LMFDB - Embedded newform 1000.2.v.g.507.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1000,2,Mod(43,1000)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1000.43"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1000, base_ring=CyclotomicField(20)) chi = DirichletCharacter(H, H._module([10, 10, 19])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 1000 = 2^{3} \cdot 5^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1000.v (of order $20$, degree $8$, not minimal)

Newform invariants

comment:select newform

sage:traces = [208,-8,4,10,0,-26,0,46,20,0,-4,-32,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(13)] == traces)

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

Self dual:	no
Analytic conductor:	$7.98504020213$
Analytic rank:	$0$
Dimension:	$208$
Relative dimension:	$26$ over $\Q(\zeta_{20})$
Twist minimal:	no (minimal twist has level 200)
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			507.5
Character	$\chi$	$=$	1000.507
Dual form			1000.2.v.g.643.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.20125 + 0.746320i) q^{2} +(1.50506 - 0.238378i) q^{3} +(0.886011 - 1.79304i) q^{4} +(-1.63005 + 1.40961i) q^{6} +(0.599487 - 0.599487i) q^{7} +(0.273858 + 2.81514i) q^{8} +(-0.644782 + 0.209502i) q^{9} +(-0.504364 + 1.55227i) q^{11} +(0.906081 - 2.90984i) q^{12} +(2.63223 - 5.16603i) q^{13} +(-0.272725 + 1.16754i) q^{14} +(-2.42997 - 3.17730i) q^{16} +(2.68282 + 0.424918i) q^{17} +(0.618190 - 0.732879i) q^{18} +(-1.03303 - 1.42184i) q^{19} +(0.759360 - 1.04517i) q^{21} +(-0.552625 - 2.24109i) q^{22} +(6.43220 - 3.27737i) q^{23} +(1.08324 + 4.17168i) q^{24} +(0.693551 + 8.17019i) q^{26} +(-4.99370 + 2.54442i) q^{27} +(-0.543750 - 1.60605i) q^{28} +(6.49732 + 4.72058i) q^{29} +(-1.09301 - 1.50440i) q^{31} +(5.29029 + 2.00321i) q^{32} +(-0.389071 + 2.45650i) q^{33} +(-3.53987 + 1.49181i) q^{34} +(-0.195639 + 1.34174i) q^{36} +(-0.781804 - 0.398349i) q^{37} +(2.30208 + 0.937020i) q^{38} +(2.73019 - 8.40267i) q^{39} +(-1.42918 - 4.39856i) q^{41} +(-0.132151 + 1.82224i) q^{42} +(3.23259 - 3.23259i) q^{43} +(2.33641 + 2.27967i) q^{44} +(-5.28072 + 8.73743i) q^{46} +(6.42640 - 1.01784i) q^{47} +(-4.41465 - 4.20279i) q^{48} +6.28123i q^{49} +4.13911 q^{51} +(-6.93071 - 9.29685i) q^{52} +(-2.10822 - 13.3108i) q^{53} +(4.09974 - 6.78339i) q^{54} +(1.85181 + 1.52346i) q^{56} +(-1.89371 - 1.89371i) q^{57} +(-11.3280 - 0.821520i) q^{58} +(2.90867 - 0.945085i) q^{59} +(-1.24919 - 0.405886i) q^{61} +(2.43575 + 0.991428i) q^{62} +(-0.260944 + 0.512132i) q^{63} +(-7.85000 + 1.54190i) q^{64} +(-1.36596 - 3.24124i) q^{66} +(10.9543 + 1.73499i) q^{67} +(3.13891 - 4.43392i) q^{68} +(8.89961 - 6.46594i) q^{69} +(-0.426288 + 0.586736i) q^{71} +(-0.766357 - 1.75778i) q^{72} +(-2.36670 - 4.64490i) q^{73} +(1.23644 - 0.104959i) q^{74} +(-3.46469 + 0.592491i) q^{76} +(0.628207 + 1.23293i) q^{77} +(2.99143 + 12.1313i) q^{78} +(-9.40528 - 6.83334i) q^{79} +(-5.26385 + 3.82441i) q^{81} +(4.99954 + 4.21715i) q^{82} +(-2.18069 + 13.7683i) q^{83} +(-1.20123 - 2.28759i) q^{84} +(-1.47061 + 6.29571i) q^{86} +(10.9041 + 5.55594i) q^{87} +(-4.50798 - 0.994752i) q^{88} +(4.46859 + 1.45193i) q^{89} +(-1.51898 - 4.67495i) q^{91} +(-0.177444 - 14.4370i) q^{92} +(-2.00367 - 2.00367i) q^{93} +(-6.96009 + 6.01884i) q^{94} +(8.43973 + 1.75386i) q^{96} +(-0.249026 - 1.57229i) q^{97} +(-4.68781 - 7.54534i) q^{98} -1.10654i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 208 q - 8 q^{2} + 4 q^{3} + 10 q^{4} - 26 q^{6} + 46 q^{8} + 20 q^{9} - 4 q^{11} - 32 q^{12} + 30 q^{14} + 18 q^{16} - 12 q^{17} - 20 q^{18} + 38 q^{22} - 8 q^{26} - 8 q^{27} - 40 q^{28} + 22 q^{32} + 16 q^{33}+ \cdots - 34 q^{98}+O(q^{100}) $ 208 * q - 8 * q^2 + 4 * q^3 + 10 * q^4 - 26 * q^6 + 46 * q^8 + 20 * q^9 - 4 * q^11 - 32 * q^12 + 30 * q^14 + 18 * q^16 - 12 * q^17 - 20 * q^18 + 38 * q^22 - 8 * q^26 - 8 * q^27 - 40 * q^28 + 22 * q^32 + 16 * q^33 - 30 * q^34 - 38 * q^36 + 74 * q^38 - 44 * q^41 + 60 * q^42 - 8 * q^43 - 60 * q^44 + 2 * q^46 - 16 * q^48 + 8 * q^51 + 100 * q^52 + 140 * q^54 + 2 * q^56 + 92 * q^57 + 90 * q^58 + 40 * q^59 - 40 * q^62 - 20 * q^64 - 2 * q^66 - 72 * q^67 - 46 * q^68 - 150 * q^72 + 4 * q^73 - 24 * q^76 - 110 * q^78 + 16 * q^81 - 22 * q^82 + 44 * q^83 + 10 * q^84 - 26 * q^86 - 126 * q^88 + 100 * q^89 + 4 * q^91 - 110 * q^92 - 150 * q^94 - 26 * q^96 - 76 * q^97 - 34 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1000\mathbb{Z}\right)^\times$.

$n$	$377$	$501$	$751$
$\chi(n)$	$e\left(\frac{17}{20}\right)$	$-1$	$-1$

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 $

$2$	−1.20125	+	0.746320i	−0.849413	+	0.527728i
$2$	−1.20125	+	0.746320i	−0.849413	+	0.527728i
$3$	1.50506	−	0.238378i	0.868948	−	0.137628i	0.293988	−	0.955809i	$-0.405018\pi$
$3$	1.50506	−	0.238378i	0.868948	−	0.137628i	0.574960	+	0.818181i	$0.305018\pi$
$4$	0.886011	−	1.79304i	0.443006	−	0.896519i
$5$		0			0
$5$		0			0
$6$	−1.63005	+	1.40961i	−0.665466	+	0.575471i
$7$	0.599487	−	0.599487i	0.226585	−	0.226585i	−0.584680	−	0.811264i	$-0.698780\pi$
$7$	0.599487	−	0.599487i	0.226585	−	0.226585i	0.811264	+	0.584680i	$0.198780\pi$
$8$	0.273858	+	2.81514i	0.0968234	+	0.995302i
$9$	−0.644782	+	0.209502i	−0.214927	+	0.0698341i
$10$		0			0
$11$	−0.504364	+	1.55227i	−0.152071	+	0.468028i	−0.997852	−	0.0655026i	$-0.979135\pi$
$11$	−0.504364	+	1.55227i	−0.152071	+	0.468028i	0.845781	+	0.533530i	$0.179135\pi$
$12$	0.906081	−	2.90984i	0.261563	−	0.839998i
$13$	2.63223	−	5.16603i	0.730048	−	1.43280i	−0.164753	−	0.986335i	$-0.552683\pi$
$13$	2.63223	−	5.16603i	0.730048	−	1.43280i	0.894801	−	0.446465i	$-0.147317\pi$
$14$	−0.272725	+	1.16754i	−0.0728889	+	0.312039i
$15$		0			0
$16$	−2.42997	−	3.17730i	−0.607492	−	0.794326i
$17$	2.68282	+	0.424918i	0.650681	+	0.103058i	0.473044	−	0.881039i	$-0.343155\pi$
$17$	2.68282	+	0.424918i	0.650681	+	0.103058i	0.177636	+	0.984096i	$0.443155\pi$
$18$	0.618190	−	0.732879i	0.145709	−	0.172741i
$19$	−1.03303	−	1.42184i	−0.236993	−	0.326193i	0.673910	−	0.738813i	$-0.264614\pi$
$19$	−1.03303	−	1.42184i	−0.236993	−	0.326193i	−0.910903	+	0.412621i	$0.864614\pi$
$20$		0			0
$21$	0.759360	−	1.04517i	0.165706	−	0.228075i
$22$	−0.552625	−	2.24109i	−0.117820	−	0.477801i
$23$	6.43220	−	3.27737i	1.34121	−	0.683379i	0.371679	−	0.928361i	$-0.378782\pi$
$23$	6.43220	−	3.27737i	1.34121	−	0.683379i	0.969528	+	0.244982i	$0.0787822\pi$
$24$	1.08324	+	4.17168i	0.221116	+	0.851540i
$25$		0			0
$26$	0.693551	+	8.17019i	0.136017	+	1.60231i
$27$	−4.99370	+	2.54442i	−0.961039	+	0.489674i
$28$	−0.543750	−	1.60605i	−0.102759	−	0.303516i
$29$	6.49732	+	4.72058i	1.20652	+	0.876589i	0.994910	−	0.100765i	$-0.0321290\pi$
$29$	6.49732	+	4.72058i	1.20652	+	0.876589i	0.211611	+	0.977354i	$0.432129\pi$
$30$		0			0
$31$	−1.09301	−	1.50440i	−0.196311	−	0.270199i	0.699502	−	0.714631i	$-0.253405\pi$
$31$	−1.09301	−	1.50440i	−0.196311	−	0.270199i	−0.895812	+	0.444432i	$0.853405\pi$
$32$	5.29029	+	2.00321i	0.935200	+	0.354120i
$33$	−0.389071	+	2.45650i	−0.0677285	+	0.427621i
$34$	−3.53987	+	1.49181i	−0.607083	+	0.255844i
$35$		0			0
$36$	−0.195639	+	1.34174i	−0.0326064	+	0.223623i
$37$	−0.781804	−	0.398349i	−0.128528	−	0.0654882i	0.388544	−	0.921430i	$-0.372978\pi$
$37$	−0.781804	−	0.398349i	−0.128528	−	0.0654882i	−0.517072	+	0.855942i	$0.672978\pi$
$38$	2.30208	+	0.937020i	0.373446	+	0.152005i
$39$	2.73019	−	8.40267i	0.437181	−	1.34550i
$40$		0			0
$41$	−1.42918	−	4.39856i	−0.223200	−	0.686939i	−0.998469	−	0.0553084i	$-0.982386\pi$
$41$	−1.42918	−	4.39856i	−0.223200	−	0.686939i	0.775269	−	0.631631i	$-0.217614\pi$
$42$	−0.132151	+	1.82224i	−0.0203914	+	0.281177i
$43$	3.23259	−	3.23259i	0.492966	−	0.492966i	−0.416274	−	0.909239i	$-0.636664\pi$
$43$	3.23259	−	3.23259i	0.492966	−	0.492966i	0.909239	+	0.416274i	$0.136664\pi$
$44$	2.33641	+	2.27967i	0.352227	+	0.343674i
$45$		0			0
$46$	−5.28072	+	8.73743i	−0.778600	+	1.28826i
$47$	6.42640	−	1.01784i	0.937387	−	0.148467i	0.330994	−	0.943633i	$-0.392616\pi$
$47$	6.42640	−	1.01784i	0.937387	−	0.148467i	0.606393	+	0.795165i	$0.292616\pi$
$48$	−4.41465	−	4.20279i	−0.637200	−	0.606620i
$49$			6.28123i			0.897319i
$50$		0			0
$51$	4.13911			0.579591
$52$	−6.93071	−	9.29685i	−0.961117	−	1.28924i
$53$	−2.10822	−	13.3108i	−0.289587	−	1.82838i	−0.518673	−	0.854973i	$-0.673574\pi$
$53$	−2.10822	−	13.3108i	−0.289587	−	1.82838i	0.229086	−	0.973406i	$-0.426426\pi$
$54$	4.09974	−	6.78339i	0.557904	−	0.923103i
$55$		0			0
$56$	1.85181	+	1.52346i	0.247459	+	0.203581i
$57$	−1.89371	−	1.89371i	−0.250828	−	0.250828i
$58$	−11.3280	−	0.821520i	−1.48744	−	0.107871i
$59$	2.90867	−	0.945085i	0.378677	−	0.123040i	−0.113493	−	0.993539i	$-0.536204\pi$
$59$	2.90867	−	0.945085i	0.378677	−	0.123040i	0.492170	+	0.870499i	$0.336204\pi$
$60$		0			0
$61$	−1.24919	−	0.405886i	−0.159942	−	0.0519684i	0.227951	−	0.973673i	$-0.426797\pi$
$61$	−1.24919	−	0.405886i	−0.159942	−	0.0519684i	−0.387894	+	0.921704i	$0.626797\pi$
$62$	2.43575	+	0.991428i	0.309340	+	0.125911i
$63$	−0.260944	+	0.512132i	−0.0328759	+	0.0645226i
$64$	−7.85000	+	1.54190i	−0.981250	+	0.192737i
$65$		0			0
$66$	−1.36596	−	3.24124i	−0.168138	−	0.398969i
$67$	10.9543	+	1.73499i	1.33828	+	0.211963i	0.784204	−	0.620503i	$-0.213071\pi$
$67$	10.9543	+	1.73499i	1.33828	+	0.211963i	0.554077	+	0.832466i	$0.313071\pi$
$68$	3.13891	−	4.43392i	0.380648	−	0.537692i
$69$	8.89961	−	6.46594i	1.07139	−	0.778408i
$70$		0			0
$71$	−0.426288	+	0.586736i	−0.0505911	+	0.0696327i	−0.833563	−	0.552424i	$-0.813703\pi$
$71$	−0.426288	+	0.586736i	−0.0505911	+	0.0696327i	0.782972	+	0.622057i	$0.213703\pi$
$72$	−0.766357	−	1.75778i	−0.0903160	−	0.207156i
$73$	−2.36670	−	4.64490i	−0.277001	−	0.543645i	0.710031	−	0.704171i	$-0.248681\pi$
$73$	−2.36670	−	4.64490i	−0.277001	−	0.543645i	−0.987032	+	0.160526i	$0.948681\pi$
$74$	1.23644	−	0.104959i	0.143733	−	0.0122012i
$75$		0			0
$76$	−3.46469	+	0.592491i	−0.397427	+	0.0679634i
$77$	0.628207	+	1.23293i	0.0715909	+	0.140505i
$78$	2.99143	+	12.1313i	0.338713	+	1.37360i
$79$	−9.40528	−	6.83334i	−1.05818	−	0.768810i	−0.0844264	−	0.996430i	$-0.526906\pi$
$79$	−9.40528	−	6.83334i	−1.05818	−	0.768810i	−0.973750	+	0.227619i	$0.926906\pi$
$80$		0			0
$81$	−5.26385	+	3.82441i	−0.584872	+	0.424934i
$82$	4.99954	+	4.21715i	0.552107	+	0.465706i
$83$	−2.18069	+	13.7683i	−0.239362	+	1.51127i	0.516357	+	0.856374i	$0.327288\pi$
$83$	−2.18069	+	13.7683i	−0.239362	+	1.51127i	−0.755718	+	0.654897i	$0.772712\pi$
$84$	−1.20123	−	2.28759i	−0.131065	−	0.249597i
$85$		0			0
$86$	−1.47061	+	6.29571i	−0.158580	+	0.678884i
$87$	10.9041	+	5.55594i	1.16905	+	0.595659i
$88$	−4.50798	−	0.994752i	−0.480553	−	0.106041i
$89$	4.46859	+	1.45193i	0.473670	+	0.153905i	0.536117	−	0.844144i	$-0.319891\pi$
$89$	4.46859	+	1.45193i	0.473670	+	0.153905i	−0.0624475	+	0.998048i	$0.519891\pi$
$90$		0			0
$91$	−1.51898	−	4.67495i	−0.159233	−	0.490068i
$92$	−0.177444	−	14.4370i	−0.0184998	−	1.50516i
$93$	−2.00367	−	2.00367i	−0.207771	−	0.207771i
$94$	−6.96009	+	6.01884i	−0.717878	+	0.620796i
$95$		0			0
$96$	8.43973	+	1.75386i	0.861377	+	0.179003i
$97$	−0.249026	−	1.57229i	−0.0252848	−	0.159642i	0.971815	−	0.235744i	$-0.0757526\pi$
$97$	−0.249026	−	1.57229i	−0.0252848	−	0.159642i	−0.997100	+	0.0761018i	$0.975753\pi$
$98$	−4.68781	−	7.54534i	−0.473540	−	0.762194i
$99$		−	1.10654i		−	0.111212i
$100$		0			0
$101$		−	10.7533i		−	1.06999i	−0.844855	−	0.534995i	$-0.820314\pi$
$101$		−	10.7533i		−	1.06999i	0.844855	−	0.534995i	$-0.179686\pi$
$102$	−4.97211	+	3.08910i	−0.492312	+	0.305867i
$103$	2.21866	+	14.0081i	0.218611	+	1.38025i	0.815883	+	0.578216i	$0.196251\pi$
$103$	2.21866	+	14.0081i	0.218611	+	1.38025i	−0.597273	+	0.802038i	$0.703749\pi$
$104$	15.2640	+	5.99532i	1.49675	+	0.587889i
$105$		0			0
$106$	12.4666	+	14.4162i	1.21087	+	1.40023i
$107$	−11.1004	−	11.1004i	−1.07312	−	1.07312i	−0.997107	−	0.0760098i	$-0.975782\pi$
$107$	−11.1004	−	11.1004i	−1.07312	−	1.07312i	−0.0760098	−	0.997107i	$-0.524218\pi$
$108$	0.137760	+	11.2083i	0.0132560	+	1.07852i
$109$	−0.0984171	−	0.302897i	−0.00942665	−	0.0290122i	0.946233	−	0.323487i	$-0.104855\pi$
$109$	−0.0984171	−	0.302897i	−0.00942665	−	0.0290122i	−0.955659	+	0.294475i	$0.904855\pi$
$110$		0			0
$111$	−1.27162	−	0.413175i	−0.120697	−	0.0392168i
$112$	−3.36149	−	0.448018i	−0.317630	−	0.0423337i
$113$	9.42226	+	4.80088i	0.886372	+	0.451629i	0.837033	−	0.547153i	$-0.184288\pi$
$113$	9.42226	+	4.80088i	0.886372	+	0.451629i	0.0493393	+	0.998782i	$0.484288\pi$
$114$	3.68813	+	0.861507i	0.345425	+	0.0806875i
$115$		0			0
$116$	14.2209	−	7.46745i	1.32037	−	0.693335i
$117$	−0.614916	+	3.88242i	−0.0568490	+	0.358930i
$118$	−2.78871	+	3.30609i	−0.256722	+	0.304350i
$119$	1.86305	−	1.35359i	0.170786	−	0.124083i
$120$		0			0
$121$	6.74402	+	4.89982i	0.613093	+	0.445438i
$122$	1.80351	−	0.444724i	0.163282	−	0.0402634i
$123$	−3.19952	−	6.27942i	−0.288491	−	0.566196i
$124$	−3.66587	+	0.626894i	−0.329205	+	0.0562968i
$125$		0			0
$126$	−0.0687549	−	0.809948i	−0.00612517	−	0.0721559i
$127$	5.30653	+	10.4147i	0.470879	+	0.924152i	0.997265	+	0.0739061i	$0.0235465\pi$
$127$	5.30653	+	10.4147i	0.470879	+	0.924152i	−0.526386	+	0.850245i	$0.676453\pi$
$128$	8.27908	−	7.71082i	0.731774	−	0.681547i
$129$	4.09467	−	5.63583i	0.360516	−	0.496208i
$130$		0			0
$131$	−9.80424	+	7.12319i	−0.856600	+	0.622356i	−0.926958	−	0.375165i	$-0.877586\pi$
$131$	−9.80424	+	7.12319i	−0.856600	+	0.622356i	0.0703578	+	0.997522i	$0.477586\pi$
$132$	4.05987	+	2.87410i	0.353366	+	0.250158i
$133$	−1.47166	−	0.233088i	−0.127609	−	0.0202113i
$134$	−14.4537	+	6.09126i	−1.24861	+	0.526205i
$135$		0			0
$136$	−0.461489	+	7.66889i	−0.0395724	+	0.657602i
$137$	−4.82667	+	9.47288i	−0.412370	+	0.809322i	0.587630	+	0.809130i	$0.300061\pi$
$137$	−4.82667	+	9.47288i	−0.412370	+	0.809322i	−1.00000		0.000192369i	$0.999939\pi$
$138$	−5.86500	+	14.4092i	−0.499262	+	1.22659i
$139$	10.9546	+	3.55938i	0.929161	+	0.301903i	0.734219	−	0.678912i	$-0.237548\pi$
$139$	10.9546	+	3.55938i	0.929161	+	0.301903i	0.194941	+	0.980815i	$0.437548\pi$
$140$		0			0
$141$	9.42950	−	3.06383i	0.794107	−	0.258021i
$142$	0.0741868	−	1.02296i	0.00622562	−	0.0858453i
$143$	6.69149	+	6.69149i	0.559571	+	0.559571i
$144$	2.23245	+	1.53958i	0.186038	+	0.128299i
$145$		0			0
$146$	6.30958	+	3.81338i	0.522185	+	0.315598i
$147$	1.49731	+	9.45364i	0.123496	+	0.779723i
$148$	−1.40694	+	1.04886i	−0.115650	+	0.0862160i
$149$	10.5617			0.865244			0.432622	−	0.901575i	$-0.357588\pi$
$149$	10.5617			0.865244			0.432622	+	0.901575i	$0.357588\pi$
$150$		0			0
$151$			5.53163i			0.450158i	0.974341	+	0.225079i	$0.0722640\pi$
$151$			5.53163i			0.450158i	−0.974341	+	0.225079i	$0.927736\pi$
$152$	3.71978	−	3.29750i	0.301714	−	0.267463i
$153$	−1.81886	+	0.288079i	−0.147046	+	0.0232898i
$154$	−1.67479	−	1.01221i	−0.134959	−	0.0815663i
$155$		0			0
$156$	−12.6473	−	12.3402i	−1.01260	−	0.988006i
$157$	2.85061	−	2.85061i	0.227503	−	0.227503i	−0.584146	−	0.811649i	$-0.698570\pi$
$157$	2.85061	−	2.85061i	0.227503	−	0.227503i	0.811649	+	0.584146i	$0.198570\pi$
$158$	16.3980	+	1.18920i	1.30455	+	0.0946079i
$159$	−6.34601	−	19.5310i	−0.503272	−	1.54891i
$160$		0			0
$161$	1.89128	−	5.82076i	0.149054	−	0.458740i
$162$	3.46897	−	8.52259i	0.272548	−	0.669598i
$163$	−13.7399	−	7.00084i	−1.07619	−	0.548348i	−0.176246	−	0.984346i	$-0.556395\pi$
$163$	−13.7399	−	7.00084i	−1.07619	−	0.548348i	−0.899948	+	0.435998i	$0.856395\pi$
$164$	−9.15305	−	1.33460i	−0.714733	−	0.104215i
$165$		0			0
$166$	−7.65603	−	18.1667i	−0.594223	−	1.41001i
$167$	−3.46646	+	21.8863i	−0.268243	+	1.69362i	0.374253	+	0.927327i	$0.377899\pi$
$167$	−3.46646	+	21.8863i	−0.268243	+	1.69362i	−0.642495	+	0.766290i	$0.722101\pi$
$168$	3.15025	+	1.85148i	0.243047	+	0.142844i
$169$	−12.1181	−	16.6791i	−0.932161	−	1.28301i
$170$		0			0
$171$	0.963958	+	0.700356i	0.0737157	+	0.0535576i
$172$	−2.93205	−	8.66028i	−0.223566	−	0.660340i
$173$	11.1786	−	5.69578i	0.849893	−	0.433042i	0.0259151	−	0.999664i	$-0.491750\pi$
$173$	11.1786	−	5.69578i	0.849893	−	0.433042i	0.823978	+	0.566622i	$0.191750\pi$
$174$	−17.2451	+	1.46391i	−1.30735	+	0.110978i
$175$		0			0
$176$	6.15763	−	2.16945i	0.464149	−	0.163529i
$177$	4.15244	−	2.11578i	0.312117	−	0.159031i
$178$	−6.45151	+	1.59086i	−0.483561	+	0.119240i
$179$	−12.0112	+	16.5320i	−0.897761	+	1.23566i	0.0734160	+	0.997301i	$0.476610\pi$
$179$	−12.0112	+	16.5320i	−0.897761	+	1.23566i	−0.971177	+	0.238360i	$0.923390\pi$
$180$		0			0
$181$	−13.1045	−	18.0368i	−0.974049	−	1.34066i	−0.939975	−	0.341244i	$-0.889152\pi$
$181$	−13.1045	−	18.0368i	−0.974049	−	1.34066i	−0.0340747	−	0.999419i	$-0.510848\pi$
$182$	5.31370	+	4.48215i	0.393877	+	0.332239i
$183$	−1.97686	−	0.313104i	−0.146134	−	0.0231453i
$184$	10.9878	+	17.2100i	0.810028	+	1.26874i
$185$		0			0
$186$	3.90229	+	0.911531i	0.286130	+	0.0668367i
$187$	−2.01271	+	3.95016i	−0.147184	+	0.288864i
$188$	3.86884	−	12.4246i	0.282164	−	0.906157i
$189$	−1.46831	+	4.51901i	−0.106804	+	0.328709i
$190$		0			0
$191$	−10.5039	+	3.41293i	−0.760036	+	0.246951i	−0.663294	−	0.748359i	$-0.730842\pi$
$191$	−10.5039	+	3.41293i	−0.760036	+	0.246951i	−0.0967418	+	0.995310i	$0.530842\pi$
$192$	−11.4472	+	4.19192i	−0.826130	+	0.302526i
$193$	2.33162	−	2.33162i	0.167834	−	0.167834i	−0.618193	−	0.786027i	$-0.712135\pi$
$193$	2.33162	−	2.33162i	0.167834	−	0.167834i	0.786027	+	0.618193i	$0.212135\pi$
$194$	1.47258	+	1.70286i	0.105725	+	0.122258i
$195$		0			0
$196$	11.2625	+	5.56524i	0.804463	+	0.397517i
$197$	−13.5058	+	2.13910i	−0.962246	+	0.152405i	−0.617743	−	0.786380i	$-0.711953\pi$
$197$	−13.5058	+	2.13910i	−0.962246	+	0.152405i	−0.344503	+	0.938785i	$0.611953\pi$
$198$	0.825836	+	1.32924i	0.0586896	+	0.0944647i
$199$	−10.9851			−0.778711			−0.389355	−	0.921088i	$-0.627302\pi$
$199$	−10.9851			−0.778711			−0.389355	+	0.921088i	$0.627302\pi$
$200$		0			0
$201$	16.9005			1.19207
$202$	8.02538	+	12.9174i	0.564664	+	0.908863i
$203$	6.72498	−	1.06513i	0.472001	−	0.0747576i
$204$	3.66730	−	7.42158i	0.256762	−	0.519614i
$205$		0			0
$206$	−13.1197	−	15.1714i	−0.914090	−	1.05704i
$207$	−3.46075	+	3.46075i	−0.240539	+	0.240539i
$208$	−22.8103	+	4.18991i	−1.58161	+	0.290518i
$209$	2.72811	−	0.886416i	0.188707	−	0.0613147i
$210$		0			0
$211$	5.60549	−	17.2519i	0.385898	−	1.18767i	−0.549929	−	0.835212i	$-0.685345\pi$
$211$	5.60549	−	17.2519i	0.385898	−	1.18767i	0.935827	−	0.352461i	$-0.114655\pi$
$212$	−25.7347	−	8.01340i	−1.76746	−	0.550362i
$213$	−0.501725	+	0.984691i	−0.0343777	+	0.0674699i
$214$	21.6188	+	5.04992i	1.47783	+	0.345206i
$215$		0			0
$216$	−8.53046	−	13.3612i	−0.580424	−	0.909112i
$217$	−1.55712	−	0.246623i	−0.105704	−	0.0167418i
$218$	0.344282	+	0.290405i	0.0233177	+	0.0196687i
$219$	−4.66927	−	6.42670i	−0.315520	−	0.434276i
$220$		0			0
$221$	9.25694	−	12.7411i	0.622689	−	0.857058i
$222$	1.83590	−	0.452710i	0.123217	−	0.0303839i
$223$	−16.5296	+	8.42226i	−1.10691	+	0.563996i	−0.909240	−	0.416273i	$-0.863336\pi$
$223$	−16.5296	+	8.42226i	−1.10691	+	0.563996i	−0.197666	+	0.980270i	$0.563336\pi$
$224$	4.37235	−	1.97056i	0.292140	−	0.131664i
$225$		0			0
$226$	−14.9015	+	1.26496i	−0.991233	+	0.0841438i
$227$	9.25018	−	4.71320i	0.613956	−	0.312826i	−0.119217	−	0.992868i	$-0.538038\pi$
$227$	9.25018	−	4.71320i	0.613956	−	0.312826i	0.733173	+	0.680042i	$0.238038\pi$
$228$	−5.07334	+	1.71764i	−0.335990	+	0.113754i
$229$	−5.69094	−	4.13471i	−0.376068	−	0.273229i	0.383655	−	0.923477i	$-0.374665\pi$
$229$	−5.69094	−	4.13471i	−0.376068	−	0.273229i	−0.759723	+	0.650247i	$0.774665\pi$
$230$		0			0
$231$	1.23939	+	1.70588i	0.0815461	+	0.112239i
$232$	−11.5097	+	19.5836i	−0.755651	+	1.28573i
$233$	0.704644	−	4.44895i	0.0461628	−	0.291460i	−0.953797	−	0.300452i	$-0.902862\pi$
$233$	0.704644	−	4.44895i	0.0461628	−	0.291460i	0.999960	+	0.00899219i	$0.00286234\pi$
$234$	−2.15886	−	5.12269i	−0.141129	−	0.334881i
$235$		0			0
$236$	0.882544	−	6.05271i	0.0574487	−	0.393998i
$237$	−15.7844	−	8.04258i	−1.02531	−	0.522422i
$238$	−1.22778	+	3.01643i	−0.0795854	+	0.195526i
$239$	−7.49866	+	23.0785i	−0.485048	+	1.49282i	0.346863	+	0.937916i	$0.387247\pi$
$239$	−7.49866	+	23.0785i	−0.485048	+	1.49282i	−0.831911	+	0.554909i	$0.812753\pi$
$240$		0			0
$241$	2.40482	+	7.40128i	0.154908	+	0.476758i	0.998152	−	0.0607736i	$-0.0193568\pi$
$241$	2.40482	+	7.40128i	0.154908	+	0.476758i	−0.843243	+	0.537532i	$0.819357\pi$
$242$	−11.7581	−	0.852714i	−0.755839	−	0.0548145i
$243$	4.87832	−	4.87832i	0.312944	−	0.312944i
$244$	−1.83457	+	1.88022i	−0.117446	+	0.120369i
$245$		0			0
$246$	8.52989	+	5.15529i	0.543846	+	0.328689i
$247$	−10.0644	+	1.59405i	−0.640386	+	0.101427i
$248$	3.93577	−	3.48897i	0.249922	−	0.221550i
$249$			21.2420i			1.34616i
$250$		0			0
$251$	17.0826			1.07824			0.539121	−	0.842228i	$-0.318756\pi$
$251$	17.0826			1.07824			0.539121	+	0.842228i	$0.318756\pi$
$252$	0.687073	+	0.921638i	0.0432815	+	0.0580578i
$253$	1.84320	+	11.6375i	0.115881	+	0.731644i
$254$	−14.1472	−	8.55025i	−0.887672	−	0.536491i
$255$		0			0
$256$	−4.19052	+	15.4415i	−0.261907	+	0.965093i
$257$	−9.52969	−	9.52969i	−0.594445	−	0.594445i	0.344384	−	0.938829i	$-0.388088\pi$
$257$	−9.52969	−	9.52969i	−0.594445	−	0.594445i	−0.938829	+	0.344384i	$0.888088\pi$
$258$	−0.712595	+	9.82599i	−0.0443642	+	0.611740i
$259$	−0.707486	+	0.229876i	−0.0439611	+	0.0142838i
$260$		0			0
$261$	−5.17833	−	1.68254i	−0.320530	−	0.104147i
$262$	6.46117	−	15.8739i	0.399172	−	0.980690i
$263$	−4.30589	+	8.45079i	−0.265513	+	0.521098i	−0.984817	−	0.173597i	$-0.944461\pi$
$263$	−4.30589	+	8.45079i	−0.265513	+	0.521098i	0.719304	+	0.694695i	$0.244461\pi$
$264$	−7.02192	−	0.422557i	−0.432169	−	0.0260066i
$265$		0			0
$266$	1.94180	−	0.818334i	0.119059	−	0.0501753i
$267$	7.07161	+	1.12003i	0.432776	+	0.0685449i
$268$	12.8165	−	18.1043i	0.782895	−	1.10589i
$269$	−12.5762	+	9.13718i	−0.766787	+	0.557104i	−0.900985	−	0.433851i	$-0.857154\pi$
$269$	−12.5762	+	9.13718i	−0.766787	+	0.557104i	0.134197	+	0.990955i	$0.457154\pi$
$270$		0			0
$271$	−10.0546	+	13.8390i	−0.610775	+	0.840660i	−0.996641	−	0.0818949i	$-0.973903\pi$
$271$	−10.0546	+	13.8390i	−0.610775	+	0.840660i	0.385866	+	0.922555i	$0.373903\pi$
$272$	−5.16908	−	9.55668i	−0.313422	−	0.579459i
$273$	−3.40057	−	6.67400i	−0.205812	−	0.403929i
$274$	−1.27175	−	14.9816i	−0.0768295	−	0.905069i
$275$		0			0
$276$	−3.70853	−	21.6862i	−0.223227	−	1.30536i
$277$	−7.97194	−	15.6458i	−0.478987	−	0.940066i	−0.996436	−	0.0843515i	$-0.973118\pi$
$277$	−7.97194	−	15.6458i	−0.478987	−	0.940066i	0.517449	−	0.855714i	$-0.326882\pi$
$278$	−15.8157	+	3.89996i	−0.948564	+	0.233904i
$279$	1.01993	+	0.741023i	0.0610616	+	0.0443639i
$280$		0			0
$281$	−21.3524	+	15.5134i	−1.27378	+	0.925454i	−0.999346	−	0.0361521i	$-0.988490\pi$
$281$	−21.3524	+	15.5134i	−1.27378	+	0.925454i	−0.274432	+	0.961606i	$0.588490\pi$
$282$	−9.04060	+	10.7179i	−0.538360	+	0.638239i
$283$	−2.52621	+	15.9498i	−0.150167	+	0.948119i	0.791401	+	0.611297i	$0.209352\pi$
$283$	−2.52621	+	15.9498i	−0.150167	+	0.948119i	−0.941568	+	0.336822i	$0.890648\pi$
$284$	0.674343	+	1.28421i	0.0400149	+	0.0762036i
$285$		0			0
$286$	−13.0322	−	3.04417i	−0.770608	−	0.180005i
$287$	−3.49365	−	1.78010i	−0.206224	−	0.105076i
$288$	−3.83076	−	0.183304i	−0.225730	−	0.0108013i
$289$	−9.15097	−	2.97333i	−0.538292	−	0.174902i
$290$		0			0
$291$	−0.749600	−	2.30703i	−0.0439424	−	0.135241i
$292$	−10.4254	+	0.128138i	−0.610101	+	0.00749871i
$293$	−9.63162	−	9.63162i	−0.562685	−	0.562685i	0.367384	−	0.930069i	$-0.380253\pi$
$293$	−9.63162	−	9.63162i	−0.562685	−	0.562685i	−0.930069	+	0.367384i	$0.880253\pi$
$294$	−8.85409	−	10.2387i	−0.516381	−	0.597135i
$295$		0			0
$296$	0.907305	−	2.30998i	0.0527360	−	0.134265i
$297$	−1.43099	−	9.03490i	−0.0830343	−	0.524258i
$298$	−12.6872	+	7.88238i	−0.734950	+	0.456614i
$299$		−	41.8558i		−	2.42058i
$300$		0			0
$301$		−	3.87579i		−	0.223397i
$302$	−4.12837	−	6.64488i	−0.237561	−	0.382370i
$303$	−2.56335	−	16.1843i	−0.147260	−	0.929765i
$304$	−2.00740	+	6.73727i	−0.115132	+	0.386409i
$305$		0			0
$306$	1.96991	−	1.70351i	0.112612	−	0.0973830i
$307$	−15.0324	−	15.0324i	−0.857947	−	0.857947i	0.133149	−	0.991096i	$-0.457491\pi$
$307$	−15.0324	−	15.0324i	−0.857947	−	0.857947i	−0.991096	+	0.133149i	$0.957491\pi$
$308$	2.76728	−	0.0340125i	0.157681	−	0.00193804i
$309$	6.67844	+	20.5541i	0.379923	+	1.16928i
$310$		0			0
$311$	9.39383	+	3.05224i	0.532675	+	0.173077i	0.562990	−	0.826464i	$-0.309651\pi$
$311$	9.39383	+	3.05224i	0.532675	+	0.173077i	−0.0303149	+	0.999540i	$0.509651\pi$
$312$	24.4024	+	5.38473i	1.38151	+	0.304850i
$313$	15.9926	+	8.14863i	0.903954	+	0.460588i	0.843221	−	0.537566i	$-0.180656\pi$
$313$	15.9926	+	8.14863i	0.903954	+	0.460588i	0.0607328	+	0.998154i	$0.480656\pi$
$314$	−1.29683	+	5.55176i	−0.0731844	+	0.313304i
$315$		0			0
$316$	−20.5856	+	10.8096i	−1.15803	+	0.608088i
$317$	4.30065	−	27.1533i	0.241549	−	1.52508i	−0.506969	−	0.861964i	$-0.669234\pi$
$317$	4.30065	−	27.1533i	0.241549	−	1.52508i	0.748518	−	0.663115i	$-0.230766\pi$
$318$	22.1996	+	18.7255i	1.24489	+	1.05007i
$319$	−10.6046	+	7.70471i	−0.593745	+	0.431381i
$320$		0			0
$321$	−19.3529	−	14.0607i	−1.08017	−	0.784792i
$322$	2.07225	+	8.40370i	0.115482	+	0.468320i
$323$	−2.16727	−	4.25350i	−0.120590	−	0.236671i
$324$	2.19348	+	12.8267i	0.121860	+	0.712597i
$325$		0			0
$326$	21.7300	−	1.84461i	1.20351	−	0.102164i
$327$	−0.220328	−	0.432418i	−0.0121842	−	0.0239128i
$328$	11.9912	−	5.22791i	0.662101	−	0.288663i
$329$	3.24236	−	4.46273i	0.178757	−	0.246038i
$330$		0			0
$331$	−20.4129	+	14.8308i	−1.12199	+	0.815175i	−0.984510	−	0.175329i	$-0.943901\pi$
$331$	−20.4129	+	14.8308i	−1.12199	+	0.815175i	−0.137483	+	0.990504i	$0.543901\pi$
$332$	22.7550	+	16.1090i	1.24884	+	0.884094i
$333$	0.587549	+	0.0930586i	0.0321975	+	0.00509958i
$334$	−12.1701	−	28.8781i	−0.665921	−	1.58014i
$335$		0			0
$336$	−5.16604	+	0.127010i	−0.281831	+	0.00692898i
$337$	−11.7526	+	23.0657i	−0.640204	+	1.25647i	0.311731	+	0.950170i	$0.399091\pi$
$337$	−11.7526	+	23.0657i	−0.640204	+	1.25647i	−0.951935	+	0.306300i	$0.900909\pi$
$338$	27.0048	+	10.9918i	1.46887	+	0.597877i
$339$	15.3255	+	4.97956i	0.832368	+	0.270453i
$340$		0			0
$341$	2.88652	−	0.937886i	0.156314	−	0.0507894i
$342$	−1.68065	−	0.121883i	−0.0908789	−	0.00659067i
$343$	7.96192	+	7.96192i	0.429903	+	0.429903i
$344$	9.98547	+	8.21493i	0.538380	+	0.442919i
$345$		0			0
$346$	−9.17743	+	15.1849i	−0.493382	+	0.816344i
$347$	2.00576	+	12.6639i	0.107675	+	0.679832i	0.981191	+	0.193038i	$0.0618340\pi$
$347$	2.00576	+	12.6639i	0.107675	+	0.679832i	−0.873516	+	0.486795i	$0.838166\pi$
$348$	19.6232	−	14.6289i	1.05191	−	0.784192i
$349$	−9.62259			−0.515086			−0.257543	−	0.966267i	$-0.582913\pi$
$349$	−9.62259			−0.515086			−0.257543	+	0.966267i	$0.582913\pi$
$350$		0			0
$351$			32.4951i			1.73446i
$352$	−5.77775	+	7.20162i	−0.307955	+	0.383848i
$353$	−26.3215	+	4.16891i	−1.40095	+	0.221889i	−0.810761	−	0.585377i	$-0.800947\pi$
$353$	−26.3215	+	4.16891i	−1.40095	+	0.221889i	−0.590188	+	0.807266i	$0.700947\pi$
$354$	−3.40908	+	5.64063i	−0.181191	+	0.299796i
$355$		0			0
$356$	6.56259	−	6.72592i	0.347817	−	0.356473i
$357$	2.48134	−	2.48134i	0.131326	−	0.131326i
$358$	2.09031	−	28.8233i	0.110476	−	1.52336i
$359$	11.0131	+	33.8947i	0.581247	+	1.78889i	0.613845	+	0.789426i	$0.289622\pi$
$359$	11.0131	+	33.8947i	0.581247	+	1.78889i	−0.0325983	+	0.999469i	$0.510378\pi$
$360$		0			0
$361$	4.91684	−	15.1325i	0.258781	−	0.796446i
$362$	29.2030	+	11.8866i	1.53488	+	0.624744i
$363$	11.3182	+	5.76690i	0.594050	+	0.302684i
$364$	−9.72821	−	1.41847i	−0.509897	−	0.0743478i
$365$		0			0
$366$	2.60839	−	1.09926i	0.136343	−	0.0574590i
$367$	3.99779	−	25.2411i	0.208683	−	1.31757i	−0.631545	−	0.775339i	$-0.717579\pi$
$367$	3.99779	−	25.2411i	0.208683	−	1.31757i	0.840228	−	0.542234i	$-0.182421\pi$
$368$	−26.0432	−	12.4732i	−1.35760	−	0.650208i
$369$	1.84302	+	2.53670i	0.0959437	+	0.132055i
$370$		0			0
$371$	−9.24350	−	6.71580i	−0.479899	−	0.348667i
$372$	−5.36792	+	1.81738i	−0.278314	+	0.0942267i
$373$	−2.34473	+	1.19470i	−0.121406	+	0.0618592i	−0.513638	−	0.858007i	$-0.671703\pi$
$373$	−2.34473	+	1.19470i	−0.121406	+	0.0618592i	0.392233	+	0.919866i	$0.371703\pi$
$374$	−0.530318	−	6.24726i	−0.0274221	−	0.323038i
$375$		0			0
$376$	4.62529	+	17.8125i	0.238531	+	0.918607i
$377$	41.4891	−	21.1397i	2.13680	−	1.08875i
$378$	−1.60881	−	6.52430i	−0.0827484	−	0.335574i
$379$	−13.0709	+	17.9905i	−0.671405	+	0.924110i	−0.999791	−	0.0204337i	$-0.993495\pi$
$379$	−13.0709	+	17.9905i	−0.671405	+	0.924110i	0.328386	+	0.944544i	$0.393495\pi$
$380$		0			0
$381$	10.4693	+	14.4097i	0.536358	+	0.738234i
$382$	10.0707	−	11.9391i	0.515262	−	0.610855i
$383$	−2.57923	−	0.408510i	−0.131793	−	0.0208739i	0.0901896	−	0.995925i	$-0.471253\pi$
$383$	−2.57923	−	0.408510i	−0.131793	−	0.0208739i	−0.221982	+	0.975051i	$0.571253\pi$
$384$	10.6224	−	13.5788i	0.542074	−	0.692941i
$385$		0			0
$386$	−1.06073	+	4.54100i	−0.0539896	+	0.231131i
$387$	−1.40708	+	2.76156i	−0.0715260	+	0.140378i
$388$	−3.03982	−	0.946554i	−0.154323	−	0.0480540i
$389$	2.82279	−	8.68765i	0.143121	−	0.440481i	−0.853644	−	0.520858i	$-0.825612\pi$
$389$	2.82279	−	8.68765i	0.143121	−	0.440481i	0.996765	+	0.0803764i	$0.0256122\pi$
$390$		0			0
$391$	18.6491	−	6.05945i	0.943125	−	0.306440i
$392$	−17.6825	+	1.72016i	−0.893103	+	0.0868814i
$393$	−13.0580	+	13.0580i	−0.658687	+	0.658687i
$394$	14.6274	−	12.6492i	0.736916	−	0.637259i
$395$		0			0
$396$	−1.98407	−	0.980410i	−0.0997034	−	0.0492674i
$397$	22.0201	−	3.48764i	1.10516	−	0.175040i	0.422917	−	0.906169i	$-0.361006\pi$
$397$	22.0201	−	3.48764i	1.10516	−	0.175040i	0.682239	+	0.731129i	$0.261006\pi$
$398$	13.1958	−	8.19838i	0.661447	−	0.410948i
$399$	−2.27051			−0.113667
$400$		0			0
$401$	24.5825			1.22759			0.613795	−	0.789465i	$-0.289642\pi$
$401$	24.5825			1.22759			0.613795	+	0.789465i	$0.289642\pi$
$402$	−20.3017	+	12.6132i	−1.01256	+	0.629088i
$403$	−10.6488	+	1.68661i	−0.530457	+	0.0840161i
$404$	−19.2810	−	9.52751i	−0.959266	−	0.474012i
$405$		0			0
$406$	−7.28346	+	6.29848i	−0.361472	+	0.312588i
$407$	1.01266	−	1.01266i	0.0501957	−	0.0501957i
$408$	1.13353	+	11.6522i	0.0561180	+	0.576868i
$409$	12.4251	−	4.03716i	0.614381	−	0.199624i	0.0147370	−	0.999891i	$-0.495309\pi$
$409$	12.4251	−	4.03716i	0.614381	−	0.199624i	0.599644	+	0.800267i	$0.295309\pi$
$410$		0			0
$411$	−5.00631	+	15.4078i	−0.246943	+	0.760013i
$412$	27.0827	+	8.43316i	1.33427	+	0.415472i
$413$	1.17714	−	2.31028i	0.0579235	−	0.113681i
$414$	1.57440	−	6.74006i	0.0773777	−	0.331256i
$415$		0			0
$416$	24.2739	−	22.0569i	1.19012	−	1.08143i
$417$	17.3359	+	2.74574i	0.848942	+	0.134459i
$418$	−2.61559	+	3.10085i	−0.127933	+	0.151668i
$419$	13.5174	+	18.6051i	0.660367	+	0.908918i	0.999494	−	0.0318232i	$-0.0101314\pi$
$419$	13.5174	+	18.6051i	0.660367	+	0.908918i	−0.339126	+	0.940741i	$0.610131\pi$
$420$		0			0
$421$	−1.27992	+	1.76165i	−0.0623792	+	0.0858577i	−0.839067	−	0.544028i	$-0.816898\pi$
$421$	−1.27992	+	1.76165i	−0.0623792	+	0.0858577i	0.776688	+	0.629886i	$0.216898\pi$
$422$	6.14186	+	24.9074i	0.298981	+	1.21247i
$423$	−3.93039	+	2.00263i	−0.191102	+	0.0973713i
$424$	36.8944	−	9.58021i	1.79175	−	0.465256i
$425$		0			0
$426$	−0.132197	−	1.55731i	−0.00640496	−	0.0754519i
$427$	−0.992196	+	0.505549i	−0.0480158	+	0.0244652i
$428$	−29.7385	+	10.0684i	−1.43747	+	0.486673i
$429$	11.6662	+	8.47600i	0.563250	+	0.409225i
$430$		0			0
$431$	3.07549	+	4.23304i	0.148141	+	0.203899i	0.876638	−	0.481150i	$-0.159781\pi$
$431$	3.07549	+	4.23304i	0.148141	+	0.203899i	−0.728497	+	0.685049i	$0.759781\pi$
$432$	20.2189	+	9.68366i	0.972784	+	0.465905i
$433$	2.60589	−	16.4529i	0.125231	−	0.790677i	−0.842501	−	0.538695i	$-0.818918\pi$
$433$	2.60589	−	16.4529i	0.125231	−	0.790677i	0.967732	−	0.251982i	$-0.0810824\pi$
$434$	2.05455	−	0.865851i	0.0986214	−	0.0415622i
$435$		0			0
$436$	−0.630304	−	0.0919044i	−0.0301861	−	0.00440142i
$437$	−11.3046	−	5.75996i	−0.540770	−	0.275536i
$438$	10.4053	+	4.23531i	0.497187	+	0.202371i
$439$	4.46164	−	13.7315i	0.212943	−	0.655370i	−0.786351	−	0.617780i	$-0.788032\pi$
$439$	4.46164	−	13.7315i	0.212943	−	0.655370i	0.999293	−	0.0375894i	$-0.0119679\pi$
$440$		0			0
$441$	−1.31593	−	4.05003i	−0.0626635	−	0.192858i
$442$	−1.61098	+	22.2139i	−0.0766266	+	1.05661i
$443$	17.2334	−	17.2334i	0.818783	−	0.818783i	−0.167149	−	0.985932i	$-0.553456\pi$
$443$	17.2334	−	17.2334i	0.818783	−	0.818783i	0.985932	+	0.167149i	$0.0534560\pi$
$444$	−1.86751	+	1.91399i	−0.0886281	+	0.0908338i
$445$		0			0
$446$	13.5705	−	22.4537i	0.642583	−	1.06321i
$447$	15.8959	−	2.51767i	0.751852	−	0.119082i
$448$	−3.78163	+	5.63032i	−0.178665	+	0.266008i
$449$			29.7838i			1.40558i	0.711396	+	0.702792i	$0.248063\pi$
$449$			29.7838i			1.40558i	−0.711396	+	0.702792i	$0.751937\pi$
$450$		0			0
$451$	7.54859			0.355449
$452$	16.9564	−	12.6408i	0.797562	−	0.594575i
$453$	1.31862	+	8.32544i	0.0619542	+	0.391164i
$454$	−7.59424	+	12.5653i	−0.356415	+	0.589721i
$455$		0			0
$456$	4.81244	−	5.84966i	0.225363	−	0.273935i
$457$	−2.99043	−	2.99043i	−0.139887	−	0.139887i	0.633696	−	0.773582i	$-0.281537\pi$
$457$	−2.99043	−	2.99043i	−0.139887	−	0.139887i	−0.773582	+	0.633696i	$0.781537\pi$
$458$	9.92207	+	0.719562i	0.463628	+	0.0336229i
$459$	−14.4784	+	4.70432i	−0.675794	+	0.219579i
$460$		0			0
$461$	25.4014	+	8.25343i	1.18306	+	0.384400i	0.833504	−	0.552514i	$-0.186331\pi$
$461$	25.4014	+	8.25343i	1.18306	+	0.384400i	0.349559	+	0.936914i	$0.386331\pi$
$462$	−2.76196	−	1.12421i	−0.128498	−	0.0523028i
$463$	−7.35271	+	14.4305i	−0.341710	+	0.670643i	−0.996356	−	0.0852925i	$-0.972818\pi$
$463$	−7.35271	+	14.4305i	−0.341710	+	0.670643i	0.654646	+	0.755935i	$0.272818\pi$
$464$	−0.789562	−	32.1148i	−0.0366545	−	1.49089i
$465$		0			0
$466$	2.47389	+	5.87020i	0.114601	+	0.271932i
$467$	9.61404	+	1.52271i	0.444885	+	0.0704628i	0.374858	−	0.927082i	$-0.377692\pi$
$467$	9.61404	+	1.52271i	0.444885	+	0.0704628i	0.0700268	+	0.997545i	$0.477692\pi$
$468$	6.41651	+	4.54244i	0.296603	+	0.209974i
$469$	7.60707	−	5.52686i	0.351262	−	0.255207i
$470$		0			0
$471$	3.61082	−	4.96986i	0.166378	−	0.228999i
$472$	3.45711	+	7.92949i	0.159126	+	0.364985i
$473$	3.38746	+	6.64827i	0.155756	+	0.305688i
$474$	24.9634	−	2.11910i	1.14661	−	0.0973333i
$475$		0			0
$476$	−0.776345	−	4.53981i	−0.0355837	−	0.208082i
$477$	4.14799	+	8.14089i	0.189923	+	0.372746i
$478$	−8.21619	−	33.3195i	−0.375800	−	1.52400i
$479$	9.26622	+	6.73230i	0.423384	+	0.307607i	0.778998	−	0.627026i	$-0.215728\pi$
$479$	9.26622	+	6.73230i	0.423384	+	0.307607i	−0.355614	+	0.934633i	$0.615728\pi$
$480$		0			0
$481$	−4.11577	+	2.99028i	−0.187663	+	0.136345i
$482$	−8.41252	−	7.09603i	−0.383180	−	0.323215i
$483$	1.45895	−	9.21145i	0.0663845	−	0.419135i
$484$	14.7608	−	7.75099i	0.670947	−	0.352318i
$485$		0			0
$486$	−2.21930	+	9.50088i	−0.100669	+	0.430969i
$487$	−18.5583	−	9.45591i	−0.840955	−	0.428488i	−0.0202192	−	0.999796i	$-0.506436\pi$
$487$	−18.5583	−	9.45591i	−0.840955	−	0.428488i	−0.820736	+	0.571307i	$0.806436\pi$
$488$	0.800526	−	3.62780i	0.0362381	−	0.164223i
$489$	−22.3483	−	7.26140i	−1.01062	−	0.328372i
$490$		0			0
$491$	6.15155	+	18.9325i	0.277616	+	0.854413i	0.988515	+	0.151120i	$0.0482879\pi$
$491$	6.15155	+	18.9325i	0.277616	+	0.854413i	−0.710900	+	0.703293i	$0.751712\pi$
$492$	−14.0940	+	0.173229i	−0.635409	+	0.00780977i
$493$	15.4253	+	15.4253i	0.694721	+	0.694721i
$494$	10.9003	−	9.42616i	0.490426	−	0.424103i
$495$		0			0
$496$	−2.12396	+	7.12848i	−0.0953685	+	0.320078i
$497$	0.0961860	+	0.607295i	0.00431453	+	0.0272409i
$498$	−15.8534	−	25.5170i	−0.710406	−	1.14344i
$499$		−	25.0399i		−	1.12094i	−0.828175	−	0.560469i	$-0.810621\pi$
$499$		−	25.0399i		−	1.12094i	0.828175	−	0.560469i	$-0.189379\pi$
$500$		0			0
$501$			33.7666i			1.50858i
$502$	−20.5205	+	12.7491i	−0.915873	+	0.569019i
$503$	0.394723	+	2.49218i	0.0175998	+	0.111121i	0.994924	−	0.100626i	$-0.0320846\pi$
$503$	0.394723	+	2.49218i	0.0175998	+	0.111121i	−0.977324	+	0.211747i	$0.932085\pi$
$504$	−1.51319	−	0.594343i	−0.0674026	−	0.0264742i
$505$		0			0
$506$	−10.8995	−	12.6040i	−0.484540	−	0.560315i
$507$	−22.2144	−	22.2144i	−0.986577	−	0.986577i
$508$	23.3755	−	0.287307i	1.03712	−	0.0127472i
$509$	−1.71006	−	5.26302i	−0.0757970	−	0.233279i	0.905978	−	0.423324i	$-0.139137\pi$
$509$	−1.71006	−	5.26302i	−0.0757970	−	0.233279i	−0.981775	+	0.190045i	$0.939137\pi$
$510$		0			0
$511$	−4.20336	−	1.36575i	−0.185946	−	0.0604174i
$512$	−6.49043	−	21.6766i	−0.286839	−	0.957979i
$513$	8.77640	+	4.47180i	0.387488	+	0.197435i
$514$	18.5598	+	4.33535i	0.818636	+	0.191224i
$515$		0			0
$516$	−6.47733	−	12.3353i	−0.285149	−	0.543032i
$517$	−1.66128	+	10.4889i	−0.0730628	+	0.461301i
$518$	0.678308	−	0.804151i	0.0298031	−	0.0353324i
$519$	15.4667	−	11.2372i	0.678914	−	0.493260i
$520$		0			0
$521$	−2.44987	−	1.77994i	−0.107331	−	0.0779804i	0.532825	−	0.846225i	$-0.321130\pi$
$521$	−2.44987	−	1.77994i	−0.107331	−	0.0779804i	−0.640156	+	0.768245i	$0.721130\pi$
$522$	7.47619	−	1.84354i	0.327224	−	0.0806894i
$523$	3.95831	+	7.76863i	0.173085	+	0.339698i	0.961210	−	0.275816i	$-0.0889482\pi$
$523$	3.95831	+	7.76863i	0.173085	+	0.339698i	−0.788125	+	0.615515i	$0.788948\pi$
$524$	4.08549	+	23.8906i	0.178475	+	1.04367i
$525$		0			0
$526$	−1.13454	−	13.3651i	−0.0494682	−	0.582746i
$527$	−2.29311	−	4.50049i	−0.0998895	−	0.196044i
$528$	8.75046	−	4.73301i	0.380815	−	0.205978i
$529$	17.1130	−	23.5540i	0.744043	−	1.02409i
$530$		0			0
$531$	−1.67746	+	1.21875i	−0.0727957	+	0.0528891i
$532$	−1.72185	+	2.43223i	−0.0746515	+	0.105450i
$533$	−26.4850	−	4.19482i	−1.14719	−	0.181698i
$534$	−9.33069	+	3.93225i	−0.403779	+	0.170165i
$535$		0			0
$536$	−1.88432	+	31.3130i	−0.0813901	+	1.35252i
$537$	−14.1368	+	27.7449i	−0.610046	+	1.19728i
$538$	8.28798	−	20.3620i	0.357320	−	0.877867i
$539$	−9.75018	−	3.16803i	−0.419970	−	0.136457i
$540$		0			0
$541$	−17.7647	+	5.77210i	−0.763764	+	0.248162i	−0.664894	−	0.746938i	$-0.731523\pi$
$541$	−17.7647	+	5.77210i	−0.763764	+	0.248162i	−0.0988709	+	0.995100i	$0.531523\pi$
$542$	1.74980	−	24.1281i	0.0751605	−	1.03639i
$543$	−24.0227	−	24.0227i	−1.03091	−	1.03091i
$544$	13.3417	+	7.62219i	0.572022	+	0.326799i
$545$		0			0
$546$	9.06589	+	5.47924i	0.387984	+	0.234490i
$547$	1.04697	+	6.61028i	0.0447650	+	0.282635i	0.999909	−	0.0135073i	$-0.00429965\pi$
$547$	1.04697	+	6.61028i	0.0447650	+	0.282635i	−0.955144	+	0.296143i	$0.904300\pi$
$548$	12.7087	+	17.0475i	0.542890	+	0.728232i
$549$	0.890490			0.0380052
$550$		0			0
$551$		−	14.1146i		−	0.601304i
$552$	20.6398	+	23.2829i	0.878486	+	0.990985i
$553$	−9.73483	+	1.54185i	−0.413967	+	0.0655660i
$554$	21.2531	+	12.8449i	0.902958	+	0.545729i
$555$		0			0
$556$	16.0880	−	16.4884i	0.682285	−	0.699265i
$557$	8.28968	−	8.28968i	0.351245	−	0.351245i	−0.509328	−	0.860573i	$-0.670106\pi$
$557$	8.28968	−	8.28968i	0.351245	−	0.351245i	0.860573	+	0.509328i	$0.170106\pi$
$558$	−1.77823	−	0.128960i	−0.0752786	−	0.00545931i
$559$	−8.19077	−	25.2086i	−0.346433	−	1.06621i
$560$		0			0
$561$	−2.08762	+	6.42502i	−0.0881392	+	0.271265i
$562$	14.0716	−	34.5713i	0.593576	−	1.45830i
$563$	−9.63212	−	4.90781i	−0.405946	−	0.206840i	0.239081	−	0.971000i	$-0.423154\pi$
$563$	−9.63212	−	4.90781i	−0.405946	−	0.206840i	−0.645027	+	0.764160i	$0.723154\pi$
$564$	2.86108	−	19.6220i	0.120473	−	0.826237i
$565$		0			0
$566$	−8.86908	−	21.0451i	−0.372795	−	0.884593i
$567$	−0.862924	+	5.44829i	−0.0362394	+	0.228807i
$568$	−1.76848	−	1.03938i	−0.0742039	−	0.0436114i
$569$	13.6521	+	18.7905i	0.572326	+	0.787739i	0.992828	−	0.119552i	$-0.0381459\pi$
$569$	13.6521	+	18.7905i	0.572326	+	0.787739i	−0.420502	+	0.907292i	$0.638146\pi$
$570$		0			0
$571$	−1.84713	−	1.34202i	−0.0772998	−	0.0561616i	0.548464	−	0.836174i	$-0.315213\pi$
$571$	−1.84713	−	1.34202i	−0.0772998	−	0.0561616i	−0.625764	+	0.780012i	$0.715213\pi$
$572$	17.9268	−	6.06936i	0.749559	−	0.253773i
$573$	−14.9955	+	7.64057i	−0.626444	+	0.319189i
$574$	5.52528	−	0.469030i	0.230621	−	0.0195769i
$575$		0			0
$576$	4.73851	−	2.63878i	0.197438	−	0.109949i
$577$	10.7554	−	5.48015i	0.447753	−	0.228142i	−0.215549	−	0.976493i	$-0.569154\pi$
$577$	10.7554	−	5.48015i	0.447753	−	0.228142i	0.663303	+	0.748351i	$0.269154\pi$
$578$	13.2117	−	3.25784i	0.549533	−	0.135508i
$579$	2.95343	−	4.06504i	0.122740	−	0.168937i
$580$		0			0
$581$	6.94664	+	9.56123i	0.288195	+	0.396667i
$582$	2.62224	+	2.21189i	0.108696	+	0.0916856i
$583$	21.7253	+	3.44095i	0.899770	+	0.142510i
$584$	12.4279	−	7.93462i	0.514270	−	0.328337i
$585$		0			0
$586$	18.7583	+	4.38172i	0.774897	+	0.181007i
$587$	−13.2680	+	26.0399i	−0.547628	+	1.07478i	0.436893	+	0.899514i	$0.356079\pi$
$587$	−13.2680	+	26.0399i	−0.547628	+	1.07478i	−0.984521	+	0.175267i	$0.943921\pi$
$588$	18.2774	+	5.69130i	0.753746	+	0.234705i
$589$	−1.00991	+	3.10818i	−0.0416126	+	0.128070i
$590$		0			0
$591$	−19.8171	+	6.43897i	−0.815167	+	0.264864i
$592$	0.634083	+	3.45201i	0.0260606	+	0.141877i
$593$	10.4158	−	10.4158i	0.427727	−	0.427727i	−0.460126	−	0.887853i	$-0.652196\pi$
$593$	10.4158	−	10.4158i	0.427727	−	0.427727i	0.887853	+	0.460126i	$0.152196\pi$
$594$	8.46191	+	9.78522i	0.347196	+	0.401492i
$595$		0			0
$596$	9.35775	−	18.9374i	0.383308	−	0.775708i
$597$	−16.5332	+	2.61860i	−0.676659	+	0.107172i
$598$	31.2378	+	50.2793i	1.27741	+	2.05607i
$599$	25.5565			1.04421			0.522105	−	0.852881i	$-0.325147\pi$
$599$	25.5565			1.04421			0.522105	+	0.852881i	$0.325147\pi$
$600$		0			0
$601$	−27.3859			−1.11709			−0.558547	−	0.829473i	$-0.688641\pi$
$601$	−27.3859			−1.11709			−0.558547	+	0.829473i	$0.688641\pi$
$602$	2.89258	+	4.65580i	0.117893	+	0.189756i
$603$	−7.42663	+	1.17626i	−0.302436	+	0.0479011i
$604$	9.91842	+	4.90109i	0.403575	+	0.199422i
$605$		0			0
$606$	15.1579	+	17.5284i	0.615748	+	0.712041i
$607$	33.4675	−	33.4675i	1.35841	−	1.35841i	0.482522	−	0.875884i	$-0.339721\pi$
$607$	33.4675	−	33.4675i	1.35841	−	1.35841i	0.875884	−	0.482522i	$-0.160279\pi$
$608$	−2.61678	−	9.59133i	−0.106124	−	0.388980i
$609$	9.86760	−	3.20618i	0.399856	−	0.129921i
$610$		0			0
$611$	11.6575	−	35.8782i	0.471613	−	1.45148i
$612$	−1.09499	+	3.51652i	−0.0442625	+	0.142147i
$613$	−10.1959	+	20.0105i	−0.411808	+	0.808218i	−1.00000		0.000502907i	$-0.999840\pi$
$613$	−10.1959	+	20.0105i	−0.411808	+	0.808218i	0.588192	+	0.808721i	$0.299840\pi$
$614$	29.2768	+	6.83873i	1.18151	+	0.275989i
$615$		0			0
$616$	−3.29882	+	2.10614i	−0.132913	+	0.0848587i
$617$	−38.9539	−	6.16968i	−1.56822	−	0.248382i	−0.688989	−	0.724772i	$-0.741945\pi$
$617$	−38.9539	−	6.16968i	−1.56822	−	0.248382i	−0.879234	+	0.476390i	$0.841945\pi$
$618$	−23.3624	−	19.7064i	−0.939775	−	0.792708i
$619$	10.9094	+	15.0155i	0.438487	+	0.603525i	0.969875	−	0.243603i	$-0.0783294\pi$
$619$	10.9094	+	15.0155i	0.438487	+	0.603525i	−0.531388	+	0.847128i	$0.678329\pi$
$620$		0			0
$621$	−23.7815	+	32.7324i	−0.954319	+	1.31351i
$622$	−13.5623	+	3.34430i	−0.543799	+	0.134094i
$623$	3.54927	−	1.80845i	0.142199	−	0.0724539i
$624$	−33.3321	+	11.7436i	−1.33435	+	0.470119i
$625$		0			0
$626$	−25.2926	+	2.14704i	−1.01090	+	0.0858129i
$627$	3.89467	−	1.98443i	0.155538	−	0.0792506i
$628$	−2.58557	−	7.63692i	−0.103176	−	0.304746i
$629$	−1.92818	−	1.40090i	−0.0768815	−	0.0558577i
$630$		0			0
$631$	4.93488	+	6.79228i	0.196454	+	0.270396i	0.895867	−	0.444321i	$-0.146555\pi$
$631$	4.93488	+	6.79228i	0.196454	+	0.270396i	−0.699413	+	0.714718i	$0.746555\pi$
$632$	16.6611	−	28.3485i	0.662742	−	1.12764i
$633$	4.32413	−	27.3015i	0.171869	−	1.08514i
$634$	15.0989	+	35.8276i	0.599653	+	1.42289i
$635$		0			0
$636$	−40.6425	−	5.92607i	−1.61158	−	0.234984i
$637$	32.4491	+	16.5336i	1.28568	+	0.655086i
$638$	6.98864	−	17.1698i	0.276683	−	0.679757i
$639$	0.151941	−	0.467625i	0.00601068	−	0.0184990i
$640$		0			0
$641$	1.94986	+	6.00105i	0.0770148	+	0.237027i	0.982151	−	0.188095i	$-0.0602312\pi$
$641$	1.94986	+	6.00105i	0.0770148	+	0.237027i	−0.905136	+	0.425122i	$0.860231\pi$
$642$	33.7415	+	2.44698i	1.33167	+	0.0965746i
$643$	−9.08027	+	9.08027i	−0.358091	+	0.358091i	−0.863109	−	0.505018i	$-0.831486\pi$
$643$	−9.08027	+	9.08027i	−0.358091	+	0.358091i	0.505018	+	0.863109i	$0.331486\pi$
$644$	−8.76115	−	8.54840i	−0.345238	−	0.336854i
$645$		0			0
$646$	5.77791	+	3.49205i	0.227329	+	0.137393i
$647$	−31.5384	+	4.99520i	−1.23990	+	0.196381i	−0.741731	−	0.670697i	$-0.765995\pi$
$647$	−31.5384	+	4.99520i	−1.23990	+	0.196381i	−0.498172	+	0.867078i	$0.665995\pi$
$648$	−12.2078	−	13.7711i	−0.479567	−	0.540980i
$649$			4.99172i			0.195942i
$650$		0			0
$651$	−2.40234			−0.0941553
$652$	−24.7265	+	18.4334i	−0.968364	+	0.721906i
$653$	−3.93441	−	24.8409i	−0.153965	−	0.972099i	−0.936799	−	0.349868i	$-0.886227\pi$
$653$	−3.93441	−	24.8409i	−0.153965	−	0.972099i	0.782834	−	0.622231i	$-0.213773\pi$
$654$	0.587392	+	0.355007i	0.0229688	+	0.0138819i
$655$		0			0
$656$	−10.5027	+	15.2293i	−0.410061	+	0.594604i
$657$	2.49912	+	2.49912i	0.0975000	+	0.0975000i
$658$	−0.564267	+	7.78070i	−0.0219974	+	0.303323i
$659$	−19.1414	+	6.21943i	−0.745645	+	0.242275i	−0.657106	−	0.753798i	$-0.728220\pi$
$659$	−19.1414	+	6.21943i	−0.745645	+	0.242275i	−0.0885388	+	0.996073i	$0.528220\pi$
$660$		0			0
$661$	−12.2360	−	3.97571i	−0.475924	−	0.154637i	0.0612256	−	0.998124i	$-0.480499\pi$
$661$	−12.2360	−	3.97571i	−0.475924	−	0.154637i	−0.537150	+	0.843487i	$0.680499\pi$
$662$	13.4524	−	33.0501i	0.522844	−	1.28453i
$663$	10.8951	−	21.3828i	0.423129	−	0.830438i
$664$	−39.3569	−	2.36838i	−1.52735	−	0.0919108i
$665$		0			0
$666$	−0.775245	+	0.326713i	−0.0300401	+	0.0126599i
$667$	57.2631	+	9.06959i	2.21724	+	0.351176i
$668$	36.1717	+	25.6070i	1.39953	+	0.990766i
$669$	−22.8704	+	16.6163i	−0.884221	+	0.642424i
$670$		0			0
$671$	1.26009	−	1.73437i	0.0486453	−	0.0669545i
$672$	6.11093	−	4.00809i	0.235734	−	0.154616i
$673$	8.13657	+	15.9689i	0.313642	+	0.615557i	0.992982	−	0.118267i	$-0.0377339\pi$
$673$	8.13657	+	15.9689i	0.313642	+	0.615557i	−0.679340	+	0.733824i	$0.737734\pi$
$674$	−3.09662	−	36.4789i	−0.119278	−	1.40512i
$675$		0			0
$676$	−40.6430	+	6.95030i	−1.56319	+	0.267319i
$677$	5.15738	+	10.1219i	0.198214	+	0.389017i	0.968624	−	0.248532i	$-0.0799482\pi$
$677$	5.15738	+	10.1219i	0.198214	+	0.389017i	−0.770409	+	0.637549i	$0.779948\pi$
$678$	−22.1262	+	5.45604i	−0.849750	+	0.209538i
$679$	−1.09186	−	0.793280i	−0.0419016	−	0.0304433i
$680$		0			0
$681$	12.7986	−	9.29870i	0.490442	−	0.356327i
$682$	−2.76747	+	3.28090i	−0.105972	+	0.125632i
$683$	0.137671	−	0.869222i	0.00526784	−	0.0332598i	−0.984914	−	0.173042i	$-0.944640\pi$
$683$	0.137671	−	0.869222i	0.00526784	−	0.0332598i	0.990182	+	0.139782i	$0.0446403\pi$
$684$	2.10984	−	1.10789i	0.0806719	−	0.0423612i
$685$		0			0
$686$	−15.5064	−	3.62213i	−0.592038	−	0.138293i
$687$	−9.55084	−	4.86640i	−0.364387	−	0.185665i
$688$	−18.1260	−	2.41583i	−0.691048	−	0.0921028i
$689$	−74.3134	−	24.1459i	−2.83111	−	0.919885i
$690$		0			0
$691$	4.21965	+	12.9867i	0.160523	+	0.494039i	0.998679	−	0.0513922i	$-0.0163659\pi$
$691$	4.21965	+	12.9867i	0.160523	+	0.494039i	−0.838155	+	0.545431i	$0.816366\pi$
$692$	−0.308382	−	25.0902i	−0.0117229	−	0.953785i
$693$	−0.663358	−	0.663358i	−0.0251989	−	0.0251989i
$694$	−11.8607	−	13.7156i	−0.450227	−	0.520636i
$695$		0			0
$696$	−12.6546	+	32.2182i	−0.479670	+	1.22123i
$697$	−1.96521	−	12.4078i	−0.0744376	−	0.469981i
$698$	11.5592	−	7.18154i	0.437521	−	0.271825i
$699$		−	6.86391i		−	0.259617i
$700$		0			0
$701$			30.3530i			1.14642i	0.819410	+	0.573208i	$0.194301\pi$
$701$			30.3530i			1.14642i	−0.819410	+	0.573208i	$0.805699\pi$
$702$	−24.2518	−	39.0348i	−0.915325	−	1.47327i
$703$	0.241237	+	1.52311i	0.00909841	+	0.0574451i
$704$	1.56582	−	12.9630i	0.0590139	−	0.488562i
$705$		0			0
$706$	28.5074	−	24.6522i	1.07289	−	0.927796i
$707$	−6.44644	−	6.44644i	−0.242443	−	0.242443i
$708$	−0.114553	−	9.32009i	−0.00430515	−	0.350270i
$709$	−8.73436	−	26.8816i	−0.328026	−	1.00956i	−0.970056	−	0.242880i	$-0.921908\pi$
$709$	−8.73436	−	26.8816i	−0.328026	−	1.00956i	0.642031	−	0.766679i	$-0.278092\pi$
$710$		0			0
$711$	7.49596	+	2.43558i	0.281120	+	0.0913415i
$712$	−2.86363	+	12.9773i	−0.107319	+	0.486346i
$713$	−11.9610	−	6.09441i	−0.447941	−	0.228237i
$714$	−1.12884	+	4.83259i	−0.0422458	+	0.180855i
$715$		0			0
$716$	19.0005	+	36.1841i	0.710081	+	1.35226i
$717$	−5.78453	+	36.5221i	−0.216027	+	1.36394i
$718$	−38.5258	−	32.4968i	−1.43777	−	1.21277i
$719$	−37.2617	+	27.0722i	−1.38963	+	1.00962i	−0.393719	+	0.919231i	$0.628812\pi$
$719$	−37.2617	+	27.0722i	−1.38963	+	1.00962i	−0.995906	+	0.0903910i	$0.971188\pi$
$720$		0			0
$721$	9.72770	+	7.06759i	0.362279	+	0.263211i
$722$	5.38731	+	21.8474i	0.200495	+	0.813077i
$723$	5.38371	+	10.5661i	0.200222	+	0.392958i
$724$	−43.9514	+	7.51605i	−1.63344	+	0.279332i
$725$		0			0
$726$	−17.8999	+	1.51949i	−0.664329	+	0.0563936i
$727$	−13.1018	−	25.7138i	−0.485920	−	0.953672i	−0.995635	−	0.0933286i	$-0.970249\pi$
$727$	−13.1018	−	25.7138i	−0.485920	−	0.953672i	0.509715	−	0.860343i	$-0.329751\pi$
$728$	12.7447	−	5.55642i	0.472348	−	0.205935i
$729$	17.6525	−	24.2966i	0.653797	−	0.899874i
$730$		0			0
$731$	10.0461	−	7.29890i	0.371567	−	0.269959i
$732$	−2.31293	+	3.26718i	−0.0854884	+	0.120758i
$733$	49.0422	+	7.76752i	1.81142	+	0.286900i	0.968108	−	0.250532i	$-0.0806057\pi$
$733$	49.0422	+	7.76752i	1.81142	+	0.286900i	0.843307	+	0.537432i	$0.180606\pi$
$734$	14.0356	+	33.3045i	0.518062	+	1.22929i
$735$		0			0
$736$	40.5935	−	4.45321i	1.49629	−	0.164147i
$737$	−8.21813	+	16.1290i	−0.302719	+	0.594119i
$738$	−4.10712	−	1.67173i	−0.151185	−	0.0615372i
$739$	26.6502	+	8.65917i	0.980343	+	0.318533i	0.754984	−	0.655743i	$-0.227645\pi$
$739$	26.6502	+	8.65917i	0.980343	+	0.318533i	0.225359	+	0.974276i	$0.427645\pi$
$740$		0			0
$741$	−14.7676	+	4.79829i	−0.542502	+	0.176270i
$742$	16.1159	+	1.16875i	0.591634	+	0.0429061i
$743$	17.1558	+	17.1558i	0.629384	+	0.629384i	0.947913	−	0.318529i	$-0.103189\pi$
$743$	17.1558	+	17.1558i	0.629384	+	0.629384i	−0.318529	+	0.947913i	$0.603189\pi$
$744$	5.09188	−	6.18932i	0.186677	−	0.226911i
$745$		0			0
$746$	1.92498	−	3.18506i	0.0704786	−	0.116613i
$747$	−1.47843	−	9.33443i	−0.0540929	−	0.341529i
$748$	5.29950	+	7.10875i	0.193769	+	0.259922i
$749$	−13.3091			−0.486304
$750$		0			0
$751$		−	54.0781i		−	1.97334i	−0.162738	−	0.986669i	$-0.552032\pi$
$751$		−	54.0781i		−	1.97334i	0.162738	−	0.986669i	$-0.447968\pi$
$752$	−18.8499	−	17.9453i	−0.687386	−	0.654398i
$753$	25.7103	−	4.07212i	0.936936	−	0.148396i
$754$	−34.0618	+	56.3583i	−1.24046	+	2.05245i
$755$		0			0
$756$	6.80180	+	6.63663i	0.247379	+	0.241372i
$757$	−23.3426	+	23.3426i	−0.848401	+	0.848401i	−0.989934	−	0.141532i	$-0.954797\pi$
$757$	−23.3426	+	23.3426i	−0.848401	+	0.848401i	0.141532	+	0.989934i	$0.454797\pi$
$758$	2.27472	−	31.3662i	0.0826215	−	1.13927i
$759$	5.54826	+	17.0758i	0.201389	+	0.619812i
$760$		0			0
$761$	−1.58617	+	4.88172i	−0.0574985	+	0.176962i	−0.975681	−	0.219196i	$-0.929657\pi$
$761$	−1.58617	+	4.88172i	−0.0574985	+	0.176962i	0.918182	+	0.396158i	$0.129657\pi$
$762$	−23.3305	−	9.49628i	−0.845176	−	0.344014i
$763$	−0.240582	−	0.122583i	−0.00870967	−	0.00443780i
$764$	−3.18708	+	21.8578i	−0.115304	+	0.790787i
$765$		0			0
$766$	3.40319	−	1.43421i	0.122962	−	0.0518201i
$767$	2.77394	−	17.5140i	0.100161	−	0.632393i
$768$	−2.62607	+	24.2393i	−0.0947601	+	0.874661i
$769$	10.5565	+	14.5298i	0.380679	+	0.523959i	0.955764	−	0.294134i	$-0.0950312\pi$
$769$	10.5565	+	14.5298i	0.380679	+	0.523959i	−0.575085	+	0.818093i	$0.695031\pi$
$770$		0			0
$771$	−16.6144	−	12.0711i	−0.598354	−	0.434730i
$772$	−2.11484	−	6.24653i	−0.0761148	−	0.224817i
$773$	−22.5768	+	11.5035i	−0.812033	+	0.413751i	−0.810133	−	0.586247i	$-0.800605\pi$
$773$	−22.5768	+	11.5035i	−0.812033	+	0.413751i	−0.00190030	+	0.999998i	$0.500605\pi$
$774$	−0.370745	−	4.36746i	−0.0133261	−	0.156985i
$775$		0			0
$776$	4.35802	−	1.13163i	0.156444	−	0.0406231i
$777$	−1.01001	+	0.514628i	−0.0362340	+	0.0184622i
$778$	3.09289	+	12.5428i	0.110885	+	0.449680i
$779$	−4.77767	+	6.57590i	−0.171178	+	0.235606i
$780$		0			0
$781$	−0.695769	−	0.957644i	−0.0248966	−	0.0342672i
$782$	−17.8799	+	21.1971i	−0.639386	+	0.758007i
$783$	−44.4568	−	7.04127i	−1.58876	−	0.251634i
$784$	19.9574	−	15.2632i	0.712764	−	0.545114i
$785$		0			0
$786$	5.94048	−	25.4313i	0.211890	−	0.907106i
$787$	15.5649	−	30.5479i	0.554829	−	1.08891i	−0.427893	−	0.903829i	$-0.640744\pi$
$787$	15.5649	−	30.5479i	0.554829	−	1.08891i	0.982723	−	0.185085i	$-0.0592560\pi$
$788$	−8.13077	+	26.1116i	−0.289647	+	0.930188i
$789$	−4.46615	+	13.7454i	−0.158999	+	0.489349i
$790$		0			0
$791$	8.52659	−	2.77046i	0.303171	−	0.0985061i
$792$	3.11507	−	0.303036i	0.110689	−	0.0107679i
$793$	−5.38497	+	5.38497i	−0.191226	+	0.191226i
$794$	−23.8488	+	20.6236i	−0.846361	+	0.731903i
$795$		0			0
$796$	−9.73289	+	19.6966i	−0.344973	+	0.698129i
$797$	7.38252	−	1.16928i	0.261502	−	0.0414179i	−0.0243065	−	0.999705i	$-0.507738\pi$
$797$	7.38252	−	1.16928i	0.261502	−	0.0414179i	0.285809	+	0.958287i	$0.407738\pi$
$798$	2.72745	−	1.69453i	0.0965507	−	0.0599856i
$799$	17.6734			0.625240
$800$		0			0
$801$	−3.18545			−0.112552
$802$	−29.5297	+	18.3464i	−1.04273	+	0.647834i
$803$	8.40383	−	1.33104i	0.296565	−	0.0469712i
$804$	14.9740	−	30.3032i	0.528093	−	1.06871i
$805$		0			0
$806$	11.5332	−	9.97350i	0.406239	−	0.351301i
$807$	−16.7499	+	16.7499i	−0.589625	+	0.589625i
$808$	30.2719	−	2.94487i	1.06496	−	0.103600i
$809$	6.69119	−	2.17410i	0.235250	−	0.0764373i	−0.189020	−	0.981973i	$-0.560531\pi$
$809$	6.69119	−	2.17410i	0.235250	−	0.0764373i	0.424269	+	0.905536i	$0.360531\pi$
$810$		0			0
$811$	1.88146	−	5.79054i	0.0660670	−	0.203333i	−0.912573	−	0.408913i	$-0.865908\pi$
$811$	1.88146	−	5.79054i	0.0660670	−	0.203333i	0.978640	+	0.205580i	$0.0659080\pi$
$812$	4.04859	−	13.0019i	0.142078	−	0.456276i
$813$	−11.8339	+	23.2254i	−0.415034	+	0.814550i
$814$	−0.460691	+	1.97223i	−0.0161472	+	0.0691266i
$815$		0			0
$816$	−10.0579	−	13.1512i	−0.352097	−	0.460384i
$817$	−7.93560	−	1.25688i	−0.277631	−	0.0439725i
$818$	−11.9126	+	14.1227i	−0.416516	+	0.493790i
$819$	1.95883	+	2.69610i	0.0684470	+	0.0942092i
$820$		0			0
$821$	−4.36281	+	6.00490i	−0.152263	+	0.209572i	−0.878334	−	0.478048i	$-0.841345\pi$
$821$	−4.36281	+	6.00490i	−0.152263	+	0.209572i	0.726071	+	0.687620i	$0.241345\pi$
$822$	−5.48535	−	22.2450i	−0.191323	−	0.775884i
$823$	38.5098	−	19.6217i	1.34237	−	0.683970i	0.372598	−	0.927993i	$-0.378467\pi$
$823$	38.5098	−	19.6217i	1.34237	−	0.683970i	0.969769	+	0.244023i	$0.0784672\pi$
$824$	−38.8270	+	10.0820i	−1.35260	+	0.351225i
$825$		0			0
$826$	0.310160	+	3.65375i	0.0107918	+	0.127130i
$827$	−0.546569	+	0.278491i	−0.0190061	+	0.00968408i	−0.463468	−	0.886114i	$-0.653395\pi$
$827$	−0.546569	+	0.278491i	−0.0190061	+	0.00968408i	0.444462	+	0.895798i	$0.353395\pi$
$828$	3.13899	+	9.27152i	0.109088	+	0.322208i
$829$	−25.2713	−	18.3607i	−0.877709	−	0.637693i	0.0549352	−	0.998490i	$-0.482505\pi$
$829$	−25.2713	−	18.3607i	−0.877709	−	0.637693i	−0.932644	+	0.360797i	$0.882505\pi$
$830$		0			0
$831$	−15.7279	−	21.6476i	−0.545594	−	0.750946i
$832$	−12.6975	+	44.6120i	−0.440207	+	1.54664i
$833$	−2.66901	+	16.8514i	−0.0924756	+	0.583868i
$834$	−22.8740	+	9.63981i	−0.792061	+	0.333799i
$835$		0			0
$836$	0.827758	−	5.67697i	0.0286286	−	0.196342i
$837$	9.28601	+	4.73146i	0.320971	+	0.163543i
$838$	−30.1231	−	12.2611i	−1.04059	−	0.423552i
$839$	−2.67652	+	8.23749i	−0.0924038	+	0.284390i	−0.986568	−	0.163349i	$-0.947770\pi$
$839$	−2.67652	+	8.23749i	−0.0924038	+	0.284390i	0.894165	+	0.447738i	$0.147770\pi$
$840$		0			0
$841$	10.9698	+	33.7615i	0.378268	+	1.16419i
$842$	0.222743	−	3.07141i	0.00767624	−	0.105848i
$843$	−28.4386	+	28.4386i	−0.979479	+	0.979479i
$844$	−25.9668	−	25.3363i	−0.893815	−	0.872111i
$845$		0			0
$846$	3.22678	−	5.33900i	0.110939	−	0.183558i
$847$	6.98033	−	1.10558i	0.239847	−	0.0379880i
$848$	−37.1695	+	39.0433i	−1.27641	+	1.34075i
$849$			24.6077i			0.844534i
$850$		0			0
$851$	−6.33426			−0.217136
$852$	1.32105	+	1.77206i	0.0452586	+	0.0607098i
$853$	1.44745	+	9.13882i	0.0495596	+	0.312907i	0.999998	+	0.00199425i	$0.000634791\pi$
$853$	1.44745	+	9.13882i	0.0495596	+	0.312907i	−0.950438	+	0.310913i	$0.899365\pi$
$854$	0.814576	−	1.34779i	0.0278742	−	0.0461204i
$855$		0			0
$856$	28.2092	−	34.2891i	0.964172	−	1.17198i
$857$	25.2568	+	25.2568i	0.862757	+	0.862757i	0.991658	−	0.128901i	$-0.0411449\pi$
$857$	25.2568	+	25.2568i	0.862757	+	0.862757i	−0.128901	+	0.991658i	$0.541145\pi$
$858$	−20.3399	−	1.47508i	−0.694392	−	0.0503583i
$859$	−3.73920	+	1.21494i	−0.127580	+	0.0414532i	−0.372111	−	0.928188i	$-0.621366\pi$
$859$	−3.73920	+	1.21494i	−0.127580	+	0.0414532i	0.244531	+	0.969641i	$0.421366\pi$
$860$		0			0
$861$	−5.68250	−	1.84636i	−0.193659	−	0.0629237i
$862$	−6.85364	−	2.78965i	−0.233436	−	0.0950160i
$863$	17.5562	−	34.4560i	0.597620	−	1.17290i	−0.371989	−	0.928237i	$-0.621324\pi$
$863$	17.5562	−	34.4560i	0.597620	−	1.17290i	0.969609	−	0.244659i	$-0.0786759\pi$
$864$	−31.5151	+	3.45729i	−1.07217	+	0.117619i
$865$		0			0
$866$	9.14882	+	21.7089i	0.310890	+	0.737699i
$867$	−14.4816	−	2.29365i	−0.491819	−	0.0778965i
$868$	−1.82183	+	2.57346i	−0.0618368	+	0.0873488i
$869$	15.3509	−	11.1531i	0.520743	−	0.378342i
$870$		0			0
$871$	37.7972	−	52.0234i	1.28071	−	1.76275i
$872$	0.825744	−	0.360008i	0.0279632	−	0.0121914i
$873$	0.489967	+	0.961614i	0.0165829	+	0.0325457i
$874$	17.8784	−	1.51766i	0.604745	−	0.0513356i
$875$		0			0
$876$	−15.6603	+	2.67805i	−0.529114	+	0.0904828i
$877$	8.04946	+	15.7980i	0.271811	+	0.533459i	0.986051	−	0.166441i	$-0.0532276\pi$
$877$	8.04946	+	15.7980i	0.271811	+	0.533459i	−0.714240	+	0.699901i	$0.753228\pi$
$878$	4.88856	+	19.8248i	0.164981	+	0.669055i
$879$	−16.7922	−	12.2002i	−0.566385	−	0.411503i
$880$		0			0
$881$	−0.144449	+	0.104948i	−0.00486661	+	0.00353580i	−0.590216	−	0.807245i	$-0.700957\pi$
$881$	−0.144449	+	0.104948i	−0.00486661	+	0.00353580i	0.585349	+	0.810781i	$0.300957\pi$
$882$	4.60338	+	3.88299i	0.155004	+	0.130747i
$883$	5.34973	−	33.7769i	0.180033	−	1.13668i	−0.717769	−	0.696282i	$-0.754836\pi$
$883$	5.34973	−	33.7769i	0.180033	−	1.13668i	0.897801	−	0.440400i	$-0.145164\pi$
$884$	−14.6435	−	27.8868i	−0.492514	−	0.937934i
$885$		0			0
$886$	−7.84001	+	33.5633i	−0.263390	+	1.12758i
$887$	8.81412	+	4.49102i	0.295949	+	0.150794i	0.595661	−	0.803236i	$-0.296890\pi$
$887$	8.81412	+	4.49102i	0.295949	+	0.150794i	−0.299711	+	0.954030i	$0.596890\pi$
$888$	0.814901	−	3.69294i	0.0273463	−	0.123927i
$889$	9.42465	+	3.06225i	0.316093	+	0.102705i
$890$		0			0
$891$	−3.28163	−	10.0998i	−0.109939	−	0.338357i
$892$	0.456000	+	37.1005i	0.0152680	+	1.24221i
$893$	−8.08587	−	8.08587i	−0.270583	−	0.270583i
$894$	−17.2160	+	14.8878i	−0.575791	+	0.497923i
$895$		0			0
$896$	0.340664	−	9.58574i	0.0113808	−	0.320237i
$897$	−9.97751	−	62.9955i	−0.333139	−	2.10336i
$898$	−22.2282	−	35.7778i	−0.741766	−	1.19392i
$899$		−	14.9342i		−	0.498084i
$900$		0			0
$901$		−	36.6064i		−	1.21953i
$902$	−9.06775	+	5.63366i	−0.301923	+	0.187580i
$903$	−0.923906	−	5.83331i	−0.0307457	−	0.194120i
$904$	−10.9348	+	27.8397i	−0.363686	+	0.925936i
$905$		0			0
$906$	−7.79745	−	9.01684i	−0.259053	−	0.299564i
$907$	−7.87950	−	7.87950i	−0.261634	−	0.261634i	0.564083	−	0.825718i	$-0.309230\pi$
$907$	−7.87950	−	7.87950i	−0.261634	−	0.261634i	−0.825718	+	0.564083i	$0.809230\pi$
$908$	−0.255183	−	20.7619i	−0.00846855	−	0.689007i
$909$	2.25283	+	6.93351i	0.0747218	+	0.229970i
$910$		0			0
$911$	−25.3951	−	8.25137i	−0.841377	−	0.273380i	−0.143547	−	0.989643i	$-0.545851\pi$
$911$	−25.3951	−	8.25137i	−0.841377	−	0.273380i	−0.697830	+	0.716263i	$0.745851\pi$
$912$	−1.41524	+	10.6185i	−0.0468632	+	0.351615i
$913$	−20.2723	−	10.3293i	−0.670916	−	0.341849i
$914$	5.82409	+	1.36044i	0.192644	+	0.0449994i
$915$		0			0
$916$	−12.4559	+	6.54067i	−0.411555	+	0.216110i
$917$	−1.60725	+	10.1478i	−0.0530760	+	0.335109i
$918$	13.8813	−	16.4566i	0.458150	−	0.543149i
$919$	46.3097	−	33.6460i	1.52762	−	1.10988i	0.570071	−	0.821596i	$-0.306916\pi$
$919$	46.3097	−	33.6460i	1.52762	−	1.10988i	0.957545	−	0.288282i	$-0.0930842\pi$
$920$		0			0
$921$	−26.2082	−	19.0414i	−0.863589	−	0.627434i
$922$	−36.6732	+	9.04317i	−1.20777	+	0.297821i
$923$	1.90901	+	3.74664i	0.0628358	+	0.123322i
$924$	4.15682	−	0.710851i	0.136749	−	0.0233853i
$925$		0			0
$926$	−1.93733	−	22.8222i	−0.0636645	−	0.749983i
$927$	−4.36527	−	8.56733i	−0.143374	−	0.281388i
$928$	24.9164	+	37.9887i	0.817921	+	1.24704i
$929$	23.3033	−	32.0743i	0.764557	−	1.05232i	−0.232264	−	0.972653i	$-0.574613\pi$
$929$	23.3033	−	32.0743i	0.764557	−	1.05232i	0.996821	−	0.0796697i	$-0.0253865\pi$
$930$		0			0
$931$	8.93092	−	6.48869i	0.292699	−	0.212658i
$932$	−7.35281	−	5.20527i	−0.240849	−	0.170504i
$933$	14.8659	+	2.35452i	0.486687	+	0.0770837i
$934$	−12.6853	+	5.34599i	−0.415076	+	0.174926i
$935$		0			0
$936$	−11.0980	−	0.667840i	−0.362748	−	0.0218290i
$937$	−7.10250	+	13.9394i	−0.232028	+	0.455381i	−0.977437	−	0.211226i	$-0.932254\pi$
$937$	−7.10250	+	13.9394i	−0.232028	+	0.455381i	0.745409	+	0.666608i	$0.232254\pi$
$938$	−5.01319	+	12.3165i	−0.163687	+	0.402147i
$939$	26.0123	+	8.45190i	0.848879	+	0.275817i
$940$		0			0
$941$	0.332851	−	0.108150i	0.0108506	−	0.00352559i	−0.303587	−	0.952804i	$-0.598184\pi$
$941$	0.332851	−	0.108150i	0.0108506	−	0.00352559i	0.314437	+	0.949278i	$0.398184\pi$
$942$	−0.628389	+	8.66488i	−0.0204740	+	0.282317i
$943$	−23.6085	−	23.6085i	−0.768797	−	0.768797i
$944$	−10.0708	−	6.94521i	−0.327777	−	0.226047i
$945$		0			0
$946$	−9.03093	−	5.45811i	−0.293621	−	0.177459i
$947$	2.97102	+	18.7583i	0.0965450	+	0.609561i	0.987760	+	0.155980i	$0.0498537\pi$
$947$	2.97102	+	18.7583i	0.0965450	+	0.609561i	−0.891215	+	0.453581i	$0.850146\pi$
$948$	−28.4058	+	21.1763i	−0.922579	+	0.687774i
$949$	−30.2254			−0.981158
$950$		0			0
$951$		−	41.8925i		−	1.35846i
$952$	4.32074	+	4.87405i	0.140036	+	0.157969i
$953$	27.2740	−	4.31977i	0.883491	−	0.139931i	0.301829	−	0.953362i	$-0.402403\pi$
$953$	27.2740	−	4.31977i	0.883491	−	0.139931i	0.581662	+	0.813431i	$0.302403\pi$
$954$	−11.0585	−	6.68353i	−0.358032	−	0.216387i
$955$		0			0
$956$	34.7367	+	33.8932i	1.12347	+	1.09618i
$957$	−14.1240	+	14.1240i	−0.456564	+	0.456564i
$958$	−16.1555	−	1.17162i	−0.521961	−	0.0378533i
$959$	2.78534	+	8.57239i	0.0899433	+	0.276817i
$960$		0			0
$961$	8.51098	−	26.1941i	0.274548	−	0.844971i
$962$	2.71237	−	6.66377i	0.0874502	−	0.214848i
$963$	9.48291	+	4.83178i	0.305582	+	0.155702i
$964$	15.4015	+	2.24568i	0.496048	+	0.0723286i
$965$		0			0
$966$	5.12212	+	12.1541i	0.164802	+	0.391052i
$967$	−3.59773	+	22.7152i	−0.115695	+	0.730471i	0.859830	+	0.510581i	$0.170570\pi$
$967$	−3.59773	+	22.7152i	−0.115695	+	0.730471i	−0.975525	+	0.219890i	$0.929430\pi$
$968$	−11.9468	+	20.3272i	−0.383983	+	0.653341i
$969$	−4.27582	−	5.88516i	−0.137359	−	0.189059i
$970$		0			0
$971$	−5.28369	−	3.83882i	−0.169562	−	0.123194i	0.499768	−	0.866159i	$-0.333419\pi$
$971$	−5.28369	−	3.83882i	−0.169562	−	0.123194i	−0.669330	+	0.742966i	$0.733419\pi$
$972$	−4.42476	−	13.0693i	−0.141924	−	0.419197i
$973$	8.70096	−	4.43336i	0.278940	−	0.142127i
$974$	29.3503	−	2.49149i	0.940444	−	0.0798324i
$975$		0			0
$976$	1.74587	+	4.95535i	0.0558838	+	0.158617i
$977$	11.4089	−	5.81313i	0.365003	−	0.185978i	−0.261863	−	0.965105i	$-0.584337\pi$
$977$	11.4089	−	5.81313i	0.365003	−	0.185978i	0.626867	+	0.779126i	$0.284337\pi$
$978$	32.2652	−	7.95621i	1.03173	−	0.254412i
$979$	−4.50759	+	6.20416i	−0.144063	+	0.198286i
$980$		0			0
$981$	0.126915	+	0.174684i	0.00405209	+	0.00557722i
$982$	−21.5193	−	18.1517i	−0.686708	−	0.579244i
$983$	29.2673	+	4.63549i	0.933482	+	0.147849i	0.604607	−	0.796524i	$-0.293330\pi$
$983$	29.2673	+	4.63549i	0.933482	+	0.147849i	0.328876	+	0.944373i	$0.393330\pi$
$984$	16.8012	−	10.7268i	0.535603	−	0.341957i
$985$		0			0
$986$	−30.0419	−	7.01745i	−0.956729	−	0.223481i
$987$	3.81613	−	7.48959i	0.121469	−	0.238396i
$988$	−6.05902	+	19.4583i	−0.192763	+	0.619050i
$989$	10.1983	−	31.3871i	0.324287	−	0.998052i
$990$		0			0
$991$	22.3204	−	7.25233i	0.709030	−	0.230378i	0.0677695	−	0.997701i	$-0.478412\pi$
$991$	22.3204	−	7.25233i	0.709030	−	0.230378i	0.641261	+	0.767323i	$0.278412\pi$
$992$	−2.76872	−	10.1482i	−0.0879070	−	0.322207i
$993$	−27.1873	+	27.1873i	−0.862762	+	0.862762i
$994$	−0.568780	−	0.657728i	−0.0180406	−	0.0208619i
$995$		0			0
$996$	38.0877	+	18.8207i	1.20686	+	0.596356i
$997$	44.2857	−	7.01416i	1.40254	−	0.222141i	0.591111	−	0.806590i	$-0.298690\pi$
$997$	44.2857	−	7.01416i	1.40254	−	0.222141i	0.811430	+	0.584450i	$0.198690\pi$
$998$	18.6878	+	30.0792i	0.591551	+	0.952140i
$999$	4.91767			0.155588

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1000.2.v.g.507.5		208
5.2	odd	4		1000.2.v.h.243.9		208
5.3	odd	4		200.2.v.c.3.18	yes	208
5.4	even	2		1000.2.v.i.507.22		208
8.3	odd	2	inner	1000.2.v.g.507.4		208
20.3	even	4		800.2.bp.c.303.5		208
25.6	even	5		200.2.v.c.67.15	yes	208
25.8	odd	20	inner	1000.2.v.g.643.4		208
25.17	odd	20		1000.2.v.i.643.23		208
25.19	even	10		1000.2.v.h.107.12		208
40.3	even	4		200.2.v.c.3.15	✓	208
40.13	odd	4		800.2.bp.c.303.6		208
40.19	odd	2		1000.2.v.i.507.23		208
40.27	even	4		1000.2.v.h.243.12		208
100.31	odd	10		800.2.bp.c.367.6		208
200.19	odd	10		1000.2.v.h.107.9		208
200.67	even	20		1000.2.v.i.643.22		208
200.83	even	20	inner	1000.2.v.g.643.5		208
200.131	odd	10		200.2.v.c.67.18	yes	208
200.181	even	10		800.2.bp.c.367.5		208

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
200.2.v.c.3.15	✓	208	40.3	even	4
200.2.v.c.3.18	yes	208	5.3	odd	4
200.2.v.c.67.15	yes	208	25.6	even	5
200.2.v.c.67.18	yes	208	200.131	odd	10
800.2.bp.c.303.5		208	20.3	even	4
800.2.bp.c.303.6		208	40.13	odd	4
800.2.bp.c.367.5		208	200.181	even	10
800.2.bp.c.367.6		208	100.31	odd	10
1000.2.v.g.507.4		208	8.3	odd	2	inner
1000.2.v.g.507.5		208	1.1	even	1	trivial
1000.2.v.g.643.4		208	25.8	odd	20	inner
1000.2.v.g.643.5		208	200.83	even	20	inner
1000.2.v.h.107.9		208	200.19	odd	10
1000.2.v.h.107.12		208	25.19	even	10
1000.2.v.h.243.9		208	5.2	odd	4
1000.2.v.h.243.12		208	40.27	even	4
1000.2.v.i.507.22		208	5.4	even	2
1000.2.v.i.507.23		208	40.19	odd	2
1000.2.v.i.643.22		208	200.67	even	20
1000.2.v.i.643.23		208	25.17	odd	20

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 1000 = 2^{3} \cdot 5^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1000.v (of order \(20\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.20125 + 0.746320i) q^{2} +(1.50506 - 0.238378i) q^{3} +(0.886011 - 1.79304i) q^{4} +(-1.63005 + 1.40961i) q^{6} +(0.599487 - 0.599487i) q^{7} +(0.273858 + 2.81514i) q^{8} +(-0.644782 + 0.209502i) q^{9} +(-0.504364 + 1.55227i) q^{11} +(0.906081 - 2.90984i) q^{12} +(2.63223 - 5.16603i) q^{13} +(-0.272725 + 1.16754i) q^{14} +(-2.42997 - 3.17730i) q^{16} +(2.68282 + 0.424918i) q^{17} +(0.618190 - 0.732879i) q^{18} +(-1.03303 - 1.42184i) q^{19} +(0.759360 - 1.04517i) q^{21} +(-0.552625 - 2.24109i) q^{22} +(6.43220 - 3.27737i) q^{23} +(1.08324 + 4.17168i) q^{24} +(0.693551 + 8.17019i) q^{26} +(-4.99370 + 2.54442i) q^{27} +(-0.543750 - 1.60605i) q^{28} +(6.49732 + 4.72058i) q^{29} +(-1.09301 - 1.50440i) q^{31} +(5.29029 + 2.00321i) q^{32} +(-0.389071 + 2.45650i) q^{33} +(-3.53987 + 1.49181i) q^{34} +(-0.195639 + 1.34174i) q^{36} +(-0.781804 - 0.398349i) q^{37} +(2.30208 + 0.937020i) q^{38} +(2.73019 - 8.40267i) q^{39} +(-1.42918 - 4.39856i) q^{41} +(-0.132151 + 1.82224i) q^{42} +(3.23259 - 3.23259i) q^{43} +(2.33641 + 2.27967i) q^{44} +(-5.28072 + 8.73743i) q^{46} +(6.42640 - 1.01784i) q^{47} +(-4.41465 - 4.20279i) q^{48} +6.28123i q^{49} +4.13911 q^{51} +(-6.93071 - 9.29685i) q^{52} +(-2.10822 - 13.3108i) q^{53} +(4.09974 - 6.78339i) q^{54} +(1.85181 + 1.52346i) q^{56} +(-1.89371 - 1.89371i) q^{57} +(-11.3280 - 0.821520i) q^{58} +(2.90867 - 0.945085i) q^{59} +(-1.24919 - 0.405886i) q^{61} +(2.43575 + 0.991428i) q^{62} +(-0.260944 + 0.512132i) q^{63} +(-7.85000 + 1.54190i) q^{64} +(-1.36596 - 3.24124i) q^{66} +(10.9543 + 1.73499i) q^{67} +(3.13891 - 4.43392i) q^{68} +(8.89961 - 6.46594i) q^{69} +(-0.426288 + 0.586736i) q^{71} +(-0.766357 - 1.75778i) q^{72} +(-2.36670 - 4.64490i) q^{73} +(1.23644 - 0.104959i) q^{74} +(-3.46469 + 0.592491i) q^{76} +(0.628207 + 1.23293i) q^{77} +(2.99143 + 12.1313i) q^{78} +(-9.40528 - 6.83334i) q^{79} +(-5.26385 + 3.82441i) q^{81} +(4.99954 + 4.21715i) q^{82} +(-2.18069 + 13.7683i) q^{83} +(-1.20123 - 2.28759i) q^{84} +(-1.47061 + 6.29571i) q^{86} +(10.9041 + 5.55594i) q^{87} +(-4.50798 - 0.994752i) q^{88} +(4.46859 + 1.45193i) q^{89} +(-1.51898 - 4.67495i) q^{91} +(-0.177444 - 14.4370i) q^{92} +(-2.00367 - 2.00367i) q^{93} +(-6.96009 + 6.01884i) q^{94} +(8.43973 + 1.75386i) q^{96} +(-0.249026 - 1.57229i) q^{97} +(-4.68781 - 7.54534i) q^{98} -1.10654i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 208 q - 8 q^{2} + 4 q^{3} + 10 q^{4} - 26 q^{6} + 46 q^{8} + 20 q^{9} - 4 q^{11} - 32 q^{12} + 30 q^{14} + 18 q^{16} - 12 q^{17} - 20 q^{18} + 38 q^{22} - 8 q^{26} - 8 q^{27} - 40 q^{28} + 22 q^{32} + 16 q^{33}+ \cdots - 34 q^{98}+O(q^{100}) \) 208 * q - 8 * q^2 + 4 * q^3 + 10 * q^4 - 26 * q^6 + 46 * q^8 + 20 * q^9 - 4 * q^11 - 32 * q^12 + 30 * q^14 + 18 * q^16 - 12 * q^17 - 20 * q^18 + 38 * q^22 - 8 * q^26 - 8 * q^27 - 40 * q^28 + 22 * q^32 + 16 * q^33 - 30 * q^34 - 38 * q^36 + 74 * q^38 - 44 * q^41 + 60 * q^42 - 8 * q^43 - 60 * q^44 + 2 * q^46 - 16 * q^48 + 8 * q^51 + 100 * q^52 + 140 * q^54 + 2 * q^56 + 92 * q^57 + 90 * q^58 + 40 * q^59 - 40 * q^62 - 20 * q^64 - 2 * q^66 - 72 * q^67 - 46 * q^68 - 150 * q^72 + 4 * q^73 - 24 * q^76 - 110 * q^78 + 16 * q^81 - 22 * q^82 + 44 * q^83 + 10 * q^84 - 26 * q^86 - 126 * q^88 + 100 * q^89 + 4 * q^91 - 110 * q^92 - 150 * q^94 - 26 * q^96 - 76 * q^97 - 34 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more