LMFDB - Embedded newform 225.2.q.a.106.3

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			106.3
Character	$\chi$	$=$	225.106
Dual form			225.2.q.a.121.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.40744 - 0.511718i) q^{2} +(1.05412 + 1.37435i) q^{3} +(3.70683 + 1.65039i) q^{4} +(1.50334 + 1.65528i) q^{5} +(-1.83444 - 3.84808i) q^{6} +(2.55879 - 4.43196i) q^{7} +(-4.09710 - 2.97672i) q^{8} +(-0.777680 + 2.89745i) q^{9} +O(q^{10})$	\(q+(-2.40744 - 0.511718i) q^{2} +(1.05412 + 1.37435i) q^{3} +(3.70683 + 1.65039i) q^{4} +(1.50334 + 1.65528i) q^{5} +(-1.83444 - 3.84808i) q^{6} +(2.55879 - 4.43196i) q^{7} +(-4.09710 - 2.97672i) q^{8} +(-0.777680 + 2.89745i) q^{9} +(-2.77218 - 4.75428i) q^{10} +(1.54858 + 0.329161i) q^{11} +(1.63922 + 6.83418i) q^{12} +(-0.872558 + 0.185468i) q^{13} +(-8.42805 + 9.36030i) q^{14} +(-0.690238 + 3.81098i) q^{15} +(2.91012 + 3.23201i) q^{16} +(-3.04259 - 2.21057i) q^{17} +(3.35489 - 6.57749i) q^{18} +(3.69404 + 2.68388i) q^{19} +(2.84079 + 8.61695i) q^{20} +(8.78832 - 1.15512i) q^{21} +(-3.55968 - 1.58487i) q^{22} +(3.66725 - 4.07289i) q^{23} +(-0.227764 - 8.76865i) q^{24} +(-0.479912 + 4.97692i) q^{25} +2.19554 q^{26} +(-4.80188 + 1.98544i) q^{27} +(16.7994 - 12.2055i) q^{28} +(0.00441000 + 0.0419584i) q^{29} +(3.61185 - 8.82151i) q^{30} +(-0.205934 + 1.95934i) q^{31} +(-0.287768 - 0.498429i) q^{32} +(1.18000 + 2.47526i) q^{33} +(6.19366 + 6.87876i) q^{34} +(11.1829 - 2.42724i) q^{35} +(-7.66464 + 9.45688i) q^{36} +(-1.43995 + 4.43171i) q^{37} +(-7.51981 - 8.35159i) q^{38} +(-1.17468 - 1.00370i) q^{39} +(-1.23205 - 11.2569i) q^{40} +(-0.748156 + 0.159025i) q^{41} +(-21.7485 - 1.71626i) q^{42} +(-4.11709 + 7.13101i) q^{43} +(5.19708 + 3.77590i) q^{44} +(-5.96521 + 3.06859i) q^{45} +(-10.9129 + 7.92865i) q^{46} +(-0.426471 - 4.05760i) q^{47} +(-1.37432 + 7.40644i) q^{48} +(-9.59482 - 16.6187i) q^{49} +(3.70214 - 11.7361i) q^{50} +(-0.169142 - 6.51178i) q^{51} +(-3.54052 - 0.752561i) q^{52} +(-2.00012 + 1.45317i) q^{53} +(12.5762 - 2.32263i) q^{54} +(1.78319 + 3.05818i) q^{55} +(-23.6763 + 10.5414i) q^{56} +(0.205358 + 7.90603i) q^{57} +(0.0108540 - 0.103269i) q^{58} +(-9.31606 + 1.98019i) q^{59} +(-8.84819 + 12.9875i) q^{60} +(7.08784 + 1.50657i) q^{61} +(1.49840 - 4.61160i) q^{62} +(10.8514 + 10.8606i) q^{63} +(-2.25016 - 6.92529i) q^{64} +(-1.61876 - 1.16551i) q^{65} +(-1.57414 - 6.56288i) q^{66} +(-0.375946 + 3.57689i) q^{67} +(-7.63006 - 13.2156i) q^{68} +(9.46329 + 0.746785i) q^{69} +(-28.1642 + 0.120956i) q^{70} +(-1.57130 + 1.14162i) q^{71} +(11.8111 - 9.55620i) q^{72} +(-4.42033 - 13.6044i) q^{73} +(5.73438 - 9.93224i) q^{74} +(-7.34591 + 4.58668i) q^{75} +(9.26375 + 16.0453i) q^{76} +(5.42132 - 6.02098i) q^{77} +(2.31435 + 3.01744i) q^{78} +(-0.355789 - 3.38511i) q^{79} +(-0.974982 + 9.67589i) q^{80} +(-7.79043 - 4.50657i) q^{81} +1.88252 q^{82} +(-3.54787 + 1.57961i) q^{83} +(34.4832 + 10.2223i) q^{84} +(-0.914942 - 8.35958i) q^{85} +(13.5607 - 15.0607i) q^{86} +(-0.0530169 + 0.0502899i) q^{87} +(-5.36486 - 5.95828i) q^{88} +(-0.935601 - 2.87948i) q^{89} +(15.9312 - 4.33494i) q^{90} +(-1.41071 + 4.34171i) q^{91} +(20.3157 - 9.04514i) q^{92} +(-2.90989 + 1.78234i) q^{93} +(-1.04964 + 9.98667i) q^{94} +(1.11084 + 10.1495i) q^{95} +(0.381675 - 0.920896i) q^{96} +(0.544048 + 5.17627i) q^{97} +(14.5949 + 44.9184i) q^{98} +(-2.15803 + 4.23095i) 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 $

$2$	−2.40744	−	0.511718i	−1.70232	−	0.361839i	−0.748712	−	0.662895i	$-0.769327\pi$
$2$	−2.40744	−	0.511718i	−1.70232	−	0.361839i	−0.953606	+	0.301056i	$0.902661\pi$
$3$	1.05412	+	1.37435i	0.608594	+	0.793482i
$3$	1.05412	+	1.37435i	0.608594	+	0.793482i
$4$	3.70683	+	1.65039i	1.85341	+	0.825193i
$5$	1.50334	+	1.65528i	0.672316	+	0.740264i
$5$	1.50334	+	1.65528i	0.672316	+	0.740264i
$6$	−1.83444	−	3.84808i	−0.748908	−	1.57097i
$7$	2.55879	−	4.43196i	0.967132	−	1.67512i	0.263357	−	0.964698i	$-0.415170\pi$
$7$	2.55879	−	4.43196i	0.967132	−	1.67512i	0.703775	−	0.710423i	$-0.251496\pi$
$8$	−4.09710	−	2.97672i	−1.44854	−	1.05243i
$9$	−0.777680	+	2.89745i	−0.259227	+	0.965817i
$10$	−2.77218	−	4.75428i	−0.876639	−	1.50344i
$11$	1.54858	+	0.329161i	0.466914	+	0.0992457i	0.435360	−	0.900256i	$-0.356621\pi$
$11$	1.54858	+	0.329161i	0.466914	+	0.0992457i	0.0315541	+	0.999502i	$0.489954\pi$
$12$	1.63922	+	6.83418i	0.473201	+	1.97286i
$13$	−0.872558	+	0.185468i	−0.242004	+	0.0514396i	−0.327317	−	0.944915i	$-0.606144\pi$
$13$	−0.872558	+	0.185468i	−0.242004	+	0.0514396i	0.0853127	+	0.996354i	$0.472811\pi$
$14$	−8.42805	+	9.36030i	−2.25249	+	2.50164i
$15$	−0.690238	+	3.81098i	−0.178219	+	0.983991i
$16$	2.91012	+	3.23201i	0.727529	+	0.808003i
$17$	−3.04259	−	2.21057i	−0.737936	−	0.536142i	0.154128	−	0.988051i	$-0.450743\pi$
$17$	−3.04259	−	2.21057i	−0.737936	−	0.536142i	−0.892064	+	0.451909i	$0.850743\pi$
$18$	3.35489	−	6.57749i	0.790756	−	1.55033i
$19$	3.69404	+	2.68388i	0.847472	+	0.615724i	0.924448	−	0.381309i	$-0.124527\pi$
$19$	3.69404	+	2.68388i	0.847472	+	0.615724i	−0.0769761	+	0.997033i	$0.524527\pi$
$20$	2.84079	+	8.61695i	0.635219	+	1.92681i
$21$	8.78832	−	1.15512i	1.91777	−	0.252068i
$22$	−3.55968	−	1.58487i	−0.758926	−	0.337896i
$23$	3.66725	−	4.07289i	0.764674	−	0.849257i	−0.227544	−	0.973768i	$-0.573070\pi$
$23$	3.66725	−	4.07289i	0.764674	−	0.849257i	0.992218	+	0.124511i	$0.0397363\pi$
$24$	−0.227764	−	8.76865i	−0.0464922	−	1.78989i
$25$	−0.479912	+	4.97692i	−0.0959825	+	0.995383i
$26$	2.19554			0.430581
$27$	−4.80188	+	1.98544i	−0.924122	+	0.382099i
$28$	16.7994	−	12.2055i	3.17480	−	2.30662i
$29$	0.00441000	+	0.0419584i	0.000818917	+	0.00779148i	0.994924	−	0.100632i	$-0.0320864\pi$
$29$	0.00441000	+	0.0419584i	0.000818917	+	0.00779148i	−0.994105	+	0.108423i	$0.965420\pi$
$30$	3.61185	−	8.82151i	0.659431	−	1.61058i
$31$	−0.205934	+	1.95934i	−0.0369869	+	0.351907i	0.960340	+	0.278833i	$0.0899476\pi$
$31$	−0.205934	+	1.95934i	−0.0369869	+	0.351907i	−0.997327	+	0.0730740i	$0.976719\pi$
$32$	−0.287768	−	0.498429i	−0.0508707	−	0.0881106i
$33$	1.18000	+	2.47526i	0.205412	+	0.430888i
$34$	6.19366	+	6.87876i	1.06220	+	1.17970i
$35$	11.1829	−	2.42724i	1.89025	−	0.410278i
$36$	−7.66464	+	9.45688i	−1.27744	+	1.57615i
$37$	−1.43995	+	4.43171i	−0.236726	+	0.728569i	0.760161	+	0.649734i	$0.225120\pi$
$37$	−1.43995	+	4.43171i	−0.236726	+	0.728569i	−0.996888	+	0.0788345i	$0.974880\pi$
$38$	−7.51981	−	8.35159i	−1.21987	−	1.35481i
$39$	−1.17468	−	1.00370i	−0.188099	−	0.160720i
$40$	−1.23205	−	11.2569i	−0.194804	−	1.77987i
$41$	−0.748156	+	0.159025i	−0.116842	+	0.0248356i	−0.265962	−	0.963984i	$-0.585689\pi$
$41$	−0.748156	+	0.159025i	−0.116842	+	0.0248356i	0.149119	+	0.988819i	$0.452356\pi$
$42$	−21.7485	−	1.71626i	−3.35586	−	0.264824i
$43$	−4.11709	+	7.13101i	−0.627850	+	1.08747i	0.360132	+	0.932901i	$0.382732\pi$
$43$	−4.11709	+	7.13101i	−0.627850	+	1.08747i	−0.987982	+	0.154567i	$0.950602\pi$
$44$	5.19708	+	3.77590i	0.783489	+	0.569238i
$45$	−5.96521	+	3.06859i	−0.889242	+	0.457438i
$46$	−10.9129	+	7.92865i	−1.60901	+	1.16902i
$47$	−0.426471	−	4.05760i	−0.0622072	−	0.591862i	−0.980576	−	0.196137i	$-0.937160\pi$
$47$	−0.426471	−	4.05760i	−0.0622072	−	0.591862i	0.918369	−	0.395725i	$-0.129507\pi$
$48$	−1.37432	+	7.40644i	−0.198366	+	1.06903i
$49$	−9.59482	−	16.6187i	−1.37069	−	2.37410i
$50$	3.70214	−	11.7361i	0.523561	−	1.65973i
$51$	−0.169142	−	6.51178i	−0.0236847	−	0.911831i
$52$	−3.54052	−	0.752561i	−0.490982	−	0.104361i
$53$	−2.00012	+	1.45317i	−0.274737	+	0.199608i	−0.716619	−	0.697465i	$-0.754311\pi$
$53$	−2.00012	+	1.45317i	−0.274737	+	0.199608i	0.441882	+	0.897073i	$0.354311\pi$
$54$	12.5762	−	2.32263i	1.71141	−	0.316071i
$55$	1.78319	+	3.05818i	0.240446	+	0.412364i
$56$	−23.6763	+	10.5414i	−3.16388	+	1.40865i
$57$	0.205358	+	7.90603i	0.0272003	+	1.04718i
$58$	0.0108540	−	0.103269i	0.00142520	−	0.0135599i
$59$	−9.31606	+	1.98019i	−1.21285	+	0.257799i	−0.769557	−	0.638579i	$-0.779523\pi$
$59$	−9.31606	+	1.98019i	−1.21285	+	0.257799i	−0.443292	+	0.896377i	$0.646189\pi$
$60$	−8.84819	+	12.9875i	−1.14230	+	1.67668i
$61$	7.08784	+	1.50657i	0.907505	+	0.192896i	0.637940	−	0.770086i	$-0.279787\pi$
$61$	7.08784	+	1.50657i	0.907505	+	0.192896i	0.269565	+	0.962982i	$0.413120\pi$
$62$	1.49840	−	4.61160i	0.190297	−	0.585674i
$63$	10.8514	+	10.8606i	1.36715	+	1.36831i
$64$	−2.25016	−	6.92529i	−0.281270	−	0.865661i
$65$	−1.61876	−	1.16551i	−0.200782	−	0.144563i
$66$	−1.57414	−	6.56288i	−0.193764	−	0.807835i
$67$	−0.375946	+	3.57689i	−0.0459291	+	0.436986i	0.947259	+	0.320468i	$0.103840\pi$
$67$	−0.375946	+	3.57689i	−0.0459291	+	0.436986i	−0.993189	+	0.116519i	$0.962827\pi$
$68$	−7.63006	−	13.2156i	−0.925280	−	1.60263i
$69$	9.46329	+	0.746785i	1.13925	+	0.0899024i
$70$	−28.1642	+	0.120956i	−3.36626	+	0.0144570i
$71$	−1.57130	+	1.14162i	−0.186479	+	0.135485i	−0.677108	−	0.735884i	$-0.736767\pi$
$71$	−1.57130	+	1.14162i	−0.186479	+	0.135485i	0.490629	+	0.871369i	$0.336767\pi$
$72$	11.8111	−	9.55620i	1.39195	−	1.12621i
$73$	−4.42033	−	13.6044i	−0.517361	−	1.59227i	−0.778945	−	0.627093i	$-0.784245\pi$
$73$	−4.42033	−	13.6044i	−0.517361	−	1.59227i	0.261584	−	0.965181i	$-0.415755\pi$
$74$	5.73438	−	9.93224i	0.666608	−	1.15460i
$75$	−7.34591	+	4.58668i	−0.848233	+	0.529624i
$76$	9.26375	+	16.0453i	1.06262	+	1.84052i
$77$	5.42132	−	6.02098i	0.617816	−	0.686155i
$78$	2.31435	+	3.01744i	0.262049	+	0.341658i
$79$	−0.355789	−	3.38511i	−0.0400294	−	0.380855i	−0.996135	−	0.0878329i	$-0.972006\pi$
$79$	−0.355789	−	3.38511i	−0.0400294	−	0.380855i	0.956106	−	0.293022i	$-0.0946608\pi$
$80$	−0.974982	+	9.67589i	−0.109006	+	1.08180i
$81$	−7.79043	−	4.50657i	−0.865603	−	0.500731i
$82$	1.88252			0.207889
$83$	−3.54787	+	1.57961i	−0.389429	+	0.173385i	−0.592105	−	0.805861i	$-0.701703\pi$
$83$	−3.54787	+	1.57961i	−0.389429	+	0.173385i	0.202676	+	0.979246i	$0.435036\pi$
$84$	34.4832	+	10.2223i	3.76243	+	1.11534i
$85$	−0.914942	−	8.35958i	−0.0992394	−	0.906724i
$86$	13.5607	−	15.0607i	1.46229	−	1.62404i
$87$	−0.0530169	+	0.0502899i	−0.00568401	+	0.00539164i
$88$	−5.36486	−	5.95828i	−0.571896	−	0.635155i
$89$	−0.935601	−	2.87948i	−0.0991735	−	0.305225i	0.889145	−	0.457625i	$-0.151300\pi$
$89$	−0.935601	−	2.87948i	−0.0991735	−	0.305225i	−0.988319	+	0.152400i	$0.951300\pi$
$90$	15.9312	−	4.33494i	1.67929	−	0.456942i
$91$	−1.41071	+	4.34171i	−0.147882	+	0.455135i
$92$	20.3157	−	9.04514i	2.11806	−	0.943021i
$93$	−2.90989	+	1.78234i	−0.301742	+	0.184820i
$94$	−1.04964	+	9.98667i	−0.108262	+	1.03005i
$95$	1.11084	+	10.1495i	0.113970	+	1.04131i
$96$	0.381675	−	0.920896i	0.0389546	−	0.0939886i
$97$	0.544048	+	5.17627i	0.0552397	+	0.525571i	0.986795	+	0.161972i	$0.0517854\pi$
$97$	0.544048	+	5.17627i	0.0552397	+	0.525571i	−0.931556	+	0.363599i	$0.881548\pi$
$98$	14.5949	+	44.9184i	1.47431	+	4.53744i
$99$	−2.15803	+	4.23095i	−0.216890	+	0.425226i
$100$	−9.99279	+	17.6565i	−0.999279	+	1.76565i
$101$	7.78401	−	13.4823i	0.774538	−	1.34154i	−0.160516	−	0.987033i	$-0.551316\pi$
$101$	7.78401	−	13.4823i	0.774538	−	1.34154i	0.935054	−	0.354506i	$-0.115351\pi$
$102$	−2.92499	+	15.7633i	−0.289617	+	1.56080i
$103$	−14.5392	−	6.47329i	−1.43259	−	0.637832i	−0.463854	−	0.885912i	$-0.653534\pi$
$103$	−14.5392	−	6.47329i	−1.43259	−	0.637832i	−0.968740	+	0.248080i	$0.920200\pi$
$104$	4.12704	+	1.83748i	0.404690	+	0.180179i
$105$	15.1239	+	12.8106i	1.47594	+	1.25019i
$106$	5.55878	−	2.47493i	0.539916	−	0.240386i
$107$	2.75485			0.266322			0.133161	−	0.991094i	$-0.457487\pi$
$107$	2.75485			0.266322			0.133161	+	0.991094i	$0.457487\pi$
$108$	−21.0765	−	0.565254i	−2.02809	−	0.0543916i
$109$	3.89734	−	11.9948i	0.373297	−	1.14889i	−0.571323	−	0.820726i	$-0.693570\pi$
$109$	3.89734	−	11.9948i	0.373297	−	1.14889i	0.944620	−	0.328166i	$-0.106430\pi$
$110$	−2.72801	−	8.27487i	−0.260106	−	0.788978i
$111$	−7.60860	+	2.69254i	−0.722176	+	0.255565i
$112$	21.7705	−	4.62747i	2.05712	−	0.437254i
$113$	12.4858	−	2.65395i	1.17457	−	0.249662i	0.421018	−	0.907052i	$-0.361673\pi$
$113$	12.4858	−	2.65395i	1.17457	−	0.249662i	0.753550	+	0.657390i	$0.228340\pi$
$114$	3.55127	−	19.1384i	0.332607	−	1.79247i
$115$	12.2549	−	0.0526309i	1.14278	−	0.00490785i
$116$	−0.0529004	+	0.162811i	−0.00491168	+	0.0151166i
$117$	0.141187	−	2.67243i	0.0130527	−	0.247066i
$118$	23.4412			2.15794
$119$	−17.5825	+	7.82823i	−1.61178	+	0.717612i
$120$	14.1722	−	13.5593i	1.29374	−	1.23779i
$121$	−7.75925	−	3.45464i	−0.705386	−	0.314058i
$122$	−16.2926	−	7.25394i	−1.47506	−	0.656741i
$123$	−1.00720	−	0.860597i	−0.0908161	−	0.0775974i
$124$	−3.99702	+	6.92305i	−0.358943	+	0.621708i
$125$	−8.95967	+	6.68763i	−0.801377	+	0.598160i
$126$	−20.5667	−	31.6992i	−1.83222	−	2.82399i
$127$	−2.35801	−	7.25722i	−0.209240	−	0.643974i	−0.999513	−	0.0312188i	$-0.990061\pi$
$127$	−2.35801	−	7.25722i	−0.209240	−	0.643974i	0.790273	−	0.612755i	$-0.209939\pi$
$128$	1.99366	+	18.9684i	0.176217	+	1.67659i
$129$	−14.1404	+	1.85858i	−1.24499	+	0.163639i
$130$	3.30065	+	3.63424i	0.289486	+	0.318744i
$131$	−0.271722	+	2.58526i	−0.0237404	+	0.225875i	0.976218	+	0.216790i	$0.0695586\pi$
$131$	−0.271722	+	2.58526i	−0.0237404	+	0.225875i	−0.999959	+	0.00908528i	$0.997108\pi$
$132$	0.288914	+	11.1228i	0.0251467	+	0.968119i
$133$	21.3471	−	9.50435i	1.85103	−	0.824131i
$134$	2.73542	−	8.41877i	0.236305	−	0.727271i
$135$	−10.5053	−	4.96365i	−0.904156	−	0.427203i
$136$	5.88554	+	18.1138i	0.504681	+	1.55325i
$137$	3.75593	+	4.17139i	0.320891	+	0.356386i	0.881910	−	0.471417i	$-0.156257\pi$
$137$	3.75593	+	4.17139i	0.320891	+	0.356386i	−0.561019	+	0.827803i	$0.689591\pi$
$138$	−22.4002	−	6.64037i	−1.90683	−	0.565266i
$139$	−1.15390	+	1.28154i	−0.0978727	+	0.108699i	−0.790091	−	0.612989i	$-0.789967\pi$
$139$	−1.15390	+	1.28154i	−0.0978727	+	0.108699i	0.692218	+	0.721688i	$0.256633\pi$
$140$	45.4589	+	9.45872i	3.84198	+	0.799408i
$141$	5.12702	−	4.86330i	0.431773	−	0.409564i
$142$	4.36700	−	1.94432i	0.366471	−	0.163163i
$143$	−1.41227			−0.118100
$144$	−11.6277	+	5.91845i	−0.968978	+	0.493204i
$145$	−0.0628232	+	0.0703777i	−0.00521718	+	0.00584455i
$146$	3.68009	+	35.0137i	0.304567	+	2.89776i
$147$	12.7259	−	30.7047i	1.04961	−	2.53248i
$148$	−12.6517	+	14.0511i	−1.03996	+	1.15500i
$149$	−6.23532	−	10.7999i	−0.510817	−	0.884761i	−0.999921	−	0.0125357i	$-0.996010\pi$
$149$	−6.23532	−	10.7999i	−0.510817	−	0.884761i	0.489104	−	0.872225i	$-0.337324\pi$
$150$	20.0319	−	7.28313i	1.63560	−	0.594665i
$151$	−3.71371	+	6.43234i	−0.302218	+	0.523457i	−0.976638	−	0.214891i	$-0.931060\pi$
$151$	−3.71371	+	6.43234i	−0.302218	+	0.523457i	0.674420	+	0.738348i	$0.264394\pi$
$152$	−7.14571	−	21.9922i	−0.579594	−	1.78381i
$153$	8.77117	−	7.09663i	0.709107	−	0.573728i
$154$	−16.1325	+	11.7210i	−1.30000	+	0.944503i
$155$	−3.55284	+	2.60468i	−0.285371	+	0.209213i
$156$	−2.69783	−	5.65920i	−0.216000	−	0.453099i
$157$	4.70564	+	8.15040i	0.375551	+	0.650473i	0.990409	−	0.138164i	$-0.0441202\pi$
$157$	4.70564	+	8.15040i	0.375551	+	0.650473i	−0.614859	+	0.788637i	$0.710787\pi$
$158$	−0.875678	+	8.33152i	−0.0696652	+	0.662820i
$159$	−4.10552	−	1.21705i	−0.325589	−	0.0965185i
$160$	0.392426	−	1.22565i	0.0310240	−	0.0968960i
$161$	−8.66715	−	26.6748i	−0.683067	−	2.10227i
$162$	16.4489	+	14.8358i	1.29235	+	1.16561i
$163$	−0.969935	+	2.98515i	−0.0759712	+	0.233815i	−0.981829	−	0.189766i	$-0.939227\pi$
$163$	−0.969935	+	2.98515i	−0.0759712	+	0.233815i	0.905858	+	0.423581i	$0.139227\pi$
$164$	−3.03574	−	0.645266i	−0.237051	−	0.0503868i
$165$	−2.32331	+	5.67441i	−0.180870	+	0.441752i
$166$	9.34960	−	1.98732i	0.725669	−	0.154246i
$167$	−0.299893	+	2.85329i	−0.0232064	+	0.220794i	0.976772	+	0.214279i	$0.0687403\pi$
$167$	−0.299893	+	2.85329i	−0.0232064	+	0.220794i	−0.999979	+	0.00651456i	$0.997926\pi$
$168$	−39.4451	−	21.4277i	−3.04325	−	1.65318i
$169$	−11.1491	+	4.96391i	−0.857625	+	0.381839i
$170$	−2.07507	+	20.5934i	−0.159151	+	1.57944i
$171$	−10.6492	+	8.61611i	−0.814364	+	0.658890i
$172$	−27.0303	+	19.6386i	−2.06104	+	1.49743i
$173$	−15.5462	−	3.30444i	−1.18195	−	0.251232i	−0.425303	−	0.905051i	$-0.639832\pi$
$173$	−15.5462	−	3.30444i	−1.18195	−	0.251232i	−0.756651	+	0.653819i	$0.773166\pi$
$174$	0.153369	−	0.0939403i	0.0116269	−	0.00712160i
$175$	20.8295	+	14.8618i	1.57456	+	1.12345i
$176$	3.44270	+	5.96292i	0.259503	+	0.449472i
$177$	−12.5417	−	10.7162i	−0.942691	−	0.805478i
$178$	0.778923	+	7.41096i	0.0583827	+	0.555475i
$179$	14.4077	−	10.4678i	1.07688	−	0.782399i	0.0997433	−	0.995013i	$-0.468198\pi$
$179$	14.4077	−	10.4678i	1.07688	−	0.782399i	0.977136	+	0.212614i	$0.0681978\pi$
$180$	−27.1764	+	1.52981i	−2.02561	+	0.114026i
$181$	14.8249	+	10.7709i	1.10192	+	0.800594i	0.981373	−	0.192114i	$-0.0615342\pi$
$181$	14.8249	+	10.7709i	1.10192	+	0.800594i	0.120550	+	0.992707i	$0.461534\pi$
$182$	5.61793	−	9.73054i	0.416429	−	0.721275i
$183$	5.40085	+	11.3293i	0.399242	+	0.837484i
$184$	−27.1489	+	5.77068i	−2.00144	+	0.425420i
$185$	−9.50047	+	4.27886i	−0.698488	+	0.314588i
$186$	7.91745	−	2.80184i	0.580536	−	0.205441i
$187$	−3.98405	−	4.42474i	−0.291343	−	0.323569i
$188$	5.11576	−	15.7447i	0.373105	−	1.14830i
$189$	−3.48760	+	26.3620i	−0.253686	+	1.91756i
$190$	2.51937	−	25.0027i	0.182775	−	1.81389i
$191$	7.36816	+	8.18317i	0.533141	+	0.592114i	0.948197	−	0.317682i	$-0.102905\pi$
$191$	7.36816	+	8.18317i	0.533141	+	0.592114i	−0.415056	+	0.909796i	$0.636238\pi$
$192$	7.14584	−	10.3926i	0.515707	−	0.750019i
$193$	−3.22947	−	5.59361i	−0.232463	−	0.402637i	0.726070	−	0.687621i	$-0.241345\pi$
$193$	−3.22947	−	5.59361i	−0.232463	−	0.402637i	−0.958532	+	0.284984i	$0.908012\pi$
$194$	1.33902	−	12.7400i	0.0961364	−	0.914676i
$195$	−0.104542	−	3.45332i	−0.00748641	−	0.247297i
$196$	−8.13905	−	77.4379i	−0.581361	−	5.53128i
$197$	−20.4081	+	14.8274i	−1.45402	+	1.05641i	−0.469145	+	0.883121i	$0.655438\pi$
$197$	−20.4081	+	14.8274i	−1.45402	+	1.05641i	−0.984872	+	0.173284i	$0.944562\pi$
$198$	7.36037	−	9.08147i	0.523079	−	0.645392i
$199$	2.48202			0.175946			0.0879729	−	0.996123i	$-0.471961\pi$
$199$	2.48202			0.175946			0.0879729	+	0.996123i	$0.471961\pi$
$200$	16.7811	−	18.9623i	1.18660	−	1.34084i
$201$	−5.31219	+	3.25377i	−0.374693	+	0.229503i
$202$	−25.6387	+	28.4746i	−1.80393	+	2.00347i
$203$	0.197242	+	0.0878178i	0.0138437	+	0.00616360i
$204$	10.1200	−	24.4172i	0.708539	−	1.70955i
$205$	−1.38797	−	0.999338i	−0.0969399	−	0.0697968i
$206$	31.6899	+	23.0240i	2.20794	+	1.60416i
$207$	8.94905	+	13.7931i	0.622002	+	0.958685i
$208$	−3.13868	−	2.28039i	−0.217628	−	0.158116i
$209$	4.83709	+	5.37213i	0.334589	+	0.371598i
$210$	−29.8545	−	38.5800i	−2.06016	−	2.66227i
$211$	−4.61440	+	5.12481i	−0.317669	+	0.352807i	−0.880739	−	0.473602i	$-0.842953\pi$
$211$	−4.61440	+	5.12481i	−0.317669	+	0.352807i	0.563070	+	0.826409i	$0.309620\pi$
$212$	−9.81238	+	2.08569i	−0.673917	+	0.143246i
$213$	−3.22532	−	0.956123i	−0.220995	−	0.0655124i
$214$	−6.63215	−	1.40971i	−0.453365	−	0.0963656i
$215$	−17.9932	+	3.90542i	−1.22713	+	0.266347i
$216$	25.5839	+	6.15927i	1.74076	+	0.419085i
$217$	8.15674	+	5.92622i	0.553716	+	0.402298i
$218$	−15.5206	+	26.8824i	−1.05118	+	1.82071i
$219$	14.0377	−	20.4157i	0.948577	−	1.37956i
$220$	1.56282	+	14.2791i	0.105366	+	0.962697i
$221$	3.06482	+	1.36455i	0.206162	+	0.0917894i
$222$	19.6951	−	2.58868i	1.32185	−	0.173741i
$223$	12.9012	+	2.74223i	0.863927	+	0.183633i	0.618503	−	0.785782i	$-0.287739\pi$
$223$	12.9012	+	2.74223i	0.863927	+	0.183633i	0.245424	+	0.969416i	$0.421073\pi$
$224$	−2.94535			−0.196795
$225$	−14.0471	−	5.26097i	−0.936476	−	0.350731i
$226$	−31.4170			−2.08983
$227$	17.1480	+	3.64491i	1.13815	+	0.241921i	0.738178	−	0.674606i	$-0.235686\pi$
$227$	17.1480	+	3.64491i	1.13815	+	0.241921i	0.399973	+	0.916527i	$0.369020\pi$
$228$	−12.2868	+	29.6452i	−0.813712	+	1.96330i
$229$	14.8442	+	6.60908i	0.980935	+	0.436740i	0.833613	−	0.552348i	$-0.186268\pi$
$229$	14.8442	+	6.60908i	0.980935	+	0.436740i	0.147321	+	0.989089i	$0.452935\pi$
$230$	−29.5299	−	6.14435i	−1.94715	−	0.405146i
$231$	13.9896	+	1.10398i	0.920450	+	0.0726364i
$232$	0.106830	−	0.185035i	0.00701373	−	0.0121481i
$233$	−15.4281	−	11.2092i	−1.01073	−	0.734339i	−0.0463684	−	0.998924i	$-0.514765\pi$
$233$	−15.4281	−	11.2092i	−1.01073	−	0.734339i	−0.964362	+	0.264586i	$0.914765\pi$
$234$	−1.70743	+	6.36147i	−0.111618	+	0.415862i
$235$	6.07534	−	6.80590i	0.396311	−	0.443968i
$236$	−37.8011	−	8.03488i	−2.46064	−	0.523026i
$237$	4.27728	−	4.05728i	0.277839	−	0.263548i
$238$	46.3346	−	9.84873i	3.00343	−	0.638398i
$239$	−4.66262	+	5.17837i	−0.301600	+	0.334961i	−0.874827	−	0.484436i	$-0.839025\pi$
$239$	−4.66262	+	5.17837i	−0.301600	+	0.334961i	0.573227	+	0.819397i	$0.305691\pi$
$240$	−14.3258	+	8.85954i	−0.924727	+	0.571881i
$241$	−2.02990	−	2.25444i	−0.130758	−	0.145221i	0.674210	−	0.738539i	$-0.264484\pi$
$241$	−2.02990	−	2.25444i	−0.130758	−	0.145221i	−0.804968	+	0.593318i	$0.797817\pi$
$242$	16.9121	+	12.2874i	1.08715	+	0.789863i
$243$	−2.01840	−	15.4572i	−0.129480	−	0.991582i
$244$	23.7870	+	17.2823i	1.52281	+	1.10638i
$245$	13.0843	−	40.8658i	0.835927	−	2.61082i
$246$	1.98439	+	2.58724i	0.126520	+	0.164956i
$247$	−3.72104	−	1.65671i	−0.236764	−	0.105414i
$248$	6.67612	−	7.41458i	0.423934	−	0.470826i
$249$	−5.91080	−	3.21092i	−0.374582	−	0.203484i
$250$	24.9921	−	11.5153i	1.58064	−	0.728288i
$251$	14.6208			0.922854			0.461427	−	0.887178i	$-0.347338\pi$
$251$	14.6208			0.922854			0.461427	+	0.887178i	$0.347338\pi$
$252$	22.3003	+	58.1675i	1.40478	+	3.66421i
$253$	7.01966	−	5.10008i	0.441322	−	0.320639i
$254$	1.96313	+	18.6780i	0.123178	+	1.17196i
$255$	10.5245	−	10.0694i	0.659072	−	0.630571i
$256$	3.38457	−	32.2020i	0.211536	−	2.01263i
$257$	8.94002	+	15.4846i	0.557663	+	0.965900i	0.997691	+	0.0679164i	$0.0216351\pi$
$257$	8.94002	+	15.4846i	0.557663	+	0.965900i	−0.440028	+	0.897984i	$0.645032\pi$
$258$	34.9932	+	2.76145i	2.17858	+	0.171921i
$259$	15.9566	+	17.7216i	0.991496	+	1.10117i
$260$	−4.07692	−	6.99191i	−0.252840	−	0.433620i
$261$	−0.125002	−	0.0198524i	−0.00773742	−	0.00122883i
$262$	1.97708	−	6.08482i	0.122144	−	0.375921i
$263$	8.20941	+	9.11748i	0.506214	+	0.562208i	0.941035	−	0.338309i	$-0.109855\pi$
$263$	8.20941	+	9.11748i	0.506214	+	0.562208i	−0.434821	+	0.900517i	$0.643188\pi$
$264$	2.53358	−	13.6539i	0.155931	−	0.840341i
$265$	−5.41227	−	1.12614i	−0.332473	−	0.0691783i
$266$	−56.2555	+	11.9575i	−3.44924	+	0.733160i
$267$	2.97119	−	4.32115i	0.181834	−	0.264450i
$268$	−7.29682	+	12.6385i	−0.445724	+	0.772017i
$269$	−18.8007	−	13.6595i	−1.14630	−	0.832835i	−0.158314	−	0.987389i	$-0.550606\pi$
$269$	−18.8007	−	13.6595i	−1.14630	−	0.832835i	−0.987984	+	0.154554i	$0.950606\pi$
$270$	22.7510	+	17.3255i	1.38458	+	1.05439i
$271$	22.0116	−	15.9923i	1.33711	−	0.971466i	0.337563	−	0.941303i	$-0.390397\pi$
$271$	22.0116	−	15.9923i	1.33711	−	0.971466i	0.999545	−	0.0301632i	$-0.00960270\pi$
$272$	−1.70970	−	16.2667i	−0.103666	−	0.986313i
$273$	−7.45409	+	2.63786i	−0.451142	+	0.159651i
$274$	−6.90762	−	11.9643i	−0.417305	−	0.722793i
$275$	−2.38139	+	7.54918i	−0.143603	+	0.455233i
$276$	33.8463	+	18.3863i	2.03731	+	1.10672i
$277$	−17.2246	−	3.66120i	−1.03493	−	0.219980i	−0.341028	−	0.940053i	$-0.610775\pi$
$277$	−17.2246	−	3.66120i	−1.03493	−	0.219980i	−0.693898	+	0.720073i	$0.744108\pi$
$278$	3.43374	−	2.49476i	0.205942	−	0.149626i
$279$	−5.51692	−	2.12042i	−0.330290	−	0.126946i
$280$	−53.0425	−	23.3436i	−3.16990	−	1.39505i
$281$	13.1803	−	5.86826i	0.786272	−	0.350071i	0.0259884	−	0.999662i	$-0.491727\pi$
$281$	13.1803	−	5.86826i	0.786272	−	0.350071i	0.760283	+	0.649591i	$0.225060\pi$
$282$	−14.8316	+	9.08453i	−0.883211	+	0.540976i
$283$	1.29863	−	12.3556i	0.0771954	−	0.734465i	−0.885639	−	0.464374i	$-0.846279\pi$
$283$	1.29863	−	12.3556i	0.0771954	−	0.734465i	0.962835	−	0.270091i	$-0.0870539\pi$
$284$	−7.70866	+	1.63853i	−0.457425	+	0.0972286i
$285$	−12.7780	+	12.2254i	−0.756902	+	0.724171i
$286$	3.39997	+	0.722686i	0.201044	+	0.0427333i
$287$	−1.20958	+	3.72271i	−0.0713993	+	0.219744i
$288$	1.66796	−	0.446176i	0.0982858	−	0.0262912i
$289$	−0.882569	−	2.71627i	−0.0519158	−	0.159781i
$290$	0.187257	−	0.137282i	0.0109961	−	0.00806151i
$291$	−6.54052	+	6.20410i	−0.383412	+	0.363691i
$292$	6.06708	−	57.7244i	0.355049	−	3.37807i
$293$	11.2824	+	19.5417i	0.659125	+	1.14164i	0.980843	+	0.194802i	$0.0624064\pi$
$293$	11.2824	+	19.5417i	0.659125	+	1.14164i	−0.321718	+	0.946836i	$0.604260\pi$
$294$	−46.3490	+	67.4077i	−2.70313	+	3.93130i
$295$	−17.2830	−	12.4438i	−1.00626	−	0.724506i
$296$	19.0916	−	13.8708i	1.10967	−	0.806226i
$297$	−8.08962	+	1.49403i	−0.469407	+	0.0866923i
$298$	9.48467	+	29.1908i	0.549432	+	1.69098i
$299$	−2.44450	+	4.23399i	−0.141369	+	0.244858i
$300$	−34.7998	+	4.87844i	−2.00917	+	0.281657i
$301$	21.0695	+	36.4935i	1.21443	+	2.10345i
$302$	12.2321	−	13.5851i	0.703878	−	0.781735i
$303$	26.7347	−	3.51395i	1.53587	−	0.201871i
$304$	2.07577	+	19.7496i	0.119053	+	1.13272i
$305$	8.16167	+	13.9973i	0.467336	+	0.801480i
$306$	−24.7475	+	12.5964i	−1.41472	+	0.720086i
$307$	−27.5455			−1.57211			−0.786054	−	0.618158i	$-0.787879\pi$
$307$	−27.5455			−1.57211			−0.786054	+	0.618158i	$0.787879\pi$
$308$	30.0328	−	13.3715i	1.71128	−	0.761911i
$309$	−6.42948	−	26.8056i	−0.365760	−	1.52492i
$310$	9.88612	−	4.45255i	0.561494	−	0.252888i
$311$	0.339314	−	0.376846i	0.0192407	−	0.0213690i	−0.733448	−	0.679746i	$-0.762090\pi$
$311$	0.339314	−	0.376846i	0.0192407	−	0.0213690i	0.752688	+	0.658377i	$0.228757\pi$
$312$	1.82504	+	7.60892i	0.103323	+	0.430770i
$313$	−8.84725	−	9.82587i	−0.500076	−	0.555391i	0.439273	−	0.898354i	$-0.355236\pi$
$313$	−8.84725	−	9.82587i	−0.500076	−	0.555391i	−0.939349	+	0.342963i	$0.888570\pi$
$314$	−7.15784	−	22.0296i	−0.403941	−	1.24320i
$315$	−1.66390	+	34.2894i	−0.0937501	+	1.93199i
$316$	4.26789	−	13.1352i	0.240088	−	0.738914i
$317$	−9.58348	+	4.26684i	−0.538262	+	0.239650i	−0.657817	−	0.753178i	$-0.728520\pi$
$317$	−9.58348	+	4.26684i	−0.538262	+	0.239650i	0.119555	+	0.992828i	$0.461853\pi$
$318$	9.26101	+	5.03085i	0.519332	+	0.282116i
$319$	−0.00698181	+	0.0664275i	−0.000390906	+	0.00371923i
$320$	8.08053	−	14.1357i	0.451715	−	0.790212i
$321$	2.90394	+	3.78614i	0.162082	+	0.211322i
$322$	7.21573	+	68.6530i	0.402117	+	3.82588i
$323$	−5.30655	−	16.3319i	−0.295264	−	0.908730i
$324$	−21.4402	−	29.5623i	−1.19112	−	1.64235i
$325$	−0.504307	−	4.43166i	−0.0279739	−	0.245824i
$326$	3.86262	−	6.69025i	0.213931	−	0.370539i
$327$	20.5933	−	7.28757i	1.13881	−	0.403004i
$328$	3.53864	+	1.57550i	0.195389	+	0.0869927i
$329$	−19.0744	−	8.49245i	−1.05160	−	0.468204i
$330$	8.49694	−	12.4719i	0.467741	−	0.686557i
$331$	−2.23440	+	0.994818i	−0.122814	+	0.0546801i	−0.467224	−	0.884139i	$-0.654746\pi$
$331$	−2.23440	+	0.994818i	−0.122814	+	0.0546801i	0.344410	+	0.938819i	$0.388079\pi$
$332$	−15.7583			−0.864850
$333$	−11.7208	−	7.61863i	−0.642298	−	0.417499i
$334$	2.18205	−	6.71566i	0.119397	−	0.367465i
$335$	−6.48593	+	4.75500i	−0.354364	+	0.259793i
$336$	29.3084	+	25.0424i	1.59890	+	1.36618i
$337$	−1.79424	+	0.381377i	−0.0977383	+	0.0207749i	−0.256521	−	0.966539i	$-0.582576\pi$
$337$	−1.79424	+	0.381377i	−0.0977383	+	0.0207749i	0.158783	+	0.987314i	$0.449243\pi$
$338$	29.3810	−	6.24513i	1.59812	−	0.339690i
$339$	16.8090	+	14.3623i	0.912938	+	0.780055i
$340$	10.4050	−	32.4976i	0.564291	−	1.76243i
$341$	−0.963842	+	2.96640i	−0.0521950	+	0.160640i
$342$	30.0463	−	15.2934i	1.62472	−	0.826972i
$343$	−62.3814			−3.36828
$344$	38.0951	−	16.9610i	2.05395	−	0.914477i
$345$	12.9904	+	16.7871i	0.699382	+	0.903786i
$346$	35.7356	+	15.9105i	1.92116	+	0.855354i
$347$	−0.272573	−	0.121357i	−0.0146325	−	0.00651481i	0.399407	−	0.916774i	$-0.369216\pi$
$347$	−0.272573	−	0.121357i	−0.0146325	−	0.00651481i	−0.414040	+	0.910259i	$0.635883\pi$
$348$	−0.279522	+	0.0989177i	−0.0149840	+	0.00530255i
$349$	−8.44783	+	14.6321i	−0.452202	+	0.783237i	−0.998523	−	0.0543395i	$-0.982695\pi$
$349$	−8.44783	+	14.6321i	−0.452202	+	0.783237i	0.546321	+	0.837576i	$0.316028\pi$
$350$	−42.5407	−	46.4378i	−2.27389	−	2.48220i
$351$	3.82168	−	2.62301i	0.203986	−	0.140006i
$352$	−0.281569	−	0.866579i	−0.0150077	−	0.0461888i
$353$	−0.760861	−	7.23910i	−0.0404965	−	0.385299i	−0.995933	−	0.0901008i	$-0.971281\pi$
$353$	−0.760861	−	7.23910i	−0.0404965	−	0.385299i	0.955436	−	0.295198i	$-0.0953856\pi$
$354$	24.7097	+	32.2164i	1.31331	+	1.71228i
$355$	−4.25191	−	0.884702i	−0.225668	−	0.0469551i
$356$	1.28415	−	12.2179i	0.0680598	−	0.647545i
$357$	−29.2927	−	15.9126i	−1.55033	−	0.842186i
$358$	−40.0422	+	17.8279i	−2.11629	+	0.942235i
$359$	−8.36007	+	25.7297i	−0.441228	+	1.35796i	0.445340	+	0.895361i	$0.353083\pi$
$359$	−8.36007	+	25.7297i	−0.441228	+	1.35796i	−0.886568	+	0.462598i	$0.846917\pi$
$360$	33.5744	+	5.18445i	1.76952	+	0.273245i
$361$	0.571423	+	1.75866i	0.0300749	+	0.0925610i
$362$	−30.1783	−	33.5164i	−1.58614	−	1.76158i
$363$	−3.43126	−	14.3055i	−0.180094	−	0.750845i
$364$	−12.3948	+	13.7658i	−0.649662	+	0.721523i
$365$	15.8738	−	27.7690i	0.830873	−	1.45349i
$366$	−7.20485	−	30.0383i	−0.376603	−	1.57013i
$367$	7.03463	−	3.13202i	0.367205	−	0.163490i	−0.214835	−	0.976650i	$-0.568921\pi$
$367$	7.03463	−	3.13202i	0.367205	−	0.163490i	0.582040	+	0.813160i	$0.302255\pi$
$368$	23.8358			1.24252
$369$	0.121057	−	2.29141i	0.00630199	−	0.119286i
$370$	25.0614	−	5.43956i	1.30288	−	0.282789i
$371$	1.32250	+	12.5828i	0.0686610	+	0.653265i
$372$	−13.7280	+	1.80438i	−0.711765	+	0.0935529i
$373$	−15.6677	+	17.4007i	−0.811241	+	0.900974i	−0.996658	−	0.0816856i	$-0.973970\pi$
$373$	−15.6677	+	17.4007i	−0.811241	+	0.900974i	0.185417	+	0.982660i	$0.440636\pi$
$374$	7.32716	+	12.6910i	0.378879	+	0.656237i
$375$	−18.6357	−	5.26419i	−0.962342	−	0.271842i
$376$	−10.3310	+	17.8939i	−0.532782	+	0.922806i
$377$	−0.0116299	−	0.0357932i	−0.000598972	−	0.00184345i
$378$	21.8861	−	61.6804i	1.12570	−	3.17250i
$379$	−5.93052	+	4.30878i	−0.304630	+	0.221327i	−0.729589	−	0.683886i	$-0.760289\pi$
$379$	−5.93052	+	4.30878i	−0.304630	+	0.221327i	0.424959	+	0.905213i	$0.360289\pi$
$380$	−12.6329	+	39.4557i	−0.648052	+	2.02403i
$381$	7.48835	−	10.8907i	0.383640	−	0.557947i
$382$	−13.5509	−	23.4709i	−0.693327	−	1.20088i
$383$	−1.83428	+	17.4521i	−0.0937276	+	0.891758i	0.842105	+	0.539314i	$0.181316\pi$
$383$	−1.83428	+	17.4521i	−0.0937276	+	0.891758i	−0.935833	+	0.352445i	$0.885350\pi$
$384$	−23.9677	+	22.7349i	−1.22310	+	1.16019i
$385$	18.1165	−	0.0778046i	0.923303	−	0.00396529i
$386$	4.91242	+	15.1189i	0.250035	+	0.769530i
$387$	−17.4600	−	17.4747i	−0.887540	−	0.888289i
$388$	−6.52616	+	20.0854i	−0.331315	+	1.01968i
$389$	−0.325778	−	0.0692462i	−0.0165176	−	0.00351092i	0.199645	−	0.979868i	$-0.436021\pi$
$389$	−0.325778	−	0.0692462i	−0.0165176	−	0.00351092i	−0.216163	+	0.976357i	$0.569354\pi$
$390$	−1.51545	+	8.36716i	−0.0767376	+	0.423688i
$391$	−20.1613	+	4.28542i	−1.01960	+	0.216723i
$392$	−10.1583	+	96.6495i	−0.513070	+	4.88154i
$393$	−3.83948	+	2.35172i	−0.193676	+	0.118629i
$394$	56.7187	−	25.2528i	2.85745	−	1.27222i
$395$	5.06843	−	5.67792i	0.255021	−	0.285687i
$396$	−14.9821	+	12.1218i	−0.752881	+	0.609145i
$397$	19.6674	−	14.2892i	0.987079	−	0.717155i	0.0277993	−	0.999614i	$-0.491150\pi$
$397$	19.6674	−	14.2892i	0.987079	−	0.717155i	0.959279	+	0.282459i	$0.0911501\pi$
$398$	−5.97532	−	1.27009i	−0.299516	−	0.0636640i
$399$	35.5646	+	19.3197i	1.78046	+	0.967197i
$400$	−17.4821	+	12.9323i	−0.874103	+	0.646616i
$401$	−10.6053	−	18.3689i	−0.529604	−	0.917301i	−0.999404	−	0.0345279i	$-0.989007\pi$
$401$	−10.6053	−	18.3689i	−0.529604	−	0.917301i	0.469800	−	0.882773i	$-0.344326\pi$
$402$	14.4538	−	5.11493i	0.720890	−	0.255109i
$403$	−0.183704	−	1.74783i	−0.00915096	−	0.0870655i
$404$	51.1050	−	37.1300i	2.54257	−	1.84729i
$405$	−4.25205	−	19.6703i	−0.211286	−	0.977424i
$406$	−0.429911	−	0.312348i	−0.0213361	−	0.0155016i
$407$	−3.68862	+	6.38888i	−0.182838	+	0.316685i
$408$	−18.6907	+	27.1829i	−0.925328	+	1.34575i
$409$	15.8046	−	3.35938i	0.781489	−	0.166111i	0.200143	−	0.979767i	$-0.435859\pi$
$409$	15.8046	−	3.35938i	0.781489	−	0.166111i	0.581347	+	0.813656i	$0.302526\pi$
$410$	2.83007	+	3.11610i	0.139767	+	0.153893i
$411$	−1.77376	+	9.55910i	−0.0874931	+	0.471515i
$412$	−43.2110	−	47.9907i	−2.12886	−	2.36433i
$413$	−15.0617	+	46.3553i	−0.741140	+	2.28099i
$414$	−14.4862	−	37.7854i	−0.711956	−	1.85705i
$415$	−7.94837	−	3.49802i	−0.390170	−	0.171711i
$416$	0.343537	+	0.381537i	0.0168433	+	0.0187064i
$417$	−2.97763	−	0.234976i	−0.145815	−	0.0115068i
$418$	−8.89600	−	15.4083i	−0.435118	−	0.753646i
$419$	−1.47939	+	14.0755i	−0.0722731	+	0.687633i	0.897064	+	0.441900i	$0.145695\pi$
$419$	−1.47939	+	14.0755i	−0.0722731	+	0.687633i	−0.969338	+	0.245733i	$0.920971\pi$
$420$	34.9193	+	72.4470i	1.70389	+	3.53505i
$421$	2.61246	+	24.8559i	0.127324	+	1.21140i	0.852458	+	0.522796i	$0.175111\pi$
$421$	2.61246	+	24.8559i	0.127324	+	1.21140i	−0.725134	+	0.688607i	$0.758222\pi$
$422$	13.7314	−	9.97642i	0.668432	−	0.485644i
$423$	12.0884	+	1.91984i	0.587756	+	0.0933456i
$424$	12.5203			0.608042
$425$	12.4620	−	14.0818i	0.604495	−	0.683068i
$426$	7.27550	+	3.95226i	0.352499	+	0.191488i
$427$	24.8133	−	27.5580i	1.20080	−	1.33362i
$428$	10.2118	+	4.54658i	0.493605	+	0.219767i
$429$	−1.48870	−	1.94096i	−0.0718752	−	0.0937105i
$430$	45.3161	−	0.194618i	2.18534	−	0.00938531i
$431$	4.09020	+	2.97170i	0.197018	+	0.143142i	0.681921	−	0.731426i	$-0.261145\pi$
$431$	4.09020	+	2.97170i	0.197018	+	0.143142i	−0.484903	+	0.874568i	$0.661145\pi$
$432$	−20.3910	−	9.74185i	−0.981062	−	0.468705i
$433$	16.2872	+	11.8334i	0.782715	+	0.568676i	0.905793	−	0.423721i	$-0.139276\pi$
$433$	16.2872	+	11.8334i	0.782715	+	0.568676i	−0.123078	+	0.992397i	$0.539276\pi$
$434$	−16.6043	−	18.4410i	−0.797033	−	0.885195i
$435$	−0.162947	−	0.0121548i	−0.00781269	−	0.000582780i
$436$	34.2428	−	38.0305i	1.63993	−	1.82133i
$437$	24.4781	−	5.20299i	1.17095	−	0.248893i
$438$	−44.2419	+	41.9663i	−2.11396	+	2.00523i
$439$	38.8328	+	8.25417i	1.85339	+	0.393950i	0.993239	−	0.116090i	$-0.0370360\pi$
$439$	38.8328	+	8.25417i	1.85339	+	0.393950i	0.860151	+	0.510040i	$0.170369\pi$
$440$	1.79740	−	17.8377i	0.0856877	−	0.850380i
$441$	55.6136	−	14.8765i	2.64827	−	0.708403i
$442$	−6.68012	−	4.85339i	−0.317741	−	0.230852i
$443$	14.2137	−	24.6188i	0.675313	−	1.16968i	−0.301065	−	0.953604i	$-0.597342\pi$
$443$	14.2137	−	24.6188i	0.675313	−	1.16968i	0.976377	−	0.216072i	$-0.0693246\pi$
$444$	−32.6475	−	2.57634i	−1.54938	−	0.122268i
$445$	3.35983	−	5.87754i	0.159271	−	0.278622i
$446$	−29.6556	−	13.2035i	−1.40423	−	0.625205i
$447$	8.27008	−	19.9538i	0.391161	−	0.943784i
$448$	−36.4503	−	7.74774i	−1.72211	−	0.366046i
$449$	−32.9656			−1.55574			−0.777871	−	0.628424i	$-0.783700\pi$
$449$	−32.9656			−1.55574			−0.777871	+	0.628424i	$0.783700\pi$
$450$	31.1255	+	19.8536i	1.46727	+	0.935910i
$451$	−1.21092			−0.0570202
$452$	50.6629	+	10.7687i	2.38298	+	0.506518i
$453$	−12.7550	+	1.67649i	−0.599281	+	0.0787683i
$454$	−39.4176	−	17.5498i	−1.84996	−	0.823655i
$455$	−9.30754	+	4.19197i	−0.436344	+	0.196523i
$456$	22.6926	−	33.0031i	1.06268	−	1.54551i
$457$	14.1520	−	24.5120i	0.662004	−	1.14663i	−0.318084	−	0.948063i	$-0.603039\pi$
$457$	14.1520	−	24.5120i	0.662004	−	1.14663i	0.980088	−	0.198563i	$-0.0636273\pi$
$458$	−32.3547	−	23.5070i	−1.51183	−	1.09841i
$459$	18.9991	+	4.57399i	0.886801	+	0.213496i
$460$	45.5137	+	20.0303i	2.12209	+	0.933916i
$461$	−16.2616	−	3.45651i	−0.757378	−	0.160986i	−0.186991	−	0.982362i	$-0.559874\pi$
$461$	−16.2616	−	3.45651i	−0.757378	−	0.160986i	−0.570387	+	0.821376i	$0.693207\pi$
$462$	−33.1143	−	9.81650i	−1.54062	−	0.456705i
$463$	−10.6551	+	2.26481i	−0.495185	+	0.105255i	−0.448733	−	0.893666i	$-0.648125\pi$
$463$	−10.6551	+	2.26481i	−0.495185	+	0.105255i	−0.0464518	+	0.998921i	$0.514791\pi$
$464$	−0.122776	+	0.136357i	−0.00569975	+	0.00633022i
$465$	−7.32484	−	2.13722i	−0.339681	−	0.0991112i
$466$	31.4064	+	34.8803i	1.45487	+	1.61580i
$467$	19.9438	+	14.4900i	0.922888	+	0.670517i	0.944241	−	0.329255i	$-0.106797\pi$
$467$	19.9438	+	14.4900i	0.922888	+	0.670517i	−0.0213532	+	0.999772i	$0.506797\pi$
$468$	4.93390	−	9.67322i	0.228069	−	0.447145i
$469$	14.8906	+	10.8187i	0.687586	+	0.499560i
$470$	−18.1087	+	13.2760i	−0.835293	+	0.612374i
$471$	−6.24123	+	15.0587i	−0.287580	+	0.693867i
$472$	44.0633	+	19.6182i	2.02818	+	0.903003i
$473$	−8.72289	+	9.68775i	−0.401079	+	0.445443i
$474$	−12.3735	+	7.57890i	−0.568333	+	0.348110i
$475$	−15.1303	+	17.0969i	−0.694224	+	0.784460i
$476$	−78.0949			−3.57947
$477$	−2.65504	−	6.92534i	−0.121566	−	0.317089i
$478$	13.8749	−	10.0807i	0.634621	−	0.461079i
$479$	4.05028	+	38.5358i	0.185062	+	1.76075i	0.555150	+	0.831750i	$0.312661\pi$
$479$	4.05028	+	38.5358i	0.185062	+	1.76075i	−0.370089	+	0.928996i	$0.620673\pi$
$480$	2.09813	−	0.752644i	0.0957662	−	0.0343533i
$481$	0.434500	−	4.13399i	0.0198115	−	0.188494i
$482$	3.73324	+	6.46616i	0.170044	+	0.294526i
$483$	27.5243	−	40.0300i	1.25240	−	1.82143i
$484$	−23.0607	−	25.6115i	−1.04821	−	1.16416i
$485$	−7.75029	+	8.68227i	−0.351923	+	0.394242i
$486$	−3.05055	+	38.2452i	−0.138376	+	1.73484i
$487$	−0.280386	+	0.862940i	−0.0127055	+	0.0391036i	−0.957208	−	0.289400i	$-0.906544\pi$
$487$	−0.280386	+	0.862940i	−0.0127055	+	0.0391036i	0.944503	+	0.328503i	$0.106544\pi$
$488$	−24.5549	−	27.2710i	−1.11155	−	1.23450i
$489$	−5.12507	+	1.81367i	−0.231764	+	0.0820168i
$490$	−52.4115	+	91.6865i	−2.36771	+	4.14197i
$491$	−4.57995	+	0.973499i	−0.206690	+	0.0439334i	−0.310093	−	0.950706i	$-0.600360\pi$
$491$	−4.57995	+	0.973499i	−0.206690	+	0.0439334i	0.103403	+	0.994640i	$0.467027\pi$
$492$	−2.31320	−	4.85236i	−0.104287	−	0.218761i
$493$	0.0793341	−	0.137411i	0.00357303	−	0.00618866i
$494$	8.11042	+	5.89257i	0.364905	+	0.265119i
$495$	−10.2477	+	2.78843i	−0.460598	+	0.125331i
$496$	−6.93189	+	5.03631i	−0.311251	+	0.226137i
$497$	1.03897	+	9.88510i	0.0466040	+	0.443407i
$498$	12.5868	+	10.7548i	0.564029	+	0.481932i
$499$	7.00291	+	12.1294i	0.313493	+	0.542986i	0.979116	−	0.203302i	$-0.0651673\pi$
$499$	7.00291	+	12.1294i	0.313493	+	0.542986i	−0.665623	+	0.746288i	$0.731834\pi$
$500$	−44.2491	+	10.0030i	−1.97888	+	0.447347i
$501$	−4.23754	+	2.59554i	−0.189319	+	0.115960i
$502$	−35.1986	−	7.48170i	−1.57099	−	0.333925i
$503$	23.8114	−	17.3000i	1.06170	−	0.771370i	0.0872979	−	0.996182i	$-0.472177\pi$
$503$	23.8114	−	17.3000i	1.06170	−	0.771370i	0.974402	+	0.224812i	$0.0721768\pi$
$504$	−12.1305	−	76.7986i	−0.540335	−	3.42088i
$505$	34.0191	−	7.38381i	1.51383	−	0.328575i
$506$	−19.5092	+	8.68607i	−0.867291	+	0.386143i
$507$	−18.5746	−	10.0903i	−0.824928	−	0.448125i
$508$	3.23647	−	30.7929i	0.143595	−	1.36621i
$509$	−5.59125	+	1.18846i	−0.247828	+	0.0526774i	−0.330150	−	0.943928i	$-0.607099\pi$
$509$	−5.59125	+	1.18846i	−0.247828	+	0.0526774i	0.0823228	+	0.996606i	$0.473766\pi$
$510$	−30.4899	+	18.8559i	−1.35012	+	0.834955i
$511$	−71.6048	−	15.2201i	−3.16761	−	0.673296i
$512$	−12.8388	+	39.5137i	−0.567399	+	1.74628i
$513$	−23.0670	−	5.55334i	−1.01843	−	0.245186i
$514$	−13.5988	−	41.8529i	−0.599819	−	1.84605i
$515$	−11.1424	−	33.7981i	−0.490991	−	1.48932i
$516$	−55.4834	−	16.4477i	−2.44252	−	0.724068i
$517$	0.675179	−	6.42390i	0.0296943	−	0.282523i
$518$	−29.3462	−	50.8290i	−1.28940	−	2.23330i
$519$	−11.8460	−	24.8492i	−0.519982	−	1.09076i
$520$	3.16282	+	9.59378i	0.138699	+	0.420715i
$521$	−6.83148	+	4.96336i	−0.299293	+	0.217449i	−0.727288	−	0.686332i	$-0.759220\pi$
$521$	−6.83148	+	4.96336i	−0.299293	+	0.217449i	0.427996	+	0.903781i	$0.359220\pi$
$522$	0.290776	+	0.111759i	0.0127269	+	0.00489157i
$523$	−0.335514	−	1.03260i	−0.0146710	−	0.0451527i	0.943453	−	0.331506i	$-0.107557\pi$
$523$	−0.335514	−	1.03260i	−0.0146710	−	0.0451527i	−0.958124	+	0.286354i	$0.907557\pi$
$524$	−5.27390	+	9.13467i	−0.230392	+	0.399050i
$525$	1.53130	+	44.2931i	0.0668316	+	1.93311i
$526$	−15.0981	−	26.1507i	−0.658309	−	1.14022i
$527$	4.95782	−	5.50621i	0.215966	−	0.239854i
$528$	−4.56615	+	11.0171i	−0.198716	+	0.479457i
$529$	−0.735583	−	6.99860i	−0.0319819	−	0.304287i
$530$	12.4535	+	5.48067i	0.540943	+	0.238065i
$531$	1.50741	−	28.5328i	0.0654160	−	1.23822i
$532$	94.8160			4.11079
$533$	0.623315	−	0.277518i	0.0269988	−	0.0120206i
$534$	−9.36418	+	8.88252i	−0.405228	+	0.384384i
$535$	4.14149	+	4.56006i	0.179052	+	0.197149i
$536$	12.1877	−	13.5358i	0.526427	−	0.584656i
$537$	29.5738	+	8.76693i	1.27620	+	0.378321i
$538$	38.2718	+	42.5051i	1.65001	+	1.83253i
$539$	−9.38811	−	28.8936i	−0.404375	−	1.24454i
$540$	−30.7496	−	35.7373i	−1.32325	−	1.53789i
$541$	3.62252	−	11.1490i	0.155744	−	0.479331i	−0.842491	−	0.538710i	$-0.818912\pi$
$541$	3.62252	−	11.1490i	0.155744	−	0.479331i	0.998236	+	0.0593787i	$0.0189120\pi$
$542$	−61.1752	+	27.2369i	−2.62770	+	1.16993i
$543$	0.824138	+	31.7283i	0.0353671	+	1.36159i
$544$	−0.226252	+	2.15264i	−0.00970048	+	0.0922939i
$545$	25.7138	−	11.5811i	1.10146	−	0.496079i
$546$	19.2951	−	2.53611i	0.825755	−	0.108535i
$547$	2.00229	+	19.0505i	0.0856115	+	0.814539i	0.950112	+	0.311908i	$0.100968\pi$
$547$	2.00229	+	19.0505i	0.0856115	+	0.814539i	−0.864501	+	0.502631i	$0.832365\pi$
$548$	7.03820	+	21.6614i	0.300657	+	0.925328i
$549$	−9.87727	+	19.3650i	−0.421551	+	0.826479i
$550$	9.59610	−	16.9556i	0.409179	−	0.722990i
$551$	−0.0963205	+	0.166832i	−0.00410339	+	0.00710728i
$552$	−36.5490	−	31.2292i	−1.55563	−	1.32920i
$553$	−15.9130	−	7.08494i	−0.676691	−	0.301282i
$554$	39.5937	+	17.6283i	1.68218	+	0.748953i
$555$	−15.8953	−	8.54656i	−0.674716	−	0.362781i
$556$	−6.39235	+	2.84606i	−0.271096	+	0.120700i
$557$	18.2151			0.771799			0.385899	−	0.922541i	$-0.373891\pi$
$557$	18.2151			0.771799			0.385899	+	0.922541i	$0.373891\pi$
$558$	12.1966	+	7.92789i	0.516324	+	0.335614i
$559$	2.26983	−	6.98581i	0.0960034	−	0.295468i
$560$	40.3883	+	29.0796i	1.70672	+	1.22884i
$561$	1.88149	−	10.1397i	0.0794366	−	0.428098i
$562$	−34.7337	+	7.38288i	−1.46515	+	0.311428i
$563$	13.2459	−	2.81550i	0.558248	−	0.118659i	0.0798570	−	0.996806i	$-0.474554\pi$
$563$	13.2459	−	2.81550i	0.558248	−	0.118659i	0.478391	+	0.878147i	$0.341220\pi$
$564$	27.0313	−	9.56587i	1.13822	−	0.402796i
$565$	23.1635	+	16.6778i	0.974497	+	0.701639i
$566$	−9.44896	+	29.0809i	−0.397169	+	1.22236i
$567$	−39.9070	+	22.9955i	−1.67594	+	0.965718i
$568$	9.83605			0.412711
$569$	21.6080	−	9.62051i	0.905855	−	0.403313i	0.0997002	−	0.995018i	$-0.468212\pi$
$569$	21.6080	−	9.62051i	0.905855	−	0.403313i	0.806155	+	0.591705i	$0.201545\pi$
$570$	37.0182	−	22.8932i	1.55052	−	0.958893i
$571$	−33.2067	−	14.7846i	−1.38966	−	0.618715i	−0.430760	−	0.902467i	$-0.641754\pi$
$571$	−33.2067	−	14.7846i	−1.38966	−	0.618715i	−0.958898	+	0.283751i	$0.908421\pi$
$572$	−5.23506	−	2.33080i	−0.218889	−	0.0974556i
$573$	−3.47965	+	18.7525i	−0.145365	+	0.783395i
$574$	4.81697	−	8.34323i	0.201056	−	0.348240i
$575$	18.5105	+	20.2062i	0.771940	+	0.842657i
$576$	21.8156	−	1.13408i	0.908982	−	0.0472532i
$577$	10.9221	+	33.6148i	0.454694	+	1.39940i	0.871494	+	0.490406i	$0.163151\pi$
$577$	10.9221	+	33.6148i	0.454694	+	1.39940i	−0.416801	+	0.908998i	$0.636849\pi$
$578$	0.734772	+	6.99088i	0.0305625	+	0.290782i
$579$	4.28334	−	10.3347i	0.178010	−	0.429497i
$580$	−0.349025	+	0.157196i	−0.0144925	+	0.00652719i
$581$	−2.07748	+	19.7659i	−0.0861883	+	0.820027i
$582$	18.9207	−	11.5891i	0.784287	−	0.480384i
$583$	−3.57567	+	1.59199i	−0.148089	+	0.0659334i
$584$	−22.3859	+	68.8966i	−0.926334	+	2.85096i
$585$	4.63587	−	3.78388i	0.191670	−	0.156444i
$586$	−17.1619	−	52.8189i	−0.708951	−	2.18193i
$587$	25.3314	+	28.1334i	1.04554	+	1.16119i	0.986638	+	0.162925i	$0.0520928\pi$
$587$	25.3314	+	28.1334i	1.04554	+	1.16119i	0.0589006	+	0.998264i	$0.481240\pi$
$588$	97.8473	−	92.8144i	4.03515	−	3.82760i
$589$	−6.01935	+	6.68517i	−0.248023	+	0.275457i
$590$	35.2402	+	38.8017i	1.45081	+	1.59744i
$591$	−41.8905	−	12.4181i	−1.72314	−	0.510814i
$592$	−18.5138	+	8.24286i	−0.760911	+	0.338780i
$593$	33.1095			1.35964			0.679822	−	0.733377i	$-0.262057\pi$
$593$	33.1095			1.35964			0.679822	+	0.733377i	$0.262057\pi$
$594$	20.2398	+	0.542814i	0.830449	+	0.0222719i
$595$	−39.3904	−	17.3354i	−1.61485	−	0.710684i
$596$	−5.28927	−	50.3240i	−0.216657	−	2.06135i
$597$	2.61634	+	3.41117i	0.107080	+	0.139610i
$598$	8.05159	−	8.94220i	0.329254	−	0.365674i
$599$	16.9563	+	29.3692i	0.692816	+	1.19999i	0.970912	+	0.239439i	$0.0769634\pi$
$599$	16.9563	+	29.3692i	0.692816	+	1.19999i	−0.278096	+	0.960553i	$0.589703\pi$
$600$	43.7501	+	3.07462i	1.78609	+	0.125521i
$601$	7.45268	−	12.9084i	0.304001	−	0.526545i	−0.673037	−	0.739608i	$-0.735011\pi$
$601$	7.45268	−	12.9084i	0.304001	−	0.526545i	0.977038	+	0.213063i	$0.0683441\pi$
$602$	−32.0493	−	98.6376i	−1.30623	−	4.02017i
$603$	−10.0715	−	3.87096i	−0.410143	−	0.157638i
$604$	−24.3820	+	17.7145i	−0.992088	+	0.720794i
$605$	−5.94642	−	18.0373i	−0.241756	−	0.733319i
$606$	−66.1603	−	5.22097i	−2.68758	−	0.212087i
$607$	−1.90528	−	3.30004i	−0.0773328	−	0.133944i	0.824766	−	0.565475i	$-0.191307\pi$
$607$	−1.90528	−	3.30004i	−0.0773328	−	0.133944i	−0.902098	+	0.431530i	$0.857974\pi$
$608$	0.274696	−	2.61355i	0.0111404	−	0.105994i
$609$	0.0872235	+	0.363650i	0.00353447	+	0.0147358i
$610$	−12.4861	−	37.8740i	−0.505547	−	1.53347i
$611$	1.12468	+	3.46140i	0.0454995	+	0.140033i
$612$	44.2254	−	11.8302i	1.78771	−	0.478206i
$613$	0.301134	−	0.926794i	0.0121627	−	0.0374329i	−0.944791	−	0.327674i	$-0.893735\pi$
$613$	0.301134	−	0.926794i	0.0121627	−	0.0374329i	0.956954	+	0.290241i	$0.0937354\pi$
$614$	66.3143	+	14.0955i	2.67623	+	0.568850i
$615$	−0.0896372	−	2.96097i	−0.00361452	−	0.119398i
$616$	−40.1344	+	8.53083i	−1.61706	+	0.343717i
$617$	−3.08552	+	29.3567i	−0.124218	+	1.18186i	0.737814	+	0.675004i	$0.235858\pi$
$617$	−3.08552	+	29.3567i	−0.124218	+	1.18186i	−0.862032	+	0.506853i	$0.830809\pi$
$618$	1.76169	+	67.8230i	0.0708656	+	2.72824i
$619$	−3.98573	+	1.77456i	−0.160200	+	0.0713256i	−0.485270	−	0.874364i	$-0.661279\pi$
$619$	−3.98573	+	1.77456i	−0.160200	+	0.0713256i	0.325070	+	0.945690i	$0.394612\pi$
$620$	−17.4685	+	3.79153i	−0.701552	+	0.152271i
$621$	−9.52318	+	26.8386i	−0.382152	+	1.07700i
$622$	−1.00972	+	0.733602i	−0.0404859	+	0.0294148i
$623$	−15.1558	−	3.22146i	−0.607203	−	0.129065i
$624$	−0.174484	−	6.71744i	−0.00698497	−	0.268913i
$625$	−24.5394	−	4.77697i	−0.981575	−	0.191079i
$626$	16.2712	+	28.1825i	0.650327	+	1.12640i
$627$	−2.28434	+	12.3107i	−0.0912278	+	0.491643i
$628$	3.99168	+	37.9783i	0.159285	+	1.51550i
$629$	14.1778	−	10.3008i	0.565305	−	0.410718i
$630$	21.5522	−	81.6984i	0.858662	−	3.25494i
$631$	39.3657	+	28.6008i	1.56712	+	1.13858i	0.929848	+	0.367944i	$0.119938\pi$
$631$	39.3657	+	28.6008i	1.56712	+	1.13858i	0.637274	+	0.770637i	$0.280062\pi$
$632$	−8.61881	+	14.9282i	−0.342838	+	0.593812i
$633$	−11.9074	−	0.939660i	−0.473277	−	0.0373481i
$634$	25.2551	−	5.36814i	1.00301	−	0.213196i
$635$	8.46783	−	14.8133i	0.336036	−	0.587847i
$636$	−13.2099	−	11.2871i	−0.523805	−	0.447563i
$637$	11.4543	+	12.7213i	0.453835	+	0.504035i
$638$	0.0508004	−	0.156348i	0.00201121	−	0.00618986i
$639$	−2.08581	−	5.44058i	−0.0825134	−	0.215226i
$640$	−28.4009	+	31.8162i	−1.12265	+	1.25764i
$641$	3.32735	+	3.69539i	0.131422	+	0.145959i	0.805264	−	0.592917i	$-0.202024\pi$
$641$	3.32735	+	3.69539i	0.131422	+	0.145959i	−0.673842	+	0.738876i	$0.735357\pi$
$642$	−5.05362	−	10.6009i	−0.199451	−	0.418384i
$643$	1.30748	+	2.26463i	0.0515621	+	0.0893081i	0.890654	−	0.454681i	$-0.150247\pi$
$643$	1.30748	+	2.26463i	0.0515621	+	0.0893081i	−0.839092	+	0.543989i	$0.816913\pi$
$644$	11.8960	−	113.183i	0.468768	−	4.46003i
$645$	−24.3344	−	20.6122i	−0.958164	−	0.811606i
$646$	4.41790	+	42.0335i	0.173820	+	1.65379i
$647$	13.0683	−	9.49465i	0.513767	−	0.373273i	−0.300484	−	0.953787i	$-0.597148\pi$
$647$	13.0683	−	9.49465i	0.513767	−	0.373273i	0.814251	+	0.580514i	$0.197148\pi$
$648$	18.5034	+	41.6538i	0.726881	+	1.63631i
$649$	−15.0785			−0.591882
$650$	−1.05367	+	10.9270i	−0.0413282	+	0.428593i
$651$	0.453447	+	17.4571i	0.0177720	+	0.684199i
$652$	−8.52204	+	9.46469i	−0.333749	+	0.370666i
$653$	−15.8839	−	7.07197i	−0.621585	−	0.276748i	0.0716826	−	0.997427i	$-0.477163\pi$
$653$	−15.8839	−	7.07197i	−0.621585	−	0.276748i	−0.693268	+	0.720680i	$0.743830\pi$
$654$	−53.3063	+	7.00647i	−2.08444	+	0.273975i
$655$	−4.68782	+	3.43676i	−0.183168	+	0.134285i
$656$	−2.69119	−	1.95527i	−0.105073	−	0.0763403i
$657$	42.8556	−	2.22784i	1.67196	−	0.0869163i
$658$	41.5747	+	30.2058i	1.62075	+	1.17754i
$659$	−30.1579	−	33.4938i	−1.17479	−	1.30473i	−0.943319	−	0.331889i	$-0.892314\pi$
$659$	−30.1579	−	33.4938i	−1.17479	−	1.30473i	−0.231467	−	0.972843i	$-0.574353\pi$
$660$	−17.9771	+	17.1997i	−0.699757	+	0.669497i
$661$	−20.4456	+	22.7072i	−0.795243	+	0.883207i	−0.995326	−	0.0965717i	$-0.969212\pi$
$661$	−20.4456	+	22.7072i	−0.795243	+	0.883207i	0.200083	+	0.979779i	$0.435879\pi$
$662$	5.88825	−	1.25159i	0.228853	−	0.0486443i
$663$	1.35531	+	5.65053i	0.0526360	+	0.219449i
$664$	19.2380	+	4.08917i	0.746580	+	0.158690i
$665$	47.8244	+	21.0472i	1.85455	+	0.816174i
$666$	24.3187	+	24.3392i	0.942329	+	0.943124i
$667$	0.187065	+	0.135910i	0.00724317	+	0.00526247i
$668$	−5.82068	+	10.0817i	−0.225209	+	0.390073i
$669$	9.83056	+	20.6214i	0.380071	+	0.797269i
$670$	18.0477	−	8.12841i	0.697244	−	0.314028i
$671$	10.4802	+	4.66608i	0.404583	+	0.180132i
$672$	−3.10474	−	4.04795i	−0.119768	−	0.156153i
$673$	14.1717	+	3.01229i	0.546279	+	0.116115i	0.472781	−	0.881180i	$-0.343250\pi$
$673$	14.1717	+	3.01229i	0.546279	+	0.116115i	0.0734983	+	0.997295i	$0.476584\pi$
$674$	4.51468			0.173899
$675$	−7.57690	−	24.8514i	−0.291635	−	0.956530i
$676$	−49.5203			−1.90463
$677$	11.5152	+	2.44762i	0.442563	+	0.0940697i	0.423803	−	0.905754i	$-0.360695\pi$
$677$	11.5152	+	2.44762i	0.442563	+	0.0940697i	0.0187600	+	0.999824i	$0.494028\pi$
$678$	−33.1171	−	43.1779i	−1.27186	−	1.65824i
$679$	24.3331	+	10.8338i	0.933819	+	0.415763i
$680$	−21.1355	+	36.9735i	−0.810509	+	1.41787i
$681$	13.0666	+	27.4095i	0.500712	+	1.05033i
$682$	3.83835	−	6.64822i	0.146978	−	0.254574i
$683$	−7.80859	−	5.67327i	−0.298787	−	0.217082i	0.428283	−	0.903645i	$-0.359119\pi$
$683$	−7.80859	−	5.67327i	−0.298787	−	0.217082i	−0.727070	+	0.686563i	$0.759119\pi$
$684$	−53.6946	+	14.3632i	−2.05307	+	0.549189i
$685$	−1.25836	+	12.4882i	−0.0480794	+	0.477148i
$686$	150.180	+	31.9217i	5.73389	+	1.21878i
$687$	6.56435	+	27.3679i	0.250446	+	1.04415i
$688$	−35.0287	+	7.44558i	−1.33546	+	0.283860i
$689$	1.47570	−	1.63893i	0.0562198	−	0.0624384i
$690$	−22.6835	−	47.0613i	−0.863545	−	1.79159i
$691$	0.577170	+	0.641012i	0.0219566	+	0.0243852i	0.754023	−	0.656848i	$-0.228111\pi$
$691$	0.577170	+	0.641012i	0.0219566	+	0.0243852i	−0.732067	+	0.681233i	$0.761444\pi$
$692$	−52.1734	−	37.9062i	−1.98334	−	1.44098i
$693$	13.2294	+	20.3904i	0.502545	+	0.774567i
$694$	0.594103	+	0.431641i	0.0225518	+	0.0163849i
$695$	−3.85602	+	0.0165603i	−0.146267	+	0.000628170i
$696$	0.366914	−	0.0482264i	0.0139078	−	0.00182802i
$697$	2.62787	+	1.17000i	0.0995375	+	0.0443170i
$698$	27.8251	−	30.9029i	1.05320	−	1.16969i
$699$	−0.857675	−	33.0195i	−0.0324403	−	1.24891i
$700$	52.6835	+	89.4670i	1.99125	+	3.38153i
$701$	−9.06128			−0.342240			−0.171120	−	0.985250i	$-0.554739\pi$
$701$	−9.06128			−0.342240			−0.171120	+	0.985250i	$0.554739\pi$
$702$	−10.5427	+	4.35912i	−0.397909	+	0.164524i
$703$	−17.2134	+	12.5063i	−0.649216	+	0.471683i
$704$	−1.20502	−	11.4650i	−0.0454160	−	0.432104i
$705$	15.7578	+	1.17544i	0.593473	+	0.0442695i
$706$	−1.87265	+	17.8171i	−0.0704781	+	0.670554i
$707$	−39.8353	−	68.9968i	−1.49816	−	2.59489i
$708$	−28.8040	−	60.4217i	−1.08252	−	2.27079i
$709$	−28.8143	−	32.0015i	−1.08214	−	1.20184i	−0.978288	−	0.207251i	$-0.933548\pi$
$709$	−28.8143	−	32.0015i	−1.08214	−	1.20184i	−0.103856	−	0.994592i	$-0.533118\pi$
$710$	9.78350	+	4.30564i	0.367168	+	0.161588i
$711$	10.0849	+	1.60165i	0.378212	+	0.0600665i
$712$	−4.73816	+	14.5825i	−0.177570	+	0.546504i
$713$	7.22495	+	8.02412i	0.270576	+	0.300506i
$714$	62.3777	+	53.2983i	2.33443	+	1.99464i
$715$	−2.12314	−	2.33771i	−0.0794007	−	0.0874255i
$716$	70.6826	−	15.0241i	2.64153	−	0.561476i
$717$	−12.0318	−	0.949480i	−0.449337	−	0.0354590i
$718$	33.2927	−	57.6647i	1.24247	−	2.15203i
$719$	22.4736	+	16.3280i	0.838124	+	0.608933i	0.921846	−	0.387556i	$-0.126681\pi$
$719$	22.4736	+	16.3280i	0.838124	+	0.608933i	−0.0837219	+	0.996489i	$0.526681\pi$
$720$	−27.2772	−	10.3497i	−1.01656	−	0.385711i
$721$	−65.8922	+	47.8735i	−2.45395	+	1.78290i
$722$	−0.475731	−	4.52628i	−0.0177049	−	0.168451i
$723$	0.958633	−	5.16624i	0.0356519	−	0.192134i
$724$	37.1771	+	64.3926i	1.38167	+	2.39313i
$725$	−0.210940	+	0.00181187i	−0.00783411	+	6.72911e-5i
$726$	0.940174	+	36.1955i	0.0348931	+	1.34334i
$727$	−28.1735	−	5.98845i	−1.04490	−	0.222099i	−0.346677	−	0.937984i	$-0.612690\pi$
$727$	−28.1735	−	5.98845i	−1.04490	−	0.222099i	−0.698218	+	0.715885i	$0.746023\pi$
$728$	18.7039	−	13.5891i	0.693211	−	0.503647i
$729$	19.1160	−	19.0677i	0.708001	−	0.706211i
$730$	−52.4251	+	58.7293i	−1.94034	+	2.17367i
$731$	28.2902	−	12.5956i	1.04635	−	0.465865i
$732$	1.32236	+	50.9092i	0.0488758	+	1.88166i
$733$	−1.31486	+	12.5100i	−0.0485654	+	0.462069i	0.943032	+	0.332703i	$0.107961\pi$
$733$	−1.31486	+	12.5100i	−0.0485654	+	0.462069i	−0.991597	+	0.129366i	$0.958706\pi$
$734$	−18.5382	+	3.94041i	−0.684256	+	0.145443i
$735$	69.9563	−	25.0948i	2.58038	−	0.925635i
$736$	−3.08536	−	0.655815i	−0.113728	−	0.0241736i
$737$	−1.75955	+	5.41535i	−0.0648140	+	0.199477i
$738$	−1.46400	+	5.45450i	−0.0538904	+	0.200783i
$739$	−14.5062	−	44.6456i	−0.533620	−	1.64231i	−0.746612	−	0.665259i	$-0.768321\pi$
$739$	−14.5062	−	44.6456i	−0.533620	−	1.64231i	0.212992	−	0.977054i	$-0.431679\pi$
$740$	−42.2784	+	0.181572i	−1.55419	+	0.00667472i
$741$	−1.64550	−	6.86039i	−0.0604490	−	0.252023i
$742$	3.25498	−	30.9691i	0.119494	−	1.13691i
$743$	3.97180	+	6.87937i	0.145711	+	0.252379i	0.929638	−	0.368474i	$-0.120120\pi$
$743$	3.97180	+	6.87937i	0.145711	+	0.252379i	−0.783927	+	0.620853i	$0.786786\pi$
$744$	17.2276	+	1.35950i	0.631596	+	0.0498417i
$745$	8.50302	−	26.5571i	0.311527	−	0.972978i
$746$	46.6232	−	33.8738i	1.70700	−	1.24021i
$747$	−1.81774	−	11.5082i	−0.0665077	−	0.421063i
$748$	−7.46568	−	22.9770i	−0.272972	−	0.840122i
$749$	7.04910	−	12.2094i	0.257568	−	0.446121i
$750$	42.1705	+	22.2094i	1.53985	+	0.810974i
$751$	6.40667	+	11.0967i	0.233783	+	0.404923i	0.958918	−	0.283683i	$-0.0915563\pi$
$751$	6.40667	+	11.0967i	0.233783	+	0.404923i	−0.725136	+	0.688606i	$0.758223\pi$
$752$	11.8731	−	13.1865i	0.432969	−	0.480861i
$753$	15.4120	+	20.0941i	0.561644	+	0.732268i
$754$	0.00968234	+	0.0921213i	0.000352610	+	0.00335486i
$755$	−16.2303	+	3.52278i	−0.590682	+	0.128207i
$756$	−56.4355	+	91.9637i	−2.05254	+	3.34469i
$757$	4.66915			0.169703			0.0848516	−	0.996394i	$-0.472958\pi$
$757$	4.66915			0.169703			0.0848516	+	0.996394i	$0.472958\pi$
$758$	16.4823	−	7.33838i	0.598663	−	0.266542i
$759$	14.4088	+	4.27140i	0.523008	+	0.155042i
$760$	25.6609	−	44.8901i	0.930818	−	1.62833i
$761$	−0.322089	+	0.357716i	−0.0116757	+	0.0129672i	−0.748954	−	0.662622i	$-0.769444\pi$
$761$	−0.322089	+	0.357716i	−0.0116757	+	0.0129672i	0.737279	+	0.675589i	$0.236110\pi$
$762$	−23.6007	+	22.3868i	−0.854964	+	0.810987i
$763$	−43.1878	−	47.9650i	−1.56350	−	1.73645i
$764$	13.8071	+	42.4939i	0.499524	+	1.53738i
$765$	24.9330	+	3.85008i	0.901455	+	0.139200i
$766$	13.3465	−	41.0762i	0.482227	−	1.48414i
$767$	7.76155	−	3.45566i	0.280253	−	0.124777i
$768$	47.8246	−	29.2931i	1.72572	−	1.05702i
$769$	−1.23257	+	11.7271i	−0.0444476	+	0.422890i	0.949561	+	0.313584i	$0.101530\pi$
$769$	−1.23257	+	11.7271i	−0.0444476	+	0.422890i	−0.994008	+	0.109306i	$0.965137\pi$
$770$	−43.6543	−	9.08323i	−1.57319	−	0.327337i
$771$	−11.8574	+	28.6092i	−0.427034	+	1.03034i
$772$	−2.73948	−	26.0644i	−0.0985961	−	0.938080i
$773$	−9.94328	−	30.6023i	−0.357635	−	1.10069i	−0.954466	−	0.298320i	$-0.903574\pi$
$773$	−9.94328	−	30.6023i	−0.357635	−	1.10069i	0.596831	−	0.802367i	$-0.296426\pi$
$774$	33.0917	+	51.0039i	1.18946	+	1.83330i
$775$	−9.65261	−	1.96523i	−0.346732	−	0.0705930i
$776$	13.1793	−	22.8272i	0.473108	−	0.819447i
$777$	−7.53559	+	40.6106i	−0.270338	+	1.45690i
$778$	0.748856	+	0.333412i	0.0268478	+	0.0119534i
$779$	−3.19053	−	1.42051i	−0.114312	−	0.0508952i
$780$	5.31179	−	12.9734i	0.190193	−	0.464522i
$781$	−2.80906	+	1.25067i	−0.100516	+	0.0447527i
$782$	50.7301			1.81411
$783$	−0.104482	−	0.192723i	−0.00373389	−	0.00688736i
$784$	25.7898	−	79.3730i	0.921066	−	2.83475i
$785$	−6.41702	+	20.0420i	−0.229033	+	0.715330i
$786$	10.4467	−	3.69690i	0.372623	−	0.131864i
$787$	22.7154	−	4.82831i	0.809717	−	0.172111i	0.215592	−	0.976483i	$-0.430832\pi$
$787$	22.7154	−	4.82831i	0.809717	−	0.172111i	0.594125	+	0.804373i	$0.297498\pi$
$788$	−100.120	+	21.2812i	−3.56664	+	0.758112i
$789$	−3.87694	+	20.8935i	−0.138023	+	0.743828i
$790$	−15.1075	+	11.0756i	−0.537499	+	0.394054i
$791$	20.1865	−	62.1275i	0.717748	−	2.20900i
$792$	21.4360	−	10.9108i	0.761694	−	0.387698i
$793$	−6.46397			−0.229542
$794$	−54.6602	+	24.3363i	−1.93982	+	0.863662i
$795$	−4.15744	−	8.62544i	−0.147449	−	0.305913i
$796$	9.20042	+	4.09629i	0.326100	+	0.145189i
$797$	−43.4005	−	19.3232i	−1.53733	−	0.684462i	−0.548861	−	0.835913i	$-0.684938\pi$
$797$	−43.4005	−	19.3232i	−1.53733	−	0.684462i	−0.988465	+	0.151452i	$0.951605\pi$
$798$	−75.7335	−	64.7102i	−2.68094	−	2.29072i
$799$	−7.67203	+	13.2883i	−0.271417	+	0.470108i
$800$	2.61874	−	1.19300i	0.0925865	−	0.0421788i
$801$	9.07076	−	0.471541i	0.320500	−	0.0166611i
$802$	16.1320	+	49.6491i	0.569639	+	1.75317i
$803$	−2.36721	−	22.5225i	−0.0835370	−	0.794801i
$804$	−25.0614	+	3.29401i	−0.883846	+	0.116171i
$805$	31.1245	−	54.4479i	1.09699	−	1.91904i
$806$	−0.452137	+	4.30180i	−0.0159259	+	0.151524i
$807$	−1.04516	−	40.2375i	−0.0367914	−	1.41643i
$808$	−72.0248	+	32.0675i	−2.53383	+	1.12813i
$809$	8.12369	−	25.0022i	0.285614	−	0.879029i	−0.700600	−	0.713554i	$-0.747084\pi$
$809$	8.12369	−	25.0022i	0.285614	−	0.879029i	0.986214	−	0.165475i	$-0.0529157\pi$
$810$	0.170928	+	49.5309i	0.00600580	+	1.74034i
$811$	−4.66526	−	14.3582i	−0.163819	−	0.504184i	0.835128	−	0.550056i	$-0.185394\pi$
$811$	−4.66526	−	14.3582i	−0.163819	−	0.504184i	−0.998947	+	0.0458715i	$0.985394\pi$
$812$	0.586209	+	0.651051i	0.0205719	+	0.0228474i
$813$	45.1819	+	13.3938i	1.58460	+	0.469743i
$814$	12.1494	−	13.4933i	0.425838	−	0.472941i
$815$	−6.39941	+	2.88220i	−0.224162	+	0.100959i
$816$	20.5539	−	19.4967i	0.719531	−	0.682521i
$817$	−34.3475	+	15.2925i	−1.20167	+	0.535016i
$818$	−39.7678			−1.39045
$819$	−11.4828	−	7.46392i	−0.401242	−	0.260810i
$820$	−3.49566	−	5.99506i	−0.122074	−	0.209357i
$821$	−0.421988	−	4.01495i	−0.0147275	−	0.140123i	0.984687	−	0.174330i	$-0.0557760\pi$
$821$	−0.421988	−	4.01495i	−0.0147275	−	0.140123i	−0.999415	+	0.0342074i	$0.989109\pi$
$822$	9.16178	−	22.1053i	0.319554	−	0.771011i
$823$	26.5904	−	29.5316i	0.926882	−	1.02941i	−0.0726049	−	0.997361i	$-0.523131\pi$
$823$	26.5904	−	29.5316i	0.926882	−	1.02941i	0.999486	−	0.0320455i	$-0.0102021\pi$
$824$	40.2995	+	69.8009i	1.40390	+	2.43163i
$825$	−12.8855	+	4.68485i	−0.448615	+	0.163106i
$826$	59.9811	−	103.890i	2.08701	−	3.61480i
$827$	11.8321	+	36.4154i	0.411441	+	1.26629i	0.915396	+	0.402556i	$0.131878\pi$
$827$	11.8321	+	36.4154i	0.411441	+	1.26629i	−0.503954	+	0.863730i	$0.668122\pi$
$828$	10.4087	+	65.8980i	0.361728	+	2.29011i
$829$	31.2683	−	22.7178i	1.08599	−	0.789020i	0.107275	−	0.994229i	$-0.465787\pi$
$829$	31.2683	−	22.7178i	1.08599	−	0.789020i	0.978718	+	0.205209i	$0.0657874\pi$
$830$	17.3452	+	12.4886i	0.602062	+	0.433485i
$831$	−13.1249	−	27.5320i	−0.455299	−	0.955074i
$832$	3.24782	+	5.62538i	0.112598	+	0.195025i
$833$	−7.54374	+	71.7739i	−0.261375	+	2.48682i
$834$	7.04823	+	2.08940i	0.244060	+	0.0723499i
$835$	−5.17384	+	3.79307i	−0.179048	+	0.131264i
$836$	9.06417	+	27.8967i	0.313491	+	0.964826i
$837$	−2.90128	−	9.81736i	−0.100283	−	0.339337i
$838$	10.7642	−	33.1289i	0.371844	−	1.14442i
$839$	32.3088	+	6.86746i	1.11543	+	0.237091i	0.728517	−	0.685027i	$-0.240210\pi$
$839$	32.3088	+	6.86746i	1.11543	+	0.237091i	0.386908	+	0.922118i	$0.373543\pi$
$840$	−23.8306	−	97.5059i	−0.822235	−	3.36427i
$841$	28.3645	−	6.02907i	0.978088	−	0.207899i
$842$	6.42986	−	61.1760i	0.221588	−	2.10826i
$843$	21.9586	+	11.9286i	0.756295	+	0.410841i
$844$	−25.5627	+	11.3813i	−0.879905	+	0.391759i
$845$	−24.9777	−	10.9925i	−0.859257	−	0.378153i
$846$	−28.1196	−	10.8077i	−0.966772	−	0.371577i
$847$	−35.1651	+	25.5489i	−1.20829	+	0.877872i
$848$	−10.5172	−	2.23551i	−0.361163	−	0.0767676i
$849$	18.3499	−	11.2395i	0.629766	−	0.385738i
$850$	−37.2074	+	27.5241i	−1.27620	+	0.944070i
$851$	12.7692	+	22.1169i	0.437723	+	0.758159i
$852$	−10.3777	−	8.86720i	−0.355535	−	0.303785i
$853$	−1.64958	−	15.6947i	−0.0564807	−	0.537378i	−0.985779	−	0.168047i	$-0.946254\pi$
$853$	−1.64958	−	15.6947i	−0.0564807	−	0.537378i	0.929298	−	0.369330i	$-0.120413\pi$
$854$	−73.8385	+	53.6468i	−2.52670	+	1.83576i
$855$	−30.2715	−	4.67443i	−1.03526	−	0.159862i
$856$	−11.2869	−	8.20042i	−0.385779	−	0.280285i
$857$	−19.9971	+	34.6359i	−0.683086	+	1.18314i	0.290948	+	0.956739i	$0.406029\pi$
$857$	−19.9971	+	34.6359i	−0.683086	+	1.18314i	−0.974034	+	0.226401i	$0.927304\pi$
$858$	2.59074	+	5.43454i	0.0884463	+	0.185532i
$859$	−54.6043	+	11.6065i	−1.86307	+	0.396009i	−0.994953	−	0.100344i	$-0.968006\pi$
$859$	−54.6043	+	11.6065i	−1.86307	+	0.396009i	−0.868121	+	0.496352i	$0.834672\pi$
$860$	−73.1433	−	15.2191i	−2.49416	−	0.518966i
$861$	−6.39134	+	2.26178i	−0.217816	+	0.0770811i
$862$	−8.32625	−	9.24723i	−0.283593	−	0.314962i
$863$	2.37722	−	7.31633i	0.0809215	−	0.249051i	−0.902408	−	0.430882i	$-0.858203\pi$
$863$	2.37722	−	7.31633i	0.0809215	−	0.249051i	0.983330	+	0.181831i	$0.0582025\pi$
$864$	2.37143	+	1.82205i	0.0806777	+	0.0619873i
$865$	−17.9015	−	30.7010i	−0.608668	−	1.04387i
$866$	−33.1552	−	36.8226i	−1.12666	−	1.25128i
$867$	2.80278	−	4.07622i	0.0951873	−	0.138436i
$868$	20.4551	+	35.4293i	0.694291	+	1.20255i
$869$	0.563277	−	5.35922i	0.0191079	−	0.181799i
$870$	0.386064	+	0.112645i	0.0130888	+	0.00381901i
$871$	−0.335363	−	3.19077i	−0.0113634	−	0.108115i
$872$	−51.6728	+	37.5425i	−1.74986	+	1.27135i
$873$	−15.4211	−	2.44913i	−0.521924	−	0.0828904i
$874$	−61.5921			−2.08338
$875$	6.71335	+	56.8211i	0.226953	+	1.92090i
$876$	85.7290	−	52.5099i	2.89651	−	1.77415i
$877$	−4.00898	+	4.45243i	−0.135374	+	0.150348i	−0.807020	−	0.590524i	$-0.798921\pi$
$877$	−4.00898	+	4.45243i	−0.135374	+	0.150348i	0.671646	+	0.740872i	$0.265588\pi$
$878$	−89.2639	−	39.7429i	−3.01251	−	1.34126i
$879$	−14.9642	+	36.1052i	−0.504729	+	1.21780i
$880$	−4.69476	+	14.6630i	−0.158260	+	0.494288i
$881$	−35.8213	−	26.0257i	−1.20685	−	0.876829i	−0.211910	−	0.977289i	$-0.567968\pi$
$881$	−35.8213	−	26.0257i	−1.20685	−	0.876829i	−0.994941	+	0.100461i	$0.967968\pi$
$882$	−141.499	+	7.35579i	−4.76452	+	0.247682i
$883$	37.8054	+	27.4673i	1.27225	+	0.924347i	0.999290	−	0.0376774i	$-0.0119959\pi$
$883$	37.8054	+	27.4673i	1.27225	+	0.924347i	0.272964	+	0.962024i	$0.411996\pi$
$884$	9.10875	+	10.1163i	0.306360	+	0.340248i
$885$	−1.11617	−	36.8701i	−0.0375195	−	1.23938i
$886$	−46.8165	+	51.9950i	−1.57283	+	1.74681i
$887$	−35.6071	+	7.56852i	−1.19557	+	0.254126i	−0.762352	−	0.647163i	$-0.775955\pi$
$887$	−35.6071	+	7.56852i	−1.19557	+	0.254126i	−0.433218	+	0.901289i	$0.642622\pi$
$888$	39.1881	+	11.6170i	1.31507	+	0.389842i
$889$	−38.1973	−	8.11909i	−1.28110	−	0.272306i
$890$	−11.0962	+	12.4306i	−0.371946	+	0.416673i
$891$	−10.5807	−	9.54309i	−0.354467	−	0.319706i
$892$	43.2968	+	31.4569i	1.44968	+	1.05326i
$893$	9.31471	−	16.1336i	0.311705	−	0.539889i
$894$	−30.1205	+	43.8058i	−1.00738	+	1.46508i
$895$	38.9868	+	8.11206i	1.30319	+	0.271156i
$896$	89.1686	+	39.7004i	2.97892	+	1.32630i
$897$	−8.39577	+	1.10352i	−0.280327	+	0.0368456i
$898$	79.3627	+	16.8691i	2.64837	+	0.562928i
$899$	−0.0831187			−0.00277216
$900$	−43.3877	−	42.6847i	−1.44626	−	1.42282i
$901$	9.29786			0.309757
$902$	2.91523	+	0.619651i	0.0970665	+	0.0206321i
$903$	−27.9451	+	67.4253i	−0.929956	+	2.24377i
$904$	−59.0557	−	26.2933i	−1.96416	−	0.874502i
$905$	4.45801	+	40.7316i	0.148189	+	1.35397i
$906$	31.5648	+	2.49090i	1.04867	+	0.0827546i
$907$	7.52629	−	13.0359i	0.249906	−	0.432850i	−0.713593	−	0.700560i	$-0.752934\pi$
$907$	7.52629	−	13.0359i	0.249906	−	0.432850i	0.963500	+	0.267710i	$0.0862669\pi$
$908$	57.5491	+	41.8119i	1.90983	+	1.38758i
$909$	33.0108	+	33.0387i	1.09490	+	1.09582i
$910$	24.5525	−	5.32909i	0.813906	−	0.176658i
$911$	−57.3475	−	12.1896i	−1.90001	−	0.403859i	−0.900488	−	0.434881i	$-0.856791\pi$
$911$	−57.3475	−	12.1896i	−1.90001	−	0.403859i	−0.999519	+	0.0310218i	$0.990124\pi$
$912$	−24.9548	+	23.6712i	−0.826335	+	0.783832i
$913$	−6.01410	+	1.27834i	−0.199038	+	0.0423068i
$914$	−46.6134	+	51.7695i	−1.54184	+	1.71238i
$915$	−10.6338	+	25.9717i	−0.351542	+	0.858599i
$916$	44.1175	+	48.9975i	1.45768	+	1.61892i
$917$	10.7625	+	7.81939i	0.355408	+	0.258219i
$918$	−43.3986	−	20.7338i	−1.43237	−	0.684317i
$919$	−5.91856	−	4.30008i	−0.195235	−	0.141847i	0.485873	−	0.874029i	$-0.338502\pi$
$919$	−5.91856	−	4.30008i	−0.195235	−	0.141847i	−0.681108	+	0.732183i	$0.738502\pi$
$920$	−50.3663	−	36.2638i	−1.66053	−	1.19558i
$921$	−29.0362	−	37.8572i	−0.956775	−	1.24744i
$922$	37.3801	+	16.6427i	1.23105	+	0.548098i
$923$	1.15932	−	1.28755i	0.0381594	−	0.0423804i
$924$	50.0352	+	27.1806i	1.64604	+	0.894175i
$925$	−21.3652	−	9.29334i	−0.702484	−	0.305563i
$926$	26.8105			0.881048
$927$	30.0629	−	37.0926i	0.987395	−	1.21828i
$928$	0.0196442	−	0.0142724i	0.000644853	−	0.000468513i
$929$	2.08049	+	19.7945i	0.0682585	+	0.649437i	0.974146	+	0.225919i	$0.0725383\pi$
$929$	2.08049	+	19.7945i	0.0682585	+	0.649437i	−0.905888	+	0.423518i	$0.860795\pi$
$930$	16.5405	+	8.89348i	0.542384	+	0.291629i
$931$	9.15895	−	87.1416i	0.300172	−	2.85595i
$932$	−38.6899	−	67.0130i	−1.26733	−	2.19508i
$933$	0.875594	+	0.0690966i	0.0286657	+	0.00226212i
$934$	−40.5987	−	45.0894i	−1.32843	−	1.47537i
$935$	1.33479	−	13.2466i	0.0436522	−	0.433211i
$936$	−8.53351	+	10.5289i	−0.278927	+	0.344149i
$937$	5.65299	−	17.3981i	0.184675	−	0.568371i	−0.815268	−	0.579084i	$-0.803410\pi$
$937$	5.65299	−	17.3981i	0.184675	−	0.568371i	0.999943	+	0.0107132i	$0.00341019\pi$
$938$	−30.3122	−	33.6651i	−0.989730	−	1.09921i
$939$	4.17816	−	22.5168i	0.136349	−	0.734809i
$940$	33.7526	−	15.2017i	1.10089	−	0.495823i
$941$	18.4320	−	3.91785i	0.600867	−	0.127718i	0.102572	−	0.994726i	$-0.467293\pi$
$941$	18.4320	−	3.91785i	0.600867	−	0.127718i	0.498295	+	0.867007i	$0.333960\pi$
$942$	22.7312	−	33.0591i	0.740622	−	1.07712i
$943$	−2.09598	+	3.63034i	−0.0682545	+	0.118220i
$944$	−33.5108	−	24.3470i	−1.09068	−	0.792429i
$945$	−48.8796	+	33.8583i	−1.59005	+	1.10141i
$946$	25.9572	−	18.8590i	0.843942	−	0.613160i
$947$	−3.18036	−	30.2591i	−0.103348	−	0.983288i	−0.916174	−	0.400782i	$-0.868739\pi$
$947$	−3.18036	−	30.2591i	−0.103348	−	0.983288i	0.812826	−	0.582507i	$-0.197928\pi$
$948$	22.5512	−	7.98046i	0.732430	−	0.259193i
$949$	6.38018	+	11.0508i	0.207109	+	0.358724i
$950$	45.1740	−	33.4174i	1.46564	−	1.08420i
$951$	−15.9662	−	8.67332i	−0.517741	−	0.281252i
$952$	95.3395	+	20.2650i	3.08997	+	0.656794i
$953$	−6.16233	+	4.47720i	−0.199617	+	0.145031i	−0.683104	−	0.730321i	$-0.739370\pi$
$953$	−6.16233	+	4.47720i	−0.199617	+	0.145031i	0.483486	+	0.875352i	$0.339370\pi$
$954$	2.84803	+	18.0310i	0.0922083	+	0.583774i
$955$	−2.46857	+	24.4985i	−0.0798810	+	0.792753i
$956$	−25.8299	+	11.5002i	−0.835397	+	0.371943i
$957$	−0.0986543	+	0.0604268i	−0.00318904	+	0.00195332i
$958$	9.96865	−	94.8453i	0.322072	−	3.06431i
$959$	28.0980	−	5.97242i	0.907333	−	0.192860i
$960$	27.9453	−	3.79523i	0.901930	−	0.122490i
$961$	26.5260	+	5.63827i	0.855677	+	0.181880i
$962$	−3.16147	+	9.73000i	−0.101930	+	0.313708i
$963$	−2.14239	+	7.98205i	−0.0690377	+	0.257218i
$964$	−3.80381	−	11.7069i	−0.122513	−	0.377055i
$965$	4.40399	−	13.7548i	0.141769	−	0.442783i
$966$	−86.7471	+	82.2852i	−2.79104	+	2.64748i
$967$	−5.19009	+	49.3804i	−0.166902	+	1.58797i	0.515435	+	0.856929i	$0.327630\pi$
$967$	−5.19009	+	49.3804i	−0.166902	+	1.58797i	−0.682337	+	0.731038i	$0.739036\pi$
$968$	21.5069	+	37.2511i	0.691258	+	1.19729i
$969$	16.8520	−	24.5087i	0.541364	−	0.787334i
$970$	23.1012	−	16.9361i	0.741736	−	0.543785i
$971$	−0.472976	+	0.343637i	−0.0151785	+	0.0110278i	−0.595349	−	0.803467i	$-0.702986\pi$
$971$	−0.472976	+	0.343637i	−0.0151785	+	0.0110278i	0.580170	+	0.814495i	$0.302986\pi$
$972$	18.0285	−	60.6285i	0.578266	−	1.94466i
$973$	2.72713	+	8.39323i	0.0874276	+	0.269075i
$974$	1.11660	−	1.93400i	0.0357780	−	0.0619693i
$975$	5.55905	−	5.36457i	0.178032	−	0.171804i
$976$	15.7572	+	27.2923i	0.504376	+	0.873604i
$977$	36.8148	−	40.8870i	1.17781	−	1.30809i	0.236075	−	0.971735i	$-0.424139\pi$
$977$	36.8148	−	40.8870i	1.17781	−	1.30809i	0.941735	−	0.336356i	$-0.109194\pi$
$978$	13.2664	−	1.74371i	0.424213	−	0.0557576i
$979$	−0.501040	−	4.76707i	−0.0160133	−	0.152356i
$980$	115.946	−	129.888i	3.70375	−	4.14913i
$981$	31.7234	+	20.6204i	1.01285	+	0.658360i
$982$	11.5241			0.367750
$983$	53.4151	−	23.7819i	1.70368	−	0.758526i	0.704889	−	0.709317i	$-0.250997\pi$
$983$	53.4151	−	23.7819i	1.70368	−	0.758526i	0.998789	−	0.0492089i	$-0.0156700\pi$
$984$	1.56484	+	6.52410i	0.0498853	+	0.207981i
$985$	−55.2238	−	11.4905i	−1.75958	−	0.366119i
$986$	−0.261308	+	0.290211i	−0.00832173	+	0.00924222i
$987$	−8.43498	−	35.1669i	−0.268488	−	1.11937i
$988$	−11.0590	−	12.2823i	−0.351835	−	0.390753i
$989$	13.9454	+	42.9196i	0.443439	+	1.36476i
$990$	26.0976	−	1.46908i	0.829435	−	0.0466905i
$991$	−14.9966	+	46.1549i	−0.476384	+	1.46616i	0.367699	+	0.929945i	$0.380146\pi$
$991$	−14.9966	+	46.1549i	−0.476384	+	1.46616i	−0.844082	+	0.536213i	$0.819854\pi$
$992$	1.03585	−	0.461191i	0.0328883	−	0.0146428i
$993$	−3.72254	−	2.02219i	−0.118131	−	0.0641723i
$994$	2.55713	−	24.3295i	0.0811072	−	0.771684i
$995$	3.73133	+	4.10844i	0.118291	+	0.130246i
$996$	−16.6111	−	21.6574i	−0.526342	−	0.686242i
$997$	−4.86241	−	46.2628i	−0.153994	−	1.46516i	−0.749606	−	0.661884i	$-0.769757\pi$
$997$	−4.86241	−	46.2628i	−0.153994	−	1.46516i	0.595612	−	0.803273i	$-0.296910\pi$
$998$	−10.6523	−	32.7843i	−0.337192	−	1.03777i
$999$	−1.88445	−	24.1395i	−0.0596213	−	0.763739i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	225.2.q.a.106.3	yes	224
3.2	odd	2		675.2.r.a.181.26		224
9.4	even	3	inner	225.2.q.a.31.26	✓	224
9.5	odd	6		675.2.r.a.631.3		224
25.21	even	5	inner	225.2.q.a.196.26	yes	224
75.71	odd	10		675.2.r.a.46.3		224
225.121	even	15	inner	225.2.q.a.121.3	yes	224
225.221	odd	30		675.2.r.a.496.26		224

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
225.2.q.a.31.26	✓	224	9.4	even	3	inner
225.2.q.a.106.3	yes	224	1.1	even	1	trivial
225.2.q.a.121.3	yes	224	225.121	even	15	inner
225.2.q.a.196.26	yes	224	25.21	even	5	inner
675.2.r.a.46.3		224	75.71	odd	10
675.2.r.a.181.26		224	3.2	odd	2
675.2.r.a.496.26		224	225.221	odd	30
675.2.r.a.631.3		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)

\(f(q)\)	\(=\)	\(q+(-2.40744 - 0.511718i) q^{2} +(1.05412 + 1.37435i) q^{3} +(3.70683 + 1.65039i) q^{4} +(1.50334 + 1.65528i) q^{5} +(-1.83444 - 3.84808i) q^{6} +(2.55879 - 4.43196i) q^{7} +(-4.09710 - 2.97672i) q^{8} +(-0.777680 + 2.89745i) q^{9} +O(q^{10})\)	\(q+(-2.40744 - 0.511718i) q^{2} +(1.05412 + 1.37435i) q^{3} +(3.70683 + 1.65039i) q^{4} +(1.50334 + 1.65528i) q^{5} +(-1.83444 - 3.84808i) q^{6} +(2.55879 - 4.43196i) q^{7} +(-4.09710 - 2.97672i) q^{8} +(-0.777680 + 2.89745i) q^{9} +(-2.77218 - 4.75428i) q^{10} +(1.54858 + 0.329161i) q^{11} +(1.63922 + 6.83418i) q^{12} +(-0.872558 + 0.185468i) q^{13} +(-8.42805 + 9.36030i) q^{14} +(-0.690238 + 3.81098i) q^{15} +(2.91012 + 3.23201i) q^{16} +(-3.04259 - 2.21057i) q^{17} +(3.35489 - 6.57749i) q^{18} +(3.69404 + 2.68388i) q^{19} +(2.84079 + 8.61695i) q^{20} +(8.78832 - 1.15512i) q^{21} +(-3.55968 - 1.58487i) q^{22} +(3.66725 - 4.07289i) q^{23} +(-0.227764 - 8.76865i) q^{24} +(-0.479912 + 4.97692i) q^{25} +2.19554 q^{26} +(-4.80188 + 1.98544i) q^{27} +(16.7994 - 12.2055i) q^{28} +(0.00441000 + 0.0419584i) q^{29} +(3.61185 - 8.82151i) q^{30} +(-0.205934 + 1.95934i) q^{31} +(-0.287768 - 0.498429i) q^{32} +(1.18000 + 2.47526i) q^{33} +(6.19366 + 6.87876i) q^{34} +(11.1829 - 2.42724i) q^{35} +(-7.66464 + 9.45688i) q^{36} +(-1.43995 + 4.43171i) q^{37} +(-7.51981 - 8.35159i) q^{38} +(-1.17468 - 1.00370i) q^{39} +(-1.23205 - 11.2569i) q^{40} +(-0.748156 + 0.159025i) q^{41} +(-21.7485 - 1.71626i) q^{42} +(-4.11709 + 7.13101i) q^{43} +(5.19708 + 3.77590i) q^{44} +(-5.96521 + 3.06859i) q^{45} +(-10.9129 + 7.92865i) q^{46} +(-0.426471 - 4.05760i) q^{47} +(-1.37432 + 7.40644i) q^{48} +(-9.59482 - 16.6187i) q^{49} +(3.70214 - 11.7361i) q^{50} +(-0.169142 - 6.51178i) q^{51} +(-3.54052 - 0.752561i) q^{52} +(-2.00012 + 1.45317i) q^{53} +(12.5762 - 2.32263i) q^{54} +(1.78319 + 3.05818i) q^{55} +(-23.6763 + 10.5414i) q^{56} +(0.205358 + 7.90603i) q^{57} +(0.0108540 - 0.103269i) q^{58} +(-9.31606 + 1.98019i) q^{59} +(-8.84819 + 12.9875i) q^{60} +(7.08784 + 1.50657i) q^{61} +(1.49840 - 4.61160i) q^{62} +(10.8514 + 10.8606i) q^{63} +(-2.25016 - 6.92529i) q^{64} +(-1.61876 - 1.16551i) q^{65} +(-1.57414 - 6.56288i) q^{66} +(-0.375946 + 3.57689i) q^{67} +(-7.63006 - 13.2156i) q^{68} +(9.46329 + 0.746785i) q^{69} +(-28.1642 + 0.120956i) q^{70} +(-1.57130 + 1.14162i) q^{71} +(11.8111 - 9.55620i) q^{72} +(-4.42033 - 13.6044i) q^{73} +(5.73438 - 9.93224i) q^{74} +(-7.34591 + 4.58668i) q^{75} +(9.26375 + 16.0453i) q^{76} +(5.42132 - 6.02098i) q^{77} +(2.31435 + 3.01744i) q^{78} +(-0.355789 - 3.38511i) q^{79} +(-0.974982 + 9.67589i) q^{80} +(-7.79043 - 4.50657i) q^{81} +1.88252 q^{82} +(-3.54787 + 1.57961i) q^{83} +(34.4832 + 10.2223i) q^{84} +(-0.914942 - 8.35958i) q^{85} +(13.5607 - 15.0607i) q^{86} +(-0.0530169 + 0.0502899i) q^{87} +(-5.36486 - 5.95828i) q^{88} +(-0.935601 - 2.87948i) q^{89} +(15.9312 - 4.33494i) q^{90} +(-1.41071 + 4.34171i) q^{91} +(20.3157 - 9.04514i) q^{92} +(-2.90989 + 1.78234i) q^{93} +(-1.04964 + 9.98667i) q^{94} +(1.11084 + 10.1495i) q^{95} +(0.381675 - 0.920896i) q^{96} +(0.544048 + 5.17627i) q^{97} +(14.5949 + 44.9184i) q^{98} +(-2.15803 + 4.23095i) 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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