LMFDB - Embedded newform 425.2.n.f.274.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [425,2,Mod(49,425)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(425, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([4, 3]))

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

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

chi := DirichletCharacter("425.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 425 = 5^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	425.n (of order $8$, degree $4$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.39364208590$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$6$ over $\Q(\zeta_{8})$
Twist minimal:	no (minimal twist has level 85)
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			274.5
Character	$\chi$	$=$	425.274
Dual form			425.2.n.f.349.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.01710 - 1.01710i) q^{2} +(-0.0420595 - 0.101541i) q^{3} -0.0689897i q^{4} +(-0.146056 - 0.0604983i) q^{6} +(0.642174 + 0.265997i) q^{7} +(1.96403 + 1.96403i) q^{8} +(2.11278 - 2.11278i) q^{9} +(-4.48163 - 1.85635i) q^{11} +(-0.00700526 + 0.00290167i) q^{12} +5.63906 q^{13} +(0.923703 - 0.382610i) q^{14} +4.13322 q^{16} +(3.78674 - 1.63113i) q^{17} -4.29782i q^{18} +(1.64241 + 1.64241i) q^{19} -0.0763945i q^{21} +(-6.44637 + 2.67018i) q^{22} +(-1.77445 + 4.28390i) q^{23} +(0.116823 - 0.282035i) q^{24} +(5.73549 - 5.73549i) q^{26} +(-0.608017 - 0.251849i) q^{27} +(0.0183511 - 0.0443034i) q^{28} +(-2.48981 - 6.01093i) q^{29} +(-6.12711 + 2.53793i) q^{31} +(0.275837 - 0.275837i) q^{32} +0.533145i q^{33} +(2.19248 - 5.51052i) q^{34} +(-0.145760 - 0.145760i) q^{36} +(-0.0453958 - 0.109595i) q^{37} +3.34100 q^{38} +(-0.237176 - 0.572593i) q^{39} +(-0.412826 + 0.996650i) q^{41} +(-0.0777010 - 0.0777010i) q^{42} +(-0.453332 - 0.453332i) q^{43} +(-0.128069 + 0.309187i) q^{44} +(2.55237 + 6.16195i) q^{46} -4.93703 q^{47} +(-0.173841 - 0.419690i) q^{48} +(-4.60811 - 4.60811i) q^{49} +(-0.324894 - 0.315904i) q^{51} -0.389037i q^{52} +(-8.47565 + 8.47565i) q^{53} +(-0.874571 + 0.362259i) q^{54} +(0.738824 + 1.78368i) q^{56} +(0.0976925 - 0.235850i) q^{57} +(-8.64611 - 3.58134i) q^{58} +(-7.01329 + 7.01329i) q^{59} +(0.613413 - 1.48091i) q^{61} +(-3.65056 + 8.81322i) q^{62} +(1.91877 - 0.794779i) q^{63} +7.70533i q^{64} +(0.542263 + 0.542263i) q^{66} -2.99411i q^{67} +(-0.112531 - 0.261246i) q^{68} +0.509622 q^{69} +(-4.33163 + 1.79422i) q^{71} +8.29913 q^{72} +(5.08052 - 2.10442i) q^{73} +(-0.157641 - 0.0652972i) q^{74} +(0.113309 - 0.113309i) q^{76} +(-2.38421 - 2.38421i) q^{77} +(-0.823617 - 0.341153i) q^{78} +(13.7140 + 5.68053i) q^{79} -8.89143i q^{81} +(0.593808 + 1.43358i) q^{82} +(3.56033 - 3.56033i) q^{83} -0.00527044 q^{84} -0.922169 q^{86} +(-0.505633 + 0.505633i) q^{87} +(-5.15614 - 12.4480i) q^{88} +2.35657i q^{89} +(3.62126 + 1.49997i) q^{91} +(0.295545 + 0.122419i) q^{92} +(0.515406 + 0.515406i) q^{93} +(-5.02145 + 5.02145i) q^{94} +(-0.0396102 - 0.0164071i) q^{96} +(-2.49522 + 1.03355i) q^{97} -9.37384 q^{98} +(-13.3908 + 5.54664i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 8 q^{3} - 8 q^{6} + 24 q^{9} - 8 q^{11} - 40 q^{12} - 16 q^{13} - 24 q^{16} + 8 q^{19} + 24 q^{22} - 8 q^{23} + 8 q^{24} + 16 q^{26} - 16 q^{27} + 40 q^{28} + 8 q^{29} - 16 q^{34} - 24 q^{36} + 16 q^{37}+ \cdots + 8 q^{99}+O(q^{100}) $ 24 * q + 8 * q^3 - 8 * q^6 + 24 * q^9 - 8 * q^11 - 40 * q^12 - 16 * q^13 - 24 * q^16 + 8 * q^19 + 24 * q^22 - 8 * q^23 + 8 * q^24 + 16 * q^26 - 16 * q^27 + 40 * q^28 + 8 * q^29 - 16 * q^34 - 24 * q^36 + 16 * q^37 + 48 * q^38 - 8 * q^39 + 16 * q^41 + 24 * q^42 + 8 * q^43 - 16 * q^44 + 8 * q^46 + 64 * q^47 + 8 * q^48 - 56 * q^51 - 24 * q^53 + 32 * q^54 + 64 * q^56 - 16 * q^57 - 56 * q^58 - 32 * q^59 + 32 * q^61 + 32 * q^62 - 80 * q^63 + 96 * q^66 - 24 * q^68 - 96 * q^69 - 24 * q^71 + 24 * q^72 + 64 * q^73 + 64 * q^74 - 8 * q^76 - 24 * q^77 - 8 * q^78 + 16 * q^82 + 96 * q^83 + 64 * q^84 - 16 * q^86 - 48 * q^87 - 8 * q^88 - 24 * q^91 - 112 * q^92 + 64 * q^93 - 56 * q^94 - 168 * q^96 - 48 * q^97 - 120 * q^98 + 8 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/425\mathbb{Z}\right)^\times$.

$n$	$52$	$326$
$\chi(n)$	$-1$	$e\left(\frac{7}{8}\right)$

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 $

$2$	1.01710	−	1.01710i	0.719199	−	0.719199i	−0.249242	−	0.968441i	$-0.580181\pi$
$2$	1.01710	−	1.01710i	0.719199	−	0.719199i	0.968441	+	0.249242i	$0.0801815\pi$
$3$	−0.0420595	−	0.101541i	−0.0242831	−	0.0586245i	0.911273	−	0.411803i	$-0.135101\pi$
$3$	−0.0420595	−	0.101541i	−0.0242831	−	0.0586245i	−0.935556	+	0.353179i	$0.885101\pi$
$4$		−	0.0689897i		−	0.0344949i
$5$		0			0
$5$		0			0
$6$	−0.146056	−	0.0604983i	−0.0596271	−	0.0246983i
$7$	0.642174	+	0.265997i	0.242719	+	0.100538i	0.500727	−	0.865605i	$-0.333066\pi$
$7$	0.642174	+	0.265997i	0.242719	+	0.100538i	−0.258008	+	0.966143i	$0.583066\pi$
$8$	1.96403	+	1.96403i	0.694390	+	0.694390i
$9$	2.11278	−	2.11278i	0.704260	−	0.704260i
$10$		0			0
$11$	−4.48163	−	1.85635i	−1.35126	−	0.559712i	−0.414620	−	0.909995i	$-0.636085\pi$
$11$	−4.48163	−	1.85635i	−1.35126	−	0.559712i	−0.936644	+	0.350283i	$0.886085\pi$
$12$	−0.00700526	+	0.00290167i	−0.00202224	+	0.000837641i
$13$	5.63906			1.56399			0.781996	−	0.623283i	$-0.214202\pi$
$13$	5.63906			1.56399			0.781996	+	0.623283i	$0.214202\pi$
$14$	0.923703	−	0.382610i	0.246870	−	0.102257i
$15$		0			0
$16$	4.13322			1.03330
$17$	3.78674	−	1.63113i	0.918420	−	0.395606i
$17$	3.78674	−	1.63113i	0.918420	−	0.395606i
$18$		−	4.29782i		−	1.01301i
$19$	1.64241	+	1.64241i	0.376795	+	0.376795i	0.869945	−	0.493150i	$-0.164154\pi$
$19$	1.64241	+	1.64241i	0.376795	+	0.376795i	−0.493150	+	0.869945i	$0.664154\pi$
$20$		0			0
$21$		−	0.0763945i		−	0.0166706i
$22$	−6.44637	+	2.67018i	−1.37437	+	0.569283i
$23$	−1.77445	+	4.28390i	−0.369998	+	0.893255i	0.623751	+	0.781623i	$0.285608\pi$
$23$	−1.77445	+	4.28390i	−0.369998	+	0.893255i	−0.993750	+	0.111632i	$0.964392\pi$
$24$	0.116823	−	0.282035i	0.0238464	−	0.0575702i
$25$		0			0
$26$	5.73549	−	5.73549i	1.12482	−	1.12482i
$27$	−0.608017	−	0.251849i	−0.117013	−	0.0484684i
$28$	0.0183511	−	0.0443034i	0.00346803	−	0.00837256i
$29$	−2.48981	−	6.01093i	−0.462346	−	1.11620i	−0.967432	−	0.253132i	$-0.918539\pi$
$29$	−2.48981	−	6.01093i	−0.462346	−	1.11620i	0.505086	−	0.863069i	$-0.331461\pi$
$30$		0			0
$31$	−6.12711	+	2.53793i	−1.10046	+	0.455826i	−0.857643	−	0.514246i	$-0.828072\pi$
$31$	−6.12711	+	2.53793i	−1.10046	+	0.455826i	−0.242819	+	0.970072i	$0.578072\pi$
$32$	0.275837	−	0.275837i	0.0487616	−	0.0487616i
$33$			0.533145i			0.0928087i
$34$	2.19248	−	5.51052i	0.376008	−	0.945047i
$35$		0			0
$36$	−0.145760	−	0.145760i	−0.0242933	−	0.0242933i
$37$	−0.0453958	−	0.109595i	−0.00746302	−	0.0180173i	0.920104	−	0.391674i	$-0.128104\pi$
$37$	−0.0453958	−	0.109595i	−0.00746302	−	0.0180173i	−0.927567	+	0.373657i	$0.878104\pi$
$38$	3.34100			0.541981
$39$	−0.237176	−	0.572593i	−0.0379785	−	0.0916883i
$40$		0			0
$41$	−0.412826	+	0.996650i	−0.0644726	+	0.155651i	−0.952832	−	0.303498i	$-0.901845\pi$
$41$	−0.412826	+	0.996650i	−0.0644726	+	0.155651i	0.888359	+	0.459149i	$0.151845\pi$
$42$	−0.0777010	−	0.0777010i	−0.0119895	−	0.0119895i
$43$	−0.453332	−	0.453332i	−0.0691325	−	0.0691325i	0.671695	−	0.740828i	$-0.265566\pi$
$43$	−0.453332	−	0.453332i	−0.0691325	−	0.0691325i	−0.740828	+	0.671695i	$0.765566\pi$
$44$	−0.128069	+	0.309187i	−0.0193072	+	0.0466116i
$45$		0			0
$46$	2.55237	+	6.16195i	0.376326	+	0.908531i
$47$	−4.93703			−0.720139			−0.360070	−	0.932925i	$-0.617247\pi$
$47$	−4.93703			−0.720139			−0.360070	+	0.932925i	$0.617247\pi$
$48$	−0.173841	−	0.419690i	−0.0250918	−	0.0605770i
$49$	−4.60811	−	4.60811i	−0.658302	−	0.658302i
$50$		0			0
$51$	−0.324894	−	0.315904i	−0.0454943	−	0.0442354i
$52$		−	0.389037i		−	0.0539497i
$53$	−8.47565	+	8.47565i	−1.16422	+	1.16422i	−0.180678	+	0.983542i	$0.557829\pi$
$53$	−8.47565	+	8.47565i	−1.16422	+	1.16422i	−0.983542	+	0.180678i	$0.942171\pi$
$54$	−0.874571	+	0.362259i	−0.119014	+	0.0492972i
$55$		0			0
$56$	0.738824	+	1.78368i	0.0987295	+	0.238354i
$57$	0.0976925	−	0.235850i	0.0129397	−	0.0312392i
$58$	−8.64611	−	3.58134i	−1.13529	−	0.470252i
$59$	−7.01329	+	7.01329i	−0.913053	+	0.913053i	−0.996511	−	0.0834587i	$-0.973403\pi$
$59$	−7.01329	+	7.01329i	−0.913053	+	0.913053i	0.0834587	+	0.996511i	$0.473403\pi$
$60$		0			0
$61$	0.613413	−	1.48091i	0.0785394	−	0.189611i	−0.879733	−	0.475469i	$-0.842278\pi$
$61$	0.613413	−	1.48091i	0.0785394	−	0.189611i	0.958272	+	0.285858i	$0.0922785\pi$
$62$	−3.65056	+	8.81322i	−0.463621	+	1.11928i
$63$	1.91877	−	0.794779i	0.241742	−	0.100133i
$64$			7.70533i			0.963166i
$65$		0			0
$66$	0.542263	+	0.542263i	0.0667479	+	0.0667479i
$67$		−	2.99411i		−	0.365789i	−0.983133	−	0.182894i	$-0.941453\pi$
$67$		−	2.99411i		−	0.365789i	0.983133	−	0.182894i	$-0.0585467\pi$
$68$	−0.112531	−	0.261246i	−0.0136464	−	0.0316808i
$69$	0.509622			0.0613513
$70$		0			0
$71$	−4.33163	+	1.79422i	−0.514070	+	0.212935i	−0.624610	−	0.780937i	$-0.714742\pi$
$71$	−4.33163	+	1.79422i	−0.514070	+	0.212935i	0.110540	+	0.993872i	$0.464742\pi$
$72$	8.29913			0.978062
$73$	5.08052	−	2.10442i	0.594629	−	0.246304i	−0.0650115	−	0.997885i	$-0.520708\pi$
$73$	5.08052	−	2.10442i	0.594629	−	0.246304i	0.659641	+	0.751581i	$0.270708\pi$
$74$	−0.157641	−	0.0652972i	−0.0183254	−	0.00759065i
$75$		0			0
$76$	0.113309	−	0.113309i	0.0129975	−	0.0129975i
$77$	−2.38421	−	2.38421i	−0.271705	−	0.271705i
$78$	−0.823617	−	0.341153i	−0.0932563	−	0.0386280i
$79$	13.7140	+	5.68053i	1.54295	+	0.639110i	0.982024	−	0.188757i	$-0.0604460\pi$
$79$	13.7140	+	5.68053i	1.54295	+	0.639110i	0.560924	+	0.827867i	$0.310446\pi$
$80$		0			0
$81$		−	8.89143i		−	0.987937i
$82$	0.593808	+	1.43358i	0.0655752	+	0.158312i
$83$	3.56033	−	3.56033i	0.390797	−	0.390797i	−0.484175	−	0.874971i	$-0.660880\pi$
$83$	3.56033	−	3.56033i	0.390797	−	0.390797i	0.874971	+	0.484175i	$0.160880\pi$
$84$	−0.00527044			−0.000575052
$85$		0			0
$86$	−0.922169			−0.0994400
$87$	−0.505633	+	0.505633i	−0.0542096	+	0.0542096i
$88$	−5.15614	−	12.4480i	−0.549646	−	1.32696i
$89$			2.35657i			0.249796i	0.992170	+	0.124898i	$0.0398604\pi$
$89$			2.35657i			0.249796i	−0.992170	+	0.124898i	$0.960140\pi$
$90$		0			0
$91$	3.62126	+	1.49997i	0.379611	+	0.157240i
$92$	0.295545	+	0.122419i	0.0308127	+	0.0127630i
$93$	0.515406	+	0.515406i	0.0534452	+	0.0534452i
$94$	−5.02145	+	5.02145i	−0.517924	+	0.517924i
$95$		0			0
$96$	−0.0396102	−	0.0164071i	−0.00404270	−	0.00167454i
$97$	−2.49522	+	1.03355i	−0.253351	+	0.104941i	−0.505745	−	0.862683i	$-0.668782\pi$
$97$	−2.49522	+	1.03355i	−0.253351	+	0.104941i	0.252394	+	0.967625i	$0.418782\pi$
$98$	−9.37384			−0.946900
$99$	−13.3908	+	5.54664i	−1.34582	+	0.557458i
$100$		0			0
$101$	−14.3025			−1.42315			−0.711575	−	0.702610i	$-0.752018\pi$
$101$	−14.3025			−1.42315			−0.711575	+	0.702610i	$0.752018\pi$
$102$	−0.651756	+	0.00914379i	−0.0645335	+	0.000905370i
$103$		−	10.8963i		−	1.07365i	−0.843694	−	0.536824i	$-0.819624\pi$
$103$		−	10.8963i		−	1.07365i	0.843694	−	0.536824i	$-0.180376\pi$
$104$	11.0753	+	11.0753i	1.08602	+	1.08602i
$105$		0			0
$106$			17.2412i			1.67461i
$107$	15.3616	−	6.36300i	1.48507	−	0.615134i	0.514829	−	0.857293i	$-0.327855\pi$
$107$	15.3616	−	6.36300i	1.48507	−	0.615134i	0.970237	+	0.242158i	$0.0778553\pi$
$108$	−0.0173750	+	0.0419469i	−0.00167191	+	0.00403635i
$109$	−4.05640	+	9.79302i	−0.388533	+	0.938002i	0.601718	+	0.798708i	$0.294483\pi$
$109$	−4.05640	+	9.79302i	−0.388533	+	0.938002i	−0.990251	+	0.139293i	$0.955517\pi$
$110$		0			0
$111$	−0.00921903	+	0.00921903i	−0.000875032	+	0.000875032i
$112$	2.65425	+	1.09943i	0.250803	+	0.103886i
$113$	−4.41604	+	10.6613i	−0.415426	+	1.00293i	0.568230	+	0.822869i	$0.307628\pi$
$113$	−4.41604	+	10.6613i	−0.415426	+	1.00293i	−0.983656	+	0.180057i	$0.942372\pi$
$114$	−0.140521	−	0.339247i	−0.0131610	−	0.0317734i
$115$		0			0
$116$	−0.414692	+	0.171771i	−0.0385032	+	0.0159485i
$117$	11.9141	−	11.9141i	1.10146	−	1.10146i
$118$			14.2665i			1.31333i
$119$	2.86563	−	0.0402032i	0.262691	−	0.00368542i
$120$		0			0
$121$	8.86082	+	8.86082i	0.805529	+	0.805529i
$122$	−0.882332	−	2.13014i	−0.0798825	−	0.192854i
$123$	0.118564			0.0106905
$124$	0.175091	+	0.422708i	0.0157237	+	0.0379603i
$125$		0			0
$126$	1.14321	−	2.75995i	0.101845	−	0.245876i
$127$	−0.352520	−	0.352520i	−0.0312811	−	0.0312811i	0.691293	−	0.722574i	$-0.257041\pi$
$127$	−0.352520	−	0.352520i	−0.0312811	−	0.0312811i	−0.722574	+	0.691293i	$0.757041\pi$
$128$	8.38878	+	8.38878i	0.741470	+	0.741470i
$129$	−0.0269647	+	0.0650985i	−0.00237411	+	0.00573160i
$130$		0			0
$131$	−7.47537	−	18.0471i	−0.653126	−	1.57679i	−0.808217	−	0.588885i	$-0.799567\pi$
$131$	−7.47537	−	18.0471i	−0.653126	−	1.57679i	0.155091	−	0.987900i	$-0.450433\pi$
$132$	0.0367815			0.00320142
$133$	0.617838	+	1.49159i	0.0535733	+	0.129337i
$134$	−3.04531	−	3.04531i	−0.263075	−	0.263075i
$135$		0			0
$136$	10.6409	+	4.23371i	0.912447	+	0.363037i
$137$			3.81724i			0.326129i	0.986615	+	0.163065i	$0.0521379\pi$
$137$			3.81724i			0.326129i	−0.986615	+	0.163065i	$0.947862\pi$
$138$	0.518337	−	0.518337i	0.0441238	−	0.0441238i
$139$	−12.2437	+	5.07150i	−1.03850	+	0.430159i	−0.835772	−	0.549076i	$-0.814980\pi$
$139$	−12.2437	+	5.07150i	−1.03850	+	0.430159i	−0.202725	+	0.979236i	$0.564980\pi$
$140$		0			0
$141$	0.207649	+	0.501309i	0.0174872	+	0.0422178i
$142$	−2.58080	+	6.23061i	−0.216576	+	0.522861i
$143$	−25.2722	−	10.4681i	−2.11337	−	0.875385i
$144$	8.73258	−	8.73258i	0.727715	−	0.727715i
$145$		0			0
$146$	3.02699	−	7.30780i	0.250516	−	0.604798i
$147$	−0.274096	+	0.661726i	−0.0226070	+	0.0545782i
$148$	−0.00756094	+	0.00313184i	−0.000621505	+	0.000257436i
$149$		−	17.4543i		−	1.42991i	−0.699171	−	0.714955i	$-0.746447\pi$
$149$		−	17.4543i		−	1.42991i	0.699171	−	0.714955i	$-0.253553\pi$
$150$		0			0
$151$	7.97016	+	7.97016i	0.648602	+	0.648602i	0.952655	−	0.304053i	$-0.0983400\pi$
$151$	7.97016	+	7.97016i	0.648602	+	0.648602i	−0.304053	+	0.952655i	$0.598340\pi$
$152$			6.45150i			0.523286i
$153$	4.55435	−	11.4468i	0.368197	−	0.925416i
$154$	−4.84996			−0.390821
$155$		0			0
$156$	−0.0395030	+	0.0163627i	−0.00316277	+	0.00131006i
$157$	−6.14541			−0.490457			−0.245229	−	0.969465i	$-0.578863\pi$
$157$	−6.14541			−0.490457			−0.245229	+	0.969465i	$0.578863\pi$
$158$	19.7262	−	8.17087i	1.56933	−	0.650039i
$159$	1.21710	+	0.504141i	0.0965227	+	0.0399810i
$160$		0			0
$161$	−2.27901	+	2.27901i	−0.179611	+	0.179611i
$162$	−9.04348	−	9.04348i	−0.710523	−	0.710523i
$163$	10.3485	+	4.28650i	0.810560	+	0.335745i	0.749177	−	0.662369i	$-0.230449\pi$
$163$	10.3485	+	4.28650i	0.810560	+	0.335745i	0.0613824	+	0.998114i	$0.480449\pi$
$164$	0.0687586	+	0.0284808i	0.00536915	+	0.00222397i
$165$		0			0
$166$		−	7.24243i		−	0.562121i
$167$	2.18360	+	5.27168i	0.168972	+	0.407935i	0.985569	−	0.169273i	$-0.0541420\pi$
$167$	2.18360	+	5.27168i	0.168972	+	0.407935i	−0.816597	+	0.577208i	$0.804142\pi$
$168$	0.150041	−	0.150041i	0.0115759	−	0.0115759i
$169$	18.7989			1.44607
$170$		0			0
$171$	6.94010			0.530723
$172$	−0.0312752	+	0.0312752i	−0.00238471	+	0.00238471i
$173$	−1.73644	−	4.19214i	−0.132019	−	0.318722i	0.844022	−	0.536309i	$-0.180182\pi$
$173$	−1.73644	−	4.19214i	−0.132019	−	0.318722i	−0.976041	+	0.217586i	$0.930182\pi$
$174$			1.02856i			0.0779750i
$175$		0			0
$176$	−18.5236	−	7.67272i	−1.39627	−	0.578353i
$177$	1.00711	+	0.417158i	0.0756990	+	0.0313555i
$178$	2.39687	+	2.39687i	0.179653	+	0.179653i
$179$	12.9935	−	12.9935i	0.971179	−	0.971179i	−0.0284174	−	0.999596i	$-0.509047\pi$
$179$	12.9935	−	12.9935i	0.971179	−	0.971179i	0.999596	+	0.0284174i	$0.00904677\pi$
$180$		0			0
$181$	−9.90234	−	4.10168i	−0.736035	−	0.304876i	−0.0170058	−	0.999855i	$-0.505413\pi$
$181$	−9.90234	−	4.10168i	−0.736035	−	0.304876i	−0.719029	+	0.694980i	$0.755413\pi$
$182$	5.20881	−	2.15756i	0.386103	−	0.159929i
$183$	−0.176172			−0.0130230
$184$	−11.8988	+	4.92864i	−0.877191	+	0.363344i
$185$		0			0
$186$	1.04844			0.0768754
$187$	−19.9987	+	0.280571i	−1.46245	+	0.0205174i
$188$			0.340604i			0.0248411i
$189$	−0.323462	−	0.323462i	−0.0235284	−	0.0235284i
$190$		0			0
$191$			18.5397i			1.34149i	0.741690	+	0.670743i	$0.234024\pi$
$191$			18.5397i			1.34149i	−0.741690	+	0.670743i	$0.765976\pi$
$192$	0.782404	−	0.324082i	0.0564652	−	0.0233886i
$193$	−3.78317	+	9.13339i	−0.272319	+	0.657435i	−0.999582	−	0.0289235i	$-0.990792\pi$
$193$	−3.78317	+	9.13339i	−0.272319	+	0.657435i	0.727263	+	0.686359i	$0.240792\pi$
$194$	−1.48666	+	3.58912i	−0.106736	+	0.257684i
$195$		0			0
$196$	−0.317912	+	0.317912i	−0.0227080	+	0.0227080i
$197$	−12.8913	−	5.33973i	−0.918464	−	0.380440i	−0.127173	−	0.991881i	$-0.540590\pi$
$197$	−12.8913	−	5.33973i	−0.918464	−	0.380440i	−0.791291	+	0.611440i	$0.790590\pi$
$198$	−7.97827	+	19.2613i	−0.566991	+	1.36884i
$199$	−4.87410	−	11.7671i	−0.345516	−	0.834148i	−0.997138	−	0.0756048i	$-0.975911\pi$
$199$	−4.87410	−	11.7671i	−0.345516	−	0.834148i	0.651622	−	0.758544i	$-0.274089\pi$
$200$		0			0
$201$	−0.304024	+	0.125931i	−0.0214442	+	0.00888248i
$202$	−14.5471	+	14.5471i	−1.02353	+	1.02353i
$203$		−	4.52235i		−	0.317407i
$204$	−0.0217941	+	0.0224143i	−0.00152589	+	0.00156932i
$205$		0			0
$206$	−11.0827	−	11.0827i	−0.772167	−	0.772167i
$207$	5.30191	+	12.8000i	0.368509	+	0.889658i
$208$	23.3075			1.61608
$209$	−4.31179	−	10.4096i	−0.298253	−	0.720046i
$210$		0			0
$211$	4.92813	−	11.8976i	0.339266	−	0.819061i	−0.658520	−	0.752563i	$-0.728817\pi$
$211$	4.92813	−	11.8976i	0.339266	−	0.819061i	0.997787	−	0.0664982i	$-0.0211827\pi$
$212$	0.584733	+	0.584733i	0.0401596	+	0.0401596i
$213$	0.364372	+	0.364372i	0.0249664	+	0.0249664i
$214$	9.15253	−	22.0962i	0.625654	−	1.51046i
$215$		0			0
$216$	−0.699526	−	1.68881i	−0.0475967	−	0.114909i
$217$	−4.60976			−0.312931
$218$	5.83472	+	14.0863i	0.395177	+	0.954042i
$219$	−0.427368	−	0.427368i	−0.0288788	−	0.0288788i
$220$		0			0
$221$	21.3537	−	9.19801i	1.43640	−	0.618725i
$222$			0.0187534i			0.00125864i
$223$	−14.4397	+	14.4397i	−0.966952	+	0.966952i	−0.999471	−	0.0325195i	$-0.989647\pi$
$223$	−14.4397	+	14.4397i	−0.966952	+	0.966952i	0.0325195	+	0.999471i	$0.489647\pi$
$224$	0.250507	−	0.103764i	0.0167377	−	0.00693300i
$225$		0			0
$226$	6.35202	+	15.3351i	0.422530	+	1.02008i
$227$	0.466985	−	1.12740i	0.0309949	−	0.0748282i	−0.907624	−	0.419784i	$-0.862106\pi$
$227$	0.466985	−	1.12740i	0.0309949	−	0.0748282i	0.938619	+	0.344955i	$0.112106\pi$
$228$	−0.0162713	−	0.00673977i	−0.00107759	−	0.000446352i
$229$	2.48862	−	2.48862i	0.164453	−	0.164453i	−0.620083	−	0.784536i	$-0.712901\pi$
$229$	2.48862	−	2.48862i	0.164453	−	0.164453i	0.784536	+	0.620083i	$0.212901\pi$
$230$		0			0
$231$	−0.141815	+	0.342372i	−0.00933076	+	0.0225264i
$232$	6.91560	−	16.6957i	0.454031	−	1.09613i
$233$	26.7949	−	11.0988i	1.75539	−	0.727107i	0.758215	−	0.652005i	$-0.226072\pi$
$233$	26.7949	−	11.0988i	1.75539	−	0.727107i	0.997176	−	0.0751019i	$-0.0239282\pi$
$234$		−	24.2356i		−	1.58433i
$235$		0			0
$236$	0.483845	+	0.483845i	0.0314956	+	0.0314956i
$237$		−	1.63145i		−	0.105974i
$238$	2.87374	−	2.95552i	0.186277	−	0.191578i
$239$	−7.87133			−0.509154			−0.254577	−	0.967053i	$-0.581936\pi$
$239$	−7.87133			−0.509154			−0.254577	+	0.967053i	$0.581936\pi$
$240$		0			0
$241$	10.7419	−	4.44945i	0.691947	−	0.286614i	−0.00886385	−	0.999961i	$-0.502821\pi$
$241$	10.7419	−	4.44945i	0.691947	−	0.286614i	0.700811	+	0.713347i	$0.252821\pi$
$242$	18.0247			1.15867
$243$	−2.72689	+	1.12952i	−0.174930	+	0.0724585i
$244$	−0.102167	−	0.0423192i	−0.00654060	−	0.00270921i
$245$		0			0
$246$	0.120591	−	0.120591i	0.00768862	−	0.00768862i
$247$	9.26165	+	9.26165i	0.589305	+	0.589305i
$248$	−17.0184	−	7.04926i	−1.08067	−	0.447629i
$249$	−0.511263	−	0.211772i	−0.0324000	−	0.0134205i
$250$		0			0
$251$			7.94692i			0.501605i	0.968038	+	0.250803i	$0.0806945\pi$
$251$			7.94692i			0.501605i	−0.968038	+	0.250803i	$0.919306\pi$
$252$	−0.0548316	−	0.132375i	−0.00345406	−	0.00833885i
$253$	15.9049	−	15.9049i	0.999930	−	0.999930i
$254$	−0.717097			−0.0449947
$255$		0			0
$256$	1.65381			0.103363
$257$	−5.60542	+	5.60542i	−0.349657	+	0.349657i	−0.859982	−	0.510325i	$-0.829525\pi$
$257$	−5.60542	+	5.60542i	−0.349657	+	0.349657i	0.510325	+	0.859982i	$0.329525\pi$
$258$	0.0387860	+	0.0936376i	0.00241471	+	0.00582962i
$259$		−	0.0824544i		−	0.00512347i
$260$		0			0
$261$	−17.9602	−	7.43935i	−1.11171	−	0.460484i
$262$	−25.9590	−	10.7526i	−1.60375	−	0.664295i
$263$	−6.03602	−	6.03602i	−0.372197	−	0.372197i	0.496080	−	0.868277i	$-0.334772\pi$
$263$	−6.03602	−	6.03602i	−0.372197	−	0.372197i	−0.868277	+	0.496080i	$0.834772\pi$
$264$	−1.04711	+	1.04711i	−0.0644454	+	0.0644454i
$265$		0			0
$266$	2.14550	+	0.888696i	0.131549	+	0.0544895i
$267$	0.239288	−	0.0991163i	0.0146442	−	0.00606582i
$268$	−0.206563			−0.0126178
$269$	14.7662	−	6.11636i	0.900311	−	0.372921i	0.115971	−	0.993253i	$-0.463002\pi$
$269$	14.7662	−	6.11636i	0.900311	−	0.372921i	0.784340	+	0.620331i	$0.213002\pi$
$270$		0			0
$271$	22.5289			1.36853			0.684266	−	0.729232i	$-0.260123\pi$
$271$	22.5289			1.36853			0.684266	+	0.729232i	$0.260123\pi$
$272$	15.6514	−	6.74180i	0.949008	−	0.408782i
$273$		−	0.430793i		−	0.0260728i
$274$	3.88252	+	3.88252i	0.234552	+	0.234552i
$275$		0			0
$276$		−	0.0351587i		−	0.00211630i
$277$	6.37672	−	2.64132i	0.383140	−	0.158702i	−0.182796	−	0.983151i	$-0.558515\pi$
$277$	6.37672	−	2.64132i	0.383140	−	0.158702i	0.565936	+	0.824449i	$0.308515\pi$
$278$	−7.29484	+	17.6113i	−0.437516	+	1.05626i
$279$	−7.58314	+	18.3073i	−0.453991	+	1.09603i
$280$		0			0
$281$	6.63310	−	6.63310i	0.395698	−	0.395698i	−0.481015	−	0.876712i	$-0.659732\pi$
$281$	6.63310	−	6.63310i	0.395698	−	0.395698i	0.876712	+	0.481015i	$0.159732\pi$
$282$	0.721082	+	0.298682i	0.0429398	+	0.0177862i
$283$	−7.87443	+	19.0106i	−0.468086	+	1.13006i	0.496911	+	0.867802i	$0.334468\pi$
$283$	−7.87443	+	19.0106i	−0.468086	+	1.13006i	−0.964997	+	0.262259i	$0.915532\pi$
$284$	0.123783	+	0.298838i	0.00734515	+	0.0177328i
$285$		0			0
$286$	−36.3515	+	15.0573i	−2.14951	+	0.890355i
$287$	−0.530213	+	0.530213i	−0.0312975	+	0.0312975i
$288$		−	1.16557i		−	0.0686816i
$289$	11.6789	−	12.3533i	0.686992	−	0.726665i
$290$		0			0
$291$	0.209895	+	0.209895i	0.0123043	+	0.0123043i
$292$	−0.145183	−	0.350503i	−0.00849620	−	0.0205117i
$293$	23.4539			1.37019			0.685097	−	0.728452i	$-0.259760\pi$
$293$	23.4539			1.37019			0.685097	+	0.728452i	$0.259760\pi$
$294$	0.394259	+	0.951825i	0.0229936	+	0.0555116i
$295$		0			0
$296$	0.126090	−	0.304407i	0.00732881	−	0.0176933i
$297$	2.25739	+	2.25739i	0.130987	+	0.130987i
$298$	−17.7528	−	17.7528i	−1.02839	−	1.02839i
$299$	−10.0062	+	24.1572i	−0.578675	+	1.39704i
$300$		0			0
$301$	−0.170533	−	0.411703i	−0.00982936	−	0.0237302i
$302$	16.2129			0.932948
$303$	0.601555	+	1.45228i	0.0345585	+	0.0834315i
$304$	6.78845	+	6.78845i	0.389344	+	0.389344i
$305$		0			0
$306$	−7.01028	−	16.2747i	−0.400751	−	0.930365i
$307$		−	30.4260i		−	1.73650i	−0.496126	−	0.868251i	$-0.665244\pi$
$307$		−	30.4260i		−	1.73650i	0.496126	−	0.868251i	$-0.334756\pi$
$308$	−0.164486	+	0.164486i	−0.00937244	+	0.00937244i
$309$	−1.10642	+	0.458294i	−0.0629421	+	0.0260715i
$310$		0			0
$311$	0.413255	+	0.997685i	0.0234335	+	0.0565735i	0.935163	−	0.354217i	$-0.115253\pi$
$311$	0.413255	+	0.997685i	0.0234335	+	0.0565735i	−0.911730	+	0.410791i	$0.865253\pi$
$312$	0.658771	−	1.59041i	0.0372955	−	0.0900394i
$313$	3.34956	+	1.38743i	0.189328	+	0.0784224i	0.475333	−	0.879806i	$-0.342327\pi$
$313$	3.34956	+	1.38743i	0.189328	+	0.0784224i	−0.286005	+	0.958228i	$0.592327\pi$
$314$	−6.25051	+	6.25051i	−0.352737	+	0.352737i
$315$		0			0
$316$	0.391898	−	0.946126i	0.0220460	−	0.0532238i
$317$	−3.36564	+	8.12537i	−0.189033	+	0.456366i	−0.989774	−	0.142645i	$-0.954439\pi$
$317$	−3.36564	+	8.12537i	−0.189033	+	0.456366i	0.800741	+	0.599011i	$0.204439\pi$
$318$	1.75068	−	0.725156i	0.0981733	−	0.0406647i
$319$			31.5607i			1.76706i
$320$		0			0
$321$	−1.29221	−	1.29221i	−0.0721239	−	0.0721239i
$322$			4.63597i			0.258353i
$323$	8.89837	+	3.54041i	0.495119	+	0.196994i
$324$	−0.613417			−0.0340787
$325$		0			0
$326$	14.8853	−	6.16570i	0.824421	−	0.341486i
$327$	1.16500			0.0644246
$328$	−2.76826	+	1.14665i	−0.152851	+	0.0633132i
$329$	−3.17043	−	1.31324i	−0.174792	−	0.0724010i
$330$		0			0
$331$	−24.8643	+	24.8643i	−1.36666	+	1.36666i	−0.501515	+	0.865149i	$0.667224\pi$
$331$	−24.8643	+	24.8643i	−1.36666	+	1.36666i	−0.865149	+	0.501515i	$0.832776\pi$
$332$	−0.245626	−	0.245626i	−0.0134805	−	0.0134805i
$333$	−0.327462	−	0.135639i	−0.0179448	−	0.00743297i
$334$	7.58278	+	3.14089i	0.414911	+	0.171862i
$335$		0			0
$336$		−	0.315755i		−	0.0172259i
$337$	12.0603	+	29.1162i	0.656968	+	1.58606i	0.802463	+	0.596702i	$0.203523\pi$
$337$	12.0603	+	29.1162i	0.656968	+	1.58606i	−0.145494	+	0.989359i	$0.546477\pi$
$338$	19.1204	−	19.1204i	1.04001	−	1.04001i
$339$	1.26829			0.0688839
$340$		0			0
$341$	32.1708			1.74214
$342$	7.05879	−	7.05879i	0.381696	−	0.381696i
$343$	−3.59545	−	8.68018i	−0.194136	−	0.468686i
$344$		−	1.78072i		−	0.0960098i
$345$		0			0
$346$	−6.02997	−	2.49769i	−0.324173	−	0.134277i
$347$	0.406795	+	0.168500i	0.0218379	+	0.00904556i	0.393576	−	0.919292i	$-0.371238\pi$
$347$	0.406795	+	0.168500i	0.0218379	+	0.00904556i	−0.371738	+	0.928338i	$0.621238\pi$
$348$	0.0348835	+	0.0348835i	0.00186995	+	0.00186995i
$349$	8.78380	−	8.78380i	0.470186	−	0.470186i	−0.431789	−	0.901975i	$-0.642117\pi$
$349$	8.78380	−	8.78380i	0.470186	−	0.470186i	0.901975	+	0.431789i	$0.142117\pi$
$350$		0			0
$351$	−3.42864	−	1.42019i	−0.183007	−	0.0758041i
$352$	−1.74825	+	0.724150i	−0.0931821	+	0.0385973i
$353$	−7.38055			−0.392827			−0.196414	−	0.980521i	$-0.562929\pi$
$353$	−7.38055			−0.392827			−0.196414	+	0.980521i	$0.562929\pi$
$354$	1.44862	−	0.600040i	0.0769935	−	0.0318918i
$355$		0			0
$356$	0.162579			0.00861668
$357$	−0.124609	−	0.289286i	−0.00659501	−	0.0153107i
$358$		−	26.4314i		−	1.39694i
$359$	4.98636	+	4.98636i	0.263170	+	0.263170i	0.826341	−	0.563171i	$-0.190419\pi$
$359$	4.98636	+	4.98636i	0.263170	+	0.263170i	−0.563171	+	0.826341i	$0.690419\pi$
$360$		0			0
$361$		−	13.6050i		−	0.716051i
$362$	−14.2435	+	5.89986i	−0.748622	+	0.310090i
$363$	0.527051	−	1.27241i	0.0276630	−	0.0667844i
$364$	0.103483	−	0.249830i	0.00542397	−	0.0130946i
$365$		0			0
$366$	−0.179185	+	0.179185i	−0.00936615	+	0.00936615i
$367$	15.0747	+	6.24413i	0.786891	+	0.325941i	0.739693	−	0.672945i	$-0.234971\pi$
$367$	15.0747	+	6.24413i	0.786891	+	0.325941i	0.0471982	+	0.998886i	$0.484971\pi$
$368$	−7.33419	+	17.7063i	−0.382321	+	0.923005i
$369$	1.23349	+	2.97791i	0.0642130	+	0.155024i
$370$		0			0
$371$	−7.69735	+	3.18835i	−0.399626	+	0.165531i
$372$	0.0355577	−	0.0355577i	0.00184358	−	0.00184358i
$373$			18.3821i			0.951787i	0.879503	+	0.475893i	$0.157875\pi$
$373$			18.3821i			0.951787i	−0.879503	+	0.475893i	$0.842125\pi$
$374$	−20.0554	+	20.6261i	−1.03704	+	1.06655i
$375$		0			0
$376$	−9.69648	−	9.69648i	−0.500058	−	0.500058i
$377$	−14.0402	−	33.8960i	−0.723105	−	1.74573i
$378$	−0.657987			−0.0338432
$379$	6.31254	+	15.2398i	0.324253	+	0.782817i	0.998998	+	0.0447652i	$0.0142540\pi$
$379$	6.31254	+	15.2398i	0.324253	+	0.782817i	−0.674744	+	0.738052i	$0.735746\pi$
$380$		0			0
$381$	−0.0209683	+	0.0506219i	−0.00107424	+	0.00259344i
$382$	18.8567	+	18.8567i	0.964795	+	0.964795i
$383$	−25.6981	−	25.6981i	−1.31311	−	1.31311i	−0.919110	−	0.394002i	$-0.871090\pi$
$383$	−25.6981	−	25.6981i	−1.31311	−	1.31311i	−0.394002	−	0.919110i	$-0.628910\pi$
$384$	0.498974	−	1.20463i	0.0254631	−	0.0614735i
$385$		0			0
$386$	5.44171	+	13.1374i	0.276976	+	0.668678i
$387$	−1.91558			−0.0973744
$388$	0.0713045	+	0.172144i	0.00361994	+	0.00873930i
$389$	4.50312	+	4.50312i	0.228317	+	0.228317i	0.811989	−	0.583672i	$-0.198385\pi$
$389$	4.50312	+	4.50312i	0.228317	+	0.228317i	−0.583672	+	0.811989i	$0.698385\pi$
$390$		0			0
$391$	0.268192	+	19.1164i	0.0135631	+	0.966757i
$392$		−	18.1010i		−	0.914237i
$393$	−1.51811	+	1.51811i	−0.0765784	+	0.0765784i
$394$	−18.5428	+	7.68066i	−0.934171	+	0.386946i
$395$		0			0
$396$	0.382661	+	0.923825i	0.0192294	+	0.0464240i
$397$	−12.7731	+	30.8370i	−0.641065	+	1.54767i	0.184181	+	0.982892i	$0.441037\pi$
$397$	−12.7731	+	30.8370i	−0.641065	+	1.54767i	−0.825245	+	0.564774i	$0.808963\pi$
$398$	−16.9258	−	7.01089i	−0.848413	−	0.351424i
$399$	0.125471	−	0.125471i	0.00628142	−	0.00628142i
$400$		0			0
$401$	−4.49654	+	10.8556i	−0.224547	+	0.542104i	−0.995497	−	0.0947914i	$-0.969782\pi$
$401$	−4.49654	+	10.8556i	−0.224547	+	0.542104i	0.770950	+	0.636895i	$0.219782\pi$
$402$	−0.181139	+	0.437307i	−0.00903438	+	0.0218109i
$403$	−34.5511	+	14.3115i	−1.72111	+	0.712909i
$404$			0.986724i			0.0490914i
$405$		0			0
$406$	−4.59968	−	4.59968i	−0.228278	−	0.228278i
$407$			0.575436i			0.0285233i
$408$	−0.0176567	−	1.25855i	−0.000874139	−	0.0623074i
$409$	−12.6834			−0.627154			−0.313577	−	0.949563i	$-0.601527\pi$
$409$	−12.6834			−0.627154			−0.313577	+	0.949563i	$0.601527\pi$
$410$		0			0
$411$	0.387605	−	0.160551i	0.0191192	−	0.00791941i
$412$	−0.751735			−0.0370353
$413$	−6.36927	+	2.63824i	−0.313411	+	0.129819i
$414$	18.4114	+	7.62626i	0.904872	+	0.374810i
$415$		0			0
$416$	1.55546	−	1.55546i	0.0762627	−	0.0762627i
$417$	1.02993	+	1.02993i	0.0504358	+	0.0504358i
$418$	−14.9731	−	6.20207i	−0.732359	−	0.303353i
$419$	−32.3564	−	13.4025i	−1.58072	−	0.654754i	−0.592189	−	0.805799i	$-0.701736\pi$
$419$	−32.3564	−	13.4025i	−1.58072	−	0.654754i	−0.988527	+	0.151045i	$0.951736\pi$
$420$		0			0
$421$			10.0231i			0.488497i	0.969713	+	0.244248i	$0.0785412\pi$
$421$			10.0231i			0.488497i	−0.969713	+	0.244248i	$0.921459\pi$
$422$	−7.08861	−	17.1134i	−0.345068	−	0.833068i
$423$	−10.4308	+	10.4308i	−0.507165	+	0.507165i
$424$	−33.2929			−1.61685
$425$		0			0
$426$	0.741207			0.0359116
$427$	0.787836	−	0.787836i	0.0381260	−	0.0381260i
$428$	−0.438982	−	1.05980i	−0.0212190	−	0.0512271i
$429$			3.00643i			0.145152i
$430$		0			0
$431$	21.9385	+	9.08724i	1.05674	+	0.437717i	0.842294	−	0.539019i	$-0.181205\pi$
$431$	21.9385	+	9.08724i	1.05674	+	0.437717i	0.214448	+	0.976735i	$0.431205\pi$
$432$	−2.51307	−	1.04095i	−0.120910	−	0.0500826i
$433$	22.8337	+	22.8337i	1.09732	+	1.09732i	0.994724	+	0.102592i	$0.0327135\pi$
$433$	22.8337	+	22.8337i	1.09732	+	1.09732i	0.102592	+	0.994724i	$0.467286\pi$
$434$	−4.68859	+	4.68859i	−0.225059	+	0.225059i
$435$		0			0
$436$	0.675618	+	0.279850i	0.0323562	+	0.0134024i
$437$	−9.95030	+	4.12155i	−0.475987	+	0.197160i
$438$	−0.869353			−0.0415393
$439$	19.7035	−	8.16145i	0.940396	−	0.389525i	0.140783	−	0.990040i	$-0.455038\pi$
$439$	19.7035	−	8.16145i	0.940396	−	0.389525i	0.799613	+	0.600515i	$0.205038\pi$
$440$		0			0
$441$	−19.4719			−0.927231
$442$	12.3635	−	31.0741i	0.588073	−	1.47805i
$443$		−	13.8187i		−	0.656546i	−0.944583	−	0.328273i	$-0.893533\pi$
$443$		−	13.8187i		−	0.656546i	0.944583	−	0.328273i	$-0.106467\pi$
$444$	0.000636019	0	0.000636019i	3.01841e−5	0	3.01841e-5i
$445$		0			0
$446$			29.3732i			1.39086i
$447$	−1.77232	+	0.734118i	−0.0838277	+	0.0347226i
$448$	−2.04960	+	4.94817i	−0.0968344	+	0.233779i
$449$	2.53099	−	6.11035i	0.119445	−	0.288365i	−0.852837	−	0.522177i	$-0.825120\pi$
$449$	2.53099	−	6.11035i	0.119445	−	0.288365i	0.972282	+	0.233812i	$0.0751199\pi$
$450$		0			0
$451$	3.70027	−	3.70027i	0.174239	−	0.174239i
$452$	0.735517	+	0.304661i	0.0345958	+	0.0143301i
$453$	0.474074	−	1.14452i	0.0222739	−	0.0537740i
$454$	−0.671710	−	1.62165i	−0.0315249	−	0.0761079i
$455$		0			0
$456$	0.655089	−	0.271347i	0.0306774	−	0.0127070i
$457$	−3.54288	+	3.54288i	−0.165729	+	0.165729i	−0.785099	−	0.619370i	$-0.787388\pi$
$457$	−3.54288	+	3.54288i	−0.165729	+	0.165729i	0.619370	+	0.785099i	$0.287388\pi$
$458$		−	5.06236i		−	0.236548i
$459$	−2.71320	+	0.0380648i	−0.126641	+	0.00177671i
$460$		0			0
$461$	11.5839	+	11.5839i	0.539518	+	0.539518i	0.923387	−	0.383869i	$-0.125409\pi$
$461$	11.5839	+	11.5839i	0.539518	+	0.539518i	−0.383869	+	0.923387i	$0.625409\pi$
$462$	0.203987	+	0.492468i	0.00949032	+	0.0229117i
$463$	27.3768			1.27231			0.636153	−	0.771563i	$-0.280525\pi$
$463$	27.3768			1.27231			0.636153	+	0.771563i	$0.280525\pi$
$464$	−10.2909	−	24.8445i	−0.477744	−	1.15338i
$465$		0			0
$466$	15.9645	−	38.5417i	0.739541	−	1.78541i
$467$	−0.457032	−	0.457032i	−0.0211489	−	0.0211489i	0.696453	−	0.717602i	$-0.254760\pi$
$467$	−0.457032	−	0.457032i	−0.0211489	−	0.0211489i	−0.717602	+	0.696453i	$0.754760\pi$
$468$	−0.821949	−	0.821949i	−0.0379946	−	0.0379946i
$469$	0.796426	−	1.92274i	0.0367755	−	0.0887840i
$470$		0			0
$471$	0.258473	+	0.624009i	0.0119098	+	0.0287528i
$472$	−27.5487			−1.26803
$473$	1.19012	+	2.87321i	0.0547219	+	0.132110i
$474$	−1.65935	−	1.65935i	−0.0762165	−	0.0762165i
$475$		0			0
$476$	−0.00277360	−	0.197699i	−0.000127128	−	0.00906150i
$477$			35.8144i			1.63983i
$478$	−8.00594	+	8.00594i	−0.366183	+	0.366183i
$479$	12.5323	−	5.19106i	0.572616	−	0.237185i	−0.0775357	−	0.996990i	$-0.524705\pi$
$479$	12.5323	−	5.19106i	0.572616	−	0.237185i	0.650152	+	0.759804i	$0.274705\pi$
$480$		0			0
$481$	−0.255989	−	0.618013i	−0.0116721	−	0.0281790i
$482$	6.40008	−	15.4511i	0.291515	−	0.703781i
$483$	0.327266	+	0.135558i	0.0148911	+	0.00616811i
$484$	0.611305	−	0.611305i	0.0277866	−	0.0277866i
$485$		0			0
$486$	−1.62469	+	3.92236i	−0.0736976	+	0.177922i
$487$	−11.1108	+	26.8238i	−0.503478	+	1.21550i	0.444099	+	0.895978i	$0.353524\pi$
$487$	−11.1108	+	26.8238i	−0.503478	+	1.21550i	−0.947577	+	0.319527i	$0.896476\pi$
$488$	4.11332	−	1.70379i	0.186201	−	0.0771270i
$489$		−	1.23108i		−	0.0556716i
$490$		0			0
$491$	−9.28419	−	9.28419i	−0.418990	−	0.418990i	0.465866	−	0.884855i	$-0.345743\pi$
$491$	−9.28419	−	9.28419i	−0.418990	−	0.418990i	−0.884855	+	0.465866i	$0.845743\pi$
$492$		−	0.00817968i		−	0.000368768i
$493$	−19.2328	−	18.7007i	−0.866204	−	0.842235i
$494$	18.8401			0.847655
$495$		0			0
$496$	−25.3247	+	10.4898i	−1.13711	+	0.471007i
$497$	−3.25892			−0.146183
$498$	−0.735400	+	0.304613i	−0.0329541	+	0.0136500i
$499$	−10.4777	−	4.34000i	−0.469045	−	0.194285i	0.135626	−	0.990760i	$-0.456695\pi$
$499$	−10.4777	−	4.34000i	−0.469045	−	0.194285i	−0.604671	+	0.796475i	$0.706695\pi$
$500$		0			0
$501$	0.443449	−	0.443449i	0.0198118	−	0.0198118i
$502$	8.08282	+	8.08282i	0.360754	+	0.360754i
$503$	18.9798	+	7.86171i	0.846269	+	0.350536i	0.763322	−	0.646018i	$-0.223567\pi$
$503$	18.9798	+	7.86171i	0.846269	+	0.350536i	0.0829468	+	0.996554i	$0.473567\pi$
$504$	5.32949	+	2.20755i	0.237394	+	0.0983320i
$505$		0			0
$506$		−	32.3537i		−	1.43830i
$507$	−0.790674	−	1.90886i	−0.0351151	−	0.0847753i
$508$	−0.0243203	+	0.0243203i	−0.00107904	+	0.00107904i
$509$	8.40900			0.372722			0.186361	−	0.982481i	$-0.440331\pi$
$509$	8.40900			0.372722			0.186361	+	0.982481i	$0.440331\pi$
$510$		0			0
$511$	3.82235			0.169091
$512$	−15.0955	+	15.0955i	−0.667132	+	0.667132i
$513$	−0.584975	−	1.41225i	−0.0258273	−	0.0623525i
$514$			11.4026i			0.502946i
$515$		0			0
$516$	0.00449113	+	0.00186029i	0.000197711	+	8.18945e-5i
$517$	22.1259	+	9.16486i	0.973098	+	0.403070i
$518$	−0.0838644	−	0.0838644i	−0.00368479	−	0.00368479i
$519$	−0.352639	+	0.352639i	−0.0154791	+	0.0154791i
$520$		0			0
$521$	−19.7304	−	8.17262i	−0.864406	−	0.358049i	−0.0939770	−	0.995574i	$-0.529958\pi$
$521$	−19.7304	−	8.17262i	−0.864406	−	0.358049i	−0.770429	+	0.637526i	$0.779958\pi$
$522$	−25.8339	+	10.7007i	−1.13072	+	0.468359i
$523$	−24.4644			−1.06975			−0.534877	−	0.844930i	$-0.679642\pi$
$523$	−24.4644			−1.06975			−0.534877	+	0.844930i	$0.679642\pi$
$524$	−1.24507	+	0.515723i	−0.0543910	+	0.0225295i
$525$		0			0
$526$	−12.2785			−0.535367
$527$	−19.0621	+	19.6046i	−0.830359	+	0.853989i
$528$			2.20361i			0.0958996i
$529$	1.06033	+	1.06033i	0.0461012	+	0.0461012i
$530$		0			0
$531$			29.6351i			1.28605i
$532$	0.102904	−	0.0426244i	0.00446148	−	0.00184800i
$533$	−2.32795	+	5.62017i	−0.100835	+	0.243436i
$534$	0.142569	−	0.344191i	0.00616955	−	0.0148946i
$535$		0			0
$536$	5.88053	−	5.88053i	0.254000	−	0.254000i
$537$	−1.86587	−	0.772867i	−0.0805181	−	0.0333517i
$538$	8.79776	−	21.2397i	0.379299	−	0.915708i
$539$	12.0976	+	29.2062i	0.521080	+	1.25800i
$540$		0			0
$541$	1.77760	−	0.736307i	0.0764251	−	0.0316563i	−0.344143	−	0.938917i	$-0.611831\pi$
$541$	1.77760	−	0.736307i	0.0764251	−	0.0316563i	0.420569	+	0.907261i	$0.361831\pi$
$542$	22.9142	−	22.9142i	0.984248	−	0.984248i
$543$			1.17800i			0.0505530i
$544$	0.594600	−	1.49445i	0.0254932	−	0.0640740i
$545$		0			0
$546$	−0.438160	−	0.438160i	−0.0187515	−	0.0187515i
$547$	−5.63393	−	13.6015i	−0.240890	−	0.581559i	0.756482	−	0.654014i	$-0.226916\pi$
$547$	−5.63393	−	13.6015i	−0.240890	−	0.581559i	−0.997372	+	0.0724556i	$0.976916\pi$
$548$	0.263350			0.0112498
$549$	−1.83283	−	4.42484i	−0.0782232	−	0.188847i
$550$		0			0
$551$	5.78313	−	13.9617i	0.246369	−	0.594789i
$552$	1.00092	+	1.00092i	0.0426018	+	0.0426018i
$553$	7.29579	+	7.29579i	0.310248	+	0.310248i
$554$	3.79928	−	9.17226i	0.161416	−	0.389692i
$555$		0			0
$556$	0.349882	+	0.844689i	0.0148383	+	0.0358228i
$557$	24.3617			1.03224			0.516119	−	0.856517i	$-0.327376\pi$
$557$	24.3617			1.03224			0.516119	+	0.856517i	$0.327376\pi$
$558$	10.9076	+	26.3332i	0.461754	+	1.11477i
$559$	−2.55636	−	2.55636i	−0.108123	−	0.108123i
$560$		0			0
$561$	0.869627	+	2.01888i	0.0367157	+	0.0852374i
$562$		−	13.4931i		−	0.569171i
$563$	21.7224	−	21.7224i	0.915488	−	0.915488i	−0.0812090	−	0.996697i	$-0.525878\pi$
$563$	21.7224	−	21.7224i	0.915488	−	0.915488i	0.996697	+	0.0812090i	$0.0258781\pi$
$564$	0.0345851	−	0.0143256i	0.00145630	−	0.000603218i
$565$		0			0
$566$	11.3266	+	27.3448i	0.476091	+	1.14939i
$567$	2.36510	−	5.70985i	0.0993247	−	0.239791i
$568$	−12.0314	−	4.98356i	−0.504825	−	0.209105i
$569$	3.78820	−	3.78820i	0.158809	−	0.158809i	−0.623230	−	0.782039i	$-0.714180\pi$
$569$	3.78820	−	3.78820i	0.158809	−	0.158809i	0.782039	+	0.623230i	$0.214180\pi$
$570$		0			0
$571$	13.7904	−	33.2930i	0.577110	−	1.39327i	−0.318285	−	0.947995i	$-0.603107\pi$
$571$	13.7904	−	33.2930i	0.577110	−	1.39327i	0.895395	−	0.445272i	$-0.146893\pi$
$572$	−0.722190	+	1.74352i	−0.0301963	+	0.0729003i
$573$	1.88253	−	0.779770i	0.0786439	−	0.0325754i
$574$			1.07856i			0.0450182i
$575$		0			0
$576$	16.2797	+	16.2797i	0.678319	+	0.678319i
$577$		−	39.5472i		−	1.64637i	−0.567772	−	0.823186i	$-0.692194\pi$
$577$		−	39.5472i		−	1.64637i	0.567772	−	0.823186i	$-0.307806\pi$
$578$	−0.685983	−	24.4431i	−0.0285331	−	1.01670i
$579$	1.08653			0.0451546
$580$		0			0
$581$	3.23339	−	1.33931i	0.134144	−	0.0555641i
$582$	0.426969			0.0176984
$583$	53.7186	−	22.2510i	2.22480	−	0.921541i
$584$	14.1114	+	5.84515i	0.583936	+	0.241874i
$585$		0			0
$586$	23.8550	−	23.8550i	0.985442	−	0.985442i
$587$	−12.6771	−	12.6771i	−0.523242	−	0.523242i	0.395307	−	0.918549i	$-0.370638\pi$
$587$	−12.6771	−	12.6771i	−0.523242	−	0.523242i	−0.918549	+	0.395307i	$0.870638\pi$
$588$	0.0456523	+	0.0189098i	0.00188267	+	0.000779827i
$589$	−14.2316	−	5.89491i	−0.586401	−	0.242895i
$590$		0			0
$591$			1.53357i			0.0630827i
$592$	−0.187631	−	0.452981i	−0.00771158	−	0.0186174i
$593$	−10.8169	+	10.8169i	−0.444199	+	0.444199i	−0.893420	−	0.449222i	$-0.851701\pi$
$593$	−10.8169	+	10.8169i	−0.444199	+	0.444199i	0.449222	+	0.893420i	$0.351701\pi$
$594$	4.59199			0.188412
$595$		0			0
$596$	−1.20416			−0.0493245
$597$	−0.989838	+	0.989838i	−0.0405114	+	0.0405114i
$598$	14.3929	+	34.7476i	0.588571	+	1.42094i
$599$		−	34.6498i		−	1.41575i	−0.706336	−	0.707877i	$-0.749653\pi$
$599$		−	34.6498i		−	1.41575i	0.706336	−	0.707877i	$-0.250347\pi$
$600$		0			0
$601$	−14.8154	−	6.13675i	−0.604333	−	0.250323i	0.0594701	−	0.998230i	$-0.481059\pi$
$601$	−14.8154	−	6.13675i	−0.604333	−	0.250323i	−0.663804	+	0.747907i	$0.731059\pi$
$602$	−0.592193	−	0.245294i	−0.0241360	−	0.00999746i
$603$	−6.32590	−	6.32590i	−0.257610	−	0.257610i
$604$	0.549859	−	0.549859i	0.0223734	−	0.0223734i
$605$		0			0
$606$	2.08896	+	0.865276i	0.0848583	+	0.0351494i
$607$	33.7326	−	13.9725i	1.36916	−	0.567126i	0.427602	−	0.903967i	$-0.359359\pi$
$607$	33.7326	−	13.9725i	1.36916	−	0.567126i	0.941561	+	0.336841i	$0.109359\pi$
$608$	0.906076			0.0367462
$609$	−0.459202	+	0.190208i	−0.0186078	+	0.00770760i
$610$		0			0
$611$	−27.8402			−1.12629
$612$	−0.789709	−	0.314203i	−0.0319221	−	0.0127009i
$613$			33.2758i			1.34400i	0.740553	+	0.671998i	$0.234564\pi$
$613$			33.2758i			1.34400i	−0.740553	+	0.671998i	$0.765436\pi$
$614$	−30.9463	−	30.9463i	−1.24889	−	1.24889i
$615$		0			0
$616$		−	9.36532i		−	0.377339i
$617$	29.2948	−	12.1343i	1.17936	−	0.488508i	0.295086	−	0.955471i	$-0.404652\pi$
$617$	29.2948	−	12.1343i	1.17936	−	0.488508i	0.884277	+	0.466963i	$0.154652\pi$
$618$	−0.659210	+	1.59147i	−0.0265173	+	0.0640185i
$619$	15.6250	−	37.7222i	0.628023	−	1.51618i	−0.214052	−	0.976822i	$-0.568666\pi$
$619$	15.6250	−	37.7222i	0.628023	−	1.51618i	0.842075	−	0.539360i	$-0.181334\pi$
$620$		0			0
$621$	2.15779	−	2.15779i	0.0865892	−	0.0865892i
$622$	1.43507	+	0.594425i	0.0575410	+	0.0238343i
$623$	−0.626842	+	1.51333i	−0.0251139	+	0.0606303i
$624$	−0.980300	−	2.36665i	−0.0392434	−	0.0947420i
$625$		0			0
$626$	4.81800	−	1.99568i	0.192566	−	0.0797635i
$627$	−0.875644	+	0.875644i	−0.0349698	+	0.0349698i
$628$			0.423970i			0.0169183i
$629$	−0.350666	−	0.340963i	−0.0139820	−	0.0135951i
$630$		0			0
$631$	−11.1724	−	11.1724i	−0.444764	−	0.444764i	0.448845	−	0.893610i	$-0.351835\pi$
$631$	−11.1724	−	11.1724i	−0.444764	−	0.444764i	−0.893610	+	0.448845i	$0.851835\pi$
$632$	15.7780	+	38.0915i	0.627616	+	1.51520i
$633$	−1.41536			−0.0562555
$634$	4.84113	+	11.6875i	0.192266	+	0.464171i
$635$		0			0
$636$	0.0347806	−	0.0839677i	0.00137914	−	0.00332954i
$637$	−25.9854	−	25.9854i	−1.02958	−	1.02958i
$638$	32.1005	+	32.1005i	1.27087	+	1.27087i
$639$	−5.36099	+	12.9426i	−0.212077	+	0.512000i
$640$		0			0
$641$	9.54180	+	23.0359i	0.376878	+	0.909865i	0.992547	+	0.121860i	$0.0388859\pi$
$641$	9.54180	+	23.0359i	0.376878	+	0.909865i	−0.615669	+	0.788005i	$0.711114\pi$
$642$	−2.62861			−0.103743
$643$	9.19057	+	22.1880i	0.362441	+	0.875009i	0.994942	+	0.100450i	$0.0320283\pi$
$643$	9.19057	+	22.1880i	0.362441	+	0.875009i	−0.632501	+	0.774559i	$0.717972\pi$
$644$	0.157228	+	0.157228i	0.00619567	+	0.00619567i
$645$		0			0
$646$	12.6515	−	5.44959i	0.497767	−	0.214411i
$647$			23.8307i			0.936882i	0.883495	+	0.468441i	$0.155184\pi$
$647$			23.8307i			0.936882i	−0.883495	+	0.468441i	$0.844816\pi$
$648$	17.4631	−	17.4631i	0.686014	−	0.686014i
$649$	44.4501	−	18.4119i	1.74482	−	0.722728i
$650$		0			0
$651$	0.193884	+	0.468078i	0.00759892	+	0.0183454i
$652$	0.295725	−	0.713942i	0.0115815	−	0.0279601i
$653$	15.2616	+	6.32157i	0.597234	+	0.247382i	0.660759	−	0.750598i	$-0.270234\pi$
$653$	15.2616	+	6.32157i	0.597234	+	0.247382i	−0.0635255	+	0.997980i	$0.520234\pi$
$654$	1.18492	−	1.18492i	0.0463341	−	0.0463341i
$655$		0			0
$656$	−1.70630	+	4.11938i	−0.0666199	+	0.160835i
$657$	6.28783	−	15.1802i	0.245312	−	0.592235i
$658$	−4.56034	+	1.88896i	−0.177781	+	0.0736392i
$659$			10.2510i			0.399324i	0.979865	+	0.199662i	$0.0639843\pi$
$659$			10.2510i			0.399324i	−0.979865	+	0.199662i	$0.936016\pi$
$660$		0			0
$661$	15.0908	+	15.0908i	0.586962	+	0.586962i	0.936808	−	0.349845i	$-0.113766\pi$
$661$	15.0908	+	15.0908i	0.586962	+	0.586962i	−0.349845	+	0.936808i	$0.613766\pi$
$662$			50.5790i			1.96581i
$663$	−1.83210	−	1.78140i	−0.0711527	−	0.0691839i
$664$	13.9852			0.542731
$665$		0			0
$666$	−0.471020	+	0.195103i	−0.0182517	+	0.00756009i
$667$	30.1683			1.16812
$668$	0.363692	−	0.150646i	0.0140717	−	0.00582867i
$669$	2.07354	+	0.858887i	0.0801676	+	0.0332065i
$670$		0			0
$671$	−5.49818	+	5.49818i	−0.212255	+	0.212255i
$672$	−0.0210724	−	0.0210724i	−0.000812887	−	0.000812887i
$673$	−25.4214	−	10.5299i	−0.979924	−	0.405898i	−0.165526	−	0.986205i	$-0.552932\pi$
$673$	−25.4214	−	10.5299i	−0.979924	−	0.405898i	−0.814397	+	0.580308i	$0.802932\pi$
$674$	41.8807	+	17.3476i	1.61319	+	0.668203i
$675$		0			0
$676$		−	1.29693i		−	0.0498821i
$677$	−6.52233	−	15.7463i	−0.250674	−	0.605180i	0.747585	−	0.664166i	$-0.231213\pi$
$677$	−6.52233	−	15.7463i	−0.250674	−	0.605180i	−0.998259	+	0.0589863i	$0.981213\pi$
$678$	1.28998	−	1.28998i	0.0495412	−	0.0495412i
$679$	−1.87729			−0.0720437
$680$		0			0
$681$	−0.134118			−0.00513942
$682$	32.7209	−	32.7209i	1.25295	−	1.25295i
$683$	−1.19505	−	2.88510i	−0.0457273	−	0.110395i	0.899366	−	0.437198i	$-0.144029\pi$
$683$	−1.19505	−	2.88510i	−0.0457273	−	0.110395i	−0.945093	+	0.326802i	$0.894029\pi$
$684$		−	0.478796i		−	0.0183072i
$685$		0			0
$686$	−12.4856	−	5.17169i	−0.476701	−	0.197456i
$687$	−0.357366	−	0.148026i	−0.0136344	−	0.00564754i
$688$	−1.87372	−	1.87372i	−0.0714349	−	0.0714349i
$689$	−47.7947	+	47.7947i	−1.82083	+	1.82083i
$690$		0			0
$691$	−33.3778	−	13.8255i	−1.26975	−	0.525948i	−0.356862	−	0.934157i	$-0.616153\pi$
$691$	−33.3778	−	13.8255i	−1.26975	−	0.525948i	−0.912888	+	0.408210i	$0.866153\pi$
$692$	−0.289214	+	0.119797i	−0.0109943	+	0.00455398i
$693$	−10.0746			−0.382702
$694$	0.585134	−	0.242370i	0.0222114	−	0.00920025i
$695$		0			0
$696$	−1.98616			−0.0752852
$697$	0.0623950	+	4.44743i	0.00236338	+	0.168458i
$698$		−	17.8680i		−	0.676315i
$699$	−2.25396	−	2.25396i	−0.0852525	−	0.0852525i
$700$		0			0
$701$		−	18.1677i		−	0.686185i	−0.939302	−	0.343093i	$-0.888526\pi$
$701$		−	18.1677i		−	0.686185i	0.939302	−	0.343093i	$-0.111474\pi$
$702$	−4.93175	+	2.04280i	−0.186137	+	0.0771005i
$703$	0.105442	−	0.254559i	0.00397681	−	0.00960087i
$704$	14.3038	−	34.5325i	0.539095	−	1.30149i
$705$		0			0
$706$	−7.50677	+	7.50677i	−0.282521	+	0.282521i
$707$	−9.18469	−	3.80442i	−0.345426	−	0.143080i
$708$	0.0287796	−	0.0694802i	0.00108160	−	0.00261123i
$709$	−4.44086	−	10.7212i	−0.166780	−	0.402643i	0.818288	−	0.574809i	$-0.194923\pi$
$709$	−4.44086	−	10.7212i	−0.166780	−	0.402643i	−0.985068	+	0.172166i	$0.944923\pi$
$710$		0			0
$711$	40.9764	−	16.9730i	1.53674	−	0.636536i
$712$	−4.62839	+	4.62839i	−0.173456	+	0.173456i
$713$		−	30.7514i		−	1.15165i
$714$	−0.420974	−	0.167494i	−0.0157545	−	0.00626829i
$715$		0			0
$716$	−0.896417	−	0.896417i	−0.0335007	−	0.0335007i
$717$	0.331064	+	0.799260i	0.0123638	+	0.0298489i
$718$	10.1433			0.378543
$719$	9.86790	+	23.8232i	0.368011	+	0.888456i	0.994076	+	0.108686i	$0.0346642\pi$
$719$	9.86790	+	23.8232i	0.368011	+	0.888456i	−0.626066	+	0.779770i	$0.715336\pi$
$720$		0			0
$721$	2.89840	−	6.99735i	0.107942	−	0.260595i
$722$	−13.8376	−	13.8376i	−0.514983	−	0.514983i
$723$	−0.903599	−	0.903599i	−0.0336052	−	0.0336052i
$724$	−0.282974	+	0.683160i	−0.0105166	+	0.0253894i
$725$		0			0
$726$	−0.758110	−	1.83024i	−0.0281361	−	0.0679265i
$727$	−17.7430			−0.658051			−0.329025	−	0.944321i	$-0.606720\pi$
$727$	−17.7430			−0.658051			−0.329025	+	0.944321i	$0.606720\pi$
$728$	4.16627	+	10.0583i	0.154412	+	0.372784i
$729$	−18.6322	−	18.6322i	−0.690081	−	0.690081i
$730$		0			0
$731$	−2.45609	−	0.977211i	−0.0908419	−	0.0361434i
$732$			0.0121541i			0.000449227i
$733$	18.9661	−	18.9661i	0.700527	−	0.700527i	−0.263996	−	0.964524i	$-0.585041\pi$
$733$	18.9661	−	18.9661i	0.700527	−	0.700527i	0.964524	+	0.263996i	$0.0850407\pi$
$734$	21.6834	−	8.98155i	0.800348	−	0.331515i
$735$		0			0
$736$	0.692200	+	1.67112i	0.0255148	+	0.0615982i
$737$	−5.55813	+	13.4185i	−0.204736	+	0.494277i
$738$	4.28342	+	1.77425i	0.157675	+	0.0653111i
$739$	0.319229	−	0.319229i	0.0117430	−	0.0117430i	−0.701211	−	0.712954i	$-0.747357\pi$
$739$	0.319229	−	0.319229i	0.0117430	−	0.0117430i	0.712954	+	0.701211i	$0.247357\pi$
$740$		0			0
$741$	0.550893	−	1.32997i	0.0202376	−	0.0488578i
$742$	−4.58611	+	11.0719i	−0.168361	+	0.406460i
$743$	−19.0750	+	7.90111i	−0.699793	+	0.289864i	−0.704073	−	0.710127i	$-0.748637\pi$
$743$	−19.0750	+	7.90111i	−0.699793	+	0.289864i	0.00428071	+	0.999991i	$0.498637\pi$
$744$			2.02455i			0.0742236i
$745$		0			0
$746$	18.6964	+	18.6964i	0.684524	+	0.684524i
$747$		−	15.0444i		−	0.550445i
$748$	0.0193565	+	1.37971i	0.000707745	+	0.0504471i
$749$	11.5574			0.422298
$750$		0			0
$751$	24.6731	−	10.2199i	0.900333	−	0.372930i	0.115985	−	0.993251i	$-0.462998\pi$
$751$	24.6731	−	10.2199i	0.900333	−	0.372930i	0.784348	+	0.620321i	$0.212998\pi$
$752$	−20.4058			−0.744123
$753$	0.806935	−	0.334243i	0.0294064	−	0.0121805i
$754$	−48.7559	−	20.1953i	−1.77558	−	0.735471i
$755$		0			0
$756$	−0.0223155	+	0.0223155i	−0.000811609	+	0.000811609i
$757$	−13.6672	−	13.6672i	−0.496742	−	0.496742i	0.413680	−	0.910422i	$-0.364243\pi$
$757$	−13.6672	−	13.6672i	−0.496742	−	0.496742i	−0.910422	+	0.413680i	$0.864243\pi$
$758$	21.9209	+	9.07995i	0.796204	+	0.329799i
$759$	−2.28394	−	0.946039i	−0.0829018	−	0.0343390i
$760$		0			0
$761$			9.52382i			0.345238i	0.984989	+	0.172619i	$0.0552230\pi$
$761$			9.52382i			0.345238i	−0.984989	+	0.172619i	$0.944777\pi$
$762$	0.0301607	+	0.0728145i	0.00109261	+	0.00263779i
$763$	−5.20984	+	5.20984i	−0.188609	+	0.188609i
$764$	1.27905			0.0462743
$765$		0			0
$766$	−52.2751			−1.88878
$767$	−39.5483	+	39.5483i	−1.42801	+	1.42801i
$768$	−0.0695582	−	0.167928i	−0.00250997	−	0.00605960i
$769$		−	21.8393i		−	0.787544i	−0.919208	−	0.393772i	$-0.871170\pi$
$769$		−	21.8393i		−	0.787544i	0.919208	−	0.393772i	$-0.128830\pi$
$770$		0			0
$771$	0.804939	+	0.333417i	0.0289892	+	0.0120077i
$772$	0.630110	+	0.261000i	0.0226781	+	0.00939359i
$773$	12.8920	+	12.8920i	0.463693	+	0.463693i	0.899864	−	0.436171i	$-0.143666\pi$
$773$	12.8920	+	12.8920i	0.463693	+	0.463693i	−0.436171	+	0.899864i	$0.643666\pi$
$774$	−1.94834	+	1.94834i	−0.0700316	+	0.0700316i
$775$		0			0
$776$	−6.93062	−	2.87076i	−0.248795	−	0.103054i
$777$	−0.00837247	+	0.00346799i	−0.000300361	+	0.000124413i
$778$	9.16025			0.328411
$779$	−2.31494	+	0.958880i	−0.0829413	+	0.0343554i
$780$		0			0
$781$	22.7435			0.813826
$782$	19.7161	+	19.1705i	0.705045	+	0.685536i
$783$			4.28180i			0.153019i
$784$	−19.0463	−	19.0463i	−0.680227	−	0.680227i
$785$		0			0
$786$			3.08814i			0.110150i
$787$	9.32964	−	3.86446i	0.332566	−	0.137753i	−0.210151	−	0.977669i	$-0.567396\pi$
$787$	9.32964	−	3.86446i	0.332566	−	0.137753i	0.542717	+	0.839916i	$0.317396\pi$
$788$	−0.368387	+	0.889364i	−0.0131232	+	0.0316823i
$789$	−0.359029	+	0.866773i	−0.0127818	+	0.0308579i
$790$		0			0
$791$	−5.67173	+	5.67173i	−0.201664	+	0.201664i
$792$	−37.1937	−	15.4061i	−1.32162	−	0.547433i
$793$	3.45907	−	8.35093i	0.122835	−	0.296550i
$794$	18.3728	+	44.3559i	0.652028	+	1.57413i
$795$		0			0
$796$	−0.811810	+	0.336263i	−0.0287738	+	0.0119185i
$797$	21.3651	−	21.3651i	0.756792	−	0.756792i	−0.218945	−	0.975737i	$-0.570262\pi$
$797$	21.3651	−	21.3651i	0.756792	−	0.756792i	0.975737	+	0.218945i	$0.0702615\pi$
$798$		−	0.255234i		−	0.00903518i
$799$	−18.6953	+	8.05291i	−0.661390	+	0.284891i
$800$		0			0
$801$	4.97892	+	4.97892i	0.175921	+	0.175921i
$802$	6.46782	+	15.6147i	0.228387	+	0.551374i
$803$	−26.6756			−0.941360
$804$	0.00868793	+	0.0209745i	0.000306400	+	0.000739714i
$805$		0			0
$806$	−20.5857	+	49.6983i	−0.725100	+	1.75055i
$807$	−1.24212	−	1.24212i	−0.0437246	−	0.0437246i
$808$	−28.0905	−	28.0905i	−0.988222	−	0.988222i
$809$	−9.87604	+	23.8429i	−0.347223	+	0.838270i	0.649723	+	0.760171i	$0.274885\pi$
$809$	−9.87604	+	23.8429i	−0.347223	+	0.838270i	−0.996946	+	0.0780990i	$0.975115\pi$
$810$		0			0
$811$	−18.0534	−	43.5848i	−0.633941	−	1.53047i	−0.834628	−	0.550814i	$-0.814317\pi$
$811$	−18.0534	−	43.5848i	−0.633941	−	1.53047i	0.200686	−	0.979656i	$-0.435683\pi$
$812$	−0.311995			−0.0109489
$813$	−0.947554	−	2.28760i	−0.0332322	−	0.0802296i
$814$	0.585277	+	0.585277i	0.0205139	+	0.0205139i
$815$		0			0
$816$	−1.34286	−	1.30570i	−0.0470095	−	0.0457087i
$817$		−	1.48911i		−	0.0520975i
$818$	−12.9003	+	12.9003i	−0.451049	+	0.451049i
$819$	10.8200	−	4.48180i	0.378082	−	0.156607i
$820$		0			0
$821$	−13.3232	−	32.1651i	−0.464983	−	1.12257i	−0.966326	−	0.257320i	$-0.917161\pi$
$821$	−13.3232	−	32.1651i	−0.464983	−	1.12257i	0.501343	−	0.865249i	$-0.332839\pi$
$822$	0.230937	−	0.557531i	0.00805484	−	0.0194461i
$823$	11.0211	+	4.56508i	0.384171	+	0.159129i	0.566406	−	0.824126i	$-0.308333\pi$
$823$	11.0211	+	4.56508i	0.384171	+	0.159129i	−0.182236	+	0.983255i	$0.558333\pi$
$824$	21.4008	−	21.4008i	0.745531	−	0.745531i
$825$		0			0
$826$	−3.79484	+	9.16155i	−0.132039	+	0.318771i
$827$	−2.90175	+	7.00545i	−0.100904	+	0.243603i	−0.966267	−	0.257541i	$-0.917088\pi$
$827$	−2.90175	+	7.00545i	−0.100904	+	0.243603i	0.865363	+	0.501145i	$0.167088\pi$
$828$	0.883065	−	0.365778i	0.0306886	−	0.0127116i
$829$			24.5064i			0.851141i	0.904925	+	0.425570i	$0.139927\pi$
$829$			24.5064i			0.851141i	−0.904925	+	0.425570i	$0.860073\pi$
$830$		0			0
$831$	−0.536403	−	0.536403i	−0.0186076	−	0.0186076i
$832$			43.4508i			1.50639i
$833$	−24.9662	−	9.93334i	−0.865026	−	0.344170i
$834$	2.09508			0.0725467
$835$		0			0
$836$	−0.718154	+	0.297469i	−0.0248379	+	0.0102882i
$837$	4.36456			0.150861
$838$	−46.5415	+	19.2781i	−1.60775	+	0.665951i
$839$	12.9110	+	5.34790i	0.445737	+	0.184630i	0.594250	−	0.804280i	$-0.297449\pi$
$839$	12.9110	+	5.34790i	0.445737	+	0.184630i	−0.148514	+	0.988910i	$0.547449\pi$
$840$		0			0
$841$	−9.42601	+	9.42601i	−0.325035	+	0.325035i
$842$	10.1945	+	10.1945i	0.351326	+	0.351326i
$843$	−0.952514	−	0.394544i	−0.0328063	−	0.0135888i
$844$	−0.820809	−	0.339990i	−0.0282534	−	0.0117029i
$845$		0			0
$846$			21.2184i			0.729505i
$847$	3.33324	+	8.04714i	0.114531	+	0.276503i
$848$	−35.0317	+	35.0317i	−1.20299	+	1.20299i
$849$	2.26154			0.0776158
$850$		0			0
$851$	0.550047			0.0188554
$852$	0.0251379	−	0.0251379i	0.000861212	−	0.000861212i
$853$	−2.83189	−	6.83679i	−0.0969621	−	0.234087i	0.867955	−	0.496644i	$-0.165434\pi$
$853$	−2.83189	−	6.83679i	−0.0969621	−	0.234087i	−0.964917	+	0.262556i	$0.915434\pi$
$854$		−	1.60262i		−	0.0548404i
$855$		0			0
$856$	42.6679	+	17.6736i	1.45836	+	0.604072i
$857$	−44.6404	−	18.4907i	−1.52489	−	0.631629i	−0.546324	−	0.837574i	$-0.683973\pi$
$857$	−44.6404	−	18.4907i	−1.52489	−	0.631629i	−0.978564	+	0.205944i	$0.933973\pi$
$858$	3.05785	+	3.05785i	0.104393	+	0.104393i
$859$	3.68462	−	3.68462i	0.125718	−	0.125718i	−0.641448	−	0.767166i	$-0.721666\pi$
$859$	3.68462	−	3.68462i	0.125718	−	0.125718i	0.767166	+	0.641448i	$0.221666\pi$
$860$		0			0
$861$	0.0761386	+	0.0315377i	0.00259480	+	0.00107480i
$862$	31.5564	−	13.0711i	1.07481	−	0.445202i
$863$	7.90307			0.269024			0.134512	−	0.990912i	$-0.457053\pi$
$863$	7.90307			0.269024			0.134512	+	0.990912i	$0.457053\pi$
$864$	−0.237183	+	0.0982444i	−0.00806913	+	0.00334234i
$865$		0			0
$866$	46.4483			1.57838
$867$	−1.74557	−	0.666305i	−0.0592827	−	0.0226289i
$868$			0.318026i			0.0107945i
$869$	−50.9161	−	50.9161i	−1.72721	−	1.72721i
$870$		0			0
$871$		−	16.8840i		−	0.572091i
$872$	−27.2007	+	11.2669i	−0.921133	+	0.381546i
$873$	−3.08817	+	7.45551i	−0.104519	+	0.252331i
$874$	−5.92843	+	14.3125i	−0.200532	+	0.484127i
$875$		0			0
$876$	−0.0294840	+	0.0294840i	−0.000996172	+	0.000996172i
$877$	25.4126	+	10.5262i	0.858121	+	0.355445i	0.767972	−	0.640483i	$-0.221266\pi$
$877$	25.4126	+	10.5262i	0.858121	+	0.355445i	0.0901488	+	0.995928i	$0.471266\pi$
$878$	11.7394	−	28.3415i	0.396186	−	0.956478i
$879$	−0.986461	−	2.38153i	−0.0332725	−	0.0803269i
$880$		0			0
$881$	18.2295	−	7.55089i	0.614166	−	0.254396i	−0.0538426	−	0.998549i	$-0.517147\pi$
$881$	18.2295	−	7.55089i	0.614166	−	0.254396i	0.668009	+	0.744154i	$0.267147\pi$
$882$	−19.8048	+	19.8048i	−0.666864	+	0.666864i
$883$		−	21.8566i		−	0.735534i	−0.929918	−	0.367767i	$-0.880122\pi$
$883$		−	21.8566i		−	0.735534i	0.929918	−	0.367767i	$-0.119878\pi$
$884$	−0.634568	−	1.47318i	−0.0213428	−	0.0495485i
$885$		0			0
$886$	−14.0550	−	14.0550i	−0.472187	−	0.472187i
$887$	−1.06338	−	2.56722i	−0.0357048	−	0.0861989i	0.905021	−	0.425366i	$-0.139855\pi$
$887$	−1.06338	−	2.56722i	−0.0357048	−	0.0861989i	−0.940726	+	0.339167i	$0.889855\pi$
$888$	−0.0362130			−0.00121523
$889$	−0.132610	−	0.320149i	−0.00444759	−	0.0107374i
$890$		0			0
$891$	−16.5056	+	39.8481i	−0.552960	+	1.33496i
$892$	0.996188	+	0.996188i	0.0333549	+	0.0333549i
$893$	−8.10863	−	8.10863i	−0.271345	−	0.271345i
$894$	−1.05595	+	2.54930i	−0.0353164	+	0.0852613i
$895$		0			0
$896$	3.15567	+	7.61845i	0.105423	+	0.254515i
$897$	2.87379			0.0959530
$898$	−3.64057	−	8.78912i	−0.121488	−	0.293297i
$899$	30.5107	+	30.5107i	1.01759	+	1.01759i
$900$		0			0
$901$	−18.2703	+	45.9200i	−0.608671	+	1.52982i
$902$		−	7.52710i		−	0.250625i
$903$	−0.0346321	+	0.0346321i	−0.00115248	+	0.00115248i
$904$	−29.6123	+	12.2658i	−0.984890	+	0.407955i
$905$		0			0
$906$	−0.681907	−	1.64627i	−0.0226548	−	0.0546936i
$907$	16.2552	−	39.2435i	0.539745	−	1.30306i	−0.385156	−	0.922851i	$-0.625853\pi$
$907$	16.2552	−	39.2435i	0.539745	−	1.30306i	0.924901	−	0.380208i	$-0.124147\pi$
$908$	−0.0777791	−	0.0322171i	−0.00258119	−	0.00106916i
$909$	−30.2180	+	30.2180i	−1.00227	+	1.00227i
$910$		0			0
$911$	−22.6043	+	54.5717i	−0.748915	+	1.80804i	−0.183933	+	0.982939i	$0.558883\pi$
$911$	−22.6043	+	54.5717i	−0.748915	+	1.80804i	−0.564982	+	0.825103i	$0.691117\pi$
$912$	0.403784	−	0.974822i	0.0133706	−	0.0322796i
$913$	−22.5653	+	9.34686i	−0.746803	+	0.309336i
$914$			7.20694i			0.238384i
$915$		0			0
$916$	−0.171689	−	0.171689i	−0.00567277	−	0.00567277i
$917$		−	13.5778i		−	0.448380i
$918$	−2.72089	+	2.79832i	−0.0898026	+	0.0923582i
$919$	−26.5657			−0.876323			−0.438161	−	0.898896i	$-0.644370\pi$
$919$	−26.5657			−0.876323			−0.438161	+	0.898896i	$0.644370\pi$
$920$		0			0
$921$	−3.08947	+	1.27970i	−0.101802	+	0.0421676i
$922$	23.5641			0.776042
$923$	−24.4263	+	10.1177i	−0.804001	+	0.333028i
$924$	0.0236202	+	0.00978379i	0.000777046	+	0.000321863i
$925$		0			0
$926$	27.8450	−	27.8450i	0.915042	−	0.915042i
$927$	−23.0215	−	23.0215i	−0.756127	−	0.756127i
$928$	−2.34482	−	0.971255i	−0.0769724	−	0.0318830i
$929$	−36.0284	−	14.9234i	−1.18205	−	0.489622i	−0.296894	−	0.954911i	$-0.595951\pi$
$929$	−36.0284	−	14.9234i	−1.18205	−	0.489622i	−0.885159	+	0.465288i	$0.845951\pi$
$930$		0			0
$931$		−	15.1368i		−	0.496090i
$932$	−0.765703	−	1.84857i	−0.0250814	−	0.0605519i
$933$	0.0839243	−	0.0839243i	0.00274756	−	0.00274756i
$934$	−0.929695			−0.0304206
$935$		0			0
$936$	46.7993			1.52968
$937$	6.93328	−	6.93328i	0.226500	−	0.226500i	−0.584729	−	0.811229i	$-0.698799\pi$
$937$	6.93328	−	6.93328i	0.226500	−	0.226500i	0.811229	+	0.584729i	$0.198799\pi$
$938$	−1.14558	−	2.76567i	−0.0374044	−	0.0903023i
$939$		−	0.398471i		−	0.0130036i
$940$		0			0
$941$	−45.4770	−	18.8372i	−1.48251	−	0.614075i	−0.512837	−	0.858486i	$-0.671405\pi$
$941$	−45.4770	−	18.8372i	−1.48251	−	0.614075i	−0.969672	+	0.244411i	$0.921405\pi$
$942$	0.897574	+	0.371787i	0.0292445	+	0.0121135i
$943$	−3.53701	−	3.53701i	−0.115181	−	0.115181i
$944$	−28.9875	+	28.9875i	−0.943462	+	0.943462i
$945$		0			0
$946$	4.13282	+	1.71187i	0.134370	+	0.0556577i
$947$	16.8123	−	6.96387i	0.546326	−	0.226295i	−0.0924110	−	0.995721i	$-0.529457\pi$
$947$	16.8123	−	6.96387i	0.546326	−	0.226295i	0.638737	+	0.769425i	$0.279457\pi$
$948$	−0.112553			−0.00365556
$949$	28.6493	−	11.8669i	0.929996	−	0.385217i
$950$		0			0
$951$	0.966612			0.0313445
$952$	5.70714	+	5.54922i	0.184970	+	0.179851i
$953$		−	5.23591i		−	0.169608i	−0.996398	−	0.0848039i	$-0.972974\pi$
$953$		−	5.23591i		−	0.169608i	0.996398	−	0.0848039i	$-0.0270264\pi$
$954$	36.4268	+	36.4268i	1.17936	+	1.17936i
$955$		0			0
$956$			0.543041i			0.0175632i
$957$	3.20470	−	1.32743i	0.103593	−	0.0429097i
$958$	7.46681	−	18.0265i	0.241242	−	0.582409i
$959$	−1.01538	+	2.45134i	−0.0327882	+	0.0791578i
$960$		0			0
$961$	9.18007	−	9.18007i	0.296131	−	0.296131i
$962$	−0.888949	−	0.368215i	−0.0286609	−	0.0118717i
$963$	19.0121	−	45.8994i	0.612658	−	1.47909i
$964$	−0.306966	−	0.741081i	−0.00988671	−	0.0238686i
$965$		0			0
$966$	0.470740	−	0.194987i	0.0151458	−	0.00627359i
$967$	−2.25894	+	2.25894i	−0.0726426	+	0.0726426i	−0.742495	−	0.669852i	$-0.766358\pi$
$967$	−2.25894	+	2.25894i	−0.0726426	+	0.0726426i	0.669852	+	0.742495i	$0.266358\pi$
$968$			34.8059i			1.11870i
$969$	−0.0147654	−	1.05245i	−0.000474332	−	0.0338097i
$970$		0			0
$971$	−19.2766	−	19.2766i	−0.618617	−	0.618617i	0.326560	−	0.945176i	$-0.394110\pi$
$971$	−19.2766	−	19.2766i	−0.618617	−	0.618617i	−0.945176	+	0.326560i	$0.894110\pi$
$972$	0.0779250	+	0.188128i	0.00249944	+	0.00603419i
$973$	−9.21160			−0.295310
$974$	15.9818	+	38.5834i	0.512089	+	1.23629i
$975$		0			0
$976$	2.53537	−	6.12092i	0.0811552	−	0.195926i
$977$	5.66117	+	5.66117i	0.181117	+	0.181117i	0.791842	−	0.610726i	$-0.209122\pi$
$977$	5.66117	+	5.66117i	0.181117	+	0.181117i	−0.610726	+	0.791842i	$0.709122\pi$
$978$	−1.25214	−	1.25214i	−0.0400390	−	0.0400390i
$979$	4.37463	−	10.5613i	0.139814	−	0.337540i
$980$		0			0
$981$	12.1202	+	29.2608i	0.386969	+	0.934225i
$982$	−18.8859			−0.602674
$983$	4.18902	+	10.1132i	0.133609	+	0.322561i	0.976498	−	0.215527i	$-0.0691469\pi$
$983$	4.18902	+	10.1132i	0.133609	+	0.322561i	−0.842889	+	0.538088i	$0.819147\pi$
$984$	0.232863	+	0.232863i	0.00742341	+	0.00742341i
$985$		0			0
$986$	−38.5822	+	0.541287i	−1.22871	+	0.0172381i
$987$			0.377162i			0.0120052i
$988$	0.638958	−	0.638958i	0.0203280	−	0.0203280i
$989$	2.74644	−	1.13761i	0.0873318	−	0.0361740i
$990$		0			0
$991$	−11.1297	−	26.8695i	−0.353547	−	0.853539i	−0.996177	−	0.0873614i	$-0.972157\pi$
$991$	−11.1297	−	26.8695i	−0.353547	−	0.853539i	0.642629	−	0.766177i	$-0.277843\pi$
$992$	−0.990028	+	2.39014i	−0.0314334	+	0.0758870i
$993$	3.57051	+	1.47895i	0.113307	+	0.0469332i
$994$	−3.31465	+	3.31465i	−0.105134	+	0.105134i
$995$		0			0
$996$	−0.0146101	+	0.0352719i	−0.000462939	+	0.00111763i
$997$	5.24110	−	12.6531i	0.165987	−	0.400728i	−0.818898	−	0.573940i	$-0.805414\pi$
$997$	5.24110	−	12.6531i	0.165987	−	0.400728i	0.984885	+	0.173211i	$0.0554144\pi$
$998$	−15.0711	+	6.24264i	−0.477067	+	0.197607i
$999$			0.0780686i			0.00246998i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	425.2.n.f.274.5		24
5.2	odd	4		85.2.l.a.36.5	yes	24
5.3	odd	4		425.2.m.b.376.2		24
5.4	even	2		425.2.n.c.274.2		24
15.2	even	4		765.2.be.b.631.2		24
17.9	even	8		425.2.n.c.349.2		24
85.3	even	16		7225.2.a.bq.1.3		12
85.9	even	8	inner	425.2.n.f.349.5		24
85.12	even	16		1445.2.d.j.866.6		24
85.22	even	16		1445.2.d.j.866.5		24
85.37	even	16		1445.2.a.q.1.10		12
85.43	odd	8		425.2.m.b.26.2		24
85.48	even	16		7225.2.a.bs.1.3		12
85.77	odd	8		85.2.l.a.26.5	✓	24
85.82	even	16		1445.2.a.p.1.10		12
255.77	even	8		765.2.be.b.451.2		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
85.2.l.a.26.5	✓	24	85.77	odd	8
85.2.l.a.36.5	yes	24	5.2	odd	4
425.2.m.b.26.2		24	85.43	odd	8
425.2.m.b.376.2		24	5.3	odd	4
425.2.n.c.274.2		24	5.4	even	2
425.2.n.c.349.2		24	17.9	even	8
425.2.n.f.274.5		24	1.1	even	1	trivial
425.2.n.f.349.5		24	85.9	even	8	inner
765.2.be.b.451.2		24	255.77	even	8
765.2.be.b.631.2		24	15.2	even	4
1445.2.a.p.1.10		12	85.82	even	16
1445.2.a.q.1.10		12	85.37	even	16
1445.2.d.j.866.5		24	85.22	even	16
1445.2.d.j.866.6		24	85.12	even	16
7225.2.a.bq.1.3		12	85.3	even	16
7225.2.a.bs.1.3		12	85.48	even	16

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:	\( N \)	\(=\)	\( 425 = 5^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	425.n (of order \(8\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.01710 - 1.01710i) q^{2} +(-0.0420595 - 0.101541i) q^{3} -0.0689897i q^{4} +(-0.146056 - 0.0604983i) q^{6} +(0.642174 + 0.265997i) q^{7} +(1.96403 + 1.96403i) q^{8} +(2.11278 - 2.11278i) q^{9} +(-4.48163 - 1.85635i) q^{11} +(-0.00700526 + 0.00290167i) q^{12} +5.63906 q^{13} +(0.923703 - 0.382610i) q^{14} +4.13322 q^{16} +(3.78674 - 1.63113i) q^{17} -4.29782i q^{18} +(1.64241 + 1.64241i) q^{19} -0.0763945i q^{21} +(-6.44637 + 2.67018i) q^{22} +(-1.77445 + 4.28390i) q^{23} +(0.116823 - 0.282035i) q^{24} +(5.73549 - 5.73549i) q^{26} +(-0.608017 - 0.251849i) q^{27} +(0.0183511 - 0.0443034i) q^{28} +(-2.48981 - 6.01093i) q^{29} +(-6.12711 + 2.53793i) q^{31} +(0.275837 - 0.275837i) q^{32} +0.533145i q^{33} +(2.19248 - 5.51052i) q^{34} +(-0.145760 - 0.145760i) q^{36} +(-0.0453958 - 0.109595i) q^{37} +3.34100 q^{38} +(-0.237176 - 0.572593i) q^{39} +(-0.412826 + 0.996650i) q^{41} +(-0.0777010 - 0.0777010i) q^{42} +(-0.453332 - 0.453332i) q^{43} +(-0.128069 + 0.309187i) q^{44} +(2.55237 + 6.16195i) q^{46} -4.93703 q^{47} +(-0.173841 - 0.419690i) q^{48} +(-4.60811 - 4.60811i) q^{49} +(-0.324894 - 0.315904i) q^{51} -0.389037i q^{52} +(-8.47565 + 8.47565i) q^{53} +(-0.874571 + 0.362259i) q^{54} +(0.738824 + 1.78368i) q^{56} +(0.0976925 - 0.235850i) q^{57} +(-8.64611 - 3.58134i) q^{58} +(-7.01329 + 7.01329i) q^{59} +(0.613413 - 1.48091i) q^{61} +(-3.65056 + 8.81322i) q^{62} +(1.91877 - 0.794779i) q^{63} +7.70533i q^{64} +(0.542263 + 0.542263i) q^{66} -2.99411i q^{67} +(-0.112531 - 0.261246i) q^{68} +0.509622 q^{69} +(-4.33163 + 1.79422i) q^{71} +8.29913 q^{72} +(5.08052 - 2.10442i) q^{73} +(-0.157641 - 0.0652972i) q^{74} +(0.113309 - 0.113309i) q^{76} +(-2.38421 - 2.38421i) q^{77} +(-0.823617 - 0.341153i) q^{78} +(13.7140 + 5.68053i) q^{79} -8.89143i q^{81} +(0.593808 + 1.43358i) q^{82} +(3.56033 - 3.56033i) q^{83} -0.00527044 q^{84} -0.922169 q^{86} +(-0.505633 + 0.505633i) q^{87} +(-5.15614 - 12.4480i) q^{88} +2.35657i q^{89} +(3.62126 + 1.49997i) q^{91} +(0.295545 + 0.122419i) q^{92} +(0.515406 + 0.515406i) q^{93} +(-5.02145 + 5.02145i) q^{94} +(-0.0396102 - 0.0164071i) q^{96} +(-2.49522 + 1.03355i) q^{97} -9.37384 q^{98} +(-13.3908 + 5.54664i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 8 q^{3} - 8 q^{6} + 24 q^{9} - 8 q^{11} - 40 q^{12} - 16 q^{13} - 24 q^{16} + 8 q^{19} + 24 q^{22} - 8 q^{23} + 8 q^{24} + 16 q^{26} - 16 q^{27} + 40 q^{28} + 8 q^{29} - 16 q^{34} - 24 q^{36} + 16 q^{37}+ \cdots + 8 q^{99}+O(q^{100}) \) 24 * q + 8 * q^3 - 8 * q^6 + 24 * q^9 - 8 * q^11 - 40 * q^12 - 16 * q^13 - 24 * q^16 + 8 * q^19 + 24 * q^22 - 8 * q^23 + 8 * q^24 + 16 * q^26 - 16 * q^27 + 40 * q^28 + 8 * q^29 - 16 * q^34 - 24 * q^36 + 16 * q^37 + 48 * q^38 - 8 * q^39 + 16 * q^41 + 24 * q^42 + 8 * q^43 - 16 * q^44 + 8 * q^46 + 64 * q^47 + 8 * q^48 - 56 * q^51 - 24 * q^53 + 32 * q^54 + 64 * q^56 - 16 * q^57 - 56 * q^58 - 32 * q^59 + 32 * q^61 + 32 * q^62 - 80 * q^63 + 96 * q^66 - 24 * q^68 - 96 * q^69 - 24 * q^71 + 24 * q^72 + 64 * q^73 + 64 * q^74 - 8 * q^76 - 24 * q^77 - 8 * q^78 + 16 * q^82 + 96 * q^83 + 64 * q^84 - 16 * q^86 - 48 * q^87 - 8 * q^88 - 24 * q^91 - 112 * q^92 + 64 * q^93 - 56 * q^94 - 168 * q^96 - 48 * q^97 - 120 * q^98 + 8 * q^99

Introduction

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