LMFDB - Embedded newform 690.2.w.b.217.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [690,2,Mod(7,690)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(690, base_ring=CyclotomicField(44))

chi = DirichletCharacter(H, H._module([0, 11, 38]))

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

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

chi := DirichletCharacter("690.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 690 = 2 \cdot 3 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	690.w (of order $44$, 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:	$5.50967773947$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$12$ over $\Q(\zeta_{44})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{44}]$

Embedding invariants

Embedding label			217.7
Character	$\chi$	$=$	690.217
Dual form			690.2.w.b.283.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.0713392 - 0.997452i) q^{2} +(-0.977147 + 0.212565i) q^{3} +(-0.989821 - 0.142315i) q^{4} +(-2.10209 - 0.762373i) q^{5} +(0.142315 + 0.989821i) q^{6} +(-2.42181 + 1.32241i) q^{7} +(-0.212565 + 0.977147i) q^{8} +(0.909632 - 0.415415i) q^{9} +O(q^{10})$	\(q+(0.0713392 - 0.997452i) q^{2} +(-0.977147 + 0.212565i) q^{3} +(-0.989821 - 0.142315i) q^{4} +(-2.10209 - 0.762373i) q^{5} +(0.142315 + 0.989821i) q^{6} +(-2.42181 + 1.32241i) q^{7} +(-0.212565 + 0.977147i) q^{8} +(0.909632 - 0.415415i) q^{9} +(-0.910392 + 2.04235i) q^{10} +(1.06157 + 0.919855i) q^{11} +(0.997452 - 0.0713392i) q^{12} +(-0.203857 + 0.373337i) q^{13} +(1.14627 + 2.50998i) q^{14} +(2.21611 + 0.298118i) q^{15} +(0.959493 + 0.281733i) q^{16} +(4.88142 + 3.65418i) q^{17} +(-0.349464 - 0.936950i) q^{18} +(1.15607 - 8.04065i) q^{19} +(1.97220 + 1.05377i) q^{20} +(2.08536 - 1.80698i) q^{21} +(0.993243 - 0.993243i) q^{22} +(4.06472 + 2.54521i) q^{23} -1.00000i q^{24} +(3.83758 + 3.20515i) q^{25} +(0.357843 + 0.229972i) q^{26} +(-0.800541 + 0.599278i) q^{27} +(2.58536 - 0.964288i) q^{28} +(-5.63176 + 0.809725i) q^{29} +(0.455454 - 2.18919i) q^{30} +(5.70892 - 3.66890i) q^{31} +(0.349464 - 0.936950i) q^{32} +(-1.23284 - 0.673180i) q^{33} +(3.99311 - 4.60829i) q^{34} +(6.09903 - 0.933501i) q^{35} +(-0.959493 + 0.281733i) q^{36} +(3.26096 + 1.21628i) q^{37} +(-7.93769 - 1.72674i) q^{38} +(0.119840 - 0.408138i) q^{39} +(1.19178 - 1.89200i) q^{40} +(-1.16152 + 2.54337i) q^{41} +(-1.65361 - 2.20896i) q^{42} +(-0.510219 - 2.34544i) q^{43} +(-0.919855 - 1.06157i) q^{44} +(-2.22883 + 0.179762i) q^{45} +(2.82870 - 3.87279i) q^{46} +(9.19442 + 9.19442i) q^{47} +(-0.997452 - 0.0713392i) q^{48} +(0.331909 - 0.516460i) q^{49} +(3.47076 - 3.59915i) q^{50} +(-5.54661 - 2.53305i) q^{51} +(0.254914 - 0.340525i) q^{52} +(1.38785 + 2.54165i) q^{53} +(0.540641 + 0.841254i) q^{54} +(-1.53024 - 2.74293i) q^{55} +(-0.777394 - 2.64756i) q^{56} +(0.579512 + 8.10264i) q^{57} +(0.405897 + 5.67518i) q^{58} +(-2.60440 - 8.86977i) q^{59} +(-2.15112 - 0.610469i) q^{60} +(6.21286 + 9.66741i) q^{61} +(-3.25228 - 5.95611i) q^{62} +(-1.65361 + 2.20896i) q^{63} +(-0.909632 - 0.415415i) q^{64} +(0.713149 - 0.629373i) q^{65} +(-0.759415 + 1.18167i) q^{66} +(8.61929 + 0.616464i) q^{67} +(-4.31169 - 4.31169i) q^{68} +(-4.51285 - 1.62302i) q^{69} +(-0.496022 - 6.15009i) q^{70} +(3.18033 + 3.67030i) q^{71} +(0.212565 + 0.977147i) q^{72} +(-4.25471 - 5.68363i) q^{73} +(1.44581 - 3.16589i) q^{74} +(-4.43118 - 2.31617i) q^{75} +(-2.28861 + 7.79429i) q^{76} +(-3.78734 - 0.823885i) q^{77} +(-0.398549 - 0.148651i) q^{78} +(-4.39954 + 1.29182i) q^{79} +(-1.80216 - 1.32372i) q^{80} +(0.654861 - 0.755750i) q^{81} +(2.45403 + 1.34000i) q^{82} +(-1.36418 + 3.65752i) q^{83} +(-2.32130 + 1.49181i) q^{84} +(-7.47534 - 11.4029i) q^{85} +(-2.37586 + 0.341597i) q^{86} +(5.33094 - 1.98834i) q^{87} +(-1.12449 + 0.841780i) q^{88} +(0.0406320 + 0.0261126i) q^{89} +(0.0203007 + 2.23598i) q^{90} -1.17373i q^{91} +(-3.66112 - 3.09777i) q^{92} +(-4.79857 + 4.79857i) q^{93} +(9.82692 - 8.51507i) q^{94} +(-8.56014 + 16.0208i) q^{95} +(-0.142315 + 0.989821i) q^{96} +(-0.982139 - 2.63322i) q^{97} +(-0.491466 - 0.367907i) q^{98} +(1.34776 + 0.395738i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q + 24 q^{6}+O(q^{10}) $ 240 * q + 24 * q^6	$ 240 q + 24 q^{6} - 44 q^{10} + 24 q^{16} - 44 q^{21} + 96 q^{23} + 16 q^{25} + 16 q^{26} + 44 q^{28} - 16 q^{31} + 44 q^{33} + 16 q^{35} - 24 q^{36} + 44 q^{37} - 88 q^{43} + 8 q^{46} + 96 q^{47} - 24 q^{50} - 24 q^{55} + 44 q^{57} - 16 q^{58} + 88 q^{61} + 56 q^{62} - 88 q^{65} + 132 q^{67} - 56 q^{70} + 16 q^{71} + 48 q^{73} + 24 q^{81} - 24 q^{82} + 44 q^{85} - 16 q^{87} + 44 q^{88} - 124 q^{92} + 32 q^{93} + 20 q^{95} - 24 q^{96} - 56 q^{98}+O(q^{100}) $ 240 * q + 24 * q^6 - 44 * q^10 + 24 * q^16 - 44 * q^21 + 96 * q^23 + 16 * q^25 + 16 * q^26 + 44 * q^28 - 16 * q^31 + 44 * q^33 + 16 * q^35 - 24 * q^36 + 44 * q^37 - 88 * q^43 + 8 * q^46 + 96 * q^47 - 24 * q^50 - 24 * q^55 + 44 * q^57 - 16 * q^58 + 88 * q^61 + 56 * q^62 - 88 * q^65 + 132 * q^67 - 56 * q^70 + 16 * q^71 + 48 * q^73 + 24 * q^81 - 24 * q^82 + 44 * q^85 - 16 * q^87 + 44 * q^88 - 124 * q^92 + 32 * q^93 + 20 * q^95 - 24 * q^96 - 56 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/690\mathbb{Z}\right)^\times$.

$n$	$277$	$461$	$511$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$e\left(\frac{3}{22}\right)$

Coefficient data

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

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

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

$2$	0.0713392	−	0.997452i	0.0504444	−	0.705305i
$2$	0.0713392	−	0.997452i	0.0504444	−	0.705305i
$3$	−0.977147	+	0.212565i	−0.564156	+	0.122725i
$3$	−0.977147	+	0.212565i	−0.564156	+	0.122725i
$4$	−0.989821	−	0.142315i	−0.494911	−	0.0711574i
$5$	−2.10209	−	0.762373i	−0.940084	−	0.340943i
$5$	−2.10209	−	0.762373i	−0.940084	−	0.340943i
$6$	0.142315	+	0.989821i	0.0580998	+	0.404093i
$7$	−2.42181	+	1.32241i	−0.915358	+	0.499823i	−0.866609	−	0.498988i	$-0.833705\pi$
$7$	−2.42181	+	1.32241i	−0.915358	+	0.499823i	−0.0487487	+	0.998811i	$0.515523\pi$
$8$	−0.212565	+	0.977147i	−0.0751532	+	0.345474i
$9$	0.909632	−	0.415415i	0.303211	−	0.138472i
$10$	−0.910392	+	2.04235i	−0.287891	+	0.645847i
$11$	1.06157	+	0.919855i	0.320075	+	0.277347i	0.800047	−	0.599937i	$-0.204808\pi$
$11$	1.06157	+	0.919855i	0.320075	+	0.277347i	−0.479972	+	0.877284i	$0.659353\pi$
$12$	0.997452	−	0.0713392i	0.287940	−	0.0205938i
$13$	−0.203857	+	0.373337i	−0.0565399	+	0.103545i	−0.904421	−	0.426642i	$-0.859696\pi$
$13$	−0.203857	+	0.373337i	−0.0565399	+	0.103545i	0.847881	+	0.530187i	$0.177878\pi$
$14$	1.14627	+	2.50998i	0.306353	+	0.670820i
$15$	2.21611	+	0.298118i	0.572196	+	0.0769738i
$16$	0.959493	+	0.281733i	0.239873	+	0.0704331i
$17$	4.88142	+	3.65418i	1.18392	+	0.886270i	0.995401	−	0.0958003i	$-0.0305410\pi$
$17$	4.88142	+	3.65418i	1.18392	+	0.886270i	0.188517	+	0.982070i	$0.439632\pi$
$18$	−0.349464	−	0.936950i	−0.0823695	−	0.220841i
$19$	1.15607	−	8.04065i	0.265221	−	1.84465i	−0.226640	−	0.973979i	$-0.572774\pi$
$19$	1.15607	−	8.04065i	0.265221	−	1.84465i	0.491861	−	0.870674i	$-0.336317\pi$
$20$	1.97220	+	1.05377i	0.440997	+	0.235630i
$21$	2.08536	−	1.80698i	0.455064	−	0.394315i
$22$	0.993243	−	0.993243i	0.211760	−	0.211760i
$23$	4.06472	+	2.54521i	0.847552	+	0.530713i
$23$	4.06472	+	2.54521i	0.847552	+	0.530713i
$24$		−	1.00000i		−	0.204124i
$25$	3.83758	+	3.20515i	0.767515	+	0.641031i
$26$	0.357843	+	0.229972i	0.0701787	+	0.0451011i
$27$	−0.800541	+	0.599278i	−0.154064	+	0.115331i
$28$	2.58536	−	0.964288i	0.488586	−	0.182233i
$29$	−5.63176	+	0.809725i	−1.04579	+	0.150362i	−0.643732	−	0.765251i	$-0.722615\pi$
$29$	−5.63176	+	0.809725i	−1.04579	+	0.150362i	−0.402060	+	0.915613i	$0.631706\pi$
$30$	0.455454	−	2.18919i	0.0831541	−	0.399690i
$31$	5.70892	−	3.66890i	1.02535	−	0.658954i	0.0840297	−	0.996463i	$-0.473221\pi$
$31$	5.70892	−	3.66890i	1.02535	−	0.658954i	0.941322	+	0.337510i	$0.109585\pi$
$32$	0.349464	−	0.936950i	0.0617771	−	0.165631i
$33$	−1.23284	−	0.673180i	−0.214610	−	0.117186i
$34$	3.99311	−	4.60829i	0.684813	−	0.790316i
$35$	6.09903	−	0.933501i	1.03092	−	0.157790i
$36$	−0.959493	+	0.281733i	−0.159915	+	0.0469554i
$37$	3.26096	+	1.21628i	0.536099	+	0.199955i	0.602907	−	0.797811i	$-0.294009\pi$
$37$	3.26096	+	1.21628i	0.536099	+	0.199955i	−0.0668083	+	0.997766i	$0.521282\pi$
$38$	−7.93769	−	1.72674i	−1.28766	−	0.280114i
$39$	0.119840	−	0.408138i	0.0191898	−	0.0653544i
$40$	1.19178	−	1.89200i	0.188437	−	0.299151i
$41$	−1.16152	+	2.54337i	−0.181399	+	0.397208i	−0.978386	−	0.206788i	$-0.933699\pi$
$41$	−1.16152	+	2.54337i	−0.181399	+	0.397208i	0.796987	+	0.603997i	$0.206426\pi$
$42$	−1.65361	−	2.20896i	−0.255157	−	0.340850i
$43$	−0.510219	−	2.34544i	−0.0778077	−	0.357676i	0.921738	−	0.387813i	$-0.126769\pi$
$43$	−0.510219	−	2.34544i	−0.0778077	−	0.357676i	−0.999546	+	0.0301368i	$0.990406\pi$
$44$	−0.919855	−	1.06157i	−0.138673	−	0.160038i
$45$	−2.22883	+	0.179762i	−0.332254	+	0.0267973i
$46$	2.82870	−	3.87279i	0.417069	−	0.571011i
$47$	9.19442	+	9.19442i	1.34114	+	1.34114i	0.894923	+	0.446221i	$0.147231\pi$
$47$	9.19442	+	9.19442i	1.34114	+	1.34114i	0.446221	+	0.894923i	$0.352769\pi$
$48$	−0.997452	−	0.0713392i	−0.143970	−	0.0102969i
$49$	0.331909	−	0.516460i	0.0474155	−	0.0737800i
$50$	3.47076	−	3.59915i	0.490839	−	0.508996i
$51$	−5.54661	−	2.53305i	−0.776681	−	0.354698i
$52$	0.254914	−	0.340525i	0.0353502	−	0.0472223i
$53$	1.38785	+	2.54165i	0.190635	+	0.349123i	0.955462	−	0.295113i	$-0.0953573\pi$
$53$	1.38785	+	2.54165i	0.190635	+	0.349123i	−0.764827	+	0.644236i	$0.777175\pi$
$54$	0.540641	+	0.841254i	0.0735719	+	0.114480i
$55$	−1.53024	−	2.74293i	−0.206338	−	0.369857i
$56$	−0.777394	−	2.64756i	−0.103884	−	0.353795i
$57$	0.579512	+	8.10264i	0.0767583	+	1.07322i
$58$	0.405897	+	5.67518i	0.0532968	+	0.745187i
$59$	−2.60440	−	8.86977i	−0.339064	−	1.15475i	−0.935866	−	0.352357i	$-0.885380\pi$
$59$	−2.60440	−	8.86977i	−0.339064	−	1.15475i	0.596802	−	0.802389i	$-0.296438\pi$
$60$	−2.15112	−	0.610469i	−0.277709	−	0.0788112i
$61$	6.21286	+	9.66741i	0.795476	+	1.23778i	0.967545	+	0.252700i	$0.0813184\pi$
$61$	6.21286	+	9.66741i	0.795476	+	1.23778i	−0.172069	+	0.985085i	$0.555045\pi$
$62$	−3.25228	−	5.95611i	−0.413040	−	0.756426i
$63$	−1.65361	+	2.20896i	−0.208335	+	0.278303i
$64$	−0.909632	−	0.415415i	−0.113704	−	0.0519269i
$65$	0.713149	−	0.629373i	0.0884552	−	0.0780641i
$66$	−0.759415	+	1.18167i	−0.0934775	+	0.145454i
$67$	8.61929	+	0.616464i	1.05301	+	0.0753131i	0.587098	−	0.809516i	$-0.300270\pi$
$67$	8.61929	+	0.616464i	1.05301	+	0.0753131i	0.465916	+	0.884829i	$0.345725\pi$
$68$	−4.31169	−	4.31169i	−0.522869	−	0.522869i
$69$	−4.51285	−	1.62302i	−0.543283	−	0.195389i
$70$	−0.496022	−	6.15009i	−0.0592860	−	0.735076i
$71$	3.18033	+	3.67030i	0.377436	+	0.435585i	0.912406	−	0.409287i	$-0.134222\pi$
$71$	3.18033	+	3.67030i	0.377436	+	0.435585i	−0.534970	+	0.844871i	$0.679677\pi$
$72$	0.212565	+	0.977147i	0.0250511	+	0.115158i
$73$	−4.25471	−	5.68363i	−0.497977	−	0.665219i	0.479186	−	0.877714i	$-0.340932\pi$
$73$	−4.25471	−	5.68363i	−0.497977	−	0.665219i	−0.977162	+	0.212495i	$0.931841\pi$
$74$	1.44581	−	3.16589i	0.168072	−	0.368027i
$75$	−4.43118	−	2.31617i	−0.511669	−	0.267448i
$76$	−2.28861	+	7.79429i	−0.262521	+	0.894066i
$77$	−3.78734	−	0.823885i	−0.431607	−	0.0938904i
$78$	−0.398549	−	0.148651i	−0.0451268	−	0.0168314i
$79$	−4.39954	+	1.29182i	−0.494986	+	0.145341i	−0.519692	−	0.854354i	$-0.673953\pi$
$79$	−4.39954	+	1.29182i	−0.494986	+	0.145341i	0.0247057	+	0.999695i	$0.492135\pi$
$80$	−1.80216	−	1.32372i	−0.201487	−	0.147996i
$81$	0.654861	−	0.755750i	0.0727623	−	0.0839722i
$82$	2.45403	+	1.34000i	0.271003	+	0.147979i
$83$	−1.36418	+	3.65752i	−0.149739	+	0.401464i	−0.990064	−	0.140618i	$-0.955091\pi$
$83$	−1.36418	+	3.65752i	−0.149739	+	0.401464i	0.840325	+	0.542082i	$0.182364\pi$
$84$	−2.32130	+	1.49181i	−0.253274	+	0.162770i
$85$	−7.47534	−	11.4029i	−0.810814	−	1.23682i
$86$	−2.37586	+	0.341597i	−0.256196	+	0.0368354i
$87$	5.33094	−	1.98834i	0.571536	−	0.213172i
$88$	−1.12449	+	0.841780i	−0.119871	+	0.0897340i
$89$	0.0406320	+	0.0261126i	0.00430698	+	0.00276793i	0.542793	−	0.839867i	$-0.317367\pi$
$89$	0.0406320	+	0.0261126i	0.00430698	+	0.00276793i	−0.538486	+	0.842635i	$0.681003\pi$
$90$	0.0203007	+	2.23598i	0.00213989	+	0.235693i
$91$		−	1.17373i		−	0.123041i
$92$	−3.66112	−	3.09777i	−0.381698	−	0.322965i
$93$	−4.79857	+	4.79857i	−0.497589	+	0.497589i
$94$	9.82692	−	8.51507i	1.01357	−	0.878263i
$95$	−8.56014	+	16.0208i	−0.878252	+	1.64370i
$96$	−0.142315	+	0.989821i	−0.0145249	+	0.101023i
$97$	−0.982139	−	2.63322i	−0.0997211	−	0.267363i	0.877503	−	0.479570i	$-0.159207\pi$
$97$	−0.982139	−	2.63322i	−0.0997211	−	0.267363i	−0.977225	+	0.212208i	$0.931935\pi$
$98$	−0.491466	−	0.367907i	−0.0496456	−	0.0371642i
$99$	1.34776	+	0.395738i	0.135455	+	0.0397731i
$100$	−3.34237	−	3.71867i	−0.334237	−	0.371867i
$101$	6.54239	+	14.3258i	0.650992	+	1.42547i	0.890683	+	0.454624i	$0.150226\pi$
$101$	6.54239	+	14.3258i	0.650992	+	1.42547i	−0.239691	+	0.970849i	$0.577046\pi$
$102$	−2.92229	+	5.35178i	−0.289350	+	0.529905i
$103$	17.1092	−	1.22367i	1.68582	−	0.120572i	0.804768	−	0.593590i	$-0.202290\pi$
$103$	17.1092	−	1.22367i	1.68582	−	0.120572i	0.881053	+	0.473018i	$0.156835\pi$
$104$	−0.321472	−	0.278557i	−0.0315229	−	0.0273148i
$105$	−5.76122	+	2.20861i	−0.562237	+	0.215538i
$106$	2.63418	−	1.20299i	0.255855	−	0.116845i
$107$	0.255271	−	1.17346i	0.0246779	−	0.113443i	−0.963160	−	0.268928i	$-0.913331\pi$
$107$	0.255271	−	1.17346i	0.0246779	−	0.113443i	0.987838	+	0.155486i	$0.0496942\pi$
$108$	0.877679	−	0.479249i	0.0844547	−	0.0461158i
$109$	1.13944	+	7.92495i	0.109138	+	0.759073i	0.968735	+	0.248099i	$0.0798059\pi$
$109$	1.13944	+	7.92495i	0.109138	+	0.759073i	−0.859596	+	0.510974i	$0.829285\pi$
$110$	−2.84511	+	1.33067i	−0.271270	+	0.126874i
$111$	−3.44498	−	0.495313i	−0.326983	−	0.0470130i
$112$	−2.69627	+	0.586538i	−0.254774	+	0.0554227i
$113$	−0.714937	+	9.99612i	−0.0672556	+	0.940356i	0.846056	+	0.533094i	$0.178971\pi$
$113$	−0.714937	+	9.99612i	−0.0672556	+	0.940356i	−0.913311	+	0.407262i	$0.866484\pi$
$114$	8.12334			0.760820
$115$	−6.60401	−	8.44909i	−0.615827	−	0.787882i
$116$	5.68967			0.528273
$117$	−0.0303454	+	0.424285i	−0.00280544	+	0.0392251i
$118$	−9.03297	+	1.96500i	−0.831552	+	0.180893i
$119$	−16.6542	−	2.39451i	−1.52669	−	0.219504i
$120$	−0.762373	+	2.10209i	−0.0695948	+	0.191894i
$121$	−1.28467	−	8.93506i	−0.116788	−	0.812278i
$122$	10.0860	−	5.50737i	0.913143	−	0.498614i
$123$	0.594343	−	2.73215i	0.0535901	−	0.246350i
$124$	−6.17295	+	2.81909i	−0.554347	+	0.253162i
$125$	−5.62341	−	9.66319i	−0.502973	−	0.864302i
$126$	2.08536	+	1.80698i	0.185779	+	0.160978i
$127$	−19.6301	+	1.40397i	−1.74189	+	0.124583i	−0.905718	−	0.423881i	$-0.860667\pi$
$127$	−19.6301	+	1.40397i	−1.74189	+	0.124583i	−0.836174	+	0.548464i	$0.815213\pi$
$128$	−0.479249	+	0.877679i	−0.0423600	+	0.0775766i
$129$	0.997118	+	2.18338i	0.0877913	+	0.192236i
$130$	−0.576894	−	0.756231i	−0.0505969	−	0.0663258i
$131$	−7.37918	−	2.16672i	−0.644722	−	0.189307i	−0.0570048	−	0.998374i	$-0.518155\pi$
$131$	−7.37918	−	2.16672i	−0.644722	−	0.189307i	−0.587717	+	0.809066i	$0.699973\pi$
$132$	1.12449	+	0.841780i	0.0978739	+	0.0732675i
$133$	7.83324	+	21.0017i	0.679228	+	1.82108i
$134$	1.22979	−	8.55335i	0.106237	−	0.738897i
$135$	2.13968	−	0.649426i	0.184155	−	0.0558937i
$136$	−4.60829	+	3.99311i	−0.395158	+	0.342406i
$137$	3.48169	−	3.48169i	0.297461	−	0.297461i	−0.542558	−	0.840018i	$-0.682544\pi$
$137$	3.48169	−	3.48169i	0.297461	−	0.297461i	0.840018	+	0.542558i	$0.182544\pi$
$138$	−1.94083	+	4.38556i	−0.165215	+	0.373324i
$139$		−	21.3396i		−	1.81000i	−0.425410	−	0.905001i	$-0.639870\pi$
$139$		−	21.3396i		−	1.81000i	0.425410	−	0.905001i	$-0.360130\pi$
$140$	−6.16980	+	0.0560165i	−0.521443	+	0.00473426i
$141$	−10.9387	−	7.02988i	−0.921206	−	0.592023i
$142$	3.88783	−	2.91039i	0.326260	−	0.244235i
$143$	−0.559824	+	0.208804i	−0.0468149	+	0.0174610i
$144$	0.989821	−	0.142315i	0.0824851	−	0.0118596i
$145$	12.4558	+	2.59138i	1.03440	+	0.215203i
$146$	−5.97268	+	3.83841i	−0.494302	+	0.317669i
$147$	−0.214542	+	0.575210i	−0.0176951	+	0.0474425i
$148$	−3.05468	−	1.66798i	−0.251093	−	0.137107i
$149$	10.4181	−	12.0232i	0.853487	−	0.984977i	−0.146504	−	0.989210i	$-0.546802\pi$
$149$	10.4181	−	12.0232i	0.853487	−	0.984977i	0.999991	+	0.00423317i	$0.00134746\pi$
$150$	−2.62639	+	4.25466i	−0.214444	+	0.347391i
$151$	10.6427	−	3.12498i	0.866091	−	0.254307i	0.181639	−	0.983365i	$-0.441860\pi$
$151$	10.6427	−	3.12498i	0.866091	−	0.254307i	0.684452	+	0.729058i	$0.260042\pi$
$152$	7.61116	+	2.83882i	0.617347	+	0.230258i
$153$	5.95830	+	1.29615i	0.481700	+	0.104787i
$154$	−1.09197	+	3.71891i	−0.0879936	+	0.299679i
$155$	−14.7977	+	3.36004i	−1.18858	+	0.269885i
$156$	−0.176704	+	0.386929i	−0.0141477	+	0.0309791i
$157$	7.76412	+	10.3716i	0.619644	+	0.827747i	0.995077	−	0.0991019i	$-0.0315970\pi$
$157$	7.76412	+	10.3716i	0.619644	+	0.827747i	−0.375433	+	0.926849i	$0.622506\pi$
$158$	0.974669	+	4.48048i	0.0775405	+	0.356448i
$159$	−1.89640	−	2.18856i	−0.150394	−	0.173564i
$160$	−1.44891	+	1.70313i	−0.114546	+	0.134644i
$161$	−13.2098	−	0.788797i	−1.04108	−	0.0621659i
$162$	−0.707107	−	0.707107i	−0.0555556	−	0.0555556i
$163$	−12.7139	−	0.909317i	−0.995831	−	0.0712232i	−0.436100	−	0.899898i	$-0.643641\pi$
$163$	−12.7139	−	0.909317i	−0.995831	−	0.0712232i	−0.559730	+	0.828675i	$0.689095\pi$
$164$	1.51166	−	2.35219i	0.118041	−	0.183675i
$165$	2.07832	+	2.35497i	0.161797	+	0.183334i
$166$	3.55088	+	1.62163i	0.275602	+	0.125863i
$167$	−2.94203	+	3.93009i	−0.227661	+	0.304120i	−0.899798	−	0.436308i	$-0.856286\pi$
$167$	−2.94203	+	3.93009i	−0.227661	+	0.304120i	0.672136	+	0.740427i	$0.265377\pi$
$168$	1.32241	+	2.42181i	0.102026	+	0.186847i
$169$	6.93051	+	10.7841i	0.533116	+	0.829545i
$170$	−11.9071	+	6.64282i	−0.913234	+	0.509481i
$171$	−2.28861	−	7.79429i	−0.175014	−	0.596044i
$172$	0.171235	+	2.39418i	0.0130565	+	0.182554i
$173$	1.45189	+	20.3001i	0.110385	+	1.54339i	0.687174	+	0.726493i	$0.258851\pi$
$173$	1.45189	+	20.3001i	0.110385	+	1.54339i	−0.576789	+	0.816894i	$0.695694\pi$
$174$	−1.60297	−	5.45920i	−0.121521	−	0.413861i
$175$	−13.5324	−	2.68743i	−1.02295	−	0.203151i
$176$	0.759415	+	1.18167i	0.0572431	+	0.0890719i
$177$	4.43029	+	8.11346i	0.333001	+	0.609845i
$178$	0.0289447	−	0.0386656i	0.00216950	−	0.00289811i
$179$	20.0852	+	9.17261i	1.50124	+	0.685593i	0.985269	−	0.171013i	$-0.0547041\pi$
$179$	20.0852	+	9.17261i	1.50124	+	0.685593i	0.515971	+	0.856606i	$0.327431\pi$
$180$	2.23173	+	0.139264i	0.166343	+	0.0103801i
$181$	−5.00103	+	7.78176i	−0.371724	+	0.578414i	−0.975841	−	0.218482i	$-0.929890\pi$
$181$	−5.00103	+	7.78176i	−0.371724	+	0.578414i	0.604117	+	0.796896i	$0.293526\pi$
$182$	−1.17074	−	0.0837332i	−0.0867812	−	0.00620671i
$183$	−8.12584	−	8.12584i	−0.600679	−	0.600679i
$184$	−3.35106	+	3.43080i	−0.247043	+	0.252922i
$185$	−5.92759	−	5.04279i	−0.435805	−	0.370753i
$186$	4.44402	+	5.12867i	0.325851	+	0.376052i
$187$	1.82064	+	8.36936i	0.133139	+	0.612028i
$188$	−7.79233	−	10.4093i	−0.568314	−	0.759179i
$189$	1.14627	−	2.50998i	0.0833787	−	0.182574i
$190$	15.3693	+	9.68125i	1.11501	+	0.702351i
$191$	−2.53171	+	8.62222i	−0.183188	+	0.623882i	0.815776	+	0.578369i	$0.196310\pi$
$191$	−2.53171	+	8.62222i	−0.183188	+	0.623882i	−0.998964	+	0.0455131i	$0.985508\pi$
$192$	0.977147	+	0.212565i	0.0705195	+	0.0153406i
$193$	−13.9545	−	5.20476i	−1.00447	−	0.374647i	−0.207216	−	0.978295i	$-0.566440\pi$
$193$	−13.9545	−	5.20476i	−1.00447	−	0.374647i	−0.797251	+	0.603649i	$0.793713\pi$
$194$	−2.69657	+	0.791785i	−0.193603	+	0.0568469i
$195$	−0.563068	+	0.766580i	−0.0403221	+	0.0548960i
$196$	−0.402030	+	0.463968i	−0.0287164	+	0.0331405i
$197$	−10.0511	−	5.48829i	−0.716108	−	0.391025i	0.0795010	−	0.996835i	$-0.474667\pi$
$197$	−10.0511	−	5.48829i	−0.716108	−	0.391025i	−0.795609	+	0.605810i	$0.792849\pi$
$198$	0.490877	−	1.31609i	0.0348851	−	0.0935307i
$199$	12.2869	−	7.89633i	0.870997	−	0.559756i	−0.0270606	−	0.999634i	$-0.508615\pi$
$199$	12.2869	−	7.89633i	0.870997	−	0.559756i	0.898057	+	0.439878i	$0.144978\pi$
$200$	−3.94764	+	3.06857i	−0.279140	+	0.216981i
$201$	−8.55335	+	1.22979i	−0.603307	+	0.0867425i
$202$	14.7561	−	5.50373i	1.03823	−	0.387241i
$203$	12.5683	−	9.40848i	0.882119	−	0.660346i
$204$	5.12967	+	3.29664i	0.359148	+	0.230811i
$205$	4.38062	−	4.46089i	0.305956	−	0.311562i
$206$		−	17.1529i		−	1.19510i
$207$	4.75471	+	0.626659i	0.330475	+	0.0435558i
$208$	−0.300781	+	0.300781i	−0.0208554	+	0.0208554i
$209$	8.62348	−	7.47229i	0.596499	−	0.516869i
$210$	1.79198	+	5.90410i	0.123658	+	0.407422i
$211$	−0.237553	+	1.65221i	−0.0163538	+	0.113743i	−0.996363	−	0.0852082i	$-0.972844\pi$
$211$	−0.237553	+	1.65221i	−0.0163538	+	0.113743i	0.980009	+	0.198951i	$0.0637536\pi$
$212$	−1.01201	−	2.71329i	−0.0695049	−	0.186350i
$213$	−3.88783	−	2.91039i	−0.266390	−	0.199417i
$214$	−1.15226	−	0.338334i	−0.0787668	−	0.0231280i
$215$	−0.715572	+	5.31930i	−0.0488016	+	0.362773i
$216$	−0.415415	−	0.909632i	−0.0282654	−	0.0618926i
$217$	−8.97413	+	16.4349i	−0.609203	+	1.11567i
$218$	7.98605	−	0.571174i	0.540884	−	0.0386848i
$219$	5.36562	+	4.64934i	0.362575	+	0.314173i
$220$	1.12431	+	2.93279i	0.0758008	+	0.197728i
$221$	−2.35935	+	1.07748i	−0.158707	+	0.0724792i
$222$	−0.739813	+	3.40087i	−0.0496530	+	0.228251i
$223$	−0.965561	+	0.527236i	−0.0646588	+	0.0353064i	−0.511253	−	0.859430i	$-0.670819\pi$
$223$	−0.965561	+	0.527236i	−0.0646588	+	0.0353064i	0.446594	+	0.894737i	$0.352637\pi$
$224$	0.392694	+	2.73125i	0.0262380	+	0.182489i
$225$	4.82225	+	1.32132i	0.321483	+	0.0880883i
$226$	9.91965	+	1.42623i	0.659845	+	0.0948714i
$227$	−6.23920	+	1.35726i	−0.414110	+	0.0900842i	−0.414793	−	0.909916i	$-0.636146\pi$
$227$	−6.23920	+	1.35726i	−0.414110	+	0.0900842i	0.000683157		1.00000i	$0.499783\pi$
$228$	0.579512	−	8.10264i	0.0383791	−	0.536610i
$229$	19.0008			1.25561			0.627803	−	0.778373i	$-0.283955\pi$
$229$	19.0008			1.25561			0.627803	+	0.778373i	$0.283955\pi$
$230$	−8.89869	+	5.98443i	−0.586762	+	0.394602i
$231$	3.87592			0.255017
$232$	0.405897	−	5.67518i	0.0266484	−	0.372594i
$233$	6.62813	−	1.44186i	0.434223	−	0.0944594i	0.00985959	−	0.999951i	$-0.496862\pi$
$233$	6.62813	−	1.44186i	0.434223	−	0.0944594i	0.424363	+	0.905492i	$0.360498\pi$
$234$	0.421039	+	0.0605362i	0.0275242	+	0.00395738i
$235$	−12.3179	−	26.3371i	−0.803534	−	1.71804i
$236$	1.31559	+	9.15013i	0.0856377	+	0.595623i
$237$	4.02440	−	2.19749i	0.261413	−	0.142742i
$238$	−3.57650	+	16.4409i	−0.231830	+	1.06571i
$239$	−26.6353	+	12.1639i	−1.72289	+	0.786820i	−0.728037	+	0.685538i	$0.759567\pi$
$239$	−26.6353	+	12.1639i	−1.72289	+	0.786820i	−0.994858	+	0.101282i	$0.967706\pi$
$240$	2.04235	+	0.910392i	0.131833	+	0.0587655i
$241$	−0.709128	−	0.614463i	−0.0456789	−	0.0395810i	0.631722	−	0.775195i	$-0.282348\pi$
$241$	−0.709128	−	0.614463i	−0.0456789	−	0.0395810i	−0.677401	+	0.735614i	$0.736894\pi$
$242$	−9.00394	+	0.643974i	−0.578795	+	0.0413962i
$243$	−0.479249	+	0.877679i	−0.0307438	+	0.0563031i
$244$	−4.77381	−	10.4532i	−0.305612	−	0.669197i
$245$	−1.09144	+	0.832608i	−0.0697294	+	0.0531934i
$246$	−2.68279	−	0.787738i	−0.171048	−	0.0502243i
$247$	2.76620	+	2.07075i	0.176009	+	0.131759i
$248$	2.37153	+	6.35833i	0.150593	+	0.403754i
$249$	0.555546	−	3.86391i	0.0352063	−	0.244865i
$250$	−10.0397	+	4.91972i	−0.634969	+	0.311150i
$251$	16.7160	−	14.4845i	1.05510	−	0.914253i	0.0586411	−	0.998279i	$-0.481323\pi$
$251$	16.7160	−	14.4845i	1.05510	−	0.914253i	0.996464	+	0.0840257i	$0.0267778\pi$
$252$	1.95114	−	1.95114i	0.122910	−	0.122910i
$253$	1.97375	+	6.44086i	0.124089	+	0.404934i
$254$			19.6803i			1.23485i
$255$	9.72836	+	9.55330i	0.609213	+	0.598251i
$256$	0.841254	+	0.540641i	0.0525783	+	0.0337901i
$257$	−0.561384	+	0.420247i	−0.0350182	+	0.0262143i	−0.616643	−	0.787243i	$-0.711508\pi$
$257$	−0.561384	+	0.420247i	−0.0350182	+	0.0262143i	0.581625	+	0.813457i	$0.302417\pi$
$258$	2.24895	−	0.838816i	0.140014	−	0.0522224i
$259$	−9.50584	+	1.36673i	−0.590664	+	0.0849247i
$260$	−0.795459	+	0.521475i	−0.0493323	+	0.0323405i
$261$	−4.78646	+	3.07607i	−0.296274	+	0.190404i
$262$	−2.68763	+	7.20581i	−0.166042	+	0.445176i
$263$	−1.85614	−	1.01353i	−0.114454	−	0.0624969i	0.421002	−	0.907060i	$-0.361679\pi$
$263$	−1.85614	−	1.01353i	−0.114454	−	0.0624969i	−0.535456	+	0.844563i	$0.679860\pi$
$264$	0.919855	−	1.06157i	0.0566131	−	0.0653351i
$265$	−0.979695	−	6.40084i	−0.0601822	−	0.393201i
$266$	21.5070	−	6.31503i	1.31868	−	0.387200i
$267$	−0.0452540	−	0.0168789i	−0.00276950	−	0.00103297i
$268$	−8.44383	−	1.83684i	−0.515789	−	0.112203i
$269$	1.75446	−	5.97516i	0.106972	−	0.364312i	−0.888558	−	0.458765i	$-0.848292\pi$
$269$	1.75446	−	5.97516i	0.106972	−	0.364312i	0.995529	+	0.0944531i	$0.0301102\pi$
$270$	−0.495128	−	2.18056i	−0.0301325	−	0.132705i
$271$	13.5030	−	29.5675i	0.820251	−	1.79610i	0.265429	−	0.964130i	$-0.414486\pi$
$271$	13.5030	−	29.5675i	0.820251	−	1.79610i	0.554822	−	0.831969i	$-0.312786\pi$
$272$	3.65418	+	4.88142i	0.221567	+	0.295979i
$273$	0.249495	+	1.14691i	0.0151001	+	0.0694141i
$274$	−3.22443	−	3.72120i	−0.194795	−	0.224806i
$275$	1.12558	+	6.93250i	0.0678747	+	0.418046i
$276$	4.23593	+	2.24875i	0.254973	+	0.135359i
$277$	−5.91674	−	5.91674i	−0.355503	−	0.355503i	0.506649	−	0.862152i	$-0.330884\pi$
$277$	−5.91674	−	5.91674i	−0.355503	−	0.355503i	−0.862152	+	0.506649i	$0.830884\pi$
$278$	−21.2852	−	1.52235i	−1.27660	−	0.0913045i
$279$	3.66890	−	5.70892i	0.219651	−	0.341784i
$280$	−0.384275	+	6.15808i	−0.0229648	+	0.368016i
$281$	17.0485	+	7.78579i	1.01703	+	0.464461i	0.852954	−	0.521987i	$-0.174809\pi$
$281$	17.0485	+	7.78579i	1.01703	+	0.464461i	0.164075	+	0.986448i	$0.447536\pi$
$282$	−7.79233	+	10.4093i	−0.464027	+	0.619867i
$283$	−1.41517	−	2.59168i	−0.0841229	−	0.154060i	0.832231	−	0.554429i	$-0.187063\pi$
$283$	−1.41517	−	2.59168i	−0.0841229	−	0.154060i	−0.916354	+	0.400370i	$0.868882\pi$
$284$	−2.62562	−	4.08555i	−0.155802	−	0.242433i
$285$	4.95904	−	17.4743i	0.293748	−	1.03509i
$286$	0.168334	+	0.573294i	0.00995381	+	0.0338996i
$287$	−0.550398	−	7.69557i	−0.0324890	−	0.454255i
$288$	−0.0713392	−	0.997452i	−0.00420370	−	0.0587754i
$289$	5.68573	+	19.3638i	0.334455	+	1.13905i
$290$	3.47337	−	12.2392i	0.203963	−	0.718710i
$291$	1.51942	+	2.36427i	0.0890703	+	0.138596i
$292$	3.40254	+	6.23129i	0.199119	+	0.364659i
$293$	11.5881	−	15.4798i	0.676981	−	0.904341i	−0.322121	−	0.946698i	$-0.604396\pi$
$293$	11.5881	−	15.4798i	0.676981	−	0.904341i	0.999103	+	0.0423574i	$0.0134868\pi$
$294$	0.558439	+	0.255030i	0.0325688	+	0.0148737i
$295$	−1.28738	+	20.6306i	−0.0749544	+	1.20116i
$296$	−1.88165	+	2.92790i	−0.109369	+	0.170181i
$297$	−1.40108	−	0.100207i	−0.0812988	−	0.00581460i
$298$	−11.2493	−	11.2493i	−0.651656	−	0.651656i
$299$	−1.77884	+	0.998649i	−0.102873	+	0.0577534i
$300$	4.05645	+	2.92322i	0.234199	+	0.168772i
$301$	4.33728	+	5.00549i	0.249997	+	0.288511i
$302$	−2.35778	−	10.8385i	−0.135675	−	0.623687i
$303$	−9.43805	−	12.6078i	−0.542202	−	0.724297i
$304$	3.37456	−	7.38925i	0.193544	−	0.423802i
$305$	−5.68984	−	25.0583i	−0.325799	−	1.43483i
$306$	1.71791	−	5.85065i	0.0982061	−	0.334459i
$307$	4.07917	+	0.887368i	0.232810	+	0.0506448i	0.327457	−	0.944866i	$-0.393808\pi$
$307$	4.07917	+	0.887368i	0.232810	+	0.0506448i	−0.0946464	+	0.995511i	$0.530172\pi$
$308$	3.63154	+	1.35449i	0.206926	+	0.0771795i
$309$	−16.4581	+	4.83253i	−0.936268	+	0.274913i
$310$	2.29582	+	14.9997i	0.130394	+	0.851928i
$311$	18.3292	−	21.1530i	1.03935	−	1.19948i	0.0598156	−	0.998209i	$-0.480949\pi$
$311$	18.3292	−	21.1530i	1.03935	−	1.19948i	0.979536	−	0.201267i	$-0.0645058\pi$
$312$	0.373337	+	0.203857i	0.0211360	+	0.0115412i
$313$	3.90278	−	10.4637i	0.220598	−	0.591446i	−0.778758	−	0.627324i	$-0.784150\pi$
$313$	3.90278	−	10.4637i	0.220598	−	0.591446i	0.999356	+	0.0358782i	$0.0114228\pi$
$314$	10.8991	−	7.00443i	0.615072	−	0.395283i
$315$	5.16008	−	3.38277i	0.290738	−	0.190598i
$316$	4.53860	−	0.652552i	0.255316	−	0.0367089i
$317$	−12.5404	+	4.67732i	−0.704338	+	0.262704i	−0.676008	−	0.736894i	$-0.736292\pi$
$317$	−12.5404	+	4.67732i	−0.704338	+	0.262704i	−0.0283297	+	0.999599i	$0.509019\pi$
$318$	−2.31827	+	1.73544i	−0.130002	+	0.0973184i
$319$	−6.72333	−	4.32082i	−0.376434	−	0.241920i
$320$	1.59543	+	1.56672i	0.0891872	+	0.0875822i
$321$			1.20090i			0.0670279i
$322$	−1.72916	+	13.1198i	−0.0963624	+	0.731140i
$323$	35.0253	−	35.0253i	1.94886	−	1.94886i
$324$	−0.755750	+	0.654861i	−0.0419861	+	0.0363812i
$325$	−1.97892	+	0.779314i	−0.109771	+	0.0432286i
$326$	−1.81400	+	12.6167i	−0.100468	+	0.698772i
$327$	−2.79797	−	7.50164i	−0.154728	−	0.414842i
$328$	−2.23835	−	1.67561i	−0.123592	−	0.0925200i
$329$	−34.4259	−	10.1084i	−1.89796	−	0.557292i
$330$	2.49723	−	1.90503i	0.137468	−	0.104868i
$331$	−6.38596	−	13.9833i	−0.351004	−	0.768591i	−0.999970	−	0.00777386i	$-0.997525\pi$
$331$	−6.38596	−	13.9833i	−0.351004	−	0.768591i	0.648966	−	0.760818i	$-0.275202\pi$
$332$	1.87082	−	3.42614i	0.102674	−	0.188034i
$333$	3.47154	−	0.248289i	0.190239	−	0.0136062i
$334$	3.71020	+	3.21491i	0.203013	+	0.175912i
$335$	−17.6486	−	7.86698i	−0.964244	−	0.429819i
$336$	2.50998	−	1.14627i	0.136930	−	0.0625341i
$337$	−2.84957	+	13.0993i	−0.155226	+	0.713563i	0.832070	+	0.554671i	$0.187156\pi$
$337$	−2.84957	+	13.0993i	−0.155226	+	0.713563i	−0.987296	+	0.158892i	$0.949208\pi$
$338$	11.2510	−	6.14352i	0.611975	−	0.334164i
$339$	−1.42623	−	9.91965i	−0.0774622	−	0.538761i
$340$	5.77645	+	12.3507i	0.313272	+	0.669809i
$341$	9.43526	+	1.35659i	0.510948	+	0.0734633i
$342$	−7.93769	+	1.72674i	−0.429221	+	0.0933714i
$343$	1.25709	−	17.5764i	0.0678765	−	0.949038i
$344$	2.40029			0.129415
$345$	8.24907	+	6.85222i	0.444115	+	0.368911i
$346$	20.3519			1.09413
$347$	1.20459	−	16.8424i	0.0646659	−	0.904147i	−0.856790	−	0.515665i	$-0.827545\pi$
$347$	1.20459	−	16.8424i	0.0646659	−	0.904147i	0.921456	−	0.388482i	$-0.127001\pi$
$348$	−5.55965	+	1.20943i	−0.298028	+	0.0648321i
$349$	12.2393	+	1.75974i	0.655154	+	0.0941970i	0.461872	−	0.886946i	$-0.347178\pi$
$349$	12.2393	+	1.75974i	0.655154	+	0.0941970i	0.193282	+	0.981143i	$0.438087\pi$
$350$	−3.64597	+	13.3062i	−0.194885	+	0.711246i
$351$	−0.0605362	−	0.421039i	−0.00323119	−	0.0224734i
$352$	1.23284	−	0.673180i	0.0657105	−	0.0358806i
$353$	−0.390694	+	1.79599i	−0.0207946	+	0.0955911i	−0.986375	−	0.164515i	$-0.947394\pi$
$353$	−0.390694	+	1.79599i	−0.0207946	+	0.0955911i	0.965580	+	0.260106i	$0.0837576\pi$
$354$	8.40884	−	3.84019i	0.446925	−	0.204104i
$355$	−3.88722	−	10.1399i	−0.206312	−	0.538170i
$356$	−0.0365022	−	0.0316293i	−0.00193461	−	0.00167635i
$357$	16.7826	−	1.20031i	0.888228	−	0.0635273i
$358$	10.5821	−	19.3797i	0.559281	−	1.02425i
$359$	12.4367	+	27.2326i	0.656386	+	1.43728i	0.885852	+	0.463968i	$0.153575\pi$
$359$	12.4367	+	27.2326i	0.656386	+	1.43728i	−0.229467	+	0.973317i	$0.573698\pi$
$360$	0.298118	−	2.21611i	0.0157122	−	0.116799i
$361$	−45.0853	−	13.2382i	−2.37291	−	0.696749i
$362$	7.40516	+	5.54344i	0.389207	+	0.291357i
$363$	3.15459	+	8.45779i	0.165573	+	0.443919i
$364$	−0.167040	+	1.16179i	−0.00875525	+	0.0608941i
$365$	4.61075	+	15.1912i	0.241338	+	0.795143i
$366$	−8.68482	+	7.52544i	−0.453963	+	0.393361i
$367$	−6.98787	+	6.98787i	−0.364764	+	0.364764i	−0.865563	−	0.500799i	$-0.833039\pi$
$367$	−6.98787	+	6.98787i	−0.364764	+	0.364764i	0.500799	+	0.865563i	$0.333039\pi$
$368$	3.18300	+	3.58727i	0.165925	+	0.186999i
$369$			2.79605i			0.145556i
$370$	−5.45281	+	5.55273i	−0.283478	+	0.288673i
$371$	−6.72220	−	4.32010i	−0.348999	−	0.224288i
$372$	5.43264	−	4.06682i	0.281669	−	0.210855i
$373$	−11.3429	+	4.23068i	−0.587313	+	0.219056i	−0.625513	−	0.780214i	$-0.715110\pi$
$373$	−11.3429	+	4.23068i	−0.587313	+	0.219056i	0.0382002	+	0.999270i	$0.487838\pi$
$374$	8.47792	−	1.21894i	0.438383	−	0.0630299i
$375$	7.54896	+	8.24701i	0.389827	+	0.425874i
$376$	−10.9387	+	7.02988i	−0.564121	+	0.362539i
$377$	0.845776	−	2.26761i	0.0435597	−	0.116788i
$378$	−2.42181	−	1.32241i	−0.124564	−	0.0680173i
$379$	−0.0468847	+	0.0541079i	−0.00240831	+	0.00277933i	−0.756952	−	0.653470i	$-0.773313\pi$
$379$	−0.0468847	+	0.0541079i	−0.00240831	+	0.00277933i	0.754544	+	0.656249i	$0.227858\pi$
$380$	10.7530	−	14.6395i	0.551618	−	0.750992i
$381$	18.8831	−	5.54457i	0.967409	−	0.284057i
$382$	8.41964	+	3.14036i	0.430786	+	0.160675i
$383$	32.1375	+	6.99109i	1.64215	+	0.357228i	0.936319	−	0.351152i	$-0.114210\pi$
$383$	32.1375	+	6.99109i	1.64215	+	0.357228i	0.705832	+	0.708380i	$0.250573\pi$
$384$	0.281733	−	0.959493i	0.0143771	−	0.0489639i
$385$	7.33323	+	4.61925i	0.373736	+	0.235419i
$386$	−6.18700	+	13.5476i	−0.314910	+	0.689557i
$387$	−1.43844	−	1.92153i	−0.0731201	−	0.0976770i
$388$	0.597397	+	2.74619i	0.0303282	+	0.139417i
$389$	−21.2818	−	24.5605i	−1.07903	−	1.24527i	−0.967866	−	0.251465i	$-0.919088\pi$
$389$	−21.2818	−	24.5605i	−1.07903	−	1.24527i	−0.111164	−	0.993802i	$-0.535458\pi$
$390$	0.724459	+	0.616321i	0.0366844	+	0.0312086i
$391$	10.5409	+	27.2774i	0.533077	+	1.37948i
$392$	0.434105	+	0.434105i	0.0219256	+	0.0219256i
$393$	7.67111	+	0.548649i	0.386956	+	0.0276757i
$394$	−6.19134	+	9.63392i	−0.311915	+	0.485350i
$395$	10.2331	+	0.638562i	0.514882	+	0.0321295i
$396$	−1.27772	−	0.583516i	−0.0642079	−	0.0293228i
$397$	15.1677	−	20.2616i	0.761244	−	1.01690i	−0.237717	−	0.971334i	$-0.576399\pi$
$397$	15.1677	−	20.2616i	0.761244	−	1.01690i	0.998961	−	0.0455684i	$-0.0145099\pi$
$398$	−6.99967	−	12.8189i	−0.350862	−	0.642555i
$399$	−12.1185	−	18.8567i	−0.606682	−	0.944015i
$400$	2.77913	+	4.15649i	0.138957	+	0.207825i
$401$	2.09126	+	7.12219i	0.104433	+	0.355665i	0.995086	−	0.0990188i	$-0.0315704\pi$
$401$	2.09126	+	7.12219i	0.104433	+	0.355665i	−0.890653	+	0.454684i	$0.849752\pi$
$402$	0.616464	+	8.61929i	0.0307464	+	0.429891i
$403$	0.205930	+	2.87928i	0.0102581	+	0.143427i
$404$	−4.43702	−	15.1111i	−0.220750	−	0.751805i
$405$	−1.95274	+	1.08941i	−0.0970324	+	0.0541331i
$406$	−8.48790	−	13.2074i	−0.421247	−	0.655474i
$407$	2.34294	+	4.29077i	0.116135	+	0.212686i
$408$	3.65418	−	4.88142i	0.180909	−	0.241666i
$409$	3.86292	+	1.76414i	0.191009	+	0.0872309i	0.508624	−	0.860989i	$-0.330155\pi$
$409$	3.86292	+	1.76414i	0.191009	+	0.0872309i	−0.317614	+	0.948220i	$0.602882\pi$
$410$	−4.13702	−	4.68770i	−0.204313	−	0.231509i
$411$	−2.66203	+	4.14220i	−0.131308	+	0.204320i
$412$	−17.1092	−	1.22367i	−0.842910	−	0.0602861i
$413$	18.0368	+	18.0368i	0.887533	+	0.887533i
$414$	0.964260	−	4.69789i	0.0473908	−	0.230889i
$415$	5.65603	−	6.64842i	0.277643	−	0.326358i
$416$	0.278557	+	0.321472i	0.0136574	+	0.0157615i
$417$	4.53606	+	20.8519i	0.222132	+	1.02112i
$418$	−6.83806	−	9.13458i	−0.334460	−	0.446787i
$419$	4.65611	−	10.1954i	0.227466	−	0.498080i	−0.761144	−	0.648583i	$-0.775362\pi$
$419$	4.65611	−	10.1954i	0.227466	−	0.498080i	0.988610	+	0.150503i	$0.0480892\pi$
$420$	6.01689	−	1.36622i	0.293594	−	0.0666648i
$421$	−3.47897	+	11.8483i	−0.169555	+	0.577450i	0.830244	+	0.557400i	$0.188201\pi$
$421$	−3.47897	+	11.8483i	−0.169555	+	0.577450i	−0.999799	+	0.0200507i	$0.993617\pi$
$422$	1.63106	+	0.354815i	0.0793986	+	0.0172721i
$423$	12.1830	+	4.54404i	0.592360	+	0.220939i
$424$	−2.77858	+	0.815864i	−0.134940	+	0.0396218i
$425$	7.02059	+	29.6689i	0.340549	+	1.43915i
$426$	−3.18033	+	3.67030i	−0.154088	+	0.177827i
$427$	−27.8306	−	15.1967i	−1.34682	−	0.735418i
$428$	−0.419673	+	1.12519i	−0.0202857	+	0.0543880i
$429$	0.502646	−	0.323031i	0.0242680	−	0.0155961i
$430$	5.25470	+	1.09322i	0.253404	+	0.0527199i
$431$	−1.08505	+	0.156007i	−0.0522651	+	0.00751459i	−0.168398	−	0.985719i	$-0.553859\pi$
$431$	−1.08505	+	0.156007i	−0.0522651	+	0.00751459i	0.116133	+	0.993234i	$0.462950\pi$
$432$	−0.936950	+	0.349464i	−0.0450790	+	0.0168136i
$433$	−15.3412	+	11.4843i	−0.737250	+	0.551898i	−0.900589	−	0.434672i	$-0.856864\pi$
$433$	−15.3412	+	11.4843i	−0.737250	+	0.551898i	0.163339	+	0.986570i	$0.447773\pi$
$434$	15.7528	+	10.1237i	0.756159	+	0.485954i
$435$	−12.7220	+	0.115505i	−0.609972	+	0.00553802i
$436$		−	8.00645i		−	0.383439i
$437$	25.1642	−	29.7405i	1.20377	−	1.42268i
$438$	5.02027	−	5.02027i	0.239878	−	0.239878i
$439$	−9.52773	+	8.25583i	−0.454734	+	0.394029i	−0.851889	−	0.523722i	$-0.824543\pi$
$439$	−9.52773	+	8.25583i	−0.454734	+	0.394029i	0.397155	+	0.917751i	$0.369997\pi$
$440$	3.00552	−	0.912220i	0.143283	−	0.0434884i
$441$	0.0873695	−	0.607668i	0.00416045	−	0.0289366i
$442$	0.906421	+	2.43021i	0.0431141	+	0.115593i
$443$	−6.72791	−	5.03645i	−0.319653	−	0.239289i	0.427386	−	0.904069i	$-0.359434\pi$
$443$	−6.72791	−	5.03645i	−0.319653	−	0.239289i	−0.747039	+	0.664780i	$0.768525\pi$
$444$	3.33942	+	0.980543i	0.158482	+	0.0465345i
$445$	−0.0655046	−	0.0858677i	−0.00310522	−	0.00407052i
$446$	0.457011	+	1.00071i	0.0216401	+	0.0473852i
$447$	−7.62434	+	13.9629i	−0.360619	+	0.660425i
$448$	2.75230	−	0.196849i	0.130034	−	0.00930022i
$449$	26.3276	+	22.8130i	1.24248	+	1.07661i	0.994158	+	0.107934i	$0.0344236\pi$
$449$	26.3276	+	22.8130i	1.24248	+	1.07661i	0.248319	+	0.968678i	$0.420122\pi$
$450$	1.66197	−	4.71570i	0.0783462	−	0.222300i
$451$	−3.57257	+	1.63154i	−0.168226	+	0.0768261i
$452$	2.13026	−	9.79263i	0.100199	−	0.460607i
$453$	−9.73522	+	5.31583i	−0.457401	+	0.249760i
$454$	0.908698	+	6.32013i	0.0426473	+	0.296618i
$455$	−0.894822	+	2.46729i	−0.0419499	+	0.115669i
$456$	−8.04065	−	1.15607i	−0.376538	−	0.0541380i
$457$	17.2325	−	3.74870i	0.806102	−	0.175357i	0.209411	−	0.977828i	$-0.432845\pi$
$457$	17.2325	−	3.74870i	0.806102	−	0.175357i	0.596691	+	0.802471i	$0.296482\pi$
$458$	1.35550	−	18.9523i	0.0633383	−	0.885585i
$459$	−6.09765			−0.284614
$460$	5.33436	+	9.30294i	0.248716	+	0.433752i
$461$	6.58334			0.306617			0.153308	−	0.988178i	$-0.451007\pi$
$461$	6.58334			0.306617			0.153308	+	0.988178i	$0.451007\pi$
$462$	0.276505	−	3.86604i	0.0128642	−	0.179864i
$463$	−22.4040	+	4.87369i	−1.04120	+	0.226499i	−0.700485	−	0.713667i	$-0.747033\pi$
$463$	−22.4040	+	4.87369i	−1.04120	+	0.226499i	−0.340716	+	0.940166i	$0.610669\pi$
$464$	−5.63176	−	0.809725i	−0.261448	−	0.0375905i
$465$	13.7453	−	6.42873i	0.637424	−	0.298125i
$466$	−0.965342	−	6.71410i	−0.0447186	−	0.311025i
$467$	1.77648	−	0.970033i	0.0822058	−	0.0448878i	−0.437620	−	0.899160i	$-0.644179\pi$
$467$	1.77648	−	0.970033i	0.0822058	−	0.0448878i	0.519826	+	0.854272i	$0.325997\pi$
$468$	0.0904186	−	0.415647i	0.00417960	−	0.0192133i
$469$	−21.6895	+	9.90526i	−1.00153	+	0.457382i
$470$	−27.1487	+	10.4077i	−1.25228	+	0.480071i
$471$	−9.79133	−	8.48424i	−0.451161	−	0.390933i
$472$	9.22067	−	0.659476i	0.424416	−	0.0303548i
$473$	1.61583	−	2.95917i	0.0742960	−	0.136063i
$474$	−1.90479	−	4.17091i	−0.0874899	−	0.191576i
$475$	30.2080	−	27.1512i	1.38604	−	1.24578i
$476$	16.1439	+	4.74027i	0.739954	+	0.217270i
$477$	2.31827	+	1.73544i	0.106146	+	0.0794602i
$478$	10.2328	+	27.4352i	0.468038	+	1.25486i
$479$	−0.648613	+	4.51120i	−0.0296359	+	0.206122i	−0.999259	−	0.0384803i	$-0.987748\pi$
$479$	−0.648613	+	4.51120i	−0.0296359	+	0.206122i	0.969623	+	0.244602i	$0.0786574\pi$
$480$	1.05377	−	1.97220i	0.0480979	−	0.0900181i
$481$	−1.11885	+	0.969491i	−0.0510153	+	0.0442050i
$482$	−0.663486	+	0.663486i	−0.0302209	+	0.0302209i
$483$	13.0756	−	2.03717i	0.594958	−	0.0926943i
$484$			9.02694i			0.410315i
$485$	0.0570535	+	6.28402i	0.00259067	+	0.285343i
$486$	0.841254	+	0.540641i	0.0381600	+	0.0245240i
$487$	−19.6605	+	14.7176i	−0.890901	+	0.666920i	−0.943384	−	0.331702i	$-0.892377\pi$
$487$	−19.6605	+	14.7176i	−0.890901	+	0.666920i	0.0524833	+	0.998622i	$0.483286\pi$
$488$	−10.7671	+	4.01593i	−0.487404	+	0.181792i
$489$	12.6167	−	1.81400i	0.570545	−	0.0820320i
$490$	0.752624	+	1.14805i	0.0340001	+	0.0518638i
$491$	8.64445	−	5.55545i	0.390118	−	0.250714i	−0.330848	−	0.943684i	$-0.607335\pi$
$491$	8.64445	−	5.55545i	0.390118	−	0.250714i	0.720966	+	0.692970i	$0.243698\pi$
$492$	−0.977119	+	2.61976i	−0.0440519	+	0.118108i
$493$	−30.4499	−	16.6269i	−1.37139	−	0.748837i
$494$	2.26281	−	2.61143i	0.101809	−	0.117494i
$495$	−2.53141	−	1.85937i	−0.113779	−	0.0835725i
$496$	6.51131	−	1.91189i	0.292367	−	0.0858466i
$497$	−12.5558	−	4.68307i	−0.563204	−	0.210064i
$498$	−3.81443	−	0.829779i	−0.170929	−	0.0371833i
$499$	−10.4187	+	35.4829i	−0.466406	+	1.58843i	0.305171	+	0.952298i	$0.401287\pi$
$499$	−10.4187	+	35.4829i	−0.466406	+	1.58843i	−0.771577	+	0.636136i	$0.780532\pi$
$500$	4.19096	+	10.3651i	0.187425	+	0.463543i
$501$	2.03940	−	4.46565i	0.0911135	−	0.199511i
$502$	−13.2551	−	17.7067i	−0.591604	−	0.790290i
$503$	4.00839	+	18.4263i	0.178725	+	0.821587i	0.975965	+	0.217925i	$0.0699289\pi$
$503$	4.00839	+	18.4263i	0.178725	+	0.821587i	−0.797240	+	0.603662i	$0.793708\pi$
$504$	−1.80698	−	2.08536i	−0.0804892	−	0.0928895i
$505$	−2.83107	−	35.1019i	−0.125981	−	1.56202i
$506$	6.56526	−	1.50924i	0.291861	−	0.0670939i
$507$	−9.06445	−	9.06445i	−0.402566	−	0.402566i
$508$	19.6301	+	1.40397i	0.870946	+	0.0622913i
$509$	−18.3847	+	28.6071i	−0.814887	+	1.26799i	0.145511	+	0.989357i	$0.453517\pi$
$509$	−18.3847	+	28.6071i	−0.814887	+	1.26799i	−0.960398	+	0.278632i	$0.910119\pi$
$510$	10.2230	−	9.02205i	0.452681	−	0.399503i
$511$	17.8202	+	8.13820i	0.788318	+	0.360013i
$512$	0.599278	−	0.800541i	0.0264846	−	0.0353793i
$513$	3.89310	+	7.12968i	0.171885	+	0.314783i
$514$	0.379127	+	0.589933i	0.0167226	+	0.0260208i
$515$	−36.8980	−	10.4713i	−1.62592	−	0.461421i
$516$	−0.676241	−	2.30306i	−0.0297698	−	0.101387i
$517$	1.30298	+	18.2180i	0.0573050	+	0.801229i
$518$	0.685112	+	9.57912i	0.0301021	+	0.420882i
$519$	−5.73380	−	19.5275i	−0.251686	−	0.857164i
$520$	0.463399	+	0.830634i	0.0203214	+	0.0364257i
$521$	2.70606	+	4.21071i	0.118555	+	0.184474i	0.895459	−	0.445144i	$-0.146848\pi$
$521$	2.70606	+	4.21071i	0.118555	+	0.184474i	−0.776904	+	0.629619i	$0.783211\pi$
$522$	2.72677	+	4.99371i	0.119347	+	0.218569i
$523$	−23.9014	+	31.9286i	−1.04514	+	1.39614i	−0.130695	+	0.991423i	$0.541721\pi$
$523$	−23.9014	+	31.9286i	−1.04514	+	1.39614i	−0.914442	+	0.404717i	$0.867370\pi$
$524$	6.99571	+	3.19484i	0.305609	+	0.139567i
$525$	13.7944	−	0.250503i	0.602037	−	0.0109329i
$526$	−1.14336	+	1.77911i	−0.0498529	+	0.0775727i
$527$	41.2744	+	2.95201i	1.79794	+	0.128591i
$528$	−0.993243	−	0.993243i	−0.0432253	−	0.0432253i
$529$	10.0438	+	20.6911i	0.436688	+	0.899613i
$530$	−6.45442	+	0.520568i	−0.280362	+	0.0226120i
$531$	−6.05368	−	6.98632i	−0.262707	−	0.303180i
$532$	−4.76465	−	21.9027i	−0.206574	−	0.949604i
$533$	−0.712751	−	0.952124i	−0.0308727	−	0.0412411i
$534$	−0.0200643	+	0.0439346i	−0.000868265	+	0.00190124i
$535$	−1.43122	+	2.27211i	−0.0618768	+	0.0982318i
$536$	−2.43454	+	8.29128i	−0.105156	+	0.358129i
$537$	−21.5760	−	4.69357i	−0.931072	−	0.202542i
$538$	−5.83477	−	2.17626i	−0.251555	−	0.0938251i
$539$	0.827412	−	0.242950i	0.0356392	−	0.0104646i
$540$	−2.21033	+	0.338307i	−0.0951174	+	0.0145584i
$541$	7.96628	−	9.19358i	0.342497	−	0.395263i	−0.558203	−	0.829705i	$-0.688509\pi$
$541$	7.96628	−	9.19358i	0.342497	−	0.395263i	0.900700	+	0.434442i	$0.143054\pi$
$542$	−28.5289	−	15.5780i	−1.22542	−	0.669131i
$543$	3.23261	−	8.66697i	0.138725	−	0.371935i
$544$	5.12967	−	3.29664i	0.219933	−	0.141342i
$545$	3.64657	−	17.5277i	0.156202	−	0.750802i
$546$	1.16179	−	0.167040i	0.0497199	−	0.00714864i
$547$	−1.68316	+	0.627785i	−0.0719665	+	0.0268421i	−0.385190	−	0.922837i	$-0.625864\pi$
$547$	−1.68316	+	0.627785i	−0.0719665	+	0.0268421i	0.313223	+	0.949680i	$0.398591\pi$
$548$	−3.94174	+	2.95075i	−0.168383	+	0.126050i
$549$	9.66741	+	6.21286i	0.412595	+	0.265159i
$550$	6.99514	−	0.628148i	0.298274	−	0.0267843i
$551$			46.2191i			1.96900i
$552$	2.54521	−	4.06472i	0.108331	−	0.173006i
$553$	8.94652	−	8.94652i	0.380445	−	0.380445i
$554$	−6.32376	+	5.47957i	−0.268671	+	0.232805i
$555$	6.86404	+	3.66755i	0.291362	+	0.155679i
$556$	−3.03694	+	21.1224i	−0.128795	+	0.895789i
$557$	−13.4107	−	35.9555i	−0.568229	−	1.52348i	−0.829665	−	0.558261i	$-0.811469\pi$
$557$	−13.4107	−	35.9555i	−0.568229	−	1.52348i	0.261436	−	0.965221i	$-0.415804\pi$
$558$	−5.43264	−	4.06682i	−0.229982	−	0.172162i
$559$	0.979651	+	0.287651i	0.0414348	+	0.0121664i
$560$	6.11497	+	0.822608i	0.258405	+	0.0347615i
$561$	−3.55807	−	7.79109i	−0.150222	−	0.328940i
$562$	8.98218	−	16.4496i	0.378890	−	0.693886i
$563$	−5.42504	+	0.388006i	−0.228638	+	0.0163525i	−0.185188	−	0.982703i	$-0.559289\pi$
$563$	−5.42504	+	0.388006i	−0.228638	+	0.0163525i	−0.0434499	+	0.999056i	$0.513835\pi$
$564$	9.82692	+	8.51507i	0.413788	+	0.358549i
$565$	9.12363	−	20.4677i	0.383834	−	0.861083i
$566$	−2.68604	+	1.22667i	−0.112903	+	0.0515609i
$567$	−0.586538	+	2.69627i	−0.0246323	+	0.113233i
$568$	−4.26245	+	2.32747i	−0.178849	+	0.0976587i
$569$	0.175779	+	1.22257i	0.00736904	+	0.0512528i	0.993174	−	0.116641i	$-0.0372126\pi$
$569$	0.175779	+	1.22257i	0.00736904	+	0.0512528i	−0.985805	+	0.167894i	$0.946304\pi$
$570$	−17.0760	−	6.19301i	−0.715235	−	0.259397i
$571$	18.9867	+	2.72988i	0.794570	+	0.114242i	0.527633	−	0.849472i	$-0.323079\pi$
$571$	18.9867	+	2.72988i	0.794570	+	0.114242i	0.266937	+	0.963714i	$0.413989\pi$
$572$	0.583842	−	0.127007i	0.0244117	−	0.00531043i
$573$	0.641070	−	8.96333i	0.0267811	−	0.374448i
$574$	−7.71523			−0.322027
$575$	7.44087	+	22.7955i	0.310306	+	0.950637i
$576$	−1.00000			−0.0416667
$577$	−1.52587	+	21.3344i	−0.0635226	+	0.888162i	0.861381	+	0.507960i	$0.169600\pi$
$577$	−1.52587	+	21.3344i	−0.0635226	+	0.888162i	−0.924903	+	0.380202i	$0.875854\pi$
$578$	19.7201	−	4.28984i	0.820247	−	0.178434i
$579$	14.7419	+	2.11957i	0.612654	+	0.0880864i
$580$	−11.9602	−	4.33765i	−0.496621	−	0.180111i
$581$	−1.53294	−	10.6618i	−0.0635969	−	0.442326i
$582$	2.46664	−	1.34689i	0.102246	−	0.0558303i
$583$	−0.864656	+	3.97476i	−0.0358104	+	0.164618i
$584$	6.45815	−	2.94934i	0.267240	−	0.122044i
$585$	0.387252	−	0.868750i	0.0160109	−	0.0359184i
$586$	−14.6137	−	12.6628i	−0.603686	−	0.523097i
$587$	−5.79133	+	0.414204i	−0.239034	+	0.0170960i	−0.190342	−	0.981718i	$-0.560960\pi$
$587$	−5.79133	+	0.414204i	−0.239034	+	0.0170960i	−0.0486918	+	0.998814i	$0.515505\pi$
$588$	0.294219	−	0.538822i	0.0121334	−	0.0222207i
$589$	−22.9004	−	50.1449i	−0.943596	−	2.06619i
$590$	20.4862	+	2.75587i	0.843403	+	0.113458i
$591$	10.9880	+	3.22636i	0.451985	+	0.132715i
$592$	2.78621	+	2.08573i	0.114512	+	0.0857229i
$593$	5.81334	+	15.5862i	0.238725	+	0.640047i	0.999965	−	0.00842413i	$-0.00268152\pi$
$593$	5.81334	+	15.5862i	0.238725	+	0.640047i	−0.761239	+	0.648471i	$0.775409\pi$
$594$	−0.199904	+	1.39036i	−0.00820214	+	0.0570471i
$595$	33.1831	+	17.7302i	1.36037	+	0.726866i
$596$	−12.0232	+	10.4181i	−0.492488	+	0.426744i
$597$	−10.3276	+	10.3276i	−0.422682	+	0.422682i
$598$	0.869203	+	1.84555i	0.0355444	+	0.0754703i
$599$			14.2196i			0.580996i	0.956876	+	0.290498i	$0.0938210\pi$
$599$			14.2196i			0.580996i	−0.956876	+	0.290498i	$0.906179\pi$
$600$	3.20515	−	3.83758i	0.130850	−	0.156668i
$601$	−14.9018	−	9.57678i	−0.607856	−	0.390645i	0.200197	−	0.979756i	$-0.435842\pi$
$601$	−14.9018	−	9.57678i	−0.607856	−	0.390645i	−0.808052	+	0.589111i	$0.799478\pi$
$602$	5.30215	−	3.96914i	0.216100	−	0.161770i
$603$	8.09647	−	3.01983i	0.329714	−	0.122977i
$604$	−10.9791	+	1.57856i	−0.446733	+	0.0642306i
$605$	−4.11136	+	19.7617i	−0.167150	+	0.803427i
$606$	−13.2489	+	8.51457i	−0.538201	+	0.345881i
$607$	−0.836274	+	2.24214i	−0.0339433	+	0.0910055i	−0.952816	−	0.303549i	$-0.901828\pi$
$607$	−0.836274	+	2.24214i	−0.0339433	+	0.0910055i	0.918873	+	0.394555i	$0.129101\pi$
$608$	−7.12968	−	3.89310i	−0.289147	−	0.157886i
$609$	−10.2811	+	11.8650i	−0.416612	+	0.480796i
$610$	−25.4004	+	3.88771i	−1.02843	+	0.157409i
$611$	−5.30697	+	1.55827i	−0.214697	+	0.0630407i
$612$	−5.71319	−	2.13091i	−0.230942	−	0.0861369i
$613$	1.71911	+	0.373970i	0.0694343	+	0.0151045i	0.247148	−	0.968978i	$-0.420507\pi$
$613$	1.71911	+	0.373970i	0.0694343	+	0.0151045i	−0.177714	+	0.984082i	$0.556870\pi$
$614$	1.17611	−	4.00547i	0.0474640	−	0.161648i
$615$	−3.33228	+	5.29012i	−0.134370	+	0.213318i
$616$	1.61011	−	3.52566i	0.0648733	−	0.142053i
$617$	2.96478	+	3.96048i	0.119357	+	0.159443i	0.856241	−	0.516577i	$-0.172794\pi$
$617$	2.96478	+	3.96048i	0.119357	+	0.159443i	−0.736883	+	0.676020i	$0.763703\pi$
$618$	3.64611	+	16.7609i	0.146668	+	0.674223i
$619$	3.47128	+	4.00607i	0.139523	+	0.161018i	0.821210	−	0.570626i	$-0.193299\pi$
$619$	3.47128	+	4.00607i	0.139523	+	0.161018i	−0.681688	+	0.731643i	$0.738754\pi$
$620$	15.1253	−	1.21990i	0.607447	−	0.0489923i
$621$	−4.77926	+	0.398349i	−0.191785	+	0.0159852i
$622$	−19.7915	−	19.7915i	−0.793567	−	0.793567i
$623$	−0.132934	−	0.00950765i	−0.00532590	−	0.000380916i
$624$	0.229972	−	0.357843i	0.00920623	−	0.0143252i
$625$	4.45398	+	24.6000i	0.178159	+	0.984002i
$626$	−10.1587	−	4.63931i	−0.406022	−	0.185424i
$627$	−6.83806	+	9.13458i	−0.273086	+	0.364800i
$628$	−6.20905	−	11.3710i	−0.247768	−	0.453753i
$629$	11.4736	+	17.8533i	0.457483	+	0.711858i
$630$	−3.00604	−	5.38826i	−0.119763	−	0.214673i
$631$	−3.88451	−	13.2294i	−0.154640	−	0.526655i	0.845331	−	0.534243i	$-0.179403\pi$
$631$	−3.88451	−	13.2294i	−0.154640	−	0.526655i	−0.999971	+	0.00758712i	$0.997585\pi$
$632$	−0.327109	−	4.57359i	−0.0130117	−	0.181928i
$633$	−0.119080	−	1.66495i	−0.00473299	−	0.0661759i
$634$	3.77078	+	12.8421i	0.149757	+	0.510025i
$635$	42.3347	+	12.0142i	1.68000	+	0.476769i
$636$	1.56563	+	2.43617i	0.0620813	+	0.0966004i
$637$	0.125152	+	0.229198i	0.00495868	+	0.00908115i
$638$	−4.78945	+	6.39796i	−0.189616	+	0.253298i
$639$	4.41763	+	2.01746i	0.174759	+	0.0798097i
$640$	1.67654	−	1.47960i	0.0662712	−	0.0584861i
$641$	−15.2158	+	23.6763i	−0.600988	+	0.935156i	0.398847	+	0.917017i	$0.369410\pi$
$641$	−15.2158	+	23.6763i	−0.600988	+	0.935156i	−0.999835	+	0.0181386i	$0.994226\pi$
$642$	1.19784	+	0.0856715i	0.0472751	+	0.00338118i
$643$	23.3062	+	23.3062i	0.919106	+	0.919106i	0.996964	−	0.0778584i	$-0.0248082\pi$
$643$	23.3062	+	23.3062i	0.919106	+	0.919106i	−0.0778584	+	0.996964i	$0.524808\pi$
$644$	12.9631	+	2.66071i	0.510816	+	0.104847i
$645$	−0.431481	−	5.34985i	−0.0169895	−	0.210650i
$646$	−32.4374	−	37.4347i	−1.27623	−	1.47285i
$647$	−7.58657	−	34.8749i	−0.298259	−	1.37107i	−0.845445	−	0.534063i	$-0.820664\pi$
$647$	−7.58657	−	34.8749i	−0.298259	−	1.37107i	0.547186	−	0.837011i	$-0.315699\pi$
$648$	0.599278	+	0.800541i	0.0235419	+	0.0314482i
$649$	5.39415	−	11.8115i	0.211739	−	0.463644i
$650$	0.636154	+	2.02947i	0.0249520	+	0.0796025i
$651$	5.27555	−	17.9669i	0.206765	−	0.704178i
$652$	12.4551	+	2.70944i	0.487779	+	0.106110i
$653$	−37.4503	−	13.9683i	−1.46555	−	0.546620i	−0.514996	−	0.857193i	$-0.672206\pi$
$653$	−37.4503	−	13.9683i	−1.46555	−	0.546620i	−0.950550	+	0.310573i	$0.899479\pi$
$654$	−7.68213	+	2.25568i	−0.300395	+	0.0882040i
$655$	13.8599	+	10.1803i	0.541550	+	0.397779i
$656$	−1.83102	+	2.11311i	−0.0714894	+	0.0825032i
$657$	−6.23129	−	3.40254i	−0.243106	−	0.132746i
$658$	−12.5385	+	33.6171i	−0.488802	+	1.31053i
$659$	−18.8922	+	12.1413i	−0.735936	+	0.472957i	−0.854147	−	0.520031i	$-0.825920\pi$
$659$	−18.8922	+	12.1413i	−0.735936	+	0.472957i	0.118212	+	0.992988i	$0.462284\pi$
$660$	−1.72202	−	2.62677i	−0.0670296	−	0.102247i
$661$	−27.4770	+	3.95059i	−1.06873	+	0.153660i	−0.654160	−	0.756357i	$-0.726978\pi$
$661$	−27.4770	+	3.95059i	−1.06873	+	0.153660i	−0.414571	+	0.910017i	$0.636068\pi$
$662$	−14.4032	+	5.37213i	−0.559798	+	0.208794i
$663$	2.07640	−	1.55437i	0.0806407	−	0.0603669i
$664$	−3.28395	−	2.11047i	−0.127442	−	0.0819020i
$665$	−0.455041	−	50.1194i	−0.0176457	−	1.94355i
$666$		−	3.48040i		−	0.134863i
$667$	−24.9524	−	11.0427i	−0.966162	−	0.427575i
$668$	3.47140	−	3.47140i	0.134312	−	0.134312i
$669$	0.831423	−	0.720432i	0.0321447	−	0.0278535i
$670$	−9.10597	+	17.0424i	−0.351794	+	0.658404i
$671$	−2.29723	+	15.9776i	−0.0886834	+	0.616807i
$672$	−0.964288	−	2.58536i	−0.0371982	−	0.0997323i
$673$	33.3072	+	24.9334i	1.28390	+	0.961114i	0.999997	+	0.00225987i	$0.000719339\pi$
$673$	33.3072	+	24.9334i	1.28390	+	0.961114i	0.283900	+	0.958854i	$0.408372\pi$
$674$	12.8626	+	3.77680i	0.495449	+	0.145477i
$675$	−4.99291	−	0.266084i	−0.192177	−	0.0102416i
$676$	−5.32523	−	11.6606i	−0.204817	−	0.448486i
$677$	−5.80549	+	10.6320i	−0.223123	+	0.408620i	−0.965129	−	0.261773i	$-0.915693\pi$
$677$	−5.80549	+	10.6320i	−0.223123	+	0.408620i	0.742006	+	0.670393i	$0.233875\pi$
$678$	−9.99612	+	0.714937i	−0.383899	+	0.0274570i
$679$	5.86074	+	5.07836i	0.224914	+	0.194890i
$680$	12.7313	−	4.88064i	0.488223	−	0.187164i
$681$	5.80811	−	2.65248i	0.222567	−	0.101643i
$682$	2.02623	−	9.31445i	0.0775885	−	0.356669i
$683$	−40.4828	+	22.1053i	−1.54903	+	0.845834i	−0.549081	+	0.835769i	$0.685022\pi$
$683$	−40.4828	+	22.1053i	−1.54903	+	0.845834i	−0.999949	+	0.0100652i	$0.996796\pi$
$684$	1.15607	+	8.04065i	0.0442035	+	0.307442i
$685$	−9.97317	+	4.66448i	−0.381055	+	0.178221i
$686$	−17.4420	−	2.50778i	−0.665937	−	0.0957473i
$687$	−18.5665	+	4.03890i	−0.708357	+	0.154094i
$688$	0.171235	−	2.39418i	0.00652827	−	0.0912771i
$689$	−1.23182			−0.0469284
$690$	7.42324	−	7.73922i	0.282598	−	0.294627i
$691$	−23.4157			−0.890777			−0.445388	−	0.895337i	$-0.646934\pi$
$691$	−23.4157			−0.890777			−0.445388	+	0.895337i	$0.646934\pi$
$692$	1.45189	−	20.3001i	0.0551926	−	0.771693i
$693$	−3.78734	+	0.823885i	−0.143869	+	0.0312968i
$694$	−16.7136	−	2.40305i	−0.634438	−	0.0912184i
$695$	−16.2687	+	44.8578i	−0.617108	+	1.70155i
$696$	0.809725	+	5.63176i	0.0306925	+	0.213471i
$697$	−14.9638	+	8.17087i	−0.566795	+	0.309494i
$698$	2.62840	−	12.0826i	0.0994865	−	0.457332i
$699$	−6.17016	+	2.81782i	−0.233377	+	0.106580i
$700$	13.0122	+	4.58594i	0.491815	+	0.173332i
$701$	−35.3441	−	30.6258i	−1.33493	−	1.15672i	−0.974614	−	0.223891i	$-0.928124\pi$
$701$	−35.3441	−	30.6258i	−1.33493	−	1.15672i	−0.360314	−	0.932831i	$-0.617331\pi$
$702$	−0.424285	+	0.0303454i	−0.0160136	+	0.00114531i
$703$	13.5496	−	24.8142i	0.511031	−	0.935884i
$704$	−0.583516	−	1.27772i	−0.0219921	−	0.0481559i
$705$	17.6348	+	23.1168i	0.664164	+	0.870630i
$706$	1.76355	+	0.517824i	0.0663719	+	0.0194885i
$707$	−34.7890	−	26.0427i	−1.30837	−	0.979437i
$708$	−3.23053	−	8.66138i	−0.121411	−	0.325514i
$709$	0.880387	−	6.12323i	0.0330636	−	0.229963i	−0.966589	−	0.256333i	$-0.917486\pi$
$709$	0.880387	−	6.12323i	0.0330636	−	0.229963i	0.999652	+	0.0263701i	$0.00839483\pi$
$710$	−10.3914	+	3.15394i	−0.389982	+	0.118365i
$711$	−3.46532	+	3.00271i	−0.129960	+	0.112611i
$712$	−0.0341528	+	0.0341528i	−0.00127993	+	0.00127993i
$713$	32.5432	−	0.382645i	1.21875	−	0.0143302i
$714$		−	16.8254i		−	0.629676i
$715$	1.33599	−	0.0121296i	0.0499631	−	0.000453622i
$716$	−18.5754	−	11.9377i	−0.694194	−	0.446132i
$717$	23.4410	−	17.5477i	0.875419	−	0.655331i
$718$	28.0505	−	10.4623i	1.04683	−	0.390449i
$719$	−33.9576	+	4.88236i	−1.26640	+	0.182081i	−0.742587	−	0.669750i	$-0.766401\pi$
$719$	−33.9576	+	4.88236i	−1.26640	+	0.182081i	−0.523816	+	0.851831i	$0.675492\pi$
$720$	−2.18919	−	0.455454i	−0.0815864	−	0.0169738i
$721$	−39.8170	+	25.5888i	−1.48286	+	0.952979i
$722$	−16.4208	+	44.0260i	−0.611120	+	1.63848i
$723$	0.823535	+	0.449684i	0.0306276	+	0.0167239i
$724$	6.05759	−	6.99083i	0.225129	−	0.259812i
$725$	−24.2076	−	14.9433i	−0.899048	−	0.554979i
$726$	8.66128	−	2.54318i	0.321450	−	0.0943864i
$727$	−42.6338	−	15.9016i	−1.58120	−	0.589758i	−0.603060	−	0.797696i	$-0.706052\pi$
$727$	−42.6338	−	15.9016i	−1.58120	−	0.589758i	−0.978142	+	0.207938i	$0.933325\pi$
$728$	1.14691	+	0.249495i	0.0425073	+	0.00924690i
$729$	0.281733	−	0.959493i	0.0104345	−	0.0355368i
$730$	15.4814	−	3.51528i	0.572993	−	0.130106i
$731$	6.08007	−	13.3135i	0.224880	−	0.492418i
$732$	6.88670	+	9.19955i	0.254540	+	0.340025i
$733$	−8.25104	−	37.9294i	−0.304759	−	1.40096i	−0.833663	−	0.552274i	$-0.813760\pi$
$733$	−8.25104	−	37.9294i	−0.304759	−	1.40096i	0.528903	−	0.848682i	$-0.322603\pi$
$734$	6.47156	+	7.46858i	0.238870	+	0.275670i
$735$	0.889511	−	1.04558i	0.0328101	−	0.0385669i
$736$	3.80520	−	2.91898i	0.140262	−	0.107595i
$737$	8.58292	+	8.58292i	0.316156	+	0.316156i
$738$	2.78892	+	0.199468i	0.102662	+	0.00734251i
$739$	9.94703	−	15.4779i	0.365907	−	0.569363i	−0.608667	−	0.793426i	$-0.708296\pi$
$739$	9.94703	−	15.4779i	0.365907	−	0.569363i	0.974575	+	0.224062i	$0.0719320\pi$
$740$	5.14959	+	5.83505i	0.189303	+	0.214501i
$741$	−3.14315	−	1.43543i	−0.115467	−	0.0527318i
$742$	−4.78865	+	6.39688i	−0.175797	+	0.234837i
$743$	0.324938	+	0.595079i	0.0119208	+	0.0218313i	0.883572	−	0.468296i	$-0.155132\pi$
$743$	0.324938	+	0.595079i	0.0119208	+	0.0218313i	−0.871651	+	0.490128i	$0.836950\pi$
$744$	−3.66890	−	5.70892i	−0.134508	−	0.209299i
$745$	−31.0660	+	17.3313i	−1.13817	+	0.634970i
$746$	3.41071	+	11.6158i	0.124875	+	0.425285i
$747$	0.278483	+	3.89370i	0.0101891	+	0.142463i
$748$	−0.611027	−	8.54328i	−0.0223414	−	0.312373i
$749$	0.933575	+	3.17947i	0.0341121	+	0.116175i
$750$	8.76454	−	6.94139i	0.320036	−	0.253464i
$751$	11.1671	+	17.3764i	0.407494	+	0.634072i	0.982974	−	0.183743i	$-0.0588214\pi$
$751$	11.1671	+	17.3764i	0.407494	+	0.634072i	−0.575481	+	0.817815i	$0.695185\pi$
$752$	6.23161	+	11.4123i	0.227244	+	0.416166i
$753$	−13.2551	+	17.7067i	−0.483042	+	0.645269i
$754$	−2.20150	−	1.00539i	−0.0801738	−	0.0366142i
$755$	−24.7543	−	1.54471i	−0.900902	−	0.0562179i
$756$	−1.49181	+	2.32130i	−0.0542565	+	0.0844248i
$757$	39.9066	+	2.85418i	1.45043	+	0.103737i	0.774195	−	0.632948i	$-0.218155\pi$
$757$	39.9066	+	2.85418i	1.45043	+	0.103737i	0.676237	+	0.736685i	$0.263610\pi$
$758$	0.0506253	+	0.0506253i	0.00183879	+	0.00183879i
$759$	−3.29775	−	5.87412i	−0.119701	−	0.213217i
$760$	−13.8351	−	11.7700i	−0.501852	−	0.426942i
$761$	−3.30561	−	3.81487i	−0.119828	−	0.138289i	0.692666	−	0.721259i	$-0.256436\pi$
$761$	−3.30561	−	3.81487i	−0.119828	−	0.138289i	−0.812494	+	0.582970i	$0.801891\pi$
$762$	−4.18334	−	19.2305i	−0.151546	−	0.696648i
$763$	−13.2395	−	17.6859i	−0.479303	−	0.640273i
$764$	3.73301	−	8.17416i	0.135056	−	0.295731i
$765$	−11.5367	−	7.26706i	−0.417112	−	0.262741i
$766$	9.26594	−	31.5569i	0.334792	−	1.14020i
$767$	3.84234	+	0.835850i	0.138739	+	0.0301808i
$768$	−0.936950	−	0.349464i	−0.0338093	−	0.0126102i
$769$	5.69413	−	1.67195i	0.205336	−	0.0602920i	−0.177447	−	0.984130i	$-0.556784\pi$
$769$	5.69413	−	1.67195i	0.205336	−	0.0602920i	0.382783	+	0.923838i	$0.374966\pi$
$770$	5.13062	−	6.98501i	0.184895	−	0.251722i
$771$	0.459225	−	0.529973i	0.0165386	−	0.0190865i
$772$	13.0717	+	7.13771i	0.470462	+	0.256892i
$773$	2.07991	−	5.57645i	0.0748091	−	0.200571i	−0.894163	−	0.447742i	$-0.852228\pi$
$773$	2.07991	−	5.57645i	0.0748091	−	0.200571i	0.968972	+	0.247171i	$0.0795010\pi$
$774$	−2.01925	+	1.29770i	−0.0725806	+	0.0466447i
$775$	33.6678	+	4.21828i	1.20938	+	0.151525i
$776$	2.78181	−	0.399964i	0.0998611	−	0.0143579i
$777$	8.99808	−	3.35611i	0.322804	−	0.120400i
$778$	−26.0162	+	19.4755i	−0.932724	+	0.698229i
$779$	19.1076	+	12.2797i	0.684601	+	0.439966i
$780$	0.666433	−	0.678645i	0.0238621	−	0.0242994i
$781$			6.82172i			0.244100i
$782$	27.9599	−	8.56811i	0.999845	−	0.306395i
$783$	4.02321	−	4.02321i	0.143778	−	0.143778i
$784$	0.463968	−	0.402030i	0.0165703	−	0.0143582i
$785$	−8.41382	−	27.7213i	−0.300302	−	0.989416i
$786$	1.09450	−	7.61243i	0.0390396	−	0.271526i
$787$	12.8004	+	34.3193i	0.456286	+	1.22335i	0.937881	+	0.346957i	$0.112785\pi$
$787$	12.8004	+	34.3193i	0.456286	+	1.22335i	−0.481595	+	0.876394i	$0.659942\pi$
$788$	9.16769	+	6.86285i	0.326585	+	0.244479i
$789$	2.02916	+	0.595816i	0.0722401	+	0.0212116i
$790$	1.36695	−	10.1614i	0.0486340	−	0.361528i
$791$	−11.4875	−	25.1541i	−0.408449	−	0.894378i
$792$	−0.673180	+	1.23284i	−0.0239204	+	0.0438070i
$793$	−4.87574	+	0.348720i	−0.173143	+	0.0123834i
$794$	−19.1280	−	16.5745i	−0.678826	−	0.588206i
$795$	2.31790	+	6.04631i	0.0822076	+	0.214441i
$796$	−13.2856	+	6.06734i	−0.470896	+	0.215051i
$797$	−3.22166	+	14.8097i	−0.114117	+	0.524588i	0.884227	+	0.467058i	$0.154686\pi$
$797$	−3.22166	+	14.8097i	−0.114117	+	0.524588i	−0.998344	+	0.0575300i	$0.981678\pi$
$798$	−19.6732	+	10.7424i	−0.696423	+	0.380276i
$799$	11.2837	+	78.4799i	0.399189	+	2.77642i
$800$	4.34416	−	2.47553i	0.153589	−	0.0875232i
$801$	0.0478077	+	0.00687371i	0.00168920	+	0.000242871i
$802$	7.25323	−	1.57784i	0.256120	−	0.0557156i
$803$	0.711444	−	9.94729i	0.0251063	−	0.351032i
$804$	8.64131			0.304755
$805$	27.1668	+	11.7289i	0.957503	+	0.413389i
$806$	2.88664			0.101677
$807$	−0.444258	+	6.21154i	−0.0156386	+	0.218657i
$808$	−15.3891	+	3.34770i	−0.541388	+	0.117772i
$809$	−33.2259	−	4.77717i	−1.16816	−	0.167956i	−0.469185	−	0.883100i	$-0.655452\pi$
$809$	−33.2259	−	4.77717i	−1.16816	−	0.167956i	−0.698977	+	0.715144i	$0.746361\pi$
$810$	0.947324	+	2.02548i	0.0332856	+	0.0711682i
$811$	−0.994990	−	6.92031i	−0.0349388	−	0.243005i	0.964866	−	0.262741i	$-0.0846265\pi$
$811$	−0.994990	−	6.92031i	−0.0349388	−	0.243005i	−0.999805	+	0.0197361i	$0.993717\pi$
$812$	−13.7793	+	7.52407i	−0.483559	+	0.264043i
$813$	−6.90942	+	31.7621i	−0.242324	+	1.11395i
$814$	4.44698	−	2.03087i	0.155867	−	0.0711819i
$815$	26.0326	+	11.6042i	0.911881	+	0.406478i
$816$	−4.60829	−	3.99311i	−0.161323	−	0.139787i
$817$	−19.4487	+	1.39100i	−0.680424	+	0.0486649i
$818$	2.03522	−	3.72722i	0.0711598	−	0.130319i
$819$	−0.487586	−	1.06767i	−0.0170376	−	0.0373072i
$820$	−4.97088	+	3.79206i	−0.173591	+	0.132425i
$821$	14.8638	+	4.36441i	0.518751	+	0.152319i	0.530619	−	0.847611i	$-0.321960\pi$
$821$	14.8638	+	4.36441i	0.518751	+	0.152319i	−0.0118679	+	0.999930i	$0.503778\pi$
$822$	3.94174	+	2.95075i	0.137484	+	0.102919i
$823$	8.37247	+	22.4475i	0.291846	+	0.782469i	0.997281	+	0.0736945i	$0.0234790\pi$
$823$	8.37247	+	22.4475i	0.291846	+	0.782469i	−0.705435	+	0.708775i	$0.749248\pi$
$824$	−2.44111	+	16.9783i	−0.0850402	+	0.591468i
$825$	−2.57346	−	6.53482i	−0.0895965	−	0.227513i
$826$	19.2776	−	16.7041i	0.670753	−	0.581211i
$827$	31.2203	−	31.2203i	1.08564	−	1.08564i	0.0896649	−	0.995972i	$-0.471420\pi$
$827$	31.2203	−	31.2203i	1.08564	−	1.08564i	0.995972	−	0.0896649i	$-0.0285796\pi$
$828$	−4.61713	−	1.29695i	−0.160457	−	0.0450720i
$829$		−	1.81499i		−	0.0630373i	−0.999503	−	0.0315187i	$-0.989966\pi$
$829$		−	1.81499i		−	0.0630373i	0.999503	−	0.0315187i	$-0.0100344\pi$
$830$	−6.22798	−	6.11591i	−0.216176	−	0.212286i
$831$	7.03922	+	4.52383i	0.244188	+	0.156930i
$832$	0.340525	−	0.254914i	0.0118056	−	0.00883755i
$833$	3.50742	−	1.30820i	0.121525	−	0.0453265i
$834$	21.1224	−	3.03694i	0.731409	−	0.105161i
$835$	9.18062	−	6.01849i	0.317708	−	0.208279i
$836$	−9.59913	+	6.16898i	−0.331993	+	0.213359i
$837$	−2.37153	+	6.35833i	−0.0819722	+	0.219776i
$838$	−9.83731	−	5.37158i	−0.339824	−	0.185558i
$839$	30.1662	−	34.8136i	1.04145	−	1.20190i	0.0624512	−	0.998048i	$-0.480108\pi$
$839$	30.1662	−	34.8136i	1.04145	−	1.20190i	0.979002	−	0.203853i	$-0.0653463\pi$
$840$	−0.933501	−	6.09903i	−0.0322088	−	0.210437i
$841$	3.23577	−	0.950108i	0.111578	−	0.0327624i
$842$	11.5699	+	4.31536i	0.398726	+	0.148717i
$843$	−18.3139	−	3.98394i	−0.630764	−	0.137214i
$844$	0.470269	−	1.60159i	0.0161873	−	0.0551290i
$845$	−6.34707	−	27.9528i	−0.218346	−	0.961604i
$846$	5.40159	−	11.8278i	0.185710	−	0.406649i
$847$	14.9270	+	19.9401i	0.512898	+	0.685151i
$848$	0.615563	+	2.82970i	0.0211385	+	0.0971723i
$849$	1.93373	+	2.23164i	0.0663654	+	0.0765897i
$850$	30.0941	−	4.88615i	1.03222	−	0.167593i
$851$	10.1592	+	13.2436i	0.348253	+	0.453986i
$852$	3.43407	+	3.43407i	0.117649	+	0.117649i
$853$	6.92673	+	0.495409i	0.237167	+	0.0169625i	0.189417	−	0.981897i	$-0.439340\pi$
$853$	6.92673	+	0.495409i	0.237167	+	0.0169625i	0.0477501	+	0.998859i	$0.484795\pi$
$854$	−17.1434	+	26.6756i	−0.586634	+	0.912820i
$855$	−1.13129	+	18.1291i	−0.0386892	+	0.620001i
$856$	1.09238	+	0.498874i	0.0373368	+	0.0170511i
$857$	18.7344	−	25.0262i	0.639955	−	0.854879i	−0.356899	−	0.934143i	$-0.616166\pi$
$857$	18.7344	−	25.0262i	0.639955	−	0.854879i	0.996854	+	0.0792635i	$0.0252569\pi$
$858$	−0.286350	−	0.524410i	−0.00977582	−	0.0179031i
$859$	−3.65630	−	5.68931i	−0.124751	−	0.194117i	0.773260	−	0.634089i	$-0.218625\pi$
$859$	−3.65630	−	5.68931i	−0.124751	−	0.194117i	−0.898011	+	0.439972i	$0.854988\pi$
$860$	1.46530	−	5.16332i	0.0499664	−	0.176068i
$861$	2.17363	+	7.40271i	0.0740771	+	0.252284i
$862$	0.0782027	+	1.09342i	0.00266359	+	0.0372419i
$863$	−2.45947	−	34.3879i	−0.0837214	−	1.17058i	−0.849541	−	0.527522i	$-0.823121\pi$
$863$	−2.45947	−	34.3879i	−0.0837214	−	1.17058i	0.765820	−	0.643055i	$-0.222333\pi$
$864$	0.281733	+	0.959493i	0.00958474	+	0.0326426i
$865$	12.4242	−	43.7795i	0.422436	−	1.48855i
$866$	10.3606	+	16.1214i	0.352066	+	0.547826i
$867$	−9.67186	−	17.7127i	−0.328474	−	0.601555i
$868$	11.2217	−	14.9904i	0.380890	−	0.508809i
$869$	−5.85870	−	2.67558i	−0.198743	−	0.0907627i
$870$	−0.792365	+	12.6978i	−0.0268637	+	0.430496i
$871$	−1.98726	+	3.09223i	−0.0673356	+	0.104776i
$872$	−7.98605	−	0.571174i	−0.270442	−	0.0193424i
$873$	−1.98726	−	1.98726i	−0.0672587	−	0.0672587i
$874$	−27.8696	−	27.2218i	−0.942702	−	0.920791i
$875$	26.3975	+	15.9659i	0.892398	+	0.539748i
$876$	−4.64934	−	5.36562i	−0.157087	−	0.181288i
$877$	11.1854	+	51.4183i	0.377703	+	1.73627i	0.637356	+	0.770570i	$0.280028\pi$
$877$	11.1854	+	51.4183i	0.377703	+	1.73627i	−0.259653	+	0.965702i	$0.583608\pi$
$878$	7.55509	+	10.0924i	0.254972	+	0.340603i
$879$	−8.03275	+	17.5893i	−0.270938	+	0.593272i
$880$	−0.695485	−	3.06294i	−0.0234448	−	0.103252i
$881$	13.3240	−	45.3773i	0.448896	−	1.52880i	−0.355482	−	0.934683i	$-0.615683\pi$
$881$	13.3240	−	45.3773i	0.448896	−	1.52880i	0.804378	−	0.594117i	$-0.202499\pi$
$882$	−0.599887	−	0.130497i	−0.0201993	−	0.00439408i
$883$	33.0924	+	12.3428i	1.11365	+	0.415369i	0.837880	−	0.545855i	$-0.183795\pi$
$883$	33.0924	+	12.3428i	1.11365	+	0.415369i	0.275769	+	0.961224i	$0.411068\pi$
$884$	2.48868	−	0.730743i	0.0837034	−	0.0245775i
$885$	−3.12738	−	20.4328i	−0.105126	−	0.686840i
$886$	−5.50358	+	6.35147i	−0.184896	+	0.213382i
$887$	−9.35337	−	5.10733i	−0.314055	−	0.171487i	0.314489	−	0.949261i	$-0.398167\pi$
$887$	−9.35337	−	5.10733i	−0.314055	−	0.171487i	−0.628544	+	0.777774i	$0.716349\pi$
$888$	1.21628	−	3.26096i	0.0408156	−	0.109431i
$889$	45.6838	−	29.3592i	1.53218	−	0.984675i
$890$	−0.0903220	+	0.0592120i	−0.00302760	+	0.00198479i
$891$	1.39036	−	0.199904i	0.0465788	−	0.00669702i
$892$	1.03077	−	0.384456i	0.0345126	−	0.0128725i
$893$	84.5586	−	63.2997i	2.82964	−	2.11825i
$894$	13.3835	+	8.60102i	0.447610	+	0.287661i
$895$	−35.2280	−	34.5941i	−1.17754	−	1.15635i
$896$		−	2.75933i		−	0.0921828i
$897$	1.52591	−	1.35395i	0.0509487	−	0.0452070i
$898$	24.6331	−	24.6331i	0.822016	−	0.822016i
$899$	−29.1805	+	25.2850i	−0.973223	+	0.843302i
$900$	−4.58512	−	1.99415i	−0.152837	−	0.0664718i
$901$	−2.51300	+	17.4783i	−0.0837202	+	0.582287i
$902$	1.37252	+	3.67986i	0.0456998	+	0.122526i
$903$	−5.30215	−	3.96914i	−0.176445	−	0.132085i
$904$	−9.61571	−	2.82343i	−0.319814	−	0.0939058i
$905$	16.4452	−	12.5453i	0.546658	−	0.417020i
$906$	4.60779	+	10.0896i	0.153083	+	0.335206i
$907$	21.5157	−	39.4031i	0.714417	−	1.30836i	−0.227916	−	0.973681i	$-0.573191\pi$
$907$	21.5157	−	39.4031i	0.714417	−	1.30836i	0.942333	−	0.334677i	$-0.108627\pi$
$908$	6.36885	−	0.455509i	0.211358	−	0.0151166i
$909$	11.9023	+	10.3134i	0.394775	+	0.342075i
$910$	2.39717	+	1.06856i	0.0794655	+	0.0354223i
$911$	−4.76006	+	2.17384i	−0.157708	+	0.0720227i	−0.492705	−	0.870196i	$-0.663992\pi$
$911$	−4.76006	+	2.17384i	−0.157708	+	0.0720227i	0.334997	+	0.942219i	$0.391265\pi$
$912$	−1.72674	+	7.93769i	−0.0571781	+	0.262843i
$913$	−4.81256	+	2.62786i	−0.159272	+	0.0869693i
$914$	−2.50980	−	17.4560i	−0.0830167	−	0.577394i
$915$	10.8863	+	23.2762i	0.359891	+	0.769486i
$916$	−18.8074	−	2.70409i	−0.621412	−	0.0893456i
$917$	20.7363	−	4.51090i	0.684771	−	0.148963i
$918$	−0.435001	+	6.08211i	−0.0143572	+	0.200740i
$919$	−51.6838			−1.70489			−0.852445	−	0.522817i	$-0.824881\pi$
$919$	−51.6838			−1.70489			−0.852445	+	0.522817i	$0.824881\pi$
$920$	9.65978	−	4.65710i	0.318474	−	0.153540i
$921$	−4.17457			−0.137557
$922$	0.469650	−	6.56657i	0.0154671	−	0.216258i
$923$	−2.01859	+	0.439118i	−0.0664428	+	0.0144537i
$924$	−3.83646	−	0.551600i	−0.126210	−	0.0181463i
$925$	8.61584	+	15.1194i	0.283287	+	0.497124i
$926$	3.26299	+	22.6946i	0.107228	+	0.745790i
$927$	15.0548	−	8.22052i	0.494463	−	0.269997i
$928$	−1.20943	+	5.55965i	−0.0397014	+	0.182504i
$929$	−53.3504	+	24.3643i	−1.75037	+	0.799366i	−0.761946	+	0.647641i	$0.775756\pi$
$929$	−53.3504	+	24.3643i	−1.75037	+	0.799366i	−0.988423	+	0.151725i	$0.951517\pi$
$930$	−5.43177	−	14.1689i	−0.178115	−	0.464618i
$931$	−3.76897	−	3.26583i	−0.123523	−	0.107033i
$932$	−6.76586	+	0.483904i	−0.221623	+	0.0158508i
$933$	−13.4139	+	24.5657i	−0.439151	+	0.804246i
$934$	−0.840829	−	1.84116i	−0.0275128	−	0.0602445i
$935$	2.55341	−	18.9812i	0.0835056	−	0.620751i
$936$	−0.408138	−	0.119840i	−0.0133404	−	0.00391710i
$937$	12.4203	+	9.29768i	0.405752	+	0.303742i	0.782590	−	0.622537i	$-0.213898\pi$
$937$	12.4203	+	9.29768i	0.405752	+	0.303742i	−0.376839	+	0.926279i	$0.622989\pi$
$938$	8.33271	+	22.3409i	0.272073	+	0.729455i
$939$	−1.58936	+	11.0542i	−0.0518667	+	0.360741i
$940$	8.44440	+	27.8220i	0.275426	+	0.907455i
$941$	−12.9992	+	11.2639i	−0.423762	+	0.367192i	−0.840479	−	0.541844i	$-0.817726\pi$
$941$	−12.9992	+	11.2639i	−0.423762	+	0.367192i	0.416717	+	0.909036i	$0.363181\pi$
$942$	−9.16113	+	9.16113i	−0.298486	+	0.298486i
$943$	−11.1947	+	7.38178i	−0.364549	+	0.240384i
$944$		−	9.24423i		−	0.300874i
$945$	−4.32310	+	4.40232i	−0.140630	+	0.143207i
$946$	−2.83636	−	1.82282i	−0.0922180	−	0.0592649i
$947$	−19.6514	+	14.7108i	−0.638584	+	0.478038i	−0.868840	−	0.495092i	$-0.835134\pi$
$947$	−19.6514	+	14.7108i	−0.638584	+	0.478038i	0.230257	+	0.973130i	$0.426043\pi$
$948$	−4.29617	+	1.60239i	−0.139533	+	0.0520431i
$949$	2.98926	−	0.429791i	0.0970356	−	0.0139516i
$950$	−24.9270	−	32.0680i	−0.808740	−	1.04042i
$951$	11.2596	−	7.23608i	0.365116	−	0.234646i
$952$	5.87989	−	15.7646i	0.190568	−	0.510933i
$953$	−27.1379	−	14.8184i	−0.879082	−	0.480015i	−0.0247207	−	0.999694i	$-0.507870\pi$
$953$	−27.1379	−	14.8184i	−0.879082	−	0.480015i	−0.854361	+	0.519679i	$0.826051\pi$
$954$	1.89640	−	2.18856i	0.0613981	−	0.0708572i
$955$	11.8952	−	16.1946i	0.384921	−	0.524044i
$956$	28.0953	−	8.24953i	0.908667	−	0.266809i
$957$	7.48814	+	2.79293i	0.242057	+	0.0902826i
$958$	4.45344	+	0.968786i	0.143884	+	0.0313000i
$959$	−3.82777	+	13.0362i	−0.123605	+	0.420960i
$960$	−1.89200	−	1.19178i	−0.0610640	−	0.0384646i
$961$	6.25306	−	13.6923i	0.201711	−	0.441687i
$962$	0.887203	+	1.18516i	0.0286046	+	0.0382112i
$963$	−0.255271	−	1.17346i	−0.00822598	−	0.0378142i
$964$	0.614463	+	0.709128i	0.0197905	+	0.0228395i
$965$	25.3657	+	21.5794i	0.816549	+	0.694665i
$966$	−1.09918	−	13.1876i	−0.0353655	−	0.424303i
$967$	−28.2059	−	28.2059i	−0.907040	−	0.907040i	0.0889923	−	0.996032i	$-0.471635\pi$
$967$	−28.2059	−	28.2059i	−0.907040	−	0.907040i	−0.996032	+	0.0889923i	$0.971635\pi$
$968$	9.00394	+	0.643974i	0.289398	+	0.0206981i
$969$	−26.7797	+	41.6700i	−0.860288	+	1.33863i
$970$	6.27208	+	0.391389i	0.201384	+	0.0125667i
$971$	38.8011	+	17.7199i	1.24519	+	0.568657i	0.925457	−	0.378852i	$-0.123681\pi$
$971$	38.8011	+	17.7199i	1.24519	+	0.568657i	0.319728	+	0.947509i	$0.396408\pi$
$972$	0.599278	−	0.800541i	0.0192218	−	0.0256774i
$973$	28.2197	+	51.6804i	0.904680	+	1.65680i
$974$	13.2776	+	20.6603i	0.425441	+	0.661999i
$975$	1.76804	−	1.18215i	0.0566226	−	0.0378592i
$976$	3.23758	+	11.0262i	0.103632	+	0.352939i
$977$	−4.05973	−	56.7624i	−0.129882	−	1.81599i	−0.477805	−	0.878466i	$-0.658567\pi$
$977$	−4.05973	−	56.7624i	−0.129882	−	1.81599i	0.347922	−	0.937523i	$-0.386887\pi$
$978$	−0.909317	−	12.7139i	−0.0290768	−	0.406546i
$979$	0.0191139	+	0.0650958i	0.000610881	+	0.00208047i
$980$	1.19882	−	0.668805i	0.0382949	−	0.0213642i
$981$	4.32861	+	6.73545i	0.138202	+	0.215046i
$982$	−4.92461	−	9.01874i	−0.157150	−	0.287800i
$983$	−19.5672	+	26.1387i	−0.624096	+	0.833694i	−0.995498	−	0.0947775i	$-0.969786\pi$
$983$	−19.5672	+	26.1387i	−0.624096	+	0.833694i	0.371403	+	0.928472i	$0.378877\pi$
$984$	2.54337	+	1.16152i	0.0810798	+	0.0370279i
$985$	16.9441	+	19.1995i	0.539885	+	0.611748i
$986$	−18.7568	+	29.1861i	−0.597338	+	0.929476i
$987$	35.7878	+	2.55960i	1.13914	+	0.0814729i
$988$	−2.44334	−	2.44334i	−0.0777332	−	0.0777332i
$989$	3.89574	−	10.8322i	0.123877	−	0.344442i
$990$	−2.03522	+	2.39232i	−0.0646836	+	0.0760328i
$991$	−5.15430	−	5.94838i	−0.163732	−	0.188957i	0.667955	−	0.744202i	$-0.267170\pi$
$991$	−5.15430	−	5.94838i	−0.163732	−	0.188957i	−0.831687	+	0.555245i	$0.812624\pi$
$992$	−1.44251	−	6.63112i	−0.0457998	−	0.210538i
$993$	9.21238	+	12.3063i	0.292346	+	0.390529i
$994$	−5.56686	+	12.1897i	−0.176570	+	0.386634i
$995$	−31.8482	+	7.23158i	−1.00966	+	0.229257i
$996$	−1.09978	+	3.74552i	−0.0348480	+	0.118681i
$997$	35.1391	+	7.64404i	1.11287	+	0.242089i	0.731168	−	0.682198i	$-0.238976\pi$
$997$	35.1391	+	7.64404i	1.11287	+	0.242089i	0.381698	+	0.924287i	$0.375339\pi$
$998$	34.6493	+	12.9235i	1.09680	+	0.409086i
$999$	−3.33942	+	0.980543i	−0.105655	+	0.0310230i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	690.2.w.b.217.7	yes	240
5.3	odd	4	inner	690.2.w.b.493.1	yes	240
23.7	odd	22	inner	690.2.w.b.7.1	✓	240
115.53	even	44	inner	690.2.w.b.283.7	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.2.w.b.7.1	✓	240	23.7	odd	22	inner
690.2.w.b.217.7	yes	240	1.1	even	1	trivial
690.2.w.b.283.7	yes	240	115.53	even	44	inner
690.2.w.b.493.1	yes	240	5.3	odd	4	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:	\( N \)	\(=\)	\( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	690.w (of order \(44\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(0.0713392 - 0.997452i) q^{2} +(-0.977147 + 0.212565i) q^{3} +(-0.989821 - 0.142315i) q^{4} +(-2.10209 - 0.762373i) q^{5} +(0.142315 + 0.989821i) q^{6} +(-2.42181 + 1.32241i) q^{7} +(-0.212565 + 0.977147i) q^{8} +(0.909632 - 0.415415i) q^{9} +O(q^{10})\)	\(q+(0.0713392 - 0.997452i) q^{2} +(-0.977147 + 0.212565i) q^{3} +(-0.989821 - 0.142315i) q^{4} +(-2.10209 - 0.762373i) q^{5} +(0.142315 + 0.989821i) q^{6} +(-2.42181 + 1.32241i) q^{7} +(-0.212565 + 0.977147i) q^{8} +(0.909632 - 0.415415i) q^{9} +(-0.910392 + 2.04235i) q^{10} +(1.06157 + 0.919855i) q^{11} +(0.997452 - 0.0713392i) q^{12} +(-0.203857 + 0.373337i) q^{13} +(1.14627 + 2.50998i) q^{14} +(2.21611 + 0.298118i) q^{15} +(0.959493 + 0.281733i) q^{16} +(4.88142 + 3.65418i) q^{17} +(-0.349464 - 0.936950i) q^{18} +(1.15607 - 8.04065i) q^{19} +(1.97220 + 1.05377i) q^{20} +(2.08536 - 1.80698i) q^{21} +(0.993243 - 0.993243i) q^{22} +(4.06472 + 2.54521i) q^{23} -1.00000i q^{24} +(3.83758 + 3.20515i) q^{25} +(0.357843 + 0.229972i) q^{26} +(-0.800541 + 0.599278i) q^{27} +(2.58536 - 0.964288i) q^{28} +(-5.63176 + 0.809725i) q^{29} +(0.455454 - 2.18919i) q^{30} +(5.70892 - 3.66890i) q^{31} +(0.349464 - 0.936950i) q^{32} +(-1.23284 - 0.673180i) q^{33} +(3.99311 - 4.60829i) q^{34} +(6.09903 - 0.933501i) q^{35} +(-0.959493 + 0.281733i) q^{36} +(3.26096 + 1.21628i) q^{37} +(-7.93769 - 1.72674i) q^{38} +(0.119840 - 0.408138i) q^{39} +(1.19178 - 1.89200i) q^{40} +(-1.16152 + 2.54337i) q^{41} +(-1.65361 - 2.20896i) q^{42} +(-0.510219 - 2.34544i) q^{43} +(-0.919855 - 1.06157i) q^{44} +(-2.22883 + 0.179762i) q^{45} +(2.82870 - 3.87279i) q^{46} +(9.19442 + 9.19442i) q^{47} +(-0.997452 - 0.0713392i) q^{48} +(0.331909 - 0.516460i) q^{49} +(3.47076 - 3.59915i) q^{50} +(-5.54661 - 2.53305i) q^{51} +(0.254914 - 0.340525i) q^{52} +(1.38785 + 2.54165i) q^{53} +(0.540641 + 0.841254i) q^{54} +(-1.53024 - 2.74293i) q^{55} +(-0.777394 - 2.64756i) q^{56} +(0.579512 + 8.10264i) q^{57} +(0.405897 + 5.67518i) q^{58} +(-2.60440 - 8.86977i) q^{59} +(-2.15112 - 0.610469i) q^{60} +(6.21286 + 9.66741i) q^{61} +(-3.25228 - 5.95611i) q^{62} +(-1.65361 + 2.20896i) q^{63} +(-0.909632 - 0.415415i) q^{64} +(0.713149 - 0.629373i) q^{65} +(-0.759415 + 1.18167i) q^{66} +(8.61929 + 0.616464i) q^{67} +(-4.31169 - 4.31169i) q^{68} +(-4.51285 - 1.62302i) q^{69} +(-0.496022 - 6.15009i) q^{70} +(3.18033 + 3.67030i) q^{71} +(0.212565 + 0.977147i) q^{72} +(-4.25471 - 5.68363i) q^{73} +(1.44581 - 3.16589i) q^{74} +(-4.43118 - 2.31617i) q^{75} +(-2.28861 + 7.79429i) q^{76} +(-3.78734 - 0.823885i) q^{77} +(-0.398549 - 0.148651i) q^{78} +(-4.39954 + 1.29182i) q^{79} +(-1.80216 - 1.32372i) q^{80} +(0.654861 - 0.755750i) q^{81} +(2.45403 + 1.34000i) q^{82} +(-1.36418 + 3.65752i) q^{83} +(-2.32130 + 1.49181i) q^{84} +(-7.47534 - 11.4029i) q^{85} +(-2.37586 + 0.341597i) q^{86} +(5.33094 - 1.98834i) q^{87} +(-1.12449 + 0.841780i) q^{88} +(0.0406320 + 0.0261126i) q^{89} +(0.0203007 + 2.23598i) q^{90} -1.17373i q^{91} +(-3.66112 - 3.09777i) q^{92} +(-4.79857 + 4.79857i) q^{93} +(9.82692 - 8.51507i) q^{94} +(-8.56014 + 16.0208i) q^{95} +(-0.142315 + 0.989821i) q^{96} +(-0.982139 - 2.63322i) q^{97} +(-0.491466 - 0.367907i) q^{98} +(1.34776 + 0.395738i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q + 24 q^{6}+O(q^{10}) \) 240 * q + 24 * q^6	\( 240 q + 24 q^{6} - 44 q^{10} + 24 q^{16} - 44 q^{21} + 96 q^{23} + 16 q^{25} + 16 q^{26} + 44 q^{28} - 16 q^{31} + 44 q^{33} + 16 q^{35} - 24 q^{36} + 44 q^{37} - 88 q^{43} + 8 q^{46} + 96 q^{47} - 24 q^{50} - 24 q^{55} + 44 q^{57} - 16 q^{58} + 88 q^{61} + 56 q^{62} - 88 q^{65} + 132 q^{67} - 56 q^{70} + 16 q^{71} + 48 q^{73} + 24 q^{81} - 24 q^{82} + 44 q^{85} - 16 q^{87} + 44 q^{88} - 124 q^{92} + 32 q^{93} + 20 q^{95} - 24 q^{96} - 56 q^{98}+O(q^{100}) \) 240 * q + 24 * q^6 - 44 * q^10 + 24 * q^16 - 44 * q^21 + 96 * q^23 + 16 * q^25 + 16 * q^26 + 44 * q^28 - 16 * q^31 + 44 * q^33 + 16 * q^35 - 24 * q^36 + 44 * q^37 - 88 * q^43 + 8 * q^46 + 96 * q^47 - 24 * q^50 - 24 * q^55 + 44 * q^57 - 16 * q^58 + 88 * q^61 + 56 * q^62 - 88 * q^65 + 132 * q^67 - 56 * q^70 + 16 * q^71 + 48 * q^73 + 24 * q^81 - 24 * q^82 + 44 * q^85 - 16 * q^87 + 44 * q^88 - 124 * q^92 + 32 * q^93 + 20 * q^95 - 24 * q^96 - 56 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more