LMFDB - Embedded newform 950.2.l.i.101.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("950.101");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.58578819202$
Analytic rank:	$0$
Dimension:	$18$
Relative dimension:	$3$ over $\Q(\zeta_{9})$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} + 24 x^{16} - 12 x^{15} + 393 x^{14} - 222 x^{13} + 3518 x^{12} - 2478 x^{11} + 22809 x^{10} + \cdots + 64 $ x^18 + 24x^16 - 12x^15 + 393x^14 - 222x^13 + 3518x^12 - 2478x^11 + 22809x^10 - 12862x^9 + 77397x^8 - 24822x^7 + 178501x^6 - 39408x^5 + 132588x^4 + 45584x^3 + 50640x^2 + 1824x + 64
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 190)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			101.1
Root			$1.18566 + 2.05362i$ of defining polynomial
Character	$\chi$	$=$	950.101
Dual form			950.2.l.i.301.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.766044 - 0.642788i) q^{2} +(-2.22831 - 0.811037i) q^{3} +(0.173648 - 0.984808i) q^{4} +(-2.22831 + 0.811037i) q^{6} +(1.57771 - 2.73267i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(2.00943 + 1.68611i) q^{9} +O(q^{10})$	\(q+(0.766044 - 0.642788i) q^{2} +(-2.22831 - 0.811037i) q^{3} +(0.173648 - 0.984808i) q^{4} +(-2.22831 + 0.811037i) q^{6} +(1.57771 - 2.73267i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(2.00943 + 1.68611i) q^{9} +(-0.688886 - 1.19319i) q^{11} +(-1.18566 + 2.05362i) q^{12} +(-4.06437 + 1.47931i) q^{13} +(-0.547933 - 3.10748i) q^{14} +(-0.939693 - 0.342020i) q^{16} +(0.993253 - 0.833438i) q^{17} +2.62313 q^{18} +(1.08907 - 4.22066i) q^{19} +(-5.73192 + 4.80965i) q^{21} +(-1.29468 - 0.471226i) q^{22} +(0.369001 - 2.09271i) q^{23} +(0.411774 + 2.33529i) q^{24} +(-2.16260 + 3.74574i) q^{26} +(0.446842 + 0.773953i) q^{27} +(-2.41719 - 2.02826i) q^{28} +(-0.0998515 - 0.0837854i) q^{29} +(-0.173355 + 0.300259i) q^{31} +(-0.939693 + 0.342020i) q^{32} +(0.567331 + 3.21749i) q^{33} +(0.225152 - 1.27690i) q^{34} +(2.00943 - 1.68611i) q^{36} -10.3150 q^{37} +(-1.87871 - 3.93325i) q^{38} +10.2564 q^{39} +(-10.3451 - 3.76531i) q^{41} +(-1.29932 + 7.36881i) q^{42} +(2.00132 + 11.3501i) q^{43} +(-1.29468 + 0.471226i) q^{44} +(-1.06250 - 1.84030i) q^{46} +(-0.0585581 - 0.0491361i) q^{47} +(1.81653 + 1.52425i) q^{48} +(-1.47834 - 2.56055i) q^{49} +(-2.88922 + 1.05159i) q^{51} +(0.751065 + 4.25950i) q^{52} +(-1.08002 + 6.12511i) q^{53} +(0.839788 + 0.305658i) q^{54} -3.15542 q^{56} +(-5.84988 + 8.52164i) q^{57} -0.130347 q^{58} +(-6.27104 + 5.26202i) q^{59} +(1.36244 - 7.72680i) q^{61} +(0.0602055 + 0.341442i) q^{62} +(7.77790 - 2.83092i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(2.50277 + 2.10007i) q^{66} +(0.789546 + 0.662508i) q^{67} +(-0.648300 - 1.12289i) q^{68} +(-2.51951 + 4.36392i) q^{69} +(2.02349 + 11.4758i) q^{71} +(0.455501 - 2.58328i) q^{72} +(-11.5052 - 4.18756i) q^{73} +(-7.90176 + 6.63036i) q^{74} +(-3.96742 - 1.80543i) q^{76} -4.34745 q^{77} +(7.85688 - 6.59270i) q^{78} +(-13.1650 - 4.79168i) q^{79} +(-1.73450 - 9.83684i) q^{81} +(-10.3451 + 3.76531i) q^{82} +(5.68946 - 9.85443i) q^{83} +(3.74124 + 6.48003i) q^{84} +(8.82879 + 7.40823i) q^{86} +(0.154547 + 0.267683i) q^{87} +(-0.688886 + 1.19319i) q^{88} +(17.1195 - 6.23099i) q^{89} +(-2.36992 + 13.4405i) q^{91} +(-1.99684 - 0.726790i) q^{92} +(0.629809 - 0.528473i) q^{93} -0.0764422 q^{94} +2.37131 q^{96} +(12.4265 - 10.4271i) q^{97} +(-2.77836 - 1.01124i) q^{98} +(0.627577 - 3.55916i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q - 9 q^{8} - 18 q^{9}+O(q^{10}) $ 18 * q - 9 * q^8 - 18 * q^9	$ 18 q - 9 q^{8} - 18 q^{9} - 12 q^{11} + 6 q^{13} + 6 q^{14} + 42 q^{18} + 12 q^{21} + 3 q^{22} - 9 q^{23} - 9 q^{26} + 18 q^{27} - 3 q^{28} - 6 q^{29} - 6 q^{31} - 66 q^{33} + 18 q^{34} - 18 q^{36} + 12 q^{37} + 6 q^{38} + 48 q^{39} - 21 q^{41} - 42 q^{42} - 18 q^{43} + 3 q^{44} + 18 q^{46} + 54 q^{47} - 39 q^{49} + 42 q^{51} - 12 q^{52} + 24 q^{53} - 54 q^{54} + 18 q^{57} - 30 q^{59} + 48 q^{61} + 30 q^{62} + 57 q^{63} - 9 q^{64} + 24 q^{66} + 6 q^{67} + 6 q^{68} - 30 q^{69} + 30 q^{71} - 6 q^{73} - 3 q^{74} - 21 q^{76} - 30 q^{77} + 24 q^{78} + 30 q^{79} + 18 q^{81} - 21 q^{82} - 6 q^{83} + 6 q^{84} + 36 q^{86} - 24 q^{87} - 12 q^{88} + 30 q^{89} - 60 q^{91} + 18 q^{92} + 12 q^{93} + 6 q^{94} + 12 q^{97} + 18 q^{98} + 171 q^{99}+O(q^{100}) $ 18 * q - 9 * q^8 - 18 * q^9 - 12 * q^11 + 6 * q^13 + 6 * q^14 + 42 * q^18 + 12 * q^21 + 3 * q^22 - 9 * q^23 - 9 * q^26 + 18 * q^27 - 3 * q^28 - 6 * q^29 - 6 * q^31 - 66 * q^33 + 18 * q^34 - 18 * q^36 + 12 * q^37 + 6 * q^38 + 48 * q^39 - 21 * q^41 - 42 * q^42 - 18 * q^43 + 3 * q^44 + 18 * q^46 + 54 * q^47 - 39 * q^49 + 42 * q^51 - 12 * q^52 + 24 * q^53 - 54 * q^54 + 18 * q^57 - 30 * q^59 + 48 * q^61 + 30 * q^62 + 57 * q^63 - 9 * q^64 + 24 * q^66 + 6 * q^67 + 6 * q^68 - 30 * q^69 + 30 * q^71 - 6 * q^73 - 3 * q^74 - 21 * q^76 - 30 * q^77 + 24 * q^78 + 30 * q^79 + 18 * q^81 - 21 * q^82 - 6 * q^83 + 6 * q^84 + 36 * q^86 - 24 * q^87 - 12 * q^88 + 30 * q^89 - 60 * q^91 + 18 * q^92 + 12 * q^93 + 6 * q^94 + 12 * q^97 + 18 * q^98 + 171 * 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 $

$2$	0.766044	−	0.642788i	0.541675	−	0.454519i
$2$	0.766044	−	0.642788i	0.541675	−	0.454519i
$3$	−2.22831	−	0.811037i	−1.28651	−	0.468252i	−0.393932	−	0.919140i	$-0.628885\pi$
$3$	−2.22831	−	0.811037i	−1.28651	−	0.468252i	−0.892581	+	0.450887i	$0.851108\pi$
$4$	0.173648	−	0.984808i	0.0868241	−	0.492404i
$5$		0			0
$5$		0			0
$6$	−2.22831	+	0.811037i	−0.909702	+	0.331104i
$7$	1.57771	−	2.73267i	0.596318	−	1.03285i	−0.397041	−	0.917801i	$-0.629963\pi$
$7$	1.57771	−	2.73267i	0.596318	−	1.03285i	0.993359	−	0.115053i	$-0.0367037\pi$
$8$	−0.500000	−	0.866025i	−0.176777	−	0.306186i
$9$	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	$0.899933\pi$
$12$	−1.18566	+	2.05362i	−0.342270	+	0.592828i
$13$	−4.06437	+	1.47931i	−1.12725	+	0.410286i	−0.837294	−	0.546753i	$-0.815864\pi$
$13$	−4.06437	+	1.47931i	−1.12725	+	0.410286i	−0.289958	+	0.957039i	$0.593641\pi$
$14$	−0.547933	−	3.10748i	−0.146441	−	0.830509i
$15$		0			0
$16$	−0.939693	−	0.342020i	−0.234923	−	0.0855050i
$17$	0.993253	−	0.833438i	0.240899	−	0.202138i	−0.514342	−	0.857585i	$-0.671964\pi$
$17$	0.993253	−	0.833438i	0.240899	−	0.202138i	0.755242	+	0.655446i	$0.227520\pi$
$18$	2.62313			0.618277
$19$	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
$22$	−1.29468	−	0.471226i	−0.276027	−	0.100466i
$23$	0.369001	−	2.09271i	0.0769420	−	0.436360i	−0.921864	−	0.387513i	$-0.873334\pi$
$23$	0.369001	−	2.09271i	0.0769420	−	0.436360i	0.998806	−	0.0488468i	$-0.0155546\pi$
$24$	0.411774	+	2.33529i	0.0840531	+	0.476689i
$25$		0			0
$26$	−2.16260	+	3.74574i	−0.424122	+	0.734600i
$27$	0.446842	+	0.773953i	0.0859948	+	0.148947i
$28$	−2.41719	−	2.02826i	−0.456806	−	0.383306i
$29$	−0.0998515	−	0.0837854i	−0.0185420	−	0.0155586i	0.633470	−	0.773768i	$-0.281630\pi$
$29$	−0.0998515	−	0.0837854i	−0.0185420	−	0.0155586i	−0.652012	+	0.758209i	$0.726075\pi$
$30$		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	$0.176579\pi$
$32$	−0.939693	+	0.342020i	−0.166116	+	0.0604612i
$33$	0.567331	+	3.21749i	0.0987596	+	0.560094i
$34$	0.225152	−	1.27690i	0.0386133	−	0.218987i
$35$		0			0
$36$	2.00943	−	1.68611i	0.334905	−	0.281019i
$37$	−10.3150			−1.69578			−0.847889	−	0.530174i	$-0.822127\pi$
$37$	−10.3150			−1.69578			−0.847889	+	0.530174i	$0.822127\pi$
$38$	−1.87871	−	3.93325i	−0.304768	−	0.638057i
$39$	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	$0.940436\pi$
$42$	−1.29932	+	7.36881i	−0.200490	+	1.13703i
$43$	2.00132	+	11.3501i	0.305199	+	1.73087i	0.622566	+	0.782567i	$0.286090\pi$
$43$	2.00132	+	11.3501i	0.305199	+	1.73087i	−0.317367	+	0.948303i	$0.602799\pi$
$44$	−1.29468	+	0.471226i	−0.195181	+	0.0710400i
$45$		0			0
$46$	−1.06250	−	1.84030i	−0.156656	−	0.271337i
$47$	−0.0585581	−	0.0491361i	−0.00854158	−	0.00716723i	0.638507	−	0.769616i	$-0.279552\pi$
$47$	−0.0585581	−	0.0491361i	−0.00854158	−	0.00716723i	−0.647048	+	0.762449i	$0.723997\pi$
$48$	1.81653	+	1.52425i	0.262194	+	0.220007i
$49$	−1.47834	−	2.56055i	−0.211191	−	0.365793i
$50$		0			0
$51$	−2.88922	+	1.05159i	−0.404572	+	0.147252i
$52$	0.751065	+	4.25950i	0.104154	+	0.590686i
$53$	−1.08002	+	6.12511i	−0.148352	+	0.841348i	0.816262	+	0.577682i	$0.196043\pi$
$53$	−1.08002	+	6.12511i	−0.148352	+	0.841348i	−0.964614	+	0.263666i	$0.915068\pi$
$54$	0.839788	+	0.305658i	0.114281	+	0.0415948i
$55$		0			0
$56$	−3.15542			−0.421661
$57$	−5.84988	+	8.52164i	−0.774835	+	1.12872i
$58$	−0.130347			−0.0171154
$59$	−6.27104	+	5.26202i	−0.816419	+	0.685057i	−0.952131	−	0.305691i	$-0.901112\pi$
$59$	−6.27104	+	5.26202i	−0.816419	+	0.685057i	0.135711	+	0.990748i	$0.456668\pi$
$60$		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	$-0.111953\pi$
$62$	0.0602055	+	0.341442i	0.00764611	+	0.0433632i
$63$	7.77790	−	2.83092i	0.979923	−	0.356663i
$64$	−0.500000	+	0.866025i	−0.0625000	+	0.108253i
$65$		0			0
$66$	2.50277	+	2.10007i	0.308069	+	0.258501i
$67$	0.789546	+	0.662508i	0.0964584	+	0.0809382i	0.689742	−	0.724056i	$-0.257724\pi$
$67$	0.789546	+	0.662508i	0.0964584	+	0.0809382i	−0.593283	+	0.804994i	$0.702169\pi$
$68$	−0.648300	−	1.12289i	−0.0786179	−	0.136170i
$69$	−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	$0.701409\pi$
$72$	0.455501	−	2.58328i	0.0536813	−	0.304442i
$73$	−11.5052	−	4.18756i	−1.34659	−	0.490117i	−0.434705	−	0.900573i	$-0.643147\pi$
$73$	−11.5052	−	4.18756i	−1.34659	−	0.490117i	−0.911881	+	0.410456i	$0.865370\pi$
$74$	−7.90176	+	6.63036i	−0.918561	+	0.770764i
$75$		0			0
$76$	−3.96742	−	1.80543i	−0.455094	−	0.207097i
$77$	−4.34745			−0.495438
$78$	7.85688	−	6.59270i	0.889616	−	0.746477i
$79$	−13.1650	−	4.79168i	−1.48118	−	0.539106i	−0.530070	−	0.847954i	$-0.677834\pi$
$79$	−13.1650	−	4.79168i	−1.48118	−	0.539106i	−0.951111	+	0.308848i	$0.900056\pi$
$80$		0			0
$81$	−1.73450	−	9.83684i	−0.192722	−	1.09298i
$82$	−10.3451	+	3.76531i	−1.14242	+	0.415808i
$83$	5.68946	−	9.85443i	0.624499	−	1.08166i	−0.364138	−	0.931345i	$-0.618636\pi$
$83$	5.68946	−	9.85443i	0.624499	−	1.08166i	0.988637	−	0.150319i	$-0.0480302\pi$
$84$	3.74124	+	6.48003i	0.408203	+	0.707029i
$85$		0			0
$86$	8.82879	+	7.40823i	0.952033	+	0.798850i
$87$	0.154547	+	0.267683i	0.0165691	+	0.0286986i
$88$	−0.688886	+	1.19319i	−0.0734355	+	0.127194i
$89$	17.1195	−	6.23099i	1.81466	−	0.660484i	0.818348	−	0.574723i	$-0.194890\pi$
$89$	17.1195	−	6.23099i	1.81466	−	0.660484i	0.996316	−	0.0857608i	$-0.0273321\pi$
$90$		0			0
$91$	−2.36992	+	13.4405i	−0.248436	+	1.40895i
$92$	−1.99684	−	0.726790i	−0.208185	−	0.0757731i
$93$	0.629809	−	0.528473i	0.0653082	−	0.0548000i
$94$	−0.0764422			−0.00788441
$95$		0			0
$96$	2.37131			0.242021
$97$	12.4265	−	10.4271i	1.26172	−	1.05871i	0.266227	−	0.963910i	$-0.414223\pi$
$97$	12.4265	−	10.4271i	1.26172	−	1.05871i	0.995496	−	0.0948014i	$-0.0302216\pi$
$98$	−2.77836	−	1.01124i	−0.280657	−	0.102151i
$99$	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	$0.495775\pi$
$102$	−1.53732	+	2.66272i	−0.152218	+	0.263649i
$103$	−6.17880	−	10.7020i	−0.608815	−	1.05450i	−0.991436	−	0.130594i	$-0.958312\pi$
$103$	−6.17880	−	10.7020i	−0.608815	−	1.05450i	0.382621	−	0.923906i	$-0.375022\pi$
$104$	3.31330	+	2.78019i	0.324896	+	0.272620i
$105$		0			0
$106$	3.10980	+	5.38633i	0.302050	+	0.523167i
$107$	5.47740	−	9.48714i	0.529521	−	0.917156i	−0.469887	−	0.882727i	$-0.655705\pi$
$107$	5.47740	−	9.48714i	0.529521	−	0.917156i	0.999407	−	0.0344297i	$-0.0109615\pi$
$108$	0.839788	−	0.305658i	0.0808087	−	0.0294120i
$109$	1.29211	+	7.32792i	0.123762	+	0.701887i	0.982036	+	0.188695i	$0.0604259\pi$
$109$	1.29211	+	7.32792i	0.123762	+	0.701887i	−0.858274	+	0.513192i	$0.828463\pi$
$110$		0			0
$111$	22.9850	+	8.36586i	2.18164	+	0.794052i
$112$	−2.41719	+	2.02826i	−0.228403	+	0.191653i
$113$	11.6014			1.09137			0.545686	−	0.837990i	$-0.316269\pi$
$113$	11.6014			1.09137			0.545686	+	0.837990i	$0.316269\pi$
$114$	0.996338	+	10.2882i	0.0933156	+	0.963577i
$115$		0			0
$116$	−0.0998515	+	0.0837854i	−0.00927098	+	0.00777928i
$117$	−10.6613	−	3.88041i	−0.985642	−	0.358744i
$118$	−1.42153	+	8.06189i	−0.130862	+	0.742157i
$119$	−0.710449	−	4.02916i	−0.0651268	−	0.369352i
$120$		0			0
$121$	4.55087	−	7.88234i	0.413716	−	0.716577i
$122$	−3.92300	−	6.79483i	−0.355172	−	0.615175i
$123$	19.9982	+	16.7805i	1.80318	+	1.51305i
$124$	0.265595	+	0.222861i	0.0238511	+	0.0200135i
$125$		0			0
$126$	4.13853	−	7.16815i	0.368690	−	0.638589i
$127$	15.4096	−	5.60862i	1.36738	−	0.497685i	0.449050	−	0.893507i	$-0.351763\pi$
$127$	15.4096	−	5.60862i	1.36738	−	0.497685i	0.918327	+	0.395822i	$0.129540\pi$
$128$	0.173648	+	0.984808i	0.0153485	+	0.0870455i
$129$	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	$0.116048\pi$
$132$	3.26713			0.284367
$133$	−9.81545	−	9.63503i	−0.851107	−	0.835463i
$134$	1.03068			0.0890371
$135$		0			0
$136$	−1.21840	−	0.443463i	−0.104477	−	0.0380266i
$137$	−1.27486	+	7.23011i	−0.108919	+	0.617710i	0.880663	+	0.473743i	$0.157097\pi$
$137$	−1.27486	+	7.23011i	−0.108919	+	0.617710i	−0.989582	+	0.143968i	$0.954014\pi$
$138$	0.875017	+	4.96247i	0.0744864	+	0.422433i
$139$	−11.0992	+	4.03978i	−0.941422	+	0.342650i	−0.766727	−	0.641973i	$-0.778116\pi$
$139$	−11.0992	+	4.03978i	−0.941422	+	0.342650i	−0.174695	+	0.984623i	$0.555894\pi$
$140$		0			0
$141$	0.0906342	+	0.156983i	0.00763277	+	0.0132203i
$142$	8.92657	+	7.49028i	0.749101	+	0.628570i
$143$	4.56497	+	3.83047i	0.381742	+	0.320320i
$144$	−1.31156	−	2.27169i	−0.109297	−	0.189308i
$145$		0			0
$146$	−11.5052	+	4.18756i	−0.952180	+	0.346565i
$147$	1.21748	+	6.90468i	0.100416	+	0.569488i
$148$	−1.79118	+	10.1583i	−0.147234	+	0.835007i
$149$	−3.30256	−	1.20203i	−0.270556	−	0.0984745i	0.203179	−	0.979142i	$-0.434873\pi$
$149$	−3.30256	−	1.20203i	−0.270556	−	0.0984745i	−0.473736	+	0.880667i	$0.657095\pi$
$150$		0			0
$151$	−0.212620			−0.0173028			−0.00865139	−	0.999963i	$-0.502754\pi$
$151$	−0.212620			−0.0173028			−0.00865139	+	0.999963i	$0.502754\pi$
$152$	−4.19973	+	1.16717i	−0.340643	+	0.0946700i
$153$	3.40114			0.274966
$154$	−3.33034	+	2.79449i	−0.268366	+	0.225186i
$155$		0			0
$156$	1.78101	−	10.1006i	0.142595	−	0.808696i
$157$	−1.33492	−	7.57072i	−0.106538	−	0.604210i	−0.990595	−	0.136829i	$-0.956309\pi$
$157$	−1.33492	−	7.57072i	−0.106538	−	0.604210i	0.884056	−	0.467381i	$-0.154802\pi$
$158$	−13.1650	+	4.79168i	−1.04735	+	0.381205i
$159$	7.37431	−	12.7727i	0.584821	−	1.01294i
$160$		0			0
$161$	−5.13651	−	4.31004i	−0.404814	−	0.339679i
$162$	−7.65170	−	6.42054i	−0.601174	−	0.504445i
$163$	−3.66350	−	6.34537i	−0.286948	−	0.497008i	0.686132	−	0.727477i	$-0.259307\pi$
$163$	−3.66350	−	6.34537i	−0.286948	−	0.497008i	−0.973080	+	0.230469i	$0.925974\pi$
$164$	−5.50451	+	9.53409i	−0.429830	+	0.744487i
$165$		0			0
$166$	−1.97593	−	11.2060i	−0.153362	−	0.869758i
$167$	2.75126	−	15.6032i	0.212899	−	1.20741i	−0.671617	−	0.740899i	$-0.734400\pi$
$167$	2.75126	−	15.6032i	0.212899	−	1.20741i	0.884515	−	0.466511i	$-0.154489\pi$
$168$	7.03124	+	2.55916i	0.542472	+	0.197444i
$169$	4.37215	−	3.66867i	0.336319	−	0.282205i
$170$		0			0
$171$	9.30491	−	6.64483i	0.711564	−	0.508143i
$172$	11.5252			0.878786
$173$	−12.7471	+	10.6961i	−0.969147	+	0.813211i	−0.982417	−	0.186701i	$-0.940220\pi$
$173$	−12.7471	+	10.6961i	−0.969147	+	0.813211i	0.0132697	+	0.999912i	$0.495776\pi$
$174$	0.290453	+	0.105716i	0.0220192	+	0.00801432i
$175$		0			0
$176$	0.239248	+	1.35684i	0.0180340	+	0.102276i
$177$	18.2415	−	6.63936i	1.37111	−	0.499045i
$178$	9.10910	−	15.7774i	0.682756	−	1.18257i
$179$	2.28553	+	3.95866i	0.170829	+	0.295884i	0.938710	−	0.344708i	$-0.112022\pi$
$179$	2.28553	+	3.95866i	0.170829	+	0.295884i	−0.767881	+	0.640592i	$0.778689\pi$
$180$		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	$0.702236\pi$
$182$	6.82392	+	11.8194i	0.505823	+	0.876111i
$183$	−9.30266	+	16.1127i	−0.687673	+	1.19108i
$184$	−1.99684	+	0.726790i	−0.147209	+	0.0535796i
$185$		0			0
$186$	0.142766	−	0.809667i	0.0104681	−	0.0593677i
$187$	−1.67868	−	0.610991i	−0.122758	−	0.0446801i
$188$	−0.0585581	+	0.0491361i	−0.00427079	+	0.00358362i
$189$	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	$0.366941\pi$
$192$	1.81653	−	1.52425i	0.131097	−	0.110003i
$193$	−20.1920	−	7.34927i	−1.45345	−	0.529012i	−0.509897	−	0.860236i	$-0.670316\pi$
$193$	−20.1920	−	7.34927i	−1.45345	−	0.529012i	−0.943552	+	0.331223i	$0.892539\pi$
$194$	2.81687	−	15.9752i	0.202239	−	1.14696i
$195$		0			0
$196$	−2.77836	+	1.01124i	−0.198455	+	0.0722315i
$197$	7.63921	−	13.2315i	0.544271	−	0.942705i	−0.454381	−	0.890807i	$-0.650140\pi$
$197$	7.63921	−	13.2315i	0.544271	−	0.942705i	0.998652	−	0.0518981i	$-0.0165271\pi$
$198$	−1.80704	−	3.12988i	−0.128420	−	0.222431i
$199$	0.542940	+	0.455581i	0.0384880	+	0.0322953i	0.661829	−	0.749655i	$-0.269781\pi$
$199$	0.542940	+	0.455581i	0.0384880	+	0.0322953i	−0.623341	+	0.781950i	$0.714225\pi$
$200$		0			0
$201$	−1.22203	−	2.11662i	−0.0861955	−	0.149295i
$202$	−3.31162	+	5.73590i	−0.233005	+	0.403576i
$203$	−0.386495	+	0.140673i	−0.0271266	+	0.00987328i
$204$	0.533906	+	3.02793i	0.0373809	+	0.211998i
$205$		0			0
$206$	−11.6123	−	4.22655i	−0.809071	−	0.294478i
$207$	4.27002	−	3.58298i	0.296787	−	0.249034i
$208$	4.32521			0.299899
$209$	−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	$0.116735\pi$
$212$	5.84451	+	2.12723i	0.401403	+	0.146099i
$213$	4.79832	−	27.2126i	0.328776	−	1.86458i
$214$	−1.90228	−	10.7884i	−0.130037	−	0.737478i
$215$		0			0
$216$	0.446842	−	0.773953i	0.0304038	−	0.0526608i
$217$	0.547007	+	0.947444i	0.0371333	+	0.0643167i
$218$	5.70011	+	4.78296i	0.386060	+	0.323943i
$219$	22.2409	+	18.6623i	1.50290	+	1.26108i
$220$		0			0
$221$	−2.80403	+	4.85673i	−0.188620	+	0.326699i
$222$	22.9850	−	8.36586i	1.54265	−	0.561479i
$223$	−2.03461	−	11.5389i	−0.136248	−	0.772699i	−0.973983	−	0.226622i	$-0.927232\pi$
$223$	−2.03461	−	11.5389i	−0.136248	−	0.772699i	0.837735	−	0.546077i	$-0.183879\pi$
$224$	−0.547933	+	3.10748i	−0.0366103	+	0.207627i
$225$		0			0
$226$	8.88722	−	7.45727i	0.591169	−	0.496050i
$227$	10.2265			0.678758			0.339379	−	0.940650i	$-0.389783\pi$
$227$	10.2265			0.678758			0.339379	+	0.940650i	$0.389783\pi$
$228$	7.37636	+	7.24077i	0.488511	+	0.479532i
$229$	−5.05689			−0.334169			−0.167084	−	0.985943i	$-0.553435\pi$
$229$	−5.05689			−0.334169			−0.167084	+	0.985943i	$0.553435\pi$
$230$		0			0
$231$	9.68744	+	3.52594i	0.637387	+	0.231990i
$232$	−0.0226345	+	0.128367i	−0.00148603	+	0.00842768i
$233$	1.26042	+	7.14818i	0.0825727	+	0.468293i	0.997854	+	0.0654778i	$0.0208571\pi$
$233$	1.26042	+	7.14818i	0.0825727	+	0.468293i	−0.915281	+	0.402815i	$0.868032\pi$
$234$	−10.6613	+	3.88041i	−0.696954	+	0.253671i
$235$		0			0
$236$	4.09313	+	7.08951i	0.266440	+	0.461488i
$237$	25.4495	+	21.3546i	1.65312	+	1.38713i
$238$	−3.13413	−	2.62985i	−0.203155	−	0.170468i
$239$	−7.98657	−	13.8331i	−0.516608	−	0.894792i	−0.999814	−	0.0192850i	$-0.993861\pi$
$239$	−7.98657	−	13.8331i	−0.516608	−	0.894792i	0.483206	−	0.875507i	$-0.339472\pi$
$240$		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	$0.642394\pi$
$242$	−1.58050	−	8.96347i	−0.101598	−	0.576194i
$243$	−3.64748	+	20.6859i	−0.233986	+	1.32700i
$244$	−7.37283	−	2.68349i	−0.471997	−	0.171793i
$245$		0			0
$246$	26.1058			1.66445
$247$	1.81729	+	18.7654i	0.115632	+	1.19401i
$248$	0.346710			0.0220161
$249$	−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	$-0.196544\pi$
$252$	−1.43730	−	8.15132i	−0.0905412	−	0.513485i
$253$	−2.75119	+	1.00135i	−0.172966	+	0.0629544i
$254$	8.19925	−	14.2015i	0.514467	−	0.891083i
$255$		0			0
$256$	0.766044	+	0.642788i	0.0478778	+	0.0401742i
$257$	−8.20783	−	6.88718i	−0.511990	−	0.429611i	0.349839	−	0.936810i	$-0.386236\pi$
$257$	−8.20783	−	6.88718i	−0.511990	−	0.429611i	−0.861829	+	0.507199i	$0.830681\pi$
$258$	−13.6649	−	23.6683i	−0.850739	−	1.47352i
$259$	−16.2741	+	28.1876i	−1.01122	+	1.75149i
$260$		0			0
$261$	−0.0593732	−	0.336722i	−0.00367511	−	0.0208426i
$262$	1.93386	−	10.9675i	0.119474	−	0.677573i
$263$	25.0584	+	9.12051i	1.54517	+	0.562395i	0.967278	−	0.253720i	$-0.0816542\pi$
$263$	25.0584	+	9.12051i	1.54517	+	0.562395i	0.577890	+	0.816115i	$0.303876\pi$
$264$	2.50277	−	2.10007i	0.154035	−	0.129250i
$265$		0			0
$266$	−13.7123	−	1.07161i	−0.840758	−	0.0657049i
$267$	−43.2011			−2.64386
$268$	0.789546	−	0.662508i	0.0482292	−	0.0404691i
$269$	−1.34180	−	0.488375i	−0.0818110	−	0.0297768i	0.300790	−	0.953690i	$-0.402750\pi$
$269$	−1.34180	−	0.488375i	−0.0818110	−	0.0297768i	−0.382601	+	0.923913i	$0.624972\pi$
$270$		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	$0.872588\pi$
$272$	−1.21840	+	0.443463i	−0.0738766	+	0.0268889i
$273$	16.1817	−	28.0275i	0.979359	−	1.69630i
$274$	3.67083	+	6.35806i	0.221763	+	0.384104i
$275$		0			0
$276$	3.86011	+	3.23902i	0.232351	+	0.194966i
$277$	−1.26266	−	2.18698i	−0.0758656	−	0.131403i	0.825597	−	0.564261i	$-0.190839\pi$
$277$	−1.26266	−	2.18698i	−0.0758656	−	0.131403i	−0.901462	+	0.432857i	$0.857505\pi$
$278$	−5.90576	+	10.2291i	−0.354204	+	0.613500i
$279$	−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	$-0.116241\pi$
$282$	0.170336	+	0.0619974i	0.0101434	+	0.00369189i
$283$	−21.6184	+	18.1400i	−1.28508	+	1.07831i	−0.292556	+	0.956248i	$0.594506\pi$
$283$	−21.6184	+	18.1400i	−1.28508	+	1.07831i	−0.992523	+	0.122061i	$0.961050\pi$
$284$	11.6528			0.691467
$285$		0			0
$286$	5.95915			0.352372
$287$	−26.6109	+	22.3292i	−1.57079	+	1.31805i
$288$	−2.46493	−	0.897162i	−0.145248	−	0.0528658i
$289$	−2.66009	+	15.0861i	−0.156476	+	0.887418i
$290$		0			0
$291$	−36.1469	+	13.1564i	−2.11897	+	0.771241i
$292$	−6.12181	+	10.6033i	−0.358252	+	0.620510i
$293$	−6.30904	−	10.9276i	−0.368578	−	0.638396i	0.620766	−	0.783996i	$-0.286822\pi$
$293$	−6.30904	−	10.9276i	−0.368578	−	0.638396i	−0.989343	+	0.145601i	$0.953489\pi$
$294$	5.37089	+	4.50671i	0.313237	+	0.262837i
$295$		0			0
$296$	5.15751	+	8.93306i	0.299774	+	0.519224i
$297$	0.615647	−	1.06633i	0.0357234	−	0.0618748i
$298$	−3.30256	+	1.20203i	−0.191312	+	0.0696320i
$299$	1.59601	+	9.05140i	0.0922994	+	0.523456i
$300$		0			0
$301$	34.1735	+	12.4382i	1.96973	+	0.716923i
$302$	−0.162877	+	0.136670i	−0.00937249	+	0.00786445i
$303$	15.7058			0.902274
$304$	−2.46694	+	3.59364i	−0.141488	+	0.206109i
$305$		0			0
$306$	2.60543	−	2.18621i	0.148942	−	0.124978i
$307$	8.51802	+	3.10031i	0.486149	+	0.176944i	0.573454	−	0.819238i	$-0.305603\pi$
$307$	8.51802	+	3.10031i	0.486149	+	0.176944i	−0.0873047	+	0.996182i	$0.527825\pi$
$308$	−0.754926	+	4.28140i	−0.0430159	+	0.243955i
$309$	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	$-0.0444192\pi$
$312$	−5.12821	−	8.88232i	−0.290328	−	0.502863i
$313$	7.69570	+	6.45746i	0.434987	+	0.364997i	0.833829	−	0.552022i	$-0.186144\pi$
$313$	7.69570	+	6.45746i	0.434987	+	0.364997i	−0.398843	+	0.917019i	$0.630588\pi$
$314$	−5.88898	−	4.94144i	−0.332334	−	0.278862i
$315$		0			0
$316$	−7.00496	+	12.1330i	−0.394060	+	0.682532i
$317$	−1.98130	+	0.721135i	−0.111281	+	0.0405030i	−0.397061	−	0.917792i	$-0.629970\pi$
$317$	−1.98130	+	0.721135i	−0.111281	+	0.0405030i	0.285780	+	0.958295i	$0.407747\pi$
$318$	−2.56107	−	14.5245i	−0.143618	−	0.814496i
$319$	−0.0311852	+	0.176860i	−0.00174604	+	0.00990226i
$320$		0			0
$321$	−19.8997	+	16.6979i	−1.11070	+	0.931984i
$322$	−6.70524			−0.373668
$323$	−2.43594	−	5.09985i	−0.135539	−	0.283763i
$324$	−9.98859			−0.554921
$325$		0			0
$326$	−6.88513	−	2.50598i	−0.381332	−	0.138794i
$327$	3.06400	−	17.3768i	0.169439	−	0.960939i
$328$	1.91170	+	10.8418i	0.105556	+	0.598636i
$329$	−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	$0.803159\pi$
$332$	−8.71676	−	7.31423i	−0.478394	−	0.401420i
$333$	−20.7273	−	17.3923i	−1.13585	−	0.953091i
$334$	−7.92194	−	13.7212i	−0.433469	−	0.750791i
$335$		0			0
$336$	7.03124	−	2.55916i	0.383586	−	0.139614i
$337$	4.49031	+	25.4658i	0.244603	+	1.38721i	0.821414	+	0.570332i	$0.193186\pi$
$337$	4.49031	+	25.4658i	0.244603	+	1.38721i	−0.576811	+	0.816877i	$0.695703\pi$
$338$	0.991085	−	5.62072i	0.0539079	−	0.305727i
$339$	−25.8516	−	9.40920i	−1.40406	−	0.511038i
$340$		0			0
$341$	0.477687			0.0258682
$342$	2.85676	−	11.0713i	0.154476	−	0.598668i
$343$	12.7584			0.688889
$344$	8.82879	−	7.40823i	0.476016	−	0.399425i
$345$		0			0
$346$	−2.88954	+	16.3874i	−0.155343	+	0.880992i
$347$	−0.438152	−	2.48488i	−0.0235212	−	0.133395i	0.970786	−	0.239947i	$-0.0771301\pi$
$347$	−0.438152	−	2.48488i	−0.0235212	−	0.133395i	−0.994307	+	0.106552i	$0.966019\pi$
$348$	0.290453	−	0.105716i	0.0155699	−	0.00566698i
$349$	−1.83973	+	3.18650i	−0.0984782	+	0.170569i	−0.911055	−	0.412285i	$-0.864731\pi$
$349$	−1.83973	+	3.18650i	−0.0984782	+	0.170569i	0.812577	+	0.582854i	$0.198064\pi$
$350$		0			0
$351$	−2.96105	−	2.48461i	−0.158049	−	0.132619i
$352$	1.05543	+	0.885615i	0.0562548	+	0.0472034i
$353$	1.39818	+	2.42172i	0.0744175	+	0.128895i	0.900833	−	0.434166i	$-0.142957\pi$
$353$	1.39818	+	2.42172i	0.0744175	+	0.128895i	−0.826415	+	0.563061i	$0.809624\pi$
$354$	9.70609	−	16.8114i	0.515873	−	0.893518i
$355$		0			0
$356$	−3.16356	−	17.9414i	−0.167668	−	0.950893i
$357$	−1.68470	+	9.55440i	−0.0891637	+	0.505672i
$358$	4.29540	+	1.56340i	0.227019	+	0.0826281i
$359$	15.4284	−	12.9460i	0.814280	−	0.683262i	−0.137345	−	0.990523i	$-0.543857\pi$
$359$	15.4284	−	12.9460i	0.814280	−	0.683262i	0.951625	+	0.307261i	$0.0994125\pi$
$360$		0			0
$361$	−16.6279	−	9.19314i	−0.875151	−	0.483849i
$362$	1.68838			0.0887395
$363$	−16.5336	+	13.8733i	−0.867789	+	0.728162i
$364$	12.8248	+	4.66784i	0.672201	+	0.244661i
$365$		0			0
$366$	3.23078	+	18.3227i	0.168876	+	0.957741i
$367$	−4.24866	+	1.54639i	−0.221778	+	0.0807207i	−0.450520	−	0.892767i	$-0.648761\pi$
$367$	−4.24866	+	1.54639i	−0.221778	+	0.0807207i	0.228741	+	0.973487i	$0.426539\pi$
$368$	−1.06250	+	1.84030i	−0.0553864	+	0.0959321i
$369$	−14.4390	−	25.0091i	−0.751666	−	1.30192i
$370$		0			0
$371$	15.0340	+	12.6150i	0.780524	+	0.654938i
$372$	−0.411079	−	0.712009i	−0.0213134	−	0.0369160i
$373$	11.6352	−	20.1528i	0.602449	−	1.04347i	−0.390000	−	0.920815i	$-0.627525\pi$
$373$	11.6352	−	20.1528i	0.602449	−	1.04347i	0.992449	−	0.122657i	$-0.0391416\pi$
$374$	−1.67868	+	0.610991i	−0.0868027	+	0.0315936i
$375$		0			0
$376$	−0.0132740	+	0.0752808i	−0.000684556	+	0.00388231i
$377$	0.529778	+	0.192823i	0.0272849	+	0.00993091i
$378$	2.16021	−	1.81263i	0.111109	−	0.0932315i
$379$	9.34667			0.480106			0.240053	−	0.970760i	$-0.422835\pi$
$379$	9.34667			0.480106			0.240053	+	0.970760i	$0.422835\pi$
$380$		0			0
$381$	−38.8860			−1.99219
$382$	8.59555	−	7.21252i	0.439787	−	0.369025i
$383$	30.8559	+	11.2306i	1.57666	+	0.573858i	0.974475	−	0.224497i	$-0.0720738\pi$
$383$	30.8559	+	11.2306i	1.57666	+	0.573858i	0.602187	+	0.798355i	$0.294296\pi$
$384$	0.411774	−	2.33529i	0.0210133	−	0.119172i
$385$		0			0
$386$	−20.1920	+	7.34927i	−1.02774	+	0.374068i
$387$	−15.1160	+	26.1817i	−0.768389	+	1.33089i
$388$	−8.11084	−	14.0484i	−0.411766	−	0.713199i
$389$	8.17650	+	6.86090i	0.414565	+	0.347862i	0.826091	−	0.563537i	$-0.190560\pi$
$389$	8.17650	+	6.86090i	0.414565	+	0.347862i	−0.411526	+	0.911398i	$0.635004\pi$
$390$		0			0
$391$	−1.37763	−	2.38613i	−0.0696698	−	0.120672i
$392$	−1.47834	+	2.56055i	−0.0746673	+	0.129327i
$393$	−24.8159	+	9.03225i	−1.25180	+	0.455617i
$394$	−2.65307	−	15.0463i	−0.133660	−	0.758022i
$395$		0			0
$396$	−3.39612	−	1.23608i	−0.170661	−	0.0621156i
$397$	−7.70354	+	6.46404i	−0.386630	+	0.324421i	−0.815299	−	0.579041i	$-0.803427\pi$
$397$	−7.70354	+	6.46404i	−0.386630	+	0.324421i	0.428669	+	0.903462i	$0.358983\pi$
$398$	0.708758			0.0355268
$399$	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	$0.180257\pi$
$402$	−2.29667	−	0.835919i	−0.114547	−	0.0416918i
$403$	0.260401	−	1.47681i	0.0129715	−	0.0735651i
$404$	1.15011	+	6.52262i	0.0572203	+	0.324513i
$405$		0			0
$406$	−0.205650	+	0.356196i	−0.0102062	+	0.0176777i
$407$	7.10587	+	12.3077i	0.352225	+	0.610071i
$408$	2.35531	+	1.97634i	0.116605	+	0.0978435i
$409$	−30.2942	−	25.4198i	−1.49795	−	1.25693i	−0.883911	−	0.467655i	$-0.845099\pi$
$409$	−30.2942	−	25.4198i	−1.49795	−	1.25693i	−0.614040	−	0.789275i	$-0.710457\pi$
$410$		0			0
$411$	8.70468	−	15.0769i	0.429370	−	0.743691i
$412$	−11.6123	+	4.22655i	−0.572099	+	0.208227i
$413$	4.48552	+	25.4386i	0.220718	+	1.25175i
$414$	0.967936	−	5.48944i	0.0475715	−	0.269791i
$415$		0			0
$416$	3.31330	−	2.78019i	0.162448	−	0.136310i
$417$	28.0088			1.37160
$418$	−3.39887	+	4.95121i	−0.166244	+	0.242172i
$419$	28.5326			1.39391			0.696954	−	0.717116i	$-0.254538\pi$
$419$	28.5326			1.39391			0.696954	+	0.717116i	$0.254538\pi$
$420$		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	$0.626934\pi$
$422$	2.44481	−	13.8652i	0.119012	−	0.674949i
$423$	−0.0348195	−	0.197471i	−0.00169298	−	0.00960138i
$424$	5.84451	−	2.12723i	0.283834	−	0.103307i
$425$		0			0
$426$	−13.8162	−	23.9304i	−0.669398	−	1.15943i
$427$	−18.9653	−	15.9138i	−0.917794	−	0.770121i
$428$	−8.39187	−	7.04161i	−0.405636	−	0.340369i
$429$	−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	$0.494873\pi$
$432$	−0.155187	−	0.880107i	−0.00746642	−	0.0423442i
$433$	−5.02952	+	28.5238i	−0.241703	+	1.37077i	0.586323	+	0.810078i	$0.300575\pi$
$433$	−5.02952	+	28.5238i	−0.241703	+	1.37077i	−0.828026	+	0.560690i	$0.810536\pi$
$434$	1.02804	+	0.374175i	0.0493474	+	0.0179610i
$435$		0			0
$436$	7.44096			0.356357
$437$	−8.43073	−	3.83652i	−0.403297	−	0.183526i
$438$	29.0334			1.38727
$439$	−8.59028	+	7.20810i	−0.409992	+	0.344024i	−0.824341	−	0.566094i	$-0.808454\pi$
$439$	−8.59028	+	7.20810i	−0.409992	+	0.344024i	0.414349	+	0.910118i	$0.364009\pi$
$440$		0			0
$441$	1.34677	−	7.63790i	0.0641318	−	0.363710i
$442$	0.973830	+	5.52286i	0.0463204	+	0.262696i
$443$	7.00068	−	2.54804i	0.332612	−	0.121061i	−0.170315	−	0.985390i	$-0.554479\pi$
$443$	7.00068	−	2.54804i	0.332612	−	0.121061i	0.502927	+	0.864329i	$0.332256\pi$
$444$	12.2301	−	21.1831i	0.580413	−	1.00530i
$445$		0			0
$446$	−8.97564	−	7.53146i	−0.425009	−	0.356625i
$447$	6.38422	+	5.35700i	0.301963	+	0.253377i
$448$	1.57771	+	2.73267i	0.0745398	+	0.129107i
$449$	−2.65192	+	4.59326i	−0.125152	+	0.216769i	−0.921792	−	0.387684i	$-0.873275\pi$
$449$	−2.65192	+	4.59326i	−0.125152	+	0.216769i	0.796640	+	0.604453i	$0.206608\pi$
$450$		0			0
$451$	2.63388	+	14.9375i	0.124025	+	0.703378i
$452$	2.01457	−	11.4252i	0.0947574	−	0.537396i
$453$	0.473783	+	0.172443i	0.0222603	+	0.00810207i
$454$	7.83397	−	6.57348i	0.367667	−	0.308509i
$455$		0			0
$456$	10.3049	+	0.805323i	0.482571	+	0.0377127i
$457$	−14.9890			−0.701154			−0.350577	−	0.936534i	$-0.614014\pi$
$457$	−14.9890			−0.701154			−0.350577	+	0.936534i	$0.614014\pi$
$458$	−3.87381	+	3.25051i	−0.181011	+	0.151886i
$459$	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	$0.995528\pi$
$462$	9.68744	−	3.52594i	0.450701	−	0.164042i
$463$	10.3194	−	17.8738i	0.479585	−	0.830665i	−0.520141	−	0.854080i	$-0.674121\pi$
$463$	10.3194	−	17.8738i	0.479585	−	0.830665i	0.999726	+	0.0234152i	$0.00745396\pi$
$464$	0.0651735	+	0.112884i	0.00302560	+	0.00524050i
$465$		0			0
$466$	5.56030	+	4.66564i	0.257576	+	0.216132i
$467$	−6.01750	−	10.4226i	−0.278457	−	0.482301i	0.692545	−	0.721375i	$-0.256490\pi$
$467$	−6.01750	−	10.4226i	−0.278457	−	0.482301i	−0.971001	+	0.239074i	$0.923156\pi$
$468$	−5.67279	+	9.82555i	−0.262225	+	0.454186i
$469$	3.05609	−	1.11233i	0.141117	−	0.0513625i
$470$		0			0
$471$	−3.16552	+	17.9526i	−0.145859	+	0.827210i
$472$	7.69256	+	2.79986i	0.354079	+	0.128874i
$473$	12.1641	−	10.2069i	0.559304	−	0.469312i
$474$	33.2219			1.52593
$475$		0			0
$476$	−4.09132			−0.187525
$477$	−12.4979	+	10.4869i	−0.572238	+	0.480164i
$478$	−15.0098	−	5.46314i	−0.686534	−	0.249878i
$479$	3.95553	−	22.4329i	0.180733	−	1.02499i	−0.750583	−	0.660776i	$-0.770227\pi$
$479$	3.95553	−	22.4329i	0.180733	−	1.02499i	0.931316	−	0.364211i	$-0.118661\pi$
$480$		0			0
$481$	41.9240	−	15.2591i	1.91157	−	0.695754i
$482$	−11.0975	+	19.2214i	−0.505475	+	0.875509i
$483$	7.95011	+	13.7700i	0.361743	+	0.626556i
$484$	−6.97234	−	5.85049i	−0.316925	−	0.265931i
$485$		0			0
$486$	10.5025	+	18.1909i	0.476403	+	0.825155i
$487$	3.22456	−	5.58510i	0.146119	−	0.253085i	−0.783671	−	0.621176i	$-0.786655\pi$
$487$	3.22456	−	5.58510i	0.146119	−	0.253085i	0.929790	+	0.368091i	$0.119989\pi$
$488$	−7.37283	+	2.68349i	−0.333752	+	0.121476i
$489$	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	$0.425830\pi$
$492$	19.9982	−	16.7805i	0.901590	−	0.756524i
$493$	−0.169008			−0.00761173
$494$	13.4543	+	13.2070i	0.605336	+	0.594209i
$495$		0			0
$496$	0.265595	−	0.222861i	0.0119256	−	0.0100067i
$497$	34.5520	+	12.5759i	1.54987	+	0.564106i
$498$	−4.68554	+	26.5730i	−0.209964	+	1.19077i
$499$	0.282127	+	1.60002i	0.0126298	+	0.0716269i	0.990471	−	0.137720i	$-0.0439774\pi$
$499$	0.282127	+	1.60002i	0.0126298	+	0.0716269i	−0.977841	+	0.209347i	$0.932866\pi$
$500$		0			0
$501$	−18.7854	+	32.5373i	−0.839270	+	1.45366i
$502$	−11.2763	−	19.5311i	−0.503286	−	0.871717i
$503$	−26.9615	−	22.6234i	−1.20215	−	1.00873i	−0.999566	−	0.0294632i	$-0.990620\pi$
$503$	−26.9615	−	22.6234i	−1.20215	−	1.00873i	−0.202588	−	0.979264i	$-0.564935\pi$
$504$	−6.34060	−	5.32040i	−0.282433	−	0.236989i
$505$		0			0
$506$	−1.46388	+	2.53551i	−0.0650772	+	0.112717i
$507$	−12.7179	+	4.62894i	−0.564822	+	0.205578i
$508$	−2.84757	−	16.1494i	−0.126341	−	0.716513i
$509$	−4.20711	+	23.8597i	−0.186477	+	1.05756i	0.737567	+	0.675274i	$0.235975\pi$
$509$	−4.20711	+	23.8597i	−0.186477	+	1.05756i	−0.924043	+	0.382288i	$0.875136\pi$
$510$		0			0
$511$	−29.5952	+	24.8333i	−1.30921	+	1.09856i
$512$	1.00000			0.0441942
$513$	3.75323	−	1.04308i	0.165709	−	0.0460532i
$514$	−10.7146			−0.472599
$515$		0			0
$516$	−25.6816	−	9.34733i	−1.13057	−	0.411493i
$517$	−0.0182886	+	0.103720i	−0.000804332	+	0.00456159i
$518$	5.65193	+	32.0537i	0.248332	+	1.40836i
$519$	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	$0.777849\pi$
$522$	−0.261923	−	0.219780i	−0.0114641	−	0.00961950i
$523$	1.88229	+	1.57943i	0.0823069	+	0.0690637i	0.683013	−	0.730406i	$-0.260669\pi$
$523$	1.88229	+	1.57943i	0.0823069	+	0.0690637i	−0.600706	+	0.799470i	$0.705114\pi$
$524$	−5.56833	−	9.64464i	−0.243254	−	0.421328i
$525$		0			0
$526$	25.0584	−	9.12051i	1.09260	−	0.397673i
$527$	0.0780624	+	0.442714i	0.00340045	+	0.0192849i
$528$	0.567331	−	3.21749i	0.0246899	−	0.140023i
$529$	17.3697	+	6.32204i	0.755203	+	0.274871i
$530$		0			0
$531$	−21.4736			−0.931874
$532$	−11.1931	+	7.99322i	−0.485282	+	0.346550i
$533$	47.6163			2.06249
$534$	−33.0939	+	27.7691i	−1.43211	+	1.20169i
$535$		0			0
$536$	0.178976	−	1.01502i	0.00773057	−	0.0438422i
$537$	−1.88225	−	10.6748i	−0.0812250	−	0.460650i
$538$	−1.34180	+	0.488375i	−0.0578491	+	0.0210554i
$539$	−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	$0.561756\pi$
$542$	5.64532	+	4.73699i	0.242487	+	0.203471i
$543$	−2.00184	−	3.46730i	−0.0859074	−	0.148796i
$544$	−0.648300	+	1.12289i	−0.0277956	+	0.0481434i
$545$		0			0
$546$	−5.61983	−	31.8717i	−0.240507	−	1.36398i
$547$	4.65342	−	26.3908i	0.198966	−	1.12839i	−0.707691	−	0.706522i	$-0.750263\pi$
$547$	4.65342	−	26.3908i	0.198966	−	1.12839i	0.906657	−	0.421869i	$-0.138626\pi$
$548$	6.89889	+	2.51099i	0.294706	+	0.107264i
$549$	15.7660	−	13.2292i	0.672876	−	0.564610i
$550$		0			0
$551$	−0.462374	+	0.330191i	−0.0196978	+	0.0140666i
$552$	5.03902			0.214475
$553$	−33.8647	+	28.4158i	−1.44007	+	1.20836i
$554$	−2.37302	−	0.863707i	−0.100820	−	0.0366954i
$555$		0			0
$556$	2.05105	+	11.6321i	0.0869839	+	0.493310i
$557$	−36.7473	+	13.3749i	−1.55704	+	0.566714i	−0.970055	−	0.242887i	$-0.921906\pi$
$557$	−36.7473	+	13.3749i	−1.55704	+	0.566714i	−0.586980	+	0.809601i	$0.699683\pi$
$558$	−0.454732	+	0.787619i	−0.0192503	+	0.0333426i
$559$	−24.9244	−	43.1703i	−1.05419	−	1.82591i
$560$		0			0
$561$	3.24508	+	2.72295i	0.137008	+	0.114963i
$562$	−8.61440	−	14.9206i	−0.363377	−	0.629387i
$563$	4.31076	−	7.46645i	0.181677	−	0.314673i	−0.760775	−	0.649016i	$-0.775181\pi$
$563$	4.31076	−	7.46645i	0.181677	−	0.314673i	0.942452	+	0.334343i	$0.108514\pi$
$564$	0.170336	−	0.0619974i	0.00717246	−	0.00261056i
$565$		0			0
$566$	−4.90049	+	27.7920i	−0.205983	+	1.16819i
$567$	−29.6174	−	10.7799i	−1.24381	−	0.452711i
$568$	8.92657	−	7.49028i	0.374550	−	0.314285i
$569$	23.0260			0.965300			0.482650	−	0.875813i	$-0.339674\pi$
$569$	23.0260			0.965300			0.482650	+	0.875813i	$0.339674\pi$
$570$		0			0
$571$	−29.9673			−1.25409			−0.627047	−	0.778981i	$-0.715737\pi$
$571$	−29.9673			−1.25409			−0.627047	+	0.778981i	$0.715737\pi$
$572$	4.56497	−	3.83047i	0.190871	−	0.160160i
$573$	−25.0031	−	9.10040i	−1.04452	−	0.380175i
$574$	−6.03220	+	34.2103i	−0.251779	+	1.42791i
$575$		0			0
$576$	−2.46493	+	0.897162i	−0.102706	+	0.0373818i
$577$	2.27258	−	3.93622i	0.0946087	−	0.163867i	−0.814837	−	0.579691i	$-0.803173\pi$
$577$	2.27258	−	3.93622i	0.0946087	−	0.163867i	0.909445	+	0.415824i	$0.136507\pi$
$578$	7.65941	+	13.2665i	0.318590	+	0.551813i
$579$	39.0333	+	32.7529i	1.62217	+	1.36116i
$580$		0			0
$581$	−17.9526	−	31.0949i	−0.744800	−	1.29003i
$582$	−19.2334	+	33.3131i	−0.797248	+	1.38087i
$583$	8.05240	−	2.93083i	0.333496	−	0.121383i
$584$	2.12608	+	12.0576i	0.0879779	+	0.498947i
$585$		0			0
$586$	−11.8571	−	4.31563i	−0.489813	−	0.178277i
$587$	−14.1471	+	11.8709i	−0.583915	+	0.489963i	−0.886230	−	0.463245i	$-0.846685\pi$
$587$	−14.1471	+	11.8709i	−0.583915	+	0.489963i	0.302315	+	0.953208i	$0.402240\pi$
$588$	7.01120			0.289137
$589$	1.07850	+	1.05867i	0.0444387	+	0.0436219i
$590$		0			0
$591$	−27.7537	+	23.2881i	−1.14164	+	0.957946i
$592$	9.69294	+	3.52794i	0.398377	+	0.144998i
$593$	2.77694	−	15.7488i	0.114035	−	0.646726i	−0.873188	−	0.487384i	$-0.837951\pi$
$593$	2.77694	−	15.7488i	0.114035	−	0.646726i	0.987223	−	0.159343i	$-0.0509375\pi$
$594$	−0.213812	−	1.21259i	−0.00877280	−	0.0497530i
$595$		0			0
$596$	−1.75726	+	3.04366i	−0.0719800	+	0.124673i
$597$	−0.840343	−	1.45552i	−0.0343930	−	0.0595704i
$598$	7.04074	+	5.90788i	0.287917	+	0.241591i
$599$	3.02967	+	2.54220i	0.123789	+	0.103871i	0.702581	−	0.711604i	$-0.252031\pi$
$599$	3.02967	+	2.54220i	0.123789	+	0.103871i	−0.578792	+	0.815476i	$0.696476\pi$
$600$		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	$0.152268\pi$
$602$	34.1735	−	12.4382i	1.39281	−	0.506941i
$603$	0.469476	+	2.66253i	0.0191185	+	0.108427i
$604$	−0.0369211	+	0.209390i	−0.00150230	+	0.00851996i
$605$		0			0
$606$	12.0313	−	10.0955i	0.488739	−	0.410101i
$607$	−17.4964			−0.710155			−0.355078	−	0.934837i	$-0.615546\pi$
$607$	−17.4964			−0.710155			−0.355078	+	0.934837i	$0.615546\pi$
$608$	0.420163	+	4.33860i	0.0170399	+	0.175954i
$609$	0.975319			0.0395219
$610$		0			0
$611$	0.310689	+	0.113082i	0.0125691	+	0.00457479i
$612$	0.590603	−	3.34947i	0.0238737	−	0.135394i
$613$	−1.58504	−	8.98922i	−0.0640193	−	0.363071i	−0.999941	−	0.0108633i	$-0.996542\pi$
$613$	−1.58504	−	8.98922i	−0.0640193	−	0.363071i	0.935922	−	0.352208i	$-0.114569\pi$
$614$	8.51802	−	3.10031i	0.343759	−	0.125118i
$615$		0			0
$616$	2.17372	+	3.76500i	0.0875818	+	0.151696i
$617$	−1.19206	−	1.00026i	−0.0479906	−	0.0402689i	0.618477	−	0.785803i	$-0.287750\pi$
$617$	−1.19206	−	1.00026i	−0.0479906	−	0.0402689i	−0.666467	+	0.745534i	$0.732194\pi$
$618$	22.4480	+	18.8361i	0.902990	+	0.757699i
$619$	−16.2140	−	28.0835i	−0.651695	−	1.12877i	−0.982711	−	0.185144i	$-0.940725\pi$
$619$	−16.2140	−	28.0835i	−0.651695	−	1.12877i	0.331016	−	0.943625i	$-0.392609\pi$
$620$		0			0
$621$	1.78454	−	0.649520i	0.0716112	−	0.0260644i
$622$	−3.77032	−	21.3826i	−0.151176	−	0.857362i
$623$	9.98235	−	56.6127i	0.399934	−	2.26814i
$624$	−9.63789	−	3.50790i	−0.385824	−	0.140429i
$625$		0			0
$626$	10.0460			0.401520
$627$	14.1978	+	1.10955i	0.567005	+	0.0443112i
$628$	−7.68751			−0.306765
$629$	−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	$0.993968\pi$
$632$	2.43280	+	13.7971i	0.0967715	+	0.548819i
$633$	−31.3726	+	11.4187i	−1.24695	+	0.453852i
$634$	−1.05423	+	1.82598i	−0.0418688	+	0.0725189i
$635$		0			0
$636$	−11.2981	−	9.48023i	−0.447999	−	0.375915i
$637$	9.79635	+	8.22011i	0.388145	+	0.325693i
$638$	0.0897942	+	0.155528i	0.00355498	+	0.00615741i
$639$	−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	$0.647864\pi$
$642$	−4.51091	+	25.5826i	−0.178031	+	1.00967i
$643$	−39.5312	−	14.3882i	−1.55896	−	0.567414i	−0.588460	−	0.808526i	$-0.700266\pi$
$643$	−39.5312	−	14.3882i	−1.55896	−	0.567414i	−0.970497	+	0.241112i	$0.922488\pi$
$644$	−5.13651	+	4.31004i	−0.202407	+	0.169840i
$645$		0			0
$646$	−5.14416	−	2.34092i	−0.202394	−	0.0921022i
$647$	−18.0072			−0.707936			−0.353968	−	0.935258i	$-0.615168\pi$
$647$	−18.0072			−0.707936			−0.353968	+	0.935258i	$0.615168\pi$
$648$	−7.65170	+	6.42054i	−0.300587	+	0.252223i
$649$	10.5986	+	3.85757i	0.416031	+	0.151423i
$650$		0			0
$651$	−0.450487	−	2.55484i	−0.0176560	−	0.100132i
$652$	−6.88513	+	2.50598i	−0.269643	+	0.0981419i
$653$	19.7435	−	34.1968i	0.772624	−	1.33822i	−0.163496	−	0.986544i	$-0.552277\pi$
$653$	19.7435	−	34.1968i	0.772624	−	1.33822i	0.936120	−	0.351680i	$-0.114390\pi$
$654$	−8.82243	−	15.2809i	−0.344984	−	0.597530i
$655$		0			0
$656$	8.43340	+	7.07646i	0.329269	+	0.276289i
$657$	−16.0583	−	27.8138i	−0.626493	−	1.08512i
$658$	−0.120604	+	0.208891i	−0.00470162	+	0.00814344i
$659$	−33.6395	+	12.2438i	−1.31041	+	0.476949i	−0.900372	−	0.435120i	$-0.856706\pi$
$659$	−33.6395	+	12.2438i	−1.31041	+	0.476949i	−0.410035	+	0.912070i	$0.634484\pi$
$660$		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	$-0.0296772\pi$
$662$	3.23639	+	1.17795i	0.125786	+	0.0457822i
$663$	10.1872	−	8.54809i	0.395639	−	0.331980i
$664$	−11.3789			−0.441588
$665$		0			0
$666$	−27.0576			−1.04846
$667$	−0.212184	+	0.178043i	−0.00821578	+	0.00689386i
$668$	−14.8884	−	5.41893i	−0.576049	−	0.209665i
$669$	−4.82470	+	27.3623i	−0.186534	+	1.05789i
$670$		0			0
$671$	−10.1581	+	3.69724i	−0.392148	+	0.142730i
$672$	3.74124	−	6.48003i	0.144322	−	0.249972i
$673$	−21.1108	−	36.5649i	−0.813760	−	1.40947i	−0.910215	−	0.414136i	$-0.864084\pi$
$673$	−21.1108	−	36.5649i	−0.813760	−	1.40947i	0.0964549	−	0.995337i	$-0.469250\pi$
$674$	19.8089	+	16.6216i	0.763009	+	0.640241i
$675$		0			0
$676$	−2.85372	−	4.94278i	−0.109758	−	0.190107i
$677$	−21.8355	+	37.8202i	−0.839207	+	1.45355i	0.0513514	+	0.998681i	$0.483647\pi$
$677$	−21.8355	+	37.8202i	−0.839207	+	1.45355i	−0.890558	+	0.454869i	$0.849686\pi$
$678$	−25.8516	+	9.40920i	−0.992824	+	0.361358i
$679$	−8.88840	−	50.4086i	−0.341105	−	1.93450i
$680$		0			0
$681$	−22.7878	−	8.29409i	−0.873231	−	0.317830i
$682$	0.365929	−	0.307051i	0.0140122	−	0.0117576i
$683$	−9.22100			−0.352832			−0.176416	−	0.984316i	$-0.556450\pi$
$683$	−9.22100			−0.352832			−0.176416	+	0.984316i	$0.556450\pi$
$684$	−4.92810	−	10.3174i	−0.188431	−	0.394496i
$685$		0			0
$686$	9.77350	−	8.20094i	0.373154	−	0.313113i
$687$	11.2683	+	4.10133i	0.429913	+	0.156475i
$688$	2.00132	−	11.3501i	0.0762998	−	0.432717i
$689$	−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	$-0.108626\pi$
$692$	8.32010	+	14.4108i	0.316283	+	0.547818i
$693$	−8.73590	−	7.33029i	−0.331849	−	0.278455i
$694$	−1.93290	−	1.62189i	−0.0733717	−	0.0615662i
$695$		0			0
$696$	0.154547	−	0.267683i	0.00585808	−	0.0101465i
$697$	−13.4134	+	4.88209i	−0.508070	+	0.184922i
$698$	0.638930	+	3.62355i	0.0241839	+	0.137153i
$699$	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	$0.288582\pi$
$702$	−3.86537			−0.145889
$703$	−11.2337	+	43.5361i	−0.423688	+	1.64200i
$704$	1.37777			0.0519267
$705$		0			0
$706$	2.62772	+	0.956410i	0.0988954	+	0.0359950i
$707$	−3.62909	+	20.5816i	−0.136486	+	0.774051i
$708$	−3.37089	−	19.1173i	−0.126686	−	0.718471i
$709$	−31.8904	+	11.6072i	−1.19767	+	0.435916i	−0.862410	−	0.506210i	$-0.831046\pi$
$709$	−31.8904	+	11.6072i	−1.19767	+	0.435916i	−0.335259	+	0.942126i	$0.608824\pi$
$710$		0			0
$711$	−18.3749	−	31.8263i	−0.689113	−	1.19358i
$712$	−13.9559	−	11.7104i	−0.523021	−	0.438867i
$713$	0.564387	+	0.473577i	0.0211365	+	0.0177356i
$714$	4.85090	+	8.40200i	0.181540	+	0.314437i
$715$		0			0
$716$	4.29540	−	1.56340i	0.160527	−	0.0584269i
$717$	6.57733	+	37.3019i	0.245635	+	1.39306i
$718$	3.49734	−	19.8344i	0.130519	−	0.740212i
$719$	4.77790	+	1.73901i	0.178186	+	0.0648542i	0.429572	−	0.903033i	$-0.358664\pi$
$719$	4.77790	+	1.73901i	0.178186	+	0.0648542i	−0.251387	+	0.967887i	$0.580887\pi$
$720$		0			0
$721$	−38.9934			−1.45219
$722$	−18.6469	+	3.64584i	−0.693967	+	0.135684i
$723$	52.6311			1.95737
$724$	1.29338	−	1.08527i	0.0480680	−	0.0403338i
$725$		0			0
$726$	−3.74786	+	21.2552i	−0.139096	+	0.788854i
$727$	3.74747	+	21.2529i	0.138986	+	0.788228i	0.972001	+	0.234977i	$0.0755016\pi$
$727$	3.74747	+	21.2529i	0.138986	+	0.788228i	−0.833015	+	0.553250i	$0.813387\pi$
$728$	12.8248	−	4.66784i	0.475318	−	0.173002i
$729$	9.92186	−	17.1852i	0.367476	−	0.636487i
$730$		0			0
$731$	11.4474	+	9.60551i	0.423397	+	0.355273i
$732$	14.2525	+	11.9593i	0.526788	+	0.442027i
$733$	4.73774	+	8.20601i	0.174993	+	0.303096i	0.940159	−	0.340737i	$-0.110677\pi$
$733$	4.73774	+	8.20601i	0.174993	+	0.303096i	−0.765166	+	0.643833i	$0.777343\pi$
$734$	−2.26066	+	3.91559i	−0.0834426	+	0.144527i
$735$		0			0
$736$	0.369001	+	2.09271i	0.0136015	+	0.0771382i
$737$	0.246588	−	1.39847i	0.00908317	−	0.0515132i
$738$	−27.1365	−	9.87687i	−0.998908	−	0.363573i
$739$	−6.02954	+	5.05938i	−0.221800	+	0.186112i	−0.746916	−	0.664918i	$-0.768466\pi$
$739$	−6.02954	+	5.05938i	−0.221800	+	0.186112i	0.525116	+	0.851031i	$0.324022\pi$
$740$		0			0
$741$	11.1699	−	43.2888i	0.410337	−	1.59026i
$742$	19.6254			0.720473
$743$	−37.0651	+	31.1013i	−1.35979	+	1.14100i	−0.383737	+	0.923442i	$0.625363\pi$
$743$	−37.0651	+	31.1013i	−1.35979	+	1.14100i	−0.976049	+	0.217553i	$0.930193\pi$
$744$	−0.772575	−	0.281194i	−0.0283240	−	0.0103091i
$745$		0			0
$746$	−4.04087	−	22.9169i	−0.147947	−	0.839048i
$747$	28.0483	−	10.2087i	1.02623	−	0.373518i
$748$	−0.893209	+	1.54708i	−0.0326590	+	0.0565670i
$749$	−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	$0.793337\pi$
$752$	0.0382211	+	0.0662008i	0.00139378	+	0.00241410i
$753$	−26.7397	+	46.3145i	−0.974447	+	1.68779i
$754$	0.529778	−	0.192823i	0.0192934	−	0.00702221i
$755$		0			0
$756$	0.489679	−	2.77711i	0.0178095	−	0.101002i
$757$	32.8586	+	11.9596i	1.19427	+	0.434677i	0.861220	−	0.508233i	$-0.169701\pi$
$757$	32.8586	+	11.9596i	1.19427	+	0.434677i	0.333046	+	0.942910i	$0.391923\pi$
$758$	7.15997	−	6.00792i	0.260062	−	0.218218i
$759$	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	$0.176485\pi$
$762$	−29.7884	+	24.9954i	−1.07912	+	0.905489i
$763$	22.0634	+	8.03041i	0.798748	+	0.290720i
$764$	1.94845	−	11.0502i	0.0704926	−	0.399783i
$765$		0			0
$766$	30.8559	−	11.2306i	1.11487	−	0.405779i
$767$	17.7036	−	30.6636i	0.639241	−	1.10720i
$768$	−1.18566	−	2.05362i	−0.0427837	−	0.0741035i
$769$	1.06182	+	0.890969i	0.0382900	+	0.0321292i	0.661732	−	0.749741i	$-0.269822\pi$
$769$	1.06182	+	0.890969i	0.0382900	+	0.0321292i	−0.623442	+	0.781870i	$0.714266\pi$
$770$		0			0
$771$	12.7038	+	22.0036i	0.457516	+	0.792440i
$772$	−10.7439	+	18.6090i	−0.386682	+	0.669753i
$773$	6.05111	−	2.20242i	0.217643	−	0.0792157i	−0.230897	−	0.972978i	$-0.574166\pi$
$773$	6.05111	−	2.20242i	0.217643	−	0.0792157i	0.448541	+	0.893762i	$0.351944\pi$
$774$	5.24973	+	29.7727i	0.188698	+	1.07016i
$775$		0			0
$776$	−15.2434	−	5.54814i	−0.547206	−	0.199167i
$777$	59.1248	−	49.6116i	2.12109	−	1.77981i
$778$	10.6737			0.382670
$779$	−27.1585	+	39.5624i	−0.973056	+	1.41747i
$780$		0			0
$781$	12.2988	−	10.3199i	0.440085	−	0.369275i
$782$	−2.58910	−	0.942355i	−0.0925860	−	0.0336985i
$783$	0.0202281	−	0.114719i	0.000722893	−	0.00409973i
$784$	0.513421	+	2.91175i	0.0183365	+	0.103991i
$785$		0			0
$786$	−13.2043	+	22.8705i	−0.470981	+	0.815762i
$787$	4.21842	+	7.30651i	0.150370	+	0.260449i	0.931364	−	0.364090i	$-0.118620\pi$
$787$	4.21842	+	7.30651i	0.150370	+	0.260449i	−0.780993	+	0.624539i	$0.785287\pi$
$788$	−11.7040	−	9.82078i	−0.416936	−	0.349851i
$789$	−48.4407	−	40.6466i	−1.72453	−	1.44706i
$790$		0			0
$791$	18.3037	−	31.7030i	0.650805	−	1.12723i
$792$	−3.39612	+	1.23608i	−0.120676	+	0.0439224i
$793$	5.89285	+	33.4200i	0.209261	+	1.18678i
$794$	−1.74625	+	9.90348i	−0.0619721	+	0.351461i
$795$		0			0
$796$	0.542940	−	0.455581i	0.0192440	−	0.0161476i
$797$	32.4342			1.14888			0.574438	−	0.818548i	$-0.305221\pi$
$797$	32.4342			1.14888			0.574438	+	0.818548i	$0.305221\pi$
$798$	29.6862	+	13.5091i	1.05088	+	0.478217i
$799$	−0.0991149			−0.00350643
$800$		0			0
$801$	44.9066	+	16.3447i	1.58670	+	0.577511i
$802$	2.09751	−	11.8956i	0.0740657	−	0.420047i
$803$	2.92926	+	16.6126i	0.103371	+	0.586247i
$804$	−2.29667	+	0.835919i	−0.0809973	+	0.0294806i
$805$		0			0
$806$	−0.749796	−	1.29868i	−0.0264104	−	0.0457442i
$807$	2.59385	+	2.17650i	0.0913079	+	0.0766164i
$808$	5.07370	+	4.25734i	0.178492	+	0.149773i
$809$	9.01013	+	15.6060i	0.316779	+	0.548678i	0.979814	−	0.199911i	$-0.0640652\pi$
$809$	9.01013	+	15.6060i	0.316779	+	0.548678i	−0.663035	+	0.748589i	$0.730732\pi$
$810$		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	$0.236985\pi$
$812$	0.0714214	+	0.405051i	0.00250640	+	0.0142145i
$813$	3.03455	−	17.2098i	0.106426	−	0.603573i
$814$	13.3547	+	4.86070i	0.468081	+	0.170367i
$815$		0			0
$816$	3.07464			0.107634
$817$	50.0843	+	3.91407i	1.75223	+	0.136936i
$818$	−39.5462			−1.38270
$819$	−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	$0.891213\pi$
$822$	−3.02310	−	17.1449i	−0.105443	−	0.597996i
$823$	46.9427	−	17.0857i	1.63632	−	0.595571i	0.649929	−	0.759995i	$-0.274799\pi$
$823$	46.9427	−	17.0857i	1.63632	−	0.595571i	0.986390	+	0.164424i	$0.0525765\pi$
$824$	−6.17880	+	10.7020i	−0.215249	+	0.372822i
$825$		0			0
$826$	19.7878	+	16.6039i	0.688504	+	0.577723i
$827$	4.06949	+	3.41471i	0.141510	+	0.118741i	0.710795	−	0.703399i	$-0.248335\pi$
$827$	4.06949	+	3.41471i	0.141510	+	0.118741i	−0.569285	+	0.822140i	$0.692780\pi$
$828$	−2.78706	−	4.82733i	−0.0968570	−	0.167761i
$829$	−18.4308	+	31.9231i	−0.640129	+	1.10874i	0.345275	+	0.938502i	$0.387786\pi$
$829$	−18.4308	+	31.9231i	−0.640129	+	1.10874i	−0.985404	+	0.170234i	$0.945548\pi$
$830$		0			0
$831$	1.03986	+	5.89733i	0.0360723	+	0.204576i
$832$	0.751065	−	4.25950i	0.0260385	−	0.147672i
$833$	−3.60242	−	1.31118i	−0.124817	−	0.0454295i
$834$	21.4560	−	18.0037i	0.742961	−	0.623418i
$835$		0			0
$836$	0.578889	+	5.97760i	0.0200213	+	0.206740i
$837$	−0.309849			−0.0107099
$838$	21.8572	−	18.3404i	0.755045	−	0.633558i
$839$	42.0154	+	15.2924i	1.45053	+	0.527951i	0.942740	−	0.333528i	$-0.108239\pi$
$839$	42.0154	+	15.2924i	1.45053	+	0.527951i	0.507793	+	0.861479i	$0.330462\pi$
$840$		0			0
$841$	−5.03285	−	28.5427i	−0.173546	−	0.984231i
$842$	−1.91607	+	0.697393i	−0.0660321	+	0.0240337i
$843$	−20.4275	+	35.3814i	−0.703559	+	1.21860i
$844$	−7.03956	−	12.1929i	−0.242312	−	0.419696i
$845$		0			0
$846$	−0.153605	−	0.128890i	−0.00528106	−	0.00443133i
$847$	−14.3599	−	24.8721i	−0.493412	−	0.854615i
$848$	3.10980	−	5.38633i	0.106791	−	0.184967i
$849$	62.8845	−	22.8881i	2.15819	−	0.785517i
$850$		0			0
$851$	−3.80625	+	21.5863i	−0.130476	+	0.739969i
$852$	−25.9660	−	9.45085i	−0.889581	−	0.323781i
$853$	22.5705	−	18.9389i	0.772800	−	0.648457i	−0.168624	−	0.985680i	$-0.553932\pi$
$853$	22.5705	−	18.9389i	0.772800	−	0.648457i	0.941424	+	0.337224i	$0.109488\pi$
$854$	−24.7574			−0.847181
$855$		0			0
$856$	−10.9548			−0.374428
$857$	36.3667	−	30.5152i	1.24226	−	1.04238i	0.244917	−	0.969544i	$-0.421239\pi$
$857$	36.3667	−	30.5152i	1.24226	−	1.04238i	0.997344	−	0.0728369i	$-0.0232053\pi$
$858$	−13.2788	−	4.83309i	−0.453331	−	0.164999i
$859$	0.165772	−	0.940140i	0.00565607	−	0.0320772i	−0.981849	−	0.189664i	$-0.939260\pi$
$859$	0.165772	−	0.940140i	0.00565607	−	0.0320772i	0.987505	+	0.157587i	$0.0503713\pi$
$860$		0			0
$861$	77.4070	−	28.1739i	2.63802	−	0.960162i
$862$	−6.78537	+	11.7526i	−0.231111	+	0.400295i
$863$	23.5130	+	40.7257i	0.800392	+	1.38632i	0.919359	+	0.393421i	$0.128708\pi$
$863$	23.5130	+	40.7257i	0.800392	+	1.38632i	−0.118967	+	0.992898i	$0.537958\pi$
$864$	−0.684602	−	0.574449i	−0.0232906	−	0.0195432i
$865$		0			0
$866$	14.4819	+	25.0834i	0.492116	+	0.852370i
$867$	18.1629	−	31.4590i	0.616843	−	1.06840i
$868$	1.02804	−	0.374175i	0.0348939	−	0.0127003i
$869$	3.35184	+	19.0092i	0.113703	+	0.644844i
$870$		0			0
$871$	−4.18906	−	1.52469i	−0.141941	−	0.0516622i
$872$	5.70011	−	4.78296i	0.193030	−	0.161971i
$873$	42.5515			1.44015
$874$	−8.92438	+	2.48023i	−0.301872	+	0.0838949i
$875$		0			0
$876$	22.2409	−	18.6623i	0.751451	−	0.630542i
$877$	−40.2114	−	14.6358i	−1.35784	−	0.494215i	−0.442457	−	0.896790i	$-0.645893\pi$
$877$	−40.2114	−	14.6358i	−1.35784	−	0.494215i	−0.915387	+	0.402575i	$0.868115\pi$
$878$	−1.94726	+	11.0435i	−0.0657168	+	0.372699i
$879$	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	$0.215510\pi$
$882$	−3.87786	−	6.71666i	−0.130574	−	0.226162i
$883$	23.9939	+	20.1333i	0.807460	+	0.677539i	0.950000	−	0.312250i	$-0.101083\pi$
$883$	23.9939	+	20.1333i	0.807460	+	0.677539i	−0.142540	+	0.989789i	$0.545527\pi$
$884$	4.29603	+	3.60479i	0.144491	+	0.121242i
$885$		0			0
$886$	3.72498	−	6.45186i	0.125143	−	0.216755i
$887$	−3.18973	+	1.16097i	−0.107101	+	0.0389814i	−0.395015	−	0.918675i	$-0.629260\pi$
$887$	−3.18973	+	1.16097i	−0.107101	+	0.0389814i	0.287914	+	0.957656i	$0.407038\pi$
$888$	−4.24746	−	24.0885i	−0.142535	−	0.808358i
$889$	8.98528	−	50.9581i	0.301357	−	1.70908i
$890$		0			0
$891$	−10.5423	+	8.84604i	−0.353180	+	0.296353i
$892$	−11.7169			−0.392310
$893$	−0.271160	+	0.193641i	−0.00907402	+	0.00647995i
$894$	8.33401			0.278731
$895$		0			0
$896$	2.96512	+	1.07922i	0.0990579	+	0.0360541i
$897$	3.78463	−	21.4637i	0.126365	−	0.716652i
$898$	0.921002	+	5.22326i	0.0307342	+	0.174303i
$899$	0.0424671	−	0.0154568i	0.00141636	−	0.000515512i
$900$		0			0
$901$	4.03216	+	6.98391i	0.134331	+	0.232668i
$902$	11.6193	+	9.74975i	0.386880	+	0.324631i
$903$	−66.0613	−	55.4320i	−2.19838	−	1.84466i
$904$	−5.80072	−	10.0471i	−0.192929	−	0.334163i
$905$		0			0
$906$	0.473783	−	0.172443i	0.0157404	−	0.00572903i
$907$	−6.87769	−	39.0053i	−0.228370	−	1.29515i	−0.856137	−	0.516749i	$-0.827142\pi$
$907$	−6.87769	−	39.0053i	−0.228370	−	1.29515i	0.627767	−	0.778401i	$-0.283969\pi$
$908$	1.77582	−	10.0712i	0.0589326	−	0.334223i
$909$	−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	$0.630331\pi$
$912$	8.41166	−	6.00695i	0.278538	−	0.198910i
$913$	−15.6776			−0.518851
$914$	−11.4822	+	9.63471i	−0.379798	+	0.318688i
$915$		0			0
$916$	−0.878120	+	4.98007i	−0.0290139	+	0.164546i
$917$	−6.10215	−	34.6070i	−0.201511	−	1.14282i
$918$	1.08887	−	0.396316i	0.0359380	−	0.0130804i
$919$	−1.92860	+	3.34044i	−0.0636187	+	0.110191i	−0.896080	−	0.443892i	$-0.853597\pi$
$919$	−1.92860	+	3.34044i	−0.0636187	+	0.110191i	0.832462	+	0.554083i	$0.186931\pi$
$920$		0			0
$921$	−16.4663	−	13.8169i	−0.542583	−	0.455281i
$922$	−5.25656	−	4.41078i	−0.173116	−	0.145261i
$923$	−25.2004	−	43.6484i	−0.829481	−	1.43670i
$924$	5.15458	−	8.92800i	0.169573	−	0.293710i
$925$		0			0
$926$	−3.58390	−	20.3253i	−0.117774	−	0.667931i
$927$	5.62890	−	31.9231i	0.184877	−	1.04849i
$928$	0.122486	+	0.0445813i	0.00402080	+	0.00146345i
$929$	15.5371	−	13.0371i	0.509755	−	0.427735i	−0.351288	−	0.936267i	$-0.614256\pi$
$929$	15.5371	−	13.0371i	0.509755	−	0.427735i	0.861043	+	0.508532i	$0.169812\pi$
$930$		0			0
$931$	−12.4172	+	3.45094i	−0.406958	+	0.113100i
$932$	7.25845			0.237759
$933$	−39.4413	+	33.0952i	−1.29125	+	1.08349i
$934$	−11.3092	−	4.11621i	−0.370048	−	0.134687i
$935$		0			0
$936$	1.97014	+	11.1732i	0.0643960	+	0.365208i
$937$	−25.9286	+	9.43723i	−0.847050	+	0.308301i	−0.728837	−	0.684687i	$-0.759939\pi$
$937$	−25.9286	+	9.43723i	−0.847050	+	0.308301i	−0.118213	+	0.992988i	$0.537717\pi$
$938$	1.62611	−	2.81651i	0.0530945	−	0.0919623i
$939$	−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	$0.844187\pi$
$942$	9.11475	+	15.7872i	0.296975	+	0.514375i
$943$	−11.6970	+	20.2599i	−0.380908	+	0.659752i
$944$	7.69256	−	2.79986i	0.250372	−	0.0911278i
$945$		0			0
$946$	2.75737	−	15.6378i	0.0896498	−	0.508429i
$947$	26.3822	+	9.60233i	0.857306	+	0.312034i	0.733016	−	0.680212i	$-0.238112\pi$
$947$	26.3822	+	9.60233i	0.857306	+	0.312034i	0.124291	+	0.992246i	$0.460334\pi$
$948$	25.4495	−	21.3546i	0.826560	−	0.693566i
$949$	52.9562			1.71903
$950$		0			0
$951$	4.99982			0.162130
$952$	−3.13413	+	2.62985i	−0.101578	+	0.0852338i
$953$	32.2346	+	11.7324i	1.04418	+	0.380050i	0.806463	−	0.591284i	$-0.201379\pi$
$953$	32.2346	+	11.7324i	1.04418	+	0.380050i	0.237717	+	0.971335i	$0.423601\pi$
$954$	−2.83303	+	16.0669i	−0.0917229	+	0.520186i
$955$		0			0
$956$	−15.0098	+	5.46314i	−0.485453	+	0.176690i
$957$	0.212930	−	0.368806i	0.00688305	−	0.0119218i
$958$	−11.3895	−	19.7272i	−0.367978	−	0.637357i
$959$	17.7462	+	14.8908i	0.573054	+	0.480849i
$960$		0			0
$961$	15.4399	+	26.7427i	0.498061	+	0.862667i
$962$	22.3073	−	38.6374i	0.719216	−	1.24572i
$963$	27.0029	−	9.82824i	0.870155	−	0.316711i
$964$	3.85411	+	21.8577i	0.124132	+	0.703990i
$965$		0			0
$966$	14.9413	+	5.43820i	0.480729	+	0.174971i
$967$	−11.1331	+	9.34181i	−0.358017	+	0.300412i	−0.804000	−	0.594629i	$-0.797299\pi$
$967$	−11.1331	+	9.34181i	−0.358017	+	0.300412i	0.445983	+	0.895042i	$0.352854\pi$
$968$	−9.10174			−0.292541
$969$	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	$-0.0137300\pi$
$972$	19.7383	+	7.18414i	0.633105	+	0.230431i
$973$	−6.47192	+	36.7041i	−0.207480	+	1.17668i
$974$	−1.11988	−	6.35114i	−0.0358832	−	0.203504i
$975$		0			0
$976$	−3.92300	+	6.79483i	−0.125572	+	0.217497i
$977$	−1.45577	−	2.52147i	−0.0465743	−	0.0806691i	0.841798	−	0.539792i	$-0.181497\pi$
$977$	−1.45577	−	2.52147i	−0.0465743	−	0.0806691i	−0.888373	+	0.459123i	$0.848164\pi$
$978$	13.3097	+	11.1682i	0.425599	+	0.357120i
$979$	−19.2281	−	16.1343i	−0.614533	−	0.515655i
$980$		0			0
$981$	−9.75929	+	16.9036i	−0.311590	+	0.539690i
$982$	22.8944	−	8.33289i	0.730591	−	0.265913i
$983$	−7.16313	−	40.6242i	−0.228469	−	1.29571i	−0.855942	−	0.517072i	$-0.827022\pi$
$983$	−7.16313	−	40.6242i	−0.228469	−	1.29571i	0.627474	−	0.778638i	$-0.284089\pi$
$984$	4.53323	−	25.7092i	0.144514	−	0.819580i
$985$		0			0
$986$	−0.129467	+	0.108636i	−0.00412308	+	0.00345968i
$987$	0.571978			0.0182062
$988$	18.7958	+	1.46889i	0.597975	+	0.0467315i
$989$	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	$0.458998\pi$
$992$	0.0602055	−	0.341442i	0.00191153	−	0.0108408i
$993$	−1.41819	−	8.04294i	−0.0450048	−	0.255235i
$994$	34.5520	−	12.5759i	1.09592	−	0.398883i
$995$		0			0
$996$	13.4915	+	23.3679i	0.427494	+	0.740442i
$997$	−0.503657	−	0.422618i	−0.0159510	−	0.0133844i	0.634777	−	0.772695i	$-0.281092\pi$
$997$	−0.503657	−	0.422618i	−0.0159510	−	0.0133844i	−0.650728	+	0.759311i	$0.725536\pi$
$998$	1.24460	+	1.04434i	0.0393970	+	0.0330580i
$999$	−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.l.i.101.1		18
5.2	odd	4		950.2.u.g.899.4		36
5.3	odd	4		950.2.u.g.899.3		36
5.4	even	2		190.2.k.d.101.3	✓	18
19.16	even	9	inner	950.2.l.i.301.1		18
95.4	even	18		3610.2.a.bi.1.2		9
95.34	odd	18		3610.2.a.bj.1.8		9
95.54	even	18		190.2.k.d.111.3	yes	18
95.73	odd	36		950.2.u.g.149.4		36
95.92	odd	36		950.2.u.g.149.3		36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
190.2.k.d.101.3	✓	18	5.4	even	2
190.2.k.d.111.3	yes	18	95.54	even	18
950.2.l.i.101.1		18	1.1	even	1	trivial
950.2.l.i.301.1		18	19.16	even	9	inner
950.2.u.g.149.3		36	95.92	odd	36
950.2.u.g.149.4		36	95.73	odd	36
950.2.u.g.899.3		36	5.3	odd	4
950.2.u.g.899.4		36	5.2	odd	4
3610.2.a.bi.1.2		9	95.4	even	18
3610.2.a.bj.1.8		9	95.34	odd	18

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(0.766044 - 0.642788i) q^{2} +(-2.22831 - 0.811037i) q^{3} +(0.173648 - 0.984808i) q^{4} +(-2.22831 + 0.811037i) q^{6} +(1.57771 - 2.73267i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(2.00943 + 1.68611i) q^{9} +O(q^{10})\)	\(q+(0.766044 - 0.642788i) q^{2} +(-2.22831 - 0.811037i) q^{3} +(0.173648 - 0.984808i) q^{4} +(-2.22831 + 0.811037i) q^{6} +(1.57771 - 2.73267i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(2.00943 + 1.68611i) q^{9} +(-0.688886 - 1.19319i) q^{11} +(-1.18566 + 2.05362i) q^{12} +(-4.06437 + 1.47931i) q^{13} +(-0.547933 - 3.10748i) q^{14} +(-0.939693 - 0.342020i) q^{16} +(0.993253 - 0.833438i) q^{17} +2.62313 q^{18} +(1.08907 - 4.22066i) q^{19} +(-5.73192 + 4.80965i) q^{21} +(-1.29468 - 0.471226i) q^{22} +(0.369001 - 2.09271i) q^{23} +(0.411774 + 2.33529i) q^{24} +(-2.16260 + 3.74574i) q^{26} +(0.446842 + 0.773953i) q^{27} +(-2.41719 - 2.02826i) q^{28} +(-0.0998515 - 0.0837854i) q^{29} +(-0.173355 + 0.300259i) q^{31} +(-0.939693 + 0.342020i) q^{32} +(0.567331 + 3.21749i) q^{33} +(0.225152 - 1.27690i) q^{34} +(2.00943 - 1.68611i) q^{36} -10.3150 q^{37} +(-1.87871 - 3.93325i) q^{38} +10.2564 q^{39} +(-10.3451 - 3.76531i) q^{41} +(-1.29932 + 7.36881i) q^{42} +(2.00132 + 11.3501i) q^{43} +(-1.29468 + 0.471226i) q^{44} +(-1.06250 - 1.84030i) q^{46} +(-0.0585581 - 0.0491361i) q^{47} +(1.81653 + 1.52425i) q^{48} +(-1.47834 - 2.56055i) q^{49} +(-2.88922 + 1.05159i) q^{51} +(0.751065 + 4.25950i) q^{52} +(-1.08002 + 6.12511i) q^{53} +(0.839788 + 0.305658i) q^{54} -3.15542 q^{56} +(-5.84988 + 8.52164i) q^{57} -0.130347 q^{58} +(-6.27104 + 5.26202i) q^{59} +(1.36244 - 7.72680i) q^{61} +(0.0602055 + 0.341442i) q^{62} +(7.77790 - 2.83092i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(2.50277 + 2.10007i) q^{66} +(0.789546 + 0.662508i) q^{67} +(-0.648300 - 1.12289i) q^{68} +(-2.51951 + 4.36392i) q^{69} +(2.02349 + 11.4758i) q^{71} +(0.455501 - 2.58328i) q^{72} +(-11.5052 - 4.18756i) q^{73} +(-7.90176 + 6.63036i) q^{74} +(-3.96742 - 1.80543i) q^{76} -4.34745 q^{77} +(7.85688 - 6.59270i) q^{78} +(-13.1650 - 4.79168i) q^{79} +(-1.73450 - 9.83684i) q^{81} +(-10.3451 + 3.76531i) q^{82} +(5.68946 - 9.85443i) q^{83} +(3.74124 + 6.48003i) q^{84} +(8.82879 + 7.40823i) q^{86} +(0.154547 + 0.267683i) q^{87} +(-0.688886 + 1.19319i) q^{88} +(17.1195 - 6.23099i) q^{89} +(-2.36992 + 13.4405i) q^{91} +(-1.99684 - 0.726790i) q^{92} +(0.629809 - 0.528473i) q^{93} -0.0764422 q^{94} +2.37131 q^{96} +(12.4265 - 10.4271i) q^{97} +(-2.77836 - 1.01124i) q^{98} +(0.627577 - 3.55916i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q - 9 q^{8} - 18 q^{9}+O(q^{10}) \) 18 * q - 9 * q^8 - 18 * q^9	\( 18 q - 9 q^{8} - 18 q^{9} - 12 q^{11} + 6 q^{13} + 6 q^{14} + 42 q^{18} + 12 q^{21} + 3 q^{22} - 9 q^{23} - 9 q^{26} + 18 q^{27} - 3 q^{28} - 6 q^{29} - 6 q^{31} - 66 q^{33} + 18 q^{34} - 18 q^{36} + 12 q^{37} + 6 q^{38} + 48 q^{39} - 21 q^{41} - 42 q^{42} - 18 q^{43} + 3 q^{44} + 18 q^{46} + 54 q^{47} - 39 q^{49} + 42 q^{51} - 12 q^{52} + 24 q^{53} - 54 q^{54} + 18 q^{57} - 30 q^{59} + 48 q^{61} + 30 q^{62} + 57 q^{63} - 9 q^{64} + 24 q^{66} + 6 q^{67} + 6 q^{68} - 30 q^{69} + 30 q^{71} - 6 q^{73} - 3 q^{74} - 21 q^{76} - 30 q^{77} + 24 q^{78} + 30 q^{79} + 18 q^{81} - 21 q^{82} - 6 q^{83} + 6 q^{84} + 36 q^{86} - 24 q^{87} - 12 q^{88} + 30 q^{89} - 60 q^{91} + 18 q^{92} + 12 q^{93} + 6 q^{94} + 12 q^{97} + 18 q^{98} + 171 q^{99}+O(q^{100}) \) 18 * q - 9 * q^8 - 18 * q^9 - 12 * q^11 + 6 * q^13 + 6 * q^14 + 42 * q^18 + 12 * q^21 + 3 * q^22 - 9 * q^23 - 9 * q^26 + 18 * q^27 - 3 * q^28 - 6 * q^29 - 6 * q^31 - 66 * q^33 + 18 * q^34 - 18 * q^36 + 12 * q^37 + 6 * q^38 + 48 * q^39 - 21 * q^41 - 42 * q^42 - 18 * q^43 + 3 * q^44 + 18 * q^46 + 54 * q^47 - 39 * q^49 + 42 * q^51 - 12 * q^52 + 24 * q^53 - 54 * q^54 + 18 * q^57 - 30 * q^59 + 48 * q^61 + 30 * q^62 + 57 * q^63 - 9 * q^64 + 24 * q^66 + 6 * q^67 + 6 * q^68 - 30 * q^69 + 30 * q^71 - 6 * q^73 - 3 * q^74 - 21 * q^76 - 30 * q^77 + 24 * q^78 + 30 * q^79 + 18 * q^81 - 21 * q^82 - 6 * q^83 + 6 * q^84 + 36 * q^86 - 24 * q^87 - 12 * q^88 + 30 * q^89 - 60 * q^91 + 18 * q^92 + 12 * q^93 + 6 * q^94 + 12 * q^97 + 18 * q^98 + 171 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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