LMFDB - Embedded newform 360.2.bo.a.43.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [360,2,Mod(43,360)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(360, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 6, 8, 9]))

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

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

chi := DirichletCharacter("360.43");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 360 = 2^{3} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	360.bo (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:	$2.87461447277$
Analytic rank:	$0$
Dimension:	$272$
Relative dimension:	$68$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			43.9
Character	$\chi$	$=$	360.43
Dual form			360.2.bo.a.67.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.32591 - 0.491884i) q^{2} +(1.50731 + 0.853236i) q^{3} +(1.51610 + 1.30439i) q^{4} +(-1.08846 + 1.95327i) q^{5} +(-1.57887 - 1.87274i) q^{6} +(-0.188817 + 0.0505935i) q^{7} +(-1.36861 - 2.47526i) q^{8} +(1.54398 + 2.57218i) q^{9} +O(q^{10})$	\(q+(-1.32591 - 0.491884i) q^{2} +(1.50731 + 0.853236i) q^{3} +(1.51610 + 1.30439i) q^{4} +(-1.08846 + 1.95327i) q^{5} +(-1.57887 - 1.87274i) q^{6} +(-0.188817 + 0.0505935i) q^{7} +(-1.36861 - 2.47526i) q^{8} +(1.54398 + 2.57218i) q^{9} +(2.40398 - 2.05448i) q^{10} +(-0.232924 + 0.403435i) q^{11} +(1.17228 + 3.25972i) q^{12} +(2.07510 + 0.556021i) q^{13} +(0.275242 + 0.0257936i) q^{14} +(-3.30724 + 2.01548i) q^{15} +(0.597122 + 3.95518i) q^{16} +(-0.920977 + 0.920977i) q^{17} +(-0.781967 - 4.16996i) q^{18} +4.46687i q^{19} +(-4.19804 + 1.54158i) q^{20} +(-0.327775 - 0.0848457i) q^{21} +(0.507280 - 0.420350i) q^{22} +(-3.71507 - 0.995450i) q^{23} +(0.0490559 - 4.89873i) q^{24} +(-2.63053 - 4.25210i) q^{25} +(-2.47791 - 1.75794i) q^{26} +(0.132575 + 5.19446i) q^{27} +(-0.352260 - 0.169587i) q^{28} +(-3.38365 + 5.86065i) q^{29} +(5.37650 - 1.04557i) q^{30} +(3.98667 - 2.30170i) q^{31} +(1.15376 - 5.53795i) q^{32} +(-0.695314 + 0.409364i) q^{33} +(1.67415 - 0.768123i) q^{34} +(0.106697 - 0.423880i) q^{35} +(-1.01431 + 5.91364i) q^{36} +(-1.27866 - 1.27866i) q^{37} +(2.19718 - 5.92268i) q^{38} +(2.65340 + 2.60864i) q^{39} +(6.32452 + 0.0209428i) q^{40} +(3.27828 + 5.67815i) q^{41} +(0.392867 + 0.273725i) q^{42} +(7.90763 - 2.11884i) q^{43} +(-0.879373 + 0.307825i) q^{44} +(-6.70472 + 0.216096i) q^{45} +(4.43622 + 3.14727i) q^{46} +(2.03363 - 0.544910i) q^{47} +(-2.47465 + 6.47117i) q^{48} +(-6.02909 + 3.48089i) q^{49} +(1.39632 + 6.93183i) q^{50} +(-2.17401 + 0.602389i) q^{51} +(2.42079 + 3.54972i) q^{52} +(5.40217 - 5.40217i) q^{53} +(2.37929 - 6.95262i) q^{54} +(-0.534491 - 0.894084i) q^{55} +(0.383650 + 0.398129i) q^{56} +(-3.81129 + 6.73296i) q^{57} +(7.36919 - 6.10636i) q^{58} +(9.85225 - 5.68820i) q^{59} +(-7.64308 - 1.25827i) q^{60} +(12.8871 + 7.44037i) q^{61} +(-6.41815 + 1.09089i) q^{62} +(-0.421666 - 0.407558i) q^{63} +(-4.25381 + 6.77533i) q^{64} +(-3.34471 + 3.44802i) q^{65} +(1.12329 - 0.200768i) q^{66} +(-9.07697 - 2.43217i) q^{67} +(-2.59761 + 0.194979i) q^{68} +(-4.75042 - 4.67029i) q^{69} +(-0.349971 + 0.509547i) q^{70} -12.3092i q^{71} +(4.25372 - 7.34206i) q^{72} +(-8.43399 - 8.43399i) q^{73} +(1.06644 + 2.32435i) q^{74} +(-0.336985 - 8.65370i) q^{75} +(-5.82655 + 6.77222i) q^{76} +(0.0235688 - 0.0879600i) q^{77} +(-2.23504 - 4.76401i) q^{78} +(5.78276 - 10.0160i) q^{79} +(-8.37547 - 3.13870i) q^{80} +(-4.23227 + 7.94279i) q^{81} +(-1.55373 - 9.14128i) q^{82} +(7.75492 - 2.07792i) q^{83} +(-0.386268 - 0.556182i) q^{84} +(-0.796474 - 2.80136i) q^{85} +(-11.5271 - 1.08023i) q^{86} +(-10.1007 + 5.94678i) q^{87} +(1.31739 + 0.0243999i) q^{88} +1.96777i q^{89} +(8.99619 + 3.01142i) q^{90} -0.419946 q^{91} +(-4.33396 - 6.35511i) q^{92} +(7.97305 - 0.0678175i) q^{93} +(-2.96445 - 0.277806i) q^{94} +(-8.72500 - 4.86199i) q^{95} +(6.46424 - 7.36299i) q^{96} +(-3.27183 - 12.2106i) q^{97} +(9.70625 - 1.64976i) q^{98} +(-1.39734 + 0.0237728i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 272 q - 2 q^{2} - 8 q^{3} - 8 q^{6} - 8 q^{8}+O(q^{10}) $ 272 * q - 2 * q^2 - 8 * q^3 - 8 * q^6 - 8 * q^8	$ 272 q - 2 q^{2} - 8 q^{3} - 8 q^{6} - 8 q^{8} - 8 q^{10} - 8 q^{11} - 10 q^{12} - 4 q^{16} - 16 q^{17} + 20 q^{18} + 14 q^{20} + 6 q^{22} - 4 q^{25} - 48 q^{26} - 8 q^{27} + 8 q^{28} - 34 q^{30} - 22 q^{32} + 4 q^{33} - 16 q^{35} - 8 q^{36} - 26 q^{38} - 2 q^{40} - 8 q^{41} - 66 q^{42} - 4 q^{43} - 40 q^{46} - 38 q^{48} - 42 q^{50} - 16 q^{51} + 14 q^{52} + 24 q^{56} + 16 q^{57} + 6 q^{58} + 14 q^{60} - 76 q^{62} - 4 q^{65} - 44 q^{66} - 4 q^{67} - 46 q^{68} + 18 q^{70} + 38 q^{72} - 16 q^{73} - 120 q^{75} - 38 q^{78} + 92 q^{80} - 32 q^{81} - 4 q^{83} - 40 q^{86} - 42 q^{88} - 14 q^{90} - 32 q^{91} + 52 q^{92} + 108 q^{96} - 4 q^{97} - 140 q^{98}+O(q^{100}) $ 272 * q - 2 * q^2 - 8 * q^3 - 8 * q^6 - 8 * q^8 - 8 * q^10 - 8 * q^11 - 10 * q^12 - 4 * q^16 - 16 * q^17 + 20 * q^18 + 14 * q^20 + 6 * q^22 - 4 * q^25 - 48 * q^26 - 8 * q^27 + 8 * q^28 - 34 * q^30 - 22 * q^32 + 4 * q^33 - 16 * q^35 - 8 * q^36 - 26 * q^38 - 2 * q^40 - 8 * q^41 - 66 * q^42 - 4 * q^43 - 40 * q^46 - 38 * q^48 - 42 * q^50 - 16 * q^51 + 14 * q^52 + 24 * q^56 + 16 * q^57 + 6 * q^58 + 14 * q^60 - 76 * q^62 - 4 * q^65 - 44 * q^66 - 4 * q^67 - 46 * q^68 + 18 * q^70 + 38 * q^72 - 16 * q^73 - 120 * q^75 - 38 * q^78 + 92 * q^80 - 32 * q^81 - 4 * q^83 - 40 * q^86 - 42 * q^88 - 14 * q^90 - 32 * q^91 + 52 * q^92 + 108 * q^96 - 4 * q^97 - 140 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/360\mathbb{Z}\right)^\times$.

$n$	$181$	$217$	$271$	$281$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$	$-1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	−1.32591	−	0.491884i	−0.937563	−	0.347814i
$2$	−1.32591	−	0.491884i	−0.937563	−	0.347814i
$3$	1.50731	+	0.853236i	0.870247	+	0.492616i
$3$	1.50731	+	0.853236i	0.870247	+	0.492616i
$4$	1.51610	+	1.30439i	0.758050	+	0.652196i
$5$	−1.08846	+	1.95327i	−0.486772	+	0.873529i
$5$	−1.08846	+	1.95327i	−0.486772	+	0.873529i
$6$	−1.57887	−	1.87274i	−0.644573	−	0.764543i
$7$	−0.188817	+	0.0505935i	−0.0713663	+	0.0191225i	−0.294326	−	0.955705i	$-0.595095\pi$
$7$	−0.188817	+	0.0505935i	−0.0713663	+	0.0191225i	0.222959	+	0.974828i	$0.428428\pi$
$8$	−1.36861	−	2.47526i	−0.483877	−	0.875136i
$9$	1.54398	+	2.57218i	0.514659	+	0.857395i
$10$	2.40398	−	2.05448i	0.760206	−	0.649682i
$11$	−0.232924	+	0.403435i	−0.0702291	+	0.121640i	−0.899002	−	0.437945i	$-0.855706\pi$
$11$	−0.232924	+	0.403435i	−0.0702291	+	0.121640i	0.828773	+	0.559586i	$0.189040\pi$
$12$	1.17228	+	3.25972i	0.338409	+	0.940999i
$13$	2.07510	+	0.556021i	0.575529	+	0.154212i	0.534831	−	0.844959i	$-0.320375\pi$
$13$	2.07510	+	0.556021i	0.575529	+	0.154212i	0.0406976	+	0.999172i	$0.487042\pi$
$14$	0.275242	+	0.0257936i	0.0735615	+	0.00689363i
$15$	−3.30724	+	2.01548i	−0.853926	+	0.520394i
$16$	0.597122	+	3.95518i	0.149280	+	0.988795i
$17$	−0.920977	+	0.920977i	−0.223370	+	0.223370i	−0.809916	−	0.586546i	$-0.800487\pi$
$17$	−0.920977	+	0.920977i	−0.223370	+	0.223370i	0.586546	+	0.809916i	$0.300487\pi$
$18$	−0.781967	−	4.16996i	−0.184311	−	0.982868i
$19$			4.46687i			1.02477i	0.858756	+	0.512385i	$0.171238\pi$
$19$			4.46687i			1.02477i	−0.858756	+	0.512385i	$0.828762\pi$
$20$	−4.19804	+	1.54158i	−0.938710	+	0.344708i
$21$	−0.327775	−	0.0848457i	−0.0715264	−	0.0185148i
$22$	0.507280	−	0.420350i	0.108152	−	0.0896188i
$23$	−3.71507	−	0.995450i	−0.774646	−	0.207566i	−0.150223	−	0.988652i	$-0.547999\pi$
$23$	−3.71507	−	0.995450i	−0.774646	−	0.207566i	−0.624423	+	0.781086i	$0.714666\pi$
$24$	0.0490559	−	4.89873i	0.0100135	−	0.999950i
$25$	−2.63053	−	4.25210i	−0.526106	−	0.850419i
$26$	−2.47791	−	1.75794i	−0.485957	−	0.344761i
$27$	0.132575	+	5.19446i	0.0255142	+	0.999674i
$28$	−0.352260	−	0.169587i	−0.0665709	−	0.0320490i
$29$	−3.38365	+	5.86065i	−0.628328	+	1.08830i	0.359559	+	0.933122i	$0.382927\pi$
$29$	−3.38365	+	5.86065i	−0.628328	+	1.08830i	−0.987887	+	0.155174i	$0.950406\pi$
$30$	5.37650	−	1.04557i	0.981611	−	0.190895i
$31$	3.98667	−	2.30170i	0.716027	−	0.413398i	−0.0972617	−	0.995259i	$-0.531008\pi$
$31$	3.98667	−	2.30170i	0.716027	−	0.413398i	0.813289	+	0.581861i	$0.197675\pi$
$32$	1.15376	−	5.53795i	0.203957	−	0.978980i
$33$	−0.695314	+	0.409364i	−0.121039	+	0.0712612i
$34$	1.67415	−	0.768123i	0.287115	−	0.131732i
$35$	0.106697	−	0.423880i	0.0180350	−	0.0716488i
$36$	−1.01431	+	5.91364i	−0.169052	+	0.985607i
$37$	−1.27866	−	1.27866i	−0.210210	−	0.210210i	0.594147	−	0.804357i	$-0.297490\pi$
$37$	−1.27866	−	1.27866i	−0.210210	−	0.210210i	−0.804357	+	0.594147i	$0.797490\pi$
$38$	2.19718	−	5.92268i	0.356430	−	0.960786i
$39$	2.65340	+	2.60864i	0.424884	+	0.417717i
$40$	6.32452	+	0.0209428i	0.999995	+	0.00331134i
$41$	3.27828	+	5.67815i	0.511982	+	0.886779i	0.999904	+	0.0138912i	$0.00442183\pi$
$41$	3.27828	+	5.67815i	0.511982	+	0.886779i	−0.487922	+	0.872887i	$0.662245\pi$
$42$	0.392867	+	0.273725i	0.0606208	+	0.0422367i
$43$	7.90763	−	2.11884i	1.20590	−	0.323121i	0.400750	−	0.916188i	$-0.368750\pi$
$43$	7.90763	−	2.11884i	1.20590	−	0.323121i	0.805153	+	0.593067i	$0.202083\pi$
$44$	−0.879373	+	0.307825i	−0.132571	+	0.0464064i
$45$	−6.70472	+	0.216096i	−0.999481	+	0.0322137i
$46$	4.43622	+	3.14727i	0.654085	+	0.464039i
$47$	2.03363	−	0.544910i	0.296636	−	0.0794833i	−0.107432	−	0.994212i	$-0.534263\pi$
$47$	2.03363	−	0.544910i	0.296636	−	0.0794833i	0.404067	+	0.914729i	$0.367596\pi$
$48$	−2.47465	+	6.47117i	−0.357185	+	0.934034i
$49$	−6.02909	+	3.48089i	−0.861298	+	0.497271i
$50$	1.39632	+	6.93183i	0.197469	+	0.980309i
$51$	−2.17401	+	0.602389i	−0.304422	+	0.0843513i
$52$	2.42079	+	3.54972i	0.335703	+	0.492258i
$53$	5.40217	−	5.40217i	0.742045	−	0.742045i	−0.230927	−	0.972971i	$-0.574176\pi$
$53$	5.40217	−	5.40217i	0.742045	−	0.742045i	0.972971	+	0.230927i	$0.0741757\pi$
$54$	2.37929	−	6.95262i	0.323780	−	0.946132i
$55$	−0.534491	−	0.894084i	−0.0720708	−	0.120558i
$56$	0.383650	+	0.398129i	0.0512673	+	0.0532023i
$57$	−3.81129	+	6.73296i	−0.504818	+	0.891802i
$58$	7.36919	−	6.10636i	0.967622	−	0.801805i
$59$	9.85225	−	5.68820i	1.28265	−	0.740541i	0.305321	−	0.952249i	$-0.401236\pi$
$59$	9.85225	−	5.68820i	1.28265	−	0.740541i	0.977333	+	0.211709i	$0.0679028\pi$
$60$	−7.64308	−	1.25827i	−0.986718	−	0.162443i
$61$	12.8871	+	7.44037i	1.65002	+	0.952642i	0.977059	+	0.212967i	$0.0683128\pi$
$61$	12.8871	+	7.44037i	1.65002	+	0.952642i	0.672965	+	0.739675i	$0.265021\pi$
$62$	−6.41815	+	1.09089i	−0.815106	+	0.138543i
$63$	−0.421666	−	0.407558i	−0.0531249	−	0.0513475i
$64$	−4.25381	+	6.77533i	−0.531726	+	0.846916i
$65$	−3.34471	+	3.44802i	−0.414860	+	0.427674i
$66$	1.12329	−	0.200768i	0.138267	−	0.0247129i
$67$	−9.07697	−	2.43217i	−1.10893	−	0.297136i	−0.342533	−	0.939506i	$-0.611285\pi$
$67$	−9.07697	−	2.43217i	−1.10893	−	0.297136i	−0.766395	+	0.642369i	$0.777952\pi$
$68$	−2.59761	+	0.194979i	−0.315006	+	0.0236446i
$69$	−4.75042	−	4.67029i	−0.571883	−	0.562236i
$70$	−0.349971	+	0.509547i	−0.0418295	+	0.0609025i
$71$		−	12.3092i		−	1.46083i	−0.683004	−	0.730415i	$-0.739327\pi$
$71$		−	12.3092i		−	1.46083i	0.683004	−	0.730415i	$-0.260673\pi$
$72$	4.25372	−	7.34206i	0.501305	−	0.865270i
$73$	−8.43399	−	8.43399i	−0.987124	−	0.987124i	0.0127944	−	0.999918i	$-0.495927\pi$
$73$	−8.43399	−	8.43399i	−0.987124	−	0.987124i	−0.999918	+	0.0127944i	$0.995927\pi$
$74$	1.06644	+	2.32435i	0.123971	+	0.270200i
$75$	−0.336985	−	8.65370i	−0.0389117	−	0.999243i
$76$	−5.82655	+	6.77222i	−0.668351	+	0.776827i
$77$	0.0235688	−	0.0879600i	0.00268592	−	0.0100240i
$78$	−2.23504	−	4.76401i	−0.253068	−	0.539417i
$79$	5.78276	−	10.0160i	0.650611	−	1.12689i	−0.332364	−	0.943151i	$-0.607846\pi$
$79$	5.78276	−	10.0160i	0.650611	−	1.12689i	0.982975	−	0.183740i	$-0.0588206\pi$
$80$	−8.37547	−	3.13870i	−0.936407	−	0.350917i
$81$	−4.23227	+	7.94279i	−0.470252	+	0.882532i
$82$	−1.55373	−	9.14128i	−0.171581	−	1.00949i
$83$	7.75492	−	2.07792i	0.851213	−	0.228082i	0.193266	−	0.981146i	$-0.438092\pi$
$83$	7.75492	−	2.07792i	0.851213	−	0.228082i	0.657947	+	0.753065i	$0.271425\pi$
$84$	−0.386268	−	0.556182i	−0.0421453	−	0.0606844i
$85$	−0.796474	−	2.80136i	−0.0863898	−	0.303850i
$86$	−11.5271	−	1.08023i	−1.24300	−	0.116484i
$87$	−10.1007	+	5.94678i	−1.08291	+	0.637562i
$88$	1.31739	+	0.0243999i	0.140434	+	0.00260104i
$89$			1.96777i			0.208584i	0.994547	+	0.104292i	$0.0332576\pi$
$89$			1.96777i			0.208584i	−0.994547	+	0.104292i	$0.966742\pi$
$90$	8.99619	+	3.01142i	0.948281	+	0.317432i
$91$	−0.419946			−0.0440223
$92$	−4.33396	−	6.35511i	−0.451847	−	0.662566i
$93$	7.97305	−	0.0678175i	0.826767	−	0.00703235i
$94$	−2.96445	−	0.277806i	−0.305760	−	0.0286535i
$95$	−8.72500	−	4.86199i	−0.895166	−	0.498829i
$96$	6.46424	−	7.36299i	0.659754	−	0.751482i
$97$	−3.27183	−	12.2106i	−0.332204	−	1.23980i	−0.906868	−	0.421414i	$-0.861534\pi$
$97$	−3.27183	−	12.2106i	−0.332204	−	1.23980i	0.574664	−	0.818389i	$-0.305133\pi$
$98$	9.70625	−	1.64976i	0.980479	−	0.166651i
$99$	−1.39734	+	0.0237728i	−0.140438	+	0.00238926i
$100$	1.55826	−	9.87785i	0.155826	−	0.987785i
$101$	2.65936	+	1.53538i	0.264616	+	0.152776i	0.626439	−	0.779471i	$-0.284512\pi$
$101$	2.65936	+	1.53538i	0.264616	+	0.152776i	−0.361822	+	0.932247i	$0.617845\pi$
$102$	3.17886	+	0.270644i	0.314754	+	0.0267977i
$103$	−3.96466	−	1.06233i	−0.390650	−	0.104674i	0.0581472	−	0.998308i	$-0.481481\pi$
$103$	−3.96466	−	1.06233i	−0.390650	−	0.104674i	−0.448797	+	0.893634i	$0.648147\pi$
$104$	−1.46371	−	5.89738i	−0.143528	−	0.578286i
$105$	0.522495	−	0.547882i	0.0509903	−	0.0534678i
$106$	−9.82005	+	4.50557i	−0.953808	+	0.437620i
$107$	13.3206	−	13.3206i	1.28775	−	1.28775i	0.351605	−	0.936148i	$-0.385636\pi$
$107$	13.3206	−	13.3206i	1.28775	−	1.28775i	0.936148	−	0.351605i	$-0.114364\pi$
$108$	−6.57462	+	8.04826i	−0.632643	+	0.774444i
$109$	−13.8421			−1.32583			−0.662914	−	0.748695i	$-0.730681\pi$
$109$	−13.8421			−1.32583			−0.662914	+	0.748695i	$0.730681\pi$
$110$	0.268904	+	1.44839i	0.0256390	+	0.138098i
$111$	−0.836340	−	3.01834i	−0.0793819	−	0.286488i
$112$	−0.312853	−	0.716596i	−0.0295619	−	0.0677120i
$113$	−2.01876	+	7.53412i	−0.189909	+	0.708751i	0.803617	+	0.595147i	$0.202906\pi$
$113$	−2.01876	+	7.53412i	−0.189909	+	0.708751i	−0.993526	+	0.113604i	$0.963761\pi$
$114$	8.36528	−	7.05262i	0.783480	−	0.660538i
$115$	5.98807	−	6.17303i	0.558391	−	0.575638i
$116$	−12.7745	+	4.47173i	−1.18609	+	0.415190i
$117$	1.77372	+	6.19602i	0.163980	+	0.572822i
$118$	−15.8612	+	2.69591i	−1.46014	+	0.248178i
$119$	0.127301	−	0.220492i	0.0116697	−	0.0202125i
$120$	9.51516	+	5.42787i	0.868611	+	0.495495i
$121$	5.39149	+	9.33834i	0.490136	+	0.848940i
$122$	−13.4274	−	16.2043i	−1.21566	−	1.46706i
$123$	0.0965915	+	11.3559i	0.00870936	+	1.02393i
$124$	9.04652	+	1.71056i	0.812401	+	0.153613i
$125$	11.1687	−	0.509913i	0.998959	−	0.0456080i
$126$	0.358622	+	0.747798i	0.0319485	+	0.0666191i
$127$	6.44664	+	6.44664i	0.572047	+	0.572047i	0.932700	−	0.360653i	$-0.117446\pi$
$127$	6.44664	+	6.44664i	0.572047	+	0.572047i	−0.360653	+	0.932700i	$0.617446\pi$
$128$	8.97286	−	6.89113i	0.793097	−	0.609096i
$129$	13.7271	+	3.55332i	1.20861	+	0.312852i
$130$	6.13083	−	2.92657i	0.537709	−	0.256678i
$131$	0.622881	+	1.07886i	0.0544213	+	0.0942605i	0.891953	−	0.452129i	$-0.149335\pi$
$131$	0.622881	+	1.07886i	0.0544213	+	0.0942605i	−0.837531	+	0.546389i	$0.816002\pi$
$132$	−1.58814	−	0.286325i	−0.138230	−	0.0249214i
$133$	−0.225994	−	0.843422i	−0.0195962	−	0.0731340i
$134$	10.8389	+	7.68966i	0.936342	+	0.664286i
$135$	−10.2905	−	5.39499i	−0.885664	−	0.464326i
$136$	3.54012	+	1.01920i	0.303562	+	0.0873954i
$137$	−2.85902	−	10.6700i	−0.244262	−	0.911599i	−0.973753	−	0.227608i	$-0.926909\pi$
$137$	−2.85902	−	10.6700i	−0.244262	−	0.911599i	0.729491	−	0.683991i	$-0.239757\pi$
$138$	4.00141	+	8.52906i	0.340623	+	0.726041i
$139$	0.555969	−	0.320989i	0.0471566	−	0.0272259i	−0.476236	−	0.879317i	$-0.657999\pi$
$139$	0.555969	−	0.320989i	0.0471566	−	0.0272259i	0.523393	+	0.852091i	$0.324666\pi$
$140$	0.714669	−	0.503471i	0.0604006	−	0.0425510i
$141$	3.53025	+	0.913818i	0.297301	+	0.0769574i
$142$	−6.05468	+	16.3209i	−0.508098	+	1.36962i
$143$	−0.707657	+	0.707657i	−0.0591773	+	0.0591773i
$144$	−9.25151	+	7.64262i	−0.770959	+	0.636885i
$145$	−7.76448	−	12.9882i	−0.644805	−	1.07861i
$146$	7.03421	+	15.3313i	0.582155	+	1.26883i
$147$	−12.0577	+	0.102561i	−0.994505	+	0.00845911i
$148$	−0.270703	−	3.60645i	−0.0222516	−	0.296448i
$149$	1.05975	+	1.83555i	0.0868183	+	0.150374i	0.906165	−	0.422925i	$-0.138997\pi$
$149$	1.05975	+	1.83555i	0.0868183	+	0.150374i	−0.819346	+	0.573299i	$0.805663\pi$
$150$	−3.80980	+	11.6398i	−0.311069	+	0.950387i
$151$	1.19601	+	0.690518i	0.0973301	+	0.0561935i	0.547875	−	0.836560i	$-0.315437\pi$
$151$	1.19601	+	0.690518i	0.0973301	+	0.0561935i	−0.450545	+	0.892754i	$0.648770\pi$
$152$	11.0566	−	6.11340i	0.896813	−	0.495862i
$153$	−3.79089	−	0.946955i	−0.306475	−	0.0765568i
$154$	−0.0745164	+	0.105034i	−0.00600470	+	0.00846391i
$155$	0.156538	+	10.2923i	0.0125734	+	0.826701i
$156$	0.620130	+	7.41604i	0.0496501	+	0.593759i
$157$	−5.00630	+	18.6838i	−0.399547	+	1.49113i	0.414349	+	0.910118i	$0.364009\pi$
$157$	−5.00630	+	18.6838i	−0.399547	+	1.49113i	−0.813896	+	0.581010i	$0.802658\pi$
$158$	−12.5942	+	10.4360i	−1.00194	+	0.830241i
$159$	12.7521	−	3.53343i	1.01130	−	0.280219i
$160$	9.56129	+	8.28141i	0.755886	+	0.654703i
$161$	0.751834			0.0592528
$162$	9.51856	−	8.44968i	0.747848	−	0.663870i
$163$	−2.50128	−	2.50128i	−0.195915	−	0.195915i	0.602331	−	0.798246i	$-0.294239\pi$
$163$	−2.50128	−	2.50128i	−0.195915	−	0.195915i	−0.798246	+	0.602331i	$0.794239\pi$
$164$	−2.43633	+	12.8848i	−0.190246	+	1.00614i
$165$	−0.0427805	−	1.80371i	−0.00333046	−	0.140419i
$166$	−11.3045	−	1.05937i	−0.877396	−	0.0822230i
$167$	−3.25838	+	12.1604i	−0.252141	+	0.941002i	0.717518	+	0.696540i	$0.245278\pi$
$167$	−3.25838	+	12.1604i	−0.252141	+	0.941002i	−0.969659	+	0.244462i	$0.921389\pi$
$168$	0.238581	+	0.927448i	0.0184070	+	0.0715542i
$169$	−7.26146	−	4.19241i	−0.558574	−	0.322493i
$170$	−0.321887	+	4.10614i	−0.0246876	+	0.314926i
$171$	−11.4896	+	6.89674i	−0.878632	+	0.527407i
$172$	14.7526	+	7.10227i	1.12487	+	0.541543i
$173$	2.62507	+	9.79689i	0.199580	+	0.744844i	0.991033	+	0.133614i	$0.0426582\pi$
$173$	2.62507	+	9.79689i	0.199580	+	0.744844i	−0.791453	+	0.611230i	$0.790675\pi$
$174$	16.3178	−	2.91654i	1.23705	−	0.221102i
$175$	0.711818	+	0.669782i	0.0538084	+	0.0506308i
$176$	−1.73474	−	0.680354i	−0.130761	−	0.0512836i
$177$	19.7038	−	0.167597i	1.48103	−	0.0125974i
$178$	0.967916	−	2.60910i	0.0725483	−	0.195560i
$179$		−	24.7190i		−	1.84759i	−0.382891	−	0.923793i	$-0.625072\pi$
$179$		−	24.7190i		−	1.84759i	0.382891	−	0.923793i	$-0.374928\pi$
$180$	−10.4469	−	8.41796i	−0.778666	−	0.627438i
$181$		−	9.90140i		−	0.735966i	−0.929833	−	0.367983i	$-0.880049\pi$
$181$		−	9.90140i		−	0.735966i	0.929833	−	0.367983i	$-0.119951\pi$
$182$	0.556812	+	0.206564i	0.0412737	+	0.0153116i
$183$	13.0765	+	22.2107i	0.966642	+	1.64186i
$184$	2.62049	+	10.5581i	0.193185	+	0.778357i
$185$	3.88933	−	1.10580i	0.285949	−	0.0813003i
$186$	−10.6049	−	3.83189i	−0.777592	−	0.280968i
$187$	−0.157038	−	0.586072i	−0.0114837	−	0.0428578i
$188$	3.79397	+	1.82651i	0.276703	+	0.133212i
$189$	−0.287838	−	0.974097i	−0.0209372	−	0.0708552i
$190$	9.17707	+	10.7383i	0.665775	+	0.779036i
$191$	1.94988	+	1.12576i	0.141088	+	0.0814573i	0.568883	−	0.822419i	$-0.307376\pi$
$191$	1.94988	+	1.12576i	0.141088	+	0.0814573i	−0.427794	+	0.903876i	$0.640709\pi$
$192$	−12.1928	+	6.58303i	−0.879937	+	0.475090i
$193$	3.04772	−	11.3742i	0.219380	−	0.818736i	−0.765199	−	0.643794i	$-0.777359\pi$
$193$	3.04772	−	11.3742i	0.219380	−	0.818736i	0.984579	−	0.174942i	$-0.0559739\pi$
$194$	−1.66805	+	17.7996i	−0.119759	+	1.27794i
$195$	−7.98350	+	2.34342i	−0.571710	+	0.167816i
$196$	−13.6812	−	2.58691i	−0.977225	−	0.184779i
$197$	15.5805	+	15.5805i	1.11006	+	1.11006i	0.993141	+	0.116921i	$0.0373025\pi$
$197$	15.5805	+	15.5805i	1.11006	+	1.11006i	0.116921	+	0.993141i	$0.462698\pi$
$198$	1.86445	+	0.655808i	0.132500	+	0.0466062i
$199$	14.7179			1.04333			0.521664	−	0.853151i	$-0.325312\pi$
$199$	14.7179			1.04333			0.521664	+	0.853151i	$0.325312\pi$
$200$	−6.92487	+	12.3307i	−0.489662	+	0.871912i
$201$	−11.6066	−	11.4108i	−0.818667	−	0.804858i
$202$	−2.77086	−	3.34388i	−0.194957	−	0.235275i
$203$	0.342381	−	1.27778i	0.0240305	−	0.0896829i
$204$	−4.08177	−	1.92248i	−0.285781	−	0.134601i
$205$	−14.6592	+	0.222954i	−1.02385	+	0.0155718i
$206$	4.73426	+	3.35871i	0.329852	+	0.234012i
$207$	−3.17550	−	11.0928i	−0.220713	−	0.771003i
$208$	−0.960076	+	8.53940i	−0.0665693	+	0.592101i
$209$	−1.80209	−	1.04044i	−0.124653	−	0.0719686i
$210$	−0.962278	+	0.469438i	−0.0664035	+	0.0323943i
$211$	6.76693	+	11.7207i	0.465855	+	0.806884i	0.999240	−	0.0389884i	$-0.0124135\pi$
$211$	6.76693	+	11.7207i	0.465855	+	0.806884i	−0.533385	+	0.845873i	$0.679080\pi$
$212$	15.2368	−	1.14368i	1.04647	−	0.0785485i
$213$	10.5026	−	18.5538i	0.719628	−	1.27128i
$214$	−24.2142	+	11.1098i	−1.65525	+	0.759451i
$215$	−4.46843	+	17.7520i	−0.304745	+	1.21068i
$216$	12.6762	−	7.43735i	0.862505	−	0.506048i
$217$	−0.636301	+	0.636301i	−0.0431950	+	0.0431950i
$218$	18.3534	+	6.80869i	1.24305	+	0.461142i
$219$	−5.51647	−	19.9088i	−0.372768	−	1.34531i
$220$	0.355894	−	2.05271i	0.0239944	−	0.138394i
$221$	−2.42320	+	1.39903i	−0.163002	+	0.0941093i
$222$	−0.375755	+	4.41344i	−0.0252190	+	0.296211i
$223$	−3.97663	−	14.8410i	−0.266295	−	0.993826i	−0.961453	−	0.274969i	$-0.911332\pi$
$223$	−3.97663	−	14.8410i	−0.266295	−	0.993826i	0.695158	−	0.718857i	$-0.255334\pi$
$224$	0.0623347	+	1.10403i	0.00416491	+	0.0737663i
$225$	6.87570	−	13.3313i	0.458380	−	0.888756i
$226$	6.38262	−	8.99661i	0.424566	−	0.598446i
$227$	3.61148	+	13.4782i	0.239702	+	0.894581i	0.975973	+	0.217894i	$0.0699186\pi$
$227$	3.61148	+	13.4782i	0.239702	+	0.894581i	−0.736270	+	0.676688i	$0.763415\pi$
$228$	−14.5607	+	5.23643i	−0.964307	+	0.346791i
$229$	−10.1887	−	17.6474i	−0.673291	−	1.16617i	−0.976965	−	0.213398i	$-0.931547\pi$
$229$	−10.1887	−	17.6474i	−0.673291	−	1.16617i	0.303675	−	0.952776i	$-0.401786\pi$
$230$	−10.9761	+	5.23948i	−0.723742	+	0.345481i
$231$	0.110576	−	0.112473i	0.00727538	−	0.00740021i
$232$	19.1375	+	0.354454i	1.25644	+	0.0232711i
$233$	11.5108	+	11.5108i	0.754099	+	0.754099i	0.975242	−	0.221142i	$-0.0709785\pi$
$233$	11.5108	+	11.5108i	0.754099	+	0.754099i	−0.221142	+	0.975242i	$0.570979\pi$
$234$	0.695925	−	9.08785i	0.0454940	−	0.594092i
$235$	−1.14916	+	4.56534i	−0.0749630	+	0.297810i
$236$	22.3567	+	4.22732i	1.45529	+	0.275175i
$237$	17.2625	−	10.1632i	1.12132	−	0.660173i
$238$	−0.277247	+	0.229736i	−0.0179712	+	0.0148916i
$239$	−2.91026	−	5.04071i	−0.188249	−	0.326057i	0.756418	−	0.654089i	$-0.226948\pi$
$239$	−2.91026	−	5.04071i	−0.188249	−	0.326057i	−0.944666	+	0.328032i	$0.893614\pi$
$240$	−9.94640	−	11.8773i	−0.642037	−	0.766673i
$241$	7.27235	−	12.5961i	0.468453	−	0.811384i	−0.530897	−	0.847436i	$-0.678145\pi$
$241$	7.27235	−	12.5961i	0.468453	−	0.811384i	0.999350	+	0.0360521i	$0.0114782\pi$
$242$	−2.55528	−	15.0338i	−0.164260	−	0.966411i
$243$	−13.1564	+	8.36114i	−0.843985	+	0.536367i
$244$	9.83298	+	28.0902i	0.629492	+	1.79829i
$245$	−0.236734	−	15.5652i	−0.0151244	−	0.994426i
$246$	5.45771	−	15.1045i	0.347971	−	0.963025i
$247$	−2.48367	+	9.26918i	−0.158032	+	0.589784i
$248$	−11.1535	−	6.71790i	−0.708249	−	0.426587i
$249$	13.4620	+	3.48469i	0.853122	+	0.220834i
$250$	−15.0596	−	4.81760i	−0.952451	−	0.304692i
$251$	−9.31145			−0.587733			−0.293867	−	0.955846i	$-0.594942\pi$
$251$	−9.31145			−0.587733			−0.293867	+	0.955846i	$0.594942\pi$
$252$	−0.107672	−	1.16792i	−0.00678269	−	0.0735718i
$253$	1.26693	−	1.26693i	0.0796510	−	0.0796510i
$254$	−5.37670	−	11.7187i	−0.337364	−	0.735297i
$255$	1.18969	−	4.90210i	0.0745010	−	0.306982i
$256$	−15.2869	+	4.72345i	−0.955431	+	0.295215i
$257$	−10.6956	−	2.86589i	−0.667176	−	0.178769i	−0.0906936	−	0.995879i	$-0.528908\pi$
$257$	−10.6956	−	2.86589i	−0.667176	−	0.178769i	−0.576482	+	0.817110i	$0.695575\pi$
$258$	−16.4532	−	11.4636i	−1.02433	−	0.713690i
$259$	0.306125	+	0.176741i	0.0190217	+	0.0109822i
$260$	−9.56849	+	0.864734i	−0.593413	+	0.0536285i
$261$	−20.2990	+	0.345345i	−1.25647	+	0.0213763i
$262$	−0.295212	−	1.73686i	−0.0182383	−	0.107304i
$263$	6.90342	+	25.7639i	0.425683	+	1.58867i	0.762426	+	0.647075i	$0.224008\pi$
$263$	6.90342	+	25.7639i	0.425683	+	1.58867i	−0.336743	+	0.941597i	$0.609325\pi$
$264$	1.96490	+	1.16082i	0.120931	+	0.0714436i
$265$	4.67187	+	16.4319i	0.286991	+	1.00940i
$266$	−0.115217	+	1.22947i	−0.00706438	+	0.0753836i
$267$	−1.67897	+	2.96605i	−0.102752	+	0.181519i
$268$	−10.5891	−	15.5273i	−0.646832	−	0.948483i
$269$	−13.0412			−0.795136			−0.397568	−	0.917573i	$-0.630146\pi$
$269$	−13.0412			−0.795136			−0.397568	+	0.917573i	$0.630146\pi$
$270$	10.9906	+	12.2150i	0.668867	+	0.743382i
$271$		−	13.1765i		−	0.800418i	−0.916424	−	0.400209i	$-0.868937\pi$
$271$		−	13.1765i		−	0.800418i	0.916424	−	0.400209i	$-0.131063\pi$
$272$	−4.19257	−	3.09269i	−0.254212	−	0.187522i
$273$	−0.632989	−	0.358313i	−0.0383102	−	0.0216861i
$274$	−1.45759	+	15.5538i	−0.0880559	+	0.939640i
$275$	2.32816	−	0.0708349i	0.140393	−	0.00427150i
$276$	−1.11023	−	13.2770i	−0.0668277	−	0.799183i
$277$	−18.8396	+	5.04804i	−1.13196	+	0.303308i	−0.775714	−	0.631085i	$-0.782610\pi$
$277$	−18.8396	+	5.04804i	−1.13196	+	0.303308i	−0.356245	+	0.934392i	$0.615943\pi$
$278$	−0.895056	+	0.152132i	−0.0536819	+	0.00912425i
$279$	12.0757	+	6.70067i	0.722955	+	0.401159i
$280$	−1.19524	+	0.316025i	−0.0714292	+	0.0188861i
$281$	11.3874	−	19.7236i	0.679317	−	1.17661i	−0.295870	−	0.955228i	$-0.595610\pi$
$281$	11.3874	−	19.7236i	0.679317	−	1.17661i	0.975187	−	0.221383i	$-0.0710571\pi$
$282$	−4.23132	−	2.94812i	−0.251972	−	0.175558i
$283$	−2.64552	+	9.87322i	−0.157260	+	0.586902i	0.841641	+	0.540037i	$0.181590\pi$
$283$	−2.64552	+	9.87322i	−0.157260	+	0.586902i	−0.998901	+	0.0468650i	$0.985077\pi$
$284$	16.0560	−	18.6619i	0.952747	−	1.10738i
$285$	−9.00287	−	14.7730i	−0.533284	−	0.875078i
$286$	1.28638	−	0.590208i	0.0760652	−	0.0348997i
$287$	−0.906275	−	0.906275i	−0.0534957	−	0.0534957i
$288$	16.0260	−	5.58279i	0.944341	−	0.328969i
$289$			15.3036i			0.900212i
$290$	3.90634	+	21.0405i	0.229388	+	1.23554i
$291$	5.48689	−	21.1969i	0.321647	−	1.24258i
$292$	−1.78555	−	23.7880i	−0.104491	−	1.39209i
$293$	−8.03221	−	2.15222i	−0.469247	−	0.125734i	0.0164443	−	0.999865i	$-0.494765\pi$
$293$	−8.03221	−	2.15222i	−0.469247	−	0.125734i	−0.485691	+	0.874130i	$0.661432\pi$
$294$	16.0380	+	5.79502i	0.935354	+	0.337972i
$295$	0.386851	+	25.4355i	0.0225233	+	1.48091i
$296$	−1.41503	+	4.91500i	−0.0822467	+	0.285679i
$297$	−2.12651	−	1.15643i	−0.123393	−	0.0671027i
$298$	−0.502267	−	2.95505i	−0.0290955	−	0.171182i
$299$	−7.15565	−	4.13131i	−0.413822	−	0.238920i
$300$	10.7769	−	13.5594i	0.622205	−	0.782854i
$301$	−1.38590	+	0.800149i	−0.0798819	+	0.0461198i
$302$	−1.24616	−	1.50387i	−0.0717082	−	0.0865378i
$303$	2.69844	+	4.58336i	0.155022	+	0.263307i
$304$	−17.6673	+	2.66726i	−1.01329	+	0.152978i
$305$	−28.5601	+	17.0735i	−1.63535	+	0.977624i
$306$	4.56061	+	3.12026i	0.260713	+	0.178373i
$307$	−17.6869	+	17.6869i	−1.00944	+	1.00944i	−0.00948742	+	0.999955i	$0.503020\pi$
$307$	−17.6869	+	17.6869i	−1.00944	+	1.00944i	−0.999955	+	0.00948742i	$0.996980\pi$
$308$	0.150467	−	0.102613i	0.00857366	−	0.00584693i
$309$	−5.06957	−	4.98405i	−0.288398	−	0.283533i
$310$	4.85508	−	13.7238i	0.275750	−	0.779458i
$311$	11.2543	−	6.49767i	0.638172	−	0.368449i	−0.145738	−	0.989323i	$-0.546556\pi$
$311$	11.2543	−	6.49767i	0.638172	−	0.368449i	0.783910	+	0.620874i	$0.213222\pi$
$312$	2.82559	−	10.1381i	0.159968	−	0.573955i
$313$	6.77905	−	1.81644i	0.383174	−	0.102671i	−0.0620897	−	0.998071i	$-0.519776\pi$
$313$	6.77905	−	1.81644i	0.383174	−	0.102671i	0.445264	+	0.895399i	$0.353110\pi$
$314$	15.8282	−	22.3106i	0.893236	−	1.25906i
$315$	1.25504	−	0.380018i	0.0707132	−	0.0214116i
$316$	21.8321	−	7.64233i	1.22815	−	0.429914i
$317$	−7.12309	+	1.90863i	−0.400073	+	0.107199i	−0.453245	−	0.891386i	$-0.649734\pi$
$317$	−7.12309	+	1.90863i	−0.400073	+	0.107199i	0.0531719	+	0.998585i	$0.483067\pi$
$318$	−18.6462	−	1.58751i	−1.04563	−	0.0890233i
$319$	−1.57626	−	2.73017i	−0.0882538	−	0.152860i
$320$	−8.60397	−	15.6835i	−0.480976	−	0.876734i
$321$	31.4440	−	8.71270i	1.75503	−	0.486296i
$322$	−0.996867	−	0.369815i	−0.0555533	−	0.0206090i
$323$	−4.11388	−	4.11388i	−0.228903	−	0.228903i
$324$	−16.7771	+	6.52153i	−0.932059	+	0.362307i
$325$	−3.09435	−	10.2861i	−0.171644	−	0.570573i
$326$	2.08614	+	4.54682i	0.115541	+	0.251825i
$327$	−20.8643	−	11.8105i	−1.15380	−	0.653124i
$328$	9.56820	−	15.8858i	0.528316	−	0.877146i
$329$	−0.356416	+	0.205777i	−0.0196499	+	0.0113449i
$330$	−0.830493	+	2.41261i	−0.0457171	+	0.132810i
$331$	−9.15059	+	15.8493i	−0.502962	+	0.871156i	0.497032	+	0.867732i	$0.334423\pi$
$331$	−9.15059	+	15.8493i	−0.502962	+	0.871156i	−0.999994	+	0.00342373i	$0.998910\pi$
$332$	14.4677	+	6.96511i	0.794016	+	0.382260i
$333$	1.31473	−	5.26317i	0.0720466	−	0.288420i
$334$	10.3018	−	14.5209i	0.563692	−	0.794551i
$335$	14.6306	−	15.0825i	0.799353	−	0.824043i
$336$	0.139858	−	1.34707i	0.00762989	−	0.0734888i
$337$	8.47040	+	2.26964i	0.461412	+	0.123635i	0.482034	−	0.876152i	$-0.339898\pi$
$337$	8.47040	+	2.26964i	0.461412	+	0.123635i	−0.0206222	+	0.999787i	$0.506565\pi$
$338$	7.56590	+	9.13057i	0.411531	+	0.496637i
$339$	−9.47129	+	9.63379i	−0.514410	+	0.523236i
$340$	2.44654	−	5.28606i	0.132682	−	0.286677i
$341$			2.14448i			0.116130i
$342$	18.6266	−	3.49294i	1.00721	−	0.188877i
$343$	1.92985	−	1.92985i	0.104202	−	0.104202i
$344$	−16.0672	−	16.6736i	−0.866283	−	0.898978i
$345$	14.2929	−	4.19545i	0.769507	−	0.225875i
$346$	1.33831	−	14.2811i	0.0719482	−	0.767755i
$347$	−11.7649	−	3.15239i	−0.631573	−	0.169229i	−0.0711893	−	0.997463i	$-0.522679\pi$
$347$	−11.7649	−	3.15239i	−0.631573	−	0.169229i	−0.560383	+	0.828233i	$0.689346\pi$
$348$	−23.0707	−	4.15940i	−1.23672	−	0.222967i
$349$	1.93383	−	3.34949i	0.103516	−	0.179294i	−0.809615	−	0.586961i	$-0.800324\pi$
$349$	1.93383	−	3.34949i	0.103516	−	0.179294i	0.913131	+	0.407667i	$0.133658\pi$
$350$	−0.614355	−	1.23821i	−0.0328387	−	0.0661849i
$351$	−2.61312	+	10.8527i	−0.139478	+	0.579276i
$352$	1.96547	+	1.75538i	0.104760	+	0.0935623i
$353$	3.95631	−	1.06009i	0.210573	−	0.0564229i	−0.151990	−	0.988382i	$-0.548568\pi$
$353$	3.95631	−	1.06009i	0.210573	−	0.0564229i	0.362564	+	0.931959i	$0.381902\pi$
$354$	−26.2080	−	9.46976i	−1.39294	−	0.503312i
$355$	24.0431	+	13.3980i	1.27608	+	0.711091i
$356$	−2.56675	+	2.98334i	−0.136037	+	0.158117i
$357$	0.380014	−	0.223732i	0.0201125	−	0.0118412i
$358$	−12.1589	+	32.7753i	−0.642617	+	1.73223i
$359$	−36.5561			−1.92936			−0.964680	−	0.263425i	$-0.915148\pi$
$359$	−36.5561			−1.92936			−0.964680	+	0.263425i	$0.915148\pi$
$360$	9.71105	+	16.3002i	0.511817	+	0.859094i
$361$	−0.952897			−0.0501525
$362$	−4.87034	+	13.1284i	−0.255979	+	0.690014i
$363$	0.158855	+	18.6760i	0.00833774	+	0.980236i
$364$	−0.636680	−	0.547774i	−0.0333711	−	0.0287112i
$365$	25.6539	−	7.29383i	1.34279	−	0.381777i
$366$	−6.41323	−	35.8816i	−0.335225	−	1.87556i
$367$	10.0058	−	2.68106i	0.522301	−	0.139950i	0.0119701	−	0.999928i	$-0.496190\pi$
$367$	10.0058	−	2.68106i	0.522301	−	0.139950i	0.510331	+	0.859978i	$0.329523\pi$
$368$	1.71884	−	15.2882i	0.0896005	−	0.796952i
$369$	−9.54366	+	17.1993i	−0.496823	+	0.895359i
$370$	−5.70085	−	0.446899i	−0.296373	−	0.0232332i
$371$	−0.746709	+	1.29334i	−0.0387672	+	0.0671467i
$372$	12.1764	+	10.2972i	0.631317	+	0.533883i
$373$	−2.30653	−	0.618034i	−0.119428	−	0.0320006i	0.198610	−	0.980079i	$-0.436357\pi$
$373$	−2.30653	−	0.618034i	−0.119428	−	0.0320006i	−0.318038	+	0.948078i	$0.603024\pi$
$374$	−0.0800610	+	0.854326i	−0.00413985	+	0.0441761i
$375$	17.2698	+	8.76094i	0.891809	+	0.452413i
$376$	−4.13204	−	4.28799i	−0.213094	−	0.221136i
$377$	−10.2800	+	10.2800i	−0.529449	+	0.529449i
$378$	−0.0974935	+	1.43315i	−0.00501453	+	0.0737135i
$379$			19.6935i			1.01158i	0.862655	+	0.505792i	$0.168800\pi$
$379$			19.6935i			1.01158i	−0.862655	+	0.505792i	$0.831200\pi$
$380$	−6.88603	−	18.7521i	−0.353246	−	0.961961i
$381$	4.21660	+	15.2176i	0.216023	+	0.779622i
$382$	−2.03163	−	2.45178i	−0.103947	−	0.125444i
$383$	−3.69752	−	0.990747i	−0.188934	−	0.0506248i	0.163111	−	0.986608i	$-0.447847\pi$
$383$	−3.69752	−	0.990747i	−0.188934	−	0.0506248i	−0.352045	+	0.935983i	$0.614514\pi$
$384$	19.4047	−	2.73112i	0.990240	−	0.139372i
$385$	0.146156	+	0.141777i	0.00744881	+	0.00722562i
$386$	−9.63583	+	13.5822i	−0.490451	+	0.691314i
$387$	17.6593	+	17.0684i	0.897671	+	0.867638i
$388$	10.9670	−	22.7803i	0.556767	−	1.15650i
$389$	−4.86357	+	8.42395i	−0.246593	+	0.427111i	−0.962578	−	0.271004i	$-0.912644\pi$
$389$	−4.86357	+	8.42395i	−0.246593	+	0.427111i	0.715986	+	0.698115i	$0.245978\pi$
$390$	11.7381	+	0.819781i	0.594383	+	0.0415112i
$391$	4.33828	−	2.50471i	0.219396	−	0.126669i
$392$	16.8676	+	10.1596i	0.851942	+	0.513135i
$393$	0.0183526	+	2.15764i	0.000925766	+	0.108839i
$394$	−12.9946	−	28.3222i	−0.654658	−	1.42685i
$395$	13.2697	+	22.1973i	0.667673	+	1.11687i
$396$	−2.14952	−	1.78664i	−0.108017	−	0.0897818i
$397$	17.0512	+	17.0512i	0.855773	+	0.855773i	0.990837	−	0.135064i	$-0.0431239\pi$
$397$	17.0512	+	17.0512i	0.855773	+	0.855773i	−0.135064	+	0.990837i	$0.543124\pi$
$398$	−19.5147	−	7.23952i	−0.978186	−	0.362884i
$399$	0.378994	−	1.46413i	0.0189734	−	0.0732980i
$400$	15.2471	−	12.9432i	0.762353	−	0.647162i
$401$	9.09930	+	15.7604i	0.454397	+	0.787039i	0.998653	−	0.0518800i	$-0.0165213\pi$
$401$	9.09930	+	15.7604i	0.454397	+	0.787039i	−0.544256	+	0.838919i	$0.683188\pi$
$402$	9.77658	+	20.8389i	0.487611	+	1.03935i
$403$	9.55252	−	2.55959i	0.475845	−	0.127502i
$404$	2.02912	+	5.79665i	0.100952	+	0.288394i
$405$	−10.9078	−	16.9121i	−0.542012	−	0.840371i
$406$	−1.08249	+	1.52582i	−0.0537231	+	0.0757252i
$407$	0.813686	−	0.218027i	0.0403329	−	0.0108072i
$408$	4.46644	+	4.55680i	0.221122	+	0.225595i
$409$	20.9062	−	12.0702i	1.03374	−	0.596833i	0.115689	−	0.993285i	$-0.463092\pi$
$409$	20.9062	−	12.0702i	1.03374	−	0.596833i	0.918055	+	0.396453i	$0.129759\pi$
$410$	19.5466	+	6.91502i	0.965336	+	0.341509i
$411$	4.79459	−	18.5224i	0.236500	−	0.913644i
$412$	−4.62514	−	6.78207i	−0.227864	−	0.334129i
$413$	−1.57249	+	1.57249i	−0.0773773	+	0.0773773i
$414$	−1.24592	+	16.2701i	−0.0612337	+	0.799631i
$415$	−4.38214	+	17.4092i	−0.215111	+	0.854583i
$416$	5.47337	−	10.8503i	0.268354	−	0.531978i
$417$	1.11190	−	0.00945763i	0.0544498	−	0.000463142i
$418$	1.87765	+	2.26595i	0.0918387	+	0.110831i
$419$	−28.0572	+	16.1988i	−1.37068	+	0.791364i	−0.991014	−	0.133759i	$-0.957295\pi$
$419$	−28.0572	+	16.1988i	−1.37068	+	0.791364i	−0.379669	+	0.925123i	$0.623962\pi$
$420$	1.50681	−	0.149106i	0.0735247	−	0.00727564i
$421$	32.4773	+	18.7508i	1.58285	+	0.913857i	0.994442	+	0.105290i	$0.0335770\pi$
$421$	32.4773	+	18.7508i	1.58285	+	0.913857i	0.588404	+	0.808567i	$0.299756\pi$
$422$	−3.20717	−	18.8692i	−0.156122	−	0.918536i
$423$	4.54149	+	4.38955i	0.220815	+	0.213427i
$424$	−20.7652	−	5.97829i	−1.00845	−	0.290332i
$425$	6.33874	+	1.49343i	0.307474	+	0.0724419i
$426$	−23.0519	+	19.4346i	−1.11687	+	0.941611i
$427$	−2.80974	−	0.752869i	−0.135973	−	0.0364339i
$428$	37.5707	−	2.82009i	1.81605	−	0.136314i
$429$	−1.67046	+	0.462862i	−0.0806505	+	0.0223472i
$430$	14.6567	−	21.3397i	0.706808	−	1.02909i
$431$		−	35.6049i		−	1.71503i	−0.514460	−	0.857515i	$-0.672008\pi$
$431$		−	35.6049i		−	1.71503i	0.514460	−	0.857515i	$-0.327992\pi$
$432$	−20.4659	+	3.62609i	−0.984664	+	0.174460i
$433$	−6.47693	−	6.47693i	−0.311261	−	0.311261i	0.534137	−	0.845398i	$-0.320637\pi$
$433$	−6.47693	−	6.47693i	−0.311261	−	0.311261i	−0.845398	+	0.534137i	$0.820637\pi$
$434$	1.15667	−	0.530695i	0.0555218	−	0.0254742i
$435$	−0.621466	−	26.2023i	−0.0297970	−	1.25630i
$436$	−20.9860	−	18.0555i	−1.00504	−	0.864700i
$437$	4.44654	−	16.5947i	0.212707	−	0.793834i
$438$	−2.47846	+	29.1109i	−0.118426	+	1.39097i
$439$	−7.39780	+	12.8134i	−0.353078	+	0.611549i	−0.986787	−	0.162023i	$-0.948198\pi$
$439$	−7.39780	+	12.8134i	−0.353078	+	0.611549i	0.633709	+	0.773571i	$0.281532\pi$
$440$	−1.48158	+	2.54666i	−0.0706315	+	0.121407i
$441$	−18.2623	−	10.1335i	−0.869632	−	0.482548i
$442$	3.90112	−	0.663069i	0.185557	−	0.0315390i
$443$	−9.69296	+	2.59722i	−0.460527	+	0.123398i	−0.481621	−	0.876380i	$-0.659952\pi$
$443$	−9.69296	+	2.59722i	−0.460527	+	0.123398i	0.0210941	+	0.999777i	$0.493285\pi$
$444$	2.66912	−	5.66702i	0.126671	−	0.268945i
$445$	−3.84359	−	2.14183i	−0.182204	−	0.101533i
$446$	−2.02737	+	21.6339i	−0.0959987	+	1.02440i
$447$	0.0312246	+	3.67096i	0.00147687	+	0.173630i
$448$	0.460406	−	1.49452i	0.0217521	−	0.0706092i
$449$			22.1944i			1.04742i	0.851898	+	0.523708i	$0.175452\pi$
$449$			22.1944i			1.04742i	−0.851898	+	0.523708i	$0.824548\pi$
$450$	−15.6741	+	14.2942i	−0.738883	+	0.673834i
$451$	−3.05436			−0.143824
$452$	−12.8881	+	8.78923i	−0.606205	+	0.413411i
$453$	1.21359	+	2.06131i	0.0570193	+	0.0968486i
$454$	1.84121	−	19.6474i	0.0864121	−	0.922099i
$455$	0.457092	−	0.820267i	0.0214288	−	0.0384547i
$456$	21.8820	+	0.219126i	1.02472	+	0.0102615i
$457$	7.84284	+	29.2699i	0.366872	+	1.36919i	0.864865	+	0.502005i	$0.167404\pi$
$457$	7.84284	+	29.2699i	0.366872	+	1.36919i	−0.497992	+	0.867182i	$0.665929\pi$
$458$	4.82892	+	28.4106i	0.225641	+	1.32754i
$459$	−4.90608	−	4.66188i	−0.228996	−	0.217598i
$460$	17.1306	−	1.54814i	0.798718	−	0.0721825i
$461$	−32.8488	−	18.9653i	−1.52992	−	0.883301i	−0.999364	−	0.0356524i	$-0.988649\pi$
$461$	−32.8488	−	18.9653i	−1.52992	−	0.883301i	−0.530558	−	0.847649i	$-0.678018\pi$
$462$	−0.201939	+	0.0947396i	−0.00939503	+	0.00440768i
$463$	−25.5974	−	6.85881i	−1.18961	−	0.318756i	−0.390881	−	0.920441i	$-0.627830\pi$
$463$	−25.5974	−	6.85881i	−1.18961	−	0.318756i	−0.798733	+	0.601685i	$0.794496\pi$
$464$	−25.2004	−	9.88342i	−1.16990	−	0.458826i
$465$	−8.54585	+	15.6473i	−0.396304	+	0.725628i
$466$	−9.60039	−	20.9244i	−0.444729	−	0.969302i
$467$	−1.64391	+	1.64391i	−0.0760711	+	0.0760711i	−0.744119	−	0.668048i	$-0.767130\pi$
$467$	−1.64391	+	1.64391i	−0.0760711	+	0.0760711i	0.668048	+	0.744119i	$0.267130\pi$
$468$	−5.39291	+	11.7074i	−0.249287	+	0.541175i
$469$	1.83694			0.0848221
$470$	3.76931	−	5.48800i	0.173865	−	0.253143i
$471$	−23.4877	+	23.8907i	−1.08226	+	1.10083i
$472$	−27.5637	−	16.6019i	−1.26872	−	0.764166i
$473$	−0.987057	+	3.68375i	−0.0453849	+	0.169379i
$474$	−27.8877	+	4.98445i	−1.28092	+	0.228943i
$475$	18.9935	−	11.7502i	0.871484	−	0.539137i
$476$	0.480609	−	0.168237i	0.0220287	−	0.00771115i
$477$	22.2362	+	5.55455i	1.01813	+	0.254325i
$478$	1.37931	+	8.11506i	0.0630881	+	0.371174i
$479$	14.1745	−	24.5509i	0.647649	−	1.12176i	−0.336034	−	0.941850i	$-0.609086\pi$
$479$	14.1745	−	24.5509i	0.647649	−	1.12176i	0.983683	−	0.179911i	$-0.0575808\pi$
$480$	7.34585	+	20.6407i	0.335291	+	0.942115i
$481$	−1.94238	−	3.36430i	−0.0885650	−	0.153399i
$482$	−15.8383	+	13.1242i	−0.721415	+	0.597790i
$483$	1.13325	+	0.641491i	0.0515646	+	0.0291889i
$484$	−4.00681	+	21.1905i	−0.182128	+	0.963204i
$485$	27.4119	+	6.89998i	1.24471	+	0.313312i
$486$	21.5570	−	4.61473i	0.977845	−	0.209328i
$487$	−30.5533	−	30.5533i	−1.38450	−	1.38450i	−0.836434	−	0.548068i	$-0.815363\pi$
$487$	−30.5533	−	30.5533i	−1.38450	−	1.38450i	−0.548068	−	0.836434i	$-0.684637\pi$
$488$	0.779416	−	42.0819i	0.0352825	−	1.90496i
$489$	−1.63603	−	5.90439i	−0.0739837	−	0.267006i
$490$	−7.34240	+	20.7546i	−0.331696	+	0.937598i
$491$	−16.0111	−	27.7321i	−0.722573	−	1.25153i	−0.959965	−	0.280119i	$-0.909626\pi$
$491$	−16.0111	−	27.7321i	−0.722573	−	1.25153i	0.237392	−	0.971414i	$-0.423707\pi$
$492$	−14.6661	+	17.3427i	−0.661199	+	0.781868i
$493$	−2.28126	−	8.51379i	−0.102743	−	0.383442i
$494$	7.85250	−	11.0685i	0.353301	−	0.497994i
$495$	1.47451	−	2.75526i	0.0662742	−	0.123840i
$496$	11.4842	+	14.3936i	0.515655	+	0.646291i
$497$	0.622764	+	2.32419i	0.0279348	+	0.104254i
$498$	−16.1355	−	11.2422i	−0.723047	−	0.503774i
$499$	20.8466	−	12.0358i	0.933223	−	0.538797i	0.0453938	−	0.998969i	$-0.485546\pi$
$499$	20.8466	−	12.0358i	0.933223	−	0.538797i	0.887830	+	0.460172i	$0.152212\pi$
$500$	17.5980	+	13.7953i	0.787007	+	0.616944i
$501$	−15.2871	+	15.5494i	−0.682977	+	0.694696i
$502$	12.3462	+	4.58015i	0.551037	+	0.204422i
$503$	13.4239	−	13.4239i	0.598540	−	0.598540i	−0.341384	−	0.939924i	$-0.610896\pi$
$503$	13.4239	−	13.4239i	0.598540	−	0.598540i	0.939924	+	0.341384i	$0.110896\pi$
$504$	−0.431716	+	1.60152i	−0.0192301	+	0.0713374i
$505$	−5.89362	+	3.52325i	−0.262262	+	0.156783i
$506$	−2.30302	+	1.05666i	−0.102382	+	0.0469741i
$507$	−7.36817	−	12.5150i	−0.327232	−	0.555811i
$508$	1.36481	+	18.1827i	0.0605536	+	0.806727i
$509$	2.14413	+	3.71374i	0.0950369	+	0.164609i	0.909624	−	0.415433i	$-0.136370\pi$
$509$	2.14413	+	3.71374i	0.0950369	+	0.164609i	−0.814587	+	0.580041i	$0.803036\pi$
$510$	−3.98869	+	5.91458i	−0.176622	+	0.261902i
$511$	2.01919	+	1.16578i	0.0893237	+	0.0515710i
$512$	22.5925	+	1.25649i	0.998457	+	0.0555293i
$513$	−23.2030	+	0.592197i	−1.02444	+	0.0261461i
$514$	12.7718	+	9.06094i	0.563341	+	0.399661i
$515$	6.39038	−	6.58776i	0.281594	−	0.290291i
$516$	16.1768	+	23.2928i	0.712144	+	1.02541i
$517$	−0.253845	+	0.947361i	−0.0111641	+	0.0416649i
$518$	−0.318960	−	0.384922i	−0.0140143	−	0.0169125i
$519$	−4.40226	+	17.0068i	−0.193238	+	0.746514i
$520$	13.1124	+	3.56002i	0.575015	+	0.156117i
$521$	−7.13723			−0.312688			−0.156344	−	0.987703i	$-0.549971\pi$
$521$	−7.13723			−0.312688			−0.156344	+	0.987703i	$0.549971\pi$
$522$	27.0846	+	9.52683i	1.18546	+	0.416978i
$523$	−22.5211	−	22.5211i	−0.984780	−	0.984780i	0.0151057	−	0.999886i	$-0.495192\pi$
$523$	−22.5211	−	22.5211i	−0.984780	−	0.984780i	−0.999886	+	0.0151057i	$0.995192\pi$
$524$	−0.462908	+	2.44814i	−0.0202222	+	0.106948i
$525$	0.501449	+	1.61692i	0.0218850	+	0.0705681i
$526$	3.51951	−	37.5564i	0.153458	−	1.63754i
$527$	−1.55181	+	5.79145i	−0.0675981	+	0.252279i
$528$	−2.03430	−	2.50565i	−0.0885314	−	0.109044i
$529$	−7.10775	−	4.10366i	−0.309033	−	0.178420i
$530$	1.88809	−	24.0853i	0.0820133	−	1.04620i
$531$	29.8428	+	16.5594i	1.29507	+	0.718615i
$532$	0.757523	−	1.57350i	0.0328428	−	0.0682198i
$533$	3.64559	+	13.6055i	0.157908	+	0.589320i
$534$	3.68513	−	3.10687i	0.159471	−	0.134447i
$535$	11.5199	+	40.5177i	0.498047	+	1.75173i
$536$	6.40260	+	25.7965i	0.276550	+	1.11424i
$537$	21.0912	−	37.2593i	0.910151	−	1.60786i
$538$	17.2915	+	6.41475i	0.745490	+	0.276560i
$539$		−	3.24313i		−	0.139691i
$540$	−8.56424	−	21.6022i	−0.368546	−	0.929609i
$541$			9.19452i			0.395303i	0.980272	+	0.197652i	$0.0633315\pi$
$541$			9.19452i			0.395303i	−0.980272	+	0.197652i	$0.936669\pi$
$542$	−6.48133	+	17.4710i	−0.278397	+	0.750443i
$543$	8.44823	−	14.9245i	0.362548	−	0.640472i
$544$	4.03774	+	6.16290i	0.173117	+	0.264232i
$545$	15.0665	−	27.0373i	0.645377	−	1.15815i
$546$	0.663041	+	0.786449i	0.0283756	+	0.0336569i
$547$	−0.780613	−	2.91329i	−0.0333766	−	0.124563i	0.947228	−	0.320562i	$-0.103872\pi$
$547$	−0.780613	−	2.91329i	−0.0333766	−	0.124563i	−0.980604	+	0.195999i	$0.937205\pi$
$548$	9.58330	−	19.9061i	0.409378	−	0.850345i
$549$	0.759385	+	44.6358i	0.0324098	+	1.90501i
$550$	−3.12178	−	1.05126i	−0.133113	−	0.0448260i
$551$	−26.1788	−	15.1143i	−1.11525	−	0.643891i
$552$	−5.05869	+	18.1503i	−0.215312	+	0.772529i
$553$	−0.585140	+	2.18377i	−0.0248827	+	0.0928634i
$554$	27.4627	+	2.57360i	1.16678	+	0.109342i
$555$	6.80595	+	1.65173i	0.288896	+	0.0701119i
$556$	1.26160	+	0.238550i	0.0535037	+	0.0101168i
$557$	−24.3679	−	24.3679i	−1.03250	−	1.03250i	−0.999454	−	0.0330478i	$-0.989479\pi$
$557$	−24.3679	−	24.3679i	−1.03250	−	1.03250i	−0.0330478	−	0.999454i	$-0.510521\pi$
$558$	−12.7154	−	14.8244i	−0.538288	−	0.627566i
$559$	17.5872			0.743861
$560$	1.74023	+	0.168897i	0.0735383	+	0.00713718i
$561$	0.263353	−	1.01738i	0.0111188	−	0.0429539i
$562$	−24.8005	+	20.5505i	−1.04614	+	0.866871i
$563$	3.94584	−	14.7261i	0.166297	−	0.620630i	−0.831574	−	0.555414i	$-0.812560\pi$
$563$	3.94584	−	14.7261i	0.166297	−	0.620630i	0.997871	−	0.0652157i	$-0.0207735\pi$
$564$	4.16024	+	5.99027i	0.175178	+	0.252236i
$565$	−12.5188	−	12.1437i	−0.526672	−	0.510891i
$566$	8.36421	−	11.7898i	0.351574	−	0.495561i
$567$	0.397273	−	1.71386i	0.0166839	−	0.0719755i
$568$	−30.4684	+	16.8465i	−1.27842	+	0.706862i
$569$	−28.1232	−	16.2370i	−1.17899	−	0.680689i	−0.223207	−	0.974771i	$-0.571653\pi$
$569$	−28.1232	−	16.2370i	−1.17899	−	0.680689i	−0.955780	+	0.294082i	$0.904986\pi$
$570$	4.67043	+	24.0161i	0.195623	+	1.00592i
$571$	1.81476	+	3.14325i	0.0759452	+	0.131541i	0.901497	−	0.432786i	$-0.142469\pi$
$571$	1.81476	+	3.14325i	0.0759452	+	0.131541i	−0.825552	+	0.564326i	$0.809136\pi$
$572$	−1.99594	+	0.149817i	−0.0834546	+	0.00626416i
$573$	1.97853	+	3.36058i	0.0826544	+	0.140390i
$574$	0.755861	+	1.64742i	0.0315490	+	0.0687622i
$575$	5.53985	+	18.4154i	0.231028	+	0.767975i
$576$	−23.9952	−	0.480623i	−0.999799	−	0.0200260i
$577$	11.2348	−	11.2348i	0.467712	−	0.467712i	−0.433461	−	0.901172i	$-0.642708\pi$
$577$	11.2348	−	11.2348i	0.467712	−	0.467712i	0.901172	+	0.433461i	$0.142708\pi$
$578$	7.52759	−	20.2913i	0.313107	−	0.844006i
$579$	14.2988	−	14.5441i	0.594237	−	0.604433i
$580$	5.17002	−	29.8194i	0.214673	−	1.23818i
$581$	−1.35913	+	0.784697i	−0.0563864	+	0.0325547i
$582$	−17.7016	+	25.4064i	−0.733753	+	1.05313i
$583$	0.921133	+	3.43772i	0.0381494	+	0.142376i
$584$	−9.33345	+	32.4192i	−0.386221	+	1.34151i
$585$	−14.0331	−	3.27954i	−0.580198	−	0.135592i
$586$	9.59139	+	6.80458i	0.396216	+	0.281095i
$587$	6.78917	+	25.3375i	0.280219	+	1.04579i	0.952262	+	0.305281i	$0.0987502\pi$
$587$	6.78917	+	25.3375i	0.280219	+	1.04579i	−0.672043	+	0.740512i	$0.734583\pi$
$588$	−18.4145	−	15.5725i	−0.759402	−	0.642200i
$589$	10.2814	+	17.8079i	0.423638	+	0.733762i
$590$	11.9984	−	33.9156i	0.493965	−	1.39628i
$591$	10.1908	+	36.7784i	0.419194	+	1.51286i
$592$	4.29381	−	5.82084i	0.176475	−	0.239235i
$593$	−13.5488	−	13.5488i	−0.556383	−	0.556383i	0.371893	−	0.928276i	$-0.378709\pi$
$593$	−13.5488	−	13.5488i	−0.556383	−	0.556383i	−0.928276	+	0.371893i	$0.878709\pi$
$594$	2.25074	+	2.57932i	0.0923491	+	0.105831i
$595$	0.292119	+	0.488649i	0.0119757	+	0.0200327i
$596$	−0.787579	+	4.16520i	−0.0322605	+	0.170613i
$597$	22.1845	+	12.5579i	0.907953	+	0.513960i
$598$	7.45565	+	8.99752i	0.304884	+	0.367936i
$599$	18.6761	+	32.3479i	0.763085	+	1.32170i	0.941253	+	0.337701i	$0.109649\pi$
$599$	18.6761	+	32.3479i	0.763085	+	1.32170i	−0.178169	+	0.984000i	$0.557017\pi$
$600$	−20.9589	+	12.6777i	−0.855645	+	0.517564i
$601$	−4.14864	+	7.18566i	−0.169227	+	0.293109i	−0.938148	−	0.346234i	$-0.887460\pi$
$601$	−4.14864	+	7.18566i	−0.169227	+	0.293109i	0.768922	+	0.639343i	$0.220794\pi$
$602$	2.23117	−	0.379228i	0.0909355	−	0.0154562i
$603$	−7.75865	−	27.1029i	−0.315957	−	1.10371i
$604$	0.912568	+	2.60696i	0.0371319	+	0.106076i
$605$	−24.1087	+	0.366672i	−0.980158	+	0.0149073i
$606$	−1.32342	−	7.40447i	−0.0537604	−	0.300786i
$607$	8.18355	−	30.5414i	0.332160	−	1.23964i	−0.574756	−	0.818325i	$-0.694903\pi$
$607$	8.18355	−	30.5414i	0.332160	−	1.23964i	0.906916	−	0.421312i	$-0.138430\pi$
$608$	24.7373	+	5.15368i	1.00323	+	0.209009i
$609$	1.60633	−	1.63389i	0.0650916	−	0.0662084i
$610$	46.2664	−	8.58972i	1.87327	−	0.347788i
$611$	4.52296			0.182980
$612$	−4.51217	−	6.38049i	−0.182394	−	0.257916i
$613$	−13.7605	+	13.7605i	−0.555780	+	0.555780i	−0.928103	−	0.372323i	$-0.878561\pi$
$613$	−13.7605	+	13.7605i	−0.555780	+	0.555780i	0.372323	+	0.928103i	$0.378561\pi$
$614$	32.1512	−	14.7514i	1.29751	−	0.595318i
$615$	−22.2863	−	12.1717i	−0.898669	−	0.490811i
$616$	−0.249980	+	0.0620441i	−0.0100720	+	0.00249983i
$617$	−0.825327	−	0.221146i	−0.0332264	−	0.00890300i	0.242168	−	0.970234i	$-0.422142\pi$
$617$	−0.825327	−	0.221146i	−0.0332264	−	0.00890300i	−0.275394	+	0.961331i	$0.588808\pi$
$618$	4.27024	+	9.10207i	0.171774	+	0.366139i
$619$	−0.920705	−	0.531569i	−0.0370062	−	0.0213656i	0.481383	−	0.876510i	$-0.340135\pi$
$619$	−0.920705	−	0.531569i	−0.0370062	−	0.0213656i	−0.518389	+	0.855145i	$0.673468\pi$
$620$	−13.1879	+	15.8084i	−0.529640	+	0.634881i
$621$	4.67830	−	19.4298i	0.187734	−	0.779690i
$622$	−18.1183	+	3.07955i	−0.726479	+	0.123479i
$623$	−0.0995565	−	0.371550i	−0.00398865	−	0.0148858i
$624$	−8.73325	+	12.0524i	−0.349610	+	0.482481i
$625$	−11.1606	+	22.3705i	−0.446426	+	0.894821i
$626$	−9.88192	−	0.926059i	−0.394961	−	0.0370128i
$627$	−1.82858	−	3.10587i	−0.0730263	−	0.124037i
$628$	−31.9610	+	21.7963i	−1.27538	+	0.869767i
$629$	2.35523			0.0939093
$630$	−1.85100	−	0.113460i	−0.0737454	−	0.00452037i
$631$			9.31691i			0.370900i	0.982654	+	0.185450i	$0.0593743\pi$
$631$			9.31691i			0.370900i	−0.982654	+	0.185450i	$0.940626\pi$
$632$	−32.7066	−	0.605773i	−1.30100	−	0.0240964i
$633$	0.199381	+	23.4405i	0.00792469	+	0.931676i
$634$	10.3834	+	0.973057i	0.412379	+	0.0386450i
$635$	−19.6089	+	5.57515i	−0.778156	+	0.221243i
$636$	23.9424	+	11.2767i	0.949378	+	0.447149i
$637$	−14.4464	+	3.87090i	−0.572387	+	0.153371i
$638$	0.747065	+	4.39531i	0.0295766	+	0.174012i
$639$	31.6615	−	19.0051i	1.25251	−	0.751829i
$640$	3.69368	+	25.0271i	0.146005	+	0.989284i
$641$	−2.21360	+	3.83407i	−0.0874321	+	0.151437i	−0.906425	−	0.422367i	$-0.861199\pi$
$641$	−2.21360	+	3.83407i	−0.0874321	+	0.151437i	0.818993	+	0.573804i	$0.194533\pi$
$642$	−45.9777	−	3.91448i	−1.81459	−	0.154492i
$643$	−3.27705	+	12.2301i	−0.129234	+	0.482309i	−0.999955	−	0.00946835i	$-0.996986\pi$
$643$	−3.27705	+	12.2301i	−0.129234	+	0.482309i	0.870721	+	0.491778i	$0.163653\pi$
$644$	1.13986	+	0.980686i	0.0449166	+	0.0386444i
$645$	−21.8820	+	22.9452i	−0.861602	+	0.903466i
$646$	3.43111	+	7.47821i	0.134995	+	0.294226i
$647$	−2.79686	−	2.79686i	−0.109956	−	0.109956i	0.649988	−	0.759944i	$-0.274774\pi$
$647$	−2.79686	−	2.79686i	−0.109956	−	0.109956i	−0.759944	+	0.649988i	$0.774774\pi$
$648$	25.4528	−	0.394633i	0.999880	−	0.0155026i
$649$			5.29966i			0.208030i
$650$	−0.956744	+	15.1606i	−0.0375266	+	0.594648i
$651$	−1.50202	+	0.416189i	−0.0588688	+	0.0163118i
$652$	−0.529542	−	7.05484i	−0.0207384	−	0.276289i
$653$	−37.5186	−	10.0531i	−1.46821	−	0.393407i	−0.565896	−	0.824477i	$-0.691470\pi$
$653$	−37.5186	−	10.0531i	−1.46821	−	0.393407i	−0.902319	+	0.431070i	$0.858136\pi$
$654$	21.8549	+	25.9226i	0.854593	+	1.01365i
$655$	−2.78529	+	0.0423617i	−0.108830	+	0.00165521i
$656$	−20.5006	+	16.3567i	−0.800413	+	0.638624i
$657$	8.67189	−	34.7157i	0.338323	−	1.35439i
$658$	0.573796	−	0.0975274i	0.0223689	−	0.00380201i
$659$	8.68171	+	5.01238i	0.338191	+	0.195255i	0.659472	−	0.751729i	$-0.270780\pi$
$659$	8.68171	+	5.01238i	0.338191	+	0.195255i	−0.321281	+	0.946984i	$0.604113\pi$
$660$	2.28789	−	2.79041i	0.0890559	−	0.108617i
$661$	42.5684	−	24.5769i	1.65572	−	0.955930i	0.681061	−	0.732226i	$-0.261519\pi$
$661$	42.5684	−	24.5769i	1.65572	−	0.955930i	0.974657	−	0.223703i	$-0.0718146\pi$
$662$	19.9289	−	16.5138i	0.774559	−	0.641826i
$663$	−4.84622	+	0.0412212i	−0.188212	+	0.00160090i
$664$	−15.7569	−	16.3516i	−0.611485	−	0.634564i
$665$	1.89342	+	0.476600i	0.0734235	+	0.0184818i
$666$	−4.33208	+	6.33182i	−0.167865	+	0.245353i
$667$	18.4045	−	18.4045i	0.712625	−	0.712625i
$668$	−20.8020	+	14.1862i	−0.804853	+	0.548882i
$669$	6.66884	−	25.7630i	0.257832	−	0.996055i
$670$	−26.8177	+	12.8015i	−1.03606	+	0.494566i
$671$	−6.00342	+	3.46607i	−0.231759	+	0.133806i
$672$	−0.848043	+	1.71731i	−0.0327140	+	0.0662466i
$673$	17.9878	−	4.81981i	0.693377	−	0.185790i	0.105115	−	0.994460i	$-0.466479\pi$
$673$	17.9878	−	4.81981i	0.693377	−	0.185790i	0.588262	+	0.808670i	$0.299812\pi$
$674$	−10.1146	−	7.17580i	−0.389601	−	0.276401i
$675$	21.7386	−	14.2279i	0.836719	−	0.547632i
$676$	−5.54056	−	15.8279i	−0.213099	−	0.608765i
$677$	36.7124	−	9.83705i	1.41097	−	0.378069i	0.528700	−	0.848809i	$-0.322680\pi$
$677$	36.7124	−	9.83705i	1.41097	−	0.378069i	0.882272	+	0.470740i	$0.156013\pi$
$678$	17.2968	−	8.11482i	0.664281	−	0.311648i
$679$	1.23556	+	2.14005i	0.0474164	+	0.0821276i
$680$	−5.84403	+	5.80545i	−0.224108	+	0.222629i
$681$	−6.05648	+	23.3973i	−0.232085	+	0.896588i
$682$	1.05484	−	2.84340i	0.0403918	−	0.108880i
$683$	3.54056	+	3.54056i	0.135476	+	0.135476i	0.771593	−	0.636117i	$-0.219460\pi$
$683$	3.54056	+	3.54056i	0.135476	+	0.135476i	−0.636117	+	0.771593i	$0.719460\pi$
$684$	−26.4155	−	4.53080i	−1.01002	−	0.173239i
$685$	23.9533	+	6.02938i	0.915208	+	0.230371i
$686$	−3.50809	+	1.60956i	−0.133939	+	0.0614532i
$687$	−0.300201	−	35.2935i	−0.0114534	−	1.34653i
$688$	13.1022	+	30.0109i	0.499518	+	1.14415i
$689$	14.2137	−	8.20631i	0.541500	−	0.312635i
$690$	−21.0149	−	1.46766i	−0.800024	−	0.0558730i
$691$	−4.51257	+	7.81600i	−0.171666	+	0.297335i	−0.939003	−	0.343910i	$-0.888248\pi$
$691$	−4.51257	+	7.81600i	−0.171666	+	0.297335i	0.767336	+	0.641245i	$0.221582\pi$
$692$	−8.79912	+	18.2772i	−0.334492	+	0.694794i
$693$	0.262639	−	0.0751850i	0.00997684	−	0.00285604i
$694$	14.0486	+	9.96677i	0.533279	+	0.378333i
$695$	0.0218302	+	1.43534i	0.000828068	+	0.0544455i
$696$	28.5438	+	16.8631i	1.08195	+	0.639194i
$697$	−8.24867	−	2.21023i	−0.312441	−	0.0837183i
$698$	−4.21166	+	3.48992i	−0.159414	+	0.132096i
$699$	7.52895	+	27.1718i	0.284771	+	1.02773i
$700$	0.205529	+	1.94395i	0.00776825	+	0.0734743i
$701$			13.3585i			0.504544i	0.967656	+	0.252272i	$0.0811778\pi$
$701$			13.3585i			0.504544i	−0.967656	+	0.252272i	$0.918822\pi$
$702$	8.80306	−	13.1044i	0.332250	−	0.494595i
$703$	5.71160	−	5.71160i	0.215417	−	0.215417i
$704$	−1.74260	−	3.29427i	−0.0656766	−	0.124158i
$705$	−5.62746	+	5.90089i	−0.211942	+	0.222240i
$706$	−5.76718	−	0.540456i	−0.217051	−	0.0203403i
$707$	−0.579814	−	0.155361i	−0.0218062	−	0.00584294i
$708$	30.0915	+	25.4474i	1.13091	+	0.956371i
$709$	8.51169	−	14.7427i	0.319663	−	0.553673i	−0.660754	−	0.750602i	$-0.729764\pi$
$709$	8.51169	−	14.7427i	0.319663	−	0.553673i	0.980418	+	0.196929i	$0.0630969\pi$
$710$	−25.2889	−	29.5910i	−0.949075	−	1.11053i
$711$	34.6915	−	0.590205i	1.30103	−	0.0221344i
$712$	4.87075	−	2.69312i	0.182539	−	0.100929i
$713$	−17.1020	+	4.58247i	−0.640475	+	0.171615i
$714$	−0.613917	+	0.109727i	−0.0229753	+	0.00410644i
$715$	−0.611992	−	2.15250i	−0.0228872	−	0.0804989i
$716$	32.2433	−	37.4765i	1.20499	−	1.40056i
$717$	−0.0857480	−	10.0811i	−0.00320232	−	0.376484i
$718$	48.4703	+	17.9814i	1.80890	+	0.671059i
$719$	−9.93645			−0.370567			−0.185283	−	0.982685i	$-0.559320\pi$
$719$	−9.93645			−0.370567			−0.185283	+	0.982685i	$0.559320\pi$
$720$	−4.85823	−	26.3893i	−0.181056	−	0.983473i
$721$	0.802345			0.0298809
$722$	1.26346	+	0.468715i	0.0470211	+	0.0174438i
$723$	21.7091	−	12.7812i	0.807371	−	0.475337i
$724$	12.9153	−	15.0115i	0.479994	−	0.557899i
$725$	33.8208	−	1.02901i	1.25607	−	0.0382164i
$726$	8.97580	−	24.8409i	0.333123	−	0.921933i
$727$	30.0313	−	8.04687i	1.11380	−	0.298442i	0.345428	−	0.938445i	$-0.387734\pi$
$727$	30.0313	−	8.04687i	1.11380	−	0.298442i	0.768372	+	0.640004i	$0.221067\pi$
$728$	0.574742	+	1.03947i	0.0213014	+	0.0385255i
$729$	−26.9648	+	1.37732i	−0.998698	+	0.0510117i
$730$	−37.6026	−	2.94773i	−1.39173	−	0.109100i
$731$	−5.33134	+	9.23415i	−0.197187	+	0.341538i
$732$	−9.14619	+	50.7305i	−0.338053	+	1.87505i
$733$	2.05449	+	0.550498i	0.0758842	+	0.0203331i	0.296561	−	0.955014i	$-0.404160\pi$
$733$	2.05449	+	0.550498i	0.0758842	+	0.0203331i	−0.220677	+	0.975347i	$0.570827\pi$
$734$	−14.5857	−	1.36686i	−0.538367	−	0.0504517i
$735$	12.9240	−	23.6636i	0.476708	−	0.872847i
$736$	−9.79904	+	19.4254i	−0.361197	+	0.716028i
$737$	3.09546	−	3.09546i	0.114023	−	0.114023i
$738$	21.1141	−	18.1104i	0.777222	−	0.666654i
$739$		−	42.6335i		−	1.56830i	−0.620573	−	0.784149i	$-0.713100\pi$
$739$		−	42.6335i		−	1.56830i	0.620573	−	0.784149i	$-0.286900\pi$
$740$	7.33902	+	3.39671i	0.269788	+	0.124865i
$741$	−11.6525	+	11.8524i	−0.428064	+	0.435409i
$742$	1.62624	−	1.34756i	0.0597013	−	0.0494705i
$743$	1.77494	+	0.475593i	0.0651162	+	0.0174478i	0.291230	−	0.956653i	$-0.405935\pi$
$743$	1.77494	+	0.475593i	0.0651162	+	0.0174478i	−0.226114	+	0.974101i	$0.572602\pi$
$744$	−11.0799	−	19.6425i	−0.406208	−	0.720131i
$745$	−4.73881	+	0.0720731i	−0.173617	+	0.00264056i
$746$	2.75427	+	1.95401i	0.100841	+	0.0715413i
$747$	17.3182	+	16.7388i	0.633641	+	0.612441i
$748$	0.526383	−	1.09338i	0.0192465	−	0.0399780i
$749$	−1.84123	+	3.18910i	−0.0672771	+	0.116527i
$750$	−18.5889	−	20.1110i	−0.678771	−	0.734350i
$751$	−6.16320	+	3.55832i	−0.224898	+	0.129845i	−0.608216	−	0.793771i	$-0.708115\pi$
$751$	−6.16320	+	3.55832i	−0.224898	+	0.129845i	0.383318	+	0.923616i	$0.374781\pi$
$752$	3.36954	+	7.71800i	0.122875	+	0.281446i
$753$	−14.0353	−	7.94486i	−0.511473	−	0.289527i
$754$	18.6871	−	8.57388i	0.680542	−	0.312242i
$755$	−2.65057	+	1.58454i	−0.0964642	+	0.0576672i
$756$	0.834213	−	1.85228i	0.0303400	−	0.0673669i
$757$	−33.2356	−	33.2356i	−1.20797	−	1.20797i	−0.971684	−	0.236286i	$-0.924070\pi$
$757$	−33.2356	−	33.2356i	−1.20797	−	1.20797i	−0.236286	−	0.971684i	$-0.575930\pi$
$758$	9.68689	−	26.1118i	0.351844	−	0.948425i
$759$	2.99064	−	0.828667i	0.108553	−	0.0300787i
$760$	−0.0935486	+	28.2508i	−0.00339336	+	1.02476i
$761$	2.53174	+	4.38511i	0.0917757	+	0.158960i	0.908258	−	0.418410i	$-0.137412\pi$
$761$	2.53174	+	4.38511i	0.0917757	+	0.158960i	−0.816483	+	0.577370i	$0.804079\pi$
$762$	1.89445	−	22.2513i	0.0686287	−	0.806081i
$763$	2.61362	−	0.700318i	0.0946195	−	0.0253532i
$764$	1.48777	+	4.25017i	0.0538258	+	0.153766i
$765$	5.97588	−	6.37392i	0.216058	−	0.230449i
$766$	4.41526	+	3.13239i	0.159530	+	0.113178i
$767$	23.6071	−	6.32552i	0.852405	−	0.228401i
$768$	−27.0723	−	5.92361i	−0.976888	−	0.213750i
$769$	1.20299	−	0.694545i	0.0433808	−	0.0250459i	−0.478153	−	0.878277i	$-0.658693\pi$
$769$	1.20299	−	0.694545i	0.0433808	−	0.0250459i	0.521534	+	0.853231i	$0.325360\pi$
$770$	−0.124053	−	0.259876i	−0.00447055	−	0.00936528i
$771$	−13.6764	−	13.4457i	−0.492543	−	0.484235i
$772$	19.4571	−	13.2691i	0.700277	−	0.477565i
$773$	−30.3401	+	30.3401i	−1.09126	+	1.09126i	−0.0958611	+	0.995395i	$0.530560\pi$
$773$	−30.3401	+	30.3401i	−1.09126	+	1.09126i	−0.995395	+	0.0958611i	$0.969440\pi$
$774$	−15.0190	−	31.3176i	−0.539846	−	1.12569i
$775$	−20.2741	−	10.8970i	−0.728268	−	0.391432i
$776$	−25.7466	+	24.8103i	−0.924251	+	0.890636i
$777$	0.310624	+	0.527601i	0.0111436	+	0.0189276i
$778$	10.5923	−	8.77713i	0.379752	−	0.314675i
$779$	−25.3636	+	14.6437i	−0.908744	+	0.524663i
$780$	−15.1605	−	6.86076i	−0.542834	−	0.245654i
$781$	4.96595	+	2.86710i	0.177696	+	0.102593i
$782$	−6.98422	+	1.18710i	−0.249755	+	0.0424506i
$783$	−30.8915	−	16.7993i	−1.10397	−	0.600356i
$784$	−17.3677	−	21.7676i	−0.620274	−	0.777414i
$785$	−31.0453	−	30.1151i	−1.10806	−	1.07486i
$786$	1.03698	−	2.86988i	0.0369877	−	0.102365i
$787$	−17.8013	−	4.76984i	−0.634547	−	0.170026i	−0.0728149	−	0.997345i	$-0.523198\pi$
$787$	−17.8013	−	4.76984i	−0.634547	−	0.170026i	−0.561732	+	0.827319i	$0.689865\pi$
$788$	3.29851	+	43.9446i	0.117505	+	1.56546i
$789$	−11.5771	+	44.7245i	−0.412155	+	1.59223i
$790$	−6.67605	−	35.9589i	−0.237523	−	1.27936i
$791$		−	1.52471i		−	0.0542125i
$792$	1.97126	+	3.42624i	0.0700456	+	0.121746i
$793$	22.6050	+	22.6050i	0.802727	+	0.802727i
$794$	−14.2212	−	30.9956i	−0.504691	−	1.09999i
$795$	−6.97833	+	28.7542i	−0.247496	+	1.01981i
$796$	22.3139	+	19.1980i	0.790895	+	0.680454i
$797$	10.6103	−	39.5980i	0.375835	−	1.40263i	−0.476286	−	0.879290i	$-0.658017\pi$
$797$	10.6103	−	39.5980i	0.375835	−	1.40263i	0.852121	−	0.523345i	$-0.175316\pi$
$798$	−1.22269	+	1.75489i	−0.0432829	+	0.0621223i
$799$	−1.37108	+	2.37478i	−0.0485053	+	0.0840136i
$800$	−26.5829	+	9.66184i	−0.939846	+	0.341598i
$801$	−5.06147	+	3.03820i	−0.178838	+	0.107349i
$802$	−4.31259	−	25.3728i	−0.152283	−	0.895945i
$803$	5.36704	−	1.43810i	0.189399	−	0.0507493i
$804$	−2.71259	−	32.4395i	−0.0956658	−	1.14405i
$805$	−0.818338	+	1.46853i	−0.0288426	+	0.0517590i
$806$	−13.9249	−	1.30493i	−0.490482	−	0.0459643i
$807$	−19.6571	−	11.1272i	−0.691964	−	0.391696i
$808$	0.160839	−	8.68395i	0.00565830	−	0.305500i
$809$		−	40.9872i		−	1.44103i	−0.693437	−	0.720517i	$-0.743904\pi$
$809$		−	40.9872i		−	1.44103i	0.693437	−	0.720517i	$-0.256096\pi$
$810$	6.14398	+	27.7894i	0.215877	+	0.976420i
$811$	2.11957			0.0744281			0.0372140	−	0.999307i	$-0.488152\pi$
$811$	2.11957			0.0744281			0.0372140	+	0.999307i	$0.488152\pi$
$812$	2.18582	−	1.49065i	0.0767071	−	0.0523116i
$813$	11.2427	−	19.8612i	0.394299	−	0.696561i
$814$	−1.18612	−	0.111154i	−0.0415736	−	0.00389596i
$815$	7.60821	−	2.16314i	0.266504	−	0.0757716i
$816$	−3.68071	−	8.23890i	−0.128850	−	0.288419i
$817$	9.46459	+	35.3223i	0.331124	+	1.23577i
$818$	−33.6570	+	5.72063i	−1.17679	+	0.200017i
$819$	−0.648387	−	1.08018i	−0.0226565	−	0.0377445i
$820$	−22.5157	−	18.7834i	−0.786282	−	0.655944i
$821$	−7.15582	−	4.13142i	−0.249740	−	0.144187i	0.369905	−	0.929069i	$-0.379390\pi$
$821$	−7.15582	−	4.13142i	−0.249740	−	0.144187i	−0.619645	+	0.784882i	$0.712723\pi$
$822$	−15.4681	+	22.2008i	−0.539512	+	0.774341i
$823$	−35.4977	−	9.51159i	−1.23737	−	0.331553i	−0.419927	−	0.907558i	$-0.637944\pi$
$823$	−35.4977	−	9.51159i	−1.23737	−	0.331553i	−0.817447	+	0.576004i	$0.804611\pi$
$824$	2.79654	+	11.2675i	0.0974222	+	0.392521i
$825$	3.56970	+	1.87970i	0.124281	+	0.0654427i
$826$	2.85847	−	1.31151i	0.0994590	−	0.0456332i
$827$	25.5181	−	25.5181i	0.887351	−	0.887351i	−0.106917	−	0.994268i	$-0.534098\pi$
$827$	25.5181	−	25.5181i	0.887351	−	0.887351i	0.994268	+	0.106917i	$0.0340978\pi$
$828$	9.65498	−	20.9599i	0.335534	−	0.728407i
$829$	36.5185			1.26834			0.634170	−	0.773194i	$-0.281342\pi$
$829$	36.5185			1.26834			0.634170	+	0.773194i	$0.281342\pi$
$830$	14.3736	−	20.9276i	0.498916	−	0.726407i
$831$	−32.7043	−	8.46561i	−1.13450	−	0.293669i
$832$	−12.5943	+	11.6943i	−0.436629	+	0.405426i
$833$	2.34683	−	8.75847i	0.0813127	−	0.303463i
$834$	−1.47893	−	0.534384i	−0.0512113	−	0.0185042i
$835$	−20.2060	−	19.6006i	−0.699257	−	0.678306i
$836$	−1.37501	−	3.92804i	−0.0475558	−	0.135854i
$837$	12.4846	+	20.4034i	0.431533	+	0.705246i
$838$	45.1694	−	7.67738i	1.56035	−	0.265211i
$839$	−2.04896	+	3.54891i	−0.0707381	+	0.122522i	−0.899225	−	0.437486i	$-0.855869\pi$
$839$	−2.04896	+	3.54891i	−0.0707381	+	0.122522i	0.828487	+	0.560008i	$0.189202\pi$
$840$	−2.07124	−	0.543473i	−0.0714647	−	0.0187516i
$841$	−8.39816	−	14.5460i	−0.289592	−	0.501588i
$842$	−33.8389	−	40.8370i	−1.16617	−	1.40734i
$843$	33.9933	−	20.0135i	1.17079	−	0.689300i
$844$	−5.02900	+	26.5965i	−0.173105	+	0.915488i
$845$	16.0927	−	9.62034i	0.553605	−	0.330950i
$846$	−3.86248	−	8.05405i	−0.132795	−	0.276904i
$847$	−1.49047	−	1.49047i	−0.0512131	−	0.0512131i
$848$	24.5923	+	18.1408i	0.844503	+	0.622957i
$849$	−12.4118	+	12.6248i	−0.425972	+	0.433281i
$850$	−7.67004	−	5.09808i	−0.263080	−	0.174863i
$851$	3.47747	+	6.02315i	0.119206	+	0.206471i
$852$	40.1244	−	14.4298i	1.37464	−	0.494357i
$853$	0.264172	+	0.985905i	0.00904509	+	0.0337567i	0.970301	−	0.241901i	$-0.0777710\pi$
$853$	0.264172	+	0.985905i	0.00904509	+	0.0337567i	−0.961256	+	0.275658i	$0.911104\pi$
$854$	3.35516	+	2.38031i	0.114811	+	0.0814524i
$855$	−0.965271	−	29.9491i	−0.0330116	−	1.02424i
$856$	−51.2028	−	14.7412i	−1.75007	−	0.503845i
$857$	2.42082	+	9.03464i	0.0826938	+	0.308617i	0.994867	−	0.101186i	$-0.0322639\pi$
$857$	2.42082	+	9.03464i	0.0826938	+	0.308617i	−0.912174	+	0.409804i	$0.865597\pi$
$858$	2.44256	+	0.207957i	0.0833876	+	0.00709952i
$859$	16.7171	−	9.65161i	0.570379	−	0.329309i	−0.186922	−	0.982375i	$-0.559851\pi$
$859$	16.7171	−	9.65161i	0.570379	−	0.329309i	0.757301	+	0.653066i	$0.226518\pi$
$860$	−29.9302	+	21.0852i	−1.02061	+	0.719001i
$861$	−0.592773	−	2.13930i	−0.0202016	−	0.0729073i
$862$	−17.5135	+	47.2091i	−0.596512	+	1.60795i
$863$	−0.779595	+	0.779595i	−0.0265377	+	0.0265377i	−0.720251	−	0.693713i	$-0.755973\pi$
$863$	−0.779595	+	0.779595i	−0.0265377	+	0.0265377i	0.693713	+	0.720251i	$0.255973\pi$
$864$	28.9196	+	5.25895i	0.983865	+	0.178913i
$865$	−21.9932	−	5.53601i	−0.747793	−	0.188230i
$866$	5.40196	+	11.7738i	0.183566	+	0.400088i
$867$	−13.0576	+	23.0673i	−0.443459	+	0.783407i
$868$	−1.79468	+	0.134710i	−0.0609155	+	0.00457237i
$869$	2.69388	+	4.66594i	0.0913837	+	0.158281i
$870$	−12.0645	+	35.0477i	−0.409023	+	1.18823i
$871$	−17.4833	−	10.0940i	−0.592398	−	0.342021i
$872$	18.9444	+	34.2627i	0.641538	+	1.16028i
$873$	26.3564	−	27.2687i	0.892029	−	0.922907i
$874$	−14.0584	+	19.8160i	−0.475533	+	0.670287i
$875$	−2.08305	+	0.661344i	−0.0704199	+	0.0223575i
$876$	17.6054	−	37.3794i	0.594831	−	1.26293i
$877$	−6.13647	+	22.9016i	−0.207214	+	0.773332i	0.781550	+	0.623843i	$0.214430\pi$
$877$	−6.13647	+	22.9016i	−0.207214	+	0.773332i	−0.988763	+	0.149489i	$0.952237\pi$
$878$	16.1115	−	13.3506i	0.543738	−	0.450560i
$879$	−10.2707	−	10.0974i	−0.346422	−	0.340578i
$880$	3.21711	−	2.64789i	0.108449	−	0.0892602i
$881$	11.3625			0.382812			0.191406	−	0.981511i	$-0.438695\pi$
$881$	11.3625			0.382812			0.191406	+	0.981511i	$0.438695\pi$
$882$	19.2297	+	22.4191i	0.647498	+	0.754890i
$883$	16.2651	+	16.2651i	0.547365	+	0.547365i	0.925678	−	0.378313i	$-0.123496\pi$
$883$	16.2651	+	16.2651i	0.547365	+	0.547365i	−0.378313	+	0.925678i	$0.623496\pi$
$884$	−5.49870	−	1.03973i	−0.184941	−	0.0349697i
$885$	−21.1193	+	38.6693i	−0.709919	+	1.29985i
$886$	14.1296	+	1.32412i	0.474692	+	0.0444846i
$887$	−12.7316	+	47.5149i	−0.427484	+	1.59539i	0.330952	+	0.943647i	$0.392630\pi$
$887$	−12.7316	+	47.5149i	−0.427484	+	1.59539i	−0.758437	+	0.651746i	$0.774037\pi$
$888$	−6.32654	+	6.20109i	−0.212305	+	0.208095i
$889$	−1.54340	−	0.891081i	−0.0517639	−	0.0298859i
$890$	4.04274	+	4.73049i	0.135513	+	0.158566i
$891$	−2.21861	−	3.55751i	−0.0743262	−	0.119181i
$892$	13.3295	−	27.6875i	0.446305	−	0.927047i
$893$	2.43404	+	9.08396i	0.0814520	+	0.303983i
$894$	1.76428	−	4.88274i	0.0590065	−	0.163303i
$895$	48.2829	+	26.9056i	1.61392	+	0.899354i
$896$	−1.34559	+	1.75513i	−0.0449529	+	0.0586349i
$897$	−7.26080	−	12.3326i	−0.242431	−	0.411775i
$898$	10.9171	−	29.4278i	0.364307	−	0.982020i
$899$			31.1526i			1.03900i
$900$	27.8136	−	11.2430i	0.927119	−	0.374768i
$901$			9.95054i			0.331501i
$902$	4.04982	+	1.50239i	0.134844	+	0.0500241i
$903$	−2.77170	+	0.0235756i	−0.0922363	+	0.000784548i
$904$	21.4118	−	5.31433i	0.712146	−	0.176752i
$905$	19.3401	+	10.7772i	0.642887	+	0.358248i
$906$	−0.595192	−	3.33006i	−0.0197739	−	0.110634i
$907$	−12.6278	−	47.1274i	−0.419298	−	1.56484i	−0.776069	−	0.630648i	$-0.782789\pi$
$907$	−12.6278	−	47.1274i	−0.419298	−	1.56484i	0.356771	−	0.934192i	$-0.383878\pi$
$908$	−12.1055	+	25.1451i	−0.401736	+	0.834471i
$909$	0.156705	+	9.21097i	0.00519759	+	0.305508i
$910$	−1.00954	+	0.862768i	−0.0334660	+	0.0286005i
$911$	−2.42041	−	1.39742i	−0.0801916	−	0.0462987i	0.459368	−	0.888246i	$-0.348076\pi$
$911$	−2.42041	−	1.39742i	−0.0801916	−	0.0462987i	−0.539560	+	0.841947i	$0.681409\pi$
$912$	−28.9059	−	11.0539i	−0.957169	−	0.366033i
$913$	−0.967995	+	3.61261i	−0.0320360	+	0.119560i
$914$	3.99844	−	42.6671i	0.132257	−	1.41130i
$915$	−57.6167	+	1.36655i	−1.90475	+	0.0451769i
$916$	7.57199	−	40.0454i	0.250186	−	1.32314i
$917$	−0.172194	−	0.172194i	−0.00568635	−	0.00568635i
$918$	4.21194	+	8.59448i	0.139015	+	0.283660i
$919$	−13.1955			−0.435280			−0.217640	−	0.976029i	$-0.569836\pi$
$919$	−13.1955			−0.435280			−0.217640	+	0.976029i	$0.569836\pi$
$920$	−23.4752	−	6.37355i	−0.773954	−	0.210130i
$921$	−41.7507	+	11.5686i	−1.37573	+	0.381197i
$922$	34.2260	+	41.3041i	1.12717	+	1.36028i
$923$	6.84415	−	25.5427i	0.225278	−	0.840749i
$924$	0.314354	−	0.0262863i	0.0103415	−	0.000864756i
$925$	−2.07343	+	8.80053i	−0.0681741	+	0.289360i
$926$	30.5663	+	21.6852i	1.00447	+	0.712619i
$927$	−3.38885	−	11.8381i	−0.111304	−	0.388813i
$928$	28.5521	+	25.5002i	0.937268	+	0.837086i
$929$	14.7287	+	8.50362i	0.483233	+	0.278995i	0.721763	−	0.692140i	$-0.243332\pi$
$929$	14.7287	+	8.50362i	0.483233	+	0.278995i	−0.238530	+	0.971135i	$0.576665\pi$
$930$	19.0277	−	16.5435i	0.623944	−	0.542482i
$931$	−15.5487	−	26.9311i	−0.509588	−	0.882632i
$932$	2.43694	+	32.4662i	0.0798245	+	1.06347i
$933$	22.5078	−	0.191448i	0.736871	−	0.00626772i
$934$	2.98830	−	1.37107i	0.0977801	−	0.0448628i
$935$	1.31569	+	0.331177i	0.0430275	+	0.0108306i
$936$	12.9092	−	12.8703i	0.421951	−	0.420680i
$937$	1.51284	−	1.51284i	0.0494223	−	0.0494223i	−0.681964	−	0.731386i	$-0.738874\pi$
$937$	1.51284	−	1.51284i	0.0494223	−	0.0494223i	0.731386	+	0.681964i	$0.238874\pi$
$938$	−2.43563	−	0.903562i	−0.0795261	−	0.0295023i
$939$	11.7680	+	3.04618i	0.384034	+	0.0994085i
$940$	−7.69724	+	5.42256i	−0.251056	+	0.176864i
$941$	4.39477	−	2.53732i	0.143265	−	0.0827143i	−0.426654	−	0.904415i	$-0.640308\pi$
$941$	4.39477	−	2.53732i	0.143265	−	0.0827143i	0.569919	+	0.821701i	$0.306974\pi$
$942$	42.8942	−	20.1238i	1.39757	−	0.655670i
$943$	−6.52674	−	24.3581i	−0.212540	−	0.793209i
$944$	28.3809	+	35.5709i	0.923718	+	1.15773i
$945$	2.21597	+	0.498036i	0.0720857	+	0.0162011i
$946$	3.12073	−	4.39882i	0.101464	−	0.143018i
$947$	3.84084	+	14.3342i	0.124811	+	0.465799i	0.999833	−	0.0182833i	$-0.00582008\pi$
$947$	3.84084	+	14.3342i	0.124811	+	0.465799i	−0.875022	+	0.484083i	$0.839153\pi$
$948$	39.4285	+	7.10854i	1.28058	+	0.230875i
$949$	−12.8119	−	22.1908i	−0.415891	−	0.720345i
$950$	−30.9636	+	6.23717i	−1.00459	+	0.202361i
$951$	−12.3652	−	3.20078i	−0.400970	−	0.103792i
$952$	−0.720000	−	0.0133354i	−0.0233353	−	0.000432204i
$953$	1.85933	+	1.85933i	0.0602297	+	0.0602297i	0.736580	−	0.676350i	$-0.236439\pi$
$953$	1.85933	+	1.85933i	0.0602297	+	0.0602297i	−0.676350	+	0.736580i	$0.736439\pi$
$954$	−26.7511	−	18.3025i	−0.866099	−	0.592565i
$955$	−4.32127	+	2.58330i	−0.139833	+	0.0835935i
$956$	2.16282	−	11.4383i	0.0699507	−	0.369942i
$957$	−0.0464431	−	5.46014i	−0.00150129	−	0.176501i
$958$	−30.8704	+	25.5802i	−0.997376	+	0.826460i
$959$	1.07966	+	1.87003i	0.0348642	+	0.0603865i
$960$	0.412848	−	30.9811i	0.0133246	−	0.999911i
$961$	−4.90431	+	8.49452i	−0.158204	+	0.274017i
$962$	0.920586	+	5.41621i	0.0296809	+	0.174626i
$963$	54.8299	+	13.6964i	1.76687	+	0.441359i
$964$	27.4558	−	9.61092i	0.884293	−	0.309547i
$965$	18.8997	+	18.3334i	0.608402	+	0.590173i
$966$	−1.18705	−	1.40799i	−0.0381927	−	0.0453013i
$967$	−2.94239	+	10.9812i	−0.0946209	+	0.353130i	−0.996962	−	0.0778933i	$-0.975181\pi$
$967$	−2.94239	+	10.9812i	−0.0946209	+	0.353130i	0.902341	+	0.431023i	$0.141847\pi$
$968$	15.7359	−	26.1259i	0.505773	−	0.839718i
$969$	−2.69079	−	9.71101i	−0.0864407	−	0.311963i
$970$	−32.9519	−	22.6323i	−1.05802	−	0.726678i
$971$	18.9190			0.607141			0.303570	−	0.952809i	$-0.401821\pi$
$971$	18.9190			0.607141			0.303570	+	0.952809i	$0.401821\pi$
$972$	−30.8527	−	4.48480i	−0.989599	−	0.143850i
$973$	−0.0887367	+	0.0887367i	−0.00284477	+	0.00284477i
$974$	25.4824	+	55.5397i	0.816509	+	1.77961i
$975$	4.11236	−	18.1446i	0.131701	−	0.581093i
$976$	−21.7328	+	55.4136i	−0.695651	+	1.77375i
$977$	26.3213	+	7.05278i	0.842094	+	0.225638i	0.653983	−	0.756509i	$-0.273097\pi$
$977$	26.3213	+	7.05278i	0.842094	+	0.225638i	0.188111	+	0.982148i	$0.439764\pi$
$978$	−0.735041	+	8.63345i	−0.0235040	+	0.276067i
$979$	−0.793869	−	0.458341i	−0.0253722	−	0.0146486i
$980$	19.9443	−	23.9072i	0.637096	−	0.763689i
$981$	−21.3718	−	35.6043i	−0.682350	−	1.13676i
$982$	7.58843	+	44.6460i	0.242157	+	1.42471i
$983$	3.64466	+	13.6020i	0.116246	+	0.433838i	0.999377	−	0.0352894i	$-0.0112353\pi$
$983$	3.64466	+	13.6020i	0.116246	+	0.433838i	−0.883131	+	0.469127i	$0.844569\pi$
$984$	27.9766	−	15.7809i	0.891861	−	0.503076i
$985$	−47.3915	+	13.4742i	−1.51002	+	0.429324i
$986$	−1.16304	+	12.4107i	−0.0370386	+	0.395236i
$987$	−0.712807	+	0.00606302i	−0.0226889	+	0.000192988i
$988$	−15.8561	+	10.8133i	−0.504451	+	0.344018i
$989$	−31.4866			−1.00122
$990$	−3.31034	+	2.92795i	−0.105209	+	0.0930563i
$991$			40.7213i			1.29356i	0.762679	+	0.646778i	$0.223884\pi$
$991$			40.7213i			1.29356i	−0.762679	+	0.646778i	$0.776116\pi$
$992$	−8.14707	−	24.7336i	−0.258670	−	0.785291i
$993$	−27.3160	+	16.0822i	−0.866846	+	0.510354i
$994$	0.317498	−	3.38800i	0.0100704	−	0.107461i
$995$	−16.0198	+	28.7481i	−0.507863	+	0.911377i
$996$	15.8644	+	22.8429i	0.502683	+	0.723806i
$997$	3.18470	−	0.853339i	0.100861	−	0.0270255i	−0.208036	−	0.978121i	$-0.566707\pi$
$997$	3.18470	−	0.853339i	0.100861	−	0.0270255i	0.308896	+	0.951096i	$0.400040\pi$
$998$	−33.5611	+	5.70434i	−1.06236	+	0.180568i
$999$	6.47243	−	6.81147i	0.204779	−	0.215505i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	360.2.bo.a.43.9	✓	272
5.2	odd	4	inner	360.2.bo.a.187.43	yes	272
8.3	odd	2	inner	360.2.bo.a.43.48	yes	272
9.4	even	3	inner	360.2.bo.a.283.54	yes	272
40.27	even	4	inner	360.2.bo.a.187.54	yes	272
45.22	odd	12	inner	360.2.bo.a.67.48	yes	272
72.67	odd	6	inner	360.2.bo.a.283.43	yes	272
360.67	even	12	inner	360.2.bo.a.67.9	yes	272

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
360.2.bo.a.43.9	✓	272	1.1	even	1	trivial
360.2.bo.a.43.48	yes	272	8.3	odd	2	inner
360.2.bo.a.67.9	yes	272	360.67	even	12	inner
360.2.bo.a.67.48	yes	272	45.22	odd	12	inner
360.2.bo.a.187.43	yes	272	5.2	odd	4	inner
360.2.bo.a.187.54	yes	272	40.27	even	4	inner
360.2.bo.a.283.43	yes	272	72.67	odd	6	inner
360.2.bo.a.283.54	yes	272	9.4	even	3	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 360 = 2^{3} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	360.bo (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.32591 - 0.491884i) q^{2} +(1.50731 + 0.853236i) q^{3} +(1.51610 + 1.30439i) q^{4} +(-1.08846 + 1.95327i) q^{5} +(-1.57887 - 1.87274i) q^{6} +(-0.188817 + 0.0505935i) q^{7} +(-1.36861 - 2.47526i) q^{8} +(1.54398 + 2.57218i) q^{9} +O(q^{10})\)	\(q+(-1.32591 - 0.491884i) q^{2} +(1.50731 + 0.853236i) q^{3} +(1.51610 + 1.30439i) q^{4} +(-1.08846 + 1.95327i) q^{5} +(-1.57887 - 1.87274i) q^{6} +(-0.188817 + 0.0505935i) q^{7} +(-1.36861 - 2.47526i) q^{8} +(1.54398 + 2.57218i) q^{9} +(2.40398 - 2.05448i) q^{10} +(-0.232924 + 0.403435i) q^{11} +(1.17228 + 3.25972i) q^{12} +(2.07510 + 0.556021i) q^{13} +(0.275242 + 0.0257936i) q^{14} +(-3.30724 + 2.01548i) q^{15} +(0.597122 + 3.95518i) q^{16} +(-0.920977 + 0.920977i) q^{17} +(-0.781967 - 4.16996i) q^{18} +4.46687i q^{19} +(-4.19804 + 1.54158i) q^{20} +(-0.327775 - 0.0848457i) q^{21} +(0.507280 - 0.420350i) q^{22} +(-3.71507 - 0.995450i) q^{23} +(0.0490559 - 4.89873i) q^{24} +(-2.63053 - 4.25210i) q^{25} +(-2.47791 - 1.75794i) q^{26} +(0.132575 + 5.19446i) q^{27} +(-0.352260 - 0.169587i) q^{28} +(-3.38365 + 5.86065i) q^{29} +(5.37650 - 1.04557i) q^{30} +(3.98667 - 2.30170i) q^{31} +(1.15376 - 5.53795i) q^{32} +(-0.695314 + 0.409364i) q^{33} +(1.67415 - 0.768123i) q^{34} +(0.106697 - 0.423880i) q^{35} +(-1.01431 + 5.91364i) q^{36} +(-1.27866 - 1.27866i) q^{37} +(2.19718 - 5.92268i) q^{38} +(2.65340 + 2.60864i) q^{39} +(6.32452 + 0.0209428i) q^{40} +(3.27828 + 5.67815i) q^{41} +(0.392867 + 0.273725i) q^{42} +(7.90763 - 2.11884i) q^{43} +(-0.879373 + 0.307825i) q^{44} +(-6.70472 + 0.216096i) q^{45} +(4.43622 + 3.14727i) q^{46} +(2.03363 - 0.544910i) q^{47} +(-2.47465 + 6.47117i) q^{48} +(-6.02909 + 3.48089i) q^{49} +(1.39632 + 6.93183i) q^{50} +(-2.17401 + 0.602389i) q^{51} +(2.42079 + 3.54972i) q^{52} +(5.40217 - 5.40217i) q^{53} +(2.37929 - 6.95262i) q^{54} +(-0.534491 - 0.894084i) q^{55} +(0.383650 + 0.398129i) q^{56} +(-3.81129 + 6.73296i) q^{57} +(7.36919 - 6.10636i) q^{58} +(9.85225 - 5.68820i) q^{59} +(-7.64308 - 1.25827i) q^{60} +(12.8871 + 7.44037i) q^{61} +(-6.41815 + 1.09089i) q^{62} +(-0.421666 - 0.407558i) q^{63} +(-4.25381 + 6.77533i) q^{64} +(-3.34471 + 3.44802i) q^{65} +(1.12329 - 0.200768i) q^{66} +(-9.07697 - 2.43217i) q^{67} +(-2.59761 + 0.194979i) q^{68} +(-4.75042 - 4.67029i) q^{69} +(-0.349971 + 0.509547i) q^{70} -12.3092i q^{71} +(4.25372 - 7.34206i) q^{72} +(-8.43399 - 8.43399i) q^{73} +(1.06644 + 2.32435i) q^{74} +(-0.336985 - 8.65370i) q^{75} +(-5.82655 + 6.77222i) q^{76} +(0.0235688 - 0.0879600i) q^{77} +(-2.23504 - 4.76401i) q^{78} +(5.78276 - 10.0160i) q^{79} +(-8.37547 - 3.13870i) q^{80} +(-4.23227 + 7.94279i) q^{81} +(-1.55373 - 9.14128i) q^{82} +(7.75492 - 2.07792i) q^{83} +(-0.386268 - 0.556182i) q^{84} +(-0.796474 - 2.80136i) q^{85} +(-11.5271 - 1.08023i) q^{86} +(-10.1007 + 5.94678i) q^{87} +(1.31739 + 0.0243999i) q^{88} +1.96777i q^{89} +(8.99619 + 3.01142i) q^{90} -0.419946 q^{91} +(-4.33396 - 6.35511i) q^{92} +(7.97305 - 0.0678175i) q^{93} +(-2.96445 - 0.277806i) q^{94} +(-8.72500 - 4.86199i) q^{95} +(6.46424 - 7.36299i) q^{96} +(-3.27183 - 12.2106i) q^{97} +(9.70625 - 1.64976i) q^{98} +(-1.39734 + 0.0237728i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 272 q - 2 q^{2} - 8 q^{3} - 8 q^{6} - 8 q^{8}+O(q^{10}) \) 272 * q - 2 * q^2 - 8 * q^3 - 8 * q^6 - 8 * q^8	\( 272 q - 2 q^{2} - 8 q^{3} - 8 q^{6} - 8 q^{8} - 8 q^{10} - 8 q^{11} - 10 q^{12} - 4 q^{16} - 16 q^{17} + 20 q^{18} + 14 q^{20} + 6 q^{22} - 4 q^{25} - 48 q^{26} - 8 q^{27} + 8 q^{28} - 34 q^{30} - 22 q^{32} + 4 q^{33} - 16 q^{35} - 8 q^{36} - 26 q^{38} - 2 q^{40} - 8 q^{41} - 66 q^{42} - 4 q^{43} - 40 q^{46} - 38 q^{48} - 42 q^{50} - 16 q^{51} + 14 q^{52} + 24 q^{56} + 16 q^{57} + 6 q^{58} + 14 q^{60} - 76 q^{62} - 4 q^{65} - 44 q^{66} - 4 q^{67} - 46 q^{68} + 18 q^{70} + 38 q^{72} - 16 q^{73} - 120 q^{75} - 38 q^{78} + 92 q^{80} - 32 q^{81} - 4 q^{83} - 40 q^{86} - 42 q^{88} - 14 q^{90} - 32 q^{91} + 52 q^{92} + 108 q^{96} - 4 q^{97} - 140 q^{98}+O(q^{100}) \) 272 * q - 2 * q^2 - 8 * q^3 - 8 * q^6 - 8 * q^8 - 8 * q^10 - 8 * q^11 - 10 * q^12 - 4 * q^16 - 16 * q^17 + 20 * q^18 + 14 * q^20 + 6 * q^22 - 4 * q^25 - 48 * q^26 - 8 * q^27 + 8 * q^28 - 34 * q^30 - 22 * q^32 + 4 * q^33 - 16 * q^35 - 8 * q^36 - 26 * q^38 - 2 * q^40 - 8 * q^41 - 66 * q^42 - 4 * q^43 - 40 * q^46 - 38 * q^48 - 42 * q^50 - 16 * q^51 + 14 * q^52 + 24 * q^56 + 16 * q^57 + 6 * q^58 + 14 * q^60 - 76 * q^62 - 4 * q^65 - 44 * q^66 - 4 * q^67 - 46 * q^68 + 18 * q^70 + 38 * q^72 - 16 * q^73 - 120 * q^75 - 38 * q^78 + 92 * q^80 - 32 * q^81 - 4 * q^83 - 40 * q^86 - 42 * q^88 - 14 * q^90 - 32 * q^91 + 52 * q^92 + 108 * q^96 - 4 * q^97 - 140 * q^98

Introduction

L-functions

Modular forms

Varieties

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Database

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