LMFDB - Embedded newform 504.2.ca.a.101.61

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [504,2,Mod(5,504)]

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([0, 3, 5, 5]))

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

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

chi := DirichletCharacter("504.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 504 = 2^{3} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	504.ca (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			101.61
Character	$\chi$	$=$	504.101
Dual form			504.2.ca.a.5.61

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.657114 - 1.25228i) q^{2} +(-1.49163 + 0.880361i) q^{3} +(-1.13640 - 1.64578i) q^{4} +(0.161865 + 0.0934530i) q^{5} +(0.122285 + 2.44644i) q^{6} +(-2.28020 + 1.34189i) q^{7} +(-2.80772 + 0.341626i) q^{8} +(1.44993 - 2.62635i) q^{9} +O(q^{10})$	\(q+(0.657114 - 1.25228i) q^{2} +(-1.49163 + 0.880361i) q^{3} +(-1.13640 - 1.64578i) q^{4} +(0.161865 + 0.0934530i) q^{5} +(0.122285 + 2.44644i) q^{6} +(-2.28020 + 1.34189i) q^{7} +(-2.80772 + 0.341626i) q^{8} +(1.44993 - 2.62635i) q^{9} +(0.223393 - 0.141291i) q^{10} +(1.79813 + 3.11445i) q^{11} +(3.14397 + 1.45445i) q^{12} +(1.86968 + 3.23838i) q^{13} +(0.182067 + 3.73723i) q^{14} +(-0.323716 + 0.00310256i) q^{15} +(-1.41718 + 3.74053i) q^{16} +(1.02476 - 1.77494i) q^{17} +(-2.33615 - 3.54152i) q^{18} +(3.05081 + 5.28416i) q^{19} +(-0.0301411 - 0.372595i) q^{20} +(2.21987 - 4.00901i) q^{21} +(5.08173 - 0.205208i) q^{22} +(1.61923 + 0.934863i) q^{23} +(3.88733 - 2.98139i) q^{24} +(-2.48253 - 4.29987i) q^{25} +(5.28395 - 0.213374i) q^{26} +(0.149378 + 5.19400i) q^{27} +(4.79969 + 2.22778i) q^{28} +(-3.68322 + 6.37953i) q^{29} +(-0.208833 + 0.407421i) q^{30} +4.84319i q^{31} +(3.75294 + 4.23266i) q^{32} +(-5.42398 - 3.06261i) q^{33} +(-1.54933 - 2.44962i) q^{34} +(-0.494490 + 0.00411386i) q^{35} +(-5.97009 + 0.598326i) q^{36} +(1.33193 - 0.768992i) q^{37} +(8.62198 - 0.348169i) q^{38} +(-5.63982 - 3.18448i) q^{39} +(-0.486399 - 0.207092i) q^{40} +(5.23920 + 9.07456i) q^{41} +(-3.56169 - 5.41428i) q^{42} +(-8.77963 - 5.06892i) q^{43} +(3.08230 - 6.49858i) q^{44} +(0.480133 - 0.289615i) q^{45} +(2.23473 - 1.41342i) q^{46} +3.32000 q^{47} +(-1.17911 - 6.82713i) q^{48} +(3.39866 - 6.11957i) q^{49} +(-7.01595 + 0.283315i) q^{50} +(0.0340211 + 3.54971i) q^{51} +(3.20495 - 6.75719i) q^{52} +(1.25602 - 2.17549i) q^{53} +(6.60250 + 3.22599i) q^{54} +0.672161i q^{55} +(5.94375 - 4.54663i) q^{56} +(-9.20266 - 5.19621i) q^{57} +(5.56865 + 8.80450i) q^{58} -3.16376i q^{59} +(0.372977 + 0.529239i) q^{60} -1.60808 q^{61} +(6.06503 + 3.18253i) q^{62} +(0.218144 + 7.93426i) q^{63} +(7.76658 - 1.91838i) q^{64} +0.698909i q^{65} +(-7.39941 + 4.77985i) q^{66} -4.61691i q^{67} +(-4.08570 + 0.330512i) q^{68} +(-3.23831 + 0.0310366i) q^{69} +(-0.319785 + 0.621942i) q^{70} +10.3929i q^{71} +(-3.17376 + 7.86939i) q^{72} +(-10.1047 - 5.83396i) q^{73} +(-0.0877598 - 2.17327i) q^{74} +(7.48847 + 4.22830i) q^{75} +(5.22962 - 11.0259i) q^{76} +(-8.27934 - 4.68868i) q^{77} +(-7.69386 + 4.97006i) q^{78} -16.0762 q^{79} +(-0.578957 + 0.473023i) q^{80} +(-4.79542 - 7.61603i) q^{81} +(14.8066 - 0.597914i) q^{82} +(2.62532 + 1.51573i) q^{83} +(-9.12062 + 0.902424i) q^{84} +(0.331746 - 0.191534i) q^{85} +(-12.1169 + 7.66368i) q^{86} +(-0.122280 - 12.7585i) q^{87} +(-6.11261 - 8.13021i) q^{88} +(3.54615 + 6.14211i) q^{89} +(-0.0471759 - 0.791571i) q^{90} +(-8.60881 - 4.87526i) q^{91} +(-0.301518 - 3.72728i) q^{92} +(-4.26376 - 7.22426i) q^{93} +(2.18162 - 4.15757i) q^{94} +1.14043i q^{95} +(-9.32428 - 3.00963i) q^{96} +(9.38981 + 5.42121i) q^{97} +(-5.43010 - 8.27732i) q^{98} +(10.7868 - 0.206784i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 184 q - 2 q^{4} - 6 q^{6} - 2 q^{7} - 2 q^{9}+O(q^{10}) $ 184 * q - 2 * q^4 - 6 * q^6 - 2 * q^7 - 2 * q^9	$ 184 q - 2 q^{4} - 6 q^{6} - 2 q^{7} - 2 q^{9} - 6 q^{10} + 12 q^{12} - 18 q^{14} - 2 q^{15} - 2 q^{16} + 12 q^{18} - 6 q^{22} - 6 q^{23} - 12 q^{24} + 78 q^{25} - 6 q^{26} - 8 q^{28} + 7 q^{30} - 6 q^{33} + 6 q^{34} + 22 q^{36} - 33 q^{38} - 8 q^{39} - 18 q^{40} - 42 q^{42} - 9 q^{44} + 2 q^{46} - 12 q^{47} + 9 q^{48} - 2 q^{49} + 9 q^{50} + 21 q^{52} + 33 q^{54} + 18 q^{56} + 4 q^{57} - 3 q^{58} - 59 q^{60} + 12 q^{62} - 72 q^{63} - 8 q^{64} - 42 q^{66} - 18 q^{68} - 27 q^{70} + 12 q^{72} - 12 q^{73} - 57 q^{74} + 12 q^{76} + 19 q^{78} - 4 q^{79} - 57 q^{80} - 18 q^{81} + 69 q^{84} - 27 q^{86} - 6 q^{87} + 9 q^{88} - 24 q^{89} - 75 q^{90} - 36 q^{92} - 45 q^{96} - 45 q^{98}+O(q^{100}) $ 184 * q - 2 * q^4 - 6 * q^6 - 2 * q^7 - 2 * q^9 - 6 * q^10 + 12 * q^12 - 18 * q^14 - 2 * q^15 - 2 * q^16 + 12 * q^18 - 6 * q^22 - 6 * q^23 - 12 * q^24 + 78 * q^25 - 6 * q^26 - 8 * q^28 + 7 * q^30 - 6 * q^33 + 6 * q^34 + 22 * q^36 - 33 * q^38 - 8 * q^39 - 18 * q^40 - 42 * q^42 - 9 * q^44 + 2 * q^46 - 12 * q^47 + 9 * q^48 - 2 * q^49 + 9 * q^50 + 21 * q^52 + 33 * q^54 + 18 * q^56 + 4 * q^57 - 3 * q^58 - 59 * q^60 + 12 * q^62 - 72 * q^63 - 8 * q^64 - 42 * q^66 - 18 * q^68 - 27 * q^70 + 12 * q^72 - 12 * q^73 - 57 * q^74 + 12 * q^76 + 19 * q^78 - 4 * q^79 - 57 * q^80 - 18 * q^81 + 69 * q^84 - 27 * q^86 - 6 * q^87 + 9 * q^88 - 24 * q^89 - 75 * q^90 - 36 * q^92 - 45 * q^96 - 45 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$73$	$127$	$253$	$281$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$	$-1$	$e\left(\frac{1}{6}\right)$

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 $

$2$	0.657114	−	1.25228i	0.464650	−	0.885494i
$2$	0.657114	−	1.25228i	0.464650	−	0.885494i
$3$	−1.49163	+	0.880361i	−0.861194	+	0.508277i
$3$	−1.49163	+	0.880361i	−0.861194	+	0.508277i
$4$	−1.13640	−	1.64578i	−0.568201	−	0.822890i
$5$	0.161865	+	0.0934530i	0.0723884	+	0.0417935i	0.535757	−	0.844372i	$-0.320026\pi$
$5$	0.161865	+	0.0934530i	0.0723884	+	0.0417935i	−0.463369	+	0.886165i	$0.653360\pi$
$6$	0.122285	+	2.44644i	0.0499227	+	0.998753i
$7$	−2.28020	+	1.34189i	−0.861836	+	0.507187i
$7$	−2.28020	+	1.34189i	−0.861836	+	0.507187i
$8$	−2.80772	+	0.341626i	−0.992679	+	0.120783i
$9$	1.44993	−	2.62635i	0.483309	−	0.875450i
$10$	0.223393	−	0.141291i	0.0706431	−	0.0446802i
$11$	1.79813	+	3.11445i	0.542156	+	0.939041i	0.998780	+	0.0493815i	$0.0157250\pi$
$11$	1.79813	+	3.11445i	0.542156	+	0.939041i	−0.456624	+	0.889660i	$0.650942\pi$
$12$	3.14397	+	1.45445i	0.907587	+	0.419864i
$13$	1.86968	+	3.23838i	0.518556	+	0.898166i	0.999768	+	0.0215611i	$0.00686363\pi$
$13$	1.86968	+	3.23838i	0.518556	+	0.898166i	−0.481211	+	0.876605i	$0.659803\pi$
$14$	0.182067	+	3.73723i	0.0486596	+	0.998815i
$15$	−0.323716	+	0.00310256i	−0.0835831	+	0.000801077i
$16$	−1.41718	+	3.74053i	−0.354295	+	0.935134i
$17$	1.02476	−	1.77494i	0.248541	−	0.430485i	−0.714580	−	0.699553i	$-0.753382\pi$
$17$	1.02476	−	1.77494i	0.248541	−	0.430485i	0.963121	+	0.269068i	$0.0867156\pi$
$18$	−2.33615	−	3.54152i	−0.550636	−	0.834745i
$19$	3.05081	+	5.28416i	0.699905	+	1.21227i	0.968499	+	0.249017i	$0.0801075\pi$
$19$	3.05081	+	5.28416i	0.699905	+	1.21227i	−0.268595	+	0.963253i	$0.586559\pi$
$20$	−0.0301411	−	0.372595i	−0.00673974	−	0.0833148i
$21$	2.21987	−	4.00901i	0.484416	−	0.874838i
$22$	5.08173	−	0.205208i	1.08343	−	0.0437505i
$23$	1.61923	+	0.934863i	0.337633	+	0.194932i	0.659225	−	0.751946i	$-0.270885\pi$
$23$	1.61923	+	0.934863i	0.337633	+	0.194932i	−0.321592	+	0.946878i	$0.604218\pi$
$24$	3.88733	−	2.98139i	0.793498	−	0.608573i
$25$	−2.48253	−	4.29987i	−0.496507	−	0.859975i
$26$	5.28395	−	0.213374i	1.03627	−	0.0418461i
$27$	0.149378	+	5.19400i	0.0287478	+	0.999587i
$28$	4.79969	+	2.22778i	0.907055	+	0.421012i
$29$	−3.68322	+	6.37953i	−0.683957	+	1.18465i	0.289806	+	0.957085i	$0.406409\pi$
$29$	−3.68322	+	6.37953i	−0.683957	+	1.18465i	−0.973763	+	0.227563i	$0.926924\pi$
$30$	−0.208833	+	0.407421i	−0.0381275	+	0.0743846i
$31$			4.84319i			0.869863i	0.900464	+	0.434932i	$0.143227\pi$
$31$			4.84319i			0.869863i	−0.900464	+	0.434932i	$0.856773\pi$
$32$	3.75294	+	4.23266i	0.663432	+	0.748236i
$33$	−5.42398	−	3.06261i	−0.944194	−	0.533131i
$34$	−1.54933	−	2.44962i	−0.265708	−	0.420107i
$35$	−0.494490	+	0.00411386i	−0.0835840	+	0.000695369i
$36$	−5.97009	+	0.598326i	−0.995015	+	0.0997210i
$37$	1.33193	−	0.768992i	0.218968	−	0.126422i	−0.386504	−	0.922288i	$-0.626317\pi$
$37$	1.33193	−	0.768992i	0.218968	−	0.126422i	0.605473	+	0.795866i	$0.292984\pi$
$38$	8.62198	−	0.348169i	1.39867	−	0.0564804i
$39$	−5.63982	−	3.18448i	−0.903094	−	0.509925i
$40$	−0.486399	−	0.207092i	−0.0769064	−	0.0327442i
$41$	5.23920	+	9.07456i	0.818226	+	1.41721i	0.906988	+	0.421155i	$0.138375\pi$
$41$	5.23920	+	9.07456i	0.818226	+	1.41721i	−0.0887629	+	0.996053i	$0.528291\pi$
$42$	−3.56169	−	5.41428i	−0.549580	−	0.835441i
$43$	−8.77963	−	5.06892i	−1.33888	−	0.773004i	−0.352240	−	0.935910i	$-0.614580\pi$
$43$	−8.77963	−	5.06892i	−1.33888	−	0.773004i	−0.986642	+	0.162906i	$0.947913\pi$
$44$	3.08230	−	6.49858i	0.464674	−	0.979698i
$45$	0.480133	−	0.289615i	0.0715741	−	0.0431732i
$46$	2.23473	−	1.41342i	0.329493	−	0.208397i
$47$	3.32000			0.484272			0.242136	−	0.970242i	$-0.422152\pi$
$47$	3.32000			0.484272			0.242136	+	0.970242i	$0.422152\pi$
$48$	−1.17911	−	6.82713i	−0.170190	−	0.985411i
$49$	3.39866	−	6.11957i	0.485522	−	0.874224i
$50$	−7.01595	+	0.283315i	−0.992205	+	0.0400667i
$51$	0.0340211	+	3.54971i	0.00476391	+	0.497059i
$52$	3.20495	−	6.75719i	0.444447	−	0.937053i
$53$	1.25602	−	2.17549i	0.172527	−	0.298826i	−0.766775	−	0.641915i	$-0.778140\pi$
$53$	1.25602	−	2.17549i	0.172527	−	0.298826i	0.939303	+	0.343089i	$0.111473\pi$
$54$	6.60250	+	3.22599i	0.898486	+	0.439002i
$55$			0.672161i			0.0906342i
$56$	5.94375	−	4.54663i	0.794267	−	0.607569i
$57$	−9.20266	−	5.19621i	−1.21892	−	0.688254i
$58$	5.56865	+	8.80450i	0.731199	+	1.15609i
$59$		−	3.16376i		−	0.411887i	−0.978564	−	0.205944i	$-0.933974\pi$
$59$		−	3.16376i		−	0.411887i	0.978564	−	0.205944i	$-0.0660263\pi$
$60$	0.372977	+	0.529239i	0.0481512	+	0.0683245i
$61$	−1.60808			−0.205893			−0.102947	−	0.994687i	$-0.532827\pi$
$61$	−1.60808			−0.205893			−0.102947	+	0.994687i	$0.532827\pi$
$62$	6.06503	+	3.18253i	0.770259	+	0.404182i
$63$	0.218144	+	7.93426i	0.0274836	+	0.999622i
$64$	7.76658	−	1.91838i	0.970823	−	0.239798i
$65$			0.698909i			0.0866890i
$66$	−7.39941	+	4.77985i	−0.910804	+	0.588359i
$67$		−	4.61691i		−	0.564046i	−0.959408	−	0.282023i	$-0.908995\pi$
$67$		−	4.61691i		−	0.564046i	0.959408	−	0.282023i	$-0.0910054\pi$
$68$	−4.08570	+	0.330512i	−0.495463	+	0.0400805i
$69$	−3.23831	+	0.0310366i	−0.389847	+	0.00373637i
$70$	−0.319785	+	0.621942i	−0.0382216	+	0.0743363i
$71$			10.3929i			1.23341i	0.787193	+	0.616707i	$0.211533\pi$
$71$			10.3929i			1.23341i	−0.787193	+	0.616707i	$0.788467\pi$
$72$	−3.17376	+	7.86939i	−0.374031	+	0.927416i
$73$	−10.1047	−	5.83396i	−1.18267	−	0.682813i	−0.226037	−	0.974119i	$-0.572577\pi$
$73$	−10.1047	−	5.83396i	−1.18267	−	0.682813i	−0.956630	+	0.291306i	$0.905910\pi$
$74$	−0.0877598	−	2.17327i	−0.0102019	−	0.252637i
$75$	7.48847	+	4.22830i	0.864694	+	0.488242i
$76$	5.22962	−	11.0259i	0.599878	−	1.26476i
$77$	−8.27934	−	4.68868i	−0.943519	−	0.534325i
$78$	−7.69386	+	4.97006i	−0.871158	+	0.562748i
$79$	−16.0762			−1.80871			−0.904354	−	0.426783i	$-0.859647\pi$
$79$	−16.0762			−1.80871			−0.904354	+	0.426783i	$0.859647\pi$
$80$	−0.578957	+	0.473023i	−0.0647293	+	0.0528856i
$81$	−4.79542	−	7.61603i	−0.532824	−	0.846226i
$82$	14.8066	−	0.597914i	1.63512	−	0.0660286i
$83$	2.62532	+	1.51573i	0.288166	+	0.166373i	0.637115	−	0.770769i	$-0.280128\pi$
$83$	2.62532	+	1.51573i	0.288166	+	0.166373i	−0.348948	+	0.937142i	$0.613461\pi$
$84$	−9.12062	+	0.902424i	−0.995141	+	0.0984625i
$85$	0.331746	−	0.191534i	0.0359830	−	0.0207748i
$86$	−12.1169	+	7.66368i	−1.30660	+	0.826396i
$87$	−0.122280	−	12.7585i	−0.0131098	−	1.36785i
$88$	−6.11261	−	8.13021i	−0.651607	−	0.866683i
$89$	3.54615	+	6.14211i	0.375891	+	0.651063i	0.990460	−	0.137801i	$-0.0440033\pi$
$89$	3.54615	+	6.14211i	0.375891	+	0.651063i	−0.614569	+	0.788863i	$0.710670\pi$
$90$	−0.0471759	−	0.791571i	−0.00497277	−	0.0834389i
$91$	−8.60881	−	4.87526i	−0.902449	−	0.511066i
$92$	−0.301518	−	3.72728i	−0.0314354	−	0.388595i
$93$	−4.26376	−	7.22426i	−0.442131	−	0.749121i
$94$	2.18162	−	4.15757i	0.225017	−	0.428820i
$95$			1.14043i			0.117006i
$96$	−9.32428	−	3.00963i	−0.951655	−	0.307169i
$97$	9.38981	+	5.42121i	0.953391	+	0.550440i	0.894133	−	0.447802i	$-0.147793\pi$
$97$	9.38981	+	5.42121i	0.953391	+	0.550440i	0.0592580	+	0.998243i	$0.481127\pi$
$98$	−5.43010	−	8.27732i	−0.548523	−	0.836135i
$99$	10.7868	−	0.206784i	1.08411	−	0.0207826i
$100$	−4.25549	+	8.97209i	−0.425549	+	0.897209i
$101$	−14.0054	+	8.08602i	−1.39359	+	0.804589i	−0.993711	−	0.111979i	$-0.964281\pi$
$101$	−14.0054	+	8.08602i	−1.39359	+	0.804589i	−0.399878	+	0.916568i	$0.630948\pi$
$102$	4.46758	+	2.28996i	0.442357	+	0.226740i
$103$	−7.26837	−	4.19640i	−0.716174	−	0.413483i	0.0971689	−	0.995268i	$-0.469021\pi$
$103$	−7.26837	−	4.19640i	−0.716174	−	0.413483i	−0.813343	+	0.581785i	$0.802355\pi$
$104$	−6.35586	−	8.45374i	−0.623243	−	0.828957i
$105$	0.733975	−	0.441466i	0.0716286	−	0.0430827i
$106$	−1.89897	−	3.00243i	−0.184444	−	0.291621i
$107$	2.40802	+	4.17081i	0.232792	+	0.403208i	0.958629	−	0.284659i	$-0.0918805\pi$
$107$	2.40802	+	4.17081i	0.232792	+	0.403208i	−0.725837	+	0.687867i	$0.758547\pi$
$108$	8.37843	−	6.14832i	0.806215	−	0.591622i
$109$	0.567963	+	0.327914i	0.0544010	+	0.0314084i	0.526954	−	0.849894i	$-0.323334\pi$
$109$	0.567963	+	0.327914i	0.0544010	+	0.0314084i	−0.472553	+	0.881302i	$0.656667\pi$
$110$	0.841733	+	0.441687i	0.0802561	+	0.0421132i
$111$	−1.30976	+	2.31964i	−0.124317	+	0.220170i
$112$	−1.78793	−	10.4309i	−0.168943	−	0.985626i
$113$	12.0747	−	6.97134i	1.13589	−	0.655808i	0.190483	−	0.981691i	$-0.438995\pi$
$113$	12.0747	−	6.97134i	1.13589	−	0.655808i	0.945410	+	0.325882i	$0.105661\pi$
$114$	−12.5543	+	8.10979i	−1.17582	+	0.759552i
$115$	0.174732	+	0.302644i	0.0162938	+	0.0282217i
$116$	14.6849	−	1.18794i	1.36346	−	0.110297i
$117$	11.2160	−	0.215013i	1.03692	−	0.0198780i
$118$	−3.96191	−	2.07895i	−0.364724	−	0.191383i
$119$	0.0451106	+	5.42233i	0.00413528	+	0.497065i
$120$	0.907844	−	0.119301i	0.0828744	−	0.0108906i
$121$	−0.966520	+	1.67406i	−0.0878655	+	0.152188i
$122$	−1.05669	+	2.01376i	−0.0956682	+	0.182317i
$123$	−15.8038	−	8.92351i	−1.42498	−	0.804606i
$124$	7.97083	−	5.50381i	0.715802	−	0.494257i
$125$		−	1.86253i		−	0.166590i
$126$	10.0792	+	4.94053i	0.897930	+	0.440138i
$127$	9.93306			0.881416			0.440708	−	0.897650i	$-0.354727\pi$
$127$	9.93306			0.881416			0.440708	+	0.897650i	$0.354727\pi$
$128$	2.70118	−	10.9865i	0.238753	−	0.971080i
$129$	17.5585	−	0.168284i	1.54594	−	0.0148166i
$130$	0.875229	+	0.459263i	0.0767627	+	0.0402800i
$131$	10.3353	+	5.96707i	0.902997	+	0.521346i	0.878171	−	0.478346i	$-0.158764\pi$
$131$	10.3353	+	5.96707i	0.902997	+	0.521346i	0.0248258	+	0.999692i	$0.492097\pi$
$132$	1.12345	+	12.4070i	0.0977837	+	1.07989i
$133$	−14.0472	−	7.95511i	−1.21805	−	0.689795i
$134$	−5.78166	−	3.03384i	−0.499459	−	0.262084i
$135$	−0.461216	+	0.854689i	−0.0396952	+	0.0735599i
$136$	−2.27087	+	5.33361i	−0.194726	+	0.457353i
$137$	15.4604	−	8.92607i	1.32087	−	0.762606i	0.337004	−	0.941503i	$-0.390586\pi$
$137$	15.4604	−	8.92607i	1.32087	−	0.762606i	0.983868	+	0.178897i	$0.0572529\pi$
$138$	−2.08907	+	4.07566i	−0.177834	+	0.346943i
$139$	−4.27906	−	7.41155i	−0.362945	−	0.628640i	0.625499	−	0.780225i	$-0.284896\pi$
$139$	−4.27906	−	7.41155i	−0.362945	−	0.628640i	−0.988444	+	0.151585i	$0.951562\pi$
$140$	0.568710	+	0.809146i	0.0480647	+	0.0683853i
$141$	−4.95222	+	2.92280i	−0.417052	+	0.246144i
$142$	13.0148	+	6.82934i	1.09218	+	0.573105i
$143$	−6.72385	+	11.6460i	−0.562276	+	0.973891i
$144$	7.76914	+	9.14552i	0.647428	+	0.762127i
$145$	−1.19237	+	0.688416i	−0.0990211	+	0.0571699i
$146$	−13.9457	+	8.82033i	−1.15415	+	0.729976i
$147$	0.317892	+	12.1202i	0.0262193	+	0.999656i
$148$	−2.77920	−	1.31818i	−0.228449	−	0.108354i
$149$	−11.4137	+	19.7690i	−0.935043	+	1.61954i	−0.160487	+	0.987038i	$0.551307\pi$
$149$	−11.4137	+	19.7690i	−0.935043	+	1.61954i	−0.774556	+	0.632505i	$0.782027\pi$
$150$	10.2158	−	6.59917i	0.834115	−	0.538820i
$151$	4.30322	+	7.45340i	0.350191	+	0.606549i	0.986283	−	0.165065i	$-0.0527833\pi$
$151$	4.30322	+	7.45340i	0.350191	+	0.606549i	−0.636092	+	0.771614i	$0.719450\pi$
$152$	−10.3710	−	13.7942i	−0.841202	−	1.11886i
$153$	−3.17578	−	5.26491i	−0.256746	−	0.425643i
$154$	−11.3120	+	7.28704i	−0.911548	+	0.587207i
$155$	−0.452611	+	0.783945i	−0.0363546	+	0.0629680i
$156$	1.16815	+	12.9007i	0.0935272	+	1.03289i
$157$	2.49375			0.199023			0.0995116	−	0.995036i	$-0.468272\pi$
$157$	2.49375			0.199023			0.0995116	+	0.995036i	$0.468272\pi$
$158$	−10.5639	+	20.1318i	−0.840416	+	1.60160i
$159$	0.0416987	+	4.35077i	0.00330692	+	0.345039i
$160$	0.211916	+	1.03585i	0.0167534	+	0.0818908i
$161$	−4.94666	+	0.0411532i	−0.389851	+	0.00324333i
$162$	−12.6885	+	1.00059i	−0.996905	+	0.0786140i
$163$	−1.55387	+	0.897128i	−0.121709	+	0.0702684i	−0.559618	−	0.828750i	$-0.689052\pi$
$163$	−1.55387	+	0.897128i	−0.121709	+	0.0702684i	0.437910	+	0.899019i	$0.355719\pi$
$164$	8.98089	−	18.9349i	0.701290	−	1.47857i
$165$	−0.591745	−	1.00262i	−0.0460673	−	0.0780536i
$166$	3.62325	−	2.29163i	0.281219	−	0.177865i
$167$	−4.90949	−	8.50349i	−0.379908	−	0.658020i	0.611141	−	0.791522i	$-0.290711\pi$
$167$	−4.90949	−	8.50349i	−0.379908	−	0.658020i	−0.991049	+	0.133502i	$0.957378\pi$
$168$	−4.86320	+	12.0145i	−0.375204	+	0.926942i
$169$	−0.491414	+	0.851153i	−0.0378010	+	0.0654733i
$170$	−0.0218585	−	0.541299i	−0.00167647	−	0.0415157i
$171$	18.3015	−	0.350843i	1.39955	−	0.0268296i
$172$	1.63486	+	20.2097i	0.124657	+	1.54097i
$173$		−	6.02868i		−	0.458352i	−0.973385	−	0.229176i	$-0.926397\pi$
$173$		−	6.02868i		−	0.458352i	0.973385	−	0.229176i	$-0.0736031\pi$
$174$	−16.0575	−	8.23064i	−1.21732	−	0.623963i
$175$	11.4306	+	6.47330i	0.864075	+	0.489335i
$176$	−14.1980	+	2.31222i	−1.07021	+	0.174290i
$177$	2.78526	+	4.71917i	0.209353	+	0.354715i
$178$	10.0219	−	0.404698i	0.751170	−	0.0303334i
$179$	1.95012	−	3.37771i	0.145759	−	0.252462i	−0.783897	−	0.620891i	$-0.786771\pi$
$179$	1.95012	−	3.37771i	0.145759	−	0.252462i	0.929656	+	0.368429i	$0.120104\pi$
$180$	−1.02227	−	0.461075i	−0.0761953	−	0.0343665i
$181$	21.3467			1.58669			0.793344	−	0.608774i	$-0.208338\pi$
$181$	21.3467			1.58669			0.793344	+	0.608774i	$0.208338\pi$
$182$	−11.7622	+	7.57702i	−0.871869	+	0.561646i
$183$	2.39866	−	1.41569i	0.177314	−	0.104651i
$184$	−4.86572	−	2.07166i	−0.358706	−	0.152725i
$185$	0.287458			0.0211344
$186$	−11.8486	+	0.592251i	−0.868779	+	0.0434260i
$187$	7.37060			0.538991
$188$	−3.77286	−	5.46399i	−0.275164	−	0.398503i
$189$	−7.31040	−	11.6429i	−0.531753	−	0.846899i
$190$	1.42814	+	0.749393i	0.103608	+	0.0543667i
$191$		−	11.4262i		−	0.826768i	−0.910557	−	0.413384i	$-0.864347\pi$
$191$		−	11.4262i		−	0.826768i	0.910557	−	0.413384i	$-0.135653\pi$
$192$	−9.89601	+	9.69892i	−0.714183	+	0.699959i
$193$	18.0295			1.29779			0.648897	−	0.760876i	$-0.275230\pi$
$193$	18.0295			1.29779			0.648897	+	0.760876i	$0.275230\pi$
$194$	12.9590	−	8.19630i	0.930405	−	0.588460i
$195$	−0.615293	−	1.04251i	−0.0440620	−	0.0746560i
$196$	−13.9337	+	1.36085i	−0.995264	+	0.0972039i
$197$	−2.03503			−0.144990			−0.0724950	−	0.997369i	$-0.523096\pi$
$197$	−2.03503			−0.144990			−0.0724950	+	0.997369i	$0.523096\pi$
$198$	6.82919	−	13.6439i	0.485330	−	0.969632i
$199$	−15.9489	−	9.20812i	−1.13059	−	0.652747i	−0.186507	−	0.982454i	$-0.559717\pi$
$199$	−15.9489	−	9.20812i	−1.13059	−	0.652747i	−0.944083	+	0.329707i	$0.893050\pi$
$200$	8.43921	+	11.2247i	0.596742	+	0.793709i
$201$	4.06455	+	6.88673i	0.286691	+	0.485753i
$202$	0.922802	+	22.8521i	0.0649281	+	1.60787i
$203$	−0.162138	−	19.4891i	−0.0113798	−	1.36787i
$204$	5.80338	−	4.08989i	0.406318	−	0.286350i
$205$			1.95848i			0.136786i
$206$	−10.0312	+	6.34451i	−0.698907	+	0.442043i
$207$	4.80304	−	2.89718i	0.333835	−	0.201368i
$208$	−14.7630	+	2.40423i	−1.02363	+	0.166703i
$209$	−10.9715	+	19.0032i	−0.758914	+	1.31448i
$210$	−0.0705331	−	1.20923i	−0.00486725	−	0.0834451i
$211$	11.2790	−	6.51192i	0.776476	−	0.448299i	−0.0587038	−	0.998275i	$-0.518697\pi$
$211$	11.2790	−	6.51192i	0.776476	−	0.448299i	0.835180	+	0.549977i	$0.185363\pi$
$212$	−5.00771	+	0.405099i	−0.343931	+	0.0278223i
$213$	−9.14953	−	15.5024i	−0.626915	−	1.06221i
$214$	6.80536	−	0.274811i	0.465205	−	0.0187857i
$215$	−0.947413	−	1.64097i	−0.0646130	−	0.111913i
$216$	−2.19382	−	14.5323i	−0.149271	−	0.988796i
$217$	−6.49904	−	11.0435i	−0.441184	−	0.749679i
$218$	0.783856	−	0.495771i	0.0530894	−	0.0335779i
$219$	20.2085	−	0.193682i	1.36556	−	0.0130878i
$220$	1.10623	−	0.763846i	0.0745820	−	0.0514985i
$221$	7.66390			0.515530
$222$	2.04417	+	3.16445i	0.137195	+	0.212384i
$223$	18.0840	+	10.4408i	1.21099	+	0.699168i	0.962976	−	0.269587i	$-0.0868873\pi$
$223$	18.0840	+	10.4408i	1.21099	+	0.699168i	0.248018	+	0.968755i	$0.420221\pi$
$224$	−14.2372	−	4.61530i	−0.951266	−	0.308372i
$225$	−14.8925	+	0.285491i	−0.992831	+	0.0190327i
$226$	−0.795591	−	19.7019i	−0.0529219	−	1.31055i
$227$	−1.81412	+	1.04738i	−0.120408	+	0.0695174i	−0.558994	−	0.829172i	$-0.688813\pi$
$227$	−1.81412	+	1.04738i	−0.120408	+	0.0695174i	0.438587	+	0.898689i	$0.355479\pi$
$228$	1.90611	+	21.0505i	0.126235	+	1.39411i
$229$	7.43748	−	12.8821i	0.491483	−	0.851273i	−0.508469	−	0.861080i	$-0.669788\pi$
$229$	7.43748	−	12.8821i	0.491483	−	0.851273i	0.999952	+	0.00980726i	$0.00312180\pi$
$230$	0.493813	−	0.0199409i	0.0325611	−	0.00131487i
$231$	16.4775	−	0.295029i	1.08414	−	0.0194115i
$232$	8.16204	−	19.1702i	0.535864	−	1.25859i
$233$	2.36217	−	1.36380i	0.154751	−	0.0893454i	−0.420625	−	0.907235i	$-0.638189\pi$
$233$	2.36217	−	1.36380i	0.154751	−	0.0893454i	0.575376	+	0.817889i	$0.304856\pi$
$234$	7.10095	−	14.1869i	0.464204	−	0.927425i
$235$	0.537393	+	0.310264i	0.0350557	+	0.0202394i
$236$	−5.20686	+	3.59531i	−0.338938	+	0.234035i
$237$	23.9797	−	14.1528i	1.55765	−	0.919325i
$238$	6.81992	+	3.50660i	0.442069	+	0.227299i
$239$	20.2522	−	11.6926i	1.31001	−	0.756333i	0.327910	−	0.944709i	$-0.393656\pi$
$239$	20.2522	−	11.6926i	1.31001	−	0.756333i	0.982097	+	0.188376i	$0.0603225\pi$
$240$	0.447159	−	1.21527i	0.0288640	−	0.0784452i
$241$	−13.0680	+	7.54481i	−0.841784	+	0.486004i	−0.857870	−	0.513867i	$-0.828213\pi$
$241$	−13.0680	+	7.54481i	−0.841784	+	0.486004i	0.0160864	+	0.999871i	$0.494879\pi$
$242$	1.46128	+	2.31040i	0.0939345	+	0.148518i
$243$	13.8579	+	7.13862i	0.888982	+	0.457942i
$244$	1.82742	+	2.64654i	0.116989	+	0.169427i
$245$	1.12202	−	0.672932i	0.0716830	−	0.0429920i
$246$	−21.5596	+	13.9270i	−1.37459	+	0.887956i
$247$	−11.4081	+	19.7594i	−0.725880	+	1.25726i
$248$	−1.65456	−	13.5983i	−0.105065	−	0.863495i
$249$	−5.25040	+	0.0503209i	−0.332731	+	0.00318896i
$250$	−2.33241	−	1.22390i	−0.147514	−	0.0774059i
$251$		−	2.44518i		−	0.154338i	−0.997018	−	0.0771692i	$-0.975412\pi$
$251$		−	2.44518i		−	0.154338i	0.997018	−	0.0771692i	$-0.0245882\pi$
$252$	12.8101	−	9.37552i	0.806963	−	0.590602i
$253$			6.72401i			0.422735i
$254$	6.52715	−	12.4389i	0.409550	−	0.780489i
$255$	−0.326224	+	0.577755i	−0.0204290	+	0.0361804i
$256$	−11.9832	−	10.6020i	−0.748950	−	0.662627i
$257$	0.545436	−	0.944723i	0.0340234	−	0.0589302i	−0.848512	−	0.529176i	$-0.822501\pi$
$257$	0.545436	−	0.944723i	0.0340234	−	0.0589302i	0.882536	+	0.470245i	$0.155835\pi$
$258$	11.3272	−	22.0987i	0.705199	−	1.37580i
$259$	−2.00518	+	3.54077i	−0.124596	+	0.220013i
$260$	1.15025	−	0.794242i	0.0713355	−	0.0492568i
$261$	11.4145	+	18.9233i	0.706537	+	1.17132i
$262$	14.2639	−	9.02159i	0.881226	−	0.557356i
$263$	13.4846	−	7.78535i	0.831497	−	0.480065i	−0.0228680	−	0.999738i	$-0.507280\pi$
$263$	13.4846	−	7.78535i	0.831497	−	0.480065i	0.854365	+	0.519674i	$0.173946\pi$
$264$	16.2753	+	6.74596i	1.00167	+	0.415185i
$265$	0.406612	−	0.234757i	0.0249779	−	0.0144210i
$266$	−19.1927	+	12.3637i	−1.17678	+	0.758064i
$267$	−10.6968	−	6.03987i	−0.654635	−	0.369634i
$268$	−7.59842	+	5.24667i	−0.464147	+	0.320491i
$269$	25.2905	+	14.6015i	1.54199	+	0.890268i	0.998713	+	0.0507137i	$0.0161496\pi$
$269$	25.2905	+	14.6015i	1.54199	+	0.890268i	0.543276	+	0.839554i	$0.317184\pi$
$270$	0.767237	+	1.13920i	0.0466926	+	0.0693295i
$271$	−8.67784	+	5.01015i	−0.527141	+	0.304345i	−0.739852	−	0.672770i	$-0.765104\pi$
$271$	−8.67784	+	5.01015i	−0.527141	+	0.304345i	0.212710	+	0.977115i	$0.431771\pi$
$272$	5.18694	+	6.34856i	0.314505	+	0.384938i
$273$	17.1332	−	0.306770i	1.03695	−	0.0185665i
$274$	−1.01867	−	25.2262i	−0.0615402	−	1.52397i
$275$	8.92782	−	15.4634i	0.538368	−	0.932480i
$276$	3.73110	+	5.29428i	0.224586	+	0.318678i
$277$	−17.7570	+	10.2520i	−1.06692	+	0.615985i	−0.927338	−	0.374226i	$-0.877908\pi$
$277$	−17.7570	+	10.2520i	−1.06692	+	0.615985i	−0.139580	+	0.990211i	$0.544575\pi$
$278$	−12.0932	+	0.488340i	−0.725300	+	0.0292887i
$279$	12.7199	+	7.02228i	0.761521	+	0.420413i
$280$	1.38698	−	0.180481i	0.0828881	−	0.0107858i
$281$	−6.18481	−	3.57080i	−0.368955	−	0.213016i	0.304047	−	0.952657i	$-0.401662\pi$
$281$	−6.18481	−	3.57080i	−0.368955	−	0.213016i	−0.673002	+	0.739641i	$0.734995\pi$
$282$	0.405987	+	8.12217i	0.0241762	+	0.483668i
$283$	−31.3995			−1.86651			−0.933254	−	0.359217i	$-0.883044\pi$
$283$	−31.3995			−1.86651			−0.933254	+	0.359217i	$0.883044\pi$
$284$	17.1045	−	11.8105i	1.01496	−	0.700827i
$285$	−1.00399	−	1.70110i	−0.0594713	−	0.100765i
$286$	10.1658	+	16.0729i	0.601114	+	0.950411i
$287$	−24.1235	−	13.6614i	−1.42397	−	0.806407i
$288$	16.5579	−	3.71947i	0.975686	−	0.219172i
$289$	6.39973	+	11.0847i	0.376455	+	0.652039i
$290$	0.0785643	+	1.94555i	0.00461345	+	0.114247i
$291$	−18.7788	+	0.179979i	−1.10083	+	0.0105506i
$292$	1.88160	+	23.2598i	0.110113	+	1.36118i
$293$	9.92881	−	5.73240i	0.580047	−	0.334890i	−0.181105	−	0.983464i	$-0.557967\pi$
$293$	9.92881	−	5.73240i	0.580047	−	0.334890i	0.761152	+	0.648573i	$0.224634\pi$
$294$	15.3867	+	7.56626i	0.897373	+	0.441273i
$295$	0.295663	−	0.512104i	0.0172142	−	0.0298158i
$296$	−3.47699	+	2.61414i	−0.202096	+	0.151944i
$297$	−15.9079	+	9.80471i	−0.923067	+	0.568927i
$298$	17.2563	+	27.2836i	0.999628	+	1.58050i
$299$			6.99158i			0.404334i
$300$	−1.55106	−	17.1294i	−0.0895504	−	0.988967i
$301$	26.8213	−	0.223137i	1.54595	−	0.0128614i
$302$	12.1614	−	0.491097i	0.699812	−	0.0282595i
$303$	13.7723	−	24.3912i	0.791196	−	1.40124i
$304$	−24.0892	+	3.92305i	−1.38161	+	0.225003i
$305$	−0.260292	−	0.150280i	−0.0149043	−	0.00860498i
$306$	−8.67998	+	0.517308i	−0.496201	+	0.0295725i
$307$	−10.2367			−0.584239			−0.292119	−	0.956382i	$-0.594360\pi$
$307$	−10.2367			−0.584239			−0.292119	+	0.956382i	$0.594360\pi$
$308$	1.69213	+	18.9542i	0.0964178	+	1.08002i
$309$	14.5361	−	0.139317i	0.826928	−	0.00792545i
$310$	0.684301	+	1.08194i	0.0388657	+	0.0614499i
$311$	−9.87692			−0.560069			−0.280034	−	0.959990i	$-0.590346\pi$
$311$	−9.87692			−0.560069			−0.280034	+	0.959990i	$0.590346\pi$
$312$	16.9229	+	7.01441i	0.958073	+	0.397113i
$313$		−	9.75571i		−	0.551425i	−0.961240	−	0.275713i	$-0.911086\pi$
$313$		−	9.75571i		−	0.551425i	0.961240	−	0.275713i	$-0.0889138\pi$
$314$	1.63868	−	3.12287i	0.0924761	−	0.176234i
$315$	−0.706170	+	1.30467i	−0.0397882	+	0.0735097i
$316$	18.2690	+	26.4578i	1.02771	+	1.48837i
$317$	−17.8635			−1.00331			−0.501656	−	0.865067i	$-0.667276\pi$
$317$	−17.8635			−1.00331			−0.501656	+	0.865067i	$0.667276\pi$
$318$	5.47578	+	2.80674i	0.307066	+	0.157394i
$319$	−26.4916			−1.48324
$320$	1.43642	+	0.415291i	0.0802983	+	0.0232155i
$321$	−7.26370	−	4.10139i	−0.405420	−	0.228917i
$322$	−3.19898	+	6.22164i	−0.178272	+	0.346718i
$323$	12.5054			0.695820
$324$	−7.08479	+	16.5471i	−0.393600	+	0.919282i
$325$	9.28309	−	16.0788i	0.514933	−	0.891890i
$326$	0.102383	+	2.53539i	0.00567047	+	0.140422i
$327$	−1.13587	+	0.0108864i	−0.0628140	+	0.000602022i
$328$	−17.8103	−	23.6890i	−0.983410	−	1.30800i
$329$	−7.57028	+	4.45508i	−0.417363	+	0.245617i
$330$	−1.64440	+	0.0821954i	−0.0905212	+	0.00452471i
$331$		−	27.5324i		−	1.51332i	−0.653810	−	0.756659i	$-0.726831\pi$
$331$		−	27.5324i		−	1.51332i	0.653810	−	0.756659i	$-0.273169\pi$
$332$	−0.488863	−	6.04318i	−0.0268298	−	0.331663i
$333$	−0.0884340	−	4.61310i	−0.00484615	−	0.252797i
$334$	−13.8748	+	0.560287i	−0.759197	+	0.0306575i
$335$	0.431464	−	0.747318i	0.0235734	−	0.0408304i
$336$	11.8499	+	13.9850i	0.646464	+	0.762945i
$337$	−2.76289	−	4.78546i	−0.150504	−	0.260681i	0.780909	−	0.624645i	$-0.214756\pi$
$337$	−2.76289	−	4.78546i	−0.150504	−	0.260681i	−0.931413	+	0.363964i	$0.881423\pi$
$338$	0.742966	+	1.17469i	0.0404120	+	0.0638948i
$339$	−11.8737	+	21.0288i	−0.644892	+	1.14213i
$340$	−0.692220	−	0.328322i	−0.0375409	−	0.0178058i
$341$	−15.0839	+	8.70868i	−0.816837	+	0.471601i
$342$	11.5868	−	23.1491i	0.626544	−	1.25176i
$343$	0.462173	+	18.5145i	0.0249550	+	0.999689i
$344$	26.3824	+	11.2328i	1.42245	+	0.605630i
$345$	−0.527071	−	0.297606i	−0.0283766	−	0.0160226i
$346$	−7.54958	−	3.96153i	−0.405868	−	0.212973i
$347$	−10.0012			−0.536894			−0.268447	−	0.963294i	$-0.586510\pi$
$347$	−10.0012			−0.536894			−0.268447	+	0.963294i	$0.586510\pi$
$348$	−20.8587	+	14.7000i	−1.11814	+	0.788002i
$349$	−7.64270	+	13.2375i	−0.409104	+	0.708590i	−0.994790	−	0.101949i	$-0.967492\pi$
$349$	−7.64270	+	13.2375i	−0.409104	+	0.708590i	0.585685	+	0.810539i	$0.300825\pi$
$350$	15.6176	−	10.0607i	0.834796	−	0.537764i
$351$	−16.5409	+	10.1949i	−0.882887	+	0.544162i
$352$	−6.43414	+	19.2992i	−0.342941	+	1.02865i
$353$	9.55634	+	16.5521i	0.508633	+	0.880978i	0.999950	+	0.00999723i	$0.00318227\pi$
$353$	9.55634	+	16.5521i	0.508633	+	0.880978i	−0.491317	+	0.870981i	$0.663484\pi$
$354$	7.73995	−	0.386882i	0.411373	−	0.0205625i
$355$	−0.971250	+	1.68225i	−0.0515486	+	0.0892848i
$356$	6.07871	−	12.8161i	0.322171	−	0.679252i
$357$	−4.84090	−	8.04841i	−0.256208	−	0.425967i
$358$	−2.94838	−	4.66164i	−0.155827	−	0.246375i
$359$	24.6224	−	14.2158i	1.29952	−	0.750280i	0.319201	−	0.947687i	$-0.396586\pi$
$359$	24.6224	−	14.2158i	1.29952	−	0.750280i	0.980322	+	0.197408i	$0.0632522\pi$
$360$	−1.24914	+	0.977183i	−0.0658355	+	0.0515021i
$361$	−9.11492	+	15.7875i	−0.479733	+	0.830922i
$362$	14.0272	−	26.7320i	0.737254	−	1.40500i
$363$	−0.0320876	−	3.34797i	−0.00168416	−	0.175723i
$364$	1.75946	+	19.7085i	0.0922209	+	1.03300i
$365$	−1.09040	−	1.88863i	−0.0570742	−	0.0988555i
$366$	−0.196644	−	3.93406i	−0.0102787	−	0.205636i
$367$	2.89913	−	1.67381i	0.151333	−	0.0873723i	−0.422421	−	0.906400i	$-0.638820\pi$
$367$	2.89913	−	1.67381i	0.151333	−	0.0873723i	0.573755	+	0.819027i	$0.305486\pi$
$368$	−5.79163	+	4.73192i	−0.301910	+	0.246668i
$369$	31.4294	−	0.602507i	1.63615	−	0.0313653i
$370$	0.188893	−	0.359978i	0.00982008	−	0.0187144i
$371$	0.0552906	+	6.64599i	0.00287055	+	0.345043i
$372$	−7.04419	+	15.2269i	−0.365224	+	0.789476i
$373$	7.18502	+	4.14828i	0.372026	+	0.214790i	0.674343	−	0.738418i	$-0.264427\pi$
$373$	7.18502	+	4.14828i	0.372026	+	0.214790i	−0.302317	+	0.953207i	$0.597760\pi$
$374$	4.84332	−	9.23004i	0.250442	−	0.477274i
$375$	1.63970	+	2.77821i	0.0846737	+	0.143466i
$376$	−9.32164	+	1.13420i	−0.480727	+	0.0584919i
$377$	−27.5458			−1.41868
$378$	−19.3840	+	1.50392i	−0.997004	+	0.0773532i
$379$			3.07229i			0.157813i	0.996882	+	0.0789065i	$0.0251428\pi$
$379$			3.07229i			0.157813i	−0.996882	+	0.0789065i	$0.974857\pi$
$380$	1.87690	−	1.29599i	0.0962828	−	0.0664828i
$381$	−14.8165	+	8.74468i	−0.759070	+	0.448003i
$382$	−14.3087	−	7.50829i	−0.732098	−	0.384157i
$383$	−9.02646	+	15.6343i	−0.461231	+	0.798875i	−0.999023	−	0.0442026i	$-0.985925\pi$
$383$	−9.02646	+	15.6343i	−0.461231	+	0.798875i	0.537792	+	0.843078i	$0.319259\pi$
$384$	5.64294	+	18.7659i	0.287965	+	0.957641i
$385$	−0.901968	−	1.53266i	−0.0459685	−	0.0781118i
$386$	11.8475	−	22.5780i	0.603020	−	1.14919i
$387$	−26.0426	+	15.7088i	−1.32382	+	0.798524i
$388$	−1.74848	−	21.6142i	−0.0887657	−	1.09730i
$389$	−18.1165	−	31.3786i	−0.918541	−	1.59096i	−0.801632	−	0.597818i	$-0.796035\pi$
$389$	−18.1165	−	31.3786i	−0.918541	−	1.59096i	−0.116909	−	0.993143i	$-0.537299\pi$
$390$	−1.70984	+	0.0854663i	−0.0865809	+	0.00432775i
$391$	3.31865	−	1.91602i	0.167831	−	0.0968974i
$392$	−7.45187	+	18.3431i	−0.376376	+	0.926467i
$393$	−20.6696	+	0.198102i	−1.04264	+	0.00999290i
$394$	−1.33725	+	2.54843i	−0.0673696	+	0.128388i
$395$	−2.60217	−	1.50236i	−0.130929	−	0.0755922i
$396$	−12.5984	−	17.5177i	−0.633095	−	0.880296i
$397$	5.22076	+	9.04263i	0.262023	+	0.453836i	0.966779	−	0.255613i	$-0.0822772\pi$
$397$	5.22076	+	9.04263i	0.262023	+	0.453836i	−0.704757	+	0.709449i	$0.748944\pi$
$398$	−22.0114	+	13.9217i	−1.10333	+	0.697833i
$399$	27.9567	−	0.500565i	1.39958	−	0.0250596i
$400$	19.6020	−	3.19230i	0.980101	−	0.159615i
$401$	32.5034	+	18.7658i	1.62314	+	0.937122i	0.986073	+	0.166316i	$0.0531871\pi$
$401$	32.5034	+	18.7658i	1.62314	+	0.937122i	0.637070	+	0.770806i	$0.280146\pi$
$402$	11.2950	−	0.564580i	0.563342	−	0.0281587i
$403$	−15.6841	+	9.05523i	−0.781281	+	0.451073i
$404$	29.2236	+	13.8608i	1.45393	+	0.689602i
$405$	−0.0644706	−	1.68092i	−0.00320357	−	0.0835255i
$406$	−24.5123	−	12.6035i	−1.21653	−	0.625502i
$407$	4.78997	+	2.76549i	0.237430	+	0.137080i
$408$	−1.30820	−	9.95497i	−0.0647654	−	0.492845i
$409$		−	13.1844i		−	0.651929i	−0.945382	−	0.325965i	$-0.894311\pi$
$409$		−	13.1844i		−	0.651929i	0.945382	−	0.325965i	$-0.105689\pi$
$410$	2.45256	+	1.28694i	0.121123	+	0.0635576i
$411$	−15.2031	+	26.9252i	−0.749912	+	1.32812i
$412$	1.35345	+	16.7309i	0.0666796	+	0.824274i
$413$	4.24543	+	7.21403i	0.208904	+	0.354979i
$414$	−0.471927	−	7.91853i	−0.0231939	−	0.389174i
$415$	0.283299	+	0.490688i	0.0139066	+	0.0240869i
$416$	−6.69018	+	20.0672i	−0.328013	+	0.983875i
$417$	12.9076	+	7.28818i	0.632089	+	0.356904i
$418$	16.5878	+	26.2266i	0.811334	+	1.28279i
$419$	23.1171	−	13.3467i	1.12935	−	0.652028i	0.185576	−	0.982630i	$-0.440585\pi$
$419$	23.1171	−	13.3467i	1.12935	−	0.652028i	0.943770	+	0.330601i	$0.107252\pi$
$420$	−1.56065	−	0.706278i	−0.0761517	−	0.0344628i
$421$	19.5174	+	11.2684i	0.951221	+	0.549188i	0.893460	−	0.449143i	$-0.148271\pi$
$421$	19.5174	+	11.2684i	0.951221	+	0.549188i	0.0577610	+	0.998330i	$0.481604\pi$
$422$	−0.743161	−	18.4035i	−0.0361765	−	0.895867i
$423$	4.81377	−	8.71949i	0.234053	−	0.423956i
$424$	−2.78334	+	6.53725i	−0.135171	+	0.317477i
$425$	−10.1760			−0.493609
$426$	−25.4256	+	1.27090i	−1.23188	+	0.0615754i
$427$	3.66674	−	2.15786i	0.177446	−	0.104426i
$428$	4.12776	−	8.70279i	0.199523	−	0.420665i
$429$	−0.223226	−	23.2910i	−0.0107774	−	1.12450i
$430$	−2.67751	+	0.108122i	−0.129121	+	0.00521409i
$431$	4.62836	+	2.67218i	0.222940	+	0.128715i	0.607311	−	0.794464i	$-0.292248\pi$
$431$	4.62836	+	2.67218i	0.222940	+	0.128715i	−0.384371	+	0.923179i	$0.625582\pi$
$432$	−19.6400	−	6.80209i	−0.944932	−	0.327266i
$433$			34.2107i			1.64406i	0.569444	+	0.822030i	$0.307159\pi$
$433$			34.2107i			1.64406i	−0.569444	+	0.822030i	$0.692841\pi$
$434$	−18.1001	+	0.881788i	−0.868833	+	0.0423272i
$435$	1.17252	−	2.07658i	0.0562182	−	0.0995645i
$436$	−0.105761	−	1.30738i	−0.00506502	−	0.0626123i
$437$			11.4084i			0.545736i
$438$	13.0367	−	25.4339i	0.622920	−	1.21528i
$439$		−	8.36863i		−	0.399413i	−0.979856	−	0.199707i	$-0.936001\pi$
$439$		−	8.36863i		−	0.399413i	0.979856	−	0.199707i	$-0.0639989\pi$
$440$	−0.229628	−	1.88724i	−0.0109471	−	0.0899707i
$441$	−11.1443	−	17.7990i	−0.530682	−	0.847571i
$442$	5.03606	−	9.59734i	0.239541	−	0.456499i
$443$	7.85931			0.373407			0.186704	−	0.982416i	$-0.440220\pi$
$443$	7.85931			0.373407			0.186704	+	0.982416i	$0.440220\pi$
$444$	5.30602	−	0.480457i	0.251813	−	0.0228015i
$445$			1.32559i			0.0628392i
$446$	24.9580	−	15.7854i	1.18180	−	0.747461i
$447$	−0.378923	−	39.5363i	−0.0179225	−	1.87000i
$448$	−15.1351	+	14.7962i	−0.715068	+	0.699055i
$449$			15.6275i			0.737506i	0.929527	+	0.368753i	$0.120215\pi$
$449$			15.6275i			0.737506i	−0.929527	+	0.368753i	$0.879785\pi$
$450$	−9.42853	+	18.8371i	−0.444465	+	0.887990i
$451$	−18.8415	+	32.6344i	−0.887211	+	1.53669i
$452$	−25.1950	−	11.9501i	−1.18507	−	0.562084i
$453$	−12.9805	−	7.32933i	−0.609877	−	0.344362i
$454$	0.119531	+	2.96004i	0.00560986	+	0.138921i
$455$	−0.937860	−	1.59366i	−0.0439676	−	0.0747117i
$456$	27.6137	+	11.4456i	1.29313	+	0.535990i
$457$	−30.5320			−1.42823			−0.714114	−	0.700029i	$-0.753170\pi$
$457$	−30.5320			−1.42823			−0.714114	+	0.700029i	$0.753170\pi$
$458$	−11.2447	−	17.7788i	−0.525430	−	0.830749i
$459$	9.37211	+	5.05747i	0.437453	+	0.236063i
$460$	0.299520	−	0.631495i	0.0139652	−	0.0294436i
$461$	9.28126	+	5.35854i	0.432271	+	0.249572i	0.700314	−	0.713835i	$-0.253043\pi$
$461$	9.28126	+	5.35854i	0.432271	+	0.249572i	−0.268042	+	0.963407i	$0.586377\pi$
$462$	10.4581	−	20.8282i	0.486556	−	0.969017i
$463$	−1.09777	−	1.90140i	−0.0510179	−	0.0883656i	0.839389	−	0.543532i	$-0.182913\pi$
$463$	−1.09777	−	1.90140i	−0.0510179	−	0.0883656i	−0.890407	+	0.455166i	$0.849580\pi$
$464$	−18.6430	−	22.8182i	−0.865482	−	1.05931i
$465$	−0.0150263	−	1.56782i	−0.000696827	−	0.0727058i
$466$	−0.155641	−	3.85426i	−0.00720993	−	0.178545i
$467$	−17.5040	+	10.1059i	−0.809988	+	0.467647i	−0.846952	−	0.531670i	$-0.821565\pi$
$467$	−17.5040	+	10.1059i	−0.809988	+	0.467647i	0.0369639	+	0.999317i	$0.488231\pi$
$468$	−13.0998	−	18.2148i	−0.605537	−	0.841978i
$469$	6.19539	+	10.5275i	0.286077	+	0.486115i
$470$	0.741666	−	0.469087i	0.0342105	−	0.0216374i
$471$	−3.71976	+	2.19540i	−0.171397	+	0.101159i
$472$	1.08083	+	8.88296i	0.0497490	+	0.408872i
$473$		−	36.4583i		−	1.67635i
$474$	−1.96588	−	39.3293i	−0.0902957	−	1.80645i
$475$	15.1475	−	26.2362i	0.695015	−	1.20380i
$476$	8.87270	−	6.23619i	0.406680	−	0.285835i
$477$	−3.89245	−	6.45304i	−0.178223	−	0.295464i
$478$	−1.33440	−	33.0448i	−0.0610340	−	1.51143i
$479$	−18.5419	−	32.1155i	−0.847201	−	1.46740i	−0.883696	−	0.468062i	$-0.844952\pi$
$479$	−18.5419	−	32.1155i	−0.847201	−	1.46740i	0.0364941	−	0.999334i	$-0.488381\pi$
$480$	−1.22802	−	1.35854i	−0.0560511	−	0.0620084i
$481$	4.98058	+	2.87554i	0.227095	+	0.131113i
$482$	0.861038	+	21.3226i	0.0392192	+	0.971217i
$483$	7.34236	−	4.41623i	0.334089	−	0.200946i
$484$	3.85349	−	0.311728i	0.175159	−	0.0141695i
$485$	1.01326	+	1.75501i	0.0460096	+	0.0796910i
$486$	18.0457	−	12.6630i	0.818571	−	0.574406i
$487$	16.0989	−	27.8840i	0.729509	−	1.26355i	−0.227582	−	0.973759i	$-0.573082\pi$
$487$	16.0989	−	27.8840i	0.729509	−	1.26355i	0.957091	−	0.289788i	$-0.0935848\pi$
$488$	4.51503	−	0.549361i	0.204386	−	0.0248684i
$489$	1.52801	−	2.70615i	0.0690988	−	0.122376i
$490$	−0.105405	−	1.84727i	−0.00476171	−	0.0834512i
$491$	−4.44228	−	7.69425i	−0.200477	−	0.347237i	0.748205	−	0.663467i	$-0.230916\pi$
$491$	−4.44228	−	7.69425i	−0.200477	−	0.347237i	−0.948682	+	0.316231i	$0.897583\pi$
$492$	3.27339	+	36.1503i	0.147576	+	1.62978i
$493$	7.54884	+	13.0750i	0.339983	+	0.588867i
$494$	17.2478	+	27.2703i	0.776017	+	1.22695i
$495$	1.76533	+	0.974586i	0.0793457	+	0.0438044i
$496$	−18.1161	−	6.86368i	−0.813438	−	0.308188i
$497$	−13.9462	−	23.6980i	−0.625571	−	1.06300i
$498$	−3.38710	+	6.60803i	−0.151779	+	0.296113i
$499$	−9.75634	−	5.63283i	−0.436754	−	0.252160i	0.265466	−	0.964120i	$-0.414474\pi$
$499$	−9.75634	−	5.63283i	−0.436754	−	0.252160i	−0.702220	+	0.711960i	$0.747808\pi$
$500$	−3.06532	+	2.11658i	−0.137085	+	0.0946565i
$501$	14.8093	+	8.36195i	0.661631	+	0.373584i
$502$	−3.06205	−	1.60676i	−0.136666	−	0.0717133i
$503$	−7.35421			−0.327908			−0.163954	−	0.986468i	$-0.552425\pi$
$503$	−7.35421			−0.327908			−0.163954	+	0.986468i	$0.552425\pi$
$504$	−3.32304	−	22.2026i	−0.148020	−	0.988984i
$505$	−3.02265			−0.134506
$506$	8.42033	+	4.41844i	0.374329	+	0.196424i
$507$	−0.0163145	−	1.70223i	−0.000724552	−	0.0755986i
$508$	−11.2879	−	16.3476i	−0.500821	−	0.725308i
$509$	−17.7203	−	10.2308i	−0.785439	−	0.453473i	0.0529155	−	0.998599i	$-0.483149\pi$
$509$	−17.7203	−	10.2308i	−0.785439	−	0.453473i	−0.838354	+	0.545126i	$0.816482\pi$
$510$	0.509143	+	0.788174i	0.0225452	+	0.0349010i
$511$	30.8693	−	0.256814i	1.36558	−	0.0113608i
$512$	−21.1510	+	8.03955i	−0.934752	+	0.355301i
$513$	−26.9902	+	16.6353i	−1.19165	+	0.734465i
$514$	−0.824643	−	1.30383i	−0.0363734	−	0.0575094i
$515$	−0.784332	−	1.35850i	−0.0345618	−	0.0598628i
$516$	−20.2304	−	28.7061i	−0.890595	−	1.26372i
$517$	5.96979	+	10.3400i	0.262551	+	0.454752i
$518$	3.11640	+	4.83773i	0.136927	+	0.212557i
$519$	5.30741	+	8.99257i	0.232970	+	0.394730i
$520$	−0.238766	−	1.96234i	−0.0104706	−	0.0860544i
$521$	0.229817	−	0.398055i	0.0100685	−	0.0174391i	−0.860947	−	0.508694i	$-0.830128\pi$
$521$	0.229817	−	0.398055i	0.0100685	−	0.0174391i	0.871016	+	0.491255i	$0.163462\pi$
$522$	31.1978	−	1.85932i	1.36549	−	0.0813803i
$523$	−12.5802	−	21.7895i	−0.550092	−	0.952787i	−0.998267	−	0.0588414i	$-0.981259\pi$
$523$	−12.5802	−	21.7895i	−0.550092	−	0.952787i	0.448176	−	0.893946i	$-0.352074\pi$
$524$	−1.92454	−	23.7906i	−0.0840738	−	1.03930i
$525$	−22.7491	+	0.407324i	−0.992854	+	0.0177771i
$526$	−0.888488	−	22.0024i	−0.0387399	−	0.959348i
$527$	8.59636	+	4.96311i	0.374463	+	0.216197i
$528$	19.1425	−	15.9483i	0.833072	−	0.694062i
$529$	−9.75206	−	16.8911i	−0.424003	−	0.734394i
$530$	−0.0267913	−	0.663453i	−0.00116374	−	0.0288186i
$531$	−8.30915	−	4.58723i	−0.360586	−	0.199069i
$532$	2.87097	+	32.1589i	0.124472	+	1.39426i
$533$	−19.5913	+	33.9331i	−0.848592	+	1.46980i
$534$	−14.5926	+	9.42652i	−0.631485	+	0.407925i
$535$			0.900147i			0.0389167i
$536$	1.57726	+	12.9630i	0.0681272	+	0.559916i
$537$	0.0647424	+	6.75512i	0.00279384	+	0.291505i
$538$	34.9039	−	22.0759i	1.50481	−	0.951760i
$539$	25.1703	−	0.418832i	1.08416	−	0.0180404i
$540$	1.93076	−	0.212210i	0.0830866	−	0.00913207i
$541$	−5.88606	+	3.39832i	−0.253061	+	0.146105i	−0.621165	−	0.783680i	$-0.713340\pi$
$541$	−5.88606	+	3.39832i	−0.253061	+	0.146105i	0.368104	+	0.929785i	$0.380007\pi$
$542$	0.571775	+	14.1593i	0.0245598	+	0.608195i
$543$	−31.8414	+	18.7928i	−1.36644	+	0.806476i
$544$	11.3586	−	2.32377i	0.486995	−	0.0996307i
$545$	0.0612890	+	0.106156i	0.00262533	+	0.00454721i
$546$	10.8743	−	21.6571i	0.465376	−	0.926837i
$547$	−15.2713	−	8.81688i	−0.652953	−	0.376982i	0.136634	−	0.990622i	$-0.456372\pi$
$547$	−15.2713	−	8.81688i	−0.652953	−	0.376982i	−0.789587	+	0.613639i	$0.789705\pi$
$548$	−32.2596	−	15.3008i	−1.37806	−	0.653619i
$549$	−2.33160	+	4.22337i	−0.0995101	+	0.180249i
$550$	−13.4979	−	21.3414i	−0.575554	−	0.909999i
$551$	−44.9473			−1.91482
$552$	9.08167	−	1.19344i	0.386542	−	0.0507960i
$553$	36.6569	−	21.5724i	1.55881	−	0.917354i
$554$	1.16999	+	28.9735i	0.0497083	+	1.23097i
$555$	−0.428782	+	0.253067i	−0.0182008	+	0.0107421i
$556$	−7.33505	+	15.4649i	−0.311075	+	0.655858i
$557$	−3.82739	+	6.62923i	−0.162172	+	0.280890i	−0.935647	−	0.352936i	$-0.885183\pi$
$557$	−3.82739	+	6.62923i	−0.162172	+	0.280890i	0.773476	+	0.633826i	$0.218517\pi$
$558$	17.1523	−	11.3144i	0.726114	−	0.478978i
$559$		−	37.9091i		−	1.60338i
$560$	0.685394	−	1.85549i	0.0289632	−	0.0784086i
$561$	−10.9942	+	6.48879i	−0.464176	+	0.273957i
$562$	−8.53576	+	5.39868i	−0.360059	+	0.227730i
$563$		−	21.7089i		−	0.914920i	−0.889230	−	0.457460i	$-0.848759\pi$
$563$		−	21.7089i		−	0.914920i	0.889230	−	0.457460i	$-0.151241\pi$
$564$	10.4380	+	4.82879i	0.439519	+	0.203329i
$565$	2.60597			0.109634
$566$	−20.6331	+	39.3209i	−0.867273	+	1.65278i
$567$	21.1544	+	10.9312i	0.888402	+	0.459066i
$568$	−3.55050	−	29.1804i	−0.148976	−	1.22438i
$569$		−	19.3980i		−	0.813209i	−0.913604	−	0.406604i	$-0.866713\pi$
$569$		−	19.3980i		−	0.813209i	0.913604	−	0.406604i	$-0.133287\pi$
$570$	−2.78999	+	0.139458i	−0.116860	+	0.00584125i
$571$			2.96254i			0.123979i	0.998077	+	0.0619893i	$0.0197445\pi$
$571$			2.96254i			0.123979i	−0.998077	+	0.0619893i	$0.980256\pi$
$572$	26.8078	−	2.16862i	1.12089	−	0.0906744i
$573$	10.0591	+	17.0436i	0.420227	+	0.712007i
$574$	−32.9598	+	21.2323i	−1.37571	+	0.886217i
$575$		−	9.28331i		−	0.387141i
$576$	6.22264	−	23.1793i	0.259277	−	0.965803i
$577$	20.7429	+	11.9759i	0.863536	+	0.498563i	0.865195	−	0.501436i	$-0.167195\pi$
$577$	20.7429	+	11.9759i	0.863536	+	0.498563i	−0.00165862	+	0.999999i	$0.500528\pi$
$578$	18.0864	−	0.730358i	0.752297	−	0.0303789i
$579$	−26.8934	+	15.8725i	−1.11765	+	0.659639i
$580$	2.48800	+	1.18006i	0.103308	+	0.0489995i
$581$	−8.02021	+	0.0667233i	−0.332734	+	0.00276815i
$582$	−12.1144	+	23.6345i	−0.502158	+	0.979681i
$583$	9.03392			0.374147
$584$	30.3642	+	12.9281i	1.25648	+	0.534968i
$585$	1.83558	+	1.01337i	0.0758919	+	0.0418976i
$586$	−0.654200	−	16.2005i	−0.0270247	−	0.669235i
$587$	−16.4199	−	9.48005i	−0.677723	−	0.391283i	0.121274	−	0.992619i	$-0.461302\pi$
$587$	−16.4199	−	9.48005i	−0.677723	−	0.391283i	−0.798997	+	0.601336i	$0.794635\pi$
$588$	19.5859	−	14.2966i	0.807709	−	0.589581i
$589$	−25.5922	+	14.7757i	−1.05451	+	0.608821i
$590$	−0.447012	−	0.706763i	−0.0184032	−	0.0290970i
$591$	3.03552	−	1.79156i	0.124864	−	0.0736950i
$592$	0.988850	+	6.07194i	0.0406415	+	0.249555i
$593$	10.0275	+	17.3681i	0.411779	+	0.713223i	0.995084	−	0.0990304i	$-0.0315741\pi$
$593$	10.0275	+	17.3681i	0.411779	+	0.713223i	−0.583305	+	0.812253i	$0.698241\pi$
$594$	1.82495	+	26.3639i	0.0748785	+	1.08172i
$595$	−0.499432	+	0.881904i	−0.0204747	+	0.0361545i
$596$	45.5060	−	3.68121i	1.86400	−	0.150788i
$597$	31.8964	−	0.305702i	1.30543	−	0.0125115i
$598$	8.75541	+	4.59427i	0.358035	+	0.187874i
$599$		−	15.4185i		−	0.629982i	−0.949095	−	0.314991i	$-0.897999\pi$
$599$		−	15.4185i		−	0.629982i	0.949095	−	0.314991i	$-0.102001\pi$
$600$	−22.4700	−	9.31362i	−0.917335	−	0.380227i
$601$	1.22512	+	0.707326i	0.0499739	+	0.0288524i	0.524779	−	0.851239i	$-0.324148\pi$
$601$	1.22512	+	0.707326i	0.0499739	+	0.0288524i	−0.474805	+	0.880091i	$0.657481\pi$
$602$	17.3452	−	33.7344i	0.706939	−	1.37491i
$603$	−12.1256	−	6.69419i	−0.493794	−	0.272609i
$604$	7.37646	−	15.5522i	0.300144	−	0.632810i
$605$	−0.312892	+	0.180648i	−0.0127209	+	0.00734441i
$606$	−21.4946	−	33.2745i	−0.873157	−	1.35168i
$607$	−32.6358	−	18.8423i	−1.32465	−	0.764785i	−0.340181	−	0.940360i	$-0.610488\pi$
$607$	−32.6358	−	18.8423i	−1.32465	−	0.764785i	−0.984466	+	0.175575i	$0.943822\pi$
$608$	−10.9166	+	32.7442i	−0.442725	+	1.32795i
$609$	17.3993	+	28.9278i	0.705055	+	1.17221i
$610$	−0.359233	+	0.227207i	−0.0145449	+	0.00919934i
$611$	6.20735	+	10.7514i	0.251122	+	0.434957i
$612$	−5.05592	+	11.2097i	−0.204374	+	0.453124i
$613$	−5.53531	−	3.19581i	−0.223569	−	0.129078i	0.384033	−	0.923319i	$-0.374535\pi$
$613$	−5.53531	−	3.19581i	−0.223569	−	0.129078i	−0.607602	+	0.794242i	$0.707868\pi$
$614$	−6.72668	+	12.8192i	−0.271467	+	0.517340i
$615$	−1.72417	−	2.92132i	−0.0695251	−	0.117799i
$616$	24.8479	+	10.3361i	1.00115	+	0.416452i
$617$	−31.7666	+	18.3405i	−1.27888	+	0.738359i	−0.976642	−	0.214875i	$-0.931066\pi$
$617$	−31.7666	+	18.3405i	−1.27888	+	0.738359i	−0.302234	+	0.953234i	$0.597732\pi$
$618$	9.37740	−	18.2948i	0.377214	−	0.735923i
$619$	14.7050	+	25.4699i	0.591045	+	1.02372i	0.994092	+	0.108541i	$0.0346180\pi$
$619$	14.7050	+	25.4699i	0.591045	+	1.02372i	−0.403046	+	0.915180i	$0.632049\pi$
$620$	1.80455	−	0.145979i	0.0724724	−	0.00586266i
$621$	−4.61381	+	8.54994i	−0.185146	+	0.343097i
$622$	−6.49027	+	12.3687i	−0.260236	+	0.495938i
$623$	−16.3280	−	9.24672i	−0.654167	−	0.370462i
$624$	19.9043	−	16.5830i	0.796810	−	0.663850i
$625$	−12.2386	+	21.1979i	−0.489544	+	0.847916i
$626$	−12.2169	−	6.41061i	−0.488284	−	0.256220i
$627$	−0.364244	−	38.0046i	−0.0145465	−	1.51776i
$628$	−2.83391	−	4.10417i	−0.113085	−	0.163774i
$629$		−	3.15213i		−	0.125684i
$630$	1.16977	+	1.74164i	0.0466048	+	0.0693885i
$631$	19.7989			0.788183			0.394092	−	0.919071i	$-0.371059\pi$
$631$	19.7989			0.788183			0.394092	+	0.919071i	$0.371059\pi$
$632$	45.1373	−	5.49204i	1.79547	−	0.218462i
$633$	−11.0912	+	19.6429i	−0.440837	+	0.780737i
$634$	−11.7383	+	22.3700i	−0.466189	+	0.888428i
$635$	1.60782	+	0.928274i	0.0638043	+	0.0368374i
$636$	7.11303	−	5.01285i	0.282050	−	0.198773i
$637$	26.1719	−	0.435499i	1.03697	−	0.0172551i
$638$	−17.4080	+	33.1749i	−0.689190	+	1.31341i
$639$	27.2954	+	15.0690i	1.07979	+	0.596120i
$640$	1.46395	−	1.52590i	0.0578678	−	0.0603166i
$641$	−16.6542	+	9.61531i	−0.657801	+	0.379782i	−0.791439	−	0.611248i	$-0.790668\pi$
$641$	−16.6542	+	9.61531i	−0.657801	+	0.379782i	0.133637	+	0.991030i	$0.457334\pi$
$642$	−9.90916	+	6.40109i	−0.391083	+	0.252631i
$643$	21.0103	+	36.3910i	0.828567	+	1.43512i	0.899162	+	0.437615i	$0.144177\pi$
$643$	21.0103	+	36.3910i	0.828567	+	1.43512i	−0.0705951	+	0.997505i	$0.522490\pi$
$644$	5.68912	+	8.09435i	0.224183	+	0.318962i
$645$	2.85783	+	1.61365i	0.112527	+	0.0635375i
$646$	8.21748	−	15.6603i	0.323313	−	0.616145i
$647$	10.0641	−	17.4315i	0.395659	−	0.685302i	−0.597526	−	0.801850i	$-0.703849\pi$
$647$	10.0641	−	17.4315i	0.395659	−	0.685302i	0.993185	+	0.116548i	$0.0371828\pi$
$648$	16.0660	+	19.7454i	0.631133	+	0.775675i
$649$	9.85338	−	5.68885i	0.386779	−	0.223307i
$650$	−14.0351	−	22.1906i	−0.550500	−	0.870387i
$651$	19.4164	+	10.7513i	0.760989	+	0.421376i
$652$	3.24230	+	1.53783i	0.126978	+	0.0602261i
$653$	19.7672	−	34.2378i	0.773551	−	1.33983i	−0.162054	−	0.986782i	$-0.551812\pi$
$653$	19.7672	−	34.2378i	0.773551	−	1.33983i	0.935605	−	0.353048i	$-0.114855\pi$
$654$	−0.732766	+	1.42958i	−0.0286534	+	0.0559012i
$655$	1.11528	+	1.93173i	0.0435777	+	0.0754787i
$656$	−41.3686	+	6.73711i	−1.61517	+	0.263040i
$657$	−29.9731	+	18.0797i	−1.16936	+	0.705355i
$658$	0.604465	+	12.4076i	0.0235645	+	0.483699i
$659$	0.351137	−	0.608186i	0.0136783	−	0.0236916i	−0.859105	−	0.511799i	$-0.828979\pi$
$659$	0.351137	−	0.608186i	0.0136783	−	0.0236916i	0.872784	+	0.488107i	$0.162313\pi$
$660$	−0.977627	+	2.11326i	−0.0380541	+	0.0822584i
$661$	−28.1818			−1.09615			−0.548073	−	0.836431i	$-0.684638\pi$
$661$	−28.1818			−1.09615			−0.548073	+	0.836431i	$0.684638\pi$
$662$	−34.4782	−	18.0919i	−1.34003	−	0.703163i
$663$	−11.4317	+	6.74700i	−0.443971	+	0.262032i
$664$	−7.88898	−	3.35887i	−0.306152	−	0.130349i
$665$	−1.53033	−	2.60041i	−0.0593438	−	0.100840i
$666$	−5.83500	−	2.92059i	−0.226102	−	0.113171i
$667$	−11.9280	+	6.88662i	−0.461853	+	0.266651i
$668$	−8.41571	+	17.7433i	−0.325614	+	0.686510i
$669$	−36.1663	+	0.346626i	−1.39827	+	0.0134013i
$670$	−0.652329	−	1.03139i	−0.0252017	−	0.0398459i
$671$	−2.89153	−	5.00827i	−0.111626	−	0.193342i
$672$	25.2998	−	5.64960i	0.975963	−	0.217938i
$673$	16.0280	−	27.7613i	0.617833	−	1.07012i	−0.372047	−	0.928214i	$-0.621344\pi$
$673$	16.0280	−	27.7613i	0.617833	−	1.07012i	0.989880	−	0.141905i	$-0.0453226\pi$
$674$	−7.80826	+	0.315310i	−0.300763	+	0.0121453i
$675$	21.9627	−	13.5366i	0.845346	−	0.521024i
$676$	1.95925	−	0.158494i	0.0753559	−	0.00609591i
$677$		−	21.4563i		−	0.824634i	−0.911040	−	0.412317i	$-0.864720\pi$
$677$		−	21.4563i		−	0.824634i	0.911040	−	0.412317i	$-0.135280\pi$
$678$	18.5315	+	28.6875i	0.711697	+	1.10174i
$679$	−28.6853	+	0.238645i	−1.10084	+	0.00915834i
$680$	−0.866018	+	0.651107i	−0.0332103	+	0.0249688i
$681$	1.78393	−	3.15940i	0.0683602	−	0.121068i
$682$	0.993862	+	24.6118i	0.0380569	+	0.942434i
$683$	−14.3033	+	24.7740i	−0.547300	+	0.947951i	0.451158	+	0.892444i	$0.351011\pi$
$683$	−14.3033	+	24.7740i	−0.547300	+	0.947951i	−0.998458	+	0.0555074i	$0.982322\pi$
$684$	−21.3753	−	29.7216i	−0.817305	−	1.13643i
$685$	3.33667			0.127488
$686$	23.4890	+	11.5874i	0.896814	+	0.442408i
$687$	0.246918	+	25.7630i	0.00942050	+	0.982920i
$688$	31.4028	−	25.6569i	1.19722	−	0.978162i
$689$	9.39341			0.357860
$690$	−0.719032	+	0.464478i	−0.0273731	+	0.0176824i
$691$	44.1860			1.68092			0.840458	−	0.541876i	$-0.182286\pi$
$691$	44.1860			1.68092			0.840458	+	0.541876i	$0.182286\pi$
$692$	−9.92188	+	6.85100i	−0.377173	+	0.260436i
$693$	−24.3186	+	14.9462i	−0.923786	+	0.567759i
$694$	−6.57195	+	12.5243i	−0.249468	+	0.475417i
$695$		−	1.59957i		−	0.0606750i
$696$	4.70196	+	35.7804i	0.178227	+	1.35625i
$697$	21.4757			0.813450
$698$	11.5550	+	18.2694i	0.437362	+	0.691506i
$699$	−2.32285	+	4.11384i	−0.0878582	+	0.155600i
$700$	−2.33619	−	26.1686i	−0.0882995	−	0.989080i
$701$	18.1914			0.687078			0.343539	−	0.939138i	$-0.388374\pi$
$701$	18.1914			0.687078			0.343539	+	0.939138i	$0.388374\pi$
$702$	1.89757	+	27.4130i	0.0716192	+	1.03464i
$703$	8.12696	+	4.69210i	0.306514	+	0.176966i
$704$	19.9400	+	20.7391i	0.751517	+	0.781635i
$705$	−1.07474	+	0.0103005i	−0.0404770	+	0.000387939i
$706$	27.0074	−	1.09060i	1.01644	−	0.0410453i
$707$	21.0846	−	37.2315i	0.792968	−	1.40023i
$708$	4.60154	−	9.94679i	0.172937	−	0.373823i
$709$		−	9.67006i		−	0.363167i	−0.983376	−	0.181583i	$-0.941878\pi$
$709$		−	9.67006i		−	0.363167i	0.983376	−	0.181583i	$-0.0581222\pi$
$710$	1.46843	+	2.32171i	0.0551091	+	0.0871322i
$711$	−23.3093	+	42.2216i	−0.874166	+	1.58343i
$712$	−12.0549	−	16.0339i	−0.451777	−	0.600895i
$713$	−4.52772	+	7.84225i	−0.169565	+	0.293694i
$714$	−13.2599	+	0.773432i	−0.496238	+	0.0289450i
$715$	−2.17672	+	1.25673i	−0.0814046	+	0.0469989i
$716$	−7.77510	+	0.628966i	−0.290569	+	0.0235056i
$717$	−19.9151	+	35.2703i	−0.743743	+	1.31720i
$718$	−1.62235	−	40.1755i	−0.0605455	−	1.49934i
$719$	18.9102	+	32.7535i	0.705233	+	1.22150i	0.966608	+	0.256261i	$0.0824907\pi$
$719$	18.9102	+	32.7535i	0.705233	+	1.22150i	−0.261375	+	0.965237i	$0.584176\pi$
$720$	0.402878	+	2.20639i	0.0150144	+	0.0822274i
$721$	22.2045	−	0.184728i	0.826938	−	0.00687962i
$722$	13.7808	+	21.7886i	0.512869	+	0.810889i
$723$	12.8505	−	22.7586i	0.477914	−	0.846403i
$724$	−24.2584	−	35.1319i	−0.901557	−	1.30567i
$725$	36.5749			1.35836
$726$	−4.21368	−	2.15982i	−0.156384	−	0.0801583i
$727$	25.0543	+	14.4651i	0.929213	+	0.536482i	0.886563	−	0.462608i	$-0.153086\pi$
$727$	25.0543	+	14.4651i	0.929213	+	0.536482i	0.0426506	+	0.999090i	$0.486420\pi$
$728$	25.8366	+	10.7474i	0.957570	+	0.398324i
$729$	−26.9554	+	1.55174i	−0.998347	+	0.0574718i
$730$	−3.08161	+	0.124440i	−0.114055	+	0.00460573i
$731$	−17.9940	+	10.3889i	−0.665534	+	0.384246i
$732$	−5.05575	−	2.33887i	−0.186866	−	0.0864471i
$733$	9.86767	−	17.0913i	0.364471	−	0.631282i	−0.624220	−	0.781248i	$-0.714583\pi$
$733$	9.86767	−	17.0913i	0.364471	−	0.631282i	0.988691	+	0.149967i	$0.0479166\pi$
$734$	−0.191021	−	4.73040i	−0.00705071	−	0.174602i
$735$	−1.08121	+	1.99155i	−0.0398811	+	0.0734593i
$736$	2.11991	+	10.3621i	0.0781411	+	0.381954i
$737$	14.3791	−	8.30179i	0.529662	−	0.305801i
$738$	19.8982	−	39.7543i	0.732463	−	1.46338i
$739$	37.9102	+	21.8875i	1.39455	+	0.805143i	0.993815	−	0.111051i	$-0.0354218\pi$
$739$	37.9102	+	21.8875i	1.39455	+	0.805143i	0.400734	+	0.916194i	$0.368755\pi$
$740$	−0.326668	−	0.473093i	−0.0120086	−	0.0173913i
$741$	−0.378739	−	39.5170i	−0.0139133	−	1.45169i
$742$	8.35896	+	4.29794i	0.306867	+	0.157782i
$743$	−0.221046	+	0.127621i	−0.00810940	+	0.00468196i	−0.504049	−	0.863675i	$-0.668157\pi$
$743$	−0.221046	+	0.127621i	−0.00810940	+	0.00468196i	0.495940	+	0.868357i	$0.334824\pi$
$744$	14.4394	+	18.8271i	0.529376	+	0.690234i
$745$	−3.69495	+	2.13328i	−0.135373	+	0.0781574i
$746$	9.91618	−	6.27176i	0.363057	−	0.229625i
$747$	7.78736	−	4.69731i	0.284925	−	0.171866i
$748$	−8.37596	−	12.1304i	−0.306255	−	0.443531i
$749$	−11.0876	−	6.27900i	−0.405130	−	0.229430i
$750$	4.55656	−	0.227760i	0.166382	−	0.00831662i
$751$	0.182415	−	0.315953i	0.00665643	−	0.0115293i	−0.862678	−	0.505754i	$-0.831215\pi$
$751$	0.182415	−	0.315953i	0.00665643	−	0.0115293i	0.869334	+	0.494224i	$0.164548\pi$
$752$	−4.70505	+	12.4186i	−0.171575	+	0.452859i
$753$	2.15264	+	3.64731i	0.0784466	+	0.132915i
$754$	−18.1007	+	34.4950i	−0.659190	+	1.25623i
$755$			1.60860i			0.0585428i
$756$	−10.8542	+	25.2624i	−0.394762	+	0.918783i
$757$			19.4967i			0.708619i	0.935128	+	0.354309i	$0.115284\pi$
$757$			19.4967i			0.708619i	−0.935128	+	0.354309i	$0.884716\pi$
$758$	3.84736	+	2.01885i	0.139742	+	0.0733278i
$759$	−5.91956	−	10.0297i	−0.214866	−	0.364057i
$760$	−0.389601	−	3.20201i	−0.0141323	−	0.116149i
$761$	−21.3757	+	37.0237i	−0.774867	+	1.34211i	0.160002	+	0.987117i	$0.448850\pi$
$761$	−21.3757	+	37.0237i	−0.774867	+	1.34211i	−0.934869	+	0.354992i	$0.884484\pi$
$762$	1.21467	+	24.3006i	0.0440027	+	0.880317i
$763$	−1.73510	+	0.0144350i	−0.0628147	+	0.000522580i
$764$	−18.8049	+	12.9847i	−0.680339	+	0.469770i
$765$	−0.0220264	−	1.14899i	−0.000796365	−	0.0415419i
$766$	13.6471	+	21.5772i	0.493089	+	0.779614i
$767$	10.2455	−	5.91523i	0.369943	−	0.213587i
$768$	27.2081	+	5.26478i	0.981789	+	0.189976i
$769$	22.0296	−	12.7188i	0.794409	−	0.458652i	−0.0471032	−	0.998890i	$-0.514999\pi$
$769$	22.0296	−	12.7188i	0.794409	−	0.458652i	0.841513	+	0.540238i	$0.181666\pi$
$770$	−2.51202	+	0.122379i	−0.0905269	+	0.00441022i
$771$	0.0181080	+	1.88936i	0.000652144	+	0.0680436i
$772$	−20.4888	−	29.6727i	−0.737408	−	1.06794i
$773$	39.0057	+	22.5199i	1.40294	+	0.809986i	0.994693	−	0.102887i	$-0.0328081\pi$
$773$	39.0057	+	22.5199i	1.40294	+	0.809986i	0.408244	+	0.912873i	$0.366141\pi$
$774$	2.55884	+	42.9351i	0.0919755	+	1.54327i
$775$	20.8251	−	12.0234i	0.748060	−	0.431893i
$776$	−28.2160	−	12.0134i	−1.01289	−	0.431257i
$777$	−0.126173	−	7.04680i	−0.00452643	−	0.252803i
$778$	−51.1994	+	2.06751i	−1.83559	+	0.0741238i
$779$	−31.9676	+	55.3696i	−1.14536	+	1.98382i
$780$	−1.01653	+	2.19735i	−0.0363976	+	0.0786778i
$781$	−32.3682	+	18.6878i	−1.15823	+	0.668702i
$782$	−0.218663	−	5.41491i	−0.00781936	−	0.193637i
$783$	−33.6855	−	18.1777i	−1.20382	−	0.649618i
$784$	18.0740	+	21.3853i	0.645498	+	0.763762i
$785$	0.403652	+	0.233049i	0.0144070	+	0.00831787i
$786$	−13.3342	+	26.0143i	−0.475616	+	0.927898i
$787$	24.6562			0.878897			0.439449	−	0.898268i	$-0.355174\pi$
$787$	24.6562			0.878897			0.439449	+	0.898268i	$0.355174\pi$
$788$	2.31261	+	3.34921i	0.0823834	+	0.119311i
$789$	−13.2602	+	23.4842i	−0.472074	+	0.836060i
$790$	−3.59130	+	2.27142i	−0.127773	+	0.0808134i
$791$	−18.1780	+	32.0990i	−0.646336	+	1.14131i
$792$	−30.2156	+	4.26564i	−1.07367	+	0.151573i
$793$	−3.00659	−	5.20757i	−0.106767	−	0.184926i
$794$	14.7545	−	0.595810i	0.523618	−	0.0211445i
$795$	−0.399843	+	0.708136i	−0.0141810	+	0.0251150i
$796$	2.96986	+	36.7126i	0.105264	+	1.30124i
$797$	−19.0282	+	10.9859i	−0.674012	+	0.389141i	−0.797595	−	0.603193i	$-0.793895\pi$
$797$	−19.0282	+	10.9859i	−0.674012	+	0.389141i	0.123583	+	0.992334i	$0.460561\pi$
$798$	17.7439	−	35.3385i	0.628127	−	1.25097i
$799$	3.40221	−	5.89280i	0.120361	−	0.208472i
$800$	8.88312	−	26.6449i	0.314066	−	0.942039i
$801$	21.2730	−	0.407807i	0.751644	−	0.0144091i
$802$	44.8585	−	28.3720i	1.58401	−	1.00185i
$803$		−	41.9608i		−	1.48076i
$804$	6.71508	−	14.5154i	0.236823	−	0.511920i
$805$	−0.804539	−	0.455619i	−0.0283563	−	0.0160585i
$806$	1.03341	+	25.5912i	0.0364004	+	0.901411i
$807$	−50.5787	+	0.484756i	−1.78045	+	0.0170642i
$808$	36.5608	−	27.4879i	1.28621	−	0.967020i
$809$	−6.85501	−	3.95774i	−0.241009	−	0.139147i	0.374631	−	0.927174i	$-0.377769\pi$
$809$	−6.85501	−	3.95774i	−0.241009	−	0.139147i	−0.615640	+	0.788027i	$0.711103\pi$
$810$	−2.14734	−	1.02382i	−0.0754499	−	0.0359734i
$811$	−26.5888			−0.933658			−0.466829	−	0.884348i	$-0.654604\pi$
$811$	−26.5888			−0.933658			−0.466829	+	0.884348i	$0.654604\pi$
$812$	−31.8905	+	22.4143i	−1.11914	+	0.786588i
$813$	8.53339	−	15.1129i	0.299279	−	0.530034i
$814$	6.61072	−	4.18113i	0.231706	−	0.146549i
$815$	−0.335357			−0.0117470
$816$	−13.3260	−	4.90333i	−0.466504	−	0.171651i
$817$		−	61.8574i		−	2.16412i
$818$	−16.5106	−	8.66369i	−0.577280	−	0.302919i
$819$	−25.2863	+	15.5410i	−0.883575	+	0.543045i
$820$	3.22322	−	2.22562i	0.112560	−	0.0777219i
$821$	52.5867			1.83529			0.917644	−	0.397404i	$-0.130089\pi$
$821$	52.5867			1.83529			0.917644	+	0.397404i	$0.130089\pi$
$822$	23.7276	+	36.7314i	0.827597	+	1.28115i
$823$	36.6887			1.27889			0.639444	−	0.768838i	$-0.279165\pi$
$823$	36.6887			1.27889			0.639444	+	0.768838i	$0.279165\pi$
$824$	21.8412	+	9.29924i	0.760873	+	0.323954i
$825$	0.296396	+	30.9255i	0.0103192	+	1.07669i
$826$	11.8237	−	0.576019i	0.411399	−	0.0200423i
$827$	53.0150			1.84351			0.921756	−	0.387771i	$-0.126755\pi$
$827$	53.0150			1.84351			0.921756	+	0.387771i	$0.126755\pi$
$828$	−10.2263	−	4.61239i	−0.355389	−	0.160292i
$829$	24.1125	−	41.7641i	0.837463	−	1.45053i	−0.0545466	−	0.998511i	$-0.517371\pi$
$829$	24.1125	−	41.7641i	0.837463	−	1.45053i	0.892009	−	0.452017i	$-0.149295\pi$
$830$	0.800638	−	0.0323310i	0.0277906	−	0.00112223i
$831$	17.4615	−	30.9249i	0.605732	−	1.07277i
$832$	20.7335	+	21.5644i	0.718804	+	0.747611i
$833$	−7.37905	−	12.3035i	−0.255669	−	0.426291i
$834$	17.6086	−	11.3748i	0.609737	−	0.393876i
$835$		−	1.83523i		−	0.0635107i
$836$	43.7431	−	3.53860i	1.51289	−	0.122385i
$837$	−25.1556	+	0.723465i	−0.869504	+	0.0250066i
$838$	−1.52317	−	37.7194i	−0.0526169	−	1.30299i
$839$	−0.606303	+	1.05015i	−0.0209319	+	0.0362551i	−0.876302	−	0.481763i	$-0.839997\pi$
$839$	−0.606303	+	1.05015i	−0.0209319	+	0.0362551i	0.855370	+	0.518018i	$0.173330\pi$
$840$	−1.90998	+	1.49026i	−0.0659005	+	0.0514188i
$841$	−12.6322	−	21.8797i	−0.435595	−	0.754472i
$842$	26.9363	−	17.0366i	0.928287	−	0.587121i
$843$	12.3691	−	0.118547i	0.426013	−	0.00408299i
$844$	−23.5346	−	11.1625i	−0.810095	−	0.384231i
$845$	−0.159086	+	0.0918481i	−0.00547271	+	0.00315967i
$846$	−7.75603	−	11.7579i	−0.266658	−	0.404244i
$847$	−0.0425468	−	5.11417i	−0.00146193	−	0.175725i
$848$	6.35748	+	7.78124i	0.218317	+	0.267209i
$849$	46.8365	−	27.6429i	1.60743	−	0.948703i
$850$	−6.68680	+	12.7432i	−0.229355	+	0.437088i
$851$	2.87561			0.0985746
$852$	−15.1160	+	32.6751i	−0.517866	+	1.11943i
$853$	3.90131	−	6.75726i	0.133578	−	0.231364i	−0.791475	−	0.611201i	$-0.790687\pi$
$853$	3.90131	−	6.75726i	0.133578	−	0.231364i	0.925053	+	0.379837i	$0.124020\pi$
$854$	−0.292778	−	6.00974i	−0.0100187	−	0.205649i
$855$	2.99517	+	1.65354i	0.102433	+	0.0565500i
$856$	−8.18590	−	10.8878i	−0.279788	−	0.372138i
$857$	−20.4850	−	35.4811i	−0.699755	−	1.21201i	−0.968551	−	0.248814i	$-0.919959\pi$
$857$	−20.4850	−	35.4811i	−0.699755	−	1.21201i	0.268796	−	0.963197i	$-0.413374\pi$
$858$	−29.3135	−	15.0253i	−1.00075	−	0.512956i
$859$	−11.0580	+	19.1530i	−0.377294	+	0.653492i	−0.990667	−	0.136301i	$-0.956479\pi$
$859$	−11.0580	+	19.1530i	−0.377294	+	0.653492i	0.613374	+	0.789793i	$0.289812\pi$
$860$	−1.62403	+	3.42403i	−0.0553789	+	0.116758i
$861$	48.0104	−	0.859627i	1.63619	−	0.0292960i
$862$	6.38768	−	4.04006i	0.217565	−	0.137605i
$863$	−17.5708	+	10.1445i	−0.598116	+	0.345322i	−0.768300	−	0.640090i	$-0.778897\pi$
$863$	−17.5708	+	10.1445i	−0.598116	+	0.345322i	0.170184	+	0.985412i	$0.445564\pi$
$864$	−21.4239	+	20.1251i	−0.728855	+	0.684668i
$865$	0.563398	−	0.975834i	0.0191561	−	0.0331794i
$866$	42.8413	+	22.4803i	1.45581	+	0.763912i
$867$	−19.3045	−	10.9002i	−0.655617	−	0.370189i
$868$	−10.7896	+	23.2458i	−0.366223	+	0.789014i
$869$	−28.9070	−	50.0683i	−0.980601	−	1.69845i
$870$	−1.82998	−	2.83288i	−0.0620420	−	0.0960436i
$871$	14.9513	−	8.63215i	0.506606	−	0.292489i
$872$	−1.70671	−	0.726659i	−0.0577963	−	0.0246078i
$873$	27.8525	−	16.8006i	0.942665	−	0.568613i
$874$	14.2865	+	7.49660i	0.483247	+	0.253576i
$875$	2.49931	+	4.24695i	0.0844922	+	0.143573i
$876$	−23.2837	−	33.0386i	−0.786684	−	1.11627i
$877$	−43.9004	−	25.3459i	−1.48241	−	0.855871i	−0.482611	−	0.875835i	$-0.660312\pi$
$877$	−43.9004	−	25.3459i	−1.48241	−	0.855871i	−0.999801	+	0.0199639i	$0.993645\pi$
$878$	−10.4799	−	5.49915i	−0.353678	−	0.185587i
$879$	−9.76354	+	17.2916i	−0.329316	+	0.583230i
$880$	−2.51424	−	0.952575i	−0.0847551	−	0.0321113i
$881$	11.0756			0.373145			0.186572	−	0.982441i	$-0.440262\pi$
$881$	11.0756			0.373145			0.186572	+	0.982441i	$0.440262\pi$
$882$	−29.6124	+	2.25982i	−0.997101	+	0.0760922i
$883$		−	32.4150i		−	1.09085i	−0.838159	−	0.545425i	$-0.816368\pi$
$883$		−	32.4150i		−	1.09085i	0.838159	−	0.545425i	$-0.183632\pi$
$884$	−8.70927	−	12.6131i	−0.292924	−	0.424224i
$885$	0.00981576	+	1.02416i	0.000329953	+	0.0344268i
$886$	5.16447	−	9.84205i	0.173504	−	0.330650i
$887$	−8.45794	+	14.6496i	−0.283990	+	0.491885i	−0.972364	−	0.233471i	$-0.924992\pi$
$887$	−8.45794	+	14.6496i	−0.283990	+	0.491885i	0.688374	+	0.725356i	$0.258325\pi$
$888$	2.88500	−	6.96034i	0.0968142	−	0.233574i
$889$	−22.6494	+	13.3291i	−0.759636	+	0.447043i
$890$	1.66001	+	0.871067i	0.0556437	+	0.0291982i
$891$	15.0970	−	28.6297i	0.505767	−	0.959130i
$892$	−3.36743	−	41.6272i	−0.112750	−	1.39378i
$893$	10.1287	+	17.5434i	0.338944	+	0.587069i
$894$	−49.7594	−	25.5053i	−1.66420	−	0.853026i
$895$	0.631315	−	0.364490i	0.0211025	−	0.0121836i
$896$	8.58347	+	28.6762i	0.286754	+	0.958004i
$897$	−6.15512	−	10.4289i	−0.205513	−	0.348210i
$898$	19.5699	+	10.2690i	0.653058	+	0.342682i
$899$	−30.8973	−	17.8386i	−1.03048	−	0.594949i
$900$	17.3937	+	24.1853i	0.579789	+	0.806176i
$901$	−2.57423	−	4.45871i	−0.0857602	−	0.148541i
$902$	28.4864	+	45.0393i	0.948492	+	1.49965i
$903$	−39.8110	+	23.9453i	−1.32483	+	0.796849i
$904$	−31.5208	+	23.6986i	−1.04837	+	0.788204i
$905$	3.45529	+	1.99491i	0.114858	+	0.0663131i
$906$	−17.7080	+	11.4390i	−0.588310	+	0.380035i
$907$	26.8760	−	15.5168i	0.892402	−	0.515228i	0.0176745	−	0.999844i	$-0.494374\pi$
$907$	26.8760	−	15.5168i	0.892402	−	0.515228i	0.874727	+	0.484615i	$0.161040\pi$
$908$	3.78534	+	1.79540i	0.125621	+	0.0595824i
$909$	0.929891	+	48.5072i	0.0308425	+	1.60888i
$910$	−2.61198	+	0.127249i	−0.0865863	+	0.00421825i
$911$	43.4959	+	25.1124i	1.44108	+	0.832010i	0.997922	−	0.0644318i	$-0.0205235\pi$
$911$	43.4959	+	25.1124i	1.44108	+	0.832010i	0.443161	+	0.896442i	$0.353857\pi$
$912$	32.4784	−	27.0589i	1.07547	−	0.896010i
$913$			10.9019i			0.360800i
$914$	−20.0630	+	38.2346i	−0.663626	+	1.26469i
$915$	0.520560	−	0.00498915i	0.0172092	−	0.000164936i
$916$	−29.6531	+	2.39878i	−0.979765	+	0.0792580i
$917$	−31.5737	+	0.262674i	−1.04266	+	0.00867426i
$918$	12.4919	−	8.41315i	0.412295	−	0.277675i
$919$	−14.6299	−	25.3397i	−0.482595	−	0.835878i	0.517206	−	0.855861i	$-0.326972\pi$
$919$	−14.6299	−	25.3397i	−0.482595	−	0.835878i	−0.999800	+	0.0199828i	$0.993639\pi$
$920$	−0.593988	−	0.790046i	−0.0195832	−	0.0260471i
$921$	15.2694	−	9.01199i	0.503143	−	0.296955i
$922$	12.8092	−	8.10155i	0.421850	−	0.266810i
$923$	−33.6563	+	19.4315i	−1.10781	+	0.639594i
$924$	−19.2106	−	26.7830i	−0.631982	−	0.881096i
$925$	−6.61314	−	3.81810i	−0.217439	−	0.125538i
$926$	−3.10245	+	0.125281i	−0.101953	+	0.00411701i
$927$	−21.5598	+	13.0048i	−0.708117	+	0.427134i
$928$	−40.8253	+	8.35215i	−1.34016	+	0.274173i
$929$	49.3492			1.61909			0.809547	−	0.587055i	$-0.199713\pi$
$929$	49.3492			1.61909			0.809547	+	0.587055i	$0.199713\pi$
$930$	−1.97322	−	1.01142i	−0.0647044	−	0.0331657i
$931$	42.7055	−	0.710617i	1.39962	−	0.0232895i
$932$	−4.92888	−	2.33778i	−0.161451	−	0.0765767i
$933$	14.7327	−	8.69526i	0.482328	−	0.284670i
$934$	1.15332	+	28.5606i	0.0377378	+	0.934532i
$935$	1.19304	+	0.688804i	0.0390167	+	0.0225263i
$936$	−31.4180	+	4.43539i	−1.02693	+	0.144975i
$937$			12.4009i			0.405120i	0.979270	+	0.202560i	$0.0649261\pi$
$937$			12.4009i			0.405120i	−0.979270	+	0.202560i	$0.935074\pi$
$938$	17.2544	−	0.840590i	0.563377	−	0.0274462i
$939$	8.58855	+	14.5519i	0.280277	+	0.474884i
$940$	−0.100068	−	1.23702i	−0.00326387	−	0.0403470i
$941$		−	3.87843i		−	0.126433i	−0.998000	−	0.0632166i	$-0.979864\pi$
$941$		−	3.87843i		−	0.126433i	0.998000	−	0.0632166i	$-0.0201359\pi$
$942$	0.304949	+	6.10081i	0.00993578	+	0.198775i
$943$			19.5917i			0.637995i
$944$	11.8342	+	4.48363i	0.385169	+	0.145930i
$945$	−0.0952331	−	2.56777i	−0.00309793	−	0.0835295i
$946$	−45.6559	−	23.9573i	−1.48440	−	0.778917i
$947$	5.23245			0.170032			0.0850159	−	0.996380i	$-0.472906\pi$
$947$	5.23245			0.170032			0.0850159	+	0.996380i	$0.472906\pi$
$948$	−50.5430	−	23.3820i	−1.64156	−	0.759412i
$949$		−	43.6305i		−	1.41631i
$950$	−22.9014	−	36.2091i	−0.743020	−	1.17478i
$951$	26.6457	−	15.7263i	0.864047	−	0.509961i
$952$	−1.97907	−	15.2090i	−0.0641420	−	0.492926i
$953$			5.43209i			0.175963i	0.996122	+	0.0879813i	$0.0280416\pi$
$953$			5.43209i			0.175963i	−0.996122	+	0.0879813i	$0.971958\pi$
$954$	−10.6388	+	0.634049i	−0.344443	+	0.0205281i
$955$	1.06781	−	1.84950i	0.0345535	−	0.0598484i
$956$	−42.2581	−	20.0432i	−1.36673	−	0.648242i
$957$	39.5157	−	23.3222i	1.27736	−	0.753899i
$958$	−52.4017	+	2.11606i	−1.69302	+	0.0683669i
$959$	−23.2751	+	41.0995i	−0.751591	+	1.32717i
$960$	−2.50821	+	0.645107i	−0.0809523	+	0.0208207i
$961$	7.54348			0.243338
$962$	6.87379	−	4.34752i	0.221620	−	0.140170i
$963$	14.4455	−	0.276922i	0.465499	−	0.00892368i
$964$	27.2676	+	12.9331i	0.878230	+	0.416547i
$965$	2.91836	+	1.68491i	0.0939453	+	0.0542393i
$966$	−0.705582	−	12.0967i	−0.0227017	−	0.389203i
$967$	19.1585	+	33.1835i	0.616096	+	1.06711i	0.990191	+	0.139719i	$0.0446198\pi$
$967$	19.1585	+	33.1835i	0.616096	+	1.06711i	−0.374096	+	0.927390i	$0.622047\pi$
$968$	2.14181	−	5.03049i	0.0688405	−	0.161686i
$969$	−18.6535	+	11.0093i	−0.599236	+	0.353669i
$970$	2.86359	−	0.115636i	0.0919443	−	0.00371285i
$971$	−18.3260	+	10.5805i	−0.588109	+	0.339545i	−0.764350	−	0.644802i	$-0.776940\pi$
$971$	−18.3260	+	10.5805i	−0.588109	+	0.339545i	0.176240	+	0.984347i	$0.443606\pi$
$972$	−3.99951	−	30.9193i	−0.128284	−	0.991737i
$973$	19.7026	+	11.1578i	0.631637	+	0.357703i
$974$	−24.3398	−	38.4833i	−0.779897	−	1.23308i
$975$	0.308190	+	32.1561i	0.00986999	+	1.02982i
$976$	2.27894	−	6.01507i	0.0729470	−	0.192538i
$977$		−	6.04764i		−	0.193481i	−0.995310	−	0.0967406i	$-0.969158\pi$
$977$		−	6.04764i		−	0.193481i	0.995310	−	0.0967406i	$-0.0308417\pi$
$978$	−2.38478	−	3.69174i	−0.0762569	−	0.118049i
$979$	−12.7529	+	22.0886i	−0.407583	+	0.705955i
$980$	−2.38256	−	1.08187i	−0.0761081	−	0.0345591i
$981$	1.68472	−	1.01622i	0.0537890	−	0.0324454i
$982$	−12.5544	+	0.506967i	−0.400628	+	0.0161780i
$983$	13.1121	+	22.7109i	0.418212	+	0.724364i	0.995760	−	0.0919926i	$-0.0293236\pi$
$983$	13.1121	+	22.7109i	0.418212	+	0.724364i	−0.577548	+	0.816357i	$0.695990\pi$
$984$	47.4213	+	19.6557i	1.51174	+	0.626601i
$985$	−0.329401	−	0.190180i	−0.0104956	−	0.00605963i
$986$	21.3340	−	0.861498i	0.679412	−	0.0274357i
$987$	7.36999	−	13.3099i	0.234589	−	0.423660i
$988$	45.4838	−	3.67941i	1.44703	−	0.117058i
$989$	−9.47750	−	16.4155i	−0.301367	−	0.521983i
$990$	2.38048	−	1.57027i	0.0756565	−	0.0499065i
$991$	7.11351	−	12.3210i	0.225968	−	0.391388i	−0.730641	−	0.682761i	$-0.760779\pi$
$991$	7.11351	−	12.3210i	0.225968	−	0.391388i	0.956609	+	0.291373i	$0.0941122\pi$
$992$	−20.4996	+	18.1762i	−0.650863	+	0.577095i
$993$	24.2385	+	41.0682i	0.769184	+	1.30326i
$994$	−38.8407	+	1.89221i	−1.23195	+	0.0600174i
$995$	−1.72105	−	2.98095i	−0.0545611	−	0.0945026i
$996$	6.04938	+	8.58382i	0.191682	+	0.271989i
$997$	10.2150	+	17.6928i	0.323511	+	0.560338i	0.981210	−	0.192943i	$-0.0618033\pi$
$997$	10.2150	+	17.6928i	0.323511	+	0.560338i	−0.657699	+	0.753281i	$0.728470\pi$
$998$	−13.4649	+	8.51625i	−0.426224	+	0.269577i
$999$	4.19311	+	6.80320i	0.132664	+	0.215244i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	504.2.ca.a.101.61	yes	184
7.5	odd	6		504.2.y.a.173.1	✓	184
8.5	even	2	inner	504.2.ca.a.101.32	yes	184
9.5	odd	6		504.2.y.a.437.29	yes	184
56.5	odd	6		504.2.y.a.173.29	yes	184
63.5	even	6	inner	504.2.ca.a.5.32	yes	184
72.5	odd	6		504.2.y.a.437.1	yes	184
504.5	even	6	inner	504.2.ca.a.5.61	yes	184

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.y.a.173.1	✓	184	7.5	odd	6
504.2.y.a.173.29	yes	184	56.5	odd	6
504.2.y.a.437.1	yes	184	72.5	odd	6
504.2.y.a.437.29	yes	184	9.5	odd	6
504.2.ca.a.5.32	yes	184	63.5	even	6	inner
504.2.ca.a.5.61	yes	184	504.5	even	6	inner
504.2.ca.a.101.32	yes	184	8.5	even	2	inner
504.2.ca.a.101.61	yes	184	1.1	even	1	trivial

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.ca (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.657114 - 1.25228i) q^{2} +(-1.49163 + 0.880361i) q^{3} +(-1.13640 - 1.64578i) q^{4} +(0.161865 + 0.0934530i) q^{5} +(0.122285 + 2.44644i) q^{6} +(-2.28020 + 1.34189i) q^{7} +(-2.80772 + 0.341626i) q^{8} +(1.44993 - 2.62635i) q^{9} +O(q^{10})\)	\(q+(0.657114 - 1.25228i) q^{2} +(-1.49163 + 0.880361i) q^{3} +(-1.13640 - 1.64578i) q^{4} +(0.161865 + 0.0934530i) q^{5} +(0.122285 + 2.44644i) q^{6} +(-2.28020 + 1.34189i) q^{7} +(-2.80772 + 0.341626i) q^{8} +(1.44993 - 2.62635i) q^{9} +(0.223393 - 0.141291i) q^{10} +(1.79813 + 3.11445i) q^{11} +(3.14397 + 1.45445i) q^{12} +(1.86968 + 3.23838i) q^{13} +(0.182067 + 3.73723i) q^{14} +(-0.323716 + 0.00310256i) q^{15} +(-1.41718 + 3.74053i) q^{16} +(1.02476 - 1.77494i) q^{17} +(-2.33615 - 3.54152i) q^{18} +(3.05081 + 5.28416i) q^{19} +(-0.0301411 - 0.372595i) q^{20} +(2.21987 - 4.00901i) q^{21} +(5.08173 - 0.205208i) q^{22} +(1.61923 + 0.934863i) q^{23} +(3.88733 - 2.98139i) q^{24} +(-2.48253 - 4.29987i) q^{25} +(5.28395 - 0.213374i) q^{26} +(0.149378 + 5.19400i) q^{27} +(4.79969 + 2.22778i) q^{28} +(-3.68322 + 6.37953i) q^{29} +(-0.208833 + 0.407421i) q^{30} +4.84319i q^{31} +(3.75294 + 4.23266i) q^{32} +(-5.42398 - 3.06261i) q^{33} +(-1.54933 - 2.44962i) q^{34} +(-0.494490 + 0.00411386i) q^{35} +(-5.97009 + 0.598326i) q^{36} +(1.33193 - 0.768992i) q^{37} +(8.62198 - 0.348169i) q^{38} +(-5.63982 - 3.18448i) q^{39} +(-0.486399 - 0.207092i) q^{40} +(5.23920 + 9.07456i) q^{41} +(-3.56169 - 5.41428i) q^{42} +(-8.77963 - 5.06892i) q^{43} +(3.08230 - 6.49858i) q^{44} +(0.480133 - 0.289615i) q^{45} +(2.23473 - 1.41342i) q^{46} +3.32000 q^{47} +(-1.17911 - 6.82713i) q^{48} +(3.39866 - 6.11957i) q^{49} +(-7.01595 + 0.283315i) q^{50} +(0.0340211 + 3.54971i) q^{51} +(3.20495 - 6.75719i) q^{52} +(1.25602 - 2.17549i) q^{53} +(6.60250 + 3.22599i) q^{54} +0.672161i q^{55} +(5.94375 - 4.54663i) q^{56} +(-9.20266 - 5.19621i) q^{57} +(5.56865 + 8.80450i) q^{58} -3.16376i q^{59} +(0.372977 + 0.529239i) q^{60} -1.60808 q^{61} +(6.06503 + 3.18253i) q^{62} +(0.218144 + 7.93426i) q^{63} +(7.76658 - 1.91838i) q^{64} +0.698909i q^{65} +(-7.39941 + 4.77985i) q^{66} -4.61691i q^{67} +(-4.08570 + 0.330512i) q^{68} +(-3.23831 + 0.0310366i) q^{69} +(-0.319785 + 0.621942i) q^{70} +10.3929i q^{71} +(-3.17376 + 7.86939i) q^{72} +(-10.1047 - 5.83396i) q^{73} +(-0.0877598 - 2.17327i) q^{74} +(7.48847 + 4.22830i) q^{75} +(5.22962 - 11.0259i) q^{76} +(-8.27934 - 4.68868i) q^{77} +(-7.69386 + 4.97006i) q^{78} -16.0762 q^{79} +(-0.578957 + 0.473023i) q^{80} +(-4.79542 - 7.61603i) q^{81} +(14.8066 - 0.597914i) q^{82} +(2.62532 + 1.51573i) q^{83} +(-9.12062 + 0.902424i) q^{84} +(0.331746 - 0.191534i) q^{85} +(-12.1169 + 7.66368i) q^{86} +(-0.122280 - 12.7585i) q^{87} +(-6.11261 - 8.13021i) q^{88} +(3.54615 + 6.14211i) q^{89} +(-0.0471759 - 0.791571i) q^{90} +(-8.60881 - 4.87526i) q^{91} +(-0.301518 - 3.72728i) q^{92} +(-4.26376 - 7.22426i) q^{93} +(2.18162 - 4.15757i) q^{94} +1.14043i q^{95} +(-9.32428 - 3.00963i) q^{96} +(9.38981 + 5.42121i) q^{97} +(-5.43010 - 8.27732i) q^{98} +(10.7868 - 0.206784i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 184 q - 2 q^{4} - 6 q^{6} - 2 q^{7} - 2 q^{9}+O(q^{10}) \) 184 * q - 2 * q^4 - 6 * q^6 - 2 * q^7 - 2 * q^9	\( 184 q - 2 q^{4} - 6 q^{6} - 2 q^{7} - 2 q^{9} - 6 q^{10} + 12 q^{12} - 18 q^{14} - 2 q^{15} - 2 q^{16} + 12 q^{18} - 6 q^{22} - 6 q^{23} - 12 q^{24} + 78 q^{25} - 6 q^{26} - 8 q^{28} + 7 q^{30} - 6 q^{33} + 6 q^{34} + 22 q^{36} - 33 q^{38} - 8 q^{39} - 18 q^{40} - 42 q^{42} - 9 q^{44} + 2 q^{46} - 12 q^{47} + 9 q^{48} - 2 q^{49} + 9 q^{50} + 21 q^{52} + 33 q^{54} + 18 q^{56} + 4 q^{57} - 3 q^{58} - 59 q^{60} + 12 q^{62} - 72 q^{63} - 8 q^{64} - 42 q^{66} - 18 q^{68} - 27 q^{70} + 12 q^{72} - 12 q^{73} - 57 q^{74} + 12 q^{76} + 19 q^{78} - 4 q^{79} - 57 q^{80} - 18 q^{81} + 69 q^{84} - 27 q^{86} - 6 q^{87} + 9 q^{88} - 24 q^{89} - 75 q^{90} - 36 q^{92} - 45 q^{96} - 45 q^{98}+O(q^{100}) \) 184 * q - 2 * q^4 - 6 * q^6 - 2 * q^7 - 2 * q^9 - 6 * q^10 + 12 * q^12 - 18 * q^14 - 2 * q^15 - 2 * q^16 + 12 * q^18 - 6 * q^22 - 6 * q^23 - 12 * q^24 + 78 * q^25 - 6 * q^26 - 8 * q^28 + 7 * q^30 - 6 * q^33 + 6 * q^34 + 22 * q^36 - 33 * q^38 - 8 * q^39 - 18 * q^40 - 42 * q^42 - 9 * q^44 + 2 * q^46 - 12 * q^47 + 9 * q^48 - 2 * q^49 + 9 * q^50 + 21 * q^52 + 33 * q^54 + 18 * q^56 + 4 * q^57 - 3 * q^58 - 59 * q^60 + 12 * q^62 - 72 * q^63 - 8 * q^64 - 42 * q^66 - 18 * q^68 - 27 * q^70 + 12 * q^72 - 12 * q^73 - 57 * q^74 + 12 * q^76 + 19 * q^78 - 4 * q^79 - 57 * q^80 - 18 * q^81 + 69 * q^84 - 27 * q^86 - 6 * q^87 + 9 * q^88 - 24 * q^89 - 75 * q^90 - 36 * q^92 - 45 * q^96 - 45 * q^98

Introduction

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