LMFDB - Embedded newform 676.2.l.i.427.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [676,2,Mod(19,676)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(676, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 5]))

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

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

chi := DirichletCharacter("676.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 676 = 2^{2} \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	676.l (of order $12$, 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:	$5.39788717664$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{12})$
Coefficient field:	16.0.102930383934669717504.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 4 x^{15} + 5 x^{14} - 2 x^{13} + 5 x^{12} - 8 x^{11} - 12 x^{10} + 32 x^{9} - 36 x^{8} + \cdots + 256 $ x^16 - 4x^15 + 5x^14 - 2x^13 + 5x^12 - 8x^11 - 12x^10 + 32x^9 - 36x^8 + 64x^7 - 48x^6 - 64x^5 + 80x^4 - 64x^3 + 320x^2 - 512*x + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 52)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			427.4
Root			$1.08916 - 0.902074i$ of defining polynomial
Character	$\chi$	$=$	676.427
Dual form			676.2.l.i.19.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.39427 - 0.236640i) q^{2} +(0.736159 - 0.425021i) q^{3} +(1.88800 - 0.659882i) q^{4} +(0.166404 + 0.166404i) q^{5} +(0.925830 - 0.766801i) q^{6} +(2.55416 - 0.684384i) q^{7} +(2.47624 - 1.36683i) q^{8} +(-1.13871 + 1.97231i) q^{9} +(0.271390 + 0.192635i) q^{10} +(-0.373247 + 1.39298i) q^{11} +(1.10941 - 1.28822i) q^{12} +(3.39924 - 1.55864i) q^{14} +(0.193225 + 0.0517744i) q^{15} +(3.12911 - 2.49172i) q^{16} +(-1.21178 - 0.699622i) q^{17} +(-1.12095 + 3.01941i) q^{18} +(1.44475 + 5.39188i) q^{19} +(0.423978 + 0.204364i) q^{20} +(1.58939 - 1.58939i) q^{21} +(-0.190775 + 2.03052i) q^{22} +(-4.37216 - 7.57279i) q^{23} +(1.24197 - 2.05866i) q^{24} -4.94462i q^{25} +4.48604i q^{27} +(4.37064 - 2.97756i) q^{28} +(-2.11023 - 3.65503i) q^{29} +(0.281660 + 0.0264630i) q^{30} +(-3.88100 + 3.88100i) q^{31} +(3.77320 - 4.21461i) q^{32} +(0.317276 + 1.18409i) q^{33} +(-1.85511 - 0.688709i) q^{34} +(0.538906 + 0.311137i) q^{35} +(-0.848402 + 4.47514i) q^{36} +(-0.500000 - 0.133975i) q^{37} +(3.29032 + 7.17588i) q^{38} +(0.639502 + 0.184609i) q^{40} +(1.50000 - 5.59808i) q^{41} +(1.83993 - 2.59215i) q^{42} +(-4.59362 + 7.95638i) q^{43} +(0.214509 + 2.87624i) q^{44} +(-0.517686 + 0.138714i) q^{45} +(-7.88801 - 9.52393i) q^{46} +(2.80318 + 2.80318i) q^{47} +(1.24449 - 3.16424i) q^{48} +(-0.00684229 + 0.00395040i) q^{49} +(-1.17009 - 6.89416i) q^{50} -1.18942 q^{51} -5.94462 q^{53} +(1.06158 + 6.25477i) q^{54} +(-0.293906 + 0.169687i) q^{55} +(5.38927 - 5.18581i) q^{56} +(3.35523 + 3.35523i) q^{57} +(-3.80717 - 4.59675i) q^{58} +(8.22961 - 2.20512i) q^{59} +(0.398974 - 0.0297554i) q^{60} +(3.61102 - 6.25448i) q^{61} +(-4.49277 + 6.32957i) q^{62} +(-1.55864 + 5.81691i) q^{63} +(4.26353 - 6.76922i) q^{64} +(0.722573 + 1.57587i) q^{66} +(-2.43624 - 0.652790i) q^{67} +(-2.74951 - 0.521255i) q^{68} +(-6.43720 - 3.71652i) q^{69} +(0.825010 + 0.306284i) q^{70} +(2.81352 + 10.5002i) q^{71} +(-0.123908 + 6.44034i) q^{72} +(-5.05407 + 5.05407i) q^{73} +(-0.728841 - 0.0684774i) q^{74} +(-2.10157 - 3.64002i) q^{75} +(6.28570 + 9.22653i) q^{76} +3.81333i q^{77} +8.51654i q^{79} +(0.935328 + 0.106064i) q^{80} +(-1.50948 - 2.61449i) q^{81} +(0.766683 - 8.16022i) q^{82} +(6.91195 - 6.91195i) q^{83} +(1.95196 - 4.04958i) q^{84} +(-0.0852251 - 0.318065i) q^{85} +(-4.52197 + 12.1804i) q^{86} +(-3.10694 - 1.79379i) q^{87} +(0.979719 + 3.95951i) q^{88} +(-6.41693 - 1.71941i) q^{89} +(-0.688971 + 0.315910i) q^{90} +(-13.2518 - 11.4124i) q^{92} +(-1.20752 + 4.50653i) q^{93} +(4.57175 + 3.24506i) q^{94} +(-0.656818 + 1.13764i) q^{95} +(0.986372 - 4.70632i) q^{96} +(-14.9459 + 4.00474i) q^{97} +(-0.00860521 + 0.00712710i) q^{98} +(-2.32236 - 2.32236i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 4 q^{2} + 6 q^{4} + 12 q^{5} - 10 q^{6} - 10 q^{8} + 4 q^{9} + 8 q^{14} - 2 q^{16} - 12 q^{17} + 6 q^{18} - 20 q^{20} + 28 q^{21} + 14 q^{24} - 24 q^{28} - 8 q^{29} - 42 q^{30} + 26 q^{32} + 8 q^{33}+ \cdots + 68 q^{98}+O(q^{100}) $ 16 * q - 4 * q^2 + 6 * q^4 + 12 * q^5 - 10 * q^6 - 10 * q^8 + 4 * q^9 + 8 * q^14 - 2 * q^16 - 12 * q^17 + 6 * q^18 - 20 * q^20 + 28 * q^21 + 14 * q^24 - 24 * q^28 - 8 * q^29 - 42 * q^30 + 26 * q^32 + 8 * q^33 - 14 * q^34 + 6 * q^36 - 8 * q^37 - 40 * q^40 + 24 * q^41 - 28 * q^42 + 8 * q^44 + 40 * q^45 + 10 * q^46 - 10 * q^48 - 60 * q^49 - 22 * q^50 - 32 * q^53 + 28 * q^54 + 60 * q^56 - 12 * q^57 - 18 * q^58 + 24 * q^60 + 4 * q^61 + 18 * q^62 + 56 * q^66 + 16 * q^68 + 12 * q^69 - 28 * q^70 + 10 * q^72 - 20 * q^73 + 4 * q^74 + 14 * q^76 + 22 * q^80 + 48 * q^81 + 36 * q^84 - 32 * q^85 - 16 * q^86 - 36 * q^88 - 8 * q^89 - 12 * q^92 + 20 * q^93 - 38 * q^94 + 72 * q^96 - 80 * q^97 + 68 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/676\mathbb{Z}\right)^\times$.

$n$	$339$	$509$
$\chi(n)$	$-1$	$e\left(\frac{7}{12}\right)$

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 $

$2$	1.39427	−	0.236640i	0.985901	−	0.167330i
$2$	1.39427	−	0.236640i	0.985901	−	0.167330i
$3$	0.736159	−	0.425021i	0.425021	−	0.245386i	−0.272202	−	0.962240i	$-0.587752\pi$
$3$	0.736159	−	0.425021i	0.425021	−	0.245386i	0.697223	+	0.716854i	$0.254419\pi$
$4$	1.88800	−	0.659882i	0.944001	−	0.329941i
$5$	0.166404	+	0.166404i	0.0744180	+	0.0744180i	0.743336	−	0.668918i	$-0.233242\pi$
$5$	0.166404	+	0.166404i	0.0744180	+	0.0744180i	−0.668918	+	0.743336i	$0.733242\pi$
$6$	0.925830	−	0.766801i	0.377969	−	0.313045i
$7$	2.55416	−	0.684384i	0.965381	−	0.258673i	0.258504	−	0.966010i	$-0.416770\pi$
$7$	2.55416	−	0.684384i	0.965381	−	0.258673i	0.706876	+	0.707337i	$0.250104\pi$
$8$	2.47624	−	1.36683i	0.875483	−	0.483249i
$9$	−1.13871	+	1.97231i	−0.379571	+	0.657437i
$10$	0.271390	+	0.192635i	0.0858212	+	0.0609165i
$11$	−0.373247	+	1.39298i	−0.112538	+	0.419998i	−0.999091	−	0.0426292i	$-0.986427\pi$
$11$	−0.373247	+	1.39298i	−0.112538	+	0.419998i	0.886553	+	0.462628i	$0.153093\pi$
$12$	1.10941	−	1.28822i	0.320258	−	0.371877i
$13$		0			0
$13$		0			0
$14$	3.39924	−	1.55864i	0.908486	−	0.416563i
$15$	0.193225	+	0.0517744i	0.0498904	+	0.0133681i
$16$	3.12911	−	2.49172i	0.782278	−	0.622930i
$17$	−1.21178	−	0.699622i	−0.293900	−	0.169683i	0.345799	−	0.938308i	$-0.387608\pi$
$17$	−1.21178	−	0.699622i	−0.293900	−	0.169683i	−0.639699	+	0.768625i	$0.720941\pi$
$18$	−1.12095	+	3.01941i	−0.264211	+	0.711681i
$19$	1.44475	+	5.39188i	0.331449	+	1.23698i	0.907668	+	0.419688i	$0.137861\pi$
$19$	1.44475	+	5.39188i	0.331449	+	1.23698i	−0.576220	+	0.817295i	$0.695473\pi$
$20$	0.423978	+	0.204364i	0.0948043	+	0.0456972i
$21$	1.58939	−	1.58939i	0.346833	−	0.346833i
$22$	−0.190775	+	2.03052i	−0.0406733	+	0.432908i
$23$	−4.37216	−	7.57279i	−0.911657	−	1.57904i	−0.811723	−	0.584043i	$-0.801470\pi$
$23$	−4.37216	−	7.57279i	−0.911657	−	1.57904i	−0.0999345	−	0.994994i	$-0.531863\pi$
$24$	1.24197	−	2.05866i	0.253516	−	0.420223i
$25$		−	4.94462i		−	0.988924i
$26$		0			0
$27$			4.48604i			0.863339i
$28$	4.37064	−	2.97756i	0.825974	−	0.562706i
$29$	−2.11023	−	3.65503i	−0.391861	−	0.678723i	0.600834	−	0.799374i	$-0.294835\pi$
$29$	−2.11023	−	3.65503i	−0.391861	−	0.678723i	−0.992695	+	0.120651i	$0.961502\pi$
$30$	0.281660	+	0.0264630i	0.0514239	+	0.00483147i
$31$	−3.88100	+	3.88100i	−0.697047	+	0.697047i	−0.963773	−	0.266725i	$-0.914058\pi$
$31$	−3.88100	+	3.88100i	−0.697047	+	0.697047i	0.266725	+	0.963773i	$0.414058\pi$
$32$	3.77320	−	4.21461i	0.667014	−	0.745046i
$33$	0.317276	+	1.18409i	0.0552307	+	0.206124i
$34$	−1.85511	−	0.688709i	−0.318149	−	0.118113i
$35$	0.538906	+	0.311137i	0.0910917	+	0.0525918i
$36$	−0.848402	+	4.47514i	−0.141400	+	0.745857i
$37$	−0.500000	−	0.133975i	−0.0821995	−	0.0220253i	0.217485	−	0.976064i	$-0.430215\pi$
$37$	−0.500000	−	0.133975i	−0.0821995	−	0.0220253i	−0.299684	+	0.954038i	$0.596881\pi$
$38$	3.29032	+	7.17588i	0.533760	+	1.16408i
$39$		0			0
$40$	0.639502	+	0.184609i	0.101114	+	0.0291893i
$41$	1.50000	−	5.59808i	0.234261	−	0.874273i	−0.744220	−	0.667934i	$-0.767179\pi$
$41$	1.50000	−	5.59808i	0.234261	−	0.874273i	0.978481	−	0.206338i	$-0.0661547\pi$
$42$	1.83993	−	2.59215i	0.283907	−	0.399978i
$43$	−4.59362	+	7.95638i	−0.700520	+	1.21334i	0.267764	+	0.963484i	$0.413715\pi$
$43$	−4.59362	+	7.95638i	−0.700520	+	1.21334i	−0.968284	+	0.249852i	$0.919618\pi$
$44$	0.214509	+	2.87624i	0.0323385	+	0.433610i
$45$	−0.517686	+	0.138714i	−0.0771721	+	0.0206782i
$46$	−7.88801	−	9.52393i	−1.16302	−	1.40423i
$47$	2.80318	+	2.80318i	0.408886	+	0.408886i	0.881350	−	0.472464i	$-0.156635\pi$
$47$	2.80318	+	2.80318i	0.408886	+	0.408886i	−0.472464	+	0.881350i	$0.656635\pi$
$48$	1.24449	−	3.16424i	0.179626	−	0.456719i
$49$	−0.00684229	+	0.00395040i	−0.000977470	+	0.000564343i
$50$	−1.17009	−	6.89416i	−0.165476	−	0.974981i
$51$	−1.18942			−0.166552
$52$		0			0
$53$	−5.94462			−0.816556			−0.408278	−	0.912858i	$-0.633871\pi$
$53$	−5.94462			−0.816556			−0.408278	+	0.912858i	$0.633871\pi$
$54$	1.06158	+	6.25477i	0.144462	+	0.851166i
$55$	−0.293906	+	0.169687i	−0.0396303	+	0.0228806i
$56$	5.38927	−	5.18581i	0.720171	−	0.692983i
$57$	3.35523	+	3.35523i	0.444411	+	0.444411i
$58$	−3.80717	−	4.59675i	−0.499906	−	0.603583i
$59$	8.22961	−	2.20512i	1.07140	−	0.287082i	0.320334	−	0.947305i	$-0.396205\pi$
$59$	8.22961	−	2.20512i	1.07140	−	0.287082i	0.751070	+	0.660223i	$0.229538\pi$
$60$	0.398974	−	0.0297554i	0.0515073	−	0.00384140i
$61$	3.61102	−	6.25448i	0.462344	−	0.800804i	−0.536733	−	0.843752i	$-0.680342\pi$
$61$	3.61102	−	6.25448i	0.462344	−	0.800804i	0.999077	+	0.0429485i	$0.0136751\pi$
$62$	−4.49277	+	6.32957i	−0.570583	+	0.803856i
$63$	−1.55864	+	5.81691i	−0.196370	+	0.732861i
$64$	4.26353	−	6.76922i	0.532941	−	0.846152i
$65$		0			0
$66$	0.722573	+	1.57587i	0.0889426	+	0.193976i
$67$	−2.43624	−	0.652790i	−0.297635	−	0.0797510i	0.106912	−	0.994269i	$-0.465904\pi$
$67$	−2.43624	−	0.652790i	−0.297635	−	0.0797510i	−0.404546	+	0.914518i	$0.632571\pi$
$68$	−2.74951	−	0.521255i	−0.333427	−	0.0632115i
$69$	−6.43720	−	3.71652i	−0.774948	−	0.447416i
$70$	0.825010	+	0.306284i	0.0986075	+	0.0366080i
$71$	2.81352	+	10.5002i	0.333903	+	1.24614i	0.905053	+	0.425298i	$0.139831\pi$
$71$	2.81352	+	10.5002i	0.333903	+	1.24614i	−0.571150	+	0.820846i	$0.693502\pi$
$72$	−0.123908	+	6.44034i	−0.0146026	+	0.759002i
$73$	−5.05407	+	5.05407i	−0.591534	+	0.591534i	−0.938046	−	0.346512i	$-0.887366\pi$
$73$	−5.05407	+	5.05407i	−0.591534	+	0.591534i	0.346512	+	0.938046i	$0.387366\pi$
$74$	−0.728841	−	0.0684774i	−0.0847260	−	0.00796033i
$75$	−2.10157	−	3.64002i	−0.242668	−	0.420314i
$76$	6.28570	+	9.22653i	0.721020	+	1.05836i
$77$			3.81333i			0.434569i
$78$		0			0
$79$			8.51654i			0.958186i	0.877764	+	0.479093i	$0.159034\pi$
$79$			8.51654i			0.958186i	−0.877764	+	0.479093i	$0.840966\pi$
$80$	0.935328	+	0.106064i	0.104573	+	0.0118583i
$81$	−1.50948	−	2.61449i	−0.167720	−	0.290499i
$82$	0.766683	−	8.16022i	0.0846660	−	0.901145i
$83$	6.91195	−	6.91195i	0.758685	−	0.758685i	−0.217398	−	0.976083i	$-0.569757\pi$
$83$	6.91195	−	6.91195i	0.758685	−	0.758685i	0.976083	+	0.217398i	$0.0697570\pi$
$84$	1.95196	−	4.04958i	0.212976	−	0.441845i
$85$	−0.0852251	−	0.318065i	−0.00924396	−	0.0344989i
$86$	−4.52197	+	12.1804i	−0.487616	+	1.31345i
$87$	−3.10694	−	1.79379i	−0.333098	−	0.192314i
$88$	0.979719	+	3.95951i	0.104438	+	0.422085i
$89$	−6.41693	−	1.71941i	−0.680193	−	0.182257i	−0.0978511	−	0.995201i	$-0.531197\pi$
$89$	−6.41693	−	1.71941i	−0.680193	−	0.182257i	−0.582342	+	0.812944i	$0.697864\pi$
$90$	−0.688971	+	0.315910i	−0.0726240	+	0.0332998i
$91$		0			0
$92$	−13.2518	−	11.4124i	−1.38160	−	1.18982i
$93$	−1.20752	+	4.50653i	−0.125214	+	0.467306i
$94$	4.57175	+	3.24506i	0.471540	+	0.334703i
$95$	−0.656818	+	1.13764i	−0.0673881	+	0.116720i
$96$	0.986372	−	4.70632i	0.100671	−	0.480336i
$97$	−14.9459	+	4.00474i	−1.51753	+	0.406620i	−0.918926	−	0.394429i	$-0.870942\pi$
$97$	−14.9459	+	4.00474i	−1.51753	+	0.406620i	−0.598599	+	0.801049i	$0.704276\pi$
$98$	−0.00860521	+	0.00712710i	−0.000869257	+	0.000719946i
$99$	−2.32236	−	2.32236i	−0.233406	−	0.233406i
$100$	−3.26287	−	9.33546i	−0.326287	−	0.933546i
$101$	7.94541	−	4.58728i	0.790598	−	0.456452i	−0.0495752	−	0.998770i	$-0.515787\pi$
$101$	7.94541	−	4.58728i	0.790598	−	0.456452i	0.840173	+	0.542319i	$0.182453\pi$
$102$	−1.65837	+	0.281464i	−0.164203	+	0.0278690i
$103$	−10.9080			−1.07480			−0.537398	−	0.843329i	$-0.680593\pi$
$103$	−10.9080			−1.07480			−0.537398	+	0.843329i	$0.680593\pi$
$104$		0			0
$105$	0.528960			0.0516212
$106$	−8.28843	+	1.40673i	−0.805044	+	0.136634i
$107$	−8.53605	+	4.92829i	−0.825211	+	0.476436i	−0.852210	−	0.523200i	$-0.824738\pi$
$107$	−8.53605	+	4.92829i	−0.825211	+	0.476436i	0.0269990	+	0.999635i	$0.491405\pi$
$108$	2.96026	+	8.46966i	0.284851	+	0.814993i
$109$	−0.0243171	−	0.0243171i	−0.00232916	−	0.00232916i	0.705941	−	0.708270i	$-0.250524\pi$
$109$	−0.0243171	−	0.0243171i	−0.00232916	−	0.00232916i	−0.708270	+	0.705941i	$0.750524\pi$
$110$	−0.369631	+	0.306140i	−0.0352430	+	0.0291893i
$111$	−0.425021	+	0.113884i	−0.0403412	+	0.0108094i
$112$	6.28695	−	8.50576i	0.594061	−	0.803718i
$113$	−2.27664	+	3.94325i	−0.214168	+	0.370950i	−0.953015	−	0.302923i	$-0.902037\pi$
$113$	−2.27664	+	3.94325i	−0.214168	+	0.370950i	0.738847	+	0.673873i	$0.235371\pi$
$114$	5.47210	+	3.88413i	0.512509	+	0.363782i
$115$	0.532599	−	1.98769i	0.0496651	−	0.185353i
$116$	−6.39602	−	5.50821i	−0.593856	−	0.511424i
$117$		0			0
$118$	10.9525	−	5.02200i	1.00826	−	0.462312i
$119$	−3.57389	−	0.957620i	−0.327618	−	0.0877849i
$120$	0.549238	−	0.135900i	0.0501383	−	0.0124059i
$121$	7.72521	+	4.46015i	0.702292	+	0.405468i
$122$	3.55470	−	9.57497i	0.321827	−	0.866877i
$123$	−1.27506	−	4.75860i	−0.114969	−	0.429069i
$124$	−4.76633	+	9.88833i	−0.428029	+	0.887998i
$125$	1.65482	−	1.65482i	0.148012	−	0.148012i
$126$	−0.796653	+	8.47920i	−0.0709715	+	0.755387i
$127$	2.67207	+	4.62816i	0.237108	+	0.410683i	0.959883	−	0.280400i	$-0.0904672\pi$
$127$	2.67207	+	4.62816i	0.237108	+	0.410683i	−0.722775	+	0.691083i	$0.757134\pi$
$128$	4.34266	−	10.4471i	0.383841	−	0.923399i
$129$			7.80954i			0.687592i
$130$		0			0
$131$		−	11.2254i		−	0.980764i	−0.871508	−	0.490382i	$-0.836857\pi$
$131$		−	11.2254i		−	0.980764i	0.871508	−	0.490382i	$-0.163143\pi$
$132$	1.38038	+	2.02620i	0.120146	+	0.176358i
$133$	7.38024	+	12.7830i	0.639948	+	1.10842i
$134$	−3.55127	−	0.333655i	−0.306783	−	0.0288234i
$135$	−0.746494	+	0.746494i	−0.0642480	+	0.0642480i
$136$	−3.95693	−	0.0761283i	−0.339304	−	0.00652795i
$137$	1.24442	+	4.64424i	0.106318	+	0.396784i	0.998491	−	0.0549089i	$-0.0174868\pi$
$137$	1.24442	+	4.64424i	0.106318	+	0.396784i	−0.892173	+	0.451693i	$0.850820\pi$
$138$	−9.85470	−	3.65855i	−0.838888	−	0.311436i
$139$	6.01080	+	3.47034i	0.509830	+	0.294350i	0.732764	−	0.680483i	$-0.238230\pi$
$139$	6.01080	+	3.47034i	0.509830	+	0.294350i	−0.222934	+	0.974834i	$0.571563\pi$
$140$	1.22277	+	0.231814i	0.103343	+	0.0195918i
$141$	3.25500	+	0.872175i	0.274121	+	0.0734504i
$142$	6.40759	+	13.9744i	0.537713	+	1.17270i
$143$		0			0
$144$	1.35128	+	9.00893i	0.112607	+	0.750744i
$145$	0.257060	−	0.959363i	0.0213477	−	0.0796707i
$146$	−5.85076	+	8.24275i	−0.484212	+	0.682175i
$147$	−0.00335801	+	0.00581624i	−0.000276964	+	0.000479715i
$148$	−1.03241	+	0.0769967i	−0.0848635	+	0.00632909i
$149$	14.6408	−	3.92298i	1.19942	−	0.321383i	0.396817	−	0.917898i	$-0.370115\pi$
$149$	14.6408	−	3.92298i	1.19942	−	0.321383i	0.802602	+	0.596515i	$0.203448\pi$
$150$	−3.79154	−	4.57788i	−0.309578	−	0.373782i
$151$	0.480824	+	0.480824i	0.0391289	+	0.0391289i	0.726401	−	0.687272i	$-0.241192\pi$
$151$	0.480824	+	0.480824i	0.0391289	+	0.0391289i	−0.687272	+	0.726401i	$0.741192\pi$
$152$	10.9474	+	11.3769i	0.887948	+	0.922786i
$153$	2.75974	−	1.59334i	0.223112	−	0.128814i
$154$	0.902385	+	5.31682i	0.0727163	+	0.428442i
$155$	−1.29162			−0.103746
$156$		0			0
$157$	5.90408			0.471197			0.235598	−	0.971851i	$-0.424295\pi$
$157$	5.90408			0.471197			0.235598	+	0.971851i	$0.424295\pi$
$158$	2.01535	+	11.8744i	0.160333	+	0.944676i
$159$	−4.37618	+	2.52659i	−0.347054	+	0.200372i
$160$	1.32920	−	0.0734532i	0.105083	−	0.00580699i
$161$	−16.3499	−	16.3499i	−1.28855	−	1.28855i
$162$	−2.72332	−	3.28812i	−0.213964	−	0.258339i
$163$	−15.1967	+	4.07194i	−1.19030	+	0.318939i	−0.799003	−	0.601327i	$-0.794639\pi$
$163$	−15.1967	+	4.07194i	−1.19030	+	0.318939i	−0.391294	+	0.920266i	$0.627972\pi$
$164$	−0.862067	−	11.5590i	−0.0673161	−	0.902607i
$165$	−0.144241	+	0.249833i	−0.0112292	+	0.0194495i
$166$	8.00151	−	11.2728i	0.621038	−	0.874939i
$167$	1.45106	−	5.41542i	0.112286	−	0.419058i	−0.886783	−	0.462185i	$-0.847065\pi$
$167$	1.45106	−	5.41542i	0.112286	−	0.419058i	0.999070	+	0.0431274i	$0.0137321\pi$
$168$	1.76327	−	6.10813i	0.136040	−	0.471253i
$169$		0			0
$170$	−0.194094	−	0.423302i	−0.0148863	−	0.0324658i
$171$	−12.2796	−	3.29032i	−0.939046	−	0.251617i
$172$	−3.42249	+	18.0529i	−0.260962	+	1.37652i
$173$	−1.87129	−	1.08039i	−0.142272	−	0.0821405i	0.427175	−	0.904169i	$-0.359509\pi$
$173$	−1.87129	−	1.08039i	−0.142272	−	0.0821405i	−0.569446	+	0.822029i	$0.692842\pi$
$174$	−4.75640	−	1.76581i	−0.360582	−	0.133866i
$175$	−3.38402	−	12.6293i	−0.255808	−	0.954688i
$176$	2.30298	+	5.28881i	0.173593	+	0.398659i
$177$	5.12108	−	5.12108i	0.384924	−	0.384924i
$178$	−9.35384	−	0.878829i	−0.701100	−	0.0658710i
$179$	5.06638	+	8.77523i	0.378679	+	0.655892i	0.990870	−	0.134818i	$-0.0430450\pi$
$179$	5.06638	+	8.77523i	0.378679	+	0.655892i	−0.612191	+	0.790710i	$0.709712\pi$
$180$	−0.885858	+	0.603504i	−0.0660280	+	0.0449825i
$181$		−	13.8528i		−	1.02967i	−0.857289	−	0.514836i	$-0.827853\pi$
$181$		−	13.8528i		−	1.02967i	0.857289	−	0.514836i	$-0.172147\pi$
$182$		0			0
$183$		−	6.13905i		−	0.453812i
$184$	−21.1773	−	12.7760i	−1.56121	−	0.941863i
$185$	−0.0609080	−	0.105496i	−0.00447805	−	0.00775620i
$186$	−0.617191	+	6.56910i	−0.0452547	+	0.481669i
$187$	1.42685	−	1.42685i	0.104342	−	0.104342i
$188$	7.14219	+	3.44265i	0.520898	+	0.251081i
$189$	3.07017	+	11.4580i	0.223322	+	0.833450i
$190$	−0.646573	+	1.74162i	−0.0469073	+	0.126350i
$191$	3.35193	+	1.93524i	0.242537	+	0.140029i	0.616342	−	0.787478i	$-0.288614\pi$
$191$	3.35193	+	1.93524i	0.242537	+	0.140029i	−0.373805	+	0.927507i	$0.621947\pi$
$192$	0.261570	−	6.79531i	0.0188772	−	0.490409i
$193$	7.94409	+	2.12861i	0.571828	+	0.153221i	0.533135	−	0.846030i	$-0.321014\pi$
$193$	7.94409	+	2.12861i	0.571828	+	0.153221i	0.0386934	+	0.999251i	$0.487680\pi$
$194$	−19.8910	+	9.12050i	−1.42809	+	0.654814i
$195$		0			0
$196$	−0.0103115	+	0.0119735i	−0.000736533	+	0.000855248i
$197$	−3.20436	+	11.9588i	−0.228301	+	0.852032i	0.752754	+	0.658302i	$0.228725\pi$
$197$	−3.20436	+	11.9588i	−0.228301	+	0.852032i	−0.981055	+	0.193730i	$0.937942\pi$
$198$	−3.78757	−	2.68844i	−0.269171	−	0.191059i
$199$	1.21698	−	2.10788i	0.0862696	−	0.149423i	−0.819662	−	0.572848i	$-0.805839\pi$
$199$	1.21698	−	2.10788i	0.0862696	−	0.149423i	0.905932	+	0.423424i	$0.139172\pi$
$200$	−6.75848	−	12.2441i	−0.477896	−	0.865786i
$201$	−2.07091	+	0.554899i	−0.146071	+	0.0391396i
$202$	9.99255	−	8.27613i	0.703073	−	0.582307i
$203$	−7.89132	−	7.89132i	−0.553862	−	0.553862i
$204$	−2.24562	+	0.784875i	−0.157225	+	0.0549522i
$205$	1.18115	−	0.681935i	0.0824949	−	0.0476284i
$206$	−15.2087	+	2.58127i	−1.05964	+	0.179845i
$207$	19.9145			1.38416
$208$		0			0
$209$	−8.05002			−0.556831
$210$	0.737516	−	0.125173i	0.0508934	−	0.00863777i
$211$	3.62910	−	2.09526i	0.249838	−	0.144244i	−0.369852	−	0.929091i	$-0.620592\pi$
$211$	3.62910	−	2.09526i	0.249838	−	0.144244i	0.619690	+	0.784847i	$0.287258\pi$
$212$	−11.2235	+	3.92275i	−0.770830	+	0.269416i
$213$	6.53401	+	6.53401i	0.447703	+	0.447703i
$214$	−10.7354	+	8.89136i	−0.733855	+	0.607801i
$215$	−2.08837	+	0.559576i	−0.142425	+	0.0381628i
$216$	6.13167	+	11.1085i	0.417207	+	0.755838i
$217$	−7.25658	+	12.5688i	−0.492609	+	0.853223i
$218$	−0.0396591	−	0.0281503i	−0.00268606	−	0.00190658i
$219$	−1.57251	+	5.86868i	−0.106260	+	0.396569i
$220$	−0.442923	+	0.514313i	−0.0298618	+	0.0346750i
$221$		0			0
$222$	−0.565647	+	0.259363i	−0.0379637	+	0.0174073i
$223$	18.1869	+	4.87316i	1.21788	+	0.326331i	0.809850	−	0.586636i	$-0.199548\pi$
$223$	18.1869	+	4.87316i	1.21788	+	0.326331i	0.408033	+	0.912967i	$0.366215\pi$
$224$	6.75293	−	13.3471i	0.451199	−	0.891791i
$225$	9.75232	+	5.63051i	0.650155	+	0.375367i
$226$	−2.24113	+	6.03672i	−0.149078	+	0.401557i
$227$	−1.92558	−	7.18635i	−0.127805	−	0.476974i	0.872119	−	0.489293i	$-0.162745\pi$
$227$	−1.92558	−	7.18635i	−0.127805	−	0.476974i	−0.999924	+	0.0123190i	$0.996079\pi$
$228$	8.54875	+	4.12063i	0.566155	+	0.272895i
$229$	3.17720	−	3.17720i	0.209955	−	0.209955i	−0.594293	−	0.804248i	$-0.702568\pi$
$229$	3.17720	−	3.17720i	0.209955	−	0.209955i	0.804248	+	0.594293i	$0.202568\pi$
$230$	0.272223	−	2.89741i	0.0179498	−	0.191050i
$231$	1.62075	+	2.80721i	0.106637	+	0.184701i
$232$	−10.2213	−	6.16640i	−0.671059	−	0.404844i
$233$			13.3205i			0.872655i	0.899788	+	0.436328i	$0.143721\pi$
$233$			13.3205i			0.872655i	−0.899788	+	0.436328i	$0.856279\pi$
$234$		0			0
$235$			0.932921i			0.0608571i
$236$	14.0824	−	9.59385i	0.916687	−	0.624506i
$237$	3.61971	+	6.26953i	0.235126	+	0.407250i
$238$	−5.20959	−	0.489461i	−0.337688	−	0.0317270i
$239$	5.96641	−	5.96641i	0.385935	−	0.385935i	−0.487300	−	0.873235i	$-0.662018\pi$
$239$	5.96641	−	5.96641i	0.385935	−	0.385935i	0.873235	+	0.487300i	$0.162018\pi$
$240$	0.733629	−	0.319454i	0.0473556	−	0.0206207i
$241$	−4.00333	−	14.9406i	−0.257877	−	0.962410i	−0.966467	−	0.256790i	$-0.917335\pi$
$241$	−4.00333	−	14.9406i	−0.257877	−	0.962410i	0.708590	−	0.705620i	$-0.249332\pi$
$242$	11.8265	+	4.39058i	0.760237	+	0.282237i
$243$	−13.8775	−	8.01218i	−0.890242	−	0.513982i
$244$	2.69040	−	14.1913i	0.172236	−	0.908506i
$245$	−0.00179594		0.000481222i	−0.000114739		3.07441e-5i
$246$	−2.90387	−	6.33307i	−0.185144	−	0.403782i
$247$		0			0
$248$	−4.30560	+	14.9150i	−0.273406	+	0.947101i
$249$	2.15056	−	8.02602i	0.136287	−	0.508628i
$250$	1.91568	−	2.69887i	0.121158	−	0.170692i
$251$	13.7387	−	23.7962i	0.867182	−	1.50200i	0.00231697	−	0.999997i	$-0.499262\pi$
$251$	13.7387	−	23.7962i	0.867182	−	1.50200i	0.864865	−	0.502005i	$-0.167404\pi$
$252$	0.895766	+	12.0109i	0.0564279	+	0.756613i
$253$	12.1806	−	3.26379i	0.765789	−	0.205193i
$254$	4.82081	+	5.82061i	0.302484	+	0.365217i
$255$	−0.197923	−	0.197923i	−0.0123944	−	0.0123944i
$256$	3.58267	−	15.5937i	0.223917	−	0.974608i
$257$	−24.1060	+	13.9176i	−1.50369	+	0.868157i	−0.503702	+	0.863878i	$0.668029\pi$
$257$	−24.1060	+	13.9176i	−1.50369	+	0.868157i	−0.999991	+	0.00427985i	$0.998638\pi$
$258$	1.84805	+	10.8886i	0.115055	+	0.677897i
$259$	−1.36877			−0.0850511
$260$		0			0
$261$	9.61181			0.594956
$262$	−2.65637	−	15.6512i	−0.164111	−	0.966936i
$263$	20.6166	−	11.9030i	1.27128	−	0.733972i	0.296048	−	0.955173i	$-0.404331\pi$
$263$	20.6166	−	11.9030i	1.27128	−	0.733972i	0.975228	+	0.221201i	$0.0709978\pi$
$264$	2.40411	+	2.49843i	0.147962	+	0.153768i
$265$	−0.989207	−	0.989207i	−0.0607665	−	0.0607665i
$266$	13.3150	+	16.0765i	0.816398	+	0.985713i
$267$	−5.45466	+	1.46157i	−0.333820	+	0.0894468i
$268$	−5.03040	+	0.375166i	−0.307281	+	0.0229169i
$269$	10.3559	−	17.9370i	0.631412	−	1.09364i	−0.355851	−	0.934543i	$-0.615809\pi$
$269$	10.3559	−	17.9370i	0.631412	−	1.09364i	0.987263	−	0.159095i	$-0.0508576\pi$
$270$	−0.864167	+	1.21747i	−0.0525915	+	0.0740927i
$271$	3.57684	−	13.3489i	0.217277	−	0.810890i	−0.768075	−	0.640360i	$-0.778785\pi$
$271$	3.57684	−	13.3489i	0.217277	−	0.810890i	0.985352	−	0.170530i	$-0.0545480\pi$
$272$	−5.53506	+	0.830223i	−0.335612	+	0.0503397i
$273$		0			0
$274$	2.83408	+	6.18087i	0.171213	+	0.373400i
$275$	6.88774	+	1.84556i	0.415346	+	0.111292i
$276$	−14.6059	−	2.76900i	−0.879173	−	0.166674i
$277$	−11.0276	−	6.36681i	−0.662587	−	0.382545i	0.130675	−	0.991425i	$-0.458286\pi$
$277$	−11.0276	−	6.36681i	−0.662587	−	0.382545i	−0.793262	+	0.608880i	$0.791619\pi$
$278$	9.20193	+	3.41621i	0.551895	+	0.204891i
$279$	−3.23518	−	12.0739i	−0.193685	−	0.722844i
$280$	1.75973	+	0.0338560i	0.105164	+	0.00202328i
$281$	−15.4454	+	15.4454i	−0.921396	+	0.921396i	−0.997128	−	0.0757324i	$-0.975871\pi$
$281$	−15.4454	+	15.4454i	−0.921396	+	0.921396i	0.0757324	+	0.997128i	$0.475871\pi$
$282$	4.74476	+	0.445788i	0.282546	+	0.0265463i
$283$	10.3449	+	17.9178i	0.614939	+	1.06511i	0.990395	+	0.138265i	$0.0441527\pi$
$283$	10.3449	+	17.9178i	0.614939	+	1.06511i	−0.375456	+	0.926840i	$0.622514\pi$
$284$	12.2408	+	17.9678i	0.726360	+	1.06619i
$285$			1.11665i			0.0661445i
$286$		0			0
$287$		−	15.3249i		−	0.904603i
$288$	4.01593	+	12.2412i	0.236641	+	0.721317i
$289$	−7.52106	−	13.0269i	−0.442415	−	0.766286i
$290$	0.131389	−	1.39845i	0.00771544	−	0.0821196i
$291$	−9.30045	+	9.30045i	−0.545202	+	0.545202i
$292$	−6.20700	+	12.8772i	−0.363237	+	0.753580i
$293$	−5.96815	−	22.2734i	−0.348663	−	1.30123i	−0.888274	−	0.459314i	$-0.848095\pi$
$293$	−5.96815	−	22.2734i	−0.348663	−	1.30123i	0.539611	−	0.841914i	$-0.318571\pi$
$294$	−0.00330563	+	0.00890407i	−0.000192788	+	0.000519296i
$295$	1.73638	+	1.00250i	0.101096	+	0.0583677i
$296$	−1.42124	+	0.351664i	−0.0826080	+	0.0204400i
$297$	−6.24895	−	1.67440i	−0.362601	−	0.0971586i
$298$	19.4849	−	8.93431i	1.12873	−	0.517551i
$299$		0			0
$300$	−6.36976	−	5.48559i	−0.367758	−	0.316711i
$301$	−6.28760	+	23.4656i	−0.362411	+	1.35254i
$302$	0.784183	+	0.556619i	0.0451247	+	0.0320298i
$303$	3.89939	−	6.75394i	0.224014	−	0.388004i
$304$	17.9559	+	13.2719i	1.02984	+	0.761195i
$305$	1.64166	−	0.439881i	0.0940010	−	0.0251875i
$306$	3.47079	−	2.87461i	0.198412	−	0.164331i
$307$	16.3164	+	16.3164i	0.931228	+	0.931228i	0.997783	−	0.0665547i	$-0.0212007\pi$
$307$	16.3164	+	16.3164i	0.931228	+	0.931228i	−0.0665547	+	0.997783i	$0.521201\pi$
$308$	2.51635	+	7.19957i	0.143382	+	0.410234i
$309$	−8.03001	+	4.63613i	−0.456811	+	0.263740i
$310$	−1.80088	+	0.305650i	−0.102283	+	0.0173598i
$311$	8.54527			0.484558			0.242279	−	0.970207i	$-0.422105\pi$
$311$	8.54527			0.484558			0.242279	+	0.970207i	$0.422105\pi$
$312$		0			0
$313$	5.88378			0.332571			0.166285	−	0.986078i	$-0.446823\pi$
$313$	5.88378			0.332571			0.166285	+	0.986078i	$0.446823\pi$
$314$	8.23191	−	1.39714i	0.464553	−	0.0788452i
$315$	−1.22732	+	0.708592i	−0.0691515	+	0.0399247i
$316$	5.61992	+	16.0793i	0.316145	+	0.904529i
$317$	16.5045	+	16.5045i	0.926984	+	0.926984i	0.997510	−	0.0705258i	$-0.0224677\pi$
$317$	16.5045	+	16.5045i	0.926984	+	0.926984i	−0.0705258	+	0.997510i	$0.522468\pi$
$318$	−5.50371	+	4.55834i	−0.308633	+	0.255619i
$319$	5.87902	−	1.57528i	0.329162	−	0.0881986i
$320$	1.83589	−	0.416956i	0.102629	−	0.0233086i
$321$	−4.18926	+	7.25601i	−0.233822	+	0.404991i
$322$	−26.6652	−	18.9272i	−1.48600	−	1.05477i
$323$	2.02156	−	7.54456i	0.112483	−	0.419790i
$324$	−4.57516	−	3.94009i	−0.254175	−	0.218894i
$325$		0			0
$326$	−20.2248	+	9.27355i	−1.12015	+	0.513614i
$327$	−0.0282365	−	0.00756596i	−0.00156148	−	0.000418399i
$328$	−3.93728	−	15.9124i	−0.217400	−	0.878617i
$329$	9.07823	+	5.24132i	0.500499	+	0.288963i
$330$	−0.141991	+	0.382469i	−0.00781636	+	0.0210542i
$331$	−3.71829	−	13.8768i	−0.204375	−	0.762740i	−0.989639	−	0.143578i	$-0.954139\pi$
$331$	−3.71829	−	13.8768i	−0.204375	−	0.762740i	0.785264	−	0.619162i	$-0.212527\pi$
$332$	8.48871	−	17.6109i	0.465878	−	0.966521i
$333$	0.833596	−	0.833596i	0.0456808	−	0.0456808i
$334$	0.741668	−	7.89396i	0.0405822	−	0.431939i
$335$	−0.296774	−	0.514027i	−0.0162145	−	0.0280843i
$336$	1.01306	−	8.93367i	0.0552670	−	0.487372i
$337$		−	14.3427i		−	0.781297i	−0.920540	−	0.390649i	$-0.872251\pi$
$337$		−	14.3427i		−	0.781297i	0.920540	−	0.390649i	$-0.127749\pi$
$338$		0			0
$339$			3.87048i			0.210216i
$340$	−0.370790	−	0.544268i	−0.0201089	−	0.0295171i
$341$	−3.95757	−	6.85471i	−0.214314	−	0.371203i
$342$	−17.8998	−	1.68175i	−0.967910	−	0.0909388i
$343$	−13.1032	+	13.1032i	−0.707505	+	0.707505i
$344$	−0.499848	+	25.9806i	−0.0269500	+	1.40078i
$345$	−0.452732	−	1.68962i	−0.0243743	−	0.0909659i
$346$	−2.86476	−	1.06354i	−0.154010	−	0.0571762i
$347$	−0.407300	−	0.235155i	−0.0218650	−	0.0126238i	0.489028	−	0.872268i	$-0.337352\pi$
$347$	−0.407300	−	0.235155i	−0.0218650	−	0.0126238i	−0.510893	+	0.859645i	$0.670685\pi$
$348$	−7.04959	−	1.33647i	−0.377898	−	0.0716423i
$349$	27.3192	+	7.32017i	1.46237	+	0.391840i	0.900306	−	0.435257i	$-0.143343\pi$
$349$	27.3192	+	7.32017i	1.46237	+	0.391840i	0.562059	+	0.827097i	$0.310009\pi$
$350$	−7.70686	−	16.8080i	−0.411949	−	0.898423i
$351$		0			0
$352$	4.46252	+	6.82907i	0.237853	+	0.363991i
$353$	9.30507	−	34.7270i	0.495259	−	1.84833i	−0.0333153	−	0.999445i	$-0.510607\pi$
$353$	9.30507	−	34.7270i	0.495259	−	1.84833i	0.528574	−	0.848887i	$-0.322727\pi$
$354$	5.92834	−	8.35204i	0.315088	−	0.443906i
$355$	−1.27909	+	2.21545i	−0.0678872	+	0.117584i
$356$	−13.2498	+	0.988165i	−0.702238	+	0.0523726i
$357$	−3.03796	+	0.814018i	−0.160786	+	0.0430824i
$358$	9.14050	+	11.0362i	0.483091	+	0.583280i
$359$	−11.7167	−	11.7167i	−0.618383	−	0.618383i	0.326733	−	0.945117i	$-0.394052\pi$
$359$	−11.7167	−	11.7167i	−0.618383	−	0.618383i	−0.945117	+	0.326733i	$0.894052\pi$
$360$	−1.09232	+	1.05108i	−0.0575701	+	0.0553967i
$361$	−10.5306	+	6.07986i	−0.554244	+	0.319993i
$362$	−3.27813	−	19.3146i	−0.172295	−	1.01515i
$363$	7.58264			0.397985
$364$		0			0
$365$	−1.68203			−0.0880416
$366$	−1.45274	−	8.55952i	−0.0759362	−	0.447413i
$367$	8.79501	−	5.07780i	0.459096	−	0.265059i	−0.252568	−	0.967579i	$-0.581275\pi$
$367$	8.79501	−	5.07780i	0.459096	−	0.265059i	0.711664	+	0.702520i	$0.247942\pi$
$368$	−32.5502	−	12.8019i	−1.69680	−	0.667347i
$369$	9.33307	+	9.33307i	0.485860	+	0.485860i
$370$	−0.109887	−	0.132677i	−0.00571275	−	0.00689754i
$371$	−15.1835	+	4.06840i	−0.788288	+	0.211221i
$372$	0.693977	+	9.30517i	0.0359810	+	0.482451i
$373$	7.50790	−	13.0041i	0.388744	−	0.673325i	−0.603537	−	0.797335i	$-0.706242\pi$
$373$	7.50790	−	13.0041i	0.388744	−	0.673325i	0.992281	+	0.124010i	$0.0395756\pi$
$374$	1.65177	−	2.32707i	0.0854110	−	0.120330i
$375$	0.514877	−	1.92155i	0.0265881	−	0.0992283i
$376$	10.7728	+	3.10987i	0.555567	+	0.160379i
$377$		0			0
$378$	6.99210	+	15.2491i	0.359635	+	0.784331i
$379$	32.2202	+	8.63337i	1.65504	+	0.443467i	0.961018	−	0.276487i	$-0.0891702\pi$
$379$	32.2202	+	8.63337i	1.65504	+	0.443467i	0.694022	+	0.719953i	$0.255837\pi$
$380$	−0.489364	+	2.58129i	−0.0251039	+	0.132418i
$381$	3.93413	+	2.27137i	0.201552	+	0.116366i
$382$	5.13147	+	1.90505i	0.262549	+	0.0974711i
$383$	5.41837	+	20.2216i	0.276866	+	1.03328i	0.954581	+	0.297953i	$0.0963037\pi$
$383$	5.41837	+	20.2216i	0.276866	+	1.03328i	−0.677715	+	0.735325i	$0.737030\pi$
$384$	−1.24334	−	9.53643i	−0.0634490	−	0.486654i
$385$	−0.634552	+	0.634552i	−0.0323398	+	0.0323398i
$386$	11.5800	+	1.08798i	0.589405	+	0.0553768i
$387$	−10.4616	−	18.1201i	−0.531794	−	0.921095i
$388$	−25.5752	+	17.4235i	−1.29839	+	0.884544i
$389$			9.60410i			0.486947i	0.969908	+	0.243474i	$0.0782870\pi$
$389$			9.60410i			0.486947i	−0.969908	+	0.243474i	$0.921713\pi$
$390$		0			0
$391$			12.2354i			0.618772i
$392$	−0.0115436	+	0.0191344i	−0.000583040	+	0.000966434i
$393$	−4.77101	−	8.26364i	−0.240666	−	0.416846i
$394$	−1.63782	+	17.4322i	−0.0825121	+	0.878221i
$395$	−1.41718	+	1.41718i	−0.0713063	+	0.0713063i
$396$	−5.91711	−	2.85214i	−0.297346	−	0.143325i
$397$	0.668462	+	2.49473i	0.0335492	+	0.125207i	0.980670	−	0.195671i	$-0.0626886\pi$
$397$	0.668462	+	2.49473i	0.0335492	+	0.125207i	−0.947120	+	0.320878i	$0.896022\pi$
$398$	1.19800	−	3.22694i	0.0600503	−	0.161752i
$399$	10.8661	+	6.27352i	0.543983	+	0.314069i
$400$	−12.3206	−	15.4723i	−0.616030	−	0.773613i
$401$	−26.1295	−	7.00137i	−1.30484	−	0.349632i	−0.461563	−	0.887107i	$-0.652711\pi$
$401$	−26.1295	−	7.00137i	−1.30484	−	0.349632i	−0.843279	+	0.537476i	$0.819378\pi$
$402$	−2.75611	+	1.26374i	−0.137462	+	0.0630298i
$403$		0			0
$404$	11.9739	−	13.9038i	0.595723	−	0.691742i
$405$	0.183879	−	0.686244i	0.00913700	−	0.0340998i
$406$	−12.8701	−	9.13526i	−0.638731	−	0.453375i
$407$	0.373247	−	0.646483i	0.0185012	−	0.0320450i
$408$	−2.94528	+	1.62574i	−0.145813	+	0.0804859i
$409$	4.63129	−	1.24095i	0.229003	−	0.0613611i	−0.142493	−	0.989796i	$-0.545512\pi$
$409$	4.63129	−	1.24095i	0.229003	−	0.0613611i	0.371496	+	0.928435i	$0.378845\pi$
$410$	1.48547	−	1.23031i	0.0733621	−	0.0607608i
$411$	2.88999	+	2.88999i	0.142553	+	0.142553i
$412$	−20.5943	+	7.19799i	−1.01461	+	0.354619i
$413$	19.5106	−	11.2644i	0.960053	−	0.554287i
$414$	27.7663	−	4.71257i	1.36464	−	0.231610i
$415$	2.30035			0.112920
$416$		0			0
$417$	5.89987			0.288918
$418$	−11.2239	+	1.90496i	−0.548981	+	0.0931745i
$419$	4.85410	−	2.80251i	0.237138	−	0.136912i	−0.376723	−	0.926326i	$-0.622949\pi$
$419$	4.85410	−	2.80251i	0.237138	−	0.136912i	0.613861	+	0.789414i	$0.289616\pi$
$420$	0.998678	−	0.349051i	0.0487305	−	0.0170320i
$421$	−3.55354	−	3.55354i	−0.173189	−	0.173189i	0.615190	−	0.788379i	$-0.289079\pi$
$421$	−3.55354	−	3.55354i	−0.173189	−	0.173189i	−0.788379	+	0.615190i	$0.789079\pi$
$422$	4.56414	−	3.78016i	0.222179	−	0.184015i
$423$	−8.72077	+	2.33672i	−0.424018	+	0.113615i
$424$	−14.7203	+	8.12531i	−0.714881	+	0.394600i
$425$	−3.45936	+	5.99179i	−0.167804	+	0.290645i
$426$	10.6564	+	7.56399i	0.516305	+	0.366477i
$427$	4.94266	−	18.4462i	0.239192	−	0.892676i
$428$	−12.8640	+	14.9374i	−0.621805	+	0.722027i
$429$		0			0
$430$	−2.77934	+	1.27439i	−0.134032	+	0.0614567i
$431$	−3.33989	−	0.894922i	−0.160877	−	0.0431069i	0.177482	−	0.984124i	$-0.443205\pi$
$431$	−3.33989	−	0.894922i	−0.160877	−	0.0431069i	−0.338359	+	0.941017i	$0.609872\pi$
$432$	11.1780	+	14.0373i	0.537799	+	0.675371i
$433$	4.73943	+	2.73631i	0.227762	+	0.131499i	0.609539	−	0.792756i	$-0.291354\pi$
$433$	4.73943	+	2.73631i	0.227762	+	0.131499i	−0.381777	+	0.924254i	$0.624688\pi$
$434$	−7.14339	+	19.2415i	−0.342894	+	0.923622i
$435$	−0.218512	−	0.815499i	−0.0104769	−	0.0391002i
$436$	−0.0619572	−	0.0298643i	−0.00296721	−	0.00143024i
$437$	34.5150	−	34.5150i	1.65107	−	1.65107i
$438$	−0.803743	+	8.55467i	−0.0384043	+	0.408758i
$439$	15.2532	+	26.4193i	0.727994	+	1.26092i	0.957730	+	0.287669i	$0.0928804\pi$
$439$	15.2532	+	26.4193i	0.727994	+	1.26092i	−0.229736	+	0.973253i	$0.573786\pi$
$440$	−0.495849	+	0.821907i	−0.0236387	+	0.0391829i
$441$		−	0.0179935i		−	0.000856833i
$442$		0			0
$443$		−	12.8994i		−	0.612869i	−0.951892	−	0.306434i	$-0.900864\pi$
$443$		−	12.8994i		−	0.612869i	0.951892	−	0.306434i	$-0.0991360\pi$
$444$	−0.727292	+	0.495478i	−0.0345157	+	0.0235143i
$445$	−0.781685	−	1.35392i	−0.0370554	−	0.0641819i
$446$	26.5107	+	2.49078i	1.25532	+	0.117942i
$447$	9.11058	−	9.11058i	0.430916	−	0.430916i
$448$	6.25697	−	20.2075i	0.295614	−	0.954716i
$449$	2.55455	+	9.53370i	0.120557	+	0.449923i	0.999642	−	0.0267403i	$-0.00851273\pi$
$449$	2.55455	+	9.53370i	0.120557	+	0.449923i	−0.879086	+	0.476663i	$0.841846\pi$
$450$	14.9298	+	5.54268i	0.703798	+	0.261284i
$451$	7.23812	+	4.17893i	0.340830	+	0.196778i
$452$	−1.69622	+	8.94719i	−0.0797833	+	0.420840i
$453$	0.558323	+	0.149602i	0.0262323	+	0.00702893i
$454$	−4.38536	−	9.56407i	−0.205815	−	0.448864i
$455$		0			0
$456$	12.8944	+	3.72231i	0.603836	+	0.174313i
$457$	2.68710	−	10.0284i	0.125697	−	0.469108i	−0.874166	−	0.485626i	$-0.838592\pi$
$457$	2.68710	−	10.0284i	0.125697	−	0.469108i	0.999864	+	0.0165184i	$0.00525822\pi$
$458$	3.67803	−	5.18174i	0.171863	−	0.242127i
$459$	3.13853	−	5.43609i	0.146494	−	0.253735i
$460$	−0.306091	−	4.10421i	−0.0142715	−	0.191360i
$461$	27.7556	−	7.43710i	1.29271	−	0.346380i	0.454021	−	0.890991i	$-0.349989\pi$
$461$	27.7556	−	7.43710i	1.29271	−	0.346380i	0.838689	+	0.544611i	$0.183323\pi$
$462$	2.92406	+	3.53049i	0.136040	+	0.164253i
$463$	5.89061	+	5.89061i	0.273760	+	0.273760i	0.830612	−	0.556852i	$-0.187991\pi$
$463$	5.89061	+	5.89061i	0.273760	+	0.273760i	−0.556852	+	0.830612i	$0.687991\pi$
$464$	−15.7105	−	6.17889i	−0.729341	−	0.286848i
$465$	−0.950841	+	0.548968i	−0.0440942	+	0.0254578i
$466$	3.15217	+	18.5724i	0.146021	+	0.860352i
$467$	3.30334			0.152860			0.0764301	−	0.997075i	$-0.475648\pi$
$467$	3.30334			0.152860			0.0764301	+	0.997075i	$0.475648\pi$
$468$		0			0
$469$	−6.66931			−0.307960
$470$	0.220766	+	1.30075i	0.0101832	+	0.0599990i
$471$	4.34634	−	2.50936i	0.200269	−	0.115625i
$472$	17.3645	−	16.7089i	0.799264	−	0.769090i
$473$	−9.36849	−	9.36849i	−0.430764	−	0.430764i
$474$	6.53049	+	7.88487i	0.299956	+	0.362164i
$475$	26.6608	−	7.14374i	1.22328	−	0.327777i
$476$	−7.37943	+	0.550355i	−0.338235	+	0.0252255i
$477$	6.76922	−	11.7246i	0.309941	−	0.536834i
$478$	6.90693	−	9.73071i	0.315915	−	0.445072i
$479$	−7.19847	+	26.8650i	−0.328906	+	1.22750i	0.581420	+	0.813604i	$0.302497\pi$
$479$	−7.19847	+	26.8650i	−0.328906	+	1.22750i	−0.910326	+	0.413892i	$0.864169\pi$
$480$	0.947285	−	0.619013i	0.0432374	−	0.0282539i
$481$		0			0
$482$	−9.11729	−	19.8840i	−0.415281	−	0.905691i
$483$	−18.9851	−	5.08705i	−0.863854	−	0.231469i
$484$	17.5284	+	3.32305i	0.796745	+	0.151048i
$485$	−3.15346	−	1.82065i	−0.143191	−	0.0826714i
$486$	−21.2451	−	7.88721i	−0.963695	−	0.357771i
$487$	−2.67032	−	9.96577i	−0.121004	−	0.451592i	0.878662	−	0.477444i	$-0.158437\pi$
$487$	−2.67032	−	9.96577i	−0.121004	−	0.451592i	−0.999666	+	0.0258522i	$0.991770\pi$
$488$	0.392928	−	20.4233i	0.0177870	−	0.924517i
$489$	−9.45652	+	9.45652i	−0.427638	+	0.427638i
$490$	−0.00261792		0.000245963i	−0.000118265		1.11115e-5i
$491$	−6.81243	−	11.7995i	−0.307441	−	0.532503i	0.670361	−	0.742035i	$-0.266139\pi$
$491$	−6.81243	−	11.7995i	−0.307441	−	0.532503i	−0.977802	+	0.209532i	$0.932806\pi$
$492$	−5.54744	−	8.14287i	−0.250098	−	0.367109i
$493$			5.90546i			0.265969i
$494$		0			0
$495$		−	0.772899i		−	0.0347392i
$496$	−2.47371	+	21.8144i	−0.111073	+	0.979496i
$497$	14.3723	+	24.8936i	0.644688	+	1.11663i
$498$	1.09920	−	11.6994i	0.0492564	−	0.524262i
$499$	−11.2288	+	11.2288i	−0.502670	+	0.502670i	−0.912267	−	0.409597i	$-0.865669\pi$
$499$	−11.2288	+	11.2288i	−0.502670	+	0.502670i	0.409597	+	0.912267i	$0.365669\pi$
$500$	2.03232	−	4.21630i	0.0908882	−	0.188559i
$501$	−1.23346	−	4.60334i	−0.0551070	−	0.205662i
$502$	13.5244	−	36.4296i	0.603625	−	1.62593i
$503$	−19.7978	−	11.4303i	−0.882739	−	0.509650i	−0.0111787	−	0.999938i	$-0.503558\pi$
$503$	−19.7978	−	11.4303i	−0.882739	−	0.509650i	−0.871561	+	0.490288i	$0.836892\pi$
$504$	4.09119	+	16.5345i	0.182236	+	0.736503i
$505$	2.08549	+	0.558805i	0.0928030	+	0.0248665i
$506$	16.2108	−	7.43304i	0.720657	−	0.330439i
$507$		0			0
$508$	8.09892	+	6.97473i	0.359331	+	0.309454i
$509$	−2.55291	+	9.52759i	−0.113156	+	0.422303i	−0.999142	−	0.0414078i	$-0.986816\pi$
$509$	−2.55291	+	9.52759i	−0.113156	+	0.422303i	0.885987	+	0.463711i	$0.153482\pi$
$510$	−0.322796	−	0.229123i	−0.0142937	−	0.0101457i
$511$	−9.44995	+	16.3678i	−0.418041	+	0.724069i
$512$	1.30512	−	22.5897i	0.0576787	−	0.998335i
$513$	−24.1882	+	6.48121i	−1.06794	+	0.286152i
$514$	−30.3170	+	25.1094i	−1.33722	+	1.10753i
$515$	−1.81513	−	1.81513i	−0.0799842	−	0.0799842i
$516$	5.15338	+	14.7444i	0.226865	+	0.649088i
$517$	−4.95105	+	2.85849i	−0.217747	+	0.125716i
$518$	−1.90844	+	0.323905i	−0.0838520	+	0.0142316i
$519$	−1.83676			−0.0806246
$520$		0			0
$521$	15.9204			0.697486			0.348743	−	0.937218i	$-0.386609\pi$
$521$	15.9204			0.697486			0.348743	+	0.937218i	$0.386609\pi$
$522$	13.4015	−	2.27454i	0.586568	−	0.0995539i
$523$	−1.86869	+	1.07889i	−0.0817122	+	0.0471766i	−0.540299	−	0.841473i	$-0.681689\pi$
$523$	−1.86869	+	1.07889i	−0.0817122	+	0.0471766i	0.458587	+	0.888649i	$0.348356\pi$
$524$	−7.40741	−	21.1935i	−0.323594	−	0.925842i
$525$	−7.85891	−	7.85891i	−0.342991	−	0.342991i
$526$	25.9285	−	21.4748i	1.13054	−	0.936346i
$527$	7.41814	−	1.98769i	0.323139	−	0.0865849i
$528$	3.94321	+	2.91459i	0.171606	+	0.126841i
$529$	−26.7315	+	46.3003i	−1.16224	+	2.01306i
$530$	−1.61331	−	1.14514i	−0.0700778	−	0.0497417i
$531$	−5.02200	+	18.7423i	−0.217936	+	0.813348i
$532$	22.3692	+	19.2642i	0.969826	+	0.835207i
$533$		0			0
$534$	−7.25943	+	3.32863i	−0.314146	+	0.144044i
$535$	−2.24052	−	0.600345i	−0.0968660	−	0.0259552i
$536$	−6.92498	+	1.71348i	−0.299114	+	0.0740110i
$537$	7.45933	+	4.30664i	0.321894	+	0.185845i
$538$	10.1944	−	27.4597i	0.439512	−	1.18387i
$539$	−0.00294895	−	0.0110056i	−0.000127020	−	0.000474046i
$540$	−0.916785	+	1.90198i	−0.0394521	+	0.0818482i
$541$	−8.15947	+	8.15947i	−0.350803	+	0.350803i	−0.860408	−	0.509605i	$-0.829791\pi$
$541$	−8.15947	+	8.15947i	−0.350803	+	0.350803i	0.509605	+	0.860408i	$0.329791\pi$
$542$	1.82820	−	19.4585i	0.0785279	−	0.835814i
$543$	−5.88774	−	10.1979i	−0.252667	−	0.437632i
$544$	−7.52092	+	2.46737i	−0.322457	+	0.105788i
$545$		−	0.00809292i		−	0.000346663i
$546$		0			0
$547$			8.11076i			0.346791i	0.984852	+	0.173396i	$0.0554739\pi$
$547$			8.11076i			0.346791i	−0.984852	+	0.173396i	$0.944526\pi$
$548$	5.41412	+	7.94717i	0.231280	+	0.339486i
$549$	8.22384	+	14.2441i	0.350985	+	0.607924i
$550$	10.0401	+	0.943308i	0.428113	+	0.0402228i
$551$	16.6588	−	16.6588i	0.709687	−	0.709687i
$552$	−21.0199	−	0.404408i	−0.894667	−	0.0172127i
$553$	5.82859	+	21.7526i	0.247857	+	0.925014i
$554$	−16.8822	−	6.26750i	−0.717256	−	0.266281i
$555$	−0.0896759	−	0.0517744i	−0.00380653	−	0.00219770i
$556$	13.6384	+	2.58559i	0.578398	+	0.109653i
$557$	−3.31359	−	0.887873i	−0.140401	−	0.0376204i	0.187934	−	0.982182i	$-0.439821\pi$
$557$	−3.31359	−	0.887873i	−0.140401	−	0.0376204i	−0.328335	+	0.944561i	$0.606488\pi$
$558$	−7.36789	−	16.0687i	−0.311908	−	0.680243i
$559$		0			0
$560$	2.46156	−	0.369219i	0.104020	−	0.0156023i
$561$	0.443946	−	1.65683i	0.0187434	−	0.0699514i
$562$	−17.8801	+	25.1901i	−0.754228	+	1.06258i
$563$	−3.12130	+	5.40625i	−0.131547	+	0.227846i	−0.924273	−	0.381732i	$-0.875328\pi$
$563$	−3.12130	+	5.40625i	−0.131547	+	0.227846i	0.792726	+	0.609578i	$0.208661\pi$
$564$	6.72099	−	0.501249i	0.283005	−	0.0211064i
$565$	−1.03501	+	0.277331i	−0.0435434	+	0.0116674i
$566$	18.6637	+	22.5344i	0.784493	+	0.947191i
$567$	−5.64476	−	5.64476i	−0.237058	−	0.237058i
$568$	21.3190	+	22.1554i	0.894525	+	0.929620i
$569$	27.8969	−	16.1063i	1.16950	−	0.675211i	0.215937	−	0.976407i	$-0.430719\pi$
$569$	27.8969	−	16.1063i	1.16950	−	0.675211i	0.953562	+	0.301197i	$0.0973861\pi$
$570$	0.264243	+	1.55691i	0.0110679	+	0.0652119i
$571$	−41.4189			−1.73333			−0.866663	−	0.498894i	$-0.833740\pi$
$571$	−41.4189			−1.73333			−0.866663	+	0.498894i	$0.833740\pi$
$572$		0			0
$573$	3.29007			0.137445
$574$	−3.62649	−	21.3672i	−0.151367	−	0.891849i
$575$	−37.4446	+	21.6186i	−1.56155	+	0.901560i
$576$	8.49606	+	16.1172i	0.354002	+	0.671550i
$577$	−12.3408	−	12.3408i	−0.513753	−	0.513753i	0.401921	−	0.915674i	$-0.368343\pi$
$577$	−12.3408	−	12.3408i	−0.513753	−	0.513753i	−0.915674	+	0.401921i	$0.868343\pi$
$578$	−13.5691	−	16.3832i	−0.564400	−	0.681453i
$579$	6.75282	−	1.80941i	0.280638	−	0.0751966i
$580$	−0.147736	−	1.98091i	−0.00613439	−	0.0822528i
$581$	12.9238	−	22.3846i	0.536168	−	0.928671i
$582$	−10.7665	+	15.1682i	−0.446287	+	0.628744i
$583$	2.21881	−	8.28072i	0.0918938	−	0.342952i
$584$	−5.60701	+	19.4231i	−0.232020	+	0.803736i
$585$		0			0
$586$	−13.5920	−	29.6430i	−0.561481	−	1.22454i
$587$	−22.3181	−	5.98011i	−0.921165	−	0.246825i	−0.233082	−	0.972457i	$-0.574881\pi$
$587$	−22.3181	−	5.98011i	−0.921165	−	0.246825i	−0.688083	+	0.725632i	$0.741548\pi$
$588$	−0.00250189	+	0.0131970i	−0.000103176	+	0.000544234i
$589$	−26.5330	−	15.3188i	−1.09327	−	0.631200i
$590$	2.65822	+	0.986862i	0.109437	+	0.0406285i
$591$	2.72384	+	10.1655i	0.112044	+	0.418154i
$592$	−1.89838	+	0.826639i	−0.0780230	+	0.0339746i
$593$	−11.0244	+	11.0244i	−0.452717	+	0.452717i	−0.896255	−	0.443538i	$-0.853723\pi$
$593$	−11.0244	+	11.0244i	−0.452717	+	0.452717i	0.443538	+	0.896255i	$0.353723\pi$
$594$	−9.10898	−	0.855823i	−0.373746	−	0.0351148i
$595$	−0.435357	−	0.754060i	−0.0178479	−	0.0309134i
$596$	25.0531	−	17.0678i	1.02622	−	0.699124i
$597$		−	2.06898i		−	0.0846775i
$598$		0			0
$599$			10.6090i			0.433471i	0.976230	+	0.216735i	$0.0695409\pi$
$599$			10.6090i			0.433471i	−0.976230	+	0.216735i	$0.930459\pi$
$600$	−10.1793	−	6.14108i	−0.415568	−	0.250708i
$601$	−14.1251	−	24.4655i	−0.576177	−	0.997967i	−0.995913	−	0.0903210i	$-0.971211\pi$
$601$	−14.1251	−	24.4655i	−0.576177	−	0.997967i	0.419736	−	0.907646i	$-0.362123\pi$
$602$	−3.21373	+	34.2054i	−0.130982	+	1.39411i
$603$	4.06169	−	4.06169i	0.165405	−	0.165405i
$604$	1.22508	+	0.590510i	0.0498480	+	0.0240275i
$605$	0.543318	+	2.02769i	0.0220890	+	0.0824373i
$606$	3.83856	−	10.3396i	0.155931	−	0.420017i
$607$	8.89476	+	5.13539i	0.361027	+	0.208439i	0.669531	−	0.742784i	$-0.266495\pi$
$607$	8.89476	+	5.13539i	0.361027	+	0.208439i	−0.308504	+	0.951223i	$0.599828\pi$
$608$	28.1760	+	14.2556i	1.14269	+	0.578140i
$609$	−9.16324	−	2.45528i	−0.371313	−	0.0994931i
$610$	2.18483	−	1.00180i	0.0884610	−	0.0405615i
$611$		0			0
$612$	4.15898	−	4.82933i	0.168117	−	0.195214i
$613$	−9.17089	+	34.2262i	−0.370409	+	1.38238i	0.489530	+	0.871986i	$0.337168\pi$
$613$	−9.17089	+	34.2262i	−0.370409	+	1.38238i	−0.859939	+	0.510397i	$0.829498\pi$
$614$	26.6107	+	18.8885i	1.07392	+	0.762277i
$615$	0.579674	−	1.00403i	0.0233747	−	0.0404862i
$616$	5.21218	+	9.44271i	0.210005	+	0.380458i
$617$	−40.4828	+	10.8473i	−1.62978	+	0.436697i	−0.953853	−	0.300275i	$-0.902922\pi$
$617$	−40.4828	+	10.8473i	−1.62978	+	0.436697i	−0.675923	+	0.736972i	$0.736255\pi$
$618$	−10.0989	+	8.36426i	−0.406239	+	0.336460i
$619$	−12.0880	−	12.0880i	−0.485858	−	0.485858i	0.421138	−	0.906996i	$-0.361631\pi$
$619$	−12.0880	−	12.0880i	−0.485858	−	0.485858i	−0.906996	+	0.421138i	$0.861631\pi$
$620$	−2.43859	+	0.852320i	−0.0979362	+	0.0342300i
$621$	33.9719	−	19.6137i	1.36324	−	0.787069i
$622$	11.9145	−	2.02215i	0.477726	−	0.0810809i
$623$	−17.5666			−0.703790
$624$		0			0
$625$	−24.1724			−0.966894
$626$	8.20360	−	1.39234i	0.327882	−	0.0556490i
$627$	−5.92609	+	3.42143i	−0.236665	+	0.136639i
$628$	11.1469	−	3.89600i	0.444810	−	0.155467i
$629$	0.512159	+	0.512159i	0.0204211	+	0.0204211i
$630$	−1.54354	+	1.27841i	−0.0614960	+	0.0509329i
$631$	−11.6470	+	3.12081i	−0.463660	+	0.124237i	−0.483084	−	0.875574i	$-0.660483\pi$
$631$	−11.6470	+	3.12081i	−0.463660	+	0.124237i	0.0194238	+	0.999811i	$0.493817\pi$
$632$	11.6407	+	21.0890i	0.463042	+	0.838875i
$633$	1.78106	−	3.08489i	0.0707909	−	0.122613i
$634$	26.9174	+	19.1062i	1.06903	+	0.758803i
$635$	−0.325501	+	1.21479i	−0.0129171	+	0.0482073i
$636$	−6.59499	+	7.65798i	−0.261509	+	0.303659i
$637$		0			0
$638$	7.82419	−	3.58758i	0.309763	−	0.142034i
$639$	−23.9134	−	6.40759i	−0.946001	−	0.253480i
$640$	2.46107	−	1.01580i	0.0972822	−	0.0401529i
$641$	1.81632	+	1.04865i	0.0717404	+	0.0414193i	0.535441	−	0.844573i	$-0.320145\pi$
$641$	1.81632	+	1.04865i	0.0717404	+	0.0414193i	−0.463701	+	0.885992i	$0.653479\pi$
$642$	−4.12391	+	11.1082i	−0.162758	+	0.438406i
$643$	10.9696	+	40.9391i	0.432599	+	1.61448i	0.746747	+	0.665108i	$0.231614\pi$
$643$	10.9696	+	40.9391i	0.432599	+	1.61448i	−0.314148	+	0.949374i	$0.601719\pi$
$644$	−41.6576	−	20.0796i	−1.64154	−	0.791248i
$645$	−1.29954	+	1.29954i	−0.0511692	+	0.0511692i
$646$	1.03326	−	10.9976i	0.0406532	−	0.432693i
$647$	−21.5400	−	37.3083i	−0.846824	−	1.46674i	−0.884028	−	0.467434i	$-0.845179\pi$
$647$	−21.5400	−	37.3083i	−0.846824	−	1.46674i	0.0372042	−	0.999308i	$-0.488155\pi$
$648$	−7.31141	−	4.41090i	−0.287219	−	0.173277i
$649$			12.2867i			0.482296i
$650$		0			0
$651$			12.3368i			0.483518i
$652$	−26.0044	+	17.7159i	−1.01841	+	0.693807i
$653$	5.56059	+	9.63123i	0.217603	+	0.376899i	0.954075	−	0.299569i	$-0.0968429\pi$
$653$	5.56059	+	9.63123i	0.217603	+	0.376899i	−0.736472	+	0.676468i	$0.763510\pi$
$654$	−0.0411599	−	0.00386713i	−0.00160948	−	0.000151217i
$655$	1.86794	−	1.86794i	0.0729865	−	0.0729865i
$656$	−9.25517	−	21.2546i	−0.361354	−	0.829852i
$657$	−4.21305	−	15.7233i	−0.164367	−	0.613425i
$658$	13.8978	+	5.15956i	0.541795	+	0.201141i
$659$	13.2010	+	7.62162i	0.514239	+	0.296896i	0.734575	−	0.678528i	$-0.237382\pi$
$659$	13.2010	+	7.62162i	0.514239	+	0.296896i	−0.220335	+	0.975424i	$0.570715\pi$
$660$	−0.107467	+	0.566868i	−0.00418316	+	0.0220653i
$661$	−9.97516	−	2.67284i	−0.387989	−	0.103961i	0.0595512	−	0.998225i	$-0.481033\pi$
$661$	−9.97516	−	2.67284i	−0.387989	−	0.103961i	−0.447540	+	0.894264i	$0.647700\pi$
$662$	−8.46813	−	18.4682i	−0.329123	−	0.717788i
$663$		0			0
$664$	7.66815	−	26.5631i	0.297582	−	1.03085i
$665$	−0.899032	+	3.35523i	−0.0348630	+	0.130110i
$666$	0.965000	−	1.35952i	0.0373930	−	0.0526805i
$667$	−18.4525	+	31.9607i	−0.714485	+	1.23753i
$668$	−0.833940	−	11.1819i	−0.0322661	−	0.432639i
$669$	15.4596	−	4.14239i	0.597704	−	0.160154i
$670$	−0.535423	−	0.646466i	−0.0206852	−	0.0249752i
$671$	7.36454	+	7.36454i	0.284305	+	0.284305i
$672$	−0.701580	−	12.6957i	−0.0270640	−	0.489748i
$673$	−25.8030	+	14.8974i	−0.994631	+	0.574251i	−0.906655	−	0.421872i	$-0.861373\pi$
$673$	−25.8030	+	14.8974i	−0.994631	+	0.574251i	−0.0879759	+	0.996123i	$0.528040\pi$
$674$	−3.39406	−	19.9977i	−0.130734	−	0.770282i
$675$	22.1818			0.853776
$676$		0			0
$677$	−29.1021			−1.11849			−0.559243	−	0.829004i	$-0.688908\pi$
$677$	−29.1021			−1.11849			−0.559243	+	0.829004i	$0.688908\pi$
$678$	0.915911	+	5.39651i	0.0351753	+	0.207252i
$679$	−35.4334	+	20.4575i	−1.35981	+	0.785085i
$680$	−0.645779	−	0.671115i	−0.0247645	−	0.0257361i
$681$	−4.47188	−	4.47188i	−0.171363	−	0.171363i
$682$	−7.14003	−	8.62082i	−0.273406	−	0.330108i
$683$	−4.87499	+	1.30625i	−0.186536	+	0.0499823i	−0.350878	−	0.936421i	$-0.614117\pi$
$683$	−4.87499	+	1.30625i	−0.186536	+	0.0499823i	0.164342	+	0.986404i	$0.447450\pi$
$684$	−25.3552	+	1.89098i	−0.969480	+	0.0723035i
$685$	−0.565743	+	0.979896i	−0.0216159	+	0.0374399i
$686$	−15.1687	+	21.3702i	−0.579143	+	0.815917i
$687$	0.988544	−	3.68930i	0.0377153	−	0.140755i
$688$	5.45113	+	36.3424i	0.207822	+	1.38554i
$689$		0			0
$690$	−1.03106	−	2.24866i	−0.0392519	−	0.0856049i
$691$	10.7956	+	2.89268i	0.410685	+	0.110043i	0.458246	−	0.888826i	$-0.348478\pi$
$691$	10.7956	+	2.89268i	0.410685	+	0.110043i	−0.0475604	+	0.998868i	$0.515145\pi$
$692$	−4.24593	−	0.804948i	−0.161406	−	0.0305995i
$693$	−7.52106	−	4.34229i	−0.285701	−	0.164950i
$694$	−0.623535	−	0.231487i	−0.0236691	−	0.00878711i
$695$	0.422743	+	1.57770i	0.0160355	+	0.0598455i
$696$	−10.1453	−	0.195189i	−0.384558	−	0.00739861i
$697$	−5.73421	+	5.73421i	−0.217199	+	0.217199i
$698$	39.8228	+	3.74150i	1.50731	+	0.141618i
$699$	5.66150	+	9.80601i	0.214138	+	0.370897i
$700$	−14.7229	−	21.6112i	−0.556474	−	0.816825i
$701$		−	27.1476i		−	1.02535i	−0.858582	−	0.512676i	$-0.828654\pi$
$701$		−	27.1476i		−	1.02535i	0.858582	−	0.512676i	$-0.171346\pi$
$702$		0			0
$703$		−	2.88950i		−	0.108980i
$704$	7.83802	+	8.46559i	0.295406	+	0.319059i
$705$	0.396511	+	0.686778i	0.0149335	+	0.0258656i
$706$	4.75603	−	50.6209i	0.178995	−	1.90514i
$707$	17.1544	−	17.1544i	0.645156	−	0.645156i
$708$	6.28930	−	13.0479i	0.236366	−	0.490371i
$709$	10.9821	+	40.9857i	0.412441	+	1.53925i	0.789906	+	0.613228i	$0.210129\pi$
$709$	10.9821	+	40.9857i	0.412441	+	1.53925i	−0.377465	+	0.926024i	$0.623204\pi$
$710$	−1.25914	+	3.39163i	−0.0472547	+	0.127286i
$711$	−16.7973	−	9.69790i	−0.629946	−	0.363700i
$712$	−18.2400	+	4.51320i	−0.683573	+	0.169139i
$713$	46.3583	+	12.4217i	1.73613	+	0.465195i
$714$	−4.04312	+	1.85387i	−0.151310	+	0.0693792i
$715$		0			0
$716$	15.3560	+	13.2245i	0.573880	+	0.494221i
$717$	1.85637	−	6.92808i	0.0693275	−	0.258734i
$718$	−19.1089	−	13.5636i	−0.713139	−	0.506191i
$719$	−8.21566	+	14.2299i	−0.306392	+	0.530687i	−0.977570	−	0.210609i	$-0.932455\pi$
$719$	−8.21566	+	14.2299i	−0.306392	+	0.530687i	0.671178	+	0.741296i	$0.265789\pi$
$720$	−1.27426	+	1.72398i	−0.0474889	+	0.0642489i
$721$	−27.8607	+	7.46526i	−1.03759	+	0.278021i
$722$	−13.2439	+	10.9690i	−0.492885	+	0.408223i
$723$	−9.29717	−	9.29717i	−0.345765	−	0.345765i
$724$	−9.14123	−	26.1542i	−0.339731	−	0.972012i
$725$	−18.0728	+	10.4343i	−0.671205	+	0.387520i
$726$	10.5723	−	1.79436i	0.392374	−	0.0665948i
$727$	−32.1429			−1.19211			−0.596057	−	0.802942i	$-0.703267\pi$
$727$	−32.1429			−1.19211			−0.596057	+	0.802942i	$0.703267\pi$
$728$		0			0
$729$	−4.56452			−0.169056
$730$	−2.34521	+	0.398036i	−0.0868003	+	0.0147320i
$731$	11.1329	−	6.42759i	0.411765	−	0.237733i
$732$	−4.05105	−	11.5905i	−0.149731	−	0.428399i
$733$	19.2047	+	19.2047i	0.709343	+	0.709343i	0.966397	−	0.257054i	$-0.0827518\pi$
$733$	19.2047	+	19.2047i	0.709343	+	0.709343i	−0.257054	+	0.966397i	$0.582752\pi$
$734$	11.0610	−	9.16110i	0.408270	−	0.338142i
$735$	−0.00152663		0.000409059i	−5.63106e−5		1.50884e-5i
$736$	−48.4134	−	10.1467i	−1.78454	−	0.374013i
$737$	1.81864	−	3.14998i	0.0669905	−	0.116031i
$738$	15.2214	+	10.8043i	0.560309	+	0.397711i
$739$	−6.01290	+	22.4404i	−0.221188	+	0.825485i	0.762708	+	0.646743i	$0.223869\pi$
$739$	−6.01290	+	22.4404i	−0.221188	+	0.825485i	−0.983896	+	0.178742i	$0.942797\pi$
$740$	−0.184609	−	0.158984i	−0.00678637	−	0.00584438i
$741$		0			0
$742$	−20.2072	+	9.26549i	−0.741830	+	0.340147i
$743$	−37.2749	−	9.98778i	−1.36748	−	0.366416i	−0.500925	−	0.865491i	$-0.667007\pi$
$743$	−37.2749	−	9.98778i	−1.36748	−	0.366416i	−0.866559	+	0.499075i	$0.833673\pi$
$744$	3.16957	+	12.8097i	0.116202	+	0.469628i
$745$	3.08908	+	1.78348i	0.113175	+	0.0653417i
$746$	7.39079	−	19.9079i	0.270596	−	0.728880i
$747$	5.76177	+	21.5032i	0.210812	+	0.786762i
$748$	1.75234	−	3.63545i	0.0640720	−	0.132925i
$749$	−18.4296	+	18.4296i	−0.673402	+	0.673402i
$750$	0.263165	−	2.80100i	0.00960942	−	0.102278i
$751$	−0.646973	−	1.12059i	−0.0236084	−	0.0408909i	0.853980	−	0.520306i	$-0.174182\pi$
$751$	−0.646973	−	1.12059i	−0.0236084	−	0.0408909i	−0.877588	+	0.479415i	$0.840849\pi$
$752$	15.7562	+	1.78672i	0.574570	+	0.0651551i
$753$		−	23.3570i		−	0.851178i
$754$		0			0
$755$			0.160022i			0.00582380i
$756$	13.3575	+	19.6069i	0.485806	+	0.713095i
$757$	11.2800	+	19.5376i	0.409979	+	0.710104i	0.994887	−	0.100995i	$-0.0322027\pi$
$757$	11.2800	+	19.5376i	0.409979	+	0.710104i	−0.584908	+	0.811100i	$0.698869\pi$
$758$	46.9668	+	4.41271i	1.70591	+	0.160277i
$759$	7.57969	−	7.57969i	0.275125	−	0.275125i
$760$	−0.0714707	+	3.71484i	−0.00259252	+	0.134751i
$761$	2.25142	+	8.40241i	0.0816138	+	0.304587i	0.994651	−	0.103288i	$-0.0329365\pi$
$761$	2.25142	+	8.40241i	0.0816138	+	0.304587i	−0.913038	+	0.407875i	$0.866270\pi$
$762$	6.02276	+	2.23594i	0.218182	+	0.0809997i
$763$	−0.0787520	−	0.0454675i	−0.00285101	−	0.00164603i
$764$	7.60549	+	1.44186i	0.275157	+	0.0521646i
$765$	0.724369	+	0.194094i	0.0261896	+	0.00701748i
$766$	12.3399	+	26.9123i	0.445860	+	0.972381i
$767$		0			0
$768$	−3.99026	−	13.0022i	−0.143986	−	0.469175i
$769$	−2.50537	+	9.35018i	−0.0903461	+	0.337176i	−0.996273	−	0.0862584i	$-0.972509\pi$
$769$	−2.50537	+	9.35018i	−0.0903461	+	0.337176i	0.905927	+	0.423434i	$0.139176\pi$
$770$	−0.734579	+	1.03490i	−0.0264724	+	0.0372952i
$771$	−11.8306	+	20.4912i	−0.426068	+	0.737971i
$772$	16.4031	−	1.22334i	0.590361	−	0.0440289i
$773$	−18.5456	+	4.96928i	−0.667039	+	0.178732i	−0.576420	−	0.817153i	$-0.695551\pi$
$773$	−18.5456	+	4.96928i	−0.667039	+	0.178732i	−0.0906182	+	0.995886i	$0.528884\pi$
$774$	−18.8743	−	22.7887i	−0.678423	−	0.819123i
$775$	19.1900	+	19.1900i	0.689327	+	0.689327i
$776$	−31.5358	+	30.3452i	−1.13207	+	1.08933i
$777$	−1.00763	+	0.581756i	−0.0361486	+	0.0208704i
$778$	2.27272	+	13.3908i	0.0814808	+	0.480082i
$779$	32.3513			1.15911
$780$		0			0
$781$	−15.6767			−0.560955
$782$	2.89539	+	17.0595i	0.103539	+	0.610048i
$783$	16.3966	−	9.46660i	0.585968	−	0.338309i
$784$	−0.0115670	+	0.0294103i	−0.000413107	+	0.00105037i
$785$	0.982461	+	0.982461i	0.0350655	+	0.0350655i
$786$	−8.60761	−	10.3928i	−0.307023	−	0.370698i
$787$	28.8763	−	7.73737i	1.02933	−	0.275808i	0.295644	−	0.955298i	$-0.404466\pi$
$787$	28.8763	−	7.73737i	1.02933	−	0.275808i	0.733684	+	0.679491i	$0.237799\pi$
$788$	1.84158	+	24.6928i	0.0656037	+	0.879645i
$789$	10.1181	−	17.5250i	0.360213	−	0.623907i
$790$	−1.64058	+	2.31131i	−0.0583693	+	0.0822326i
$791$	−3.11619	+	11.6298i	−0.110799	+	0.413508i
$792$	−8.92500	−	2.57644i	−0.317136	−	0.0915498i
$793$		0			0
$794$	1.52237	+	3.32016i	0.0540270	+	0.117828i
$795$	−1.14865	−	0.307779i	−0.0407383	−	0.0109158i
$796$	0.906717	−	4.78274i	0.0321377	−	0.169520i
$797$	−32.2562	−	18.6231i	−1.14257	−	0.659665i	−0.195507	−	0.980702i	$-0.562635\pi$
$797$	−32.2562	−	18.6231i	−1.14257	−	0.659665i	−0.947067	+	0.321037i	$0.895969\pi$
$798$	16.6348	+	6.17567i	0.588867	+	0.218616i
$799$	−1.43567	−	5.35801i	−0.0507905	−	0.189553i
$800$	−20.8397	−	18.6570i	−0.736793	−	0.659626i
$801$	10.6983	−	10.6983i	0.378004	−	0.378004i
$802$	−38.0884	−	3.57855i	−1.34495	−	0.126363i
$803$	−5.15378	−	8.92661i	−0.181873	−	0.315013i
$804$	−3.54372	+	2.41421i	−0.124977	+	0.0851426i
$805$		−	5.44136i		−	0.191783i
$806$		0			0
$807$		−	17.6060i		−	0.619759i
$808$	13.4047	−	22.2193i	0.471575	−	0.781671i
$809$	−20.9090	−	36.2154i	−0.735121	−	1.27327i	−0.954670	−	0.297665i	$-0.903792\pi$
$809$	−20.9090	−	36.2154i	−0.735121	−	1.27327i	0.219550	−	0.975601i	$-0.429541\pi$
$810$	0.0939844	−	1.00033i	0.00330228	−	0.0351479i
$811$	4.29617	−	4.29617i	0.150859	−	0.150859i	−0.627643	−	0.778502i	$-0.715980\pi$
$811$	4.29617	−	4.29617i	0.150859	−	0.150859i	0.778502	+	0.627643i	$0.215980\pi$
$812$	−20.1062	−	9.69149i	−0.705588	−	0.340105i
$813$	−3.04046	−	11.3472i	−0.106634	−	0.397962i
$814$	0.367425	−	0.989700i	0.0128782	−	0.0346890i
$815$	−3.20637	−	1.85120i	−0.112314	−	0.0648447i
$816$	−3.72182	+	2.96369i	−0.130290	+	0.103750i
$817$	−49.5365	−	13.2733i	−1.73306	−	0.464373i
$818$	6.16364	−	2.82618i	0.215506	−	0.0988149i
$819$		0			0
$820$	1.78001	−	2.06691i	0.0621607	−	0.0721798i
$821$	4.88681	−	18.2378i	0.170551	−	0.636505i	−0.826716	−	0.562620i	$-0.809793\pi$
$821$	4.88681	−	18.2378i	0.170551	−	0.636505i	0.997267	−	0.0738852i	$-0.0235398\pi$
$822$	4.71333	+	3.34556i	0.164396	+	0.116690i
$823$	6.80437	−	11.7855i	0.237185	−	0.410817i	−0.722720	−	0.691141i	$-0.757108\pi$
$823$	6.80437	−	11.7855i	0.237185	−	0.410817i	0.959906	+	0.280324i	$0.0904418\pi$
$824$	−27.0108	+	14.9094i	−0.940966	+	0.519394i
$825$	5.85487	−	1.56881i	0.203841	−	0.0546189i
$826$	24.5375	−	20.3227i	0.853768	−	0.707117i
$827$	17.0815	+	17.0815i	0.593982	+	0.593982i	0.938705	−	0.344723i	$-0.112027\pi$
$827$	17.0815	+	17.0815i	0.593982	+	0.593982i	−0.344723	+	0.938705i	$0.612027\pi$
$828$	37.5987	−	13.1412i	1.30664	−	0.456690i
$829$	23.8014	−	13.7417i	0.826657	−	0.477270i	−0.0260500	−	0.999661i	$-0.508293\pi$
$829$	23.8014	−	13.7417i	0.826657	−	0.477270i	0.852707	+	0.522390i	$0.174960\pi$
$830$	3.20732	−	0.544355i	0.111328	−	0.0188948i
$831$	−10.8241			−0.375485
$832$		0			0
$833$	0.0110551			0.000383038
$834$	8.22604	−	1.39615i	0.284844	−	0.0483446i
$835$	1.14261	−	0.659685i	0.0395416	−	0.0228294i
$836$	−15.1985	+	5.31207i	−0.525650	+	0.183722i
$837$	−17.4103	−	17.4103i	−0.601788	−	0.601788i
$838$	6.10476	−	5.05615i	0.210885	−	0.174662i
$839$	38.5731	−	10.3356i	1.33169	−	0.356825i	0.478345	−	0.878172i	$-0.341237\pi$
$839$	38.5731	−	10.3356i	1.33169	−	0.356825i	0.853345	+	0.521347i	$0.174570\pi$
$840$	1.30983	−	0.723001i	0.0451935	−	0.0249459i
$841$	5.59382	−	9.68878i	0.192890	−	0.334096i
$842$	−5.79552	−	4.11370i	−0.199727	−	0.141767i
$843$	−4.80564	+	17.9349i	−0.165515	+	0.617711i
$844$	5.46913	−	6.35064i	0.188255	−	0.218598i
$845$		0			0
$846$	−11.6062	+	5.32172i	−0.399029	+	0.182964i
$847$	22.7839	+	6.10491i	0.782862	+	0.209767i
$848$	−18.6014	+	14.8123i	−0.638774	+	0.508657i
$849$	15.2309	+	8.79359i	0.522725	+	0.301795i
$850$	−3.40540	+	9.17283i	−0.116804	+	0.314625i
$851$	1.17152	+	4.37216i	0.0401590	+	0.149876i
$852$	16.6479	+	8.02455i	0.570348	+	0.274916i
$853$	6.78242	−	6.78242i	0.232226	−	0.232226i	−0.581395	−	0.813621i	$-0.697493\pi$
$853$	6.78242	−	6.78242i	0.232226	−	0.232226i	0.813621	+	0.581395i	$0.197493\pi$
$854$	2.52630	−	26.8888i	0.0864482	−	0.920114i
$855$	−1.49586	−	2.59090i	−0.0511572	−	0.0886068i
$856$	−14.4012	+	23.8710i	−0.492221	+	0.815894i
$857$			25.7579i			0.879872i	0.898029	+	0.439936i	$0.144999\pi$
$857$			25.7579i			0.879872i	−0.898029	+	0.439936i	$0.855001\pi$
$858$		0			0
$859$			51.8251i			1.76825i	0.467252	+	0.884124i	$0.345244\pi$
$859$			51.8251i			1.76825i	−0.467252	+	0.884124i	$0.654756\pi$
$860$	−3.57359	+	2.43456i	−0.121858	+	0.0830177i
$861$	−6.51343	−	11.2816i	−0.221977	−	0.384476i
$862$	−4.86850	−	0.457414i	−0.165822	−	0.0155796i
$863$	−35.1233	+	35.1233i	−1.19561	+	1.19561i	−0.220144	+	0.975467i	$0.570653\pi$
$863$	−35.1233	+	35.1233i	−1.19561	+	1.19561i	−0.975467	+	0.220144i	$0.929347\pi$
$864$	18.9069	+	16.9267i	0.643227	+	0.575859i
$865$	−0.131609	−	0.491171i	−0.00447483	−	0.0167003i
$866$	7.25558	+	2.69363i	0.246555	+	0.0915332i
$867$	−11.0734	−	6.39322i	−0.376072	−	0.217125i
$868$	−5.40654	+	28.5184i	−0.183510	+	0.967976i
$869$	−11.8633	−	3.17877i	−0.402436	−	0.107833i
$870$	−0.497646	−	1.08532i	−0.0168718	−	0.0367958i
$871$		0			0
$872$	−0.0934525	−	0.0269775i	−0.00316470	−	0.000913575i
$873$	9.12050	−	34.0382i	0.308682	−	1.15202i
$874$	39.9557	−	56.2910i	1.35152	−	1.90407i
$875$	3.09414	−	5.35921i	0.104601	−	0.181174i
$876$	0.903738	+	12.1178i	0.0305345	+	0.409421i
$877$	35.8746	−	9.61256i	1.21140	−	0.324593i	0.404088	−	0.914720i	$-0.367589\pi$
$877$	35.8746	−	9.61256i	1.21140	−	0.324593i	0.807310	+	0.590127i	$0.200922\pi$
$878$	27.5190	+	33.2262i	0.928720	+	1.12133i
$879$	−13.8602	−	13.8602i	−0.467493	−	0.467493i
$880$	−0.496853	+	1.26330i	−0.0167489	+	0.0425859i
$881$	1.73014	−	0.998897i	0.0582899	−	0.0336537i	−0.470572	−	0.882362i	$-0.655952\pi$
$881$	1.73014	−	0.998897i	0.0582899	−	0.0336537i	0.528862	+	0.848708i	$0.322619\pi$
$882$	−0.00425798	−	0.0250879i	−0.000143374	−	0.000844752i
$883$	−16.1625			−0.543913			−0.271956	−	0.962310i	$-0.587671\pi$
$883$	−16.1625			−0.543913			−0.271956	+	0.962310i	$0.587671\pi$
$884$		0			0
$885$	1.70433			0.0572906
$886$	−3.05251	−	17.9853i	−0.102551	−	0.604228i
$887$	−15.2472	+	8.80298i	−0.511951	+	0.295575i	−0.733635	−	0.679543i	$-0.762178\pi$
$887$	−15.2472	+	8.80298i	−0.511951	+	0.295575i	0.221684	+	0.975119i	$0.428845\pi$
$888$	−0.896794	+	0.862938i	−0.0300944	+	0.0289583i
$889$	9.99232	+	9.99232i	0.335132	+	0.335132i
$890$	−1.41027	−	1.70276i	−0.0472725	−	0.0570765i
$891$	4.20534	−	1.12682i	0.140884	−	0.0377498i
$892$	37.5526	−	2.80066i	1.25735	−	0.0937730i
$893$	−11.0645	+	19.1644i	−0.370261	+	0.641311i
$894$	10.5467	−	14.8586i	0.352735	−	0.496945i
$895$	−0.617167	+	2.30330i	−0.0206296	+	0.0769908i
$896$	3.94203	−	29.6555i	0.131694	−	0.990721i
$897$		0			0
$898$	5.81779	+	12.6881i	0.194142	+	0.423407i
$899$	22.3750	+	5.99536i	0.746247	+	0.199956i
$900$	22.1279	+	4.19503i	0.737596	+	0.139834i
$901$	7.20357	+	4.15898i	0.239986	+	0.138556i
$902$	11.0808	+	4.11375i	0.368951	+	0.136973i
$903$	5.34473	+	19.9468i	0.177861	+	0.663788i
$904$	−0.247729	+	12.8762i	−0.00823935	+	0.428257i
$905$	2.30516	−	2.30516i	0.0766261	−	0.0766261i
$906$	0.813858	+	0.0764650i	0.0270386	+	0.00254038i
$907$	−14.7054	−	25.4704i	−0.488283	−	0.845731i	0.511626	−	0.859208i	$-0.329043\pi$
$907$	−14.7054	−	25.4704i	−0.488283	−	0.845731i	−0.999909	+	0.0134769i	$0.995710\pi$
$908$	−8.37763	−	12.2972i	−0.278022	−	0.408097i
$909$			20.8944i			0.693024i
$910$		0			0
$911$			20.5091i			0.679495i	0.940517	+	0.339748i	$0.110342\pi$
$911$			20.5091i			0.679495i	−0.940517	+	0.339748i	$0.889658\pi$
$912$	18.8592	+	2.13859i	0.624490	+	0.0708160i
$913$	7.04832	+	12.2080i	0.233265	+	0.404027i
$914$	1.37343	−	14.6182i	0.0454292	−	0.483527i
$915$	1.02156	−	1.02156i	0.0337718	−	0.0337718i
$916$	3.90198	−	8.09513i	0.128925	−	0.267471i
$917$	−7.68245	−	28.6713i	−0.253697	−	0.946810i
$918$	3.08958	−	8.32211i	0.101971	−	0.274671i
$919$	42.4137	+	24.4876i	1.39910	+	0.807770i	0.994298	−	0.106635i	$-0.0340077\pi$
$919$	42.4137	+	24.4876i	1.39910	+	0.807770i	0.404800	+	0.914405i	$0.367341\pi$
$920$	−1.39799	−	5.64996i	−0.0460905	−	0.186274i
$921$	18.9463	+	5.07665i	0.624302	+	0.167281i
$922$	36.9391	−	16.9375i	1.21652	−	0.557806i
$923$		0			0
$924$	4.91240	+	4.23053i	0.161606	+	0.139174i
$925$	−0.662453	+	2.47231i	−0.0217813	+	0.0812890i
$926$	9.60708	+	6.81917i	0.315708	+	0.224092i
$927$	12.4211	−	21.5139i	0.407962	−	0.706610i
$928$	−23.3669	−	4.89734i	−0.767056	−	0.160763i
$929$	−6.61751	+	1.77316i	−0.217113	+	0.0581754i	−0.365736	−	0.930719i	$-0.619183\pi$
$929$	−6.61751	+	1.77316i	−0.217113	+	0.0581754i	0.148623	+	0.988894i	$0.452516\pi$
$930$	−1.19583	+	0.990419i	−0.0392127	+	0.0324771i
$931$	−0.0311855	−	0.0311855i	−0.00102206	−	0.00102206i
$932$	8.78997	+	25.1492i	0.287925	+	0.823788i
$933$	6.29067	−	3.63192i	0.205947	−	0.118904i
$934$	4.60576	−	0.781702i	0.150705	−	0.0255781i
$935$	0.474867			0.0155298
$936$		0			0
$937$	11.1107			0.362970			0.181485	−	0.983394i	$-0.441910\pi$
$937$	11.1107			0.362970			0.181485	+	0.983394i	$0.441910\pi$
$938$	−9.29885	+	1.57823i	−0.303618	+	0.0515309i
$939$	4.33139	−	2.50073i	0.141350	−	0.0816083i
$940$	0.615618	+	1.76136i	0.0200793	+	0.0574492i
$941$	20.5970	+	20.5970i	0.671442	+	0.671442i	0.958048	−	0.286606i	$-0.0925272\pi$
$941$	20.5970	+	20.5970i	0.671442	+	0.671442i	−0.286606	+	0.958048i	$0.592527\pi$
$942$	5.46617	−	4.52725i	0.178098	−	0.147506i
$943$	−48.9513	+	13.1165i	−1.59407	+	0.427131i
$944$	20.2568	−	27.4059i	0.659304	−	0.891988i
$945$	−1.39577	+	2.41755i	−0.0454045	+	0.0786430i
$946$	−15.2792	−	10.8453i	−0.496770	−	0.352611i
$947$	7.59297	−	28.3374i	0.246739	−	0.920841i	−0.725763	−	0.687945i	$-0.758513\pi$
$947$	7.59297	−	28.3374i	0.246739	−	0.920841i	0.972502	−	0.232896i	$-0.0748202\pi$
$948$	10.9712	+	9.44830i	0.356327	+	0.306867i
$949$		0			0
$950$	35.4820	−	16.2694i	1.15119	−	0.527848i
$951$	19.1647	+	5.13516i	0.621457	+	0.166519i
$952$	−10.1587	+	2.51361i	−0.329246	+	0.0814667i
$953$	11.3638	+	6.56091i	0.368110	+	0.212529i	0.672633	−	0.739977i	$-0.265163\pi$
$953$	11.3638	+	6.56091i	0.368110	+	0.212529i	−0.304522	+	0.952505i	$0.598497\pi$
$954$	6.66363	−	17.9492i	0.215743	−	0.581128i
$955$	0.235743	+	0.879806i	0.00762847	+	0.0284699i
$956$	7.32748	−	15.2017i	0.236987	−	0.491659i
$957$	3.65836	−	3.65836i	0.118258	−	0.118258i
$958$	−3.67929	+	39.1607i	−0.118873	+	1.26522i
$959$	6.35689	+	11.0105i	0.205275	+	0.355546i
$960$	1.17429	−	1.08724i	0.0379001	−	0.0350905i
$961$			0.875747i			0.0282499i
$962$		0			0
$963$		−	22.4477i		−	0.723365i
$964$	−17.4173	−	25.5662i	−0.560975	−	0.823432i
$965$	0.967718	+	1.67614i	0.0311519	+	0.0539568i
$966$	−27.6743	−	2.60011i	−0.890406	−	0.0836570i
$967$	−13.0476	+	13.0476i	−0.419581	+	0.419581i	−0.885059	−	0.465478i	$-0.845882\pi$
$967$	−13.0476	+	13.0476i	−0.419581	+	0.419581i	0.465478	+	0.885059i	$0.345882\pi$
$968$	25.2258	+	0.485325i	0.810787	+	0.0155989i
$969$	−1.71841	−	6.41320i	−0.0552033	−	0.206022i
$970$	−4.82762	−	1.79225i	−0.155006	−	0.0575457i
$971$	−38.3512	−	22.1421i	−1.23075	−	0.710573i	−0.263562	−	0.964642i	$-0.584897\pi$
$971$	−38.3512	−	22.1421i	−1.23075	−	0.710573i	−0.967186	+	0.254070i	$0.918231\pi$
$972$	−31.4879	−	5.96950i	−1.00997	−	0.191472i
$973$	17.7276	+	4.75009i	0.568320	+	0.152281i
$974$	−6.08146	−	13.2631i	−0.194862	−	0.424978i
$975$		0			0
$976$	−4.28511	−	28.5686i	−0.137163	−	0.914459i
$977$	0.0641402	−	0.239374i	0.00205203	−	0.00765826i	−0.964892	−	0.262646i	$-0.915405\pi$
$977$	0.0641402	−	0.239374i	0.00205203	−	0.00765826i	0.966944	+	0.254988i	$0.0820715\pi$
$978$	−10.9472	+	15.4228i	−0.350053	+	0.493166i
$979$	4.79020	−	8.29687i	0.153095	−	0.265169i
$980$	−0.00370830		0.000276564i	−0.000118457		8.83450e-6i
$981$	0.0756511	−	0.0202707i	0.00241535	−	0.000647192i
$982$	−12.2906	−	14.8396i	−0.392210	−	0.473551i
$983$	−8.44991	−	8.44991i	−0.269510	−	0.269510i	0.559393	−	0.828903i	$-0.311034\pi$
$983$	−8.44991	−	8.44991i	−0.269510	−	0.269510i	−0.828903	+	0.559393i	$0.811034\pi$
$984$	−9.66159	−	10.0406i	−0.308000	−	0.320084i
$985$	−2.52321	+	1.45678i	−0.0803963	+	0.0464168i
$986$	1.39747	+	8.23384i	0.0445045	+	0.262219i
$987$	8.91069			0.283630
$988$		0			0
$989$	80.3360			2.55454
$990$	−0.182899	−	1.07763i	−0.00581291	−	0.0342494i
$991$	36.2254	−	20.9147i	1.15074	−	0.664379i	0.201671	−	0.979453i	$-0.435363\pi$
$991$	36.2254	−	20.9147i	1.15074	−	0.664379i	0.949067	+	0.315074i	$0.102029\pi$
$992$	1.71313	+	31.0007i	0.0543920	+	0.984272i
$993$	−8.63520	−	8.63520i	−0.274030	−	0.274030i
$994$	25.9298	+	31.3075i	0.822444	+	0.993013i
$995$	0.553269	−	0.148248i	0.0175398	−	0.00469978i
$996$	−1.23595	−	16.5723i	−0.0391627	−	0.525112i
$997$	−6.38088	+	11.0520i	−0.202085	+	0.350021i	−0.949200	−	0.314674i	$-0.898105\pi$
$997$	−6.38088	+	11.0520i	−0.202085	+	0.350021i	0.747115	+	0.664694i	$0.231438\pi$
$998$	−12.9988	+	18.3132i	−0.411471	+	0.579694i
$999$	0.601015	−	2.24302i	0.0190153	−	0.0709660i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	676.2.l.i.427.4		16
4.3	odd	2	inner	676.2.l.i.427.2		16
13.2	odd	12		676.2.f.i.239.8		16
13.3	even	3		676.2.f.i.99.3		16
13.4	even	6		52.2.l.b.7.4	yes	16
13.5	odd	4		676.2.l.k.587.2		16
13.6	odd	12	inner	676.2.l.i.19.2		16
13.7	odd	12		676.2.l.m.19.3		16
13.8	odd	4		52.2.l.b.15.3	yes	16
13.9	even	3		676.2.l.k.319.1		16
13.10	even	6		676.2.f.h.99.6		16
13.11	odd	12		676.2.f.h.239.1		16
13.12	even	2		676.2.l.m.427.1		16
39.8	even	4		468.2.cb.f.379.2		16
39.17	odd	6		468.2.cb.f.163.1		16
52.3	odd	6		676.2.f.i.99.8		16
52.7	even	12		676.2.l.m.19.1		16
52.11	even	12		676.2.f.h.239.6		16
52.15	even	12		676.2.f.i.239.3		16
52.19	even	12	inner	676.2.l.i.19.4		16
52.23	odd	6		676.2.f.h.99.1		16
52.31	even	4		676.2.l.k.587.1		16
52.35	odd	6		676.2.l.k.319.2		16
52.43	odd	6		52.2.l.b.7.3	✓	16
52.47	even	4		52.2.l.b.15.4	yes	16
52.51	odd	2		676.2.l.m.427.3		16
104.21	odd	4		832.2.bu.n.639.2		16
104.43	odd	6		832.2.bu.n.319.2		16
104.69	even	6		832.2.bu.n.319.3		16
104.99	even	4		832.2.bu.n.639.3		16
156.47	odd	4		468.2.cb.f.379.1		16
156.95	even	6		468.2.cb.f.163.2		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
52.2.l.b.7.3	✓	16	52.43	odd	6
52.2.l.b.7.4	yes	16	13.4	even	6
52.2.l.b.15.3	yes	16	13.8	odd	4
52.2.l.b.15.4	yes	16	52.47	even	4
468.2.cb.f.163.1		16	39.17	odd	6
468.2.cb.f.163.2		16	156.95	even	6
468.2.cb.f.379.1		16	156.47	odd	4
468.2.cb.f.379.2		16	39.8	even	4
676.2.f.h.99.1		16	52.23	odd	6
676.2.f.h.99.6		16	13.10	even	6
676.2.f.h.239.1		16	13.11	odd	12
676.2.f.h.239.6		16	52.11	even	12
676.2.f.i.99.3		16	13.3	even	3
676.2.f.i.99.8		16	52.3	odd	6
676.2.f.i.239.3		16	52.15	even	12
676.2.f.i.239.8		16	13.2	odd	12
676.2.l.i.19.2		16	13.6	odd	12	inner
676.2.l.i.19.4		16	52.19	even	12	inner
676.2.l.i.427.2		16	4.3	odd	2	inner
676.2.l.i.427.4		16	1.1	even	1	trivial
676.2.l.k.319.1		16	13.9	even	3
676.2.l.k.319.2		16	52.35	odd	6
676.2.l.k.587.1		16	52.31	even	4
676.2.l.k.587.2		16	13.5	odd	4
676.2.l.m.19.1		16	52.7	even	12
676.2.l.m.19.3		16	13.7	odd	12
676.2.l.m.427.1		16	13.12	even	2
676.2.l.m.427.3		16	52.51	odd	2
832.2.bu.n.319.2		16	104.43	odd	6
832.2.bu.n.319.3		16	104.69	even	6
832.2.bu.n.639.2		16	104.21	odd	4
832.2.bu.n.639.3		16	104.99	even	4

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:	\( N \)	\(=\)	\( 676 = 2^{2} \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	676.l (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.39427 - 0.236640i) q^{2} +(0.736159 - 0.425021i) q^{3} +(1.88800 - 0.659882i) q^{4} +(0.166404 + 0.166404i) q^{5} +(0.925830 - 0.766801i) q^{6} +(2.55416 - 0.684384i) q^{7} +(2.47624 - 1.36683i) q^{8} +(-1.13871 + 1.97231i) q^{9} +(0.271390 + 0.192635i) q^{10} +(-0.373247 + 1.39298i) q^{11} +(1.10941 - 1.28822i) q^{12} +(3.39924 - 1.55864i) q^{14} +(0.193225 + 0.0517744i) q^{15} +(3.12911 - 2.49172i) q^{16} +(-1.21178 - 0.699622i) q^{17} +(-1.12095 + 3.01941i) q^{18} +(1.44475 + 5.39188i) q^{19} +(0.423978 + 0.204364i) q^{20} +(1.58939 - 1.58939i) q^{21} +(-0.190775 + 2.03052i) q^{22} +(-4.37216 - 7.57279i) q^{23} +(1.24197 - 2.05866i) q^{24} -4.94462i q^{25} +4.48604i q^{27} +(4.37064 - 2.97756i) q^{28} +(-2.11023 - 3.65503i) q^{29} +(0.281660 + 0.0264630i) q^{30} +(-3.88100 + 3.88100i) q^{31} +(3.77320 - 4.21461i) q^{32} +(0.317276 + 1.18409i) q^{33} +(-1.85511 - 0.688709i) q^{34} +(0.538906 + 0.311137i) q^{35} +(-0.848402 + 4.47514i) q^{36} +(-0.500000 - 0.133975i) q^{37} +(3.29032 + 7.17588i) q^{38} +(0.639502 + 0.184609i) q^{40} +(1.50000 - 5.59808i) q^{41} +(1.83993 - 2.59215i) q^{42} +(-4.59362 + 7.95638i) q^{43} +(0.214509 + 2.87624i) q^{44} +(-0.517686 + 0.138714i) q^{45} +(-7.88801 - 9.52393i) q^{46} +(2.80318 + 2.80318i) q^{47} +(1.24449 - 3.16424i) q^{48} +(-0.00684229 + 0.00395040i) q^{49} +(-1.17009 - 6.89416i) q^{50} -1.18942 q^{51} -5.94462 q^{53} +(1.06158 + 6.25477i) q^{54} +(-0.293906 + 0.169687i) q^{55} +(5.38927 - 5.18581i) q^{56} +(3.35523 + 3.35523i) q^{57} +(-3.80717 - 4.59675i) q^{58} +(8.22961 - 2.20512i) q^{59} +(0.398974 - 0.0297554i) q^{60} +(3.61102 - 6.25448i) q^{61} +(-4.49277 + 6.32957i) q^{62} +(-1.55864 + 5.81691i) q^{63} +(4.26353 - 6.76922i) q^{64} +(0.722573 + 1.57587i) q^{66} +(-2.43624 - 0.652790i) q^{67} +(-2.74951 - 0.521255i) q^{68} +(-6.43720 - 3.71652i) q^{69} +(0.825010 + 0.306284i) q^{70} +(2.81352 + 10.5002i) q^{71} +(-0.123908 + 6.44034i) q^{72} +(-5.05407 + 5.05407i) q^{73} +(-0.728841 - 0.0684774i) q^{74} +(-2.10157 - 3.64002i) q^{75} +(6.28570 + 9.22653i) q^{76} +3.81333i q^{77} +8.51654i q^{79} +(0.935328 + 0.106064i) q^{80} +(-1.50948 - 2.61449i) q^{81} +(0.766683 - 8.16022i) q^{82} +(6.91195 - 6.91195i) q^{83} +(1.95196 - 4.04958i) q^{84} +(-0.0852251 - 0.318065i) q^{85} +(-4.52197 + 12.1804i) q^{86} +(-3.10694 - 1.79379i) q^{87} +(0.979719 + 3.95951i) q^{88} +(-6.41693 - 1.71941i) q^{89} +(-0.688971 + 0.315910i) q^{90} +(-13.2518 - 11.4124i) q^{92} +(-1.20752 + 4.50653i) q^{93} +(4.57175 + 3.24506i) q^{94} +(-0.656818 + 1.13764i) q^{95} +(0.986372 - 4.70632i) q^{96} +(-14.9459 + 4.00474i) q^{97} +(-0.00860521 + 0.00712710i) q^{98} +(-2.32236 - 2.32236i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 4 q^{2} + 6 q^{4} + 12 q^{5} - 10 q^{6} - 10 q^{8} + 4 q^{9} + 8 q^{14} - 2 q^{16} - 12 q^{17} + 6 q^{18} - 20 q^{20} + 28 q^{21} + 14 q^{24} - 24 q^{28} - 8 q^{29} - 42 q^{30} + 26 q^{32} + 8 q^{33}+ \cdots + 68 q^{98}+O(q^{100}) \) 16 * q - 4 * q^2 + 6 * q^4 + 12 * q^5 - 10 * q^6 - 10 * q^8 + 4 * q^9 + 8 * q^14 - 2 * q^16 - 12 * q^17 + 6 * q^18 - 20 * q^20 + 28 * q^21 + 14 * q^24 - 24 * q^28 - 8 * q^29 - 42 * q^30 + 26 * q^32 + 8 * q^33 - 14 * q^34 + 6 * q^36 - 8 * q^37 - 40 * q^40 + 24 * q^41 - 28 * q^42 + 8 * q^44 + 40 * q^45 + 10 * q^46 - 10 * q^48 - 60 * q^49 - 22 * q^50 - 32 * q^53 + 28 * q^54 + 60 * q^56 - 12 * q^57 - 18 * q^58 + 24 * q^60 + 4 * q^61 + 18 * q^62 + 56 * q^66 + 16 * q^68 + 12 * q^69 - 28 * q^70 + 10 * q^72 - 20 * q^73 + 4 * q^74 + 14 * q^76 + 22 * q^80 + 48 * q^81 + 36 * q^84 - 32 * q^85 - 16 * q^86 - 36 * q^88 - 8 * q^89 - 12 * q^92 + 20 * q^93 - 38 * q^94 + 72 * q^96 - 80 * q^97 + 68 * q^98

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