LMFDB - Embedded newform 637.2.bl.a.235.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [637,2,Mod(53,637)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(637, base_ring=CyclotomicField(42))

chi = DirichletCharacter(H, H._module([10, 0]))

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

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

chi := DirichletCharacter("637.53");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 637 = 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	637.bl (of order $21$, degree $12$, 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:	$5.08647060876$
Analytic rank:	$0$
Dimension:	$324$
Relative dimension:	$27$ over $\Q(\zeta_{21})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label			235.13
Character	$\chi$	$=$	637.235
Dual form			637.2.bl.a.534.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.0482185 + 0.00726776i) q^{2} +(1.72594 - 1.17672i) q^{3} +(-1.90887 - 0.588809i) q^{4} +(-0.208146 - 2.77752i) q^{5} +(0.0917741 - 0.0441961i) q^{6} +(1.61347 - 2.09684i) q^{7} +(-0.175632 - 0.0845798i) q^{8} +(0.498154 - 1.26928i) q^{9} +O(q^{10})$	\(q+(0.0482185 + 0.00726776i) q^{2} +(1.72594 - 1.17672i) q^{3} +(-1.90887 - 0.588809i) q^{4} +(-0.208146 - 2.77752i) q^{5} +(0.0917741 - 0.0441961i) q^{6} +(1.61347 - 2.09684i) q^{7} +(-0.175632 - 0.0845798i) q^{8} +(0.498154 - 1.26928i) q^{9} +(0.0101499 - 0.135440i) q^{10} +(-0.0497559 - 0.126776i) q^{11} +(-3.98746 + 1.22997i) q^{12} +(-0.623490 + 0.781831i) q^{13} +(0.0930382 - 0.0893800i) q^{14} +(-3.62762 - 4.54889i) q^{15} +(3.29317 + 2.24525i) q^{16} +(-0.921886 - 0.855385i) q^{17} +(0.0332450 - 0.0575821i) q^{18} +(-1.13153 - 1.95987i) q^{19} +(-1.23810 + 5.42449i) q^{20} +(0.317343 - 5.51761i) q^{21} +(-0.00147778 - 0.00647456i) q^{22} +(-3.55870 + 3.30199i) q^{23} +(-0.402656 + 0.0606906i) q^{24} +(-2.72712 + 0.411047i) q^{25} +(-0.0357459 + 0.0331673i) q^{26} +(0.760672 + 3.33272i) q^{27} +(-4.31454 + 3.05257i) q^{28} +(0.352487 - 1.54435i) q^{29} +(-0.141858 - 0.245705i) q^{30} +(3.15912 - 5.47176i) q^{31} +(0.428271 + 0.397377i) q^{32} +(-0.235056 - 0.160258i) q^{33} +(-0.0382352 - 0.0479454i) q^{34} +(-6.15984 - 4.04498i) q^{35} +(-1.69828 + 2.12957i) q^{36} +(-2.96942 + 0.915944i) q^{37} +(-0.0403169 - 0.102726i) q^{38} +(-0.156104 + 2.08307i) q^{39} +(-0.198365 + 0.505425i) q^{40} +(-3.94223 - 1.89848i) q^{41} +(0.0554025 - 0.263744i) q^{42} +(-2.74895 + 1.32383i) q^{43} +(0.0203308 + 0.271296i) q^{44} +(-3.62913 - 1.11944i) q^{45} +(-0.195593 + 0.133353i) q^{46} +(6.49479 + 0.978932i) q^{47} +8.32584 q^{48} +(-1.79345 - 6.76635i) q^{49} -0.134485 q^{50} +(-2.59767 - 0.391536i) q^{51} +(1.65051 - 1.12530i) q^{52} +(4.29211 + 1.32394i) q^{53} +(0.0124570 + 0.166227i) q^{54} +(-0.341766 + 0.164586i) q^{55} +(-0.460726 + 0.231804i) q^{56} +(-4.25919 - 2.05112i) q^{57} +(0.0282203 - 0.0719042i) q^{58} +(0.910351 - 12.1478i) q^{59} +(4.24623 + 10.8192i) q^{60} +(7.93443 - 2.44745i) q^{61} +(0.192095 - 0.240880i) q^{62} +(-1.85771 - 3.09248i) q^{63} +(-4.95237 - 6.21008i) q^{64} +(2.30133 + 1.56902i) q^{65} +(-0.0101693 - 0.00943574i) q^{66} +(0.797322 - 1.38100i) q^{67} +(1.25611 + 2.17564i) q^{68} +(-2.25656 + 9.88664i) q^{69} +(-0.267620 - 0.239811i) q^{70} +(2.64783 + 11.6009i) q^{71} +(-0.194847 + 0.180791i) q^{72} +(12.3066 - 1.85492i) q^{73} +(-0.149838 + 0.0225844i) q^{74} +(-4.22315 + 3.91851i) q^{75} +(1.00596 + 4.40741i) q^{76} +(-0.346108 - 0.100219i) q^{77} +(-0.0226663 + 0.0993077i) q^{78} +(-0.0499915 - 0.0865879i) q^{79} +(5.55075 - 9.61418i) q^{80} +(8.23318 + 7.63928i) q^{81} +(-0.176291 - 0.120193i) q^{82} +(5.75041 + 7.21078i) q^{83} +(-3.85459 + 10.3456i) q^{84} +(-2.18396 + 2.73860i) q^{85} +(-0.142171 + 0.0438541i) q^{86} +(-1.20890 - 3.08022i) q^{87} +(-0.00198397 + 0.0264742i) q^{88} +(-1.17904 + 3.00415i) q^{89} +(-0.166855 - 0.0803532i) q^{90} +(0.633393 + 2.56882i) q^{91} +(8.73736 - 4.20769i) q^{92} +(-0.986304 - 13.1613i) q^{93} +(0.306054 + 0.0944052i) q^{94} +(-5.20806 + 3.55080i) q^{95} +(1.20677 + 0.181891i) q^{96} -1.95504 q^{97} +(-0.0373012 - 0.339298i) q^{98} -0.185700 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 324 q - 3 q^{2} + 25 q^{4} + q^{5} - 24 q^{6} - 21 q^{7} + 24 q^{8} + 11 q^{9}+O(q^{10}) $ 324 * q - 3 * q^2 + 25 * q^4 + q^5 - 24 * q^6 - 21 * q^7 + 24 * q^8 + 11 * q^9	\( 324 q - 3 q^{2} + 25 q^{4} + q^{5} - 24 q^{6} - 21 q^{7} + 24 q^{8} + 11 q^{9} - 5 q^{10} - 18 q^{11} - 40 q^{12} + 54 q^{13} - 15 q^{14} + 6 q^{15} + 29 q^{16} - 6 q^{17} + 49 q^{18} - 24 q^{19} + 11 q^{20} - 6 q^{22} - 42 q^{23} + 20 q^{24} + 14 q^{25} + 3 q^{26} - 33 q^{27} + 7 q^{28} - 22 q^{29} + 57 q^{30} - 31 q^{31} - 139 q^{32} + 6 q^{33} + 50 q^{34} + 42 q^{35} - 78 q^{36} - 4 q^{37} - 90 q^{38} + 40 q^{40} + 8 q^{41} + 20 q^{42} + 34 q^{43} - 256 q^{44} + 19 q^{45} + 85 q^{46} + 34 q^{47} - 10 q^{48} + 51 q^{49} - 54 q^{50} + 74 q^{51} - 25 q^{52} + 10 q^{53} + 111 q^{54} - 10 q^{55} - 196 q^{56} - 5 q^{57} - 21 q^{58} + 65 q^{59} + 87 q^{60} + 3 q^{61} - 54 q^{62} - 35 q^{63} - 28 q^{64} - q^{65} - 110 q^{66} + 135 q^{67} - 158 q^{68} + 42 q^{69} + 44 q^{70} + 9 q^{71} - 133 q^{72} + 31 q^{73} - 97 q^{74} - 315 q^{75} - 177 q^{76} + 6 q^{77} - 25 q^{78} + 43 q^{79} - 20 q^{80} - 259 q^{81} + 96 q^{82} + 59 q^{83} + 285 q^{84} + 6 q^{85} + 95 q^{86} - 206 q^{87} + 228 q^{88} + 43 q^{89} - 61 q^{90} - 7 q^{91} + 53 q^{92} - 10 q^{93} - 36 q^{94} - 17 q^{95} + 277 q^{96} + 66 q^{97} + 260 q^{98} - 206 q^{99}+O(q^{100}) \) 324 * q - 3 * q^2 + 25 * q^4 + q^5 - 24 * q^6 - 21 * q^7 + 24 * q^8 + 11 * q^9 - 5 * q^10 - 18 * q^11 - 40 * q^12 + 54 * q^13 - 15 * q^14 + 6 * q^15 + 29 * q^16 - 6 * q^17 + 49 * q^18 - 24 * q^19 + 11 * q^20 - 6 * q^22 - 42 * q^23 + 20 * q^24 + 14 * q^25 + 3 * q^26 - 33 * q^27 + 7 * q^28 - 22 * q^29 + 57 * q^30 - 31 * q^31 - 139 * q^32 + 6 * q^33 + 50 * q^34 + 42 * q^35 - 78 * q^36 - 4 * q^37 - 90 * q^38 + 40 * q^40 + 8 * q^41 + 20 * q^42 + 34 * q^43 - 256 * q^44 + 19 * q^45 + 85 * q^46 + 34 * q^47 - 10 * q^48 + 51 * q^49 - 54 * q^50 + 74 * q^51 - 25 * q^52 + 10 * q^53 + 111 * q^54 - 10 * q^55 - 196 * q^56 - 5 * q^57 - 21 * q^58 + 65 * q^59 + 87 * q^60 + 3 * q^61 - 54 * q^62 - 35 * q^63 - 28 * q^64 - q^65 - 110 * q^66 + 135 * q^67 - 158 * q^68 + 42 * q^69 + 44 * q^70 + 9 * q^71 - 133 * q^72 + 31 * q^73 - 97 * q^74 - 315 * q^75 - 177 * q^76 + 6 * q^77 - 25 * q^78 + 43 * q^79 - 20 * q^80 - 259 * q^81 + 96 * q^82 + 59 * q^83 + 285 * q^84 + 6 * q^85 + 95 * q^86 - 206 * q^87 + 228 * q^88 + 43 * q^89 - 61 * q^90 - 7 * q^91 + 53 * q^92 - 10 * q^93 - 36 * q^94 - 17 * q^95 + 277 * q^96 + 66 * q^97 + 260 * q^98 - 206 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/637\mathbb{Z}\right)^\times$.

$n$	$197$	$248$
$\chi(n)$	$1$	$e\left(\frac{17}{21}\right)$

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 $

$2$	0.0482185	+	0.00726776i	0.0340956	+	0.00513909i	0.166068	−	0.986114i	$-0.446893\pi$
$2$	0.0482185	+	0.00726776i	0.0340956	+	0.00513909i	−0.131972	+	0.991253i	$0.542131\pi$
$3$	1.72594	−	1.17672i	0.996470	−	0.679381i	0.0488578	−	0.998806i	$-0.484442\pi$
$3$	1.72594	−	1.17672i	0.996470	−	0.679381i	0.947612	+	0.319424i	$0.103489\pi$
$4$	−1.90887	−	0.588809i	−0.954437	−	0.294405i
$5$	−0.208146	−	2.77752i	−0.0930858	−	1.24214i	−0.826726	−	0.562605i	$-0.809799\pi$
$5$	−0.208146	−	2.77752i	−0.0930858	−	1.24214i	0.733640	−	0.679538i	$-0.237820\pi$
$6$	0.0917741	−	0.0441961i	0.0374666	−	0.0180430i
$7$	1.61347	−	2.09684i	0.609833	−	0.792530i
$7$	1.61347	−	2.09684i	0.609833	−	0.792530i
$8$	−0.175632	−	0.0845798i	−0.0620952	−	0.0299035i
$9$	0.498154	−	1.26928i	0.166051	−	0.423092i
$10$	0.0101499	−	0.135440i	0.00320966	−	0.0428300i
$11$	−0.0497559	−	0.126776i	−0.0150020	−	0.0382244i	0.923177	−	0.384376i	$-0.125583\pi$
$11$	−0.0497559	−	0.126776i	−0.0150020	−	0.0382244i	−0.938179	+	0.346152i	$0.887488\pi$
$12$	−3.98746	+	1.22997i	−1.15108	+	0.355061i
$13$	−0.623490	+	0.781831i	−0.172925	+	0.216841i
$13$	−0.623490	+	0.781831i	−0.172925	+	0.216841i
$14$	0.0930382	−	0.0893800i	0.0248655	−	0.0238878i
$15$	−3.62762	−	4.54889i	−0.936646	−	1.17452i
$16$	3.29317	+	2.24525i	0.823293	+	0.561312i
$17$	−0.921886	−	0.855385i	−0.223590	−	0.207461i	0.560421	−	0.828208i	$-0.310639\pi$
$17$	−0.921886	−	0.855385i	−0.223590	−	0.207461i	−0.784012	+	0.620746i	$0.786830\pi$
$18$	0.0332450	−	0.0575821i	0.00783593	−	0.0135722i
$19$	−1.13153	−	1.95987i	−0.259592	−	0.449626i	0.706541	−	0.707672i	$-0.250255\pi$
$19$	−1.13153	−	1.95987i	−0.259592	−	0.449626i	−0.966133	+	0.258046i	$0.916921\pi$
$20$	−1.23810	+	5.42449i	−0.276848	+	1.21295i
$21$	0.317343	−	5.51761i	0.0692500	−	1.20404i
$22$	−0.00147778	−	0.00647456i	−0.000315063	−	0.00138038i
$23$	−3.55870	+	3.30199i	−0.742041	+	0.688513i	−0.957640	−	0.287969i	$-0.907020\pi$
$23$	−3.55870	+	3.30199i	−0.742041	+	0.688513i	0.215599	+	0.976482i	$0.430830\pi$
$24$	−0.402656	+	0.0606906i	−0.0821918	+	0.0123884i
$25$	−2.72712	+	0.411047i	−0.545424	+	0.0822095i
$26$	−0.0357459	+	0.0331673i	−0.00701035	+	0.00650465i
$27$	0.760672	+	3.33272i	0.146391	+	0.641382i
$28$	−4.31454	+	3.05257i	−0.815372	+	0.576882i
$29$	0.352487	−	1.54435i	0.0654552	−	0.286778i	−0.931598	−	0.363490i	$-0.881585\pi$
$29$	0.352487	−	1.54435i	0.0654552	−	0.286778i	0.997053	+	0.0767121i	$0.0244422\pi$
$30$	−0.141858	−	0.245705i	−0.0258996	−	0.0448594i
$31$	3.15912	−	5.47176i	0.567395	−	0.982756i	−0.429428	−	0.903101i	$-0.641285\pi$
$31$	3.15912	−	5.47176i	0.567395	−	0.982756i	0.996822	−	0.0796553i	$-0.0253819\pi$
$32$	0.428271	+	0.397377i	0.0757083	+	0.0702470i
$33$	−0.235056	−	0.160258i	−0.0409180	−	0.0278974i
$34$	−0.0382352	−	0.0479454i	−0.00655728	−	0.00822257i
$35$	−6.15984	−	4.04498i	−1.04120	−	0.683727i
$36$	−1.69828	+	2.12957i	−0.283046	+	0.354928i
$37$	−2.96942	+	0.915944i	−0.488169	+	0.150580i	−0.529062	−	0.848583i	$-0.677456\pi$
$37$	−2.96942	+	0.915944i	−0.488169	+	0.150580i	0.0408926	+	0.999164i	$0.486980\pi$
$38$	−0.0403169	−	0.102726i	−0.00654027	−	0.0166643i
$39$	−0.156104	+	2.08307i	−0.0249967	+	0.333558i
$40$	−0.198365	+	0.505425i	−0.0313642	+	0.0799147i
$41$	−3.94223	−	1.89848i	−0.615674	−	0.296493i	0.0999354	−	0.994994i	$-0.468136\pi$
$41$	−3.94223	−	1.89848i	−0.615674	−	0.296493i	−0.715609	+	0.698501i	$0.753851\pi$
$42$	0.0554025	−	0.263744i	0.00854879	−	0.0406966i
$43$	−2.74895	+	1.32383i	−0.419211	+	0.201881i	−0.631584	−	0.775307i	$-0.717595\pi$
$43$	−2.74895	+	1.32383i	−0.419211	+	0.201881i	0.212373	+	0.977189i	$0.431881\pi$
$44$	0.0203308	+	0.271296i	0.00306499	+	0.0408994i
$45$	−3.62913	−	1.11944i	−0.540998	−	0.166876i
$46$	−0.195593	+	0.133353i	−0.0288387	+	0.0196619i
$47$	6.49479	+	0.978932i	0.947362	+	0.142792i	0.604510	−	0.796597i	$-0.293369\pi$
$47$	6.49479	+	0.978932i	0.947362	+	0.142792i	0.342852	+	0.939389i	$0.388607\pi$
$48$	8.32584			1.20173
$49$	−1.79345	−	6.76635i	−0.256207	−	0.966622i
$50$	−0.134485			−0.0190191
$51$	−2.59767	−	0.391536i	−0.363746	−	0.0548259i
$52$	1.65051	−	1.12530i	0.228885	−	0.156051i
$53$	4.29211	+	1.32394i	0.589567	+	0.181857i	0.575163	−	0.818039i	$-0.304939\pi$
$53$	4.29211	+	1.32394i	0.589567	+	0.181857i	0.0144039	+	0.999896i	$0.495415\pi$
$54$	0.0124570	+	0.166227i	0.00169518	+	0.0226206i
$55$	−0.341766	+	0.164586i	−0.0460837	+	0.0221928i
$56$	−0.460726	+	0.231804i	−0.0615671	+	0.0309762i
$57$	−4.25919	−	2.05112i	−0.564143	−	0.271677i
$58$	0.0282203	−	0.0719042i	0.00370551	−	0.00944148i
$59$	0.910351	−	12.1478i	0.118518	−	1.58151i	−0.548296	−	0.836284i	$-0.684723\pi$
$59$	0.910351	−	12.1478i	0.118518	−	1.58151i	0.666814	−	0.745224i	$-0.267658\pi$
$60$	4.24623	+	10.8192i	0.548186	+	1.39676i
$61$	7.93443	−	2.44745i	1.01590	−	0.313364i	0.258287	−	0.966068i	$-0.416842\pi$
$61$	7.93443	−	2.44745i	1.01590	−	0.313364i	0.757612	+	0.652705i	$0.226366\pi$
$62$	0.192095	−	0.240880i	0.0243961	−	0.0305918i
$63$	−1.85771	−	3.09248i	−0.234050	−	0.389616i
$64$	−4.95237	−	6.21008i	−0.619047	−	0.776260i
$65$	2.30133	+	1.56902i	0.285445	+	0.194613i
$66$	−0.0101693	−	0.00943574i	−0.00125176	−	0.00116146i
$67$	0.797322	−	1.38100i	0.0974084	−	0.168716i	−0.813203	−	0.581980i	$-0.802278\pi$
$67$	0.797322	−	1.38100i	0.0974084	−	0.168716i	0.910611	+	0.413264i	$0.135611\pi$
$68$	1.25611	+	2.17564i	0.152325	+	0.263835i
$69$	−2.25656	+	9.88664i	−0.271658	+	1.19021i
$70$	−0.267620	−	0.239811i	−0.0319867	−	0.0286629i
$71$	2.64783	+	11.6009i	0.314239	+	1.37677i	0.847488	+	0.530814i	$0.178114\pi$
$71$	2.64783	+	11.6009i	0.314239	+	1.37677i	−0.533249	+	0.845959i	$0.679029\pi$
$72$	−0.194847	+	0.180791i	−0.0229629	+	0.0213065i
$73$	12.3066	−	1.85492i	1.44038	−	0.217102i	0.618061	−	0.786130i	$-0.287918\pi$
$73$	12.3066	−	1.85492i	1.44038	−	0.217102i	0.822319	+	0.569027i	$0.192680\pi$
$74$	−0.149838	+	0.0225844i	−0.0174183	+	0.00262538i
$75$	−4.22315	+	3.91851i	−0.487647	+	0.452470i
$76$	1.00596	+	4.40741i	0.115392	+	0.505565i
$77$	−0.346108	−	0.100219i	−0.0394427	−	0.0114210i
$78$	−0.0226663	+	0.0993077i	−0.00256646	+	0.0112444i
$79$	−0.0499915	−	0.0865879i	−0.00562449	−	0.00974190i	0.863199	−	0.504863i	$-0.168457\pi$
$79$	−0.0499915	−	0.0865879i	−0.00562449	−	0.00974190i	−0.868824	+	0.495121i	$0.835124\pi$
$80$	5.55075	−	9.61418i	0.620593	−	1.07490i
$81$	8.23318	+	7.63928i	0.914798	+	0.848808i
$82$	−0.176291	−	0.120193i	−0.0194681	−	0.0132731i
$83$	5.75041	+	7.21078i	0.631189	+	0.791486i	0.989870	−	0.141974i	$-0.0453450\pi$
$83$	5.75041	+	7.21078i	0.631189	+	0.791486i	−0.358681	+	0.933460i	$0.616774\pi$
$84$	−3.85459	+	10.3456i	−0.420570	+	1.12879i
$85$	−2.18396	+	2.73860i	−0.236884	+	0.297043i
$86$	−0.142171	+	0.0438541i	−0.0153307	+	0.00472891i
$87$	−1.20890	−	3.08022i	−0.129607	−	0.330234i
$88$	−0.00198397	+	0.0264742i	−0.000211492	+	0.00282216i
$89$	−1.17904	+	3.00415i	−0.124978	+	0.318439i	−0.979645	−	0.200738i	$-0.935666\pi$
$89$	−1.17904	+	3.00415i	−0.124978	+	0.318439i	0.854667	+	0.519177i	$0.173761\pi$
$90$	−0.166855	−	0.0803532i	−0.0175881	−	0.00846997i
$91$	0.633393	+	2.56882i	0.0663976	+	0.269285i
$92$	8.73736	−	4.20769i	0.910933	−	0.438682i
$93$	−0.986304	−	13.1613i	−0.102275	−	1.36476i
$94$	0.306054	+	0.0944052i	0.0315671	+	0.00973715i
$95$	−5.20806	+	3.55080i	−0.534336	+	0.364304i
$96$	1.20677	+	0.181891i	0.123166	+	0.0185642i
$97$	−1.95504			−0.198504			−0.0992519	−	0.995062i	$-0.531645\pi$
$97$	−1.95504			−0.198504			−0.0992519	+	0.995062i	$0.531645\pi$
$98$	−0.0373012	−	0.339298i	−0.00376799	−	0.0342742i
$99$	−0.185700			−0.0186636
$100$	5.44776	+	0.821117i	0.544776	+	0.0821117i
$101$	2.82382	−	1.92525i	0.280981	−	0.191570i	−0.414626	−	0.909992i	$-0.636088\pi$
$101$	2.82382	−	1.92525i	0.280981	−	0.191570i	0.695607	+	0.718422i	$0.255135\pi$
$102$	−0.122410	−	0.0377585i	−0.0121204	−	0.00373865i
$103$	−0.986250	−	13.1606i	−0.0971781	−	1.29675i	−0.806233	−	0.591598i	$-0.798497\pi$
$103$	−0.986250	−	13.1606i	−0.0971781	−	1.29675i	0.709055	−	0.705153i	$-0.249122\pi$
$104$	0.175632	−	0.0845798i	0.0172221	−	0.00829373i
$105$	−15.3913	+	0.267043i	−1.50204	+	0.0260607i
$106$	0.197337	+	0.0950324i	0.0191671	+	0.00923037i
$107$	−0.651062	+	1.65888i	−0.0629405	+	0.160370i	−0.958884	−	0.283798i	$-0.908405\pi$
$107$	−0.651062	+	1.65888i	−0.0629405	+	0.160370i	0.895944	+	0.444168i	$0.146501\pi$
$108$	0.510311	−	6.80963i	0.0491047	−	0.655257i
$109$	1.14836	+	2.92598i	0.109993	+	0.280258i	0.975263	−	0.221049i	$-0.0709480\pi$
$109$	1.14836	+	2.92598i	0.109993	+	0.280258i	−0.865270	+	0.501307i	$0.832853\pi$
$110$	−0.0176756	+	0.00545220i	−0.00168530	+	0.000519847i
$111$	−4.04721	+	5.07504i	−0.384144	+	0.481702i
$112$	10.0213	−	3.28261i	0.946928	−	0.310178i
$113$	−7.55524	−	9.47397i	−0.710737	−	0.891236i	0.287037	−	0.957919i	$-0.407330\pi$
$113$	−7.55524	−	9.47397i	−0.710737	−	0.891236i	−0.997774	+	0.0666835i	$0.978758\pi$
$114$	−0.190464	−	0.129856i	−0.0178386	−	0.0121622i
$115$	9.91207	+	9.19706i	0.924306	+	0.857630i
$116$	−1.58218	+	2.74041i	−0.146902	+	0.254441i
$117$	0.681766	+	1.18085i	0.0630293	+	0.109170i
$118$	0.132183	−	0.579132i	0.0121684	−	0.0533134i
$119$	−3.28104	+	0.552909i	−0.300772	+	0.0506851i
$120$	0.252381	+	1.10575i	0.0230391	+	0.100941i
$121$	8.04997	−	7.46928i	0.731816	−	0.679026i
$122$	0.400373	−	0.0603466i	0.0362481	−	0.00546352i
$123$	−9.03803	+	1.36226i	−0.814932	+	0.122831i
$124$	−9.25218	+	8.58477i	−0.830871	+	0.770935i
$125$	−1.38961	−	6.08829i	−0.124291	−	0.544553i
$126$	−0.0671005	−	0.162616i	−0.00597779	−	0.0144870i
$127$	−0.969278	+	4.24668i	−0.0860095	+	0.376832i	−0.999553	−	0.0299097i	$-0.990478\pi$
$127$	−0.969278	+	4.24668i	−0.0860095	+	0.376832i	0.913543	+	0.406742i	$0.133335\pi$
$128$	−0.777892	−	1.34735i	−0.0687566	−	0.119090i
$129$	−3.18674	+	5.51959i	−0.280577	+	0.485973i
$130$	0.0995632	+	0.0923812i	0.00873227	+	0.00810236i
$131$	9.05216	+	6.17166i	0.790891	+	0.539220i	0.890056	−	0.455851i	$-0.150665\pi$
$131$	9.05216	+	6.17166i	0.790891	+	0.539220i	−0.0991655	+	0.995071i	$0.531617\pi$
$132$	0.354330	+	0.444316i	0.0308405	+	0.0386728i
$133$	−5.93523	−	0.789550i	−0.514650	−	0.0684626i
$134$	0.0484825	−	0.0607951i	0.00418825	−	0.00525189i
$135$	9.09836	−	2.80647i	0.783062	−	0.241543i
$136$	0.0895641	+	0.228206i	0.00768006	+	0.0195685i
$137$	0.480525	−	6.41216i	0.0410540	−	0.547828i	−0.938319	−	0.345770i	$-0.887618\pi$
$137$	0.480525	−	6.41216i	0.0410540	−	0.547828i	0.979373	−	0.202058i	$-0.0647631\pi$
$138$	−0.180662	+	0.460318i	−0.0153789	+	0.0391849i
$139$	−6.76934	−	3.25994i	−0.574168	−	0.276505i	0.124184	−	0.992259i	$-0.460369\pi$
$139$	−6.76934	−	3.25994i	−0.574168	−	0.276505i	−0.698352	+	0.715754i	$0.746083\pi$
$140$	9.37663	+	11.3483i	0.792469	+	0.959109i
$141$	12.3615	−	5.95300i	1.04103	−	0.501333i
$142$	0.0433617	+	0.578621i	0.00363883	+	0.0485568i
$143$	0.130140	+	0.0401428i	0.0108828	+	0.00335691i
$144$	4.49035	−	3.06147i	0.374196	−	0.255122i
$145$	−4.36282	−	0.657589i	−0.362312	−	0.0546098i
$146$	0.606887			0.0502263
$147$	−11.0575	−	9.56790i	−0.912008	−	0.789147i
$148$	6.20756			0.510258
$149$	−16.2778	−	2.45348i	−1.33353	−	0.200997i	−0.556702	−	0.830712i	$-0.687934\pi$
$149$	−16.2778	−	2.45348i	−1.33353	−	0.200997i	−0.776826	+	0.629715i	$0.783172\pi$
$150$	−0.232113	+	0.158252i	−0.0189519	+	0.0129212i
$151$	19.4328	+	5.99422i	1.58142	+	0.487802i	0.956216	−	0.292662i	$-0.0945409\pi$
$151$	19.4328	+	5.99422i	1.58142	+	0.487802i	0.625201	+	0.780464i	$0.285017\pi$
$152$	0.0329675	+	0.439921i	0.00267402	+	0.0356823i
$153$	−1.54496	+	0.744015i	−0.124903	+	0.0601500i
$154$	−0.0159604	−	0.00734783i	−0.00128613	−	0.000592105i
$155$	−15.8555	−	7.63558i	−1.27354	−	0.613305i
$156$	1.52451	−	3.88439i	0.122059	−	0.311000i
$157$	−1.58141	+	21.1025i	−0.126210	+	1.68416i	0.471044	+	0.882110i	$0.343877\pi$
$157$	−1.58141	+	21.1025i	−0.126210	+	1.68416i	−0.597255	+	0.802052i	$0.703742\pi$
$158$	−0.00178121	−	0.00453846i	−0.000141706	−	0.000361061i
$159$	8.96582	−	2.76559i	0.711036	−	0.219325i
$160$	1.01458	−	1.27224i	0.0802095	−	0.100580i
$161$	1.18189	+	12.7897i	0.0931463	+	1.00797i
$162$	0.341471	+	0.428191i	0.0268285	+	0.0336419i
$163$	4.08658	+	2.78619i	0.320086	+	0.218231i	0.712694	−	0.701475i	$-0.247475\pi$
$163$	4.08658	+	2.78619i	0.320086	+	0.218231i	−0.392608	+	0.919706i	$0.628427\pi$
$164$	6.40738	+	5.94518i	0.500333	+	0.464241i
$165$	−0.396194	+	0.686229i	−0.0308437	+	0.0534228i
$166$	0.224869	+	0.389485i	0.0174533	+	0.0302299i
$167$	−4.77276	+	20.9108i	−0.369327	+	1.61813i	0.359304	+	0.933221i	$0.383014\pi$
$167$	−4.77276	+	20.9108i	−0.369327	+	1.61813i	−0.728631	+	0.684906i	$0.759843\pi$
$168$	−0.522414	+	0.942226i	−0.0403051	+	0.0726943i
$169$	−0.222521	−	0.974928i	−0.0171170	−	0.0749945i
$170$	−0.125211	+	0.116179i	−0.00960322	+	0.00891049i
$171$	−3.05130	+	0.459910i	−0.233339	+	0.0351702i
$172$	6.02688	−	0.908406i	0.459545	−	0.0692653i
$173$	−4.04100	+	3.74950i	−0.307231	+	0.285069i	−0.818686	−	0.574241i	$-0.805297\pi$
$173$	−4.04100	+	3.74950i	−0.307231	+	0.285069i	0.511455	+	0.859310i	$0.329107\pi$
$174$	−0.0359049	−	0.157310i	−0.00272194	−	0.0119256i
$175$	−3.53822	+	6.38154i	−0.267464	+	0.482399i
$176$	0.120789	−	0.529210i	0.00910479	−	0.0398907i
$177$	−12.7234	−	22.0376i	−0.956348	−	1.65644i
$178$	−0.0786849	+	0.136286i	−0.00589769	+	0.0102151i
$179$	2.65962	+	2.46776i	0.198789	+	0.184449i	0.773286	−	0.634057i	$-0.218612\pi$
$179$	2.65962	+	2.46776i	0.198789	+	0.184449i	−0.574497	+	0.818507i	$0.694802\pi$
$180$	6.26841	+	4.27373i	0.467220	+	0.318545i
$181$	6.33060	+	7.93832i	0.470550	+	0.590051i	0.959306	−	0.282370i	$-0.0911205\pi$
$181$	6.33060	+	7.93832i	0.470550	+	0.590051i	−0.488756	+	0.872421i	$0.662549\pi$
$182$	0.0118717	+	0.128468i	0.000879989	+	0.00952266i
$183$	10.8143	−	13.5608i	0.799420	−	1.00244i
$184$	0.904303	−	0.278940i	0.0666661	−	0.0205638i
$185$	3.16212	+	8.05696i	0.232484	+	0.592359i
$186$	0.0480952	−	0.641786i	0.00352651	−	0.0470581i
$187$	−0.0625731	+	0.159434i	−0.00457580	+	0.0116589i
$188$	−11.8213	−	5.69285i	−0.862159	−	0.415194i
$189$	8.21549	+	3.78223i	0.597589	+	0.275117i
$190$	−0.276931	+	0.133363i	−0.0200907	+	0.00967517i
$191$	0.833999	+	11.1289i	0.0603461	+	0.805262i	0.942480	+	0.334263i	$0.108487\pi$
$191$	0.833999	+	11.1289i	0.0603461	+	0.805262i	−0.882134	+	0.470999i	$0.843893\pi$
$192$	−15.8550	−	4.89063i	−1.14424	−	0.352951i
$193$	8.83456	−	6.02330i	0.635926	−	0.433567i	−0.201974	−	0.979391i	$-0.564736\pi$
$193$	8.83456	−	6.02330i	0.635926	−	0.433567i	0.837900	+	0.545824i	$0.183783\pi$
$194$	−0.0942689	−	0.0142087i	−0.00676811	−	0.00102013i
$195$	5.81824			0.416653
$196$	−0.560622	+	13.9721i	−0.0400444	+	0.998008i
$197$	24.0314			1.71217			0.856083	−	0.516838i	$-0.172891\pi$
$197$	24.0314			1.71217			0.856083	+	0.516838i	$0.172891\pi$
$198$	−0.00895417	−	0.00134962i	−0.000636345	−	9.59136e-5i
$199$	3.31450	−	2.25979i	0.234958	−	0.160192i	−0.440117	−	0.897940i	$-0.645063\pi$
$199$	3.31450	−	2.25979i	0.234958	−	0.160192i	0.675076	+	0.737748i	$0.264111\pi$
$200$	0.513735	+	0.158466i	0.0363266	+	0.0112053i
$201$	−0.248931	−	3.32175i	−0.0175582	−	0.234298i
$202$	0.150153	−	0.0723097i	0.0105647	−	0.00508769i
$203$	−2.66952	−	3.23086i	−0.187363	−	0.226762i
$204$	4.72808	+	2.27692i	0.331032	+	0.159417i
$205$	−4.45250	+	11.3448i	−0.310976	+	0.792354i
$206$	0.0480926	−	0.641751i	0.00335077	−	0.0447129i
$207$	2.41836	+	6.16188i	0.168088	+	0.428280i
$208$	−3.80866	+	1.17482i	−0.264083	+	0.0814589i
$209$	−0.192165	+	0.240967i	−0.0132923	+	0.0166680i
$210$	−0.744086	−	0.0989840i	−0.0513468	−	0.00683055i
$211$	−10.8159	−	13.5627i	−0.744597	−	0.933695i	0.254849	−	0.966981i	$-0.417974\pi$
$211$	−10.8159	−	13.5627i	−0.744597	−	0.933695i	−0.999446	+	0.0332859i	$0.989403\pi$
$212$	−7.41355	−	5.05447i	−0.509164	−	0.347142i
$213$	18.2210	+	16.9066i	1.24848	+	1.15842i
$214$	−0.0434495	+	0.0752568i	−0.00297015	+	0.00514445i
$215$	4.24913	+	7.35971i	0.289788	+	0.501928i
$216$	0.148283	−	0.649669i	0.0100894	−	0.0442044i
$217$	−6.37625	−	15.4527i	−0.432848	−	1.04899i
$218$	0.0341070	+	0.149432i	0.00231001	+	0.0101208i
$219$	19.0577	−	17.6830i	1.28780	−	1.19490i
$220$	0.749298	−	0.112938i	0.0505177	−	0.00761431i
$221$	1.24355	−	0.187436i	0.0836505	−	0.0126083i
$222$	−0.232035	+	0.215297i	−0.0155731	+	0.0144498i
$223$	−1.41629	−	6.20517i	−0.0948418	−	0.415529i	0.905112	−	0.425174i	$-0.139787\pi$
$223$	−1.41629	−	6.20517i	−0.0948418	−	0.415529i	−0.999953	+	0.00964477i	$0.996930\pi$
$224$	1.52424	−	0.256859i	0.101842	−	0.0171621i
$225$	−0.836795	+	3.66624i	−0.0557863	+	0.244416i
$226$	−0.295447	−	0.511730i	−0.0196529	−	0.0340398i
$227$	1.76151	−	3.05102i	0.116915	−	0.202503i	−0.801629	−	0.597822i	$-0.796033\pi$
$227$	1.76151	−	3.05102i	0.116915	−	0.202503i	0.918544	+	0.395319i	$0.129366\pi$
$228$	6.92253	+	6.42317i	0.458456	+	0.425385i
$229$	19.5915	+	13.3573i	1.29464	+	0.882673i	0.997395	−	0.0721268i	$-0.0229786\pi$
$229$	19.5915	+	13.3573i	1.29464	+	0.882673i	0.297248	+	0.954800i	$0.403931\pi$
$230$	0.411103	+	0.515507i	0.0271073	+	0.0339915i
$231$	−0.715291	+	0.234302i	−0.0470627	+	0.0154160i
$232$	−0.192528	+	0.241423i	−0.0126401	+	0.0158502i
$233$	−18.6610	+	5.75615i	−1.22252	+	0.377098i	−0.837821	−	0.545944i	$-0.816171\pi$
$233$	−18.6610	+	5.75615i	−1.22252	+	0.377098i	−0.384699	+	0.923042i	$0.625695\pi$
$234$	0.0242916	+	0.0618939i	0.00158799	+	0.00404613i
$235$	1.36713	−	18.2431i	0.0891820	−	1.19005i
$236$	−8.89048	+	22.6526i	−0.578721	+	1.47456i
$237$	−0.188172	−	0.0906189i	−0.0122231	−	0.00588633i
$238$	−0.162225	+	0.00281464i	−0.0105155	+	0.000182446i
$239$	−9.42497	+	4.53883i	−0.609651	+	0.293592i	−0.713122	−	0.701040i	$-0.752719\pi$
$239$	−9.42497	+	4.53883i	−0.609651	+	0.293592i	0.103471	+	0.994632i	$0.467005\pi$
$240$	−1.73299	−	23.1252i	−0.111864	−	1.49272i
$241$	10.8194	+	3.33734i	0.696939	+	0.214977i	0.622927	−	0.782280i	$-0.285943\pi$
$241$	10.8194	+	3.33734i	0.696939	+	0.214977i	0.0740123	+	0.997257i	$0.476420\pi$
$242$	0.442442	−	0.301652i	0.0284413	−	0.0193909i
$243$	13.0585	+	1.96825i	0.837704	+	0.126264i
$244$	−16.5869			−1.06187
$245$	−18.4204	+	6.38973i	−1.17683	+	0.408225i
$246$	−0.445700			−0.0284168
$247$	2.23779	+	0.337293i	0.142387	+	0.0214614i
$248$	−1.01764	+	0.693816i	−0.0646203	+	0.0440574i
$249$	18.4099	+	5.67871i	1.16668	+	0.359874i
$250$	−0.0227567	−	0.303667i	−0.00143926	−	0.0192056i
$251$	−25.7708	+	12.4106i	−1.62664	+	0.783349i	−0.626649	+	0.779302i	$0.715574\pi$
$251$	−25.7708	+	12.4106i	−1.62664	+	0.783349i	−0.999992	+	0.00404699i	$0.998712\pi$
$252$	1.72525	+	6.99700i	0.108681	+	0.440770i
$253$	0.595680	+	0.286864i	0.0374501	+	0.0180350i
$254$	−0.0776010	+	0.197724i	−0.00486912	+	0.0124063i
$255$	−0.546802	+	7.29657i	−0.0342421	+	0.456929i
$256$	5.77608	+	14.7172i	0.361005	+	0.919826i
$257$	−6.75453	+	2.08350i	−0.421336	+	0.129965i	−0.498171	−	0.867079i	$-0.665995\pi$
$257$	−6.75453	+	2.08350i	−0.421336	+	0.129965i	0.0768349	+	0.997044i	$0.475519\pi$
$258$	−0.193775	+	0.242986i	−0.0120639	+	0.0151276i
$259$	−2.87047	+	7.70423i	−0.178362	+	0.478718i
$260$	−3.46909	−	4.35010i	−0.215144	−	0.269782i
$261$	−1.78461	−	1.21673i	−0.110465	−	0.0753135i
$262$	0.391627	+	0.363377i	0.0241948	+	0.0224495i
$263$	11.9905	−	20.7682i	0.739369	−	1.28062i	−0.213412	−	0.976962i	$-0.568458\pi$
$263$	11.9905	−	20.7682i	0.739369	−	1.28062i	0.952780	−	0.303661i	$-0.0982092\pi$
$264$	0.0277286	+	0.0480274i	0.00170658	+	0.00295588i
$265$	2.78388	−	12.1970i	0.171012	−	0.749255i
$266$	−0.280449	−	0.0812067i	−0.0171955	−	0.00497910i
$267$	1.50010	+	6.57237i	0.0918046	+	0.402222i
$268$	−2.33513	+	2.16669i	−0.142641	+	0.132352i
$269$	−25.9951	+	3.91813i	−1.58495	+	0.238893i	−0.881616	−	0.471967i	$-0.843544\pi$
$269$	−25.9951	+	3.91813i	−1.58495	+	0.238893i	−0.703334	+	0.710859i	$0.748306\pi$
$270$	0.459106	−	0.0691990i	0.0279403	−	0.00421132i
$271$	11.0453	−	10.2486i	0.670956	−	0.622556i	−0.269287	−	0.963060i	$-0.586788\pi$
$271$	11.0453	−	10.2486i	0.670956	−	0.622556i	0.940243	+	0.340504i	$0.110598\pi$
$272$	−1.11538	−	4.88679i	−0.0676298	−	0.296305i
$273$	4.11598	+	3.68828i	0.249111	+	0.223225i
$274$	0.0697723	−	0.305692i	0.00421510	−	0.0184675i
$275$	0.187801	+	0.325282i	0.0113249	+	0.0196152i
$276$	10.1288	−	17.5437i	0.609684	−	1.05600i
$277$	0.435133	+	0.403745i	0.0261446	+	0.0242587i	0.693137	−	0.720806i	$-0.256228\pi$
$277$	0.435133	+	0.403745i	0.0261446	+	0.0242587i	−0.666992	+	0.745065i	$0.732419\pi$
$278$	−0.302715	−	0.206388i	−0.0181556	−	0.0123783i
$279$	−5.37144	−	6.73558i	−0.321580	−	0.403249i
$280$	0.739739	+	1.23142i	0.0442079	+	0.0735917i
$281$	−2.52674	+	3.16843i	−0.150733	+	0.189013i	−0.851465	−	0.524412i	$-0.824285\pi$
$281$	−2.52674	+	3.16843i	−0.150733	+	0.189013i	0.700732	+	0.713424i	$0.252857\pi$
$282$	0.639319	−	0.197204i	0.0380709	−	0.0117433i
$283$	−8.86508	−	22.5879i	−0.526974	−	1.34271i	−0.908320	−	0.418276i	$-0.862635\pi$
$283$	−8.86508	−	22.5879i	−0.526974	−	1.34271i	0.381346	−	0.924432i	$-0.375461\pi$
$284$	1.77635	−	23.7037i	0.105407	−	1.40656i
$285$	−4.81048	+	12.2569i	−0.284948	+	0.726036i
$286$	0.00598339	+	0.00288145i	0.000353805	+	0.000170384i
$287$	−10.3415	+	5.20309i	−0.610437	+	0.307129i
$288$	0.717727	−	0.345639i	0.0422925	−	0.0203670i
$289$	−1.15222	−	15.3753i	−0.0677777	−	0.904431i
$290$	−0.205589	−	0.0634158i	−0.0120726	−	0.00372391i
$291$	−3.37427	+	2.30054i	−0.197803	+	0.134860i
$292$	−24.5840	−	3.70544i	−1.43867	−	0.216844i
$293$	−11.3054			−0.660469			−0.330234	−	0.943899i	$-0.607128\pi$
$293$	−11.3054			−0.660469			−0.330234	+	0.943899i	$0.607128\pi$
$294$	−0.463639	−	0.541713i	−0.0270400	−	0.0315933i
$295$	−33.9302			−1.97549
$296$	0.598994	+	0.0902838i	0.0348158	+	0.00524764i
$297$	0.384661	−	0.262258i	0.0223203	−	0.0152177i
$298$	−0.767059	−	0.236606i	−0.0444345	−	0.0137062i
$299$	−0.362788	−	4.84107i	−0.0209806	−	0.279966i
$300$	10.3687	−	4.99331i	0.598638	−	0.288289i
$301$	−1.65950	+	7.90005i	−0.0956517	+	0.455351i
$302$	0.893454	+	0.430265i	0.0514125	+	0.0247590i
$303$	2.60825	−	6.64572i	0.149840	−	0.381786i
$304$	0.674065	−	8.99478i	0.0386603	−	0.515886i
$305$	−8.44935	−	21.5286i	−0.483808	−	1.23272i
$306$	−0.0799031	+	0.0246468i	−0.00456775	+	0.00140897i
$307$	15.2479	−	19.1202i	0.870242	−	1.09125i	−0.124838	−	0.992177i	$-0.539841\pi$
$307$	15.2479	−	19.1202i	0.870242	−	1.09125i	0.995080	−	0.0990722i	$-0.0315875\pi$
$308$	0.601667	+	0.395097i	0.0342832	+	0.0225127i
$309$	−17.1886	−	21.5538i	−0.977824	−	1.22615i
$310$	−0.709032	−	0.483410i	−0.0402703	−	0.0274558i
$311$	6.96692	+	6.46435i	0.395058	+	0.366560i	0.852543	−	0.522657i	$-0.175059\pi$
$311$	6.96692	+	6.46435i	0.395058	+	0.366560i	−0.457485	+	0.889217i	$0.651250\pi$
$312$	0.203602	−	0.352649i	0.0115267	−	0.0199648i
$313$	12.3071	+	21.3166i	0.695641	+	1.20488i	0.969964	+	0.243248i	$0.0782127\pi$
$313$	12.3071	+	21.3166i	0.695641	+	1.20488i	−0.274324	+	0.961637i	$0.588454\pi$
$314$	−0.229621	+	1.00604i	−0.0129583	+	0.0567739i
$315$	−8.20275	+	5.80351i	−0.462173	+	0.326991i
$316$	0.0444438	+	0.194721i	0.00250016	+	0.0109539i
$317$	19.2651	−	17.8754i	1.08204	−	1.00398i	0.0820631	−	0.996627i	$-0.473849\pi$
$317$	19.2651	−	17.8754i	1.08204	−	1.00398i	0.999973	−	0.00735556i	$-0.00234137\pi$
$318$	0.452418	−	0.0681910i	0.0253703	−	0.00382396i
$319$	−0.213324	+	0.0321535i	−0.0119439	+	0.00180025i
$320$	−16.2178	+	15.0479i	−0.906602	+	0.841203i
$321$	0.828350	+	3.62924i	0.0462340	+	0.202564i
$322$	−0.0359632	+	0.625288i	−0.00200415	+	0.0348460i
$323$	−0.633303	+	2.77468i	−0.0352379	+	0.154387i
$324$	−11.2180	−	19.4302i	−0.623224	−	1.07945i
$325$	1.37896	−	2.38843i	0.0764911	−	0.132486i
$326$	0.176799	+	0.164046i	0.00979202	+	0.00908566i
$327$	5.42507	+	3.69875i	0.300007	+	0.204541i
$328$	0.531808	+	0.666866i	0.0293642	+	0.0368215i
$329$	12.5318	−	12.0390i	0.690900	−	0.663734i
$330$	−0.0240912	+	0.0302095i	−0.00132618	+	0.00166298i
$331$	−4.25171	+	1.31148i	−0.233695	+	0.0720855i	−0.409391	−	0.912359i	$-0.634259\pi$
$331$	−4.25171	+	1.31148i	−0.233695	+	0.0720855i	0.175696	+	0.984445i	$0.443783\pi$
$332$	−6.73102	−	17.1504i	−0.369413	−	0.941248i
$333$	−0.316642	+	4.22529i	−0.0173519	+	0.231545i
$334$	−0.382110	+	0.973600i	−0.0209081	+	0.0532730i
$335$	−4.00172	−	1.92713i	−0.218637	−	0.105290i
$336$	13.4335	−	17.4579i	0.732855	−	0.952408i
$337$	−14.8370	+	7.14514i	−0.808225	+	0.389221i	−0.791904	−	0.610646i	$-0.790910\pi$
$337$	−14.8370	+	7.14514i	−0.808225	+	0.389221i	−0.0163216	+	0.999867i	$0.505196\pi$
$338$	−0.00364407	−	0.0486268i	−0.000198211	−	0.00264495i
$339$	−24.1881	−	7.46104i	−1.31372	−	0.405228i
$340$	5.78142	−	3.94170i	0.313541	−	0.213769i
$341$	−0.850873	−	0.128248i	−0.0460773	−	0.00694504i
$342$	−0.150472			−0.00813658
$343$	−17.0816	−	7.15671i	−0.922320	−	0.386426i
$344$	0.594772			0.0320679
$345$	27.9300	+	4.20977i	1.50370	+	0.226646i
$346$	−0.222101	+	0.151426i	−0.0119402	+	0.00814071i
$347$	−25.1589	−	7.76050i	−1.35060	−	0.416606i	−0.466757	−	0.884385i	$-0.654578\pi$
$347$	−25.1589	−	7.76050i	−1.35060	−	0.416606i	−0.883845	+	0.467780i	$0.845054\pi$
$348$	0.493969	+	6.59156i	0.0264795	+	0.353345i
$349$	−18.4370	+	8.87880i	−0.986910	+	0.475271i	−0.856477	−	0.516186i	$-0.827351\pi$
$349$	−18.4370	+	8.87880i	−0.986910	+	0.475271i	−0.130434	+	0.991457i	$0.541637\pi$
$350$	−0.216987	+	0.281993i	−0.0115984	+	0.0150732i
$351$	−3.07990	−	1.48320i	−0.164393	−	0.0791674i
$352$	0.0290689	−	0.0740664i	0.00154938	−	0.00394775i
$353$	−0.851571	+	11.3634i	−0.0453246	+	0.604814i	0.927583	+	0.373618i	$0.121883\pi$
$353$	−0.851571	+	11.3634i	−0.0453246	+	0.604814i	−0.972907	+	0.231196i	$0.925736\pi$
$354$	−0.453338	−	1.15509i	−0.0240947	−	0.0613922i
$355$	31.6705	−	9.76907i	1.68090	−	0.518488i
$356$	4.01951	−	5.04030i	0.213034	−	0.267136i
$357$	−5.01224	+	4.81516i	−0.265276	+	0.254845i
$358$	0.110308	+	0.138321i	0.00582993	+	0.00731051i
$359$	−16.5291	−	11.2693i	−0.872372	−	0.594773i	0.0422392	−	0.999108i	$-0.486551\pi$
$359$	−16.5291	−	11.2693i	−0.872372	−	0.594773i	−0.914611	+	0.404334i	$0.867503\pi$
$360$	0.542708	+	0.503559i	0.0286032	+	0.0265399i
$361$	6.93926	−	12.0192i	0.365224	−	0.632587i
$362$	0.247558	+	0.428783i	0.0130114	+	0.0225363i
$363$	5.10446	−	22.3641i	0.267915	−	1.17381i
$364$	0.303475	−	5.27649i	0.0159064	−	0.276563i
$365$	−7.71365	−	33.7957i	−0.403751	−	1.76895i
$366$	0.620008	−	0.575283i	0.0324083	−	0.0300705i
$367$	6.72766	−	1.01403i	0.351181	−	0.0529320i	0.0289168	−	0.999582i	$-0.490794\pi$
$367$	6.72766	−	1.01403i	0.351181	−	0.0529320i	0.322264	+	0.946650i	$0.395556\pi$
$368$	−19.1332	+	2.88387i	−0.997387	+	0.150332i
$369$	−4.37354	+	4.05805i	−0.227677	+	0.211254i
$370$	0.0939166	+	0.411476i	0.00488249	+	0.0213916i
$371$	9.70126	−	6.86372i	0.503665	−	0.356347i
$372$	−5.86678	+	25.7040i	−0.304178	+	1.33269i
$373$	10.3948	+	18.0044i	0.538224	+	0.932231i	0.999000	+	0.0447144i	$0.0142378\pi$
$373$	10.3948	+	18.0044i	0.538224	+	0.932231i	−0.460776	+	0.887516i	$0.652429\pi$
$374$	−0.00417590	+	0.00723288i	−0.000215931	+	0.000374003i
$375$	−9.56262	−	8.87281i	−0.493811	−	0.458190i
$376$	−1.05789	−	0.721259i	−0.0545567	−	0.0371961i
$377$	0.987646	+	1.23847i	0.0508664	+	0.0637844i
$378$	0.368650	+	0.242082i	0.0189613	+	0.0124513i
$379$	4.87665	−	6.11512i	0.250497	−	0.314113i	−0.640646	−	0.767837i	$-0.721333\pi$
$379$	4.87665	−	6.11512i	0.250497	−	0.314113i	0.891142	+	0.453724i	$0.149905\pi$
$380$	12.0323	−	3.71146i	0.617243	−	0.190394i
$381$	3.32426	+	8.47007i	0.170307	+	0.433935i
$382$	−0.0406684	+	0.542682i	−0.00208078	+	0.0277660i
$383$	−11.4400	+	29.1486i	−0.584555	+	1.48942i	0.266230	+	0.963910i	$0.414222\pi$
$383$	−11.4400	+	29.1486i	−0.584555	+	1.48942i	−0.850785	+	0.525514i	$0.823873\pi$
$384$	−2.92805	−	1.41007i	−0.149421	−	0.0719576i
$385$	−0.206318	+	0.982182i	−0.0105150	+	0.0500566i
$386$	0.469765	−	0.226227i	0.0239104	−	0.0115146i
$387$	0.310898	+	4.14865i	0.0158038	+	0.210888i
$388$	3.73192	+	1.15114i	0.189459	+	0.0584405i
$389$	−6.82376	+	4.65236i	−0.345978	+	0.235884i	−0.723824	−	0.689984i	$-0.757617\pi$
$389$	−6.82376	+	4.65236i	−0.345978	+	0.235884i	0.377846	+	0.925869i	$0.376665\pi$
$390$	0.280547	+	0.0422856i	0.0142060	+	0.00214122i
$391$	6.10520			0.308753
$392$	−0.257310	+	1.34008i	−0.0129961	+	0.0676840i
$393$	22.8858			1.15443
$394$	1.15876	+	0.174655i	0.0583773	+	0.00879897i
$395$	−0.230094	+	0.156875i	−0.0115773	+	0.00789325i
$396$	0.354478	+	0.109342i	0.0178132	+	0.00549464i
$397$	−1.24259	−	16.5812i	−0.0623638	−	0.832188i	−0.937428	−	0.348180i	$-0.886800\pi$
$397$	−1.24259	−	16.5812i	−0.0623638	−	0.832188i	0.875064	−	0.484008i	$-0.160819\pi$
$398$	0.176244	−	0.0848744i	0.00883429	−	0.00425437i
$399$	−11.1729	+	5.62141i	−0.559345	+	0.281423i
$400$	−9.90378	−	4.76941i	−0.495189	−	0.238471i
$401$	−13.8865	+	35.3822i	−0.693458	+	1.76690i	−0.0534044	+	0.998573i	$0.517007\pi$
$401$	−13.8865	+	35.3822i	−0.693458	+	1.76690i	−0.640054	+	0.768330i	$0.721088\pi$
$402$	0.0121386	−	0.161979i	0.000605420	−	0.00807877i
$403$	2.30831	+	5.88148i	0.114985	+	0.292978i
$404$	−6.52393	+	2.01236i	−0.324577	+	0.100119i
$405$	19.5045	−	24.4579i	0.969187	−	1.21532i
$406$	−0.105239	−	0.175188i	−0.00522292	−	0.00869446i
$407$	0.263866	+	0.330877i	0.0130793	+	0.0164010i
$408$	0.423117	+	0.288476i	0.0209474	+	0.0142817i
$409$	26.3719	+	24.4696i	1.30401	+	1.20994i	0.962881	+	0.269926i	$0.0869994\pi$
$409$	26.3719	+	24.4696i	1.30401	+	1.20994i	0.341128	+	0.940017i	$0.389191\pi$
$410$	−0.297144	+	0.514668i	−0.0146749	+	0.0254177i
$411$	−6.71599	−	11.6324i	−0.331275	−	0.573785i
$412$	−5.86645	+	25.7026i	−0.289019	+	1.26628i
$413$	−24.0031	−	21.5089i	−1.18112	−	1.05838i
$414$	0.0718265	+	0.314693i	0.00353008	+	0.0154663i
$415$	18.8311	−	17.4727i	0.924384	−	0.857703i
$416$	−0.577705	+	0.0870750i	−0.0283243	+	0.00426920i
$417$	−15.5195	+	2.33919i	−0.759994	+	0.114551i
$418$	−0.0110172	+	0.0102224i	−0.000538868	+	0.000499996i
$419$	−2.45004	−	10.7343i	−0.119692	−	0.524406i	−0.998853	−	0.0478808i	$-0.984753\pi$
$419$	−2.45004	−	10.7343i	−0.119692	−	0.524406i	0.879161	−	0.476525i	$-0.158104\pi$
$420$	29.5373	+	8.55280i	1.44127	+	0.417334i
$421$	−5.96192	+	26.1209i	−0.290566	+	1.27305i	0.593173	+	0.805075i	$0.297875\pi$
$421$	−5.96192	+	26.1209i	−0.290566	+	1.27305i	−0.883740	+	0.467979i	$0.844982\pi$
$422$	−0.422955	−	0.732580i	−0.0205891	−	0.0356614i
$423$	4.47794	−	7.75603i	0.217725	−	0.377111i
$424$	−0.641852	−	0.595552i	−0.0311711	−	0.0289225i
$425$	2.86570	+	1.95380i	0.139007	+	0.0947733i
$426$	0.755716	+	0.947638i	0.0366146	+	0.0459132i
$427$	7.67004	−	20.5861i	0.371179	−	0.996230i
$428$	2.21956	−	2.78324i	0.107286	−	0.134533i
$429$	0.271850	−	0.0838546i	0.0131250	−	0.00404854i
$430$	0.151398	+	0.385756i	0.00730105	+	0.0186028i
$431$	0.867233	−	11.5724i	0.0417731	−	0.557424i	−0.936576	−	0.350464i	$-0.886024\pi$
$431$	0.867233	−	11.5724i	0.0417731	−	0.557424i	0.978349	−	0.206960i	$-0.0663570\pi$
$432$	−4.97776	+	12.6831i	−0.239492	+	0.610217i
$433$	33.9657	+	16.3570i	1.63229	+	0.786069i	0.999935	+	0.0113890i	$0.00362531\pi$
$433$	33.9657	+	16.3570i	1.63229	+	0.786069i	0.632354	+	0.774680i	$0.282089\pi$
$434$	−0.195147	−	0.791444i	−0.00936733	−	0.0379905i
$435$	−8.30374	+	3.99887i	−0.398134	+	0.191731i
$436$	−0.469234	−	6.26149i	−0.0224722	−	0.299871i
$437$	10.4983	+	3.23829i	0.502201	+	0.154909i
$438$	1.04745	−	0.714138i	0.0500490	−	0.0341228i
$439$	−11.3002	−	1.70324i	−0.539331	−	0.0812911i	−0.126273	−	0.991996i	$-0.540301\pi$
$439$	−11.3002	−	1.70324i	−0.539331	−	0.0812911i	−0.413059	+	0.910704i	$0.635540\pi$
$440$	0.0739456			0.00352522
$441$	−9.48179	−	1.09430i	−0.451514	−	0.0521097i
$442$	0.0613245			0.00291691
$443$	−4.65977	−	0.702347i	−0.221392	−	0.0333695i	0.0374092	−	0.999300i	$-0.488089\pi$
$443$	−4.65977	−	0.702347i	−0.221392	−	0.0333695i	−0.258802	+	0.965930i	$0.583328\pi$
$444$	10.7138	−	7.30458i	0.508457	−	0.346660i
$445$	8.58948	+	2.64950i	0.407180	+	0.125599i
$446$	−0.0231936	−	0.309497i	−0.00109825	−	0.0146551i
$447$	−30.9815	+	14.9199i	−1.46537	+	0.705687i
$448$	−21.0120	+	0.364563i	−0.992724	+	0.0172240i
$449$	−5.01072	−	2.41304i	−0.236471	−	0.113878i	0.311896	−	0.950116i	$-0.399036\pi$
$449$	−5.01072	−	2.41304i	−0.236471	−	0.113878i	−0.548367	+	0.836238i	$0.684750\pi$
$450$	−0.0669943	+	0.170699i	−0.00315814	+	0.00804681i
$451$	−0.0445322	+	0.594241i	−0.00209694	+	0.0279817i
$452$	8.84363	+	22.5332i	0.415969	+	1.05987i
$453$	40.5933	−	12.5214i	1.90724	−	0.588305i
$454$	0.107111	−	0.134313i	0.00502697	−	0.00630363i
$455$	7.00309	−	2.29395i	0.328310	−	0.107542i
$456$	0.574565	+	0.720482i	0.0269065	+	0.0337397i
$457$	25.5591	+	17.4259i	1.19561	+	0.815150i	0.986663	−	0.162778i	$-0.0520454\pi$
$457$	25.5591	+	17.4259i	1.19561	+	0.815150i	0.208943	+	0.977928i	$0.432998\pi$
$458$	0.847595	+	0.786454i	0.0396055	+	0.0367486i
$459$	2.14951	−	3.72306i	0.100330	−	0.173777i
$460$	−13.5056	−	23.3923i	−0.629701	−	1.09067i
$461$	−1.09427	+	4.79432i	−0.0509653	+	0.223294i	−0.993997	−	0.109410i	$-0.965104\pi$
$461$	−1.09427	+	4.79432i	−0.0509653	+	0.223294i	0.943031	+	0.332704i	$0.107961\pi$
$462$	−0.0361931	+	0.00609913i	−0.00168385	+	0.000283757i
$463$	−1.40323	−	6.14796i	−0.0652137	−	0.285720i	0.931797	−	0.362979i	$-0.118240\pi$
$463$	−1.40323	−	6.14796i	−0.0652137	−	0.285720i	−0.997011	+	0.0772591i	$0.975383\pi$
$464$	4.62824	−	4.29438i	0.214861	−	0.199361i
$465$	−36.3505	+	5.47895i	−1.68571	+	0.254080i
$466$	−0.941637	+	0.141929i	−0.0436205	+	0.00657473i
$467$	−14.6512	+	13.5944i	−0.677979	+	0.629072i	−0.942066	−	0.335426i	$-0.891120\pi$
$467$	−14.6512	+	13.5944i	−0.677979	+	0.629072i	0.264088	+	0.964499i	$0.414929\pi$
$468$	−0.606108	−	2.65553i	−0.0280173	−	0.122752i
$469$	−1.60928	−	3.90006i	−0.0743099	−	0.180088i
$470$	0.198508	−	0.869720i	0.00915649	−	0.0401172i
$471$	22.1024	+	38.2824i	1.01842	+	1.76396i
$472$	−1.18734	+	2.05654i	−0.0546520	+	0.0946600i
$473$	0.304606	+	0.282633i	0.0140058	+	0.0129955i
$474$	−0.00841478	−	0.00573710i	−0.000386503	−	0.000263514i
$475$	3.89143	+	4.87970i	0.178551	+	0.223896i
$476$	6.58864	+	0.876471i	0.301990	+	0.0401730i
$477$	3.81858	−	4.78835i	0.174841	−	0.219243i
$478$	−0.487445	+	0.150357i	−0.0222952	+	0.00687716i
$479$	−2.86197	−	7.29219i	−0.130767	−	0.333189i	0.850462	−	0.526037i	$-0.176323\pi$
$479$	−2.86197	−	7.29219i	−0.130767	−	0.333189i	−0.981229	+	0.192848i	$0.938227\pi$
$480$	0.254022	−	3.38969i	0.0115945	−	0.154717i
$481$	1.13529	−	2.89267i	0.0517647	−	0.131894i
$482$	0.497440	+	0.239555i	0.0226578	+	0.0109114i
$483$	17.0898	+	20.6834i	0.777612	+	0.941127i
$484$	−19.7644	+	9.51802i	−0.898380	+	0.432637i
$485$	0.406933	+	5.43015i	0.0184779	+	0.246570i
$486$	0.615357	+	0.189812i	0.0279132	+	0.00861007i
$487$	−0.282872	+	0.192859i	−0.0128181	+	0.00873925i	−0.569712	−	0.821844i	$-0.692945\pi$
$487$	−0.282872	+	0.192859i	−0.0128181	+	0.00873925i	0.556894	+	0.830584i	$0.311993\pi$
$488$	−1.60054	−	0.241243i	−0.0724531	−	0.0109206i
$489$	10.3318			0.467218
$490$	−0.934641	+	0.174228i	−0.0422228	+	0.00787083i
$491$	−10.9403			−0.493729			−0.246864	−	0.969050i	$-0.579400\pi$
$491$	−10.9403			−0.493729			−0.246864	+	0.969050i	$0.579400\pi$
$492$	18.0546	+	2.72129i	0.813963	+	0.122685i
$493$	−1.64596	+	1.12220i	−0.0741305	+	0.0505413i
$494$	0.105452	+	0.0325275i	0.00474449	+	0.00146348i
$495$	0.0386527	+	0.515785i	0.00173731	+	0.0231828i
$496$	22.6890	−	10.9264i	1.01876	−	0.490611i
$497$	28.5974	+	13.1656i	1.28277	+	0.590558i
$498$	0.846427	+	0.407618i	0.0379293	+	0.0182658i
$499$	−3.18544	+	8.11638i	−0.142600	+	0.363339i	−0.984274	−	0.176647i	$-0.943475\pi$
$499$	−3.18544	+	8.11638i	−0.142600	+	0.363339i	0.841674	+	0.539985i	$0.181570\pi$
$500$	−0.932249	+	12.4400i	−0.0416914	+	0.556333i
$501$	16.3688	+	41.7069i	0.731302	+	1.86333i
$502$	−1.33283	+	0.411123i	−0.0594870	+	0.0183493i
$503$	−26.6967	+	33.4766i	−1.19035	+	1.49265i	−0.362232	+	0.932088i	$0.617985\pi$
$503$	−26.6967	+	33.4766i	−1.19035	+	1.49265i	−0.828115	+	0.560559i	$0.810586\pi$
$504$	0.0647113	+	0.700263i	0.00288247	+	0.0311922i
$505$	−5.93518	−	7.44248i	−0.264112	−	0.331186i
$506$	0.0266379	+	0.0181614i	0.00118420	+	0.000807374i
$507$	−1.53128	−	1.42082i	−0.0680064	−	0.0631007i
$508$	4.35072	−	7.53566i	0.193032	−	0.334341i
$509$	20.0860	+	34.7900i	0.890297	+	1.54204i	0.839520	+	0.543329i	$0.182836\pi$
$509$	20.0860	+	34.7900i	0.890297	+	1.54204i	0.0507765	+	0.998710i	$0.483830\pi$
$510$	−0.0793957	+	0.347855i	−0.00351570	+	0.0154033i
$511$	15.9668	−	28.7978i	0.706331	−	1.27394i
$512$	0.863942	+	3.78518i	0.0381812	+	0.167283i
$513$	5.67099	−	5.26191i	0.250380	−	0.232319i
$514$	−0.340835	+	0.0513727i	−0.0150336	+	0.00226595i
$515$	−36.3485	+	5.47865i	−1.60171	+	0.241418i
$516$	9.33307	−	8.65982i	0.410865	−	0.381227i
$517$	−0.199049	−	0.872091i	−0.00875417	−	0.0383545i
$518$	−0.194402	+	0.350624i	−0.00854154	+	0.0154055i
$519$	−2.56238	+	11.2265i	−0.112476	+	0.492790i
$520$	−0.271479	−	0.470215i	−0.0119051	−	0.0206203i
$521$	−7.68695	+	13.3142i	−0.336771	+	0.583305i	−0.983823	−	0.179141i	$-0.942668\pi$
$521$	−7.68695	+	13.3142i	−0.336771	+	0.583305i	0.647052	+	0.762446i	$0.276002\pi$
$522$	−0.0772083	−	0.0716388i	−0.00337931	−	0.00313554i
$523$	−31.4079	−	21.4135i	−1.37337	−	0.936348i	−0.999962	−	0.00868126i	$-0.997237\pi$
$523$	−31.4079	−	21.4135i	−1.37337	−	0.936348i	−0.373408	−	0.927667i	$-0.621811\pi$
$524$	−13.6455	−	17.1109i	−0.596106	−	0.747494i
$525$	1.40257	+	15.1776i	0.0612130	+	0.662406i
$526$	0.729104	−	0.914268i	0.0317904	−	0.0398640i
$527$	−7.59281	+	2.34207i	−0.330748	+	0.102022i
$528$	−0.414260	−	1.05552i	−0.0180283	−	0.0459355i
$529$	0.0424114	−	0.565941i	0.00184397	−	0.0246061i
$530$	0.222879	−	0.567887i	0.00968126	−	0.0246674i
$531$	−14.9654	−	7.20697i	−0.649444	−	0.312756i
$532$	10.8647	+	5.00187i	0.471045	+	0.216859i
$533$	3.94223	−	1.89848i	0.170757	−	0.0822323i
$534$	0.0245661	+	0.327812i	0.00106308	+	0.0141858i
$535$	4.74308	+	1.46305i	0.205061	+	0.0632530i
$536$	−0.256840	+	0.175111i	−0.0110938	+	0.00756362i
$537$	7.49420	+	1.12957i	0.323399	+	0.0487445i
$538$	−1.28192			−0.0552675
$539$	−0.768577	+	0.564033i	−0.0331049	+	0.0242946i
$540$	−19.0201			−0.818494
$541$	−42.9515	−	6.47390i	−1.84663	−	0.278335i	−0.869967	−	0.493110i	$-0.835860\pi$
$541$	−42.9515	−	6.47390i	−1.84663	−	0.278335i	−0.976663	+	0.214776i	$0.931098\pi$
$542$	0.607073	−	0.413895i	0.0260760	−	0.0177783i
$543$	20.2674	+	6.25167i	0.869758	+	0.268285i
$544$	−0.0549063	−	0.732673i	−0.00235409	−	0.0314131i
$545$	7.88793	−	3.79863i	0.337882	−	0.162715i
$546$	0.171661	+	0.207757i	0.00734640	+	0.00889119i
$547$	25.5774	+	12.3174i	1.09361	+	0.526656i	0.891645	−	0.452736i	$-0.149552\pi$
$547$	25.5774	+	12.3174i	1.09361	+	0.526656i	0.201968	+	0.979392i	$0.435266\pi$
$548$	−4.69280	+	11.9571i	−0.200467	+	0.510781i
$549$	0.846083	−	11.2902i	0.0361099	−	0.481854i
$550$	0.00669143	+	0.0170495i	0.000285323	+	0.000726992i
$551$	−3.42558	+	1.05665i	−0.145934	+	0.0450148i
$552$	1.23253	−	1.54555i	0.0524601	−	0.0657829i
$553$	−0.262220	−	0.0348826i	−0.0111507	−	0.00148336i
$554$	0.0180471	+	0.0226304i	0.000766750	+	0.000961474i
$555$	14.9384	+	10.1848i	0.634101	+	0.432323i
$556$	11.0023	+	10.2087i	0.466603	+	0.432944i
$557$	−6.00703	+	10.4045i	−0.254526	+	0.440852i	−0.964767	−	0.263107i	$-0.915253\pi$
$557$	−6.00703	+	10.4045i	−0.254526	+	0.440852i	0.710241	+	0.703959i	$0.248586\pi$
$558$	−0.210050	−	0.363818i	−0.00889213	−	0.0154016i
$559$	0.678935	−	2.97461i	0.0287159	−	0.125813i
$560$	−11.2034	−	27.1512i	−0.473431	−	1.14735i
$561$	0.0796121	+	0.348803i	0.00336123	+	0.0147265i
$562$	−0.144863	+	0.134413i	−0.00611068	+	0.00566988i
$563$	14.8213	−	2.23395i	0.624644	−	0.0941500i	0.170909	−	0.985287i	$-0.445329\pi$
$563$	14.8213	−	2.23395i	0.624644	−	0.0941500i	0.453735	+	0.891137i	$0.350091\pi$
$564$	−27.1018	+	4.08493i	−1.14119	+	0.172007i
$565$	−24.7415	+	22.9568i	−1.04088	+	0.965799i
$566$	−0.263297	−	1.15358i	−0.0110672	−	0.0484886i
$567$	29.3023	−	4.93792i	1.23058	−	0.207373i
$568$	0.516158	−	2.26144i	0.0216575	−	0.0948878i
$569$	11.3587	+	19.6739i	0.476183	+	0.824773i	0.999628	−	0.0272867i	$-0.00868669\pi$
$569$	11.3587	+	19.6739i	0.476183	+	0.824773i	−0.523445	+	0.852060i	$0.675353\pi$
$570$	−0.321034	+	0.556047i	−0.0134466	+	0.0232903i
$571$	13.8463	+	12.8475i	0.579451	+	0.537652i	0.914520	−	0.404542i	$-0.132569\pi$
$571$	13.8463	+	12.8475i	0.579451	+	0.537652i	−0.335068	+	0.942194i	$0.608759\pi$
$572$	−0.224784	−	0.153255i	−0.00939869	−	0.00640792i
$573$	14.5351	+	18.2265i	0.607213	+	0.761422i
$574$	−0.536464	+	0.175726i	−0.0223916	+	0.00733464i
$575$	8.34774	−	10.4677i	0.348125	−	0.436535i
$576$	−10.3494	+	3.19235i	−0.431223	+	0.133015i
$577$	−3.54565	−	9.03418i	−0.147608	−	0.376098i	0.837878	−	0.545858i	$-0.183796\pi$
$577$	−3.54565	−	9.03418i	−0.147608	−	0.376098i	−0.985485	+	0.169760i	$0.945701\pi$
$578$	0.0561859	−	0.749749i	0.00233703	−	0.0311854i
$579$	8.16013	−	20.7917i	0.339123	−	0.864072i
$580$	7.94087	+	3.82412i	0.329727	+	0.158788i
$581$	24.3979	−	0.423309i	1.01220	−	0.0175618i
$582$	−0.179422	+	0.0864050i	−0.00743727	+	0.00358160i
$583$	−0.0457140	−	0.610011i	−0.00189328	−	0.0252641i
$584$	−2.31832	−	0.715107i	−0.0959328	−	0.0295913i
$585$	3.13794	−	2.13941i	0.129738	−	0.0884536i
$586$	−0.545129	−	0.0821650i	−0.0225191	−	0.00339420i
$587$	41.3692			1.70749			0.853744	−	0.520692i	$-0.174326\pi$
$587$	41.3692			1.70749			0.853744	+	0.520692i	$0.174326\pi$
$588$	15.4737	+	24.7747i	0.638125	+	1.02169i
$589$	−14.2986			−0.589164
$590$	−1.63606	−	0.246597i	−0.0673556	−	0.0101522i
$591$	41.4767	−	28.2783i	1.70612	−	1.16321i
$592$	−11.8353	−	3.65071i	−0.486429	−	0.150043i
$593$	−1.49836	−	19.9942i	−0.0615301	−	0.821062i	−0.939544	−	0.342428i	$-0.888751\pi$
$593$	−1.49836	−	19.9942i	−0.0615301	−	0.821062i	0.878014	−	0.478635i	$-0.158868\pi$
$594$	0.0204538	−	0.00985003i	0.000839230	−	0.000404152i
$595$	2.21865	+	8.99805i	0.0909558	+	0.368884i
$596$	29.6276	+	14.2679i	1.21359	+	0.584436i
$597$	3.06147	−	7.80049i	0.125298	−	0.319253i
$598$	0.0176907	−	0.236065i	0.000723425	−	0.00965343i
$599$	−12.6239	−	32.1652i	−0.515799	−	1.31424i	−0.917234	−	0.398348i	$-0.869584\pi$
$599$	−12.6239	−	32.1652i	−0.515799	−	1.31424i	0.401435	−	0.915887i	$-0.368512\pi$
$600$	1.07315	−	0.331021i	0.0438110	−	0.0135139i
$601$	−16.4324	+	20.6056i	−0.670293	+	0.840521i	−0.994420	−	0.105493i	$-0.966358\pi$
$601$	−16.4324	+	20.6056i	−0.670293	+	0.840521i	0.324127	+	0.946014i	$0.394929\pi$
$602$	−0.137434	+	0.368867i	−0.00560139	+	0.0150339i
$603$	−1.35569	−	1.69998i	−0.0552078	−	0.0692284i
$604$	−33.5653	−	22.8844i	−1.36575	−	0.931153i
$605$	−22.4216	−	20.8042i	−0.911569	−	0.845813i
$606$	0.174065	−	0.301490i	0.00707092	−	0.0122472i
$607$	−1.21069	−	2.09698i	−0.0491405	−	0.0851138i	0.840409	−	0.541953i	$-0.182315\pi$
$607$	−1.21069	−	2.09698i	−0.0491405	−	0.0851138i	−0.889549	+	0.456839i	$0.848982\pi$
$608$	0.294207	−	1.28900i	0.0119317	−	0.0522760i
$609$	−8.40924	−	2.43497i	−0.340760	−	0.0986701i
$610$	−0.250950	−	1.09948i	−0.0101607	−	0.0445168i
$611$	−4.81479	+	4.46748i	−0.194786	+	0.180735i
$612$	3.38722	−	0.510541i	0.136920	−	0.0206374i
$613$	17.0595	−	2.57131i	0.689028	−	0.103854i	0.204810	−	0.978802i	$-0.434342\pi$
$613$	17.0595	−	2.57131i	0.689028	−	0.103854i	0.484218	+	0.874948i	$0.339104\pi$
$614$	0.874191	−	0.811130i	0.0352795	−	0.0327346i
$615$	5.66494	+	24.8197i	0.228432	+	1.00083i
$616$	0.0523111	+	0.0468754i	0.00210767	+	0.00188866i
$617$	1.80244	−	7.89701i	0.0725636	−	0.317922i	−0.925600	−	0.378504i	$-0.876439\pi$
$617$	1.80244	−	7.89701i	0.0725636	−	0.317922i	0.998163	+	0.0605823i	$0.0192958\pi$
$618$	−0.672159	−	1.16421i	−0.0270382	−	0.0468315i
$619$	7.07243	−	12.2498i	0.284265	−	0.492361i	−0.688166	−	0.725554i	$-0.741584\pi$
$619$	7.07243	−	12.2498i	0.284265	−	0.492361i	0.972431	+	0.233192i	$0.0749171\pi$
$620$	25.7702	+	23.9112i	1.03495	+	0.960297i
$621$	−13.7116	−	9.34843i	−0.550229	−	0.375140i
$622$	0.288953	+	0.362335i	0.0115859	+	0.0145283i
$623$	4.39686	+	7.31934i	0.176157	+	0.293243i
$624$	−5.19107	+	6.50940i	−0.207809	+	0.260585i
$625$	−29.7981	+	9.19149i	−1.19192	+	0.367660i
$626$	0.438507	+	1.11730i	0.0175263	+	0.0446562i
$627$	−0.0481126	+	0.642018i	−0.00192143	+	0.0256397i
$628$	15.4441	−	39.3508i	0.616285	−	1.57027i
$629$	3.52095	+	1.69560i	0.140389	+	0.0676080i
$630$	−0.437703	+	0.220221i	−0.0174385	+	0.00877381i
$631$	−29.8297	+	14.3652i	−1.18750	+	0.571871i	−0.920088	−	0.391711i	$-0.871883\pi$
$631$	−29.8297	+	14.3652i	−1.18750	+	0.571871i	−0.267414	+	0.963582i	$0.586169\pi$
$632$	0.00145652	+	0.0194358i	5.79371e−5	+	0.000773117i
$633$	−34.6271	−	10.6810i	−1.37630	−	0.424533i
$634$	1.05885	−	0.721910i	0.0420522	−	0.0286707i
$635$	11.9970	+	1.80825i	0.476086	+	0.0717584i
$636$	−18.7430			−0.743209
$637$	6.40835	+	2.81658i	0.253908	+	0.111597i
$638$	−0.0105199			−0.000416485
$639$	16.0438	+	2.41821i	0.634682	+	0.0956629i
$640$	−3.58037	+	2.44105i	−0.141527	+	0.0964912i
$641$	34.1750	+	10.5416i	1.34983	+	0.416368i	0.883579	−	0.468283i	$-0.155127\pi$
$641$	34.1750	+	10.5416i	1.34983	+	0.416368i	0.466254	+	0.884651i	$0.345603\pi$
$642$	0.0135653	+	0.181017i	0.000535380	+	0.00714415i
$643$	16.6176	−	8.00262i	0.655335	−	0.315593i	−0.0765051	−	0.997069i	$-0.524376\pi$
$643$	16.6176	−	8.00262i	0.655335	−	0.315593i	0.731840	+	0.681477i	$0.238662\pi$
$644$	5.27460	−	25.1098i	0.207848	−	0.989464i
$645$	15.9941	+	7.70234i	0.629766	+	0.303279i
$646$	−0.0507026	+	0.129188i	−0.00199487	+	0.00508284i
$647$	0.765378	−	10.2133i	0.0300901	−	0.401524i	−0.961740	−	0.273962i	$-0.911666\pi$
$647$	0.765378	−	10.2133i	0.0300901	−	0.401524i	0.991831	−	0.127562i	$-0.0407153\pi$
$648$	−0.799879	−	2.03806i	−0.0314222	−	0.0800625i
$649$	−1.58534	+	0.489014i	−0.0622302	+	0.0191955i
$650$	0.0838500	−	0.105145i	0.00328887	−	0.00412411i
$651$	−29.1885	−	19.1672i	−1.14399	−	0.751223i
$652$	−6.16024	−	7.72470i	−0.241254	−	0.302522i
$653$	8.99749	+	6.13439i	0.352099	+	0.240057i	0.726434	−	0.687237i	$-0.241176\pi$
$653$	8.99749	+	6.13439i	0.352099	+	0.240057i	−0.374335	+	0.927294i	$0.622129\pi$
$654$	0.234707	+	0.217776i	0.00917777	+	0.00851572i
$655$	15.2577	−	26.4271i	0.596168	−	1.03259i
$656$	−8.71990	−	15.1033i	−0.340455	−	0.589685i
$657$	3.77618	−	16.5445i	0.147323	−	0.645464i
$658$	0.691760	−	0.489426i	0.0269676	−	0.0190798i
$659$	−2.71468	−	11.8938i	−0.105749	−	0.463317i	−0.999880	−	0.0155107i	$-0.995063\pi$
$659$	−2.71468	−	11.8938i	−0.105749	−	0.463317i	0.894131	−	0.447806i	$-0.147795\pi$
$660$	1.16034	−	1.07664i	0.0451663	−	0.0419082i
$661$	−29.6808	+	4.47366i	−1.15445	+	0.174005i	−0.698238	−	0.715866i	$-0.746032\pi$
$661$	−29.6808	+	4.47366i	−1.15445	+	0.174005i	−0.456212	+	0.889871i	$0.650794\pi$
$662$	−0.214543	+	0.0323371i	−0.00833844	+	0.00125682i
$663$	1.92573	−	1.78682i	0.0747893	−	0.0693944i
$664$	−0.400067	−	1.75281i	−0.0155256	−	0.0680222i
$665$	−0.957593	+	16.6495i	−0.0371338	+	0.645642i
$666$	−0.0459764	+	0.201436i	−0.00178155	+	0.00780548i
$667$	3.84502	+	6.65978i	0.148880	+	0.257868i
$668$	21.4231	−	37.1058i	0.828883	−	1.43567i
$669$	−9.74620	−	9.04315i	−0.376810	−	0.349628i
$670$	−0.178951	−	0.122007i	−0.00691347	−	0.00471353i
$671$	−0.705063	−	0.884121i	−0.0272186	−	0.0341311i
$672$	2.32848	−	2.23693i	0.0898231	−	0.0862913i
$673$	18.6182	−	23.3465i	0.717679	−	0.899941i	−0.280525	−	0.959847i	$-0.590508\pi$
$673$	18.6182	−	23.3465i	0.717679	−	0.899941i	0.998204	+	0.0599054i	$0.0190799\pi$
$674$	−0.767349	+	0.236696i	−0.0295572	+	0.00911718i
$675$	−3.44435	−	8.77606i	−0.132573	−	0.337791i
$676$	−0.149282	+	1.99204i	−0.00574163	+	0.0766168i
$677$	−11.1271	+	28.3513i	−0.427648	+	1.08963i	0.540963	+	0.841046i	$0.318060\pi$
$677$	−11.1271	+	28.3513i	−0.427648	+	1.08963i	−0.968611	+	0.248582i	$0.920035\pi$
$678$	−1.11209	−	0.535553i	−0.0427095	−	0.0205678i
$679$	−3.15439	+	4.09939i	−0.121054	+	0.157320i
$680$	0.615203	−	0.296266i	0.0235920	−	0.0113613i
$681$	−0.549957	−	7.33866i	−0.0210744	−	0.281218i
$682$	−0.0400957	−	0.0123679i	−0.00153534	−	0.000473591i
$683$	−3.91075	+	2.66630i	−0.149641	+	0.102023i	−0.635826	−	0.771832i	$-0.719340\pi$
$683$	−3.91075	+	2.66630i	−0.149641	+	0.102023i	0.486185	+	0.873856i	$0.338388\pi$
$684$	6.09535	+	0.918726i	0.233062	+	0.0351284i
$685$	−17.9099			−0.684303
$686$	−0.771636	−	0.469231i	−0.0294612	−	0.0179153i
$687$	49.5315			1.88975
$688$	−12.0251	−	1.81249i	−0.458452	−	0.0691005i
$689$	−3.71119	+	2.53024i	−0.141385	+	0.0963946i
$690$	1.31615	+	0.405977i	0.0501048	+	0.0154553i
$691$	−3.14775	−	42.0038i	−0.119746	−	1.59790i	−0.656610	−	0.754230i	$-0.728010\pi$
$691$	−3.14775	−	42.0038i	−0.119746	−	1.59790i	0.536864	−	0.843669i	$-0.319609\pi$
$692$	9.92149	−	4.77794i	0.377158	−	0.181630i
$693$	−0.299621	+	0.389383i	−0.0113817	+	0.0147914i
$694$	−1.15672	−	0.557049i	−0.0439086	−	0.0211453i
$695$	−7.64554	+	19.4805i	−0.290012	+	0.738938i
$696$	−0.0482036	+	0.643233i	−0.00182715	+	0.0243817i
$697$	2.01036	+	5.12231i	0.0761478	+	0.194021i
$698$	−0.953533	+	0.294126i	−0.0360918	+	0.0111328i
$699$	−25.4342	+	31.8935i	−0.962012	+	1.20632i
$700$	10.5115	−	10.0982i	0.397298	−	0.381677i
$701$	10.4583	+	13.1142i	0.395003	+	0.495318i	0.939071	−	0.343723i	$-0.111688\pi$
$701$	10.4583	+	13.1142i	0.395003	+	0.495318i	−0.544068	+	0.839041i	$0.683117\pi$
$702$	−0.137728	−	0.0939016i	−0.00519822	−	0.00354409i
$703$	5.15513	+	4.78326i	0.194430	+	0.180404i
$704$	−0.540879	+	0.936830i	−0.0203852	+	0.0353081i
$705$	−19.1075	−	33.0952i	−0.719632	−	1.24644i
$706$	−0.123648	+	0.541738i	−0.00465356	+	0.0203886i
$707$	0.519209	−	9.02742i	0.0195269	−	0.339511i
$708$	11.3114	+	49.5585i	0.425109	+	1.86252i
$709$	−1.91053	+	1.77271i	−0.0717514	+	0.0665756i	−0.715233	−	0.698886i	$-0.753680\pi$
$709$	−1.91053	+	1.77271i	−0.0717514	+	0.0665756i	0.643482	+	0.765461i	$0.277489\pi$
$710$	1.59810	−	0.240875i	0.0599758	−	0.00903990i
$711$	−0.134808	+	0.0203190i	−0.00505568	+	0.000762021i
$712$	0.461167	−	0.427900i	0.0172830	−	0.0160362i
$713$	6.82534	+	29.9037i	0.255611	+	1.11990i
$714$	−0.276678	+	0.195752i	−0.0103544	+	0.00732583i
$715$	0.0844093	−	0.369821i	0.00315673	−	0.0138305i
$716$	−3.62383	−	6.27666i	−0.135429	−	0.234570i
$717$	−10.9260	+	18.9243i	−0.408037	+	0.706741i
$718$	−0.715104	−	0.663520i	−0.0266875	−	0.0247623i
$719$	32.4029	+	22.0919i	1.20842	+	0.823889i	0.988440	−	0.151614i	$-0.0484472\pi$
$719$	32.4029	+	22.0919i	1.20842	+	0.823889i	0.219984	+	0.975504i	$0.429400\pi$
$720$	−9.43793	−	11.8348i	−0.351731	−	0.441056i
$721$	−29.1869	−	19.1662i	−1.08698	−	0.713785i
$722$	0.421953	−	0.529112i	0.0157035	−	0.0196915i
$723$	22.6007	−	6.97140i	0.840530	−	0.259269i
$724$	−7.41016	−	18.8808i	−0.275396	−	0.701698i
$725$	−0.326475	+	4.35651i	−0.0121250	+	0.161797i
$726$	0.408666	−	1.04126i	0.0151670	−	0.0386449i
$727$	16.2321	+	7.81698i	0.602016	+	0.289916i	0.709961	−	0.704241i	$-0.248713\pi$
$727$	16.2321	+	7.81698i	0.602016	+	0.289916i	−0.107944	+	0.994157i	$0.534427\pi$
$728$	0.106026	−	0.504738i	0.00392958	−	0.0187068i
$729$	−5.50310	+	2.65015i	−0.203819	+	0.0981539i
$730$	−0.126321	−	1.68564i	−0.00467536	−	0.0623883i
$731$	3.66660	+	1.13100i	0.135614	+	0.0418314i
$732$	−28.6279	+	19.5182i	−1.05812	+	0.721413i
$733$	6.51840	+	0.982491i	0.240763	+	0.0362891i	0.268315	−	0.963331i	$-0.413533\pi$
$733$	6.51840	+	0.982491i	0.240763	+	0.0362891i	−0.0275524	+	0.999620i	$0.508771\pi$
$734$	0.331767			0.0122457
$735$	−24.2734	+	32.7039i	−0.895339	+	1.20630i
$736$	−2.83623			−0.104545
$737$	−0.214750	−	0.0323683i	−0.00791040	−	0.00119230i
$738$	−0.240378	+	0.163887i	−0.00884845	+	0.00603277i
$739$	−40.8934	−	12.6140i	−1.50429	−	0.464012i	−0.570338	−	0.821410i	$-0.693188\pi$
$739$	−40.8934	−	12.6140i	−1.50429	−	0.464012i	−0.933952	+	0.357398i	$0.883664\pi$
$740$	−1.29208	−	17.2416i	−0.0474978	−	0.633814i
$741$	4.25919	−	2.05112i	0.156465	−	0.0753496i
$742$	0.517664	−	0.260452i	0.0190040	−	0.00956148i
$743$	27.9009	+	13.4364i	1.02359	+	0.492933i	0.868878	−	0.495027i	$-0.164842\pi$
$743$	27.9009	+	13.4364i	1.02359	+	0.492933i	0.154709	+	0.987960i	$0.450556\pi$
$744$	−0.939954	+	2.39496i	−0.0344604	+	0.0878037i
$745$	−3.42643	+	45.7225i	−0.125535	+	1.67514i
$746$	0.370371	+	0.943690i	0.0135602	+	0.0345509i
$747$	12.0171	−	3.70677i	0.439681	−	0.135624i
$748$	0.213320	−	0.267495i	0.00779976	−	0.00978058i
$749$	2.42793	+	4.04172i	0.0887147	+	0.147681i
$750$	−0.396609	−	0.497332i	−0.0144821	−	0.0181600i
$751$	40.5562	+	27.6507i	1.47992	+	1.00899i	0.990586	+	0.136892i	$0.0437112\pi$
$751$	40.5562	+	27.6507i	1.47992	+	1.00899i	0.489331	+	0.872098i	$0.337241\pi$
$752$	19.1905	+	17.8062i	0.699806	+	0.649325i
$753$	−29.8750	+	51.7450i	−1.08871	+	1.88569i
$754$	0.0386219	+	0.0668951i	0.00140653	+	0.00243617i
$755$	12.6042	−	55.2225i	0.458713	−	2.00975i
$756$	−13.4553	−	12.0572i	−0.489365	−	0.438514i
$757$	10.2616	+	44.9590i	0.372964	+	1.63406i	0.718407	+	0.695623i	$0.244872\pi$
$757$	10.2616	+	44.9590i	0.372964	+	1.63406i	−0.345443	+	0.938440i	$0.612271\pi$
$758$	0.279588	−	0.259419i	0.0101551	−	0.00942254i
$759$	1.36567	−	0.205841i	0.0495705	−	0.00747156i
$760$	1.21503	−	0.183136i	0.0440736	−	0.00664303i
$761$	25.2556	−	23.4338i	0.915515	−	0.849474i	−0.0734988	−	0.997295i	$-0.523416\pi$
$761$	25.2556	−	23.4338i	0.915515	−	0.849474i	0.989014	+	0.147821i	$0.0472260\pi$
$762$	0.0987322	+	0.432574i	0.00357669	+	0.0156705i
$763$	7.98815	+	2.31304i	0.289190	+	0.0837378i
$764$	4.96083	−	21.7348i	0.179477	−	0.786338i
$765$	2.38809	+	4.13630i	0.0863416	+	0.149548i
$766$	−0.763463	+	1.32236i	−0.0275850	+	0.0477787i
$767$	8.92993	+	8.28577i	0.322441	+	0.299182i
$768$	27.2872	+	18.6041i	0.984644	+	0.671319i
$769$	21.5521	+	27.0255i	0.777189	+	0.974564i	1.00000		0.000297346i	$-9.46483e-5\pi$
$769$	21.5521	+	27.0255i	0.777189	+	0.974564i	−0.222811	+	0.974862i	$0.571523\pi$
$770$	−0.0170866	+	0.0458598i	−0.000615759	+	0.00165267i
$771$	−9.20619	+	11.5442i	−0.331553	+	0.415754i
$772$	−20.4106	+	6.29585i	−0.734595	+	0.226593i
$773$	9.73409	+	24.8021i	0.350111	+	0.892068i	0.992111	+	0.125364i	$0.0400097\pi$
$773$	9.73409	+	24.8021i	0.350111	+	0.892068i	−0.642000	+	0.766705i	$0.721895\pi$
$774$	−0.0151604	+	0.202301i	−0.000544928	+	0.00727156i
$775$	−6.36615	+	16.2207i	−0.228679	+	0.582665i
$776$	0.343366	+	0.165357i	0.0123261	+	0.00593595i
$777$	4.11150	+	16.6748i	0.147499	+	0.598204i
$778$	−0.362844	+	0.174736i	−0.0130086	+	0.00626460i
$779$	0.739990	+	9.87448i	0.0265129	+	0.353790i
$780$	−11.1063	−	3.42584i	−0.397669	−	0.122665i
$781$	1.33897	−	0.912895i	0.0479121	−	0.0326659i
$782$	0.294383	+	0.0443711i	0.0105271	+	0.00158671i
$783$	5.41500			0.193516
$784$	9.28599	−	26.3095i	0.331642	−	0.939625i
$785$	58.9417			2.10372
$786$	1.10352	+	0.166328i	0.0393612	+	0.00593274i
$787$	−38.4989	+	26.2481i	−1.37234	+	0.935645i	−0.372368	+	0.928085i	$0.621454\pi$
$787$	−38.4989	+	26.2481i	−1.37234	+	0.935645i	−0.999971	+	0.00755982i	$0.997594\pi$
$788$	−45.8729	−	14.1499i	−1.63415	−	0.504070i
$789$	−3.74355	−	49.9542i	−0.133274	−	1.77842i
$790$	−0.0122349	+	0.00589202i	−0.000435298	+	0.000209629i
$791$	−32.0555	+	0.556170i	−1.13976	+	0.0197751i
$792$	0.0326148	+	0.0157065i	0.00115892	+	0.000558105i
$793$	−3.03354	+	7.72935i	−0.107724	+	0.274477i
$794$	0.0605926	−	0.808552i	0.00215035	−	0.0286944i
$795$	−9.54767	−	24.3271i	−0.338621	−	0.862792i
$796$	−7.65754	+	2.36204i	−0.271414	+	0.0837202i
$797$	−8.50502	+	10.6650i	−0.301263	+	0.377772i	−0.909303	−	0.416134i	$-0.863385\pi$
$797$	−8.50502	+	10.6650i	−0.301263	+	0.377772i	0.608040	+	0.793906i	$0.291956\pi$
$798$	−0.579596	+	0.189854i	−0.0205175	+	0.00672075i
$799$	−5.15009	−	6.45801i	−0.182197	−	0.228468i
$800$	−1.33129	−	0.907657i	−0.0470681	−	0.0320905i
$801$	3.22575	+	2.99306i	0.113976	+	0.105754i
$802$	−0.926735	+	1.60515i	−0.0327241	+	0.0566799i
$803$	−0.847487	−	1.46789i	−0.0299072	−	0.0518007i
$804$	−1.48070	+	6.48737i	−0.0522203	+	0.228792i
$805$	35.2775	−	5.94485i	1.24337	−	0.209529i
$806$	0.0685580	+	0.300372i	0.00241485	+	0.0105802i
$807$	−40.2554	+	37.3515i	−1.41706	+	1.31484i
$808$	−0.658790	+	0.0992966i	−0.0231762	+	0.00349324i
$809$	3.82754	−	0.576909i	0.134569	−	0.0202830i	−0.0814123	−	0.996681i	$-0.525943\pi$
$809$	3.82754	−	0.576909i	0.134569	−	0.0202830i	0.215981	+	0.976397i	$0.430705\pi$
$810$	1.11823	−	1.03757i	0.0392907	−	0.0364564i
$811$	−9.29016	−	40.7028i	−0.326222	−	1.42927i	−0.826271	−	0.563273i	$-0.809542\pi$
$811$	−9.29016	−	40.7028i	−0.326222	−	1.42927i	0.500049	−	0.865997i	$-0.333315\pi$
$812$	3.19341	+	7.73914i	0.112067	+	0.271590i
$813$	7.00380	−	30.6857i	0.245634	−	1.07619i
$814$	0.0103185	+	0.0178721i	0.000361662	+	0.000626417i
$815$	6.88807	−	11.9305i	0.241279	−	0.417907i
$816$	−7.67548	−	7.12180i	−0.268695	−	0.249313i
$817$	5.70506	+	3.88965i	0.199595	+	0.136082i
$818$	1.09378	+	1.37155i	0.0382430	+	0.0479552i
$819$	3.57607	+	0.475716i	0.124958	+	0.0166228i
$820$	15.1792	−	19.0341i	0.530080	−	0.664699i
$821$	−53.8317	+	16.6049i	−1.87874	+	0.579514i	−0.885318	+	0.464986i	$0.846059\pi$
$821$	−53.8317	+	16.6049i	−1.87874	+	0.579514i	−0.993420	+	0.114528i	$0.963465\pi$
$822$	−0.239293	−	0.609708i	−0.00834629	−	0.0212660i
$823$	−4.06046	+	54.1831i	−0.141539	+	1.88870i	0.249566	+	0.968358i	$0.419712\pi$
$823$	−4.06046	+	54.1831i	−0.141539	+	1.88870i	−0.391105	+	0.920346i	$0.627907\pi$
$824$	−0.939903	+	2.39483i	−0.0327431	+	0.0834280i
$825$	0.706900	+	0.340425i	0.0246111	+	0.0118521i
$826$	−1.00107	−	1.21158i	−0.0348318	−	0.0421561i
$827$	26.4275	−	12.7268i	0.918973	−	0.442554i	0.0862686	−	0.996272i	$-0.472506\pi$
$827$	26.4275	−	12.7268i	0.918973	−	0.442554i	0.832704	+	0.553718i	$0.186791\pi$
$828$	−0.988170	−	13.1862i	−0.0343413	−	0.458252i
$829$	−35.6529	−	10.9975i	−1.23828	−	0.381958i	−0.394621	−	0.918844i	$-0.629124\pi$
$829$	−35.6529	−	10.9975i	−1.23828	−	0.381958i	−0.843655	+	0.536886i	$0.819600\pi$
$830$	1.03500	−	0.705649i	0.0359252	−	0.0244934i
$831$	1.22611	+	0.184806i	0.0425332	+	0.00641085i
$832$	7.94299			0.275374
$833$	−4.13448	+	7.77190i	−0.143251	+	0.269280i
$834$	−0.765328			−0.0265011
$835$	59.0736	+	8.90391i	2.04432	+	0.308132i
$836$	0.508702	−	0.346827i	0.0175938	−	0.0119953i
$837$	20.6389	+	6.36625i	0.713384	+	0.220050i
$838$	−0.0401226	−	0.535399i	−0.00138601	−	0.0184950i
$839$	−1.00135	+	0.482226i	−0.0345705	+	0.0166483i	−0.451089	−	0.892479i	$-0.648964\pi$
$839$	−1.00135	+	0.482226i	−0.0345705	+	0.0166483i	0.416519	+	0.909127i	$0.363250\pi$
$840$	2.72579	+	1.25489i	0.0940486	+	0.0432979i
$841$	23.8673	+	11.4939i	0.823012	+	0.396342i
$842$	−0.477315	+	1.21618i	−0.0164494	+	0.0419123i
$843$	−0.632625	+	8.44179i	−0.0217887	+	0.290751i
$844$	12.6603	+	32.2580i	0.435786	+	1.11037i
$845$	−2.66156	+	0.820983i	−0.0915605	+	0.0282427i
$846$	0.272289	−	0.341439i	0.00936147	−	0.0117389i
$847$	−2.67351	−	28.9309i	−0.0918628	−	0.994078i
$848$	11.1621	+	13.9968i	0.383307	+	0.480652i
$849$	−41.8802	−	28.5534i	−1.43733	−	0.979952i
$850$	0.123980	+	0.115037i	0.00425247	+	0.00394572i
$851$	7.54283	−	13.0646i	0.258565	−	0.447848i
$852$	−24.8268	−	43.0014i	−0.850554	−	1.47320i
$853$	−7.61821	+	33.3775i	−0.260842	+	1.14283i	0.659498	+	0.751706i	$0.270769\pi$
$853$	−7.61821	+	33.3775i	−0.260842	+	1.14283i	−0.920340	+	0.391119i	$0.872088\pi$
$854$	0.519452	−	0.936885i	0.0177753	−	0.0320595i
$855$	1.91252	+	8.37932i	0.0654070	+	0.286567i
$856$	0.254655	−	0.236285i	0.00870392	−	0.00807606i
$857$	−1.75563	+	0.264618i	−0.0599711	+	0.00903919i	−0.178959	−	0.983856i	$-0.557273\pi$
$857$	−1.75563	+	0.264618i	−0.0599711	+	0.00903919i	0.118988	+	0.992896i	$0.462035\pi$
$858$	0.0137176	−	0.00206760i	0.000468312	−	7.05867e-5i
$859$	−19.6839	+	18.2640i	−0.671606	+	0.623159i	−0.940413	−	0.340035i	$-0.889561\pi$
$859$	−19.6839	+	18.2640i	−0.671606	+	0.623159i	0.268807	+	0.963194i	$0.413371\pi$
$860$	−3.77758	−	16.5507i	−0.128815	−	0.564374i
$861$	−11.7261	+	21.1492i	−0.399625	+	0.720764i
$862$	0.125922	−	0.551701i	0.00428893	−	0.0187910i
$863$	2.51868	+	4.36248i	0.0857368	+	0.148501i	0.905705	−	0.423909i	$-0.139342\pi$
$863$	2.51868	+	4.36248i	0.0857368	+	0.148501i	−0.819968	+	0.572409i	$0.806009\pi$
$864$	−0.998574	+	1.72958i	−0.0339722	+	0.0588415i
$865$	11.2554	+	10.4435i	0.382695	+	0.355089i
$866$	1.51890	+	1.03557i	0.0516142	+	0.0351900i
$867$	−20.0812	−	25.1810i	−0.681992	−	0.855191i
$868$	3.07278	+	33.2516i	0.104297	+	1.12863i
$869$	−0.00848989	+	0.0106460i	−0.000288000	+	0.000361140i
$870$	−0.429456	+	0.132470i	−0.0145599	+	0.00449115i
$871$	0.582589	+	1.48441i	0.0197403	+	0.0502974i
$872$	0.0457899	−	0.611023i	0.00155064	−	0.0206919i
$873$	−0.973910	+	2.48148i	−0.0329619	+	0.0839855i
$874$	0.482676	+	0.232445i	0.0163268	+	0.00786256i
$875$	−15.0082	−	6.90946i	−0.507371	−	0.233582i
$876$	−46.7906	+	22.5332i	−1.58091	+	0.761325i
$877$	0.597936	+	7.97890i	0.0201909	+	0.269428i	0.998158	+	0.0606691i	$0.0193234\pi$
$877$	0.597936	+	7.97890i	0.0201909	+	0.269428i	−0.977967	+	0.208759i	$0.933058\pi$
$878$	−0.532502	−	0.164255i	−0.0179711	−	0.00554334i
$879$	−19.5124	+	13.3033i	−0.658137	+	0.448710i
$880$	−1.49503	−	0.225340i	−0.0503975	−	0.00759620i
$881$	31.4499			1.05957			0.529787	−	0.848131i	$-0.322272\pi$
$881$	31.4499			1.05957			0.529787	+	0.848131i	$0.322272\pi$
$882$	−0.449244	−	0.121677i	−0.0151268	−	0.00409708i
$883$	−17.0418			−0.573502			−0.286751	−	0.958005i	$-0.592575\pi$
$883$	−17.0418			−0.573502			−0.286751	+	0.958005i	$0.592575\pi$
$884$	−2.48415	−	0.374426i	−0.0835510	−	0.0125933i
$885$	−58.5613	+	39.9265i	−1.96852	+	1.34211i
$886$	−0.219582	−	0.0677322i	−0.00737702	−	0.00227551i
$887$	−3.58592	−	47.8508i	−0.120403	−	1.60667i	−0.651021	−	0.759060i	$-0.725659\pi$
$887$	−3.58592	−	47.8508i	−0.120403	−	1.60667i	0.530618	−	0.847611i	$-0.321960\pi$
$888$	1.14006	−	0.549026i	0.0382581	−	0.0184241i
$889$	7.34070	+	8.88430i	0.246199	+	0.297970i
$890$	0.394916	+	0.190181i	0.0132376	+	0.00637489i
$891$	0.558828	−	1.42387i	0.0187214	−	0.0477014i
$892$	−0.950146	+	12.6788i	−0.0318132	+	0.424518i
$893$	−5.43049	−	13.8367i	−0.181725	−	0.463026i
$894$	−1.60231	+	0.494249i	−0.0535894	+	0.0165301i
$895$	6.30067	−	7.90079i	0.210608	−	0.264094i
$896$	−4.08027	−	0.542789i	−0.136312	−	0.0181333i
$897$	−6.32274	−	7.92847i	−0.211110	−	0.264724i
$898$	−0.224072	−	0.152770i	−0.00747738	−	0.00509799i
$899$	−7.33674	−	6.80750i	−0.244694	−	0.227043i
$900$	3.75605	−	6.50567i	0.125202	−	0.216856i
$901$	−2.82436	−	4.89193i	−0.0940930	−	0.162974i
$902$	−0.00646608	+	0.0283298i	−0.000215297	+	0.000943278i
$903$	6.43199	+	15.5877i	0.214043	+	0.518728i
$904$	0.525633	+	2.30295i	0.0174823	+	0.0765950i
$905$	20.7311	−	19.2357i	0.689126	−	0.639416i
$906$	2.04835	−	0.308739i	0.0680518	−	0.0102572i
$907$	−43.8593	+	6.61072i	−1.45632	+	0.219505i	−0.828998	−	0.559252i	$-0.811088\pi$
$907$	−43.8593	+	6.61072i	−1.45632	+	0.219505i	−0.627325	+	0.778757i	$0.715850\pi$
$908$	−5.15896	+	4.78681i	−0.171206	+	0.158856i
$909$	−1.03698	−	4.54329i	−0.0343943	−	0.150691i
$910$	0.354350	−	0.0597139i	0.0117466	−	0.00197950i
$911$	7.93606	−	34.7701i	0.262933	−	1.15199i	−0.655119	−	0.755526i	$-0.727381\pi$
$911$	7.93606	−	34.7701i	0.262933	−	1.15199i	0.918052	−	0.396460i	$-0.129762\pi$
$912$	−9.42097	−	16.3176i	−0.311960	−	0.540330i
$913$	0.628037	−	1.08779i	0.0207850	−	0.0360007i
$914$	1.10577	+	1.02601i	0.0365758	+	0.0339373i
$915$	−39.9162	−	27.2144i	−1.31959	−	0.899681i
$916$	−29.5328	−	37.0330i	−0.975793	−	1.22361i
$917$	27.5463	−	9.02314i	0.909659	−	0.297970i
$918$	0.130704	−	0.163898i	0.00431388	−	0.00540944i
$919$	6.54260	−	2.01812i	0.215820	−	0.0665718i	−0.184960	−	0.982746i	$-0.559215\pi$
$919$	6.54260	−	2.01812i	0.215820	−	0.0665718i	0.400780	+	0.916174i	$0.368739\pi$
$920$	−0.962989	−	2.45366i	−0.0317488	−	0.0808946i
$921$	3.81764	−	50.9428i	0.125795	−	1.67862i
$922$	−0.0876081	+	0.223222i	−0.00288522	+	0.00735142i
$923$	−10.7208	−	5.16288i	−0.352881	−	0.169938i
$924$	1.50336	−	0.0260836i	0.0494569	−	0.000858088i
$925$	7.72147	−	3.71846i	0.253880	−	0.122262i
$926$	−0.0229797	−	0.306643i	−0.000755161	−	0.0100769i
$927$	−17.1957	−	5.30418i	−0.564782	−	0.174212i
$928$	0.764648	−	0.521328i	0.0251008	−	0.0171134i
$929$	8.60541	+	1.29706i	0.282334	+	0.0425551i	0.288683	−	0.957425i	$-0.406783\pi$
$929$	8.60541	+	1.29706i	0.282334	+	0.0425551i	−0.00634844	+	0.999980i	$0.502021\pi$
$930$	−1.79258			−0.0587811
$931$	−11.2319	+	11.1713i	−0.368109	+	0.366125i
$932$	39.0107			1.27784
$933$	19.6312	+	2.95893i	0.642697	+	0.0968710i
$934$	−0.805261	+	0.549018i	−0.0263489	+	0.0179644i
$935$	0.455854	+	0.140612i	0.0149080	+	0.00459851i
$936$	−0.0198634	−	0.265059i	−0.000649257	−	0.00866373i
$937$	51.9967	−	25.0403i	1.69866	−	0.818031i	0.704548	−	0.709657i	$-0.251150\pi$
$937$	51.9967	−	25.0403i	1.69866	−	0.818031i	0.994110	−	0.108374i	$-0.0345644\pi$
$938$	−0.0492525	−	0.199751i	−0.00160815	−	0.00652209i
$939$	46.3251	+	22.3090i	1.51176	+	0.728026i
$940$	−13.3514	+	34.0189i	−0.435475	+	1.10957i
$941$	0.131229	−	1.75113i	0.00427794	−	0.0570852i	−0.994656	−	0.103242i	$-0.967078\pi$
$941$	0.131229	−	1.75113i	0.00427794	−	0.0570852i	0.998934	+	0.0461569i	$0.0146974\pi$
$942$	0.787514	+	2.00655i	0.0256586	+	0.0653771i
$943$	20.2980	−	6.26111i	0.660994	−	0.203890i
$944$	30.2727	−	37.9608i	0.985294	−	1.23552i
$945$	8.79518	−	23.6059i	0.286107	−	0.767901i
$946$	0.0126335	+	0.0158419i	0.000410751	+	0.000515066i
$947$	−15.2279	−	10.3822i	−0.494842	−	0.337377i	0.290049	−	0.957012i	$-0.406328\pi$
$947$	−15.2279	−	10.3822i	−0.494842	−	0.337377i	−0.784891	+	0.619634i	$0.787281\pi$
$948$	0.305840	+	0.283778i	0.00993321	+	0.00921667i
$949$	−6.22281	+	10.7782i	−0.202001	+	0.349876i
$950$	0.152174	+	0.263574i	0.00493719	+	0.00855146i
$951$	12.2159	−	53.5215i	0.396129	−	1.73555i
$952$	0.623019	+	0.180401i	0.0201922	+	0.00584683i
$953$	−2.67510	−	11.7204i	−0.0866549	−	0.379660i	0.912941	−	0.408092i	$-0.133806\pi$
$953$	−2.67510	−	11.7204i	−0.0866549	−	0.379660i	−0.999596	+	0.0284320i	$0.990949\pi$
$954$	0.218927	−	0.203134i	0.00708801	−	0.00657672i
$955$	30.7372	−	4.63289i	0.994634	−	0.149917i
$956$	20.6636	−	3.11453i	0.668308	−	0.100731i
$957$	−0.330348	+	0.306519i	−0.0106786	+	0.00990834i
$958$	−0.0850021	−	0.372418i	−0.00274629	−	0.0120323i
$959$	−12.6699	−	11.3534i	−0.409134	−	0.366620i
$960$	−10.2836	+	45.0556i	−0.331903	+	1.45416i
$961$	−4.46008	−	7.72508i	−0.143874	−	0.249196i
$962$	0.0757650	−	0.131229i	0.00244276	−	0.00423099i
$963$	1.78125	+	1.65276i	0.0573999	+	0.0532593i
$964$	−18.6878	−	12.7411i	−0.601894	−	0.410364i
$965$	−18.5687	−	23.2844i	−0.597748	−	0.749552i
$966$	0.673721	+	1.12153i	0.0216766	+	0.0360845i
$967$	0.0577327	−	0.0723945i	0.00185656	−	0.00232805i	−0.780902	−	0.624653i	$-0.785240\pi$
$967$	0.0577327	−	0.0723945i	0.00185656	−	0.00232805i	0.782759	+	0.622325i	$0.213812\pi$
$968$	−2.04558	+	0.630978i	−0.0657475	+	0.0202804i
$969$	2.17199	+	5.53414i	0.0697744	+	0.177782i
$970$	−0.0198433	+	0.264791i	−0.000637131	+	0.00850192i
$971$	−1.55596	+	3.96453i	−0.0499333	+	0.127228i	−0.953664	−	0.300873i	$-0.902722\pi$
$971$	−1.55596	+	3.96453i	−0.0499333	+	0.127228i	0.903731	+	0.428101i	$0.140817\pi$
$972$	−23.7681	−	11.4461i	−0.762363	−	0.367135i
$973$	−17.7577	+	8.93440i	−0.569285	+	0.286424i
$974$	−0.0150413	+	0.00724350i	−0.000481954	+	0.000232097i
$975$	−0.430524	−	5.74494i	−0.0137878	−	0.183985i
$976$	31.6246	+	9.75489i	1.01228	+	0.312246i
$977$	−1.21530	+	0.828575i	−0.0388808	+	0.0265085i	−0.582605	−	0.812756i	$-0.697966\pi$
$977$	−1.21530	+	0.828575i	−0.0388808	+	0.0265085i	0.543724	+	0.839264i	$0.317014\pi$
$978$	0.498181	+	0.0750887i	0.0159301	+	0.00240107i
$979$	0.439518			0.0140471
$980$	38.9245	−	1.35110i	1.24340	−	0.0431594i
$981$	4.28594			0.136840
$982$	−0.527525	−	0.0795115i	−0.0168340	−	0.00253731i
$983$	−14.1878	+	9.67310i	−0.452522	+	0.308524i	−0.768047	−	0.640393i	$-0.778772\pi$
$983$	−14.1878	+	9.67310i	−0.452522	+	0.308524i	0.315526	+	0.948917i	$0.397819\pi$
$984$	1.70258	+	0.525178i	0.0542764	+	0.0167421i
$985$	−5.00204	−	66.7476i	−0.159378	−	2.12676i
$986$	−0.0875217	+	0.0421482i	−0.00278726	+	0.00134227i
$987$	7.46244	−	35.5251i	0.237532	−	1.13077i
$988$	−4.07306	−	1.96148i	−0.129581	−	0.0624031i
$989$	5.41144	−	13.7881i	0.172074	−	0.438437i
$990$	−0.00188483	+	0.0251513i	−5.99038e−5	+	0.000799360i
$991$	−19.5866	−	49.9058i	−0.622188	−	1.58531i	−0.799177	−	0.601096i	$-0.794731\pi$
$991$	−19.5866	−	49.9058i	−0.622188	−	1.58531i	0.176989	−	0.984213i	$-0.443364\pi$
$992$	3.52731	−	1.08803i	0.111992	−	0.0345450i
$993$	−5.79494	+	7.26662i	−0.183897	+	0.230599i
$994$	1.28324	+	0.842664i	0.0407018	+	0.0267277i
$995$	−6.96649	−	8.73571i	−0.220853	−	0.276941i
$996$	−31.7985	−	21.6799i	−1.00758	−	0.686953i
$997$	−26.7958	−	24.8628i	−0.848630	−	0.787414i	0.130329	−	0.991471i	$-0.458397\pi$
$997$	−26.7958	−	24.8628i	−0.848630	−	0.787414i	−0.978959	+	0.204057i	$0.934587\pi$
$998$	−0.212585	+	0.368208i	−0.00672926	+	0.0116554i
$999$	−5.31134	−	9.19951i	−0.168043	−	0.291059i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	637.2.bl.a.235.13	✓	324
49.44	even	21	inner	637.2.bl.a.534.13	yes	324

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
637.2.bl.a.235.13	✓	324	1.1	even	1	trivial
637.2.bl.a.534.13	yes	324	49.44	even	21	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:	\( N \)	\(=\)	\( 637 = 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	637.bl (of order \(21\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(0.0482185 + 0.00726776i) q^{2} +(1.72594 - 1.17672i) q^{3} +(-1.90887 - 0.588809i) q^{4} +(-0.208146 - 2.77752i) q^{5} +(0.0917741 - 0.0441961i) q^{6} +(1.61347 - 2.09684i) q^{7} +(-0.175632 - 0.0845798i) q^{8} +(0.498154 - 1.26928i) q^{9} +O(q^{10})\)	\(q+(0.0482185 + 0.00726776i) q^{2} +(1.72594 - 1.17672i) q^{3} +(-1.90887 - 0.588809i) q^{4} +(-0.208146 - 2.77752i) q^{5} +(0.0917741 - 0.0441961i) q^{6} +(1.61347 - 2.09684i) q^{7} +(-0.175632 - 0.0845798i) q^{8} +(0.498154 - 1.26928i) q^{9} +(0.0101499 - 0.135440i) q^{10} +(-0.0497559 - 0.126776i) q^{11} +(-3.98746 + 1.22997i) q^{12} +(-0.623490 + 0.781831i) q^{13} +(0.0930382 - 0.0893800i) q^{14} +(-3.62762 - 4.54889i) q^{15} +(3.29317 + 2.24525i) q^{16} +(-0.921886 - 0.855385i) q^{17} +(0.0332450 - 0.0575821i) q^{18} +(-1.13153 - 1.95987i) q^{19} +(-1.23810 + 5.42449i) q^{20} +(0.317343 - 5.51761i) q^{21} +(-0.00147778 - 0.00647456i) q^{22} +(-3.55870 + 3.30199i) q^{23} +(-0.402656 + 0.0606906i) q^{24} +(-2.72712 + 0.411047i) q^{25} +(-0.0357459 + 0.0331673i) q^{26} +(0.760672 + 3.33272i) q^{27} +(-4.31454 + 3.05257i) q^{28} +(0.352487 - 1.54435i) q^{29} +(-0.141858 - 0.245705i) q^{30} +(3.15912 - 5.47176i) q^{31} +(0.428271 + 0.397377i) q^{32} +(-0.235056 - 0.160258i) q^{33} +(-0.0382352 - 0.0479454i) q^{34} +(-6.15984 - 4.04498i) q^{35} +(-1.69828 + 2.12957i) q^{36} +(-2.96942 + 0.915944i) q^{37} +(-0.0403169 - 0.102726i) q^{38} +(-0.156104 + 2.08307i) q^{39} +(-0.198365 + 0.505425i) q^{40} +(-3.94223 - 1.89848i) q^{41} +(0.0554025 - 0.263744i) q^{42} +(-2.74895 + 1.32383i) q^{43} +(0.0203308 + 0.271296i) q^{44} +(-3.62913 - 1.11944i) q^{45} +(-0.195593 + 0.133353i) q^{46} +(6.49479 + 0.978932i) q^{47} +8.32584 q^{48} +(-1.79345 - 6.76635i) q^{49} -0.134485 q^{50} +(-2.59767 - 0.391536i) q^{51} +(1.65051 - 1.12530i) q^{52} +(4.29211 + 1.32394i) q^{53} +(0.0124570 + 0.166227i) q^{54} +(-0.341766 + 0.164586i) q^{55} +(-0.460726 + 0.231804i) q^{56} +(-4.25919 - 2.05112i) q^{57} +(0.0282203 - 0.0719042i) q^{58} +(0.910351 - 12.1478i) q^{59} +(4.24623 + 10.8192i) q^{60} +(7.93443 - 2.44745i) q^{61} +(0.192095 - 0.240880i) q^{62} +(-1.85771 - 3.09248i) q^{63} +(-4.95237 - 6.21008i) q^{64} +(2.30133 + 1.56902i) q^{65} +(-0.0101693 - 0.00943574i) q^{66} +(0.797322 - 1.38100i) q^{67} +(1.25611 + 2.17564i) q^{68} +(-2.25656 + 9.88664i) q^{69} +(-0.267620 - 0.239811i) q^{70} +(2.64783 + 11.6009i) q^{71} +(-0.194847 + 0.180791i) q^{72} +(12.3066 - 1.85492i) q^{73} +(-0.149838 + 0.0225844i) q^{74} +(-4.22315 + 3.91851i) q^{75} +(1.00596 + 4.40741i) q^{76} +(-0.346108 - 0.100219i) q^{77} +(-0.0226663 + 0.0993077i) q^{78} +(-0.0499915 - 0.0865879i) q^{79} +(5.55075 - 9.61418i) q^{80} +(8.23318 + 7.63928i) q^{81} +(-0.176291 - 0.120193i) q^{82} +(5.75041 + 7.21078i) q^{83} +(-3.85459 + 10.3456i) q^{84} +(-2.18396 + 2.73860i) q^{85} +(-0.142171 + 0.0438541i) q^{86} +(-1.20890 - 3.08022i) q^{87} +(-0.00198397 + 0.0264742i) q^{88} +(-1.17904 + 3.00415i) q^{89} +(-0.166855 - 0.0803532i) q^{90} +(0.633393 + 2.56882i) q^{91} +(8.73736 - 4.20769i) q^{92} +(-0.986304 - 13.1613i) q^{93} +(0.306054 + 0.0944052i) q^{94} +(-5.20806 + 3.55080i) q^{95} +(1.20677 + 0.181891i) q^{96} -1.95504 q^{97} +(-0.0373012 - 0.339298i) q^{98} -0.185700 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 324 q - 3 q^{2} + 25 q^{4} + q^{5} - 24 q^{6} - 21 q^{7} + 24 q^{8} + 11 q^{9}+O(q^{10}) \) 324 * q - 3 * q^2 + 25 * q^4 + q^5 - 24 * q^6 - 21 * q^7 + 24 * q^8 + 11 * q^9	\( 324 q - 3 q^{2} + 25 q^{4} + q^{5} - 24 q^{6} - 21 q^{7} + 24 q^{8} + 11 q^{9} - 5 q^{10} - 18 q^{11} - 40 q^{12} + 54 q^{13} - 15 q^{14} + 6 q^{15} + 29 q^{16} - 6 q^{17} + 49 q^{18} - 24 q^{19} + 11 q^{20} - 6 q^{22} - 42 q^{23} + 20 q^{24} + 14 q^{25} + 3 q^{26} - 33 q^{27} + 7 q^{28} - 22 q^{29} + 57 q^{30} - 31 q^{31} - 139 q^{32} + 6 q^{33} + 50 q^{34} + 42 q^{35} - 78 q^{36} - 4 q^{37} - 90 q^{38} + 40 q^{40} + 8 q^{41} + 20 q^{42} + 34 q^{43} - 256 q^{44} + 19 q^{45} + 85 q^{46} + 34 q^{47} - 10 q^{48} + 51 q^{49} - 54 q^{50} + 74 q^{51} - 25 q^{52} + 10 q^{53} + 111 q^{54} - 10 q^{55} - 196 q^{56} - 5 q^{57} - 21 q^{58} + 65 q^{59} + 87 q^{60} + 3 q^{61} - 54 q^{62} - 35 q^{63} - 28 q^{64} - q^{65} - 110 q^{66} + 135 q^{67} - 158 q^{68} + 42 q^{69} + 44 q^{70} + 9 q^{71} - 133 q^{72} + 31 q^{73} - 97 q^{74} - 315 q^{75} - 177 q^{76} + 6 q^{77} - 25 q^{78} + 43 q^{79} - 20 q^{80} - 259 q^{81} + 96 q^{82} + 59 q^{83} + 285 q^{84} + 6 q^{85} + 95 q^{86} - 206 q^{87} + 228 q^{88} + 43 q^{89} - 61 q^{90} - 7 q^{91} + 53 q^{92} - 10 q^{93} - 36 q^{94} - 17 q^{95} + 277 q^{96} + 66 q^{97} + 260 q^{98} - 206 q^{99}+O(q^{100}) \) 324 * q - 3 * q^2 + 25 * q^4 + q^5 - 24 * q^6 - 21 * q^7 + 24 * q^8 + 11 * q^9 - 5 * q^10 - 18 * q^11 - 40 * q^12 + 54 * q^13 - 15 * q^14 + 6 * q^15 + 29 * q^16 - 6 * q^17 + 49 * q^18 - 24 * q^19 + 11 * q^20 - 6 * q^22 - 42 * q^23 + 20 * q^24 + 14 * q^25 + 3 * q^26 - 33 * q^27 + 7 * q^28 - 22 * q^29 + 57 * q^30 - 31 * q^31 - 139 * q^32 + 6 * q^33 + 50 * q^34 + 42 * q^35 - 78 * q^36 - 4 * q^37 - 90 * q^38 + 40 * q^40 + 8 * q^41 + 20 * q^42 + 34 * q^43 - 256 * q^44 + 19 * q^45 + 85 * q^46 + 34 * q^47 - 10 * q^48 + 51 * q^49 - 54 * q^50 + 74 * q^51 - 25 * q^52 + 10 * q^53 + 111 * q^54 - 10 * q^55 - 196 * q^56 - 5 * q^57 - 21 * q^58 + 65 * q^59 + 87 * q^60 + 3 * q^61 - 54 * q^62 - 35 * q^63 - 28 * q^64 - q^65 - 110 * q^66 + 135 * q^67 - 158 * q^68 + 42 * q^69 + 44 * q^70 + 9 * q^71 - 133 * q^72 + 31 * q^73 - 97 * q^74 - 315 * q^75 - 177 * q^76 + 6 * q^77 - 25 * q^78 + 43 * q^79 - 20 * q^80 - 259 * q^81 + 96 * q^82 + 59 * q^83 + 285 * q^84 + 6 * q^85 + 95 * q^86 - 206 * q^87 + 228 * q^88 + 43 * q^89 - 61 * q^90 - 7 * q^91 + 53 * q^92 - 10 * q^93 - 36 * q^94 - 17 * q^95 + 277 * q^96 + 66 * q^97 + 260 * q^98 - 206 * q^99

Introduction

L-functions

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