LMFDB - Embedded newform 950.2.u.g.899.3

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:	$36$
Relative dimension:	$6$ over $\Q(\zeta_{18})$
Twist minimal:	no (minimal twist has level 190)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			899.3
Character	$\chi$	$=$	950.899
Dual form			950.2.u.g.149.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.642788 - 0.766044i) q^{2} +(0.811037 - 2.22831i) q^{3} +(-0.173648 + 0.984808i) q^{4} +(-2.22831 + 0.811037i) q^{6} +(-2.73267 - 1.57771i) q^{7} +(0.866025 - 0.500000i) q^{8} +(-2.00943 - 1.68611i) q^{9} +O(q^{10})$	\(q+(-0.642788 - 0.766044i) q^{2} +(0.811037 - 2.22831i) q^{3} +(-0.173648 + 0.984808i) q^{4} +(-2.22831 + 0.811037i) q^{6} +(-2.73267 - 1.57771i) q^{7} +(0.866025 - 0.500000i) q^{8} +(-2.00943 - 1.68611i) q^{9} +(-0.688886 - 1.19319i) q^{11} +(2.05362 + 1.18566i) q^{12} +(-1.47931 - 4.06437i) q^{13} +(0.547933 + 3.10748i) q^{14} +(-0.939693 - 0.342020i) q^{16} +(-0.833438 - 0.993253i) q^{17} +2.62313i q^{18} +(-1.08907 + 4.22066i) q^{19} +(-5.73192 + 4.80965i) q^{21} +(-0.471226 + 1.29468i) q^{22} +(2.09271 + 0.369001i) q^{23} +(-0.411774 - 2.33529i) q^{24} +(-2.16260 + 3.74574i) q^{26} +(0.773953 - 0.446842i) q^{27} +(2.02826 - 2.41719i) q^{28} +(0.0998515 + 0.0837854i) q^{29} +(-0.173355 + 0.300259i) q^{31} +(0.342020 + 0.939693i) q^{32} +(-3.21749 + 0.567331i) q^{33} +(-0.225152 + 1.27690i) q^{34} +(2.00943 - 1.68611i) q^{36} +10.3150i q^{37} +(3.93325 - 1.87871i) q^{38} -10.2564 q^{39} +(-10.3451 - 3.76531i) q^{41} +(7.36881 + 1.29932i) q^{42} +(-11.3501 + 2.00132i) q^{43} +(1.29468 - 0.471226i) q^{44} +(-1.06250 - 1.84030i) q^{46} +(-0.0491361 + 0.0585581i) q^{47} +(-1.52425 + 1.81653i) q^{48} +(1.47834 + 2.56055i) q^{49} +(-2.88922 + 1.05159i) q^{51} +(4.25950 - 0.751065i) q^{52} +(-6.12511 - 1.08002i) q^{53} +(-0.839788 - 0.305658i) q^{54} -3.15542 q^{56} +(8.52164 + 5.84988i) q^{57} -0.130347i q^{58} +(6.27104 - 5.26202i) q^{59} +(1.36244 - 7.72680i) q^{61} +(0.341442 - 0.0602055i) q^{62} +(2.83092 + 7.77790i) q^{63} +(0.500000 - 0.866025i) q^{64} +(2.50277 + 2.10007i) q^{66} +(0.662508 - 0.789546i) q^{67} +(1.12289 - 0.648300i) q^{68} +(2.51951 - 4.36392i) q^{69} +(2.02349 + 11.4758i) q^{71} +(-2.58328 - 0.455501i) q^{72} +(4.18756 - 11.5052i) q^{73} +(7.90176 - 6.63036i) q^{74} +(-3.96742 - 1.80543i) q^{76} +4.34745i q^{77} +(6.59270 + 7.85688i) q^{78} +(13.1650 + 4.79168i) q^{79} +(-1.73450 - 9.83684i) q^{81} +(3.76531 + 10.3451i) q^{82} +(9.85443 + 5.68946i) q^{83} +(-3.74124 - 6.48003i) q^{84} +(8.82879 + 7.40823i) q^{86} +(0.267683 - 0.154547i) q^{87} +(-1.19319 - 0.688886i) q^{88} +(-17.1195 + 6.23099i) q^{89} +(-2.36992 + 13.4405i) q^{91} +(-0.726790 + 1.99684i) q^{92} +(0.528473 + 0.629809i) q^{93} +0.0764422 q^{94} +2.37131 q^{96} +(-10.4271 - 12.4265i) q^{97} +(1.01124 - 2.77836i) q^{98} +(-0.627577 + 3.55916i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + 36 q^{9}+O(q^{10}) $ 36 * q + 36 * q^9	$ 36 q + 36 q^{9} - 24 q^{11} - 12 q^{14} + 24 q^{21} - 18 q^{26} + 12 q^{29} - 12 q^{31} - 36 q^{34} - 36 q^{36} - 96 q^{39} - 42 q^{41} - 6 q^{44} + 36 q^{46} + 78 q^{49} + 84 q^{51} + 108 q^{54} + 60 q^{59} + 96 q^{61} + 18 q^{64} + 48 q^{66} + 60 q^{69} + 60 q^{71} + 6 q^{74} - 42 q^{76} - 60 q^{79} + 36 q^{81} - 12 q^{84} + 72 q^{86} - 60 q^{89} - 120 q^{91} - 12 q^{94} - 342 q^{99}+O(q^{100}) $ 36 * q + 36 * q^9 - 24 * q^11 - 12 * q^14 + 24 * q^21 - 18 * q^26 + 12 * q^29 - 12 * q^31 - 36 * q^34 - 36 * q^36 - 96 * q^39 - 42 * q^41 - 6 * q^44 + 36 * q^46 + 78 * q^49 + 84 * q^51 + 108 * q^54 + 60 * q^59 + 96 * q^61 + 18 * q^64 + 48 * q^66 + 60 * q^69 + 60 * q^71 + 6 * q^74 - 42 * q^76 - 60 * q^79 + 36 * q^81 - 12 * q^84 + 72 * q^86 - 60 * q^89 - 120 * q^91 - 12 * q^94 - 342 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$77$	$401$
$\chi(n)$	$-1$	$e\left(\frac{7}{9}\right)$

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 $

$2$	−0.642788	−	0.766044i	−0.454519	−	0.541675i
$2$	−0.642788	−	0.766044i	−0.454519	−	0.541675i
$3$	0.811037	−	2.22831i	0.468252	−	1.28651i	−0.450887	−	0.892581i	$-0.648892\pi$
$3$	0.811037	−	2.22831i	0.468252	−	1.28651i	0.919140	−	0.393932i	$-0.128885\pi$
$4$	−0.173648	+	0.984808i	−0.0868241	+	0.492404i
$5$		0			0
$5$		0			0
$6$	−2.22831	+	0.811037i	−0.909702	+	0.331104i
$7$	−2.73267	−	1.57771i	−1.03285	−	0.596318i	−0.115053	−	0.993359i	$-0.536704\pi$
$7$	−2.73267	−	1.57771i	−1.03285	−	0.596318i	−0.917801	+	0.397041i	$0.870037\pi$
$8$	0.866025	−	0.500000i	0.306186	−	0.176777i
$9$	−2.00943	−	1.68611i	−0.669811	−	0.562038i
$10$		0			0
$11$	−0.688886	−	1.19319i	−0.207707	−	0.359759i	0.743285	−	0.668975i	$-0.233267\pi$
$11$	−0.688886	−	1.19319i	−0.207707	−	0.359759i	−0.950992	+	0.309216i	$0.899933\pi$
$12$	2.05362	+	1.18566i	0.592828	+	0.342270i
$13$	−1.47931	−	4.06437i	−0.410286	−	1.12725i	−0.957039	−	0.289958i	$-0.906359\pi$
$13$	−1.47931	−	4.06437i	−0.410286	−	1.12725i	0.546753	−	0.837294i	$-0.315864\pi$
$14$	0.547933	+	3.10748i	0.146441	+	0.830509i
$15$		0			0
$16$	−0.939693	−	0.342020i	−0.234923	−	0.0855050i
$17$	−0.833438	−	0.993253i	−0.202138	−	0.240899i	0.655446	−	0.755242i	$-0.272480\pi$
$17$	−0.833438	−	0.993253i	−0.202138	−	0.240899i	−0.857585	+	0.514342i	$0.828036\pi$
$18$			2.62313i			0.618277i
$19$	−1.08907	+	4.22066i	−0.249849	+	0.968285i
$19$	−1.08907	+	4.22066i	−0.249849	+	0.968285i
$20$		0			0
$21$	−5.73192	+	4.80965i	−1.25081	+	1.04955i
$22$	−0.471226	+	1.29468i	−0.100466	+	0.276027i
$23$	2.09271	+	0.369001i	0.436360	+	0.0769420i	0.387513	−	0.921864i	$-0.373334\pi$
$23$	2.09271	+	0.369001i	0.436360	+	0.0769420i	0.0488468	+	0.998806i	$0.484445\pi$
$24$	−0.411774	−	2.33529i	−0.0840531	−	0.476689i
$25$		0			0
$26$	−2.16260	+	3.74574i	−0.424122	+	0.734600i
$27$	0.773953	−	0.446842i	0.148947	−	0.0859948i
$28$	2.02826	−	2.41719i	0.383306	−	0.456806i
$29$	0.0998515	+	0.0837854i	0.0185420	+	0.0155586i	0.652012	−	0.758209i	$-0.273925\pi$
$29$	0.0998515	+	0.0837854i	0.0185420	+	0.0155586i	−0.633470	+	0.773768i	$0.718370\pi$
$30$		0			0
$31$	−0.173355	+	0.300259i	−0.0311355	+	0.0539282i	−0.881173	−	0.472793i	$-0.843246\pi$
$31$	−0.173355	+	0.300259i	−0.0311355	+	0.0539282i	0.850038	+	0.526722i	$0.176579\pi$
$32$	0.342020	+	0.939693i	0.0604612	+	0.166116i
$33$	−3.21749	+	0.567331i	−0.560094	+	0.0987596i
$34$	−0.225152	+	1.27690i	−0.0386133	+	0.218987i
$35$		0			0
$36$	2.00943	−	1.68611i	0.334905	−	0.281019i
$37$			10.3150i			1.69578i	0.530174	+	0.847889i	$0.322127\pi$
$37$			10.3150i			1.69578i	−0.530174	+	0.847889i	$0.677873\pi$
$38$	3.93325	−	1.87871i	0.638057	−	0.304768i
$39$	−10.2564			−1.64234
$40$		0			0
$41$	−10.3451	−	3.76531i	−1.61563	−	0.588042i	−0.633089	−	0.774079i	$-0.718213\pi$
$41$	−10.3451	−	3.76531i	−1.61563	−	0.588042i	−0.982543	+	0.186037i	$0.940436\pi$
$42$	7.36881	+	1.29932i	1.13703	+	0.200490i
$43$	−11.3501	+	2.00132i	−1.73087	+	0.305199i	−0.948303	−	0.317367i	$-0.897201\pi$
$43$	−11.3501	+	2.00132i	−1.73087	+	0.305199i	−0.782567	+	0.622566i	$0.786090\pi$
$44$	1.29468	−	0.471226i	0.195181	−	0.0710400i
$45$		0			0
$46$	−1.06250	−	1.84030i	−0.156656	−	0.271337i
$47$	−0.0491361	+	0.0585581i	−0.00716723	+	0.00854158i	−0.769616	−	0.638507i	$-0.779552\pi$
$47$	−0.0491361	+	0.0585581i	−0.00716723	+	0.00854158i	0.762449	+	0.647048i	$0.223997\pi$
$48$	−1.52425	+	1.81653i	−0.220007	+	0.262194i
$49$	1.47834	+	2.56055i	0.211191	+	0.365793i
$50$		0			0
$51$	−2.88922	+	1.05159i	−0.404572	+	0.147252i
$52$	4.25950	−	0.751065i	0.590686	−	0.104154i
$53$	−6.12511	−	1.08002i	−0.841348	−	0.148352i	−0.263666	−	0.964614i	$-0.584932\pi$
$53$	−6.12511	−	1.08002i	−0.841348	−	0.148352i	−0.577682	+	0.816262i	$0.696043\pi$
$54$	−0.839788	−	0.305658i	−0.114281	−	0.0415948i
$55$		0			0
$56$	−3.15542			−0.421661
$57$	8.52164	+	5.84988i	1.12872	+	0.774835i
$58$		−	0.130347i		−	0.0171154i
$59$	6.27104	−	5.26202i	0.816419	−	0.685057i	−0.135711	−	0.990748i	$-0.543332\pi$
$59$	6.27104	−	5.26202i	0.816419	−	0.685057i	0.952131	+	0.305691i	$0.0988875\pi$
$60$		0			0
$61$	1.36244	−	7.72680i	0.174443	−	0.989315i	−0.764342	−	0.644811i	$-0.776936\pi$
$61$	1.36244	−	7.72680i	0.174443	−	0.989315i	0.938785	−	0.344504i	$-0.111953\pi$
$62$	0.341442	−	0.0602055i	0.0433632	−	0.00764611i
$63$	2.83092	+	7.77790i	0.356663	+	0.979923i
$64$	0.500000	−	0.866025i	0.0625000	−	0.108253i
$65$		0			0
$66$	2.50277	+	2.10007i	0.308069	+	0.258501i
$67$	0.662508	−	0.789546i	0.0809382	−	0.0964584i	−0.724056	−	0.689742i	$-0.757724\pi$
$67$	0.662508	−	0.789546i	0.0809382	−	0.0964584i	0.804994	+	0.593283i	$0.202169\pi$
$68$	1.12289	−	0.648300i	0.136170	−	0.0786179i
$69$	2.51951	−	4.36392i	0.303313	−	0.525354i
$70$		0			0
$71$	2.02349	+	11.4758i	0.240144	+	1.36192i	0.831505	+	0.555517i	$0.187480\pi$
$71$	2.02349	+	11.4758i	0.240144	+	1.36192i	−0.591361	+	0.806407i	$0.701409\pi$
$72$	−2.58328	−	0.455501i	−0.304442	−	0.0536813i
$73$	4.18756	−	11.5052i	0.490117	−	1.34659i	−0.410456	−	0.911881i	$-0.634630\pi$
$73$	4.18756	−	11.5052i	0.490117	−	1.34659i	0.900573	−	0.434705i	$-0.143147\pi$
$74$	7.90176	−	6.63036i	0.918561	−	0.770764i
$75$		0			0
$76$	−3.96742	−	1.80543i	−0.455094	−	0.207097i
$77$			4.34745i			0.495438i
$78$	6.59270	+	7.85688i	0.746477	+	0.889616i
$79$	13.1650	+	4.79168i	1.48118	+	0.539106i	0.951111	−	0.308848i	$-0.0999436\pi$
$79$	13.1650	+	4.79168i	1.48118	+	0.539106i	0.530070	+	0.847954i	$0.322166\pi$
$80$		0			0
$81$	−1.73450	−	9.83684i	−0.192722	−	1.09298i
$82$	3.76531	+	10.3451i	0.415808	+	1.14242i
$83$	9.85443	+	5.68946i	1.08166	+	0.624499i	0.931345	−	0.364138i	$-0.118636\pi$
$83$	9.85443	+	5.68946i	1.08166	+	0.624499i	0.150319	+	0.988637i	$0.451970\pi$
$84$	−3.74124	−	6.48003i	−0.408203	−	0.707029i
$85$		0			0
$86$	8.82879	+	7.40823i	0.952033	+	0.798850i
$87$	0.267683	−	0.154547i	0.0286986	−	0.0165691i
$88$	−1.19319	−	0.688886i	−0.127194	−	0.0734355i
$89$	−17.1195	+	6.23099i	−1.81466	+	0.660484i	−0.818348	+	0.574723i	$0.805110\pi$
$89$	−17.1195	+	6.23099i	−1.81466	+	0.660484i	−0.996316	+	0.0857608i	$0.972668\pi$
$90$		0			0
$91$	−2.36992	+	13.4405i	−0.248436	+	1.40895i
$92$	−0.726790	+	1.99684i	−0.0757731	+	0.208185i
$93$	0.528473	+	0.629809i	0.0548000	+	0.0653082i
$94$	0.0764422			0.00788441
$95$		0			0
$96$	2.37131			0.242021
$97$	−10.4271	−	12.4265i	−1.05871	−	1.26172i	−0.963910	−	0.266227i	$-0.914223\pi$
$97$	−10.4271	−	12.4265i	−1.05871	−	1.26172i	−0.0948014	−	0.995496i	$-0.530222\pi$
$98$	1.01124	−	2.77836i	0.102151	−	0.280657i
$99$	−0.627577	+	3.55916i	−0.0630738	+	0.357710i
$100$		0			0
$101$	−6.22381	+	2.26528i	−0.619293	+	0.225404i	−0.632564	−	0.774508i	$-0.717998\pi$
$101$	−6.22381	+	2.26528i	−0.619293	+	0.225404i	0.0132716	+	0.999912i	$0.495775\pi$
$102$	2.66272	+	1.53732i	0.263649	+	0.152218i
$103$	10.7020	−	6.17880i	1.05450	−	0.608815i	0.130594	−	0.991436i	$-0.458312\pi$
$103$	10.7020	−	6.17880i	1.05450	−	0.608815i	0.923906	+	0.382621i	$0.124978\pi$
$104$	−3.31330	−	2.78019i	−0.324896	−	0.272620i
$105$		0			0
$106$	3.10980	+	5.38633i	0.302050	+	0.523167i
$107$	−9.48714	−	5.47740i	−0.917156	−	0.529521i	−0.0344297	−	0.999407i	$-0.510961\pi$
$107$	−9.48714	−	5.47740i	−0.917156	−	0.529521i	−0.882727	+	0.469887i	$0.844295\pi$
$108$	0.305658	+	0.839788i	0.0294120	+	0.0808087i
$109$	−1.29211	−	7.32792i	−0.123762	−	0.701887i	−0.982036	−	0.188695i	$-0.939574\pi$
$109$	−1.29211	−	7.32792i	−0.123762	−	0.701887i	0.858274	−	0.513192i	$-0.171537\pi$
$110$		0			0
$111$	22.9850	+	8.36586i	2.18164	+	0.794052i
$112$	2.02826	+	2.41719i	0.191653	+	0.228403i
$113$			11.6014i			1.09137i	0.837990	+	0.545686i	$0.183731\pi$
$113$			11.6014i			1.09137i	−0.837990	+	0.545686i	$0.816269\pi$
$114$	−0.996338	−	10.2882i	−0.0933156	−	0.963577i
$115$		0			0
$116$	−0.0998515	+	0.0837854i	−0.00927098	+	0.00777928i
$117$	−3.88041	+	10.6613i	−0.358744	+	0.985642i
$118$	−8.06189	−	1.42153i	−0.742157	−	0.130862i
$119$	0.710449	+	4.02916i	0.0651268	+	0.369352i
$120$		0			0
$121$	4.55087	−	7.88234i	0.413716	−	0.716577i
$122$	−6.79483	+	3.92300i	−0.615175	+	0.355172i
$123$	−16.7805	+	19.9982i	−1.51305	+	1.80318i
$124$	−0.265595	−	0.222861i	−0.0238511	−	0.0200135i
$125$		0			0
$126$	4.13853	−	7.16815i	0.368690	−	0.638589i
$127$	−5.60862	−	15.4096i	−0.497685	−	1.36738i	−0.893507	−	0.449050i	$-0.851763\pi$
$127$	−5.60862	−	15.4096i	−0.497685	−	1.36738i	0.395822	−	0.918327i	$-0.370460\pi$
$128$	−0.984808	+	0.173648i	−0.0870455	+	0.0153485i
$129$	−4.74577	+	26.9146i	−0.417841	+	2.36970i
$130$		0			0
$131$	8.53118	−	7.15851i	0.745373	−	0.625442i	−0.188902	−	0.981996i	$-0.560493\pi$
$131$	8.53118	−	7.15851i	0.745373	−	0.625442i	0.934275	+	0.356554i	$0.116048\pi$
$132$		−	3.26713i		−	0.284367i
$133$	9.63503	−	9.81545i	0.835463	−	0.851107i
$134$	−1.03068			−0.0890371
$135$		0			0
$136$	−1.21840	−	0.443463i	−0.104477	−	0.0380266i
$137$	7.23011	+	1.27486i	0.617710	+	0.108919i	0.473743	−	0.880663i	$-0.342903\pi$
$137$	7.23011	+	1.27486i	0.617710	+	0.108919i	0.143968	+	0.989582i	$0.454014\pi$
$138$	−4.96247	+	0.875017i	−0.422433	+	0.0744864i
$139$	11.0992	−	4.03978i	0.941422	−	0.342650i	0.174695	−	0.984623i	$-0.444106\pi$
$139$	11.0992	−	4.03978i	0.941422	−	0.342650i	0.766727	+	0.641973i	$0.221884\pi$
$140$		0			0
$141$	0.0906342	+	0.156983i	0.00763277	+	0.0132203i
$142$	7.49028	−	8.92657i	0.628570	−	0.749101i
$143$	−3.83047	+	4.56497i	−0.320320	+	0.381742i
$144$	1.31156	+	2.27169i	0.109297	+	0.189308i
$145$		0			0
$146$	−11.5052	+	4.18756i	−0.952180	+	0.346565i
$147$	6.90468	−	1.21748i	0.569488	−	0.100416i
$148$	−10.1583	−	1.79118i	−0.835007	−	0.147234i
$149$	3.30256	+	1.20203i	0.270556	+	0.0984745i	0.473736	−	0.880667i	$-0.342905\pi$
$149$	3.30256	+	1.20203i	0.270556	+	0.0984745i	−0.203179	+	0.979142i	$0.565127\pi$
$150$		0			0
$151$	−0.212620			−0.0173028			−0.00865139	−	0.999963i	$-0.502754\pi$
$151$	−0.212620			−0.0173028			−0.00865139	+	0.999963i	$0.502754\pi$
$152$	1.16717	+	4.19973i	0.0946700	+	0.340643i
$153$			3.40114i			0.274966i
$154$	3.33034	−	2.79449i	0.268366	−	0.225186i
$155$		0			0
$156$	1.78101	−	10.1006i	0.142595	−	0.808696i
$157$	−7.57072	+	1.33492i	−0.604210	+	0.106538i	−0.467381	−	0.884056i	$-0.654802\pi$
$157$	−7.57072	+	1.33492i	−0.604210	+	0.106538i	−0.136829	+	0.990595i	$0.543691\pi$
$158$	−4.79168	−	13.1650i	−0.381205	−	1.04735i
$159$	−7.37431	+	12.7727i	−0.584821	+	1.01294i
$160$		0			0
$161$	−5.13651	−	4.31004i	−0.404814	−	0.339679i
$162$	−6.42054	+	7.65170i	−0.504445	+	0.601174i
$163$	6.34537	−	3.66350i	0.497008	−	0.286948i	−0.230469	−	0.973080i	$-0.574026\pi$
$163$	6.34537	−	3.66350i	0.497008	−	0.286948i	0.727477	+	0.686132i	$0.240693\pi$
$164$	5.50451	−	9.53409i	0.429830	−	0.744487i
$165$		0			0
$166$	−1.97593	−	11.2060i	−0.153362	−	0.869758i
$167$	−15.6032	−	2.75126i	−1.20741	−	0.212899i	−0.466511	−	0.884515i	$-0.654489\pi$
$167$	−15.6032	−	2.75126i	−1.20741	−	0.212899i	−0.740899	+	0.671617i	$0.765600\pi$
$168$	−2.55916	+	7.03124i	−0.197444	+	0.542472i
$169$	−4.37215	+	3.66867i	−0.336319	+	0.282205i
$170$		0			0
$171$	9.30491	−	6.64483i	0.711564	−	0.508143i
$172$		−	11.5252i		−	0.878786i
$173$	−10.6961	−	12.7471i	−0.813211	−	0.969147i	0.186701	−	0.982417i	$-0.440220\pi$
$173$	−10.6961	−	12.7471i	−0.813211	−	0.969147i	−0.999912	+	0.0132697i	$0.995776\pi$
$174$	−0.290453	−	0.105716i	−0.0220192	−	0.00801432i
$175$		0			0
$176$	0.239248	+	1.35684i	0.0180340	+	0.102276i
$177$	−6.63936	−	18.2415i	−0.499045	−	1.37111i
$178$	15.7774	+	9.10910i	1.18257	+	0.682756i
$179$	−2.28553	−	3.95866i	−0.170829	−	0.295884i	0.767881	−	0.640592i	$-0.221311\pi$
$179$	−2.28553	−	3.95866i	−0.170829	−	0.295884i	−0.938710	+	0.344708i	$0.887978\pi$
$180$		0			0
$181$	1.29338	+	1.08527i	0.0961360	+	0.0806677i	0.689589	−	0.724201i	$-0.257791\pi$
$181$	1.29338	+	1.08527i	0.0961360	+	0.0806677i	−0.593453	+	0.804869i	$0.702236\pi$
$182$	11.8194	−	6.82392i	0.876111	−	0.505823i
$183$	−16.1127	−	9.30266i	−1.19108	−	0.687673i
$184$	1.99684	−	0.726790i	0.147209	−	0.0535796i
$185$		0			0
$186$	0.142766	−	0.809667i	0.0104681	−	0.0593677i
$187$	−0.610991	+	1.67868i	−0.0446801	+	0.122758i
$188$	−0.0491361	−	0.0585581i	−0.00358362	−	0.00427079i
$189$	−2.81995			−0.205121
$190$		0			0
$191$	11.2207			0.811901			0.405951	−	0.913895i	$-0.366941\pi$
$191$	11.2207			0.811901			0.405951	+	0.913895i	$0.366941\pi$
$192$	−1.52425	−	1.81653i	−0.110003	−	0.131097i
$193$	7.34927	−	20.1920i	0.529012	−	1.45345i	−0.331223	−	0.943552i	$-0.607461\pi$
$193$	7.34927	−	20.1920i	0.529012	−	1.45345i	0.860236	−	0.509897i	$-0.170316\pi$
$194$	−2.81687	+	15.9752i	−0.202239	+	1.14696i
$195$		0			0
$196$	−2.77836	+	1.01124i	−0.198455	+	0.0722315i
$197$	−13.2315	−	7.63921i	−0.942705	−	0.544271i	−0.0518981	−	0.998652i	$-0.516527\pi$
$197$	−13.2315	−	7.63921i	−0.942705	−	0.544271i	−0.890807	+	0.454381i	$0.849860\pi$
$198$	3.12988	−	1.80704i	0.222431	−	0.128420i
$199$	−0.542940	−	0.455581i	−0.0384880	−	0.0322953i	0.623341	−	0.781950i	$-0.285775\pi$
$199$	−0.542940	−	0.455581i	−0.0384880	−	0.0322953i	−0.661829	+	0.749655i	$0.730219\pi$
$200$		0			0
$201$	−1.22203	−	2.11662i	−0.0861955	−	0.149295i
$202$	5.73590	+	3.31162i	0.403576	+	0.233005i
$203$	−0.140673	−	0.386495i	−0.00987328	−	0.0271266i
$204$	−0.533906	−	3.02793i	−0.0373809	−	0.211998i
$205$		0			0
$206$	−11.6123	−	4.22655i	−0.809071	−	0.294478i
$207$	−3.58298	−	4.27002i	−0.249034	−	0.296787i
$208$			4.32521i			0.299899i
$209$	5.78627	−	1.60809i	0.400244	−	0.111234i
$210$		0			0
$211$	10.7852	−	9.04988i	0.742486	−	0.623020i	−0.191018	−	0.981586i	$-0.561179\pi$
$211$	10.7852	−	9.04988i	0.742486	−	0.623020i	0.933504	+	0.358567i	$0.116735\pi$
$212$	2.12723	−	5.84451i	0.146099	−	0.401403i
$213$	27.2126	+	4.79832i	1.86458	+	0.328776i
$214$	1.90228	+	10.7884i	0.130037	+	0.737478i
$215$		0			0
$216$	0.446842	−	0.773953i	0.0304038	−	0.0526608i
$217$	0.947444	−	0.547007i	0.0643167	−	0.0371333i
$218$	−4.78296	+	5.70011i	−0.323943	+	0.386060i
$219$	−22.2409	−	18.6623i	−1.50290	−	1.26108i
$220$		0			0
$221$	−2.80403	+	4.85673i	−0.188620	+	0.326699i
$222$	−8.36586	−	22.9850i	−0.561479	−	1.54265i
$223$	11.5389	−	2.03461i	0.772699	−	0.136248i	0.226622	−	0.973983i	$-0.427232\pi$
$223$	11.5389	−	2.03461i	0.772699	−	0.136248i	0.546077	+	0.837735i	$0.316121\pi$
$224$	0.547933	−	3.10748i	0.0366103	−	0.207627i
$225$		0			0
$226$	8.88722	−	7.45727i	0.591169	−	0.496050i
$227$		−	10.2265i		−	0.678758i	−0.940650	−	0.339379i	$-0.889783\pi$
$227$		−	10.2265i		−	0.678758i	0.940650	−	0.339379i	$-0.110217\pi$
$228$	−7.24077	+	7.37636i	−0.479532	+	0.488511i
$229$	5.05689			0.334169			0.167084	−	0.985943i	$-0.446565\pi$
$229$	5.05689			0.334169			0.167084	+	0.985943i	$0.446565\pi$
$230$		0			0
$231$	9.68744	+	3.52594i	0.637387	+	0.231990i
$232$	0.128367	+	0.0226345i	0.00842768	+	0.00148603i
$233$	−7.14818	+	1.26042i	−0.468293	+	0.0825727i	−0.402815	−	0.915281i	$-0.631968\pi$
$233$	−7.14818	+	1.26042i	−0.468293	+	0.0825727i	−0.0654778	+	0.997854i	$0.520857\pi$
$234$	10.6613	−	3.88041i	0.696954	−	0.253671i
$235$		0			0
$236$	4.09313	+	7.08951i	0.266440	+	0.461488i
$237$	21.3546	−	25.4495i	1.38713	−	1.65312i
$238$	2.62985	−	3.13413i	0.170468	−	0.203155i
$239$	7.98657	+	13.8331i	0.516608	+	0.894792i	0.999814	+	0.0192850i	$0.00613899\pi$
$239$	7.98657	+	13.8331i	0.516608	+	0.894792i	−0.483206	+	0.875507i	$0.660528\pi$
$240$		0			0
$241$	−20.8564	+	7.59111i	−1.34348	+	0.488986i	−0.910906	−	0.412613i	$-0.864616\pi$
$241$	−20.8564	+	7.59111i	−1.34348	+	0.488986i	−0.432572	+	0.901599i	$0.642394\pi$
$242$	−8.96347	+	1.58050i	−0.576194	+	0.101598i
$243$	−20.6859	−	3.64748i	−1.32700	−	0.233986i
$244$	7.37283	+	2.68349i	0.471997	+	0.171793i
$245$		0			0
$246$	26.1058			1.66445
$247$	18.7654	−	1.81729i	1.19401	−	0.115632i
$248$			0.346710i			0.0220161i
$249$	20.6702	−	17.3443i	1.30992	−	1.09915i
$250$		0			0
$251$	3.91622	−	22.2100i	0.247190	−	1.40188i	−0.568162	−	0.822917i	$-0.692345\pi$
$251$	3.91622	−	22.2100i	0.247190	−	1.40188i	0.815352	−	0.578966i	$-0.196544\pi$
$252$	−8.15132	+	1.43730i	−0.513485	+	0.0905412i
$253$	−1.00135	−	2.75119i	−0.0629544	−	0.172966i
$254$	−8.19925	+	14.2015i	−0.514467	+	0.891083i
$255$		0			0
$256$	0.766044	+	0.642788i	0.0478778	+	0.0401742i
$257$	−6.88718	+	8.20783i	−0.429611	+	0.511990i	−0.936810	−	0.349839i	$-0.886236\pi$
$257$	−6.88718	+	8.20783i	−0.429611	+	0.511990i	0.507199	+	0.861829i	$0.330681\pi$
$258$	23.6683	−	13.6649i	1.47352	−	0.850739i
$259$	16.2741	−	28.1876i	1.01122	−	1.75149i
$260$		0			0
$261$	−0.0593732	−	0.336722i	−0.00367511	−	0.0208426i
$262$	−10.9675	−	1.93386i	−0.677573	−	0.119474i
$263$	−9.12051	+	25.0584i	−0.562395	+	1.54517i	0.253720	+	0.967278i	$0.418346\pi$
$263$	−9.12051	+	25.0584i	−0.562395	+	1.54517i	−0.816115	+	0.577890i	$0.803876\pi$
$264$	−2.50277	+	2.10007i	−0.154035	+	0.129250i
$265$		0			0
$266$	−13.7123	−	1.07161i	−0.840758	−	0.0657049i
$267$			43.2011i			2.64386i
$268$	0.662508	+	0.789546i	0.0404691	+	0.0482292i
$269$	1.34180	+	0.488375i	0.0818110	+	0.0297768i	0.382601	−	0.923913i	$-0.375028\pi$
$269$	1.34180	+	0.488375i	0.0818110	+	0.0297768i	−0.300790	+	0.953690i	$0.597250\pi$
$270$		0			0
$271$	1.27969	+	7.25749i	0.0777357	+	0.440861i	0.998689	+	0.0511882i	$0.0163008\pi$
$271$	1.27969	+	7.25749i	0.0777357	+	0.440861i	−0.920953	+	0.389673i	$0.872588\pi$
$272$	0.443463	+	1.21840i	0.0268889	+	0.0738766i
$273$	28.0275	+	16.1817i	1.69630	+	0.979359i
$274$	−3.67083	−	6.35806i	−0.221763	−	0.384104i
$275$		0			0
$276$	3.86011	+	3.23902i	0.232351	+	0.194966i
$277$	−2.18698	+	1.26266i	−0.131403	+	0.0758656i	−0.564261	−	0.825597i	$-0.690839\pi$
$277$	−2.18698	+	1.26266i	−0.131403	+	0.0758656i	0.432857	+	0.901462i	$0.357505\pi$
$278$	−10.2291	−	5.90576i	−0.613500	−	0.354204i
$279$	0.854616	−	0.311055i	0.0511645	−	0.0186224i
$280$		0			0
$281$	2.99175	−	16.9671i	0.178473	−	1.01217i	−0.755586	−	0.655050i	$-0.772648\pi$
$281$	2.99175	−	16.9671i	0.178473	−	1.01217i	0.934058	−	0.357120i	$-0.116241\pi$
$282$	0.0619974	−	0.170336i	0.00369189	−	0.0101434i
$283$	−18.1400	−	21.6184i	−1.07831	−	1.28508i	−0.956248	−	0.292556i	$-0.905494\pi$
$283$	−18.1400	−	21.6184i	−1.07831	−	1.28508i	−0.122061	−	0.992523i	$-0.538950\pi$
$284$	−11.6528			−0.691467
$285$		0			0
$286$	5.95915			0.352372
$287$	22.3292	+	26.6109i	1.31805	+	1.57079i
$288$	0.897162	−	2.46493i	0.0528658	−	0.145248i
$289$	2.66009	−	15.0861i	0.156476	−	0.887418i
$290$		0			0
$291$	−36.1469	+	13.1564i	−2.11897	+	0.771241i
$292$	10.6033	+	6.12181i	0.620510	+	0.358252i
$293$	10.9276	−	6.30904i	0.638396	−	0.368578i	−0.145601	−	0.989343i	$-0.546511\pi$
$293$	10.9276	−	6.30904i	0.638396	−	0.368578i	0.783996	+	0.620766i	$0.213178\pi$
$294$	−5.37089	−	4.50671i	−0.313237	−	0.262837i
$295$		0			0
$296$	5.15751	+	8.93306i	0.299774	+	0.519224i
$297$	−1.06633	−	0.615647i	−0.0618748	−	0.0357234i
$298$	−1.20203	−	3.30256i	−0.0696320	−	0.191312i
$299$	−1.59601	−	9.05140i	−0.0922994	−	0.523456i
$300$		0			0
$301$	34.1735	+	12.4382i	1.96973	+	0.716923i
$302$	0.136670	+	0.162877i	0.00786445	+	0.00937249i
$303$			15.7058i			0.902274i
$304$	2.46694	−	3.59364i	0.141488	−	0.206109i
$305$		0			0
$306$	2.60543	−	2.18621i	0.148942	−	0.124978i
$307$	3.10031	−	8.51802i	0.176944	−	0.486149i	−0.819238	−	0.573454i	$-0.805603\pi$
$307$	3.10031	−	8.51802i	0.176944	−	0.486149i	0.996182	+	0.0873047i	$0.0278254\pi$
$308$	−4.28140	−	0.754926i	−0.243955	−	0.0430159i
$309$	−5.08854	−	28.8586i	−0.289477	−	1.64171i
$310$		0			0
$311$	10.8562	−	18.8035i	0.615599	−	1.06625i	−0.374680	−	0.927154i	$-0.622247\pi$
$311$	10.8562	−	18.8035i	0.615599	−	1.06625i	0.990279	−	0.139095i	$-0.0444192\pi$
$312$	−8.88232	+	5.12821i	−0.502863	+	0.290328i
$313$	−6.45746	+	7.69570i	−0.364997	+	0.434987i	−0.917019	−	0.398843i	$-0.869412\pi$
$313$	−6.45746	+	7.69570i	−0.364997	+	0.434987i	0.552022	+	0.833829i	$0.313856\pi$
$314$	5.88898	+	4.94144i	0.332334	+	0.278862i
$315$		0			0
$316$	−7.00496	+	12.1330i	−0.394060	+	0.682532i
$317$	0.721135	+	1.98130i	0.0405030	+	0.111281i	0.958295	−	0.285780i	$-0.0922525\pi$
$317$	0.721135	+	1.98130i	0.0405030	+	0.111281i	−0.917792	+	0.397061i	$0.870030\pi$
$318$	14.5245	−	2.56107i	0.814496	−	0.143618i
$319$	0.0311852	−	0.176860i	0.00174604	−	0.00990226i
$320$		0			0
$321$	−19.8997	+	16.6979i	−1.11070	+	0.931984i
$322$			6.70524i			0.373668i
$323$	5.09985	−	2.43594i	0.283763	−	0.135539i
$324$	9.98859			0.554921
$325$		0			0
$326$	−6.88513	−	2.50598i	−0.381332	−	0.138794i
$327$	−17.3768	−	3.06400i	−0.960939	−	0.169439i
$328$	−10.8418	+	1.91170i	−0.598636	+	0.105556i
$329$	0.226661	−	0.0824977i	0.0124962	−	0.00454824i
$330$		0			0
$331$	1.72204	+	2.98267i	0.0946521	+	0.163942i	0.909463	−	0.415784i	$-0.136493\pi$
$331$	1.72204	+	2.98267i	0.0946521	+	0.163942i	−0.814811	+	0.579726i	$0.803159\pi$
$332$	−7.31423	+	8.71676i	−0.401420	+	0.478394i
$333$	17.3923	−	20.7273i	0.953091	−	1.13585i
$334$	7.92194	+	13.7212i	0.433469	+	0.750791i
$335$		0			0
$336$	7.03124	−	2.55916i	0.383586	−	0.139614i
$337$	25.4658	−	4.49031i	1.38721	−	0.244603i	0.570332	−	0.821414i	$-0.306814\pi$
$337$	25.4658	−	4.49031i	1.38721	−	0.244603i	0.816877	+	0.576811i	$0.195703\pi$
$338$	5.62072	+	0.991085i	0.305727	+	0.0539079i
$339$	25.8516	+	9.40920i	1.40406	+	0.511038i
$340$		0			0
$341$	0.477687			0.0258682
$342$	−11.0713	−	2.85676i	−0.598668	−	0.154476i
$343$			12.7584i			0.688889i
$344$	−8.82879	+	7.40823i	−0.476016	+	0.399425i
$345$		0			0
$346$	−2.88954	+	16.3874i	−0.155343	+	0.880992i
$347$	−2.48488	+	0.438152i	−0.133395	+	0.0235212i	−0.239947	−	0.970786i	$-0.577130\pi$
$347$	−2.48488	+	0.438152i	−0.133395	+	0.0235212i	0.106552	+	0.994307i	$0.466019\pi$
$348$	0.105716	+	0.290453i	0.00566698	+	0.0155699i
$349$	1.83973	−	3.18650i	0.0984782	−	0.170569i	−0.812577	−	0.582854i	$-0.801936\pi$
$349$	1.83973	−	3.18650i	0.0984782	−	0.170569i	0.911055	+	0.412285i	$0.135269\pi$
$350$		0			0
$351$	−2.96105	−	2.48461i	−0.158049	−	0.132619i
$352$	0.885615	−	1.05543i	0.0472034	−	0.0562548i
$353$	−2.42172	+	1.39818i	−0.128895	+	0.0744175i	−0.563061	−	0.826415i	$-0.690376\pi$
$353$	−2.42172	+	1.39818i	−0.128895	+	0.0744175i	0.434166	+	0.900833i	$0.357043\pi$
$354$	−9.70609	+	16.8114i	−0.515873	+	0.893518i
$355$		0			0
$356$	−3.16356	−	17.9414i	−0.167668	−	0.950893i
$357$	9.55440	+	1.68470i	0.505672	+	0.0891637i
$358$	−1.56340	+	4.29540i	−0.0826281	+	0.227019i
$359$	−15.4284	+	12.9460i	−0.814280	+	0.683262i	−0.951625	−	0.307261i	$-0.900587\pi$
$359$	−15.4284	+	12.9460i	−0.814280	+	0.683262i	0.137345	+	0.990523i	$0.456143\pi$
$360$		0			0
$361$	−16.6279	−	9.19314i	−0.875151	−	0.483849i
$362$		−	1.68838i		−	0.0887395i
$363$	−13.8733	−	16.5336i	−0.728162	−	0.867789i
$364$	−12.8248	−	4.66784i	−0.672201	−	0.244661i
$365$		0			0
$366$	3.23078	+	18.3227i	0.168876	+	0.957741i
$367$	1.54639	+	4.24866i	0.0807207	+	0.221778i	0.973487	−	0.228741i	$-0.0734610\pi$
$367$	1.54639	+	4.24866i	0.0807207	+	0.221778i	−0.892767	+	0.450520i	$0.851239\pi$
$368$	−1.84030	−	1.06250i	−0.0959321	−	0.0553864i
$369$	14.4390	+	25.0091i	0.751666	+	1.30192i
$370$		0			0
$371$	15.0340	+	12.6150i	0.780524	+	0.654938i
$372$	−0.712009	+	0.411079i	−0.0369160	+	0.0213134i
$373$	20.1528	+	11.6352i	1.04347	+	0.602449i	0.920815	−	0.390000i	$-0.127525\pi$
$373$	20.1528	+	11.6352i	1.04347	+	0.602449i	0.122657	+	0.992449i	$0.460858\pi$
$374$	1.67868	−	0.610991i	0.0868027	−	0.0315936i
$375$		0			0
$376$	−0.0132740	+	0.0752808i	−0.000684556	+	0.00388231i
$377$	0.192823	−	0.529778i	0.00993091	−	0.0272849i
$378$	1.81263	+	2.16021i	0.0932315	+	0.111109i
$379$	−9.34667			−0.480106			−0.240053	−	0.970760i	$-0.577165\pi$
$379$	−9.34667			−0.480106			−0.240053	+	0.970760i	$0.577165\pi$
$380$		0			0
$381$	−38.8860			−1.99219
$382$	−7.21252	−	8.59555i	−0.369025	−	0.439787i
$383$	−11.2306	+	30.8559i	−0.573858	+	1.57666i	0.224497	+	0.974475i	$0.427926\pi$
$383$	−11.2306	+	30.8559i	−0.573858	+	1.57666i	−0.798355	+	0.602187i	$0.794296\pi$
$384$	−0.411774	+	2.33529i	−0.0210133	+	0.119172i
$385$		0			0
$386$	−20.1920	+	7.34927i	−1.02774	+	0.374068i
$387$	26.1817	+	15.1160i	1.33089	+	0.768389i
$388$	14.0484	−	8.11084i	0.713199	−	0.411766i
$389$	−8.17650	−	6.86090i	−0.414565	−	0.347862i	0.411526	−	0.911398i	$-0.364996\pi$
$389$	−8.17650	−	6.86090i	−0.414565	−	0.347862i	−0.826091	+	0.563537i	$0.809440\pi$
$390$		0			0
$391$	−1.37763	−	2.38613i	−0.0696698	−	0.120672i
$392$	2.56055	+	1.47834i	0.129327	+	0.0746673i
$393$	−9.03225	−	24.8159i	−0.455617	−	1.25180i
$394$	2.65307	+	15.0463i	0.133660	+	0.758022i
$395$		0			0
$396$	−3.39612	−	1.23608i	−0.170661	−	0.0621156i
$397$	6.46404	+	7.70354i	0.324421	+	0.386630i	0.903462	−	0.428669i	$-0.141017\pi$
$397$	6.46404	+	7.70354i	0.324421	+	0.386630i	−0.579041	+	0.815299i	$0.696573\pi$
$398$			0.708758i			0.0355268i
$399$	−14.0574	−	29.4305i	−0.703753	−	1.47337i
$400$		0			0
$401$	9.25312	−	7.76429i	0.462079	−	0.387730i	−0.381817	−	0.924238i	$-0.624701\pi$
$401$	9.25312	−	7.76429i	0.462079	−	0.387730i	0.843895	+	0.536508i	$0.180257\pi$
$402$	−0.835919	+	2.29667i	−0.0416918	+	0.114547i
$403$	1.47681	+	0.260401i	0.0735651	+	0.0129715i
$404$	−1.15011	−	6.52262i	−0.0572203	−	0.324513i
$405$		0			0
$406$	−0.205650	+	0.356196i	−0.0102062	+	0.0176777i
$407$	12.3077	−	7.10587i	0.610071	−	0.352225i
$408$	−1.97634	+	2.35531i	−0.0978435	+	0.116605i
$409$	30.2942	+	25.4198i	1.49795	+	1.25693i	0.883911	+	0.467655i	$0.154901\pi$
$409$	30.2942	+	25.4198i	1.49795	+	1.25693i	0.614040	+	0.789275i	$0.289543\pi$
$410$		0			0
$411$	8.70468	−	15.0769i	0.429370	−	0.743691i
$412$	4.22655	+	11.6123i	0.208227	+	0.572099i
$413$	−25.4386	+	4.48552i	−1.25175	+	0.220718i
$414$	−0.967936	+	5.48944i	−0.0475715	+	0.269791i
$415$		0			0
$416$	3.31330	−	2.78019i	0.162448	−	0.136310i
$417$		−	28.0088i		−	1.37160i
$418$	−4.95121	−	3.39887i	−0.242172	−	0.166244i
$419$	−28.5326			−1.39391			−0.696954	−	0.717116i	$-0.745462\pi$
$419$	−28.5326			−1.39391			−0.696954	+	0.717116i	$0.745462\pi$
$420$		0			0
$421$	−1.91607	−	0.697393i	−0.0933836	−	0.0339888i	0.294906	−	0.955526i	$-0.404712\pi$
$421$	−1.91607	−	0.697393i	−0.0933836	−	0.0339888i	−0.388289	+	0.921537i	$0.626934\pi$
$422$	−13.8652	−	2.44481i	−0.674949	−	0.119012i
$423$	0.197471	−	0.0348195i	0.00960138	−	0.00169298i
$424$	−5.84451	+	2.12723i	−0.283834	+	0.103307i
$425$		0			0
$426$	−13.8162	−	23.9304i	−0.669398	−	1.15943i
$427$	−15.9138	+	18.9653i	−0.770121	+	0.917794i
$428$	7.04161	−	8.39187i	0.340369	−	0.405636i
$429$	7.06551	+	12.2378i	0.341126	+	0.590847i
$430$		0			0
$431$	−12.7523	+	4.64147i	−0.614258	+	0.223572i	−0.630365	−	0.776299i	$-0.717095\pi$
$431$	−12.7523	+	4.64147i	−0.614258	+	0.223572i	0.0161074	+	0.999870i	$0.494873\pi$
$432$	−0.880107	+	0.155187i	−0.0423442	+	0.00746642i
$433$	−28.5238	−	5.02952i	−1.37077	−	0.241703i	−0.560690	−	0.828026i	$-0.689464\pi$
$433$	−28.5238	−	5.02952i	−1.37077	−	0.241703i	−0.810078	+	0.586323i	$0.800575\pi$
$434$	−1.02804	−	0.374175i	−0.0493474	−	0.0179610i
$435$		0			0
$436$	7.44096			0.356357
$437$	−3.83652	+	8.43073i	−0.183526	+	0.403297i
$438$			29.0334i			1.38727i
$439$	8.59028	−	7.20810i	0.409992	−	0.344024i	−0.414349	−	0.910118i	$-0.635991\pi$
$439$	8.59028	−	7.20810i	0.409992	−	0.344024i	0.824341	+	0.566094i	$0.191546\pi$
$440$		0			0
$441$	1.34677	−	7.63790i	0.0641318	−	0.363710i
$442$	5.52286	−	0.973830i	0.262696	−	0.0463204i
$443$	2.54804	+	7.00068i	0.121061	+	0.332612i	0.985390	−	0.170315i	$-0.0544785\pi$
$443$	2.54804	+	7.00068i	0.121061	+	0.332612i	−0.864329	+	0.502927i	$0.832256\pi$
$444$	−12.2301	+	21.1831i	−0.580413	+	1.00530i
$445$		0			0
$446$	−8.97564	−	7.53146i	−0.425009	−	0.356625i
$447$	5.35700	−	6.38422i	0.253377	−	0.301963i
$448$	−2.73267	+	1.57771i	−0.129107	+	0.0745398i
$449$	2.65192	−	4.59326i	0.125152	−	0.216769i	−0.796640	−	0.604453i	$-0.793392\pi$
$449$	2.65192	−	4.59326i	0.125152	−	0.216769i	0.921792	+	0.387684i	$0.126725\pi$
$450$		0			0
$451$	2.63388	+	14.9375i	0.124025	+	0.703378i
$452$	−11.4252	−	2.01457i	−0.537396	−	0.0947574i
$453$	−0.172443	+	0.473783i	−0.00810207	+	0.0222603i
$454$	−7.83397	+	6.57348i	−0.367667	+	0.308509i
$455$		0			0
$456$	10.3049	+	0.805323i	0.482571	+	0.0377127i
$457$			14.9890i			0.701154i	0.936534	+	0.350577i	$0.114014\pi$
$457$			14.9890i			0.701154i	−0.936534	+	0.350577i	$0.885986\pi$
$458$	−3.25051	−	3.87381i	−0.151886	−	0.181011i
$459$	−1.08887	−	0.396316i	−0.0508241	−	0.0184984i
$460$		0			0
$461$	−1.19157	−	6.75771i	−0.0554968	−	0.314738i	0.944405	−	0.328786i	$-0.106639\pi$
$461$	−1.19157	−	6.75771i	−0.0554968	−	0.314738i	−0.999901	+	0.0140479i	$0.995528\pi$
$462$	−3.52594	−	9.68744i	−0.164042	−	0.450701i
$463$	17.8738	+	10.3194i	0.830665	+	0.479585i	0.854080	−	0.520141i	$-0.174121\pi$
$463$	17.8738	+	10.3194i	0.830665	+	0.479585i	−0.0234152	+	0.999726i	$0.507454\pi$
$464$	−0.0651735	−	0.112884i	−0.00302560	−	0.00524050i
$465$		0			0
$466$	5.56030	+	4.66564i	0.257576	+	0.216132i
$467$	−10.4226	+	6.01750i	−0.482301	+	0.278457i	−0.721375	−	0.692545i	$-0.756490\pi$
$467$	−10.4226	+	6.01750i	−0.482301	+	0.278457i	0.239074	+	0.971001i	$0.423156\pi$
$468$	−9.82555	−	5.67279i	−0.454186	−	0.262225i
$469$	−3.05609	+	1.11233i	−0.141117	+	0.0513625i
$470$		0			0
$471$	−3.16552	+	17.9526i	−0.145859	+	0.827210i
$472$	2.79986	−	7.69256i	0.128874	−	0.354079i
$473$	10.2069	+	12.1641i	0.469312	+	0.559304i
$474$	−33.2219			−1.52593
$475$		0			0
$476$	−4.09132			−0.187525
$477$	10.4869	+	12.4979i	0.480164	+	0.572238i
$478$	5.46314	−	15.0098i	0.249878	−	0.686534i
$479$	−3.95553	+	22.4329i	−0.180733	+	1.02499i	0.750583	+	0.660776i	$0.229773\pi$
$479$	−3.95553	+	22.4329i	−0.180733	+	1.02499i	−0.931316	+	0.364211i	$0.881339\pi$
$480$		0			0
$481$	41.9240	−	15.2591i	1.91157	−	0.695754i
$482$	19.2214	+	11.0975i	0.875509	+	0.505475i
$483$	−13.7700	+	7.95011i	−0.626556	+	0.361743i
$484$	6.97234	+	5.85049i	0.316925	+	0.265931i
$485$		0			0
$486$	10.5025	+	18.1909i	0.476403	+	0.825155i
$487$	−5.58510	−	3.22456i	−0.253085	−	0.146119i	0.368091	−	0.929790i	$-0.380011\pi$
$487$	−5.58510	−	3.22456i	−0.253085	−	0.146119i	−0.621176	+	0.783671i	$0.713345\pi$
$488$	−2.68349	−	7.37283i	−0.121476	−	0.333752i
$489$	−3.01707	−	17.1107i	−0.136437	−	0.773771i
$490$		0			0
$491$	22.8944	+	8.33289i	1.03321	+	0.376058i	0.802303	−	0.596917i	$-0.203608\pi$
$491$	22.8944	+	8.33289i	1.03321	+	0.376058i	0.230908	+	0.972975i	$0.425830\pi$
$492$	−16.7805	−	19.9982i	−0.756524	−	0.901590i
$493$		−	0.169008i		−	0.00761173i
$494$	−13.4543	−	13.2070i	−0.605336	−	0.594209i
$495$		0			0
$496$	0.265595	−	0.222861i	0.0119256	−	0.0100067i
$497$	12.5759	−	34.5520i	0.564106	−	1.54987i
$498$	−26.5730	−	4.68554i	−1.19077	−	0.209964i
$499$	−0.282127	−	1.60002i	−0.0126298	−	0.0716269i	0.977841	−	0.209347i	$-0.0671337\pi$
$499$	−0.282127	−	1.60002i	−0.0126298	−	0.0716269i	−0.990471	+	0.137720i	$0.956023\pi$
$500$		0			0
$501$	−18.7854	+	32.5373i	−0.839270	+	1.45366i
$502$	−19.5311	+	11.2763i	−0.871717	+	0.503286i
$503$	22.6234	−	26.9615i	1.00873	−	1.20215i	0.0294632	−	0.999566i	$-0.490620\pi$
$503$	22.6234	−	26.9615i	1.00873	−	1.20215i	0.979264	−	0.202588i	$-0.0649353\pi$
$504$	6.34060	+	5.32040i	0.282433	+	0.236989i
$505$		0			0
$506$	−1.46388	+	2.53551i	−0.0650772	+	0.112717i
$507$	4.62894	+	12.7179i	0.205578	+	0.564822i
$508$	16.1494	−	2.84757i	0.716513	−	0.126341i
$509$	4.20711	−	23.8597i	0.186477	−	1.05756i	−0.737567	−	0.675274i	$-0.764025\pi$
$509$	4.20711	−	23.8597i	0.186477	−	1.05756i	0.924043	−	0.382288i	$-0.124864\pi$
$510$		0			0
$511$	−29.5952	+	24.8333i	−1.30921	+	1.09856i
$512$		−	1.00000i		−	0.0441942i
$513$	1.04308	+	3.75323i	0.0460532	+	0.165709i
$514$	10.7146			0.472599
$515$		0			0
$516$	−25.6816	−	9.34733i	−1.13057	−	0.411493i
$517$	0.103720	+	0.0182886i	0.00456159	+	0.000804332i
$518$	−32.0537	+	5.65193i	−1.40836	+	0.248332i
$519$	−37.0795	+	13.4958i	−1.62761	+	0.592401i
$520$		0			0
$521$	3.95859	+	6.85648i	0.173429	+	0.300388i	0.939616	−	0.342229i	$-0.111182\pi$
$521$	3.95859	+	6.85648i	0.173429	+	0.300388i	−0.766187	+	0.642617i	$0.777849\pi$
$522$	−0.219780	+	0.261923i	−0.00961950	+	0.0114641i
$523$	−1.57943	+	1.88229i	−0.0690637	+	0.0823069i	−0.799470	−	0.600706i	$-0.794886\pi$
$523$	−1.57943	+	1.88229i	−0.0690637	+	0.0823069i	0.730406	+	0.683013i	$0.239331\pi$
$524$	5.56833	+	9.64464i	0.243254	+	0.421328i
$525$		0			0
$526$	25.0584	−	9.12051i	1.09260	−	0.397673i
$527$	0.442714	−	0.0780624i	0.0192849	−	0.00340045i
$528$	3.21749	+	0.567331i	0.140023	+	0.0246899i
$529$	−17.3697	−	6.32204i	−0.755203	−	0.274871i
$530$		0			0
$531$	−21.4736			−0.931874
$532$	7.99322	+	11.1931i	0.346550	+	0.485282i
$533$			47.6163i			2.06249i
$534$	33.0939	−	27.7691i	1.43211	−	1.20169i
$535$		0			0
$536$	0.178976	−	1.01502i	0.00773057	−	0.0438422i
$537$	−10.6748	+	1.88225i	−0.460650	+	0.0812250i
$538$	−0.488375	−	1.34180i	−0.0210554	−	0.0578491i
$539$	2.03681	−	3.52786i	0.0877316	−	0.151956i
$540$		0			0
$541$	17.2132	+	14.4436i	0.740054	+	0.620979i	0.932852	−	0.360260i	$-0.117312\pi$
$541$	17.2132	+	14.4436i	0.740054	+	0.620979i	−0.192798	+	0.981238i	$0.561756\pi$
$542$	4.73699	−	5.64532i	0.203471	−	0.242487i
$543$	3.46730	−	2.00184i	0.148796	−	0.0859074i
$544$	0.648300	−	1.12289i	0.0277956	−	0.0481434i
$545$		0			0
$546$	−5.61983	−	31.8717i	−0.240507	−	1.36398i
$547$	−26.3908	−	4.65342i	−1.12839	−	0.198966i	−0.421869	−	0.906657i	$-0.638626\pi$
$547$	−26.3908	−	4.65342i	−1.12839	−	0.198966i	−0.706522	+	0.707691i	$0.749737\pi$
$548$	−2.51099	+	6.89889i	−0.107264	+	0.294706i
$549$	−15.7660	+	13.2292i	−0.672876	+	0.564610i
$550$		0			0
$551$	−0.462374	+	0.330191i	−0.0196978	+	0.0140666i
$552$		−	5.03902i		−	0.214475i
$553$	−28.4158	−	33.8647i	−1.20836	−	1.44007i
$554$	2.37302	+	0.863707i	0.100820	+	0.0366954i
$555$		0			0
$556$	2.05105	+	11.6321i	0.0869839	+	0.493310i
$557$	13.3749	+	36.7473i	0.566714	+	1.55704i	0.809601	+	0.586980i	$0.199683\pi$
$557$	13.3749	+	36.7473i	0.566714	+	1.55704i	−0.242887	+	0.970055i	$0.578094\pi$
$558$	−0.787619	−	0.454732i	−0.0333426	−	0.0192503i
$559$	24.9244	+	43.1703i	1.05419	+	1.82591i
$560$		0			0
$561$	3.24508	+	2.72295i	0.137008	+	0.114963i
$562$	−14.9206	+	8.61440i	−0.629387	+	0.363377i
$563$	7.46645	+	4.31076i	0.314673	+	0.181677i	0.649016	−	0.760775i	$-0.275181\pi$
$563$	7.46645	+	4.31076i	0.314673	+	0.181677i	−0.334343	+	0.942452i	$0.608514\pi$
$564$	−0.170336	+	0.0619974i	−0.00717246	+	0.00261056i
$565$		0			0
$566$	−4.90049	+	27.7920i	−0.205983	+	1.16819i
$567$	−10.7799	+	29.6174i	−0.452711	+	1.24381i
$568$	7.49028	+	8.92657i	0.314285	+	0.374550i
$569$	−23.0260			−0.965300			−0.482650	−	0.875813i	$-0.660326\pi$
$569$	−23.0260			−0.965300			−0.482650	+	0.875813i	$0.660326\pi$
$570$		0			0
$571$	−29.9673			−1.25409			−0.627047	−	0.778981i	$-0.715737\pi$
$571$	−29.9673			−1.25409			−0.627047	+	0.778981i	$0.715737\pi$
$572$	−3.83047	−	4.56497i	−0.160160	−	0.190871i
$573$	9.10040	−	25.0031i	0.380175	−	1.04452i
$574$	6.03220	−	34.2103i	0.251779	−	1.42791i
$575$		0			0
$576$	−2.46493	+	0.897162i	−0.102706	+	0.0373818i
$577$	−3.93622	−	2.27258i	−0.163867	−	0.0946087i	0.415824	−	0.909445i	$-0.363493\pi$
$577$	−3.93622	−	2.27258i	−0.163867	−	0.0946087i	−0.579691	+	0.814837i	$0.696827\pi$
$578$	−13.2665	+	7.65941i	−0.551813	+	0.318590i
$579$	−39.0333	−	32.7529i	−1.62217	−	1.36116i
$580$		0			0
$581$	−17.9526	−	31.0949i	−0.744800	−	1.29003i
$582$	33.3131	+	19.2334i	1.38087	+	0.797248i
$583$	2.93083	+	8.05240i	0.121383	+	0.333496i
$584$	−2.12608	−	12.0576i	−0.0879779	−	0.498947i
$585$		0			0
$586$	−11.8571	−	4.31563i	−0.489813	−	0.178277i
$587$	11.8709	+	14.1471i	0.489963	+	0.583915i	0.953208	−	0.302315i	$-0.0977595\pi$
$587$	11.8709	+	14.1471i	0.489963	+	0.583915i	−0.463245	+	0.886230i	$0.653315\pi$
$588$			7.01120i			0.289137i
$589$	−1.07850	−	1.05867i	−0.0444387	−	0.0436219i
$590$		0			0
$591$	−27.7537	+	23.2881i	−1.14164	+	0.957946i
$592$	3.52794	−	9.69294i	0.144998	−	0.398377i
$593$	15.7488	+	2.77694i	0.646726	+	0.114035i	0.487384	−	0.873188i	$-0.337951\pi$
$593$	15.7488	+	2.77694i	0.646726	+	0.114035i	0.159343	+	0.987223i	$0.449062\pi$
$594$	0.213812	+	1.21259i	0.00877280	+	0.0497530i
$595$		0			0
$596$	−1.75726	+	3.04366i	−0.0719800	+	0.124673i
$597$	−1.45552	+	0.840343i	−0.0595704	+	0.0343930i
$598$	−5.90788	+	7.04074i	−0.241591	+	0.287917i
$599$	−3.02967	−	2.54220i	−0.123789	−	0.103871i	0.578792	−	0.815476i	$-0.303524\pi$
$599$	−3.02967	−	2.54220i	−0.123789	−	0.103871i	−0.702581	+	0.711604i	$0.747969\pi$
$600$		0			0
$601$	1.10855	−	1.92006i	0.0452186	−	0.0783209i	−0.842530	−	0.538649i	$-0.818935\pi$
$601$	1.10855	−	1.92006i	0.0452186	−	0.0783209i	0.887749	+	0.460328i	$0.152268\pi$
$602$	−12.4382	−	34.1735i	−0.506941	−	1.39281i
$603$	−2.66253	+	0.469476i	−0.108427	+	0.0191185i
$604$	0.0369211	−	0.209390i	0.00150230	−	0.00851996i
$605$		0			0
$606$	12.0313	−	10.0955i	0.488739	−	0.410101i
$607$			17.4964i			0.710155i	0.934837	+	0.355078i	$0.115546\pi$
$607$			17.4964i			0.710155i	−0.934837	+	0.355078i	$0.884454\pi$
$608$	−4.33860	+	0.420163i	−0.175954	+	0.0170399i
$609$	−0.975319			−0.0395219
$610$		0			0
$611$	0.310689	+	0.113082i	0.0125691	+	0.00457479i
$612$	−3.34947	−	0.590603i	−0.135394	−	0.0238737i
$613$	8.98922	−	1.58504i	0.363071	−	0.0640193i	0.0108633	−	0.999941i	$-0.496542\pi$
$613$	8.98922	−	1.58504i	0.363071	−	0.0640193i	0.352208	+	0.935922i	$0.385431\pi$
$614$	−8.51802	+	3.10031i	−0.343759	+	0.125118i
$615$		0			0
$616$	2.17372	+	3.76500i	0.0875818	+	0.151696i
$617$	−1.00026	+	1.19206i	−0.0402689	+	0.0479906i	−0.785803	−	0.618477i	$-0.787750\pi$
$617$	−1.00026	+	1.19206i	−0.0402689	+	0.0479906i	0.745534	+	0.666467i	$0.232194\pi$
$618$	−18.8361	+	22.4480i	−0.757699	+	0.902990i
$619$	16.2140	+	28.0835i	0.651695	+	1.12877i	0.982711	+	0.185144i	$0.0592753\pi$
$619$	16.2140	+	28.0835i	0.651695	+	1.12877i	−0.331016	+	0.943625i	$0.607391\pi$
$620$		0			0
$621$	1.78454	−	0.649520i	0.0716112	−	0.0260644i
$622$	−21.3826	+	3.77032i	−0.857362	+	0.151176i
$623$	56.6127	+	9.98235i	2.26814	+	0.399934i
$624$	9.63789	+	3.50790i	0.385824	+	0.140429i
$625$		0			0
$626$	10.0460			0.401520
$627$	1.10955	−	14.1978i	0.0443112	−	0.567005i
$628$		−	7.68751i		−	0.306765i
$629$	10.2454	−	8.59692i	0.408511	−	0.342782i
$630$		0			0
$631$	−1.67744	+	9.51323i	−0.0667778	+	0.378716i	0.933043	+	0.359766i	$0.117143\pi$
$631$	−1.67744	+	9.51323i	−0.0667778	+	0.378716i	−0.999820	+	0.0189499i	$0.993968\pi$
$632$	13.7971	−	2.43280i	0.548819	−	0.0967715i
$633$	−11.4187	−	31.3726i	−0.453852	−	1.24695i
$634$	1.05423	−	1.82598i	0.0418688	−	0.0725189i
$635$		0			0
$636$	−11.2981	−	9.48023i	−0.447999	−	0.375915i
$637$	8.22011	−	9.79635i	0.325693	−	0.388145i
$638$	−0.155528	+	0.0897942i	−0.00615741	+	0.00355498i
$639$	15.2834	−	26.4716i	0.604602	−	1.04720i
$640$		0			0
$641$	7.05763	+	40.0258i	0.278759	+	1.58092i	0.726761	+	0.686891i	$0.241025\pi$
$641$	7.05763	+	40.0258i	0.278759	+	1.58092i	−0.448001	+	0.894033i	$0.647864\pi$
$642$	25.5826	+	4.51091i	1.00967	+	0.178031i
$643$	14.3882	−	39.5312i	0.567414	−	1.55896i	−0.241112	−	0.970497i	$-0.577512\pi$
$643$	14.3882	−	39.5312i	0.567414	−	1.55896i	0.808526	−	0.588460i	$-0.200266\pi$
$644$	5.13651	−	4.31004i	0.202407	−	0.169840i
$645$		0			0
$646$	−5.14416	−	2.34092i	−0.202394	−	0.0921022i
$647$			18.0072i			0.707936i	0.935258	+	0.353968i	$0.115168\pi$
$647$			18.0072i			0.707936i	−0.935258	+	0.353968i	$0.884832\pi$
$648$	−6.42054	−	7.65170i	−0.252223	−	0.300587i
$649$	−10.5986	−	3.85757i	−0.416031	−	0.151423i
$650$		0			0
$651$	−0.450487	−	2.55484i	−0.0176560	−	0.100132i
$652$	2.50598	+	6.88513i	0.0981419	+	0.269643i
$653$	34.1968	+	19.7435i	1.33822	+	0.772624i	0.986544	−	0.163496i	$-0.0522772\pi$
$653$	34.1968	+	19.7435i	1.33822	+	0.772624i	0.351680	+	0.936120i	$0.385610\pi$
$654$	8.82243	+	15.2809i	0.344984	+	0.597530i
$655$		0			0
$656$	8.43340	+	7.07646i	0.329269	+	0.276289i
$657$	−27.8138	+	16.0583i	−1.08512	+	0.626493i
$658$	−0.208891	−	0.120604i	−0.00814344	−	0.00470162i
$659$	33.6395	−	12.2438i	1.31041	−	0.476949i	0.410035	−	0.912070i	$-0.365516\pi$
$659$	33.6395	−	12.2438i	1.31041	−	0.476949i	0.900372	+	0.435120i	$0.143294\pi$
$660$		0			0
$661$	2.36241	−	13.3979i	0.0918871	−	0.521118i	−0.903770	−	0.428019i	$-0.859212\pi$
$661$	2.36241	−	13.3979i	0.0918871	−	0.521118i	0.995657	−	0.0930988i	$-0.0296772\pi$
$662$	1.17795	−	3.23639i	0.0457822	−	0.125786i
$663$	8.54809	+	10.1872i	0.331980	+	0.395639i
$664$	11.3789			0.441588
$665$		0			0
$666$	−27.0576			−1.04846
$667$	0.178043	+	0.212184i	0.00689386	+	0.00821578i
$668$	5.41893	−	14.8884i	0.209665	−	0.576049i
$669$	4.82470	−	27.3623i	0.186534	−	1.05789i
$670$		0			0
$671$	−10.1581	+	3.69724i	−0.392148	+	0.142730i
$672$	−6.48003	−	3.74124i	−0.249972	−	0.144322i
$673$	36.5649	−	21.1108i	1.40947	−	0.813760i	0.414136	−	0.910215i	$-0.364084\pi$
$673$	36.5649	−	21.1108i	1.40947	−	0.813760i	0.995337	+	0.0964549i	$0.0307504\pi$
$674$	−19.8089	−	16.6216i	−0.763009	−	0.640241i
$675$		0			0
$676$	−2.85372	−	4.94278i	−0.109758	−	0.190107i
$677$	37.8202	+	21.8355i	1.45355	+	0.839207i	0.998681	−	0.0513514i	$-0.0163528\pi$
$677$	37.8202	+	21.8355i	1.45355	+	0.839207i	0.454869	+	0.890558i	$0.349686\pi$
$678$	−9.40920	−	25.8516i	−0.361358	−	0.992824i
$679$	8.88840	+	50.4086i	0.341105	+	1.93450i
$680$		0			0
$681$	−22.7878	−	8.29409i	−0.873231	−	0.317830i
$682$	−0.307051	−	0.365929i	−0.0117576	−	0.0140122i
$683$		−	9.22100i		−	0.352832i	−0.984316	−	0.176416i	$-0.943550\pi$
$683$		−	9.22100i		−	0.352832i	0.984316	−	0.176416i	$-0.0564504\pi$
$684$	4.92810	+	10.3174i	0.188431	+	0.394496i
$685$		0			0
$686$	9.77350	−	8.20094i	0.373154	−	0.313113i
$687$	4.10133	−	11.2683i	0.156475	−	0.429913i
$688$	11.3501	+	2.00132i	0.432717	+	0.0762998i
$689$	4.67132	+	26.4924i	0.177963	+	1.00928i
$690$		0			0
$691$	20.0044	−	34.6487i	0.761004	−	1.31810i	−0.181330	−	0.983422i	$-0.558040\pi$
$691$	20.0044	−	34.6487i	0.761004	−	1.31810i	0.942334	−	0.334675i	$-0.108626\pi$
$692$	14.4108	−	8.32010i	0.547818	−	0.316283i
$693$	7.33029	−	8.73590i	0.278455	−	0.331849i
$694$	1.93290	+	1.62189i	0.0733717	+	0.0615662i
$695$		0			0
$696$	0.154547	−	0.267683i	0.00585808	−	0.0101465i
$697$	4.88209	+	13.4134i	0.184922	+	0.508070i
$698$	−3.62355	+	0.638930i	−0.137153	+	0.0241839i
$699$	−2.98884	+	16.9506i	−0.113048	+	0.641130i
$700$		0			0
$701$	−1.37655	+	1.15507i	−0.0519917	+	0.0436262i	−0.668413	−	0.743790i	$-0.733026\pi$
$701$	−1.37655	+	1.15507i	−0.0519917	+	0.0436262i	0.616422	+	0.787416i	$0.288582\pi$
$702$			3.86537i			0.145889i
$703$	−43.5361	−	11.2337i	−1.64200	−	0.423688i
$704$	−1.37777			−0.0519267
$705$		0			0
$706$	2.62772	+	0.956410i	0.0988954	+	0.0359950i
$707$	20.5816	+	3.62909i	0.774051	+	0.136486i
$708$	19.1173	−	3.37089i	0.718471	−	0.126686i
$709$	31.8904	−	11.6072i	1.19767	−	0.435916i	0.335259	−	0.942126i	$-0.391176\pi$
$709$	31.8904	−	11.6072i	1.19767	−	0.435916i	0.862410	+	0.506210i	$0.168954\pi$
$710$		0			0
$711$	−18.3749	−	31.8263i	−0.689113	−	1.19358i
$712$	−11.7104	+	13.9559i	−0.438867	+	0.523021i
$713$	−0.473577	+	0.564387i	−0.0177356	+	0.0211365i
$714$	−4.85090	−	8.40200i	−0.181540	−	0.314437i
$715$		0			0
$716$	4.29540	−	1.56340i	0.160527	−	0.0584269i
$717$	37.3019	−	6.57733i	1.39306	−	0.245635i
$718$	19.8344	+	3.49734i	0.740212	+	0.130519i
$719$	−4.77790	−	1.73901i	−0.178186	−	0.0648542i	0.251387	−	0.967887i	$-0.419113\pi$
$719$	−4.77790	−	1.73901i	−0.178186	−	0.0648542i	−0.429572	+	0.903033i	$0.641336\pi$
$720$		0			0
$721$	−38.9934			−1.45219
$722$	3.64584	+	18.6469i	0.135684	+	0.693967i
$723$			52.6311i			1.95737i
$724$	−1.29338	+	1.08527i	−0.0480680	+	0.0403338i
$725$		0			0
$726$	−3.74786	+	21.2552i	−0.139096	+	0.788854i
$727$	21.2529	−	3.74747i	0.788228	−	0.138986i	0.234977	−	0.972001i	$-0.424498\pi$
$727$	21.2529	−	3.74747i	0.788228	−	0.138986i	0.553250	+	0.833015i	$0.313387\pi$
$728$	4.66784	+	12.8248i	0.173002	+	0.475318i
$729$	−9.92186	+	17.1852i	−0.367476	+	0.636487i
$730$		0			0
$731$	11.4474	+	9.60551i	0.423397	+	0.355273i
$732$	11.9593	−	14.2525i	0.442027	−	0.526788i
$733$	−8.20601	+	4.73774i	−0.303096	+	0.174993i	−0.643833	−	0.765166i	$-0.722657\pi$
$733$	−8.20601	+	4.73774i	−0.303096	+	0.174993i	0.340737	+	0.940159i	$0.389323\pi$
$734$	2.26066	−	3.91559i	0.0834426	−	0.144527i
$735$		0			0
$736$	0.369001	+	2.09271i	0.0136015	+	0.0771382i
$737$	−1.39847	−	0.246588i	−0.0515132	−	0.00908317i
$738$	9.87687	−	27.1365i	0.363573	−	0.998908i
$739$	6.02954	−	5.05938i	0.221800	−	0.186112i	−0.525116	−	0.851031i	$-0.675978\pi$
$739$	6.02954	−	5.05938i	0.221800	−	0.186112i	0.746916	+	0.664918i	$0.231534\pi$
$740$		0			0
$741$	11.1699	−	43.2888i	0.410337	−	1.59026i
$742$		−	19.6254i		−	0.720473i
$743$	−31.1013	−	37.0651i	−1.14100	−	1.35979i	−0.923442	−	0.383737i	$-0.874637\pi$
$743$	−31.1013	−	37.0651i	−1.14100	−	1.35979i	−0.217553	−	0.976049i	$-0.569807\pi$
$744$	0.772575	+	0.281194i	0.0283240	+	0.0103091i
$745$		0			0
$746$	−4.04087	−	22.9169i	−0.147947	−	0.839048i
$747$	−10.2087	−	28.0483i	−0.373518	−	1.02623i
$748$	−1.54708	−	0.893209i	−0.0565670	−	0.0326590i
$749$	17.2835	+	29.9359i	0.631525	+	1.09383i
$750$		0			0
$751$	−9.30243	−	7.80567i	−0.339451	−	0.284833i	0.457087	−	0.889422i	$-0.348893\pi$
$751$	−9.30243	−	7.80567i	−0.339451	−	0.284833i	−0.796537	+	0.604589i	$0.793337\pi$
$752$	0.0662008	−	0.0382211i	0.00241410	−	0.00139378i
$753$	−46.3145	−	26.7397i	−1.68779	−	0.974447i
$754$	−0.529778	+	0.192823i	−0.0192934	+	0.00702221i
$755$		0			0
$756$	0.489679	−	2.77711i	0.0178095	−	0.101002i
$757$	11.9596	−	32.8586i	0.434677	−	1.19427i	−0.508233	−	0.861220i	$-0.669701\pi$
$757$	11.9596	−	32.8586i	0.434677	−	1.19427i	0.942910	−	0.333046i	$-0.108077\pi$
$758$	6.00792	+	7.15997i	0.218218	+	0.260062i
$759$	−6.94262			−0.252001
$760$		0			0
$761$	46.9073			1.70039			0.850194	−	0.526470i	$-0.176485\pi$
$761$	46.9073			1.70039			0.850194	+	0.526470i	$0.176485\pi$
$762$	24.9954	+	29.7884i	0.905489	+	1.07912i
$763$	−8.03041	+	22.0634i	−0.290720	+	0.798748i
$764$	−1.94845	+	11.0502i	−0.0704926	+	0.399783i
$765$		0			0
$766$	30.8559	−	11.2306i	1.11487	−	0.405779i
$767$	−30.6636	−	17.7036i	−1.10720	−	0.639241i
$768$	2.05362	−	1.18566i	0.0741035	−	0.0427837i
$769$	−1.06182	−	0.890969i	−0.0382900	−	0.0321292i	0.623442	−	0.781870i	$-0.285734\pi$
$769$	−1.06182	−	0.890969i	−0.0382900	−	0.0321292i	−0.661732	+	0.749741i	$0.730178\pi$
$770$		0			0
$771$	12.7038	+	22.0036i	0.457516	+	0.792440i
$772$	18.6090	+	10.7439i	0.669753	+	0.386682i
$773$	2.20242	+	6.05111i	0.0792157	+	0.217643i	0.972978	−	0.230897i	$-0.0741662\pi$
$773$	2.20242	+	6.05111i	0.0792157	+	0.217643i	−0.893762	+	0.448541i	$0.851944\pi$
$774$	−5.24973	−	29.7727i	−0.188698	−	1.07016i
$775$		0			0
$776$	−15.2434	−	5.54814i	−0.547206	−	0.199167i
$777$	−49.6116	−	59.1248i	−1.77981	−	2.12109i
$778$			10.6737i			0.382670i
$779$	27.1585	−	39.5624i	0.973056	−	1.41747i
$780$		0			0
$781$	12.2988	−	10.3199i	0.440085	−	0.369275i
$782$	−0.942355	+	2.58910i	−0.0336985	+	0.0925860i
$783$	0.114719	+	0.0202281i	0.00409973	+	0.000722893i
$784$	−0.513421	−	2.91175i	−0.0183365	−	0.103991i
$785$		0			0
$786$	−13.2043	+	22.8705i	−0.470981	+	0.815762i
$787$	7.30651	−	4.21842i	0.260449	−	0.150370i	−0.364090	−	0.931364i	$-0.618620\pi$
$787$	7.30651	−	4.21842i	0.260449	−	0.150370i	0.624539	+	0.780993i	$0.285287\pi$
$788$	9.82078	−	11.7040i	0.349851	−	0.416936i
$789$	48.4407	+	40.6466i	1.72453	+	1.44706i
$790$		0			0
$791$	18.3037	−	31.7030i	0.650805	−	1.12723i
$792$	1.23608	+	3.39612i	0.0439224	+	0.120676i
$793$	−33.4200	+	5.89285i	−1.18678	+	0.209261i
$794$	1.74625	−	9.90348i	0.0619721	−	0.351461i
$795$		0			0
$796$	0.542940	−	0.455581i	0.0192440	−	0.0161476i
$797$		−	32.4342i		−	1.14888i	−0.818548	−	0.574438i	$-0.805221\pi$
$797$		−	32.4342i		−	1.14888i	0.818548	−	0.574438i	$-0.194779\pi$
$798$	−13.5091	+	29.6862i	−0.478217	+	1.05088i
$799$	0.0991149			0.00350643
$800$		0			0
$801$	44.9066	+	16.3447i	1.58670	+	0.577511i
$802$	−11.8956	−	2.09751i	−0.420047	−	0.0740657i
$803$	−16.6126	+	2.92926i	−0.586247	+	0.103371i
$804$	2.29667	−	0.835919i	0.0809973	−	0.0294806i
$805$		0			0
$806$	−0.749796	−	1.29868i	−0.0264104	−	0.0457442i
$807$	2.17650	−	2.59385i	0.0766164	−	0.0913079i
$808$	−4.25734	+	5.07370i	−0.149773	+	0.178492i
$809$	−9.01013	−	15.6060i	−0.316779	−	0.548678i	0.663035	−	0.748589i	$-0.269268\pi$
$809$	−9.01013	−	15.6060i	−0.316779	−	0.548678i	−0.979814	+	0.199911i	$0.935935\pi$
$810$		0			0
$811$	24.5830	−	8.94748i	0.863226	−	0.314189i	0.127805	−	0.991799i	$-0.459207\pi$
$811$	24.5830	−	8.94748i	0.863226	−	0.314189i	0.735421	+	0.677611i	$0.236985\pi$
$812$	0.405051	−	0.0714214i	0.0142145	−	0.00250640i
$813$	17.2098	+	3.03455i	0.603573	+	0.106426i
$814$	−13.3547	−	4.86070i	−0.468081	−	0.170367i
$815$		0			0
$816$	3.07464			0.107634
$817$	3.91407	−	50.0843i	0.136936	−	1.75223i
$818$		−	39.5462i		−	1.38270i
$819$	27.4244	−	23.0118i	0.958287	−	0.804098i
$820$		0			0
$821$	−4.91249	+	27.8601i	−0.171447	+	0.972325i	0.770718	+	0.637176i	$0.219898\pi$
$821$	−4.91249	+	27.8601i	−0.171447	+	0.972325i	−0.942165	+	0.335149i	$0.891213\pi$
$822$	−17.1449	+	3.02310i	−0.597996	+	0.105443i
$823$	17.0857	+	46.9427i	0.595571	+	1.63632i	0.759995	+	0.649929i	$0.225201\pi$
$823$	17.0857	+	46.9427i	0.595571	+	1.63632i	−0.164424	+	0.986390i	$0.552577\pi$
$824$	6.17880	−	10.7020i	0.215249	−	0.372822i
$825$		0			0
$826$	19.7878	+	16.6039i	0.688504	+	0.577723i
$827$	3.41471	−	4.06949i	0.118741	−	0.141510i	−0.703399	−	0.710795i	$-0.748335\pi$
$827$	3.41471	−	4.06949i	0.118741	−	0.141510i	0.822140	+	0.569285i	$0.192780\pi$
$828$	4.82733	−	2.78706i	0.167761	−	0.0968570i
$829$	18.4308	−	31.9231i	0.640129	−	1.10874i	−0.345275	−	0.938502i	$-0.612214\pi$
$829$	18.4308	−	31.9231i	0.640129	−	1.10874i	0.985404	−	0.170234i	$-0.0544524\pi$
$830$		0			0
$831$	1.03986	+	5.89733i	0.0360723	+	0.204576i
$832$	−4.25950	−	0.751065i	−0.147672	−	0.0260385i
$833$	1.31118	−	3.60242i	0.0454295	−	0.124817i
$834$	−21.4560	+	18.0037i	−0.742961	+	0.623418i
$835$		0			0
$836$	0.578889	+	5.97760i	0.0200213	+	0.206740i
$837$			0.309849i			0.0107099i
$838$	18.3404	+	21.8572i	0.633558	+	0.755045i
$839$	−42.0154	−	15.2924i	−1.45053	−	0.527951i	−0.507793	−	0.861479i	$-0.669538\pi$
$839$	−42.0154	−	15.2924i	−1.45053	−	0.527951i	−0.942740	+	0.333528i	$0.891761\pi$
$840$		0			0
$841$	−5.03285	−	28.5427i	−0.173546	−	0.984231i
$842$	0.697393	+	1.91607i	0.0240337	+	0.0660321i
$843$	−35.3814	−	20.4275i	−1.21860	−	0.703559i
$844$	7.03956	+	12.1929i	0.242312	+	0.419696i
$845$		0			0
$846$	−0.153605	−	0.128890i	−0.00528106	−	0.00443133i
$847$	−24.8721	+	14.3599i	−0.854615	+	0.493412i
$848$	5.38633	+	3.10980i	0.184967	+	0.106791i
$849$	−62.8845	+	22.8881i	−2.15819	+	0.785517i
$850$		0			0
$851$	−3.80625	+	21.5863i	−0.130476	+	0.739969i
$852$	−9.45085	+	25.9660i	−0.323781	+	0.889581i
$853$	18.9389	+	22.5705i	0.648457	+	0.772800i	0.985680	−	0.168624i	$-0.0539324\pi$
$853$	18.9389	+	22.5705i	0.648457	+	0.772800i	−0.337224	+	0.941424i	$0.609488\pi$
$854$	24.7574			0.847181
$855$		0			0
$856$	−10.9548			−0.374428
$857$	−30.5152	−	36.3667i	−1.04238	−	1.24226i	−0.969544	−	0.244917i	$-0.921239\pi$
$857$	−30.5152	−	36.3667i	−1.04238	−	1.24226i	−0.0728369	−	0.997344i	$-0.523205\pi$
$858$	4.83309	−	13.2788i	0.164999	−	0.453331i
$859$	−0.165772	+	0.940140i	−0.00565607	+	0.0320772i	−0.987505	−	0.157587i	$-0.949629\pi$
$859$	−0.165772	+	0.940140i	−0.00565607	+	0.0320772i	0.981849	+	0.189664i	$0.0607398\pi$
$860$		0			0
$861$	77.4070	−	28.1739i	2.63802	−	0.960162i
$862$	11.7526	+	6.78537i	0.400295	+	0.231111i
$863$	−40.7257	+	23.5130i	−1.38632	+	0.800392i	−0.992898	−	0.118967i	$-0.962042\pi$
$863$	−40.7257	+	23.5130i	−1.38632	+	0.800392i	−0.393421	+	0.919359i	$0.628708\pi$
$864$	0.684602	+	0.574449i	0.0232906	+	0.0195432i
$865$		0			0
$866$	14.4819	+	25.0834i	0.492116	+	0.852370i
$867$	−31.4590	−	18.1629i	−1.06840	−	0.616843i
$868$	0.374175	+	1.02804i	0.0127003	+	0.0348939i
$869$	−3.35184	−	19.0092i	−0.113703	−	0.644844i
$870$		0			0
$871$	−4.18906	−	1.52469i	−0.141941	−	0.0516622i
$872$	−4.78296	−	5.70011i	−0.161971	−	0.193030i
$873$			42.5515i			1.44015i
$874$	8.92438	−	2.48023i	0.301872	−	0.0838949i
$875$		0			0
$876$	22.2409	−	18.6623i	0.751451	−	0.630542i
$877$	−14.6358	+	40.2114i	−0.494215	+	1.35784i	0.402575	+	0.915387i	$0.368115\pi$
$877$	−14.6358	+	40.2114i	−0.494215	+	1.35784i	−0.896790	+	0.442457i	$0.854107\pi$
$878$	−11.0435	−	1.94726i	−0.372699	−	0.0657168i
$879$	−5.19580	−	29.4668i	−0.175250	−	0.993891i
$880$		0			0
$881$	−4.53664	+	7.85770i	−0.152843	+	0.264733i	−0.932272	−	0.361759i	$-0.882176\pi$
$881$	−4.53664	+	7.85770i	−0.152843	+	0.264733i	0.779428	+	0.626491i	$0.215510\pi$
$882$	−6.71666	+	3.87786i	−0.226162	+	0.130574i
$883$	−20.1333	+	23.9939i	−0.677539	+	0.807460i	−0.989789	−	0.142540i	$-0.954473\pi$
$883$	−20.1333	+	23.9939i	−0.677539	+	0.807460i	0.312250	+	0.950000i	$0.398917\pi$
$884$	−4.29603	−	3.60479i	−0.144491	−	0.121242i
$885$		0			0
$886$	3.72498	−	6.45186i	0.125143	−	0.216755i
$887$	1.16097	+	3.18973i	0.0389814	+	0.107101i	0.957656	−	0.287914i	$-0.0929617\pi$
$887$	1.16097	+	3.18973i	0.0389814	+	0.107101i	−0.918675	+	0.395015i	$0.870740\pi$
$888$	24.0885	−	4.24746i	0.808358	−	0.142535i
$889$	−8.98528	+	50.9581i	−0.301357	+	1.70908i
$890$		0			0
$891$	−10.5423	+	8.84604i	−0.353180	+	0.296353i
$892$			11.7169i			0.392310i
$893$	−0.193641	−	0.271160i	−0.00647995	−	0.00907402i
$894$	−8.33401			−0.278731
$895$		0			0
$896$	2.96512	+	1.07922i	0.0990579	+	0.0360541i
$897$	−21.4637	−	3.78463i	−0.716652	−	0.126365i
$898$	−5.22326	+	0.921002i	−0.174303	+	0.0307342i
$899$	−0.0424671	+	0.0154568i	−0.00141636	+	0.000515512i
$900$		0			0
$901$	4.03216	+	6.98391i	0.134331	+	0.232668i
$902$	9.74975	−	11.6193i	0.324631	−	0.386880i
$903$	55.4320	−	66.0613i	1.84466	−	2.19838i
$904$	5.80072	+	10.0471i	0.192929	+	0.334163i
$905$		0			0
$906$	0.473783	−	0.172443i	0.0157404	−	0.00572903i
$907$	−39.0053	+	6.87769i	−1.29515	+	0.228370i	−0.778401	−	0.627767i	$-0.783969\pi$
$907$	−39.0053	+	6.87769i	−1.29515	+	0.228370i	−0.516749	+	0.856137i	$0.672858\pi$
$908$	10.0712	+	1.77582i	0.334223	+	0.0589326i
$909$	16.3259	+	5.94213i	0.541494	+	0.197088i
$910$		0			0
$911$	−24.0316			−0.796204			−0.398102	−	0.917341i	$-0.630331\pi$
$911$	−24.0316			−0.796204			−0.398102	+	0.917341i	$0.630331\pi$
$912$	−6.00695	−	8.41166i	−0.198910	−	0.278538i
$913$		−	15.6776i		−	0.518851i
$914$	11.4822	−	9.63471i	0.379798	−	0.318688i
$915$		0			0
$916$	−0.878120	+	4.98007i	−0.0290139	+	0.164546i
$917$	−34.6070	+	6.10215i	−1.14282	+	0.201511i
$918$	0.396316	+	1.08887i	0.0130804	+	0.0359380i
$919$	1.92860	−	3.34044i	0.0636187	−	0.110191i	−0.832462	−	0.554083i	$-0.813069\pi$
$919$	1.92860	−	3.34044i	0.0636187	−	0.110191i	0.896080	+	0.443892i	$0.146403\pi$
$920$		0			0
$921$	−16.4663	−	13.8169i	−0.542583	−	0.455281i
$922$	−4.41078	+	5.25656i	−0.145261	+	0.173116i
$923$	43.6484	−	25.2004i	1.43670	−	0.829481i
$924$	−5.15458	+	8.92800i	−0.169573	+	0.293710i
$925$		0			0
$926$	−3.58390	−	20.3253i	−0.117774	−	0.667931i
$927$	−31.9231	−	5.62890i	−1.04849	−	0.184877i
$928$	−0.0445813	+	0.122486i	−0.00146345	+	0.00402080i
$929$	−15.5371	+	13.0371i	−0.509755	+	0.427735i	−0.861043	−	0.508532i	$-0.830188\pi$
$929$	−15.5371	+	13.0371i	−0.509755	+	0.427735i	0.351288	+	0.936267i	$0.385744\pi$
$930$		0			0
$931$	−12.4172	+	3.45094i	−0.406958	+	0.113100i
$932$		−	7.25845i		−	0.237759i
$933$	−33.0952	−	39.4413i	−1.08349	−	1.29125i
$934$	11.3092	+	4.11621i	0.370048	+	0.134687i
$935$		0			0
$936$	1.97014	+	11.1732i	0.0643960	+	0.365208i
$937$	9.43723	+	25.9286i	0.308301	+	0.847050i	0.992988	+	0.118213i	$0.0377166\pi$
$937$	9.43723	+	25.9286i	0.308301	+	0.847050i	−0.684687	+	0.728837i	$0.740061\pi$
$938$	2.81651	+	1.62611i	0.0919623	+	0.0530945i
$939$	11.9111	+	20.6307i	0.388705	+	0.673257i
$940$		0			0
$941$	−17.5704	−	14.7433i	−0.572780	−	0.480619i	0.309787	−	0.950806i	$-0.399742\pi$
$941$	−17.5704	−	14.7433i	−0.572780	−	0.480619i	−0.882567	+	0.470187i	$0.844187\pi$
$942$	15.7872	−	9.11475i	0.514375	−	0.296975i
$943$	−20.2599	−	11.6970i	−0.659752	−	0.380908i
$944$	−7.69256	+	2.79986i	−0.250372	+	0.0911278i
$945$		0			0
$946$	2.75737	−	15.6378i	0.0896498	−	0.508429i
$947$	9.60233	−	26.3822i	0.312034	−	0.857306i	−0.680212	−	0.733016i	$-0.738112\pi$
$947$	9.60233	−	26.3822i	0.312034	−	0.857306i	0.992246	−	0.124291i	$-0.0396655\pi$
$948$	21.3546	+	25.4495i	0.693566	+	0.826560i
$949$	−52.9562			−1.71903
$950$		0			0
$951$	4.99982			0.162130
$952$	2.62985	+	3.13413i	0.0852338	+	0.101578i
$953$	−11.7324	+	32.2346i	−0.380050	+	1.04418i	0.591284	+	0.806463i	$0.298621\pi$
$953$	−11.7324	+	32.2346i	−0.380050	+	1.04418i	−0.971335	+	0.237717i	$0.923601\pi$
$954$	2.83303	−	16.0669i	0.0917229	−	0.520186i
$955$		0			0
$956$	−15.0098	+	5.46314i	−0.485453	+	0.176690i
$957$	−0.368806	−	0.212930i	−0.0119218	−	0.00688305i
$958$	19.7272	−	11.3895i	0.637357	−	0.367978i
$959$	−17.7462	−	14.8908i	−0.573054	−	0.480849i
$960$		0			0
$961$	15.4399	+	26.7427i	0.498061	+	0.862667i
$962$	−38.6374	−	22.3073i	−1.24572	−	0.719216i
$963$	9.82824	+	27.0029i	0.316711	+	0.870155i
$964$	−3.85411	−	21.8577i	−0.124132	−	0.703990i
$965$		0			0
$966$	14.9413	+	5.43820i	0.480729	+	0.174971i
$967$	9.34181	+	11.1331i	0.300412	+	0.358017i	0.895042	−	0.445983i	$-0.147146\pi$
$967$	9.34181	+	11.1331i	0.300412	+	0.358017i	−0.594629	+	0.804000i	$0.702701\pi$
$968$		−	9.10174i		−	0.292541i
$969$	−1.29185	−	13.3397i	−0.0415002	−	0.428531i
$970$		0			0
$971$	37.8612	−	31.7693i	1.21502	−	1.01952i	0.215952	−	0.976404i	$-0.430714\pi$
$971$	37.8612	−	31.7693i	1.21502	−	1.01952i	0.999070	−	0.0431208i	$-0.0137300\pi$
$972$	7.18414	−	19.7383i	0.230431	−	0.633105i
$973$	−36.7041	−	6.47192i	−1.17668	−	0.207480i
$974$	1.11988	+	6.35114i	0.0358832	+	0.203504i
$975$		0			0
$976$	−3.92300	+	6.79483i	−0.125572	+	0.217497i
$977$	−2.52147	+	1.45577i	−0.0806691	+	0.0465743i	−0.539792	−	0.841798i	$-0.681497\pi$
$977$	−2.52147	+	1.45577i	−0.0806691	+	0.0465743i	0.459123	+	0.888373i	$0.348164\pi$
$978$	−11.1682	+	13.3097i	−0.357120	+	0.425599i
$979$	19.2281	+	16.1343i	0.614533	+	0.515655i
$980$		0			0
$981$	−9.75929	+	16.9036i	−0.311590	+	0.539690i
$982$	−8.33289	−	22.8944i	−0.265913	−	0.730591i
$983$	40.6242	−	7.16313i	1.29571	−	0.228469i	0.517072	−	0.855942i	$-0.327022\pi$
$983$	40.6242	−	7.16313i	1.29571	−	0.228469i	0.778638	+	0.627474i	$0.215911\pi$
$984$	−4.53323	+	25.7092i	−0.144514	+	0.819580i
$985$		0			0
$986$	−0.129467	+	0.108636i	−0.00412308	+	0.00345968i
$987$		−	0.571978i		−	0.0182062i
$988$	−1.46889	+	18.7958i	−0.0467315	+	0.597975i
$989$	−24.4909			−0.778764
$990$		0			0
$991$	27.2089	+	9.90324i	0.864320	+	0.314587i	0.735865	−	0.677129i	$-0.236776\pi$
$991$	27.2089	+	9.90324i	0.864320	+	0.314587i	0.128455	+	0.991715i	$0.458998\pi$
$992$	−0.341442	−	0.0602055i	−0.0108408	−	0.00191153i
$993$	8.04294	−	1.41819i	0.255235	−	0.0450048i
$994$	−34.5520	+	12.5759i	−1.09592	+	0.398883i
$995$		0			0
$996$	13.4915	+	23.3679i	0.427494	+	0.740442i
$997$	−0.422618	+	0.503657i	−0.0133844	+	0.0159510i	−0.772695	−	0.634777i	$-0.781092\pi$
$997$	−0.422618	+	0.503657i	−0.0133844	+	0.0159510i	0.759311	+	0.650728i	$0.225536\pi$
$998$	−1.04434	+	1.24460i	−0.0330580	+	0.0393970i
$999$	4.60918	+	7.98334i	0.145828	+	0.252582i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	950.2.u.g.899.3		36
5.2	odd	4		950.2.l.i.101.1		18
5.3	odd	4		190.2.k.d.101.3	✓	18
5.4	even	2	inner	950.2.u.g.899.4		36
19.16	even	9	inner	950.2.u.g.149.4		36
95.23	odd	36		3610.2.a.bi.1.2		9
95.53	even	36		3610.2.a.bj.1.8		9
95.54	even	18	inner	950.2.u.g.149.3		36
95.73	odd	36		190.2.k.d.111.3	yes	18
95.92	odd	36		950.2.l.i.301.1		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
190.2.k.d.101.3	✓	18	5.3	odd	4
190.2.k.d.111.3	yes	18	95.73	odd	36
950.2.l.i.101.1		18	5.2	odd	4
950.2.l.i.301.1		18	95.92	odd	36
950.2.u.g.149.3		36	95.54	even	18	inner
950.2.u.g.149.4		36	19.16	even	9	inner
950.2.u.g.899.3		36	1.1	even	1	trivial
950.2.u.g.899.4		36	5.4	even	2	inner
3610.2.a.bi.1.2		9	95.23	odd	36
3610.2.a.bj.1.8		9	95.53	even	36

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)

\(f(q)\)	\(=\)	\(q+(-0.642788 - 0.766044i) q^{2} +(0.811037 - 2.22831i) q^{3} +(-0.173648 + 0.984808i) q^{4} +(-2.22831 + 0.811037i) q^{6} +(-2.73267 - 1.57771i) q^{7} +(0.866025 - 0.500000i) q^{8} +(-2.00943 - 1.68611i) q^{9} +O(q^{10})\)	\(q+(-0.642788 - 0.766044i) q^{2} +(0.811037 - 2.22831i) q^{3} +(-0.173648 + 0.984808i) q^{4} +(-2.22831 + 0.811037i) q^{6} +(-2.73267 - 1.57771i) q^{7} +(0.866025 - 0.500000i) q^{8} +(-2.00943 - 1.68611i) q^{9} +(-0.688886 - 1.19319i) q^{11} +(2.05362 + 1.18566i) q^{12} +(-1.47931 - 4.06437i) q^{13} +(0.547933 + 3.10748i) q^{14} +(-0.939693 - 0.342020i) q^{16} +(-0.833438 - 0.993253i) q^{17} +2.62313i q^{18} +(-1.08907 + 4.22066i) q^{19} +(-5.73192 + 4.80965i) q^{21} +(-0.471226 + 1.29468i) q^{22} +(2.09271 + 0.369001i) q^{23} +(-0.411774 - 2.33529i) q^{24} +(-2.16260 + 3.74574i) q^{26} +(0.773953 - 0.446842i) q^{27} +(2.02826 - 2.41719i) q^{28} +(0.0998515 + 0.0837854i) q^{29} +(-0.173355 + 0.300259i) q^{31} +(0.342020 + 0.939693i) q^{32} +(-3.21749 + 0.567331i) q^{33} +(-0.225152 + 1.27690i) q^{34} +(2.00943 - 1.68611i) q^{36} +10.3150i q^{37} +(3.93325 - 1.87871i) q^{38} -10.2564 q^{39} +(-10.3451 - 3.76531i) q^{41} +(7.36881 + 1.29932i) q^{42} +(-11.3501 + 2.00132i) q^{43} +(1.29468 - 0.471226i) q^{44} +(-1.06250 - 1.84030i) q^{46} +(-0.0491361 + 0.0585581i) q^{47} +(-1.52425 + 1.81653i) q^{48} +(1.47834 + 2.56055i) q^{49} +(-2.88922 + 1.05159i) q^{51} +(4.25950 - 0.751065i) q^{52} +(-6.12511 - 1.08002i) q^{53} +(-0.839788 - 0.305658i) q^{54} -3.15542 q^{56} +(8.52164 + 5.84988i) q^{57} -0.130347i q^{58} +(6.27104 - 5.26202i) q^{59} +(1.36244 - 7.72680i) q^{61} +(0.341442 - 0.0602055i) q^{62} +(2.83092 + 7.77790i) q^{63} +(0.500000 - 0.866025i) q^{64} +(2.50277 + 2.10007i) q^{66} +(0.662508 - 0.789546i) q^{67} +(1.12289 - 0.648300i) q^{68} +(2.51951 - 4.36392i) q^{69} +(2.02349 + 11.4758i) q^{71} +(-2.58328 - 0.455501i) q^{72} +(4.18756 - 11.5052i) q^{73} +(7.90176 - 6.63036i) q^{74} +(-3.96742 - 1.80543i) q^{76} +4.34745i q^{77} +(6.59270 + 7.85688i) q^{78} +(13.1650 + 4.79168i) q^{79} +(-1.73450 - 9.83684i) q^{81} +(3.76531 + 10.3451i) q^{82} +(9.85443 + 5.68946i) q^{83} +(-3.74124 - 6.48003i) q^{84} +(8.82879 + 7.40823i) q^{86} +(0.267683 - 0.154547i) q^{87} +(-1.19319 - 0.688886i) q^{88} +(-17.1195 + 6.23099i) q^{89} +(-2.36992 + 13.4405i) q^{91} +(-0.726790 + 1.99684i) q^{92} +(0.528473 + 0.629809i) q^{93} +0.0764422 q^{94} +2.37131 q^{96} +(-10.4271 - 12.4265i) q^{97} +(1.01124 - 2.77836i) q^{98} +(-0.627577 + 3.55916i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 36 q^{9}+O(q^{10}) \) 36 * q + 36 * q^9	\( 36 q + 36 q^{9} - 24 q^{11} - 12 q^{14} + 24 q^{21} - 18 q^{26} + 12 q^{29} - 12 q^{31} - 36 q^{34} - 36 q^{36} - 96 q^{39} - 42 q^{41} - 6 q^{44} + 36 q^{46} + 78 q^{49} + 84 q^{51} + 108 q^{54} + 60 q^{59} + 96 q^{61} + 18 q^{64} + 48 q^{66} + 60 q^{69} + 60 q^{71} + 6 q^{74} - 42 q^{76} - 60 q^{79} + 36 q^{81} - 12 q^{84} + 72 q^{86} - 60 q^{89} - 120 q^{91} - 12 q^{94} - 342 q^{99}+O(q^{100}) \) 36 * q + 36 * q^9 - 24 * q^11 - 12 * q^14 + 24 * q^21 - 18 * q^26 + 12 * q^29 - 12 * q^31 - 36 * q^34 - 36 * q^36 - 96 * q^39 - 42 * q^41 - 6 * q^44 + 36 * q^46 + 78 * q^49 + 84 * q^51 + 108 * q^54 + 60 * q^59 + 96 * q^61 + 18 * q^64 + 48 * q^66 + 60 * q^69 + 60 * q^71 + 6 * q^74 - 42 * q^76 - 60 * q^79 + 36 * q^81 - 12 * q^84 + 72 * q^86 - 60 * q^89 - 120 * q^91 - 12 * q^94 - 342 * q^99

Introduction

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