LMFDB - Embedded newform 225.2.q.a.16.10

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			16.10
Character	$\chi$	$=$	225.16
Dual form			225.2.q.a.211.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.16983 + 0.520841i) q^{2} +(1.71766 - 0.222825i) q^{3} +(-0.241041 + 0.267703i) q^{4} +(2.12080 + 0.708681i) q^{5} +(-1.89331 + 1.15529i) q^{6} +(1.38994 - 2.40744i) q^{7} +(0.933960 - 2.87443i) q^{8} +(2.90070 - 0.765476i) q^{9} +O(q^{10})$	\(q+(-1.16983 + 0.520841i) q^{2} +(1.71766 - 0.222825i) q^{3} +(-0.241041 + 0.267703i) q^{4} +(2.12080 + 0.708681i) q^{5} +(-1.89331 + 1.15529i) q^{6} +(1.38994 - 2.40744i) q^{7} +(0.933960 - 2.87443i) q^{8} +(2.90070 - 0.765476i) q^{9} +(-2.85007 + 0.275562i) q^{10} +(-3.72952 + 1.66049i) q^{11} +(-0.354375 + 0.513533i) q^{12} +(1.61140 + 0.717440i) q^{13} +(-0.372093 + 3.54022i) q^{14} +(3.80071 + 0.744704i) q^{15} +(0.329241 + 3.13252i) q^{16} +(-1.70650 + 5.25207i) q^{17} +(-2.99462 + 2.40627i) q^{18} +(2.48610 - 7.65144i) q^{19} +(-0.700915 + 0.396922i) q^{20} +(1.85100 - 4.44487i) q^{21} +(3.49804 - 3.88497i) q^{22} +(-0.403397 + 3.83806i) q^{23} +(0.963727 - 5.14540i) q^{24} +(3.99554 + 3.00593i) q^{25} -2.25873 q^{26} +(4.81184 - 1.96117i) q^{27} +(0.309448 + 0.952382i) q^{28} +(3.00335 + 0.638381i) q^{29} +(-4.83405 + 1.10839i) q^{30} +(-7.56593 + 1.60819i) q^{31} +(1.00566 + 1.74185i) q^{32} +(-6.03603 + 3.68318i) q^{33} +(-0.739181 - 7.03283i) q^{34} +(4.65388 - 4.12067i) q^{35} +(-0.494267 + 0.961037i) q^{36} +(-5.00145 + 3.63377i) q^{37} +(1.07687 + 10.2457i) q^{38} +(2.92769 + 0.873256i) q^{39} +(4.01779 - 5.43420i) q^{40} +(-8.98876 - 4.00205i) q^{41} +(0.149724 + 6.16381i) q^{42} +(1.87556 - 3.24857i) q^{43} +(0.454449 - 1.39865i) q^{44} +(6.69426 + 0.432252i) q^{45} +(-1.52712 - 4.69998i) q^{46} +(-0.343135 - 0.0729356i) q^{47} +(1.26353 + 5.30723i) q^{48} +(-0.363847 - 0.630202i) q^{49} +(-6.23971 - 1.43538i) q^{50} +(-1.76089 + 9.40152i) q^{51} +(-0.580473 + 0.258443i) q^{52} +(-2.83919 - 8.73813i) q^{53} +(-4.60756 + 4.80044i) q^{54} +(-9.08629 + 0.878518i) q^{55} +(-5.62188 - 6.24373i) q^{56} +(2.56534 - 13.6965i) q^{57} +(-3.84589 + 0.817469i) q^{58} +(-10.7721 - 4.79604i) q^{59} +(-1.11549 + 0.837959i) q^{60} +(3.54472 - 1.57821i) q^{61} +(8.01322 - 5.82194i) q^{62} +(2.18895 - 8.04722i) q^{63} +(-7.18012 - 5.21666i) q^{64} +(2.90901 + 2.66351i) q^{65} +(5.14277 - 7.45249i) q^{66} +(-6.62308 + 1.40778i) q^{67} +(-0.994660 - 1.72280i) q^{68} +(0.162320 + 6.68237i) q^{69} +(-3.29802 + 7.24440i) q^{70} +(-1.46059 - 4.49524i) q^{71} +(0.508827 - 9.05278i) q^{72} +(1.59230 + 1.15687i) q^{73} +(3.95822 - 6.85584i) q^{74} +(7.53278 + 4.27286i) q^{75} +(1.44906 + 2.50985i) q^{76} +(-1.18627 + 11.2866i) q^{77} +(-3.87972 + 0.503301i) q^{78} +(-3.83783 - 0.815756i) q^{79} +(-1.52170 + 6.87676i) q^{80} +(7.82809 - 4.44083i) q^{81} +12.5997 q^{82} +(8.05282 + 8.94357i) q^{83} +(0.743740 + 1.56691i) q^{84} +(-7.34118 + 9.92921i) q^{85} +(-0.502096 + 4.77713i) q^{86} +(5.30097 + 0.427298i) q^{87} +(1.28974 + 12.2711i) q^{88} +(-2.09393 - 1.52133i) q^{89} +(-8.05626 + 2.98098i) q^{90} +(3.96693 - 2.88214i) q^{91} +(-0.930227 - 1.03312i) q^{92} +(-12.6373 + 4.44820i) q^{93} +(0.439396 - 0.0933965i) q^{94} +(10.6949 - 14.4653i) q^{95} +(2.11551 + 2.76782i) q^{96} +(-0.0744158 - 0.0158176i) q^{97} +(0.753873 + 0.547721i) q^{98} +(-9.54714 + 7.67143i) 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 $\left(\mathbb{Z}/225\mathbb{Z}\right)^\times$.

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

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.16983	+	0.520841i	−0.827193	+	0.368290i	−0.776261	−	0.630412i	$-0.782886\pi$
$2$	−1.16983	+	0.520841i	−0.827193	+	0.368290i	−0.0509320	+	0.998702i	$0.516219\pi$
$3$	1.71766	−	0.222825i	0.991690	−	0.128648i
$3$	1.71766	−	0.222825i	0.991690	−	0.128648i
$4$	−0.241041	+	0.267703i	−0.120521	+	0.133852i
$5$	2.12080	+	0.708681i	0.948448	+	0.316932i
$5$	2.12080	+	0.708681i	0.948448	+	0.316932i
$6$	−1.89331	+	1.15529i	−0.772939	+	0.471646i
$7$	1.38994	−	2.40744i	0.525347	−	0.909927i	−0.474218	−	0.880408i	$-0.657269\pi$
$7$	1.38994	−	2.40744i	0.525347	−	0.909927i	0.999564	−	0.0295194i	$-0.00939768\pi$
$8$	0.933960	−	2.87443i	0.330205	−	1.01627i
$9$	2.90070	−	0.765476i	0.966899	−	0.255159i
$10$	−2.85007	+	0.275562i	−0.901272	+	0.0871405i
$11$	−3.72952	+	1.66049i	−1.12449	+	0.500656i	−0.882824	−	0.469703i	$-0.844361\pi$
$11$	−3.72952	+	1.66049i	−1.12449	+	0.500656i	−0.241667	+	0.970359i	$0.577694\pi$
$12$	−0.354375	+	0.513533i	−0.102299	+	0.148244i
$13$	1.61140	+	0.717440i	0.446921	+	0.198982i	0.617841	−	0.786303i	$-0.288007\pi$
$13$	1.61140	+	0.717440i	0.446921	+	0.198982i	−0.170920	+	0.985285i	$0.554674\pi$
$14$	−0.372093	+	3.54022i	−0.0994459	+	0.946165i
$15$	3.80071	+	0.744704i	0.981340	+	0.192282i
$16$	0.329241	+	3.13252i	0.0823103	+	0.783130i
$17$	−1.70650	+	5.25207i	−0.413888	+	1.27382i	0.499355	+	0.866398i	$0.333571\pi$
$17$	−1.70650	+	5.25207i	−0.413888	+	1.27382i	−0.913242	+	0.407417i	$0.866429\pi$
$18$	−2.99462	+	2.40627i	−0.705840	+	0.567164i
$19$	2.48610	−	7.65144i	0.570351	−	1.75536i	−0.0811386	−	0.996703i	$-0.525856\pi$
$19$	2.48610	−	7.65144i	0.570351	−	1.75536i	0.651490	−	0.758657i	$-0.274144\pi$
$20$	−0.700915	+	0.396922i	−0.156729	+	0.0887546i
$21$	1.85100	−	4.44487i	0.403921	−	0.969951i
$22$	3.49804	−	3.88497i	0.745784	−	0.828278i
$23$	−0.403397	+	3.83806i	−0.0841141	+	0.800292i	0.868414	+	0.495840i	$0.165140\pi$
$23$	−0.403397	+	3.83806i	−0.0841141	+	0.800292i	−0.952528	+	0.304452i	$0.901527\pi$
$24$	0.963727	−	5.14540i	0.196720	−	1.05030i
$25$	3.99554	+	3.00593i	0.799109	+	0.601187i
$26$	−2.25873			−0.442973
$27$	4.81184	−	1.96117i	0.926039	−	0.377428i
$28$	0.309448	+	0.952382i	0.0584801	+	0.179983i
$29$	3.00335	+	0.638381i	0.557707	+	0.118544i	0.478138	−	0.878285i	$-0.341312\pi$
$29$	3.00335	+	0.638381i	0.557707	+	0.118544i	0.0795697	+	0.996829i	$0.474645\pi$
$30$	−4.83405	+	1.10839i	−0.882572	+	0.202363i
$31$	−7.56593	+	1.60819i	−1.35888	+	0.288839i	−0.829007	−	0.559238i	$-0.811094\pi$
$31$	−7.56593	+	1.60819i	−1.35888	+	0.288839i	−0.529873	+	0.848077i	$0.677761\pi$
$32$	1.00566	+	1.74185i	0.177777	+	0.307919i
$33$	−6.03603	+	3.68318i	−1.05074	+	0.641159i
$34$	−0.739181	−	7.03283i	−0.126768	−	1.20612i
$35$	4.65388	−	4.12067i	0.786649	−	0.696520i
$36$	−0.494267	+	0.961037i	−0.0823778	+	0.160173i
$37$	−5.00145	+	3.63377i	−0.822234	+	0.597388i	−0.917352	−	0.398078i	$-0.869677\pi$
$37$	−5.00145	+	3.63377i	−0.822234	+	0.597388i	0.0951175	+	0.995466i	$0.469677\pi$
$38$	1.07687	+	10.2457i	0.174691	+	1.66208i
$39$	2.92769	+	0.873256i	0.468806	+	0.139833i
$40$	4.01779	−	5.43420i	0.635269	−	0.859223i
$41$	−8.98876	−	4.00205i	−1.40381	−	0.625015i	−0.441570	−	0.897227i	$-0.645578\pi$
$41$	−8.98876	−	4.00205i	−1.40381	−	0.625015i	−0.962238	+	0.272211i	$0.912245\pi$
$42$	0.149724	+	6.16381i	0.0231029	+	0.951096i
$43$	1.87556	−	3.24857i	0.286020	−	0.495402i	−0.686836	−	0.726813i	$-0.741001\pi$
$43$	1.87556	−	3.24857i	0.286020	−	0.495402i	0.972856	+	0.231411i	$0.0743342\pi$
$44$	0.454449	−	1.39865i	0.0685107	−	0.210854i
$45$	6.69426	+	0.432252i	0.997922	+	0.0644362i
$46$	−1.52712	−	4.69998i	−0.225161	−	0.692974i
$47$	−0.343135	−	0.0729356i	−0.0500514	−	0.0106387i	0.182818	−	0.983147i	$-0.441478\pi$
$47$	−0.343135	−	0.0729356i	−0.0500514	−	0.0106387i	−0.232869	+	0.972508i	$0.574811\pi$
$48$	1.26353	+	5.30723i	0.182375	+	0.766033i
$49$	−0.363847	−	0.630202i	−0.0519782	−	0.0900289i
$50$	−6.23971	−	1.43538i	−0.882428	−	0.202993i
$51$	−1.76089	+	9.40152i	−0.246574	+	1.31648i
$52$	−0.580473	+	0.258443i	−0.0804972	+	0.0358397i
$53$	−2.83919	−	8.73813i	−0.389993	−	1.20027i	−0.932793	−	0.360413i	$-0.882636\pi$
$53$	−2.83919	−	8.73813i	−0.389993	−	1.20027i	0.542800	−	0.839862i	$-0.317364\pi$
$54$	−4.60756	+	4.80044i	−0.627010	+	0.653256i
$55$	−9.08629	+	0.878518i	−1.22520	+	0.118459i
$56$	−5.62188	−	6.24373i	−0.751256	−	0.834354i
$57$	2.56534	−	13.6965i	0.339788	−	1.81415i
$58$	−3.84589	+	0.817469i	−0.504990	+	0.107339i
$59$	−10.7721	−	4.79604i	−1.40241	−	0.624391i	−0.440495	−	0.897755i	$-0.645197\pi$
$59$	−10.7721	−	4.79604i	−1.40241	−	0.624391i	−0.961911	+	0.273364i	$0.911864\pi$
$60$	−1.11549	+	0.837959i	−0.144009	+	0.108180i
$61$	3.54472	−	1.57821i	0.453855	−	0.202069i	−0.167061	−	0.985947i	$-0.553428\pi$
$61$	3.54472	−	1.57821i	0.453855	−	0.202069i	0.620916	+	0.783877i	$0.286761\pi$
$62$	8.01322	−	5.82194i	1.01768	−	0.739387i
$63$	2.18895	−	8.04722i	0.275782	−	1.01385i
$64$	−7.18012	−	5.21666i	−0.897515	−	0.652082i
$65$	2.90901	+	2.66351i	0.360818	+	0.330367i
$66$	5.14277	−	7.45249i	0.633031	−	0.917339i
$67$	−6.62308	+	1.40778i	−0.809138	+	0.171988i	−0.593863	−	0.804566i	$-0.702398\pi$
$67$	−6.62308	+	1.40778i	−0.809138	+	0.171988i	−0.215275	+	0.976554i	$0.569065\pi$
$68$	−0.994660	−	1.72280i	−0.120620	−	0.208920i
$69$	0.162320	+	6.68237i	0.0195411	+	0.804463i
$70$	−3.29802	+	7.24440i	−0.394189	+	0.865871i
$71$	−1.46059	−	4.49524i	−0.173340	−	0.533486i	0.826214	−	0.563357i	$-0.190490\pi$
$71$	−1.46059	−	4.49524i	−0.173340	−	0.533486i	−0.999554	+	0.0298707i	$0.990490\pi$
$72$	0.508827	−	9.05278i	0.0599659	−	1.06688i
$73$	1.59230	+	1.15687i	0.186365	+	0.135402i	0.677056	−	0.735932i	$-0.263256\pi$
$73$	1.59230	+	1.15687i	0.186365	+	0.135402i	−0.490691	+	0.871334i	$0.663256\pi$
$74$	3.95822	−	6.85584i	0.460134	−	0.796975i
$75$	7.53278	+	4.27286i	0.869810	+	0.493387i
$76$	1.44906	+	2.50985i	0.166219	+	0.287899i
$77$	−1.18627	+	11.2866i	−0.135187	+	1.28622i
$78$	−3.87972	+	0.503301i	−0.439292	+	0.0569877i
$79$	−3.83783	−	0.815756i	−0.431789	−	0.0917797i	−0.0131106	−	0.999914i	$-0.504173\pi$
$79$	−3.83783	−	0.815756i	−0.431789	−	0.0917797i	−0.418679	+	0.908134i	$0.637507\pi$
$80$	−1.52170	+	6.87676i	−0.170132	+	0.768845i
$81$	7.82809	−	4.44083i	0.869788	−	0.493425i
$82$	12.5997			1.39141
$83$	8.05282	+	8.94357i	0.883912	+	0.981684i	0.999933	−	0.0115627i	$-0.00368061\pi$
$83$	8.05282	+	8.94357i	0.883912	+	0.981684i	−0.116021	+	0.993247i	$0.537014\pi$
$84$	0.743740	+	1.56691i	0.0811487	+	0.170964i
$85$	−7.34118	+	9.92921i	−0.796263	+	1.07697i
$86$	−0.502096	+	4.77713i	−0.0541425	+	0.515131i
$87$	5.30097	+	0.427298i	0.568323	+	0.0458112i
$88$	1.28974	+	12.2711i	0.137487	+	1.30810i
$89$	−2.09393	−	1.52133i	−0.221956	−	0.161260i	0.471251	−	0.881999i	$-0.343803\pi$
$89$	−2.09393	−	1.52133i	−0.221956	−	0.161260i	−0.693207	+	0.720739i	$0.743803\pi$
$90$	−8.05626	+	2.98098i	−0.849205	+	0.314223i
$91$	3.96693	−	2.88214i	0.415847	−	0.302131i
$92$	−0.930227	−	1.03312i	−0.0969829	−	0.107710i
$93$	−12.6373	+	4.44820i	−1.31043	+	0.461256i
$94$	0.439396	−	0.0933965i	0.0453202	−	0.00963312i
$95$	10.6949	−	14.4653i	1.09728	−	1.48411i
$96$	2.11551	+	2.76782i	0.215913	+	0.282490i
$97$	−0.0744158	−	0.0158176i	−0.00755578	−	0.00160603i	0.204132	−	0.978943i	$-0.434563\pi$
$97$	−0.0744158	−	0.0158176i	−0.00755578	−	0.00160603i	−0.211688	+	0.977337i	$0.567896\pi$
$98$	0.753873	+	0.547721i	0.0761527	+	0.0553282i
$99$	−9.54714	+	7.67143i	−0.959523	+	0.771007i
$100$	−1.76779	+	0.345067i	−0.176779	+	0.0345067i
$101$	2.68749	−	4.65486i	0.267415	−	0.463176i	−0.700779	−	0.713379i	$-0.747164\pi$
$101$	2.68749	−	4.65486i	0.267415	−	0.463176i	0.968193	+	0.250203i	$0.0804972\pi$
$102$	−2.83675	−	11.9153i	−0.280880	−	1.17979i
$103$	4.32876	−	4.80758i	0.426526	−	0.473705i	−0.491127	−	0.871088i	$-0.663415\pi$
$103$	4.32876	−	4.80758i	0.426526	−	0.473705i	0.917653	+	0.397383i	$0.130082\pi$
$104$	3.56721	−	3.96179i	0.349794	−	0.388485i
$105$	7.07558	−	8.11490i	0.690506	−	0.791933i
$106$	7.87254	+	8.74334i	0.764648	+	0.849228i
$107$	5.75730			0.556579			0.278289	−	0.960497i	$-0.410233\pi$
$107$	5.75730			0.556579			0.278289	+	0.960497i	$0.410233\pi$
$108$	−0.634838	+	1.76087i	−0.0610873	+	0.169440i
$109$	−6.85039	+	4.97710i	−0.656149	+	0.476720i	−0.865360	−	0.501151i	$-0.832910\pi$
$109$	−6.85039	+	4.97710i	−0.656149	+	0.476720i	0.209211	+	0.977870i	$0.432910\pi$
$110$	10.1718	−	5.76022i	0.969845	−	0.549216i
$111$	−7.78109	+	7.35602i	−0.738549	+	0.698203i
$112$	7.99898	+	3.56137i	0.755832	+	0.336518i
$113$	2.18503	+	0.972840i	0.205551	+	0.0915171i	0.506930	−	0.861987i	$-0.330780\pi$
$113$	2.18503	+	0.972840i	0.205551	+	0.0915171i	−0.301379	+	0.953504i	$0.597447\pi$
$114$	4.13270	+	17.3587i	0.387063	+	1.62579i
$115$	−3.57548	+	7.85387i	−0.333416	+	0.732377i
$116$	−0.894826	+	0.650129i	−0.0830825	+	0.0603630i
$117$	5.22336	+	0.847592i	0.482899	+	0.0783599i
$118$	15.0994			1.39002
$119$	10.2721	+	11.4084i	0.941644	+	1.04580i
$120$	5.69031	−	10.2294i	0.519452	−	0.933809i
$121$	3.79163	−	4.21104i	0.344694	−	0.382822i
$122$	−3.32471	+	3.69247i	−0.301005	+	0.334300i
$123$	−16.3314	−	4.87123i	−1.47255	−	0.439224i
$124$	1.39318	−	2.41306i	0.125111	−	0.216699i
$125$	6.34348	+	9.20653i	0.567378	+	0.823457i
$126$	1.63063	+	10.5539i	0.145268	+	0.940220i
$127$	0.560712	+	0.407381i	0.0497551	+	0.0361492i	0.612385	−	0.790560i	$-0.290210\pi$
$127$	0.560712	+	0.407381i	0.0497551	+	0.0361492i	−0.562630	+	0.826709i	$0.690210\pi$
$128$	7.18181	+	1.52654i	0.634788	+	0.134928i
$129$	2.49771	−	5.99785i	0.219911	−	0.528081i
$130$	−4.79030	−	1.60072i	−0.420137	−	0.140392i
$131$	5.48003	−	1.16482i	0.478792	−	0.101770i	0.0378076	−	0.999285i	$-0.487963\pi$
$131$	5.48003	−	1.16482i	0.478792	−	0.101770i	0.440985	+	0.897515i	$0.354629\pi$
$132$	0.468933	−	2.50366i	0.0408154	−	0.217916i
$133$	−14.9649	−	16.6202i	−1.29762	−	1.44115i
$134$	7.01463	−	5.09643i	0.605972	−	0.440264i
$135$	11.5948	−	0.749191i	0.997919	−	0.0644801i
$136$	13.5029	+	9.81045i	1.15787	+	0.841239i
$137$	0.544353	+	5.17917i	0.0465072	+	0.442486i	0.992854	+	0.119334i	$0.0380759\pi$
$137$	0.544353	+	5.17917i	0.0465072	+	0.442486i	−0.946347	+	0.323152i	$0.895257\pi$
$138$	−3.67034	−	7.73267i	−0.312440	−	0.658249i
$139$	−1.28216	+	12.1990i	−0.108752	+	1.03470i	0.794989	+	0.606623i	$0.207476\pi$
$139$	−1.28216	+	12.1990i	−0.108752	+	1.03470i	−0.903741	+	0.428079i	$0.859190\pi$
$140$	−0.0186596	+	2.23911i	−0.00157702	+	0.189239i
$141$	−0.605640	−	0.0488192i	−0.0510041	−	0.00411132i
$142$	4.04994	+	4.49791i	0.339863	+	0.377457i
$143$	−7.20103			−0.602180
$144$	3.35290	+	8.83447i	0.279408	+	0.736205i
$145$	5.91707	+	3.48229i	0.491386	+	0.289188i
$146$	−2.46526	−	0.524008i	−0.204027	−	0.0433672i
$147$	−0.765390	−	1.00140i	−0.0631283	−	0.0825939i
$148$	0.232784	−	2.21479i	0.0191347	−	0.182055i
$149$	−1.22686	−	2.12499i	−0.100508	−	0.174086i	0.811386	−	0.584511i	$-0.198714\pi$
$149$	−1.22686	−	2.12499i	−0.100508	−	0.174086i	−0.911894	+	0.410425i	$0.865380\pi$
$150$	−11.0375	−	1.07513i	−0.901210	−	0.0877838i
$151$	2.75815	−	4.77726i	0.224455	−	0.388768i	−0.731700	−	0.681626i	$-0.761273\pi$
$151$	2.75815	−	4.77726i	0.224455	−	0.388768i	0.956156	+	0.292858i	$0.0946063\pi$
$152$	−19.6716	−	14.2923i	−1.59558	−	1.15926i
$153$	−0.929713	+	16.5410i	−0.0751628	+	1.33726i
$154$	−4.49077	−	13.8212i	−0.361877	−	1.11374i
$155$	−17.1855	−	1.95119i	−1.38037	−	0.156723i
$156$	−0.939467	+	0.573262i	−0.0752176	+	0.0458977i
$157$	3.31278	+	5.73791i	0.264389	+	0.457935i	0.967403	−	0.253241i	$-0.0814964\pi$
$157$	3.31278	+	5.73791i	0.264389	+	0.457935i	−0.703014	+	0.711176i	$0.748163\pi$
$158$	4.91447	−	1.04460i	0.390974	−	0.0831042i
$159$	−6.82384	−	14.3765i	−0.541166	−	1.14013i
$160$	0.898380	+	4.40680i	0.0710232	+	0.348389i
$161$	8.67922	+	6.30582i	0.684018	+	0.496968i
$162$	−6.84455	+	9.27219i	−0.537759	+	0.728492i
$163$	12.9210	−	9.38766i	1.01205	−	0.735298i	0.0474126	−	0.998875i	$-0.484902\pi$
$163$	12.9210	−	9.38766i	1.01205	−	0.735298i	0.964638	+	0.263577i	$0.0849024\pi$
$164$	3.23802	−	1.44166i	0.252847	−	0.112575i
$165$	−15.4114	+	3.53365i	−1.19978	+	0.275094i
$166$	−14.0786	−	6.26819i	−1.09271	−	0.486506i
$167$	−7.78229	+	1.65418i	−0.602212	+	0.128004i	−0.498922	−	0.866647i	$-0.666270\pi$
$167$	−7.78229	+	1.65418i	−0.602212	+	0.128004i	−0.103290	+	0.994651i	$0.532937\pi$
$168$	−11.0477	−	9.47190i	−0.852351	−	0.730773i
$169$	−6.61682	−	7.34872i	−0.508986	−	0.565286i
$170$	3.41638	−	15.4390i	0.262025	−	1.18412i
$171$	1.35444	−	24.0976i	0.103577	−	1.84279i
$172$	0.417564	+	1.28513i	0.0318390	+	0.0979903i
$173$	−5.70311	+	2.53919i	−0.433599	+	0.193051i	−0.611917	−	0.790922i	$-0.709601\pi$
$173$	−5.70311	+	2.53919i	−0.433599	+	0.193051i	0.178317	+	0.983973i	$0.442935\pi$
$174$	−6.42377	+	2.26109i	−0.486985	+	0.171413i
$175$	12.7902	−	5.44098i	0.966845	−	0.411299i
$176$	−6.42942	−	11.1361i	−0.484636	−	0.839414i
$177$	−19.5714	−	5.83766i	−1.47108	−	0.438786i
$178$	3.24190	+	0.689087i	0.242991	+	0.0516492i
$179$	4.57781	+	14.0890i	0.342161	+	1.05306i	0.963086	+	0.269194i	$0.0867573\pi$
$179$	4.57781	+	14.0890i	0.342161	+	1.05306i	−0.620925	+	0.783870i	$0.713243\pi$
$180$	−1.72931	+	1.68789i	−0.128895	+	0.125808i
$181$	−7.23295	+	22.2607i	−0.537621	+	1.65463i	0.200297	+	0.979735i	$0.435809\pi$
$181$	−7.23295	+	22.2607i	−0.537621	+	1.65463i	−0.737917	+	0.674891i	$0.764191\pi$
$182$	−3.13949	+	5.43775i	−0.232714	+	0.403073i
$183$	5.73695	−	3.50068i	0.424088	−	0.258778i
$184$	10.6555	+	4.74414i	0.785534	+	0.349742i
$185$	−13.1822	+	4.16205i	−0.969178	+	0.306000i
$186$	12.4667	−	11.7857i	0.914102	−	0.864166i
$187$	−2.35658	−	22.4213i	−0.172330	−	1.63961i
$188$	0.102235	−	0.0742778i	0.00745623	−	0.00541727i
$189$	1.96674	−	14.3101i	0.143059	−	1.04091i
$190$	−4.97713	+	22.4922i	−0.361079	+	1.63176i
$191$	−1.53450	−	14.5998i	−0.111032	−	1.05640i	−0.898177	−	0.439634i	$-0.855108\pi$
$191$	−1.53450	−	14.5998i	−0.111032	−	1.05640i	0.787145	−	0.616769i	$-0.211559\pi$
$192$	−13.4954	−	7.36053i	−0.973946	−	0.531200i
$193$	1.55719	+	2.69714i	0.112089	+	0.194144i	0.916612	−	0.399777i	$-0.130912\pi$
$193$	1.55719	+	2.69714i	0.112089	+	0.194144i	−0.804523	+	0.593921i	$0.797579\pi$
$194$	0.0952921	−	0.0202550i	0.00684157	−	0.00145422i
$195$	5.59017	+	3.92680i	0.400321	+	0.281204i
$196$	0.256409	+	0.0545015i	0.0183149	+	0.00389296i
$197$	0.0685498	+	0.210975i	0.00488397	+	0.0150313i	0.953469	−	0.301492i	$-0.0974846\pi$
$197$	0.0685498	+	0.210975i	0.00488397	+	0.0150313i	−0.948585	+	0.316523i	$0.897485\pi$
$198$	7.17291	−	13.9468i	0.509756	−	0.991154i
$199$	6.14533			0.435631			0.217815	−	0.975990i	$-0.430107\pi$
$199$	6.14533			0.435631			0.217815	+	0.975990i	$0.430107\pi$
$200$	12.3720	−	8.67750i	0.874834	−	0.613592i
$201$	−11.0625	+	3.89387i	−0.780289	+	0.274653i
$202$	−0.719453	+	6.84514i	−0.0506205	+	0.481622i
$203$	5.71132	−	6.34307i	0.400856	−	0.445196i
$204$	−2.09237	−	2.73755i	−0.146495	−	0.191667i
$205$	−16.2271	−	14.8577i	−1.13335	−	1.03771i
$206$	−2.55992	+	7.87863i	−0.178358	+	0.548930i
$207$	1.76781	+	11.4419i	0.122871	+	0.795264i
$208$	−1.71686	+	5.28394i	−0.119043	+	0.366375i
$209$	3.43316	+	32.6643i	0.237476	+	2.25944i
$210$	−4.05064	+	13.1783i	−0.279520	+	0.909387i
$211$	−2.10709	+	20.0476i	−0.145058	+	1.38014i	0.643627	+	0.765339i	$0.277429\pi$
$211$	−2.10709	+	20.0476i	−0.145058	+	1.38014i	−0.788685	+	0.614797i	$0.789238\pi$
$212$	3.02359	+	1.34619i	0.207661	+	0.0924566i
$213$	−3.51045	−	7.39582i	−0.240532	−	0.506753i
$214$	−6.73504	+	2.99863i	−0.460398	+	0.204982i
$215$	6.27988	−	5.56037i	0.428284	−	0.379214i
$216$	−1.14320	−	15.6630i	−0.0777848	−	1.06573i
$217$	−6.64454	+	20.4498i	−0.451061	+	1.38822i
$218$	5.42150	−	9.39031i	0.367190	−	0.635992i
$219$	2.99281	+	1.63231i	0.202235	+	0.110301i
$220$	1.95499	−	2.64419i	0.131805	−	0.178271i
$221$	−6.51790	+	7.23886i	−0.438441	+	0.486938i
$222$	5.27122	−	12.6580i	0.353781	−	0.849548i
$223$	10.6275	−	4.73168i	0.711672	−	0.316857i	−0.0187775	−	0.999824i	$-0.505977\pi$
$223$	10.6275	−	4.73168i	0.711672	−	0.316857i	0.730449	+	0.682967i	$0.239311\pi$
$224$	5.59121			0.373579
$225$	13.8908	+	5.66081i	0.926055	+	0.377387i
$226$	−3.06281			−0.203735
$227$	1.58999	−	0.707911i	0.105532	−	0.0469857i	−0.353292	−	0.935513i	$-0.614938\pi$
$227$	1.58999	−	0.707911i	0.105532	−	0.0469857i	0.458823	+	0.888527i	$0.348271\pi$
$228$	3.04825	+	3.98817i	0.201875	+	0.264123i
$229$	2.56118	−	2.84448i	0.169247	−	0.187968i	−0.652554	−	0.757742i	$-0.726302\pi$
$229$	2.56118	−	2.84448i	0.169247	−	0.187968i	0.821802	+	0.569774i	$0.192969\pi$
$230$	0.0920844	−	11.0499i	0.00607187	−	0.728610i
$231$	0.477334	+	19.6508i	0.0314063	+	1.29293i
$232$	4.63999	−	8.03669i	0.304630	−	0.527635i
$233$	−0.641036	+	1.97290i	−0.0419956	+	0.129249i	−0.969856	−	0.243678i	$-0.921646\pi$
$233$	−0.641036	+	1.97290i	−0.0419956	+	0.129249i	0.927861	+	0.372927i	$0.121646\pi$
$234$	−6.55188	+	1.72900i	−0.428310	+	0.113028i
$235$	−0.676031	−	0.397854i	−0.0440994	−	0.0259532i
$236$	3.88043	−	1.72768i	0.252594	−	0.112462i
$237$	−6.77385	−	0.546024i	−0.440009	−	0.0354680i
$238$	−17.9585	−	7.99566i	−1.16408	−	0.518282i
$239$	2.73653	−	26.0363i	0.177011	−	1.68415i	−0.440629	−	0.897689i	$-0.645245\pi$
$239$	2.73653	−	26.0363i	0.177011	−	1.68415i	0.617640	−	0.786461i	$-0.288089\pi$
$240$	−1.08145	+	12.1510i	−0.0698072	+	0.784343i
$241$	2.58033	+	24.5502i	0.166214	+	1.58142i	0.686310	+	0.727309i	$0.259229\pi$
$241$	2.58033	+	24.5502i	0.166214	+	1.58142i	−0.520097	+	0.854107i	$0.674104\pi$
$242$	−2.24228	+	6.90102i	−0.144139	+	0.443614i
$243$	12.4565	−	9.37212i	0.799082	−	0.601222i
$244$	−0.431931	+	1.32935i	−0.0276515	+	0.0851027i
$245$	−0.325034	−	1.59438i	−0.0207656	−	0.101861i
$246$	21.6420	−	2.80754i	1.37984	−	0.179002i
$247$	9.49554	−	10.5459i	0.604187	−	0.671017i
$248$	−2.44365	+	23.2497i	−0.155172	+	1.47636i
$249$	15.8249	+	13.5676i	1.00286	+	0.859813i
$250$	−12.2159	−	7.46611i	−0.772602	−	0.472198i
$251$	−19.5268			−1.23252			−0.616262	−	0.787542i	$-0.711354\pi$
$251$	−19.5268			−1.23252			−0.616262	+	0.787542i	$0.711354\pi$
$252$	1.62664	+	2.52570i	0.102469	+	0.159104i
$253$	−4.86858	−	14.9840i	−0.306085	−	0.942034i
$254$	−0.868116	−	0.184524i	−0.0544704	−	0.0115780i
$255$	−10.3972	+	18.6908i	−0.651096	+	1.17046i
$256$	8.16578	−	1.73569i	0.510361	−	0.108481i
$257$	10.9988	+	19.0506i	0.686089	+	1.18834i	0.973093	+	0.230411i	$0.0740072\pi$
$257$	10.9988	+	19.0506i	0.686089	+	1.18834i	−0.287004	+	0.957929i	$0.592659\pi$
$258$	0.202035	+	8.31735i	0.0125782	+	0.517816i
$259$	1.79638	+	17.0914i	0.111622	+	1.06201i
$260$	−1.41422	+	0.136735i	−0.0877061	+	0.00847996i
$261$	9.20046	−	0.447238i	0.569494	−	0.0276833i
$262$	−5.80400	+	4.21685i	−0.358572	+	0.260518i
$263$	−1.62985	−	15.5070i	−0.100501	−	0.956201i	−0.922313	−	0.386443i	$-0.873704\pi$
$263$	−1.62985	−	15.5070i	−0.100501	−	0.956201i	0.821813	−	0.569758i	$-0.192963\pi$
$264$	4.94964	+	20.7901i	0.304629	+	1.27954i
$265$	0.171202	−	20.5439i	0.0105169	−	1.26200i
$266$	26.1627	+	11.6484i	1.60414	+	0.714210i
$267$	−3.93564	−	2.14654i	−0.240857	−	0.131366i
$268$	1.21957	−	2.11235i	0.0744969	−	0.129032i
$269$	5.15923	−	15.8785i	0.314564	−	0.968127i	−0.661370	−	0.750060i	$-0.730025\pi$
$269$	5.15923	−	15.8785i	0.314564	−	0.968127i	0.975934	−	0.218067i	$-0.0699753\pi$
$270$	−13.1737	+	6.91545i	−0.801724	+	0.420861i
$271$	−6.30794	−	19.4138i	−0.383180	−	1.17931i	−0.937792	−	0.347197i	$-0.887133\pi$
$271$	−6.30794	−	19.4138i	−0.383180	−	1.17931i	0.554612	−	0.832109i	$-0.312867\pi$
$272$	−17.0141	−	3.61645i	−1.03163	−	0.219280i
$273$	6.17162	−	5.83447i	0.373523	−	0.353118i
$274$	−3.33432	−	5.77521i	−0.201434	−	0.348893i
$275$	−19.8928	−	4.57612i	−1.19958	−	0.275951i
$276$	−1.82802	−	1.56727i	−0.110034	−	0.0943387i
$277$	3.29047	−	1.46501i	0.197705	−	0.0880239i	−0.305496	−	0.952193i	$-0.598822\pi$
$277$	3.29047	−	1.46501i	0.197705	−	0.0880239i	0.503201	+	0.864169i	$0.332156\pi$
$278$	−4.85381	−	14.9385i	−0.291112	−	0.895951i
$279$	−20.7154	+	10.4564i	−1.24020	+	0.626008i
$280$	−7.49805	−	17.2258i	−0.448094	−	1.02944i
$281$	−0.828322	−	0.919945i	−0.0494136	−	0.0548793i	0.717931	−	0.696114i	$-0.245089\pi$
$281$	−0.828322	−	0.919945i	−0.0494136	−	0.0548793i	−0.767345	+	0.641235i	$0.778423\pi$
$282$	0.733921	−	0.258332i	0.0437044	−	0.0153834i
$283$	12.8466	−	2.73064i	0.763653	−	0.162319i	0.190410	−	0.981705i	$-0.439018\pi$
$283$	12.8466	−	2.73064i	0.763653	−	0.162319i	0.573243	+	0.819385i	$0.305685\pi$
$284$	1.55545	+	0.692532i	0.0922991	+	0.0410942i
$285$	15.1470	−	27.2295i	0.897232	−	1.61294i
$286$	8.42396	−	3.75059i	0.498119	−	0.221777i
$287$	−22.1285	+	16.0773i	−1.30620	+	0.949013i
$288$	4.25046	+	4.28278i	0.250461	+	0.252365i
$289$	−10.9188	−	7.93300i	−0.642285	−	0.466647i
$290$	−8.73567	−	0.991823i	−0.512976	−	0.0582418i
$291$	−0.131345	−	0.0105874i	−0.00769961	−	0.000620647i
$292$	−0.693508	+	0.147410i	−0.0405845	+	0.00862650i
$293$	−0.196240	−	0.339898i	−0.0114645	−	0.0198571i	0.860236	−	0.509896i	$-0.170316\pi$
$293$	−0.196240	−	0.339898i	−0.0114645	−	0.0198571i	−0.871701	+	0.490039i	$0.836983\pi$
$294$	1.41694	+	0.772815i	0.0826378	+	0.0450715i
$295$	−19.4465	−	17.8054i	−1.13222	−	1.03667i
$296$	5.77387	+	17.7701i	0.335599	+	1.03287i
$297$	−14.6893	+	15.3042i	−0.852361	+	0.888041i
$298$	2.54199	+	1.84687i	0.147254	+	0.106986i
$299$	−3.40361	+	5.89523i	−0.196836	+	0.340930i
$300$	−2.95956	+	0.986614i	−0.170871	+	0.0569622i
$301$	−5.21382	−	9.03060i	−0.300520	−	0.520515i
$302$	−0.738371	+	7.02513i	−0.0424885	+	0.404251i
$303$	3.57896	−	8.59430i	0.205606	−	0.493730i
$304$	24.7868	+	5.26860i	1.42162	+	0.302175i
$305$	8.63607	−	0.834988i	0.494500	−	0.0478113i
$306$	−7.52760	−	19.8343i	−0.430324	−	1.13385i
$307$	−5.56125			−0.317397			−0.158699	−	0.987327i	$-0.550730\pi$
$307$	−5.56125			−0.317397			−0.158699	+	0.987327i	$0.550730\pi$
$308$	−2.73551	−	3.03809i	−0.155870	−	0.173111i
$309$	6.36408	−	9.22233i	0.362040	−	0.524640i
$310$	21.1203	−	6.66834i	1.19955	−	0.378736i
$311$	0.406248	−	3.86519i	0.0230362	−	0.219175i	−0.976948	−	0.213479i	$-0.931520\pi$
$311$	0.406248	−	3.86519i	0.0230362	−	0.219175i	0.999984	−	0.00569549i	$-0.00181294\pi$
$312$	5.24446	−	7.59986i	0.296909	−	0.430258i
$313$	3.00956	+	28.6340i	0.170110	+	1.61849i	0.663152	+	0.748484i	$0.269218\pi$
$313$	3.00956	+	28.6340i	0.170110	+	1.61849i	−0.493042	+	0.870005i	$0.664115\pi$
$314$	−6.86392	−	4.98693i	−0.387353	−	0.281429i
$315$	10.3452	−	15.5152i	0.582887	−	0.874185i
$316$	1.14345	−	0.830768i	0.0643243	−	0.0467344i
$317$	5.54854	+	6.16227i	0.311637	+	0.346108i	0.878533	−	0.477681i	$-0.158523\pi$
$317$	5.54854	+	6.16227i	0.311637	+	0.346108i	−0.566896	+	0.823789i	$0.691856\pi$
$318$	15.4706	+	13.2639i	0.867546	+	0.743800i
$319$	−12.2610	+	2.60617i	−0.686487	+	0.145917i
$320$	−11.5306	−	16.1519i	−0.644581	−	0.902917i
$321$	9.88906	−	1.28287i	0.551954	−	0.0716029i
$322$	−13.4375	−	2.85623i	−0.748843	−	0.159172i
$323$	35.9434	+	26.1144i	1.99994	+	1.45304i
$324$	−0.698069	+	3.16603i	−0.0387816	+	0.175890i
$325$	4.28183	+	7.71031i	0.237513	+	0.427691i
$326$	−10.2259	+	17.7117i	−0.566358	+	0.980961i
$327$	−10.6576	+	10.0754i	−0.589367	+	0.557171i
$328$	−19.8988	+	22.0998i	−1.09873	+	1.22026i
$329$	−0.652524	+	0.724701i	−0.0359748	+	0.0399541i
$330$	16.1882	−	12.1606i	0.891131	−	0.669421i
$331$	10.8411	+	12.0403i	0.595882	+	0.661794i	0.963352	−	0.268242i	$-0.0864425\pi$
$331$	10.8411	+	12.0403i	0.595882	+	0.661794i	−0.367470	+	0.930035i	$0.619776\pi$
$332$	−4.33528			−0.237930
$333$	−11.7261	+	14.3690i	−0.642589	+	0.787414i
$334$	8.24237	−	5.98843i	0.451003	−	0.327673i
$335$	−15.0439	−	1.70804i	−0.821934	−	0.0933201i
$336$	14.5331	+	4.33485i	0.792844	+	0.236485i
$337$	15.9058	+	7.08173i	0.866445	+	0.385766i	0.791316	−	0.611408i	$-0.209396\pi$
$337$	15.9058	+	7.08173i	0.866445	+	0.385766i	0.0751293	+	0.997174i	$0.476063\pi$
$338$	11.5680	+	5.15043i	0.629219	+	0.280146i
$339$	3.96991	+	1.18413i	0.215616	+	0.0643129i
$340$	−0.888554	−	4.35860i	−0.0481886	−	0.236379i
$341$	25.5469	−	18.5609i	1.38344	−	1.00513i
$342$	10.9665	+	28.8954i	0.593001	+	1.56249i
$343$	17.4362			0.941467
$344$	−7.58609	−	8.42520i	−0.409014	−	0.454257i
$345$	−4.39142	+	14.2870i	−0.236426	+	0.769185i
$346$	5.34914	−	5.94082i	0.287571	−	0.319380i
$347$	13.3243	−	14.7981i	0.715287	−	0.794406i	−0.270444	−	0.962736i	$-0.587171\pi$
$347$	13.3243	−	14.7981i	0.715287	−	0.794406i	0.985731	+	0.168329i	$0.0538372\pi$
$348$	−1.39214	+	1.31609i	−0.0746265	+	0.0705498i
$349$	−4.68392	+	8.11279i	−0.250724	+	0.434268i	−0.963725	−	0.266895i	$-0.914002\pi$
$349$	−4.68392	+	8.11279i	−0.250724	+	0.434268i	0.713001	+	0.701163i	$0.247335\pi$
$350$	−12.1284	+	13.0266i	−0.648290	+	0.696303i
$351$	9.16080	+	0.291976i	0.488967	+	0.0155845i
$352$	−6.64295	−	4.82638i	−0.354070	−	0.257247i
$353$	17.1619	+	3.64788i	0.913438	+	0.194157i	0.640575	−	0.767896i	$-0.278696\pi$
$353$	17.1619	+	3.64788i	0.913438	+	0.194157i	0.272863	+	0.962053i	$0.412029\pi$
$354$	25.9357	−	3.36454i	1.37847	−	0.178823i
$355$	0.0880730	−	10.5686i	0.00467443	−	0.560921i
$356$	0.911986	−	0.193849i	0.0483351	−	0.0102740i
$357$	20.1861	+	17.3068i	1.06836	+	0.915971i
$358$	−12.6934	−	14.0974i	−0.670866	−	0.745072i
$359$	0.187026	−	0.135882i	0.00987085	−	0.00717159i	−0.582839	−	0.812588i	$-0.698058\pi$
$359$	0.187026	−	0.135882i	0.00987085	−	0.00717159i	0.592710	+	0.805416i	$0.298058\pi$
$360$	7.49465	−	18.8385i	0.395003	−	0.992876i
$361$	−36.9925	−	26.8766i	−1.94697	−	1.41456i
$362$	−3.13299	−	29.8084i	−0.164666	−	1.56669i
$363$	5.57441	−	8.07799i	0.292580	−	0.423985i
$364$	−0.184634	+	1.75668i	−0.00967745	+	0.0920748i
$365$	2.55709	+	3.58192i	0.133844	+	0.187486i
$366$	−4.88794	+	7.08323i	−0.255497	+	0.370246i
$367$	8.64380	+	9.59991i	0.451203	+	0.501111i	0.925234	−	0.379397i	$-0.123868\pi$
$367$	8.64380	+	9.59991i	0.451203	+	0.501111i	−0.474031	+	0.880508i	$0.657202\pi$
$368$	−12.1556			−0.633656
$369$	−29.1371	−	4.72807i	−1.51682	−	0.246134i
$370$	13.2532	−	11.7347i	0.689000	−	0.610059i
$371$	−24.9828	−	5.31027i	−1.29704	−	0.275695i
$372$	1.85532	−	4.45525i	0.0961938	−	0.230994i
$373$	3.65381	−	34.7637i	0.189187	−	1.80000i	−0.328583	−	0.944475i	$-0.606571\pi$
$373$	3.65381	−	34.7637i	0.189187	−	1.80000i	0.517770	−	0.855520i	$-0.326762\pi$
$374$	14.4347	+	25.0017i	0.746401	+	1.29281i
$375$	12.9474	+	14.4002i	0.668600	+	0.743622i
$376$	−0.530122	+	0.918199i	−0.0273390	+	0.0473525i
$377$	4.38158	+	3.18340i	0.225663	+	0.163954i
$378$	5.15255	+	17.7647i	0.265018	+	0.913719i
$379$	5.46807	+	16.8290i	0.280876	+	0.864448i	0.987605	+	0.156963i	$0.0501702\pi$
$379$	5.46807	+	16.8290i	0.280876	+	0.864448i	−0.706728	+	0.707485i	$0.749830\pi$
$380$	1.29448	+	6.34980i	0.0664055	+	0.325738i
$381$	1.05389	+	0.574800i	0.0539922	+	0.0294479i
$382$	9.39925	+	16.2800i	0.480908	+	0.832956i
$383$	−26.9136	+	5.72065i	−1.37522	+	0.292312i	−0.835480	−	0.549521i	$-0.814810\pi$
$383$	−26.9136	+	5.72065i	−1.37522	+	0.292312i	−0.539739	+	0.841833i	$0.681477\pi$
$384$	12.6760	+	1.02179i	0.646872	+	0.0521428i
$385$	−10.5144	+	23.0958i	−0.535863	+	1.17707i
$386$	−3.22643	−	2.34414i	−0.164221	−	0.119313i
$387$	2.95374	−	10.8588i	0.150147	−	0.551984i
$388$	0.0221717	−	0.0161087i	0.00112560	−	0.000817794i
$389$	3.19923	−	1.42439i	0.162207	−	0.0722193i	−0.324027	−	0.946048i	$-0.605037\pi$
$389$	3.19923	−	1.42439i	0.162207	−	0.0722193i	0.486234	+	0.873829i	$0.338370\pi$
$390$	−8.58477	−	1.68208i	−0.434707	−	0.0851755i
$391$	−19.4694	−	8.66834i	−0.984610	−	0.438377i
$392$	−2.15129	+	0.457271i	−0.108657	+	0.0230957i
$393$	9.15326	−	3.22184i	0.461721	−	0.162521i
$394$	−0.190076	−	0.211100i	−0.00957587	−	0.0106351i
$395$	−7.56114	−	4.44984i	−0.380442	−	0.223896i
$396$	0.247586	−	4.40493i	0.0124417	−	0.221356i
$397$	3.68101	+	11.3290i	0.184745	+	0.568586i	0.999944	−	0.0105951i	$-0.00337259\pi$
$397$	3.68101	+	11.3290i	0.184745	+	0.568586i	−0.815199	+	0.579181i	$0.803373\pi$
$398$	−7.18897	+	3.20074i	−0.360350	+	0.160438i
$399$	−29.4079	−	25.2132i	−1.47224	−	1.26224i
$400$	−8.10065	+	13.5058i	−0.405032	+	0.675290i
$401$	−7.08207	−	12.2665i	−0.353661	−	0.612560i	0.633226	−	0.773967i	$-0.281730\pi$
$401$	−7.08207	−	12.2665i	−0.353661	−	0.612560i	−0.986888	+	0.161407i	$0.948397\pi$
$402$	10.9131	−	10.3170i	0.544297	−	0.514563i
$403$	−13.3455	−	2.83667i	−0.664786	−	0.141305i
$404$	0.598327	+	1.84146i	0.0297679	+	0.0916161i
$405$	19.7489	−	3.87046i	0.981331	−	0.192325i
$406$	−3.37753	+	10.3950i	−0.167624	+	0.515894i
$407$	12.6192	−	21.8571i	0.625509	−	1.08341i
$408$	25.3794	+	13.8422i	1.25647	+	0.685291i
$409$	1.73143	+	0.770882i	0.0856136	+	0.0381176i	0.449097	−	0.893483i	$-0.351746\pi$
$409$	1.73143	+	0.770882i	0.0856136	+	0.0381176i	−0.363483	+	0.931601i	$0.618413\pi$
$410$	26.7214	+	8.92918i	1.31968	+	0.440981i
$411$	2.08906	+	8.77475i	0.103046	+	0.432826i
$412$	0.243594	+	2.31765i	0.0120010	+	0.114182i
$413$	−26.5187	+	19.2670i	−1.30490	+	0.948065i
$414$	−8.02742	−	12.4642i	−0.394526	−	0.612584i
$415$	10.7403	+	24.6744i	0.527218	+	1.21122i
$416$	0.370841	+	3.52832i	0.0181820	+	0.172990i
$417$	0.515922	+	21.2393i	0.0252648	+	1.04010i
$418$	−21.0291	−	36.4235i	−1.02857	−	1.78153i
$419$	23.4165	−	4.97733i	1.14397	−	0.243159i	0.403327	−	0.915056i	$-0.367854\pi$
$419$	23.4165	−	4.97733i	1.14397	−	0.243159i	0.740644	+	0.671897i	$0.234520\pi$
$420$	0.466879	+	3.85018i	0.0227814	+	0.187869i
$421$	−8.69537	−	1.84826i	−0.423787	−	0.0900786i	−0.00891857	−	0.999960i	$-0.502839\pi$
$421$	−8.69537	−	1.84826i	−0.423787	−	0.0900786i	−0.414868	+	0.909882i	$0.636172\pi$
$422$	−7.97669	−	24.5497i	−0.388299	−	1.19506i
$423$	−1.05116	+	0.0510973i	−0.0511092	+	0.00248444i
$424$	−27.7689			−1.34858
$425$	−22.6058	+	15.8553i	−1.09654	+	0.769093i
$426$	7.95866	+	6.82345i	0.385598	+	0.330597i
$427$	1.12749	−	10.7273i	0.0545629	−	0.519131i
$428$	−1.38774	+	1.54125i	−0.0670792	+	0.0744989i
$429$	−12.3689	+	1.60457i	−0.597176	+	0.0774694i
$430$	−4.45030	+	9.77549i	−0.214613	+	0.471416i
$431$	0.186360	−	0.573557i	0.00897664	−	0.0276273i	−0.946468	−	0.322798i	$-0.895377\pi$
$431$	0.186360	−	0.573557i	0.00897664	−	0.0276273i	0.955445	+	0.295171i	$0.0953765\pi$
$432$	7.72767	+	14.4275i	0.371798	+	0.694142i
$433$	11.7310	−	36.1042i	0.563754	−	1.73506i	−0.107871	−	0.994165i	$-0.534403\pi$
$433$	11.7310	−	36.1042i	0.563754	−	1.73506i	0.671625	−	0.740891i	$-0.265597\pi$
$434$	−2.87812	−	27.3835i	−0.138154	−	1.31445i
$435$	10.9394	+	4.66291i	0.524506	+	0.223569i
$436$	0.318840	−	3.03356i	0.0152697	−	0.145281i
$437$	28.3638	+	12.6284i	1.35683	+	0.604098i
$438$	−4.35124	−	0.350743i	−0.207910	−	0.0167591i
$439$	34.7392	−	15.4669i	1.65801	−	0.738193i	0.658118	−	0.752915i	$-0.271353\pi$
$439$	34.7392	−	15.4669i	1.65801	−	0.738193i	0.999892	+	0.0147216i	$0.00468620\pi$
$440$	−5.96099	+	26.9384i	−0.284179	+	1.28424i
$441$	−1.53782	−	1.54951i	−0.0732293	−	0.0737862i
$442$	3.85452	−	11.8630i	0.183341	−	0.564265i
$443$	−16.7070	+	28.9373i	−0.793772	+	1.37485i	0.129844	+	0.991534i	$0.458552\pi$
$443$	−16.7070	+	28.9373i	−0.793772	+	1.37485i	−0.923616	+	0.383319i	$0.874781\pi$
$444$	−0.0936685	−	3.85613i	−0.00444531	−	0.183004i
$445$	−3.36265	−	4.71034i	−0.159405	−	0.223292i
$446$	−9.96792	+	11.0705i	−0.471994	+	0.524203i
$447$	−2.58083	−	3.37662i	−0.122069	−	0.159709i
$448$	−22.5387	+	10.0349i	−1.06485	+	0.474103i
$449$	4.99449			0.235705			0.117852	−	0.993031i	$-0.462399\pi$
$449$	4.99449			0.235705			0.117852	+	0.993031i	$0.462399\pi$
$450$	−19.1982	+	0.612738i	−0.905014	+	0.0288848i
$451$	40.1691			1.89149
$452$	−0.787115	+	0.350446i	−0.0370228	+	0.0164836i
$453$	3.67307	−	8.82029i	0.172576	−	0.414413i
$454$	−1.49131	+	1.65627i	−0.0699906	+	0.0777324i
$455$	10.4556	−	3.30115i	0.490165	−	0.154760i
$456$	−36.9738	−	20.1659i	−1.73146	−	0.944355i
$457$	14.1253	−	24.4658i	0.660756	−	1.14446i	−0.319662	−	0.947532i	$-0.603569\pi$
$457$	14.1253	−	24.4658i	0.660756	−	1.14446i	0.980417	−	0.196931i	$-0.0630974\pi$
$458$	−1.51462	+	4.66151i	−0.0707734	+	0.217818i
$459$	2.08882	+	28.6189i	0.0974976	+	1.33582i
$460$	−1.24067	−	2.85027i	−0.0578464	−	0.132895i
$461$	18.6354	−	8.29700i	0.867936	−	0.386430i	0.0760535	−	0.997104i	$-0.475768\pi$
$461$	18.6354	−	8.29700i	0.867936	−	0.386430i	0.791882	+	0.610674i	$0.209101\pi$
$462$	−10.7933	−	22.7394i	−0.502151	−	1.05793i
$463$	22.2020	+	9.88497i	1.03182	+	0.459394i	0.851577	−	0.524229i	$-0.175647\pi$
$463$	22.2020	+	9.88497i	1.03182	+	0.459394i	0.180238	+	0.983623i	$0.442313\pi$
$464$	−1.01092	+	9.61822i	−0.0469306	+	0.446515i
$465$	−29.9535	+	0.477882i	−1.38906	+	0.0221613i
$466$	−0.277668	−	2.64183i	−0.0128627	−	0.122381i
$467$	0.349452	−	1.07550i	0.0161707	−	0.0497683i	−0.942646	−	0.333795i	$-0.891671\pi$
$467$	0.349452	−	1.07550i	0.0161707	−	0.0497683i	0.958816	+	0.284027i	$0.0916706\pi$
$468$	−1.48595	+	1.19400i	−0.0686879	+	0.0551929i
$469$	−5.81652	+	17.9014i	−0.268582	+	0.826610i
$470$	0.998057	+	0.113317i	0.0460370	+	0.00522691i
$471$	6.96878	+	9.11759i	0.321104	+	0.420117i
$472$	−23.8466	+	26.4843i	−1.09763	+	1.21904i
$473$	−1.60073	+	15.2299i	−0.0736016	+	0.700273i
$474$	8.20862	−	2.88934i	0.377034	−	0.132712i
$475$	32.9330	−	23.0986i	1.51107	−	1.05984i
$476$	−5.53006			−0.253470
$477$	−14.9245	−	23.1733i	−0.683344	−	1.06103i
$478$	10.3595	+	31.8833i	0.473833	+	1.45831i
$479$	−26.9399	−	5.72626i	−1.23092	−	0.261640i	−0.453862	−	0.891072i	$-0.649954\pi$
$479$	−26.9399	−	5.72626i	−1.23092	−	0.261640i	−0.777055	+	0.629432i	$0.783287\pi$
$480$	2.52506	+	7.36920i	0.115253	+	0.336357i
$481$	−10.6663	+	2.26720i	−0.486343	+	0.103375i
$482$	−15.8053	−	27.3755i	−0.719910	−	1.24692i
$483$	16.3130	+	8.89729i	0.742268	+	0.404841i
$484$	0.213368	+	2.03007i	0.00969857	+	0.0922757i
$485$	−0.146611	−	0.0862829i	−0.00665727	−	0.00391790i
$486$	−9.69052	+	17.4516i	−0.439571	+	0.791620i
$487$	−3.20834	+	2.33100i	−0.145384	+	0.105628i	−0.658100	−	0.752931i	$-0.728639\pi$
$487$	−3.20834	+	2.33100i	−0.145384	+	0.105628i	0.512716	+	0.858558i	$0.328639\pi$
$488$	−1.22584	−	11.6630i	−0.0554910	−	0.527961i
$489$	20.1021	−	19.0039i	0.909046	−	0.859386i
$490$	1.21065	+	1.69586i	0.0546917	+	0.0766111i
$491$	35.2505	+	15.6945i	1.59083	+	0.708284i	0.995461	−	0.0951663i	$-0.0303383\pi$
$491$	35.2505	+	15.6945i	1.59083	+	0.708284i	0.595371	+	0.803451i	$0.297005\pi$
$492$	5.24057	−	3.19779i	0.236263	−	0.144168i
$493$	−8.47804	+	14.6844i	−0.381832	+	0.661352i
$494$	−5.61543	+	17.2825i	−0.252650	+	0.777577i
$495$	−25.6841	+	9.50365i	−1.15441	+	0.427157i
$496$	−7.52869	−	23.1709i	−0.338048	−	1.04041i
$497$	−12.8521	−	2.73181i	−0.576497	−	0.122538i
$498$	−25.5789	−	7.62954i	−1.14622	−	0.341888i
$499$	1.12601	+	1.95031i	0.0504073	+	0.0873081i	0.890128	−	0.455710i	$-0.150615\pi$
$499$	1.12601	+	1.95031i	0.0504073	+	0.0873081i	−0.839721	+	0.543018i	$0.817281\pi$
$500$	−3.99366	−	0.520981i	−0.178602	−	0.0232990i
$501$	−12.9987	+	4.57540i	−0.580740	+	0.204414i
$502$	22.8430	−	10.1704i	1.01953	−	0.453926i
$503$	−9.99411	−	30.7587i	−0.445615	−	1.37146i	−0.881808	−	0.471609i	$-0.843673\pi$
$503$	−9.99411	−	30.7587i	−0.445615	−	1.37146i	0.436192	−	0.899853i	$-0.356327\pi$
$504$	−21.0868	−	13.8078i	−0.939281	−	0.615047i
$505$	8.99842	−	7.96744i	0.400424	−	0.354547i
$506$	13.4997	+	14.9929i	0.600133	+	0.666515i
$507$	−13.0029	−	11.1482i	−0.577480	−	0.495109i
$508$	−0.244212	+	0.0519088i	−0.0108351	+	0.00230308i
$509$	−28.2990	−	12.5995i	−1.25433	−	0.558463i	−0.331421	−	0.943483i	$-0.607528\pi$
$509$	−28.2990	−	12.5995i	−1.25433	−	0.558463i	−0.922908	+	0.385020i	$0.874195\pi$
$510$	2.42797	−	27.2802i	0.107512	−	1.20799i
$511$	4.99830	−	2.22539i	0.221112	−	0.0984453i
$512$	−20.5286	+	14.9149i	−0.907242	+	0.659150i
$513$	−3.04308	−	41.6932i	−0.134355	−	1.84080i
$514$	−22.7890	−	16.5572i	−1.00518	−	0.730307i
$515$	12.5875	−	7.12818i	0.554669	−	0.314105i
$516$	1.00359	+	2.11437i	0.0441807	+	0.0930800i
$517$	1.40084	−	0.297757i	0.0616087	−	0.0130953i
$518$	−11.0034	−	19.0584i	−0.483460	−	0.837377i
$519$	−9.23019	+	5.63225i	−0.405161	+	0.247228i
$520$	10.3730	−	5.87413i	0.454885	−	0.257598i
$521$	4.77195	+	14.6865i	0.209063	+	0.643429i	0.999522	+	0.0309144i	$0.00984194\pi$
$521$	4.77195	+	14.6865i	0.209063	+	0.643429i	−0.790459	+	0.612515i	$0.790158\pi$
$522$	−10.5300	+	5.31516i	−0.460886	+	0.232638i
$523$	−19.9676	−	14.5073i	−0.873123	−	0.634361i	0.0583005	−	0.998299i	$-0.481432\pi$
$523$	−19.9676	−	14.5073i	−0.873123	−	0.634361i	−0.931423	+	0.363938i	$0.881432\pi$
$524$	−1.00909	+	1.74779i	−0.0440822	+	0.0763525i
$525$	20.7567	−	12.1957i	0.905898	−	0.532264i
$526$	9.98330	+	17.2916i	0.435293	+	0.753949i
$527$	4.46495	−	42.4812i	0.194496	−	1.85051i
$528$	−13.5249	−	17.6953i	−0.588598	−	0.770091i
$529$	7.92938	+	1.68544i	0.344756	+	0.0732801i
$530$	10.4998	+	24.1219i	0.456082	+	1.04779i
$531$	−34.9178	−	5.66610i	−1.51530	−	0.245888i
$532$	8.05641			0.349290
$533$	−11.6132	−	12.8978i	−0.503024	−	0.558665i
$534$	5.72202	+	0.461238i	0.247616	+	0.0199597i
$535$	12.2100	+	4.08008i	0.527886	+	0.176397i
$536$	−2.13912	+	20.3524i	−0.0923961	+	0.879090i
$537$	11.0025	+	23.1801i	0.474793	+	1.00030i
$538$	2.23475	+	21.2622i	0.0963468	+	0.916678i
$539$	2.40342	+	1.74619i	0.103523	+	0.0752135i
$540$	−2.59425	+	3.28454i	−0.111639	+	0.141344i
$541$	−0.625472	+	0.454432i	−0.0268911	+	0.0195376i	−0.601150	−	0.799136i	$-0.705290\pi$
$541$	−0.625472	+	0.454432i	−0.0268911	+	0.0195376i	0.574259	+	0.818674i	$0.305290\pi$
$542$	17.4907	+	19.4254i	0.751290	+	0.834392i
$543$	−7.46347	+	39.8480i	−0.320288	+	1.71004i
$544$	−10.8645	+	2.30932i	−0.465812	+	0.0990113i
$545$	−18.0555	+	5.70067i	−0.773411	+	0.244190i
$546$	−4.18089	+	10.0398i	−0.178926	+	0.429662i
$547$	−6.50128	−	1.38189i	−0.277975	−	0.0590853i	0.0668148	−	0.997765i	$-0.478716\pi$
$547$	−6.50128	−	1.38189i	−0.277975	−	0.0590853i	−0.344789	+	0.938680i	$0.612050\pi$
$548$	−1.51769	−	1.10267i	−0.0648326	−	0.0471036i
$549$	9.07408	−	7.29131i	0.387272	−	0.311186i
$550$	25.6545	−	5.00768i	1.09391	−	0.213528i
$551$	12.3512	−	21.3928i	0.526177	−	0.911365i
$552$	19.3596	+	5.77449i	0.824000	+	0.245778i
$553$	−7.29822	+	8.10550i	−0.310352	+	0.344681i
$554$	−3.08624	+	3.42762i	−0.131122	+	0.145625i
$555$	−21.7152	+	10.0863i	−0.921758	+	0.428140i
$556$	−2.95665	−	3.28369i	−0.125390	−	0.139259i
$557$	32.9287			1.39523			0.697616	−	0.716472i	$-0.254244\pi$
$557$	32.9287			1.39523			0.697616	+	0.716472i	$0.254244\pi$
$558$	18.7874	−	23.0216i	0.795332	−	0.974583i
$559$	5.35292	−	3.88913i	0.226404	−	0.164492i
$560$	14.4403	+	13.2217i	0.610215	+	0.558717i
$561$	−9.04383	−	37.9871i	−0.381831	−	1.60381i
$562$	1.44814	+	0.644753i	0.0610860	+	0.0271973i
$563$	−14.9570	−	6.65930i	−0.630364	−	0.280656i	0.0665809	−	0.997781i	$-0.478791\pi$
$563$	−14.9570	−	6.65930i	−0.630364	−	0.280656i	−0.696944	+	0.717125i	$0.745458\pi$
$564$	0.159053	−	0.150364i	0.00669735	−	0.00633148i
$565$	3.94458	+	3.61169i	0.165950	+	0.151945i
$566$	−13.6061	+	9.88542i	−0.571907	+	0.415515i
$567$	0.189529	−	25.0181i	0.00795945	−	1.05066i
$568$	−14.2854			−0.599402
$569$	−12.4687	−	13.8479i	−0.522715	−	0.580534i	0.422754	−	0.906244i	$-0.361063\pi$
$569$	−12.4687	−	13.8479i	−0.522715	−	0.580534i	−0.945470	+	0.325710i	$0.894397\pi$
$570$	−3.53716	+	39.7430i	−0.148155	+	1.66465i
$571$	−26.2483	+	29.1517i	−1.09846	+	1.21996i	−0.124741	+	0.992189i	$0.539810\pi$
$571$	−26.2483	+	29.1517i	−1.09846	+	1.21996i	−0.973715	+	0.227770i	$0.926857\pi$
$572$	1.73574	−	1.92774i	0.0725751	−	0.0806028i
$573$	−5.88894	−	24.7355i	−0.246014	−	1.03334i
$574$	17.5128	−	30.3331i	0.730971	−	1.26608i
$575$	−13.1488	+	14.1226i	−0.548341	+	0.588952i
$576$	−24.8206	−	9.63575i	−1.03419	−	0.401490i
$577$	−35.2940	−	25.6426i	−1.46931	−	1.06751i	−0.980814	−	0.194946i	$-0.937547\pi$
$577$	−35.2940	−	25.6426i	−1.46931	−	1.06751i	−0.488493	−	0.872568i	$-0.662453\pi$
$578$	16.9050	+	3.59327i	0.703155	+	0.149460i
$579$	3.27572	+	4.28578i	0.136134	+	0.178111i
$580$	−2.35848	+	0.744645i	−0.0979304	+	0.0309197i
$581$	32.7240	−	6.95571i	1.35762	−	0.288571i
$582$	0.159166	−	0.0560246i	0.00659764	−	0.00232229i
$583$	25.0984	+	27.8746i	1.03947	+	1.15445i
$584$	4.81250	−	3.49649i	0.199143	−	0.144686i
$585$	10.4770	+	5.49926i	0.433170	+	0.227366i
$586$	0.406600	+	0.295412i	0.0167965	+	0.0122034i
$587$	−0.0391166	−	0.372170i	−0.00161452	−	0.0153611i	0.993685	−	0.112206i	$-0.0357916\pi$
$587$	−0.0391166	−	0.372170i	−0.00161452	−	0.0153611i	−0.995299	+	0.0968448i	$0.969125\pi$
$588$	0.452568	+	0.0364804i	0.0186636	+	0.00150443i
$589$	−6.50473	+	61.8883i	−0.268023	+	2.55006i
$590$	32.0228	+	10.7007i	1.31836	+	0.440540i
$591$	0.164756	+	0.347108i	0.00677714	+	0.0142781i
$592$	−13.0295	−	14.4708i	−0.535511	−	0.594745i
$593$	35.6235			1.46288			0.731442	−	0.681904i	$-0.238848\pi$
$593$	35.6235			1.46288			0.731442	+	0.681904i	$0.238848\pi$
$594$	9.21291	−	25.5541i	0.378010	−	1.04850i
$595$	13.7002	+	31.4744i	0.561653	+	1.29033i
$596$	0.864590	+	0.183774i	0.0354150	+	0.00752768i
$597$	10.5556	−	1.36933i	0.432011	−	0.0560431i
$598$	0.911163	−	8.66914i	0.0372602	−	0.354507i
$599$	9.58076	+	16.5944i	0.391459	+	0.678027i	0.992642	−	0.121084i	$-0.0386370\pi$
$599$	9.58076	+	16.5944i	0.391459	+	0.678027i	−0.601183	+	0.799111i	$0.705304\pi$
$600$	19.3173	−	17.6618i	0.788627	−	0.721039i
$601$	10.7112	−	18.5524i	0.436919	−	0.756767i	−0.560531	−	0.828134i	$-0.689403\pi$
$601$	10.7112	−	18.5524i	0.436919	−	0.756767i	0.997450	+	0.0713671i	$0.0227362\pi$
$602$	10.8028	+	7.84867i	0.440288	+	0.319888i
$603$	−18.1339	+	9.15335i	−0.738471	+	0.372753i
$604$	0.614060	+	1.88988i	0.0249858	+	0.0768983i
$605$	11.0256	−	6.24369i	0.448253	−	0.253842i
$606$	0.289496	+	11.9179i	0.0117600	+	0.484132i
$607$	−10.9680	−	18.9971i	−0.445177	−	0.771069i	0.552888	−	0.833256i	$-0.313526\pi$
$607$	−10.9680	−	18.9971i	−0.445177	−	0.771069i	−0.998065	+	0.0621867i	$0.980193\pi$
$608$	15.8279	−	3.36431i	0.641904	−	0.136441i
$609$	8.39670	−	12.1678i	0.340252	−	0.493066i
$610$	−9.66782	+	5.47481i	−0.391438	+	0.221669i
$611$	−0.500599	−	0.363707i	−0.0202521	−	0.0147140i
$612$	−4.20397	−	4.23594i	−0.169935	−	0.171228i
$613$	−30.6633	+	22.2782i	−1.23848	+	0.899808i	−0.997496	−	0.0707211i	$-0.977470\pi$
$613$	−30.6633	+	22.2782i	−1.23848	+	0.899808i	−0.240983	+	0.970529i	$0.577470\pi$
$614$	6.50570	−	2.89652i	0.262549	−	0.116894i
$615$	−31.1833	−	21.9046i	−1.25743	−	0.883279i
$616$	31.3345	+	13.9510i	1.26250	+	0.562103i
$617$	1.13655	−	0.241582i	0.0457559	−	0.00972572i	−0.184977	−	0.982743i	$-0.559221\pi$
$617$	1.13655	−	0.241582i	0.0457559	−	0.00972572i	0.230733	+	0.973017i	$0.425888\pi$
$618$	−2.64151	+	14.1032i	−0.106257	+	0.567314i
$619$	−21.8780	−	24.2979i	−0.879349	−	0.976616i	0.120521	−	0.992711i	$-0.461543\pi$
$619$	−21.8780	−	24.2979i	−0.879349	−	0.976616i	−0.999870	+	0.0160944i	$0.994877\pi$
$620$	4.66474	−	4.13029i	0.187341	−	0.165876i
$621$	5.58603	+	19.2593i	0.224160	+	0.772848i
$622$	1.53791	+	4.73319i	0.0616645	+	0.189784i
$623$	−6.57292	+	2.92645i	−0.263339	+	0.117246i
$624$	−1.77158	+	9.45856i	−0.0709198	+	0.378645i
$625$	6.92874	+	24.0207i	0.277149	+	0.960827i
$626$	−18.4344	−	31.9293i	−0.736787	−	1.27615i
$627$	13.1754	+	55.3411i	0.526176	+	2.21011i
$628$	−2.33457	−	0.496229i	−0.0931596	−	0.0198017i
$629$	−10.5498	−	32.4690i	−0.420649	−	1.29463i
$630$	−4.02115	+	23.5384i	−0.160207	+	0.937791i
$631$	9.90042	−	30.4703i	0.394129	−	1.21301i	−0.535508	−	0.844530i	$-0.679880\pi$
$631$	9.90042	−	30.4703i	0.394129	−	1.21301i	0.929638	−	0.368475i	$-0.120120\pi$
$632$	−5.92921	+	10.2697i	−0.235851	+	0.408507i
$633$	0.847860	+	34.9045i	0.0336994	+	1.38733i
$634$	−9.70039	−	4.31889i	−0.385252	−	0.171525i
$635$	0.900451	+	1.26134i	0.0357333	+	0.0500546i
$636$	5.49345	+	1.63856i	0.217830	+	0.0649731i
$637$	−0.134170	−	1.27654i	−0.00531602	−	0.0505785i
$638$	12.9859	−	9.43482i	0.514117	−	0.373528i
$639$	−7.67773	−	11.9213i	−0.303726	−	0.471598i
$640$	14.1493	+	8.32709i	0.559301	+	0.329157i
$641$	−0.407249	−	3.87472i	−0.0160854	−	0.153042i	0.983531	−	0.180740i	$-0.0578491\pi$
$641$	−0.407249	−	3.87472i	−0.0160854	−	0.153042i	−0.999616	+	0.0276975i	$0.991182\pi$
$642$	−10.9003	+	6.65136i	−0.430201	+	0.262508i
$643$	19.1932	+	33.2436i	0.756906	+	1.31100i	0.944421	+	0.328737i	$0.106623\pi$
$643$	19.1932	+	33.2436i	0.756906	+	1.31100i	−0.187516	+	0.982262i	$0.560044\pi$
$644$	−3.78014	+	0.803493i	−0.148958	+	0.0316620i
$645$	9.54769	−	10.9501i	0.375940	−	0.431161i
$646$	−55.6490	−	11.8286i	−2.18948	−	0.465388i
$647$	4.44041	+	13.6662i	0.174570	+	0.537272i	0.999614	−	0.0277973i	$-0.00884929\pi$
$647$	4.44041	+	13.6662i	0.174570	+	0.537272i	−0.825043	+	0.565070i	$0.808849\pi$
$648$	−5.45373	−	26.6489i	−0.214243	−	1.04687i
$649$	48.1384			1.88960
$650$	−9.02484	−	6.78958i	−0.353983	−	0.266309i
$651$	−6.85632	+	36.6063i	−0.268720	+	1.43472i
$652$	−0.601386	+	5.72180i	−0.0235521	+	0.224083i
$653$	17.4904	−	19.4251i	0.684454	−	0.760163i	−0.296367	−	0.955074i	$-0.595775\pi$
$653$	17.4904	−	19.4251i	0.684454	−	0.760163i	0.980821	+	0.194911i	$0.0624418\pi$
$654$	7.21988	−	17.3374i	0.282320	−	0.677946i
$655$	12.4475	+	1.41325i	0.486364	+	0.0552204i
$656$	9.57704	−	29.4751i	0.373920	−	1.15081i
$657$	5.50434	+	2.13687i	0.214745	+	0.0833674i
$658$	0.385886	−	1.18764i	0.0150434	−	0.0462988i
$659$	0.0665847	+	0.633511i	0.00259377	+	0.0246781i	0.995742	−	0.0921814i	$-0.0293840\pi$
$659$	0.0665847	+	0.633511i	0.00259377	+	0.0246781i	−0.993148	+	0.116859i	$0.962717\pi$
$660$	2.76881	−	4.97743i	0.107776	−	0.193746i
$661$	−0.131816	+	1.25414i	−0.00512704	+	0.0487805i	−0.996786	−	0.0801068i	$-0.974474\pi$
$661$	−0.131816	+	1.25414i	−0.00512704	+	0.0487805i	0.991659	+	0.128887i	$0.0411405\pi$
$662$	−18.9533	−	8.43855i	−0.736641	−	0.327974i
$663$	−9.58252	+	13.8862i	−0.372154	+	0.539297i
$664$	33.2287	−	14.7944i	1.28952	−	0.574133i
$665$	−19.9590	−	45.8533i	−0.773977	−	1.77811i
$666$	6.23363	−	22.9166i	0.241548	−	0.888002i
$667$	−3.66169	+	11.2695i	−0.141781	+	0.436357i
$668$	1.43302	−	2.48207i	0.0554453	−	0.0960341i
$669$	17.2001	−	10.4955i	0.664995	−	0.405779i
$670$	18.4883	−	5.83735i	0.714267	−	0.225516i
$671$	−10.5995	+	11.7719i	−0.409189	+	0.454450i
$672$	9.60379	−	1.24586i	0.370474	−	0.0480602i
$673$	−2.56181	+	1.14059i	−0.0987505	+	0.0439666i	−0.455517	−	0.890227i	$-0.650546\pi$
$673$	−2.56181	+	1.14059i	−0.0987505	+	0.0439666i	0.356767	+	0.934193i	$0.383879\pi$
$674$	−22.2955			−0.858791
$675$	25.1211	+	6.62811i	0.966910	+	0.255116i
$676$	3.56220			0.137008
$677$	37.3176	−	16.6149i	1.43423	−	0.638561i	0.465134	−	0.885240i	$-0.346006\pi$
$677$	37.3176	−	16.6149i	1.43423	−	0.638561i	0.969097	+	0.246680i	$0.0793395\pi$
$678$	−5.26085	+	0.682471i	−0.202042	+	0.0262101i
$679$	−0.141513	+	0.157166i	−0.00543078	+	0.00603149i
$680$	21.6845	+	30.3752i	0.831561	+	1.16484i
$681$	2.57332	−	1.57024i	0.0986100	−	0.0601717i
$682$	−20.2182	+	35.0189i	−0.774193	+	1.34094i
$683$	−1.79495	+	5.52428i	−0.0686817	+	0.211381i	−0.979506	−	0.201413i	$-0.935447\pi$
$683$	−1.79495	+	5.52428i	−0.0686817	+	0.211381i	0.910825	+	0.412793i	$0.135447\pi$
$684$	6.12452	+	6.17109i	0.234177	+	0.235957i
$685$	−2.51592	+	11.3697i	−0.0961282	+	0.434415i
$686$	−20.3974	+	9.08149i	−0.778774	+	0.346733i
$687$	3.76541	−	5.45654i	0.143659	−	0.208180i
$688$	10.7937	+	4.80567i	0.411506	+	0.183214i
$689$	1.69402	−	16.1175i	0.0645371	−	0.614029i
$690$	−2.30403	−	19.0005i	−0.0877131	−	0.723337i
$691$	3.28063	+	31.2131i	0.124801	+	1.18740i	0.860268	+	0.509842i	$0.170296\pi$
$691$	3.28063	+	31.2131i	0.124801	+	1.18740i	−0.735467	+	0.677560i	$0.763037\pi$
$692$	0.694935	−	2.13879i	0.0264174	−	0.0813045i
$693$	5.19859	+	33.6470i	0.197478	+	1.27814i
$694$	−7.87967	+	24.2511i	−0.299108	+	0.920560i
$695$	−11.3644	+	24.9629i	−0.431075	+	0.946895i
$696$	6.17913	−	14.8382i	0.234219	−	0.562440i
$697$	36.3584	−	40.3801i	1.37717	−	1.52951i
$698$	1.25391	−	11.9301i	0.0474611	−	0.451562i
$699$	−0.661467	+	3.53161i	−0.0250190	+	0.133578i
$700$	−1.62639	+	4.73546i	−0.0614716	+	0.178984i
$701$	−28.7744			−1.08679			−0.543397	−	0.839476i	$-0.682862\pi$
$701$	−28.7744			−1.08679			−0.543397	+	0.839476i	$0.682862\pi$
$702$	−10.8686	+	4.42976i	−0.410210	+	0.167190i
$703$	15.3694	+	47.3022i	0.579669	+	1.78404i
$704$	35.4406	+	7.53312i	1.33572	+	0.283915i
$705$	−1.24984	−	0.532741i	−0.0470717	−	0.0200642i
$706$	−21.9765	+	4.67124i	−0.827095	+	0.175805i
$707$	−7.47087	−	12.9399i	−0.280971	−	0.486656i
$708$	6.28028	−	3.83222i	0.236027	−	0.144024i
$709$	3.85894	+	36.7153i	0.144925	+	1.37887i	0.789227	+	0.614102i	$0.210481\pi$
$709$	3.85894	+	36.7153i	0.144925	+	1.37887i	−0.644302	+	0.764771i	$0.722852\pi$
$710$	5.40151	+	12.4093i	0.202715	+	0.465712i
$711$	−11.7568	+	0.571503i	−0.440915	+	0.0214330i
$712$	−6.32859	+	4.59799i	−0.237174	+	0.172317i
$713$	−3.12026	−	29.6873i	−0.116855	−	1.11180i
$714$	−32.6283	−	9.73219i	−1.22108	−	0.364218i
$715$	−15.2719	−	5.10323i	−0.571137	−	0.190850i
$716$	−4.87512	−	2.17054i	−0.182192	−	0.0811170i
$717$	−1.10113	−	45.3313i	−0.0411226	−	1.69293i
$718$	−0.148015	+	0.256369i	−0.00552387	+	0.00956762i
$719$	−9.45641	+	29.1038i	−0.352665	+	1.08539i	0.604687	+	0.796463i	$0.293298\pi$
$719$	−9.45641	+	29.1038i	−0.352665	+	1.08539i	−0.957351	+	0.288926i	$0.906702\pi$
$720$	0.849990	+	21.1122i	0.0316773	+	0.786806i
$721$	−5.55725	−	17.1035i	−0.206963	−	0.636966i
$722$	57.2732	+	12.1738i	2.13149	+	0.453062i
$723$	9.90252	+	41.5939i	0.368279	+	1.54689i
$724$	−4.21583	−	7.30203i	−0.156680	−	0.271378i
$725$	10.0811	+	11.5785i	0.374401	+	0.430016i
$726$	−2.31374	+	12.3532i	−0.0858711	+	0.458471i
$727$	−39.8104	+	17.7247i	−1.47649	+	0.657374i	−0.977825	−	0.209422i	$-0.932842\pi$
$727$	−39.8104	+	17.7247i	−1.47649	+	0.657374i	−0.498662	+	0.866797i	$0.666175\pi$
$728$	−4.57958	−	14.0945i	−0.169730	−	0.522376i
$729$	19.3076	−	18.8737i	0.715096	−	0.699026i
$730$	−4.85696	−	2.85840i	−0.179764	−	0.105794i
$731$	13.8611	+	15.3943i	0.512670	+	0.569378i
$732$	−0.445697	+	2.37961i	−0.0164734	+	0.0879528i
$733$	−39.8802	+	8.47680i	−1.47301	+	0.313098i	−0.873325	−	0.487139i	$-0.838041\pi$
$733$	−39.8802	+	8.47680i	−1.47301	+	0.313098i	−0.599685	+	0.800236i	$0.704707\pi$
$734$	−15.1118	−	6.72820i	−0.557786	−	0.248342i
$735$	−0.913565	−	2.66618i	−0.0336974	−	0.0983434i
$736$	−7.09103	+	3.15713i	−0.261379	+	0.116373i
$737$	22.3633	−	16.2479i	0.823762	−	0.598498i
$738$	36.5480	−	9.64478i	1.34535	−	0.355029i
$739$	10.9000	+	7.91934i	0.400965	+	0.291318i	0.769934	−	0.638124i	$-0.220289\pi$
$739$	10.9000	+	7.91934i	0.400965	+	0.291318i	−0.368969	+	0.929442i	$0.620289\pi$
$740$	2.06327	−	4.53215i	0.0758472	−	0.166605i
$741$	13.9602	−	20.2300i	0.512841	−	0.743169i
$742$	31.9914	−	6.79998i	1.17444	−	0.249635i
$743$	−11.5451	−	19.9968i	−0.423550	−	0.733610i	0.572734	−	0.819742i	$-0.305883\pi$
$743$	−11.5451	−	19.9968i	−0.423550	−	0.733610i	−0.996284	+	0.0861312i	$0.972550\pi$
$744$	0.983283	+	40.4796i	0.0360489	+	1.48405i
$745$	−1.09599	−	5.37611i	−0.0401538	−	0.196966i
$746$	13.8320	+	42.5705i	0.506426	+	1.55862i
$747$	30.2049	+	19.7783i	1.10514	+	0.723652i
$748$	6.57029	+	4.77359i	0.240234	+	0.174540i
$749$	8.00228	−	13.8603i	0.292397	−	0.506446i
$750$	−22.6464	−	10.1022i	−0.826929	−	0.368880i
$751$	−14.0513	−	24.3376i	−0.512739	−	0.888090i	−0.999891	−	0.0147729i	$-0.995297\pi$
$751$	−14.0513	−	24.3376i	−0.512739	−	0.888090i	0.487152	−	0.873317i	$-0.338036\pi$
$752$	0.115498	−	1.09889i	0.00421178	−	0.0400724i
$753$	−33.5404	+	4.35107i	−1.22228	+	0.158562i
$754$	−6.78374	−	1.44193i	−0.247049	−	0.0525119i
$755$	9.23503	−	8.17695i	0.336097	−	0.297590i
$756$	3.35680	+	3.97583i	0.122086	+	0.144600i
$757$	−17.4304			−0.633517			−0.316759	−	0.948506i	$-0.602595\pi$
$757$	−17.4304			−0.633517			−0.316759	+	0.948506i	$0.602595\pi$
$758$	−15.1619	−	16.8390i	−0.550706	−	0.611621i
$759$	−11.7014	−	24.6525i	−0.424733	−	0.894828i
$760$	−31.5908	−	44.2519i	−1.14592	−	1.60518i
$761$	2.25392	−	21.4446i	0.0817044	−	0.777365i	−0.874571	−	0.484898i	$-0.838857\pi$
$761$	2.25392	−	21.4446i	0.0817044	−	0.777365i	0.956275	−	0.292468i	$-0.0944764\pi$
$762$	−1.53224	−	0.123510i	−0.0555073	−	0.00447431i
$763$	2.46047	+	23.4098i	0.0890749	+	0.847491i
$764$	4.27828	+	3.10835i	0.154783	+	0.112456i
$765$	−13.6940	+	34.4211i	−0.495107	+	1.24450i
$766$	28.5047	−	20.7098i	1.02992	−	0.748277i
$767$	−13.9172	−	15.4566i	−0.502522	−	0.558107i
$768$	13.6393	−	4.80087i	0.492165	−	0.173236i
$769$	51.2684	−	10.8974i	1.84879	−	0.392972i	0.856419	−	0.516282i	$-0.172684\pi$
$769$	51.2684	−	10.8974i	1.84879	−	0.392972i	0.992368	+	0.123310i	$0.0393510\pi$
$770$	0.270792	−	32.4944i	0.00975866	−	1.17102i
$771$	23.1372	+	30.2715i	0.833266	+	1.09020i
$772$	−1.09738	−	0.233255i	−0.0394956	−	0.00839504i
$773$	−2.85019	−	2.07078i	−0.102514	−	0.0744809i	0.535347	−	0.844632i	$-0.320181\pi$
$773$	−2.85019	−	2.07078i	−0.102514	−	0.0744809i	−0.637861	+	0.770151i	$0.720181\pi$
$774$	2.20035	+	14.2413i	0.0790898	+	0.511895i
$775$	−35.0641	−	16.3171i	−1.25954	−	0.586127i
$776$	−0.114968	+	0.199130i	−0.00412711	+	0.00714836i
$777$	6.89397	+	28.9569i	0.247320	+	1.03882i
$778$	−3.00066	+	3.33257i	−0.107579	+	0.119479i
$779$	−52.9684	+	58.8274i	−1.89779	+	2.10771i
$780$	−2.39868	+	0.549988i	−0.0858864	+	0.0196927i
$781$	12.9116	+	14.3398i	0.462013	+	0.513117i
$782$	27.2907			0.975912
$783$	15.7036	−	2.81830i	0.561201	−	0.100718i
$784$	1.85433	−	1.34725i	0.0662260	−	0.0481160i
$785$	2.95939	+	14.5166i	0.105625	+	0.518121i
$786$	−9.02967	+	8.53639i	−0.322078	+	0.304483i
$787$	−1.65307	−	0.735994i	−0.0589256	−	0.0262354i	0.377062	−	0.926188i	$-0.376934\pi$
$787$	−1.65307	−	0.735994i	−0.0589256	−	0.0262354i	−0.435988	+	0.899953i	$0.643601\pi$
$788$	−0.0730019	−	0.0325025i	−0.00260058	−	0.00115785i
$789$	−6.25487	−	26.2725i	−0.222679	−	0.935326i
$790$	11.1629	+	1.26740i	0.397157	+	0.0450921i
$791$	5.37911	−	3.90815i	0.191259	−	0.138958i
$792$	13.1344	+	34.6074i	0.466709	+	1.22972i
$793$	6.84422			0.243045
$794$	−10.2067	−	11.3357i	−0.362224	−	0.402290i
$795$	−4.28363	−	35.3255i	−0.151925	−	1.25287i
$796$	−1.48128	+	1.64512i	−0.0525024	+	0.0583099i
$797$	−19.0851	+	21.1961i	−0.676028	+	0.750805i	−0.979370	−	0.202077i	$-0.935231\pi$
$797$	−19.0851	+	21.1961i	−0.676028	+	0.750805i	0.303342	+	0.952882i	$0.401898\pi$
$798$	47.5342	+	14.1783i	1.68269	+	0.501905i
$799$	0.968623	−	1.67770i	0.0342674	−	0.0593529i
$800$	−1.21774	+	9.98259i	−0.0430535	+	0.352938i
$801$	−7.23838	−	2.81006i	−0.255756	−	0.0992885i
$802$	14.6737	+	10.6611i	0.518146	+	0.376455i
$803$	−7.85948	−	1.67058i	−0.277355	−	0.0589537i
$804$	1.62411	−	3.90005i	0.0572781	−	0.137544i
$805$	13.9380	+	19.5241i	0.491251	+	0.688136i
$806$	17.0894	−	3.63245i	0.601947	−	0.127948i
$807$	5.32366	−	28.4234i	0.187402	−	1.00055i
$808$	−10.8701	−	12.0725i	−0.382408	−	0.424707i
$809$	6.47021	−	4.70088i	0.227480	−	0.165274i	−0.468207	−	0.883619i	$-0.655100\pi$
$809$	6.47021	−	4.70088i	0.227480	−	0.165274i	0.695687	+	0.718345i	$0.255100\pi$
$810$	−21.0869	+	14.8138i	−0.740919	+	0.520504i
$811$	15.9314	+	11.5749i	0.559429	+	0.406449i	0.831250	−	0.555899i	$-0.187626\pi$
$811$	15.9314	+	11.5749i	0.559429	+	0.406449i	−0.271821	+	0.962348i	$0.587626\pi$
$812$	0.321396	+	3.05788i	0.0112788	+	0.107311i
$813$	−15.1608	−	31.9408i	−0.531711	−	1.12021i
$814$	−3.37821	+	32.1415i	−0.118406	+	1.12656i
$815$	34.0556	−	10.7524i	1.19292	−	0.376641i
$816$	−30.0302	−	2.42066i	−1.05127	−	0.0847401i
$817$	−20.1934	−	22.4270i	−0.706477	−	0.784622i
$818$	−2.42698			−0.0848573
$819$	9.30066	−	11.3968i	0.324991	−	0.398237i
$820$	7.88885	−	0.762742i	0.275491	−	0.0266361i
$821$	4.52384	+	0.961572i	0.157883	+	0.0335591i	0.286175	−	0.958177i	$-0.407616\pi$
$821$	4.52384	+	0.961572i	0.157883	+	0.0335591i	−0.128292	+	0.991736i	$0.540949\pi$
$822$	−7.01409	−	9.17687i	−0.244644	−	0.320080i
$823$	0.715412	−	6.80669i	0.0249377	−	0.237266i	−0.974952	−	0.222415i	$-0.928606\pi$
$823$	0.715412	−	6.80669i	0.0249377	−	0.237266i	0.999890	−	0.0148510i	$-0.00472739\pi$
$824$	−9.77617	−	16.9328i	−0.340569	−	0.589883i
$825$	−35.1886	−	3.42761i	−1.22511	−	0.119334i
$826$	20.9873	−	36.3510i	0.730240	−	1.26481i
$827$	15.7497	+	11.4428i	0.547669	+	0.397905i	0.826925	−	0.562312i	$-0.190088\pi$
$827$	15.7497	+	11.4428i	0.547669	+	0.397905i	−0.279256	+	0.960217i	$0.590088\pi$
$828$	−3.48914	−	2.28471i	−0.121256	−	0.0793991i
$829$	−13.1862	−	40.5830i	−0.457976	−	1.40950i	−0.867606	−	0.497253i	$-0.834342\pi$
$829$	−13.1862	−	40.5830i	−0.457976	−	1.40950i	0.409630	−	0.912252i	$-0.365658\pi$
$830$	−25.4156	−	23.2708i	−0.882190	−	0.807740i
$831$	5.32546	−	3.24959i	0.184738	−	0.112727i
$832$	−7.82737	−	13.5574i	−0.271365	−	0.470018i
$833$	3.93078	−	0.835512i	0.136193	−	0.0289488i
$834$	−11.6659	−	24.5776i	−0.403955	−	0.851054i
$835$	−17.6769	−	2.00699i	−0.611735	−	0.0694547i
$836$	−9.57187	−	6.95437i	−0.331050	−	0.240522i
$837$	−33.2521	+	22.5764i	−1.14936	+	0.780356i
$838$	−24.8009	+	18.0189i	−0.856731	+	0.622452i
$839$	−34.8793	+	15.5292i	−1.20417	+	0.536129i	−0.907985	−	0.419003i	$-0.862380\pi$
$839$	−34.8793	+	15.5292i	−1.20417	+	0.536129i	−0.296181	+	0.955132i	$0.595713\pi$
$840$	−16.7174	−	27.9173i	−0.576806	−	0.963237i
$841$	−17.8803	−	7.96081i	−0.616561	−	0.274511i
$842$	11.1347	−	2.36676i	0.383728	−	0.0815639i
$843$	−1.62776	−	1.39558i	−0.0560631	−	0.0480663i
$844$	−4.85892	−	5.39638i	−0.167251	−	0.185751i
$845$	−8.82502	−	20.2743i	−0.303590	−	0.697459i
$846$	1.20306	−	0.607262i	0.0413621	−	0.0208781i
$847$	−4.86769	−	14.9812i	−0.167256	−	0.514760i
$848$	26.4376	−	11.7708i	0.907871	−	0.404210i
$849$	21.4577	−	7.55285i	0.736425	−	0.259213i
$850$	18.1868	−	30.3219i	0.623802	−	1.04003i
$851$	−11.9291	−	20.6618i	−0.408923	−	0.708276i
$852$	2.82605	+	0.842938i	0.0968188	+	0.0288786i
$853$	31.2209	+	6.63621i	1.06898	+	0.227219i	0.708618	−	0.705592i	$-0.249319\pi$
$853$	31.2209	+	6.63621i	1.06898	+	0.227219i	0.360365	+	0.932811i	$0.382652\pi$
$854$	4.26826	+	13.1363i	0.146057	+	0.449517i
$855$	19.9500	−	50.1461i	0.682275	−	1.71496i
$856$	5.37708	−	16.5490i	0.183785	−	0.565632i
$857$	−13.2538	+	22.9563i	−0.452742	+	0.784172i	−0.998555	−	0.0537346i	$-0.982887\pi$
$857$	−13.2538	+	22.9563i	−0.452742	+	0.784172i	0.545813	+	0.837907i	$0.316221\pi$
$858$	13.6337	−	8.31930i	0.465448	−	0.284016i
$859$	−25.3769	−	11.2985i	−0.865849	−	0.385501i	−0.0747601	−	0.997202i	$-0.523819\pi$
$859$	−25.3769	−	11.2985i	−0.865849	−	0.385501i	−0.791089	+	0.611701i	$0.790486\pi$
$860$	−0.0251790	+	3.02142i	−0.000858596	+	0.103030i
$861$	−34.4268	+	32.5461i	−1.17326	+	1.10917i
$862$	0.0807228	+	0.768026i	0.00274943	+	0.0261591i
$863$	−26.8507	+	19.5082i	−0.914010	+	0.664067i	−0.942026	−	0.335540i	$-0.891081\pi$
$863$	−26.8507	+	19.5082i	−0.914010	+	0.664067i	0.0280160	+	0.999607i	$0.491081\pi$
$864$	8.25515	+	6.40924i	0.280846	+	0.218047i
$865$	−13.8946	+	1.34341i	−0.472431	+	0.0456774i
$866$	5.08133	+	48.3456i	0.172671	+	1.64285i
$867$	−20.5225	−	11.1932i	−0.696981	−	0.380141i
$868$	−3.87287	−	6.70801i	−0.131454	−	0.227685i
$869$	15.6678	−	3.33029i	0.531493	−	0.112972i
$870$	−15.2259	+	0.242916i	−0.516206	+	0.00823561i
$871$	−11.6824	−	2.48317i	−0.395843	−	0.0841391i
$872$	7.90835	+	24.3394i	0.267811	+	0.824236i
$873$	−0.227966	+	0.0110815i	−0.00771547	+	0.000375052i
$874$	−39.7581			−1.34484
$875$	30.9812	−	2.47506i	1.04736	−	0.0836724i
$876$	−1.15836	+	0.407731i	−0.0391375	+	0.0137759i
$877$	−1.96772	+	18.7216i	−0.0664453	+	0.632185i	0.909730	+	0.415201i	$0.136289\pi$
$877$	−1.96772	+	18.7216i	−0.0664453	+	0.632185i	−0.976175	+	0.216984i	$0.930378\pi$
$878$	−32.5830	+	36.1871i	−1.09962	+	1.22126i
$879$	−0.412812	−	0.540102i	−0.0139238	−	0.0182172i
$880$	−5.74356	−	28.1737i	−0.193615	−	0.949737i
$881$	12.0961	−	37.2279i	0.407528	−	1.25424i	−0.511238	−	0.859439i	$-0.670813\pi$
$881$	12.0961	−	37.2279i	0.407528	−	1.25424i	0.918766	−	0.394802i	$-0.129187\pi$
$882$	2.60603	+	1.01170i	0.0877495	+	0.0340658i
$883$	1.53348	−	4.71957i	0.0516058	−	0.158826i	−0.921932	−	0.387351i	$-0.873390\pi$
$883$	1.53348	−	4.71957i	0.0516058	−	0.158826i	0.973538	+	0.228525i	$0.0733902\pi$
$884$	−0.366785	−	3.48972i	−0.0123363	−	0.117372i
$885$	−37.3700	−	26.2504i	−1.25618	−	0.882397i
$886$	4.47253	−	42.5533i	0.150258	−	1.42961i
$887$	−28.7633	−	12.8062i	−0.965775	−	0.429991i	−0.137617	−	0.990485i	$-0.543944\pi$
$887$	−28.7633	−	12.8062i	−0.965775	−	0.429991i	−0.828158	+	0.560495i	$0.810611\pi$
$888$	13.8772	+	29.2365i	0.465687	+	0.981111i
$889$	1.76010	−	0.783646i	0.0590318	−	0.0262827i
$890$	6.38706	+	3.75888i	0.214095	+	0.125998i
$891$	−21.8211	+	29.5606i	−0.731033	+	0.990317i
$892$	−1.29498	+	3.98555i	−0.0433593	+	0.133446i
$893$	−1.41113	+	2.44415i	−0.0472217	+	0.0817903i
$894$	4.77781	+	2.60587i	0.159794	+	0.0871532i
$895$	−0.276040	+	33.1242i	−0.00922700	+	1.10722i
$896$	13.6573	−	15.1680i	0.456259	−	0.506727i
$897$	−4.53264	+	10.8844i	−0.151340	+	0.363420i
$898$	−5.84269	+	2.60133i	−0.194973	+	0.0868076i
$899$	−23.7497			−0.792098
$900$	−4.86368	+	2.35413i	−0.162123	+	0.0784711i
$901$	50.7384			1.69034
$902$	−46.9909	+	20.9217i	−1.56462	+	0.696616i
$903$	−10.9678	−	14.3497i	−0.364986	−	0.477529i
$904$	4.83710	−	5.37214i	0.160879	−	0.178675i
$905$	−31.1153	+	42.0846i	−1.03431	+	1.39894i
$906$	0.297109	+	12.2313i	0.00987077	+	0.406358i
$907$	−28.0817	+	48.6389i	−0.932436	+	1.61503i	−0.153293	+	0.988181i	$0.548988\pi$
$907$	−28.0817	+	48.6389i	−0.932436	+	1.61503i	−0.779143	+	0.626846i	$0.784346\pi$
$908$	−0.193744	+	0.596282i	−0.00642961	+	0.0197883i
$909$	4.23240	−	15.5596i	0.140380	−	0.516078i
$910$	−10.5118	+	9.30746i	−0.348464	+	0.308539i
$911$	5.58252	−	2.48550i	0.184957	−	0.0823483i	−0.312169	−	0.950027i	$-0.601055\pi$
$911$	5.58252	−	2.48550i	0.184957	−	0.0823483i	0.497126	+	0.867678i	$0.334389\pi$
$912$	43.7492	+	3.52652i	1.44868	+	0.116775i
$913$	−44.8838	−	19.9836i	−1.48544	−	0.661359i
$914$	−3.78142	+	35.9778i	−0.125078	+	1.19004i
$915$	14.6478	−	3.35856i	0.484240	−	0.111031i
$916$	0.144126	+	1.37127i	0.00476207	+	0.0453081i
$917$	4.81267	−	14.8119i	0.158928	−	0.489131i
$918$	−17.3494	−	32.3912i	−0.572616	−	1.06907i
$919$	−2.31734	+	7.13203i	−0.0764419	+	0.235264i	−0.981975	−	0.189012i	$-0.939471\pi$
$919$	−2.31734	+	7.13203i	−0.0764419	+	0.235264i	0.905533	+	0.424276i	$0.139471\pi$
$920$	19.2361	+	17.6127i	0.634194	+	0.580673i
$921$	−9.55232	+	1.23919i	−0.314760	+	0.0408326i
$922$	−17.4787	+	19.4121i	−0.575632	+	0.639304i
$923$	0.871471	−	8.29149i	0.0286848	−	0.272918i
$924$	−5.37563	−	4.60886i	−0.176845	−	0.151620i
$925$	−30.9064	−	0.515152i	−1.01620	−	0.0169381i
$926$	−31.1210			−1.02270
$927$	8.87635	−	17.2589i	0.291537	−	0.566856i
$928$	1.90838	+	5.87338i	0.0626455	+	0.192803i
$929$	−28.4509	−	6.04742i	−0.933443	−	0.198409i	−0.284004	−	0.958823i	$-0.591663\pi$
$929$	−28.4509	−	6.04742i	−0.933443	−	0.198409i	−0.649439	+	0.760414i	$0.724996\pi$
$930$	34.7916	−	16.1601i	1.14086	−	0.529909i
$931$	−5.72652	+	1.21721i	−0.187679	+	0.0398924i
$932$	−0.373637	−	0.647158i	−0.0122389	−	0.0211984i
$933$	−0.163468	−	6.72960i	−0.00535169	−	0.220317i
$934$	0.151367	+	1.44016i	0.00495288	+	0.0471235i
$935$	10.8917	−	49.2211i	0.356198	−	1.60970i
$936$	7.31475	−	14.2226i	0.239090	−	0.464879i
$937$	−4.48748	+	3.26034i	−0.146599	+	0.106511i	−0.658667	−	0.752434i	$-0.728880\pi$
$937$	−4.48748	+	3.26034i	−0.146599	+	0.106511i	0.512068	+	0.858945i	$0.328880\pi$
$938$	−2.51946	−	23.9710i	−0.0822632	−	0.782682i
$939$	11.5498	+	48.5128i	0.376912	+	1.58316i
$940$	0.269458	−	0.0850763i	0.00878875	−	0.00277488i
$941$	−0.691697	−	0.307963i	−0.0225487	−	0.0100393i	0.395431	−	0.918496i	$-0.370595\pi$
$941$	−0.691697	−	0.307963i	−0.0225487	−	0.0100393i	−0.417980	+	0.908456i	$0.637262\pi$
$942$	−12.9011	−	7.03638i	−0.420340	−	0.229258i
$943$	18.9862	−	32.8850i	0.618275	−	1.07088i
$944$	11.4771	−	35.3228i	0.373547	−	1.14966i
$945$	14.3124	−	28.9551i	0.465581	−	0.941908i
$946$	−6.05979	−	18.6501i	−0.197021	−	0.606367i
$947$	11.0397	+	2.34657i	0.358743	+	0.0762531i	0.383757	−	0.923434i	$-0.374630\pi$
$947$	11.0397	+	2.34657i	0.358743	+	0.0762531i	−0.0250146	+	0.999687i	$0.507963\pi$
$948$	1.77895	−	1.68177i	0.0577775	−	0.0546212i
$949$	1.73584	+	3.00656i	0.0563477	+	0.0975971i
$950$	−26.4953	+	44.1742i	−0.859620	+	1.43320i
$951$	10.9036	+	9.34832i	0.353573	+	0.303140i
$952$	42.3863	−	18.8716i	1.37375	−	0.611632i
$953$	9.88820	+	30.4328i	0.320310	+	0.985814i	0.973513	+	0.228631i	$0.0734248\pi$
$953$	9.88820	+	30.4328i	0.320310	+	0.985814i	−0.653203	+	0.757183i	$0.726575\pi$
$954$	29.5287	+	19.3355i	0.956026	+	0.626011i
$955$	7.09222	−	32.0506i	0.229499	−	1.03713i
$956$	6.31039	+	7.00840i	0.204093	+	0.226668i
$957$	−20.4796	+	7.20858i	−0.662010	+	0.233020i
$958$	34.4975	−	7.33268i	1.11456	−	0.236908i
$959$	13.2252	+	5.88822i	0.427063	+	0.190141i
$960$	−23.4047	−	25.1741i	−0.755383	−	0.812490i
$961$	26.3371	−	11.7260i	0.849583	−	0.378259i
$962$	11.2969	−	8.20769i	0.364227	−	0.264627i
$963$	16.7002	−	4.40707i	0.538156	−	0.142016i
$964$	−7.19413	−	5.22684i	−0.231707	−	0.168345i
$965$	1.39108	+	6.82363i	0.0447804	+	0.219660i
$966$	−23.7175	−	1.91181i	−0.763098	−	0.0615115i
$967$	−13.1135	+	2.78737i	−0.421703	+	0.0896356i	−0.413875	−	0.910334i	$-0.635825\pi$
$967$	−13.1135	+	2.78737i	−0.421703	+	0.0896356i	−0.00782753	+	0.999969i	$0.502492\pi$
$968$	−8.56311	−	14.8317i	−0.275229	−	0.476710i
$969$	67.5574	+	36.8465i	2.17026	+	1.18368i
$970$	0.216449	+	0.0245750i	0.00694977	+	0.000789057i
$971$	−2.88021	−	8.86439i	−0.0924305	−	0.284472i	0.894145	−	0.447777i	$-0.147784\pi$
$971$	−2.88021	−	8.86439i	−0.0924305	−	0.284472i	−0.986576	+	0.163306i	$0.947784\pi$
$972$	−0.493572	+	5.59370i	−0.0158313	+	0.179418i
$973$	27.5862	+	20.0425i	0.884372	+	0.642534i
$974$	2.53913	−	4.39790i	0.0813589	−	0.140918i
$975$	9.07277	+	12.2896i	0.290561	+	0.393581i
$976$	6.11084	+	10.5843i	0.195603	+	0.338795i
$977$	−2.75929	+	26.2529i	−0.0882774	+	0.839903i	0.857368	+	0.514704i	$0.172098\pi$
$977$	−2.75929	+	26.2529i	−0.0882774	+	0.839903i	−0.945645	+	0.325199i	$0.894569\pi$
$978$	−13.6179	+	32.7012i	−0.435453	+	1.04567i
$979$	10.3355	+	2.19687i	0.330323	+	0.0702123i
$980$	0.505167	+	0.297299i	0.0161370	+	0.00949686i
$981$	−16.0611	+	19.6809i	−0.512790	+	0.628362i
$982$	−49.4113			−1.57678
$983$	8.05428	+	8.94518i	0.256892	+	0.285307i	0.857770	−	0.514033i	$-0.171849\pi$
$983$	8.05428	+	8.94518i	0.256892	+	0.285307i	−0.600879	+	0.799340i	$0.705183\pi$
$984$	−29.2549	+	42.3939i	−0.932611	+	1.35147i
$985$	−0.00413353	+	0.496014i	−0.000131705	+	0.0158043i
$986$	2.26961	−	21.5939i	0.0722791	−	0.687690i
$987$	−0.959331	+	1.39019i	−0.0305358	+	0.0442501i
$988$	0.534347	+	5.08397i	0.0169998	+	0.161743i
$989$	11.7116	+	8.50899i	0.372408	+	0.270570i
$990$	25.0961	−	24.4950i	0.797606	−	0.778501i
$991$	−41.4190	+	30.0926i	−1.31572	+	0.955924i	−0.315741	+	0.948845i	$0.602253\pi$
$991$	−41.4190	+	30.0926i	−1.31572	+	0.955924i	−0.999975	+	0.00707861i	$0.997747\pi$
$992$	−10.4100	−	11.5614i	−0.330517	−	0.367076i
$993$	21.3042	+	18.2654i	0.676069	+	0.579635i
$994$	16.4576	−	3.49818i	0.522004	−	0.110955i
$995$	13.0330	+	4.35507i	0.413173	+	0.138065i
$996$	−7.44653	+	0.966011i	−0.235952	+	0.0306092i
$997$	−24.6904	−	5.24811i	−0.781953	−	0.166209i	−0.200396	−	0.979715i	$-0.564223\pi$
$997$	−24.6904	−	5.24811i	−0.781953	−	0.166209i	−0.581557	+	0.813506i	$0.697556\pi$
$998$	−2.33305	−	1.69506i	−0.0738513	−	0.0536561i
$999$	−16.9397	+	27.2938i	−0.535950	+	0.863539i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	225.2.q.a.16.10	✓	224
3.2	odd	2		675.2.r.a.316.19		224
9.4	even	3	inner	225.2.q.a.166.19	yes	224
9.5	odd	6		675.2.r.a.91.10		224
25.11	even	5	inner	225.2.q.a.61.19	yes	224
75.11	odd	10		675.2.r.a.586.10		224
225.86	odd	30		675.2.r.a.361.19		224
225.211	even	15	inner	225.2.q.a.211.10	yes	224

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
225.2.q.a.16.10	✓	224	1.1	even	1	trivial
225.2.q.a.61.19	yes	224	25.11	even	5	inner
225.2.q.a.166.19	yes	224	9.4	even	3	inner
225.2.q.a.211.10	yes	224	225.211	even	15	inner
675.2.r.a.91.10		224	9.5	odd	6
675.2.r.a.316.19		224	3.2	odd	2
675.2.r.a.361.19		224	225.86	odd	30
675.2.r.a.586.10		224	75.11	odd	10

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-1.16983 + 0.520841i) q^{2} +(1.71766 - 0.222825i) q^{3} +(-0.241041 + 0.267703i) q^{4} +(2.12080 + 0.708681i) q^{5} +(-1.89331 + 1.15529i) q^{6} +(1.38994 - 2.40744i) q^{7} +(0.933960 - 2.87443i) q^{8} +(2.90070 - 0.765476i) q^{9} +O(q^{10})\)	\(q+(-1.16983 + 0.520841i) q^{2} +(1.71766 - 0.222825i) q^{3} +(-0.241041 + 0.267703i) q^{4} +(2.12080 + 0.708681i) q^{5} +(-1.89331 + 1.15529i) q^{6} +(1.38994 - 2.40744i) q^{7} +(0.933960 - 2.87443i) q^{8} +(2.90070 - 0.765476i) q^{9} +(-2.85007 + 0.275562i) q^{10} +(-3.72952 + 1.66049i) q^{11} +(-0.354375 + 0.513533i) q^{12} +(1.61140 + 0.717440i) q^{13} +(-0.372093 + 3.54022i) q^{14} +(3.80071 + 0.744704i) q^{15} +(0.329241 + 3.13252i) q^{16} +(-1.70650 + 5.25207i) q^{17} +(-2.99462 + 2.40627i) q^{18} +(2.48610 - 7.65144i) q^{19} +(-0.700915 + 0.396922i) q^{20} +(1.85100 - 4.44487i) q^{21} +(3.49804 - 3.88497i) q^{22} +(-0.403397 + 3.83806i) q^{23} +(0.963727 - 5.14540i) q^{24} +(3.99554 + 3.00593i) q^{25} -2.25873 q^{26} +(4.81184 - 1.96117i) q^{27} +(0.309448 + 0.952382i) q^{28} +(3.00335 + 0.638381i) q^{29} +(-4.83405 + 1.10839i) q^{30} +(-7.56593 + 1.60819i) q^{31} +(1.00566 + 1.74185i) q^{32} +(-6.03603 + 3.68318i) q^{33} +(-0.739181 - 7.03283i) q^{34} +(4.65388 - 4.12067i) q^{35} +(-0.494267 + 0.961037i) q^{36} +(-5.00145 + 3.63377i) q^{37} +(1.07687 + 10.2457i) q^{38} +(2.92769 + 0.873256i) q^{39} +(4.01779 - 5.43420i) q^{40} +(-8.98876 - 4.00205i) q^{41} +(0.149724 + 6.16381i) q^{42} +(1.87556 - 3.24857i) q^{43} +(0.454449 - 1.39865i) q^{44} +(6.69426 + 0.432252i) q^{45} +(-1.52712 - 4.69998i) q^{46} +(-0.343135 - 0.0729356i) q^{47} +(1.26353 + 5.30723i) q^{48} +(-0.363847 - 0.630202i) q^{49} +(-6.23971 - 1.43538i) q^{50} +(-1.76089 + 9.40152i) q^{51} +(-0.580473 + 0.258443i) q^{52} +(-2.83919 - 8.73813i) q^{53} +(-4.60756 + 4.80044i) q^{54} +(-9.08629 + 0.878518i) q^{55} +(-5.62188 - 6.24373i) q^{56} +(2.56534 - 13.6965i) q^{57} +(-3.84589 + 0.817469i) q^{58} +(-10.7721 - 4.79604i) q^{59} +(-1.11549 + 0.837959i) q^{60} +(3.54472 - 1.57821i) q^{61} +(8.01322 - 5.82194i) q^{62} +(2.18895 - 8.04722i) q^{63} +(-7.18012 - 5.21666i) q^{64} +(2.90901 + 2.66351i) q^{65} +(5.14277 - 7.45249i) q^{66} +(-6.62308 + 1.40778i) q^{67} +(-0.994660 - 1.72280i) q^{68} +(0.162320 + 6.68237i) q^{69} +(-3.29802 + 7.24440i) q^{70} +(-1.46059 - 4.49524i) q^{71} +(0.508827 - 9.05278i) q^{72} +(1.59230 + 1.15687i) q^{73} +(3.95822 - 6.85584i) q^{74} +(7.53278 + 4.27286i) q^{75} +(1.44906 + 2.50985i) q^{76} +(-1.18627 + 11.2866i) q^{77} +(-3.87972 + 0.503301i) q^{78} +(-3.83783 - 0.815756i) q^{79} +(-1.52170 + 6.87676i) q^{80} +(7.82809 - 4.44083i) q^{81} +12.5997 q^{82} +(8.05282 + 8.94357i) q^{83} +(0.743740 + 1.56691i) q^{84} +(-7.34118 + 9.92921i) q^{85} +(-0.502096 + 4.77713i) q^{86} +(5.30097 + 0.427298i) q^{87} +(1.28974 + 12.2711i) q^{88} +(-2.09393 - 1.52133i) q^{89} +(-8.05626 + 2.98098i) q^{90} +(3.96693 - 2.88214i) q^{91} +(-0.930227 - 1.03312i) q^{92} +(-12.6373 + 4.44820i) q^{93} +(0.439396 - 0.0933965i) q^{94} +(10.6949 - 14.4653i) q^{95} +(2.11551 + 2.76782i) q^{96} +(-0.0744158 - 0.0158176i) q^{97} +(0.753873 + 0.547721i) q^{98} +(-9.54714 + 7.67143i) 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

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more