LMFDB - Embedded newform 225.2.q.a.31.24

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			31.24
Character	$\chi$	$=$	225.31
Dual form			225.2.q.a.196.24

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.53828 - 1.70844i) q^{2} +(-0.365394 - 1.69307i) q^{3} +(-0.343384 - 3.26708i) q^{4} +(0.322490 + 2.21269i) q^{5} +(-3.45458 - 1.98017i) q^{6} +(-1.62043 - 2.80667i) q^{7} +(-2.39008 - 1.73649i) q^{8} +(-2.73297 + 1.23728i) q^{9} +O(q^{10})$	\(q+(1.53828 - 1.70844i) q^{2} +(-0.365394 - 1.69307i) q^{3} +(-0.343384 - 3.26708i) q^{4} +(0.322490 + 2.21269i) q^{5} +(-3.45458 - 1.98017i) q^{6} +(-1.62043 - 2.80667i) q^{7} +(-2.39008 - 1.73649i) q^{8} +(-2.73297 + 1.23728i) q^{9} +(4.27633 + 2.85279i) q^{10} +(1.30655 - 1.45107i) q^{11} +(-5.40593 + 1.77515i) q^{12} +(2.38463 + 2.64840i) q^{13} +(-7.28770 - 1.54905i) q^{14} +(3.62841 - 1.35450i) q^{15} +(-0.216735 + 0.0460685i) q^{16} +(0.726639 + 0.527934i) q^{17} +(-2.09028 + 6.57240i) q^{18} +(0.733140 + 0.532657i) q^{19} +(7.11830 - 1.81340i) q^{20} +(-4.15979 + 3.76904i) q^{21} +(-0.469217 - 4.46430i) q^{22} +(8.31379 + 1.76715i) q^{23} +(-2.06669 + 4.68108i) q^{24} +(-4.79200 + 1.42714i) q^{25} +8.19288 q^{26} +(3.09341 + 4.17502i) q^{27} +(-8.61318 + 6.25784i) q^{28} +(-6.82216 - 3.03742i) q^{29} +(3.26744 - 8.28251i) q^{30} +(-7.07738 + 3.15105i) q^{31} +(2.69961 - 4.67586i) q^{32} +(-2.93416 - 1.68186i) q^{33} +(2.01972 - 0.429305i) q^{34} +(5.68771 - 4.49063i) q^{35} +(4.98074 + 8.50399i) q^{36} +(-1.33249 + 4.10099i) q^{37} +(2.03779 - 0.433145i) q^{38} +(3.61260 - 5.00507i) q^{39} +(3.07155 - 5.84851i) q^{40} +(3.03574 + 3.37153i) q^{41} +(0.0402345 + 12.9046i) q^{42} +(-0.885445 - 1.53364i) q^{43} +(-5.18939 - 3.77032i) q^{44} +(-3.61907 - 5.64822i) q^{45} +(15.8080 - 11.4852i) q^{46} +(7.06685 + 3.14637i) q^{47} +(0.157191 + 0.350115i) q^{48} +(-1.75159 + 3.03384i) q^{49} +(-4.93328 + 10.3822i) q^{50} +(0.628320 - 1.42316i) q^{51} +(7.83371 - 8.70021i) q^{52} +(5.94096 - 4.31636i) q^{53} +(11.8913 + 1.13748i) q^{54} +(3.63211 + 2.42303i) q^{55} +(-1.00081 + 9.52203i) q^{56} +(0.633941 - 1.43589i) q^{57} +(-15.6837 + 6.98281i) q^{58} +(-9.23740 - 10.2592i) q^{59} +(-5.67120 - 11.3892i) q^{60} +(-4.22089 + 4.68777i) q^{61} +(-5.50365 + 16.9385i) q^{62} +(7.90122 + 5.66563i) q^{63} +(-3.97259 - 12.2264i) q^{64} +(-5.09108 + 6.13054i) q^{65} +(-7.38693 + 2.42565i) q^{66} +(-11.0747 + 4.93079i) q^{67} +(1.47529 - 2.55527i) q^{68} +(-0.0458994 - 14.7215i) q^{69} +(1.07736 - 16.6250i) q^{70} +(-8.02747 + 5.83230i) q^{71} +(8.68055 + 1.78861i) q^{72} +(0.246766 + 0.759468i) q^{73} +(4.95654 + 8.58498i) q^{74} +(4.16722 + 7.59173i) q^{75} +(1.48849 - 2.57813i) q^{76} +(-6.18982 - 1.31569i) q^{77} +(-2.99363 - 13.8711i) q^{78} +(-0.222600 - 0.0991078i) q^{79} +(-0.171830 - 0.464711i) q^{80} +(5.93830 - 6.76289i) q^{81} +10.4299 q^{82} +(-0.483482 + 4.60003i) q^{83} +(13.7422 + 12.2961i) q^{84} +(-0.933822 + 1.77808i) q^{85} +(-3.98219 - 0.846440i) q^{86} +(-2.64979 + 12.6602i) q^{87} +(-5.64252 + 1.19935i) q^{88} +(2.11267 + 6.50212i) q^{89} +(-15.2168 - 2.50562i) q^{90} +(3.56906 - 10.9844i) q^{91} +(2.91860 - 27.7686i) q^{92} +(7.92099 + 10.8311i) q^{93} +(16.2462 - 7.23327i) q^{94} +(-0.942175 + 1.79399i) q^{95} +(-8.90297 - 2.86209i) q^{96} +(-4.33055 - 1.92809i) q^{97} +(2.48869 + 7.65939i) q^{98} +(-1.77539 + 5.58228i) 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 $\left(\mathbb{Z}/225\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{5}\right)$

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 $

$2$	1.53828	−	1.70844i	1.08773	−	1.20805i	0.110946	−	0.993826i	$-0.464612\pi$
$2$	1.53828	−	1.70844i	1.08773	−	1.20805i	0.976785	−	0.214221i	$-0.0687214\pi$
$3$	−0.365394	−	1.69307i	−0.210960	−	0.977495i
$3$	−0.365394	−	1.69307i	−0.210960	−	0.977495i
$4$	−0.343384	−	3.26708i	−0.171692	−	1.63354i
$5$	0.322490	+	2.21269i	0.144222	+	0.989545i
$5$	0.322490	+	2.21269i	0.144222	+	0.989545i
$6$	−3.45458	−	1.98017i	−1.41033	−	0.808401i
$7$	−1.62043	−	2.80667i	−0.612465	−	1.06082i	−0.990824	−	0.135161i	$-0.956845\pi$
$7$	−1.62043	−	2.80667i	−0.612465	−	1.06082i	0.378359	−	0.925659i	$-0.376489\pi$
$8$	−2.39008	−	1.73649i	−0.845021	−	0.613944i
$9$	−2.73297	+	1.23728i	−0.910991	+	0.412425i
$10$	4.27633	+	2.85279i	1.35229	+	0.902132i
$11$	1.30655	−	1.45107i	0.393938	−	0.437513i	−0.513249	−	0.858240i	$-0.671558\pi$
$11$	1.30655	−	1.45107i	0.393938	−	0.437513i	0.907187	+	0.420727i	$0.138225\pi$
$12$	−5.40593	+	1.77515i	−1.56056	+	0.512440i
$13$	2.38463	+	2.64840i	0.661379	+	0.734535i	0.976738	−	0.214437i	$-0.0687917\pi$
$13$	2.38463	+	2.64840i	0.661379	+	0.734535i	−0.315359	+	0.948972i	$0.602125\pi$
$14$	−7.28770	−	1.54905i	−1.94772	−	0.414001i
$15$	3.62841	−	1.35450i	0.936850	−	0.349731i
$16$	−0.216735	+	0.0460685i	−0.0541838	+	0.0115171i
$17$	0.726639	+	0.527934i	0.176236	+	0.128043i	0.672406	−	0.740182i	$-0.265261\pi$
$17$	0.726639	+	0.527934i	0.176236	+	0.128043i	−0.496170	+	0.868225i	$0.665261\pi$
$18$	−2.09028	+	6.57240i	−0.492684	+	1.54913i
$19$	0.733140	+	0.532657i	0.168194	+	0.122200i	0.668698	−	0.743534i	$-0.266852\pi$
$19$	0.733140	+	0.532657i	0.168194	+	0.122200i	−0.500504	+	0.865734i	$0.666852\pi$
$20$	7.11830	−	1.81340i	1.59170	−	0.405489i
$21$	−4.15979	+	3.76904i	−0.907741	+	0.822472i
$22$	−0.469217	−	4.46430i	−0.100037	−	0.951792i
$23$	8.31379	+	1.76715i	1.73354	+	0.368476i	0.963124	−	0.269059i	$-0.0867127\pi$
$23$	8.31379	+	1.76715i	1.73354	+	0.368476i	0.770421	+	0.637535i	$0.220046\pi$
$24$	−2.06669	+	4.68108i	−0.421861	+	0.955521i
$25$	−4.79200	+	1.42714i	−0.958400	+	0.285428i
$26$	8.19288			1.60676
$27$	3.09341	+	4.17502i	0.595327	+	0.803484i
$28$	−8.61318	+	6.25784i	−1.62774	+	1.18262i
$29$	−6.82216	−	3.03742i	−1.26684	−	0.564035i	−0.340333	−	0.940305i	$-0.610540\pi$
$29$	−6.82216	−	3.03742i	−1.26684	−	0.564035i	−0.926510	+	0.376270i	$0.877206\pi$
$30$	3.26744	−	8.28251i	0.596549	−	1.51217i
$31$	−7.07738	+	3.15105i	−1.27114	+	0.565946i	−0.927734	−	0.373243i	$-0.878246\pi$
$31$	−7.07738	+	3.15105i	−1.27114	+	0.565946i	−0.343402	+	0.939189i	$0.611579\pi$
$32$	2.69961	−	4.67586i	0.477228	−	0.826582i
$33$	−2.93416	−	1.68186i	−0.510772	−	0.292775i
$34$	2.01972	−	0.429305i	0.346379	−	0.0736252i
$35$	5.68771	−	4.49063i	0.961399	−	0.759055i
$36$	4.98074	+	8.50399i	0.830123	+	1.41733i
$37$	−1.33249	+	4.10099i	−0.219061	+	0.674199i	0.779780	+	0.626054i	$0.215331\pi$
$37$	−1.33249	+	4.10099i	−0.219061	+	0.674199i	−0.998840	+	0.0481453i	$0.984669\pi$
$38$	2.03779	−	0.433145i	0.330573	−	0.0702655i
$39$	3.61260	−	5.00507i	0.578480	−	0.801452i
$40$	3.07155	−	5.84851i	0.485655	−	0.924731i
$41$	3.03574	+	3.37153i	0.474103	+	0.526545i	0.931999	−	0.362461i	$-0.118063\pi$
$41$	3.03574	+	3.37153i	0.474103	+	0.526545i	−0.457896	+	0.889006i	$0.651397\pi$
$42$	0.0402345	+	12.9046i	0.00620832	+	1.99122i
$43$	−0.885445	−	1.53364i	−0.135029	−	0.233877i	0.790579	−	0.612359i	$-0.209779\pi$
$43$	−0.885445	−	1.53364i	−0.135029	−	0.233877i	−0.925609	+	0.378482i	$0.876446\pi$
$44$	−5.18939	−	3.77032i	−0.782331	−	0.568397i
$45$	−3.61907	−	5.64822i	−0.539498	−	0.841987i
$46$	15.8080	−	11.4852i	2.33077	−	1.69340i
$47$	7.06685	+	3.14637i	1.03081	+	0.458945i	0.851226	−	0.524799i	$-0.175859\pi$
$47$	7.06685	+	3.14637i	1.03081	+	0.458945i	0.179580	+	0.983743i	$0.442526\pi$
$48$	0.157191	+	0.350115i	0.0226886	+	0.0505347i
$49$	−1.75159	+	3.03384i	−0.250227	+	0.433406i
$50$	−4.93328	+	10.3822i	−0.697671	+	1.46826i
$51$	0.628320	−	1.42316i	0.0879824	−	0.199282i
$52$	7.83371	−	8.70021i	1.08634	−	1.20650i
$53$	5.94096	−	4.31636i	0.816053	−	0.592897i	−0.0995259	−	0.995035i	$-0.531733\pi$
$53$	5.94096	−	4.31636i	0.816053	−	0.592897i	0.915579	+	0.402137i	$0.131733\pi$
$54$	11.8913	+	1.13748i	1.61820	+	0.154791i
$55$	3.63211	+	2.42303i	0.489753	+	0.326721i
$56$	−1.00081	+	9.52203i	−0.133738	+	1.27243i
$57$	0.633941	−	1.43589i	0.0839675	−	0.190188i
$58$	−15.6837	+	6.98281i	−2.05937	+	0.916888i
$59$	−9.23740	−	10.2592i	−1.20261	−	1.33563i	−0.927321	−	0.374267i	$-0.877894\pi$
$59$	−9.23740	−	10.2592i	−1.20261	−	1.33563i	−0.275286	−	0.961362i	$-0.588772\pi$
$60$	−5.67120	−	11.3892i	−0.732149	−	1.47034i
$61$	−4.22089	+	4.68777i	−0.540429	+	0.600207i	−0.950069	−	0.312040i	$-0.898988\pi$
$61$	−4.22089	+	4.68777i	−0.540429	+	0.600207i	0.409640	+	0.912247i	$0.365654\pi$
$62$	−5.50365	+	16.9385i	−0.698964	+	2.15119i
$63$	7.90122	+	5.66563i	0.995460	+	0.713802i
$64$	−3.97259	−	12.2264i	−0.496573	−	1.52830i
$65$	−5.09108	+	6.13054i	−0.631471	+	0.760400i
$66$	−7.38693	+	2.42565i	−0.909268	+	0.298576i
$67$	−11.0747	+	4.93079i	−1.35300	+	0.602392i	−0.949839	−	0.312739i	$-0.898754\pi$
$67$	−11.0747	+	4.93079i	−1.35300	+	0.602392i	−0.403156	+	0.915131i	$0.632087\pi$
$68$	1.47529	−	2.55527i	0.178905	−	0.309872i
$69$	−0.0458994	−	14.7215i	−0.00552564	−	1.77226i
$70$	1.07736	−	16.6250i	0.128769	−	1.98706i
$71$	−8.02747	+	5.83230i	−0.952686	+	0.692167i	−0.951441	−	0.307833i	$-0.900396\pi$
$71$	−8.02747	+	5.83230i	−0.952686	+	0.692167i	−0.00124504	+	0.999999i	$0.500396\pi$
$72$	8.68055	+	1.78861i	1.02301	+	0.210789i
$73$	0.246766	+	0.759468i	0.0288818	+	0.0888891i	0.964458	−	0.264235i	$-0.0851194\pi$
$73$	0.246766	+	0.759468i	0.0288818	+	0.0888891i	−0.935577	+	0.353124i	$0.885119\pi$
$74$	4.95654	+	8.58498i	0.576186	+	0.997983i
$75$	4.16722	+	7.59173i	0.481189	+	0.876617i
$76$	1.48849	−	2.57813i	0.170741	−	0.295732i
$77$	−6.18982	−	1.31569i	−0.705396	−	0.149937i
$78$	−2.99363	−	13.8711i	−0.338962	−	1.57060i
$79$	−0.222600	−	0.0991078i	−0.0250444	−	0.0111505i	0.394176	−	0.919035i	$-0.371030\pi$
$79$	−0.222600	−	0.0991078i	−0.0250444	−	0.0111505i	−0.419221	+	0.907884i	$0.637697\pi$
$80$	−0.171830	−	0.464711i	−0.0192112	−	0.0519563i
$81$	5.93830	−	6.76289i	0.659811	−	0.751432i
$82$	10.4299			1.15179
$83$	−0.483482	+	4.60003i	−0.0530691	+	0.504919i	0.935410	+	0.353564i	$0.115030\pi$
$83$	−0.483482	+	4.60003i	−0.0530691	+	0.504919i	−0.988479	+	0.151355i	$0.951636\pi$
$84$	13.7422	+	12.2961i	1.49939	+	1.34162i
$85$	−0.933822	+	1.77808i	−0.101287	+	0.192860i
$86$	−3.98219	−	0.846440i	−0.429410	−	0.0912740i
$87$	−2.64979	+	12.6602i	−0.284087	+	1.35732i
$88$	−5.64252	+	1.19935i	−0.601494	+	0.127852i
$89$	2.11267	+	6.50212i	0.223942	+	0.689224i	0.998397	+	0.0565946i	$0.0180243\pi$
$89$	2.11267	+	6.50212i	0.223942	+	0.689224i	−0.774455	+	0.632629i	$0.781976\pi$
$90$	−15.2168	−	2.50562i	−1.60399	−	0.264115i
$91$	3.56906	−	10.9844i	0.374139	−	1.15148i
$92$	2.91860	−	27.7686i	0.304285	−	2.89508i
$93$	7.92099	+	10.8311i	0.821368	+	1.12314i
$94$	16.2462	−	7.23327i	1.67567	−	0.746055i
$95$	−0.942175	+	1.79399i	−0.0966652	+	0.184059i
$96$	−8.90297	−	2.86209i	−0.908656	−	0.292111i
$97$	−4.33055	−	1.92809i	−0.439701	−	0.195767i	0.174932	−	0.984580i	$-0.444029\pi$
$97$	−4.33055	−	1.92809i	−0.439701	−	0.195767i	−0.614633	+	0.788813i	$0.710696\pi$
$98$	2.48869	+	7.65939i	0.251395	+	0.773715i
$99$	−1.77539	+	5.58228i	−0.178433	+	0.561040i
$100$	6.30808	+	15.1658i	0.630808	+	1.51658i
$101$	5.99315	+	10.3804i	0.596341	+	1.03289i	0.993356	+	0.115080i	$0.0367126\pi$
$101$	5.99315	+	10.3804i	0.596341	+	1.03289i	−0.397016	+	0.917812i	$0.629954\pi$
$102$	−1.46484	−	3.26266i	−0.145041	−	0.323052i
$103$	−0.230552	−	2.19355i	−0.0227169	−	0.216137i	−0.999991	−	0.00415917i	$-0.998676\pi$
$103$	−0.230552	−	2.19355i	−0.0227169	−	0.216137i	0.977274	−	0.211978i	$-0.0679906\pi$
$104$	−1.10053	−	10.4708i	−0.107915	−	1.02675i
$105$	−9.68121	−	7.98885i	−0.944790	−	0.779632i
$106$	1.76465	−	16.7895i	0.171398	−	1.63074i
$107$	−4.62059			−0.446689			−0.223344	−	0.974740i	$-0.571697\pi$
$107$	−4.62059			−0.446689			−0.223344	+	0.974740i	$0.571697\pi$
$108$	12.5779	−	11.5401i	1.21031	−	1.11044i
$109$	−4.18621	+	12.8838i	−0.400966	+	1.23405i	0.523251	+	0.852178i	$0.324719\pi$
$109$	−4.18621	+	12.8838i	−0.400966	+	1.23405i	−0.924217	+	0.381867i	$0.875281\pi$
$110$	9.72680	−	2.47792i	0.927414	−	0.236261i
$111$	7.43016	+	0.757527i	0.705239	+	0.0719012i
$112$	0.480503	+	0.533653i	0.0454033	+	0.0504255i
$113$	−11.3213	−	12.5736i	−1.06502	−	1.18282i	−0.982505	−	0.186234i	$-0.940372\pi$
$113$	−11.3213	−	12.5736i	−1.06502	−	1.18282i	−0.0825140	−	0.996590i	$-0.526295\pi$
$114$	−1.47794	−	3.29185i	−0.138422	−	0.308310i
$115$	−1.22904	+	18.9657i	−0.114609	+	1.76856i
$116$	−7.58088	+	23.3315i	−0.703867	+	2.16628i
$117$	−9.79395	−	4.28757i	−0.905451	−	0.396386i
$118$	−31.7369			−2.92162
$119$	0.304268	−	2.89492i	0.0278922	−	0.265377i
$120$	−11.0243	−	3.06334i	−1.00637	−	0.279643i
$121$	0.751283	+	7.14798i	0.0682984	+	0.649816i
$122$	1.51584	+	14.4222i	0.137238	+	1.30573i
$123$	4.59900	−	6.37166i	0.414678	−	0.574514i
$124$	12.7250	+	22.0404i	1.14274	+	1.97928i
$125$	−4.70319	−	10.1430i	−0.420666	−	0.907215i
$126$	21.8337	−	4.78338i	1.94510	−	0.426138i
$127$	−2.60072	−	8.00418i	−0.230776	−	0.710256i	−0.997654	−	0.0684626i	$-0.978191\pi$
$127$	−2.60072	−	8.00418i	−0.230776	−	0.710256i	0.766877	−	0.641794i	$-0.221809\pi$
$128$	−17.1341	−	7.62859i	−1.51446	−	0.674279i
$129$	−2.27302	+	2.05950i	−0.200128	+	0.181329i
$130$	2.64212	+	18.1283i	0.231729	+	1.58996i
$131$	13.2541	−	5.90112i	1.15802	−	0.515584i	0.264402	−	0.964413i	$-0.414825\pi$
$131$	13.2541	−	5.90112i	1.15802	−	0.515584i	0.893618	+	0.448829i	$0.148159\pi$
$132$	−4.48724	+	10.1637i	−0.390564	+	0.884633i
$133$	0.306990	−	2.92081i	0.0266194	−	0.253267i
$134$	−8.61215	+	26.5055i	−0.743976	+	2.28972i
$135$	−8.24045	+	8.19116i	−0.709225	+	0.704983i
$136$	−0.819971	−	2.52361i	−0.0703119	−	0.216398i
$137$	5.89389	−	1.25278i	0.503549	−	0.107033i	0.0508682	−	0.998705i	$-0.483801\pi$
$137$	5.89389	−	1.25278i	0.503549	−	0.107033i	0.452681	+	0.891673i	$0.350468\pi$
$138$	−25.2214	−	22.5675i	−2.14699	−	1.92107i
$139$	8.08068	+	1.71760i	0.685394	+	0.145685i	0.537431	−	0.843308i	$-0.319395\pi$
$139$	8.08068	+	1.71760i	0.685394	+	0.145685i	0.147963	+	0.988993i	$0.452728\pi$
$140$	−16.6243	−	17.0402i	−1.40501	−	1.44016i
$141$	2.74483	−	13.1143i	0.231157	−	1.10443i
$142$	−2.38441	+	22.6862i	−0.200095	+	1.90378i
$143$	6.95864			0.581911
$144$	0.535332	−	0.394065i	0.0446110	−	0.0328388i
$145$	4.52079	−	16.0749i	0.375432	−	1.33494i
$146$	1.67710	+	0.746693i	0.138798	+	0.0617968i
$147$	5.77652	+	1.85701i	0.476440	+	0.153164i
$148$	13.8558	+	2.94515i	1.13894	+	0.242090i
$149$	5.47333	−	9.48009i	0.448393	−	0.776639i	−0.549889	−	0.835238i	$-0.685330\pi$
$149$	5.47333	−	9.48009i	0.448393	−	0.776639i	0.998282	+	0.0585987i	$0.0186632\pi$
$150$	19.3804	+	4.55880i	1.58240	+	0.372224i
$151$	−10.5024	−	18.1907i	−0.854675	−	1.48034i	−0.876946	−	0.480589i	$-0.840423\pi$
$151$	−10.5024	−	18.1907i	−0.854675	−	1.48034i	0.0222707	−	0.999752i	$-0.492910\pi$
$152$	−0.827306	−	2.54619i	−0.0671034	−	0.206523i
$153$	−2.63909	−	0.543778i	−0.213358	−	0.0439618i
$154$	−11.7695	+	8.55102i	−0.948411	+	0.689061i
$155$	−9.25469	−	14.6439i	−0.743355	−	1.17622i
$156$	−17.5925	−	10.0840i	−1.40852	−	0.807367i
$157$	3.25622	−	5.63994i	0.259875	−	0.450116i	−0.706333	−	0.707879i	$-0.749652\pi$
$157$	3.25622	−	5.63994i	0.259875	−	0.450116i	0.966208	+	0.257763i	$0.0829854\pi$
$158$	−0.511741	+	0.227842i	−0.0407119	+	0.0181261i
$159$	−9.47869	−	8.48129i	−0.751709	−	0.672610i
$160$	11.2168	+	4.46548i	0.886767	+	0.353027i
$161$	−8.51211	−	26.1976i	−0.670848	−	2.06466i
$162$	−2.41918	−	20.5485i	−0.190069	−	1.61444i
$163$	−1.26328	+	3.88796i	−0.0989474	+	0.304529i	−0.988262	−	0.152766i	$-0.951182\pi$
$163$	−1.26328	+	3.88796i	−0.0989474	+	0.304529i	0.889315	+	0.457295i	$0.151182\pi$
$164$	9.97265	−	11.0757i	0.778733	−	0.864871i
$165$	2.77520	−	7.03477i	0.216049	−	0.547656i
$166$	7.11513	+	7.90215i	0.552241	+	0.613326i
$167$	15.3149	−	6.81865i	1.18511	−	0.527643i	0.282984	−	0.959125i	$-0.408676\pi$
$167$	15.3149	−	6.81865i	1.18511	−	0.527643i	0.902122	+	0.431482i	$0.142009\pi$
$168$	16.4872	−	1.78486i	1.27201	−	0.137705i
$169$	0.0313031	−	0.297829i	0.00240793	−	0.0229099i
$170$	1.60126	+	4.33057i	0.122811	+	0.332140i
$171$	−2.66270	−	0.548642i	−0.203621	−	0.0419557i
$172$	−4.70647	+	3.41945i	−0.358865	+	0.260730i
$173$	−4.40487	+	4.89211i	−0.334896	+	0.371940i	−0.886948	−	0.461870i	$-0.847179\pi$
$173$	−4.40487	+	4.89211i	−0.334896	+	0.371940i	0.552051	+	0.833810i	$0.313845\pi$
$174$	17.5531	+	24.0021i	1.33070	+	1.81959i
$175$	11.7706	+	11.1370i	0.889775	+	0.841876i
$176$	−0.216326	+	0.374687i	−0.0163062	+	0.0282431i
$177$	−13.9942	+	19.3882i	−1.05187	+	1.45731i
$178$	14.3584	+	6.39275i	1.07620	+	0.479157i
$179$	−8.82628	+	6.41267i	−0.659707	+	0.479305i	−0.866564	−	0.499066i	$-0.833677\pi$
$179$	−8.82628	+	6.41267i	−0.659707	+	0.479305i	0.206857	+	0.978371i	$0.433677\pi$
$180$	−17.2105	+	13.7633i	−1.28279	+	1.02585i
$181$	7.04839	+	5.12096i	0.523903	+	0.380638i	0.818072	−	0.575116i	$-0.195043\pi$
$181$	7.04839	+	5.12096i	0.523903	+	0.380638i	−0.294169	+	0.955753i	$0.595043\pi$
$182$	−13.2760	−	22.9947i	−0.984082	−	1.70448i
$183$	9.47901	+	5.43337i	0.700708	+	0.401646i
$184$	−16.8020	−	18.6605i	−1.23866	−	1.37567i
$185$	−9.50395	−	1.62587i	−0.698744	−	0.119536i
$186$	30.6890	+	3.12884i	2.25023	+	0.229418i
$187$	1.71545	−	0.364631i	0.125446	−	0.0266645i
$188$	7.85279	−	24.1684i	0.572723	−	1.76266i
$189$	6.70525	−	15.4475i	0.487735	−	1.12364i
$190$	1.61558	+	4.36931i	0.117207	+	0.316983i
$191$	9.78604	−	2.08009i	0.708093	−	0.150510i	0.160232	−	0.987079i	$-0.448776\pi$
$191$	9.78604	−	2.08009i	0.708093	−	0.150510i	0.547861	+	0.836570i	$0.315442\pi$
$192$	−19.2485	+	11.1933i	−1.38914	+	0.807808i
$193$	5.77682	−	10.0057i	0.415824	−	0.720229i	−0.579690	−	0.814837i	$-0.696826\pi$
$193$	5.77682	−	10.0057i	0.415824	−	0.720229i	0.995515	+	0.0946081i	$0.0301598\pi$
$194$	−9.95563	+	4.43253i	−0.714773	+	0.318237i
$195$	12.2397	+	6.37949i	0.876502	+	0.456845i
$196$	10.5133	+	4.68081i	0.750948	+	0.334343i
$197$	10.5844	−	7.69002i	0.754108	−	0.547891i	−0.142990	−	0.989724i	$-0.545672\pi$
$197$	10.5844	−	7.69002i	0.754108	−	0.547891i	0.897097	+	0.441833i	$0.145672\pi$
$198$	6.80593	+	11.6203i	0.483676	+	0.825817i
$199$	2.60687			0.184796			0.0923980	−	0.995722i	$-0.470547\pi$
$199$	2.60687			0.184796			0.0923980	+	0.995722i	$0.470547\pi$
$200$	13.9315	+	4.91030i	0.985105	+	0.347211i
$201$	12.3948	+	16.9486i	0.874264	+	1.19546i
$202$	26.9535	+	5.72914i	1.89644	+	0.403101i
$203$	2.52980	+	24.0695i	0.177557	+	1.68934i
$204$	−4.86532	−	1.56408i	−0.340641	−	0.109508i
$205$	−6.48117	+	7.80445i	−0.452664	+	0.545086i
$206$	−4.10221	−	2.98043i	−0.285814	−	0.207656i
$207$	−24.9078	+	5.45687i	−1.73121	+	0.379279i
$208$	−0.638842	−	0.464146i	−0.0442957	−	0.0321827i
$209$	1.73080	−	0.367893i	0.119722	−	0.0254477i
$210$	−28.5409	+	4.25063i	−1.96951	+	0.293321i
$211$	−26.1057	−	5.54894i	−1.79719	−	0.382005i	−0.816466	−	0.577394i	$-0.804070\pi$
$211$	−26.1057	−	5.54894i	−1.79719	−	0.382005i	−0.980726	+	0.195389i	$0.937403\pi$
$212$	−16.1419	−	17.9274i	−1.10863	−	1.23126i
$213$	12.8077	+	11.4600i	0.877568	+	0.785225i
$214$	−7.10777	+	7.89398i	−0.485877	+	0.539622i
$215$	3.10791	−	2.45380i	0.211958	−	0.167348i
$216$	−0.143584	−	15.3503i	−0.00976962	−	1.04446i
$217$	20.3124	+	14.7578i	1.37889	+	1.00182i
$218$	15.5716	+	26.9708i	1.05464	+	1.82670i
$219$	1.19567	−	0.695298i	0.0807957	−	0.0469839i
$220$	6.66902	−	12.6984i	0.449625	−	0.856127i
$221$	0.334585	+	3.18337i	0.0225066	+	0.214136i
$222$	12.7239	−	11.5287i	0.853971	−	0.773754i
$223$	14.3624	−	15.9511i	0.961780	−	1.06817i	−0.0358496	−	0.999357i	$-0.511414\pi$
$223$	14.3624	−	15.9511i	0.961780	−	1.06817i	0.997630	−	0.0688080i	$-0.0219196\pi$
$224$	−17.4981			−1.16914
$225$	11.3306	−	9.82937i	0.755377	−	0.655291i
$226$	−38.8966			−2.58736
$227$	−3.52007	+	3.90944i	−0.233636	+	0.259479i	−0.848550	−	0.529115i	$-0.822524\pi$
$227$	−3.52007	+	3.90944i	−0.233636	+	0.259479i	0.614914	+	0.788594i	$0.289191\pi$
$228$	−4.90884	−	1.57808i	−0.325096	−	0.104511i
$229$	−1.82919	−	17.4036i	−0.120877	−	1.15006i	−0.871864	−	0.489747i	$-0.837089\pi$
$229$	−1.82919	−	17.4036i	−0.120877	−	1.15006i	0.750988	−	0.660316i	$-0.229578\pi$
$230$	30.5111	+	31.2744i	2.01185	+	2.06217i
$231$	0.0341733	+	10.9605i	0.00224844	+	0.721151i
$232$	11.0310	+	19.1063i	0.724223	+	1.25439i
$233$	−7.95794	−	5.78178i	−0.521342	−	0.378777i	0.295767	−	0.955260i	$-0.404425\pi$
$233$	−7.95794	−	5.78178i	−0.521342	−	0.378777i	−0.817109	+	0.576483i	$0.804425\pi$
$234$	−22.3909	+	10.1369i	−1.46374	+	0.662667i
$235$	−4.68294	+	16.6514i	−0.305482	+	1.08622i
$236$	−30.3456	+	33.7022i	−1.97533	+	2.19382i
$237$	−0.0864598	+	0.413090i	−0.00561617	+	0.0268331i
$238$	−4.47773	−	4.97303i	−0.290248	−	0.322353i
$239$	16.3019	+	3.46507i	1.05448	+	0.224136i	0.702362	−	0.711820i	$-0.252129\pi$
$239$	16.3019	+	3.46507i	1.05448	+	0.224136i	0.352117	+	0.935956i	$0.385462\pi$
$240$	−0.724003	+	0.460723i	−0.0467342	+	0.0297396i
$241$	−21.6986	+	4.61217i	−1.39773	+	0.297096i	−0.844331	−	0.535822i	$-0.820002\pi$
$241$	−21.6986	+	4.61217i	−1.39773	+	0.297096i	−0.553396	+	0.832918i	$0.686668\pi$
$242$	13.3676	+	9.71210i	0.859299	+	0.624317i
$243$	−13.6199	−	7.58284i	−0.873714	−	0.486439i
$244$	16.7647	+	12.1803i	1.07325	+	0.779762i
$245$	−7.27782	−	2.89734i	−0.464963	−	0.185104i
$246$	−3.81102	−	17.6585i	−0.242982	−	1.12587i
$247$	0.337578	+	3.21184i	0.0214796	+	0.204365i
$248$	22.3873	+	4.75857i	1.42160	+	0.302169i
$249$	7.96483	−	0.862253i	0.504751	−	0.0546431i
$250$	−24.5635	−	7.56767i	−1.55353	−	0.478621i
$251$	−7.63595			−0.481977			−0.240989	−	0.970528i	$-0.577472\pi$
$251$	−7.63595			−0.481977			−0.240989	+	0.970528i	$0.577472\pi$
$252$	15.7969	−	27.7594i	0.995113	−	1.74868i
$253$	13.4266	−	9.75499i	0.844122	−	0.613291i
$254$	−17.6753	−	7.86954i	−1.10905	−	0.493779i
$255$	3.35163	+	0.931325i	0.209887	+	0.0583219i
$256$	−15.9018	+	7.07994i	−0.993863	+	0.442496i
$257$	−3.94709	+	6.83657i	−0.246213	+	0.426453i	−0.962472	−	0.271381i	$-0.912520\pi$
$257$	−3.94709	+	6.83657i	−0.246213	+	0.426453i	0.716259	+	0.697835i	$0.245853\pi$
$258$	0.0219852	+	7.05141i	0.00136874	+	0.439001i
$259$	13.6693	−	2.90551i	0.849371	−	0.180539i
$260$	21.7772	+	14.5278i	1.35056	+	0.900979i
$261$	22.4029	−	0.139699i	1.38671	−	0.00864714i
$262$	10.3069	−	31.7215i	0.636764	−	1.95976i
$263$	9.10099	−	1.93448i	0.561191	−	0.119285i	0.0814223	−	0.996680i	$-0.474054\pi$
$263$	9.10099	−	1.93448i	0.561191	−	0.119285i	0.479769	+	0.877395i	$0.340720\pi$
$264$	4.09233	+	9.11494i	0.251866	+	0.560986i
$265$	11.4667	+	11.7535i	0.704392	+	0.722013i
$266$	−4.51779	−	5.01751i	−0.277003	−	0.307643i
$267$	10.2366	−	5.95273i	0.626470	−	0.364301i
$268$	19.9122	+	34.4889i	1.21633	+	2.10675i
$269$	12.3841	+	8.99756i	0.755071	+	0.548591i	0.897394	−	0.441229i	$-0.145457\pi$
$269$	12.3841	+	8.99756i	0.755071	+	0.548591i	−0.142324	+	0.989820i	$0.545457\pi$
$270$	1.31794	+	26.6786i	0.0802070	+	1.62361i
$271$	−6.20201	+	4.50602i	−0.376745	+	0.273721i	−0.760002	−	0.649920i	$-0.774802\pi$
$271$	−6.20201	+	4.50602i	−0.376745	+	0.273721i	0.383257	+	0.923642i	$0.374802\pi$
$272$	−0.181809	−	0.0809468i	−0.0110238	−	0.00490812i
$273$	−19.9015	−	2.02902i	−1.20450	−	0.122802i
$274$	6.92617	−	11.9965i	0.418425	−	0.724734i
$275$	−4.19009	+	8.81813i	−0.252672	+	0.531753i
$276$	−48.0807	+	5.20510i	−2.89412	+	0.313310i
$277$	0.345420	−	0.383628i	0.0207543	−	0.0230500i	−0.732678	−	0.680575i	$-0.761730\pi$
$277$	0.345420	−	0.383628i	0.0207543	−	0.0230500i	0.753433	+	0.657525i	$0.228397\pi$
$278$	15.3648	−	11.1632i	0.921519	−	0.669523i
$279$	15.4436	−	17.3684i	0.924583	−	1.03982i
$280$	−21.3921	+	0.856285i	−1.27842	+	0.0511728i
$281$	−0.275106	+	2.61746i	−0.0164115	+	0.156145i	−0.999658	−	0.0261336i	$-0.991680\pi$
$281$	−0.275106	+	2.61746i	−0.0164115	+	0.156145i	0.983247	+	0.182278i	$0.0583471\pi$
$282$	−18.1827	−	24.8630i	−1.08276	−	1.48057i
$283$	28.0092	−	12.4705i	1.66497	−	0.741293i	0.664987	−	0.746855i	$-0.268437\pi$
$283$	28.0092	−	12.4705i	1.66497	−	0.741293i	0.999985	+	0.00556193i	$0.00177043\pi$
$284$	21.8111	+	24.2237i	1.29425	+	1.43741i
$285$	3.38161	+	0.939657i	0.200309	+	0.0556605i
$286$	10.7044	−	11.8884i	0.632962	−	0.702976i
$287$	4.54357	−	13.9837i	0.268198	−	0.825429i
$288$	−1.59263	+	16.1192i	−0.0938468	+	0.949830i
$289$	−5.00400	−	15.4007i	−0.294353	−	0.905925i
$290$	−20.5086	−	32.4512i	−1.20431	−	1.90560i
$291$	−1.68203	+	8.03644i	−0.0986022	+	0.471104i
$292$	2.39651	−	1.06699i	0.140245	−	0.0624411i
$293$	−14.6607	+	25.3931i	−0.856488	+	1.48348i	0.0187704	+	0.999824i	$0.494025\pi$
$293$	−14.6607	+	25.3931i	−0.856488	+	1.48348i	−0.875258	+	0.483656i	$0.839309\pi$
$294$	12.0585	−	7.01221i	0.703268	−	0.408961i
$295$	19.7214	−	23.7480i	1.14822	−	1.38266i
$296$	10.3061	−	7.48784i	0.599031	−	0.435222i
$297$	10.0999	+	0.966121i	0.586056	+	0.0560600i
$298$	−7.77660	−	23.9339i	−0.450486	−	1.38645i
$299$	15.1452	+	26.2323i	0.875871	+	1.51705i
$300$	23.3718	−	16.2215i	1.34937	−	0.936550i
$301$	−2.86960	+	4.97030i	−0.165401	+	0.286483i
$302$	−47.2334	−	10.0398i	−2.71798	−	0.577724i
$303$	15.3850	−	13.9398i	0.883842	−	0.800819i
$304$	−0.183436	−	0.0816709i	−0.0105208	−	0.00468415i
$305$	−11.7338	−	7.82776i	−0.671874	−	0.448216i
$306$	−4.98868	+	3.67223i	−0.285184	+	0.209927i
$307$	9.35518			0.533929			0.266964	−	0.963706i	$-0.413979\pi$
$307$	9.35518			0.533929			0.266964	+	0.963706i	$0.413979\pi$
$308$	−2.17297	+	20.6744i	−0.123817	+	1.17804i
$309$	−3.62960	+	1.19185i	−0.206481	+	0.0678021i
$310$	−39.2545	−	6.71538i	−2.22951	−	0.381408i
$311$	−20.1764	−	4.28863i	−1.14410	−	0.243186i	−0.403401	−	0.915023i	$-0.632172\pi$
$311$	−20.1764	−	4.28863i	−1.14410	−	0.243186i	−0.740699	+	0.671837i	$0.765505\pi$
$312$	−17.3257	+	5.68924i	−0.980874	+	0.322090i
$313$	−19.9912	+	4.24926i	−1.12997	+	0.240183i	−0.734707	−	0.678385i	$-0.762680\pi$
$313$	−19.9912	+	4.24926i	−1.12997	+	0.240183i	−0.395264	+	0.918568i	$0.629347\pi$
$314$	−4.62649	−	14.2389i	−0.261088	−	0.803547i
$315$	−9.98823	+	19.3101i	−0.562773	+	1.08800i
$316$	−0.247356	+	0.761283i	−0.0139149	+	0.0428255i
$317$	0.00914898	−	0.0870467i	0.000513858	−	0.00488903i	−0.994262	−	0.106973i	$-0.965884\pi$
$317$	0.00914898	−	0.0870467i	0.000513858	−	0.00488903i	0.994776	+	0.102084i	$0.0325509\pi$
$318$	−29.0707	+	3.14712i	−1.63020	+	0.176482i
$319$	−13.3210	+	5.93087i	−0.745830	+	0.332065i
$320$	25.7721	−	12.7330i	1.44070	−	0.711796i
$321$	1.68834	+	7.82298i	0.0942337	+	0.436636i
$322$	−57.8510	−	25.7569i	−3.22391	−	1.43538i
$323$	0.251520	+	0.774099i	0.0139950	+	0.0430720i
$324$	−24.1340	−	17.0786i	−1.34078	−	0.948813i
$325$	−15.2068	−	9.28795i	−0.843522	−	0.515203i
$326$	4.69907	+	8.13902i	0.260257	+	0.450779i
$327$	23.3428	+	2.37987i	1.29086	+	0.131607i
$328$	−1.40102	−	13.3298i	−0.0773582	−	0.736014i
$329$	−2.62054	−	24.9328i	−0.144475	−	1.37459i
$330$	−7.74942	−	15.5627i	−0.426591	−	0.856701i
$331$	−2.35991	+	22.4531i	−0.129713	+	1.23413i	0.715082	+	0.699041i	$0.246390\pi$
$331$	−2.35991	+	22.4531i	−0.129713	+	1.23413i	−0.844794	+	0.535091i	$0.820277\pi$
$332$	15.1947			0.833917
$333$	−1.43239	−	12.8566i	−0.0784945	−	0.704536i
$334$	11.9095	−	36.6536i	0.651658	−	2.00560i
$335$	−14.4818	−	22.9149i	−0.791226	−	1.25197i
$336$	0.727939	−	1.00852i	0.0397123	−	0.0550192i
$337$	2.22518	+	2.47131i	0.121213	+	0.134621i	0.800697	−	0.599070i	$-0.204463\pi$
$337$	2.22518	+	2.47131i	0.121213	+	0.134621i	−0.679484	+	0.733691i	$0.737796\pi$
$338$	−0.460669	−	0.511625i	−0.0250571	−	0.0278287i
$339$	−17.1512	+	23.7621i	−0.931527	+	1.29058i
$340$	6.12980	+	2.44031i	0.332435	+	0.132344i
$341$	−4.67454	+	14.3867i	−0.253140	+	0.779086i
$342$	−5.03330	+	3.70508i	−0.272170	+	0.200348i
$343$	−11.3327			−0.611909
$344$	−0.546866	+	5.20308i	−0.0294850	+	0.280531i
$345$	32.5594	−	4.84911i	1.75294	−	0.261067i
$346$	1.58191	+	15.0509i	0.0850442	+	0.809142i
$347$	1.44171	+	13.7170i	0.0773951	+	0.736365i	0.962557	+	0.271081i	$0.0873811\pi$
$347$	1.44171	+	13.7170i	0.0773951	+	0.736365i	−0.885162	+	0.465284i	$0.845952\pi$
$348$	42.2719	+	4.30975i	2.26601	+	0.231027i
$349$	−7.45084	−	12.9052i	−0.398834	−	0.690801i	0.594748	−	0.803912i	$-0.297252\pi$
$349$	−7.45084	−	12.9052i	−0.398834	−	0.690801i	−0.993582	+	0.113111i	$0.963918\pi$
$350$	37.1334	−	2.97753i	1.98486	−	0.159156i
$351$	−3.68051	+	18.1485i	−0.196451	+	0.968695i
$352$	−3.25781	−	10.0265i	−0.173642	−	0.534415i
$353$	−8.63336	−	3.84382i	−0.459508	−	0.204586i	0.163910	−	0.986475i	$-0.447589\pi$
$353$	−8.63336	−	3.84382i	−0.459508	−	0.204586i	−0.623417	+	0.781889i	$0.714256\pi$
$354$	11.5965	+	53.7328i	0.616346	+	2.85587i
$355$	−15.4939	−	15.8815i	−0.822328	−	0.842900i
$356$	20.5175	−	9.13498i	1.08743	−	0.484153i
$357$	−5.01247	+	0.542638i	−0.265288	+	0.0287195i
$358$	−2.62168	+	24.9436i	−0.138560	+	1.31831i
$359$	0.603190	−	1.85643i	0.0318351	−	0.0979785i	−0.933876	−	0.357596i	$-0.883596\pi$
$359$	0.603190	−	1.85643i	0.0318351	−	0.0979785i	0.965712	+	0.259618i	$0.0835965\pi$
$360$	−1.15825	+	19.7842i	−0.0610449	+	1.04272i
$361$	−5.61755	−	17.2890i	−0.295661	−	0.909950i
$362$	19.5913	−	4.16425i	1.02969	−	0.218868i
$363$	11.8275	−	3.88380i	0.620783	−	0.203847i
$364$	−37.1126	−	7.88852i	−1.94523	−	0.413471i
$365$	−1.60089	+	0.790938i	−0.0837944	+	0.0413996i
$366$	23.8640	−	7.83622i	1.24739	−	0.409606i
$367$	0.759966	−	7.23059i	0.0396699	−	0.377434i	−0.956618	−	0.291346i	$-0.905897\pi$
$367$	0.759966	−	7.23059i	0.0396699	−	0.377434i	0.996288	−	0.0860876i	$-0.0274365\pi$
$368$	−1.88330			−0.0981738
$369$	−12.4681	−	5.45826i	−0.649065	−	0.284146i
$370$	−17.3975	+	13.7359i	−0.904451	+	0.714093i
$371$	−21.7415	−	9.67994i	−1.12876	−	0.502557i
$372$	32.6662	−	29.5978i	1.69367	−	1.53457i
$373$	12.7293	+	2.70570i	0.659098	+	0.140096i	0.525305	−	0.850914i	$-0.323951\pi$
$373$	12.7293	+	2.70570i	0.659098	+	0.140096i	0.133793	+	0.991009i	$0.457284\pi$
$374$	2.01591	−	3.49165i	0.104240	−	0.180549i
$375$	−15.4543	+	11.6690i	−0.798054	+	0.602586i
$376$	−11.4267	−	19.7916i	−0.589287	−	1.02067i
$377$	−8.22403	−	25.3110i	−0.423559	−	1.30358i
$378$	−16.0765	−	35.2182i	−0.826886	−	1.81143i
$379$	0.718684	−	0.522154i	0.0369163	−	0.0268213i	−0.569174	−	0.822217i	$-0.692737\pi$
$379$	0.718684	−	0.522154i	0.0369163	−	0.0268213i	0.606090	+	0.795396i	$0.292737\pi$
$380$	6.18463	+	2.46214i	0.317265	+	0.126305i
$381$	−12.6014	+	7.32787i	−0.645587	+	0.375418i
$382$	11.5000	−	19.9186i	0.588391	−	1.01912i
$383$	17.1982	−	7.65712i	0.878785	−	0.391261i	0.0827928	−	0.996567i	$-0.473616\pi$
$383$	17.1982	−	7.65712i	0.878785	−	0.391261i	0.795993	+	0.605306i	$0.206949\pi$
$384$	−6.65505	+	31.7967i	−0.339614	+	1.62262i
$385$	0.915054	−	14.1205i	0.0466355	−	0.719645i
$386$	−8.20780	−	25.2610i	−0.417766	−	1.28575i
$387$	4.31743	+	3.09585i	0.219467	+	0.157371i
$388$	−4.81217	+	14.8103i	−0.244301	+	0.751881i
$389$	−21.7409	+	24.1457i	−1.10231	+	1.22423i	−0.129754	+	0.991546i	$0.541419\pi$
$389$	−21.7409	+	24.1457i	−1.10231	+	1.22423i	−0.972551	+	0.232688i	$0.925248\pi$
$390$	29.7271	−	11.0973i	1.50529	−	0.561932i
$391$	5.10819	+	5.67322i	0.258332	+	0.286907i
$392$	9.45468	−	4.20950i	0.477534	−	0.212612i
$393$	−14.8340	−	20.2840i	−0.748276	−	1.02319i
$394$	3.14390	−	29.9122i	0.158387	−	1.50696i
$395$	0.147509	−	0.524506i	0.00742197	−	0.0263907i
$396$	18.8474	+	3.88346i	0.947118	+	0.195151i
$397$	−15.9764	+	11.6075i	−0.801832	+	0.582565i	−0.911451	−	0.411409i	$-0.865037\pi$
$397$	−15.9764	+	11.6075i	−0.801832	+	0.582565i	0.109619	+	0.993974i	$0.465037\pi$
$398$	4.01010	−	4.45367i	0.201008	−	0.223242i
$399$	−5.05731	+	0.547492i	−0.253182	+	0.0274089i
$400$	0.972849	−	0.530072i	0.0486424	−	0.0265036i
$401$	5.22664	−	9.05280i	0.261006	−	0.452075i	−0.705504	−	0.708706i	$-0.749279\pi$
$401$	5.22664	−	9.05280i	0.261006	−	0.452075i	0.966509	+	0.256631i	$0.0826125\pi$
$402$	48.0225	+	4.89603i	2.39514	+	0.244192i
$403$	−25.2222	−	11.2297i	−1.25641	−	0.559389i
$404$	31.8558	−	23.1446i	1.58488	−	1.15149i
$405$	16.8792	+	10.9587i	0.838735	+	0.544540i
$406$	45.0127	+	32.7036i	2.23394	+	1.62305i
$407$	4.20985	+	7.29167i	0.208674	+	0.361435i
$408$	−3.97304	+	2.31038i	−0.196695	+	0.114381i
$409$	4.93192	+	5.47746i	0.243868	+	0.270843i	0.852636	−	0.522506i	$-0.175003\pi$
$409$	4.93192	+	5.47746i	0.243868	+	0.270843i	−0.608768	+	0.793348i	$0.708336\pi$
$410$	3.36353	+	23.0781i	0.166113	+	1.13975i
$411$	−4.27464	−	9.52101i	−0.210853	−	0.469637i
$412$	−7.08735	+	1.50646i	−0.349169	+	0.0742181i
$413$	−13.8255	+	42.5506i	−0.680309	+	2.09378i
$414$	−28.9926	+	50.9477i	−1.42491	+	2.50394i
$415$	−10.3344	+	0.413665i	−0.507294	+	0.0203060i
$416$	18.8211	−	4.00056i	0.922782	−	0.196143i
$417$	−0.0446125	−	14.3088i	−0.00218468	−	0.700703i
$418$	2.03394	−	3.52289i	0.0994833	−	0.172310i
$419$	−1.97295	+	0.878413i	−0.0963849	+	0.0429133i	−0.454363	−	0.890817i	$-0.650133\pi$
$419$	−1.97295	+	0.878413i	−0.0963849	+	0.0429133i	0.357978	+	0.933730i	$0.383466\pi$
$420$	−22.7758	+	34.3726i	−1.11135	+	1.67721i
$421$	28.8887	+	12.8621i	1.40795	+	0.626859i	0.963197	−	0.268796i	$-0.0866258\pi$
$421$	28.8887	+	12.8621i	1.40795	+	0.626859i	0.444750	+	0.895655i	$0.353292\pi$
$422$	−49.6380	+	36.0641i	−2.41634	+	1.75557i
$423$	−23.2064	+	0.144710i	−1.12834	+	0.00703602i
$424$	−21.6947			−1.05359
$425$	−4.23549	−	1.49285i	−0.205452	−	0.0724136i
$426$	39.2805	−	4.25241i	1.90315	−	0.206030i
$427$	19.9967	+	4.25042i	0.967706	+	0.205692i
$428$	1.58664	+	15.0958i	0.0766929	+	0.729685i
$429$	−2.54265	−	11.7815i	−0.122760	−	0.568815i
$430$	0.588695	−	9.08432i	0.0283894	−	0.438085i
$431$	14.4718	+	10.5144i	0.697081	+	0.506459i	0.878980	−	0.476858i	$-0.158225\pi$
$431$	14.4718	+	10.5144i	0.697081	+	0.506459i	−0.181899	+	0.983317i	$0.558225\pi$
$432$	−0.862787	−	0.762366i	−0.0415109	−	0.0366794i
$433$	26.2239	+	19.0528i	1.26024	+	0.915620i	0.998770	−	0.0495910i	$-0.0157918\pi$
$433$	26.2239	+	19.0528i	1.26024	+	0.915620i	0.261473	+	0.965211i	$0.415792\pi$
$434$	56.4590	−	12.0007i	2.71012	−	0.576053i
$435$	−28.8677	−	1.78036i	−1.38410	−	0.0853619i
$436$	43.5300	+	9.25258i	2.08471	+	0.443118i
$437$	5.15388	+	5.72397i	0.246544	+	0.273814i
$438$	0.651402	−	3.11229i	0.0311252	−	0.148711i
$439$	8.09745	−	8.99313i	0.386470	−	0.429219i	−0.518247	−	0.855231i	$-0.673415\pi$
$439$	8.09745	−	8.99313i	0.386470	−	0.429219i	0.904717	+	0.426012i	$0.140082\pi$
$440$	−4.47345	−	12.0984i	−0.213263	−	0.576767i
$441$	1.03335	−	10.4586i	0.0492071	−	0.498029i
$442$	5.95327	+	4.32530i	0.283168	+	0.205734i
$443$	−5.38308	−	9.32377i	−0.255758	−	0.442986i	0.709343	−	0.704863i	$-0.248992\pi$
$443$	−5.38308	−	9.32377i	−0.255758	−	0.442986i	−0.965101	+	0.261878i	$0.915658\pi$
$444$	−0.0764964	−	24.5350i	−0.00363036	−	1.16438i
$445$	−13.7059	+	6.77155i	−0.649721	+	0.321002i
$446$	−5.15796	−	49.0747i	−0.244236	−	2.32375i
$447$	−18.0504	−	5.80277i	−0.853754	−	0.274462i
$448$	−27.8780	+	30.9617i	−1.31711	+	1.46280i
$449$	−27.1471			−1.28115			−0.640575	−	0.767896i	$-0.721304\pi$
$449$	−27.1471			−1.28115			−0.640575	+	0.767896i	$0.721304\pi$
$450$	0.636899	−	34.4781i	0.0300237	−	1.62531i
$451$	8.85865			0.417138
$452$	−37.1914	+	41.3052i	−1.74934	+	1.94283i
$453$	−26.9607	+	24.4281i	−1.26672	+	1.14773i
$454$	1.26416	+	12.0277i	0.0593298	+	0.564486i
$455$	25.4561	+	4.35485i	1.19340	+	0.204159i
$456$	−4.00858	+	2.33105i	−0.187719	+	0.109161i
$457$	7.80737	+	13.5228i	0.365213	+	0.632568i	0.988810	−	0.149178i	$-0.0476627\pi$
$457$	7.80737	+	13.5228i	0.365213	+	0.632568i	−0.623597	+	0.781746i	$0.714329\pi$
$458$	−32.5468	−	23.6466i	−1.52081	−	1.10493i
$459$	0.0436527	+	4.66685i	0.00203753	+	0.217830i
$460$	62.3846	−	2.49714i	2.90870	−	0.116430i
$461$	5.02063	−	5.57598i	0.233834	−	0.259699i	−0.614795	−	0.788687i	$-0.710761\pi$
$461$	5.02063	−	5.57598i	0.233834	−	0.259699i	0.848630	+	0.528987i	$0.177428\pi$
$462$	18.7780	+	16.8021i	0.873631	+	0.781702i
$463$	−22.1504	−	24.6005i	−1.02941	−	1.14328i	−0.989567	−	0.144075i	$-0.953979\pi$
$463$	−22.1504	−	24.6005i	−1.02941	−	1.14328i	−0.0398480	−	0.999206i	$-0.512687\pi$
$464$	1.61853	+	0.344029i	0.0751384	+	0.0159712i
$465$	−21.4115	+	21.0196i	−0.992935	+	0.974762i
$466$	−22.1194	+	4.70162i	−1.02466	+	0.217798i
$467$	−2.65707	−	1.93048i	−0.122955	−	0.0893318i	0.524608	−	0.851344i	$-0.324212\pi$
$467$	−2.65707	−	1.93048i	−0.122955	−	0.0893318i	−0.647563	+	0.762012i	$0.724212\pi$
$468$	−10.6448	+	33.4699i	−0.492054	+	1.54715i
$469$	31.7849	+	23.0931i	1.46769	+	1.06634i
$470$	21.2442	+	33.6151i	0.979923	+	1.55055i
$471$	−10.7386	−	3.45221i	−0.494810	−	0.159069i
$472$	4.26313	+	40.5609i	0.196226	+	1.86697i
$473$	−3.38228	−	0.718926i	−0.155517	−	0.0330562i
$474$	0.572739	+	0.783161i	0.0263068	+	0.0359718i
$475$	−4.27338	−	1.50620i	−0.196076	−	0.0691092i
$476$	−9.56241			−0.438292
$477$	−10.8960	+	19.1471i	−0.498892	+	0.876686i
$478$	30.9967	−	22.5204i	1.41776	−	1.03006i
$479$	7.52723	+	3.35134i	0.343928	+	0.153127i	0.571430	−	0.820651i	$-0.306389\pi$
$479$	7.52723	+	3.35134i	0.343928	+	0.153127i	−0.227502	+	0.973778i	$0.573056\pi$
$480$	3.46181	−	20.6225i	0.158009	−	0.941285i
$481$	−14.0386	+	6.25039i	−0.640105	+	0.284993i
$482$	−25.4989	+	44.1655i	−1.16145	+	2.01168i
$483$	−41.2441	+	23.9840i	−1.87667	+	1.09131i
$484$	23.0950	−	4.90900i	1.04977	−	0.223136i
$485$	2.86970	−	10.2040i	0.130306	−	0.463338i
$486$	−33.9060	+	11.6041i	−1.53801	+	0.526374i
$487$	4.69938	−	14.4632i	0.212949	−	0.655391i	−0.786343	−	0.617790i	$-0.788028\pi$
$487$	4.69938	−	14.4632i	0.212949	−	0.655391i	0.999293	−	0.0376012i	$-0.0119716\pi$
$488$	18.2285	−	3.87460i	0.825167	−	0.175395i
$489$	7.04419	+	0.718176i	0.318549	+	0.0324771i
$490$	−16.1453	+	7.97677i	−0.729369	+	0.360354i
$491$	1.05842	+	1.17550i	0.0477660	+	0.0530495i	0.766554	−	0.642179i	$-0.221970\pi$
$491$	1.05842	+	1.17550i	0.0477660	+	0.0530495i	−0.718788	+	0.695229i	$0.755303\pi$
$492$	−22.3960	−	12.8374i	−1.00969	−	0.578754i
$493$	−3.35369	−	5.80876i	−0.151043	−	0.261613i
$494$	6.00653	+	4.36400i	0.270246	+	0.196345i
$495$	−12.9244	−	2.12815i	−0.580909	−	0.0956533i
$496$	1.38875	−	1.00899i	0.0623569	−	0.0453049i
$497$	29.3773	+	13.0796i	1.31775	+	0.586701i
$498$	10.7791	−	14.9338i	0.483022	−	0.669200i
$499$	−15.4879	+	26.8258i	−0.693333	+	1.20089i	0.277407	+	0.960753i	$0.410525\pi$
$499$	−15.4879	+	26.8258i	−0.693333	+	1.20089i	−0.970739	+	0.240135i	$0.922808\pi$
$500$	−31.5229	+	18.8486i	−1.40975	+	0.842937i
$501$	−17.1404	−	23.4378i	−0.765778	−	1.04712i
$502$	−11.7463	+	13.0456i	−0.524262	+	0.582251i
$503$	24.3048	−	17.6585i	1.08370	−	0.787354i	0.105375	−	0.994433i	$-0.466396\pi$
$503$	24.3048	−	17.6585i	1.08370	−	0.787354i	0.978324	+	0.207079i	$0.0663957\pi$
$504$	−9.04620	−	27.2617i	−0.402950	−	1.21433i
$505$	−21.0360	+	16.6086i	−0.936088	+	0.739072i
$506$	3.98812	−	37.9444i	0.177294	−	1.68684i
$507$	−0.515683	+	0.0558266i	−0.0229023	+	0.00247935i
$508$	−25.2573	+	11.2453i	−1.12061	+	0.498928i
$509$	13.6021	+	15.1067i	0.602903	+	0.669592i	0.964909	−	0.262584i	$-0.0845747\pi$
$509$	13.6021	+	15.1067i	0.602903	+	0.669592i	−0.362006	+	0.932176i	$0.617908\pi$
$510$	6.74687	−	4.29341i	0.298756	−	0.190115i
$511$	1.73171	−	1.92326i	0.0766062	−	0.0850799i
$512$	−0.774259	+	2.38292i	−0.0342177	+	0.105311i
$513$	0.0440432	+	4.70860i	0.00194455	+	0.207890i
$514$	5.60810	+	17.2599i	0.247363	+	0.761304i
$515$	4.77931	−	1.21754i	0.210601	−	0.0536512i
$516$	7.50908	+	6.71893i	0.330569	+	0.295784i
$517$	13.7987	−	6.14360i	0.606868	−	0.270195i
$518$	16.0634	−	27.8227i	0.705787	−	1.22246i
$519$	9.89220	+	5.67022i	0.434219	+	0.248895i
$520$	22.8137	−	5.81185i	1.00045	−	0.254867i
$521$	−14.7886	+	10.7445i	−0.647898	+	0.470726i	−0.862555	−	0.505964i	$-0.831137\pi$
$521$	−14.7886	+	10.7445i	−0.647898	+	0.470726i	0.214656	+	0.976690i	$0.431137\pi$
$522$	34.2234	−	38.4889i	1.49792	−	1.68461i
$523$	0.681075	+	2.09613i	0.0297813	+	0.0916575i	0.964842	−	0.262829i	$-0.0846556\pi$
$523$	0.681075	+	2.09613i	0.0297813	+	0.0916575i	−0.935061	+	0.354487i	$0.884656\pi$
$524$	−23.8307	−	41.2760i	−1.04105	−	1.80315i
$525$	14.5548	−	23.9979i	0.635222	−	1.04735i
$526$	10.6950	−	18.5243i	0.466323	−	0.807696i
$527$	−6.80626	−	1.44671i	−0.296485	−	0.0630199i
$528$	0.713416	+	0.229346i	0.0310475	+	0.00998102i
$529$	44.9847	+	20.0285i	1.95586	+	0.870804i
$530$	37.7191	−	1.50983i	1.63842	−	0.0655827i
$531$	37.9390	+	16.6088i	1.64641	+	0.720762i
$532$	−9.64795			−0.418292
$533$	−1.69005	+	16.0798i	−0.0732042	+	0.696491i
$534$	5.57692	−	26.6456i	0.241337	−	1.15307i
$535$	−1.49009	−	10.2239i	−0.0644223	−	0.442019i
$536$	35.0318	+	7.44624i	1.51314	+	0.321629i
$537$	14.0822	+	12.6004i	0.607690	+	0.543746i
$538$	34.4220	−	7.31662i	1.48404	−	0.315442i
$539$	2.11377	+	6.50552i	0.0910465	+	0.280212i
$540$	29.5908	+	24.1095i	1.27339	+	1.03751i
$541$	0.946056	−	2.91166i	0.0406741	−	0.125182i	−0.928658	−	0.370938i	$-0.879036\pi$
$541$	0.946056	−	2.91166i	0.0406741	−	0.125182i	0.969332	+	0.245756i	$0.0790362\pi$
$542$	−1.84219	+	17.5273i	−0.0791289	+	0.752861i
$543$	6.09470	−	13.8046i	0.261549	−	0.592412i
$544$	4.43019	−	1.97245i	0.189943	−	0.0845679i
$545$	−29.8579	−	5.10788i	−1.27897	−	0.218797i
$546$	−34.0807	+	30.8793i	−1.45852	+	1.32151i
$547$	4.66778	+	2.07823i	0.199580	+	0.0888586i	0.504093	−	0.863650i	$-0.331827\pi$
$547$	4.66778	+	2.07823i	0.199580	+	0.0888586i	−0.304513	+	0.952508i	$0.598494\pi$
$548$	−6.11682	−	18.8256i	−0.261297	−	0.804191i
$549$	5.73551	−	18.0339i	0.244786	−	0.769670i
$550$	8.61967	+	20.7233i	0.367544	+	0.883644i
$551$	−3.38369	−	5.86072i	−0.144150	−	0.249675i
$552$	−25.4542	+	35.2654i	−1.08340	+	1.50099i
$553$	0.0825447	+	0.785361i	0.00351016	+	0.0333969i
$554$	−0.124050	−	1.18026i	−0.00527039	−	0.0501444i
$555$	0.719978	+	16.6849i	0.0305614	+	0.708236i
$556$	2.83677	−	26.9900i	0.120306	−	1.14463i
$557$	23.7393			1.00587			0.502934	−	0.864325i	$-0.332254\pi$
$557$	23.7393			1.00587			0.502934	+	0.864325i	$0.332254\pi$
$558$	−5.91625	−	53.1020i	−0.250455	−	2.24799i
$559$	1.95023	−	6.00218i	0.0824858	−	0.253865i
$560$	−1.02585	+	1.23530i	−0.0433501	+	0.0522011i
$561$	−1.24416	−	2.77115i	−0.0525286	−	0.116998i
$562$	4.04857	+	4.49640i	0.170779	+	0.189669i
$563$	13.0121	+	14.4514i	0.548394	+	0.609054i	0.952082	−	0.305843i	$-0.0989384\pi$
$563$	13.0121	+	14.4514i	0.548394	+	0.609054i	−0.403687	+	0.914897i	$0.632272\pi$
$564$	−43.7881	−	4.46433i	−1.84381	−	0.187982i
$565$	24.1705	−	29.1054i	1.01686	−	1.22447i
$566$	21.7810	−	67.0350i	0.915524	−	2.81769i
$567$	−28.6038	−	5.70804i	−1.20125	−	0.239715i
$568$	29.3141			1.22999
$569$	0.0692037	−	0.658430i	0.00290117	−	0.0276028i	−0.992976	−	0.118320i	$-0.962249\pi$
$569$	0.0692037	−	0.658430i	0.00290117	−	0.0276028i	0.995877	+	0.0907170i	$0.0289159\pi$
$570$	6.80723	−	4.33182i	0.285123	−	0.181440i
$571$	−1.92300	−	18.2961i	−0.0804749	−	0.765668i	−0.958122	−	0.286360i	$-0.907555\pi$
$571$	−1.92300	−	18.2961i	−0.0804749	−	0.765668i	0.877647	−	0.479307i	$-0.159112\pi$
$572$	−2.38949	−	22.7344i	−0.0999094	−	0.950575i
$573$	−7.09749	−	15.8084i	−0.296502	−	0.660405i
$574$	−16.9009	−	29.2732i	−0.705430	−	1.22184i
$575$	−42.3617	+	3.39676i	−1.76660	+	0.141655i
$576$	25.9844	+	28.4992i	1.08268	+	1.18747i
$577$	−2.40887	−	7.41374i	−0.100283	−	0.308638i	0.888312	−	0.459241i	$-0.151878\pi$
$577$	−2.40887	−	7.41374i	−0.100283	−	0.308638i	−0.988594	+	0.150603i	$0.951878\pi$
$578$	−34.0087	−	15.1417i	−1.41458	−	0.629810i
$579$	−19.0512	−	6.12452i	−0.791742	−	0.254526i
$580$	−54.0702	−	9.24995i	−2.24514	−	0.384083i
$581$	13.6942	−	6.09705i	0.568131	−	0.252948i
$582$	11.1423	+	15.2360i	0.461864	+	0.631551i
$583$	1.49881	−	14.2602i	0.0620744	−	0.590599i
$584$	0.729022	−	2.24370i	0.0301671	−	0.0928449i
$585$	6.32862	−	23.0537i	0.261656	−	0.953153i
$586$	20.8302	+	64.1087i	0.860487	+	2.64831i
$587$	−14.2893	+	3.03728i	−0.589782	+	0.125362i	−0.493129	−	0.869956i	$-0.664147\pi$
$587$	−14.2893	+	3.03728i	−0.589782	+	0.125362i	−0.0966531	+	0.995318i	$0.530814\pi$
$588$	4.08345	−	19.5100i	0.168399	−	0.804581i
$589$	−6.86714	−	1.45966i	−0.282956	−	0.0601441i
$590$	−10.2348	−	70.2239i	−0.421361	−	2.89107i
$591$	−16.8872	−	15.1103i	−0.694647	−	0.621553i
$592$	0.0998717	−	0.950216i	0.00410470	−	0.0390536i
$593$	−17.7208			−0.727707			−0.363853	−	0.931456i	$-0.618539\pi$
$593$	−17.7208			−0.727707			−0.363853	+	0.931456i	$0.618539\pi$
$594$	17.1871	−	15.7689i	0.705195	−	0.647006i
$595$	6.50368	−	0.260330i	0.266625	−	0.0106725i
$596$	−32.8517	−	14.6265i	−1.34566	−	0.599125i
$597$	−0.952534	−	4.41361i	−0.0389846	−	0.180637i
$598$	68.1139	+	14.4781i	2.78538	+	0.592052i
$599$	7.37178	−	12.7683i	0.301203	−	0.521699i	−0.675206	−	0.737629i	$-0.735945\pi$
$599$	7.37178	−	12.7683i	0.301203	−	0.521699i	0.976409	+	0.215931i	$0.0692785\pi$
$600$	3.22301	−	25.3812i	0.131579	−	1.03618i
$601$	6.78135	+	11.7456i	0.276617	+	0.479115i	0.970542	−	0.240933i	$-0.0774533\pi$
$601$	6.78135	+	11.7456i	0.276617	+	0.479115i	−0.693925	+	0.720048i	$0.744120\pi$
$602$	4.07718	+	12.5483i	0.166173	+	0.511429i
$603$	24.1662	−	27.1782i	0.984125	−	1.10678i
$604$	−55.8242	+	40.5587i	−2.27146	+	1.65031i
$605$	−15.5740	+	3.96751i	−0.633172	+	0.161302i
$606$	−0.148807	−	47.7276i	−0.00604487	−	1.93880i
$607$	−16.6848	+	28.8989i	−0.677216	+	1.17297i	0.298600	+	0.954378i	$0.403480\pi$
$607$	−16.6848	+	28.8989i	−0.677216	+	1.17297i	−0.975816	+	0.218594i	$0.929853\pi$
$608$	4.46982	−	1.99009i	0.181275	−	0.0807088i
$609$	39.8269	−	13.0780i	1.61387	−	0.529946i
$610$	−31.4231	+	8.00511i	−1.27228	+	0.324117i
$611$	8.51901	+	26.2188i	0.344642	+	1.06070i
$612$	−0.870346	+	8.80884i	−0.0351816	+	0.356076i
$613$	5.32757	−	16.3966i	0.215178	−	0.662251i	−0.783962	−	0.620808i	$-0.786805\pi$
$613$	5.32757	−	16.3966i	0.215178	−	0.662251i	0.999141	−	0.0414429i	$-0.0131955\pi$
$614$	14.3909	−	15.9827i	0.580771	−	0.645011i
$615$	15.5817	+	8.12137i	0.628313	+	0.327485i
$616$	12.5095	+	13.8932i	0.504022	+	0.559773i
$617$	22.8977	−	10.1947i	0.921827	−	0.410424i	0.109740	−	0.993960i	$-0.464998\pi$
$617$	22.8977	−	10.1947i	0.921827	−	0.410424i	0.812087	+	0.583537i	$0.198332\pi$
$618$	−3.54715	+	8.03435i	−0.142687	+	0.323189i
$619$	−1.63152	+	15.5229i	−0.0655762	+	0.623916i	0.911540	+	0.411211i	$0.134894\pi$
$619$	−1.63152	+	15.5229i	−0.0655762	+	0.623916i	−0.977116	+	0.212705i	$0.931773\pi$
$620$	−44.6648	+	35.2643i	−1.79378	+	1.41625i
$621$	18.3400	+	40.1768i	0.735961	+	1.61224i
$622$	−38.3639	+	27.8730i	−1.53825	+	1.11761i
$623$	14.8259	−	16.4658i	0.593986	−	0.659688i
$624$	−0.552403	+	1.25120i	−0.0221138	+	0.0500881i
$625$	20.9265	−	13.6777i	0.837062	−	0.547109i
$626$	−23.4926	+	40.6903i	−0.938952	+	1.62631i
$627$	−1.25529	−	2.79594i	−0.0501316	−	0.111659i
$628$	−19.5443	−	8.70167i	−0.779902	−	0.347235i
$629$	−3.13330	+	2.27647i	−0.124933	+	0.0907690i
$630$	17.6253	+	46.7686i	0.702209	+	1.86331i
$631$	−4.14912	−	3.01451i	−0.165174	−	0.120006i	0.502128	−	0.864793i	$-0.332551\pi$
$631$	−4.14912	−	3.01451i	−0.165174	−	0.120006i	−0.667301	+	0.744788i	$0.732551\pi$
$632$	0.359931	+	0.623419i	0.0143173	+	0.0247983i
$633$	0.144127	+	46.2264i	0.00572852	+	1.83733i
$634$	−0.134640	−	0.149533i	−0.00534724	−	0.00593872i
$635$	16.8721	−	8.33585i	0.669548	−	0.330798i
$636$	−24.4542	+	33.8800i	−0.969673	+	1.34343i
$637$	−12.2117	+	2.59568i	−0.483846	+	0.102845i
$638$	−10.3589	+	31.8814i	−0.410112	+	1.26220i
$639$	14.7227	−	25.8717i	0.582421	−	1.02347i
$640$	11.3541	−	40.3726i	0.448812	−	1.59587i
$641$	−2.92267	+	0.621233i	−0.115439	+	0.0245372i	−0.265269	−	0.964175i	$-0.585461\pi$
$641$	−2.92267	+	0.621233i	−0.115439	+	0.0245372i	0.149830	+	0.988712i	$0.452127\pi$
$642$	15.9622	+	9.14955i	0.629978	+	0.361104i
$643$	−14.7308	+	25.5144i	−0.580925	+	1.00619i	0.414445	+	0.910074i	$0.363976\pi$
$643$	−14.7308	+	25.5144i	−0.580925	+	1.00619i	−0.995370	+	0.0961173i	$0.969358\pi$
$644$	−82.6667	+	36.8056i	−3.25752	+	1.45034i
$645$	−5.29007	−	4.36532i	−0.208296	−	0.171884i
$646$	1.70941	+	0.761078i	0.0672558	+	0.0299442i
$647$	18.7975	−	13.6572i	0.739005	−	0.536919i	−0.153394	−	0.988165i	$-0.549020\pi$
$647$	18.7975	−	13.6572i	0.739005	−	0.536919i	0.892399	+	0.451246i	$0.149020\pi$
$648$	−25.9367	+	5.85202i	−1.01889	+	0.229889i
$649$	−26.9558			−1.05811
$650$	−39.2603	+	11.6924i	−1.53992	+	0.458613i
$651$	17.5640	−	39.7827i	0.688386	−	1.55921i
$652$	13.1361	+	2.79216i	0.514449	+	0.109349i
$653$	−0.136446	−	1.29820i	−0.00533956	−	0.0508025i	0.991528	−	0.129896i	$-0.0414642\pi$
$653$	−0.136446	−	1.29820i	−0.00533956	−	0.0508025i	−0.996867	+	0.0790931i	$0.974798\pi$
$654$	39.9738	−	36.2188i	1.56310	−	1.41627i
$655$	17.3317	+	27.4243i	0.677205	+	1.07155i
$656$	−0.813274	−	0.590878i	−0.0317530	−	0.0230699i
$657$	−1.61408	−	1.77029i	−0.0629712	−	0.0690656i
$658$	−46.6272	−	33.8767i	−1.81772	−	1.32065i
$659$	21.2157	−	4.50954i	0.826447	−	0.175667i	0.224776	−	0.974411i	$-0.427835\pi$
$659$	21.2157	−	4.50954i	0.826447	−	0.175667i	0.601671	+	0.798744i	$0.294502\pi$
$660$	−23.9361	−	6.65119i	−0.931712	−	0.258897i
$661$	5.58421	+	1.18696i	0.217201	+	0.0461674i	0.315227	−	0.949016i	$-0.397920\pi$
$661$	5.58421	+	1.18696i	0.217201	+	0.0461674i	−0.0980260	+	0.995184i	$0.531253\pi$
$662$	34.7295	+	38.5710i	1.34980	+	1.49910i
$663$	5.26741	−	1.72966i	0.204569	−	0.0671744i
$664$	9.14349	−	10.1549i	0.354836	−	0.394085i
$665$	6.56186	−	0.262659i	0.254458	−	0.0101855i
$666$	−24.1681	−	17.3299i	−0.936494	−	0.671521i
$667$	−51.3504	−	37.3082i	−1.98830	−	1.44458i
$668$	−27.5360	−	47.6937i	−1.06540	−	1.84533i
$669$	−32.2543	−	18.4882i	−1.24702	−	0.714795i
$670$	−61.4257	−	10.5083i	−2.37308	−	0.405970i
$671$	1.28748	+	12.2496i	0.0497026	+	0.472889i
$672$	6.39370	+	29.6255i	0.246642	+	1.14283i
$673$	−2.27945	+	2.53159i	−0.0878664	+	0.0975855i	−0.785474	−	0.618894i	$-0.787581\pi$
$673$	−2.27945	+	2.53159i	−0.0878664	+	0.0975855i	0.697608	+	0.716480i	$0.254248\pi$
$674$	7.64505			0.294476
$675$	−20.7820	−	15.5920i	−0.799898	−	0.600136i
$676$	−0.983780			−0.0378377
$677$	−25.2631	+	28.0575i	−0.970939	+	1.07834i	0.0259612	+	0.999663i	$0.491735\pi$
$677$	−25.2631	+	28.0575i	−0.970939	+	1.07834i	−0.996900	+	0.0786743i	$0.974931\pi$
$678$	14.2126	+	65.8547i	0.545831	+	2.52913i
$679$	1.60586	+	15.2787i	0.0616273	+	0.586345i
$680$	5.31954	−	2.62818i	0.203995	−	0.100786i
$681$	7.90517	+	4.53125i	0.302927	+	0.173638i
$682$	17.3881	+	30.1170i	0.665824	+	1.15324i
$683$	10.4985	+	7.62763i	0.401715	+	0.291863i	0.770239	−	0.637755i	$-0.220137\pi$
$683$	10.4985	+	7.62763i	0.401715	+	0.291863i	−0.368524	+	0.929618i	$0.620137\pi$
$684$	−0.878132	+	8.88764i	−0.0335762	+	0.339827i
$685$	4.67274	+	12.6373i	0.178536	+	0.482848i
$686$	−17.4329	+	19.3612i	−0.665593	+	0.739216i
$687$	−28.7972	+	9.45613i	−1.09868	+	0.360774i
$688$	0.262559	+	0.291602i	0.0100100	+	0.0111172i
$689$	25.5985	+	5.44112i	0.975224	+	0.207290i
$690$	41.8012	−	63.0850i	1.59135	−	2.40161i
$691$	−47.5179	+	10.1002i	−1.80767	+	0.384232i	−0.983325	−	0.181859i	$-0.941788\pi$
$691$	−47.5179	+	10.1002i	−1.80767	+	0.384232i	−0.824343	+	0.566091i	$0.808455\pi$
$692$	17.4955	+	12.7112i	0.665078	+	0.483208i
$693$	18.5445	−	4.06278i	0.704447	−	0.154332i
$694$	25.6523	+	18.6375i	0.973749	+	0.707470i
$695$	−1.19458	+	18.4339i	−0.0453131	+	0.699239i
$696$	28.3177	−	25.6577i	1.07338	−	0.972551i
$697$	0.425941	+	4.05256i	0.0161337	+	0.153502i
$698$	−33.5093	−	7.12262i	−1.26835	−	0.269595i
$699$	−6.88118	+	15.5860i	−0.260270	+	0.589516i
$700$	32.3435	−	42.2798i	1.22247	−	1.59803i
$701$	32.6872			1.23458			0.617290	−	0.786736i	$-0.288231\pi$
$701$	32.6872			1.23458			0.617290	+	0.786736i	$0.288231\pi$
$702$	25.3439	+	34.2055i	0.956545	+	1.29100i
$703$	−3.16133	+	2.29684i	−0.119232	+	0.0866269i
$704$	−22.9316	−	10.2098i	−0.864268	−	0.384797i
$705$	29.9032	+	1.84422i	1.12622	+	0.0694574i
$706$	−19.8475	+	8.83667i	−0.746970	+	0.332573i
$707$	19.4230	−	33.6416i	0.730476	−	1.26522i
$708$	68.1482	+	39.0626i	2.56117	+	1.46806i
$709$	−9.83705	+	2.09093i	−0.369438	+	0.0785265i	−0.388890	−	0.921284i	$-0.627141\pi$
$709$	−9.83705	+	2.09093i	−0.369438	+	0.0785265i	0.0194515	+	0.999811i	$0.493808\pi$
$710$	−50.9664	+	2.04009i	−1.91274	+	0.0765633i
$711$	0.730983	−	0.00455822i	0.0274140	−	0.000170947i
$712$	6.24146	−	19.2092i	0.233909	−	0.719897i
$713$	−64.4083	+	13.6904i	−2.41211	+	0.512709i
$714$	−6.78355	+	9.39823i	−0.253868	+	0.351720i
$715$	2.24409	+	15.3973i	0.0839243	+	0.575827i
$716$	23.9815	+	26.6342i	0.896231	+	0.995365i
$717$	−0.0900006	−	28.8663i	−0.00336113	−	1.07803i
$718$	−2.24371	−	3.88622i	−0.0837346	−	0.145033i
$719$	−1.59555	−	1.15923i	−0.0595039	−	0.0432321i	0.557636	−	0.830086i	$-0.311709\pi$
$719$	−1.59555	−	1.15923i	−0.0595039	−	0.0432321i	−0.617140	+	0.786854i	$0.711709\pi$
$720$	1.04458	+	1.05744i	0.0389293	+	0.0394086i
$721$	−5.78298	+	4.20158i	−0.215370	+	0.156475i
$722$	−38.1787	−	16.9982i	−1.42086	−	0.632609i
$723$	15.7373	+	35.0519i	0.585275	+	1.30360i
$724$	14.3103	−	24.7861i	0.531837	−	0.921169i
$725$	37.0266	+	4.81914i	1.37513	+	0.178978i
$726$	11.5588	−	26.1810i	0.428989	−	0.971667i
$727$	4.42436	−	4.91374i	0.164090	−	0.182241i	−0.655492	−	0.755202i	$-0.727539\pi$
$727$	4.42436	−	4.91374i	0.164090	−	0.182241i	0.819582	+	0.572961i	$0.194205\pi$
$728$	−27.6047	+	20.0560i	−1.02310	+	0.743326i
$729$	−7.86166	+	25.8301i	−0.291173	+	0.956671i
$730$	−1.11135	+	3.95171i	−0.0411330	+	0.146259i
$731$	0.166260	−	1.58186i	0.00614934	−	0.0585071i
$732$	14.4963	−	32.8344i	0.535800	−	1.21359i
$733$	12.7008	−	5.65477i	0.469116	−	0.208864i	−0.158543	−	0.987352i	$-0.550680\pi$
$733$	12.7008	−	5.65477i	0.469116	−	0.208864i	0.627659	+	0.778488i	$0.284013\pi$
$734$	−11.1840	−	12.4211i	−0.412808	−	0.458470i
$735$	−2.24613	+	13.3805i	−0.0828497	+	0.493548i
$736$	30.7069	−	34.1035i	1.13187	−	1.25707i
$737$	−7.31475	+	22.5125i	−0.269442	+	0.829258i
$738$	−28.5046	+	12.9047i	−1.04927	+	0.475027i
$739$	−0.707775	−	2.17831i	−0.0260359	−	0.0801304i	0.937194	−	0.348808i	$-0.113413\pi$
$739$	−0.707775	−	2.17831i	−0.0260359	−	0.0801304i	−0.963230	+	0.268677i	$0.913413\pi$
$740$	−2.04834	+	31.6085i	−0.0752984	+	1.16195i
$741$	5.31453	−	1.74513i	0.195234	−	0.0641090i
$742$	−49.9822	+	22.2535i	−1.83490	+	0.816951i
$743$	−12.7978	+	22.1664i	−0.469506	+	0.813207i	−0.999392	−	0.0348611i	$-0.988901\pi$
$743$	−12.7978	+	22.1664i	−0.469506	+	0.813207i	0.529887	+	0.848068i	$0.322234\pi$
$744$	−0.123598	−	39.6420i	−0.00453131	−	1.45335i
$745$	22.7416	+	9.05356i	0.833188	+	0.331697i
$746$	24.2038	−	17.5851i	0.886164	−	0.643836i
$747$	−4.37016	−	13.1700i	−0.159896	−	0.481864i
$748$	−1.78034	−	5.47932i	−0.0650956	−	0.200344i
$749$	7.48734	+	12.9684i	0.273581	+	0.473857i
$750$	−3.83724	+	44.3529i	−0.140116	+	1.61954i
$751$	18.1894	−	31.5050i	0.663742	−	1.14963i	−0.315883	−	0.948798i	$-0.602301\pi$
$751$	18.1894	−	31.5050i	0.663742	−	1.14963i	0.979625	−	0.200836i	$-0.0643660\pi$
$752$	−1.67658	−	0.356369i	−0.0611387	−	0.0129954i
$753$	2.79013	+	12.9282i	0.101678	+	0.471130i
$754$	−55.8931	−	24.8852i	−2.03551	−	0.906266i
$755$	36.8635	−	29.1049i	1.34160	−	1.05924i
$756$	−52.7707	−	16.6022i	−1.91925	−	0.603816i
$757$	35.2024			1.27945			0.639727	−	0.768602i	$-0.279048\pi$
$757$	35.2024			1.27945			0.639727	+	0.768602i	$0.279048\pi$
$758$	0.213472	−	2.03105i	0.00775364	−	0.0737710i
$759$	−21.4219	−	19.1677i	−0.777565	−	0.695745i
$760$	5.36713	−	2.65169i	0.194686	−	0.0961870i
$761$	21.9059	+	4.65623i	0.794087	+	0.168788i	0.587056	−	0.809546i	$-0.300287\pi$
$761$	21.9059	+	4.65623i	0.794087	+	0.168788i	0.207031	+	0.978334i	$0.433620\pi$
$762$	−6.86525	+	32.8010i	−0.248702	+	1.18825i
$763$	42.9440	−	9.12804i	1.55468	−	0.330457i
$764$	−10.1562	−	31.2575i	−0.367438	−	1.13086i
$765$	0.352133	−	6.01485i	0.0127314	−	0.217467i
$766$	13.3740	−	41.1608i	0.483221	−	1.48720i
$767$	5.14262	−	48.9287i	0.185689	−	1.76671i
$768$	17.7973	+	24.3359i	0.642204	+	0.878147i
$769$	6.82840	−	3.04020i	0.246238	−	0.109632i	−0.279907	−	0.960027i	$-0.590304\pi$
$769$	6.82840	−	3.04020i	0.246238	−	0.109632i	0.526145	+	0.850395i	$0.323637\pi$
$770$	−22.7163	−	23.2846i	−0.818639	−	0.839118i
$771$	13.0170	+	4.18467i	0.468797	+	0.150707i
$772$	−34.6732	−	15.4375i	−1.24792	−	0.555608i
$773$	−5.32348	−	16.3840i	−0.191472	−	0.589291i	−1.00000		0.000832682i	$-0.999735\pi$
$773$	−5.32348	−	16.3840i	−0.191472	−	0.589291i	0.808527	−	0.588459i	$-0.200265\pi$
$774$	11.9305	−	2.61377i	0.428833	−	0.0939498i
$775$	29.4178	−	25.2003i	1.05672	−	0.905221i
$776$	7.00225	+	12.1283i	0.251366	+	0.435379i
$777$	−9.91392	−	22.0815i	−0.355660	−	0.792169i
$778$	7.80775	+	74.2858i	0.279922	+	2.66328i
$779$	0.429752	+	4.08882i	0.0153975	+	0.146497i
$780$	16.6394	−	42.1787i	0.595786	−	1.51024i
$781$	−2.02521	+	19.2685i	−0.0724676	+	0.689483i
$782$	17.5502			0.627593
$783$	−8.42241	−	37.8787i	−0.300992	−	1.35367i
$784$	0.239866	−	0.738233i	0.00856666	−	0.0263655i
$785$	13.5295	+	5.38619i	0.482890	+	0.192241i
$786$	−57.4728	−	5.85952i	−2.04999	−	0.209002i
$787$	−0.344436	−	0.382535i	−0.0122778	−	0.0136359i	0.736975	−	0.675920i	$-0.236254\pi$
$787$	−0.344436	−	0.382535i	−0.0122778	−	0.0136359i	−0.749252	+	0.662284i	$0.769587\pi$
$788$	−28.7584	−	31.9395i	−1.02448	−	1.13780i
$789$	−6.60065	−	14.7018i	−0.234989	−	0.523397i
$790$	−0.669175	−	1.05885i	−0.0238082	−	0.0376721i
$791$	−16.9445	+	52.1498i	−0.602477	+	1.85423i
$792$	13.9369	−	10.2591i	0.495227	−	0.364543i
$793$	−22.4804			−0.798302
$794$	−4.74549	+	45.1503i	−0.168411	+	1.60233i
$795$	15.7097	−	23.7085i	0.557165	−	0.840855i
$796$	−0.895157	−	8.51685i	−0.0317280	−	0.301872i
$797$	−0.835956	−	7.95359i	−0.0296111	−	0.281731i	−0.999301	−	0.0373908i	$-0.988095\pi$
$797$	−0.835956	−	7.95359i	−0.0296111	−	0.281731i	0.969690	−	0.244340i	$-0.0785713\pi$
$798$	−6.84423	+	9.48230i	−0.242283	+	0.335670i
$799$	3.47398	+	6.01711i	0.122901	+	0.212870i
$800$	−6.26341	+	26.2594i	−0.221445	+	0.928411i
$801$	−13.8188	−	15.1562i	−0.488263	−	0.535517i
$802$	−7.42609	−	22.8552i	−0.262224	−	0.807044i
$803$	1.42445	+	0.634206i	0.0502677	+	0.0223806i
$804$	51.1164	−	46.3148i	1.80274	−	1.63340i
$805$	55.2221	−	27.2831i	1.94632	−	0.961604i
$806$	−57.9842	+	25.8162i	−2.04240	+	0.909337i
$807$	10.7084	−	24.2548i	0.376955	−	0.853808i
$808$	3.70147	−	35.2172i	0.130217	−	1.23894i
$809$	−1.50879	+	4.64358i	−0.0530463	+	0.163260i	−0.974070	−	0.226247i	$-0.927354\pi$
$809$	−1.50879	+	4.64358i	−0.0530463	+	0.163260i	0.921024	+	0.389506i	$0.127354\pi$
$810$	44.6872	−	11.9796i	1.57015	−	0.420919i
$811$	−13.8925	−	42.7567i	−0.487832	−	1.50139i	−0.827838	−	0.560968i	$-0.810429\pi$
$811$	−13.8925	−	42.7567i	−0.487832	−	1.50139i	0.340006	−	0.940423i	$-0.389571\pi$
$812$	77.7682	−	16.5301i	2.72913	−	0.580094i
$813$	9.89519	+	8.85396i	0.347039	+	0.310522i
$814$	18.9333	+	4.02440i	0.663612	+	0.141055i
$815$	−9.01026	−	1.54141i	−0.315616	−	0.0539933i
$816$	−0.0706165	+	0.337394i	−0.00247207	+	0.0118111i
$817$	0.167747	−	1.59601i	0.00586873	−	0.0558373i
$818$	16.9446			0.592454
$819$	3.83663	+	34.4361i	0.134063	+	1.20329i
$820$	27.7233	+	18.4946i	0.968139	+	0.645858i
$821$	48.5944	+	21.6356i	1.69595	+	0.755088i	0.999289	+	0.0376913i	$0.0120004\pi$
$821$	48.5944	+	21.6356i	1.69595	+	0.755088i	0.696665	+	0.717396i	$0.254666\pi$
$822$	−22.8417	−	7.34305i	−0.796694	−	0.256118i
$823$	−48.5319	−	10.3158i	−1.69171	−	0.359585i	−0.741445	−	0.671014i	$-0.765859\pi$
$823$	−48.5319	−	10.3158i	−1.69171	−	0.359585i	−0.950269	+	0.311429i	$0.899192\pi$
$824$	−3.25806	+	5.64312i	−0.113500	+	0.196588i
$825$	16.4607	+	3.87203i	0.573090	+	0.134807i
$826$	51.4274	+	89.0749i	1.78939	+	3.09931i
$827$	−3.93599	−	12.1137i	−0.136868	−	0.421236i	0.859008	−	0.511962i	$-0.171081\pi$
$827$	−3.93599	−	12.1137i	−0.136868	−	0.421236i	−0.995876	+	0.0907261i	$0.971081\pi$
$828$	26.3810	+	79.5021i	0.916803	+	2.76289i
$829$	−42.5264	+	30.8972i	−1.47700	+	1.07310i	−0.498494	+	0.866893i	$0.666113\pi$
$829$	−42.5264	+	30.8972i	−1.47700	+	1.07310i	−0.978507	+	0.206211i	$0.933887\pi$
$830$	−15.1905	+	18.2919i	−0.527269	+	0.634923i
$831$	−0.775724	−	0.444645i	−0.0269096	−	0.0154246i
$832$	22.9072	−	39.6764i	0.794164	−	1.37553i
$833$	−2.87444	+	1.27978i	−0.0995935	+	0.0443419i
$834$	−24.5142	−	21.9347i	−0.848859	−	0.759537i
$835$	20.0265	+	31.6883i	0.693045	+	1.09662i
$836$	−1.79627	−	5.52834i	−0.0621251	−	0.191202i
$837$	−35.0490	−	19.8008i	−1.21147	−	0.684414i
$838$	−1.53424	+	4.72191i	−0.0529995	+	0.163116i
$839$	−25.1976	+	27.9848i	−0.869919	+	0.966142i	−0.999677	−	0.0254031i	$-0.991913\pi$
$839$	−25.1976	+	27.9848i	−0.869919	+	0.966142i	0.129759	+	0.991546i	$0.458580\pi$
$840$	9.26628	+	35.9054i	0.319717	+	1.23885i
$841$	17.9111	+	19.8923i	0.617625	+	0.685942i
$842$	66.4130	−	29.5690i	2.28874	−	1.01901i
$843$	4.53207	−	0.490630i	0.156093	−	0.0168982i
$844$	−9.16455	+	87.1949i	−0.315457	+	3.00137i
$845$	0.669098	−	0.0267828i	0.0230177	−	0.000921355i
$846$	−35.4509	+	39.8694i	−1.21883	+	1.37074i
$847$	18.8446	−	13.6914i	0.647508	−	0.470442i
$848$	−1.08877	+	1.20920i	−0.0373884	+	0.0415240i
$849$	−31.3478	−	42.8648i	−1.07585	−	1.47112i
$850$	−9.06582	+	4.93965i	−0.310955	+	0.169429i
$851$	−18.3251	+	31.7401i	−0.628178	+	1.08804i
$852$	33.0427	−	45.7789i	1.13203	−	1.56836i
$853$	−25.4196	−	11.3175i	−0.870349	−	0.387504i	−0.0775507	−	0.996988i	$-0.524710\pi$
$853$	−25.4196	−	11.3175i	−0.870349	−	0.387504i	−0.792798	+	0.609484i	$0.791377\pi$
$854$	38.0221	−	27.6247i	1.30109	−	0.945297i
$855$	0.355283	−	6.06865i	0.0121504	−	0.207544i
$856$	11.0436	+	8.02363i	0.377462	+	0.274242i
$857$	17.5755	+	30.4416i	0.600366	+	1.03986i	0.992765	+	0.120070i	$0.0383118\pi$
$857$	17.5755	+	30.4416i	0.600366	+	1.03986i	−0.392399	+	0.919795i	$0.628355\pi$
$858$	−24.0392	−	13.7793i	−0.820685	−	0.470417i
$859$	−16.2497	−	18.0471i	−0.554431	−	0.615758i	0.399153	−	0.916884i	$-0.369304\pi$
$859$	−16.2497	−	18.0471i	−0.554431	−	0.615758i	−0.953584	+	0.301126i	$0.902637\pi$
$860$	−9.08397	−	9.31121i	−0.309761	−	0.317510i
$861$	−25.3355	−	2.58303i	−0.863432	−	0.0880294i
$862$	40.2248	−	8.55005i	1.37006	−	0.291216i
$863$	−2.53910	+	7.81456i	−0.0864321	+	0.266011i	−0.984926	−	0.172975i	$-0.944662\pi$
$863$	−2.53910	+	7.81456i	−0.0864321	+	0.266011i	0.898494	+	0.438985i	$0.144662\pi$
$864$	27.8728	−	3.19340i	0.948252	−	0.108642i
$865$	−12.2453	−	8.16897i	−0.416351	−	0.277753i
$866$	72.8904	−	15.4933i	2.47692	−	0.526485i
$867$	−24.2461	+	14.0995i	−0.823440	+	0.478843i
$868$	41.2400	−	71.4297i	1.39978	−	2.42448i
$869$	−0.434648	+	0.193518i	−0.0147444	+	0.00656465i
$870$	−47.4484	+	46.5800i	−1.60865	+	1.57921i
$871$	−39.4680	−	17.5723i	−1.33732	−	0.595413i
$872$	32.3781	−	23.5240i	1.09646	−	0.796624i
$873$	14.2209	−	0.0886777i	0.481303	−	0.00300129i
$874$	17.7072			0.598954
$875$	−20.8468	+	29.6363i	−0.704749	+	1.00189i
$876$	−2.68217	−	3.66759i	−0.0906220	−	0.123916i
$877$	−30.2206	−	6.42358i	−1.02048	−	0.216909i	−0.332855	−	0.942978i	$-0.608012\pi$
$877$	−30.2206	−	6.42358i	−1.02048	−	0.216909i	−0.687622	+	0.726069i	$0.741345\pi$
$878$	−2.90802	−	27.6680i	−0.0981410	−	0.933749i
$879$	48.3492	+	15.5431i	1.63078	+	0.524257i
$880$	−0.898830	−	0.357829i	−0.0302996	−	0.0120624i
$881$	−14.6144	−	10.6180i	−0.492373	−	0.357730i	0.313723	−	0.949514i	$-0.398424\pi$
$881$	−14.6144	−	10.6180i	−0.492373	−	0.357730i	−0.806096	+	0.591785i	$0.798424\pi$
$882$	−16.2783	−	17.8537i	−0.548118	−	0.601166i
$883$	22.5517	+	16.3848i	0.758925	+	0.551391i	0.898580	−	0.438809i	$-0.144599\pi$
$883$	22.5517	+	16.3848i	0.758925	+	0.551391i	−0.139655	+	0.990200i	$0.544599\pi$
$884$	10.2854	−	2.18623i	0.345936	−	0.0735310i
$885$	−47.4131	−	24.7123i	−1.59377	−	0.830696i
$886$	−24.2098	−	5.14595i	−0.813344	−	0.172882i
$887$	−15.2446	−	16.9308i	−0.511863	−	0.568482i	0.430706	−	0.902492i	$-0.358265\pi$
$887$	−15.2446	−	16.9308i	−0.511863	−	0.568482i	−0.942569	+	0.334011i	$0.891598\pi$
$888$	−16.4432	−	14.7130i	−0.551799	−	0.493735i
$889$	−18.2508	+	20.2696i	−0.612112	+	0.679819i
$890$	−9.51476	+	33.8322i	−0.318935	+	1.13406i
$891$	−2.05474	−	17.4529i	−0.0688363	−	0.584693i
$892$	−57.0454	−	41.4459i	−1.91002	−	1.38771i
$893$	3.50506	+	6.07093i	0.117292	+	0.203156i
$894$	−37.6803	+	21.9116i	−1.26022	+	0.732835i
$895$	−17.0356	−	17.4618i	−0.569438	−	0.583684i
$896$	6.35369	+	60.4513i	0.212262	+	2.01954i
$897$	38.8791	−	35.2270i	1.29814	−	1.17620i
$898$	−41.7599	+	46.3791i	−1.39355	+	1.54769i
$899$	57.8541			1.92954
$900$	−36.0041	−	33.6429i	−1.20014	−	1.12143i
$901$	6.59569			0.219734
$902$	13.6271	−	15.1345i	0.453734	−	0.503922i
$903$	9.46360	+	3.04232i	0.314929	+	0.101242i
$904$	5.22487	+	49.7113i	0.173777	+	1.65337i
$905$	−9.05806	+	17.2474i	−0.301100	+	0.573322i
$906$	0.260770	+	83.6380i	0.00866351	+	2.77869i
$907$	−0.183281	−	0.317451i	−0.00608574	−	0.0105408i	0.862966	−	0.505261i	$-0.168604\pi$
$907$	−0.183281	−	0.317451i	−0.00608574	−	0.0105408i	−0.869052	+	0.494720i	$0.835270\pi$
$908$	13.9812	+	10.1579i	0.463982	+	0.337103i
$909$	−29.2226	−	20.9543i	−0.969252	−	0.695010i
$910$	46.5988	−	36.7912i	1.54473	−	1.21962i
$911$	36.2540	−	40.2641i	1.20115	−	1.33401i	0.272903	−	0.962042i	$-0.412016\pi$
$911$	36.2540	−	40.2641i	1.20115	−	1.33401i	0.928245	−	0.371969i	$-0.121317\pi$
$912$	−0.0712482	+	0.340412i	−0.00235926	+	0.0112722i
$913$	6.04325	+	6.71171i	0.200002	+	0.222125i
$914$	35.1127	+	7.46344i	1.16143	+	0.246869i
$915$	−8.96549	+	22.7263i	−0.296390	+	0.751309i
$916$	−56.2309	+	11.9522i	−1.85792	+	0.394913i
$917$	−38.0399	−	27.6376i	−1.25619	−	0.912674i
$918$	8.04018	+	7.10437i	0.265365	+	0.234479i
$919$	−29.1500	−	21.1787i	−0.961568	−	0.698620i	−0.00805385	−	0.999968i	$-0.502564\pi$
$919$	−29.1500	−	21.1787i	−0.961568	−	0.698620i	−0.953514	+	0.301347i	$0.902564\pi$
$920$	35.8714	−	43.1954i	1.18265	−	1.42411i
$921$	−3.41833	−	15.8390i	−0.112638	−	0.521912i
$922$	−1.80305	−	17.1549i	−0.0593803	−	0.564966i
$923$	−34.5889	−	7.35209i	−1.13851	−	0.241997i
$924$	35.7973	−	3.87532i	1.17764	−	0.127489i
$925$	0.532615	−	21.5536i	0.0175123	−	0.708679i
$926$	−76.1019			−2.50086
$927$	3.34412	+	5.70967i	0.109835	+	0.187530i
$928$	−32.6197	+	23.6996i	−1.07079	+	0.777977i
$929$	−9.18536	−	4.08959i	−0.301362	−	0.134175i	0.250485	−	0.968121i	$-0.419410\pi$
$929$	−9.18536	−	4.08959i	−0.301362	−	0.134175i	−0.551847	+	0.833946i	$0.686077\pi$
$930$	2.97375	+	68.9144i	0.0975132	+	2.25979i
$931$	−2.90016	+	1.29123i	−0.0950487	+	0.0423184i
$932$	−16.1569	+	27.9846i	−0.529237	+	0.916666i
$933$	0.111392	+	35.7271i	0.00364680	+	1.16965i
$934$	−7.38543	+	1.56982i	−0.241659	+	0.0513661i
$935$	1.36003	+	3.67818i	0.0444778	+	0.120289i
$936$	15.9630	+	27.2548i	0.521766	+	0.890851i
$937$	−5.85784	+	18.0286i	−0.191367	+	0.588968i	0.808633	+	0.588314i	$0.200208\pi$
$937$	−5.85784	+	18.0286i	−0.191367	+	0.588968i	−1.00000		0.000653814i	$0.999792\pi$
$938$	88.3474	−	18.7788i	2.88465	−	0.613150i
$939$	14.4990	+	32.2939i	0.473156	+	1.05387i
$940$	56.0096	+	9.58173i	1.82683	+	0.312521i
$941$	−32.0921	−	35.6419i	−1.04617	−	1.16189i	−0.986515	−	0.163672i	$-0.947666\pi$
$941$	−32.0921	−	35.6419i	−1.04617	−	1.16189i	−0.0596570	−	0.998219i	$-0.519001\pi$
$942$	−22.4169	+	13.0358i	−0.730383	+	0.424729i
$943$	19.2805	+	33.3948i	0.627860	+	1.08749i
$944$	2.47469	+	1.79797i	0.0805444	+	0.0585189i
$945$	36.3429	+	9.85499i	1.18224	+	0.320583i
$946$	−6.43115	+	4.67250i	−0.209095	+	0.151916i
$947$	−35.1348	−	15.6430i	−1.14173	−	0.508330i	−0.253319	−	0.967383i	$-0.581522\pi$
$947$	−35.1348	−	15.6430i	−1.14173	−	0.508330i	−0.888409	+	0.459052i	$0.848189\pi$
$948$	1.37929	+	0.140623i	0.0447972	+	0.00456721i
$949$	−1.42293	+	2.46459i	−0.0461903	+	0.0800040i
$950$	−9.14692	+	4.98384i	−0.296765	+	0.161697i
$951$	−0.150719	+	0.0163165i	−0.00488741	+	0.000529099i
$952$	−5.75423	+	6.39072i	−0.186496	+	0.207124i
$953$	26.9203	−	19.5587i	0.872034	−	0.633569i	−0.0590983	−	0.998252i	$-0.518823\pi$
$953$	26.9203	−	19.5587i	0.872034	−	0.633569i	0.931132	+	0.364683i	$0.118823\pi$
$954$	15.9505	+	48.0687i	0.516418	+	1.55628i
$955$	7.75848	+	20.9827i	0.251059	+	0.678983i
$956$	5.72285	−	54.4493i	0.185090	−	1.76102i
$957$	14.9088	+	20.3862i	0.481932	+	0.658992i
$958$	17.3046	−	7.70450i	0.559086	−	0.248921i
$959$	−13.0668	−	14.5121i	−0.421948	−	0.468621i
$960$	−30.9748	−	38.9813i	−0.999707	−	1.25812i
$961$	19.4172	−	21.5649i	0.626360	−	0.695643i
$962$	−10.9170	+	33.5990i	−0.351977	+	1.08327i
$963$	12.6279	−	5.71694i	0.406930	−	0.184226i
$964$	22.5193	+	69.3072i	0.725297	+	2.23224i
$965$	24.0026	+	9.55556i	0.772670	+	0.307604i
$966$	−22.4699	+	107.357i	−0.722956	+	3.45416i
$967$	40.1904	−	17.8939i	1.29244	−	0.575429i	0.358720	−	0.933445i	$-0.383213\pi$
$967$	40.1904	−	17.8939i	1.29244	−	0.575429i	0.933715	+	0.358016i	$0.116547\pi$
$968$	10.6168	−	18.3888i	0.341237	−	0.591040i
$969$	1.21870	−	0.708693i	0.0391503	−	0.0227665i
$970$	−13.0184	−	20.5993i	−0.417996	−	0.661403i
$971$	15.7738	−	11.4603i	0.506204	−	0.367779i	−0.305178	−	0.952295i	$-0.598716\pi$
$971$	15.7738	−	11.4603i	0.506204	−	0.367779i	0.811382	+	0.584517i	$0.198716\pi$
$972$	−20.0969	+	47.1010i	−0.644608	+	1.51077i
$973$	−8.27344	−	25.4630i	−0.265234	−	0.816307i
$974$	−17.4805	−	30.2771i	−0.560112	−	0.970142i
$975$	−10.1687	+	29.1400i	−0.325658	+	0.933226i
$976$	0.698856	−	1.21045i	0.0223698	−	0.0387457i
$977$	43.9214	+	9.33578i	1.40517	+	0.298678i	0.847240	−	0.531210i	$-0.178263\pi$
$977$	43.9214	+	9.33578i	1.40517	+	0.298678i	0.557930	+	0.829888i	$0.311596\pi$
$978$	12.0629	−	10.9298i	0.385730	−	0.349497i
$979$	12.1953	+	5.42970i	0.389764	+	0.173534i
$980$	−6.96676	+	24.7721i	−0.222545	+	0.791316i
$981$	−4.50004	−	40.3906i	−0.143675	−	1.28957i
$982$	3.63642			0.116043
$983$	5.36159	−	51.0121i	0.171008	−	1.62703i	−0.486567	−	0.873643i	$-0.661751\pi$
$983$	5.36159	−	51.0121i	0.171008	−	1.62703i	0.657575	−	0.753389i	$-0.271582\pi$
$984$	−22.0563	+	7.24265i	−0.703131	+	0.230887i
$985$	20.4290	+	20.9401i	0.650922	+	0.667206i
$986$	−15.0828	−	3.20595i	−0.480335	−	0.102098i
$987$	−41.2554	+	13.5470i	−1.31317	+	0.431207i
$988$	10.3774	−	2.20579i	0.330150	−	0.0701756i
$989$	−4.65124	−	14.3150i	−0.147901	−	0.455192i
$990$	−23.5172	+	18.8068i	−0.747426	+	0.597721i
$991$	2.34318	−	7.21156i	0.0744335	−	0.229083i	−0.906917	−	0.421309i	$-0.861571\pi$
$991$	2.34318	−	7.21156i	0.0744335	−	0.229083i	0.981351	+	0.192226i	$0.0615708\pi$
$992$	−4.37228	+	41.5994i	−0.138820	+	1.32078i
$993$	38.8769	−	4.20872i	1.23372	−	0.133560i
$994$	67.5363	−	30.0691i	2.14212	−	0.953734i
$995$	0.840689	+	5.76819i	0.0266516	+	0.182864i
$996$	−5.55205	−	25.7257i	−0.175923	−	0.815149i
$997$	21.4035	+	9.52945i	0.677855	+	0.301801i	0.716636	−	0.697447i	$-0.245681\pi$
$997$	21.4035	+	9.52945i	0.677855	+	0.301801i	−0.0387810	+	0.999248i	$0.512347\pi$
$998$	22.0054	+	67.7258i	0.696570	+	2.14382i
$999$	−21.2437	+	7.12285i	−0.672121	+	0.225357i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	225.2.q.a.31.24	✓	224
3.2	odd	2		675.2.r.a.631.5		224
9.2	odd	6		675.2.r.a.181.24		224
9.7	even	3	inner	225.2.q.a.106.5	yes	224
25.21	even	5	inner	225.2.q.a.121.5	yes	224
75.71	odd	10		675.2.r.a.496.24		224
225.146	odd	30		675.2.r.a.46.5		224
225.196	even	15	inner	225.2.q.a.196.24	yes	224

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
225.2.q.a.31.24	✓	224	1.1	even	1	trivial
225.2.q.a.106.5	yes	224	9.7	even	3	inner
225.2.q.a.121.5	yes	224	25.21	even	5	inner
225.2.q.a.196.24	yes	224	225.196	even	15	inner
675.2.r.a.46.5		224	225.146	odd	30
675.2.r.a.181.24		224	9.2	odd	6
675.2.r.a.496.24		224	75.71	odd	10
675.2.r.a.631.5		224	3.2	odd	2

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)

\(f(q)\)	\(=\)	\(q+(1.53828 - 1.70844i) q^{2} +(-0.365394 - 1.69307i) q^{3} +(-0.343384 - 3.26708i) q^{4} +(0.322490 + 2.21269i) q^{5} +(-3.45458 - 1.98017i) q^{6} +(-1.62043 - 2.80667i) q^{7} +(-2.39008 - 1.73649i) q^{8} +(-2.73297 + 1.23728i) q^{9} +O(q^{10})\)	\(q+(1.53828 - 1.70844i) q^{2} +(-0.365394 - 1.69307i) q^{3} +(-0.343384 - 3.26708i) q^{4} +(0.322490 + 2.21269i) q^{5} +(-3.45458 - 1.98017i) q^{6} +(-1.62043 - 2.80667i) q^{7} +(-2.39008 - 1.73649i) q^{8} +(-2.73297 + 1.23728i) q^{9} +(4.27633 + 2.85279i) q^{10} +(1.30655 - 1.45107i) q^{11} +(-5.40593 + 1.77515i) q^{12} +(2.38463 + 2.64840i) q^{13} +(-7.28770 - 1.54905i) q^{14} +(3.62841 - 1.35450i) q^{15} +(-0.216735 + 0.0460685i) q^{16} +(0.726639 + 0.527934i) q^{17} +(-2.09028 + 6.57240i) q^{18} +(0.733140 + 0.532657i) q^{19} +(7.11830 - 1.81340i) q^{20} +(-4.15979 + 3.76904i) q^{21} +(-0.469217 - 4.46430i) q^{22} +(8.31379 + 1.76715i) q^{23} +(-2.06669 + 4.68108i) q^{24} +(-4.79200 + 1.42714i) q^{25} +8.19288 q^{26} +(3.09341 + 4.17502i) q^{27} +(-8.61318 + 6.25784i) q^{28} +(-6.82216 - 3.03742i) q^{29} +(3.26744 - 8.28251i) q^{30} +(-7.07738 + 3.15105i) q^{31} +(2.69961 - 4.67586i) q^{32} +(-2.93416 - 1.68186i) q^{33} +(2.01972 - 0.429305i) q^{34} +(5.68771 - 4.49063i) q^{35} +(4.98074 + 8.50399i) q^{36} +(-1.33249 + 4.10099i) q^{37} +(2.03779 - 0.433145i) q^{38} +(3.61260 - 5.00507i) q^{39} +(3.07155 - 5.84851i) q^{40} +(3.03574 + 3.37153i) q^{41} +(0.0402345 + 12.9046i) q^{42} +(-0.885445 - 1.53364i) q^{43} +(-5.18939 - 3.77032i) q^{44} +(-3.61907 - 5.64822i) q^{45} +(15.8080 - 11.4852i) q^{46} +(7.06685 + 3.14637i) q^{47} +(0.157191 + 0.350115i) q^{48} +(-1.75159 + 3.03384i) q^{49} +(-4.93328 + 10.3822i) q^{50} +(0.628320 - 1.42316i) q^{51} +(7.83371 - 8.70021i) q^{52} +(5.94096 - 4.31636i) q^{53} +(11.8913 + 1.13748i) q^{54} +(3.63211 + 2.42303i) q^{55} +(-1.00081 + 9.52203i) q^{56} +(0.633941 - 1.43589i) q^{57} +(-15.6837 + 6.98281i) q^{58} +(-9.23740 - 10.2592i) q^{59} +(-5.67120 - 11.3892i) q^{60} +(-4.22089 + 4.68777i) q^{61} +(-5.50365 + 16.9385i) q^{62} +(7.90122 + 5.66563i) q^{63} +(-3.97259 - 12.2264i) q^{64} +(-5.09108 + 6.13054i) q^{65} +(-7.38693 + 2.42565i) q^{66} +(-11.0747 + 4.93079i) q^{67} +(1.47529 - 2.55527i) q^{68} +(-0.0458994 - 14.7215i) q^{69} +(1.07736 - 16.6250i) q^{70} +(-8.02747 + 5.83230i) q^{71} +(8.68055 + 1.78861i) q^{72} +(0.246766 + 0.759468i) q^{73} +(4.95654 + 8.58498i) q^{74} +(4.16722 + 7.59173i) q^{75} +(1.48849 - 2.57813i) q^{76} +(-6.18982 - 1.31569i) q^{77} +(-2.99363 - 13.8711i) q^{78} +(-0.222600 - 0.0991078i) q^{79} +(-0.171830 - 0.464711i) q^{80} +(5.93830 - 6.76289i) q^{81} +10.4299 q^{82} +(-0.483482 + 4.60003i) q^{83} +(13.7422 + 12.2961i) q^{84} +(-0.933822 + 1.77808i) q^{85} +(-3.98219 - 0.846440i) q^{86} +(-2.64979 + 12.6602i) q^{87} +(-5.64252 + 1.19935i) q^{88} +(2.11267 + 6.50212i) q^{89} +(-15.2168 - 2.50562i) q^{90} +(3.56906 - 10.9844i) q^{91} +(2.91860 - 27.7686i) q^{92} +(7.92099 + 10.8311i) q^{93} +(16.2462 - 7.23327i) q^{94} +(-0.942175 + 1.79399i) q^{95} +(-8.90297 - 2.86209i) q^{96} +(-4.33055 - 1.92809i) q^{97} +(2.48869 + 7.65939i) q^{98} +(-1.77539 + 5.58228i) 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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