LMFDB - Embedded newform 805.2.bs.a.37.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [805,2,Mod(37,805)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(805, base_ring=CyclotomicField(132))

chi = DirichletCharacter(H, H._module([33, 44, 126]))

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

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

chi := DirichletCharacter("805.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 805 = 5 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	805.bs (of order $132$, degree $40$, 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:	$6.42795736271$
Analytic rank:	$0$
Dimension:	$3680$
Relative dimension:	$92$ over $\Q(\zeta_{132})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{132}]$

Embedding invariants

Embedding label			37.8
Character	$\chi$	$=$	805.37
Dual form			805.2.bs.a.718.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.08232 + 1.26924i) q^{2} +(0.0668818 + 0.137682i) q^{3} +(1.80864 - 3.50827i) q^{4} +(0.447044 - 2.19092i) q^{5} +(-0.314021 - 0.201809i) q^{6} +(0.109828 - 2.64347i) q^{7} +(0.338730 + 4.73606i) q^{8} +(1.83999 - 2.33974i) q^{9} +O(q^{10})$	\(q+(-2.08232 + 1.26924i) q^{2} +(0.0668818 + 0.137682i) q^{3} +(1.80864 - 3.50827i) q^{4} +(0.447044 - 2.19092i) q^{5} +(-0.314021 - 0.201809i) q^{6} +(0.109828 - 2.64347i) q^{7} +(0.338730 + 4.73606i) q^{8} +(1.83999 - 2.33974i) q^{9} +(1.84992 + 5.12962i) q^{10} +(-4.54781 + 1.10329i) q^{11} +(0.603991 + 0.0143777i) q^{12} +(4.20759 + 1.56935i) q^{13} +(3.12651 + 5.64396i) q^{14} +(0.331550 - 0.0849832i) q^{15} +(-2.13753 - 3.00175i) q^{16} +(2.70732 + 2.97815i) q^{17} +(-0.861761 + 7.20749i) q^{18} +(-0.176571 - 3.70668i) q^{19} +(-6.87781 - 5.53094i) q^{20} +(0.371304 - 0.161679i) q^{21} +(8.06967 - 8.06967i) q^{22} +(4.54062 + 1.54363i) q^{23} +(-0.629416 + 0.363393i) q^{24} +(-4.60030 - 1.95888i) q^{25} +(-10.7534 + 2.07256i) q^{26} +(0.893910 + 0.194458i) q^{27} +(-9.07537 - 5.16639i) q^{28} +(1.03455 - 1.60979i) q^{29} +(-0.582530 + 0.597780i) q^{30} +(-2.29202 - 0.441750i) q^{31} +(-0.468612 - 0.200672i) q^{32} +(-0.456069 - 0.552363i) q^{33} +(-9.41750 - 2.76523i) q^{34} +(-5.74255 - 1.42237i) q^{35} +(-4.88056 - 10.6869i) q^{36} +(3.51507 - 0.420279i) q^{37} +(5.07235 + 7.49439i) q^{38} +(0.0653399 + 0.684271i) q^{39} +(10.5278 + 1.37509i) q^{40} +(-1.01513 - 7.06036i) q^{41} +(-0.567965 + 0.807942i) q^{42} +(0.772384 - 10.7993i) q^{43} +(-4.35472 + 17.9504i) q^{44} +(-4.30364 - 5.07726i) q^{45} +(-11.4143 + 2.54882i) q^{46} +(-10.6488 + 2.85335i) q^{47} +(0.270325 - 0.495062i) q^{48} +(-6.97588 - 0.580652i) q^{49} +(12.0656 - 1.75988i) q^{50} +(-0.228968 + 0.571934i) q^{51} +(13.1157 - 11.9230i) q^{52} +(1.80109 + 1.48710i) q^{53} +(-2.10822 + 0.729663i) q^{54} +(0.384149 + 10.4571i) q^{55} +(12.5568 - 0.375272i) q^{56} +(0.498534 - 0.272220i) q^{57} +(-0.111052 + 4.66520i) q^{58} +(-8.42647 - 6.00047i) q^{59} +(0.301511 - 1.31687i) q^{60} +(4.38975 - 1.51931i) q^{61} +(5.33340 - 1.98926i) q^{62} +(-5.98296 - 5.12094i) q^{63} +(8.52557 - 1.22579i) q^{64} +(5.31930 - 8.51694i) q^{65} +(1.65076 + 0.571335i) q^{66} +(8.08189 - 0.192385i) q^{67} +(15.3447 - 4.11160i) q^{68} +(0.0911553 + 0.728403i) q^{69} +(13.7632 - 4.32685i) q^{70} +(2.26106 - 0.663906i) q^{71} +(11.7044 + 7.92178i) q^{72} +(-5.90094 + 1.88633i) q^{73} +(-6.78608 + 5.33663i) q^{74} +(-0.0379743 - 0.764393i) q^{75} +(-13.3234 - 6.08458i) q^{76} +(2.41703 + 12.1432i) q^{77} +(-1.00456 - 1.34194i) q^{78} +(-15.5317 - 1.48310i) q^{79} +(-7.53217 + 3.34126i) q^{80} +(-2.07225 - 8.54192i) q^{81} +(11.0751 + 13.4135i) q^{82} +(-6.42511 + 4.80978i) q^{83} +(0.104342 - 1.59505i) q^{84} +(7.73520 - 4.60017i) q^{85} +(12.0986 + 23.4680i) q^{86} +(0.290832 + 0.0347732i) q^{87} +(-6.76571 - 21.1650i) q^{88} +(8.29079 - 1.59792i) q^{89} +(15.4058 + 5.11012i) q^{90} +(4.61064 - 10.9503i) q^{91} +(13.6278 - 13.1378i) q^{92} +(-0.0924732 - 0.345115i) q^{93} +(18.5527 - 19.4575i) q^{94} +(-8.19999 - 1.27019i) q^{95} +(-0.00371278 - 0.0779408i) q^{96} +(1.65742 + 1.24073i) q^{97} +(15.2630 - 7.64497i) q^{98} +(-5.78654 + 12.6708i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3680 q - 18 q^{2} - 18 q^{3} - 22 q^{5} - 160 q^{6} - 44 q^{7} - 56 q^{8}+O(q^{10}) $ 3680 * q - 18 * q^2 - 18 * q^3 - 22 * q^5 - 160 * q^6 - 44 * q^7 - 56 * q^8	$ 3680 q - 18 q^{2} - 18 q^{3} - 22 q^{5} - 160 q^{6} - 44 q^{7} - 56 q^{8} - 22 q^{10} - 44 q^{11} + 14 q^{12} - 72 q^{13} - 88 q^{15} - 196 q^{16} - 22 q^{17} - 62 q^{18} - 88 q^{20} - 88 q^{21} - 44 q^{23} - 30 q^{25} - 28 q^{26} - 48 q^{27} + 132 q^{28} - 22 q^{30} - 40 q^{31} - 50 q^{32} - 22 q^{33} - 40 q^{35} - 416 q^{36} - 110 q^{37} - 22 q^{38} - 22 q^{40} - 192 q^{41} - 264 q^{42} - 88 q^{43} - 44 q^{47} + 24 q^{48} - 44 q^{51} - 374 q^{52} - 22 q^{53} - 32 q^{55} - 220 q^{56} + 88 q^{57} - 58 q^{58} - 22 q^{60} - 220 q^{61} + 8 q^{62} - 44 q^{63} - 22 q^{65} - 44 q^{66} - 22 q^{67} - 96 q^{70} - 136 q^{71} - 46 q^{72} + 18 q^{73} - 34 q^{75} - 176 q^{76} - 116 q^{77} + 80 q^{78} + 176 q^{80} - 236 q^{81} - 2 q^{82} - 88 q^{83} - 448 q^{85} - 86 q^{87} - 110 q^{88} - 88 q^{90} - 228 q^{92} + 4 q^{93} - 236 q^{95} - 332 q^{96} - 88 q^{97} + 84 q^{98}+O(q^{100}) $ 3680 * q - 18 * q^2 - 18 * q^3 - 22 * q^5 - 160 * q^6 - 44 * q^7 - 56 * q^8 - 22 * q^10 - 44 * q^11 + 14 * q^12 - 72 * q^13 - 88 * q^15 - 196 * q^16 - 22 * q^17 - 62 * q^18 - 88 * q^20 - 88 * q^21 - 44 * q^23 - 30 * q^25 - 28 * q^26 - 48 * q^27 + 132 * q^28 - 22 * q^30 - 40 * q^31 - 50 * q^32 - 22 * q^33 - 40 * q^35 - 416 * q^36 - 110 * q^37 - 22 * q^38 - 22 * q^40 - 192 * q^41 - 264 * q^42 - 88 * q^43 - 44 * q^47 + 24 * q^48 - 44 * q^51 - 374 * q^52 - 22 * q^53 - 32 * q^55 - 220 * q^56 + 88 * q^57 - 58 * q^58 - 22 * q^60 - 220 * q^61 + 8 * q^62 - 44 * q^63 - 22 * q^65 - 44 * q^66 - 22 * q^67 - 96 * q^70 - 136 * q^71 - 46 * q^72 + 18 * q^73 - 34 * q^75 - 176 * q^76 - 116 * q^77 + 80 * q^78 + 176 * q^80 - 236 * q^81 - 2 * q^82 - 88 * q^83 - 448 * q^85 - 86 * q^87 - 110 * q^88 - 88 * q^90 - 228 * q^92 + 4 * q^93 - 236 * q^95 - 332 * q^96 - 88 * q^97 + 84 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/805\mathbb{Z}\right)^\times$.

$n$	$162$	$281$	$346$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	−2.08232	+	1.26924i	−1.47242	+	0.897489i	−0.472555	+	0.881301i	$0.656668\pi$
$2$	−2.08232	+	1.26924i	−1.47242	+	0.897489i	−0.999869	+	0.0161882i	$0.994847\pi$
$3$	0.0668818	+	0.137682i	0.0386142	+	0.0794908i	0.917917	−	0.396772i	$-0.129870\pi$
$3$	0.0668818	+	0.137682i	0.0386142	+	0.0794908i	−0.879303	+	0.476263i	$0.841991\pi$
$4$	1.80864	−	3.50827i	0.904319	−	1.75413i
$5$	0.447044	−	2.19092i	0.199924	−	0.979811i
$5$	0.447044	−	2.19092i	0.199924	−	0.979811i
$6$	−0.314021	−	0.201809i	−0.128199	−	0.0823883i
$7$	0.109828	−	2.64347i	0.0415109	−	0.999138i
$7$	0.109828	−	2.64347i	0.0415109	−	0.999138i
$8$	0.338730	+	4.73606i	0.119759	+	1.67445i
$9$	1.83999	−	2.33974i	0.613331	−	0.779914i
$10$	1.84992	+	5.12962i	0.584997	+	1.62213i
$11$	−4.54781	+	1.10329i	−1.37122	+	0.332654i	−0.852694	−	0.522410i	$-0.825033\pi$
$11$	−4.54781	+	1.10329i	−1.37122	+	0.332654i	−0.518523	+	0.855064i	$0.673518\pi$
$12$	0.603991	+	0.0143777i	0.174357	+	0.00415047i
$13$	4.20759	+	1.56935i	1.16698	+	0.435259i	0.856915	−	0.515458i	$-0.172378\pi$
$13$	4.20759	+	1.56935i	1.16698	+	0.435259i	0.310060	+	0.950717i	$0.399651\pi$
$14$	3.12651	+	5.64396i	0.835594	+	1.50841i
$15$	0.331550	−	0.0849832i	0.0856059	−	0.0219426i
$16$	−2.13753	−	3.00175i	−0.534383	−	0.750436i
$17$	2.70732	+	2.97815i	0.656621	+	0.722308i	0.974140	−	0.225944i	$-0.0725467\pi$
$17$	2.70732	+	2.97815i	0.656621	+	0.722308i	−0.317519	+	0.948252i	$0.602850\pi$
$18$	−0.861761	+	7.20749i	−0.203119	+	1.69882i
$19$	−0.176571	−	3.70668i	−0.0405081	−	0.850370i	−0.924109	−	0.382129i	$-0.875191\pi$
$19$	−0.176571	−	3.70668i	−0.0405081	−	0.850370i	0.883601	−	0.468241i	$-0.155112\pi$
$20$	−6.87781	−	5.53094i	−1.53793	−	1.23676i
$21$	0.371304	−	0.161679i	0.0810252	−	0.0352812i
$22$	8.06967	−	8.06967i	1.72046	−	1.72046i
$23$	4.54062	+	1.54363i	0.946784	+	0.321868i
$23$	4.54062	+	1.54363i	0.946784	+	0.321868i
$24$	−0.629416	+	0.363393i	−0.128479	+	0.0741774i
$25$	−4.60030	−	1.95888i	−0.920061	−	0.391776i
$26$	−10.7534	+	2.07256i	−2.10892	+	0.406462i
$27$	0.893910	+	0.194458i	0.172033	+	0.0374235i
$28$	−9.07537	−	5.16639i	−1.71508	−	0.976355i
$29$	1.03455	−	1.60979i	0.192111	−	0.298931i	−0.731814	−	0.681505i	$-0.761326\pi$
$29$	1.03455	−	1.60979i	0.192111	−	0.298931i	0.923925	+	0.382574i	$0.124962\pi$
$30$	−0.582530	+	0.597780i	−0.106355	+	0.109139i
$31$	−2.29202	−	0.441750i	−0.411658	−	0.0793406i	−0.0207824	−	0.999784i	$-0.506616\pi$
$31$	−2.29202	−	0.441750i	−0.411658	−	0.0793406i	−0.390876	+	0.920443i	$0.627828\pi$
$32$	−0.468612	−	0.200672i	−0.0828398	−	0.0354741i
$33$	−0.456069	−	0.552363i	−0.0793914	−	0.0961540i
$34$	−9.41750	−	2.76523i	−1.61509	−	0.474233i
$35$	−5.74255	−	1.42237i	−0.970668	−	0.240425i
$36$	−4.88056	−	10.6869i	−0.813427	−	1.78116i
$37$	3.51507	−	0.420279i	0.577875	−	0.0690934i	0.175356	−	0.984505i	$-0.443892\pi$
$37$	3.51507	−	0.420279i	0.577875	−	0.0690934i	0.402519	+	0.915412i	$0.368135\pi$
$38$	5.07235	+	7.49439i	0.822844	+	1.21575i
$39$	0.0653399	+	0.684271i	0.0104628	+	0.109571i
$40$	10.5278	+	1.37509i	1.66459	+	0.217422i
$41$	−1.01513	−	7.06036i	−0.158536	−	1.10264i	−0.901333	−	0.433127i	$-0.857410\pi$
$41$	−1.01513	−	7.06036i	−0.158536	−	1.10264i	0.742797	−	0.669517i	$-0.233499\pi$
$42$	−0.567965	+	0.807942i	−0.0876389	+	0.124668i
$43$	0.772384	−	10.7993i	0.117787	−	1.64688i	−0.504004	−	0.863701i	$-0.668140\pi$
$43$	0.772384	−	10.7993i	0.117787	−	1.64688i	0.621792	−	0.783183i	$-0.286405\pi$
$44$	−4.35472	+	17.9504i	−0.656499	+	2.70612i
$45$	−4.30364	−	5.07726i	−0.641549	−	0.756873i
$46$	−11.4143	+	2.54882i	−1.68294	+	0.375802i
$47$	−10.6488	+	2.85335i	−1.55329	+	0.416203i	−0.930532	−	0.366210i	$-0.880655\pi$
$47$	−10.6488	+	2.85335i	−1.55329	+	0.416203i	−0.622760	+	0.782413i	$0.713989\pi$
$48$	0.270325	−	0.495062i	0.0390180	−	0.0714561i
$49$	−6.97588	−	0.580652i	−0.996554	−	0.0829503i
$50$	12.0656	−	1.75988i	1.70633	−	0.248885i
$51$	−0.228968	+	0.571934i	−0.0320619	+	0.0800867i
$52$	13.1157	−	11.9230i	1.81882	−	1.65342i
$53$	1.80109	+	1.48710i	0.247399	+	0.204269i	0.752144	−	0.658999i	$-0.229020\pi$
$53$	1.80109	+	1.48710i	0.247399	+	0.204269i	−0.504746	+	0.863268i	$0.668414\pi$
$54$	−2.10822	+	0.729663i	−0.286893	+	0.0992946i
$55$	0.384149	+	10.4571i	0.0517986	+	1.41004i
$56$	12.5568	−	0.375272i	1.67798	−	0.0501478i
$57$	0.498534	−	0.272220i	0.0660324	−	0.0360564i
$58$	−0.111052	+	4.66520i	−0.0145819	+	0.612571i
$59$	−8.42647	−	6.00047i	−1.09703	−	0.781194i	−0.119681	−	0.992812i	$-0.538187\pi$
$59$	−8.42647	−	6.00047i	−1.09703	−	0.781194i	−0.977352	+	0.211618i	$0.932127\pi$
$60$	0.301511	−	1.31687i	0.0389249	−	0.170007i
$61$	4.38975	−	1.51931i	0.562050	−	0.194528i	−0.0312459	−	0.999512i	$-0.509947\pi$
$61$	4.38975	−	1.51931i	0.562050	−	0.194528i	0.593296	+	0.804984i	$0.297826\pi$
$62$	5.33340	−	1.98926i	0.677343	−	0.252636i
$63$	−5.98296	−	5.12094i	−0.753782	−	0.645178i
$64$	8.52557	−	1.22579i	1.06570	−	0.153224i
$65$	5.31930	−	8.51694i	0.659778	−	1.05640i
$66$	1.65076	+	0.571335i	0.203195	+	0.0703265i
$67$	8.08189	−	0.192385i	0.987360	−	0.0235035i	0.472986	−	0.881070i	$-0.343176\pi$
$67$	8.08189	−	0.192385i	0.987360	−	0.0235035i	0.514374	+	0.857566i	$0.328024\pi$
$68$	15.3447	−	4.11160i	1.86082	−	0.498605i
$69$	0.0911553	+	0.728403i	0.0109738	+	0.0876894i
$70$	13.7632	−	4.32685i	1.64501	−	0.517157i
$71$	2.26106	−	0.663906i	0.268338	−	0.0787912i	−0.144795	−	0.989462i	$-0.546252\pi$
$71$	2.26106	−	0.663906i	0.268338	−	0.0787912i	0.413134	+	0.910670i	$0.364434\pi$
$72$	11.7044	+	7.92178i	1.37938	+	0.933591i
$73$	−5.90094	+	1.88633i	−0.690653	+	0.220778i	−0.629098	−	0.777326i	$-0.716576\pi$
$73$	−5.90094	+	1.88633i	−0.690653	+	0.220778i	−0.0615549	+	0.998104i	$0.519606\pi$
$74$	−6.78608	+	5.33663i	−0.788866	+	0.620371i
$75$	−0.0379743	−	0.764393i	−0.00438489	−	0.0882645i
$76$	−13.3234	−	6.08458i	−1.52830	−	0.697950i
$77$	2.41703	+	12.1432i	0.275446	+	1.38384i
$78$	−1.00456	−	1.34194i	−0.113744	−	0.151945i
$79$	−15.5317	−	1.48310i	−1.74745	−	0.166862i	−0.828176	−	0.560469i	$-0.810621\pi$
$79$	−15.5317	−	1.48310i	−1.74745	−	0.166862i	−0.919279	+	0.393607i	$0.871227\pi$
$80$	−7.53217	+	3.34126i	−0.842122	+	0.373565i
$81$	−2.07225	−	8.54192i	−0.230250	−	0.949102i
$82$	11.0751	+	13.4135i	1.22304	+	1.48127i
$83$	−6.42511	+	4.80978i	−0.705247	+	0.527942i	−0.890632	−	0.454724i	$-0.849738\pi$
$83$	−6.42511	+	4.80978i	−0.705247	+	0.527942i	0.185385	+	0.982666i	$0.440647\pi$
$84$	0.104342	−	1.59505i	0.0113846	−	0.174035i
$85$	7.73520	−	4.60017i	0.839000	−	0.498958i
$86$	12.0986	+	23.4680i	1.30463	+	2.53062i
$87$	0.290832	+	0.0347732i	0.0311805	+	0.00372808i
$88$	−6.76571	−	21.1650i	−0.721228	−	2.25620i
$89$	8.29079	−	1.59792i	0.878822	−	0.169379i	0.270167	−	0.962814i	$-0.412921\pi$
$89$	8.29079	−	1.59792i	0.878822	−	0.169379i	0.608656	+	0.793434i	$0.291709\pi$
$90$	15.4058	+	5.11012i	1.62392	+	0.538654i
$91$	4.61064	−	10.9503i	0.483326	−	1.14790i
$92$	13.6278	−	13.1378i	1.42080	−	1.36972i
$93$	−0.0924732	−	0.345115i	−0.00958902	−	0.0357867i
$94$	18.5527	−	19.4575i	1.91357	−	2.00689i
$95$	−8.19999	−	1.27019i	−0.841301	−	0.130319i
$96$	−0.00371278	−	0.0779408i	−0.000378934	−	0.00795480i
$97$	1.65742	+	1.24073i	0.168286	+	0.125977i	0.680101	−	0.733118i	$-0.261936\pi$
$97$	1.65742	+	1.24073i	0.168286	+	0.125977i	−0.511815	+	0.859095i	$0.671027\pi$
$98$	15.2630	−	7.64497i	1.54180	−	0.772258i
$99$	−5.78654	+	12.6708i	−0.581569	+	1.27346i
$100$	−15.1926	+	12.5962i	−1.51926	+	1.25962i
$101$	2.07709	−	0.831540i	0.206678	−	0.0827413i	−0.266014	−	0.963969i	$-0.585707\pi$
$101$	2.07709	−	0.831540i	0.206678	−	0.0827413i	0.472692	+	0.881228i	$0.343282\pi$
$102$	−0.249137	−	1.48157i	−0.0246683	−	0.146697i
$103$	17.2072	+	0.409608i	1.69548	+	0.0403599i	0.860352	−	0.509701i	$-0.170244\pi$
$103$	17.2072	+	0.409608i	1.69548	+	0.0403599i	0.835125	+	0.550061i	$0.185395\pi$
$104$	−6.00730	+	20.4590i	−0.589064	+	2.00617i
$105$	−0.188237	−	0.885777i	−0.0183701	−	0.0864430i
$106$	−5.63794	−	0.810614i	−0.547605	−	0.0787337i
$107$	−4.61588	−	2.24226i	−0.446234	−	0.216767i	0.200172	−	0.979761i	$-0.435850\pi$
$107$	−4.61588	−	2.24226i	−0.446234	−	0.216767i	−0.646406	+	0.762994i	$0.723729\pi$
$108$	2.29897	−	2.78437i	0.221219	−	0.267926i
$109$	−0.179906	+	3.77668i	−0.0172318	+	0.361741i	0.973739	+	0.227666i	$0.0731093\pi$
$109$	−0.179906	+	3.77668i	−0.0172318	+	0.361741i	−0.990971	+	0.134075i	$0.957194\pi$
$110$	−14.0725	−	21.2875i	−1.34176	−	2.02969i
$111$	0.292959	+	0.455854i	0.0278065	+	0.0432677i
$112$	−8.16979	+	5.32083i	−0.771972	+	0.502771i
$113$	13.8045	+	7.53781i	1.29861	+	0.709097i	0.971759	−	0.235977i	$-0.0758290\pi$
$113$	13.8045	+	7.53781i	1.29861	+	0.709097i	0.326856	+	0.945074i	$0.394011\pi$
$114$	−0.692595	+	1.19961i	−0.0648675	+	0.112354i
$115$	5.41182	−	9.25809i	0.504655	−	0.863321i
$116$	−3.77645	−	6.54101i	−0.350635	−	0.607317i
$117$	11.4138	−	6.95708i	1.05521	−	0.643182i
$118$	25.1627	+	1.79967i	2.31641	+	0.165673i
$119$	8.17000	−	6.82964i	0.748942	−	0.626072i
$120$	0.514791	+	1.54146i	0.0469938	+	0.140715i
$121$	9.68816	−	4.99460i	0.880742	−	0.454054i
$122$	−7.21251	+	8.73535i	−0.652990	+	0.790861i
$123$	0.904192	−	0.611975i	0.0815283	−	0.0551799i
$124$	−5.69521	+	7.24204i	−0.511445	+	0.650355i
$125$	−6.34829	+	9.20322i	−0.567809	+	0.823161i
$126$	18.9582	+	3.06962i	1.68893	+	0.273464i
$127$	−9.68443	−	17.7357i	−0.859354	−	1.57379i	−0.818415	−	0.574628i	$-0.805147\pi$
$127$	−9.68443	−	17.7357i	−0.859354	−	1.57379i	−0.0409394	−	0.999162i	$-0.513035\pi$
$128$	−15.4110	+	12.7244i	−1.36215	+	1.12469i
$129$	1.53853	−	0.615936i	0.135460	−	0.0542302i
$130$	−0.266444	+	24.4865i	−0.0233687	+	2.14761i
$131$	3.09344	+	4.34413i	0.270275	+	0.379548i	0.927299	−	0.374321i	$-0.122124\pi$
$131$	3.09344	+	4.34413i	0.270275	+	0.379548i	−0.657024	+	0.753870i	$0.728185\pi$
$132$	−2.76270	+	0.600989i	−0.240462	+	0.0523093i
$133$	−9.81789	+	0.0596643i	−0.851319	+	0.00517355i
$134$	−16.5849	+	10.6585i	−1.43272	+	0.920752i
$135$	0.825660	−	1.87156i	0.0710615	−	0.161078i
$136$	−13.1877	+	13.8308i	−1.13083	+	1.18598i
$137$	−15.7527	−	4.22093i	−1.34585	−	0.360618i	−0.487246	−	0.873265i	$-0.661998\pi$
$137$	−15.7527	−	4.22093i	−1.34585	−	0.360618i	−0.858600	+	0.512647i	$0.828665\pi$
$138$	−1.11433	−	1.40107i	−0.0948584	−	0.119267i
$139$		−	9.73150i		−	0.825415i	−0.910864	−	0.412707i	$-0.864583\pi$
$139$		−	9.73150i		−	0.825415i	0.910864	−	0.412707i	$-0.135417\pi$
$140$	−15.3763	+	17.5738i	−1.29953	+	1.48526i
$141$	−1.10507	−	1.27532i	−0.0930635	−	0.107401i
$142$	−3.86559	+	4.25229i	−0.324393	+	0.356845i
$143$	−20.8668	−	2.49493i	−1.74497	−	0.208636i
$144$	−10.9564	−	0.521916i	−0.913030	−	0.0434930i
$145$	−3.06444	−	2.98627i	−0.254488	−	0.247996i
$146$	9.89346	−	11.4177i	0.818788	−	0.944932i
$147$	−0.386614	−	0.999288i	−0.0318874	−	0.0824199i
$148$	4.88305	−	13.0920i	0.401384	−	1.07615i
$149$	−14.7020	+	14.0184i	−1.20444	+	1.14843i	−0.219483	+	0.975616i	$0.570437\pi$
$149$	−14.7020	+	14.0184i	−1.20444	+	1.14843i	−0.984955	+	0.172813i	$0.944714\pi$
$150$	1.04927	+	1.54351i	0.0856729	+	0.126027i
$151$	−1.20377	+	1.69045i	−0.0979610	+	0.137567i	−0.860647	−	0.509202i	$-0.829941\pi$
$151$	−1.20377	+	1.69045i	−0.0979610	+	0.137567i	0.762686	+	0.646769i	$0.223880\pi$
$152$	17.4952	−	2.09181i	1.41905	−	0.169668i
$153$	11.9496	−	0.854649i	0.966065	−	0.0690943i
$154$	−20.4457	−	22.2182i	−1.64756	−	1.79039i
$155$	−1.99247	+	4.82415i	−0.160039	+	0.387485i
$156$	2.51878	+	1.00837i	0.201664	+	0.0807341i
$157$	−16.6023	+	5.30719i	−1.32501	+	0.423560i	−0.881277	−	0.472599i	$-0.843316\pi$
$157$	−16.6023	+	5.30719i	−1.32501	+	0.423560i	−0.443733	+	0.896159i	$0.646346\pi$
$158$	34.2244	−	16.6252i	2.72275	−	1.32263i
$159$	−0.0842875	+	0.347438i	−0.00668444	+	0.0275536i
$160$	−0.649147	+	0.936986i	−0.0513195	+	0.0740752i
$161$	4.57921	−	11.8335i	0.360893	−	0.932607i
$162$	15.1568	+	15.1568i	1.19083	+	1.19083i
$163$	6.59763	+	10.8241i	0.516767	+	0.847809i	0.999611	−	0.0278972i	$-0.00888111\pi$
$163$	6.59763	+	10.8241i	0.516767	+	0.847809i	−0.482844	+	0.875706i	$0.660396\pi$
$164$	−26.6056	−	9.20830i	−2.07755	−	0.719048i
$165$	−1.41407	+	0.752283i	−0.110085	+	0.0585651i
$166$	7.27438	−	18.1705i	0.564601	−	1.41031i
$167$	−0.386499	−	1.77671i	−0.0299082	−	0.137486i	0.959772	−	0.280782i	$-0.0905936\pi$
$167$	−0.386499	−	1.77671i	−0.0299082	−	0.137486i	−0.989680	+	0.143296i	$0.954230\pi$
$168$	0.891493	+	1.70375i	0.0687802	+	0.131447i
$169$	5.41620	+	4.69317i	0.416631	+	0.361013i
$170$	−10.2684	+	19.3969i	−0.787554	+	1.48767i
$171$	−8.99756	−	6.40714i	−0.688061	−	0.489966i
$172$	−36.4900	−	22.2418i	−2.78234	−	1.69592i
$173$	−0.000378801		0.0159130i	−2.87997e−5		0.00120985i	−0.999731	−	0.0231928i	$-0.992617\pi$
$173$	−0.000378801		0.0159130i	−2.87997e−5		0.00120985i	0.999702	+	0.0244026i	$0.00776837\pi$
$174$	−0.649742	+	0.296727i	−0.0492568	+	0.0224948i
$175$	−5.68348	+	11.9456i	−0.429631	+	0.903005i
$176$	13.0329	+	11.2931i	0.982391	+	0.851247i
$177$	0.262579	−	1.56150i	0.0197366	−	0.117369i
$178$	−15.2360	+	13.8504i	−1.14198	+	1.03813i
$179$	11.4433	+	14.5514i	0.855316	+	1.08762i	0.995239	+	0.0974600i	$0.0310718\pi$
$179$	11.4433	+	14.5514i	0.855316	+	1.08762i	−0.139924	+	0.990162i	$0.544686\pi$
$180$	−25.5961	+	5.91541i	−1.90782	+	0.440909i
$181$	4.07132	−	3.52782i	0.302619	−	0.262221i	−0.490292	−	0.871558i	$-0.663110\pi$
$181$	4.07132	−	3.52782i	0.302619	−	0.262221i	0.792911	+	0.609337i	$0.208565\pi$
$182$	4.29772	+	28.6540i	0.318568	+	2.12398i
$183$	0.502776	+	0.502776i	0.0371663	+	0.0371663i
$184$	−5.77266	+	22.0275i	−0.425566	+	1.62389i
$185$	0.650593	−	7.88915i	0.0478326	−	0.580022i
$186$	0.630593	+	0.601269i	0.0462373	+	0.0440872i
$187$	−15.5981	−	10.5571i	−1.14065	−	0.772013i
$188$	−9.24958	+	42.5196i	−0.674595	+	3.10106i
$189$	0.612221	−	2.34167i	0.0445325	−	0.170331i
$190$	18.6872	−	7.76282i	1.35571	−	0.563174i
$191$	9.12799	−	6.50001i	0.660478	−	0.470325i	−0.200010	−	0.979794i	$-0.564098\pi$
$191$	9.12799	−	6.50001i	0.660478	−	0.470325i	0.860489	+	0.509469i	$0.170158\pi$
$192$	0.738975	+	1.09183i	0.0533309	+	0.0787964i
$193$	−3.65266	+	8.52976i	−0.262924	+	0.613986i	−0.997946	−	0.0640573i	$-0.979596\pi$
$193$	−3.65266	+	8.52976i	−0.262924	+	0.613986i	0.735022	+	0.678043i	$0.237172\pi$
$194$	−5.02607	−	0.479931i	−0.360851	−	0.0344571i
$195$	1.52840	+	0.162744i	0.109451	+	0.0116543i
$196$	−14.6539	+	23.4231i	−1.04671	+	1.67308i
$197$	−0.169955	+	0.455666i	−0.0121088	+	0.0324649i	−0.942863	−	0.333179i	$-0.891879\pi$
$197$	−0.169955	+	0.455666i	−0.0121088	+	0.0324649i	0.930755	+	0.365644i	$0.119151\pi$
$198$	−4.03281	−	33.7291i	−0.286599	−	2.39702i
$199$	14.9708	+	2.88539i	1.06125	+	0.204540i	0.689865	−	0.723938i	$-0.257670\pi$
$199$	14.9708	+	2.88539i	1.06125	+	0.204540i	0.371388	+	0.928478i	$0.378882\pi$
$200$	7.71911	−	22.4508i	0.545823	−	1.58751i
$201$	0.567020	+	1.09986i	0.0399945	+	0.0775785i
$202$	−3.26974	+	4.36786i	−0.230058	+	0.307321i
$203$	−4.14181	−	2.91160i	−0.290698	−	0.204354i
$204$	1.59238	+	1.83770i	0.111489	+	0.128665i
$205$	−15.9225	−	0.932224i	−1.11208	−	0.0651094i
$206$	−36.3508	+	20.9872i	−2.53268	+	1.46224i
$207$	11.9664	−	7.78362i	0.831722	−	0.540999i
$208$	−4.28307	−	15.9847i	−0.296978	−	1.10834i
$209$	4.89254	+	16.6625i	0.338424	+	1.15257i
$210$	1.51624	+	1.60555i	0.104630	+	0.110794i
$211$	−7.99148	+	5.13581i	−0.550156	+	0.353564i	−0.785999	−	0.618227i	$-0.787851\pi$
$211$	−7.99148	+	5.13581i	−0.550156	+	0.353564i	0.235843	+	0.971791i	$0.424215\pi$
$212$	8.47468	−	3.62907i	0.582043	−	0.249245i
$213$	0.242632	+	0.266904i	0.0166249	+	0.0182880i
$214$	12.4577	−	1.18957i	0.851592	−	0.0813172i
$215$	−23.3153	−	6.52001i	−1.59009	−	0.444661i
$216$	−0.618172	+	4.29948i	−0.0420613	+	0.292543i
$217$	−1.41948	+	6.01036i	−0.0963606	+	0.408010i
$218$	−4.41890	−	8.09262i	−0.299286	−	0.548101i
$219$	−0.654379	−	0.686293i	−0.0442188	−	0.0463754i
$220$	37.3812	+	17.5655i	2.52024	+	1.18426i
$221$	6.71753	+	16.7796i	0.451870	+	1.12872i
$222$	−1.18862	−	0.577398i	−0.0797753	−	0.0387524i
$223$	−5.71924	−	15.3339i	−0.382989	−	1.02683i	−0.975254	−	0.221089i	$-0.929039\pi$
$223$	−5.71924	−	15.3339i	−0.382989	−	1.02683i	0.592265	−	0.805743i	$-0.298234\pi$
$224$	−0.581936	+	1.21672i	−0.0388822	+	0.0812958i
$225$	−13.0478	+	7.15920i	−0.869853	+	0.477280i
$226$	−38.3126	+	1.82506i	−2.54852	+	0.121401i
$227$	−1.65601	−	3.40904i	−0.109913	−	0.226266i	0.837389	−	0.546608i	$-0.184081\pi$
$227$	−1.65601	−	3.40904i	−0.109913	−	0.226266i	−0.947302	+	0.320342i	$0.896202\pi$
$228$	−0.0533538	−	2.24134i	−0.00353344	−	0.148436i
$229$	−4.50952	+	7.81073i	−0.297998	+	0.516147i	−0.975678	−	0.219210i	$-0.929652\pi$
$229$	−4.50952	+	7.81073i	−0.297998	+	0.516147i	0.677680	+	0.735357i	$0.262985\pi$
$230$	0.481590	+	26.1472i	0.0317551	+	1.72410i
$231$	−1.51024	+	1.14494i	−0.0993667	+	0.0753315i
$232$	7.97450	+	4.35441i	0.523552	+	0.285881i
$233$	1.88051	−	2.77845i	0.123196	−	0.182022i	−0.761535	−	0.648124i	$-0.775554\pi$
$233$	1.88051	−	2.77845i	0.123196	−	0.182022i	0.884731	+	0.466102i	$0.154342\pi$
$234$	−14.9370	+	28.9738i	−0.976463	+	1.89407i
$235$	1.49097	+	24.6064i	0.0972604	+	1.60514i
$236$	−36.2917	+	18.7097i	−2.36239	+	1.21790i
$237$	−0.834593	−	2.23763i	−0.0542127	−	0.145350i
$238$	−8.34410	+	24.5912i	−0.540868	+	1.59401i
$239$	15.3750	+	2.21059i	0.994526	+	0.142991i	0.620315	−	0.784352i	$-0.287005\pi$
$239$	15.3750	+	2.21059i	0.994526	+	0.142991i	0.374211	+	0.927344i	$0.377914\pi$
$240$	−0.963798	−	0.813575i	−0.0622129	−	0.0525161i
$241$	21.8654	−	5.30449i	1.40848	−	0.341692i	0.541776	−	0.840523i	$-0.317752\pi$
$241$	21.8654	−	5.30449i	1.40848	−	0.341692i	0.866700	+	0.498831i	$0.166237\pi$
$242$	−13.8345	+	22.6970i	−0.889317	+	1.45902i
$243$	3.15377	−	2.60397i	0.202315	−	0.167045i
$244$	2.60933	−	18.1483i	0.167045	−	1.16183i
$245$	−4.39069	+	15.0240i	−0.280511	+	0.959851i
$246$	−1.10608	+	2.42197i	−0.0705208	+	0.154419i
$247$	5.07414	−	15.8733i	0.322860	−	1.00999i
$248$	1.31578	−	11.0048i	0.0835521	−	0.698803i
$249$	−1.09194	−	0.562936i	−0.0691991	−	0.0356746i
$250$	1.53809	−	27.2216i	0.0972771	−	1.72164i
$251$	−1.80658	−	6.15265i	−0.114030	−	0.388352i	0.882624	−	0.470079i	$-0.155775\pi$
$251$	−1.80658	−	6.15265i	−0.114030	−	0.388352i	−0.996655	+	0.0817272i	$0.973956\pi$
$252$	−28.7866	+	11.7279i	−1.81339	+	0.738788i
$253$	−22.3529	−	2.01051i	−1.40532	−	0.126400i
$254$	42.6770	+	24.6396i	2.67779	+	1.54602i
$255$	1.15071	+	0.757330i	0.0720600	+	0.0474259i
$256$	10.3061	−	29.7774i	0.644129	−	1.86109i
$257$	8.56805	−	9.42517i	0.534460	−	0.587926i	−0.411824	−	0.911264i	$-0.635108\pi$
$257$	8.56805	−	9.42517i	0.534460	−	0.587926i	0.946284	+	0.323338i	$0.104805\pi$
$258$	−2.42195	+	3.23535i	−0.150784	+	0.201424i
$259$	−0.724942	−	9.33815i	−0.0450457	−	0.580245i
$260$	−20.2590	−	34.0656i	−1.25641	−	2.11266i
$261$	−1.86293	−	5.38259i	−0.115313	−	0.333174i
$262$	−11.9553	−	5.11955i	−0.738600	−	0.316287i
$263$	7.26700	−	1.22201i	0.448103	−	0.0753521i	0.0625579	−	0.998041i	$-0.480074\pi$
$263$	7.26700	−	1.22201i	0.448103	−	0.0753521i	0.385545	+	0.922689i	$0.374014\pi$
$264$	2.46154	−	2.34707i	0.151497	−	0.144452i
$265$	4.06330	−	3.28125i	0.249606	−	0.201566i
$266$	20.3683	−	12.5855i	1.24886	−	0.771667i
$267$	0.774508	+	1.03462i	0.0473991	+	0.0633178i
$268$	13.9423	−	28.7014i	0.851660	−	1.75322i
$269$	−2.74444	−	28.7410i	−0.167331	−	1.75237i	−0.556173	−	0.831067i	$-0.687731\pi$
$269$	−2.74444	−	28.7410i	−0.167331	−	1.75237i	0.388841	−	0.921305i	$-0.372875\pi$
$270$	0.656169	+	4.94515i	0.0399332	+	0.300952i
$271$	20.6643	+	8.27272i	1.25526	+	0.502532i	0.901490	−	0.432799i	$-0.142474\pi$
$271$	20.6643	+	8.27272i	1.25526	+	0.502532i	0.353774	+	0.935331i	$0.384898\pi$
$272$	3.15267	−	14.4926i	0.191159	−	0.878742i
$273$	1.81603	−	0.0975724i	0.109911	−	0.00590535i
$274$	38.1596	−	11.2047i	2.30531	−	0.676899i
$275$	23.0825	+	3.83315i	1.39193	+	0.231148i
$276$	2.72030	+	0.997619i	0.163743	+	0.0600496i
$277$	1.72497	−	6.43766i	0.103643	−	0.386802i	−0.894545	−	0.446979i	$-0.852500\pi$
$277$	1.72497	−	6.43766i	0.103643	−	0.386802i	0.998188	+	0.0601772i	$0.0191666\pi$
$278$	12.3516	+	20.2641i	0.740801	+	1.21536i
$279$	−5.25088	+	4.54991i	−0.314362	+	0.272396i
$280$	4.79126	−	27.6789i	0.286333	−	1.65413i
$281$	7.73022	−	1.11144i	0.461146	−	0.0663028i	0.0921733	−	0.995743i	$-0.470619\pi$
$281$	7.73022	−	1.11144i	0.461146	−	0.0663028i	0.368973	+	0.929440i	$0.379710\pi$
$282$	3.91979	+	1.25302i	0.233420	+	0.0746164i
$283$	16.9661	+	14.0084i	1.00853	+	0.832713i	0.985951	−	0.167032i	$-0.0534184\pi$
$283$	16.9661	+	14.0084i	1.00853	+	0.832713i	0.0225787	+	0.999745i	$0.492812\pi$
$284$	1.76027	−	9.13316i	0.104453	−	0.541953i
$285$	−0.373547	−	1.21394i	−0.0221270	−	0.0719079i
$286$	46.6180	−	21.2897i	2.75658	−	1.25889i
$287$	−18.7754	+	1.90804i	−1.10827	+	0.112628i
$288$	−1.33176	+	0.727198i	−0.0784749	+	0.0428506i
$289$	0.0761432	−	0.797407i	0.00447901	−	0.0469063i
$290$	10.1715	+	2.32885i	0.597288	+	0.136755i
$291$	−0.0599749	+	0.311179i	−0.00351579	+	0.0182417i
$292$	−4.05493	+	24.1138i	−0.237297	+	1.41115i
$293$	−0.305270	−	1.40331i	−0.0178341	−	0.0819820i	0.967370	−	0.253369i	$-0.0815387\pi$
$293$	−0.305270	−	1.40331i	−0.0178341	−	0.0819820i	−0.985204	+	0.171387i	$0.945175\pi$
$294$	2.07339	+	1.59013i	0.120923	+	0.0927385i
$295$	−16.9136	+	15.7793i	−0.984746	+	0.918707i
$296$	3.18112	+	16.5052i	0.184899	+	0.959348i
$297$	−4.27988	+	0.101880i	−0.248344	+	0.00591168i
$298$	12.8217	−	47.8512i	0.742740	−	2.77194i
$299$	16.6826	+	13.6208i	0.964778	+	0.787709i
$300$	−2.75038	−	1.24929i	−0.158793	−	0.0721276i
$301$	−28.4629	−	3.22784i	−1.64058	−	0.186050i
$302$	0.361035	−	5.04793i	0.0207752	−	0.290476i
$303$	0.253408	+	0.230363i	0.0145579	+	0.0132340i
$304$	−10.7491	+	8.45317i	−0.616502	+	0.484823i
$305$	−1.36628	−	10.2968i	−0.0782329	−	0.589594i
$306$	−23.7981	+	16.9465i	−1.36045	+	0.968769i
$307$	−15.8566	+	1.13409i	−0.904984	+	0.0647258i	−0.516068	−	0.856547i	$-0.672605\pi$
$307$	−15.8566	+	1.13409i	−0.904984	+	0.0647258i	−0.388916	+	0.921273i	$0.627150\pi$
$308$	46.9731	+	13.4830i	2.67654	+	0.768266i
$309$	1.09445	+	2.39652i	0.0622613	+	0.136333i
$310$	−1.97405	−	12.5744i	−0.112118	−	0.714176i
$311$	−5.17737	−	21.3414i	−0.293582	−	1.21016i	−0.907248	−	0.420596i	$-0.861821\pi$
$311$	−5.17737	−	21.3414i	−0.293582	−	1.21016i	0.613666	−	0.789565i	$-0.289694\pi$
$312$	−3.21861	+	0.541237i	−0.182218	+	0.0306415i
$313$	−0.394681	−	3.30099i	−0.0223087	−	0.186583i	0.977381	−	0.211485i	$-0.0678301\pi$
$313$	−0.394681	−	3.30099i	−0.0223087	−	0.186583i	−0.999690	+	0.0249025i	$0.992072\pi$
$314$	27.8353	−	32.1236i	1.57084	−	1.81284i
$315$	−13.8942	+	10.8189i	−0.782851	+	0.609578i
$316$	−33.2944	+	51.8070i	−1.87295	+	2.91437i
$317$	9.11455	+	21.2845i	0.511924	+	1.19546i	0.954361	+	0.298656i	$0.0965383\pi$
$317$	9.11455	+	21.2845i	0.511924	+	1.19546i	−0.442437	+	0.896800i	$0.645886\pi$
$318$	−0.265469	−	0.830459i	−0.0148868	−	0.0465698i
$319$	−2.92888	+	8.46243i	−0.163986	+	0.473805i
$320$	1.12568	−	19.2269i	0.0629277	−	1.07481i
$321$		−	0.785491i		−	0.0438418i
$322$	5.48412	+	30.4532i	0.305618	+	1.69709i
$323$	10.5610	−	10.5610i	0.587631	−	0.587631i
$324$	−33.7153	−	8.17924i	−1.87307	−	0.454402i
$325$	−16.2820	−	15.4616i	−0.903164	−	0.857658i
$326$	−27.4768	−	14.1653i	−1.52180	−	0.784542i
$327$	−0.532014	+	0.227822i	−0.0294205	+	0.0125986i
$328$	33.0944	−	7.19926i	1.82734	−	0.397512i
$329$	6.37320	+	28.4633i	0.351366	+	1.56923i
$330$	1.98972	−	3.36129i	0.109530	−	0.185033i
$331$	6.54748	+	5.14900i	0.359882	+	0.283015i	0.781685	−	0.623673i	$-0.214360\pi$
$331$	6.54748	+	5.14900i	0.359882	+	0.283015i	−0.421803	+	0.906687i	$0.638603\pi$
$332$	5.25329	+	31.2402i	0.288312	+	1.71453i
$333$	5.48437	−	8.99768i	0.300542	−	0.493070i
$334$	3.05989	+	3.20912i	0.167430	+	0.175595i
$335$	3.19146	−	17.7928i	0.174368	−	0.972125i
$336$	−1.27899	−	0.768966i	−0.0697748	−	0.0419506i
$337$	1.91844	+	26.8234i	0.104504	+	1.46116i	0.731342	+	0.682011i	$0.238894\pi$
$337$	1.91844	+	26.8234i	0.104504	+	1.46116i	−0.626837	+	0.779150i	$0.715651\pi$
$338$	−17.2350	−	2.89822i	−0.937463	−	0.157642i
$339$	−0.114553	+	2.40477i	−0.00622168	+	0.130609i
$340$	−2.14846	−	35.4572i	−0.116516	−	1.92294i
$341$	10.9110	−	0.519757i	0.590866	−	0.0281464i
$342$	26.8680	+	1.92164i	1.45286	+	0.103910i
$343$	−2.30108	+	18.3768i	−0.124247	+	0.992251i
$344$	51.4080			2.77173
$345$	1.63663	+	0.125913i	0.0881130	+	0.00677895i
$346$	−0.0194087	−	0.0336169i	−0.00104342	−	0.00180725i
$347$	−0.134109	−	5.63376i	−0.00719933	−	0.302436i	−0.991814	−	0.127694i	$-0.959242\pi$
$347$	−0.134109	−	5.63376i	−0.00719933	−	0.302436i	0.984614	−	0.174742i	$-0.0559092\pi$
$348$	0.648004	−	0.957425i	0.0347367	−	0.0513234i
$349$	−13.3843	−	20.8264i	−0.716445	−	1.11481i	−0.988307	−	0.152474i	$-0.951276\pi$
$349$	−13.3843	−	20.8264i	−0.716445	−	1.11481i	0.271862	−	0.962336i	$-0.412360\pi$
$350$	−3.32706	−	32.0884i	−0.177839	−	1.71519i
$351$	3.45603	+	2.22106i	0.184469	+	0.118551i
$352$	2.35256	+	0.395602i	0.125392	+	0.0210857i
$353$	18.2708	−	12.3660i	0.972455	−	0.658176i	0.0324986	−	0.999472i	$-0.489654\pi$
$353$	18.2708	−	12.3660i	0.972455	−	0.658176i	0.939956	+	0.341295i	$0.110866\pi$
$354$	1.43514	+	3.58482i	0.0762770	+	0.190531i
$355$	−0.443777	−	5.25060i	−0.0235533	−	0.278673i
$356$	9.38911	−	31.9764i	0.497622	−	1.69475i
$357$	1.48674	+	0.668084i	0.0786868	+	0.0353587i
$358$	−42.2980	−	15.7763i	−2.23552	−	0.833805i
$359$	6.74314	+	5.30286i	0.355889	+	0.279874i	0.780056	−	0.625710i	$-0.215191\pi$
$359$	6.74314	+	5.30286i	0.355889	+	0.279874i	−0.424167	+	0.905584i	$0.639433\pi$
$360$	22.5884	−	22.1021i	1.19051	−	1.16488i
$361$	5.20567	−	0.497082i	0.273983	−	0.0261622i
$362$	−4.00014	+	12.5135i	−0.210243	+	0.657697i
$363$	1.33563	+	0.999839i	0.0701023	+	0.0524779i
$364$	−30.0775	−	35.9805i	−1.57649	−	1.88589i
$365$	1.49482	+	13.7718i	0.0782424	+	0.720848i
$366$	−1.68509	−	0.408798i	−0.0880809	−	0.0213682i
$367$	28.9649	+	7.76112i	1.51196	+	0.405127i	0.917084	−	0.398694i	$-0.130536\pi$
$367$	28.9649	+	7.76112i	1.51196	+	0.405127i	0.594871	+	0.803821i	$0.297203\pi$
$368$	−5.07215	−	16.9293i	−0.264404	−	0.882503i
$369$	−18.3873	−	10.6159i	−0.957202	−	0.552641i
$370$	8.65849	+	17.2535i	0.450133	+	0.896967i
$371$	4.12893	−	4.59780i	0.214363	−	0.238706i
$372$	−1.37801	−	0.299767i	−0.0714463	−	0.0155422i
$373$	5.75541	+	13.4402i	0.298004	+	0.695905i	0.999865	−	0.0164086i	$-0.00522326\pi$
$373$	5.75541	+	13.4402i	0.298004	+	0.695905i	−0.701862	+	0.712313i	$0.747648\pi$
$374$	45.8799	+	2.18553i	2.37239	+	0.113011i
$375$	−1.69170	−	0.258518i	−0.0873592	−	0.0133498i
$376$	−17.1207	−	49.4670i	−0.882932	−	2.55107i
$377$	6.87929	−	5.14977i	0.354301	−	0.265227i
$378$	1.69730	+	5.65316i	0.0872998	+	0.290767i
$379$	−10.5756	−	3.10528i	−0.543233	−	0.159508i	−0.00140836	−	0.999999i	$-0.500448\pi$
$379$	−10.5756	−	3.10528i	−0.543233	−	0.159508i	−0.541825	+	0.840491i	$0.682266\pi$
$380$	−19.2870	+	26.4704i	−0.989402	+	1.35791i
$381$	1.79418	−	2.51957i	0.0919185	−	0.129081i
$382$	−10.7573	+	25.1208i	−0.550393	+	1.28529i
$383$	13.5117	−	27.8150i	0.690415	−	1.42128i	−0.206218	−	0.978506i	$-0.566116\pi$
$383$	13.5117	−	27.8150i	0.690415	−	1.42128i	0.896633	−	0.442774i	$-0.146005\pi$
$384$	−2.78263	−	1.27078i	−0.142001	−	0.0648495i
$385$	27.6853	+	0.132996i	1.41097	+	0.00677810i
$386$	−3.22032	−	22.3978i	−0.163910	−	1.14002i
$387$	−23.8465	−	21.6779i	−1.21219	−	1.10195i
$388$	7.35049	−	3.57065i	0.373164	−	0.181272i
$389$	22.5118	+	21.4650i	1.14139	+	1.08832i	0.995080	+	0.0990785i	$0.0315895\pi$
$389$	22.5118	+	21.4650i	1.14139	+	1.08832i	0.146314	+	0.989238i	$0.453259\pi$
$390$	−3.38917	+	1.60102i	−0.171617	+	0.0810707i
$391$	7.69575	+	17.7017i	0.389191	+	0.895215i
$392$	0.387067	−	33.2348i	0.0195498	−	1.67861i
$393$	−0.391214	+	0.716455i	−0.0197341	+	0.0361404i
$394$	−0.224450	−	1.16456i	−0.0113076	−	0.0586695i
$395$	−10.1927	+	33.3658i	−0.512851	+	1.67882i
$396$	33.9866	+	43.2175i	1.70789	+	2.17176i
$397$	29.7505	+	9.51020i	1.49313	+	0.477303i	0.935663	−	0.352894i	$-0.114802\pi$
$397$	29.7505	+	9.51020i	1.49313	+	0.477303i	0.557470	+	0.830197i	$0.311772\pi$
$398$	−34.8363	+	12.9933i	−1.74619	+	0.651294i
$399$	−0.664853	−	1.34776i	−0.0332843	−	0.0674723i
$400$	3.95325	+	17.9961i	0.197662	+	0.899806i
$401$	1.13059	−	11.8400i	0.0564587	−	0.591263i	−0.922332	−	0.386399i	$-0.873719\pi$
$401$	1.13059	−	11.8400i	0.0564587	−	0.591263i	0.978791	−	0.204864i	$-0.0656751\pi$
$402$	−2.57671	−	1.57059i	−0.128515	−	0.0783338i
$403$	−8.95060	−	5.45568i	−0.445861	−	0.271767i
$404$	0.839432	−	8.79093i	0.0417633	−	0.437365i
$405$	−19.6411	+	0.721526i	−0.975973	+	0.0358529i
$406$	12.3201	+	0.805931i	0.611437	+	0.0399977i
$407$	−15.5222	+	5.78949i	−0.769407	+	0.286974i
$408$	−2.78627	−	0.890674i	−0.137941	−	0.0440949i
$409$	3.61660	+	4.59888i	0.178829	+	0.227400i	0.867201	−	0.497958i	$-0.165917\pi$
$409$	3.61660	+	4.59888i	0.178829	+	0.227400i	−0.688372	+	0.725358i	$0.741674\pi$
$410$	34.3391	−	18.2683i	1.69589	−	0.902209i
$411$	−0.472424	−	2.45117i	−0.0233030	−	0.120907i
$412$	32.5586	−	59.6267i	1.60405	−	2.93759i
$413$	−16.7875	+	21.6161i	−0.826060	+	1.06366i
$414$	−15.0386	+	31.3962i	−0.739107	+	1.54304i
$415$	7.66555	+	16.2271i	0.376287	+	0.796558i
$416$	−1.65680	−	1.57976i	−0.0812315	−	0.0774541i
$417$	1.33985	−	0.650861i	0.0656129	−	0.0318728i
$418$	−31.3366	−	28.4868i	−1.53272	−	1.39334i
$419$	3.03240	+	21.0908i	0.148142	+	1.03035i	0.919257	+	0.393657i	$0.128790\pi$
$419$	3.03240	+	21.0908i	0.148142	+	1.03035i	−0.771115	+	0.636696i	$0.780301\pi$
$420$	−3.44800	−	0.941664i	−0.168245	−	0.0459485i
$421$	7.76442	+	3.54589i	0.378415	+	0.172816i	0.595536	−	0.803328i	$-0.296940\pi$
$421$	7.76442	+	3.54589i	0.378415	+	0.172816i	−0.217122	+	0.976145i	$0.569667\pi$
$422$	10.1222	−	20.8375i	0.492743	−	1.01435i
$423$	−12.9177	+	30.1657i	−0.628080	+	1.46670i
$424$	−6.43293	+	9.03379i	−0.312411	+	0.438720i
$425$	−6.62065	−	19.0037i	−0.321149	−	0.921815i
$426$	−0.844003	−	0.247822i	−0.0408921	−	0.0120070i
$427$	−3.53413	−	11.7710i	−0.171029	−	0.569641i
$428$	−16.2149	+	12.1383i	−0.783777	+	0.586728i
$429$	−1.05210	−	3.03985i	−0.0507959	−	0.146765i
$430$	56.8253	−	16.0159i	2.74036	−	0.772356i
$431$	−12.0527	−	0.574140i	−0.580557	−	0.0276553i	−0.244750	−	0.969586i	$-0.578706\pi$
$431$	−12.0527	−	0.574140i	−0.580557	−	0.0276553i	−0.335807	+	0.941931i	$0.609009\pi$
$432$	−1.32705	−	3.09895i	−0.0638476	−	0.149098i
$433$	4.20004	+	0.913664i	0.201841	+	0.0439079i	0.312349	−	0.949967i	$-0.398884\pi$
$433$	4.20004	+	0.913664i	0.201841	+	0.0439079i	−0.110508	+	0.993875i	$0.535248\pi$
$434$	−4.67279	−	14.3172i	−0.224301	−	0.687246i
$435$	0.206200	−	0.621646i	0.00988654	−	0.0298056i
$436$	12.9242	+	7.46181i	0.618959	+	0.357356i
$437$	4.91998	−	17.1032i	0.235355	−	0.818156i
$438$	2.23370	+	0.598518i	0.106730	+	0.0285983i
$439$	−11.2170	−	2.72122i	−0.535359	−	0.129877i	−0.0410405	−	0.999157i	$-0.513067\pi$
$439$	−11.2170	−	2.72122i	−0.535359	−	0.129877i	−0.494319	+	0.869281i	$0.664582\pi$
$440$	−49.3955	+	5.36149i	−2.35484	+	0.255599i
$441$	−14.1941	+	15.2534i	−0.675912	+	0.726350i
$442$	−35.2854	−	26.4143i	−1.67835	−	1.25640i
$443$	−6.95174	+	21.7469i	−0.330287	+	1.03323i	0.635105	+	0.772425i	$0.280957\pi$
$443$	−6.95174	+	21.7469i	−0.330287	+	1.03323i	−0.965392	+	0.260802i	$0.916013\pi$
$444$	2.12912	−	0.203306i	0.101043	−	0.00964847i
$445$	0.205426	−	18.8788i	0.00973811	−	0.894943i
$446$	31.3717	+	24.6710i	1.48549	+	1.16821i
$447$	−2.91338	−	1.08663i	−0.137798	−	0.0513960i
$448$	−2.30400	−	22.6717i	−0.108854	−	1.07114i
$449$	4.47161	−	15.2289i	0.211028	−	0.718697i	−0.784146	−	0.620576i	$-0.786899\pi$
$449$	4.47161	−	15.2289i	0.211028	−	0.718697i	0.995175	−	0.0981205i	$-0.0312831\pi$
$450$	18.0830	−	31.4686i	0.852439	−	1.48344i
$451$	12.4062	+	30.9892i	0.584186	+	1.45923i
$452$	51.4119	−	34.7966i	2.41821	−	1.63669i
$453$	−0.313255	−	0.0526764i	−0.0147180	−	0.00247495i
$454$	7.77525	+	4.99685i	0.364910	+	0.234514i
$455$	−21.9301	−	14.9968i	−1.02810	−	0.703062i
$456$	1.45812	+	2.26888i	0.0682827	+	0.106250i
$457$	−13.5669	+	20.0450i	−0.634631	+	0.937666i	0.365346	+	0.930872i	$0.380951\pi$
$457$	−13.5669	+	20.0450i	−0.634631	+	0.937666i	−0.999977	+	0.00679449i	$0.997837\pi$
$458$	−0.523415	−	21.9881i	−0.0244576	−	1.02744i
$459$	1.84097	+	3.18866i	0.0859293	+	0.148834i
$460$	−22.6918	−	35.7307i	−1.05801	−	1.66595i
$461$	13.0091			0.605894			0.302947	−	0.953007i	$-0.402030\pi$
$461$	13.0091			0.605894			0.302947	+	0.953007i	$0.402030\pi$
$462$	1.69161	−	4.30100i	0.0787007	−	0.200101i
$463$	−20.7694	−	1.48546i	−0.965237	−	0.0690351i	−0.420186	−	0.907438i	$-0.638035\pi$
$463$	−20.7694	−	1.48546i	−0.965237	−	0.0690351i	−0.545051	+	0.838403i	$0.683490\pi$
$464$	−7.04357	+	0.335527i	−0.326990	+	0.0155764i
$465$	−0.797460	+	0.0483205i	−0.0369813	+	0.00224081i
$466$	−0.389301	+	8.17243i	−0.0180340	+	0.378581i
$467$	−12.4892	−	2.10016i	−0.577931	−	0.0971839i	−0.130415	−	0.991460i	$-0.541631\pi$
$467$	−12.4892	−	2.10016i	−0.577931	−	0.0971839i	−0.447517	+	0.894276i	$0.647691\pi$
$468$	−3.76385	−	52.6256i	−0.173984	−	2.43262i
$469$	0.379051	−	21.3854i	0.0175029	−	0.987484i
$470$	−34.3361	−	49.3460i	−1.58381	−	2.27616i
$471$	−1.84110	−	1.93089i	−0.0848334	−	0.0889707i
$472$	25.5643	−	41.9408i	1.17669	−	1.93048i
$473$	8.40212	+	49.9655i	0.386330	+	2.29742i
$474$	4.57799	+	3.60017i	0.210274	+	0.165361i
$475$	−6.44865	+	17.3977i	−0.295885	+	0.798263i
$476$	−9.18363	−	41.0149i	−0.420931	−	1.87991i
$477$	6.79343	−	1.47782i	0.311050	−	0.0676648i
$478$	−34.8215	+	14.9114i	−1.59270	+	0.682033i
$479$	−9.19780	−	4.74179i	−0.420258	−	0.216658i	0.235108	−	0.971969i	$-0.424455\pi$
$479$	−9.19780	−	4.74179i	−0.420258	−	0.216658i	−0.655366	+	0.755311i	$0.727486\pi$
$480$	−0.172422	−	0.0267085i	−0.00786996	−	0.00121907i
$481$	15.4496	+	3.74802i	0.704439	+	0.170895i
$482$	−38.7982	+	38.7982i	−1.76721	+	1.76721i
$483$	1.93552	−	0.160968i	0.0880693	−	0.00732428i
$484$		−	43.0221i		−	1.95555i
$485$	3.45928	−	3.07662i	0.157078	−	0.139702i
$486$	−3.26210	+	9.42521i	−0.147972	+	0.427536i
$487$	5.58139	+	17.4601i	0.252917	+	0.791192i	0.992941	+	0.118612i	$0.0378444\pi$
$487$	5.58139	+	17.4601i	0.252917	+	0.791192i	−0.740024	+	0.672581i	$0.765186\pi$
$488$	8.68248	+	20.2755i	0.393037	+	0.917829i
$489$	−1.04902	+	1.63231i	−0.0474385	+	0.0738157i
$490$	−9.92632	−	36.8577i	−0.448425	−	1.66506i
$491$	−15.5265	+	17.9185i	−0.700700	+	0.808651i	−0.988847	−	0.148935i	$-0.952415\pi$
$491$	−15.5265	+	17.9185i	−0.700700	+	0.808651i	0.288147	+	0.957586i	$0.406961\pi$
$492$	−0.511616	−	4.27899i	−0.0230654	−	0.192912i
$493$	7.59506	−	1.27717i	0.342064	−	0.0575209i
$494$	9.58104	+	39.4936i	0.431071	+	1.77690i
$495$	25.1738	+	18.3423i	1.13148	+	0.824423i
$496$	3.57324	+	7.82430i	0.160443	+	0.351322i
$497$	−1.50669	−	6.04995i	−0.0675843	−	0.271378i
$498$	2.98828	−	0.213726i	0.133908	−	0.00957729i
$499$	−14.6084	+	10.4026i	−0.653961	+	0.465684i	−0.858253	−	0.513226i	$-0.828450\pi$
$499$	−14.6084	+	10.4026i	−0.653961	+	0.465684i	0.204292	+	0.978910i	$0.434511\pi$
$500$	20.8056	+	38.9168i	0.930454	+	1.74041i
$501$	0.218771	−	0.172044i	0.00977397	−	0.00768634i
$502$	11.5711	+	10.5188i	0.516443	+	0.469477i
$503$	2.34914	−	32.8453i	0.104743	−	1.46450i	−0.624918	−	0.780690i	$-0.714868\pi$
$503$	2.34914	−	32.8453i	0.104743	−	1.46450i	0.729661	−	0.683809i	$-0.239678\pi$
$504$	22.2265	−	30.0703i	0.990045	−	1.33944i
$505$	−0.893293	−	4.92248i	−0.0397510	−	0.219047i
$506$	49.0979	−	24.1848i	2.18267	−	1.07514i
$507$	−0.283920	+	1.05960i	−0.0126093	+	0.0470586i
$508$	−79.7373	+	1.89810i	−3.53777	+	0.0842146i
$509$	0.476940	+	2.47460i	0.0211400	+	0.109685i	0.990966	−	0.134114i	$-0.0428187\pi$
$509$	0.476940	+	2.47460i	0.0211400	+	0.109685i	−0.969826	+	0.243798i	$0.921607\pi$
$510$	−3.35737	−	0.116483i	−0.148667	−	0.00515796i
$511$	4.33836	+	15.8061i	0.191918	+	0.699222i
$512$	7.83789	+	36.0302i	0.346389	+	1.59232i
$513$	0.562956	−	3.34777i	0.0248551	−	0.147808i
$514$	−5.87862	+	30.5012i	−0.259295	+	1.34535i
$515$	8.58979	−	37.5166i	0.378511	−	1.65318i
$516$	0.621782	−	6.51160i	0.0273724	−	0.286657i
$517$	45.2808	−	24.7252i	1.99145	−	1.08741i
$518$	13.3619	+	18.5249i	0.587090	+	0.813938i
$519$	−0.00221628	+	0.00101214i	−9.72838e−5	+	4.44280e-5i
$520$	42.1386	+	22.3076i	1.84790	+	0.978253i
$521$	0.675866	−	3.50672i	0.0296102	−	0.153632i	−0.964114	−	0.265487i	$-0.914467\pi$
$521$	0.675866	−	3.50672i	0.0296102	−	0.153632i	0.993725	+	0.111855i	$0.0356792\pi$
$522$	10.7110	+	8.84377i	0.468809	+	0.387081i
$523$	21.4627	+	6.86090i	0.938501	+	0.300006i	0.734224	−	0.678907i	$-0.237546\pi$
$523$	21.4627	+	6.86090i	0.938501	+	0.300006i	0.204276	+	0.978913i	$0.434516\pi$
$524$	20.8353	−	2.99566i	0.910194	−	0.130866i
$525$	−2.02482	+	0.0164324i	−0.0883704	+	0.000717169i
$526$	−13.5812	+	11.7682i	−0.592169	+	0.513118i
$527$	−4.88962	−	8.02193i	−0.212995	−	0.349441i
$528$	−0.683189	+	2.54970i	−0.0297320	+	0.110961i
$529$	18.2344	+	14.0180i	0.792802	+	0.609480i
$530$	−4.29640	+	11.9899i	−0.186624	+	0.520809i
$531$	−29.5442	+	8.67496i	−1.28211	+	0.376461i
$532$	−17.5477	+	34.5517i	−0.760789	+	1.49801i
$533$	6.80894	−	31.3002i	0.294928	−	1.35576i
$534$	−2.92596	−	1.17138i	−0.126619	−	0.0506905i
$535$	−6.97612	+	9.11066i	−0.301604	+	0.393888i
$536$	3.64872	+	38.2111i	0.157601	+	1.65047i
$537$	−1.23811	+	2.54877i	−0.0534286	+	0.109987i
$538$	42.1941	+	56.3647i	1.81912	+	2.43006i
$539$	32.3656	−	5.05570i	1.39409	−	0.217764i
$540$	−5.07261	−	6.28161i	−0.218290	−	0.270317i
$541$	6.29928	−	6.00635i	0.270827	−	0.258233i	−0.542479	−	0.840070i	$-0.682514\pi$
$541$	6.29928	−	6.00635i	0.270827	−	0.258233i	0.813306	+	0.581836i	$0.197666\pi$
$542$	−53.5297	+	9.00147i	−2.29930	+	0.386646i
$543$	0.758015	+	0.324601i	0.0325295	+	0.0139300i
$544$	−0.671053	−	1.93888i	−0.0287712	−	0.0831288i
$545$	8.19401	+	2.08250i	0.350993	+	0.0892046i
$546$	−3.65771	+	2.50815i	−0.156535	+	0.107339i
$547$	−13.7907	+	18.4222i	−0.589646	+	0.787675i	−0.991787	−	0.127903i	$-0.959175\pi$
$547$	−13.7907	+	18.4222i	−0.589646	+	0.787675i	0.402140	+	0.915578i	$0.368266\pi$
$548$	−43.2991	+	47.6306i	−1.84965	+	2.03468i
$549$	4.52233	−	13.0664i	0.193008	−	0.557661i
$550$	−52.9304	+	21.3154i	−2.25696	+	0.908893i
$551$	−6.14965	−	3.55050i	−0.261984	−	0.151257i
$552$	−3.41888	+	0.678449i	−0.145517	+	0.0288767i
$553$	−5.62634	+	40.8947i	−0.239256	+	1.73902i
$554$	4.57901	+	15.5947i	0.194544	+	0.662555i
$555$	1.12971	−	0.438066i	0.0479534	−	0.0185949i
$556$	−34.1407	−	17.6008i	−1.44789	−	0.746438i
$557$	−0.355522	+	2.97347i	−0.0150640	+	0.125990i	−0.998460	−	0.0554849i	$-0.982330\pi$
$557$	−0.355522	+	2.97347i	−0.0150640	+	0.125990i	0.983396	+	0.181475i	$0.0580871\pi$
$558$	5.15908	−	16.1390i	0.218401	−	0.683219i
$559$	20.1978	−	44.2271i	0.854277	−	1.87060i
$560$	8.00529	+	20.2780i	0.338285	+	0.856903i
$561$	0.410295	−	2.85366i	0.0173227	−	0.120482i
$562$	−14.6861	+	12.1259i	−0.619497	+	0.511500i
$563$	−17.9378	+	29.4288i	−0.755988	+	1.24028i	0.208983	+	0.977919i	$0.432985\pi$
$563$	−17.9378	+	29.4288i	−0.755988	+	1.24028i	−0.964971	+	0.262357i	$0.915500\pi$
$564$	−6.47282	+	1.57029i	−0.272555	+	0.0661211i
$565$	22.6860	−	26.8748i	0.954406	−	1.13063i
$566$	−53.1089	−	7.63591i	−2.23233	−	0.320961i
$567$	−22.8079	+	4.53978i	−0.957842	+	0.190653i
$568$	3.91019	+	10.4836i	0.164068	+	0.439883i
$569$	27.1580	−	14.0009i	1.13852	−	0.586950i	0.217347	−	0.976094i	$-0.430260\pi$
$569$	27.1580	−	14.0009i	1.13852	−	0.586950i	0.921177	+	0.389145i	$0.127229\pi$
$570$	2.31864	+	2.05370i	0.0971169	+	0.0860201i
$571$	−2.61642	+	5.07515i	−0.109494	+	0.212388i	−0.937216	−	0.348750i	$-0.886606\pi$
$571$	−2.61642	+	5.07515i	−0.109494	+	0.212388i	0.827722	+	0.561138i	$0.189636\pi$
$572$	−46.4933	+	68.6938i	−1.94398	+	2.87223i
$573$	1.50543	+	0.822028i	0.0628904	+	0.0343407i
$574$	36.6746	−	27.8036i	1.53077	−	1.16050i
$575$	−17.8645	−	15.9957i	−0.744999	−	0.667065i
$576$	12.8190	−	22.2031i	0.534123	−	0.925128i
$577$	0.482071	+	20.2513i	0.0200689	+	0.843073i	0.916533	+	0.399958i	$0.130975\pi$
$577$	0.482071	+	20.2513i	0.0200689	+	0.843073i	−0.896465	+	0.443115i	$0.853873\pi$
$578$	0.853548	+	1.75710i	0.0355029	+	0.0730858i
$579$	−1.41869	+	0.0675806i	−0.0589588	+	0.00280856i
$580$	−16.0191	+	5.34981i	−0.665157	+	0.222139i
$581$	12.0088	+	17.5128i	0.498211	+	0.726555i
$582$	−0.270075	−	0.724098i	−0.0111950	−	0.0300148i
$583$	−9.83172	−	4.77595i	−0.407188	−	0.197800i
$584$	−10.9326	−	27.3083i	−0.452393	−	1.13002i
$585$	−10.1400	−	28.1169i	−0.419236	−	1.16249i
$586$	2.41681	+	2.53467i	0.0998373	+	0.104706i
$587$	11.5436	+	21.1406i	0.476457	+	0.872566i	0.999791	+	0.0204387i	$0.00650628\pi$
$587$	11.5436	+	21.1406i	0.476457	+	0.872566i	−0.523334	+	0.852128i	$0.675312\pi$
$588$	−4.20502	−	0.451005i	−0.173412	−	0.0185991i
$589$	−1.23272	+	8.57377i	−0.0507934	+	0.353276i
$590$	15.1918	−	54.3250i	0.625435	−	2.23652i
$591$	−0.0741039	+	0.00707607i	−0.00304823	+	0.000291070i
$592$	−8.77516	−	9.65300i	−0.360657	−	0.396736i
$593$	25.0273	−	10.7173i	1.02775	−	0.440108i	0.187475	−	0.982269i	$-0.439970\pi$
$593$	25.0273	−	10.7173i	1.02775	−	0.440108i	0.840274	+	0.542162i	$0.182394\pi$
$594$	8.78277	−	5.64435i	0.360362	−	0.231590i
$595$	−11.3109	−	20.9530i	−0.463701	−	0.858989i
$596$	22.5895	+	76.9328i	0.925303	+	3.15129i
$597$	0.604010	+	2.25420i	0.0247205	+	0.0922581i
$598$	−52.0265	−	7.18860i	−2.12752	−	0.293964i
$599$	−32.1729	+	18.5750i	−1.31455	+	0.758956i	−0.982846	−	0.184428i	$-0.940957\pi$
$599$	−32.1729	+	18.5750i	−1.31455	+	0.758956i	−0.331704	+	0.943384i	$0.607623\pi$
$600$	3.60735	−	0.438771i	0.147269	−	0.0179127i
$601$	−18.7664	−	21.6575i	−0.765496	−	0.883430i	0.230477	−	0.973078i	$-0.425971\pi$
$601$	−18.7664	−	21.6575i	−0.765496	−	0.883430i	−0.995974	+	0.0896478i	$0.971426\pi$
$602$	63.3659	−	29.4049i	2.58260	−	1.19845i
$603$	14.4205	−	19.2635i	0.587248	−	0.784471i
$604$	3.75338	+	7.28055i	0.152723	+	0.296241i
$605$	−6.61175	−	23.4588i	−0.268806	−	0.953738i
$606$	−0.820062	−	0.158054i	−0.0333127	−	0.00642051i
$607$	3.39736	+	28.4144i	0.137895	+	1.15331i	0.877265	+	0.480007i	$0.159366\pi$
$607$	3.39736	+	28.4144i	0.137895	+	1.15331i	−0.739370	+	0.673299i	$0.764877\pi$
$608$	−0.661082	+	1.77243i	−0.0268104	+	0.0718815i
$609$	0.123863	−	0.764987i	0.00501920	−	0.0309988i
$610$	15.9142	+	19.7072i	0.644346	+	0.797919i
$611$	−49.2838	−	4.70603i	−1.99381	−	0.190386i
$612$	18.6141	−	43.4680i	0.752430	−	1.75709i
$613$	24.6154	+	36.3693i	0.994208	+	1.46894i	0.879706	+	0.475518i	$0.157739\pi$
$613$	24.6154	+	36.3693i	0.994208	+	1.46894i	0.114502	+	0.993423i	$0.463473\pi$
$614$	31.5791	−	22.4874i	1.27443	−	0.907518i
$615$	−0.936578	−	2.25460i	−0.0377665	−	0.0909141i
$616$	−56.6921	+	15.5605i	−2.28419	+	0.626949i
$617$	4.48656	−	20.6244i	0.180622	−	0.830306i	−0.794259	−	0.607579i	$-0.792141\pi$
$617$	4.48656	−	20.6244i	0.180622	−	0.830306i	0.974881	−	0.222727i	$-0.0714957\pi$
$618$	−5.32077	−	3.60120i	−0.214033	−	0.144861i
$619$	−6.44977	−	6.14984i	−0.259238	−	0.247183i	0.549302	−	0.835624i	$-0.314894\pi$
$619$	−6.44977	−	6.14984i	−0.259238	−	0.247183i	−0.808540	+	0.588441i	$0.799742\pi$
$620$	13.3208	+	15.7153i	0.534975	+	0.631141i
$621$	3.75873	+	2.26282i	0.150833	+	0.0908040i
$622$	37.8684	+	37.8684i	1.51838	+	1.51838i
$623$	−3.31350	−	22.0920i	−0.132752	−	0.885096i
$624$	1.91434	−	1.65879i	0.0766350	−	0.0664046i
$625$	17.3256	+	18.0229i	0.693024	+	0.720915i
$626$	5.01160	+	6.37277i	0.200304	+	0.254707i
$627$	−1.96690	+	1.78803i	−0.0785505	+	0.0714071i
$628$	−11.4086	+	67.8442i	−0.455251	+	2.70728i
$629$	10.7681	+	9.33060i	0.429352	+	0.372035i
$630$	15.2004	−	40.1636i	0.605600	−	1.60016i
$631$	42.7223	−	19.5106i	1.70075	−	0.776705i	0.702888	−	0.711301i	$-0.251894\pi$
$631$	42.7223	−	19.5106i	1.70075	−	0.776705i	0.997859	−	0.0654043i	$-0.0208337\pi$
$632$	1.76299	−	74.0615i	0.0701281	−	2.94601i
$633$	−1.24159	−	0.756791i	−0.0493489	−	0.0300797i
$634$	−45.9946	−	32.7526i	−1.82668	−	1.30077i
$635$	−43.1870	+	13.2892i	−1.71382	+	0.527367i
$636$	1.06646	+	0.924093i	0.0422879	+	0.0366427i
$637$	−28.4404	−	13.3907i	−1.12685	−	0.530560i
$638$	−4.64201	−	21.3390i	−0.183779	−	0.844818i
$639$	2.60696	−	6.51188i	0.103130	−	0.257606i
$640$	20.9888	+	39.4526i	0.829653	+	1.55950i
$641$	−36.2469	−	12.5452i	−1.43167	−	0.495505i	−0.502311	−	0.864687i	$-0.667517\pi$
$641$	−36.2469	−	12.5452i	−1.43167	−	0.495505i	−0.929357	+	0.369182i	$0.879638\pi$
$642$	0.996977	+	1.63564i	0.0393476	+	0.0645537i
$643$	19.8812	+	19.8812i	0.784039	+	0.784039i	0.980510	−	0.196471i	$-0.0629481\pi$
$643$	19.8812	+	19.8812i	0.784039	+	0.784039i	−0.196471	+	0.980510i	$0.562948\pi$
$644$	−33.2328	−	37.4676i	−1.30956	−	1.47643i
$645$	−0.661678	−	3.64616i	−0.0260535	−	0.143568i
$646$	−8.58696	+	35.3959i	−0.337849	+	1.39263i
$647$	19.3392	−	9.39439i	0.760301	−	0.369331i	−0.0158534	−	0.999874i	$-0.505047\pi$
$647$	19.3392	−	9.39439i	0.760301	−	0.369331i	0.776154	+	0.630543i	$0.217168\pi$
$648$	39.7531	−	12.7077i	1.56165	−	0.499205i
$649$	44.9423	+	17.9922i	1.76414	+	0.706254i
$650$	53.5290	+	11.5303i	2.09958	+	0.452255i
$651$	−0.922457	+	0.206547i	−0.0361539	+	0.00809522i
$652$	49.9066	−	3.56939i	1.95449	−	0.139788i
$653$	−30.6938	+	3.66989i	−1.20114	+	0.143614i	−0.695111	−	0.718903i	$-0.744645\pi$
$653$	−30.6938	+	3.66989i	−1.20114	+	0.143614i	−0.506029	+	0.862516i	$0.668887\pi$
$654$	0.818664	−	1.14965i	0.0320123	−	0.0449550i
$655$	10.9006	−	4.83548i	0.425920	−	0.188938i
$656$	−19.0235	+	18.1389i	−0.742745	+	0.708206i
$657$	−6.44418	+	17.2775i	−0.251411	+	0.674060i
$658$	−49.3978	−	51.1805i	−1.92573	−	1.99522i
$659$	0.774394	−	0.893698i	0.0301661	−	0.0348135i	−0.740466	−	0.672094i	$-0.765395\pi$
$659$	0.774394	−	0.893698i	0.0301661	−	0.0348135i	0.770632	+	0.637280i	$0.219941\pi$
$660$	0.0816732	+	6.32154i	0.00317912	+	0.246065i
$661$	10.0978	+	0.481019i	0.392760	+	0.0187095i	0.243033	−	0.970018i	$-0.421858\pi$
$661$	10.0978	+	0.481019i	0.392760	+	0.0187095i	0.149727	+	0.988727i	$0.452161\pi$
$662$	−20.1693	−	2.41153i	−0.783902	−	0.0937269i
$663$	−1.86097	+	2.04713i	−0.0722739	+	0.0795040i
$664$	−24.9558	−	28.8005i	−0.968472	−	1.11768i
$665$	−4.25831	+	21.5369i	−0.165130	+	0.835166i
$666$			25.6971i			0.995741i
$667$	7.18241	−	5.71249i	0.278104	−	0.221189i
$668$	−6.93221	−	1.85748i	−0.268215	−	0.0718680i
$669$	1.72869	−	1.81300i	0.0668349	−	0.0700945i
$670$	15.9377	+	41.1011i	0.615729	+	1.58787i
$671$	−18.2875	+	11.7527i	−0.705983	+	0.453708i
$672$	−0.206442	+	0.00125457i	−0.00796368	+	4.83961e-5i
$673$	8.85793	−	1.92693i	0.341448	−	0.0742775i	−0.0385716	−	0.999256i	$-0.512281\pi$
$673$	8.85793	−	1.92693i	0.341448	−	0.0742775i	0.380020	+	0.924978i	$0.375917\pi$
$674$	−38.0401	−	53.4199i	−1.46525	−	2.05766i
$675$	−3.73134	−	2.64563i	−0.143619	−	0.101830i
$676$	26.2608	−	10.5133i	1.01003	−	0.404356i
$677$	−15.3737	+	12.6936i	−0.590857	+	0.487853i	−0.883539	−	0.468357i	$-0.844846\pi$
$677$	−15.3737	+	12.6936i	−0.590857	+	0.487853i	0.292682	+	0.956210i	$0.405452\pi$
$678$	−2.81370	−	5.15290i	−0.108059	−	0.197896i
$679$	3.46186	−	4.24508i	0.132854	−	0.162911i
$680$	24.4068	+	35.0761i	0.935959	+	1.34511i
$681$	0.358607	−	0.456006i	0.0137419	−	0.0174742i
$682$	−22.0606	+	14.9310i	−0.844744	+	0.571739i
$683$	9.65627	−	11.6951i	0.369487	−	0.447500i	−0.553201	−	0.833048i	$-0.686594\pi$
$683$	9.65627	−	11.6951i	0.369487	−	0.447500i	0.922688	+	0.385548i	$0.125988\pi$
$684$	−38.7513	+	19.9777i	−1.48169	+	0.763866i
$685$	−16.2899	+	32.6261i	−0.622405	+	1.24658i
$686$	−18.5329	−	41.1869i	−0.707591	−	1.57252i
$687$	−1.37700	−	0.0984852i	−0.0525359	−	0.00375744i
$688$	−34.0679	+	20.7655i	−1.29883	+	0.791675i
$689$	5.24445	+	9.08366i	0.199798	+	0.346060i
$690$	−3.56780	+	1.81508i	−0.135824	+	0.0690990i
$691$	7.49922	−	12.9890i	0.285284	−	0.494126i	−0.687394	−	0.726284i	$-0.741246\pi$
$691$	7.49922	−	12.9890i	0.285284	−	0.494126i	0.972678	+	0.232159i	$0.0745789\pi$
$692$	0.0551421	+	0.0301099i	0.00209619	+	0.00114461i
$693$	32.8592	+	16.6881i	1.24822	+	0.633930i
$694$	7.42987	+	11.5611i	0.282034	+	0.438853i
$695$	−21.3210	−	4.35041i	−0.808751	−	0.165020i
$696$	−0.0661747	+	1.38918i	−0.00250834	+	0.0526566i
$697$	18.2786	−	22.1379i	0.692350	−	0.838531i
$698$	54.3041	+	26.3793i	2.05544	+	0.998472i
$699$	0.508314	+	0.0730845i	0.0192262	+	0.00276431i
$700$	31.6291	+	41.5445i	1.19547	+	1.57023i
$701$	0.929444	−	3.16540i	0.0351046	−	0.119555i	−0.940077	−	0.340963i	$-0.889247\pi$
$701$	0.929444	−	3.16540i	0.0351046	−	0.119555i	0.975181	+	0.221408i	$0.0710651\pi$
$702$	−10.0156	−	0.238417i	−0.378016	−	0.00899845i
$703$	−2.17850	−	12.9550i	−0.0821636	−	0.488609i
$704$	−37.4203	+	14.9808i	−1.41033	+	0.564611i
$705$	−3.28814	+	1.85100i	−0.123838	+	0.0697127i
$706$	−22.3502	+	48.9400i	−0.841160	+	1.84188i
$707$	−1.97003	−	5.58204i	−0.0740906	−	0.209934i
$708$	−5.00324	−	3.74538i	−0.188033	−	0.140760i
$709$	0.956411	+	20.0775i	0.0359188	+	0.754028i	0.942944	+	0.332952i	$0.108045\pi$
$709$	0.956411	+	20.0775i	0.0359188	+	0.754028i	−0.907025	+	0.421076i	$0.861652\pi$
$710$	7.58837	+	10.3702i	0.284786	+	0.389186i
$711$	−32.0483	+	33.6113i	−1.20191	+	1.26052i
$712$	10.3762	+	38.7244i	0.388864	+	1.45126i
$713$	−9.72528	−	5.54383i	−0.364214	−	0.207618i
$714$	−3.94384	+	0.495871i	−0.147594	+	0.0185575i
$715$	−14.7946	+	44.6022i	−0.553285	+	1.66803i
$716$	71.7471	−	13.8281i	2.68131	−	0.516781i
$717$	0.723949	+	2.26471i	0.0270364	+	0.0845772i
$718$	−20.7720	−	2.48360i	−0.775204	−	0.0926870i
$719$	−8.57112	−	16.6256i	−0.319649	−	0.620032i	0.673193	−	0.739467i	$-0.264922\pi$
$719$	−8.57112	−	16.6256i	−0.319649	−	0.620032i	−0.992842	+	0.119434i	$0.961892\pi$
$720$	−6.04145	+	23.7712i	−0.225152	+	0.885902i
$721$	2.97261	−	45.4418i	0.110706	−	1.69234i
$722$	−10.2090	+	7.64234i	−0.379939	+	0.284419i
$723$	2.19273	+	2.65570i	0.0815486	+	0.0987666i
$724$	−5.01299	−	20.6638i	−0.186306	−	0.767965i
$725$	−7.91263	+	5.37897i	−0.293868	+	0.199770i
$726$	−4.05025	−	0.386752i	−0.150319	−	0.0143537i
$727$	4.43648	+	5.92644i	0.164540	+	0.219800i	0.875232	−	0.483704i	$-0.160709\pi$
$727$	4.43648	+	5.92644i	0.164540	+	0.219800i	−0.710692	+	0.703504i	$0.751618\pi$
$728$	53.4229	+	18.1271i	1.97999	+	0.671834i
$729$	−23.4167	−	10.6940i	−0.867284	−	0.396076i
$730$	−20.5924	−	26.7800i	−0.762160	−	0.991173i
$731$	34.2532	−	26.9370i	1.26690	−	0.996301i
$732$	2.67322	−	0.854534i	0.0988049	−	0.0315845i
$733$	20.8295	+	14.0978i	0.769355	+	0.520715i	0.881047	−	0.473028i	$-0.156839\pi$
$733$	20.8295	+	14.0978i	0.769355	+	0.520715i	−0.111692	+	0.993743i	$0.535627\pi$
$734$	−70.1650	+	20.6023i	−2.58984	+	0.760445i
$735$	−2.36220	+	0.400317i	−0.0871310	+	0.0147659i
$736$	−1.81803	−	1.63454i	−0.0670134	−	0.0602498i
$737$	−36.5427	+	9.79158i	−1.34607	+	0.360677i
$738$	51.7623	−	1.23217i	1.90540	−	0.0453569i
$739$	37.6391	+	13.0270i	1.38458	+	0.479207i	0.914917	−	0.403641i	$-0.132256\pi$
$739$	37.6391	+	13.0270i	1.38458	+	0.479207i	0.469659	+	0.882848i	$0.344377\pi$
$740$	−26.5006	−	16.5511i	−0.974180	−	0.608429i
$741$	2.52483	−	0.363016i	0.0927521	−	0.0133357i
$742$	−2.76203	+	14.8147i	−0.101397	+	0.543865i
$743$	−47.4945	+	17.7145i	−1.74240	+	0.649883i	−0.999803	−	0.0198531i	$-0.993680\pi$
$743$	−47.4945	+	17.7145i	−1.74240	+	0.649883i	−0.742600	+	0.669736i	$0.766407\pi$
$744$	1.60316	−	0.554859i	0.0587747	−	0.0203421i
$745$	24.1407	+	38.4779i	0.884448	+	1.40972i
$746$	−29.0434	−	20.6817i	−1.06336	−	0.757212i
$747$	−0.568523	+	23.8831i	−0.0208012	+	0.873835i
$748$	−65.2486	+	35.6284i	−2.38573	+	1.30270i
$749$	−6.43429	+	11.9557i	−0.235104	+	0.436851i
$750$	3.85079	−	1.60886i	0.140611	−	0.0587473i
$751$	−26.3838	+	9.13151i	−0.962757	+	0.333213i	−0.762831	−	0.646598i	$-0.776191\pi$
$751$	−26.3838	+	9.13151i	−0.962757	+	0.333213i	−0.199926	+	0.979811i	$0.564070\pi$
$752$	31.3273	+	25.8660i	1.14239	+	0.943235i
$753$	0.726282	−	0.660234i	0.0264672	−	0.0240603i
$754$	−7.78859	+	19.4550i	−0.283644	+	0.708508i
$755$	3.16552	+	3.39306i	0.115205	+	0.123486i
$756$	−7.10792	−	6.38306i	−0.258512	−	0.232150i
$757$	4.48654	−	8.21648i	0.163066	−	0.298633i	−0.783351	−	0.621579i	$-0.786491\pi$
$757$	4.48654	−	8.21648i	0.163066	−	0.298633i	0.946417	+	0.322946i	$0.104673\pi$
$758$	25.9632	−	6.95682i	0.943026	−	0.252683i
$759$	−1.21819	−	3.21207i	−0.0442177	−	0.116591i
$760$	3.23813	−	39.2659i	0.117459	−	1.42432i
$761$	3.77936	−	15.5787i	0.137002	−	0.564729i	−0.861385	−	0.507952i	$-0.830403\pi$
$761$	3.77936	−	15.5787i	0.137002	−	0.564729i	0.998387	−	0.0567766i	$-0.0180823\pi$
$762$	−0.538113	+	7.52380i	−0.0194938	+	0.272558i
$763$	9.96380	+	0.890359i	0.360714	+	0.0322332i
$764$	−6.29456	−	43.7796i	−0.227729	−	1.58389i
$765$	3.46950	−	26.5627i	0.125440	−	0.960375i
$766$	7.16826	+	75.0694i	0.259000	+	2.71237i
$767$	−26.0383	−	38.4716i	−0.940189	−	1.38913i
$768$	4.78911	−	0.572608i	0.172812	−	0.0206622i
$769$	−0.599313	−	1.31231i	−0.0216118	−	0.0473232i	0.898518	−	0.438936i	$-0.144645\pi$
$769$	−0.599313	−	1.31231i	−0.0216118	−	0.0473232i	−0.920130	+	0.391613i	$0.871917\pi$
$770$	−57.8185	+	34.8624i	−2.08364	+	1.25635i
$771$	1.87072	+	0.549294i	0.0673725	+	0.0197823i
$772$	23.3184	+	28.2418i	0.839246	+	1.01644i
$773$	−14.6988	−	6.29441i	−0.528680	−	0.226394i	0.112684	−	0.993631i	$-0.464055\pi$
$773$	−14.6988	−	6.29441i	−0.528680	−	0.226394i	−0.641364	+	0.767237i	$0.721631\pi$
$774$	77.1706	+	14.8734i	2.77384	+	0.534614i
$775$	9.67864	+	6.52197i	0.347667	+	0.234276i
$776$	−5.31475	+	8.26991i	−0.190788	+	0.296873i
$777$	1.23721	−	0.724365i	0.0443847	−	0.0259864i
$778$	−74.1210	−	16.1240i	−2.65737	−	0.578075i
$779$	−25.9913	+	5.00940i	−0.931233	+	0.179481i
$780$	3.33526	−	5.06768i	0.119422	−	0.181452i
$781$	−9.55038	+	5.51392i	−0.341740	+	0.197303i
$782$	−38.4928	−	27.0930i	−1.37650	−	0.968842i
$783$	1.23783	−	1.23783i	0.0442365	−	0.0442365i
$784$	13.1682	+	22.1810i	0.470293	+	0.792177i
$785$	4.20568	+	38.7470i	0.150107	+	1.38294i
$786$	−0.0947208	−	1.98843i	−0.00337858	−	0.0709251i
$787$	1.88053	−	15.7281i	0.0670336	−	0.560648i	−0.919019	−	0.394213i	$-0.871017\pi$
$787$	1.88053	−	15.7281i	0.0670336	−	0.560648i	0.986053	−	0.166434i	$-0.0532254\pi$
$788$	1.29121	+	1.42038i	0.0459975	+	0.0505990i
$789$	0.654279	+	0.918806i	0.0232929	+	0.0327104i
$790$	−21.1248	−	82.4154i	−0.751585	−	2.93221i
$791$	21.4421	−	35.6638i	0.762393	−	1.26806i
$792$	−61.9695	−	23.1134i	−2.20199	−	0.821300i
$793$	20.8546	+	0.496432i	0.740569	+	0.0176288i
$794$	−74.0208	+	17.9573i	−2.62690	+	0.637279i
$795$	0.723530	+	0.339988i	0.0256610	+	0.0120581i
$796$	37.1995	−	47.3031i	1.31850	−	1.67661i
$797$	−0.498508	−	6.97006i	−0.0176581	−	0.246892i	−0.998613	−	0.0526553i	$-0.983232\pi$
$797$	−0.498508	−	6.97006i	−0.0176581	−	0.246892i	0.980955	−	0.194237i	$-0.0622230\pi$
$798$	3.09507	+	1.96261i	0.109564	+	0.0694755i
$799$	−37.3275	−	23.9889i	−1.32055	−	0.848667i
$800$	1.76267	+	1.84110i	0.0623197	+	0.0650929i
$801$	11.5163	−	22.3385i	0.406908	−	0.789291i
$802$	12.6736	+	26.0897i	0.447521	+	0.921260i
$803$	24.7552	−	15.0891i	0.873593	−	0.532482i
$804$	4.88415			0.172251
$805$	−23.8791	−	15.3228i	−0.841628	−	0.540057i
$806$	25.5626			0.900405
$807$	3.77357	−	2.30011i	0.132836	−	0.0809678i
$808$	4.64179	+	9.55554i	0.163298	+	0.336163i
$809$	13.3830	−	25.9594i	0.470522	−	0.912685i	−0.527484	−	0.849565i	$-0.676865\pi$
$809$	13.3830	−	25.9594i	0.470522	−	0.912685i	0.998006	−	0.0631203i	$-0.0201052\pi$
$810$	39.9833	−	26.4317i	1.40487	−	0.928716i
$811$	−6.89687	−	4.43235i	−0.242182	−	0.155641i	0.413920	−	0.910313i	$-0.364159\pi$
$811$	−6.89687	−	4.43235i	−0.242182	−	0.155641i	−0.656102	+	0.754672i	$0.727796\pi$
$812$	−17.7057	+	9.26456i	−0.621349	+	0.325122i
$813$	0.243058	+	3.39839i	0.00852441	+	0.119187i
$814$	24.9740	−	31.7570i	0.875338	−	1.11308i
$815$	26.6642	−	9.61607i	0.934007	−	0.336836i
$816$	2.20623	−	0.535225i	0.0772333	−	0.0187366i
$817$	−40.1661	−	0.956131i	−1.40523	−	0.0334508i
$818$	−13.3680	−	4.98601i	−0.467402	−	0.174332i
$819$	−17.1373	−	30.9362i	−0.598825	−	1.08100i
$820$	−32.0686	+	54.1745i	−1.11988	+	1.89185i
$821$	−12.0397	−	16.9074i	−0.420188	−	0.590072i	0.549174	−	0.835708i	$-0.314943\pi$
$821$	−12.0397	−	16.9074i	−0.420188	−	0.590072i	−0.969362	+	0.245636i	$0.921003\pi$
$822$	4.09487	+	4.50451i	0.142825	+	0.157113i
$823$	0.0445231	−	0.372377i	0.00155198	−	0.0129802i	−0.992131	−	0.125207i	$-0.960041\pi$
$823$	0.0445231	−	0.372377i	0.00155198	−	0.0129802i	0.993683	+	0.112226i	$0.0357982\pi$
$824$	3.88866	+	81.6331i	0.135468	+	2.84382i
$825$	1.01604	+	3.43442i	0.0353741	+	0.119571i
$826$	7.52093	−	66.3191i	0.261687	−	2.30754i
$827$	26.7393	−	26.7393i	0.929818	−	0.929818i	−0.0678757	−	0.997694i	$-0.521622\pi$
$827$	26.7393	−	26.7393i	0.929818	−	0.929818i	0.997694	+	0.0678757i	$0.0216221\pi$
$828$	−5.66414	−	56.0591i	−0.196842	−	1.94819i
$829$	−45.4495	+	26.2403i	−1.57853	+	0.911363i	−0.583463	+	0.812140i	$0.698302\pi$
$829$	−45.4495	+	26.2403i	−1.57853	+	0.911363i	−0.995065	+	0.0992233i	$0.968364\pi$
$830$	−36.5583	−	24.0606i	−1.26896	−	0.835157i
$831$	1.00172	−	0.193066i	0.0347493	−	0.00669738i
$832$	37.7958	+	8.22197i	1.31033	+	0.285045i
$833$	−17.1567	−	22.3472i	−0.594443	−	0.774286i
$834$	−1.96391	+	3.05590i	−0.0680045	+	0.105817i
$835$	−4.06542	+	0.0525245i	−0.140690	+	0.00181768i
$836$	67.3053	+	12.9720i	2.32780	+	0.448647i
$837$	−1.96295	−	0.840586i	−0.0678496	−	0.0290549i
$838$	−33.0837	−	40.0690i	−1.14286	−	1.38416i
$839$	41.1224	+	12.0746i	1.41970	+	0.416862i	0.899403	−	0.437121i	$-0.144002\pi$
$839$	41.1224	+	12.0746i	1.41970	+	0.416862i	0.520300	+	0.853984i	$0.325820\pi$
$840$	4.13133	−	1.19154i	0.142544	−	0.0411121i
$841$	10.5259	+	23.0485i	0.362962	+	0.794776i
$842$	−20.6686	+	2.47124i	−0.712287	+	0.0851644i
$843$	0.670036	+	0.989978i	0.0230773	+	0.0340966i
$844$	3.56411	+	37.3251i	0.122682	+	1.28478i
$845$	12.7037	−	9.76845i	0.437019	−	0.336045i
$846$	−11.3887	−	79.2103i	−0.391552	−	2.72331i
$847$	−12.1390	−	26.1589i	−0.417102	−	0.898831i
$848$	0.614022	−	8.58514i	0.0210856	−	0.294815i
$849$	−0.793981	+	3.27284i	−0.0272494	+	0.112323i
$850$	37.9066	+	31.1686i	1.30019	+	1.06908i
$851$	16.6094	+	3.51763i	0.569362	+	0.120583i
$852$	1.37520	−	0.368485i	0.0471137	−	0.0126241i
$853$	26.5557	−	48.6331i	0.909249	−	1.66517i	0.176909	−	0.984227i	$-0.443390\pi$
$853$	26.5557	−	48.6331i	0.909249	−	1.66517i	0.732340	−	0.680939i	$-0.238428\pi$
$854$	22.2995	+	20.0254i	0.763073	+	0.685257i
$855$	−18.0599	+	16.8487i	−0.617634	+	0.576214i
$856$	9.05593	−	22.6206i	0.309525	−	0.773157i
$857$	5.53533	−	5.03195i	0.189083	−	0.171888i	−0.572606	−	0.819831i	$-0.694067\pi$
$857$	5.53533	−	5.03195i	0.189083	−	0.171888i	0.761689	+	0.647943i	$0.224370\pi$
$858$	6.04911	+	4.99457i	0.206513	+	0.170512i
$859$	0.962406	−	0.333092i	0.0328369	−	0.0113650i	−0.310600	−	0.950541i	$-0.600530\pi$
$859$	0.962406	−	0.333092i	0.0328369	−	0.0113650i	0.343437	+	0.939176i	$0.388409\pi$
$860$	−65.0428	+	70.0038i	−2.21794	+	2.38711i
$861$	−1.51843	−	2.45742i	−0.0517480	−	0.0837486i
$862$	25.8263	−	14.1022i	0.879646	−	0.480323i
$863$	−0.701384	+	29.4644i	−0.0238754	+	1.00298i	0.852898	+	0.522077i	$0.174843\pi$
$863$	−0.701384	+	29.4644i	−0.0238754	+	1.00298i	−0.876774	+	0.480904i	$0.840309\pi$
$864$	−0.379875	−	0.270508i	−0.0129236	−	0.00920286i
$865$	0.0346950	+	0.00794375i	0.00117966	+	0.000270096i
$866$	−9.90550	+	3.42833i	−0.336603	+	0.116499i
$867$	0.114881	−	0.0428485i	0.00390157	−	0.00145521i
$868$	18.5186	+	15.8505i	0.628564	+	0.538001i
$869$	72.2716	−	10.3911i	2.45165	−	0.352494i
$870$	0.359644	+	1.55619i	0.0121931	+	0.0527596i
$871$	34.3072	+	11.8738i	1.16245	+	0.402329i
$872$	−17.9475	+	0.427231i	−0.607780	+	0.0144679i
$873$	5.95263	−	1.59500i	0.201466	−	0.0539827i
$874$	11.4631	+	41.8590i	0.387744	+	1.41590i
$875$	23.6312	+	17.7923i	0.798881	+	0.601489i
$876$	−3.59124	+	1.05448i	−0.121337	+	0.0356276i
$877$	−22.3515	−	15.1280i	−0.754758	−	0.510835i	0.121551	−	0.992585i	$-0.461213\pi$
$877$	−22.3515	−	15.1280i	−0.754758	−	0.510835i	−0.876309	+	0.481750i	$0.840001\pi$
$878$	26.8113	−	8.57065i	0.904839	−	0.289246i
$879$	0.172793	−	0.135886i	0.00582816	−	0.00458332i
$880$	30.5685	−	23.5056i	1.03046	−	0.792373i
$881$	25.2734	+	11.5420i	0.851483	+	0.388859i	0.792847	−	0.609420i	$-0.208598\pi$
$881$	25.2734	+	11.5420i	0.851483	+	0.388859i	0.0586353	+	0.998279i	$0.481325\pi$
$882$	10.1966	−	49.7782i	0.343337	−	1.67612i
$883$	24.5842	+	32.8406i	0.827323	+	1.10517i	0.992897	+	0.118977i	$0.0379615\pi$
$883$	24.5842	+	32.8406i	0.827323	+	1.10517i	−0.165574	+	0.986197i	$0.552948\pi$
$884$	71.0168	+	6.78128i	2.38855	+	0.228079i
$885$	−3.30374	−	1.27335i	−0.111054	−	0.0428031i
$886$	−13.1263	−	54.1075i	−0.440988	−	1.81778i
$887$	7.46339	+	9.03919i	0.250596	+	0.303506i	0.881338	−	0.472486i	$-0.156643\pi$
$887$	7.46339	+	9.03919i	0.250596	+	0.303506i	−0.630742	+	0.775993i	$0.717249\pi$
$888$	−2.05972	+	1.54188i	−0.0691196	+	0.0517423i
$889$	−47.9474	+	23.6526i	−1.60811	+	0.793284i
$890$	23.5341	+	39.5726i	0.788863	+	1.32648i
$891$	18.8484	+	36.5607i	0.631444	+	1.22483i
$892$	−64.1394	−	7.66881i	−2.14755	−	0.256771i
$893$	12.4567	+	38.9680i	0.416848	+	1.30401i
$894$	7.44579	−	1.43506i	0.249025	−	0.0479955i
$895$	36.9967	−	18.5664i	1.23666	−	0.620606i
$896$	31.9439	+	42.1359i	1.06717	+	1.40766i
$897$	−0.759574	+	3.20787i	−0.0253614	+	0.107108i
$898$	10.0178	+	37.3871i	0.334299	+	1.24762i
$899$	−3.08233	+	3.23266i	−0.102801	+	0.107815i
$900$	1.51765	+	58.7236i	0.0505884	+	1.95745i
$901$	0.447300	+	9.38998i	0.0149017	+	0.312826i
$902$	−65.1666	−	48.7831i	−2.16981	−	1.62430i
$903$	−1.45924	−	4.13472i	−0.0485603	−	0.137595i
$904$	−31.0235	+	67.9320i	−1.03183	+	2.25939i
$905$	−5.90913	−	10.4970i	−0.196426	−	0.348934i
$906$	0.719157	−	0.287907i	0.0238924	−	0.00956507i
$907$	1.42778	+	8.49070i	0.0474087	+	0.281929i	0.999732	−	0.0231625i	$-0.00737352\pi$
$907$	1.42778	+	8.49070i	0.0474087	+	0.281929i	−0.952323	+	0.305092i	$0.901313\pi$
$908$	−14.9550	−	0.355994i	−0.496298	−	0.0118141i
$909$	1.87624	−	6.38988i	0.0622309	−	0.211939i
$910$	64.7001	+	3.39363i	2.14479	+	0.112498i
$911$	37.3264	+	5.36672i	1.23668	+	0.177807i	0.729468	−	0.684015i	$-0.239768\pi$
$911$	37.3264	+	5.36672i	1.23668	+	0.177807i	0.507210	+	0.861823i	$0.330677\pi$
$912$	−1.88277	−	0.914593i	−0.0623447	−	0.0302852i
$913$	23.9136	−	28.9627i	0.791425	−	0.958526i
$914$	2.80860	−	58.9598i	0.0929003	−	1.95022i
$915$	1.32631	−	0.876782i	0.0438464	−	0.0289855i
$916$	19.2460	+	29.9474i	0.635907	+	0.989490i
$917$	11.8233	−	7.70031i	0.390441	−	0.254287i
$918$	−7.88068	−	4.30318i	−0.260101	−	0.142026i
$919$	11.5287	−	19.9683i	0.380298	−	0.658695i	−0.610807	−	0.791779i	$-0.709155\pi$
$919$	11.5287	−	19.9683i	0.380298	−	0.658695i	0.991105	+	0.133085i	$0.0424882\pi$
$920$	45.6800	+	22.4947i	1.50602	+	0.741629i
$921$	−1.21666	−	2.10732i	−0.0400904	−	0.0694386i
$922$	−27.0891	+	16.5117i	−0.892133	+	0.543783i
$923$	10.5555	+	0.754944i	0.347439	+	0.0248493i
$924$	1.28528	+	7.36912i	0.0422824	+	0.242426i
$925$	−16.9937	−	4.95219i	−0.558749	−	0.162827i
$926$	45.1340	−	23.2682i	1.48320	−	0.764641i
$927$	32.6195	−	39.5067i	1.07137	−	1.29757i
$928$	−0.807842	+	0.546763i	−0.0265187	+	0.0179484i
$929$	−18.3453	+	23.3280i	−0.601890	+	0.765366i	−0.987555	−	0.157273i	$-0.949730\pi$
$929$	−18.3453	+	23.3280i	−0.601890	+	0.765366i	0.385665	+	0.922639i	$0.373972\pi$
$930$	1.59924	−	1.11279i	0.0524411	−	0.0364898i
$931$	−0.920554	+	25.9599i	−0.0301699	+	0.850800i
$932$	−6.34638	−	11.6225i	−0.207883	−	0.380708i
$933$	2.59206	−	2.14019i	0.0848602	−	0.0700665i
$934$	28.6722	−	11.4786i	0.938182	−	0.375591i
$935$	−30.1029	+	29.4549i	−0.984471	+	0.963277i
$936$	36.8154	+	51.6999i	1.20335	+	1.68986i
$937$	−25.0439	+	5.44798i	−0.818150	+	0.177978i	−0.602116	−	0.798408i	$-0.705676\pi$
$937$	−25.0439	+	5.44798i	−0.818150	+	0.177978i	−0.216034	+	0.976386i	$0.569312\pi$
$938$	26.3539	+	45.0123i	0.860485	+	1.46970i
$939$	0.428090	−	0.275117i	0.0139702	−	0.00897809i
$940$	89.0224	+	39.2733i	2.90359	+	1.28095i
$941$	27.8452	−	29.2032i	0.907727	−	0.951996i	−0.0913125	−	0.995822i	$-0.529106\pi$
$941$	27.8452	−	29.2032i	0.907727	−	0.951996i	0.999039	+	0.0438260i	$0.0139547\pi$
$942$	6.28453	+	1.68393i	0.204761	+	0.0548655i
$943$	6.28925	−	33.6254i	0.204806	−	1.09499i
$944$			38.1203i			1.24071i
$945$	−4.85673	−	2.38816i	−0.157989	−	0.0776868i
$946$	−80.9143	−	93.3800i	−2.63075	−	3.03605i
$947$	16.8623	−	18.5491i	0.547950	−	0.602765i	−0.401818	−	0.915719i	$-0.631622\pi$
$947$	16.8623	−	18.5491i	0.547950	−	0.602765i	0.949768	+	0.312954i	$0.101319\pi$
$948$	−9.35969	−	1.11909i	−0.303989	−	0.0363463i
$949$	−27.7890	−	1.32376i	−0.902071	−	0.0429709i
$950$	−8.65375	−	44.4126i	−0.280765	−	1.44093i
$951$	−2.32089	+	2.67845i	−0.0752602	+	0.0868549i
$952$	35.1130	+	36.3802i	1.13802	+	1.17909i
$953$	8.58522	−	23.0179i	0.278103	−	0.745622i	−0.720534	−	0.693420i	$-0.756103\pi$
$953$	8.58522	−	23.0179i	0.278103	−	0.745622i	0.998637	−	0.0522021i	$-0.0166240\pi$
$954$	−12.2704	+	11.6998i	−0.397269	+	0.378795i
$955$	−10.1604	−	22.9045i	−0.328784	−	0.741173i
$956$	35.5632	−	49.9415i	1.15019	−	1.61522i
$957$	−1.36101	+	0.162729i	−0.0439954	+	0.00526029i
$958$	25.1713	−	1.80028i	0.813246	−	0.0581645i
$959$	−12.8880	+	41.1783i	−0.416175	+	1.32972i
$960$	2.72248	−	1.13094i	0.0878677	−	0.0365010i
$961$	−23.7212	−	9.49654i	−0.765200	−	0.306340i
$962$	−36.9281	+	11.8046i	−1.19061	+	0.380596i
$963$	−13.7395	+	6.67424i	−0.442749	+	0.215074i
$964$	20.9370	−	86.3037i	0.674337	−	2.77965i
$965$	17.0552	+	11.8159i	0.549025	+	0.380366i
$966$	−3.82607	+	2.79183i	−0.123102	+	0.0898257i
$967$	−8.15168	−	8.15168i	−0.262140	−	0.262140i	0.563783	−	0.825923i	$-0.309346\pi$
$967$	−8.15168	−	8.15168i	−0.262140	−	0.262140i	−0.825923	+	0.563783i	$0.809346\pi$
$968$	26.9364	+	44.1919i	0.865768	+	1.42038i
$969$	2.16040	+	0.747723i	0.0694022	+	0.0240203i
$970$	−3.29837	+	10.7972i	−0.105904	+	0.346677i
$971$	3.91377	−	9.77612i	0.125599	−	0.313731i	−0.852220	−	0.523184i	$-0.824744\pi$
$971$	3.91377	−	9.77612i	0.125599	−	0.313731i	0.977819	+	0.209453i	$0.0671684\pi$
$972$	−3.43141	−	15.7739i	−0.110062	−	0.505949i
$973$	−25.7249	−	1.06879i	−0.824704	−	0.0342637i
$974$	−33.7833	−	29.2734i	−1.08249	−	0.937981i
$975$	1.03982	−	3.27585i	0.0333009	−	0.104911i
$976$	−13.9438	−	9.92935i	−0.446331	−	0.317831i
$977$	38.5283	+	23.4842i	1.23263	+	0.751327i	0.976542	−	0.215327i	$-0.0690818\pi$
$977$	38.5283	+	23.4842i	1.23263	+	0.751327i	0.256087	+	0.966654i	$0.417567\pi$
$978$	0.112606	−	4.73046i	0.00360074	−	0.151264i
$979$	−35.9420	+	16.4142i	−1.14871	+	0.524599i
$980$	44.7672	+	42.5768i	1.43004	+	1.36006i
$981$	8.50544	+	7.37001i	0.271558	+	0.235306i
$982$	9.58821	−	57.0190i	0.305972	−	1.81955i
$983$	38.3618	−	34.8732i	1.22355	−	1.11228i	0.233385	−	0.972384i	$-0.425020\pi$
$983$	38.3618	−	34.8732i	1.22355	−	1.11228i	0.990166	−	0.139897i	$-0.0446772\pi$
$984$	3.20463	+	4.07501i	0.102160	+	0.129907i
$985$	0.922353	+	0.576060i	0.0293886	+	0.0183548i
$986$	−14.1943	+	12.2994i	−0.452039	+	0.391694i
$987$	−3.49263	+	2.78115i	−0.111172	+	0.0885250i
$988$	−46.5105	−	46.5105i	−1.47969	−	1.47969i
$989$	20.1772	−	47.8434i	0.641599	−	1.52133i
$990$	−75.7008	−	6.24280i	−2.40593	−	0.198409i
$991$	32.0602	+	30.5694i	1.01843	+	0.971068i	0.999587	−	0.0287541i	$-0.00915398\pi$
$991$	32.0602	+	30.5694i	1.01843	+	0.971068i	0.0188407	+	0.999822i	$0.494002\pi$
$992$	0.985421	+	0.666952i	0.0312871	+	0.0211757i
$993$	−0.271017	+	1.24585i	−0.00860047	+	0.0395357i
$994$	10.8163	+	10.6856i	0.343071	+	0.338927i
$995$	13.0143	−	31.5101i	0.412581	−	0.998936i
$996$	−3.94986	+	2.81268i	−0.125156	+	0.0891233i
$997$	−22.9137	−	33.8549i	−0.725683	−	1.07220i	−0.994055	−	0.108881i	$-0.965273\pi$
$997$	−22.9137	−	33.8549i	−0.725683	−	1.07220i	0.268372	−	0.963315i	$-0.413515\pi$
$998$	17.2160	−	40.2031i	0.544962	−	1.27261i
$999$	3.22389	+	0.307844i	0.101999	+	0.00973975i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	805.2.bs.a.37.8	✓	3680
5.3	odd	4	inner	805.2.bs.a.198.85	yes	3680
7.4	even	3	inner	805.2.bs.a.382.8	yes	3680
23.5	odd	22	inner	805.2.bs.a.212.8	yes	3680
35.18	odd	12	inner	805.2.bs.a.543.8	yes	3680
115.28	even	44	inner	805.2.bs.a.373.8	yes	3680
161.74	odd	66	inner	805.2.bs.a.557.85	yes	3680
805.718	even	132	inner	805.2.bs.a.718.8	yes	3680

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
805.2.bs.a.37.8	✓	3680	1.1	even	1	trivial
805.2.bs.a.198.85	yes	3680	5.3	odd	4	inner
805.2.bs.a.212.8	yes	3680	23.5	odd	22	inner
805.2.bs.a.373.8	yes	3680	115.28	even	44	inner
805.2.bs.a.382.8	yes	3680	7.4	even	3	inner
805.2.bs.a.543.8	yes	3680	35.18	odd	12	inner
805.2.bs.a.557.85	yes	3680	161.74	odd	66	inner
805.2.bs.a.718.8	yes	3680	805.718	even	132	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:	\( N \)	\(=\)	\( 805 = 5 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	805.bs (of order \(132\), degree \(40\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.08232 + 1.26924i) q^{2} +(0.0668818 + 0.137682i) q^{3} +(1.80864 - 3.50827i) q^{4} +(0.447044 - 2.19092i) q^{5} +(-0.314021 - 0.201809i) q^{6} +(0.109828 - 2.64347i) q^{7} +(0.338730 + 4.73606i) q^{8} +(1.83999 - 2.33974i) q^{9} +O(q^{10})\)	\(q+(-2.08232 + 1.26924i) q^{2} +(0.0668818 + 0.137682i) q^{3} +(1.80864 - 3.50827i) q^{4} +(0.447044 - 2.19092i) q^{5} +(-0.314021 - 0.201809i) q^{6} +(0.109828 - 2.64347i) q^{7} +(0.338730 + 4.73606i) q^{8} +(1.83999 - 2.33974i) q^{9} +(1.84992 + 5.12962i) q^{10} +(-4.54781 + 1.10329i) q^{11} +(0.603991 + 0.0143777i) q^{12} +(4.20759 + 1.56935i) q^{13} +(3.12651 + 5.64396i) q^{14} +(0.331550 - 0.0849832i) q^{15} +(-2.13753 - 3.00175i) q^{16} +(2.70732 + 2.97815i) q^{17} +(-0.861761 + 7.20749i) q^{18} +(-0.176571 - 3.70668i) q^{19} +(-6.87781 - 5.53094i) q^{20} +(0.371304 - 0.161679i) q^{21} +(8.06967 - 8.06967i) q^{22} +(4.54062 + 1.54363i) q^{23} +(-0.629416 + 0.363393i) q^{24} +(-4.60030 - 1.95888i) q^{25} +(-10.7534 + 2.07256i) q^{26} +(0.893910 + 0.194458i) q^{27} +(-9.07537 - 5.16639i) q^{28} +(1.03455 - 1.60979i) q^{29} +(-0.582530 + 0.597780i) q^{30} +(-2.29202 - 0.441750i) q^{31} +(-0.468612 - 0.200672i) q^{32} +(-0.456069 - 0.552363i) q^{33} +(-9.41750 - 2.76523i) q^{34} +(-5.74255 - 1.42237i) q^{35} +(-4.88056 - 10.6869i) q^{36} +(3.51507 - 0.420279i) q^{37} +(5.07235 + 7.49439i) q^{38} +(0.0653399 + 0.684271i) q^{39} +(10.5278 + 1.37509i) q^{40} +(-1.01513 - 7.06036i) q^{41} +(-0.567965 + 0.807942i) q^{42} +(0.772384 - 10.7993i) q^{43} +(-4.35472 + 17.9504i) q^{44} +(-4.30364 - 5.07726i) q^{45} +(-11.4143 + 2.54882i) q^{46} +(-10.6488 + 2.85335i) q^{47} +(0.270325 - 0.495062i) q^{48} +(-6.97588 - 0.580652i) q^{49} +(12.0656 - 1.75988i) q^{50} +(-0.228968 + 0.571934i) q^{51} +(13.1157 - 11.9230i) q^{52} +(1.80109 + 1.48710i) q^{53} +(-2.10822 + 0.729663i) q^{54} +(0.384149 + 10.4571i) q^{55} +(12.5568 - 0.375272i) q^{56} +(0.498534 - 0.272220i) q^{57} +(-0.111052 + 4.66520i) q^{58} +(-8.42647 - 6.00047i) q^{59} +(0.301511 - 1.31687i) q^{60} +(4.38975 - 1.51931i) q^{61} +(5.33340 - 1.98926i) q^{62} +(-5.98296 - 5.12094i) q^{63} +(8.52557 - 1.22579i) q^{64} +(5.31930 - 8.51694i) q^{65} +(1.65076 + 0.571335i) q^{66} +(8.08189 - 0.192385i) q^{67} +(15.3447 - 4.11160i) q^{68} +(0.0911553 + 0.728403i) q^{69} +(13.7632 - 4.32685i) q^{70} +(2.26106 - 0.663906i) q^{71} +(11.7044 + 7.92178i) q^{72} +(-5.90094 + 1.88633i) q^{73} +(-6.78608 + 5.33663i) q^{74} +(-0.0379743 - 0.764393i) q^{75} +(-13.3234 - 6.08458i) q^{76} +(2.41703 + 12.1432i) q^{77} +(-1.00456 - 1.34194i) q^{78} +(-15.5317 - 1.48310i) q^{79} +(-7.53217 + 3.34126i) q^{80} +(-2.07225 - 8.54192i) q^{81} +(11.0751 + 13.4135i) q^{82} +(-6.42511 + 4.80978i) q^{83} +(0.104342 - 1.59505i) q^{84} +(7.73520 - 4.60017i) q^{85} +(12.0986 + 23.4680i) q^{86} +(0.290832 + 0.0347732i) q^{87} +(-6.76571 - 21.1650i) q^{88} +(8.29079 - 1.59792i) q^{89} +(15.4058 + 5.11012i) q^{90} +(4.61064 - 10.9503i) q^{91} +(13.6278 - 13.1378i) q^{92} +(-0.0924732 - 0.345115i) q^{93} +(18.5527 - 19.4575i) q^{94} +(-8.19999 - 1.27019i) q^{95} +(-0.00371278 - 0.0779408i) q^{96} +(1.65742 + 1.24073i) q^{97} +(15.2630 - 7.64497i) q^{98} +(-5.78654 + 12.6708i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3680 q - 18 q^{2} - 18 q^{3} - 22 q^{5} - 160 q^{6} - 44 q^{7} - 56 q^{8}+O(q^{10}) \) 3680 * q - 18 * q^2 - 18 * q^3 - 22 * q^5 - 160 * q^6 - 44 * q^7 - 56 * q^8	\( 3680 q - 18 q^{2} - 18 q^{3} - 22 q^{5} - 160 q^{6} - 44 q^{7} - 56 q^{8} - 22 q^{10} - 44 q^{11} + 14 q^{12} - 72 q^{13} - 88 q^{15} - 196 q^{16} - 22 q^{17} - 62 q^{18} - 88 q^{20} - 88 q^{21} - 44 q^{23} - 30 q^{25} - 28 q^{26} - 48 q^{27} + 132 q^{28} - 22 q^{30} - 40 q^{31} - 50 q^{32} - 22 q^{33} - 40 q^{35} - 416 q^{36} - 110 q^{37} - 22 q^{38} - 22 q^{40} - 192 q^{41} - 264 q^{42} - 88 q^{43} - 44 q^{47} + 24 q^{48} - 44 q^{51} - 374 q^{52} - 22 q^{53} - 32 q^{55} - 220 q^{56} + 88 q^{57} - 58 q^{58} - 22 q^{60} - 220 q^{61} + 8 q^{62} - 44 q^{63} - 22 q^{65} - 44 q^{66} - 22 q^{67} - 96 q^{70} - 136 q^{71} - 46 q^{72} + 18 q^{73} - 34 q^{75} - 176 q^{76} - 116 q^{77} + 80 q^{78} + 176 q^{80} - 236 q^{81} - 2 q^{82} - 88 q^{83} - 448 q^{85} - 86 q^{87} - 110 q^{88} - 88 q^{90} - 228 q^{92} + 4 q^{93} - 236 q^{95} - 332 q^{96} - 88 q^{97} + 84 q^{98}+O(q^{100}) \) 3680 * q - 18 * q^2 - 18 * q^3 - 22 * q^5 - 160 * q^6 - 44 * q^7 - 56 * q^8 - 22 * q^10 - 44 * q^11 + 14 * q^12 - 72 * q^13 - 88 * q^15 - 196 * q^16 - 22 * q^17 - 62 * q^18 - 88 * q^20 - 88 * q^21 - 44 * q^23 - 30 * q^25 - 28 * q^26 - 48 * q^27 + 132 * q^28 - 22 * q^30 - 40 * q^31 - 50 * q^32 - 22 * q^33 - 40 * q^35 - 416 * q^36 - 110 * q^37 - 22 * q^38 - 22 * q^40 - 192 * q^41 - 264 * q^42 - 88 * q^43 - 44 * q^47 + 24 * q^48 - 44 * q^51 - 374 * q^52 - 22 * q^53 - 32 * q^55 - 220 * q^56 + 88 * q^57 - 58 * q^58 - 22 * q^60 - 220 * q^61 + 8 * q^62 - 44 * q^63 - 22 * q^65 - 44 * q^66 - 22 * q^67 - 96 * q^70 - 136 * q^71 - 46 * q^72 + 18 * q^73 - 34 * q^75 - 176 * q^76 - 116 * q^77 + 80 * q^78 + 176 * q^80 - 236 * q^81 - 2 * q^82 - 88 * q^83 - 448 * q^85 - 86 * q^87 - 110 * q^88 - 88 * q^90 - 228 * q^92 + 4 * q^93 - 236 * q^95 - 332 * q^96 - 88 * q^97 + 84 * q^98

Introduction

L-functions

Modular forms

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