LMFDB - Embedded newform 224.2.bd.a.37.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [224,2,Mod(37,224)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(224, base_ring=CyclotomicField(24))

chi = DirichletCharacter(H, H._module([0, 3, 8]))

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

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

chi := DirichletCharacter("224.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 224 = 2^{5} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	224.bd (of order $24$, degree $8$, 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:	$1.78864900528$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$30$ over $\Q(\zeta_{24})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{24}]$

Embedding invariants

Embedding label			37.8
Character	$\chi$	$=$	224.37
Dual form			224.2.bd.a.109.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.940911 + 1.05579i) q^{2} +(-1.04486 + 1.36169i) q^{3} +(-0.229373 - 1.98680i) q^{4} +(1.80014 - 1.38129i) q^{5} +(-0.454533 - 2.38438i) q^{6} +(2.29881 + 1.30976i) q^{7} +(2.31346 + 1.62724i) q^{8} +(0.0139922 + 0.0522197i) q^{9} +O(q^{10})$	\(q+(-0.940911 + 1.05579i) q^{2} +(-1.04486 + 1.36169i) q^{3} +(-0.229373 - 1.98680i) q^{4} +(1.80014 - 1.38129i) q^{5} +(-0.454533 - 2.38438i) q^{6} +(2.29881 + 1.30976i) q^{7} +(2.31346 + 1.62724i) q^{8} +(0.0139922 + 0.0522197i) q^{9} +(-0.235417 + 3.20024i) q^{10} +(-0.940800 + 0.123859i) q^{11} +(2.94507 + 1.76360i) q^{12} +(2.44244 - 1.01169i) q^{13} +(-3.54580 + 1.19469i) q^{14} +3.89449i q^{15} +(-3.89478 + 0.911438i) q^{16} +(0.0434878 - 0.0251077i) q^{17} +(-0.0682984 - 0.0343613i) q^{18} +(-0.771600 + 5.86089i) q^{19} +(-3.15726 - 3.25969i) q^{20} +(-4.18543 + 1.76175i) q^{21} +(0.754441 - 1.10982i) q^{22} +(-0.0591965 - 0.220924i) q^{23} +(-4.63304 + 1.44998i) q^{24} +(0.0384260 - 0.143408i) q^{25} +(-1.22999 + 3.53060i) q^{26} +(-4.84289 - 2.00599i) q^{27} +(2.07495 - 4.86771i) q^{28} +(-0.876670 - 2.11647i) q^{29} +(-4.11175 - 3.66437i) q^{30} +(4.67044 + 8.08944i) q^{31} +(2.70235 - 4.96964i) q^{32} +(0.814349 - 1.41049i) q^{33} +(-0.0144098 + 0.0695380i) q^{34} +(5.94734 - 0.817591i) q^{35} +(0.100541 - 0.0397776i) q^{36} +(4.71785 - 3.62013i) q^{37} +(-5.46184 - 6.32922i) q^{38} +(-1.17440 + 4.38292i) q^{39} +(6.41224 - 0.266321i) q^{40} +(1.81397 - 1.81397i) q^{41} +(2.07808 - 6.07657i) q^{42} +(3.88053 - 9.36842i) q^{43} +(0.461877 + 1.84078i) q^{44} +(0.0973188 + 0.0746753i) q^{45} +(0.288948 + 0.145371i) q^{46} +(5.15262 + 2.97487i) q^{47} +(2.82841 - 6.25581i) q^{48} +(3.56907 + 6.02177i) q^{49} +(0.115253 + 0.175504i) q^{50} +(-0.0112499 + 0.0854511i) q^{51} +(-2.57026 - 4.62059i) q^{52} +(-12.4313 + 1.63662i) q^{53} +(6.67463 - 3.22560i) q^{54} +(-1.52248 + 1.52248i) q^{55} +(3.18693 + 6.77078i) q^{56} +(-7.17450 - 7.17450i) q^{57} +(3.05941 + 1.06583i) q^{58} +(-1.13971 - 8.65692i) q^{59} +(7.73759 - 0.893291i) q^{60} +(-1.78778 - 0.235366i) q^{61} +(-12.9352 - 2.68045i) q^{62} +(-0.0362297 + 0.138370i) q^{63} +(2.70420 + 7.52910i) q^{64} +(2.99928 - 5.19490i) q^{65} +(0.722951 + 2.18693i) q^{66} +(4.75222 - 6.19321i) q^{67} +(-0.0598590 - 0.0806428i) q^{68} +(0.362683 + 0.150228i) q^{69} +(-4.73271 + 7.04840i) q^{70} +(-7.65167 - 7.65167i) q^{71} +(-0.0526034 + 0.143577i) q^{72} +(0.769926 + 0.206301i) q^{73} +(-0.616986 + 8.38727i) q^{74} +(0.155127 + 0.202166i) q^{75} +(11.8214 + 0.188690i) q^{76} +(-2.32495 - 0.947492i) q^{77} +(-3.52242 - 5.36385i) q^{78} +(-10.5808 - 6.10885i) q^{79} +(-5.75217 + 7.02054i) q^{80} +(7.65124 - 4.41745i) q^{81} +(0.208382 + 3.62196i) q^{82} +(-13.0219 + 5.39387i) q^{83} +(4.46028 + 7.91152i) q^{84} +(0.0436030 - 0.105267i) q^{85} +(6.23983 + 12.9119i) q^{86} +(3.79797 + 1.01766i) q^{87} +(-2.37805 - 1.24436i) q^{88} +(-2.08390 + 0.558378i) q^{89} +(-0.170410 + 0.0324851i) q^{90} +(6.93977 + 0.873315i) q^{91} +(-0.425355 + 0.168286i) q^{92} +(-15.8953 - 2.09265i) q^{93} +(-7.98898 + 2.64099i) q^{94} +(6.70662 + 11.6162i) q^{95} +(3.94352 + 8.87235i) q^{96} +18.1541 q^{97} +(-9.71589 - 1.89777i) q^{98} +(-0.0196318 - 0.0473953i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q - 4 q^{2} - 4 q^{3} - 4 q^{4} - 4 q^{5} - 16 q^{6} - 8 q^{7} - 16 q^{8} - 4 q^{9}+O(q^{10}) $ 240 * q - 4 * q^2 - 4 * q^3 - 4 * q^4 - 4 * q^5 - 16 * q^6 - 8 * q^7 - 16 * q^8 - 4 * q^9	\( 240 q - 4 q^{2} - 4 q^{3} - 4 q^{4} - 4 q^{5} - 16 q^{6} - 8 q^{7} - 16 q^{8} - 4 q^{9} - 4 q^{10} - 4 q^{11} - 4 q^{12} - 16 q^{13} + 24 q^{14} - 24 q^{16} - 24 q^{18} - 4 q^{19} - 48 q^{20} - 8 q^{21} - 24 q^{22} - 12 q^{23} + 36 q^{24} - 4 q^{25} - 4 q^{26} - 16 q^{27} + 12 q^{28} - 16 q^{29} + 44 q^{30} - 56 q^{31} - 4 q^{32} - 8 q^{33} - 32 q^{34} - 32 q^{35} - 96 q^{36} - 4 q^{37} + 36 q^{38} - 4 q^{39} - 68 q^{40} - 16 q^{41} - 28 q^{42} + 44 q^{44} + 8 q^{45} - 4 q^{46} - 16 q^{48} + 8 q^{50} - 28 q^{51} - 28 q^{52} - 20 q^{53} - 92 q^{54} - 16 q^{55} - 48 q^{56} - 16 q^{57} + 28 q^{58} - 36 q^{59} + 60 q^{60} - 4 q^{61} - 16 q^{63} + 56 q^{64} - 8 q^{65} - 36 q^{66} + 36 q^{67} - 36 q^{68} - 16 q^{69} - 44 q^{70} + 48 q^{71} - 4 q^{72} - 4 q^{73} + 68 q^{74} + 16 q^{75} - 16 q^{76} - 8 q^{77} - 120 q^{78} - 16 q^{80} - 44 q^{82} - 96 q^{83} - 28 q^{84} - 56 q^{85} - 4 q^{86} - 4 q^{87} + 40 q^{88} - 4 q^{89} + 224 q^{90} - 56 q^{91} - 80 q^{92} + 20 q^{93} + 4 q^{94} - 8 q^{95} - 32 q^{96} - 32 q^{97} + 96 q^{98} + 8 q^{99}+O(q^{100}) \) 240 * q - 4 * q^2 - 4 * q^3 - 4 * q^4 - 4 * q^5 - 16 * q^6 - 8 * q^7 - 16 * q^8 - 4 * q^9 - 4 * q^10 - 4 * q^11 - 4 * q^12 - 16 * q^13 + 24 * q^14 - 24 * q^16 - 24 * q^18 - 4 * q^19 - 48 * q^20 - 8 * q^21 - 24 * q^22 - 12 * q^23 + 36 * q^24 - 4 * q^25 - 4 * q^26 - 16 * q^27 + 12 * q^28 - 16 * q^29 + 44 * q^30 - 56 * q^31 - 4 * q^32 - 8 * q^33 - 32 * q^34 - 32 * q^35 - 96 * q^36 - 4 * q^37 + 36 * q^38 - 4 * q^39 - 68 * q^40 - 16 * q^41 - 28 * q^42 + 44 * q^44 + 8 * q^45 - 4 * q^46 - 16 * q^48 + 8 * q^50 - 28 * q^51 - 28 * q^52 - 20 * q^53 - 92 * q^54 - 16 * q^55 - 48 * q^56 - 16 * q^57 + 28 * q^58 - 36 * q^59 + 60 * q^60 - 4 * q^61 - 16 * q^63 + 56 * q^64 - 8 * q^65 - 36 * q^66 + 36 * q^67 - 36 * q^68 - 16 * q^69 - 44 * q^70 + 48 * q^71 - 4 * q^72 - 4 * q^73 + 68 * q^74 + 16 * q^75 - 16 * q^76 - 8 * q^77 - 120 * q^78 - 16 * q^80 - 44 * q^82 - 96 * q^83 - 28 * q^84 - 56 * q^85 - 4 * q^86 - 4 * q^87 + 40 * q^88 - 4 * q^89 + 224 * q^90 - 56 * q^91 - 80 * q^92 + 20 * q^93 + 4 * q^94 - 8 * q^95 - 32 * q^96 - 32 * q^97 + 96 * q^98 + 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/224\mathbb{Z}\right)^\times$.

$n$	$127$	$129$	$197$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{8}\right)$

Coefficient data

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

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

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

$2$	−0.940911	+	1.05579i	−0.665325	+	0.746554i
$2$	−0.940911	+	1.05579i	−0.665325	+	0.746554i
$3$	−1.04486	+	1.36169i	−0.603251	+	0.786172i	−0.990750	−	0.135698i	$-0.956672\pi$
$3$	−1.04486	+	1.36169i	−0.603251	+	0.786172i	0.387499	+	0.921870i	$0.373339\pi$
$4$	−0.229373	−	1.98680i	−0.114686	−	0.993402i
$5$	1.80014	−	1.38129i	0.805046	−	0.617733i	−0.122064	−	0.992522i	$-0.538951\pi$
$5$	1.80014	−	1.38129i	0.805046	−	0.617733i	0.927110	+	0.374789i	$0.122285\pi$
$6$	−0.454533	−	2.38438i	−0.185562	−	0.973420i
$7$	2.29881	+	1.30976i	0.868869	+	0.495042i
$7$	2.29881	+	1.30976i	0.868869	+	0.495042i
$8$	2.31346	+	1.62724i	0.817932	+	0.575315i
$9$	0.0139922	+	0.0522197i	0.00466408	+	0.0174066i
$10$	−0.235417	+	3.20024i	−0.0744453	+	1.01200i
$11$	−0.940800	+	0.123859i	−0.283662	+	0.0373448i	−0.271015	−	0.962575i	$-0.587359\pi$
$11$	−0.940800	+	0.123859i	−0.283662	+	0.0373448i	−0.0126472	+	0.999920i	$0.504026\pi$
$12$	2.94507	+	1.76360i	0.850170	+	0.509108i
$13$	2.44244	−	1.01169i	0.677410	−	0.280592i	−0.0173337	−	0.999850i	$-0.505518\pi$
$13$	2.44244	−	1.01169i	0.677410	−	0.280592i	0.694744	+	0.719257i	$0.255518\pi$
$14$	−3.54580	+	1.19469i	−0.947656	+	0.319294i
$15$			3.89449i			1.00555i
$16$	−3.89478	+	0.911438i	−0.973694	+	0.227859i
$17$	0.0434878	−	0.0251077i	0.0105474	−	0.00608952i	−0.494717	−	0.869054i	$-0.664728\pi$
$17$	0.0434878	−	0.0251077i	0.0105474	−	0.00608952i	0.505264	+	0.862965i	$0.331395\pi$
$18$	−0.0682984	−	0.0343613i	−0.0160981	−	0.00809904i
$19$	−0.771600	+	5.86089i	−0.177017	+	1.34458i	0.640182	+	0.768224i	$0.278859\pi$
$19$	−0.771600	+	5.86089i	−0.177017	+	1.34458i	−0.817199	+	0.576356i	$0.804474\pi$
$20$	−3.15726	−	3.25969i	−0.705985	−	0.728888i
$21$	−4.18543	+	1.76175i	−0.913335	+	0.384446i
$22$	0.754441	−	1.10982i	0.160847	−	0.236615i
$23$	−0.0591965	−	0.220924i	−0.0123433	−	0.0460659i	0.959480	−	0.281778i	$-0.0909243\pi$
$23$	−0.0591965	−	0.220924i	−0.0123433	−	0.0460659i	−0.971823	+	0.235712i	$0.924258\pi$
$24$	−4.63304	+	1.44998i	−0.945715	+	0.295976i
$25$	0.0384260	−	0.143408i	0.00768520	−	0.0286816i
$26$	−1.22999	+	3.53060i	−0.241220	+	0.692408i
$27$	−4.84289	−	2.00599i	−0.932015	−	0.386053i
$28$	2.07495	−	4.86771i	0.392128	−	0.919911i
$29$	−0.876670	−	2.11647i	−0.162793	−	0.393018i	0.821342	−	0.570436i	$-0.193226\pi$
$29$	−0.876670	−	2.11647i	−0.162793	−	0.393018i	−0.984136	+	0.177418i	$0.943226\pi$
$30$	−4.11175	−	3.66437i	−0.750700	−	0.669019i
$31$	4.67044	+	8.08944i	0.838836	+	1.45291i	0.890868	+	0.454262i	$0.150097\pi$
$31$	4.67044	+	8.08944i	0.838836	+	1.45291i	−0.0520321	+	0.998645i	$0.516570\pi$
$32$	2.70235	−	4.96964i	0.477713	−	0.878516i
$33$	0.814349	−	1.41049i	0.141760	−	0.245535i
$34$	−0.0144098	+	0.0695380i	−0.00247126	+	0.0119257i
$35$	5.94734	−	0.817591i	1.00528	−	0.138198i
$36$	0.100541	−	0.0397776i	0.0167568	−	0.00662960i
$37$	4.71785	−	3.62013i	0.775609	−	0.595146i	−0.143270	−	0.989684i	$-0.545762\pi$
$37$	4.71785	−	3.62013i	0.775609	−	0.595146i	0.918880	+	0.394538i	$0.129095\pi$
$38$	−5.46184	−	6.32922i	−0.886027	−	1.02673i
$39$	−1.17440	+	4.38292i	−0.188054	+	0.701829i
$40$	6.41224	−	0.266321i	1.01386	−	0.0421090i
$41$	1.81397	−	1.81397i	0.283295	−	0.283295i	−0.551127	−	0.834422i	$-0.685802\pi$
$41$	1.81397	−	1.81397i	0.283295	−	0.283295i	0.834422	+	0.551127i	$0.185802\pi$
$42$	2.07808	−	6.07657i	0.320654	−	0.937636i
$43$	3.88053	−	9.36842i	0.591775	−	1.42867i	−0.290012	−	0.957023i	$-0.593659\pi$
$43$	3.88053	−	9.36842i	0.591775	−	1.42867i	0.881787	−	0.471648i	$-0.156341\pi$
$44$	0.461877	+	1.84078i	0.0696306	+	0.277507i
$45$	0.0973188	+	0.0746753i	0.0145074	+	0.0111319i
$46$	0.288948	+	0.145371i	0.0426030	+	0.0214338i
$47$	5.15262	+	2.97487i	0.751587	+	0.433929i	0.826267	−	0.563279i	$-0.190460\pi$
$47$	5.15262	+	2.97487i	0.751587	+	0.433929i	−0.0746801	+	0.997208i	$0.523794\pi$
$48$	2.82841	−	6.25581i	0.408245	−	0.902948i
$49$	3.56907	+	6.02177i	0.509867	+	0.860253i
$50$	0.115253	+	0.175504i	0.0162992	+	0.0248200i
$51$	−0.0112499	+	0.0854511i	−0.00157529	+	0.0119655i
$52$	−2.57026	−	4.62059i	−0.356431	−	0.640760i
$53$	−12.4313	+	1.63662i	−1.70758	+	0.224807i	−0.920140	−	0.391589i	$-0.871926\pi$
$53$	−12.4313	+	1.63662i	−1.70758	+	0.224807i	−0.787437	+	0.616396i	$0.788592\pi$
$54$	6.67463	−	3.22560i	0.908303	−	0.438949i
$55$	−1.52248	+	1.52248i	−0.205292	+	0.205292i
$56$	3.18693	+	6.77078i	0.425871	+	0.904784i
$57$	−7.17450	−	7.17450i	−0.950285	−	0.950285i
$58$	3.05941	+	1.06583i	0.401720	+	0.139951i
$59$	−1.13971	−	8.65692i	−0.148377	−	1.12704i	−0.889916	−	0.456125i	$-0.849237\pi$
$59$	−1.13971	−	8.65692i	−0.148377	−	1.12704i	0.741539	−	0.670910i	$-0.234096\pi$
$60$	7.73759	−	0.893291i	0.998918	−	0.115323i
$61$	−1.78778	−	0.235366i	−0.228902	−	0.0301355i	0.0152027	−	0.999884i	$-0.495161\pi$
$61$	−1.78778	−	0.235366i	−0.228902	−	0.0301355i	−0.244104	+	0.969749i	$0.578494\pi$
$62$	−12.9352	−	2.68045i	−1.64277	−	0.340418i
$63$	−0.0362297	+	0.138370i	−0.00456451	+	0.0174330i
$64$	2.70420	+	7.52910i	0.338025	+	0.941137i
$65$	2.99928	−	5.19490i	0.372015	−	0.644349i
$66$	0.722951	+	2.18693i	0.0889892	+	0.269192i
$67$	4.75222	−	6.19321i	0.580576	−	0.756621i	−0.407058	−	0.913403i	$-0.633445\pi$
$67$	4.75222	−	6.19321i	0.580576	−	0.756621i	0.987633	+	0.156781i	$0.0501118\pi$
$68$	−0.0598590	−	0.0806428i	−0.00725898	−	0.00977937i
$69$	0.362683	+	0.150228i	0.0436619	+	0.0180853i
$70$	−4.73271	+	7.04840i	−0.565667	+	0.842445i
$71$	−7.65167	−	7.65167i	−0.908086	−	0.908086i	0.0880320	−	0.996118i	$-0.471942\pi$
$71$	−7.65167	−	7.65167i	−0.908086	−	0.908086i	−0.996118	+	0.0880320i	$0.971942\pi$
$72$	−0.0526034	+	0.143577i	−0.00619937	+	0.0169207i
$73$	0.769926	+	0.206301i	0.0901130	+	0.0241457i	0.303594	−	0.952802i	$-0.401813\pi$
$73$	0.769926	+	0.206301i	0.0901130	+	0.0241457i	−0.213481	+	0.976947i	$0.568480\pi$
$74$	−0.616986	+	8.38727i	−0.0717232	+	0.975000i
$75$	0.155127	+	0.202166i	0.0179125	+	0.0233441i
$76$	11.8214	+	0.188690i	1.35601	+	0.0216442i
$77$	−2.32495	−	0.947492i	−0.264952	−	0.107977i
$78$	−3.52242	−	5.36385i	−0.398836	−	0.607337i
$79$	−10.5808	−	6.10885i	−1.19044	−	0.687299i	−0.232032	−	0.972708i	$-0.574537\pi$
$79$	−10.5808	−	6.10885i	−1.19044	−	0.687299i	−0.958406	+	0.285409i	$0.907871\pi$
$80$	−5.75217	+	7.02054i	−0.643112	+	0.784921i
$81$	7.65124	−	4.41745i	0.850138	−	0.490827i
$82$	0.208382	+	3.62196i	0.0230120	+	0.399978i
$83$	−13.0219	+	5.39387i	−1.42934	+	0.592054i	−0.957189	−	0.289462i	$-0.906524\pi$
$83$	−13.0219	+	5.39387i	−1.42934	+	0.592054i	−0.472154	+	0.881516i	$0.656524\pi$
$84$	4.46028	+	7.91152i	0.486657	+	0.863218i
$85$	0.0436030	−	0.105267i	0.00472940	−	0.0114178i
$86$	6.23983	+	12.9119i	0.672858	+	1.39232i
$87$	3.79797	+	1.01766i	0.407185	+	0.109105i
$88$	−2.37805	−	1.24436i	−0.253501	−	0.132649i
$89$	−2.08390	+	0.558378i	−0.220892	+	0.0591880i	−0.367568	−	0.929997i	$-0.619809\pi$
$89$	−2.08390	+	0.558378i	−0.220892	+	0.0591880i	0.146675	+	0.989185i	$0.453143\pi$
$90$	−0.170410	+	0.0324851i	−0.0179627	+	0.00342423i
$91$	6.93977	+	0.873315i	0.727486	+	0.0915482i
$92$	−0.425355	+	0.168286i	−0.0443463	+	0.0175450i
$93$	−15.8953	−	2.09265i	−1.64826	−	0.216998i
$94$	−7.98898	+	2.64099i	−0.824001	+	0.272397i
$95$	6.70662	+	11.6162i	0.688085	+	1.19180i
$96$	3.94352	+	8.87235i	0.402484	+	0.905531i
$97$	18.1541			1.84327			0.921633	−	0.388063i	$-0.126856\pi$
$97$	18.1541			1.84327			0.921633	+	0.388063i	$0.126856\pi$
$98$	−9.71589	−	1.89777i	−0.981453	−	0.191704i
$99$	−0.0196318	−	0.0473953i	−0.00197307	−	0.00476341i
$100$	−0.293737	−	0.0434511i	−0.0293737	−	0.00434511i
$101$	−0.817611	−	6.21037i	−0.0813554	−	0.617955i	−0.982748	−	0.184952i	$-0.940787\pi$
$101$	−0.817611	−	6.21037i	−0.0813554	−	0.617955i	0.901392	−	0.433004i	$-0.142546\pi$
$102$	−0.0796331	−	0.0922793i	−0.00788485	−	0.00913702i
$103$	−0.407621	+	0.109222i	−0.0401641	+	0.0107619i	−0.278845	−	0.960336i	$-0.589952\pi$
$103$	−0.407621	+	0.109222i	−0.0401641	+	0.0107619i	0.238681	+	0.971098i	$0.423285\pi$
$104$	7.29674	+	1.63392i	0.715504	+	0.160219i
$105$	−5.10084	+	8.95270i	−0.497791	+	0.873694i
$106$	9.96887	−	14.6648i	0.968262	−	1.42437i
$107$	−5.19947	−	6.77608i	−0.502652	−	0.655069i	0.471260	−	0.881994i	$-0.343799\pi$
$107$	−5.19947	−	6.77608i	−0.502652	−	0.655069i	−0.973912	+	0.226926i	$0.927133\pi$
$108$	−2.87468	+	10.0820i	−0.276617	+	0.970141i
$109$	−5.45362	−	4.18471i	−0.522362	−	0.400822i	0.313646	−	0.949540i	$-0.398450\pi$
$109$	−5.45362	−	4.18471i	−0.522362	−	0.400822i	−0.836008	+	0.548718i	$0.815116\pi$
$110$	−0.174897	−	3.03994i	−0.0166758	−	0.289847i
$111$			10.2068i			0.968786i
$112$	−10.1471	−	3.00599i	−0.958813	−	0.284039i
$113$		−	17.1078i		−	1.60937i	−0.593705	−	0.804683i	$-0.702335\pi$
$113$		−	17.1078i		−	1.60937i	0.593705	−	0.804683i	$-0.297665\pi$
$114$	14.3253	−	0.824178i	1.34169	−	0.0771914i
$115$	−0.411723	−	0.315926i	−0.0383934	−	0.0294603i
$116$	−4.00392	+	2.22723i	−0.371755	+	0.206793i
$117$	0.0870054	+	0.113388i	0.00804365	+	0.0104827i
$118$	10.2122	+	6.94211i	0.940112	+	0.639073i
$119$	0.132855		0.000759378i	0.0121788		6.96120e-5i
$120$	−6.33726	+	9.00975i	−0.578510	+	0.822474i
$121$	−9.75542	+	2.61396i	−0.886856	+	0.237632i
$122$	1.93064	−	1.66606i	0.174792	−	0.150838i
$123$	0.574719	+	4.36542i	0.0518206	+	0.393617i
$124$	15.0009	−	11.1348i	1.34712	−	0.999930i
$125$	4.21267	+	10.1703i	0.376793	+	0.909658i
$126$	−0.112000	−	0.168445i	−0.00997777	−	0.0150062i
$127$	−3.31241			−0.293928			−0.146964	−	0.989142i	$-0.546950\pi$
$127$	−3.31241			−0.293928			−0.146964	+	0.989142i	$0.546950\pi$
$128$	−10.4935	−	4.22915i	−0.927506	−	0.373807i
$129$	8.70228	+	15.0728i	0.766193	+	1.32708i
$130$	2.66266	+	8.05454i	0.233531	+	0.706430i
$131$	3.93085	+	0.517506i	0.343440	+	0.0452147i	0.300273	−	0.953853i	$-0.402922\pi$
$131$	3.93085	+	0.517506i	0.343440	+	0.0452147i	0.0431665	+	0.999068i	$0.486255\pi$
$132$	−2.98916	−	1.29442i	−0.260173	−	0.112665i
$133$	−9.45010	+	12.4625i	−0.819428	+	1.08063i
$134$	2.06730	+	10.8446i	0.178587	+	0.936830i
$135$	−11.4887	+	3.07840i	−0.988793	+	0.264946i
$136$	0.141464	+	0.0126793i	0.0121304	+	0.00108724i
$137$	10.0344	+	2.68870i	0.857294	+	0.229711i	0.660585	−	0.750751i	$-0.270308\pi$
$137$	10.0344	+	2.68870i	0.857294	+	0.229711i	0.196708	+	0.980462i	$0.436975\pi$
$138$	−0.499861	+	0.241565i	−0.0425510	+	0.0205633i
$139$	0.721994	−	1.74305i	0.0612387	−	0.147843i	−0.890298	−	0.455378i	$-0.849504\pi$
$139$	0.721994	−	1.74305i	0.0612387	−	0.147843i	0.951537	+	0.307535i	$0.0995041\pi$
$140$	−2.98855	−	11.6287i	−0.252579	−	0.982801i
$141$	−9.43463	+	3.90795i	−0.794539	+	0.329109i
$142$	15.2781	−	0.878993i	1.28211	−	0.0737635i
$143$	−2.17254	+	1.25432i	−0.181677	+	0.104891i
$144$	−0.102092	−	0.190631i	−0.00850764	−	0.0158859i
$145$	−4.50159	−	2.59899i	−0.373837	−	0.215835i
$146$	−0.942242	+	0.618767i	−0.0779805	+	0.0512095i
$147$	−11.9290	−	1.43195i	−0.983885	−	0.118105i
$148$	−8.27464	−	8.54308i	−0.680171	−	0.702237i
$149$	10.5975	+	13.8109i	0.868180	+	1.13143i	0.990304	+	0.138920i	$0.0443630\pi$
$149$	10.5975	+	13.8109i	0.868180	+	1.13143i	−0.122123	+	0.992515i	$0.538970\pi$
$150$	−0.359405	−	0.0264386i	−0.0293453	−	0.00215871i
$151$	0.571811	+	0.153216i	0.0465333	+	0.0124686i	0.282011	−	0.959411i	$-0.408999\pi$
$151$	0.571811	+	0.153216i	0.0465333	+	0.0124686i	−0.235477	+	0.971880i	$0.575665\pi$
$152$	−11.3221	+	12.3034i	−0.918345	+	0.997934i
$153$	0.00191961	+	0.00191961i	0.000155191	+	0.000155191i
$154$	3.18792	−	1.56314i	0.256890	−	0.125962i
$155$	19.5813	+	8.11086i	1.57281	+	0.651480i
$156$	8.97738	+	1.32798i	0.718765	+	0.106323i
$157$	12.4540	−	16.2303i	0.993935	−	1.29532i	0.0387694	−	0.999248i	$-0.487656\pi$
$157$	12.4540	−	16.2303i	0.993935	−	1.29532i	0.955165	−	0.296073i	$-0.0956771\pi$
$158$	16.4053	−	5.42323i	1.30513	−	0.431449i
$159$	10.7605	−	18.6377i	0.853361	−	1.47806i
$160$	−1.99992	−	12.6788i	−0.158108	−	1.00234i
$161$	0.153276	−	0.585396i	0.0120798	−	0.0461357i
$162$	−2.53525	+	12.2345i	−0.199188	+	0.961233i
$163$	−10.3097	−	1.35730i	−0.807521	−	0.106312i	−0.284548	−	0.958662i	$-0.591844\pi$
$163$	−10.3097	−	1.35730i	−0.807521	−	0.106312i	−0.522972	+	0.852350i	$0.675177\pi$
$164$	−4.02008	−	3.18793i	−0.313916	−	0.248936i
$165$	−0.482367	−	3.66394i	−0.0375522	−	0.285237i
$166$	6.55772	−	18.8235i	0.508977	−	1.46099i
$167$	−6.21642	−	6.21642i	−0.481041	−	0.481041i	0.424423	−	0.905464i	$-0.360477\pi$
$167$	−6.21642	−	6.21642i	−0.481041	−	0.481041i	−0.905464	+	0.424423i	$0.860477\pi$
$168$	−12.5496	−	2.73493i	−0.968223	−	0.211004i
$169$	−4.25041	+	4.25041i	−0.326955	+	0.326955i
$170$	0.0701129	+	0.145082i	0.00537741	+	0.0111273i
$171$	−0.316850	+	0.0417141i	−0.0242302	+	0.00318996i
$172$	−19.5033	−	5.56098i	−1.48711	−	0.424021i
$173$	−0.778550	+	5.91368i	−0.0591921	+	0.449609i	0.936026	+	0.351931i	$0.114475\pi$
$173$	−0.778550	+	5.91368i	−0.0591921	+	0.449609i	−0.995218	+	0.0976777i	$0.968859\pi$
$174$	−4.64799	+	3.05232i	−0.352363	+	0.231396i
$175$	0.276164	−	0.279339i	0.0208760	−	0.0211160i
$176$	3.55132	−	1.33988i	0.267691	−	0.100997i
$177$	12.9789	+	7.49336i	0.975553	+	0.563236i
$178$	1.37123	−	2.72553i	0.102778	−	0.204287i
$179$	−10.4355	−	8.00741i	−0.779983	−	0.598502i	0.140140	−	0.990132i	$-0.455245\pi$
$179$	−10.4355	−	8.00741i	−0.779983	−	0.598502i	−0.920123	+	0.391630i	$0.871911\pi$
$180$	0.126043	−	0.210482i	0.00939468	−	0.0156884i
$181$	−9.30204	+	22.4571i	−0.691415	+	1.66922i	0.0504948	+	0.998724i	$0.483920\pi$
$181$	−9.30204	+	22.4571i	−0.691415	+	1.66922i	−0.741910	+	0.670500i	$0.766080\pi$
$182$	−7.45174	+	6.50521i	−0.552360	+	0.482198i
$183$	2.18848	−	2.18848i	0.161777	−	0.161777i
$184$	0.222547	−	0.607427i	0.0164064	−	0.0447801i
$185$	3.49231	−	13.0335i	0.256760	−	0.958240i
$186$	17.1654	−	14.8130i	1.25863	−	1.08614i
$187$	−0.0378036	+	0.0290077i	−0.00276447	+	0.00212125i
$188$	4.72860	−	10.9196i	0.344869	−	0.796394i
$189$	−8.50554	−	10.9544i	−0.618687	−	0.796817i
$190$	−18.5746	−	3.84905i	−1.34754	−	0.279240i
$191$	12.2545	−	21.2254i	0.886705	−	1.53582i	0.0429586	−	0.999077i	$-0.486322\pi$
$191$	12.2545	−	21.2254i	0.886705	−	1.53582i	0.843747	−	0.536742i	$-0.180345\pi$
$192$	−13.0778	−	4.18458i	−0.943810	−	0.301996i
$193$	−7.24339	−	12.5459i	−0.521391	−	0.903075i	−0.999690	−	0.0248786i	$-0.992080\pi$
$193$	−7.24339	−	12.5459i	−0.521391	−	0.903075i	0.478300	−	0.878197i	$-0.341253\pi$
$194$	−17.0814	+	19.1668i	−1.22637	+	1.37610i
$195$	3.94002	+	9.51205i	0.282151	+	0.681172i
$196$	11.1454	−	8.47227i	0.796102	−	0.605162i
$197$	24.0632	+	9.96730i	1.71443	+	0.710141i	0.999945	+	0.0104922i	$0.00333983\pi$
$197$	24.0632	+	9.96730i	1.71443	+	0.710141i	0.714487	+	0.699649i	$0.246660\pi$
$198$	0.0685111	+	0.0238678i	0.00486887	+	0.00169621i
$199$	3.13222	−	11.6896i	0.222038	−	0.828655i	−0.761532	−	0.648127i	$-0.775553\pi$
$199$	3.13222	−	11.6896i	0.222038	−	0.828655i	0.983570	−	0.180528i	$-0.0577807\pi$
$200$	0.322255	−	0.269240i	0.0227869	−	0.0190382i
$201$	3.46783	+	12.9421i	0.244602	+	0.912865i
$202$	7.32613	+	4.98019i	0.515465	+	0.350405i
$203$	0.756761	−	6.01359i	0.0531142	−	0.422071i
$204$	0.172355	+	0.00275108i	0.0120673	+	0.000192614i
$205$	0.759770	−	5.77103i	0.0530647	−	0.403066i
$206$	0.268220	−	0.533128i	0.0186878	−	0.0371448i
$207$	0.0107083	−	0.00618245i	0.000744280	−	0.000429710i
$208$	−8.59065	+	6.16644i	−0.595654	+	0.427565i
$209$		−	5.60949i		−	0.388017i
$210$	−4.65271	−	13.8091i	−0.321068	−	0.952918i
$211$	9.72932	−	4.03002i	0.669794	−	0.277438i	−0.0217592	−	0.999763i	$-0.506927\pi$
$211$	9.72932	−	4.03002i	0.669794	−	0.277438i	0.691553	+	0.722325i	$0.256927\pi$
$212$	6.10305	+	24.3232i	0.419159	+	1.67053i
$213$	18.4141	−	2.42427i	1.26172	−	0.166108i
$214$	12.0463	+	0.886156i	0.823471	+	0.0605764i
$215$	−5.95506	−	22.2246i	−0.406132	−	1.51570i
$216$	−7.93962	−	12.5213i	−0.540223	−	0.851968i
$217$	0.141257	+	24.7133i	0.00958912	+	1.67765i
$218$	9.54953	−	1.82042i	0.646776	−	0.123295i
$219$	−1.08538	+	0.832845i	−0.0733435	+	0.0562784i
$220$	3.37409	+	2.67566i	0.227481	+	0.180393i
$221$	0.0808151	−	0.105320i	0.00543621	−	0.00708461i
$222$	−10.7762	−	9.60368i	−0.723251	−	0.644557i
$223$	−5.83435			−0.390697			−0.195349	−	0.980734i	$-0.562584\pi$
$223$	−5.83435			−0.390697			−0.195349	+	0.980734i	$0.562584\pi$
$224$	12.7212	−	7.88483i	0.849972	−	0.526827i
$225$	0.00802638			0.000535092
$226$	18.0622	+	16.0969i	1.20148	+	1.07075i
$227$	−0.313067	+	0.407997i	−0.0207790	+	0.0270797i	−0.803627	−	0.595133i	$-0.797099\pi$
$227$	−0.313067	+	0.407997i	−0.0207790	+	0.0270797i	0.782848	+	0.622213i	$0.213766\pi$
$228$	−12.6087	+	15.9000i	−0.835030	+	1.05300i
$229$	−12.2415	+	9.39321i	−0.808939	+	0.620720i	−0.928174	−	0.372145i	$-0.878622\pi$
$229$	−12.2415	+	9.39321i	−0.808939	+	0.620720i	0.119236	+	0.992866i	$0.461956\pi$
$230$	0.720946	−	0.137434i	0.0475378	−	0.00906210i
$231$	3.71944	−	2.17586i	0.244721	−	0.143161i
$232$	1.41585	−	6.32291i	0.0929553	−	0.415120i
$233$	−5.68909	−	21.2320i	−0.372705	−	1.39095i	−0.856670	−	0.515865i	$-0.827470\pi$
$233$	−5.68909	−	21.2320i	−0.372705	−	1.39095i	0.483965	−	0.875087i	$-0.339196\pi$
$234$	−0.201577	−	0.0148285i	−0.0131775	−	0.000969369i
$235$	13.3846	−	1.76211i	0.873114	−	0.114948i
$236$	−16.9382	+	4.25003i	−1.10258	+	0.276654i
$237$	19.3739	−	8.02492i	1.25847	−	0.521275i
$238$	−0.124203	+	0.140982i	−0.00805091	+	0.00913848i
$239$			27.2393i			1.76196i	0.473149	+	0.880982i	$0.343117\pi$
$239$			27.2393i			1.76196i	−0.473149	+	0.880982i	$0.656883\pi$
$240$	−3.54959	−	15.1682i	−0.229125	−	0.979101i
$241$	−23.4339	+	13.5295i	−1.50951	+	0.871515i	−0.509569	+	0.860430i	$0.670195\pi$
$241$	−23.4339	+	13.5295i	−1.50951	+	0.871515i	−0.999939	+	0.0110847i	$0.996472\pi$
$242$	6.41920	−	12.7591i	0.412642	−	0.820189i
$243$	0.0733242	−	0.556953i	0.00470375	−	0.0357285i
$244$	−0.0575571	+	3.60595i	−0.00368472	+	0.230848i
$245$	14.7427	+	5.91008i	0.941873	+	0.377581i
$246$	−5.14971	−	3.50069i	−0.328334	−	0.223196i
$247$	4.04482	+	15.0955i	0.257366	+	0.960501i
$248$	−2.35855	+	26.3145i	−0.149768	+	1.67097i
$249$	6.26136	−	23.3677i	0.396797	−	1.48087i
$250$	−14.7014	−	5.12165i	−0.929799	−	0.323922i
$251$	−15.4531	−	6.40088i	−0.975390	−	0.404020i	−0.162674	−	0.986680i	$-0.552012\pi$
$251$	−15.4531	−	6.40088i	−0.975390	−	0.404020i	−0.812716	+	0.582660i	$0.802012\pi$
$252$	0.283224	+	0.0402430i	0.0178414	+	0.00253507i
$253$	0.0830555	+	0.200514i	0.00522165	+	0.0126062i
$254$	3.11668	−	3.49719i	0.195558	−	0.219434i
$255$	0.0977818	+	0.169363i	0.00612333	+	0.0106059i
$256$	14.3386	−	7.09969i	0.896160	−	0.443731i
$257$	−1.68247	+	2.91413i	−0.104950	+	0.181778i	−0.913718	−	0.406350i	$-0.866802\pi$
$257$	−1.68247	+	2.91413i	−0.104950	+	0.181778i	0.808768	+	0.588128i	$0.200135\pi$
$258$	−24.1017	−	4.99440i	−1.50051	−	0.310938i
$259$	15.5869	−	2.14276i	0.968525	−	0.133145i
$260$	−11.0092	−	4.76741i	−0.682762	−	0.295662i
$261$	0.0982548	−	0.0753936i	0.00608182	−	0.00466675i
$262$	−4.24496	+	3.66321i	−0.262254	+	0.226314i
$263$	−4.72463	+	17.6325i	−0.291333	+	1.08727i	0.652753	+	0.757571i	$0.273614\pi$
$263$	−4.72463	+	17.6325i	−0.291333	+	1.08727i	−0.944086	+	0.329699i	$0.893053\pi$
$264$	4.17917	−	1.93798i	0.257210	−	0.119275i
$265$	−20.1175	+	20.1175i	−1.23581	+	1.23581i
$266$	−4.26600	−	21.7034i	−0.261565	−	1.33072i
$267$	1.41704	−	3.42105i	0.0867217	−	0.209365i
$268$	−13.3947	−	8.02117i	−0.818213	−	0.489971i
$269$	5.35106	+	4.10601i	0.326260	+	0.250348i	0.758883	−	0.651227i	$-0.225745\pi$
$269$	5.35106	+	4.10601i	0.326260	+	0.250348i	−0.432623	+	0.901575i	$0.642412\pi$
$270$	7.55975	−	15.0262i	0.460072	−	0.914463i
$271$	8.29501	+	4.78912i	0.503886	+	0.290919i	0.730317	−	0.683109i	$-0.239372\pi$
$271$	8.29501	+	4.78912i	0.503886	+	0.290919i	−0.226431	+	0.974027i	$0.572706\pi$
$272$	−0.146491	+	0.137425i	−0.00888234	+	0.00833264i
$273$	−8.44029	+	8.53733i	−0.510829	+	0.516703i
$274$	−12.2801	+	8.06433i	−0.741870	+	0.487184i
$275$	−0.0183889	+	0.139677i	−0.00110889	+	0.00842287i
$276$	0.215284	−	0.755038i	0.0129586	−	0.0454479i
$277$	−12.9532	+	1.70532i	−0.778282	+	0.102463i	−0.509193	−	0.860652i	$-0.670056\pi$
$277$	−12.9532	+	1.70532i	−0.778282	+	0.102463i	−0.269089	+	0.963115i	$0.586723\pi$
$278$	1.16095	+	2.40232i	0.0696294	+	0.144082i
$279$	−0.357079	+	0.357079i	−0.0213777	+	0.0213777i
$280$	15.0893	+	7.78626i	0.901761	+	0.465318i
$281$	6.54883	+	6.54883i	0.390670	+	0.390670i	0.874926	−	0.484256i	$-0.160910\pi$
$281$	6.54883	+	6.54883i	0.390670	+	0.390670i	−0.484256	+	0.874926i	$0.660910\pi$
$282$	4.75118	−	13.6380i	0.282929	−	0.812131i
$283$	−1.89112	−	14.3645i	−0.112415	−	0.853878i	−0.951018	−	0.309135i	$-0.899961\pi$
$283$	−1.89112	−	14.3645i	−0.112415	−	0.853878i	0.838603	−	0.544743i	$-0.183373\pi$
$284$	−13.4473	+	16.9574i	−0.797949	+	1.00624i
$285$	−22.8252	−	3.00499i	−1.35205	−	0.178000i
$286$	0.719875	−	3.47394i	0.0425671	−	0.205418i
$287$	6.54585	−	1.79412i	0.386389	−	0.105903i
$288$	0.297325	+	0.0715799i	0.0175201	+	0.00421789i
$289$	−8.49874	+	14.7202i	−0.499926	+	0.865897i
$290$	6.97958	−	2.30730i	0.409855	−	0.135489i
$291$	−18.9685	+	24.7202i	−1.11195	+	1.44912i
$292$	0.233279	−	1.57701i	0.0136516	−	0.0922876i
$293$	2.86102	+	1.18507i	0.167143	+	0.0692328i	0.464686	−	0.885476i	$-0.346167\pi$
$293$	2.86102	+	1.18507i	0.167143	+	0.0692328i	−0.297543	+	0.954708i	$0.596167\pi$
$294$	12.7359	−	11.2471i	0.742775	−	0.655945i
$295$	−14.0094	−	14.0094i	−0.815657	−	0.815657i
$296$	16.8054	−	0.697981i	0.976792	−	0.0405693i
$297$	4.80465	+	1.28740i	0.278794	+	0.0747027i
$298$	−24.5527	−	1.80615i	−1.42230	−	0.104628i
$299$	−0.368091	−	0.479705i	−0.0212872	−	0.0277421i
$300$	0.366081	−	0.354579i	0.0211357	−	0.0204716i
$301$	21.1910	−	16.4537i	1.22143	−	0.948375i
$302$	−0.699787	+	0.459548i	−0.0402682	+	0.0264440i
$303$	9.31090	+	5.37565i	0.534897	+	0.308823i
$304$	−2.33662	−	23.5301i	−0.134014	−	1.34954i
$305$	−3.54336	+	2.04576i	−0.202892	+	0.117140i
$306$	−0.00383288		0.000220517i	−0.000219111		1.26061e-5i
$307$	5.22184	−	2.16296i	0.298026	−	0.123447i	−0.228660	−	0.973506i	$-0.573434\pi$
$307$	5.22184	−	2.16296i	0.298026	−	0.123447i	0.526686	+	0.850060i	$0.323434\pi$
$308$	−1.34920	+	4.83654i	−0.0768779	+	0.275588i
$309$	0.277181	−	0.669175i	0.0157683	−	0.0380680i
$310$	−26.9876	+	13.0421i	−1.53279	+	0.740743i
$311$	7.01313	+	1.87916i	0.397678	+	0.106558i	0.452115	−	0.891960i	$-0.350670\pi$
$311$	7.01313	+	1.87916i	0.397678	+	0.106558i	−0.0544368	+	0.998517i	$0.517336\pi$
$312$	−9.84897	+	8.22869i	−0.557588	+	0.465858i
$313$	−2.83478	+	0.759576i	−0.160231	+	0.0429338i	−0.338043	−	0.941131i	$-0.609765\pi$
$313$	−2.83478	+	0.759576i	−0.160231	+	0.0429338i	0.177812	+	0.984065i	$0.443098\pi$
$314$	5.41769	+	28.4200i	0.305738	+	1.60384i
$315$	0.125911	+	0.299128i	0.00709428	+	0.0168540i
$316$	−9.71013	+	22.4233i	−0.546237	+	1.26141i
$317$	14.2195	+	1.87203i	0.798645	+	0.105144i	0.518793	−	0.854900i	$-0.326381\pi$
$317$	14.2195	+	1.87203i	0.798645	+	0.105144i	0.279852	+	0.960043i	$0.409715\pi$
$318$	9.55278	+	28.8972i	0.535693	+	1.62047i
$319$	1.08691	+	1.88259i	0.0608555	+	0.105405i
$320$	15.2678	+	9.81811i	0.853498	+	0.548849i
$321$	14.6597			0.818222
$322$	0.473835	+	0.712633i	0.0264058	+	0.0397135i
$323$	0.113598	+	0.274250i	0.00632078	+	0.0152597i
$324$	−10.5316	−	14.1883i	−0.585088	−	0.788237i
$325$	−0.0512312	−	0.389140i	−0.00284180	−	0.0215856i
$326$	11.1336	−	9.60778i	0.616631	−	0.532126i
$327$	11.3966	−	3.05370i	0.630231	−	0.168870i
$328$	7.14832	−	1.24479i	0.394700	−	0.0687322i
$329$	7.94855	+	13.5873i	0.438218	+	0.749094i
$330$	4.32220	+	2.93816i	0.237929	+	0.161741i
$331$	9.65849	+	12.5872i	0.530879	+	0.691854i	0.979403	−	0.201916i	$-0.0647169\pi$
$331$	9.65849	+	12.5872i	0.530879	+	0.691854i	−0.448524	+	0.893771i	$0.648050\pi$
$332$	13.7034	+	24.6348i	0.752073	+	1.35201i
$333$	0.255056	+	0.195711i	0.0139770	+	0.0107249i
$334$	12.4123	−	0.714118i	0.679172	−	0.0390748i
$335$		−	17.7128i		−	0.967756i
$336$	14.6956	−	10.6764i	0.801709	−	0.582445i
$337$			8.12319i			0.442499i	0.975217	+	0.221249i	$0.0710134\pi$
$337$			8.12319i			0.442499i	−0.975217	+	0.221249i	$0.928987\pi$
$338$	−0.488270	−	8.48678i	−0.0265584	−	0.461620i
$339$	23.2955	+	17.8753i	1.26524	+	0.970852i
$340$	−0.219146	−	0.0624851i	−0.0118849	−	0.00338873i
$341$	−5.39590	−	7.03207i	−0.292204	−	0.380808i
$342$	0.254087	−	0.373776i	0.0137394	−	0.0202115i
$343$	0.317556	+	18.5175i	0.0171464	+	0.999853i
$344$	24.2221	−	15.3589i	1.30597	−	0.828099i
$345$	0.860388	−	0.230540i	0.0463217	−	0.0124119i
$346$	−5.51104	−	6.38623i	−0.296275	−	0.343326i
$347$	2.25177	+	17.1039i	0.120881	+	0.918185i	0.939188	+	0.343403i	$0.111580\pi$
$347$	2.25177	+	17.1039i	0.120881	+	0.918185i	−0.818307	+	0.574782i	$0.805087\pi$
$348$	1.15075	−	7.77925i	0.0616865	−	0.417012i
$349$	0.275206	+	0.664405i	0.0147314	+	0.0355648i	0.931074	−	0.364830i	$-0.118873\pi$
$349$	0.275206	+	0.664405i	0.0147314	+	0.0355648i	−0.916343	+	0.400395i	$0.868873\pi$
$350$	0.0350769	+	0.554403i	0.00187494	+	0.0296341i
$351$	−13.8579			−0.739680
$352$	−1.92684	+	5.01014i	−0.102701	+	0.267042i
$353$	−10.2028	−	17.6718i	−0.543041	−	0.940574i	−0.998727	−	0.0504339i	$-0.983940\pi$
$353$	−10.2028	−	17.6718i	−0.543041	−	0.940574i	0.455687	−	0.890140i	$-0.349394\pi$
$354$	−20.1234	+	6.65235i	−1.06954	+	0.353568i
$355$	−24.3432	−	3.20485i	−1.29201	−	0.170096i
$356$	1.58738	+	4.01221i	0.0841308	+	0.212647i
$357$	−0.137782	+	0.181701i	−0.00729217	+	0.00961666i
$358$	18.2730	−	3.48336i	0.965756	−	0.184101i
$359$	−11.6399	+	3.11891i	−0.614333	+	0.164610i	−0.552550	−	0.833480i	$-0.686345\pi$
$359$	−11.6399	+	3.11891i	−0.614333	+	0.164610i	−0.0617827	+	0.998090i	$0.519679\pi$
$360$	0.103629	+	0.331119i	0.00546172	+	0.0174515i
$361$	−15.4020	−	4.12696i	−0.810633	−	0.217208i
$362$	−14.9575	−	30.9511i	−0.786151	−	1.62675i
$363$	6.63367	−	16.0151i	0.348177	−	0.840574i
$364$	0.143309	−	13.9883i	0.00751144	−	0.733185i
$365$	1.67093	−	0.692124i	0.0874607	−	0.0362274i
$366$	0.251404	+	4.36973i	0.0131411	+	0.228409i
$367$	20.3624	−	11.7562i	1.06291	−	0.613671i	0.136674	−	0.990616i	$-0.456359\pi$
$367$	20.3624	−	11.7562i	1.06291	−	0.613671i	0.926236	+	0.376945i	$0.123025\pi$
$368$	0.431916	+	0.806497i	0.0225152	+	0.0420416i
$369$	0.120107	+	0.0693437i	0.00625251	+	0.00360989i
$370$	10.4746	+	15.9505i	0.544549	+	0.829225i
$371$	−30.7209	−	12.5198i	−1.59495	−	0.649994i
$372$	−0.511745	+	32.0608i	−0.0265327	+	1.66228i
$373$	−7.45759	−	9.71892i	−0.386139	−	0.503226i	0.559327	−	0.828947i	$-0.311060\pi$
$373$	−7.45759	−	9.71892i	−0.386139	−	0.503226i	−0.945466	+	0.325721i	$0.894393\pi$
$374$	0.00494384	−	0.0672062i	0.000255640	−	0.00347515i
$375$	−18.2504	−	4.89019i	−0.942449	−	0.252528i
$376$	7.07958	+	15.2668i	0.365101	+	0.787324i
$377$	−4.28242	−	4.28242i	−0.220556	−	0.220556i
$378$	19.5685	+	1.32709i	1.00649	+	0.0682584i
$379$	23.3198	+	9.65936i	1.19786	+	0.496168i	0.890306	−	0.455364i	$-0.150491\pi$
$379$	23.3198	+	9.65936i	1.19786	+	0.496168i	0.307550	+	0.951532i	$0.400491\pi$
$380$	21.5408	−	15.9892i	1.10502	−	0.820227i
$381$	3.46101	−	4.51047i	0.177313	−	0.231078i
$382$	10.8791	+	32.9094i	0.556625	+	1.68379i
$383$	13.1708	−	22.8125i	0.672998	−	1.16567i	−0.304052	−	0.952655i	$-0.598340\pi$
$383$	13.1708	−	22.8125i	0.672998	−	1.16567i	0.977050	−	0.213011i	$-0.0683269\pi$
$384$	16.7231	−	9.87008i	0.853396	−	0.503680i
$385$	−5.49399	+	1.50582i	−0.280000	+	0.0767436i
$386$	20.0612	+	4.15712i	1.02109	+	0.211592i
$387$	0.543514	+	0.0715550i	0.0276284	+	0.00363734i
$388$	−4.16405	−	36.0685i	−0.211398	−	1.83110i
$389$	−0.883693	−	6.71232i	−0.0448050	−	0.340328i	−0.999135	−	0.0415747i	$-0.986763\pi$
$389$	−0.883693	−	6.71232i	−0.0448050	−	0.340328i	0.954330	−	0.298753i	$-0.0965708\pi$
$390$	−13.7499	−	4.79017i	−0.696254	−	0.242560i
$391$	−0.00812123	−	0.00812123i	−0.000410709	−	0.000410709i
$392$	−1.54194	+	19.7389i	−0.0778799	+	0.996963i
$393$	−4.81188	+	4.81188i	−0.242727	+	0.242727i
$394$	−33.1647	+	16.0273i	−1.67081	+	0.807442i
$395$	−27.4851	+	3.61848i	−1.38292	+	0.182065i
$396$	−0.0896621	+	0.0498757i	−0.00450569	+	0.00250635i
$397$	−2.02284	+	15.3650i	−0.101523	+	0.771146i	0.862637	+	0.505824i	$0.168812\pi$
$397$	−2.02284	+	15.3650i	−0.101523	+	0.771146i	−0.964160	+	0.265322i	$0.914522\pi$
$398$	9.39461	+	14.3059i	0.470909	+	0.717088i
$399$	−7.09596	−	25.8897i	−0.355243	−	1.29610i
$400$	−0.0189534	+	0.593564i	−0.000947670	+	0.0296782i
$401$	−1.80550	−	1.04241i	−0.0901625	−	0.0520553i	0.454241	−	0.890879i	$-0.349911\pi$
$401$	−1.80550	−	1.04241i	−0.0901625	−	0.0520553i	−0.544403	+	0.838824i	$0.683244\pi$
$402$	−16.9270	−	8.51608i	−0.844243	−	0.424743i
$403$	19.5913	+	15.0329i	0.975911	+	0.748843i
$404$	−12.1513	+	3.04892i	−0.604548	+	0.151690i
$405$	7.67149	−	18.5206i	0.381200	−	0.920297i
$406$	5.63702	+	6.45723i	0.279761	+	0.320467i
$407$	−3.99017	+	3.99017i	−0.197785	+	0.197785i
$408$	−0.165075	+	0.179382i	−0.00817244	+	0.00888071i
$409$	4.51629	−	16.8550i	0.223316	−	0.833427i	−0.759756	−	0.650208i	$-0.774682\pi$
$409$	4.51629	−	16.8550i	0.223316	−	0.833427i	0.983072	−	0.183219i	$-0.0586517\pi$
$410$	5.37810	+	6.23218i	0.265606	+	0.307785i
$411$	−14.1457	+	10.8544i	−0.697756	+	0.535407i
$412$	0.310499	+	0.784810i	0.0152972	+	0.0386648i
$413$	8.71850	−	21.3934i	0.429009	−	1.05270i
$414$	−0.00354822	+	0.0171228i	−0.000174386	+	0.000841542i
$415$	−15.9908	+	27.6968i	−0.784956	+	1.35958i
$416$	1.57259	−	14.8720i	0.0771028	−	0.729158i
$417$	1.61911	+	2.80438i	0.0792880	+	0.137331i
$418$	5.92243	+	5.27803i	0.289675	+	0.258157i
$419$	−1.85032	−	4.46707i	−0.0903942	−	0.218231i	0.872216	−	0.489120i	$-0.162682\pi$
$419$	−1.85032	−	4.46707i	−0.0903942	−	0.218231i	−0.962610	+	0.270890i	$0.912682\pi$
$420$	18.9573	+	8.08086i	0.925019	+	0.394306i
$421$	−19.5246	−	8.08736i	−0.951572	−	0.394154i	−0.147750	−	0.989025i	$-0.547203\pi$
$421$	−19.5246	−	8.08736i	−0.951572	−	0.394154i	−0.803821	+	0.594871i	$0.797203\pi$
$422$	−4.89959	+	14.0640i	−0.238508	+	0.684624i
$423$	−0.0832501	+	0.310694i	−0.00404776	+	0.0151064i
$424$	−31.4226	−	16.4425i	−1.52602	−	0.798518i
$425$	−0.00192958	−	0.00720129i	−9.35983e−5	−	0.000349314i
$426$	−14.7666	+	21.7224i	−0.715442	+	1.05246i
$427$	−3.80150	−	2.88262i	−0.183967	−	0.139500i
$428$	−12.2701	+	11.8846i	−0.593099	+	0.574463i
$429$	0.562013	−	4.26891i	0.0271342	−	0.206105i
$430$	29.0676	+	14.6241i	1.40177	+	0.705236i
$431$	5.91156	−	3.41304i	0.284750	−	0.164400i	−0.350822	−	0.936442i	$-0.614098\pi$
$431$	5.91156	−	3.41304i	0.284750	−	0.164400i	0.635572	+	0.772042i	$0.280764\pi$
$432$	20.6903	+	3.39890i	0.995464	+	0.163529i
$433$		−	5.72011i		−	0.274891i	−0.990509	−	0.137446i	$-0.956111\pi$
$433$		−	5.72011i		−	0.274891i	0.990509	−	0.137446i	$-0.0438892\pi$
$434$	−26.2248	−	23.1038i	−1.25883	−	1.10902i
$435$	8.24257	−	3.41418i	0.395201	−	0.163698i
$436$	−7.06328	+	11.7951i	−0.338270	+	0.564884i
$437$	1.34049	−	0.176479i	0.0641242	−	0.00844212i
$438$	0.141943	−	1.92957i	0.00678232	−	0.0921983i
$439$	−8.16557	−	30.4743i	−0.389721	−	1.45446i	−0.830588	−	0.556887i	$-0.811995\pi$
$439$	−8.16557	−	30.4743i	−0.389721	−	1.45446i	0.440867	−	0.897573i	$-0.354671\pi$
$440$	−5.99965	+	1.04477i	−0.286022	+	0.0498073i
$441$	−0.264516	+	0.270634i	−0.0125960	+	0.0128873i
$442$	0.0351560	+	0.184421i	0.00167220	+	0.00877199i
$443$	−10.4853	+	8.04566i	−0.498172	+	0.382261i	−0.827065	−	0.562106i	$-0.809991\pi$
$443$	−10.4853	+	8.04566i	−0.498172	+	0.382261i	0.328893	+	0.944367i	$0.393325\pi$
$444$	20.2789	−	2.34116i	0.962393	−	0.111107i
$445$	−2.98001	+	3.88363i	−0.141266	+	0.184102i
$446$	5.48961	−	6.15983i	0.259940	−	0.291677i
$447$	−29.8791			−1.41323
$448$	−3.64484	+	20.8498i	−0.172202	+	0.985062i
$449$	−12.5172			−0.590722			−0.295361	−	0.955386i	$-0.595440\pi$
$449$	−12.5172			−0.590722			−0.295361	+	0.955386i	$0.595440\pi$
$450$	−0.00755211	+	0.00847415i	−0.000356010	+	0.000399475i
$451$	−1.48191	+	1.93126i	−0.0697804	+	0.0909396i
$452$	−33.9898	+	3.92406i	−1.59875	+	0.184572i
$453$	−0.806096	+	0.618539i	−0.0378737	+	0.0290615i
$454$	−0.136190	−	0.714422i	−0.00639171	−	0.0335295i
$455$	13.6988	−	8.01378i	0.642212	−	0.375692i
$456$	−4.92332	−	28.2725i	−0.230555	−	1.32398i
$457$	−8.50530	−	31.7422i	−0.397861	−	1.48484i	−0.816852	−	0.576848i	$-0.804283\pi$
$457$	−8.50530	−	31.7422i	−0.397861	−	1.48484i	0.418991	−	0.907991i	$-0.362384\pi$
$458$	1.60090	−	21.7625i	0.0748053	−	1.01690i
$459$	−0.260973	+	0.0343577i	−0.0121812	+	0.00160368i
$460$	−0.533245	+	0.890478i	−0.0248627	+	0.0415188i
$461$	−2.08517	+	0.863705i	−0.0971160	+	0.0402268i	−0.430712	−	0.902489i	$-0.641738\pi$
$461$	−2.08517	+	0.863705i	−0.0971160	+	0.0402268i	0.333597	+	0.942716i	$0.391738\pi$
$462$	−1.20242	+	5.97423i	−0.0559415	+	0.277946i
$463$			4.71931i			0.219325i	0.993969	+	0.109663i	$0.0349770\pi$
$463$			4.71931i			0.219325i	−0.993969	+	0.109663i	$0.965023\pi$
$464$	5.34346	+	7.44414i	0.248064	+	0.345585i
$465$	−31.5043	+	18.1890i	−1.46098	+	0.843495i
$466$	27.7694	+	13.9709i	1.28639	+	0.647191i
$467$	−4.27839	+	32.4976i	−0.197980	+	1.50381i	0.547230	+	0.836982i	$0.315682\pi$
$467$	−4.27839	+	32.4976i	−0.197980	+	1.50381i	−0.745211	+	0.666829i	$0.767651\pi$
$468$	0.205322	−	0.198871i	0.00949102	−	0.00919280i
$469$	19.0361	−	8.01277i	0.879003	−	0.369995i
$470$	−10.7333	+	15.7893i	−0.495090	+	0.728305i
$471$	9.08801	+	33.9169i	0.418753	+	1.56281i
$472$	11.4502	−	21.8820i	0.527038	−	1.00720i
$473$	−2.49044	+	9.29445i	−0.114511	+	0.427359i
$474$	−9.75649	+	28.0054i	−0.448130	+	1.28633i
$475$	0.810847	+	0.335864i	0.0372042	+	0.0154105i
$476$	−0.0319822	−	0.263783i	−0.00146590	−	0.0120905i
$477$	−0.259406	−	0.626262i	−0.0118774	−	0.0286746i
$478$	−28.7589	−	25.6298i	−1.31540	−	1.17228i
$479$	14.5613	+	25.2209i	0.665322	+	1.15237i	0.979198	+	0.202907i	$0.0650390\pi$
$479$	14.5613	+	25.2209i	0.665322	+	1.15237i	−0.313876	+	0.949464i	$0.601628\pi$
$480$	19.3542	+	10.5243i	0.883395	+	0.480366i
$481$	7.86059	−	13.6149i	0.358412	−	0.620788i
$482$	7.76486	−	37.4713i	0.353680	−	1.70677i
$483$	0.636977	+	0.820373i	0.0289835	+	0.0373283i
$484$	7.43105	+	18.7825i	0.337775	+	0.853751i
$485$	32.6798	−	25.0761i	1.48391	−	1.13865i
$486$	0.519032	+	0.601458i	0.0235438	+	0.0272827i
$487$	2.45624	−	9.16682i	0.111303	−	0.415388i	−0.887681	−	0.460459i	$-0.847685\pi$
$487$	2.45624	−	9.16682i	0.111303	−	0.415388i	0.998984	+	0.0450711i	$0.0143514\pi$
$488$	−3.75296	−	3.45365i	−0.169889	−	0.156339i
$489$	12.6205	−	12.6205i	0.570718	−	0.570718i
$490$	−20.1113	+	10.0042i	−0.908537	+	0.451946i
$491$	−11.6185	+	28.0495i	−0.524334	+	1.26586i	0.410853	+	0.911702i	$0.365231\pi$
$491$	−11.6185	+	28.0495i	−0.524334	+	1.26586i	−0.935187	+	0.354153i	$0.884769\pi$
$492$	8.54141	−	2.14316i	0.385076	−	0.0966212i
$493$	−0.0912642	−	0.0700295i	−0.00411033	−	0.00315397i
$494$	−19.7434	−	9.93302i	−0.888298	−	0.446908i
$495$	−0.100807	−	0.0582008i	−0.00453092	−	0.00261593i
$496$	−25.5634	−	27.2498i	−1.14783	−	1.22355i
$497$	−7.56791	−	27.6116i	−0.339467	−	1.23855i
$498$	18.7799	+	28.5976i	0.841549	+	1.28149i
$499$	3.00596	−	22.8325i	0.134565	−	1.02212i	−0.782293	−	0.622910i	$-0.785950\pi$
$499$	3.00596	−	22.8325i	0.134565	−	1.02212i	0.916858	−	0.399213i	$-0.130717\pi$
$500$	19.2401	−	10.7025i	0.860443	−	0.478632i
$501$	14.9601	−	1.96954i	0.668370	−	0.0879926i
$502$	21.2979	−	10.2925i	0.950573	−	0.459377i
$503$	−3.99460	+	3.99460i	−0.178110	+	0.178110i	−0.790532	−	0.612421i	$-0.790196\pi$
$503$	−3.99460	+	3.99460i	−0.178110	+	0.178110i	0.612421	+	0.790532i	$0.290196\pi$
$504$	−0.308976	+	0.261159i	−0.0137629	+	0.0116329i
$505$	−10.0502	−	10.0502i	−0.447226	−	0.447226i
$506$	−0.289848	−	0.100977i	−0.0128853	−	0.00448896i
$507$	−1.34665	−	10.2288i	−0.0598069	−	0.454278i
$508$	0.759776	+	6.58110i	0.0337096	+	0.291989i
$509$	−0.373014	−	0.0491082i	−0.0165336	−	0.00217668i	0.122255	−	0.992499i	$-0.460987\pi$
$509$	−0.373014	−	0.0491082i	−0.0165336	−	0.00217668i	−0.138788	+	0.990322i	$0.544321\pi$
$510$	−0.270815	−	0.0561188i	−0.0119919	−	0.00248498i
$511$	1.49971	+	1.48266i	0.0663433	+	0.0655892i
$512$	−5.99555	+	21.8186i	−0.264968	+	0.964257i
$513$	15.4937	−	26.8358i	0.684062	−	1.18483i
$514$	−1.49364	−	4.51827i	−0.0658818	−	0.199292i
$515$	−0.582906	+	0.759658i	−0.0256859	+	0.0334745i
$516$	27.9506	−	20.7470i	1.23046	−	0.913336i
$517$	−5.21605	−	2.16056i	−0.229402	−	0.0950212i
$518$	−12.4036	+	18.4726i	−0.544984	+	0.811641i
$519$	−7.23912	−	7.23912i	−0.317762	−	0.317762i
$520$	15.3921	−	7.13767i	0.674986	−	0.313008i
$521$	−11.6347	−	3.11751i	−0.509725	−	0.136581i	−0.00521550	−	0.999986i	$-0.501660\pi$
$521$	−11.6347	−	3.11751i	−0.509725	−	0.136581i	−0.504510	+	0.863406i	$0.668327\pi$
$522$	−0.0128495	+	0.174675i	−0.000562406	+	0.00764531i
$523$	21.6218	+	28.1780i	0.945454	+	1.23214i	0.972594	+	0.232508i	$0.0746932\pi$
$523$	21.6218	+	28.1780i	0.945454	+	1.23214i	−0.0271405	+	0.999632i	$0.508640\pi$
$524$	0.126553	−	7.92853i	0.00552848	−	0.346359i
$525$	0.0918201	+	0.667920i	0.00400736	+	0.0291504i
$526$	−14.1708	−	21.5789i	−0.617875	−	0.940883i
$527$	0.406215	+	0.234528i	0.0176950	+	0.0102162i
$528$	−1.88613	+	6.23579i	−0.0820833	+	0.271378i
$529$	19.8733	−	11.4738i	0.864056	−	0.498863i
$530$	−2.31102	−	40.1685i	−0.100384	−	1.74481i
$531$	0.436115	−	0.180645i	0.0189258	−	0.00783932i
$532$	26.9281	+	15.9169i	1.16748	+	0.690087i
$533$	2.59533	−	6.26569i	0.112416	−	0.271397i
$534$	2.27859	+	4.71500i	0.0986041	+	0.204038i
$535$	−18.7195	−	5.01588i	−0.809316	−	0.216855i
$536$	21.0719	−	6.59477i	0.910167	−	0.284851i
$537$	21.8072	−	5.84323i	0.941051	−	0.252154i
$538$	−9.36994	+	1.78619i	−0.403967	+	0.0770080i
$539$	−4.10363	−	5.22322i	−0.176756	−	0.224980i
$540$	8.75138	+	22.1198i	0.376599	+	0.951883i
$541$	13.9320	+	1.83418i	0.598982	+	0.0788575i	0.423920	−	0.905700i	$-0.360654\pi$
$541$	13.9320	+	1.83418i	0.598982	+	0.0788575i	0.175063	+	0.984557i	$0.443987\pi$
$542$	−12.8612	+	4.25162i	−0.552434	+	0.182623i
$543$	−20.8603	−	36.1311i	−0.895201	−	1.55053i
$544$	−0.00725669	−	0.283969i	−0.000311128	−	0.0121751i
$545$	−15.5976			−0.668127
$546$	−1.07204	−	16.9440i	−0.0458792	−	0.725137i
$547$	−4.13041	−	9.97168i	−0.176603	−	0.426358i	0.810647	−	0.585536i	$-0.199116\pi$
$547$	−4.13041	−	9.97168i	−0.176603	−	0.426358i	−0.987250	+	0.159177i	$0.949116\pi$
$548$	3.04031	−	20.5530i	0.129875	−	0.877982i
$549$	−0.0127243	−	0.0966507i	−0.000543060	−	0.00412495i
$550$	−0.130167	−	0.150839i	−0.00555035	−	0.00643179i
$551$	13.0808	−	3.50499i	0.557261	−	0.149318i
$552$	0.594596	+	0.937718i	0.0253077	+	0.0399119i
$553$	−16.3222	−	27.9014i	−0.694092	−	1.18649i
$554$	10.3874	−	15.2804i	0.441316	−	0.649201i
$555$	14.0986	+	18.3736i	0.598451	+	0.779917i
$556$	−3.62870	−	1.03465i	−0.153891	−	0.0438790i
$557$	15.5397	+	11.9241i	0.658439	+	0.505238i	0.883092	−	0.469201i	$-0.155458\pi$
$557$	15.5397	+	11.9241i	0.658439	+	0.505238i	−0.224652	+	0.974439i	$0.572125\pi$
$558$	−0.0410198	−	0.712979i	−0.00173651	−	0.0301828i
$559$		−	26.8077i		−	1.13384i
$560$	−22.4184	+	8.60496i	−0.947349	+	0.363626i
$561$		−	0.0817858i		−	0.00345300i
$562$	−13.0760	+	0.752304i	−0.551579	+	0.0317340i
$563$	24.8644	+	19.0791i	1.04791	+	0.804088i	0.981066	−	0.193675i	$-0.0620409\pi$
$563$	24.8644	+	19.0791i	1.04791	+	0.804088i	0.0668424	+	0.997764i	$0.478708\pi$
$564$	9.92838	+	17.8484i	0.418060	+	0.751552i
$565$	−23.6309	−	30.7964i	−0.994159	−	1.29561i
$566$	16.9452	+	11.5191i	0.712259	+	0.484182i
$567$	23.3745	−	0.133605i	0.981639	−	0.00561087i
$568$	−5.25076	−	30.1529i	−0.220317	−	1.26519i
$569$	−36.8872	+	9.88389i	−1.54639	+	0.414354i	−0.928324	−	0.371771i	$-0.878751\pi$
$569$	−36.8872	+	9.88389i	−1.54639	+	0.414354i	−0.618067	+	0.786125i	$0.712084\pi$
$570$	24.6491	−	21.2711i	1.03244	−	0.890948i
$571$	2.87503	+	21.8380i	0.120316	+	0.913894i	0.940023	+	0.341110i	$0.110803\pi$
$571$	2.87503	+	21.8380i	0.120316	+	0.913894i	−0.819707	+	0.572783i	$0.805864\pi$
$572$	2.99040	+	4.02870i	0.125035	+	0.168448i
$573$	16.0982	+	38.8645i	0.672512	+	1.62359i
$574$	−4.26485	+	8.59912i	−0.178012	+	0.358921i
$575$	−0.0339570			−0.00141610
$576$	−0.355330	+	0.246562i	−0.0148054	+	0.0102734i
$577$	2.30610	+	3.99428i	0.0960042	+	0.166284i	0.910027	−	0.414548i	$-0.136060\pi$
$577$	2.30610	+	3.99428i	0.0960042	+	0.166284i	−0.814023	+	0.580833i	$0.802727\pi$
$578$	−7.54489	−	22.8233i	−0.313826	−	0.949324i
$579$	24.6520	+	3.24550i	1.02450	+	0.134878i
$580$	−4.13115	+	9.53991i	−0.171537	+	0.396123i
$581$	−36.9996	−	4.65611i	−1.53500	−	0.193168i
$582$	−8.25162	−	43.2862i	−0.342041	−	1.79427i
$583$	11.4927	−	3.07946i	0.475979	−	0.127538i
$584$	1.44549	+	1.73012i	0.0598149	+	0.0715929i
$585$	0.313243	+	0.0839333i	0.0129510	+	0.00347021i
$586$	−3.94315	+	1.90558i	−0.162890	+	0.0787188i
$587$	8.83831	−	21.3376i	0.364796	−	0.880695i	−0.629789	−	0.776766i	$-0.716859\pi$
$587$	8.83831	−	21.3376i	0.364796	−	0.880695i	0.994585	−	0.103929i	$-0.0331415\pi$
$588$	−0.108824	+	24.0290i	−0.00448782	+	0.990939i
$589$	−51.0150	+	21.1311i	−2.10204	+	0.870692i
$590$	27.9725	−	1.60934i	1.15161	−	0.0662556i
$591$	−38.7151	+	22.3522i	−1.59253	+	0.919446i
$592$	−15.0754	+	18.3996i	−0.619597	+	0.756220i
$593$	31.6538	+	18.2753i	1.29986	+	0.750477i	0.980380	−	0.197115i	$-0.0631572\pi$
$593$	31.6538	+	18.2753i	1.29986	+	0.750477i	0.319484	+	0.947592i	$0.396491\pi$
$594$	−5.87998	+	3.86136i	−0.241258	+	0.158434i
$595$	0.238109	−	0.184879i	0.00976152	−	0.00757931i
$596$	25.0088	−	24.2230i	1.02440	−	0.992212i
$597$	12.6449	+	16.4792i	0.517522	+	0.674447i
$598$	0.852807	+	0.0627344i	0.0348739	+	0.00256540i
$599$	6.61863	+	1.77346i	0.270430	+	0.0724614i	0.391485	−	0.920184i	$-0.371961\pi$
$599$	6.61863	+	1.77346i	0.270430	+	0.0724614i	−0.121056	+	0.992646i	$0.538628\pi$
$600$	0.0299093	+	0.720131i	0.00122104	+	0.0293992i
$601$	27.8002	+	27.8002i	1.13400	+	1.13400i	0.989506	+	0.144489i	$0.0461538\pi$
$601$	27.8002	+	27.8002i	1.13400	+	1.13400i	0.144489	+	0.989506i	$0.453846\pi$
$602$	−2.56722	+	37.8546i	−0.104632	+	1.54284i
$603$	0.389902	+	0.161503i	0.0158780	+	0.00657690i
$604$	0.173253	−	1.17122i	0.00704955	−	0.0476562i
$605$	−13.9505	+	18.1806i	−0.567167	+	0.739146i
$606$	−14.4363	+	4.77232i	−0.586433	+	0.193862i
$607$	−17.2445	+	29.8684i	−0.699933	+	1.21232i	0.268556	+	0.963264i	$0.413454\pi$
$607$	−17.2445	+	29.8684i	−0.699933	+	1.21232i	−0.968489	+	0.249056i	$0.919880\pi$
$608$	27.0413	+	19.6728i	1.09667	+	0.797836i
$609$	7.39793	+	7.31384i	0.299779	+	0.296372i
$610$	1.17410	−	5.66591i	0.0475379	−	0.229406i
$611$	15.5946	+	2.05307i	0.630890	+	0.0830582i
$612$	0.00337358	−	0.00425420i	0.000136369	−	0.000171966i
$613$	2.22063	+	16.8674i	0.0896904	+	0.681266i	0.975937	+	0.218053i	$0.0699704\pi$
$613$	2.22063	+	16.8674i	0.0896904	+	0.681266i	−0.886247	+	0.463214i	$0.846696\pi$
$614$	−2.62967	+	7.54831i	−0.106125	+	0.304625i
$615$	7.06450	+	7.06450i	0.284868	+	0.284868i
$616$	−3.83688	−	5.97522i	−0.154592	−	0.240749i
$617$	21.9050	−	21.9050i	0.881864	−	0.881864i	−0.111860	−	0.993724i	$-0.535681\pi$
$617$	21.9050	−	21.9050i	0.881864	−	0.881864i	0.993724	+	0.111860i	$0.0356808\pi$
$618$	0.445703	+	0.922278i	0.0179288	+	0.0370995i
$619$	−28.6865	+	3.77665i	−1.15301	+	0.151796i	−0.682695	−	0.730704i	$-0.739192\pi$
$619$	−28.6865	+	3.77665i	−1.15301	+	0.151796i	−0.470312	+	0.882500i	$0.655859\pi$
$620$	11.6232	−	40.7647i	0.466801	−	1.63715i
$621$	−0.156490	+	1.18866i	−0.00627973	+	0.0476993i
$622$	−8.58273	+	5.63625i	−0.344136	+	0.225993i
$623$	−5.52182	−	1.44579i	−0.221227	−	0.0579244i
$624$	0.579266	−	18.1409i	0.0231892	−	0.726217i
$625$	22.2744	+	12.8601i	0.890977	+	0.514406i
$626$	1.86532	−	3.70761i	0.0745533	−	0.148186i
$627$	7.63839	+	5.86114i	0.305048	+	0.234072i
$628$	−35.1031	−	21.0208i	−1.40077	−	0.838821i
$629$	0.114276	−	0.275886i	0.00455647	−	0.0110003i
$630$	−0.434287	−	0.148518i	−0.0173024	−	0.00591710i
$631$	11.4925	−	11.4925i	0.457510	−	0.457510i	−0.440327	−	0.897837i	$-0.645137\pi$
$631$	11.4925	−	11.4925i	0.457510	−	0.457510i	0.897837	+	0.440327i	$0.145137\pi$
$632$	−14.5378	−	31.3501i	−0.578283	−	1.24704i
$633$	−4.67816	+	17.4591i	−0.185940	+	0.693938i
$634$	−15.3557	+	13.2513i	−0.609854	+	0.526277i
$635$	−5.96278	+	4.57541i	−0.236626	+	0.181569i
$636$	−39.4976	−	17.1040i	−1.56618	−	0.678216i
$637$	14.8094	+	11.0970i	0.586770	+	0.439679i
$638$	−3.01030	−	0.623800i	−0.119179	−	0.0246965i
$639$	0.292504	−	0.506632i	0.0115713	−	0.0200421i
$640$	−24.7315	+	6.88162i	−0.977598	+	0.272020i
$641$	−0.491952	−	0.852086i	−0.0194309	−	0.0336554i	0.856146	−	0.516733i	$-0.172852\pi$
$641$	−0.491952	−	0.852086i	−0.0194309	−	0.0336554i	−0.875577	+	0.483078i	$0.839519\pi$
$642$	−13.7934	+	15.4775i	−0.544383	+	0.610847i
$643$	5.00573	+	12.0849i	0.197407	+	0.476582i	0.991324	−	0.131444i	$-0.0419615\pi$
$643$	5.00573	+	12.0849i	0.197407	+	0.476582i	−0.793917	+	0.608026i	$0.791961\pi$
$644$	−1.19823	−	0.170255i	−0.0472167	−	0.00670898i
$645$	36.4852	+	15.1127i	1.43660	+	0.595061i
$646$	−0.396436	−	0.138110i	−0.0155976	−	0.00543385i
$647$	−0.519900	+	1.94029i	−0.0204394	+	0.0762808i	−0.975392	−	0.220477i	$-0.929239\pi$
$647$	−0.519900	+	1.94029i	−0.0204394	+	0.0762808i	0.954953	+	0.296758i	$0.0959053\pi$
$648$	24.8891	+	2.23079i	0.977735	+	0.0876336i
$649$	2.14447	+	8.00327i	0.0841778	+	0.314156i
$650$	0.459053	+	0.312057i	0.0180055	+	0.0122399i
$651$	−33.7994	−	25.6296i	−1.32470	−	1.00450i
$652$	−0.331919	+	20.7947i	−0.0129990	+	0.814385i
$653$	−4.87594	+	37.0365i	−0.190810	+	1.44935i	0.581211	+	0.813753i	$0.302579\pi$
$653$	−4.87594	+	37.0365i	−0.190810	+	1.44935i	−0.772022	+	0.635596i	$0.780754\pi$
$654$	−7.49909	+	14.9056i	−0.293238	+	0.582855i
$655$	7.79090	−	4.49808i	0.304416	−	0.175754i
$656$	−5.41169	+	8.71834i	−0.211291	+	0.340394i
$657$			0.0430919i			0.00168118i
$658$	−21.8242	−	4.39250i	−0.850797	−	0.171238i
$659$	−1.18124	+	0.489288i	−0.0460148	+	0.0190599i	−0.405572	−	0.914063i	$-0.632928\pi$
$659$	−1.18124	+	0.489288i	−0.0460148	+	0.0190599i	0.359557	+	0.933123i	$0.382928\pi$
$660$	−7.16888	+	1.79878i	−0.279048	+	0.0700172i
$661$	−26.5473	+	3.49502i	−1.03257	+	0.135940i	−0.627717	−	0.778441i	$-0.716011\pi$
$661$	−26.5473	+	3.49502i	−1.03257	+	0.135940i	−0.404853	+	0.914382i	$0.632677\pi$
$662$	−22.3772	−	1.64612i	−0.869713	−	0.0639781i
$663$	0.0589730	+	0.220090i	0.00229032	+	0.00854760i
$664$	−38.9028	−	8.71128i	−1.50972	−	0.338063i
$665$	0.202840	+	35.4875i	0.00786581	+	1.37615i
$666$	−0.446614	+	0.0851378i	−0.0173059	+	0.00329902i
$667$	−0.415683	+	0.318965i	−0.0160953	+	0.0123504i
$668$	−10.9249	+	13.7767i	−0.422698	+	0.533036i
$669$	6.09609	−	7.94458i	0.235689	−	0.307155i
$670$	18.7010	+	16.6662i	0.722482	+	0.643872i
$671$	1.71110			0.0660561
$672$	−2.55522	+	25.5609i	−0.0985698	+	0.986034i
$673$	−32.0683			−1.23614			−0.618072	−	0.786122i	$-0.712086\pi$
$673$	−32.0683			−1.23614			−0.618072	+	0.786122i	$0.712086\pi$
$674$	−8.57636	−	7.64320i	−0.330349	−	0.294405i
$675$	−0.473768	+	0.617426i	−0.0182353	+	0.0237648i
$676$	9.41966	+	7.46980i	0.362294	+	0.287300i
$677$	−1.13981	+	0.874607i	−0.0438065	+	0.0336139i	−0.630433	−	0.776244i	$-0.717122\pi$
$677$	−1.13981	+	0.874607i	−0.0438065	+	0.0336139i	0.586626	+	0.809858i	$0.300456\pi$
$678$	−40.7915	+	7.77606i	−1.56659	+	0.298638i
$679$	41.7328	+	23.7774i	1.60156	+	0.912494i
$680$	0.272168	−	0.172578i	0.0104372	−	0.00661808i
$681$	−0.228454	−	0.852602i	−0.00875438	−	0.0326718i
$682$	12.5014	+	0.919634i	0.478705	+	0.0352146i
$683$	−0.311033	+	0.0409483i	−0.0119014	+	0.00156684i	−0.136475	−	0.990644i	$-0.543577\pi$
$683$	−0.311033	+	0.0409483i	−0.0119014	+	0.00156684i	0.124573	+	0.992210i	$0.460244\pi$
$684$	0.155555	+	0.619951i	0.00594778	+	0.0237044i
$685$	21.7771	−	9.02038i	0.832061	−	0.344651i
$686$	−19.8494	−	17.0881i	−0.757852	−	0.652426i
$687$		−	26.4837i		−	1.01042i
$688$	−6.57505	+	40.0248i	−0.250672	+	1.52593i
$689$	−28.7070	+	16.5740i	−1.09365	+	0.631419i
$690$	−0.566147	+	1.12530i	−0.0215529	+	0.0428396i
$691$	2.08532	−	15.8396i	0.0793294	−	0.602566i	−0.904894	−	0.425637i	$-0.860050\pi$
$691$	2.08532	−	15.8396i	0.0793294	−	0.602566i	0.984223	−	0.176930i	$-0.0566165\pi$
$692$	11.9279	+	0.190389i	0.453431	+	0.00723752i
$693$	0.0169466	−	0.134666i	0.000643748	−	0.00511553i
$694$	−20.1768	−	13.7158i	−0.765900	−	0.520646i
$695$	−1.10797	−	4.13501i	−0.0420278	−	0.156850i
$696$	7.13048	+	8.53453i	0.270280	+	0.323500i
$697$	0.0333410	−	0.124430i	0.00126288	−	0.00471314i
$698$	−0.960414	−	0.334587i	−0.0363522	−	0.0126643i
$699$	34.8557	+	14.4377i	1.31836	+	0.546084i
$700$	−0.618336	−	0.484610i	−0.0233709	−	0.0183165i
$701$	15.4207	+	37.2289i	0.582433	+	1.40612i	0.890601	+	0.454785i	$0.150284\pi$
$701$	15.4207	+	37.2289i	0.582433	+	1.40612i	−0.308168	+	0.951332i	$0.599716\pi$
$702$	13.0391	−	14.6310i	0.492127	−	0.552211i
$703$	17.5769	+	30.4441i	0.662925	+	1.14822i
$704$	−3.47666	−	6.74843i	−0.131032	−	0.254341i
$705$	−11.5856	+	20.0668i	−0.436339	+	0.755761i
$706$	28.2576	+	5.85558i	1.06349	+	0.220378i
$707$	6.25455	−	15.3474i	0.235227	−	0.577197i
$708$	11.9108	−	27.5053i	0.447636	−	1.03371i
$709$	2.50969	−	1.92575i	0.0942533	−	0.0723231i	−0.560560	−	0.828114i	$-0.689414\pi$
$709$	2.50969	−	1.92575i	0.0942533	−	0.0723231i	0.654813	+	0.755791i	$0.272747\pi$
$710$	26.2885	−	22.6858i	0.986589	−	0.851383i
$711$	0.170953	−	0.638005i	0.00641124	−	0.0239271i
$712$	−5.72962	−	2.09920i	−0.214727	−	0.0786710i
$713$	1.51068	−	1.51068i	0.0565755	−	0.0565755i
$714$	−0.0621979	−	0.316433i	−0.00232770	−	0.0118422i
$715$	−2.17829	+	5.25885i	−0.0814634	+	0.196670i
$716$	−13.5155	+	22.5699i	−0.505099	+	0.843476i
$717$	−37.0915	−	28.4613i	−1.38521	−	1.06291i
$718$	7.65925	−	15.2239i	0.285840	−	0.568152i
$719$	−18.2626	−	10.5439i	−0.681082	−	0.393223i	0.119181	−	0.992873i	$-0.461973\pi$
$719$	−18.2626	−	10.5439i	−0.681082	−	0.393223i	−0.800262	+	0.599650i	$0.795307\pi$
$720$	−0.447097	−	0.202144i	−0.0166623	−	0.00753345i
$721$	−1.08010	−	0.282804i	−0.0402249	−	0.0105322i
$722$	18.8491	−	12.3782i	0.701492	−	0.460667i
$723$	6.06209	−	46.0462i	0.225452	−	1.71248i
$724$	46.7515	+	13.3303i	1.73751	+	0.495416i
$725$	−0.337205	+	0.0443939i	−0.0125235	+	0.00164875i
$726$	10.6668	+	22.0725i	0.395883	+	0.819188i
$727$	1.49231	−	1.49231i	0.0553467	−	0.0553467i	−0.678892	−	0.734238i	$-0.737539\pi$
$727$	1.49231	−	1.49231i	0.0553467	−	0.0553467i	0.734238	+	0.678892i	$0.237539\pi$
$728$	14.6338	+	13.3130i	0.542365	+	0.493414i
$729$	19.4234	+	19.4234i	0.719386	+	0.719386i
$730$	−0.841465	+	2.41538i	−0.0311440	+	0.0893971i
$731$	−0.0664639	−	0.504844i	−0.00245826	−	0.0186723i
$732$	−4.85005	−	3.84610i	−0.179263	−	0.142156i
$733$	−16.1713	−	2.12900i	−0.597302	−	0.0786363i	−0.174187	−	0.984713i	$-0.555730\pi$
$733$	−16.1713	−	2.12900i	−0.597302	−	0.0786363i	−0.423114	+	0.906076i	$0.639063\pi$
$734$	−6.74713	+	32.5600i	−0.249041	+	1.20181i
$735$	−23.4517	+	13.8997i	−0.865031	+	0.512699i
$736$	−1.25788	−	0.302831i	−0.0463662	−	0.0111625i
$737$	−3.70380	+	6.41518i	−0.136431	+	0.236306i
$738$	−0.186222	+	0.0615609i	−0.00685492	+	0.00226609i
$739$	17.8434	−	23.2540i	0.656380	−	0.855412i	−0.339999	−	0.940426i	$-0.610427\pi$
$739$	17.8434	−	23.2540i	0.656380	−	0.855412i	0.996380	+	0.0850140i	$0.0270935\pi$
$740$	−26.6960	−	3.94900i	−0.981364	−	0.145168i
$741$	−24.7816	−	10.2649i	−0.910376	−	0.377090i
$742$	42.1238	−	20.6547i	1.54642	−	0.758259i
$743$	22.4851	+	22.4851i	0.824899	+	0.824899i	0.986806	−	0.161907i	$-0.0517644\pi$
$743$	22.4851	+	22.4851i	0.824899	+	0.824899i	−0.161907	+	0.986806i	$0.551764\pi$
$744$	−33.3679	−	30.7067i	−1.22333	−	1.12576i
$745$	38.1539	+	10.2233i	1.39785	+	0.374553i
$746$	17.2780	+	1.27101i	0.632594	+	0.0465350i
$747$	−0.463872	−	0.604530i	−0.0169722	−	0.0221186i
$748$	0.0663037	+	0.0684547i	0.00242430	+	0.00250295i
$749$	−3.07758	−	22.3870i	−0.112452	−	0.818003i
$750$	22.3351	−	14.6674i	0.815561	−	0.535576i
$751$	26.9574	+	15.5639i	0.983690	+	0.567934i	0.903382	−	0.428837i	$-0.141076\pi$
$751$	26.9574	+	15.5639i	0.983690	+	0.567934i	0.0803077	+	0.996770i	$0.474410\pi$
$752$	−22.7797	−	6.89015i	−0.830691	−	0.251258i
$753$	24.8624	−	14.3543i	0.906034	−	0.523099i
$754$	8.55070	−	0.491948i	0.311398	−	0.0179157i
$755$	1.24097	−	0.514028i	0.0451637	−	0.0187074i
$756$	−19.8133	+	19.4115i	−0.720604	+	0.705989i
$757$	1.79118	−	4.32429i	0.0651016	−	0.157169i	−0.887980	−	0.459881i	$-0.847892\pi$
$757$	1.79118	−	4.32429i	0.0651016	−	0.157169i	0.953082	+	0.302712i	$0.0978920\pi$
$758$	−32.1401	+	15.5321i	−1.16738	+	0.564152i
$759$	−0.359819	−	0.0964132i	−0.0130606	−	0.00349958i
$760$	−3.38681	+	37.7869i	−0.122852	+	1.37067i
$761$	21.0021	−	5.62750i	0.761326	−	0.203997i	0.142790	−	0.989753i	$-0.454393\pi$
$761$	21.0021	−	5.62750i	0.761326	−	0.203997i	0.618536	+	0.785756i	$0.287726\pi$
$762$	1.50560	+	7.89804i	0.0545421	+	0.286116i
$763$	−7.05589	−	16.7628i	−0.255440	−	0.606853i
$764$	−44.9816	−	19.4788i	−1.62738	−	0.704717i
$765$	0.00610711		0.000804016i	0.000220803		2.90693e-5i
$766$	11.6926	+	35.3701i	0.422471	+	1.27798i
$767$	−11.5418	−	19.9909i	−0.416750	−	0.721831i
$768$	−5.31424	+	26.9429i	−0.191761	+	0.972218i
$769$	−36.3367			−1.31033			−0.655167	−	0.755484i	$-0.727402\pi$
$769$	−36.3367			−1.31033			−0.655167	+	0.755484i	$0.727402\pi$
$770$	3.57953	−	7.21732i	0.128997	−	0.260094i
$771$	−2.21019	−	5.33587i	−0.0795981	−	0.192167i
$772$	−23.2648	+	17.2689i	−0.837320	+	0.621521i
$773$	4.61541	+	35.0575i	0.166005	+	1.26093i	0.848167	+	0.529730i	$0.177707\pi$
$773$	4.61541	+	35.0575i	0.166005	+	1.26093i	−0.682162	+	0.731201i	$0.738960\pi$
$774$	−0.586945	+	0.506508i	−0.0210973	+	0.0182061i
$775$	1.33956	−	0.358933i	0.0481183	−	0.0128932i
$776$	41.9987	+	29.5409i	1.50767	+	1.06046i
$777$	−13.3684	+	23.4635i	−0.479589	+	0.841748i
$778$	7.91825	+	5.38270i	0.283883	+	0.192979i
$779$	9.23182	+	12.0311i	0.330764	+	0.431061i
$780$	17.9948	−	10.0099i	0.644319	−	0.358410i
$781$	8.14641	+	6.25096i	0.291502	+	0.223677i
$782$	0.0162157		0.000932936i	0.000579871		3.33617e-5i
$783$			12.0084i			0.429146i
$784$	−19.3892	−	20.2005i	−0.692471	−	0.721445i
$785$		−	46.4194i		−	1.65678i
$786$	−0.552770	−	9.60787i	−0.0197167	−	0.342701i
$787$	−34.4340	−	26.4222i	−1.22744	−	0.941848i	−0.227947	−	0.973673i	$-0.573201\pi$
$787$	−34.4340	−	26.4222i	−1.22744	−	0.941848i	−0.999493	+	0.0318250i	$0.989868\pi$
$788$	14.2836	−	50.0951i	0.508833	−	1.78456i
$789$	−19.0735	−	24.8571i	−0.679034	−	0.884935i
$790$	22.0407	−	32.4231i	0.784172	−	1.15356i
$791$	22.4071	−	39.3276i	0.796703	−	1.39833i
$792$	0.0317060	−	0.141593i	0.00112662	−	0.00503128i
$793$	−4.60466	+	1.23381i	−0.163516	+	0.0438140i
$794$	−14.3188	−	16.5928i	−0.508156	−	0.588855i
$795$	−6.37379	−	48.4138i	−0.226055	−	1.71706i
$796$	−23.9434	−	3.54183i	−0.848652	−	0.125537i
$797$	−9.23619	−	22.2981i	−0.327163	−	0.789841i	−0.998801	−	0.0489611i	$-0.984409\pi$
$797$	−9.23619	−	22.2981i	−0.327163	−	0.789841i	0.671638	−	0.740879i	$-0.265591\pi$
$798$	34.0107	+	16.8680i	1.20396	+	0.597122i
$799$	0.298769			0.0105697
$800$	−0.608844	−	0.578502i	−0.0215259	−	0.0204531i
$801$	−0.0583167	−	0.101008i	−0.00206052	−	0.00356893i
$802$	2.79938	−	0.925413i	0.0988494	−	0.0326775i
$803$	−0.749898	−	0.0987260i	−0.0264633	−	0.00348397i
$804$	24.9180	−	9.85845i	0.878790	−	0.347681i
$805$	−0.532687	−	1.26551i	−0.0187748	−	0.0446035i
$806$	−34.3052	+	6.53958i	−1.20835	+	0.230347i
$807$	−11.1822	+	2.99627i	−0.393633	+	0.105474i
$808$	8.21424	−	15.6979i	0.288976	−	0.552250i
$809$	29.1859	+	7.82034i	1.02612	+	0.274949i	0.732351	−	0.680927i	$-0.238423\pi$
$809$	29.1859	+	7.82034i	1.02612	+	0.274949i	0.293771	+	0.955876i	$0.405090\pi$
$810$	12.3356	+	25.5257i	0.433430	+	0.896882i
$811$	−3.30832	+	7.98700i	−0.116171	+	0.280461i	−0.971261	−	0.238019i	$-0.923502\pi$
$811$	−3.30832	+	7.98700i	−0.116171	+	0.280461i	0.855090	+	0.518480i	$0.173502\pi$
$812$	−12.1214	−	0.124183i	−0.425377	−	0.00435797i
$813$	−15.1884	+	6.29126i	−0.532682	+	0.220644i
$814$	−0.458375	−	7.96716i	−0.0160660	−	0.279249i
$815$	−20.4338	+	11.7974i	−0.715764	+	0.413246i
$816$	−0.0340677	−	0.343066i	−0.00119261	−	0.0120097i
$817$	51.9130	+	29.9720i	1.81621	+	1.04859i
$818$	13.5459	+	20.6273i	0.473621	+	0.721217i
$819$	0.0514987	+	0.374613i	0.00179951	+	0.0130900i
$820$	−11.6402	−	0.185797i	−0.406492	−	0.00648831i
$821$	−17.9919	−	23.4475i	−0.627921	−	0.818323i	0.365743	−	0.930716i	$-0.380815\pi$
$821$	−17.9919	−	23.4475i	−0.627921	−	0.818323i	−0.993664	+	0.112393i	$0.964148\pi$
$822$	1.84993	−	25.1479i	0.0645238	−	0.877132i
$823$	−9.85062	−	2.63947i	−0.343371	−	0.0920060i	0.0830124	−	0.996549i	$-0.473546\pi$
$823$	−9.85062	−	2.63947i	−0.343371	−	0.0920060i	−0.426383	+	0.904543i	$0.640213\pi$
$824$	−1.12074	−	0.410615i	−0.0390430	−	0.0143045i
$825$	−0.170984	−	0.170984i	−0.00595289	−	0.00595289i
$826$	14.3835	+	29.3341i	0.500466	+	1.02067i
$827$	−36.1787	−	14.9857i	−1.25806	−	0.521105i	−0.348745	−	0.937218i	$-0.613392\pi$
$827$	−36.1787	−	14.9857i	−1.25806	−	0.521105i	−0.909313	+	0.416113i	$0.863392\pi$
$828$	−0.0147395	−	0.0198572i	−0.000512234	−	0.000690087i
$829$	16.5305	−	21.5430i	0.574129	−	0.748220i	−0.412544	−	0.910938i	$-0.635360\pi$
$829$	16.5305	−	21.5430i	0.574129	−	0.748220i	0.986673	+	0.162718i	$0.0520262\pi$
$830$	−14.1961	−	42.9431i	−0.492752	−	1.49058i
$831$	11.2122	−	19.4201i	0.388946	−	0.673675i
$832$	14.2220	+	15.6535i	0.493058	+	0.542688i
$833$	0.306404	+	0.172263i	0.0106163	+	0.00596855i
$834$	−4.48426	−	0.929236i	−0.155277	−	0.0321768i
$835$	−19.7771	−	2.60371i	−0.684415	−	0.0901050i
$836$	−11.1450	+	1.28667i	−0.385456	+	0.0445002i
$837$	−6.39110	−	48.5452i	−0.220909	−	1.67797i
$838$	6.45727	+	2.24957i	0.223063	+	0.0777102i
$839$	28.0292	+	28.0292i	0.967677	+	0.967677i	0.999494	−	0.0318170i	$-0.0101294\pi$
$839$	28.0292	+	28.0292i	0.967677	+	0.967677i	−0.0318170	+	0.999494i	$0.510129\pi$
$840$	−26.3688	+	12.4115i	−0.909809	+	0.428236i
$841$	16.7952	−	16.7952i	0.579145	−	0.579145i
$842$	26.9095	−	13.0044i	0.927361	−	0.448160i
$843$	−15.7601	+	2.07486i	−0.542807	+	0.0714619i
$844$	−10.2385	−	18.4059i	−0.352423	−	0.633556i
$845$	−1.78026	+	13.5224i	−0.0612427	+	0.465184i
$846$	−0.249695	−	0.380229i	−0.00858470	−	0.0130726i
$847$	−25.8495	−	6.76824i	−0.888200	−	0.232560i
$848$	46.9256	−	17.7047i	1.61143	−	0.607980i
$849$	21.5359	+	12.4338i	0.739110	+	0.426725i
$850$	0.00941859	+	0.00473854i	0.000323055	+	0.000162531i
$851$	−1.07906	−	0.827988i	−0.0369895	−	0.0283831i
$852$	−9.04025	−	36.0292i	−0.309714	−	1.23434i
$853$	−1.68705	+	4.07290i	−0.0577635	+	0.139453i	−0.950126	−	0.311865i	$-0.899046\pi$
$853$	−1.68705	+	4.07290i	−0.0577635	+	0.139453i	0.892363	+	0.451319i	$0.149046\pi$
$854$	6.62030	−	1.30128i	0.226542	−	0.0445290i
$855$	−0.512755	+	0.512755i	−0.0175358	+	0.0175358i
$856$	−1.00249	−	24.1370i	−0.0342642	−	0.824985i
$857$	5.73079	−	21.3876i	0.195760	−	0.730586i	−0.796309	−	0.604890i	$-0.793217\pi$
$857$	5.73079	−	21.3876i	0.195760	−	0.730586i	0.992069	−	0.125696i	$-0.0401164\pi$
$858$	3.97826	+	4.61003i	0.135815	+	0.157384i
$859$	2.05759	−	1.57885i	0.0702042	−	0.0538696i	−0.573063	−	0.819511i	$-0.694245\pi$
$859$	2.05759	−	1.57885i	0.0702042	−	0.0538696i	0.643267	+	0.765642i	$0.277578\pi$
$860$	−42.7900	+	16.9293i	−1.45913	+	0.577283i
$861$	−4.39647	+	10.7880i	−0.149831	+	0.367655i
$862$	−1.95881	+	9.45271i	−0.0667172	+	0.321961i
$863$	−0.598235	+	1.03617i	−0.0203642	+	0.0352718i	−0.876028	−	0.482260i	$-0.839816\pi$
$863$	−0.598235	+	1.03617i	−0.0203642	+	0.0352718i	0.855664	+	0.517532i	$0.173149\pi$
$864$	−23.0563	+	18.6465i	−0.784390	+	0.634368i
$865$	6.76703	+	11.7208i	0.230086	+	0.398520i
$866$	6.03922	+	5.38212i	0.205221	+	0.182892i
$867$	−11.1644	−	26.9533i	−0.379163	−	0.915381i
$868$	49.0680	−	5.94920i	1.66548	−	0.201929i
$869$	10.7111	+	4.43668i	0.363349	+	0.150504i
$870$	−4.15087	+	11.9148i	−0.140728	+	0.403951i
$871$	5.34138	−	19.9343i	0.180986	−	0.675448i
$872$	−5.80722	−	18.5555i	−0.196657	−	0.628368i
$873$	0.254016	+	0.948000i	0.00859714	+	0.0320850i
$874$	−1.07496	+	1.58132i	−0.0363609	+	0.0534890i
$875$	−3.63648	+	28.8972i	−0.122935	+	0.976902i
$876$	1.90366	+	1.96541i	0.0643186	+	0.0664052i
$877$	−1.08659	+	8.25344i	−0.0366914	+	0.278699i	0.963257	+	0.268580i	$0.0865544\pi$
$877$	−1.08659	+	8.25344i	−0.0366914	+	0.278699i	−0.999949	+	0.0101190i	$0.996779\pi$
$878$	39.8575	+	20.0525i	1.34512	+	0.676740i
$879$	−4.60308	+	2.65759i	−0.155258	+	0.0896382i
$880$	4.54209	−	7.31738i	0.153114	−	0.246669i
$881$		−	44.7478i		−	1.50759i	−0.657108	−	0.753797i	$-0.728220\pi$
$881$		−	44.7478i		−	1.50759i	0.657108	−	0.753797i	$-0.271780\pi$
$882$	−0.0368457	−	0.533915i	−0.00124066	−	0.0179779i
$883$	42.5710	−	17.6335i	1.43263	−	0.593414i	0.474629	−	0.880186i	$-0.342582\pi$
$883$	42.5710	−	17.6335i	1.43263	−	0.593414i	0.957999	+	0.286772i	$0.0925823\pi$
$884$	−0.227787	−	0.136406i	−0.00766132	−	0.00458783i
$885$	33.7143	−	4.43857i	1.13329	−	0.149201i
$886$	1.37124	−	18.6405i	0.0460677	−	0.626240i
$887$	11.7135	+	43.7152i	0.393299	+	1.46781i	0.824657	+	0.565633i	$0.191368\pi$
$887$	11.7135	+	43.7152i	0.393299	+	1.46781i	−0.431358	+	0.902181i	$0.641965\pi$
$888$	−16.6089	+	23.6130i	−0.557357	+	0.792401i
$889$	−7.61460	−	4.33845i	−0.255385	−	0.145507i
$890$	−1.29636	−	6.80041i	−0.0434540	−	0.227950i
$891$	−6.65115	+	5.10361i	−0.222822	+	0.170977i
$892$	1.33824	+	11.5917i	0.0448077	+	0.388119i
$893$	−21.4111	+	27.9035i	−0.716496	+	0.933755i
$894$	28.1136	−	31.5460i	0.940259	−	1.05506i
$895$	−29.8458			−0.997636
$896$	−18.5835	−	23.4660i	−0.620831	−	0.783944i
$897$	1.03781			0.0346516
$898$	11.7775	−	13.2155i	0.393022	−	0.441006i
$899$	13.0266	−	16.9766i	0.434462	−	0.566202i
$900$	−0.00184103	−	0.0159468i	−6.13678e−5	−	0.000531562i
$901$	−0.499521	+	0.383296i	−0.0166414	+	0.0127694i
$902$	−0.644657	−	3.38173i	−0.0214647	−	0.112599i
$903$	0.263198	+	46.0474i	0.00875870	+	1.53236i
$904$	27.8384	−	39.5782i	0.925892	−	1.31635i
$905$	14.2749	+	53.2747i	0.474514	+	1.77091i
$906$	0.105419	−	1.43306i	0.00350231	−	0.0476101i
$907$	21.4541	−	2.82449i	0.712372	−	0.0937856i	0.234374	−	0.972146i	$-0.424696\pi$
$907$	21.4541	−	2.82449i	0.712372	−	0.0937856i	0.477998	+	0.878361i	$0.341363\pi$
$908$	0.882420	+	0.528420i	0.0292841	+	0.0175362i
$909$	0.312864	−	0.129592i	0.0103770	−	0.00429831i
$910$	−4.42855	+	22.0033i	−0.146805	+	0.729403i
$911$			36.0398i			1.19405i	0.802222	+	0.597026i	$0.203651\pi$
$911$			36.0398i			1.19405i	−0.802222	+	0.597026i	$0.796349\pi$
$912$	34.4822	+	21.4040i	1.14182	+	0.708756i
$913$	11.5830	−	6.68743i	0.383340	−	0.221322i
$914$	41.5158	+	20.8868i	1.37322	+	0.690874i
$915$	0.916630	−	6.96249i	0.0303028	−	0.230173i
$916$	21.4703	+	22.1668i	0.709399	+	0.732413i
$917$	8.35848	+	6.33811i	0.276021	+	0.209303i
$918$	0.209278	−	0.307859i	0.00690720	−	0.0101609i
$919$	−10.4994	−	39.1843i	−0.346344	−	1.29257i	−0.891035	−	0.453935i	$-0.850020\pi$
$919$	−10.4994	−	39.1843i	−0.346344	−	1.29257i	0.544691	−	0.838637i	$-0.316647\pi$
$920$	−0.438419	−	1.40085i	−0.0144542	−	0.0461848i
$921$	−2.51083	+	9.37053i	−0.0827345	+	0.308769i
$922$	1.05007	−	3.01416i	0.0345822	−	0.0992662i
$923$	−26.4298	−	10.9476i	−0.869948	−	0.360344i
$924$	−5.17614	−	6.89071i	−0.170283	−	0.226688i
$925$	−0.337867	−	0.815683i	−0.0111090	−	0.0268195i
$926$	−4.98259	−	4.44045i	−0.163738	−	0.145922i
$927$	−0.0114071	−	0.0197576i	−0.000374657	−	0.000648924i
$928$	−12.8871	−	1.36272i	−0.423041	−	0.0447333i
$929$	−13.6580	+	23.6564i	−0.448106	+	0.776142i	−0.998263	−	0.0589191i	$-0.981235\pi$
$929$	−13.6580	+	23.6564i	−0.448106	+	0.776142i	0.550157	+	0.835061i	$0.314568\pi$
$930$	10.4390	−	50.3760i	0.342308	−	1.65190i
$931$	−38.0468	+	16.2715i	−1.24693	+	0.533277i
$932$	−40.8788	+	16.1731i	−1.33903	+	0.529769i
$933$	−9.88659	+	7.58625i	−0.323673	+	0.248363i
$934$	−30.2850	−	35.0945i	−0.990955	−	1.14833i
$935$	−0.0279835	+	0.104436i	−0.000915157	+	0.00341541i
$936$	0.0167751	+	0.403896i	0.000548311	+	0.0132018i
$937$	39.8612	−	39.8612i	1.30221	−	1.30221i	0.375311	−	0.926899i	$-0.377536\pi$
$937$	39.8612	−	39.8612i	1.30221	−	1.30221i	0.926899	−	0.375311i	$-0.122464\pi$
$938$	−9.45146	+	27.6373i	−0.308601	+	0.902391i
$939$	1.92764	−	4.65374i	0.0629062	−	0.151869i
$940$	−6.57104	−	26.1884i	−0.214324	−	0.854170i
$941$	−8.87982	−	6.81373i	−0.289474	−	0.222121i	0.453808	−	0.891100i	$-0.350065\pi$
$941$	−8.87982	−	6.81373i	−0.289474	−	0.222121i	−0.743282	+	0.668978i	$0.766732\pi$
$942$	−44.3600	−	22.3178i	−1.44533	−	0.727153i
$943$	−0.508132	−	0.293370i	−0.0165470	−	0.00955344i
$944$	12.3291	+	32.6780i	0.401279	+	1.06358i
$945$	−30.4424	−	7.97081i	−0.990291	−	0.259290i
$946$	−7.46968	−	11.3746i	−0.242860	−	0.369821i
$947$	2.01830	−	15.3305i	0.0655860	−	0.498175i	−0.926852	−	0.375427i	$-0.877496\pi$
$947$	2.01830	−	15.3305i	0.0655860	−	0.498175i	0.992438	−	0.122748i	$-0.0391707\pi$
$948$	−20.3878	−	36.6514i	−0.662165	−	1.19038i
$949$	2.08921	−	0.275049i	0.0678186	−	0.00892848i
$950$	−1.11754	+	0.540064i	−0.0362576	+	0.0175220i
$951$	−17.4065	+	17.4065i	−0.564445	+	0.564445i
$952$	0.308591	+	0.214430i	0.0100015	+	0.00694973i
$953$	−36.3082	−	36.3082i	−1.17614	−	1.17614i	−0.980720	−	0.195417i	$-0.937394\pi$
$953$	−36.3082	−	36.3082i	−1.17614	−	1.17614i	−0.195417	−	0.980720i	$-0.562606\pi$
$954$	0.905277	+	0.315379i	0.0293094	+	0.0102108i
$955$	−7.25876	−	55.1358i	−0.234888	−	1.78415i
$956$	54.1192	−	6.24796i	1.75034	−	0.202073i
$957$	−3.69918	−	0.487006i	−0.119578	−	0.0157427i
$958$	−40.3287	−	8.35699i	−1.30296	−	0.270002i
$959$	19.5456	+	19.3234i	0.631159	+	0.623985i
$960$	−29.3220	+	10.5315i	−0.946363	+	0.339903i
$961$	−28.1261	+	48.7158i	−0.907293	+	1.57148i
$962$	6.97837	+	21.1096i	0.224992	+	0.680600i
$963$	0.281093	−	0.366328i	0.00905810	−	0.0118047i
$964$	32.2556	+	43.4552i	1.03888	+	1.39960i
$965$	−30.3687	−	12.5791i	−0.977603	−	0.404936i
$966$	−1.46548	−	0.0993857i	−0.0471510	−	0.00319768i
$967$	1.50632	+	1.50632i	0.0484399	+	0.0484399i	0.730912	−	0.682472i	$-0.239095\pi$
$967$	1.50632	+	1.50632i	0.0484399	+	0.0484399i	−0.682472	+	0.730912i	$0.739095\pi$
$968$	−26.8223	−	9.82709i	−0.862102	−	0.315855i
$969$	−0.492139	−	0.131868i	−0.0158098	−	0.00423622i
$970$	−4.27377	+	58.0973i	−0.137222	+	1.86539i
$971$	0.0239539	+	0.0312174i	0.000768718	+	0.00100181i	0.793738	−	0.608260i	$-0.208132\pi$
$971$	0.0239539	+	0.0312174i	0.000768718	+	0.00100181i	−0.792969	+	0.609262i	$0.791466\pi$
$972$	−1.12337	−	0.0179310i	−0.0360322	−	0.000575136i
$973$	3.94270	−	3.06130i	0.126397	−	0.0981408i
$974$	7.36710	+	11.2184i	0.236057	+	0.359462i
$975$	0.583417	+	0.336836i	0.0186843	+	0.0107874i
$976$	7.17752	−	0.712753i	0.229747	−	0.0228147i
$977$	−29.9664	+	17.3011i	−0.958710	+	0.553511i	−0.895776	−	0.444506i	$-0.853379\pi$
$977$	−29.9664	+	17.3011i	−0.958710	+	0.553511i	−0.0629341	+	0.998018i	$0.520046\pi$
$978$	1.44979	+	25.1993i	0.0463592	+	0.805784i
$979$	1.89137	−	0.783431i	0.0604484	−	0.0250386i
$980$	8.36061	−	30.6464i	0.267070	−	0.978962i
$981$	0.142216	−	0.343340i	0.00454061	−	0.0109620i
$982$	−18.6823	−	38.6587i	−0.596177	−	1.23365i
$983$	−4.66428	−	1.24979i	−0.148767	−	0.0398621i	0.183667	−	0.982989i	$-0.441203\pi$
$983$	−4.66428	−	1.24979i	−0.148767	−	0.0398621i	−0.332434	+	0.943126i	$0.607870\pi$
$984$	−5.77398	+	11.0344i	−0.184068	+	0.351765i
$985$	57.0848	−	15.2958i	1.81887	−	0.487366i
$986$	0.159808	−	0.0304640i	0.00508931	−	0.000970173i
$987$	−26.8069	−	3.37343i	−0.853273	−	0.107378i
$988$	29.0639	−	11.4987i	0.924647	−	0.365824i
$989$	−2.29943	−	0.302725i	−0.0731175	−	0.00962610i
$990$	0.156298	−	0.0516687i	0.00496747	−	0.00164214i
$991$	5.73345	+	9.93063i	0.182129	+	0.315457i	0.942605	−	0.333909i	$-0.108368\pi$
$991$	5.73345	+	9.93063i	0.182129	+	0.315457i	−0.760476	+	0.649366i	$0.775034\pi$
$992$	52.8228	−	1.34986i	1.67713	−	0.0428582i
$993$	−27.2316			−0.864170
$994$	36.2727	+	17.9899i	1.15050	+	0.570606i
$995$	−10.5084	−	25.3694i	−0.333138	−	0.804265i
$996$	−47.8632	−	7.08017i	−1.51660	−	0.224344i
$997$	5.22587	+	39.6944i	0.165505	+	1.25713i	0.849477	+	0.527626i	$0.176918\pi$
$997$	5.22587	+	39.6944i	0.165505	+	1.25713i	−0.683972	+	0.729508i	$0.739749\pi$
$998$	21.2779	+	24.6570i	0.673541	+	0.780504i
$999$	−30.1100	+	8.06795i	−0.952638	+	0.255259i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	224.2.bd.a.37.8	✓	240
4.3	odd	2		896.2.bh.a.625.24		240
7.4	even	3	inner	224.2.bd.a.165.12	yes	240
28.11	odd	6		896.2.bh.a.753.7		240
32.13	even	8	inner	224.2.bd.a.205.12	yes	240
32.19	odd	8		896.2.bh.a.401.7		240
224.109	even	24	inner	224.2.bd.a.109.8	yes	240
224.179	odd	24		896.2.bh.a.529.24		240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
224.2.bd.a.37.8	✓	240	1.1	even	1	trivial
224.2.bd.a.109.8	yes	240	224.109	even	24	inner
224.2.bd.a.165.12	yes	240	7.4	even	3	inner
224.2.bd.a.205.12	yes	240	32.13	even	8	inner
896.2.bh.a.401.7		240	32.19	odd	8
896.2.bh.a.529.24		240	224.179	odd	24
896.2.bh.a.625.24		240	4.3	odd	2
896.2.bh.a.753.7		240	28.11	odd	6

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:	\( N \)	\(=\)	\( 224 = 2^{5} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	224.bd (of order \(24\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.940911 + 1.05579i) q^{2} +(-1.04486 + 1.36169i) q^{3} +(-0.229373 - 1.98680i) q^{4} +(1.80014 - 1.38129i) q^{5} +(-0.454533 - 2.38438i) q^{6} +(2.29881 + 1.30976i) q^{7} +(2.31346 + 1.62724i) q^{8} +(0.0139922 + 0.0522197i) q^{9} +O(q^{10})\)	\(q+(-0.940911 + 1.05579i) q^{2} +(-1.04486 + 1.36169i) q^{3} +(-0.229373 - 1.98680i) q^{4} +(1.80014 - 1.38129i) q^{5} +(-0.454533 - 2.38438i) q^{6} +(2.29881 + 1.30976i) q^{7} +(2.31346 + 1.62724i) q^{8} +(0.0139922 + 0.0522197i) q^{9} +(-0.235417 + 3.20024i) q^{10} +(-0.940800 + 0.123859i) q^{11} +(2.94507 + 1.76360i) q^{12} +(2.44244 - 1.01169i) q^{13} +(-3.54580 + 1.19469i) q^{14} +3.89449i q^{15} +(-3.89478 + 0.911438i) q^{16} +(0.0434878 - 0.0251077i) q^{17} +(-0.0682984 - 0.0343613i) q^{18} +(-0.771600 + 5.86089i) q^{19} +(-3.15726 - 3.25969i) q^{20} +(-4.18543 + 1.76175i) q^{21} +(0.754441 - 1.10982i) q^{22} +(-0.0591965 - 0.220924i) q^{23} +(-4.63304 + 1.44998i) q^{24} +(0.0384260 - 0.143408i) q^{25} +(-1.22999 + 3.53060i) q^{26} +(-4.84289 - 2.00599i) q^{27} +(2.07495 - 4.86771i) q^{28} +(-0.876670 - 2.11647i) q^{29} +(-4.11175 - 3.66437i) q^{30} +(4.67044 + 8.08944i) q^{31} +(2.70235 - 4.96964i) q^{32} +(0.814349 - 1.41049i) q^{33} +(-0.0144098 + 0.0695380i) q^{34} +(5.94734 - 0.817591i) q^{35} +(0.100541 - 0.0397776i) q^{36} +(4.71785 - 3.62013i) q^{37} +(-5.46184 - 6.32922i) q^{38} +(-1.17440 + 4.38292i) q^{39} +(6.41224 - 0.266321i) q^{40} +(1.81397 - 1.81397i) q^{41} +(2.07808 - 6.07657i) q^{42} +(3.88053 - 9.36842i) q^{43} +(0.461877 + 1.84078i) q^{44} +(0.0973188 + 0.0746753i) q^{45} +(0.288948 + 0.145371i) q^{46} +(5.15262 + 2.97487i) q^{47} +(2.82841 - 6.25581i) q^{48} +(3.56907 + 6.02177i) q^{49} +(0.115253 + 0.175504i) q^{50} +(-0.0112499 + 0.0854511i) q^{51} +(-2.57026 - 4.62059i) q^{52} +(-12.4313 + 1.63662i) q^{53} +(6.67463 - 3.22560i) q^{54} +(-1.52248 + 1.52248i) q^{55} +(3.18693 + 6.77078i) q^{56} +(-7.17450 - 7.17450i) q^{57} +(3.05941 + 1.06583i) q^{58} +(-1.13971 - 8.65692i) q^{59} +(7.73759 - 0.893291i) q^{60} +(-1.78778 - 0.235366i) q^{61} +(-12.9352 - 2.68045i) q^{62} +(-0.0362297 + 0.138370i) q^{63} +(2.70420 + 7.52910i) q^{64} +(2.99928 - 5.19490i) q^{65} +(0.722951 + 2.18693i) q^{66} +(4.75222 - 6.19321i) q^{67} +(-0.0598590 - 0.0806428i) q^{68} +(0.362683 + 0.150228i) q^{69} +(-4.73271 + 7.04840i) q^{70} +(-7.65167 - 7.65167i) q^{71} +(-0.0526034 + 0.143577i) q^{72} +(0.769926 + 0.206301i) q^{73} +(-0.616986 + 8.38727i) q^{74} +(0.155127 + 0.202166i) q^{75} +(11.8214 + 0.188690i) q^{76} +(-2.32495 - 0.947492i) q^{77} +(-3.52242 - 5.36385i) q^{78} +(-10.5808 - 6.10885i) q^{79} +(-5.75217 + 7.02054i) q^{80} +(7.65124 - 4.41745i) q^{81} +(0.208382 + 3.62196i) q^{82} +(-13.0219 + 5.39387i) q^{83} +(4.46028 + 7.91152i) q^{84} +(0.0436030 - 0.105267i) q^{85} +(6.23983 + 12.9119i) q^{86} +(3.79797 + 1.01766i) q^{87} +(-2.37805 - 1.24436i) q^{88} +(-2.08390 + 0.558378i) q^{89} +(-0.170410 + 0.0324851i) q^{90} +(6.93977 + 0.873315i) q^{91} +(-0.425355 + 0.168286i) q^{92} +(-15.8953 - 2.09265i) q^{93} +(-7.98898 + 2.64099i) q^{94} +(6.70662 + 11.6162i) q^{95} +(3.94352 + 8.87235i) q^{96} +18.1541 q^{97} +(-9.71589 - 1.89777i) q^{98} +(-0.0196318 - 0.0473953i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q - 4 q^{2} - 4 q^{3} - 4 q^{4} - 4 q^{5} - 16 q^{6} - 8 q^{7} - 16 q^{8} - 4 q^{9}+O(q^{10}) \) 240 * q - 4 * q^2 - 4 * q^3 - 4 * q^4 - 4 * q^5 - 16 * q^6 - 8 * q^7 - 16 * q^8 - 4 * q^9	\( 240 q - 4 q^{2} - 4 q^{3} - 4 q^{4} - 4 q^{5} - 16 q^{6} - 8 q^{7} - 16 q^{8} - 4 q^{9} - 4 q^{10} - 4 q^{11} - 4 q^{12} - 16 q^{13} + 24 q^{14} - 24 q^{16} - 24 q^{18} - 4 q^{19} - 48 q^{20} - 8 q^{21} - 24 q^{22} - 12 q^{23} + 36 q^{24} - 4 q^{25} - 4 q^{26} - 16 q^{27} + 12 q^{28} - 16 q^{29} + 44 q^{30} - 56 q^{31} - 4 q^{32} - 8 q^{33} - 32 q^{34} - 32 q^{35} - 96 q^{36} - 4 q^{37} + 36 q^{38} - 4 q^{39} - 68 q^{40} - 16 q^{41} - 28 q^{42} + 44 q^{44} + 8 q^{45} - 4 q^{46} - 16 q^{48} + 8 q^{50} - 28 q^{51} - 28 q^{52} - 20 q^{53} - 92 q^{54} - 16 q^{55} - 48 q^{56} - 16 q^{57} + 28 q^{58} - 36 q^{59} + 60 q^{60} - 4 q^{61} - 16 q^{63} + 56 q^{64} - 8 q^{65} - 36 q^{66} + 36 q^{67} - 36 q^{68} - 16 q^{69} - 44 q^{70} + 48 q^{71} - 4 q^{72} - 4 q^{73} + 68 q^{74} + 16 q^{75} - 16 q^{76} - 8 q^{77} - 120 q^{78} - 16 q^{80} - 44 q^{82} - 96 q^{83} - 28 q^{84} - 56 q^{85} - 4 q^{86} - 4 q^{87} + 40 q^{88} - 4 q^{89} + 224 q^{90} - 56 q^{91} - 80 q^{92} + 20 q^{93} + 4 q^{94} - 8 q^{95} - 32 q^{96} - 32 q^{97} + 96 q^{98} + 8 q^{99}+O(q^{100}) \) 240 * q - 4 * q^2 - 4 * q^3 - 4 * q^4 - 4 * q^5 - 16 * q^6 - 8 * q^7 - 16 * q^8 - 4 * q^9 - 4 * q^10 - 4 * q^11 - 4 * q^12 - 16 * q^13 + 24 * q^14 - 24 * q^16 - 24 * q^18 - 4 * q^19 - 48 * q^20 - 8 * q^21 - 24 * q^22 - 12 * q^23 + 36 * q^24 - 4 * q^25 - 4 * q^26 - 16 * q^27 + 12 * q^28 - 16 * q^29 + 44 * q^30 - 56 * q^31 - 4 * q^32 - 8 * q^33 - 32 * q^34 - 32 * q^35 - 96 * q^36 - 4 * q^37 + 36 * q^38 - 4 * q^39 - 68 * q^40 - 16 * q^41 - 28 * q^42 + 44 * q^44 + 8 * q^45 - 4 * q^46 - 16 * q^48 + 8 * q^50 - 28 * q^51 - 28 * q^52 - 20 * q^53 - 92 * q^54 - 16 * q^55 - 48 * q^56 - 16 * q^57 + 28 * q^58 - 36 * q^59 + 60 * q^60 - 4 * q^61 - 16 * q^63 + 56 * q^64 - 8 * q^65 - 36 * q^66 + 36 * q^67 - 36 * q^68 - 16 * q^69 - 44 * q^70 + 48 * q^71 - 4 * q^72 - 4 * q^73 + 68 * q^74 + 16 * q^75 - 16 * q^76 - 8 * q^77 - 120 * q^78 - 16 * q^80 - 44 * q^82 - 96 * q^83 - 28 * q^84 - 56 * q^85 - 4 * q^86 - 4 * q^87 + 40 * q^88 - 4 * q^89 + 224 * q^90 - 56 * q^91 - 80 * q^92 + 20 * q^93 + 4 * q^94 - 8 * q^95 - 32 * q^96 - 32 * q^97 + 96 * q^98 + 8 * q^99

Introduction

L-functions

Modular forms

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