LMFDB - Embedded newform 225.2.q.a.121.27

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			121.27
Character	$\chi$	$=$	225.121
Dual form			225.2.q.a.106.27

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.43022 - 0.516560i) q^{2} +(0.810393 + 1.53077i) q^{3} +(3.81206 - 1.69724i) q^{4} +(-2.22233 - 0.247525i) q^{5} +(2.76017 + 3.30150i) q^{6} +(-0.644527 - 1.11635i) q^{7} +(4.36740 - 3.17310i) q^{8} +(-1.68652 + 2.48105i) q^{9} +O(q^{10})$	\(q+(2.43022 - 0.516560i) q^{2} +(0.810393 + 1.53077i) q^{3} +(3.81206 - 1.69724i) q^{4} +(-2.22233 - 0.247525i) q^{5} +(2.76017 + 3.30150i) q^{6} +(-0.644527 - 1.11635i) q^{7} +(4.36740 - 3.17310i) q^{8} +(-1.68652 + 2.48105i) q^{9} +(-5.52861 + 0.546422i) q^{10} +(0.502326 - 0.106773i) q^{11} +(5.68735 + 4.45996i) q^{12} +(-4.87743 - 1.03673i) q^{13} +(-2.14301 - 2.38005i) q^{14} +(-1.42205 - 3.60247i) q^{15} +(3.39033 - 3.76535i) q^{16} +(5.60571 - 4.07278i) q^{17} +(-2.81702 + 6.90071i) q^{18} +(-4.21905 + 3.06532i) q^{19} +(-8.89175 + 2.82823i) q^{20} +(1.18656 - 1.89131i) q^{21} +(1.16561 - 0.518963i) q^{22} +(2.78826 + 3.09668i) q^{23} +(8.39660 + 4.11403i) q^{24} +(4.87746 + 1.10016i) q^{25} -12.3888 q^{26} +(-5.16468 - 0.571054i) q^{27} +(-4.35169 - 3.16169i) q^{28} +(0.724325 - 6.89149i) q^{29} +(-5.31680 - 8.02022i) q^{30} +(0.160665 + 1.52862i) q^{31} +(0.895838 - 1.55164i) q^{32} +(0.570526 + 0.682419i) q^{33} +(11.5193 - 12.7935i) q^{34} +(1.15602 + 2.64044i) q^{35} +(-2.21819 + 12.3204i) q^{36} +(2.27325 + 6.99635i) q^{37} +(-8.66982 + 9.62881i) q^{38} +(-2.36564 - 8.30640i) q^{39} +(-10.4912 + 5.97062i) q^{40} +(-3.98547 - 0.847138i) q^{41} +(1.90663 - 5.20923i) q^{42} +(2.08364 + 3.60897i) q^{43} +(1.73368 - 1.25959i) q^{44} +(4.36213 - 5.09625i) q^{45} +(8.37572 + 6.08531i) q^{46} +(0.841878 - 8.00993i) q^{47} +(8.51139 + 2.13841i) q^{48} +(2.66917 - 4.62314i) q^{49} +(12.4216 + 0.154142i) q^{50} +(10.7773 + 5.28050i) q^{51} +(-20.3526 + 4.32609i) q^{52} +(2.21350 + 1.60820i) q^{53} +(-12.8463 + 1.28008i) q^{54} +(-1.14276 + 0.112945i) q^{55} +(-6.35720 - 2.83041i) q^{56} +(-8.11140 - 3.97429i) q^{57} +(-1.79960 - 17.1220i) q^{58} +(2.99263 + 0.636103i) q^{59} +(-11.5352 - 11.3193i) q^{60} +(-7.17717 + 1.52555i) q^{61} +(1.18008 + 3.63190i) q^{62} +(3.85674 + 0.283651i) q^{63} +(-1.75586 + 5.40400i) q^{64} +(10.5826 + 3.51124i) q^{65} +(1.73902 + 1.36372i) q^{66} +(0.0475303 + 0.452221i) q^{67} +(14.4568 - 25.0399i) q^{68} +(-2.48072 + 6.77772i) q^{69} +(4.17334 + 5.81969i) q^{70} +(1.33759 + 0.971819i) q^{71} +(0.506910 + 16.1873i) q^{72} +(-2.72548 + 8.38816i) q^{73} +(9.13854 + 15.8284i) q^{74} +(2.26856 + 8.35785i) q^{75} +(-10.8807 + 18.8459i) q^{76} +(-0.442959 - 0.491955i) q^{77} +(-10.0398 - 18.9644i) q^{78} +(0.359882 - 3.42405i) q^{79} +(-8.46644 + 7.52863i) q^{80} +(-3.31127 - 8.36872i) q^{81} -10.1232 q^{82} +(13.4120 + 5.97142i) q^{83} +(1.31324 - 9.22366i) q^{84} +(-13.4658 + 7.66350i) q^{85} +(6.92795 + 7.69427i) q^{86} +(11.1363 - 4.47604i) q^{87} +(1.85506 - 2.06025i) q^{88} +(-2.98202 + 9.17771i) q^{89} +(7.96843 - 14.6383i) q^{90} +(1.98628 + 6.11314i) q^{91} +(15.8848 + 7.07238i) q^{92} +(-2.20977 + 1.48473i) q^{93} +(-2.09166 - 19.9008i) q^{94} +(10.1349 - 5.76782i) q^{95} +(3.10118 + 0.113887i) q^{96} +(-0.842924 + 8.01989i) q^{97} +(4.09855 - 12.6140i) q^{98} +(-0.582277 + 1.42637i) 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 $\left(\mathbb{Z}/225\mathbb{Z}\right)^\times$.

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

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 $

$2$	2.43022	−	0.516560i	1.71843	−	0.365263i	0.759851	−	0.650098i	$-0.225272\pi$
$2$	2.43022	−	0.516560i	1.71843	−	0.365263i	0.958577	+	0.284835i	$0.0919388\pi$
$3$	0.810393	+	1.53077i	0.467881	+	0.883792i
$3$	0.810393	+	1.53077i	0.467881	+	0.883792i
$4$	3.81206	−	1.69724i	1.90603	−	0.848619i
$5$	−2.22233	−	0.247525i	−0.993854	−	0.110697i
$5$	−2.22233	−	0.247525i	−0.993854	−	0.110697i
$6$	2.76017	+	3.30150i	1.12684	+	1.34783i
$7$	−0.644527	−	1.11635i	−0.243608	−	0.421942i	0.718131	−	0.695908i	$-0.244998\pi$
$7$	−0.644527	−	1.11635i	−0.243608	−	0.421942i	−0.961739	+	0.273966i	$0.911664\pi$
$8$	4.36740	−	3.17310i	1.54411	−	1.12186i
$9$	−1.68652	+	2.48105i	−0.562175	+	0.827018i
$10$	−5.52861	+	0.546422i	−1.74830	+	0.172794i
$11$	0.502326	−	0.106773i	0.151457	−	0.0321932i	−0.131559	−	0.991308i	$-0.541998\pi$
$11$	0.502326	−	0.106773i	0.151457	−	0.0321932i	0.283016	+	0.959115i	$0.408665\pi$
$12$	5.68735	+	4.45996i	1.64180	+	1.28748i
$13$	−4.87743	−	1.03673i	−1.35276	−	0.287537i	−0.526185	−	0.850370i	$-0.676378\pi$
$13$	−4.87743	−	1.03673i	−1.35276	−	0.287537i	−0.826571	+	0.562833i	$0.809712\pi$
$14$	−2.14301	−	2.38005i	−0.572743	−	0.636095i
$15$	−1.42205	−	3.60247i	−0.367173	−	0.930153i
$16$	3.39033	−	3.76535i	0.847583	−	0.941337i
$17$	5.60571	−	4.07278i	1.35958	−	0.987795i	0.361113	−	0.932522i	$-0.382397\pi$
$17$	5.60571	−	4.07278i	1.35958	−	0.987795i	0.998471	−	0.0552732i	$-0.0176030\pi$
$18$	−2.81702	+	6.90071i	−0.663978	+	1.62651i
$19$	−4.21905	+	3.06532i	−0.967917	+	0.703233i	−0.954976	−	0.296683i	$-0.904119\pi$
$19$	−4.21905	+	3.06532i	−0.967917	+	0.703233i	−0.0129412	+	0.999916i	$0.504119\pi$
$20$	−8.89175	+	2.82823i	−1.98825	+	0.632412i
$21$	1.18656	−	1.89131i	0.258929	−	0.412717i
$22$	1.16561	−	0.518963i	0.248509	−	0.110643i
$23$	2.78826	+	3.09668i	0.581393	+	0.645702i	0.960048	−	0.279836i	$-0.0902800\pi$
$23$	2.78826	+	3.09668i	0.581393	+	0.645702i	−0.378655	+	0.925538i	$0.623613\pi$
$24$	8.39660	+	4.11403i	1.71395	+	0.839773i
$25$	4.87746	+	1.10016i	0.975492	+	0.220033i
$26$	−12.3888			−2.42964
$27$	−5.16468	−	0.571054i	−0.993943	−	0.109899i
$28$	−4.35169	−	3.16169i	−0.822392	−	0.597503i
$29$	0.724325	−	6.89149i	0.134504	−	1.27972i	−0.694098	−	0.719880i	$-0.744197\pi$
$29$	0.724325	−	6.89149i	0.134504	−	1.27972i	0.828602	−	0.559838i	$-0.189137\pi$
$30$	−5.31680	−	8.02022i	−0.970710	−	1.46429i
$31$	0.160665	+	1.52862i	0.0288562	+	0.274548i	0.999430	+	0.0337463i	$0.0107438\pi$
$31$	0.160665	+	1.52862i	0.0288562	+	0.274548i	−0.970574	+	0.240802i	$0.922590\pi$
$32$	0.895838	−	1.55164i	0.158363	−	0.274293i
$33$	0.570526	+	0.682419i	0.0993159	+	0.118794i
$34$	11.5193	−	12.7935i	1.97554	−	2.19406i
$35$	1.15602	+	2.64044i	0.195403	+	0.446315i
$36$	−2.21819	+	12.3204i	−0.369699	+	2.05339i
$37$	2.27325	+	6.99635i	0.373720	+	1.15019i	0.944338	+	0.328977i	$0.106704\pi$
$37$	2.27325	+	6.99635i	0.373720	+	1.15019i	−0.570618	+	0.821216i	$0.693296\pi$
$38$	−8.66982	+	9.62881i	−1.40643	+	1.56200i
$39$	−2.36564	−	8.30640i	−0.378806	−	1.33009i
$40$	−10.4912	+	5.97062i	−1.65880	+	0.944038i
$41$	−3.98547	−	0.847138i	−0.622426	−	0.132301i	−0.114105	−	0.993469i	$-0.536400\pi$
$41$	−3.98547	−	0.847138i	−0.622426	−	0.132301i	−0.508321	+	0.861168i	$0.669733\pi$
$42$	1.90663	−	5.20923i	0.294200	−	0.803802i
$43$	2.08364	+	3.60897i	0.317752	+	0.550362i	0.980019	−	0.198906i	$-0.0637387\pi$
$43$	2.08364	+	3.60897i	0.317752	+	0.550362i	−0.662267	+	0.749268i	$0.730405\pi$
$44$	1.73368	−	1.25959i	0.261362	−	0.189890i
$45$	4.36213	−	5.09625i	0.650268	−	0.759705i
$46$	8.37572	+	6.08531i	1.23493	+	0.897231i
$47$	0.841878	−	8.00993i	0.122801	−	1.16837i	−0.743461	−	0.668779i	$-0.766817\pi$
$47$	0.841878	−	8.00993i	0.122801	−	1.16837i	0.866262	−	0.499590i	$-0.166516\pi$
$48$	8.51139	+	2.13841i	1.22851	+	0.308654i
$49$	2.66917	−	4.62314i	0.381310	−	0.660448i
$50$	12.4216	+	0.154142i	1.75668	+	0.0217990i
$51$	10.7773	+	5.28050i	1.50913	+	0.739418i
$52$	−20.3526	+	4.32609i	−2.82240	+	0.599920i
$53$	2.21350	+	1.60820i	0.304047	+	0.220903i	0.729338	−	0.684153i	$-0.239828\pi$
$53$	2.21350	+	1.60820i	0.304047	+	0.220903i	−0.425291	+	0.905057i	$0.639828\pi$
$54$	−12.8463	+	1.28008i	−1.74816	+	0.174196i
$55$	−1.14276	+	0.112945i	−0.154090	+	0.0152295i
$56$	−6.35720	−	2.83041i	−0.849517	−	0.378229i
$57$	−8.11140	−	3.97429i	−1.07438	−	0.526408i
$58$	−1.79960	−	17.1220i	−0.236299	−	2.24823i
$59$	2.99263	+	0.636103i	0.389607	+	0.0828136i	0.398550	−	0.917146i	$-0.369513\pi$
$59$	2.99263	+	0.636103i	0.389607	+	0.0828136i	−0.00894310	+	0.999960i	$0.502847\pi$
$60$	−11.5352	−	11.3193i	−1.48919	−	1.46131i
$61$	−7.17717	+	1.52555i	−0.918942	+	0.195327i	−0.643017	−	0.765852i	$-0.722318\pi$
$61$	−7.17717	+	1.52555i	−0.918942	+	0.195327i	−0.275925	+	0.961179i	$0.588984\pi$
$62$	1.18008	+	3.63190i	0.149870	+	0.461251i
$63$	3.85674	+	0.283651i	0.485904	+	0.0357367i
$64$	−1.75586	+	5.40400i	−0.219483	+	0.675499i
$65$	10.5826	+	3.51124i	1.31261	+	0.435516i
$66$	1.73902	+	1.36372i	0.214058	+	0.167862i
$67$	0.0475303	+	0.452221i	0.00580675	+	0.0552476i	0.997042	−	0.0768644i	$-0.0244908\pi$
$67$	0.0475303	+	0.452221i	0.00580675	+	0.0552476i	−0.991235	+	0.132112i	$0.957824\pi$
$68$	14.4568	−	25.0399i	1.75314	−	3.03654i
$69$	−2.48072	+	6.77772i	−0.298643	+	0.815942i
$70$	4.17334	+	5.81969i	0.498809	+	0.695587i
$71$	1.33759	+	0.971819i	0.158743	+	0.115334i	0.664321	−	0.747447i	$-0.268721\pi$
$71$	1.33759	+	0.971819i	0.158743	+	0.115334i	−0.505578	+	0.862781i	$0.668721\pi$
$72$	0.506910	+	16.1873i	0.0597400	+	1.90769i
$73$	−2.72548	+	8.38816i	−0.318993	+	0.981760i	0.655086	+	0.755554i	$0.272632\pi$
$73$	−2.72548	+	8.38816i	−0.318993	+	0.981760i	−0.974079	+	0.226206i	$0.927368\pi$
$74$	9.13854	+	15.8284i	1.06233	+	1.84002i
$75$	2.26856	+	8.35785i	0.261951	+	0.965081i
$76$	−10.8807	+	18.8459i	−1.24810	+	2.16178i
$77$	−0.442959	−	0.491955i	−0.0504798	−	0.0560635i
$78$	−10.0398	−	18.9644i	−1.13678	−	2.14730i
$79$	0.359882	−	3.42405i	0.0404899	−	0.385236i	−0.955446	−	0.295167i	$-0.904625\pi$
$79$	0.359882	−	3.42405i	0.0404899	−	0.385236i	0.995936	−	0.0900686i	$-0.0287086\pi$
$80$	−8.46644	+	7.52863i	−0.946577	+	0.841727i
$81$	−3.31127	−	8.36872i	−0.367919	−	0.929858i
$82$	−10.1232			−1.11792
$83$	13.4120	+	5.97142i	1.47216	+	0.655448i	0.976978	−	0.213341i	$-0.0684344\pi$
$83$	13.4120	+	5.97142i	1.47216	+	0.655448i	0.495183	+	0.868789i	$0.335101\pi$
$84$	1.31324	−	9.22366i	0.143286	−	1.00638i
$85$	−13.4658	+	7.66350i	−1.46057	+	0.831223i
$86$	6.92795	+	7.69427i	0.747061	+	0.829695i
$87$	11.1363	−	4.47604i	1.19394	−	0.479882i
$88$	1.85506	−	2.06025i	0.197750	−	0.219623i
$89$	−2.98202	+	9.17771i	−0.316093	+	0.972835i	0.659209	+	0.751960i	$0.270891\pi$
$89$	−2.98202	+	9.17771i	−0.316093	+	0.972835i	−0.975302	+	0.220875i	$0.929109\pi$
$90$	7.96843	−	14.6383i	0.839947	−	1.54302i
$91$	1.98628	+	6.11314i	0.208219	+	0.640831i
$92$	15.8848	+	7.07238i	1.65611	+	0.737346i
$93$	−2.20977	+	1.48473i	−0.229142	+	0.153959i
$94$	−2.09166	−	19.9008i	−0.215738	−	2.05261i
$95$	10.1349	−	5.76782i	1.03981	−	0.591766i
$96$	3.10118	+	0.113887i	0.316513	+	0.0116236i
$97$	−0.842924	+	8.01989i	−0.0855860	+	0.814296i	0.864568	+	0.502516i	$0.167592\pi$
$97$	−0.842924	+	8.01989i	−0.0855860	+	0.814296i	−0.950154	+	0.311781i	$0.899075\pi$
$98$	4.09855	−	12.6140i	0.414016	−	1.27421i
$99$	−0.582277	+	1.42637i	−0.0585210	+	0.143356i
$100$	20.4604	−	4.08432i	2.04604	−	0.408432i
$101$	−7.80298	−	13.5152i	−0.776425	−	1.34481i	−0.933990	−	0.357299i	$-0.883698\pi$
$101$	−7.80298	−	13.5152i	−0.776425	−	1.34481i	0.157565	−	0.987509i	$-0.449636\pi$
$102$	28.9190	+	7.26566i	2.86341	+	0.719407i
$103$	13.8836	−	6.18136i	1.36799	−	0.609068i	0.414376	−	0.910106i	$-0.364000\pi$
$103$	13.8836	−	6.18136i	1.36799	−	0.609068i	0.953612	+	0.301038i	$0.0973330\pi$
$104$	−24.5913	+	10.9488i	−2.41138	+	1.07361i
$105$	−3.10507	+	3.90940i	−0.303024	+	0.381518i
$106$	6.21002	+	2.76488i	0.603171	+	0.268549i
$107$	−10.6981			−1.03422			−0.517111	−	0.855919i	$-0.672992\pi$
$107$	−10.6981			−1.03422			−0.517111	+	0.855919i	$0.672992\pi$
$108$	−20.6573	+	6.58879i	−1.98775	+	0.634007i
$109$	−4.10780	−	12.6425i	−0.393456	−	1.21093i	−0.930158	−	0.367160i	$-0.880330\pi$
$109$	−4.10780	−	12.6425i	−0.393456	−	1.21093i	0.536702	−	0.843772i	$-0.319670\pi$
$110$	−2.71882	+	0.864787i	−0.259229	+	0.0824542i
$111$	−8.86758	+	9.14962i	−0.841674	+	0.868444i
$112$	−6.38861	−	1.35794i	−0.603667	−	0.128313i
$113$	9.31537	+	1.98004i	0.876316	+	0.186267i	0.624044	−	0.781390i	$-0.285489\pi$
$113$	9.31537	+	1.98004i	0.876316	+	0.186267i	0.252272	+	0.967656i	$0.418822\pi$
$114$	−21.7655	−	5.46839i	−2.03852	−	0.512162i
$115$	−5.42992	−	7.57199i	−0.506343	−	0.706092i
$116$	−8.93533	−	27.5001i	−0.829625	−	2.55332i
$117$	10.7981	−	10.3527i	0.998284	−	0.957108i
$118$	7.60135			0.699761
$119$	−8.15969	−	3.63293i	−0.747998	−	0.333030i
$120$	−17.6417	−	11.2211i	−1.61046	−	1.02434i
$121$	−9.80807	+	4.36683i	−0.891643	+	0.396985i
$122$	−16.6541	+	7.41487i	−1.50779	+	0.671311i
$123$	−1.93302	−	6.78736i	−0.174295	−	0.611996i
$124$	3.20690	+	5.55451i	0.287988	+	0.498810i
$125$	−10.5670	−	3.65222i	−0.945140	−	0.326664i
$126$	9.51927	−	1.30290i	0.848044	−	0.116072i
$127$	4.08839	−	12.5828i	0.362786	−	1.11654i	−0.588570	−	0.808447i	$-0.700309\pi$
$127$	4.08839	−	12.5828i	0.362786	−	1.11654i	0.951356	−	0.308094i	$-0.0996913\pi$
$128$	−1.85022	+	17.6036i	−0.163538	+	1.55596i
$129$	−3.83594	+	6.11426i	−0.337736	+	0.538331i
$130$	27.5319	+	3.06654i	2.41471	+	0.268953i
$131$	−1.04806	−	9.97167i	−0.0915699	−	0.871229i	−0.939828	−	0.341647i	$-0.889015\pi$
$131$	−1.04806	−	9.97167i	−0.0915699	−	0.871229i	0.848259	−	0.529582i	$-0.177651\pi$
$132$	3.33311	+	1.63310i	0.290110	+	0.142143i
$133$	6.14127	+	2.73427i	0.532516	+	0.237091i
$134$	0.349108	+	1.07445i	0.0301584	+	0.0928179i
$135$	11.3362	+	2.54746i	0.975669	+	0.219250i
$136$	11.5590	−	35.5749i	0.991176	−	3.05053i
$137$	7.07228	−	7.85456i	0.604226	−	0.671060i	−0.360974	−	0.932576i	$-0.617556\pi$
$137$	7.07228	−	7.85456i	0.604226	−	0.671060i	0.965199	+	0.261516i	$0.0842223\pi$
$138$	−2.52760	+	17.7528i	−0.215164	+	1.51122i
$139$	0.398014	+	0.442039i	0.0337591	+	0.0374933i	0.759788	−	0.650171i	$-0.225303\pi$
$139$	0.398014	+	0.442039i	0.0337591	+	0.0374933i	−0.726029	+	0.687664i	$0.758636\pi$
$140$	8.88827	+	8.10345i	0.751196	+	0.684867i
$141$	12.9436	−	5.20247i	1.09005	−	0.438127i
$142$	3.75266	+	1.67079i	0.314916	+	0.140210i
$143$	−2.56076			−0.214141
$144$	3.62415	+	14.7620i	0.302012	+	1.23016i
$145$	−3.31550	+	15.1358i	−0.275338	+	1.25696i
$146$	−2.29053	+	21.7930i	−0.189566	+	1.80360i
$147$	9.24005	+	0.339330i	0.762107	+	0.0279874i
$148$	20.5402	+	22.8122i	1.68840	+	1.87515i
$149$	−1.01642	+	1.76049i	−0.0832683	+	0.144225i	−0.904652	−	0.426151i	$-0.859869\pi$
$149$	−1.01642	+	1.76049i	−0.0832683	+	0.144225i	0.821384	+	0.570376i	$0.193203\pi$
$150$	9.83044	+	19.1396i	0.802652	+	1.56274i
$151$	−2.10363	−	3.64359i	−0.171191	−	0.296511i	0.767646	−	0.640874i	$-0.221428\pi$
$151$	−2.10363	−	3.64359i	−0.171191	−	0.296511i	−0.938836	+	0.344363i	$0.888095\pi$
$152$	−8.69971	+	26.7750i	−0.705640	+	2.17174i
$153$	0.650637	+	20.7769i	0.0526009	+	1.67971i
$154$	−1.33061	−	0.966746i	−0.107224	−	0.0779027i
$155$	0.0213235	−	3.43686i	0.00171275	−	0.276055i
$156$	−23.1159	−	27.6494i	−1.85075	−	2.21372i
$157$	0.279109	−	0.483431i	0.0222753	−	0.0385820i	−0.854673	−	0.519167i	$-0.826242\pi$
$157$	0.279109	−	0.483431i	0.0222753	−	0.0385820i	0.876948	+	0.480585i	$0.159576\pi$
$158$	−0.894133	−	8.50710i	−0.0711334	−	0.676789i
$159$	−0.667984	+	4.69163i	−0.0529745	+	0.372071i
$160$	−2.37491	+	3.22650i	−0.187753	+	0.255077i
$161$	1.65988	−	5.10858i	0.130817	−	0.402612i
$162$	−12.3701	−	18.6274i	−0.971884	−	1.46351i
$163$	−5.35439	−	16.4791i	−0.419388	−	1.29074i	−0.908267	−	0.418392i	$-0.862594\pi$
$163$	−5.35439	−	16.4791i	−0.419388	−	1.29074i	0.488879	−	0.872352i	$-0.337406\pi$
$164$	−16.6306	+	3.53495i	−1.29864	+	0.276033i
$165$	−1.09898	−	1.65778i	−0.0855554	−	0.129058i
$166$	35.6788	+	7.58376i	2.76921	+	0.588614i
$167$	0.685292	+	6.52012i	0.0530295	+	0.504542i	0.988509	+	0.151161i	$0.0483013\pi$
$167$	0.685292	+	6.52012i	0.0530295	+	0.504542i	−0.935480	+	0.353381i	$0.885032\pi$
$168$	−0.819125	−	12.0252i	−0.0631969	−	0.927762i
$169$	10.8384	+	4.82559i	0.833727	+	0.371199i
$170$	−28.7663	+	25.5799i	−2.20627	+	1.96189i
$171$	−0.489693	−	15.6374i	−0.0374477	−	1.19583i
$172$	14.0682	+	10.2212i	1.07269	+	0.779357i
$173$	1.05159	−	0.223521i	0.0799506	−	0.0169940i	−0.167763	−	0.985827i	$-0.553654\pi$
$173$	1.05159	−	0.223521i	0.0799506	−	0.0169940i	0.247713	+	0.968833i	$0.420321\pi$
$174$	24.7515	−	16.6303i	1.87641	−	1.26074i
$175$	−1.91548	−	6.15405i	−0.144797	−	0.465203i
$176$	1.30102	−	2.25343i	0.0980678	−	0.169858i
$177$	1.45148	+	5.09653i	0.109100	+	0.383079i
$178$	−2.50613	+	23.8443i	−0.187843	+	1.78720i
$179$	15.2398	+	11.0724i	1.13908	+	0.827587i	0.986990	−	0.160781i	$-0.0514012\pi$
$179$	15.2398	+	11.0724i	1.13908	+	0.827587i	0.152085	+	0.988367i	$0.451401\pi$
$180$	7.97915	−	26.8308i	0.594730	−	1.99985i
$181$	−11.6647	+	8.47488i	−0.867029	+	0.629933i	−0.929788	−	0.368096i	$-0.880010\pi$
$181$	−11.6647	+	8.47488i	−0.867029	+	0.629933i	0.0627594	+	0.998029i	$0.480010\pi$
$182$	7.98490	+	13.8303i	0.591880	+	1.02517i
$183$	−8.15161	−	9.75031i	−0.602584	−	0.720764i
$184$	22.0035	+	4.67699i	1.62212	+	0.344792i
$185$	−3.32013	−	16.1109i	−0.244101	−	1.18449i
$186$	−4.60328	+	4.74969i	−0.337529	+	0.348264i
$187$	2.38103	−	2.64440i	0.174118	−	0.193378i
$188$	−10.3855	−	31.9632i	−0.757439	−	2.33116i
$189$	2.69127	+	6.13366i	0.195761	+	0.446158i
$190$	21.6505	−	19.2523i	1.57069	−	1.39671i
$191$	−12.3893	+	13.7597i	−0.896455	+	0.995614i	0.103544	+	0.994625i	$0.466982\pi$
$191$	−12.3893	+	13.7597i	−0.896455	+	0.995614i	−1.00000		0.000989586i	$0.999685\pi$
$192$	−9.69522	+	1.69153i	−0.699693	+	0.122076i
$193$	−2.70053	+	4.67746i	−0.194388	+	0.336691i	−0.946700	−	0.322117i	$-0.895606\pi$
$193$	−2.70053	+	4.67746i	−0.194388	+	0.336691i	0.752311	+	0.658808i	$0.228939\pi$
$194$	2.09426	+	19.9255i	0.150359	+	1.43057i
$195$	3.20118	+	19.0451i	0.229241	+	1.36385i
$196$	2.32847	−	22.1539i	0.166319	−	1.58242i
$197$	−12.6037	−	9.15716i	−0.897980	−	0.652421i	0.0399665	−	0.999201i	$-0.487275\pi$
$197$	−12.6037	−	9.15716i	−0.897980	−	0.652421i	−0.937946	+	0.346780i	$0.887275\pi$
$198$	−0.678255	+	3.76719i	−0.0482015	+	0.267722i
$199$	−17.1285			−1.21421			−0.607104	−	0.794623i	$-0.707669\pi$
$199$	−17.1285			−1.21421			−0.607104	+	0.794623i	$0.707669\pi$
$200$	24.7927	−	10.6718i	1.75311	−	0.754612i
$201$	−0.653729	+	0.439235i	−0.0461105	+	0.0309812i
$202$	−25.9444	−	28.8141i	−1.82544	−	2.02736i
$203$	−8.16018	+	3.63315i	−0.572733	+	0.254997i
$204$	50.0461	+	1.83788i	3.50393	+	0.128678i
$205$	8.64733	+	2.86912i	0.603955	+	0.200388i
$206$	30.5471	−	22.1938i	2.12832	−	1.54631i
$207$	−12.3855	+	1.69520i	−0.860852	+	0.117825i
$208$	−20.4398	+	14.8504i	−1.41724	+	1.02969i
$209$	−1.79205	+	1.99027i	−0.123959	+	0.137670i
$210$	−5.52658	+	11.1047i	−0.381370	+	0.766295i
$211$	−9.68372	−	10.7549i	−0.666655	−	0.740395i	0.311047	−	0.950395i	$-0.399320\pi$
$211$	−9.68372	−	10.7549i	−0.666655	−	0.740395i	−0.977702	+	0.209999i	$0.932654\pi$
$212$	11.1675	+	2.37372i	0.766986	+	0.163028i
$213$	−0.403656	+	2.83511i	−0.0276580	+	0.194258i
$214$	−25.9987	+	5.52619i	−1.77723	+	0.377763i
$215$	−3.73721	−	8.53606i	−0.254876	−	0.582154i
$216$	−24.3682	+	13.8940i	−1.65805	+	0.945368i
$217$	1.60293	−	1.16460i	0.108814	−	0.0790579i
$218$	−16.5135	−	28.6022i	−1.11843	−	1.93718i
$219$	−15.0491	+	2.62563i	−1.01692	+	0.177423i
$220$	−4.16458	+	2.37009i	−0.280776	+	0.159792i
$221$	−31.5638	+	14.0531i	−2.12321	+	0.945316i
$222$	−16.8239	+	26.8163i	−1.12914	+	1.79979i
$223$	18.2430	−	3.87767i	1.22164	−	0.259668i	0.448431	−	0.893818i	$-0.351983\pi$
$223$	18.2430	−	3.87767i	1.22164	−	0.259668i	0.773210	+	0.634150i	$0.218650\pi$
$224$	−2.30957			−0.154314
$225$	−10.9555	+	10.2458i	−0.730369	+	0.683053i
$226$	23.6612			1.57392
$227$	−16.6360	+	3.53610i	−1.10417	+	0.234699i	−0.723714	−	0.690100i	$-0.757567\pi$
$227$	−16.6360	+	3.53610i	−1.10417	+	0.234699i	−0.380457	+	0.924799i	$0.624233\pi$
$228$	−37.6665	−	1.38326i	−2.49452	−	0.0916083i
$229$	−19.8898	+	8.85552i	−1.31436	+	0.585189i	−0.939708	−	0.341977i	$-0.888903\pi$
$229$	−19.8898	+	8.85552i	−1.31436	+	0.585189i	−0.374649	+	0.927167i	$0.622237\pi$
$230$	−17.1073	−	15.5968i	−1.12802	−	1.02842i
$231$	0.394101	−	1.07675i	0.0259299	−	0.0708447i
$232$	−18.7040	−	32.3962i	−1.22798	−	2.12692i
$233$	−7.60150	+	5.52281i	−0.497991	+	0.361811i	−0.808249	−	0.588841i	$-0.799584\pi$
$233$	−7.60150	+	5.52281i	−0.497991	+	0.361811i	0.310258	+	0.950652i	$0.399584\pi$
$234$	20.8940	−	30.7372i	1.36588	−	2.00936i
$235$	−3.85359	+	17.5923i	−0.251380	+	1.14759i
$236$	12.4877	−	2.65434i	0.812880	−	0.172783i
$237$	5.53308	−	2.22393i	0.359412	−	0.144460i
$238$	−21.7065	−	4.61386i	−1.40702	−	0.299072i
$239$	3.28802	+	3.65172i	0.212684	+	0.236210i	0.840042	−	0.542521i	$-0.182530\pi$
$239$	3.28802	+	3.65172i	0.212684	+	0.236210i	−0.627358	+	0.778731i	$0.715864\pi$
$240$	−18.3858	−	6.85904i	−1.18680	−	0.442749i
$241$	−5.34404	+	5.93515i	−0.344240	+	0.382317i	−0.890258	−	0.455456i	$-0.849476\pi$
$241$	−5.34404	+	5.93515i	−0.344240	+	0.382317i	0.546019	+	0.837773i	$0.316143\pi$
$242$	−21.5801	+	15.6788i	−1.38722	+	1.00787i
$243$	10.1272	−	11.8508i	0.649659	−	0.760226i
$244$	−24.7706	+	17.9969i	−1.58577	+	1.15213i
$245$	−7.07611	+	9.61343i	−0.452076	+	0.614180i
$246$	−8.20376	−	15.4963i	−0.523053	−	0.988007i
$247$	23.7561	−	10.5769i	1.51156	−	0.672991i
$248$	5.55215	+	6.16629i	0.352562	+	0.391560i
$249$	1.72814	+	25.3699i	0.109516	+	1.60775i
$250$	−27.5667	−	3.41722i	−1.74347	−	0.216124i
$251$	21.5099			1.35769			0.678847	−	0.734279i	$-0.262480\pi$
$251$	21.5099			1.35769			0.678847	+	0.734279i	$0.262480\pi$
$252$	15.1836	−	5.46452i	0.956474	−	0.344232i
$253$	1.73126	+	1.25783i	0.108843	+	0.0790792i
$254$	3.43595	−	32.6909i	0.215591	−	2.05121i
$255$	−22.6437	−	14.4027i	−1.41800	−	0.901929i
$256$	3.40901	+	32.4346i	0.213063	+	2.02716i
$257$	4.80713	−	8.32619i	0.299860	−	0.519373i	−0.676243	−	0.736678i	$-0.736393\pi$
$257$	4.80713	−	8.32619i	0.299860	−	0.519373i	0.976104	+	0.217305i	$0.0697266\pi$
$258$	−6.16381	+	16.8405i	−0.383742	+	1.04844i
$259$	6.34522	−	7.04708i	0.394273	−	0.437884i
$260$	46.3010	−	4.57618i	2.87147	−	0.283803i
$261$	15.8766	+	13.4198i	0.982735	+	0.830662i
$262$	−7.69800	−	23.6920i	−0.475584	−	1.46370i
$263$	6.46203	−	7.17681i	0.398466	−	0.442541i	−0.510206	−	0.860052i	$-0.670431\pi$
$263$	6.46203	−	7.17681i	0.398466	−	0.442541i	0.908672	+	0.417511i	$0.137098\pi$
$264$	4.65710	+	1.17006i	0.286625	+	0.0720120i
$265$	−4.52104	−	4.12184i	−0.277725	−	0.253203i
$266$	16.3371	+	3.47255i	1.00169	+	0.212916i
$267$	−16.4656	+	2.87276i	−1.00768	+	0.175810i
$268$	0.948715	+	1.64322i	0.0579520	+	0.100376i
$269$	14.7015	−	10.6812i	0.896364	−	0.651246i	−0.0411659	−	0.999152i	$-0.513107\pi$
$269$	14.7015	−	10.6812i	0.896364	−	0.651246i	0.937529	+	0.347906i	$0.113107\pi$
$270$	28.8655	+	0.335041i	1.75670	+	0.0203899i
$271$	−2.02436	−	1.47078i	−0.122971	−	0.0893437i	0.524600	−	0.851349i	$-0.324215\pi$
$271$	−2.02436	−	1.47078i	−0.122971	−	0.0893437i	−0.647571	+	0.762005i	$0.724215\pi$
$272$	3.66977	−	34.9155i	0.222512	−	2.11706i
$273$	−7.74815	+	7.99458i	−0.468939	+	0.483854i
$274$	13.1299	−	22.7416i	0.793204	−	1.37387i
$275$	2.56754	+	0.0318612i	0.154829	+	0.00192130i
$276$	2.04676	+	30.0474i	0.123200	+	1.80864i
$277$	−13.1783	+	2.80114i	−0.791809	+	0.168304i	−0.586025	−	0.810293i	$-0.699308\pi$
$277$	−13.1783	+	2.80114i	−0.791809	+	0.168304i	−0.205784	+	0.978597i	$0.565974\pi$
$278$	1.19560	+	0.868656i	0.0717075	+	0.0520985i
$279$	−4.06356	−	2.17944i	−0.243279	−	0.130480i
$280$	13.4272	+	7.86366i	0.802427	+	0.469944i
$281$	−0.690611	−	0.307480i	−0.0411984	−	0.0183427i	0.386034	−	0.922485i	$-0.373845\pi$
$281$	−0.690611	−	0.307480i	−0.0411984	−	0.0183427i	−0.427232	+	0.904142i	$0.640511\pi$
$282$	28.7685	−	19.3293i	1.71314	−	1.15105i
$283$	0.437736	+	4.16478i	0.0260207	+	0.247571i	0.999799	+	0.0200697i	$0.00638881\pi$
$283$	0.437736	+	4.16478i	0.0260207	+	0.247571i	−0.973778	+	0.227501i	$0.926945\pi$
$284$	6.74840	+	1.43442i	0.400444	+	0.0851169i
$285$	17.0424	+	10.8399i	1.00951	+	0.642103i
$286$	−6.22321	+	1.32278i	−0.367986	+	0.0782178i
$287$	1.62304	+	4.99519i	0.0958049	+	0.294857i
$288$	2.33884	+	4.83950i	0.137818	+	0.285170i
$289$	9.58309	−	29.4937i	0.563711	−	1.73492i
$290$	−0.238844	+	38.4961i	−0.0140254	+	2.26057i
$291$	−12.9597	+	5.20894i	−0.759712	+	0.305353i
$292$	3.84702	+	36.6020i	0.225130	+	2.14197i
$293$	−13.1006	+	22.6909i	−0.765344	+	1.32561i	0.174721	+	0.984618i	$0.444098\pi$
$293$	−13.1006	+	22.6909i	−0.765344	+	1.32561i	−0.940065	+	0.340997i	$0.889236\pi$
$294$	22.6307	−	3.94839i	1.31985	−	0.230275i
$295$	−6.49315	−	2.15438i	−0.378046	−	0.125433i
$296$	32.1283	+	23.3426i	1.86742	+	1.35676i
$297$	−2.65533	+	0.264591i	−0.154078	+	0.0153531i
$298$	−1.56073	+	4.80343i	−0.0904105	+	0.278255i
$299$	−10.3891	−	17.9945i	−0.600819	−	1.04065i
$300$	22.8332	+	28.0103i	1.31827	+	1.61718i
$301$	2.68592	−	4.65215i	0.154814	−	0.268146i
$302$	−6.99441	−	7.76808i	−0.402483	−	0.447003i
$303$	14.3651	−	22.8972i	0.825256	−	1.31541i
$304$	−2.76200	+	26.2787i	−0.158411	+	1.50718i
$305$	16.3276	−	1.61375i	0.934917	−	0.0924029i
$306$	12.3137	+	50.1565i	0.703928	+	2.86725i
$307$	13.6647			0.779887			0.389944	−	0.920839i	$-0.372495\pi$
$307$	13.6647			0.779887			0.389944	+	0.920839i	$0.372495\pi$
$308$	−2.52355	−	1.12356i	−0.143793	−	0.0640206i
$309$	20.7134	+	16.2432i	1.17834	+	0.924046i
$310$	−1.72352	−	8.36336i	−0.0978896	−	0.475007i
$311$	0.639250	+	0.709959i	0.0362486	+	0.0402581i	0.760996	−	0.648756i	$-0.224710\pi$
$311$	0.639250	+	0.709959i	0.0362486	+	0.0402581i	−0.724748	+	0.689014i	$0.758044\pi$
$312$	−36.6887	−	28.7709i	−2.07709	−	1.62883i
$313$	−8.02015	+	8.90728i	−0.453326	+	0.503469i	−0.925872	−	0.377836i	$-0.876668\pi$
$313$	−8.02015	+	8.90728i	−0.453326	+	0.503469i	0.472547	+	0.881306i	$0.343335\pi$
$314$	0.428576	−	1.31902i	0.0241859	−	0.0744367i
$315$	−8.50073	−	1.58501i	−0.478962	−	0.0893050i
$316$	−4.43953	−	13.6635i	−0.249743	−	0.768631i
$317$	2.06249	+	0.918281i	0.115841	+	0.0515758i	0.463839	−	0.885920i	$-0.346472\pi$
$317$	2.06249	+	0.918281i	0.115841	+	0.0515758i	−0.347998	+	0.937495i	$0.613138\pi$
$318$	0.800161	+	11.7468i	0.0448708	+	0.658726i
$319$	−0.371976	−	3.53911i	−0.0208266	−	0.198152i
$320$	5.23973	−	11.5748i	0.292910	−	0.647052i
$321$	−8.66964	−	16.3763i	−0.483892	−	0.914036i
$322$	1.39499	−	13.2724i	0.0777395	−	0.739642i
$323$	−11.1664	+	34.3666i	−0.621314	+	1.91221i
$324$	−26.8265	−	26.2821i	−1.49036	−	1.46011i
$325$	−22.6489	−	10.4226i	−1.25634	−	0.578141i
$326$	−21.5248	−	37.2821i	−1.19215	−	2.06486i
$327$	16.0239	−	16.5335i	0.886121	−	0.914305i
$328$	−20.0942	+	8.94651i	−1.10952	+	0.493988i
$329$	−9.48453	+	4.22278i	−0.522899	+	0.232810i
$330$	−3.52711	−	3.46108i	−0.194161	−	0.190526i
$331$	12.2444	+	5.45156i	0.673014	+	0.299645i	0.714644	−	0.699488i	$-0.246589\pi$
$331$	12.2444	+	5.45156i	0.673014	+	0.299645i	−0.0416306	+	0.999133i	$0.513255\pi$
$332$	61.2623			3.36221
$333$	−21.1922	−	6.15945i	−1.16133	−	0.337536i
$334$	5.03344	+	15.4913i	0.275418	+	0.847649i
$335$	0.00630826	−	1.01675i	0.000344657	−	0.0555508i
$336$	−3.09859	−	10.8800i	−0.169042	−	0.593552i
$337$	−11.7817	−	2.50428i	−0.641790	−	0.136417i	−0.124490	−	0.992221i	$-0.539730\pi$
$337$	−11.7817	−	2.50428i	−0.641790	−	0.136417i	−0.517300	+	0.855804i	$0.673063\pi$
$338$	28.8326	+	6.12855i	1.56828	+	0.333349i
$339$	4.51812	+	15.8643i	0.245390	+	0.861631i
$340$	−38.3257	+	52.0684i	−2.07850	+	2.82381i
$341$	0.243921	+	0.750712i	0.0132091	+	0.0406533i
$342$	−9.26774	−	37.7495i	−0.501142	−	2.04126i
$343$	−15.9048			−0.858777
$344$	20.5517	+	9.15020i	1.10807	+	0.493346i
$345$	7.19062	−	14.4483i	0.387130	−	0.777868i
$346$	2.44013	−	1.08641i	0.131182	−	0.0584060i
$347$	0.638552	−	0.284302i	0.0342793	−	0.0152621i	−0.389525	−	0.921016i	$-0.627361\pi$
$347$	0.638552	−	0.284302i	0.0342793	−	0.0152621i	0.423805	+	0.905754i	$0.360694\pi$
$348$	34.8553	−	35.9639i	1.86844	−	1.92787i
$349$	8.65614	+	14.9929i	0.463353	+	0.802551i	0.999126	−	0.0418117i	$-0.0133130\pi$
$349$	8.65614	+	14.9929i	0.463353	+	0.802551i	−0.535773	+	0.844362i	$0.679980\pi$
$350$	−7.83399	−	13.9663i	−0.418744	−	0.746528i
$351$	24.5983	+	8.13966i	1.31296	+	0.434463i
$352$	0.284330	−	0.875079i	0.0151549	−	0.0466419i
$353$	0.551935	−	5.25131i	0.0293765	−	0.279499i	−0.969966	−	0.243241i	$-0.921789\pi$
$353$	0.551935	−	5.25131i	0.0293765	−	0.279499i	0.999342	−	0.0362582i	$-0.0115439\pi$
$354$	6.16008	+	11.6359i	0.327405	+	0.618442i
$355$	−2.73202	−	2.49079i	−0.145001	−	0.132197i
$356$	4.20912	+	40.0471i	0.223083	+	2.12249i
$357$	−1.05138	−	15.4347i	−0.0556447	−	0.816893i
$358$	42.7556	+	19.0360i	2.25970	+	1.00609i
$359$	0.334961	+	1.03090i	0.0176786	+	0.0544091i	0.959507	−	0.281686i	$-0.0908937\pi$
$359$	0.334961	+	1.03090i	0.0176786	+	0.0544091i	−0.941828	+	0.336095i	$0.890894\pi$
$360$	2.88024	−	36.0988i	0.151802	−	1.90258i
$361$	2.53289	−	7.79543i	0.133310	−	0.410286i
$362$	−23.9700	+	26.6214i	−1.25983	+	1.39919i
$363$	−14.6330	−	11.4751i	−0.768034	−	0.602285i
$364$	17.9473	+	19.9324i	0.940692	+	1.04474i
$365$	8.13319	−	17.9666i	0.425710	−	0.940415i
$366$	−24.8468	−	19.4846i	−1.29877	−	1.01848i
$367$	28.5328	+	12.7036i	1.48940	+	0.663123i	0.980287	−	0.197578i	$-0.0633075\pi$
$367$	28.5328	+	12.7036i	1.48940	+	0.663123i	0.509111	+	0.860701i	$0.329974\pi$
$368$	21.1132			1.10060
$369$	8.82339	−	8.45945i	0.459327	−	0.440381i
$370$	−16.3909	−	37.4379i	−0.852121	−	1.94630i
$371$	0.368661	−	3.50757i	0.0191399	−	0.182104i
$372$	−5.90384	+	9.41036i	−0.306100	+	0.487905i
$373$	−0.165419	−	0.183716i	−0.00856507	−	0.00951248i	0.738847	−	0.673873i	$-0.235371\pi$
$373$	−0.165419	−	0.183716i	−0.00856507	−	0.00951248i	−0.747412	+	0.664361i	$0.768704\pi$
$374$	4.42044	−	7.65643i	0.228576	−	0.395905i
$375$	−2.97271	−	19.1354i	−0.153510	−	0.988147i
$376$	−21.7395	−	37.6539i	−1.12113	−	1.94185i
$377$	−10.6775	+	32.8619i	−0.549917	+	1.69247i
$378$	9.70880	+	13.5160i	0.499367	+	0.695186i
$379$	18.0726	+	13.1305i	0.928325	+	0.674467i	0.945582	−	0.325384i	$-0.105493\pi$
$379$	18.0726	+	13.1305i	0.928325	+	0.674467i	−0.0172574	+	0.999851i	$0.505493\pi$
$380$	28.8453	−	39.1885i	1.47973	−	2.01033i
$381$	22.5746	−	3.93860i	1.15653	−	0.201781i
$382$	−23.0010	+	39.8388i	−1.17683	+	2.03833i
$383$	−2.77196	−	26.3735i	−0.141641	−	1.34762i	−0.802293	−	0.596930i	$-0.796387\pi$
$383$	−2.77196	−	26.3735i	−0.141641	−	1.34762i	0.660653	−	0.750692i	$-0.270280\pi$
$384$	−28.4466	+	11.4336i	−1.45166	+	0.583469i
$385$	0.862627	+	1.20293i	0.0439635	+	0.0613069i
$386$	−4.14671	+	12.7622i	−0.211062	+	0.649581i
$387$	−12.4682	−	0.916993i	−0.633792	−	0.0466134i
$388$	10.3984	+	32.0029i	0.527898	+	1.62470i
$389$	12.7219	−	2.70413i	0.645028	−	0.137105i	0.126229	−	0.992001i	$-0.459713\pi$
$389$	12.7219	−	2.70413i	0.645028	−	0.137105i	0.518799	+	0.854896i	$0.326379\pi$
$390$	17.6175	+	44.6302i	0.892097	+	2.25994i
$391$	28.2423	+	6.00308i	1.42827	+	0.303589i
$392$	−3.01235	−	28.6606i	−0.152147	−	1.44758i
$393$	14.4150	−	9.68533i	0.727141	−	0.488560i
$394$	−35.3601	−	15.7433i	−1.78142	−	0.793138i
$395$	−1.64731	+	7.52027i	−0.0828854	+	0.378386i
$396$	0.201223	+	6.42568i	0.0101118	+	0.322903i
$397$	24.8748	+	18.0726i	1.24843	+	0.907040i	0.998130	−	0.0611280i	$-0.0194698\pi$
$397$	24.8748	+	18.0726i	1.24843	+	0.907040i	0.250303	+	0.968168i	$0.419470\pi$
$398$	−41.6261	+	8.84790i	−2.08653	+	0.443505i
$399$	0.791302	+	11.6167i	0.0396147	+	0.581564i
$400$	20.6787	−	14.6354i	1.03394	−	0.731771i
$401$	5.05931	−	8.76298i	0.252650	−	0.437602i	−0.711605	−	0.702580i	$-0.752031\pi$
$401$	5.05931	−	8.76298i	0.252650	−	0.437602i	0.964255	+	0.264978i	$0.0853646\pi$
$402$	−1.36182	+	1.40513i	−0.0679212	+	0.0700814i
$403$	0.801137	−	7.62231i	0.0399075	−	0.379694i
$404$	−52.6838	−	38.2771i	−2.62112	−	1.90435i
$405$	5.28724	+	19.4176i	0.262725	+	0.964871i
$406$	−17.9543	+	13.0446i	−0.891058	+	0.647392i
$407$	1.88893	+	3.27173i	0.0936309	+	0.162173i
$408$	63.8245	−	11.1355i	3.15978	−	0.551290i
$409$	17.3238	+	3.68229i	0.856607	+	0.182077i	0.615224	−	0.788353i	$-0.289066\pi$
$409$	17.3238	+	3.68229i	0.856607	+	0.182077i	0.241383	+	0.970430i	$0.422399\pi$
$410$	22.4970	+	2.50574i	1.11105	+	0.123750i
$411$	17.7549	+	4.46076i	0.875783	+	0.220033i
$412$	42.4337	−	47.1274i	2.09056	−	2.32180i
$413$	−1.21871	−	3.75082i	−0.0599690	−	0.184566i
$414$	−29.2239	+	10.5176i	−1.43627	+	0.516911i
$415$	−28.3278	−	16.5902i	−1.39056	−	0.814383i
$416$	−5.97802	+	6.63927i	−0.293097	+	0.325517i
$417$	−0.354113	+	0.967494i	−0.0173410	+	0.0473784i
$418$	−3.32698	+	5.76250i	−0.162728	+	0.281853i
$419$	1.40339	+	13.3523i	0.0685600	+	0.652305i	0.973800	+	0.227405i	$0.0730241\pi$
$419$	1.40339	+	13.3523i	0.0685600	+	0.652305i	−0.905240	+	0.424900i	$0.860309\pi$
$420$	−5.20154	+	20.1729i	−0.253809	+	0.984337i
$421$	3.40776	−	32.4227i	0.166084	−	1.58019i	−0.520967	−	0.853577i	$-0.674428\pi$
$421$	3.40776	−	32.4227i	0.166084	−	1.58019i	0.687051	−	0.726609i	$-0.258905\pi$
$422$	−29.0891	−	21.1345i	−1.41604	−	1.02881i
$423$	18.4532	+	15.5977i	0.897227	+	0.758386i
$424$	14.7702			0.717304
$425$	31.8224	−	13.6977i	1.54361	−	0.664434i
$426$	0.483529	+	7.09846i	0.0234271	+	0.343921i
$427$	6.32893	+	7.02899i	0.306279	+	0.340157i
$428$	−40.7817	+	18.1572i	−1.97126	+	0.877660i
$429$	−2.07522	−	3.91993i	−0.100193	−	0.189256i
$430$	−13.4916	−	18.8140i	−0.650625	−	0.907293i
$431$	7.24479	−	5.26365i	0.348969	−	0.253541i	−0.399467	−	0.916747i	$-0.630805\pi$
$431$	7.24479	−	5.26365i	0.348969	−	0.253541i	0.748436	+	0.663206i	$0.230805\pi$
$432$	−19.6602	+	17.5107i	−0.945902	+	0.842486i
$433$	22.5500	−	16.3836i	1.08369	−	0.787344i	0.105364	−	0.994434i	$-0.466399\pi$
$433$	22.5500	−	16.3836i	1.08369	−	0.787344i	0.978322	+	0.207090i	$0.0663992\pi$
$434$	3.29389	−	3.65823i	0.158112	−	0.175601i
$435$	−25.8564	+	7.19071i	−1.23972	+	0.344768i
$436$	−37.1165	−	41.2220i	−1.77756	−	1.97418i
$437$	−21.2561	−	4.51813i	−1.01682	−	0.216132i
$438$	−35.2163	+	14.1546i	−1.68270	+	0.676333i
$439$	3.07587	−	0.653797i	0.146803	−	0.0312040i	−0.133924	−	0.990992i	$-0.542758\pi$
$439$	3.07587	−	0.653797i	0.146803	−	0.0312040i	0.280727	+	0.959788i	$0.409424\pi$
$440$	−4.63250	+	4.11937i	−0.220846	+	0.196383i
$441$	6.96864	+	14.4194i	0.331840	+	0.686638i
$442$	−69.4479	+	50.4568i	−3.30330	+	2.39999i
$443$	9.86697	+	17.0901i	0.468794	+	0.811975i	0.999364	−	0.0356665i	$-0.0113554\pi$
$443$	9.86697	+	17.0901i	0.468794	+	0.811975i	−0.530570	+	0.847641i	$0.678022\pi$
$444$	−18.2747	+	49.9293i	−0.867277	+	2.36954i
$445$	8.89873	−	19.6577i	0.421840	−	0.931866i
$446$	42.3315	−	18.8472i	2.00445	−	0.892440i
$447$	−3.51861	−	0.129217i	−0.166425	−	0.00611174i
$448$	7.16447	−	1.52285i	0.338489	−	0.0719481i
$449$	−13.7726			−0.649970			−0.324985	−	0.945719i	$-0.605359\pi$
$449$	−13.7726			−0.649970			−0.324985	+	0.945719i	$0.605359\pi$
$450$	−21.3318	+	30.5588i	−1.00559	+	1.44055i
$451$	−2.09246			−0.0985300
$452$	38.8713	−	8.26235i	1.82835	−	0.388628i
$453$	3.87274	−	6.17291i	0.181957	−	0.290029i
$454$	−38.6026	+	17.1870i	−1.81171	+	0.806626i
$455$	−2.90100	−	14.0770i	−0.136001	−	0.659942i
$456$	−48.0365	+	8.38098i	−2.24952	+	0.392475i
$457$	8.03370	+	13.9148i	0.375801	+	0.650906i	0.990447	−	0.137897i	$-0.0440344\pi$
$457$	8.03370	+	13.9148i	0.375801	+	0.650906i	−0.614646	+	0.788803i	$0.710701\pi$
$458$	−43.7623	+	31.7952i	−2.04488	+	1.48569i
$459$	−31.2775	+	17.8335i	−1.45991	+	0.832395i
$460$	−33.5506	−	19.6490i	−1.56431	−	0.916140i
$461$	−10.0438	+	2.13487i	−0.467785	+	0.0994309i	−0.435773	−	0.900057i	$-0.643525\pi$
$461$	−10.0438	+	2.13487i	−0.467785	+	0.0994309i	−0.0320125	+	0.999487i	$0.510192\pi$
$462$	0.401549	−	2.82031i	0.0186817	−	0.131213i
$463$	−17.6285	−	3.74706i	−0.819268	−	0.174141i	−0.220832	−	0.975312i	$-0.570877\pi$
$463$	−17.6285	−	3.74706i	−0.819268	−	0.174141i	−0.598435	+	0.801171i	$0.704211\pi$
$464$	−23.4931	−	26.0918i	−1.09064	−	1.21128i
$465$	5.27833	−	2.75257i	0.244777	−	0.127647i
$466$	−15.6205	+	17.3483i	−0.723604	+	0.803644i
$467$	28.5731	−	20.7596i	1.32221	−	0.960639i	0.322304	−	0.946636i	$-0.395543\pi$
$467$	28.5731	−	20.7596i	1.32221	−	0.960639i	0.999902	−	0.0140027i	$-0.00445734\pi$
$468$	23.5920	−	57.7921i	1.09054	−	2.67144i
$469$	0.474203	−	0.344529i	0.0218967	−	0.0159089i
$470$	−0.277607	+	44.7438i	−0.0128050	+	2.06388i
$471$	0.966210	+	0.0354829i	0.0445206	+	0.00163497i
$472$	15.0884	−	6.71780i	0.694501	−	0.309212i
$473$	1.43201	+	1.59040i	0.0658437	+	0.0731268i
$474$	12.2978	−	8.26281i	0.564858	−	0.379524i
$475$	−23.9506	+	10.3093i	−1.09893	+	0.473025i
$476$	−37.2712			−1.70832
$477$	−7.72315	+	2.77954i	−0.353619	+	0.127266i
$478$	9.87695	+	7.17603i	0.451761	+	0.328224i
$479$	0.178641	−	1.69966i	0.00816233	−	0.0776594i	−0.989682	−	0.143278i	$-0.954236\pi$
$479$	0.178641	−	1.69966i	0.00816233	−	0.0776594i	0.997845	+	0.0656191i	$0.0209022\pi$
$480$	−6.86365	−	1.02072i	−0.313281	−	0.0465891i
$481$	−3.83430	−	36.4810i	−0.174829	−	1.66339i
$482$	−9.92134	+	17.1843i	−0.451905	+	0.782722i
$483$	9.16522	−	1.59906i	0.417032	−	0.0727599i
$484$	−29.9774	+	33.2933i	−1.36261	+	1.51333i
$485$	3.85838	−	17.6142i	0.175200	−	0.799818i
$486$	18.4897	−	34.0313i	0.838709	−	1.54369i
$487$	10.1084	+	31.1106i	0.458057	+	1.40975i	0.867509	+	0.497422i	$0.165720\pi$
$487$	10.1084	+	31.1106i	0.458057	+	1.40975i	−0.409452	+	0.912332i	$0.634280\pi$
$488$	−26.5048	+	29.4366i	−1.19982	+	1.33253i
$489$	20.8866	−	21.5509i	0.944525	−	0.974566i
$490$	−12.2306	+	27.0180i	−0.552523	+	1.22055i
$491$	−40.3627	−	8.57936i	−1.82154	−	0.387181i	−0.834943	−	0.550336i	$-0.814500\pi$
$491$	−40.3627	−	8.57936i	−1.82154	−	0.387181i	−0.986600	+	0.163155i	$0.947833\pi$
$492$	−18.8886	−	22.5930i	−0.851562	−	1.01857i
$493$	−24.0072	−	41.5817i	−1.08123	−	1.87275i
$494$	52.2689	−	37.9756i	2.35169	−	1.70860i
$495$	1.64707	−	3.02574i	0.0740304	−	0.135997i
$496$	6.30049	+	4.57758i	0.282901	+	0.205539i
$497$	0.222778	−	2.11959i	0.00999296	−	0.0950766i
$498$	17.3049	+	60.7619i	0.775449	+	2.72281i
$499$	1.73929	−	3.01255i	0.0778615	−	0.134860i	−0.824466	−	0.565912i	$-0.808524\pi$
$499$	1.73929	−	3.01255i	0.0778615	−	0.134860i	0.902327	+	0.431052i	$0.141857\pi$
$500$	−46.4807	+	4.01223i	−2.07868	+	0.179432i
$501$	−9.42546	+	6.33289i	−0.421098	+	0.282933i
$502$	52.2739	−	11.1112i	2.33310	−	0.495916i
$503$	13.8073	+	10.0316i	0.615638	+	0.447287i	0.851395	−	0.524525i	$-0.175757\pi$
$503$	13.8073	+	10.0316i	0.615638	+	0.447287i	−0.235757	+	0.971812i	$0.575757\pi$
$504$	17.7440	−	10.9990i	0.790380	−	0.489935i
$505$	13.9954	+	31.9665i	0.622788	+	1.42249i
$506$	4.85709	+	2.16251i	0.215924	+	0.0961355i
$507$	1.39653	+	20.5018i	0.0620222	+	0.910518i
$508$	−5.77078	−	54.9053i	−0.256037	−	2.43603i
$509$	−7.62861	−	1.62151i	−0.338132	−	0.0718723i	0.0357163	−	0.999362i	$-0.488629\pi$
$509$	−7.62861	−	1.62151i	−0.338132	−	0.0718723i	−0.373849	+	0.927490i	$0.621962\pi$
$510$	−62.4690	−	23.3048i	−2.76618	−	1.03196i
$511$	11.1208	−	2.36380i	0.491955	−	0.104568i
$512$	14.0995	+	43.3938i	0.623115	+	1.91775i
$513$	23.5405	−	13.4221i	1.03934	−	0.592600i
$514$	7.38142	−	22.7177i	0.325580	−	1.00203i
$515$	−32.3839	+	10.3005i	−1.42700	+	0.453893i
$516$	−4.24547	+	29.8184i	−0.186897	+	1.31268i
$517$	−0.432345	−	4.11349i	−0.0190145	−	0.180911i
$518$	11.7801	−	20.4037i	0.517586	−	0.896486i
$519$	1.19436	+	1.42860i	0.0524265	+	0.0627085i
$520$	57.3601	−	18.2447i	2.51540	−	0.800085i
$521$	−9.24944	−	6.72011i	−0.405225	−	0.294413i	0.366441	−	0.930441i	$-0.380576\pi$
$521$	−9.24944	−	6.72011i	−0.405225	−	0.294413i	−0.771666	+	0.636028i	$0.780576\pi$
$522$	45.5157	+	24.4118i	1.99217	+	1.06848i
$523$	6.03668	−	18.5790i	0.263966	−	0.812403i	−0.727964	−	0.685615i	$-0.759533\pi$
$523$	6.03668	−	18.5790i	0.263966	−	0.812403i	0.991930	−	0.126788i	$-0.0404667\pi$
$524$	−20.9196	−	36.2338i	−0.913876	−	1.58288i
$525$	7.86816	−	7.91937i	0.343395	−	0.345630i
$526$	11.9969	−	20.7793i	0.523090	−	0.906019i
$527$	7.12638	+	7.91465i	0.310430	+	0.344768i
$528$	4.50382	+	0.165397i	0.196003	+	0.00719799i
$529$	0.589142	−	5.60531i	0.0256149	−	0.243709i
$530$	−13.1163	−	7.68160i	−0.569736	−	0.333668i
$531$	−6.62535	+	6.35208i	−0.287516	+	0.275657i
$532$	28.0516			1.21619
$533$	18.5606	+	8.26372i	0.803949	+	0.357941i
$534$	−38.5311	+	15.4869i	−1.66740	+	0.670184i
$535$	23.7746	+	2.64804i	1.02786	+	0.114485i
$536$	1.64253	+	1.82421i	0.0709463	+	0.0787938i
$537$	−4.59902	+	32.3016i	−0.198463	+	1.39392i
$538$	30.2103	−	33.5520i	1.30246	−	1.44653i
$539$	0.847169	−	2.60732i	0.0364902	−	0.112305i
$540$	47.5381	−	9.52925i	2.04571	−	0.410074i
$541$	2.36879	+	7.29039i	0.101842	+	0.313439i	0.988976	−	0.148073i	$-0.0473072\pi$
$541$	2.36879	+	7.29039i	0.101842	+	0.313439i	−0.887134	+	0.461512i	$0.847307\pi$
$542$	−5.67939	−	2.52863i	−0.243951	−	0.108614i
$543$	−22.4261	−	10.9880i	−0.962396	−	0.471539i
$544$	−1.29768	−	12.3466i	−0.0556375	−	0.529355i
$545$	5.99952	+	29.1125i	0.256991	+	1.24704i
$546$	−14.7001	+	23.4310i	−0.629104	+	1.00275i
$547$	1.50602	−	14.3288i	0.0643929	−	0.612657i	−0.913973	−	0.405775i	$-0.867002\pi$
$547$	1.50602	−	14.3288i	0.0643929	−	0.612657i	0.978366	−	0.206882i	$-0.0663317\pi$
$548$	13.6289	−	41.9454i	0.582197	−	1.79182i
$549$	8.31949	−	20.3798i	0.355067	−	0.869790i
$550$	6.25616	−	1.24886i	0.266764	−	0.0532516i
$551$	18.0687	+	31.2959i	0.769751	+	1.33325i
$552$	10.6721	+	37.4726i	0.454235	+	1.59494i
$553$	−4.05440	+	1.80514i	−0.172411	+	0.0767622i
$554$	−30.5793	+	13.6148i	−1.29919	+	0.578437i
$555$	21.9714	−	18.1385i	0.932635	−	0.769936i
$556$	2.26750	+	1.00956i	0.0961633	+	0.0428147i
$557$	11.9602			0.506771			0.253386	−	0.967365i	$-0.418456\pi$
$557$	11.9602			0.506771			0.253386	+	0.967365i	$0.418456\pi$
$558$	−11.0012	−	3.19745i	−0.465716	−	0.135359i
$559$	−6.42128	−	19.7627i	−0.271591	−	0.835872i
$560$	13.8615	+	4.59913i	0.585753	+	0.194349i
$561$	5.97755	+	1.50181i	0.252372	+	0.0634064i
$562$	−1.83717	−	0.390502i	−0.0774963	−	0.0164724i
$563$	40.3973	+	8.58670i	1.70254	+	0.361886i	0.953676	−	0.300836i	$-0.0972657\pi$
$563$	40.3973	+	8.58670i	1.70254	+	0.361886i	0.748865	+	0.662722i	$0.230599\pi$
$564$	40.5121	−	41.8006i	1.70587	−	1.76012i
$565$	−20.2117	−	6.70609i	−0.850311	−	0.282127i
$566$	3.21516	+	9.89523i	0.135143	+	0.415928i
$567$	−7.20825	+	9.09041i	−0.302718	+	0.381761i
$568$	8.92549			0.374505
$569$	−13.3805	−	5.95739i	−0.560941	−	0.249747i	0.106623	−	0.994300i	$-0.465996\pi$
$569$	−13.3805	−	5.95739i	−0.560941	−	0.249747i	−0.667564	+	0.744553i	$0.732663\pi$
$570$	47.0164	+	17.5401i	1.96930	+	0.734672i
$571$	−21.3865	+	9.52187i	−0.894996	+	0.398478i	−0.802094	−	0.597197i	$-0.796281\pi$
$571$	−21.3865	+	9.52187i	−0.894996	+	0.398478i	−0.0929016	+	0.995675i	$0.529614\pi$
$572$	−9.76175	+	4.34621i	−0.408159	+	0.181724i
$573$	−31.1031	−	7.81439i	−1.29935	−	0.326451i
$574$	6.52466	+	11.3010i	0.272334	+	0.471696i
$575$	10.1928	+	18.1715i	0.425069	+	0.757803i
$576$	−10.4463	−	13.4704i	−0.435262	−	0.561265i
$577$	0.219132	−	0.674419i	0.00912259	−	0.0280764i	−0.946392	−	0.323022i	$-0.895301\pi$
$577$	0.219132	−	0.674419i	0.00912259	−	0.0280764i	0.955514	+	0.294945i	$0.0953014\pi$
$578$	8.05378	−	76.6266i	0.334993	−	3.18724i
$579$	−9.34861	−	0.343316i	−0.388515	−	0.0142677i
$580$	13.0502	+	63.3259i	0.541882	+	2.62947i
$581$	−1.97820	−	18.8213i	−0.0820694	−	0.780839i
$582$	−28.8043	+	19.3534i	−1.19398	+	0.802222i
$583$	1.28361	+	0.571500i	0.0531617	+	0.0236691i
$584$	14.7132	+	45.2827i	0.608838	+	1.87381i
$585$	−26.5594	+	20.3343i	−1.09810	+	0.840719i
$586$	−20.1161	+	61.9111i	−0.830990	+	2.55752i
$587$	−7.12521	+	7.91335i	−0.294089	+	0.326619i	−0.872023	−	0.489464i	$-0.837192\pi$
$587$	−7.12521	+	7.91335i	−0.294089	+	0.326619i	0.577934	+	0.816083i	$0.303859\pi$
$588$	35.7995	−	14.3890i	1.47635	−	0.593393i
$589$	−5.36357	−	5.95685i	−0.221002	−	0.245448i
$590$	−16.8927	−	1.88153i	−0.695460	−	0.0774612i
$591$	3.80353	−	26.7144i	0.156456	−	1.09888i
$592$	34.0507	+	15.1604i	1.39948	+	0.623087i
$593$	−47.7160			−1.95946			−0.979730	−	0.200323i	$-0.935801\pi$
$593$	−47.7160			−1.95946			−0.979730	+	0.200323i	$0.935801\pi$
$594$	−6.31636	+	2.01465i	−0.259163	+	0.0826621i
$595$	17.2343	+	10.0933i	0.706535	+	0.413784i
$596$	−0.886680	+	8.43620i	−0.0363198	+	0.345560i
$597$	−13.8808	−	26.2198i	−0.568104	−	1.07311i
$598$	−34.5432	−	38.3641i	−1.41257	−	1.56882i
$599$	1.95259	−	3.38199i	0.0797808	−	0.138184i	−0.823374	−	0.567498i	$-0.807911\pi$
$599$	1.95259	−	3.38199i	0.0797808	−	0.138184i	0.903155	+	0.429314i	$0.141245\pi$
$600$	36.4280	+	29.3037i	1.48717	+	1.19632i
$601$	−3.54162	−	6.13427i	−0.144466	−	0.250222i	0.784708	−	0.619866i	$-0.212813\pi$
$601$	−3.54162	−	6.13427i	−0.144466	−	0.250222i	−0.929174	+	0.369644i	$0.879480\pi$
$602$	4.12427	−	12.6932i	0.168093	−	0.517336i
$603$	−1.20215	−	0.644756i	−0.0489552	−	0.0262565i
$604$	−14.2032	−	10.3192i	−0.577920	−	0.419883i
$605$	22.8776	−	7.27678i	0.930108	−	0.295843i
$606$	23.0827	−	63.0657i	0.937672	−	2.56187i
$607$	2.38982	−	4.13929i	0.0969997	−	0.168008i	−0.813442	−	0.581646i	$-0.802409\pi$
$607$	2.38982	−	4.13929i	0.0969997	−	0.168008i	0.910441	+	0.413638i	$0.135742\pi$
$608$	0.976678	+	9.29247i	0.0396095	+	0.376860i
$609$	−12.1745	−	9.54710i	−0.493335	−	0.386868i
$610$	38.8462	−	12.3560i	1.57284	−	0.500278i
$611$	−12.4103	+	38.1951i	−0.502069	+	1.54521i
$612$	37.7436	+	78.0986i	1.52570	+	3.15695i
$613$	14.0778	+	43.3269i	0.568596	+	1.74996i	0.657018	+	0.753875i	$0.271818\pi$
$613$	14.0778	+	43.3269i	0.568596	+	1.74996i	−0.0884219	+	0.996083i	$0.528182\pi$
$614$	33.2083	−	7.05865i	1.34018	−	0.284864i
$615$	2.61577	+	15.5622i	0.105478	+	0.627528i
$616$	−3.49560	−	0.743013i	−0.140842	−	0.0299368i
$617$	2.02983	+	19.3126i	0.0817179	+	0.777494i	0.956255	+	0.292535i	$0.0944989\pi$
$617$	2.02983	+	19.3126i	0.0817179	+	0.777494i	−0.874537	+	0.484959i	$0.838834\pi$
$618$	58.7288	+	28.7750i	2.36242	+	1.15750i
$619$	24.9267	+	11.0981i	1.00189	+	0.446070i	0.841077	−	0.540915i	$-0.181922\pi$
$619$	24.9267	+	11.0981i	1.00189	+	0.446070i	0.160812	+	0.986985i	$0.448589\pi$
$620$	−5.75189	−	13.1377i	−0.231001	−	0.527623i
$621$	−12.6321	−	17.5856i	−0.506909	−	0.705686i
$622$	1.92026	+	1.39515i	0.0769953	+	0.0559404i
$623$	12.1675	−	2.58629i	0.487482	−	0.103618i
$624$	−39.2968	−	19.2540i	−1.57313	−	0.770776i
$625$	22.5793	+	10.7320i	0.903171	+	0.429281i
$626$	−14.8896	+	25.7896i	−0.595109	+	1.03076i
$627$	−4.49891	−	1.13031i	−0.179669	−	0.0451404i
$628$	0.243482	−	2.31658i	0.00971601	−	0.0924416i
$629$	41.2378	+	29.9610i	1.64426	+	1.19462i
$630$	−21.4774	+	0.539215i	−0.855681	+	0.0214828i
$631$	12.6772	−	9.21053i	0.504672	−	0.366665i	−0.306127	−	0.951991i	$-0.599033\pi$
$631$	12.6772	−	9.21053i	0.504672	−	0.366665i	0.810799	+	0.585325i	$0.199033\pi$
$632$	−9.29310	−	16.0961i	−0.369660	−	0.640269i
$633$	8.61562	−	23.5392i	0.342440	−	0.935601i
$634$	5.48667	+	1.16623i	0.217903	+	0.0463168i
$635$	−12.2003	+	26.9511i	−0.484154	+	1.06952i
$636$	5.41643	+	19.0185i	0.214775	+	0.754133i
$637$	−17.8116	+	19.7818i	−0.705723	+	0.783785i
$638$	−2.73215	−	8.40869i	−0.108167	−	0.332903i
$639$	−4.66702	+	1.67965i	−0.184625	+	0.0664458i
$640$	8.46913	−	38.6631i	0.334772	−	1.52829i
$641$	23.6349	−	26.2493i	0.933524	−	1.03678i	−0.0657170	−	0.997838i	$-0.520933\pi$
$641$	23.6349	−	26.2493i	0.933524	−	1.03678i	0.999241	−	0.0389455i	$-0.0123999\pi$
$642$	−29.5285	−	35.3197i	−1.16540	−	1.39396i
$643$	5.45444	−	9.44736i	0.215102	−	0.372567i	−0.738202	−	0.674580i	$-0.764325\pi$
$643$	5.45444	−	9.44736i	0.215102	−	0.372567i	0.953304	+	0.302012i	$0.0976583\pi$
$644$	−2.34292	−	22.2914i	−0.0923240	−	0.878404i
$645$	10.0381	−	12.6384i	0.395251	−	0.497636i
$646$	−9.38440	+	89.2866i	−0.369224	+	3.51293i
$647$	−28.4306	−	20.6560i	−1.11772	−	0.812072i	−0.133860	−	0.991000i	$-0.542737\pi$
$647$	−28.4306	−	20.6560i	−1.11772	−	0.812072i	−0.983862	+	0.178928i	$0.942737\pi$
$648$	−41.0164	−	26.0426i	−1.61128	−	1.02305i
$649$	1.57119			0.0616748
$650$	−60.4258	−	13.6297i	−2.37010	−	0.534600i
$651$	3.08173	+	1.50994i	0.120783	+	0.0591791i
$652$	−48.3802	−	53.7317i	−1.89472	−	2.10429i
$653$	−11.5270	+	5.13214i	−0.451086	+	0.200836i	−0.619689	−	0.784848i	$-0.712741\pi$
$653$	−11.5270	+	5.13214i	−0.451086	+	0.200836i	0.168603	+	0.985684i	$0.446074\pi$
$654$	30.4010	−	48.4574i	1.18877	−	1.89483i
$655$	−0.139100	+	22.4197i	−0.00543509	+	0.876011i
$656$	−16.7018	+	12.1346i	−0.652097	+	0.473776i
$657$	−16.2149	−	20.9089i	−0.632604	−	0.815734i
$658$	−20.8682	+	15.1616i	−0.813527	+	0.591062i
$659$	−11.9432	+	13.2643i	−0.465242	+	0.516703i	−0.929413	−	0.369043i	$-0.879686\pi$
$659$	−11.9432	+	13.2643i	−0.465242	+	0.516703i	0.464171	+	0.885746i	$0.346352\pi$
$660$	−7.00302	−	4.45431i	−0.272592	−	0.173384i
$661$	24.5369	+	27.2510i	0.954375	+	1.05994i	0.998144	+	0.0608991i	$0.0193968\pi$
$661$	24.5369	+	27.2510i	0.954375	+	1.05994i	−0.0437689	+	0.999042i	$0.513937\pi$
$662$	32.5727	+	6.92354i	1.26597	+	0.269091i
$663$	−47.0913	−	36.9285i	−1.82887	−	1.43418i
$664$	77.5235	−	16.4781i	3.00850	−	0.639476i
$665$	−12.9711	−	7.59656i	−0.502998	−	0.294582i
$666$	−54.6835	−	4.02180i	−2.11894	−	0.155842i
$667$	23.3603	−	16.9723i	0.904516	−	0.657169i
$668$	13.6786	+	23.6920i	0.529240	+	0.916670i
$669$	20.7198	+	24.7834i	0.801075	+	0.958182i
$670$	−0.509880	−	2.47418i	−0.0196984	−	0.0955859i
$671$	−3.44239	+	1.53265i	−0.132892	+	0.0591674i
$672$	−1.87166	−	3.53542i	−0.0722008	−	0.136382i
$673$	−20.3716	+	4.33013i	−0.785269	+	0.166914i	−0.583061	−	0.812428i	$-0.698145\pi$
$673$	−20.3716	+	4.33013i	−0.785269	+	0.166914i	−0.202208	+	0.979343i	$0.564812\pi$
$674$	−29.9258			−1.15270
$675$	−24.5623	−	8.46729i	−0.945402	−	0.325906i
$676$	49.5070			1.90411
$677$	−6.76634	+	1.43823i	−0.260052	+	0.0552757i	−0.336092	−	0.941829i	$-0.609105\pi$
$677$	−6.76634	+	1.43823i	−0.260052	+	0.0552757i	0.0760407	+	0.997105i	$0.475772\pi$
$678$	19.1749	+	36.2199i	0.736408	+	1.39102i
$679$	9.49631	−	4.22803i	0.364435	−	0.162257i
$680$	−34.4936	+	76.1980i	−1.32277	+	2.92206i
$681$	−18.8947	−	22.6003i	−0.724046	−	0.866046i
$682$	0.980570	+	1.69840i	0.0375480	+	0.0650350i
$683$	25.6445	−	18.6318i	0.981258	−	0.712926i	0.0232689	−	0.999729i	$-0.492593\pi$
$683$	25.6445	−	18.6318i	0.981258	−	0.712926i	0.957989	+	0.286803i	$0.0925926\pi$
$684$	−28.4072	−	58.7797i	−1.08618	−	2.24750i
$685$	−17.6611	+	15.7048i	−0.674796	+	0.600050i
$686$	−38.6522	+	8.21577i	−1.47575	+	0.313680i
$687$	−29.6744	−	23.2703i	−1.13215	−	0.887819i
$688$	20.6532	+	4.38998i	0.787398	+	0.167367i
$689$	−9.12892	−	10.1387i	−0.347784	−	0.386253i
$690$	10.0114	−	38.8269i	0.381128	−	1.47811i
$691$	−2.74243	+	3.04578i	−0.104327	+	0.115867i	−0.793047	−	0.609161i	$-0.791506\pi$
$691$	−2.74243	+	3.04578i	−0.104327	+	0.115867i	0.688720	+	0.725028i	$0.258173\pi$
$692$	3.62934	−	2.63687i	0.137967	−	0.100239i
$693$	1.96763	−	0.269310i	0.0747440	−	0.0102302i
$694$	1.40496	−	1.02077i	0.0533317	−	0.0387478i
$695$	−0.775101	−	1.08087i	−0.0294012	−	0.0409999i
$696$	34.4337	−	54.8852i	1.30520	−	2.08042i
$697$	−25.7916	+	11.4832i	−0.976926	+	0.434956i
$698$	28.7811	+	31.9646i	1.08938	+	1.20988i
$699$	−14.6144	−	7.16051i	−0.552766	−	0.270835i
$700$	−17.7468	−	20.2086i	−0.670767	−	0.763813i
$701$	1.75231			0.0661838			0.0330919	−	0.999452i	$-0.489465\pi$
$701$	1.75231			0.0661838			0.0330919	+	0.999452i	$0.489465\pi$
$702$	63.9841	+	7.07467i	2.41492	+	0.267016i
$703$	−31.0370	−	22.5497i	−1.17058	−	0.850479i
$704$	−0.305017	+	2.90205i	−0.0114958	+	0.109375i
$705$	−30.0527	+	8.35771i	−1.13185	+	0.314770i
$706$	−1.37129	−	13.0470i	−0.0516092	−	0.491029i
$707$	−10.0585	+	17.4218i	−0.378287	+	0.655213i
$708$	14.1831	+	16.9648i	0.533035	+	0.637575i
$709$	−17.0356	+	18.9200i	−0.639787	+	0.710556i	−0.972612	−	0.232433i	$-0.925331\pi$
$709$	−17.0356	+	18.9200i	−0.639787	+	0.710556i	0.332825	+	0.942989i	$0.391998\pi$
$710$	−7.92606	−	4.64192i	−0.297460	−	0.174208i
$711$	7.88830	+	6.66763i	0.295835	+	0.250056i
$712$	16.0981	+	49.5449i	0.603303	+	1.85677i
$713$	−4.28567	+	4.75972i	−0.160500	+	0.178253i
$714$	−10.5280	−	36.9667i	−0.394002	−	1.38345i
$715$	5.69083	+	0.633852i	0.212825	+	0.0237047i
$716$	76.8874	+	16.3429i	2.87342	+	0.610763i
$717$	−2.92535	+	7.99254i	−0.109249	+	0.298487i
$718$	1.34655	+	2.33230i	0.0502530	+	0.0870407i
$719$	9.49736	−	6.90024i	0.354192	−	0.257335i	−0.396434	−	0.918063i	$-0.629752\pi$
$719$	9.49736	−	6.90024i	0.354192	−	0.257335i	0.750625	+	0.660728i	$0.229752\pi$
$720$	−4.40008	−	33.7029i	−0.163981	−	1.25603i
$721$	−15.8489	−	11.5149i	−0.590244	−	0.428838i
$722$	2.12868	−	20.2530i	0.0792213	−	0.753740i
$723$	−13.4161	−	3.37069i	−0.498952	−	0.125357i
$724$	−30.0825	+	52.1045i	−1.11801	+	1.93645i
$725$	11.1146	−	32.8161i	0.412787	−	1.21876i
$726$	−41.4891	−	20.3281i	−1.53980	−	0.754448i
$727$	−19.9336	+	4.23701i	−0.739295	+	0.157142i	−0.562141	−	0.827041i	$-0.690022\pi$
$727$	−19.9336	+	4.23701i	−0.739295	+	0.157142i	−0.177154	+	0.984183i	$0.556689\pi$
$728$	28.0725	+	20.3958i	1.04043	+	0.755920i
$729$	26.3478	+	5.89862i	0.975844	+	0.218468i
$730$	10.4846	−	47.8641i	0.388054	−	1.77153i
$731$	26.3788	+	11.7446i	0.975656	+	0.434390i
$732$	−47.6230	−	23.3335i	−1.76020	−	0.862432i
$733$	4.53737	+	43.1702i	0.167592	+	1.59453i	0.678308	+	0.734778i	$0.262714\pi$
$733$	4.53737	+	43.1702i	0.167592	+	1.59453i	−0.510716	+	0.859749i	$0.670620\pi$
$734$	75.9032	+	16.1337i	2.80164	+	0.595506i
$735$	−20.4504	−	3.04125i	−0.754325	−	0.112178i
$736$	7.30275	−	1.55225i	0.269183	−	0.0572166i
$737$	0.0721606	+	0.222087i	0.00265807	+	0.00818069i
$738$	17.0730	−	25.1162i	0.628466	−	0.924539i
$739$	−2.42742	+	7.47084i	−0.0892942	+	0.274819i	−0.985725	−	0.168365i	$-0.946151\pi$
$739$	−2.42742	+	7.47084i	−0.0892942	+	0.274819i	0.896431	+	0.443184i	$0.146151\pi$
$740$	−40.0005	−	55.7805i	−1.47045	−	2.05053i
$741$	35.4425	+	27.7937i	1.30201	+	1.02103i
$742$	−0.915943	−	8.71462i	−0.0336253	−	0.319924i
$743$	−16.6131	+	28.7747i	−0.609475	+	1.05564i	0.381852	+	0.924223i	$0.375286\pi$
$743$	−16.6131	+	28.7747i	−0.609475	+	1.05564i	−0.991327	+	0.131418i	$0.958047\pi$
$744$	−4.93976	+	13.4962i	−0.181100	+	0.494795i
$745$	2.69458	−	3.66079i	0.0987218	−	0.134121i
$746$	−0.496906	−	0.361023i	−0.0181930	−	0.0132180i
$747$	−37.4351	+	23.2050i	−1.36968	+	0.849027i
$748$	4.58845	−	14.1218i	0.167770	−	0.516344i
$749$	6.89519	+	11.9428i	0.251945	+	0.436381i
$750$	−17.1089	−	44.9677i	−0.624729	−	1.64199i
$751$	−16.9328	+	29.3284i	−0.617886	+	1.07021i	0.371985	+	0.928239i	$0.378677\pi$
$751$	−16.9328	+	29.3284i	−0.617886	+	1.07021i	−0.989871	+	0.141971i	$0.954656\pi$
$752$	−27.3059	−	30.3263i	−0.995745	−	1.10589i
$753$	17.4315	+	32.9268i	0.635239	+	1.19992i
$754$	−8.97350	+	85.3772i	−0.326796	+	3.10925i
$755$	3.77306	+	8.61794i	0.137316	+	0.313639i
$756$	20.6696	+	18.8142i	0.751745	+	0.684264i
$757$	−9.25569			−0.336404			−0.168202	−	0.985753i	$-0.553796\pi$
$757$	−9.25569			−0.336404			−0.168202	+	0.985753i	$0.553796\pi$
$758$	50.7030	+	22.5744i	1.84162	+	0.819940i
$759$	−0.522454	+	3.66950i	−0.0189639	+	0.133194i
$760$	25.9611	−	57.3493i	0.941707	−	2.08028i
$761$	10.3134	+	11.4542i	0.373861	+	0.415214i	0.900487	−	0.434882i	$-0.143210\pi$
$761$	10.3134	+	11.4542i	0.373861	+	0.415214i	−0.526627	+	0.850097i	$0.676543\pi$
$762$	52.8267	−	21.2328i	1.91371	−	0.769183i
$763$	−11.4659	+	12.7342i	−0.415094	+	0.461008i
$764$	−23.8752	+	73.4802i	−0.863773	+	2.65842i
$765$	3.69689	−	46.3341i	0.133661	−	1.67521i
$766$	−20.3600	−	62.6615i	−0.735636	−	2.26405i
$767$	−13.9369	−	6.20510i	−0.503232	−	0.224053i
$768$	−46.8873	+	31.5032i	−1.69190	+	1.13677i
$769$	−1.77895	−	16.9256i	−0.0641505	−	0.610351i	−0.978617	−	0.205690i	$-0.934056\pi$
$769$	−1.77895	−	16.9256i	−0.0641505	−	0.610351i	0.914467	−	0.404661i	$-0.132611\pi$
$770$	2.71776	+	2.47779i	0.0979413	+	0.0892932i
$771$	16.6412	+	0.611127i	0.599317	+	0.0220092i
$772$	−2.35583	+	22.4142i	−0.0847880	+	0.806704i
$773$	8.95270	−	27.5536i	0.322006	−	0.991033i	−0.650768	−	0.759277i	$-0.725553\pi$
$773$	8.95270	−	27.5536i	0.322006	−	0.991033i	0.972774	−	0.231756i	$-0.0744471\pi$
$774$	−30.7741	+	4.21205i	−1.10615	+	0.151399i
$775$	−0.898098	+	7.63255i	−0.0322606	+	0.274169i
$776$	21.7665	+	37.7007i	0.781372	+	1.35338i
$777$	15.9296	+	4.00218i	0.571471	+	0.143577i
$778$	29.5203	−	13.1433i	1.05835	−	0.471210i
$779$	19.4117	−	8.64263i	0.695495	−	0.309654i
$780$	44.5271	+	67.1678i	1.59433	+	2.40499i
$781$	0.775672	+	0.345352i	0.0277557	+	0.0123576i
$782$	71.7360			2.56527
$783$	−7.67632	+	35.1787i	−0.274329	+	1.25718i
$784$	−8.35834	−	25.7243i	−0.298512	−	0.918726i
$785$	−0.739932	+	1.00525i	−0.0264093	+	0.0358791i
$786$	30.0286	−	30.9837i	1.07109	−	1.10515i
$787$	−7.31133	−	1.55407i	−0.260621	−	0.0553967i	0.0757480	−	0.997127i	$-0.475866\pi$
$787$	−7.31133	−	1.55407i	−0.260621	−	0.0553967i	−0.336369	+	0.941730i	$0.609199\pi$
$788$	−63.5881	−	13.5161i	−2.26523	−	0.481490i
$789$	16.2228	+	4.07585i	0.577548	+	0.145104i
$790$	−0.118670	+	19.1269i	−0.00422209	+	0.680504i
$791$	−3.79358	−	11.6754i	−0.134884	−	0.415130i
$792$	1.98299	+	8.07716i	0.0704626	+	0.287009i
$793$	36.5877			1.29927
$794$	69.7870	+	31.0712i	2.47665	+	1.10268i
$795$	2.64578	−	10.2610i	0.0938360	−	0.363920i
$796$	−65.2949	+	29.0711i	−2.31431	+	1.03040i
$797$	14.5045	−	6.45782i	0.513776	−	0.228748i	−0.133437	−	0.991057i	$-0.542601\pi$
$797$	14.5045	−	6.45782i	0.513776	−	0.228748i	0.647212	+	0.762310i	$0.275935\pi$
$798$	7.92377	+	27.8225i	0.280499	+	0.984905i
$799$	−27.9034	−	48.3301i	−0.987152	−	1.70980i
$800$	6.07647	−	6.58249i	0.214836	−	0.232726i
$801$	−17.7411	−	22.8770i	−0.626853	−	0.808318i
$802$	7.76865	−	23.9094i	0.274320	−	0.844271i
$803$	−0.473453	+	4.50460i	−0.0167078	+	0.158964i
$804$	−1.74657	+	2.78392i	−0.0615966	+	0.0981814i
$805$	−4.95329	+	10.9421i	−0.174580	+	0.385657i
$806$	−1.99044	−	18.9378i	−0.0701102	−	0.667054i
$807$	28.2645	+	13.8486i	0.994957	+	0.487493i
$808$	−76.9636	−	34.2664i	−2.70757	−	1.20549i
$809$	−0.927281	−	2.85388i	−0.0326015	−	0.100337i	0.933432	−	0.358755i	$-0.116799\pi$
$809$	−0.927281	−	2.85388i	−0.0326015	−	0.100337i	−0.966033	+	0.258418i	$0.916799\pi$
$810$	22.8796	+	44.4580i	0.803906	+	1.56210i
$811$	−11.0539	+	34.0205i	−0.388156	+	1.19462i	0.546009	+	0.837779i	$0.316146\pi$
$811$	−11.0539	+	34.0205i	−0.388156	+	1.19462i	−0.934165	+	0.356841i	$0.883854\pi$
$812$	−24.9408	+	27.6995i	−0.875250	+	0.972063i
$813$	0.610906	−	4.29074i	0.0214254	−	0.150483i
$814$	6.28057	+	6.97528i	0.220134	+	0.244483i
$815$	7.82020	+	37.9473i	0.273930	+	1.32924i
$816$	56.4217	−	22.6777i	1.97515	−	0.793879i
$817$	−19.8536	−	8.83941i	−0.694591	−	0.309252i
$818$	44.0028			1.53852
$819$	−18.5169	−	5.38189i	−0.647034	−	0.188059i
$820$	37.8337	−	3.73931i	1.32121	−	0.130582i
$821$	4.85653	−	46.2068i	0.169494	−	1.61263i	−0.497430	−	0.867504i	$-0.665723\pi$
$821$	4.85653	−	46.2068i	0.169494	−	1.61263i	0.666924	−	0.745126i	$-0.267611\pi$
$822$	45.4525	+	1.66919i	1.58534	+	0.0582197i
$823$	27.4590	+	30.4963i	0.957159	+	1.06303i	0.997959	+	0.0638657i	$0.0203429\pi$
$823$	27.4590	+	30.4963i	0.957159	+	1.06303i	−0.0407992	+	0.999167i	$0.512990\pi$
$824$	41.0210	−	71.0504i	1.42903	−	2.47516i
$825$	2.03195	+	3.95614i	0.0707434	+	0.137735i
$826$	−4.89927	−	8.48578i	−0.170467	−	0.295258i
$827$	12.0368	−	37.0454i	0.418560	−	1.28820i	−0.490468	−	0.871459i	$-0.663174\pi$
$827$	12.0368	−	37.0454i	0.418560	−	1.28820i	0.909028	−	0.416736i	$-0.136826\pi$
$828$	−44.3371	+	27.4834i	−1.54082	+	0.955113i
$829$	−4.44553	−	3.22987i	−0.154400	−	0.112178i	0.507903	−	0.861414i	$-0.330421\pi$
$829$	−4.44553	−	3.22987i	−0.154400	−	0.112178i	−0.662303	+	0.749236i	$0.730421\pi$
$830$	−77.4127	−	25.6850i	−2.68704	−	0.891539i
$831$	−14.9675	−	17.9030i	−0.519218	−	0.621048i
$832$	14.1666	−	24.5373i	0.491138	−	0.850677i
$833$	−3.86646	−	36.7869i	−0.133965	−	1.27459i
$834$	−0.360806	+	2.53415i	−0.0124937	+	0.0877503i
$835$	0.0909525	−	14.6595i	0.00314754	−	0.507311i
$836$	−3.45343	+	10.6286i	−0.119439	+	0.367596i
$837$	0.0431451	−	7.98658i	0.00149131	−	0.276057i
$838$	10.3078	+	31.7242i	0.356078	+	1.09590i
$839$	−15.3782	+	3.26874i	−0.530916	+	0.112850i	−0.465567	−	0.885013i	$-0.654149\pi$
$839$	−15.3782	+	3.26874i	−0.530916	+	0.112850i	−0.0653491	+	0.997862i	$0.520816\pi$
$840$	−1.15617	+	26.9266i	−0.0398918	+	0.929056i
$841$	−18.6017	−	3.95392i	−0.641439	−	0.136342i
$842$	−8.46664	−	80.5547i	−0.291780	−	2.77610i
$843$	−0.0889851	−	1.30635i	−0.00306481	−	0.0449930i
$844$	−55.1685	−	24.5626i	−1.89898	−	0.845479i
$845$	−22.8921	−	13.4068i	−0.787512	−	0.461209i
$846$	52.9026	+	28.3737i	1.81883	+	0.975507i
$847$	11.1965	+	8.13473i	0.384716	+	0.279512i
$848$	13.5599	−	2.88225i	0.465650	−	0.0989769i
$849$	−6.02059	+	4.04519i	−0.206626	+	0.138830i
$850$	70.2598	−	49.7265i	2.40989	−	1.70561i
$851$	−15.3270	+	26.5472i	−0.525403	+	0.910025i
$852$	3.27309	+	11.4927i	0.112134	+	0.393733i
$853$	−0.145516	+	1.38449i	−0.00498237	+	0.0474041i	−0.996731	−	0.0807967i	$-0.974254\pi$
$853$	−0.145516	+	1.38449i	−0.00498237	+	0.0474041i	0.991748	+	0.128201i	$0.0409202\pi$
$854$	19.0116	+	13.8127i	0.650564	+	0.472662i
$855$	−2.78241	+	34.8727i	−0.0951563	+	1.19262i
$856$	−46.7227	+	33.9460i	−1.59695	+	1.16025i
$857$	−12.7340	−	22.0559i	−0.434985	−	0.753415i	0.562310	−	0.826927i	$-0.309913\pi$
$857$	−12.7340	−	22.0559i	−0.434985	−	0.753415i	−0.997294	+	0.0735113i	$0.976580\pi$
$858$	−7.06813	−	8.45434i	−0.241302	−	0.288626i
$859$	6.26793	+	1.33229i	0.213859	+	0.0454572i	0.313595	−	0.949557i	$-0.398467\pi$
$859$	6.26793	+	1.33229i	0.213859	+	0.0454572i	−0.0997361	+	0.995014i	$0.531800\pi$
$860$	−28.7342	−	26.1970i	−0.979828	−	0.893311i
$861$	−6.33120	+	6.53257i	−0.215767	+	0.222629i
$862$	14.8875	−	16.5342i	0.507069	−	0.563157i
$863$	−3.68829	−	11.3514i	−0.125551	−	0.386406i	0.868450	−	0.495777i	$-0.165117\pi$
$863$	−3.68829	−	11.3514i	−0.125551	−	0.386406i	−0.994001	+	0.109370i	$0.965117\pi$
$864$	−5.51279	+	7.50214i	−0.187549	+	0.255228i
$865$	−2.39229	+	0.236443i	−0.0813404	+	0.00803931i
$866$	46.3386	−	51.4642i	1.57465	−	1.74882i
$867$	52.9142	−	9.23199i	1.79706	−	0.313535i
$868$	4.13386	−	7.16006i	0.140312	−	0.243028i
$869$	−0.184817	−	1.75841i	−0.00626948	−	0.0596501i
$870$	−59.1224	+	30.8314i	−2.00444	+	1.04528i
$871$	0.237005	−	2.25495i	0.00803061	−	0.0764062i
$872$	−58.0563	−	42.1804i	−1.96603	−	1.42841i
$873$	−18.4762	−	15.6171i	−0.625323	−	0.528558i
$874$	−53.9910			−1.82627
$875$	2.73354	+	14.1504i	0.0924106	+	0.478372i
$876$	−52.9116	+	35.5509i	−1.78772	+	1.20115i
$877$	−0.560532	−	0.622534i	−0.0189278	−	0.0210215i	0.733607	−	0.679574i	$-0.237836\pi$
$877$	−0.560532	−	0.622534i	−0.0189278	−	0.0210215i	−0.752534	+	0.658553i	$0.771169\pi$
$878$	7.13733	−	3.17775i	0.240873	−	0.107244i
$879$	−45.3512	−	1.66547i	−1.52966	−	0.0561748i
$880$	−3.44906	+	4.68581i	−0.116268	+	0.157959i
$881$	−8.77572	+	6.37593i	−0.295661	+	0.214811i	−0.725720	−	0.687991i	$-0.758493\pi$
$881$	−8.77572	+	6.37593i	−0.295661	+	0.214811i	0.430058	+	0.902801i	$0.358493\pi$
$882$	24.3838	+	31.4426i	0.821046	+	1.05873i
$883$	−29.2715	+	21.2670i	−0.985064	+	0.715691i	−0.958835	−	0.283965i	$-0.908350\pi$
$883$	−29.2715	+	21.2670i	−0.985064	+	0.715691i	−0.0262292	+	0.999656i	$0.508350\pi$
$884$	−96.4717	+	107.143i	−3.24469	+	3.60360i
$885$	−1.96414	−	11.6854i	−0.0660238	−	0.392801i
$886$	32.8070	+	36.4358i	1.10217	+	1.22409i
$887$	44.3753	+	9.43226i	1.48998	+	0.316704i	0.879717	−	0.475497i	$-0.157732\pi$
$887$	44.3753	+	9.43226i	1.48998	+	0.316704i	0.610259	+	0.792202i	$0.291065\pi$
$888$	−9.69560	+	68.0978i	−0.325363	+	2.28521i
$889$	−16.6819	+	3.54585i	−0.559493	+	0.118924i
$890$	11.4715	−	52.3694i	0.384526	−	1.75543i
$891$	−2.55689	−	3.85027i	−0.0856589	−	0.128989i
$892$	62.9620	−	45.7446i	2.10812	−	1.53164i
$893$	21.0011	+	36.3750i	0.702775	+	1.21724i
$894$	−8.61775	+	1.50355i	−0.288221	+	0.0502861i
$895$	−31.1271	−	28.3786i	−1.04046	−	0.948592i
$896$	20.8444	−	9.28052i	0.696362	−	0.310041i
$897$	19.1262	−	30.4860i	0.638605	−	1.01790i
$898$	−33.4705	+	7.11438i	−1.11693	+	0.237410i
$899$	10.6509			0.355226
$900$	−24.3736	+	57.6517i	−0.812452	+	1.92172i
$901$	18.9581			0.631585
$902$	−5.08514	+	1.08088i	−0.169317	+	0.0359893i
$903$	9.29804	+	0.341459i	0.309419	+	0.0113631i
$904$	46.9668	−	20.9110i	1.56209	−	0.695488i
$905$	28.0205	−	15.9466i	0.931432	−	0.530084i
$906$	6.22294	−	17.0021i	0.206743	−	0.564856i
$907$	−8.10153	−	14.0323i	−0.269007	−	0.465933i	0.699599	−	0.714536i	$-0.253362\pi$
$907$	−8.10153	−	14.0323i	−0.269007	−	0.465933i	−0.968606	+	0.248602i	$0.920029\pi$
$908$	−57.4159	+	41.7151i	−1.90541	+	1.38436i
$909$	46.6918	+	3.43403i	1.54867	+	0.113900i
$910$	−14.3217	−	32.7118i	−0.474760	−	1.08439i
$911$	13.5590	−	2.88206i	0.449231	−	0.0954869i	0.0222596	−	0.999752i	$-0.492914\pi$
$911$	13.5590	−	2.88206i	0.449231	−	0.0954869i	0.426971	+	0.904265i	$0.359581\pi$
$912$	−42.4649	+	17.0681i	−1.40615	+	0.565180i
$913$	7.37479	+	1.56756i	0.244070	+	0.0518787i
$914$	26.7115	+	29.6661i	0.883538	+	0.981268i
$915$	15.7021	+	23.6861i	0.519095	+	0.783038i
$916$	−60.7913	+	67.5156i	−2.00860	+	2.23078i
$917$	−10.4564	+	7.59702i	−0.345301	+	0.250876i
$918$	−66.7991	+	59.4960i	−2.20470	+	1.96366i
$919$	33.8071	−	24.5623i	1.11519	−	0.810236i	0.131720	−	0.991287i	$-0.457950\pi$
$919$	33.8071	−	24.5623i	1.11519	−	0.810236i	0.983474	+	0.181051i	$0.0579500\pi$
$920$	−47.7413	−	15.8402i	−1.57398	−	0.522237i
$921$	11.0738	+	20.9176i	0.364894	+	0.689258i
$922$	−23.3058	+	10.3764i	−0.767537	+	0.341729i
$923$	−5.51651	−	6.12671i	−0.181578	−	0.201663i
$924$	−0.325159	−	4.77350i	−0.0106969	−	0.157037i
$925$	3.39057	+	36.6254i	0.111481	+	1.20423i
$926$	−44.7769			−1.47146
$927$	−8.07868	+	44.8709i	−0.265339	+	1.47375i
$928$	−10.0442	−	7.29755i	−0.329718	−	0.239554i
$929$	3.25692	−	30.9875i	0.106856	−	1.01667i	−0.801365	−	0.598176i	$-0.795892\pi$
$929$	3.25692	−	30.9875i	0.106856	−	1.01667i	0.908221	−	0.418491i	$-0.137441\pi$
$930$	11.4057	−	9.41593i	0.374006	−	0.308761i
$931$	2.91004	+	27.6871i	0.0953726	+	0.907409i
$932$	−19.6038	+	33.9548i	−0.642145	+	1.11223i
$933$	−0.568742	+	1.55389i	−0.0186198	+	0.0508722i
$934$	58.7155	−	65.2101i	1.92123	−	2.13374i
$935$	−5.94598	+	5.28736i	−0.194454	+	0.172915i
$936$	14.3094	−	79.4778i	0.467718	−	2.59781i
$937$	−11.2706	−	34.6872i	−0.368193	−	1.13318i	−0.947957	−	0.318398i	$-0.896855\pi$
$937$	−11.2706	−	34.6872i	−0.368193	−	1.13318i	0.579764	−	0.814784i	$-0.303145\pi$
$938$	0.974450	−	1.08224i	0.0318169	−	0.0353363i
$939$	−20.1345	−	5.05862i	−0.657064	−	0.165082i
$940$	15.1682	+	73.6033i	0.494732	+	2.40068i
$941$	−15.2034	−	3.23158i	−0.495617	−	0.105347i	−0.0466795	−	0.998910i	$-0.514864\pi$
$941$	−15.2034	−	3.23158i	−0.495617	−	0.105347i	−0.448937	+	0.893563i	$0.648197\pi$
$942$	2.36644	−	0.412874i	0.0771026	−	0.0134522i
$943$	−8.48922	−	14.7038i	−0.276447	−	0.478820i
$944$	12.5412	−	9.11169i	0.408180	−	0.296560i
$945$	−4.46265	−	14.2972i	−0.145170	−	0.465086i
$946$	4.30163	+	3.12532i	0.139858	+	0.101613i
$947$	1.69965	−	16.1711i	0.0552313	−	0.525490i	−0.931571	−	0.363560i	$-0.881561\pi$
$947$	1.69965	−	16.1711i	0.0552313	−	0.525490i	0.986802	−	0.161931i	$-0.0517721\pi$
$948$	17.3179	−	17.8687i	0.562459	−	0.580349i
$949$	21.9896	−	38.0871i	0.713813	−	1.23636i
$950$	−52.8800	+	37.4259i	−1.71565	+	1.21426i
$951$	0.265752	+	3.90138i	0.00861760	+	0.126511i
$952$	−47.1643	+	10.0251i	−1.52860	+	0.324915i
$953$	29.6469	+	21.5397i	0.960357	+	0.697741i	0.953234	−	0.302234i	$-0.0977324\pi$
$953$	29.6469	+	21.5397i	0.960357	+	0.697741i	0.00712369	+	0.999975i	$0.497732\pi$
$954$	−17.3332	+	10.7444i	−0.561183	+	0.347862i
$955$	30.9388	−	27.5118i	1.00116	−	0.890261i
$956$	18.7320	+	8.34000i	0.605835	+	0.269735i
$957$	5.11613	−	3.43748i	0.165381	−	0.111118i
$958$	−0.443837	−	4.22283i	−0.0143397	−	0.136433i
$959$	−13.3267	−	2.83268i	−0.430343	−	0.0914722i
$960$	21.9646	−	1.35933i	0.708906	−	0.0438721i
$961$	28.0117	−	5.95407i	0.903603	−	0.192067i
$962$	−28.1628	−	86.6762i	−0.908006	−	2.79455i
$963$	18.0426	−	26.5425i	0.581413	−	0.855320i
$964$	−10.2984	+	31.6953i	−0.331690	+	1.02084i
$965$	7.15925	−	9.72638i	0.230464	−	0.313103i
$966$	21.4475	−	8.62046i	0.690062	−	0.277359i
$967$	4.26366	+	40.5660i	0.137110	+	1.30452i	0.819310	+	0.573350i	$0.194357\pi$
$967$	4.26366	+	40.5660i	0.137110	+	1.30452i	−0.682200	+	0.731165i	$0.738977\pi$
$968$	−28.9793	+	50.1937i	−0.931431	+	1.61329i
$969$	−61.6566	+	10.7573i	−1.98069	+	0.345573i
$970$	0.277952	−	44.7994i	0.00892449	−	1.43842i
$971$	36.3301	+	26.3954i	1.16589	+	0.847068i	0.990511	−	0.137433i	$-0.0438852\pi$
$971$	36.3301	+	26.3954i	1.16589	+	0.847068i	0.175378	+	0.984501i	$0.443885\pi$
$972$	18.4918	−	62.3640i	0.593126	−	2.00033i
$973$	0.236941	−	0.729230i	0.00759599	−	0.0233780i
$974$	40.6362	+	70.3840i	1.30207	+	2.25525i
$975$	−2.39993	−	43.1167i	−0.0768593	−	1.38084i
$976$	−18.5888	+	32.1967i	−0.595011	+	1.03059i
$977$	−4.45973	−	4.95303i	−0.142679	−	0.158462i	0.667569	−	0.744548i	$-0.267335\pi$
$977$	−4.45973	−	4.95303i	−0.142679	−	0.158462i	−0.810249	+	0.586086i	$0.800668\pi$
$978$	39.6268	−	63.1627i	1.26712	−	2.01972i
$979$	−0.518017	+	4.92860i	−0.0165559	+	0.157519i
$980$	−10.6583	+	48.6568i	−0.340466	+	1.55429i
$981$	38.2946	+	11.1302i	1.22265	+	0.355361i
$982$	−102.522			−3.27161
$983$	−28.5768	−	12.7232i	−0.911458	−	0.405807i	−0.103217	−	0.994659i	$-0.532914\pi$
$983$	−28.5768	−	12.7232i	−0.911458	−	0.405807i	−0.808241	+	0.588851i	$0.799580\pi$
$984$	−29.9793	−	23.5094i	−0.955704	−	0.749453i
$985$	25.7430	+	23.4699i	0.820240	+	0.747814i
$986$	−79.8223	−	88.6517i	−2.54206	−	2.82324i
$987$	−14.1503	−	11.0965i	−0.450409	−	0.353206i
$988$	72.6080	−	80.6394i	2.30997	−	2.56548i
$989$	−5.36608	+	16.5151i	−0.170632	+	0.525150i
$990$	2.43978	−	8.20403i	0.0775412	−	0.260741i
$991$	−1.60963	−	4.95394i	−0.0511317	−	0.157367i	0.922230	−	0.386641i	$-0.126365\pi$
$991$	−1.60963	−	4.95394i	−0.0511317	−	0.157367i	−0.973362	+	0.229274i	$0.926365\pi$
$992$	2.51580	+	1.12010i	0.0798766	+	0.0355634i
$993$	1.57769	+	23.1613i	0.0500665	+	0.735002i
$994$	−0.553495	−	5.26616i	−0.0175558	−	0.167032i
$995$	38.0651	+	4.23974i	1.20675	+	0.134409i
$996$	49.6466	+	93.7787i	1.57311	+	2.97149i
$997$	2.39822	−	22.8176i	0.0759524	−	0.722639i	−0.888588	−	0.458705i	$-0.848313\pi$
$997$	2.39822	−	22.8176i	0.0759524	−	0.722639i	0.964541	−	0.263934i	$-0.0850200\pi$
$998$	2.67071	−	8.21961i	0.0845399	−	0.260187i
$999$	−7.74532	−	37.4320i	−0.245051	−	1.18430i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	225.2.q.a.121.27	yes	224
3.2	odd	2		675.2.r.a.496.2		224
9.2	odd	6		675.2.r.a.46.27		224
9.7	even	3	inner	225.2.q.a.196.2	yes	224
25.6	even	5	inner	225.2.q.a.31.2	✓	224
75.56	odd	10		675.2.r.a.631.27		224
225.56	odd	30		675.2.r.a.181.2		224
225.106	even	15	inner	225.2.q.a.106.27	yes	224

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
225.2.q.a.31.2	✓	224	25.6	even	5	inner
225.2.q.a.106.27	yes	224	225.106	even	15	inner
225.2.q.a.121.27	yes	224	1.1	even	1	trivial
225.2.q.a.196.2	yes	224	9.7	even	3	inner
675.2.r.a.46.27		224	9.2	odd	6
675.2.r.a.181.2		224	225.56	odd	30
675.2.r.a.496.2		224	3.2	odd	2
675.2.r.a.631.27		224	75.56	odd	10

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)

\(f(q)\)	\(=\)	\(q+(2.43022 - 0.516560i) q^{2} +(0.810393 + 1.53077i) q^{3} +(3.81206 - 1.69724i) q^{4} +(-2.22233 - 0.247525i) q^{5} +(2.76017 + 3.30150i) q^{6} +(-0.644527 - 1.11635i) q^{7} +(4.36740 - 3.17310i) q^{8} +(-1.68652 + 2.48105i) q^{9} +O(q^{10})\)	\(q+(2.43022 - 0.516560i) q^{2} +(0.810393 + 1.53077i) q^{3} +(3.81206 - 1.69724i) q^{4} +(-2.22233 - 0.247525i) q^{5} +(2.76017 + 3.30150i) q^{6} +(-0.644527 - 1.11635i) q^{7} +(4.36740 - 3.17310i) q^{8} +(-1.68652 + 2.48105i) q^{9} +(-5.52861 + 0.546422i) q^{10} +(0.502326 - 0.106773i) q^{11} +(5.68735 + 4.45996i) q^{12} +(-4.87743 - 1.03673i) q^{13} +(-2.14301 - 2.38005i) q^{14} +(-1.42205 - 3.60247i) q^{15} +(3.39033 - 3.76535i) q^{16} +(5.60571 - 4.07278i) q^{17} +(-2.81702 + 6.90071i) q^{18} +(-4.21905 + 3.06532i) q^{19} +(-8.89175 + 2.82823i) q^{20} +(1.18656 - 1.89131i) q^{21} +(1.16561 - 0.518963i) q^{22} +(2.78826 + 3.09668i) q^{23} +(8.39660 + 4.11403i) q^{24} +(4.87746 + 1.10016i) q^{25} -12.3888 q^{26} +(-5.16468 - 0.571054i) q^{27} +(-4.35169 - 3.16169i) q^{28} +(0.724325 - 6.89149i) q^{29} +(-5.31680 - 8.02022i) q^{30} +(0.160665 + 1.52862i) q^{31} +(0.895838 - 1.55164i) q^{32} +(0.570526 + 0.682419i) q^{33} +(11.5193 - 12.7935i) q^{34} +(1.15602 + 2.64044i) q^{35} +(-2.21819 + 12.3204i) q^{36} +(2.27325 + 6.99635i) q^{37} +(-8.66982 + 9.62881i) q^{38} +(-2.36564 - 8.30640i) q^{39} +(-10.4912 + 5.97062i) q^{40} +(-3.98547 - 0.847138i) q^{41} +(1.90663 - 5.20923i) q^{42} +(2.08364 + 3.60897i) q^{43} +(1.73368 - 1.25959i) q^{44} +(4.36213 - 5.09625i) q^{45} +(8.37572 + 6.08531i) q^{46} +(0.841878 - 8.00993i) q^{47} +(8.51139 + 2.13841i) q^{48} +(2.66917 - 4.62314i) q^{49} +(12.4216 + 0.154142i) q^{50} +(10.7773 + 5.28050i) q^{51} +(-20.3526 + 4.32609i) q^{52} +(2.21350 + 1.60820i) q^{53} +(-12.8463 + 1.28008i) q^{54} +(-1.14276 + 0.112945i) q^{55} +(-6.35720 - 2.83041i) q^{56} +(-8.11140 - 3.97429i) q^{57} +(-1.79960 - 17.1220i) q^{58} +(2.99263 + 0.636103i) q^{59} +(-11.5352 - 11.3193i) q^{60} +(-7.17717 + 1.52555i) q^{61} +(1.18008 + 3.63190i) q^{62} +(3.85674 + 0.283651i) q^{63} +(-1.75586 + 5.40400i) q^{64} +(10.5826 + 3.51124i) q^{65} +(1.73902 + 1.36372i) q^{66} +(0.0475303 + 0.452221i) q^{67} +(14.4568 - 25.0399i) q^{68} +(-2.48072 + 6.77772i) q^{69} +(4.17334 + 5.81969i) q^{70} +(1.33759 + 0.971819i) q^{71} +(0.506910 + 16.1873i) q^{72} +(-2.72548 + 8.38816i) q^{73} +(9.13854 + 15.8284i) q^{74} +(2.26856 + 8.35785i) q^{75} +(-10.8807 + 18.8459i) q^{76} +(-0.442959 - 0.491955i) q^{77} +(-10.0398 - 18.9644i) q^{78} +(0.359882 - 3.42405i) q^{79} +(-8.46644 + 7.52863i) q^{80} +(-3.31127 - 8.36872i) q^{81} -10.1232 q^{82} +(13.4120 + 5.97142i) q^{83} +(1.31324 - 9.22366i) q^{84} +(-13.4658 + 7.66350i) q^{85} +(6.92795 + 7.69427i) q^{86} +(11.1363 - 4.47604i) q^{87} +(1.85506 - 2.06025i) q^{88} +(-2.98202 + 9.17771i) q^{89} +(7.96843 - 14.6383i) q^{90} +(1.98628 + 6.11314i) q^{91} +(15.8848 + 7.07238i) q^{92} +(-2.20977 + 1.48473i) q^{93} +(-2.09166 - 19.9008i) q^{94} +(10.1349 - 5.76782i) q^{95} +(3.10118 + 0.113887i) q^{96} +(-0.842924 + 8.01989i) q^{97} +(4.09855 - 12.6140i) q^{98} +(-0.582277 + 1.42637i) 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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