LMFDB - Embedded newform 507.2.t.b.4.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [507,2,Mod(4,507)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(507, base_ring=CyclotomicField(78))

chi = DirichletCharacter(H, H._module([0, 1]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("507.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 507 = 3 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	507.t (of order $78$, degree $24$, 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:	$4.04841538248$
Analytic rank:	$0$
Dimension:	$360$
Relative dimension:	$15$ over $\Q(\zeta_{78})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{78}]$

Embedding invariants

Embedding label			4.7
Character	$\chi$	$=$	507.4
Dual form			507.2.t.b.127.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.218325 - 0.00879818i) q^{2} +(-0.278217 + 0.960518i) q^{3} +(-1.94593 - 0.157091i) q^{4} +(-3.83328 - 1.45377i) q^{5} +(0.0691925 - 0.207257i) q^{6} +(1.70758 + 4.00784i) q^{7} +(0.857279 + 0.104093i) q^{8} +(-0.845190 - 0.534466i) q^{9} +O(q^{10})$	\(q+(-0.218325 - 0.00879818i) q^{2} +(-0.278217 + 0.960518i) q^{3} +(-1.94593 - 0.157091i) q^{4} +(-3.83328 - 1.45377i) q^{5} +(0.0691925 - 0.207257i) q^{6} +(1.70758 + 4.00784i) q^{7} +(0.857279 + 0.104093i) q^{8} +(-0.845190 - 0.534466i) q^{9} +(0.824109 + 0.351120i) q^{10} +(-0.471741 - 0.745999i) q^{11} +(0.692280 - 1.82539i) q^{12} +(0.0746234 - 3.60478i) q^{13} +(-0.337546 - 0.890034i) q^{14} +(2.46286 - 3.27747i) q^{15} +(3.66770 + 0.596060i) q^{16} +(-2.47890 + 1.05616i) q^{17} +(0.179823 + 0.124123i) q^{18} +(5.33520 - 3.08028i) q^{19} +(7.23091 + 3.43111i) q^{20} +(-4.32468 + 0.525112i) q^{21} +(0.0964293 + 0.167020i) q^{22} +(2.74639 - 4.75689i) q^{23} +(-0.338493 + 0.794472i) q^{24} +(8.83804 + 7.82982i) q^{25} +(-0.0480076 + 0.786356i) q^{26} +(0.748511 - 0.663123i) q^{27} +(-2.69323 - 8.06721i) q^{28} +(0.160201 - 3.97535i) q^{29} +(-0.566539 + 0.693884i) q^{30} +(-5.18259 - 5.84993i) q^{31} +(-2.48775 - 0.507878i) q^{32} +(0.847792 - 0.245566i) q^{33} +(0.550498 - 0.208776i) q^{34} +(-0.719154 - 17.8456i) q^{35} +(1.56072 + 1.17280i) q^{36} +(1.36128 - 0.277908i) q^{37} +(-1.19191 + 0.625561i) q^{38} +(3.44169 + 1.07459i) q^{39} +(-3.13487 - 1.64530i) q^{40} +(8.14041 + 2.35790i) q^{41} +(0.948805 - 0.0765955i) q^{42} +(-0.847610 + 4.15187i) q^{43} +(0.800783 + 1.52577i) q^{44} +(2.46286 + 3.27747i) q^{45} +(-0.641458 + 1.01438i) q^{46} +(-1.15310 + 0.795930i) q^{47} +(-1.59294 + 3.35706i) q^{48} +(-8.29789 + 8.63902i) q^{49} +(-1.86067 - 1.78720i) q^{50} +(-0.324789 - 2.67488i) q^{51} +(-0.711492 + 7.00291i) q^{52} +(-0.436224 + 3.59263i) q^{53} +(-0.169253 + 0.138190i) q^{54} +(0.723804 + 3.54543i) q^{55} +(1.04669 + 3.61359i) q^{56} +(1.47432 + 5.98155i) q^{57} +(-0.0699517 + 0.866508i) q^{58} +(-1.39690 - 8.59548i) q^{59} +(-5.30741 + 5.99082i) q^{60} +(9.91335 - 7.44940i) q^{61} +(1.08002 + 1.32278i) q^{62} +(0.698823 - 4.30003i) q^{63} +(-6.67702 - 1.64574i) q^{64} +(-5.52658 + 13.7096i) q^{65} +(-0.187254 + 0.0461541i) q^{66} +(0.132931 + 1.64665i) q^{67} +(4.98968 - 1.66580i) q^{68} +(3.80499 + 3.96141i) q^{69} +3.90247i q^{70} +(2.58919 - 2.48695i) q^{71} +(-0.668930 - 0.546164i) q^{72} +(-3.89183 + 7.41526i) q^{73} +(-0.299646 + 0.0486973i) q^{74} +(-9.97959 + 6.31071i) q^{75} +(-10.8658 + 5.15588i) q^{76} +(2.18431 - 3.16452i) q^{77} +(-0.741952 - 0.264890i) q^{78} +(-1.09155 - 1.58138i) q^{79} +(-13.1928 - 7.61687i) q^{80} +(0.428693 + 0.903450i) q^{81} +(-1.75651 - 0.586408i) q^{82} +(1.12885 - 4.57991i) q^{83} +(8.49801 - 0.342458i) q^{84} +(11.0378 - 0.444806i) q^{85} +(0.221583 - 0.898998i) q^{86} +(3.77383 + 1.25989i) q^{87} +(-0.326761 - 0.688634i) q^{88} +(-12.4332 - 7.17831i) q^{89} +(-0.508867 - 0.737222i) q^{90} +(14.5748 - 5.85638i) q^{91} +(-6.09155 + 8.82513i) q^{92} +(7.06086 - 3.35042i) q^{93} +(0.258754 - 0.163626i) q^{94} +(-24.9294 + 4.05141i) q^{95} +(1.17996 - 2.24823i) q^{96} +(-13.8277 - 11.2900i) q^{97} +(1.88764 - 1.81310i) q^{98} +0.882640i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 360 q - 15 q^{3} - 14 q^{4} + 3 q^{7} + 15 q^{9}+O(q^{10}) $ 360 * q - 15 * q^3 - 14 * q^4 + 3 * q^7 + 15 * q^9	$ 360 q - 15 q^{3} - 14 q^{4} + 3 q^{7} + 15 q^{9} + 6 q^{11} - 28 q^{12} + 6 q^{13} + 4 q^{14} - 6 q^{15} + 20 q^{16} - 6 q^{19} - 12 q^{20} - 28 q^{22} + 46 q^{23} - 6 q^{25} - 39 q^{26} + 30 q^{27} - 6 q^{28} + 43 q^{29} + 26 q^{31} - 195 q^{32} + 19 q^{33} + 65 q^{34} + 84 q^{35} - 14 q^{36} - 65 q^{38} - 2 q^{39} + 12 q^{41} - 128 q^{42} + 83 q^{43} - 39 q^{44} - 6 q^{45} - 20 q^{48} + 72 q^{49} - 52 q^{50} - 55 q^{52} + 49 q^{53} - 49 q^{55} - 2 q^{56} + 26 q^{57} + 26 q^{58} - 202 q^{59} - 182 q^{60} - 3 q^{61} - 65 q^{62} - 3 q^{63} - 14 q^{64} - 58 q^{65} + 48 q^{66} - 41 q^{67} + 139 q^{68} + 6 q^{69} - 60 q^{71} - 52 q^{73} - 269 q^{74} + 23 q^{75} - 14 q^{76} + 70 q^{77} - 65 q^{78} + 18 q^{79} + 492 q^{80} + 15 q^{81} - 65 q^{82} + 78 q^{83} - 6 q^{84} - 91 q^{85} - 169 q^{86} + 48 q^{87} - 522 q^{88} - 12 q^{89} + 373 q^{91} + 72 q^{92} - 3 q^{93} - 13 q^{94} - 110 q^{95} + 65 q^{96} - 121 q^{97} - 104 q^{98}+O(q^{100}) $ 360 * q - 15 * q^3 - 14 * q^4 + 3 * q^7 + 15 * q^9 + 6 * q^11 - 28 * q^12 + 6 * q^13 + 4 * q^14 - 6 * q^15 + 20 * q^16 - 6 * q^19 - 12 * q^20 - 28 * q^22 + 46 * q^23 - 6 * q^25 - 39 * q^26 + 30 * q^27 - 6 * q^28 + 43 * q^29 + 26 * q^31 - 195 * q^32 + 19 * q^33 + 65 * q^34 + 84 * q^35 - 14 * q^36 - 65 * q^38 - 2 * q^39 + 12 * q^41 - 128 * q^42 + 83 * q^43 - 39 * q^44 - 6 * q^45 - 20 * q^48 + 72 * q^49 - 52 * q^50 - 55 * q^52 + 49 * q^53 - 49 * q^55 - 2 * q^56 + 26 * q^57 + 26 * q^58 - 202 * q^59 - 182 * q^60 - 3 * q^61 - 65 * q^62 - 3 * q^63 - 14 * q^64 - 58 * q^65 + 48 * q^66 - 41 * q^67 + 139 * q^68 + 6 * q^69 - 60 * q^71 - 52 * q^73 - 269 * q^74 + 23 * q^75 - 14 * q^76 + 70 * q^77 - 65 * q^78 + 18 * q^79 + 492 * q^80 + 15 * q^81 - 65 * q^82 + 78 * q^83 - 6 * q^84 - 91 * q^85 - 169 * q^86 + 48 * q^87 - 522 * q^88 - 12 * q^89 + 373 * q^91 + 72 * q^92 - 3 * q^93 - 13 * q^94 - 110 * q^95 + 65 * q^96 - 121 * q^97 - 104 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/507\mathbb{Z}\right)^\times$.

$n$	$170$	$340$
$\chi(n)$	$1$	$e\left(\frac{1}{78}\right)$

Coefficient data

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

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

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

$2$	−0.218325	−	0.00879818i	−0.154379	−	0.00622125i	−0.0370438	−	0.999314i	$-0.511794\pi$
$2$	−0.218325	−	0.00879818i	−0.154379	−	0.00622125i	−0.117335	+	0.993092i	$0.537435\pi$
$3$	−0.278217	+	0.960518i	−0.160629	+	0.554555i
$3$	−0.278217	+	0.960518i	−0.160629	+	0.554555i
$4$	−1.94593	−	0.157091i	−0.972963	−	0.0785457i
$5$	−3.83328	−	1.45377i	−1.71430	−	0.650147i	−0.715472	−	0.698641i	$-0.753788\pi$
$5$	−3.83328	−	1.45377i	−1.71430	−	0.650147i	−0.998823	+	0.0484944i	$0.984558\pi$
$6$	0.0691925	−	0.207257i	0.0282477	−	0.0846123i
$7$	1.70758	+	4.00784i	0.645405	+	1.51482i	0.844901	+	0.534923i	$0.179659\pi$
$7$	1.70758	+	4.00784i	0.645405	+	1.51482i	−0.199495	+	0.979899i	$0.563930\pi$
$8$	0.857279	+	0.104093i	0.303094	+	0.0368023i
$9$	−0.845190	−	0.534466i	−0.281730	−	0.178155i
$10$	0.824109	+	0.351120i	0.260606	+	0.111034i
$11$	−0.471741	−	0.745999i	−0.142235	−	0.224927i	0.766557	−	0.642177i	$-0.221968\pi$
$11$	−0.471741	−	0.745999i	−0.142235	−	0.224927i	−0.908792	+	0.417250i	$0.862994\pi$
$12$	0.692280	−	1.82539i	0.199844	−	0.526945i
$13$	0.0746234	−	3.60478i	0.0206968	−	0.999786i
$13$	0.0746234	−	3.60478i	0.0206968	−	0.999786i
$14$	−0.337546	−	0.890034i	−0.0902128	−	0.237872i
$15$	2.46286	−	3.27747i	0.635908	−	0.846240i
$16$	3.66770	+	0.596060i	0.916926	+	0.149015i
$17$	−2.47890	+	1.05616i	−0.601223	+	0.256157i	−0.671062	−	0.741401i	$-0.734162\pi$
$17$	−2.47890	+	1.05616i	−0.601223	+	0.256157i	0.0698394	+	0.997558i	$0.477751\pi$
$18$	0.179823	+	0.124123i	0.0423848	+	0.0292561i
$19$	5.33520	−	3.08028i	1.22398	−	0.706665i	0.258215	−	0.966087i	$-0.416866\pi$
$19$	5.33520	−	3.08028i	1.22398	−	0.706665i	0.965764	+	0.259423i	$0.0835323\pi$
$20$	7.23091	+	3.43111i	1.61688	+	0.767219i
$21$	−4.32468	+	0.525112i	−0.943723	+	0.114589i
$22$	0.0964293	+	0.167020i	0.0205588	+	0.0356089i
$23$	2.74639	−	4.75689i	0.572663	−	0.991881i	−0.423629	−	0.905836i	$-0.639244\pi$
$23$	2.74639	−	4.75689i	0.572663	−	0.991881i	0.996291	−	0.0860449i	$-0.0274229\pi$
$24$	−0.338493	+	0.794472i	−0.0690945	+	0.162171i
$25$	8.83804	+	7.82982i	1.76761	+	1.56596i
$26$	−0.0480076	+	0.786356i	−0.00941507	+	0.154217i
$27$	0.748511	−	0.663123i	0.144051	−	0.127618i
$28$	−2.69323	−	8.06721i	−0.508973	−	1.52456i
$29$	0.160201	−	3.97535i	0.0297486	−	0.738204i	−0.913642	−	0.406520i	$-0.866742\pi$
$29$	0.160201	−	3.97535i	0.0297486	−	0.738204i	0.943390	−	0.331684i	$-0.107617\pi$
$30$	−0.566539	+	0.693884i	−0.103435	+	0.126685i
$31$	−5.18259	−	5.84993i	−0.930821	−	1.05068i	−0.998596	−	0.0529787i	$-0.983128\pi$
$31$	−5.18259	−	5.84993i	−0.930821	−	1.05068i	0.0677750	−	0.997701i	$-0.478410\pi$
$32$	−2.48775	−	0.507878i	−0.439777	−	0.0897810i
$33$	0.847792	−	0.245566i	0.147582	−	0.0427475i
$34$	0.550498	−	0.208776i	0.0944097	−	0.0358049i
$35$	−0.719154	−	17.8456i	−0.121559	−	3.01646i
$36$	1.56072	+	1.17280i	0.260120	+	0.195467i
$37$	1.36128	−	0.277908i	0.223793	−	0.0456877i	−0.0868203	−	0.996224i	$-0.527671\pi$
$37$	1.36128	−	0.277908i	0.223793	−	0.0456877i	0.310614	+	0.950536i	$0.399465\pi$
$38$	−1.19191	+	0.625561i	−0.193353	+	0.101479i
$39$	3.44169	+	1.07459i	0.551112	+	0.172072i
$40$	−3.13487	−	1.64530i	−0.495666	−	0.260145i
$41$	8.14041	+	2.35790i	1.27132	+	0.368242i	0.844236	−	0.535971i	$-0.180054\pi$
$41$	8.14041	+	2.35790i	1.27132	+	0.368242i	0.427082	+	0.904213i	$0.359542\pi$
$42$	0.948805	−	0.0765955i	0.146404	−	0.0118189i
$43$	−0.847610	+	4.15187i	−0.129259	+	0.633154i	0.862607	+	0.505874i	$0.168830\pi$
$43$	−0.847610	+	4.15187i	−0.129259	+	0.633154i	−0.991867	+	0.127280i	$0.959375\pi$
$44$	0.800783	+	1.52577i	0.120723	+	0.230018i
$45$	2.46286	+	3.27747i	0.367142	+	0.488577i
$46$	−0.641458	+	1.01438i	−0.0945778	+	0.149563i
$47$	−1.15310	+	0.795930i	−0.168198	+	0.116098i	−0.649190	−	0.760626i	$-0.724892\pi$
$47$	−1.15310	+	0.795930i	−0.168198	+	0.116098i	0.480992	+	0.876725i	$0.340277\pi$
$48$	−1.59294	+	3.35706i	−0.229922	+	0.484550i
$49$	−8.29789	+	8.63902i	−1.18541	+	1.23415i
$50$	−1.86067	−	1.78720i	−0.263139	−	0.252749i
$51$	−0.324789	−	2.67488i	−0.0454795	−	0.374557i
$52$	−0.711492	+	7.00291i	−0.0986661	+	0.971129i
$53$	−0.436224	+	3.59263i	−0.0599200	+	0.493486i	0.931595	+	0.363497i	$0.118417\pi$
$53$	−0.436224	+	3.59263i	−0.0599200	+	0.493486i	−0.991515	+	0.129989i	$0.958506\pi$
$54$	−0.169253	+	0.138190i	−0.0230324	+	0.0188053i
$55$	0.723804	+	3.54543i	0.0975977	+	0.478065i
$56$	1.04669	+	3.61359i	0.139870	+	0.482886i
$57$	1.47432	+	5.98155i	0.195278	+	0.792275i
$58$	−0.0699517	+	0.866508i	−0.00918511	+	0.113778i
$59$	−1.39690	−	8.59548i	−0.181861	−	1.11904i	−0.904077	−	0.427369i	$-0.859441\pi$
$59$	−1.39690	−	8.59548i	−0.181861	−	1.11904i	0.722217	−	0.691667i	$-0.243123\pi$
$60$	−5.30741	+	5.99082i	−0.685183	+	0.773412i
$61$	9.91335	−	7.44940i	1.26927	−	0.953798i	0.269317	−	0.963051i	$-0.413202\pi$
$61$	9.91335	−	7.44940i	1.26927	−	0.953798i	0.999957	+	0.00925353i	$0.00294553\pi$
$62$	1.08002	+	1.32278i	0.137162	+	0.167994i
$63$	0.698823	−	4.30003i	0.0880435	−	0.541753i
$64$	−6.67702	−	1.64574i	−0.834628	−	0.205717i
$65$	−5.52658	+	13.7096i	−0.685488	+	1.70047i
$66$	−0.187254	+	0.0461541i	−0.0230494	+	0.00568117i
$67$	0.132931	+	1.64665i	0.0162401	+	0.201170i	0.999789	+	0.0205291i	$0.00653508\pi$
$67$	0.132931	+	1.64665i	0.0162401	+	0.201170i	−0.983549	+	0.180641i	$0.942183\pi$
$68$	4.98968	−	1.66580i	0.605088	−	0.202008i
$69$	3.80499	+	3.96141i	0.458067	+	0.476898i
$70$			3.90247i			0.466434i
$71$	2.58919	−	2.48695i	0.307280	−	0.295147i	−0.523183	−	0.852221i	$-0.675255\pi$
$71$	2.58919	−	2.48695i	0.307280	−	0.295147i	0.830463	+	0.557074i	$0.188076\pi$
$72$	−0.668930	−	0.546164i	−0.0788341	−	0.0643661i
$73$	−3.89183	+	7.41526i	−0.455504	+	0.867891i	0.544079	+	0.839034i	$0.316879\pi$
$73$	−3.89183	+	7.41526i	−0.455504	+	0.867891i	−0.999584	+	0.0288568i	$0.990813\pi$
$74$	−0.299646	+	0.0486973i	−0.0348332	+	0.00566094i
$75$	−9.97959	+	6.31071i	−1.15234	+	0.728698i
$76$	−10.8658	+	5.15588i	−1.24639	+	0.591420i
$77$	2.18431	−	3.16452i	0.248925	−	0.360630i
$78$	−0.741952	−	0.264890i	−0.0840095	−	0.0299929i
$79$	−1.09155	−	1.58138i	−0.122809	−	0.177919i	0.756757	−	0.653696i	$-0.226782\pi$
$79$	−1.09155	−	1.58138i	−0.122809	−	0.177919i	−0.879566	+	0.475777i	$0.842167\pi$
$80$	−13.1928	−	7.61687i	−1.47500	−	0.851592i
$81$	0.428693	+	0.903450i	0.0476325	+	0.100383i
$82$	−1.75651	−	0.586408i	−0.193974	−	0.0647579i
$83$	1.12885	−	4.57991i	0.123907	−	0.502710i	−0.875889	−	0.482513i	$-0.839724\pi$
$83$	1.12885	−	4.57991i	0.123907	−	0.502710i	0.999796	−	0.0201978i	$-0.00642959\pi$
$84$	8.49801	−	0.342458i	0.927209	−	0.0373652i
$85$	11.0378	−	0.444806i	1.19721	−	0.0482460i
$86$	0.221583	−	0.898998i	0.0238939	−	0.0969414i
$87$	3.77383	+	1.25989i	0.404597	+	0.135074i
$88$	−0.326761	−	0.688634i	−0.0348328	−	0.0734086i
$89$	−12.4332	−	7.17831i	−1.31792	−	0.760899i	−0.334523	−	0.942388i	$-0.608575\pi$
$89$	−12.4332	−	7.17831i	−1.31792	−	0.760899i	−0.983393	+	0.181488i	$0.941909\pi$
$90$	−0.508867	−	0.737222i	−0.0536393	−	0.0777100i
$91$	14.5748	−	5.85638i	1.52786	−	0.613915i
$92$	−6.09155	+	8.82513i	−0.635088	+	0.920083i
$93$	7.06086	−	3.35042i	0.732177	−	0.347422i
$94$	0.258754	−	0.163626i	0.0266884	−	0.0168767i
$95$	−24.9294	+	4.05141i	−2.55770	+	0.415666i
$96$	1.17996	−	2.24823i	0.120429	−	0.229459i
$97$	−13.8277	−	11.2900i	−1.40399	−	1.14632i	−0.969339	−	0.245726i	$-0.920974\pi$
$97$	−13.8277	−	11.2900i	−1.40399	−	1.14632i	−0.434652	−	0.900598i	$-0.643129\pi$
$98$	1.88764	−	1.81310i	0.190681	−	0.183151i
$99$			0.882640i			0.0887087i
$100$	−15.9682	−	16.6246i	−1.59682	−	1.66246i
$101$	15.4034	−	5.14241i	1.53270	−	0.511689i	0.579741	−	0.814801i	$-0.303154\pi$
$101$	15.4034	−	5.14241i	1.53270	−	0.511689i	0.952955	+	0.303111i	$0.0980254\pi$
$102$	0.0473753	+	0.586849i	0.00469086	+	0.0581067i
$103$	10.2907	−	2.53644i	1.01398	−	0.249923i	0.302888	−	0.953026i	$-0.402049\pi$
$103$	10.2907	−	2.53644i	1.01398	−	0.249923i	0.711088	+	0.703103i	$0.248203\pi$
$104$	0.439204	−	3.08253i	0.0430675	−	0.302267i
$105$	17.3411	+	4.27420i	1.69232	+	0.417120i
$106$	0.126847	−	0.780522i	0.0123205	−	0.0758110i
$107$	−6.98643	−	8.55682i	−0.675403	−	0.827219i	0.317234	−	0.948347i	$-0.397246\pi$
$107$	−6.98643	−	8.55682i	−0.675403	−	0.827219i	−0.992637	+	0.121129i	$0.961349\pi$
$108$	−1.56072	+	1.17280i	−0.150180	+	0.112853i
$109$	4.33164	−	4.88941i	0.414896	−	0.468320i	−0.503493	−	0.863999i	$-0.667952\pi$
$109$	4.33164	−	4.88941i	0.414896	−	0.468320i	0.918389	+	0.395679i	$0.129491\pi$
$110$	−0.126831	−	0.780422i	−0.0120929	−	0.0744104i
$111$	−0.111797	+	1.38485i	−0.0106113	+	0.131445i
$112$	3.87399	+	15.7174i	0.366058	+	1.48515i
$113$	3.79442	+	13.0999i	0.356949	+	1.23233i	0.915316	+	0.402737i	$0.131941\pi$
$113$	3.79442	+	13.0999i	0.356949	+	1.23233i	−0.558367	+	0.829594i	$0.688572\pi$
$114$	−0.269253	−	1.31889i	−0.0252179	−	0.123525i
$115$	−17.4431	+	14.2419i	−1.62658	+	1.32806i
$116$	−0.936233	+	7.71058i	−0.0869271	+	0.715909i
$117$	−1.98970	+	3.00684i	−0.183948	+	0.277982i
$118$	0.229353	+	1.88889i	0.0211137	+	0.173887i
$119$	−8.46587	−	8.13157i	−0.776065	−	0.745420i
$120$	2.45252	−	2.55334i	0.223883	−	0.233087i
$121$	4.38164	−	9.23412i	0.398331	−	0.839465i
$122$	−2.22987	+	1.53917i	−0.201883	+	0.139350i
$123$	−4.52961	+	7.16300i	−0.408421	+	0.645866i
$124$	9.16596	+	12.1977i	0.823128	+	1.09538i
$125$	−12.9698	−	24.7119i	−1.16006	−	2.21030i
$126$	−0.190403	+	0.932655i	−0.0169624	+	0.0830875i
$127$	−0.0175567	+	0.00141732i	−0.00155790	+	0.000125767i	−0.0812455	−	0.996694i	$-0.525890\pi$
$127$	−0.0175567	+	0.00141732i	−0.00155790	+	0.000125767i	0.0796876	+	0.996820i	$0.474608\pi$
$128$	6.32091	+	1.83088i	0.558695	+	0.161828i
$129$	−3.75213	−	1.96927i	−0.330356	−	0.173384i
$130$	1.32721	−	2.94453i	0.116404	−	0.258252i
$131$	10.1399	−	5.32185i	0.885931	−	0.464972i	0.0405754	−	0.999176i	$-0.487081\pi$
$131$	10.1399	−	5.32185i	0.885931	−	0.464972i	0.845356	+	0.534204i	$0.179389\pi$
$132$	−1.68832	+	0.344672i	−0.146949	+	0.0299999i
$133$	21.4556	+	16.1228i	1.86043	+	1.39803i
$134$	−0.0145346	−	0.360673i	−0.00125560	−	0.0311574i
$135$	−3.83328	+	1.45377i	−0.329916	+	0.125121i
$136$	−2.23505	+	0.647391i	−0.191654	+	0.0555133i
$137$	−10.0156	−	2.04469i	−0.855688	−	0.174690i	−0.247896	−	0.968787i	$-0.579739\pi$
$137$	−10.0156	−	2.04469i	−0.855688	−	0.174690i	−0.607792	+	0.794097i	$0.707944\pi$
$138$	−0.795869	−	0.898351i	−0.0677489	−	0.0764727i
$139$	−1.50720	+	1.84598i	−0.127839	+	0.156574i	−0.834558	−	0.550920i	$-0.814277\pi$
$139$	−1.50720	+	1.84598i	−0.127839	+	0.156574i	0.706719	+	0.707494i	$0.250174\pi$
$140$	−1.40397	+	34.8392i	−0.118657	+	2.94445i
$141$	−0.443692	−	1.32902i	−0.0373656	−	0.111924i
$142$	−0.587164	+	0.520182i	−0.0492737	+	0.0436527i
$143$	−2.72436	+	1.64485i	−0.227823	+	0.137550i
$144$	−2.78133	−	2.46405i	−0.231778	−	0.205337i
$145$	−6.39335	+	15.0057i	−0.530939	+	1.24616i
$146$	0.914923	−	1.58469i	0.0757196	−	0.131150i
$147$	−5.98932	−	10.3738i	−0.493991	−	0.855617i
$148$	−2.69261	+	0.326942i	−0.221331	+	0.0268745i
$149$	−13.7821	−	6.53968i	−1.12907	−	0.535751i	−0.229842	−	0.973228i	$-0.573821\pi$
$149$	−13.7821	−	6.53968i	−1.12907	−	0.535751i	−0.899230	+	0.437477i	$0.855872\pi$
$150$	2.23431	−	1.28998i	0.182431	−	0.105326i
$151$	3.56037	+	2.45754i	0.289739	+	0.199992i	0.704064	−	0.710137i	$-0.251367\pi$
$151$	3.56037	+	2.45754i	0.289739	+	0.199992i	−0.414325	+	0.910129i	$0.635982\pi$
$152$	4.89439	−	2.08530i	0.396987	−	0.169141i
$153$	2.65963	+	0.432232i	0.215018	+	0.0349439i
$154$	−0.504730	+	0.671674i	−0.0406723	+	0.0541251i
$155$	11.3619	+	29.9588i	0.912606	+	2.40635i
$156$	−6.52847	−	2.63173i	−0.522696	−	0.210707i
$157$	0.993322	−	2.61917i	0.0792757	−	0.209033i	−0.889519	−	0.456899i	$-0.848960\pi$
$157$	0.993322	−	2.61917i	0.0792757	−	0.209033i	0.968794	+	0.247866i	$0.0797293\pi$
$158$	0.224399	+	0.354858i	0.0178522	+	0.0282310i
$159$	−3.32942	−	1.41853i	−0.264040	−	0.112497i
$160$	8.79792	+	5.56346i	0.695536	+	0.439830i
$161$	23.7546	+	2.88433i	1.87212	+	0.227317i
$162$	−0.0856454	−	0.201017i	−0.00672894	−	0.0157934i
$163$	0.677858	−	2.03043i	0.0530940	−	0.159036i	−0.918650	−	0.395071i	$-0.870720\pi$
$163$	0.677858	−	2.03043i	0.0530940	−	0.159036i	0.971744	+	0.236035i	$0.0758481\pi$
$164$	−15.4702	−	5.86708i	−1.20802	−	0.458142i
$165$	−3.60682	−	0.291173i	−0.280791	−	0.0226678i
$166$	−0.286750	+	0.989975i	−0.0222561	+	0.0768370i
$167$	8.66553	+	0.349209i	0.670559	+	0.0270226i	0.373211	−	0.927747i	$-0.378257\pi$
$167$	8.66553	+	0.349209i	0.670559	+	0.0270226i	0.297348	+	0.954769i	$0.403898\pi$
$168$	−3.76212			−0.290254
$169$	−12.9889	−	0.538002i	−0.999143	−	0.0413848i
$170$	−2.41373			−0.185125
$171$	−6.15556	−	0.248061i	−0.470728	−	0.0189697i
$172$	2.30161	−	7.94608i	0.175496	−	0.605883i
$173$	−5.06059	−	0.408533i	−0.384750	−	0.0310602i	−0.113421	−	0.993547i	$-0.536181\pi$
$173$	−5.06059	−	0.408533i	−0.384750	−	0.0310602i	−0.271328	+	0.962487i	$0.587463\pi$
$174$	−0.812835	−	0.308268i	−0.0616208	−	0.0233697i
$175$	−16.2890	+	48.7915i	−1.23133	+	3.68829i
$176$	−1.28555	−	3.01729i	−0.0969017	−	0.227437i
$177$	8.64475	+	1.04966i	0.649779	+	0.0788975i
$178$	2.65132	+	1.67659i	0.198725	+	0.125666i
$179$	21.6362	+	9.21831i	1.61716	+	0.689009i	0.995543	−	0.0943107i	$-0.0300647\pi$
$179$	21.6362	+	9.21831i	1.61716	+	0.689009i	0.621620	+	0.783319i	$0.286475\pi$
$180$	−4.27768	−	6.76461i	−0.318840	−	0.504205i
$181$	0.0278091	−	0.0733266i	0.00206703	−	0.00545032i	−0.933979	−	0.357329i	$-0.883688\pi$
$181$	0.0278091	−	0.0733266i	0.00206703	−	0.00545032i	0.936046	+	0.351878i	$0.114457\pi$
$182$	−3.23357	+	1.15036i	−0.239688	+	0.0852703i
$183$	4.39722	+	11.5945i	0.325052	+	0.857091i
$184$	2.84958	−	3.79211i	0.210074	−	0.279558i
$185$	−5.62219	−	0.913695i	−0.413352	−	0.0671762i
$186$	−1.57104	+	0.669356i	−0.115194	+	0.0490796i
$187$	1.95730	+	1.35102i	0.143132	+	0.0987967i
$188$	2.36889	−	1.36768i	0.172769	−	0.0997483i
$189$	3.93583	+	1.86758i	0.286290	+	0.135846i
$190$	5.47834	−	0.665191i	0.397440	−	0.0482580i
$191$	−5.35993	−	9.28368i	−0.387831	−	0.671743i	0.604326	−	0.796737i	$-0.293442\pi$
$191$	−5.35993	−	9.28368i	−0.387831	−	0.671743i	−0.992158	+	0.124994i	$0.960109\pi$
$192$	3.43843	−	5.95553i	0.248147	−	0.429803i
$193$	7.66329	−	17.9864i	0.551616	−	1.29469i	−0.377879	−	0.925855i	$-0.623347\pi$
$193$	7.66329	−	17.9864i	0.551616	−	1.29469i	0.929495	−	0.368835i	$-0.120243\pi$
$194$	2.91960	+	2.58654i	0.209615	+	0.185703i
$195$	−11.6308	−	9.12264i	−0.832897	−	0.653286i
$196$	17.5042	−	15.5074i	1.25030	−	1.10767i
$197$	3.27059	+	9.79660i	0.233020	+	0.697979i	0.998512	+	0.0545340i	$0.0173673\pi$
$197$	3.27059	+	9.79660i	0.233020	+	0.697979i	−0.765492	+	0.643445i	$0.777504\pi$
$198$	0.00776563	−	0.192702i	0.000551879	−	0.0136947i
$199$	14.1191	−	17.2928i	1.00088	−	1.22585i	0.0268012	−	0.999641i	$-0.491468\pi$
$199$	14.1191	−	17.2928i	1.00088	−	1.22585i	0.974078	−	0.226213i	$-0.0726347\pi$
$200$	6.76164	+	7.63232i	0.478120	+	0.539686i
$201$	−1.61862	−	0.330443i	−0.114168	−	0.0233077i
$202$	−3.40819	+	0.987194i	−0.239799	+	0.0694587i
$203$	16.2061	−	6.14618i	1.13745	−	0.431377i
$204$	0.211815	+	5.25613i	0.0148300	+	0.368003i
$205$	−27.7766	−	20.8728i	−1.94000	−	1.45782i
$206$	−2.26904	+	0.463227i	−0.158091	+	0.0322746i
$207$	−4.86362	+	2.55263i	−0.338045	+	0.177420i
$208$	2.42236	−	13.1768i	0.167960	−	0.913645i
$209$	−4.81472	−	2.52696i	−0.333041	−	0.174793i
$210$	−3.74839	−	1.08573i	−0.258663	−	0.0749228i
$211$	−12.2850	+	0.991749i	−0.845735	+	0.0682748i	−0.495734	−	0.868474i	$-0.665101\pi$
$211$	−12.2850	+	0.991749i	−0.845735	+	0.0682748i	−0.350001	+	0.936749i	$0.613819\pi$
$212$	1.41323	−	6.92247i	0.0970612	−	0.475437i
$213$	1.66840	+	3.17888i	0.114317	+	0.217813i
$214$	1.45002	+	1.92963i	0.0991216	+	0.131907i
$215$	9.28500	−	14.6831i	0.633232	−	1.00138i
$216$	0.710709	−	0.490567i	0.0483576	−	0.0333788i
$217$	14.5959	−	30.7602i	0.990836	−	2.08814i
$218$	−0.988721	+	1.02937i	−0.0669646	+	0.0697176i
$219$	−6.03972	−	5.80123i	−0.408126	−	0.392011i
$220$	−0.851513	−	7.01284i	−0.0574090	−	0.472806i
$221$	3.62225	+	9.01472i	0.243659	+	0.606395i
$222$	0.0365922	−	0.301364i	0.00245591	−	0.0202262i
$223$	−8.73140	+	7.12897i	−0.584698	+	0.477391i	−0.878021	−	0.478622i	$-0.841136\pi$
$223$	−8.73140	+	7.12897i	−0.584698	+	0.477391i	0.293323	+	0.956013i	$0.405239\pi$
$224$	−2.21254	−	10.8378i	−0.147832	−	0.724128i
$225$	−3.28505	−	11.3413i	−0.219004	−	0.756088i
$226$	−0.713160	−	2.89341i	−0.0474387	−	0.192466i
$227$	−0.808581	+	10.0161i	−0.0536674	+	0.664790i	0.912868	+	0.408256i	$0.133863\pi$
$227$	−0.808581	+	10.0161i	−0.0536674	+	0.664790i	−0.966535	+	0.256534i	$0.917419\pi$
$228$	−1.92927	−	11.8712i	−0.127769	−	0.786193i
$229$	−4.66898	+	5.27018i	−0.308535	+	0.348264i	−0.882242	−	0.470797i	$-0.843966\pi$
$229$	−4.66898	+	5.27018i	−0.308535	+	0.348264i	0.573707	+	0.819061i	$0.305505\pi$
$230$	3.93357	−	2.95589i	0.259372	−	0.194905i
$231$	2.43186	+	2.97849i	0.160005	+	0.195970i
$232$	0.551141	−	3.39131i	0.0361842	−	0.222650i
$233$	0.808998	+	0.199400i	0.0529993	+	0.0130631i	0.265726	−	0.964049i	$-0.414388\pi$
$233$	0.808998	+	0.199400i	0.0529993	+	0.0130631i	−0.212727	+	0.977112i	$0.568234\pi$
$234$	0.460856	−	0.638961i	0.0301271	−	0.0417702i
$235$	5.57728	−	1.37467i	0.363821	−	0.0896739i
$236$	1.36799	+	16.9456i	0.0890486	+	1.10306i
$237$	1.82263	−	0.608485i	0.118393	−	0.0395253i
$238$	1.77676	+	1.84981i	0.115171	+	0.119905i
$239$			4.23266i			0.273788i	0.990586	+	0.136894i	$0.0437119\pi$
$239$			4.23266i			0.273788i	−0.990586	+	0.136894i	$0.956288\pi$
$240$	10.9866	−	10.5528i	0.709182	−	0.681179i
$241$	−13.5604	−	11.0717i	−0.873503	−	0.713193i	0.0855761	−	0.996332i	$-0.472727\pi$
$241$	−13.5604	−	11.0717i	−0.873503	−	0.713193i	−0.959079	+	0.283139i	$0.908624\pi$
$242$	−1.03786	+	1.97749i	−0.0667164	+	0.127118i
$243$	−0.987050	+	0.160411i	−0.0633193	+	0.0102904i
$244$	−20.4609	+	12.9387i	−1.30987	+	0.828314i
$245$	44.3673	−	21.0526i	2.83452	−	1.34500i
$246$	1.05195	−	1.52401i	0.0670696	−	0.0971671i
$247$	−10.7056	−	19.4621i	−0.681181	−	1.23834i
$248$	−3.83399	−	5.55450i	−0.243459	−	0.352711i
$249$	4.08502	+	2.35849i	0.258878	+	0.149463i
$250$	2.61421	+	5.50933i	0.165337	+	0.348441i
$251$	5.72230	+	1.91039i	0.361189	+	0.120582i	0.491470	−	0.870895i	$-0.336460\pi$
$251$	5.72230	+	1.91039i	0.361189	+	0.120582i	−0.130281	+	0.991477i	$0.541588\pi$
$252$	−2.03536	+	8.25777i	−0.128215	+	0.520190i
$253$	−4.84422	+	0.195216i	−0.304554	+	0.0122731i
$254$	0.00384552		0.000154969i	0.000241290		9.72364e-6i
$255$	−2.64365	+	10.7257i	−0.165552	+	0.671671i
$256$	11.6820	+	3.90002i	0.730124	+	0.243751i
$257$	3.97914	+	8.38586i	0.248212	+	0.523096i	0.988869	−	0.148787i	$-0.0475370\pi$
$257$	3.97914	+	8.38586i	0.248212	+	0.523096i	−0.740657	+	0.671883i	$0.765486\pi$
$258$	0.801855	+	0.462951i	0.0499213	+	0.0288221i
$259$	3.43831	+	4.98125i	0.213646	+	0.309520i
$260$	12.9080	−	25.8098i	0.800519	−	1.60066i
$261$	−2.26009	+	3.27431i	−0.139896	+	0.202674i
$262$	−2.26062	+	1.07268i	−0.139662	+	0.0662703i
$263$	5.87779	−	3.71689i	0.362440	−	0.229193i	−0.340816	−	0.940130i	$-0.610703\pi$
$263$	5.87779	−	3.71689i	0.362440	−	0.229193i	0.703256	+	0.710937i	$0.251729\pi$
$264$	0.752356	−	0.122270i	0.0463043	−	0.00752518i
$265$	6.89504	−	13.1374i	0.423559	−	0.807024i
$266$	−4.54243	−	3.70878i	−0.278514	−	0.227400i
$267$	10.3540	−	9.94518i	0.633656	−	0.608635i
$268$		−	3.22514i		−	0.197006i
$269$	15.0217	+	15.6393i	0.915890	+	0.953543i	0.999075	−	0.0429915i	$-0.0136888\pi$
$269$	15.0217	+	15.6393i	0.915890	+	0.953543i	−0.0831853	+	0.996534i	$0.526509\pi$
$270$	0.849690	−	0.283668i	0.0517105	−	0.0172635i
$271$	−1.30141	−	16.1208i	−0.0790549	−	0.979271i	−0.907734	−	0.419547i	$-0.862189\pi$
$271$	−1.30141	−	16.1208i	−0.0790549	−	0.979271i	0.828679	−	0.559724i	$-0.189093\pi$
$272$	−9.72142	+	2.39611i	−0.589448	+	0.145286i
$273$	1.57019	+	15.6287i	0.0950322	+	0.945893i
$274$	2.16866	+	0.534526i	0.131013	+	0.0322919i
$275$	1.67177	−	10.2868i	0.100812	−	0.620318i
$276$	−6.78192	−	8.30635i	−0.408224	−	0.499983i
$277$	−4.08198	+	3.06741i	−0.245262	+	0.184303i	−0.716263	−	0.697830i	$-0.754149\pi$
$277$	−4.08198	+	3.06741i	−0.245262	+	0.184303i	0.471001	+	0.882133i	$0.343893\pi$
$278$	0.345300	−	0.389763i	0.0207097	−	0.0233764i
$279$	1.25368	+	7.71422i	0.0750561	+	0.461839i
$280$	1.24108	−	15.3735i	0.0741687	−	0.918745i
$281$	6.04370	+	24.5203i	0.360537	+	1.46276i	0.818872	+	0.573977i	$0.194600\pi$
$281$	6.04370	+	24.5203i	0.360537	+	1.46276i	−0.458334	+	0.888780i	$0.651554\pi$
$282$	0.0851759	+	0.294061i	0.00507215	+	0.0175111i
$283$	0.522041	+	2.55713i	0.0310321	+	0.152005i	0.992354	−	0.123420i	$-0.0393863\pi$
$283$	0.522041	+	2.55713i	0.0310321	+	0.152005i	−0.961322	+	0.275426i	$0.911181\pi$
$284$	−5.42905	+	4.43268i	−0.322155	+	0.263031i
$285$	3.04433	−	25.0723i	0.180330	−	1.48515i
$286$	0.609267	−	0.335143i	0.0360267	−	0.0198174i
$287$	4.45033	+	36.6518i	0.262695	+	2.16349i
$288$	1.83118	+	1.75887i	0.107903	+	0.103643i
$289$	−6.74683	+	7.02419i	−0.396872	+	0.413188i
$290$	1.52785	−	3.21987i	0.0897184	−	0.189078i
$291$	14.6913	−	10.1407i	0.861222	−	0.594458i
$292$	8.73809	−	13.8182i	0.511358	−	0.808648i
$293$	−13.1161	−	17.4544i	−0.766251	−	1.01970i	−0.998889	−	0.0471318i	$-0.984992\pi$
$293$	−13.1161	−	17.4544i	−0.766251	−	1.01970i	0.232637	−	0.972564i	$-0.425265\pi$
$294$	1.21635	+	2.31755i	0.0709387	+	0.135162i
$295$	−7.14115	+	34.9797i	−0.415774	+	2.03659i
$296$	1.19593	−	0.0965451i	0.0695118	−	0.00561157i
$297$	−0.847792	−	0.245566i	−0.0491939	−	0.0142492i
$298$	2.95143	+	1.54903i	0.170972	+	0.0897329i
$299$	−16.9426	−	10.2551i	−0.979816	−	0.593069i
$300$	20.4109	−	10.7125i	1.17842	−	0.618484i
$301$	−18.0874	+	3.69257i	−1.04254	+	0.212836i
$302$	−0.755694	−	0.567867i	−0.0434853	−	0.0326771i
$303$	0.653884	+	16.2260i	0.0375646	+	0.932157i
$304$	21.4040	−	8.11745i	1.22760	−	0.465568i
$305$	−48.8304	+	14.1439i	−2.79602	+	0.809877i
$306$	−0.576860	−	0.117767i	−0.0329769	−	0.00673228i
$307$	5.46691	+	6.17087i	0.312013	+	0.352190i	0.883508	−	0.468415i	$-0.155175\pi$
$307$	5.46691	+	6.17087i	0.312013	+	0.352190i	−0.571495	+	0.820605i	$0.693636\pi$
$308$	−4.74762	+	5.81478i	−0.270521	+	0.331328i
$309$	−0.426767	+	10.5901i	−0.0242779	+	0.602451i
$310$	−2.21699	−	6.64070i	−0.125917	−	0.377166i
$311$	−15.0507	+	13.3338i	−0.853450	+	0.756090i	−0.971531	−	0.236913i	$-0.923864\pi$
$311$	−15.0507	+	13.3338i	−0.853450	+	0.756090i	0.118081	+	0.993004i	$0.462326\pi$
$312$	2.83864	+	1.27948i	0.160706	+	0.0724362i
$313$	20.5445	+	18.2008i	1.16124	+	1.02877i	0.999118	+	0.0420012i	$0.0133733\pi$
$313$	20.5445	+	18.2008i	1.16124	+	1.02877i	0.162125	+	0.986770i	$0.448165\pi$
$314$	−0.239911	+	0.563091i	−0.0135389	+	0.0317771i
$315$	−8.93005	+	15.4673i	−0.503152	+	0.871484i
$316$	1.87565	+	3.24873i	0.105514	+	0.182755i
$317$	20.3546	−	2.47149i	1.14323	−	0.138813i	0.473065	−	0.881027i	$-0.343148\pi$
$317$	20.3546	−	2.47149i	1.14323	−	0.138813i	0.670162	+	0.742215i	$0.266224\pi$
$318$	0.714414	+	0.338994i	0.0400624	+	0.0190098i
$319$	−3.04118	+	1.75583i	−0.170273	+	0.0983074i
$320$	23.2024	+	16.0154i	1.29705	+	0.895291i
$321$	10.1627	−	4.32993i	0.567228	−	0.241673i
$322$	−5.16083	−	0.838717i	−0.287602	−	0.0467399i
$323$	−9.97218	+	13.2706i	−0.554867	+	0.738394i
$324$	−0.692280	−	1.82539i	−0.0384600	−	0.101411i
$325$	28.8843	−	31.2749i	1.60221	−	1.73482i
$326$	−0.165857	+	0.437330i	−0.00918599	+	0.0242215i
$327$	3.49123	+	5.52094i	0.193065	+	0.305308i
$328$	6.73316	+	2.86873i	0.371777	+	0.158399i
$329$	−5.15898	−	3.26234i	−0.284424	−	0.179859i
$330$	0.784896	+	0.0953037i	0.0432071	+	0.00524629i
$331$	−5.41469	−	12.7088i	−0.297619	−	0.698536i	0.702292	−	0.711889i	$-0.252160\pi$
$331$	−5.41469	−	12.7088i	−0.297619	−	0.698536i	−0.999911	+	0.0133523i	$0.995750\pi$
$332$	−2.91612	+	8.73484i	−0.160043	+	0.479386i
$333$	−1.29907	−	0.492674i	−0.0711888	−	0.0269984i
$334$	−1.88883	−	0.152482i	−0.103352	−	0.00834344i
$335$	1.88429	−	6.50531i	0.102950	−	0.355423i
$336$	−16.1747	−	0.651816i	−0.882400	−	0.0355595i
$337$	30.6392			1.66902			0.834511	−	0.550991i	$-0.185750\pi$
$337$	30.6392			1.66902			0.834511	+	0.550991i	$0.185750\pi$
$338$	2.83106	+	0.231737i	0.153989	+	0.0126049i
$339$	−13.6383			−0.740732
$340$	−21.5485	−	0.868377i	−1.16863	−	0.0470943i
$341$	−1.91920	+	6.62586i	−0.103931	+	0.358810i
$342$	1.34173	+	0.108316i	0.0725524	+	0.00585703i
$343$	−20.2797	−	7.69108i	−1.09500	−	0.415280i
$344$	−1.15882	+	3.47108i	−0.0624792	+	0.187148i
$345$	−8.82660	−	20.7168i	−0.475208	−	1.11535i
$346$	1.10126	+	0.133717i	0.0592039	+	0.00718866i
$347$	−14.2286	−	8.99762i	−0.763831	−	0.483017i	0.0948730	−	0.995489i	$-0.469756\pi$
$347$	−14.2286	−	8.99762i	−0.763831	−	0.483017i	−0.858704	+	0.512472i	$0.828730\pi$
$348$	−7.14567	−	3.04449i	−0.383048	−	0.163202i
$349$	−13.1533	−	20.8003i	−0.704081	−	1.11341i	−0.987983	−	0.154561i	$-0.950604\pi$
$349$	−13.1533	−	20.8003i	−0.704081	−	1.11341i	0.283903	−	0.958853i	$-0.408371\pi$
$350$	3.98557	−	10.5091i	0.213038	−	0.561734i
$351$	−2.33455	−	2.74770i	−0.124609	−	0.146661i
$352$	0.794698	+	2.09545i	0.0423576	+	0.111688i
$353$	18.8122	−	25.0345i	1.00127	−	1.33245i	0.0587620	−	0.998272i	$-0.481285\pi$
$353$	18.8122	−	25.0345i	1.00127	−	1.33245i	0.942510	−	0.334179i	$-0.108459\pi$
$354$	−1.87813	−	0.305225i	−0.0998213	−	0.0162225i
$355$	−13.5405	+	5.76909i	−0.718658	+	0.306191i
$356$	23.0664	+	15.9216i	1.22252	+	0.843844i
$357$	10.1659	−	5.86927i	0.538035	−	0.310635i
$358$	−4.64260	−	2.20294i	−0.245369	−	0.116429i
$359$	−25.6427	+	3.11359i	−1.35337	+	0.164329i	−0.764879	−	0.644175i	$-0.777201\pi$
$359$	−25.6427	+	3.11359i	−1.35337	+	0.164329i	−0.588492	+	0.808503i	$0.700278\pi$
$360$	1.77020	+	3.06607i	0.0932976	+	0.161596i
$361$	9.47625	−	16.4133i	0.498750	−	0.863860i
$362$	−0.00671655	+	0.0157643i	−0.000353014	+	0.000828555i
$363$	7.65049	+	6.77774i	0.401546	+	0.355739i
$364$	−29.2815	+	9.10650i	−1.53477	+	0.477310i
$365$	25.6986	−	22.7670i	1.34512	−	1.19168i
$366$	−0.858010	−	2.57005i	−0.0448489	−	0.134339i
$367$	0.650452	−	16.1408i	0.0339533	−	0.842543i	−0.889064	−	0.457784i	$-0.848643\pi$
$367$	0.650452	−	16.1408i	0.0339533	−	0.842543i	0.923017	−	0.384759i	$-0.125716\pi$
$368$	12.9083	−	15.8099i	0.672894	−	0.824146i
$369$	−5.61998	−	6.34364i	−0.292564	−	0.330237i
$370$	1.21942	+	0.248947i	0.0633948	+	0.0129421i
$371$	−15.1436	+	4.38639i	−0.786216	+	0.227730i
$372$	−14.2662	+	5.41047i	−0.739669	+	0.280520i
$373$	−0.177489	−	4.40434i	−0.00919003	−	0.228048i	−0.997257	−	0.0740212i	$-0.976417\pi$
$373$	−0.177489	−	4.40434i	−0.00919003	−	0.228048i	0.988067	−	0.154027i	$-0.0492243\pi$
$374$	−0.415440	−	0.312183i	−0.0214819	−	0.0161426i
$375$	27.3447	−	5.58246i	1.41207	−	0.288277i
$376$	−1.07138	+	0.562305i	−0.0552523	+	0.0289987i
$377$	−14.3183	−	0.874144i	−0.737430	−	0.0450207i
$378$	−0.842858	−	0.442366i	−0.0433520	−	0.0227529i
$379$	−2.44264	−	0.707518i	−0.125470	−	0.0363428i	0.214889	−	0.976639i	$-0.431061\pi$
$379$	−2.44264	−	0.707518i	−0.125470	−	0.0363428i	−0.340358	+	0.940296i	$0.610548\pi$
$380$	49.1471	−	3.96757i	2.52119	−	0.203532i
$381$	0.00352321	−	0.0172578i	0.000180499	−	0.000884145i
$382$	1.08853	+	2.07401i	0.0556938	+	0.106116i
$383$	−0.0566584	−	0.0753987i	−0.00289511	−	0.00385269i	0.797993	−	0.602667i	$-0.205895\pi$
$383$	−0.0566584	−	0.0753987i	−0.00289511	−	0.00385269i	−0.800888	+	0.598814i	$0.795639\pi$
$384$	−3.51718	+	5.56197i	−0.179485	+	0.283833i
$385$	−12.9736	+	8.95500i	−0.661194	+	0.456389i
$386$	−1.83133	+	3.85945i	−0.0932124	+	0.196441i
$387$	2.93542	−	3.05610i	0.149216	−	0.155350i
$388$	25.1342	+	24.1417i	1.27599	+	1.22561i
$389$	4.54006	+	37.3907i	0.230190	+	1.89579i	0.410001	+	0.912085i	$0.365528\pi$
$389$	4.54006	+	37.3907i	0.230190	+	1.89579i	−0.179811	+	0.983701i	$0.557549\pi$
$390$	2.45902	+	2.09403i	0.124517	+	0.106035i
$391$	−1.78400	+	14.6925i	−0.0902205	+	0.743033i
$392$	−8.01287	+	6.54230i	−0.404711	+	0.330436i
$393$	2.29063	+	11.2202i	0.115547	+	0.565986i
$394$	−0.627858	−	2.16762i	−0.0316310	−	0.109203i
$395$	1.88525	+	7.64875i	0.0948571	+	0.384850i
$396$	0.138655	−	1.71755i	0.00696769	−	0.0863103i
$397$	−4.41777	−	27.1836i	−0.221721	−	1.36431i	−0.824258	−	0.566215i	$-0.808407\pi$
$397$	−4.41777	−	27.1836i	−0.221721	−	1.36431i	0.602536	−	0.798091i	$-0.294157\pi$
$398$	−3.23470	+	3.65122i	−0.162141	+	0.183019i
$399$	−21.4556	+	16.1228i	−1.07412	+	0.807150i
$400$	27.7483	+	33.9855i	1.38741	+	1.69927i
$401$	2.40001	−	14.7679i	0.119851	−	0.737472i	−0.855663	−	0.517534i	$-0.826850\pi$
$401$	2.40001	−	14.7679i	0.119851	−	0.737472i	0.975514	−	0.219938i	$-0.0705857\pi$
$402$	0.350477	+	0.0863848i	0.0174802	+	0.00430848i
$403$	−21.4745	+	18.2455i	−1.06972	+	0.908876i
$404$	−30.7817	+	7.58701i	−1.53145	+	0.377468i
$405$	−0.329888	−	4.08640i	−0.0163923	−	0.203055i
$406$	−3.59227	+	1.19928i	−0.178282	+	0.0595191i
$407$	−0.849491	−	0.884414i	−0.0421077	−	0.0438388i
$408$		−	2.32692i		−	0.115200i
$409$	−11.7984	+	11.3326i	−0.583396	+	0.560359i	−0.925233	−	0.379400i	$-0.876130\pi$
$409$	−11.7984	+	11.3326i	−0.583396	+	0.560359i	0.341837	+	0.939759i	$0.388951\pi$
$410$	5.88068	+	4.80143i	0.290426	+	0.237126i
$411$	4.75047	−	9.05127i	0.234323	−	0.446466i
$412$	−20.4235	+	3.31913i	−1.00619	+	0.163522i
$413$	32.0640	−	20.2760i	1.57777	−	0.997719i
$414$	1.08431	−	0.514510i	0.0532908	−	0.0252868i
$415$	−10.9853	+	15.9150i	−0.539249	+	0.781237i
$416$	−2.01643	+	8.92990i	−0.0988638	+	0.437824i
$417$	−1.35377	−	1.96128i	−0.0662945	−	0.0960441i
$418$	1.02894	+	0.594058i	0.0503271	+	0.0290563i
$419$	0.925596	+	1.95065i	0.0452183	+	0.0952956i	0.924802	−	0.380448i	$-0.124230\pi$
$419$	0.925596	+	1.95065i	0.0452183	+	0.0952956i	−0.879584	+	0.475744i	$0.842179\pi$
$420$	−33.0731	−	11.0414i	−1.61380	−	0.538767i
$421$	2.14039	−	8.68392i	0.104316	−	0.423228i	−0.895443	−	0.445177i	$-0.853141\pi$
$421$	2.14039	−	8.68392i	0.104316	−	0.423228i	0.999759	+	0.0219484i	$0.00698696\pi$
$422$	2.69085	−	0.108437i	0.130988	−	0.00527865i
$423$	1.39999	−	0.0564177i	0.0680698	−	0.00274312i
$424$	−0.747932	+	3.03448i	−0.0363228	+	0.147367i
$425$	−30.1782	−	10.0750i	−1.46386	−	0.488708i
$426$	−0.336285	−	0.708706i	−0.0162931	−	0.0343369i
$427$	46.7839	+	27.0107i	2.26403	+	1.30714i
$428$	12.2509	+	17.7484i	0.592168	+	0.857903i
$429$	−0.821946	−	3.07443i	−0.0396839	−	0.148435i
$430$	−2.15633	+	3.12398i	−0.103987	+	0.150652i
$431$	−12.5179	+	5.93981i	−0.602966	+	0.286111i	−0.705602	−	0.708608i	$-0.749323\pi$
$431$	−12.5179	+	5.93981i	−0.602966	+	0.286111i	0.102637	+	0.994719i	$0.467272\pi$
$432$	3.14058	−	1.98598i	0.151101	−	0.0955505i
$433$	−7.33471	+	1.19201i	−0.352484	+	0.0572842i	−0.334075	−	0.942546i	$-0.608424\pi$
$433$	−7.33471	+	1.19201i	−0.352484	+	0.0572842i	−0.0184085	+	0.999831i	$0.505860\pi$
$434$	−3.45728	+	6.58730i	−0.165955	+	0.316201i
$435$	−12.6346	−	10.3158i	−0.605780	−	0.494604i
$436$	−9.19713	+	8.83396i	−0.440463	+	0.423070i
$437$		−	33.8387i		−	1.61872i
$438$	1.26758	+	1.31969i	0.0605673	+	0.0630572i
$439$	4.86093	−	1.62282i	0.232000	−	0.0774528i	−0.198291	−	0.980143i	$-0.563539\pi$
$439$	4.86093	−	1.62282i	0.232000	−	0.0774528i	0.430291	+	0.902690i	$0.358411\pi$
$440$	0.251450	+	3.11476i	0.0119874	+	0.148491i
$441$	11.6306	−	2.86668i	0.553836	−	0.136508i
$442$	−0.711513	−	2.00000i	−0.0338432	−	0.0951305i
$443$	−21.1013	−	5.20101i	−1.00255	−	0.247107i	−0.296322	−	0.955088i	$-0.595760\pi$
$443$	−21.1013	−	5.20101i	−1.00255	−	0.247107i	−0.706232	+	0.707981i	$0.749606\pi$
$444$	0.435097	−	2.67726i	0.0206488	−	0.127057i
$445$	37.2243	+	45.5915i	1.76460	+	2.16125i
$446$	1.96900	−	1.47961i	0.0932349	−	0.0700615i
$447$	10.1159	−	11.4185i	0.478465	−	0.540076i
$448$	−4.80570	−	29.5707i	−0.227048	−	1.39708i
$449$	−1.70774	+	21.1542i	−0.0805932	+	0.998326i	0.822467	+	0.568813i	$0.192597\pi$
$449$	−1.70774	+	21.1542i	−0.0805932	+	0.998326i	−0.903060	+	0.429514i	$0.858685\pi$
$450$	0.617425	+	2.50499i	0.0291057	+	0.118086i
$451$	−2.08118	−	7.18505i	−0.0979987	−	0.338331i
$452$	−5.32579	−	26.0874i	−0.250504	−	1.22705i
$453$	−3.35107	+	2.73607i	−0.157447	+	0.128552i
$454$	0.264656	−	2.17964i	0.0124209	−	0.102296i
$455$	−64.3832	+	1.26069i	−3.01833	+	0.0591020i
$456$	0.641268	+	5.28132i	0.0300301	+	0.247320i
$457$	2.12573	+	2.04179i	0.0994373	+	0.0955108i	0.740795	−	0.671731i	$-0.234449\pi$
$457$	2.12573	+	2.04179i	0.0994373	+	0.0955108i	−0.641358	+	0.767242i	$0.721628\pi$
$458$	1.06572	−	1.10953i	0.0497979	−	0.0518451i
$459$	−1.15512	+	2.43437i	−0.0539164	+	0.113627i
$460$	36.1803	−	24.9735i	1.68692	−	1.16440i
$461$	−3.31300	+	5.23909i	−0.154302	+	0.244009i	−0.913489	−	0.406864i	$-0.866622\pi$
$461$	−3.31300	+	5.23909i	−0.154302	+	0.244009i	0.759187	+	0.650872i	$0.225597\pi$
$462$	−0.504730	−	0.671674i	−0.0234822	−	0.0312491i
$463$	12.3270	+	23.4871i	0.572884	+	1.09154i	0.983699	+	0.179820i	$0.0575517\pi$
$463$	12.3270	+	23.4871i	0.572884	+	1.09154i	−0.410816	+	0.911718i	$0.634756\pi$
$464$	2.95712	−	14.4849i	0.137281	−	0.672445i
$465$	−31.9370	+	2.57822i	−1.48104	+	0.119562i
$466$	−0.174870	−	0.0506517i	−0.00810069	−	0.00234639i
$467$	−14.9977	−	7.87140i	−0.694011	−	0.364245i	0.0805444	−	0.996751i	$-0.474334\pi$
$467$	−14.9977	−	7.87140i	−0.694011	−	0.364245i	−0.774556	+	0.632506i	$0.782026\pi$
$468$	4.34416	−	5.53852i	0.200809	−	0.256018i
$469$	−6.37251	+	3.34455i	−0.294255	+	0.154437i
$470$	−1.22975	+	0.251056i	−0.0567242	+	0.0115803i
$471$	2.23941	+	1.68280i	0.103186	+	0.0775395i
$472$	−0.302809	−	7.51413i	−0.0139379	−	0.345866i
$473$	3.49714	−	1.32629i	0.160799	−	0.0609829i
$474$	−0.403280	+	0.116811i	−0.0185232	+	0.00536532i
$475$	71.2708	+	14.5500i	3.27013	+	0.667601i
$476$	15.1965	+	17.1534i	0.696533	+	0.786223i
$477$	2.28883	−	2.80331i	0.104798	−	0.128355i
$478$	0.0372397	−	0.924093i	0.00170330	−	0.0422670i
$479$	−10.1891	−	30.5200i	−0.465551	−	1.39450i	−0.875867	−	0.482552i	$-0.839710\pi$
$479$	−10.1891	−	30.5200i	−0.465551	−	1.39450i	0.410316	−	0.911943i	$-0.365418\pi$
$480$	−7.79154	+	6.90270i	−0.355634	+	0.315064i
$481$	−0.900212	−	4.92786i	−0.0410461	−	0.224691i
$482$	2.86316	+	2.53654i	0.130413	+	0.115536i
$483$	−9.37939	+	22.0142i	−0.426777	+	1.00168i
$484$	−9.97696	+	17.2806i	−0.453498	+	0.785482i
$485$	36.5925	+	63.3800i	1.66158	+	2.87794i
$486$	0.216909	−	0.0263375i	0.00983918	−	0.00119469i
$487$	21.5943	+	10.2466i	0.978533	+	0.464320i	0.849654	−	0.527340i	$-0.176811\pi$
$487$	21.5943	+	10.2466i	0.978533	+	0.464320i	0.128879	+	0.991660i	$0.458862\pi$
$488$	9.27393	−	5.35431i	0.419811	−	0.242378i
$489$	1.76168	+	1.21600i	0.0796658	+	0.0549893i
$490$	−9.87171	+	4.20594i	−0.445958	+	0.190005i
$491$	−40.6965	−	6.61383i	−1.83661	−	0.298478i	−0.859486	−	0.511159i	$-0.829217\pi$
$491$	−40.6965	−	6.61383i	−1.83661	−	0.298478i	−0.977122	+	0.212681i	$0.931781\pi$
$492$	9.93953	−	13.2271i	0.448109	−	0.596324i
$493$	3.80149	+	10.0237i	0.171211	+	0.451445i
$494$	2.16606	+	4.34324i	0.0974559	+	0.195412i
$495$	1.28316	−	3.38341i	0.0576736	−	0.152073i
$496$	−15.5213	−	24.5450i	−0.696926	−	1.10210i
$497$	14.3886	+	6.13039i	0.645415	+	0.274986i
$498$	−0.871110	−	0.550857i	−0.0390354	−	0.0246845i
$499$	−27.9188	−	3.38995i	−1.24982	−	0.151755i	−0.531251	−	0.847214i	$-0.678278\pi$
$499$	−27.9188	−	3.38995i	−1.24982	−	0.151755i	−0.718566	+	0.695459i	$0.755201\pi$
$500$	21.3563	+	50.1250i	0.955082	+	2.24166i
$501$	−2.74632	+	8.22625i	−0.122697	+	0.367522i
$502$	−1.23251	−	0.467430i	−0.0550097	−	0.0208624i
$503$	16.3402	+	1.31912i	0.728575	+	0.0588167i	0.439188	−	0.898395i	$-0.355266\pi$
$503$	16.3402	+	1.31912i	0.728575	+	0.0588167i	0.289388	+	0.957212i	$0.406548\pi$
$504$	1.04669	−	3.61359i	0.0466232	−	0.160962i
$505$	−66.5215	−	2.68072i	−2.96017	−	0.119291i
$506$	1.05933			0.0470930
$507$	4.13049	−	12.3264i	0.183441	−	0.547433i
$508$	0.0343866			0.00152566
$509$	32.6023	+	1.31383i	1.44507	+	0.0582343i	0.750347	−	0.661044i	$-0.229886\pi$
$509$	32.6023	+	1.31383i	1.44507	+	0.0582343i	0.694722	+	0.719278i	$0.255527\pi$
$510$	0.671541	−	2.31843i	0.0297364	−	0.102662i
$511$	−36.3648	−	2.93567i	−1.60868	−	0.129866i
$512$	−14.8223	−	5.62137i	−0.655061	−	0.248432i
$513$	1.95085	−	5.84352i	0.0861322	−	0.257998i
$514$	−0.794964	−	1.86585i	−0.0350644	−	0.0822991i
$515$	−43.1347	−	5.23750i	−1.90074	−	0.230792i
$516$	6.99200	+	4.42148i	0.307806	+	0.194645i
$517$	1.13773	+	0.484741i	0.0500373	+	0.0213189i
$518$	−0.706842	−	1.11778i	−0.0310568	−	0.0491125i
$519$	1.80035	−	4.74713i	0.0790265	−	0.208376i
$520$	−6.16489	+	11.1777i	−0.270348	+	0.490175i
$521$	4.30005	+	11.3383i	0.188388	+	0.496740i	0.995620	−	0.0934958i	$-0.0298042\pi$
$521$	4.30005	+	11.3383i	0.188388	+	0.496740i	−0.807231	+	0.590235i	$0.799035\pi$
$522$	0.522241	−	0.694977i	0.0228579	−	0.0304183i
$523$	−32.7882	−	5.32860i	−1.43373	−	0.233003i	−0.606595	−	0.795011i	$-0.707465\pi$
$523$	−32.7882	−	5.32860i	−1.43373	−	0.233003i	−0.827132	+	0.562007i	$0.810029\pi$
$524$	−20.5676	+	8.76304i	−0.898500	+	0.382815i
$525$	−42.3333	−	29.2206i	−1.84758	−	1.27529i
$526$	−1.31597	+	0.759774i	−0.0573789	+	0.0331277i
$527$	19.0256	+	9.02777i	0.828769	+	0.393256i
$528$	3.25582	−	0.395328i	0.141691	−	0.0172044i
$529$	−3.58536	−	6.21003i	−0.155885	−	0.270001i
$530$	−1.62094	+	2.80755i	−0.0704092	+	0.121952i
$531$	−3.41334	+	8.01141i	−0.148126	+	0.347665i
$532$	−39.2182	−	34.7443i	−1.70032	−	1.50636i
$533$	9.10717	−	29.1684i	0.394475	−	1.26342i
$534$	−2.34804	+	2.08018i	−0.101610	+	0.0900182i
$535$	14.3413	+	42.9574i	0.620027	+	1.85721i
$536$	−0.0574446	+	1.42547i	−0.00248123	+	0.0615710i
$537$	−14.8739	+	18.2172i	−0.641856	+	0.786131i
$538$	−3.14201	−	3.54660i	−0.135462	−	0.152905i
$539$	10.3592	+	2.11484i	0.446200	+	0.0910925i
$540$	7.68766	−	2.22676i	0.330824	−	0.0958244i
$541$	−5.53103	+	2.09764i	−0.237798	+	0.0901848i	−0.470625	−	0.882333i	$-0.655972\pi$
$541$	−5.53103	+	2.09764i	−0.237798	+	0.0901848i	0.232827	+	0.972518i	$0.425202\pi$
$542$	0.142295	+	3.53102i	0.00611211	+	0.151671i
$543$	0.0626945	+	0.0471119i	0.00269048	+	0.00202176i
$544$	6.70330	−	1.36849i	0.287402	−	0.0586735i
$545$	−23.7125	+	12.4453i	−1.01573	+	0.533097i
$546$	−0.205307	−	3.42595i	−0.00878631	−	0.146617i
$547$	−25.9486	−	13.6189i	−1.10948	−	0.582301i	−0.192527	−	0.981292i	$-0.561668\pi$
$547$	−25.9486	−	13.6189i	−1.10948	−	0.582301i	−0.916955	+	0.398990i	$0.869361\pi$
$548$	19.1684	+	5.55218i	0.818832	+	0.237177i
$549$	−12.3601	+	0.997812i	−0.527517	+	0.0425856i
$550$	−0.455494	+	2.23116i	−0.0194223	+	0.0951369i
$551$	−11.3905	−	21.7028i	−0.485251	−	0.924569i
$552$	2.84958	+	3.79211i	0.121286	+	0.161403i
$553$	4.47402	−	7.07510i	0.190255	−	0.300864i
$554$	0.918184	−	0.633776i	0.0390099	−	0.0269266i
$555$	2.44181	−	5.14601i	0.103649	−	0.218436i
$556$	3.22289	−	3.35538i	0.136681	−	0.142300i
$557$	10.9714	+	10.5382i	0.464873	+	0.446517i	0.888198	−	0.459461i	$-0.151958\pi$
$557$	10.9714	+	10.5382i	0.464873	+	0.446517i	−0.423325	+	0.905978i	$0.639137\pi$
$558$	−0.205839	−	1.69524i	−0.00871385	−	0.0717650i
$559$	14.9033	+	3.36527i	0.630343	+	0.142336i
$560$	7.99941	−	65.8811i	0.338037	−	2.78398i
$561$	−1.84224	+	1.50414i	−0.0777793	+	0.0635049i
$562$	−1.10376	−	5.40655i	−0.0465591	−	0.228062i
$563$	5.73034	+	19.7834i	0.241505	+	0.833771i	0.986086	+	0.166239i	$0.0531623\pi$
$563$	5.73034	+	19.7834i	0.241505	+	0.833771i	−0.744581	+	0.667532i	$0.767351\pi$
$564$	0.654614	+	2.65587i	0.0275642	+	0.111832i
$565$	4.49912	−	55.7317i	0.189280	−	2.34465i
$566$	−0.0914764	−	0.562877i	−0.00384504	−	0.0236595i
$567$	−2.88886	+	3.26085i	−0.121321	+	0.136943i
$568$	2.47853	−	1.86249i	0.103997	−	0.0781485i
$569$	2.79257	+	3.42028i	0.117071	+	0.143386i	0.829815	−	0.558038i	$-0.188446\pi$
$569$	2.79257	+	3.42028i	0.117071	+	0.143386i	−0.712745	+	0.701424i	$0.752548\pi$
$570$	−0.885242	+	5.44711i	−0.0370787	+	0.228154i
$571$	14.8376	+	3.65715i	0.620936	+	0.153047i	0.537219	−	0.843443i	$-0.319475\pi$
$571$	14.8376	+	3.65715i	0.620936	+	0.153047i	0.0837166	+	0.996490i	$0.473321\pi$
$572$	5.55980	−	2.77279i	0.232467	−	0.115936i
$573$	10.4084	−	2.56543i	0.434816	−	0.107172i
$574$	−0.649148	−	8.04114i	−0.0270949	−	0.335631i
$575$	61.5184	−	20.5379i	2.56549	−	0.856488i
$576$	4.76376	+	4.95960i	0.198490	+	0.206650i
$577$			13.9832i			0.582129i	0.956703	+	0.291064i	$0.0940094\pi$
$577$			13.9832i			0.582129i	−0.956703	+	0.291064i	$0.905991\pi$
$578$	1.53480	−	1.47419i	0.0638392	−	0.0613184i
$579$	15.1442	+	12.3649i	0.629372	+	0.513866i
$580$	14.7983	−	28.1957i	0.614465	−	1.17076i
$581$	20.2832	−	3.29633i	0.841487	−	0.136755i
$582$	−3.29670	+	2.08471i	−0.136653	+	0.0864139i
$583$	2.88588	−	1.36937i	0.119521	−	0.0567135i
$584$	−4.10826	+	5.95184i	−0.170001	+	0.246289i
$585$	11.9983	−	8.63349i	0.496071	−	0.356951i
$586$	2.71000	+	3.92612i	0.111949	+	0.162186i
$587$	−26.8078	−	15.4775i	−1.10648	−	0.638824i	−0.168562	−	0.985691i	$-0.553912\pi$
$587$	−26.8078	−	15.4775i	−1.10648	−	0.638824i	−0.937914	+	0.346867i	$0.887246\pi$
$588$	10.0251	+	21.1275i	0.413430	+	0.871285i
$589$	−45.6696	−	15.2468i	−1.88178	−	0.628232i
$590$	1.86685	−	7.57409i	0.0768568	−	0.311820i
$591$	−10.3198	+	0.415872i	−0.424498	+	0.0171067i
$592$	5.15842	−	0.207877i	0.212010	−	0.00854371i
$593$	−9.15941	+	37.1612i	−0.376132	+	1.52603i	0.412383	+	0.911011i	$0.364697\pi$
$593$	−9.15941	+	37.1612i	−0.376132	+	1.52603i	−0.788514	+	0.615016i	$0.789149\pi$
$594$	0.182933	+	0.0610721i	0.00750585	+	0.00250582i
$595$	20.6306	+	43.4781i	0.845772	+	1.78243i
$596$	25.7916	+	14.8908i	1.05646	+	0.609950i
$597$	12.6819	+	18.3728i	0.519034	+	0.751950i
$598$	3.60876	+	2.38801i	0.147573	+	0.0976530i
$599$	−11.7101	+	16.9651i	−0.478463	+	0.693174i	−0.985677	−	0.168647i	$-0.946060\pi$
$599$	−11.7101	+	16.9651i	−0.478463	+	0.693174i	0.507213	+	0.861821i	$0.330676\pi$
$600$	−9.21219	+	4.37124i	−0.376086	+	0.178455i
$601$	12.9403	−	8.18298i	0.527848	−	0.333791i	−0.243816	−	0.969822i	$-0.578399\pi$
$601$	12.9403	−	8.18298i	0.527848	−	0.333791i	0.771664	+	0.636031i	$0.219425\pi$
$602$	3.98141	−	0.647043i	0.162270	−	0.0263715i
$603$	0.767724	−	1.46278i	0.0312641	−	0.0595689i
$604$	−6.54215	−	5.34150i	−0.266196	−	0.217343i
$605$	−30.2204	+	29.0271i	−1.22863	+	1.18012i
$606$		−	3.54828i		−	0.144139i
$607$	5.34929	+	5.56920i	0.217121	+	0.226047i	0.820852	−	0.571141i	$-0.193499\pi$
$607$	5.34929	+	5.56920i	0.217121	+	0.226047i	−0.603731	+	0.797188i	$0.706320\pi$
$608$	−14.8371	+	4.95334i	−0.601722	+	0.200884i
$609$	1.39468	+	17.2763i	0.0565155	+	0.700070i
$610$	10.7853	−	2.65834i	0.436685	−	0.107633i
$611$	2.78310	+	4.21608i	0.112592	+	0.170564i
$612$	−5.10754	−	1.25890i	−0.206460	−	0.0508878i
$613$	5.04450	−	31.0401i	0.203745	−	1.25370i	−0.660577	−	0.750758i	$-0.729688\pi$
$613$	5.04450	−	31.0401i	0.203745	−	1.25370i	0.864322	−	0.502938i	$-0.167748\pi$
$614$	−1.13927	−	1.39535i	−0.0459771	−	0.0563118i
$615$	27.7766	−	20.8728i	1.12006	−	0.841672i
$616$	2.20196	−	2.48550i	0.0887197	−	0.100144i
$617$	3.79502	+	23.3517i	0.152782	+	0.940104i	0.944331	+	0.328998i	$0.106711\pi$
$617$	3.79502	+	23.3517i	0.152782	+	0.940104i	−0.791549	+	0.611106i	$0.790725\pi$
$618$	0.186348	−	2.30833i	0.00749600	−	0.0928546i
$619$	3.34759	+	13.5817i	0.134551	+	0.545895i	0.999063	+	0.0432827i	$0.0137816\pi$
$619$	3.34759	+	13.5817i	0.134551	+	0.545895i	−0.864512	+	0.502613i	$0.832372\pi$
$620$	−17.4031	−	60.0824i	−0.698924	−	2.41297i
$621$	−1.09870	−	5.38178i	−0.0440893	−	0.215963i
$622$	3.40326	−	2.77868i	0.136458	−	0.111415i
$623$	7.53883	−	62.0878i	0.302037	−	2.48750i
$624$	11.9826	+	5.99273i	0.479687	+	0.239901i
$625$	6.67528	+	54.9758i	0.267011	+	2.19903i
$626$	−4.32523	−	4.15444i	−0.172871	−	0.166045i
$627$	3.76673	−	3.92158i	0.150429	−	0.156613i
$628$	−2.34438	+	4.94068i	−0.0935510	+	0.197155i
$629$	−3.08097	+	2.12664i	−0.122846	+	0.0847947i
$630$	2.08574	−	3.29833i	0.0830977	−	0.131408i
$631$	−1.29079	−	1.71773i	−0.0513857	−	0.0683819i	0.773018	−	0.634384i	$-0.218746\pi$
$631$	−1.29079	−	1.71773i	−0.0513857	−	0.0683819i	−0.824404	+	0.566002i	$0.808490\pi$
$632$	−0.771152	−	1.46931i	−0.0306748	−	0.0584459i
$633$	2.46531	−	12.0759i	0.0979874	−	0.479974i
$634$	−4.46565	+	0.360505i	−0.177354	+	0.0143175i
$635$	0.0693601	+	0.0200904i	0.00275247	+	0.000797263i
$636$	6.25597	+	3.28339i	0.248065	+	0.130195i
$637$	30.5225	+	30.5567i	1.20935	+	1.21070i
$638$	0.679413	−	0.356583i	0.0268982	−	0.0141173i
$639$	−3.51755	+	0.718112i	−0.139152	+	0.0284081i
$640$	−21.5682	−	16.2074i	−0.852557	−	0.640655i
$641$	1.77484	+	44.0421i	0.0701019	+	1.73956i	0.526845	+	0.849961i	$0.323375\pi$
$641$	1.77484	+	44.0421i	0.0701019	+	1.73956i	−0.456743	+	0.889599i	$0.650984\pi$
$642$	−2.25687	+	0.855917i	−0.0890715	+	0.0337804i
$643$	26.3962	−	7.64575i	1.04096	−	0.301519i	0.286652	−	0.958035i	$-0.407458\pi$
$643$	26.3962	−	7.64575i	1.04096	−	0.301519i	0.754312	+	0.656516i	$0.227971\pi$
$644$	−45.7715	−	9.34433i	−1.80365	−	0.368218i
$645$	11.5201	+	13.0035i	0.453603	+	0.512012i
$646$	2.29393	−	2.80955i	0.0902534	−	0.110540i
$647$	−1.48510	+	36.8525i	−0.0583854	+	1.44882i	0.659000	+	0.752143i	$0.270980\pi$
$647$	−1.48510	+	36.8525i	−0.0583854	+	1.44882i	−0.717385	+	0.696677i	$0.754661\pi$
$648$	0.273467	+	0.819133i	0.0107428	+	0.0321786i
$649$	−5.75324	+	5.09692i	−0.225834	+	0.200072i
$650$	−6.58132	+	6.57395i	−0.258141	+	0.257852i
$651$	25.4849	+	22.5777i	0.998833	+	0.884889i
$652$	−1.63803	+	3.84459i	−0.0641501	+	0.150566i
$653$	−5.80764	+	10.0591i	−0.227271	+	0.393644i	−0.956998	−	0.290094i	$-0.906314\pi$
$653$	−5.80764	+	10.0591i	−0.227271	+	0.393644i	0.729728	+	0.683738i	$0.239647\pi$
$654$	−0.713647	−	1.23607i	−0.0279058	−	0.0483343i
$655$	−46.6060	+	5.65900i	−1.82105	+	0.221115i
$656$	28.4511	+	13.5002i	1.11083	+	0.527096i
$657$	7.25254	−	4.18725i	0.282948	−	0.163360i
$658$	1.09763	+	0.757640i	0.0427901	+	0.0295359i
$659$	26.6030	−	11.3345i	1.03631	−	0.441529i	0.194269	−	0.980948i	$-0.437766\pi$
$659$	26.6030	−	11.3345i	1.03631	−	0.441529i	0.842037	+	0.539419i	$0.181356\pi$
$660$	6.97287	+	1.13320i	0.271419	+	0.0441098i
$661$	−17.1129	+	22.7732i	−0.665616	+	0.885774i	−0.998360	−	0.0572431i	$-0.981769\pi$
$661$	−17.1129	+	22.7732i	−0.665616	+	0.885774i	0.332744	+	0.943017i	$0.392025\pi$
$662$	1.07035	+	2.82227i	0.0416002	+	0.109691i
$663$	−9.66657	+	0.971183i	−0.375419	+	0.0377176i
$664$	1.44447	−	3.80876i	0.0560563	−	0.147808i
$665$	−58.8064	−	92.9948i	−2.28041	−	3.60618i
$666$	0.279285	+	0.118992i	0.0108221	+	0.00461086i
$667$	−18.4704	−	11.6799i	−0.715175	−	0.452249i
$668$	−16.8076	−	2.04082i	−0.650307	−	0.0789615i
$669$	−4.41827	−	10.3701i	−0.170820	−	0.400930i
$670$	−0.468621	+	1.40369i	−0.0181044	+	0.0542293i
$671$	−10.2338	−	3.88116i	−0.395071	−	0.149831i
$672$	11.0254	+	0.890065i	0.425315	+	0.0343350i
$673$	2.69991	−	9.32115i	0.104074	−	0.359304i	−0.891531	−	0.452960i	$-0.850368\pi$
$673$	2.69991	−	9.32115i	0.104074	−	0.359304i	0.995605	+	0.0936557i	$0.0298553\pi$
$674$	−6.68929	−	0.269569i	−0.257662	−	0.0103834i
$675$	11.8075			0.454471
$676$	25.1909	+	3.08735i	0.968879	+	0.118744i
$677$	3.00788			0.115602			0.0578011	−	0.998328i	$-0.481591\pi$
$677$	3.00788			0.115602			0.0578011	+	0.998328i	$0.481591\pi$
$678$	2.97758	+	0.119992i	0.114353	+	0.00460828i
$679$	21.6365	−	74.6979i	0.830333	−	2.86664i
$680$	9.50874	+	0.767625i	0.364644	+	0.0294371i
$681$	−9.39566	−	3.56330i	−0.360042	−	0.136546i
$682$	0.477305	−	1.42970i	0.0182770	−	0.0547462i
$683$	6.42229	+	15.0737i	0.245742	+	0.576778i	0.996481	−	0.0838213i	$-0.0267125\pi$
$683$	6.42229	+	15.0737i	0.245742	+	0.576778i	−0.750739	+	0.660599i	$0.770302\pi$
$684$	11.9393	+	1.44969i	0.456511	+	0.0554304i
$685$	35.4200	+	22.3982i	1.35333	+	0.855793i
$686$	4.35990	+	1.85758i	0.166462	+	0.0709227i
$687$	−3.76312	−	5.95089i	−0.143572	−	0.227041i
$688$	−5.58354	+	14.7226i	−0.212871	+	0.561294i
$689$	12.9181	+	1.84059i	0.492140	+	0.0701208i
$690$	1.74479	+	4.60065i	0.0664232	+	0.175144i
$691$	3.73276	−	4.96741i	0.142001	−	0.188969i	−0.722839	−	0.691016i	$-0.757163\pi$
$691$	3.73276	−	4.96741i	0.142001	−	0.188969i	0.864840	+	0.502047i	$0.167420\pi$
$692$	9.78336	+	1.58995i	0.371907	+	0.0604408i
$693$	−3.53748	+	1.50718i	−0.134378	+	0.0572531i
$694$	3.02729	+	2.08959i	0.114914	+	0.0793197i
$695$	8.46116	−	4.88505i	0.320950	−	0.185301i
$696$	3.10408	+	1.47290i	0.117660	+	0.0558302i
$697$	−22.6696	+	2.75259i	−0.858673	+	0.104262i
$698$	2.68869	+	4.65694i	0.101768	+	0.176268i
$699$	−0.416605	+	0.721581i	−0.0157574	+	0.0272927i
$700$	39.3620	−	92.3859i	1.48774	−	3.49186i
$701$	−7.83320	−	6.93961i	−0.295856	−	0.262105i	0.502116	−	0.864800i	$-0.332555\pi$
$701$	−7.83320	−	6.93961i	−0.295856	−	0.262105i	−0.797972	+	0.602695i	$0.794094\pi$
$702$	0.485516	+	0.620431i	0.0183246	+	0.0234166i
$703$	6.40668	−	5.67582i	0.241632	−	0.214068i
$704$	1.92211	+	5.75741i	0.0724421	+	0.216991i
$705$	−0.231295	+	5.73953i	−0.00871108	+	0.216163i
$706$	−4.32742	+	5.30013i	−0.162865	+	0.199473i
$707$	46.9126	+	52.9533i	1.76433	+	1.99152i
$708$	−16.6572	−	3.40058i	−0.626014	−	0.127802i
$709$	−20.5972	+	5.96605i	−0.773544	+	0.224060i	−0.641437	−	0.767176i	$-0.721661\pi$
$709$	−20.5972	+	5.96605i	−0.773544	+	0.224060i	−0.132107	+	0.991235i	$0.542174\pi$
$710$	3.00699	−	1.14040i	0.112850	−	0.0427985i
$711$	0.0773719	+	1.91996i	0.00290167	+	0.0720043i
$712$	−9.91151	−	7.44802i	−0.371450	−	0.279126i
$713$	−42.0610	+	8.58681i	−1.57520	+	0.321578i
$714$	−2.27110	+	1.19197i	−0.0849938	+	0.0446082i
$715$	12.8345	−	2.34458i	0.479983	−	0.0876824i
$716$	−40.6543	−	21.3370i	−1.51932	−	0.797401i
$717$	−4.06554	−	1.17760i	−0.151830	−	0.0439782i
$718$	5.62583	−	0.454164i	0.209954	−	0.0169492i
$719$	6.04248	−	29.5980i	0.225347	−	1.10382i	−0.696885	−	0.717183i	$-0.745431\pi$
$719$	6.04248	−	29.5980i	0.225347	−	1.10382i	0.922232	−	0.386638i	$-0.126364\pi$
$720$	7.07947	+	13.4888i	0.263836	+	0.502698i
$721$	27.7379	+	36.9125i	1.03301	+	1.37469i
$722$	−2.21331	+	3.50006i	−0.0823707	+	0.130259i
$723$	14.4073	−	9.94467i	0.535815	−	0.369846i
$724$	−0.0656334	+	0.138320i	−0.00243925	+	0.00514061i
$725$	32.5422	−	33.8800i	1.20859	−	1.25827i
$726$	−1.61066	−	1.54706i	−0.0597771	−	0.0574167i
$727$	−1.82713	−	15.0478i	−0.0677645	−	0.558091i	−0.986565	−	0.163369i	$-0.947764\pi$
$727$	−1.82713	−	15.0478i	−0.0677645	−	0.558091i	0.918801	−	0.394722i	$-0.129159\pi$
$728$	13.1043	−	3.50342i	0.485677	−	0.129845i
$729$	0.120537	−	0.992709i	0.00446432	−	0.0367670i
$730$	−5.81094	+	4.74449i	−0.215073	+	0.175601i
$731$	−2.28390	−	11.1873i	−0.0844732	−	0.413777i
$732$	−6.73526	−	23.2528i	−0.248942	−	0.859449i
$733$	2.54070	+	10.3080i	0.0938428	+	0.380735i	0.999018	−	0.0443032i	$-0.0141068\pi$
$733$	2.54070	+	10.3080i	0.0938428	+	0.380735i	−0.905175	+	0.425038i	$0.860261\pi$
$734$	−0.284019	+	3.51821i	−0.0104834	+	0.129860i
$735$	7.87760	+	48.4728i	0.290570	+	1.78795i
$736$	−9.24827	+	10.4391i	−0.340896	+	0.384792i
$737$	1.16569	−	0.875957i	0.0429386	−	0.0322663i
$738$	1.17117	+	1.43442i	0.0431112	+	0.0528017i
$739$	−5.93582	+	36.5245i	−0.218353	+	1.34358i	0.613989	+	0.789314i	$0.289564\pi$
$739$	−5.93582	+	36.5245i	−0.218353	+	1.34358i	−0.832342	+	0.554263i	$0.813000\pi$
$740$	10.7968	+	2.66118i	0.396900	+	0.0978269i
$741$	21.6722	−	4.86823i	0.796147	−	0.178839i
$742$	3.34481	−	0.824422i	0.122792	−	0.0302655i
$743$	−1.92127	−	23.7992i	−0.0704847	−	0.873110i	−0.931314	−	0.364216i	$-0.881337\pi$
$743$	−1.92127	−	23.7992i	−0.0704847	−	0.873110i	0.860830	−	0.508893i	$-0.169945\pi$
$744$	6.40188	−	2.13726i	0.234704	−	0.0783558i
$745$	43.3234	+	45.1044i	1.58725	+	1.65250i
$746$			0.963138i			0.0352630i
$747$	−3.40190	+	3.26756i	−0.124469	+	0.119554i
$748$	−3.59652	−	2.93647i	−0.131502	−	0.107368i
$749$	22.3645	−	42.6120i	0.817180	−	1.55701i
$750$	−6.01913	+	0.978204i	−0.219788	+	0.0357190i
$751$	28.5275	−	18.0397i	1.04098	−	0.658279i	0.0993976	−	0.995048i	$-0.468308\pi$
$751$	28.5275	−	18.0397i	1.04098	−	0.658279i	0.941587	+	0.336769i	$0.109334\pi$
$752$	−4.70367	+	2.23192i	−0.171525	+	0.0813896i
$753$	−3.42701	+	4.96487i	−0.124887	+	0.180930i
$754$	3.11835	+	0.316822i	0.113564	+	0.0115380i
$755$	−10.0752	−	14.5964i	−0.366673	−	0.531218i
$756$	−7.36546	−	4.25245i	−0.267879	−	0.154660i
$757$	−4.29071	−	9.04247i	−0.155948	−	0.328654i	0.810406	−	0.585869i	$-0.199247\pi$
$757$	−4.29071	−	9.04247i	−0.155948	−	0.328654i	−0.966354	+	0.257214i	$0.917195\pi$
$758$	0.527063	+	0.175959i	0.0191438	+	0.00639113i
$759$	1.16024	−	4.70728i	0.0421140	−	0.170863i
$760$	−21.7931	+	0.878233i	−0.790520	+	0.0318569i
$761$	−7.19986	+	0.290144i	−0.260995	+	0.0105177i	−0.170418	−	0.985372i	$-0.554512\pi$
$761$	−7.19986	+	0.290144i	−0.260995	+	0.0105177i	−0.0905763	+	0.995890i	$0.528871\pi$
$762$	−0.000921041		0.00373681i	−3.33658e−5		0.000135370i
$763$	26.9926	+	9.01145i	0.977198	+	0.326237i
$764$	8.97165	+	18.9074i	0.324583	+	0.684044i
$765$	−9.56674	−	5.52336i	−0.345886	−	0.199697i
$766$	0.0117066	+	0.0169599i	0.000422975	+	0.000612786i
$767$	−31.0890	+	4.39409i	−1.12256	+	0.158662i
$768$	−6.99617	+	10.1357i	−0.252453	+	0.365741i
$769$	−2.64851	+	1.25673i	−0.0955076	+	0.0453189i	−0.475847	−	0.879528i	$-0.657858\pi$
$769$	−2.64851	+	1.25673i	−0.0955076	+	0.0453189i	0.380339	+	0.924847i	$0.375807\pi$
$770$	2.91124	−	1.84095i	0.104914	−	0.0663434i
$771$	−9.16184	+	1.48894i	−0.329956	+	0.0536230i
$772$	−17.7377	+	33.7964i	−0.638394	+	1.21636i
$773$	−13.5304	−	11.0472i	−0.486655	−	0.397342i	0.357103	−	0.934065i	$-0.383764\pi$
$773$	−13.5304	−	11.0472i	−0.486655	−	0.397342i	−0.843758	+	0.536723i	$0.819662\pi$
$774$	−0.667763	+	0.641395i	−0.0240023	+	0.0230545i
$775$		−	92.2807i		−	3.31482i
$776$	−10.6790	−	11.1180i	−0.383354	−	0.399114i
$777$	−5.74118	+	1.91669i	−0.205964	+	0.0687608i
$778$	−0.662236	−	8.20327i	−0.0237423	−	0.294101i
$779$	50.6937	−	12.4949i	1.81629	−	0.447675i
$780$	21.1995	+	19.5791i	0.759065	+	0.701044i
$781$	−3.07669	−	0.758335i	−0.110093	−	0.0271354i
$782$	0.518758	−	3.19204i	0.0185507	−	0.114147i
$783$	−2.51623	−	3.08183i	−0.0899228	−	0.110135i
$784$	−35.5836	+	26.7393i	−1.27084	+	0.954976i
$785$	−7.61537	+	8.59597i	−0.271804	+	0.306803i
$786$	−0.401383	−	2.46981i	−0.0143168	−	0.0880951i
$787$	0.783212	−	9.70182i	0.0279185	−	0.345832i	−0.967685	−	0.252163i	$-0.918858\pi$
$787$	0.783212	−	9.70182i	0.0279185	−	0.345832i	0.995603	−	0.0936697i	$-0.0298598\pi$
$788$	−4.82536	−	19.5773i	−0.171896	−	0.697411i
$789$	1.93483	+	6.67982i	0.0688819	+	0.237808i
$790$	−0.344301	−	1.68650i	−0.0122497	−	0.0600029i
$791$	−46.0229	+	37.5765i	−1.63638	+	1.33607i
$792$	−0.0918762	+	0.756669i	−0.00326468	+	0.0268871i
$793$	−26.1137	−	36.2913i	−0.927324	−	1.28874i
$794$	0.725341	+	5.97372i	0.0257414	+	0.211999i
$795$	10.7004	+	10.2779i	0.379504	+	0.364518i
$796$	−30.1913	+	31.4325i	−1.07010	+	1.11410i
$797$	11.4709	−	24.1744i	0.406321	−	0.856303i	−0.592396	−	0.805647i	$-0.701818\pi$
$797$	11.4709	−	24.1744i	0.406321	−	0.856303i	0.998716	−	0.0506554i	$-0.0161310\pi$
$798$	4.82613	−	3.33124i	0.170843	−	0.117925i
$799$	2.01780	−	3.19090i	0.0713848	−	0.112886i
$800$	−18.0103	−	23.9673i	−0.636759	−	0.847372i
$801$	6.67185	+	12.7122i	0.235738	+	0.449162i
$802$	−0.653912	+	3.20307i	−0.0230904	+	0.113104i
$803$	7.36771	−	0.594783i	0.260001	−	0.0209894i
$804$	3.09780	+	0.897289i	0.109251	+	0.0316449i
$805$	−86.8648	−	45.5902i	−3.06158	−	1.60684i
$806$	4.84893	−	3.79452i	0.170796	−	0.133656i
$807$	−19.2011	+	10.0775i	−0.675911	+	0.354745i
$808$	13.7403	−	2.80510i	0.483382	−	0.0986832i
$809$	−4.13371	−	3.10628i	−0.145333	−	0.109211i	0.525589	−	0.850739i	$-0.323845\pi$
$809$	−4.13371	−	3.10628i	−0.145333	−	0.109211i	−0.670922	+	0.741528i	$0.734102\pi$
$810$	0.0360699	+	0.895065i	0.00126737	+	0.0314494i
$811$	25.0310	−	9.49302i	0.878958	−	0.333345i	0.126486	−	0.991968i	$-0.459630\pi$
$811$	25.0310	−	9.49302i	0.878958	−	0.333345i	0.752473	+	0.658623i	$0.228861\pi$
$812$	−32.5015	+	9.41416i	−1.14058	+	0.330372i
$813$	15.8464	+	3.23507i	0.555758	+	0.113459i
$814$	0.177684	+	0.200563i	0.00622781	+	0.00702974i
$815$	−5.55021	+	6.79777i	−0.194415	+	0.238116i
$816$	0.403157	−	10.0042i	0.0141133	−	0.350218i
$817$	8.26675	+	24.7619i	0.289217	+	0.866310i
$818$	2.67560	−	2.37037i	0.0935501	−	0.0828781i
$819$	−15.4485	−	2.83999i	−0.539815	−	0.0992372i
$820$	50.7723	+	44.9804i	1.77305	+	1.57078i
$821$	18.6241	−	43.7124i	0.649986	−	1.52557i	−0.189320	−	0.981915i	$-0.560629\pi$
$821$	18.6241	−	43.7124i	0.649986	−	1.52557i	0.839307	−	0.543658i	$-0.182961\pi$
$822$	−1.11678	+	1.93432i	−0.0389522	+	0.0674671i
$823$	6.30446	+	10.9197i	0.219760	+	0.380635i	0.954734	−	0.297459i	$-0.0961393\pi$
$823$	6.30446	+	10.9197i	0.219760	+	0.380635i	−0.734975	+	0.678095i	$0.762806\pi$
$824$	9.08605	−	1.10325i	0.316528	−	0.0384334i
$825$	9.41556	+	4.46774i	0.327808	+	0.155547i
$826$	−7.17875	+	4.14465i	−0.249781	+	0.144211i
$827$	−39.9344	−	27.5647i	−1.38865	−	0.958519i	−0.999299	−	0.0374316i	$-0.988082\pi$
$827$	−39.9344	−	27.5647i	−1.38865	−	0.958519i	−0.389356	−	0.921088i	$-0.627302\pi$
$828$	9.86525	−	4.20319i	0.342841	−	0.146071i
$829$	32.5585	+	5.29128i	1.13080	+	0.183774i	0.696889	−	0.717179i	$-0.254567\pi$
$829$	32.5585	+	5.29128i	1.13080	+	0.183774i	0.433916	+	0.900953i	$0.357131\pi$
$830$	2.53839	−	3.37799i	0.0881089	−	0.117252i
$831$	−1.81062	−	4.77422i	−0.0628098	−	0.165616i
$832$	−6.43079	+	23.9464i	−0.222947	+	0.830191i
$833$	11.4455	−	30.1792i	0.396562	−	1.04565i
$834$	0.278306	+	0.440106i	0.00963695	+	0.0152396i
$835$	−32.7098	−	13.9363i	−1.13197	−	0.482286i
$836$	8.97212	+	5.67363i	0.310307	+	0.196227i
$837$	−7.75845	−	0.942046i	−0.268171	−	0.0325619i
$838$	−0.184918	−	0.434019i	−0.00638790	−	0.0149929i
$839$	14.0692	−	42.1423i	0.485722	−	1.45491i	−0.365849	−	0.930674i	$-0.619221\pi$
$839$	14.0692	−	42.1423i	0.485722	−	1.45491i	0.851570	−	0.524240i	$-0.175651\pi$
$840$	14.4213	+	5.46927i	0.497581	+	0.188708i
$841$	13.1282	+	1.05982i	0.452697	+	0.0365455i
$842$	−0.543704	+	1.87708i	−0.0187373	+	0.0646885i
$843$	−25.2336	−	1.01688i	−0.869092	−	0.0350232i
$844$	24.0615			0.828232
$845$	49.0078	+	20.9452i	1.68592	+	0.720535i
$846$	−0.306149			−0.0105256
$847$	44.4909	+	1.79292i	1.52873	+	0.0616055i
$848$	−3.74136	+	12.9167i	−0.128479	+	0.443561i
$849$	−2.60141	−	0.210007i	−0.0892801	−	0.00720744i
$850$	6.50001	+	2.46513i	0.222949	+	0.0845532i
$851$	2.41664	−	7.23872i	0.0828413	−	0.248140i
$852$	−2.74721	−	6.44795i	−0.0941180	−	0.220903i
$853$	10.6395	+	1.29187i	0.364291	+	0.0442329i	0.300636	−	0.953739i	$-0.402801\pi$
$853$	10.6395	+	1.29187i	0.364291	+	0.0442329i	0.0636551	+	0.997972i	$0.479724\pi$
$854$	−9.97643	−	6.30871i	−0.341386	−	0.215880i
$855$	23.2354	+	9.89967i	0.794634	+	0.338562i
$856$	−5.09862	−	8.06281i	−0.174267	−	0.275581i
$857$	3.90907	−	10.3074i	0.133531	−	0.352093i	−0.851528	−	0.524310i	$-0.824323\pi$
$857$	3.90907	−	10.3074i	0.133531	−	0.352093i	0.985059	+	0.172216i	$0.0550927\pi$
$858$	0.152402	+	0.678455i	0.00520291	+	0.0231621i
$859$	12.6178	+	33.2704i	0.430513	+	1.13517i	0.958293	+	0.285789i	$0.0922556\pi$
$859$	12.6178	+	33.2704i	0.430513	+	1.13517i	−0.527779	+	0.849382i	$0.676975\pi$
$860$	−20.3745	+	27.1135i	−0.694765	+	0.924564i
$861$	−36.4429	−	5.92254i	−1.24197	−	0.201840i
$862$	2.78522	−	1.18667i	0.0948651	−	0.0404182i
$863$	4.23369	+	2.92230i	0.144116	+	0.0994763i	0.637941	−	0.770085i	$-0.279786\pi$
$863$	4.23369	+	2.92230i	0.144116	+	0.0994763i	−0.493825	+	0.869561i	$0.664402\pi$
$864$	−2.19889	+	1.26953i	−0.0748079	+	0.0431904i
$865$	18.8048	+	8.92297i	0.639381	+	0.303390i
$866$	1.61184	−	0.195712i	0.0547724	−	0.00665058i
$867$	−4.86978	−	8.43470i	−0.165386	−	0.286457i
$868$	−33.2348	+	57.5643i	−1.12806	+	1.95386i
$869$	−0.664781	+	1.56030i	−0.0225511	+	0.0529295i
$870$	2.66767	+	2.36335i	0.0904426	+	0.0801252i
$871$	5.94572	−	0.356309i	0.201463	−	0.0120731i
$872$	4.22237	−	3.74070i	0.142988	−	0.126676i
$873$	5.65294	+	16.9326i	0.191323	+	0.573082i
$874$	−0.297719	+	7.38781i	−0.0100705	+	0.249896i
$875$	76.8945	−	94.1786i	2.59951	−	3.18382i
$876$	10.8415	+	12.2375i	0.366301	+	0.413468i
$877$	50.2682	+	10.2623i	1.69744	+	0.346534i	0.948662	−	0.316291i	$-0.102438\pi$
$877$	50.2682	+	10.2623i	1.69744	+	0.346534i	0.748774	+	0.662825i	$0.230643\pi$
$878$	−1.07554	+	0.311534i	−0.0362977	+	0.0105137i
$879$	20.4144	−	7.74215i	0.688560	−	0.261136i
$880$	0.541412	+	13.4350i	0.0182510	+	0.452894i
$881$	−19.4529	−	14.6179i	−0.655386	−	0.492491i	0.220262	−	0.975441i	$-0.429309\pi$
$881$	−19.4529	−	14.6179i	−0.655386	−	0.492491i	−0.875648	+	0.482950i	$0.839565\pi$
$882$	−2.56446	+	0.523538i	−0.0863498	+	0.0176284i
$883$	13.4462	−	7.05713i	0.452502	−	0.237491i	−0.223045	−	0.974808i	$-0.571600\pi$
$883$	13.4462	−	7.05713i	0.452502	−	0.237491i	0.675547	+	0.737317i	$0.263908\pi$
$884$	−5.63249	−	18.1110i	−0.189441	−	0.609139i
$885$	−31.6118	−	16.5912i	−1.06262	−	0.557706i
$886$	4.56118	+	1.32116i	0.153236	+	0.0443853i
$887$	19.2519	−	1.55418i	0.646417	−	0.0521841i	0.247090	−	0.968993i	$-0.420526\pi$
$887$	19.2519	−	1.55418i	0.646417	−	0.0521841i	0.399327	+	0.916809i	$0.369244\pi$
$888$	−0.239994	+	1.17557i	−0.00805368	+	0.0394495i
$889$	−0.0356598	−	0.0679442i	−0.00119599	−	0.00227877i
$890$	−7.72586	−	10.2813i	−0.258972	−	0.344629i
$891$	0.471741	−	0.745999i	0.0158039	−	0.0249919i
$892$	18.1106	−	12.5008i	0.606387	−	0.418558i
$893$	−3.70036	+	7.79833i	−0.123828	+	0.260961i
$894$	−2.30901	+	2.40393i	−0.0772249	+	0.0803996i
$895$	−69.5362	−	66.7904i	−2.32434	−	2.23256i
$896$	3.45562	+	28.4596i	0.115444	+	0.950768i
$897$	14.5640	−	13.4205i	0.486276	−	0.448098i
$898$	0.558960	−	4.60345i	0.0186527	−	0.153619i
$899$	−24.0858	+	19.6655i	−0.803307	+	0.655880i
$900$	4.61085	+	22.5854i	0.153695	+	0.752848i
$901$	−2.71304	−	9.36651i	−0.0903846	−	0.312044i
$902$	0.391156	+	1.58698i	0.0130241	+	0.0528408i
$903$	1.48545	−	18.4006i	0.0494327	−	0.612334i
$904$	1.88928	+	11.6252i	0.0628365	+	0.386648i
$905$	−0.213200	+	0.240653i	−0.00708702	+	0.00799959i
$906$	0.755694	−	0.567867i	0.0251063	−	0.0188661i
$907$	−8.04568	−	9.85417i	−0.267152	−	0.327202i	0.623555	−	0.781780i	$-0.285688\pi$
$907$	−8.04568	−	9.85417i	−0.267152	−	0.327202i	−0.890707	+	0.454577i	$0.849790\pi$
$908$	3.14688	−	19.3635i	0.104433	−	0.642601i
$909$	−15.7673	−	3.88628i	−0.522967	−	0.128900i
$910$	14.0675	+	0.291215i	0.466334	+	0.00965370i
$911$	−5.14346	+	1.26775i	−0.170410	+	0.0420024i	−0.323598	−	0.946195i	$-0.604892\pi$
$911$	−5.14346	+	1.26775i	−0.170410	+	0.0420024i	0.153187	+	0.988197i	$0.451046\pi$
$912$	1.84200	+	22.8173i	0.0609948	+	0.755557i
$913$	−3.94913	+	1.31841i	−0.130697	+	0.0436331i
$914$	−0.446135	−	0.464475i	−0.0147568	−	0.0153635i
$915$		−	50.8376i		−	1.68064i
$916$	9.91338	−	9.52193i	0.327547	−	0.314614i
$917$	38.6439	+	31.5518i	1.27613	+	1.04193i
$918$	0.273609	−	0.521319i	0.00903046	−	0.0172061i
$919$	−44.5838	+	7.24558i	−1.47068	+	0.239009i	−0.842349	−	0.538933i	$-0.818828\pi$
$919$	−44.5838	+	7.24558i	−1.47068	+	0.239009i	−0.628336	+	0.777942i	$0.716264\pi$
$920$	−16.4361	+	10.3936i	−0.541883	+	0.342666i
$921$	−7.44822	+	3.53422i	−0.245427	+	0.116457i
$922$	0.769404	−	1.11467i	0.0253390	−	0.0367098i
$923$	−8.77169	−	9.51904i	−0.288724	−	0.313323i
$924$	−4.26433	−	6.17795i	−0.140286	−	0.203240i
$925$	14.2070	+	8.20243i	0.467124	+	0.269694i
$926$	−2.48464	−	5.23627i	−0.0816504	−	0.172075i
$927$	−10.0533	−	3.35627i	−0.330192	−	0.110234i
$928$	−2.41754	+	9.80833i	−0.0793595	+	0.321974i
$929$	−0.0130598		0.000526293i	−0.000428479		1.72671e-5i	−0.0404802	−	0.999180i	$-0.512889\pi$
$929$	−0.0130598		0.000526293i	−0.000428479		1.72671e-5i	0.0400517	+	0.999198i	$0.487248\pi$
$930$	6.99532	−	0.281902i	0.229385	−	0.00924392i
$931$	−17.6603	+	71.6508i	−0.578794	+	2.34826i
$932$	−1.54293	−	0.515105i	−0.0505403	−	0.0168728i
$933$	−8.61998	−	18.1662i	−0.282205	−	0.594735i
$934$	3.20512	+	1.85047i	0.104875	+	0.0605494i
$935$	−5.53879	−	8.02432i	−0.181138	−	0.262423i
$936$	−2.01872	+	2.37059i	−0.0659839	+	0.0774851i
$937$	17.6790	−	25.6124i	0.577547	−	0.836722i	−0.419941	−	0.907551i	$-0.637949\pi$
$937$	17.6790	−	25.6124i	0.577547	−	0.836722i	0.997488	+	0.0708295i	$0.0225646\pi$
$938$	1.42070	−	0.674131i	0.0463876	−	0.0220112i
$939$	−23.1981	+	14.6696i	−0.757040	+	0.478723i
$940$	−11.0689	+	1.79887i	−0.361028	+	0.0586728i
$941$	17.2799	−	32.9242i	0.563310	−	1.07330i	−0.422646	−	0.906295i	$-0.638899\pi$
$941$	17.2799	−	32.9242i	0.563310	−	1.07330i	0.985956	−	0.167003i	$-0.0534089\pi$
$942$	−0.474112	−	0.387100i	−0.0154474	−	0.0126124i
$943$	33.5730	−	32.2473i	1.09329	−	1.05012i
$944$		−	32.3583i		−	1.05317i
$945$	−12.3721	−	12.8808i	−0.402465	−	0.419011i
$946$	−0.775181	+	0.258793i	−0.0252033	+	0.00841410i
$947$	4.75905	+	58.9514i	0.154648	+	1.91566i	0.353158	+	0.935564i	$0.385108\pi$
$947$	4.75905	+	58.9514i	0.154648	+	1.91566i	−0.198510	+	0.980099i	$0.563610\pi$
$948$	−3.64230	+	0.897746i	−0.118296	+	0.0291574i
$949$	26.4400	+	14.5825i	0.858277	+	0.473369i
$950$	−15.4322	−	3.80369i	−0.500685	−	0.123408i
$951$	−3.28909	+	20.2386i	−0.106656	+	0.656280i
$952$	−6.41117	−	7.85226i	−0.207787	−	0.254493i
$953$	−21.7280	+	16.3275i	−0.703839	+	0.528900i	−0.891324	−	0.453367i	$-0.850223\pi$
$953$	−21.7280	+	16.3275i	−0.703839	+	0.528900i	0.187485	+	0.982267i	$0.439966\pi$
$954$	−0.524372	+	0.591894i	−0.0169772	+	0.0191633i
$955$	7.04979	+	43.3791i	0.228126	+	1.40371i
$956$	0.664914	−	8.23644i	0.0215049	−	0.266385i
$957$	−0.840394	−	3.40961i	−0.0271661	−	0.110217i
$958$	1.95601	+	6.75292i	0.0631957	+	0.218177i
$959$	−8.90760	−	43.6323i	−0.287641	−	1.40896i
$960$	−21.8384	+	17.8305i	−0.704833	+	0.575478i
$961$	−3.62586	+	29.8617i	−0.116963	+	0.963279i
$962$	0.153182	+	1.08379i	0.00493880	+	0.0349429i
$963$	1.33153	+	10.9661i	0.0429080	+	0.353379i
$964$	24.6483	+	23.6750i	0.793868	+	0.762521i
$965$	−55.5237	+	57.8063i	−1.78737	+	1.86085i
$966$	2.24144	−	4.72373i	0.0721170	−	0.151983i
$967$	0.455932	−	0.314707i	0.0146618	−	0.0101203i	−0.560711	−	0.828011i	$-0.689472\pi$
$967$	0.455932	−	0.314707i	0.0146618	−	0.0101203i	0.575373	+	0.817891i	$0.304857\pi$
$968$	4.71749	−	7.46012i	0.151626	−	0.239777i
$969$	−9.97218	−	13.2706i	−0.320353	−	0.426312i
$970$	−7.43141	−	14.1594i	−0.238608	−	0.454630i
$971$	9.59519	−	47.0003i	0.307924	−	1.50831i	−0.471528	−	0.881851i	$-0.656297\pi$
$971$	9.59519	−	47.0003i	0.307924	−	1.50831i	0.779452	−	0.626462i	$-0.215497\pi$
$972$	1.94593	−	0.157091i	0.0624156	−	0.00503871i
$973$	−9.97208	−	2.88845i	−0.319690	−	0.0925994i
$974$	−4.62443	−	2.42709i	−0.148176	−	0.0777689i
$975$	22.0040	+	36.4451i	0.704692	+	1.16718i
$976$	40.7995	−	21.4132i	1.30596	−	0.685421i
$977$	−3.73064	+	0.761616i	−0.119354	+	0.0243663i	−0.259331	−	0.965788i	$-0.583502\pi$
$977$	−3.73064	+	0.761616i	−0.119354	+	0.0243663i	0.139977	+	0.990155i	$0.455297\pi$
$978$	−0.373919	−	0.280982i	−0.0119566	−	0.00898481i
$979$	0.510239	+	12.6615i	0.0163073	+	0.404662i
$980$	−89.6427	+	33.9970i	−2.86353	+	1.08599i
$981$	−6.27428	+	1.81737i	−0.200322	+	0.0580241i
$982$	8.82686	+	1.80202i	0.281677	+	0.0575047i
$983$	22.3292	+	25.2045i	0.712192	+	0.803899i	0.987527	−	0.157450i	$-0.0503272\pi$
$983$	22.3292	+	25.2045i	0.712192	+	0.803899i	−0.275335	+	0.961348i	$0.588789\pi$
$984$	−4.62875	+	5.66919i	−0.147559	+	0.180727i
$985$	1.70495	−	42.3078i	0.0543241	−	1.34804i
$986$	−0.741769	−	2.22187i	−0.0236227	−	0.0707588i
$987$	4.56886	−	4.04766i	0.145428	−	0.128838i
$988$	17.7750	+	39.5535i	0.565497	+	1.25837i
$989$	17.4221	+	15.4347i	0.553991	+	0.490794i
$990$	−0.309913	+	0.727392i	−0.00984968	+	0.0231180i
$991$	6.27067	−	10.8611i	0.199194	−	0.345015i	−0.749073	−	0.662487i	$-0.769501\pi$
$991$	6.27067	−	10.8611i	0.199194	−	0.345015i	0.948267	+	0.317473i	$0.102834\pi$
$992$	9.92194	+	17.1853i	0.315022	+	0.545634i
$993$	13.7135	−	1.66511i	0.435183	−	0.0528408i
$994$	−3.08744	−	1.46501i	−0.0979276	−	0.0464672i
$995$	−79.2624	+	45.7622i	−2.51279	+	1.45076i
$996$	−7.57865	−	5.23117i	−0.240139	−	0.165756i
$997$	−13.0023	+	5.53976i	−0.411787	+	0.175446i	−0.587918	−	0.808921i	$-0.700052\pi$
$997$	−13.0023	+	5.53976i	−0.411787	+	0.175446i	0.176131	+	0.984367i	$0.443642\pi$
$998$	6.06553	+	0.985745i	0.192001	+	0.0312032i
$999$	0.834647	−	1.11071i	0.0264071	−	0.0351414i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	507.2.t.b.4.7	✓	360
169.127	even	78	inner	507.2.t.b.127.7	yes	360

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
507.2.t.b.4.7	✓	360	1.1	even	1	trivial
507.2.t.b.127.7	yes	360	169.127	even	78	inner

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:	\( N \)	\(=\)	\( 507 = 3 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	507.t (of order \(78\), degree \(24\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.218325 - 0.00879818i) q^{2} +(-0.278217 + 0.960518i) q^{3} +(-1.94593 - 0.157091i) q^{4} +(-3.83328 - 1.45377i) q^{5} +(0.0691925 - 0.207257i) q^{6} +(1.70758 + 4.00784i) q^{7} +(0.857279 + 0.104093i) q^{8} +(-0.845190 - 0.534466i) q^{9} +O(q^{10})\)	\(q+(-0.218325 - 0.00879818i) q^{2} +(-0.278217 + 0.960518i) q^{3} +(-1.94593 - 0.157091i) q^{4} +(-3.83328 - 1.45377i) q^{5} +(0.0691925 - 0.207257i) q^{6} +(1.70758 + 4.00784i) q^{7} +(0.857279 + 0.104093i) q^{8} +(-0.845190 - 0.534466i) q^{9} +(0.824109 + 0.351120i) q^{10} +(-0.471741 - 0.745999i) q^{11} +(0.692280 - 1.82539i) q^{12} +(0.0746234 - 3.60478i) q^{13} +(-0.337546 - 0.890034i) q^{14} +(2.46286 - 3.27747i) q^{15} +(3.66770 + 0.596060i) q^{16} +(-2.47890 + 1.05616i) q^{17} +(0.179823 + 0.124123i) q^{18} +(5.33520 - 3.08028i) q^{19} +(7.23091 + 3.43111i) q^{20} +(-4.32468 + 0.525112i) q^{21} +(0.0964293 + 0.167020i) q^{22} +(2.74639 - 4.75689i) q^{23} +(-0.338493 + 0.794472i) q^{24} +(8.83804 + 7.82982i) q^{25} +(-0.0480076 + 0.786356i) q^{26} +(0.748511 - 0.663123i) q^{27} +(-2.69323 - 8.06721i) q^{28} +(0.160201 - 3.97535i) q^{29} +(-0.566539 + 0.693884i) q^{30} +(-5.18259 - 5.84993i) q^{31} +(-2.48775 - 0.507878i) q^{32} +(0.847792 - 0.245566i) q^{33} +(0.550498 - 0.208776i) q^{34} +(-0.719154 - 17.8456i) q^{35} +(1.56072 + 1.17280i) q^{36} +(1.36128 - 0.277908i) q^{37} +(-1.19191 + 0.625561i) q^{38} +(3.44169 + 1.07459i) q^{39} +(-3.13487 - 1.64530i) q^{40} +(8.14041 + 2.35790i) q^{41} +(0.948805 - 0.0765955i) q^{42} +(-0.847610 + 4.15187i) q^{43} +(0.800783 + 1.52577i) q^{44} +(2.46286 + 3.27747i) q^{45} +(-0.641458 + 1.01438i) q^{46} +(-1.15310 + 0.795930i) q^{47} +(-1.59294 + 3.35706i) q^{48} +(-8.29789 + 8.63902i) q^{49} +(-1.86067 - 1.78720i) q^{50} +(-0.324789 - 2.67488i) q^{51} +(-0.711492 + 7.00291i) q^{52} +(-0.436224 + 3.59263i) q^{53} +(-0.169253 + 0.138190i) q^{54} +(0.723804 + 3.54543i) q^{55} +(1.04669 + 3.61359i) q^{56} +(1.47432 + 5.98155i) q^{57} +(-0.0699517 + 0.866508i) q^{58} +(-1.39690 - 8.59548i) q^{59} +(-5.30741 + 5.99082i) q^{60} +(9.91335 - 7.44940i) q^{61} +(1.08002 + 1.32278i) q^{62} +(0.698823 - 4.30003i) q^{63} +(-6.67702 - 1.64574i) q^{64} +(-5.52658 + 13.7096i) q^{65} +(-0.187254 + 0.0461541i) q^{66} +(0.132931 + 1.64665i) q^{67} +(4.98968 - 1.66580i) q^{68} +(3.80499 + 3.96141i) q^{69} +3.90247i q^{70} +(2.58919 - 2.48695i) q^{71} +(-0.668930 - 0.546164i) q^{72} +(-3.89183 + 7.41526i) q^{73} +(-0.299646 + 0.0486973i) q^{74} +(-9.97959 + 6.31071i) q^{75} +(-10.8658 + 5.15588i) q^{76} +(2.18431 - 3.16452i) q^{77} +(-0.741952 - 0.264890i) q^{78} +(-1.09155 - 1.58138i) q^{79} +(-13.1928 - 7.61687i) q^{80} +(0.428693 + 0.903450i) q^{81} +(-1.75651 - 0.586408i) q^{82} +(1.12885 - 4.57991i) q^{83} +(8.49801 - 0.342458i) q^{84} +(11.0378 - 0.444806i) q^{85} +(0.221583 - 0.898998i) q^{86} +(3.77383 + 1.25989i) q^{87} +(-0.326761 - 0.688634i) q^{88} +(-12.4332 - 7.17831i) q^{89} +(-0.508867 - 0.737222i) q^{90} +(14.5748 - 5.85638i) q^{91} +(-6.09155 + 8.82513i) q^{92} +(7.06086 - 3.35042i) q^{93} +(0.258754 - 0.163626i) q^{94} +(-24.9294 + 4.05141i) q^{95} +(1.17996 - 2.24823i) q^{96} +(-13.8277 - 11.2900i) q^{97} +(1.88764 - 1.81310i) q^{98} +0.882640i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 360 q - 15 q^{3} - 14 q^{4} + 3 q^{7} + 15 q^{9}+O(q^{10}) \) 360 * q - 15 * q^3 - 14 * q^4 + 3 * q^7 + 15 * q^9	\( 360 q - 15 q^{3} - 14 q^{4} + 3 q^{7} + 15 q^{9} + 6 q^{11} - 28 q^{12} + 6 q^{13} + 4 q^{14} - 6 q^{15} + 20 q^{16} - 6 q^{19} - 12 q^{20} - 28 q^{22} + 46 q^{23} - 6 q^{25} - 39 q^{26} + 30 q^{27} - 6 q^{28} + 43 q^{29} + 26 q^{31} - 195 q^{32} + 19 q^{33} + 65 q^{34} + 84 q^{35} - 14 q^{36} - 65 q^{38} - 2 q^{39} + 12 q^{41} - 128 q^{42} + 83 q^{43} - 39 q^{44} - 6 q^{45} - 20 q^{48} + 72 q^{49} - 52 q^{50} - 55 q^{52} + 49 q^{53} - 49 q^{55} - 2 q^{56} + 26 q^{57} + 26 q^{58} - 202 q^{59} - 182 q^{60} - 3 q^{61} - 65 q^{62} - 3 q^{63} - 14 q^{64} - 58 q^{65} + 48 q^{66} - 41 q^{67} + 139 q^{68} + 6 q^{69} - 60 q^{71} - 52 q^{73} - 269 q^{74} + 23 q^{75} - 14 q^{76} + 70 q^{77} - 65 q^{78} + 18 q^{79} + 492 q^{80} + 15 q^{81} - 65 q^{82} + 78 q^{83} - 6 q^{84} - 91 q^{85} - 169 q^{86} + 48 q^{87} - 522 q^{88} - 12 q^{89} + 373 q^{91} + 72 q^{92} - 3 q^{93} - 13 q^{94} - 110 q^{95} + 65 q^{96} - 121 q^{97} - 104 q^{98}+O(q^{100}) \) 360 * q - 15 * q^3 - 14 * q^4 + 3 * q^7 + 15 * q^9 + 6 * q^11 - 28 * q^12 + 6 * q^13 + 4 * q^14 - 6 * q^15 + 20 * q^16 - 6 * q^19 - 12 * q^20 - 28 * q^22 + 46 * q^23 - 6 * q^25 - 39 * q^26 + 30 * q^27 - 6 * q^28 + 43 * q^29 + 26 * q^31 - 195 * q^32 + 19 * q^33 + 65 * q^34 + 84 * q^35 - 14 * q^36 - 65 * q^38 - 2 * q^39 + 12 * q^41 - 128 * q^42 + 83 * q^43 - 39 * q^44 - 6 * q^45 - 20 * q^48 + 72 * q^49 - 52 * q^50 - 55 * q^52 + 49 * q^53 - 49 * q^55 - 2 * q^56 + 26 * q^57 + 26 * q^58 - 202 * q^59 - 182 * q^60 - 3 * q^61 - 65 * q^62 - 3 * q^63 - 14 * q^64 - 58 * q^65 + 48 * q^66 - 41 * q^67 + 139 * q^68 + 6 * q^69 - 60 * q^71 - 52 * q^73 - 269 * q^74 + 23 * q^75 - 14 * q^76 + 70 * q^77 - 65 * q^78 + 18 * q^79 + 492 * q^80 + 15 * q^81 - 65 * q^82 + 78 * q^83 - 6 * q^84 - 91 * q^85 - 169 * q^86 + 48 * q^87 - 522 * q^88 - 12 * q^89 + 373 * q^91 + 72 * q^92 - 3 * q^93 - 13 * q^94 - 110 * q^95 + 65 * q^96 - 121 * q^97 - 104 * q^98

Introduction

L-functions

Modular forms

Varieties

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Database

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