LMFDB - Embedded newform 950.2.l.l.701.3

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:	$30$
Relative dimension:	$5$ over $\Q(\zeta_{9})$
Twist minimal:	no (minimal twist has level 190)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			701.3
Character	$\chi$	$=$	950.701
Dual form			950.2.l.l.351.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.173648 + 0.984808i) q^{2} +(0.0864812 + 0.0725664i) q^{3} +(-0.939693 - 0.342020i) q^{4} +(-0.0864812 + 0.0725664i) q^{6} +(0.772138 + 1.33738i) q^{7} +(0.500000 - 0.866025i) q^{8} +(-0.518731 - 2.94187i) q^{9} +O(q^{10})$	\(q+(-0.173648 + 0.984808i) q^{2} +(0.0864812 + 0.0725664i) q^{3} +(-0.939693 - 0.342020i) q^{4} +(-0.0864812 + 0.0725664i) q^{6} +(0.772138 + 1.33738i) q^{7} +(0.500000 - 0.866025i) q^{8} +(-0.518731 - 2.94187i) q^{9} +(0.653254 - 1.13147i) q^{11} +(-0.0564466 - 0.0977684i) q^{12} +(-0.437630 + 0.367216i) q^{13} +(-1.45115 + 0.528174i) q^{14} +(0.766044 + 0.642788i) q^{16} +(0.878205 - 4.98055i) q^{17} +2.98726 q^{18} +(-0.546051 - 4.32456i) q^{19} +(-0.0302735 + 0.171690i) q^{21} +(1.00084 + 0.839807i) q^{22} +(4.86607 + 1.77110i) q^{23} +(0.106085 - 0.0386118i) q^{24} +(-0.285643 - 0.494748i) q^{26} +(0.337960 - 0.585364i) q^{27} +(-0.268161 - 1.52082i) q^{28} +(0.660543 + 3.74612i) q^{29} +(-1.49337 - 2.58659i) q^{31} +(-0.766044 + 0.642788i) q^{32} +(0.138601 - 0.0504466i) q^{33} +(4.75238 + 1.72973i) q^{34} +(-0.518731 + 2.94187i) q^{36} +3.31366 q^{37} +(4.35368 + 0.213197i) q^{38} -0.0644943 q^{39} +(-8.57613 - 7.19623i) q^{41} +(-0.163824 - 0.0596272i) q^{42} +(8.85190 - 3.22183i) q^{43} +(-1.00084 + 0.839807i) q^{44} +(-2.58918 + 4.48459i) q^{46} +(0.368346 + 2.08900i) q^{47} +(0.0196037 + 0.111178i) q^{48} +(2.30761 - 3.99689i) q^{49} +(0.437368 - 0.366996i) q^{51} +(0.536833 - 0.195391i) q^{52} +(7.19438 + 2.61854i) q^{53} +(0.517785 + 0.434473i) q^{54} +1.54428 q^{56} +(0.266595 - 0.413618i) q^{57} -3.80391 q^{58} +(-0.0463006 + 0.262584i) q^{59} +(3.05865 + 1.11326i) q^{61} +(2.80661 - 1.02152i) q^{62} +(3.53388 - 2.96527i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(0.0256124 + 0.145255i) q^{66} +(1.57745 + 8.94618i) q^{67} +(-2.52869 + 4.37982i) q^{68} +(0.292301 + 0.506280i) q^{69} +(15.2634 - 5.55544i) q^{71} +(-2.80710 - 1.02170i) q^{72} +(2.14696 + 1.80151i) q^{73} +(-0.575412 + 3.26332i) q^{74} +(-0.965967 + 4.25052i) q^{76} +2.01761 q^{77} +(0.0111993 - 0.0635145i) q^{78} +(3.19682 + 2.68245i) q^{79} +(-8.34960 + 3.03901i) q^{81} +(8.57613 - 7.19623i) q^{82} +(-4.63728 - 8.03200i) q^{83} +(0.0871692 - 0.150981i) q^{84} +(1.63576 + 9.27688i) q^{86} +(-0.214718 + 0.371903i) q^{87} +(-0.653254 - 1.13147i) q^{88} +(-4.42254 + 3.71095i) q^{89} +(-0.829019 - 0.301738i) q^{91} +(-3.96686 - 3.32859i) q^{92} +(0.0585510 - 0.332059i) q^{93} -2.12122 q^{94} -0.112893 q^{96} +(0.500011 - 2.83571i) q^{97} +(3.53546 + 2.96660i) q^{98} +(-3.66750 - 1.33486i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q - 12 q^{7} + 15 q^{8}+O(q^{10}) $ 30 * q - 12 * q^7 + 15 * q^8	$ 30 q - 12 q^{7} + 15 q^{8} + 6 q^{11} + 6 q^{14} - 30 q^{18} + 24 q^{19} + 24 q^{21} + 3 q^{22} + 3 q^{23} + 3 q^{26} - 18 q^{27} + 3 q^{28} + 12 q^{29} - 30 q^{33} + 24 q^{37} - 12 q^{38} - 24 q^{39} - 3 q^{41} + 12 q^{42} + 6 q^{43} - 3 q^{44} + 48 q^{47} + 15 q^{49} - 90 q^{51} - 18 q^{53} + 18 q^{54} - 24 q^{56} - 42 q^{57} + 36 q^{58} - 18 q^{59} - 60 q^{61} - 24 q^{62} - 21 q^{63} - 15 q^{64} - 78 q^{66} - 30 q^{67} - 12 q^{68} + 24 q^{69} + 30 q^{73} - 9 q^{74} - 3 q^{76} + 78 q^{77} - 6 q^{79} + 60 q^{81} + 3 q^{82} - 42 q^{83} - 6 q^{84} + 12 q^{86} - 54 q^{87} - 6 q^{88} - 30 q^{89} - 6 q^{91} - 6 q^{92} + 72 q^{93} - 78 q^{94} - 42 q^{97} + 6 q^{98} - 99 q^{99}+O(q^{100}) $ 30 * q - 12 * q^7 + 15 * q^8 + 6 * q^11 + 6 * q^14 - 30 * q^18 + 24 * q^19 + 24 * q^21 + 3 * q^22 + 3 * q^23 + 3 * q^26 - 18 * q^27 + 3 * q^28 + 12 * q^29 - 30 * q^33 + 24 * q^37 - 12 * q^38 - 24 * q^39 - 3 * q^41 + 12 * q^42 + 6 * q^43 - 3 * q^44 + 48 * q^47 + 15 * q^49 - 90 * q^51 - 18 * q^53 + 18 * q^54 - 24 * q^56 - 42 * q^57 + 36 * q^58 - 18 * q^59 - 60 * q^61 - 24 * q^62 - 21 * q^63 - 15 * q^64 - 78 * q^66 - 30 * q^67 - 12 * q^68 + 24 * q^69 + 30 * q^73 - 9 * q^74 - 3 * q^76 + 78 * q^77 - 6 * q^79 + 60 * q^81 + 3 * q^82 - 42 * q^83 - 6 * q^84 + 12 * q^86 - 54 * q^87 - 6 * q^88 - 30 * q^89 - 6 * q^91 - 6 * q^92 + 72 * q^93 - 78 * q^94 - 42 * q^97 + 6 * q^98 - 99 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$77$	$401$
$\chi(n)$	$1$	$e\left(\frac{5}{9}\right)$

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 $

$2$	−0.173648	+	0.984808i	−0.122788	+	0.696364i
$2$	−0.173648	+	0.984808i	−0.122788	+	0.696364i
$3$	0.0864812	+	0.0725664i	0.0499300	+	0.0418962i	0.667411	−	0.744689i	$-0.267402\pi$
$3$	0.0864812	+	0.0725664i	0.0499300	+	0.0418962i	−0.617481	+	0.786586i	$0.711847\pi$
$4$	−0.939693	−	0.342020i	−0.469846	−	0.171010i
$5$		0			0
$5$		0			0
$6$	−0.0864812	+	0.0725664i	−0.0353058	+	0.0296251i
$7$	0.772138	+	1.33738i	0.291841	+	0.505483i	0.974245	−	0.225492i	$-0.0723989\pi$
$7$	0.772138	+	1.33738i	0.291841	+	0.505483i	−0.682404	+	0.730975i	$0.739066\pi$
$8$	0.500000	−	0.866025i	0.176777	−	0.306186i
$9$	−0.518731	−	2.94187i	−0.172910	−	0.980624i
$10$		0			0
$11$	0.653254	−	1.13147i	0.196963	−	0.341151i	−0.750579	−	0.660781i	$-0.770225\pi$
$11$	0.653254	−	1.13147i	0.196963	−	0.341151i	0.947542	+	0.319630i	$0.103559\pi$
$12$	−0.0564466	−	0.0977684i	−0.0162947	−	0.0282233i
$13$	−0.437630	+	0.367216i	−0.121377	+	0.101847i	−0.701456	−	0.712713i	$-0.747466\pi$
$13$	−0.437630	+	0.367216i	−0.121377	+	0.101847i	0.580079	+	0.814560i	$0.303022\pi$
$14$	−1.45115	+	0.528174i	−0.387835	+	0.141160i
$15$		0			0
$16$	0.766044	+	0.642788i	0.191511	+	0.160697i
$17$	0.878205	−	4.98055i	0.212996	−	1.20796i	−0.671355	−	0.741136i	$-0.734287\pi$
$17$	0.878205	−	4.98055i	0.212996	−	1.20796i	0.884351	−	0.466824i	$-0.154602\pi$
$18$	2.98726			0.704103
$19$	−0.546051	−	4.32456i	−0.125273	−	0.992122i
$19$	−0.546051	−	4.32456i	−0.125273	−	0.992122i
$20$		0			0
$21$	−0.0302735	+	0.171690i	−0.00660623	+	0.0374658i
$22$	1.00084	+	0.839807i	0.213380	+	0.179047i
$23$	4.86607	+	1.77110i	1.01465	+	0.369301i	0.795215	−	0.606327i	$-0.207358\pi$
$23$	4.86607	+	1.77110i	1.01465	+	0.369301i	0.219430	+	0.975628i	$0.429580\pi$
$24$	0.106085	−	0.0386118i	0.0216545	−	0.00788159i
$25$		0			0
$26$	−0.285643	−	0.494748i	−0.0560192	−	0.0970281i
$27$	0.337960	−	0.585364i	0.0650405	−	0.112653i
$28$	−0.268161	−	1.52082i	−0.0506776	−	0.287407i
$29$	0.660543	+	3.74612i	0.122660	+	0.695638i	0.982670	+	0.185362i	$0.0593457\pi$
$29$	0.660543	+	3.74612i	0.122660	+	0.695638i	−0.860011	+	0.510276i	$0.829543\pi$
$30$		0			0
$31$	−1.49337	−	2.58659i	−0.268217	−	0.464565i	0.700185	−	0.713962i	$-0.253101\pi$
$31$	−1.49337	−	2.58659i	−0.268217	−	0.464565i	−0.968401	+	0.249397i	$0.919768\pi$
$32$	−0.766044	+	0.642788i	−0.135419	+	0.113630i
$33$	0.138601	−	0.0504466i	0.0241273	−	0.00878162i
$34$	4.75238	+	1.72973i	0.815027	+	0.296645i
$35$		0			0
$36$	−0.518731	+	2.94187i	−0.0864552	+	0.490312i
$37$	3.31366			0.544763			0.272381	−	0.962189i	$-0.412189\pi$
$37$	3.31366			0.544763			0.272381	+	0.962189i	$0.412189\pi$
$38$	4.35368	+	0.213197i	0.706260	+	0.0345851i
$39$	−0.0644943			−0.0103274
$40$		0			0
$41$	−8.57613	−	7.19623i	−1.33937	−	1.12386i	−0.981788	−	0.189980i	$-0.939158\pi$
$41$	−8.57613	−	7.19623i	−1.33937	−	1.12386i	−0.357579	−	0.933883i	$-0.616398\pi$
$42$	−0.163824	−	0.0596272i	−0.0252787	−	0.00920068i
$43$	8.85190	−	3.22183i	1.34990	−	0.491324i	0.436984	−	0.899469i	$-0.356046\pi$
$43$	8.85190	−	3.22183i	1.34990	−	0.491324i	0.912917	+	0.408145i	$0.133824\pi$
$44$	−1.00084	+	0.839807i	−0.150883	+	0.126606i
$45$		0			0
$46$	−2.58918	+	4.48459i	−0.381754	+	0.661217i
$47$	0.368346	+	2.08900i	0.0537288	+	0.304711i	0.999816	−	0.0192019i	$-0.00611253\pi$
$47$	0.368346	+	2.08900i	0.0537288	+	0.304711i	−0.946087	+	0.323913i	$0.895001\pi$
$48$	0.0196037	+	0.111178i	0.00282955	+	0.0160472i
$49$	2.30761	−	3.99689i	0.329658	−	0.570984i
$50$		0			0
$51$	0.437368	−	0.366996i	0.0612438	−	0.0513897i
$52$	0.536833	−	0.195391i	0.0744454	−	0.0270959i
$53$	7.19438	+	2.61854i	0.988225	+	0.359684i	0.785033	−	0.619455i	$-0.212646\pi$
$53$	7.19438	+	2.61854i	0.988225	+	0.359684i	0.203192	+	0.979139i	$0.434868\pi$
$54$	0.517785	+	0.434473i	0.0704616	+	0.0591243i
$55$		0			0
$56$	1.54428			0.206363
$57$	0.266595	−	0.413618i	0.0353113	−	0.0547851i
$58$	−3.80391			−0.499479
$59$	−0.0463006	+	0.262584i	−0.00602782	+	0.0341855i	−0.987673	−	0.156529i	$-0.949969\pi$
$59$	−0.0463006	+	0.262584i	−0.00602782	+	0.0341855i	0.981645	+	0.190715i	$0.0610806\pi$
$60$		0			0
$61$	3.05865	+	1.11326i	0.391620	+	0.142538i	0.530322	−	0.847796i	$-0.322071\pi$
$61$	3.05865	+	1.11326i	0.391620	+	0.142538i	−0.138702	+	0.990334i	$0.544293\pi$
$62$	2.80661	−	1.02152i	0.356440	−	0.129734i
$63$	3.53388	−	2.96527i	0.445227	−	0.373589i
$64$	−0.500000	−	0.866025i	−0.0625000	−	0.108253i
$65$		0			0
$66$	0.0256124	+	0.145255i	0.00315267	+	0.0178797i
$67$	1.57745	+	8.94618i	0.192716	+	1.09295i	0.915633	+	0.402014i	$0.131690\pi$
$67$	1.57745	+	8.94618i	0.192716	+	1.09295i	−0.722917	+	0.690935i	$0.757199\pi$
$68$	−2.52869	+	4.37982i	−0.306649	+	0.531131i
$69$	0.292301	+	0.506280i	0.0351889	+	0.0609490i
$70$		0			0
$71$	15.2634	−	5.55544i	1.81144	−	0.659309i	0.814583	−	0.580048i	$-0.196966\pi$
$71$	15.2634	−	5.55544i	1.81144	−	0.659309i	0.996854	−	0.0792613i	$-0.0252562\pi$
$72$	−2.80710	−	1.02170i	−0.330820	−	0.120409i
$73$	2.14696	+	1.80151i	0.251283	+	0.210851i	0.759724	−	0.650245i	$-0.225334\pi$
$73$	2.14696	+	1.80151i	0.251283	+	0.210851i	−0.508442	+	0.861096i	$0.669778\pi$
$74$	−0.575412	+	3.26332i	−0.0668902	+	0.379353i
$75$		0			0
$76$	−0.965967	+	4.25052i	−0.110804	+	0.487568i
$77$	2.01761			0.229928
$78$	0.0111993	−	0.0635145i	0.00126807	−	0.00719160i
$79$	3.19682	+	2.68245i	0.359671	+	0.301800i	0.804660	−	0.593737i	$-0.202348\pi$
$79$	3.19682	+	2.68245i	0.359671	+	0.301800i	−0.444989	+	0.895536i	$0.646792\pi$
$80$		0			0
$81$	−8.34960	+	3.03901i	−0.927733	+	0.337667i
$82$	8.57613	−	7.19623i	0.947076	−	0.794691i
$83$	−4.63728	−	8.03200i	−0.509007	−	0.881627i	−0.999946	−	0.0104323i	$-0.996679\pi$
$83$	−4.63728	−	8.03200i	−0.509007	−	0.881627i	0.490938	−	0.871194i	$-0.336654\pi$
$84$	0.0871692	−	0.150981i	0.00951094	−	0.0164734i
$85$		0			0
$86$	1.63576	+	9.27688i	0.176389	+	1.00035i
$87$	−0.214718	+	0.371903i	−0.0230202	+	0.0398722i
$88$	−0.653254	−	1.13147i	−0.0696371	−	0.120615i
$89$	−4.42254	+	3.71095i	−0.468788	+	0.393360i	−0.846352	−	0.532623i	$-0.821206\pi$
$89$	−4.42254	+	3.71095i	−0.468788	+	0.393360i	0.377564	+	0.925983i	$0.376762\pi$
$90$		0			0
$91$	−0.829019	−	0.301738i	−0.0869048	−	0.0316308i
$92$	−3.96686	−	3.32859i	−0.413573	−	0.347029i
$93$	0.0585510	−	0.332059i	0.00607146	−	0.0344330i
$94$	−2.12122			−0.218787
$95$		0			0
$96$	−0.112893			−0.0115221
$97$	0.500011	−	2.83571i	0.0507685	−	0.287922i	−0.948844	−	0.315744i	$-0.897746\pi$
$97$	0.500011	−	2.83571i	0.0507685	−	0.287922i	0.999613	+	0.0278217i	$0.00885706\pi$
$98$	3.53546	+	2.96660i	0.357135	+	0.299672i
$99$	−3.66750	−	1.33486i	−0.368598	−	0.134159i
$100$		0			0
$101$	7.83588	−	6.57509i	0.779699	−	0.654245i	−0.163474	−	0.986548i	$-0.552270\pi$
$101$	7.83588	−	6.57509i	0.779699	−	0.654245i	0.943173	+	0.332302i	$0.107825\pi$
$102$	0.285472	+	0.494452i	0.0282659	+	0.0489580i
$103$	−2.48830	+	4.30986i	−0.245180	+	0.424663i	−0.962182	−	0.272407i	$-0.912180\pi$
$103$	−2.48830	+	4.30986i	−0.245180	+	0.424663i	0.717003	+	0.697071i	$0.245514\pi$
$104$	0.0992028	+	0.562607i	0.00972763	+	0.0551681i
$105$		0			0
$106$	−3.82805	+	6.63038i	−0.371813	+	0.643999i
$107$	−6.69352	−	11.5935i	−0.647087	−	1.12079i	−0.983815	−	0.179185i	$-0.942654\pi$
$107$	−6.69352	−	11.5935i	−0.647087	−	1.12079i	0.336729	−	0.941602i	$-0.390680\pi$
$108$	−0.517785	+	0.434473i	−0.0498239	+	0.0418072i
$109$	−9.28707	+	3.38022i	−0.889540	+	0.323766i	−0.746053	−	0.665886i	$-0.768054\pi$
$109$	−9.28707	+	3.38022i	−0.889540	+	0.323766i	−0.143487	+	0.989652i	$0.545831\pi$
$110$		0			0
$111$	0.286570	+	0.240461i	0.0272000	+	0.0228235i
$112$	−0.268161	+	1.52082i	−0.0253388	+	0.143704i
$113$	−15.3970			−1.44843			−0.724215	−	0.689575i	$-0.757798\pi$
$113$	−15.3970			−1.44843			−0.724215	+	0.689575i	$0.757798\pi$
$114$	0.361041	+	0.334368i	0.0338146	+	0.0313165i
$115$		0			0
$116$	0.660543	−	3.74612i	0.0613299	−	0.347819i
$117$	1.30731	+	1.09697i	0.120861	+	0.101415i
$118$	−0.250554	−	0.0911943i	−0.0230654	−	0.00839512i
$119$	7.33899	−	2.67117i	0.672764	−	0.244866i
$120$		0			0
$121$	4.64652	+	8.04801i	0.422411	+	0.731637i
$122$	−1.62747	+	2.81887i	−0.147345	+	0.255208i
$123$	−0.219470	−	1.24468i	−0.0197890	−	0.112229i
$124$	0.518641	+	2.94136i	0.0465753	+	0.264142i
$125$		0			0
$126$	2.30657	+	3.99510i	0.205486	+	0.355912i
$127$	−12.7214	+	10.6745i	−1.12884	+	0.947212i	−0.999017	−	0.0443246i	$-0.985886\pi$
$127$	−12.7214	+	10.6745i	−1.12884	+	0.947212i	−0.129826	+	0.991537i	$0.541442\pi$
$128$	0.939693	−	0.342020i	0.0830579	−	0.0302306i
$129$	0.999319	+	0.363722i	0.0879852	+	0.0320240i
$130$		0			0
$131$	2.64192	−	14.9831i	0.230825	−	1.30908i	−0.620404	−	0.784282i	$-0.713032\pi$
$131$	2.64192	−	14.9831i	0.230825	−	1.30908i	0.851230	−	0.524793i	$-0.175857\pi$
$132$	−0.147496			−0.0128379
$133$	5.36197	−	4.06944i	0.464941	−	0.352865i
$134$	−9.08419			−0.784754
$135$		0			0
$136$	−3.87418	−	3.25082i	−0.332208	−	0.278756i
$137$	11.1596	+	4.06178i	0.953432	+	0.347021i	0.771456	−	0.636282i	$-0.219529\pi$
$137$	11.1596	+	4.06178i	0.953432	+	0.347021i	0.181976	+	0.983303i	$0.441751\pi$
$138$	−0.549346	+	0.199946i	−0.0467635	+	0.0170205i
$139$	−0.888380	+	0.745439i	−0.0753514	+	0.0632273i	−0.679685	−	0.733504i	$-0.737884\pi$
$139$	−0.888380	+	0.745439i	−0.0753514	+	0.0632273i	0.604334	+	0.796731i	$0.293439\pi$
$140$		0			0
$141$	−0.119736	+	0.207388i	−0.0100836	+	0.0174653i
$142$	2.82057	+	15.9962i	0.236697	+	1.34237i
$143$	0.129609	+	0.735050i	0.0108385	+	0.0614680i
$144$	1.49363	−	2.58704i	0.124469	−	0.215587i
$145$		0			0
$146$	−2.14696	+	1.80151i	−0.177684	+	0.149094i
$147$	0.489604	−	0.178201i	0.0403819	−	0.0146978i
$148$	−3.11383	−	1.13334i	−0.255955	−	0.0931599i
$149$	12.3996	+	10.4045i	1.01581	+	0.852369i	0.989096	−	0.147274i	$-0.0470498\pi$
$149$	12.3996	+	10.4045i	1.01581	+	0.852369i	0.0267185	+	0.999643i	$0.491494\pi$
$150$		0			0
$151$	−11.5646			−0.941115			−0.470557	−	0.882369i	$-0.655947\pi$
$151$	−11.5646			−0.941115			−0.470557	+	0.882369i	$0.655947\pi$
$152$	−4.01821	−	1.68939i	−0.325919	−	0.137027i
$153$	−15.1077			−1.22138
$154$	−0.350354	+	1.98696i	−0.0282323	+	0.160114i
$155$		0			0
$156$	0.0606048	+	0.0220584i	0.00485227	+	0.00176608i
$157$	−13.4719	+	4.90336i	−1.07517	+	0.391331i	−0.818108	−	0.575064i	$-0.804977\pi$
$157$	−13.4719	+	4.90336i	−1.07517	+	0.391331i	−0.257063	+	0.966395i	$0.582755\pi$
$158$	−3.19682	+	2.68245i	−0.254326	+	0.213405i
$159$	0.432161	+	0.748525i	0.0342726	+	0.0593619i
$160$		0			0
$161$	1.38863	+	7.87533i	0.109440	+	0.620663i
$162$	−1.54294	−	8.75047i	−0.121225	−	0.687502i
$163$	−3.74257	+	6.48232i	−0.293141	+	0.507735i	−0.974551	−	0.224167i	$-0.928034\pi$
$163$	−3.74257	+	6.48232i	−0.293141	+	0.507735i	0.681410	+	0.731902i	$0.261367\pi$
$164$	5.59767	+	9.69546i	0.437105	+	0.757088i
$165$		0			0
$166$	8.71523	−	3.17209i	0.676433	−	0.246202i
$167$	5.05451	+	1.83969i	0.391130	+	0.142360i	0.530096	−	0.847937i	$-0.322156\pi$
$167$	5.05451	+	1.83969i	0.391130	+	0.142360i	−0.138966	+	0.990297i	$0.544378\pi$
$168$	0.133551	+	0.112063i	0.0103037	+	0.00864581i
$169$	−2.20075	+	12.4811i	−0.169289	+	0.960084i
$170$		0			0
$171$	−12.4391	+	3.84970i	−0.951238	+	0.294394i
$172$	−9.41999			−0.718268
$173$	−1.18783	+	6.73649i	−0.0903087	+	0.512166i	0.905776	+	0.423758i	$0.139289\pi$
$173$	−1.18783	+	6.73649i	−0.0903087	+	0.512166i	−0.996084	+	0.0884084i	$0.971822\pi$
$174$	−0.328967	−	0.276036i	−0.0249389	−	0.0209263i
$175$		0			0
$176$	1.22772	−	0.446852i	0.0925426	−	0.0336827i
$177$	−0.0230589	+	0.0193487i	−0.00173321	+	0.00145434i
$178$	−2.88661	−	4.99975i	−0.216360	−	0.374747i
$179$	12.9332	−	22.4009i	0.966670	−	1.67432i	0.261612	−	0.965173i	$-0.415746\pi$
$179$	12.9332	−	22.4009i	0.966670	−	1.67432i	0.705058	−	0.709149i	$-0.250921\pi$
$180$		0			0
$181$	−0.983005	−	5.57490i	−0.0730662	−	0.414379i	−0.999299	−	0.0374279i	$-0.988084\pi$
$181$	−0.983005	−	5.57490i	−0.0730662	−	0.414379i	0.926233	−	0.376951i	$-0.123028\pi$
$182$	0.441112	−	0.764028i	0.0326974	−	0.0566335i
$183$	0.183731	+	0.318231i	0.0135818	+	0.0235243i
$184$	3.96686	−	3.32859i	0.292440	−	0.245387i
$185$		0			0
$186$	0.316847	+	0.115323i	0.0232324	+	0.00845589i
$187$	−5.06164	−	4.24722i	−0.370144	−	0.310588i
$188$	0.368346	−	2.08900i	0.0268644	−	0.152356i
$189$	1.04381			0.0759259
$190$		0			0
$191$	−3.80022			−0.274974			−0.137487	−	0.990504i	$-0.543903\pi$
$191$	−3.80022			−0.274974			−0.137487	+	0.990504i	$0.543903\pi$
$192$	0.0196037	−	0.111178i	0.00141478	−	0.00802359i
$193$	−1.49718	−	1.25628i	−0.107769	−	0.0904291i	0.587311	−	0.809361i	$-0.300187\pi$
$193$	−1.49718	−	1.25628i	−0.107769	−	0.0904291i	−0.695080	+	0.718932i	$0.744631\pi$
$194$	2.70580	+	0.984830i	0.194265	+	0.0707067i
$195$		0			0
$196$	−3.53546	+	2.96660i	−0.252533	+	0.211900i
$197$	−9.25912	−	16.0373i	−0.659685	−	1.14261i	−0.980697	−	0.195533i	$-0.937356\pi$
$197$	−9.25912	−	16.0373i	−0.659685	−	1.14261i	0.321012	−	0.947075i	$-0.395977\pi$
$198$	1.95144	−	3.37999i	0.138683	−	0.240205i
$199$	−4.20620	−	23.8545i	−0.298170	−	1.69100i	−0.654033	−	0.756466i	$-0.726924\pi$
$199$	−4.20620	−	23.8545i	−0.298170	−	1.69100i	0.355863	−	0.934538i	$-0.384187\pi$
$200$		0			0
$201$	−0.512772	+	0.888146i	−0.0361681	+	0.0626450i
$202$	5.11451	+	8.85859i	0.359856	+	0.623288i
$203$	−4.49997	+	3.77592i	−0.315836	+	0.265018i
$204$	−0.536512	+	0.195274i	−0.0375633	+	0.0136719i
$205$		0			0
$206$	−3.81230	−	3.19890i	−0.265615	−	0.222878i
$207$	2.68618	−	15.2341i	0.186702	−	1.05884i
$208$	−0.571286			−0.0396116
$209$	−5.24982	−	2.20720i	−0.363137	−	0.152675i
$210$		0			0
$211$	2.09667	−	11.8908i	0.144341	−	0.818596i	−0.823554	−	0.567239i	$-0.808012\pi$
$211$	2.09667	−	11.8908i	0.144341	−	0.818596i	0.967894	−	0.251358i	$-0.0808771\pi$
$212$	−5.86492	−	4.92125i	−0.402804	−	0.337993i
$213$	1.72314	+	0.627171i	0.118068	+	0.0429731i
$214$	12.5797	−	4.57864i	0.859931	−	0.312989i
$215$		0			0
$216$	−0.337960	−	0.585364i	−0.0229953	−	0.0398290i
$217$	2.30617	−	3.99440i	0.156553	−	0.271158i
$218$	−1.71618	−	9.73295i	−0.116235	−	0.659199i
$219$	0.0549425	+	0.311594i	0.00371267	+	0.0210556i
$220$		0			0
$221$	1.44460	+	2.50213i	0.0971746	+	0.168311i
$222$	−0.286570	+	0.240461i	−0.0192333	+	0.0161387i
$223$	−23.8939	+	8.69666i	−1.60005	+	0.582371i	−0.979438	−	0.201745i	$-0.935339\pi$
$223$	−23.8939	+	8.69666i	−1.60005	+	0.582371i	−0.620614	+	0.784116i	$0.713117\pi$
$224$	−1.45115	−	0.528174i	−0.0969587	−	0.0352901i
$225$		0			0
$226$	2.67366	−	15.1631i	0.177849	−	1.00863i
$227$	13.2055			0.876477			0.438239	−	0.898859i	$-0.355602\pi$
$227$	13.2055			0.876477			0.438239	+	0.898859i	$0.355602\pi$
$228$	−0.391983	+	0.297493i	−0.0259597	+	0.0197020i
$229$	−22.5334			−1.48905			−0.744525	−	0.667594i	$-0.767324\pi$
$229$	−22.5334			−1.48905			−0.744525	+	0.667594i	$0.767324\pi$
$230$		0			0
$231$	0.174485	+	0.146411i	0.0114803	+	0.00963311i
$232$	3.57451	+	1.30102i	0.234678	+	0.0854159i
$233$	−11.5483	+	4.20325i	−0.756557	+	0.275364i	−0.691362	−	0.722508i	$-0.742989\pi$
$233$	−11.5483	+	4.20325i	−0.756557	+	0.275364i	−0.0651947	+	0.997873i	$0.520767\pi$
$234$	−1.30731	+	1.09697i	−0.0854618	+	0.0717109i
$235$		0			0
$236$	0.133317	−	0.230912i	0.00867821	−	0.0150311i
$237$	0.0818093	+	0.463964i	0.00531409	+	0.0301377i
$238$	1.35619	+	7.69134i	0.0879088	+	0.498555i
$239$	3.95320	−	6.84714i	0.255711	−	0.442905i	−0.709377	−	0.704829i	$-0.751024\pi$
$239$	3.95320	−	6.84714i	0.255711	−	0.442905i	0.965088	+	0.261924i	$0.0843570\pi$
$240$		0			0
$241$	−11.6806	+	9.80119i	−0.752414	+	0.631350i	−0.936140	−	0.351627i	$-0.885629\pi$
$241$	−11.6806	+	9.80119i	−0.752414	+	0.631350i	0.183726	+	0.982977i	$0.441184\pi$
$242$	−8.73260	+	3.17841i	−0.561353	+	0.204316i
$243$	−2.84809	−	1.03662i	−0.182705	−	0.0664991i
$244$	−2.49343	−	2.09224i	−0.159626	−	0.133942i
$245$		0			0
$246$	1.26388			0.0805820
$247$	1.82701	+	1.69204i	0.116250	+	0.107662i
$248$	−2.98673			−0.189658
$249$	0.181816	−	1.03113i	0.0115221	−	0.0653451i
$250$		0			0
$251$	11.4134	+	4.15415i	0.720409	+	0.262207i	0.676099	−	0.736810i	$-0.263669\pi$
$251$	11.4134	+	4.15415i	0.720409	+	0.262207i	0.0443097	+	0.999018i	$0.485891\pi$
$252$	−4.33494	+	1.57779i	−0.273076	+	0.0993914i
$253$	5.18273	−	4.34883i	0.325835	−	0.273408i
$254$	−8.30332	−	14.3818i	−0.520996	−	0.902392i
$255$		0			0
$256$	0.173648	+	0.984808i	0.0108530	+	0.0615505i
$257$	0.872967	+	4.95084i	0.0544542	+	0.308825i	0.999854	−	0.0170879i	$-0.00543952\pi$
$257$	0.872967	+	4.95084i	0.0544542	+	0.308825i	−0.945400	+	0.325913i	$0.894328\pi$
$258$	−0.531727	+	0.920978i	−0.0331039	+	0.0573376i
$259$	2.55861	+	4.43164i	0.158984	+	0.275368i
$260$		0			0
$261$	10.6780	−	3.88647i	0.660950	−	0.240566i
$262$	14.2967	+	5.20356i	0.883251	+	0.321477i
$263$	−5.08686	−	4.26839i	−0.313669	−	0.263200i	0.472337	−	0.881418i	$-0.343410\pi$
$263$	−5.08686	−	4.26839i	−0.313669	−	0.263200i	−0.786007	+	0.618218i	$0.787855\pi$
$264$	0.0256124	−	0.145255i	0.00157633	−	0.00893983i
$265$		0			0
$266$	3.07652	+	5.98716i	0.188633	+	0.367096i
$267$	−0.651757			−0.0398869
$268$	1.57745	−	8.94618i	0.0963582	−	0.546475i
$269$	7.49299	+	6.28737i	0.456856	+	0.383348i	0.841973	−	0.539520i	$-0.181394\pi$
$269$	7.49299	+	6.28737i	0.456856	+	0.383348i	−0.385117	+	0.922868i	$0.625839\pi$
$270$		0			0
$271$	1.66984	−	0.607771i	0.101435	−	0.0369195i	−0.290804	−	0.956783i	$-0.593923\pi$
$271$	1.66984	−	0.607771i	0.101435	−	0.0369195i	0.392239	+	0.919863i	$0.371701\pi$
$272$	3.87418	−	3.25082i	0.234906	−	0.197110i
$273$	−0.0497985	−	0.0862536i	−0.00301394	−	0.00522030i
$274$	−5.93792	+	10.2848i	−0.358723	+	0.621326i
$275$		0			0
$276$	−0.101515	−	0.575721i	−0.00611049	−	0.0346543i
$277$	−15.5653	+	26.9600i	−0.935231	+	1.61987i	−0.161010	+	0.986953i	$0.551475\pi$
$277$	−15.5653	+	26.9600i	−0.935231	+	1.61987i	−0.774221	+	0.632915i	$0.781858\pi$
$278$	−0.579849	−	1.00433i	−0.0347770	−	0.0602356i
$279$	−6.83475	+	5.73504i	−0.409186	+	0.343348i
$280$		0			0
$281$	0.167999	+	0.0611467i	0.0100220	+	0.00364771i	0.347026	−	0.937855i	$-0.387191\pi$
$281$	0.167999	+	0.0611467i	0.0100220	+	0.00364771i	−0.337004	+	0.941503i	$0.609414\pi$
$282$	−0.183446	−	0.153929i	−0.0109240	−	0.00916636i
$283$	−0.157929	+	0.895660i	−0.00938791	+	0.0532415i	−0.989142	−	0.146964i	$-0.953050\pi$
$283$	−0.157929	+	0.895660i	−0.00938791	+	0.0532415i	0.979754	+	0.200205i	$0.0641610\pi$
$284$	−16.2430			−0.963845
$285$		0			0
$286$	−0.746390			−0.0441349
$287$	3.00215	−	17.0261i	0.177212	−	1.00502i
$288$	2.28837	+	1.92017i	0.134844	+	0.113147i
$289$	−8.05982	−	2.93353i	−0.474107	−	0.172561i
$290$		0			0
$291$	0.249018	−	0.208951i	0.0145977	−	0.0122489i
$292$	−1.40133	−	2.42717i	−0.0820066	−	0.142040i
$293$	14.9376	−	25.8728i	0.872666	−	1.51150i	0.0134380	−	0.999910i	$-0.495722\pi$
$293$	14.9376	−	25.8728i	0.872666	−	1.51150i	0.859228	−	0.511593i	$-0.170944\pi$
$294$	0.0904752	+	0.513111i	0.00527662	+	0.0299252i
$295$		0			0
$296$	1.65683	−	2.86972i	0.0963014	−	0.166799i
$297$	−0.441548	−	0.764783i	−0.0256212	−	0.0443772i
$298$	−12.3996	+	10.4045i	−0.718289	+	0.602716i
$299$	−2.77992	+	1.01181i	−0.160767	+	0.0585143i
$300$		0			0
$301$	11.1437	+	9.35068i	0.642312	+	0.538964i
$302$	2.00817	−	11.3889i	0.115557	−	0.655359i
$303$	1.15479			0.0663408
$304$	2.36147	−	3.66380i	0.135440	−	0.210133i
$305$		0			0
$306$	2.62342	−	14.8782i	0.149971	−	0.850528i
$307$	17.1837	+	14.4188i	0.980724	+	0.822925i	0.984198	−	0.177069i	$-0.0566616\pi$
$307$	17.1837	+	14.4188i	0.980724	+	0.822925i	−0.00347485	+	0.999994i	$0.501106\pi$
$308$	−1.89593	−	0.690063i	−0.108031	−	0.0393200i
$309$	−0.527942	+	0.192155i	−0.0300336	+	0.0109313i
$310$		0			0
$311$	6.75504	+	11.7001i	0.383043	+	0.663451i	0.991496	−	0.130140i	$-0.0415426\pi$
$311$	6.75504	+	11.7001i	0.383043	+	0.663451i	−0.608452	+	0.793590i	$0.708209\pi$
$312$	−0.0322472	+	0.0558537i	−0.00182564	+	0.00316209i
$313$	4.77485	+	27.0795i	0.269891	+	1.53063i	0.754738	+	0.656027i	$0.227764\pi$
$313$	4.77485	+	27.0795i	0.269891	+	1.53063i	−0.484847	+	0.874599i	$0.661125\pi$
$314$	−2.48950	−	14.1187i	−0.140491	−	0.796762i
$315$		0			0
$316$	−2.08658	−	3.61406i	−0.117379	−	0.203307i
$317$	−21.8404	+	18.3263i	−1.22668	+	1.02931i	−0.228234	+	0.973606i	$0.573295\pi$
$317$	−21.8404	+	18.3263i	−1.22668	+	1.02931i	−0.998447	+	0.0557019i	$0.982260\pi$
$318$	−0.812197	+	0.295616i	−0.0455458	+	0.0165773i
$319$	4.67013	+	1.69979i	0.261477	+	0.0951698i
$320$		0			0
$321$	0.262435	−	1.48835i	0.0146477	−	0.0830714i
$322$	−7.99682			−0.445645
$323$	−22.0182	−	1.07822i	−1.22513	−	0.0599936i
$324$	8.88546			0.493637
$325$		0			0
$326$	−5.73395	−	4.81136i	−0.317574	−	0.266476i
$327$	−1.04845	−	0.381604i	−0.0579793	−	0.0211027i
$328$	−10.5202	+	3.82903i	−0.580880	+	0.211423i
$329$	−2.50937	+	2.10561i	−0.138346	+	0.116086i
$330$		0			0
$331$	−6.19337	+	10.7272i	−0.340418	+	0.589622i	−0.984510	−	0.175326i	$-0.943902\pi$
$331$	−6.19337	+	10.7272i	−0.340418	+	0.589622i	0.644092	+	0.764948i	$0.277235\pi$
$332$	1.61051	+	9.13366i	0.0883882	+	0.501274i
$333$	−1.71890	−	9.74837i	−0.0941952	−	0.534208i
$334$	−2.68945	+	4.65826i	−0.147160	+	0.254889i
$335$		0			0
$336$	−0.133551	+	0.112063i	−0.00728580	+	0.00611351i
$337$	20.5859	−	7.49265i	1.12138	−	0.408150i	0.286227	−	0.958162i	$-0.407599\pi$
$337$	20.5859	−	7.49265i	1.12138	−	0.408150i	0.835157	+	0.550011i	$0.185377\pi$
$338$	−11.9093	−	4.33464i	−0.647782	−	0.235773i
$339$	−1.33155	−	1.11731i	−0.0723200	−	0.0606837i
$340$		0			0
$341$	−3.90219			−0.211315
$342$	−1.63119	−	12.9186i	−0.0882049	−	0.698556i
$343$	17.9371			0.968512
$344$	1.63576	−	9.27688i	0.0881945	−	0.500176i
$345$		0			0
$346$	−6.42789	−	2.33956i	−0.345565	−	0.125775i
$347$	−25.4259	+	9.25427i	−1.36493	+	0.496795i	−0.917576	−	0.397560i	$-0.869857\pi$
$347$	−25.4259	+	9.25427i	−1.36493	+	0.496795i	−0.447357	+	0.894355i	$0.647635\pi$
$348$	0.328967	−	0.276036i	0.0176345	−	0.0147971i
$349$	8.85115	+	15.3306i	0.473791	+	0.820631i	0.999550	−	0.0300032i	$-0.00955175\pi$
$349$	8.85115	+	15.3306i	0.473791	+	0.820631i	−0.525758	+	0.850634i	$0.676218\pi$
$350$		0			0
$351$	0.0670532	+	0.380278i	0.00357903	+	0.0202977i
$352$	0.226873	+	1.28666i	0.0120924	+	0.0685792i
$353$	10.0955	−	17.4859i	0.537329	−	0.930682i	−0.461717	−	0.887027i	$-0.652767\pi$
$353$	10.0955	−	17.4859i	0.537329	−	0.930682i	0.999047	−	0.0436546i	$-0.0139001\pi$
$354$	−0.0150506	−	0.0260684i	−0.000799931	−	0.00138552i
$355$		0			0
$356$	5.42505	−	1.97456i	0.287527	−	0.104651i
$357$	0.828522	+	0.301557i	0.0438501	+	0.0159601i
$358$	19.8148	+	16.6266i	1.04724	+	0.878741i
$359$	4.59095	−	26.0366i	0.242301	−	1.37416i	−0.584377	−	0.811482i	$-0.698661\pi$
$359$	4.59095	−	26.0366i	0.242301	−	1.37416i	0.826678	−	0.562675i	$-0.190228\pi$
$360$		0			0
$361$	−18.4037	+	4.72286i	−0.968613	+	0.248572i
$362$	5.66090			0.297530
$363$	−0.182178	+	1.03318i	−0.00956186	+	0.0542280i
$364$	0.675822	+	0.567082i	0.0354227	+	0.0297232i
$365$		0			0
$366$	−0.345301	+	0.125679i	−0.0180492	+	0.00656936i
$367$	12.8221	−	10.7590i	0.669307	−	0.561615i	−0.243553	−	0.969887i	$-0.578313\pi$
$367$	12.8221	−	10.7590i	0.669307	−	0.561615i	0.912860	+	0.408272i	$0.133869\pi$
$368$	2.58918	+	4.48459i	0.134970	+	0.233776i
$369$	−16.7217	+	28.9628i	−0.870496	+	1.50774i
$370$		0			0
$371$	2.05307	+	11.6435i	0.106590	+	0.604501i
$372$	−0.168591	+	0.292008i	−0.00874103	+	0.0151399i
$373$	0.597506	+	1.03491i	0.0309377	+	0.0535857i	0.881080	−	0.472968i	$-0.156817\pi$
$373$	0.597506	+	1.03491i	0.0309377	+	0.0535857i	−0.850142	+	0.526553i	$0.823484\pi$
$374$	5.06164	−	4.24722i	0.261731	−	0.219619i
$375$		0			0
$376$	1.99330	+	0.725500i	0.102796	+	0.0374148i
$377$	−1.66471	−	1.39686i	−0.0857369	−	0.0719418i
$378$	−0.181255	+	1.02795i	−0.00932277	+	0.0528721i
$379$	8.65379			0.444515			0.222258	−	0.974988i	$-0.428657\pi$
$379$	8.65379			0.444515			0.222258	+	0.974988i	$0.428657\pi$
$380$		0			0
$381$	−1.87478			−0.0960477
$382$	0.659901	−	3.74249i	0.0337635	−	0.191482i
$383$	12.4656	+	10.4599i	0.636964	+	0.534476i	0.903084	−	0.429464i	$-0.141297\pi$
$383$	12.4656	+	10.4599i	0.636964	+	0.534476i	−0.266120	+	0.963940i	$0.585742\pi$
$384$	0.106085	+	0.0386118i	0.00541362	+	0.00197040i
$385$		0			0
$386$	1.49718	−	1.25628i	0.0762043	−	0.0639430i
$387$	−14.0700	−	24.3699i	−0.715216	−	1.23879i
$388$	−1.43973	+	2.49368i	−0.0730910	+	0.126597i
$389$	2.76086	+	15.6576i	0.139981	+	0.793874i	0.971261	+	0.238019i	$0.0764980\pi$
$389$	2.76086	+	15.6576i	0.139981	+	0.793874i	−0.831279	+	0.555855i	$0.812391\pi$
$390$		0			0
$391$	13.0945	−	22.6803i	0.662216	−	1.14699i
$392$	−2.30761	−	3.99689i	−0.116552	−	0.201873i
$393$	1.31574	−	1.10404i	0.0663704	−	0.0556914i
$394$	17.4015	−	6.33361i	0.876673	−	0.319083i
$395$		0			0
$396$	2.98977	+	2.50872i	0.150242	+	0.126068i
$397$	−3.78984	+	21.4933i	−0.190207	+	1.07872i	0.728874	+	0.684648i	$0.240044\pi$
$397$	−3.78984	+	21.4933i	−0.190207	+	1.07872i	−0.919081	+	0.394069i	$0.871067\pi$
$398$	24.2225			1.21417
$399$	0.759014	+	0.0371684i	0.0379982	+	0.00186075i
$400$		0			0
$401$	−3.57252	+	20.2608i	−0.178403	+	1.01177i	0.755739	+	0.654873i	$0.227278\pi$
$401$	−3.57252	+	20.2608i	−0.178403	+	1.01177i	−0.934142	+	0.356902i	$0.883833\pi$
$402$	−0.785612	−	0.659206i	−0.0391827	−	0.0328782i
$403$	1.60338	+	0.583582i	0.0798699	+	0.0290703i
$404$	−9.61213	+	3.49853i	−0.478221	+	0.174058i
$405$		0			0
$406$	−2.93715	−	5.08729i	−0.145768	−	0.252478i
$407$	2.16466	−	3.74931i	0.107298	−	0.185846i
$408$	−0.0991434	−	0.562270i	−0.00490833	−	0.0278365i
$409$	1.48671	+	8.43154i	0.0735130	+	0.416913i	0.999249	+	0.0387431i	$0.0123354\pi$
$409$	1.48671	+	8.43154i	0.0735130	+	0.416913i	−0.925736	+	0.378170i	$0.876553\pi$
$410$		0			0
$411$	0.670351	+	1.16108i	0.0330660	+	0.0572719i
$412$	3.81230	−	3.19890i	0.187818	−	0.157598i
$413$	−0.386925	+	0.140829i	−0.0190393	+	0.00692975i
$414$	14.5362	+	5.29074i	0.714415	+	0.260026i
$415$		0			0
$416$	0.0992028	−	0.562607i	0.00486382	−	0.0275841i
$417$	−0.130922			−0.00641128
$418$	3.08529	−	4.78678i	0.150906	−	0.234129i
$419$	29.2900			1.43091			0.715454	−	0.698660i	$-0.246220\pi$
$419$	29.2900			1.43091			0.715454	+	0.698660i	$0.246220\pi$
$420$		0			0
$421$	−5.82441	−	4.88726i	−0.283864	−	0.238190i	0.489726	−	0.871876i	$-0.337097\pi$
$421$	−5.82441	−	4.88726i	−0.283864	−	0.238190i	−0.773591	+	0.633686i	$0.781541\pi$
$422$	11.3461	+	4.12963i	0.552318	+	0.201027i
$423$	5.95448	−	2.16725i	0.289517	−	0.105376i
$424$	5.86492	−	4.92125i	0.284825	−	0.238997i
$425$		0			0
$426$	−0.916863	+	1.58805i	−0.0444222	+	0.0769414i
$427$	0.872849	+	4.95017i	0.0422401	+	0.239556i
$428$	2.32463	+	13.1837i	0.112365	+	0.637256i
$429$	−0.0421312	+	0.0729733i	−0.00203411	+	0.00352319i
$430$		0			0
$431$	−20.9007	+	17.5378i	−1.00675	+	0.844766i	−0.987906	−	0.155056i	$-0.950444\pi$
$431$	−20.9007	+	17.5378i	−1.00675	+	0.844766i	−0.0188473	+	0.999822i	$0.506000\pi$
$432$	0.635158	−	0.231178i	0.0305590	−	0.0111226i
$433$	26.4150	+	9.61426i	1.26942	+	0.462032i	0.886920	−	0.461923i	$-0.152840\pi$
$433$	26.4150	+	9.61426i	1.26942	+	0.462032i	0.382502	+	0.923955i	$0.375063\pi$
$434$	3.53326	+	2.96476i	0.169602	+	0.142313i
$435$		0			0
$436$	9.88310			0.473315
$437$	5.00213	−	22.0107i	0.239284	−	1.05292i
$438$	−0.316401			−0.0151182
$439$	−0.977251	+	5.54227i	−0.0466416	+	0.264518i	−0.999207	−	0.0398161i	$-0.987323\pi$
$439$	−0.977251	+	5.54227i	−0.0466416	+	0.264518i	0.952565	+	0.304334i	$0.0984339\pi$
$440$		0			0
$441$	−12.9554	−	4.71537i	−0.616922	−	0.224541i
$442$	−2.71497	+	0.988168i	−0.129138	+	0.0470024i
$443$	21.2082	−	17.7958i	1.00763	−	0.845505i	0.0196101	−	0.999808i	$-0.493758\pi$
$443$	21.2082	−	17.7958i	1.00763	−	0.845505i	0.988024	+	0.154303i	$0.0493131\pi$
$444$	−0.187045	−	0.323972i	−0.00887677	−	0.0153750i
$445$		0			0
$446$	−4.41541	−	25.0410i	−0.209076	−	1.18573i
$447$	0.317316	+	1.79959i	0.0150085	+	0.0851175i
$448$	0.772138	−	1.33738i	0.0364801	−	0.0631854i
$449$	4.23719	+	7.33903i	0.199965	+	0.346350i	0.948517	−	0.316726i	$-0.102584\pi$
$449$	4.23719	+	7.33903i	0.199965	+	0.346350i	−0.748552	+	0.663077i	$0.769250\pi$
$450$		0			0
$451$	−13.7447	+	5.00266i	−0.647213	+	0.235566i
$452$	14.4685	+	5.26609i	0.680539	+	0.247696i
$453$	−1.00012	−	0.839202i	−0.0469898	−	0.0394291i
$454$	−2.29310	+	13.0048i	−0.107621	+	0.610348i
$455$		0			0
$456$	−0.224907	−	0.437687i	−0.0105322	−	0.0204966i
$457$	3.63083			0.169843			0.0849215	−	0.996388i	$-0.472936\pi$
$457$	3.63083			0.169843			0.0849215	+	0.996388i	$0.472936\pi$
$458$	3.91289	−	22.1911i	0.182837	−	1.03692i
$459$	−2.61864	−	2.19730i	−0.122227	−	0.102561i
$460$		0			0
$461$	19.6828	−	7.16395i	0.916719	−	0.333658i	0.159787	−	0.987152i	$-0.448919\pi$
$461$	19.6828	−	7.16395i	0.916719	−	0.333658i	0.756932	+	0.653493i	$0.226697\pi$
$462$	−0.174485	+	0.146411i	−0.00811779	+	0.00681164i
$463$	−10.0978	−	17.4900i	−0.469286	−	0.812828i	0.530097	−	0.847937i	$-0.322155\pi$
$463$	−10.0978	−	17.4900i	−0.469286	−	0.812828i	−0.999383	+	0.0351092i	$0.988822\pi$
$464$	−1.90196	+	3.29429i	−0.0882962	+	0.152933i
$465$		0			0
$466$	−2.13405	−	12.1028i	−0.0988578	−	0.560651i
$467$	−1.35695	+	2.35031i	−0.0627922	+	0.108759i	−0.895712	−	0.444634i	$-0.853334\pi$
$467$	−1.35695	+	2.35031i	−0.0627922	+	0.108759i	0.832920	+	0.553393i	$0.186667\pi$
$468$	−0.853288	−	1.47794i	−0.0394433	−	0.0683178i
$469$	−10.7464	+	9.01734i	−0.496225	+	0.416382i
$470$		0			0
$471$	−1.52088	−	0.553556i	−0.0700786	−	0.0255065i
$472$	0.204254	+	0.171389i	0.00940154	+	0.00788883i
$473$	2.13714	−	12.1203i	0.0982658	−	0.557293i
$474$	−0.471121			−0.0216393
$475$		0			0
$476$	−7.80999			−0.357970
$477$	3.97146	−	22.5233i	0.181841	−	1.03127i
$478$	6.05665	+	5.08214i	0.277025	+	0.232452i
$479$	13.6940	+	4.98421i	0.625694	+	0.227734i	0.635356	−	0.772219i	$-0.280853\pi$
$479$	13.6940	+	4.98421i	0.625694	+	0.227734i	−0.00966182	+	0.999953i	$0.503075\pi$
$480$		0			0
$481$	−1.45016	+	1.21683i	−0.0661216	+	0.0554826i
$482$	−7.62398	−	13.2051i	−0.347263	−	0.601476i
$483$	−0.451394	+	0.781837i	−0.0205391	+	0.0355748i
$484$	−1.61372	−	9.15186i	−0.0733509	−	0.415993i
$485$		0			0
$486$	1.51543	−	2.62481i	0.0687415	−	0.119064i
$487$	17.6475	+	30.5664i	0.799685	+	1.38510i	0.919821	+	0.392338i	$0.128334\pi$
$487$	17.6475	+	30.5664i	0.799685	+	1.38510i	−0.120136	+	0.992757i	$0.538333\pi$
$488$	2.49343	−	2.09224i	0.112872	−	0.0947112i
$489$	−0.794061	+	0.289014i	−0.0359087	+	0.0130697i
$490$		0			0
$491$	25.1844	+	21.1322i	1.13655	+	0.953683i	0.999321	−	0.0368558i	$-0.0117342\pi$
$491$	25.1844	+	21.1322i	1.13655	+	0.953683i	0.137234	+	0.990539i	$0.456179\pi$
$492$	−0.219470	+	1.24468i	−0.00989449	+	0.0561144i
$493$	19.2378			0.866429
$494$	−1.98359	+	1.50544i	−0.0892461	+	0.0677329i
$495$		0			0
$496$	0.518641	−	2.94136i	0.0232877	−	0.132071i
$497$	19.2152	+	16.1235i	0.861921	+	0.723237i
$498$	0.983891	+	0.358107i	0.0440892	+	0.0160472i
$499$	−15.3897	+	5.60139i	−0.688937	+	0.250753i	−0.662680	−	0.748903i	$-0.730581\pi$
$499$	−15.3897	+	5.60139i	−0.688937	+	0.250753i	−0.0262571	+	0.999655i	$0.508359\pi$
$500$		0			0
$501$	0.303621	+	0.525886i	0.0135648	+	0.0234949i
$502$	−6.07296	+	10.5187i	−0.271049	+	0.469471i
$503$	4.68146	+	26.5499i	0.208736	+	1.18380i	0.891451	+	0.453117i	$0.149688\pi$
$503$	4.68146	+	26.5499i	0.208736	+	1.18380i	−0.682715	+	0.730685i	$0.739201\pi$
$504$	−0.801065	−	4.54306i	−0.0356823	−	0.202364i
$505$		0			0
$506$	3.38279	+	5.85916i	0.150383	+	0.260471i
$507$	−1.09603	+	0.919680i	−0.0486765	+	0.0408444i
$508$	15.6051	−	5.67980i	0.692366	−	0.252001i
$509$	−27.5004	−	10.0093i	−1.21894	−	0.443656i	−0.349141	−	0.937070i	$-0.613527\pi$
$509$	−27.5004	−	10.0093i	−1.21894	−	0.443656i	−0.869795	+	0.493414i	$0.835749\pi$
$510$		0			0
$511$	−0.751563	+	4.26232i	−0.0332472	+	0.188554i
$512$	−1.00000			−0.0441942
$513$	−2.71599	−	1.14189i	−0.119914	−	0.0504157i
$514$	−5.02721			−0.221741
$515$		0			0
$516$	−0.814652	−	0.683575i	−0.0358631	−	0.0300927i
$517$	2.60426	+	0.947872i	0.114535	+	0.0416874i
$518$	−4.80861	+	1.75019i	−0.211278	+	0.0768989i
$519$	−0.591567	+	0.496384i	−0.0259669	+	0.0217888i
$520$		0			0
$521$	−10.3667	+	17.9557i	−0.454174	+	0.786652i	−0.998640	−	0.0521303i	$-0.983399\pi$
$521$	−10.3667	+	17.9557i	−0.454174	+	0.786652i	0.544466	+	0.838783i	$0.316732\pi$
$522$	1.97321	+	11.1906i	0.0863651	+	0.489801i
$523$	2.93923	+	16.6692i	0.128524	+	0.728893i	0.979152	+	0.203127i	$0.0651104\pi$
$523$	2.93923	+	16.6692i	0.128524	+	0.728893i	−0.850629	+	0.525767i	$0.823779\pi$
$524$	−7.60709	+	13.1759i	−0.332317	+	0.575591i
$525$		0			0
$526$	5.08686	−	4.26839i	0.221798	−	0.186110i
$527$	−14.1941	+	5.16623i	−0.618304	+	0.225044i
$528$	0.138601	+	0.0504466i	0.00603183	+	0.00219541i
$529$	2.92279	+	2.45251i	0.127078	+	0.106631i
$530$		0			0
$531$	0.796505			0.0345654
$532$	−6.43043	+	1.99012i	−0.278794	+	0.0862827i
$533$	6.39575			0.277030
$534$	0.113176	−	0.641855i	0.00489762	−	0.0277758i
$535$		0			0
$536$	8.53634	+	3.10697i	0.368714	+	0.134201i
$537$	2.74403	−	0.998745i	0.118414	−	0.0430990i
$538$	−7.49299	+	6.28737i	−0.323046	+	0.271068i
$539$	−3.01490	−	5.22197i	−0.129861	−	0.224926i
$540$		0			0
$541$	0.541156	+	3.06905i	0.0232661	+	0.131949i	0.994228	−	0.107284i	$-0.0342153\pi$
$541$	0.541156	+	3.06905i	0.0232661	+	0.131949i	−0.970962	+	0.239232i	$0.923104\pi$
$542$	0.308574	+	1.75001i	0.0132544	+	0.0751693i
$543$	0.319539	−	0.553457i	0.0137127	−	0.0237511i
$544$	2.52869	+	4.37982i	0.108417	+	0.187783i
$545$		0			0
$546$	0.0935906	−	0.0340642i	0.00400531	−	0.00145781i
$547$	39.9731	+	14.5490i	1.70912	+	0.622070i	0.996812	−	0.0797916i	$-0.0254255\pi$
$547$	39.9731	+	14.5490i	1.70912	+	0.622070i	0.712313	+	0.701862i	$0.247648\pi$
$548$	−9.09742	−	7.63364i	−0.388622	−	0.326093i
$549$	1.68844	−	9.57564i	0.0720610	−	0.408678i
$550$		0			0
$551$	15.8397	−	4.90213i	0.674792	−	0.208838i
$552$	0.584602			0.0248823
$553$	−1.11908	+	6.34660i	−0.0475880	+	0.269885i
$554$	−23.8475	−	20.0104i	−1.01318	−	0.850161i
$555$		0			0
$556$	1.08976	−	0.396640i	0.0462161	−	0.0168213i
$557$	15.2692	−	12.8123i	0.646975	−	0.542877i	−0.259176	−	0.965830i	$-0.583451\pi$
$557$	15.2692	−	12.8123i	0.646975	−	0.542877i	0.906151	+	0.422953i	$0.139007\pi$
$558$	−4.46107	−	7.72679i	−0.188852	−	0.327101i
$559$	−2.69075	+	4.66052i	−0.113807	+	0.197119i
$560$		0			0
$561$	−0.129532	−	0.734610i	−0.00546883	−	0.0310153i
$562$	−0.0893905	+	0.154829i	−0.00377071	+	0.00653107i
$563$	12.5834	+	21.7950i	0.530326	+	0.918552i	0.999374	+	0.0353789i	$0.0112638\pi$
$563$	12.5834	+	21.7950i	0.530326	+	0.918552i	−0.469048	+	0.883173i	$0.655403\pi$
$564$	0.183446	−	0.153929i	0.00772446	−	0.00648159i
$565$		0			0
$566$	−0.854629	−	0.311059i	−0.0359227	−	0.0130748i
$567$	−10.5114	−	8.82008i	−0.441436	−	0.370408i
$568$	2.82057	−	15.9962i	0.118348	−	0.671187i
$569$	12.7385			0.534025			0.267012	−	0.963693i	$-0.413964\pi$
$569$	12.7385			0.534025			0.267012	+	0.963693i	$0.413964\pi$
$570$		0			0
$571$	20.5911			0.861713			0.430856	−	0.902421i	$-0.358212\pi$
$571$	20.5911			0.861713			0.430856	+	0.902421i	$0.358212\pi$
$572$	0.129609	−	0.735050i	0.00541923	−	0.0307340i
$573$	−0.328648	−	0.275768i	−0.0137295	−	0.0115204i
$574$	16.2461	+	5.91309i	0.678098	+	0.246808i
$575$		0			0
$576$	−2.28837	+	1.92017i	−0.0953488	+	0.0800071i
$577$	−18.8879	−	32.7148i	−0.786313	−	1.36193i	−0.928212	−	0.372052i	$-0.878654\pi$
$577$	−18.8879	−	32.7148i	−0.786313	−	1.36193i	0.141899	−	0.989881i	$-0.454679\pi$
$578$	4.28854	−	7.42797i	0.178380	−	0.308963i
$579$	−0.0383140	−	0.217290i	−0.00159228	−	0.00903024i
$580$		0			0
$581$	7.16124	−	12.4036i	0.297098	−	0.514589i
$582$	0.162535	+	0.281519i	0.00673730	+	0.0116693i
$583$	7.66256	−	6.42965i	0.317351	−	0.266289i
$584$	2.63364	−	0.958565i	0.108981	−	0.0396657i
$585$		0			0
$586$	22.8858	+	19.2035i	0.945403	+	0.793288i
$587$	6.83556	−	38.7664i	0.282134	−	1.60006i	−0.433215	−	0.901291i	$-0.642621\pi$
$587$	6.83556	−	38.7664i	0.282134	−	1.60006i	0.715348	−	0.698768i	$-0.246268\pi$
$588$	−0.521026			−0.0214868
$589$	−10.3704	+	7.87056i	−0.427305	+	0.324301i
$590$		0			0
$591$	0.363026	−	2.05882i	0.0149329	−	0.0846887i
$592$	2.53841	+	2.12998i	0.104328	+	0.0875417i
$593$	0.756583	+	0.275374i	0.0310691	+	0.0113082i	0.357508	−	0.933910i	$-0.383626\pi$
$593$	0.756583	+	0.275374i	0.0310691	+	0.0113082i	−0.326439	+	0.945218i	$0.605849\pi$
$594$	0.829838	−	0.302036i	0.0340487	−	0.0123927i
$595$		0			0
$596$	−8.09326	−	14.0179i	−0.331513	−	0.574197i
$597$	1.36728	−	2.36820i	0.0559591	−	0.0969240i
$598$	−0.513708	−	2.91338i	−0.0210071	−	0.119137i
$599$	3.95984	+	22.4574i	0.161795	+	0.917582i	0.952308	+	0.305138i	$0.0987026\pi$
$599$	3.95984	+	22.4574i	0.161795	+	0.917582i	−0.790514	+	0.612444i	$0.790186\pi$
$600$		0			0
$601$	20.3517	+	35.2502i	0.830163	+	1.43788i	0.897909	+	0.440181i	$0.145086\pi$
$601$	20.3517	+	35.2502i	0.830163	+	1.43788i	−0.0677462	+	0.997703i	$0.521581\pi$
$602$	−11.1437	+	9.35068i	−0.454183	+	0.381105i
$603$	25.5002	−	9.28133i	1.03845	−	0.377965i
$604$	10.8672	+	3.95533i	0.442179	+	0.160940i
$605$		0			0
$606$	−0.200527	+	1.13724i	−0.00814584	+	0.0461973i
$607$	46.9728			1.90657			0.953283	−	0.302080i	$-0.0976809\pi$
$607$	46.9728			1.90657			0.953283	+	0.302080i	$0.0976809\pi$
$608$	3.19807	+	2.96181i	0.129699	+	0.120117i
$609$	−0.663168			−0.0268729
$610$		0			0
$611$	−0.928311	−	0.778945i	−0.0375554	−	0.0315128i
$612$	14.1966	+	5.16713i	0.573863	+	0.208869i
$613$	−23.5041	+	8.55480i	−0.949322	+	0.345525i	−0.769840	−	0.638236i	$-0.779664\pi$
$613$	−23.5041	+	8.55480i	−0.949322	+	0.345525i	−0.179482	+	0.983761i	$0.557442\pi$
$614$	−17.1837	+	14.4188i	−0.693476	+	0.581896i
$615$		0			0
$616$	1.00880	−	1.74730i	0.0406459	−	0.0704008i
$617$	2.69182	+	15.2660i	0.108368	+	0.614588i	0.989821	+	0.142316i	$0.0454549\pi$
$617$	2.69182	+	15.2660i	0.108368	+	0.614588i	−0.881453	+	0.472272i	$0.843434\pi$
$618$	−0.0975598	−	0.553289i	−0.00392443	−	0.0222566i
$619$	11.2933	−	19.5606i	0.453916	−	0.786205i	−0.544709	−	0.838625i	$-0.683360\pi$
$619$	11.2933	−	19.5606i	0.453916	−	0.786205i	0.998625	+	0.0524196i	$0.0166933\pi$
$620$		0			0
$621$	2.68128	−	2.24986i	0.107596	−	0.0902838i
$622$	−12.6953	+	4.62072i	−0.509036	+	0.185274i
$623$	−8.37777	−	3.04926i	−0.335648	−	0.122166i
$624$	−0.0494055	−	0.0414561i	−0.00197780	−	0.00165957i
$625$		0			0
$626$	−27.4973			−1.09901
$627$	−0.293842	−	0.571841i	−0.0117349	−	0.0228371i
$628$	14.3365			0.572087
$629$	2.91007	−	16.5039i	0.116032	−	0.658052i
$630$		0			0
$631$	−28.9589	−	10.5402i	−1.15284	−	0.419598i	−0.306303	−	0.951934i	$-0.599092\pi$
$631$	−28.9589	−	10.5402i	−1.15284	−	0.419598i	−0.846533	+	0.532336i	$0.821314\pi$
$632$	3.92149	−	1.42730i	0.155988	−	0.0567751i
$633$	1.04419	−	0.876183i	0.0415030	−	0.0348252i
$634$	−14.2553	−	24.6910i	−0.566152	−	0.980604i
$635$		0			0
$636$	−0.150088	−	0.851191i	−0.00595138	−	0.0337519i
$637$	0.457842	+	2.59655i	0.0181403	+	0.102879i
$638$	−2.48492	+	4.30401i	−0.0983790	+	0.170397i
$639$	−24.2610	−	42.0213i	−0.959750	−	1.66234i
$640$		0			0
$641$	−42.0764	+	15.3146i	−1.66192	+	0.604889i	−0.990663	−	0.136336i	$-0.956467\pi$
$641$	−42.0764	+	15.3146i	−1.66192	+	0.604889i	−0.671257	+	0.741225i	$0.734245\pi$
$642$	1.42016	+	0.516897i	0.0560494	+	0.0204003i
$643$	−8.34048	−	6.99849i	−0.328916	−	0.275994i	0.463342	−	0.886180i	$-0.346650\pi$
$643$	−8.34048	−	6.99849i	−0.328916	−	0.275994i	−0.792258	+	0.610186i	$0.791095\pi$
$644$	1.38863	−	7.87533i	0.0547198	−	0.310332i
$645$		0			0
$646$	4.88526	−	21.4965i	0.192208	−	0.845768i
$647$	−40.9224			−1.60882			−0.804412	−	0.594072i	$-0.797519\pi$
$647$	−40.9224			−1.60882			−0.804412	+	0.594072i	$0.797519\pi$
$648$	−1.54294	+	8.75047i	−0.0606126	+	0.343751i
$649$	0.266859	+	0.223921i	0.0104751	+	0.00878969i
$650$		0			0
$651$	0.489300	−	0.178091i	0.0191772	−	0.00697992i
$652$	5.73395	−	4.81136i	0.224559	−	0.188427i
$653$	1.90571	+	3.30078i	0.0745762	+	0.129170i	0.900902	−	0.434023i	$-0.142906\pi$
$653$	1.90571	+	3.30078i	0.0745762	+	0.129170i	−0.826326	+	0.563193i	$0.809573\pi$
$654$	0.557867	−	0.966255i	0.0218143	−	0.0377836i
$655$		0			0
$656$	−1.94405	−	11.0253i	−0.0759025	−	0.430464i
$657$	4.18613	−	7.25058i	0.163316	−	0.282872i
$658$	−1.63788	−	2.83688i	−0.0638511	−	0.110593i
$659$	3.17564	−	2.66468i	0.123705	−	0.103801i	−0.578836	−	0.815444i	$-0.696493\pi$
$659$	3.17564	−	2.66468i	0.123705	−	0.103801i	0.702542	+	0.711643i	$0.252049\pi$
$660$		0			0
$661$	21.2808	+	7.74559i	0.827728	+	0.301268i	0.720926	−	0.693012i	$-0.243717\pi$
$661$	21.2808	+	7.74559i	0.827728	+	0.301268i	0.106802	+	0.994280i	$0.465939\pi$
$662$	−9.48879	−	7.96204i	−0.368792	−	0.309454i
$663$	−0.0566392	+	0.321217i	−0.00219968	+	0.0124750i
$664$	−9.27456			−0.359923
$665$		0			0
$666$	9.89876			0.383569
$667$	−3.42053	+	19.3988i	−0.132443	+	0.751124i
$668$	−4.12047	−	3.45749i	−0.159426	−	0.133774i
$669$	−2.69746	−	0.981794i	−0.104290	−	0.0379583i
$670$		0			0
$671$	3.25769	−	2.73353i	0.125762	−	0.105527i
$672$	−0.0871692	−	0.150981i	−0.00336262	−	0.00582424i
$673$	−11.5322	+	19.9743i	−0.444533	+	0.769955i	−0.998020	−	0.0629039i	$-0.979964\pi$
$673$	−11.5322	+	19.9743i	−0.444533	+	0.769955i	0.553486	+	0.832858i	$0.313297\pi$
$674$	3.80412	+	21.5742i	0.146529	+	0.831008i
$675$		0			0
$676$	6.33682	−	10.9757i	0.243724	−	0.422142i
$677$	−7.56037	−	13.0949i	−0.290569	−	0.503280i	0.683376	−	0.730067i	$-0.260511\pi$
$677$	−7.56037	−	13.0949i	−0.290569	−	0.503280i	−0.973944	+	0.226787i	$0.927178\pi$
$678$	1.33155	−	1.11731i	0.0511380	−	0.0429099i
$679$	4.17850	−	1.52085i	0.160356	−	0.0583649i
$680$		0			0
$681$	1.14202	+	0.958273i	0.0437625	+	0.0367211i
$682$	0.677608	−	3.84291i	0.0259470	−	0.147153i
$683$	2.26803			0.0867838			0.0433919	−	0.999058i	$-0.486184\pi$
$683$	2.26803			0.0867838			0.0433919	+	0.999058i	$0.486184\pi$
$684$	13.0056	+	0.636873i	0.497280	+	0.0243514i
$685$		0			0
$686$	−3.11474	+	17.6646i	−0.118921	+	0.674437i
$687$	−1.94872	−	1.63517i	−0.0743482	−	0.0623856i
$688$	8.85190	+	3.22183i	0.337475	+	0.122831i
$689$	−4.11005	+	1.49594i	−0.156580	+	0.0569906i
$690$		0			0
$691$	−16.6481	−	28.8353i	−0.633323	−	1.09695i	−0.986868	−	0.161530i	$-0.948357\pi$
$691$	−16.6481	−	28.8353i	−0.633323	−	1.09695i	0.353545	−	0.935418i	$-0.384976\pi$
$692$	3.42021	−	5.92397i	0.130017	−	0.225196i
$693$	−1.04660	−	5.93555i	−0.0397569	−	0.225473i
$694$	−4.69851	−	26.6466i	−0.178353	−	1.01149i
$695$		0			0
$696$	0.214718	+	0.371903i	0.00813887	+	0.0140969i
$697$	−43.3728	+	36.3941i	−1.64286	+	1.37852i
$698$	−16.6347	+	6.05455i	−0.629634	+	0.229168i
$699$	−1.30373	−	0.474519i	−0.0493116	−	0.0179479i
$700$		0			0
$701$	6.34263	−	35.9709i	0.239558	−	1.35860i	−0.593241	−	0.805025i	$-0.702152\pi$
$701$	6.34263	−	35.9709i	0.239558	−	1.35860i	0.832799	−	0.553576i	$-0.186737\pi$
$702$	−0.386144			−0.0145741
$703$	−1.80943	−	14.3301i	−0.0682439	−	0.540471i
$704$	−1.30651			−0.0492409
$705$		0			0
$706$	15.4672	+	12.9785i	0.582116	+	0.488453i
$707$	14.8438	+	5.40270i	0.558258	+	0.203189i
$708$	0.0282859	−	0.0102952i	0.00106305	−	0.000386918i
$709$	31.3347	−	26.2929i	1.17680	−	0.987451i	0.176804	−	0.984246i	$-0.443424\pi$
$709$	31.3347	−	26.2929i	1.17680	−	0.987451i	0.999995	−	0.00320540i	$-0.00102031\pi$
$710$		0			0
$711$	6.23314	−	10.7961i	0.233761	−	0.404886i
$712$	1.00251	+	5.68551i	0.0375706	+	0.213073i
$713$	−2.68571	−	15.2314i	−0.100581	−	0.570421i
$714$	−0.440848	+	0.763570i	−0.0164983	+	0.0285759i
$715$		0			0
$716$	−19.8148	+	16.6266i	−0.740513	+	0.621364i
$717$	0.838750	−	0.305280i	0.0313237	−	0.0114009i
$718$	24.8438	+	9.04240i	0.927162	+	0.337459i
$719$	6.19986	+	5.20230i	0.231216	+	0.194013i	0.751033	−	0.660264i	$-0.229556\pi$
$719$	6.19986	+	5.20230i	0.231216	+	0.194013i	−0.519818	+	0.854277i	$0.674000\pi$
$720$		0			0
$721$	−7.68525			−0.286214
$722$	−1.45535	−	18.9442i	−0.0541626	−	0.705029i
$723$	−1.72139			−0.0640192
$724$	−0.983005	+	5.57490i	−0.0365331	+	0.207190i
$725$		0			0
$726$	−0.985851	−	0.358821i	−0.0365884	−	0.0133171i
$727$	−40.3129	+	14.6727i	−1.49512	+	0.544180i	−0.954793	−	0.297273i	$-0.903923\pi$
$727$	−40.3129	+	14.6727i	−1.49512	+	0.544180i	−0.540330	+	0.841453i	$0.681701\pi$
$728$	−0.675822	+	0.567082i	−0.0250476	+	0.0210175i
$729$	13.1571	+	22.7888i	0.487300	+	0.844029i
$730$		0			0
$731$	−8.27268	−	46.9167i	−0.305976	−	1.73528i
$732$	−0.0638090	−	0.361879i	−0.00235845	−	0.0133754i
$733$	−16.3017	+	28.2353i	−0.602116	+	1.04290i	0.390384	+	0.920652i	$0.372342\pi$
$733$	−16.3017	+	28.2353i	−0.602116	+	1.04290i	−0.992500	+	0.122244i	$0.960991\pi$
$734$	8.36901	+	14.4956i	0.308906	+	0.535041i
$735$		0			0
$736$	−4.86607	+	1.77110i	−0.179366	+	0.0652838i
$737$	11.1528	+	4.05929i	0.410819	+	0.149526i
$738$	−25.6191	−	21.4970i	−0.943052	−	0.791315i
$739$	4.84735	−	27.4907i	0.178313	−	1.01126i	−0.755938	−	0.654643i	$-0.772819\pi$
$739$	4.84735	−	27.4907i	0.178313	−	1.01126i	0.934251	−	0.356617i	$-0.116070\pi$
$740$		0			0
$741$	0.0352172	+	0.278910i	0.00129374	+	0.0102460i
$742$	−11.8231			−0.434041
$743$	7.49138	−	42.4857i	0.274832	−	1.55865i	−0.464663	−	0.885488i	$-0.653825\pi$
$743$	7.49138	−	42.4857i	0.274832	−	1.55865i	0.739495	−	0.673162i	$-0.235064\pi$
$744$	−0.258296	−	0.216736i	−0.00946960	−	0.00794594i
$745$		0			0
$746$	−1.12294	+	0.408718i	−0.0411139	+	0.0149642i
$747$	−21.2236	+	17.8087i	−0.776532	+	0.651587i
$748$	3.30375	+	5.72227i	0.120797	+	0.209227i
$749$	10.3366	−	17.9036i	0.377693	−	0.654183i
$750$		0			0
$751$	5.16332	+	29.2826i	0.188412	+	1.06854i	0.921492	+	0.388397i	$0.126971\pi$
$751$	5.16332	+	29.2826i	0.188412	+	1.06854i	−0.733080	+	0.680142i	$0.761918\pi$
$752$	−1.06061	+	1.83703i	−0.0386765	+	0.0669897i
$753$	0.685596	+	1.18749i	0.0249845	+	0.0432744i
$754$	1.66471	−	1.39686i	0.0606251	−	0.0508705i
$755$		0			0
$756$	−0.980859	−	0.357003i	−0.0356735	−	0.0129841i
$757$	0.00914056	+	0.00766984i	0.000332219	+	0.000278765i	0.642954	−	0.765905i	$-0.277709\pi$
$757$	0.00914056	+	0.00766984i	0.000332219	+	0.000278765i	−0.642621	+	0.766184i	$0.722153\pi$
$758$	−1.50272	+	8.52232i	−0.0545811	+	0.309545i
$759$	0.763787			0.0277237
$760$		0			0
$761$	−47.1667			−1.70979			−0.854896	−	0.518800i	$-0.826379\pi$
$761$	−47.1667			−1.70979			−0.854896	+	0.518800i	$0.826379\pi$
$762$	0.325552	−	1.84629i	0.0117935	−	0.0668842i
$763$	−11.6915	−	9.81037i	−0.423263	−	0.355159i
$764$	3.57104	+	1.29975i	0.129196	+	0.0470234i
$765$		0			0
$766$	−12.4656	+	10.4599i	−0.450401	+	0.377932i
$767$	−0.0761622	−	0.131917i	−0.00275006	−	0.00476324i
$768$	−0.0564466	+	0.0977684i	−0.00203684	+	0.00352791i
$769$	4.60798	+	26.1332i	0.166168	+	0.942387i	0.947852	+	0.318711i	$0.103250\pi$
$769$	4.60798	+	26.1332i	0.166168	+	0.942387i	−0.781684	+	0.623675i	$0.785639\pi$
$770$		0			0
$771$	−0.283769	+	0.491503i	−0.0102197	+	0.0177010i
$772$	0.977213	+	1.69258i	0.0351707	+	0.0609174i
$773$	−30.3191	+	25.4408i	−1.09050	+	0.915041i	−0.996750	−	0.0805550i	$-0.974331\pi$
$773$	−30.3191	+	25.4408i	−1.09050	+	0.915041i	−0.0937527	+	0.995596i	$0.529886\pi$
$774$	26.4429	−	9.62442i	0.950469	−	0.345943i
$775$		0			0
$776$	−2.20579	−	1.85088i	−0.0791831	−	0.0664425i
$777$	−0.100316	+	0.568922i	−0.00359883	+	0.0204100i
$778$	−15.8992			−0.570013
$779$	−26.4375	+	41.0175i	−0.947223	+	1.46961i
$780$		0			0
$781$	3.68510	−	20.8992i	0.131863	−	0.747833i
$782$	20.0619	+	16.8339i	0.717412	+	0.601980i
$783$	2.41609	+	0.879383i	0.0863439	+	0.0314266i
$784$	4.33688	−	1.57850i	0.154889	−	0.0563748i
$785$		0			0
$786$	0.858789	+	1.48747i	0.0306320	+	0.0530562i
$787$	7.90292	−	13.6883i	0.281709	−	0.487934i	−0.690097	−	0.723717i	$-0.742432\pi$
$787$	7.90292	−	13.6883i	0.281709	−	0.487934i	0.971806	+	0.235783i	$0.0757655\pi$
$788$	3.21566	+	18.2369i	0.114553	+	0.649663i
$789$	−0.130177	−	0.738270i	−0.00463442	−	0.0262831i
$790$		0			0
$791$	−11.8886	−	20.5917i	−0.422711	−	0.732157i
$792$	−2.98977	+	2.50872i	−0.106237	+	0.0891434i
$793$	−1.74736	+	0.635988i	−0.0620507	+	0.0225846i
$794$	−20.5086	−	7.46453i	−0.727824	−	0.264906i
$795$		0			0
$796$	−4.20620	+	23.8545i	−0.149085	+	0.845502i
$797$	8.79105			0.311395			0.155697	−	0.987805i	$-0.450238\pi$
$797$	8.79105			0.311395			0.155697	+	0.987805i	$0.450238\pi$
$798$	−0.168405	+	0.741028i	−0.00596147	+	0.0262321i
$799$	10.7278			0.379523
$800$		0			0
$801$	13.2113	+	11.0856i	0.466797	+	0.391689i
$802$	−19.3326	−	7.03649i	−0.682658	−	0.248467i
$803$	3.44087	−	1.25237i	0.121426	−	0.0441953i
$804$	0.785612	−	0.659206i	0.0277064	−	0.0232484i
$805$		0			0
$806$	−0.853139	+	1.47768i	−0.0300506	+	0.0520491i
$807$	0.191752	+	1.08748i	0.00674999	+	0.0382811i
$808$	−1.77625	−	10.0736i	−0.0624883	−	0.354389i
$809$	−6.21165	+	10.7589i	−0.218390	+	0.378262i	−0.954316	−	0.298800i	$-0.903414\pi$
$809$	−6.21165	+	10.7589i	−0.218390	+	0.378262i	0.735926	+	0.677062i	$0.236747\pi$
$810$		0			0
$811$	5.72281	−	4.80201i	0.200955	−	0.168621i	−0.536757	−	0.843737i	$-0.680351\pi$
$811$	5.72281	−	4.80201i	0.200955	−	0.168621i	0.737712	+	0.675116i	$0.235906\pi$
$812$	5.52003	−	2.00913i	0.193715	−	0.0705066i
$813$	0.188513	+	0.0686133i	0.00661145	+	0.00240637i
$814$	3.31646	+	2.78284i	0.116242	+	0.0975384i
$815$		0			0
$816$	0.570944			0.0199870
$817$	−18.7666	−	36.5213i	−0.656559	−	1.27772i
$818$	−8.56161			−0.299350
$819$	−0.457637	+	2.59539i	−0.0159911	+	0.0906902i
$820$		0			0
$821$	10.0532	+	3.65908i	0.350860	+	0.127703i	0.511437	−	0.859321i	$-0.329113\pi$
$821$	10.0532	+	3.65908i	0.350860	+	0.127703i	−0.160577	+	0.987023i	$0.551336\pi$
$822$	−1.25985	+	0.458547i	−0.0439422	+	0.0159937i
$823$	−1.31967	+	1.10734i	−0.0460010	+	0.0385994i	−0.665498	−	0.746399i	$-0.731781\pi$
$823$	−1.31967	+	1.10734i	−0.0460010	+	0.0385994i	0.619497	+	0.784999i	$0.287336\pi$
$824$	2.48830	+	4.30986i	0.0866841	+	0.150141i
$825$		0			0
$826$	−0.0715009	−	0.405502i	−0.00248783	−	0.0141092i
$827$	2.65866	+	15.0780i	0.0924507	+	0.524314i	0.995499	+	0.0947744i	$0.0302130\pi$
$827$	2.65866	+	15.0780i	0.0924507	+	0.524314i	−0.903048	+	0.429539i	$0.858676\pi$
$828$	−7.73454	+	13.3966i	−0.268794	+	0.465565i
$829$	−14.5352	−	25.1757i	−0.504829	−	0.874389i	−0.999984	−	0.00558497i	$-0.998222\pi$
$829$	−14.5352	−	25.1757i	−0.504829	−	0.874389i	0.495155	−	0.868804i	$-0.335111\pi$
$830$		0			0
$831$	−3.30250	+	1.20201i	−0.114562	+	0.0416973i
$832$	0.536833	+	0.195391i	0.0186113	+	0.00677397i
$833$	−17.8801	−	15.0032i	−0.619510	−	0.519831i
$834$	0.0227344	−	0.128933i	0.000787227	−	0.00446458i
$835$		0			0
$836$	4.17831	+	3.86963i	0.144510	+	0.133834i
$837$	−2.01879			−0.0697797
$838$	−5.08615	+	28.8450i	−0.175698	+	0.996433i
$839$	−17.7060	−	14.8571i	−0.611280	−	0.512925i	0.283769	−	0.958893i	$-0.408415\pi$
$839$	−17.7060	−	14.8571i	−0.611280	−	0.512925i	−0.895049	+	0.445968i	$0.852860\pi$
$840$		0			0
$841$	13.6540	−	4.96963i	0.470826	−	0.171367i
$842$	5.82441	−	4.88726i	0.200722	−	0.168426i
$843$	0.0100916	+	0.0174791i	0.000347573	+	0.000602014i
$844$	−6.03712	+	10.4566i	−0.207806	+	0.359931i
$845$		0			0
$846$	1.10034	+	6.24036i	0.0378306	+	0.214548i
$847$	−7.17551	+	12.4283i	−0.246553	+	0.427043i
$848$	3.82805	+	6.63038i	0.131456	+	0.227688i
$849$	−0.0786527	+	0.0659975i	−0.00269935	+	0.00226503i
$850$		0			0
$851$	16.1245	+	5.86884i	0.552741	+	0.201181i
$852$	−1.40472	−	1.17870i	−0.0481248	−	0.0403815i
$853$	3.20750	−	18.1906i	0.109823	−	0.622835i	−0.879361	−	0.476155i	$-0.842030\pi$
$853$	3.20750	−	18.1906i	0.109823	−	0.622835i	0.989184	−	0.146680i	$-0.0468588\pi$
$854$	−5.02654			−0.172005
$855$		0			0
$856$	−13.3870			−0.457559
$857$	5.04158	−	28.5922i	0.172217	−	0.976691i	−0.769090	−	0.639140i	$-0.779290\pi$
$857$	5.04158	−	28.5922i	0.172217	−	0.976691i	0.941307	−	0.337551i	$-0.109599\pi$
$858$	−0.0645487	−	0.0541628i	−0.00220366	−	0.00184909i
$859$	−30.8358	−	11.2233i	−1.05210	−	0.382935i	−0.242648	−	0.970114i	$-0.578016\pi$
$859$	−30.8358	−	11.2233i	−1.05210	−	0.382935i	−0.809457	+	0.587179i	$0.800238\pi$
$860$		0			0
$861$	1.49515	−	1.25458i	0.0509545	−	0.0427559i
$862$	−13.6420	−	23.6286i	−0.464648	−	0.804794i
$863$	−27.5310	+	47.6851i	−0.937167	+	1.62322i	−0.166443	+	0.986051i	$0.553228\pi$
$863$	−27.5310	+	47.6851i	−0.937167	+	1.62322i	−0.770724	+	0.637170i	$0.780105\pi$
$864$	0.117372	+	0.665652i	0.00399309	+	0.0226459i
$865$		0			0
$866$	−14.0551	+	24.3442i	−0.477612	+	0.827248i
$867$	−0.484147	−	0.838567i	−0.0164425	−	0.0284792i
$868$	−3.53326	+	2.96476i	−0.119927	+	0.100630i
$869$	5.12345	−	1.86478i	0.173801	−	0.0632585i
$870$		0			0
$871$	−3.97552	−	3.33585i	−0.134705	−	0.113031i
$872$	−1.71618	+	9.73295i	−0.0581173	+	0.329599i
$873$	−8.60165			−0.291122
$874$	20.8077	+	8.74825i	0.703832	+	0.295914i
$875$		0			0
$876$	0.0549425	−	0.311594i	0.00185633	−	0.0105278i
$877$	31.9817	+	26.8358i	1.07995	+	0.906182i	0.995916	−	0.0902817i	$-0.0287767\pi$
$877$	31.9817	+	26.8358i	1.07995	+	0.906182i	0.0840289	+	0.996463i	$0.473221\pi$
$878$	−5.28837	−	1.92481i	−0.178474	−	0.0649591i
$879$	3.16932	−	1.15354i	0.106898	−	0.0389078i
$880$		0			0
$881$	9.79330	+	16.9625i	0.329945	+	0.571481i	0.982501	−	0.186260i	$-0.0596366\pi$
$881$	9.79330	+	16.9625i	0.329945	+	0.571481i	−0.652556	+	0.757741i	$0.726303\pi$
$882$	6.89341	−	11.9397i	0.232113	−	0.402032i
$883$	−5.09807	−	28.9126i	−0.171564	−	0.972986i	−0.942036	−	0.335512i	$-0.891091\pi$
$883$	−5.09807	−	28.9126i	−0.171564	−	0.972986i	0.770472	−	0.637474i	$-0.220021\pi$
$884$	−0.501706	−	2.84532i	−0.0168742	−	0.0956983i
$885$		0			0
$886$	13.8427	+	23.9762i	0.465054	+	0.805498i
$887$	−29.7620	+	24.9733i	−0.999311	+	0.838521i	−0.986889	−	0.161402i	$-0.948399\pi$
$887$	−29.7620	+	24.9733i	−0.999311	+	0.838521i	−0.0124219	+	0.999923i	$0.503954\pi$
$888$	0.351530	−	0.127946i	0.0117966	−	0.00429360i
$889$	−24.0986	−	8.77119i	−0.808242	−	0.294176i
$890$		0			0
$891$	−2.01587	+	11.4326i	−0.0675341	+	0.383005i
$892$	25.4273			0.851370
$893$	8.83285	−	2.73363i	0.295580	−	0.0914776i
$894$	−1.82735			−0.0611157
$895$		0			0
$896$	1.18298	+	0.992642i	0.0395207	+	0.0331618i
$897$	−0.313834	−	0.114226i	−0.0104786	−	0.00381390i
$898$	−7.96332	+	2.89841i	−0.265739	+	0.0967212i
$899$	8.70324	−	7.30289i	0.290269	−	0.243565i
$900$		0			0
$901$	19.3599	−	33.5323i	0.644972	−	1.11712i
$902$	−2.53992	−	14.4046i	−0.0845701	−	0.479621i
$903$	0.285176	+	1.61732i	0.00949008	+	0.0538209i
$904$	−7.69851	+	13.3342i	−0.256049	+	0.443489i
$905$		0			0
$906$	1.00012	−	0.839202i	0.0332268	−	0.0278806i
$907$	−37.1516	+	13.5221i	−1.23360	+	0.448993i	−0.874828	−	0.484433i	$-0.839026\pi$
$907$	−37.1516	+	13.5221i	−1.23360	+	0.448993i	−0.358770	+	0.933426i	$0.616804\pi$
$908$	−12.4091	−	4.51654i	−0.411810	−	0.149886i
$909$	−23.4078	−	19.6415i	−0.776387	−	0.651466i
$910$		0			0
$911$	23.6770			0.784453			0.392227	−	0.919869i	$-0.371705\pi$
$911$	23.6770			0.784453			0.392227	+	0.919869i	$0.371705\pi$
$912$	0.470092	−	0.145486i	0.0155663	−	0.00481754i
$913$	−12.1173			−0.401024
$914$	−0.630487	+	3.57567i	−0.0208546	+	0.118273i
$915$		0			0
$916$	21.1745	+	7.70688i	0.699625	+	0.254643i
$917$	22.0780	−	8.03573i	0.729080	−	0.265363i
$918$	2.61864	−	2.19730i	0.0864279	−	0.0725216i
$919$	20.0206	+	34.6767i	0.660419	+	1.14388i	0.980506	+	0.196490i	$0.0629545\pi$
$919$	20.0206	+	34.6767i	0.660419	+	1.14388i	−0.320087	+	0.947388i	$0.603712\pi$
$920$		0			0
$921$	0.439744	+	2.49391i	0.0144901	+	0.0821772i
$922$	3.63723	+	20.6278i	0.119786	+	0.679340i
$923$	−4.63970	+	8.03620i	−0.152718	+	0.264515i
$924$	−0.113887	−	0.197258i	−0.00374661	−	0.00648933i
$925$		0			0
$926$	18.9777	−	6.90733i	0.623647	−	0.226989i
$927$	13.9698	+	5.08460i	0.458829	+	0.167000i
$928$	−2.91397	−	2.44511i	−0.0956557	−	0.0802646i
$929$	1.53316	−	8.69500i	0.0503014	−	0.285274i	−0.949273	−	0.314454i	$-0.898179\pi$
$929$	1.53316	−	8.69500i	0.0503014	−	0.285274i	0.999574	+	0.0291803i	$0.00928970\pi$
$930$		0			0
$931$	−18.5449	−	7.79687i	−0.607783	−	0.255532i
$932$	12.2895			0.402556
$933$	−0.264848	+	1.50203i	−0.00867073	+	0.0491741i
$934$	−2.07897	−	1.74446i	−0.0680259	−	0.0570805i
$935$		0			0
$936$	1.60366	−	0.583684i	0.0524172	−	0.0190783i
$937$	41.9098	−	35.1665i	1.36914	−	1.14884i	0.396094	−	0.918210i	$-0.370366\pi$
$937$	41.9098	−	35.1665i	1.36914	−	1.14884i	0.973041	−	0.230631i	$-0.0740789\pi$
$938$	−7.01425	−	12.1490i	−0.229023	−	0.396680i
$939$	−1.55213	+	2.68836i	−0.0506518	+	0.0877315i
$940$		0			0
$941$	−6.00049	−	34.0305i	−0.195610	−	1.10936i	−0.911547	−	0.411196i	$-0.865111\pi$
$941$	−6.00049	−	34.0305i	−0.195610	−	1.10936i	0.715937	−	0.698165i	$-0.246000\pi$
$942$	0.809245	−	1.40165i	0.0263666	−	0.0456683i
$943$	−28.9868	−	50.2066i	−0.943940	−	1.63495i
$944$	−0.204254	+	0.171389i	−0.00664789	+	0.00557825i
$945$		0			0
$946$	11.5651	+	4.20934i	0.376013	+	0.136858i
$947$	−31.1977	−	26.1780i	−1.01379	−	0.850670i	−0.0249541	−	0.999689i	$-0.507944\pi$
$947$	−31.1977	−	26.1780i	−1.01379	−	0.850670i	−0.988834	+	0.149019i	$0.952388\pi$
$948$	0.0818093	−	0.463964i	0.00265704	−	0.0150688i
$949$	−1.60112			−0.0519745
$950$		0			0
$951$	−3.21866			−0.104372
$952$	1.35619	−	7.69134i	0.0439544	−	0.249278i
$953$	−12.6748	−	10.6354i	−0.410576	−	0.344514i	0.413988	−	0.910282i	$-0.364135\pi$
$953$	−12.6748	−	10.6354i	−0.410576	−	0.344514i	−0.824565	+	0.565768i	$0.808580\pi$
$954$	21.4915	+	7.82225i	0.695812	+	0.253255i
$955$		0			0
$956$	−6.05665	+	5.08214i	−0.195886	+	0.164368i
$957$	0.280531	+	0.485894i	0.00906828	+	0.0157067i
$958$	−7.28642	+	12.6205i	−0.235414	+	0.407748i
$959$	3.18463	+	18.0610i	0.102837	+	0.583219i
$960$		0			0
$961$	11.0397	−	19.1213i	0.356120	−	0.616818i
$962$	−0.946525	−	1.63943i	−0.0305172	−	0.0528573i
$963$	−30.6345	+	25.7054i	−0.987183	+	0.828345i
$964$	14.3284	−	5.21511i	0.461486	−	0.167967i
$965$		0			0
$966$	−0.691575	−	0.580300i	−0.0222511	−	0.0186709i
$967$	5.39597	−	30.6021i	0.173523	−	0.984096i	−0.766312	−	0.642468i	$-0.777911\pi$
$967$	5.39597	−	30.6021i	0.173523	−	0.984096i	0.939835	−	0.341628i	$-0.110978\pi$
$968$	9.29304			0.298690
$969$	−1.82592	−	1.69103i	−0.0586570	−	0.0543236i
$970$		0			0
$971$	0.647741	−	3.67352i	0.0207870	−	0.117889i	−0.972649	−	0.232281i	$-0.925381\pi$
$971$	0.647741	−	3.67352i	0.0207870	−	0.117889i	0.993436	+	0.114392i	$0.0364921\pi$
$972$	2.32178	+	1.94821i	0.0744712	+	0.0624887i
$973$	−1.68289	−	0.612522i	−0.0539510	−	0.0196365i
$974$	−33.1665	+	12.0716i	−1.06272	+	0.386799i
$975$		0			0
$976$	1.62747	+	2.81887i	0.0520942	+	0.0902297i
$977$	−23.6192	+	40.9097i	−0.755646	+	1.30882i	0.189406	+	0.981899i	$0.439344\pi$
$977$	−23.6192	+	40.9097i	−0.755646	+	1.30882i	−0.945052	+	0.326919i	$0.893990\pi$
$978$	−0.146736	−	0.832184i	−0.00469212	−	0.0266103i
$979$	1.30979	+	7.42816i	0.0418609	+	0.237405i
$980$		0			0
$981$	14.7617	+	25.5680i	0.471304	+	0.816322i
$982$	−25.1844	+	21.1322i	−0.803666	+	0.674356i
$983$	27.9743	−	10.1818i	0.892240	−	0.324749i	0.145101	−	0.989417i	$-0.453649\pi$
$983$	27.9743	−	10.1818i	0.892240	−	0.324749i	0.747139	+	0.664668i	$0.231427\pi$
$984$	−1.18766	−	0.432272i	−0.0378611	−	0.0137803i
$985$		0			0
$986$	−3.34062	+	18.9456i	−0.106387	+	0.603350i
$987$	−0.369810			−0.0117712
$988$	−1.13812	−	2.21487i	−0.0362084	−	0.0704645i
$989$	48.7801			1.55112
$990$		0			0
$991$	18.1298	+	15.2127i	0.575912	+	0.483247i	0.883602	−	0.468239i	$-0.155112\pi$
$991$	18.1298	+	15.2127i	0.575912	+	0.483247i	−0.307690	+	0.951487i	$0.599556\pi$
$992$	2.80661	+	1.02152i	0.0891100	+	0.0324334i
$993$	−1.31405	+	0.478274i	−0.0417000	+	0.0151776i
$994$	−19.2152	+	16.1235i	−0.609470	+	0.511406i
$995$		0			0
$996$	−0.523517	+	0.906759i	−0.0165883	+	0.0287317i
$997$	3.51128	+	19.9135i	0.111203	+	0.630666i	0.988560	+	0.150827i	$0.0481938\pi$
$997$	3.51128	+	19.9135i	0.111203	+	0.630666i	−0.877357	+	0.479839i	$0.840695\pi$
$998$	−2.84390	−	16.1286i	−0.0900221	−	0.510541i
$999$	1.11989	−	1.93970i	0.0354316	−	0.0613694i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	950.2.l.l.701.3		30
5.2	odd	4		190.2.p.a.169.3	yes	60
5.3	odd	4		190.2.p.a.169.8	yes	60
5.4	even	2		950.2.l.m.701.3		30
19.9	even	9	inner	950.2.l.l.351.3		30
95.9	even	18		950.2.l.m.351.3		30
95.28	odd	36		190.2.p.a.9.3	✓	60
95.47	odd	36		190.2.p.a.9.8	yes	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
190.2.p.a.9.3	✓	60	95.28	odd	36
190.2.p.a.9.8	yes	60	95.47	odd	36
190.2.p.a.169.3	yes	60	5.2	odd	4
190.2.p.a.169.8	yes	60	5.3	odd	4
950.2.l.l.351.3		30	19.9	even	9	inner
950.2.l.l.701.3		30	1.1	even	1	trivial
950.2.l.m.351.3		30	95.9	even	18
950.2.l.m.701.3		30	5.4	even	2

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)

\(f(q)\)	\(=\)	\(q+(-0.173648 + 0.984808i) q^{2} +(0.0864812 + 0.0725664i) q^{3} +(-0.939693 - 0.342020i) q^{4} +(-0.0864812 + 0.0725664i) q^{6} +(0.772138 + 1.33738i) q^{7} +(0.500000 - 0.866025i) q^{8} +(-0.518731 - 2.94187i) q^{9} +O(q^{10})\)	\(q+(-0.173648 + 0.984808i) q^{2} +(0.0864812 + 0.0725664i) q^{3} +(-0.939693 - 0.342020i) q^{4} +(-0.0864812 + 0.0725664i) q^{6} +(0.772138 + 1.33738i) q^{7} +(0.500000 - 0.866025i) q^{8} +(-0.518731 - 2.94187i) q^{9} +(0.653254 - 1.13147i) q^{11} +(-0.0564466 - 0.0977684i) q^{12} +(-0.437630 + 0.367216i) q^{13} +(-1.45115 + 0.528174i) q^{14} +(0.766044 + 0.642788i) q^{16} +(0.878205 - 4.98055i) q^{17} +2.98726 q^{18} +(-0.546051 - 4.32456i) q^{19} +(-0.0302735 + 0.171690i) q^{21} +(1.00084 + 0.839807i) q^{22} +(4.86607 + 1.77110i) q^{23} +(0.106085 - 0.0386118i) q^{24} +(-0.285643 - 0.494748i) q^{26} +(0.337960 - 0.585364i) q^{27} +(-0.268161 - 1.52082i) q^{28} +(0.660543 + 3.74612i) q^{29} +(-1.49337 - 2.58659i) q^{31} +(-0.766044 + 0.642788i) q^{32} +(0.138601 - 0.0504466i) q^{33} +(4.75238 + 1.72973i) q^{34} +(-0.518731 + 2.94187i) q^{36} +3.31366 q^{37} +(4.35368 + 0.213197i) q^{38} -0.0644943 q^{39} +(-8.57613 - 7.19623i) q^{41} +(-0.163824 - 0.0596272i) q^{42} +(8.85190 - 3.22183i) q^{43} +(-1.00084 + 0.839807i) q^{44} +(-2.58918 + 4.48459i) q^{46} +(0.368346 + 2.08900i) q^{47} +(0.0196037 + 0.111178i) q^{48} +(2.30761 - 3.99689i) q^{49} +(0.437368 - 0.366996i) q^{51} +(0.536833 - 0.195391i) q^{52} +(7.19438 + 2.61854i) q^{53} +(0.517785 + 0.434473i) q^{54} +1.54428 q^{56} +(0.266595 - 0.413618i) q^{57} -3.80391 q^{58} +(-0.0463006 + 0.262584i) q^{59} +(3.05865 + 1.11326i) q^{61} +(2.80661 - 1.02152i) q^{62} +(3.53388 - 2.96527i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(0.0256124 + 0.145255i) q^{66} +(1.57745 + 8.94618i) q^{67} +(-2.52869 + 4.37982i) q^{68} +(0.292301 + 0.506280i) q^{69} +(15.2634 - 5.55544i) q^{71} +(-2.80710 - 1.02170i) q^{72} +(2.14696 + 1.80151i) q^{73} +(-0.575412 + 3.26332i) q^{74} +(-0.965967 + 4.25052i) q^{76} +2.01761 q^{77} +(0.0111993 - 0.0635145i) q^{78} +(3.19682 + 2.68245i) q^{79} +(-8.34960 + 3.03901i) q^{81} +(8.57613 - 7.19623i) q^{82} +(-4.63728 - 8.03200i) q^{83} +(0.0871692 - 0.150981i) q^{84} +(1.63576 + 9.27688i) q^{86} +(-0.214718 + 0.371903i) q^{87} +(-0.653254 - 1.13147i) q^{88} +(-4.42254 + 3.71095i) q^{89} +(-0.829019 - 0.301738i) q^{91} +(-3.96686 - 3.32859i) q^{92} +(0.0585510 - 0.332059i) q^{93} -2.12122 q^{94} -0.112893 q^{96} +(0.500011 - 2.83571i) q^{97} +(3.53546 + 2.96660i) q^{98} +(-3.66750 - 1.33486i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q - 12 q^{7} + 15 q^{8}+O(q^{10}) \) 30 * q - 12 * q^7 + 15 * q^8	\( 30 q - 12 q^{7} + 15 q^{8} + 6 q^{11} + 6 q^{14} - 30 q^{18} + 24 q^{19} + 24 q^{21} + 3 q^{22} + 3 q^{23} + 3 q^{26} - 18 q^{27} + 3 q^{28} + 12 q^{29} - 30 q^{33} + 24 q^{37} - 12 q^{38} - 24 q^{39} - 3 q^{41} + 12 q^{42} + 6 q^{43} - 3 q^{44} + 48 q^{47} + 15 q^{49} - 90 q^{51} - 18 q^{53} + 18 q^{54} - 24 q^{56} - 42 q^{57} + 36 q^{58} - 18 q^{59} - 60 q^{61} - 24 q^{62} - 21 q^{63} - 15 q^{64} - 78 q^{66} - 30 q^{67} - 12 q^{68} + 24 q^{69} + 30 q^{73} - 9 q^{74} - 3 q^{76} + 78 q^{77} - 6 q^{79} + 60 q^{81} + 3 q^{82} - 42 q^{83} - 6 q^{84} + 12 q^{86} - 54 q^{87} - 6 q^{88} - 30 q^{89} - 6 q^{91} - 6 q^{92} + 72 q^{93} - 78 q^{94} - 42 q^{97} + 6 q^{98} - 99 q^{99}+O(q^{100}) \) 30 * q - 12 * q^7 + 15 * q^8 + 6 * q^11 + 6 * q^14 - 30 * q^18 + 24 * q^19 + 24 * q^21 + 3 * q^22 + 3 * q^23 + 3 * q^26 - 18 * q^27 + 3 * q^28 + 12 * q^29 - 30 * q^33 + 24 * q^37 - 12 * q^38 - 24 * q^39 - 3 * q^41 + 12 * q^42 + 6 * q^43 - 3 * q^44 + 48 * q^47 + 15 * q^49 - 90 * q^51 - 18 * q^53 + 18 * q^54 - 24 * q^56 - 42 * q^57 + 36 * q^58 - 18 * q^59 - 60 * q^61 - 24 * q^62 - 21 * q^63 - 15 * q^64 - 78 * q^66 - 30 * q^67 - 12 * q^68 + 24 * q^69 + 30 * q^73 - 9 * q^74 - 3 * q^76 + 78 * q^77 - 6 * q^79 + 60 * q^81 + 3 * q^82 - 42 * q^83 - 6 * q^84 + 12 * q^86 - 54 * q^87 - 6 * q^88 - 30 * q^89 - 6 * q^91 - 6 * q^92 + 72 * q^93 - 78 * q^94 - 42 * q^97 + 6 * q^98 - 99 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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