LMFDB - Embedded newform 225.2.q.a.211.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [225,2,Mod(16,225)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(225, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([20, 6]))

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

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

chi := DirichletCharacter("225.16");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 225 = 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	225.q (of order $15$, degree $8$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.79663404548$
Analytic rank:	$0$
Dimension:	$224$
Relative dimension:	$28$ over $\Q(\zeta_{15})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			211.12
Character	$\chi$	$=$	225.211
Dual form			225.2.q.a.16.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.808045 - 0.359765i) q^{2} +(0.558868 - 1.63941i) q^{3} +(-0.814755 - 0.904878i) q^{4} +(1.09577 - 1.94918i) q^{5} +(-1.04139 + 1.12366i) q^{6} +(-0.458035 - 0.793340i) q^{7} +(0.879476 + 2.70675i) q^{8} +(-2.37533 - 1.83243i) q^{9} +O(q^{10})$	\(q+(-0.808045 - 0.359765i) q^{2} +(0.558868 - 1.63941i) q^{3} +(-0.814755 - 0.904878i) q^{4} +(1.09577 - 1.94918i) q^{5} +(-1.04139 + 1.12366i) q^{6} +(-0.458035 - 0.793340i) q^{7} +(0.879476 + 2.70675i) q^{8} +(-2.37533 - 1.83243i) q^{9} +(-1.58668 + 1.18080i) q^{10} +(1.33506 + 0.594408i) q^{11} +(-1.93881 + 0.830012i) q^{12} +(-1.67311 + 0.744918i) q^{13} +(0.0846971 + 0.805839i) q^{14} +(-2.58311 - 2.88575i) q^{15} +(0.00858220 - 0.0816542i) q^{16} +(1.50326 + 4.62656i) q^{17} +(1.26013 + 2.33524i) q^{18} +(-2.04373 - 6.28996i) q^{19} +(-2.65655 + 0.596562i) q^{20} +(-1.55659 + 0.307535i) q^{21} +(-0.864943 - 0.960617i) q^{22} +(-0.0683526 - 0.650331i) q^{23} +(4.92898 + 0.0708924i) q^{24} +(-2.59857 - 4.27170i) q^{25} +1.61995 q^{26} +(-4.33160 + 2.87006i) q^{27} +(-0.344689 + 1.06084i) q^{28} +(6.29829 - 1.33874i) q^{29} +(1.04907 + 3.26113i) q^{30} +(2.87587 + 0.611285i) q^{31} +(2.80973 - 4.86660i) q^{32} +(1.72060 - 1.85652i) q^{33} +(0.449771 - 4.27929i) q^{34} +(-2.04826 + 0.0234710i) q^{35} +(0.277194 + 3.64237i) q^{36} +(-4.86137 - 3.53200i) q^{37} +(-0.611478 + 5.81783i) q^{38} +(0.286177 + 3.15923i) q^{39} +(6.23963 + 1.25173i) q^{40} +(2.26096 - 1.00664i) q^{41} +(1.36844 + 0.311504i) q^{42} +(2.01308 + 3.48676i) q^{43} +(-0.549883 - 1.69237i) q^{44} +(-6.17455 + 2.62202i) q^{45} +(-0.178734 + 0.550087i) q^{46} +(5.26308 - 1.11870i) q^{47} +(-0.129068 - 0.0597036i) q^{48} +(3.08041 - 5.33542i) q^{49} +(0.562952 + 4.38660i) q^{50} +(8.42495 + 0.121174i) q^{51} +(2.03724 + 0.907036i) q^{52} +(-3.46201 + 10.6550i) q^{53} +(4.53267 - 0.760783i) q^{54} +(2.62153 - 1.95093i) q^{55} +(1.74454 - 1.93751i) q^{56} +(-11.4540 - 0.164740i) q^{57} +(-5.57093 - 1.18414i) q^{58} +(1.82813 - 0.813937i) q^{59} +(-0.506651 + 4.68858i) q^{60} +(11.5472 + 5.14113i) q^{61} +(-2.10391 - 1.52858i) q^{62} +(-0.365752 + 2.72376i) q^{63} +(-4.15407 + 3.01811i) q^{64} +(-0.381374 + 4.07745i) q^{65} +(-2.05823 + 0.881139i) q^{66} +(8.34092 + 1.77292i) q^{67} +(2.96168 - 5.12978i) q^{68} +(-1.10436 - 0.251391i) q^{69} +(1.66353 + 0.717926i) q^{70} +(5.09668 - 15.6860i) q^{71} +(2.87087 - 8.04101i) q^{72} +(-2.01962 + 1.46734i) q^{73} +(2.65752 + 4.60296i) q^{74} +(-8.45533 + 1.87280i) q^{75} +(-4.02650 + 6.97410i) q^{76} +(-0.139938 - 1.33142i) q^{77} +(0.905335 - 2.65576i) q^{78} +(-6.05809 + 1.28769i) q^{79} +(-0.149754 - 0.106203i) q^{80} +(2.28442 + 8.70525i) q^{81} -2.18911 q^{82} +(2.67975 - 2.97617i) q^{83} +(1.54652 + 1.15796i) q^{84} +(10.6652 + 2.13954i) q^{85} +(-0.372247 - 3.54169i) q^{86} +(1.32516 - 11.0737i) q^{87} +(-0.434758 + 4.13645i) q^{88} +(-11.4149 + 8.29340i) q^{89} +(5.93262 + 0.102674i) q^{90} +(1.35732 + 0.986149i) q^{91} +(-0.532779 + 0.591712i) q^{92} +(2.60938 - 4.37310i) q^{93} +(-4.65527 - 0.989508i) q^{94} +(-14.4997 - 2.90877i) q^{95} +(-6.40809 - 7.32609i) q^{96} +(-5.89193 + 1.25237i) q^{97} +(-4.40860 + 3.20304i) q^{98} +(-2.08201 - 3.85832i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 224 q - 3 q^{2} - 8 q^{3} + 23 q^{4} - 8 q^{5} - 10 q^{6} - 8 q^{7} - 20 q^{8} - 8 q^{9}+O(q^{10}) $ 224 * q - 3 * q^2 - 8 * q^3 + 23 * q^4 - 8 * q^5 - 10 * q^6 - 8 * q^7 - 20 * q^8 - 8 * q^9	\( 224 q - 3 q^{2} - 8 q^{3} + 23 q^{4} - 8 q^{5} - 10 q^{6} - 8 q^{7} - 20 q^{8} - 8 q^{9} - 20 q^{10} - 11 q^{11} - 4 q^{12} - 3 q^{13} + q^{14} - 48 q^{15} + 23 q^{16} - 24 q^{17} - 12 q^{19} + q^{20} + 15 q^{21} - 11 q^{22} + q^{23} - 30 q^{24} - 16 q^{25} - 136 q^{26} + 7 q^{27} + 4 q^{28} - 15 q^{29} - 24 q^{30} + 3 q^{31} + 12 q^{32} - 5 q^{33} + q^{34} + 14 q^{35} + 38 q^{36} - 24 q^{37} + 55 q^{38} + 20 q^{39} + q^{40} - 19 q^{41} - 38 q^{42} - 8 q^{43} + 4 q^{44} - 38 q^{45} - 20 q^{46} - 10 q^{47} - 25 q^{48} - 72 q^{49} - 3 q^{50} - 26 q^{51} - 25 q^{52} - 12 q^{53} + 53 q^{54} - 20 q^{55} - 60 q^{56} + 38 q^{57} - 23 q^{58} - 30 q^{59} - 33 q^{60} - 3 q^{61} - 44 q^{62} + 46 q^{63} - 44 q^{64} + 51 q^{65} - 134 q^{66} - 12 q^{67} - 156 q^{68} + 4 q^{69} - 16 q^{70} + 42 q^{71} + 74 q^{72} - 12 q^{73} + 90 q^{74} + 67 q^{75} - 8 q^{76} + 31 q^{77} - 92 q^{78} - 15 q^{79} + 298 q^{80} - 104 q^{81} + 8 q^{82} + 59 q^{83} + 115 q^{84} - 11 q^{85} + 9 q^{86} - 59 q^{87} - 23 q^{88} + 106 q^{89} + 107 q^{90} + 30 q^{91} + 11 q^{92} + 32 q^{93} + 25 q^{94} + 7 q^{95} + 35 q^{96} - 21 q^{97} + 146 q^{98} - 20 q^{99}+O(q^{100}) \) 224 * q - 3 * q^2 - 8 * q^3 + 23 * q^4 - 8 * q^5 - 10 * q^6 - 8 * q^7 - 20 * q^8 - 8 * q^9 - 20 * q^10 - 11 * q^11 - 4 * q^12 - 3 * q^13 + q^14 - 48 * q^15 + 23 * q^16 - 24 * q^17 - 12 * q^19 + q^20 + 15 * q^21 - 11 * q^22 + q^23 - 30 * q^24 - 16 * q^25 - 136 * q^26 + 7 * q^27 + 4 * q^28 - 15 * q^29 - 24 * q^30 + 3 * q^31 + 12 * q^32 - 5 * q^33 + q^34 + 14 * q^35 + 38 * q^36 - 24 * q^37 + 55 * q^38 + 20 * q^39 + q^40 - 19 * q^41 - 38 * q^42 - 8 * q^43 + 4 * q^44 - 38 * q^45 - 20 * q^46 - 10 * q^47 - 25 * q^48 - 72 * q^49 - 3 * q^50 - 26 * q^51 - 25 * q^52 - 12 * q^53 + 53 * q^54 - 20 * q^55 - 60 * q^56 + 38 * q^57 - 23 * q^58 - 30 * q^59 - 33 * q^60 - 3 * q^61 - 44 * q^62 + 46 * q^63 - 44 * q^64 + 51 * q^65 - 134 * q^66 - 12 * q^67 - 156 * q^68 + 4 * q^69 - 16 * q^70 + 42 * q^71 + 74 * q^72 - 12 * q^73 + 90 * q^74 + 67 * q^75 - 8 * q^76 + 31 * q^77 - 92 * q^78 - 15 * q^79 + 298 * q^80 - 104 * q^81 + 8 * q^82 + 59 * q^83 + 115 * q^84 - 11 * q^85 + 9 * q^86 - 59 * q^87 - 23 * q^88 + 106 * q^89 + 107 * q^90 + 30 * q^91 + 11 * q^92 + 32 * q^93 + 25 * q^94 + 7 * q^95 + 35 * q^96 - 21 * q^97 + 146 * q^98 - 20 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/225\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{4}{5}\right)$

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 $

$2$	−0.808045	−	0.359765i	−0.571374	−	0.254392i	0.100649	−	0.994922i	$-0.467908\pi$
$2$	−0.808045	−	0.359765i	−0.571374	−	0.254392i	−0.672023	+	0.740530i	$0.734575\pi$
$3$	0.558868	−	1.63941i	0.322662	−	0.946514i
$3$	0.558868	−	1.63941i	0.322662	−	0.946514i
$4$	−0.814755	−	0.904878i	−0.407378	−	0.452439i
$5$	1.09577	−	1.94918i	0.490044	−	0.871698i
$5$	1.09577	−	1.94918i	0.490044	−	0.871698i
$6$	−1.04139	+	1.12366i	−0.425147	+	0.458731i
$7$	−0.458035	−	0.793340i	−0.173121	−	0.299854i	0.766388	−	0.642377i	$-0.222052\pi$
$7$	−0.458035	−	0.793340i	−0.173121	−	0.299854i	−0.939509	+	0.342523i	$0.888718\pi$
$8$	0.879476	+	2.70675i	0.310942	+	0.956981i
$9$	−2.37533	−	1.83243i	−0.791778	−	0.610809i
$10$	−1.58668	+	1.18080i	−0.501751	+	0.373402i
$11$	1.33506	+	0.594408i	0.402536	+	0.179221i	0.598011	−	0.801488i	$-0.295958\pi$
$11$	1.33506	+	0.594408i	0.402536	+	0.179221i	−0.195474	+	0.980709i	$0.562625\pi$
$12$	−1.93881	+	0.830012i	−0.559685	+	0.239604i
$13$	−1.67311	+	0.744918i	−0.464038	+	0.206603i	−0.625419	−	0.780289i	$-0.715072\pi$
$13$	−1.67311	+	0.744918i	−0.464038	+	0.206603i	0.161381	+	0.986892i	$0.448405\pi$
$14$	0.0846971	+	0.805839i	0.0226362	+	0.215370i
$15$	−2.58311	−	2.88575i	−0.666955	−	0.745098i
$16$	0.00858220	−	0.0816542i	0.00214555	−	0.0204135i
$17$	1.50326	+	4.62656i	0.364594	+	1.12211i	0.950235	+	0.311535i	$0.100843\pi$
$17$	1.50326	+	4.62656i	0.364594	+	1.12211i	−0.585641	+	0.810571i	$0.699157\pi$
$18$	1.26013	+	2.33524i	0.297016	+	0.550422i
$19$	−2.04373	−	6.28996i	−0.468864	−	1.44301i	−0.854057	−	0.520179i	$-0.825865\pi$
$19$	−2.04373	−	6.28996i	−0.468864	−	1.44301i	0.385193	−	0.922836i	$-0.374135\pi$
$20$	−2.65655	+	0.596562i	−0.594023	+	0.133395i
$21$	−1.55659	+	0.307535i	−0.339676	+	0.0671097i
$22$	−0.864943	−	0.960617i	−0.184406	−	0.204804i
$23$	−0.0683526	−	0.650331i	−0.0142525	−	0.135603i	0.985082	−	0.172087i	$-0.0550510\pi$
$23$	−0.0683526	−	0.650331i	−0.0142525	−	0.135603i	−0.999334	+	0.0364836i	$0.988384\pi$
$24$	4.92898	+	0.0708924i	1.00612	+	0.0144708i
$25$	−2.59857	−	4.27170i	−0.519714	−	0.854341i
$26$	1.61995			0.317697
$27$	−4.33160	+	2.87006i	−0.833616	+	0.552344i
$28$	−0.344689	+	1.06084i	−0.0651401	+	0.200481i
$29$	6.29829	−	1.33874i	1.16956	−	0.248598i	0.418117	−	0.908393i	$-0.362690\pi$
$29$	6.29829	−	1.33874i	1.16956	−	0.248598i	0.751446	+	0.659795i	$0.229357\pi$
$30$	1.04907	+	3.26113i	0.191534	+	0.595398i
$31$	2.87587	+	0.611285i	0.516521	+	0.109790i	0.458794	−	0.888542i	$-0.348281\pi$
$31$	2.87587	+	0.611285i	0.516521	+	0.109790i	0.0577267	+	0.998332i	$0.481615\pi$
$32$	2.80973	−	4.86660i	0.496695	−	0.860302i
$33$	1.72060	−	1.85652i	0.299518	−	0.323179i
$34$	0.449771	−	4.27929i	0.0771351	−	0.733892i
$35$	−2.04826	+	0.0234710i	−0.346219	+	0.00396732i
$36$	0.277194	+	3.64237i	0.0461990	+	0.607061i
$37$	−4.86137	−	3.53200i	−0.799205	−	0.580656i	0.111476	−	0.993767i	$-0.464442\pi$
$37$	−4.86137	−	3.53200i	−0.799205	−	0.580656i	−0.910681	+	0.413111i	$0.864442\pi$
$38$	−0.611478	+	5.81783i	−0.0991949	+	0.943776i
$39$	0.286177	+	3.15923i	0.0458250	+	0.505882i
$40$	6.23963	+	1.25173i	0.986573	+	0.197915i
$41$	2.26096	−	1.00664i	0.353103	−	0.157212i	−0.222517	−	0.974929i	$-0.571427\pi$
$41$	2.26096	−	1.00664i	0.353103	−	0.157212i	0.575620	+	0.817717i	$0.304761\pi$
$42$	1.36844	+	0.311504i	0.211154	+	0.0480661i
$43$	2.01308	+	3.48676i	0.306992	+	0.531725i	0.977703	−	0.209993i	$-0.0673443\pi$
$43$	2.01308	+	3.48676i	0.306992	+	0.531725i	−0.670711	+	0.741719i	$0.734011\pi$
$44$	−0.549883	−	1.69237i	−0.0828980	−	0.255134i
$45$	−6.17455	+	2.62202i	−0.920447	+	0.390868i
$46$	−0.178734	+	0.550087i	−0.0263529	+	0.0811060i
$47$	5.26308	−	1.11870i	0.767699	−	0.163179i	0.192615	−	0.981274i	$-0.438303\pi$
$47$	5.26308	−	1.11870i	0.767699	−	0.163179i	0.575083	+	0.818095i	$0.304970\pi$
$48$	−0.129068	−	0.0597036i	−0.0186294	−	0.00861748i
$49$	3.08041	−	5.33542i	0.440058	−	0.762203i
$50$	0.562952	+	4.38660i	0.0796134	+	0.620359i
$51$	8.42495	+	0.121174i	1.17973	+	0.0169678i
$52$	2.03724	+	0.907036i	0.282514	+	0.125783i
$53$	−3.46201	+	10.6550i	−0.475543	+	1.46357i	0.369680	+	0.929159i	$0.379467\pi$
$53$	−3.46201	+	10.6550i	−0.475543	+	1.46357i	−0.845223	+	0.534413i	$0.820533\pi$
$54$	4.53267	−	0.760783i	0.616819	−	0.103529i
$55$	2.62153	−	1.95093i	0.353487	−	0.263064i
$56$	1.74454	−	1.93751i	0.233124	−	0.258911i
$57$	−11.4540	−	0.164740i	−1.51712	−	0.0218203i
$58$	−5.57093	−	1.18414i	−0.731499	−	0.155485i
$59$	1.82813	−	0.813937i	0.238003	−	0.105966i	−0.284270	−	0.958744i	$-0.591751\pi$
$59$	1.82813	−	0.813937i	0.238003	−	0.105966i	0.522272	+	0.852779i	$0.325084\pi$
$60$	−0.506651	+	4.68858i	−0.0654084	+	0.605293i
$61$	11.5472	+	5.14113i	1.47846	+	0.658254i	0.978209	−	0.207624i	$-0.0665730\pi$
$61$	11.5472	+	5.14113i	1.47846	+	0.658254i	0.500255	+	0.865878i	$0.333240\pi$
$62$	−2.10391	−	1.52858i	−0.267197	−	0.194130i
$63$	−0.365752	+	2.72376i	−0.0460804	+	0.343162i
$64$	−4.15407	+	3.01811i	−0.519259	+	0.377264i
$65$	−0.381374	+	4.07745i	−0.0473037	+	0.505745i
$66$	−2.05823	+	0.881139i	−0.253351	+	0.108461i
$67$	8.34092	+	1.77292i	1.01901	+	0.216596i	0.686982	−	0.726675i	$-0.258935\pi$
$67$	8.34092	+	1.77292i	1.01901	+	0.216596i	0.332024	+	0.943271i	$0.392269\pi$
$68$	2.96168	−	5.12978i	0.359156	−	0.622077i
$69$	−1.10436	−	0.251391i	−0.132949	−	0.0302639i
$70$	1.66353	+	0.717926i	0.198830	+	0.0858086i
$71$	5.09668	−	15.6860i	0.604865	−	1.86158i	0.107148	−	0.994243i	$-0.465828\pi$
$71$	5.09668	−	15.6860i	0.604865	−	1.86158i	0.497717	−	0.867340i	$-0.334172\pi$
$72$	2.87087	−	8.04101i	0.338336	−	0.947642i
$73$	−2.01962	+	1.46734i	−0.236378	+	0.171739i	−0.699668	−	0.714468i	$-0.746669\pi$
$73$	−2.01962	+	1.46734i	−0.236378	+	0.171739i	0.463290	+	0.886207i	$0.346669\pi$
$74$	2.65752	+	4.60296i	0.308931	+	0.535083i
$75$	−8.45533	+	1.87280i	−0.976337	+	0.216253i
$76$	−4.02650	+	6.97410i	−0.461871	+	0.799984i
$77$	−0.139938	−	1.33142i	−0.0159474	−	0.151729i
$78$	0.905335	−	2.65576i	0.102509	−	0.300705i
$79$	−6.05809	+	1.28769i	−0.681589	+	0.144876i	−0.535679	−	0.844422i	$-0.679944\pi$
$79$	−6.05809	+	1.28769i	−0.681589	+	0.144876i	−0.145910	+	0.989298i	$0.546611\pi$
$80$	−0.149754	−	0.106203i	−0.0167430	−	0.0118738i
$81$	2.28442	+	8.70525i	0.253825	+	0.967250i
$82$	−2.18911			−0.241747
$83$	2.67975	−	2.97617i	0.294141	−	0.326677i	−0.577902	−	0.816106i	$-0.696128\pi$
$83$	2.67975	−	2.97617i	0.294141	−	0.326677i	0.872043	+	0.489430i	$0.162795\pi$
$84$	1.54652	+	1.15796i	0.168739	+	0.126344i
$85$	10.6652	+	2.13954i	1.15680	+	0.232065i
$86$	−0.372247	−	3.54169i	−0.0401404	−	0.381910i
$87$	1.32516	−	11.0737i	0.142072	−	1.18722i
$88$	−0.434758	+	4.13645i	−0.0463454	+	0.440947i
$89$	−11.4149	+	8.29340i	−1.20998	+	0.879098i	−0.995229	−	0.0975715i	$-0.968893\pi$
$89$	−11.4149	+	8.29340i	−1.20998	+	0.879098i	−0.214746	+	0.976670i	$0.568893\pi$
$90$	5.93262	+	0.102674i	0.625353	+	0.0108228i
$91$	1.35732	+	0.986149i	0.142285	+	0.103376i
$92$	−0.532779	+	0.591712i	−0.0555461	+	0.0616902i
$93$	2.60938	−	4.37310i	0.270580	−	0.453469i
$94$	−4.65527	−	0.989508i	−0.480155	−	0.102060i
$95$	−14.4997	−	2.90877i	−1.48764	−	0.298433i
$96$	−6.40809	−	7.32609i	−0.654023	−	0.747716i
$97$	−5.89193	+	1.25237i	−0.598235	+	0.127159i	−0.497069	−	0.867711i	$-0.665591\pi$
$97$	−5.89193	+	1.25237i	−0.598235	+	0.127159i	−0.101166	+	0.994870i	$0.532257\pi$
$98$	−4.40860	+	3.20304i	−0.445336	+	0.323556i
$99$	−2.08201	−	3.85832i	−0.209250	−	0.387776i
$100$	−1.74817	+	5.83178i	−0.174817	+	0.583178i
$101$	−1.94183	−	3.36335i	−0.193219	−	0.334666i	0.753096	−	0.657911i	$-0.228560\pi$
$101$	−1.94183	−	3.36335i	−0.193219	−	0.334666i	−0.946315	+	0.323245i	$0.895226\pi$
$102$	−6.76414	−	3.12891i	−0.669750	−	0.309809i
$103$	−8.86425	−	9.84474i	−0.873420	−	0.970031i	0.126339	−	0.991987i	$-0.459677\pi$
$103$	−8.86425	−	9.84474i	−0.873420	−	0.970031i	−0.999759	+	0.0219558i	$0.993011\pi$
$104$	−3.48777	−	3.87356i	−0.342004	−	0.379834i
$105$	−1.10623	+	3.37106i	−0.107957	+	0.328981i
$106$	6.63074	−	7.36418i	0.644034	−	0.715273i
$107$	0.575014			0.0555887			0.0277944	−	0.999614i	$-0.491152\pi$
$107$	0.575014			0.0555887			0.0277944	+	0.999614i	$0.491152\pi$
$108$	6.12625	+	1.58117i	0.589499	+	0.152148i
$109$	10.4238	+	7.57330i	0.998415	+	0.725391i	0.961748	−	0.273936i	$-0.0883258\pi$
$109$	10.4238	+	7.57330i	0.998415	+	0.725391i	0.0366673	+	0.999328i	$0.488326\pi$
$110$	−2.82019	+	0.633309i	−0.268895	+	0.0603836i
$111$	−8.50726	+	5.99587i	−0.807473	+	0.569103i
$112$	−0.0687104	+	0.0305919i	−0.00649253	+	0.00289066i
$113$	6.68184	−	2.97495i	0.628575	−	0.279859i	−0.0676216	−	0.997711i	$-0.521541\pi$
$113$	6.68184	−	2.97495i	0.628575	−	0.279859i	0.696196	+	0.717852i	$0.254874\pi$
$114$	9.19607	+	4.25386i	0.861291	+	0.398411i
$115$	−1.34251	−	0.579383i	−0.125190	−	0.0540278i
$116$	−6.34297	−	4.60843i	−0.588930	−	0.427882i
$117$	5.33921	+	1.29643i	0.493610	+	0.119855i
$118$	−1.77004			−0.162945
$119$	2.98189	−	3.31172i	0.273349	−	0.303585i
$120$	5.53922	−	9.52977i	0.505660	−	0.869945i
$121$	−5.93137	−	6.58745i	−0.539215	−	0.598859i
$122$	−7.48103	−	8.30853i	−0.677301	−	0.752219i
$123$	−0.386726	−	4.26923i	−0.0348699	−	0.384943i
$124$	−1.78999	−	3.10036i	−0.160746	−	0.278420i
$125$	−11.1737	+	0.384254i	−0.999409	+	0.0343687i
$126$	1.27546	−	2.06934i	0.113627	−	0.184351i
$127$	8.89523	−	6.46276i	0.789324	−	0.573477i	−0.118439	−	0.992961i	$-0.537789\pi$
$127$	8.89523	−	6.46276i	0.789324	−	0.573477i	0.907763	+	0.419484i	$0.137789\pi$
$128$	−6.55086	+	1.39243i	−0.579019	+	0.123074i
$129$	6.84127	−	1.35163i	0.602340	−	0.119004i
$130$	1.77509	−	3.15756i	0.155686	−	0.276936i
$131$	−9.44760	−	2.00815i	−0.825441	−	0.175453i	−0.224223	−	0.974538i	$-0.571984\pi$
$131$	−9.44760	−	2.00815i	−0.825441	−	0.175453i	−0.601218	+	0.799085i	$0.705318\pi$
$132$	−3.08179	−	0.0443247i	−0.268236	−	0.00385797i
$133$	−4.05397	+	4.50239i	−0.351524	+	0.390407i
$134$	−6.10200	−	4.43336i	−0.527133	−	0.382984i
$135$	0.847812	+	11.5880i	0.0729681	+	0.997334i
$136$	−11.2009	+	8.13790i	−0.960465	+	0.697819i
$137$	−2.04237	+	19.4319i	−0.174492	+	1.66018i	0.460501	+	0.887659i	$0.347670\pi$
$137$	−2.04237	+	19.4319i	−0.174492	+	1.66018i	−0.634992	+	0.772518i	$0.718997\pi$
$138$	0.801930	+	0.600445i	0.0682648	+	0.0511133i
$139$	−1.68243	−	16.0073i	−0.142702	−	1.35772i	−0.798140	−	0.602472i	$-0.794183\pi$
$139$	−1.68243	−	16.0073i	−0.142702	−	1.35772i	0.655438	−	0.755249i	$-0.272484\pi$
$140$	1.69007	+	1.83430i	0.142837	+	0.155027i
$141$	1.10735	−	9.25355i	0.0932559	−	0.779289i
$142$	−9.76161	+	10.8414i	−0.819176	+	0.909787i
$143$	−2.67649			−0.223820
$144$	−0.170011	+	0.178230i	−0.0141676	+	0.0148525i
$145$	4.29204	−	13.7434i	0.356435	−	1.14133i
$146$	2.15984	−	0.459087i	0.178749	−	0.0379943i
$147$	−7.02541	−	8.03185i	−0.579446	−	0.662456i
$148$	0.764808	+	7.27666i	0.0628668	+	0.598138i
$149$	−5.73913	+	9.94047i	−0.470168	+	0.814355i	−0.999418	−	0.0341109i	$-0.989140\pi$
$149$	−5.73913	+	9.94047i	−0.470168	+	0.814355i	0.529250	+	0.848466i	$0.322473\pi$
$150$	7.50605	+	1.52862i	0.612867	+	0.124811i
$151$	7.22503	+	12.5141i	0.587964	+	1.01838i	0.994499	+	0.104749i	$0.0334038\pi$
$151$	7.22503	+	12.5141i	0.587964	+	1.01838i	−0.406534	+	0.913636i	$0.633263\pi$
$152$	15.2279	−	11.0637i	1.23515	−	0.897387i
$153$	4.90709	−	13.7442i	0.396715	−	1.11116i
$154$	−0.365921	+	1.12619i	−0.0294868	+	0.0907510i
$155$	4.34280	−	4.93574i	0.348822	−	0.396448i
$156$	2.62555	−	2.83295i	0.210212	−	0.226818i
$157$	−11.2855	+	19.5471i	−0.900683	+	1.56003i	−0.0740732	+	0.997253i	$0.523600\pi$
$157$	−11.2855	+	19.5471i	−0.900683	+	1.56003i	−0.826610	+	0.562776i	$0.809733\pi$
$158$	5.35848	+	1.13898i	0.426298	+	0.0906123i
$159$	15.5331	+	11.6304i	1.23185	+	0.922348i
$160$	−6.40703	−	10.8093i	−0.506520	−	0.854554i
$161$	−0.484626	+	0.352101i	−0.0381939	+	0.0277495i
$162$	1.28593	−	7.85609i	0.101032	−	0.617233i
$163$	13.3225	+	9.67938i	1.04350	+	0.758148i	0.970966	−	0.239218i	$-0.0768910\pi$
$163$	13.3225	+	9.67938i	1.04350	+	0.758148i	0.0725352	+	0.997366i	$0.476891\pi$
$164$	−2.75302	−	1.22572i	−0.214975	−	0.0957130i
$165$	−1.73330	−	5.38808i	−0.134937	−	0.419461i
$166$	−3.23608	+	1.44080i	−0.251168	+	0.111827i
$167$	20.1378	+	4.28042i	1.55831	+	0.331229i	0.904850	−	0.425731i	$-0.139983\pi$
$167$	20.1378	+	4.28042i	1.55831	+	0.331229i	0.653461	+	0.756960i	$0.273316\pi$
$168$	−2.20141	−	3.94283i	−0.169842	−	0.304196i
$169$	−6.45429	+	7.16822i	−0.496484	+	0.551402i
$170$	−7.84823	−	5.56580i	−0.601932	−	0.426878i
$171$	−6.67134	+	18.6857i	−0.510170	+	1.42893i
$172$	1.51492	−	4.66244i	0.115512	−	0.355508i
$173$	20.0490	+	8.92638i	1.52430	+	0.678660i	0.986402	−	0.164352i	$-0.0525533\pi$
$173$	20.0490	+	8.92638i	1.52430	+	0.678660i	0.537894	+	0.843012i	$0.319220\pi$
$174$	−5.05470	+	8.47127i	−0.383196	+	0.642205i
$175$	−2.19868	+	4.01814i	−0.166204	+	0.303743i
$176$	0.0599937	−	0.103912i	0.00452219	−	0.00783267i
$177$	−0.312693	−	3.45194i	−0.0235034	−	0.259464i
$178$	12.2074	−	2.59476i	0.914984	−	0.194486i
$179$	−3.58817	+	11.0432i	−0.268192	+	0.825410i	0.722749	+	0.691111i	$0.242878\pi$
$179$	−3.58817	+	11.0432i	−0.268192	+	0.825410i	−0.990941	+	0.134299i	$0.957122\pi$
$180$	7.40335	+	3.45090i	0.551813	+	0.257215i
$181$	4.13289	+	12.7197i	0.307196	+	0.945451i	0.978849	+	0.204585i	$0.0655845\pi$
$181$	4.13289	+	12.7197i	0.307196	+	0.945451i	−0.671653	+	0.740866i	$0.734415\pi$
$182$	−0.741991	−	1.28517i	−0.0550001	−	0.0952629i
$183$	14.8818	−	16.0573i	1.10009	−	1.18699i
$184$	1.70017	−	0.756964i	0.125338	−	0.0558041i
$185$	−12.2114	+	5.60541i	−0.897803	+	0.412118i
$186$	−3.68178	+	2.59490i	−0.269961	+	0.190267i
$187$	−0.743118	+	7.07029i	−0.0543422	+	0.517031i
$188$	−5.30041	−	3.85097i	−0.386572	−	0.280861i
$189$	4.26096	+	2.12184i	0.309939	+	0.154341i
$190$	10.6699	+	7.56689i	0.774078	+	0.548960i
$191$	−0.737405	+	7.01594i	−0.0533568	+	0.507656i	0.934906	+	0.354895i	$0.115483\pi$
$191$	−0.737405	+	7.01594i	−0.0533568	+	0.507656i	−0.988263	+	0.152761i	$0.951183\pi$
$192$	2.62634	+	8.49695i	0.189540	+	0.613214i
$193$	−2.80358	+	4.85594i	−0.201806	+	0.349538i	−0.949110	−	0.314944i	$-0.898014\pi$
$193$	−2.80358	+	4.85594i	−0.201806	+	0.349538i	0.747304	+	0.664482i	$0.231348\pi$
$194$	5.21151	+	1.10774i	0.374164	+	0.0795311i
$195$	6.47148	+	2.90398i	0.463432	+	0.207959i
$196$	−7.33768	+	1.55967i	−0.524120	+	0.111405i
$197$	0.644829	−	1.98458i	0.0459422	−	0.141395i	−0.925454	−	0.378860i	$-0.876316\pi$
$197$	0.644829	−	1.98458i	0.0459422	−	0.141395i	0.971396	+	0.237464i	$0.0763163\pi$
$198$	0.294268	+	3.86673i	0.0209127	+	0.274797i
$199$	3.06579			0.217328			0.108664	−	0.994079i	$-0.465343\pi$
$199$	3.06579			0.217328			0.108664	+	0.994079i	$0.465343\pi$
$200$	9.27705	−	10.7905i	0.655987	−	0.763006i
$201$	7.56801	−	12.6834i	0.533806	−	0.894615i
$202$	0.359072	+	3.41634i	0.0252642	+	0.240373i
$203$	−3.94692	−	4.38349i	−0.277019	−	0.307661i
$204$	−6.75463	−	7.72228i	−0.472919	−	0.540668i
$205$	0.515371	−	5.51006i	0.0359950	−	0.384840i
$206$	3.62092	+	11.1440i	0.252281	+	0.776442i
$207$	−1.02932	+	1.67000i	−0.0715430	+	0.116073i
$208$	0.0464667	+	0.143010i	0.00322188	+	0.00991594i
$209$	1.01029	−	9.61229i	0.0698834	−	0.664896i
$210$	2.10667	−	2.32598i	0.145374	−	0.160508i
$211$	0.214854	+	2.04420i	0.0147911	+	0.140728i	0.999425	−	0.0339024i	$-0.0107935\pi$
$211$	0.214854	+	2.04420i	0.0147911	+	0.140728i	−0.984634	+	0.174631i	$0.944127\pi$
$212$	12.4621	−	5.54850i	0.855903	−	0.381072i
$213$	−22.8674	−	17.1219i	−1.56685	−	1.17318i
$214$	−0.464637	−	0.206870i	−0.0317619	−	0.0141413i
$215$	9.00217	−	0.103156i	0.613943	−	0.00703517i
$216$	−11.5781	−	9.20040i	−0.787788	−	0.626008i
$217$	−0.832292	−	2.56153i	−0.0564996	−	0.173888i
$218$	−5.69826	−	9.86967i	−0.385935	−	0.668458i
$219$	1.27687	+	4.13103i	0.0862829	+	0.279149i
$220$	−3.90126	−	0.782628i	−0.263023	−	0.0527648i
$221$	−5.96153	−	6.62095i	−0.401016	−	0.445373i
$222$	9.03135	−	1.78432i	0.606144	−	0.119756i
$223$	−20.7361	−	9.23232i	−1.38859	−	0.618242i	−0.429950	−	0.902852i	$-0.641469\pi$
$223$	−20.7361	−	9.23232i	−1.38859	−	0.618242i	−0.958643	+	0.284611i	$0.908136\pi$
$224$	−5.14783			−0.343954
$225$	−1.65512	+	14.9084i	−0.110341	+	0.993894i
$226$	−6.46951			−0.430345
$227$	6.01094	+	2.67624i	0.398960	+	0.177628i	0.596401	−	0.802686i	$-0.296597\pi$
$227$	6.01094	+	2.67624i	0.398960	+	0.177628i	−0.197442	+	0.980315i	$0.563263\pi$
$228$	9.18314	+	10.4987i	0.608168	+	0.695293i
$229$	4.35897	+	4.84112i	0.288049	+	0.319910i	0.869751	−	0.493492i	$-0.164280\pi$
$229$	4.35897	+	4.84112i	0.288049	+	0.319910i	−0.581702	+	0.813402i	$0.697613\pi$
$230$	0.876365	+	0.951155i	0.0577858	+	0.0627173i
$231$	−2.26095	−	0.514671i	−0.148759	−	0.0338629i
$232$	9.16284	+	15.8705i	0.601570	+	1.04195i
$233$	1.15048	+	3.54081i	0.0753703	+	0.231966i	0.981643	−	0.190727i	$-0.0610847\pi$
$233$	1.15048	+	3.54081i	0.0753703	+	0.231966i	−0.906273	+	0.422694i	$0.861085\pi$
$234$	−3.84791	−	2.96843i	−0.251546	−	0.194052i
$235$	3.58659	−	11.4845i	0.233963	−	0.749166i
$236$	−2.22599	−	0.991077i	−0.144900	−	0.0645136i
$237$	−1.27462	+	10.6514i	−0.0827958	+	0.691880i
$238$	−3.60094	+	1.60324i	−0.233414	+	0.103923i
$239$	0.596567	+	5.67596i	0.0385887	+	0.367147i	0.996727	+	0.0808412i	$0.0257607\pi$
$239$	0.596567	+	5.67596i	0.0385887	+	0.367147i	−0.958138	+	0.286306i	$0.907573\pi$
$240$	−0.257802	+	0.186155i	−0.0166411	+	0.0120163i
$241$	3.12340	−	29.7171i	0.201196	−	1.91425i	−0.169563	−	0.985519i	$-0.554236\pi$
$241$	3.12340	−	29.7171i	0.201196	−	1.91425i	0.370759	−	0.928729i	$-0.379098\pi$
$242$	2.42288	+	7.45685i	0.155748	+	0.479345i
$243$	15.5482	+	1.11998i	0.997416	+	0.0718468i
$244$	−4.75602	−	14.6375i	−0.304473	−	0.937072i
$245$	−7.02425	−	11.8507i	−0.448763	−	0.757111i
$246$	−1.22342	+	3.58886i	−0.0780027	+	0.228817i
$247$	8.10489	+	9.00139i	0.515702	+	0.572745i
$248$	0.874663	+	8.32186i	0.0555412	+	0.528439i
$249$	−3.38153	−	6.05650i	−0.214296	−	0.383815i
$250$	9.16712	+	3.70942i	0.579780	+	0.234604i
$251$	−4.00907			−0.253050			−0.126525	−	0.991963i	$-0.540382\pi$
$251$	−4.00907			−0.253050			−0.126525	+	0.991963i	$0.540382\pi$
$252$	2.76267	−	1.88824i	0.174032	−	0.118948i
$253$	0.295307	−	0.908862i	0.0185658	−	0.0571397i
$254$	−9.51282	+	2.02201i	−0.596887	+	0.126872i
$255$	9.46801	−	16.2889i	0.592910	−	1.02005i
$256$	15.8393	+	3.36676i	0.989959	+	0.210422i
$257$	−5.23224	+	9.06250i	−0.326378	+	0.565303i	−0.981790	−	0.189968i	$-0.939162\pi$
$257$	−5.23224	+	9.06250i	−0.326378	+	0.565303i	0.655412	+	0.755271i	$0.272495\pi$
$258$	−6.01432	−	1.36907i	−0.374435	−	0.0852346i
$259$	−0.575393	+	5.47450i	−0.0357532	+	0.340169i
$260$	4.00032	−	2.97703i	0.248089	−	0.184627i
$261$	−17.4137	−	8.36120i	−1.07788	−	0.517545i
$262$	6.91162	+	5.02159i	0.427001	+	0.310235i
$263$	1.04740	−	9.96535i	0.0645855	−	0.614490i	−0.913580	−	0.406660i	$-0.866693\pi$
$263$	1.04740	−	9.96535i	0.0645855	−	0.614490i	0.978165	−	0.207830i	$-0.0666400\pi$
$264$	6.53836	+	3.02447i	0.402408	+	0.186144i
$265$	16.9748	+	18.4235i	1.04276	+	1.13175i
$266$	4.89559	−	2.17966i	0.300168	−	0.133643i
$267$	7.21687	+	23.3486i	0.441665	+	1.42891i
$268$	−5.19154	−	8.99200i	−0.317124	−	0.549274i
$269$	6.60992	+	20.3433i	0.403014	+	1.24035i	0.922542	+	0.385896i	$0.126108\pi$
$269$	6.60992	+	20.3433i	0.403014	+	1.24035i	−0.519528	+	0.854453i	$0.673892\pi$
$270$	3.48388	−	9.66862i	0.212022	−	0.588413i
$271$	2.51483	−	7.73984i	0.152765	−	0.470162i	−0.845163	−	0.534509i	$-0.820497\pi$
$271$	2.51483	−	7.73984i	0.152765	−	0.470162i	0.997928	+	0.0643473i	$0.0204965\pi$
$272$	0.390679	−	0.0830414i	0.0236884	−	0.00503512i
$273$	2.37526	−	1.67407i	0.143757	−	0.101320i
$274$	8.64124	−	14.9671i	0.522036	−	0.904193i
$275$	−0.930116	−	7.24760i	−0.0560881	−	0.437047i
$276$	0.672305	+	1.20413i	0.0404680	+	0.0724803i
$277$	0.0811277	+	0.0361204i	0.00487449	+	0.00217026i	0.409172	−	0.912457i	$-0.365817\pi$
$277$	0.0811277	+	0.0361204i	0.00487449	+	0.00217026i	−0.404298	+	0.914627i	$0.632484\pi$
$278$	−4.39938	+	13.5399i	−0.263857	+	0.812069i
$279$	−5.71101	−	6.72182i	−0.341909	−	0.402425i
$280$	−1.86493	−	5.52349i	−0.111451	−	0.330091i
$281$	−13.6010	+	15.1054i	−0.811365	+	0.901112i	−0.996668	−	0.0815694i	$-0.974007\pi$
$281$	−13.6010	+	15.1054i	−0.811365	+	0.901112i	0.185303	+	0.982681i	$0.440673\pi$
$282$	−4.22389	+	7.07890i	−0.251529	+	0.421542i
$283$	−27.2002	−	5.78158i	−1.61688	−	0.343679i	−0.691402	−	0.722471i	$-0.743007\pi$
$283$	−27.2002	−	5.78158i	−1.61688	−	0.343679i	−0.925482	+	0.378791i	$0.876340\pi$
$284$	−18.3464	+	8.16836i	−1.08866	+	0.484703i
$285$	−12.8721	+	22.1453i	−0.762476	+	1.31178i
$286$	2.16273	+	0.962908i	0.127885	+	0.0569380i
$287$	−1.83421	−	1.33263i	−0.108270	−	0.0786628i
$288$	−15.5918	+	6.41117i	−0.918753	+	0.377782i
$289$	−5.39197	+	3.91749i	−0.317174	+	0.230441i
$290$	−8.41257	+	9.56118i	−0.494003	+	0.561452i
$291$	−1.23966	+	10.3592i	−0.0726704	+	0.607268i
$292$	2.97325	+	0.631985i	0.173997	+	0.0369841i
$293$	−5.17974	+	8.97157i	−0.302604	+	0.524125i	−0.976725	−	0.214496i	$-0.931189\pi$
$293$	−5.17974	+	8.97157i	−0.302604	+	0.524125i	0.674121	+	0.738621i	$0.264523\pi$
$294$	2.78727	+	9.01759i	0.162557	+	0.525916i
$295$	0.416710	−	4.45524i	0.0242618	−	0.259394i
$296$	5.28476	−	16.2648i	0.307171	−	0.945374i
$297$	−7.48894	+	1.25698i	−0.434552	+	0.0729371i
$298$	8.21371	−	5.96761i	0.475807	−	0.345694i
$299$	0.598805	+	1.03716i	0.0346298	+	0.0599805i
$300$	8.58368	+	6.12516i	0.495579	+	0.353636i
$301$	1.84412	−	3.19411i	0.106293	−	0.184106i
$302$	−1.33601	−	12.7113i	−0.0768787	−	0.731452i
$303$	−6.59913	+	1.30379i	−0.379110	+	0.0749008i
$304$	−0.531141	+	0.112897i	−0.0304630	+	0.00647511i
$305$	22.6740	−	16.8739i	1.29831	−	0.966200i
$306$	−8.90984	+	9.34056i	−0.509342	+	0.533964i
$307$	−26.4065			−1.50710			−0.753550	−	0.657391i	$-0.771660\pi$
$307$	−26.4065			−1.50710			−0.753550	+	0.657391i	$0.771660\pi$
$308$	−1.09076	+	1.21141i	−0.0621515	+	0.0690263i
$309$	−21.0935	+	9.03023i	−1.19997	+	0.513712i
$310$	−5.28488	+	2.42592i	−0.300161	+	0.137783i
$311$	0.852094	+	8.10713i	0.0483178	+	0.459713i	0.991754	+	0.128158i	$0.0409066\pi$
$311$	0.852094	+	8.10713i	0.0483178	+	0.459713i	−0.943436	+	0.331555i	$0.892427\pi$
$312$	−8.29956	+	3.55308i	−0.469870	+	0.201153i
$313$	3.04832	−	29.0029i	0.172301	−	1.63934i	−0.477069	−	0.878866i	$-0.658301\pi$
$313$	3.04832	−	29.0029i	0.172301	−	1.63934i	0.649370	−	0.760472i	$-0.275032\pi$
$314$	16.1516	−	11.7348i	0.911486	−	0.662233i
$315$	4.90831	+	3.69754i	0.276552	+	0.208333i
$316$	6.10107	+	4.43268i	0.343212	+	0.249358i
$317$	−7.21022	+	8.00776i	−0.404966	+	0.449761i	−0.910786	−	0.412878i	$-0.864523\pi$
$317$	−7.21022	+	8.00776i	−0.404966	+	0.449761i	0.505820	+	0.862639i	$0.331190\pi$
$318$	−8.36721	−	14.9861i	−0.469210	−	0.840379i
$319$	9.20437	+	1.95645i	0.515346	+	0.109540i
$320$	1.33091	+	11.4042i	0.0744001	+	0.637512i
$321$	0.321357	−	0.942684i	0.0179364	−	0.0526155i
$322$	0.518273	−	0.110162i	0.0288822	−	0.00613910i
$323$	26.0286	−	18.9109i	1.44827	−	1.05223i
$324$	6.01594	−	9.15977i	0.334219	−	0.508876i
$325$	7.52976	+	5.21132i	0.417676	+	0.289072i
$326$	−7.28290	−	12.6144i	−0.403362	−	0.698644i
$327$	18.2413	−	12.8563i	1.00874	−	0.710958i
$328$	4.71320	+	5.23454i	0.260243	+	0.289029i
$329$	−3.29818	−	3.66300i	−0.181835	−	0.201948i
$330$	−0.537860	+	4.97739i	−0.0296082	+	0.273996i
$331$	10.0456	−	11.1567i	0.552154	−	0.613229i	−0.400866	−	0.916137i	$-0.631291\pi$
$331$	10.0456	−	11.1567i	0.552154	−	0.613229i	0.953020	+	0.302908i	$0.0979574\pi$
$332$	−4.87641			−0.267628
$333$	5.07526	+	17.2978i	0.278123	+	0.947913i
$334$	−14.7323	−	10.7036i	−0.806116	−	0.585678i
$335$	12.5955	−	14.3152i	0.688164	−	0.782123i
$336$	0.0117526	+	0.129741i	0.000641155	+	0.00707798i
$337$	1.21087	−	0.539114i	0.0659603	−	0.0293674i	−0.373491	−	0.927634i	$-0.621839\pi$
$337$	1.21087	−	0.539114i	0.0659603	−	0.0293674i	0.439452	+	0.898266i	$0.355173\pi$
$338$	7.79423	−	3.47022i	0.423950	−	0.188755i
$339$	−1.14289	−	12.6169i	−0.0620735	−	0.685255i
$340$	−6.75352	−	11.3939i	−0.366261	−	0.617921i
$341$	3.47611	+	2.52554i	0.188242	+	0.136766i
$342$	12.1132	−	12.6988i	0.655007	−	0.686672i
$343$	−12.0562			−0.650975
$344$	−7.66732	+	8.51542i	−0.413394	+	0.459121i
$345$	−1.70013	+	1.87712i	−0.0915320	+	0.101061i
$346$	−12.9891	−	14.4258i	−0.698297	−	0.775538i
$347$	−5.31615	−	5.90418i	−0.285386	−	0.316953i	0.583358	−	0.812215i	$-0.301739\pi$
$347$	−5.31615	−	5.90418i	−0.285386	−	0.316953i	−0.868743	+	0.495262i	$0.835072\pi$
$348$	−11.1000	+	7.82322i	−0.595022	+	0.419369i
$349$	6.48550	+	11.2332i	0.347161	+	0.601300i	0.985744	−	0.168253i	$-0.0538124\pi$
$349$	6.48550	+	11.2332i	0.347161	+	0.601300i	−0.638583	+	0.769553i	$0.720479\pi$
$350$	3.22221	−	2.45583i	0.172235	−	0.131270i
$351$	5.10929	−	8.02862i	0.272714	−	0.428536i
$352$	6.64392	−	4.82709i	0.354122	−	0.257285i
$353$	−4.30300	+	0.914630i	−0.229025	+	0.0486809i	−0.320995	−	0.947081i	$-0.604017\pi$
$353$	−4.30300	+	0.914630i	−0.229025	+	0.0486809i	0.0919693	+	0.995762i	$0.470684\pi$
$354$	−0.989217	+	2.90182i	−0.0525763	+	0.154230i
$355$	−24.9899	−	27.1226i	−1.32633	−	1.43952i
$356$	16.8048	+	3.57198i	0.890655	+	0.189315i
$357$	−3.76279	−	6.73935i	−0.199148	−	0.356684i
$358$	6.87237	−	7.63253i	0.363216	−	0.403392i
$359$	11.0737	+	8.04552i	0.584448	+	0.424627i	0.840325	−	0.542083i	$-0.182364\pi$
$359$	11.0737	+	8.04552i	0.584448	+	0.424627i	−0.255877	+	0.966709i	$0.582364\pi$
$360$	−12.5275	−	14.4069i	−0.660258	−	0.759313i
$361$	−20.0154	+	14.5420i	−1.05344	+	0.765370i
$362$	1.23655	−	11.7650i	0.0649916	−	0.618354i
$363$	−14.1144	+	6.04243i	−0.740813	+	0.317145i
$364$	−0.213538	−	2.03168i	−0.0111924	−	0.106489i
$365$	0.647059	+	5.54445i	0.0338686	+	0.290210i
$366$	−17.8020	+	7.62111i	−0.930525	+	0.398362i
$367$	3.50752	−	3.89550i	0.183091	−	0.203343i	−0.644611	−	0.764510i	$-0.722981\pi$
$367$	3.50752	−	3.89550i	0.183091	−	0.203343i	0.827703	+	0.561167i	$0.189648\pi$
$368$	−0.0536889			−0.00279873
$369$	−7.21514	−	1.75193i	−0.375605	−	0.0912018i
$370$	11.8840	−	0.136179i	0.617821	−	0.00707960i
$371$	10.0387	−	2.13380i	0.521185	−	0.110781i
$372$	−6.08312	+	1.20184i	−0.315395	+	0.0623126i
$373$	−0.885927	−	8.42903i	−0.0458716	−	0.436439i	−0.993221	−	0.116238i	$-0.962916\pi$
$373$	−0.885927	−	8.42903i	−0.0458716	−	0.436439i	0.947350	−	0.320201i	$-0.103750\pi$
$374$	3.14411	−	5.44577i	0.162578	−	0.281594i
$375$	−5.61469	+	18.5331i	−0.289941	+	0.957044i
$376$	7.65680	+	13.2620i	0.394869	+	0.683933i
$377$	−9.54050	+	6.93158i	−0.491361	+	0.356994i
$378$	−2.67968	−	3.24748i	−0.137828	−	0.167033i
$379$	−7.97105	+	24.5324i	−0.409445	+	1.26014i	0.507680	+	0.861545i	$0.330503\pi$
$379$	−7.97105	+	24.5324i	−0.409445	+	1.26014i	−0.917126	+	0.398598i	$0.869497\pi$
$380$	9.18162	+	15.4904i	0.471007	+	0.794640i
$381$	−5.62386	−	18.1948i	−0.288119	−	0.932146i
$382$	3.11995	−	5.40390i	0.159630	−	0.276488i
$383$	7.46117	+	1.58592i	0.381248	+	0.0810367i	0.394549	−	0.918875i	$-0.370901\pi$
$383$	7.46117	+	1.58592i	0.381248	+	0.0810367i	−0.0133014	+	0.999912i	$0.504234\pi$
$384$	−1.37830	+	11.5177i	−0.0703362	+	0.587761i
$385$	−2.74851	−	1.18617i	−0.140077	−	0.0604527i
$386$	4.01241	−	2.91519i	0.204226	−	0.148379i
$387$	1.60749	−	11.9710i	0.0817133	−	0.608522i
$388$	5.93373	+	4.31110i	0.301239	+	0.218863i
$389$	−32.4386	−	14.4426i	−1.64470	−	0.732268i	−0.645204	−	0.764011i	$-0.723228\pi$
$389$	−32.4386	−	14.4426i	−1.64470	−	0.732268i	−0.999496	+	0.0317430i	$0.989894\pi$
$390$	−4.18449	−	4.67476i	−0.211890	−	0.236716i
$391$	2.90604	−	1.29385i	0.146965	−	0.0654330i
$392$	17.1508	+	3.64552i	0.866246	+	0.184126i
$393$	−8.57214	+	14.3662i	−0.432407	+	0.724679i
$394$	−1.23503	+	1.37164i	−0.0622200	+	0.0691024i
$395$	−4.12836	+	13.2193i	−0.207720	+	0.665135i
$396$	−1.79498	+	5.02755i	−0.0902012	+	0.252644i
$397$	8.38450	−	25.8048i	0.420806	−	1.29511i	−0.486148	−	0.873877i	$-0.661598\pi$
$397$	8.38450	−	25.8048i	0.420806	−	1.29511i	0.906954	−	0.421230i	$-0.138402\pi$
$398$	−2.47729	−	1.10296i	−0.124176	−	0.0552865i
$399$	5.11564	+	9.16237i	0.256102	+	0.458692i
$400$	−0.371104	+	0.175523i	−0.0185552	+	0.00877617i
$401$	11.5052	−	19.9276i	0.574543	−	0.995138i	−0.421548	−	0.906806i	$-0.638513\pi$
$401$	11.5052	−	19.9276i	0.574543	−	0.995138i	0.996091	−	0.0883319i	$-0.0281536\pi$
$402$	−10.6783	+	7.52602i	−0.532586	+	0.375364i
$403$	−5.26701	+	1.11954i	−0.262368	+	0.0557681i
$404$	−1.46130	+	4.49742i	−0.0727025	+	0.223755i
$405$	19.4713	+	5.08623i	0.967535	+	0.252737i
$406$	1.61226	+	4.96202i	0.0800150	+	0.246261i
$407$	−4.39079	−	7.60507i	−0.217643	−	0.376970i
$408$	7.08156	+	22.9108i	0.350589	+	1.13425i
$409$	16.5641	−	7.37483i	0.819044	−	0.364662i	0.0459421	−	0.998944i	$-0.485371\pi$
$409$	16.5641	−	7.37483i	0.819044	−	0.364662i	0.773101	+	0.634282i	$0.218704\pi$
$410$	−2.39877	+	4.26697i	−0.118467	+	0.210730i
$411$	30.7154	+	14.2081i	1.51508	+	0.700836i
$412$	−1.68609	+	16.0421i	−0.0830679	+	0.790338i
$413$	−1.48308	−	1.07752i	−0.0729775	−	0.0530212i
$414$	1.43255	−	0.979124i	0.0704059	−	0.0481213i
$415$	−2.86467	−	8.48451i	−0.140621	−	0.416488i
$416$	−1.07578	+	10.2354i	−0.0527446	+	0.501831i
$417$	−27.1828	−	6.18776i	−1.33115	−	0.303016i
$418$	−4.27453	+	7.40370i	−0.209074	+	0.362127i
$419$	3.16469	+	0.672676i	0.154605	+	0.0328624i	0.284564	−	0.958657i	$-0.408151\pi$
$419$	3.16469	+	0.672676i	0.154605	+	0.0328624i	−0.129959	+	0.991519i	$0.541484\pi$
$420$	3.95170	−	1.74559i	0.192823	−	0.0851759i
$421$	10.1780	−	2.16341i	0.496047	−	0.105438i	0.0469065	−	0.998899i	$-0.485064\pi$
$421$	10.1780	−	2.16341i	0.496047	−	0.105438i	0.449140	+	0.893461i	$0.351730\pi$
$422$	0.561818	−	1.72910i	0.0273489	−	0.0841712i
$423$	−14.5515	−	6.98692i	−0.707518	−	0.339715i
$424$	−31.8851			−1.54848
$425$	15.8570	−	18.4439i	0.769175	−	0.894661i
$426$	12.3180	+	22.0622i	0.596809	+	1.06892i
$427$	−1.21034	−	11.5156i	−0.0585726	−	0.557281i
$428$	−0.468496	−	0.520318i	−0.0226456	−	0.0251505i
$429$	−1.49581	+	4.38787i	−0.0722182	+	0.211849i
$430$	−7.31127	−	3.15531i	−0.352581	−	0.152163i
$431$	6.18249	+	19.0277i	0.297800	+	0.916534i	0.982267	+	0.187490i	$0.0600351\pi$
$431$	6.18249	+	19.0277i	0.297800	+	0.916534i	−0.684467	+	0.729044i	$0.739965\pi$
$432$	0.197178	+	0.378324i	0.00948673	+	0.0182021i
$433$	−1.29700	−	3.99175i	−0.0623297	−	0.191831i	0.915043	−	0.403357i	$-0.132157\pi$
$433$	−1.29700	−	3.99175i	−0.0623297	−	0.191831i	−0.977372	+	0.211526i	$0.932157\pi$
$434$	−0.249019	+	2.36926i	−0.0119533	+	0.113728i
$435$	−20.1324	−	14.7172i	−0.965277	−	0.705635i
$436$	−1.63990	−	15.6026i	−0.0785370	−	0.747230i
$437$	−3.95086	+	1.75904i	−0.188995	+	0.0841461i
$438$	0.454430	−	3.79743i	0.0217135	−	0.181448i
$439$	29.5520	+	13.1574i	1.41044	+	0.627969i	0.963771	−	0.266730i	$-0.0859431\pi$
$439$	29.5520	+	13.1574i	1.41044	+	0.627969i	0.446670	+	0.894699i	$0.352610\pi$
$440$	7.58626	+	5.38002i	0.361661	+	0.256482i
$441$	−17.0938	+	7.02879i	−0.813989	+	0.334704i
$442$	2.43520	+	7.49477i	0.115831	+	0.356490i
$443$	−0.881739	−	1.52722i	−0.0418927	−	0.0725602i	0.844319	−	0.535841i	$-0.180005\pi$
$443$	−0.881739	−	1.52722i	−0.0418927	−	0.0725602i	−0.886211	+	0.463281i	$0.846672\pi$
$444$	12.3569	+	2.81286i	0.586431	+	0.133492i
$445$	3.65718	+	31.3373i	0.173367	+	1.48553i
$446$	13.4343	+	14.9203i	0.636130	+	0.706494i
$447$	13.0891	+	14.9642i	0.619093	+	0.707783i
$448$	4.29709	+	1.91319i	0.203019	+	0.0903897i
$449$	4.06171			0.191684			0.0958420	−	0.995397i	$-0.469446\pi$
$449$	4.06171			0.191684			0.0958420	+	0.995397i	$0.469446\pi$
$450$	6.70093	−	11.4512i	0.315885	−	0.539815i
$451$	3.61688			0.170312
$452$	−8.13603	−	3.62239i	−0.382687	−	0.170383i
$453$	24.5536	−	4.85105i	1.15363	−	0.227922i
$454$	−3.89429	−	4.32504i	−0.182768	−	0.202984i
$455$	3.40949	−	1.56505i	0.159839	−	0.0733709i
$456$	−9.62761	−	31.1480i	−0.450854	−	1.45864i
$457$	−17.6151	−	30.5103i	−0.824002	−	1.42721i	−0.902680	−	0.430313i	$-0.858403\pi$
$457$	−17.6151	−	30.5103i	−0.824002	−	1.42721i	0.0786783	−	0.996900i	$-0.474930\pi$
$458$	−1.78057	−	5.48004i	−0.0832008	−	0.256066i
$459$	−19.7900	−	15.7259i	−0.923720	−	0.734024i
$460$	0.569545	+	1.68686i	0.0265552	+	0.0786503i
$461$	−0.00623691	−	0.00277685i	−0.000290482	−	0.000129331i	0.406591	−	0.913610i	$-0.366717\pi$
$461$	−0.00623691	−	0.00277685i	−0.000290482	−	0.000129331i	−0.406882	+	0.913481i	$0.633384\pi$
$462$	1.64179	+	1.22929i	0.0763828	+	0.0571916i
$463$	26.7037	−	11.8893i	1.24103	−	0.552541i	0.322001	−	0.946739i	$-0.395644\pi$
$463$	26.7037	−	11.8893i	1.24103	−	0.552541i	0.919025	+	0.394198i	$0.128978\pi$
$464$	−0.0552608	−	0.525771i	−0.00256542	−	0.0244083i
$465$	−5.66466	−	9.87805i	−0.262692	−	0.458084i
$466$	0.344220	−	3.27503i	0.0159457	−	0.151713i
$467$	−5.25864	−	16.1844i	−0.243341	−	0.748926i	−0.995905	−	0.0904068i	$-0.971183\pi$
$467$	−5.25864	−	16.1844i	−0.243341	−	0.748926i	0.752564	−	0.658519i	$-0.228817\pi$
$468$	−3.17704	−	5.88760i	−0.146859	−	0.272155i
$469$	−2.41391	−	7.42924i	−0.111464	−	0.343050i
$470$	−7.02984	+	7.98966i	−0.324262	+	0.368536i
$471$	25.7386	+	29.4259i	1.18597	+	1.35587i
$472$	3.81092	+	4.23246i	0.175412	+	0.194815i
$473$	0.615031	+	5.85163i	0.0282791	+	0.269058i
$474$	4.86193	−	8.14820i	0.223316	−	0.374259i
$475$	−21.5580	+	25.0751i	−0.989151	+	1.15052i
$476$	−5.42621			−0.248710
$477$	27.7479	−	18.9652i	1.27049	−	0.868358i
$478$	1.55996	−	4.80105i	0.0713507	−	0.219595i
$479$	38.6010	−	8.20489i	1.76372	−	0.374891i	0.791909	−	0.610640i	$-0.209088\pi$
$479$	38.6010	−	8.20489i	1.76372	−	0.374891i	0.971814	+	0.235749i	$0.0757542\pi$
$480$	−21.3016	+	4.46276i	−0.972283	+	0.203696i
$481$	10.7647	+	2.28810i	0.490827	+	0.104328i
$482$	−13.2150	+	22.8891i	−0.601928	+	1.04257i
$483$	0.306397	+	0.991278i	0.0139415	+	0.0451047i
$484$	−1.12822	+	10.7343i	−0.0512828	+	0.487924i
$485$	−4.01513	+	12.8567i	−0.182318	+	0.583794i
$486$	−12.1607	−	6.49868i	−0.551620	−	0.294786i
$487$	−4.96283	−	3.60570i	−0.224887	−	0.163390i	0.469637	−	0.882860i	$-0.344385\pi$
$487$	−4.96283	−	3.60570i	−0.224887	−	0.163390i	−0.694524	+	0.719470i	$0.744385\pi$
$488$	−3.76029	+	35.7768i	−0.170220	+	1.61954i
$489$	23.3140	−	16.4316i	1.05430	−	0.743063i
$490$	1.41246	+	12.1029i	0.0638084	+	0.546755i
$491$	−37.8652	+	16.8587i	−1.70883	+	0.760821i	−0.710462	+	0.703736i	$0.751514\pi$
$491$	−37.8652	+	16.8587i	−1.70883	+	0.760821i	−0.998369	+	0.0570848i	$0.981819\pi$
$492$	−3.54804	+	3.82831i	−0.159958	+	0.172594i
$493$	15.6617	+	27.1269i	0.705369	+	1.22174i
$494$	−3.31073	−	10.1894i	−0.148957	−	0.458442i
$495$	−9.80195	−	0.169640i	−0.440565	−	0.00762475i
$496$	0.0745952	−	0.229580i	0.00334942	−	0.0103085i
$497$	−14.7788	+	3.14132i	−0.662918	+	0.140908i
$498$	0.553515	+	6.11048i	0.0248036	+	0.273817i
$499$	−21.5077	+	37.2524i	−0.962815	+	1.66765i	−0.247442	+	0.968903i	$0.579590\pi$
$499$	−21.5077	+	37.2524i	−0.962815	+	1.66765i	−0.715373	+	0.698742i	$0.753743\pi$
$500$	9.45156	+	9.79779i	0.422687	+	0.438170i
$501$	18.2717	−	30.6219i	0.816321	−	1.36809i
$502$	3.23951	+	1.44232i	0.144586	+	0.0643740i
$503$	−3.68891	+	11.3533i	−0.164481	+	0.506219i	−0.998998	−	0.0447630i	$-0.985747\pi$
$503$	−3.68891	+	11.3533i	−0.164481	+	0.506219i	0.834517	+	0.550982i	$0.185747\pi$
$504$	−7.69421	+	1.40549i	−0.342728	+	0.0626053i
$505$	−8.68356	+	0.0995048i	−0.386413	+	0.00442790i
$506$	−0.565598	+	0.628160i	−0.0251439	+	0.0279251i
$507$	8.14456	+	14.5873i	0.361713	+	0.647846i
$508$	−13.0954	−	2.78352i	−0.581017	−	0.123499i
$509$	15.8268	−	7.04652i	0.701509	−	0.312332i	−0.0248079	−	0.999692i	$-0.507897\pi$
$509$	15.8268	−	7.04652i	0.701509	−	0.312332i	0.726316	+	0.687361i	$0.241231\pi$
$510$	−13.5108	+	9.75593i	−0.598267	+	0.432000i
$511$	2.08915	+	0.930150i	0.0924186	+	0.0411474i
$512$	−0.751353	−	0.545890i	−0.0332054	−	0.0241252i
$513$	26.9052	+	21.3799i	1.18789	+	0.943947i
$514$	7.48825	−	5.44053i	0.330293	−	0.239972i
$515$	−28.9023	+	6.49038i	−1.27359	+	0.286000i
$516$	−6.79702	−	5.08926i	−0.299222	−	0.224042i
$517$	7.69150	+	1.63488i	0.338272	+	0.0719019i
$518$	2.43448	−	4.21663i	0.106965	−	0.185268i
$519$	25.8387	−	27.8798i	1.13419	−	1.22379i
$520$	−11.3720	+	2.55374i	−0.498697	+	0.111989i
$521$	6.41731	−	19.7505i	0.281147	−	0.865283i	−0.706380	−	0.707833i	$-0.749673\pi$
$521$	6.41731	−	19.7505i	0.281147	−	0.865283i	0.987527	−	0.157450i	$-0.0503272\pi$
$522$	11.0630	+	13.0211i	0.484213	+	0.569916i
$523$	−13.4985	+	9.80721i	−0.590247	+	0.428839i	−0.842404	−	0.538847i	$-0.818860\pi$
$523$	−13.4985	+	9.80721i	−0.590247	+	0.428839i	0.252157	+	0.967686i	$0.418860\pi$
$524$	5.88035	+	10.1851i	0.256884	+	0.444937i
$525$	5.35861	+	5.85014i	0.233869	+	0.255321i
$526$	−4.43153	+	7.67563i	−0.193224	+	0.334674i
$527$	1.49503	+	14.2243i	0.0651247	+	0.619620i
$528$	−0.136826	−	0.156427i	−0.00595459	−	0.00680763i
$529$	22.0791	−	4.69307i	0.959962	−	0.204046i
$530$	−7.08830	−	20.9939i	−0.307896	−	0.911918i
$531$	−5.83390	−	1.41655i	−0.253170	−	0.0614729i
$532$	7.37711			0.319838
$533$	−3.03298	+	3.36846i	−0.131373	+	0.145904i
$534$	2.56844	−	21.4631i	0.111147	−	0.928798i
$535$	0.630084	−	1.12080i	0.0272409	−	0.0484566i
$536$	2.53680	+	24.1360i	0.109573	+	1.04252i
$537$	16.0991	+	12.0542i	0.694727	+	0.520176i
$538$	1.97767	−	18.8163i	0.0852634	−	0.811227i
$539$	7.28395	−	5.29210i	0.313742	−	0.227947i
$540$	9.79494	−	10.2085i	0.421507	−	0.439305i
$541$	−1.25243	−	0.909945i	−0.0538462	−	0.0391216i	0.560537	−	0.828130i	$-0.310595\pi$
$541$	−1.25243	−	0.909945i	−0.0538462	−	0.0391216i	−0.614383	+	0.789008i	$0.710595\pi$
$542$	−4.81661	+	5.34939i	−0.206891	+	0.229776i
$543$	23.1626	+	0.333142i	0.994003	+	0.0142965i
$544$	26.7394	+	5.68363i	1.14644	+	0.243684i
$545$	26.1838	−	12.0191i	1.12159	−	0.514843i
$546$	−2.52159	+	0.498190i	−0.107914	+	0.0213206i
$547$	−18.4672	+	3.92532i	−0.789599	+	0.167834i	−0.585023	−	0.811016i	$-0.698915\pi$
$547$	−18.4672	+	3.92532i	−0.789599	+	0.167834i	−0.204575	+	0.978851i	$0.565581\pi$
$548$	19.2475	−	13.9841i	0.822213	−	0.597373i
$549$	−18.0076	−	33.3712i	−0.768547	−	1.42425i
$550$	−1.85585	+	6.19101i	−0.0791339	+	0.263985i
$551$	−21.2926	−	36.8799i	−0.907097	−	1.57114i
$552$	−0.290805	−	3.21032i	−0.0123775	−	0.136640i
$553$	3.79639	+	4.21632i	0.161439	+	0.179296i
$554$	−0.0525600	−	0.0583738i	−0.00223306	−	0.00248006i
$555$	2.36499	+	23.1522i	0.100388	+	0.982758i
$556$	−13.1139	+	14.5644i	−0.556152	+	0.617669i
$557$	−16.8643			−0.714561			−0.357281	−	0.933997i	$-0.616296\pi$
$557$	−16.8643			−0.714561			−0.357281	+	0.933997i	$0.616296\pi$
$558$	2.19648	+	7.48615i	0.0929843	+	0.316914i
$559$	−5.96545	−	4.33416i	−0.252312	−	0.183315i
$560$	−0.0156621	+	0.167450i	−0.000661843	+	0.00707607i
$561$	11.1758	+	5.16963i	0.471843	+	0.218262i
$562$	16.4246	−	7.31269i	0.692829	−	0.308467i
$563$	−1.64115	+	0.730685i	−0.0691660	+	0.0307947i	−0.441028	−	0.897493i	$-0.645386\pi$
$563$	−1.64115	+	0.730685i	−0.0691660	+	0.0307947i	0.371862	+	0.928288i	$0.378719\pi$
$564$	−9.27555	+	6.53736i	−0.390571	+	0.275273i
$565$	1.52308	−	16.2839i	0.0640764	−	0.685070i
$566$	19.8990	+	14.4574i	0.836416	+	0.607692i
$567$	5.85988	−	5.79963i	0.246092	−	0.243562i
$568$	46.9404			1.96958
$569$	−3.03944	+	3.37564i	−0.127420	+	0.141514i	−0.803479	−	0.595334i	$-0.797020\pi$
$569$	−3.03944	+	3.37564i	−0.127420	+	0.141514i	0.676059	+	0.736848i	$0.263687\pi$
$570$	18.3683	−	13.2635i	0.769364	−	0.555547i
$571$	−26.9761	−	29.9600i	−1.12891	−	1.25379i	−0.963543	−	0.267554i	$-0.913785\pi$
$571$	−26.9761	−	29.9600i	−1.12891	−	1.25379i	−0.165370	−	0.986232i	$-0.552882\pi$
$572$	2.18069	+	2.42190i	0.0911792	+	0.101265i
$573$	11.0899	+	5.12989i	0.463287	+	0.214304i
$574$	1.00269	+	1.73671i	0.0418515	+	0.0724889i
$575$	−2.60040	+	1.98191i	−0.108444	+	0.0826514i
$576$	15.3978	+	0.443016i	0.641574	+	0.0184590i
$577$	−14.4803	+	10.5206i	−0.602824	+	0.437978i	−0.846880	−	0.531784i	$-0.821522\pi$
$577$	−14.4803	+	10.5206i	−0.602824	+	0.437978i	0.244056	+	0.969761i	$0.421522\pi$
$578$	5.76633	−	1.22567i	0.239848	−	0.0509812i
$579$	6.39405	+	7.31004i	0.265727	+	0.303795i
$580$	−15.9331	+	7.31376i	−0.661586	+	0.303687i
$581$	−3.58853	−	0.762766i	−0.148877	−	0.0316449i
$582$	4.72858	−	7.92472i	0.196006	−	0.328490i
$583$	−10.9554	+	12.1672i	−0.453726	+	0.503914i
$584$	−5.74792	−	4.17611i	−0.237851	−	0.172809i
$585$	8.37752	−	8.98646i	0.346368	−	0.371545i
$586$	7.41312	−	5.38595i	0.306233	−	0.222491i
$587$	4.04407	−	38.4768i	0.166917	−	1.58811i	−0.515335	−	0.856989i	$-0.672333\pi$
$587$	4.04407	−	38.4768i	0.166917	−	1.58811i	0.682252	−	0.731117i	$-0.261001\pi$
$588$	−1.54385	+	12.9011i	−0.0636673	+	0.532034i
$589$	−2.03255	−	19.3384i	−0.0837496	−	0.796824i
$590$	−1.93956	+	3.45012i	−0.0798504	+	0.142039i
$591$	−2.89317	−	2.16626i	−0.119009	−	0.0891079i
$592$	−0.330123	+	0.366639i	−0.0135680	+	0.0150688i
$593$	0.135281			0.00555534			0.00277767	−	0.999996i	$-0.499116\pi$
$593$	0.135281			0.00555534			0.00277767	+	0.999996i	$0.499116\pi$
$594$	6.50362	+	1.67856i	0.266847	+	0.0688723i
$595$	−3.18766	−	9.44111i	−0.130681	−	0.387048i
$596$	13.6709	−	2.90584i	0.559982	−	0.119028i
$597$	1.71337	−	5.02608i	0.0701236	−	0.205704i
$598$	−0.110727	−	1.05350i	−0.00452798	−	0.0430808i
$599$	−0.290350	+	0.502901i	−0.0118634	+	0.0205480i	−0.871896	−	0.489691i	$-0.837110\pi$
$599$	−0.290350	+	0.502901i	−0.0118634	+	0.0205480i	0.860033	+	0.510239i	$0.170443\pi$
$600$	−12.5055	−	21.2394i	−0.510534	−	0.867094i
$601$	11.2892	+	19.5535i	0.460496	+	0.797602i	0.998986	−	0.0450300i	$-0.0143383\pi$
$601$	11.2892	+	19.5535i	0.460496	+	0.797602i	−0.538490	+	0.842632i	$0.681005\pi$
$602$	−2.63926	+	1.91754i	−0.107568	+	0.0781529i
$603$	−16.5637	−	19.4954i	−0.674527	−	0.793914i
$604$	5.43711	−	16.7337i	0.221233	−	0.680885i
$605$	−19.3395	+	4.34293i	−0.786263	+	0.176565i
$606$	5.80145	+	1.32062i	0.235668	+	0.0536463i
$607$	5.42862	−	9.40265i	0.220341	−	0.381642i	−0.734570	−	0.678532i	$-0.762616\pi$
$607$	5.42862	−	9.40265i	0.220341	−	0.381642i	0.954912	+	0.296891i	$0.0959496\pi$
$608$	−36.3531	−	7.72708i	−1.47431	−	0.313374i
$609$	−9.39215	+	4.02082i	−0.380589	+	0.162932i
$610$	−24.3923	+	5.47759i	−0.987615	+	0.221781i
$611$	−7.97238	+	5.79227i	−0.322528	+	0.234330i
$612$	−16.4349	+	6.75788i	−0.664343	+	0.273171i
$613$	32.2624	+	23.4400i	1.30307	+	0.946733i	0.999981	−	0.00623024i	$-0.00198316\pi$
$613$	32.2624	+	23.4400i	1.30307	+	0.946733i	0.303086	+	0.952963i	$0.401983\pi$
$614$	21.3377	+	9.50014i	0.861118	+	0.383394i
$615$	−8.74523	−	3.92430i	−0.352642	−	0.158243i
$616$	3.48074	−	1.54973i	0.140243	−	0.0624403i
$617$	−25.4813	−	5.41621i	−1.02584	−	0.218048i	−0.335885	−	0.941903i	$-0.609035\pi$
$617$	−25.4813	−	5.41621i	−1.02584	−	0.218048i	−0.689952	+	0.723855i	$0.742369\pi$
$618$	20.2933	+	0.291873i	0.816315	+	0.0117409i
$619$	−6.20324	+	6.88940i	−0.249329	+	0.276908i	−0.854798	−	0.518961i	$-0.826319\pi$
$619$	−6.20324	+	6.88940i	−0.249329	+	0.276908i	0.605469	+	0.795869i	$0.292986\pi$
$620$	−8.00456	+	0.0917241i	−0.321471	+	0.00368373i
$621$	2.16257	+	2.62080i	0.0867808	+	0.105169i
$622$	2.22813	−	6.85748i	0.0893399	−	0.274960i
$623$	11.8079	+	5.25721i	0.473073	+	0.210626i
$624$	0.260420	+	0.00374556i	0.0104252	+	0.000149942i
$625$	−11.4949	+	22.2006i	−0.459795	+	0.888025i
$626$	−12.8974	+	22.3389i	−0.515483	+	0.892843i
$627$	−15.1939	−	7.02828i	−0.606785	−	0.280683i
$628$	26.8827	−	5.71409i	1.07274	−	0.228017i
$629$	9.03307	−	27.8009i	0.360172	−	1.10850i
$630$	−2.63589	−	4.75361i	−0.105016	−	0.189388i
$631$	−2.38628	−	7.34421i	−0.0949963	−	0.292368i	0.892256	−	0.451529i	$-0.149121\pi$
$631$	−2.38628	−	7.34421i	−0.0949963	−	0.292368i	−0.987253	+	0.159161i	$0.949121\pi$
$632$	−8.81340	−	15.2653i	−0.350578	−	0.607219i
$633$	3.47135	+	0.790202i	0.137974	+	0.0314077i
$634$	8.70709	−	3.87665i	0.345803	−	0.153961i
$635$	−2.84992	−	24.4201i	−0.113095	−	0.969081i
$636$	−2.13158	−	23.5314i	−0.0845228	−	0.933082i
$637$	−1.17942	+	11.2214i	−0.0467303	+	0.444609i
$638$	−6.73368	−	4.89231i	−0.266589	−	0.193688i
$639$	−40.8497	+	27.9201i	−1.61599	+	1.10450i
$640$	−4.46416	+	14.2945i	−0.176461	+	0.565042i
$641$	−3.03061	+	28.8343i	−0.119702	+	1.13889i	0.755507	+	0.655141i	$0.227391\pi$
$641$	−3.03061	+	28.8343i	−0.119702	+	1.13889i	−0.875208	+	0.483746i	$0.839276\pi$
$642$	−0.598815	+	0.646118i	−0.0236334	+	0.0255003i
$643$	−19.9683	+	34.5861i	−0.787473	+	1.36394i	0.140038	+	0.990146i	$0.455278\pi$
$643$	−19.9683	+	34.5861i	−0.787473	+	1.36394i	−0.927511	+	0.373797i	$0.878056\pi$
$644$	0.713460	+	0.151651i	0.0281143	+	0.00597587i
$645$	4.86191	−	14.8159i	0.191437	−	0.583376i
$646$	−27.8357	+	5.91667i	−1.09518	+	0.232788i
$647$	−1.22692	+	3.77608i	−0.0482353	+	0.148453i	−0.972273	−	0.233848i	$-0.924868\pi$
$647$	−1.22692	+	3.77608i	−0.0482353	+	0.148453i	0.924038	+	0.382301i	$0.124868\pi$
$648$	−21.5538	+	13.8394i	−0.846715	+	0.543664i
$649$	2.92448			0.114796
$650$	−4.20954	−	6.91992i	−0.165112	−	0.271422i
$651$	−4.66454	−	0.0670889i	−0.182818	−	0.00262942i
$652$	−2.09595	−	19.9416i	−0.0820836	−	0.780973i
$653$	−23.3941	−	25.9818i	−0.915483	−	1.01675i	−0.999794	−	0.0203078i	$-0.993535\pi$
$653$	−23.3941	−	25.9818i	−0.915483	−	1.01675i	0.0843104	−	0.996440i	$-0.473131\pi$
$654$	−19.3650	+	3.82594i	−0.757232	+	0.149606i
$655$	−14.2666	+	16.2146i	−0.557444	+	0.633555i
$656$	−0.0627927	−	0.193256i	−0.00245164	−	0.00754538i
$657$	7.48605	+	0.215385i	0.292059	+	0.00840295i
$658$	1.34726	+	4.14644i	0.0525217	+	0.161645i
$659$	2.85250	−	27.1397i	0.111118	−	1.05721i	−0.786848	−	0.617147i	$-0.788288\pi$
$659$	2.85250	−	27.1397i	0.111118	−	1.05721i	0.897965	−	0.440066i	$-0.145045\pi$
$660$	−3.46334	+	5.95839i	−0.134810	+	0.231930i
$661$	−3.82476	−	36.3902i	−0.148766	−	1.41541i	−0.773114	−	0.634267i	$-0.781302\pi$
$661$	−3.82476	−	36.3902i	−0.148766	−	1.41541i	0.624348	−	0.781146i	$-0.285365\pi$
$662$	−12.1311	+	5.40109i	−0.471487	+	0.209919i
$663$	−14.1862	+	6.07316i	−0.550945	+	0.235862i
$664$	10.4125	+	4.63595i	0.404084	+	0.179910i
$665$	4.33372	+	12.8355i	0.168055	+	0.497739i
$666$	2.12209	−	15.8033i	0.0822294	−	0.612365i
$667$	−1.30113	−	4.00447i	−0.0503800	−	0.155054i
$668$	−12.5341	−	21.7098i	−0.484960	−	0.839976i
$669$	−26.7243	+	28.8354i	−1.03322	+	1.11484i
$670$	−15.3278	+	7.03592i	−0.592165	+	0.271821i
$671$	12.3603	+	13.7275i	0.477163	+	0.529943i
$672$	−2.87695	+	8.43940i	−0.110981	+	0.325557i
$673$	−23.0242	−	10.2510i	−0.887518	−	0.395148i	−0.0882323	−	0.996100i	$-0.528122\pi$
$673$	−23.0242	−	10.2510i	−0.887518	−	0.395148i	−0.799285	+	0.600952i	$0.794788\pi$
$674$	−1.17239			−0.0451589
$675$	23.5160	+	11.0452i	0.905132	+	0.425132i
$676$	11.7450			0.451732
$677$	10.8854	+	4.84649i	0.418360	+	0.186266i	0.605110	−	0.796142i	$-0.293129\pi$
$677$	10.8854	+	4.84649i	0.418360	+	0.186266i	−0.186751	+	0.982407i	$0.559796\pi$
$678$	−3.61560	+	10.6062i	−0.138856	+	0.407328i
$679$	3.69227	+	4.10068i	0.141696	+	0.157370i
$680$	3.58861	+	30.7497i	0.137617	+	1.17920i
$681$	7.74678	−	8.35873i	0.296857	−	0.320307i
$682$	−1.90025	−	3.29133i	−0.0727644	−	0.126032i
$683$	−10.9564	−	33.7204i	−0.419236	−	1.29028i	−0.908407	−	0.418088i	$-0.862701\pi$
$683$	−10.9564	−	33.7204i	−0.419236	−	1.29028i	0.489171	−	0.872188i	$-0.337299\pi$
$684$	22.3438	−	9.18755i	0.854337	−	0.351295i
$685$	35.6382	+	25.2739i	1.36166	+	0.965664i
$686$	9.74197	+	4.33741i	0.371950	+	0.165603i
$687$	10.3727	−	4.44059i	0.395742	−	0.169419i
$688$	0.301985	−	0.134452i	0.0115131	−	0.00512594i
$689$	−2.14474	−	20.4059i	−0.0817082	−	0.777402i
$690$	2.04911	−	0.905152i	0.0780081	−	0.0344586i
$691$	−1.82303	+	17.3450i	−0.0693513	+	0.659834i	0.903529	+	0.428526i	$0.140967\pi$
$691$	−1.82303	+	17.3450i	−0.0693513	+	0.659834i	−0.972881	+	0.231307i	$0.925700\pi$
$692$	−8.25774	−	25.4147i	−0.313912	−	0.966122i
$693$	−2.10733	+	3.41899i	−0.0800508	+	0.129877i
$694$	2.17157	+	6.68341i	0.0824317	+	0.253699i
$695$	−33.0446	−	14.2610i	−1.25345	−	0.540950i
$696$	31.1391	−	6.15214i	1.18032	−	0.233196i
$697$	8.05612	+	8.94722i	0.305147	+	0.338900i
$698$	−1.19926	−	11.4102i	−0.0453927	−	0.431882i
$699$	6.44780	+	0.0927371i	0.243878	+	0.00350764i
$700$	5.42731	−	1.28427i	0.205133	−	0.0485407i
$701$	−23.1265			−0.873476			−0.436738	−	0.899589i	$-0.643866\pi$
$701$	−23.1265			−0.873476			−0.436738	+	0.899589i	$0.643866\pi$
$702$	−7.01695	+	4.64934i	−0.264838	+	0.175478i
$703$	−12.2808	+	37.7963i	−0.463177	+	1.42551i
$704$	−7.33993	+	1.56015i	−0.276634	+	0.0588004i
$705$	−16.8234	−	12.2982i	−0.633605	−	0.463177i
$706$	3.80607	+	0.809004i	0.143243	+	0.0304473i
$707$	−1.77885	+	3.08106i	−0.0669006	+	0.115875i
$708$	−2.86882	+	3.09544i	−0.107817	+	0.116334i
$709$	−1.08114	+	10.2864i	−0.0406030	+	0.386312i	0.955283	+	0.295694i	$0.0955509\pi$
$709$	−1.08114	+	10.2864i	−0.0406030	+	0.386312i	−0.995886	+	0.0906180i	$0.971116\pi$
$710$	10.4352	+	30.9067i	0.391627	+	1.15991i
$711$	16.7496	+	8.04233i	0.628159	+	0.301611i
$712$	−32.4873	−	23.6034i	−1.21751	−	0.884574i
$713$	0.200964	−	1.91205i	0.00752618	−	0.0716068i
$714$	0.615922	+	6.79942i	0.0230503	+	0.254462i
$715$	−2.93283	+	5.21696i	−0.109682	+	0.195103i
$716$	12.9163	−	5.75069i	0.482703	−	0.214913i
$717$	9.63862	+	2.19409i	0.359961	+	0.0819398i
$718$	−6.05356	−	10.4851i	−0.225917	−	0.391300i
$719$	−11.2080	−	34.4945i	−0.417986	−	1.28643i	−0.909552	−	0.415589i	$-0.863575\pi$
$719$	−11.2080	−	34.4945i	−0.417986	−	1.28643i	0.491566	−	0.870840i	$-0.336425\pi$
$720$	0.161108	+	0.526680i	0.00600413	+	0.0196282i
$721$	−3.75009	+	11.5416i	−0.139661	+	0.429832i
$722$	21.4050	−	4.54978i	0.796613	−	0.169325i
$723$	−46.9730	−	21.7285i	−1.74694	−	0.808091i
$724$	8.14251	−	14.1032i	0.302614	−	0.524143i
$725$	−22.0853	−	23.4256i	−0.820226	−	0.870005i
$726$	13.5789	+	0.195302i	0.503961	+	0.00724834i
$727$	−18.3260	−	8.15926i	−0.679674	−	0.302610i	0.0377098	−	0.999289i	$-0.487994\pi$
$727$	−18.3260	−	8.15926i	−0.679674	−	0.302610i	−0.717383	+	0.696679i	$0.754660\pi$
$728$	−1.47553	+	4.54121i	−0.0546867	+	0.168309i
$729$	10.5255	−	24.8639i	0.389833	−	0.920886i
$730$	1.47185	−	4.71296i	0.0544755	−	0.174434i
$731$	−13.1055	+	14.5551i	−0.484724	+	0.538341i
$732$	−26.6549	−	0.383371i	−0.985194	−	0.0141698i
$733$	28.4700	+	6.05149i	1.05156	+	0.223517i	0.701103	−	0.713060i	$-0.252692\pi$
$733$	28.4700	+	6.05149i	1.05156	+	0.223517i	0.350461	+	0.936577i	$0.386025\pi$
$734$	−4.23569	+	1.88585i	−0.156342	+	0.0696081i
$735$	−23.3537	+	4.89268i	−0.861415	+	0.180469i
$736$	−3.35696	−	1.49461i	−0.123739	−	0.0550922i
$737$	10.0818	+	7.32486i	0.371368	+	0.269815i
$738$	5.19988	+	4.01139i	0.191410	+	0.147661i
$739$	−13.5848	+	9.86991i	−0.499724	+	0.363071i	−0.808912	−	0.587930i	$-0.799943\pi$
$739$	−13.5848	+	9.86991i	−0.499724	+	0.363071i	0.309188	+	0.951001i	$0.399943\pi$
$740$	15.0215	+	6.48282i	0.552203	+	0.238313i
$741$	19.2865	−	8.25666i	0.708509	−	0.303316i
$742$	−8.87941	−	1.88738i	−0.325973	−	0.0692878i
$743$	−22.2483	+	38.5352i	−0.816211	+	1.41372i	0.0922434	+	0.995736i	$0.470596\pi$
$743$	−22.2483	+	38.5352i	−0.816211	+	1.41372i	−0.908455	+	0.417983i	$0.862737\pi$
$744$	14.1318	+	3.21689i	0.518096	+	0.117937i
$745$	13.0869	+	22.0791i	0.479468	+	0.808914i
$746$	−2.31660	+	7.12976i	−0.0848168	+	0.261039i
$747$	−11.8189	+	2.15894i	−0.432431	+	0.0789914i
$748$	7.00321	−	5.08813i	0.256063	−	0.186040i
$749$	−0.263377	−	0.456182i	−0.00962357	−	0.0166685i
$750$	11.2045	−	12.9556i	0.409129	−	0.473071i
$751$	−18.8265	+	32.6085i	−0.686990	+	1.18990i	0.285817	+	0.958284i	$0.407735\pi$
$751$	−18.8265	+	32.6085i	−0.686990	+	1.18990i	−0.972807	+	0.231617i	$0.925598\pi$
$752$	−0.0461779	−	0.439353i	−0.00168393	−	0.0160216i
$753$	−2.24054	+	6.57251i	−0.0816498	+	0.239516i
$754$	10.2029	−	2.16869i	0.371567	−	0.0789790i
$755$	32.3092	−	0.370231i	1.17585	−	0.0134741i
$756$	−1.55163	−	5.58443i	−0.0564324	−	0.203104i
$757$	23.9415			0.870167			0.435084	−	0.900390i	$-0.356719\pi$
$757$	23.9415			0.870167			0.435084	+	0.900390i	$0.356719\pi$
$758$	15.2668	−	16.9556i	0.554517	−	0.615853i
$759$	−1.32496	−	0.992063i	−0.0480930	−	0.0360096i
$760$	−4.87883	−	41.8052i	−0.176974	−	1.51643i
$761$	−2.60057	−	24.7428i	−0.0942706	−	0.896924i	−0.934804	−	0.355164i	$-0.884425\pi$
$761$	−2.60057	−	24.7428i	−0.0942706	−	0.896924i	0.840533	−	0.541760i	$-0.182242\pi$
$762$	−2.00150	+	16.7255i	−0.0725067	+	0.605899i
$763$	1.23376	−	11.7384i	0.0446650	−	0.424959i
$764$	6.94938	−	5.04902i	0.251420	−	0.182667i
$765$	−21.4129	−	24.6253i	−0.774184	−	0.890330i
$766$	−5.45840	−	3.96576i	−0.197220	−	0.143289i
$767$	−2.45236	+	2.72362i	−0.0885494	+	0.0983441i
$768$	14.3716	−	24.0856i	0.518590	−	0.869115i
$769$	−20.7844	−	4.41785i	−0.749503	−	0.159312i	−0.182704	−	0.983168i	$-0.558485\pi$
$769$	−20.7844	−	4.41785i	−0.749503	−	0.159312i	−0.566799	+	0.823856i	$0.691818\pi$
$770$	1.79418	+	1.94729i	0.0646576	+	0.0701755i
$771$	11.9330	+	13.6425i	0.429758	+	0.491323i
$772$	6.67826	−	1.41951i	0.240356	−	0.0510892i
$773$	−4.02099	+	2.92142i	−0.144625	+	0.105076i	−0.657745	−	0.753241i	$-0.728490\pi$
$773$	−4.02099	+	2.92142i	−0.144625	+	0.105076i	0.513120	+	0.858317i	$0.328490\pi$
$774$	−5.60568	+	9.09481i	−0.201492	+	0.326906i
$775$	−4.86191	−	13.8733i	−0.174645	−	0.498344i
$776$	−8.57167	−	14.8466i	−0.307705	−	0.532961i
$777$	8.65338	+	4.00283i	0.310438	+	0.143601i
$778$	21.0159	+	23.3405i	0.753456	+	0.836797i
$779$	−10.9525	−	12.1640i	−0.392416	−	0.435822i
$780$	−2.64492	−	8.22193i	−0.0947033	−	0.294392i
$781$	16.1283	−	17.9122i	0.577114	−	0.640951i
$782$	−2.81370			−0.100618
$783$	−23.4394	+	23.8754i	−0.837655	+	0.853237i
$784$	−0.409223	−	0.297318i	−0.0146151	−	0.0106185i
$785$	25.7344	+	43.4166i	0.918499	+	1.54961i
$786$	12.0951	−	8.52458i	0.431419	−	0.304062i
$787$	43.9427	−	19.5646i	1.56639	−	0.697401i	0.573808	−	0.818990i	$-0.305466\pi$
$787$	43.9427	−	19.5646i	1.56639	−	0.697401i	0.992581	+	0.121589i	$0.0387990\pi$
$788$	−2.32118	+	1.03346i	−0.0826886	+	0.0368153i
$789$	−15.7519	−	7.28643i	−0.560784	−	0.259404i
$790$	8.09174	−	9.19655i	0.287891	−	0.327199i
$791$	−5.42066	−	3.93834i	−0.192736	−	0.140031i
$792$	8.61243	−	9.02878i	0.306030	−	0.320824i
$793$	−23.1494			−0.822060
$794$	−16.0587	+	17.8350i	−0.569902	+	0.632941i
$795$	39.6903	−	17.5324i	1.40767	−	0.621811i
$796$	−2.49787	−	2.77416i	−0.0885346	−	0.0983276i
$797$	3.58369	+	3.98009i	0.126941	+	0.140982i	0.803264	−	0.595623i	$-0.203095\pi$
$797$	3.58369	+	3.98009i	0.126941	+	0.140982i	−0.676324	+	0.736605i	$0.736428\pi$
$798$	−0.837366	−	9.24403i	−0.0296424	−	0.327235i
$799$	13.0875	+	22.6682i	0.463003	+	0.801944i
$800$	−28.0900	+	0.643850i	−0.993130	+	0.0227635i
$801$	42.3112	+	1.21735i	1.49499	+	0.0430131i
$802$	−16.4660	+	11.9632i	−0.581434	+	0.422437i
$803$	−3.56851	+	0.758510i	−0.125930	+	0.0267673i
$804$	−17.6430	+	3.48572i	−0.622220	+	0.122932i
$805$	0.155268	+	1.33044i	0.00547247	+	0.0468920i
$806$	4.65875	+	0.990247i	0.164097	+	0.0348800i
$807$	37.0450	+	0.532809i	1.30405	+	0.0187558i
$808$	7.39595	−	8.21403i	0.260189	−	0.288969i
$809$	8.50974	+	6.18268i	0.299186	+	0.217372i	0.727243	−	0.686380i	$-0.240801\pi$
$809$	8.50974	+	6.18268i	0.299186	+	0.217372i	−0.428056	+	0.903752i	$0.640801\pi$
$810$	−13.9038	−	11.1150i	−0.488530	−	0.390541i
$811$	14.8190	−	10.7667i	0.520367	−	0.378068i	−0.296375	−	0.955072i	$-0.595778\pi$
$811$	14.8190	−	10.7667i	0.520367	−	0.378068i	0.816742	+	0.577003i	$0.195778\pi$
$812$	−0.750754	+	7.14295i	−0.0263463	+	0.250668i
$813$	−11.2833	−	8.44838i	−0.395723	−	0.296298i
$814$	0.811919	+	7.72489i	0.0284577	+	0.270757i
$815$	33.4653	−	15.3615i	1.17224	−	0.538092i
$816$	0.0821990	−	0.686893i	0.00287754	−	0.0240460i
$817$	17.8173	−	19.7882i	0.623350	−	0.692300i
$818$	−16.0378			−0.560747
$819$	−1.41704	−	4.82962i	−0.0495152	−	0.168760i
$820$	−5.40583	+	4.02301i	−0.188780	+	0.140490i
$821$	47.7890	−	10.1579i	1.66785	−	0.354512i	0.725261	−	0.688474i	$-0.241719\pi$
$821$	47.7890	−	10.1579i	1.66785	−	0.354512i	0.942586	+	0.333963i	$0.108386\pi$
$822$	−19.7078	−	22.5311i	−0.687390	−	0.785864i
$823$	1.51205	+	14.3861i	0.0527066	+	0.501470i	0.988749	+	0.149583i	$0.0477931\pi$
$823$	1.51205	+	14.3861i	0.0527066	+	0.501470i	−0.936043	+	0.351887i	$0.885540\pi$
$824$	18.8514	−	32.6515i	0.656718	−	1.13747i
$825$	−12.4016	−	2.52561i	−0.431768	−	0.0879303i
$826$	0.810740	+	1.40424i	0.0282092	+	0.0488598i
$827$	−15.1725	+	11.0234i	−0.527598	+	0.383322i	−0.819458	−	0.573139i	$-0.805726\pi$
$827$	−15.1725	+	11.0234i	−0.527598	+	0.383322i	0.291861	+	0.956461i	$0.405726\pi$
$828$	2.34980	−	0.429233i	0.0816611	−	0.0149169i
$829$	1.12241	−	3.45444i	0.0389830	−	0.119977i	−0.929671	−	0.368390i	$-0.879909\pi$
$829$	1.12241	−	3.45444i	0.0389830	−	0.119977i	0.968654	+	0.248413i	$0.0799090\pi$
$830$	−0.737642	+	7.88647i	−0.0256039	+	0.273743i
$831$	0.104556	−	0.112815i	0.00362700	−	0.00391351i
$832$	4.70198	−	8.14408i	0.163012	−	0.282345i
$833$	29.3153	+	6.23116i	1.01572	+	0.215897i
$834$	19.7388	+	14.7794i	0.683498	+	0.511769i
$835$	30.4097	−	34.5618i	1.05237	−	1.19606i
$836$	−9.52109	+	6.91748i	−0.329294	+	0.239246i
$837$	−14.2115	+	5.60608i	−0.491222	+	0.193775i
$838$	−2.31521	−	1.68210i	−0.0799776	−	0.0581071i
$839$	10.7379	+	4.78083i	0.370714	+	0.165052i	0.583633	−	0.812017i	$-0.301631\pi$
$839$	10.7379	+	4.78083i	0.370714	+	0.165052i	−0.212920	+	0.977070i	$0.568297\pi$
$840$	−10.0975	−	0.0295178i	−0.348397	−	0.00101846i
$841$	11.3834	−	5.06822i	0.392532	−	0.174766i
$842$	−9.00262	−	1.91357i	−0.310251	−	0.0659458i
$843$	17.1628	+	30.7395i	0.591118	+	1.05872i
$844$	1.67469	−	1.85994i	0.0576454	−	0.0640217i
$845$	6.89968	+	20.4353i	0.237356	+	0.702995i
$846$	9.24462	+	10.8809i	0.317837	+	0.374092i
$847$	−2.50931	+	7.72287i	−0.0862210	+	0.265361i
$848$	0.840311	+	0.374130i	0.0288564	+	0.0128477i
$849$	−24.6797	+	41.3612i	−0.847005	+	1.41951i
$850$	−19.4486	+	9.19873i	−0.667081	+	0.315514i
$851$	−1.96468	+	3.40292i	−0.0673483	+	0.116651i
$852$	3.13806	+	34.6424i	0.107508	+	1.18683i
$853$	44.4770	−	9.45388i	1.52286	−	0.323695i	0.630923	−	0.775846i	$-0.282677\pi$
$853$	44.4770	−	9.45388i	1.52286	−	0.323695i	0.891941	+	0.452151i	$0.149343\pi$
$854$	−3.16491	+	9.74060i	−0.108301	+	0.333316i
$855$	29.1115	+	33.4789i	0.995592	+	1.14495i
$856$	0.505711	+	1.55642i	0.0172849	+	0.0531973i
$857$	15.6168	+	27.0491i	0.533460	+	0.923980i	0.999236	+	0.0390776i	$0.0124419\pi$
$857$	15.6168	+	27.0491i	0.533460	+	0.923980i	−0.465776	+	0.884903i	$0.654225\pi$
$858$	2.78728	−	3.00746i	0.0951562	−	0.102673i
$859$	−28.5380	+	12.7059i	−0.973704	+	0.433521i	−0.831017	−	0.556247i	$-0.812241\pi$
$859$	−28.5380	+	12.7059i	−0.973704	+	0.433521i	−0.142687	+	0.989768i	$0.545574\pi$
$860$	−7.42791	−	8.06182i	−0.253290	−	0.274906i
$861$	−3.20981	+	2.26226i	−0.109390	+	0.0770976i
$862$	1.84978	−	17.5995i	0.0630038	−	0.599442i
$863$	−7.17033	−	5.20955i	−0.244081	−	0.177335i	0.459019	−	0.888427i	$-0.348201\pi$
$863$	−7.17033	−	5.20955i	−0.244081	−	0.177335i	−0.703099	+	0.711092i	$0.748201\pi$
$864$	1.79682	+	29.1443i	0.0611289	+	0.991508i
$865$	39.3682	−	29.2977i	1.33856	−	0.996152i
$866$	−0.388058	+	3.69212i	−0.0131867	+	0.125463i
$867$	3.40898	+	11.0290i	0.115775	+	0.374565i
$868$	−1.63976	+	2.84014i	−0.0556570	+	0.0964007i
$869$	−8.85335	−	1.88184i	−0.300329	−	0.0638369i
$870$	10.9732	+	19.1351i	0.372026	+	0.648740i
$871$	−15.2760	+	3.24701i	−0.517607	+	0.110021i
$872$	−11.3316	+	34.8751i	−0.383736	+	1.18102i
$873$	16.2902	+	7.82175i	0.551339	+	0.264726i
$874$	3.82531			0.129393
$875$	5.42280	+	8.68857i	0.183324	+	0.293727i
$876$	2.69774	−	4.52119i	0.0911481	−	0.152757i
$877$	−0.186003	−	1.76970i	−0.00628086	−	0.0597584i	0.990933	−	0.134360i	$-0.0428980\pi$
$877$	−0.186003	−	1.76970i	−0.00628086	−	0.0597584i	−0.997213	+	0.0746021i	$0.976231\pi$
$878$	−19.1458	−	21.2636i	−0.646139	−	0.717610i
$879$	11.8133	+	13.5056i	0.398453	+	0.455534i
$880$	−0.136803	−	0.230802i	−0.00461164	−	0.00778034i
$881$	8.34381	+	25.6796i	0.281110	+	0.865168i	0.987538	+	0.157382i	$0.0503055\pi$
$881$	8.34381	+	25.6796i	0.281110	+	0.865168i	−0.706428	+	0.707785i	$0.749694\pi$
$882$	16.3412	+	0.470161i	0.550238	+	0.0158312i
$883$	−0.231224	−	0.711635i	−0.00778131	−	0.0239484i	0.947090	−	0.320967i	$-0.104008\pi$
$883$	−0.231224	−	0.711635i	−0.00778131	−	0.0239484i	−0.954872	+	0.297018i	$0.904008\pi$
$884$	−1.13396	+	10.7889i	−0.0381392	+	0.362870i
$885$	−7.07108	−	3.17305i	−0.237692	−	0.106661i
$886$	0.163046	+	1.55128i	0.00547763	+	0.0521162i
$887$	−29.8287	+	13.2806i	−1.00155	+	0.445919i	−0.840957	−	0.541102i	$-0.818007\pi$
$887$	−29.8287	+	13.2806i	−1.00155	+	0.445919i	−0.160593	+	0.987021i	$0.551341\pi$
$888$	−23.7112	−	17.7538i	−0.795697	−	0.595778i
$889$	−9.20149	−	4.09677i	−0.308608	−	0.137401i
$890$	8.31888	−	26.6376i	0.278850	−	0.892896i
$891$	−2.12463	+	12.9799i	−0.0711777	+	0.434844i
$892$	8.54075	+	26.2857i	0.285966	+	0.880112i
$893$	−17.7929	−	30.8182i	−0.595416	−	1.03129i
$894$	−5.19298	−	16.8007i	−0.173679	−	0.561901i
$895$	17.5934	+	19.0948i	0.588082	+	0.638270i
$896$	4.10519	+	4.55927i	0.137145	+	0.152315i
$897$	2.03498	−	0.402051i	0.0679461	−	0.0134241i
$898$	−3.28204	−	1.46126i	−0.109523	−	0.0487629i
$899$	18.9314			0.631398
$900$	14.8388	−	10.6490i	0.494627	−	0.354968i
$901$	−54.5001			−1.81566
$902$	−2.92260	−	1.30123i	−0.0973120	−	0.0433261i
$903$	−4.20584	−	4.80836i	−0.139962	−	0.160012i
$904$	13.9290	+	15.4697i	0.463270	+	0.514514i
$905$	29.3217	+	5.88220i	0.974687	+	0.195531i
$906$	−21.5857	−	4.91365i	−0.717135	−	0.163245i
$907$	−9.80283	−	16.9790i	−0.325498	−	0.563778i	0.656115	−	0.754661i	$-0.272198\pi$
$907$	−9.80283	−	16.9790i	−0.325498	−	0.563778i	−0.981613	+	0.190882i	$0.938865\pi$
$908$	−2.47577	−	7.61964i	−0.0821614	−	0.252867i
$909$	−1.55060	+	11.5473i	−0.0514300	+	0.383001i
$910$	−3.31807	+	0.0380217i	−0.109993	+	0.00126041i
$911$	−6.69634	−	2.98140i	−0.221860	−	0.0987782i	0.292797	−	0.956175i	$-0.405414\pi$
$911$	−6.69634	−	2.98140i	−0.221860	−	0.0987782i	−0.514657	+	0.857396i	$0.672081\pi$
$912$	−0.111752	+	0.933853i	−0.00370048	+	0.0309229i
$913$	5.34669	−	2.38050i	0.176950	−	0.0787831i
$914$	3.25729	+	30.9910i	0.107741	+	1.02509i
$915$	−14.9915	−	46.6023i	−0.495605	−	1.54063i
$916$	0.829132	−	7.88866i	0.0273953	−	0.260649i
$917$	2.73419	+	8.41496i	0.0902908	+	0.277886i
$918$	10.3336	+	19.8270i	0.341059	+	0.654389i
$919$	−0.919198	−	2.82900i	−0.0303215	−	0.0933201i	0.934750	−	0.355305i	$-0.115623\pi$
$919$	−0.919198	−	2.82900i	−0.0303215	−	0.0933201i	−0.965072	+	0.261985i	$0.915623\pi$
$920$	0.387542	−	4.14339i	0.0127769	−	0.136603i
$921$	−14.7578	+	43.2911i	−0.486285	+	1.42649i
$922$	0.00404069	+	0.00448764i	0.000133073	+	0.000147793i
$923$	3.15744	+	30.0410i	0.103928	+	0.988812i
$924$	1.37640	+	2.46521i	0.0452804	+	0.0810995i
$925$	−2.45502	+	29.9445i	−0.0807206	+	0.984568i
$926$	−25.8551			−0.849652
$927$	3.01577	+	39.6276i	0.0990508	+	1.30154i
$928$	11.1814	−	34.4128i	0.367047	−	1.12966i
$929$	0.682954	−	0.145166i	0.0224070	−	0.00476275i	−0.196695	−	0.980465i	$-0.563021\pi$
$929$	0.682954	−	0.145166i	0.0224070	−	0.00476275i	0.219102	+	0.975702i	$0.429687\pi$
$930$	1.02352	+	10.0199i	0.0335627	+	0.328564i
$931$	−39.8551	−	8.47146i	−1.30620	−	0.277641i
$932$	2.26664	−	3.92593i	0.0742462	−	0.128598i
$933$	13.7671	+	3.13388i	0.450716	+	0.102599i
$934$	−1.57337	+	14.9696i	−0.0514822	+	0.489821i
$935$	12.9670	+	9.19590i	0.424065	+	0.300738i
$936$	1.18660	+	15.5921i	0.0387852	+	0.509643i
$937$	−6.03529	−	4.38490i	−0.197164	−	0.143248i	0.484823	−	0.874612i	$-0.338884\pi$
$937$	−6.03529	−	4.38490i	−0.197164	−	0.143248i	−0.681987	+	0.731364i	$0.738884\pi$
$938$	−0.722234	+	6.87160i	−0.0235818	+	0.224366i
$939$	−45.8440	−	21.2062i	−1.49606	−	0.692038i
$940$	−13.3143	+	6.11164i	−0.434263	+	0.199340i
$941$	34.9240	−	15.5492i	1.13849	−	0.506888i	0.251124	−	0.967955i	$-0.419200\pi$
$941$	34.9240	−	15.5492i	1.13849	−	0.506888i	0.887366	+	0.461067i	$0.152533\pi$
$942$	−10.2116	−	33.0372i	−0.332711	−	1.07641i
$943$	−0.809195	−	1.40157i	−0.0263510	−	0.0456413i
$944$	−0.0507719	−	0.156260i	−0.00165249	−	0.00508583i
$945$	8.80488	−	5.98030i	0.286423	−	0.194539i
$946$	1.60824	−	4.94964i	0.0522883	−	0.160927i
$947$	15.0237	−	3.19339i	0.488206	−	0.103771i	0.0427694	−	0.999085i	$-0.486382\pi$
$947$	15.0237	−	3.19339i	0.488206	−	0.103771i	0.445436	+	0.895314i	$0.353049\pi$
$948$	10.6767	−	7.52487i	0.346762	−	0.244396i
$949$	2.28600	−	3.95947i	0.0742067	−	0.128530i
$950$	26.4410	−	12.5060i	0.857859	−	0.405747i
$951$	9.09845	+	16.2958i	0.295037	+	0.528427i
$952$	11.5865	+	5.15864i	0.375521	+	0.167193i
$953$	−12.6455	+	38.9188i	−0.409628	+	1.26070i	0.507341	+	0.861745i	$0.330628\pi$
$953$	−12.6455	+	38.9188i	−0.409628	+	1.26070i	−0.916969	+	0.398959i	$0.869372\pi$
$954$	−29.2445	+	5.34204i	−0.946827	+	0.172955i
$955$	12.8673	+	9.12521i	0.416375	+	0.295285i
$956$	4.64999	−	5.16434i	0.150391	−	0.167027i
$957$	8.35145	−	13.9963i	0.269964	−	0.452438i
$958$	−34.1431	−	7.25735i	−1.10311	−	0.234474i
$959$	16.3516	−	7.28019i	0.528020	−	0.235089i
$960$	19.4399	+	4.19151i	0.627421	+	0.135281i
$961$	−20.4230	−	9.09289i	−0.658805	−	0.293319i
$962$	−7.87516	−	5.72164i	−0.253905	−	0.184473i
$963$	−1.36585	−	1.05367i	−0.0440139	−	0.0339541i
$964$	−29.4352	+	21.3859i	−0.948043	+	0.688794i
$965$	6.39299	+	10.7857i	0.205798	+	0.347203i
$966$	0.109045	−	0.911228i	0.00350846	−	0.0293183i
$967$	16.3259	+	3.47018i	0.525007	+	0.111594i	0.462788	−	0.886469i	$-0.346849\pi$
$967$	16.3259	+	3.47018i	0.525007	+	0.111594i	0.0622185	+	0.998063i	$0.480182\pi$
$968$	12.6141	−	21.8482i	0.405432	−	0.702229i
$969$	−16.4562	−	53.2402i	−0.528648	−	1.71032i
$970$	7.86980	−	8.94431i	0.252684	−	0.287184i
$971$	−10.2477	+	31.5391i	−0.328863	+	1.01214i	0.640803	+	0.767705i	$0.278601\pi$
$971$	−10.2477	+	31.5391i	−0.328863	+	1.01214i	−0.969667	+	0.244432i	$0.921399\pi$
$972$	−11.6545	−	14.9817i	−0.373819	−	0.480538i
$973$	−11.9286	+	8.66664i	−0.382414	+	0.277840i
$974$	2.71298	+	4.69902i	0.0869295	+	0.150566i
$975$	12.7516	−	9.43194i	0.408379	−	0.302064i
$976$	0.518895	−	0.898752i	0.0166094	−	0.0287684i
$977$	2.04222	+	19.4304i	0.0653363	+	0.621633i	0.977373	+	0.211524i	$0.0678427\pi$
$977$	2.04222	+	19.4304i	0.0653363	+	0.621633i	−0.912036	+	0.410109i	$0.865491\pi$
$978$	−24.7503	+	4.88991i	−0.791427	+	0.156362i
$979$	−20.1692	+	4.28710i	−0.644612	+	0.137016i
$980$	−5.00035	+	16.0115i	−0.159730	+	0.511468i
$981$	−10.8824	−	37.0899i	−0.347448	−	1.18419i
$982$	36.6619			1.16993
$983$	22.9263	−	25.4622i	0.731234	−	0.812117i	−0.256782	−	0.966469i	$-0.582662\pi$
$983$	22.9263	−	25.4622i	0.731234	−	0.812117i	0.988016	+	0.154352i	$0.0493289\pi$
$984$	11.2156	−	4.80145i	0.357541	−	0.153065i
$985$	−3.16171	−	3.43153i	−0.100740	−	0.109338i
$986$	−2.89608	−	27.5543i	−0.0922298	−	0.877508i
$987$	−7.84842	+	3.35994i	−0.249818	+	0.106948i
$988$	1.54166	−	14.6679i	0.0490466	−	0.466647i
$989$	2.12995	−	1.54750i	0.0677284	−	0.0492075i
$990$	7.85939	+	3.66347i	0.249788	+	0.116433i
$991$	1.53877	+	1.11799i	0.0488808	+	0.0355140i	0.611957	−	0.790891i	$-0.290382\pi$
$991$	1.53877	+	1.11799i	0.0488808	+	0.0355140i	−0.563077	+	0.826405i	$0.690382\pi$
$992$	11.0553	−	12.2782i	0.351006	−	0.389832i
$993$	−12.6763	−	22.7039i	−0.402271	−	0.720487i
$994$	13.0720	+	2.77855i	0.414620	+	0.0881302i
$995$	3.35940	−	5.97576i	0.106500	−	0.189444i
$996$	−2.72527	+	7.99444i	−0.0863534	+	0.253313i
$997$	−37.4240	+	7.95471i	−1.18523	+	0.251928i	−0.758024	−	0.652226i	$-0.773835\pi$
$997$	−37.4240	+	7.95471i	−1.18523	+	0.251928i	−0.427205	+	0.904155i	$0.640502\pi$
$998$	30.7812	−	22.3639i	0.974363	−	0.707916i
$999$	31.1946	+	1.34673i	0.986952	+	0.0426088i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	225.2.q.a.211.12	yes	224
3.2	odd	2		675.2.r.a.361.17		224
9.2	odd	6		675.2.r.a.586.12		224
9.7	even	3	inner	225.2.q.a.61.17	yes	224
25.16	even	5	inner	225.2.q.a.166.17	yes	224
75.41	odd	10		675.2.r.a.91.12		224
225.16	even	15	inner	225.2.q.a.16.12	✓	224
225.191	odd	30		675.2.r.a.316.17		224

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
225.2.q.a.16.12	✓	224	225.16	even	15	inner
225.2.q.a.61.17	yes	224	9.7	even	3	inner
225.2.q.a.166.17	yes	224	25.16	even	5	inner
225.2.q.a.211.12	yes	224	1.1	even	1	trivial
675.2.r.a.91.12		224	75.41	odd	10
675.2.r.a.316.17		224	225.191	odd	30
675.2.r.a.361.17		224	3.2	odd	2
675.2.r.a.586.12		224	9.2	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 225 = 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	225.q (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.808045 - 0.359765i) q^{2} +(0.558868 - 1.63941i) q^{3} +(-0.814755 - 0.904878i) q^{4} +(1.09577 - 1.94918i) q^{5} +(-1.04139 + 1.12366i) q^{6} +(-0.458035 - 0.793340i) q^{7} +(0.879476 + 2.70675i) q^{8} +(-2.37533 - 1.83243i) q^{9} +O(q^{10})\)	\(q+(-0.808045 - 0.359765i) q^{2} +(0.558868 - 1.63941i) q^{3} +(-0.814755 - 0.904878i) q^{4} +(1.09577 - 1.94918i) q^{5} +(-1.04139 + 1.12366i) q^{6} +(-0.458035 - 0.793340i) q^{7} +(0.879476 + 2.70675i) q^{8} +(-2.37533 - 1.83243i) q^{9} +(-1.58668 + 1.18080i) q^{10} +(1.33506 + 0.594408i) q^{11} +(-1.93881 + 0.830012i) q^{12} +(-1.67311 + 0.744918i) q^{13} +(0.0846971 + 0.805839i) q^{14} +(-2.58311 - 2.88575i) q^{15} +(0.00858220 - 0.0816542i) q^{16} +(1.50326 + 4.62656i) q^{17} +(1.26013 + 2.33524i) q^{18} +(-2.04373 - 6.28996i) q^{19} +(-2.65655 + 0.596562i) q^{20} +(-1.55659 + 0.307535i) q^{21} +(-0.864943 - 0.960617i) q^{22} +(-0.0683526 - 0.650331i) q^{23} +(4.92898 + 0.0708924i) q^{24} +(-2.59857 - 4.27170i) q^{25} +1.61995 q^{26} +(-4.33160 + 2.87006i) q^{27} +(-0.344689 + 1.06084i) q^{28} +(6.29829 - 1.33874i) q^{29} +(1.04907 + 3.26113i) q^{30} +(2.87587 + 0.611285i) q^{31} +(2.80973 - 4.86660i) q^{32} +(1.72060 - 1.85652i) q^{33} +(0.449771 - 4.27929i) q^{34} +(-2.04826 + 0.0234710i) q^{35} +(0.277194 + 3.64237i) q^{36} +(-4.86137 - 3.53200i) q^{37} +(-0.611478 + 5.81783i) q^{38} +(0.286177 + 3.15923i) q^{39} +(6.23963 + 1.25173i) q^{40} +(2.26096 - 1.00664i) q^{41} +(1.36844 + 0.311504i) q^{42} +(2.01308 + 3.48676i) q^{43} +(-0.549883 - 1.69237i) q^{44} +(-6.17455 + 2.62202i) q^{45} +(-0.178734 + 0.550087i) q^{46} +(5.26308 - 1.11870i) q^{47} +(-0.129068 - 0.0597036i) q^{48} +(3.08041 - 5.33542i) q^{49} +(0.562952 + 4.38660i) q^{50} +(8.42495 + 0.121174i) q^{51} +(2.03724 + 0.907036i) q^{52} +(-3.46201 + 10.6550i) q^{53} +(4.53267 - 0.760783i) q^{54} +(2.62153 - 1.95093i) q^{55} +(1.74454 - 1.93751i) q^{56} +(-11.4540 - 0.164740i) q^{57} +(-5.57093 - 1.18414i) q^{58} +(1.82813 - 0.813937i) q^{59} +(-0.506651 + 4.68858i) q^{60} +(11.5472 + 5.14113i) q^{61} +(-2.10391 - 1.52858i) q^{62} +(-0.365752 + 2.72376i) q^{63} +(-4.15407 + 3.01811i) q^{64} +(-0.381374 + 4.07745i) q^{65} +(-2.05823 + 0.881139i) q^{66} +(8.34092 + 1.77292i) q^{67} +(2.96168 - 5.12978i) q^{68} +(-1.10436 - 0.251391i) q^{69} +(1.66353 + 0.717926i) q^{70} +(5.09668 - 15.6860i) q^{71} +(2.87087 - 8.04101i) q^{72} +(-2.01962 + 1.46734i) q^{73} +(2.65752 + 4.60296i) q^{74} +(-8.45533 + 1.87280i) q^{75} +(-4.02650 + 6.97410i) q^{76} +(-0.139938 - 1.33142i) q^{77} +(0.905335 - 2.65576i) q^{78} +(-6.05809 + 1.28769i) q^{79} +(-0.149754 - 0.106203i) q^{80} +(2.28442 + 8.70525i) q^{81} -2.18911 q^{82} +(2.67975 - 2.97617i) q^{83} +(1.54652 + 1.15796i) q^{84} +(10.6652 + 2.13954i) q^{85} +(-0.372247 - 3.54169i) q^{86} +(1.32516 - 11.0737i) q^{87} +(-0.434758 + 4.13645i) q^{88} +(-11.4149 + 8.29340i) q^{89} +(5.93262 + 0.102674i) q^{90} +(1.35732 + 0.986149i) q^{91} +(-0.532779 + 0.591712i) q^{92} +(2.60938 - 4.37310i) q^{93} +(-4.65527 - 0.989508i) q^{94} +(-14.4997 - 2.90877i) q^{95} +(-6.40809 - 7.32609i) q^{96} +(-5.89193 + 1.25237i) q^{97} +(-4.40860 + 3.20304i) q^{98} +(-2.08201 - 3.85832i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 224 q - 3 q^{2} - 8 q^{3} + 23 q^{4} - 8 q^{5} - 10 q^{6} - 8 q^{7} - 20 q^{8} - 8 q^{9}+O(q^{10}) \) 224 * q - 3 * q^2 - 8 * q^3 + 23 * q^4 - 8 * q^5 - 10 * q^6 - 8 * q^7 - 20 * q^8 - 8 * q^9	\( 224 q - 3 q^{2} - 8 q^{3} + 23 q^{4} - 8 q^{5} - 10 q^{6} - 8 q^{7} - 20 q^{8} - 8 q^{9} - 20 q^{10} - 11 q^{11} - 4 q^{12} - 3 q^{13} + q^{14} - 48 q^{15} + 23 q^{16} - 24 q^{17} - 12 q^{19} + q^{20} + 15 q^{21} - 11 q^{22} + q^{23} - 30 q^{24} - 16 q^{25} - 136 q^{26} + 7 q^{27} + 4 q^{28} - 15 q^{29} - 24 q^{30} + 3 q^{31} + 12 q^{32} - 5 q^{33} + q^{34} + 14 q^{35} + 38 q^{36} - 24 q^{37} + 55 q^{38} + 20 q^{39} + q^{40} - 19 q^{41} - 38 q^{42} - 8 q^{43} + 4 q^{44} - 38 q^{45} - 20 q^{46} - 10 q^{47} - 25 q^{48} - 72 q^{49} - 3 q^{50} - 26 q^{51} - 25 q^{52} - 12 q^{53} + 53 q^{54} - 20 q^{55} - 60 q^{56} + 38 q^{57} - 23 q^{58} - 30 q^{59} - 33 q^{60} - 3 q^{61} - 44 q^{62} + 46 q^{63} - 44 q^{64} + 51 q^{65} - 134 q^{66} - 12 q^{67} - 156 q^{68} + 4 q^{69} - 16 q^{70} + 42 q^{71} + 74 q^{72} - 12 q^{73} + 90 q^{74} + 67 q^{75} - 8 q^{76} + 31 q^{77} - 92 q^{78} - 15 q^{79} + 298 q^{80} - 104 q^{81} + 8 q^{82} + 59 q^{83} + 115 q^{84} - 11 q^{85} + 9 q^{86} - 59 q^{87} - 23 q^{88} + 106 q^{89} + 107 q^{90} + 30 q^{91} + 11 q^{92} + 32 q^{93} + 25 q^{94} + 7 q^{95} + 35 q^{96} - 21 q^{97} + 146 q^{98} - 20 q^{99}+O(q^{100}) \) 224 * q - 3 * q^2 - 8 * q^3 + 23 * q^4 - 8 * q^5 - 10 * q^6 - 8 * q^7 - 20 * q^8 - 8 * q^9 - 20 * q^10 - 11 * q^11 - 4 * q^12 - 3 * q^13 + q^14 - 48 * q^15 + 23 * q^16 - 24 * q^17 - 12 * q^19 + q^20 + 15 * q^21 - 11 * q^22 + q^23 - 30 * q^24 - 16 * q^25 - 136 * q^26 + 7 * q^27 + 4 * q^28 - 15 * q^29 - 24 * q^30 + 3 * q^31 + 12 * q^32 - 5 * q^33 + q^34 + 14 * q^35 + 38 * q^36 - 24 * q^37 + 55 * q^38 + 20 * q^39 + q^40 - 19 * q^41 - 38 * q^42 - 8 * q^43 + 4 * q^44 - 38 * q^45 - 20 * q^46 - 10 * q^47 - 25 * q^48 - 72 * q^49 - 3 * q^50 - 26 * q^51 - 25 * q^52 - 12 * q^53 + 53 * q^54 - 20 * q^55 - 60 * q^56 + 38 * q^57 - 23 * q^58 - 30 * q^59 - 33 * q^60 - 3 * q^61 - 44 * q^62 + 46 * q^63 - 44 * q^64 + 51 * q^65 - 134 * q^66 - 12 * q^67 - 156 * q^68 + 4 * q^69 - 16 * q^70 + 42 * q^71 + 74 * q^72 - 12 * q^73 + 90 * q^74 + 67 * q^75 - 8 * q^76 + 31 * q^77 - 92 * q^78 - 15 * q^79 + 298 * q^80 - 104 * q^81 + 8 * q^82 + 59 * q^83 + 115 * q^84 - 11 * q^85 + 9 * q^86 - 59 * q^87 - 23 * q^88 + 106 * q^89 + 107 * q^90 + 30 * q^91 + 11 * q^92 + 32 * q^93 + 25 * q^94 + 7 * q^95 + 35 * q^96 - 21 * q^97 + 146 * q^98 - 20 * q^99

Introduction

L-functions

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