LMFDB - Embedded newform 600.2.k.f.301.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [600,2,Mod(301,600)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(600, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1, 0, 0]))

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

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

chi := DirichletCharacter("600.301");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 600 = 2^{3} \cdot 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	600.k (of order $2$, degree $1$, 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:	$4.79102412128$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	12.0.180227832610816.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + x^{10} - 8x^{6} + 16x^{2} + 64 $ x^12 + x^10 - 8x^6 + 16x^2 + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{8} $
Twist minimal:	no (minimal twist has level 120)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			301.6
Root			$-0.450129 + 1.34067i$ of defining polynomial
Character	$\chi$	$=$	600.301
Dual form			600.2.k.f.301.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.450129 + 1.34067i) q^{2} +1.00000i q^{3} +(-1.59477 - 1.20695i) q^{4} +(-1.34067 - 0.450129i) q^{6} +2.64265 q^{7} +(2.33596 - 1.59477i) q^{8} -1.00000 q^{9} +O(q^{10})$	\(q+(-0.450129 + 1.34067i) q^{2} +1.00000i q^{3} +(-1.59477 - 1.20695i) q^{4} +(-1.34067 - 0.450129i) q^{6} +2.64265 q^{7} +(2.33596 - 1.59477i) q^{8} -1.00000 q^{9} -1.51363i q^{11} +(1.20695 - 1.59477i) q^{12} +3.87086i q^{13} +(-1.18953 + 3.54291i) q^{14} +(1.08656 + 3.84959i) q^{16} +3.31415 q^{17} +(0.450129 - 1.34067i) q^{18} +7.08582i q^{19} +2.64265i q^{21} +(2.02927 + 0.681331i) q^{22} +4.82778 q^{23} +(1.59477 + 2.33596i) q^{24} +(-5.18953 - 1.74239i) q^{26} -1.00000i q^{27} +(-4.21441 - 3.18953i) q^{28} -2.18513i q^{29} -7.36266 q^{31} +(-5.65011 - 0.276098i) q^{32} +1.51363 q^{33} +(-1.49180 + 4.44317i) q^{34} +(1.59477 + 1.20695i) q^{36} +7.87086i q^{37} +(-9.49971 - 3.18953i) q^{38} -3.87086 q^{39} +8.72532 q^{41} +(-3.54291 - 1.18953i) q^{42} +1.01641i q^{43} +(-1.82687 + 2.41389i) q^{44} +(-2.17313 + 6.47244i) q^{46} -7.08582 q^{47} +(-3.84959 + 1.08656i) q^{48} -0.0164068 q^{49} +3.31415i q^{51} +(4.67192 - 6.17313i) q^{52} +4.50820i q^{53} +(1.34067 + 0.450129i) q^{54} +(6.17313 - 4.21441i) q^{56} -7.08582 q^{57} +(2.92953 + 0.983593i) q^{58} -6.79893i q^{59} -3.60104i q^{61} +(3.31415 - 9.87086i) q^{62} -2.64265 q^{63} +(2.91344 - 7.45063i) q^{64} +(-0.681331 + 2.02927i) q^{66} +1.01641i q^{67} +(-5.28530 - 4.00000i) q^{68} +4.82778i q^{69} -6.72532 q^{71} +(-2.33596 + 1.59477i) q^{72} +15.5146 q^{73} +(-10.5522 - 3.54291i) q^{74} +(8.55220 - 11.3002i) q^{76} -4.00000i q^{77} +(1.74239 - 5.18953i) q^{78} -7.36266 q^{79} +1.00000 q^{81} +(-3.92752 + 11.6977i) q^{82} +7.74173i q^{83} +(3.18953 - 4.21441i) q^{84} +(-1.36266 - 0.457515i) q^{86} +2.18513 q^{87} +(-2.41389 - 3.53579i) q^{88} +14.7581 q^{89} +10.2293i q^{91} +(-7.69919 - 5.82687i) q^{92} -7.36266i q^{93} +(3.18953 - 9.49971i) q^{94} +(0.276098 - 5.65011i) q^{96} +11.1444 q^{97} +(0.00738516 - 0.0219960i) q^{98} +1.51363i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 2 q^{4} - 2 q^{6} - 12 q^{9}+O(q^{10}) $ 12 * q - 2 * q^4 - 2 * q^6 - 12 * q^9	$ 12 q - 2 q^{4} - 2 q^{6} - 12 q^{9} + 20 q^{14} + 2 q^{16} + 2 q^{24} - 28 q^{26} - 32 q^{31} - 24 q^{34} + 2 q^{36} + 16 q^{39} - 8 q^{41} - 44 q^{44} - 4 q^{46} + 12 q^{49} + 2 q^{54} + 52 q^{56} + 46 q^{64} + 20 q^{66} + 32 q^{71} - 36 q^{74} + 12 q^{76} - 32 q^{79} + 12 q^{81} + 4 q^{84} + 40 q^{86} + 40 q^{89} + 4 q^{94} - 42 q^{96}+O(q^{100}) $ 12 * q - 2 * q^4 - 2 * q^6 - 12 * q^9 + 20 * q^14 + 2 * q^16 + 2 * q^24 - 28 * q^26 - 32 * q^31 - 24 * q^34 + 2 * q^36 + 16 * q^39 - 8 * q^41 - 44 * q^44 - 4 * q^46 + 12 * q^49 + 2 * q^54 + 52 * q^56 + 46 * q^64 + 20 * q^66 + 32 * q^71 - 36 * q^74 + 12 * q^76 - 32 * q^79 + 12 * q^81 + 4 * q^84 + 40 * q^86 + 40 * q^89 + 4 * q^94 - 42 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/600\mathbb{Z}\right)^\times$.

$n$	$151$	$301$	$401$	$577$
$\chi(n)$	$1$	$-1$	$1$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.450129	+	1.34067i	−0.318290	+	0.947994i
$2$	−0.450129	+	1.34067i	−0.318290	+	0.947994i
$3$			1.00000i			0.577350i
$3$			1.00000i			0.577350i
$4$	−1.59477	−	1.20695i	−0.797384	−	0.603473i
$5$		0			0
$5$		0			0
$6$	−1.34067	−	0.450129i	−0.547324	−	0.183765i
$7$	2.64265			0.998827			0.499414	−	0.866364i	$-0.333549\pi$
$7$	2.64265			0.998827			0.499414	+	0.866364i	$0.333549\pi$
$8$	2.33596	−	1.59477i	0.825887	−	0.563835i
$9$	−1.00000			−0.333333
$10$		0			0
$11$		−	1.51363i		−	0.456377i	−0.973617	−	0.228189i	$-0.926720\pi$
$11$		−	1.51363i		−	0.456377i	0.973617	−	0.228189i	$-0.0732803\pi$
$12$	1.20695	−	1.59477i	0.348415	−	0.460370i
$13$			3.87086i			1.07358i	0.843714	+	0.536792i	$0.180364\pi$
$13$			3.87086i			1.07358i	−0.843714	+	0.536792i	$0.819636\pi$
$14$	−1.18953	+	3.54291i	−0.317916	+	0.946882i
$15$		0			0
$16$	1.08656	+	3.84959i	0.271641	+	0.962399i
$17$	3.31415			0.803800			0.401900	−	0.915684i	$-0.368350\pi$
$17$	3.31415			0.803800			0.401900	+	0.915684i	$0.368350\pi$
$18$	0.450129	−	1.34067i	0.106097	−	0.315998i
$19$			7.08582i			1.62560i	0.582545	+	0.812799i	$0.302057\pi$
$19$			7.08582i			1.62560i	−0.582545	+	0.812799i	$0.697943\pi$
$20$		0			0
$21$			2.64265i			0.576673i
$22$	2.02927	+	0.681331i	0.432643	+	0.145260i
$23$	4.82778			1.00666			0.503331	−	0.864094i	$-0.332108\pi$
$23$	4.82778			1.00666			0.503331	+	0.864094i	$0.332108\pi$
$24$	1.59477	+	2.33596i	0.325530	+	0.476826i
$25$		0			0
$26$	−5.18953	−	1.74239i	−1.01775	−	0.341711i
$27$		−	1.00000i		−	0.192450i
$28$	−4.21441	−	3.18953i	−0.796448	−	0.602765i
$29$		−	2.18513i		−	0.405769i	−0.979203	−	0.202885i	$-0.934968\pi$
$29$		−	2.18513i		−	0.405769i	0.979203	−	0.202885i	$-0.0650316\pi$
$30$		0			0
$31$	−7.36266			−1.32237			−0.661187	−	0.750222i	$-0.729947\pi$
$31$	−7.36266			−1.32237			−0.661187	+	0.750222i	$0.729947\pi$
$32$	−5.65011	−	0.276098i	−0.998808	−	0.0488076i
$33$	1.51363			0.263490
$34$	−1.49180	+	4.44317i	−0.255841	+	0.761997i
$35$		0			0
$36$	1.59477	+	1.20695i	0.265795	+	0.201158i
$37$			7.87086i			1.29396i	0.762506	+	0.646981i	$0.223969\pi$
$37$			7.87086i			1.29396i	−0.762506	+	0.646981i	$0.776031\pi$
$38$	−9.49971	−	3.18953i	−1.54106	−	0.517411i
$39$	−3.87086			−0.619834
$40$		0			0
$41$	8.72532			1.36267			0.681333	−	0.731973i	$-0.261400\pi$
$41$	8.72532			1.36267			0.681333	+	0.731973i	$0.261400\pi$
$42$	−3.54291	−	1.18953i	−0.546683	−	0.183549i
$43$			1.01641i			0.155001i	0.996992	+	0.0775003i	$0.0246939\pi$
$43$			1.01641i			0.155001i	−0.996992	+	0.0775003i	$0.975306\pi$
$44$	−1.82687	+	2.41389i	−0.275411	+	0.363908i
$45$		0			0
$46$	−2.17313	+	6.47244i	−0.320410	+	0.954309i
$47$	−7.08582			−1.03357			−0.516786	−	0.856114i	$-0.672872\pi$
$47$	−7.08582			−1.03357			−0.516786	+	0.856114i	$0.672872\pi$
$48$	−3.84959	+	1.08656i	−0.555641	+	0.156832i
$49$	−0.0164068			−0.00234382
$50$		0			0
$51$			3.31415i			0.464074i
$52$	4.67192	−	6.17313i	0.647879	−	0.856059i
$53$			4.50820i			0.619249i	0.950859	+	0.309625i	$0.100203\pi$
$53$			4.50820i			0.619249i	−0.950859	+	0.309625i	$0.899797\pi$
$54$	1.34067	+	0.450129i	0.182441	+	0.0612549i
$55$		0			0
$56$	6.17313	−	4.21441i	0.824919	−	0.563174i
$57$	−7.08582			−0.938539
$58$	2.92953	+	0.983593i	0.384667	+	0.129152i
$59$		−	6.79893i		−	0.885145i	−0.896733	−	0.442573i	$-0.854066\pi$
$59$		−	6.79893i		−	0.885145i	0.896733	−	0.442573i	$-0.145934\pi$
$60$		0			0
$61$		−	3.60104i		−	0.461065i	−0.973065	−	0.230533i	$-0.925953\pi$
$61$		−	3.60104i		−	0.461065i	0.973065	−	0.230533i	$-0.0740469\pi$
$62$	3.31415	−	9.87086i	0.420898	−	1.25360i
$63$	−2.64265			−0.332942
$64$	2.91344	−	7.45063i	0.364180	−	0.931329i
$65$		0			0
$66$	−0.681331	+	2.02927i	−0.0838660	+	0.249786i
$67$			1.01641i			0.124174i	0.998071	+	0.0620869i	$0.0197756\pi$
$67$			1.01641i			0.124174i	−0.998071	+	0.0620869i	$0.980224\pi$
$68$	−5.28530	−	4.00000i	−0.640937	−	0.485071i
$69$			4.82778i			0.581197i
$70$		0			0
$71$	−6.72532			−0.798149			−0.399074	−	0.916919i	$-0.630669\pi$
$71$	−6.72532			−0.798149			−0.399074	+	0.916919i	$0.630669\pi$
$72$	−2.33596	+	1.59477i	−0.275296	+	0.187945i
$73$	15.5146			1.81585			0.907925	−	0.419132i	$-0.137666\pi$
$73$	15.5146			1.81585			0.907925	+	0.419132i	$0.137666\pi$
$74$	−10.5522	−	3.54291i	−1.22667	−	0.411855i
$75$		0			0
$76$	8.55220	−	11.3002i	0.981004	−	1.29622i
$77$		−	4.00000i		−	0.455842i
$78$	1.74239	−	5.18953i	0.197287	−	0.587599i
$79$	−7.36266			−0.828364			−0.414182	−	0.910194i	$-0.635932\pi$
$79$	−7.36266			−0.828364			−0.414182	+	0.910194i	$0.635932\pi$
$80$		0			0
$81$	1.00000			0.111111
$82$	−3.92752	+	11.6977i	−0.433723	+	1.29180i
$83$			7.74173i			0.849765i	0.905248	+	0.424883i	$0.139685\pi$
$83$			7.74173i			0.849765i	−0.905248	+	0.424883i	$0.860315\pi$
$84$	3.18953	−	4.21441i	0.348007	−	0.459830i
$85$		0			0
$86$	−1.36266	−	0.457515i	−0.146940	−	0.0493351i
$87$	2.18513			0.234271
$88$	−2.41389	−	3.53579i	−0.257322	−	0.376916i
$89$	14.7581			1.56436			0.782180	−	0.623053i	$-0.214108\pi$
$89$	14.7581			1.56436			0.782180	+	0.623053i	$0.214108\pi$
$90$		0			0
$91$			10.2293i			1.07233i
$92$	−7.69919	−	5.82687i	−0.802696	−	0.607493i
$93$		−	7.36266i		−	0.763472i
$94$	3.18953	−	9.49971i	0.328975	−	0.979820i
$95$		0			0
$96$	0.276098	−	5.65011i	0.0281791	−	0.576662i
$97$	11.1444			1.13154			0.565769	−	0.824563i	$-0.308579\pi$
$97$	11.1444			1.13154			0.565769	+	0.824563i	$0.308579\pi$
$98$	0.00738516	−	0.0219960i	0.000746014	−	0.00222193i
$99$			1.51363i			0.152126i
$100$		0			0
$101$		−	13.3295i		−	1.32633i	−0.748471	−	0.663167i	$-0.769212\pi$
$101$		−	13.3295i		−	1.32633i	0.748471	−	0.663167i	$-0.230788\pi$
$102$	−4.44317	−	1.49180i	−0.439939	−	0.147710i
$103$	−0.958386			−0.0944326			−0.0472163	−	0.998885i	$-0.515035\pi$
$103$	−0.958386			−0.0944326			−0.0472163	+	0.998885i	$0.515035\pi$
$104$	6.17313	+	9.04219i	0.605325	+	0.886660i
$105$		0			0
$106$	−6.04399	−	2.02927i	−0.587044	−	0.197101i
$107$			4.00000i			0.386695i	0.981130	+	0.193347i	$0.0619344\pi$
$107$			4.00000i			0.386695i	−0.981130	+	0.193347i	$0.938066\pi$
$108$	−1.20695	+	1.59477i	−0.116138	+	0.153457i
$109$			0.769233i			0.0736792i	0.999321	+	0.0368396i	$0.0117291\pi$
$109$			0.769233i			0.0736792i	−0.999321	+	0.0368396i	$0.988271\pi$
$110$		0			0
$111$	−7.87086			−0.747069
$112$	2.87141	+	10.1731i	0.271322	+	0.961270i
$113$	−14.4585			−1.36014			−0.680071	−	0.733146i	$-0.738051\pi$
$113$	−14.4585			−1.36014			−0.680071	+	0.733146i	$0.738051\pi$
$114$	3.18953	−	9.49971i	0.298727	−	0.889729i
$115$		0			0
$116$	−2.63734	+	3.48478i	−0.244871	+	0.323554i
$117$		−	3.87086i		−	0.357862i
$118$	9.11509	+	3.06040i	0.839112	+	0.281733i
$119$	8.75814			0.802857
$120$		0			0
$121$	8.70892			0.791720
$122$	4.82778	+	1.62093i	0.437087	+	0.146752i
$123$			8.72532i			0.786736i
$124$	11.7417	+	8.88633i	1.05444	+	0.798016i
$125$		0			0
$126$	1.18953	−	3.54291i	0.105972	−	0.315627i
$127$	11.5290			1.02303			0.511516	−	0.859274i	$-0.329084\pi$
$127$	11.5290			1.02303			0.511516	+	0.859274i	$0.329084\pi$
$128$	8.67738	+	7.25969i	0.766979	+	0.641672i
$129$	−1.01641			−0.0894896
$130$		0			0
$131$			7.37270i			0.644156i	0.946713	+	0.322078i	$0.104381\pi$
$131$			7.37270i			0.644156i	−0.946713	+	0.322078i	$0.895619\pi$
$132$	−2.41389	−	1.82687i	−0.210102	−	0.159009i
$133$			18.7253i			1.62369i
$134$	−1.36266	−	0.457515i	−0.117716	−	0.0395232i
$135$		0			0
$136$	7.74173	−	5.28530i	0.663848	−	0.453211i
$137$	−3.88792			−0.332167			−0.166084	−	0.986112i	$-0.553112\pi$
$137$	−3.88792			−0.332167			−0.166084	+	0.986112i	$0.553112\pi$
$138$	−6.47244	−	2.17313i	−0.550971	−	0.184989i
$139$		−	14.6291i		−	1.24083i	−0.784275	−	0.620414i	$-0.786965\pi$
$139$		−	14.6291i		−	1.24083i	0.784275	−	0.620414i	$-0.213035\pi$
$140$		0			0
$141$		−	7.08582i		−	0.596733i
$142$	3.02727	−	9.01641i	0.254042	−	0.756640i
$143$	5.85907			0.489960
$144$	−1.08656	−	3.84959i	−0.0905470	−	0.320800i
$145$		0			0
$146$	−6.98359	+	20.7999i	−0.577966	+	1.72141i
$147$		−	0.0164068i		−	0.00135321i
$148$	9.49971	−	12.5522i	0.780871	−	1.03178i
$149$		−	11.0715i		−	0.907010i	−0.891254	−	0.453505i	$-0.850173\pi$
$149$		−	11.0715i		−	0.907010i	0.891254	−	0.453505i	$-0.149827\pi$
$150$		0			0
$151$	0.637339			0.0518659			0.0259329	−	0.999664i	$-0.491744\pi$
$151$	0.637339			0.0518659			0.0259329	+	0.999664i	$0.491744\pi$
$152$	11.3002	+	16.5522i	0.916569	+	1.34256i
$153$	−3.31415			−0.267933
$154$	5.36266	+	1.80052i	0.432136	+	0.145090i
$155$		0			0
$156$	6.17313	+	4.67192i	0.494246	+	0.374053i
$157$		−	0.129135i		−	0.0103061i	−0.999987	−	0.00515306i	$-0.998360\pi$
$157$		−	0.129135i		−	0.0103061i	0.999987	−	0.00515306i	$-0.00164028\pi$
$158$	3.31415	−	9.87086i	0.263660	−	0.785284i
$159$	−4.50820			−0.357524
$160$		0			0
$161$	12.7581			1.00548
$162$	−0.450129	+	1.34067i	−0.0353655	+	0.105333i
$163$		−	19.4835i		−	1.52606i	−0.646362	−	0.763031i	$-0.723710\pi$
$163$		−	19.4835i		−	1.52606i	0.646362	−	0.763031i	$-0.276290\pi$
$164$	−13.9149	−	10.5310i	−1.08657	−	0.822332i
$165$		0			0
$166$	−10.3791	−	3.48478i	−0.805572	−	0.270471i
$167$	1.80052			0.139328			0.0696641	−	0.997571i	$-0.477807\pi$
$167$	1.80052			0.139328			0.0696641	+	0.997571i	$0.477807\pi$
$168$	4.21441	+	6.17313i	0.325149	+	0.476267i
$169$	−1.98359			−0.152584
$170$		0			0
$171$		−	7.08582i		−	0.541866i
$172$	1.22675	−	1.62093i	0.0935386	−	0.123595i
$173$		−	23.2335i		−	1.76641i	−0.468985	−	0.883206i	$-0.655380\pi$
$173$		−	23.2335i		−	1.76641i	0.468985	−	0.883206i	$-0.344620\pi$
$174$	−0.983593	+	2.92953i	−0.0745660	+	0.222087i
$175$		0			0
$176$	5.82687	−	1.64466i	0.439217	−	0.123971i
$177$	6.79893			0.511039
$178$	−6.64307	+	19.7857i	−0.497919	+	1.48300i
$179$		−	2.85664i		−	0.213515i	−0.994285	−	0.106757i	$-0.965953\pi$
$179$		−	2.85664i		−	0.213515i	0.994285	−	0.106757i	$-0.0340468\pi$
$180$		0			0
$181$			5.28530i			0.392853i	0.980519	+	0.196427i	$0.0629337\pi$
$181$			5.28530i			0.392853i	−0.980519	+	0.196427i	$0.937066\pi$
$182$	−13.7141	−	4.60453i	−1.01656	−	0.341310i
$183$	3.60104			0.266196
$184$	11.2775	−	7.69919i	0.831390	−	0.567592i
$185$		0			0
$186$	9.87086	+	3.31415i	0.723767	+	0.243005i
$187$		−	5.01641i		−	0.366836i
$188$	11.3002	+	8.55220i	0.824154	+	0.623733i
$189$		−	2.64265i		−	0.192224i
$190$		0			0
$191$	−5.96719			−0.431770			−0.215885	−	0.976419i	$-0.569264\pi$
$191$	−5.96719			−0.431770			−0.215885	+	0.976419i	$0.569264\pi$
$192$	7.45063	+	2.91344i	0.537703	+	0.210259i
$193$	−14.9409			−1.07547			−0.537733	−	0.843115i	$-0.680719\pi$
$193$	−14.9409			−1.07547			−0.537733	+	0.843115i	$0.680719\pi$
$194$	−5.01641	+	14.9409i	−0.360157	+	1.07269i
$195$		0			0
$196$	0.0261649	+	0.0198021i	0.00186892	+	0.00141443i
$197$		−	3.23353i		−	0.230379i	−0.993344	−	0.115190i	$-0.963252\pi$
$197$		−	3.23353i		−	0.230379i	0.993344	−	0.115190i	$-0.0367476\pi$
$198$	−2.02927	−	0.681331i	−0.144214	−	0.0484201i
$199$	−8.12080			−0.575668			−0.287834	−	0.957680i	$-0.592935\pi$
$199$	−8.12080			−0.575668			−0.287834	+	0.957680i	$0.592935\pi$
$200$		0			0
$201$	−1.01641			−0.0716918
$202$	17.8704	+	6.00000i	1.25736	+	0.422159i
$203$		−	5.77454i		−	0.405293i
$204$	4.00000	−	5.28530i	0.280056	−	0.370045i
$205$		0			0
$206$	0.431398	−	1.28488i	0.0300569	−	0.0895215i
$207$	−4.82778			−0.335554
$208$	−14.9013	+	4.20594i	−1.03322	+	0.291630i
$209$	10.7253			0.741886
$210$		0			0
$211$		−	13.7141i		−	0.944119i	−0.881567	−	0.472059i	$-0.843511\pi$
$211$		−	13.7141i		−	0.944119i	0.881567	−	0.472059i	$-0.156489\pi$
$212$	5.44116	−	7.18953i	0.373700	−	0.493779i
$213$		−	6.72532i		−	0.460812i
$214$	−5.36266	−	1.80052i	−0.366584	−	0.123081i
$215$		0			0
$216$	−1.59477	−	2.33596i	−0.108510	−	0.158942i
$217$	−19.4569			−1.32082
$218$	−1.03128	−	0.346255i	−0.0698474	−	0.0234513i
$219$			15.5146i			1.04838i
$220$		0			0
$221$			12.8286i			0.862947i
$222$	3.54291	−	10.5522i	0.237784	−	0.708217i
$223$	−9.84472			−0.659251			−0.329626	−	0.944112i	$-0.606923\pi$
$223$	−9.84472			−0.659251			−0.329626	+	0.944112i	$0.606923\pi$
$224$	−14.9313	−	0.729629i	−0.997637	−	0.0487504i
$225$		0			0
$226$	6.50820	−	19.3840i	0.432919	−	1.28941i
$227$			5.70892i			0.378914i	0.981889	+	0.189457i	$0.0606728\pi$
$227$			5.70892i			0.378914i	−0.981889	+	0.189457i	$0.939327\pi$
$228$	11.3002	+	8.55220i	0.748376	+	0.566383i
$229$		−	0.769233i		−	0.0508324i	−0.999677	−	0.0254162i	$-0.991909\pi$
$229$		−	0.769233i		−	0.0508324i	0.999677	−	0.0254162i	$-0.00809109\pi$
$230$		0			0
$231$	4.00000			0.263181
$232$	−3.48478	−	5.10439i	−0.228787	−	0.335120i
$233$	18.4008			1.20548			0.602739	−	0.797939i	$-0.294076\pi$
$233$	18.4008			1.20548			0.602739	+	0.797939i	$0.294076\pi$
$234$	5.18953	+	1.74239i	0.339250	+	0.113904i
$235$		0			0
$236$	−8.20594	+	10.8427i	−0.534161	+	0.705800i
$237$		−	7.36266i		−	0.478256i
$238$	−3.94229	+	11.7417i	−0.255541	+	0.761103i
$239$	10.0328			0.648969			0.324484	−	0.945891i	$-0.394809\pi$
$239$	10.0328			0.648969			0.324484	+	0.945891i	$0.394809\pi$
$240$		0			0
$241$	10.7581			0.692992			0.346496	−	0.938051i	$-0.387371\pi$
$241$	10.7581			0.692992			0.346496	+	0.938051i	$0.387371\pi$
$242$	−3.92014	+	11.6757i	−0.251996	+	0.750545i
$243$			1.00000i			0.0641500i
$244$	−4.34625	+	5.74281i	−0.278240	+	0.367646i
$245$		0			0
$246$	−11.6977	−	3.92752i	−0.745820	−	0.250410i
$247$	−27.4282			−1.74522
$248$	−17.1989	+	11.7417i	−1.09213	+	0.745601i
$249$	−7.74173			−0.490612
$250$		0			0
$251$		−	12.6580i		−	0.798966i	−0.916741	−	0.399483i	$-0.869190\pi$
$251$		−	12.6580i		−	0.798966i	0.916741	−	0.399483i	$-0.130810\pi$
$252$	4.21441	+	3.18953i	0.265483	+	0.200922i
$253$		−	7.30749i		−	0.459418i
$254$	−5.18953	+	15.4565i	−0.325620	+	0.969827i
$255$		0			0
$256$	−13.6388	+	8.36566i	−0.852422	+	0.522854i
$257$	−13.3110			−0.830316			−0.415158	−	0.909749i	$-0.636274\pi$
$257$	−13.3110			−0.830316			−0.415158	+	0.909749i	$0.636274\pi$
$258$	0.457515	−	1.36266i	0.0284836	−	0.0848356i
$259$			20.7999i			1.29244i
$260$		0			0
$261$			2.18513i			0.135256i
$262$	−9.88432	−	3.31867i	−0.610656	−	0.205028i
$263$	−18.4256			−1.13617			−0.568087	−	0.822969i	$-0.692316\pi$
$263$	−18.4256			−1.13617			−0.568087	+	0.822969i	$0.692316\pi$
$264$	3.53579	−	2.41389i	0.217613	−	0.148565i
$265$		0			0
$266$	−25.1044	−	8.42882i	−1.53925	−	0.516804i
$267$			14.7581i			0.903183i
$268$	1.22675	−	1.62093i	0.0749356	−	0.0990142i
$269$		−	3.86940i		−	0.235921i	−0.993018	−	0.117961i	$-0.962364\pi$
$269$		−	3.86940i		−	0.235921i	0.993018	−	0.117961i	$-0.0376357\pi$
$270$		0			0
$271$	−17.3955			−1.05670			−0.528350	−	0.849027i	$-0.677189\pi$
$271$	−17.3955			−1.05670			−0.528350	+	0.849027i	$0.677189\pi$
$272$	3.60104	+	12.7581i	0.218345	+	0.773576i
$273$	−10.2293			−0.619108
$274$	1.75007	−	5.21240i	0.105725	−	0.314893i
$275$		0			0
$276$	5.82687	−	7.69919i	0.350737	−	0.463437i
$277$		−	0.887271i		−	0.0533110i	−0.999645	−	0.0266555i	$-0.991514\pi$
$277$		−	0.887271i		−	0.0533110i	0.999645	−	0.0266555i	$-0.00848571\pi$
$278$	19.6128	+	6.58501i	1.17630	+	0.394943i
$279$	7.36266			0.440791
$280$		0			0
$281$	−13.4835			−0.804356			−0.402178	−	0.915562i	$-0.631747\pi$
$281$	−13.4835			−0.804356			−0.402178	+	0.915562i	$0.631747\pi$
$282$	9.49971	+	3.18953i	0.565699	+	0.189934i
$283$		−	28.4342i		−	1.69024i	−0.534577	−	0.845120i	$-0.679529\pi$
$283$		−	28.4342i		−	1.69024i	0.534577	−	0.845120i	$-0.320471\pi$
$284$	10.7253	+	8.11710i	0.636431	+	0.481661i
$285$		0			0
$286$	−2.63734	+	7.85505i	−0.155949	+	0.464479i
$287$	23.0580			1.36107
$288$	5.65011	+	0.276098i	0.332936	+	0.0162692i
$289$	−6.01641			−0.353906
$290$		0			0
$291$			11.1444i			0.653294i
$292$	−24.7422	−	18.7253i	−1.44793	−	1.09582i
$293$		−	7.99166i		−	0.466878i	−0.972371	−	0.233439i	$-0.925002\pi$
$293$		−	7.99166i		−	0.466878i	0.972371	−	0.233439i	$-0.0749979\pi$
$294$	0.0219960	+	0.00738516i	0.00128283	+	0.000430711i
$295$		0			0
$296$	12.5522	+	18.3860i	0.729582	+	1.06867i
$297$	−1.51363			−0.0878299
$298$	14.8431	+	4.98359i	0.859840	+	0.288692i
$299$			18.6877i			1.08074i
$300$		0			0
$301$			2.68601i			0.154819i
$302$	−0.286885	+	0.854458i	−0.0165084	+	0.0491685i
$303$	13.3295			0.765760
$304$	−27.2775	+	7.69919i	−1.56447	+	0.441579i
$305$		0			0
$306$	1.49180	−	4.44317i	0.0852803	−	0.253999i
$307$		−	17.4506i		−	0.995961i	−0.867188	−	0.497980i	$-0.834075\pi$
$307$		−	17.4506i		−	0.995961i	0.867188	−	0.497980i	$-0.165925\pi$
$308$	−4.82778	+	6.37907i	−0.275088	+	0.363481i
$309$		−	0.958386i		−	0.0545207i
$310$		0			0
$311$	21.4506			1.21635			0.608177	−	0.793801i	$-0.291901\pi$
$311$	21.4506			1.21635			0.608177	+	0.793801i	$0.291901\pi$
$312$	−9.04219	+	6.17313i	−0.511913	+	0.349485i
$313$	−7.73879			−0.437422			−0.218711	−	0.975790i	$-0.570185\pi$
$313$	−7.73879			−0.437422			−0.218711	+	0.975790i	$0.570185\pi$
$314$	0.173127	+	0.0581276i	0.00977014	+	0.00328033i
$315$		0			0
$316$	11.7417	+	8.88633i	0.660524	+	0.499895i
$317$		−	11.2335i		−	0.630938i	−0.948936	−	0.315469i	$-0.897838\pi$
$317$		−	11.2335i		−	0.630938i	0.948936	−	0.315469i	$-0.102162\pi$
$318$	2.02927	−	6.04399i	0.113796	−	0.338930i
$319$	−3.30749			−0.185184
$320$		0			0
$321$	−4.00000			−0.223258
$322$	−5.74281	+	17.1044i	−0.320034	+	0.953190i
$323$			23.4835i			1.30665i
$324$	−1.59477	−	1.20695i	−0.0885982	−	0.0670525i
$325$		0			0
$326$	26.1208	+	8.77008i	1.44670	+	0.485730i
$327$	−0.769233			−0.0425387
$328$	20.3820	−	13.9149i	1.12541	−	0.768319i
$329$	−18.7253			−1.03236
$330$		0			0
$331$			8.00084i			0.439766i	0.975526	+	0.219883i	$0.0705676\pi$
$331$			8.00084i			0.439766i	−0.975526	+	0.219883i	$0.929432\pi$
$332$	9.34385	−	12.3463i	0.512810	−	0.677589i
$333$		−	7.87086i		−	0.431321i
$334$	−0.810466	+	2.41389i	−0.0443467	+	0.132082i
$335$		0			0
$336$	−10.1731	+	2.87141i	−0.554990	+	0.156648i
$337$	21.5692			1.17495			0.587474	−	0.809243i	$-0.300123\pi$
$337$	21.5692			1.17495			0.587474	+	0.809243i	$0.300123\pi$
$338$	0.892874	−	2.65933i	0.0485659	−	0.144649i
$339$		−	14.4585i		−	0.785279i
$340$		0			0
$341$			11.1444i			0.603501i
$342$	9.49971	+	3.18953i	0.513685	+	0.172470i
$343$	−18.5419			−1.00117
$344$	1.62093	+	2.37429i	0.0873948	+	0.128013i
$345$		0			0
$346$	31.1484	+	10.4581i	1.67455	+	0.562231i
$347$		−	21.7089i		−	1.16540i	−0.812689	−	0.582698i	$-0.801997\pi$
$347$		−	21.7089i		−	1.16540i	0.812689	−	0.582698i	$-0.198003\pi$
$348$	−3.48478	−	2.63734i	−0.186804	−	0.141376i
$349$			24.7422i			1.32442i	0.749318	+	0.662211i	$0.230382\pi$
$349$			24.7422i			1.32442i	−0.749318	+	0.662211i	$0.769618\pi$
$350$		0			0
$351$	3.87086			0.206611
$352$	−0.417910	+	8.55220i	−0.0222747	+	0.455834i
$353$	−3.31415			−0.176394			−0.0881972	−	0.996103i	$-0.528111\pi$
$353$	−3.31415			−0.176394			−0.0881972	+	0.996103i	$0.528111\pi$
$354$	−3.06040	+	9.11509i	−0.162658	+	0.484462i
$355$		0			0
$356$	−23.5358	−	17.8123i	−1.24739	−	0.944048i
$357$			8.75814i			0.463530i
$358$	3.82979	+	1.28586i	0.202411	+	0.0679596i
$359$	−16.7581			−0.884461			−0.442230	−	0.896902i	$-0.645813\pi$
$359$	−16.7581			−0.884461			−0.442230	+	0.896902i	$0.645813\pi$
$360$		0			0
$361$	−31.2088			−1.64257
$362$	−7.08582	−	2.37907i	−0.372422	−	0.125041i
$363$			8.70892i			0.457100i
$364$	12.3463	−	16.3134i	0.647120	−	0.855055i
$365$		0			0
$366$	−1.62093	+	4.82778i	−0.0847275	+	0.252352i
$367$	−28.5324			−1.48938			−0.744690	−	0.667411i	$-0.767403\pi$
$367$	−28.5324			−1.48938			−0.744690	+	0.667411i	$0.767403\pi$
$368$	5.24569	+	18.5850i	0.273451	+	0.968811i
$369$	−8.72532			−0.454222
$370$		0			0
$371$			11.9136i			0.618523i
$372$	−8.88633	+	11.7417i	−0.460735	+	0.608780i
$373$			37.5798i			1.94581i	0.231211	+	0.972904i	$0.425731\pi$
$373$			37.5798i			1.94581i	−0.231211	+	0.972904i	$0.574269\pi$
$374$	6.72532	+	2.25803i	0.347758	+	0.116760i
$375$		0			0
$376$	−16.5522	+	11.3002i	−0.853614	+	0.582765i
$377$	8.45836			0.435628
$378$	3.54291	+	1.18953i	0.182228	+	0.0611830i
$379$		−	6.74456i		−	0.346445i	−0.984883	−	0.173222i	$-0.944582\pi$
$379$		−	6.74456i		−	0.346445i	0.984883	−	0.173222i	$-0.0554179\pi$
$380$		0			0
$381$			11.5290i			0.590648i
$382$	2.68601	−	8.00000i	0.137428	−	0.409316i
$383$	−21.8312			−1.11552			−0.557762	−	0.830001i	$-0.688340\pi$
$383$	−21.8312			−1.11552			−0.557762	+	0.830001i	$0.688340\pi$
$384$	−7.25969	+	8.67738i	−0.370470	+	0.442816i
$385$		0			0
$386$	6.72532	−	20.0307i	0.342310	−	1.01954i
$387$		−	1.01641i		−	0.0516669i
$388$	−17.7727	−	13.4506i	−0.902270	−	0.682853i
$389$			8.81344i			0.446859i	0.974720	+	0.223429i	$0.0717252\pi$
$389$			8.81344i			0.446859i	−0.974720	+	0.223429i	$0.928275\pi$
$390$		0			0
$391$	16.0000			0.809155
$392$	−0.0383256	+	0.0261649i	−0.00193573	+	0.00132153i
$393$	−7.37270			−0.371904
$394$	4.33508	+	1.45551i	0.218398	+	0.0733273i
$395$		0			0
$396$	1.82687	−	2.41389i	0.0918038	−	0.121303i
$397$			0.821644i			0.0412372i	0.999787	+	0.0206186i	$0.00656356\pi$
$397$			0.821644i			0.0412372i	−0.999787	+	0.0206186i	$0.993436\pi$
$398$	3.65541	−	10.8873i	0.183229	−	0.545730i
$399$	−18.7253			−0.937439
$400$		0			0
$401$	−12.7253			−0.635472			−0.317736	−	0.948179i	$-0.602923\pi$
$401$	−12.7253			−0.635472			−0.317736	+	0.948179i	$0.602923\pi$
$402$	0.457515	−	1.36266i	0.0228188	−	0.0679634i
$403$		−	28.4999i		−	1.41968i
$404$	−16.0880	+	21.2574i	−0.800407	+	1.05760i
$405$		0			0
$406$	7.74173	+	2.59929i	0.384216	+	0.129001i
$407$	11.9136			0.590535
$408$	5.28530	+	7.74173i	0.261661	+	0.383273i
$409$	2.25827			0.111664			0.0558321	−	0.998440i	$-0.482219\pi$
$409$	2.25827			0.111664			0.0558321	+	0.998440i	$0.482219\pi$
$410$		0			0
$411$		−	3.88792i		−	0.191777i
$412$	1.52840	+	1.15672i	0.0752990	+	0.0569875i
$413$		−	17.9672i		−	0.884107i
$414$	2.17313	−	6.47244i	0.106803	−	0.318103i
$415$		0			0
$416$	1.06874	−	21.8708i	0.0523991	−	1.07231i
$417$	14.6291			0.716392
$418$	−4.82778	+	14.3791i	−0.236135	+	0.703303i
$419$		−	33.4579i		−	1.63453i	−0.576264	−	0.817263i	$-0.695490\pi$
$419$		−	33.4579i		−	1.63453i	0.576264	−	0.817263i	$-0.304510\pi$
$420$		0			0
$421$		−	11.3398i		−	0.552669i	−0.961061	−	0.276335i	$-0.910880\pi$
$421$		−	11.3398i		−	0.552669i	0.961061	−	0.276335i	$-0.0891198\pi$
$422$	18.3860	+	6.17313i	0.895018	+	0.300503i
$423$	7.08582			0.344524
$424$	7.18953	+	10.5310i	0.349155	+	0.511430i
$425$		0			0
$426$	9.01641	+	3.02727i	0.436846	+	0.146671i
$427$		−	9.51627i		−	0.460525i
$428$	4.82778	−	6.37907i	0.233360	−	0.308344i
$429$			5.85907i			0.282878i
$430$		0			0
$431$	10.6597			0.513459			0.256730	−	0.966483i	$-0.417355\pi$
$431$	10.6597			0.513459			0.256730	+	0.966483i	$0.417355\pi$
$432$	3.84959	−	1.08656i	0.185214	−	0.0522773i
$433$	26.5132			1.27414			0.637072	−	0.770805i	$-0.280146\pi$
$433$	26.5132			1.27414			0.637072	+	0.770805i	$0.280146\pi$
$434$	8.75814	−	26.0852i	0.420404	−	1.25213i
$435$		0			0
$436$	0.928423	−	1.22675i	0.0444634	−	0.0587506i
$437$			34.2088i			1.63643i
$438$	−20.7999	−	6.98359i	−0.993859	−	0.333689i
$439$	32.8789			1.56923			0.784613	−	0.619986i	$-0.212862\pi$
$439$	32.8789			1.56923			0.784613	+	0.619986i	$0.212862\pi$
$440$		0			0
$441$	0.0164068			0.000781274
$442$	−17.1989	−	5.77454i	−0.818068	−	0.274667i
$443$			5.70892i			0.271239i	0.990761	+	0.135619i	$0.0433024\pi$
$443$			5.70892i			0.271239i	−0.990761	+	0.135619i	$0.956698\pi$
$444$	12.5522	+	9.49971i	0.595701	+	0.450836i
$445$		0			0
$446$	4.43140	−	13.1985i	0.209833	−	0.624966i
$447$	11.0715			0.523662
$448$	7.69919	−	19.6894i	0.363753	−	0.930237i
$449$	−2.00000			−0.0943858			−0.0471929	−	0.998886i	$-0.515028\pi$
$449$	−2.00000			−0.0943858			−0.0471929	+	0.998886i	$0.515028\pi$
$450$		0			0
$451$		−	13.2069i		−	0.621890i
$452$	23.0580	+	17.4506i	1.08456	+	0.820809i
$453$			0.637339i			0.0299448i
$454$	−7.65375	−	2.56975i	−0.359208	−	0.120604i
$455$		0			0
$456$	−16.5522	+	11.3002i	−0.775128	+	0.529182i
$457$	−3.94229			−0.184413			−0.0922064	−	0.995740i	$-0.529392\pi$
$457$	−3.94229			−0.184413			−0.0922064	+	0.995740i	$0.529392\pi$
$458$	1.03128	+	0.346255i	0.0481888	+	0.0161794i
$459$		−	3.31415i		−	0.154691i
$460$		0			0
$461$		−	33.8969i		−	1.57874i	−0.613920	−	0.789369i	$-0.710408\pi$
$461$		−	33.8969i		−	1.57874i	0.613920	−	0.789369i	$-0.289592\pi$
$462$	−1.80052	+	5.36266i	−0.0837677	+	0.249494i
$463$	22.8688			1.06280			0.531402	−	0.847120i	$-0.321665\pi$
$463$	22.8688			1.06280			0.531402	+	0.847120i	$0.321665\pi$
$464$	8.41188	−	2.37429i	0.390512	−	0.110224i
$465$		0			0
$466$	−8.28275	+	24.6693i	−0.383691	+	1.14278i
$467$			15.7417i			0.728440i	0.931313	+	0.364220i	$0.118664\pi$
$467$			15.7417i			0.728440i	−0.931313	+	0.364220i	$0.881336\pi$
$468$	−4.67192	+	6.17313i	−0.215960	+	0.285353i
$469$			2.68601i			0.124028i
$470$		0			0
$471$	0.129135			0.00595024
$472$	−10.8427	−	15.8820i	−0.499076	−	0.731030i
$473$	1.53847			0.0707388
$474$	9.87086	+	3.31415i	0.453384	+	0.152224i
$475$		0			0
$476$	−13.9672	−	10.5706i	−0.640185	−	0.484502i
$477$		−	4.50820i		−	0.206416i
$478$	−4.51606	+	13.4506i	−0.206560	+	0.615218i
$479$	20.6925			0.945465			0.472732	−	0.881206i	$-0.343268\pi$
$479$	20.6925			0.945465			0.472732	+	0.881206i	$0.343268\pi$
$480$		0			0
$481$	−30.4671			−1.38918
$482$	−4.84255	+	14.4231i	−0.220572	+	0.656952i
$483$			12.7581i			0.580515i
$484$	−13.8887	−	10.5112i	−0.631304	−	0.477781i
$485$		0			0
$486$	−1.34067	−	0.450129i	−0.0608138	−	0.0204183i
$487$	30.8401			1.39750			0.698750	−	0.715366i	$-0.253740\pi$
$487$	30.8401			1.39750			0.698750	+	0.715366i	$0.253740\pi$
$488$	−5.74281	−	8.41188i	−0.259965	−	0.380788i
$489$	19.4835			0.881072
$490$		0			0
$491$		−	10.9737i		−	0.495238i	−0.968858	−	0.247619i	$-0.920352\pi$
$491$		−	10.9737i		−	0.495238i	0.968858	−	0.247619i	$-0.0796481\pi$
$492$	10.5310	−	13.9149i	0.474774	−	0.627330i
$493$		−	7.24186i		−	0.326157i
$494$	12.3463	−	36.7721i	0.555484	−	1.65445i
$495$		0			0
$496$	−8.00000	−	28.3433i	−0.359211	−	1.27265i
$497$	−17.7727			−0.797213
$498$	3.48478	−	10.3791i	0.156157	−	0.465097i
$499$			3.71729i			0.166409i	0.996533	+	0.0832044i	$0.0265154\pi$
$499$			3.71729i			0.166409i	−0.996533	+	0.0832044i	$0.973485\pi$
$500$		0			0
$501$			1.80052i			0.0804412i
$502$	16.9701	+	5.69774i	0.757414	+	0.254302i
$503$	39.9451			1.78107			0.890533	−	0.454919i	$-0.150332\pi$
$503$	39.9451			1.78107			0.890533	+	0.454919i	$0.150332\pi$
$504$	−6.17313	+	4.21441i	−0.274973	+	0.187725i
$505$		0			0
$506$	9.79690	+	3.28932i	0.435525	+	0.146228i
$507$		−	1.98359i		−	0.0880945i
$508$	−18.3860	−	13.9149i	−0.815749	−	0.617372i
$509$		−	0.0728979i		−	0.00323114i	−0.999999	−	0.00161557i	$-0.999486\pi$
$509$		−	0.0728979i		−	0.00323114i	0.999999	−	0.00161557i	$-0.000514253\pi$
$510$		0			0
$511$	40.9997			1.81372
$512$	−5.07634	−	22.0506i	−0.224345	−	0.974510i
$513$	7.08582			0.312846
$514$	5.99166	−	17.8456i	0.264281	−	0.787134i
$515$		0			0
$516$	1.62093	+	1.22675i	0.0713576	+	0.0540046i
$517$			10.7253i			0.471699i
$518$	−27.8857	−	9.36266i	−1.22523	−	0.411372i
$519$	23.2335			1.01984
$520$		0			0
$521$	−11.9672			−0.524292			−0.262146	−	0.965028i	$-0.584430\pi$
$521$	−11.9672			−0.524292			−0.262146	+	0.965028i	$0.584430\pi$
$522$	−2.92953	−	0.983593i	−0.128222	−	0.0430507i
$523$			16.0656i			0.702501i	0.936282	+	0.351250i	$0.114243\pi$
$523$			16.0656i			0.702501i	−0.936282	+	0.351250i	$0.885757\pi$
$524$	8.89845	−	11.7577i	0.388731	−	0.513639i
$525$		0			0
$526$	8.29392	−	24.7026i	0.361632	−	1.07709i
$527$	−24.4010			−1.06292
$528$	1.64466	+	5.82687i	0.0715746	+	0.253582i
$529$	0.307491			0.0133692
$530$		0			0
$531$			6.79893i			0.295048i
$532$	22.6004	−	29.8625i	0.979854	−	1.29470i
$533$			33.7745i			1.46294i
$534$	−19.7857	−	6.64307i	−0.856212	−	0.287474i
$535$		0			0
$536$	1.62093	+	2.37429i	0.0700136	+	0.102554i
$537$	2.85664			0.123273
$538$	5.18757	+	1.74173i	0.223652	+	0.0750913i
$539$			0.0248338i			0.00106967i
$540$		0			0
$541$			15.8559i			0.681698i	0.940118	+	0.340849i	$0.110715\pi$
$541$			15.8559i			0.681698i	−0.940118	+	0.340849i	$0.889285\pi$
$542$	7.83021	−	23.3215i	0.336337	−	1.00174i
$543$	−5.28530			−0.226814
$544$	−18.7253	−	0.915029i	−0.802842	−	0.0392316i
$545$		0			0
$546$	4.60453	−	13.7141i	0.197055	−	0.586910i
$547$		−	4.95078i		−	0.211680i	−0.994383	−	0.105840i	$-0.966247\pi$
$547$		−	4.95078i		−	0.211680i	0.994383	−	0.105840i	$-0.0337531\pi$
$548$	6.20033	+	4.69251i	0.264865	+	0.200454i
$549$			3.60104i			0.153688i
$550$		0			0
$551$	15.4835			0.659618
$552$	7.69919	+	11.2775i	0.327699	+	0.480003i
$553$	−19.4569			−0.827393
$554$	1.18953	+	0.399387i	0.0505385	+	0.0169683i
$555$		0			0
$556$	−17.6566	+	23.3301i	−0.748806	+	0.989416i
$557$			1.26634i			0.0536565i	0.999640	+	0.0268283i	$0.00854073\pi$
$557$			1.26634i			0.0536565i	−0.999640	+	0.0268283i	$0.991459\pi$
$558$	−3.31415	+	9.87086i	−0.140299	+	0.417867i
$559$	−3.93437			−0.166406
$560$		0			0
$561$	5.01641			0.211793
$562$	6.06930	−	18.0768i	0.256018	−	0.762524i
$563$		−	5.70892i		−	0.240602i	−0.992737	−	0.120301i	$-0.961614\pi$
$563$		−	5.70892i		−	0.240602i	0.992737	−	0.120301i	$-0.0383860\pi$
$564$	−8.55220	+	11.3002i	−0.360112	+	0.475825i
$565$		0			0
$566$	38.1208	+	12.7991i	1.60234	+	0.537986i
$567$	2.64265			0.110981
$568$	−15.7101	+	10.7253i	−0.659181	+	0.450025i
$569$	−2.75814			−0.115627			−0.0578135	−	0.998327i	$-0.518413\pi$
$569$	−2.75814			−0.115627			−0.0578135	+	0.998327i	$0.518413\pi$
$570$		0			0
$571$			25.7735i			1.07859i	0.842118	+	0.539294i	$0.181309\pi$
$571$			25.7735i			1.07859i	−0.842118	+	0.539294i	$0.818691\pi$
$572$	−9.34385	−	7.07158i	−0.390686	−	0.295677i
$573$		−	5.96719i		−	0.249283i
$574$	−10.3791	+	30.9130i	−0.433214	+	1.29028i
$575$		0			0
$576$	−2.91344	+	7.45063i	−0.121393	+	0.310443i
$577$	−32.7135			−1.36188			−0.680941	−	0.732338i	$-0.738429\pi$
$577$	−32.7135			−1.36188			−0.680941	+	0.732338i	$0.738429\pi$
$578$	2.70816	−	8.06599i	0.112645	−	0.335501i
$579$		−	14.9409i		−	0.620921i
$580$		0			0
$581$			20.4587i			0.848769i
$582$	−14.9409	−	5.01641i	−0.619319	−	0.207937i
$583$	6.82376			0.282611
$584$	36.2416	−	24.7422i	1.49969	−	1.02384i
$585$		0			0
$586$	10.7141	+	3.59728i	0.442597	+	0.148602i
$587$			43.4835i			1.79475i	0.441264	+	0.897377i	$0.354530\pi$
$587$			43.4835i			1.79475i	−0.441264	+	0.897377i	$0.645470\pi$
$588$	−0.0198021	+	0.0261649i	−0.000816623	+	0.00107902i
$589$		−	52.1705i		−	2.14965i
$590$		0			0
$591$	3.23353			0.133009
$592$	−30.2996	+	8.55220i	−1.24531	+	0.351493i
$593$	7.83021			0.321548			0.160774	−	0.986991i	$-0.448601\pi$
$593$	7.83021			0.321548			0.160774	+	0.986991i	$0.448601\pi$
$594$	0.681331	−	2.02927i	0.0279553	−	0.0832622i
$595$		0			0
$596$	−13.3627	+	17.6564i	−0.547356	+	0.723235i
$597$		−	8.12080i		−	0.332362i
$598$	−25.0539	−	8.41188i	−1.02453	−	0.343987i
$599$	−32.7581			−1.33846			−0.669231	−	0.743055i	$-0.733376\pi$
$599$	−32.7581			−1.33846			−0.669231	+	0.743055i	$0.733376\pi$
$600$		0			0
$601$	17.8074			0.726377			0.363189	−	0.931716i	$-0.381688\pi$
$601$	17.8074			0.726377			0.363189	+	0.931716i	$0.381688\pi$
$602$	−3.60104	−	1.20905i	−0.146767	−	0.0492772i
$603$		−	1.01641i		−	0.0413913i
$604$	−1.01641	−	0.769233i	−0.0413570	−	0.0312997i
$605$		0			0
$606$	−6.00000	+	17.8704i	−0.243733	+	0.725935i
$607$	−3.41188			−0.138484			−0.0692420	−	0.997600i	$-0.522058\pi$
$607$	−3.41188			−0.138484			−0.0692420	+	0.997600i	$0.522058\pi$
$608$	1.95638	−	40.0357i	0.0793416	−	1.62366i
$609$	5.77454			0.233996
$610$		0			0
$611$		−	27.4282i		−	1.10963i
$612$	5.28530	+	4.00000i	0.213646	+	0.161690i
$613$			36.6290i			1.47943i	0.672920	+	0.739716i	$0.265040\pi$
$613$			36.6290i			1.47943i	−0.672920	+	0.739716i	$0.734960\pi$
$614$	23.3955	+	7.85505i	0.944165	+	0.317004i
$615$		0			0
$616$	−6.37907	−	9.34385i	−0.257020	−	0.376474i
$617$	40.3979			1.62636			0.813180	−	0.582012i	$-0.197734\pi$
$617$	40.3979			1.62636			0.813180	+	0.582012i	$0.197734\pi$
$618$	1.28488	+	0.431398i	0.0516853	+	0.0173534i
$619$		−	24.5172i		−	0.985430i	−0.870191	−	0.492715i	$-0.836004\pi$
$619$		−	24.5172i		−	0.985430i	0.870191	−	0.492715i	$-0.163996\pi$
$620$		0			0
$621$		−	4.82778i		−	0.193732i
$622$	−9.65557	+	28.7581i	−0.387153	+	1.15310i
$623$	39.0006			1.56252
$624$	−4.20594	−	14.9013i	−0.168372	−	0.596528i
$625$		0			0
$626$	3.48346	−	10.3751i	0.139227	−	0.414674i
$627$			10.7253i			0.428328i
$628$	−0.155859	+	0.205941i	−0.00621947	+	0.00821793i
$629$			26.0852i			1.04009i
$630$		0			0
$631$	18.7805			0.747640			0.373820	−	0.927501i	$-0.378048\pi$
$631$	18.7805			0.747640			0.373820	+	0.927501i	$0.378048\pi$
$632$	−17.1989	+	11.7417i	−0.684135	+	0.467061i
$633$	13.7141			0.545087
$634$	15.0604	+	5.05654i	0.598125	+	0.200821i
$635$		0			0
$636$	7.18953	+	5.44116i	0.285084	+	0.215756i
$637$		−	0.0635083i		−	0.00251629i
$638$	1.48880	−	4.43424i	0.0589421	−	0.175553i
$639$	6.72532			0.266050
$640$		0			0
$641$	−15.5163			−0.612856			−0.306428	−	0.951894i	$-0.599134\pi$
$641$	−15.5163			−0.612856			−0.306428	+	0.951894i	$0.599134\pi$
$642$	1.80052	−	5.36266i	0.0710608	−	0.211647i
$643$			17.4506i			0.688186i	0.938936	+	0.344093i	$0.111814\pi$
$643$			17.4506i			0.688186i	−0.938936	+	0.344093i	$0.888186\pi$
$644$	−20.3463	−	15.3984i	−0.801755	−	0.606781i
$645$		0			0
$646$	−31.4835	−	10.5706i	−1.23870	−	0.415895i
$647$	−13.1403			−0.516600			−0.258300	−	0.966065i	$-0.583162\pi$
$647$	−13.1403			−0.516600			−0.258300	+	0.966065i	$0.583162\pi$
$648$	2.33596	−	1.59477i	0.0917653	−	0.0626484i
$649$	−10.2911			−0.403960
$650$		0			0
$651$		−	19.4569i		−	0.762577i
$652$	−23.5155	+	31.0716i	−0.920937	+	1.21686i
$653$		−	14.7993i		−	0.579141i	−0.957157	−	0.289570i	$-0.906488\pi$
$653$		−	14.7993i		−	0.579141i	0.957157	−	0.289570i	$-0.0935124\pi$
$654$	0.346255	−	1.03128i	0.0135396	−	0.0403264i
$655$		0			0
$656$	9.48062	+	33.5890i	0.370156	+	1.31143i
$657$	−15.5146			−0.605284
$658$	8.42882	−	25.1044i	0.328590	−	0.978671i
$659$			7.99614i			0.311485i	0.987798	+	0.155743i	$0.0497771\pi$
$659$			7.99614i			0.311485i	−0.987798	+	0.155743i	$0.950223\pi$
$660$		0			0
$661$		−	0.915029i		−	0.0355905i	−0.999842	−	0.0177953i	$-0.994335\pi$
$661$		−	0.915029i		−	0.0355905i	0.999842	−	0.0177953i	$-0.00566470\pi$
$662$	−10.7265	−	3.60142i	−0.416896	−	0.139973i
$663$	−12.8286			−0.498223
$664$	12.3463	+	18.0844i	0.479128	+	0.701810i
$665$		0			0
$666$	10.5522	+	3.54291i	0.408889	+	0.137285i
$667$		−	10.5494i		−	0.408473i
$668$	−2.87141	−	2.17313i	−0.111098	−	0.0840808i
$669$		−	9.84472i		−	0.380619i
$670$		0			0
$671$	−5.45065			−0.210420
$672$	0.729629	−	14.9313i	0.0281461	−	0.575986i
$673$	34.3978			1.32594			0.662969	−	0.748647i	$-0.269296\pi$
$673$	34.3978			1.32594			0.662969	+	0.748647i	$0.269296\pi$
$674$	−9.70892	+	28.9170i	−0.373973	+	1.11384i
$675$		0			0
$676$	3.16337	+	2.39409i	0.121668	+	0.0920804i
$677$		−	40.1676i		−	1.54377i	−0.635764	−	0.771884i	$-0.719315\pi$
$677$		−	40.1676i		−	1.54377i	0.635764	−	0.771884i	$-0.280685\pi$
$678$	19.3840	+	6.50820i	0.744439	+	0.249946i
$679$	29.4506			1.13021
$680$		0			0
$681$	−5.70892			−0.218766
$682$	−14.9409	−	5.01641i	−0.572115	−	0.192088i
$683$			33.2580i			1.27258i	0.771449	+	0.636291i	$0.219532\pi$
$683$			33.2580i			1.27258i	−0.771449	+	0.636291i	$0.780468\pi$
$684$	−8.55220	+	11.3002i	−0.327001	+	0.432075i
$685$		0			0
$686$	8.34625	−	24.8585i	0.318661	−	0.949101i
$687$	0.769233			0.0293481
$688$	−3.91275	+	1.10439i	−0.149172	+	0.0421045i
$689$	−17.4506			−0.664817
$690$		0			0
$691$		−	50.2241i		−	1.91062i	−0.295611	−	0.955308i	$-0.595523\pi$
$691$		−	50.2241i		−	1.91062i	0.295611	−	0.955308i	$-0.404477\pi$
$692$	−28.0416	+	37.0521i	−1.06598	+	1.40851i
$693$			4.00000i			0.151947i
$694$	29.1044	+	9.77182i	1.10479	+	0.370933i
$695$		0			0
$696$	5.10439	−	3.48478i	0.193481	−	0.132090i
$697$	28.9170			1.09531
$698$	−33.1710	−	11.1372i	−1.25554	−	0.421549i
$699$			18.4008i			0.695983i
$700$		0			0
$701$			23.7543i			0.897188i	0.893736	+	0.448594i	$0.148075\pi$
$701$			23.7543i			0.897188i	−0.893736	+	0.448594i	$0.851925\pi$
$702$	−1.74239	+	5.18953i	−0.0657623	+	0.195866i
$703$	−55.7715			−2.10346
$704$	−11.2775	−	4.40987i	−0.425037	−	0.166203i
$705$		0			0
$706$	1.49180	−	4.44317i	0.0561445	−	0.167221i
$707$		−	35.2252i		−	1.32478i
$708$	−10.8427	−	8.20594i	−0.407494	−	0.308398i
$709$		−	36.3146i		−	1.36382i	−0.731435	−	0.681911i	$-0.761149\pi$
$709$		−	36.3146i		−	1.36382i	0.731435	−	0.681911i	$-0.238851\pi$
$710$		0			0
$711$	7.36266			0.276121
$712$	34.4744	−	23.5358i	1.29198	−	0.882041i
$713$	−35.5453			−1.33118
$714$	−11.7417	−	3.94229i	−0.439423	−	0.147537i
$715$		0			0
$716$	−3.44780	+	4.55567i	−0.128851	+	0.170253i
$717$			10.0328i			0.374682i
$718$	7.54333	−	22.4671i	0.281515	−	0.838463i
$719$	30.7253			1.14586			0.572931	−	0.819604i	$-0.305806\pi$
$719$	30.7253			1.14586			0.572931	+	0.819604i	$0.305806\pi$
$720$		0			0
$721$	−2.53268			−0.0943219
$722$	14.0480	−	41.8405i	0.522812	−	1.55714i
$723$			10.7581i			0.400099i
$724$	6.37907	−	8.42882i	0.237076	−	0.313255i
$725$		0			0
$726$	−11.6757	−	3.92014i	−0.433327	−	0.145490i
$727$	5.47445			0.203036			0.101518	−	0.994834i	$-0.467630\pi$
$727$	5.47445			0.203036			0.101518	+	0.994834i	$0.467630\pi$
$728$	16.3134	+	23.8953i	0.604615	+	0.885620i
$729$	−1.00000			−0.0370370
$730$		0			0
$731$			3.36852i			0.124589i
$732$	−5.74281	−	4.34625i	−0.212260	−	0.160642i
$733$		−	17.1455i		−	0.633285i	−0.948545	−	0.316643i	$-0.897444\pi$
$733$		−	17.1455i		−	0.633285i	0.948545	−	0.316643i	$-0.102556\pi$
$734$	12.8433	−	38.2524i	0.474054	−	1.41192i
$735$		0			0
$736$	−27.2775	−	1.33294i	−1.00546	−	0.0491328i
$737$	1.53847			0.0566701
$738$	3.92752	−	11.6977i	0.144574	−	0.430600i
$739$			11.6019i			0.426782i	0.976967	+	0.213391i	$0.0684508\pi$
$739$			11.6019i			0.426782i	−0.976967	+	0.213391i	$0.931549\pi$
$740$		0			0
$741$		−	27.4282i		−	1.00760i
$742$	−15.9721	−	5.36266i	−0.586356	−	0.196869i
$743$	−23.6613			−0.868048			−0.434024	−	0.900901i	$-0.642907\pi$
$743$	−23.6613			−0.868048			−0.434024	+	0.900901i	$0.642907\pi$
$744$	−11.7417	−	17.1989i	−0.430473	−	0.630542i
$745$		0			0
$746$	−50.3819	−	16.9158i	−1.84461	−	0.619330i
$747$		−	7.74173i		−	0.283255i
$748$	−6.05453	+	8.00000i	−0.221376	+	0.292509i
$749$			10.5706i			0.386241i
$750$		0			0
$751$	−11.4283			−0.417024			−0.208512	−	0.978020i	$-0.566862\pi$
$751$	−11.4283			−0.417024			−0.208512	+	0.978020i	$0.566862\pi$
$752$	−7.69919	−	27.2775i	−0.280761	−	0.994709i
$753$	12.6580			0.461283
$754$	−3.80736	+	11.3398i	−0.138656	+	0.412972i
$755$		0			0
$756$	−3.18953	+	4.21441i	−0.116002	+	0.153277i
$757$			19.1784i			0.697049i	0.937300	+	0.348525i	$0.113317\pi$
$757$			19.1784i			0.697049i	−0.937300	+	0.348525i	$0.886683\pi$
$758$	9.04219	+	3.03592i	0.328427	+	0.110270i
$759$	7.30749			0.265245
$760$		0			0
$761$	4.03281			0.146189			0.0730947	−	0.997325i	$-0.476712\pi$
$761$	4.03281			0.146189			0.0730947	+	0.997325i	$0.476712\pi$
$762$	−15.4565	−	5.18953i	−0.559930	−	0.187997i
$763$			2.03281i			0.0735928i
$764$	9.51627	+	7.20207i	0.344287	+	0.260562i
$765$		0			0
$766$	9.82687	−	29.2684i	0.355059	−	1.05751i
$767$	26.3177			0.950279
$768$	−8.36566	−	13.6388i	−0.301870	−	0.492146i
$769$	−2.95078			−0.106408			−0.0532039	−	0.998584i	$-0.516943\pi$
$769$	−2.95078			−0.106408			−0.0532039	+	0.998584i	$0.516943\pi$
$770$		0			0
$771$		−	13.3110i		−	0.479383i
$772$	23.8272	+	18.0328i	0.857560	+	0.649015i
$773$			45.2663i			1.62812i	0.580783	+	0.814059i	$0.302747\pi$
$773$			45.2663i			1.62812i	−0.580783	+	0.814059i	$0.697253\pi$
$774$	1.36266	+	0.457515i	0.0489798	+	0.0164450i
$775$		0			0
$776$	26.0328	−	17.7727i	0.934524	−	0.638002i
$777$	−20.7999			−0.746193
$778$	−11.8159	−	3.96719i	−0.423619	−	0.142231i
$779$			61.8260i			2.21515i
$780$		0			0
$781$			10.1797i			0.364257i
$782$	−7.20207	+	21.4506i	−0.257546	+	0.767074i
$783$	−2.18513			−0.0780903
$784$	−0.0178270	−	0.0631594i	−0.000636678	−	0.00225569i
$785$		0			0
$786$	3.31867	−	9.88432i	0.118373	−	0.352562i
$787$			52.9997i			1.88924i	0.328171	+	0.944618i	$0.393568\pi$
$787$			52.9997i			1.88924i	−0.328171	+	0.944618i	$0.606432\pi$
$788$	−3.90269	+	5.15672i	−0.139028	+	0.183701i
$789$		−	18.4256i		−	0.655970i
$790$		0			0
$791$	−38.2088			−1.35855
$792$	2.41389	+	3.53579i	0.0857739	+	0.125639i
$793$	13.9391			0.494993
$794$	−1.10155	−	0.369846i	−0.0390926	−	0.0131254i
$795$		0			0
$796$	12.9508	+	9.80136i	0.459028	+	0.347400i
$797$		−	16.5738i		−	0.587075i	−0.955948	−	0.293538i	$-0.905167\pi$
$797$		−	16.5738i		−	0.587075i	0.955948	−	0.293538i	$-0.0948326\pi$
$798$	8.42882	−	25.1044i	0.298377	−	0.888686i
$799$	−23.4835			−0.830785
$800$		0			0
$801$	−14.7581			−0.521453
$802$	5.72804	−	17.0604i	0.202264	−	0.602424i
$803$		−	23.4835i		−	0.828713i
$804$	1.62093	+	1.22675i	0.0571659	+	0.0432641i
$805$		0			0
$806$	38.2088	+	12.8286i	1.34585	+	0.451869i
$807$	3.86940			0.136209
$808$	−21.2574	−	31.1372i	−0.747834	−	1.09540i
$809$	−37.5491			−1.32016			−0.660078	−	0.751197i	$-0.729477\pi$
$809$	−37.5491			−1.32016			−0.660078	+	0.751197i	$0.729477\pi$
$810$		0			0
$811$			32.1102i			1.12754i	0.825931	+	0.563771i	$0.190650\pi$
$811$			32.1102i			1.12754i	−0.825931	+	0.563771i	$0.809350\pi$
$812$	−6.96956	+	9.20905i	−0.244584	+	0.323174i
$813$		−	17.3955i		−	0.610086i
$814$	−5.36266	+	15.9721i	−0.187961	+	0.559824i
$815$		0			0
$816$	−12.7581	+	3.60104i	−0.446624	+	0.126061i
$817$	−7.20207			−0.251969
$818$	−1.01651	+	3.02759i	−0.0355416	+	0.105857i
$819$		−	10.2293i		−	0.357442i
$820$		0			0
$821$			29.3809i			1.02540i	0.858568	+	0.512699i	$0.171354\pi$
$821$			29.3809i			1.02540i	−0.858568	+	0.512699i	$0.828646\pi$
$822$	5.21240	+	1.75007i	0.181803	+	0.0610406i
$823$	28.3866			0.989495			0.494748	−	0.869037i	$-0.335260\pi$
$823$	28.3866			0.989495			0.494748	+	0.869037i	$0.335260\pi$
$824$	−2.23875	+	1.52840i	−0.0779907	+	0.0532444i
$825$		0			0
$826$	24.0880	+	8.08756i	0.838128	+	0.281402i
$827$			1.45065i			0.0504439i	0.999682	+	0.0252219i	$0.00802924\pi$
$827$			1.45065i			0.0504439i	−0.999682	+	0.0252219i	$0.991971\pi$
$828$	7.69919	+	5.82687i	0.267565	+	0.202498i
$829$			37.4621i			1.30111i	0.759458	+	0.650556i	$0.225464\pi$
$829$			37.4621i			1.30111i	−0.759458	+	0.650556i	$0.774536\pi$
$830$		0			0
$831$	0.887271			0.0307791
$832$	28.8404	+	11.2775i	0.999860	+	0.390978i
$833$	−0.0543744			−0.00188396
$834$	−6.58501	+	19.6128i	−0.228020	+	0.679135i
$835$		0			0
$836$	−17.1044	−	12.9449i	−0.591568	−	0.447708i
$837$			7.36266i			0.254491i
$838$	44.8559	+	15.0604i	1.54952	+	0.520253i
$839$	−48.7581			−1.68332			−0.841659	−	0.540010i	$-0.818421\pi$
$839$	−48.7581			−1.68332			−0.841659	+	0.540010i	$0.818421\pi$
$840$		0			0
$841$	24.2252			0.835351
$842$	15.2029	+	5.10439i	0.523927	+	0.175909i
$843$		−	13.4835i		−	0.464395i
$844$	−16.5522	+	21.8708i	−0.569750	+	0.752825i
$845$		0			0
$846$	−3.18953	+	9.49971i	−0.109658	+	0.326607i
$847$	23.0146			0.790791
$848$	−17.3548	+	4.89845i	−0.595965	+	0.168213i
$849$	28.4342			0.975861
$850$		0			0
$851$			37.9988i			1.30258i
$852$	−8.11710	+	10.7253i	−0.278087	+	0.367443i
$853$		−	4.37073i		−	0.149651i	−0.997197	−	0.0748255i	$-0.976160\pi$
$853$		−	4.37073i		−	0.149651i	0.997197	−	0.0748255i	$-0.0238400\pi$
$854$	12.7581	+	4.28355i	0.436574	+	0.146580i
$855$		0			0
$856$	6.37907	+	9.34385i	0.218032	+	0.319366i
$857$	20.5130			0.700712			0.350356	−	0.936617i	$-0.386061\pi$
$857$	20.5130			0.700712			0.350356	+	0.936617i	$0.386061\pi$
$858$	−7.85505	−	2.63734i	−0.268167	−	0.0900373i
$859$		−	10.1131i		−	0.345054i	−0.985005	−	0.172527i	$-0.944807\pi$
$859$		−	10.1131i		−	0.345054i	0.985005	−	0.172527i	$-0.0551932\pi$
$860$		0			0
$861$			23.0580i			0.785813i
$862$	−4.79824	+	14.2911i	−0.163429	+	0.486756i
$863$	13.2861			0.452266			0.226133	−	0.974096i	$-0.427392\pi$
$863$	13.2861			0.452266			0.226133	+	0.974096i	$0.427392\pi$
$864$	−0.276098	+	5.65011i	−0.00939303	+	0.192221i
$865$		0			0
$866$	−11.9344	+	35.5453i	−0.405547	+	1.20788i
$867$		−	6.01641i		−	0.204328i
$868$	31.0293	+	23.4835i	1.05320	+	0.797081i
$869$			11.1444i			0.378047i
$870$		0			0
$871$	−3.93437			−0.133311
$872$	1.22675	+	1.79690i	0.0415429	+	0.0608507i
$873$	−11.1444			−0.377180
$874$	−45.8625	−	15.3984i	−1.55132	−	0.520858i
$875$		0			0
$876$	18.7253	−	24.7422i	0.632670	−	0.835962i
$877$		−	33.6454i		−	1.13612i	−0.822986	−	0.568062i	$-0.807693\pi$
$877$		−	33.6454i		−	1.13612i	0.822986	−	0.568062i	$-0.192307\pi$
$878$	−14.7998	+	44.0796i	−0.499468	+	1.48762i
$879$	7.99166			0.269552
$880$		0			0
$881$	−32.7909			−1.10476			−0.552378	−	0.833594i	$-0.686279\pi$
$881$	−32.7909			−1.10476			−0.552378	+	0.833594i	$0.686279\pi$
$882$	−0.00738516	+	0.0219960i	−0.000248671	+	0.000740643i
$883$			33.4506i			1.12570i	0.826558	+	0.562852i	$0.190296\pi$
$883$			33.4506i			1.12570i	−0.826558	+	0.562852i	$0.809704\pi$
$884$	15.4835	−	20.4587i	0.520765	−	0.688100i
$885$		0			0
$886$	−7.65375	−	2.56975i	−0.257133	−	0.0863325i
$887$	−34.8924			−1.17157			−0.585785	−	0.810466i	$-0.699214\pi$
$887$	−34.8924			−1.17157			−0.585785	+	0.810466i	$0.699214\pi$
$888$	−18.3860	+	12.5522i	−0.616995	+	0.421224i
$889$	30.4671			1.02183
$890$		0			0
$891$		−	1.51363i		−	0.0507086i
$892$	15.7000	+	11.8820i	0.525676	+	0.397840i
$893$		−	50.2088i		−	1.68017i
$894$	−4.98359	+	14.8431i	−0.166676	+	0.496429i
$895$		0			0
$896$	22.9313	+	19.1848i	0.766080	+	0.640920i
$897$	−18.6877			−0.623964
$898$	0.900259	−	2.68133i	0.0300420	−	0.0894772i
$899$			16.0884i			0.536578i
$900$		0			0
$901$			14.9409i			0.497752i
$902$	17.7061	+	5.94483i	0.589548	+	0.197941i
$903$	−2.68601			−0.0893847
$904$	−33.7745	+	23.0580i	−1.12332	+	0.766896i
$905$		0			0
$906$	−0.854458	−	0.286885i	−0.0283875	−	0.00953111i
$907$			30.9836i			1.02879i	0.857552	+	0.514397i	$0.171984\pi$
$907$			30.9836i			1.02879i	−0.857552	+	0.514397i	$0.828016\pi$
$908$	6.89035	−	9.10439i	0.228664	−	0.302140i
$909$			13.3295i			0.442112i
$910$		0			0
$911$	16.0000			0.530104			0.265052	−	0.964234i	$-0.414611\pi$
$911$	16.0000			0.530104			0.265052	+	0.964234i	$0.414611\pi$
$912$	−7.69919	−	27.2775i	−0.254946	−	0.903249i
$913$	11.7181			0.387814
$914$	1.77454	−	5.28530i	0.0586967	−	0.174822i
$915$		0			0
$916$	−0.928423	+	1.22675i	−0.0306760	+	0.0405329i
$917$			19.4835i			0.643400i
$918$	4.44317	+	1.49180i	0.146646	+	0.0492366i
$919$	−15.6043			−0.514737			−0.257368	−	0.966313i	$-0.582855\pi$
$919$	−15.6043			−0.514737			−0.257368	+	0.966313i	$0.582855\pi$
$920$		0			0
$921$	17.4506			0.575018
$922$	45.4444	+	15.2580i	1.49663	+	0.502496i
$923$		−	26.0328i		−	0.856880i
$924$	−6.37907	−	4.82778i	−0.209856	−	0.158822i
$925$		0			0
$926$	−10.2939	+	30.6594i	−0.338279	+	1.00753i
$927$	0.958386			0.0314775
$928$	−0.603310	+	12.3463i	−0.0198046	+	0.405286i
$929$	−38.9341			−1.27739			−0.638693	−	0.769461i	$-0.720525\pi$
$929$	−38.9341			−1.27739			−0.638693	+	0.769461i	$0.720525\pi$
$930$		0			0
$931$		−	0.116255i		−	0.00381011i
$932$	−29.3450	−	22.2088i	−0.961228	−	0.727473i
$933$			21.4506i			0.702263i
$934$	−21.1044	−	7.08582i	−0.690557	−	0.231855i
$935$		0			0
$936$	−6.17313	−	9.04219i	−0.201775	−	0.295553i
$937$	19.6027			0.640393			0.320197	−	0.947351i	$-0.396251\pi$
$937$	19.6027			0.640393			0.320197	+	0.947351i	$0.396251\pi$
$938$	−3.60104	−	1.20905i	−0.117578	−	0.0394769i
$939$		−	7.73879i		−	0.252546i
$940$		0			0
$941$		−	25.0476i		−	0.816530i	−0.912864	−	0.408265i	$-0.866134\pi$
$941$		−	25.0476i		−	0.816530i	0.912864	−	0.408265i	$-0.133866\pi$
$942$	−0.0581276	+	0.173127i	−0.00189390	+	0.00564079i
$943$	42.1240			1.37175
$944$	26.1731	−	7.38747i	0.851863	−	0.240442i
$945$		0			0
$946$	−0.692509	+	2.06257i	−0.0225154	+	0.0670599i
$947$			7.93437i			0.257832i	0.991655	+	0.128916i	$0.0411498\pi$
$947$			7.93437i			0.257832i	−0.991655	+	0.128916i	$0.958850\pi$
$948$	−8.88633	+	11.7417i	−0.288615	+	0.381354i
$949$			60.0550i			1.94947i
$950$		0			0
$951$	11.2335			0.364272
$952$	20.4587	−	13.9672i	0.663069	−	0.452679i
$953$	−11.4809			−0.371903			−0.185952	−	0.982559i	$-0.559537\pi$
$953$	−11.4809			−0.371903			−0.185952	+	0.982559i	$0.559537\pi$
$954$	6.04399	+	2.02927i	0.195681	+	0.0657002i
$955$		0			0
$956$	−16.0000	−	12.1091i	−0.517477	−	0.391635i
$957$		−	3.30749i		−	0.106916i
$958$	−9.31431	+	27.7417i	−0.300932	+	0.896295i
$959$	−10.2744			−0.331778
$960$		0			0
$961$	23.2088			0.748670
$962$	13.7141	−	40.8461i	0.442161	−	1.31693i
$963$		−	4.00000i		−	0.128898i
$964$	−17.1567	−	12.9845i	−0.552581	−	0.418202i
$965$		0			0
$966$	−17.1044	−	5.74281i	−0.550325	−	0.184772i
$967$	15.8993			0.511285			0.255643	−	0.966771i	$-0.417713\pi$
$967$	15.8993			0.511285			0.255643	+	0.966771i	$0.417713\pi$
$968$	20.3437	−	13.8887i	0.653871	−	0.446399i
$969$	−23.4835			−0.754397
$970$		0			0
$971$			40.6600i			1.30484i	0.757857	+	0.652421i	$0.226246\pi$
$971$			40.6600i			1.30484i	−0.757857	+	0.652421i	$0.773754\pi$
$972$	1.20695	−	1.59477i	0.0387128	−	0.0511522i
$973$		−	38.6597i		−	1.23937i
$974$	−13.8820	+	41.3463i	−0.444809	+	1.32482i
$975$		0			0
$976$	13.8625	−	3.91275i	0.443729	−	0.125244i
$977$	−26.5676			−0.849972			−0.424986	−	0.905200i	$-0.639721\pi$
$977$	−26.5676			−0.849972			−0.424986	+	0.905200i	$0.639721\pi$
$978$	−8.77008	+	26.1208i	−0.280436	+	0.835251i
$979$		−	22.3384i		−	0.713938i
$980$		0			0
$981$		−	0.769233i		−	0.0245597i
$982$	14.7121	+	4.93960i	0.469482	+	0.157629i
$983$	9.88057			0.315141			0.157571	−	0.987508i	$-0.449634\pi$
$983$	9.88057			0.315141			0.157571	+	0.987508i	$0.449634\pi$
$984$	13.9149	+	20.3820i	0.443589	+	0.649755i
$985$		0			0
$986$	9.70892	+	3.25978i	0.309195	+	0.103812i
$987$		−	18.7253i		−	0.596034i
$988$	43.7416	+	33.1044i	1.39161	+	1.05319i
$989$			4.90699i			0.156033i
$990$		0			0
$991$	−53.0549			−1.68534			−0.842672	−	0.538427i	$-0.819019\pi$
$991$	−53.0549			−1.68534			−0.842672	+	0.538427i	$0.819019\pi$
$992$	41.5999	+	2.03281i	1.32080	+	0.0645419i
$993$	−8.00084			−0.253899
$994$	8.00000	−	23.8272i	0.253745	−	0.755753i
$995$		0			0
$996$	12.3463	+	9.34385i	0.391206	+	0.296071i
$997$			32.3051i			1.02311i	0.859250	+	0.511556i	$0.170931\pi$
$997$			32.3051i			1.02311i	−0.859250	+	0.511556i	$0.829069\pi$
$998$	−4.98364	−	1.67326i	−0.157754	−	0.0529662i
$999$	7.87086			0.249023

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	600.2.k.f.301.6		12
3.2	odd	2		1800.2.k.u.901.7		12
4.3	odd	2		2400.2.k.f.1201.2		12
5.2	odd	4		120.2.d.a.109.1	✓	6
5.3	odd	4		120.2.d.b.109.6	yes	6
5.4	even	2	inner	600.2.k.f.301.7		12
8.3	odd	2		2400.2.k.f.1201.8		12
8.5	even	2	inner	600.2.k.f.301.5		12
12.11	even	2		7200.2.k.u.3601.3		12
15.2	even	4		360.2.d.f.109.6		6
15.8	even	4		360.2.d.e.109.1		6
15.14	odd	2		1800.2.k.u.901.6		12
20.3	even	4		480.2.d.b.49.4		6
20.7	even	4		480.2.d.a.49.4		6
20.19	odd	2		2400.2.k.f.1201.11		12
24.5	odd	2		1800.2.k.u.901.8		12
24.11	even	2		7200.2.k.u.3601.4		12
40.3	even	4		480.2.d.a.49.3		6
40.13	odd	4		120.2.d.a.109.2	yes	6
40.19	odd	2		2400.2.k.f.1201.5		12
40.27	even	4		480.2.d.b.49.3		6
40.29	even	2	inner	600.2.k.f.301.8		12
40.37	odd	4		120.2.d.b.109.5	yes	6
60.23	odd	4		1440.2.d.f.1009.3		6
60.47	odd	4		1440.2.d.e.1009.3		6
60.59	even	2		7200.2.k.u.3601.9		12
80.3	even	4		3840.2.f.m.769.12		12
80.13	odd	4		3840.2.f.l.769.6		12
80.27	even	4		3840.2.f.m.769.7		12
80.37	odd	4		3840.2.f.l.769.1		12
80.43	even	4		3840.2.f.m.769.1		12
80.53	odd	4		3840.2.f.l.769.7		12
80.67	even	4		3840.2.f.m.769.6		12
80.77	odd	4		3840.2.f.l.769.12		12
120.29	odd	2		1800.2.k.u.901.5		12
120.53	even	4		360.2.d.f.109.5		6
120.59	even	2		7200.2.k.u.3601.10		12
120.77	even	4		360.2.d.e.109.2		6
120.83	odd	4		1440.2.d.e.1009.4		6
120.107	odd	4		1440.2.d.f.1009.4		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
120.2.d.a.109.1	✓	6	5.2	odd	4
120.2.d.a.109.2	yes	6	40.13	odd	4
120.2.d.b.109.5	yes	6	40.37	odd	4
120.2.d.b.109.6	yes	6	5.3	odd	4
360.2.d.e.109.1		6	15.8	even	4
360.2.d.e.109.2		6	120.77	even	4
360.2.d.f.109.5		6	120.53	even	4
360.2.d.f.109.6		6	15.2	even	4
480.2.d.a.49.3		6	40.3	even	4
480.2.d.a.49.4		6	20.7	even	4
480.2.d.b.49.3		6	40.27	even	4
480.2.d.b.49.4		6	20.3	even	4
600.2.k.f.301.5		12	8.5	even	2	inner
600.2.k.f.301.6		12	1.1	even	1	trivial
600.2.k.f.301.7		12	5.4	even	2	inner
600.2.k.f.301.8		12	40.29	even	2	inner
1440.2.d.e.1009.3		6	60.47	odd	4
1440.2.d.e.1009.4		6	120.83	odd	4
1440.2.d.f.1009.3		6	60.23	odd	4
1440.2.d.f.1009.4		6	120.107	odd	4
1800.2.k.u.901.5		12	120.29	odd	2
1800.2.k.u.901.6		12	15.14	odd	2
1800.2.k.u.901.7		12	3.2	odd	2
1800.2.k.u.901.8		12	24.5	odd	2
2400.2.k.f.1201.2		12	4.3	odd	2
2400.2.k.f.1201.5		12	40.19	odd	2
2400.2.k.f.1201.8		12	8.3	odd	2
2400.2.k.f.1201.11		12	20.19	odd	2
3840.2.f.l.769.1		12	80.37	odd	4
3840.2.f.l.769.6		12	80.13	odd	4
3840.2.f.l.769.7		12	80.53	odd	4
3840.2.f.l.769.12		12	80.77	odd	4
3840.2.f.m.769.1		12	80.43	even	4
3840.2.f.m.769.6		12	80.67	even	4
3840.2.f.m.769.7		12	80.27	even	4
3840.2.f.m.769.12		12	80.3	even	4
7200.2.k.u.3601.3		12	12.11	even	2
7200.2.k.u.3601.4		12	24.11	even	2
7200.2.k.u.3601.9		12	60.59	even	2
7200.2.k.u.3601.10		12	120.59	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 600 = 2^{3} \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	600.k (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.450129 + 1.34067i) q^{2} +1.00000i q^{3} +(-1.59477 - 1.20695i) q^{4} +(-1.34067 - 0.450129i) q^{6} +2.64265 q^{7} +(2.33596 - 1.59477i) q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q+(-0.450129 + 1.34067i) q^{2} +1.00000i q^{3} +(-1.59477 - 1.20695i) q^{4} +(-1.34067 - 0.450129i) q^{6} +2.64265 q^{7} +(2.33596 - 1.59477i) q^{8} -1.00000 q^{9} -1.51363i q^{11} +(1.20695 - 1.59477i) q^{12} +3.87086i q^{13} +(-1.18953 + 3.54291i) q^{14} +(1.08656 + 3.84959i) q^{16} +3.31415 q^{17} +(0.450129 - 1.34067i) q^{18} +7.08582i q^{19} +2.64265i q^{21} +(2.02927 + 0.681331i) q^{22} +4.82778 q^{23} +(1.59477 + 2.33596i) q^{24} +(-5.18953 - 1.74239i) q^{26} -1.00000i q^{27} +(-4.21441 - 3.18953i) q^{28} -2.18513i q^{29} -7.36266 q^{31} +(-5.65011 - 0.276098i) q^{32} +1.51363 q^{33} +(-1.49180 + 4.44317i) q^{34} +(1.59477 + 1.20695i) q^{36} +7.87086i q^{37} +(-9.49971 - 3.18953i) q^{38} -3.87086 q^{39} +8.72532 q^{41} +(-3.54291 - 1.18953i) q^{42} +1.01641i q^{43} +(-1.82687 + 2.41389i) q^{44} +(-2.17313 + 6.47244i) q^{46} -7.08582 q^{47} +(-3.84959 + 1.08656i) q^{48} -0.0164068 q^{49} +3.31415i q^{51} +(4.67192 - 6.17313i) q^{52} +4.50820i q^{53} +(1.34067 + 0.450129i) q^{54} +(6.17313 - 4.21441i) q^{56} -7.08582 q^{57} +(2.92953 + 0.983593i) q^{58} -6.79893i q^{59} -3.60104i q^{61} +(3.31415 - 9.87086i) q^{62} -2.64265 q^{63} +(2.91344 - 7.45063i) q^{64} +(-0.681331 + 2.02927i) q^{66} +1.01641i q^{67} +(-5.28530 - 4.00000i) q^{68} +4.82778i q^{69} -6.72532 q^{71} +(-2.33596 + 1.59477i) q^{72} +15.5146 q^{73} +(-10.5522 - 3.54291i) q^{74} +(8.55220 - 11.3002i) q^{76} -4.00000i q^{77} +(1.74239 - 5.18953i) q^{78} -7.36266 q^{79} +1.00000 q^{81} +(-3.92752 + 11.6977i) q^{82} +7.74173i q^{83} +(3.18953 - 4.21441i) q^{84} +(-1.36266 - 0.457515i) q^{86} +2.18513 q^{87} +(-2.41389 - 3.53579i) q^{88} +14.7581 q^{89} +10.2293i q^{91} +(-7.69919 - 5.82687i) q^{92} -7.36266i q^{93} +(3.18953 - 9.49971i) q^{94} +(0.276098 - 5.65011i) q^{96} +11.1444 q^{97} +(0.00738516 - 0.0219960i) q^{98} +1.51363i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 2 q^{4} - 2 q^{6} - 12 q^{9}+O(q^{10}) \) 12 * q - 2 * q^4 - 2 * q^6 - 12 * q^9	\( 12 q - 2 q^{4} - 2 q^{6} - 12 q^{9} + 20 q^{14} + 2 q^{16} + 2 q^{24} - 28 q^{26} - 32 q^{31} - 24 q^{34} + 2 q^{36} + 16 q^{39} - 8 q^{41} - 44 q^{44} - 4 q^{46} + 12 q^{49} + 2 q^{54} + 52 q^{56} + 46 q^{64} + 20 q^{66} + 32 q^{71} - 36 q^{74} + 12 q^{76} - 32 q^{79} + 12 q^{81} + 4 q^{84} + 40 q^{86} + 40 q^{89} + 4 q^{94} - 42 q^{96}+O(q^{100}) \) 12 * q - 2 * q^4 - 2 * q^6 - 12 * q^9 + 20 * q^14 + 2 * q^16 + 2 * q^24 - 28 * q^26 - 32 * q^31 - 24 * q^34 + 2 * q^36 + 16 * q^39 - 8 * q^41 - 44 * q^44 - 4 * q^46 + 12 * q^49 + 2 * q^54 + 52 * q^56 + 46 * q^64 + 20 * q^66 + 32 * q^71 - 36 * q^74 + 12 * q^76 - 32 * q^79 + 12 * q^81 + 4 * q^84 + 40 * q^86 + 40 * q^89 + 4 * q^94 - 42 * q^96

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