LMFDB - Embedded newform 507.2.q.b.16.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [507,2,Mod(16,507)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(507, base_ring=CyclotomicField(78))

chi = DirichletCharacter(H, H._module([0, 2]))

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

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

chi := DirichletCharacter("507.16");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 507 = 3 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	507.q (of order $39$, degree $24$, 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:	$4.04841538248$
Analytic rank:	$0$
Dimension:	$384$
Relative dimension:	$16$ over $\Q(\zeta_{39})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{39}]$

Embedding invariants

Embedding label			16.4
Character	$\chi$	$=$	507.16
Dual form			507.2.q.b.412.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.82353 - 0.147211i) q^{2} +(-0.845190 - 0.534466i) q^{3} +(1.32950 + 0.216064i) q^{4} +(1.37382 + 1.21710i) q^{5} +(1.46255 + 1.09904i) q^{6} +(-0.320915 + 0.334108i) q^{7} +(1.16003 + 0.285923i) q^{8} +(0.428693 + 0.903450i) q^{9} +O(q^{10})$	\(q+(-1.82353 - 0.147211i) q^{2} +(-0.845190 - 0.534466i) q^{3} +(1.32950 + 0.216064i) q^{4} +(1.37382 + 1.21710i) q^{5} +(1.46255 + 1.09904i) q^{6} +(-0.320915 + 0.334108i) q^{7} +(1.16003 + 0.285923i) q^{8} +(0.428693 + 0.903450i) q^{9} +(-2.32603 - 2.42166i) q^{10} +(0.581356 - 1.22518i) q^{11} +(-1.00820 - 0.893186i) q^{12} +(1.87275 - 3.08104i) q^{13} +(0.634382 - 0.562014i) q^{14} +(-0.510641 - 1.76294i) q^{15} +(-4.62851 - 1.54522i) q^{16} +(-5.20715 + 5.42122i) q^{17} +(-0.648737 - 1.71058i) q^{18} +(-2.22407 + 3.85220i) q^{19} +(1.56352 + 1.91496i) q^{20} +(0.449803 - 0.110866i) q^{21} +(-1.24048 + 2.14858i) q^{22} +(3.02753 + 5.24383i) q^{23} +(-0.827633 - 0.861657i) q^{24} +(-0.196631 - 1.61940i) q^{25} +(-3.86857 + 5.34269i) q^{26} +(0.120537 - 0.992709i) q^{27} +(-0.498844 + 0.374857i) q^{28} +(6.60783 + 0.533439i) q^{29} +(0.671647 + 3.28995i) q^{30} +(0.779433 - 6.41921i) q^{31} +(6.01447 + 2.56253i) q^{32} +(-1.14617 + 0.724796i) q^{33} +(10.2935 - 9.11922i) q^{34} +(-0.847520 + 0.0684189i) q^{35} +(0.374742 + 1.29376i) q^{36} +(-0.708808 + 0.301995i) q^{37} +(4.62275 - 6.69721i) q^{38} +(-3.22954 + 1.60315i) q^{39} +(1.24568 + 1.80468i) q^{40} +(7.24842 + 4.58362i) q^{41} +(-0.836551 + 0.135953i) q^{42} +(5.49838 + 2.34264i) q^{43} +(1.03763 - 1.50326i) q^{44} +(-0.510641 + 1.76294i) q^{45} +(-4.74884 - 10.0080i) q^{46} +(-3.37054 + 8.88739i) q^{47} +(3.08610 + 3.77979i) q^{48} +(0.273220 + 6.77988i) q^{49} +(0.120170 + 2.98198i) q^{50} +(7.29849 - 1.79892i) q^{51} +(3.15551 - 3.69160i) q^{52} +(11.8624 + 2.92382i) q^{53} +(-0.365940 + 1.79249i) q^{54} +(2.28984 - 0.975611i) q^{55} +(-0.467801 + 0.295819i) q^{56} +(3.93863 - 2.06715i) q^{57} +(-11.9711 - 1.94549i) q^{58} +(-4.07623 + 1.36085i) q^{59} +(-0.297988 - 2.45415i) q^{60} +(-0.671460 + 2.31815i) q^{61} +(-2.36630 + 11.5909i) q^{62} +(-0.439423 - 0.146701i) q^{63} +(-1.94895 - 1.02289i) q^{64} +(6.32274 - 1.95348i) q^{65} +(2.19678 - 1.15296i) q^{66} +(-0.786388 + 0.127801i) q^{67} +(-8.09423 + 6.08242i) q^{68} +(0.243812 - 6.05014i) q^{69} +1.55555 q^{70} +(-0.0561751 + 1.39397i) q^{71} +(0.238981 + 1.17061i) q^{72} +(9.24294 + 13.3907i) q^{73} +(1.33699 - 0.446353i) q^{74} +(-0.699324 + 1.47379i) q^{75} +(-3.78922 + 4.64095i) q^{76} +(0.222777 + 0.587414i) q^{77} +(6.12517 - 2.44797i) q^{78} +(4.95845 - 13.0744i) q^{79} +(-4.47805 - 7.75620i) q^{80} +(-0.632445 + 0.774605i) q^{81} +(-12.5430 - 9.42543i) q^{82} +(-11.0923 - 5.82169i) q^{83} +(0.621966 - 0.0502103i) q^{84} +(-13.7518 + 1.11016i) q^{85} +(-9.68160 - 5.08130i) q^{86} +(-5.29977 - 3.98252i) q^{87} +(1.02470 - 1.25503i) q^{88} +(-2.28056 - 3.95004i) q^{89} +(1.19069 - 3.13960i) q^{90} +(0.428408 + 1.61445i) q^{91} +(2.89208 + 7.62580i) q^{92} +(-4.08962 + 5.00887i) q^{93} +(7.45461 - 15.7103i) q^{94} +(-7.74398 + 2.58532i) q^{95} +(-3.71379 - 5.38035i) q^{96} +(3.03876 + 14.8848i) q^{97} +(0.499846 - 12.4036i) q^{98} +1.35611 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 384 q + q^{2} + 16 q^{3} + 17 q^{4} + 6 q^{5} + q^{6} - 3 q^{7} - 18 q^{8} + 16 q^{9}+O(q^{10}) $ 384 * q + q^2 + 16 * q^3 + 17 * q^4 + 6 * q^5 + q^6 - 3 * q^7 - 18 * q^8 + 16 * q^9	\( 384 q + q^{2} + 16 q^{3} + 17 q^{4} + 6 q^{5} + q^{6} - 3 q^{7} - 18 q^{8} + 16 q^{9} + 3 q^{10} - 4 q^{11} - 34 q^{12} - 15 q^{13} + 24 q^{14} - 3 q^{15} + 11 q^{16} - 3 q^{17} - 2 q^{18} + 6 q^{19} + q^{20} + 6 q^{21} - 86 q^{22} - 52 q^{23} + 9 q^{24} - 74 q^{25} - 64 q^{26} - 32 q^{27} - 16 q^{28} - 44 q^{29} + 3 q^{30} - 28 q^{31} + 74 q^{32} - 17 q^{33} - 83 q^{34} + 70 q^{35} + 17 q^{36} + 11 q^{37} - 29 q^{38} + q^{39} - 5 q^{40} + q^{41} + 118 q^{42} - 79 q^{43} - 19 q^{44} - 3 q^{45} + 314 q^{46} + 11 q^{48} - 69 q^{49} - 76 q^{50} + 6 q^{51} - 37 q^{52} - 102 q^{53} + q^{54} - 73 q^{55} - 36 q^{56} + 14 q^{57} - 51 q^{58} + 194 q^{59} + 76 q^{60} + 4 q^{61} - 89 q^{62} - 3 q^{63} - 184 q^{64} - 49 q^{65} - 36 q^{66} - 73 q^{67} + 4 q^{68} - 100 q^{70} + 106 q^{71} + 9 q^{72} - 132 q^{73} - 45 q^{74} + 11 q^{75} + 24 q^{76} - 54 q^{77} - 39 q^{78} - 2 q^{79} + 177 q^{80} + 16 q^{81} - 76 q^{82} - 58 q^{83} - 16 q^{84} - 123 q^{85} - 157 q^{86} - 57 q^{87} + 476 q^{88} + 18 q^{89} - 6 q^{90} + 233 q^{91} - 12 q^{92} + q^{93} - 111 q^{94} + 64 q^{95} - 83 q^{96} - 143 q^{97} - 79 q^{98} - 18 q^{99}+O(q^{100}) \) 384 * q + q^2 + 16 * q^3 + 17 * q^4 + 6 * q^5 + q^6 - 3 * q^7 - 18 * q^8 + 16 * q^9 + 3 * q^10 - 4 * q^11 - 34 * q^12 - 15 * q^13 + 24 * q^14 - 3 * q^15 + 11 * q^16 - 3 * q^17 - 2 * q^18 + 6 * q^19 + q^20 + 6 * q^21 - 86 * q^22 - 52 * q^23 + 9 * q^24 - 74 * q^25 - 64 * q^26 - 32 * q^27 - 16 * q^28 - 44 * q^29 + 3 * q^30 - 28 * q^31 + 74 * q^32 - 17 * q^33 - 83 * q^34 + 70 * q^35 + 17 * q^36 + 11 * q^37 - 29 * q^38 + q^39 - 5 * q^40 + q^41 + 118 * q^42 - 79 * q^43 - 19 * q^44 - 3 * q^45 + 314 * q^46 + 11 * q^48 - 69 * q^49 - 76 * q^50 + 6 * q^51 - 37 * q^52 - 102 * q^53 + q^54 - 73 * q^55 - 36 * q^56 + 14 * q^57 - 51 * q^58 + 194 * q^59 + 76 * q^60 + 4 * q^61 - 89 * q^62 - 3 * q^63 - 184 * q^64 - 49 * q^65 - 36 * q^66 - 73 * q^67 + 4 * q^68 - 100 * q^70 + 106 * q^71 + 9 * q^72 - 132 * q^73 - 45 * q^74 + 11 * q^75 + 24 * q^76 - 54 * q^77 - 39 * q^78 - 2 * q^79 + 177 * q^80 + 16 * q^81 - 76 * q^82 - 58 * q^83 - 16 * q^84 - 123 * q^85 - 157 * q^86 - 57 * q^87 + 476 * q^88 + 18 * q^89 - 6 * q^90 + 233 * q^91 - 12 * q^92 + q^93 - 111 * q^94 + 64 * q^95 - 83 * q^96 - 143 * q^97 - 79 * q^98 - 18 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/507\mathbb{Z}\right)^\times$.

$n$	$170$	$340$
$\chi(n)$	$1$	$e\left(\frac{1}{39}\right)$

Coefficient data

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

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

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

$2$	−1.82353	−	0.147211i	−1.28943	−	0.104094i	−0.583348	−	0.812222i	$-0.698258\pi$
$2$	−1.82353	−	0.147211i	−1.28943	−	0.104094i	−0.706084	+	0.708128i	$0.749540\pi$
$3$	−0.845190	−	0.534466i	−0.487971	−	0.308574i
$3$	−0.845190	−	0.534466i	−0.487971	−	0.308574i
$4$	1.32950	+	0.216064i	0.664749	+	0.108032i
$5$	1.37382	+	1.21710i	0.614391	+	0.544303i	0.911898	−	0.410417i	$-0.134617\pi$
$5$	1.37382	+	1.21710i	0.614391	+	0.544303i	−0.297507	+	0.954720i	$0.596155\pi$
$6$	1.46255	+	1.09904i	0.597084	+	0.448680i
$7$	−0.320915	+	0.334108i	−0.121294	+	0.126281i	−0.779080	−	0.626924i	$-0.784314\pi$
$7$	−0.320915	+	0.334108i	−0.121294	+	0.126281i	0.657786	+	0.753205i	$0.271493\pi$
$8$	1.16003	+	0.285923i	0.410134	+	0.101089i
$9$	0.428693	+	0.903450i	0.142898	+	0.301150i
$10$	−2.32603	−	2.42166i	−0.735556	−	0.765795i
$11$	0.581356	−	1.22518i	0.175285	−	0.369406i	−0.796726	−	0.604341i	$-0.793436\pi$
$11$	0.581356	−	1.22518i	0.175285	−	0.369406i	0.972011	+	0.234935i	$0.0754877\pi$
$12$	−1.00820	−	0.893186i	−0.291042	−	0.257841i
$13$	1.87275	−	3.08104i	0.519406	−	0.854527i
$13$	1.87275	−	3.08104i	0.519406	−	0.854527i
$14$	0.634382	−	0.562014i	0.169546	−	0.150204i
$15$	−0.510641	−	1.76294i	−0.131847	−	0.455189i
$16$	−4.62851	−	1.54522i	−1.15713	−	0.386306i
$17$	−5.20715	+	5.42122i	−1.26292	+	1.31484i	−0.334927	+	0.942244i	$0.608712\pi$
$17$	−5.20715	+	5.42122i	−1.26292	+	1.31484i	−0.927994	+	0.372595i	$0.878468\pi$
$18$	−0.648737	−	1.71058i	−0.152909	−	0.403187i
$19$	−2.22407	+	3.85220i	−0.510237	+	0.883756i	0.489693	+	0.871895i	$0.337109\pi$
$19$	−2.22407	+	3.85220i	−0.510237	+	0.883756i	−0.999930	+	0.0118610i	$0.996224\pi$
$20$	1.56352	+	1.91496i	0.349613	+	0.428198i
$21$	0.449803	−	0.110866i	0.0981551	−	0.0241930i
$22$	−1.24048	+	2.14858i	−0.264471	+	0.458078i
$23$	3.02753	+	5.24383i	0.631283	+	1.09341i	0.987290	+	0.158931i	$0.0508046\pi$
$23$	3.02753	+	5.24383i	0.631283	+	1.09341i	−0.356007	+	0.934483i	$0.615862\pi$
$24$	−0.827633	−	0.861657i	−0.168940	−	0.175885i
$25$	−0.196631	−	1.61940i	−0.0393262	−	0.323880i
$26$	−3.86857	+	5.34269i	−0.758690	+	1.04779i
$27$	0.120537	−	0.992709i	0.0231973	−	0.191047i
$28$	−0.498844	+	0.374857i	−0.0942726	+	0.0708413i
$29$	6.60783	+	0.533439i	1.22704	+	0.0990572i	0.676939	−	0.736039i	$-0.263306\pi$
$29$	6.60783	+	0.533439i	1.22704	+	0.0990572i	0.550104	+	0.835096i	$0.314588\pi$
$30$	0.671647	+	3.28995i	0.122625	+	0.600659i
$31$	0.779433	−	6.41921i	0.139990	−	1.15292i	−0.738189	−	0.674594i	$-0.764319\pi$
$31$	0.779433	−	6.41921i	0.139990	−	1.15292i	0.878180	−	0.478331i	$-0.158758\pi$
$32$	6.01447	+	2.56253i	1.06322	+	0.452995i
$33$	−1.14617	+	0.724796i	−0.199523	+	0.126171i
$34$	10.2935	−	9.11922i	1.76532	−	1.56393i
$35$	−0.847520	+	0.0684189i	−0.143257	+	0.0115649i
$36$	0.374742	+	1.29376i	0.0624570	+	0.215627i
$37$	−0.708808	+	0.301995i	−0.116527	+	0.0496476i	−0.449443	−	0.893309i	$-0.648378\pi$
$37$	−0.708808	+	0.301995i	−0.116527	+	0.0496476i	0.332916	+	0.942956i	$0.391967\pi$
$38$	4.62275	−	6.69721i	0.749909	−	1.08643i
$39$	−3.22954	+	1.60315i	−0.517140	+	0.256709i
$40$	1.24568	+	1.80468i	0.196959	+	0.285345i
$41$	7.24842	+	4.58362i	1.13201	+	0.715842i	0.962928	−	0.269760i	$-0.0869443\pi$
$41$	7.24842	+	4.58362i	1.13201	+	0.715842i	0.169085	+	0.985601i	$0.445919\pi$
$42$	−0.836551	+	0.135953i	−0.129083	+	0.0209780i
$43$	5.49838	+	2.34264i	0.838494	+	0.357249i	0.768147	−	0.640273i	$-0.221179\pi$
$43$	5.49838	+	2.34264i	0.838494	+	0.357249i	0.0703474	+	0.997523i	$0.477589\pi$
$44$	1.03763	−	1.50326i	0.156428	−	0.226626i
$45$	−0.510641	+	1.76294i	−0.0761219	+	0.262803i
$46$	−4.74884	−	10.0080i	−0.700179	−	1.47560i
$47$	−3.37054	+	8.88739i	−0.491644	+	1.29636i	0.428061	+	0.903750i	$0.359197\pi$
$47$	−3.37054	+	8.88739i	−0.491644	+	1.29636i	−0.919705	+	0.392610i	$0.871572\pi$
$48$	3.08610	+	3.77979i	0.445440	+	0.545565i
$49$	0.273220	+	6.77988i	0.0390314	+	0.968555i
$50$	0.120170	+	2.98198i	0.0169945	+	0.421715i
$51$	7.29849	−	1.79892i	1.02199	−	0.251899i
$52$	3.15551	−	3.69160i	0.437591	−	0.511933i
$53$	11.8624	+	2.92382i	1.62943	+	0.401617i	0.944897	−	0.327368i	$-0.106162\pi$
$53$	11.8624	+	2.92382i	1.62943	+	0.401617i	0.684529	+	0.728986i	$0.260008\pi$
$54$	−0.365940	+	1.79249i	−0.0497981	+	0.243927i
$55$	2.28984	−	0.975611i	0.308762	−	0.131551i
$56$	−0.467801	+	0.295819i	−0.0625125	+	0.0395305i
$57$	3.93863	−	2.06715i	0.521685	−	0.273801i
$58$	−11.9711	−	1.94549i	−1.57188	−	0.255455i
$59$	−4.07623	+	1.36085i	−0.530680	+	0.177167i	−0.569366	−	0.822084i	$-0.692811\pi$
$59$	−4.07623	+	1.36085i	−0.530680	+	0.177167i	0.0386855	+	0.999251i	$0.487683\pi$
$60$	−0.297988	−	2.45415i	−0.0384701	−	0.316830i
$61$	−0.671460	+	2.31815i	−0.0859716	+	0.296808i	−0.991970	−	0.126472i	$-0.959634\pi$
$61$	−0.671460	+	2.31815i	−0.0859716	+	0.296808i	0.905999	+	0.423281i	$0.139122\pi$
$62$	−2.36630	+	11.5909i	−0.300520	+	1.47205i
$63$	−0.439423	−	0.146701i	−0.0553621	−	0.0184826i
$64$	−1.94895	−	1.02289i	−0.243618	−	0.127861i
$65$	6.32274	−	1.95348i	0.784240	−	0.242300i
$66$	2.19678	−	1.15296i	0.270405	−	0.141920i
$67$	−0.786388	+	0.127801i	−0.0960726	+	0.0156133i	−0.208258	−	0.978074i	$-0.566779\pi$
$67$	−0.786388	+	0.127801i	−0.0960726	+	0.0156133i	0.112185	+	0.993687i	$0.464215\pi$
$68$	−8.09423	+	6.08242i	−0.981570	+	0.737602i
$69$	0.243812	−	6.05014i	0.0293516	−	0.728351i
$70$	1.55555			0.185924
$71$	−0.0561751	+	1.39397i	−0.00666676	+	0.165434i	0.992426	+	0.122845i	$0.0392017\pi$
$71$	−0.0561751	+	1.39397i	−0.00666676	+	0.165434i	−0.999093	+	0.0425892i	$0.986439\pi$
$72$	0.238981	+	1.17061i	0.0281642	+	0.137957i
$73$	9.24294	+	13.3907i	1.08180	+	1.56726i	0.792344	+	0.610075i	$0.208861\pi$
$73$	9.24294	+	13.3907i	1.08180	+	1.56726i	0.289461	+	0.957190i	$0.406524\pi$
$74$	1.33699	−	0.446353i	0.155422	−	0.0518875i
$75$	−0.699324	+	1.47379i	−0.0807510	+	0.170179i
$76$	−3.78922	+	4.64095i	−0.434653	+	0.532354i
$77$	0.222777	+	0.587414i	0.0253878	+	0.0669420i
$78$	6.12517	−	2.44797i	0.693539	−	0.277178i
$79$	4.95845	−	13.0744i	0.557869	−	1.47098i	−0.298395	−	0.954442i	$-0.596451\pi$
$79$	4.95845	−	13.0744i	0.557869	−	1.47098i	0.856265	−	0.516538i	$-0.172779\pi$
$80$	−4.47805	−	7.75620i	−0.500661	−	0.867170i
$81$	−0.632445	+	0.774605i	−0.0702717	+	0.0860672i
$82$	−12.5430	−	9.42543i	−1.38514	−	1.04086i
$83$	−11.0923	−	5.82169i	−1.21754	−	0.639013i	−0.271303	−	0.962494i	$-0.587455\pi$
$83$	−11.0923	−	5.82169i	−1.21754	−	0.639013i	−0.946235	+	0.323481i	$0.895147\pi$
$84$	0.621966	−	0.0502103i	0.0678621	−	0.00547839i
$85$	−13.7518	+	1.11016i	−1.49160	+	0.120414i
$86$	−9.68160	−	5.08130i	−1.04399	−	0.547930i
$87$	−5.29977	−	3.98252i	−0.568195	−	0.426971i
$88$	1.02470	−	1.25503i	0.109233	−	0.133786i
$89$	−2.28056	−	3.95004i	−0.241739	−	0.418704i	0.719471	−	0.694523i	$-0.244384\pi$
$89$	−2.28056	−	3.95004i	−0.241739	−	0.418704i	−0.961210	+	0.275819i	$0.911051\pi$
$90$	1.19069	−	3.13960i	0.125510	−	0.330943i
$91$	0.428408	+	1.61445i	0.0449094	+	0.169240i
$92$	2.89208	+	7.62580i	0.301520	+	0.795044i
$93$	−4.08962	+	5.00887i	−0.424074	+	0.519396i
$94$	7.45461	−	15.7103i	0.768885	−	1.62039i
$95$	−7.74398	+	2.58532i	−0.794515	+	0.265248i
$96$	−3.71379	−	5.38035i	−0.379037	−	0.549130i
$97$	3.03876	+	14.8848i	0.308539	+	1.51132i	0.777940	+	0.628338i	$0.216265\pi$
$97$	3.03876	+	14.8848i	0.308539	+	1.51132i	−0.469401	+	0.882985i	$0.655530\pi$
$98$	0.499846	−	12.4036i	0.0504921	−	1.25295i
$99$	1.35611			0.136295
$100$	0.0884746	−	2.19547i	0.00884746	−	0.219547i
$101$	10.3017	−	7.74120i	1.02505	−	0.770278i	0.0514857	−	0.998674i	$-0.483604\pi$
$101$	10.3017	−	7.74120i	1.02505	−	0.770278i	0.973568	+	0.228396i	$0.0733479\pi$
$102$	−13.5739	+	2.20597i	−1.34401	+	0.218423i
$103$	−8.42122	+	4.41980i	−0.829767	+	0.435495i	−0.825436	−	0.564495i	$-0.809071\pi$
$103$	−8.42122	+	4.41980i	−0.829767	+	0.435495i	−0.00433086	+	0.999991i	$0.501379\pi$
$104$	3.05339	−	3.03865i	0.299409	−	0.297964i
$105$	0.752883	+	0.395144i	0.0734739	+	0.0385621i
$106$	−21.2010	−	7.07795i	−2.05923	−	0.687471i
$107$	0.865291	−	4.23848i	0.0836509	−	0.409749i	−0.916306	−	0.400478i	$-0.868844\pi$
$107$	0.865291	−	4.23848i	0.0836509	−	0.409749i	0.999957	−	0.00927054i	$-0.00295095\pi$
$108$	0.374742	−	1.29376i	0.0360596	−	0.124492i
$109$	0.279938	+	2.30550i	0.0268132	+	0.220827i	0.999956	−	0.00937546i	$-0.00298435\pi$
$109$	0.279938	+	2.30550i	0.0268132	+	0.220827i	−0.973143	+	0.230202i	$0.926061\pi$
$110$	−4.31922	+	1.44197i	−0.411822	+	0.137486i
$111$	0.760483	+	0.123591i	0.0721818	+	0.0117307i
$112$	2.00163	−	1.05054i	0.189136	−	0.0992662i
$113$	−10.7514	+	6.79880i	−1.01141	+	0.639578i	−0.933945	−	0.357417i	$-0.883657\pi$
$113$	−10.7514	+	6.79880i	−1.01141	+	0.639578i	−0.0774662	+	0.996995i	$0.524683\pi$
$114$	−7.48653	+	3.18971i	−0.701178	+	0.298744i
$115$	−2.22298	+	10.8889i	−0.207294	+	1.01539i
$116$	8.66983	+	2.13692i	0.804974	+	0.198408i
$117$	3.58640	+	0.371113i	0.331563	+	0.0343094i
$118$	7.63347	−	1.88148i	0.702718	−	0.173204i
$119$	−0.140219	−	3.47950i	−0.0128539	−	0.318965i
$120$	−0.0882971	−	2.19107i	−0.00806039	−	0.200016i
$121$	5.79380	+	7.09612i	0.526710	+	0.645102i
$122$	1.56568	−	4.12837i	0.141750	−	0.373765i
$123$	−3.67650	−	7.74806i	−0.331499	−	0.698619i
$124$	2.42322	−	8.36591i	0.217611	−	0.751281i
$125$	6.91397	−	10.0166i	0.618405	−	0.895914i
$126$	0.779707	+	0.332202i	0.0694618	+	0.0295949i
$127$	11.0814	−	1.80091i	0.983319	−	0.159805i	0.352564	−	0.935788i	$-0.385310\pi$
$127$	11.0814	−	1.80091i	0.983319	−	0.159805i	0.630754	+	0.775983i	$0.282746\pi$
$128$	−7.64767	−	4.83609i	−0.675965	−	0.427454i
$129$	−3.39511	−	4.91867i	−0.298923	−	0.433065i
$130$	−11.8173	+	2.63146i	−1.03645	+	0.230794i
$131$	−9.57682	+	13.8744i	−0.836731	+	1.21221i	0.138354	+	0.990383i	$0.455819\pi$
$131$	−9.57682	+	13.8744i	−0.836731	+	1.21221i	−0.975085	+	0.221831i	$0.928797\pi$
$132$	−1.68044	+	0.715967i	−0.146263	+	0.0623170i
$133$	−0.573313	−	1.97931i	−0.0497126	−	0.171628i
$134$	1.45282	−	0.117284i	0.125504	−	0.0101318i
$135$	1.37382	−	1.21710i	0.118240	−	0.104751i
$136$	−7.59052	+	4.79995i	−0.650882	+	0.411593i
$137$	−1.72499	−	0.734949i	−0.147376	−	0.0627909i	0.317019	−	0.948419i	$-0.397318\pi$
$137$	−1.72499	−	0.734949i	−0.147376	−	0.0627909i	−0.464395	+	0.885628i	$0.653728\pi$
$138$	−1.33525	+	10.9967i	−0.113664	+	0.936104i
$139$	−3.92531	−	19.2274i	−0.332940	−	1.63085i	−0.709675	−	0.704529i	$-0.751158\pi$
$139$	−3.92531	−	19.2274i	−0.332940	−	1.63085i	0.376735	−	0.926321i	$-0.377047\pi$
$140$	−1.14156	−	0.0921561i	−0.0964793	−	0.00778862i
$141$	7.59876	−	5.71010i	0.639931	−	0.480877i
$142$	0.307644	−	2.53368i	0.0258170	−	0.212622i
$143$	−2.68610	−	4.08563i	−0.224623	−	0.341658i
$144$	−0.588175	−	4.84405i	−0.0490146	−	0.403671i
$145$	8.42871	+	8.77522i	0.699967	+	0.728742i
$146$	−14.8835	−	25.7791i	−1.23177	−	2.13349i
$147$	3.39269	−	5.87632i	0.279825	−	0.484670i
$148$	−1.00761	+	0.248353i	−0.0828249	+	0.0204145i
$149$	−2.01924	−	2.47312i	−0.165422	−	0.202606i	0.685241	−	0.728316i	$-0.259697\pi$
$149$	−2.01924	−	2.47312i	−0.165422	−	0.202606i	−0.850663	+	0.525711i	$0.823799\pi$
$150$	1.49220	−	2.58456i	0.121837	−	0.211029i
$151$	−2.85463	−	7.52703i	−0.232306	−	0.612541i	0.767280	−	0.641312i	$-0.221610\pi$
$151$	−2.85463	−	7.52703i	−0.232306	−	0.612541i	−0.999586	+	0.0287715i	$0.990840\pi$
$152$	−3.68143	+	3.83277i	−0.298603	+	0.310879i
$153$	−7.13007	−	2.38037i	−0.576432	−	0.192441i
$154$	−0.319767	−	1.10396i	−0.0257675	−	0.0889599i
$155$	8.88361	−	7.87019i	0.713548	−	0.632149i
$156$	−4.64004	+	1.43359i	−0.371501	+	0.114779i
$157$	−2.11105	−	1.87023i	−0.168480	−	0.149260i	0.574670	−	0.818385i	$-0.305131\pi$
$157$	−2.11105	−	1.87023i	−0.168480	−	0.149260i	−0.743150	+	0.669125i	$0.766669\pi$
$158$	−10.9666	+	23.1116i	−0.872454	+	1.83866i
$159$	−8.46330	−	8.81123i	−0.671183	−	0.698776i
$160$	5.14395	+	10.8406i	0.406665	+	0.857028i
$161$	−2.72358	−	0.671302i	−0.214648	−	0.0529060i
$162$	1.26731	−	1.31941i	0.0995696	−	0.103663i
$163$	6.04276	+	4.54084i	0.473305	+	0.355666i	0.810470	−	0.585780i	$-0.199212\pi$
$163$	6.04276	+	4.54084i	0.473305	+	0.355666i	−0.337165	+	0.941446i	$0.609468\pi$
$164$	8.64640	+	7.66004i	0.675170	+	0.598148i
$165$	−2.45678	−	0.399266i	−0.191260	−	0.0310828i
$166$	19.3701	+	12.2489i	1.50341	+	0.950702i
$167$	−20.4289	−	1.64919i	−1.58084	−	0.127618i	−0.741396	−	0.671067i	$-0.765836\pi$
$167$	−20.4289	−	1.64919i	−1.58084	−	0.127618i	−0.839442	+	0.543449i	$0.817118\pi$
$168$	0.553486			0.0427023
$169$	−5.98565	−	11.5400i	−0.460434	−	0.887694i
$170$	25.2404			1.93585
$171$	−4.43372	−	0.357927i	−0.339055	−	0.0273713i
$172$	6.80391	+	4.30254i	0.518794	+	0.328065i
$173$	19.9337	+	3.23955i	1.51553	+	0.246298i	0.860558	−	0.509352i	$-0.170115\pi$
$173$	19.9337	+	3.23955i	1.51553	+	0.246298i	0.654975	+	0.755650i	$0.272679\pi$
$174$	9.07803	+	8.04243i	0.688203	+	0.609695i
$175$	0.604156	+	0.453994i	0.0456699	+	0.0343187i
$176$	−4.58399	+	4.77244i	−0.345531	+	0.359736i
$177$	4.17252	+	1.02843i	0.313626	+	0.0773018i
$178$	3.57718	+	7.53876i	0.268121	+	0.565054i
$179$	11.1082	+	11.5648i	0.830265	+	0.864397i	0.992486	−	0.122357i	$-0.0390453\pi$
$179$	11.1082	+	11.5648i	0.830265	+	0.864397i	−0.162221	+	0.986754i	$0.551866\pi$
$180$	−1.05980	+	2.23349i	−0.0789931	+	0.166475i
$181$	−1.55755	−	1.37986i	−0.115771	−	0.102565i	0.603251	−	0.797551i	$-0.293872\pi$
$181$	−1.55755	−	1.37986i	−0.115771	−	0.102565i	−0.719022	+	0.694987i	$0.755410\pi$
$182$	−0.543551	−	3.00707i	−0.0402907	−	0.222899i
$183$	1.80648	−	1.60040i	0.133539	−	0.118305i
$184$	2.01270	+	6.94865i	0.148378	+	0.512261i
$185$	−1.34133	−	0.447802i	−0.0986166	−	0.0329230i
$186$	8.19491	−	8.53180i	0.600880	−	0.625582i
$187$	3.61477	+	9.53137i	0.264338	+	0.697003i
$188$	−6.40138	+	11.0875i	−0.466868	+	0.808640i
$189$	0.292990	+	0.358847i	0.0213119	+	0.0261023i
$190$	14.5020	−	3.57442i	1.05208	−	0.259315i
$191$	10.9948	−	19.0436i	0.795559	−	1.37795i	−0.126925	−	0.991912i	$-0.540511\pi$
$191$	10.9948	−	19.0436i	0.795559	−	1.37795i	0.922484	−	0.386036i	$-0.126156\pi$
$192$	1.10053	+	1.90618i	0.0794241	+	0.137567i
$193$	−3.58276	−	3.73005i	−0.257893	−	0.268495i	0.579651	−	0.814865i	$-0.303189\pi$
$193$	−3.58276	−	3.73005i	−0.257893	−	0.268495i	−0.837544	+	0.546370i	$0.816009\pi$
$194$	−3.35006	−	27.5903i	−0.240521	−	1.98087i
$195$	−6.38799	−	1.72823i	−0.457453	−	0.123761i
$196$	−1.10165	+	9.07287i	−0.0786890	+	0.648062i
$197$	−21.1910	+	15.9240i	−1.50980	+	1.13454i	−0.557167	+	0.830400i	$0.688112\pi$
$197$	−21.1910	+	15.9240i	−1.50980	+	1.13454i	−0.952628	+	0.304137i	$0.901632\pi$
$198$	−2.47292	−	0.199634i	−0.175742	−	0.0141874i
$199$	0.573304	+	2.80823i	0.0406404	+	0.199070i	0.995042	−	0.0994559i	$-0.0317102\pi$
$199$	0.573304	+	2.80823i	0.0406404	+	0.199070i	−0.954402	+	0.298526i	$0.903505\pi$
$200$	0.234925	−	1.93478i	0.0166117	−	0.136810i
$201$	0.732953	+	0.312282i	0.0516985	+	0.0220267i
$202$	−19.9250	+	12.5998i	−1.40192	+	0.886520i
$203$	−2.29878	+	2.03654i	−0.161342	+	0.142937i
$204$	10.0920	−	0.814711i	0.706582	−	0.0570412i
$205$	4.37930	+	15.1191i	0.305864	+	1.05596i
$206$	16.0070	−	6.81995i	1.11526	−	0.475168i
$207$	−3.43966	+	4.98321i	−0.239073	+	0.346357i
$208$	−13.4289	+	11.3668i	−0.931128	+	0.788147i
$209$	3.42667	+	4.96439i	0.237028	+	0.343394i
$210$	−1.31474	−	0.831389i	−0.0907255	−	0.0573713i
$211$	15.0642	−	2.44818i	1.03707	−	0.168540i	0.382040	−	0.924146i	$-0.375222\pi$
$211$	15.0642	−	2.44818i	1.03707	−	0.168540i	0.655026	+	0.755606i	$0.272658\pi$
$212$	15.1393	+	6.45025i	1.03977	+	0.443005i
$213$	0.792508	−	1.14815i	0.0543018	−	0.0786697i
$214$	−2.20184	+	7.60162i	−0.150514	+	0.519636i
$215$	4.70255	+	9.91042i	0.320711	+	0.675885i
$216$	0.423664	−	1.11711i	0.0288267	−	0.0760098i
$217$	1.89458	+	2.32043i	0.128612	+	0.157521i
$218$	−0.171082	−	4.24536i	−0.0115871	−	0.287532i
$219$	−0.655164	−	16.2577i	−0.0442719	−	1.09860i
$220$	3.25513	−	0.802318i	0.219461	−	0.0540923i
$221$	6.95134	+	26.1960i	0.467598	+	1.76214i
$222$	−1.36857	−	0.337322i	−0.0918525	−	0.0226396i
$223$	1.44636	−	7.08476i	0.0968557	−	0.474431i	−0.902213	−	0.431290i	$-0.858059\pi$
$223$	1.44636	−	7.08476i	0.0968557	−	0.474431i	0.999069	−	0.0431406i	$-0.0137363\pi$
$224$	−2.78629	+	1.18713i	−0.186167	+	0.0793183i
$225$	1.37875	−	0.871871i	0.0919170	−	0.0581248i
$226$	20.6065	−	10.8151i	1.37072	−	0.719410i
$227$	−0.896517	−	0.145698i	−0.0595039	−	0.00967033i	0.130586	−	0.991437i	$-0.458314\pi$
$227$	−0.896517	−	0.145698i	−0.0595039	−	0.00967033i	−0.190090	+	0.981767i	$0.560878\pi$
$228$	5.68304	−	1.89728i	0.376369	−	0.125650i
$229$	−0.983649	−	8.10107i	−0.0650013	−	0.535334i	−0.988443	−	0.151595i	$-0.951559\pi$
$229$	−0.983649	−	8.10107i	−0.0650013	−	0.535334i	0.923441	−	0.383739i	$-0.125364\pi$
$230$	5.65663	−	19.5289i	0.372987	−	1.28770i
$231$	0.125664	−	0.615543i	0.00826808	−	0.0404998i
$232$	7.51278	+	2.50813i	0.493238	+	0.164667i
$233$	−11.5646	−	6.06956i	−0.757621	−	0.397630i	0.0412371	−	0.999149i	$-0.486870\pi$
$233$	−11.5646	−	6.06956i	−0.757621	−	0.397630i	−0.798858	+	0.601519i	$0.794562\pi$
$234$	−6.48529	−	1.20469i	−0.423956	−	0.0787532i
$235$	−15.4473	+	8.10739i	−1.00767	+	0.528868i
$236$	−5.71337	+	0.928513i	−0.371909	+	0.0604410i
$237$	−11.1786	+	8.40019i	−0.726130	+	0.545651i
$238$	−0.256526	+	6.36562i	−0.0166281	+	0.412622i
$239$	0.676815			0.0437795			0.0218898	−	0.999760i	$-0.493032\pi$
$239$	0.676815			0.0437795			0.0218898	+	0.999760i	$0.493032\pi$
$240$	−0.360626	+	8.94883i	−0.0232783	+	0.577645i
$241$	−4.69433	−	22.9944i	−0.302388	−	1.48120i	−0.792680	−	0.609638i	$-0.791315\pi$
$241$	−4.69433	−	22.9944i	−0.302388	−	1.48120i	0.490292	−	0.871558i	$-0.336890\pi$
$242$	−9.52056	−	13.7929i	−0.612005	−	0.886642i
$243$	0.948536	−	0.316668i	0.0608486	−	0.0203143i
$244$	−1.39357	+	2.93689i	−0.0892144	+	0.188015i
$245$	−7.87642	+	9.64687i	−0.503206	+	0.616316i
$246$	5.56362	+	14.6701i	0.354724	+	0.935329i
$247$	7.70368	+	14.0667i	0.490174	+	0.895040i
$248$	2.73957	−	7.22364i	0.173963	−	0.458702i
$249$	6.26361	+	10.8489i	0.396940	+	0.687520i
$250$	−14.0824	+	17.2478i	−0.890649	+	1.09085i
$251$	4.95159	+	3.72088i	0.312542	+	0.234860i	0.745424	−	0.666590i	$-0.232247\pi$
$251$	4.95159	+	3.72088i	0.312542	+	0.234860i	−0.432882	+	0.901450i	$0.642503\pi$
$252$	−0.552515	−	0.289982i	−0.0348052	−	0.0182672i
$253$	8.18471	−	0.660738i	0.514568	−	0.0415402i
$254$	−20.4725	+	1.65271i	−1.28456	+	0.103700i
$255$	12.2163	+	6.41159i	0.765012	+	0.401509i
$256$	16.7531	+	12.5891i	1.04707	+	0.786821i
$257$	−0.388642	+	0.476001i	−0.0242428	+	0.0296921i	−0.786584	−	0.617483i	$-0.788152\pi$
$257$	−0.388642	+	0.476001i	−0.0242428	+	0.0296921i	0.762341	+	0.647175i	$0.224050\pi$
$258$	5.46701	+	9.46915i	0.340361	+	0.589523i
$259$	0.126568	−	0.333732i	0.00786456	−	0.0207371i
$260$	8.82815	−	1.23103i	0.547498	−	0.0763451i
$261$	2.35079	+	6.19853i	0.145510	+	0.383679i
$262$	19.5061	−	23.8906i	1.20509	−	1.47597i
$263$	2.93106	−	6.17707i	0.180737	−	0.380895i	−0.792781	−	0.609507i	$-0.791368\pi$
$263$	2.93106	−	6.17707i	0.180737	−	0.380895i	0.973518	+	0.228612i	$0.0734188\pi$
$264$	−1.53683	+	0.513071i	−0.0945857	+	0.0315773i
$265$	12.7382	+	18.4545i	0.782502	+	1.13365i
$266$	0.754080	+	3.69373i	0.0462356	+	0.226477i
$267$	−0.183658	+	4.55742i	−0.0112397	+	0.278910i
$268$	−1.07311			−0.0655509
$269$	0.498788	−	12.3773i	0.0304116	−	0.754657i	−0.909998	−	0.414613i	$-0.863917\pi$
$269$	0.498788	−	12.3773i	0.0304116	−	0.754657i	0.940410	−	0.340044i	$-0.110442\pi$
$270$	−2.68437	+	2.01718i	−0.163366	+	0.122761i
$271$	−22.5115	+	3.65847i	−1.36747	+	0.222236i	−0.799429	−	0.600761i	$-0.794865\pi$
$271$	−22.5115	+	3.65847i	−1.36747	+	0.222236i	−0.568046	+	0.822997i	$0.692300\pi$
$272$	32.4784	−	17.0460i	1.96929	−	1.03356i
$273$	0.500782	−	1.59349i	0.0303087	−	0.0964422i
$274$	3.03738	+	1.59414i	0.183495	+	0.0963055i
$275$	−2.09837	−	0.700540i	−0.126537	−	0.0422441i
$276$	1.63137	−	7.99097i	0.0981968	−	0.481000i
$277$	−3.23326	+	11.1625i	−0.194267	+	0.670689i	0.802944	+	0.596055i	$0.203266\pi$
$277$	−3.23326	+	11.1625i	−0.194267	+	0.670689i	−0.997211	+	0.0746340i	$0.976221\pi$
$278$	4.32744	+	35.6397i	0.259543	+	2.13753i
$279$	6.13358	−	2.04769i	0.367208	−	0.122592i
$280$	−1.00271	−	0.162957i	−0.0599236	−	0.00973854i
$281$	17.4768	−	9.17253i	1.04258	−	0.547187i	0.145637	−	0.989338i	$-0.453477\pi$
$281$	17.4768	−	9.17253i	1.04258	−	0.547187i	0.896941	+	0.442151i	$0.145784\pi$
$282$	−14.6972	+	9.29393i	−0.875204	+	0.553445i
$283$	−11.3571	+	4.83882i	−0.675112	+	0.287638i	−0.702184	−	0.711995i	$-0.747792\pi$
$283$	−11.3571	+	4.83882i	−0.675112	+	0.287638i	0.0270725	+	0.999633i	$0.491381\pi$
$284$	−0.375872	+	1.84114i	−0.0223039	+	0.109252i
$285$	7.92690	+	1.95380i	0.469549	+	0.115733i
$286$	4.29675	+	7.84571i	0.254072	+	0.463926i
$287$	−3.85755	+	0.950800i	−0.227704	+	0.0561239i
$288$	0.263243	+	6.53231i	0.0155118	+	0.384920i
$289$	−1.59067	−	39.4721i	−0.0935688	−	2.32189i
$290$	−14.0782	−	17.2427i	−0.826702	−	1.01253i
$291$	5.38710	−	14.2046i	0.315797	−	0.832689i
$292$	9.39521	+	19.8000i	0.549813	+	1.15871i
$293$	3.13479	−	10.8226i	0.183137	−	0.632261i	−0.815436	−	0.578847i	$-0.803503\pi$
$293$	3.13479	−	10.8226i	0.183137	−	0.632261i	0.998572	−	0.0534135i	$-0.0170101\pi$
$294$	−7.05174	+	10.2162i	−0.411266	+	0.595821i
$295$	−7.25629	−	3.09162i	−0.422477	−	0.180001i
$296$	−0.908587	+	0.147660i	−0.0528106	+	0.00858255i
$297$	−1.14617	−	0.724796i	−0.0665077	−	0.0420569i
$298$	3.31807	+	4.80706i	0.192211	+	0.278465i
$299$	21.8262	+	0.492421i	1.26224	+	0.0284774i
$300$	−1.24818	+	1.80831i	−0.0720639	+	0.104403i
$301$	−2.54720	+	1.08526i	−0.146818	+	0.0625534i
$302$	4.09744	+	14.1460i	0.235781	+	0.814011i
$303$	−12.8443	+	1.03690i	−0.737884	+	0.0595682i
$304$	16.2466	−	14.3933i	0.931809	−	0.825511i
$305$	−3.74388	+	2.36748i	−0.214374	+	0.135562i
$306$	12.6515	+	5.39030i	0.723238	+	0.308143i
$307$	2.58174	−	21.2625i	0.147347	−	1.21352i	−0.712021	−	0.702158i	$-0.752220\pi$
$307$	2.58174	−	21.2625i	0.147347	−	1.21352i	0.859368	−	0.511357i	$-0.170857\pi$
$308$	0.169262	+	0.829099i	0.00964459	+	0.0472423i
$309$	9.47976	+	0.765285i	0.539285	+	0.0435356i
$310$	−17.3581	+	13.0438i	−0.985875	+	0.740837i
$311$	−2.01303	+	16.5788i	−0.114148	+	0.940095i	0.817298	+	0.576216i	$0.195471\pi$
$311$	−2.01303	+	16.5788i	−0.114148	+	0.940095i	−0.931446	+	0.363880i	$0.881452\pi$
$312$	−4.20475	+	0.936307i	−0.238047	+	0.0530080i
$313$	−0.579250	−	4.77055i	−0.0327411	−	0.269647i	−0.999881	−	0.0154039i	$-0.995097\pi$
$313$	−0.579250	−	4.77055i	−0.0327411	−	0.269647i	0.967140	−	0.254244i	$-0.0818265\pi$
$314$	3.57425	+	3.72119i	0.201707	+	0.209999i
$315$	−0.425139	−	0.736362i	−0.0239539	−	0.0414893i
$316$	9.41715	−	16.3110i	0.529756	−	0.917564i
$317$	−6.48034	+	1.59726i	−0.363972	+	0.0897111i	−0.417060	−	0.908879i	$-0.636940\pi$
$317$	−6.48034	+	1.59726i	−0.363972	+	0.0897111i	0.0530883	+	0.998590i	$0.483094\pi$
$318$	14.1360	+	17.3134i	0.792707	+	0.970890i
$319$	4.49506	−	7.78567i	0.251675	−	0.435914i
$320$	−1.43255	−	3.77732i	−0.0800818	−	0.211158i
$321$	−2.99666	+	3.11985i	−0.167257	+	0.174133i
$322$	4.86771	+	1.62508i	0.271267	+	0.0905622i
$323$	−9.30257	−	32.1162i	−0.517609	−	1.78699i
$324$	−1.00820	+	0.893186i	−0.0560110	+	0.0496215i
$325$	−5.35768	−	2.42690i	−0.297191	−	0.134620i
$326$	−10.3507	−	9.16992i	−0.573272	−	0.507875i
$327$	0.995609	−	2.09820i	0.0550573	−	0.116031i
$328$	7.09785	+	7.38964i	0.391913	+	0.408025i
$329$	−1.88769	−	3.97822i	−0.104072	−	0.219326i
$330$	4.42125	+	1.08974i	0.243382	+	0.0599882i
$331$	−16.1442	+	16.8079i	−0.887368	+	0.923847i	−0.997542	−	0.0700647i	$-0.977679\pi$
$331$	−16.1442	+	16.8079i	−0.887368	+	0.923847i	0.110175	+	0.993912i	$0.464859\pi$
$332$	−13.4893	−	10.1366i	−0.740322	−	0.556316i
$333$	−0.576698	−	0.510910i	−0.0316028	−	0.0279977i
$334$	37.0100	+	6.01472i	2.02510	+	0.329111i
$335$	−1.23590	−	0.781536i	−0.0675245	−	0.0426999i
$336$	−2.25323	−	0.181900i	−0.122924	−	0.00992344i
$337$	−16.7411			−0.911944			−0.455972	−	0.889994i	$-0.650708\pi$
$337$	−16.7411			−0.911944			−0.455972	+	0.889994i	$0.650708\pi$
$338$	9.21621	+	21.9247i	0.501295	+	1.19255i
$339$	12.7207			0.690896
$340$	−18.5229	−	1.49532i	−1.00455	−	0.0810953i
$341$	−7.41157	−	4.68679i	−0.401359	−	0.253804i
$342$	8.03233	+	1.30538i	0.434339	+	0.0705869i
$343$	−4.78020	−	4.23489i	−0.258107	−	0.228662i
$344$	5.70849	+	4.28965i	0.307781	+	0.231282i
$345$	7.69856	−	8.01505i	0.414477	−	0.431516i
$346$	−35.8729	−	8.84187i	−1.92854	−	0.475342i
$347$	−6.18082	−	13.0258i	−0.331804	−	0.699262i	0.667153	−	0.744921i	$-0.267513\pi$
$347$	−6.18082	−	13.0258i	−0.331804	−	0.699262i	−0.998957	+	0.0456586i	$0.985461\pi$
$348$	−6.18555	−	6.43984i	−0.331580	−	0.345211i
$349$	0.928318	−	1.95639i	0.0496917	−	0.104723i	−0.877086	−	0.480333i	$-0.840516\pi$
$349$	0.928318	−	1.95639i	0.0496917	−	0.104723i	0.926778	+	0.375610i	$0.122567\pi$
$350$	−1.03486	−	0.916810i	−0.0553159	−	0.0490056i
$351$	−2.83284	−	2.23047i	−0.151206	−	0.119054i
$352$	6.63611	−	5.87908i	0.353706	−	0.313356i
$353$	7.11725	+	24.5716i	0.378813	+	1.30781i	0.892969	+	0.450118i	$0.148618\pi$
$353$	7.11725	+	24.5716i	0.378813	+	1.30781i	−0.514156	+	0.857696i	$0.671895\pi$
$354$	−7.45732	−	2.48962i	−0.396352	−	0.132322i
$355$	−1.77377	+	1.84669i	−0.0941421	+	0.0980123i
$356$	−2.17853	−	5.74432i	−0.115462	−	0.304448i
$357$	−1.74116	+	3.01578i	−0.0921521	+	0.159612i
$358$	−18.5537	−	22.7241i	−0.980592	−	1.20101i
$359$	−15.1177	+	3.72617i	−0.797880	+	0.196660i	−0.617121	−	0.786868i	$-0.711701\pi$
$359$	−15.1177	+	3.72617i	−0.797880	+	0.196660i	−0.180758	+	0.983528i	$0.557855\pi$
$360$	−1.09642	+	1.89906i	−0.0577866	+	0.100089i
$361$	−0.392977	−	0.680657i	−0.0206830	−	0.0358240i
$362$	2.63710	+	2.74552i	0.138603	+	0.144301i
$363$	−1.10423	−	9.09416i	−0.0579571	−	0.477320i
$364$	0.220742	+	2.23897i	0.0115700	+	0.117354i
$365$	−3.59967	+	29.6460i	−0.188416	+	1.55174i
$366$	−3.52977	+	2.65245i	−0.184504	+	0.138646i
$367$	31.9913	+	2.58260i	1.66993	+	0.134811i	0.878913	−	0.476982i	$-0.158269\pi$
$367$	31.9913	+	2.58260i	1.66993	+	0.134811i	0.791018	+	0.611793i	$0.209551\pi$
$368$	−5.91004	−	28.9493i	−0.308082	−	1.50909i
$369$	−1.03373	+	8.51355i	−0.0538140	+	0.443198i
$370$	2.38004	+	1.01404i	0.123732	+	0.0527174i
$371$	−4.78369	+	3.02502i	−0.248357	+	0.157051i
$372$	−6.51937	+	5.77566i	−0.338014	+	0.299454i
$373$	8.58372	−	0.692950i	0.444448	−	0.0358796i	0.143783	−	0.989609i	$-0.454073\pi$
$373$	8.58372	−	0.692950i	0.444448	−	0.0358796i	0.300665	+	0.953730i	$0.402791\pi$
$374$	−5.18853	−	17.9129i	−0.268293	−	0.926253i
$375$	−11.1972	+	4.77066i	−0.578219	+	0.246356i
$376$	−6.45105	+	9.34596i	−0.332687	+	0.481981i
$377$	14.0183	−	19.3600i	0.721981	−	0.997091i
$378$	−0.481450	−	0.697500i	−0.0247631	−	0.0358755i
$379$	−0.370708	−	0.234422i	−0.0190420	−	0.0120414i	0.524911	−	0.851157i	$-0.324099\pi$
$379$	−0.370708	−	0.234422i	−0.0190420	−	0.0120414i	−0.543953	+	0.839116i	$0.683073\pi$
$380$	−10.8542	+	1.76398i	−0.556808	+	0.0904901i
$381$	−10.3284	−	4.40054i	−0.529142	−	0.225446i
$382$	−22.8529	+	33.1081i	−1.16925	+	1.69396i
$383$	4.52821	−	15.6332i	0.231381	−	0.798820i	−0.757847	−	0.652433i	$-0.773748\pi$
$383$	4.52821	−	15.6332i	0.231381	−	0.798820i	0.989227	−	0.146387i	$-0.0467644\pi$
$384$	3.87901	+	8.17483i	0.197950	+	0.417170i
$385$	−0.408885	+	1.07814i	−0.0208387	+	0.0549472i
$386$	5.98418	+	7.32929i	0.304587	+	0.373051i
$387$	0.240655	+	5.97178i	0.0122332	+	0.303563i
$388$	0.823941	+	20.4459i	0.0418293	+	1.03798i
$389$	8.21427	−	2.02464i	0.416480	−	0.102653i	−0.0255068	−	0.999675i	$-0.508120\pi$
$389$	8.21427	−	2.02464i	0.416480	−	0.102653i	0.441987	+	0.897022i	$0.354274\pi$
$390$	11.3943	+	4.09186i	0.576972	+	0.207199i
$391$	−44.1928	−	10.8925i	−2.23492	−	0.550859i
$392$	−1.62158	+	7.94301i	−0.0819020	+	0.401183i
$393$	15.5096	−	6.60804i	0.782358	−	0.333331i
$394$	40.9866	−	25.9184i	2.06488	−	1.30575i
$395$	22.7248	−	11.9269i	1.14341	−	0.600107i
$396$	1.80295	+	0.293008i	0.0906016	+	0.0147242i
$397$	−16.1379	+	5.38764i	−0.809940	+	0.270398i	−0.691326	−	0.722543i	$-0.742973\pi$
$397$	−16.1379	+	5.38764i	−0.809940	+	0.270398i	−0.118614	+	0.992940i	$0.537845\pi$
$398$	−0.632037	−	5.20529i	−0.0316811	−	0.260918i
$399$	−0.573313	+	1.97931i	−0.0287016	+	0.0990893i
$400$	−1.59223	+	7.79925i	−0.0796114	+	0.389963i
$401$	−29.3044	−	9.78324i	−1.46339	−	0.488552i	−0.530181	−	0.847884i	$-0.677876\pi$
$401$	−29.3044	−	9.78324i	−1.46339	−	0.488552i	−0.933210	+	0.359332i	$0.883004\pi$
$402$	−1.29059	−	0.677355i	−0.0643688	−	0.0337834i
$403$	−18.3182	−	14.4230i	−0.912494	−	0.718462i
$404$	15.3686	−	8.06608i	0.764618	−	0.401303i
$405$	−1.81164	+	0.294419i	−0.0900209	+	0.0146298i
$406$	4.49169	−	3.37529i	0.222919	−	0.167513i
$407$	−0.0420711	+	1.04398i	−0.00208539	+	0.0517484i
$408$	8.98085			0.444618
$409$	0.406525	−	10.0878i	0.0201013	−	0.498810i	−0.957511	−	0.288396i	$-0.906878\pi$
$409$	0.406525	−	10.0878i	0.0201013	−	0.498810i	0.977612	−	0.210413i	$-0.0674810\pi$
$410$	−5.76010	−	28.2148i	−0.284471	−	1.39343i
$411$	1.06514	+	1.54312i	0.0525394	+	0.0761164i
$412$	−12.1509	+	4.05658i	−0.598634	+	0.199853i
$413$	0.853454	−	1.79862i	0.0419957	−	0.0885041i
$414$	7.00591	−	8.58069i	0.344322	−	0.421718i
$415$	−8.15325	−	21.4983i	−0.400227	−	1.05531i
$416$	19.1588	−	13.7319i	0.939339	−	0.673261i
$417$	−6.95878	+	18.3488i	−0.340773	+	0.898544i
$418$	−5.51783	−	9.55717i	−0.269886	−	0.467456i
$419$	−3.80079	+	4.65513i	−0.185681	+	0.227418i	−0.859054	−	0.511885i	$-0.828947\pi$
$419$	−3.80079	+	4.65513i	−0.185681	+	0.227418i	0.673373	+	0.739303i	$0.264845\pi$
$420$	0.915580	+	0.688014i	0.0446757	+	0.0335716i
$421$	10.2799	+	5.39533i	0.501013	+	0.262952i	0.696244	−	0.717805i	$-0.254853\pi$
$421$	10.2799	+	5.39533i	0.501013	+	0.262952i	−0.195230	+	0.980757i	$0.562545\pi$
$422$	−27.8305	+	2.24671i	−1.35477	+	0.109368i
$423$	−9.47425	+	0.764840i	−0.460654	+	0.0371878i
$424$	12.9248	+	6.78345i	0.627683	+	0.329434i
$425$	9.80302	+	7.36649i	0.475516	+	0.357327i
$426$	−1.61418	+	1.97702i	−0.0782074	+	0.0957867i
$427$	−0.559030	−	0.968268i	−0.0270533	−	0.0468578i
$428$	2.06619	−	5.44808i	0.0998729	−	0.263343i
$429$	0.0866366	+	4.88877i	0.00418286	+	0.236032i
$430$	−7.11634	−	18.7642i	−0.343180	−	0.904892i
$431$	−12.5338	+	15.3511i	−0.603732	+	0.739438i	−0.982543	−	0.186036i	$-0.940436\pi$
$431$	−12.5338	+	15.3511i	−0.603732	+	0.739438i	0.378811	+	0.925474i	$0.376333\pi$
$432$	−2.09186	+	4.40851i	−0.100645	+	0.212104i
$433$	13.9887	−	4.67012i	0.672255	−	0.224432i	0.0400092	−	0.999199i	$-0.487261\pi$
$433$	13.9887	−	4.67012i	0.672255	−	0.224432i	0.632246	+	0.774767i	$0.282133\pi$
$434$	−3.11323	−	4.51029i	−0.149440	−	0.216501i
$435$	−2.43381	−	11.9216i	−0.116692	−	0.571597i
$436$	−0.125959	+	3.12564i	−0.00603234	+	0.149691i
$437$	−26.9337			−1.28841
$438$	−1.19860	+	29.7430i	−0.0572713	+	1.42117i
$439$	−6.90197	+	5.18649i	−0.329413	+	0.247538i	−0.752561	−	0.658523i	$-0.771182\pi$
$439$	−6.90197	+	5.18649i	−0.329413	+	0.247538i	0.423148	+	0.906061i	$0.360925\pi$
$440$	2.93524	−	0.477023i	0.139932	−	0.0227412i
$441$	−6.00816	+	3.15333i	−0.286103	+	0.150158i
$442$	−8.81965	−	48.7926i	−0.419508	−	2.32083i
$443$	−5.57125	−	2.92402i	−0.264698	−	0.138924i	0.327153	−	0.944971i	$-0.393911\pi$
$443$	−5.57125	−	2.92402i	−0.264698	−	0.138924i	−0.591852	+	0.806047i	$0.701603\pi$
$444$	0.984356	+	0.328626i	0.0467155	+	0.0155959i
$445$	1.67451	−	8.20231i	0.0793796	−	0.388827i
$446$	−3.68044	+	12.7064i	−0.174274	+	0.601664i
$447$	0.384843	+	3.16947i	0.0182024	+	0.149911i
$448$	0.967199	−	0.322899i	0.0456959	−	0.0152555i
$449$	−11.8275	−	1.92215i	−0.558173	−	0.0907119i	−0.125221	−	0.992129i	$-0.539964\pi$
$449$	−11.8275	−	1.92215i	−0.558173	−	0.0907119i	−0.432952	+	0.901417i	$0.642528\pi$
$450$	−2.64255	+	1.38692i	−0.124571	+	0.0653799i
$451$	9.82968	−	6.21591i	0.462861	−	0.292696i
$452$	−15.7630	+	6.71598i	−0.741429	+	0.315893i
$453$	−1.61024	+	7.88747i	−0.0756556	+	0.370586i
$454$	1.61338	+	0.397662i	0.0757196	+	0.0186632i
$455$	−1.37639	+	2.73938i	−0.0645261	+	0.128424i
$456$	5.15999	−	1.27182i	0.241639	−	0.0595586i
$457$	−1.15712	−	28.7136i	−0.0541278	−	1.34317i	−0.766898	−	0.641769i	$-0.778201\pi$
$457$	−1.15712	−	28.7136i	−0.0541278	−	1.34317i	0.712770	−	0.701398i	$-0.247440\pi$
$458$	0.601150	+	14.9174i	0.0280899	+	0.697043i
$459$	4.75404	+	5.82264i	0.221900	+	0.271778i
$460$	−5.30814	+	13.9964i	−0.247493	+	0.652586i
$461$	−10.3146	−	21.7375i	−0.480397	−	1.01242i	−0.988514	−	0.151128i	$-0.951709\pi$
$461$	−10.3146	−	21.7375i	−0.480397	−	1.01242i	0.508117	−	0.861288i	$-0.330342\pi$
$462$	−0.319767	+	1.10396i	−0.0148769	+	0.0513610i
$463$	14.4439	−	20.9256i	0.671264	−	0.972493i	−0.328346	−	0.944558i	$-0.606491\pi$
$463$	14.4439	−	20.9256i	0.671264	−	0.972493i	0.999610	−	0.0279359i	$-0.00889344\pi$
$464$	−29.7601	−	12.6796i	−1.38158	−	0.588636i
$465$	−11.7147	+	1.90382i	−0.543255	+	0.0882876i
$466$	20.1949	+	12.7705i	0.935510	+	0.591581i
$467$	7.85565	+	11.3809i	0.363516	+	0.526644i	0.961478	−	0.274880i	$-0.0886382\pi$
$467$	7.85565	+	11.3809i	0.363516	+	0.526644i	−0.597962	+	0.801524i	$0.704023\pi$
$468$	4.68793	+	1.26829i	0.216699	+	0.0586266i
$469$	0.209664	−	0.303751i	0.00968140	−	0.0140259i
$470$	29.3622	−	12.5101i	1.35438	−	0.577047i
$471$	0.784666	+	2.70898i	0.0361555	+	0.124823i
$472$	−5.11766	+	0.413140i	−0.235559	+	0.0190163i
$473$	6.06667	−	5.37460i	0.278946	−	0.247124i
$474$	21.6212	−	13.6724i	0.993094	−	0.627995i
$475$	6.67558	+	2.84420i	0.306297	+	0.130501i
$476$	0.565375	−	4.65628i	0.0259139	−	0.213420i
$477$	2.44380	+	11.9705i	0.111894	+	0.548092i
$478$	−1.23419	−	0.0996344i	−0.0564507	−	0.00455717i
$479$	12.0077	−	9.02321i	0.548647	−	0.412281i	−0.289944	−	0.957044i	$-0.593637\pi$
$479$	12.0077	−	9.02321i	0.548647	−	0.412281i	0.838590	+	0.544763i	$0.183380\pi$
$480$	1.44634	−	11.9117i	0.0660160	−	0.543691i
$481$	−0.396958	+	2.74943i	−0.0180997	+	0.125363i
$482$	5.17525	+	42.6220i	0.235726	+	1.94138i
$483$	1.94315	+	2.02304i	0.0884166	+	0.0920514i
$484$	6.16963	+	10.6861i	0.280438	+	0.485732i
$485$	−13.9416	+	24.1475i	−0.633054	+	1.09648i
$486$	−1.77630	+	0.437819i	−0.0805748	+	0.0198599i
$487$	−3.72980	−	4.56818i	−0.169013	−	0.207004i	0.683152	−	0.730276i	$-0.260609\pi$
$487$	−3.72980	−	4.56818i	−0.169013	−	0.207004i	−0.852166	+	0.523272i	$0.824711\pi$
$488$	−1.44173	+	2.49714i	−0.0652639	+	0.113040i
$489$	−2.68036	−	7.06752i	−0.121210	−	0.319604i
$490$	15.7830	−	16.4319i	0.713005	−	0.742317i
$491$	−5.72799	−	1.91228i	−0.258500	−	0.0863001i	0.184464	−	0.982839i	$-0.440945\pi$
$491$	−5.72799	−	1.91228i	−0.258500	−	0.0863001i	−0.442965	+	0.896539i	$0.646073\pi$
$492$	−3.21382	−	11.0954i	−0.144890	−	0.500219i
$493$	−37.2999	+	33.0448i	−1.67990	+	1.48826i
$494$	−11.9772	−	26.7851i	−0.538877	−	1.20512i
$495$	1.86305	+	1.65052i	0.0837381	+	0.0741855i
$496$	−13.5267	+	28.5070i	−0.607368	+	1.28000i
$497$	−0.447709	−	0.466114i	−0.0200825	−	0.0209081i
$498$	−9.82481	−	20.7054i	−0.440260	−	0.927829i
$499$	7.45232	+	1.83683i	0.333612	+	0.0822279i	0.402563	−	0.915392i	$-0.368119\pi$
$499$	7.45232	+	1.83683i	0.333612	+	0.0822279i	−0.0689518	+	0.997620i	$0.521965\pi$
$500$	11.3563	−	11.8232i	0.507871	−	0.528750i
$501$	16.3849	+	12.3125i	0.732023	+	0.550080i
$502$	−8.48164	−	7.51407i	−0.378554	−	0.335370i
$503$	13.5539	+	2.20273i	0.604340	+	0.0982147i	0.454879	−	0.890553i	$-0.349682\pi$
$503$	13.5539	+	2.20273i	0.604340	+	0.0982147i	0.149460	+	0.988768i	$0.452246\pi$
$504$	−0.467801	−	0.295819i	−0.0208375	−	0.0131768i
$505$	23.5744	+	1.90312i	1.04905	+	0.0846879i
$506$	−15.0223			−0.667825
$507$	−1.10874	+	12.9526i	−0.0492407	+	0.575247i
$508$	15.1219			0.670924
$509$	−20.6691	−	1.66859i	−0.916143	−	0.0739587i	−0.386606	−	0.922245i	$-0.626353\pi$
$509$	−20.6691	−	1.66859i	−0.916143	−	0.0739587i	−0.529538	+	0.848286i	$0.677635\pi$
$510$	−21.3329	−	13.4901i	−0.944637	−	0.597352i
$511$	−7.44014	−	1.20914i	−0.329132	−	0.0534892i
$512$	−15.1508	−	13.4224i	−0.669577	−	0.593194i
$513$	3.55603	+	2.67219i	0.157003	+	0.117980i
$514$	0.778774	−	0.810790i	0.0343503	−	0.0357624i
$515$	−16.9486	−	4.17744i	−0.746842	−	0.184080i
$516$	−3.45104	−	7.27292i	−0.151924	−	0.320172i
$517$	8.92918	+	9.29626i	0.392705	+	0.408849i
$518$	−0.279930	+	0.589940i	−0.0122994	+	0.0259205i
$519$	−15.1164	−	13.3919i	−0.663535	−	0.587840i
$520$	7.89314	−	0.458288i	0.346137	−	0.0200973i
$521$	−5.07779	+	4.49853i	−0.222462	+	0.197084i	−0.766991	−	0.641658i	$-0.778247\pi$
$521$	−5.07779	+	4.49853i	−0.222462	+	0.197084i	0.544529	+	0.838742i	$0.316708\pi$
$522$	−3.37425	−	11.6493i	−0.147687	−	0.509875i
$523$	−21.9520	−	7.32866i	−0.959895	−	0.320460i	−0.206808	−	0.978382i	$-0.566308\pi$
$523$	−21.9520	−	7.32866i	−0.959895	−	0.320460i	−0.753086	+	0.657922i	$0.771436\pi$
$524$	−15.7301	+	16.3768i	−0.687174	+	0.715424i
$525$	−0.267982	−	0.706612i	−0.0116957	−	0.0308391i
$526$	−6.25421	+	10.8326i	−0.272696	+	0.472324i
$527$	30.7413	+	37.6513i	1.33911	+	1.64012i
$528$	6.42505	−	1.58363i	0.279614	−	0.0689187i
$529$	−6.83182	+	11.8331i	−0.297036	+	0.514481i
$530$	−20.5118	−	35.5276i	−0.890978	−	1.54322i
$531$	−2.97691	−	3.09929i	−0.129187	−	0.134498i
$532$	−0.334561	−	2.75536i	−0.0145050	−	0.119460i
$533$	27.6968	−	13.7487i	1.19968	−	0.595524i
$534$	1.00581	−	8.28356i	0.0435255	−	0.358465i
$535$	6.34739	−	4.76976i	0.274422	−	0.206215i
$536$	−0.948778	−	0.0765932i	−0.0409809	−	0.00330832i
$537$	−3.20751	−	15.7114i	−0.138414	−	0.677999i
$538$	−2.73162	+	22.4970i	−0.117769	+	0.969913i
$539$	8.46542	+	3.60678i	0.364632	+	0.155355i
$540$	2.08946	−	1.32129i	0.0899160	−	0.0568595i
$541$	15.9112	−	14.0961i	0.684077	−	0.606039i	−0.247801	−	0.968811i	$-0.579708\pi$
$541$	15.9112	−	14.0961i	0.684077	−	0.606039i	0.931878	+	0.362772i	$0.118170\pi$
$542$	41.5890	−	3.35741i	1.78640	−	0.144213i
$543$	0.578931	+	1.99870i	0.0248443	+	0.0857726i
$544$	−45.2103	+	19.2623i	−1.93838	+	0.825865i
$545$	−2.42143	+	3.50805i	−0.103723	+	0.150268i
$546$	−1.14777	+	2.83205i	−0.0491201	+	0.121201i
$547$	0.751693	+	1.08902i	0.0321401	+	0.0465629i	0.838725	−	0.544556i	$-0.183302\pi$
$547$	0.751693	+	1.08902i	0.0321401	+	0.0465629i	−0.806584	+	0.591119i	$0.798686\pi$
$548$	−2.13457	−	1.34982i	−0.0911844	−	0.0576615i
$549$	−2.38218	+	0.387142i	−0.101669	+	0.0165228i
$550$	3.72332	+	1.58636i	0.158763	+	0.0676426i
$551$	−16.7512	+	24.2683i	−0.713625	+	1.03386i
$552$	2.01270	−	6.94865i	0.0856663	−	0.295754i
$553$	2.77700	+	5.85241i	0.118090	+	0.248870i
$554$	7.53918	−	19.8792i	0.320309	−	0.844586i
$555$	0.894344	+	1.09537i	0.0379628	+	0.0464960i
$556$	−1.06432	−	26.4109i	−0.0451374	−	1.12007i
$557$	0.825661	+	20.4886i	0.0349844	+	0.868129i	0.917474	+	0.397796i	$0.130225\pi$
$557$	0.825661	+	20.4886i	0.0349844	+	0.868129i	−0.882489	+	0.470332i	$0.844134\pi$
$558$	−11.4862	+	2.83110i	−0.486250	+	0.119850i
$559$	17.5148	−	12.5536i	0.740798	−	0.530959i
$560$	4.02848	+	0.992931i	0.170234	+	0.0419590i
$561$	2.03902	−	9.98779i	0.0860876	−	0.421685i
$562$	−33.2198	+	14.1536i	−1.40129	+	0.597035i
$563$	17.7326	−	11.2134i	0.747340	−	0.472589i	−0.105724	−	0.994396i	$-0.533716\pi$
$563$	17.7326	−	11.2134i	0.747340	−	0.472589i	0.853064	+	0.521806i	$0.174742\pi$
$564$	11.3363	−	5.94974i	0.477343	−	0.250529i
$565$	−23.0453	−	3.74523i	−0.969525	−	0.157563i
$566$	21.4224	−	7.15186i	0.900452	−	0.300615i
$567$	−0.0558404	−	0.459887i	−0.00234508	−	0.0193134i
$568$	−0.463732	+	1.60099i	−0.0194578	+	0.0671761i
$569$	8.32403	−	40.7738i	0.348962	−	1.70933i	−0.304622	−	0.952473i	$-0.598530\pi$
$569$	8.32403	−	40.7738i	0.348962	−	1.70933i	0.653584	−	0.756854i	$-0.273265\pi$
$570$	−14.1673	−	4.72975i	−0.593404	−	0.198107i
$571$	6.40082	+	3.35941i	0.267866	+	0.140587i	0.593309	−	0.804975i	$-0.297821\pi$
$571$	6.40082	+	3.35941i	0.267866	+	0.140587i	−0.325443	+	0.945562i	$0.605513\pi$
$572$	−2.68841	−	6.01221i	−0.112408	−	0.251383i
$573$	−19.4709	+	10.2191i	−0.813408	+	0.426910i
$574$	7.17433	−	1.16594i	0.299451	−	0.0486655i
$575$	7.89656	−	5.93388i	0.329309	−	0.247460i
$576$	0.0886279	−	2.19928i	0.00369283	−	0.0916366i
$577$	−0.337982			−0.0140704			−0.00703519	−	0.999975i	$-0.502239\pi$
$577$	−0.337982			−0.0140704			−0.00703519	+	0.999975i	$0.502239\pi$
$578$	−2.91007	+	72.2127i	−0.121043	+	3.00365i
$579$	1.03453	+	5.06746i	0.0429936	+	0.210597i
$580$	9.30994	+	13.4878i	0.386574	+	0.560049i
$581$	5.50475	−	1.83776i	0.228376	−	0.0762429i
$582$	−11.9146	+	25.1095i	−0.493877	+	1.04082i
$583$	10.4785	−	12.8338i	0.433974	−	0.531522i
$584$	6.89341	+	18.1764i	0.285252	+	0.752146i
$585$	4.47539	+	4.87484i	0.185034	+	0.201550i
$586$	−7.30959	+	19.2738i	−0.301957	+	0.796194i
$587$	−8.60440	−	14.9033i	−0.355141	−	0.615123i	0.632001	−	0.774968i	$-0.282234\pi$
$587$	−8.60440	−	14.9033i	−0.355141	−	0.615123i	−0.987142	+	0.159845i	$0.948901\pi$
$588$	5.78024	−	7.07951i	0.238373	−	0.291954i
$589$	22.9946	+	17.2793i	0.947475	+	0.711982i
$590$	12.7770	+	6.70586i	0.526019	+	0.276076i
$591$	26.4212	−	2.13294i	1.08682	−	0.0877376i
$592$	3.74737	−	0.302519i	0.154016	−	0.0124335i
$593$	11.9094	+	6.25055i	0.489062	+	0.256679i	0.691181	−	0.722682i	$-0.257091\pi$
$593$	11.9094	+	6.25055i	0.489062	+	0.256679i	−0.202120	+	0.979361i	$0.564783\pi$
$594$	1.98339	+	1.49042i	0.0813793	+	0.0611526i
$595$	4.04225	−	4.95086i	0.165716	−	0.202966i
$596$	−2.15022	−	3.72429i	−0.0880763	−	0.152553i
$597$	1.01635	−	2.67990i	0.0415965	−	0.109681i
$598$	−39.7284	−	4.11100i	−1.62461	−	0.168111i
$599$	10.2453	+	27.0146i	0.418611	+	1.10379i	0.964070	+	0.265649i	$0.0855864\pi$
$599$	10.2453	+	27.0146i	0.418611	+	1.10379i	−0.545458	+	0.838138i	$0.683644\pi$
$600$	−1.23263	+	1.50970i	−0.0503219	+	0.0616332i
$601$	−1.97289	+	4.15778i	−0.0804758	+	0.169599i	−0.939700	−	0.342000i	$-0.888896\pi$
$601$	−1.97289	+	4.15778i	−0.0804758	+	0.169599i	0.859224	+	0.511600i	$0.170947\pi$
$602$	4.80467	−	1.60403i	0.195824	−	0.0653755i
$603$	−0.452580	−	0.655676i	−0.0184305	−	0.0267012i
$604$	−2.16889	−	10.6239i	−0.0882510	−	0.432282i
$605$	−0.677033	+	16.8004i	−0.0275253	+	0.683034i
$606$	23.5746			0.957652
$607$	0.936889	−	23.2487i	0.0380271	−	0.943634i	−0.861763	−	0.507311i	$-0.830640\pi$
$607$	0.936889	−	23.2487i	0.0380271	−	0.943634i	0.899790	−	0.436323i	$-0.143719\pi$
$608$	−23.2480	+	17.4697i	−0.942830	+	0.708491i
$609$	3.03136	−	0.492644i	0.122837	−	0.0199630i
$610$	7.17560	−	3.76604i	0.290531	−	0.152483i
$611$	21.0703	+	27.0286i	0.852412	+	1.09346i
$612$	−8.96510	−	4.70525i	−0.362393	−	0.190198i
$613$	−0.637989	−	0.212992i	−0.0257681	−	0.00860267i	0.303755	−	0.952750i	$-0.401760\pi$
$613$	−0.637989	−	0.212992i	−0.0257681	−	0.00860267i	−0.329523	+	0.944148i	$0.606888\pi$
$614$	−7.83794	+	38.3928i	−0.316314	+	1.54941i
$615$	4.37930	−	15.1191i	0.176590	−	0.609661i
$616$	0.0904735	+	0.745117i	0.00364528	+	0.0300216i
$617$	18.3959	−	6.14147i	0.740593	−	0.247246i	0.0787557	−	0.996894i	$-0.474905\pi$
$617$	18.3959	−	6.14147i	0.740593	−	0.247246i	0.661837	+	0.749648i	$0.269777\pi$
$618$	−17.1740	−	2.79104i	−0.690839	−	0.112272i
$619$	24.1788	−	12.6900i	0.971826	−	0.510054i	0.0974175	−	0.995244i	$-0.468942\pi$
$619$	24.1788	−	12.6900i	0.971826	−	0.510054i	0.874409	+	0.485190i	$0.161249\pi$
$620$	13.5112	−	8.54396i	0.542623	−	0.343134i
$621$	5.57052	−	2.37338i	0.223537	−	0.0952404i
$622$	6.11139	−	29.9356i	0.245044	−	1.20031i
$623$	2.05160	+	0.505675i	0.0821958	+	0.0202594i
$624$	17.4252	−	2.42983i	0.697565	−	0.0972710i
$625$	13.7703	−	3.39407i	0.550811	−	0.135763i
$626$	0.354004	+	8.78452i	0.0141489	+	0.351100i
$627$	−0.242892	−	6.02729i	−0.00970015	−	0.240707i
$628$	−2.40255	−	2.94258i	−0.0958720	−	0.117422i
$629$	2.05369	−	5.41514i	0.0818860	−	0.215916i
$630$	0.666854	+	1.40536i	0.0265681	+	0.0559911i
$631$	10.9191	−	37.6972i	0.434683	−	1.50070i	−0.382299	−	0.924039i	$-0.624868\pi$
$631$	10.9191	−	37.6972i	0.434683	−	1.50070i	0.816983	−	0.576662i	$-0.195645\pi$
$632$	9.49022	−	13.7490i	0.377501	−	0.546904i
$633$	−14.0406	−	5.98215i	−0.558065	−	0.237769i
$634$	12.0522	−	1.95868i	0.478656	−	0.0777891i
$635$	17.4158	+	11.0131i	0.691124	+	0.437040i
$636$	−9.34814	−	13.5431i	−0.370678	−	0.537020i
$637$	21.4008	+	11.8552i	0.847930	+	0.469720i
$638$	−9.34302	+	13.5357i	−0.369894	+	0.535883i
$639$	−1.28347	+	0.546833i	−0.0507731	+	0.0216324i
$640$	−4.62052	−	15.9519i	−0.182642	−	0.630553i
$641$	−12.7969	+	1.03307i	−0.505448	+	0.0408040i	−0.330561	−	0.943785i	$-0.607238\pi$
$641$	−12.7969	+	1.03307i	−0.505448	+	0.0408040i	−0.174887	+	0.984589i	$0.555956\pi$
$642$	5.92377	−	5.24801i	0.233793	−	0.207122i
$643$	18.6170	−	11.7727i	0.734183	−	0.464270i	−0.114330	−	0.993443i	$-0.536472\pi$
$643$	18.6170	−	11.7727i	0.734183	−	0.464270i	0.848514	+	0.529173i	$0.177498\pi$
$644$	−3.47595	−	1.48096i	−0.136972	−	0.0583581i
$645$	1.32223	−	10.8895i	0.0520628	−	0.428775i
$646$	12.2357	+	59.9343i	0.481407	+	2.35809i
$647$	−4.12933	−	0.333354i	−0.162341	−	0.0131055i	−0.000971081	−	1.00000i	$-0.500309\pi$
$647$	−4.12933	−	0.333354i	−0.162341	−	0.0131055i	−0.161370	+	0.986894i	$0.551591\pi$
$648$	−0.955135	+	0.717737i	−0.0375212	+	0.0281954i
$649$	−0.702458	+	5.78526i	−0.0275739	+	0.227091i
$650$	9.41264	+	5.21423i	0.369194	+	0.204519i
$651$	−0.361084	−	2.97379i	−0.0141520	−	0.116552i
$652$	7.05272	+	7.34266i	0.276206	+	0.287561i
$653$	22.7030	+	39.3227i	0.888436	+	1.53882i	0.841724	+	0.539908i	$0.181541\pi$
$653$	22.7030	+	39.3227i	0.888436	+	1.53882i	0.0467123	+	0.998908i	$0.485126\pi$
$654$	−2.12440	+	3.67957i	−0.0830707	+	0.143883i
$655$	−30.0433	+	7.40502i	−1.17389	+	0.289338i
$656$	−26.4667	−	32.4158i	−1.03335	−	1.26562i
$657$	−8.13547	+	14.0910i	−0.317395	+	0.549744i
$658$	2.85662	+	7.53230i	0.111363	+	0.293640i
$659$	−34.4210	+	35.8361i	−1.34085	+	1.39597i	−0.488913	+	0.872332i	$0.662607\pi$
$659$	−34.4210	+	35.8361i	−1.34085	+	1.39597i	−0.851938	+	0.523642i	$0.824573\pi$
$660$	−3.18002	−	1.06165i	−0.123782	−	0.0413245i
$661$	10.3331	+	35.6741i	0.401912	+	1.38756i	0.865232	+	0.501371i	$0.167171\pi$
$661$	10.3331	+	35.6741i	0.401912	+	1.38756i	−0.463320	+	0.886191i	$0.653342\pi$
$662$	31.9138	−	28.2732i	1.24037	−	1.09887i
$663$	8.12568	−	25.8559i	0.315575	−	1.00416i
$664$	−11.2029	−	9.92489i	−0.434756	−	0.385160i
$665$	1.62138	−	3.41699i	0.0628745	−	0.132505i
$666$	0.976415	+	1.01656i	0.0378353	+	0.0393907i
$667$	17.2081	+	36.2653i	0.666301	+	1.40420i
$668$	−26.8039	−	6.60656i	−1.03707	−	0.255616i
$669$	−5.00902	+	5.21494i	−0.193660	+	0.201621i
$670$	2.13865	+	1.60709i	0.0826234	+	0.0620875i
$671$	2.44979	+	2.17033i	0.0945733	+	0.0837846i
$672$	2.98942	+	0.485829i	0.115320	+	0.0187413i
$673$	13.7318	+	8.68346i	0.529322	+	0.334723i	0.772247	−	0.635322i	$-0.219133\pi$
$673$	13.7318	+	8.68346i	0.529322	+	0.334723i	−0.242925	+	0.970045i	$0.578107\pi$
$674$	30.5279	+	2.46446i	1.17589	+	0.0949276i
$675$	−1.63130			−0.0627886
$676$	−5.46452	−	16.6357i	−0.210174	−	0.639835i
$677$	−7.63914			−0.293596			−0.146798	−	0.989166i	$-0.546897\pi$
$677$	−7.63914			−0.293596			−0.146798	+	0.989166i	$0.546897\pi$
$678$	−23.1967	−	1.87263i	−0.890863	−	0.0719179i
$679$	−5.94831	−	3.76148i	−0.228275	−	0.144352i
$680$	−16.2700	−	2.64413i	−0.623927	−	0.101398i
$681$	0.679857	+	0.602300i	0.0260522	+	0.0230802i
$682$	12.8253	+	9.63758i	0.491106	+	0.369042i
$683$	−20.7233	+	21.5752i	−0.792954	+	0.825553i	−0.987873	−	0.155267i	$-0.950376\pi$
$683$	−20.7233	+	21.5752i	−0.792954	+	0.825553i	0.194918	+	0.980819i	$0.437556\pi$
$684$	−5.81728	−	1.43383i	−0.222429	−	0.0548239i
$685$	−1.47532	−	3.10917i	−0.0563690	−	0.118795i
$686$	8.09343	+	8.42615i	0.309008	+	0.321712i
$687$	−3.49838	+	7.37267i	−0.133471	+	0.281285i
$688$	−21.8294	−	19.3391i	−0.832237	−	0.737298i
$689$	31.2237	−	31.0730i	1.18953	−	1.18379i
$690$	−15.2185	+	13.4824i	−0.579358	+	0.513266i
$691$	11.7284	+	40.4912i	0.446170	+	1.54036i	0.797037	+	0.603931i	$0.206400\pi$
$691$	11.7284	+	40.4912i	0.446170	+	1.54036i	−0.350867	+	0.936425i	$0.614113\pi$
$692$	25.8019	+	8.61393i	0.980840	+	0.327453i
$693$	−0.435197	+	0.453088i	−0.0165318	+	0.0172114i
$694$	9.35339	+	24.6629i	0.355050	+	0.936189i
$695$	18.0090	−	31.1925i	0.683120	−	1.18320i
$696$	−5.00921	−	6.13517i	−0.189874	−	0.232553i
$697$	−62.5925	+	15.4277i	−2.37086	+	0.584364i
$698$	−1.98082	+	3.43088i	−0.0749751	+	0.129861i
$699$	6.53030	+	11.3108i	0.246999	+	0.427814i
$700$	0.705132	+	0.734120i	0.0266515	+	0.0277471i
$701$	−3.94519	−	32.4916i	−0.149008	−	1.22719i	−0.854871	−	0.518841i	$-0.826364\pi$
$701$	−3.94519	−	32.4916i	−0.149008	−	1.22719i	0.705863	−	0.708348i	$-0.250559\pi$
$702$	4.83743	+	4.48436i	0.182577	+	0.169251i
$703$	0.413093	−	3.40213i	0.0155801	−	0.128314i
$704$	−2.38625	+	1.79315i	−0.0899352	+	0.0675819i
$705$	17.3891	+	1.40379i	0.654910	+	0.0528698i
$706$	−9.36133	−	45.8548i	−0.352318	−	1.72577i
$707$	−0.719562	+	5.92613i	−0.0270619	+	0.222875i
$708$	5.32514	+	2.26883i	0.200131	+	0.0852679i
$709$	−0.414288	+	0.261980i	−0.0155589	+	0.00983887i	−0.542223	−	0.840235i	$-0.682417\pi$
$709$	−0.414288	+	0.261980i	−0.0155589	+	0.00983887i	0.526664	+	0.850074i	$0.323443\pi$
$710$	3.50638	−	3.10638i	0.131592	−	0.116581i
$711$	13.9377	−	1.12517i	0.522704	−	0.0421970i
$712$	−1.51612	−	5.23425i	−0.0568189	−	0.196162i
$713$	36.0210	−	15.3471i	1.34900	−	0.574754i
$714$	3.61902	−	5.24305i	0.135438	−	0.196216i
$715$	1.28239	−	8.88217i	0.0479588	−	0.332174i
$716$	12.2696	+	17.7755i	0.458535	+	0.664302i
$717$	−0.572037	−	0.361734i	−0.0213631	−	0.0135092i
$718$	28.1161	−	4.56931i	1.04928	−	0.170525i
$719$	−48.1822	−	20.5285i	−1.79689	−	0.765585i	−0.982755	−	0.184915i	$-0.940799\pi$
$719$	−48.1822	−	20.5285i	−1.79689	−	0.765585i	−0.814139	−	0.580670i	$-0.802791\pi$
$720$	5.08764	−	7.37072i	0.189605	−	0.274691i
$721$	1.22581	−	4.23197i	0.0456514	−	0.157607i
$722$	0.616407	+	1.29905i	0.0229403	+	0.0483456i
$723$	−8.32209	+	21.9436i	−0.309502	+	0.816090i
$724$	−1.77261	−	2.17106i	−0.0658786	−	0.0806867i
$725$	−0.435452	−	10.8056i	−0.0161723	−	0.401311i
$726$	0.674843	+	16.7461i	0.0250458	+	0.621504i
$727$	−36.7766	+	9.06462i	−1.36397	+	0.336188i	−0.852326	−	0.523010i	$-0.824809\pi$
$727$	−36.7766	+	9.06462i	−1.36397	+	0.336188i	−0.511642	+	0.859199i	$0.670963\pi$
$728$	0.0353600	+	1.99531i	0.00131053	+	0.0739510i
$729$	−0.970942	−	0.239316i	−0.0359608	−	0.00886354i
$730$	10.9283	−	53.5305i	0.404476	−	1.98125i
$731$	−41.3309	+	17.6094i	−1.52868	+	0.651308i
$732$	2.74750	−	1.73742i	0.101551	−	0.0642167i
$733$	4.16665	−	2.18683i	0.153899	−	0.0807723i	−0.386016	−	0.922492i	$-0.626149\pi$
$733$	4.16665	−	2.18683i	0.153899	−	0.0807723i	0.539914	+	0.841720i	$0.318457\pi$
$734$	−57.9569	−	9.41892i	−2.13923	−	0.347659i
$735$	11.8130	−	3.94376i	0.435729	−	0.145468i
$736$	4.77151	+	39.2970i	0.175880	+	1.44851i
$737$	−0.300593	+	1.03777i	−0.0110725	+	0.0382266i
$738$	3.13833	−	15.3726i	0.115524	−	0.565872i
$739$	24.0414	+	8.02619i	0.884376	+	0.295248i	0.722341	−	0.691537i	$-0.243066\pi$
$739$	24.0414	+	8.02619i	0.884376	+	0.295248i	0.162035	+	0.986785i	$0.448194\pi$
$740$	−1.68654	−	0.885165i	−0.0619985	−	0.0325393i
$741$	1.00707	−	16.0063i	0.0369956	−	0.588008i
$742$	9.16852	−	4.81201i	0.336587	−	0.176655i
$743$	−26.4499	+	4.29853i	−0.970353	+	0.157698i	−0.624871	−	0.780728i	$-0.714849\pi$
$743$	−26.4499	+	4.29853i	−0.970353	+	0.157698i	−0.345482	+	0.938425i	$0.612284\pi$
$744$	−6.17624	+	4.64114i	−0.226432	+	0.170153i
$745$	0.235957	−	5.85522i	0.00864481	−	0.214519i
$746$	−15.7547			−0.576820
$747$	0.504420	−	12.5171i	0.0184558	−	0.457975i
$748$	2.74644	+	13.4529i	0.100420	+	0.491889i
$749$	1.13842	+	1.64929i	0.0415971	+	0.0602637i
$750$	21.1207	−	7.05112i	0.771218	−	0.257470i
$751$	−20.0066	+	42.1629i	−0.730050	+	1.53855i	0.108727	+	0.994072i	$0.465322\pi$
$751$	−20.0066	+	42.1629i	−0.730050	+	1.53855i	−0.838777	+	0.544475i	$0.816729\pi$
$752$	29.3336	−	35.9271i	1.06969	−	1.31013i
$753$	−2.19635	−	5.79131i	−0.0800396	−	0.211047i
$754$	−28.4129	+	33.2399i	−1.03474	+	1.21053i
$755$	5.23939	−	13.8151i	0.190681	−	0.502784i
$756$	0.311995	+	0.540391i	0.0113471	+	0.0196538i
$757$	−3.38842	+	4.15006i	−0.123154	+	0.150837i	−0.832502	−	0.554022i	$-0.813092\pi$
$757$	−3.38842	+	4.15006i	−0.123154	+	0.150837i	0.709348	+	0.704859i	$0.248990\pi$
$758$	0.641489	+	0.482048i	0.0232999	+	0.0175088i
$759$	−7.27078	−	3.81600i	−0.263912	−	0.138512i
$760$	−9.72247	+	0.784879i	−0.352671	+	0.0284706i
$761$	−23.1383	+	1.86792i	−0.838763	+	0.0677120i	−0.492379	−	0.870381i	$-0.663873\pi$
$761$	−23.1383	+	1.86792i	−0.838763	+	0.0677120i	−0.346384	+	0.938093i	$0.612591\pi$
$762$	18.1864	+	9.54498i	0.658825	+	0.345778i
$763$	−0.860121	−	0.646339i	−0.0311385	−	0.0233990i
$764$	18.7323	−	22.9429i	0.677709	−	0.830043i
$765$	−6.89829	−	11.9482i	−0.249408	−	0.431988i
$766$	−10.5587	+	27.8411i	−0.381502	+	1.00594i
$767$	−3.44092	+	15.1076i	−0.124244	+	0.545503i
$768$	−7.43109	−	19.5942i	−0.268146	−	0.707043i
$769$	26.1005	−	31.9674i	0.941210	−	1.15277i	−0.0468809	−	0.998900i	$-0.514928\pi$
$769$	26.1005	−	31.9674i	0.941210	−	1.15277i	0.988091	−	0.153872i	$-0.0491744\pi$
$770$	0.904329	−	1.90583i	0.0325898	−	0.0686815i
$771$	0.582883	−	0.194595i	0.0209920	−	0.00700816i
$772$	−3.95734	−	5.73320i	−0.142428	−	0.206342i
$773$	−4.10497	−	20.1075i	−0.147646	−	0.723216i	−0.984443	−	0.175704i	$-0.943780\pi$
$773$	−4.10497	−	20.1075i	−0.147646	−	0.723216i	0.836797	−	0.547513i	$-0.184425\pi$
$774$	0.440269	−	10.9252i	0.0158251	−	0.392697i
$775$	−10.5485			−0.378915
$776$	−0.730845	+	18.1357i	−0.0262358	+	0.651035i
$777$	−0.285343	+	0.214421i	−0.0102366	+	0.00769231i
$778$	−15.2770	+	2.48276i	−0.547708	+	0.0890112i
$779$	−33.7780	+	17.7281i	−1.21022	+	0.635174i
$780$	−8.11940	−	3.67789i	−0.290721	−	0.131690i
$781$	1.67521	+	0.879217i	0.0599437	+	0.0314609i
$782$	78.9834	+	26.3685i	2.82444	+	0.942937i
$783$	1.32604	−	6.49535i	0.0473886	−	0.232125i
$784$	9.21183	−	31.8029i	0.328994	−	1.13582i
$785$	−0.623952	−	5.13871i	−0.0222698	−	0.183408i
$786$	−29.2551	+	9.76678i	−1.04349	+	0.348370i
$787$	39.0585	+	6.34763i	1.39229	+	0.226268i	0.809864	−	0.586618i	$-0.199541\pi$
$787$	39.0585	+	6.34763i	1.39229	+	0.226268i	0.582422	+	0.812887i	$0.302105\pi$
$788$	−31.6140	+	16.5923i	−1.12620	+	0.591076i
$789$	−5.77873	+	3.65425i	−0.205728	+	0.130095i
$790$	−43.1951	+	18.4037i	−1.53681	+	0.654775i
$791$	1.17877	−	5.77397i	0.0419121	−	0.205299i
$792$	1.57314	+	0.387743i	0.0558990	+	0.0137779i
$793$	5.88484	+	6.41010i	0.208977	+	0.227629i
$794$	30.2212	−	7.44885i	1.07251	−	0.264350i
$795$	−0.902919	−	22.4057i	−0.0320232	−	0.794648i
$796$	0.155448	+	3.85740i	0.00550971	+	0.136722i
$797$	−4.51844	−	5.53408i	−0.160051	−	0.196027i	0.688353	−	0.725376i	$-0.258334\pi$
$797$	−4.51844	−	5.53408i	−0.160051	−	0.196027i	−0.848405	+	0.529348i	$0.822436\pi$
$798$	1.33683	−	3.52493i	0.0473233	−	0.124781i
$799$	−30.6296	−	64.5505i	−1.08360	−	2.28363i
$800$	2.96713	−	10.2437i	0.104904	−	0.362170i
$801$	2.59101	−	3.75373i	0.0915489	−	0.132631i
$802$	51.9973	+	22.1540i	1.83609	+	0.782284i
$803$	21.7795	−	3.53951i	0.768582	−	0.124907i
$804$	0.906985	+	0.573543i	0.0319869	+	0.0202273i
$805$	−2.92467	−	4.23711i	−0.103081	−	0.149339i
$806$	31.2806	+	28.9975i	1.10181	+	1.02139i
$807$	−7.03681	+	10.1946i	−0.247707	+	0.358866i
$808$	14.1637	−	6.03457i	0.498276	−	0.212295i
$809$	6.65208	+	22.9656i	0.233875	+	0.807429i	0.988493	+	0.151265i	$0.0483348\pi$
$809$	6.65208	+	22.9656i	0.233875	+	0.807429i	−0.754618	+	0.656164i	$0.772178\pi$
$810$	3.34692	−	0.270191i	0.117599	−	0.00949354i
$811$	−10.2198	+	9.05396i	−0.358866	+	0.317927i	−0.823220	−	0.567722i	$-0.807825\pi$
$811$	−10.2198	+	9.05396i	−0.358866	+	0.317927i	0.464354	+	0.885649i	$0.346286\pi$
$812$	−3.49624	+	2.21089i	−0.122694	+	0.0775869i
$813$	20.9818	+	8.93951i	0.735864	+	0.313522i
$814$	0.230404	−	1.89754i	0.00807564	−	0.0665089i
$815$	2.77501	+	13.5929i	0.0972045	+	0.476139i
$816$	−36.5609	−	2.95150i	−1.27989	−	0.103323i
$817$	−21.2531	+	15.9707i	−0.743552	+	0.558743i
$818$	−2.22634	+	18.3356i	−0.0778423	+	0.641089i
$819$	−1.27492	+	1.07915i	−0.0445493	+	0.0377085i
$820$	2.55557	+	21.0470i	0.0892444	+	0.734994i
$821$	28.5774	+	29.7522i	0.997359	+	1.03836i	0.999264	+	0.0383622i	$0.0122141\pi$
$821$	28.5774	+	29.7522i	0.997359	+	1.03836i	−0.00190519	+	0.999998i	$0.500606\pi$
$822$	−1.71515	−	2.97073i	−0.0598227	−	0.103616i
$823$	18.6594	−	32.3190i	0.650424	−	1.12657i	−0.332596	−	0.943070i	$-0.607924\pi$
$823$	18.6594	−	32.3190i	0.650424	−	1.12657i	0.983020	−	0.183498i	$-0.0587422\pi$
$824$	−11.0326	+	2.71929i	−0.384339	+	0.0947311i
$825$	1.39911	+	1.71360i	0.0487107	+	0.0596598i
$826$	−1.82108	+	3.15420i	−0.0633633	+	0.109748i
$827$	−2.37820	−	6.27081i	−0.0826982	−	0.218057i	0.887289	−	0.461215i	$-0.152586\pi$
$827$	−2.37820	−	6.27081i	−0.0826982	−	0.218057i	−0.969987	+	0.243157i	$0.921817\pi$
$828$	−5.64971	+	5.88198i	−0.196341	+	0.204413i
$829$	37.6676	+	12.5753i	1.30825	+	0.436758i	0.883448	−	0.468529i	$-0.155216\pi$
$829$	37.6676	+	12.5753i	1.30825	+	0.436758i	0.424801	+	0.905287i	$0.360344\pi$
$830$	11.7029	+	40.4032i	0.406214	+	1.40241i
$831$	8.69869	−	7.70636i	0.301754	−	0.267331i
$832$	−6.80143	+	4.08918i	−0.235797	+	0.141767i
$833$	−38.1780	−	33.8227i	−1.32279	−	1.17189i
$834$	15.3907	−	32.4352i	0.532936	−	1.12314i
$835$	−26.0584	−	27.1297i	−0.901789	−	0.938862i
$836$	3.48312	+	7.34052i	0.120466	+	0.253877i
$837$	−6.27846	−	1.54750i	−0.217015	−	0.0534894i
$838$	7.61615	−	7.92926i	0.263096	−	0.273912i
$839$	−16.8011	−	12.6252i	−0.580039	−	0.435871i	0.269798	−	0.962917i	$-0.413043\pi$
$839$	−16.8011	−	12.6252i	−0.580039	−	0.435871i	−0.849837	+	0.527046i	$0.823299\pi$
$840$	0.760389	+	0.673646i	0.0262359	+	0.0232430i
$841$	14.7544	+	2.39782i	0.508772	+	0.0826836i
$842$	−17.9515	−	11.3519i	−0.618651	−	0.391211i
$843$	−19.6736	−	1.58822i	−0.677595	−	0.0547011i
$844$	20.5568			0.707596
$845$	5.82213	−	23.1390i	0.200287	−	0.796006i
$846$	17.3892			0.597853
$847$	−4.23019	−	0.341496i	−0.145351	−	0.0117339i
$848$	−50.3873	−	31.8630i	−1.73031	−	1.09418i
$849$	12.1851	+	1.98028i	0.418192	+	0.0679629i
$850$	−16.7917	−	14.8761i	−0.575950	−	0.510248i
$851$	−3.72954	−	2.80257i	−0.127847	−	0.0960708i
$852$	1.30171	−	1.35522i	0.0445959	−	0.0464292i
$853$	−8.31322	−	2.04903i	−0.284639	−	0.0701573i	0.0944111	−	0.995533i	$-0.469903\pi$
$853$	−8.31322	−	2.04903i	−0.284639	−	0.0701573i	−0.379050	+	0.925376i	$0.623749\pi$
$854$	0.876869	+	1.84796i	0.0300058	+	0.0632360i
$855$	−5.65549	−	5.88799i	−0.193414	−	0.201365i
$856$	2.21564	−	4.66937i	0.0757291	−	0.159596i
$857$	−2.25525	−	1.99798i	−0.0770380	−	0.0682497i	0.623725	−	0.781644i	$-0.285619\pi$
$857$	−2.25525	−	1.99798i	−0.0770380	−	0.0682497i	−0.700763	+	0.713394i	$0.747157\pi$
$858$	0.561695	−	8.92758i	0.0191759	−	0.304783i
$859$	−8.89760	+	7.88258i	−0.303582	+	0.268950i	−0.801135	−	0.598483i	$-0.795770\pi$
$859$	−8.89760	+	7.88258i	−0.303582	+	0.268950i	0.497553	+	0.867433i	$0.334232\pi$
$860$	4.11074	+	14.1919i	0.140175	+	0.483941i
$861$	3.76853	+	1.25812i	0.128431	+	0.0428766i
$862$	25.1156	−	26.1482i	0.855442	−	0.890610i
$863$	13.0481	+	34.4049i	0.444162	+	1.17116i	0.951020	+	0.309129i	$0.100037\pi$
$863$	13.0481	+	34.4049i	0.444162	+	1.17116i	−0.506859	+	0.862029i	$0.669193\pi$
$864$	3.26881	−	5.66174i	0.111207	−	0.192616i
$865$	23.4425	+	28.7118i	0.797069	+	0.976232i
$866$	−26.1964	+	6.45683i	−0.890190	+	0.219412i
$867$	−19.7521	+	34.2116i	−0.670815	+	1.16189i
$868$	2.01747	+	3.49436i	0.0684774	+	0.118606i
$869$	−13.1358	−	13.6759i	−0.445603	−	0.463921i
$870$	2.68314	+	22.0977i	0.0909671	+	0.749182i
$871$	−1.07895	+	2.66223i	−0.0365587	+	0.0902063i
$872$	−0.334456	+	2.75449i	−0.0113261	+	0.0932790i
$873$	−12.1450	+	9.12637i	−0.411046	+	0.308881i
$874$	49.1145	+	3.96493i	1.66132	+	0.134116i
$875$	1.12783	+	5.52449i	0.0381277	+	0.186762i
$876$	2.64168	−	21.7562i	0.0892540	−	0.735073i
$877$	−9.63330	−	4.10437i	−0.325294	−	0.138595i	0.223146	−	0.974785i	$-0.428367\pi$
$877$	−9.63330	−	4.10437i	−0.325294	−	0.138595i	−0.548439	+	0.836190i	$0.684778\pi$
$878$	13.3495	−	8.44169i	0.450523	−	0.284893i
$879$	−8.43379	+	7.47168i	−0.284465	+	0.252014i
$880$	−12.1061	+	0.977305i	−0.408096	+	0.0329449i
$881$	12.9821	+	44.8194i	0.437378	+	1.51000i	0.812462	+	0.583014i	$0.198127\pi$
$881$	12.9821	+	44.8194i	0.437378	+	1.51000i	−0.375084	+	0.926991i	$0.622386\pi$
$882$	11.4203	−	4.86573i	0.384541	−	0.163837i
$883$	5.26135	−	7.62239i	0.177059	−	0.256514i	−0.724399	−	0.689381i	$-0.757883\pi$
$883$	5.26135	−	7.62239i	0.177059	−	0.256514i	0.901458	+	0.432867i	$0.142498\pi$
$884$	3.58176	+	36.3295i	0.120468	+	1.22189i
$885$	4.48058	+	6.49124i	0.150613	+	0.218201i
$886$	9.72891	+	6.15219i	0.326849	+	0.206687i
$887$	33.9571	−	5.51857i	1.14017	−	0.185295i	0.439133	−	0.898422i	$-0.355286\pi$
$887$	33.9571	−	5.51857i	1.14017	−	0.185295i	0.701035	+	0.713126i	$0.252721\pi$
$888$	0.846848	+	0.360808i	0.0284184	+	0.0121079i
$889$	−2.95450	+	4.28033i	−0.0990907	+	0.143558i
$890$	−4.26100	+	14.7107i	−0.142829	+	0.493103i
$891$	0.581356	+	1.22518i	0.0194761	+	0.0410451i
$892$	3.45370	−	9.10666i	0.115638	−	0.304914i
$893$	−26.7397	−	32.7502i	−0.894811	−	1.09594i
$894$	−0.235194	−	5.83628i	−0.00786606	−	0.195194i
$895$	1.18509	+	29.4078i	0.0396133	+	0.982993i
$896$	4.07002	−	1.00317i	0.135970	−	0.0335136i
$897$	−18.1841	−	12.0816i	−0.607151	−	0.403392i
$898$	21.2848	+	5.24623i	0.710283	+	0.175069i
$899$	8.57462	−	42.0013i	0.285980	−	1.40082i
$900$	2.02143	−	0.861251i	0.0673810	−	0.0287084i
$901$	−77.6200	+	49.0839i	−2.58590	+	1.63522i
$902$	−18.8398	+	9.88788i	−0.627296	+	0.329230i
$903$	2.73291	+	0.444140i	0.0909454	+	0.0147801i
$904$	−14.4160	+	4.81276i	−0.479468	+	0.160070i
$905$	−0.460356	−	3.79137i	−0.0153027	−	0.126029i
$906$	4.09744	−	14.1460i	0.136128	−	0.469970i
$907$	2.42387	−	11.8729i	0.0804834	−	0.394234i	−0.919516	−	0.393053i	$-0.871419\pi$
$907$	2.42387	−	11.8729i	0.0804834	−	0.394234i	0.999999	−	0.00118089i	$-0.000375888\pi$
$908$	−1.16044	−	0.387411i	−0.0385104	−	0.0128567i
$909$	11.4100	+	5.98845i	0.378447	+	0.198624i
$910$	2.91315	−	4.79272i	0.0965701	−	0.158877i
$911$	38.2770	−	20.0893i	1.26817	−	0.665589i	0.309718	−	0.950829i	$-0.399765\pi$
$911$	38.2770	−	20.0893i	1.26817	−	0.665589i	0.958456	+	0.285240i	$0.0920732\pi$
$912$	−21.4242	+	3.48177i	−0.709427	+	0.115293i
$913$	−13.5812	+	10.2056i	−0.449472	+	0.337756i
$914$	−2.11691	+	52.5306i	−0.0700211	+	1.73756i
$915$	4.42963			0.146439
$916$	0.442595	−	10.9829i	0.0146238	−	0.362885i
$917$	−1.56221	−	7.65219i	−0.0515886	−	0.252698i
$918$	−7.81199	−	11.3176i	−0.257834	−	0.373537i
$919$	20.9431	−	6.99182i	0.690848	−	0.230639i	0.0505003	−	0.998724i	$-0.483918\pi$
$919$	20.9431	−	6.99182i	0.690848	−	0.230639i	0.640348	+	0.768085i	$0.278790\pi$
$920$	−5.69210	+	11.9958i	−0.187663	+	0.395491i
$921$	−13.5461	+	16.5910i	−0.446360	+	0.546692i
$922$	15.6090	+	41.1574i	0.514054	+	1.35545i
$923$	4.18968	+	2.78363i	0.137905	+	0.0916243i
$924$	0.300067	−	0.791211i	0.00987147	−	0.0260289i
$925$	0.628424	+	1.08846i	0.0206625	+	0.0357884i
$926$	−29.4193	+	36.0321i	−0.966779	+	1.18409i
$927$	−7.60318	−	5.71342i	−0.249721	−	0.187653i
$928$	38.3756	+	20.1411i	1.25974	+	0.661164i
$929$	18.8760	−	1.52383i	0.619301	−	0.0499951i	0.233165	−	0.972437i	$-0.425092\pi$
$929$	18.8760	−	1.52383i	0.619301	−	0.0499951i	0.386136	+	0.922442i	$0.373810\pi$
$930$	21.6424	−	1.74715i	0.709681	−	0.0572914i
$931$	−26.7251	−	14.0264i	−0.875881	−	0.459698i
$932$	−14.0637	−	10.5682i	−0.460671	−	0.346172i
$933$	10.5622	−	12.9363i	0.345790	−	0.423516i
$934$	−12.6496	−	21.9098i	−0.413909	−	0.716911i
$935$	−6.63456	+	17.4939i	−0.216973	+	0.572112i
$936$	4.05424	+	1.45594i	0.132517	+	0.0475888i
$937$	−18.6022	−	49.0501i	−0.607709	−	1.60240i	−0.785868	−	0.618395i	$-0.787783\pi$
$937$	−18.6022	−	49.0501i	−0.607709	−	1.60240i	0.178159	−	0.984002i	$-0.442986\pi$
$938$	−0.427045	+	0.523035i	−0.0139435	+	0.0170777i
$939$	−2.06012	+	4.34161i	−0.0672295	+	0.141683i
$940$	−22.2889	+	7.44113i	−0.726984	+	0.242703i
$941$	14.3406	+	20.7760i	0.467490	+	0.677277i	0.983830	−	0.179107i	$-0.0573210\pi$
$941$	14.3406	+	20.7760i	0.467490	+	0.677277i	−0.516339	+	0.856384i	$0.672706\pi$
$942$	−1.03207	−	5.05542i	−0.0336267	−	0.164715i
$943$	−2.09095	+	51.8865i	−0.0680908	+	1.68966i
$944$	20.9697			0.682505
$945$	−0.0342372	+	0.849588i	−0.00111374	+	0.0276371i
$946$	−11.8540	+	8.90768i	−0.385406	+	0.289614i
$947$	4.35140	−	0.707172i	0.141402	−	0.0229800i	−0.0892985	−	0.996005i	$-0.528462\pi$
$947$	4.35140	−	0.707172i	0.141402	−	0.0229800i	0.230700	+	0.973025i	$0.425898\pi$
$948$	−16.6769	+	8.75273i	−0.541642	+	0.284276i
$949$	58.5671	−	3.40050i	1.90117	−	0.110385i
$950$	−11.7544	−	6.16921i	−0.381364	−	0.200155i
$951$	6.33080	+	2.11353i	0.205290	+	0.0685360i
$952$	0.832208	−	4.07643i	0.0269720	−	0.132118i
$953$	4.99792	−	17.2548i	0.161898	−	0.558938i	−0.838013	−	0.545650i	$-0.816283\pi$
$953$	4.99792	−	17.2548i	0.161898	−	0.558938i	0.999912	−	0.0132883i	$-0.00422993\pi$
$954$	−2.69415	−	22.1884i	−0.0872265	−	0.718375i
$955$	38.2829	−	12.7807i	1.23880	−	0.413574i
$956$	0.899823	+	0.146236i	0.0291024	+	0.00472959i
$957$	−7.96035	+	4.17792i	−0.257322	+	0.135053i
$958$	−23.2248	+	14.6865i	−0.750358	+	0.474498i
$959$	0.799126	−	0.340476i	0.0258051	−	0.0109945i
$960$	−0.808072	+	3.95820i	−0.0260804	+	0.127750i
$961$	−10.4996	−	2.58791i	−0.338695	−	0.0834809i
$962$	1.12861	−	4.95523i	0.0363878	−	0.159763i
$963$	4.20020	−	1.03526i	0.135349	−	0.0333606i
$964$	−1.27284	−	31.5852i	−0.0409954	−	1.01729i
$965$	−0.382232	−	9.48498i	−0.0123045	−	0.305332i
$966$	−3.24559	−	3.97513i	−0.104425	−	0.127898i
$967$	17.4836	−	46.1004i	0.562234	−	1.48249i	−0.288805	−	0.957388i	$-0.593258\pi$
$967$	17.4836	−	46.1004i	0.562234	−	1.48249i	0.851039	−	0.525102i	$-0.175973\pi$
$968$	4.69206	+	9.88832i	0.150809	+	0.317823i
$969$	−9.30257	+	32.1162i	−0.298842	+	1.03172i
$970$	28.9777	−	41.9814i	0.930417	−	1.34794i
$971$	17.0533	+	7.26573i	0.547266	+	0.233168i	0.647860	−	0.761759i	$-0.275664\pi$
$971$	17.0533	+	7.26573i	0.547266	+	0.233168i	−0.100594	+	0.994928i	$0.532074\pi$
$972$	1.32950	−	0.216064i	0.0426436	−	0.00693027i
$973$	7.68372	+	4.85889i	0.246329	+	0.155769i
$974$	6.12893	+	8.87929i	0.196384	+	0.284511i
$975$	3.23117	+	4.91469i	0.103480	+	0.157396i
$976$	6.68992	−	9.69202i	0.214139	−	0.310234i
$977$	7.70660	−	3.28347i	0.246556	−	0.105048i	−0.265154	−	0.964206i	$-0.585423\pi$
$977$	7.70660	−	3.28347i	0.246556	−	0.105048i	0.511709	+	0.859159i	$0.329012\pi$
$978$	3.84730	+	13.2824i	0.123023	+	0.424725i
$979$	−6.16534	+	0.497717i	−0.197045	+	0.0159071i
$980$	−12.5560	+	11.1237i	−0.401088	+	0.355333i
$981$	−1.96290	+	1.24126i	−0.0626704	+	0.0396304i
$982$	10.1637	+	4.33033i	0.324335	+	0.138186i
$983$	−2.86211	+	23.5716i	−0.0912872	+	0.751817i	0.873140	+	0.487469i	$0.162080\pi$
$983$	−2.86211	+	23.5716i	−0.0912872	+	0.751817i	−0.964427	+	0.264348i	$0.914843\pi$
$984$	−2.04952	−	10.0392i	−0.0653363	−	0.320038i
$985$	−48.4936	−	3.91481i	−1.54514	−	0.124736i
$986$	72.8821	−	54.7673i	2.32104	−	1.74415i
$987$	−0.530767	+	4.37126i	−0.0168945	+	0.139139i
$988$	7.20272	+	20.3661i	0.229149	+	0.647931i
$989$	4.36208	+	35.9249i	0.138706	+	1.14235i
$990$	−3.15436	−	3.28404i	−0.100252	−	0.104374i
$991$	−0.443691	−	0.768495i	−0.0140943	−	0.0244121i	0.858892	−	0.512156i	$-0.171153\pi$
$991$	−0.443691	−	0.768495i	−0.0140943	−	0.0244121i	−0.872987	+	0.487744i	$0.837820\pi$
$992$	21.1373	−	36.6108i	0.671109	−	1.16240i
$993$	22.6282	−	5.57735i	0.718085	−	0.176992i
$994$	0.747794	+	0.915882i	0.0237186	+	0.0290500i
$995$	−2.63027	+	4.55576i	−0.0833852	+	0.144427i
$996$	5.98339	+	15.7769i	0.189591	+	0.499910i
$997$	11.4607	−	11.9319i	0.362965	−	0.377887i	−0.514530	−	0.857472i	$-0.672034\pi$
$997$	11.4607	−	11.9319i	0.362965	−	0.377887i	0.877495	+	0.479586i	$0.159213\pi$
$998$	−13.3191	−	4.44658i	−0.421610	−	0.140754i
$999$	0.214355	+	0.740041i	0.00678191	+	0.0234139i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	507.2.q.b.16.4	✓	384
169.74	even	39	inner	507.2.q.b.412.4	yes	384

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
507.2.q.b.16.4	✓	384	1.1	even	1	trivial
507.2.q.b.412.4	yes	384	169.74	even	39	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:	\( N \)	\(=\)	\( 507 = 3 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	507.q (of order \(39\), degree \(24\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.82353 - 0.147211i) q^{2} +(-0.845190 - 0.534466i) q^{3} +(1.32950 + 0.216064i) q^{4} +(1.37382 + 1.21710i) q^{5} +(1.46255 + 1.09904i) q^{6} +(-0.320915 + 0.334108i) q^{7} +(1.16003 + 0.285923i) q^{8} +(0.428693 + 0.903450i) q^{9} +O(q^{10})\)	\(q+(-1.82353 - 0.147211i) q^{2} +(-0.845190 - 0.534466i) q^{3} +(1.32950 + 0.216064i) q^{4} +(1.37382 + 1.21710i) q^{5} +(1.46255 + 1.09904i) q^{6} +(-0.320915 + 0.334108i) q^{7} +(1.16003 + 0.285923i) q^{8} +(0.428693 + 0.903450i) q^{9} +(-2.32603 - 2.42166i) q^{10} +(0.581356 - 1.22518i) q^{11} +(-1.00820 - 0.893186i) q^{12} +(1.87275 - 3.08104i) q^{13} +(0.634382 - 0.562014i) q^{14} +(-0.510641 - 1.76294i) q^{15} +(-4.62851 - 1.54522i) q^{16} +(-5.20715 + 5.42122i) q^{17} +(-0.648737 - 1.71058i) q^{18} +(-2.22407 + 3.85220i) q^{19} +(1.56352 + 1.91496i) q^{20} +(0.449803 - 0.110866i) q^{21} +(-1.24048 + 2.14858i) q^{22} +(3.02753 + 5.24383i) q^{23} +(-0.827633 - 0.861657i) q^{24} +(-0.196631 - 1.61940i) q^{25} +(-3.86857 + 5.34269i) q^{26} +(0.120537 - 0.992709i) q^{27} +(-0.498844 + 0.374857i) q^{28} +(6.60783 + 0.533439i) q^{29} +(0.671647 + 3.28995i) q^{30} +(0.779433 - 6.41921i) q^{31} +(6.01447 + 2.56253i) q^{32} +(-1.14617 + 0.724796i) q^{33} +(10.2935 - 9.11922i) q^{34} +(-0.847520 + 0.0684189i) q^{35} +(0.374742 + 1.29376i) q^{36} +(-0.708808 + 0.301995i) q^{37} +(4.62275 - 6.69721i) q^{38} +(-3.22954 + 1.60315i) q^{39} +(1.24568 + 1.80468i) q^{40} +(7.24842 + 4.58362i) q^{41} +(-0.836551 + 0.135953i) q^{42} +(5.49838 + 2.34264i) q^{43} +(1.03763 - 1.50326i) q^{44} +(-0.510641 + 1.76294i) q^{45} +(-4.74884 - 10.0080i) q^{46} +(-3.37054 + 8.88739i) q^{47} +(3.08610 + 3.77979i) q^{48} +(0.273220 + 6.77988i) q^{49} +(0.120170 + 2.98198i) q^{50} +(7.29849 - 1.79892i) q^{51} +(3.15551 - 3.69160i) q^{52} +(11.8624 + 2.92382i) q^{53} +(-0.365940 + 1.79249i) q^{54} +(2.28984 - 0.975611i) q^{55} +(-0.467801 + 0.295819i) q^{56} +(3.93863 - 2.06715i) q^{57} +(-11.9711 - 1.94549i) q^{58} +(-4.07623 + 1.36085i) q^{59} +(-0.297988 - 2.45415i) q^{60} +(-0.671460 + 2.31815i) q^{61} +(-2.36630 + 11.5909i) q^{62} +(-0.439423 - 0.146701i) q^{63} +(-1.94895 - 1.02289i) q^{64} +(6.32274 - 1.95348i) q^{65} +(2.19678 - 1.15296i) q^{66} +(-0.786388 + 0.127801i) q^{67} +(-8.09423 + 6.08242i) q^{68} +(0.243812 - 6.05014i) q^{69} +1.55555 q^{70} +(-0.0561751 + 1.39397i) q^{71} +(0.238981 + 1.17061i) q^{72} +(9.24294 + 13.3907i) q^{73} +(1.33699 - 0.446353i) q^{74} +(-0.699324 + 1.47379i) q^{75} +(-3.78922 + 4.64095i) q^{76} +(0.222777 + 0.587414i) q^{77} +(6.12517 - 2.44797i) q^{78} +(4.95845 - 13.0744i) q^{79} +(-4.47805 - 7.75620i) q^{80} +(-0.632445 + 0.774605i) q^{81} +(-12.5430 - 9.42543i) q^{82} +(-11.0923 - 5.82169i) q^{83} +(0.621966 - 0.0502103i) q^{84} +(-13.7518 + 1.11016i) q^{85} +(-9.68160 - 5.08130i) q^{86} +(-5.29977 - 3.98252i) q^{87} +(1.02470 - 1.25503i) q^{88} +(-2.28056 - 3.95004i) q^{89} +(1.19069 - 3.13960i) q^{90} +(0.428408 + 1.61445i) q^{91} +(2.89208 + 7.62580i) q^{92} +(-4.08962 + 5.00887i) q^{93} +(7.45461 - 15.7103i) q^{94} +(-7.74398 + 2.58532i) q^{95} +(-3.71379 - 5.38035i) q^{96} +(3.03876 + 14.8848i) q^{97} +(0.499846 - 12.4036i) q^{98} +1.35611 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 384 q + q^{2} + 16 q^{3} + 17 q^{4} + 6 q^{5} + q^{6} - 3 q^{7} - 18 q^{8} + 16 q^{9}+O(q^{10}) \) 384 * q + q^2 + 16 * q^3 + 17 * q^4 + 6 * q^5 + q^6 - 3 * q^7 - 18 * q^8 + 16 * q^9	\( 384 q + q^{2} + 16 q^{3} + 17 q^{4} + 6 q^{5} + q^{6} - 3 q^{7} - 18 q^{8} + 16 q^{9} + 3 q^{10} - 4 q^{11} - 34 q^{12} - 15 q^{13} + 24 q^{14} - 3 q^{15} + 11 q^{16} - 3 q^{17} - 2 q^{18} + 6 q^{19} + q^{20} + 6 q^{21} - 86 q^{22} - 52 q^{23} + 9 q^{24} - 74 q^{25} - 64 q^{26} - 32 q^{27} - 16 q^{28} - 44 q^{29} + 3 q^{30} - 28 q^{31} + 74 q^{32} - 17 q^{33} - 83 q^{34} + 70 q^{35} + 17 q^{36} + 11 q^{37} - 29 q^{38} + q^{39} - 5 q^{40} + q^{41} + 118 q^{42} - 79 q^{43} - 19 q^{44} - 3 q^{45} + 314 q^{46} + 11 q^{48} - 69 q^{49} - 76 q^{50} + 6 q^{51} - 37 q^{52} - 102 q^{53} + q^{54} - 73 q^{55} - 36 q^{56} + 14 q^{57} - 51 q^{58} + 194 q^{59} + 76 q^{60} + 4 q^{61} - 89 q^{62} - 3 q^{63} - 184 q^{64} - 49 q^{65} - 36 q^{66} - 73 q^{67} + 4 q^{68} - 100 q^{70} + 106 q^{71} + 9 q^{72} - 132 q^{73} - 45 q^{74} + 11 q^{75} + 24 q^{76} - 54 q^{77} - 39 q^{78} - 2 q^{79} + 177 q^{80} + 16 q^{81} - 76 q^{82} - 58 q^{83} - 16 q^{84} - 123 q^{85} - 157 q^{86} - 57 q^{87} + 476 q^{88} + 18 q^{89} - 6 q^{90} + 233 q^{91} - 12 q^{92} + q^{93} - 111 q^{94} + 64 q^{95} - 83 q^{96} - 143 q^{97} - 79 q^{98} - 18 q^{99}+O(q^{100}) \) 384 * q + q^2 + 16 * q^3 + 17 * q^4 + 6 * q^5 + q^6 - 3 * q^7 - 18 * q^8 + 16 * q^9 + 3 * q^10 - 4 * q^11 - 34 * q^12 - 15 * q^13 + 24 * q^14 - 3 * q^15 + 11 * q^16 - 3 * q^17 - 2 * q^18 + 6 * q^19 + q^20 + 6 * q^21 - 86 * q^22 - 52 * q^23 + 9 * q^24 - 74 * q^25 - 64 * q^26 - 32 * q^27 - 16 * q^28 - 44 * q^29 + 3 * q^30 - 28 * q^31 + 74 * q^32 - 17 * q^33 - 83 * q^34 + 70 * q^35 + 17 * q^36 + 11 * q^37 - 29 * q^38 + q^39 - 5 * q^40 + q^41 + 118 * q^42 - 79 * q^43 - 19 * q^44 - 3 * q^45 + 314 * q^46 + 11 * q^48 - 69 * q^49 - 76 * q^50 + 6 * q^51 - 37 * q^52 - 102 * q^53 + q^54 - 73 * q^55 - 36 * q^56 + 14 * q^57 - 51 * q^58 + 194 * q^59 + 76 * q^60 + 4 * q^61 - 89 * q^62 - 3 * q^63 - 184 * q^64 - 49 * q^65 - 36 * q^66 - 73 * q^67 + 4 * q^68 - 100 * q^70 + 106 * q^71 + 9 * q^72 - 132 * q^73 - 45 * q^74 + 11 * q^75 + 24 * q^76 - 54 * q^77 - 39 * q^78 - 2 * q^79 + 177 * q^80 + 16 * q^81 - 76 * q^82 - 58 * q^83 - 16 * q^84 - 123 * q^85 - 157 * q^86 - 57 * q^87 + 476 * q^88 + 18 * q^89 - 6 * q^90 + 233 * q^91 - 12 * q^92 + q^93 - 111 * q^94 + 64 * q^95 - 83 * q^96 - 143 * q^97 - 79 * q^98 - 18 * q^99

Introduction

L-functions

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