LMFDB - Embedded newform 225.2.q.a.31.15

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			31.15
Character	$\chi$	$=$	225.31
Dual form			225.2.q.a.196.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.110043 + 0.122216i) q^{2} +(-0.385619 - 1.68858i) q^{3} +(0.206230 + 1.96215i) q^{4} +(-2.06082 + 0.867759i) q^{5} +(0.248806 + 0.138688i) q^{6} +(2.06663 + 3.57951i) q^{7} +(-0.528597 - 0.384048i) q^{8} +(-2.70260 + 1.30230i) q^{9} +O(q^{10})$	\(q+(-0.110043 + 0.122216i) q^{2} +(-0.385619 - 1.68858i) q^{3} +(0.206230 + 1.96215i) q^{4} +(-2.06082 + 0.867759i) q^{5} +(0.248806 + 0.138688i) q^{6} +(2.06663 + 3.57951i) q^{7} +(-0.528597 - 0.384048i) q^{8} +(-2.70260 + 1.30230i) q^{9} +(0.120726 - 0.347356i) q^{10} +(-0.239690 + 0.266203i) q^{11} +(3.23371 - 1.10488i) q^{12} +(1.23537 + 1.37202i) q^{13} +(-0.664892 - 0.141327i) q^{14} +(2.25997 + 3.14524i) q^{15} +(-3.75457 + 0.798059i) q^{16} +(3.22940 + 2.34629i) q^{17} +(0.138242 - 0.473609i) q^{18} +(-0.0599095 - 0.0435268i) q^{19} +(-2.12767 - 3.86468i) q^{20} +(5.24736 - 4.87000i) q^{21} +(-0.00615783 - 0.0585878i) q^{22} +(4.28234 + 0.910239i) q^{23} +(-0.444658 + 1.04067i) q^{24} +(3.49399 - 3.57660i) q^{25} -0.303627 q^{26} +(3.24120 + 4.06136i) q^{27} +(-6.59733 + 4.79324i) q^{28} +(-5.93713 - 2.64338i) q^{29} +(-0.633093 - 0.0699089i) q^{30} +(-4.95171 + 2.20464i) q^{31} +(0.969013 - 1.67838i) q^{32} +(0.541934 + 0.302083i) q^{33} +(-0.642128 + 0.136489i) q^{34} +(-7.36512 - 5.58341i) q^{35} +(-3.11265 - 5.03431i) q^{36} +(2.37480 - 7.30889i) q^{37} +(0.0119123 - 0.00253204i) q^{38} +(1.84038 - 2.61510i) q^{39} +(1.42261 + 0.332761i) q^{40} +(3.14813 + 3.49635i) q^{41} +(0.0177530 + 1.17722i) q^{42} +(1.55061 + 2.68574i) q^{43} +(-0.571760 - 0.415408i) q^{44} +(4.43949 - 5.02901i) q^{45} +(-0.582489 + 0.423203i) q^{46} +(-11.8169 - 5.26122i) q^{47} +(2.79542 + 6.03215i) q^{48} +(-5.04195 + 8.73292i) q^{49} +(0.0526256 + 0.820601i) q^{50} +(2.71659 - 6.35787i) q^{51} +(-2.43733 + 2.70693i) q^{52} +(1.53179 - 1.11291i) q^{53} +(-0.853034 - 0.0508000i) q^{54} +(0.262959 - 0.756591i) q^{55} +(0.282290 - 2.68581i) q^{56} +(-0.0503961 + 0.117947i) q^{57} +(0.976404 - 0.434723i) q^{58} +(3.31117 + 3.67743i) q^{59} +(-5.70534 + 5.08304i) q^{60} +(6.08932 - 6.76288i) q^{61} +(0.275461 - 0.847783i) q^{62} +(-10.2469 - 6.98261i) q^{63} +(-2.27380 - 6.99805i) q^{64} +(-3.73647 - 1.75549i) q^{65} +(-0.0965556 + 0.0329906i) q^{66} +(13.1648 - 5.86135i) q^{67} +(-3.93777 + 6.82042i) q^{68} +(-0.114341 - 7.58207i) q^{69} +(1.49286 - 0.285716i) q^{70} +(10.8652 - 7.89400i) q^{71} +(1.92873 + 0.349537i) q^{72} +(4.15877 + 12.7994i) q^{73} +(0.631930 + 1.09453i) q^{74} +(-7.38671 - 4.52067i) q^{75} +(0.0730507 - 0.126528i) q^{76} +(-1.44823 - 0.307831i) q^{77} +(0.117084 + 0.512698i) q^{78} +(-5.47332 - 2.43688i) q^{79} +(7.04499 - 4.90273i) q^{80} +(5.60805 - 7.03916i) q^{81} -0.773739 q^{82} +(0.301668 - 2.87018i) q^{83} +(10.6378 + 9.29174i) q^{84} +(-8.69124 - 2.03296i) q^{85} +(-0.498874 - 0.106039i) q^{86} +(-2.17408 + 11.0446i) q^{87} +(0.228934 - 0.0486615i) q^{88} +(2.21408 + 6.81425i) q^{89} +(0.126086 + 1.09598i) q^{90} +(-2.35810 + 7.25750i) q^{91} +(-0.902876 + 8.59029i) q^{92} +(5.63219 + 7.51120i) q^{93} +(1.94338 - 0.865246i) q^{94} +(0.161234 + 0.0377140i) q^{95} +(-3.20775 - 0.989039i) q^{96} +(9.65762 + 4.29985i) q^{97} +(-0.512465 - 1.57721i) q^{98} +(0.301111 - 1.03159i) 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 $

$2$	−0.110043	+	0.122216i	−0.0778125	+	0.0864195i	−0.780794	−	0.624789i	$-0.785185\pi$
$2$	−0.110043	+	0.122216i	−0.0778125	+	0.0864195i	0.702981	+	0.711208i	$0.251852\pi$
$3$	−0.385619	−	1.68858i	−0.222637	−	0.974901i
$3$	−0.385619	−	1.68858i	−0.222637	−	0.974901i
$4$	0.206230	+	1.96215i	0.103115	+	0.981073i
$5$	−2.06082	+	0.867759i	−0.921628	+	0.388074i
$5$	−2.06082	+	0.867759i	−0.921628	+	0.388074i
$6$	0.248806	+	0.138688i	0.101574	+	0.0566193i
$7$	2.06663	+	3.57951i	0.781114	+	1.35293i	0.931293	+	0.364271i	$0.118682\pi$
$7$	2.06663	+	3.57951i	0.781114	+	1.35293i	−0.150179	+	0.988659i	$0.547985\pi$
$8$	−0.528597	−	0.384048i	−0.186887	−	0.135782i
$9$	−2.70260	+	1.30230i	−0.900865	+	0.434099i
$10$	0.120726	−	0.347356i	0.0381771	−	0.109844i
$11$	−0.239690	+	0.266203i	−0.0722693	+	0.0802632i	−0.778195	−	0.628023i	$-0.783865\pi$
$11$	−0.239690	+	0.266203i	−0.0722693	+	0.0802632i	0.705926	+	0.708286i	$0.250531\pi$
$12$	3.23371	−	1.10488i	0.933492	−	0.318950i
$13$	1.23537	+	1.37202i	0.342631	+	0.380530i	0.889691	−	0.456563i	$-0.150920\pi$
$13$	1.23537	+	1.37202i	0.342631	+	0.380530i	−0.547060	+	0.837093i	$0.684253\pi$
$14$	−0.664892	−	0.141327i	−0.177700	−	0.0377713i
$15$	2.25997	+	3.14524i	0.583522	+	0.812097i
$16$	−3.75457	+	0.798059i	−0.938644	+	0.199515i
$17$	3.22940	+	2.34629i	0.783244	+	0.569060i	0.905951	−	0.423383i	$-0.139157\pi$
$17$	3.22940	+	2.34629i	0.783244	+	0.569060i	−0.122707	+	0.992443i	$0.539157\pi$
$18$	0.138242	−	0.473609i	0.0325840	−	0.111631i
$19$	−0.0599095	−	0.0435268i	−0.0137442	−	0.00998573i	0.580892	−	0.813981i	$-0.302704\pi$
$19$	−0.0599095	−	0.0435268i	−0.0137442	−	0.00998573i	−0.594636	+	0.803995i	$0.702704\pi$
$20$	−2.12767	−	3.86468i	−0.475762	−	0.864168i
$21$	5.24736	−	4.87000i	1.14507	−	1.06272i
$22$	−0.00615783	−	0.0585878i	−0.00131285	−	0.0124910i
$23$	4.28234	+	0.910239i	0.892929	+	0.189798i	0.631455	−	0.775413i	$-0.282458\pi$
$23$	4.28234	+	0.910239i	0.892929	+	0.189798i	0.261474	+	0.965210i	$0.415791\pi$
$24$	−0.444658	+	1.04067i	−0.0907655	+	0.212427i
$25$	3.49399	−	3.57660i	0.698798	−	0.715319i
$26$	−0.303627			−0.0595462
$27$	3.24120	+	4.06136i	0.623770	+	0.781608i
$28$	−6.59733	+	4.79324i	−1.24678	+	0.905837i
$29$	−5.93713	−	2.64338i	−1.10250	−	0.490863i	−0.226906	−	0.973917i	$-0.572861\pi$
$29$	−5.93713	−	2.64338i	−1.10250	−	0.490863i	−0.875591	+	0.483054i	$0.839528\pi$
$30$	−0.633093	−	0.0699089i	−0.115586	−	0.0127636i
$31$	−4.95171	+	2.20464i	−0.889353	+	0.395966i	−0.799976	−	0.600032i	$-0.795154\pi$
$31$	−4.95171	+	2.20464i	−0.889353	+	0.395966i	−0.0893776	+	0.995998i	$0.528488\pi$
$32$	0.969013	−	1.67838i	0.171299	−	0.296698i
$33$	0.541934	+	0.302083i	0.0943386	+	0.0525859i
$34$	−0.642128	+	0.136489i	−0.110124	+	0.0234076i
$35$	−7.36512	−	5.58341i	−1.24493	−	0.943768i
$36$	−3.11265	−	5.03431i	−0.518775	−	0.839052i
$37$	2.37480	−	7.30889i	0.390415	−	1.20157i	−0.542060	−	0.840340i	$-0.682355\pi$
$37$	2.37480	−	7.30889i	0.390415	−	1.20157i	0.932475	−	0.361235i	$-0.117645\pi$
$38$	0.0119123	−	0.00253204i	0.00193243	−	0.000410751i
$39$	1.84038	−	2.61510i	0.294697	−	0.418751i
$40$	1.42261	+	0.332761i	0.224934	+	0.0526141i
$41$	3.14813	+	3.49635i	0.491655	+	0.546038i	0.937004	−	0.349319i	$-0.113587\pi$
$41$	3.14813	+	3.49635i	0.491655	+	0.546038i	−0.445349	+	0.895357i	$0.646920\pi$
$42$	0.0177530	+	1.17722i	0.00273935	+	0.181649i
$43$	1.55061	+	2.68574i	0.236466	+	0.409571i	0.959698	−	0.281034i	$-0.0906775\pi$
$43$	1.55061	+	2.68574i	0.236466	+	0.409571i	−0.723232	+	0.690605i	$0.757344\pi$
$44$	−0.571760	−	0.415408i	−0.0861961	−	0.0626252i
$45$	4.43949	−	5.02901i	0.661801	−	0.749680i
$46$	−0.582489	+	0.423203i	−0.0858833	+	0.0623979i
$47$	−11.8169	−	5.26122i	−1.72367	−	0.767428i	−0.996737	−	0.0807203i	$-0.974278\pi$
$47$	−11.8169	−	5.26122i	−1.72367	−	0.767428i	−0.726934	−	0.686707i	$-0.759055\pi$
$48$	2.79542	+	6.03215i	0.403484	+	0.870666i
$49$	−5.04195	+	8.73292i	−0.720279	+	1.24756i
$50$	0.0526256	+	0.820601i	0.00744238	+	0.116051i
$51$	2.71659	−	6.35787i	0.380398	−	0.890280i
$52$	−2.43733	+	2.70693i	−0.337997	+	0.375384i
$53$	1.53179	−	1.11291i	0.210408	−	0.152870i	−0.477590	−	0.878583i	$-0.658490\pi$
$53$	1.53179	−	1.11291i	0.210408	−	0.152870i	0.687998	+	0.725712i	$0.258490\pi$
$54$	−0.853034	−	0.0508000i	−0.116083	−	0.00691300i
$55$	0.262959	−	0.756591i	0.0354574	−	0.102019i
$56$	0.282290	−	2.68581i	0.0377225	−	0.358906i
$57$	−0.0503961	+	0.117947i	−0.00667513	+	0.0156224i
$58$	0.976404	−	0.434723i	0.128208	−	0.0570820i
$59$	3.31117	+	3.67743i	0.431078	+	0.478760i	0.919074	−	0.394086i	$-0.128939\pi$
$59$	3.31117	+	3.67743i	0.431078	+	0.478760i	−0.487996	+	0.872846i	$0.662272\pi$
$60$	−5.70534	+	5.08304i	−0.736557	+	0.656217i
$61$	6.08932	−	6.76288i	0.779658	−	0.865898i	−0.214174	−	0.976796i	$-0.568706\pi$
$61$	6.08932	−	6.76288i	0.779658	−	0.865898i	0.993832	+	0.110898i	$0.0353726\pi$
$62$	0.275461	−	0.847783i	0.0349836	−	0.107669i
$63$	−10.2469	−	6.98261i	−1.29098	−	0.879726i
$64$	−2.27380	−	6.99805i	−0.284226	−	0.874756i
$65$	−3.73647	−	1.75549i	−0.463452	−	0.217741i
$66$	−0.0965556	+	0.0329906i	−0.0118852	+	0.00406086i
$67$	13.1648	−	5.86135i	1.60834	−	0.716078i	0.611184	−	0.791488i	$-0.290693\pi$
$67$	13.1648	−	5.86135i	1.60834	−	0.716078i	0.997153	+	0.0754107i	$0.0240268\pi$
$68$	−3.93777	+	6.82042i	−0.477525	+	0.827098i
$69$	−0.114341	−	7.58207i	−0.0137650	−	0.912774i
$70$	1.49286	−	0.285716i	0.178431	−	0.0341496i
$71$	10.8652	−	7.89400i	1.28946	−	0.936845i	0.289662	−	0.957129i	$-0.406457\pi$
$71$	10.8652	−	7.89400i	1.28946	−	0.936845i	0.999794	+	0.0202841i	$0.00645707\pi$
$72$	1.92873	+	0.349537i	0.227303	+	0.0411933i
$73$	4.15877	+	12.7994i	0.486747	+	1.49805i	0.829435	+	0.558603i	$0.188663\pi$
$73$	4.15877	+	12.7994i	0.486747	+	1.49805i	−0.342688	+	0.939449i	$0.611337\pi$
$74$	0.631930	+	1.09453i	0.0734603	+	0.127237i
$75$	−7.38671	−	4.52067i	−0.852944	−	0.522002i
$76$	0.0730507	−	0.126528i	0.00837950	−	0.0145137i
$77$	−1.44823	−	0.307831i	−0.165041	−	0.0350806i
$78$	0.117084	+	0.512698i	0.0132572	+	0.0580516i
$79$	−5.47332	−	2.43688i	−0.615797	−	0.274170i	0.0750407	−	0.997180i	$-0.476091\pi$
$79$	−5.47332	−	2.43688i	−0.615797	−	0.274170i	−0.690837	+	0.723010i	$0.742758\pi$
$80$	7.04499	−	4.90273i	0.787654	−	0.548141i
$81$	5.60805	−	7.03916i	0.623117	−	0.782129i
$82$	−0.773739			−0.0854452
$83$	0.301668	−	2.87018i	0.0331123	−	0.315043i	−0.965412	−	0.260730i	$-0.916037\pi$
$83$	0.301668	−	2.87018i	0.0331123	−	0.315043i	0.998524	−	0.0543124i	$-0.0172967\pi$
$84$	10.6378	+	9.29174i	1.16068	+	1.01381i
$85$	−8.69124	−	2.03296i	−0.942697	−	0.220506i
$86$	−0.498874	−	0.106039i	−0.0537949	−	0.0114345i
$87$	−2.17408	+	11.0446i	−0.233086	+	1.18411i
$88$	0.228934	−	0.0486615i	0.0244045	−	0.00518733i
$89$	2.21408	+	6.81425i	0.234692	+	0.722309i	0.997162	+	0.0752851i	$0.0239867\pi$
$89$	2.21408	+	6.81425i	0.234692	+	0.722309i	−0.762470	+	0.647024i	$0.776013\pi$
$90$	0.126086	+	1.09598i	0.0132906	+	0.115527i
$91$	−2.35810	+	7.25750i	−0.247196	+	0.760792i
$92$	−0.902876	+	8.59029i	−0.0941313	+	0.895600i
$93$	5.63219	+	7.51120i	0.584031	+	0.778875i
$94$	1.94338	−	0.865246i	0.200444	−	0.0892434i
$95$	0.161234	+	0.0377140i	0.0165422	+	0.00386938i
$96$	−3.20775	−	0.989039i	−0.327389	−	0.100943i
$97$	9.65762	+	4.29985i	0.980583	+	0.436584i	0.833487	−	0.552539i	$-0.186341\pi$
$97$	9.65762	+	4.29985i	0.980583	+	0.436584i	0.147095	+	0.989122i	$0.453008\pi$
$98$	−0.512465	−	1.57721i	−0.0517668	−	0.159322i
$99$	0.301111	−	1.03159i	0.0302628	−	0.103678i
$100$	7.73837	+	6.11811i	0.773837	+	0.611811i
$101$	8.75862	+	15.1704i	0.871516	+	1.50951i	0.860429	+	0.509571i	$0.170196\pi$
$101$	8.75862	+	15.1704i	0.871516	+	1.50951i	0.0110870	+	0.999939i	$0.496471\pi$
$102$	0.478089	+	1.03165i	0.0473378	+	0.102149i
$103$	−1.25065	−	11.8991i	−0.123230	−	1.17245i	−0.864990	−	0.501788i	$-0.832676\pi$
$103$	−1.25065	−	11.8991i	−0.123230	−	1.17245i	0.741761	−	0.670665i	$-0.233991\pi$
$104$	−0.126092	−	1.19969i	−0.0123644	−	0.117639i
$105$	−6.58789	+	14.5897i	−0.642912	+	1.42381i
$106$	−0.0325485	+	0.309678i	−0.00316138	+	0.0300786i
$107$	−8.49063			−0.820820			−0.410410	−	0.911901i	$-0.634614\pi$
$107$	−8.49063			−0.820820			−0.410410	+	0.911901i	$0.634614\pi$
$108$	−7.30054	+	7.19728i	−0.702495	+	0.692559i
$109$	2.49526	−	7.67961i	0.239002	−	0.735573i	−0.757563	−	0.652762i	$-0.773610\pi$
$109$	2.49526	−	7.67961i	0.239002	−	0.735573i	0.996565	−	0.0828110i	$-0.0263898\pi$
$110$	0.0635303	+	0.115396i	0.00605738	+	0.0110025i
$111$	−13.2574	−	1.19159i	−1.25834	−	0.113101i
$112$	−10.6160	−	11.7903i	−1.00312	−	1.11407i
$113$	5.95046	+	6.60865i	0.559772	+	0.621690i	0.954897	−	0.296938i	$-0.0959654\pi$
$113$	5.95046	+	6.60865i	0.559772	+	0.621690i	−0.395125	+	0.918627i	$0.629299\pi$
$114$	−0.00886915	−	0.0191385i	−0.000830672	−	0.00179248i
$115$	−9.61501	+	1.84020i	−0.896604	+	0.171599i
$116$	3.96228	−	12.1946i	0.367889	−	1.13224i
$117$	−5.12549	−	2.09919i	−0.473852	−	0.194071i
$118$	−0.813812			−0.0749175
$119$	−1.72461	+	16.4086i	−0.158095	+	1.50417i
$120$	0.0133085	−	2.53050i	0.00121489	−	0.231002i
$121$	1.13640	+	10.8121i	0.103309	+	0.982921i
$122$	0.156439	+	1.48842i	0.0141634	+	0.134755i
$123$	4.68988	−	6.66412i	0.422872	−	0.600883i
$124$	−5.34702	−	9.26131i	−0.480177	−	0.831691i
$125$	−4.09687	+	10.4027i	−0.366435	+	0.930444i
$126$	1.98099	−	0.483936i	0.176480	−	0.0431125i
$127$	−1.00273	−	3.08608i	−0.0889778	−	0.273845i	0.896660	−	0.442720i	$-0.145987\pi$
$127$	−1.00273	−	3.08608i	−0.0889778	−	0.273845i	−0.985637	+	0.168875i	$0.945987\pi$
$128$	4.64644	+	2.06873i	0.410691	+	0.182851i
$129$	3.93713	−	3.65400i	0.346645	−	0.321717i
$130$	0.625722	−	0.263475i	0.0548794	−	0.0231083i
$131$	−7.86032	+	3.49964i	−0.686759	+	0.305765i	−0.720290	−	0.693673i	$-0.755991\pi$
$131$	−7.86032	+	3.49964i	−0.686759	+	0.305765i	0.0335311	+	0.999438i	$0.489325\pi$
$132$	−0.480968	+	1.12565i	−0.0418629	+	0.0979754i
$133$	0.0319938	−	0.304401i	0.00277421	−	0.0263949i
$134$	−0.732352	+	2.25395i	−0.0632656	+	0.194711i
$135$	−10.2038	−	5.55715i	−0.878205	−	0.478284i
$136$	−0.805959	−	2.48049i	−0.0691105	−	0.212700i
$137$	5.60580	−	1.19155i	0.478936	−	0.101801i	0.0378831	−	0.999282i	$-0.487939\pi$
$137$	5.60580	−	1.19155i	0.478936	−	0.101801i	0.441053	+	0.897481i	$0.354605\pi$
$138$	0.939230	+	0.820383i	0.0799526	+	0.0698357i
$139$	−16.2222	−	3.44813i	−1.37595	−	0.292466i	−0.540179	−	0.841550i	$-0.681643\pi$
$139$	−16.2222	−	3.44813i	−1.37595	−	0.292466i	−0.835767	+	0.549084i	$0.814977\pi$
$140$	9.43655	−	15.6029i	0.797534	−	1.31869i
$141$	−4.32716	+	21.9826i	−0.364413	+	1.85127i
$142$	−0.230869	+	2.19657i	−0.0193741	+	0.184332i
$143$	−0.661343			−0.0553043
$144$	9.10779	−	7.04640i	0.758982	−	0.587200i
$145$	14.5292	+	0.295542i	1.20658	+	0.0245434i
$146$	−2.02193	−	0.900220i	−0.167336	−	0.0745028i
$147$	16.6905	+	5.14615i	1.37661	+	0.424447i
$148$	14.8309	+	3.15240i	1.21909	+	0.259126i
$149$	−3.50472	+	6.07035i	−0.287118	+	0.497302i	−0.973120	−	0.230297i	$-0.926030\pi$
$149$	−3.50472	+	6.07035i	−0.287118	+	0.497302i	0.686003	+	0.727599i	$0.259364\pi$
$150$	1.36536	−	0.405302i	0.111481	−	0.0330928i
$151$	2.35416	+	4.07752i	0.191579	+	0.331824i	0.945774	−	0.324827i	$-0.105306\pi$
$151$	2.35416	+	4.07752i	0.191579	+	0.331824i	−0.754195	+	0.656651i	$0.771973\pi$
$152$	0.0149516	+	0.0460162i	0.00121273	+	0.00373241i
$153$	−11.7833	−	2.13545i	−0.952626	−	0.172641i
$154$	0.196990	−	0.143122i	0.0158739	−	0.0115331i
$155$	8.29150	−	8.84027i	0.665989	−	0.710068i
$156$	5.51075	+	3.07178i	0.441213	+	0.245939i
$157$	8.51816	−	14.7539i	0.679823	−	1.17749i	−0.295210	−	0.955432i	$-0.595390\pi$
$157$	8.51816	−	14.7539i	0.679823	−	1.17749i	0.975034	−	0.222057i	$-0.0712770\pi$
$158$	0.900128	−	0.400763i	0.0716104	−	0.0318830i
$159$	−2.46993	−	2.15739i	−0.195878	−	0.171092i
$160$	−0.540535	+	4.29971i	−0.0427331	+	0.339922i
$161$	5.59181	+	17.2098i	0.440696	+	1.35632i
$162$	0.243167	+	1.46001i	0.0191050	+	0.114709i
$163$	0.313473	−	0.964770i	0.0245531	−	0.0755666i	−0.938029	−	0.346556i	$-0.887351\pi$
$163$	0.313473	−	0.964770i	0.0245531	−	0.0755666i	0.962582	+	0.270990i	$0.0873509\pi$
$164$	−6.21111	+	6.89813i	−0.485006	+	0.538654i
$165$	−1.37897	−	0.152272i	−0.107352	−	0.0118543i
$166$	0.317584	+	0.352713i	0.0246493	+	0.0273758i
$167$	3.50153	−	1.55898i	0.270956	−	0.120637i	−0.266761	−	0.963763i	$-0.585953\pi$
$167$	3.50153	−	1.55898i	0.270956	−	0.120637i	0.537717	+	0.843125i	$0.319287\pi$
$168$	−4.64405	+	0.559030i	−0.358296	+	0.0431301i
$169$	1.00258	−	9.53887i	0.0771212	−	0.733760i
$170$	1.20487	−	0.838491i	0.0924096	−	0.0643094i
$171$	0.218596	+	0.0396154i	0.0167164	+	0.00302947i
$172$	−4.95002	+	3.59640i	−0.377436	+	0.274223i
$173$	14.8429	−	16.4847i	1.12849	−	1.25331i	0.164785	−	0.986329i	$-0.447307\pi$
$173$	14.8429	−	16.4847i	1.12849	−	1.25331i	0.963701	−	0.266982i	$-0.0860265\pi$
$174$	−1.11058	−	1.48110i	−0.0841932	−	0.112282i
$175$	20.0233	+	5.11527i	1.51362	+	0.386678i
$176$	0.687489	−	1.19077i	0.0518215	−	0.0897574i
$177$	4.93277	−	7.00926i	0.370770	−	0.526848i
$178$	−1.07645	−	0.479268i	−0.0806836	−	0.0359227i
$179$	11.8426	−	8.60413i	0.885156	−	0.643103i	−0.0494548	−	0.998776i	$-0.515748\pi$
$179$	11.8426	−	8.60413i	0.885156	−	0.643103i	0.934610	+	0.355673i	$0.115748\pi$
$180$	10.7832	+	7.67380i	0.803732	+	0.571972i
$181$	−13.9341	−	10.1237i	−1.03571	−	0.752489i	−0.0662678	−	0.997802i	$-0.521109\pi$
$181$	−13.9341	−	10.1237i	−1.03571	−	0.752489i	−0.969444	+	0.245313i	$0.921109\pi$
$182$	−0.627486	−	1.08684i	−0.0465123	−	0.0805617i
$183$	−13.7678	−	7.67440i	−1.01775	−	0.567308i
$184$	−1.91405	−	2.12577i	−0.141106	−	0.156714i
$185$	1.44831	+	17.1231i	0.106482	+	1.25892i
$186$	−1.53777	−	0.138217i	−0.112755	−	0.0101346i
$187$	−1.39865	+	0.297291i	−0.102279	+	0.0217401i
$188$	7.88628	−	24.2715i	0.575166	−	1.77018i
$189$	−7.83930	+	19.9953i	−0.570225	+	1.45444i
$190$	−0.0223519	+	0.0155551i	−0.00162158	+	0.00112848i
$191$	−0.569688	+	0.121091i	−0.0412212	+	0.00876184i	−0.228476	−	0.973550i	$-0.573374\pi$
$191$	−0.569688	+	0.121091i	−0.0412212	+	0.00876184i	0.187255	+	0.982311i	$0.440041\pi$
$192$	−10.9399	+	6.53808i	−0.789522	+	0.471845i
$193$	−4.64632	+	8.04765i	−0.334449	+	0.579283i	−0.983379	−	0.181565i	$-0.941884\pi$
$193$	−4.64632	+	8.04765i	−0.334449	+	0.579283i	0.648930	+	0.760848i	$0.275217\pi$
$194$	−1.58827	+	0.707142i	−0.114031	+	0.0507698i
$195$	−1.52342	+	6.98627i	−0.109095	+	0.500297i
$196$	−18.1751	−	8.09205i	−1.29822	−	0.578004i
$197$	−3.47512	+	2.52482i	−0.247592	+	0.179886i	−0.704659	−	0.709546i	$-0.748900\pi$
$197$	−3.47512	+	2.52482i	−0.247592	+	0.179886i	0.457067	+	0.889432i	$0.348900\pi$
$198$	0.0929408	+	0.150320i	0.00660502	+	0.0106828i
$199$	−3.20175			−0.226966			−0.113483	−	0.993540i	$-0.536201\pi$
$199$	−3.20175			−0.226966			−0.113483	+	0.993540i	$0.536201\pi$
$200$	−3.22050	+	0.548719i	−0.227723	+	0.0388003i
$201$	−14.9739	−	19.9696i	−1.05618	−	1.40854i
$202$	−2.81789	−	0.598961i	−0.198266	−	0.0421427i
$203$	−2.80785	−	26.7149i	−0.197073	−	1.87502i
$204$	13.0353	+	4.01916i	0.912654	+	0.281397i
$205$	−9.52172	−	4.47354i	−0.665026	−	0.312446i
$206$	1.59188	+	1.15657i	0.110912	+	0.0805820i
$207$	−12.7588	+	3.11686i	−0.886800	+	0.216637i
$208$	−5.73325	−	4.16545i	−0.397529	−	0.288822i
$209$	0.0259467	−	0.00551514i	0.00179477	−	0.000381490i
$210$	−1.05813	−	2.41064i	−0.0730180	−	0.166350i
$211$	7.09956	+	1.50906i	0.488754	+	0.103888i	0.445695	−	0.895185i	$-0.352956\pi$
$211$	7.09956	+	1.50906i	0.488754	+	0.103888i	0.0430586	+	0.999073i	$0.486290\pi$
$212$	2.49960	+	2.77608i	0.171673	+	0.190662i
$213$	−17.5194	−	15.3026i	−1.20041	−	1.04852i
$214$	0.934339	−	1.03769i	0.0638701	−	0.0709349i
$215$	−5.52611	−	4.18927i	−0.376877	−	0.285706i
$216$	−0.153534	−	3.39160i	−0.0104466	−	0.230769i
$217$	−18.1249	−	13.1685i	−1.23040	−	0.893938i
$218$	0.663982	+	1.15005i	0.0449705	+	0.0778912i
$219$	20.0090	−	11.9581i	1.35209	−	0.808052i
$220$	1.53877	+	0.359933i	0.103744	+	0.0242667i
$221$	0.770345	+	7.32935i	0.0518190	+	0.493025i
$222$	1.60452	−	1.48914i	0.107689	−	0.0999443i
$223$	−0.398119	+	0.442156i	−0.0266600	+	0.0296090i	−0.756327	−	0.654193i	$-0.773008\pi$
$223$	−0.398119	+	0.442156i	−0.0266600	+	0.0296090i	0.729667	+	0.683802i	$0.239675\pi$
$224$	8.01038			0.535216
$225$	−4.78505	+	14.2163i	−0.319003	+	0.947754i
$226$	−1.46249			−0.0972834
$227$	−6.17937	+	6.86289i	−0.410139	+	0.455506i	−0.912454	−	0.409179i	$-0.865815\pi$
$227$	−6.17937	+	6.86289i	−0.410139	+	0.455506i	0.502315	+	0.864685i	$0.332482\pi$
$228$	−0.241822	−	0.0745605i	−0.0160150	−	0.00493789i
$229$	−0.272928	−	2.59673i	−0.0180356	−	0.171597i	0.981796	−	0.189937i	$-0.0608285\pi$
$229$	−0.272928	−	2.59673i	−0.0180356	−	0.171597i	−0.999832	+	0.0183402i	$0.994162\pi$
$230$	0.833169	−	1.37761i	0.0549375	−	0.0908367i
$231$	0.0386686	+	2.56416i	0.00254421	+	0.168709i
$232$	2.12316	+	3.67742i	0.139392	+	0.241435i
$233$	5.35177	+	3.88829i	0.350606	+	0.254730i	0.749123	−	0.662431i	$-0.230475\pi$
$233$	5.35177	+	3.88829i	0.350606	+	0.254730i	−0.398517	+	0.917161i	$0.630475\pi$
$234$	0.820581	−	0.395412i	0.0536431	−	0.0258489i
$235$	28.9180	+	0.588229i	1.88640	+	0.0383718i
$236$	−6.53279	+	7.25539i	−0.425248	+	0.472286i
$237$	−2.00425	+	10.1818i	−0.130190	+	0.661382i
$238$	−1.81561	−	2.01644i	−0.117688	−	0.130706i
$239$	−16.1587	−	3.43464i	−1.04522	−	0.222168i	−0.346861	−	0.937917i	$-0.612752\pi$
$239$	−16.1587	−	3.43464i	−1.04522	−	0.222168i	−0.698358	+	0.715748i	$0.746086\pi$
$240$	−10.9953	−	10.0054i	−0.709745	−	0.645848i
$241$	−7.35486	+	1.56332i	−0.473768	+	0.100703i	−0.438607	−	0.898679i	$-0.644528\pi$
$241$	−7.35486	+	1.56332i	−0.473768	+	0.100703i	−0.0351616	+	0.999382i	$0.511195\pi$
$242$	−1.44646	−	1.05092i	−0.0929823	−	0.0675556i
$243$	−14.0487	−	6.75520i	−0.901228	−	0.433346i
$244$	14.5256	+	10.5534i	0.929903	+	0.675614i
$245$	2.81250	−	22.3722i	0.179684	−	1.42931i
$246$	0.298369	+	1.30652i	0.0190233	+	0.0833007i
$247$	−0.0142909	−	0.135969i	−0.000909308	−	0.00865148i
$248$	3.46415	+	0.736327i	0.219974	+	0.0467568i
$249$	−4.96285	+	0.597405i	−0.314508	+	0.0378590i
$250$	−0.820536	−	1.64545i	−0.0518953	−	0.104067i
$251$	−19.2136			−1.21275			−0.606377	−	0.795177i	$-0.707378\pi$
$251$	−19.2136			−1.21275			−0.606377	+	0.795177i	$0.707378\pi$
$252$	11.5877	−	21.5459i	0.729956	−	1.35726i
$253$	−1.26874	+	0.921796i	−0.0797652	+	0.0579528i
$254$	0.487511	+	0.217054i	0.0305892	+	0.0136192i
$255$	−0.0813064	+	15.4598i	−0.00509160	+	0.968129i
$256$	12.6799	−	5.64547i	0.792496	−	0.352842i
$257$	−9.44838	+	16.3651i	−0.589374	+	1.02083i	0.404941	+	0.914343i	$0.367292\pi$
$257$	−9.44838	+	16.3651i	−0.589374	+	1.02083i	−0.994315	+	0.106483i	$0.966041\pi$
$258$	0.0133202	+	0.883278i	0.000829281	+	0.0549905i
$259$	31.0701	−	6.60416i	1.93060	−	0.410363i
$260$	2.67395	−	7.69353i	0.165831	−	0.477132i
$261$	19.4881	−	0.587913i	1.20628	−	0.0363909i
$262$	0.437266	−	1.34577i	0.0270144	−	0.0831417i
$263$	−15.8269	+	3.36410i	−0.975926	+	0.207439i	−0.668156	−	0.744021i	$-0.732916\pi$
$263$	−15.8269	+	3.36410i	−0.975926	+	0.207439i	−0.307770	+	0.951461i	$0.599583\pi$
$264$	−0.170450	−	0.367809i	−0.0104905	−	0.0226371i
$265$	−2.19101	+	3.62274i	−0.134593	+	0.222543i
$266$	0.0336818	+	0.0374075i	0.00206517	+	0.00229360i
$267$	10.6526	−	6.36636i	0.651929	−	0.389615i
$268$	14.2158	+	24.6225i	0.868368	+	1.50406i
$269$	−1.72574	−	1.25382i	−0.105220	−	0.0764469i	0.533931	−	0.845528i	$-0.320714\pi$
$269$	−1.72574	−	1.25382i	−0.105220	−	0.0764469i	−0.639151	+	0.769081i	$0.720714\pi$
$270$	1.80204	−	0.635539i	0.109668	−	0.0386776i
$271$	−13.1625	+	9.56310i	−0.799563	+	0.580917i	−0.910786	−	0.412879i	$-0.864523\pi$
$271$	−13.1625	+	9.56310i	−0.799563	+	0.580917i	0.111223	+	0.993796i	$0.464523\pi$
$272$	−13.9975	−	6.23209i	−0.848723	−	0.377876i
$273$	13.1642	+	1.18321i	0.796733	+	0.0716114i
$274$	−0.471256	+	0.816239i	−0.0284696	+	0.0493108i
$275$	0.114626	+	1.78739i	0.00691221	+	0.107783i
$276$	14.8535	−	1.78800i	0.894078	−	0.107625i
$277$	−5.70183	+	6.33252i	−0.342590	+	0.380484i	−0.889676	−	0.456591i	$-0.849070\pi$
$277$	−5.70183	+	6.33252i	−0.342590	+	0.380484i	0.547087	+	0.837076i	$0.315737\pi$
$278$	2.20656	−	1.60316i	0.132341	−	0.0961511i
$279$	10.5114	−	12.4069i	0.629299	−	0.742779i
$280$	1.74888	+	5.77993i	0.104516	+	0.345417i
$281$	0.868414	−	8.26241i	0.0518052	−	0.492894i	−0.937600	−	0.347715i	$-0.886958\pi$
$281$	0.868414	−	8.26241i	0.0518052	−	0.492894i	0.989405	−	0.145179i	$-0.0463757\pi$
$282$	−2.21044	−	2.94789i	−0.131630	−	0.175544i
$283$	4.78188	−	2.12903i	0.284253	−	0.126558i	−0.259657	−	0.965701i	$-0.583610\pi$
$283$	4.78188	−	2.12903i	0.284253	−	0.126558i	0.543911	+	0.839143i	$0.316943\pi$
$284$	17.7299	+	19.6910i	1.05208	+	1.16845i
$285$	0.00150834	−	0.286799i	8.93462e−5	−	0.0169885i
$286$	0.0727764	−	0.0808264i	0.00430336	−	0.00477937i
$287$	−6.00921	+	18.4944i	−0.354712	+	1.09169i
$288$	−0.433103	+	5.79792i	−0.0255208	+	0.341646i
$289$	−0.329378	−	1.01372i	−0.0193752	−	0.0596307i
$290$	−1.63496	+	1.74317i	−0.0960083	+	0.102363i
$291$	3.53647	−	17.9658i	0.207312	−	1.05317i
$292$	−24.2566	+	10.7997i	−1.41951	+	0.632006i
$293$	−10.1972	+	17.6621i	−0.595728	+	1.03183i	0.397715	+	0.917509i	$0.369803\pi$
$293$	−10.1972	+	17.6621i	−0.595728	+	1.03183i	−0.993444	+	0.114323i	$0.963530\pi$
$294$	−2.46562	+	1.47354i	−0.143798	+	0.0859385i
$295$	−10.0149	−	4.70523i	−0.583088	−	0.273949i
$296$	−4.06228	+	2.95142i	−0.236115	+	0.171548i
$297$	−1.85803	−	0.110650i	−0.107814	−	0.00642054i
$298$	−0.356220	−	1.09633i	−0.0206353	−	0.0635089i
$299$	4.04142	+	6.99994i	0.233721	+	0.404817i
$300$	7.34685	−	15.4261i	0.424171	−	0.890627i
$301$	−6.40909	+	11.1009i	−0.369414	+	0.639843i
$302$	−0.757397	−	0.160990i	−0.0435833	−	0.00926392i
$303$	22.2389	−	20.6396i	1.27759	−	1.18571i
$304$	0.259671	+	0.115613i	0.0148932	+	0.00663087i
$305$	−6.68047	+	19.2212i	−0.382523	+	1.10060i
$306$	1.55766	−	1.20511i	0.0890457	−	0.0688918i
$307$	8.63664			0.492919			0.246459	−	0.969153i	$-0.420733\pi$
$307$	8.63664			0.492919			0.246459	+	0.969153i	$0.420733\pi$
$308$	0.305341	−	2.90512i	0.0173984	−	0.165535i
$309$	−19.6103	+	6.70033i	−1.11559	+	0.381169i
$310$	0.167994	+	1.98617i	0.00954143	+	0.112807i
$311$	13.1734	+	2.80008i	0.746992	+	0.158778i	0.565654	−	0.824643i	$-0.308624\pi$
$311$	13.1734	+	2.80008i	0.746992	+	0.158778i	0.181338	+	0.983421i	$0.441957\pi$
$312$	−1.97714	+	0.675539i	−0.111934	+	0.0382449i
$313$	7.14512	−	1.51874i	0.403866	−	0.0858443i	−0.00150004	−	0.999999i	$-0.500477\pi$
$313$	7.14512	−	1.51874i	0.403866	−	0.0858443i	0.405366	+	0.914155i	$0.367144\pi$
$314$	0.865788	+	2.66462i	0.0488593	+	0.150373i
$315$	27.1762	+	5.49812i	1.53121	+	0.309784i
$316$	3.65275	−	11.2420i	0.205483	−	0.632413i
$317$	2.42838	−	23.1045i	0.136391	−	1.29768i	−0.685517	−	0.728057i	$-0.740424\pi$
$317$	2.42838	−	23.1045i	0.136391	−	1.29768i	0.821908	−	0.569620i	$-0.192910\pi$
$318$	0.535467	−	0.0644571i	0.0300275	−	0.00361457i
$319$	2.12675	−	0.946889i	0.119075	−	0.0530156i
$320$	10.7585	+	12.4486i	0.601420	+	0.695900i
$321$	3.27415	+	14.3371i	0.182745	+	0.800219i
$322$	−2.71865	−	1.21042i	−0.151505	−	0.0674542i
$323$	−0.0913448	−	0.281131i	−0.00508256	−	0.0156425i
$324$	14.9684	+	9.55212i	0.831578	+	0.530674i
$325$	9.22354	+	0.375392i	0.511630	+	0.0208230i
$326$	0.0834143	+	0.144478i	0.00461989	+	0.00800189i
$327$	−13.9298	−	1.25203i	−0.770322	−	0.0692376i
$328$	−0.321324	−	3.05719i	−0.0177421	−	0.168805i
$329$	−5.58858	−	53.1718i	−0.308108	−	2.93145i
$330$	0.170356	−	0.151775i	0.00937780	−	0.00835492i
$331$	−2.81073	+	26.7423i	−0.154492	+	1.46989i	0.592775	+	0.805368i	$0.298032\pi$
$331$	−2.81073	+	26.7423i	−0.154492	+	1.46989i	−0.747267	+	0.664524i	$0.768634\pi$
$332$	5.69392			0.312494
$333$	3.10021	+	22.8457i	0.169891	+	1.25194i
$334$	−0.194788	+	0.599497i	−0.0106583	+	0.0328030i
$335$	−22.0441	+	23.5031i	−1.20440	+	1.28411i
$336$	−15.8150	+	22.4725i	−0.862782	+	1.22598i
$337$	5.77004	+	6.40828i	0.314314	+	0.349081i	0.879514	−	0.475873i	$-0.157868\pi$
$337$	5.77004	+	6.40828i	0.314314	+	0.349081i	−0.565200	+	0.824954i	$0.691201\pi$
$338$	1.05547	+	1.17222i	0.0574102	+	0.0637604i
$339$	8.86462	−	12.5962i	0.481460	−	0.684134i
$340$	2.19657	−	17.4727i	0.119126	−	0.947592i
$341$	0.599994	−	1.84659i	0.0324915	−	0.0999986i
$342$	−0.0288967	+	0.0223564i	−0.00156255	+	0.00120890i
$343$	−12.7466			−0.688251
$344$	0.211804	−	2.01518i	0.0114197	−	0.108651i
$345$	6.81505	+	15.5261i	0.366910	+	0.835897i
$346$	0.381326	+	3.62808i	0.0205002	+	0.195047i
$347$	−3.67108	−	34.9280i	−0.197074	−	1.87503i	−0.430404	−	0.902636i	$-0.641629\pi$
$347$	−3.67108	−	34.9280i	−0.197074	−	1.87503i	0.233330	−	0.972398i	$-0.425038\pi$
$348$	−22.1196	−	1.98814i	−1.18573	−	0.106575i
$349$	10.5156	+	18.2135i	0.562886	+	0.974946i	0.997243	+	0.0742057i	$0.0236421\pi$
$349$	10.5156	+	18.2135i	0.562886	+	0.974946i	−0.434357	+	0.900741i	$0.643025\pi$
$350$	−2.82860	+	1.88426i	−0.151195	+	0.100718i
$351$	−1.56817	+	9.46428i	−0.0837027	+	0.505166i
$352$	0.214527	+	0.660245i	0.0114343	+	0.0351912i
$353$	17.9989	+	8.01363i	0.957985	+	0.426523i	0.825337	−	0.564641i	$-0.190985\pi$
$353$	17.9989	+	8.01363i	0.957985	+	0.426523i	0.132649	+	0.991163i	$0.457652\pi$
$354$	0.313821	+	1.37419i	0.0166794	+	0.0730371i
$355$	−15.5411	+	25.6965i	−0.824835	+	1.36383i
$356$	−12.9139	+	5.74966i	−0.684438	+	0.304731i
$357$	28.3723	−	3.41533i	1.50162	−	0.180758i
$358$	−0.251638	+	2.39418i	−0.0132995	+	0.126536i
$359$	−0.938606	+	2.88873i	−0.0495377	+	0.152461i	−0.972765	−	0.231792i	$-0.925541\pi$
$359$	−0.938606	+	2.88873i	−0.0495377	+	0.152461i	0.923228	+	0.384253i	$0.125541\pi$
$360$	−4.27808	+	0.953337i	−0.225475	+	0.0502453i
$361$	−5.86963	−	18.0649i	−0.308928	−	0.950782i
$362$	2.77063	−	0.588915i	0.145621	−	0.0309527i
$363$	17.8189	−	6.08826i	0.935250	−	0.319551i
$364$	−14.7266	−	3.13023i	−0.771882	−	0.164069i
$365$	−19.6773	−	22.7684i	−1.02995	−	1.19175i
$366$	2.45299	−	0.838124i	0.128220	−	0.0438094i
$367$	0.759260	−	7.22388i	0.0396330	−	0.377083i	−0.956670	−	0.291175i	$-0.905954\pi$
$367$	0.759260	−	7.22388i	0.0396330	−	0.377083i	0.996303	−	0.0859088i	$-0.0273794\pi$
$368$	−16.8048			−0.876010
$369$	−13.0614	−	5.34942i	−0.679949	−	0.278480i
$370$	−2.25209	−	1.70728i	−0.117080	−	0.0887572i
$371$	7.14934	+	3.18309i	0.371175	+	0.165258i
$372$	−13.5765	+	12.6002i	−0.703911	+	0.653290i
$373$	−10.3292	−	2.19554i	−0.534825	−	0.113681i	−0.0674212	−	0.997725i	$-0.521477\pi$
$373$	−10.3292	−	2.19554i	−0.534825	−	0.113681i	−0.467404	+	0.884044i	$0.654810\pi$
$374$	0.117578	−	0.203651i	0.00607983	−	0.0105306i
$375$	19.1456	+	2.90641i	0.988673	+	0.150087i
$376$	4.22581	+	7.31932i	0.217930	+	0.377465i
$377$	−3.70779	−	11.4114i	−0.190961	−	0.587718i
$378$	−1.58107	−	3.15843i	−0.0813215	−	0.162452i
$379$	−28.5159	+	20.7180i	−1.46476	+	1.06421i	−0.482673	+	0.875801i	$0.660334\pi$
$379$	−28.5159	+	20.7180i	−1.46476	+	1.06421i	−0.982090	+	0.188412i	$0.939666\pi$
$380$	−0.0407492	+	0.324142i	−0.00209039	+	0.0166281i
$381$	−4.82442	+	2.88324i	−0.247163	+	0.147713i
$382$	0.0478913	−	0.0829501i	0.00245033	−	0.00424410i
$383$	−5.70095	+	2.53823i	−0.291305	+	0.129697i	−0.547186	−	0.837011i	$-0.684301\pi$
$383$	−5.70095	+	2.53823i	−0.291305	+	0.129697i	0.255881	+	0.966708i	$0.417634\pi$
$384$	1.70145	−	8.64362i	0.0868270	−	0.441093i
$385$	3.25167	−	0.622330i	0.165720	−	0.0317169i
$386$	−0.472253	−	1.45344i	−0.0240370	−	0.0739784i
$387$	−7.68830	−	5.23910i	−0.390818	−	0.266319i
$388$	−6.44524	+	19.8364i	−0.327208	+	1.00704i
$389$	19.0702	−	21.1796i	0.966899	−	1.07385i	−0.0303363	−	0.999540i	$-0.509658\pi$
$389$	19.0702	−	21.1796i	0.966899	−	1.07385i	0.997235	−	0.0743103i	$-0.0236755\pi$
$390$	−0.686189	−	0.954979i	−0.0347465	−	0.0483573i
$391$	11.6937	+	12.9872i	0.591375	+	0.656788i
$392$	6.01902	−	2.67984i	0.304006	−	0.135352i
$393$	8.94050	+	11.9232i	0.450989	+	0.601448i
$394$	0.0738414	−	0.702554i	0.00372008	−	0.0353942i
$395$	13.3942	+	0.272455i	0.673934	+	0.0137087i
$396$	2.08622	+	0.378079i	0.104837	+	0.0189992i
$397$	−4.87063	+	3.53872i	−0.244450	+	0.177603i	−0.703263	−	0.710929i	$-0.748275\pi$
$397$	−4.87063	+	3.53872i	−0.244450	+	0.177603i	0.458814	+	0.888533i	$0.348275\pi$
$398$	0.352332	−	0.391304i	0.0176608	−	0.0196143i
$399$	−0.526342	+	0.0633587i	−0.0263501	+	0.00317190i
$400$	−10.2641	+	16.2170i	−0.513205	+	0.810851i
$401$	13.2682	−	22.9812i	0.662583	−	1.14763i	−0.317351	−	0.948308i	$-0.602793\pi$
$401$	13.2682	−	22.9812i	0.662583	−	1.14763i	0.979934	−	0.199320i	$-0.0638733\pi$
$402$	4.08838	+	0.367469i	0.203910	+	0.0183277i
$403$	−9.14202	−	4.07029i	−0.455396	−	0.202756i
$404$	−27.9602	+	20.3143i	−1.39107	+	1.01067i
$405$	−5.44890	+	19.3729i	−0.270758	+	0.962647i
$406$	3.57397	+	2.59664i	0.177373	+	0.128869i
$407$	1.37643	+	2.38405i	0.0682272	+	0.118173i
$408$	−3.87771	+	2.31745i	−0.191975	+	0.114731i
$409$	−18.2716	−	20.2927i	−0.903475	−	1.00341i	−0.999967	−	0.00807647i	$-0.997429\pi$
$409$	−18.2716	−	20.2927i	−0.903475	−	1.00341i	0.0964928	−	0.995334i	$-0.469238\pi$
$410$	1.59454	−	0.671419i	0.0787487	−	0.0331590i
$411$	−4.17373	−	9.00635i	−0.205875	−	0.444250i
$412$	23.0898	−	4.90790i	1.13755	−	0.241795i
$413$	−6.32043	+	19.4523i	−0.311008	+	0.957184i
$414$	1.02310	−	1.90232i	0.0502824	−	0.0934939i
$415$	1.86894	+	6.17670i	0.0917425	+	0.303202i
$416$	3.49986	−	0.743918i	0.171595	−	0.0364736i
$417$	0.433141	+	28.7221i	0.0212110	+	1.40653i
$418$	−0.00218123	+	0.00377800i	−0.000106687	+	0.000184788i
$419$	−10.8046	+	4.81054i	−0.527841	+	0.235010i	−0.653314	−	0.757087i	$-0.726622\pi$
$419$	−10.8046	+	4.81054i	−0.527841	+	0.235010i	0.125473	+	0.992097i	$0.459955\pi$
$420$	−29.9857	−	9.91758i	−1.46315	−	0.483928i
$421$	1.67084	+	0.743904i	0.0814316	+	0.0362557i	0.447048	−	0.894510i	$-0.352475\pi$
$421$	1.67084	+	0.743904i	0.0814316	+	0.0362557i	−0.365617	+	0.930766i	$0.619142\pi$
$422$	−0.965691	+	0.701616i	−0.0470091	+	0.0341541i
$423$	38.7879	−	1.17015i	1.88593	−	0.0568944i
$424$	−1.23711			−0.0600795
$425$	19.6752	−	3.35233i	0.954389	−	0.162612i
$426$	3.79812	−	0.457200i	0.184019	−	0.0221514i
$427$	36.7922	+	7.82043i	1.78050	+	0.378457i
$428$	−1.75102	−	16.6599i	−0.0846388	−	0.805285i
$429$	0.255026	+	1.11673i	0.0123128	+	0.0539162i
$430$	1.12011	−	0.214375i	0.0540163	−	0.0103381i
$431$	28.5016	+	20.7076i	1.37288	+	0.997452i	0.997506	+	0.0705766i	$0.0224839\pi$
$431$	28.5016	+	20.7076i	1.37288	+	0.997452i	0.375369	+	0.926876i	$0.377516\pi$
$432$	−15.4105	−	12.6620i	−0.741440	−	0.609200i
$433$	3.17805	+	2.30899i	0.152727	+	0.110963i	0.661525	−	0.749923i	$-0.269910\pi$
$433$	3.17805	+	2.30899i	0.152727	+	0.110963i	−0.508797	+	0.860886i	$0.669910\pi$
$434$	3.60393	−	0.766039i	0.172994	−	0.0367711i
$435$	−5.10368	−	24.6476i	−0.244703	−	1.18176i
$436$	15.5831	+	3.31229i	0.746295	+	0.158630i
$437$	−0.216933	−	0.240928i	−0.0103773	−	0.0115252i
$438$	−0.740399	+	3.76133i	−0.0353776	+	0.179723i
$439$	12.9252	−	14.3549i	0.616887	−	0.685123i	−0.351038	−	0.936361i	$-0.614171\pi$
$439$	12.9252	−	14.3549i	0.616887	−	0.685123i	0.967925	+	0.251238i	$0.0808378\pi$
$440$	−0.429567	+	0.298943i	−0.0204788	+	0.0142515i
$441$	2.25351	−	30.1677i	0.107310	−	1.43655i
$442$	−0.980532	−	0.712398i	−0.0466392	−	0.0338853i
$443$	−2.24077	−	3.88113i	−0.106462	−	0.184398i	0.807872	−	0.589357i	$-0.200619\pi$
$443$	−2.24077	−	3.88113i	−0.106462	−	0.184398i	−0.914335	+	0.404959i	$0.867286\pi$
$444$	−0.395993	−	26.2587i	−0.0187930	−	1.24618i
$445$	−10.4760	−	12.1217i	−0.496608	−	0.574623i
$446$	−0.0102280	−	0.0973128i	−0.000484309	−	0.00460790i
$447$	11.6017	+	3.57715i	0.548744	+	0.169193i
$448$	20.3505	−	22.6015i	0.961471	−	1.06782i
$449$	−11.2399			−0.530445			−0.265222	−	0.964187i	$-0.585445\pi$
$449$	−11.2399			−0.530445			−0.265222	+	0.964187i	$0.585445\pi$
$450$	−1.21089	−	2.14922i	−0.0570820	−	0.101315i
$451$	−1.68531			−0.0793583
$452$	−11.7400	+	13.0386i	−0.552202	+	0.613283i
$453$	5.97741	−	5.54755i	0.280843	−	0.260647i
$454$	−0.158753	−	1.51043i	−0.00745064	−	0.0708881i
$455$	−1.43812	−	17.0027i	−0.0674203	−	0.797098i
$456$	0.0719364	−	0.0429917i	0.00336873	−	0.00201327i
$457$	7.48417	+	12.9630i	0.350095	+	0.606381i	0.986266	−	0.165166i	$-0.0528161\pi$
$457$	7.48417	+	12.9630i	0.350095	+	0.606381i	−0.636171	+	0.771548i	$0.719483\pi$
$458$	0.347396	+	0.252398i	0.0162327	+	0.0117938i
$459$	0.937994	+	20.7205i	0.0437818	+	0.967152i
$460$	−5.59363	−	18.4866i	−0.260805	−	0.861940i
$461$	20.1758	−	22.4075i	0.939679	−	1.04362i	−0.0592908	−	0.998241i	$-0.518884\pi$
$461$	20.1758	−	22.4075i	0.939679	−	1.04362i	0.998970	−	0.0453786i	$-0.0144494\pi$
$462$	−0.317635	−	0.277443i	−0.0147777	−	0.0129078i
$463$	−18.4989	−	20.5451i	−0.859718	−	0.954814i	0.139655	−	0.990200i	$-0.455401\pi$
$463$	−18.4989	−	20.5451i	−0.859718	−	0.954814i	−0.999374	+	0.0353863i	$0.988734\pi$
$464$	24.4010	+	5.18658i	1.13279	+	0.240781i
$465$	−18.1249	−	10.5919i	−0.840520	−	0.491186i
$466$	−1.06414	+	0.226189i	−0.0492952	+	0.0104780i
$467$	−23.9054	−	17.3683i	−1.10621	−	0.803709i	−0.124147	−	0.992264i	$-0.539620\pi$
$467$	−23.9054	−	17.3683i	−1.10621	−	0.803709i	−0.982063	+	0.188555i	$0.939620\pi$
$468$	3.06190	−	10.4899i	0.141536	−	0.484894i
$469$	48.1876	+	35.0103i	2.22510	+	1.61663i
$470$	−3.25413	+	3.46950i	−0.150102	+	0.160036i
$471$	−28.1979	−	8.69421i	−1.29929	−	0.400608i
$472$	−0.337965	−	3.21552i	−0.0155561	−	0.148007i
$473$	−1.08662	−	0.230968i	−0.0499627	−	0.0106199i
$474$	−1.02383	−	1.36540i	−0.0470259	−	0.0627147i
$475$	−0.365001	+	0.0621900i	−0.0167474	+	0.00285347i
$476$	−32.5517			−1.49201
$477$	−2.69047	+	5.00260i	−0.123188	+	0.229053i
$478$	2.19793	−	1.59689i	0.100531	−	0.0730399i
$479$	−12.2428	−	5.45085i	−0.559389	−	0.249056i	0.107510	−	0.994204i	$-0.465712\pi$
$479$	−12.2428	−	5.45085i	−0.559389	−	0.249056i	−0.666899	+	0.745148i	$0.732379\pi$
$480$	7.46885	−	0.745315i	0.340905	−	0.0340188i
$481$	12.9617	−	5.77093i	0.591003	−	0.263132i
$482$	0.618292	−	1.07091i	0.0281624	−	0.0487788i
$483$	26.9038	−	16.0786i	1.22417	−	0.731604i
$484$	−20.9806	+	4.45957i	−0.953664	+	0.202708i
$485$	−23.6339	−	0.480743i	−1.07316	−	0.0218294i
$486$	2.37156	−	0.973612i	0.107576	−	0.0441639i
$487$	0.825534	−	2.54073i	0.0374085	−	0.115132i	−0.930608	−	0.366016i	$-0.880721\pi$
$487$	0.825534	−	2.54073i	0.0374085	−	0.115132i	0.968017	+	0.250885i	$0.0807215\pi$
$488$	−5.81607	+	1.23624i	−0.263281	+	0.0559621i
$489$	−1.74997	−	0.157290i	−0.0791364	−	0.00711288i
$490$	2.42474	+	2.80565i	0.109538	+	0.126746i
$491$	−11.9826	−	13.3080i	−0.540767	−	0.600582i	0.409388	−	0.912360i	$-0.365742\pi$
$491$	−11.9826	−	13.3080i	−0.540767	−	0.600582i	−0.950155	+	0.311778i	$0.899075\pi$
$492$	14.0432	+	7.82789i	0.633115	+	0.352909i
$493$	−12.9712	−	22.4668i	−0.584193	−	1.01185i
$494$	0.0181901	+	0.0132159i	0.000818413	+	0.000594612i
$495$	0.274633	+	2.38721i	0.0123438	+	0.107297i
$496$	16.8321	−	12.2293i	0.755785	−	0.549110i
$497$	50.7110	+	22.5780i	2.27470	+	1.01276i
$498$	0.473117	−	0.672278i	0.0212009	−	0.0301255i
$499$	−10.2734	+	17.7940i	−0.459899	+	0.796568i	−0.998955	−	0.0457019i	$-0.985448\pi$
$499$	−10.2734	+	17.7940i	−0.459899	+	0.796568i	0.539057	+	0.842270i	$0.318781\pi$
$500$	−21.2565	−	5.89331i	−0.950618	−	0.263557i
$501$	−3.98272	−	5.31143i	−0.177935	−	0.237297i
$502$	2.11433	−	2.34821i	0.0943674	−	0.104806i
$503$	−32.2593	+	23.4377i	−1.43837	+	1.04504i	−0.449990	+	0.893034i	$0.648572\pi$
$503$	−32.2593	+	23.4377i	−1.43837	+	1.04504i	−0.988380	+	0.152003i	$0.951428\pi$
$504$	2.73480	+	7.62628i	0.121818	+	0.339701i
$505$	−31.2142	−	23.6631i	−1.38901	−	1.05299i
$506$	0.0269590	−	0.256498i	0.00119847	−	0.0114027i
$507$	−16.4938	+	1.98544i	−0.732513	+	0.0881766i
$508$	5.84855	−	2.60394i	0.259487	−	0.115531i
$509$	13.2868	+	14.7564i	0.588925	+	0.654068i	0.961780	−	0.273822i	$-0.0882878\pi$
$509$	13.2868	+	14.7564i	0.588925	+	0.654068i	−0.372855	+	0.927890i	$0.621621\pi$
$510$	−1.88048	−	1.71119i	−0.0832691	−	0.0757726i
$511$	−37.2209	+	41.3380i	−1.64655	+	1.82868i
$512$	−3.84880	+	11.8454i	−0.170094	+	0.523497i
$513$	−0.0174010	−	0.384393i	−0.000768273	−	0.0169714i
$514$	−0.960336	−	2.95561i	−0.0423586	−	0.130366i
$515$	12.9029	+	23.4367i	0.568570	+	1.03274i
$516$	7.98163	+	6.97166i	0.351372	+	0.306910i
$517$	4.23295	−	1.88463i	0.186165	−	0.0828859i
$518$	−2.61193	+	4.52400i	−0.114762	+	0.198773i
$519$	−33.5595	−	18.7066i	−1.47310	−	0.821129i
$520$	1.30089	+	2.36293i	0.0570480	+	0.103621i
$521$	8.76012	−	6.36460i	0.383788	−	0.278838i	−0.379117	−	0.925349i	$-0.623772\pi$
$521$	8.76012	−	6.36460i	0.383788	−	0.278838i	0.762905	+	0.646510i	$0.223772\pi$
$522$	−2.07269	+	2.44645i	−0.0907191	+	0.107078i
$523$	4.62026	+	14.2197i	0.202030	+	0.621785i	0.999822	+	0.0188521i	$0.00600116\pi$
$523$	4.62026	+	14.2197i	0.202030	+	0.621785i	−0.797792	+	0.602932i	$0.793999\pi$
$524$	−8.48783	−	14.7014i	−0.370793	−	0.642232i
$525$	0.916171	−	35.7834i	0.0399850	−	1.56172i
$526$	1.33050	−	2.30449i	0.0580124	−	0.100480i
$527$	−21.1638	−	4.49850i	−0.921909	−	0.195958i
$528$	−2.27581	−	0.701698i	−0.0990420	−	0.0305375i
$529$	−3.50166	−	1.55904i	−0.152246	−	0.0677844i
$530$	−0.201649	−	0.666436i	−0.00875908	−	0.0289481i
$531$	−13.7379	−	5.62647i	−0.596172	−	0.244168i
$532$	0.603877			0.0261814
$533$	−0.907952	+	8.63858i	−0.0393278	+	0.374179i
$534$	−0.394181	+	2.00249i	−0.0170579	+	0.0866563i
$535$	17.4977	−	7.36782i	0.756491	−	0.318539i
$536$	−9.20991	−	1.95763i	−0.397808	−	0.0845566i
$537$	−19.0955	−	16.6792i	−0.824031	−	0.719761i
$538$	0.343143	−	0.0729373i	0.0147939	−	0.00314455i
$539$	−1.11622	−	3.43538i	−0.0480791	−	0.147972i
$540$	8.79961	−	21.1674i	0.378675	−	0.910902i
$541$	11.4490	−	35.2363i	0.492230	−	1.51493i	−0.329000	−	0.944330i	$-0.606712\pi$
$541$	11.4490	−	35.2363i	0.492230	−	1.51493i	0.821230	−	0.570597i	$-0.193288\pi$
$542$	0.279684	−	2.66102i	0.0120135	−	0.114300i
$543$	−11.7214	+	27.4327i	−0.503014	+	1.17725i
$544$	7.06730	−	3.14656i	0.303008	−	0.134908i
$545$	1.52177	+	17.9916i	0.0651854	+	0.770675i
$546$	−1.59324	+	1.47866i	−0.0681844	+	0.0632810i
$547$	−19.4966	−	8.68045i	−0.833615	−	0.371149i	−0.0548729	−	0.998493i	$-0.517475\pi$
$547$	−19.4966	−	8.68045i	−0.833615	−	0.371149i	−0.778742	+	0.627344i	$0.784142\pi$
$548$	3.49408	+	10.7537i	0.149260	+	0.459374i
$549$	−7.64971	+	26.2074i	−0.326482	+	1.11851i
$550$	−0.231060	−	0.182681i	−0.00985245	−	0.00778955i
$551$	0.240632	+	0.416787i	0.0102513	+	0.0177557i
$552$	−2.85144	+	4.05177i	−0.121365	+	0.172455i
$553$	−2.58850	−	24.6280i	−0.110074	−	1.04729i
$554$	−0.146484	−	1.39371i	−0.00622352	−	0.0592129i
$555$	28.3552	−	9.04858i	1.20361	−	0.384091i
$556$	3.42023	−	32.5414i	0.145050	−	1.38006i
$557$	38.6947			1.63955			0.819773	−	0.572689i	$-0.194100\pi$
$557$	38.6947			1.63955			0.819773	+	0.572689i	$0.194100\pi$
$558$	0.359604	+	2.64995i	0.0152232	+	0.112181i
$559$	−1.76930	+	5.44535i	−0.0748335	+	0.230314i
$560$	32.1088	+	15.0855i	1.35684	+	0.637479i
$561$	1.04134	+	2.24708i	0.0439656	+	0.0948719i
$562$	0.914232	+	1.01536i	0.0385646	+	0.0428303i
$563$	9.13347	+	10.1437i	0.384930	+	0.427508i	0.904205	−	0.427100i	$-0.140465\pi$
$563$	9.13347	+	10.1437i	0.384930	+	0.427508i	−0.519275	+	0.854607i	$0.673798\pi$
$564$	−44.0254	−	3.95706i	−1.85380	−	0.166622i
$565$	−17.9976	−	8.45570i	−0.757163	−	0.355734i
$566$	−0.266014	+	0.818707i	−0.0111814	+	0.0344128i
$567$	36.7866	+	5.52672i	1.54489	+	0.232101i
$568$	−8.77496			−0.368189
$569$	−2.42745	+	23.0956i	−0.101764	+	0.968218i	0.817860	+	0.575417i	$0.195160\pi$
$569$	−2.42745	+	23.0956i	−0.101764	+	0.968218i	−0.919624	+	0.392801i	$0.871506\pi$
$570$	0.0348853	+	0.0317447i	0.00146119	+	0.00132964i
$571$	−2.66000	−	25.3082i	−0.111317	−	1.05911i	−0.897468	−	0.441079i	$-0.854596\pi$
$571$	−2.66000	−	25.3082i	−0.111317	−	1.05911i	0.786151	−	0.618035i	$-0.212071\pi$
$572$	−0.136389	−	1.29765i	−0.00570269	−	0.0542575i
$573$	0.424154	+	0.915269i	0.0177193	+	0.0382359i
$574$	−1.59904	−	2.76961i	−0.0667425	−	0.115601i
$575$	18.2180	−	12.1358i	0.759743	−	0.506099i
$576$	15.2587	+	15.9517i	0.635780	+	0.664656i
$577$	9.47834	+	29.1713i	0.394588	+	1.21442i	0.929282	+	0.369372i	$0.120427\pi$
$577$	9.47834	+	29.1713i	0.394588	+	1.21442i	−0.534693	+	0.845046i	$0.679573\pi$
$578$	0.160139	+	0.0712983i	0.00666089	+	0.00296562i
$579$	15.3808	+	4.74234i	0.639204	+	0.197085i
$580$	2.41645	+	28.5693i	0.100338	+	1.18628i
$581$	10.8973	−	4.85178i	0.452095	−	0.201286i
$582$	1.80653	+	2.40923i	0.0748831	+	0.0998656i
$583$	−0.0708951	+	0.674522i	−0.00293618	+	0.0279359i
$584$	2.71726	−	8.36287i	0.112441	−	0.346058i
$585$	12.3843	−	0.121620i	0.512029	−	0.00502835i
$586$	−1.03645	−	3.18986i	−0.0428153	−	0.131772i
$587$	14.4830	−	3.07845i	0.597777	−	0.127061i	0.100921	−	0.994894i	$-0.467821\pi$
$587$	14.4830	−	3.07845i	0.597777	−	0.127061i	0.496856	+	0.867833i	$0.334488\pi$
$588$	−6.65542	+	33.8105i	−0.274465	+	1.39432i
$589$	0.392615	+	0.0834530i	0.0161774	+	0.00343862i
$590$	1.67712	−	0.706193i	0.0690460	−	0.0290735i
$591$	5.60343	+	4.89439i	0.230494	+	0.201328i
$592$	−3.08345	+	29.3370i	−0.126729	+	1.20574i
$593$	29.3262			1.20428			0.602140	−	0.798390i	$-0.294315\pi$
$593$	29.3262			1.20428			0.602140	+	0.798390i	$0.294315\pi$
$594$	0.217987	−	0.214904i	0.00894412	−	0.00881762i
$595$	−10.6846	−	35.3118i	−0.438026	−	1.44764i
$596$	−12.6337	−	5.62488i	−0.517496	−	0.230404i
$597$	1.23466	+	5.40641i	0.0505311	+	0.221269i
$598$	−1.30023	−	0.276373i	−0.0531705	−	0.0113017i
$599$	2.03948	−	3.53249i	0.0833310	−	0.144334i	−0.821348	−	0.570428i	$-0.806777\pi$
$599$	2.03948	−	3.53249i	0.0833310	−	0.144334i	0.904679	+	0.426094i	$0.140111\pi$
$600$	2.16844	+	5.22647i	0.0885262	+	0.213370i
$601$	−8.15219	−	14.1200i	−0.332535	−	0.575967i	0.650474	−	0.759529i	$-0.274570\pi$
$601$	−8.15219	−	14.1200i	−0.332535	−	0.575967i	−0.983008	+	0.183562i	$0.941237\pi$
$602$	−0.651421	−	2.00487i	−0.0265500	−	0.0817124i
$603$	−27.9459	+	32.9853i	−1.13805	+	1.34327i
$604$	−7.51520	+	5.46011i	−0.305789	+	0.222169i
$605$	−11.7242	−	21.2958i	−0.476658	−	0.865796i
$606$	0.0752393	+	4.98920i	0.00305639	+	0.202672i
$607$	9.93751	−	17.2123i	0.403351	−	0.698625i	−0.590777	−	0.806835i	$-0.701179\pi$
$607$	9.93751	−	17.2123i	0.403351	−	0.698625i	0.994128	+	0.108210i	$0.0345120\pi$
$608$	−0.131107	+	0.0583728i	−0.00531711	+	0.00236733i
$609$	−44.0275	+	15.0431i	−1.78408	+	0.609576i
$610$	−1.61398	−	2.93162i	−0.0653483	−	0.118698i
$611$	−7.37976	−	22.7126i	−0.298553	−	0.918852i
$612$	1.76000	−	23.5610i	0.0711437	−	0.952397i
$613$	1.01670	−	3.12907i	0.0410639	−	0.126382i	−0.928423	−	0.371525i	$-0.878835\pi$
$613$	1.01670	−	3.12907i	0.0410639	−	0.126382i	0.969487	+	0.245143i	$0.0788350\pi$
$614$	−0.950406	+	1.05553i	−0.0383552	+	0.0425978i
$615$	−3.88217	+	17.8033i	−0.156544	+	0.717897i
$616$	0.647308	+	0.718908i	0.0260808	+	0.0289656i
$617$	40.1863	−	17.8921i	1.61784	−	0.720308i	0.619912	−	0.784671i	$-0.287168\pi$
$617$	40.1863	−	17.8921i	1.61784	−	0.720308i	0.997927	+	0.0643626i	$0.0205014\pi$
$618$	1.33910	−	3.13401i	0.0538665	−	0.126068i
$619$	1.18396	−	11.2646i	0.0475873	−	0.452763i	−0.944620	−	0.328166i	$-0.893570\pi$
$619$	1.18396	−	11.2646i	0.0475873	−	0.452763i	0.992207	−	0.124597i	$-0.0397638\pi$
$620$	19.0559	+	14.4460i	0.765302	+	0.580166i
$621$	10.1831	+	20.3424i	0.408635	+	0.816311i
$622$	−1.79186	+	1.30186i	−0.0718469	+	0.0521998i
$623$	−19.8160	+	22.0079i	−0.793912	+	0.881728i
$624$	−4.82284	+	11.2873i	−0.193068	+	0.451855i
$625$	−0.584094	−	24.9932i	−0.0233638	−	0.999727i
$626$	−0.600659	+	1.04037i	−0.0240072	+	0.0415817i
$627$	−0.0193183	−	0.0416863i	−0.000771498	−	0.00166479i
$628$	30.7060	+	13.6712i	1.22530	+	0.545540i
$629$	24.8180	−	18.0313i	0.989559	−	0.718956i
$630$	−3.66252	+	2.71633i	−0.145918	+	0.108221i
$631$	19.7944	+	14.3815i	0.788005	+	0.572519i	0.907371	−	0.420331i	$-0.138086\pi$
$631$	19.7944	+	14.3815i	0.788005	+	0.572519i	−0.119366	+	0.992850i	$0.538086\pi$
$632$	1.95730	+	3.39015i	0.0778573	+	0.134853i
$633$	−0.189563	−	12.5701i	−0.00753443	−	0.499616i
$634$	2.55650	+	2.83928i	0.101532	+	0.112762i
$635$	4.74442	+	5.48974i	0.188277	+	0.217854i
$636$	3.72374	−	5.29128i	0.147656	−	0.209813i
$637$	−18.2104	+	3.87074i	−0.721523	+	0.153364i
$638$	−0.118310	+	0.364121i	−0.00468394	+	0.0144157i
$639$	−19.0838	+	35.4839i	−0.754943	+	1.40372i
$640$	−11.3706	−	0.231293i	−0.449464	−	0.00914267i
$641$	−28.6247	+	6.08438i	−1.13061	+	0.240318i	−0.734978	−	0.678091i	$-0.762808\pi$
$641$	−28.6247	+	6.08438i	−1.13061	+	0.240318i	−0.395631	+	0.918409i	$0.629474\pi$
$642$	−2.11252	−	1.17755i	−0.0833744	−	0.0464743i
$643$	−3.57430	+	6.19087i	−0.140957	+	0.244144i	−0.927857	−	0.372936i	$-0.878351\pi$
$643$	−3.57430	+	6.19087i	−0.140957	+	0.244144i	0.786900	+	0.617080i	$0.211685\pi$
$644$	−32.6150	+	14.5211i	−1.28521	+	0.572213i
$645$	−4.94294	+	10.9467i	−0.194628	+	0.431027i
$646$	0.0444105	+	0.0197728i	0.00174731	+	0.000777951i
$647$	25.5288	−	18.5478i	1.00364	−	0.729188i	0.0407758	−	0.999168i	$-0.487017\pi$
$647$	25.5288	−	18.5478i	1.00364	−	0.729188i	0.962866	+	0.269980i	$0.0870171\pi$
$648$	−5.66777	+	1.56712i	−0.222651	+	0.0615622i
$649$	−1.77260			−0.0695805
$650$	−1.06087	+	1.08595i	−0.0416107	+	0.0425945i
$651$	−15.2468	+	35.6834i	−0.597568	+	1.39854i
$652$	1.95767	+	0.416115i	0.0766681	+	0.0162963i
$653$	0.244296	+	2.32432i	0.00956003	+	0.0909576i	0.998262	−	0.0589403i	$-0.0187722\pi$
$653$	0.244296	+	2.32432i	0.00956003	+	0.0909576i	−0.988701	+	0.149898i	$0.952105\pi$
$654$	1.68591	−	1.56467i	0.0659241	−	0.0611833i
$655$	13.1619	−	14.0330i	0.514277	−	0.548315i
$656$	−14.6102	−	10.6149i	−0.570431	−	0.414443i
$657$	−27.9080	−	29.1756i	−1.08880	−	1.13825i
$658$	7.11341	+	5.16819i	0.277309	+	0.201477i
$659$	41.8091	−	8.88679i	1.62865	−	0.346180i	0.699142	−	0.714983i	$-0.253565\pi$
$659$	41.8091	−	8.88679i	1.62865	−	0.346180i	0.929508	+	0.368802i	$0.120232\pi$
$660$	0.0143952	−	2.73713i	0.000560332	−	0.106543i
$661$	−5.59291	−	1.18881i	−0.217539	−	0.0462393i	0.0978528	−	0.995201i	$-0.468803\pi$
$661$	−5.59291	−	1.18881i	−0.217539	−	0.0462393i	−0.315392	+	0.948962i	$0.602136\pi$
$662$	−2.95903	−	3.28634i	−0.115006	−	0.127727i
$663$	12.0791	−	4.12712i	0.469114	−	0.160284i
$664$	−1.26175	+	1.40131i	−0.0489652	+	0.0543814i
$665$	0.198213	+	0.655079i	0.00768637	+	0.0254029i
$666$	−3.13326	−	2.13512i	−0.121411	−	0.0827344i
$667$	−23.0187	−	16.7240i	−0.891287	−	0.647558i
$668$	3.78106	+	6.54900i	0.146294	+	0.253388i
$669$	0.900138	+	0.501752i	0.0348013	+	0.0193988i
$670$	−0.446636	−	5.28050i	−0.0172550	−	0.204003i
$671$	0.340747	+	3.24199i	0.0131544	+	0.125156i
$672$	−3.08895	−	13.5262i	−0.119159	−	0.521783i
$673$	−1.32261	+	1.46890i	−0.0509827	+	0.0566221i	−0.768097	−	0.640334i	$-0.778796\pi$
$673$	−1.32261	+	1.46890i	−0.0509827	+	0.0566221i	0.717114	+	0.696956i	$0.245463\pi$
$674$	−1.41815			−0.0546250
$675$	25.8506	+	2.59785i	0.994988	+	0.0999914i
$676$	18.9234			0.727824
$677$	−6.94407	+	7.71217i	−0.266882	+	0.296403i	−0.861659	−	0.507488i	$-0.830574\pi$
$677$	−6.94407	+	7.71217i	−0.266882	+	0.296403i	0.594776	+	0.803891i	$0.297241\pi$
$678$	0.563964	+	2.46953i	0.0216589	+	0.0948417i
$679$	4.56739	+	43.4558i	0.175280	+	1.66768i
$680$	3.81341	+	4.41247i	0.146237	+	0.169210i
$681$	13.9714	+	7.78789i	0.535385	+	0.298433i
$682$	0.159657	+	0.276534i	0.00611358	+	0.0105890i
$683$	19.2932	+	14.0174i	0.738235	+	0.536359i	0.892158	−	0.451724i	$-0.149191\pi$
$683$	19.2932	+	14.0174i	0.738235	+	0.536359i	−0.153923	+	0.988083i	$0.549191\pi$
$684$	−0.0326502	+	0.437087i	−0.00124841	+	0.0167124i
$685$	−10.5186	+	7.32006i	−0.401894	+	0.279685i
$686$	1.40268	−	1.55783i	0.0535545	−	0.0594783i
$687$	−4.27954	+	1.46221i	−0.163275	+	0.0557868i
$688$	−7.96526	−	8.84632i	−0.303673	−	0.337263i
$689$	3.41927	+	0.726789i	0.130264	+	0.0276884i
$690$	−2.64748	−	0.875639i	−0.100788	−	0.0333350i
$691$	1.00613	−	0.213859i	0.0382748	−	0.00813556i	−0.188734	−	0.982028i	$-0.560439\pi$
$691$	1.00613	−	0.213859i	0.0382748	−	0.00813556i	0.227009	+	0.973893i	$0.427105\pi$
$692$	35.4065	+	25.7243i	1.34595	+	0.977893i
$693$	4.31487	−	1.05408i	0.163908	−	0.0400413i
$694$	4.67273	+	3.39494i	0.177374	+	0.128870i
$695$	36.4232	−	6.97095i	1.38161	−	0.264423i
$696$	5.39089	−	5.00321i	0.204341	−	0.189646i
$697$	1.96309	+	18.6775i	0.0743573	+	0.707462i
$698$	−3.38314	−	0.719110i	−0.128054	−	0.0272187i
$699$	4.50193	−	10.5363i	0.170279	−	0.398518i
$700$	−5.90750	+	40.3435i	−0.223283	+	1.52484i
$701$	14.7743			0.558019			0.279009	−	0.960288i	$-0.409994\pi$
$701$	14.7743			0.558019			0.279009	+	0.960288i	$0.409994\pi$
$702$	−0.984117	−	1.23314i	−0.0371431	−	0.0465418i
$703$	−0.460406	+	0.334504i	−0.0173645	+	0.0126161i
$704$	2.40791	+	1.07207i	0.0907516	+	0.0404052i
$705$	−10.1581	−	49.0572i	−0.382575	−	1.84760i
$706$	−2.96005	+	1.31790i	−0.111403	+	0.0495999i
$707$	−36.2017	+	62.7032i	−1.36151	+	2.35820i
$708$	14.7705	+	8.23330i	0.555108	+	0.309426i
$709$	11.5131	−	2.44719i	0.432384	−	0.0919062i	0.0134224	−	0.999910i	$-0.495727\pi$
$709$	11.5131	−	2.44719i	0.432384	−	0.0919062i	0.418962	+	0.908004i	$0.362394\pi$
$710$	−1.43032	−	4.72709i	−0.0536788	−	0.177405i
$711$	17.9657	−	0.541985i	0.673767	−	0.0203260i
$712$	1.44664	−	4.45231i	0.0542152	−	0.166857i
$713$	−23.2117	+	4.93379i	−0.869283	+	0.184772i
$714$	−2.70478	+	3.84337i	−0.101224	+	0.143835i
$715$	1.36291	−	0.573886i	0.0509700	−	0.0214621i
$716$	19.3249	+	21.4624i	0.722204	+	0.802089i
$717$	0.431447	+	28.6097i	0.0161127	+	1.06845i
$718$	−0.249761	−	0.432599i	−0.00932099	−	0.0161444i
$719$	−37.9326	−	27.5596i	−1.41465	−	1.02780i	−0.992626	−	0.121213i	$-0.961321\pi$
$719$	−37.9326	−	27.5596i	−1.41465	−	1.02780i	−0.422019	−	0.906587i	$-0.638679\pi$
$720$	−12.6550	+	22.4248i	−0.471623	+	0.835721i
$721$	40.0084	−	29.0678i	1.48999	−	1.08254i
$722$	2.85372	+	1.27056i	0.106205	+	0.0472853i
$723$	5.47597	+	11.8164i	0.203654	+	0.439457i
$724$	16.9905	−	29.4285i	0.631449	−	1.09370i
$725$	−30.1985	+	11.9988i	−1.12155	+	0.445623i
$726$	−1.21677	+	2.84772i	−0.0451587	+	0.105689i
$727$	−21.0528	+	23.3815i	−0.780806	+	0.867173i	−0.993948	−	0.109848i	$-0.964964\pi$
$727$	−21.0528	+	23.3815i	−0.780806	+	0.867173i	0.213142	+	0.977021i	$0.431630\pi$
$728$	4.03371	−	2.93066i	0.149499	−	0.108618i
$729$	−5.98922	+	26.3273i	−0.221823	+	0.975087i
$730$	4.94801	+	0.100649i	0.183134	+	0.00372518i
$731$	−1.29399	+	12.3115i	−0.0478600	+	0.455357i
$732$	12.2190	−	28.5971i	0.451626	−	1.05698i
$733$	−41.4138	+	18.4386i	−1.52965	+	0.681045i	−0.987265	−	0.159083i	$-0.949146\pi$
$733$	−41.4138	+	18.4386i	−1.52965	+	0.681045i	−0.542388	+	0.840128i	$0.682480\pi$
$734$	0.799319	+	0.887734i	0.0295034	+	0.0327669i
$735$	−38.8618	+	3.87801i	−1.43344	+	0.143043i
$736$	5.67737	−	6.30535i	0.209271	−	0.232418i
$737$	−1.59517	+	4.90942i	−0.0587587	+	0.180841i
$738$	2.09110	−	1.00764i	0.0769746	−	0.0370917i
$739$	12.0961	+	37.2280i	0.444963	+	1.36945i	0.882524	+	0.470267i	$0.155842\pi$
$739$	12.0961	+	37.2280i	0.444963	+	1.36945i	−0.437562	+	0.899188i	$0.644158\pi$
$740$	−33.2993	+	6.37309i	−1.22411	+	0.234279i
$741$	−0.224083	+	0.0765634i	−0.00823190	+	0.00281263i
$742$	−1.17576	+	0.523483i	−0.0431636	+	0.0192177i
$743$	24.2958	−	42.0815i	0.891325	−	1.54382i	0.0530375	−	0.998593i	$-0.483110\pi$
$743$	24.2958	−	42.0815i	0.891325	−	1.54382i	0.838288	−	0.545228i	$-0.183557\pi$
$744$	−0.0924948	−	6.13343i	−0.00339102	−	0.224862i
$745$	1.95500	−	15.5512i	0.0716258	−	0.569750i
$746$	1.40499	−	1.02078i	0.0514403	−	0.0373735i
$747$	2.92253	+	8.14978i	0.106930	+	0.298185i
$748$	−0.871772	−	2.68304i	−0.0318751	−	0.0981016i
$749$	−17.5470	−	30.3923i	−0.641154	−	1.11051i
$750$	−2.46205	+	2.02006i	−0.0899015	+	0.0737620i
$751$	9.62073	−	16.6636i	0.351066	−	0.608063i	−0.635371	−	0.772207i	$-0.719153\pi$
$751$	9.62073	−	16.6636i	0.351066	−	0.608063i	0.986436	+	0.164144i	$0.0524861\pi$
$752$	48.5662	+	10.3231i	1.77103	+	0.376443i
$753$	7.40914	+	32.4437i	0.270004	+	1.18232i
$754$	1.80267	+	0.802601i	0.0656494	+	0.0292290i
$755$	−8.38982	−	6.36021i	−0.305337	−	0.231472i
$756$	−40.8503	−	11.2582i	−1.48571	−	0.409458i
$757$	−21.2374			−0.771886			−0.385943	−	0.922523i	$-0.626124\pi$
$757$	−21.2374			−0.771886			−0.385943	+	0.922523i	$0.626124\pi$
$758$	0.605923	−	5.76497i	0.0220081	−	0.209393i
$759$	2.04578	+	1.78691i	0.0742570	+	0.0648608i
$760$	−0.0707436	−	0.0818570i	−0.00256614	−	0.00296926i
$761$	−33.1709	−	7.05068i	−1.20244	−	0.255587i	−0.437221	−	0.899354i	$-0.644037\pi$
$761$	−33.1709	−	7.05068i	−1.20244	−	0.255587i	−0.765221	+	0.643767i	$0.777371\pi$
$762$	0.178519	−	0.906901i	0.00646706	−	0.0328536i
$763$	32.6460	−	6.93913i	1.18187	−	0.251213i
$764$	−0.355085	−	1.09284i	−0.0128465	−	0.0395375i
$765$	26.1364	−	5.82430i	0.944964	−	0.210578i
$766$	0.317141	−	0.976061i	0.0114588	−	0.0352665i
$767$	−0.954975	+	9.08598i	−0.0344822	+	0.328076i
$768$	−14.4224	−	19.2341i	−0.520425	−	0.694049i
$769$	32.2891	−	14.3760i	1.16437	−	0.518413i	0.268744	−	0.963212i	$-0.413391\pi$
$769$	32.2891	−	14.3760i	1.16437	−	0.518413i	0.895631	+	0.444799i	$0.146725\pi$
$770$	−0.281767	+	0.465888i	−0.0101542	+	0.0167894i
$771$	31.2772	+	9.64365i	1.12642	+	0.347308i
$772$	−16.7489	−	7.45708i	−0.602805	−	0.268386i
$773$	2.89307	+	8.90395i	0.104056	+	0.320253i	0.989508	−	0.144479i	$-0.0461507\pi$
$773$	2.89307	+	8.90395i	0.104056	+	0.320253i	−0.885451	+	0.464732i	$0.846151\pi$
$774$	1.48635	−	0.363101i	0.0534257	−	0.0130514i
$775$	−9.41610	+	25.4133i	−0.338236	+	0.912872i
$776$	−3.45364	−	5.98188i	−0.123978	−	0.214737i
$777$	−23.1329	−	49.9177i	−0.829888	−	1.79079i
$778$	0.489929	+	4.66136i	0.0175648	+	0.167118i
$779$	−0.0364178	−	0.346492i	−0.00130480	−	0.0124144i
$780$	−14.0223	−	1.54840i	−0.502077	−	0.0554416i
$781$	−0.502866	+	4.78445i	−0.0179940	+	0.171201i
$782$	−2.87405			−0.102776
$783$	−8.50773	−	32.6805i	−0.304041	−	1.16791i
$784$	11.9610	−	36.8122i	0.427178	−	1.31472i
$785$	−4.75161	+	37.7969i	−0.169592	+	1.34903i
$786$	−2.44105	−	0.219405i	−0.0870694	−	0.00782591i
$787$	6.25098	+	6.94241i	0.222823	+	0.247470i	0.844183	−	0.536055i	$-0.180086\pi$
$787$	6.25098	+	6.94241i	0.222823	+	0.247470i	−0.621360	+	0.783525i	$0.713419\pi$
$788$	−5.67074	−	6.29800i	−0.202012	−	0.224357i
$789$	11.7837	+	25.4276i	0.419510	+	0.905247i
$790$	−1.50724	+	1.60700i	−0.0536252	+	0.0571744i
$791$	−11.3584	+	34.9574i	−0.403857	+	1.24294i
$792$	−0.555345	+	0.429653i	−0.0197333	+	0.0152670i
$793$	16.8014			0.596635
$794$	0.103494	−	0.984680i	0.00367287	−	0.0349450i
$795$	6.96218	+	2.30270i	0.246923	+	0.0816684i
$796$	−0.660296	−	6.28230i	−0.0234036	−	0.222670i
$797$	0.912195	+	8.67896i	0.0323116	+	0.307424i	0.998727	+	0.0504398i	$0.0160623\pi$
$797$	0.912195	+	8.67896i	0.0323116	+	0.307424i	−0.966416	+	0.256985i	$0.917271\pi$
$798$	0.0501771	−	0.0712994i	0.00177625	−	0.00252397i
$799$	−25.8171	−	44.7165i	−0.913342	−	1.58196i
$800$	−2.61717	−	9.33001i	−0.0925308	−	0.329866i
$801$	−14.8579	−	15.5328i	−0.524980	−	0.548823i
$802$	1.34859	+	4.15052i	0.0476202	+	0.146560i
$803$	−4.40405	−	1.96081i	−0.155415	−	0.0691954i
$804$	36.0951	−	33.4994i	1.27298	−	1.18143i
$805$	−26.4577	−	30.6141i	−0.932512	−	1.07900i
$806$	1.50347	−	0.669389i	0.0529576	−	0.0235782i
$807$	−1.45170	+	3.39754i	−0.0511022	+	0.119599i
$808$	1.19638	−	11.3827i	0.0420883	−	0.400444i
$809$	−1.28747	+	3.96244i	−0.0452652	+	0.139312i	−0.971135	−	0.238531i	$-0.923334\pi$
$809$	−1.28747	+	3.96244i	−0.0452652	+	0.139312i	0.925870	+	0.377843i	$0.123334\pi$
$810$	−1.76806	−	2.79780i	−0.0621232	−	0.0983048i
$811$	−7.66159	−	23.5800i	−0.269035	−	0.828004i	−0.990736	−	0.135800i	$-0.956640\pi$
$811$	−7.66159	−	23.5800i	−0.269035	−	0.828004i	0.721701	−	0.692205i	$-0.243360\pi$
$812$	51.8395	−	11.0188i	1.81921	−	0.386685i
$813$	21.2237	+	18.5382i	0.744349	+	0.650162i
$814$	−0.442836	−	0.0941277i	−0.0155214	−	0.00329917i
$815$	0.191176	+	2.26024i	0.00669660	+	0.0791727i
$816$	−5.12567	+	26.0391i	−0.179434	+	0.911550i
$817$	0.0240052	−	0.228394i	0.000839835	−	0.00799050i
$818$	4.49076			0.157016
$819$	−3.07841	−	22.6850i	−0.107568	−	0.792679i
$820$	6.81408	−	19.6056i	0.237958	−	0.684657i
$821$	−26.1661	−	11.6499i	−0.913204	−	0.406584i	−0.104314	−	0.994544i	$-0.533265\pi$
$821$	−26.1661	−	11.6499i	−0.913204	−	0.406584i	−0.808890	+	0.587960i	$0.799931\pi$
$822$	1.56001	+	0.480995i	0.0544115	+	0.0167766i
$823$	−42.8413	−	9.10620i	−1.49335	−	0.317422i	−0.612371	−	0.790571i	$-0.709784\pi$
$823$	−42.8413	−	9.10620i	−1.49335	−	0.317422i	−0.880983	+	0.473149i	$0.843117\pi$
$824$	−3.90874	+	6.77013i	−0.136167	+	0.235849i
$825$	2.97394	−	0.882805i	0.103539	−	0.0307353i
$826$	−1.68185	−	2.91305i	−0.0585191	−	0.101358i
$827$	−8.39488	−	25.8368i	−0.291919	−	0.898433i	−0.984239	−	0.176843i	$-0.943411\pi$
$827$	−8.39488	−	25.8368i	−0.291919	−	0.898433i	0.692320	−	0.721590i	$-0.256589\pi$
$828$	−8.74699	−	24.3919i	−0.303979	−	0.847677i
$829$	−24.7627	+	17.9912i	−0.860045	+	0.624859i	−0.927897	−	0.372836i	$-0.878385\pi$
$829$	−24.7627	+	17.9912i	−0.860045	+	0.624859i	0.0678520	+	0.997695i	$0.478385\pi$
$830$	−0.960554	−	0.451292i	−0.0333413	−	0.0156646i
$831$	12.8917	+	7.18605i	0.447208	+	0.249281i
$832$	6.79247	−	11.7649i	0.235487	−	0.407875i
$833$	−36.7725	+	16.3722i	−1.27409	+	0.567261i
$834$	−3.55795	−	3.10774i	−0.123202	−	0.107612i
$835$	−5.86321	+	6.25126i	−0.202905	+	0.216334i
$836$	0.0161725	+	0.0497738i	0.000559337	+	0.00172146i
$837$	−25.0033	−	12.9650i	−0.864242	−	0.448135i
$838$	0.601058	−	1.84987i	0.0207632	−	0.0639025i
$839$	28.0673	−	31.1719i	0.968990	−	1.07617i	−0.0280749	−	0.999606i	$-0.508938\pi$
$839$	28.0673	−	31.1719i	0.968990	−	1.07617i	0.997065	−	0.0765661i	$-0.0243956\pi$
$840$	9.08547	−	5.18198i	0.313479	−	0.178795i
$841$	8.85722	+	9.83694i	0.305422	+	0.339205i
$842$	−0.274781	+	0.122341i	−0.00946959	+	0.00421613i
$843$	−14.2866	+	1.71976i	−0.492057	+	0.0592316i
$844$	−1.49685	+	14.2416i	−0.0515237	+	0.490216i
$845$	6.21131	+	20.5279i	0.213676	+	0.706182i
$846$	−4.12535	+	4.86926i	−0.141832	+	0.167409i
$847$	−36.3536	+	26.4125i	−1.24913	+	0.907543i
$848$	−4.86306	+	5.40097i	−0.166998	+	0.185470i
$849$	−5.43902	−	7.25359i	−0.186667	−	0.248942i
$850$	−1.75542	+	2.77352i	−0.0602105	+	0.0951311i
$851$	16.8226	−	29.1375i	0.576670	−	0.998821i
$852$	26.4129	−	37.5315i	0.904890	−	1.28581i
$853$	21.1852	+	9.43224i	0.725366	+	0.322954i	0.735992	−	0.676990i	$-0.236716\pi$
$853$	21.1852	+	9.43224i	0.725366	+	0.322954i	−0.0106265	+	0.999944i	$0.503383\pi$
$854$	−5.00452	+	3.63600i	−0.171251	+	0.124421i
$855$	−0.484864	+	0.108048i	−0.0165820	+	0.00369517i
$856$	4.48812	+	3.26081i	0.153401	+	0.111452i
$857$	−13.5979	−	23.5523i	−0.464496	−	0.804532i	0.534682	−	0.845053i	$-0.320431\pi$
$857$	−13.5979	−	23.5523i	−0.464496	−	0.804532i	−0.999179	+	0.0405217i	$0.987098\pi$
$858$	−0.164546	−	0.0917205i	−0.00561750	−	0.00313129i
$859$	−1.90895	−	2.12010i	−0.0651326	−	0.0723370i	0.709698	−	0.704506i	$-0.248831\pi$
$859$	−1.90895	−	2.12010i	−0.0651326	−	0.0723370i	−0.774830	+	0.632169i	$0.782165\pi$
$860$	7.08031	−	11.7070i	0.241437	−	0.399205i
$861$	33.5466	+	3.01521i	1.14326	+	0.102758i
$862$	−5.66722	+	1.20460i	−0.193026	+	0.0410290i
$863$	7.66135	−	23.5792i	0.260795	−	0.802646i	−0.731837	−	0.681480i	$-0.761337\pi$
$863$	7.66135	−	23.5792i	0.260795	−	0.802646i	0.992632	−	0.121166i	$-0.0386633\pi$
$864$	9.95726	−	1.50446i	0.338753	−	0.0511828i
$865$	−16.2839	+	46.8522i	−0.553668	+	1.59302i
$866$	−0.631918	+	0.134318i	−0.0214735	+	0.00456432i
$867$	−1.58474	+	0.947092i	−0.0538204	+	0.0321649i
$868$	22.1007	−	38.2795i	0.750146	−	1.29929i
$869$	1.96061	−	0.872918i	0.0665090	−	0.0296117i
$870$	3.57395	+	2.08856i	0.121168	+	0.0708089i
$871$	24.3053	+	10.8214i	0.823554	+	0.366670i
$872$	−4.26832	+	3.10112i	−0.144544	+	0.105017i
$873$	−31.7003	+	0.956327i	−1.07289	+	0.0323668i
$874$	0.0533172			0.00180348
$875$	−45.7033	+	6.83372i	−1.54505	+	0.231022i
$876$	27.5900	+	36.7945i	0.932178	+	1.24317i
$877$	24.9580	+	5.30498i	0.842771	+	0.179136i	0.609015	−	0.793159i	$-0.291565\pi$
$877$	24.9580	+	5.30498i	0.842771	+	0.179136i	0.233756	+	0.972295i	$0.424898\pi$
$878$	0.332059	+	3.15933i	0.0112064	+	0.106622i
$879$	33.7561	+	10.4080i	1.13857	+	0.351052i
$880$	−0.383496	+	3.05053i	−0.0129276	+	0.102834i
$881$	−12.7368	−	9.25380i	−0.429112	−	0.311768i	0.352181	−	0.935932i	$-0.385440\pi$
$881$	−12.7368	−	9.25380i	−0.429112	−	0.311768i	−0.781294	+	0.624163i	$0.785440\pi$
$882$	3.43898	+	3.59517i	0.115796	+	0.121056i
$883$	3.13548	+	2.27806i	0.105517	+	0.0766627i	0.639293	−	0.768964i	$-0.279227\pi$
$883$	3.13548	+	2.27806i	0.105517	+	0.0766627i	−0.533775	+	0.845626i	$0.679227\pi$
$884$	−14.2224	+	3.02306i	−0.478350	+	0.101676i
$885$	−4.08323	+	18.7253i	−0.137256	+	0.629444i
$886$	0.720918	+	0.153236i	0.0242197	+	0.00514806i
$887$	−3.41528	−	3.79305i	−0.114674	−	0.127358i	0.683075	−	0.730349i	$-0.260642\pi$
$887$	−3.41528	−	3.79305i	−0.114674	−	0.127358i	−0.797748	+	0.602990i	$0.793976\pi$
$888$	6.55020	+	5.72136i	0.219810	+	0.191996i
$889$	8.97440	−	9.96708i	0.300992	−	0.334285i
$890$	2.63427	+	0.0535844i	0.0883009	+	0.00179615i
$891$	0.529651	+	3.18010i	0.0177440	+	0.106537i
$892$	−0.949679	−	0.689982i	−0.0317976	−	0.0231023i
$893$	0.478940	+	0.829548i	0.0160271	+	0.0277598i
$894$	−1.71388	+	1.02427i	−0.0573207	+	0.0342568i
$895$	−16.9391	+	28.0081i	−0.566213	+	0.936208i
$896$	2.19745	+	20.9073i	0.0734115	+	0.698464i
$897$	10.2615	−	9.52356i	0.342621	−	0.317982i
$898$	1.23688	−	1.37369i	0.0412752	−	0.0458408i
$899$	35.2266			1.17487
$900$	−28.8813	−	6.45714i	−0.962709	−	0.215238i
$901$	7.55799			0.251793
$902$	0.185458	−	0.205972i	0.00617507	−	0.00685811i
$903$	21.2162	+	6.54154i	0.706029	+	0.217689i
$904$	−0.607353	−	5.77857i	−0.0202002	−	0.192193i
$905$	37.5006	+	8.77174i	1.24656	+	0.291582i
$906$	0.0202230	+	1.34101i	0.000671863	+	0.0445519i
$907$	−6.09501	−	10.5569i	−0.202382	−	0.350535i	0.746914	−	0.664921i	$-0.231535\pi$
$907$	−6.09501	−	10.5569i	−0.202382	−	0.350535i	−0.949295	+	0.314386i	$0.898201\pi$
$908$	−14.7404	−	10.7095i	−0.489176	−	0.355407i
$909$	−43.4274	−	29.5931i	−1.44039	−	0.981541i
$910$	2.23625	+	1.69527i	0.0741310	+	0.0561978i
$911$	−2.43329	+	2.70244i	−0.0806184	+	0.0895358i	−0.782104	−	0.623147i	$-0.785854\pi$
$911$	−2.43329	+	2.70244i	−0.0806184	+	0.0895358i	0.701486	+	0.712683i	$0.252520\pi$
$912$	0.0950877	−	0.483058i	0.00314867	−	0.0159957i
$913$	0.691743	+	0.768258i	0.0228933	+	0.0254256i
$914$	−2.40786	−	0.511806i	−0.0796449	−	0.0169291i
$915$	35.0326	+	3.86845i	1.15814	+	0.127887i
$916$	5.03889	−	1.07105i	0.166489	−	0.0353884i
$917$	−28.7714	−	20.9036i	−0.950115	−	0.690299i
$918$	−2.63560	−	2.16552i	−0.0869876	−	0.0714729i
$919$	19.4901	+	14.1604i	0.642919	+	0.467108i	0.860852	−	0.508856i	$-0.169931\pi$
$919$	19.4901	+	14.1604i	0.642919	+	0.467108i	−0.217933	+	0.975964i	$0.569931\pi$
$920$	5.78919	+	2.71991i	0.190864	+	0.0896726i
$921$	−3.33045	−	14.5836i	−0.109742	−	0.480547i
$922$	0.518331	+	4.93159i	0.0170703	+	0.162413i
$923$	24.2532	+	5.15518i	0.798305	+	0.169685i
$924$	−5.02327	+	0.604679i	−0.165254	+	0.0198925i
$925$	−17.8434	−	34.0309i	−0.586688	−	1.11893i
$926$	4.54663			0.149411
$927$	18.8761	+	30.5297i	0.619974	+	1.00273i
$928$	−10.1897	+	7.40328i	−0.334495	+	0.243025i
$929$	−14.7933	−	6.58640i	−0.485352	−	0.216093i	0.149447	−	0.988770i	$-0.452251\pi$
$929$	−14.7933	−	6.58640i	−0.485352	−	0.216093i	−0.634799	+	0.772677i	$0.718917\pi$
$930$	3.28902	−	1.04957i	0.107851	−	0.0344169i
$931$	0.682176	−	0.303724i	0.0223574	−	0.00995416i
$932$	−6.52569	+	11.3028i	−0.213756	+	0.370236i
$933$	−0.351736	−	23.3240i	−0.0115153	−	0.763594i
$934$	4.75331	−	1.01035i	0.155533	−	0.0330596i
$935$	2.62439	−	1.82635i	0.0858266	−	0.0597281i
$936$	1.90313	+	3.07806i	0.0622056	+	0.100610i
$937$	6.74493	−	20.7587i	0.220347	−	0.678159i	−0.778384	−	0.627789i	$-0.783960\pi$
$937$	6.74493	−	20.7587i	0.220347	−	0.678159i	0.998731	−	0.0503697i	$-0.0160399\pi$
$938$	−9.58155	+	2.03662i	−0.312849	+	0.0664980i
$939$	−5.31981	−	11.4794i	−0.173605	−	0.374617i
$940$	4.80956	+	56.8626i	0.156871	+	1.85465i
$941$	−15.0308	−	16.6934i	−0.489991	−	0.544190i	0.446545	−	0.894761i	$-0.352654\pi$
$941$	−15.0308	−	16.6934i	−0.489991	−	0.544190i	−0.936536	+	0.350571i	$0.885988\pi$
$942$	4.16556	−	2.48948i	0.135721	−	0.0811117i
$943$	10.2988	+	17.8381i	0.335376	+	0.580888i
$944$	−15.3668	−	11.1647i	−0.500148	−	0.363379i
$945$	−1.19565	−	48.0093i	−0.0388946	−	1.56174i
$946$	0.147803	−	0.107385i	0.00480549	−	0.00349139i
$947$	−38.8398	−	17.2926i	−1.26212	−	0.561934i	−0.336966	−	0.941517i	$-0.609401\pi$
$947$	−38.8398	−	17.2926i	−1.26212	−	0.561934i	−0.925158	+	0.379583i	$0.876067\pi$
$948$	−20.3916	−	1.83282i	−0.662288	−	0.0595273i
$949$	−12.4234	+	21.5179i	−0.403279	+	0.698500i
$950$	0.0325654	−	0.0514524i	0.00105656	−	0.00166934i
$951$	−39.9502	+	4.80902i	−1.29547	+	0.155943i
$952$	7.21332	−	8.01120i	0.233785	−	0.259645i
$953$	−22.8049	+	16.5687i	−0.738722	+	0.536713i	−0.892311	−	0.451422i	$-0.850917\pi$
$953$	−22.8049	+	16.5687i	−0.738722	+	0.536713i	0.153588	+	0.988135i	$0.450917\pi$
$954$	−0.315327	−	0.879322i	−0.0102091	−	0.0284691i
$955$	1.06895	−	0.743900i	0.0345904	−	0.0240720i
$956$	3.40685	−	32.4140i	0.110185	−	1.04834i
$957$	−2.41901	−	3.22604i	−0.0781955	−	0.104283i
$958$	2.01342	−	0.896433i	0.0650507	−	0.0289624i
$959$	15.8503	+	17.6035i	0.511833	+	0.568448i
$960$	16.8718	−	22.9671i	0.544535	−	0.741259i
$961$	−1.08407	+	1.20398i	−0.0349699	+	0.0388380i
$962$	−0.721055	+	2.21918i	−0.0232477	+	0.0715492i
$963$	22.9467	−	11.0573i	0.739449	−	0.356317i
$964$	−4.58426	−	14.1089i	−0.147649	−	0.454417i
$965$	2.59181	−	20.6167i	0.0834333	−	0.663674i
$966$	−0.995529	+	5.05742i	−0.0320306	+	0.162720i
$967$	−3.03887	+	1.35299i	−0.0977235	+	0.0435093i	−0.455016	−	0.890483i	$-0.650367\pi$
$967$	−3.03887	+	1.35299i	−0.0977235	+	0.0435093i	0.357293	+	0.933992i	$0.383700\pi$
$968$	3.55168	−	6.15169i	0.114155	−	0.197723i
$969$	−0.439487	+	0.262652i	−0.0141183	+	0.00843761i
$970$	2.65951	−	2.83553i	0.0853917	−	0.0910433i
$971$	−31.5894	+	22.9510i	−1.01375	+	0.736534i	−0.964993	−	0.262277i	$-0.915527\pi$
$971$	−31.5894	+	22.9510i	−1.01375	+	0.736534i	−0.0487589	+	0.998811i	$0.515527\pi$
$972$	10.3574	−	28.9588i	0.332214	−	0.928854i
$973$	−21.1826	−	65.1935i	−0.679085	−	2.09001i
$974$	0.219673	+	0.380484i	0.00703877	+	0.0121915i
$975$	−2.92289	−	15.7194i	−0.0936075	−	0.503425i
$976$	−17.4656	+	30.2514i	−0.559061	+	0.968323i
$977$	−24.3820	−	5.18256i	−0.780050	−	0.165805i	−0.199357	−	0.979927i	$-0.563885\pi$
$977$	−24.3820	−	5.18256i	−0.780050	−	0.165805i	−0.580694	+	0.814122i	$0.697219\pi$
$978$	0.211796	−	0.196565i	0.00677249	−	0.00628546i
$979$	−2.34467	−	1.04391i	−0.0749359	−	0.0333636i
$980$	44.4775	+	0.904730i	1.42078	+	0.0289005i
$981$	3.25746	+	24.0044i	0.104003	+	0.766403i
$982$	2.94505			0.0939804
$983$	4.20083	−	39.9683i	0.133986	−	1.27479i	−0.696422	−	0.717633i	$-0.745226\pi$
$983$	4.20083	−	39.9683i	0.133986	−	1.27479i	0.830408	−	0.557157i	$-0.188108\pi$
$984$	−5.03840	+	1.72149i	−0.160618	+	0.0548791i
$985$	4.97067	−	8.21878i	0.158379	−	0.261872i
$986$	4.17319	+	0.887038i	0.132901	+	0.0282491i
$987$	−87.6296	+	29.9408i	−2.78928	+	0.953026i
$988$	0.263843	−	0.0560816i	0.00839397	−	0.00178419i
$989$	4.19558	+	12.9127i	0.133412	+	0.410599i
$990$	−0.321976	−	0.229133i	−0.0102331	−	0.00728231i
$991$	−13.0513	+	40.1678i	−0.414588	+	1.27597i	0.498030	+	0.867160i	$0.334057\pi$
$991$	−13.0513	+	40.1678i	−0.414588	+	1.27597i	−0.912619	+	0.408812i	$0.865943\pi$
$992$	−1.09804	+	10.4472i	−0.0348629	+	0.331698i
$993$	46.2404	−	5.56621i	1.46740	−	0.176638i
$994$	−8.33979	+	3.71312i	−0.264522	+	0.117773i
$995$	6.59824	−	2.77835i	0.209178	−	0.0880795i
$996$	−2.19568	−	9.61462i	−0.0695729	−	0.304651i
$997$	43.7314	+	19.4705i	1.38499	+	0.616637i	0.957776	−	0.287514i	$-0.0928289\pi$
$997$	43.7314	+	19.4705i	1.38499	+	0.616637i	0.427213	+	0.904151i	$0.359496\pi$
$998$	−1.04419	−	3.21368i	−0.0330531	−	0.101727i
$999$	37.3812	−	14.0447i	1.18269	−	0.444354i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	225.2.q.a.31.15	✓	224
3.2	odd	2		675.2.r.a.631.14		224
9.2	odd	6		675.2.r.a.181.15		224
9.7	even	3	inner	225.2.q.a.106.14	yes	224
25.21	even	5	inner	225.2.q.a.121.14	yes	224
75.71	odd	10		675.2.r.a.496.15		224
225.146	odd	30		675.2.r.a.46.14		224
225.196	even	15	inner	225.2.q.a.196.15	yes	224

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
225.2.q.a.31.15	✓	224	1.1	even	1	trivial
225.2.q.a.106.14	yes	224	9.7	even	3	inner
225.2.q.a.121.14	yes	224	25.21	even	5	inner
225.2.q.a.196.15	yes	224	225.196	even	15	inner
675.2.r.a.46.14		224	225.146	odd	30
675.2.r.a.181.15		224	9.2	odd	6
675.2.r.a.496.15		224	75.71	odd	10
675.2.r.a.631.14		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)

\(f(q)\)	\(=\)	\(q+(-0.110043 + 0.122216i) q^{2} +(-0.385619 - 1.68858i) q^{3} +(0.206230 + 1.96215i) q^{4} +(-2.06082 + 0.867759i) q^{5} +(0.248806 + 0.138688i) q^{6} +(2.06663 + 3.57951i) q^{7} +(-0.528597 - 0.384048i) q^{8} +(-2.70260 + 1.30230i) q^{9} +O(q^{10})\)	\(q+(-0.110043 + 0.122216i) q^{2} +(-0.385619 - 1.68858i) q^{3} +(0.206230 + 1.96215i) q^{4} +(-2.06082 + 0.867759i) q^{5} +(0.248806 + 0.138688i) q^{6} +(2.06663 + 3.57951i) q^{7} +(-0.528597 - 0.384048i) q^{8} +(-2.70260 + 1.30230i) q^{9} +(0.120726 - 0.347356i) q^{10} +(-0.239690 + 0.266203i) q^{11} +(3.23371 - 1.10488i) q^{12} +(1.23537 + 1.37202i) q^{13} +(-0.664892 - 0.141327i) q^{14} +(2.25997 + 3.14524i) q^{15} +(-3.75457 + 0.798059i) q^{16} +(3.22940 + 2.34629i) q^{17} +(0.138242 - 0.473609i) q^{18} +(-0.0599095 - 0.0435268i) q^{19} +(-2.12767 - 3.86468i) q^{20} +(5.24736 - 4.87000i) q^{21} +(-0.00615783 - 0.0585878i) q^{22} +(4.28234 + 0.910239i) q^{23} +(-0.444658 + 1.04067i) q^{24} +(3.49399 - 3.57660i) q^{25} -0.303627 q^{26} +(3.24120 + 4.06136i) q^{27} +(-6.59733 + 4.79324i) q^{28} +(-5.93713 - 2.64338i) q^{29} +(-0.633093 - 0.0699089i) q^{30} +(-4.95171 + 2.20464i) q^{31} +(0.969013 - 1.67838i) q^{32} +(0.541934 + 0.302083i) q^{33} +(-0.642128 + 0.136489i) q^{34} +(-7.36512 - 5.58341i) q^{35} +(-3.11265 - 5.03431i) q^{36} +(2.37480 - 7.30889i) q^{37} +(0.0119123 - 0.00253204i) q^{38} +(1.84038 - 2.61510i) q^{39} +(1.42261 + 0.332761i) q^{40} +(3.14813 + 3.49635i) q^{41} +(0.0177530 + 1.17722i) q^{42} +(1.55061 + 2.68574i) q^{43} +(-0.571760 - 0.415408i) q^{44} +(4.43949 - 5.02901i) q^{45} +(-0.582489 + 0.423203i) q^{46} +(-11.8169 - 5.26122i) q^{47} +(2.79542 + 6.03215i) q^{48} +(-5.04195 + 8.73292i) q^{49} +(0.0526256 + 0.820601i) q^{50} +(2.71659 - 6.35787i) q^{51} +(-2.43733 + 2.70693i) q^{52} +(1.53179 - 1.11291i) q^{53} +(-0.853034 - 0.0508000i) q^{54} +(0.262959 - 0.756591i) q^{55} +(0.282290 - 2.68581i) q^{56} +(-0.0503961 + 0.117947i) q^{57} +(0.976404 - 0.434723i) q^{58} +(3.31117 + 3.67743i) q^{59} +(-5.70534 + 5.08304i) q^{60} +(6.08932 - 6.76288i) q^{61} +(0.275461 - 0.847783i) q^{62} +(-10.2469 - 6.98261i) q^{63} +(-2.27380 - 6.99805i) q^{64} +(-3.73647 - 1.75549i) q^{65} +(-0.0965556 + 0.0329906i) q^{66} +(13.1648 - 5.86135i) q^{67} +(-3.93777 + 6.82042i) q^{68} +(-0.114341 - 7.58207i) q^{69} +(1.49286 - 0.285716i) q^{70} +(10.8652 - 7.89400i) q^{71} +(1.92873 + 0.349537i) q^{72} +(4.15877 + 12.7994i) q^{73} +(0.631930 + 1.09453i) q^{74} +(-7.38671 - 4.52067i) q^{75} +(0.0730507 - 0.126528i) q^{76} +(-1.44823 - 0.307831i) q^{77} +(0.117084 + 0.512698i) q^{78} +(-5.47332 - 2.43688i) q^{79} +(7.04499 - 4.90273i) q^{80} +(5.60805 - 7.03916i) q^{81} -0.773739 q^{82} +(0.301668 - 2.87018i) q^{83} +(10.6378 + 9.29174i) q^{84} +(-8.69124 - 2.03296i) q^{85} +(-0.498874 - 0.106039i) q^{86} +(-2.17408 + 11.0446i) q^{87} +(0.228934 - 0.0486615i) q^{88} +(2.21408 + 6.81425i) q^{89} +(0.126086 + 1.09598i) q^{90} +(-2.35810 + 7.25750i) q^{91} +(-0.902876 + 8.59029i) q^{92} +(5.63219 + 7.51120i) q^{93} +(1.94338 - 0.865246i) q^{94} +(0.161234 + 0.0377140i) q^{95} +(-3.20775 - 0.989039i) q^{96} +(9.65762 + 4.29985i) q^{97} +(-0.512465 - 1.57721i) q^{98} +(0.301111 - 1.03159i) 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

Modular forms

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Database

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