LMFDB - Embedded newform 804.2.bd.a.35.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [804,2,Mod(23,804)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(804, base_ring=CyclotomicField(66))

chi = DirichletCharacter(H, H._module([33, 33, 28]))

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

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

chi := DirichletCharacter("804.23");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 804 = 2^{2} \cdot 3 \cdot 67 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	804.bd (of order $66$, degree $20$, 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:	$6.41997232251$
Analytic rank:	$0$
Dimension:	$2640$
Relative dimension:	$132$ over $\Q(\zeta_{66})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{66}]$

Embedding invariants

Embedding label			35.13
Character	$\chi$	$=$	804.35
Dual form			804.2.bd.a.23.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.33755 - 0.459299i) q^{2} +(1.70511 + 0.304307i) q^{3} +(1.57809 + 1.22867i) q^{4} +(-2.29127 - 1.04639i) q^{5} +(-2.14090 - 1.19018i) q^{6} +(-0.382733 + 0.401398i) q^{7} +(-1.54645 - 2.36823i) q^{8} +(2.81479 + 1.03775i) q^{9} +O(q^{10})$	\(q+(-1.33755 - 0.459299i) q^{2} +(1.70511 + 0.304307i) q^{3} +(1.57809 + 1.22867i) q^{4} +(-2.29127 - 1.04639i) q^{5} +(-2.14090 - 1.19018i) q^{6} +(-0.382733 + 0.401398i) q^{7} +(-1.54645 - 2.36823i) q^{8} +(2.81479 + 1.03775i) q^{9} +(2.58409 + 2.45198i) q^{10} +(3.69354 - 0.352690i) q^{11} +(2.31692 + 2.57524i) q^{12} +(-1.78432 + 0.343899i) q^{13} +(0.696287 - 0.361102i) q^{14} +(-3.58844 - 2.48146i) q^{15} +(0.980730 + 3.87791i) q^{16} +(1.28775 + 2.49788i) q^{17} +(-3.28829 - 2.68088i) q^{18} +(1.63406 + 1.71376i) q^{19} +(-2.33016 - 4.46652i) q^{20} +(-0.774749 + 0.567960i) q^{21} +(-5.10229 - 1.22470i) q^{22} +(3.38982 + 1.35708i) q^{23} +(-1.91619 - 4.50868i) q^{24} +(0.880693 + 1.01637i) q^{25} +(2.54457 + 0.359553i) q^{26} +(4.48373 + 2.62605i) q^{27} +(-1.09717 + 0.163190i) q^{28} +(1.80736 - 1.04348i) q^{29} +(3.66000 + 4.96725i) q^{30} +(1.19828 - 6.21724i) q^{31} +(0.469342 - 5.63735i) q^{32} +(6.40521 + 0.522596i) q^{33} +(-0.575153 - 3.93250i) q^{34} +(1.29696 - 0.519226i) q^{35} +(3.16694 + 5.09613i) q^{36} +(2.53488 - 4.39054i) q^{37} +(-1.39852 - 3.04276i) q^{38} +(-3.14711 + 0.0434043i) q^{39} +(1.06525 + 7.04444i) q^{40} +(9.71647 + 0.462853i) q^{41} +(1.29713 - 0.403834i) q^{42} +(1.51606 - 2.35904i) q^{43} +(6.26207 + 3.98157i) q^{44} +(-5.36356 - 5.32315i) q^{45} +(-3.91076 - 3.37211i) q^{46} +(2.11981 - 1.66704i) q^{47} +(0.492175 + 6.91070i) q^{48} +(0.318437 + 6.68481i) q^{49} +(-0.711153 - 1.76395i) q^{50} +(1.43562 + 4.65102i) q^{51} +(-3.23835 - 1.64964i) q^{52} +(1.46092 + 2.27324i) q^{53} +(-4.79109 - 5.57185i) q^{54} +(-8.83195 - 3.05677i) q^{55} +(1.54248 + 0.285656i) q^{56} +(2.26475 + 3.41940i) q^{57} +(-2.89671 + 0.565590i) q^{58} +(-5.90144 + 6.81062i) q^{59} +(-2.61399 - 8.32498i) q^{60} +(12.4227 + 1.18622i) q^{61} +(-4.45833 + 7.76552i) q^{62} +(-1.49387 + 0.732671i) q^{63} +(-3.21700 + 7.32468i) q^{64} +(4.44821 + 1.07912i) q^{65} +(-8.32727 - 3.64091i) q^{66} +(-7.02019 + 4.20915i) q^{67} +(-1.03690 + 5.52409i) q^{68} +(5.36705 + 3.34552i) q^{69} +(-1.97324 + 0.0987974i) q^{70} +(-10.5094 - 5.41795i) q^{71} +(-1.89529 - 8.27090i) q^{72} +(1.20612 + 0.115171i) q^{73} +(-5.40711 + 4.70831i) q^{74} +(1.19239 + 2.00103i) q^{75} +(0.473053 + 4.71219i) q^{76} +(-1.27207 + 1.61757i) q^{77} +(4.22936 + 1.38741i) q^{78} +(9.81221 + 3.39604i) q^{79} +(1.81068 - 9.91157i) q^{80} +(6.84613 + 5.84213i) q^{81} +(-12.7837 - 5.08186i) q^{82} +(-4.24506 - 5.96136i) q^{83} +(-1.92046 - 0.0556220i) q^{84} +(-0.336824 - 7.07080i) q^{85} +(-3.11132 + 2.45901i) q^{86} +(3.39929 - 1.22926i) q^{87} +(-6.54711 - 8.20172i) q^{88} +(10.4511 + 1.50264i) q^{89} +(4.72913 + 9.58346i) q^{90} +(0.544876 - 0.847844i) q^{91} +(3.68204 + 6.30658i) q^{92} +(3.93514 - 10.2364i) q^{93} +(-3.60103 + 1.25612i) q^{94} +(-1.95083 - 5.63655i) q^{95} +(2.51577 - 9.46947i) q^{96} +(2.46443 - 4.26851i) q^{97} +(2.64440 - 9.08754i) q^{98} +(10.7626 + 2.84024i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2640 q - 42 q^{4} - 19 q^{6} - 32 q^{9}+O(q^{10}) $ 2640 * q - 42 * q^4 - 19 * q^6 - 32 * q^9	$ 2640 q - 42 q^{4} - 19 q^{6} - 32 q^{9} - 46 q^{10} - 24 q^{12} - 88 q^{13} - 26 q^{16} - 23 q^{18} - 128 q^{22} - 22 q^{24} + 160 q^{25} + 44 q^{28} - 18 q^{30} - 44 q^{33} - 6 q^{34} - 35 q^{36} - 48 q^{37} - 92 q^{40} - 10 q^{42} + 40 q^{45} + 46 q^{46} - 11 q^{48} - 216 q^{49} - 76 q^{52} + 129 q^{54} - 42 q^{57} - 56 q^{58} - 90 q^{60} - 80 q^{61} - 48 q^{64} - 74 q^{66} - 4 q^{69} + 96 q^{70} - 20 q^{72} - 216 q^{73} + 76 q^{76} - 66 q^{78} - 16 q^{81} + 20 q^{82} - 55 q^{84} - 104 q^{85} - 30 q^{88} - 64 q^{90} - 192 q^{93} - 32 q^{94} - 205 q^{96} - 64 q^{97}+O(q^{100}) $ 2640 * q - 42 * q^4 - 19 * q^6 - 32 * q^9 - 46 * q^10 - 24 * q^12 - 88 * q^13 - 26 * q^16 - 23 * q^18 - 128 * q^22 - 22 * q^24 + 160 * q^25 + 44 * q^28 - 18 * q^30 - 44 * q^33 - 6 * q^34 - 35 * q^36 - 48 * q^37 - 92 * q^40 - 10 * q^42 + 40 * q^45 + 46 * q^46 - 11 * q^48 - 216 * q^49 - 76 * q^52 + 129 * q^54 - 42 * q^57 - 56 * q^58 - 90 * q^60 - 80 * q^61 - 48 * q^64 - 74 * q^66 - 4 * q^69 + 96 * q^70 - 20 * q^72 - 216 * q^73 + 76 * q^76 - 66 * q^78 - 16 * q^81 + 20 * q^82 - 55 * q^84 - 104 * q^85 - 30 * q^88 - 64 * q^90 - 192 * q^93 - 32 * q^94 - 205 * q^96 - 64 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/804\mathbb{Z}\right)^\times$.

$n$	$269$	$337$	$403$
$\chi(n)$	$-1$	$e\left(\frac{19}{33}\right)$	$-1$

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 $

$2$	−1.33755	−	0.459299i	−0.945792	−	0.324773i
$2$	−1.33755	−	0.459299i	−0.945792	−	0.324773i
$3$	1.70511	+	0.304307i	0.984445	+	0.175692i
$3$	1.70511	+	0.304307i	0.984445	+	0.175692i
$4$	1.57809	+	1.22867i	0.789044	+	0.614336i
$5$	−2.29127	−	1.04639i	−1.02469	−	0.467959i	−0.169090	−	0.985601i	$-0.554083\pi$
$5$	−2.29127	−	1.04639i	−1.02469	−	0.467959i	−0.855598	+	0.517641i	$0.826810\pi$
$6$	−2.14090	−	1.19018i	−0.874020	−	0.485890i
$7$	−0.382733	+	0.401398i	−0.144659	+	0.151714i	−0.792077	−	0.610421i	$-0.791000\pi$
$7$	−0.382733	+	0.401398i	−0.144659	+	0.151714i	0.647418	+	0.762135i	$0.275849\pi$
$8$	−1.54645	−	2.36823i	−0.546752	−	0.837295i
$9$	2.81479	+	1.03775i	0.938265	+	0.345918i
$10$	2.58409	+	2.45198i	0.817161	+	0.775383i
$11$	3.69354	−	0.352690i	1.11364	−	0.106340i	0.478027	−	0.878345i	$-0.341352\pi$
$11$	3.69354	−	0.352690i	1.11364	−	0.106340i	0.635616	+	0.772005i	$0.280746\pi$
$12$	2.31692	+	2.57524i	0.668837	+	0.743409i
$13$	−1.78432	+	0.343899i	−0.494881	+	0.0953805i	−0.430584	−	0.902550i	$-0.641693\pi$
$13$	−1.78432	+	0.343899i	−0.494881	+	0.0953805i	−0.0642966	+	0.997931i	$0.520480\pi$
$14$	0.696287	−	0.361102i	0.186090	−	0.0965087i
$15$	−3.58844	−	2.48146i	−0.926532	−	0.640710i
$16$	0.980730	+	3.87791i	0.245182	+	0.969477i
$17$	1.28775	+	2.49788i	0.312324	+	0.605824i	0.991789	−	0.127884i	$-0.0408184\pi$
$17$	1.28775	+	2.49788i	0.312324	+	0.605824i	−0.679465	+	0.733708i	$0.737788\pi$
$18$	−3.28829	−	2.68088i	−0.775058	−	0.631890i
$19$	1.63406	+	1.71376i	0.374880	+	0.393163i	0.883965	−	0.467554i	$-0.154865\pi$
$19$	1.63406	+	1.71376i	0.374880	+	0.393163i	−0.509085	+	0.860716i	$0.670016\pi$
$20$	−2.33016	−	4.46652i	−0.521040	−	0.998743i
$21$	−0.774749	+	0.567960i	−0.169064	+	0.123939i
$22$	−5.10229	−	1.22470i	−1.08781	−	0.261106i
$23$	3.38982	+	1.35708i	0.706827	+	0.282971i	0.697092	−	0.716982i	$-0.254477\pi$
$23$	3.38982	+	1.35708i	0.706827	+	0.282971i	0.00973519	+	0.999953i	$0.496901\pi$
$24$	−1.91619	−	4.50868i	−0.391141	−	0.920331i
$25$	0.880693	+	1.01637i	0.176139	+	0.203275i
$26$	2.54457	+	0.359553i	0.499031	+	0.0705141i
$27$	4.48373	+	2.62605i	0.862895	+	0.505383i
$28$	−1.09717	+	0.163190i	−0.207346	+	0.0308399i
$29$	1.80736	−	1.04348i	0.335619	−	0.193770i	−0.322714	−	0.946496i	$-0.604595\pi$
$29$	1.80736	−	1.04348i	0.335619	−	0.193770i	0.658333	+	0.752727i	$0.271262\pi$
$30$	3.66000	+	4.96725i	0.668221	+	0.906891i
$31$	1.19828	−	6.21724i	0.215217	−	1.11665i	−0.700140	−	0.714006i	$-0.746879\pi$
$31$	1.19828	−	6.21724i	0.215217	−	1.11665i	0.915357	−	0.402644i	$-0.131909\pi$
$32$	0.469342	−	5.63735i	0.0829688	−	0.996552i
$33$	6.40521	+	0.522596i	1.11500	+	0.0909723i
$34$	−0.575153	−	3.93250i	−0.0986380	−	0.674418i
$35$	1.29696	−	0.519226i	0.219227	−	0.0877652i
$36$	3.16694	+	5.09613i	0.527823	+	0.849355i
$37$	2.53488	−	4.39054i	0.416732	−	0.721801i	−0.578877	−	0.815415i	$-0.696509\pi$
$37$	2.53488	−	4.39054i	0.416732	−	0.721801i	0.995609	+	0.0936142i	$0.0298420\pi$
$38$	−1.39852	−	3.04276i	−0.226870	−	0.493601i
$39$	−3.14711	+	0.0434043i	−0.503941	+	0.00695025i
$40$	1.06525	+	7.04444i	0.168430	+	1.11382i
$41$	9.71647	+	0.462853i	1.51746	+	0.0722855i	0.789677	−	0.613523i	$-0.210248\pi$
$41$	9.71647	+	0.462853i	1.51746	+	0.0722855i	0.727782	+	0.685809i	$0.240551\pi$
$42$	1.29713	−	0.403834i	0.200152	−	0.0623129i
$43$	1.51606	−	2.35904i	0.231197	−	0.359750i	−0.706200	−	0.708013i	$-0.749592\pi$
$43$	1.51606	−	2.35904i	0.231197	−	0.359750i	0.937397	+	0.348263i	$0.113228\pi$
$44$	6.26207	+	3.98157i	0.944043	+	0.600244i
$45$	−5.36356	−	5.32315i	−0.799553	−	0.793528i
$46$	−3.91076	−	3.37211i	−0.576610	−	0.497190i
$47$	2.11981	−	1.66704i	0.309206	−	0.243162i	−0.451482	−	0.892280i	$-0.649104\pi$
$47$	2.11981	−	1.66704i	0.309206	−	0.243162i	0.760688	+	0.649118i	$0.224862\pi$
$48$	0.492175	+	6.91070i	0.0710393	+	0.997474i
$49$	0.318437	+	6.68481i	0.0454910	+	0.954974i
$50$	−0.711153	−	1.76395i	−0.100572	−	0.249461i
$51$	1.43562	+	4.65102i	0.201028	+	0.651274i
$52$	−3.23835	−	1.64964i	−0.449079	−	0.228764i
$53$	1.46092	+	2.27324i	0.200673	+	0.312253i	0.926975	−	0.375122i	$-0.122399\pi$
$53$	1.46092	+	2.27324i	0.200673	+	0.312253i	−0.726303	+	0.687375i	$0.758763\pi$
$54$	−4.79109	−	5.57185i	−0.651984	−	0.758233i
$55$	−8.83195	−	3.05677i	−1.19090	−	0.412174i
$56$	1.54248	+	0.285656i	0.206122	+	0.0381724i
$57$	2.26475	+	3.41940i	0.299973	+	0.452911i
$58$	−2.89671	+	0.565590i	−0.380357	+	0.0742657i
$59$	−5.90144	+	6.81062i	−0.768301	+	0.886667i	−0.996207	−	0.0870161i	$-0.972267\pi$
$59$	−5.90144	+	6.81062i	−0.768301	+	0.886667i	0.227905	+	0.973683i	$0.426812\pi$
$60$	−2.61399	−	8.32498i	−0.337464	−	1.07475i
$61$	12.4227	+	1.18622i	1.59056	+	0.151880i	0.852454	−	0.522801i	$-0.175113\pi$
$61$	12.4227	+	1.18622i	1.59056	+	0.151880i	0.738109	+	0.674682i	$0.235719\pi$
$62$	−4.45833	+	7.76552i	−0.566208	+	0.986222i
$63$	−1.49387	+	0.732671i	−0.188210	+	0.0923079i
$64$	−3.21700	+	7.32468i	−0.402125	+	0.915585i
$65$	4.44821	+	1.07912i	0.551733	+	0.133849i
$66$	−8.32727	−	3.64091i	−1.02502	−	0.448165i
$67$	−7.02019	+	4.20915i	−0.857652	+	0.514230i
$67$	−7.02019	+	4.20915i	−0.857652	+	0.514230i
$68$	−1.03690	+	5.52409i	−0.125742	+	0.669894i
$69$	5.36705	+	3.34552i	0.646117	+	0.402753i
$70$	−1.97324	+	0.0987974i	−0.235847	+	0.0118086i
$71$	−10.5094	−	5.41795i	−1.24723	−	0.642993i	−0.297101	−	0.954846i	$-0.596020\pi$
$71$	−10.5094	−	5.41795i	−1.24723	−	0.642993i	−0.950130	+	0.311853i	$0.899050\pi$
$72$	−1.89529	−	8.27090i	−0.223362	−	0.974735i
$73$	1.20612	+	0.115171i	0.141166	+	0.0134797i	0.165400	−	0.986227i	$-0.447109\pi$
$73$	1.20612	+	0.115171i	0.141166	+	0.0134797i	−0.0242337	+	0.999706i	$0.507715\pi$
$74$	−5.40711	+	4.70831i	−0.628564	+	0.547330i
$75$	1.19239	+	2.00103i	0.137685	+	0.231059i
$76$	0.473053	+	4.71219i	0.0542629	+	0.540525i
$77$	−1.27207	+	1.61757i	−0.144966	+	0.184339i
$78$	4.22936	+	1.38741i	0.478880	+	0.157093i
$79$	9.81221	+	3.39604i	1.10396	+	0.382084i	0.817454	−	0.575994i	$-0.195385\pi$
$79$	9.81221	+	3.39604i	1.10396	+	0.382084i	0.286506	+	0.958078i	$0.407506\pi$
$80$	1.81068	−	9.91157i	0.202440	−	1.10815i
$81$	6.84613	+	5.84213i	0.760681	+	0.649126i
$82$	−12.7837	−	5.08186i	−1.41172	−	0.561197i
$83$	−4.24506	−	5.96136i	−0.465956	−	0.654344i	0.513006	−	0.858385i	$-0.328532\pi$
$83$	−4.24506	−	5.96136i	−0.465956	−	0.654344i	−0.978962	+	0.204041i	$0.934592\pi$
$84$	−1.92046	−	0.0556220i	−0.209539	−	0.00606886i
$85$	−0.336824	−	7.07080i	−0.0365337	−	0.766936i
$86$	−3.11132	+	2.45901i	−0.335502	+	0.265162i
$87$	3.39929	−	1.22926i	0.364442	−	0.131790i
$88$	−6.54711	−	8.20172i	−0.697925	−	0.874306i
$89$	10.4511	+	1.50264i	1.10781	+	0.159279i	0.671851	−	0.740686i	$-0.265499\pi$
$89$	10.4511	+	1.50264i	1.10781	+	0.159279i	0.435961	+	0.899965i	$0.356408\pi$
$90$	4.72913	+	9.58346i	0.498494	+	1.01019i
$91$	0.544876	−	0.847844i	0.0571186	−	0.0888782i
$92$	3.68204	+	6.30658i	0.383879	+	0.657506i
$93$	3.93514	−	10.2364i	0.408055	−	1.06147i
$94$	−3.60103	+	1.25612i	−0.371417	+	0.129559i
$95$	−1.95083	−	5.63655i	−0.200151	−	0.578298i
$96$	2.51577	−	9.46947i	0.256764	−	0.966474i
$97$	2.46443	−	4.26851i	0.250225	−	0.433402i	−0.713363	−	0.700795i	$-0.752829\pi$
$97$	2.46443	−	4.26851i	0.250225	−	0.433402i	0.963588	+	0.267393i	$0.0861622\pi$
$98$	2.64440	−	9.08754i	0.267125	−	0.917980i
$99$	10.7626	+	2.84024i	1.08168	+	0.285454i
$100$	0.141022	+	2.68601i	0.0141022	+	0.268601i
$101$	−2.75260	+	0.667773i	−0.273894	+	0.0664459i	−0.370353	−	0.928891i	$-0.620763\pi$
$101$	−2.75260	+	0.667773i	−0.273894	+	0.0664459i	0.0964594	+	0.995337i	$0.469248\pi$
$102$	0.215990	−	6.88037i	0.0213862	−	0.681258i
$103$	−0.282492	+	1.46571i	−0.0278348	+	0.144421i	−0.993187	−	0.116528i	$-0.962823\pi$
$103$	−0.282492	+	1.46571i	−0.0278348	+	0.144421i	0.965353	+	0.260949i	$0.0840355\pi$
$104$	3.57379	+	3.69385i	0.350439	+	0.362212i
$105$	2.36947	−	0.490661i	0.231236	−	0.0478836i
$106$	−0.909962	−	3.71157i	−0.0883833	−	0.360500i
$107$	−1.89962	−	4.15960i	−0.183644	−	0.402124i	0.795311	−	0.606202i	$-0.207308\pi$
$107$	−1.89962	−	4.15960i	−0.183644	−	0.402124i	−0.978955	+	0.204078i	$0.934580\pi$
$108$	3.84918	+	9.65318i	0.370388	+	0.928877i
$109$	0.421620	+	0.486575i	0.0403839	+	0.0466055i	0.775582	−	0.631247i	$-0.217456\pi$
$109$	0.421620	+	0.486575i	0.0403839	+	0.0466055i	−0.735198	+	0.677852i	$0.762911\pi$
$110$	10.4092	+	8.14509i	0.992480	+	0.776604i
$111$	5.65833	−	6.71497i	0.537064	−	0.637357i
$112$	−1.93194	−	1.09054i	−0.182551	−	0.103046i
$113$	4.80201	+	3.41949i	0.451735	+	0.321679i	0.783179	−	0.621796i	$-0.213597\pi$
$113$	4.80201	+	3.41949i	0.451735	+	0.321679i	−0.331445	+	0.943475i	$0.607536\pi$
$114$	−1.45869	−	5.61382i	−0.136619	−	0.525782i
$115$	−6.34697	−	6.65651i	−0.591858	−	0.620723i
$116$	4.13428	+	0.573950i	0.383858	+	0.0532899i
$117$	−5.37937	−	0.883680i	−0.497323	−	0.0816962i
$118$	11.0216	−	6.39903i	1.01462	−	0.589079i
$119$	−1.49551	−	0.439120i	−0.137093	−	0.0402541i
$120$	−0.327314	+	12.3357i	−0.0298795	+	1.12609i
$121$	2.71662	−	0.523585i	0.246965	−	0.0475986i
$122$	−16.0712	−	7.29237i	−1.45501	−	0.660220i
$123$	16.4268	+	3.74601i	1.48115	+	0.337766i
$124$	9.52994	−	8.33908i	0.855814	−	0.748871i
$125$	2.59390	+	8.83400i	0.232005	+	0.790137i
$126$	2.33464	−	0.293854i	0.207986	−	0.0261786i
$127$	−7.80220	+	8.18271i	−0.692333	+	0.726098i	−0.972255	−	0.233924i	$-0.924843\pi$
$127$	−7.80220	+	8.18271i	−0.692333	+	0.726098i	0.279921	+	0.960023i	$0.409692\pi$
$128$	7.66712	−	8.31957i	0.677684	−	0.735353i
$129$	3.30293	−	3.56107i	0.290806	−	0.313535i
$130$	−5.45407	−	3.48644i	−0.478354	−	0.305781i
$131$	−1.76116	−	12.2491i	−0.153873	−	1.07021i	−0.909649	−	0.415379i	$-0.863649\pi$
$131$	−1.76116	−	12.2491i	−0.153873	−	1.07021i	0.755776	−	0.654831i	$-0.227260\pi$
$132$	9.46589	+	8.69461i	0.823900	+	0.756768i
$133$	−1.31331			−0.113878
$134$	11.3231	−	2.40560i	0.978169	−	0.207812i
$135$	−7.52559	−	10.7087i	−0.647699	−	0.921660i
$136$	3.92411	−	6.91251i	0.336490	−	0.592743i
$137$	−6.23893	+	0.897022i	−0.533028	+	0.0766378i	−0.403573	−	0.914948i	$-0.632232\pi$
$137$	−6.23893	+	0.897022i	−0.533028	+	0.0766378i	−0.129455	+	0.991585i	$0.541323\pi$
$138$	−5.64211	−	6.93989i	−0.480289	−	0.590762i
$139$	1.10489	+	0.504586i	0.0937154	+	0.0427984i	0.461721	−	0.887025i	$-0.347232\pi$
$139$	1.10489	+	0.504586i	0.0937154	+	0.0427984i	−0.368006	+	0.929824i	$0.619959\pi$
$140$	2.68468	+	0.774158i	0.226897	+	0.0654283i
$141$	4.12180	−	2.19741i	0.347118	−	0.185055i
$142$	11.5684	+	12.0737i	0.970795	+	1.01320i
$143$	−6.46916	+	1.89952i	−0.540978	+	0.158846i
$144$	−1.26377	+	11.9333i	−0.105314	+	0.994439i
$145$	−5.23305	+	0.499695i	−0.434581	+	0.0414974i
$146$	−1.56036	−	0.708019i	−0.129136	−	0.0585960i
$147$	−1.49127	+	11.4952i	−0.122998	+	0.948112i
$148$	9.39481	−	3.81413i	0.772249	−	0.313520i
$149$	3.17899	−	10.8266i	0.260433	−	0.886953i	−0.720639	−	0.693310i	$-0.756152\pi$
$149$	3.17899	−	10.8266i	0.260433	−	0.886953i	0.981072	−	0.193643i	$-0.0620303\pi$
$150$	−0.675809	−	3.22414i	−0.0551796	−	0.263250i
$151$	−4.30316	−	8.34696i	−0.350186	−	0.679266i	0.646295	−	0.763088i	$-0.276318\pi$
$151$	−4.30316	−	8.34696i	−0.350186	−	0.679266i	−0.996481	+	0.0838219i	$0.973287\pi$
$152$	1.53157	−	6.52007i	0.124227	−	0.528847i
$153$	1.03255	+	8.36737i	0.0834770	+	0.676462i
$154$	2.44440	−	1.57932i	0.196976	−	0.127265i
$155$	−9.25123	+	12.9915i	−0.743077	+	1.04351i
$156$	−5.01975	−	3.79827i	−0.401901	−	0.304105i
$157$	−20.0628	−	8.03193i	−1.60119	−	0.641018i	−0.612426	−	0.790528i	$-0.709806\pi$
$157$	−20.0628	−	8.03193i	−1.60119	−	0.641018i	−0.988760	+	0.149510i	$0.952230\pi$
$158$	−11.5645	−	9.04912i	−0.920026	−	0.719909i
$159$	1.79927	+	4.32069i	0.142691	+	0.342653i
$160$	−6.97425	+	12.4256i	−0.551363	+	0.982329i
$161$	−1.84213	+	0.841271i	−0.145180	+	0.0663014i
$162$	−6.47377	−	10.9586i	−0.508627	−	0.860987i
$163$	−19.1731	+	11.0696i	−1.50175	+	0.867036i	−0.501753	+	0.865011i	$0.667311\pi$
$163$	−19.1731	+	11.0696i	−1.50175	+	0.867036i	−0.999998	+	0.00202570i	$0.999355\pi$
$164$	14.7648	+	12.6688i	1.15293	+	0.989266i
$165$	−14.1292	−	7.89975i	−1.09996	−	0.614995i
$166$	2.93995	+	9.92338i	0.228184	+	0.770204i
$167$	−0.136417	−	0.562318i	−0.0105563	−	0.0435135i	0.966290	−	0.257457i	$-0.0828844\pi$
$167$	−0.136417	−	0.562318i	−0.0105563	−	0.0435135i	−0.976846	+	0.213943i	$0.931369\pi$
$168$	2.54317	+	0.956462i	0.196210	+	0.0737927i
$169$	−9.00326	+	3.60436i	−0.692558	+	0.277258i
$170$	−2.79709	+	9.61226i	−0.214527	+	0.737227i
$171$	2.82109	+	6.51963i	0.215734	+	0.498569i
$172$	5.29097	−	1.86003i	0.403433	−	0.141826i
$173$	−16.4853	+	5.70563i	−1.25336	+	0.433791i	−0.871484	−	0.490423i	$-0.836842\pi$
$173$	−16.4853	+	5.70563i	−1.25336	+	0.433791i	−0.381873	+	0.924215i	$0.624721\pi$
$174$	−5.11132	+	0.0829028i	−0.387488	+	0.00628485i
$175$	−0.745041	−	0.0354907i	−0.0563198	−	0.00268284i
$176$	4.99006	+	13.9773i	0.376140	+	1.05358i
$177$	−12.1351	+	9.81700i	−0.912131	+	0.737891i
$178$	−13.2887	−	6.81003i	−0.996031	−	0.510433i
$179$	1.70940	−	11.8891i	0.127767	−	0.888636i	−0.820610	−	0.571489i	$-0.806366\pi$
$179$	1.70940	−	11.8891i	0.127767	−	0.888636i	0.948376	−	0.317147i	$-0.102725\pi$
$180$	−1.92378	−	14.9905i	−0.143390	−	1.11732i
$181$	−17.2925	+	13.5990i	−1.28534	+	1.01081i	−0.286739	+	0.958009i	$0.592571\pi$
$181$	−17.2925	+	13.5990i	−1.28534	+	1.01081i	−0.998605	+	0.0527976i	$0.983186\pi$
$182$	−1.11821	+	0.883774i	−0.0828876	+	0.0655097i
$183$	20.8211	+	5.80296i	1.53914	+	0.428967i
$184$	−2.02831	−	10.1265i	−0.149529	−	0.746538i
$185$	−10.4023	+	7.40746i	−0.764794	+	0.544607i
$186$	−9.96504	+	11.8844i	−0.730672	+	0.871403i
$187$	5.63731	+	8.77183i	0.412241	+	0.641460i
$188$	5.39349	−	0.0261813i	0.393361	−	0.00190947i
$189$	−2.77016	+	0.794690i	−0.201500	+	0.0578052i
$190$	0.0204731	+	8.43519i	0.00148527	+	0.611953i
$191$	1.63644	+	1.28691i	0.118409	+	0.0931176i	0.675607	−	0.737262i	$-0.263881\pi$
$191$	1.63644	+	1.28691i	0.118409	+	0.0931176i	−0.557199	+	0.830379i	$0.688124\pi$
$192$	−7.71429	+	11.5104i	−0.556731	+	0.830693i
$193$	3.24327	−	3.74294i	0.233456	−	0.269422i	−0.626919	−	0.779085i	$-0.715684\pi$
$193$	3.24327	−	3.74294i	0.233456	−	0.269422i	0.860375	+	0.509662i	$0.170230\pi$
$194$	−5.25682	+	4.57745i	−0.377418	+	0.328642i
$195$	7.25630	+	3.19365i	0.519634	+	0.228702i
$196$	−7.71092	+	10.9405i	−0.550780	+	0.781463i
$197$	−2.36888	+	4.59499i	−0.168776	+	0.327379i	−0.958021	−	0.286699i	$-0.907442\pi$
$197$	−2.36888	+	4.59499i	−0.168776	+	0.327379i	0.789245	+	0.614079i	$0.210472\pi$
$198$	−13.0910	−	8.74219i	−0.930334	−	0.621281i
$199$	−7.15748	−	1.73639i	−0.507381	−	0.123089i	−0.0261062	−	0.999659i	$-0.508311\pi$
$199$	−7.15748	−	1.73639i	−0.507381	−	0.123089i	−0.481274	+	0.876570i	$0.659826\pi$
$200$	1.04506	−	3.65745i	0.0738968	−	0.258621i
$201$	−13.2511	+	5.04077i	−0.934658	+	0.355549i
$202$	3.98845	+	0.371085i	0.280626	+	0.0261094i
$203$	−0.272885	+	1.12485i	−0.0191528	+	0.0789488i
$204$	−3.44904	+	9.10364i	−0.241481	+	0.637382i
$205$	−21.7788	−	11.2277i	−1.52109	−	0.784179i
$206$	1.05105	−	1.83071i	0.0732299	−	0.127552i
$207$	8.13334	+	7.33771i	0.565306	+	0.510006i
$208$	−3.08354	−	6.58215i	−0.213805	−	0.456390i
$209$	6.63990	+	5.75351i	0.459292	+	0.397978i
$210$	−3.39465	−	0.432010i	−0.234253	−	0.0298115i
$211$	8.09823	−	10.2977i	0.557505	−	0.708926i	−0.422842	−	0.906203i	$-0.638968\pi$
$211$	8.09823	−	10.2977i	0.557505	−	0.708926i	0.980348	+	0.197278i	$0.0632100\pi$
$212$	−0.487600	+	5.38236i	−0.0334885	+	0.369662i
$213$	−16.2709	−	12.4363i	−1.11486	−	0.852120i
$214$	0.630347	+	6.43617i	0.0430897	+	0.439968i
$215$	−5.94218	+	3.81881i	−0.405254	+	0.260441i
$216$	−0.714784	−	14.6795i	−0.0486349	−	0.998817i
$217$	2.03697	+	2.86053i	0.138279	+	0.194185i
$218$	−0.340455	−	0.844469i	−0.0230585	−	0.0571947i
$219$	2.02153	+	0.563411i	0.136602	+	0.0380718i
$220$	−10.1818	−	15.6754i	−0.686459	−	1.05684i
$221$	−3.15677	−	4.01415i	−0.212347	−	0.270021i
$222$	−10.6525	+	6.38276i	−0.714948	+	0.428383i
$223$	19.6772	+	2.82915i	1.31768	+	0.189454i	0.765050	−	0.643971i	$-0.222714\pi$
$223$	19.6772	+	2.82915i	1.31768	+	0.189454i	0.552632	+	0.833425i	$0.313623\pi$
$224$	2.08319	+	2.34599i	0.139189	+	0.156748i
$225$	1.42422	+	3.77483i	0.0949482	+	0.251655i
$226$	−4.85236	−	6.77931i	−0.322774	−	0.450953i
$227$	1.27040	−	26.6690i	0.0843195	−	1.77009i	−0.420912	−	0.907101i	$-0.638290\pi$
$227$	1.27040	−	26.6690i	0.0843195	−	1.77009i	0.505232	−	0.862984i	$-0.331407\pi$
$228$	−0.627347	+	8.17875i	−0.0415471	+	0.541651i
$229$	−0.888025	−	2.56578i	−0.0586823	−	0.169551i	0.911849	−	0.410525i	$-0.134655\pi$
$229$	−0.888025	−	2.56578i	−0.0586823	−	0.169551i	−0.970532	+	0.240973i	$0.922533\pi$
$230$	5.43208	+	11.8186i	0.358180	+	0.779295i
$231$	−2.66125	+	2.37103i	−0.175098	+	0.156002i
$232$	−5.26619	−	2.66656i	−0.345742	−	0.175068i
$233$	−9.39412	−	23.4654i	−0.615429	−	1.53727i	−0.828357	−	0.560200i	$-0.810724\pi$
$233$	−9.39412	−	23.4654i	−0.615429	−	1.53727i	0.212928	−	0.977068i	$-0.431700\pi$
$234$	6.78932	+	3.65271i	0.443831	+	0.238785i
$235$	−6.60143	+	1.60149i	−0.430630	+	0.104470i
$236$	−17.6810	+	3.49683i	−1.15094	+	0.227625i
$237$	15.6975	+	8.77655i	1.01966	+	0.570098i
$238$	1.79863	+	1.27423i	0.116588	+	0.0825961i
$239$	8.24252	+	14.2765i	0.533165	+	0.923468i	0.999250	+	0.0387283i	$0.0123307\pi$
$239$	8.24252	+	14.2765i	0.533165	+	0.923468i	−0.466085	+	0.884740i	$0.654336\pi$
$240$	6.10357	−	16.3493i	0.393984	−	1.05534i
$241$	7.20366	+	15.7738i	0.464029	+	1.01608i	0.986551	+	0.163455i	$0.0522640\pi$
$241$	7.20366	+	15.7738i	0.464029	+	1.01608i	−0.522522	+	0.852626i	$0.675009\pi$
$242$	−3.87410	−	0.547417i	−0.249036	−	0.0351893i
$243$	9.89560	+	12.0448i	0.634803	+	0.772674i
$244$	18.1466	+	17.1354i	1.16172	+	1.09698i
$245$	6.26529	−	15.6499i	0.400275	−	0.999838i
$246$	−20.2512	−	12.5553i	−1.29117	−	0.800496i
$247$	−3.50505	−	2.49593i	−0.223021	−	0.158813i
$248$	−16.5769	+	6.77685i	−1.05264	+	0.430331i
$249$	−5.42421	−	11.4566i	−0.343745	−	0.726031i
$250$	0.587976	−	13.0073i	0.0371869	−	0.822654i
$251$	−19.2924	+	9.94590i	−1.21772	+	0.627780i	−0.942695	−	0.333656i	$-0.891717\pi$
$251$	−19.2924	+	9.94590i	−1.21772	+	0.627780i	−0.275028	+	0.961436i	$0.588687\pi$
$252$	−3.25767	−	0.679252i	−0.205214	−	0.0427888i
$253$	12.9991	+	3.81687i	0.817245	+	0.239965i
$254$	14.1942	−	7.36126i	0.890621	−	0.461887i
$255$	1.57738	−	12.1590i	0.0987791	−	0.761425i
$256$	−14.0763	+	7.60636i	−0.879771	+	0.475397i
$257$	0.414061	+	4.33624i	0.0258284	+	0.270487i	0.999156	+	0.0410689i	$0.0130763\pi$
$257$	0.414061	+	4.33624i	0.0258284	+	0.270487i	−0.973328	+	0.229418i	$0.926318\pi$
$258$	−6.05343	+	3.24609i	−0.376870	+	0.202092i
$259$	0.792176	+	2.69790i	0.0492234	+	0.167639i
$260$	5.69378	+	7.16835i	0.353113	+	0.444562i
$261$	6.17023	−	1.06159i	0.381928	−	0.0657105i
$262$	−3.27036	+	17.1927i	−0.202044	+	1.06217i
$263$	−11.2174	+	24.5627i	−0.691695	+	1.51460i	0.158063	+	0.987429i	$0.449475\pi$
$263$	−11.2174	+	24.5627i	−0.691695	+	1.51460i	−0.849759	+	0.527172i	$0.823252\pi$
$264$	−8.66770	−	15.9772i	−0.533460	−	0.983326i
$265$	−0.968677	−	6.73729i	−0.0595053	−	0.413869i
$266$	1.75662	+	0.603201i	0.107705	+	0.0369846i
$267$	17.3630	+	5.74251i	1.06260	+	0.351436i
$268$	−16.2501	−	1.98309i	−0.992636	−	0.121136i
$269$			23.0643i			1.40626i	0.711063	+	0.703129i	$0.248214\pi$
$269$			23.0643i			1.40626i	−0.711063	+	0.703129i	$0.751786\pi$
$270$	5.14736	+	17.7800i	0.313258	+	1.08205i
$271$	−30.4980	+	4.38495i	−1.85262	+	0.266367i	−0.976468	−	0.215664i	$-0.930808\pi$
$271$	−30.4980	+	4.38495i	−1.85262	+	0.266367i	−0.876154	+	0.482031i	$0.839899\pi$
$272$	−8.42361	+	7.44350i	−0.510756	+	0.451328i
$273$	1.18708	−	1.27986i	0.0718453	−	0.0774605i
$274$	8.75689	+	1.66572i	0.529023	+	0.100630i
$275$	3.61134	+	3.44340i	0.217772	+	0.207645i
$276$	4.35914	+	11.8739i	0.262389	+	0.714723i
$277$	22.8807	−	6.71837i	1.37477	−	0.403668i	0.490822	−	0.871260i	$-0.336697\pi$
$277$	22.8807	−	6.71837i	1.37477	−	0.403668i	0.883944	+	0.467592i	$0.154878\pi$
$278$	−1.24609	−	1.18238i	−0.0747355	−	0.0709146i
$279$	9.82487	−	16.2567i	0.588200	−	0.973266i
$280$	−3.23533	−	2.26855i	−0.193348	−	0.135572i
$281$	−1.97978	−	10.2721i	−0.118104	−	0.612781i	−0.991955	−	0.126588i	$-0.959597\pi$
$281$	−1.97978	−	10.2721i	−0.118104	−	0.612781i	0.873852	−	0.486193i	$-0.161615\pi$
$282$	−6.52239	+	1.04601i	−0.388403	+	0.0622888i
$283$	8.35232	−	28.4454i	0.496494	−	1.69090i	−0.205447	−	0.978668i	$-0.565865\pi$
$283$	8.35232	−	28.4454i	0.496494	−	1.69090i	0.701941	−	0.712235i	$-0.252317\pi$
$284$	−9.92782	−	21.4626i	−0.589108	−	1.27357i
$285$	−1.61113	−	10.2046i	−0.0954352	−	0.604467i
$286$	9.52528	+	0.430576i	0.563242	+	0.0254605i
$287$	−3.90460	+	3.72303i	−0.230481	+	0.219763i
$288$	7.17129	−	15.3809i	0.422572	−	0.906329i
$289$	5.27986	−	7.41453i	0.310580	−	0.436149i
$290$	7.22898	+	1.73516i	0.424500	+	0.101892i
$291$	5.50106	−	6.52834i	0.322478	−	0.382698i
$292$	1.76186	+	1.66368i	0.103105	+	0.0973596i
$293$	−13.0274	+	11.2883i	−0.761067	+	0.659469i	−0.946323	−	0.323222i	$-0.895234\pi$
$293$	−13.0274	+	11.2883i	−0.761067	+	0.659469i	0.185256	+	0.982690i	$0.440689\pi$
$294$	7.27440	−	14.6905i	0.424252	−	0.856770i
$295$	20.6483	−	9.42978i	1.20219	−	0.549023i
$296$	−14.3179	+	0.786571i	−0.832209	+	0.0457185i
$297$	17.4870	+	8.11804i	1.01470	+	0.471056i
$298$	−9.22473	+	13.0211i	−0.534374	+	0.754291i
$299$	−6.51523	−	1.25571i	−0.376785	−	0.0726194i
$300$	−0.576916	+	4.62286i	−0.0333083	+	0.266901i
$301$	0.366668	+	1.51143i	0.0211344	+	0.0871172i
$302$	1.92194	+	13.1409i	0.110596	+	0.756175i
$303$	−4.89669	+	0.300990i	−0.281307	+	0.0172914i
$304$	−5.04322	+	8.01748i	−0.289248	+	0.459834i
$305$	−27.2225	−	15.7169i	−1.55876	−	0.899949i
$306$	2.46203	−	11.6660i	0.140745	−	0.666903i
$307$	−21.9851	+	7.60913i	−1.25476	+	0.434276i	−0.871969	−	0.489561i	$-0.837157\pi$
$307$	−21.9851	+	7.60913i	−1.25476	+	0.434276i	−0.382788	+	0.923836i	$0.625036\pi$
$308$	−3.99490	+	0.989709i	−0.227630	+	0.0563939i
$309$	−0.927707	+	2.41323i	−0.0527754	+	0.137284i
$310$	18.3410	−	13.1278i	1.04170	−	0.745607i
$311$	−9.08343	−	5.83757i	−0.515074	−	0.331018i	0.257146	−	0.966372i	$-0.417218\pi$
$311$	−9.08343	−	5.83757i	−0.515074	−	0.331018i	−0.772221	+	0.635354i	$0.780854\pi$
$312$	4.96963	+	7.38595i	0.281350	+	0.418147i
$313$	−3.37788	+	23.4937i	−0.190929	+	1.32794i	0.638626	+	0.769518i	$0.279503\pi$
$313$	−3.37788	+	23.4937i	−0.190929	+	1.32794i	−0.829555	+	0.558425i	$0.811406\pi$
$314$	23.1460	+	19.9580i	1.30620	+	1.12629i
$315$	4.18951	−	0.115584i	0.236052	−	0.00651241i
$316$	11.3119	+	17.4152i	0.636345	+	0.979684i
$317$	16.1419	−	0.768935i	0.906622	−	0.0431877i	0.410911	−	0.911675i	$-0.365211\pi$
$317$	16.1419	−	0.768935i	0.906622	−	0.0431877i	0.495711	+	0.868488i	$0.334908\pi$
$318$	−0.422125	−	6.60554i	−0.0236716	−	0.370420i
$319$	6.30754	−	4.49158i	0.353154	−	0.251480i
$320$	15.0355	−	13.4166i	0.840509	−	0.750011i
$321$	−1.97327	−	7.67064i	−0.110137	−	0.428133i
$322$	2.85033	−	0.279157i	0.158843	−	0.0155568i
$323$	−2.17650	+	6.28857i	−0.121103	+	0.349906i
$324$	3.62574	+	17.6311i	0.201430	+	0.979503i
$325$	−1.92097	−	1.51067i	−0.106556	−	0.0837966i
$326$	30.7292	−	5.99996i	1.70193	−	0.332307i
$327$	0.570839	+	0.957966i	0.0315675	+	0.0529756i
$328$	−13.9299	−	23.7266i	−0.769149	−	1.31008i
$329$	−0.142174	+	1.48892i	−0.00783833	+	0.0820867i
$330$	15.2702	+	17.0559i	0.840599	+	0.938895i
$331$	4.81011	−	9.33032i	0.264388	−	0.512841i	−0.718851	−	0.695164i	$-0.755332\pi$
$331$	4.81011	−	9.33032i	0.264388	−	0.512841i	0.983239	+	0.182324i	$0.0583619\pi$
$332$	0.625466	−	14.6233i	0.0343269	−	0.802560i
$333$	11.6915	−	9.72789i	0.640689	−	0.533085i
$334$	−0.0758075	+	0.814786i	−0.00414800	+	0.0445831i
$335$	20.4896	−	2.29847i	1.11946	−	0.125579i
$336$	−2.96232	−	2.44739i	−0.161608	−	0.133516i
$337$	−4.36229	+	17.9816i	−0.237629	+	0.979520i	0.720562	+	0.693390i	$0.243884\pi$
$337$	−4.36229	+	17.9816i	−0.237629	+	0.979520i	−0.958191	+	0.286129i	$0.907631\pi$
$338$	13.6978	−	0.685832i	0.745062	−	0.0373043i
$339$	7.14737	+	7.29190i	0.388192	+	0.396041i
$340$	8.15615	−	11.5722i	0.442330	−	0.627590i
$341$	2.23312	−	23.3862i	0.120930	−	1.26644i
$342$	−0.778900	−	10.0161i	−0.0421181	−	0.541607i
$343$	−5.73923	−	4.97308i	−0.309890	−	0.268521i
$344$	−7.93125	+	0.0577508i	−0.427625	+	0.00311372i
$345$	−8.79666	−	13.2815i	−0.473596	−	0.715053i
$346$	24.6706	−	0.0598781i	1.32630	−	0.00321906i
$347$	7.76232	−	22.4277i	0.416703	−	1.20398i	−0.520094	−	0.854109i	$-0.674103\pi$
$347$	7.76232	−	22.4277i	0.416703	−	1.20398i	0.936796	−	0.349875i	$-0.113776\pi$
$348$	6.87473	+	2.23674i	0.368524	+	0.119902i
$349$	21.4470	−	13.7832i	1.14803	−	0.737795i	0.178786	−	0.983888i	$-0.442783\pi$
$349$	21.4470	−	13.7832i	1.14803	−	0.737795i	0.969246	+	0.246093i	$0.0791467\pi$
$350$	0.980230	+	0.389667i	0.0523955	+	0.0208286i
$351$	−8.90351	−	3.14375i	−0.475234	−	0.167801i
$352$	−0.254704	−	20.9873i	−0.0135758	−	1.11863i
$353$	−0.595472	+	0.0283658i	−0.0316938	+	0.00150976i	−0.0634228	−	0.997987i	$-0.520202\pi$
$353$	−0.595472	+	0.0283658i	−0.0316938	+	0.00150976i	0.0317290	+	0.999497i	$0.489899\pi$
$354$	20.7403	−	7.55710i	1.10233	−	0.401655i
$355$	18.4105	+	23.4109i	0.977129	+	1.24252i
$356$	14.6465	+	15.2123i	0.776262	+	0.806248i
$357$	−2.41637	−	1.20384i	−0.127888	−	0.0637141i
$358$	−7.74708	+	15.1172i	−0.409446	+	0.798970i
$359$	−14.8840	−	9.56537i	−0.785548	−	0.504841i	0.0853228	−	0.996353i	$-0.472808\pi$
$359$	−14.8840	−	9.56537i	−0.785548	−	0.504841i	−0.870871	+	0.491512i	$0.836444\pi$
$360$	−4.31195	+	20.9341i	−0.227260	+	1.10332i
$361$	0.637259	−	13.3777i	0.0335399	−	0.704090i
$362$	29.3757	−	10.2469i	1.54395	−	0.538567i
$363$	4.79146	−	0.0660828i	0.251486	−	0.00346845i
$364$	1.90159	−	0.668499i	0.0996702	−	0.0350389i
$365$	−2.64304	−	1.52596i	−0.138343	−	0.0798725i
$366$	−25.1840	−	17.3249i	−1.31639	−	0.905585i
$367$	−3.56422	−	8.90299i	−0.186051	−	0.464732i	0.805792	−	0.592198i	$-0.201740\pi$
$367$	−3.56422	−	8.90299i	−0.186051	−	0.464732i	−0.991843	+	0.127466i	$0.959316\pi$
$368$	−1.93813	+	14.4764i	−0.101032	+	0.754632i
$369$	26.8695	+	11.3862i	1.39877	+	0.592739i
$370$	17.3159	−	5.13008i	0.900210	−	0.266700i
$371$	−1.47162	−	0.283631i	−0.0764025	−	0.0147254i
$372$	18.7872	−	11.3190i	0.974072	−	0.586863i
$373$	−3.31657	−	5.74447i	−0.171726	−	0.297438i	0.767298	−	0.641291i	$-0.221601\pi$
$373$	−3.31657	−	5.74447i	−0.171726	−	0.297438i	−0.939023	+	0.343854i	$0.888268\pi$
$374$	−3.51130	−	14.3220i	−0.181565	−	0.740572i
$375$	1.73462	+	15.8523i	0.0895756	+	0.818608i
$376$	−7.22610	−	2.44221i	−0.372658	−	0.125947i
$377$	−2.86606	+	2.48345i	−0.147610	+	0.127904i
$378$	4.07024	+	0.209394i	0.209350	+	0.0107701i
$379$	−0.876611	+	2.18967i	−0.0450285	+	0.112476i	−0.949177	−	0.314742i	$-0.898082\pi$
$379$	−0.876611	+	2.18967i	−0.0450285	+	0.112476i	0.904149	+	0.427218i	$0.140506\pi$
$380$	3.84689	−	11.2919i	0.197341	−	0.579262i
$381$	−15.7937	+	11.5782i	−0.809134	+	0.593167i
$382$	−1.59775	−	2.47292i	−0.0817478	−	0.126526i
$383$	−18.1649	+	17.3202i	−0.928185	+	0.885022i	−0.993614	−	0.112835i	$-0.964007\pi$
$383$	−18.1649	+	17.3202i	−0.928185	+	0.885022i	0.0654289	+	0.997857i	$0.479158\pi$
$384$	15.6050	−	11.8526i	0.796338	−	0.604851i
$385$	4.60726	−	2.37521i	0.234808	−	0.121052i
$386$	−6.05717	+	3.51674i	−0.308302	+	0.178997i
$387$	6.71551	−	5.06691i	0.341369	−	0.257565i
$388$	9.13369	−	3.70812i	0.463693	−	0.188251i
$389$	1.07787	+	5.59253i	0.0546502	+	0.283552i	0.998965	−	0.0454920i	$-0.0144856\pi$
$389$	1.07787	+	5.59253i	0.0546502	+	0.283552i	−0.944314	+	0.329044i	$0.893273\pi$
$390$	−8.23884	−	7.60448i	−0.417190	−	0.385068i
$391$	0.975408	+	10.2149i	0.0493285	+	0.516592i
$392$	15.3387	−	11.0918i	0.774722	−	0.560223i
$393$	0.724531	−	21.4220i	0.0365478	−	1.08060i
$394$	5.27898	−	5.05801i	0.265951	−	0.254819i
$395$	−18.9289	−	18.0486i	−0.952415	−	0.908125i
$396$	13.4945	+	17.7058i	0.678127	+	0.889750i
$397$	−12.9107	+	28.2704i	−0.647968	+	1.41885i	0.245354	+	0.969434i	$0.421096\pi$
$397$	−12.9107	+	28.2704i	−0.647968	+	1.41885i	−0.893322	+	0.449418i	$0.851631\pi$
$398$	8.77598	+	5.60993i	0.439900	+	0.281200i
$399$	−2.23933	−	0.399650i	−0.112107	−	0.0200075i
$400$	−3.07768	+	4.41203i	−0.153884	+	0.220602i
$401$		−	21.4096i		−	1.06914i	−0.845123	−	0.534571i	$-0.820473\pi$
$401$		−	21.4096i		−	1.06914i	0.845123	−	0.534571i	$-0.179527\pi$
$402$	20.0392	−	0.656094i	0.999464	−	0.0327230i
$403$			11.5056i			0.573136i
$404$	−5.16432	−	2.32824i	−0.256935	−	0.115834i
$405$	−9.57320	−	20.5496i	−0.475696	−	1.02112i
$406$	0.881639	−	1.37921i	0.0437550	−	0.0684488i
$407$	7.81418	−	17.1107i	0.387335	−	0.848144i
$408$	8.79456	−	10.5924i	0.435396	−	0.524404i
$409$	28.0364	+	26.7326i	1.38631	+	1.32184i	0.891628	+	0.452768i	$0.149563\pi$
$409$	28.0364	+	26.7326i	1.38631	+	1.32184i	0.494680	+	0.869075i	$0.335285\pi$
$410$	23.9733	+	25.0206i	1.18396	+	1.23568i
$411$	−10.9110	−	0.369031i	−0.538201	−	0.0182030i
$412$	−2.24668	+	1.96593i	−0.110686	+	0.0968544i
$413$	−0.475100	−	4.97547i	−0.0233781	−	0.244827i
$414$	−7.50856	−	13.5502i	−0.369026	−	0.665956i
$415$	3.48870	+	18.1011i	0.171253	+	0.888547i
$416$	1.10122	+	10.2202i	0.0539920	+	0.501088i
$417$	1.73041	+	1.19660i	0.0847383	+	0.0585977i
$418$	−6.23863	−	10.7453i	−0.305141	−	0.525570i
$419$	11.8399	−	6.10389i	0.578417	−	0.298195i	−0.144083	−	0.989566i	$-0.546023\pi$
$419$	11.8399	−	6.10389i	0.578417	−	0.298195i	0.722500	+	0.691371i	$0.242993\pi$
$420$	4.34209	+	2.13699i	0.211872	+	0.104275i
$421$	−0.806541	+	0.769035i	−0.0393084	+	0.0374805i	−0.709479	−	0.704727i	$-0.751070\pi$
$421$	−0.806541	+	0.769035i	−0.0393084	+	0.0374805i	0.670170	+	0.742207i	$0.266221\pi$
$422$	−15.5615	+	10.0543i	−0.757524	+	0.489433i
$423$	7.69681	−	2.49252i	0.374232	−	0.121191i
$424$	3.12430	−	6.97523i	0.151730	−	0.338747i
$425$	−1.40467	+	3.50869i	−0.0681365	+	0.170197i
$426$	16.0512	+	24.1074i	0.777682	+	1.16801i
$427$	−5.23072	+	4.53244i	−0.253132	+	0.219340i
$428$	2.11301	−	8.89823i	0.102136	−	0.430112i
$429$	−11.6087	+	1.27027i	−0.560471	+	0.0613292i
$430$	9.70195	−	2.37862i	0.467870	−	0.114707i
$431$	−12.1487	−	21.0422i	−0.585182	−	1.01357i	−0.994853	−	0.101332i	$-0.967690\pi$
$431$	−12.1487	−	21.0422i	−0.585182	−	1.01357i	0.409670	−	0.912234i	$-0.365644\pi$
$432$	−5.78624	+	19.9630i	−0.278391	+	0.960468i
$433$	5.13435	+	0.989566i	0.246741	+	0.0475555i	0.311122	−	0.950370i	$-0.399295\pi$
$433$	5.13435	+	0.989566i	0.246741	+	0.0475555i	−0.0643809	+	0.997925i	$0.520507\pi$
$434$	−1.41072	−	4.76168i	−0.0677167	−	0.228568i
$435$	−9.07498	−	0.740420i	−0.435112	−	0.0355004i
$436$	0.0675122	+	1.28589i	0.00323325	+	0.0615830i
$437$	3.21348	+	8.02689i	0.153722	+	0.383978i
$438$	−2.44512	−	1.68208i	−0.116832	−	0.0803727i
$439$	35.1604	+	20.2999i	1.67811	+	0.968859i	0.962863	+	0.269990i	$0.0870206\pi$
$439$	35.1604	+	20.2999i	1.67811	+	0.968859i	0.715250	+	0.698869i	$0.246313\pi$
$440$	6.41903	+	25.6432i	0.306015	+	1.22249i
$441$	−6.04086	+	19.1468i	−0.287660	+	0.911754i
$442$	2.37864	+	6.81904i	0.113140	+	0.324349i
$443$	0.674702	−	14.1637i	0.0320561	−	0.672940i	−0.924463	−	0.381271i	$-0.875486\pi$
$443$	0.674702	−	14.1637i	0.0320561	−	0.672940i	0.956519	−	0.291669i	$-0.0942105\pi$
$444$	17.1798	−	3.64460i	0.815319	−	0.172965i
$445$	−22.3739	−	14.3789i	−1.06063	−	0.681623i
$446$	−25.0198	−	12.8218i	−1.18472	−	0.607132i
$447$	8.71515	−	17.4932i	0.412212	−	0.827401i
$448$	−1.70886	−	4.09469i	−0.0807362	−	0.193456i
$449$	12.0049	+	15.2655i	0.566546	+	0.720422i	0.981934	−	0.189222i	$-0.0605966\pi$
$449$	12.0049	+	15.2655i	0.566546	+	0.720422i	−0.415388	+	0.909644i	$0.636354\pi$
$450$	−0.171198	−	5.70317i	−0.00807033	−	0.268850i
$451$	36.0514	−	1.71734i	1.69759	−	0.0808664i
$452$	3.37656	+	11.2964i	0.158820	+	0.531336i
$453$	−4.79731	−	15.5420i	−0.225397	−	0.730225i
$454$	−13.9483	+	35.0877i	−0.654625	+	1.64675i
$455$	−2.13563	+	1.37249i	−0.100120	+	0.0643433i
$456$	4.59560	−	10.6514i	0.215209	−	0.498796i
$457$	2.26014	−	6.53025i	0.105725	−	0.305472i	−0.879714	−	0.475504i	$-0.842266\pi$
$457$	2.26014	−	6.53025i	0.105725	−	0.305472i	0.985439	+	0.170032i	$0.0543870\pi$
$458$	0.00931942	+	3.83973i	0.000435468	+	0.179419i
$459$	−0.785637	+	14.5815i	−0.0366704	+	0.680606i
$460$	−1.83742	−	18.3029i	−0.0856699	−	0.853378i
$461$	−19.5274	−	16.9206i	−0.909483	−	0.788071i	0.0683061	−	0.997664i	$-0.478241\pi$
$461$	−19.5274	−	16.9206i	−0.909483	−	0.788071i	−0.977789	+	0.209593i	$0.932786\pi$
$462$	4.64857	−	1.94906i	0.216271	−	0.0906785i
$463$	0.953270	−	9.98309i	0.0443022	−	0.463954i	−0.945915	−	0.324416i	$-0.894832\pi$
$463$	0.953270	−	9.98309i	0.0443022	−	0.463954i	0.990217	−	0.139538i	$-0.0445616\pi$
$464$	5.81906	+	5.98541i	0.270143	+	0.277866i
$465$	−19.7278	+	19.3368i	−0.914854	+	0.896721i
$466$	1.78750	+	35.7009i	0.0828043	+	1.65381i
$467$	−9.07646	+	37.4137i	−0.420009	+	1.73130i	0.231662	+	0.972796i	$0.425584\pi$
$467$	−9.07646	+	37.4137i	−0.420009	+	1.73130i	−0.651670	+	0.758502i	$0.725931\pi$
$468$	−7.40338	−	8.00401i	−0.342221	−	0.369986i
$469$	0.997307	−	4.42887i	0.0460513	−	0.204506i
$470$	9.56532	+	0.889955i	0.441215	+	0.0410506i
$471$	−31.7651	−	19.8006i	−1.46366	−	0.912363i
$472$	25.2554	+	3.44367i	1.16247	+	0.158508i
$473$	4.76763	−	9.24790i	0.219216	−	0.425219i
$474$	−16.9651	−	18.9489i	−0.779233	−	0.870352i
$475$	−0.302709	+	3.17011i	−0.0138892	+	0.145455i
$476$	−1.82051	−	2.53046i	−0.0834428	−	0.115983i
$477$	1.75313	+	7.91477i	0.0802702	+	0.362392i
$478$	−4.46763	−	22.8813i	−0.204345	−	1.04657i
$479$	13.2279	+	10.4025i	0.604398	+	0.475304i	0.872849	−	0.487990i	$-0.162270\pi$
$479$	13.2279	+	10.4025i	0.604398	+	0.475304i	−0.268452	+	0.963293i	$0.586512\pi$
$480$	−15.6731	+	19.0647i	−0.715374	+	0.870179i
$481$	−3.01313	+	8.70587i	−0.137387	+	0.396954i
$482$	−2.39037	−	24.4069i	−0.108878	−	1.11171i
$483$	−3.39703	+	0.873886i	−0.154570	+	0.0397632i
$484$	4.93038	+	2.51157i	0.224108	+	0.114162i
$485$	−10.1132	+	7.20158i	−0.459217	+	0.327007i
$486$	−7.70371	−	20.6556i	−0.349447	−	0.936956i
$487$	14.5554	−	0.693359i	0.659568	−	0.0314191i	0.284870	−	0.958566i	$-0.408050\pi$
$487$	14.5554	−	0.693359i	0.659568	−	0.0314191i	0.374698	+	0.927147i	$0.377747\pi$
$488$	−16.4018	−	31.2542i	−0.742475	−	1.41481i
$489$	−36.0607	+	13.0403i	−1.63072	+	0.589704i
$490$	−15.5681	+	18.0550i	−0.703297	+	0.815640i
$491$	−2.42887	+	16.8931i	−0.109613	+	0.762377i	0.858671	+	0.512527i	$0.171290\pi$
$491$	−2.42887	+	16.8931i	−0.109613	+	0.762377i	−0.968285	+	0.249850i	$0.919619\pi$
$492$	21.3203	+	26.0947i	0.961195	+	1.17644i
$493$	4.93391	+	3.17083i	0.222212	+	0.142807i
$494$	3.54181	+	4.94831i	0.159353	+	0.222635i
$495$	−21.6879	−	17.7696i	−0.974801	−	0.798683i
$496$	25.2851	−	1.45063i	1.13533	−	0.0651354i
$497$	6.19703	−	2.14481i	0.277975	−	0.0962081i
$498$	1.99317	+	17.8151i	0.0893162	+	0.798313i
$499$	10.4812	+	6.05131i	0.469202	+	0.270894i	0.715905	−	0.698197i	$-0.246014\pi$
$499$	10.4812	+	6.05131i	0.469202	+	0.270894i	−0.246704	+	0.969091i	$0.579347\pi$
$500$	−6.76069	+	17.1279i	−0.302347	+	0.765982i
$501$	−0.0614881	−	1.00033i	−0.00274709	−	0.0446913i
$502$	30.3727	−	4.44220i	1.35560	−	0.198265i
$503$	−3.13173	−	12.9092i	−0.139637	−	0.575591i	−0.998038	−	0.0626119i	$-0.980057\pi$
$503$	−3.13173	−	12.9092i	−0.139637	−	0.575591i	0.858401	−	0.512979i	$-0.171458\pi$
$504$	4.04532	+	2.40478i	0.180193	+	0.107117i
$505$	7.00570	+	1.35024i	0.311750	+	0.0600848i
$506$	−15.6338	−	11.0757i	−0.695009	−	0.492376i
$507$	−16.4484	+	3.40607i	−0.730498	+	0.151269i
$508$	−22.3664	+	3.32670i	−0.992350	+	0.147599i
$509$	0.185601	−	0.0847611i	0.00822661	−	0.00375697i	−0.411297	−	0.911501i	$-0.634924\pi$
$509$	0.185601	−	0.0847611i	0.00822661	−	0.00375697i	0.419524	+	0.907744i	$0.362197\pi$
$510$	−7.69443	+	15.5388i	−0.340715	+	0.688069i
$511$	−0.507852	+	0.440057i	−0.0224661	+	0.0194670i
$512$	22.3214	−	3.70865i	0.986477	−	0.163901i
$513$	2.82630	+	11.9752i	0.124784	+	0.528716i
$514$	1.43780	−	5.99012i	0.0634187	−	0.264213i
$515$	2.18097	−	3.06274i	0.0961050	−	0.134961i
$516$	9.58770	−	1.56147i	0.422075	−	0.0687401i
$517$	7.24165	−	6.90490i	0.318488	−	0.303677i
$518$	0.179568	−	3.97243i	0.00788976	−	0.174539i
$519$	−29.8456	+	4.71211i	−1.31008	+	0.206839i
$520$	−4.32331	−	12.2032i	−0.189590	−	0.535145i
$521$	−2.04147	+	6.95260i	−0.0894383	+	0.304599i	−0.992048	−	0.125861i	$-0.959831\pi$
$521$	−2.04147	+	6.95260i	−0.0894383	+	0.304599i	0.902610	+	0.430460i	$0.141649\pi$
$522$	−8.74059	−	1.41405i	−0.382565	−	0.0618915i
$523$	−5.46649	−	28.3629i	−0.239033	−	1.24022i	−0.880862	−	0.473373i	$-0.843036\pi$
$523$	−5.46649	−	28.3629i	−0.239033	−	1.24022i	0.641829	−	0.766848i	$-0.278176\pi$
$524$	12.2709	−	21.4941i	0.536056	−	0.938972i
$525$	−1.25958	−	0.287237i	−0.0549724	−	0.0125360i
$526$	26.2855	−	27.7017i	1.14610	−	1.20785i
$527$	17.0730	−	5.01308i	0.743711	−	0.218373i
$528$	4.25520	+	25.3513i	0.185184	+	1.10328i
$529$	−6.99664	−	6.67129i	−0.304202	−	0.290056i
$530$	−1.79878	+	9.45639i	−0.0781339	+	0.410759i
$531$	−23.6791	+	13.0462i	−1.02758	+	0.566159i
$532$	−2.07252	−	1.61363i	−0.0898551	−	0.0699596i
$533$	−17.4965	+	2.51561i	−0.757856	+	0.108963i
$534$	−20.5864	−	15.6557i	−0.890859	−	0.677488i
$535$			11.5185i			0.497989i
$536$	20.8246	+	10.1162i	0.899485	+	0.436952i
$537$	6.53267	−	19.7521i	0.281905	−	0.852366i
$538$	10.5934	−	30.8497i	0.456715	−	1.33003i
$539$	3.53383	+	24.5783i	0.152213	+	1.05866i
$540$	1.28146	−	26.1458i	0.0551451	−	1.12514i
$541$	10.5275	−	23.0520i	0.452612	−	0.991082i	−0.536498	−	0.843902i	$-0.680253\pi$
$541$	10.5275	−	23.0520i	0.452612	−	0.991082i	0.989110	−	0.147180i	$-0.0470197\pi$
$542$	42.8067	+	8.14260i	1.83870	+	0.349755i
$543$	−33.6240	+	17.9255i	−1.44294	+	0.769259i
$544$	14.6858	−	6.08711i	0.629649	−	0.260983i
$545$	−0.456899	−	1.55605i	−0.0195714	−	0.0666540i
$546$	−2.17562	+	1.16665i	−0.0931078	+	0.0499280i
$547$	−2.94362	−	30.8270i	−0.125860	−	1.31807i	−0.809012	−	0.587792i	$-0.799997\pi$
$547$	−2.94362	−	30.8270i	−0.125860	−	1.31807i	0.683152	−	0.730276i	$-0.260609\pi$
$548$	−10.9477	−	6.25002i	−0.467664	−	0.266987i
$549$	33.7363	+	16.2307i	1.43983	+	0.692709i
$550$	−3.24880	−	6.26442i	−0.138529	−	0.267116i
$551$	4.74162	+	1.39226i	0.202000	+	0.0593125i
$552$	−0.376913	−	17.8841i	−0.0160425	−	0.761196i
$553$	−5.11862	+	2.63883i	−0.217666	+	0.112215i
$554$	−33.6898	−	1.52290i	−1.43134	−	0.0647018i
$555$	−19.9912	+	9.46502i	−0.848581	+	0.401768i
$556$	1.12364	+	2.15383i	0.0476530	+	0.0913426i
$557$	10.9259	+	7.78033i	0.462947	+	0.329663i	0.787618	−	0.616164i	$-0.211314\pi$
$557$	10.9259	+	7.78033i	0.462947	+	0.329663i	−0.324671	+	0.945827i	$0.605254\pi$
$558$	−20.6080	+	17.2317i	−0.872405	+	0.729475i
$559$	−1.89387	+	4.73065i	−0.0801020	+	0.200085i
$560$	3.28548	+	4.52028i	0.138837	+	0.191017i
$561$	6.94290	+	16.6724i	0.293129	+	0.703909i
$562$	−2.06990	+	14.6488i	−0.0873133	+	0.617920i
$563$	4.86319	+	10.6489i	0.204959	+	0.448798i	0.983998	−	0.178177i	$-0.0570200\pi$
$563$	4.86319	+	10.6489i	0.204959	+	0.448798i	−0.779039	+	0.626975i	$0.784293\pi$
$564$	9.20446	+	1.59664i	0.387578	+	0.0672306i
$565$	−7.42458	−	12.8598i	−0.312355	−	0.541014i
$566$	−24.2366	+	34.2110i	−1.01874	+	1.43799i
$567$	−4.96526	+	0.512052i	−0.208521	+	0.0215042i
$568$	3.42124	+	33.2671i	0.143552	+	1.39586i
$569$	−23.2113	+	5.63100i	−0.973069	+	0.236064i	−0.690620	−	0.723218i	$-0.742662\pi$
$569$	−23.2113	+	5.63100i	−0.973069	+	0.236064i	−0.282449	+	0.959282i	$0.591147\pi$
$570$	−2.53198	+	14.3891i	−0.106053	+	0.602695i
$571$	−8.02717	−	20.0509i	−0.335927	−	0.839104i	−0.996120	−	0.0880082i	$-0.971950\pi$
$571$	−8.02717	−	20.0509i	−0.335927	−	0.839104i	0.660193	−	0.751096i	$-0.270474\pi$
$572$	−12.5428	−	4.95087i	−0.524440	−	0.207006i
$573$	2.39869	+	2.69230i	0.100207	+	0.112473i
$574$	6.93259	−	3.18636i	0.289361	−	0.132996i
$575$	1.60609	+	4.64050i	0.0669787	+	0.193522i
$576$	−16.6564	+	17.2790i	−0.694017	+	0.719959i
$577$	−1.17516	+	24.6696i	−0.0489224	+	1.02701i	0.832306	+	0.554316i	$0.187020\pi$
$577$	−1.17516	+	24.6696i	−0.0489224	+	1.02701i	−0.881228	+	0.472691i	$0.843283\pi$
$578$	−10.4676	+	7.49228i	−0.435394	+	0.311638i
$579$	6.66914	−	5.39516i	0.277160	−	0.224215i
$580$	−8.87217	−	5.64113i	−0.368397	−	0.234235i
$581$	4.01760	+	0.577644i	0.166678	+	0.0239647i
$582$	−10.3564	+	6.20536i	−0.429287	+	0.257220i
$583$	6.19771	+	7.88103i	0.256683	+	0.326399i
$584$	−1.59246	−	3.03448i	−0.0658963	−	0.125568i
$585$	11.4009	+	7.65367i	0.471371	+	0.316440i
$586$	22.6095	−	9.11521i	0.933989	−	0.376546i
$587$	−19.6378	−	27.5774i	−0.810539	−	1.13824i	−0.988051	−	0.154124i	$-0.950744\pi$
$587$	−19.6378	−	27.5774i	−0.810539	−	1.13824i	0.177512	−	0.984119i	$-0.443195\pi$
$588$	−16.4772	+	16.3082i	−0.679510	+	0.672540i
$589$	12.6129	−	8.10582i	0.519706	−	0.333994i
$590$	−31.9493	+	3.12906i	−1.31533	+	0.128821i
$591$	−5.43749	+	7.11409i	−0.223669	+	0.292635i
$592$	19.5122	+	5.52410i	0.801945	+	0.227039i
$593$	13.7094	−	17.4330i	0.562979	−	0.715886i	−0.418337	−	0.908292i	$-0.637387\pi$
$593$	13.7094	−	17.4330i	0.562979	−	0.715886i	0.981315	+	0.192406i	$0.0616291\pi$
$594$	−19.6612	−	18.8901i	−0.806708	−	0.775069i
$595$	2.96712	+	2.57102i	0.121640	+	0.105402i
$596$	18.3191	−	13.1795i	0.750380	−	0.539852i
$597$	−11.6759	−	5.13880i	−0.477863	−	0.210317i
$598$	8.13771	+	4.67201i	0.332776	+	0.191053i
$599$	17.2989	+	8.91821i	0.706814	+	0.364388i	0.773856	−	0.633362i	$-0.218326\pi$
$599$	17.2989	+	8.91821i	0.706814	+	0.364388i	−0.0670413	+	0.997750i	$0.521356\pi$
$600$	2.89493	−	5.91833i	0.118185	−	0.241615i
$601$	−5.51286	+	22.7243i	−0.224874	+	0.926944i	0.741736	+	0.670692i	$0.234003\pi$
$601$	−5.51286	+	22.7243i	−0.224874	+	0.926944i	−0.966610	+	0.256252i	$0.917512\pi$
$602$	0.203759	−	2.19002i	0.00830460	−	0.0892586i
$603$	−24.1284	+	4.56267i	−0.982586	+	0.185806i
$604$	3.46491	−	18.4594i	0.140985	−	0.751103i
$605$	−6.77238	−	1.64296i	−0.275336	−	0.0667959i
$606$	6.68782	+	1.84645i	0.271674	+	0.0750071i
$607$	−3.37870	+	6.55377i	−0.137137	+	0.266009i	−0.947396	−	0.320063i	$-0.896296\pi$
$607$	−3.37870	+	6.55377i	−0.137137	+	0.266009i	0.810259	+	0.586072i	$0.199326\pi$
$608$	10.4280	−	8.40745i	0.422911	−	0.340967i
$609$	−0.807598	+	1.83495i	−0.0327255	+	0.0743558i
$610$	29.1928	+	33.5255i	1.18198	+	1.35741i
$611$	−3.20913	+	3.70353i	−0.129827	+	0.149829i
$612$	−8.65130	+	14.4731i	−0.349708	+	0.585042i
$613$	−26.4995	−	20.8394i	−1.07030	−	0.841697i	−0.0823751	−	0.996601i	$-0.526251\pi$
$613$	−26.4995	−	20.8394i	−1.07030	−	0.841697i	−0.987929	+	0.154905i	$0.950493\pi$
$614$	32.9011	−	0.0798544i	1.32778	−	0.00322266i
$615$	−33.7185	−	25.7719i	−1.35966	−	1.03923i
$616$	5.79795	+	0.511065i	0.233606	+	0.0205914i
$617$	−0.996095	−	1.54995i	−0.0401013	−	0.0623988i	0.820624	−	0.571468i	$-0.193626\pi$
$617$	−0.996095	−	1.54995i	−0.0401013	−	0.0623988i	−0.860725	+	0.509069i	$0.829990\pi$
$618$	2.34925	−	2.80173i	0.0945007	−	0.112702i
$619$	39.0111	−	27.7797i	1.56799	−	1.11656i	0.626544	−	0.779386i	$-0.284469\pi$
$619$	39.0111	−	27.7797i	1.56799	−	1.11656i	0.941443	−	0.337173i	$-0.109471\pi$
$620$	−30.5616	+	9.13507i	−1.22738	+	0.366873i
$621$	11.6353	+	14.9866i	0.466909	+	0.601393i
$622$	9.46837	+	11.9801i	0.379647	+	0.480357i
$623$	−4.60313	+	3.61994i	−0.184420	+	0.145030i
$624$	−3.25478	−	12.1616i	−0.130296	−	0.486855i
$625$	4.25744	−	29.6111i	0.170298	−	1.18445i
$626$	15.3087	−	29.8726i	0.611860	−	1.19395i
$627$	9.57092	+	11.8309i	0.382226	+	0.472482i
$628$	−21.7923	−	37.3257i	−0.869606	−	1.48946i
$629$	14.2313	+	0.677922i	0.567440	+	0.0270305i
$630$	−5.65678	−	1.76964i	−0.225371	−	0.0705041i
$631$	17.4807	−	6.05014i	0.695897	−	0.240852i	0.0438581	−	0.999038i	$-0.486035\pi$
$631$	17.4807	−	6.05014i	0.695897	−	0.240852i	0.652039	+	0.758185i	$0.273914\pi$
$632$	−7.13148	−	28.4893i	−0.283675	−	1.13325i
$633$	16.9421	−	15.0944i	0.673386	−	0.599949i
$634$	−21.9439	−	6.38549i	−0.871502	−	0.253600i
$635$	26.4393	−	10.5847i	1.04921	−	0.420040i
$636$	−2.46930	+	9.02913i	−0.0979143	+	0.358028i
$637$	−2.86710	−	11.8183i	−0.113598	−	0.468259i
$638$	−10.4996	+	3.11067i	−0.415684	+	0.123153i
$639$	−23.9592	−	26.1566i	−0.947811	−	1.03474i
$640$	−26.2730	+	11.0396i	−1.03853	+	0.436379i
$641$	15.0548	−	8.69192i	0.594631	−	0.343310i	−0.172296	−	0.985045i	$-0.555118\pi$
$641$	15.0548	−	8.69192i	0.594631	−	0.343310i	0.766926	+	0.641735i	$0.221785\pi$
$642$	−0.883764	+	11.1662i	−0.0348794	+	0.440695i
$643$	−38.4950	+	17.5801i	−1.51809	+	0.693291i	−0.987972	−	0.154631i	$-0.950581\pi$
$643$	−38.4950	+	17.5801i	−1.51809	+	0.693291i	−0.530122	+	0.847921i	$0.677854\pi$
$644$	−3.94069	−	0.935769i	−0.155285	−	0.0368745i
$645$	−11.2942	+	4.70324i	−0.444707	+	0.185190i
$646$	5.79951	−	7.41163i	0.228179	−	0.291607i
$647$	−35.1102	−	14.0560i	−1.38032	−	0.552599i	−0.441583	−	0.897220i	$-0.645583\pi$
$647$	−35.1102	−	14.0560i	−1.38032	−	0.552599i	−0.938742	+	0.344622i	$0.888007\pi$
$648$	3.24831	−	25.2477i	0.127606	−	0.991825i
$649$	−19.3951	+	27.2367i	−0.761326	+	1.06913i
$650$	1.87555	+	2.90289i	0.0735650	+	0.113861i
$651$	2.60278	+	5.49738i	0.102011	+	0.215459i
$652$	−43.8577	−	6.08864i	−1.71760	−	0.238450i
$653$	2.00068	+	3.88078i	0.0782927	+	0.151867i	0.924732	−	0.380618i	$-0.124289\pi$
$653$	2.00068	+	3.88078i	0.0782927	+	0.151867i	−0.846440	+	0.532485i	$0.821258\pi$
$654$	−0.323534	−	1.54351i	−0.0126512	−	0.0603562i
$655$	−8.78204	+	29.9089i	−0.343143	+	1.16864i
$656$	7.73433	+	38.1335i	0.301975	+	1.48886i
$657$	3.27547	+	1.57584i	0.127788	+	0.0614795i
$658$	0.874024	−	1.92620i	0.0340730	−	0.0750913i
$659$	12.3279	−	1.17717i	0.480226	−	0.0458560i	0.147863	−	0.989008i	$-0.452760\pi$
$659$	12.3279	−	1.17717i	0.480226	−	0.0458560i	0.332362	+	0.943152i	$0.392154\pi$
$660$	−12.5910	−	29.8267i	−0.490104	−	1.16100i
$661$	1.32013	−	0.387624i	0.0513470	−	0.0150768i	−0.255958	−	0.966688i	$-0.582391\pi$
$661$	1.32013	−	0.387624i	0.0513470	−	0.0150768i	0.307305	+	0.951611i	$0.400573\pi$
$662$	−10.7192	+	10.2705i	−0.416613	+	0.399174i
$663$	−4.16109	−	7.80520i	−0.161603	−	0.303129i
$664$	−7.55308	+	19.2722i	−0.293116	+	0.747907i
$665$	3.00915	+	1.37423i	0.116690	+	0.0532904i
$666$	−20.1060	+	7.64168i	−0.779090	+	0.296109i
$667$	7.54273	−	1.08448i	0.292056	−	0.0419913i
$668$	0.475627	−	1.05500i	0.0184026	−	0.0408192i
$669$	32.6908	+	10.8119i	1.26390	+	0.418013i
$670$	−28.4615	−	6.33651i	−1.09957	−	0.244801i
$671$	46.3021			1.78747
$672$	2.83817	+	4.63410i	0.109485	+	0.178764i
$673$	−0.721875	−	5.02075i	−0.0278262	−	0.193536i	0.971167	−	0.238401i	$-0.0766232\pi$
$673$	−0.721875	−	5.02075i	−0.0278262	−	0.193536i	−0.998993	+	0.0448653i	$0.985714\pi$
$674$	14.0937	−	22.0477i	0.542869	−	0.849246i
$675$	1.27975	+	6.86989i	0.0492575	+	0.264422i
$676$	−18.6365	−	5.37405i	−0.716789	−	0.206694i
$677$	11.5172	−	12.0789i	0.442642	−	0.464230i	−0.464181	−	0.885740i	$-0.653651\pi$
$677$	11.5172	−	12.0789i	0.442642	−	0.464230i	0.906824	+	0.421510i	$0.138500\pi$
$678$	−6.21081	−	13.0361i	−0.238525	−	0.500647i
$679$	0.770158	+	2.62292i	0.0295559	+	0.100658i
$680$	−16.2244	+	11.7323i	−0.622176	+	0.449913i
$681$	10.2818	−	45.0870i	0.393998	−	1.72774i
$682$	−13.7282	+	30.2546i	−0.525679	+	1.15851i
$683$	4.90398	−	0.945165i	0.187646	−	0.0361657i	−0.0945625	−	0.995519i	$-0.530145\pi$
$683$	4.90398	−	0.945165i	0.187646	−	0.0361657i	0.282208	+	0.959353i	$0.408933\pi$
$684$	−3.55855	+	13.7548i	−0.136065	+	0.525926i
$685$	15.2337	+	4.47302i	0.582050	+	0.170905i
$686$	5.39240	+	9.28777i	0.205883	+	0.354609i
$687$	−0.733394	−	4.64517i	−0.0279807	−	0.177224i
$688$	10.6350	+	3.56557i	0.405455	+	0.135936i
$689$	−3.38851	−	3.55377i	−0.129092	−	0.135388i
$690$	5.66580	+	21.8050i	0.215693	+	0.830102i
$691$	36.9599	+	26.3190i	1.40602	+	1.00122i	0.996019	+	0.0891386i	$0.0284114\pi$
$691$	36.9599	+	26.3190i	1.40602	+	1.00122i	0.410002	+	0.912085i	$0.365528\pi$
$692$	−33.0257	−	11.2511i	−1.25545	−	0.427702i
$693$	−5.25925	+	3.23302i	−0.199782	+	0.122812i
$694$	−20.6835	+	26.4330i	−0.785136	+	1.00338i
$695$	−2.00361	−	2.31229i	−0.0760011	−	0.0877100i
$696$	−8.16798	−	6.14931i	−0.309606	−	0.233089i
$697$	11.3562	+	24.8666i	0.430147	+	0.941890i
$698$	−35.0171	+	8.58510i	−1.32542	+	0.324951i
$699$	−8.87731	−	42.8697i	−0.335771	−	1.62148i
$700$	−1.13213	−	0.971418i	−0.0427907	−	0.0367162i
$701$	−7.77199	+	40.3249i	−0.293544	+	1.52305i	0.473117	+	0.881000i	$0.343129\pi$
$701$	−7.77199	+	40.3249i	−0.293544	+	1.52305i	−0.766661	+	0.642052i	$0.778083\pi$
$702$	10.4650	+	8.29430i	0.394975	+	0.313048i
$703$	11.6665	−	2.83026i	0.440010	−	0.106745i
$704$	−9.29876	+	28.1886i	−0.350460	+	1.06240i
$705$	−11.7435	+	0.721851i	−0.442286	+	0.0271865i
$706$	0.809503	+	0.235559i	0.0304660	+	0.00886538i
$707$	0.785466	−	1.36047i	0.0295405	−	0.0511656i
$708$	−31.2122	+	0.582022i	−1.17302	+	0.0218737i
$709$	−14.2607	−	41.2035i	−0.535571	−	1.54743i	−0.810364	−	0.585927i	$-0.800730\pi$
$709$	−14.2607	−	41.2035i	−0.535571	−	1.54743i	0.274793	−	0.961504i	$-0.411391\pi$
$710$	−13.8724	−	39.7692i	−0.520623	−	1.49251i
$711$	24.0951	+	19.7418i	0.903637	+	0.740376i
$712$	−12.6035	−	27.0743i	−0.472335	−	1.01465i
$713$	12.4992	−	19.4492i	0.468100	−	0.728379i
$714$	2.67910	+	2.72004i	0.100263	+	0.101795i
$715$	16.8102	+	2.41695i	0.628667	+	0.0903887i
$716$	17.3054	−	16.6618i	0.646735	−	0.622682i
$717$	9.70997	+	26.8512i	0.362625	+	1.00278i
$718$	15.5148	+	19.6304i	0.579006	+	0.732599i
$719$	1.75669	+	36.8774i	0.0655134	+	1.37530i	0.757240	+	0.653137i	$0.226547\pi$
$719$	1.75669	+	36.8774i	0.0655134	+	1.37530i	−0.691727	+	0.722160i	$0.743150\pi$
$720$	15.3825	−	26.0200i	0.573271	−	0.969707i
$721$	−0.480215	−	0.674367i	−0.0178841	−	0.0251147i
$722$	−6.99673	+	17.6007i	−0.260391	+	0.655029i
$723$	7.48294	+	29.0882i	0.278294	+	1.08180i
$724$	−43.9979	+	0.213576i	−1.63517	+	0.00793749i
$725$	2.65230	+	0.917970i	0.0985039	+	0.0340925i
$726$	−6.43917	−	2.11232i	−0.238980	−	0.0783956i
$727$	−5.35008	+	6.80318i	−0.198424	+	0.252316i	−0.875075	−	0.483987i	$-0.839188\pi$
$727$	−5.35008	+	6.80318i	−0.198424	+	0.252316i	0.676651	+	0.736304i	$0.263430\pi$
$728$	−2.85051	+	0.0207558i	−0.105647	+	0.000769260i
$729$	13.2077	+	23.5490i	0.489176	+	0.872185i
$730$	2.83434	+	3.25500i	0.104903	+	0.120473i
$731$	7.84489	+	0.749097i	0.290154	+	0.0277063i
$732$	25.7276	+	34.7399i	0.950918	+	1.28402i
$733$	−9.25419	−	4.77087i	−0.341811	−	0.176216i	0.278770	−	0.960358i	$-0.410073\pi$
$733$	−9.25419	−	4.77087i	−0.341811	−	0.176216i	−0.620582	+	0.784142i	$0.713103\pi$
$734$	0.678194	+	13.5453i	0.0250326	+	0.499965i
$735$	15.4454	−	24.7783i	0.569712	−	0.913960i
$736$	9.24133	−	18.4727i	0.340640	−	0.680912i
$737$	−24.4448	+	18.0226i	−0.900436	+	0.663872i
$738$	−30.7098	−	27.5707i	−1.13044	−	1.01489i
$739$	−50.9440	−	12.3589i	−1.87400	−	0.454629i	−0.874468	−	0.485083i	$-0.838789\pi$
$739$	−50.9440	−	12.3589i	−1.87400	−	0.454629i	−0.999536	+	0.0304546i	$0.990304\pi$
$740$	−25.5171	−	1.09141i	−0.938028	−	0.0401211i
$741$	−5.21696	−	5.32245i	−0.191650	−	0.195525i
$742$	1.83809	+	1.05528i	0.0674784	+	0.0387406i
$743$	38.0389	+	3.63227i	1.39551	+	0.133255i	0.765553	−	0.643373i	$-0.222466\pi$
$743$	38.0389	+	3.63227i	1.39551	+	0.133255i	0.629959	+	0.776628i	$0.283072\pi$
$744$	−30.3277	+	6.51080i	−1.11187	+	0.238697i
$745$	−18.6128	+	21.4803i	−0.681920	+	0.786978i
$746$	1.79766	+	9.20683i	0.0658169	+	0.337086i
$747$	−5.76255	−	21.1853i	−0.210841	−	0.775131i
$748$	−1.88152	+	20.7691i	−0.0687952	+	0.759395i
$749$	2.39670	+	0.829508i	0.0875737	+	0.0303095i
$750$	4.96078	−	21.9999i	0.181142	−	0.803324i
$751$	14.9414	+	23.2493i	0.545221	+	0.848380i	0.999088	−	0.0426890i	$-0.0135925\pi$
$751$	14.9414	+	23.2493i	0.545221	+	0.848380i	−0.453868	+	0.891069i	$0.649956\pi$
$752$	8.54358	+	6.58552i	0.311552	+	0.240149i
$753$	−35.9222	+	11.0880i	−1.30908	+	0.404071i
$754$	4.97415	−	2.00537i	0.181148	−	0.0730313i
$755$	1.12554	+	23.6279i	0.0409625	+	0.859908i
$756$	−5.34798	−	2.14953i	−0.194504	−	0.0781777i
$757$	32.0127	−	25.1751i	1.16352	−	0.915004i	0.166054	−	0.986117i	$-0.446897\pi$
$757$	32.0127	−	25.1751i	1.16352	−	0.915004i	0.997468	+	0.0711124i	$0.0226549\pi$
$758$	2.17822	−	2.52617i	0.0791167	−	0.0917545i
$759$	21.0033	+	10.4639i	0.762373	+	0.379815i
$760$	−10.3318	+	13.3366i	−0.374773	+	0.483770i
$761$	9.32832	−	14.5151i	0.338151	−	0.526174i	−0.629982	−	0.776610i	$-0.716938\pi$
$761$	9.32832	−	14.5151i	0.338151	−	0.526174i	0.968133	+	0.250436i	$0.0805740\pi$
$762$	26.4427	−	8.23236i	0.957917	−	0.298227i
$763$	−0.356678	−	0.0169907i	−0.0129126	−	0.000615104i
$764$	1.00126	+	4.04151i	0.0362242	+	0.146217i
$765$	6.38966	−	20.2524i	0.231019	−	0.732226i
$766$	32.2517	−	14.8236i	1.16530	−	0.535597i
$767$	8.18788	−	14.1818i	0.295647	−	0.512076i
$768$	−26.3164	+	8.68614i	−0.949610	+	0.313434i
$769$	6.65068	−	2.66253i	0.239830	−	0.0960134i	−0.248634	−	0.968597i	$-0.579982\pi$
$769$	6.65068	−	2.66253i	0.239830	−	0.0960134i	0.488464	+	0.872584i	$0.337557\pi$
$770$	−7.25337	+	1.06085i	−0.261393	+	0.0382305i
$771$	−0.613531	+	7.51976i	−0.0220958	+	0.270818i
$772$	9.71701	−	1.92177i	0.349723	−	0.0691659i
$773$	−3.25888	+	16.9087i	−0.117214	+	0.608163i	0.875052	+	0.484029i	$0.160827\pi$
$773$	−3.25888	+	16.9087i	−0.117214	+	0.608163i	−0.992266	+	0.124133i	$0.960385\pi$
$774$	−11.3096	+	3.69283i	−0.406514	+	0.132736i
$775$	7.37436	−	4.25759i	0.264895	−	0.152937i
$776$	−13.9199	+	0.764709i	−0.499696	+	0.0274515i
$777$	0.529754	+	4.84128i	0.0190048	+	0.173680i
$778$	1.12693	−	7.97536i	0.0404025	−	0.285930i
$779$	15.0841	+	17.4080i	0.540445	+	0.623706i
$780$	7.52714	+	13.9555i	0.269515	+	0.499686i
$781$	−40.7276	−	16.3049i	−1.45735	−	0.583434i
$782$	3.38705	−	14.1110i	0.121121	−	0.504609i
$783$	10.8440	+	0.0675274i	0.387532	+	0.00241323i
$784$	−25.6108	+	7.79087i	−0.914671	+	0.278245i
$785$	37.5648	+	39.3968i	1.34075	+	1.40613i
$786$	−10.8082	+	28.3202i	−0.385516	+	1.01015i
$787$	−16.7586	−	32.5072i	−0.597381	−	1.15876i	−0.972744	−	0.231880i	$-0.925512\pi$
$787$	−16.7586	−	32.5072i	−0.597381	−	1.15876i	0.375363	−	0.926878i	$-0.377518\pi$
$788$	−9.38404	+	4.34072i	−0.334293	+	0.154632i
$789$	−26.6015	+	38.4685i	−0.947039	+	1.36952i
$790$	17.0286	+	32.8350i	0.605851	+	1.16822i
$791$	−3.21046	+	0.618766i	−0.114151	+	0.0220008i
$792$	−9.91740	−	29.8804i	−0.352400	−	1.06176i
$793$	−22.5740	+	2.15555i	−0.801626	+	0.0765460i
$794$	30.2533	−	31.8833i	1.07365	−	1.13150i
$795$	0.398509	−	11.7826i	0.0141337	−	0.417886i
$796$	−9.16170	−	11.5344i	−0.324728	−	0.408825i
$797$	−17.9838	+	18.8609i	−0.637020	+	0.668088i	−0.960543	−	0.278133i	$-0.910284\pi$
$797$	−17.9838	+	18.8609i	−0.637020	+	0.668088i	0.323522	+	0.946221i	$0.395133\pi$
$798$	2.81167	+	1.56308i	0.0995319	+	0.0553323i
$799$	6.89383	+	3.14831i	0.243886	+	0.111379i
$800$	6.14300	−	4.48775i	0.217188	−	0.158666i
$801$	27.8583	+	15.0753i	0.984324	+	0.532659i
$802$	−9.83339	+	28.6364i	−0.347229	+	1.01119i
$803$	4.49548			0.158642
$804$	−27.1048	−	8.32642i	−0.955913	−	0.293650i
$805$	5.10111			0.179790
$806$	5.28452	−	15.3894i	0.186139	−	0.542068i
$807$	−7.01865	+	39.3272i	−0.247068	+	1.38438i
$808$	5.83819	+	5.48610i	0.205387	+	0.193000i
$809$	19.5228	+	8.91575i	0.686384	+	0.313461i	0.727907	−	0.685676i	$-0.240493\pi$
$809$	19.5228	+	8.91575i	0.686384	+	0.313461i	−0.0415223	+	0.999138i	$0.513221\pi$
$810$	3.36624	+	31.8831i	0.118277	+	1.12026i
$811$	−20.0546	+	21.0327i	−0.704212	+	0.738556i	−0.974540	−	0.224212i	$-0.928019\pi$
$811$	−20.0546	+	21.0327i	−0.704212	+	0.738556i	0.270328	+	0.962768i	$0.412868\pi$
$812$	−1.81270	+	1.43982i	−0.0636135	+	0.0505279i
$813$	−53.3368	−	1.80395i	−1.87060	−	0.0632673i
$814$	−18.3108	+	19.2974i	−0.641793	+	0.676372i
$815$	55.5138	−	5.30093i	1.94456	−	0.185683i
$816$	−16.6283	+	10.1286i	−0.582106	+	0.354572i
$817$	6.52016	−	1.25666i	0.228112	−	0.0439649i
$818$	−25.2218	−	48.6333i	−0.881860	−	1.70042i
$819$	2.41357	−	1.82106i	0.0843369	−	0.0636329i
$820$	−20.5736	−	44.4773i	−0.718462	−	1.55322i
$821$	−25.0047	−	48.5023i	−0.872669	−	1.69274i	−0.707783	−	0.706429i	$-0.750305\pi$
$821$	−25.0047	−	48.5023i	−0.872669	−	1.69274i	−0.164886	−	0.986313i	$-0.552726\pi$
$822$	14.4246	+	5.50502i	0.503114	+	0.192010i
$823$	−16.4490	−	17.2513i	−0.573378	−	0.601341i	0.371633	−	0.928380i	$-0.378798\pi$
$823$	−16.4490	−	17.2513i	−0.573378	−	0.601341i	−0.945011	+	0.327038i	$0.893949\pi$
$824$	3.90799	−	1.59764i	0.136141	−	0.0556563i
$825$	5.10987	+	6.97034i	0.177903	+	0.242676i
$826$	−1.64976	+	6.87317i	−0.0574024	+	0.239148i
$827$	−2.74049	−	1.09713i	−0.0952962	−	0.0381509i	0.323525	−	0.946220i	$-0.395132\pi$
$827$	−2.74049	−	1.09713i	−0.0952962	−	0.0381509i	−0.418821	+	0.908069i	$0.637556\pi$
$828$	3.81950	+	21.5728i	0.132737	+	0.749705i
$829$	−1.69645	−	1.95781i	−0.0589202	−	0.0679975i	0.725524	−	0.688196i	$-0.241597\pi$
$829$	−1.69645	−	1.95781i	−0.0589202	−	0.0679975i	−0.784445	+	0.620199i	$0.787052\pi$
$830$	3.64749	−	25.8135i	0.126606	−	0.895999i
$831$	41.0585	−	4.49280i	1.42430	−	0.155853i
$832$	3.22120	−	14.1759i	0.111675	−	0.491460i
$833$	−16.2878	+	9.40376i	−0.564338	+	0.325821i
$834$	−1.76491	−	2.39529i	−0.0611139	−	0.0829420i
$835$	−0.275835	+	1.43117i	−0.00954567	+	0.0495276i
$836$	3.40918	+	17.2378i	0.117909	+	0.596182i
$837$	21.6995	−	24.7297i	0.750045	−	0.854785i
$838$	−18.6400	+	2.72622i	−0.643908	+	0.0941756i
$839$	35.8966	−	14.3708i	1.23929	−	0.496136i	0.342886	−	0.939377i	$-0.388596\pi$
$839$	35.8966	−	14.3708i	1.23929	−	0.496136i	0.896403	+	0.443241i	$0.146171\pi$
$840$	−4.82626	−	4.85266i	−0.166522	−	0.167433i
$841$	−12.3223	+	21.3428i	−0.424907	+	0.735960i
$842$	1.43201	−	0.658181i	0.0493502	−	0.0226824i
$843$	−0.249873	−	18.1175i	−0.00860607	−	0.623999i
$844$	25.4323	−	6.30068i	0.875415	−	0.216878i
$845$	24.4005	+	1.16234i	0.839402	+	0.0399856i
$846$	−11.4397	−	0.201256i	−0.393305	−	0.00691931i
$847$	−0.829572	+	1.29084i	−0.0285044	+	0.0443537i
$848$	−7.38263	+	7.89475i	−0.253521	+	0.271107i
$849$	22.8978	−	45.9608i	0.785849	−	1.57737i
$850$	3.49036	−	4.04790i	0.119718	−	0.138842i
$851$	14.5511	−	11.4431i	0.498806	−	0.392266i
$852$	−10.3968	−	39.6171i	−0.356188	−	1.35726i
$853$	−0.997437	−	20.9388i	−0.0341516	−	0.716930i	−0.949405	−	0.314053i	$-0.898313\pi$
$853$	−0.997437	−	20.9388i	−0.0341516	−	0.716930i	0.915254	−	0.402878i	$-0.131990\pi$
$854$	9.07810	−	3.65991i	0.310646	−	0.125240i
$855$	0.358174	−	17.8902i	0.0122493	−	0.611832i
$856$	−6.91320	+	10.9313i	−0.236288	+	0.373626i
$857$	19.8798	+	30.9335i	0.679080	+	1.05667i	0.994193	+	0.107614i	$0.0343212\pi$
$857$	19.8798	+	30.9335i	0.679080	+	1.05667i	−0.315113	+	0.949054i	$0.602042\pi$
$858$	16.1106	+	3.63279i	0.550007	+	0.124022i
$859$	−39.4760	−	13.6628i	−1.34690	−	0.466168i	−0.444007	−	0.896023i	$-0.646443\pi$
$859$	−39.4760	−	13.6628i	−1.34690	−	0.466168i	−0.902898	+	0.429855i	$0.858565\pi$
$860$	−14.0694	−	1.27457i	−0.479761	−	0.0434626i
$861$	−7.79071	+	5.15997i	−0.265507	+	0.175851i
$862$	6.58487	+	33.7249i	0.224282	+	1.14867i
$863$	−21.6705	+	25.0091i	−0.737674	+	0.851321i	−0.993313	−	0.115451i	$-0.963169\pi$
$863$	−21.6705	+	25.0091i	−0.737674	+	0.851321i	0.255639	+	0.966772i	$0.417714\pi$
$864$	16.9084	−	24.0439i	0.575234	−	0.817989i
$865$	43.7427	+	4.17692i	1.48730	+	0.142020i
$866$	−6.41296	−	3.68180i	−0.217921	−	0.125113i
$867$	11.2590	−	11.0359i	0.382377	−	0.374798i
$868$	−0.300127	+	7.01694i	−0.0101870	+	0.238170i
$869$	37.4395	+	9.08273i	1.27005	+	0.308111i
$870$	11.7982	+	5.15848i	0.399996	+	0.174889i
$871$	11.0787	−	9.92471i	0.375388	−	0.336286i
$872$	0.500308	−	1.75095i	0.0169426	−	0.0592948i
$873$	11.3665	−	9.45751i	0.384699	−	0.320088i
$874$	−0.611456	−	12.2123i	−0.0206828	−	0.413088i
$875$	−4.53872	−	2.33987i	−0.153437	−	0.0791021i
$876$	2.49790	+	3.37291i	0.0843962	+	0.113960i
$877$	10.9169	+	1.04244i	0.368638	+	0.0352006i	0.277731	−	0.960659i	$-0.410418\pi$
$877$	10.9169	+	1.04244i	0.368638	+	0.0352006i	0.0909063	+	0.995859i	$0.471024\pi$
$878$	−37.7051	−	43.3012i	−1.27249	−	1.46135i
$879$	−25.6482	+	15.2834i	−0.865093	+	0.515497i
$880$	3.19211	−	37.2474i	0.107606	−	1.25561i
$881$	30.6719	−	39.0025i	1.03336	−	1.31403i	0.0851580	−	0.996367i	$-0.472860\pi$
$881$	30.6719	−	39.0025i	1.03336	−	1.31403i	0.948205	−	0.317660i	$-0.102897\pi$
$882$	16.8741	−	22.8353i	0.568180	−	0.768905i
$883$	−19.0547	−	6.59489i	−0.641241	−	0.221936i	−0.0129528	−	0.999916i	$-0.504123\pi$
$883$	−19.0547	−	6.59489i	−0.641241	−	0.221936i	−0.628289	+	0.777980i	$0.716244\pi$
$884$	−0.0495779	−	10.2133i	−0.00166748	−	0.343511i
$885$	38.0772	−	9.79537i	1.27995	−	0.329268i
$886$	−7.40784	+	18.6349i	−0.248871	+	0.626050i
$887$	−12.9754	−	18.2213i	−0.435670	−	0.611813i	0.537119	−	0.843507i	$-0.319513\pi$
$887$	−12.9754	−	18.2213i	−0.435670	−	0.611813i	−0.972789	+	0.231694i	$0.925573\pi$
$888$	−24.6529	−	3.01584i	−0.827297	−	0.101205i
$889$	−0.298371	−	6.26358i	−0.0100071	−	0.210074i
$890$	23.3221	+	29.5088i	0.781758	+	0.989137i
$891$	27.3469	+	19.1636i	0.916156	+	0.642004i
$892$	27.5763	+	28.6415i	0.923321	+	0.958987i
$893$	6.32080	+	0.908794i	0.211518	+	0.0304116i
$894$	−19.6916	+	19.3952i	−0.658585	+	0.648673i
$895$	−16.3574	+	25.4526i	−0.546766	+	0.850785i
$896$	0.405007	+	6.26174i	0.0135303	+	0.209190i
$897$	−10.7270	−	4.12375i	−0.358166	−	0.137688i
$898$	−9.04576	−	25.9322i	−0.301861	−	0.865368i
$899$	−4.32186	−	12.4872i	−0.144142	−	0.416471i
$900$	−2.39047	+	7.70692i	−0.0796825	+	0.256897i
$901$	−3.79697	+	6.57655i	−0.126496	+	0.219097i
$902$	−49.0094	−	14.2613i	−1.63183	−	0.474851i
$903$	0.165271	+	2.68873i	0.00549987	+	0.0894752i
$904$	0.672084	−	16.6603i	0.0223532	−	0.554114i
$905$	53.8518	−	13.0643i	1.79009	−	0.434272i
$906$	−0.721755	+	22.9916i	−0.0239787	+	0.763844i
$907$	9.22565	−	47.8672i	0.306333	−	1.58940i	−0.423577	−	0.905860i	$-0.639226\pi$
$907$	9.22565	−	47.8672i	0.306333	−	1.58940i	0.729909	−	0.683544i	$-0.239562\pi$
$908$	34.7723	−	40.5252i	1.15396	−	1.34488i
$909$	−8.44098	−	0.976878i	−0.279970	−	0.0324010i
$910$	3.48690	−	0.854880i	0.115590	−	0.0283390i
$911$	5.84765	+	12.8046i	0.193741	+	0.424234i	0.981425	−	0.191845i	$-0.0614472\pi$
$911$	5.84765	+	12.8046i	0.193741	+	0.424234i	−0.787684	+	0.616080i	$0.788720\pi$
$912$	−11.0390	+	12.1360i	−0.365538	+	0.401863i
$913$	−17.7818	−	20.5213i	−0.588492	−	0.679156i
$914$	−6.02240	+	7.69647i	−0.199203	+	0.254577i
$915$	−41.6346	−	35.0831i	−1.37640	−	1.15981i
$916$	1.75112	−	5.14012i	0.0578586	−	0.169834i
$917$	5.59082	+	3.98121i	0.184625	+	0.131471i
$918$	7.74810	−	19.1427i	0.255725	−	0.631802i
$919$	−15.2019	−	15.9433i	−0.501463	−	0.525919i	0.423541	−	0.905877i	$-0.360787\pi$
$919$	−15.2019	−	15.9433i	−0.501463	−	0.525919i	−0.925004	+	0.379958i	$0.875939\pi$
$920$	−5.94887	+	25.3250i	−0.196129	+	0.834941i
$921$	−39.8025	+	6.28415i	−1.31154	+	0.207070i
$922$	18.3473	+	31.6011i	0.604237	+	1.04073i
$923$	20.6153	+	6.05319i	0.678560	+	0.199243i
$924$	−7.11291	+	0.471885i	−0.233998	+	0.0155239i
$925$	6.69489	−	1.29033i	0.220127	−	0.0424259i
$926$	−5.86027	+	12.9151i	−0.192580	+	0.424415i
$927$	−2.31621	+	3.83251i	−0.0760742	+	0.125876i
$928$	−5.03420	−	10.6785i	−0.165256	−	0.350538i
$929$	9.24801	+	31.4958i	0.303417	+	1.03334i	0.960211	+	0.279275i	$0.0900940\pi$
$929$	9.24801	+	31.4958i	0.303417	+	1.03334i	−0.656794	+	0.754070i	$0.728088\pi$
$930$	35.2683	−	16.8030i	1.15649	−	0.550991i
$931$	−10.9358	+	11.4691i	−0.358406	+	0.375886i
$932$	14.0065	−	48.5728i	0.458798	−	1.59105i
$933$	−13.7118	−	12.7178i	−0.448905	−	0.416364i
$934$	29.3243	−	45.8739i	0.959520	−	1.50104i
$935$	−3.73787	−	25.9975i	−0.122241	−	0.850208i
$936$	6.22617	+	14.1061i	0.203509	+	0.461074i
$937$	10.2783			0.335776			0.167888	−	0.985806i	$-0.446305\pi$
$937$	10.2783			0.335776			0.167888	+	0.985806i	$0.446305\pi$
$938$	−3.36813	+	5.46578i	−0.109973	+	0.178464i
$939$	−12.9090	+	39.0314i	−0.421268	+	1.27374i
$940$	−12.3854	−	5.58370i	−0.403966	−	0.182120i
$941$	21.8265	−	3.13818i	0.711523	−	0.102302i	0.222957	−	0.974828i	$-0.428429\pi$
$941$	21.8265	−	3.13818i	0.711523	−	0.102302i	0.488566	+	0.872527i	$0.337520\pi$
$942$	33.3931	+	41.0740i	1.08800	+	1.33826i
$943$	32.3090	+	14.7550i	1.05213	+	0.480490i
$944$	−32.1987	−	16.2058i	−1.04798	−	0.527455i
$945$	7.17875	+	1.07782i	0.233525	+	0.0350614i
$946$	−10.6245	+	10.1798i	−0.345432	+	0.330973i
$947$	−24.3176	+	7.14030i	−0.790217	+	0.232029i	−0.651845	−	0.758352i	$-0.726005\pi$
$947$	−24.3176	+	7.14030i	−0.790217	+	0.232029i	−0.138371	+	0.990380i	$0.544187\pi$
$948$	13.9885	+	33.1372i	0.454325	+	1.07625i
$949$	−2.19172	+	0.209284i	−0.0711461	+	0.00679363i
$950$	1.86092	−	4.10116i	0.0603762	−	0.133059i
$951$	27.7578	+	3.60099i	0.900107	+	0.116770i
$952$	1.27279	+	4.22077i	0.0412512	+	0.136796i
$953$	−14.2399	+	48.4966i	−0.461275	+	1.57096i	0.320405	+	0.947281i	$0.396181\pi$
$953$	−14.2399	+	48.4966i	−0.461275	+	1.57096i	−0.781680	+	0.623679i	$0.785637\pi$
$954$	1.29035	−	11.3916i	0.0417765	−	0.368817i
$955$	−2.40292	−	4.66101i	−0.0777567	−	0.150827i
$956$	−4.53367	+	32.6569i	−0.146629	+	1.05620i
$957$	12.1219	−	5.73920i	0.391844	−	0.185522i
$958$	−12.9151	−	19.9895i	−0.417268	−	0.645830i
$959$	2.02778	−	2.84762i	0.0654804	−	0.0919543i
$960$	29.7199	−	18.3014i	0.959206	−	0.590674i
$961$	−8.43885	−	3.37841i	−0.272221	−	0.108981i
$962$	8.02882	−	10.2606i	0.258860	−	0.330816i
$963$	−1.03041	−	13.6798i	−0.0332045	−	0.440824i
$964$	−8.01283	+	33.7434i	−0.258076	+	1.08680i
$965$	−11.3478	+	5.18236i	−0.365298	+	0.166826i
$966$	4.94508	+	0.391385i	0.159105	+	0.0125926i
$967$	−32.9107	+	19.0010i	−1.05834	+	0.611030i	−0.924971	−	0.380037i	$-0.875911\pi$
$967$	−32.9107	+	19.0010i	−1.05834	+	0.611030i	−0.133364	+	0.991067i	$0.542578\pi$
$968$	−5.44107	−	5.62387i	−0.174883	−	0.180758i
$969$	−5.62482	+	10.0604i	−0.180695	+	0.323186i
$970$	16.8346	−	4.98750i	0.540526	−	0.160139i
$971$	−2.12859	−	8.77418i	−0.0683098	−	0.281577i	0.927404	−	0.374060i	$-0.122035\pi$
$971$	−2.12859	−	8.77418i	−0.0683098	−	0.281577i	−0.995714	+	0.0924834i	$0.970519\pi$
$972$	0.817021	+	31.1662i	0.0262060	+	0.999657i
$973$	−0.625417	+	0.250379i	−0.0200499	+	0.00802678i
$974$	−19.7870	−	5.75787i	−0.634018	−	0.184494i
$975$	−2.81575	−	3.16041i	−0.0901762	−	0.101214i
$976$	7.58324	+	49.3374i	0.242734	+	1.57925i
$977$	−14.1134	+	4.88468i	−0.451526	+	0.156275i	−0.543360	−	0.839500i	$-0.682848\pi$
$977$	−14.1134	+	4.88468i	−0.451526	+	0.156275i	0.0918340	+	0.995774i	$0.470727\pi$
$978$	54.2225	−	0.879459i	1.73384	−	0.0281220i
$979$	39.1314	+	1.86406i	1.25065	+	0.0595756i
$980$	29.1158	−	16.9990i	0.930071	−	0.543013i
$981$	0.681827	+	1.80715i	0.0217691	+	0.0576978i
$982$	11.0077	−	21.4799i	0.351271	−	0.685450i
$983$	−0.516119	+	3.58969i	−0.0164617	+	0.114493i	−0.996395	−	0.0848300i	$-0.972965\pi$
$983$	−0.516119	+	3.58969i	−0.0164617	+	0.114493i	0.979934	+	0.199323i	$0.0638744\pi$
$984$	−16.5318	−	44.6954i	−0.527014	−	1.42484i
$985$	10.2359	−	8.04960i	0.326143	−	0.256482i
$986$	−5.14300	−	6.50729i	−0.163787	−	0.207234i
$987$	−0.695512	+	2.49550i	−0.0221384	+	0.0794328i
$988$	−2.46460	−	8.24536i	−0.0784092	−	0.262320i
$989$	8.34059	−	5.93931i	0.265215	−	0.188859i
$990$	20.8472	+	33.7290i	0.662568	+	1.07198i
$991$	9.78861	+	15.2314i	0.310945	+	0.483841i	0.961191	−	0.275883i	$-0.0889704\pi$
$991$	9.78861	+	15.2314i	0.310945	+	0.483841i	−0.650246	+	0.759724i	$0.725334\pi$
$992$	−34.4864	−	9.67312i	−1.09494	−	0.307122i
$993$	11.0411	−	14.4455i	0.350377	−	0.458413i
$994$	−9.27396	+	0.0225089i	−0.294152	+	0.000713938i
$995$	14.5828	+	11.4680i	0.462306	+	0.363561i
$996$	5.51648	−	24.7441i	0.174796	−	0.784046i
$997$	−17.9704	+	20.7390i	−0.569130	+	0.656811i	−0.965232	−	0.261396i	$-0.915817\pi$
$997$	−17.9704	+	20.7390i	−0.569130	+	0.656811i	0.396102	+	0.918206i	$0.370363\pi$
$998$	−11.2397	−	12.9079i	−0.355788	−	0.408593i
$999$	22.8955	−	13.0293i	0.724382	−	0.412229i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	804.2.bd.a.35.13	yes	2640
3.2	odd	2	inner	804.2.bd.a.35.120	yes	2640
4.3	odd	2	inner	804.2.bd.a.35.5	yes	2640
12.11	even	2	inner	804.2.bd.a.35.128	yes	2640
67.23	even	33	inner	804.2.bd.a.23.128	yes	2640
201.23	odd	66	inner	804.2.bd.a.23.5	✓	2640
268.23	odd	66	inner	804.2.bd.a.23.120	yes	2640
804.23	even	66	inner	804.2.bd.a.23.13	yes	2640

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
804.2.bd.a.23.5	✓	2640	201.23	odd	66	inner
804.2.bd.a.23.13	yes	2640	804.23	even	66	inner
804.2.bd.a.23.120	yes	2640	268.23	odd	66	inner
804.2.bd.a.23.128	yes	2640	67.23	even	33	inner
804.2.bd.a.35.5	yes	2640	4.3	odd	2	inner
804.2.bd.a.35.13	yes	2640	1.1	even	1	trivial
804.2.bd.a.35.120	yes	2640	3.2	odd	2	inner
804.2.bd.a.35.128	yes	2640	12.11	even	2	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:	\( N \)	\(=\)	\( 804 = 2^{2} \cdot 3 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	804.bd (of order \(66\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.33755 - 0.459299i) q^{2} +(1.70511 + 0.304307i) q^{3} +(1.57809 + 1.22867i) q^{4} +(-2.29127 - 1.04639i) q^{5} +(-2.14090 - 1.19018i) q^{6} +(-0.382733 + 0.401398i) q^{7} +(-1.54645 - 2.36823i) q^{8} +(2.81479 + 1.03775i) q^{9} +O(q^{10})\)	\(q+(-1.33755 - 0.459299i) q^{2} +(1.70511 + 0.304307i) q^{3} +(1.57809 + 1.22867i) q^{4} +(-2.29127 - 1.04639i) q^{5} +(-2.14090 - 1.19018i) q^{6} +(-0.382733 + 0.401398i) q^{7} +(-1.54645 - 2.36823i) q^{8} +(2.81479 + 1.03775i) q^{9} +(2.58409 + 2.45198i) q^{10} +(3.69354 - 0.352690i) q^{11} +(2.31692 + 2.57524i) q^{12} +(-1.78432 + 0.343899i) q^{13} +(0.696287 - 0.361102i) q^{14} +(-3.58844 - 2.48146i) q^{15} +(0.980730 + 3.87791i) q^{16} +(1.28775 + 2.49788i) q^{17} +(-3.28829 - 2.68088i) q^{18} +(1.63406 + 1.71376i) q^{19} +(-2.33016 - 4.46652i) q^{20} +(-0.774749 + 0.567960i) q^{21} +(-5.10229 - 1.22470i) q^{22} +(3.38982 + 1.35708i) q^{23} +(-1.91619 - 4.50868i) q^{24} +(0.880693 + 1.01637i) q^{25} +(2.54457 + 0.359553i) q^{26} +(4.48373 + 2.62605i) q^{27} +(-1.09717 + 0.163190i) q^{28} +(1.80736 - 1.04348i) q^{29} +(3.66000 + 4.96725i) q^{30} +(1.19828 - 6.21724i) q^{31} +(0.469342 - 5.63735i) q^{32} +(6.40521 + 0.522596i) q^{33} +(-0.575153 - 3.93250i) q^{34} +(1.29696 - 0.519226i) q^{35} +(3.16694 + 5.09613i) q^{36} +(2.53488 - 4.39054i) q^{37} +(-1.39852 - 3.04276i) q^{38} +(-3.14711 + 0.0434043i) q^{39} +(1.06525 + 7.04444i) q^{40} +(9.71647 + 0.462853i) q^{41} +(1.29713 - 0.403834i) q^{42} +(1.51606 - 2.35904i) q^{43} +(6.26207 + 3.98157i) q^{44} +(-5.36356 - 5.32315i) q^{45} +(-3.91076 - 3.37211i) q^{46} +(2.11981 - 1.66704i) q^{47} +(0.492175 + 6.91070i) q^{48} +(0.318437 + 6.68481i) q^{49} +(-0.711153 - 1.76395i) q^{50} +(1.43562 + 4.65102i) q^{51} +(-3.23835 - 1.64964i) q^{52} +(1.46092 + 2.27324i) q^{53} +(-4.79109 - 5.57185i) q^{54} +(-8.83195 - 3.05677i) q^{55} +(1.54248 + 0.285656i) q^{56} +(2.26475 + 3.41940i) q^{57} +(-2.89671 + 0.565590i) q^{58} +(-5.90144 + 6.81062i) q^{59} +(-2.61399 - 8.32498i) q^{60} +(12.4227 + 1.18622i) q^{61} +(-4.45833 + 7.76552i) q^{62} +(-1.49387 + 0.732671i) q^{63} +(-3.21700 + 7.32468i) q^{64} +(4.44821 + 1.07912i) q^{65} +(-8.32727 - 3.64091i) q^{66} +(-7.02019 + 4.20915i) q^{67} +(-1.03690 + 5.52409i) q^{68} +(5.36705 + 3.34552i) q^{69} +(-1.97324 + 0.0987974i) q^{70} +(-10.5094 - 5.41795i) q^{71} +(-1.89529 - 8.27090i) q^{72} +(1.20612 + 0.115171i) q^{73} +(-5.40711 + 4.70831i) q^{74} +(1.19239 + 2.00103i) q^{75} +(0.473053 + 4.71219i) q^{76} +(-1.27207 + 1.61757i) q^{77} +(4.22936 + 1.38741i) q^{78} +(9.81221 + 3.39604i) q^{79} +(1.81068 - 9.91157i) q^{80} +(6.84613 + 5.84213i) q^{81} +(-12.7837 - 5.08186i) q^{82} +(-4.24506 - 5.96136i) q^{83} +(-1.92046 - 0.0556220i) q^{84} +(-0.336824 - 7.07080i) q^{85} +(-3.11132 + 2.45901i) q^{86} +(3.39929 - 1.22926i) q^{87} +(-6.54711 - 8.20172i) q^{88} +(10.4511 + 1.50264i) q^{89} +(4.72913 + 9.58346i) q^{90} +(0.544876 - 0.847844i) q^{91} +(3.68204 + 6.30658i) q^{92} +(3.93514 - 10.2364i) q^{93} +(-3.60103 + 1.25612i) q^{94} +(-1.95083 - 5.63655i) q^{95} +(2.51577 - 9.46947i) q^{96} +(2.46443 - 4.26851i) q^{97} +(2.64440 - 9.08754i) q^{98} +(10.7626 + 2.84024i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2640 q - 42 q^{4} - 19 q^{6} - 32 q^{9}+O(q^{10}) \) 2640 * q - 42 * q^4 - 19 * q^6 - 32 * q^9	\( 2640 q - 42 q^{4} - 19 q^{6} - 32 q^{9} - 46 q^{10} - 24 q^{12} - 88 q^{13} - 26 q^{16} - 23 q^{18} - 128 q^{22} - 22 q^{24} + 160 q^{25} + 44 q^{28} - 18 q^{30} - 44 q^{33} - 6 q^{34} - 35 q^{36} - 48 q^{37} - 92 q^{40} - 10 q^{42} + 40 q^{45} + 46 q^{46} - 11 q^{48} - 216 q^{49} - 76 q^{52} + 129 q^{54} - 42 q^{57} - 56 q^{58} - 90 q^{60} - 80 q^{61} - 48 q^{64} - 74 q^{66} - 4 q^{69} + 96 q^{70} - 20 q^{72} - 216 q^{73} + 76 q^{76} - 66 q^{78} - 16 q^{81} + 20 q^{82} - 55 q^{84} - 104 q^{85} - 30 q^{88} - 64 q^{90} - 192 q^{93} - 32 q^{94} - 205 q^{96} - 64 q^{97}+O(q^{100}) \) 2640 * q - 42 * q^4 - 19 * q^6 - 32 * q^9 - 46 * q^10 - 24 * q^12 - 88 * q^13 - 26 * q^16 - 23 * q^18 - 128 * q^22 - 22 * q^24 + 160 * q^25 + 44 * q^28 - 18 * q^30 - 44 * q^33 - 6 * q^34 - 35 * q^36 - 48 * q^37 - 92 * q^40 - 10 * q^42 + 40 * q^45 + 46 * q^46 - 11 * q^48 - 216 * q^49 - 76 * q^52 + 129 * q^54 - 42 * q^57 - 56 * q^58 - 90 * q^60 - 80 * q^61 - 48 * q^64 - 74 * q^66 - 4 * q^69 + 96 * q^70 - 20 * q^72 - 216 * q^73 + 76 * q^76 - 66 * q^78 - 16 * q^81 + 20 * q^82 - 55 * q^84 - 104 * q^85 - 30 * q^88 - 64 * q^90 - 192 * q^93 - 32 * q^94 - 205 * q^96 - 64 * q^97

Introduction

L-functions

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