LMFDB - Embedded newform 504.2.be.a.139.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [504,2,Mod(139,504)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(504, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 2, 3]))

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

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

chi := DirichletCharacter("504.139");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 504 = 2^{3} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	504.be (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$4.02446026187$
Analytic rank:	$0$
Dimension:	$184$
Relative dimension:	$92$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			139.12
Character	$\chi$	$=$	504.139
Dual form			504.2.be.a.475.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.29729 + 0.563073i) q^{2} +(1.71842 + 0.216873i) q^{3} +(1.36590 - 1.46093i) q^{4} +(1.92861 - 3.34045i) q^{5} +(-2.35140 + 0.686250i) q^{6} +(-0.786580 - 2.52612i) q^{7} +(-0.949346 + 2.66435i) q^{8} +(2.90593 + 0.745357i) q^{9} +(-0.621039 + 5.41946i) q^{10} +(1.23369 + 2.13681i) q^{11} +(2.66402 - 2.21427i) q^{12} +(-1.73459 + 3.00439i) q^{13} +(2.44281 + 2.83420i) q^{14} +(4.03861 - 5.32203i) q^{15} +(-0.268649 - 3.99097i) q^{16} +2.85064i q^{17} +(-4.18951 + 0.669311i) q^{18} -6.98636i q^{19} +(-2.24589 - 7.38027i) q^{20} +(-0.803828 - 4.51153i) q^{21} +(-2.80362 - 2.07739i) q^{22} +(1.87512 + 1.08260i) q^{23} +(-2.20920 + 4.37258i) q^{24} +(-4.93906 - 8.55470i) q^{25} +(0.558561 - 4.87426i) q^{26} +(4.83196 + 1.91105i) q^{27} +(-4.76488 - 2.30128i) q^{28} +(-5.27204 + 3.04382i) q^{29} +(-2.24254 + 9.17822i) q^{30} +(4.41084 - 7.63980i) q^{31} +(2.59572 + 5.02615i) q^{32} +(1.65658 + 3.93949i) q^{33} +(-1.60512 - 3.69810i) q^{34} +(-9.95538 - 2.24437i) q^{35} +(5.05812 - 3.22729i) q^{36} +4.69167i q^{37} +(3.93383 + 9.06330i) q^{38} +(-3.63232 + 4.78663i) q^{39} +(7.06919 + 8.30972i) q^{40} +(-3.78170 - 2.18336i) q^{41} +(3.58311 + 5.40012i) q^{42} +(-1.49032 - 2.58131i) q^{43} +(4.80682 + 1.11633i) q^{44} +(8.09423 - 8.26961i) q^{45} +(-3.04214 - 0.348612i) q^{46} +(4.30072 + 7.44906i) q^{47} +(0.403881 - 6.91642i) q^{48} +(-5.76258 + 3.97400i) q^{49} +(11.2243 + 8.31683i) q^{50} +(-0.618227 + 4.89860i) q^{51} +(2.01995 + 6.63781i) q^{52} -8.09088i q^{53} +(-7.34450 + 0.241566i) q^{54} +9.51720 q^{55} +(7.47720 + 0.302442i) q^{56} +(1.51515 - 12.0055i) q^{57} +(5.12545 - 6.91724i) q^{58} +(1.67555 + 0.967379i) q^{59} +(-2.25880 - 13.1695i) q^{60} +(3.12837 + 5.41850i) q^{61} +(-1.42035 + 12.3946i) q^{62} +(-0.402886 - 7.92702i) q^{63} +(-6.19748 - 5.05878i) q^{64} +(6.69068 + 11.5886i) q^{65} +(-4.36727 - 4.17787i) q^{66} +(1.52832 - 2.64713i) q^{67} +(4.16460 + 3.89369i) q^{68} +(2.98745 + 2.26702i) q^{69} +(14.1787 - 2.69402i) q^{70} +6.26226i q^{71} +(-4.74463 + 7.03481i) q^{72} +7.36156i q^{73} +(-2.64175 - 6.08644i) q^{74} +(-6.63209 - 15.7717i) q^{75} +(-10.2066 - 9.54265i) q^{76} +(4.42745 - 4.79722i) q^{77} +(2.01694 - 8.25488i) q^{78} +(-9.84796 + 5.68572i) q^{79} +(-13.8497 - 6.79961i) q^{80} +(7.88888 + 4.33192i) q^{81} +(6.13533 + 0.703073i) q^{82} +(7.31414 - 4.22282i) q^{83} +(-7.68898 - 4.98794i) q^{84} +(9.52243 + 5.49777i) q^{85} +(3.38684 + 2.50954i) q^{86} +(-9.71971 + 4.08719i) q^{87} +(-6.86440 + 1.25840i) q^{88} +10.4879i q^{89} +(-5.84413 + 15.2857i) q^{90} +(8.95386 + 2.01858i) q^{91} +(4.14282 - 1.26070i) q^{92} +(9.23654 - 12.1718i) q^{93} +(-9.77363 - 7.24194i) q^{94} +(-23.3376 - 13.4740i) q^{95} +(3.37050 + 9.19998i) q^{96} +(-4.28025 + 2.47121i) q^{97} +(5.23806 - 8.40016i) q^{98} +(1.99233 + 7.12896i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 184 q - 2 q^{2} - 2 q^{4} - 8 q^{8} - 8 q^{9} - 4 q^{11} - 10 q^{14} - 2 q^{16} - 10 q^{18} + 6 q^{22} - 80 q^{25} - 12 q^{28} + 4 q^{30} - 12 q^{32} + 12 q^{35} - 46 q^{36} + 10 q^{42} - 4 q^{43} - 36 q^{44}+ \cdots + 28 q^{99}+O(q^{100}) $ 184 * q - 2 * q^2 - 2 * q^4 - 8 * q^8 - 8 * q^9 - 4 * q^11 - 10 * q^14 - 2 * q^16 - 10 * q^18 + 6 * q^22 - 80 * q^25 - 12 * q^28 + 4 * q^30 - 12 * q^32 + 12 * q^35 - 46 * q^36 + 10 * q^42 - 4 * q^43 - 36 * q^44 - 16 * q^46 - 2 * q^49 + 16 * q^50 - 24 * q^51 + 40 * q^56 + 16 * q^57 - 10 * q^58 + 40 * q^60 - 8 * q^64 + 36 * q^65 - 4 * q^67 - 76 * q^72 - 40 * q^74 + 60 * q^78 + 8 * q^81 + 40 * q^84 + 32 * q^86 - 18 * q^88 + 20 * q^91 - 26 * q^92 - 132 * q^98 + 28 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/504\mathbb{Z}\right)^\times$.

$n$	$73$	$127$	$253$	$281$
$\chi(n)$	$-1$	$-1$	$-1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−1.29729	+	0.563073i	−0.917319	+	0.398153i
$2$	−1.29729	+	0.563073i	−0.917319	+	0.398153i
$3$	1.71842	+	0.216873i	0.992130	+	0.125212i
$3$	1.71842	+	0.216873i	0.992130	+	0.125212i
$4$	1.36590	−	1.46093i	0.682949	−	0.730466i
$5$	1.92861	−	3.34045i	0.862500	−	1.49389i	−0.00700873	−	0.999975i	$-0.502231\pi$
$5$	1.92861	−	3.34045i	0.862500	−	1.49389i	0.869508	−	0.493918i	$-0.164436\pi$
$6$	−2.35140	+	0.686250i	−0.959953	+	0.280160i
$7$	−0.786580	−	2.52612i	−0.297299	−	0.954784i
$7$	−0.786580	−	2.52612i	−0.297299	−	0.954784i
$8$	−0.949346	+	2.66435i	−0.335645	+	0.941989i
$9$	2.90593	+	0.745357i	0.968644	+	0.248452i
$10$	−0.621039	+	5.41946i	−0.196390	+	1.71378i
$11$	1.23369	+	2.13681i	0.371971	+	0.644272i	0.989869	−	0.141986i	$-0.0453489\pi$
$11$	1.23369	+	2.13681i	0.371971	+	0.644272i	−0.617898	+	0.786258i	$0.712016\pi$
$12$	2.66402	−	2.21427i	0.769037	−	0.639205i
$13$	−1.73459	+	3.00439i	−0.481088	+	0.833269i	−0.999764	−	0.0217015i	$-0.993092\pi$
$13$	−1.73459	+	3.00439i	−0.481088	+	0.833269i	0.518676	+	0.854971i	$0.326425\pi$
$14$	2.44281	+	2.83420i	0.652868	+	0.757471i
$15$	4.03861	−	5.32203i	1.04276	−	1.37414i
$16$	−0.268649	−	3.99097i	−0.0671622	−	0.997742i
$17$			2.85064i			0.691383i	0.938348	+	0.345691i	$0.112356\pi$
$17$			2.85064i			0.691383i	−0.938348	+	0.345691i	$0.887644\pi$
$18$	−4.18951	+	0.669311i	−0.987478	+	0.157758i
$19$		−	6.98636i		−	1.60278i	−0.598141	−	0.801391i	$-0.704094\pi$
$19$		−	6.98636i		−	1.60278i	0.598141	−	0.801391i	$-0.295906\pi$
$20$	−2.24589	−	7.38027i	−0.502196	−	1.65028i
$21$	−0.803828	−	4.51153i	−0.175410	−	0.984496i
$22$	−2.80362	−	2.07739i	−0.597735	−	0.442902i
$23$	1.87512	+	1.08260i	0.390989	+	0.225738i	0.682589	−	0.730803i	$-0.260854\pi$
$23$	1.87512	+	1.08260i	0.390989	+	0.225738i	−0.291600	+	0.956540i	$0.594187\pi$
$24$	−2.20920	+	4.37258i	−0.450951	+	0.892549i
$25$	−4.93906	−	8.55470i	−0.987812	−	1.71094i
$26$	0.558561	−	4.87426i	0.109543	−	0.955920i
$27$	4.83196	+	1.91105i	0.929912	+	0.367783i
$28$	−4.76488	−	2.30128i	−0.900478	−	0.434901i
$29$	−5.27204	+	3.04382i	−0.978994	+	0.565223i	−0.901966	−	0.431806i	$-0.857876\pi$
$29$	−5.27204	+	3.04382i	−0.978994	+	0.565223i	−0.0770278	+	0.997029i	$0.524543\pi$
$30$	−2.24254	+	9.17822i	−0.409430	+	1.67571i
$31$	4.41084	−	7.63980i	0.792210	−	1.37215i	−0.132386	−	0.991198i	$-0.542264\pi$
$31$	4.41084	−	7.63980i	0.792210	−	1.37215i	0.924596	−	0.380950i	$-0.124403\pi$
$32$	2.59572	+	5.02615i	0.458863	+	0.888507i
$33$	1.65658	+	3.93949i	0.288373	+	0.685777i
$34$	−1.60512	−	3.69810i	−0.275276	−	0.634219i
$35$	−9.95538	−	2.24437i	−1.68277	−	0.379368i
$36$	5.05812	−	3.22729i	0.843020	−	0.537882i
$37$			4.69167i			0.771306i	0.922644	+	0.385653i	$0.126024\pi$
$37$			4.69167i			0.771306i	−0.922644	+	0.385653i	$0.873976\pi$
$38$	3.93383	+	9.06330i	0.638152	+	1.47026i
$39$	−3.63232	+	4.78663i	−0.581637	+	0.766474i
$40$	7.06919	+	8.30972i	1.11774	+	1.31388i
$41$	−3.78170	−	2.18336i	−0.590602	−	0.340984i	0.174734	−	0.984616i	$-0.444094\pi$
$41$	−3.78170	−	2.18336i	−0.590602	−	0.340984i	−0.765335	+	0.643632i	$0.777427\pi$
$42$	3.58311	+	5.40012i	0.552886	+	0.833257i
$43$	−1.49032	−	2.58131i	−0.227272	−	0.393646i	0.729727	−	0.683739i	$-0.239647\pi$
$43$	−1.49032	−	2.58131i	−0.227272	−	0.393646i	−0.956999	+	0.290093i	$0.906314\pi$
$44$	4.80682	+	1.11633i	0.724656	+	0.168293i
$45$	8.09423	−	8.26961i	1.20662	−	1.23276i
$46$	−3.04214	−	0.348612i	−0.448540	−	0.0514000i
$47$	4.30072	+	7.44906i	0.627324	+	1.08656i	0.988086	+	0.153900i	$0.0491833\pi$
$47$	4.30072	+	7.44906i	0.627324	+	1.08656i	−0.360762	+	0.932658i	$0.617483\pi$
$48$	0.403881	−	6.91642i	0.0582953	−	0.998299i
$49$	−5.76258	+	3.97400i	−0.823226	+	0.567714i
$50$	11.2243	+	8.31683i	1.58735	+	1.17618i
$51$	−0.618227	+	4.89860i	−0.0865692	+	0.685942i
$52$	2.01995	+	6.63781i	0.280117	+	0.920499i
$53$		−	8.09088i		−	1.11137i	−0.831394	−	0.555684i	$-0.812456\pi$
$53$		−	8.09088i		−	1.11137i	0.831394	−	0.555684i	$-0.187544\pi$
$54$	−7.34450	+	0.241566i	−0.999460	+	0.0328730i
$55$	9.51720			1.28330
$56$	7.47720	+	0.302442i	0.999183	+	0.0404155i
$57$	1.51515	−	12.0055i	0.200687	−	1.59017i
$58$	5.12545	−	6.91724i	0.673005	−	0.908279i
$59$	1.67555	+	0.967379i	0.218138	+	0.125942i	0.605088	−	0.796159i	$-0.293138\pi$
$59$	1.67555	+	0.967379i	0.218138	+	0.125942i	−0.386950	+	0.922101i	$0.626471\pi$
$60$	−2.25880	−	13.1695i	−0.291609	−	1.70017i
$61$	3.12837	+	5.41850i	0.400547	+	0.693767i	0.993792	−	0.111255i	$-0.0354869\pi$
$61$	3.12837	+	5.41850i	0.400547	+	0.693767i	−0.593245	+	0.805022i	$0.702154\pi$
$62$	−1.42035	+	12.3946i	−0.180385	+	1.57412i
$63$	−0.402886	−	7.92702i	−0.0507588	−	0.998711i
$64$	−6.19748	−	5.05878i	−0.774685	−	0.632347i
$65$	6.69068	+	11.5886i	0.829877	+	1.43739i
$66$	−4.36727	−	4.17787i	−0.537574	−	0.514260i
$67$	1.52832	−	2.64713i	0.186714	−	0.323399i	−0.757439	−	0.652907i	$-0.773549\pi$
$67$	1.52832	−	2.64713i	0.186714	−	0.323399i	0.944153	+	0.329508i	$0.106883\pi$
$68$	4.16460	+	3.89369i	0.505032	+	0.472179i
$69$	2.98745	+	2.26702i	0.359647	+	0.272917i
$70$	14.1787	−	2.69402i	1.69468	−	0.321997i
$71$			6.26226i			0.743193i	0.928394	+	0.371596i	$0.121190\pi$
$71$			6.26226i			0.743193i	−0.928394	+	0.371596i	$0.878810\pi$
$72$	−4.74463	+	7.03481i	−0.559160	+	0.829060i
$73$			7.36156i			0.861605i	0.902446	+	0.430802i	$0.141769\pi$
$73$			7.36156i			0.861605i	−0.902446	+	0.430802i	$0.858231\pi$
$74$	−2.64175	−	6.08644i	−0.307098	−	0.707534i
$75$	−6.63209	−	15.7717i	−0.765808	−	1.82116i
$76$	−10.2066	−	9.54265i	−1.17078	−	1.09462i
$77$	4.42745	−	4.79722i	0.504554	−	0.546694i
$78$	2.01694	−	8.25488i	0.228373	−	0.934681i
$79$	−9.84796	+	5.68572i	−1.10798	+	0.639694i	−0.938306	−	0.345806i	$-0.887606\pi$
$79$	−9.84796	+	5.68572i	−1.10798	+	0.639694i	−0.169676	+	0.985500i	$0.554272\pi$
$80$	−13.8497	−	6.79961i	−1.54845	−	0.760219i
$81$	7.88888	+	4.33192i	0.876543	+	0.481324i
$82$	6.13533	+	0.703073i	0.677534	+	0.0776415i
$83$	7.31414	−	4.22282i	0.802831	−	0.463515i	−0.0416289	−	0.999133i	$-0.513255\pi$
$83$	7.31414	−	4.22282i	0.802831	−	0.463515i	0.844460	+	0.535618i	$0.179921\pi$
$84$	−7.68898	−	4.98794i	−0.838937	−	0.544229i
$85$	9.52243	+	5.49777i	1.03285	+	0.596317i
$86$	3.38684	+	2.50954i	0.365212	+	0.270610i
$87$	−9.71971	+	4.08719i	−1.04206	+	0.438193i
$88$	−6.86440	+	1.25840i	−0.731747	+	0.134146i
$89$			10.4879i			1.11172i	0.831276	+	0.555860i	$0.187611\pi$
$89$			10.4879i			1.11172i	−0.831276	+	0.555860i	$0.812389\pi$
$90$	−5.84413	+	15.2857i	−0.616025	+	1.61125i
$91$	8.95386	+	2.01858i	0.938620	+	0.211605i
$92$	4.14282	−	1.26070i	0.431919	−	0.131437i
$93$	9.23654	−	12.1718i	0.957784	−	1.26216i
$94$	−9.77363	−	7.24194i	−1.00807	−	0.746949i
$95$	−23.3376	−	13.4740i	−2.39438	−	1.38240i
$96$	3.37050	+	9.19998i	0.344000	+	0.938970i
$97$	−4.28025	+	2.47121i	−0.434594	+	0.250913i	−0.701302	−	0.712865i	$-0.747397\pi$
$97$	−4.28025	+	2.47121i	−0.434594	+	0.250913i	0.266708	+	0.963777i	$0.414064\pi$
$98$	5.23806	−	8.40016i	0.529124	−	0.848544i
$99$	1.99233	+	7.12896i	0.200236	+	0.716487i
$100$	−19.2441	−	4.46921i	−1.92441	−	0.446921i
$101$	1.44860	+	2.50905i	0.144141	+	0.249660i	0.929052	−	0.369949i	$-0.120625\pi$
$101$	1.44860	+	2.50905i	0.144141	+	0.249660i	−0.784911	+	0.619609i	$0.787291\pi$
$102$	−1.95625	−	6.70299i	−0.193698	−	0.663695i
$103$	−0.567070	+	0.982194i	−0.0558750	+	0.0967784i	−0.892610	−	0.450830i	$-0.851128\pi$
$103$	−0.567070	+	0.982194i	−0.0558750	+	0.0967784i	0.836735	+	0.547608i	$0.184462\pi$
$104$	−6.35802	−	7.47376i	−0.623455	−	0.732862i
$105$	−16.6208	−	6.01582i	−1.62202	−	0.587084i
$106$	4.55576	+	10.4962i	0.442494	+	1.01948i
$107$	10.9789			1.06137			0.530685	−	0.847569i	$-0.321935\pi$
$107$	10.9789			1.06137			0.530685	+	0.847569i	$0.321935\pi$
$108$	9.39189	−	4.44887i	0.903735	−	0.428093i
$109$			0.509013i			0.0487546i	0.999703	+	0.0243773i	$0.00776031\pi$
$109$			0.509013i			0.0487546i	−0.999703	+	0.0243773i	$0.992240\pi$
$110$	−12.3465	+	5.35888i	−1.17719	+	0.510949i
$111$	−1.01750	+	8.06226i	−0.0965765	+	0.765236i
$112$	−9.87036	+	3.81786i	−0.932661	+	0.360754i
$113$	−9.53142	+	16.5089i	−0.896641	+	1.55303i	−0.0648796	+	0.997893i	$0.520666\pi$
$113$	−9.53142	+	16.5089i	−0.896641	+	1.55303i	−0.831761	+	0.555134i	$0.812667\pi$
$114$	4.79439	+	16.4277i	0.449036	+	1.53860i
$115$	7.23273	−	4.17582i	0.674456	−	0.389397i
$116$	−2.75426	+	11.8596i	−0.255727	+	1.10114i
$117$	−7.27994	+	7.43768i	−0.673031	+	0.687614i
$118$	−2.71837	−	0.311510i	−0.250246	−	0.0286768i
$119$	7.20107	−	2.24226i	0.660121	−	0.205548i
$120$	10.3457	+	15.8127i	0.944427	+	1.44350i
$121$	2.45603	−	4.25397i	0.223276	−	0.386725i
$122$	−7.10940	−	5.26783i	−0.643655	−	0.476927i
$123$	−6.02503	−	4.57208i	−0.543259	−	0.412251i
$124$	−5.13648	−	16.8791i	−0.461269	−	1.51579i
$125$	−18.8160			−1.68295
$126$	4.98615	+	10.0568i	0.444202	+	0.895927i
$127$			16.2937i			1.44583i	0.690936	+	0.722916i	$0.257199\pi$
$127$			16.2937i			1.44583i	−0.690936	+	0.722916i	$0.742801\pi$
$128$	10.8884	+	3.07304i	0.962404	+	0.271621i
$129$	−2.00118	−	4.75898i	−0.176194	−	0.419005i
$130$	−15.2050	−	11.2664i	−1.33356	−	0.988127i
$131$	−12.8422	−	7.41447i	−1.12203	−	0.647805i	−0.180112	−	0.983646i	$-0.557646\pi$
$131$	−12.8422	−	7.41447i	−1.12203	−	0.647805i	−0.941919	+	0.335841i	$0.890979\pi$
$132$	8.01804	+	2.96079i	0.697881	+	0.257704i
$133$	−17.6484	+	5.49533i	−1.53031	+	0.476506i
$134$	−0.492141	+	4.29464i	−0.0425145	+	0.371001i
$135$	15.7027	−	12.4552i	1.35148	−	1.07198i
$136$	−7.59510	−	2.70625i	−0.651275	−	0.232059i
$137$	1.67840	+	2.90708i	0.143396	+	0.248369i	0.928773	−	0.370648i	$-0.120864\pi$
$137$	1.67840	+	2.90708i	0.143396	+	0.248369i	−0.785378	+	0.619017i	$0.787531\pi$
$138$	−5.15208	−	1.25882i	−0.438574	−	0.107158i
$139$	−3.63823	−	2.10054i	−0.308591	−	0.178165i	0.337705	−	0.941252i	$-0.390349\pi$
$139$	−3.63823	−	2.10054i	−0.308591	−	0.178165i	−0.646296	+	0.763087i	$0.723683\pi$
$140$	−16.8769	+	11.4786i	−1.42636	+	0.970116i
$141$	5.77494	+	13.7333i	0.486338	+	1.15655i
$142$	−3.52611	−	8.12393i	−0.295904	−	0.681745i
$143$	−8.55976			−0.715803
$144$	2.19402	−	11.7977i	0.182835	−	0.983144i
$145$			23.4813i			1.95002i
$146$	−4.14509	−	9.55004i	−0.343050	−	0.790367i
$147$	−10.7644	+	5.57924i	−0.887832	+	0.460168i
$148$	6.85422	+	6.40834i	0.563413	+	0.526762i
$149$	−1.60283	−	0.925393i	−0.131309	−	0.0758111i	0.432907	−	0.901439i	$-0.357488\pi$
$149$	−1.60283	−	0.925393i	−0.131309	−	0.0758111i	−0.564215	+	0.825628i	$0.690821\pi$
$150$	17.4843	+	16.7261i	1.42759	+	1.36568i
$151$	7.44861	−	4.30045i	0.606159	−	0.349966i	−0.165302	−	0.986243i	$-0.552860\pi$
$151$	7.44861	−	4.30045i	0.606159	−	0.349966i	0.771461	+	0.636277i	$0.219526\pi$
$152$	18.6141	+	6.63248i	1.50980	+	0.537965i
$153$	−2.12475	+	8.28378i	−0.171776	+	0.669704i
$154$	−3.04248	+	8.71633i	−0.245170	+	0.702382i
$155$	−17.0136	−	29.4683i	−1.36656	−	2.36695i
$156$	2.03156	+	11.8446i	0.162655	+	0.948328i
$157$	3.71253	−	6.43029i	0.296292	−	0.513193i	−0.678993	−	0.734145i	$-0.737583\pi$
$157$	3.71253	−	6.43029i	0.296292	−	0.513193i	0.975285	+	0.220952i	$0.0709165\pi$
$158$	9.57414	−	12.9211i	0.761678	−	1.02795i
$159$	1.75469	−	13.9035i	0.139156	−	1.10262i
$160$	21.7957	+	1.02261i	1.72310	+	0.0808447i
$161$	1.25985	−	5.58833i	0.0992899	−	0.440422i
$162$	−12.6733	−	1.17771i	−0.995710	−	0.0925297i
$163$	8.40698			0.658485			0.329243	−	0.944245i	$-0.393207\pi$
$163$	8.40698			0.658485			0.329243	+	0.944245i	$0.393207\pi$
$164$	−8.35516	+	2.54255i	−0.652428	+	0.198540i
$165$	16.3545	+	2.06402i	1.27320	+	0.160684i
$166$	−7.11077	+	9.59660i	−0.551903	+	0.744841i
$167$	6.28622	−	10.8880i	0.486442	−	0.842542i	−0.513437	−	0.858128i	$-0.671628\pi$
$167$	6.28622	−	10.8880i	0.486442	−	0.842542i	0.999879	+	0.0155853i	$0.00496116\pi$
$168$	12.7834	+	2.14132i	0.986259	+	0.165207i
$169$	0.482408	+	0.835555i	0.0371083	+	0.0642734i
$170$	−15.4489	−	1.77036i	−1.18488	−	0.135780i
$171$	5.20734	−	20.3019i	0.398215	−	1.55252i
$172$	−5.80674	−	1.34855i	−0.442760	−	0.102826i
$173$	4.19124	+	7.25944i	0.318654	+	0.551925i	0.980207	−	0.197973i	$-0.0634358\pi$
$173$	4.19124	+	7.25944i	0.318654	+	0.551925i	−0.661553	+	0.749898i	$0.730102\pi$
$174$	10.3078	−	10.7752i	0.781436	−	0.816862i
$175$	−17.7252	+	19.2056i	−1.33990	+	1.45181i
$176$	8.19651	−	5.49766i	0.617835	−	0.414402i
$177$	2.66950	+	2.02575i	0.200652	+	0.152264i
$178$	−5.90548	−	13.6058i	−0.442634	−	1.01980i
$179$	−16.3432			−1.22155			−0.610775	−	0.791804i	$-0.709142\pi$
$179$	−16.3432			−1.22155			−0.610775	+	0.791804i	$0.709142\pi$
$180$	−1.02546	−	23.1206i	−0.0764330	−	1.72331i
$181$	3.16964			0.235597			0.117799	−	0.993037i	$-0.462416\pi$
$181$	3.16964			0.235597			0.117799	+	0.993037i	$0.462416\pi$
$182$	−12.7523	+	2.42300i	−0.945265	+	0.179605i
$183$	4.20073	+	9.98971i	0.310527	+	0.738461i
$184$	−4.66456	+	3.96820i	−0.343876	+	0.292540i
$185$	15.6723	+	9.04840i	1.15225	+	0.665251i
$186$	−5.12882	+	20.9911i	−0.376063	+	1.53914i
$187$	−6.09128	+	3.51680i	−0.445439	+	0.257174i
$188$	16.7569	+	3.89160i	1.22212	+	0.283824i
$189$	1.02683	−	13.7093i	0.0746909	−	0.997207i
$190$	37.8623	+	4.33880i	2.74682	+	0.314770i
$191$	12.3881	−	7.15227i	0.896371	−	0.517520i	0.0203499	−	0.999793i	$-0.493522\pi$
$191$	12.3881	−	7.15227i	0.896371	−	0.517520i	0.876021	+	0.482273i	$0.160189\pi$
$192$	−9.55277	−	10.0372i	−0.689411	−	0.724370i
$193$	−8.87133	+	15.3656i	−0.638572	+	1.10604i	0.347174	+	0.937801i	$0.387141\pi$
$193$	−8.87133	+	15.3656i	−0.638572	+	1.10604i	−0.985746	+	0.168239i	$0.946192\pi$
$194$	4.16124	−	5.61595i	0.298760	−	0.403202i
$195$	8.98415	+	21.3651i	0.643368	+	1.52999i
$196$	−2.06536	+	13.8468i	−0.147525	+	0.989058i
$197$		−	11.4563i		−	0.816226i	−0.912931	−	0.408113i	$-0.866187\pi$
$197$		−	11.4563i		−	0.816226i	0.912931	−	0.408113i	$-0.133813\pi$
$198$	−6.59874	−	8.12647i	−0.468952	−	0.577523i
$199$	−17.1472			−1.21553			−0.607765	−	0.794117i	$-0.707934\pi$
$199$	−17.1472			−1.21553			−0.607765	+	0.794117i	$0.707934\pi$
$200$	27.4816	−	5.03799i	1.94324	−	0.356240i
$201$	3.20039	−	4.21743i	0.225738	−	0.297475i
$202$	−3.29203	−	2.43929i	−0.231626	−	0.171628i
$203$	11.8359	+	10.9236i	0.830720	+	0.766688i
$204$	6.31209	+	7.59418i	0.441935	+	0.531699i
$205$	−14.5868	+	8.42171i	−1.01879	+	0.588197i
$206$	0.182604	−	1.59349i	0.0127226	−	0.111024i
$207$	4.64204	+	4.54359i	0.322644	+	0.315802i
$208$	12.4564	+	6.11556i	0.863699	+	0.424038i
$209$	14.9285	−	8.61899i	1.03263	−	0.596188i
$210$	24.9492	−	1.55448i	1.72166	−	0.107269i
$211$	1.54702	−	2.67952i	0.106501	−	0.184466i	−0.807849	−	0.589389i	$-0.799369\pi$
$211$	1.54702	−	2.67952i	0.106501	−	0.184466i	0.914351	+	0.404924i	$0.132702\pi$
$212$	−11.8202	−	11.0513i	−0.811817	−	0.759007i
$213$	−1.35811	+	10.7612i	−0.0930564	+	0.737344i
$214$	−14.2428	+	6.18193i	−0.973616	+	0.422588i
$215$	−11.4970			−0.784087
$216$	−9.67892	+	11.0598i	−0.658567	+	0.752522i
$217$	−22.7685	−	5.13300i	−1.54563	−	0.348451i
$218$	−0.286612	−	0.660335i	−0.0194118	−	0.0447235i
$219$	−1.59652	+	12.6502i	−0.107883	+	0.854824i
$220$	12.9995	−	13.9040i	0.876427	−	0.937406i
$221$	−8.56446	−	4.94469i	−0.576108	−	0.332616i
$222$	−3.21966	−	11.0320i	−0.216089	−	0.740418i
$223$	3.38882	+	5.86960i	0.226932	+	0.393058i	0.956897	−	0.290426i	$-0.0937971\pi$
$223$	3.38882	+	5.86960i	0.226932	+	0.393058i	−0.729965	+	0.683484i	$0.760464\pi$
$224$	10.6549	−	10.5106i	0.711913	−	0.702268i
$225$	−7.97626	−	28.5407i	−0.531751	−	1.90272i
$226$	3.06925	−	26.7836i	0.204163	−	1.78162i
$227$	−4.24310	+	2.44975i	−0.281624	+	0.162596i	−0.634159	−	0.773203i	$-0.718653\pi$
$227$	−4.24310	+	2.44975i	−0.281624	+	0.162596i	0.352534	+	0.935799i	$0.385320\pi$
$228$	−15.4697	−	18.6118i	−1.02451	−	1.23260i
$229$	2.71934	−	4.71004i	0.179699	−	0.311248i	−0.762078	−	0.647485i	$-0.775821\pi$
$229$	2.71934	−	4.71004i	0.179699	−	0.311248i	0.941777	+	0.336237i	$0.109154\pi$
$230$	−7.03162	+	9.48979i	−0.463652	+	0.625738i
$231$	8.64860	−	7.28344i	0.569036	−	0.479215i
$232$	−3.10478	−	16.9362i	−0.203839	−	1.11192i
$233$	3.90548			0.255856			0.127928	−	0.991783i	$-0.459167\pi$
$233$	3.90548			0.255856			0.127928	+	0.991783i	$0.459167\pi$
$234$	5.25620	−	13.7479i	0.343609	−	0.898730i
$235$	33.1776			2.16427
$236$	3.70191	−	1.12653i	0.240974	−	0.0733305i
$237$	−18.1560	+	7.63470i	−1.17936	+	0.495927i
$238$	−8.07929	+	6.96358i	−0.523703	+	0.451382i
$239$	−11.3161	−	6.53333i	−0.731975	−	0.422606i	0.0871691	−	0.996194i	$-0.472218\pi$
$239$	−11.3161	−	6.53333i	−0.731975	−	0.422606i	−0.819144	+	0.573587i	$0.805551\pi$
$240$	−22.3250	−	14.6882i	−1.44107	−	0.948120i
$241$	18.2614	−	10.5432i	1.17632	−	0.679149i	0.221161	−	0.975237i	$-0.429016\pi$
$241$	18.2614	−	10.5432i	1.17632	−	0.679149i	0.955161	+	0.296088i	$0.0956822\pi$
$242$	−0.790876	+	6.90154i	−0.0508395	+	0.443648i
$243$	12.6169	+	9.15493i	0.809377	+	0.587289i
$244$	12.1891	+	2.83077i	0.780327	+	0.181222i
$245$	2.16116	+	26.9139i	0.138071	+	1.71946i
$246$	10.3906	+	2.53876i	0.662480	+	0.161866i
$247$	20.9898	+	12.1185i	1.33555	+	0.771079i
$248$	16.1677	+	19.0048i	1.02665	+	1.20681i
$249$	13.4846	−	5.67034i	0.854551	−	0.359343i
$250$	24.4097	−	10.5948i	1.54380	−	0.670071i
$251$		−	0.311589i		−	0.0196673i	−0.999952	−	0.00983367i	$-0.996870\pi$
$251$		−	0.311589i		−	0.0196673i	0.999952	−	0.00983367i	$-0.00313020\pi$
$252$	−12.1311	−	10.2389i	−0.764190	−	0.644991i
$253$			5.34236i			0.335871i
$254$	−9.17455	−	21.1376i	−0.575662	−	1.32629i
$255$	15.1712	+	11.5126i	0.950058	+	0.720950i
$256$	−15.8557	+	2.14434i	−0.990978	+	0.134021i
$257$	−17.2272	−	9.94611i	−1.07460	−	0.620421i	−0.145166	−	0.989407i	$-0.546372\pi$
$257$	−17.2272	−	9.94611i	−1.07460	−	0.620421i	−0.929435	+	0.368986i	$0.879705\pi$
$258$	5.27576	+	5.04695i	0.328454	+	0.314209i
$259$	11.8517	−	3.69038i	0.736431	−	0.229309i
$260$	26.0690	+	6.05420i	1.61673	+	0.375466i
$261$	−17.5889	+	4.91557i	−1.08873	+	0.304266i
$262$	20.8349	+	2.38756i	1.28719	+	0.147504i
$263$	−12.8412	+	7.41389i	−0.791824	+	0.457160i	−0.840604	−	0.541650i	$-0.817800\pi$
$263$	−12.8412	+	7.41389i	−0.791824	+	0.457160i	0.0487800	+	0.998810i	$0.484467\pi$
$264$	−12.0688	+	0.673755i	−0.742785	+	0.0414667i
$265$	−27.0272	−	15.6041i	−1.66027	−	0.958555i
$266$	19.8007	−	17.0664i	1.21406	−	1.04641i
$267$	−2.27455	+	18.0227i	−0.139200	+	1.10297i
$268$	−1.77975	−	5.84849i	−0.108716	−	0.357253i
$269$	−17.8308			−1.08716			−0.543581	−	0.839357i	$-0.682932\pi$
$269$	−17.8308			−1.08716			−0.543581	+	0.839357i	$0.682932\pi$
$270$	−13.3577	+	24.9998i	−0.812925	+	1.52144i
$271$	−4.46709			−0.271356			−0.135678	−	0.990753i	$-0.543321\pi$
$271$	−4.46709			−0.271356			−0.135678	+	0.990753i	$0.543321\pi$
$272$	11.3768	−	0.765822i	0.689822	−	0.0464348i
$273$	14.9487	+	5.41062i	0.904737	+	0.327466i
$274$	−3.81427	−	2.82625i	−0.230428	−	0.170740i
$275$	12.1865	−	21.1076i	0.734874	−	1.27284i
$276$	7.39252	−	1.26795i	0.444977	−	0.0763214i
$277$	24.6045	−	14.2054i	1.47834	−	0.853522i	0.478644	−	0.878009i	$-0.341128\pi$
$277$	24.6045	−	14.2054i	1.47834	−	0.853522i	0.999700	+	0.0244868i	$0.00779516\pi$
$278$	5.90258	+	0.676402i	0.354013	+	0.0405679i
$279$	18.5120	−	18.9131i	1.10828	−	1.13230i
$280$	15.4309	−	24.3939i	0.922172	−	1.45781i
$281$	6.45716	+	11.1841i	0.385202	+	0.667190i	0.991797	−	0.127821i	$-0.0407984\pi$
$281$	6.45716	+	11.1841i	0.385202	+	0.667190i	−0.606595	+	0.795011i	$0.707465\pi$
$282$	−15.2246	−	14.5643i	−0.906613	−	0.867293i
$283$	−3.89933	−	2.25128i	−0.231791	−	0.133825i	0.379607	−	0.925148i	$-0.376059\pi$
$283$	−3.89933	−	2.25128i	−0.231791	−	0.133825i	−0.611398	+	0.791323i	$0.709393\pi$
$284$	9.14873	+	8.55360i	0.542877	+	0.507563i
$285$	−37.1816	−	28.2152i	−2.20245	−	1.67132i
$286$	11.1044	−	4.81977i	0.656620	−	0.284999i
$287$	−2.54083	+	11.2704i	−0.149981	+	0.665272i
$288$	3.79671	+	16.5404i	0.223723	+	0.974653i
$289$	8.87383			0.521990
$290$	−13.2217	−	30.4620i	−0.776405	−	1.78879i
$291$	−7.89121	+	3.31830i	−0.462591	+	0.194522i
$292$	10.7547	+	10.0551i	0.629373	+	0.588432i
$293$	−4.46297	+	7.73009i	−0.260729	+	0.451596i	−0.966436	−	0.256908i	$-0.917296\pi$
$293$	−4.46297	+	7.73009i	−0.260729	+	0.451596i	0.705707	+	0.708504i	$0.250630\pi$
$294$	10.8230	−	13.2990i	0.631208	−	0.775614i
$295$	6.46296	−	3.73139i	0.376288	−	0.217250i
$296$	−12.5002	−	4.45402i	−0.726562	−	0.258885i
$297$	1.87757	+	12.6826i	0.108948	+	0.735921i
$298$	2.60039	+	0.297989i	0.150636	+	0.0172621i
$299$	−6.50511	+	3.75573i	−0.376200	+	0.217199i
$300$	−32.1002	−	11.8535i	−1.85330	−	0.684362i
$301$	−5.34845	+	5.79514i	−0.308279	+	0.334026i
$302$	−7.24150	+	9.77303i	−0.416701	+	0.562374i
$303$	1.94516	+	4.62577i	0.111747	+	0.265743i
$304$	−27.8823	+	1.87688i	−1.59916	+	0.107646i
$305$	24.1336			1.38189
$306$	−1.90797	−	11.9428i	−0.109071	−	0.682725i
$307$		−	11.3307i		−	0.646678i	−0.946283	−	0.323339i	$-0.895195\pi$
$307$		−	11.3307i		−	0.646678i	0.946283	−	0.323339i	$-0.104805\pi$
$308$	−0.960974	−	13.0207i	−0.0547566	−	0.741924i
$309$	−1.18748	+	1.56484i	−0.0675531	+	0.0890206i
$310$	38.6643	+	28.6490i	2.19598	+	1.62715i
$311$	−7.03619	+	12.1870i	−0.398986	+	0.691064i	−0.993601	−	0.112947i	$-0.963971\pi$
$311$	−7.03619	+	12.1870i	−0.398986	+	0.691064i	0.594615	+	0.804010i	$0.297304\pi$
$312$	−9.30490	−	14.2219i	−0.526786	−	0.805158i
$313$	27.6908	−	15.9873i	1.56518	−	0.903656i	0.568459	−	0.822711i	$-0.307540\pi$
$313$	27.6908	−	15.9873i	1.56518	−	0.903656i	0.996719	−	0.0809447i	$-0.0257937\pi$
$314$	−1.19549	+	10.4323i	−0.0674652	+	0.588731i
$315$	−27.2568	−	13.9423i	−1.53575	−	0.785560i
$316$	−5.14485	+	22.1533i	−0.289420	+	1.24622i
$317$	−1.38300	+	0.798478i	−0.0776773	+	0.0448470i	−0.538336	−	0.842731i	$-0.680947\pi$
$317$	−1.38300	+	0.798478i	−0.0776773	+	0.0448470i	0.460658	+	0.887578i	$0.347613\pi$
$318$	5.55237	+	19.0249i	0.311361	+	1.06686i
$319$	−13.0081	−	7.51023i	−0.728314	−	0.420492i
$320$	−28.8511	+	10.9460i	−1.61282	+	0.611898i
$321$	18.8664	+	2.38103i	1.05302	+	0.132896i
$322$	1.51225	+	7.95904i	0.0842746	+	0.443540i
$323$	19.9156			1.10814
$324$	17.1040	−	5.60818i	0.950225	−	0.311565i
$325$	34.2689			1.90090
$326$	−10.9062	+	4.73374i	−0.604041	+	0.262178i
$327$	−0.110391	+	0.874698i	−0.00610464	+	0.0483709i
$328$	9.40738	−	8.00298i	0.519436	−	0.441891i
$329$	15.4344	−	16.7234i	0.850925	−	0.921993i
$330$	−22.3787	+	6.53118i	−1.23191	+	0.359529i
$331$	17.9537	+	31.0967i	0.986824	+	1.70923i	0.633533	+	0.773716i	$0.281604\pi$
$331$	17.9537	+	31.0967i	0.986824	+	1.70923i	0.353291	+	0.935514i	$0.385063\pi$
$332$	3.82111	−	16.4534i	0.209711	−	0.902998i
$333$	−3.49697	+	13.6337i	−0.191633	+	0.747121i
$334$	−2.02425	+	17.6645i	−0.110762	+	0.966558i
$335$	−5.89507	−	10.2106i	−0.322082	−	0.557863i
$336$	−17.7894	+	4.42007i	−0.970492	+	0.241134i
$337$	1.89587	−	3.28374i	0.103275	−	0.178877i	−0.809757	−	0.586765i	$-0.800401\pi$
$337$	1.89587	−	3.28374i	0.103275	−	0.178877i	0.913032	+	0.407888i	$0.133735\pi$
$338$	−1.09630	−	0.812322i	−0.0596308	−	0.0441845i
$339$	−19.9593	+	26.3021i	−1.08404	+	1.42853i
$340$	21.0385	−	6.40223i	1.14097	−	0.347209i
$341$	21.7664			1.17872
$342$	4.67605	+	29.2695i	0.252852	+	1.58271i
$343$	14.5715	+	11.4311i	0.786789	+	0.617222i
$344$	8.29233	−	1.52017i	0.447093	−	0.0819621i
$345$	13.3345	−	5.60723i	0.717905	−	0.301883i
$346$	−9.52483	−	7.05759i	−0.512058	−	0.379418i
$347$	−8.09564	+	14.0221i	−0.434597	+	0.752744i	−0.997263	−	0.0739406i	$-0.976442\pi$
$347$	−8.09564	+	14.0221i	−0.434597	+	0.752744i	0.562666	+	0.826684i	$0.309776\pi$
$348$	−7.30501	+	19.7825i	−0.391590	+	1.06045i
$349$	−14.0407	−	24.3191i	−0.751579	−	1.30177i	−0.947057	−	0.321066i	$-0.895959\pi$
$349$	−14.0407	−	24.3191i	−0.751579	−	1.30177i	0.195477	−	0.980708i	$-0.437374\pi$
$350$	12.1805	−	34.8958i	0.651077	−	1.86526i
$351$	−14.1230	+	11.2022i	−0.753832	+	0.597931i
$352$	−7.53762	+	11.7473i	−0.401757	+	0.626131i
$353$	−29.7079	+	17.1519i	−1.58119	+	0.912901i	−0.586506	+	0.809945i	$0.699497\pi$
$353$	−29.7079	+	17.1519i	−1.58119	+	0.912901i	−0.994686	+	0.102956i	$0.967170\pi$
$354$	−4.60375	−	1.12485i	−0.244686	−	0.0597849i
$355$	20.9187	+	12.0774i	1.11025	+	0.641004i
$356$	15.3222	+	14.3254i	0.812074	+	0.759247i
$357$	12.8608	−	2.29143i	0.680663	−	0.121275i
$358$	21.2018	−	9.20243i	1.12055	−	0.486363i
$359$			4.85162i			0.256059i	0.991770	+	0.128029i	$0.0408652\pi$
$359$			4.85162i			0.256059i	−0.991770	+	0.128029i	$0.959135\pi$
$360$	14.3489	+	29.4166i	0.756252	+	1.55039i
$361$	−29.8093			−1.56891
$362$	−4.11192	+	1.78474i	−0.216118	+	0.0938037i
$363$	5.14306	−	6.77746i	0.269941	−	0.355724i
$364$	15.1791	−	10.3238i	0.795599	−	0.541115i
$365$	24.5909	+	14.1976i	1.28715	+	0.743134i
$366$	−11.0745	−	10.5942i	−0.578872	−	0.553767i
$367$	−4.78514	−	8.28811i	−0.249782	−	0.432636i	0.713683	−	0.700469i	$-0.247026\pi$
$367$	−4.78514	−	8.28811i	−0.249782	−	0.432636i	−0.963465	+	0.267833i	$0.913692\pi$
$368$	3.81687	−	7.77437i	0.198968	−	0.405267i
$369$	−9.36197	−	9.16342i	−0.487365	−	0.477029i
$370$	−25.4263	−	2.91371i	−1.32185	−	0.151477i
$371$	−20.4386	+	6.36413i	−1.06112	+	0.330409i
$372$	−5.16600	−	30.1194i	−0.267845	−	1.56162i
$373$	−15.2103	−	8.78165i	−0.787557	−	0.454696i	0.0515446	−	0.998671i	$-0.483586\pi$
$373$	−15.2103	−	8.78165i	−0.787557	−	0.454696i	−0.839102	+	0.543974i	$0.816919\pi$
$374$	5.92191	−	7.99213i	0.306215	−	0.413263i
$375$	−32.3337	−	4.08067i	−1.66971	−	0.210725i
$376$	−23.9298	+	4.38686i	−1.23408	+	0.226235i
$377$		−	21.1191i		−	1.08769i
$378$	6.38726	+	18.3631i	0.328525	+	0.944495i
$379$	−33.8517			−1.73884			−0.869422	−	0.494071i	$-0.835508\pi$
$379$	−33.8517			−1.73884			−0.869422	+	0.494071i	$0.835508\pi$
$380$	−51.5613	+	15.6906i	−2.64504	+	0.804910i
$381$	−3.53366	+	27.9994i	−0.181035	+	1.43445i
$382$	−12.0436	+	16.2539i	−0.616206	+	0.831624i
$383$	2.60408	−	4.51040i	0.133062	−	0.230471i	−0.791793	−	0.610789i	$-0.790852\pi$
$383$	2.60408	−	4.51040i	0.133062	−	0.230471i	0.924856	+	0.380319i	$0.124186\pi$
$384$	18.0443	+	7.64216i	0.920820	+	0.389987i
$385$	−7.48604	−	24.0416i	−0.381524	−	1.22527i
$386$	2.85669	−	24.9288i	0.145402	−	1.26884i
$387$	−2.40677	−	8.61193i	−0.122343	−	0.437769i
$388$	−2.23612	+	9.62858i	−0.113522	+	0.488817i
$389$	13.5192	−	7.80529i	0.685449	−	0.395744i	−0.116456	−	0.993196i	$-0.537153\pi$
$389$	13.5192	−	7.80529i	0.685449	−	0.395744i	0.801905	+	0.597452i	$0.203820\pi$
$390$	−23.6851	−	22.6579i	−1.19934	−	1.14733i
$391$	−3.08611	+	5.34529i	−0.156071	+	0.270323i
$392$	−5.11741	−	19.1262i	−0.258468	−	0.966020i
$393$	−20.4603	−	15.5263i	−1.03209	−	0.783198i
$394$	6.45072	+	14.8621i	0.324983	+	0.748740i
$395$			43.8621i			2.20694i
$396$	13.1362	+	6.82677i	0.660121	+	0.343058i
$397$	−28.1909			−1.41486			−0.707431	−	0.706782i	$-0.750146\pi$
$397$	−28.1909			−1.41486			−0.707431	+	0.706782i	$0.750146\pi$
$398$	22.2448	−	9.65511i	1.11503	−	0.483967i
$399$	−31.5191	+	5.61583i	−1.57793	+	0.281143i
$400$	−32.8147	+	22.0098i	−1.64073	+	1.10049i
$401$	−5.79294	+	10.0337i	−0.289286	+	0.501057i	−0.973639	−	0.228093i	$-0.926751\pi$
$401$	−5.79294	+	10.0337i	−0.289286	+	0.501057i	0.684354	+	0.729150i	$0.260084\pi$
$402$	−1.77710	+	7.27327i	−0.0886335	+	0.362758i
$403$	15.3020	+	26.5038i	0.762246	+	1.32025i
$404$	5.64420	+	1.31080i	0.280809	+	0.0652146i
$405$	29.6851	−	17.9978i	1.47506	−	0.894320i
$406$	−21.5054	−	7.50655i	−1.06729	−	0.372544i
$407$	−10.0252	+	5.78806i	−0.496931	+	0.286903i
$408$	−12.4647	−	6.29764i	−0.617093	−	0.311780i
$409$	−10.2077	−	5.89340i	−0.504736	−	0.291410i	0.225931	−	0.974143i	$-0.427458\pi$
$409$	−10.2077	−	5.89340i	−0.504736	−	0.291410i	−0.730667	+	0.682734i	$0.760791\pi$
$410$	14.1812	−	19.1388i	0.700361	−	0.945198i
$411$	2.25374	+	5.35959i	0.111169	+	0.264369i
$412$	0.660360	+	2.17003i	0.0325336	+	0.106910i
$413$	1.12576	−	4.99357i	0.0553952	−	0.245717i
$414$	−8.58042	−	3.28053i	−0.421705	−	0.161229i
$415$		−	32.5767i		−	1.59913i
$416$	−19.6031	−	0.919738i	−0.961119	−	0.0450938i
$417$	−5.79646	−	4.39864i	−0.283854	−	0.215402i
$418$	−14.5134	+	19.5871i	−0.709875	+	0.958038i
$419$	−28.0709	−	16.2067i	−1.37135	−	0.791751i	−0.380254	−	0.924882i	$-0.624164\pi$
$419$	−28.0709	−	16.2067i	−1.37135	−	0.791751i	−0.991098	+	0.133131i	$0.957497\pi$
$420$	−31.4910	+	16.0648i	−1.53660	+	0.783884i
$421$	13.5777	−	7.83909i	0.661737	−	0.382054i	−0.131202	−	0.991356i	$-0.541884\pi$
$421$	13.5777	−	7.83909i	0.661737	−	0.382054i	0.792938	+	0.609302i	$0.208550\pi$
$422$	−0.498162	+	4.34718i	−0.0242501	+	0.211618i
$423$	6.94538	+	24.8521i	0.337696	+	1.20835i
$424$	21.5569	+	7.68105i	1.04690	+	0.373025i
$425$	24.3864	−	14.0795i	1.18291	−	0.682956i
$426$	−4.29747	−	14.7250i	−0.208213	−	0.713430i
$427$	11.2271	−	12.1647i	0.543316	−	0.588692i
$428$	14.9961	−	16.0394i	0.724862	−	0.775296i
$429$	−14.7093	−	1.85638i	−0.710170	−	0.0896268i
$430$	14.9149	−	6.47364i	0.719258	−	0.312186i
$431$		−	1.41491i		−	0.0681540i	−0.999419	−	0.0340770i	$-0.989151\pi$
$431$		−	1.41491i		−	0.0681540i	0.999419	−	0.0340770i	$-0.0108492\pi$
$432$	6.32886	−	19.7976i	0.304497	−	0.952513i
$433$			34.8956i			1.67698i	0.544919	+	0.838489i	$0.316560\pi$
$433$			34.8956i			1.67698i	−0.544919	+	0.838489i	$0.683440\pi$
$434$	32.4275	−	6.16138i	1.55657	−	0.295756i
$435$	−5.09246	+	40.3508i	−0.244165	+	1.93467i
$436$	0.743634	+	0.695260i	0.0356136	+	0.0332969i
$437$	7.56343	−	13.1002i	0.361808	−	0.626670i
$438$	−5.05187	−	17.3099i	−0.241388	−	0.827100i
$439$	−0.592169	−	1.02567i	−0.0282627	−	0.0489524i	0.851548	−	0.524276i	$-0.175664\pi$
$439$	−0.592169	−	1.02567i	−0.0282627	−	0.0489524i	−0.879811	+	0.475324i	$0.842331\pi$
$440$	−9.03512	+	25.3571i	−0.430732	+	1.20885i
$441$	−19.7077	+	7.25298i	−0.938463	+	0.345380i
$442$	13.8948	+	1.59226i	0.660907	+	0.0757361i
$443$	−4.65552	−	8.06360i	−0.221191	−	0.383113i	0.733979	−	0.679172i	$-0.237661\pi$
$443$	−4.65552	−	8.06360i	−0.221191	−	0.383113i	−0.955170	+	0.296059i	$0.904328\pi$
$444$	10.3886	+	12.4987i	0.493022	+	0.593163i
$445$	35.0344	+	20.2271i	1.66079	+	0.958858i
$446$	−7.70128	−	5.70640i	−0.364666	−	0.270206i
$447$	−2.55364	−	1.93782i	−0.120783	−	0.0916559i
$448$	−7.90426	+	19.6347i	−0.373441	+	0.927654i
$449$	−12.0779			−0.569989			−0.284995	−	0.958529i	$-0.591992\pi$
$449$	−12.0779			−0.569989			−0.284995	+	0.958529i	$0.591992\pi$
$450$	26.4180	+	32.5343i	1.24536	+	1.53368i
$451$		−	10.7744i		−	0.507344i
$452$	11.0995	+	36.4742i	0.522075	+	1.71560i
$453$	13.7325	−	5.77459i	0.645208	−	0.271314i
$454$	4.12512	−	5.56720i	0.193601	−	0.261282i
$455$	24.0115	−	26.0168i	1.12567	−	1.21969i
$456$	30.5484	+	15.4343i	1.43056	+	0.722776i
$457$	15.3112	+	26.5198i	0.716229	+	1.24054i	0.962484	+	0.271340i	$0.0874667\pi$
$457$	15.3112	+	26.5198i	0.716229	+	1.24054i	−0.246255	+	0.969205i	$0.579200\pi$
$458$	−0.875666	+	7.64145i	−0.0409172	+	0.357061i
$459$	−5.44774	+	13.7742i	−0.254279	+	0.642925i
$460$	3.77858	−	16.2703i	0.176177	−	0.758606i
$461$	−0.877473	−	1.51983i	−0.0408680	−	0.0707854i	0.844868	−	0.534975i	$-0.179679\pi$
$461$	−0.877473	−	1.51983i	−0.0408680	−	0.0707854i	−0.885736	+	0.464190i	$0.846346\pi$
$462$	−7.11859	+	14.3185i	−0.331187	+	0.666156i
$463$	−15.5100	−	8.95469i	−0.720810	−	0.416160i	0.0942410	−	0.995549i	$-0.469958\pi$
$463$	−15.5100	−	8.95469i	−0.720810	−	0.416160i	−0.815051	+	0.579390i	$0.803291\pi$
$464$	13.5641	+	20.2228i	0.629698	+	0.938822i
$465$	−22.8455	−	54.3288i	−1.05944	−	2.51944i
$466$	−5.06652	+	2.19907i	−0.234702	+	0.101870i
$467$		−	9.17435i		−	0.424538i	−0.977211	−	0.212269i	$-0.931915\pi$
$467$		−	9.17435i		−	0.424538i	0.977211	−	0.212269i	$-0.0680853\pi$
$468$	0.922295	+	20.7946i	0.0426331	+	0.961231i
$469$	−7.88913	−	1.77855i	−0.364286	−	0.0821257i
$470$	−43.0408	+	18.6814i	−1.98533	+	0.861710i
$471$	7.77424	−	10.2448i	0.358218	−	0.472055i
$472$	−4.16811	+	3.54587i	−0.191853	+	0.163212i
$473$	3.67718	−	6.36906i	0.169077	−	0.292850i
$474$	19.2546	−	20.1276i	0.884394	−	0.924489i
$475$	−59.7662	+	34.5061i	−2.74226	+	1.58325i
$476$	6.56014	−	13.5830i	0.300683	−	0.622575i
$477$	6.03060	−	23.5116i	0.276122	−	1.07652i
$478$	18.3589	+	2.10382i	0.839717	+	0.0962267i
$479$	3.38730	+	5.86698i	0.154770	+	0.268069i	0.932975	−	0.359941i	$-0.117203\pi$
$479$	3.38730	+	5.86698i	0.154770	+	0.268069i	−0.778205	+	0.628010i	$0.783870\pi$
$480$	37.2324	+	6.48418i	1.69942	+	0.295961i
$481$	−14.0956	−	8.13812i	−0.642706	−	0.371066i
$482$	−17.7537	+	23.9601i	−0.808657	+	1.09135i
$483$	3.37690	−	9.32986i	0.153654	−	0.424523i
$484$	−2.86008	−	9.39859i	−0.130004	−	0.427208i
$485$			19.0639i			0.865649i
$486$	−21.5227	−	4.77230i	−0.976288	−	0.216476i
$487$		−	7.19407i		−	0.325995i	−0.986627	−	0.162997i	$-0.947884\pi$
$487$		−	7.19407i		−	0.325995i	0.986627	−	0.162997i	$-0.0521162\pi$
$488$	−17.4067	+	3.19103i	−0.787962	+	0.144451i
$489$	14.4467	+	1.82325i	0.653303	+	0.0824500i
$490$	−17.9581	−	33.6981i	−0.811265	−	1.52232i
$491$	19.3146	−	33.4538i	0.871654	−	1.50975i	0.0113696	−	0.999935i	$-0.496381\pi$
$491$	19.3146	−	33.4538i	0.871654	−	1.50975i	0.860285	−	0.509814i	$-0.170286\pi$
$492$	−14.9091	+	2.55717i	−0.672153	+	0.115286i
$493$	−8.67684	−	15.0287i	−0.390785	−	0.676860i
$494$	−34.0533	−	3.90231i	−1.53213	−	0.175573i
$495$	27.6563	+	7.09371i	1.24306	+	0.318839i
$496$	−31.6752	−	15.5511i	−1.42226	−	0.698265i
$497$	15.8192	−	4.92577i	0.709589	−	0.220951i
$498$	−14.3005	+	14.9489i	−0.640822	+	0.669874i
$499$	12.3613	−	21.4103i	0.553366	−	0.958458i	−0.444663	−	0.895698i	$-0.646676\pi$
$499$	12.3613	−	21.4103i	0.553366	−	0.958458i	0.998029	−	0.0627597i	$-0.0199902\pi$
$500$	−25.7007	+	27.4888i	−1.14937	+	1.22934i
$501$	13.1637	−	17.3469i	0.588110	−	0.775003i
$502$	0.175447	+	0.404220i	0.00783060	+	0.0180412i
$503$	14.0570			0.626769			0.313384	−	0.949626i	$-0.398537\pi$
$503$	14.0570			0.626769			0.313384	+	0.949626i	$0.398537\pi$
$504$	21.5028	+	6.45206i	0.957811	+	0.287398i
$505$	11.1751			0.497287
$506$	−3.00814	−	6.93056i	−0.133728	−	0.308101i
$507$	0.647770	+	1.54045i	0.0287685	+	0.0684140i
$508$	23.8040	+	22.2555i	1.05613	+	0.987429i
$509$	15.8199	−	27.4009i	0.701205	−	1.21452i	−0.266838	−	0.963741i	$-0.585979\pi$
$509$	15.8199	−	27.4009i	0.701205	−	1.21452i	0.968044	−	0.250782i	$-0.0806877\pi$
$510$	−26.1638	−	6.39268i	−1.15855	−	0.283073i
$511$	18.5962	−	5.79045i	0.822647	−	0.256155i
$512$	19.3619	−	11.7097i	0.855683	−	0.517501i
$513$	13.3513	−	33.7578i	0.589475	−	1.49045i
$514$	27.9489	+	3.20278i	1.23277	+	0.141269i
$515$	2.18731	+	3.78853i	0.0963844	+	0.166943i
$516$	−9.68596	−	3.57670i	−0.426401	−	0.157455i
$517$	−10.6115	+	18.3796i	−0.466693	+	0.808335i
$518$	−13.2971	+	11.4609i	−0.584242	+	0.503561i
$519$	5.62793	+	13.3837i	0.247039	+	0.587481i
$520$	−37.2278	+	6.82470i	−1.63255	+	0.299283i
$521$		−	25.3117i		−	1.10893i	−0.832208	−	0.554463i	$-0.812924\pi$
$521$		−	25.3117i		−	1.10893i	0.832208	−	0.554463i	$-0.187076\pi$
$522$	20.0500	−	16.2807i	0.877566	−	0.712589i
$523$			25.2295i			1.10321i	0.834106	+	0.551603i	$0.185984\pi$
$523$			25.2295i			1.10321i	−0.834106	+	0.551603i	$0.814016\pi$
$524$	−28.3732	+	8.63424i	−1.23949	+	0.377188i
$525$	−34.6246	+	29.1592i	−1.51114	+	1.27261i
$526$	12.4842	−	16.8485i	0.544336	−	0.734629i
$527$	21.7783	+	12.5737i	0.948679	+	0.547720i
$528$	15.2773	−	7.66968i	0.664861	−	0.333780i
$529$	−9.15596	−	15.8586i	−0.398085	−	0.689504i
$530$	43.8482	+	5.02475i	1.90464	+	0.218261i
$531$	4.14799	+	4.06002i	0.180008	+	0.176190i
$532$	−16.0776	+	33.2892i	−0.697052	+	1.44327i
$533$	13.1194	−	7.57447i	0.568263	−	0.328087i
$534$	−7.19735	−	24.6613i	−0.311460	−	1.06720i
$535$	21.1740	−	36.6744i	0.915432	−	1.58557i
$536$	5.60197	+	6.58503i	0.241968	+	0.284430i
$537$	−28.0845	−	3.54440i	−1.21194	−	0.152952i
$538$	23.1316	−	10.0400i	0.997275	−	0.432857i
$539$	−15.6009	−	7.41087i	−0.671978	−	0.319209i
$540$	3.25206	−	39.9532i	0.139946	−	1.71931i
$541$		−	18.0204i		−	0.774758i	−0.921921	−	0.387379i	$-0.873381\pi$
$541$		−	18.0204i		−	0.774758i	0.921921	−	0.387379i	$-0.126619\pi$
$542$	5.79509	−	2.51530i	0.248920	−	0.108041i
$543$	5.44677	+	0.687409i	0.233743	+	0.0294995i
$544$	−14.3278	+	7.39948i	−0.614298	+	0.317250i
$545$	1.70033	+	0.981687i	0.0728342	+	0.0420508i
$546$	−22.4393	+	1.39810i	−0.960314	+	0.0598331i
$547$	−10.4599	−	18.1171i	−0.447234	−	0.774632i	0.550971	−	0.834524i	$-0.314258\pi$
$547$	−10.4599	−	18.1171i	−0.447234	−	0.774632i	−0.998205	+	0.0598926i	$0.980924\pi$
$548$	6.53958	+	1.51874i	0.279357	+	0.0648773i
$549$	5.05212	+	18.0775i	0.215619	+	0.771530i
$550$	−3.92422	+	34.2445i	−0.167329	+	1.46019i
$551$	21.2652	+	36.8324i	0.905928	+	1.56911i
$552$	−8.87626	+	5.80742i	−0.377799	+	0.247180i
$553$	22.1090	+	20.4049i	0.940172	+	0.867704i
$554$	−23.9204	+	32.2827i	−1.01628	+	1.37156i
$555$	24.9692	+	18.9478i	1.05988	+	0.804291i
$556$	−8.03820	+	2.44610i	−0.340895	+	0.103738i
$557$			11.5909i			0.491122i	0.969381	+	0.245561i	$0.0789721\pi$
$557$			11.5909i			0.491122i	−0.969381	+	0.245561i	$0.921028\pi$
$558$	−13.3659	+	34.9593i	−0.565822	+	1.47994i
$559$	10.3404			0.437351
$560$	−6.28270	+	40.3346i	−0.265493	+	1.70445i
$561$	−11.2301	+	4.72231i	−0.474134	+	0.199376i
$562$	−14.6743	−	10.8732i	−0.618997	−	0.458656i
$563$	−18.9519	−	10.9419i	−0.798727	−	0.461145i	0.0442991	−	0.999018i	$-0.485895\pi$
$563$	−18.9519	−	10.9419i	−0.798727	−	0.461145i	−0.843026	+	0.537873i	$0.819228\pi$
$564$	27.9514	+	10.3215i	1.17697	+	0.434614i
$565$	36.7647	+	63.6784i	1.54670	+	2.67897i
$566$	6.32617	+	0.724943i	0.265909	+	0.0304716i
$567$	4.73771	−	23.3357i	0.198965	−	0.980007i
$568$	−16.6848	−	5.94505i	−0.700079	−	0.249449i
$569$	9.88187	+	17.1159i	0.414270	+	0.717536i	0.995351	−	0.0963091i	$-0.0307037\pi$
$569$	9.88187	+	17.1159i	0.414270	+	0.717536i	−0.581082	+	0.813845i	$0.697370\pi$
$570$	64.1224	+	15.6672i	2.68579	+	0.656226i
$571$	6.31870	−	10.9443i	0.264429	−	0.458005i	−0.702985	−	0.711205i	$-0.748150\pi$
$571$	6.31870	−	10.9443i	0.264429	−	0.458005i	0.967414	+	0.253200i	$0.0814831\pi$
$572$	−11.6917	+	12.5052i	−0.488857	+	0.522870i
$573$	22.8391	−	9.60396i	0.954116	−	0.401211i
$574$	−3.04988	−	16.0516i	−0.127300	−	0.669982i
$575$		−	21.3881i		−	0.891945i
$576$	−14.2389	−	19.3198i	−0.593286	−	0.804992i
$577$		−	27.4645i		−	1.14336i	−0.820477	−	0.571680i	$-0.806292\pi$
$577$		−	27.4645i		−	1.14336i	0.820477	−	0.571680i	$-0.193708\pi$
$578$	−11.5119	+	4.99661i	−0.478831	+	0.207832i
$579$	−18.5770	+	24.4806i	−0.772036	+	1.01738i
$580$	34.3046	+	32.0731i	1.42442	+	1.33176i
$581$	−16.4205	−	15.1548i	−0.681238	−	0.628728i
$582$	8.36870	−	8.74811i	0.346894	−	0.362621i
$583$	17.2887	−	9.98162i	0.716024	−	0.413396i
$584$	−19.6137	−	6.98867i	−0.811622	−	0.289193i
$585$	10.8050	+	38.6626i	0.446733	+	1.59850i
$586$	1.43714	−	12.5411i	0.0593676	−	0.518068i
$587$	27.1220	−	15.6589i	1.11944	−	0.646311i	0.178185	−	0.983997i	$-0.442977\pi$
$587$	27.1220	−	15.6589i	1.11944	−	0.646311i	0.941259	+	0.337686i	$0.109644\pi$
$588$	−6.55215	+	23.3467i	−0.270206	+	0.962803i
$589$	−53.3744	−	30.8157i	−2.19925	−	1.26974i
$590$	−6.28326	+	8.47980i	−0.258678	+	0.349108i
$591$	2.48456	−	19.6867i	0.102201	−	0.809803i
$592$	18.7243	−	1.26041i	0.769564	−	0.0518026i
$593$		−	24.2858i		−	0.997298i	−0.866804	−	0.498649i	$-0.833830\pi$
$593$		−	24.2858i		−	0.997298i	0.866804	−	0.498649i	$-0.166170\pi$
$594$	−9.57699	−	15.3958i	−0.392949	−	0.631696i
$595$	6.39790	−	28.3792i	0.262288	−	1.16344i
$596$	−3.54123	+	1.07763i	−0.145055	+	0.0441415i
$597$	−29.4660	−	3.71876i	−1.20596	−	0.152199i
$598$	6.32424	−	8.53510i	0.258617	−	0.349026i
$599$	36.4513	+	21.0452i	1.48936	+	0.859882i	0.999926	−	0.0121589i	$-0.00387040\pi$
$599$	36.4513	+	21.0452i	1.48936	+	0.859882i	0.489433	+	0.872041i	$0.337204\pi$
$600$	48.3175	−	2.69737i	1.97255	−	0.110120i
$601$	−0.670410	+	0.387062i	−0.0273466	+	0.0157886i	−0.513611	−	0.858023i	$-0.671693\pi$
$601$	−0.670410	+	0.387062i	−0.0273466	+	0.0157886i	0.486264	+	0.873812i	$0.338359\pi$
$602$	3.67537	−	10.5295i	0.149797	−	0.429151i
$603$	6.41426	−	6.55324i	0.261209	−	0.266869i
$604$	3.89136	−	16.7559i	0.158337	−	0.681788i
$605$	−9.47344	−	16.4085i	−0.385150	−	0.667100i
$606$	−5.12807	−	4.90567i	−0.208314	−	0.199279i
$607$	20.3300	−	35.2126i	0.825171	−	1.42924i	−0.0766183	−	0.997060i	$-0.524412\pi$
$607$	20.3300	−	35.2126i	0.825171	−	1.42924i	0.901789	−	0.432177i	$-0.142254\pi$
$608$	35.1145	−	18.1346i	1.42408	−	0.735457i
$609$	17.9701	+	21.3383i	0.728184	+	0.864670i
$610$	−31.3082	+	13.5890i	−1.26763	+	0.550202i
$611$	−29.8399			−1.20719
$612$	9.19985	+	14.4189i	0.371882	+	0.582850i
$613$		−	12.2531i		−	0.494899i	−0.968901	−	0.247449i	$-0.920408\pi$
$613$		−	12.2531i		−	0.494899i	0.968901	−	0.247449i	$-0.0795924\pi$
$614$	6.38002	+	14.6992i	0.257477	+	0.593210i
$615$	−26.8927	+	11.3085i	−1.08442	+	0.456004i
$616$	8.57827	+	16.3505i	0.345628	+	0.658779i
$617$	−18.6020	+	32.2196i	−0.748887	+	1.29711i	0.199469	+	0.979904i	$0.436078\pi$
$617$	−18.6020	+	32.2196i	−0.748887	+	1.29711i	−0.948356	+	0.317207i	$0.897255\pi$
$618$	0.659375	−	2.69868i	0.0265240	−	0.108557i
$619$	−1.70406	+	0.983840i	−0.0684920	+	0.0395438i	−0.533855	−	0.845576i	$-0.679257\pi$
$619$	−1.70406	+	0.983840i	−0.0684920	+	0.0395438i	0.465363	+	0.885120i	$0.345924\pi$
$620$	−66.2900	−	15.3951i	−2.66227	−	0.618281i
$621$	6.99159	+	8.81453i	0.280563	+	0.353715i
$622$	2.26575	−	19.7720i	0.0908484	−	0.792783i
$623$	26.4938	−	8.24961i	1.06145	−	0.330513i
$624$	20.0791	+	13.2106i	0.803807	+	0.528846i
$625$	−11.5933	+	20.0802i	−0.463732	+	0.803208i
$626$	−26.9209	+	36.3321i	−1.07597	+	1.45212i
$627$	27.5227	−	11.5734i	1.09915	−	0.462199i
$628$	−4.32328	−	14.2069i	−0.172518	−	0.566916i
$629$	−13.3743			−0.533268
$630$	43.2104	+	2.73956i	1.72154	+	0.109147i
$631$		−	37.3160i		−	1.48553i	−0.669554	−	0.742763i	$-0.733515\pi$
$631$		−	37.3160i		−	1.48553i	0.669554	−	0.742763i	$-0.266485\pi$
$632$	−5.79961	−	31.6361i	−0.230696	−	1.25842i
$633$	3.23954	−	4.26903i	0.128760	−	0.169679i
$634$	1.34455	−	1.81459i	0.0533989	−	0.0720664i
$635$	54.4283	+	31.4242i	2.15992	+	1.24703i
$636$	−17.9154	−	21.5543i	−0.710392	−	0.854683i
$637$	−1.94374	−	24.2063i	−0.0770139	−	0.959089i
$638$	21.1040	+	2.41840i	0.835517	+	0.0957454i
$639$	−4.66762	+	18.1977i	−0.184648	+	0.719889i
$640$	31.2647	−	30.4453i	1.23585	−	1.20346i
$641$	−10.0408	−	17.3911i	−0.396587	−	0.686908i	0.596716	−	0.802453i	$-0.296472\pi$
$641$	−10.0408	−	17.3911i	−0.396587	−	0.686908i	−0.993302	+	0.115544i	$0.963139\pi$
$642$	−25.8157	+	7.53427i	−1.01887	+	0.297354i
$643$	12.6707	+	7.31543i	0.499683	+	0.288492i	0.728583	−	0.684958i	$-0.240179\pi$
$643$	12.6707	+	7.31543i	0.499683	+	0.288492i	−0.228899	+	0.973450i	$0.573513\pi$
$644$	−6.44335	−	9.47363i	−0.253903	−	0.373313i
$645$	−19.7566	−	2.49338i	−0.777916	−	0.0981768i
$646$	−25.8363	+	11.2140i	−1.01651	+	0.441207i
$647$	−36.8277			−1.44785			−0.723924	−	0.689880i	$-0.757663\pi$
$647$	−36.8277			−1.44785			−0.723924	+	0.689880i	$0.757663\pi$
$648$	−19.0310	+	16.9062i	−0.747609	+	0.664140i
$649$			4.77377i			0.187387i
$650$	−44.4566	+	19.2959i	−1.74373	+	0.756848i
$651$	−38.0127	−	13.7585i	−1.48983	−	0.539239i
$652$	11.4831	−	12.2820i	0.449712	−	0.481001i
$653$	−28.0627	−	16.2020i	−1.09818	−	0.634034i	−0.162437	−	0.986719i	$-0.551935\pi$
$653$	−28.0627	−	16.2020i	−1.09818	−	0.634034i	−0.935742	+	0.352685i	$0.885269\pi$
$654$	−0.349310	−	1.19689i	−0.0136591	−	0.0468021i
$655$	−49.5353	+	28.5992i	−1.93550	+	1.11746i
$656$	−7.69779	+	15.6792i	−0.300548	+	0.612170i
$657$	−5.48699	+	21.3922i	−0.214068	+	0.834589i
$658$	−10.6063	+	30.3857i	−0.413476	+	1.18456i
$659$	1.94310	+	3.36554i	0.0756923	+	0.131103i	0.901387	−	0.433014i	$-0.142550\pi$
$659$	1.94310	+	3.36554i	0.0756923	+	0.131103i	−0.825695	+	0.564117i	$0.809217\pi$
$660$	25.3540	−	21.0736i	0.986904	−	0.820290i
$661$	3.16320	−	5.47883i	0.123034	−	0.213102i	−0.797929	−	0.602752i	$-0.794071\pi$
$661$	3.16320	−	5.47883i	0.123034	−	0.213102i	0.920963	+	0.389650i	$0.127404\pi$
$662$	−40.8008	−	30.2320i	−1.58577	−	1.17500i
$663$	−13.6450	−	10.3545i	−0.529927	−	0.402134i
$664$	4.30741	+	23.4963i	0.167160	+	0.911834i
$665$	−15.6800	+	69.5519i	−0.608043	+	2.69711i
$666$	−3.14019	−	19.6558i	−0.121680	−	0.761648i
$667$	−13.1809			−0.510368
$668$	−7.32038	−	24.0557i	−0.283234	−	0.930743i
$669$	4.55045	+	10.8214i	0.175931	+	0.418379i
$670$	13.3969	+	9.92666i	0.517567	+	0.383500i
$671$	−7.71886	+	13.3695i	−0.297983	+	0.516122i
$672$	20.5891	−	15.7508i	0.794242	−	0.607601i
$673$	−8.96087	−	15.5207i	−0.345416	−	0.598278i	0.640013	−	0.768364i	$-0.278929\pi$
$673$	−8.96087	−	15.5207i	−0.345416	−	0.598278i	−0.985429	+	0.170086i	$0.945596\pi$
$674$	−0.610496	+	5.32746i	−0.0235154	+	0.205206i
$675$	−7.51685	−	50.7748i	−0.289324	−	1.95432i
$676$	1.87961	+	0.436517i	0.0722926	+	0.0167891i
$677$	−10.1673	−	17.6102i	−0.390759	−	0.676815i	0.601791	−	0.798654i	$-0.294454\pi$
$677$	−10.1673	−	17.6102i	−0.390759	−	0.676815i	−0.992550	+	0.121839i	$0.961121\pi$
$678$	11.0829	−	45.3599i	0.425636	−	1.74204i
$679$	9.60933	+	8.86864i	0.368772	+	0.340347i
$680$	−23.6881	+	20.1517i	−0.908395	+	0.772784i
$681$	−7.82271	+	3.28949i	−0.299767	+	0.126054i
$682$	−28.2372	+	12.2561i	−1.08126	+	0.469309i
$683$	22.4453			0.858846			0.429423	−	0.903103i	$-0.358717\pi$
$683$	22.4453			0.858846			0.429423	+	0.903103i	$0.358717\pi$
$684$	−22.5470	−	35.3379i	−0.862107	−	1.35118i
$685$	12.9479			0.494715
$686$	−25.3400	−	6.62458i	−0.967485	−	0.252928i
$687$	5.69445	−	7.50407i	0.217257	−	0.286298i
$688$	−9.90155	+	6.64129i	−0.377493	+	0.253197i
$689$	24.3082	+	14.0343i	0.926069	+	0.534666i
$690$	−14.1414	+	14.7825i	−0.538352	+	0.562759i
$691$	−5.69761	+	3.28951i	−0.216747	+	0.125139i	−0.604443	−	0.796648i	$-0.706604\pi$
$691$	−5.69761	+	3.28951i	−0.216747	+	0.125139i	0.387696	+	0.921787i	$0.373271\pi$
$692$	16.3304	+	3.79253i	0.620787	+	0.144170i
$693$	16.4415	−	10.6404i	0.624561	−	0.404194i
$694$	2.60691	−	22.7491i	0.0989569	−	0.863542i
$695$	−14.0335	+	8.10222i	−0.532319	+	0.307335i
$696$	−1.66232	−	29.7768i	−0.0630102	−	1.12869i
$697$	6.22399	−	10.7803i	0.235751	−	0.408332i
$698$	31.9082	+	23.6429i	1.20774	+	0.894899i
$699$	6.71125	+	0.846993i	0.253843	+	0.0320362i
$700$	3.84725	+	52.1283i	0.145412	+	1.97026i
$701$			32.7929i			1.23857i	0.785166	+	0.619285i	$0.212578\pi$
$701$			32.7929i			1.23857i	−0.785166	+	0.619285i	$0.787422\pi$
$702$	12.0139	−	22.4848i	0.453436	−	0.848634i
$703$	32.7777			1.23623
$704$	3.16388	−	19.4838i	0.119243	−	0.734323i
$705$	57.0131	+	7.19532i	2.14724	+	0.270992i
$706$	28.8819	−	38.9786i	1.08698	−	1.46698i
$707$	5.19873	−	5.63292i	0.195518	−	0.211848i
$708$	6.60574	−	1.13300i	0.248259	−	0.0425808i
$709$	0.534092	−	0.308358i	0.0200582	−	0.0115806i	−0.489937	−	0.871758i	$-0.662980\pi$
$709$	0.534092	−	0.308358i	0.0200582	−	0.0115806i	0.509996	+	0.860177i	$0.329647\pi$
$710$	−33.9380	−	3.88910i	−1.27367	−	0.145955i
$711$	−32.8554	+	9.18208i	−1.23217	+	0.344355i
$712$	−27.9435	−	9.95669i	−1.04723	−	0.373143i
$713$	16.5417	−	9.55034i	0.619491	−	0.357663i
$714$	−15.3938	+	10.2142i	−0.576099	+	0.382256i
$715$	−16.5084	+	28.5934i	−0.617380	+	1.06933i
$716$	−22.3232	+	23.8763i	−0.834256	+	0.892301i
$717$	−18.0288	−	13.6812i	−0.673300	−	0.510932i
$718$	−2.73182	−	6.29394i	−0.101951	−	0.234888i
$719$	5.70948			0.212928			0.106464	−	0.994317i	$-0.466047\pi$
$719$	5.70948			0.212928			0.106464	+	0.994317i	$0.466047\pi$
$720$	−35.1783	−	30.0822i	−1.31102	−	1.12110i
$721$	2.92719	+	0.659913i	0.109014	+	0.0245765i
$722$	38.6711	−	16.7848i	1.43919	−	0.624665i
$723$	33.6673	−	14.1573i	1.25210	−	0.526515i
$724$	4.32940	−	4.63063i	0.160901	−	0.172096i
$725$	52.0779	+	30.0672i	1.93412	+	1.11667i
$726$	−2.85581	+	11.6882i	−0.105989	+	0.433791i
$727$	6.62420	+	11.4735i	0.245678	+	0.425527i	0.962322	−	0.271912i	$-0.0876561\pi$
$727$	6.62420	+	11.4735i	0.245678	+	0.425527i	−0.716644	+	0.697439i	$0.754323\pi$
$728$	−13.8785	+	21.9399i	−0.514372	+	0.813145i
$729$	19.6957	+	18.4683i	0.729472	+	0.684011i
$730$	−39.8957	−	4.57181i	−1.47660	−	0.169210i
$731$	7.35839	−	4.24837i	0.272160	−	0.157132i
$732$	20.3321	+	7.50794i	0.751494	+	0.277501i
$733$	−12.4197	+	21.5116i	−0.458732	+	0.794547i	−0.998894	−	0.0470136i	$-0.985030\pi$
$733$	−12.4197	+	21.5116i	−0.458732	+	0.794547i	0.540162	+	0.841561i	$0.318363\pi$
$734$	10.8745	+	8.05765i	0.401385	+	0.297413i
$735$	−2.12312	+	46.7180i	−0.0783123	+	1.72322i
$736$	−0.574031	+	12.2348i	−0.0211591	+	0.450979i
$737$	7.54189			0.277809
$738$	17.3048	+	6.61610i	0.636999	+	0.243542i
$739$	−10.5465			−0.387960			−0.193980	−	0.981006i	$-0.562140\pi$
$739$	−10.5465			−0.387960			−0.193980	+	0.981006i	$0.562140\pi$
$740$	34.6258	−	10.5370i	1.27287	−	0.387347i
$741$	33.4411	+	25.3767i	1.22849	+	0.932237i
$742$	22.9312	−	19.7645i	0.841830	−	0.725577i
$743$	9.09138	+	5.24891i	0.333530	+	0.192564i	0.657407	−	0.753535i	$-0.271653\pi$
$743$	9.09138	+	5.24891i	0.333530	+	0.192564i	−0.323877	+	0.946099i	$0.604986\pi$
$744$	23.6612	+	36.1646i	0.867461	+	1.32586i
$745$	−6.18245	+	3.56944i	−0.226507	+	0.130774i
$746$	24.6768	+	2.82781i	0.903480	+	0.103534i
$747$	24.4019	−	6.81958i	0.892819	−	0.249516i
$748$	−3.18225	+	13.7025i	−0.116355	+	0.501015i
$749$	−8.63579	−	27.7340i	−0.315545	−	1.01338i
$750$	44.2437	−	12.9124i	1.61555	−	0.471496i
$751$	23.5255	+	13.5824i	0.858456	+	0.495630i	0.863495	−	0.504358i	$-0.168271\pi$
$751$	23.5255	+	13.5824i	0.858456	+	0.495630i	−0.00503894	+	0.999987i	$0.501604\pi$
$752$	28.5736	−	19.1652i	1.04197	−	0.698884i
$753$	0.0675752	−	0.535441i	0.00246258	−	0.0195126i
$754$	11.8916	+	27.3975i	0.433066	+	0.997757i
$755$		−	33.1756i		−	1.20738i
$756$	−18.6259	−	20.2257i	−0.677416	−	0.735600i
$757$			32.0077i			1.16334i	0.813425	+	0.581670i	$0.197600\pi$
$757$			32.0077i			1.16334i	−0.813425	+	0.581670i	$0.802400\pi$
$758$	43.9153	−	19.0610i	1.59507	−	0.692325i
$759$	−1.15861	+	9.18041i	−0.0420550	+	0.333228i
$760$	58.0547	−	49.3879i	2.10587	−	1.79149i
$761$	−25.7518	−	14.8678i	−0.933500	−	0.538957i	−0.0455835	−	0.998961i	$-0.514515\pi$
$761$	−25.7518	−	14.8678i	−0.933500	−	0.538957i	−0.887917	+	0.460004i	$0.847848\pi$
$762$	−11.1816	−	38.3129i	−0.405065	−	1.38793i
$763$	1.28583	−	0.400380i	0.0465501	−	0.0144947i
$764$	6.47188	−	27.8674i	0.234144	−	1.00821i
$765$	23.5737	+	23.0738i	0.852310	+	0.834234i
$766$	−0.838550	+	7.31756i	−0.0302980	+	0.264394i
$767$	−5.81278	+	3.35601i	−0.209887	+	0.121178i
$768$	−27.7117	+	0.246211i	−0.999961	+	0.00888436i
$769$	−10.0441	−	5.79895i	−0.362199	−	0.209116i	0.307846	−	0.951436i	$-0.400392\pi$
$769$	−10.0441	−	5.79895i	−0.362199	−	0.209116i	−0.670045	+	0.742321i	$0.733725\pi$
$770$	23.2487	+	26.9736i	0.837825	+	0.972062i
$771$	−27.4464	−	20.8277i	−0.988460	−	0.750091i
$772$	10.3308	+	33.9482i	0.371813	+	1.22182i
$773$	−5.58980			−0.201051			−0.100526	−	0.994934i	$-0.532052\pi$
$773$	−5.58980			−0.201051			−0.100526	+	0.994934i	$0.532052\pi$
$774$	7.97141	+	9.81694i	0.286527	+	0.352863i
$775$	−87.1416			−3.13022
$776$	−2.52070	−	13.7501i	−0.0904880	−	0.493600i
$777$	21.1666	−	3.77130i	0.759347	−	0.135294i
$778$	−13.1433	+	17.7380i	−0.471209	+	0.635937i
$779$	−15.2538	+	26.4203i	−0.546523	+	0.946606i
$780$	43.4844	+	16.0573i	1.55699	+	0.574944i
$781$	−13.3812	+	7.72566i	−0.478819	+	0.276446i
$782$	0.993769	−	8.67207i	0.0355371	−	0.310113i
$783$	−31.2912	+	4.63244i	−1.11826	+	0.165550i
$784$	17.4082	+	21.9307i	0.621721	+	0.783238i
$785$	−14.3200	−	24.8030i	−0.511104	−	0.885257i
$786$	35.2853	+	8.62136i	1.25859	+	0.307514i
$787$	32.4855	+	18.7555i	1.15798	+	0.668561i	0.950820	−	0.309745i	$-0.100244\pi$
$787$	32.4855	+	18.7555i	1.15798	+	0.668561i	0.207163	+	0.978307i	$0.433577\pi$
$788$	−16.7369	−	15.6481i	−0.596226	−	0.557441i
$789$	−23.6745	+	9.95526i	−0.842835	+	0.354417i
$790$	−24.6976	−	56.9017i	−0.878701	−	2.02447i
$791$	49.2007	+	11.0919i	1.74938	+	0.394384i
$792$	−20.8854	−	1.45961i	−0.742131	−	0.0518649i
$793$	−21.7057			−0.770793
$794$	36.5717	−	15.8736i	1.29788	−	0.563331i
$795$	−43.0599	−	32.6759i	−1.52718	−	1.15890i
$796$	−23.4213	+	25.0509i	−0.830145	+	0.887904i
$797$	−11.4471	+	19.8270i	−0.405477	+	0.702308i	−0.994377	−	0.105899i	$-0.966228\pi$
$797$	−11.4471	+	19.8270i	−0.405477	+	0.702308i	0.588899	+	0.808206i	$0.299561\pi$
$798$	37.7272	−	25.0329i	1.33553	−	0.886156i
$799$	−21.2346	+	12.2598i	−0.751227	+	0.433721i
$800$	30.1768	−	47.0301i	1.06691	−	1.66276i
$801$	−7.81726	+	30.4772i	−0.276209	+	1.07686i
$802$	1.86541	−	16.2784i	0.0658698	−	0.574809i
$803$	−15.7302	+	9.08186i	−0.555108	+	0.320492i
$804$	−1.78998	−	10.4361i	−0.0631277	−	0.368054i
$805$	−16.2378	−	14.9861i	−0.572306	−	0.528192i
$806$	−34.7746	−	25.7669i	−1.22488	−	0.907599i
$807$	−30.6408	−	3.86701i	−1.07861	−	0.136125i
$808$	−8.06021	+	1.47762i	−0.283557	+	0.0519824i
$809$	−3.40612			−0.119753			−0.0598764	−	0.998206i	$-0.519071\pi$
$809$	−3.40612			−0.119753			−0.0598764	+	0.998206i	$0.519071\pi$
$810$	−28.3759	+	40.0632i	−0.997029	+	1.40768i
$811$		−	34.9305i		−	1.22658i	−0.789859	−	0.613288i	$-0.789847\pi$
$811$		−	34.9305i		−	1.22658i	0.789859	−	0.613288i	$-0.210153\pi$
$812$	32.1254	−	2.37096i	1.12738	−	0.0832045i
$813$	−7.67634	−	0.968791i	−0.269221	−	0.0339770i
$814$	9.74645	−	13.1537i	0.341613	−	0.461036i
$815$	16.2138	−	28.0831i	0.567944	−	0.983707i
$816$	19.7163	+	1.15132i	0.690207	+	0.0403043i
$817$	−18.0340	+	10.4119i	−0.630929	+	0.364267i
$818$	16.5607	+	1.89776i	0.579030	+	0.0663535i
$819$	24.5147	+	12.5397i	0.856615	+	0.438172i
$820$	−7.62056	+	32.8136i	−0.266121	+	1.14590i
$821$	19.0029	−	10.9713i	0.663205	−	0.382902i	−0.130292	−	0.991476i	$-0.541591\pi$
$821$	19.0029	−	10.9713i	0.663205	−	0.382902i	0.793497	+	0.608574i	$0.208258\pi$
$822$	−5.94158	−	5.68389i	−0.207236	−	0.198249i
$823$	−44.0508	−	25.4327i	−1.53551	−	0.886529i	−0.999093	−	0.0425788i	$-0.986443\pi$
$823$	−44.0508	−	25.4327i	−1.53551	−	0.886529i	−0.536421	−	0.843951i	$-0.680224\pi$
$824$	−2.07856	−	2.44331i	−0.0724100	−	0.0851168i
$825$	25.5192	−	33.6289i	0.888465	−	1.17081i
$826$	1.35131	+	7.11197i	0.0470180	+	0.247457i
$827$	−2.58474			−0.0898803			−0.0449402	−	0.998990i	$-0.514310\pi$
$827$	−2.58474			−0.0898803			−0.0449402	+	0.998990i	$0.514310\pi$
$828$	12.9784	−	0.575627i	0.451032	−	0.0200044i
$829$	−44.0726			−1.53071			−0.765353	−	0.643611i	$-0.777436\pi$
$829$	−44.0726			−1.53071			−0.765353	+	0.643611i	$0.777436\pi$
$830$	18.3430	+	42.2612i	0.636696	+	1.46691i
$831$	45.3617	−	19.0749i	1.57358	−	0.661699i
$832$	25.9486	−	9.84479i	0.899607	−	0.341307i
$833$	−11.3284	−	16.4271i	−0.392507	−	0.569164i
$834$	9.99642	+	2.44245i	0.346148	+	0.0845752i
$835$	−24.2473	−	41.9975i	−0.839112	−	1.45338i
$836$	7.79907	−	33.5822i	0.269736	−	1.16147i
$837$	35.9131	−	28.4859i	1.24134	−	0.984615i
$838$	45.5415	+	5.21879i	1.57321	+	0.180280i
$839$	0.0135412	+	0.0234541i	0.000467494	+	0.000809724i	0.866259	−	0.499595i	$-0.166518\pi$
$839$	0.0135412	+	0.0234541i	0.000467494	+	0.000809724i	−0.865792	+	0.500405i	$0.833185\pi$
$840$	31.8071	−	38.5724i	1.09745	−	1.33087i
$841$	4.02964	−	6.97953i	0.138953	−	0.240674i
$842$	−13.2002	+	17.8148i	−0.454908	+	0.613937i
$843$	8.67058	+	20.6194i	0.298631	+	0.710171i
$844$	−1.80152	−	5.92004i	−0.0620110	−	0.203776i
$845$	3.72150			0.128024
$846$	−23.0037	−	28.3294i	−0.790882	−	0.973986i
$847$	−12.6779	−	2.85814i	−0.435618	−	0.0982070i
$848$	−32.2905	+	2.17361i	−1.10886	+	0.0746420i
$849$	−6.21244	−	4.71430i	−0.213210	−	0.161794i
$850$	−23.7083	+	31.9964i	−0.813189	+	1.09747i
$851$	−5.07920	+	8.79743i	−0.174113	+	0.301572i
$852$	13.8663	+	16.6828i	0.475052	+	0.571543i
$853$	−15.2459	−	26.4066i	−0.522009	−	0.904146i	−0.999672	−	0.0256029i	$-0.991849\pi$
$853$	−15.2459	−	26.4066i	−0.522009	−	0.904146i	0.477663	−	0.878543i	$-0.341484\pi$
$854$	−7.71508	+	22.1028i	−0.264004	+	0.756341i
$855$	−57.7745	−	56.5492i	−1.97585	−	1.93394i
$856$	−10.4228	+	29.2516i	−0.356243	+	0.999799i
$857$	−43.4562	+	25.0895i	−1.48444	+	0.857040i	−0.999843	−	0.0176997i	$-0.994366\pi$
$857$	−43.4562	+	25.0895i	−1.48444	+	0.857040i	−0.484593	+	0.874740i	$0.661032\pi$
$858$	20.1274	−	5.87413i	0.687137	−	0.200540i
$859$	−9.42520	−	5.44164i	−0.321584	−	0.185666i	0.330515	−	0.943801i	$-0.392778\pi$
$859$	−9.42520	−	5.44164i	−0.321584	−	0.185666i	−0.652098	+	0.758134i	$0.726111\pi$
$860$	−15.7037	+	16.7963i	−0.535491	+	0.572749i
$861$	−6.81047	+	18.8163i	−0.232100	+	0.641257i
$862$	0.796700	+	1.83555i	0.0271357	+	0.0625190i
$863$		−	49.1064i		−	1.67160i	−0.549033	−	0.835800i	$-0.685004\pi$
$863$		−	49.1064i		−	1.67160i	0.549033	−	0.835800i	$-0.314996\pi$
$864$	2.93717	+	29.2468i	0.0999246	+	0.994995i
$865$	32.3330			1.09936
$866$	−19.6488	−	45.2696i	−0.667693	−	1.53832i
$867$	15.2490	+	1.92449i	0.517882	+	0.0653592i
$868$	−38.5985	+	26.2521i	−1.31012	+	0.891056i
$869$	−24.2986	−	14.0288i	−0.824274	−	0.475895i
$870$	−16.1141	−	55.2139i	−0.546317	−	1.87193i
$871$	5.30202	+	9.18337i	0.179652	+	0.311167i
$872$	−1.35619	−	0.483230i	−0.0459263	−	0.0163642i
$873$	−14.2801	+	3.99084i	−0.483307	+	0.135069i
$874$	−2.43553	+	21.2535i	−0.0823830	+	0.718911i
$875$	14.8003	+	47.5314i	0.500340	+	1.60685i
$876$	16.3005	+	19.6113i	0.550742	+	0.662606i
$877$	29.0691	+	16.7831i	0.981595	+	0.566724i	0.902751	−	0.430163i	$-0.141544\pi$
$877$	29.0691	+	16.7831i	0.981595	+	0.566724i	0.0788439	+	0.996887i	$0.474877\pi$
$878$	1.34574	+	0.997148i	0.0454164	+	0.0336521i
$879$	−9.34570	+	12.3156i	−0.315223	+	0.415396i
$880$	−2.55678	−	37.9828i	−0.0861892	−	1.28040i
$881$			1.42156i			0.0478937i	0.999713	+	0.0239468i	$0.00762325\pi$
$881$			1.42156i			0.0478937i	−0.999713	+	0.0239468i	$0.992377\pi$
$882$	21.4826	−	20.5061i	0.723356	−	0.690475i
$883$	−0.829835			−0.0279262			−0.0139631	−	0.999903i	$-0.504445\pi$
$883$	−0.829835			−0.0279262			−0.0139631	+	0.999903i	$0.504445\pi$
$884$	−18.9220	+	5.75816i	−0.636417	+	0.193668i
$885$	11.9153	−	5.01046i	0.400529	−	0.168425i
$886$	10.5799	+	7.83939i	0.355440	+	0.263370i
$887$	−20.6951	+	35.8450i	−0.694874	+	1.20356i	0.275349	+	0.961344i	$0.411207\pi$
$887$	−20.6951	+	35.8450i	−0.694874	+	1.20356i	−0.970223	+	0.242213i	$0.922127\pi$
$888$	−20.5147	−	10.3648i	−0.688428	−	0.347821i
$889$	41.1599	−	12.8163i	1.38046	−	0.429845i
$890$	−56.8390	−	6.51341i	−1.90525	−	0.218330i
$891$	0.475940	+	22.2013i	0.0159446	+	0.743771i
$892$	13.2039	+	3.06644i	0.442098	+	0.102672i
$893$	52.0419	−	30.0464i	1.74151	−	1.00546i
$894$	4.40393	+	1.07602i	0.147289	+	0.0359876i
$895$	−31.5197	+	54.5937i	−1.05359	+	1.82487i
$896$	−0.801704	−	29.9225i	−0.0267831	−	0.999641i
$897$	−11.9930	+	5.04313i	−0.400436	+	0.168385i
$898$	15.6684	−	6.80071i	0.522862	−	0.226943i
$899$			53.7031i			1.79110i
$900$	−52.5909	−	27.3309i	−1.75303	−	0.911031i
$901$	23.0642			0.768381
$902$	6.06675	+	13.9774i	0.202001	+	0.465397i
$903$	−10.4477	+	8.79854i	−0.347677	+	0.292797i
$904$	−34.9368	−	41.0677i	−1.16198	−	1.36589i
$905$	6.11299	−	10.5880i	0.203203	−	0.351957i
$906$	−14.5634	+	15.2237i	−0.483838	+	0.505773i
$907$	−20.2557	−	35.0839i	−0.672579	−	1.16494i	−0.977170	−	0.212457i	$-0.931853\pi$
$907$	−20.2557	−	35.0839i	−0.672579	−	1.16494i	0.304592	−	0.952483i	$-0.401480\pi$
$908$	−2.21671	+	9.54499i	−0.0735641	+	0.316762i
$909$	2.33940	+	8.37086i	0.0775930	+	0.277644i
$910$	−16.5003	+	47.2715i	−0.546980	+	1.56703i
$911$	6.31530	−	3.64614i	0.209235	−	0.120802i	−0.391721	−	0.920084i	$-0.628120\pi$
$911$	6.31530	−	3.64614i	0.209235	−	0.120802i	0.600956	+	0.799282i	$0.294787\pi$
$912$	−48.3206	−	2.82166i	−1.60006	−	0.0934346i
$913$	18.0467	+	10.4193i	0.597259	+	0.344828i
$914$	−34.7956	−	25.7824i	−1.15094	−	0.852807i
$915$	41.4717	+	5.23392i	1.37101	+	0.173028i
$916$	−3.16671	−	10.4062i	−0.104631	−	0.343831i
$917$	−8.62840	+	38.2731i	−0.284935	+	1.26389i
$918$	−0.688618	−	20.9365i	−0.0227278	−	0.691009i
$919$		−	16.9526i		−	0.559214i	−0.960115	−	0.279607i	$-0.909796\pi$
$919$		−	16.9526i		−	0.559214i	0.960115	−	0.279607i	$-0.0902042\pi$
$920$	4.25946	+	23.2348i	0.140430	+	0.766029i
$921$	2.45732	−	19.4709i	0.0809716	−	0.641588i
$922$	1.99411	+	1.47757i	0.0656724	+	0.0486611i
$923$	−18.8143	−	10.8624i	−0.619280	−	0.357541i
$924$	1.17248	−	22.5834i	0.0385718	−	0.742941i
$925$	40.1358	−	23.1724i	1.31966	−	0.761905i
$926$	25.1630	+	2.88353i	0.826907	+	0.0947588i
$927$	−2.37995	+	2.43152i	−0.0781679	+	0.0798616i
$928$	−28.9834	−	18.5972i	−0.951428	−	0.610483i
$929$	−0.128590	+	0.0742417i	−0.00421891	+	0.00243579i	−0.502108	−	0.864805i	$-0.667442\pi$
$929$	−0.128590	+	0.0742417i	−0.00421891	+	0.00243579i	0.497889	+	0.867241i	$0.334109\pi$
$930$	60.2283	+	57.6162i	1.97496	+	1.88931i
$931$	27.7638	+	40.2595i	0.909921	+	1.31945i
$932$	5.33448	−	5.70564i	0.174737	−	0.186895i
$933$	−14.7342	+	19.4165i	−0.482375	+	0.635667i
$934$	5.16583	+	11.9017i	0.169031	+	0.389437i
$935$			27.1301i			0.887250i
$936$	−12.9054	−	26.4572i	−0.421825	−	0.864781i
$937$			44.3047i			1.44737i	0.690130	+	0.723685i	$0.257553\pi$
$937$			44.3047i			1.44737i	−0.690130	+	0.723685i	$0.742447\pi$
$938$	11.2359	−	2.13487i	0.366865	−	0.0697061i
$939$	51.0517	−	21.4675i	1.66601	−	0.700566i
$940$	45.3172	−	48.4703i	1.47808	−	1.58093i
$941$	−1.87919	+	3.25485i	−0.0612599	+	0.106105i	−0.895029	−	0.446008i	$-0.852845\pi$
$941$	−1.87919	+	3.25485i	−0.0612599	+	0.106105i	0.833769	+	0.552114i	$0.186179\pi$
$942$	−4.31684	+	17.6679i	−0.140650	+	0.575650i
$943$	−4.72742	−	8.18813i	−0.153946	−	0.266642i
$944$	3.41065	−	6.94695i	0.111007	−	0.226104i
$945$	−43.8149	−	29.8700i	−1.42530	−	0.971671i
$946$	−1.18410	+	10.3330i	−0.0384985	+	0.335955i
$947$	18.7203	+	32.4245i	0.608328	+	1.05365i	0.991516	+	0.129984i	$0.0414927\pi$
$947$	18.7203	+	32.4245i	0.608328	+	1.05365i	−0.383188	+	0.923670i	$0.625174\pi$
$948$	−13.6455	+	36.9529i	−0.443184	+	1.20018i
$949$	−22.1170	−	12.7693i	−0.717949	−	0.414508i
$950$	58.1044	−	78.4169i	1.88516	−	2.54418i
$951$	−2.54975	+	1.07218i	−0.0826813	+	0.0347680i
$952$	−0.862155	+	21.3148i	−0.0279426	+	0.690818i
$953$	11.7152			0.379493			0.189746	−	0.981833i	$-0.439233\pi$
$953$	11.7152			0.379493			0.189746	+	0.981833i	$0.439233\pi$
$954$	5.41532	+	33.8969i	0.175327	+	1.09745i
$955$		−	55.1757i		−	1.78544i
$956$	−25.0013	+	7.60815i	−0.808601	+	0.246065i
$957$	−20.7246	−	15.7268i	−0.669932	−	0.508377i
$958$	−7.69784	−	5.70385i	−0.248706	−	0.184283i
$959$	6.02344	−	6.52651i	0.194507	−	0.210752i
$960$	−51.9522	+	12.5528i	−1.67675	+	0.405138i
$961$	−23.4110	−	40.5490i	−0.755193	−	1.30803i
$962$	22.8684	+	2.62059i	0.737307	+	0.0844911i
$963$	31.9040	+	8.18321i	1.02809	+	0.263700i
$964$	9.54027	−	41.0797i	0.307271	−	1.32309i
$965$	34.2186	+	59.2684i	1.10154	+	1.90792i
$966$	0.872588	+	14.0049i	0.0280750	+	0.450601i
$967$	26.4981	+	15.2987i	0.852122	+	0.491973i	0.861366	−	0.507984i	$-0.169609\pi$
$967$	26.4981	+	15.2987i	0.852122	+	0.491973i	−0.00924412	+	0.999957i	$0.502943\pi$
$968$	9.00243	+	10.5822i	0.289349	+	0.340125i
$969$	34.2234	+	4.31916i	1.09941	+	0.138751i
$970$	−10.7344	−	24.7314i	−0.344661	−	0.794077i
$971$		−	62.1778i		−	1.99538i	−0.0679347	−	0.997690i	$-0.521641\pi$
$971$		−	62.1778i		−	1.99538i	0.0679347	−	0.997690i	$-0.478359\pi$
$972$	30.6082	−	5.92780i	0.981758	−	0.190134i
$973$	−2.44445	+	10.8429i	−0.0783653	+	0.347606i
$974$	4.05079	+	9.33277i	0.129796	+	0.299041i
$975$	58.8884	+	7.43200i	1.88594	+	0.238015i
$976$	20.7846	−	13.9409i	0.665299	−	0.446237i
$977$	12.3354	−	21.3655i	0.394643	−	0.683542i	−0.598412	−	0.801188i	$-0.704202\pi$
$977$	12.3354	−	21.3655i	0.394643	−	0.683542i	0.993056	+	0.117646i	$0.0375349\pi$
$978$	−19.7681	+	5.76929i	−0.632115	+	0.184482i
$979$	−22.4107	+	12.9388i	−0.716250	+	0.413527i
$980$	42.2713	+	33.6043i	1.35031	+	1.07345i
$981$	−0.379397	+	1.47916i	−0.0121132	+	0.0472259i
$982$	−6.21956	+	54.2746i	−0.198474	+	1.73197i
$983$	−9.40212	−	16.2849i	−0.299881	−	0.519409i	0.676228	−	0.736693i	$-0.263614\pi$
$983$	−9.40212	−	16.2849i	−0.299881	−	0.519409i	−0.976108	+	0.217284i	$0.930280\pi$
$984$	17.9015	−	11.7123i	0.570677	−	0.373374i
$985$	−38.2691	−	22.0947i	−1.21936	−	0.703995i
$986$	19.7186	+	14.6108i	0.627968	+	0.465304i
$987$	30.1496	−	25.3906i	0.959673	−	0.808191i
$988$	46.3742	−	14.1121i	1.47536	−	0.448966i
$989$		−	6.45368i		−	0.205215i
$990$	−39.8724	+	6.36997i	−1.26723	+	0.202451i
$991$			45.4887i			1.44500i	0.691372	+	0.722499i	$0.257006\pi$
$991$			45.4887i			1.44500i	−0.691372	+	0.722499i	$0.742994\pi$
$992$	49.8481	+	2.33878i	1.58268	+	0.0742562i
$993$	24.1079	+	57.3308i	0.765042	+	1.81934i
$994$	−17.7485	+	15.2975i	−0.562947	+	0.485207i
$995$	−33.0702	+	57.2792i	−1.04839	+	1.81587i
$996$	10.1346	−	27.4452i	0.321126	−	0.869633i
$997$	−2.38291	−	4.12733i	−0.0754676	−	0.130714i	0.825822	−	0.563931i	$-0.190712\pi$
$997$	−2.38291	−	4.12733i	−0.0754676	−	0.130714i	−0.901290	+	0.433217i	$0.857378\pi$
$998$	−3.98050	+	34.7356i	−0.126000	+	1.09954i
$999$	−8.96604	+	22.6700i	−0.283673	+	0.717247i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	504.2.be.a.139.12	yes	184
7.6	odd	2	inner	504.2.be.a.139.11	✓	184
8.3	odd	2	inner	504.2.be.a.139.74	yes	184
9.7	even	3	inner	504.2.be.a.475.73	yes	184
56.27	even	2	inner	504.2.be.a.139.73	yes	184
63.34	odd	6	inner	504.2.be.a.475.74	yes	184
72.43	odd	6	inner	504.2.be.a.475.11	yes	184
504.475	even	6	inner	504.2.be.a.475.12	yes	184

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.be.a.139.11	✓	184	7.6	odd	2	inner
504.2.be.a.139.12	yes	184	1.1	even	1	trivial
504.2.be.a.139.73	yes	184	56.27	even	2	inner
504.2.be.a.139.74	yes	184	8.3	odd	2	inner
504.2.be.a.475.11	yes	184	72.43	odd	6	inner
504.2.be.a.475.12	yes	184	504.475	even	6	inner
504.2.be.a.475.73	yes	184	9.7	even	3	inner
504.2.be.a.475.74	yes	184	63.34	odd	6	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:	\( N \)	\(=\)	\( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	504.be (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.29729 + 0.563073i) q^{2} +(1.71842 + 0.216873i) q^{3} +(1.36590 - 1.46093i) q^{4} +(1.92861 - 3.34045i) q^{5} +(-2.35140 + 0.686250i) q^{6} +(-0.786580 - 2.52612i) q^{7} +(-0.949346 + 2.66435i) q^{8} +(2.90593 + 0.745357i) q^{9} +(-0.621039 + 5.41946i) q^{10} +(1.23369 + 2.13681i) q^{11} +(2.66402 - 2.21427i) q^{12} +(-1.73459 + 3.00439i) q^{13} +(2.44281 + 2.83420i) q^{14} +(4.03861 - 5.32203i) q^{15} +(-0.268649 - 3.99097i) q^{16} +2.85064i q^{17} +(-4.18951 + 0.669311i) q^{18} -6.98636i q^{19} +(-2.24589 - 7.38027i) q^{20} +(-0.803828 - 4.51153i) q^{21} +(-2.80362 - 2.07739i) q^{22} +(1.87512 + 1.08260i) q^{23} +(-2.20920 + 4.37258i) q^{24} +(-4.93906 - 8.55470i) q^{25} +(0.558561 - 4.87426i) q^{26} +(4.83196 + 1.91105i) q^{27} +(-4.76488 - 2.30128i) q^{28} +(-5.27204 + 3.04382i) q^{29} +(-2.24254 + 9.17822i) q^{30} +(4.41084 - 7.63980i) q^{31} +(2.59572 + 5.02615i) q^{32} +(1.65658 + 3.93949i) q^{33} +(-1.60512 - 3.69810i) q^{34} +(-9.95538 - 2.24437i) q^{35} +(5.05812 - 3.22729i) q^{36} +4.69167i q^{37} +(3.93383 + 9.06330i) q^{38} +(-3.63232 + 4.78663i) q^{39} +(7.06919 + 8.30972i) q^{40} +(-3.78170 - 2.18336i) q^{41} +(3.58311 + 5.40012i) q^{42} +(-1.49032 - 2.58131i) q^{43} +(4.80682 + 1.11633i) q^{44} +(8.09423 - 8.26961i) q^{45} +(-3.04214 - 0.348612i) q^{46} +(4.30072 + 7.44906i) q^{47} +(0.403881 - 6.91642i) q^{48} +(-5.76258 + 3.97400i) q^{49} +(11.2243 + 8.31683i) q^{50} +(-0.618227 + 4.89860i) q^{51} +(2.01995 + 6.63781i) q^{52} -8.09088i q^{53} +(-7.34450 + 0.241566i) q^{54} +9.51720 q^{55} +(7.47720 + 0.302442i) q^{56} +(1.51515 - 12.0055i) q^{57} +(5.12545 - 6.91724i) q^{58} +(1.67555 + 0.967379i) q^{59} +(-2.25880 - 13.1695i) q^{60} +(3.12837 + 5.41850i) q^{61} +(-1.42035 + 12.3946i) q^{62} +(-0.402886 - 7.92702i) q^{63} +(-6.19748 - 5.05878i) q^{64} +(6.69068 + 11.5886i) q^{65} +(-4.36727 - 4.17787i) q^{66} +(1.52832 - 2.64713i) q^{67} +(4.16460 + 3.89369i) q^{68} +(2.98745 + 2.26702i) q^{69} +(14.1787 - 2.69402i) q^{70} +6.26226i q^{71} +(-4.74463 + 7.03481i) q^{72} +7.36156i q^{73} +(-2.64175 - 6.08644i) q^{74} +(-6.63209 - 15.7717i) q^{75} +(-10.2066 - 9.54265i) q^{76} +(4.42745 - 4.79722i) q^{77} +(2.01694 - 8.25488i) q^{78} +(-9.84796 + 5.68572i) q^{79} +(-13.8497 - 6.79961i) q^{80} +(7.88888 + 4.33192i) q^{81} +(6.13533 + 0.703073i) q^{82} +(7.31414 - 4.22282i) q^{83} +(-7.68898 - 4.98794i) q^{84} +(9.52243 + 5.49777i) q^{85} +(3.38684 + 2.50954i) q^{86} +(-9.71971 + 4.08719i) q^{87} +(-6.86440 + 1.25840i) q^{88} +10.4879i q^{89} +(-5.84413 + 15.2857i) q^{90} +(8.95386 + 2.01858i) q^{91} +(4.14282 - 1.26070i) q^{92} +(9.23654 - 12.1718i) q^{93} +(-9.77363 - 7.24194i) q^{94} +(-23.3376 - 13.4740i) q^{95} +(3.37050 + 9.19998i) q^{96} +(-4.28025 + 2.47121i) q^{97} +(5.23806 - 8.40016i) q^{98} +(1.99233 + 7.12896i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 184 q - 2 q^{2} - 2 q^{4} - 8 q^{8} - 8 q^{9} - 4 q^{11} - 10 q^{14} - 2 q^{16} - 10 q^{18} + 6 q^{22} - 80 q^{25} - 12 q^{28} + 4 q^{30} - 12 q^{32} + 12 q^{35} - 46 q^{36} + 10 q^{42} - 4 q^{43} - 36 q^{44}+ \cdots + 28 q^{99}+O(q^{100}) \) 184 * q - 2 * q^2 - 2 * q^4 - 8 * q^8 - 8 * q^9 - 4 * q^11 - 10 * q^14 - 2 * q^16 - 10 * q^18 + 6 * q^22 - 80 * q^25 - 12 * q^28 + 4 * q^30 - 12 * q^32 + 12 * q^35 - 46 * q^36 + 10 * q^42 - 4 * q^43 - 36 * q^44 - 16 * q^46 - 2 * q^49 + 16 * q^50 - 24 * q^51 + 40 * q^56 + 16 * q^57 - 10 * q^58 + 40 * q^60 - 8 * q^64 + 36 * q^65 - 4 * q^67 - 76 * q^72 - 40 * q^74 + 60 * q^78 + 8 * q^81 + 40 * q^84 + 32 * q^86 - 18 * q^88 + 20 * q^91 - 26 * q^92 - 132 * q^98 + 28 * q^99

Introduction

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