LMFDB - Embedded newform 52.2.l.b.15.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [52,2,Mod(7,52)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(52, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 11]))

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

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

chi := DirichletCharacter("52.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 52 = 2^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	52.l (of order $12$, degree $4$, 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:	$0.415222090511$
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:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			15.3
Root			$1.08916 + 0.902074i$ of defining polynomial
Character	$\chi$	$=$	52.15
Dual form			52.2.l.b.7.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.236640 + 1.39427i) q^{2} +(0.736159 - 0.425021i) q^{3} +(-1.88800 + 0.659882i) q^{4} +(-0.166404 + 0.166404i) q^{5} +(0.766801 + 0.925830i) q^{6} +(-0.684384 - 2.55416i) q^{7} +(-1.36683 - 2.47624i) q^{8} +(-1.13871 + 1.97231i) q^{9} +O(q^{10})$	\(q+(0.236640 + 1.39427i) q^{2} +(0.736159 - 0.425021i) q^{3} +(-1.88800 + 0.659882i) q^{4} +(-0.166404 + 0.166404i) q^{5} +(0.766801 + 0.925830i) q^{6} +(-0.684384 - 2.55416i) q^{7} +(-1.36683 - 2.47624i) q^{8} +(-1.13871 + 1.97231i) q^{9} +(-0.271390 - 0.192635i) q^{10} +(1.39298 + 0.373247i) q^{11} +(-1.10941 + 1.28822i) q^{12} +(-0.406663 - 3.58254i) q^{13} +(3.39924 - 1.55864i) q^{14} +(-0.0517744 + 0.193225i) q^{15} +(3.12911 - 2.49172i) q^{16} +(1.21178 + 0.699622i) q^{17} +(-3.01941 - 1.12095i) q^{18} +(-5.39188 + 1.44475i) q^{19} +(0.204364 - 0.423978i) q^{20} +(-1.58939 - 1.58939i) q^{21} +(-0.190775 + 2.03052i) q^{22} +(4.37216 + 7.57279i) q^{23} +(-2.05866 - 1.24197i) q^{24} +4.94462i q^{25} +(4.89882 - 1.41477i) q^{26} +4.48604i q^{27} +(2.97756 + 4.37064i) q^{28} +(-2.11023 - 3.65503i) q^{29} +(-0.281660 - 0.0264630i) q^{30} +(-3.88100 - 3.88100i) q^{31} +(4.21461 + 3.77320i) q^{32} +(1.18409 - 0.317276i) q^{33} +(-0.688709 + 1.85511i) q^{34} +(0.538906 + 0.311137i) q^{35} +(0.848402 - 4.47514i) q^{36} +(-0.133975 + 0.500000i) q^{37} +(-3.29032 - 7.17588i) q^{38} +(-1.82203 - 2.46448i) q^{39} +(0.639502 + 0.184609i) q^{40} +(5.59808 + 1.50000i) q^{41} +(1.83993 - 2.59215i) q^{42} +(4.59362 - 7.95638i) q^{43} +(-2.87624 + 0.214509i) q^{44} +(-0.138714 - 0.517686i) q^{45} +(-9.52393 + 7.88801i) q^{46} +(2.80318 - 2.80318i) q^{47} +(1.24449 - 3.16424i) q^{48} +(0.00684229 - 0.00395040i) q^{49} +(-6.89416 + 1.17009i) q^{50} +1.18942 q^{51} +(3.13184 + 6.49551i) q^{52} -5.94462 q^{53} +(-6.25477 + 1.06158i) q^{54} +(-0.293906 + 0.169687i) q^{55} +(-5.38927 + 5.18581i) q^{56} +(-3.35523 + 3.35523i) q^{57} +(4.59675 - 3.80717i) q^{58} +(-2.20512 - 8.22961i) q^{59} +(-0.0297554 - 0.398974i) q^{60} +(3.61102 - 6.25448i) q^{61} +(4.49277 - 6.32957i) q^{62} +(5.81691 + 1.55864i) q^{63} +(-4.26353 + 6.76922i) q^{64} +(0.663819 + 0.528479i) q^{65} +(0.722573 + 1.57587i) q^{66} +(0.652790 - 2.43624i) q^{67} +(-2.74951 - 0.521255i) q^{68} +(6.43720 + 3.71652i) q^{69} +(-0.306284 + 0.825010i) q^{70} +(-10.5002 + 2.81352i) q^{71} +(6.44034 + 0.123908i) q^{72} +(5.05407 + 5.05407i) q^{73} +(-0.728841 - 0.0684774i) q^{74} +(2.10157 + 3.64002i) q^{75} +(9.22653 - 6.28570i) q^{76} -3.81333i q^{77} +(3.00500 - 3.12360i) q^{78} +8.51654i q^{79} +(-0.106064 + 0.935328i) q^{80} +(-1.50948 - 2.61449i) q^{81} +(-0.766683 + 8.16022i) q^{82} +(6.91195 + 6.91195i) q^{83} +(4.04958 + 1.95196i) q^{84} +(-0.318065 + 0.0852251i) q^{85} +(12.1804 + 4.52197i) q^{86} +(-3.10694 - 1.79379i) q^{87} +(-0.979719 - 3.95951i) q^{88} +(-1.71941 + 6.41693i) q^{89} +(0.688971 - 0.315910i) q^{90} +(-8.87207 + 3.49052i) q^{91} +(-13.2518 - 11.4124i) q^{92} +(-4.50653 - 1.20752i) q^{93} +(4.57175 + 3.24506i) q^{94} +(0.656818 - 1.13764i) q^{95} +(4.70632 + 0.986372i) q^{96} +(-4.00474 - 14.9459i) q^{97} +(0.00712710 + 0.00860521i) q^{98} +(-2.32236 + 2.32236i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 2 q^{2} - 6 q^{4} - 12 q^{5} - 14 q^{6} + 10 q^{8} + 4 q^{9}+O(q^{10}) $ 16 * q - 2 * q^2 - 6 * q^4 - 12 * q^5 - 14 * q^6 + 10 * q^8 + 4 * q^9	$ 16 q - 2 q^{2} - 6 q^{4} - 12 q^{5} - 14 q^{6} + 10 q^{8} + 4 q^{9} - 12 q^{13} + 8 q^{14} - 2 q^{16} + 12 q^{17} - 6 q^{18} + 2 q^{20} - 28 q^{21} + 10 q^{24} + 16 q^{26} + 12 q^{28} - 8 q^{29} + 42 q^{30} + 28 q^{32} - 20 q^{33} + 14 q^{34} - 6 q^{36} - 16 q^{37} - 40 q^{40} + 48 q^{41} - 28 q^{42} - 8 q^{44} + 20 q^{45} - 46 q^{46} - 10 q^{48} + 60 q^{49} + 10 q^{50} - 32 q^{52} - 32 q^{53} - 16 q^{54} - 60 q^{56} + 12 q^{57} - 48 q^{58} - 24 q^{60} + 4 q^{61} - 18 q^{62} - 8 q^{65} + 56 q^{66} + 16 q^{68} - 12 q^{69} + 28 q^{70} + 56 q^{72} + 20 q^{73} + 4 q^{74} + 22 q^{76} + 68 q^{78} + 44 q^{80} + 48 q^{81} + 84 q^{84} + 20 q^{85} + 16 q^{86} + 36 q^{88} - 52 q^{89} - 12 q^{92} - 92 q^{93} - 38 q^{94} - 72 q^{96} - 28 q^{97} - 2 q^{98}+O(q^{100}) $ 16 * q - 2 * q^2 - 6 * q^4 - 12 * q^5 - 14 * q^6 + 10 * q^8 + 4 * q^9 - 12 * q^13 + 8 * q^14 - 2 * q^16 + 12 * q^17 - 6 * q^18 + 2 * q^20 - 28 * q^21 + 10 * q^24 + 16 * q^26 + 12 * q^28 - 8 * q^29 + 42 * q^30 + 28 * q^32 - 20 * q^33 + 14 * q^34 - 6 * q^36 - 16 * q^37 - 40 * q^40 + 48 * q^41 - 28 * q^42 - 8 * q^44 + 20 * q^45 - 46 * q^46 - 10 * q^48 + 60 * q^49 + 10 * q^50 - 32 * q^52 - 32 * q^53 - 16 * q^54 - 60 * q^56 + 12 * q^57 - 48 * q^58 - 24 * q^60 + 4 * q^61 - 18 * q^62 - 8 * q^65 + 56 * q^66 + 16 * q^68 - 12 * q^69 + 28 * q^70 + 56 * q^72 + 20 * q^73 + 4 * q^74 + 22 * q^76 + 68 * q^78 + 44 * q^80 + 48 * q^81 + 84 * q^84 + 20 * q^85 + 16 * q^86 + 36 * q^88 - 52 * q^89 - 12 * q^92 - 92 * q^93 - 38 * q^94 - 72 * q^96 - 28 * q^97 - 2 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/52\mathbb{Z}\right)^\times$.

$n$	$27$	$41$
$\chi(n)$	$-1$	$e\left(\frac{1}{12}\right)$

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 $

$2$	0.236640	+	1.39427i	0.167330	+	0.985901i
$2$	0.236640	+	1.39427i	0.167330	+	0.985901i
$3$	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	$-0.766758\pi$
$5$	−0.166404	+	0.166404i	−0.0744180	+	0.0744180i	0.668918	+	0.743336i	$0.266758\pi$
$6$	0.766801	+	0.925830i	0.313045	+	0.377969i
$7$	−0.684384	−	2.55416i	−0.258673	−	0.965381i	−0.966010	−	0.258504i	$-0.916770\pi$
$7$	−0.684384	−	2.55416i	−0.258673	−	0.965381i	0.707337	−	0.706876i	$-0.249896\pi$
$8$	−1.36683	−	2.47624i	−0.483249	−	0.875483i
$9$	−1.13871	+	1.97231i	−0.379571	+	0.657437i
$10$	−0.271390	−	0.192635i	−0.0858212	−	0.0609165i
$11$	1.39298	+	0.373247i	0.419998	+	0.112538i	0.462628	−	0.886553i	$-0.346907\pi$
$11$	1.39298	+	0.373247i	0.419998	+	0.112538i	−0.0426292	+	0.999091i	$0.513573\pi$
$12$	−1.10941	+	1.28822i	−0.320258	+	0.371877i
$13$	−0.406663	−	3.58254i	−0.112788	−	0.993619i
$13$	−0.406663	−	3.58254i	−0.112788	−	0.993619i
$14$	3.39924	−	1.55864i	0.908486	−	0.416563i
$15$	−0.0517744	+	0.193225i	−0.0133681	+	0.0498904i
$16$	3.12911	−	2.49172i	0.782278	−	0.622930i
$17$	1.21178	+	0.699622i	0.293900	+	0.169683i	0.639699	−	0.768625i	$-0.279059\pi$
$17$	1.21178	+	0.699622i	0.293900	+	0.169683i	−0.345799	+	0.938308i	$0.612392\pi$
$18$	−3.01941	−	1.12095i	−0.711681	−	0.264211i
$19$	−5.39188	+	1.44475i	−1.23698	+	0.331449i	−0.817295	−	0.576220i	$-0.804527\pi$
$19$	−5.39188	+	1.44475i	−1.23698	+	0.331449i	−0.419688	+	0.907668i	$0.637861\pi$
$20$	0.204364	−	0.423978i	0.0456972	−	0.0948043i
$21$	−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	$0.198530\pi$
$23$	4.37216	+	7.57279i	0.911657	+	1.57904i	0.0999345	+	0.994994i	$0.468137\pi$
$24$	−2.05866	−	1.24197i	−0.420223	−	0.253516i
$25$			4.94462i			0.988924i
$26$	4.89882	−	1.41477i	0.960737	−	0.277460i
$27$			4.48604i			0.863339i
$28$	2.97756	+	4.37064i	0.562706	+	0.825974i
$29$	−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	0.266725	−	0.963773i	$-0.414058\pi$
$31$	−3.88100	−	3.88100i	−0.697047	−	0.697047i	−0.963773	+	0.266725i	$0.914058\pi$
$32$	4.21461	+	3.77320i	0.745046	+	0.667014i
$33$	1.18409	−	0.317276i	0.206124	−	0.0552307i
$34$	−0.688709	+	1.85511i	−0.118113	+	0.318149i
$35$	0.538906	+	0.311137i	0.0910917	+	0.0525918i
$36$	0.848402	−	4.47514i	0.141400	−	0.745857i
$37$	−0.133975	+	0.500000i	−0.0220253	+	0.0821995i	−0.976064	−	0.217485i	$-0.930215\pi$
$37$	−0.133975	+	0.500000i	−0.0220253	+	0.0821995i	0.954038	+	0.299684i	$0.0968814\pi$
$38$	−3.29032	−	7.17588i	−0.533760	−	1.16408i
$39$	−1.82203	−	2.46448i	−0.291758	−	0.394633i
$40$	0.639502	+	0.184609i	0.101114	+	0.0291893i
$41$	5.59808	+	1.50000i	0.874273	+	0.234261i	0.667934	−	0.744220i	$-0.267179\pi$
$41$	5.59808	+	1.50000i	0.874273	+	0.234261i	0.206338	+	0.978481i	$0.433845\pi$
$42$	1.83993	−	2.59215i	0.283907	−	0.399978i
$43$	4.59362	−	7.95638i	0.700520	−	1.21334i	−0.267764	−	0.963484i	$-0.586285\pi$
$43$	4.59362	−	7.95638i	0.700520	−	1.21334i	0.968284	−	0.249852i	$-0.0803819\pi$
$44$	−2.87624	+	0.214509i	−0.433610	+	0.0323385i
$45$	−0.138714	−	0.517686i	−0.0206782	−	0.0771721i
$46$	−9.52393	+	7.88801i	−1.40423	+	1.16302i
$47$	2.80318	−	2.80318i	0.408886	−	0.408886i	−0.472464	−	0.881350i	$-0.656635\pi$
$47$	2.80318	−	2.80318i	0.408886	−	0.408886i	0.881350	+	0.472464i	$0.156635\pi$
$48$	1.24449	−	3.16424i	0.179626	−	0.456719i
$49$	0.00684229	−	0.00395040i	0.000977470	−	0.000564343i
$50$	−6.89416	+	1.17009i	−0.974981	+	0.165476i
$51$	1.18942			0.166552
$52$	3.13184	+	6.49551i	0.434308	+	0.900765i
$53$	−5.94462			−0.816556			−0.408278	−	0.912858i	$-0.633871\pi$
$53$	−5.94462			−0.816556			−0.408278	+	0.912858i	$0.633871\pi$
$54$	−6.25477	+	1.06158i	−0.851166	+	0.144462i
$55$	−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
$58$	4.59675	−	3.80717i	0.603583	−	0.499906i
$59$	−2.20512	−	8.22961i	−0.287082	−	1.07140i	−0.947305	−	0.320334i	$-0.896205\pi$
$59$	−2.20512	−	8.22961i	−0.287082	−	1.07140i	0.660223	−	0.751070i	$-0.270462\pi$
$60$	−0.0297554	−	0.398974i	−0.00384140	−	0.0515073i
$61$	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
$63$	5.81691	+	1.55864i	0.732861	+	0.196370i
$64$	−4.26353	+	6.76922i	−0.532941	+	0.846152i
$65$	0.663819	+	0.528479i	0.0823366	+	0.0655497i
$66$	0.722573	+	1.57587i	0.0889426	+	0.193976i
$67$	0.652790	−	2.43624i	0.0797510	−	0.297635i	−0.914518	−	0.404546i	$-0.867429\pi$
$67$	0.652790	−	2.43624i	0.0797510	−	0.297635i	0.994269	+	0.106912i	$0.0340962\pi$
$68$	−2.74951	−	0.521255i	−0.333427	−	0.0632115i
$69$	6.43720	+	3.71652i	0.774948	+	0.447416i
$70$	−0.306284	+	0.825010i	−0.0366080	+	0.0986075i
$71$	−10.5002	+	2.81352i	−1.24614	+	0.333903i	−0.820846	−	0.571150i	$-0.806498\pi$
$71$	−10.5002	+	2.81352i	−1.24614	+	0.333903i	−0.425298	+	0.905053i	$0.639831\pi$
$72$	6.44034	+	0.123908i	0.759002	+	0.0146026i
$73$	5.05407	+	5.05407i	0.591534	+	0.591534i	0.938046	−	0.346512i	$-0.112634\pi$
$73$	5.05407	+	5.05407i	0.591534	+	0.591534i	−0.346512	+	0.938046i	$0.612634\pi$
$74$	−0.728841	−	0.0684774i	−0.0847260	−	0.00796033i
$75$	2.10157	+	3.64002i	0.242668	+	0.420314i
$76$	9.22653	−	6.28570i	1.05836	−	0.721020i
$77$		−	3.81333i		−	0.434569i
$78$	3.00500	−	3.12360i	0.340249	−	0.353678i
$79$			8.51654i			0.958186i	0.877764	+	0.479093i	$0.159034\pi$
$79$			8.51654i			0.958186i	−0.877764	+	0.479093i	$0.840966\pi$
$80$	−0.106064	+	0.935328i	−0.0118583	+	0.104573i
$81$	−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	0.976083	−	0.217398i	$-0.0697570\pi$
$83$	6.91195	+	6.91195i	0.758685	+	0.758685i	−0.217398	+	0.976083i	$0.569757\pi$
$84$	4.04958	+	1.95196i	0.441845	+	0.212976i
$85$	−0.318065	+	0.0852251i	−0.0344989	+	0.00924396i
$86$	12.1804	+	4.52197i	1.31345	+	0.487616i
$87$	−3.10694	−	1.79379i	−0.333098	−	0.192314i
$88$	−0.979719	−	3.95951i	−0.104438	−	0.422085i
$89$	−1.71941	+	6.41693i	−0.182257	+	0.680193i	0.812944	+	0.582342i	$0.197864\pi$
$89$	−1.71941	+	6.41693i	−0.182257	+	0.680193i	−0.995201	+	0.0978511i	$0.968803\pi$
$90$	0.688971	−	0.315910i	0.0726240	−	0.0332998i
$91$	−8.87207	+	3.49052i	−0.930045	+	0.365906i
$92$	−13.2518	−	11.4124i	−1.38160	−	1.18982i
$93$	−4.50653	−	1.20752i	−0.467306	−	0.125214i
$94$	4.57175	+	3.24506i	0.471540	+	0.334703i
$95$	0.656818	−	1.13764i	0.0673881	−	0.116720i
$96$	4.70632	+	0.986372i	0.480336	+	0.100671i
$97$	−4.00474	−	14.9459i	−0.406620	−	1.51753i	−0.801049	−	0.598599i	$-0.795724\pi$
$97$	−4.00474	−	14.9459i	−0.406620	−	1.51753i	0.394429	−	0.918926i	$-0.370942\pi$
$98$	0.00712710	+	0.00860521i	0.000719946	+	0.000869257i
$99$	−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	−0.840173	−	0.542319i	$-0.817547\pi$
$101$	−7.94541	+	4.58728i	−0.790598	+	0.456452i	0.0495752	+	0.998770i	$0.484213\pi$
$102$	0.281464	+	1.65837i	0.0278690	+	0.164203i
$103$	10.9080			1.07480			0.537398	−	0.843329i	$-0.319407\pi$
$103$	10.9080			1.07480			0.537398	+	0.843329i	$0.319407\pi$
$104$	−8.31540	+	5.90374i	−0.815392	+	0.578909i
$105$	0.528960			0.0516212
$106$	−1.40673	−	8.28843i	−0.136634	−	0.805044i
$107$	−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	$-0.749476\pi$
$109$	0.0243171	−	0.0243171i	0.00232916	−	0.00232916i	0.708270	+	0.705941i	$0.249476\pi$
$110$	−0.306140	−	0.369631i	−0.0291893	−	0.0352430i
$111$	0.113884	+	0.425021i	0.0108094	+	0.0403412i
$112$	−8.50576	−	6.28695i	−0.803718	−	0.594061i
$113$	−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
$115$	−1.98769	−	0.532599i	−0.185353	−	0.0496651i
$116$	6.39602	+	5.50821i	0.593856	+	0.511424i
$117$	7.52896	+	3.27743i	0.696053	+	0.302998i
$118$	10.9525	−	5.02200i	1.00826	−	0.462312i
$119$	0.957620	−	3.57389i	0.0877849	−	0.327618i
$120$	0.549238	−	0.135900i	0.0501383	−	0.0124059i
$121$	−7.72521	−	4.46015i	−0.702292	−	0.405468i
$122$	9.57497	+	3.55470i	0.866877	+	0.321827i
$123$	4.75860	−	1.27506i	0.429069	−	0.114969i
$124$	9.88833	+	4.76633i	0.887998	+	0.428029i
$125$	−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	0.722775	−	0.691083i	$-0.242866\pi$
$127$	−2.67207	−	4.62816i	−0.237108	−	0.410683i	−0.959883	+	0.280400i	$0.909533\pi$
$128$	−10.4471	−	4.34266i	−0.923399	−	0.383841i
$129$		−	7.80954i		−	0.687592i
$130$	−0.579758	+	1.05061i	−0.0508482	+	0.0921442i
$131$		−	11.2254i		−	0.980764i	−0.871508	−	0.490382i	$-0.836857\pi$
$131$		−	11.2254i		−	0.980764i	0.871508	−	0.490382i	$-0.163143\pi$
$132$	−2.02620	+	1.38038i	−0.176358	+	0.120146i
$133$	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
$136$	0.0761283	−	3.95693i	0.00652795	−	0.339304i
$137$	4.64424	−	1.24442i	0.396784	−	0.106318i	−0.0549089	−	0.998491i	$-0.517487\pi$
$137$	4.64424	−	1.24442i	0.396784	−	0.106318i	0.451693	+	0.892173i	$0.350820\pi$
$138$	−3.65855	+	9.85470i	−0.311436	+	0.838888i
$139$	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
$141$	0.872175	−	3.25500i	0.0734504	−	0.274121i
$142$	−6.40759	−	13.9744i	−0.537713	−	1.17270i
$143$	0.770702	−	5.14219i	0.0644494	−	0.430011i
$144$	1.35128	+	9.00893i	0.112607	+	0.750744i
$145$	0.959363	+	0.257060i	0.0796707	+	0.0213477i
$146$	−5.85076	+	8.24275i	−0.484212	+	0.682175i
$147$	0.00335801	−	0.00581624i	0.000276964	−	0.000479715i
$148$	−0.0769967	−	1.03241i	−0.00632909	−	0.0848635i
$149$	3.92298	+	14.6408i	0.321383	+	1.19942i	0.917898	+	0.396817i	$0.129885\pi$
$149$	3.92298	+	14.6408i	0.321383	+	1.19942i	−0.596515	+	0.802602i	$0.703448\pi$
$150$	−4.57788	+	3.79154i	−0.373782	+	0.309578i
$151$	0.480824	−	0.480824i	0.0391289	−	0.0391289i	−0.687272	−	0.726401i	$-0.741192\pi$
$151$	0.480824	−	0.480824i	0.0391289	−	0.0391289i	0.726401	+	0.687272i	$0.241192\pi$
$152$	10.9474	+	11.3769i	0.887948	+	0.922786i
$153$	−2.75974	+	1.59334i	−0.223112	+	0.128814i
$154$	5.31682	−	0.902385i	0.428442	−	0.0727163i
$155$	1.29162			0.103746
$156$	5.06626	+	3.45062i	0.405625	+	0.276271i
$157$	5.90408			0.471197			0.235598	−	0.971851i	$-0.424295\pi$
$157$	5.90408			0.471197			0.235598	+	0.971851i	$0.424295\pi$
$158$	−11.8744	+	2.01535i	−0.944676	+	0.160333i
$159$	−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
$162$	3.28812	−	2.72332i	0.258339	−	0.213964i
$163$	4.07194	+	15.1967i	0.318939	+	1.19030i	0.920266	+	0.391294i	$0.127972\pi$
$163$	4.07194	+	15.1967i	0.318939	+	1.19030i	−0.601327	+	0.799003i	$0.705361\pi$
$164$	−11.5590	+	0.862067i	−0.902607	+	0.0673161i
$165$	−0.144241	+	0.249833i	−0.0112292	+	0.0194495i
$166$	−8.00151	+	11.2728i	−0.621038	+	0.874939i
$167$	−5.41542	−	1.45106i	−0.419058	−	0.112286i	0.0431274	−	0.999070i	$-0.486268\pi$
$167$	−5.41542	−	1.45106i	−0.419058	−	0.112286i	−0.462185	+	0.886783i	$0.652935\pi$
$168$	−1.76327	+	6.10813i	−0.136040	+	0.471253i
$169$	−12.6693	+	2.91377i	−0.974558	+	0.224137i
$170$	−0.194094	−	0.423302i	−0.0148863	−	0.0324658i
$171$	3.29032	−	12.2796i	0.251617	−	0.939046i
$172$	−3.42249	+	18.0529i	−0.260962	+	1.37652i
$173$	1.87129	+	1.08039i	0.142272	+	0.0821405i	0.569446	−	0.822029i	$-0.307158\pi$
$173$	1.87129	+	1.08039i	0.142272	+	0.0821405i	−0.427175	+	0.904169i	$0.640491\pi$
$174$	1.76581	−	4.75640i	0.133866	−	0.360582i
$175$	12.6293	−	3.38402i	0.954688	−	0.255808i
$176$	5.28881	−	2.30298i	0.398659	−	0.173593i
$177$	−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	0.612191	−	0.790710i	$-0.290288\pi$
$179$	−5.06638	−	8.77523i	−0.378679	−	0.655892i	−0.990870	+	0.134818i	$0.956955\pi$
$180$	0.603504	+	0.885858i	0.0449825	+	0.0660280i
$181$			13.8528i			1.02967i	0.857289	+	0.514836i	$0.172147\pi$
$181$			13.8528i			1.02967i	−0.857289	+	0.514836i	$0.827853\pi$
$182$	−6.96623	−	11.5441i	−0.516371	−	0.855706i
$183$		−	6.13905i		−	0.453812i
$184$	12.7760	−	21.1773i	0.941863	−	1.56121i
$185$	−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
$188$	−3.44265	+	7.14219i	−0.251081	+	0.520898i
$189$	11.4580	−	3.07017i	0.833450	−	0.223322i
$190$	1.74162	+	0.646573i	0.126350	+	0.0469073i
$191$	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
$193$	2.12861	−	7.94409i	0.153221	−	0.571828i	−0.846030	−	0.533135i	$-0.821014\pi$
$193$	2.12861	−	7.94409i	0.153221	−	0.571828i	0.999251	−	0.0386934i	$-0.0123196\pi$
$194$	19.8910	−	9.12050i	1.42809	−	0.654814i
$195$	0.713291	+	0.106907i	0.0510798	+	0.00765576i
$196$	−0.0103115	+	0.0119735i	−0.000736533	+	0.000855248i
$197$	−11.9588	−	3.20436i	−0.852032	−	0.228301i	−0.193730	−	0.981055i	$-0.562058\pi$
$197$	−11.9588	−	3.20436i	−0.852032	−	0.228301i	−0.658302	+	0.752754i	$0.728725\pi$
$198$	−3.78757	−	2.68844i	−0.269171	−	0.191059i
$199$	−1.21698	+	2.10788i	−0.0862696	+	0.149423i	−0.905932	−	0.423424i	$-0.860828\pi$
$199$	−1.21698	+	2.10788i	−0.0862696	+	0.149423i	0.819662	+	0.572848i	$0.194161\pi$
$200$	12.2441	−	6.75848i	0.865786	−	0.477896i
$201$	−0.554899	−	2.07091i	−0.0391396	−	0.146071i
$202$	−8.27613	−	9.99255i	−0.582307	−	0.703073i
$203$	−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
$206$	2.58127	+	15.2087i	0.179845	+	1.05964i
$207$	−19.9145			−1.38416
$208$	−10.1992	−	10.1969i	−0.707187	−	0.707027i
$209$	−8.05002			−0.556831
$210$	0.125173	+	0.737516i	0.00863777	+	0.0508934i
$211$	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
$214$	−8.89136	−	10.7354i	−0.607801	−	0.733855i
$215$	0.559576	+	2.08837i	0.0381628	+	0.142425i
$216$	11.1085	−	6.13167i	0.755838	−	0.417207i
$217$	−7.25658	+	12.5688i	−0.492609	+	0.853223i
$218$	0.0396591	+	0.0281503i	0.00268606	+	0.00190658i
$219$	5.86868	+	1.57251i	0.396569	+	0.106260i
$220$	0.442923	−	0.514313i	0.0298618	−	0.0346750i
$221$	2.01364	−	4.62577i	0.135452	−	0.311163i
$222$	−0.565647	+	0.259363i	−0.0379637	+	0.0174073i
$223$	−4.87316	+	18.1869i	−0.326331	+	1.21788i	0.586636	+	0.809850i	$0.300452\pi$
$223$	−4.87316	+	18.1869i	−0.326331	+	1.21788i	−0.912967	+	0.408033i	$0.866215\pi$
$224$	6.75293	−	13.3471i	0.451199	−	0.891791i
$225$	−9.75232	−	5.63051i	−0.650155	−	0.375367i
$226$	−6.03672	−	2.24113i	−0.401557	−	0.149078i
$227$	7.18635	−	1.92558i	0.476974	−	0.127805i	−0.0123190	−	0.999924i	$-0.503921\pi$
$227$	7.18635	−	1.92558i	0.476974	−	0.127805i	0.489293	+	0.872119i	$0.337255\pi$
$228$	4.12063	−	8.54875i	0.272895	−	0.566155i
$229$	−3.17720	−	3.17720i	−0.209955	−	0.209955i	0.594293	−	0.804248i	$-0.297432\pi$
$229$	−3.17720	−	3.17720i	−0.209955	−	0.209955i	−0.804248	+	0.594293i	$0.797432\pi$
$230$	0.272223	−	2.89741i	0.0179498	−	0.191050i
$231$	−1.62075	−	2.80721i	−0.106637	−	0.184701i
$232$	−6.16640	+	10.2213i	−0.404844	+	0.671059i
$233$		−	13.3205i		−	0.872655i	−0.899788	−	0.436328i	$-0.856279\pi$
$233$		−	13.3205i		−	0.872655i	0.899788	−	0.436328i	$-0.143721\pi$
$234$	−2.78798	+	11.2730i	−0.182256	+	0.736940i
$235$			0.932921i			0.0608571i
$236$	9.59385	+	14.0824i	0.624506	+	0.916687i
$237$	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	0.873235	−	0.487300i	$-0.162018\pi$
$239$	5.96641	+	5.96641i	0.385935	+	0.385935i	−0.487300	+	0.873235i	$0.662018\pi$
$240$	0.319454	+	0.733629i	0.0206207	+	0.0473556i
$241$	−14.9406	+	4.00333i	−0.962410	+	0.257877i	−0.705620	−	0.708590i	$-0.749332\pi$
$241$	−14.9406	+	4.00333i	−0.962410	+	0.257877i	−0.256790	+	0.966467i	$0.582665\pi$
$242$	4.39058	−	11.8265i	0.282237	−	0.760237i
$243$	−13.8775	−	8.01218i	−0.890242	−	0.513982i
$244$	−2.69040	+	14.1913i	−0.172236	+	0.908506i
$245$	−0.000481222		0.00179594i	−3.07441e−5		0.000114739i
$246$	2.90387	+	6.33307i	0.185144	+	0.403782i
$247$	7.36856	+	18.7291i	0.468851	+	1.19171i
$248$	−4.30560	+	14.9150i	−0.273406	+	0.947101i
$249$	8.02602	+	2.15056i	0.508628	+	0.136287i
$250$	1.91568	−	2.69887i	0.121158	−	0.170692i
$251$	−13.7387	+	23.7962i	−0.867182	+	1.50200i	−0.00231697	+	0.999997i	$0.500738\pi$
$251$	−13.7387	+	23.7962i	−0.867182	+	1.50200i	−0.864865	+	0.502005i	$0.832596\pi$
$252$	−12.0109	+	0.895766i	−0.756613	+	0.0564279i
$253$	3.26379	+	12.1806i	0.205193	+	0.765789i
$254$	5.82061	−	4.82081i	0.365217	−	0.302484i
$255$	−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	$-0.331971\pi$
$257$	24.1060	−	13.9176i	1.50369	−	0.868157i	0.999991	−	0.00427985i	$-0.00136232\pi$
$258$	10.8886	−	1.84805i	0.677897	−	0.115055i
$259$	1.36877			0.0850511
$260$	−1.60203	−	0.559727i	−0.0993535	−	0.0347128i
$261$	9.61181			0.594956
$262$	15.6512	−	2.65637i	0.966936	−	0.164111i
$263$	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
$266$	−16.0765	+	13.3150i	−0.985713	+	0.816398i
$267$	1.46157	+	5.45466i	0.0894468	+	0.333820i
$268$	0.375166	+	5.03040i	0.0229169	+	0.307281i
$269$	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
$271$	−13.3489	−	3.57684i	−0.810890	−	0.217277i	−0.170530	−	0.985352i	$-0.554548\pi$
$271$	−13.3489	−	3.57684i	−0.810890	−	0.217277i	−0.640360	+	0.768075i	$0.721215\pi$
$272$	5.53506	−	0.830223i	0.335612	−	0.0503397i
$273$	−5.04770	+	6.34039i	−0.305501	+	0.383738i
$274$	2.83408	+	6.18087i	0.171213	+	0.373400i
$275$	−1.84556	+	6.88774i	−0.111292	+	0.415346i
$276$	−14.6059	−	2.76900i	−0.879173	−	0.166674i
$277$	11.0276	+	6.36681i	0.662587	+	0.382545i	0.793262	−	0.608880i	$-0.208381\pi$
$277$	11.0276	+	6.36681i	0.662587	+	0.382545i	−0.130675	+	0.991425i	$0.541714\pi$
$278$	−3.41621	+	9.20193i	−0.204891	+	0.551895i
$279$	12.0739	−	3.23518i	0.722844	−	0.193685i
$280$	0.0338560	−	1.75973i	0.00202328	−	0.105164i
$281$	15.4454	+	15.4454i	0.921396	+	0.921396i	0.997128	−	0.0757324i	$-0.0241295\pi$
$281$	15.4454	+	15.4454i	0.921396	+	0.921396i	−0.0757324	+	0.997128i	$0.524129\pi$
$282$	4.74476	+	0.445788i	0.282546	+	0.0265463i
$283$	−10.3449	−	17.9178i	−0.614939	−	1.06511i	−0.990395	−	0.138265i	$-0.955847\pi$
$283$	−10.3449	−	17.9178i	−0.614939	−	1.06511i	0.375456	−	0.926840i	$-0.377486\pi$
$284$	17.9678	−	12.2408i	1.06619	−	0.726360i
$285$		−	1.11665i		−	0.0661445i
$286$	7.35200	−	0.142277i	0.434733	−	0.00841300i
$287$		−	15.3249i		−	0.904603i
$288$	−12.2412	+	4.01593i	−0.721317	+	0.236641i
$289$	−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
$292$	−12.8772	−	6.20700i	−0.753580	−	0.363237i
$293$	−22.2734	+	5.96815i	−1.30123	+	0.348663i	−0.841914	−	0.539611i	$-0.818571\pi$
$293$	−22.2734	+	5.96815i	−1.30123	+	0.348663i	−0.459314	+	0.888274i	$0.651905\pi$
$294$	0.00890407	+	0.00330563i	0.000519296	+	0.000192788i
$295$	1.73638	+	1.00250i	0.101096	+	0.0583677i
$296$	1.42124	−	0.351664i	0.0826080	−	0.0204400i
$297$	−1.67440	+	6.24895i	−0.0971586	+	0.362601i
$298$	−19.4849	+	8.93431i	−1.12873	+	0.517551i
$299$	25.3519	−	18.7430i	1.46614	−	1.08394i
$300$	−6.36976	−	5.48559i	−0.367758	−	0.316711i
$301$	−23.4656	−	6.28760i	−1.35254	−	0.362411i
$302$	0.784183	+	0.556619i	0.0451247	+	0.0320298i
$303$	−3.89939	+	6.75394i	−0.224014	+	0.388004i
$304$	−13.2719	+	17.9559i	−0.761195	+	1.02984i
$305$	0.439881	+	1.64166i	0.0251875	+	0.0940010i
$306$	−2.87461	−	3.47079i	−0.164331	−	0.198412i
$307$	16.3164	−	16.3164i	0.931228	−	0.931228i	−0.0665547	−	0.997783i	$-0.521201\pi$
$307$	16.3164	−	16.3164i	0.931228	−	0.931228i	0.997783	+	0.0665547i	$0.0212007\pi$
$308$	2.51635	+	7.19957i	0.143382	+	0.410234i
$309$	8.03001	−	4.63613i	0.456811	−	0.263740i
$310$	0.305650	+	1.80088i	0.0173598	+	0.102283i
$311$	−8.54527			−0.484558			−0.242279	−	0.970207i	$-0.577895\pi$
$311$	−8.54527			−0.484558			−0.242279	+	0.970207i	$0.577895\pi$
$312$	−3.61224	+	7.88031i	−0.204503	+	0.446135i
$313$	5.88378			0.332571			0.166285	−	0.986078i	$-0.446823\pi$
$313$	5.88378			0.332571			0.166285	+	0.986078i	$0.446823\pi$
$314$	1.39714	+	8.23191i	0.0788452	+	0.464553i
$315$	−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	$-0.977532\pi$
$317$	−16.5045	+	16.5045i	−0.926984	+	0.926984i	0.0705258	+	0.997510i	$0.477532\pi$
$318$	−4.55834	−	5.50371i	−0.255619	−	0.308633i
$319$	−1.57528	−	5.87902i	−0.0881986	−	0.329162i
$320$	−0.416956	−	1.83589i	−0.0233086	−	0.102629i
$321$	−4.18926	+	7.25601i	−0.233822	+	0.404991i
$322$	26.6652	+	18.9272i	1.48600	+	1.05477i
$323$	−7.54456	−	2.02156i	−0.419790	−	0.112483i
$324$	4.57516	+	3.94009i	0.254175	+	0.218894i
$325$	17.7143	−	2.01079i	0.982614	−	0.111539i
$326$	−20.2248	+	9.27355i	−1.12015	+	0.513614i
$327$	0.00756596	−	0.0282365i	0.000418399	−	0.00156148i
$328$	−3.93728	−	15.9124i	−0.217400	−	0.878617i
$329$	−9.07823	−	5.24132i	−0.500499	−	0.288963i
$330$	−0.382469	−	0.141991i	−0.0210542	−	0.00781636i
$331$	13.8768	−	3.71829i	0.762740	−	0.204375i	0.143578	−	0.989639i	$-0.454139\pi$
$331$	13.8768	−	3.71829i	0.762740	−	0.204375i	0.619162	+	0.785264i	$0.287473\pi$
$332$	−17.6109	−	8.48871i	−0.966521	−	0.465878i
$333$	−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
$336$	−8.93367	−	1.01306i	−0.487372	−	0.0552670i
$337$			14.3427i			0.781297i	0.920540	+	0.390649i	$0.127749\pi$
$337$			14.3427i			0.781297i	−0.920540	+	0.390649i	$0.872251\pi$
$338$	−7.06065	−	16.9749i	−0.384049	−	0.923313i
$339$			3.87048i			0.210216i
$340$	0.544268	−	0.370790i	0.0295171	−	0.0201089i
$341$	−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
$344$	−25.9806	−	0.499848i	−1.40078	−	0.0269500i
$345$	−1.68962	+	0.452732i	−0.0909659	+	0.0243743i
$346$	−1.06354	+	2.86476i	−0.0571762	+	0.154010i
$347$	−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
$349$	7.32017	−	27.3192i	0.391840	−	1.46237i	−0.435257	−	0.900306i	$-0.643343\pi$
$349$	7.32017	−	27.3192i	0.391840	−	1.46237i	0.827097	−	0.562059i	$-0.189991\pi$
$350$	7.70686	+	16.8080i	0.411949	+	0.898423i
$351$	16.0714	−	1.82431i	0.857830	−	0.0973742i
$352$	4.46252	+	6.82907i	0.237853	+	0.363991i
$353$	34.7270	+	9.30507i	1.84833	+	0.495259i	0.999445	−	0.0333153i	$-0.0106066\pi$
$353$	34.7270	+	9.30507i	1.84833	+	0.495259i	0.848887	+	0.528574i	$0.177273\pi$
$354$	5.92834	−	8.35204i	0.315088	−	0.443906i
$355$	1.27909	−	2.21545i	0.0678872	−	0.117584i
$356$	−0.988165	−	13.2498i	−0.0523726	−	0.702238i
$357$	−0.814018	−	3.03796i	−0.0430824	−	0.160786i
$358$	11.0362	−	9.14050i	0.583280	−	0.483091i
$359$	−11.7167	+	11.7167i	−0.618383	+	0.618383i	−0.945117	−	0.326733i	$-0.894052\pi$
$359$	−11.7167	+	11.7167i	−0.618383	+	0.618383i	0.326733	+	0.945117i	$0.394052\pi$
$360$	−1.09232	+	1.05108i	−0.0575701	+	0.0553967i
$361$	10.5306	−	6.07986i	0.554244	−	0.319993i
$362$	−19.3146	+	3.27813i	−1.01515	+	0.172295i
$363$	−7.58264			−0.397985
$364$	14.4472	−	12.4446i	0.757237	−	0.652276i
$365$	−1.68203			−0.0880416
$366$	8.55952	−	1.45274i	0.447413	−	0.0759362i
$367$	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
$370$	0.132677	−	0.109887i	0.00689754	−	0.00571275i
$371$	4.06840	+	15.1835i	0.211221	+	0.788288i
$372$	9.30517	−	0.693977i	0.482451	−	0.0359810i
$373$	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
$375$	−1.92155	−	0.514877i	−0.0992283	−	0.0265881i
$376$	−10.7728	−	3.10987i	−0.555567	−	0.160379i
$377$	−12.2362	+	9.04638i	−0.630195	+	0.465912i
$378$	6.99210	+	15.2491i	0.359635	+	0.784331i
$379$	−8.63337	+	32.2202i	−0.443467	+	1.65504i	0.276487	+	0.961018i	$0.410830\pi$
$379$	−8.63337	+	32.2202i	−0.443467	+	1.65504i	−0.719953	+	0.694022i	$0.755837\pi$
$380$	−0.489364	+	2.58129i	−0.0251039	+	0.132418i
$381$	−3.93413	−	2.27137i	−0.201552	−	0.116366i
$382$	−1.90505	+	5.13147i	−0.0974711	+	0.262549i
$383$	−20.2216	+	5.41837i	−1.03328	+	0.276866i	−0.735325	−	0.677715i	$-0.762970\pi$
$383$	−20.2216	+	5.41837i	−1.03328	+	0.276866i	−0.297953	+	0.954581i	$0.596304\pi$
$384$	−9.53643	+	1.24334i	−0.486654	+	0.0634490i
$385$	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
$388$	17.4235	+	25.5752i	0.884544	+	1.29839i
$389$		−	9.60410i		−	0.486947i	−0.969908	−	0.243474i	$-0.921713\pi$
$389$		−	9.60410i		−	0.486947i	0.969908	−	0.243474i	$-0.0782870\pi$
$390$	0.0197357	+	1.01982i	0.000999357	+	0.0516407i
$391$			12.2354i			0.618772i
$392$	−0.0191344	−	0.0115436i	−0.000966434	−	0.000583040i
$393$	−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
$396$	2.85214	−	5.91711i	0.143325	−	0.297346i
$397$	2.49473	−	0.668462i	0.125207	−	0.0335492i	−0.195671	−	0.980670i	$-0.562689\pi$
$397$	2.49473	−	0.668462i	0.125207	−	0.0335492i	0.320878	+	0.947120i	$0.396022\pi$
$398$	−3.22694	−	1.19800i	−0.161752	−	0.0600503i
$399$	10.8661	+	6.27352i	0.543983	+	0.314069i
$400$	12.3206	+	15.4723i	0.616030	+	0.773613i
$401$	−7.00137	+	26.1295i	−0.349632	+	1.30484i	0.537476	+	0.843279i	$0.319378\pi$
$401$	−7.00137	+	26.1295i	−0.349632	+	1.30484i	−0.887107	+	0.461563i	$0.847289\pi$
$402$	2.75611	−	1.26374i	0.137462	−	0.0630298i
$403$	−12.3256	+	15.4821i	−0.613981	+	0.771218i
$404$	11.9739	−	13.9038i	0.595723	−	0.691742i
$405$	0.686244	+	0.183879i	0.0340998	+	0.00913700i
$406$	−12.8701	−	9.13526i	−0.638731	−	0.453375i
$407$	−0.373247	+	0.646483i	−0.0185012	+	0.0320450i
$408$	−1.62574	−	2.94528i	−0.0804859	−	0.145813i
$409$	1.24095	+	4.63129i	0.0613611	+	0.229003i	0.989796	−	0.142493i	$-0.0455118\pi$
$409$	1.24095	+	4.63129i	0.0613611	+	0.229003i	−0.928435	+	0.371496i	$0.878845\pi$
$410$	−1.23031	−	1.48547i	−0.0607608	−	0.0733621i
$411$	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
$414$	−4.71257	−	27.7663i	−0.231610	−	1.36464i
$415$	−2.30035			−0.112920
$416$	11.8037	−	16.6335i	0.578725	−	0.815523i
$417$	5.89987			0.288918
$418$	−1.90496	−	11.2239i	−0.0931745	−	0.548981i
$419$	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	$-0.710921\pi$
$421$	3.55354	−	3.55354i	0.173189	−	0.173189i	0.788379	+	0.615190i	$0.210921\pi$
$422$	3.78016	+	4.56414i	0.184015	+	0.222179i
$423$	2.33672	+	8.72077i	0.113615	+	0.424018i
$424$	8.12531	+	14.7203i	0.394600	+	0.714881i
$425$	−3.45936	+	5.99179i	−0.167804	+	0.290645i
$426$	−10.6564	−	7.56399i	−0.516305	−	0.366477i
$427$	−18.4462	−	4.94266i	−0.892676	−	0.239192i
$428$	12.8640	−	14.9374i	0.621805	−	0.722027i
$429$	−1.61818	−	4.11303i	−0.0781265	−	0.198579i
$430$	−2.77934	+	1.27439i	−0.134032	+	0.0614567i
$431$	0.894922	−	3.33989i	0.0431069	−	0.160877i	−0.941017	−	0.338359i	$-0.890128\pi$
$431$	0.894922	−	3.33989i	0.0431069	−	0.160877i	0.984124	+	0.177482i	$0.0567950\pi$
$432$	11.1780	+	14.0373i	0.537799	+	0.675371i
$433$	−4.73943	−	2.73631i	−0.227762	−	0.131499i	0.381777	−	0.924254i	$-0.375312\pi$
$433$	−4.73943	−	2.73631i	−0.227762	−	0.131499i	−0.609539	+	0.792756i	$0.708646\pi$
$434$	−19.2415	−	7.14339i	−0.923622	−	0.342894i
$435$	0.815499	−	0.218512i	0.0391002	−	0.0104769i
$436$	−0.0298643	+	0.0619572i	−0.00143024	+	0.00296721i
$437$	−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	$-0.907120\pi$
$439$	−15.2532	−	26.4193i	−0.727994	−	1.26092i	0.229736	−	0.973253i	$-0.426214\pi$
$440$	0.821907	+	0.495849i	0.0391829	+	0.0236387i
$441$			0.0179935i			0.000856833i
$442$	6.92610	+	1.71293i	0.329441	+	0.0814755i
$443$		−	12.8994i		−	0.612869i	−0.951892	−	0.306434i	$-0.900864\pi$
$443$		−	12.8994i		−	0.612869i	0.951892	−	0.306434i	$-0.0991360\pi$
$444$	−0.495478	−	0.727292i	−0.0235143	−	0.0345157i
$445$	−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
$448$	20.2075	+	6.25697i	0.954716	+	0.295614i
$449$	9.53370	−	2.55455i	0.449923	−	0.120557i	−0.0267403	−	0.999642i	$-0.508513\pi$
$449$	9.53370	−	2.55455i	0.449923	−	0.120557i	0.476663	+	0.879086i	$0.341846\pi$
$450$	5.54268	−	14.9298i	0.261284	−	0.703798i
$451$	7.23812	+	4.17893i	0.340830	+	0.196778i
$452$	1.69622	−	8.94719i	0.0797833	−	0.420840i
$453$	0.149602	−	0.558323i	0.00702893	−	0.0262323i
$454$	4.38536	+	9.56407i	0.205815	+	0.448864i
$455$	0.895510	−	2.05718i	0.0419822	−	0.0964421i
$456$	12.8944	+	3.72231i	0.603836	+	0.174313i
$457$	10.0284	+	2.68710i	0.469108	+	0.125697i	0.485626	−	0.874166i	$-0.338592\pi$
$457$	10.0284	+	2.68710i	0.469108	+	0.125697i	−0.0165184	+	0.999864i	$0.505258\pi$
$458$	3.67803	−	5.18174i	0.171863	−	0.242127i
$459$	−3.13853	+	5.43609i	−0.146494	+	0.253735i
$460$	4.10421	−	0.306091i	0.191360	−	0.0142715i
$461$	7.43710	+	27.7556i	0.346380	+	1.29271i	0.890991	+	0.454021i	$0.150011\pi$
$461$	7.43710	+	27.7556i	0.346380	+	1.29271i	−0.544611	+	0.838689i	$0.683323\pi$
$462$	3.53049	−	2.92406i	0.164253	−	0.136040i
$463$	5.89061	−	5.89061i	0.273760	−	0.273760i	−0.556852	−	0.830612i	$-0.687991\pi$
$463$	5.89061	−	5.89061i	0.273760	−	0.273760i	0.830612	+	0.556852i	$0.187991\pi$
$464$	−15.7105	−	6.17889i	−0.729341	−	0.286848i
$465$	0.950841	−	0.548968i	0.0440942	−	0.0254578i
$466$	18.5724	−	3.15217i	0.860352	−	0.146021i
$467$	−3.30334			−0.152860			−0.0764301	−	0.997075i	$-0.524352\pi$
$467$	−3.30334			−0.152860			−0.0764301	+	0.997075i	$0.524352\pi$
$468$	−16.3774	−	1.21956i	−0.757046	−	0.0563744i
$469$	−6.66931			−0.307960
$470$	−1.30075	+	0.220766i	−0.0599990	+	0.0101832i
$471$	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
$474$	−7.88487	+	6.53049i	−0.362164	+	0.299956i
$475$	−7.14374	−	26.6608i	−0.327777	−	1.22328i
$476$	0.550355	+	7.37943i	0.0252255	+	0.338235i
$477$	6.76922	−	11.7246i	0.309941	−	0.536834i
$478$	−6.90693	+	9.73071i	−0.315915	+	0.445072i
$479$	26.8650	+	7.19847i	1.22750	+	0.328906i	0.813604	−	0.581420i	$-0.197503\pi$
$479$	26.8650	+	7.19847i	1.22750	+	0.328906i	0.413892	+	0.910326i	$0.364169\pi$
$480$	−0.947285	+	0.619013i	−0.0432374	+	0.0282539i
$481$	1.84575	+	0.276639i	0.0841592	+	0.0126136i
$482$	−9.11729	−	19.8840i	−0.415281	−	0.905691i
$483$	5.08705	−	18.9851i	0.231469	−	0.863854i
$484$	17.5284	+	3.32305i	0.796745	+	0.151048i
$485$	3.15346	+	1.82065i	0.143191	+	0.0826714i
$486$	7.88721	−	21.2451i	0.357771	−	0.963695i
$487$	9.96577	−	2.67032i	0.451592	−	0.121004i	−0.0258522	−	0.999666i	$-0.508230\pi$
$487$	9.96577	−	2.67032i	0.451592	−	0.121004i	0.477444	+	0.878662i	$0.341563\pi$
$488$	−20.4233	−	0.392928i	−0.924517	−	0.0177870i
$489$	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	0.977802	−	0.209532i	$-0.0671941\pi$
$491$	6.81243	+	11.7995i	0.307441	+	0.532503i	−0.670361	+	0.742035i	$0.733861\pi$
$492$	−8.14287	+	5.54744i	−0.367109	+	0.250098i
$493$		−	5.90546i		−	0.265969i
$494$	−24.3699	+	14.7059i	−1.09645	+	0.661648i
$495$		−	0.772899i		−	0.0347392i
$496$	−21.8144	−	2.47371i	−0.979496	−	0.111073i
$497$	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	0.409597	−	0.912267i	$-0.365669\pi$
$499$	−11.2288	−	11.2288i	−0.502670	−	0.502670i	−0.912267	+	0.409597i	$0.865669\pi$
$500$	4.21630	+	2.03232i	0.188559	+	0.0908882i
$501$	−4.60334	+	1.23346i	−0.205662	+	0.0551070i
$502$	−36.4296	−	13.5244i	−1.62593	−	0.603625i
$503$	−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
$505$	0.558805	−	2.08549i	0.0248665	−	0.0928030i
$506$	−16.2108	+	7.43304i	−0.720657	+	0.330439i
$507$	−8.08816	+	7.52970i	−0.359208	+	0.334406i
$508$	8.09892	+	6.97473i	0.359331	+	0.309454i
$509$	−9.52759	−	2.55291i	−0.422303	−	0.113156i	0.0414078	−	0.999142i	$-0.486816\pi$
$509$	−9.52759	−	2.55291i	−0.422303	−	0.113156i	−0.463711	+	0.885987i	$0.653482\pi$
$510$	−0.322796	−	0.229123i	−0.0142937	−	0.0101457i
$511$	9.44995	−	16.3678i	0.418041	−	0.724069i
$512$	22.5897	+	1.30512i	0.998335	+	0.0576787i
$513$	−6.48121	−	24.1882i	−0.286152	−	1.06794i
$514$	25.1094	+	30.3170i	1.10753	+	1.33722i
$515$	−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
$518$	0.323905	+	1.90844i	0.0142316	+	0.0838520i
$519$	1.83676			0.0806246
$520$	0.401309	−	2.36612i	0.0175986	−	0.103761i
$521$	15.9204			0.697486			0.348743	−	0.937218i	$-0.386609\pi$
$521$	15.9204			0.697486			0.348743	+	0.937218i	$0.386609\pi$
$522$	2.27454	+	13.4015i	0.0995539	+	0.586568i
$523$	−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
$526$	21.4748	+	25.9285i	0.936346	+	1.13054i
$527$	−1.98769	−	7.41814i	−0.0865849	−	0.323139i
$528$	2.91459	−	3.94321i	0.126841	−	0.171606i
$529$	−26.7315	+	46.3003i	−1.16224	+	2.01306i
$530$	1.61331	+	1.14514i	0.0700778	+	0.0497417i
$531$	18.7423	+	5.02200i	0.813348	+	0.217936i
$532$	−22.3692	−	19.2642i	−0.969826	−	0.835207i
$533$	3.09729	−	20.6654i	0.134158	−	0.895116i
$534$	−7.25943	+	3.32863i	−0.314146	+	0.144044i
$535$	0.600345	−	2.24052i	0.0259552	−	0.0968660i
$536$	−6.92498	+	1.71348i	−0.299114	+	0.0740110i
$537$	−7.45933	−	4.30664i	−0.321894	−	0.185845i
$538$	27.4597	+	10.1944i	1.18387	+	0.439512i
$539$	0.0110056	−	0.00294895i	0.000474046	−	0.000127020i
$540$	1.90198	+	0.916785i	0.0818482	+	0.0394521i
$541$	8.15947	+	8.15947i	0.350803	+	0.350803i	0.860408	−	0.509605i	$-0.170209\pi$
$541$	8.15947	+	8.15947i	0.350803	+	0.350803i	−0.509605	+	0.860408i	$0.670209\pi$
$542$	1.82820	−	19.4585i	0.0785279	−	0.835814i
$543$	5.88774	+	10.1979i	0.252667	+	0.437632i
$544$	2.46737	+	7.52092i	0.105788	+	0.322457i
$545$			0.00809292i			0.000346663i
$546$	−10.0347	−	5.53750i	−0.429447	−	0.236983i
$547$			8.11076i			0.346791i	0.984852	+	0.173396i	$0.0554739\pi$
$547$			8.11076i			0.346791i	−0.984852	+	0.173396i	$0.944526\pi$
$548$	−7.94717	+	5.41412i	−0.339486	+	0.231280i
$549$	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
$552$	0.404408	−	21.0199i	0.0172127	−	0.894667i
$553$	21.7526	−	5.82859i	0.925014	−	0.247857i
$554$	−6.26750	+	16.8822i	−0.266281	+	0.717256i
$555$	−0.0896759	−	0.0517744i	−0.00380653	−	0.00219770i
$556$	−13.6384	−	2.58559i	−0.578398	−	0.109653i
$557$	−0.887873	+	3.31359i	−0.0376204	+	0.140401i	−0.982182	−	0.187934i	$-0.939821\pi$
$557$	−0.887873	+	3.31359i	−0.0376204	+	0.140401i	0.944561	+	0.328335i	$0.106488\pi$
$558$	7.36789	+	16.0687i	0.311908	+	0.680243i
$559$	−30.3721	−	13.2213i	−1.28460	−	0.559200i
$560$	2.46156	−	0.369219i	0.104020	−	0.0156023i
$561$	1.65683	+	0.443946i	0.0699514	+	0.0187434i
$562$	−17.8801	+	25.1901i	−0.754228	+	1.06258i
$563$	3.12130	−	5.40625i	0.131547	−	0.227846i	−0.792726	−	0.609578i	$-0.791339\pi$
$563$	3.12130	−	5.40625i	0.131547	−	0.227846i	0.924273	+	0.381732i	$0.124672\pi$
$564$	0.501249	+	6.72099i	0.0211064	+	0.283005i
$565$	−0.277331	−	1.03501i	−0.0116674	−	0.0435434i
$566$	22.5344	−	18.6637i	0.947191	−	0.784493i
$567$	−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	−0.953562	−	0.301197i	$-0.902614\pi$
$569$	−27.8969	+	16.1063i	−1.16950	+	0.675211i	−0.215937	+	0.976407i	$0.569281\pi$
$570$	1.55691	−	0.264243i	0.0652119	−	0.0110679i
$571$	41.4189			1.73333			0.866663	−	0.498894i	$-0.166260\pi$
$571$	41.4189			1.73333			0.866663	+	0.498894i	$0.166260\pi$
$572$	1.93815	+	10.2170i	0.0810381	+	0.427196i
$573$	3.29007			0.137445
$574$	21.3672	−	3.62649i	0.891849	−	0.151367i
$575$	−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	$-0.631657\pi$
$577$	12.3408	−	12.3408i	0.513753	−	0.513753i	0.915674	+	0.401921i	$0.131657\pi$
$578$	16.3832	−	13.5691i	0.681453	−	0.564400i
$579$	−1.80941	−	6.75282i	−0.0751966	−	0.280638i
$580$	−1.98091	+	0.147736i	−0.0822528	+	0.00613439i
$581$	12.9238	−	22.3846i	0.536168	−	0.928671i
$582$	10.7665	−	15.1682i	0.446287	−	0.628744i
$583$	−8.28072	−	2.21881i	−0.342952	−	0.0918938i
$584$	5.60701	−	19.4231i	0.232020	−	0.803736i
$585$	−1.79822	+	0.707471i	−0.0743474	+	0.0292503i
$586$	−13.5920	−	29.6430i	−0.561481	−	1.22454i
$587$	5.98011	−	22.3181i	0.246825	−	0.921165i	−0.725632	−	0.688083i	$-0.758452\pi$
$587$	5.98011	−	22.3181i	0.246825	−	0.921165i	0.972457	−	0.233082i	$-0.0748810\pi$
$588$	−0.00250189	+	0.0131970i	−0.000103176	+	0.000544234i
$589$	26.5330	+	15.3188i	1.09327	+	0.631200i
$590$	−0.986862	+	2.65822i	−0.0406285	+	0.109437i
$591$	−10.1655	+	2.72384i	−0.418154	+	0.112044i
$592$	0.826639	+	1.89838i	0.0339746	+	0.0780230i
$593$	11.0244	+	11.0244i	0.452717	+	0.452717i	0.896255	−	0.443538i	$-0.146277\pi$
$593$	11.0244	+	11.0244i	0.452717	+	0.452717i	−0.443538	+	0.896255i	$0.646277\pi$
$594$	−9.10898	−	0.855823i	−0.373746	−	0.0351148i
$595$	0.435357	+	0.754060i	0.0178479	+	0.0309134i
$596$	−17.0678	−	25.0531i	−0.699124	−	1.02622i
$597$			2.06898i			0.0846775i
$598$	32.1322	+	30.9121i	1.31398	+	1.26409i
$599$			10.6090i			0.433471i	0.976230	+	0.216735i	$0.0695409\pi$
$599$			10.6090i			0.433471i	−0.976230	+	0.216735i	$0.930459\pi$
$600$	6.14108	−	10.1793i	0.250708	−	0.415568i
$601$	−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
$604$	−0.590510	+	1.22508i	−0.0240275	+	0.0498480i
$605$	2.02769	−	0.543318i	0.0824373	−	0.0220890i
$606$	−10.3396	−	3.83856i	−0.420017	−	0.155931i
$607$	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
$609$	−2.45528	+	9.16324i	−0.0994931	+	0.371313i
$610$	−2.18483	+	1.00180i	−0.0884610	+	0.0405615i
$611$	−11.1825	−	8.90258i	−0.452395	−	0.360160i
$612$	4.15898	−	4.82933i	0.168117	−	0.195214i
$613$	−34.2262	−	9.17089i	−1.38238	−	0.370409i	−0.510397	−	0.859939i	$-0.670502\pi$
$613$	−34.2262	−	9.17089i	−1.38238	−	0.370409i	−0.871986	+	0.489530i	$0.837168\pi$
$614$	26.6107	+	18.8885i	1.07392	+	0.762277i
$615$	−0.579674	+	1.00403i	−0.0233747	+	0.0404862i
$616$	−9.44271	+	5.21218i	−0.380458	+	0.210005i
$617$	−10.8473	−	40.4828i	−0.436697	−	1.62978i	−0.736972	−	0.675923i	$-0.763745\pi$
$617$	−10.8473	−	40.4828i	−0.436697	−	1.62978i	0.300275	−	0.953853i	$-0.402922\pi$
$618$	8.36426	+	10.0989i	0.336460	+	0.406239i
$619$	−12.0880	+	12.0880i	−0.485858	+	0.485858i	−0.906996	−	0.421138i	$-0.861631\pi$
$619$	−12.0880	+	12.0880i	−0.485858	+	0.485858i	0.421138	+	0.906996i	$0.361631\pi$
$620$	−2.43859	+	0.852320i	−0.0979362	+	0.0342300i
$621$	−33.9719	+	19.6137i	−1.36324	+	0.787069i
$622$	−2.02215	−	11.9145i	−0.0810809	−	0.477726i
$623$	17.5666			0.703790
$624$	−11.8421	−	3.17165i	−0.474064	−	0.126968i
$625$	−24.1724			−0.966894
$626$	1.39234	+	8.20360i	0.0556490	+	0.327882i
$627$	−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
$630$	−1.27841	−	1.54354i	−0.0509329	−	0.0614960i
$631$	3.12081	+	11.6470i	0.124237	+	0.463660i	0.999811	−	0.0194238i	$-0.00618318\pi$
$631$	3.12081	+	11.6470i	0.124237	+	0.463660i	−0.875574	+	0.483084i	$0.839517\pi$
$632$	21.0890	−	11.6407i	0.838875	−	0.463042i
$633$	1.78106	−	3.08489i	0.0707909	−	0.122613i
$634$	−26.9174	−	19.1062i	−1.06903	−	0.758803i
$635$	1.21479	+	0.325501i	0.0482073	+	0.0129171i
$636$	6.59499	−	7.65798i	0.261509	−	0.303659i
$637$	−0.0169350	−	0.0229063i	−0.000670988	−	0.000907582i
$638$	7.82419	−	3.58758i	0.309763	−	0.142034i
$639$	6.40759	−	23.9134i	0.253480	−	0.946001i
$640$	2.46107	−	1.01580i	0.0972822	−	0.0401529i
$641$	−1.81632	−	1.04865i	−0.0717404	−	0.0414193i	0.463701	−	0.885992i	$-0.346521\pi$
$641$	−1.81632	−	1.04865i	−0.0717404	−	0.0414193i	−0.535441	+	0.844573i	$0.679855\pi$
$642$	−11.1082	−	4.12391i	−0.438406	−	0.162758i
$643$	−40.9391	+	10.9696i	−1.61448	+	0.432599i	−0.949374	−	0.314148i	$-0.898281\pi$
$643$	−40.9391	+	10.9696i	−1.61448	+	0.432599i	−0.665108	+	0.746747i	$0.731614\pi$
$644$	−20.0796	+	41.6576i	−0.791248	+	1.64154i
$645$	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	$0.154821\pi$
$647$	21.5400	+	37.3083i	0.846824	+	1.46674i	−0.0372042	+	0.999308i	$0.511845\pi$
$648$	−4.41090	+	7.31141i	−0.173277	+	0.287219i
$649$		−	12.2867i		−	0.482296i
$650$	6.99551	+	24.2228i	0.274387	+	0.950096i
$651$			12.3368i			0.483518i
$652$	−17.7159	−	26.0044i	−0.693807	−	1.01841i
$653$	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
$656$	21.2546	−	9.25517i	0.829852	−	0.361354i
$657$	−15.7233	+	4.21305i	−0.613425	+	0.164367i
$658$	5.15956	−	13.8978i	0.201141	−	0.541795i
$659$	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
$661$	−2.67284	+	9.97516i	−0.103961	+	0.387989i	−0.998225	−	0.0595512i	$-0.981033\pi$
$661$	−2.67284	+	9.97516i	−0.103961	+	0.387989i	0.894264	+	0.447540i	$0.147700\pi$
$662$	8.46813	+	18.4682i	0.329123	+	0.717788i
$663$	−0.483691	−	4.26114i	−0.0187850	−	0.165489i
$664$	7.66815	−	26.5631i	0.297582	−	1.03085i
$665$	−3.35523	−	0.899032i	−0.130110	−	0.0348630i
$666$	0.965000	−	1.35952i	0.0373930	−	0.0526805i
$667$	18.4525	−	31.9607i	0.714485	−	1.23753i
$668$	11.1819	−	0.833940i	0.432639	−	0.0322661i
$669$	4.14239	+	15.4596i	0.160154	+	0.597704i
$670$	−0.646466	+	0.535423i	−0.0249752	+	0.0206852i
$671$	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	0.0879759	−	0.996123i	$-0.471960\pi$
$673$	25.8030	−	14.8974i	0.994631	−	0.574251i	0.906655	+	0.421872i	$0.138627\pi$
$674$	−19.9977	+	3.39406i	−0.770282	+	0.130734i
$675$	−22.1818			−0.853776
$676$	21.9968	−	13.8614i	0.846032	−	0.533132i
$677$	−29.1021			−1.11849			−0.559243	−	0.829004i	$-0.688908\pi$
$677$	−29.1021			−1.11849			−0.559243	+	0.829004i	$0.688908\pi$
$678$	−5.39651	+	0.915911i	−0.207252	+	0.0351753i
$679$	−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
$682$	8.62082	−	7.14003i	0.330108	−	0.273406i
$683$	1.30625	+	4.87499i	0.0499823	+	0.186536i	0.986404	−	0.164342i	$-0.0525499\pi$
$683$	1.30625	+	4.87499i	0.0499823	+	0.186536i	−0.936421	+	0.350878i	$0.885883\pi$
$684$	1.89098	+	25.3552i	0.0723035	+	0.969480i
$685$	−0.565743	+	0.979896i	−0.0216159	+	0.0374399i
$686$	15.1687	−	21.3702i	0.579143	−	0.815917i
$687$	−3.68930	−	0.988544i	−0.140755	−	0.0377153i
$688$	−5.45113	−	36.3424i	−0.207822	−	1.38554i
$689$	2.41746	+	21.2969i	0.0920977	+	0.811346i
$690$	−1.03106	−	2.24866i	−0.0392519	−	0.0856049i
$691$	−2.89268	+	10.7956i	−0.110043	+	0.410685i	−0.998868	−	0.0475604i	$-0.984855\pi$
$691$	−2.89268	+	10.7956i	−0.110043	+	0.410685i	0.888826	+	0.458246i	$0.151522\pi$
$692$	−4.24593	−	0.804948i	−0.161406	−	0.0305995i
$693$	7.52106	+	4.34229i	0.285701	+	0.164950i
$694$	0.231487	−	0.623535i	0.00878711	−	0.0236691i
$695$	−1.57770	+	0.422743i	−0.0598455	+	0.0160355i
$696$	−0.195189	+	10.1453i	−0.00739861	+	0.384558i
$697$	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
$700$	−21.6112	+	14.7229i	−0.816825	+	0.556474i
$701$			27.1476i			1.02535i	0.858582	+	0.512676i	$0.171346\pi$
$701$			27.1476i			1.02535i	−0.858582	+	0.512676i	$0.828654\pi$
$702$	6.34673	+	21.9763i	0.239542	+	0.829442i
$703$		−	2.88950i		−	0.108980i
$704$	−8.46559	+	7.83802i	−0.319059	+	0.295406i
$705$	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
$708$	13.0479	+	6.28930i	0.490371	+	0.236366i
$709$	40.9857	−	10.9821i	1.53925	−	0.412441i	0.613228	−	0.789906i	$-0.289871\pi$
$709$	40.9857	−	10.9821i	1.53925	−	0.412441i	0.926024	+	0.377465i	$0.123204\pi$
$710$	3.39163	+	1.25914i	0.127286	+	0.0472547i
$711$	−16.7973	−	9.69790i	−0.629946	−	0.363700i
$712$	18.2400	−	4.51320i	0.683573	−	0.169139i
$713$	12.4217	−	46.3583i	0.465195	−	1.73613i
$714$	4.04312	−	1.85387i	0.151310	−	0.0693792i
$715$	0.727432	+	0.983927i	0.0272044	+	0.0367968i
$716$	15.3560	+	13.2245i	0.573880	+	0.494221i
$717$	6.92808	+	1.85637i	0.258734	+	0.0693275i
$718$	−19.1089	−	13.5636i	−0.713139	−	0.506191i
$719$	8.21566	−	14.2299i	0.306392	−	0.530687i	−0.671178	−	0.741296i	$-0.734211\pi$
$719$	8.21566	−	14.2299i	0.306392	−	0.530687i	0.977570	+	0.210609i	$0.0675447\pi$
$720$	−1.72398	−	1.27426i	−0.0642489	−	0.0474889i
$721$	−7.46526	−	27.8607i	−0.278021	−	1.03759i
$722$	10.9690	+	13.2439i	0.408223	+	0.492885i
$723$	−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
$726$	−1.79436	−	10.5723i	−0.0665948	−	0.392374i
$727$	32.1429			1.19211			0.596057	−	0.802942i	$-0.296733\pi$
$727$	32.1429			1.19211			0.596057	+	0.802942i	$0.296733\pi$
$728$	20.7700	+	17.1984i	0.769788	+	0.637415i
$729$	−4.56452			−0.169056
$730$	−0.398036	−	2.34521i	−0.0147320	−	0.0868003i
$731$	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	$-0.917248\pi$
$733$	−19.2047	+	19.2047i	−0.709343	+	0.709343i	0.257054	+	0.966397i	$0.417248\pi$
$734$	9.16110	+	11.0610i	0.338142	+	0.408270i
$735$	0.000409059		0.00152663i	1.50884e−5		5.63106e-5i
$736$	−10.1467	+	48.4134i	−0.374013	+	1.78454i
$737$	1.81864	−	3.14998i	0.0669905	−	0.116031i
$738$	−15.2214	−	10.8043i	−0.560309	−	0.397711i
$739$	22.4404	+	6.01290i	0.825485	+	0.221188i	0.646743	−	0.762708i	$-0.276131\pi$
$739$	22.4404	+	6.01290i	0.825485	+	0.221188i	0.178742	+	0.983896i	$0.442797\pi$
$740$	0.184609	+	0.158984i	0.00678637	+	0.00584438i
$741$	13.3847	+	10.6558i	0.491700	+	0.391451i
$742$	−20.2072	+	9.26549i	−0.741830	+	0.340147i
$743$	9.98778	−	37.2749i	0.366416	−	1.36748i	−0.499075	−	0.866559i	$-0.666327\pi$
$743$	9.98778	−	37.2749i	0.366416	−	1.36748i	0.865491	−	0.500925i	$-0.167007\pi$
$744$	3.16957	+	12.8097i	0.116202	+	0.469628i
$745$	−3.08908	−	1.78348i	−0.113175	−	0.0653417i
$746$	19.9079	+	7.39079i	0.728880	+	0.270596i
$747$	−21.5032	+	5.76177i	−0.786762	+	0.210812i
$748$	−3.63545	−	1.75234i	−0.132925	−	0.0640720i
$749$	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	0.877588	−	0.479415i	$-0.159151\pi$
$751$	0.646973	+	1.12059i	0.0236084	+	0.0408909i	−0.853980	+	0.520306i	$0.825818\pi$
$752$	1.78672	−	15.7562i	0.0651551	−	0.574570i
$753$			23.3570i			0.851178i
$754$	−15.5087	−	14.9198i	−0.564794	−	0.543349i
$755$			0.160022i			0.00582380i
$756$	−19.6069	+	13.3575i	−0.713095	+	0.485806i
$757$	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
$760$	−3.71484	−	0.0714707i	−0.134751	−	0.00259252i
$761$	8.40241	−	2.25142i	0.304587	−	0.0816138i	−0.103288	−	0.994651i	$-0.532936\pi$
$761$	8.40241	−	2.25142i	0.304587	−	0.0816138i	0.407875	+	0.913038i	$0.366270\pi$
$762$	2.23594	−	6.02276i	0.0809997	−	0.218182i
$763$	−0.0787520	−	0.0454675i	−0.00285101	−	0.00164603i
$764$	−7.60549	−	1.44186i	−0.275157	−	0.0521646i
$765$	0.194094	−	0.724369i	0.00701748	−	0.0261896i
$766$	−12.3399	−	26.9123i	−0.445860	−	0.972381i
$767$	−28.5862	+	11.2466i	−1.03219	+	0.406092i
$768$	−3.99026	−	13.0022i	−0.143986	−	0.469175i
$769$	−9.35018	−	2.50537i	−0.337176	−	0.0903461i	0.0862584	−	0.996273i	$-0.472509\pi$
$769$	−9.35018	−	2.50537i	−0.337176	−	0.0903461i	−0.423434	+	0.905927i	$0.639176\pi$
$770$	−0.734579	+	1.03490i	−0.0264724	+	0.0372952i
$771$	11.8306	−	20.4912i	0.426068	−	0.737971i
$772$	1.22334	+	16.4031i	0.0440289	+	0.590361i
$773$	−4.96928	−	18.5456i	−0.178732	−	0.667039i	−0.995886	−	0.0906182i	$-0.971116\pi$
$773$	−4.96928	−	18.5456i	−0.178732	−	0.667039i	0.817153	−	0.576420i	$-0.195551\pi$
$774$	−22.7887	+	18.8743i	−0.819123	+	0.678423i
$775$	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
$778$	13.3908	−	2.27272i	0.480082	−	0.0814808i
$779$	−32.3513			−1.15911
$780$	−1.41724	+	0.268848i	−0.0507454	+	0.00962629i
$781$	−15.6767			−0.560955
$782$	−17.0595	+	2.89539i	−0.610048	+	0.103539i
$783$	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
$786$	10.3928	−	8.60761i	0.370698	−	0.307023i
$787$	−7.73737	−	28.8763i	−0.275808	−	1.02933i	−0.955298	−	0.295644i	$-0.904466\pi$
$787$	−7.73737	−	28.8763i	−0.275808	−	1.02933i	0.679491	−	0.733684i	$-0.262201\pi$
$788$	24.6928	−	1.84158i	0.879645	−	0.0656037i
$789$	10.1181	−	17.5250i	0.360213	−	0.623907i
$790$	1.64058	−	2.31131i	0.0583693	−	0.0822326i
$791$	11.6298	+	3.11619i	0.413508	+	0.110799i
$792$	8.92500	+	2.57644i	0.317136	+	0.0915498i
$793$	−23.8754	−	10.3932i	−0.847841	−	0.369073i
$794$	1.52237	+	3.32016i	0.0540270	+	0.117828i
$795$	0.307779	−	1.14865i	0.0109158	−	0.0407383i
$796$	0.906717	−	4.78274i	0.0321377	−	0.169520i
$797$	32.2562	+	18.6231i	1.14257	+	0.659665i	0.947067	−	0.321037i	$-0.104031\pi$
$797$	32.2562	+	18.6231i	1.14257	+	0.659665i	0.195507	+	0.980702i	$0.437365\pi$
$798$	−6.17567	+	16.6348i	−0.218616	+	0.588867i
$799$	5.35801	−	1.43567i	0.189553	−	0.0507905i
$800$	−18.6570	+	20.8397i	−0.659626	+	0.736793i
$801$	−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
$804$	2.41421	+	3.54372i	0.0851426	+	0.124977i
$805$			5.44136i			0.191783i
$806$	−24.5030	−	13.5216i	−0.863082	−	0.476277i
$807$		−	17.6060i		−	0.619759i
$808$	22.2193	+	13.4047i	0.781671	+	0.471575i
$809$	−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	0.778502	−	0.627643i	$-0.215980\pi$
$811$	4.29617	+	4.29617i	0.150859	+	0.150859i	−0.627643	+	0.778502i	$0.715980\pi$
$812$	9.69149	−	20.1062i	0.340105	−	0.705588i
$813$	−11.3472	+	3.04046i	−0.397962	+	0.106634i
$814$	−0.989700	−	0.367425i	−0.0346890	−	0.0128782i
$815$	−3.20637	−	1.85120i	−0.112314	−	0.0648447i
$816$	3.72182	−	2.96369i	0.130290	−	0.103750i
$817$	−13.2733	+	49.5365i	−0.464373	+	1.73306i
$818$	−6.16364	+	2.82618i	−0.215506	+	0.0988149i
$819$	3.21836	−	21.4732i	0.112459	−	0.750333i
$820$	1.78001	−	2.06691i	0.0621607	−	0.0721798i
$821$	18.2378	+	4.88681i	0.636505	+	0.170551i	0.562620	−	0.826716i	$-0.309793\pi$
$821$	18.2378	+	4.88681i	0.636505	+	0.170551i	0.0738852	+	0.997267i	$0.476460\pi$
$822$	4.71333	+	3.34556i	0.164396	+	0.116690i
$823$	−6.80437	+	11.7855i	−0.237185	+	0.410817i	−0.959906	−	0.280324i	$-0.909558\pi$
$823$	−6.80437	+	11.7855i	−0.237185	+	0.410817i	0.722720	+	0.691141i	$0.242892\pi$
$824$	−14.9094	−	27.0108i	−0.519394	−	0.940966i
$825$	1.56881	+	5.85487i	0.0546189	+	0.203841i
$826$	−20.3227	−	24.5375i	−0.707117	−	0.853768i
$827$	17.0815	−	17.0815i	0.593982	−	0.593982i	−0.344723	−	0.938705i	$-0.612027\pi$
$827$	17.0815	−	17.0815i	0.593982	−	0.593982i	0.938705	+	0.344723i	$0.112027\pi$
$828$	37.5987	−	13.1412i	1.30664	−	0.456690i
$829$	−23.8014	+	13.7417i	−0.826657	+	0.477270i	−0.852707	−	0.522390i	$-0.825040\pi$
$829$	−23.8014	+	13.7417i	−0.826657	+	0.477270i	0.0260500	+	0.999661i	$0.491707\pi$
$830$	−0.544355	−	3.20732i	−0.0188948	−	0.111328i
$831$	10.8241			0.375485
$832$	25.9848	+	12.5215i	0.900862	+	0.434105i
$833$	0.0110551			0.000383038
$834$	1.39615	+	8.22604i	0.0483446	+	0.284844i
$835$	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
$838$	5.05615	+	6.10476i	0.174662	+	0.210885i
$839$	−10.3356	−	38.5731i	−0.356825	−	1.33169i	−0.878172	−	0.478345i	$-0.841237\pi$
$839$	−10.3356	−	38.5731i	−0.356825	−	1.33169i	0.521347	−	0.853345i	$-0.325430\pi$
$840$	−0.723001	−	1.30983i	−0.0249459	−	0.0451935i
$841$	5.59382	−	9.68878i	0.192890	−	0.334096i
$842$	5.79552	+	4.11370i	0.199727	+	0.141767i
$843$	17.9349	+	4.80564i	0.617711	+	0.165515i
$844$	−5.46913	+	6.35064i	−0.188255	+	0.218598i
$845$	1.62335	−	2.59307i	0.0558449	−	0.0892045i
$846$	−11.6062	+	5.32172i	−0.399029	+	0.182964i
$847$	−6.10491	+	22.7839i	−0.209767	+	0.782862i
$848$	−18.6014	+	14.8123i	−0.638774	+	0.508657i
$849$	−15.2309	−	8.79359i	−0.522725	−	0.301795i
$850$	−9.17283	−	3.40540i	−0.314625	−	0.116804i
$851$	−4.37216	+	1.17152i	−0.149876	+	0.0401590i
$852$	8.02455	−	16.6479i	0.274916	−	0.570348i
$853$	−6.78242	−	6.78242i	−0.232226	−	0.232226i	0.581395	−	0.813621i	$-0.302507\pi$
$853$	−6.78242	−	6.78242i	−0.232226	−	0.232226i	−0.813621	+	0.581395i	$0.802507\pi$
$854$	2.52630	−	26.8888i	0.0864482	−	0.920114i
$855$	1.49586	+	2.59090i	0.0511572	+	0.0886068i
$856$	23.8710	+	14.4012i	0.815894	+	0.492221i
$857$		−	25.7579i		−	0.879872i	−0.898029	−	0.439936i	$-0.855001\pi$
$857$		−	25.7579i		−	0.879872i	0.898029	−	0.439936i	$-0.144999\pi$
$858$	5.35177	−	3.22950i	0.182706	−	0.110253i
$859$			51.8251i			1.76825i	0.467252	+	0.884124i	$0.345244\pi$
$859$			51.8251i			1.76825i	−0.467252	+	0.884124i	$0.654756\pi$
$860$	−2.43456	−	3.57359i	−0.0830177	−	0.121858i
$861$	−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	−0.975467	−	0.220144i	$-0.929347\pi$
$863$	−35.1233	−	35.1233i	−1.19561	−	1.19561i	−0.220144	−	0.975467i	$-0.570653\pi$
$864$	−16.9267	+	18.9069i	−0.575859	+	0.643227i
$865$	−0.491171	+	0.131609i	−0.0167003	+	0.00447483i
$866$	2.69363	−	7.25558i	0.0915332	−	0.246555i
$867$	−11.0734	−	6.39322i	−0.376072	−	0.217125i
$868$	5.40654	−	28.5184i	0.183510	−	0.967976i
$869$	−3.17877	+	11.8633i	−0.107833	+	0.402436i
$870$	0.497646	+	1.08532i	0.0168718	+	0.0367958i
$871$	−8.99342	−	1.34792i	−0.304730	−	0.0456725i
$872$	−0.0934525	−	0.0269775i	−0.00316470	−	0.000913575i
$873$	34.0382	+	9.12050i	1.15202	+	0.308682i
$874$	39.9557	−	56.2910i	1.35152	−	1.90407i
$875$	−3.09414	+	5.35921i	−0.104601	+	0.181174i
$876$	−12.1178	+	0.903738i	−0.409421	+	0.0305345i
$877$	9.61256	+	35.8746i	0.324593	+	1.21140i	0.914720	+	0.404088i	$0.132411\pi$
$877$	9.61256	+	35.8746i	0.324593	+	1.21140i	−0.590127	+	0.807310i	$0.700922\pi$
$878$	33.2262	−	27.5190i	1.12133	−	0.928720i
$879$	−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	−0.528862	−	0.848708i	$-0.677381\pi$
$881$	−1.73014	+	0.998897i	−0.0582899	+	0.0336537i	0.470572	+	0.882362i	$0.344048\pi$
$882$	−0.0250879	+	0.00425798i	−0.000844752	+	0.000143374i
$883$	16.1625			0.543913			0.271956	−	0.962310i	$-0.412329\pi$
$883$	16.1625			0.543913			0.271956	+	0.962310i	$0.412329\pi$
$884$	−0.749296	+	10.0622i	−0.0252016	+	0.338429i
$885$	1.70433			0.0572906
$886$	17.9853	−	3.05251i	0.604228	−	0.102551i
$887$	−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
$890$	1.70276	−	1.41027i	0.0570765	−	0.0472725i
$891$	−1.12682	−	4.20534i	−0.0377498	−	0.140884i
$892$	−2.80066	−	37.5526i	−0.0937730	−	1.25735i
$893$	−11.0645	+	19.1644i	−0.370261	+	0.641311i
$894$	−10.5467	+	14.8586i	−0.352735	+	0.496945i
$895$	2.30330	+	0.617167i	0.0769908	+	0.0206296i
$896$	−3.94203	+	29.6555i	−0.131694	+	0.990721i
$897$	10.6968	−	24.5729i	0.357157	−	0.820466i
$898$	5.81779	+	12.6881i	0.194142	+	0.423407i
$899$	−5.99536	+	22.3750i	−0.199956	+	0.746247i
$900$	22.1279	+	4.19503i	0.737596	+	0.139834i
$901$	−7.20357	−	4.15898i	−0.239986	−	0.138556i
$902$	−4.11375	+	11.0808i	−0.136973	+	0.368951i
$903$	−19.9468	+	5.34473i	−0.663788	+	0.177861i
$904$	12.8762	+	0.247729i	0.428257	+	0.00823935i
$905$	−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	0.999909	−	0.0134769i	$-0.00428995\pi$
$907$	14.7054	+	25.4704i	0.488283	+	0.845731i	−0.511626	+	0.859208i	$0.670957\pi$
$908$	−12.2972	+	8.37763i	−0.408097	+	0.278022i
$909$		−	20.8944i		−	0.693024i
$910$	3.08019	+	0.761776i	0.102107	+	0.0252526i
$911$			20.5091i			0.679495i	0.940517	+	0.339748i	$0.110342\pi$
$911$			20.5091i			0.679495i	−0.940517	+	0.339748i	$0.889658\pi$
$912$	−2.13859	+	18.8592i	−0.0708160	+	0.624490i
$913$	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
$916$	8.09513	+	3.90198i	0.267471	+	0.128925i
$917$	−28.6713	+	7.68245i	−0.946810	+	0.253697i
$918$	−8.32211	−	3.08958i	−0.274671	−	0.101971i
$919$	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
$921$	5.07665	−	18.9463i	0.167281	−	0.624302i
$922$	−36.9391	+	16.9375i	−1.21652	+	0.557806i
$923$	14.3496	+	36.4733i	0.472323	+	1.20053i
$924$	4.91240	+	4.23053i	0.161606	+	0.139174i
$925$	−2.47231	−	0.662453i	−0.0812890	−	0.0217813i
$926$	9.60708	+	6.81917i	0.315708	+	0.224092i
$927$	−12.4211	+	21.5139i	−0.407962	+	0.706610i
$928$	4.89734	−	23.3669i	0.160763	−	0.767056i
$929$	−1.77316	−	6.61751i	−0.0581754	−	0.217113i	0.930719	−	0.365736i	$-0.119183\pi$
$929$	−1.77316	−	6.61751i	−0.0581754	−	0.217113i	−0.988894	+	0.148623i	$0.952516\pi$
$930$	0.990419	+	1.19583i	0.0324771	+	0.0392127i
$931$	−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
$934$	−0.781702	−	4.60576i	−0.0255781	−	0.150705i
$935$	−0.474867			−0.0155298
$936$	−2.17514	−	23.1232i	−0.0710968	−	0.755806i
$937$	11.1107			0.362970			0.181485	−	0.983394i	$-0.441910\pi$
$937$	11.1107			0.362970			0.181485	+	0.983394i	$0.441910\pi$
$938$	−1.57823	−	9.29885i	−0.0515309	−	0.303618i
$939$	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	$-0.907473\pi$
$941$	−20.5970	+	20.5970i	−0.671442	+	0.671442i	0.286606	+	0.958048i	$0.407473\pi$
$942$	4.52725	+	5.46617i	0.147506	+	0.178098i
$943$	13.1165	+	48.9513i	0.427131	+	1.59407i
$944$	−27.4059	−	20.2568i	−0.891988	−	0.659304i
$945$	−1.39577	+	2.41755i	−0.0454045	+	0.0786430i
$946$	15.2792	+	10.8453i	0.496770	+	0.352611i
$947$	−28.3374	−	7.59297i	−0.920841	−	0.246739i	−0.232896	−	0.972502i	$-0.574820\pi$
$947$	−28.3374	−	7.59297i	−0.920841	−	0.246739i	−0.687945	+	0.725763i	$0.741487\pi$
$948$	−10.9712	−	9.44830i	−0.356327	−	0.306867i
$949$	16.0511	−	20.1617i	0.521041	−	0.654477i
$950$	35.4820	−	16.2694i	1.15119	−	0.527848i
$951$	−5.13516	+	19.1647i	−0.166519	+	0.621457i
$952$	−10.1587	+	2.51361i	−0.329246	+	0.0814667i
$953$	−11.3638	−	6.56091i	−0.368110	−	0.212529i	0.304522	−	0.952505i	$-0.401503\pi$
$953$	−11.3638	−	6.56091i	−0.368110	−	0.212529i	−0.672633	+	0.739977i	$0.734837\pi$
$954$	17.9492	+	6.66363i	0.581128	+	0.215743i
$955$	−0.879806	+	0.235743i	−0.0284699	+	0.00762847i
$956$	−15.2017	−	7.32748i	−0.491659	−	0.236987i
$957$	−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
$960$	−1.08724	−	1.17429i	−0.0350905	−	0.0379001i
$961$		−	0.875747i		−	0.0282499i
$962$	0.0510693	+	2.63895i	0.00164654	+	0.0850832i
$963$		−	22.4477i		−	0.723365i
$964$	25.5662	−	17.4173i	0.823432	−	0.560975i
$965$	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	0.465478	−	0.885059i	$-0.345882\pi$
$967$	−13.0476	−	13.0476i	−0.419581	−	0.419581i	−0.885059	+	0.465478i	$0.845882\pi$
$968$	−0.485325	+	25.2258i	−0.0155989	+	0.810787i
$969$	−6.41320	+	1.71841i	−0.206022	+	0.0552033i
$970$	−1.79225	+	4.82762i	−0.0575457	+	0.155006i
$971$	−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
$973$	4.75009	−	17.7276i	0.152281	−	0.568320i
$974$	6.08146	+	13.2631i	0.194862	+	0.424978i
$975$	12.1859	−	9.00923i	0.390262	−	0.288526i
$976$	−4.28511	−	28.5686i	−0.137163	−	0.914459i
$977$	0.239374	+	0.0641402i	0.00765826	+	0.00205203i	0.262646	−	0.964892i	$-0.415405\pi$
$977$	0.239374	+	0.0641402i	0.00765826	+	0.00205203i	−0.254988	+	0.966944i	$0.582071\pi$
$978$	−10.9472	+	15.4228i	−0.350053	+	0.493166i
$979$	−4.79020	+	8.29687i	−0.153095	+	0.265169i
$980$	−0.000276564	−	0.00370830i	−8.83450e−6	−	0.000118457i
$981$	0.0202707	+	0.0756511i	0.000647192	+	0.00241535i
$982$	−14.8396	+	12.2906i	−0.473551	+	0.392210i
$983$	−8.44991	+	8.44991i	−0.269510	+	0.269510i	−0.828903	−	0.559393i	$-0.811034\pi$
$983$	−8.44991	+	8.44991i	−0.269510	+	0.269510i	0.559393	+	0.828903i	$0.311034\pi$
$984$	−9.66159	−	10.0406i	−0.308000	−	0.320084i
$985$	2.52321	−	1.45678i	0.0803963	−	0.0464168i
$986$	8.23384	−	1.39747i	0.262219	−	0.0445045i
$987$	−8.91069			−0.283630
$988$	−26.2709	−	30.4983i	−0.835789	−	0.970280i
$989$	80.3360			2.55454
$990$	1.07763	−	0.182899i	0.0342494	−	0.00581291i
$991$	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
$994$	−31.3075	+	25.9298i	−0.993013	+	0.822444i
$995$	−0.148248	−	0.553269i	−0.00469978	−	0.0175398i
$996$	−16.5723	+	1.23595i	−0.525112	+	0.0391627i
$997$	−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
$999$	−2.24302	−	0.601015i	−0.0709660	−	0.0190153i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
52.2.l.b.7.3	✓	16	52.7	even	12	inner
52.2.l.b.7.4	yes	16	13.7	odd	12	inner
52.2.l.b.15.3	yes	16	1.1	even	1	trivial
52.2.l.b.15.4	yes	16	4.3	odd	2	inner
468.2.cb.f.163.1		16	39.20	even	12
468.2.cb.f.163.2		16	156.59	odd	12
468.2.cb.f.379.1		16	12.11	even	2
468.2.cb.f.379.2		16	3.2	odd	2
676.2.f.h.99.1		16	52.11	even	12
676.2.f.h.99.6		16	13.11	odd	12
676.2.f.h.239.1		16	13.3	even	3
676.2.f.h.239.6		16	52.3	odd	6
676.2.f.i.99.3		16	13.2	odd	12
676.2.f.i.99.8		16	52.15	even	12
676.2.f.i.239.3		16	52.23	odd	6
676.2.f.i.239.8		16	13.10	even	6
676.2.l.i.19.2		16	13.4	even	6
676.2.l.i.19.4		16	52.43	odd	6
676.2.l.i.427.2		16	52.31	even	4
676.2.l.i.427.4		16	13.5	odd	4
676.2.l.k.319.1		16	13.6	odd	12
676.2.l.k.319.2		16	52.19	even	12
676.2.l.k.587.1		16	52.51	odd	2
676.2.l.k.587.2		16	13.12	even	2
676.2.l.m.19.1		16	52.35	odd	6
676.2.l.m.19.3		16	13.9	even	3
676.2.l.m.427.1		16	13.8	odd	4
676.2.l.m.427.3		16	52.47	even	4
832.2.bu.n.319.2		16	104.59	even	12
832.2.bu.n.319.3		16	104.85	odd	12
832.2.bu.n.639.2		16	8.5	even	2
832.2.bu.n.639.3		16	8.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 52 = 2^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	52.l (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.236640 + 1.39427i) q^{2} +(0.736159 - 0.425021i) q^{3} +(-1.88800 + 0.659882i) q^{4} +(-0.166404 + 0.166404i) q^{5} +(0.766801 + 0.925830i) q^{6} +(-0.684384 - 2.55416i) q^{7} +(-1.36683 - 2.47624i) q^{8} +(-1.13871 + 1.97231i) q^{9} +O(q^{10})\)	\(q+(0.236640 + 1.39427i) q^{2} +(0.736159 - 0.425021i) q^{3} +(-1.88800 + 0.659882i) q^{4} +(-0.166404 + 0.166404i) q^{5} +(0.766801 + 0.925830i) q^{6} +(-0.684384 - 2.55416i) q^{7} +(-1.36683 - 2.47624i) q^{8} +(-1.13871 + 1.97231i) q^{9} +(-0.271390 - 0.192635i) q^{10} +(1.39298 + 0.373247i) q^{11} +(-1.10941 + 1.28822i) q^{12} +(-0.406663 - 3.58254i) q^{13} +(3.39924 - 1.55864i) q^{14} +(-0.0517744 + 0.193225i) q^{15} +(3.12911 - 2.49172i) q^{16} +(1.21178 + 0.699622i) q^{17} +(-3.01941 - 1.12095i) q^{18} +(-5.39188 + 1.44475i) q^{19} +(0.204364 - 0.423978i) q^{20} +(-1.58939 - 1.58939i) q^{21} +(-0.190775 + 2.03052i) q^{22} +(4.37216 + 7.57279i) q^{23} +(-2.05866 - 1.24197i) q^{24} +4.94462i q^{25} +(4.89882 - 1.41477i) q^{26} +4.48604i q^{27} +(2.97756 + 4.37064i) q^{28} +(-2.11023 - 3.65503i) q^{29} +(-0.281660 - 0.0264630i) q^{30} +(-3.88100 - 3.88100i) q^{31} +(4.21461 + 3.77320i) q^{32} +(1.18409 - 0.317276i) q^{33} +(-0.688709 + 1.85511i) q^{34} +(0.538906 + 0.311137i) q^{35} +(0.848402 - 4.47514i) q^{36} +(-0.133975 + 0.500000i) q^{37} +(-3.29032 - 7.17588i) q^{38} +(-1.82203 - 2.46448i) q^{39} +(0.639502 + 0.184609i) q^{40} +(5.59808 + 1.50000i) q^{41} +(1.83993 - 2.59215i) q^{42} +(4.59362 - 7.95638i) q^{43} +(-2.87624 + 0.214509i) q^{44} +(-0.138714 - 0.517686i) q^{45} +(-9.52393 + 7.88801i) q^{46} +(2.80318 - 2.80318i) q^{47} +(1.24449 - 3.16424i) q^{48} +(0.00684229 - 0.00395040i) q^{49} +(-6.89416 + 1.17009i) q^{50} +1.18942 q^{51} +(3.13184 + 6.49551i) q^{52} -5.94462 q^{53} +(-6.25477 + 1.06158i) q^{54} +(-0.293906 + 0.169687i) q^{55} +(-5.38927 + 5.18581i) q^{56} +(-3.35523 + 3.35523i) q^{57} +(4.59675 - 3.80717i) q^{58} +(-2.20512 - 8.22961i) q^{59} +(-0.0297554 - 0.398974i) q^{60} +(3.61102 - 6.25448i) q^{61} +(4.49277 - 6.32957i) q^{62} +(5.81691 + 1.55864i) q^{63} +(-4.26353 + 6.76922i) q^{64} +(0.663819 + 0.528479i) q^{65} +(0.722573 + 1.57587i) q^{66} +(0.652790 - 2.43624i) q^{67} +(-2.74951 - 0.521255i) q^{68} +(6.43720 + 3.71652i) q^{69} +(-0.306284 + 0.825010i) q^{70} +(-10.5002 + 2.81352i) q^{71} +(6.44034 + 0.123908i) q^{72} +(5.05407 + 5.05407i) q^{73} +(-0.728841 - 0.0684774i) q^{74} +(2.10157 + 3.64002i) q^{75} +(9.22653 - 6.28570i) q^{76} -3.81333i q^{77} +(3.00500 - 3.12360i) q^{78} +8.51654i q^{79} +(-0.106064 + 0.935328i) q^{80} +(-1.50948 - 2.61449i) q^{81} +(-0.766683 + 8.16022i) q^{82} +(6.91195 + 6.91195i) q^{83} +(4.04958 + 1.95196i) q^{84} +(-0.318065 + 0.0852251i) q^{85} +(12.1804 + 4.52197i) q^{86} +(-3.10694 - 1.79379i) q^{87} +(-0.979719 - 3.95951i) q^{88} +(-1.71941 + 6.41693i) q^{89} +(0.688971 - 0.315910i) q^{90} +(-8.87207 + 3.49052i) q^{91} +(-13.2518 - 11.4124i) q^{92} +(-4.50653 - 1.20752i) q^{93} +(4.57175 + 3.24506i) q^{94} +(0.656818 - 1.13764i) q^{95} +(4.70632 + 0.986372i) q^{96} +(-4.00474 - 14.9459i) q^{97} +(0.00712710 + 0.00860521i) q^{98} +(-2.32236 + 2.32236i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 2 q^{2} - 6 q^{4} - 12 q^{5} - 14 q^{6} + 10 q^{8} + 4 q^{9}+O(q^{10}) \) 16 * q - 2 * q^2 - 6 * q^4 - 12 * q^5 - 14 * q^6 + 10 * q^8 + 4 * q^9	\( 16 q - 2 q^{2} - 6 q^{4} - 12 q^{5} - 14 q^{6} + 10 q^{8} + 4 q^{9} - 12 q^{13} + 8 q^{14} - 2 q^{16} + 12 q^{17} - 6 q^{18} + 2 q^{20} - 28 q^{21} + 10 q^{24} + 16 q^{26} + 12 q^{28} - 8 q^{29} + 42 q^{30} + 28 q^{32} - 20 q^{33} + 14 q^{34} - 6 q^{36} - 16 q^{37} - 40 q^{40} + 48 q^{41} - 28 q^{42} - 8 q^{44} + 20 q^{45} - 46 q^{46} - 10 q^{48} + 60 q^{49} + 10 q^{50} - 32 q^{52} - 32 q^{53} - 16 q^{54} - 60 q^{56} + 12 q^{57} - 48 q^{58} - 24 q^{60} + 4 q^{61} - 18 q^{62} - 8 q^{65} + 56 q^{66} + 16 q^{68} - 12 q^{69} + 28 q^{70} + 56 q^{72} + 20 q^{73} + 4 q^{74} + 22 q^{76} + 68 q^{78} + 44 q^{80} + 48 q^{81} + 84 q^{84} + 20 q^{85} + 16 q^{86} + 36 q^{88} - 52 q^{89} - 12 q^{92} - 92 q^{93} - 38 q^{94} - 72 q^{96} - 28 q^{97} - 2 q^{98}+O(q^{100}) \) 16 * q - 2 * q^2 - 6 * q^4 - 12 * q^5 - 14 * q^6 + 10 * q^8 + 4 * q^9 - 12 * q^13 + 8 * q^14 - 2 * q^16 + 12 * q^17 - 6 * q^18 + 2 * q^20 - 28 * q^21 + 10 * q^24 + 16 * q^26 + 12 * q^28 - 8 * q^29 + 42 * q^30 + 28 * q^32 - 20 * q^33 + 14 * q^34 - 6 * q^36 - 16 * q^37 - 40 * q^40 + 48 * q^41 - 28 * q^42 - 8 * q^44 + 20 * q^45 - 46 * q^46 - 10 * q^48 + 60 * q^49 + 10 * q^50 - 32 * q^52 - 32 * q^53 - 16 * q^54 - 60 * q^56 + 12 * q^57 - 48 * q^58 - 24 * q^60 + 4 * q^61 - 18 * q^62 - 8 * q^65 + 56 * q^66 + 16 * q^68 - 12 * q^69 + 28 * q^70 + 56 * q^72 + 20 * q^73 + 4 * q^74 + 22 * q^76 + 68 * q^78 + 44 * q^80 + 48 * q^81 + 84 * q^84 + 20 * q^85 + 16 * q^86 + 36 * q^88 - 52 * q^89 - 12 * q^92 - 92 * q^93 - 38 * q^94 - 72 * q^96 - 28 * q^97 - 2 * q^98

Introduction

L-functions

Modular forms

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