LMFDB - Embedded newform 725.2.q.e.51.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [725,2,Mod(51,725)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(725, base_ring=CyclotomicField(14))

chi = DirichletCharacter(H, H._module([0, 13]))

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

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

chi := DirichletCharacter("725.51");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 725 = 5^{2} \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	725.q (of order $14$, 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:	$5.78915414654$
Analytic rank:	$0$
Dimension:	$60$
Relative dimension:	$10$ over $\Q(\zeta_{14})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{14}]$

Embedding invariants

Embedding label			51.8
Character	$\chi$	$=$	725.51
Dual form			725.2.q.e.526.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.68193 - 0.383889i) q^{2} +(-0.800342 + 1.66193i) q^{3} +(0.879573 - 0.423580i) q^{4} +(-0.708122 + 3.10248i) q^{6} +(0.672793 + 0.324000i) q^{7} +(-1.38083 + 1.10118i) q^{8} +(-0.250983 - 0.314723i) q^{9} +(0.472780 + 0.377030i) q^{11} +1.80079i q^{12} +(-2.13560 + 2.67795i) q^{13} +(1.25597 + 0.286667i) q^{14} +(-3.11710 + 3.90872i) q^{16} +0.196346i q^{17} +(-0.542955 - 0.432992i) q^{18} +(0.231001 + 0.479679i) q^{19} +(-1.07693 + 0.858822i) q^{21} +(0.939920 + 0.452642i) q^{22} +(-0.730756 + 3.20165i) q^{23} +(-0.724938 - 3.17616i) q^{24} +(-2.56388 + 5.32395i) q^{26} +(-4.67113 + 1.06616i) q^{27} +0.729011 q^{28} +(5.35102 - 0.605448i) q^{29} +(-0.869026 + 0.198350i) q^{31} +(-2.20961 + 4.58831i) q^{32} +(-1.00498 + 0.483974i) q^{33} +(0.0753752 + 0.330240i) q^{34} +(-0.354069 - 0.170511i) q^{36} +(-1.95534 + 1.55933i) q^{37} +(0.572672 + 0.718107i) q^{38} +(-2.74135 - 5.69248i) q^{39} -0.0771574i q^{41} +(-1.48162 + 1.85790i) q^{42} +(6.49672 + 1.48283i) q^{43} +(0.575547 + 0.131365i) q^{44} +5.66548i q^{46} +(2.05180 + 1.63625i) q^{47} +(-4.00126 - 8.30869i) q^{48} +(-4.01675 - 5.03685i) q^{49} +(-0.326313 - 0.157144i) q^{51} +(-0.744085 + 3.26005i) q^{52} +(0.701218 + 3.07224i) q^{53} +(-7.44723 + 3.58640i) q^{54} +(-1.28580 + 0.293474i) q^{56} -0.982072 q^{57} +(8.76761 - 3.07252i) q^{58} +2.17115 q^{59} +(3.88421 - 8.06565i) q^{61} +(-1.38550 + 0.667219i) q^{62} +(-0.0668896 - 0.293062i) q^{63} +(0.269951 - 1.18273i) q^{64} +(-1.50451 + 1.19981i) q^{66} +(3.82647 + 4.79824i) q^{67} +(0.0831684 + 0.172701i) q^{68} +(-4.73605 - 3.77688i) q^{69} +(7.63953 - 9.57966i) q^{71} +(0.693132 + 0.158203i) q^{72} +(14.5498 + 3.32090i) q^{73} +(-2.69013 + 3.37332i) q^{74} +(0.406365 + 0.324066i) q^{76} +(0.195926 + 0.406844i) q^{77} +(-6.79604 - 8.52196i) q^{78} +(-3.13538 + 2.50038i) q^{79} +(2.23536 - 9.79373i) q^{81} +(-0.0296199 - 0.129773i) q^{82} +(-6.73633 + 3.24405i) q^{83} +(-0.583458 + 1.21156i) q^{84} +11.4963 q^{86} +(-3.27644 + 9.37757i) q^{87} -1.06801 q^{88} +(13.2952 - 3.03454i) q^{89} +(-2.30447 + 1.10977i) q^{91} +(0.713403 + 3.12562i) q^{92} +(0.365875 - 1.60300i) q^{93} +(4.07912 + 1.96440i) q^{94} +(-5.85698 - 7.34442i) q^{96} +(-5.91536 - 12.2834i) q^{97} +(-8.68948 - 6.92963i) q^{98} -0.243423i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 60 q + 12 q^{4} - 16 q^{6} + 4 q^{7} + 21 q^{8} + 10 q^{9} + 14 q^{11} - 4 q^{13} + 10 q^{16} - 35 q^{22} + 37 q^{23} + 48 q^{24} - 21 q^{27} - 44 q^{28} - 4 q^{29} + 14 q^{31} - 98 q^{32} + 41 q^{33} + 10 q^{34}+ \cdots - 91 q^{98}+O(q^{100}) $ 60 * q + 12 * q^4 - 16 * q^6 + 4 * q^7 + 21 * q^8 + 10 * q^9 + 14 * q^11 - 4 * q^13 + 10 * q^16 - 35 * q^22 + 37 * q^23 + 48 * q^24 - 21 * q^27 - 44 * q^28 - 4 * q^29 + 14 * q^31 - 98 * q^32 + 41 * q^33 + 10 * q^34 + 32 * q^36 - 7 * q^37 + 14 * q^38 + 56 * q^39 + 45 * q^42 - 63 * q^44 + 42 * q^47 + 21 * q^48 - 72 * q^49 - 32 * q^51 + 80 * q^52 + 20 * q^53 - 65 * q^54 - 63 * q^56 + 28 * q^57 + 2 * q^58 - 16 * q^59 - 28 * q^61 + 70 * q^62 - 42 * q^63 + 37 * q^64 - 140 * q^66 + 24 * q^67 + 42 * q^68 - 84 * q^69 + 9 * q^71 + 105 * q^72 - 14 * q^73 - 85 * q^74 + 70 * q^76 - 21 * q^77 - 102 * q^78 + 56 * q^79 - 72 * q^81 - 36 * q^82 - 6 * q^83 - 84 * q^84 + 86 * q^86 - 5 * q^87 - 102 * q^88 + 14 * q^89 - 60 * q^91 - 91 * q^92 + 62 * q^93 - 44 * q^94 + 25 * q^96 - 14 * q^97 - 91 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/725\mathbb{Z}\right)^\times$.

$n$	$176$	$552$
$\chi(n)$	$e\left(\frac{13}{14}\right)$	$1$

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 $

$2$	1.68193	−	0.383889i	1.18930	−	0.271451i	0.418316	−	0.908302i	$-0.362621\pi$
$2$	1.68193	−	0.383889i	1.18930	−	0.271451i	0.770987	+	0.636851i	$0.219763\pi$
$3$	−0.800342	+	1.66193i	−0.462077	+	0.959514i	0.531574	+	0.847012i	$0.321601\pi$
$3$	−0.800342	+	1.66193i	−0.462077	+	0.959514i	−0.993652	+	0.112502i	$0.964114\pi$
$4$	0.879573	−	0.423580i	0.439787	−	0.211790i
$5$		0			0
$5$		0			0
$6$	−0.708122	+	3.10248i	−0.289089	+	1.26658i
$7$	0.672793	+	0.324000i	0.254292	+	0.122461i	0.556688	−	0.830722i	$-0.312072\pi$
$7$	0.672793	+	0.324000i	0.254292	+	0.122461i	−0.302396	+	0.953183i	$0.597786\pi$
$8$	−1.38083	+	1.10118i	−0.488198	+	0.389325i
$9$	−0.250983	−	0.314723i	−0.0836611	−	0.104908i
$10$		0			0
$11$	0.472780	+	0.377030i	0.142549	+	0.113679i	0.692168	−	0.721737i	$-0.256656\pi$
$11$	0.472780	+	0.377030i	0.142549	+	0.113679i	−0.549619	+	0.835415i	$0.685227\pi$
$12$			1.80079i			0.519845i
$13$	−2.13560	+	2.67795i	−0.592308	+	0.742730i	−0.984157	−	0.177299i	$-0.943264\pi$
$13$	−2.13560	+	2.67795i	−0.592308	+	0.742730i	0.391849	+	0.920029i	$0.371835\pi$
$14$	1.25597	+	0.286667i	0.335672	+	0.0766149i
$15$		0			0
$16$	−3.11710	+	3.90872i	−0.779274	+	0.977179i
$17$			0.196346i			0.0476210i	0.999716	+	0.0238105i	$0.00757983\pi$
$17$			0.196346i			0.0476210i	−0.999716	+	0.0238105i	$0.992420\pi$
$18$	−0.542955	−	0.432992i	−0.127976	−	0.102057i
$19$	0.231001	+	0.479679i	0.0529954	+	0.110046i	0.925785	−	0.378051i	$-0.123406\pi$
$19$	0.231001	+	0.479679i	0.0529954	+	0.110046i	−0.872789	+	0.488097i	$0.837691\pi$
$20$		0			0
$21$	−1.07693	+	0.858822i	−0.235005	+	0.187410i
$22$	0.939920	+	0.452642i	0.200392	+	0.0965035i
$23$	−0.730756	+	3.20165i	−0.152373	+	0.667590i	0.839818	+	0.542867i	$0.182661\pi$
$23$	−0.730756	+	3.20165i	−0.152373	+	0.667590i	−0.992192	+	0.124723i	$0.960196\pi$
$24$	−0.724938	−	3.17616i	−0.147977	−	0.648331i
$25$		0			0
$26$	−2.56388	+	5.32395i	−0.502819	+	1.04411i
$27$	−4.67113	+	1.06616i	−0.898960	+	0.205182i
$28$	0.729011			0.137770
$29$	5.35102	−	0.605448i	0.993660	−	0.112429i
$29$	5.35102	−	0.605448i	0.993660	−	0.112429i
$30$		0			0
$31$	−0.869026	+	0.198350i	−0.156082	+	0.0356246i	−0.299848	−	0.953987i	$-0.596936\pi$
$31$	−0.869026	+	0.198350i	−0.156082	+	0.0356246i	0.143766	+	0.989612i	$0.454079\pi$
$32$	−2.20961	+	4.58831i	−0.390608	+	0.811106i
$33$	−1.00498	+	0.483974i	−0.174945	+	0.0842490i
$34$	0.0753752	+	0.330240i	0.0129267	+	0.0566358i
$35$		0			0
$36$	−0.354069	−	0.170511i	−0.0590115	−	0.0284184i
$37$	−1.95534	+	1.55933i	−0.321456	+	0.256352i	−0.770900	−	0.636956i	$-0.780193\pi$
$37$	−1.95534	+	1.55933i	−0.321456	+	0.256352i	0.449445	+	0.893308i	$0.351622\pi$
$38$	0.572672	+	0.718107i	0.0928996	+	0.116492i
$39$	−2.74135	−	5.69248i	−0.438968	−	0.911526i
$40$		0			0
$41$		−	0.0771574i		−	0.0120500i	−0.999982	−	0.00602498i	$-0.998082\pi$
$41$		−	0.0771574i		−	0.0120500i	0.999982	−	0.00602498i	$-0.00191782\pi$
$42$	−1.48162	+	1.85790i	−0.228620	+	0.286680i
$43$	6.49672	+	1.48283i	0.990740	+	0.226130i	0.687026	−	0.726633i	$-0.258916\pi$
$43$	6.49672	+	1.48283i	0.990740	+	0.226130i	0.303714	+	0.952763i	$0.401773\pi$
$44$	0.575547	+	0.131365i	0.0867670	+	0.0198040i
$45$		0			0
$46$			5.66548i			0.835329i
$47$	2.05180	+	1.63625i	0.299286	+	0.238672i	0.761606	−	0.648041i	$-0.224411\pi$
$47$	2.05180	+	1.63625i	0.299286	+	0.238672i	−0.462320	+	0.886713i	$0.652983\pi$
$48$	−4.00126	−	8.30869i	−0.577532	−	1.19926i
$49$	−4.01675	−	5.03685i	−0.573822	−	0.719550i
$50$		0			0
$51$	−0.326313	−	0.157144i	−0.0456930	−	0.0220046i
$52$	−0.744085	+	3.26005i	−0.103186	+	0.452088i
$53$	0.701218	+	3.07224i	0.0963197	+	0.422004i	0.999981	−	0.00624467i	$-0.00198775\pi$
$53$	0.701218	+	3.07224i	0.0963197	+	0.422004i	−0.903661	+	0.428249i	$0.859131\pi$
$54$	−7.44723	+	3.58640i	−1.01344	+	0.488047i
$55$		0			0
$56$	−1.28580	+	0.293474i	−0.171822	+	0.0392172i
$57$	−0.982072			−0.130079
$58$	8.76761	−	3.07252i	1.15124	−	0.403441i
$59$	2.17115			0.282660			0.141330	−	0.989963i	$-0.454862\pi$
$59$	2.17115			0.282660			0.141330	+	0.989963i	$0.454862\pi$
$60$		0			0
$61$	3.88421	−	8.06565i	0.497323	−	1.03270i	−0.489666	−	0.871910i	$-0.662881\pi$
$61$	3.88421	−	8.06565i	0.497323	−	1.03270i	0.986988	−	0.160791i	$-0.0514045\pi$
$62$	−1.38550	+	0.667219i	−0.175958	+	0.0847369i
$63$	−0.0668896	−	0.293062i	−0.00842729	−	0.0369224i
$64$	0.269951	−	1.18273i	0.0337439	−	0.147842i
$65$		0			0
$66$	−1.50451	+	1.19981i	−0.185193	+	0.147686i
$67$	3.82647	+	4.79824i	0.467478	+	0.586198i	0.958551	−	0.284920i	$-0.0919669\pi$
$67$	3.82647	+	4.79824i	0.467478	+	0.586198i	−0.491074	+	0.871118i	$0.663395\pi$
$68$	0.0831684	+	0.172701i	0.0100857	+	0.0209431i
$69$	−4.73605	−	3.77688i	−0.570154	−	0.454683i
$70$		0			0
$71$	7.63953	−	9.57966i	0.906645	−	1.13690i	−0.0834518	−	0.996512i	$-0.526594\pi$
$71$	7.63953	−	9.57966i	0.906645	−	1.13690i	0.990097	−	0.140385i	$-0.0448341\pi$
$72$	0.693132	+	0.158203i	0.0816864	+	0.0186444i
$73$	14.5498	+	3.32090i	1.70293	+	0.388682i	0.959848	−	0.280521i	$-0.0905071\pi$
$73$	14.5498	+	3.32090i	1.70293	+	0.388682i	0.743080	+	0.669203i	$0.233364\pi$
$74$	−2.69013	+	3.37332i	−0.312721	+	0.392140i
$75$		0			0
$76$	0.406365	+	0.324066i	0.0466133	+	0.0371729i
$77$	0.195926	+	0.406844i	0.0223278	+	0.0463642i
$78$	−6.79604	−	8.52196i	−0.769500	−	0.964922i
$79$	−3.13538	+	2.50038i	−0.352758	+	0.281315i	−0.783796	−	0.621019i	$-0.786719\pi$
$79$	−3.13538	+	2.50038i	−0.352758	+	0.281315i	0.431038	+	0.902334i	$0.358148\pi$
$80$		0			0
$81$	2.23536	−	9.79373i	0.248373	−	1.08819i
$82$	−0.0296199	−	0.129773i	−0.00327097	−	0.0143310i
$83$	−6.73633	+	3.24405i	−0.739408	+	0.356080i	−0.765377	−	0.643582i	$-0.777447\pi$
$83$	−6.73633	+	3.24405i	−0.739408	+	0.356080i	0.0259684	+	0.999663i	$0.491733\pi$
$84$	−0.583458	+	1.21156i	−0.0636605	+	0.132192i
$85$		0			0
$86$	11.4963			1.23967
$87$	−3.27644	+	9.37757i	−0.351271	+	1.00538i
$88$	−1.06801			−0.113850
$89$	13.2952	−	3.03454i	1.40929	−	0.321661i	0.550861	−	0.834597i	$-0.314299\pi$
$89$	13.2952	−	3.03454i	1.40929	−	0.321661i	0.858427	+	0.512936i	$0.171442\pi$
$90$		0			0
$91$	−2.30447	+	1.10977i	−0.241574	+	0.116336i
$92$	0.713403	+	3.12562i	0.0743774	+	0.325868i
$93$	0.365875	−	1.60300i	0.0379395	−	0.166224i
$94$	4.07912	+	1.96440i	0.420729	+	0.202612i
$95$		0			0
$96$	−5.85698	−	7.34442i	−0.597776	−	0.749587i
$97$	−5.91536	−	12.2834i	−0.600614	−	1.24719i	−0.950596	−	0.310431i	$-0.899527\pi$
$97$	−5.91536	−	12.2834i	−0.600614	−	1.24719i	0.349982	−	0.936756i	$-0.386188\pi$
$98$	−8.68948	−	6.92963i	−0.877770	−	0.699998i
$99$		−	0.243423i		−	0.0244649i
$100$		0			0
$101$	−3.16345	−	0.722036i	−0.314775	−	0.0718453i	0.0622148	−	0.998063i	$-0.480184\pi$
$101$	−3.16345	−	0.722036i	−0.314775	−	0.0718453i	−0.376990	+	0.926217i	$0.623041\pi$
$102$	−0.609161	−	0.139037i	−0.0603159	−	0.0137667i
$103$	6.52732	−	8.18501i	0.643156	−	0.806493i	−0.348237	−	0.937406i	$-0.613220\pi$
$103$	6.52732	−	8.18501i	0.643156	−	0.806493i	0.991394	+	0.130914i	$0.0417911\pi$
$104$		−	6.04947i		−	0.593199i
$105$		0			0
$106$	2.35880	+	4.89809i	0.229107	+	0.475745i
$107$	−3.95527	−	4.95975i	−0.382370	−	0.479477i	0.552983	−	0.833193i	$-0.313490\pi$
$107$	−3.95527	−	4.95975i	−0.382370	−	0.479477i	−0.935353	+	0.353715i	$0.884918\pi$
$108$	−3.65700	+	2.91636i	−0.351895	+	0.280627i
$109$	13.2656	+	6.38838i	1.27062	+	0.611896i	0.942962	−	0.332902i	$-0.108028\pi$
$109$	13.2656	+	6.38838i	1.27062	+	0.611896i	0.327654	+	0.944798i	$0.393742\pi$
$110$		0			0
$111$	−1.02655	−	4.49763i	−0.0974362	−	0.426896i
$112$	−3.36359	+	1.61982i	−0.317829	+	0.153058i
$113$	−6.90734	+	14.3432i	−0.649788	+	1.34930i	0.272261	+	0.962223i	$0.412229\pi$
$113$	−6.90734	+	14.3432i	−0.649788	+	1.34930i	−0.922048	+	0.387074i	$0.873486\pi$
$114$	−1.65177	+	0.377007i	−0.154703	+	0.0353099i
$115$		0			0
$116$	4.45016	−	2.79912i	0.413187	−	0.259892i
$117$	1.37881			0.127471
$118$	3.65173	−	0.833483i	0.336169	−	0.0767283i
$119$	−0.0636162	+	0.132100i	−0.00583169	+	0.0121096i
$120$		0			0
$121$	−2.36636	−	10.3677i	−0.215124	−	0.942518i
$122$	3.43665	−	15.0570i	0.311140	−	1.36319i
$123$	0.128230	+	0.0617522i	0.0115621	+	0.00556801i
$124$	−0.680355	+	0.542565i	−0.0610977	+	0.0487238i
$125$		0			0
$126$	−0.225007	−	0.467231i	−0.0200452	−	0.0416243i
$127$	5.00763	+	3.99345i	0.444355	+	0.354361i	0.819962	−	0.572418i	$-0.193994\pi$
$127$	5.00763	+	3.99345i	0.444355	+	0.354361i	−0.375607	+	0.926779i	$0.622566\pi$
$128$		−	12.2782i		−	1.08525i
$129$	−7.66395	+	9.61029i	−0.674773	+	0.846139i
$130$		0			0
$131$	−5.58467	−	1.27467i	−0.487935	−	0.111368i	−0.0285265	−	0.999593i	$-0.509082\pi$
$131$	−5.58467	−	1.27467i	−0.487935	−	0.111368i	−0.459409	+	0.888225i	$0.651939\pi$
$132$	−0.678953	+	0.851380i	−0.0590953	+	0.0741031i
$133$			0.397570i			0.0344736i
$134$	8.27784	+	6.60136i	0.715096	+	0.570270i
$135$		0			0
$136$	−0.216212	−	0.271121i	−0.0185400	−	0.0232485i
$137$	8.41084	−	6.70742i	0.718586	−	0.573054i	−0.194459	−	0.980911i	$-0.562295\pi$
$137$	8.41084	−	6.70742i	0.718586	−	0.573054i	0.913046	+	0.407857i	$0.133724\pi$
$138$	−9.41561	−	4.53432i	−0.801510	−	0.385987i
$139$	0.449732	−	1.97040i	0.0381458	−	0.167127i	−0.952267	−	0.305266i	$-0.901255\pi$
$139$	0.449732	−	1.97040i	0.0381458	−	0.167127i	0.990413	+	0.138138i	$0.0441118\pi$
$140$		0			0
$141$	−4.36148	+	2.10038i	−0.367302	+	0.176884i
$142$	9.17161	−	19.0450i	0.769664	−	1.59822i
$143$	−2.01934	+	0.460900i	−0.168865	+	0.0385424i
$144$	2.01250			0.167709
$145$		0			0
$146$	25.7466			2.13080
$147$	11.5857	−	2.64435i	0.955568	−	0.218102i
$148$	−1.05936	+	2.19979i	−0.0870790	+	0.180821i
$149$	5.21579	−	2.51179i	0.427294	−	0.205774i	−0.207862	−	0.978158i	$-0.566650\pi$
$149$	5.21579	−	2.51179i	0.427294	−	0.205774i	0.635155	+	0.772384i	$0.280936\pi$
$150$		0			0
$151$	−2.37507	+	10.4059i	−0.193281	+	0.846818i	0.781545	+	0.623849i	$0.214432\pi$
$151$	−2.37507	+	10.4059i	−0.193281	+	0.846818i	−0.974826	+	0.222969i	$0.928425\pi$
$152$	−0.847186	−	0.407983i	−0.0687159	−	0.0330918i
$153$	0.0617948	−	0.0492797i	0.00499581	−	0.00398403i
$154$	0.485716	+	0.609068i	0.0391401	+	0.0490801i
$155$		0			0
$156$	−4.82244	−	3.84577i	−0.386104	−	0.307908i
$157$		−	13.2586i		−	1.05815i	−0.848574	−	0.529077i	$-0.822538\pi$
$157$		−	13.2586i		−	1.05815i	0.848574	−	0.529077i	$-0.177462\pi$
$158$	−4.31361	+	5.40910i	−0.343173	+	0.430325i
$159$	−5.66705	−	1.29347i	−0.449426	−	0.102579i
$160$		0			0
$161$	−1.52898	+	1.91728i	−0.120501	+	0.151103i
$162$		−	17.3305i		−	1.36161i
$163$	13.1423	+	10.4806i	1.02938	+	0.820904i	0.984018	−	0.178067i	$-0.0569842\pi$
$163$	13.1423	+	10.4806i	1.02938	+	0.820904i	0.0453627	+	0.998971i	$0.485556\pi$
$164$	−0.0326823	−	0.0678655i	−0.00255206	−	0.00529941i
$165$		0			0
$166$	−10.0847	+	8.04226i	−0.782722	+	0.624200i
$167$	6.66647	+	3.21041i	0.515867	+	0.248429i	0.673657	−	0.739044i	$-0.264723\pi$
$167$	6.66647	+	3.21041i	0.515867	+	0.248429i	−0.157790	+	0.987473i	$0.550437\pi$
$168$	0.541343	−	2.37178i	0.0417655	−	0.182987i
$169$	0.282113	+	1.23602i	0.0217010	+	0.0950783i
$170$		0			0
$171$	0.0929887	−	0.193093i	0.00711103	−	0.0147662i
$172$	6.34244	−	1.44762i	0.483606	−	0.110380i
$173$	−19.9824			−1.51923			−0.759617	−	0.650371i	$-0.774614\pi$
$173$	−19.9824			−1.51923			−0.759617	+	0.650371i	$0.774614\pi$
$174$	−1.91078	+	17.0302i	−0.144856	+	1.29105i
$175$		0			0
$176$	−2.94740	+	0.672726i	−0.222169	+	0.0507086i
$177$	−1.73767	+	3.60830i	−0.130611	+	0.271216i
$178$	21.1966	−	10.2078i	1.58875	−	0.765104i
$179$	5.14143	+	22.5261i	0.384289	+	1.68368i	0.683866	+	0.729607i	$0.260297\pi$
$179$	5.14143	+	22.5261i	0.384289	+	1.68368i	−0.299578	+	0.954072i	$0.596846\pi$
$180$		0			0
$181$	8.77426	+	4.22546i	0.652186	+	0.314076i	0.730561	−	0.682848i	$-0.239259\pi$
$181$	8.77426	+	4.22546i	0.652186	+	0.314076i	−0.0783750	+	0.996924i	$0.524973\pi$
$182$	−3.44992	+	2.75122i	−0.255725	+	0.203934i
$183$	10.2958	+	12.9106i	0.761089	+	0.954376i
$184$	−2.51653	−	5.22563i	−0.185521	−	0.385239i
$185$		0			0
$186$		−	2.83659i		−	0.207989i
$187$	−0.0740284	+	0.0928287i	−0.00541349	+	0.00678831i
$188$	2.49779	+	0.570105i	0.182170	+	0.0415792i
$189$	−3.48814	−	0.796146i	−0.253725	−	0.0579111i
$190$		0			0
$191$			16.7890i			1.21481i	0.794394	+	0.607403i	$0.207789\pi$
$191$			16.7890i			1.21481i	−0.794394	+	0.607403i	$0.792211\pi$
$192$	1.74956	+	1.39523i	0.126264	+	0.100692i
$193$	−5.01908	−	10.4222i	−0.361281	−	0.750208i	0.638531	−	0.769596i	$-0.279542\pi$
$193$	−5.01908	−	10.4222i	−0.361281	−	0.750208i	−0.999812	+	0.0193882i	$0.993828\pi$
$194$	−14.6647	−	18.3889i	−1.05286	−	1.32025i
$195$		0			0
$196$	−5.66654	−	2.72886i	−0.404753	−	0.194919i
$197$	5.77770	−	25.3138i	0.411644	−	1.80353i	−0.164722	−	0.986340i	$-0.552673\pi$
$197$	5.77770	−	25.3138i	0.411644	−	1.80353i	0.576366	−	0.817192i	$-0.304470\pi$
$198$	−0.0934475	−	0.409420i	−0.00664102	−	0.0290962i
$199$	−23.1330	+	11.1403i	−1.63985	+	0.789712i	−0.640082	+	0.768307i	$0.721100\pi$
$199$	−23.1330	+	11.1403i	−1.63985	+	0.789712i	−0.999771	+	0.0214050i	$0.993186\pi$
$200$		0			0
$201$	−11.0368	+	2.51908i	−0.778476	+	0.177682i
$202$	−5.59787			−0.393865
$203$	3.79630	+	1.32639i	0.266448	+	0.0930943i
$204$	−0.353579			−0.0247555
$205$		0			0
$206$	7.83636	−	16.2724i	0.545985	−	1.13375i
$207$	1.19104	−	0.573575i	0.0827831	−	0.0398663i
$208$	−3.81050	−	16.6949i	−0.264210	−	1.15758i
$209$	−0.0716405	+	0.313877i	−0.00495547	+	0.0217114i
$210$		0			0
$211$	−10.5587	+	8.42029i	−0.726891	+	0.579677i	−0.915472	−	0.402381i	$-0.868183\pi$
$211$	−10.5587	+	8.42029i	−0.726891	+	0.579677i	0.188581	+	0.982058i	$0.439611\pi$
$212$	1.91811	+	2.40524i	0.131736	+	0.165192i
$213$	9.80647	+	20.3633i	0.671928	+	1.39527i
$214$	−8.55648	−	6.82356i	−0.584909	−	0.466449i
$215$		0			0
$216$	5.27603	−	6.61593i	0.358988	−	0.450157i
$217$	−0.648940	−	0.148116i	−0.0440529	−	0.0100548i
$218$	24.7642	+	5.65228i	1.67725	+	0.382820i
$219$	−17.1639	+	21.5229i	−1.15983	+	1.45438i
$220$		0			0
$221$	−0.525806	−	0.419316i	−0.0353695	−	0.0282063i
$222$	−3.45318	−	7.17060i	−0.231762	−	0.481259i
$223$	−14.7560	−	18.5035i	−0.988137	−	1.23908i	−0.970963	−	0.239232i	$-0.923104\pi$
$223$	−14.7560	−	18.5035i	−0.988137	−	1.23908i	−0.0171742	−	0.999853i	$-0.505467\pi$
$224$	−2.97322	+	2.37107i	−0.198657	+	0.158424i
$225$		0			0
$226$	−6.11143	+	26.7759i	−0.406526	+	1.78111i
$227$	4.27370	+	18.7243i	0.283656	+	1.24278i	0.893067	+	0.449923i	$0.148549\pi$
$227$	4.27370	+	18.7243i	0.283656	+	1.24278i	−0.609412	+	0.792854i	$0.708594\pi$
$228$	−0.863804	+	0.415986i	−0.0572068	+	0.0275494i
$229$	−1.59226	+	3.30637i	−0.105220	+	0.218491i	−0.946931	−	0.321437i	$-0.895834\pi$
$229$	−1.59226	+	3.30637i	−0.105220	+	0.218491i	0.841711	+	0.539928i	$0.181548\pi$
$230$		0			0
$231$	−0.832952			−0.0548042
$232$	−6.72216	+	6.72844i	−0.441331	+	0.441744i
$233$	−16.0346			−1.05046			−0.525230	−	0.850960i	$-0.676021\pi$
$233$	−16.0346			−1.05046			−0.525230	+	0.850960i	$0.676021\pi$
$234$	2.31906	−	0.529311i	0.151602	−	0.0346022i
$235$		0			0
$236$	1.90969	−	0.919658i	0.124310	−	0.0598646i
$237$	−1.64608	−	7.21193i	−0.106924	−	0.468465i
$238$	−0.0562860	+	0.246605i	−0.00364848	+	0.0159850i
$239$	17.8984	+	8.61941i	1.15775	+	0.557543i	0.911353	−	0.411626i	$-0.135039\pi$
$239$	17.8984	+	8.61941i	1.15775	+	0.557543i	0.246397	+	0.969169i	$0.420753\pi$
$240$		0			0
$241$	−14.4296	−	18.0942i	−0.929494	−	1.16555i	−0.985933	−	0.167143i	$-0.946546\pi$
$241$	−14.4296	−	18.0942i	−0.929494	−	1.16555i	0.0564382	−	0.998406i	$-0.482026\pi$
$242$	−7.96010	−	16.5293i	−0.511694	−	1.06254i
$243$	3.24954	+	2.59142i	0.208458	+	0.166240i
$244$		−	8.73961i		−	0.559496i
$245$		0			0
$246$	0.239379	+	0.0546368i	0.0152623	+	0.00348351i
$247$	−1.77788	−	0.405790i	−0.113124	−	0.0258198i
$248$	0.981561	−	1.23084i	0.0623292	−	0.0781583i
$249$		−	13.7916i		−	0.874009i
$250$		0			0
$251$	5.85189	+	12.1516i	0.369368	+	0.767001i	0.999958	−	0.00911486i	$-0.00290139\pi$
$251$	5.85189	+	12.1516i	0.369368	+	0.767001i	−0.630590	+	0.776116i	$0.717187\pi$
$252$	−0.182970	−	0.229437i	−0.0115260	−	0.0144532i
$253$	−1.55260	+	1.23816i	−0.0976114	+	0.0778425i
$254$	9.95551	+	4.79432i	0.624665	+	0.300823i
$255$		0			0
$256$	−4.17356	−	18.2855i	−0.260847	−	1.14285i
$257$	−13.8835	+	6.68595i	−0.866030	+	0.417058i	−0.813503	−	0.581561i	$-0.802442\pi$
$257$	−13.8835	+	6.68595i	−0.866030	+	0.417058i	−0.0525275	+	0.998619i	$0.516728\pi$
$258$	−9.20093	+	19.1059i	−0.572825	+	1.18948i
$259$	−1.82076	+	0.415577i	−0.113137	+	0.0258227i
$260$		0			0
$261$	−1.53357	−	1.53213i	−0.0949254	−	0.0948367i
$262$	−9.88235			−0.610534
$263$	−17.0080	+	3.88196i	−1.04876	+	0.239372i	−0.711971	−	0.702209i	$-0.752197\pi$
$263$	−17.0080	+	3.88196i	−1.04876	+	0.239372i	−0.336786	+	0.941581i	$0.609340\pi$
$264$	0.854770	−	1.77495i	0.0526075	−	0.109241i
$265$		0			0
$266$	0.152623	+	0.668683i	0.00935789	+	0.0409996i
$267$	−5.59751	+	24.5243i	−0.342562	+	1.50086i
$268$	5.39810	+	2.59959i	0.329741	+	0.158795i
$269$	−11.5376	+	9.20097i	−0.703463	+	0.560993i	−0.908563	−	0.417748i	$-0.862819\pi$
$269$	−11.5376	+	9.20097i	−0.703463	+	0.560993i	0.205100	+	0.978741i	$0.434248\pi$
$270$		0			0
$271$	0.576227	+	1.19655i	0.0350033	+	0.0726851i	0.917737	−	0.397188i	$-0.130014\pi$
$271$	0.576227	+	1.19655i	0.0350033	+	0.0726851i	−0.882734	+	0.469873i	$0.844300\pi$
$272$	−0.767462	−	0.612031i	−0.0465342	−	0.0371098i
$273$		−	4.71806i		−	0.285550i
$274$	11.5715	−	14.5102i	0.699061	−	0.876595i
$275$		0			0
$276$	−5.76552	−	1.31594i	−0.347043	−	0.0792104i
$277$	−7.58834	+	9.51548i	−0.455939	+	0.571730i	−0.955666	−	0.294453i	$-0.904862\pi$
$277$	−7.58834	+	9.51548i	−0.455939	+	0.571730i	0.499726	+	0.866183i	$0.333434\pi$
$278$		−	3.48672i		−	0.209120i
$279$	0.280536	+	0.223720i	0.0167953	+	0.0133938i
$280$		0			0
$281$	−5.69656	−	7.14325i	−0.339828	−	0.426131i	0.582325	−	0.812956i	$-0.302143\pi$
$281$	−5.69656	−	7.14325i	−0.339828	−	0.426131i	−0.922153	+	0.386825i	$0.873572\pi$
$282$	−6.52938	+	5.20700i	−0.388819	+	0.310073i
$283$	5.33220	+	2.56785i	0.316966	+	0.152643i	0.585602	−	0.810599i	$-0.300858\pi$
$283$	5.33220	+	2.56785i	0.316966	+	0.152643i	−0.268635	+	0.963242i	$0.586573\pi$
$284$	2.66177	−	11.6620i	0.157947	−	0.692011i
$285$		0			0
$286$	−3.21944	+	1.55040i	−0.190370	+	0.0916772i
$287$	0.0249990	−	0.0519109i	0.00147564	−	0.00306421i
$288$	1.99862	−	0.456173i	0.117770	−	0.0268802i
$289$	16.9614			0.997732
$290$		0			0
$291$	25.1484			1.47422
$292$	14.2043	−	3.24204i	0.831244	−	0.189726i
$293$	−4.79506	+	9.95705i	−0.280131	+	0.581697i	−0.992797	−	0.119806i	$-0.961773\pi$
$293$	−4.79506	+	9.95705i	−0.280131	+	0.581697i	0.712667	+	0.701503i	$0.247487\pi$
$294$	18.4711	−	8.89521i	1.07726	−	0.518779i
$295$		0			0
$296$	0.982896	−	4.30635i	0.0571296	−	0.250301i
$297$	−2.61039	−	1.25710i	−0.151470	−	0.0729443i
$298$	7.80833	−	6.22693i	0.452324	−	0.360717i
$299$	−7.01327	−	8.79436i	−0.405588	−	0.508591i
$300$		0			0
$301$	3.89051	+	3.10258i	0.224245	+	0.178830i
$302$			18.4137i			1.05959i
$303$	3.73181	−	4.67954i	0.214387	−	0.268833i
$304$	−2.59498	−	0.592288i	−0.148833	−	0.0339701i
$305$		0			0
$306$	0.0850164	−	0.106607i	0.00486006	−	0.00609433i
$307$		−	0.482205i		−	0.0275209i	−0.999905	−	0.0137604i	$-0.995620\pi$
$307$		−	0.482205i		−	0.0275209i	0.999905	−	0.0137604i	$-0.00438022\pi$
$308$	0.344662	+	0.274859i	0.0196389	+	0.0156615i
$309$	8.37879	+	17.3987i	0.476653	+	0.989779i
$310$		0			0
$311$	3.38067	−	2.69599i	0.191700	−	0.152876i	−0.522936	−	0.852372i	$-0.675163\pi$
$311$	3.38067	−	2.69599i	0.191700	−	0.152876i	0.714637	+	0.699496i	$0.246592\pi$
$312$	10.0538	+	4.84164i	0.569183	+	0.274104i
$313$	1.75042	−	7.66908i	0.0989394	−	0.433482i	−0.901061	−	0.433693i	$-0.857210\pi$
$313$	1.75042	−	7.66908i	0.0989394	−	0.433482i	1.00000		0.000211367i	$6.72804e-5\pi$
$314$	−5.08985	−	22.3001i	−0.287237	−	1.25847i
$315$		0			0
$316$	−1.69868	+	3.52735i	−0.0955584	+	0.198429i
$317$	−2.18404	+	0.498493i	−0.122668	+	0.0279982i	−0.283414	−	0.958998i	$-0.591467\pi$
$317$	−2.18404	+	0.498493i	−0.122668	+	0.0279982i	0.160746	+	0.986996i	$0.448610\pi$
$318$	−10.0281			−0.562349
$319$	2.75813	+	1.73125i	0.154426	+	0.0969314i
$320$		0			0
$321$	11.4083	−	2.60387i	0.636750	−	0.145334i
$322$	−1.83561	+	3.81169i	−0.102295	+	0.212417i
$323$	−0.0941833	+	0.0453563i	−0.00524050	+	0.00252369i
$324$	−2.18227	−	9.56116i	−0.121237	−	0.531175i
$325$		0			0
$326$	26.1277	+	12.5824i	1.44708	+	0.696877i
$327$	−21.2340	+	16.9336i	−1.17425	+	0.936430i
$328$	0.0849639	+	0.106541i	0.00469135	+	0.00588276i
$329$	0.850289	+	1.76564i	0.0468780	+	0.0973431i
$330$		0			0
$331$			3.71697i			0.204303i	0.994769	+	0.102152i	$0.0325727\pi$
$331$			3.71697i			0.204303i	−0.994769	+	0.102152i	$0.967427\pi$
$332$	−4.55098	+	5.70675i	−0.249768	+	0.313199i
$333$	0.981515	+	0.224024i	0.0537867	+	0.0122765i
$334$	12.4450	+	2.84048i	0.680958	+	0.155424i
$335$		0			0
$336$		−	6.88644i		−	0.375686i
$337$	16.3319	+	13.0243i	0.889655	+	0.709476i	0.957566	−	0.288215i	$-0.0930618\pi$
$337$	16.3319	+	13.0243i	0.889655	+	0.709476i	−0.0679104	+	0.997691i	$0.521633\pi$
$338$	0.948987	+	1.97059i	0.0516181	+	0.107186i
$339$	−18.3092	−	22.9590i	−0.994418	−	1.24696i
$340$		0			0
$341$	−0.485642	−	0.233873i	−0.0262990	−	0.0126649i
$342$	0.0822740	−	0.360466i	0.00444887	−	0.0194918i
$343$	−2.23367	−	9.78634i	−0.120607	−	0.528413i
$344$	−10.6037	+	5.10649i	−0.571715	+	0.275323i
$345$		0			0
$346$	−33.6090	+	7.67103i	−1.80683	+	0.412397i
$347$	24.7314			1.32765			0.663827	−	0.747887i	$-0.268931\pi$
$347$	24.7314			1.32765			0.663827	+	0.747887i	$0.268931\pi$
$348$	1.09029	+	9.63609i	0.0584456	+	0.516549i
$349$	16.7238			0.895206			0.447603	−	0.894232i	$-0.352278\pi$
$349$	16.7238			0.895206			0.447603	+	0.894232i	$0.352278\pi$
$350$		0			0
$351$	7.12054	−	14.7860i	0.380066	−	0.789216i
$352$	−2.77459	+	1.33617i	−0.147886	+	0.0712182i
$353$	−6.91590	−	30.3006i	−0.368096	−	1.61274i	−0.732004	−	0.681301i	$-0.761415\pi$
$353$	−6.91590	−	30.3006i	−0.368096	−	1.61274i	0.363907	−	0.931435i	$-0.381443\pi$
$354$	−1.53744	+	6.73597i	−0.0817141	+	0.358013i
$355$		0			0
$356$	10.4087	−	8.30068i	0.551661	−	0.439935i
$357$	−0.168627	−	0.211451i	−0.00892466	−	0.0111912i
$358$	17.2950	+	35.9135i	0.914071	+	1.89809i
$359$	−16.5243	−	13.1777i	−0.872120	−	0.695493i	0.0814454	−	0.996678i	$-0.474046\pi$
$359$	−16.5243	−	13.1777i	−0.872120	−	0.695493i	−0.953566	+	0.301185i	$0.902618\pi$
$360$		0			0
$361$	11.6696	−	14.6332i	0.614188	−	0.770168i
$362$	16.3798	+	3.73858i	0.860902	+	0.196495i
$363$	19.1243	+	4.36499i	1.00376	+	0.229102i
$364$	−1.55687	+	1.95226i	−0.0816023	+	0.102326i
$365$		0			0
$366$	22.2731	+	17.7622i	1.16423	+	0.928444i
$367$	12.6971	+	26.3659i	0.662785	+	1.37629i	0.912945	+	0.408083i	$0.133802\pi$
$367$	12.6971	+	26.3659i	0.662785	+	1.37629i	−0.250160	+	0.968204i	$0.580483\pi$
$368$	−10.2365	−	12.8362i	−0.533615	−	0.669132i
$369$	−0.0242832	+	0.0193652i	−0.00126413	+	0.00100811i
$370$		0			0
$371$	−0.523631	+	2.29418i	−0.0271855	+	0.119108i
$372$	−0.357187	−	1.56494i	−0.0185193	−	0.0811382i
$373$	17.9684	−	8.65311i	0.930367	−	0.448041i	0.0936061	−	0.995609i	$-0.470161\pi$
$373$	17.9684	−	8.65311i	0.930367	−	0.448041i	0.836761	+	0.547568i	$0.184446\pi$
$374$	−0.0888745	+	0.184550i	−0.00459559	+	0.00954285i
$375$		0			0
$376$	−4.63500			−0.239032
$377$	−9.80626	+	15.6228i	−0.505048	+	0.804614i
$378$	−6.17243			−0.317476
$379$	33.4968	−	7.64543i	1.72061	−	0.392719i	0.755625	−	0.655005i	$-0.227333\pi$
$379$	33.4968	−	7.64543i	1.72061	−	0.392719i	0.964990	+	0.262286i	$0.0844763\pi$
$380$		0			0
$381$	−10.6446	+	5.12619i	−0.545341	+	0.262622i
$382$	6.44510	+	28.2378i	0.329760	+	1.44477i
$383$	2.47858	−	10.8594i	0.126650	−	0.554888i	−0.871292	−	0.490764i	$-0.836718\pi$
$383$	2.47858	−	10.8594i	0.126650	−	0.554888i	0.997942	−	0.0641239i	$-0.0204253\pi$
$384$	20.4054	+	9.82673i	1.04131	+	0.501468i
$385$		0			0
$386$	−12.4427	−	15.6027i	−0.633317	−	0.794154i
$387$	−1.16389	−	2.41683i	−0.0591637	−	0.122855i
$388$	−10.4060	−	8.29849i	−0.528284	−	0.421292i
$389$		−	6.83812i		−	0.346706i	−0.984860	−	0.173353i	$-0.944540\pi$
$389$		−	6.83812i		−	0.346706i	0.984860	−	0.173353i	$-0.0554602\pi$
$390$		0			0
$391$	−0.628633	−	0.143481i	−0.0317913	−	0.00725616i
$392$	11.0929	+	2.53189i	0.560277	+	0.127880i
$393$	6.58805	−	8.26115i	0.332323	−	0.416720i
$394$		−	44.7939i		−	2.25669i
$395$		0			0
$396$	−0.103109	−	0.214108i	−0.00518143	−	0.0107594i
$397$	−17.8212	−	22.3471i	−0.894420	−	1.12157i	−0.991987	−	0.126338i	$-0.959678\pi$
$397$	−17.8212	−	22.3471i	−0.894420	−	1.12157i	0.0975674	−	0.995229i	$-0.468894\pi$
$398$	−34.6314	+	27.6176i	−1.73591	+	1.38435i
$399$	−0.660731	−	0.318191i	−0.0330779	−	0.0159295i
$400$		0			0
$401$	1.37343	+	6.01739i	0.0685859	+	0.300494i	0.997574	−	0.0696154i	$-0.0221772\pi$
$401$	1.37343	+	6.01739i	0.0685859	+	0.300494i	−0.928988	+	0.370110i	$0.879320\pi$
$402$	−17.5961	+	8.47382i	−0.877612	+	0.422636i
$403$	1.32472	−	2.75080i	0.0659889	−	0.137027i
$404$	−3.08832	+	0.704890i	−0.153650	+	0.0350696i
$405$		0			0
$406$	6.89428	+	0.773536i	0.342158	+	0.0383900i
$407$	−1.51236			−0.0749649
$408$	0.623627	−	0.142339i	0.0308741	−	0.00704682i
$409$	0.145872	−	0.302906i	0.00721290	−	0.0149777i	−0.897331	−	0.441358i	$-0.854497\pi$
$409$	0.145872	−	0.302906i	0.00721290	−	0.0149777i	0.904544	+	0.426380i	$0.140211\pi$
$410$		0			0
$411$	4.41569	+	19.3464i	0.217810	+	0.954289i
$412$	2.27425	−	9.96416i	0.112044	−	0.490899i
$413$	1.46074	+	0.703454i	0.0718782	+	0.0346147i
$414$	1.78306	−	1.42194i	0.0876325	−	0.0698846i
$415$		0			0
$416$	−7.56843	−	15.7160i	−0.371073	−	0.770540i
$417$	2.91473	+	2.32442i	0.142735	+	0.113827i
$418$			0.555421i			0.0271665i
$419$	8.84314	−	11.0890i	0.432016	−	0.541731i	−0.517404	−	0.855742i	$-0.673101\pi$
$419$	8.84314	−	11.0890i	0.432016	−	0.541731i	0.949419	+	0.314011i	$0.101673\pi$
$420$		0			0
$421$	−5.31474	−	1.21306i	−0.259025	−	0.0591207i	0.0910364	−	0.995848i	$-0.470982\pi$
$421$	−5.31474	−	1.21306i	−0.259025	−	0.0591207i	−0.350061	+	0.936727i	$0.613839\pi$
$422$	−14.5265	+	18.2157i	−0.707140	+	0.886726i
$423$		−	1.05642i		−	0.0513650i
$424$	−4.35134	−	3.47008i	−0.211320	−	0.168522i
$425$		0			0
$426$	24.3110	+	30.4851i	1.17787	+	1.47701i
$427$	5.22655	−	4.16803i	0.252930	−	0.201705i
$428$	−5.57980	−	2.68709i	−0.269710	−	0.129885i
$429$	0.850176	−	3.72486i	0.0410469	−	0.179838i
$430$		0			0
$431$	−16.6504	+	8.01840i	−0.802020	+	0.386233i	−0.789547	−	0.613690i	$-0.789685\pi$
$431$	−16.6504	+	8.01840i	−0.802020	+	0.386233i	−0.0124728	+	0.999922i	$0.503970\pi$
$432$	10.3931	−	21.5815i	0.500037	−	1.03834i
$433$	5.02834	−	1.14769i	0.241647	−	0.0551542i	−0.0999822	−	0.994989i	$-0.531879\pi$
$433$	5.02834	−	1.14769i	0.241647	−	0.0551542i	0.341629	+	0.939835i	$0.389021\pi$
$434$	−1.14833			−0.0551216
$435$		0			0
$436$	14.3741			0.688393
$437$	−1.70457	+	0.389057i	−0.0815407	+	0.0186111i
$438$	−20.6061	+	42.7890i	−0.984597	+	2.04454i
$439$	18.6601	−	8.98624i	0.890598	−	0.428890i	0.0681142	−	0.997678i	$-0.478302\pi$
$439$	18.6601	−	8.98624i	0.890598	−	0.428890i	0.822484	+	0.568788i	$0.192587\pi$
$440$		0			0
$441$	−0.577075	+	2.52833i	−0.0274798	+	0.120397i
$442$	−1.04534	−	0.503409i	−0.0497217	−	0.0239447i
$443$	14.6115	−	11.6523i	0.694213	−	0.553616i	−0.211568	−	0.977363i	$-0.567857\pi$
$443$	14.6115	−	11.6523i	0.694213	−	0.553616i	0.905781	+	0.423747i	$0.139285\pi$
$444$	−2.80803	−	3.52116i	−0.133263	−	0.167107i
$445$		0			0
$446$	−31.9219	−	25.4568i	−1.51154	−	1.20542i
$447$			10.6785i			0.505078i
$448$	0.564827	−	0.708270i	0.0266856	−	0.0334626i
$449$	24.2485	+	5.53455i	1.14436	+	0.261192i	0.752345	−	0.658769i	$-0.228923\pi$
$449$	24.2485	+	5.53455i	1.14436	+	0.261192i	0.392010	+	0.919961i	$0.371780\pi$
$450$		0			0
$451$	0.0290906	−	0.0364785i	0.00136982	−	0.00171770i
$452$			15.5417i			0.731022i
$453$	−15.3929	−	12.2754i	−0.723223	−	0.576751i
$454$	14.3761	+	29.8523i	0.674705	+	1.40104i
$455$		0			0
$456$	1.35608	−	1.08143i	0.0635041	−	0.0506428i
$457$	−16.3899	−	7.89295i	−0.766686	−	0.369216i	0.00930825	−	0.999957i	$-0.497037\pi$
$457$	−16.3899	−	7.89295i	−0.766686	−	0.369216i	−0.775994	+	0.630740i	$0.782751\pi$
$458$	−1.40879	+	6.17232i	−0.0658285	+	0.288414i
$459$	−0.209336	−	0.917160i	−0.00977096	−	0.0428094i
$460$		0			0
$461$	−12.6965	+	26.3645i	−0.591334	+	1.22792i	0.363726	+	0.931506i	$0.381504\pi$
$461$	−12.6965	+	26.3645i	−0.591334	+	1.22792i	−0.955060	+	0.296412i	$0.904210\pi$
$462$	−1.40097	+	0.319761i	−0.0651788	+	0.0148766i
$463$	−5.02033			−0.233315			−0.116657	−	0.993172i	$-0.537218\pi$
$463$	−5.02033			−0.233315			−0.116657	+	0.993172i	$0.537218\pi$
$464$	−14.3131	+	22.8029i	−0.664470	+	1.05860i
$465$		0			0
$466$	−26.9690	+	6.15550i	−1.24932	+	0.285148i
$467$	−7.56929	+	15.7178i	−0.350265	+	0.727333i	−0.999445	−	0.0333015i	$-0.989398\pi$
$467$	−7.56929	+	15.7178i	−0.350265	+	0.727333i	0.649180	+	0.760635i	$0.275112\pi$
$468$	1.21277	−	0.584038i	0.0560602	−	0.0269972i
$469$	1.01979	+	4.46800i	0.0470896	+	0.206313i
$470$		0			0
$471$	22.0349	+	10.6114i	1.01531	+	0.488949i
$472$	−2.99800	+	2.39083i	−0.137994	+	0.110047i
$473$	2.51245	+	3.15051i	0.115522	+	0.144861i
$474$	−5.53716	−	11.4980i	−0.254330	−	0.528122i
$475$		0			0
$476$			0.143139i			0.00656075i
$477$	0.790911	−	0.991770i	0.0362133	−	0.0454100i
$478$	33.4127	+	7.62623i	1.52826	+	0.348816i
$479$	−33.8906	−	7.73530i	−1.54850	−	0.353435i	−0.639023	−	0.769188i	$-0.720661\pi$
$479$	−33.8906	−	7.73530i	−1.54850	−	0.353435i	−0.909478	+	0.415753i	$0.863518\pi$
$480$		0			0
$481$		−	8.56640i		−	0.390594i
$482$	−31.2158	−	24.8937i	−1.42184	−	1.13388i
$483$	−1.96268	−	4.07554i	−0.0893049	−	0.185443i
$484$	−6.47294	−	8.11681i	−0.294225	−	0.368946i
$485$		0			0
$486$	6.46030	+	3.11112i	0.293045	+	0.141123i
$487$	7.59766	−	33.2875i	0.344283	−	1.50840i	−0.445649	−	0.895208i	$-0.647027\pi$
$487$	7.59766	−	33.2875i	0.344283	−	1.50840i	0.789932	−	0.613194i	$-0.210116\pi$
$488$	3.51826	+	15.4145i	0.159264	+	0.697783i
$489$	−27.9363	+	13.4534i	−1.26332	+	0.608384i
$490$		0			0
$491$	−10.6658	+	2.43440i	−0.481340	+	0.109863i	−0.456304	−	0.889824i	$-0.650827\pi$
$491$	−10.6658	+	2.43440i	−0.481340	+	0.109863i	−0.0250360	+	0.999687i	$0.507970\pi$
$492$	0.138945			0.00626410
$493$	0.118878	+	1.05065i	0.00535397	+	0.0473191i
$494$	−3.14605			−0.141548
$495$		0			0
$496$	1.93355	−	4.01505i	0.0868188	−	0.180281i
$497$	8.24363	−	3.96992i	0.369778	−	0.178075i
$498$	−5.29446	−	23.1965i	−0.237250	−	1.03946i
$499$	1.38249	−	6.05708i	0.0618887	−	0.271152i	−0.934511	−	0.355935i	$-0.884162\pi$
$499$	1.38249	−	6.05708i	0.0618887	−	0.271152i	0.996399	+	0.0847827i	$0.0270196\pi$
$500$		0			0
$501$	−10.6709	+	8.50977i	−0.476741	+	0.380188i
$502$	14.5073	+	18.1916i	0.647494	+	0.811931i
$503$	11.9876	+	24.8924i	0.534499	+	1.10990i	0.977022	+	0.213141i	$0.0683692\pi$
$503$	11.9876	+	24.8924i	0.534499	+	1.10990i	−0.442523	+	0.896757i	$0.645917\pi$
$504$	0.415077	+	0.331013i	0.0184890	+	0.0147445i
$505$		0			0
$506$	−2.13605	+	2.67853i	−0.0949591	+	0.119075i
$507$	−2.27996	−	0.520385i	−0.101256	−	0.0231111i
$508$	6.09612	+	1.39140i	0.270472	+	0.0617334i
$509$	−25.2402	+	31.6502i	−1.11875	+	1.40287i	−0.214054	+	0.976822i	$0.568667\pi$
$509$	−25.2402	+	31.6502i	−1.11875	+	1.40287i	−0.904699	+	0.426051i	$0.859904\pi$
$510$		0			0
$511$	8.71305	+	6.94842i	0.385443	+	0.307380i
$512$	−3.38464	−	7.02827i	−0.149581	−	0.310609i
$513$	−1.59045	−	1.99436i	−0.0702202	−	0.0880533i
$514$	−20.7844	+	16.5750i	−0.916761	+	0.731093i
$515$		0			0
$516$	−2.67028	+	11.6993i	−0.117552	+	0.515031i
$517$	0.353133	+	1.54718i	0.0155308	+	0.0680448i
$518$	−2.90285	+	1.39794i	−0.127544	+	0.0614220i
$519$	15.9927	−	33.2093i	0.702004	−	1.45773i
$520$		0			0
$521$	−17.0725			−0.747960			−0.373980	−	0.927437i	$-0.622007\pi$
$521$	−17.0725			−0.747960			−0.373980	+	0.927437i	$0.622007\pi$
$522$	−3.16752	−	1.98822i	−0.138638	−	0.0870220i
$523$	−8.00592			−0.350074			−0.175037	−	0.984562i	$-0.556005\pi$
$523$	−8.00592			−0.350074			−0.175037	+	0.984562i	$0.556005\pi$
$524$	−5.45205	+	1.24440i	−0.238174	+	0.0543617i
$525$		0			0
$526$	−27.1160	+	13.0584i	−1.18231	+	0.569371i
$527$	−0.0389452	−	0.170630i	−0.00169648	−	0.00743276i
$528$	1.24091	−	5.43678i	0.0540037	−	0.236605i
$529$	11.0057	+	5.30007i	0.478509	+	0.230438i
$530$		0			0
$531$	−0.544924	−	0.683313i	−0.0236477	−	0.0296533i
$532$	0.168403	+	0.349692i	0.00730118	+	0.0151610i
$533$	0.206624	+	0.164777i	0.00894987	+	0.00713728i
$534$			43.3969i			1.87797i
$535$		0			0
$536$	−10.5674	−	2.41195i	−0.456443	−	0.104180i
$537$	−41.5516	−	9.48388i	−1.79308	−	0.409260i
$538$	−15.8733	+	19.9045i	−0.684348	+	0.858146i
$539$		−	3.89576i		−	0.167802i
$540$		0			0
$541$	10.0926	+	20.9575i	0.433914	+	0.901032i	0.997201	+	0.0747702i	$0.0238223\pi$
$541$	10.0926	+	20.9575i	0.433914	+	0.901032i	−0.563287	+	0.826261i	$0.690463\pi$
$542$	1.42851	+	1.79130i	0.0613599	+	0.0769429i
$543$	−14.0448	+	11.2004i	−0.602720	+	0.480654i
$544$	−0.900897	−	0.433849i	−0.0386256	−	0.0186011i
$545$		0			0
$546$	−1.81121	−	7.93544i	−0.0775127	−	0.339605i
$547$	15.5044	−	7.46651i	0.662919	−	0.319245i	−0.0719952	−	0.997405i	$-0.522937\pi$
$547$	15.5044	−	7.46651i	0.662919	−	0.319245i	0.734914	+	0.678160i	$0.237222\pi$
$548$	4.55682	−	9.46233i	0.194658	−	0.404211i
$549$	−3.51332	+	0.801893i	−0.149945	+	0.0342240i
$550$		0			0
$551$	1.52651	+	2.42692i	0.0650317	+	0.103390i
$552$	10.6987			0.455367
$553$	−2.91958	+	0.666376i	−0.124153	+	0.0283372i
$554$	−9.11016	+	18.9174i	−0.387054	+	0.803725i
$555$		0			0
$556$	−0.439052	−	1.92361i	−0.0186199	−	0.0815793i
$557$	−0.672945	+	2.94837i	−0.0285136	+	0.124926i	−0.987182	−	0.159601i	$-0.948979\pi$
$557$	−0.672945	+	2.94837i	−0.0285136	+	0.124926i	0.958668	+	0.284527i	$0.0918365\pi$
$558$	0.557726	+	0.268587i	0.0236104	+	0.0113702i
$559$	−17.8453	+	14.2312i	−0.754776	+	0.601914i
$560$		0			0
$561$	−0.0950264	−	0.197324i	−0.00401202	−	0.00833104i
$562$	−12.3234	−	9.82759i	−0.519832	−	0.414552i
$563$			29.5336i			1.24469i	0.782742	+	0.622346i	$0.213820\pi$
$563$			29.5336i			1.24469i	−0.782742	+	0.622346i	$0.786180\pi$
$564$	−2.94656	+	3.69487i	−0.124073	+	0.155582i
$565$		0			0
$566$	9.95415	+	2.27197i	0.418404	+	0.0954980i
$567$	4.67710	−	5.86490i	0.196420	−	0.246303i
$568$			21.6404i			0.908010i
$569$	−12.6110	−	10.0569i	−0.528680	−	0.421608i	0.322432	−	0.946593i	$-0.395500\pi$
$569$	−12.6110	−	10.0569i	−0.528680	−	0.421608i	−0.851112	+	0.524984i	$0.824071\pi$
$570$		0			0
$571$	−26.2509	−	32.9176i	−1.09857	−	1.37756i	−0.919206	−	0.393776i	$-0.871169\pi$
$571$	−26.2509	−	32.9176i	−1.09857	−	1.37756i	−0.179361	−	0.983783i	$-0.557403\pi$
$572$	−1.58093	+	1.26075i	−0.0661018	+	0.0527144i
$573$	−27.9020	−	13.4369i	−1.16562	−	0.561335i
$574$	0.0221185	−	0.0969073i	0.000923207	−	0.00404483i
$575$		0			0
$576$	−0.439987	+	0.211886i	−0.0183328	+	0.00882860i
$577$	0.848171	−	1.76124i	0.0353098	−	0.0733216i	−0.882568	−	0.470185i	$-0.844187\pi$
$577$	0.848171	−	1.76124i	0.0353098	−	0.0733216i	0.917878	+	0.396864i	$0.129901\pi$
$578$	28.5279	−	6.51131i	1.18661	−	0.270835i
$579$	21.3379			0.886775
$580$		0			0
$581$	−5.58323			−0.231631
$582$	42.2977	−	9.65418i	1.75330	−	0.400179i
$583$	−0.826803	+	1.71687i	−0.0342427	+	0.0711056i
$584$	−23.7478	+	11.4363i	−0.982689	+	0.473238i
$585$		0			0
$586$	−4.24255	+	18.5878i	−0.175258	+	0.767856i
$587$	8.53239	+	4.10898i	0.352169	+	0.169596i	0.601601	−	0.798797i	$-0.294530\pi$
$587$	8.53239	+	4.10898i	0.352169	+	0.169596i	−0.249432	+	0.968392i	$0.580244\pi$
$588$	9.07033	−	7.23335i	0.374054	−	0.298298i
$589$	−0.295890	−	0.371035i	−0.0121920	−	0.0152882i
$590$		0			0
$591$	37.4455	+	29.8618i	1.54030	+	1.22835i
$592$		−	12.5035i		−	0.513889i
$593$	22.7507	−	28.5285i	0.934259	−	1.17152i	−0.0506961	−	0.998714i	$-0.516144\pi$
$593$	22.7507	−	28.5285i	0.934259	−	1.17152i	0.984955	−	0.172810i	$-0.0552846\pi$
$594$	−4.87308	−	1.11225i	−0.199945	−	0.0456361i
$595$		0			0
$596$	3.52372	−	4.41861i	0.144337	−	0.180993i
$597$		−	47.3613i		−	1.93837i
$598$	−15.1719	−	12.0992i	−0.620424	−	0.494772i
$599$	−4.19070	−	8.70207i	−0.171227	−	0.355557i	0.797642	−	0.603132i	$-0.206081\pi$
$599$	−4.19070	−	8.70207i	−0.171227	−	0.355557i	−0.968869	+	0.247575i	$0.920366\pi$
$600$		0			0
$601$	30.7125	−	24.4924i	1.25279	−	0.999067i	0.253292	−	0.967390i	$-0.418487\pi$
$601$	30.7125	−	24.4924i	1.25279	−	0.999067i	0.999498	−	0.0316774i	$-0.0100849\pi$
$602$	7.73460	+	3.72479i	0.315239	+	0.151811i
$603$	0.549738	−	2.40856i	0.0223870	−	0.0980840i
$604$	2.31867	+	10.1588i	0.0943454	+	0.413354i
$605$		0			0
$606$	4.48021	−	9.30325i	0.181996	−	0.377919i
$607$	20.4337	−	4.66386i	0.829378	−	0.189300i	0.213301	−	0.976986i	$-0.431578\pi$
$607$	20.4337	−	4.66386i	0.829378	−	0.189300i	0.616076	+	0.787686i	$0.288721\pi$
$608$	−2.71134			−0.109959
$609$	−5.24270	+	5.24760i	−0.212445	+	0.212643i
$610$		0			0
$611$	−8.76362	+	2.00024i	−0.354538	+	0.0809211i
$612$	0.0334791	−	0.0695201i	0.00135331	−	0.00281018i
$613$	1.96499	−	0.946291i	0.0793653	−	0.0382203i	−0.393780	−	0.919205i	$-0.628833\pi$
$613$	1.96499	−	0.946291i	0.0793653	−	0.0382203i	0.473145	+	0.880984i	$0.343119\pi$
$614$	−0.185113	−	0.811034i	−0.00747056	−	0.0327307i
$615$		0			0
$616$	−0.718547	−	0.346034i	−0.0289511	−	0.0139421i
$617$	10.2213	−	8.15118i	0.411492	−	0.328154i	−0.395767	−	0.918351i	$-0.629521\pi$
$617$	10.2213	−	8.15118i	0.411492	−	0.328154i	0.807259	+	0.590197i	$0.200950\pi$
$618$	20.7717	+	26.0469i	0.835560	+	1.04776i
$619$	−8.91760	−	18.5176i	−0.358429	−	0.744285i	0.641307	−	0.767285i	$-0.278393\pi$
$619$	−8.91760	−	18.5176i	−0.358429	−	0.744285i	−0.999735	+	0.0229996i	$0.992678\pi$
$620$		0			0
$621$		−	15.7344i		−	0.631401i
$622$	4.65108	−	5.83227i	0.186491	−	0.233853i
$623$	9.92811	+	2.26603i	0.397761	+	0.0907864i
$624$	30.7954	+	7.02884i	1.23280	+	0.281379i
$625$		0			0
$626$		−	13.5708i		−	0.542398i
$627$	−0.464304	−	0.370270i	−0.0185425	−	0.0147872i
$628$	−5.61610	−	11.6619i	−0.224107	−	0.465362i
$629$	−0.306169	−	0.383924i	−0.0122078	−	0.0153080i
$630$		0			0
$631$	34.3200	+	16.5276i	1.36626	+	0.657954i	0.966022	−	0.258459i	$-0.0832146\pi$
$631$	34.3200	+	16.5276i	1.36626	+	0.657954i	0.400234	+	0.916413i	$0.368929\pi$
$632$	1.57607	−	6.90521i	0.0626927	−	0.274675i
$633$	−5.54333	−	24.2869i	−0.220327	−	0.965318i
$634$	−3.48204	+	1.67686i	−0.138289	+	0.0665966i
$635$		0			0
$636$	−5.53247	+	1.26275i	−0.219377	+	0.0500713i
$637$	22.0666			0.874311
$638$	5.30358	+	1.85302i	0.209971	+	0.0733619i
$639$	−4.93234			−0.195120
$640$		0			0
$641$	14.2194	−	29.5268i	0.561631	−	1.16624i	−0.406001	−	0.913872i	$-0.633077\pi$
$641$	14.2194	−	29.5268i	0.561631	−	1.16624i	0.967632	−	0.252366i	$-0.0812085\pi$
$642$	18.1884	−	8.75905i	0.717837	−	0.345692i
$643$	−8.67439	−	38.0050i	−0.342085	−	1.49877i	−0.794666	−	0.607047i	$-0.792354\pi$
$643$	−8.67439	−	38.0050i	−0.342085	−	1.49877i	0.452581	−	0.891723i	$-0.350503\pi$
$644$	−0.532729	+	2.33404i	−0.0209925	+	0.0919740i
$645$		0			0
$646$	−0.140998	+	0.112442i	−0.00554748	+	0.00442397i
$647$	−16.7507	−	21.0048i	−0.658540	−	0.825783i	0.334644	−	0.942345i	$-0.391384\pi$
$647$	−16.7507	−	21.0048i	−0.658540	−	0.825783i	−0.993183	+	0.116562i	$0.962813\pi$
$648$	7.69798	+	15.9850i	0.302405	+	0.627951i
$649$	1.02648	+	0.818590i	0.0402928	+	0.0321325i
$650$		0			0
$651$	0.765532	−	0.959947i	0.0300036	−	0.0376233i
$652$	15.9990	+	3.65166i	0.626567	+	0.143010i
$653$	13.3954	+	3.05740i	0.524201	+	0.119645i	0.476429	−	0.879213i	$-0.341931\pi$
$653$	13.3954	+	3.05740i	0.524201	+	0.119645i	0.0477717	+	0.998858i	$0.484788\pi$
$654$	−29.2135	+	36.6326i	−1.14234	+	1.43245i
$655$		0			0
$656$	0.301586	+	0.240507i	0.0117750	+	0.00939022i
$657$	−2.60660	−	5.41266i	−0.101693	−	0.211168i
$658$	2.10794	+	2.64327i	0.0821759	+	0.103045i
$659$	−24.5810	+	19.6027i	−0.957538	+	0.763611i	−0.971683	−	0.236289i	$-0.924069\pi$
$659$	−24.5810	+	19.6027i	−0.957538	+	0.763611i	0.0141448	+	0.999900i	$0.495497\pi$
$660$		0			0
$661$	−0.705888	+	3.09270i	−0.0274559	+	0.120292i	−0.986799	−	0.161951i	$-0.948221\pi$
$661$	−0.705888	+	3.09270i	−0.0274559	+	0.120292i	0.959343	+	0.282243i	$0.0910785\pi$
$662$	1.42691	+	6.25168i	0.0554582	+	0.242978i
$663$	1.11770	−	0.538255i	0.0434078	−	0.0209041i
$664$	5.72947	−	11.8974i	0.222347	−	0.461708i
$665$		0			0
$666$	1.73684			0.0673011
$667$	−1.97186	+	17.5745i	−0.0763506	+	0.680489i
$668$	7.22352			0.279486
$669$	42.5613	−	9.71433i	1.64551	−	0.375578i
$670$		0			0
$671$	4.87737	−	2.34882i	0.188289	−	0.0906751i
$672$	−1.56094	−	6.83894i	−0.0602147	−	0.263818i
$673$	4.59739	−	20.1425i	0.177216	−	0.776436i	−0.805691	−	0.592336i	$-0.798206\pi$
$673$	4.59739	−	20.1425i	0.177216	−	0.776436i	0.982908	−	0.184100i	$-0.0589370\pi$
$674$	32.4690	+	15.6362i	1.25066	+	0.602285i
$675$		0			0
$676$	0.771691	+	0.967670i	0.0296804	+	0.0372181i
$677$	−10.5411	−	21.8888i	−0.405126	−	0.841254i	−0.999318	−	0.0369300i	$-0.988242\pi$
$677$	−10.5411	−	21.8888i	−0.405126	−	0.841254i	0.594191	−	0.804324i	$-0.297472\pi$
$678$	−39.6084	−	31.5866i	−1.52115	−	1.21308i
$679$		−	10.1807i		−	0.390701i
$680$		0			0
$681$	−34.5389	−	7.88327i	−1.32353	−	0.302088i
$682$	−0.906596	−	0.206925i	−0.0347154	−	0.00792356i
$683$	−26.4623	+	33.1826i	−1.01255	+	1.26970i	−0.0499554	+	0.998751i	$0.515908\pi$
$683$	−26.4623	+	33.1826i	−1.01255	+	1.26970i	−0.962595	+	0.270946i	$0.912664\pi$
$684$		−	0.209228i		−	0.00800002i
$685$		0			0
$686$	−7.51374	−	15.6024i	−0.286876	−	0.595704i
$687$	−4.22058	−	5.29244i	−0.161025	−	0.201919i
$688$	−26.0469	+	20.7717i	−0.993028	+	0.791913i
$689$	−9.72483	−	4.68323i	−0.370486	−	0.178417i
$690$		0			0
$691$	−2.48942	−	10.9068i	−0.0947019	−	0.414916i	0.905248	−	0.424883i	$-0.139685\pi$
$691$	−2.48942	−	10.9068i	−0.0947019	−	0.414916i	−0.999950	+	0.00996661i	$0.996827\pi$
$692$	−17.5760	+	8.46415i	−0.668139	+	0.321759i
$693$	0.0788691	−	0.163773i	0.00299599	−	0.00622124i
$694$	41.5965	−	9.49413i	1.57898	−	0.360392i
$695$		0			0
$696$	−5.80216	−	16.5568i	−0.219930	−	0.627583i
$697$	0.0151496			0.000573831
$698$	28.1283	−	6.42009i	1.06467	−	0.243004i
$699$	12.8331	−	26.6483i	0.485394	−	1.00793i
$700$		0			0
$701$	4.62480	+	20.2626i	0.174676	+	0.765306i	0.984033	+	0.177989i	$0.0569590\pi$
$701$	4.62480	+	20.2626i	0.174676	+	0.765306i	−0.809356	+	0.587318i	$0.800184\pi$
$702$	6.30007	−	27.6024i	0.237781	−	1.04179i
$703$	−1.19966	−	0.577728i	−0.0452462	−	0.0217894i
$704$	0.573553	−	0.457393i	0.0216166	−	0.0172387i
$705$		0			0
$706$	−23.2641	−	48.3084i	−0.875556	−	1.81811i
$707$	−1.89441	−	1.51074i	−0.0712465	−	0.0568172i
$708$			3.90980i			0.146939i
$709$	−0.569564	+	0.714211i	−0.0213904	+	0.0268228i	−0.792412	−	0.609987i	$-0.791175\pi$
$709$	−0.569564	+	0.714211i	−0.0213904	+	0.0268228i	0.771021	+	0.636809i	$0.219746\pi$
$710$		0			0
$711$	1.57386	+	0.359222i	0.0590242	+	0.0134719i
$712$	−15.0169	+	18.8305i	−0.562781	+	0.705705i
$713$		−	2.92726i		−	0.109627i
$714$	−0.364791	−	0.290911i	−0.0136520	−	0.0108871i
$715$		0			0
$716$	14.0639	+	17.6355i	0.525592	+	0.659071i
$717$	−28.6496	+	22.8473i	−1.06994	+	0.853249i
$718$	−32.8515	−	15.8204i	−1.22601	−	0.590414i
$719$	6.97314	−	30.5513i	0.260054	−	1.13937i	−0.661138	−	0.750265i	$-0.729926\pi$
$719$	6.97314	−	30.5513i	0.260054	−	1.13937i	0.921192	−	0.389108i	$-0.127217\pi$
$720$		0			0
$721$	7.04348	−	3.39196i	0.262313	−	0.126323i
$722$	14.0099	−	29.0918i	0.521393	−	1.08268i
$723$	41.6198	−	9.49946i	1.54786	−	0.353289i
$724$	9.50743			0.353341
$725$		0			0
$726$	33.8413			1.25597
$727$	14.7876	−	3.37518i	0.548443	−	0.125179i	0.0606844	−	0.998157i	$-0.480672\pi$
$727$	14.7876	−	3.37518i	0.548443	−	0.125179i	0.487759	+	0.872978i	$0.337815\pi$
$728$	1.96003	−	4.07004i	0.0726435	−	0.150846i
$729$	20.2448	−	9.74939i	0.749808	−	0.361089i
$730$		0			0
$731$	−0.291149	+	1.27561i	−0.0107685	+	0.0471800i
$732$	14.5246	+	6.99467i	0.536844	+	0.258531i
$733$	−1.57785	+	1.25829i	−0.0582793	+	0.0464762i	−0.652196	−	0.758050i	$-0.726152\pi$
$733$	−1.57785	+	1.25829i	−0.0582793	+	0.0464762i	0.593917	+	0.804526i	$0.297581\pi$
$734$	31.4772	+	39.4712i	1.16185	+	1.45691i
$735$		0			0
$736$	−13.0755	−	10.4273i	−0.481968	−	0.384357i
$737$			3.71121i			0.136704i
$738$	−0.0334085	+	0.0418930i	−0.00122978	+	0.00154210i
$739$	22.3628	+	5.10416i	0.822628	+	0.187759i	0.613062	−	0.790035i	$-0.289938\pi$
$739$	22.3628	+	5.10416i	0.822628	+	0.187759i	0.209566	+	0.977794i	$0.432795\pi$
$740$		0			0
$741$	2.09731	−	2.62994i	0.0770466	−	0.0966133i
$742$			4.05965i			0.149035i
$743$	−37.6326	−	30.0110i	−1.38060	−	1.10100i	−0.983034	−	0.183424i	$-0.941282\pi$
$743$	−37.6326	−	30.0110i	−1.38060	−	1.10100i	−0.397571	−	0.917571i	$-0.630147\pi$
$744$	1.25998	+	2.61637i	0.0461931	+	0.0959209i
$745$		0			0
$746$	26.8997	−	21.4518i	0.984867	−	0.785405i
$747$	2.71168	+	1.30588i	0.0992153	+	0.0477796i
$748$	−0.0257930	+	0.113007i	−0.000943086	+	0.00413193i
$749$	−1.05412	−	4.61840i	−0.0385167	−	0.168753i
$750$		0			0
$751$	2.95072	−	6.12723i	0.107673	−	0.223586i	−0.840170	−	0.542324i	$-0.817545\pi$
$751$	2.95072	−	6.12723i	0.107673	−	0.223586i	0.947843	+	0.318738i	$0.103259\pi$
$752$	−12.7913	+	2.91953i	−0.466451	+	0.106464i
$753$	−24.8786			−0.906625
$754$	−10.4960	+	30.0409i	−0.382242	+	1.09402i
$755$		0			0
$756$	−3.40531	+	0.777239i	−0.123850	+	0.0282679i
$757$	11.7430	−	24.3845i	0.426805	−	0.886270i	−0.571057	−	0.820911i	$-0.693466\pi$
$757$	11.7430	−	24.3845i	0.426805	−	0.886270i	0.997862	−	0.0653592i	$-0.0208193\pi$
$758$	53.4042	−	25.7181i	1.93973	−	0.934124i
$759$	−0.815118	−	3.57127i	−0.0295869	−	0.129629i
$760$		0			0
$761$	−26.0670	−	12.5532i	−0.944929	−	0.455054i	−0.103024	−	0.994679i	$-0.532852\pi$
$761$	−26.0670	−	12.5532i	−0.944929	−	0.455054i	−0.841905	+	0.539625i	$0.818566\pi$
$762$	−15.9356	+	12.7082i	−0.577287	+	0.460371i
$763$	6.85518	+	8.59612i	0.248174	+	0.311200i
$764$	7.11147	+	14.7671i	0.257284	+	0.534256i
$765$		0			0
$766$		−	19.2162i		−	0.694309i
$767$	−4.63671	+	5.81425i	−0.167422	+	0.209940i
$768$	33.7295	+	7.69854i	1.21711	+	0.277797i
$769$	−25.7343	−	5.87369i	−0.928003	−	0.211811i	−0.268299	−	0.963336i	$-0.586461\pi$
$769$	−25.7343	−	5.87369i	−0.928003	−	0.211811i	−0.659704	+	0.751525i	$0.729319\pi$
$770$		0			0
$771$		−	28.4244i		−	1.02368i
$772$	−8.82929	−	7.04113i	−0.317773	−	0.253416i
$773$	−9.12471	−	18.9477i	−0.328193	−	0.681500i	0.669950	−	0.742406i	$-0.266315\pi$
$773$	−9.12471	−	18.9477i	−0.328193	−	0.681500i	−0.998144	+	0.0609058i	$0.980601\pi$
$774$	−2.88537	−	3.61814i	−0.103712	−	0.130051i
$775$		0			0
$776$	21.6943	+	10.4474i	0.778779	+	0.375040i
$777$	0.766573	−	3.35858i	0.0275007	−	0.120488i
$778$	−2.62508	−	11.5012i	−0.0941136	−	0.412339i
$779$	0.0370108	−	0.0178235i	0.00132605	−	0.000638592i
$780$		0			0
$781$	7.22364	−	1.64875i	0.258482	−	0.0589968i
$782$	−1.11240			−0.0397792
$783$	−24.3498	+	8.53315i	−0.870192	+	0.304950i
$784$	32.2082			1.15029
$785$		0			0
$786$	7.90925	−	16.4237i	0.282114	−	0.585815i
$787$	25.3140	−	12.1906i	0.902348	−	0.434548i	0.0756116	−	0.997137i	$-0.475909\pi$
$787$	25.3140	−	12.1906i	0.902348	−	0.434548i	0.826736	+	0.562589i	$0.190195\pi$
$788$	−5.64050	−	24.7126i	−0.200934	−	0.880351i
$789$	7.16066	−	31.3729i	0.254926	−	1.11691i
$790$		0			0
$791$	−9.29442	+	7.41205i	−0.330471	+	0.263542i
$792$	0.268052	+	0.336126i	0.00952481	+	0.0119437i
$793$	13.3043	+	27.6267i	0.472450	+	0.981053i
$794$	−38.5528	−	30.7448i	−1.36819	−	1.09109i
$795$		0			0
$796$	−15.6284	+	19.5973i	−0.553932	+	0.694609i
$797$	−24.8395	−	5.66946i	−0.879861	−	0.200823i	−0.241353	−	0.970437i	$-0.577591\pi$
$797$	−24.8395	−	5.66946i	−0.879861	−	0.200823i	−0.638508	+	0.769615i	$0.720448\pi$
$798$	−1.23345	−	0.281528i	−0.0436638	−	0.00996597i
$799$	−0.321273	+	0.402863i	−0.0113658	+	0.0142523i
$800$		0			0
$801$	−4.29191	−	3.42269i	−0.151647	−	0.120935i
$802$	4.62002	+	9.59358i	0.163139	+	0.338761i
$803$	5.62679	+	7.05577i	0.198565	+	0.248993i
$804$	−8.64065	+	6.89069i	−0.304732	+	0.243016i
$805$		0			0
$806$	1.17208	−	5.13520i	0.0412846	−	0.180880i
$807$	−6.05727	−	26.5386i	−0.213226	−	0.934204i
$808$	5.16328	−	2.48650i	0.181644	−	0.0874749i
$809$	2.43829	−	5.06316i	0.0857257	−	0.178011i	−0.853699	−	0.520767i	$-0.825646\pi$
$809$	2.43829	−	5.06316i	0.0857257	−	0.178011i	0.939425	+	0.342756i	$0.111360\pi$
$810$		0			0
$811$	38.9464			1.36759			0.683797	−	0.729672i	$-0.260327\pi$
$811$	38.9464			1.36759			0.683797	+	0.729672i	$0.260327\pi$
$812$	3.90095	−	0.441378i	0.136897	−	0.0154893i
$813$	−2.44975			−0.0859166
$814$	−2.54368	+	0.580578i	−0.0891559	+	0.0203493i
$815$		0			0
$816$	1.63138	−	0.785632i	0.0571098	−	0.0275026i
$817$	0.789466	+	3.45888i	0.0276199	+	0.121011i
$818$	0.129064	−	0.565464i	0.00451260	−	0.0197710i
$819$	0.927656	+	0.446735i	0.0324149	+	0.0156102i
$820$		0			0
$821$	4.56029	+	5.71843i	0.159155	+	0.199575i	0.855015	−	0.518603i	$-0.173548\pi$
$821$	4.56029	+	5.71843i	0.159155	+	0.199575i	−0.695860	+	0.718178i	$0.744976\pi$
$822$	14.8538	+	30.8442i	0.518084	+	1.07581i
$823$	−6.87216	−	5.48036i	−0.239548	−	0.191033i	0.496356	−	0.868119i	$-0.334671\pi$
$823$	−6.87216	−	5.48036i	−0.239548	−	0.191033i	−0.735904	+	0.677086i	$0.763243\pi$
$824$			18.4899i			0.644125i
$825$		0			0
$826$	2.72690	+	0.622398i	0.0948811	+	0.0216560i
$827$	0.0996373	+	0.0227416i	0.00346473	+	0.000790801i	0.224253	−	0.974531i	$-0.428006\pi$
$827$	0.0996373	+	0.0227416i	0.00346473	+	0.000790801i	−0.220788	+	0.975322i	$0.570863\pi$
$828$	0.804653	−	1.00900i	0.0279636	−	0.0350653i
$829$			42.3492i			1.47085i	0.677607	+	0.735424i	$0.263017\pi$
$829$			42.3492i			1.47085i	−0.677607	+	0.735424i	$0.736983\pi$
$830$		0			0
$831$	−9.74077	−	20.2269i	−0.337903	−	0.701664i
$832$	2.59080	+	3.24875i	0.0898197	+	0.112630i
$833$	0.988967	−	0.788675i	0.0342657	−	0.0273260i
$834$	5.79468	+	2.79057i	0.200653	+	0.0966296i
$835$		0			0
$836$	0.0699392	+	0.306424i	0.00241890	+	0.0105979i
$837$	3.84787	−	1.85303i	0.133002	−	0.0640502i
$838$	10.6166	−	22.0456i	0.366744	−	0.761553i
$839$	−23.9245	+	5.46062i	−0.825966	+	0.188521i	−0.614553	−	0.788875i	$-0.710664\pi$
$839$	−23.9245	+	5.46062i	−0.825966	+	0.188521i	−0.211413	+	0.977397i	$0.567807\pi$
$840$		0			0
$841$	28.2669	−	6.47953i	0.974719	−	0.223432i
$842$	−9.40470			−0.324107
$843$	16.4308	−	3.75021i	0.565905	−	0.129164i
$844$	−5.72049	+	11.8787i	−0.196907	+	0.408882i
$845$		0			0
$846$	−0.405549	−	1.77682i	−0.0139431	−	0.0610885i
$847$	1.76707	−	7.74202i	0.0607171	−	0.266019i
$848$	−14.1943	−	6.83560i	−0.487433	−	0.234736i
$849$	−8.53516	+	6.80656i	−0.292926	+	0.233601i
$850$		0			0
$851$	−3.56356	−	7.39980i	−0.122157	−	0.253662i
$852$	17.2510	+	13.7572i	0.591010	+	0.471315i
$853$			37.1709i			1.27271i	0.771397	+	0.636354i	$0.219558\pi$
$853$			37.1709i			1.27271i	−0.771397	+	0.636354i	$0.780442\pi$
$854$	7.19061	−	9.01674i	0.246058	−	0.308547i
$855$		0			0
$856$	10.9231	+	2.49313i	0.373345	+	0.0852135i
$857$	−16.5258	+	20.7227i	−0.564512	+	0.707876i	−0.979385	−	0.202004i	$-0.935255\pi$
$857$	−16.5258	+	20.7227i	−0.564512	+	0.707876i	0.414873	+	0.909879i	$0.363826\pi$
$858$		−	6.59133i		−	0.225024i
$859$	−28.5123	−	22.7378i	−0.972828	−	0.775805i	0.00171635	−	0.999999i	$-0.499454\pi$
$859$	−28.5123	−	22.7378i	−0.972828	−	0.775805i	−0.974545	+	0.224194i	$0.928025\pi$
$860$		0			0
$861$	0.0662644	+	0.0830930i	0.00225829	+	0.00283180i
$862$	−24.9266	+	19.8783i	−0.849002	+	0.677056i
$863$	−15.2090	−	7.32429i	−0.517722	−	0.249322i	0.156729	−	0.987642i	$-0.449905\pi$
$863$	−15.2090	−	7.32429i	−0.517722	−	0.249322i	−0.674451	+	0.738320i	$0.735619\pi$
$864$	5.42954	−	23.7884i	0.184717	−	0.809297i
$865$		0			0
$866$	8.01672	−	3.86065i	0.272419	−	0.131190i
$867$	−13.5750	+	28.1887i	−0.461030	+	0.957338i
$868$	−0.633529	+	0.144599i	−0.0215034	+	0.00490801i
$869$	−2.42506			−0.0822646
$870$		0			0
$871$	−21.0212			−0.712278
$872$	−25.3523	+	5.78650i	−0.858538	+	0.195956i
$873$	−2.38120	+	4.94462i	−0.0805916	+	0.167350i
$874$	−2.71761	+	1.30873i	−0.0919246	+	0.0442686i
$875$		0			0
$876$	−5.98026	+	26.2012i	−0.202054	+	0.885258i
$877$	6.29839	+	3.03315i	0.212682	+	0.102422i	0.537192	−	0.843460i	$-0.319485\pi$
$877$	6.29839	+	3.03315i	0.212682	+	0.102422i	−0.324510	+	0.945882i	$0.605199\pi$
$878$	27.9352	−	22.2776i	0.942769	−	0.751833i
$879$	−12.7102	−	15.9381i	−0.428704	−	0.537578i
$880$		0			0
$881$	4.91274	+	3.91778i	0.165514	+	0.131993i	0.702744	−	0.711443i	$-0.251958\pi$
$881$	4.91274	+	3.91778i	0.165514	+	0.131993i	−0.537230	+	0.843436i	$0.680529\pi$
$882$			4.47400i			0.150648i
$883$	12.0159	−	15.0675i	0.404369	−	0.507062i	−0.537398	−	0.843329i	$-0.680593\pi$
$883$	12.0159	−	15.0675i	0.404369	−	0.507062i	0.941767	+	0.336266i	$0.109164\pi$
$884$	−0.640099	−	0.146098i	−0.0215289	−	0.00491382i
$885$		0			0
$886$	20.1023	−	25.2075i	0.675350	−	0.846862i
$887$			12.8527i			0.431551i	0.976443	+	0.215775i	$0.0692279\pi$
$887$			12.8527i			0.431551i	−0.976443	+	0.215775i	$0.930772\pi$
$888$	6.37018	+	5.08005i	0.213769	+	0.170475i
$889$	2.07522	+	4.30924i	0.0696006	+	0.144527i
$890$		0			0
$891$	4.74936	−	3.78749i	0.159110	−	0.126886i
$892$	−20.8167	−	10.0248i	−0.696995	−	0.335655i
$893$	−0.310909	+	1.36218i	−0.0104042	+	0.0455837i
$894$	4.09938	+	17.9605i	0.137104	+	0.600690i
$895$		0			0
$896$	3.97813	−	8.26067i	0.132900	−	0.275970i
$897$	20.2286	−	4.61704i	0.675413	−	0.154159i
$898$	42.9088			1.43189
$899$	−4.53009	+	1.58752i	−0.151087	+	0.0529469i
$900$		0			0
$901$	−0.603223	+	0.137682i	−0.0200963	+	0.00458684i
$902$	0.0349246	−	0.0725217i	0.00116286	−	0.00241471i
$903$	−8.26999	+	3.98262i	−0.275208	+	0.132533i
$904$	−6.25656	−	27.4118i	−0.208090	−	0.911703i
$905$		0			0
$906$	−30.6022	−	14.7372i	−1.01669	−	0.489612i
$907$	41.0570	−	32.7419i	1.36328	−	1.08718i	0.376267	−	0.926511i	$-0.377208\pi$
$907$	41.0570	−	32.7419i	1.36328	−	1.08718i	0.987009	−	0.160665i	$-0.0513638\pi$
$908$	11.6903	+	14.6592i	0.387956	+	0.486481i
$909$	0.566731	+	1.17683i	0.0187973	+	0.0390330i
$910$		0			0
$911$			40.7714i			1.35082i	0.737444	+	0.675408i	$0.236032\pi$
$911$			40.7714i			1.35082i	−0.737444	+	0.675408i	$0.763968\pi$
$912$	3.06121	−	3.83864i	0.101367	−	0.127110i
$913$	−4.40791	−	1.00608i	−0.145880	−	0.0332963i
$914$	−30.5966	−	6.98347i	−1.01205	−	0.230993i
$915$		0			0
$916$			3.58264i			0.118374i
$917$	−3.34434	−	2.66702i	−0.110440	−	0.0880728i
$918$	−0.704176	−	1.46224i	−0.0232413	−	0.0482610i
$919$	−23.2227	−	29.1203i	−0.766045	−	0.960590i	0.233887	−	0.972264i	$-0.424855\pi$
$919$	−23.2227	−	29.1203i	−0.766045	−	0.960590i	−0.999932	+	0.0116740i	$0.996284\pi$
$920$		0			0
$921$	0.801389	+	0.385929i	0.0264067	+	0.0127168i
$922$	−11.2335	+	49.2172i	−0.369956	+	1.62088i
$923$	9.33894	+	40.9166i	0.307395	+	1.34679i
$924$	−0.732642	+	0.352822i	−0.0241022	+	0.0116070i
$925$		0			0
$926$	−8.44384	+	1.92725i	−0.277482	+	0.0633334i
$927$	−4.21426			−0.138415
$928$	−9.04570	+	25.8899i	−0.296940	+	0.849879i
$929$	13.2995			0.436344			0.218172	−	0.975910i	$-0.429991\pi$
$929$	13.2995			0.436344			0.218172	+	0.975910i	$0.429991\pi$
$930$		0			0
$931$	1.48820	−	3.09027i	0.0487737	−	0.101280i
$932$	−14.1036	+	6.79193i	−0.461978	+	0.222477i
$933$	1.77485	+	7.77614i	0.0581061	+	0.254579i
$934$	−6.69712	+	29.3420i	−0.219136	+	0.960099i
$935$		0			0
$936$	−1.90391	+	1.51832i	−0.0622312	+	0.0496277i
$937$	−4.76611	−	5.97651i	−0.155702	−	0.195244i	0.697862	−	0.716232i	$-0.254135\pi$
$937$	−4.76611	−	5.97651i	−0.155702	−	0.195244i	−0.853564	+	0.520988i	$0.825564\pi$
$938$	3.43043	+	7.12337i	0.112008	+	0.232586i
$939$	11.3445	+	9.04695i	0.370214	+	0.295236i
$940$		0			0
$941$	−18.0907	+	22.6850i	−0.589738	+	0.739509i	−0.983739	−	0.179601i	$-0.942519\pi$
$941$	−18.0907	+	22.6850i	−0.589738	+	0.739509i	0.394001	+	0.919110i	$0.371091\pi$
$942$	41.1347	+	9.38873i	1.34024	+	0.305901i
$943$	0.247031	+	0.0563832i	0.00804444	+	0.00183609i
$944$	−6.76770	+	8.48643i	−0.220270	+	0.276210i
$945$		0			0
$946$	5.43520	+	4.33443i	0.176714	+	0.140924i
$947$	13.4551	+	27.9399i	0.437233	+	0.907923i	0.996860	+	0.0791791i	$0.0252299\pi$
$947$	13.4551	+	27.9399i	0.437233	+	0.907923i	−0.559628	+	0.828744i	$0.689056\pi$
$948$	−4.50267	−	5.64617i	−0.146240	−	0.183379i
$949$	−39.9657	+	31.8716i	−1.29734	+	1.03460i
$950$		0			0
$951$	0.919521	−	4.02868i	0.0298175	−	0.130639i
$952$	−0.0576226	−	0.252461i	−0.00186756	−	0.00818232i
$953$	3.69492	−	1.77938i	0.119690	−	0.0576398i	−0.373080	−	0.927799i	$-0.621698\pi$
$953$	3.69492	−	1.77938i	0.119690	−	0.0576398i	0.492771	+	0.870159i	$0.335984\pi$
$954$	0.949525	−	1.97171i	0.0307420	−	0.0638364i
$955$		0			0
$956$	19.3940			0.627245
$957$	−5.08466	+	3.19822i	−0.164364	+	0.103384i
$958$	−59.9710			−1.93758
$959$	7.83196	−	1.78759i	0.252907	−	0.0577244i
$960$		0			0
$961$	−27.2142	+	13.1057i	−0.877876	+	0.422763i
$962$	−3.28855	−	14.4081i	−0.106027	−	0.464535i
$963$	−0.568242	+	2.48963i	−0.0183113	+	0.0802272i
$964$	−20.3563	−	9.80306i	−0.655631	−	0.315735i
$965$		0			0
$966$	−4.86564	−	6.10131i	−0.156549	−	0.196307i
$967$	8.62851	+	17.9173i	0.277474	+	0.576181i	0.992405	−	0.123014i	$-0.0392560\pi$
$967$	8.62851	+	17.9173i	0.277474	+	0.576181i	−0.714931	+	0.699195i	$0.753542\pi$
$968$	14.6842	+	11.7103i	0.471969	+	0.376382i
$969$		−	0.192826i		−	0.00619447i
$970$		0			0
$971$	−50.6978	−	11.5714i	−1.62697	−	0.371345i	−0.690843	−	0.723005i	$-0.742760\pi$
$971$	−50.6978	−	11.5714i	−1.62697	−	0.371345i	−0.936128	+	0.351659i	$0.885617\pi$
$972$	3.95588	+	0.902903i	0.126885	+	0.0289606i
$973$	0.940987	−	1.17996i	0.0301667	−	0.0378278i
$974$		−	58.9039i		−	1.88740i
$975$		0			0
$976$	19.4189	+	40.3237i	0.621583	+	1.29073i
$977$	−22.3926	−	28.0795i	−0.716404	−	0.898342i	0.281725	−	0.959495i	$-0.409094\pi$
$977$	−22.3926	−	28.0795i	−0.716404	−	0.898342i	−0.998128	+	0.0611534i	$0.980522\pi$
$978$	−41.8222	+	33.3521i	−1.33733	+	1.06648i
$979$	7.42982	+	3.57801i	0.237458	+	0.114354i
$980$		0			0
$981$	−1.31888	−	5.77838i	−0.0421085	−	0.184489i
$982$	−17.0046	+	8.18896i	−0.542637	+	0.261320i
$983$	2.80580	−	5.82630i	0.0894910	−	0.185830i	−0.851419	−	0.524485i	$-0.824258\pi$
$983$	2.80580	−	5.82630i	0.0894910	−	0.185830i	0.940911	+	0.338655i	$0.109972\pi$
$984$	−0.245064	+	0.0559343i	−0.00781236	+	0.00178312i
$985$		0			0
$986$	0.603278	+	1.72149i	0.0192123	+	0.0548233i
$987$	−3.61489			−0.115063
$988$	−1.73566	+	0.396154i	−0.0552188	+	0.0126033i
$989$	−9.49503	+	19.7166i	−0.301924	+	0.626952i
$990$		0			0
$991$	9.84962	+	43.1540i	0.312883	+	1.37083i	0.849759	+	0.527171i	$0.176747\pi$
$991$	9.84962	+	43.1540i	0.312883	+	1.37083i	−0.536876	+	0.843661i	$0.680396\pi$
$992$	1.01012	−	4.42563i	0.0320714	−	0.140514i
$993$	−6.17733	−	2.97485i	−0.196032	−	0.0944039i
$994$	12.3412	−	9.84177i	0.391439	−	0.312162i
$995$		0			0
$996$	−5.84186	−	12.1308i	−0.185106	−	0.384378i
$997$	−4.35205	−	3.47065i	−0.137831	−	0.109916i	0.552147	−	0.833746i	$-0.313809\pi$
$997$	−4.35205	−	3.47065i	−0.137831	−	0.109916i	−0.689978	+	0.723830i	$0.742380\pi$
$998$		−	10.7183i		−	0.339282i
$999$	7.47116	−	9.36854i	0.236377	−	0.296407i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	725.2.q.e.51.8	yes	60
5.2	odd	4		725.2.p.d.399.16		120
5.3	odd	4		725.2.p.d.399.5		120
5.4	even	2		725.2.q.d.51.3	✓	60
29.4	even	14	inner	725.2.q.e.526.8	yes	60
145.4	even	14		725.2.q.d.526.3	yes	60
145.33	odd	28		725.2.p.d.149.16		120
145.62	odd	28		725.2.p.d.149.5		120

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
725.2.p.d.149.5		120	145.62	odd	28
725.2.p.d.149.16		120	145.33	odd	28
725.2.p.d.399.5		120	5.3	odd	4
725.2.p.d.399.16		120	5.2	odd	4
725.2.q.d.51.3	✓	60	5.4	even	2
725.2.q.d.526.3	yes	60	145.4	even	14
725.2.q.e.51.8	yes	60	1.1	even	1	trivial
725.2.q.e.526.8	yes	60	29.4	even	14	inner

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:	\( N \)	\(=\)	\( 725 = 5^{2} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	725.q (of order \(14\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(1.68193 - 0.383889i) q^{2} +(-0.800342 + 1.66193i) q^{3} +(0.879573 - 0.423580i) q^{4} +(-0.708122 + 3.10248i) q^{6} +(0.672793 + 0.324000i) q^{7} +(-1.38083 + 1.10118i) q^{8} +(-0.250983 - 0.314723i) q^{9} +(0.472780 + 0.377030i) q^{11} +1.80079i q^{12} +(-2.13560 + 2.67795i) q^{13} +(1.25597 + 0.286667i) q^{14} +(-3.11710 + 3.90872i) q^{16} +0.196346i q^{17} +(-0.542955 - 0.432992i) q^{18} +(0.231001 + 0.479679i) q^{19} +(-1.07693 + 0.858822i) q^{21} +(0.939920 + 0.452642i) q^{22} +(-0.730756 + 3.20165i) q^{23} +(-0.724938 - 3.17616i) q^{24} +(-2.56388 + 5.32395i) q^{26} +(-4.67113 + 1.06616i) q^{27} +0.729011 q^{28} +(5.35102 - 0.605448i) q^{29} +(-0.869026 + 0.198350i) q^{31} +(-2.20961 + 4.58831i) q^{32} +(-1.00498 + 0.483974i) q^{33} +(0.0753752 + 0.330240i) q^{34} +(-0.354069 - 0.170511i) q^{36} +(-1.95534 + 1.55933i) q^{37} +(0.572672 + 0.718107i) q^{38} +(-2.74135 - 5.69248i) q^{39} -0.0771574i q^{41} +(-1.48162 + 1.85790i) q^{42} +(6.49672 + 1.48283i) q^{43} +(0.575547 + 0.131365i) q^{44} +5.66548i q^{46} +(2.05180 + 1.63625i) q^{47} +(-4.00126 - 8.30869i) q^{48} +(-4.01675 - 5.03685i) q^{49} +(-0.326313 - 0.157144i) q^{51} +(-0.744085 + 3.26005i) q^{52} +(0.701218 + 3.07224i) q^{53} +(-7.44723 + 3.58640i) q^{54} +(-1.28580 + 0.293474i) q^{56} -0.982072 q^{57} +(8.76761 - 3.07252i) q^{58} +2.17115 q^{59} +(3.88421 - 8.06565i) q^{61} +(-1.38550 + 0.667219i) q^{62} +(-0.0668896 - 0.293062i) q^{63} +(0.269951 - 1.18273i) q^{64} +(-1.50451 + 1.19981i) q^{66} +(3.82647 + 4.79824i) q^{67} +(0.0831684 + 0.172701i) q^{68} +(-4.73605 - 3.77688i) q^{69} +(7.63953 - 9.57966i) q^{71} +(0.693132 + 0.158203i) q^{72} +(14.5498 + 3.32090i) q^{73} +(-2.69013 + 3.37332i) q^{74} +(0.406365 + 0.324066i) q^{76} +(0.195926 + 0.406844i) q^{77} +(-6.79604 - 8.52196i) q^{78} +(-3.13538 + 2.50038i) q^{79} +(2.23536 - 9.79373i) q^{81} +(-0.0296199 - 0.129773i) q^{82} +(-6.73633 + 3.24405i) q^{83} +(-0.583458 + 1.21156i) q^{84} +11.4963 q^{86} +(-3.27644 + 9.37757i) q^{87} -1.06801 q^{88} +(13.2952 - 3.03454i) q^{89} +(-2.30447 + 1.10977i) q^{91} +(0.713403 + 3.12562i) q^{92} +(0.365875 - 1.60300i) q^{93} +(4.07912 + 1.96440i) q^{94} +(-5.85698 - 7.34442i) q^{96} +(-5.91536 - 12.2834i) q^{97} +(-8.68948 - 6.92963i) q^{98} -0.243423i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q + 12 q^{4} - 16 q^{6} + 4 q^{7} + 21 q^{8} + 10 q^{9} + 14 q^{11} - 4 q^{13} + 10 q^{16} - 35 q^{22} + 37 q^{23} + 48 q^{24} - 21 q^{27} - 44 q^{28} - 4 q^{29} + 14 q^{31} - 98 q^{32} + 41 q^{33} + 10 q^{34}+ \cdots - 91 q^{98}+O(q^{100}) \) 60 * q + 12 * q^4 - 16 * q^6 + 4 * q^7 + 21 * q^8 + 10 * q^9 + 14 * q^11 - 4 * q^13 + 10 * q^16 - 35 * q^22 + 37 * q^23 + 48 * q^24 - 21 * q^27 - 44 * q^28 - 4 * q^29 + 14 * q^31 - 98 * q^32 + 41 * q^33 + 10 * q^34 + 32 * q^36 - 7 * q^37 + 14 * q^38 + 56 * q^39 + 45 * q^42 - 63 * q^44 + 42 * q^47 + 21 * q^48 - 72 * q^49 - 32 * q^51 + 80 * q^52 + 20 * q^53 - 65 * q^54 - 63 * q^56 + 28 * q^57 + 2 * q^58 - 16 * q^59 - 28 * q^61 + 70 * q^62 - 42 * q^63 + 37 * q^64 - 140 * q^66 + 24 * q^67 + 42 * q^68 - 84 * q^69 + 9 * q^71 + 105 * q^72 - 14 * q^73 - 85 * q^74 + 70 * q^76 - 21 * q^77 - 102 * q^78 + 56 * q^79 - 72 * q^81 - 36 * q^82 - 6 * q^83 - 84 * q^84 + 86 * q^86 - 5 * q^87 - 102 * q^88 + 14 * q^89 - 60 * q^91 - 91 * q^92 + 62 * q^93 - 44 * q^94 + 25 * q^96 - 14 * q^97 - 91 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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