LMFDB - Embedded newform 507.2.t.b.127.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [507,2,Mod(4,507)]

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, 1]))

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

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

chi := DirichletCharacter("507.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 507 = 3 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	507.t (of order $78$, 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:	$360$
Relative dimension:	$15$ over $\Q(\zeta_{78})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{78}]$

Embedding invariants

Embedding label			127.2
Character	$\chi$	$=$	507.127
Dual form			507.2.t.b.4.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.53957 + 0.102341i) q^{2} +(-0.278217 - 0.960518i) q^{3} +(4.44542 - 0.358871i) q^{4} +(1.66050 - 0.629744i) q^{5} +(0.804853 + 2.41083i) q^{6} +(-2.05060 + 4.81293i) q^{7} +(-6.20652 + 0.753608i) q^{8} +(-0.845190 + 0.534466i) q^{9} +O(q^{10})$	\(q+(-2.53957 + 0.102341i) q^{2} +(-0.278217 - 0.960518i) q^{3} +(4.44542 - 0.358871i) q^{4} +(1.66050 - 0.629744i) q^{5} +(0.804853 + 2.41083i) q^{6} +(-2.05060 + 4.81293i) q^{7} +(-6.20652 + 0.753608i) q^{8} +(-0.845190 + 0.534466i) q^{9} +(-4.15250 + 1.76922i) q^{10} +(0.626521 - 0.990764i) q^{11} +(-1.58150 - 4.17006i) q^{12} +(-3.48167 - 0.936989i) q^{13} +(4.71507 - 12.4326i) q^{14} +(-1.06686 - 1.41973i) q^{15} +(6.88051 - 1.11819i) q^{16} +(-4.86253 - 2.07173i) q^{17} +(2.09172 - 1.44381i) q^{18} +(0.350140 + 0.202153i) q^{19} +(7.15562 - 3.39538i) q^{20} +(5.19341 + 0.630595i) q^{21} +(-1.48970 + 2.58023i) q^{22} +(-1.21725 - 2.10834i) q^{23} +(2.45062 + 5.75181i) q^{24} +(-1.38187 + 1.22423i) q^{25} +(8.93784 + 2.02323i) q^{26} +(0.748511 + 0.663123i) q^{27} +(-7.38854 + 22.1314i) q^{28} +(-0.322649 - 8.00644i) q^{29} +(2.85466 + 3.49633i) q^{30} +(3.37219 - 3.80642i) q^{31} +(-5.10758 + 1.04272i) q^{32} +(-1.12596 - 0.326137i) q^{33} +(12.5607 + 4.76366i) q^{34} +(-0.374101 + 9.28321i) q^{35} +(-3.56542 + 2.67924i) q^{36} +(1.51475 + 0.309239i) q^{37} +(-0.909892 - 0.477548i) q^{38} +(0.0686671 + 3.60490i) q^{39} +(-9.83135 + 5.15989i) q^{40} +(-9.64780 + 2.79452i) q^{41} +(-13.2536 - 1.06994i) q^{42} +(-1.80773 - 8.85483i) q^{43} +(2.42959 - 4.62920i) q^{44} +(-1.06686 + 1.41973i) q^{45} +(3.30706 + 5.22969i) q^{46} +(-7.01712 - 4.84357i) q^{47} +(-2.98832 - 6.29776i) q^{48} +(-14.1102 - 14.6903i) q^{49} +(3.38407 - 3.25045i) q^{50} +(-0.637093 + 5.24694i) q^{51} +(-15.8138 - 2.91584i) q^{52} +(0.532237 + 4.38337i) q^{53} +(-1.96876 - 1.60744i) q^{54} +(0.416410 - 2.03971i) q^{55} +(9.10001 - 31.4169i) q^{56} +(0.0967569 - 0.392558i) q^{57} +(1.63878 + 20.2999i) q^{58} +(0.739825 - 4.55233i) q^{59} +(-5.25215 - 5.92845i) q^{60} +(-0.780993 - 0.586878i) q^{61} +(-8.17435 + 10.0118i) q^{62} +(-0.839201 - 5.16381i) q^{63} +(-0.672112 + 0.165661i) q^{64} +(-6.37138 + 0.636694i) q^{65} +(2.89282 + 0.713016i) q^{66} +(-0.245240 + 3.03785i) q^{67} +(-22.3595 - 7.46468i) q^{68} +(-1.68644 + 1.75577i) q^{69} -23.6136i q^{70} +(5.05686 + 4.85718i) q^{71} +(4.84291 - 3.95412i) q^{72} +(1.42000 + 2.70559i) q^{73} +(-3.87846 - 0.630311i) q^{74} +(1.56036 + 0.986712i) q^{75} +(1.62906 + 0.773001i) q^{76} +(3.48373 + 5.04706i) q^{77} +(-0.543314 - 9.14786i) q^{78} +(-6.95552 + 10.0768i) q^{79} +(10.7209 - 6.18972i) q^{80} +(0.428693 - 0.903450i) q^{81} +(24.2153 - 8.08424i) q^{82} +(2.33385 + 9.46882i) q^{83} +(23.3132 + 0.939490i) q^{84} +(-9.37888 - 0.377956i) q^{85} +(5.49706 + 22.3024i) q^{86} +(-7.60056 + 2.53744i) q^{87} +(-3.14187 + 6.62135i) q^{88} +(-14.6742 + 8.47216i) q^{89} +(2.56407 - 3.71469i) q^{90} +(11.6492 - 14.8356i) q^{91} +(-6.16781 - 8.93561i) q^{92} +(-4.59433 - 2.18004i) q^{93} +(18.3161 + 11.5824i) q^{94} +(0.708711 + 0.115177i) q^{95} +(2.42257 + 4.61582i) q^{96} +(10.9636 - 8.95154i) q^{97} +(37.3373 + 35.8630i) q^{98} +1.17224i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 360 q - 15 q^{3} - 14 q^{4} + 3 q^{7} + 15 q^{9}+O(q^{10}) $ 360 * q - 15 * q^3 - 14 * q^4 + 3 * q^7 + 15 * q^9	$ 360 q - 15 q^{3} - 14 q^{4} + 3 q^{7} + 15 q^{9} + 6 q^{11} - 28 q^{12} + 6 q^{13} + 4 q^{14} - 6 q^{15} + 20 q^{16} - 6 q^{19} - 12 q^{20} - 28 q^{22} + 46 q^{23} - 6 q^{25} - 39 q^{26} + 30 q^{27} - 6 q^{28} + 43 q^{29} + 26 q^{31} - 195 q^{32} + 19 q^{33} + 65 q^{34} + 84 q^{35} - 14 q^{36} - 65 q^{38} - 2 q^{39} + 12 q^{41} - 128 q^{42} + 83 q^{43} - 39 q^{44} - 6 q^{45} - 20 q^{48} + 72 q^{49} - 52 q^{50} - 55 q^{52} + 49 q^{53} - 49 q^{55} - 2 q^{56} + 26 q^{57} + 26 q^{58} - 202 q^{59} - 182 q^{60} - 3 q^{61} - 65 q^{62} - 3 q^{63} - 14 q^{64} - 58 q^{65} + 48 q^{66} - 41 q^{67} + 139 q^{68} + 6 q^{69} - 60 q^{71} - 52 q^{73} - 269 q^{74} + 23 q^{75} - 14 q^{76} + 70 q^{77} - 65 q^{78} + 18 q^{79} + 492 q^{80} + 15 q^{81} - 65 q^{82} + 78 q^{83} - 6 q^{84} - 91 q^{85} - 169 q^{86} + 48 q^{87} - 522 q^{88} - 12 q^{89} + 373 q^{91} + 72 q^{92} - 3 q^{93} - 13 q^{94} - 110 q^{95} + 65 q^{96} - 121 q^{97} - 104 q^{98}+O(q^{100}) $ 360 * q - 15 * q^3 - 14 * q^4 + 3 * q^7 + 15 * q^9 + 6 * q^11 - 28 * q^12 + 6 * q^13 + 4 * q^14 - 6 * q^15 + 20 * q^16 - 6 * q^19 - 12 * q^20 - 28 * q^22 + 46 * q^23 - 6 * q^25 - 39 * q^26 + 30 * q^27 - 6 * q^28 + 43 * q^29 + 26 * q^31 - 195 * q^32 + 19 * q^33 + 65 * q^34 + 84 * q^35 - 14 * q^36 - 65 * q^38 - 2 * q^39 + 12 * q^41 - 128 * q^42 + 83 * q^43 - 39 * q^44 - 6 * q^45 - 20 * q^48 + 72 * q^49 - 52 * q^50 - 55 * q^52 + 49 * q^53 - 49 * q^55 - 2 * q^56 + 26 * q^57 + 26 * q^58 - 202 * q^59 - 182 * q^60 - 3 * q^61 - 65 * q^62 - 3 * q^63 - 14 * q^64 - 58 * q^65 + 48 * q^66 - 41 * q^67 + 139 * q^68 + 6 * q^69 - 60 * q^71 - 52 * q^73 - 269 * q^74 + 23 * q^75 - 14 * q^76 + 70 * q^77 - 65 * q^78 + 18 * q^79 + 492 * q^80 + 15 * q^81 - 65 * q^82 + 78 * q^83 - 6 * q^84 - 91 * q^85 - 169 * q^86 + 48 * q^87 - 522 * q^88 - 12 * q^89 + 373 * q^91 + 72 * q^92 - 3 * q^93 - 13 * q^94 - 110 * q^95 + 65 * q^96 - 121 * q^97 - 104 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$170$	$340$
$\chi(n)$	$1$	$e\left(\frac{77}{78}\right)$

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 $

$2$	−2.53957	+	0.102341i	−1.79575	+	0.0723661i	−0.915540	−	0.402226i	$-0.868237\pi$
$2$	−2.53957	+	0.102341i	−1.79575	+	0.0723661i	−0.880206	+	0.474592i	$0.842596\pi$
$3$	−0.278217	−	0.960518i	−0.160629	−	0.554555i
$3$	−0.278217	−	0.960518i	−0.160629	−	0.554555i
$4$	4.44542	−	0.358871i	2.22271	−	0.179436i
$5$	1.66050	−	0.629744i	0.742598	−	0.281630i	0.0458519	−	0.998948i	$-0.485400\pi$
$5$	1.66050	−	0.629744i	0.742598	−	0.281630i	0.696746	+	0.717318i	$0.254631\pi$
$6$	0.804853	+	2.41083i	0.328580	+	0.984217i
$7$	−2.05060	+	4.81293i	−0.775052	+	1.81911i	−0.249441	+	0.968390i	$0.580247\pi$
$7$	−2.05060	+	4.81293i	−0.775052	+	1.81911i	−0.525611	+	0.850725i	$0.676163\pi$
$8$	−6.20652	+	0.753608i	−2.19434	+	0.266441i
$9$	−0.845190	+	0.534466i	−0.281730	+	0.178155i
$10$	−4.15250	+	1.76922i	−1.31314	+	0.559475i
$11$	0.626521	−	0.990764i	0.188903	−	0.298727i	−0.737436	−	0.675417i	$-0.763964\pi$
$11$	0.626521	−	0.990764i	0.188903	−	0.298727i	0.926339	+	0.376690i	$0.122938\pi$
$12$	−1.58150	−	4.17006i	−0.456539	−	1.20379i
$13$	−3.48167	−	0.936989i	−0.965643	−	0.259874i
$13$	−3.48167	−	0.936989i	−0.965643	−	0.259874i
$14$	4.71507	−	12.4326i	1.26016	−	3.32276i
$15$	−1.06686	−	1.41973i	−0.275462	−	0.366574i
$16$	6.88051	−	1.11819i	1.72013	−	0.279548i
$17$	−4.86253	−	2.07173i	−1.17934	−	0.502468i	−0.288804	−	0.957388i	$-0.593258\pi$
$17$	−4.86253	−	2.07173i	−1.17934	−	0.502468i	−0.890532	+	0.454920i	$0.849668\pi$
$18$	2.09172	−	1.44381i	0.493023	−	0.340309i
$19$	0.350140	+	0.202153i	0.0803275	+	0.0463771i	0.539626	−	0.841905i	$-0.318566\pi$
$19$	0.350140	+	0.202153i	0.0803275	+	0.0463771i	−0.459298	+	0.888282i	$0.651899\pi$
$20$	7.15562	−	3.39538i	1.60005	−	0.759231i
$21$	5.19341	+	0.630595i	1.13330	+	0.137607i
$22$	−1.48970	+	2.58023i	−0.317605	+	0.550107i
$23$	−1.21725	−	2.10834i	−0.253814	−	0.439619i	0.710759	−	0.703436i	$-0.248352\pi$
$23$	−1.21725	−	2.10834i	−0.253814	−	0.439619i	−0.964573	+	0.263817i	$0.915018\pi$
$24$	2.45062	+	5.75181i	0.500230	+	1.17408i
$25$	−1.38187	+	1.22423i	−0.276375	+	0.244847i
$26$	8.93784	+	2.02323i	1.75285	+	0.396788i
$27$	0.748511	+	0.663123i	0.144051	+	0.127618i
$28$	−7.38854	+	22.1314i	−1.39630	+	4.18244i
$29$	−0.322649	−	8.00644i	−0.0599143	−	1.48676i	−0.697614	−	0.716474i	$-0.745755\pi$
$29$	−0.322649	−	8.00644i	−0.0599143	−	1.48676i	0.637700	−	0.770285i	$-0.279886\pi$
$30$	2.85466	+	3.49633i	0.521188	+	0.638339i
$31$	3.37219	−	3.80642i	0.605663	−	0.683652i	−0.363069	−	0.931762i	$-0.618271\pi$
$31$	3.37219	−	3.80642i	0.605663	−	0.683652i	0.968732	+	0.248110i	$0.0798094\pi$
$32$	−5.10758	+	1.04272i	−0.902901	+	0.184329i
$33$	−1.12596	−	0.326137i	−0.196004	−	0.0567732i
$34$	12.5607	+	4.76366i	2.15415	+	0.816961i
$35$	−0.374101	+	9.28321i	−0.0632345	+	1.56915i
$36$	−3.56542	+	2.67924i	−0.594237	+	0.446540i
$37$	1.51475	+	0.309239i	0.249023	+	0.0508385i	0.322916	−	0.946428i	$-0.395337\pi$
$37$	1.51475	+	0.309239i	0.249023	+	0.0508385i	−0.0738923	+	0.997266i	$0.523542\pi$
$38$	−0.909892	−	0.477548i	−0.147604	−	0.0774686i
$39$	0.0686671	+	3.60490i	0.0109955	+	0.577246i
$40$	−9.83135	+	5.15989i	−1.55447	+	0.815850i
$41$	−9.64780	+	2.79452i	−1.50673	+	0.436431i	−0.925956	−	0.377632i	$-0.876739\pi$
$41$	−9.64780	+	2.79452i	−1.50673	+	0.436431i	−0.580777	+	0.814062i	$0.697251\pi$
$42$	−13.2536	−	1.06994i	−2.04507	−	0.165095i
$43$	−1.80773	−	8.85483i	−0.275676	−	1.35035i	−0.847858	−	0.530223i	$-0.822108\pi$
$43$	−1.80773	−	8.85483i	−0.275676	−	1.35035i	0.572183	−	0.820126i	$-0.306097\pi$
$44$	2.42959	−	4.62920i	0.366275	−	0.697879i
$45$	−1.06686	+	1.41973i	−0.159038	+	0.211641i
$46$	3.30706	+	5.22969i	0.487599	+	0.771076i
$47$	−7.01712	−	4.84357i	−1.02355	−	0.706507i	−0.0669054	−	0.997759i	$-0.521313\pi$
$47$	−7.01712	−	4.84357i	−1.02355	−	0.706507i	−0.956646	+	0.291253i	$0.905928\pi$
$48$	−2.98832	−	6.29776i	−0.431327	−	0.909003i
$49$	−14.1102	−	14.6903i	−2.01575	−	2.09862i
$50$	3.38407	−	3.25045i	0.478580	−	0.459683i
$51$	−0.637093	+	5.24694i	−0.0892109	+	0.734718i
$52$	−15.8138	−	2.91584i	−2.19297	−	0.404354i
$53$	0.532237	+	4.38337i	0.0731084	+	0.602102i	0.982514	+	0.186191i	$0.0596142\pi$
$53$	0.532237	+	4.38337i	0.0731084	+	0.602102i	−0.909405	+	0.415911i	$0.863463\pi$
$54$	−1.96876	−	1.60744i	−0.267914	−	0.218745i
$55$	0.416410	−	2.03971i	0.0561487	−	0.275035i
$56$	9.10001	−	31.4169i	1.21604	−	4.19826i
$57$	0.0967569	−	0.392558i	0.0128158	−	0.0519956i
$58$	1.63878	+	20.2999i	0.215182	+	2.66551i
$59$	0.739825	−	4.55233i	0.0963170	−	0.592662i	−0.893359	−	0.449343i	$-0.851658\pi$
$59$	0.739825	−	4.55233i	0.0963170	−	0.592662i	0.989676	−	0.143320i	$-0.0457777\pi$
$60$	−5.25215	−	5.92845i	−0.678049	−	0.765359i
$61$	−0.780993	−	0.586878i	−0.0999959	−	0.0751420i	0.549568	−	0.835449i	$-0.314792\pi$
$61$	−0.780993	−	0.586878i	−0.0999959	−	0.0751420i	−0.649564	+	0.760307i	$0.725049\pi$
$62$	−8.17435	+	10.0118i	−1.03814	+	1.27150i
$63$	−0.839201	−	5.16381i	−0.105729	−	0.650579i
$64$	−0.672112	+	0.165661i	−0.0840140	+	0.0207076i
$65$	−6.37138	+	0.636694i	−0.790272	+	0.0789722i
$66$	2.89282	+	0.713016i	0.356082	+	0.0877662i
$67$	−0.245240	+	3.03785i	−0.0299609	+	0.371132i	0.964351	+	0.264626i	$0.0852485\pi$
$67$	−0.245240	+	3.03785i	−0.0299609	+	0.371132i	−0.994312	+	0.106506i	$0.966034\pi$
$68$	−22.3595	−	7.46468i	−2.71148	−	0.905226i
$69$	−1.68644	+	1.75577i	−0.203023	+	0.211369i
$70$		−	23.6136i		−	2.82237i
$71$	5.05686	+	4.85718i	0.600139	+	0.576441i	0.929987	−	0.367593i	$-0.119818\pi$
$71$	5.05686	+	4.85718i	0.600139	+	0.576441i	−0.329848	+	0.944034i	$0.606997\pi$
$72$	4.84291	−	3.95412i	0.570743	−	0.465997i
$73$	1.42000	+	2.70559i	0.166199	+	0.316665i	0.954284	−	0.298901i	$-0.0966199\pi$
$73$	1.42000	+	2.70559i	0.166199	+	0.316665i	−0.788086	+	0.615566i	$0.788928\pi$
$74$	−3.87846	−	0.630311i	−0.450862	−	0.0732722i
$75$	1.56036	+	0.986712i	0.180175	+	0.113936i
$76$	1.62906	+	0.773001i	0.186867	+	0.0886693i
$77$	3.48373	+	5.04706i	0.397008	+	0.575166i
$78$	−0.543314	−	9.14786i	−0.0615182	−	1.03579i
$79$	−6.95552	+	10.0768i	−0.782557	+	1.13373i	0.205351	+	0.978688i	$0.434166\pi$
$79$	−6.95552	+	10.0768i	−0.782557	+	1.13373i	−0.987908	+	0.155041i	$0.950449\pi$
$80$	10.7209	−	6.18972i	1.19863	−	0.692032i
$81$	0.428693	−	0.903450i	0.0476325	−	0.100383i
$82$	24.2153	−	8.08424i	2.67413	−	0.892755i
$83$	2.33385	+	9.46882i	0.256174	+	1.03934i	0.948253	+	0.317516i	$0.102849\pi$
$83$	2.33385	+	9.46882i	0.256174	+	1.03934i	−0.692079	+	0.721822i	$0.743305\pi$
$84$	23.3132	+	0.939490i	2.54368	+	0.102507i
$85$	−9.37888	−	0.377956i	−1.01728	−	0.0409951i
$86$	5.49706	+	22.3024i	0.592763	+	2.40493i
$87$	−7.60056	+	2.53744i	−0.814866	+	0.272042i
$88$	−3.14187	+	6.62135i	−0.334925	+	0.705839i
$89$	−14.6742	+	8.47216i	−1.55546	+	0.898047i	−0.557781	+	0.829988i	$0.688347\pi$
$89$	−14.6742	+	8.47216i	−1.55546	+	0.898047i	−0.997681	+	0.0680590i	$0.978319\pi$
$90$	2.56407	−	3.71469i	0.270277	−	0.391563i
$91$	11.6492	−	14.8356i	1.22116	−	1.55520i
$92$	−6.16781	−	8.93561i	−0.643038	−	0.931602i
$93$	−4.59433	−	2.18004i	−0.476410	−	0.226059i
$94$	18.3161	+	11.5824i	1.88917	+	1.19464i
$95$	0.708711	+	0.115177i	0.0727123	+	0.0118169i
$96$	2.42257	+	4.61582i	0.247252	+	0.471100i
$97$	10.9636	−	8.95154i	1.11319	−	0.908891i	0.116746	−	0.993162i	$-0.462754\pi$
$97$	10.9636	−	8.95154i	1.11319	−	0.908891i	0.996443	+	0.0842709i	$0.0268561\pi$
$98$	37.3373	+	35.8630i	3.77164	+	3.62271i
$99$			1.17224i			0.117814i
$100$	−5.70367	+	5.93815i	−0.570367	+	0.593815i
$101$	−4.35824	−	1.45499i	−0.433661	−	0.144777i	0.0914526	−	0.995809i	$-0.470849\pi$
$101$	−4.35824	−	1.45499i	−0.433661	−	0.144777i	−0.525114	+	0.851032i	$0.675977\pi$
$102$	1.08097	−	13.3902i	0.107031	−	1.32582i
$103$	4.91209	+	1.21072i	0.484002	+	0.119296i	0.473764	−	0.880652i	$-0.342895\pi$
$103$	4.91209	+	1.21072i	0.484002	+	0.119296i	0.0102380	+	0.999948i	$0.496741\pi$
$104$	22.3152	+	3.19163i	2.18819	+	0.312965i
$105$	9.02077	−	2.22342i	0.880337	−	0.216984i
$106$	−1.80025	−	11.0774i	−0.174856	−	1.07593i
$107$	−3.89438	+	4.76975i	−0.376484	+	0.461109i	−0.927740	−	0.373227i	$-0.878251\pi$
$107$	−3.89438	+	4.76975i	−0.376484	+	0.461109i	0.551256	+	0.834336i	$0.314149\pi$
$108$	3.56542	+	2.67924i	0.343083	+	0.257810i
$109$	−3.77271	−	4.25850i	−0.361360	−	0.407891i	0.539511	−	0.841979i	$-0.318609\pi$
$109$	−3.77271	−	4.25850i	−0.361360	−	0.407891i	−0.900871	+	0.434088i	$0.857071\pi$
$110$	−0.848756	+	5.22260i	−0.0809257	+	0.497956i
$111$	−0.124401	−	1.54098i	−0.0118076	−	0.146263i
$112$	−8.72738	+	35.4084i	−0.824659	+	3.34578i
$113$	3.09153	−	10.6732i	0.290827	−	1.00405i	−0.673467	−	0.739217i	$-0.735196\pi$
$113$	3.09153	−	10.6732i	0.290827	−	1.00405i	0.964294	−	0.264834i	$-0.0853172\pi$
$114$	−0.205546	+	1.00683i	−0.0192511	+	0.0942983i
$115$	−3.34896	−	2.73434i	−0.312292	−	0.254978i
$116$	−4.30759	−	35.4762i	−0.399950	−	3.29388i
$117$	3.44346	−	1.06890i	0.318348	−	0.0988200i
$118$	−1.41295	+	11.6367i	−0.130072	+	1.07124i
$119$	19.9422	−	19.1547i	1.82809	−	1.75591i
$120$	7.69142	+	8.00762i	0.702127	+	0.730992i
$121$	4.12653	+	8.69648i	0.375139	+	0.790590i
$122$	2.04345	+	1.41049i	0.185005	+	0.127700i
$123$	5.36837	+	8.48940i	0.484050	+	0.765464i
$124$	13.6248	−	18.1313i	1.22354	−	1.62824i
$125$	−5.65017	+	10.7655i	−0.505366	+	0.962895i
$126$	2.65968	+	13.0280i	0.236943	+	1.16062i
$127$	−2.62934	−	0.212262i	−0.233316	−	0.0188352i	−0.0367446	−	0.999325i	$-0.511699\pi$
$127$	−2.62934	−	0.212262i	−0.233316	−	0.0188352i	−0.196572	+	0.980489i	$0.562981\pi$
$128$	11.7041	−	3.39015i	1.03451	−	0.299650i
$129$	−8.00228	+	4.19992i	−0.704562	+	0.369783i
$130$	16.1154	−	2.26898i	1.41341	−	0.199003i
$131$	−0.0652387	−	0.0342399i	−0.00569993	−	0.00299155i	0.461871	−	0.886947i	$-0.347178\pi$
$131$	−0.0652387	−	0.0342399i	−0.00569993	−	0.00299155i	−0.467571	+	0.883956i	$0.654871\pi$
$132$	−5.12239	−	1.04574i	−0.445847	−	0.0910203i
$133$	−1.69094	+	1.27066i	−0.146623	+	0.110180i
$134$	0.311908	−	7.73992i	0.0269448	−	0.668627i
$135$	1.66050	+	0.629744i	0.142913	+	0.0541998i
$136$	31.7407	+	9.19380i	2.72174	+	0.788361i
$137$	−20.6449	+	4.21468i	−1.76381	+	0.360085i	−0.969055	−	0.246844i	$-0.920607\pi$
$137$	−20.6449	+	4.21468i	−1.76381	+	0.360085i	−0.794756	+	0.606928i	$0.792401\pi$
$138$	4.10313	−	4.63148i	0.349282	−	0.394258i
$139$	8.09968	+	9.92031i	0.687006	+	0.841430i	0.993897	−	0.110315i	$-0.0351860\pi$
$139$	8.09968	+	9.92031i	0.687006	+	0.841430i	−0.306890	+	0.951745i	$0.599289\pi$
$140$	1.66844	+	41.4020i	0.141009	+	3.49911i
$141$	−2.70005	+	8.08763i	−0.227385	+	0.681101i
$142$	−13.3393	−	11.8176i	−1.11941	−	0.991713i
$143$	−3.10968	+	2.86247i	−0.260044	+	0.239372i
$144$	−5.21771	+	4.62248i	−0.434809	+	0.385207i
$145$	−5.57777	−	13.0915i	−0.463208	−	1.08719i
$146$	−3.88308	−	6.72570i	−0.321366	−	0.556623i
$147$	−10.1846	+	17.6402i	−0.840012	+	1.45494i
$148$	6.84468	+	0.831094i	0.562629	+	0.0683155i
$149$	−2.61955	+	1.24299i	−0.214602	+	0.101830i	−0.532959	−	0.846141i	$-0.678920\pi$
$149$	−2.61955	+	1.24299i	−0.214602	+	0.101830i	0.318357	+	0.947971i	$0.396869\pi$
$150$	−4.06362	−	2.34613i	−0.331793	−	0.191561i
$151$	3.23450	−	2.23261i	0.263220	−	0.181687i	−0.429144	−	0.903236i	$-0.641185\pi$
$151$	3.23450	−	2.23261i	0.263220	−	0.181687i	0.692364	+	0.721549i	$0.256569\pi$
$152$	−2.32549	−	0.990801i	−0.188623	−	0.0803645i
$153$	5.21703	−	0.847850i	0.421772	−	0.0685446i
$154$	−9.36370	−	12.4608i	−0.754548	−	1.00412i
$155$	3.20245	−	8.44417i	0.257227	−	0.678252i
$156$	1.59895	+	16.0006i	0.128018	+	1.28108i
$157$	−6.58668	−	17.3676i	−0.525674	−	1.38609i	−0.890488	−	0.455008i	$-0.849637\pi$
$157$	−6.58668	−	17.3676i	−0.525674	−	1.38609i	0.364814	−	0.931081i	$-0.381133\pi$
$158$	16.6327	−	26.3026i	1.32323	−	2.09252i
$159$	4.06223	−	1.73075i	0.322156	−	0.137258i
$160$	−7.82449	+	4.94790i	−0.618580	+	0.391166i
$161$	12.6434	−	1.53518i	0.996436	−	0.120989i
$162$	−0.996234	+	2.33825i	−0.0782715	+	0.183710i
$163$	3.66640	+	10.9822i	0.287174	+	0.860192i	0.989009	+	0.147852i	$0.0472361\pi$
$163$	3.66640	+	10.9822i	0.287174	+	0.860192i	−0.701835	+	0.712339i	$0.747636\pi$
$164$	−41.8857	+	15.8851i	−3.27072	+	1.24042i
$165$	−2.07503	+	0.167514i	−0.161541	+	0.0130409i
$166$	−6.89603	−	23.8079i	−0.535236	−	1.84785i
$167$	5.34187	−	0.215270i	0.413366	−	0.0166581i	0.167288	−	0.985908i	$-0.446499\pi$
$167$	5.34187	−	0.215270i	0.413366	−	0.0166581i	0.246078	+	0.969250i	$0.420858\pi$
$168$	−32.7083			−2.52350
$169$	11.2441	+	6.52458i	0.864931	+	0.501891i
$170$	23.8570			1.82975
$171$	−0.403979	+	0.0162798i	−0.0308930	+	0.00124495i
$172$	−11.2138	−	38.7147i	−0.855048	−	2.95197i
$173$	−3.06641	+	0.247546i	−0.233135	+	0.0188206i	−0.196482	−	0.980507i	$-0.562952\pi$
$173$	−3.06641	+	0.247546i	−0.233135	+	0.0188206i	−0.0366531	+	0.999328i	$0.511670\pi$
$174$	19.0425	−	7.22186i	1.44361	−	0.547487i
$175$	−3.05848	−	9.16126i	−0.231199	−	0.692527i
$176$	3.20292	−	7.51754i	0.241429	−	0.566656i
$177$	−4.57842	+	0.555921i	−0.344135	+	0.0417856i
$178$	36.3991	−	23.0174i	2.72823	−	1.72523i
$179$	11.3880	−	4.85196i	0.851177	−	0.362653i	0.0780853	−	0.996947i	$-0.475119\pi$
$179$	11.3880	−	4.85196i	0.851177	−	0.362653i	0.773092	+	0.634294i	$0.218709\pi$
$180$	−4.23314	+	6.69418i	−0.315520	+	0.498955i
$181$	8.45756	+	22.3008i	0.628646	+	1.65760i	0.747155	+	0.664649i	$0.231419\pi$
$181$	8.45756	+	22.3008i	0.628646	+	1.65760i	−0.118510	+	0.992953i	$0.537812\pi$
$182$	−28.0656	+	38.8683i	−2.08036	+	2.88111i
$183$	−0.346421	+	0.913437i	−0.0256082	+	0.0675232i
$184$	9.14375	+	12.1681i	0.674086	+	0.897046i
$185$	2.70998	−	0.440415i	0.199242	−	0.0323800i
$186$	11.8907	+	5.06617i	0.871871	+	0.371469i
$187$	−5.09907	+	3.51964i	−0.372881	+	0.257381i
$188$	−32.9322	−	19.0134i	−2.40183	−	1.38670i
$189$	−4.72645	+	2.24273i	−0.343799	+	0.163135i
$190$	−1.81161	−	0.219969i	−0.131428	−	0.0159582i
$191$	13.5823	−	23.5253i	0.982782	−	1.70223i	0.331377	−	0.943499i	$-0.392487\pi$
$191$	13.5823	−	23.5253i	0.982782	−	1.70223i	0.651405	−	0.758730i	$-0.274180\pi$
$192$	0.346114	+	0.599486i	0.0249786	+	0.0432642i
$193$	0.415889	+	0.976128i	0.0299364	+	0.0702633i	0.934277	−	0.356549i	$-0.116047\pi$
$193$	0.415889	+	0.976128i	0.0299364	+	0.0702633i	−0.904340	+	0.426812i	$0.859636\pi$
$194$	−26.9268	+	23.8551i	−1.93323	+	1.71269i
$195$	2.38419	+	5.94269i	0.170735	+	0.425565i
$196$	−67.9979	−	60.2409i	−4.85699	−	4.30292i
$197$	−3.41110	+	10.2175i	−0.243031	+	0.727967i	0.754405	+	0.656409i	$0.227925\pi$
$197$	−3.41110	+	10.2175i	−0.243031	+	0.727967i	−0.997436	+	0.0715583i	$0.977203\pi$
$198$	−0.119968	−	2.97698i	−0.00852577	−	0.211565i
$199$	−13.4068	−	16.4203i	−0.950382	−	1.16401i	−0.986352	−	0.164653i	$-0.947349\pi$
$199$	−13.4068	−	16.4203i	−0.950382	−	1.16401i	0.0359699	−	0.999353i	$-0.488548\pi$
$200$	7.65404	−	8.63963i	0.541222	−	0.610914i
$201$	2.98614	−	0.609624i	0.210626	−	0.0429996i
$202$	11.2170	+	3.24903i	0.789222	+	0.228601i
$203$	39.1960	+	14.8651i	2.75102	+	1.04332i
$204$	−0.949172	+	23.5535i	−0.0664554	+	1.64907i
$205$	−14.2603	+	10.7159i	−0.995985	+	0.748434i
$206$	−12.5985	−	2.57200i	−0.877778	−	0.179200i
$207$	2.15564	+	1.13137i	0.149827	+	0.0786355i
$208$	−25.0034	−	2.55379i	−1.73368	−	0.177073i
$209$	0.419656	−	0.220253i	0.0290282	−	0.0152352i
$210$	−22.6813	+	6.56973i	−1.56516	+	0.453354i
$211$	12.7738	+	1.03121i	0.879387	+	0.0709915i	0.511908	−	0.859040i	$-0.328939\pi$
$211$	12.7738	+	1.03121i	0.879387	+	0.0709915i	0.367479	+	0.930032i	$0.380221\pi$
$212$	3.93908	+	19.2949i	0.270537	+	1.32518i
$213$	3.25850	−	6.20856i	0.223269	−	0.425404i
$214$	9.40190	−	12.5117i	0.642701	−	0.855279i
$215$	−8.57801	−	13.5650i	−0.585015	−	0.925128i
$216$	−5.14538	−	3.55160i	−0.350099	−	0.241656i
$217$	11.4050	+	24.0355i	0.774222	+	1.63164i
$218$	10.0169	+	10.4287i	0.678428	+	0.706318i
$219$	2.20370	−	2.11668i	0.148912	−	0.143032i
$220$	1.11912	−	9.21681i	0.0754513	−	0.621397i
$221$	14.9885	+	11.7692i	1.00824	+	0.791683i
$222$	0.473630	+	3.90069i	0.0317880	+	0.261798i
$223$	−10.3271	−	8.43183i	−0.691555	−	0.564637i	0.220159	−	0.975464i	$-0.429343\pi$
$223$	−10.3271	−	8.43183i	−0.691555	−	0.564637i	−0.911713	+	0.410827i	$0.865240\pi$
$224$	5.45505	−	26.7206i	0.364481	−	1.78535i
$225$	0.513635	−	1.77327i	0.0342423	−	0.118218i
$226$	−6.75886	+	27.4218i	−0.449592	+	1.82407i
$227$	−0.175912	−	2.17907i	−0.0116757	−	0.144630i	0.988293	−	0.152569i	$-0.0487547\pi$
$227$	−0.175912	−	2.17907i	−0.0116757	−	0.144630i	−0.999968	+	0.00793969i	$0.997473\pi$
$228$	0.289247	−	1.77981i	0.0191559	−	0.117871i
$229$	−16.9919	−	19.1799i	−1.12286	−	1.26744i	−0.959757	−	0.280833i	$-0.909389\pi$
$229$	−16.9919	−	19.1799i	−1.12286	−	1.26744i	−0.163099	−	0.986610i	$-0.552149\pi$
$230$	8.78474	+	6.60130i	0.579248	+	0.435277i
$231$	3.87856	−	4.75037i	0.255190	−	0.312551i
$232$	8.03625	+	49.4490i	0.527605	+	3.24649i
$233$	6.66334	−	1.64236i	0.436530	−	0.107595i	−0.0149257	−	0.999889i	$-0.504751\pi$
$233$	6.66334	−	1.64236i	0.436530	−	0.107595i	0.451455	+	0.892294i	$0.350905\pi$
$234$	−8.63552	+	3.06696i	−0.564522	+	0.200493i
$235$	−14.7021	−	3.62375i	−0.959061	−	0.236387i
$236$	1.65513	−	20.5025i	0.107740	−	1.33460i
$237$	11.6141	+	3.87736i	0.754417	+	0.251861i
$238$	−48.6842	+	50.6856i	−3.15573	+	3.28546i
$239$		−	4.50035i		−	0.291103i	−0.989351	−	0.145552i	$-0.953504\pi$
$239$		−	4.50035i		−	0.291103i	0.989351	−	0.145552i	$-0.0464957\pi$
$240$	−8.92808	−	8.57554i	−0.576305	−	0.553549i
$241$	5.79343	−	4.73019i	0.373187	−	0.304698i	−0.427228	−	0.904144i	$-0.640510\pi$
$241$	5.79343	−	4.73019i	0.373187	−	0.304698i	0.800415	+	0.599446i	$0.204612\pi$
$242$	−11.3696	−	21.6630i	−0.730867	−	1.39255i
$243$	−0.987050	−	0.160411i	−0.0633193	−	0.0102904i
$244$	−3.68245	−	2.32864i	−0.235745	−	0.149076i
$245$	−32.6812	−	15.5074i	−2.08792	−	0.990732i
$246$	−14.5022	−	21.0100i	−0.924624	−	1.33955i
$247$	−1.02966	−	1.03191i	−0.0655155	−	0.0656588i
$248$	−18.0610	+	26.1659i	−1.14688	+	1.66154i
$249$	8.44565	−	4.87610i	0.535222	−	0.309010i
$250$	13.2472	−	27.9179i	0.837828	−	1.76569i
$251$	3.50352	−	1.16965i	0.221140	−	0.0738275i	−0.203939	−	0.978984i	$-0.565374\pi$
$251$	3.50352	−	1.16965i	0.221140	−	0.0738275i	0.425079	+	0.905156i	$0.360246\pi$
$252$	−5.58374	−	22.6541i	−0.351743	−	1.42708i
$253$	−2.85150	−	0.114911i	−0.179272	−	0.00722442i
$254$	6.69911	+	0.269965i	0.420340	+	0.0169391i
$255$	2.24634	+	9.11374i	0.140671	+	0.570725i
$256$	−28.0633	+	9.36892i	−1.75396	+	0.585557i
$257$	−5.21982	+	11.0005i	−0.325604	+	0.686195i	−0.998569	−	0.0534789i	$-0.982969\pi$
$257$	−5.21982	+	11.0005i	−0.325604	+	0.686195i	0.672965	+	0.739674i	$0.265020\pi$
$258$	19.8925	−	11.4850i	1.23845	−	0.715022i
$259$	−4.59448	+	6.65626i	−0.285487	+	0.413600i
$260$	−28.0950	+	5.11688i	−1.74238	+	0.317335i
$261$	4.55187	+	6.59452i	0.281754	+	0.408190i
$262$	0.169182	+	0.0802779i	0.0104521	+	0.00495959i
$263$	−8.19110	−	5.17974i	−0.505085	−	0.319396i	0.257507	−	0.966276i	$-0.417099\pi$
$263$	−8.19110	−	5.17974i	−0.505085	−	0.319396i	−0.762592	+	0.646880i	$0.776073\pi$
$264$	7.23405	+	1.17565i	0.445225	+	0.0723561i
$265$	3.64418	+	6.94341i	0.223860	+	0.426530i
$266$	4.16423	−	3.39999i	0.255325	−	0.208466i
$267$	12.2203	+	11.7377i	0.747869	+	0.718338i
$268$			13.5925i			0.830295i
$269$	3.87878	−	4.03823i	0.236493	−	0.246215i	−0.592371	−	0.805665i	$-0.701808\pi$
$269$	3.87878	−	4.03823i	0.236493	−	0.246215i	0.828864	+	0.559450i	$0.188988\pi$
$270$	−4.28140	−	1.42934i	−0.260558	−	0.0869869i
$271$	−1.55402	+	19.2500i	−0.0943999	+	1.16935i	0.760066	+	0.649845i	$0.225166\pi$
$271$	−1.55402	+	19.2500i	−0.0943999	+	1.16935i	−0.854466	+	0.519507i	$0.826116\pi$
$272$	−35.7733	−	8.81732i	−2.16907	−	0.534628i
$273$	−17.4909	−	7.06170i	−1.05860	−	0.427393i
$274$	51.9978	−	12.8163i	3.14130	−	0.774261i
$275$	0.347153	+	2.13612i	0.0209341	+	0.128813i
$276$	−6.86682	+	8.41033i	−0.413334	+	0.506243i
$277$	−1.10520	−	0.830501i	−0.0664048	−	0.0499000i	0.567022	−	0.823703i	$-0.308096\pi$
$277$	−1.10520	−	0.830501i	−0.0664048	−	0.0499000i	−0.633426	+	0.773803i	$0.718352\pi$
$278$	−21.5850	−	24.3644i	−1.29458	−	1.46128i
$279$	−0.815742	+	5.01946i	−0.0488372	+	0.300507i
$280$	−4.67404	−	57.8984i	−0.279327	−	3.46009i
$281$	−4.88128	+	19.8041i	−0.291193	+	1.18142i	0.624983	+	0.780639i	$0.285106\pi$
$281$	−4.88128	+	19.8041i	−0.291193	+	1.18142i	−0.916175	+	0.400777i	$0.868740\pi$
$282$	6.02926	−	20.8154i	0.359037	−	1.23954i
$283$	2.40647	−	11.7877i	0.143050	−	0.700704i	−0.843485	−	0.537153i	$-0.819500\pi$
$283$	2.40647	−	11.7877i	0.143050	−	0.700704i	0.986535	−	0.163551i	$-0.0522949\pi$
$284$	24.2230	+	19.7774i	1.43737	+	1.17358i
$285$	−0.0865465	−	0.712774i	−0.00512657	−	0.0422211i
$286$	7.60429	−	7.58770i	0.449651	−	0.448670i
$287$	6.33393	−	52.1646i	0.373880	−	3.07918i
$288$	3.75958	−	3.61112i	0.221535	−	0.212787i
$289$	7.57579	+	7.88724i	0.445635	+	0.463955i
$290$	15.5049	+	32.6759i	0.910480	+	1.91880i
$291$	−11.6484	−	8.04030i	−0.682841	−	0.471331i
$292$	7.28346	+	11.5179i	0.426232	+	0.674033i
$293$	11.6884	−	15.5544i	0.682843	−	0.908699i	−0.316359	−	0.948639i	$-0.602461\pi$
$293$	11.6884	−	15.5544i	0.682843	−	0.908699i	0.999202	+	0.0399408i	$0.0127169\pi$
$294$	24.0592	−	45.8409i	1.40316	−	2.67350i
$295$	−1.63832	−	8.02504i	−0.0953868	−	0.467236i
$296$	−9.63438	−	0.777768i	−0.559987	−	0.0452068i
$297$	1.12596	−	0.326137i	0.0653346	−	0.0189244i
$298$	6.52533	−	3.42476i	0.378002	−	0.198391i
$299$	2.26257	+	8.48109i	0.130848	+	0.490474i
$300$	7.29056	+	3.82638i	0.420921	+	0.220916i
$301$	46.3246	+	9.45723i	2.67010	+	0.545105i
$302$	−7.98574	+	6.00090i	−0.459528	+	0.345313i
$303$	−0.185010	+	4.59097i	−0.0106285	+	0.263744i
$304$	2.63519	+	0.999394i	0.151138	+	0.0573192i
$305$	−1.66642	−	0.482685i	−0.0954190	−	0.0276384i
$306$	−13.1622	+	2.68709i	−0.752435	+	0.153611i
$307$	−10.9814	+	12.3955i	−0.626743	+	0.707447i	−0.973029	−	0.230682i	$-0.925904\pi$
$307$	−10.9814	+	12.3955i	−0.626743	+	0.707447i	0.346286	+	0.938129i	$0.387443\pi$
$308$	17.2979	+	21.1861i	0.985639	+	1.20719i
$309$	−0.203709	−	5.05499i	−0.0115886	−	0.287568i
$310$	−7.26866	+	21.7723i	−0.412832	+	1.23658i
$311$	−6.87699	−	6.09248i	−0.389958	−	0.345473i	0.445250	−	0.895406i	$-0.353115\pi$
$311$	−6.87699	−	6.09248i	−0.389958	−	0.345473i	−0.835209	+	0.549933i	$0.814653\pi$
$312$	−3.14287	−	22.3221i	−0.177930	−	1.26374i
$313$	−10.6567	+	9.44101i	−0.602352	+	0.533637i	−0.908251	−	0.418427i	$-0.862582\pi$
$313$	−10.6567	+	9.44101i	−0.602352	+	0.533637i	0.305898	+	0.952064i	$0.401043\pi$
$314$	18.5047	+	43.4322i	1.04428	+	2.45102i
$315$	−4.64537	−	8.04602i	−0.261737	−	0.453342i
$316$	−27.3039	+	47.2918i	−1.53597	+	2.66037i
$317$	15.7516	+	1.91260i	0.884700	+	0.107422i	0.550258	−	0.834994i	$-0.314529\pi$
$317$	15.7516	+	1.91260i	0.884700	+	0.107422i	0.334442	+	0.942416i	$0.391452\pi$
$318$	−10.1392	+	4.81110i	−0.568577	+	0.269793i
$319$	−8.13464	−	4.69654i	−0.455452	−	0.262956i
$320$	−1.01172	+	0.698338i	−0.0565567	+	0.0390383i
$321$	5.66491	+	2.41359i	0.316185	+	0.134714i
$322$	−31.9516	+	5.19263i	−1.78059	+	0.289374i
$323$	−1.28376	−	1.70837i	−0.0714301	−	0.0950563i
$324$	1.58150	−	4.17006i	0.0878609	−	0.231670i
$325$	5.95833	−	2.96758i	0.330509	−	0.164612i
$326$	−10.4350	−	27.5148i	−0.577941	−	1.52390i
$327$	−3.04074	+	4.80854i	−0.168153	+	0.265913i
$328$	57.7733	−	24.6149i	3.19000	−	1.35913i
$329$	37.7010	−	23.8407i	2.07852	−	1.31438i
$330$	5.25254	−	0.637774i	0.289143	−	0.0351083i
$331$	3.58111	−	8.40518i	0.196836	−	0.461991i	−0.792089	−	0.610405i	$-0.791007\pi$
$331$	3.58111	−	8.40518i	0.196836	−	0.461991i	0.988925	+	0.148414i	$0.0474169\pi$
$332$	13.7731	+	41.2553i	0.755894	+	2.26418i
$333$	−1.44553	+	0.548217i	−0.0792145	+	0.0300421i
$334$	−13.5440	+	1.09338i	−0.741095	+	0.0598274i
$335$	1.50585	+	5.19878i	0.0822731	+	0.284040i
$336$	36.4385	−	1.46842i	1.98788	−	0.0801089i
$337$	−25.8153			−1.40625			−0.703125	−	0.711066i	$-0.748212\pi$
$337$	−25.8153			−1.40625			−0.703125	+	0.711066i	$0.748212\pi$
$338$	−29.2229	−	15.4189i	−1.58952	−	0.838677i
$339$	−11.1119			−0.603518
$340$	−41.8287	+	1.68564i	−2.26848	+	0.0914166i
$341$	−1.65851	−	5.72585i	−0.0898134	−	0.310072i
$342$	1.02427	−	0.0826872i	0.0553859	−	0.00447121i
$343$	65.3967	−	24.8017i	3.53109	−	1.33916i
$344$	17.8928	+	53.5954i	0.964714	+	2.88967i
$345$	−1.69464	+	3.97747i	−0.0912365	+	0.214140i
$346$	7.76203	−	0.942481i	0.417289	−	0.0506681i
$347$	−6.78785	+	4.29238i	−0.364391	+	0.230427i	−0.704096	−	0.710105i	$-0.748647\pi$
$347$	−6.78785	+	4.29238i	−0.364391	+	0.230427i	0.339704	+	0.940532i	$0.389673\pi$
$348$	−32.8771	+	14.0076i	−1.76240	+	0.750887i
$349$	−13.3525	+	21.1153i	−0.714744	+	1.13028i	0.271090	+	0.962554i	$0.412616\pi$
$349$	−13.3525	+	21.1153i	−0.714744	+	1.13028i	−0.985834	+	0.167724i	$0.946358\pi$
$350$	8.70479	+	22.9527i	0.465291	+	1.22687i
$351$	−1.98473	−	3.01012i	−0.105937	−	0.160668i
$352$	−2.16692	+	5.71369i	−0.115497	+	0.304541i
$353$	−7.70961	−	10.2596i	−0.410341	−	0.546065i	0.546203	−	0.837653i	$-0.316073\pi$
$353$	−7.70961	−	10.2596i	−0.410341	−	0.546065i	−0.956544	+	0.291588i	$0.905816\pi$
$354$	11.5703	−	1.88036i	0.614956	−	0.0999401i
$355$	11.4557	+	4.88082i	0.608005	+	0.259047i
$356$	−62.1926	+	42.9284i	−3.29620	+	2.27520i
$357$	−23.9467	−	13.8256i	−1.26739	−	0.731730i
$358$	−28.4240	+	13.4873i	−1.50225	+	0.712829i
$359$	−8.32666	−	1.01104i	−0.439465	−	0.0533607i	−0.102185	−	0.994765i	$-0.532584\pi$
$359$	−8.32666	−	1.01104i	−0.439465	−	0.0533607i	−0.337279	+	0.941405i	$0.609507\pi$
$360$	5.55157	−	9.61561i	0.292594	−	0.506787i
$361$	−9.41827	−	16.3129i	−0.495698	−	0.858575i
$362$	−23.7608	−	55.7687i	−1.24884	−	2.93114i
$363$	7.20506	−	6.38312i	0.378167	−	0.335027i
$364$	46.4613	−	70.1312i	2.43524	−	3.67588i
$365$	4.06174	+	3.59839i	0.212601	+	0.188348i
$366$	0.786278	−	2.35519i	0.0410994	−	0.123108i
$367$	0.799662	+	19.8434i	0.0417420	+	1.03582i	0.875359	+	0.483474i	$0.160625\pi$
$367$	0.799662	+	19.8434i	0.0417420	+	1.03582i	−0.833617	+	0.552344i	$0.813734\pi$
$368$	−10.7328	−	13.1453i	−0.559487	−	0.685247i
$369$	6.66065	−	7.51832i	0.346740	−	0.391388i
$370$	−6.83712	+	1.39581i	−0.355445	+	0.0725646i
$371$	−22.1882	−	6.42690i	−1.15196	−	0.333668i
$372$	−21.2061	−	8.04241i	−1.09948	−	0.416980i
$373$	0.630520	−	15.6462i	0.0326471	−	0.810129i	−0.897077	−	0.441873i	$-0.854314\pi$
$373$	0.630520	−	15.6462i	0.0326471	−	0.810129i	0.929725	−	0.368256i	$-0.120045\pi$
$374$	12.5892	−	9.46020i	0.650974	−	0.489175i
$375$	11.9124	+	2.43194i	0.615155	+	0.125585i
$376$	47.2021	+	24.7735i	2.43426	+	1.27760i
$377$	−6.37859	+	28.1781i	−0.328514	+	1.45125i
$378$	11.7736	−	6.17928i	0.605570	−	0.317828i
$379$	22.3133	−	6.46314i	1.14616	−	0.331989i	0.349807	−	0.936822i	$-0.386247\pi$
$379$	22.3133	−	6.46314i	1.14616	−	0.331989i	0.796353	+	0.604833i	$0.206760\pi$
$380$	3.19185	+	0.257673i	0.163739	+	0.0132183i
$381$	0.527647	+	2.58458i	0.0270322	+	0.132412i
$382$	−32.0856	+	61.1341i	−1.64164	+	3.12789i
$383$	−18.4430	+	24.5432i	−0.942392	+	1.25410i	0.0247062	+	0.999695i	$0.492135\pi$
$383$	−18.4430	+	24.5432i	−0.942392	+	1.25410i	−0.967099	+	0.254402i	$0.918121\pi$
$384$	−6.51260	−	10.2988i	−0.332345	−	0.525561i
$385$	8.96309	+	6.18678i	0.456801	+	0.315307i
$386$	−1.15608	−	2.43638i	−0.0588428	−	0.124009i
$387$	6.26048	+	6.51785i	0.318238	+	0.331321i
$388$	45.5255	−	43.7279i	2.31121	−	2.21995i
$389$	−0.929114	+	7.65194i	−0.0471079	+	0.387969i	0.950017	+	0.312197i	$0.101065\pi$
$389$	−0.929114	+	7.65194i	−0.0471079	+	0.387969i	−0.997125	+	0.0757715i	$0.975858\pi$
$390$	−6.66298	−	14.8479i	−0.337393	−	0.751851i
$391$	1.55100	+	12.7737i	0.0784376	+	0.645992i
$392$	98.6463	+	80.5422i	4.98239	+	4.06800i
$393$	−0.0147375	+	0.0721890i	−0.000743408	+	0.00364146i
$394$	7.61706	−	26.2972i	0.383742	−	1.32483i
$395$	−5.20382	+	21.1127i	−0.261833	+	1.06230i
$396$	0.420683	+	5.21109i	0.0211401	+	0.261867i
$397$	2.68984	−	16.5512i	0.134999	−	0.830683i	−0.827911	−	0.560860i	$-0.810471\pi$
$397$	2.68984	−	16.5512i	0.134999	−	0.830683i	0.962910	−	0.269823i	$-0.0869652\pi$
$398$	35.7279	+	40.3285i	1.79088	+	2.02148i
$399$	1.69094	+	1.27066i	0.0846531	+	0.0636126i
$400$	−8.13907	+	9.96855i	−0.406954	+	0.498428i
$401$	4.26151	+	26.2221i	0.212810	+	1.30947i	0.845045	+	0.534695i	$0.179573\pi$
$401$	4.26151	+	26.2221i	0.212810	+	1.30947i	−0.632235	+	0.774776i	$0.717862\pi$
$402$	−7.52111	+	1.85379i	−0.375119	+	0.0924585i
$403$	−15.3074	+	10.0930i	−0.762518	+	0.502768i
$404$	−19.8964	−	4.90401i	−0.989881	−	0.243984i
$405$	0.142901	−	1.77015i	0.00710080	−	0.0879592i
$406$	−101.062	−	33.7396i	−5.01564	−	1.67447i
$407$	1.25541	−	1.30702i	0.0622282	−	0.0647864i
$408$		−	33.0454i		−	1.63599i
$409$	−10.2287	−	9.82484i	−0.505779	−	0.485807i	0.395852	−	0.918314i	$-0.370449\pi$
$409$	−10.2287	−	9.82484i	−0.505779	−	0.485807i	−0.901630	+	0.432507i	$0.857629\pi$
$410$	35.1184	−	28.6733i	1.73437	−	1.41607i
$411$	9.79205	+	18.6572i	0.483006	+	0.920291i
$412$	22.2708	+	3.61935i	1.09720	+	0.178313i
$413$	20.3929	+	12.8957i	1.00347	+	0.634556i
$414$	−5.59018	−	2.65258i	−0.274743	−	0.130367i
$415$	9.83830	+	14.2532i	0.482943	+	0.699664i
$416$	18.7599	+	1.15534i	0.919782	+	0.0566451i
$417$	7.27517	−	10.5399i	0.356266	−	0.516141i
$418$	−1.04320	+	0.602295i	−0.0510248	+	0.0294592i
$419$	−2.91256	+	6.13809i	−0.142288	+	0.299866i	−0.962066	−	0.272815i	$-0.912045\pi$
$419$	−2.91256	+	6.13809i	−0.142288	+	0.299866i	0.819778	+	0.572681i	$0.194097\pi$
$420$	39.3032	−	13.1213i	1.91780	−	0.640256i
$421$	8.09789	+	32.8544i	0.394667	+	1.60123i	0.746647	+	0.665220i	$0.231662\pi$
$421$	8.09789	+	32.8544i	0.394667	+	1.60123i	−0.351980	+	0.936008i	$0.614491\pi$
$422$	−32.5456	−	1.31154i	−1.58429	−	0.0638448i
$423$	8.51952	+	0.343325i	0.414233	+	0.0166930i
$424$	−6.60669	−	26.8044i	−0.320849	−	1.30174i
$425$	9.25568	−	3.09000i	0.448966	−	0.149887i
$426$	−7.63980	+	16.1005i	−0.370150	+	0.780074i
$427$	4.42610	−	2.55541i	0.214194	−	0.123665i
$428$	−15.6004	+	22.6011i	−0.754075	+	1.09247i
$429$	3.61462	+	2.19051i	0.174516	+	0.105759i
$430$	23.1727	+	33.5714i	1.11749	+	1.61896i
$431$	−32.6959	−	15.5144i	−1.57490	−	0.747302i	−0.577304	−	0.816529i	$-0.695895\pi$
$431$	−32.6959	−	15.5144i	−1.57490	−	0.747302i	−0.997601	+	0.0692278i	$0.977946\pi$
$432$	5.89164	+	3.72564i	0.283461	+	0.179250i
$433$	26.5445	+	4.31390i	1.27565	+	0.207313i	0.760246	−	0.649636i	$-0.225079\pi$
$433$	26.5445	+	4.31390i	1.27565	+	0.207313i	0.515402	+	0.856949i	$0.327643\pi$
$434$	−31.4236	−	59.8726i	−1.50838	−	2.87398i
$435$	−11.0228	+	8.99983i	−0.528502	+	0.431509i
$436$	−18.2995	−	17.5769i	−0.876388	−	0.841782i
$437$		−	0.984283i		−	0.0470847i
$438$	−5.37982	+	5.60098i	−0.257058	+	0.267625i
$439$	35.3622	+	11.8056i	1.68775	+	0.563453i	0.988472	−	0.151401i	$-0.0483783\pi$
$439$	35.3622	+	11.8056i	1.68775	+	0.563453i	0.699274	+	0.714853i	$0.253507\pi$
$440$	−1.04732	+	12.9733i	−0.0499288	+	0.618479i
$441$	19.7773	+	4.87467i	0.941776	+	0.232127i
$442$	−39.2689	−	28.3548i	−1.86783	−	1.34870i
$443$	10.1476	−	2.50117i	0.482129	−	0.118834i	0.00924189	−	0.999957i	$-0.497058\pi$
$443$	10.1476	−	2.50117i	0.482129	−	0.118834i	0.472887	+	0.881123i	$0.343212\pi$
$444$	−1.10603	−	6.80566i	−0.0524898	−	0.322982i
$445$	−19.0312	+	23.3090i	−0.902166	+	1.10495i
$446$	27.0893	+	20.3563i	1.28272	+	0.963899i
$447$	1.92272	+	2.17031i	0.0909417	+	0.102652i
$448$	0.580918	−	3.57453i	0.0274458	−	0.168881i
$449$	−0.344381	−	4.26593i	−0.0162524	−	0.201321i	−0.999788	−	0.0206056i	$-0.993441\pi$
$449$	−0.344381	−	4.26593i	−0.0162524	−	0.201321i	0.983535	−	0.180716i	$-0.0578415\pi$
$450$	−1.12293	+	4.55592i	−0.0529356	+	0.214768i
$451$	−3.27584	+	11.3095i	−0.154253	+	0.532545i
$452$	9.91286	−	48.5564i	0.466262	−	2.28390i
$453$	−3.04436	−	2.48564i	−0.143036	−	0.116786i
$454$	0.669749	+	5.51588i	0.0314329	+	0.258873i
$455$	10.0008	−	31.9706i	0.468843	−	1.49880i
$456$	−0.304689	+	2.50934i	−0.0142684	+	0.117511i
$457$	16.9026	−	16.2352i	0.790671	−	0.759450i	−0.184040	−	0.982919i	$-0.558918\pi$
$457$	16.9026	−	16.2352i	0.790671	−	0.759450i	0.974711	+	0.223469i	$0.0717382\pi$
$458$	45.1150	+	46.9697i	2.10808	+	2.19475i
$459$	−2.26584	−	4.77516i	−0.105761	−	0.222886i
$460$	−15.8688	−	10.9534i	−0.739886	−	0.510706i
$461$	−19.7039	−	31.1591i	−0.917700	−	1.45123i	−0.892246	−	0.451550i	$-0.850871\pi$
$461$	−19.7039	−	31.1591i	−0.917700	−	1.45123i	−0.0254541	−	0.999676i	$-0.508103\pi$
$462$	−9.36370	+	12.4608i	−0.435639	+	0.579730i
$463$	−0.880507	+	1.67767i	−0.0409206	+	0.0779678i	−0.905058	−	0.425289i	$-0.860173\pi$
$463$	−0.880507	+	1.67767i	−0.0409206	+	0.0779678i	0.864137	+	0.503256i	$0.167865\pi$
$464$	−11.1727	−	54.7276i	−0.518681	−	2.54067i
$465$	−9.00175	−	0.726697i	−0.417446	−	0.0336997i
$466$	−16.7539	+	4.85283i	−0.776110	+	0.224803i
$467$	10.1768	−	5.34118i	0.470925	−	0.247160i	−0.212528	−	0.977155i	$-0.568170\pi$
$467$	10.1768	−	5.34118i	0.470925	−	0.247160i	0.683453	+	0.729994i	$0.260477\pi$
$468$	14.9240	−	5.98748i	0.689864	−	0.276771i
$469$	−14.1180	−	7.40972i	−0.651911	−	0.342149i
$470$	37.7079	+	7.69812i	1.73934	+	0.355088i
$471$	−14.8494	+	11.1586i	−0.684224	+	0.514161i
$472$	−1.16107	+	28.8117i	−0.0534426	+	1.32616i
$473$	−9.90563	−	3.75671i	−0.455461	−	0.172734i
$474$	−29.8916	−	8.65821i	−1.37297	−	0.397685i
$475$	−0.731332	+	0.149302i	−0.0335558	+	0.00685046i
$476$	81.7772	−	92.3074i	3.74825	−	4.23090i
$477$	−2.79260	−	3.42032i	−0.127864	−	0.156606i
$478$	0.460571	+	11.4289i	0.0210660	+	0.522748i
$479$	−1.23950	+	3.71276i	−0.0566342	+	0.169640i	−0.973054	−	0.230579i	$-0.925938\pi$
$479$	−1.23950	+	3.71276i	−0.0566342	+	0.169640i	0.916419	+	0.400219i	$0.131066\pi$
$480$	6.92946	+	6.13897i	0.316285	+	0.280204i
$481$	−4.98411	−	2.49597i	−0.227256	−	0.113807i
$482$	−14.2287	+	12.6055i	−0.648100	+	0.574167i
$483$	−4.99217	−	11.7171i	−0.227152	−	0.533145i
$484$	21.4651	+	37.1786i	0.975686	+	1.68994i
$485$	12.5679	−	21.7683i	0.570681	−	0.988448i
$486$	2.52310	+	0.306360i	0.114450	+	0.0138968i
$487$	21.0388	−	9.98304i	0.953359	−	0.452375i	0.112514	−	0.993650i	$-0.464110\pi$
$487$	21.0388	−	9.98304i	0.953359	−	0.452375i	0.840845	+	0.541275i	$0.182058\pi$
$488$	5.28953	+	3.05391i	0.239446	+	0.138244i
$489$	9.52854	−	6.57708i	0.430896	−	0.297426i
$490$	84.5832	+	36.0375i	3.82108	+	1.62801i
$491$	14.6691	−	2.38396i	0.662007	−	0.107587i	0.179881	−	0.983688i	$-0.442429\pi$
$491$	14.6691	−	2.38396i	0.662007	−	0.107587i	0.482126	+	0.876102i	$0.339865\pi$
$492$	26.9113	+	35.8124i	1.21325	+	1.61455i
$493$	−15.0183	+	39.6000i	−0.676390	+	1.78349i
$494$	2.72049	+	2.51523i	0.122401	+	0.113165i
$495$	0.738210	+	1.94650i	0.0331801	+	0.0874887i
$496$	18.9461	−	29.9608i	0.850705	−	1.34528i
$497$	−33.7468	+	14.3782i	−1.51375	+	0.644950i
$498$	−20.9493	+	13.2475i	−0.938760	+	0.593636i
$499$	5.72449	−	0.695079i	0.256263	−	0.0311160i	0.00860327	−	0.999963i	$-0.497261\pi$
$499$	5.72449	−	0.695079i	0.256263	−	0.0311160i	0.247660	+	0.968847i	$0.420338\pi$
$500$	−21.2539	+	49.8848i	−0.950505	+	2.23092i
$501$	−1.69297	−	5.07107i	−0.0756364	−	0.226559i
$502$	−8.77773	+	3.32895i	−0.391769	+	0.148578i
$503$	11.0851	−	0.894879i	0.494259	−	0.0399007i	0.169175	−	0.985586i	$-0.445890\pi$
$503$	11.0851	−	0.894879i	0.494259	−	0.0399007i	0.325084	+	0.945685i	$0.394608\pi$
$504$	9.10001	+	31.4169i	0.405347	+	1.39942i
$505$	−8.15313	+	0.328560i	−0.362809	+	0.0146207i
$506$	7.25334			0.322450
$507$	3.13867	−	12.6154i	0.139393	−	0.560270i
$508$	−11.7647			−0.521974
$509$	−25.0664	+	1.01014i	−1.11105	+	0.0447737i	−0.588993	−	0.808138i	$-0.700475\pi$
$509$	−25.0664	+	1.01014i	−1.11105	+	0.0447737i	−0.522055	+	0.852912i	$0.674834\pi$
$510$	−6.63743	−	22.9151i	−0.293910	−	1.01470i
$511$	−15.9336	+	1.28630i	−0.704863	+	0.0569024i
$512$	47.5231	−	18.0231i	2.10024	−	0.796518i
$513$	0.128031	+	0.383499i	0.00565270	+	0.0169319i
$514$	12.1303	−	28.4708i	0.535044	−	1.25579i
$515$	8.91896	−	1.08296i	0.393016	−	0.0477208i
$516$	−34.0663	+	21.5422i	−1.49968	+	0.948343i
$517$	−9.19520	+	3.91771i	−0.404405	+	0.172301i
$518$	10.9868	−	17.3742i	0.482732	−	0.763380i
$519$	1.09090	+	2.87647i	0.0478853	+	0.126263i
$520$	39.0643	−	8.75318i	1.71308	−	0.383852i
$521$	0.559639	−	1.47565i	0.0245182	−	0.0646493i	−0.922198	−	0.386718i	$-0.873609\pi$
$521$	0.559639	−	1.47565i	0.0245182	−	0.0646493i	0.946716	+	0.322068i	$0.104378\pi$
$522$	−12.2347	−	16.2814i	−0.535497	−	0.712617i
$523$	3.47202	−	0.564258i	0.151821	−	0.0246733i	−0.0840257	−	0.996464i	$-0.526778\pi$
$523$	3.47202	−	0.564258i	0.151821	−	0.0246733i	0.235847	+	0.971790i	$0.424214\pi$
$524$	−0.302301	−	0.128798i	−0.0132061	−	0.00562658i
$525$	−7.94864	+	5.48655i	−0.346907	+	0.239453i
$526$	21.3320	+	12.3160i	0.930117	+	0.537004i
$527$	−24.2832	+	11.5225i	−1.05779	+	0.501929i
$528$	−8.11184	−	0.984956i	−0.353023	−	0.0428647i
$529$	8.53661	−	14.7858i	0.371157	−	0.642863i
$530$	−9.96524	−	17.2603i	−0.432863	−	0.749740i
$531$	1.80777	+	4.24299i	0.0784505	+	0.184130i
$532$	−7.06095	+	6.25546i	−0.306131	+	0.271208i
$533$	36.2089	−	0.689718i	1.56838	−	0.0298750i
$534$	−32.2355	−	28.5582i	−1.39497	−	1.23583i
$535$	−3.46289	+	10.3726i	−0.149714	+	0.448448i
$536$	−0.767257	−	19.0393i	−0.0331405	−	0.822372i
$537$	−7.82873	−	9.58846i	−0.337835	−	0.413772i
$538$	−9.43714	+	10.6523i	−0.406864	+	0.459254i
$539$	−23.3950	+	4.77612i	−1.00769	+	0.205722i
$540$	7.60761	+	2.20357i	0.327380	+	0.0948266i
$541$	−40.7922	−	15.4704i	−1.75379	−	0.665126i	−0.999968	−	0.00805221i	$-0.997437\pi$
$541$	−40.7922	−	15.4704i	−1.75379	−	0.665126i	−0.753826	−	0.657074i	$-0.771794\pi$
$542$	1.97647	−	49.0457i	0.0848968	−	2.10669i
$543$	19.0672	−	14.3281i	0.818254	−	0.614878i
$544$	26.9960	+	5.51127i	1.15744	+	0.236294i
$545$	−8.94634	−	4.69540i	−0.383219	−	0.201129i
$546$	45.1421	+	16.1436i	1.93190	+	0.690883i
$547$	7.32683	−	3.84542i	0.313273	−	0.164418i	−0.300758	−	0.953701i	$-0.597240\pi$
$547$	7.32683	−	3.84542i	0.313273	−	0.164418i	0.614030	+	0.789282i	$0.289547\pi$
$548$	−90.2627	+	26.1449i	−3.85583	+	1.11685i
$549$	0.973753	+	0.0786095i	0.0415588	+	0.00335497i
$550$	−1.10023	−	5.38929i	−0.0469141	−	0.229800i
$551$	1.50556	−	2.86860i	0.0641388	−	0.122206i
$552$	9.14375	−	12.1681i	0.389184	−	0.517910i
$553$	−34.2360	−	54.1399i	−1.45586	−	2.30226i
$554$	2.89172	+	1.99601i	0.122857	+	0.0848022i
$555$	−1.17699	−	2.48046i	−0.0499605	−	0.105290i
$556$	39.5666	+	41.1932i	1.67800	+	1.74698i
$557$	2.54988	−	2.44919i	0.108042	−	0.103776i	−0.636757	−	0.771064i	$-0.719725\pi$
$557$	2.54988	−	2.44919i	0.108042	−	0.103776i	0.744799	+	0.667289i	$0.232545\pi$
$558$	1.55794	−	12.8308i	0.0659527	−	0.543169i
$559$	−2.00297	+	32.5234i	−0.0847165	+	1.37560i
$560$	7.80641	+	64.2916i	0.329881	+	2.71681i
$561$	4.79932	+	3.91853i	0.202628	+	0.165440i
$562$	10.3696	−	50.7935i	0.437414	−	2.14260i
$563$	−3.35262	+	11.5746i	−0.141296	+	0.487811i	−0.999683	−	0.0251929i	$-0.991980\pi$
$563$	−3.35262	+	11.5746i	−0.141296	+	0.487811i	0.858387	+	0.513003i	$0.171467\pi$
$564$	−9.10043	+	36.9219i	−0.383197	+	1.55469i
$565$	−1.58791	−	19.6697i	−0.0668037	−	0.827512i
$566$	−4.90503	+	30.1819i	−0.206174	+	1.26864i
$567$	3.46916	+	3.91588i	0.145691	+	0.164451i
$568$	−35.0459	−	26.3353i	−1.47050	−	1.10501i
$569$	11.1745	−	13.6863i	0.468461	−	0.573760i	−0.485292	−	0.874352i	$-0.661287\pi$
$569$	11.1745	−	13.6863i	0.468461	−	0.573760i	0.953753	+	0.300592i	$0.0971842\pi$
$570$	0.292737	+	1.80128i	0.0122614	+	0.0754474i
$571$	−13.0515	+	3.21690i	−0.546187	+	0.134623i	−0.502748	−	0.864433i	$-0.667678\pi$
$571$	−13.0515	+	3.21690i	−0.546187	+	0.134623i	−0.0434389	+	0.999056i	$0.513831\pi$
$572$	−12.7966	+	13.8409i	−0.535051	+	0.578716i
$573$	−26.3753	−	6.50092i	−1.10184	−	0.271580i
$574$	−10.7469	+	133.124i	−0.448565	+	5.55648i
$575$	4.26318	+	1.42326i	0.177787	+	0.0593540i
$576$	0.479523	−	0.499236i	0.0199801	−	0.0208015i
$577$			9.43877i			0.392941i	0.980510	+	0.196470i	$0.0629480\pi$
$577$			9.43877i			0.392941i	−0.980510	+	0.196470i	$0.937052\pi$
$578$	−20.0464	−	19.2549i	−0.833822	−	0.800897i
$579$	0.821881	−	0.671045i	0.0341562	−	0.0278877i
$580$	−29.4937	−	56.1955i	−1.22466	−	2.33339i
$581$	−50.3585	−	8.18406i	−2.08922	−	0.339532i
$582$	30.4047	+	19.2268i	1.26032	+	0.796976i
$583$	4.67634	+	2.21895i	0.193674	+	0.0918996i
$584$	−10.8522	−	15.7222i	−0.449068	−	0.650588i
$585$	5.04474	−	3.94341i	0.208574	−	0.163040i
$586$	−28.0916	+	40.6977i	−1.16045	+	1.68121i
$587$	−4.49661	+	2.59612i	−0.185595	+	0.107153i	−0.589919	−	0.807463i	$-0.700840\pi$
$587$	−4.49661	+	2.59612i	−0.185595	+	0.107153i	0.404324	+	0.914616i	$0.367507\pi$
$588$	−38.9442	+	82.0732i	−1.60603	+	3.38464i
$589$	1.95022	−	0.651078i	0.0803573	−	0.0268272i
$590$	4.98192	+	20.2125i	0.205103	+	0.832134i
$591$	10.7631	+	0.433739i	0.442736	+	0.0178416i
$592$	10.7680	+	0.433937i	0.442564	+	0.0178347i
$593$	−4.92766	−	19.9923i	−0.202355	−	0.820985i	−0.981077	−	0.193616i	$-0.937978\pi$
$593$	−4.92766	−	19.9923i	−0.202355	−	0.820985i	0.778723	−	0.627368i	$-0.215868\pi$
$594$	−2.82607	+	0.943479i	−0.115955	+	0.0387114i
$595$	21.0514	−	44.3648i	0.863022	−	1.81878i
$596$	−11.1989	+	6.46571i	−0.458726	+	0.264846i
$597$	−12.0420	+	17.4459i	−0.492847	+	0.714012i
$598$	−6.61393	−	21.3068i	−0.270464	−	0.871298i
$599$	−11.4965	−	16.6555i	−0.469733	−	0.680526i	0.514482	−	0.857501i	$-0.327984\pi$
$599$	−11.4965	−	16.6555i	−0.469733	−	0.680526i	−0.984215	+	0.176975i	$0.943369\pi$
$600$	−10.4280	−	4.94815i	−0.425722	−	0.202007i
$601$	−6.87762	−	4.34914i	−0.280544	−	0.177405i	0.386782	−	0.922171i	$-0.373587\pi$
$601$	−6.87762	−	4.34914i	−0.280544	−	0.177405i	−0.667326	+	0.744766i	$0.732561\pi$
$602$	−118.612	−	19.2764i	−4.83427	−	0.785646i
$603$	−1.41635	−	2.69863i	−0.0576783	−	0.109897i
$604$	13.5775	−	11.0857i	0.552460	−	0.451070i
$605$	12.3287	+	11.8418i	0.501232	+	0.481439i
$606$		−	11.6780i		−	0.474387i
$607$	15.9913	−	16.6487i	0.649066	−	0.675749i	−0.312628	−	0.949876i	$-0.601209\pi$
$607$	15.9913	−	16.6487i	0.649066	−	0.675749i	0.961694	+	0.274126i	$0.0883887\pi$
$608$	−1.99916	−	0.667416i	−0.0810765	−	0.0270673i
$609$	3.37317	−	41.7842i	0.136688	−	1.69318i
$610$	4.28139	+	1.05527i	0.173348	+	0.0427265i
$611$	19.8929	+	23.4387i	0.804782	+	0.948227i
$612$	22.8876	−	5.64129i	0.925177	−	0.228036i
$613$	−1.99235	−	12.2594i	−0.0804703	−	0.495154i	−0.995732	−	0.0922935i	$-0.970580\pi$
$613$	−1.99235	−	12.2594i	−0.0804703	−	0.495154i	0.915262	−	0.402860i	$-0.131984\pi$
$614$	26.6195	−	32.6030i	1.07428	−	1.31575i
$615$	14.2603	+	10.7159i	0.575032	+	0.432109i
$616$	−25.4254	−	28.6993i	−1.02442	−	1.15633i
$617$	−1.37228	+	8.44397i	−0.0552459	+	0.339942i	0.944683	+	0.327986i	$0.106370\pi$
$617$	−1.37228	+	8.44397i	−0.0552459	+	0.339942i	−0.999929	+	0.0119558i	$0.996194\pi$
$618$	1.03467	+	12.8166i	0.0416204	+	0.515561i
$619$	−10.9636	+	44.4809i	−0.440662	+	1.78784i	0.158663	+	0.987333i	$0.449282\pi$
$619$	−10.9636	+	44.4809i	−0.440662	+	1.78784i	−0.599326	+	0.800505i	$0.704565\pi$
$620$	11.2059	−	38.6871i	0.450038	−	1.55371i
$621$	0.486962	−	2.38530i	0.0195411	−	0.0957187i
$622$	18.0881	+	14.7685i	0.725267	+	0.592162i
$623$	−10.6850	−	87.9988i	−0.428085	−	3.52560i
$624$	4.50343	+	24.7268i	0.180282	+	0.989863i
$625$	−1.48994	+	12.2707i	−0.0595975	+	0.490829i
$626$	26.0972	−	25.0667i	1.04305	−	1.00187i
$627$	−0.328312	−	0.341809i	−0.0131115	−	0.0136505i
$628$	−35.5133	−	74.8427i	−1.41713	−	2.98655i
$629$	−6.72486	−	4.64183i	−0.268138	−	0.185082i
$630$	12.6207	+	19.9580i	0.502820	+	0.795146i
$631$	−27.8476	+	37.0584i	−1.10860	+	1.47527i	−0.246074	+	0.969251i	$0.579141\pi$
$631$	−27.8476	+	37.0584i	−1.10860	+	1.47527i	−0.862521	+	0.506022i	$0.831116\pi$
$632$	35.5756	−	67.7837i	1.41512	−	2.69629i
$633$	−2.56341	−	12.5564i	−0.101886	−	0.499072i
$634$	−40.1981	−	3.24513i	−1.59647	−	0.128880i
$635$	−4.49969	+	1.30335i	−0.178565	+	0.0517219i
$636$	17.4372	−	9.15174i	0.691430	−	0.362890i
$637$	35.3626	+	64.3680i	1.40112	+	2.55035i
$638$	21.1391	+	11.0947i	0.836906	+	0.439242i
$639$	−6.87001	−	1.40252i	−0.271773	−	0.0554829i
$640$	17.2998	−	13.0000i	0.683835	−	0.513868i
$641$	−1.04911	+	26.0334i	−0.0414373	+	1.02826i	0.836049	+	0.548655i	$0.184860\pi$
$641$	−1.04911	+	26.0334i	−0.0414373	+	1.02826i	−0.877486	+	0.479602i	$0.840781\pi$
$642$	−14.6334	−	5.54973i	−0.577536	−	0.219031i
$643$	−44.6085	−	12.9210i	−1.75919	−	0.509555i	−0.767821	−	0.640665i	$-0.778659\pi$
$643$	−44.6085	−	12.9210i	−1.75919	−	0.509555i	−0.991368	+	0.131110i	$0.958146\pi$
$644$	55.6541	−	11.3619i	2.19308	−	0.447720i
$645$	−10.6429	+	12.0134i	−0.419064	+	0.473026i
$646$	3.43502	+	4.20714i	0.135149	+	0.165528i
$647$	−0.235335	−	5.83977i	−0.00925196	−	0.229585i	−0.997199	−	0.0747931i	$-0.976170\pi$
$647$	−0.235335	−	5.83977i	−0.00925196	−	0.229585i	0.987947	−	0.154792i	$-0.0494707\pi$
$648$	−1.97984	+	5.93035i	−0.0777756	+	0.232966i
$649$	−4.04677	−	3.58512i	−0.158849	−	0.140728i
$650$	−14.8279	+	8.14615i	−0.581597	+	0.319518i
$651$	19.9135	−	17.6418i	0.780471	−	0.691437i
$652$	20.2399	+	47.5047i	0.792654	+	1.86043i
$653$	−4.19239	−	7.26144i	−0.164061	−	0.284162i	0.772260	−	0.635306i	$-0.219126\pi$
$653$	−4.19239	−	7.26144i	−0.164061	−	0.284162i	−0.936321	+	0.351144i	$0.885793\pi$
$654$	7.23005	−	12.5228i	0.282717	−	0.489681i
$655$	−0.129891	−	0.0157716i	−0.00507527	−	0.000616249i
$656$	−63.2570	+	30.0158i	−2.46977	+	1.17192i
$657$	−2.64622	−	1.52779i	−0.103239	−	0.0596049i
$658$	−93.3044	+	64.4034i	−3.63738	+	2.51070i
$659$	11.8063	+	5.03021i	0.459910	+	0.195949i	0.609479	−	0.792802i	$-0.291379\pi$
$659$	11.8063	+	5.03021i	0.459910	+	0.195949i	−0.149570	+	0.988751i	$0.547789\pi$
$660$	−9.16427	+	1.48934i	−0.356719	+	0.0579725i
$661$	−25.9579	−	34.5437i	−1.00965	−	1.34359i	−0.938179	−	0.346151i	$-0.887488\pi$
$661$	−25.9579	−	34.5437i	−1.00965	−	1.34359i	−0.0714666	−	0.997443i	$-0.522768\pi$
$662$	−8.23429	+	21.7120i	−0.320035	+	0.843862i
$663$	7.13448	−	17.6712i	0.277080	−	0.686291i
$664$	−21.6209	−	57.0096i	−0.839054	−	2.21240i
$665$	−2.00762	+	3.17479i	−0.0778521	+	0.123113i
$666$	3.61492	−	1.54017i	0.140075	−	0.0596804i
$667$	−16.4875	+	10.4261i	−0.638400	+	0.403700i
$668$	23.6696	−	2.87401i	0.915804	−	0.111199i
$669$	−5.22574	+	12.2653i	−0.202039	+	0.474202i
$670$	−4.35625	−	13.0486i	−0.168297	−	0.504110i
$671$	−1.07077	+	0.406088i	−0.0413365	+	0.0156769i
$672$	−27.1833	+	2.19446i	−1.04862	+	0.0846533i
$673$	−9.86522	−	34.0587i	−0.380276	−	1.31287i	−0.891345	−	0.453326i	$-0.850237\pi$
$673$	−9.86522	−	34.0587i	−0.380276	−	1.31287i	0.511068	−	0.859540i	$-0.329250\pi$
$674$	65.5598	−	2.64197i	2.52527	−	0.101765i
$675$	−1.84616			−0.0710589
$676$	52.3262	+	24.9693i	2.01255	+	0.960358i
$677$	16.5357			0.635519			0.317759	−	0.948171i	$-0.397070\pi$
$677$	16.5357			0.635519			0.317759	+	0.948171i	$0.397070\pi$
$678$	28.2195	−	1.13721i	1.08376	−	0.0436742i
$679$	20.6011	+	71.1232i	0.790597	+	2.72946i
$680$	58.4951	−	4.72221i	2.24318	−	0.181089i
$681$	−2.04409	+	0.775221i	−0.0783297	+	0.0297065i
$682$	4.79789	+	14.3714i	0.183721	+	0.550311i
$683$	−5.76249	+	13.5251i	−0.220495	+	0.517522i	−0.993087	−	0.117382i	$-0.962550\pi$
$683$	−5.76249	+	13.5251i	−0.220495	+	0.517522i	0.772591	+	0.634904i	$0.218960\pi$
$684$	−1.79001	+	0.217347i	−0.0684428	+	0.00831046i
$685$	−31.6266	+	19.9995i	−1.20839	+	0.764141i
$686$	−163.541	+	69.6783i	−6.24403	+	2.66033i
$687$	−13.6952	+	21.6572i	−0.522504	+	0.826274i
$688$	−22.3395	−	58.9044i	−0.851685	−	2.24571i
$689$	2.25409	−	15.7602i	0.0858741	−	0.600414i
$690$	3.89660	−	10.2745i	0.148341	−	0.391143i
$691$	−3.74274	−	4.98069i	−0.142381	−	0.189474i	0.722619	−	0.691246i	$-0.242938\pi$
$691$	−3.74274	−	4.98069i	−0.142381	−	0.189474i	−0.865000	+	0.501772i	$0.832682\pi$
$692$	−13.5427	+	2.20090i	−0.514814	+	0.0836655i
$693$	−5.64190	−	2.40379i	−0.214318	−	0.0913123i
$694$	16.7989	−	11.5955i	0.637679	−	0.440158i
$695$	19.6968	+	11.3719i	0.747141	+	0.431362i
$696$	45.2608	−	21.4765i	1.71561	−	0.814066i
$697$	52.7022	+	6.39920i	1.99624	+	0.242387i
$698$	31.7487	−	54.9903i	1.20171	−	2.08142i
$699$	−3.43138	−	5.94332i	−0.129787	−	0.224797i
$700$	−16.8839	−	39.6281i	−0.638153	−	1.49780i
$701$	14.7567	−	13.0733i	0.557354	−	0.493772i	−0.336773	−	0.941586i	$-0.609336\pi$
$701$	14.7567	−	13.0733i	0.557354	−	0.493772i	0.894127	+	0.447813i	$0.147797\pi$
$702$	5.34842	+	7.44129i	0.201863	+	0.280854i
$703$	0.467861	+	0.414488i	0.0176457	+	0.0156327i
$704$	−0.256962	+	0.769695i	−0.00968461	+	0.0290090i
$705$	0.609712	+	15.1298i	0.0229631	+	0.569823i
$706$	20.6291	+	25.2660i	0.776385	+	0.950900i
$707$	15.9398	−	17.9923i	0.599477	−	0.676669i
$708$	−20.1535	+	4.11437i	−0.757415	+	0.154627i
$709$	−6.29144	−	1.82234i	−0.236280	−	0.0684394i	0.157965	−	0.987445i	$-0.449507\pi$
$709$	−6.29144	−	1.82234i	−0.236280	−	0.0684394i	−0.394245	+	0.919005i	$0.628994\pi$
$710$	−29.5920	−	11.2228i	−1.11057	−	0.421183i
$711$	0.493026	−	12.2343i	0.0184899	−	0.458822i
$712$	84.6911	−	63.6413i	3.17393	−	2.38506i
$713$	−12.1300	−	2.47636i	−0.454272	−	0.0927403i
$714$	62.2292	+	32.6604i	2.32887	+	1.22228i
$715$	−3.36099	+	6.71144i	−0.125694	+	0.250994i
$716$	48.8831	−	25.6558i	1.82685	−	0.958803i
$717$	−4.32267	+	1.25208i	−0.161433	+	0.0467596i
$718$	21.2496	+	1.71545i	0.793028	+	0.0640199i
$719$	7.37744	+	36.1371i	0.275132	+	1.34769i	0.848850	+	0.528634i	$0.177296\pi$
$719$	7.37744	+	36.1371i	0.275132	+	1.34769i	−0.573718	+	0.819053i	$0.694499\pi$
$720$	−5.75301	+	10.9615i	−0.214402	+	0.408509i
$721$	−15.8998	+	21.1588i	−0.592140	+	0.787995i
$722$	25.5878	+	40.4639i	0.952280	+	1.50591i
$723$	−6.15526	−	4.24867i	−0.228917	−	0.158010i
$724$	45.6005	+	96.1010i	1.69473	+	3.57157i
$725$	10.2476	+	10.6689i	0.380587	+	0.396233i
$726$	−17.6445	+	16.9478i	−0.654848	+	0.628990i
$727$	3.50957	−	28.9039i	0.130163	−	1.07199i	−0.770491	−	0.637450i	$-0.779989\pi$
$727$	3.50957	−	28.9039i	0.130163	−	1.07199i	0.900654	−	0.434537i	$-0.143088\pi$
$728$	−61.1206	+	100.857i	−2.26528	+	3.73800i
$729$	0.120537	+	0.992709i	0.00446432	+	0.0367670i
$730$	−10.6833	−	8.72267i	−0.395408	−	0.322840i
$731$	−9.55469	+	46.8020i	−0.353393	+	1.73103i
$732$	−1.21218	+	4.18493i	−0.0448035	+	0.154680i
$733$	10.7073	−	43.4411i	0.395482	−	1.60453i	−0.349155	−	0.937065i	$-0.613531\pi$
$733$	10.7073	−	43.4411i	0.395482	−	1.60453i	0.744637	−	0.667470i	$-0.232623\pi$
$734$	−4.06159	−	50.3119i	−0.149916	−	1.85705i
$735$	−5.80268	+	35.7053i	−0.214035	+	1.31701i
$736$	8.41560	+	9.49925i	0.310203	+	0.350147i
$737$	2.85614	+	2.14625i	0.105207	+	0.0790582i
$738$	−16.1457	+	19.7749i	−0.594333	+	0.727926i
$739$	−0.887574	−	5.46146i	−0.0326499	−	0.200903i	0.965601	−	0.260030i	$-0.0837325\pi$
$739$	−0.887574	−	5.46146i	−0.0326499	−	0.200903i	−0.998250	+	0.0591268i	$0.981168\pi$
$740$	11.8890	−	2.93037i	0.437047	−	0.107722i
$741$	−0.704699	+	1.27610i	−0.0258877	+	0.0468787i
$742$	57.0063	+	14.0508i	2.09277	+	0.515821i
$743$	−4.07503	+	50.4783i	−0.149498	+	1.85187i	0.294262	+	0.955725i	$0.404926\pi$
$743$	−4.07503	+	50.4783i	−0.149498	+	1.85187i	−0.443760	+	0.896145i	$0.646356\pi$
$744$	30.1577	+	10.0681i	1.10564	+	0.369116i
$745$	−3.56700	+	3.71364i	−0.130685	+	0.136057i
$746$			39.7991i			1.45715i
$747$	−7.03331	−	6.75559i	−0.257335	−	0.247174i
$748$	−21.4044	+	17.4762i	−0.782623	+	0.638992i
$749$	−14.9706	−	28.5242i	−0.547015	−	1.04225i
$750$	−30.5013	−	4.95694i	−1.11375	−	0.181002i
$751$	21.3887	+	13.5254i	0.780483	+	0.493548i	0.864326	−	0.502931i	$-0.167745\pi$
$751$	21.3887	+	13.5254i	0.780483	+	0.493548i	−0.0838432	+	0.996479i	$0.526719\pi$
$752$	−53.6974	−	25.4797i	−1.95814	−	0.929150i
$753$	−2.09821	−	3.03978i	−0.0764630	−	0.110776i
$754$	13.3151	−	72.2131i	0.484907	−	2.62985i
$755$	3.96491	−	5.74416i	0.144298	−	0.209051i
$756$	−20.2062	+	11.6661i	−0.734893	+	0.424291i
$757$	13.6685	−	28.8058i	0.496791	−	1.04696i	−0.487939	−	0.872878i	$-0.662251\pi$
$757$	13.6685	−	28.8058i	0.496791	−	1.04696i	0.984730	−	0.174087i	$-0.0556975\pi$
$758$	−56.0048	+	18.6972i	−2.03419	+	0.679111i
$759$	0.682962	+	2.77089i	0.0247900	+	0.100577i
$760$	−4.48543	−	0.180757i	−0.162704	−	0.00655674i
$761$	14.2644	+	0.574837i	0.517085	+	0.0208378i	0.297437	−	0.954741i	$-0.403868\pi$
$761$	14.2644	+	0.574837i	0.517085	+	0.0208378i	0.219648	+	0.975579i	$0.429509\pi$
$762$	−1.60450	−	6.50973i	−0.0581250	−	0.235823i
$763$	28.2322	−	9.42528i	1.02207	−	0.341218i
$764$	51.9366	−	109.454i	1.87900	−	3.95991i
$765$	8.12894	−	4.69325i	0.293903	−	0.169685i
$766$	44.3254	−	64.2165i	1.60154	−	2.32024i
$767$	−6.84131	+	15.1565i	−0.247025	+	0.547270i
$768$	16.8067	+	24.3487i	0.606460	+	0.878609i
$769$	14.6869	+	6.96903i	0.529624	+	0.251310i	0.674676	−	0.738114i	$-0.264284\pi$
$769$	14.6869	+	6.96903i	0.529624	+	0.251310i	−0.145051	+	0.989424i	$0.546335\pi$
$770$	−23.3955	−	14.7944i	−0.843117	−	0.533155i
$771$	12.0185	+	1.95319i	0.432835	+	0.0703425i
$772$	2.19911	+	4.19005i	0.0791476	+	0.150803i
$773$	−8.04322	+	6.56709i	−0.289295	+	0.236202i	−0.765968	−	0.642879i	$-0.777740\pi$
$773$	−8.04322	+	6.56709i	−0.289295	+	0.236202i	0.476673	+	0.879080i	$0.341842\pi$
$774$	−16.5660	−	15.9118i	−0.595451	−	0.571938i
$775$			9.38833i			0.337239i
$776$	−61.3002	+	63.8202i	−2.20055	+	2.29101i
$777$	7.67172	+	2.56120i	0.275221	+	0.0918824i
$778$	1.57644	−	19.5277i	0.0565181	−	0.700102i
$779$	−3.94300	−	0.971862i	−0.141273	−	0.0348206i
$780$	12.7314	+	25.5621i	0.455856	+	0.915271i
$781$	7.98055	−	1.96703i	0.285567	−	0.0703859i
$782$	−5.24615	−	32.2809i	−0.187602	−	1.15436i
$783$	5.06775	−	6.20686i	0.181106	−	0.221815i
$784$	−113.512	−	85.2989i	−4.05401	−	3.04639i
$785$	−21.8743	−	24.6910i	−0.780729	−	0.881260i
$786$	0.0300390	−	0.184837i	0.00107145	−	0.00659293i
$787$	−1.55324	−	19.2403i	−0.0553670	−	0.685843i	−0.963595	−	0.267367i	$-0.913846\pi$
$787$	−1.55324	−	19.2403i	−0.0553670	−	0.685843i	0.908228	−	0.418476i	$-0.137436\pi$
$788$	−11.4970	+	46.6453i	−0.409564	+	1.66167i
$789$	−2.69632	+	9.30879i	−0.0959917	+	0.331402i
$790$	11.0548	−	54.1498i	0.393311	−	1.92656i
$791$	45.0299	+	36.7658i	1.60108	+	1.30724i
$792$	−0.883409	−	7.27553i	−0.0313906	−	0.258525i
$793$	2.16926	+	2.77510i	0.0770328	+	0.0985466i
$794$	−5.13715	+	42.3083i	−0.182311	+	1.50146i
$795$	5.65539	−	5.43208i	0.200576	−	0.192656i
$796$	−65.4916	−	68.1839i	−2.32129	−	2.41672i
$797$	17.4620	+	36.8005i	0.618538	+	1.30354i	0.934903	+	0.354903i	$0.115486\pi$
$797$	17.4620	+	36.8005i	0.618538	+	1.30354i	−0.316366	+	0.948637i	$0.602463\pi$
$798$	−4.42431	−	3.05388i	−0.156619	−	0.108106i
$799$	24.0864	+	38.0895i	0.852114	+	1.34751i
$800$	5.78150	−	7.69378i	0.204407	−	0.272016i
$801$	7.87442	−	15.0034i	0.278229	−	0.530121i
$802$	−13.5060	−	66.1568i	−0.476914	−	2.33608i
$803$	3.57026	+	0.288221i	0.125992	+	0.0101711i
$804$	13.0559	−	3.78168i	0.460445	−	0.133369i
$805$	20.0275	−	10.5113i	0.705877	−	0.370473i
$806$	37.8414	−	27.1984i	1.33290	−	0.958023i
$807$	−4.95794	−	2.60213i	−0.174528	−	0.0915992i
$808$	28.1460	+	5.74605i	0.990173	+	0.202145i
$809$	20.2273	−	15.1998i	0.711155	−	0.534398i	−0.182471	−	0.983211i	$-0.558410\pi$
$809$	20.2273	−	15.1998i	0.711155	−	0.534398i	0.893626	+	0.448813i	$0.148153\pi$
$810$	−0.181748	+	4.51003i	−0.00638597	+	0.158466i
$811$	−11.0481	−	4.19001i	−0.387953	−	0.147131i	0.152914	−	0.988240i	$-0.451134\pi$
$811$	−11.0481	−	4.19001i	−0.387953	−	0.147131i	−0.540867	+	0.841108i	$0.681904\pi$
$812$	179.577	+	52.0152i	6.30193	+	1.82538i
$813$	18.9223	−	3.86302i	0.663634	−	0.135482i
$814$	−3.05443	+	3.44774i	−0.107058	+	0.120843i
$815$	13.0040	+	15.9270i	0.455511	+	0.557900i
$816$	1.48355	+	36.8140i	0.0519348	+	1.28875i
$817$	1.15708	−	3.46586i	0.0404810	−	0.121255i
$818$	26.9821	+	23.9040i	0.943406	+	0.835785i
$819$	−1.91661	+	18.7650i	−0.0669718	+	0.655703i
$820$	−59.5475	+	52.7545i	−2.07949	+	1.84227i
$821$	−17.3848	−	40.8035i	−0.606732	−	1.42405i	−0.885930	−	0.463819i	$-0.846479\pi$
$821$	−17.3848	−	40.8035i	−0.606732	−	1.42405i	0.279198	−	0.960234i	$-0.409932\pi$
$822$	−26.7770	−	46.3791i	−0.933954	−	1.61766i
$823$	−3.73272	+	6.46525i	−0.130114	+	0.225365i	−0.923720	−	0.383067i	$-0.874868\pi$
$823$	−3.73272	+	6.46525i	−0.130114	+	0.225365i	0.793606	+	0.608432i	$0.208201\pi$
$824$	−31.3994	−	3.81258i	−1.09385	−	0.132817i
$825$	1.95520	−	0.927753i	0.0680712	−	0.0323002i
$826$	−53.1090	−	30.6625i	−1.84790	−	1.06688i
$827$	18.8471	−	13.0092i	0.655380	−	0.452376i	−0.193402	−	0.981120i	$-0.561952\pi$
$827$	18.8471	−	13.0092i	0.655380	−	0.452376i	0.848781	+	0.528744i	$0.177337\pi$
$828$	9.98875	+	4.25581i	0.347133	+	0.147900i
$829$	6.18256	−	1.00476i	0.214729	−	0.0348969i	−0.0520949	−	0.998642i	$-0.516590\pi$
$829$	6.18256	−	1.00476i	0.214729	−	0.0348969i	0.266824	+	0.963745i	$0.414026\pi$
$830$	−26.4437	−	35.1902i	−0.917875	−	1.22147i
$831$	−0.490226	+	1.29262i	−0.0170058	+	0.0448405i
$832$	2.49530	+	0.0529852i	0.0865089	+	0.00183693i
$833$	38.1771	+	100.665i	1.32276	+	3.48782i
$834$	−17.3971	+	27.5113i	−0.602413	+	0.952640i
$835$	8.73460	−	3.72146i	0.302273	−	0.128787i
$836$	1.78651	−	1.12972i	0.0617876	−	0.0390721i
$837$	5.04824	−	0.612967i	0.174493	−	0.0211873i
$838$	6.76847	−	15.8862i	0.233813	−	0.548779i
$839$	11.1872	+	33.5098i	0.386225	+	1.15689i	0.944861	+	0.327473i	$0.106197\pi$
$839$	11.1872	+	33.5098i	0.386225	+	1.15689i	−0.558635	+	0.829413i	$0.688675\pi$
$840$	−54.3121	+	20.5978i	−1.87394	+	0.710693i
$841$	−35.0930	+	2.83300i	−1.21010	+	0.0976897i
$842$	−23.9275	−	82.6074i	−0.824597	−	2.84684i
$843$	20.3803	−	0.821298i	0.701935	−	0.0282870i
$844$	57.1551			1.96736
$845$	22.7796	+	3.75315i	0.783643	+	0.129112i
$846$	−21.6710			−0.745065
$847$	−50.3174	+	2.02772i	−1.72893	+	0.0696733i
$848$	8.56351	+	29.5647i	0.294072	+	1.01526i
$849$	−11.9918	+	0.968077i	−0.411557	+	0.0332243i
$850$	−23.1892	+	8.79450i	−0.795383	+	0.301649i
$851$	−1.19185	−	3.57003i	−0.0408561	−	0.122379i
$852$	12.2573	−	28.7690i	0.419930	−	0.985611i
$853$	11.1921	−	1.35897i	0.383210	−	0.0465301i	0.0733350	−	0.997307i	$-0.476636\pi$
$853$	11.1921	−	1.35897i	0.383210	−	0.0465301i	0.309875	+	0.950777i	$0.399713\pi$
$854$	−10.9789	+	6.94261i	−0.375689	+	0.237571i
$855$	−0.660554	+	0.281436i	−0.0225905	+	0.00962490i
$856$	20.5760	−	32.5384i	0.703274	−	1.11214i
$857$	2.57170	+	6.78102i	0.0878477	+	0.231635i	0.971739	−	0.236056i	$-0.0758550\pi$
$857$	2.57170	+	6.78102i	0.0878477	+	0.231635i	−0.883892	+	0.467692i	$0.845086\pi$
$858$	−9.40377	−	5.19303i	−0.321039	−	0.177287i
$859$	−15.3492	+	40.4725i	−0.523708	+	1.38090i	0.368647	+	0.929570i	$0.379821\pi$
$859$	−15.3492	+	40.4725i	−0.523708	+	1.38090i	−0.892355	+	0.451335i	$0.850948\pi$
$860$	−43.0009	−	57.2239i	−1.46632	−	1.95132i
$861$	−51.8672	+	8.42925i	−1.76763	+	0.287268i
$862$	84.6212	+	36.0537i	2.88221	+	1.22799i
$863$	37.2224	−	25.6927i	1.26706	−	0.874591i	0.270944	−	0.962595i	$-0.412664\pi$
$863$	37.2224	−	25.6927i	1.26706	−	0.874591i	0.996120	+	0.0880044i	$0.0280489\pi$
$864$	−4.51453	−	2.60646i	−0.153587	−	0.0886737i
$865$	−4.93588	+	2.34211i	−0.167825	+	0.0796340i
$866$	−67.8531	−	8.23885i	−2.30574	−	0.279968i
$867$	5.46812	−	9.47105i	0.185707	−	0.321654i
$868$	59.3257	+	102.755i	2.01364	+	3.48773i
$869$	5.62596	+	13.2046i	0.190848	+	0.447936i
$870$	27.0721	−	23.9838i	0.917830	−	0.813126i
$871$	3.70028	−	10.3470i	0.125379	−	0.350595i
$872$	26.6246	+	23.5874i	0.901624	+	0.798769i
$873$	−4.48207	+	13.4254i	−0.151695	+	0.454382i
$874$	0.100733	+	2.49966i	0.00340733	+	0.0845521i
$875$	−40.2273	−	49.2695i	−1.35993	−	1.66561i
$876$	9.03674	−	10.2004i	0.305323	−	0.344639i
$877$	24.6126	−	5.02470i	0.831108	−	0.169672i	0.234410	−	0.972138i	$-0.424684\pi$
$877$	24.6126	−	5.02470i	0.831108	−	0.169672i	0.596698	+	0.802466i	$0.296479\pi$
$878$	−91.0130	−	26.3622i	−3.07154	−	0.889682i
$879$	−18.1922	−	6.89940i	−0.613608	−	0.232711i
$880$	0.584325	−	14.4999i	0.0196976	−	0.488791i
$881$	20.7000	−	15.5550i	0.697399	−	0.524061i	−0.191885	−	0.981418i	$-0.561460\pi$
$881$	20.7000	−	15.5550i	0.697399	−	0.524061i	0.889284	+	0.457356i	$0.151203\pi$
$882$	−50.7247	−	10.3555i	−1.70799	−	0.348689i
$883$	8.48038	+	4.45085i	0.285387	+	0.149783i	0.601343	−	0.798991i	$-0.294633\pi$
$883$	8.48038	+	4.45085i	0.285387	+	0.149783i	−0.315955	+	0.948774i	$0.602325\pi$
$884$	70.8540	+	46.9402i	2.38308	+	1.57877i
$885$	−7.25238	+	3.80634i	−0.243786	+	0.127949i
$886$	−25.5146	+	7.39040i	−0.857181	+	0.248285i
$887$	−40.0237	−	3.23105i	−1.34386	−	0.108488i	−0.612497	−	0.790473i	$-0.709835\pi$
$887$	−40.0237	−	3.23105i	−1.34386	−	0.108488i	−0.731366	+	0.681985i	$0.761117\pi$
$888$	1.93339	+	9.47038i	0.0648804	+	0.317805i
$889$	6.41332	−	12.2196i	0.215096	−	0.409831i
$890$	45.9456	−	61.1425i	1.54010	−	2.04950i
$891$	−0.626521	−	0.990764i	−0.0209893	−	0.0331919i
$892$	−48.9343	−	33.7769i	−1.63844	−	1.13093i
$893$	−1.47783	−	3.11446i	−0.0494536	−	0.104221i
$894$	−5.10500	−	5.31487i	−0.170737	−	0.177756i
$895$	15.8542	−	15.2282i	0.529948	−	0.509022i
$896$	−7.68395	+	63.2830i	−0.256703	+	2.11414i
$897$	7.51676	−	4.53283i	0.250977	−	0.151347i
$898$	1.31116	+	10.7984i	0.0437539	+	0.360346i
$899$	−31.5639	−	25.7711i	−1.05271	−	0.859514i
$900$	1.64695	−	8.06728i	0.0548982	−	0.268909i
$901$	6.49313	−	22.4169i	0.216318	−	0.746815i
$902$	7.16180	−	29.0566i	0.238462	−	0.967478i
$903$	−3.80446	−	47.1267i	−0.126605	−	1.56828i
$904$	−11.1443	+	68.5734i	−0.370653	+	2.28072i
$905$	28.0875	+	31.7043i	0.933662	+	1.05389i
$906$	7.98574	+	6.00090i	0.265309	+	0.199366i
$907$	−11.2476	+	13.7758i	−0.373469	+	0.457417i	−0.926806	−	0.375541i	$-0.877457\pi$
$907$	−11.2476	+	13.7758i	−0.373469	+	0.457417i	0.553336	+	0.832958i	$0.313354\pi$
$908$	−1.56401	−	9.62373i	−0.0519034	−	0.319375i
$909$	4.46119	−	1.09958i	0.147968	−	0.0364709i
$910$	−22.1257	+	82.2150i	−0.733461	+	2.72540i
$911$	−14.4786	−	3.56866i	−0.479698	−	0.118235i	−0.00795015	−	0.999968i	$-0.502531\pi$
$911$	−14.4786	−	3.56866i	−0.479698	−	0.118235i	−0.471748	+	0.881733i	$0.656377\pi$
$912$	0.226782	−	2.80919i	0.00750949	−	0.0930217i
$913$	10.8436	+	3.62012i	0.358870	+	0.119808i
$914$	−41.2638	+	42.9602i	−1.36489	+	1.42100i
$915$			1.73492i			0.0573546i
$916$	−82.4192	−	79.1647i	−2.72321	−	2.61568i
$917$	0.298572	−	0.243777i	0.00985972	−	0.00805021i
$918$	6.24296	+	11.8950i	0.206048	+	0.392592i
$919$	6.47224	+	1.05184i	0.213500	+	0.0346971i	0.266220	−	0.963912i	$-0.414225\pi$
$919$	6.47224	+	1.05184i	0.213500	+	0.0346971i	−0.0527206	+	0.998609i	$0.516789\pi$
$920$	22.8460	+	14.4469i	0.753210	+	0.476301i
$921$	14.9613	+	7.09922i	0.492991	+	0.233927i
$922$	53.2281	+	77.1143i	1.75298	+	2.53962i
$923$	−13.0552	−	21.6493i	−0.429718	−	0.712597i
$924$	15.5370	−	22.5093i	0.511131	−	0.740501i
$925$	−2.47177	+	1.42708i	−0.0812714	+	0.0469221i
$926$	2.06441	−	4.35066i	0.0678409	−	0.142972i
$927$	−4.79873	+	1.60205i	−0.157611	+	0.0526183i
$928$	9.99643	+	40.5571i	0.328149	+	1.33135i
$929$	9.95862	+	0.401319i	0.326732	+	0.0131668i	0.203090	−	0.979160i	$-0.434902\pi$
$929$	9.95862	+	0.401319i	0.326732	+	0.0131668i	0.123642	+	0.992327i	$0.460543\pi$
$930$	22.9349	+	0.924246i	0.752066	+	0.0303072i
$931$	−1.97086	−	7.99609i	−0.0645923	−	0.262061i
$932$	29.0319	−	9.69228i	0.950972	−	0.317481i
$933$	−3.93864	+	8.30051i	−0.128945	+	0.271746i
$934$	−25.2980	+	14.6058i	−0.827776	+	0.477916i
$935$	−6.25054	+	9.05546i	−0.204414	+	0.296145i
$936$	−20.5664	+	9.22919i	−0.672234	+	0.301665i
$937$	4.62904	+	6.70632i	0.151224	+	0.219086i	0.891273	−	0.453467i	$-0.149813\pi$
$937$	4.62904	+	6.70632i	0.151224	+	0.219086i	−0.740049	+	0.672553i	$0.765198\pi$
$938$	36.6121	+	17.3726i	1.19543	+	0.567237i
$939$	12.0331	+	7.60930i	0.392687	+	0.248320i
$940$	−66.6576	−	10.8329i	−2.17413	−	0.353331i
$941$	−10.5043	−	20.0142i	−0.342429	−	0.652445i	0.651957	−	0.758256i	$-0.273948\pi$
$941$	−10.5043	−	20.0142i	−0.342429	−	0.652445i	−0.994386	+	0.105811i	$0.966256\pi$
$942$	36.5691	−	29.8577i	1.19149	−	0.972818i
$943$	17.6356	+	16.9392i	0.574293	+	0.551616i
$944$		−	32.1496i		−	1.04638i
$945$	−6.43593	+	6.70051i	−0.209361	+	0.217968i
$946$	25.5405	+	8.52667i	0.830393	+	0.277226i
$947$	3.59634	−	44.5486i	0.116865	−	1.44764i	−0.626851	−	0.779139i	$-0.715656\pi$
$947$	3.59634	−	44.5486i	0.116865	−	1.44764i	0.743716	−	0.668496i	$-0.233062\pi$
$948$	53.0210	+	13.0685i	1.72204	+	0.424446i
$949$	−2.40888	−	10.7505i	−0.0781954	−	0.348976i
$950$	1.84199	−	0.454009i	0.0597619	−	0.0147300i
$951$	−2.54530	−	15.6619i	−0.0825370	−	0.507870i
$952$	−109.336	+	133.913i	−3.54361	+	4.34014i
$953$	39.4237	+	29.6250i	1.27706	+	0.959647i	0.999999	−	0.00120590i	$-0.000383849\pi$
$953$	39.4237	+	29.6250i	1.27706	+	0.959647i	0.277059	+	0.960853i	$0.410640\pi$
$954$	7.44204	+	8.40033i	0.240945	+	0.271971i
$955$	7.73853	−	47.6171i	0.250413	−	1.54085i
$956$	−1.61505	−	20.0059i	−0.0522343	−	0.647038i
$957$	−2.24791	+	9.12013i	−0.0726646	+	0.294812i
$958$	2.76783	−	9.55565i	0.0894244	−	0.308729i
$959$	22.0494	−	108.005i	0.712011	−	3.48766i
$960$	0.952244	+	0.777483i	0.0307336	+	0.0250932i
$961$	0.619503	+	5.10206i	0.0199840	+	0.164583i
$962$	12.9129	+	5.82861i	0.416330	+	0.187922i
$963$	0.742223	−	6.11276i	0.0239178	−	0.196981i
$964$	24.0567	−	23.1068i	0.774814	−	0.744219i
$965$	1.30530	+	1.35896i	0.0420189	+	0.0437464i
$966$	13.8771	+	29.2454i	0.446488	+	0.940954i
$967$	−15.3226	−	10.5765i	−0.492743	−	0.340116i	0.295641	−	0.955299i	$-0.404467\pi$
$967$	−15.3226	−	10.5765i	−0.492743	−	0.340116i	−0.788384	+	0.615183i	$0.789082\pi$
$968$	−32.1652	−	50.8652i	−1.03383	−	1.63487i
$969$	−1.28376	+	1.70837i	−0.0412402	+	0.0548808i
$970$	−29.6894	+	56.5683i	−0.953268	+	1.81630i
$971$	4.95206	+	24.2568i	0.158919	+	0.778437i	0.978625	+	0.205653i	$0.0659317\pi$
$971$	4.95206	+	24.2568i	0.158919	+	0.778437i	−0.819706	+	0.572785i	$0.805863\pi$
$972$	−4.44542	−	0.358871i	−0.142587	−	0.0115108i
$973$	−64.3549	+	18.6406i	−2.06312	+	0.597591i
$974$	−52.4078	+	27.5057i	−1.67926	+	0.881341i
$975$	−4.50813	−	4.89745i	−0.144376	−	0.156844i
$976$	−6.02987	−	3.16472i	−0.193011	−	0.101300i
$977$	−22.2720	−	4.54686i	−0.712544	−	0.145467i	−0.169939	−	0.985455i	$-0.554357\pi$
$977$	−22.2720	−	4.54686i	−0.712544	−	0.145467i	−0.542606	+	0.839988i	$0.682562\pi$
$978$	−23.5253	+	17.6781i	−0.752255	+	0.565283i
$979$	−0.799793	+	19.8467i	−0.0255615	+	0.634302i
$980$	−150.847	−	57.2086i	−4.81862	−	1.82746i
$981$	5.46468	+	1.58286i	0.174474	+	0.0505369i
$982$	−37.0092	+	7.55548i	−1.18101	+	0.241105i
$983$	−11.1685	+	12.6067i	−0.356221	+	0.402090i	−0.899116	−	0.437710i	$-0.855790\pi$
$983$	−11.1685	+	12.6067i	−0.356221	+	0.402090i	0.542895	+	0.839800i	$0.317328\pi$
$984$	−39.7166	−	48.6440i	−1.26612	−	1.55072i
$985$	0.770279	+	19.1143i	0.0245431	+	0.609032i
$986$	34.0873	−	102.104i	1.08556	−	3.25165i
$987$	−33.3885	−	29.5796i	−1.06277	−	0.941529i
$988$	−4.94758	−	4.21775i	−0.157403	−	0.134185i
$989$	−16.4685	+	14.5898i	−0.523668	+	0.463930i
$990$	−2.07394	−	4.86772i	−0.0659142	−	0.154706i
$991$	−12.3092	−	21.3201i	−0.391014	−	0.677255i	0.601570	−	0.798820i	$-0.294542\pi$
$991$	−12.3092	−	21.3201i	−0.391014	−	0.677255i	−0.992583	+	0.121565i	$0.961209\pi$
$992$	−13.2547	+	22.9578i	−0.420837	+	0.728912i
$993$	−9.06966	−	1.10126i	−0.287817	−	0.0349473i
$994$	84.2309	−	39.9681i	2.67164	−	1.26771i
$995$	−32.6026	−	18.8231i	−1.03357	−	0.596732i
$996$	35.7946	−	24.7072i	1.13419	−	0.782878i
$997$	−56.2849	−	23.9808i	−1.78256	−	0.759479i	−0.988419	−	0.151747i	$-0.951510\pi$
$997$	−56.2849	−	23.9808i	−1.78256	−	0.759479i	−0.794143	−	0.607731i	$-0.792080\pi$
$998$	−14.4666	+	2.35105i	−0.457932	+	0.0744212i
$999$	0.928744	+	1.23593i	0.0293842	+	0.0391032i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	507.2.t.b.127.2	yes	360
169.4	even	78	inner	507.2.t.b.4.2	✓	360

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
507.2.t.b.4.2	✓	360	169.4	even	78	inner
507.2.t.b.127.2	yes	360	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 507 = 3 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	507.t (of order \(78\), degree \(24\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.53957 + 0.102341i) q^{2} +(-0.278217 - 0.960518i) q^{3} +(4.44542 - 0.358871i) q^{4} +(1.66050 - 0.629744i) q^{5} +(0.804853 + 2.41083i) q^{6} +(-2.05060 + 4.81293i) q^{7} +(-6.20652 + 0.753608i) q^{8} +(-0.845190 + 0.534466i) q^{9} +O(q^{10})\)	\(q+(-2.53957 + 0.102341i) q^{2} +(-0.278217 - 0.960518i) q^{3} +(4.44542 - 0.358871i) q^{4} +(1.66050 - 0.629744i) q^{5} +(0.804853 + 2.41083i) q^{6} +(-2.05060 + 4.81293i) q^{7} +(-6.20652 + 0.753608i) q^{8} +(-0.845190 + 0.534466i) q^{9} +(-4.15250 + 1.76922i) q^{10} +(0.626521 - 0.990764i) q^{11} +(-1.58150 - 4.17006i) q^{12} +(-3.48167 - 0.936989i) q^{13} +(4.71507 - 12.4326i) q^{14} +(-1.06686 - 1.41973i) q^{15} +(6.88051 - 1.11819i) q^{16} +(-4.86253 - 2.07173i) q^{17} +(2.09172 - 1.44381i) q^{18} +(0.350140 + 0.202153i) q^{19} +(7.15562 - 3.39538i) q^{20} +(5.19341 + 0.630595i) q^{21} +(-1.48970 + 2.58023i) q^{22} +(-1.21725 - 2.10834i) q^{23} +(2.45062 + 5.75181i) q^{24} +(-1.38187 + 1.22423i) q^{25} +(8.93784 + 2.02323i) q^{26} +(0.748511 + 0.663123i) q^{27} +(-7.38854 + 22.1314i) q^{28} +(-0.322649 - 8.00644i) q^{29} +(2.85466 + 3.49633i) q^{30} +(3.37219 - 3.80642i) q^{31} +(-5.10758 + 1.04272i) q^{32} +(-1.12596 - 0.326137i) q^{33} +(12.5607 + 4.76366i) q^{34} +(-0.374101 + 9.28321i) q^{35} +(-3.56542 + 2.67924i) q^{36} +(1.51475 + 0.309239i) q^{37} +(-0.909892 - 0.477548i) q^{38} +(0.0686671 + 3.60490i) q^{39} +(-9.83135 + 5.15989i) q^{40} +(-9.64780 + 2.79452i) q^{41} +(-13.2536 - 1.06994i) q^{42} +(-1.80773 - 8.85483i) q^{43} +(2.42959 - 4.62920i) q^{44} +(-1.06686 + 1.41973i) q^{45} +(3.30706 + 5.22969i) q^{46} +(-7.01712 - 4.84357i) q^{47} +(-2.98832 - 6.29776i) q^{48} +(-14.1102 - 14.6903i) q^{49} +(3.38407 - 3.25045i) q^{50} +(-0.637093 + 5.24694i) q^{51} +(-15.8138 - 2.91584i) q^{52} +(0.532237 + 4.38337i) q^{53} +(-1.96876 - 1.60744i) q^{54} +(0.416410 - 2.03971i) q^{55} +(9.10001 - 31.4169i) q^{56} +(0.0967569 - 0.392558i) q^{57} +(1.63878 + 20.2999i) q^{58} +(0.739825 - 4.55233i) q^{59} +(-5.25215 - 5.92845i) q^{60} +(-0.780993 - 0.586878i) q^{61} +(-8.17435 + 10.0118i) q^{62} +(-0.839201 - 5.16381i) q^{63} +(-0.672112 + 0.165661i) q^{64} +(-6.37138 + 0.636694i) q^{65} +(2.89282 + 0.713016i) q^{66} +(-0.245240 + 3.03785i) q^{67} +(-22.3595 - 7.46468i) q^{68} +(-1.68644 + 1.75577i) q^{69} -23.6136i q^{70} +(5.05686 + 4.85718i) q^{71} +(4.84291 - 3.95412i) q^{72} +(1.42000 + 2.70559i) q^{73} +(-3.87846 - 0.630311i) q^{74} +(1.56036 + 0.986712i) q^{75} +(1.62906 + 0.773001i) q^{76} +(3.48373 + 5.04706i) q^{77} +(-0.543314 - 9.14786i) q^{78} +(-6.95552 + 10.0768i) q^{79} +(10.7209 - 6.18972i) q^{80} +(0.428693 - 0.903450i) q^{81} +(24.2153 - 8.08424i) q^{82} +(2.33385 + 9.46882i) q^{83} +(23.3132 + 0.939490i) q^{84} +(-9.37888 - 0.377956i) q^{85} +(5.49706 + 22.3024i) q^{86} +(-7.60056 + 2.53744i) q^{87} +(-3.14187 + 6.62135i) q^{88} +(-14.6742 + 8.47216i) q^{89} +(2.56407 - 3.71469i) q^{90} +(11.6492 - 14.8356i) q^{91} +(-6.16781 - 8.93561i) q^{92} +(-4.59433 - 2.18004i) q^{93} +(18.3161 + 11.5824i) q^{94} +(0.708711 + 0.115177i) q^{95} +(2.42257 + 4.61582i) q^{96} +(10.9636 - 8.95154i) q^{97} +(37.3373 + 35.8630i) q^{98} +1.17224i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 360 q - 15 q^{3} - 14 q^{4} + 3 q^{7} + 15 q^{9}+O(q^{10}) \) 360 * q - 15 * q^3 - 14 * q^4 + 3 * q^7 + 15 * q^9	\( 360 q - 15 q^{3} - 14 q^{4} + 3 q^{7} + 15 q^{9} + 6 q^{11} - 28 q^{12} + 6 q^{13} + 4 q^{14} - 6 q^{15} + 20 q^{16} - 6 q^{19} - 12 q^{20} - 28 q^{22} + 46 q^{23} - 6 q^{25} - 39 q^{26} + 30 q^{27} - 6 q^{28} + 43 q^{29} + 26 q^{31} - 195 q^{32} + 19 q^{33} + 65 q^{34} + 84 q^{35} - 14 q^{36} - 65 q^{38} - 2 q^{39} + 12 q^{41} - 128 q^{42} + 83 q^{43} - 39 q^{44} - 6 q^{45} - 20 q^{48} + 72 q^{49} - 52 q^{50} - 55 q^{52} + 49 q^{53} - 49 q^{55} - 2 q^{56} + 26 q^{57} + 26 q^{58} - 202 q^{59} - 182 q^{60} - 3 q^{61} - 65 q^{62} - 3 q^{63} - 14 q^{64} - 58 q^{65} + 48 q^{66} - 41 q^{67} + 139 q^{68} + 6 q^{69} - 60 q^{71} - 52 q^{73} - 269 q^{74} + 23 q^{75} - 14 q^{76} + 70 q^{77} - 65 q^{78} + 18 q^{79} + 492 q^{80} + 15 q^{81} - 65 q^{82} + 78 q^{83} - 6 q^{84} - 91 q^{85} - 169 q^{86} + 48 q^{87} - 522 q^{88} - 12 q^{89} + 373 q^{91} + 72 q^{92} - 3 q^{93} - 13 q^{94} - 110 q^{95} + 65 q^{96} - 121 q^{97} - 104 q^{98}+O(q^{100}) \) 360 * q - 15 * q^3 - 14 * q^4 + 3 * q^7 + 15 * q^9 + 6 * q^11 - 28 * q^12 + 6 * q^13 + 4 * q^14 - 6 * q^15 + 20 * q^16 - 6 * q^19 - 12 * q^20 - 28 * q^22 + 46 * q^23 - 6 * q^25 - 39 * q^26 + 30 * q^27 - 6 * q^28 + 43 * q^29 + 26 * q^31 - 195 * q^32 + 19 * q^33 + 65 * q^34 + 84 * q^35 - 14 * q^36 - 65 * q^38 - 2 * q^39 + 12 * q^41 - 128 * q^42 + 83 * q^43 - 39 * q^44 - 6 * q^45 - 20 * q^48 + 72 * q^49 - 52 * q^50 - 55 * q^52 + 49 * q^53 - 49 * q^55 - 2 * q^56 + 26 * q^57 + 26 * q^58 - 202 * q^59 - 182 * q^60 - 3 * q^61 - 65 * q^62 - 3 * q^63 - 14 * q^64 - 58 * q^65 + 48 * q^66 - 41 * q^67 + 139 * q^68 + 6 * q^69 - 60 * q^71 - 52 * q^73 - 269 * q^74 + 23 * q^75 - 14 * q^76 + 70 * q^77 - 65 * q^78 + 18 * q^79 + 492 * q^80 + 15 * q^81 - 65 * q^82 + 78 * q^83 - 6 * q^84 - 91 * q^85 - 169 * q^86 + 48 * q^87 - 522 * q^88 - 12 * q^89 + 373 * q^91 + 72 * q^92 - 3 * q^93 - 13 * q^94 - 110 * q^95 + 65 * q^96 - 121 * q^97 - 104 * q^98

Introduction

L-functions

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