LMFDB - Embedded newform 225.2.q.a.106.17

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			106.17
Character	$\chi$	$=$	225.106
Dual form			225.2.q.a.121.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.367877 + 0.0781947i) q^{2} +(0.776923 - 1.54803i) q^{3} +(-1.69787 - 0.755941i) q^{4} +(1.98576 + 1.02799i) q^{5} +(0.406860 - 0.508733i) q^{6} +(1.17975 - 2.04339i) q^{7} +(-1.17403 - 0.852985i) q^{8} +(-1.79278 - 2.40540i) q^{9} +O(q^{10})$	\(q+(0.367877 + 0.0781947i) q^{2} +(0.776923 - 1.54803i) q^{3} +(-1.69787 - 0.755941i) q^{4} +(1.98576 + 1.02799i) q^{5} +(0.406860 - 0.508733i) q^{6} +(1.17975 - 2.04339i) q^{7} +(-1.17403 - 0.852985i) q^{8} +(-1.79278 - 2.40540i) q^{9} +(0.650132 + 0.533449i) q^{10} +(-0.366949 - 0.0779975i) q^{11} +(-2.48933 + 2.04104i) q^{12} +(-0.347527 + 0.0738691i) q^{13} +(0.593785 - 0.659465i) q^{14} +(3.13414 - 2.27534i) q^{15} +(2.12203 + 2.35675i) q^{16} +(3.45606 + 2.51098i) q^{17} +(-0.471434 - 1.02508i) q^{18} +(-3.26679 - 2.37346i) q^{19} +(-2.59447 - 3.24651i) q^{20} +(-2.24664 - 3.41384i) q^{21} +(-0.128893 - 0.0573870i) q^{22} +(3.07582 - 3.41605i) q^{23} +(-2.23258 + 1.15473i) q^{24} +(2.88648 + 4.08267i) q^{25} -0.133623 q^{26} +(-5.11648 + 0.906467i) q^{27} +(-3.54774 + 2.57759i) q^{28} +(0.0385018 + 0.366320i) q^{29} +(1.33090 - 0.591974i) q^{30} +(-0.614589 + 5.84742i) q^{31} +(2.04755 + 3.54645i) q^{32} +(-0.405834 + 0.507450i) q^{33} +(1.07506 + 1.19398i) q^{34} +(4.44328 - 2.84490i) q^{35} +(1.22557 + 5.43929i) q^{36} +(-3.03352 + 9.33621i) q^{37} +(-1.01618 - 1.12859i) q^{38} +(-0.155650 + 0.595372i) q^{39} +(-1.45449 - 2.90072i) q^{40} +(8.44348 - 1.79472i) q^{41} +(-0.559545 - 1.43155i) q^{42} +(-3.86472 + 6.69390i) q^{43} +(0.564071 + 0.409822i) q^{44} +(-1.08731 - 6.61950i) q^{45} +(1.39864 - 1.01617i) q^{46} +(0.0700054 + 0.666057i) q^{47} +(5.29697 - 1.45394i) q^{48} +(0.716381 + 1.24081i) q^{49} +(0.742627 + 1.72763i) q^{50} +(6.57216 - 3.39925i) q^{51} +(0.645896 + 0.137289i) q^{52} +(-8.98419 + 6.52740i) q^{53} +(-1.95312 - 0.0666126i) q^{54} +(-0.648493 - 0.532104i) q^{55} +(-3.12804 + 1.39270i) q^{56} +(-6.21222 + 3.21308i) q^{57} +(-0.0144804 + 0.137771i) q^{58} +(11.3428 - 2.41099i) q^{59} +(-7.04139 + 1.49402i) q^{60} +(-6.33351 - 1.34623i) q^{61} +(-0.683331 + 2.10308i) q^{62} +(-7.03019 + 0.825578i) q^{63} +(-1.48405 - 4.56744i) q^{64} +(-0.766041 - 0.210567i) q^{65} +(-0.188977 + 0.154945i) q^{66} +(1.33023 - 12.6563i) q^{67} +(-3.96980 - 6.87589i) q^{68} +(-2.89846 - 7.41547i) q^{69} +(1.85704 - 0.699135i) q^{70} +(-1.67206 + 1.21482i) q^{71} +(0.0530170 + 4.35323i) q^{72} +(1.94846 + 5.99673i) q^{73} +(-1.84600 + 3.19737i) q^{74} +(8.56267 - 1.29643i) q^{75} +(3.75239 + 6.49933i) q^{76} +(-0.592287 + 0.657802i) q^{77} +(-0.103815 + 0.206853i) q^{78} +(-1.24358 - 11.8319i) q^{79} +(1.79112 + 6.86136i) q^{80} +(-2.57187 + 8.62470i) q^{81} +3.24650 q^{82} +(-8.03305 + 3.57654i) q^{83} +(1.23385 + 7.49459i) q^{84} +(4.28165 + 8.53899i) q^{85} +(-1.94517 + 2.16033i) q^{86} +(0.596986 + 0.225001i) q^{87} +(0.364280 + 0.404574i) q^{88} +(-0.603343 - 1.85690i) q^{89} +(0.117613 - 2.52018i) q^{90} +(-0.259051 + 0.797278i) q^{91} +(-7.80469 + 3.47487i) q^{92} +(8.57449 + 5.49440i) q^{93} +(-0.0263287 + 0.250501i) q^{94} +(-4.04716 - 8.07133i) q^{95} +(7.08079 - 0.414337i) q^{96} +(-1.17621 - 11.1909i) q^{97} +(0.166516 + 0.512483i) q^{98} +(0.470245 + 1.02249i) 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 $\left(\mathbb{Z}/225\mathbb{Z}\right)^\times$.

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

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 $

$2$	0.367877	+	0.0781947i	0.260128	+	0.0552920i	0.336130	−	0.941816i	$-0.390882\pi$
$2$	0.367877	+	0.0781947i	0.260128	+	0.0552920i	−0.0760012	+	0.997108i	$0.524215\pi$
$3$	0.776923	−	1.54803i	0.448557	−	0.893754i
$3$	0.776923	−	1.54803i	0.448557	−	0.893754i
$4$	−1.69787	−	0.755941i	−0.848936	−	0.377971i
$5$	1.98576	+	1.02799i	0.888059	+	0.459730i
$5$	1.98576	+	1.02799i	0.888059	+	0.459730i
$6$	0.406860	−	0.508733i	0.166100	−	0.207689i
$7$	1.17975	−	2.04339i	0.445903	−	0.772327i	−0.552211	−	0.833704i	$-0.686216\pi$
$7$	1.17975	−	2.04339i	0.445903	−	0.772327i	0.998115	+	0.0613768i	$0.0195491\pi$
$8$	−1.17403	−	0.852985i	−0.415084	−	0.301576i
$9$	−1.79278	−	2.40540i	−0.597594	−	0.801799i
$10$	0.650132	+	0.533449i	0.205590	+	0.168692i
$11$	−0.366949	−	0.0779975i	−0.110639	−	0.0235171i	0.152259	−	0.988341i	$-0.451345\pi$
$11$	−0.366949	−	0.0779975i	−0.110639	−	0.0235171i	−0.262899	+	0.964823i	$0.584678\pi$
$12$	−2.48933	+	2.04104i	−0.718609	+	0.589199i
$13$	−0.347527	+	0.0738691i	−0.0963865	+	0.0204876i	−0.255852	−	0.966716i	$-0.582356\pi$
$13$	−0.347527	+	0.0738691i	−0.0963865	+	0.0204876i	0.159466	+	0.987203i	$0.449023\pi$
$14$	0.593785	−	0.659465i	0.158696	−	0.176249i
$15$	3.13414	−	2.27534i	0.809231	−	0.587491i
$16$	2.12203	+	2.35675i	0.530507	+	0.589187i
$17$	3.45606	+	2.51098i	0.838218	+	0.609001i	0.921872	−	0.387494i	$-0.126659\pi$
$17$	3.45606	+	2.51098i	0.838218	+	0.609001i	−0.0836542	+	0.996495i	$0.526659\pi$
$18$	−0.471434	−	1.02508i	−0.111118	−	0.241613i
$19$	−3.26679	−	2.37346i	−0.749452	−	0.544509i	0.146205	−	0.989254i	$-0.453294\pi$
$19$	−3.26679	−	2.37346i	−0.749452	−	0.544509i	−0.895657	+	0.444746i	$0.853294\pi$
$20$	−2.59447	−	3.24651i	−0.580140	−	0.725942i
$21$	−2.24664	−	3.41384i	−0.490258	−	0.744961i
$22$	−0.128893	−	0.0573870i	−0.0274801	−	0.0122349i
$23$	3.07582	−	3.41605i	0.641354	−	0.712295i	−0.331568	−	0.943431i	$-0.607578\pi$
$23$	3.07582	−	3.41605i	0.641354	−	0.712295i	0.972921	+	0.231136i	$0.0742442\pi$
$24$	−2.23258	+	1.15473i	−0.455723	+	0.235709i
$25$	2.88648	+	4.08267i	0.577296	+	0.816535i
$26$	−0.133623			−0.0262057
$27$	−5.11648	+	0.906467i	−0.984666	+	0.174450i
$28$	−3.54774	+	2.57759i	−0.670460	+	0.487118i
$29$	0.0385018	+	0.366320i	0.00714960	+	0.0680239i	0.997515	−	0.0704554i	$-0.0224452\pi$
$29$	0.0385018	+	0.366320i	0.00714960	+	0.0680239i	−0.990365	+	0.138479i	$0.955779\pi$
$30$	1.33090	−	0.591974i	0.242988	−	0.108079i
$31$	−0.614589	+	5.84742i	−0.110383	+	1.05023i	0.789396	+	0.613884i	$0.210394\pi$
$31$	−0.614589	+	5.84742i	−0.110383	+	1.05023i	−0.899780	+	0.436344i	$0.856273\pi$
$32$	2.04755	+	3.54645i	0.361958	+	0.626930i
$33$	−0.405834	+	0.507450i	−0.0706466	+	0.0883357i
$34$	1.07506	+	1.19398i	0.184372	+	0.204765i
$35$	4.44328	−	2.84490i	0.751051	−	0.480877i
$36$	1.22557	+	5.43929i	0.204262	+	0.906549i
$37$	−3.03352	+	9.33621i	−0.498707	+	1.53486i	0.312391	+	0.949953i	$0.398870\pi$
$37$	−3.03352	+	9.33621i	−0.498707	+	1.53486i	−0.811099	+	0.584910i	$0.801130\pi$
$38$	−1.01618	−	1.12859i	−0.164847	−	0.183081i
$39$	−0.155650	+	0.595372i	−0.0249240	+	0.0953357i
$40$	−1.45449	−	2.90072i	−0.229975	−	0.458644i
$41$	8.44348	−	1.79472i	1.31865	−	0.280288i	0.505744	−	0.862683i	$-0.331218\pi$
$41$	8.44348	−	1.79472i	1.31865	−	0.280288i	0.812905	+	0.582396i	$0.197885\pi$
$42$	−0.559545	−	1.43155i	−0.0863397	−	0.220893i
$43$	−3.86472	+	6.69390i	−0.589365	+	1.02081i	0.404951	+	0.914338i	$0.367289\pi$
$43$	−3.86472	+	6.69390i	−0.589365	+	1.02081i	−0.994316	+	0.106471i	$0.966045\pi$
$44$	0.564071	+	0.409822i	0.0850370	+	0.0617830i
$45$	−1.08731	−	6.61950i	−0.162087	−	0.986776i
$46$	1.39864	−	1.01617i	0.206219	−	0.149827i
$47$	0.0700054	+	0.666057i	0.0102113	+	0.0971544i	0.998440	−	0.0558265i	$-0.0177794\pi$
$47$	0.0700054	+	0.666057i	0.0102113	+	0.0971544i	−0.988229	+	0.152981i	$0.951113\pi$
$48$	5.29697	−	1.45394i	0.764551	−	0.209859i
$49$	0.716381	+	1.24081i	0.102340	+	0.177258i
$50$	0.742627	+	1.72763i	0.105023	+	0.244324i
$51$	6.57216	−	3.39925i	0.920286	−	0.475990i
$52$	0.645896	+	0.137289i	0.0895697	+	0.0190386i
$53$	−8.98419	+	6.52740i	−1.23407	+	0.896607i	−0.997189	−	0.0749310i	$-0.976126\pi$
$53$	−8.98419	+	6.52740i	−1.23407	+	0.896607i	−0.236885	+	0.971538i	$0.576126\pi$
$54$	−1.95312	−	0.0666126i	−0.265785	−	0.00906483i
$55$	−0.648493	−	0.532104i	−0.0874427	−	0.0717489i
$56$	−3.12804	+	1.39270i	−0.418002	+	0.186107i
$57$	−6.21222	+	3.21308i	−0.822829	+	0.425583i
$58$	−0.0144804	+	0.137771i	−0.00190136	+	0.0180903i
$59$	11.3428	−	2.41099i	1.47671	−	0.313885i	0.601987	−	0.798506i	$-0.294376\pi$
$59$	11.3428	−	2.41099i	1.47671	−	0.313885i	0.874724	+	0.484622i	$0.161043\pi$
$60$	−7.04139	+	1.49402i	−0.909039	+	0.192877i
$61$	−6.33351	−	1.34623i	−0.810923	−	0.172367i	−0.216254	−	0.976337i	$-0.569384\pi$
$61$	−6.33351	−	1.34623i	−0.810923	−	0.172367i	−0.594670	+	0.803970i	$0.702717\pi$
$62$	−0.683331	+	2.10308i	−0.0867831	+	0.267091i
$63$	−7.03019	+	0.825578i	−0.885721	+	0.104013i
$64$	−1.48405	−	4.56744i	−0.185506	−	0.570930i
$65$	−0.766041	−	0.210567i	−0.0950157	−	0.0261176i
$66$	−0.188977	+	0.154945i	−0.0232614	+	0.0190724i
$67$	1.33023	−	12.6563i	0.162513	−	1.54621i	−0.544348	−	0.838860i	$-0.683223\pi$
$67$	1.33023	−	12.6563i	0.162513	−	1.54621i	0.706861	−	0.707352i	$-0.250111\pi$
$68$	−3.96980	−	6.87589i	−0.481409	−	0.833825i
$69$	−2.89846	−	7.41547i	−0.348934	−	0.892718i
$70$	1.85704	−	0.699135i	0.221958	−	0.0835626i
$71$	−1.67206	+	1.21482i	−0.198437	+	0.144173i	−0.682567	−	0.730823i	$-0.739136\pi$
$71$	−1.67206	+	1.21482i	−0.198437	+	0.144173i	0.484129	+	0.874996i	$0.339136\pi$
$72$	0.0530170	+	4.35323i	0.00624812	+	0.513033i
$73$	1.94846	+	5.99673i	0.228050	+	0.701864i	0.997968	+	0.0637218i	$0.0202970\pi$
$73$	1.94846	+	5.99673i	0.228050	+	0.701864i	−0.769918	+	0.638143i	$0.779703\pi$
$74$	−1.84600	+	3.19737i	−0.214594	+	0.371687i
$75$	8.56267	−	1.29643i	0.988732	−	0.149699i
$76$	3.75239	+	6.49933i	0.430428	+	0.745524i
$77$	−0.592287	+	0.657802i	−0.0674974	+	0.0749635i
$78$	−0.103815	+	0.206853i	−0.0117547	+	0.0234214i
$79$	−1.24358	−	11.8319i	−0.139914	−	1.33119i	−0.808912	−	0.587930i	$-0.799943\pi$
$79$	−1.24358	−	11.8319i	−0.139914	−	1.33119i	0.668997	−	0.743265i	$-0.266724\pi$
$80$	1.79112	+	6.86136i	0.200254	+	0.767123i
$81$	−2.57187	+	8.62470i	−0.285763	+	0.958300i
$82$	3.24650			0.358516
$83$	−8.03305	+	3.57654i	−0.881741	+	0.392577i	−0.797109	−	0.603836i	$-0.793638\pi$
$83$	−8.03305	+	3.57654i	−0.881741	+	0.392577i	−0.0846325	+	0.996412i	$0.526972\pi$
$84$	1.23385	+	7.49459i	0.134624	+	0.817727i
$85$	4.28165	+	8.53899i	0.464410	+	0.926183i
$86$	−1.94517	+	2.16033i	−0.209753	+	0.232954i
$87$	0.596986	+	0.225001i	0.0640037	+	0.0241226i
$88$	0.364280	+	0.404574i	0.0388324	+	0.0431277i
$89$	−0.603343	−	1.85690i	−0.0639542	−	0.196831i	0.913974	−	0.405774i	$-0.132998\pi$
$89$	−0.603343	−	1.85690i	−0.0639542	−	0.196831i	−0.977928	+	0.208943i	$0.932998\pi$
$90$	0.117613	−	2.52018i	0.0123974	−	0.265651i
$91$	−0.259051	+	0.797278i	−0.0271560	+	0.0835775i
$92$	−7.80469	+	3.47487i	−0.813695	+	0.362280i
$93$	8.57449	+	5.49440i	0.889133	+	0.569743i
$94$	−0.0263287	+	0.250501i	−0.00271560	+	0.0258372i
$95$	−4.04716	−	8.07133i	−0.415230	−	0.828101i
$96$	7.08079	−	0.414337i	0.722680	−	0.0422881i
$97$	−1.17621	−	11.1909i	−0.119426	−	1.13626i	−0.875986	−	0.482336i	$-0.839788\pi$
$97$	−1.17621	−	11.1909i	−0.119426	−	1.13626i	0.756561	−	0.653924i	$-0.226878\pi$
$98$	0.166516	+	0.512483i	0.0168206	+	0.0517686i
$99$	0.470245	+	1.02249i	0.0472614	+	0.102764i
$100$	−1.81461	−	9.11387i	−0.181461	−	0.911387i
$101$	7.92712	−	13.7302i	0.788778	−	1.36620i	−0.137938	−	0.990441i	$-0.544048\pi$
$101$	7.92712	−	13.7302i	0.788778	−	1.36620i	0.926716	−	0.375762i	$-0.122619\pi$
$102$	2.68355	−	0.736597i	0.265711	−	0.0729340i
$103$	−1.29330	−	0.575813i	−0.127432	−	0.0567365i	0.342030	−	0.939689i	$-0.388886\pi$
$103$	−1.29330	−	0.575813i	−0.127432	−	0.0567365i	−0.469462	+	0.882953i	$0.655552\pi$
$104$	0.471017	+	0.209710i	0.0461870	+	0.0205638i
$105$	−0.951908	−	9.08859i	−0.0928967	−	0.886955i
$106$	−3.81549	+	1.69876i	−0.370593	+	0.164999i
$107$	7.97644			0.771112			0.385556	−	0.922684i	$-0.374010\pi$
$107$	7.97644			0.771112			0.385556	+	0.922684i	$0.374010\pi$
$108$	9.37235	+	2.32869i	0.901855	+	0.224078i
$109$	2.73023	−	8.40279i	0.261509	−	0.804841i	−0.730968	−	0.682411i	$-0.760931\pi$
$109$	2.73023	−	8.40279i	0.261509	−	0.804841i	0.992477	−	0.122430i	$-0.0390687\pi$
$110$	−0.196958	−	0.246458i	−0.0187792	−	0.0234988i
$111$	12.0959	+	11.9495i	1.14809	+	1.13419i
$112$	7.31921	−	1.55575i	0.691600	−	0.147004i
$113$	−16.2878	+	3.46209i	−1.53223	+	0.325686i	−0.895380	−	0.445302i	$-0.853096\pi$
$113$	−16.2878	+	3.46209i	−1.53223	+	0.325686i	−0.636850	+	0.770988i	$0.719763\pi$
$114$	−2.53658	+	0.696256i	−0.237573	+	0.0652104i
$115$	9.61951	−	3.62154i	0.897023	−	0.337710i
$116$	0.211545	−	0.651069i	0.0196415	−	0.0604503i
$117$	0.800724	+	0.703508i	0.0740269	+	0.0650394i
$118$	4.36130			0.401490
$119$	9.20818	−	4.09975i	0.844113	−	0.375823i
$120$	−5.62042	−	0.00204349i	−0.513071	−	0.000186545i
$121$	−9.92043	−	4.41686i	−0.901857	−	0.401533i
$122$	−2.22469	−	0.990495i	−0.201414	−	0.0896752i
$123$	3.78166	−	14.4651i	0.340981	−	1.30427i
$124$	5.46380	−	9.46358i	0.490664	−	0.849855i
$125$	1.53491	+	11.0745i	0.137287	+	0.990531i
$126$	−2.65080	−	0.246012i	−0.236152	−	0.0219165i
$127$	2.85948	+	8.80056i	0.253738	+	0.780924i	0.994076	+	0.108689i	$0.0346653\pi$
$127$	2.85948	+	8.80056i	0.253738	+	0.780924i	−0.740338	+	0.672235i	$0.765335\pi$
$128$	−1.04491	−	9.94162i	−0.0923575	−	0.878723i
$129$	7.35975	+	11.1833i	0.647989	+	0.984638i
$130$	−0.265344	−	0.137363i	−0.0232722	−	0.0120475i
$131$	1.66169	−	15.8099i	0.145183	−	1.38132i	−0.642994	−	0.765871i	$-0.722308\pi$
$131$	1.66169	−	15.8099i	0.145183	−	1.38132i	0.788177	−	0.615449i	$-0.211025\pi$
$132$	1.07266	−	0.554798i	0.0933627	−	0.0482890i
$133$	−8.70388	+	3.87522i	−0.754722	+	0.336024i
$134$	1.47902	−	4.55194i	0.127768	−	0.393228i
$135$	−11.0919	−	3.45965i	−0.954641	−	0.297759i
$136$	−1.91571	−	5.89594i	−0.164271	−	0.505573i
$137$	−4.68846	−	5.20706i	−0.400562	−	0.444870i	0.508794	−	0.860889i	$-0.330092\pi$
$137$	−4.68846	−	5.20706i	−0.400562	−	0.444870i	−0.909356	+	0.416019i	$0.863425\pi$
$138$	−0.486427	−	2.95463i	−0.0414074	−	0.251515i
$139$	−10.7197	+	11.9055i	−0.909236	+	1.00981i	0.0906670	+	0.995881i	$0.471100\pi$
$139$	−10.7197	+	11.9055i	−0.909236	+	1.00981i	−0.999903	+	0.0139277i	$0.995567\pi$
$140$	−9.69469	+	1.47143i	−0.819351	+	0.124358i
$141$	1.08546	+	0.409104i	0.0914125	+	0.0344528i
$142$	−0.710106	+	0.316160i	−0.0595908	+	0.0265315i
$143$	0.133286			0.0111460
$144$	1.86459	−	9.32945i	0.155382	−	0.777454i
$145$	−0.300117	+	0.767002i	−0.0249234	+	0.0636961i
$146$	0.247880	+	2.35842i	0.0205147	+	0.195184i
$147$	2.47738	−	0.144965i	0.204331	−	0.0119565i
$148$	12.2081	−	13.5585i	1.00350	−	1.11450i
$149$	5.59996	+	9.69941i	0.458766	+	0.794606i	0.998896	−	0.0469753i	$-0.0149582\pi$
$149$	5.59996	+	9.69941i	0.458766	+	0.794606i	−0.540130	+	0.841582i	$0.681625\pi$
$150$	3.25138	+	0.192629i	0.265474	+	0.0157281i
$151$	−1.72821	+	2.99334i	−0.140640	+	0.243595i	−0.927738	−	0.373233i	$-0.878249\pi$
$151$	−1.72821	+	2.99334i	−0.140640	+	0.243595i	0.787098	+	0.616828i	$0.211583\pi$
$152$	1.81079	+	5.57304i	0.146874	+	0.452033i
$153$	−0.156069	−	12.8148i	−0.0126174	−	1.03602i
$154$	−0.269326	+	0.195677i	−0.0217029	+	0.0157681i
$155$	−7.23151	+	10.9798i	−0.580849	+	0.881918i
$156$	0.714340	−	0.893202i	0.0571929	−	0.0715134i
$157$	−0.881657	−	1.52708i	−0.0703639	−	0.121874i	0.828697	−	0.559698i	$-0.189083\pi$
$157$	−0.881657	−	1.52708i	−0.0703639	−	0.121874i	−0.899061	+	0.437824i	$0.855749\pi$
$158$	0.467707	−	4.44994i	0.0372088	−	0.354018i
$159$	3.12457	+	18.9791i	0.247794	+	1.50514i
$160$	0.420220	+	9.14725i	0.0332213	+	0.723154i
$161$	−3.35161	−	10.3152i	−0.264143	−	0.812950i
$162$	−1.62054	+	2.97172i	−0.127322	+	0.233481i
$163$	2.57870	−	7.93644i	0.201980	−	0.621630i	−0.797844	−	0.602864i	$-0.794026\pi$
$163$	2.57870	−	7.93644i	0.201980	−	0.621630i	0.999824	−	0.0187660i	$-0.00597376\pi$
$164$	−15.6926	−	3.33557i	−1.22539	−	0.260465i
$165$	−1.32754	+	0.590481i	−0.103349	+	0.0459689i
$166$	−3.23484	+	0.687587i	−0.251072	+	0.0533671i
$167$	−1.20283	+	11.4442i	−0.0930778	+	0.885577i	0.843973	+	0.536385i	$0.180210\pi$
$167$	−1.20283	+	11.4442i	−0.0930778	+	0.885577i	−0.937051	+	0.349192i	$0.886456\pi$
$168$	−0.274319	+	5.92432i	−0.0211641	+	0.457071i
$169$	−11.7608	+	5.23623i	−0.904675	+	0.402787i
$170$	0.907419	+	3.47610i	0.0695959	+	0.266605i
$171$	0.147522	+	12.1130i	0.0112813	+	0.926305i
$172$	11.6220	−	8.44387i	0.886169	−	0.643839i
$173$	17.7210	+	3.76672i	1.34731	+	0.286379i	0.824398	−	0.566011i	$-0.191514\pi$
$173$	17.7210	+	3.76672i	1.34731	+	0.286379i	0.522908	+	0.852389i	$0.324847\pi$
$174$	0.202024	+	0.129454i	0.0153154	+	0.00981386i
$175$	11.7478	−	1.08166i	0.888051	−	0.0817657i
$176$	−0.594856	−	1.03032i	−0.0448389	−	0.0776633i
$177$	5.08022	−	19.4322i	0.381853	−	1.46061i
$178$	−0.0767565	−	0.730289i	−0.00575314	−	0.0547375i
$179$	−5.91468	+	4.29726i	−0.442084	+	0.321193i	−0.786462	−	0.617638i	$-0.788090\pi$
$179$	−5.91468	+	4.29726i	−0.442084	+	0.321193i	0.344379	+	0.938831i	$0.388090\pi$
$180$	−3.15784	+	12.0610i	−0.235371	+	0.898974i
$181$	−7.81043	−	5.67461i	−0.580544	−	0.421790i	0.258376	−	0.966044i	$-0.416813\pi$
$181$	−7.81043	−	5.67461i	−0.580544	−	0.421790i	−0.838920	+	0.544254i	$0.816813\pi$
$182$	−0.157642	+	0.273044i	−0.0116852	+	0.0202394i
$183$	−7.00465	+	8.75854i	−0.517799	+	0.647450i
$184$	−6.52496	+	1.38692i	−0.481026	+	0.102245i
$185$	−15.6213	+	15.4210i	−1.14850	+	1.13378i
$186$	2.72473	+	2.69174i	0.199787	+	0.197368i
$187$	−1.07235	−	1.19097i	−0.0784180	−	0.0870920i
$188$	0.384640	−	1.18380i	0.0280527	−	0.0863374i
$189$	−4.18390	+	11.5243i	−0.304334	+	0.838272i
$190$	−0.857723	−	3.28573i	−0.0622258	−	0.238372i
$191$	8.77381	+	9.74430i	0.634850	+	0.705073i	0.971629	−	0.236511i	$-0.0760040\pi$
$191$	8.77381	+	9.74430i	0.634850	+	0.705073i	−0.336778	+	0.941584i	$0.609337\pi$
$192$	−8.22352	−	1.25120i	−0.593481	−	0.0902973i
$193$	8.40007	+	14.5494i	0.604650	+	1.04729i	0.992107	+	0.125397i	$0.0400205\pi$
$193$	8.40007	+	14.5494i	0.604650	+	1.04729i	−0.387456	+	0.921888i	$0.626646\pi$
$194$	0.442367	−	4.20884i	0.0317601	−	0.302177i
$195$	−0.921119	+	1.02226i	−0.0659627	+	0.0732054i
$196$	−0.278345	−	2.64828i	−0.0198818	−	0.189163i
$197$	−9.40465	+	6.83288i	−0.670054	+	0.486823i	−0.870043	−	0.492976i	$-0.835909\pi$
$197$	−9.40465	+	6.83288i	−0.670054	+	0.486823i	0.199989	+	0.979798i	$0.435909\pi$
$198$	0.0930390	+	0.412922i	0.00661199	+	0.0293451i
$199$	7.37976			0.523137			0.261568	−	0.965185i	$-0.415760\pi$
$199$	7.37976			0.523137			0.261568	+	0.965185i	$0.415760\pi$
$200$	0.0936376	−	7.25532i	0.00662118	−	0.513029i
$201$	−18.5588	−	11.8922i	−1.30904	−	0.838811i
$202$	3.98983	−	4.43116i	0.280724	−	0.311775i
$203$	0.793955	+	0.353492i	0.0557248	+	0.0248103i
$204$	−13.7283	+	0.803320i	−0.961174	+	0.0562437i
$205$	18.6117	+	5.11592i	1.29989	+	0.357312i
$206$	−0.430749	−	0.312957i	−0.0300117	−	0.0218048i
$207$	−13.7312	−	1.27435i	−0.954387	−	0.0885735i
$208$	−0.911552	−	0.662281i	−0.0632047	−	0.0459209i
$209$	1.01362	+	1.12574i	0.0701136	+	0.0778691i
$210$	0.360494	−	3.41792i	0.0248765	−	0.235859i
$211$	7.43482	−	8.25720i	0.511834	−	0.568449i	−0.430727	−	0.902482i	$-0.641743\pi$
$211$	7.43482	−	8.25720i	0.511834	−	0.568449i	0.942561	+	0.334033i	$0.108410\pi$
$212$	20.1883	−	4.29116i	1.38654	−	0.294718i
$213$	0.581518	+	3.53222i	0.0398450	+	0.242024i
$214$	2.93435	+	0.623716i	0.200588	+	0.0426363i
$215$	−14.5557	+	9.31958i	−0.992687	+	0.635590i
$216$	6.78012	+	3.30005i	0.461329	+	0.224540i
$217$	11.2235	+	8.15434i	0.761900	+	0.553553i
$218$	1.66144	−	2.87771i	0.112527	−	0.194903i
$219$	10.7969	+	1.64273i	0.729588	+	0.111006i
$220$	0.698818	+	1.39367i	0.0471143	+	0.0939610i
$221$	−1.38656	−	0.617335i	−0.0932699	−	0.0415264i
$222$	3.51542	+	5.34178i	0.235940	+	0.358517i
$223$	2.95847	+	0.628841i	0.198114	+	0.0421103i	0.305900	−	0.952064i	$-0.401043\pi$
$223$	2.95847	+	0.628841i	0.198114	+	0.0421103i	−0.107786	+	0.994174i	$0.534376\pi$
$224$	9.66236			0.645594
$225$	4.64563	−	14.2625i	0.309708	−	0.950832i
$226$	−6.26264			−0.416585
$227$	−8.94852	−	1.90207i	−0.593934	−	0.126245i	−0.0988690	−	0.995100i	$-0.531522\pi$
$227$	−8.94852	−	1.90207i	−0.593934	−	0.126245i	−0.495065	+	0.868856i	$0.664856\pi$
$228$	12.9765	−	0.759325i	0.859387	−	0.0502875i
$229$	−26.9255	−	11.9880i	−1.77929	−	0.792191i	−0.982074	−	0.188497i	$-0.939638\pi$
$229$	−26.9255	−	11.9880i	−1.77929	−	0.792191i	−0.797216	−	0.603694i	$-0.793695\pi$
$230$	3.82198	−	0.580087i	0.252014	−	0.0382498i
$231$	0.558134	+	1.42794i	0.0367225	+	0.0939515i
$232$	0.267263	−	0.462913i	0.0175467	−	0.0303917i
$233$	6.59518	+	4.79168i	0.432064	+	0.313913i	0.782474	−	0.622683i	$-0.213958\pi$
$233$	6.59518	+	4.79168i	0.432064	+	0.313913i	−0.350409	+	0.936597i	$0.613958\pi$
$234$	0.239557	+	0.321417i	0.0156604	+	0.0210117i
$235$	−0.545685	+	1.39459i	−0.0355965	+	0.0909732i
$236$	−21.0812	−	4.48095i	−1.37227	−	0.291685i
$237$	−19.2823	−	7.26739i	−1.25252	−	0.472067i
$238$	3.70806	−	0.788172i	0.240358	−	0.0510896i
$239$	3.17374	−	3.52480i	0.205292	−	0.228000i	−0.631703	−	0.775211i	$-0.717644\pi$
$239$	3.17374	−	3.52480i	0.205292	−	0.228000i	0.836995	+	0.547211i	$0.184310\pi$
$240$	12.0131	+	2.55804i	0.775445	+	0.165121i
$241$	−16.7450	−	18.5973i	−1.07864	−	1.19795i	−0.979197	−	0.202911i	$-0.934960\pi$
$241$	−16.7450	−	18.5973i	−1.07864	−	1.19795i	−0.0994459	−	0.995043i	$-0.531707\pi$
$242$	−3.30413	−	2.40059i	−0.212397	−	0.154316i
$243$	11.3531	+	10.6821i	0.728304	+	0.685254i
$244$	9.73582	+	7.07349i	0.623272	+	0.452834i
$245$	0.147024	+	3.20038i	0.00939301	+	0.204465i
$246$	2.52228	−	5.02567i	0.160815	−	0.320425i
$247$	1.31062	+	0.583526i	0.0833928	+	0.0371288i
$248$	5.70932	−	6.34084i	0.362542	−	0.402644i
$249$	−0.704470	+	15.2141i	−0.0446440	+	0.964153i
$250$	−0.301307	+	4.19407i	−0.0190563	+	0.265256i
$251$	−20.6780			−1.30518			−0.652591	−	0.757710i	$-0.726318\pi$
$251$	−20.6780			−1.30518			−0.652591	+	0.757710i	$0.726318\pi$
$252$	12.5604	+	3.91268i	0.791234	+	0.246476i
$253$	−1.39511	+	1.01361i	−0.0877101	+	0.0637251i
$254$	0.363779	+	3.46112i	0.0228255	+	0.217170i
$255$	16.5451	+	0.00601553i	1.03609	+	0.000376707i
$256$	−0.611009	+	5.81337i	−0.0381881	+	0.363335i
$257$	0.199971	+	0.346359i	0.0124738	+	0.0216053i	0.872195	−	0.489158i	$-0.162696\pi$
$257$	0.199971	+	0.346359i	0.0124738	+	0.0216053i	−0.859721	+	0.510764i	$0.829363\pi$
$258$	1.83300	+	4.68959i	0.114118	+	0.291961i
$259$	15.4987	+	17.2130i	0.963042	+	1.06957i
$260$	1.14146	+	0.936598i	0.0707905	+	0.0580853i
$261$	0.812119	−	0.749343i	0.0502689	−	0.0463832i
$262$	1.84755	−	5.68618i	0.114142	−	0.351293i
$263$	1.78686	+	1.98451i	0.110182	+	0.122370i	0.795713	−	0.605674i	$-0.207096\pi$
$263$	1.78686	+	1.98451i	0.110182	+	0.122370i	−0.685531	+	0.728044i	$0.740430\pi$
$264$	0.909310	−	0.249593i	0.0559641	−	0.0153614i
$265$	−24.5505	+	3.72619i	−1.50813	+	0.228898i
$266$	−3.50498	+	0.745007i	−0.214904	+	0.0456793i
$267$	−3.34328	−	0.508676i	−0.204606	−	0.0311304i
$268$	−11.8260	+	20.4832i	−0.722386	+	1.25121i
$269$	15.1805	+	11.0293i	0.925574	+	0.672469i	0.944905	−	0.327344i	$-0.106154\pi$
$269$	15.1805	+	11.0293i	0.925574	+	0.672469i	−0.0193308	+	0.999813i	$0.506154\pi$
$270$	−3.80994	−	2.14006i	−0.231866	−	0.130240i
$271$	−10.8085	+	7.85283i	−0.656569	+	0.477025i	−0.865503	−	0.500905i	$-0.833001\pi$
$271$	−10.8085	+	7.85283i	−0.656569	+	0.477025i	0.208934	+	0.977930i	$0.433001\pi$
$272$	1.41611	+	13.4734i	0.0858646	+	0.816947i
$273$	1.03295	+	1.02044i	0.0625167	+	0.0617600i
$274$	−1.31761	−	2.28217i	−0.0795999	−	0.137871i
$275$	−0.740753	−	1.72327i	−0.0446691	−	0.103917i
$276$	−0.684444	+	14.7816i	−0.0411987	+	0.889747i
$277$	−22.2737	−	4.73443i	−1.33830	−	0.284464i	−0.517500	−	0.855683i	$-0.673137\pi$
$277$	−22.2737	−	4.73443i	−1.33830	−	0.284464i	−0.820798	+	0.571219i	$0.806471\pi$
$278$	−4.87449	+	3.54153i	−0.292353	+	0.212407i
$279$	15.1672	−	9.00482i	0.908037	−	0.539105i
$280$	−7.64322	−	0.450036i	−0.456770	−	0.0268948i
$281$	8.19793	−	3.64996i	0.489048	−	0.217738i	−0.147372	−	0.989081i	$-0.547081\pi$
$281$	8.19793	−	3.64996i	0.489048	−	0.217738i	0.636420	+	0.771343i	$0.280415\pi$
$282$	0.367327	+	0.235378i	0.0218740	+	0.0140165i
$283$	0.679692	−	6.46684i	0.0404035	−	0.384414i	−0.955570	−	0.294765i	$-0.904759\pi$
$283$	0.679692	−	6.46684i	0.0404035	−	0.384414i	0.995973	−	0.0896492i	$-0.0285746\pi$
$284$	3.75728	−	0.798635i	0.222954	−	0.0473903i
$285$	−15.6390	−	0.00568608i	−0.926374	−	0.000336815i
$286$	0.0490330	+	0.0104223i	0.00289938	+	0.000616282i
$287$	6.29389	−	19.3706i	0.371517	−	1.14341i
$288$	4.85983	−	11.2832i	0.286368	−	0.664867i
$289$	0.386075	+	1.18822i	0.0227103	+	0.0698951i
$290$	−0.170382	+	0.258695i	−0.0100052	+	0.0151911i
$291$	−18.2376	−	6.87364i	−1.06911	−	0.402940i
$292$	1.22495	−	11.6546i	0.0716847	−	0.682034i
$293$	8.56935	+	14.8426i	0.500627	+	0.867111i	1.00000		0.000723948i	$0.000230440\pi$
$293$	8.56935	+	14.8426i	0.500627	+	0.867111i	−0.499373	+	0.866387i	$0.666436\pi$
$294$	0.922707	+	0.140389i	0.0538134	+	0.00818763i
$295$	25.0026	+	6.87264i	1.45571	+	0.400141i
$296$	11.5251	−	8.37347i	0.669883	−	0.486698i
$297$	1.94819	+	0.0664446i	0.113045	+	0.00385551i
$298$	1.30165	+	4.00608i	0.0754028	+	0.232066i
$299$	−0.816590	+	1.41438i	−0.0472246	+	0.0817955i
$300$	−15.5183	−	4.27171i	−0.895951	−	0.246627i
$301$	9.11881	+	15.7942i	0.525599	+	0.910365i
$302$	−0.869832	+	0.966046i	−0.0500532	+	0.0555897i
$303$	−15.0959	−	22.9387i	−0.867238	−	1.31779i
$304$	−1.33856	−	12.7355i	−0.0767716	−	0.730433i
$305$	−11.1929	−	9.18407i	−0.640905	−	0.525878i
$306$	0.944638	−	4.72649i	0.0540014	−	0.270195i
$307$	−22.7466			−1.29822			−0.649109	−	0.760695i	$-0.724858\pi$
$307$	−22.7466			−1.29822			−0.649109	+	0.760695i	$0.724858\pi$
$308$	1.50289	−	0.669129i	0.0856350	−	0.0381271i
$309$	−1.89617	+	1.55470i	−0.107869	+	0.0884437i
$310$	−3.51887	+	3.47375i	−0.199858	+	0.197296i
$311$	9.62578	−	10.6905i	0.545828	−	0.606203i	−0.405609	−	0.914047i	$-0.632941\pi$
$311$	9.62578	−	10.6905i	0.545828	−	0.606203i	0.951437	+	0.307843i	$0.0996072\pi$
$312$	0.690582	−	0.566219i	0.0390965	−	0.0320558i
$313$	1.73060	+	1.92203i	0.0978194	+	0.108640i	0.790067	−	0.613021i	$-0.210046\pi$
$313$	1.73060	+	1.92203i	0.0978194	+	0.108640i	−0.692247	+	0.721660i	$0.743379\pi$
$314$	−0.204932	−	0.630717i	−0.0115650	−	0.0355934i
$315$	−14.8089	−	5.58755i	−0.834390	−	0.314823i
$316$	−6.83279	+	21.0292i	−0.384374	+	1.18298i
$317$	14.1723	−	6.30993i	0.795998	−	0.354401i	0.0318914	−	0.999491i	$-0.489847\pi$
$317$	14.1723	−	6.30993i	0.795998	−	0.354401i	0.764106	+	0.645090i	$0.223180\pi$
$318$	−0.334605	+	7.22629i	−0.0187637	+	0.405230i
$319$	0.0144438	−	0.137424i	0.000808699	−	0.00769426i
$320$	1.74831	−	10.5954i	0.0977333	−	0.592302i
$321$	6.19708	−	12.3478i	0.345887	−	0.689184i
$322$	−0.426387	−	4.05680i	−0.0237616	−	0.226077i
$323$	−5.33052	−	16.4056i	−0.296598	−	0.912834i
$324$	10.8865	−	12.6995i	0.604804	−	0.705525i
$325$	−1.30471	−	1.20562i	−0.0723724	−	0.0668756i
$326$	1.56923	−	2.71799i	0.0869119	−	0.150536i
$327$	−10.8866	−	10.7548i	−0.602029	−	0.594742i
$328$	−11.4438	−	5.09511i	−0.631878	−	0.281330i
$329$	1.44360	+	0.642732i	0.0795882	+	0.0354350i
$330$	−0.534544	+	0.113418i	−0.0294257	+	0.00624344i
$331$	7.91509	−	3.52403i	0.435053	−	0.193698i	−0.177511	−	0.984119i	$-0.556805\pi$
$331$	7.91509	−	3.52403i	0.435053	−	0.193698i	0.612564	+	0.790421i	$0.290138\pi$
$332$	16.3427			0.896924
$333$	27.8957	−	9.44096i	1.52868	−	0.517362i
$334$	−1.33737	+	4.11600i	−0.0731775	+	0.225217i
$335$	15.6520	−	23.7649i	0.855162	−	1.29841i
$336$	3.27812	−	12.5390i	0.178836	−	0.684061i
$337$	16.1508	−	3.43295i	0.879789	−	0.187005i	0.254194	−	0.967153i	$-0.418190\pi$
$337$	16.1508	−	3.43295i	0.879789	−	0.187005i	0.625594	+	0.780148i	$0.284856\pi$
$338$	−4.73597	+	1.00666i	−0.257603	+	0.0547551i
$339$	−7.29499	+	27.9038i	−0.396209	+	1.51553i
$340$	−0.814727	−	17.7348i	−0.0441848	−	0.961803i
$341$	0.681607	−	2.09777i	0.0369111	−	0.113601i
$342$	−0.892903	+	4.46764i	−0.0482827	+	0.241582i
$343$	19.8971			1.07434
$344$	10.2471	−	4.56231i	0.552487	−	0.245983i
$345$	1.86737	−	17.7049i	0.100536	−	0.953201i
$346$	6.22463	+	2.77138i	0.334638	+	0.148990i
$347$	0.512906	+	0.228361i	0.0275342	+	0.0122590i	0.420458	−	0.907312i	$-0.361870\pi$
$347$	0.512906	+	0.228361i	0.0275342	+	0.0122590i	−0.392923	+	0.919571i	$0.628536\pi$
$348$	−0.843519	−	0.833309i	−0.0452174	−	0.0446700i
$349$	−17.9910	+	31.1614i	−0.963037	+	1.66803i	−0.248239	+	0.968699i	$0.579852\pi$
$349$	−17.9910	+	31.1614i	−0.963037	+	1.66803i	−0.714798	+	0.699331i	$0.753481\pi$
$350$	4.40633	+	0.520699i	0.235528	+	0.0278325i
$351$	1.71115	−	0.692971i	0.0913345	−	0.0369880i
$352$	−0.474731	−	1.46107i	−0.0253032	−	0.0778754i
$353$	−1.37659	−	13.0974i	−0.0732685	−	0.697103i	−0.968077	−	0.250653i	$-0.919355\pi$
$353$	−1.37659	−	13.0974i	−0.0732685	−	0.697103i	0.894809	−	0.446450i	$-0.147312\pi$
$354$	3.38839	−	6.75141i	0.180091	−	0.358833i
$355$	−4.56914	+	0.693488i	−0.242505	+	0.0368065i
$356$	−0.379307	+	3.60887i	−0.0201033	+	0.191270i
$357$	0.807526	−	17.4397i	0.0427388	−	0.923007i
$358$	−2.51190	+	1.11837i	−0.132758	+	0.0591077i
$359$	11.4732	−	35.3108i	0.605532	−	1.86364i	0.112438	−	0.993659i	$-0.464134\pi$
$359$	11.4732	−	35.3108i	0.605532	−	1.86364i	0.493093	−	0.869976i	$-0.335866\pi$
$360$	−4.36979	+	8.69897i	−0.230308	+	0.458476i
$361$	−0.832742	−	2.56292i	−0.0438285	−	0.134890i
$362$	−2.42955	−	2.69829i	−0.127694	−	0.141819i
$363$	−14.5448	+	11.9255i	−0.763406	+	0.625929i
$364$	1.04253	−	1.15785i	0.0546435	−	0.0606877i
$365$	−2.29541	+	13.9111i	−0.120147	+	0.728138i
$366$	−3.26172	+	2.67434i	−0.170493	+	0.139790i
$367$	23.4860	−	10.4566i	1.22596	−	0.545832i	0.311397	−	0.950280i	$-0.399203\pi$
$367$	23.4860	−	10.4566i	1.22596	−	0.545832i	0.914561	+	0.404448i	$0.132536\pi$
$368$	14.5778			0.759918
$369$	−19.4543	−	17.0924i	−1.01275	−	0.889794i
$370$	−6.95258	+	4.45154i	−0.361448	+	0.231425i
$371$	2.73890	+	26.0589i	0.142196	+	1.35291i
$372$	−10.4049	−	15.8106i	−0.539471	−	0.819741i
$373$	−3.11442	+	3.45891i	−0.161259	+	0.179096i	−0.818359	−	0.574707i	$-0.805116\pi$
$373$	−3.11442	+	3.45891i	−0.161259	+	0.179096i	0.657101	+	0.753803i	$0.271783\pi$
$374$	−0.301366	−	0.521981i	−0.0155833	−	0.0269910i
$375$	18.3361	+	6.22793i	0.946873	+	0.321609i
$376$	0.485948	−	0.841686i	0.0250609	−	0.0434067i
$377$	−0.0404401	−	0.124462i	−0.00208277	−	0.00641011i
$378$	−2.44030	+	3.91238i	−0.125516	+	0.201231i
$379$	20.4895	−	14.8865i	1.05247	−	0.764666i	0.0797917	−	0.996812i	$-0.474574\pi$
$379$	20.4895	−	14.8865i	1.05247	−	0.764666i	0.972681	+	0.232145i	$0.0745745\pi$
$380$	0.770107	+	16.7635i	0.0395056	+	0.859950i
$381$	15.8451	+	2.41081i	0.811770	+	0.123510i
$382$	2.46573	+	4.27077i	0.126158	+	0.218512i
$383$	−0.712744	+	6.78131i	−0.0364195	+	0.346509i	0.961105	+	0.276184i	$0.0890701\pi$
$383$	−0.712744	+	6.78131i	−0.0364195	+	0.346509i	−0.997524	+	0.0703242i	$0.977597\pi$
$384$	−16.2017	−	6.10633i	−0.826790	−	0.311612i
$385$	−1.85235	+	0.697371i	−0.0944046	+	0.0355413i
$386$	1.95251	+	6.00922i	0.0993803	+	0.305861i
$387$	23.0301	−	2.70450i	1.17068	−	0.137477i
$388$	−6.46258	+	19.8898i	−0.328088	+	1.00975i
$389$	2.17285	+	0.461853i	0.110168	+	0.0234169i	0.262666	−	0.964887i	$-0.415398\pi$
$389$	2.17285	+	0.461853i	0.110168	+	0.0234169i	−0.152498	+	0.988304i	$0.548732\pi$
$390$	−0.418794	+	0.304039i	−0.0212064	+	0.0153956i
$391$	19.2079	−	4.08276i	0.971383	−	0.206474i
$392$	0.217336	−	2.06781i	0.0109771	−	0.104440i
$393$	−23.1832	−	14.8554i	−1.16944	−	0.749358i
$394$	−3.99405	+	1.77827i	−0.201217	+	0.0895878i
$395$	9.69362	−	24.7737i	0.487739	−	1.24650i
$396$	−0.0254724	−	2.09154i	−0.00128003	−	0.105104i
$397$	−18.7858	+	13.6487i	−0.942831	+	0.685007i	−0.949100	−	0.314974i	$-0.898004\pi$
$397$	−18.7858	+	13.6487i	−0.942831	+	0.685007i	0.00626974	+	0.999980i	$0.498004\pi$
$398$	2.71484	+	0.577058i	0.136083	+	0.0289253i
$399$	−0.763300	+	16.4846i	−0.0382128	+	0.825262i
$400$	−3.49665	+	15.4663i	−0.174833	+	0.773313i
$401$	7.72116	+	13.3734i	0.385576	+	0.667837i	0.991849	−	0.127419i	$-0.0406694\pi$
$401$	7.72116	+	13.3734i	0.385576	+	0.667837i	−0.606273	+	0.795257i	$0.707336\pi$
$402$	−5.89745	−	5.82607i	−0.294138	−	0.290578i
$403$	−0.218358	−	2.07753i	−0.0108772	−	0.103489i
$404$	−23.8384	+	17.3196i	−1.18601	+	0.861684i
$405$	−13.9732	+	14.4827i	−0.694334	+	0.719653i
$406$	0.264437	+	0.192125i	0.0131238	+	0.00953499i
$407$	1.84135	−	3.18931i	0.0912722	−	0.158088i
$408$	−10.6154	−	1.61512i	−0.525542	−	0.0799605i
$409$	26.5034	−	5.63347i	1.31051	−	0.278557i	0.500888	−	0.865512i	$-0.333007\pi$
$409$	26.5034	−	5.63347i	1.31051	−	0.278557i	0.809620	+	0.586955i	$0.199673\pi$
$410$	6.44677	+	3.33737i	0.318383	+	0.164821i
$411$	−11.7033	+	3.21238i	−0.577279	+	0.158455i
$412$	1.76057	+	1.95531i	0.0867371	+	0.0963314i
$413$	8.45511	−	26.0221i	0.416049	−	1.28047i
$414$	−4.95176	−	1.54251i	−0.243366	−	0.0758104i
$415$	−19.6283	−	1.15573i	−0.963517	−	0.0567323i
$416$	−0.973550	−	1.08124i	−0.0477322	−	0.0530120i
$417$	10.1016	+	25.8441i	0.494677	+	1.26559i
$418$	0.284861	+	0.493394i	0.0139330	+	0.0241327i
$419$	−1.68365	+	16.0188i	−0.0822516	+	0.782572i	0.873188	+	0.487384i	$0.162049\pi$
$419$	−1.68365	+	16.0188i	−0.0822516	+	0.782572i	−0.955439	+	0.295188i	$0.904618\pi$
$420$	−5.25422	+	16.1508i	−0.256380	+	0.788080i
$421$	−1.78347	−	16.9686i	−0.0869212	−	0.827000i	−0.947945	−	0.318435i	$-0.896843\pi$
$421$	−1.78347	−	16.9686i	−0.0869212	−	0.827000i	0.861024	−	0.508565i	$-0.169824\pi$
$422$	3.38077	−	2.45627i	0.164573	−	0.119570i
$423$	1.47663	−	1.36248i	0.0717960	−	0.0662463i
$424$	16.1155			0.782639
$425$	−0.275646	+	21.3579i	−0.0133708	+	1.03601i
$426$	−0.0622739	+	1.34490i	−0.00301718	+	0.0651604i
$427$	−10.2228	+	11.3536i	−0.494717	+	0.549439i
$428$	−13.5430	−	6.02972i	−0.654624	−	0.291458i
$429$	0.103553	−	0.206331i	0.00499959	−	0.00996175i
$430$	−6.08344	+	2.29028i	−0.293369	+	0.110447i
$431$	8.91750	+	6.47894i	0.429541	+	0.312080i	0.781465	−	0.623949i	$-0.214473\pi$
$431$	8.91750	+	6.47894i	0.429541	+	0.312080i	−0.351925	+	0.936028i	$0.614473\pi$
$432$	−12.9936	−	10.1347i	−0.625155	−	0.487606i
$433$	14.8065	+	10.7575i	0.711555	+	0.516975i	0.883675	−	0.468101i	$-0.155062\pi$
$433$	14.8065	+	10.7575i	0.711555	+	0.516975i	−0.172120	+	0.985076i	$0.555062\pi$
$434$	3.49124	+	3.87741i	0.167585	+	0.186122i
$435$	0.954173	+	1.06049i	0.0457491	+	0.0508467i
$436$	−10.9876	+	12.2030i	−0.526211	+	0.584416i
$437$	−18.1559	+	3.85916i	−0.868515	+	0.184609i
$438$	3.84348	+	1.44859i	0.183649	+	0.0692161i
$439$	20.6213	+	4.38319i	0.984200	+	0.209198i	0.671784	−	0.740747i	$-0.265528\pi$
$439$	20.6213	+	4.38319i	0.984200	+	0.209198i	0.312416	+	0.949945i	$0.398862\pi$
$440$	0.307475	+	1.17786i	0.0146583	+	0.0561524i
$441$	1.70032	−	3.94768i	0.0809678	−	0.187985i
$442$	−0.461810	−	0.335525i	−0.0219661	−	0.0159593i
$443$	−15.9033	+	27.5452i	−0.755586	+	1.30871i	0.189496	+	0.981882i	$0.439315\pi$
$443$	−15.9033	+	27.5452i	−0.755586	+	1.30871i	−0.945082	+	0.326833i	$0.894019\pi$
$444$	−11.5042	−	29.4325i	−0.545964	−	1.39680i
$445$	0.710777	−	4.30758i	0.0336940	−	0.204199i
$446$	1.03918	+	0.462673i	0.0492066	+	0.0219082i
$447$	19.3657	−	1.13320i	0.915966	−	0.0535983i
$448$	−11.0839	−	2.35595i	−0.523663	−	0.111308i
$449$	−14.3360			−0.676559			−0.338280	−	0.941046i	$-0.609845\pi$
$449$	−14.3360			−0.676559			−0.338280	+	0.941046i	$0.609845\pi$
$450$	2.82427	−	4.88358i	0.133137	−	0.230214i
$451$	−3.23831			−0.152486
$452$	30.2718	+	6.43447i	1.42387	+	0.302652i
$453$	3.29110	+	5.00091i	0.154629	+	0.234963i
$454$	−3.14323	−	1.39945i	−0.147519	−	0.0656796i
$455$	−1.33401	+	1.31690i	−0.0625392	+	0.0617373i
$456$	10.0341	+	1.52667i	0.469888	+	0.0714928i
$457$	−11.2914	+	19.5574i	−0.528191	+	0.914854i	0.471268	+	0.881990i	$0.343796\pi$
$457$	−11.2914	+	19.5574i	−0.528191	+	0.914854i	−0.999460	+	0.0328645i	$0.989537\pi$
$458$	−8.96789	−	6.51556i	−0.419042	−	0.304452i
$459$	−19.9590	−	9.71454i	−0.931605	−	0.453436i
$460$	−19.0704	−	1.12287i	−0.889160	−	0.0523541i
$461$	25.8932	+	5.50378i	1.20597	+	0.256337i	0.766692	−	0.642015i	$-0.221901\pi$
$461$	25.8932	+	5.50378i	1.20597	+	0.256337i	0.439277	+	0.898352i	$0.355235\pi$
$462$	0.0936675	+	0.568949i	0.00435780	+	0.0264699i
$463$	−5.61991	+	1.19455i	−0.261179	+	0.0555154i	−0.336640	−	0.941633i	$-0.609291\pi$
$463$	−5.61991	+	1.19455i	−0.261179	+	0.0555154i	0.0754608	+	0.997149i	$0.475957\pi$
$464$	−0.781622	+	0.868080i	−0.0362859	+	0.0402996i
$465$	11.3787	+	19.7250i	0.527674	+	0.914726i
$466$	2.05153	+	2.27846i	0.0950354	+	0.105547i
$467$	−14.6975	−	10.6783i	−0.680118	−	0.494135i	0.193279	−	0.981144i	$-0.438088\pi$
$467$	−14.6975	−	10.6783i	−0.680118	−	0.494135i	−0.873397	+	0.487009i	$0.838088\pi$
$468$	−0.827715	−	1.79977i	−0.0382611	−	0.0831943i
$469$	−24.2924	−	17.6494i	−1.12172	−	0.814975i
$470$	−0.309795	+	0.470369i	−0.0142898	+	0.0216965i
$471$	−3.04893	+	0.178410i	−0.140487	+	0.00822071i
$472$	−15.3734	−	6.84468i	−0.707618	−	0.315052i
$473$	1.94026	−	2.15488i	0.0892134	−	0.0990816i
$474$	−6.52525	−	4.18128i	−0.299715	−	0.192053i
$475$	0.260550	−	20.1882i	0.0119548	−	0.926296i
$476$	−18.7335			−0.858648
$477$	31.8077	+	9.90835i	1.45637	+	0.453672i
$478$	1.44317	−	1.04852i	0.0660090	−	0.0479583i
$479$	0.0346271	+	0.329455i	0.00158215	+	0.0150532i	0.995284	−	0.0969989i	$-0.0309243\pi$
$479$	0.0346271	+	0.329455i	0.00158215	+	0.0150532i	−0.993702	+	0.112052i	$0.964258\pi$
$480$	14.4867	+	6.45620i	0.661224	+	0.294684i
$481$	0.364571	−	3.46866i	0.0166230	−	0.158157i
$482$	−4.70591	−	8.15088i	−0.214348	−	0.371262i
$483$	−18.5721	−	2.82572i	−0.845061	−	0.128575i
$484$	13.5047	+	14.9985i	0.613852	+	0.681751i
$485$	9.16841	−	23.4315i	0.416316	−	1.06397i
$486$	3.34128	+	4.81744i	0.151564	+	0.218524i
$487$	−6.16698	+	18.9800i	−0.279452	+	0.860066i	0.708555	+	0.705656i	$0.249348\pi$
$487$	−6.16698	+	18.9800i	−0.279452	+	0.860066i	−0.988007	+	0.154410i	$0.950652\pi$
$488$	6.28744	+	6.98291i	0.284619	+	0.316102i
$489$	−10.2824	−	10.1579i	−0.464985	−	0.459356i
$490$	−0.196166	+	1.18884i	−0.00886188	+	0.0537065i
$491$	−35.3373	+	7.51118i	−1.59475	+	0.338975i	−0.917797	−	0.397050i	$-0.870034\pi$
$491$	−35.3373	+	7.51118i	−1.59475	+	0.338975i	−0.676954	+	0.736025i	$0.736701\pi$
$492$	−17.3555	+	21.7012i	−0.782448	+	0.978364i
$493$	−0.786756	+	1.36270i	−0.0354337	+	0.0613730i
$494$	0.436519	+	0.317149i	0.0196399	+	0.0142692i
$495$	−0.117316	+	2.51383i	−0.00527296	+	0.112988i
$496$	−15.0851	+	10.9600i	−0.677340	+	0.492117i
$497$	0.509741	+	4.84986i	0.0228650	+	0.217546i
$498$	−1.44882	+	5.54183i	−0.0649231	+	0.248335i
$499$	−13.7067	−	23.7407i	−0.613596	−	1.06278i	−0.990629	−	0.136579i	$-0.956389\pi$
$499$	−13.7067	−	23.7407i	−0.613596	−	1.06278i	0.377033	−	0.926200i	$-0.376944\pi$
$500$	5.76557	−	19.9633i	0.257844	−	0.892788i
$501$	16.7814	+	10.7533i	0.749737	+	0.480420i
$502$	−7.60696	−	1.61691i	−0.339515	−	0.0721662i
$503$	−1.33405	+	0.969242i	−0.0594822	+	0.0432164i	−0.617129	−	0.786862i	$-0.711704\pi$
$503$	−1.33405	+	0.969242i	−0.0594822	+	0.0432164i	0.557647	+	0.830078i	$0.311704\pi$
$504$	8.95788	+	5.02739i	0.399016	+	0.223938i
$505$	29.8558	−	19.1158i	1.32857	−	0.850643i
$506$	−0.592490	+	0.263794i	−0.0263394	+	0.0117271i
$507$	−1.03138	+	22.2742i	−0.0458051	+	0.989230i
$508$	1.79768	−	17.1038i	0.0797594	−	0.758860i
$509$	−24.1747	+	5.13850i	−1.07153	+	0.227760i	−0.709713	−	0.704491i	$-0.751176\pi$
$509$	−24.1747	+	5.13850i	−1.07153	+	0.227760i	−0.361813	+	0.932251i	$0.617842\pi$
$510$	6.08610	+	1.29595i	0.269497	+	0.0573857i
$511$	14.5523	+	3.09319i	0.643757	+	0.136835i
$512$	−6.85745	+	21.1051i	−0.303059	+	0.932721i
$513$	18.8659	+	9.18251i	0.832949	+	0.405418i
$514$	0.0464812	+	0.143054i	0.00205020	+	0.00630986i
$515$	−1.97625	−	2.47292i	−0.0870839	−	0.108970i
$516$	−4.04196	−	24.5514i	−0.177937	−	1.08082i
$517$	0.0262623	−	0.249869i	0.00115502	−	0.0109892i
$518$	4.35565	+	7.54420i	0.191376	+	0.331473i
$519$	19.5989	−	24.5062i	0.860295	−	1.07570i
$520$	0.719747	+	0.900634i	0.0315630	+	0.0394954i
$521$	0.868044	−	0.630671i	0.0380297	−	0.0276302i	−0.568608	−	0.822609i	$-0.692518\pi$
$521$	0.868044	−	0.630671i	0.0380297	−	0.0276302i	0.606638	+	0.794978i	$0.292518\pi$
$522$	0.357355	−	0.212163i	0.0156410	−	0.00928612i
$523$	−4.86221	−	14.9643i	−0.212610	−	0.654345i	−0.999315	−	0.0370160i	$-0.988215\pi$
$523$	−4.86221	−	14.9643i	−0.212610	−	0.654345i	0.786705	−	0.617329i	$-0.211785\pi$
$524$	−14.7727	+	25.5871i	−0.645349	+	1.11778i
$525$	7.45270	−	19.0263i	0.325263	−	0.830376i
$526$	0.502166	+	0.869777i	0.0218955	+	0.0379241i
$527$	−16.8068	+	18.6658i	−0.732116	+	0.813097i
$528$	−2.05712	+	0.120374i	−0.0895247	+	0.00523859i
$529$	0.195459	+	1.85967i	0.00849823	+	0.0808553i
$530$	−9.32295	−	0.548939i	−0.404963	−	0.0238444i
$531$	−26.1346	−	22.9616i	−1.13415	−	0.996450i
$532$	17.7075			0.767718
$533$	−2.80176	+	1.24742i	−0.121358	+	0.0540319i
$534$	−1.19014	−	0.448557i	−0.0515025	−	0.0194110i
$535$	15.8393	+	8.19969i	0.684792	+	0.354503i
$536$	−12.3574	+	13.7242i	−0.533757	+	0.592797i
$537$	2.05704	+	12.4947i	0.0887677	+	0.539187i
$538$	4.72214	+	5.24447i	0.203586	+	0.226105i
$539$	−0.166096	−	0.511190i	−0.00715425	−	0.0220185i
$540$	16.2174	+	14.2589i	0.697885	+	0.613605i
$541$	5.82440	−	17.9257i	0.250410	−	0.770684i	−0.744289	−	0.667858i	$-0.767211\pi$
$541$	5.82440	−	17.9257i	0.250410	−	0.770684i	0.994699	−	0.102826i	$-0.0327886\pi$
$542$	−4.59025	+	2.04371i	−0.197168	+	0.0877848i
$543$	−14.8525	+	7.68203i	−0.637384	+	0.329667i
$544$	−1.82861	+	17.3981i	−0.0784012	+	0.745937i
$545$	14.0596	−	13.8793i	0.602245	−	0.594523i
$546$	0.300204	+	0.456168i	0.0128475	+	0.0195222i
$547$	0.239907	+	2.28257i	0.0102577	+	0.0975955i	0.998453	−	0.0556048i	$-0.0177087\pi$
$547$	0.239907	+	2.28257i	0.0102577	+	0.0975955i	−0.988195	+	0.153200i	$0.951042\pi$
$548$	4.02417	+	12.3851i	0.171904	+	0.529067i
$549$	8.11639	+	17.6481i	0.346399	+	0.753203i
$550$	−0.137755	−	0.691876i	−0.00587391	−	0.0295017i
$551$	0.743668	−	1.28807i	0.0316813	−	0.0548737i
$552$	−2.92240	+	11.1784i	−0.124385	+	0.475782i
$553$	−25.6443	−	11.4176i	−1.09051	−	0.485525i
$554$	−7.82379	−	3.48337i	−0.332401	−	0.147994i
$555$	11.7356	+	36.1632i	0.498149	+	1.53504i
$556$	27.2006	−	12.1105i	1.15356	−	0.513599i
$557$	26.8111			1.13602			0.568012	−	0.823020i	$-0.307713\pi$
$557$	26.8111			1.13602			0.568012	+	0.823020i	$0.307713\pi$
$558$	6.28380	−	2.12667i	0.266014	−	0.0900293i
$559$	0.848622	−	2.61179i	0.0358929	−	0.110467i
$560$	16.1335	+	4.43473i	0.681764	+	0.187401i
$561$	−2.67678	+	0.734739i	−0.113014	+	0.0310207i
$562$	3.30124	−	0.701700i	0.139254	−	0.0295994i
$563$	−20.7742	+	4.41570i	−0.875529	+	0.186100i	−0.623692	−	0.781670i	$-0.714368\pi$
$563$	−20.7742	+	4.41570i	−0.875529	+	0.186100i	−0.251837	+	0.967770i	$0.581035\pi$
$564$	−1.53372	−	1.51515i	−0.0645812	−	0.0637995i
$565$	−35.9027	−	9.86884i	−1.51044	−	0.415185i
$566$	0.755716	−	2.32586i	0.0317651	−	0.0977630i
$567$	14.5894	+	15.4303i	0.612699	+	0.648012i
$568$	2.99928			0.125847
$569$	37.4475	−	16.6727i	1.56988	−	0.698955i	0.576853	−	0.816848i	$-0.304281\pi$
$569$	37.4475	−	16.6727i	1.56988	−	0.698955i	0.993026	+	0.117893i	$0.0376140\pi$
$570$	−5.75278	−	1.22498i	−0.240958	−	0.0513087i
$571$	40.3376	+	17.9594i	1.68807	+	0.751579i	0.999655	+	0.0262671i	$0.00836204\pi$
$571$	40.3376	+	17.9594i	1.68807	+	0.751579i	0.688420	+	0.725312i	$0.258305\pi$
$572$	−0.226303	−	0.100757i	−0.00946220	−	0.00421284i
$573$	21.9010	−	6.01153i	0.914928	−	0.251135i
$574$	3.83006	−	6.63386i	0.159864	−	0.276892i
$575$	22.8249	+	2.69723i	0.951865	+	0.112482i
$576$	−8.32593	+	11.7582i	−0.346914	+	0.489923i
$577$	−1.18692	−	3.65297i	−0.0494122	−	0.152075i	0.923306	−	0.384065i	$-0.125476\pi$
$577$	−1.18692	−	3.65297i	−0.0494122	−	0.152075i	−0.972718	+	0.231990i	$0.925476\pi$
$578$	0.0491159	+	0.467307i	0.00204295	+	0.0194374i
$579$	29.0490	−	1.69982i	1.20724	−	0.0706421i
$580$	1.08937	−	1.07540i	0.0452336	−	0.0446536i
$581$	−2.16873	+	20.6340i	−0.0899739	+	0.856044i
$582$	−6.17171	−	3.95474i	−0.255826	−	0.163929i
$583$	3.80586	−	1.69448i	0.157623	−	0.0701782i
$584$	2.82757	−	8.70237i	0.117006	−	0.360107i
$585$	0.866846	+	2.22013i	0.0358397	+	0.0917912i
$586$	1.99186	+	6.13031i	0.0822830	+	0.253241i
$587$	−26.5121	−	29.4447i	−1.09427	−	1.21531i	−0.974942	−	0.222459i	$-0.928592\pi$
$587$	−26.5121	−	29.4447i	−1.09427	−	1.21531i	−0.119332	−	0.992854i	$-0.538075\pi$
$588$	−4.31586	−	1.62662i	−0.177983	−	0.0670807i
$589$	15.8863	−	17.6436i	0.654586	−	0.726991i
$590$	8.66048	+	4.48336i	0.356546	+	0.184577i
$591$	3.27080	+	19.8673i	0.134543	+	0.817231i
$592$	−28.4403	+	12.6624i	−1.16889	+	0.520423i
$593$	−23.7687			−0.976065			−0.488033	−	0.872825i	$-0.662285\pi$
$593$	−23.7687			−0.976065			−0.488033	+	0.872825i	$0.662285\pi$
$594$	0.711499	+	0.176782i	0.0291932	+	0.00725344i
$595$	22.4997	+	1.32479i	0.922399	+	0.0543113i
$596$	−2.17582	−	20.7016i	−0.0891252	−	0.847970i
$597$	5.73350	−	11.4241i	0.234657	−	0.467556i
$598$	−0.411002	+	0.456464i	−0.0168071	+	0.0186662i
$599$	−21.3498	−	36.9790i	−0.872330	−	1.51092i	−0.859580	−	0.511001i	$-0.829275\pi$
$599$	−21.3498	−	36.9790i	−0.872330	−	1.51092i	−0.0127494	−	0.999919i	$-0.504058\pi$
$600$	−11.1587	−	5.78178i	−0.455552	−	0.236040i
$601$	15.2463	−	26.4074i	0.621910	−	1.07718i	−0.367220	−	0.930134i	$-0.619690\pi$
$601$	15.2463	−	26.4074i	0.621910	−	1.07718i	0.989130	−	0.147045i	$-0.0469764\pi$
$602$	2.11958	+	6.52338i	0.0863875	+	0.265873i
$603$	−32.8282	+	19.4902i	−1.33687	+	0.793704i
$604$	5.19707	−	3.77589i	0.211466	−	0.153639i
$605$	−15.1591	−	18.9689i	−0.616305	−	0.771196i
$606$	−3.75976	−	9.61904i	−0.152730	−	0.390747i
$607$	13.5546	+	23.4772i	0.550163	+	0.952910i	0.998262	+	0.0589263i	$0.0187677\pi$
$607$	13.5546	+	23.4772i	0.550163	+	0.952910i	−0.448099	+	0.893984i	$0.647899\pi$
$608$	1.72847	−	16.4453i	0.0700986	−	0.666943i
$609$	1.16406	−	0.954429i	0.0471700	−	0.0386754i
$610$	−3.39948	−	4.25384i	−0.137641	−	0.172233i
$611$	−0.0735297	−	0.226301i	−0.00297469	−	0.00915517i
$612$	−9.42227	+	21.8759i	−0.380873	+	0.884282i
$613$	6.76831	−	20.8307i	0.273370	−	0.841345i	−0.716277	−	0.697816i	$-0.754155\pi$
$613$	6.76831	−	20.8307i	0.273370	−	0.841345i	0.989646	−	0.143529i	$-0.0458449\pi$
$614$	−8.36797	−	1.77867i	−0.337704	−	0.0717811i
$615$	22.3794	−	24.8367i	0.902425	−	1.00151i
$616$	1.25646	−	0.267069i	0.0506242	−	0.0107605i
$617$	2.94074	−	27.9793i	0.118390	−	1.12640i	−0.760486	−	0.649354i	$-0.775039\pi$
$617$	2.94074	−	27.9793i	0.118390	−	1.12640i	0.878876	−	0.477050i	$-0.158294\pi$
$618$	−0.819126	+	0.423668i	−0.0329501	+	0.0170424i
$619$	−33.5139	+	14.9214i	−1.34704	+	0.599740i	−0.948315	−	0.317332i	$-0.897213\pi$
$619$	−33.5139	+	14.9214i	−1.34704	+	0.599740i	−0.398723	+	0.917071i	$0.630546\pi$
$620$	20.5782	−	13.1757i	0.826442	−	0.529148i
$621$	−12.6408	+	20.2663i	−0.507259	+	0.813257i
$622$	4.37705	−	3.18011i	0.175504	−	0.127511i
$623$	−4.50616	−	0.957813i	−0.180535	−	0.0383740i
$624$	−1.73343	+	0.896566i	−0.0693929	+	0.0358914i
$625$	−8.33647	+	23.5691i	−0.333459	+	0.942765i
$626$	0.486357	+	0.842395i	0.0194387	+	0.0336689i
$627$	2.53018	−	0.694500i	0.101046	−	0.0277357i
$628$	0.342562	+	3.25926i	0.0136697	+	0.130059i
$629$	−33.9270	+	24.6494i	−1.35276	+	0.982837i
$630$	−5.01096	−	3.21351i	−0.199641	−	0.128029i
$631$	−9.47939	−	6.88718i	−0.377369	−	0.274174i	0.382891	−	0.923793i	$-0.374928\pi$
$631$	−9.47939	−	6.88718i	−0.377369	−	0.274174i	−0.760260	+	0.649619i	$0.774928\pi$
$632$	−8.63244	+	14.9518i	−0.343380	+	0.594752i
$633$	−7.00610	−	17.9245i	−0.278467	−	0.712436i
$634$	5.70708	−	1.21308i	0.226657	−	0.0481775i
$635$	−3.36865	+	20.4153i	−0.133681	+	0.810157i
$636$	9.04194	−	34.5860i	0.358536	−	1.37142i
$637$	−0.340619	−	0.378296i	−0.0134958	−	0.0149886i
$638$	0.0160594	−	0.0494257i	0.000635797	−	0.00195678i
$639$	5.91978	+	1.84406i	0.234183	+	0.0729499i
$640$	8.14493	−	20.8158i	0.321957	−	0.822817i
$641$	−18.9229	−	21.0160i	−0.747410	−	0.830083i	0.242741	−	0.970091i	$-0.421954\pi$
$641$	−18.9229	−	21.0160i	−0.747410	−	0.830083i	−0.990150	+	0.140009i	$0.955287\pi$
$642$	3.24529	−	4.05788i	0.128082	−	0.160152i
$643$	−24.9228	−	43.1676i	−0.982861	−	1.70237i	−0.651081	−	0.759009i	$-0.725684\pi$
$643$	−24.9228	−	43.1676i	−0.982861	−	1.70237i	−0.331780	−	0.943357i	$-0.607649\pi$
$644$	−2.10707	+	20.0475i	−0.0830303	+	0.789981i
$645$	3.11834	+	29.7732i	0.122785	+	1.17232i
$646$	−0.678141	−	6.45208i	−0.0266811	−	0.253854i
$647$	−36.4560	+	26.4868i	−1.43323	+	1.04131i	−0.443830	+	0.896111i	$0.646381\pi$
$647$	−36.4560	+	26.4868i	−1.43323	+	1.04131i	−0.989403	+	0.145194i	$0.953619\pi$
$648$	10.3762	−	7.93192i	0.407616	−	0.311595i
$649$	−4.35029			−0.170764
$650$	−0.385701	−	0.545540i	−0.0151284	−	0.0213979i
$651$	21.3429	−	11.0390i	0.836495	−	0.432652i
$652$	−10.3778	+	11.5257i	−0.406426	+	0.451381i
$653$	39.5029	+	17.5878i	1.54587	+	0.688265i	0.989747	−	0.142835i	$-0.0456217\pi$
$653$	39.5029	+	17.5878i	1.54587	+	0.688265i	0.556123	+	0.831100i	$0.312288\pi$
$654$	−3.16395	−	4.80772i	−0.123720	−	0.187997i
$655$	19.5521	−	29.6865i	0.763965	−	1.15995i
$656$	22.1470	+	16.0907i	0.864694	+	0.628237i
$657$	10.9314	−	15.4376i	0.426473	−	0.602280i
$658$	0.480809	+	0.349328i	0.0187439	+	0.0136182i
$659$	−22.7712	−	25.2900i	−0.887039	−	0.985157i	0.112925	−	0.993604i	$-0.463978\pi$
$659$	−22.7712	−	25.2900i	−0.887039	−	0.985157i	−0.999964	+	0.00844655i	$0.997311\pi$
$660$	2.70036		0.000981808i	0.105111		3.82168e-5i
$661$	−2.00144	+	2.22282i	−0.0778469	+	0.0864577i	−0.780810	−	0.624769i	$-0.785193\pi$
$661$	−2.00144	+	2.22282i	−0.0778469	+	0.0864577i	0.702963	+	0.711226i	$0.251860\pi$
$662$	3.18734	−	0.677491i	0.123880	−	0.0263314i
$663$	−2.03290	+	1.66681i	−0.0789513	+	0.0647334i
$664$	12.4818	+	2.65309i	0.484388	+	0.102960i
$665$	−21.2675	−	1.25224i	−0.824718	−	0.0485598i
$666$	11.0004	−	1.29182i	0.426258	−	0.0500569i
$667$	1.36979	+	0.995212i	0.0530385	+	0.0385347i
$668$	10.6934	−	18.5215i	0.413739	−	0.716617i
$669$	3.27196	−	4.09123i	0.126501	−	0.158176i
$670$	7.61632	−	7.51865i	0.294244	−	0.290471i
$671$	2.21908	+	0.987996i	0.0856665	+	0.0381412i
$672$	7.50691	−	14.9576i	0.289585	−	0.577002i
$673$	6.93118	+	1.47327i	0.267178	+	0.0567903i	0.339552	−	0.940587i	$-0.389724\pi$
$673$	6.93118	+	1.47327i	0.267178	+	0.0567903i	−0.0723748	+	0.997378i	$0.523058\pi$
$674$	6.20994			0.239198
$675$	−18.4694	−	18.2724i	−0.710888	−	0.703305i
$676$	23.9266			0.920253
$677$	35.2596	+	7.49466i	1.35514	+	0.288043i	0.827519	−	0.561438i	$-0.189752\pi$
$677$	35.2596	+	7.49466i	1.35514	+	0.288043i	0.527618	+	0.849482i	$0.323085\pi$
$678$	−4.86559	+	9.69474i	−0.186862	+	0.372324i
$679$	−24.2549	−	10.7990i	−0.930817	−	0.414426i
$680$	2.25682	−	13.6772i	0.0865453	−	0.524498i
$681$	−9.89676	+	12.3748i	−0.379245	+	0.474203i
$682$	0.414783	−	0.718424i	0.0158828	−	0.0275099i
$683$	21.8805	+	15.8971i	0.837236	+	0.608287i	0.921597	−	0.388148i	$-0.126885\pi$
$683$	21.8805	+	15.8971i	0.837236	+	0.608287i	−0.0843615	+	0.996435i	$0.526885\pi$
$684$	8.90625	−	20.6779i	0.340539	−	0.790637i
$685$	−3.95736	−	15.1597i	−0.151203	−	0.579221i
$686$	7.31969	+	1.55585i	0.279467	+	0.0594026i
$687$	−39.4769	+	32.3677i	−1.50614	+	1.23491i
$688$	−23.9769	+	5.09644i	−0.914110	+	0.194300i
$689$	2.64007	−	2.93210i	0.100579	−	0.111704i
$690$	2.07139	−	6.36722i	0.0788566	−	0.242396i
$691$	−8.47233	−	9.40948i	−0.322303	−	0.357953i	0.560119	−	0.828412i	$-0.310755\pi$
$691$	−8.47233	−	9.40948i	−0.322303	−	0.357953i	−0.882422	+	0.470458i	$0.844089\pi$
$692$	−27.2406	−	19.7915i	−1.03553	−	0.752359i
$693$	2.64412	+	0.245392i	0.100442	+	0.00932166i
$694$	0.170830	+	0.124115i	0.00648462	+	0.00471135i
$695$	−33.5255	+	12.6216i	−1.27169	+	0.478766i
$696$	−0.508960	−	0.773379i	−0.0192921	−	0.0293148i
$697$	33.6877	+	14.9987i	1.27601	+	0.568117i
$698$	−9.05514	+	10.0568i	−0.342742	+	0.380654i
$699$	12.5416	−	6.48675i	0.474367	−	0.245352i
$700$	−20.7639	−	7.04413i	−0.784803	−	0.266243i
$701$	38.2015			1.44285			0.721426	−	0.692492i	$-0.243487\pi$
$701$	38.2015			1.44285			0.721426	+	0.692492i	$0.243487\pi$
$702$	0.683680	−	0.121125i	0.0258038	−	0.00457157i
$703$	32.0690	−	23.2995i	1.20950	−	0.878756i
$704$	0.188323	+	1.79177i	0.00709768	+	0.0675299i
$705$	1.73491	+	1.92823i	0.0653406	+	0.0726212i
$706$	0.517730	−	4.92587i	0.0194850	−	0.185388i
$707$	−18.7040	−	32.3963i	−0.703437	−	1.21839i
$708$	−23.3151	+	29.1530i	−0.876237	+	1.09564i
$709$	26.4187	+	29.3409i	0.992175	+	1.10192i	0.994792	+	0.101926i	$0.0325004\pi$
$709$	26.4187	+	29.3409i	0.992175	+	1.10192i	−0.00261676	+	0.999997i	$0.500833\pi$
$710$	−1.73511	−	0.102164i	−0.0651175	−	0.00383415i
$711$	−26.2310	+	24.2034i	−0.983739	+	0.907697i
$712$	−0.875563	+	2.69470i	−0.0328131	+	0.100988i
$713$	18.0847	+	20.0851i	0.677278	+	0.752194i
$714$	1.66076	−	6.35253i	0.0621525	−	0.237737i
$715$	0.264674	+	0.137017i	0.00989826	+	0.00512413i
$716$	13.2908	−	2.82506i	0.496702	−	0.105577i
$717$	−2.99073	−	7.65154i	−0.111691	−	0.285752i
$718$	6.98185	−	12.0929i	0.260560	−	0.451304i
$719$	8.24606	+	5.99111i	0.307526	+	0.223431i	0.730834	−	0.682555i	$-0.239131\pi$
$719$	8.24606	+	5.99111i	0.307526	+	0.223431i	−0.423308	+	0.905986i	$0.639131\pi$
$720$	13.2932	−	16.6093i	0.495408	−	0.618991i
$721$	−2.70238	+	1.96339i	−0.100642	+	0.0731205i
$722$	−0.105940	−	1.00795i	−0.00394269	−	0.0375122i
$723$	−41.7987	+	11.4732i	−1.55451	+	0.426691i
$724$	8.97143	+	15.5390i	0.333421	+	0.577501i
$725$	−1.38443	+	1.21457i	−0.0514165	+	0.0451078i
$726$	−6.28323	+	3.24981i	−0.233192	+	0.120612i
$727$	−26.9467	−	5.72770i	−0.999399	−	0.212429i	−0.320966	−	0.947091i	$-0.604007\pi$
$727$	−26.9467	−	5.72770i	−0.999399	−	0.212429i	−0.678433	+	0.734662i	$0.737341\pi$
$728$	0.984202	−	0.715064i	0.0364769	−	0.0265020i
$729$	25.3566	−	9.27584i	0.939135	−	0.343549i
$730$	−1.93220	+	4.93807i	−0.0715139	+	0.182766i
$731$	−30.1649	+	13.4303i	−1.11569	+	0.496737i
$732$	18.5139	−	9.57577i	0.684295	−	0.353931i
$733$	−0.396743	+	3.77476i	−0.0146540	+	0.139424i	−0.999403	−	0.0345595i	$-0.988997\pi$
$733$	−0.396743	+	3.77476i	−0.0146540	+	0.139424i	0.984749	+	0.173983i	$0.0556639\pi$
$734$	9.45761	−	2.01028i	0.349087	−	0.0742007i
$735$	5.06850	+	2.25885i	0.186955	+	0.0833190i
$736$	18.4127	+	3.91375i	0.678703	+	0.144263i
$737$	−1.47529	+	4.54046i	−0.0543428	+	0.167250i
$738$	−5.82027	−	7.80912i	−0.214247	−	0.287458i
$739$	−6.92487	−	21.3125i	−0.254735	−	0.783995i	−0.993882	−	0.110450i	$-0.964771\pi$
$739$	−6.92487	−	21.3125i	−0.254735	−	0.783995i	0.739146	−	0.673545i	$-0.235229\pi$
$740$	38.1804	−	14.3741i	1.40354	−	0.528403i
$741$	1.92156	−	1.57552i	0.0705904	−	0.0578782i
$742$	−1.03009	+	9.80063i	−0.0378157	+	0.359792i
$743$	0.543224	+	0.940891i	0.0199289	+	0.0345179i	0.875818	−	0.482642i	$-0.160323\pi$
$743$	0.543224	+	0.940891i	0.0199289	+	0.0345179i	−0.855889	+	0.517160i	$0.826989\pi$
$744$	−5.38009	−	13.7645i	−0.197244	−	0.504632i
$745$	1.14929	+	25.0174i	0.0421066	+	0.916566i
$746$	−1.41619	+	1.02892i	−0.0518505	+	0.0376716i
$747$	23.0045	+	12.9107i	0.841691	+	0.472378i
$748$	0.920413	+	2.83274i	0.0336536	+	0.103575i
$749$	9.41020	−	16.2990i	0.343841	−	0.595551i
$750$	6.25845	+	3.72490i	0.228526	+	0.136014i
$751$	−7.82702	−	13.5568i	−0.285612	−	0.494694i	0.687145	−	0.726520i	$-0.258863\pi$
$751$	−7.82702	−	13.5568i	−0.285612	−	0.494694i	−0.972757	+	0.231826i	$0.925530\pi$
$752$	−1.42118	+	1.57838i	−0.0518249	+	0.0575574i
$753$	−16.0652	+	32.0101i	−0.585448	+	1.16651i
$754$	−0.00514473	−	0.0489489i	−0.000187360	−	0.00178261i
$755$	−6.50893	+	4.16748i	−0.236884	+	0.151670i
$756$	15.8154	−	16.4041i	0.575202	−	0.596610i
$757$	−8.77489			−0.318929			−0.159464	−	0.987204i	$-0.550977\pi$
$757$	−8.77489			−0.318929			−0.159464	+	0.987204i	$0.550977\pi$
$758$	8.70165	−	3.87422i	0.316058	−	0.140718i
$759$	0.485200	+	2.94717i	0.0176117	+	0.106976i
$760$	−2.13323	+	12.9282i	−0.0773803	+	0.468955i
$761$	−12.7460	+	14.1558i	−0.462041	+	0.513149i	−0.928469	−	0.371411i	$-0.878874\pi$
$761$	−12.7460	+	14.1558i	−0.462041	+	0.513149i	0.466427	+	0.884560i	$0.345541\pi$
$762$	5.64054	+	2.12589i	0.204335	+	0.0770127i
$763$	−13.9492	−	15.4921i	−0.504993	−	0.560852i
$764$	−7.53068	−	23.1771i	−0.272450	−	0.838516i
$765$	12.8636	−	25.6076i	0.465084	−	0.925845i
$766$	−0.792465	+	2.43896i	−0.0286329	+	0.0881231i
$767$	−3.76384	+	1.67577i	−0.135904	+	0.0605085i
$768$	8.52455	+	5.46240i	0.307603	+	0.197107i
$769$	−2.89450	+	27.5393i	−0.104378	+	0.993094i	0.809504	+	0.587115i	$0.199736\pi$
$769$	−2.89450	+	27.5393i	−0.104378	+	0.993094i	−0.913882	+	0.405979i	$0.866930\pi$
$770$	−0.735969	+	0.111703i	−0.0265225	+	0.00402549i
$771$	0.691536	−	0.0404656i	0.0249051	−	0.00145733i
$772$	−3.26379	−	31.0529i	−0.117466	−	1.11762i
$773$	4.15971	+	12.8023i	0.149615	+	0.460466i	0.997576	−	0.0695925i	$-0.0221699\pi$
$773$	4.15971	+	12.8023i	0.149615	+	0.460466i	−0.847961	+	0.530059i	$0.822170\pi$
$774$	8.68372	+	0.805907i	0.312130	+	0.0289677i
$775$	−25.6471	+	14.3693i	−0.921272	+	0.516161i
$776$	−8.16473	+	14.1417i	−0.293097	+	0.507659i
$777$	38.6875	−	10.6192i	1.38791	−	0.380962i
$778$	0.763226	+	0.339810i	0.0273630	+	0.0121828i
$779$	−31.8427	−	14.1773i	−1.14088	−	0.507954i
$780$	2.33671	−	1.03935i	0.0836676	−	0.0372148i
$781$	0.708315	−	0.315362i	0.0253455	−	0.0112846i
$782$	7.38538			0.264101
$783$	−0.529050	−	1.83937i	−0.0189067	−	0.0657336i
$784$	−1.40410	+	4.32136i	−0.0501463	+	0.154334i
$785$	−0.180944	−	3.93874i	−0.00645815	−	0.140580i
$786$	−7.36696	−	7.27778i	−0.262771	−	0.259590i
$787$	11.0803	−	2.35520i	0.394972	−	0.0839538i	−0.00614432	−	0.999981i	$-0.501956\pi$
$787$	11.0803	−	2.35520i	0.394972	−	0.0839538i	0.401116	+	0.916027i	$0.368622\pi$
$788$	21.1331	−	4.49199i	0.752837	−	0.160020i
$789$	4.46032	−	1.22430i	0.158792	−	0.0435861i
$790$	5.50324	−	8.35570i	0.195796	−	0.297283i
$791$	−12.1412	+	37.3667i	−0.431691	+	1.32861i
$792$	0.320087	−	1.60155i	0.0113738	−	0.0569086i
$793$	2.30051			0.0816935
$794$	−7.97811	+	3.55208i	−0.283132	+	0.126059i
$795$	−13.3056	+	40.8999i	−0.471902	+	1.45057i
$796$	−12.5299	−	5.57866i	−0.444110	−	0.197730i
$797$	−3.70507	−	1.64960i	−0.131240	−	0.0584320i	0.340066	−	0.940402i	$-0.389551\pi$
$797$	−3.70507	−	1.64960i	−0.131240	−	0.0584320i	−0.471306	+	0.881970i	$0.656217\pi$
$798$	−1.56981	+	6.00462i	−0.0555706	+	0.212561i
$799$	−1.43051	+	2.47772i	−0.0506078	+	0.0876553i
$800$	−8.56881	+	18.5962i	−0.302953	+	0.657476i
$801$	−3.38492	+	4.78029i	−0.119600	+	0.168903i
$802$	1.79471	+	5.52354i	0.0633733	+	0.195043i
$803$	−0.247255	−	2.35247i	−0.00872543	−	0.0830169i
$804$	22.5207	+	34.2208i	0.794243	+	1.20687i
$805$	3.94840	−	23.9289i	0.139163	−	0.843382i
$806$	0.0821234	−	0.781352i	0.00289267	−	0.0275220i
$807$	28.8678	−	14.9310i	1.01619	−	0.525596i
$808$	−21.0183	+	9.35797i	−0.739423	+	0.329212i
$809$	1.08629	−	3.34324i	0.0381918	−	0.117542i	−0.930143	−	0.367198i	$-0.880317\pi$
$809$	1.08629	−	3.34324i	0.0381918	−	0.117542i	0.968335	+	0.249655i	$0.0803173\pi$
$810$	−6.27290	+	4.23524i	−0.220407	+	0.148811i
$811$	13.6058	+	41.8744i	0.477765	+	1.47041i	0.842193	+	0.539177i	$0.181265\pi$
$811$	13.6058	+	41.8744i	0.477765	+	1.47041i	−0.364428	+	0.931232i	$0.618735\pi$
$812$	−1.08082	−	1.20037i	−0.0379292	−	0.0421246i
$813$	3.75903	+	22.8329i	0.131835	+	0.800784i
$814$	0.926777	−	1.02929i	0.0324835	−	0.0360766i
$815$	13.2793	−	13.1090i	0.465152	−	0.459187i
$816$	21.9575	+	8.27563i	0.768665	+	0.289705i
$817$	28.5129	−	12.6948i	0.997540	−	0.444133i
$818$	10.1905			0.356302
$819$	2.38219	−	0.806224i	0.0832406	−	0.0281717i
$820$	−27.7329	−	22.7555i	−0.968474	−	0.794657i
$821$	−1.84739	−	17.5767i	−0.0644744	−	0.613433i	−0.978281	−	0.207283i	$-0.933538\pi$
$821$	−1.84739	−	17.5767i	−0.0644744	−	0.613433i	0.913807	−	0.406150i	$-0.133129\pi$
$822$	−4.55655	+	0.266629i	−0.158928	+	0.00929977i
$823$	21.4671	−	23.8416i	0.748295	−	0.831066i	−0.241967	−	0.970285i	$-0.577792\pi$
$823$	21.4671	−	23.8416i	0.748295	−	0.831066i	0.990262	+	0.139219i	$0.0444591\pi$
$824$	1.02721	+	1.77919i	0.0357847	+	0.0619809i
$825$	−3.24318	−	0.192143i	−0.112913	−	0.00668957i
$826$	5.14524	−	8.91181i	0.179026	−	0.310082i
$827$	−14.6544	−	45.1017i	−0.509584	−	1.56834i	−0.792925	−	0.609320i	$-0.791443\pi$
$827$	−14.6544	−	45.1017i	−0.509584	−	1.56834i	0.283341	−	0.959019i	$-0.408557\pi$
$828$	22.3505	+	12.5437i	0.776735	+	0.435923i
$829$	−1.12381	+	0.816496i	−0.0390315	+	0.0283581i	−0.607130	−	0.794603i	$-0.707679\pi$
$829$	−1.12381	+	0.816496i	−0.0390315	+	0.0283581i	0.568098	+	0.822961i	$0.307679\pi$
$830$	−7.13045	−	1.96000i	−0.247501	−	0.0680325i
$831$	−24.6340	+	30.8021i	−0.854544	+	1.06851i
$832$	0.853140	+	1.47768i	0.0295773	+	0.0512294i
$833$	−0.639783	+	6.08713i	−0.0221672	+	0.210907i
$834$	1.69528	+	10.2973i	0.0587026	+	0.356568i
$835$	−14.1530	+	21.4889i	−0.489785	+	0.743653i
$836$	−0.870005	−	2.67760i	−0.0300897	−	0.0926067i
$837$	−2.15597	−	30.4753i	−0.0745212	−	1.05338i
$838$	−1.87197	+	5.76132i	−0.0646660	+	0.199021i
$839$	−26.8889	−	5.71541i	−0.928307	−	0.197318i	−0.281141	−	0.959667i	$-0.590713\pi$
$839$	−26.8889	−	5.71541i	−0.928307	−	0.197318i	−0.647166	+	0.762349i	$0.724046\pi$
$840$	−6.63486	+	11.4823i	−0.228924	+	0.396176i
$841$	28.2336	−	6.00123i	0.973571	−	0.206939i
$842$	0.670757	−	6.38183i	0.0231158	−	0.219932i
$843$	0.718930	−	15.5264i	0.0247613	−	0.534756i
$844$	−18.8653	+	8.39939i	−0.649371	+	0.289119i
$845$	−28.7369	−	1.69204i	−0.988578	−	0.0582079i
$846$	0.649756	−	0.385763i	0.0223391	−	0.0132628i
$847$	−20.7290	+	15.0605i	−0.712256	+	0.517484i
$848$	−34.4481	−	7.32218i	−1.18295	−	0.251445i
$849$	−9.48278	−	6.07642i	−0.325448	−	0.208542i
$850$	−1.77148	+	7.83552i	−0.0607611	+	0.268756i
$851$	22.5624	+	39.0792i	0.773428	+	1.33962i
$852$	1.68281	−	6.43686i	0.0576521	−	0.220523i
$853$	0.747701	+	7.11390i	0.0256008	+	0.243575i	0.999837	+	0.0180460i	$0.00574452\pi$
$853$	0.747701	+	7.11390i	0.0256008	+	0.243575i	−0.974236	+	0.225529i	$0.927589\pi$
$854$	−4.64854	+	3.37736i	−0.159070	+	0.115571i
$855$	−12.1591	+	24.2052i	−0.415832	+	0.827799i
$856$	−9.36461	−	6.80379i	−0.320076	−	0.232549i
$857$	4.13554	−	7.16297i	0.141267	−	0.244682i	−0.786707	−	0.617327i	$-0.788216\pi$
$857$	4.13554	−	7.16297i	0.141267	−	0.244682i	0.927974	+	0.372645i	$0.121549\pi$
$858$	0.0542288	−	0.0678071i	0.00185134	−	0.00231490i
$859$	−22.2616	+	4.73184i	−0.759555	+	0.161448i	−0.571378	−	0.820687i	$-0.693591\pi$
$859$	−22.2616	+	4.73184i	−0.759555	+	0.161448i	−0.188177	+	0.982135i	$0.560258\pi$
$860$	31.7587	−	4.82022i	1.08296	−	0.164368i
$861$	−25.0964	−	24.7926i	−0.855282	−	0.844929i
$862$	2.77393	+	3.08076i	0.0944803	+	0.104931i
$863$	−6.39640	+	19.6861i	−0.217736	+	0.670123i	0.781212	+	0.624266i	$0.214602\pi$
$863$	−6.39640	+	19.6861i	−0.217736	+	0.670123i	−0.998948	+	0.0458569i	$0.985398\pi$
$864$	−13.6910	−	16.2893i	−0.465776	−	0.554173i
$865$	31.3176	+	25.6968i	1.06483	+	0.873718i
$866$	4.60579	+	5.11525i	0.156511	+	0.173823i
$867$	2.13934	+	0.325498i	0.0726559	+	0.0110545i
$868$	−12.8918	−	22.3293i	−0.437577	−	0.757906i
$869$	−0.466527	+	4.43871i	−0.0158259	+	0.150573i
$870$	0.268094	+	0.464742i	0.00908923	+	0.0157562i
$871$	0.472618	+	4.49666i	0.0160141	+	0.152364i
$872$	−10.3728	+	7.53631i	−0.351269	+	0.255212i
$873$	−24.8098	+	22.8920i	−0.839684	+	0.774777i
$874$	−6.98091			−0.236133
$875$	24.4402	+	9.92869i	0.826231	+	0.335651i
$876$	−17.0900	−	10.9510i	−0.577416	−	0.369999i
$877$	7.92995	−	8.80710i	0.267775	−	0.297395i	−0.594229	−	0.804296i	$-0.702543\pi$
$877$	7.92995	−	8.80710i	0.267775	−	0.297395i	0.862004	+	0.506902i	$0.169209\pi$
$878$	7.24336	+	3.22495i	0.244452	+	0.108837i
$879$	29.6344	−	1.73408i	0.999544	−	0.0584889i
$880$	−0.122083	−	2.65747i	−0.00411541	−	0.0895834i
$881$	0.952966	+	0.692370i	0.0321062	+	0.0233265i	0.603723	−	0.797194i	$-0.293683\pi$
$881$	0.952966	+	0.692370i	0.0321062	+	0.0233265i	−0.571616	+	0.820521i	$0.693683\pi$
$882$	0.934198	−	1.31931i	0.0314561	−	0.0444233i
$883$	−5.30098	−	3.85139i	−0.178392	−	0.129609i	0.495006	−	0.868890i	$-0.335166\pi$
$883$	−5.30098	−	3.85139i	−0.178392	−	0.129609i	−0.673398	+	0.739280i	$0.735166\pi$
$884$	1.88753	+	2.09631i	0.0634844	+	0.0705066i
$885$	30.0641	−	33.3652i	1.01060	−	1.12156i
$886$	−8.00434	+	8.88972i	−0.268911	+	0.298656i
$887$	52.1642	−	11.0878i	1.75150	−	0.372293i	0.783141	−	0.621844i	$-0.213616\pi$
$887$	52.1642	−	11.0878i	1.75150	−	0.372293i	0.968362	+	0.249551i	$0.0802830\pi$
$888$	−4.00826	−	24.3467i	−0.134508	−	0.817022i
$889$	21.3564	+	4.53945i	0.716271	+	0.152248i
$890$	0.598309	−	1.52908i	0.0200554	−	0.0512550i
$891$	1.61645	−	2.96423i	0.0541532	−	0.0993054i
$892$	−4.54773	−	3.30412i	−0.152269	−	0.110630i
$893$	1.35217	−	2.34202i	0.0452485	−	0.0783727i
$894$	7.21281	+	1.09742i	0.241232	+	0.0367031i
$895$	−16.1627	+	2.45311i	−0.540258	+	0.0819985i
$896$	−21.5473	−	9.59347i	−0.719845	−	0.320495i
$897$	1.55507	+	2.36297i	0.0519221	+	0.0788971i
$898$	−5.27390	−	1.12100i	−0.175992	−	0.0374083i
$899$	−2.16569			−0.0722298
$900$	−18.6693	+	20.7040i	−0.622309	+	0.690134i
$901$	−47.4401			−1.58046
$902$	−1.19130	−	0.253219i	−0.0396660	−	0.00843127i
$903$	31.5345	−	1.84526i	1.04940	−	0.0614065i
$904$	22.0756	+	9.82868i	0.734223	+	0.326897i
$905$	−9.67620	−	19.2974i	−0.321648	−	0.641468i
$906$	0.819674	+	2.09707i	0.0272319	+	0.0696704i
$907$	−23.7125	+	41.0712i	−0.787360	+	1.36375i	0.140220	+	0.990120i	$0.455219\pi$
$907$	−23.7125	+	41.0712i	−0.787360	+	1.36375i	−0.927579	+	0.373626i	$0.878114\pi$
$908$	13.7556	+	9.99402i	0.456495	+	0.331663i
$909$	−47.2381	+	5.54733i	−1.56679	+	0.183993i
$910$	−0.593725	+	0.380146i	−0.0196818	+	0.0126017i
$911$	9.88100	+	2.10027i	0.327372	+	0.0695851i	0.368666	−	0.929562i	$-0.379815\pi$
$911$	9.88100	+	2.10027i	0.327372	+	0.0695851i	−0.0412938	+	0.999147i	$0.513148\pi$
$912$	−20.7549	−	7.82240i	−0.687264	−	0.259026i
$913$	3.22668	−	0.685852i	0.106788	−	0.0226984i
$914$	−5.68315	+	6.31177i	−0.187982	+	0.208775i
$915$	−22.9132	+	10.1916i	−0.757488	+	0.336925i
$916$	36.6539	+	40.7083i	1.21108	+	1.34504i
$917$	−30.3454	−	22.0472i	−1.00209	−	0.728064i
$918$	−6.58283	−	5.13444i	−0.217266	−	0.169462i
$919$	16.4085	+	11.9215i	0.541266	+	0.393253i	0.824555	−	0.565782i	$-0.191426\pi$
$919$	16.4085	+	11.9215i	0.541266	+	0.393253i	−0.283289	+	0.959035i	$0.591426\pi$
$920$	−14.3827	−	3.95349i	−0.474185	−	0.130343i
$921$	−17.6724	+	35.2124i	−0.582325	+	1.16029i
$922$	9.09517	+	4.04943i	0.299533	+	0.133361i
$923$	0.491348	−	0.545697i	0.0161729	−	0.0179619i
$924$	0.131798	−	2.84637i	0.00433584	−	0.0936388i
$925$	−46.8729	+	14.5639i	−1.54117	+	0.478858i
$926$	−2.16084			−0.0710097
$927$	0.933540	+	4.14320i	0.0306615	+	0.136081i
$928$	−1.22030	+	0.886601i	−0.0400584	+	0.0291041i
$929$	3.77311	+	35.8988i	0.123792	+	1.17780i	0.863314	+	0.504668i	$0.168385\pi$
$929$	3.77311	+	35.8988i	0.123792	+	1.17780i	−0.739522	+	0.673133i	$0.764948\pi$
$930$	2.64357	+	8.14614i	0.0866860	+	0.267123i
$931$	0.604744	−	5.75376i	0.0198197	−	0.188572i
$932$	−7.57554	−	13.1212i	−0.248145	−	0.429800i
$933$	−9.07072	−	23.2067i	−0.296962	−	0.759753i
$934$	−4.57188	−	5.07758i	−0.149596	−	0.166144i
$935$	−0.905130	−	3.46733i	−0.0296009	−	0.113394i
$936$	−0.339994	−	1.50895i	−0.0111131	−	0.0493215i
$937$	−2.52174	+	7.76113i	−0.0823818	+	0.253545i	−0.983760	−	0.179487i	$-0.942556\pi$
$937$	−2.52174	+	7.76113i	−0.0823818	+	0.253545i	0.901379	+	0.433032i	$0.142556\pi$
$938$	−7.55651	−	8.39236i	−0.246729	−	0.274020i
$939$	4.31990	−	1.18575i	0.140975	−	0.0386956i
$940$	1.98073	−	1.95533i	0.0646044	−	0.0637760i
$941$	48.6857	−	10.3485i	1.58711	−	0.337350i	0.671998	−	0.740553i	$-0.265437\pi$
$941$	48.6857	−	10.3485i	1.58711	−	0.337350i	0.915111	+	0.403203i	$0.132103\pi$
$942$	−1.13558	−	0.172778i	−0.0369993	−	0.00562940i
$943$	19.8398	−	34.3636i	0.646073	−	1.11903i
$944$	29.7519	+	21.6160i	0.968342	+	0.703541i
$945$	−20.1551	+	18.5836i	−0.655645	+	0.604524i
$946$	0.882279	−	0.641013i	0.0286854	−	0.0208411i
$947$	0.803938	+	7.64896i	0.0261245	+	0.248558i	0.999788	+	0.0205697i	$0.00654801\pi$
$947$	0.803938	+	7.64896i	0.0261245	+	0.248558i	−0.973664	+	0.227988i	$0.926785\pi$
$948$	27.2452	+	26.9154i	0.884882	+	0.874171i
$949$	−1.12011	−	1.94009i	−0.0363604	−	0.0629781i
$950$	1.67446	−	7.40639i	0.0543266	−	0.240295i
$951$	1.24286	−	26.8415i	0.0403027	−	0.870395i
$952$	−14.3077	−	3.04120i	−0.463716	−	0.0985660i
$953$	8.32277	−	6.04685i	0.269601	−	0.195877i	−0.444768	−	0.895646i	$-0.646714\pi$
$953$	8.32277	−	6.04685i	0.269601	−	0.195877i	0.714369	+	0.699769i	$0.246714\pi$
$954$	10.9265	+	6.13225i	0.353760	+	0.198539i
$955$	7.40564	+	28.3692i	0.239641	+	0.918006i
$956$	−8.05314	+	3.58549i	−0.260457	+	0.115963i
$957$	−0.201514	−	0.129127i	−0.00651403	−	0.00417409i
$958$	−0.0130231	+	0.123907i	−0.000420758	+	0.00400324i
$959$	−16.1713	+	3.43731i	−0.522197	+	0.110996i
$960$	−15.0437	−	10.9383i	−0.485534	−	0.353031i
$961$	−3.49208	−	0.742264i	−0.112648	−	0.0239440i
$962$	0.405349	−	1.24753i	0.0130690	−	0.0402221i
$963$	−14.3000	−	19.1865i	−0.460812	−	0.618277i
$964$	14.3725	+	44.2340i	0.462907	+	1.42468i
$965$	1.72396	+	37.5267i	0.0554961	+	1.20803i
$966$	−6.61131	−	2.49176i	−0.212715	−	0.0801711i
$967$	1.88470	−	17.9317i	0.0606077	−	0.576644i	−0.921507	−	0.388361i	$-0.873041\pi$
$967$	1.88470	−	17.9317i	0.0606077	−	0.576644i	0.982115	−	0.188283i	$-0.0602921\pi$
$968$	7.87940	+	13.6475i	0.253254	+	0.438648i
$969$	−29.5378	−	4.49413i	−0.948890	−	0.144372i
$970$	5.20507	−	7.90299i	0.167125	−	0.253750i
$971$	21.6172	−	15.7058i	0.693730	−	0.504025i	−0.184154	−	0.982897i	$-0.558954\pi$
$971$	21.6172	−	15.7058i	0.693730	−	0.504025i	0.877884	+	0.478873i	$0.158954\pi$
$972$	−11.2012	−	26.7191i	−0.359277	−	0.857014i
$973$	11.6809	+	35.9500i	0.374472	+	1.15251i
$974$	−3.75283	+	6.50008i	−0.120248	+	0.208276i
$975$	−2.87999	+	1.08306i	−0.0922335	+	0.0346857i
$976$	−10.2672	−	17.7832i	−0.328644	−	0.569228i
$977$	−16.6448	+	18.4859i	−0.532513	+	0.591416i	−0.948034	−	0.318168i	$-0.896932\pi$
$977$	−16.6448	+	18.4859i	−0.532513	+	0.591416i	0.415521	+	0.909583i	$0.363599\pi$
$978$	−2.98836	−	4.54089i	−0.0955571	−	0.145202i
$979$	0.0765629	+	0.728447i	0.00244696	+	0.0232813i
$980$	2.16967	−	5.54498i	0.0693076	−	0.177128i
$981$	−25.1068	+	8.49707i	−0.801597	+	0.271291i
$982$	−13.5871			−0.433583
$983$	−31.5050	+	14.0269i	−1.00485	+	0.447390i	−0.842126	−	0.539281i	$-0.818696\pi$
$983$	−31.5050	+	14.0269i	−1.00485	+	0.447390i	−0.162728	+	0.986671i	$0.552029\pi$
$984$	−16.7783	+	13.7568i	−0.534873	+	0.438551i
$985$	−25.6995	+	3.90058i	−0.818854	+	0.124283i
$986$	−0.395986	+	0.439787i	−0.0126108	+	0.0140057i
$987$	2.11653	−	1.73538i	0.0673700	−	0.0552377i
$988$	−1.78415	−	1.98150i	−0.0567615	−	0.0630400i
$989$	10.9795	+	33.7913i	0.349127	+	1.07450i
$990$	−0.239726	+	0.915607i	−0.00761899	+	0.0290999i
$991$	−1.92211	+	5.91566i	−0.0610580	+	0.187917i	−0.976933	−	0.213547i	$-0.931498\pi$
$991$	−1.92211	+	5.91566i	−0.0610580	+	0.187917i	0.915875	+	0.401464i	$0.131498\pi$
$992$	−21.9960	+	9.79326i	−0.698374	+	0.310936i
$993$	0.694126	−	14.9907i	0.0220274	−	0.475715i
$994$	−0.191711	+	1.82401i	−0.00608071	+	0.0578541i
$995$	14.6544	+	7.58630i	0.464576	+	0.240502i
$996$	12.6970	−	25.2990i	0.402321	−	0.801630i
$997$	0.848789	+	8.07569i	0.0268814	+	0.255760i	0.999707	+	0.0242190i	$0.00770992\pi$
$997$	0.848789	+	8.07569i	0.0268814	+	0.255760i	−0.972825	+	0.231541i	$0.925623\pi$
$998$	−3.18598	−	9.80545i	−0.100851	−	0.310386i
$999$	7.05795	−	50.5183i	0.223304	−	1.59833i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	225.2.q.a.106.17	yes	224
3.2	odd	2		675.2.r.a.181.12		224
9.4	even	3	inner	225.2.q.a.31.12	✓	224
9.5	odd	6		675.2.r.a.631.17		224
25.21	even	5	inner	225.2.q.a.196.12	yes	224
75.71	odd	10		675.2.r.a.46.17		224
225.121	even	15	inner	225.2.q.a.121.17	yes	224
225.221	odd	30		675.2.r.a.496.12		224

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
225.2.q.a.31.12	✓	224	9.4	even	3	inner
225.2.q.a.106.17	yes	224	1.1	even	1	trivial
225.2.q.a.121.17	yes	224	225.121	even	15	inner
225.2.q.a.196.12	yes	224	25.21	even	5	inner
675.2.r.a.46.17		224	75.71	odd	10
675.2.r.a.181.12		224	3.2	odd	2
675.2.r.a.496.12		224	225.221	odd	30
675.2.r.a.631.17		224	9.5	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(0.367877 + 0.0781947i) q^{2} +(0.776923 - 1.54803i) q^{3} +(-1.69787 - 0.755941i) q^{4} +(1.98576 + 1.02799i) q^{5} +(0.406860 - 0.508733i) q^{6} +(1.17975 - 2.04339i) q^{7} +(-1.17403 - 0.852985i) q^{8} +(-1.79278 - 2.40540i) q^{9} +O(q^{10})\)	\(q+(0.367877 + 0.0781947i) q^{2} +(0.776923 - 1.54803i) q^{3} +(-1.69787 - 0.755941i) q^{4} +(1.98576 + 1.02799i) q^{5} +(0.406860 - 0.508733i) q^{6} +(1.17975 - 2.04339i) q^{7} +(-1.17403 - 0.852985i) q^{8} +(-1.79278 - 2.40540i) q^{9} +(0.650132 + 0.533449i) q^{10} +(-0.366949 - 0.0779975i) q^{11} +(-2.48933 + 2.04104i) q^{12} +(-0.347527 + 0.0738691i) q^{13} +(0.593785 - 0.659465i) q^{14} +(3.13414 - 2.27534i) q^{15} +(2.12203 + 2.35675i) q^{16} +(3.45606 + 2.51098i) q^{17} +(-0.471434 - 1.02508i) q^{18} +(-3.26679 - 2.37346i) q^{19} +(-2.59447 - 3.24651i) q^{20} +(-2.24664 - 3.41384i) q^{21} +(-0.128893 - 0.0573870i) q^{22} +(3.07582 - 3.41605i) q^{23} +(-2.23258 + 1.15473i) q^{24} +(2.88648 + 4.08267i) q^{25} -0.133623 q^{26} +(-5.11648 + 0.906467i) q^{27} +(-3.54774 + 2.57759i) q^{28} +(0.0385018 + 0.366320i) q^{29} +(1.33090 - 0.591974i) q^{30} +(-0.614589 + 5.84742i) q^{31} +(2.04755 + 3.54645i) q^{32} +(-0.405834 + 0.507450i) q^{33} +(1.07506 + 1.19398i) q^{34} +(4.44328 - 2.84490i) q^{35} +(1.22557 + 5.43929i) q^{36} +(-3.03352 + 9.33621i) q^{37} +(-1.01618 - 1.12859i) q^{38} +(-0.155650 + 0.595372i) q^{39} +(-1.45449 - 2.90072i) q^{40} +(8.44348 - 1.79472i) q^{41} +(-0.559545 - 1.43155i) q^{42} +(-3.86472 + 6.69390i) q^{43} +(0.564071 + 0.409822i) q^{44} +(-1.08731 - 6.61950i) q^{45} +(1.39864 - 1.01617i) q^{46} +(0.0700054 + 0.666057i) q^{47} +(5.29697 - 1.45394i) q^{48} +(0.716381 + 1.24081i) q^{49} +(0.742627 + 1.72763i) q^{50} +(6.57216 - 3.39925i) q^{51} +(0.645896 + 0.137289i) q^{52} +(-8.98419 + 6.52740i) q^{53} +(-1.95312 - 0.0666126i) q^{54} +(-0.648493 - 0.532104i) q^{55} +(-3.12804 + 1.39270i) q^{56} +(-6.21222 + 3.21308i) q^{57} +(-0.0144804 + 0.137771i) q^{58} +(11.3428 - 2.41099i) q^{59} +(-7.04139 + 1.49402i) q^{60} +(-6.33351 - 1.34623i) q^{61} +(-0.683331 + 2.10308i) q^{62} +(-7.03019 + 0.825578i) q^{63} +(-1.48405 - 4.56744i) q^{64} +(-0.766041 - 0.210567i) q^{65} +(-0.188977 + 0.154945i) q^{66} +(1.33023 - 12.6563i) q^{67} +(-3.96980 - 6.87589i) q^{68} +(-2.89846 - 7.41547i) q^{69} +(1.85704 - 0.699135i) q^{70} +(-1.67206 + 1.21482i) q^{71} +(0.0530170 + 4.35323i) q^{72} +(1.94846 + 5.99673i) q^{73} +(-1.84600 + 3.19737i) q^{74} +(8.56267 - 1.29643i) q^{75} +(3.75239 + 6.49933i) q^{76} +(-0.592287 + 0.657802i) q^{77} +(-0.103815 + 0.206853i) q^{78} +(-1.24358 - 11.8319i) q^{79} +(1.79112 + 6.86136i) q^{80} +(-2.57187 + 8.62470i) q^{81} +3.24650 q^{82} +(-8.03305 + 3.57654i) q^{83} +(1.23385 + 7.49459i) q^{84} +(4.28165 + 8.53899i) q^{85} +(-1.94517 + 2.16033i) q^{86} +(0.596986 + 0.225001i) q^{87} +(0.364280 + 0.404574i) q^{88} +(-0.603343 - 1.85690i) q^{89} +(0.117613 - 2.52018i) q^{90} +(-0.259051 + 0.797278i) q^{91} +(-7.80469 + 3.47487i) q^{92} +(8.57449 + 5.49440i) q^{93} +(-0.0263287 + 0.250501i) q^{94} +(-4.04716 - 8.07133i) q^{95} +(7.08079 - 0.414337i) q^{96} +(-1.17621 - 11.1909i) q^{97} +(0.166516 + 0.512483i) q^{98} +(0.470245 + 1.02249i) 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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