LMFDB - Embedded newform 690.2.m.d.271.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [690,2,Mod(31,690)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(690, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 0, 6]))

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

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

chi := DirichletCharacter("690.31");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 690 = 2 \cdot 3 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	690.m (of order $11$, degree $10$, 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:	$20$
Relative dimension:	$2$ over $\Q(\zeta_{11})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 5 x^{19} + 8 x^{18} - 32 x^{17} + 277 x^{16} - 1138 x^{15} + 2950 x^{14} - 6404 x^{13} + \cdots + 7921 $ x^20 - 5x^19 + 8x^18 - 32x^17 + 277x^16 - 1138x^15 + 2950x^14 - 6404x^13 + 24088x^12 - 93423x^11 + 318055x^10 - 798006x^9 + 1869818x^8 - 3381161x^7 + 6172602x^6 - 7296658x^5 + 10759748x^4 - 4308967x^3 + 7994447x^2 + 486652*x + 7921
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			271.2
Root			$-0.162761 - 1.13203i$ of defining polynomial
Character	$\chi$	$=$	690.271
Dual form			690.2.m.d.331.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.959493 - 0.281733i) q^{2} +(0.654861 - 0.755750i) q^{3} +(0.841254 + 0.540641i) q^{4} +(0.142315 - 0.989821i) q^{5} +(-0.841254 + 0.540641i) q^{6} +(1.42213 + 3.11402i) q^{7} +(-0.654861 - 0.755750i) q^{8} +(-0.142315 - 0.989821i) q^{9} +O(q^{10})$	\(q+(-0.959493 - 0.281733i) q^{2} +(0.654861 - 0.755750i) q^{3} +(0.841254 + 0.540641i) q^{4} +(0.142315 - 0.989821i) q^{5} +(-0.841254 + 0.540641i) q^{6} +(1.42213 + 3.11402i) q^{7} +(-0.654861 - 0.755750i) q^{8} +(-0.142315 - 0.989821i) q^{9} +(-0.415415 + 0.909632i) q^{10} +(-1.04493 + 0.306819i) q^{11} +(0.959493 - 0.281733i) q^{12} +(0.0751770 - 0.164615i) q^{13} +(-0.487199 - 3.38854i) q^{14} +(-0.654861 - 0.755750i) q^{15} +(0.415415 + 0.909632i) q^{16} +(6.04764 - 3.88658i) q^{17} +(-0.142315 + 0.989821i) q^{18} +(5.08922 + 3.27064i) q^{19} +(0.654861 - 0.755750i) q^{20} +(3.28472 + 0.964480i) q^{21} +1.08904 q^{22} +(-0.615771 + 4.75614i) q^{23} -1.00000 q^{24} +(-0.959493 - 0.281733i) q^{25} +(-0.118509 + 0.136767i) q^{26} +(-0.841254 - 0.540641i) q^{27} +(-0.487199 + 3.38854i) q^{28} +(-0.0270267 + 0.0173690i) q^{29} +(0.415415 + 0.909632i) q^{30} +(0.365303 + 0.421583i) q^{31} +(-0.142315 - 0.989821i) q^{32} +(-0.452405 + 0.990628i) q^{33} +(-6.89764 + 2.02533i) q^{34} +(3.28472 - 0.964480i) q^{35} +(0.415415 - 0.909632i) q^{36} +(0.0764072 + 0.531424i) q^{37} +(-3.96163 - 4.57196i) q^{38} +(-0.0751770 - 0.164615i) q^{39} +(-0.841254 + 0.540641i) q^{40} +(1.57106 - 10.9269i) q^{41} +(-2.87994 - 1.85082i) q^{42} +(1.12123 - 1.29396i) q^{43} +(-1.04493 - 0.306819i) q^{44} -1.00000 q^{45} +(1.93079 - 4.39000i) q^{46} +5.58621 q^{47} +(0.959493 + 0.281733i) q^{48} +(-3.09067 + 3.56682i) q^{49} +(0.841254 + 0.540641i) q^{50} +(1.02308 - 7.11567i) q^{51} +(0.152240 - 0.0978389i) q^{52} +(4.37501 + 9.57993i) q^{53} +(0.654861 + 0.755750i) q^{54} +(0.154987 + 1.07796i) q^{55} +(1.42213 - 3.11402i) q^{56} +(5.80452 - 1.70436i) q^{57} +(0.0308253 - 0.00905112i) q^{58} +(2.97306 - 6.51009i) q^{59} +(-0.142315 - 0.989821i) q^{60} +(-4.54050 - 5.24001i) q^{61} +(-0.231732 - 0.507423i) q^{62} +(2.87994 - 1.85082i) q^{63} +(-0.142315 + 0.989821i) q^{64} +(-0.152240 - 0.0978389i) q^{65} +(0.713171 - 0.823043i) q^{66} +(-0.327392 - 0.0961309i) q^{67} +7.18884 q^{68} +(3.19120 + 3.57997i) q^{69} -3.42339 q^{70} +(-13.1895 - 3.87278i) q^{71} +(-0.654861 + 0.755750i) q^{72} +(9.66213 + 6.20947i) q^{73} +(0.0764072 - 0.531424i) q^{74} +(-0.841254 + 0.540641i) q^{75} +(2.51308 + 5.50288i) q^{76} +(-2.44146 - 2.81760i) q^{77} +(0.0257545 + 0.179126i) q^{78} +(0.0896571 - 0.196322i) q^{79} +(0.959493 - 0.281733i) q^{80} +(-0.959493 + 0.281733i) q^{81} +(-4.58590 + 10.0417i) q^{82} +(0.828582 + 5.76291i) q^{83} +(2.24184 + 2.58722i) q^{84} +(-2.98635 - 6.53920i) q^{85} +(-1.44036 + 0.925664i) q^{86} +(-0.00457210 + 0.0317997i) q^{87} +(0.916161 + 0.588781i) q^{88} +(0.868066 - 1.00180i) q^{89} +(0.959493 + 0.281733i) q^{90} +0.619525 q^{91} +(-3.08938 + 3.66821i) q^{92} +0.557834 q^{93} +(-5.35993 - 1.57382i) q^{94} +(3.96163 - 4.57196i) q^{95} +(-0.841254 - 0.540641i) q^{96} +(-0.100070 + 0.695999i) q^{97} +(3.97036 - 2.55160i) q^{98} +(0.452405 + 0.990628i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 2 q^{2} + 2 q^{3} - 2 q^{4} + 2 q^{5} + 2 q^{6} + 2 q^{7} - 2 q^{8} - 2 q^{9}+O(q^{10}) $ 20 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 + 2 * q^5 + 2 * q^6 + 2 * q^7 - 2 * q^8 - 2 * q^9	\( 20 q - 2 q^{2} + 2 q^{3} - 2 q^{4} + 2 q^{5} + 2 q^{6} + 2 q^{7} - 2 q^{8} - 2 q^{9} + 2 q^{10} + 2 q^{11} + 2 q^{12} - 11 q^{13} + 2 q^{14} - 2 q^{15} - 2 q^{16} + 24 q^{17} - 2 q^{18} + 22 q^{19} + 2 q^{20} - 2 q^{21} + 2 q^{22} - 22 q^{23} - 20 q^{24} - 2 q^{25} + 11 q^{26} + 2 q^{27} + 2 q^{28} + 14 q^{29} - 2 q^{30} - 8 q^{31} - 2 q^{32} - 2 q^{33} - 9 q^{34} - 2 q^{35} - 2 q^{36} + 20 q^{37} + 11 q^{39} + 2 q^{40} - 21 q^{41} - 13 q^{42} + 34 q^{43} + 2 q^{44} - 20 q^{45} + 14 q^{47} + 2 q^{48} + 10 q^{49} - 2 q^{50} + 31 q^{51} + 2 q^{54} - 2 q^{55} + 2 q^{56} + 11 q^{57} - 19 q^{58} - 40 q^{59} - 2 q^{60} - 19 q^{61} - 8 q^{62} + 13 q^{63} - 2 q^{64} + 9 q^{66} + 18 q^{67} - 20 q^{68} - 22 q^{69} + 20 q^{70} - 85 q^{71} - 2 q^{72} + 39 q^{73} + 20 q^{74} + 2 q^{75} - 48 q^{77} - 11 q^{78} - 28 q^{79} + 2 q^{80} - 2 q^{81} + q^{82} + 49 q^{83} + 9 q^{84} - 13 q^{85} - 32 q^{86} + 8 q^{87} + 2 q^{88} + 3 q^{89} + 2 q^{90} - 34 q^{91} - 11 q^{92} - 36 q^{93} + 3 q^{94} + 2 q^{96} + 43 q^{97} + 10 q^{98} + 2 q^{99}+O(q^{100}) \) 20 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 + 2 * q^5 + 2 * q^6 + 2 * q^7 - 2 * q^8 - 2 * q^9 + 2 * q^10 + 2 * q^11 + 2 * q^12 - 11 * q^13 + 2 * q^14 - 2 * q^15 - 2 * q^16 + 24 * q^17 - 2 * q^18 + 22 * q^19 + 2 * q^20 - 2 * q^21 + 2 * q^22 - 22 * q^23 - 20 * q^24 - 2 * q^25 + 11 * q^26 + 2 * q^27 + 2 * q^28 + 14 * q^29 - 2 * q^30 - 8 * q^31 - 2 * q^32 - 2 * q^33 - 9 * q^34 - 2 * q^35 - 2 * q^36 + 20 * q^37 + 11 * q^39 + 2 * q^40 - 21 * q^41 - 13 * q^42 + 34 * q^43 + 2 * q^44 - 20 * q^45 + 14 * q^47 + 2 * q^48 + 10 * q^49 - 2 * q^50 + 31 * q^51 + 2 * q^54 - 2 * q^55 + 2 * q^56 + 11 * q^57 - 19 * q^58 - 40 * q^59 - 2 * q^60 - 19 * q^61 - 8 * q^62 + 13 * q^63 - 2 * q^64 + 9 * q^66 + 18 * q^67 - 20 * q^68 - 22 * q^69 + 20 * q^70 - 85 * q^71 - 2 * q^72 + 39 * q^73 + 20 * q^74 + 2 * q^75 - 48 * q^77 - 11 * q^78 - 28 * q^79 + 2 * q^80 - 2 * q^81 + q^82 + 49 * q^83 + 9 * q^84 - 13 * q^85 - 32 * q^86 + 8 * q^87 + 2 * q^88 + 3 * q^89 + 2 * q^90 - 34 * q^91 - 11 * q^92 - 36 * q^93 + 3 * q^94 + 2 * q^96 + 43 * q^97 + 10 * q^98 + 2 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$277$	$461$	$511$
$\chi(n)$	$1$	$1$	$e\left(\frac{6}{11}\right)$

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 $

$2$	−0.959493	−	0.281733i	−0.678464	−	0.199215i
$2$	−0.959493	−	0.281733i	−0.678464	−	0.199215i
$3$	0.654861	−	0.755750i	0.378084	−	0.436332i
$3$	0.654861	−	0.755750i	0.378084	−	0.436332i
$4$	0.841254	+	0.540641i	0.420627	+	0.270320i
$5$	0.142315	−	0.989821i	0.0636451	−	0.442662i
$5$	0.142315	−	0.989821i	0.0636451	−	0.442662i
$6$	−0.841254	+	0.540641i	−0.343440	+	0.220716i
$7$	1.42213	+	3.11402i	0.537513	+	1.17699i	0.962373	+	0.271731i	$0.0875960\pi$
$7$	1.42213	+	3.11402i	0.537513	+	1.17699i	−0.424860	+	0.905259i	$0.639677\pi$
$8$	−0.654861	−	0.755750i	−0.231528	−	0.267198i
$9$	−0.142315	−	0.989821i	−0.0474383	−	0.329940i
$10$	−0.415415	+	0.909632i	−0.131366	+	0.287651i
$11$	−1.04493	+	0.306819i	−0.315058	+	0.0925093i	−0.435439	−	0.900218i	$-0.643407\pi$
$11$	−1.04493	+	0.306819i	−0.315058	+	0.0925093i	0.120381	+	0.992728i	$0.461588\pi$
$12$	0.959493	−	0.281733i	0.276982	−	0.0813292i
$13$	0.0751770	−	0.164615i	0.0208503	−	0.0456559i	−0.898920	−	0.438112i	$-0.855647\pi$
$13$	0.0751770	−	0.164615i	0.0208503	−	0.0456559i	0.919771	+	0.392456i	$0.128375\pi$
$14$	−0.487199	−	3.38854i	−0.130209	−	0.905626i
$15$	−0.654861	−	0.755750i	−0.169084	−	0.195134i
$16$	0.415415	+	0.909632i	0.103854	+	0.227408i
$17$	6.04764	−	3.88658i	1.46677	−	0.942634i	0.468520	−	0.883453i	$-0.344787\pi$
$17$	6.04764	−	3.88658i	1.46677	−	0.942634i	0.998247	−	0.0591809i	$-0.0188489\pi$
$18$	−0.142315	+	0.989821i	−0.0335439	+	0.233303i
$19$	5.08922	+	3.27064i	1.16755	+	0.750337i	0.973056	−	0.230567i	$-0.0740581\pi$
$19$	5.08922	+	3.27064i	1.16755	+	0.750337i	0.194491	+	0.980904i	$0.437694\pi$
$20$	0.654861	−	0.755750i	0.146431	−	0.168991i
$21$	3.28472	+	0.964480i	0.716784	+	0.210467i
$22$	1.08904			0.232185
$23$	−0.615771	+	4.75614i	−0.128397	+	0.991723i
$23$	−0.615771	+	4.75614i	−0.128397	+	0.991723i
$24$	−1.00000			−0.204124
$25$	−0.959493	−	0.281733i	−0.191899	−	0.0563465i
$26$	−0.118509	+	0.136767i	−0.0232415	+	0.0268222i
$27$	−0.841254	−	0.540641i	−0.161899	−	0.104046i
$28$	−0.487199	+	3.38854i	−0.0920719	+	0.640374i
$29$	−0.0270267	+	0.0173690i	−0.00501872	+	0.00322534i	−0.543148	−	0.839637i	$-0.682768\pi$
$29$	−0.0270267	+	0.0173690i	−0.00501872	+	0.00322534i	0.538129	+	0.842862i	$0.319131\pi$
$30$	0.415415	+	0.909632i	0.0758441	+	0.166075i
$31$	0.365303	+	0.421583i	0.0656104	+	0.0757185i	0.787606	−	0.616179i	$-0.211320\pi$
$31$	0.365303	+	0.421583i	0.0656104	+	0.0757185i	−0.721995	+	0.691898i	$0.756775\pi$
$32$	−0.142315	−	0.989821i	−0.0251579	−	0.174977i
$33$	−0.452405	+	0.990628i	−0.0787535	+	0.172446i
$34$	−6.89764	+	2.02533i	−1.18294	+	0.347341i
$35$	3.28472	−	0.964480i	0.555218	−	0.163027i
$36$	0.415415	−	0.909632i	0.0692358	−	0.151605i
$37$	0.0764072	+	0.531424i	0.0125613	+	0.0873655i	0.995138	−	0.0984934i	$-0.0314023\pi$
$37$	0.0764072	+	0.531424i	0.0125613	+	0.0873655i	−0.982576	+	0.185859i	$0.940493\pi$
$38$	−3.96163	−	4.57196i	−0.642661	−	0.741670i
$39$	−0.0751770	−	0.164615i	−0.0120380	−	0.0263594i
$40$	−0.841254	+	0.540641i	−0.133014	+	0.0854828i
$41$	1.57106	−	10.9269i	0.245358	−	1.70650i	−0.379027	−	0.925386i	$-0.623741\pi$
$41$	1.57106	−	10.9269i	0.245358	−	1.70650i	0.624385	−	0.781117i	$-0.285350\pi$
$42$	−2.87994	−	1.85082i	−0.444384	−	0.285588i
$43$	1.12123	−	1.29396i	0.170985	−	0.197328i	−0.663789	−	0.747920i	$-0.731053\pi$
$43$	1.12123	−	1.29396i	0.170985	−	0.197328i	0.834774	+	0.550592i	$0.185598\pi$
$44$	−1.04493	−	0.306819i	−0.157529	−	0.0462547i
$45$	−1.00000			−0.149071
$46$	1.93079	−	4.39000i	0.284679	−	0.647270i
$47$	5.58621			0.814832			0.407416	−	0.913243i	$-0.366430\pi$
$47$	5.58621			0.814832			0.407416	+	0.913243i	$0.366430\pi$
$48$	0.959493	+	0.281733i	0.138491	+	0.0406646i
$49$	−3.09067	+	3.56682i	−0.441524	+	0.509546i
$50$	0.841254	+	0.540641i	0.118971	+	0.0764582i
$51$	1.02308	−	7.11567i	0.143260	−	0.996393i
$52$	0.152240	−	0.0978389i	0.0211119	−	0.0135678i
$53$	4.37501	+	9.57993i	0.600954	+	1.31591i	0.928592	+	0.371102i	$0.121020\pi$
$53$	4.37501	+	9.57993i	0.600954	+	1.31591i	−0.327638	+	0.944803i	$0.606253\pi$
$54$	0.654861	+	0.755750i	0.0891153	+	0.102844i
$55$	0.154987	+	1.07796i	0.0208984	+	0.145352i
$56$	1.42213	−	3.11402i	0.190040	−	0.416129i
$57$	5.80452	−	1.70436i	0.768827	−	0.225748i
$58$	0.0308253	−	0.00905112i	0.00404756	−	0.00118847i
$59$	2.97306	−	6.51009i	0.387059	−	0.847541i	−0.611361	−	0.791352i	$-0.709378\pi$
$59$	2.97306	−	6.51009i	0.387059	−	0.847541i	0.998420	−	0.0561894i	$-0.0178951\pi$
$60$	−0.142315	−	0.989821i	−0.0183728	−	0.127785i
$61$	−4.54050	−	5.24001i	−0.581351	−	0.670915i	0.386544	−	0.922271i	$-0.373669\pi$
$61$	−4.54050	−	5.24001i	−0.581351	−	0.670915i	−0.967895	+	0.251356i	$0.919123\pi$
$62$	−0.231732	−	0.507423i	−0.0294301	−	0.0644428i
$63$	2.87994	−	1.85082i	0.362838	−	0.233182i
$64$	−0.142315	+	0.989821i	−0.0177894	+	0.123728i
$65$	−0.152240	−	0.0978389i	−0.0188831	−	0.0121354i
$66$	0.713171	−	0.823043i	0.0877853	−	0.101310i
$67$	−0.327392	−	0.0961309i	−0.0399973	−	0.0117443i	0.261673	−	0.965157i	$-0.415726\pi$
$67$	−0.327392	−	0.0961309i	−0.0399973	−	0.0117443i	−0.301670	+	0.953412i	$0.597544\pi$
$68$	7.18884			0.871775
$69$	3.19120	+	3.57997i	0.384176	+	0.430978i
$70$	−3.42339			−0.409173
$71$	−13.1895	−	3.87278i	−1.56530	−	0.459614i	−0.619673	−	0.784860i	$-0.712735\pi$
$71$	−13.1895	−	3.87278i	−1.56530	−	0.459614i	−0.945630	+	0.325245i	$0.894553\pi$
$72$	−0.654861	+	0.755750i	−0.0771761	+	0.0890659i
$73$	9.66213	+	6.20947i	1.13087	+	0.726764i	0.965741	−	0.259509i	$-0.0835606\pi$
$73$	9.66213	+	6.20947i	1.13087	+	0.726764i	0.165126	+	0.986273i	$0.447197\pi$
$74$	0.0764072	−	0.531424i	0.00888216	−	0.0617768i
$75$	−0.841254	+	0.540641i	−0.0971396	+	0.0624278i
$76$	2.51308	+	5.50288i	0.288270	+	0.631224i
$77$	−2.44146	−	2.81760i	−0.278230	−	0.321095i
$78$	0.0257545	+	0.179126i	0.00291612	+	0.0202821i
$79$	0.0896571	−	0.196322i	0.0100872	−	0.0220879i	−0.904521	−	0.426428i	$-0.859772\pi$
$79$	0.0896571	−	0.196322i	0.0100872	−	0.0220879i	0.914609	+	0.404340i	$0.132499\pi$
$80$	0.959493	−	0.281733i	0.107275	−	0.0314987i
$81$	−0.959493	+	0.281733i	−0.106610	+	0.0313036i
$82$	−4.58590	+	10.0417i	−0.506427	+	1.10892i
$83$	0.828582	+	5.76291i	0.0909487	+	0.632562i	0.983404	+	0.181427i	$0.0580716\pi$
$83$	0.828582	+	5.76291i	0.0909487	+	0.632562i	−0.892456	+	0.451135i	$0.851019\pi$
$84$	2.24184	+	2.58722i	0.244605	+	0.282289i
$85$	−2.98635	−	6.53920i	−0.323915	−	0.709275i
$86$	−1.44036	+	0.925664i	−0.155318	+	0.0998169i
$87$	−0.00457210	+	0.0317997i	−0.000490181	+	0.00340928i
$88$	0.916161	+	0.588781i	0.0976631	+	0.0627642i
$89$	0.868066	−	1.00180i	0.0920148	−	0.106191i	−0.707875	−	0.706338i	$-0.750346\pi$
$89$	0.868066	−	1.00180i	0.0920148	−	0.106191i	0.799890	+	0.600147i	$0.204891\pi$
$90$	0.959493	+	0.281733i	0.101139	+	0.0296972i
$91$	0.619525			0.0649439
$92$	−3.08938	+	3.66821i	−0.322090	+	0.382437i
$93$	0.557834			0.0578447
$94$	−5.35993	−	1.57382i	−0.552834	−	0.162327i
$95$	3.96163	−	4.57196i	0.406454	−	0.469073i
$96$	−0.841254	−	0.540641i	−0.0858601	−	0.0551789i
$97$	−0.100070	+	0.695999i	−0.0101605	+	0.0706680i	−0.994271	−	0.106890i	$-0.965911\pi$
$97$	−0.100070	+	0.695999i	−0.0101605	+	0.0706680i	0.984110	+	0.177558i	$0.0568198\pi$
$98$	3.97036	−	2.55160i	0.401067	−	0.257750i
$99$	0.452405	+	0.990628i	0.0454684	+	0.0995619i
$100$	−0.654861	−	0.755750i	−0.0654861	−	0.0755750i
$101$	−1.66677	−	11.5926i	−0.165850	−	1.15351i	−0.887350	−	0.461097i	$-0.847456\pi$
$101$	−1.66677	−	11.5926i	−0.165850	−	1.15351i	0.721500	−	0.692415i	$-0.243453\pi$
$102$	−2.98635	+	6.53920i	−0.295693	+	0.647477i
$103$	8.89899	−	2.61298i	0.876844	−	0.257465i	0.187820	−	0.982203i	$-0.439858\pi$
$103$	8.89899	−	2.61298i	0.876844	−	0.257465i	0.689024	+	0.724739i	$0.258040\pi$
$104$	−0.173638	+	0.0509847i	−0.0170266	+	0.00499946i
$105$	1.42213	−	3.11402i	0.138785	−	0.303897i
$106$	−1.49881	−	10.4245i	−0.145577	−	1.01251i
$107$	2.89783	+	3.34428i	0.280144	+	0.323304i	0.878331	−	0.478053i	$-0.158657\pi$
$107$	2.89783	+	3.34428i	0.280144	+	0.323304i	−0.598187	+	0.801357i	$0.704112\pi$
$108$	−0.415415	−	0.909632i	−0.0399733	−	0.0875294i
$109$	−6.30687	+	4.05318i	−0.604088	+	0.388224i	−0.806636	−	0.591048i	$-0.798714\pi$
$109$	−6.30687	+	4.05318i	−0.604088	+	0.388224i	0.202548	+	0.979272i	$0.435078\pi$
$110$	0.154987	−	1.07796i	0.0147774	−	0.102779i
$111$	0.451659	+	0.290264i	0.0428696	+	0.0275506i
$112$	−2.24184	+	2.58722i	−0.211834	+	0.244470i
$113$	3.22430	+	0.946741i	0.303317	+	0.0890619i	0.429849	−	0.902901i	$-0.358567\pi$
$113$	3.22430	+	0.946741i	0.303317	+	0.0890619i	−0.126533	+	0.991962i	$0.540385\pi$
$114$	−6.04957			−0.566594
$115$	4.62009	+	1.28637i	0.430826	+	0.119955i
$116$	−0.0321267			−0.00298288
$117$	−0.173638	−	0.0509847i	−0.0160528	−	0.00471354i
$118$	−4.68673	+	5.40878i	−0.431449	+	0.497918i
$119$	20.7034	+	13.3053i	1.89788	+	1.21969i
$120$	−0.142315	+	0.989821i	−0.0129915	+	0.0903579i
$121$	−8.25605	+	5.30584i	−0.750550	+	0.482349i
$122$	2.88029	+	6.30696i	0.260769	+	0.571005i
$123$	−7.22921	−	8.34295i	−0.651836	−	0.752259i
$124$	0.0793880	+	0.552156i	0.00712925	+	0.0495850i
$125$	−0.415415	+	0.909632i	−0.0371558	+	0.0813600i
$126$	−3.28472	+	0.964480i	−0.292626	+	0.0859227i
$127$	5.09776	−	1.49684i	0.452353	−	0.132823i	−0.0476167	−	0.998866i	$-0.515163\pi$
$127$	5.09776	−	1.49684i	0.452353	−	0.132823i	0.499970	+	0.866043i	$0.333344\pi$
$128$	0.415415	−	0.909632i	0.0367178	−	0.0804009i
$129$	−0.243666	−	1.69473i	−0.0214536	−	0.149213i
$130$	0.118509	+	0.136767i	0.0103939	+	0.0119952i
$131$	−3.08664	−	6.75880i	−0.269681	−	0.590519i	0.725539	−	0.688181i	$-0.241591\pi$
$131$	−3.08664	−	6.75880i	−0.269681	−	0.590519i	−0.995220	+	0.0976624i	$0.968863\pi$
$132$	−0.916161	+	0.588781i	−0.0797416	+	0.0512468i
$133$	−2.94734	+	20.4992i	−0.255567	+	1.77751i
$134$	0.287047	+	0.184474i	0.0247971	+	0.0159361i
$135$	−0.654861	+	0.755750i	−0.0563614	+	0.0650446i
$136$	−6.89764	−	2.02533i	−0.591468	−	0.173671i
$137$	−18.7354			−1.60067			−0.800335	−	0.599554i	$-0.795345\pi$
$137$	−18.7354			−1.60067			−0.800335	+	0.599554i	$0.795345\pi$
$138$	−2.05334	−	4.33403i	−0.174792	−	0.368937i
$139$	−17.9025			−1.51847			−0.759237	−	0.650815i	$-0.774427\pi$
$139$	−17.9025			−1.51847			−0.759237	+	0.650815i	$0.774427\pi$
$140$	3.28472	+	0.964480i	0.277609	+	0.0815134i
$141$	3.65819	−	4.22177i	0.308075	−	0.355537i
$142$	11.5641	+	7.43181i	0.970440	+	0.623664i
$143$	−0.0280477	+	0.195076i	−0.00234547	+	0.0163131i
$144$	0.841254	−	0.540641i	0.0701045	−	0.0450534i
$145$	0.0133459	+	0.0292234i	0.00110832	+	0.00242687i
$146$	−7.52133	−	8.68008i	−0.622470	−	0.718369i
$147$	0.671666	+	4.67154i	0.0553981	+	0.385302i
$148$	−0.223032	+	0.488371i	−0.0183331	+	0.0401438i
$149$	−15.8915	+	4.66615i	−1.30188	+	0.382266i	−0.857921	−	0.513782i	$-0.828244\pi$
$149$	−15.8915	+	4.66615i	−1.30188	+	0.382266i	−0.443957	+	0.896048i	$0.646426\pi$
$150$	0.959493	−	0.281733i	0.0783423	−	0.0230034i
$151$	−4.71728	+	10.3294i	−0.383886	+	0.840594i	0.614767	+	0.788709i	$0.289250\pi$
$151$	−4.71728	+	10.3294i	−0.383886	+	0.840594i	−0.998653	+	0.0518849i	$0.983477\pi$
$152$	−0.860944	−	5.98799i	−0.0698317	−	0.485690i
$153$	−4.70769	−	5.43296i	−0.380594	−	0.439229i
$154$	1.54876	+	3.39130i	0.124802	+	0.273279i
$155$	0.469280	−	0.301588i	0.0376934	−	0.0242241i
$156$	0.0257545	−	0.179126i	0.00206201	−	0.0143416i
$157$	−4.48388	−	2.88162i	−0.357853	−	0.229978i	0.349344	−	0.936994i	$-0.386404\pi$
$157$	−4.48388	−	2.88162i	−0.357853	−	0.229978i	−0.707197	+	0.707016i	$0.750041\pi$
$158$	−0.141335	+	0.163110i	−0.0112440	+	0.0129763i
$159$	10.1051	+	2.96711i	0.801383	+	0.235307i
$160$	−1.00000			−0.0790569
$161$	−15.6864	+	4.84630i	−1.23626	+	0.381942i
$162$	1.00000			0.0785674
$163$	−7.29919	−	2.14324i	−0.571717	−	0.167871i	−0.0169196	−	0.999857i	$-0.505386\pi$
$163$	−7.29919	−	2.14324i	−0.571717	−	0.167871i	−0.554797	+	0.831986i	$0.687204\pi$
$164$	7.22921	−	8.34295i	0.564507	−	0.651475i
$165$	0.916161	+	0.588781i	0.0713230	+	0.0458365i
$166$	0.828582	−	5.76291i	0.0643104	−	0.447289i
$167$	−6.63695	+	4.26531i	−0.513583	+	0.330060i	−0.771629	−	0.636073i	$-0.780558\pi$
$167$	−6.63695	+	4.26531i	−0.513583	+	0.330060i	0.258046	+	0.966133i	$0.416921\pi$
$168$	−1.42213	−	3.11402i	−0.109719	−	0.240252i
$169$	8.49174	+	9.79999i	0.653211	+	0.753846i
$170$	1.02308	+	7.11567i	0.0784665	+	0.545747i
$171$	2.51308	−	5.50288i	0.192180	−	0.420816i
$172$	1.64281	−	0.482371i	0.125263	−	0.0367805i
$173$	−21.6195	+	6.34804i	−1.64370	+	0.482633i	−0.967243	−	0.253852i	$-0.918302\pi$
$173$	−21.6195	+	6.34804i	−1.64370	+	0.482633i	−0.676454	+	0.736485i	$0.736484\pi$
$174$	0.0133459	−	0.0292234i	0.00101175	−	0.00221542i
$175$	−0.487199	−	3.38854i	−0.0368288	−	0.256150i
$176$	−0.713171	−	0.823043i	−0.0537573	−	0.0620392i
$177$	−2.97306	−	6.51009i	−0.223469	−	0.489328i
$178$	−1.11514	+	0.716659i	−0.0835835	+	0.0537159i
$179$	−2.09229	+	14.5522i	−0.156385	+	1.08768i	0.748841	+	0.662750i	$0.230611\pi$
$179$	−2.09229	+	14.5522i	−0.156385	+	1.08768i	−0.905226	+	0.424931i	$0.860298\pi$
$180$	−0.841254	−	0.540641i	−0.0627033	−	0.0402970i
$181$	10.5668	−	12.1948i	0.785426	−	0.906429i	−0.212063	−	0.977256i	$-0.568018\pi$
$181$	10.5668	−	12.1948i	0.785426	−	0.906429i	0.997489	+	0.0708265i	$0.0225637\pi$
$182$	−0.594430	−	0.174540i	−0.0440621	−	0.0129378i
$183$	−6.93353			−0.512541
$184$	3.99769	−	2.64924i	0.294714	−	0.195304i
$185$	0.536888			0.0394728
$186$	−0.535237	−	0.157160i	−0.0392455	−	0.0115235i
$187$	−5.12687	+	5.91673i	−0.374914	+	0.432674i
$188$	4.69942	+	3.02013i	0.342740	+	0.220266i
$189$	0.487199	−	3.38854i	0.0354385	−	0.246480i
$190$	−5.08922	+	3.27064i	−0.369211	+	0.237277i
$191$	−4.13610	−	9.05679i	−0.299277	−	0.655326i	0.698929	−	0.715191i	$-0.253660\pi$
$191$	−4.13610	−	9.05679i	−0.299277	−	0.655326i	−0.998206	+	0.0598648i	$0.980933\pi$
$192$	0.654861	+	0.755750i	0.0472605	+	0.0545415i
$193$	−1.13181	−	7.87191i	−0.0814694	−	0.566632i	−0.989143	−	0.146956i	$-0.953053\pi$
$193$	−1.13181	−	7.87191i	−0.0814694	−	0.566632i	0.907674	−	0.419677i	$-0.137857\pi$
$194$	0.292102	−	0.639613i	0.0209717	−	0.0459216i
$195$	−0.173638	+	0.0509847i	−0.0124345	+	0.00365109i
$196$	−4.52840	+	1.32966i	−0.323457	+	0.0949757i
$197$	−9.97045	+	21.8322i	−0.710365	+	1.55548i	0.116568	+	0.993183i	$0.462811\pi$
$197$	−9.97045	+	21.8322i	−0.710365	+	1.55548i	−0.826933	+	0.562300i	$0.809917\pi$
$198$	−0.154987	−	1.07796i	−0.0110144	−	0.0766071i
$199$	3.89552	+	4.49567i	0.276146	+	0.318690i	0.876833	−	0.480794i	$-0.159652\pi$
$199$	3.89552	+	4.49567i	0.276146	+	0.318690i	−0.600687	+	0.799484i	$0.705106\pi$
$200$	0.415415	+	0.909632i	0.0293743	+	0.0643207i
$201$	−0.287047	+	0.184474i	−0.0202467	+	0.0130118i
$202$	−1.66677	+	11.5926i	−0.117274	+	0.815656i
$203$	−0.0925227	−	0.0594607i	−0.00649382	−	0.00417333i
$204$	4.70769	−	5.43296i	0.329604	−	0.380383i
$205$	−10.5921	−	3.11013i	−0.739787	−	0.217221i
$206$	−9.27468			−0.646198
$207$	4.79536	−	0.0673656i	0.333300	−	0.00468223i
$208$	0.180968			0.0125479
$209$	−6.32137	−	1.85612i	−0.437258	−	0.128391i
$210$	−2.24184	+	2.58722i	−0.154702	+	0.178535i
$211$	13.5547	+	8.71106i	0.933142	+	0.599694i	0.916442	−	0.400167i	$-0.131048\pi$
$211$	13.5547	+	8.71106i	0.933142	+	0.599694i	0.0166996	+	0.999861i	$0.494684\pi$
$212$	−1.49881	+	10.4245i	−0.102939	+	0.715955i
$213$	−11.5641	+	7.43181i	−0.792361	+	0.509219i
$214$	−1.83826	−	4.02523i	−0.125661	−	0.275159i
$215$	−1.12123	−	1.29396i	−0.0764670	−	0.0882477i
$216$	0.142315	+	0.989821i	0.00968330	+	0.0673488i
$217$	−0.793310	+	1.73711i	−0.0538534	+	0.117922i
$218$	7.19331	−	2.11215i	0.487192	−	0.143053i
$219$	11.0202	−	3.23581i	0.744673	−	0.218656i
$220$	−0.452405	+	0.990628i	−0.0305011	+	0.0667881i
$221$	−0.185145	−	1.28771i	−0.0124542	−	0.0866208i
$222$	−0.351587	−	0.405753i	−0.0235970	−	0.0272324i
$223$	6.04415	+	13.2349i	0.404746	+	0.886271i	0.996767	+	0.0803482i	$0.0256032\pi$
$223$	6.04415	+	13.2349i	0.404746	+	0.886271i	−0.592020	+	0.805923i	$0.701670\pi$
$224$	2.87994	−	1.85082i	0.192424	−	0.123663i
$225$	−0.142315	+	0.989821i	−0.00948766	+	0.0659881i
$226$	−2.82697	−	1.81678i	−0.188047	−	0.120851i
$227$	2.30288	−	2.65766i	0.152847	−	0.176395i	−0.674162	−	0.738584i	$-0.735495\pi$
$227$	2.30288	−	2.65766i	0.152847	−	0.176395i	0.827009	+	0.562188i	$0.190040\pi$
$228$	5.80452	+	1.70436i	0.384414	+	0.112874i
$229$	−23.9458			−1.58238			−0.791191	−	0.611570i	$-0.790538\pi$
$229$	−23.9458			−1.58238			−0.791191	+	0.611570i	$0.790538\pi$
$230$	−4.07053	−	2.53589i	−0.268403	−	0.167212i
$231$	−3.72821			−0.245298
$232$	0.0308253	+	0.00905112i	0.00202378	+	0.000594235i
$233$	−6.93713	+	8.00588i	−0.454467	+	0.524482i	−0.936026	−	0.351931i	$-0.885525\pi$
$233$	−6.93713	+	8.00588i	−0.454467	+	0.524482i	0.481559	+	0.876414i	$0.340071\pi$
$234$	0.152240	+	0.0978389i	0.00995226	+	0.00639593i
$235$	0.795000	−	5.52935i	0.0518601	−	0.360695i
$236$	6.02071	−	3.86928i	0.391915	−	0.251869i
$237$	−0.0896571	−	0.196322i	−0.00582385	−	0.0127525i
$238$	−16.1162	−	18.5991i	−1.04466	−	1.20560i
$239$	3.88975	+	27.0538i	0.251607	+	1.74996i	0.588571	+	0.808446i	$0.299691\pi$
$239$	3.88975	+	27.0538i	0.251607	+	1.74996i	−0.336964	+	0.941518i	$0.609400\pi$
$240$	0.415415	−	0.909632i	0.0268149	−	0.0587165i
$241$	23.0797	−	6.77681i	1.48669	−	0.436532i	0.565209	−	0.824948i	$-0.308796\pi$
$241$	23.0797	−	6.77681i	1.48669	−	0.436532i	0.921484	+	0.388416i	$0.126977\pi$
$242$	9.41645	−	2.76492i	0.605312	−	0.177736i
$243$	−0.415415	+	0.909632i	−0.0266489	+	0.0583529i
$244$	−0.986744	−	6.86296i	−0.0631698	−	0.439356i
$245$	3.09067	+	3.56682i	0.197455	+	0.227876i
$246$	4.58590	+	10.0417i	0.292386	+	0.640236i
$247$	0.920988	−	0.591883i	0.0586011	−	0.0376606i
$248$	0.0793880	−	0.552156i	0.00504114	−	0.0350619i
$249$	4.89793	+	3.14771i	0.310393	+	0.199478i
$250$	0.654861	−	0.755750i	0.0414170	−	0.0477978i
$251$	6.49182	+	1.90617i	0.409760	+	0.120316i	0.480115	−	0.877206i	$-0.340595\pi$
$251$	6.49182	+	1.90617i	0.409760	+	0.120316i	−0.0703548	+	0.997522i	$0.522413\pi$
$252$	3.42339			0.215653
$253$	−0.815835	−	5.15875i	−0.0512911	−	0.324328i
$254$	−5.31297			−0.333366
$255$	−6.89764	−	2.02533i	−0.431947	−	0.126831i
$256$	−0.654861	+	0.755750i	−0.0409288	+	0.0472343i
$257$	10.1444	+	6.51938i	0.632787	+	0.406668i	0.817341	−	0.576155i	$-0.195447\pi$
$257$	10.1444	+	6.51938i	0.632787	+	0.406668i	−0.184553	+	0.982823i	$0.559084\pi$
$258$	−0.243666	+	1.69473i	−0.0151700	+	0.105509i
$259$	−1.54620	+	0.993685i	−0.0960765	+	0.0617446i
$260$	−0.0751770	−	0.164615i	−0.00466228	−	0.0102090i
$261$	0.0210385	+	0.0242797i	0.00130225	+	0.00150288i
$262$	1.05744	+	7.35463i	0.0653286	+	0.454370i
$263$	9.09409	−	19.9133i	0.560765	−	1.22791i	−0.390805	−	0.920474i	$-0.627803\pi$
$263$	9.09409	−	19.9133i	0.560765	−	1.22791i	0.951570	−	0.307431i	$-0.0994695\pi$
$264$	1.04493	−	0.306819i	0.0643109	−	0.0188834i
$265$	10.1051	−	2.96711i	0.620748	−	0.182268i
$266$	8.60325	−	18.8385i	0.527499	−	1.15506i
$267$	−0.188649	−	1.31208i	−0.0115451	−	0.0802980i
$268$	−0.223447	−	0.257872i	−0.0136492	−	0.0157520i
$269$	−10.3591	−	22.6833i	−0.631608	−	1.38303i	−0.906768	−	0.421629i	$-0.861458\pi$
$269$	−10.3591	−	22.6833i	−0.631608	−	1.38303i	0.275161	−	0.961398i	$-0.411269\pi$
$270$	0.841254	−	0.540641i	0.0511971	−	0.0329024i
$271$	2.28014	−	15.8587i	0.138509	−	0.963350i	−0.795463	−	0.606003i	$-0.792772\pi$
$271$	2.28014	−	15.8587i	0.138509	−	0.963350i	0.933972	−	0.357347i	$-0.116319\pi$
$272$	6.04764	+	3.88658i	0.366692	+	0.235658i
$273$	0.405703	−	0.468206i	0.0245542	−	0.0283371i
$274$	17.9764	+	5.27836i	1.08600	+	0.318877i
$275$	1.08904			0.0656717
$276$	0.749131	+	4.73696i	0.0450924	+	0.285132i
$277$	−15.4336			−0.927316			−0.463658	−	0.886014i	$-0.653463\pi$
$277$	−15.4336			−0.927316			−0.463658	+	0.886014i	$0.653463\pi$
$278$	17.1774	+	5.04373i	1.03023	+	0.302503i
$279$	0.365303	−	0.421583i	0.0218701	−	0.0252395i
$280$	−2.87994	−	1.85082i	−0.172109	−	0.110608i
$281$	−2.87484	+	19.9950i	−0.171499	+	1.19280i	0.704221	+	0.709981i	$0.251296\pi$
$281$	−2.87484	+	19.9950i	−0.171499	+	1.19280i	−0.875720	+	0.482819i	$0.839613\pi$
$282$	−4.69942	+	3.02013i	−0.279846	+	0.179846i
$283$	−10.4767	−	22.9407i	−0.622773	−	1.36368i	−0.913485	−	0.406872i	$-0.866619\pi$
$283$	−10.4767	−	22.9407i	−0.622773	−	1.36368i	0.290712	−	0.956811i	$-0.406108\pi$
$284$	−9.00191	−	10.3888i	−0.534165	−	0.616460i
$285$	−0.860944	−	5.98799i	−0.0509979	−	0.354698i
$286$	0.0818709	−	0.179272i	0.00484113	−	0.0106006i
$287$	36.2610	−	10.6472i	2.14042	−	0.628484i
$288$	−0.959493	+	0.281733i	−0.0565387	+	0.0166013i
$289$	14.4063	−	31.5455i	0.847432	−	1.85562i
$290$	−0.00457210	−	0.0317997i	−0.000268483	−	0.00186734i
$291$	0.460469	+	0.531410i	0.0269932	+	0.0311518i
$292$	4.77120	+	10.4475i	0.279214	+	0.611393i
$293$	−6.97055	+	4.47970i	−0.407224	+	0.261707i	−0.728178	−	0.685388i	$-0.759633\pi$
$293$	−6.97055	+	4.47970i	−0.407224	+	0.261707i	0.320954	+	0.947095i	$0.395996\pi$
$294$	0.671666	−	4.67154i	0.0391724	−	0.272450i
$295$	−6.02071	−	3.86928i	−0.350540	−	0.225278i
$296$	0.351587	−	0.405753i	0.0204356	−	0.0235839i
$297$	1.04493	+	0.306819i	0.0606329	+	0.0178034i
$298$	16.5623			0.959431
$299$	0.736638	+	0.458917i	0.0426009	+	0.0265399i
$300$	−1.00000			−0.0577350
$301$	5.62396	+	1.65134i	0.324160	+	0.0951819i
$302$	7.43632	−	8.58197i	0.427912	−	0.493837i
$303$	−9.85264	−	6.33191i	−0.566019	−	0.363759i
$304$	−0.860944	+	5.98799i	−0.0493785	+	0.343435i
$305$	−5.83286	+	3.74855i	−0.333988	+	0.214641i
$306$	2.98635	+	6.53920i	0.170718	+	0.373821i
$307$	6.91806	+	7.98387i	0.394835	+	0.455663i	0.918007	−	0.396563i	$-0.129797\pi$
$307$	6.91806	+	7.98387i	0.394835	+	0.455663i	−0.523173	+	0.852227i	$0.675252\pi$
$308$	−0.530580	−	3.69027i	−0.0302326	−	0.210272i
$309$	3.85284	−	8.43655i	0.219181	−	0.479938i
$310$	−0.535237	+	0.157160i	−0.0303994	+	0.00892608i
$311$	−12.5697	+	3.69079i	−0.712761	+	0.209286i	−0.617959	−	0.786211i	$-0.712040\pi$
$311$	−12.5697	+	3.69079i	−0.712761	+	0.209286i	−0.0948024	+	0.995496i	$0.530222\pi$
$312$	−0.0751770	+	0.164615i	−0.00425606	+	0.00931947i
$313$	−4.52694	−	31.4855i	−0.255878	−	1.77967i	−0.561462	−	0.827503i	$-0.689761\pi$
$313$	−4.52694	−	31.4855i	−0.255878	−	1.77967i	0.305584	−	0.952165i	$-0.401148\pi$
$314$	3.49041	+	4.02815i	0.196975	+	0.227321i
$315$	−1.42213	−	3.11402i	−0.0801277	−	0.175455i
$316$	0.181564	−	0.116684i	0.0102138	−	0.00656398i
$317$	0.646380	−	4.49567i	0.0363043	−	0.252502i	−0.963585	−	0.267403i	$-0.913834\pi$
$317$	0.646380	−	4.49567i	0.0363043	−	0.252502i	0.999889	+	0.0149015i	$0.00474347\pi$
$318$	−8.85980	−	5.69385i	−0.496833	−	0.319295i
$319$	0.0229118	−	0.0264416i	0.00128281	−	0.00148045i
$320$	0.959493	+	0.281733i	0.0536373	+	0.0157493i
$321$	4.42511			0.246986
$322$	16.4164	−	0.230618i	0.914848	−	0.0128519i
$323$	43.4894			2.41981
$324$	−0.959493	−	0.281733i	−0.0533052	−	0.0156518i
$325$	−0.118509	+	0.136767i	−0.00657370	+	0.00758646i
$326$	6.39970	+	4.11284i	0.354447	+	0.227789i
$327$	−1.06693	+	7.42068i	−0.0590015	+	0.410365i
$328$	−9.28686	+	5.96830i	−0.512781	+	0.329544i
$329$	7.94429	+	17.3956i	0.437983	+	0.959049i
$330$	−0.713171	−	0.823043i	−0.0392588	−	0.0453070i
$331$	−2.43345	−	16.9250i	−0.133754	−	0.930282i	−0.940599	−	0.339519i	$-0.889736\pi$
$331$	−2.43345	−	16.9250i	−0.133754	−	0.930282i	0.806845	−	0.590763i	$-0.201173\pi$
$332$	−2.41862	+	5.29604i	−0.132739	+	0.290658i
$333$	0.515141	−	0.151259i	0.0282295	−	0.00828894i
$334$	7.56979	−	2.22269i	0.414200	−	0.121620i
$335$	−0.141745	+	0.310378i	−0.00774436	+	0.0169578i
$336$	0.487199	+	3.38854i	0.0265789	+	0.184860i
$337$	−23.7534	−	27.4129i	−1.29393	−	1.49327i	−0.763970	−	0.645251i	$-0.776753\pi$
$337$	−23.7534	−	27.4129i	−1.29393	−	1.49327i	−0.529959	−	0.848023i	$-0.677793\pi$
$338$	−5.38679	−	11.7954i	−0.293003	−	0.641587i
$339$	2.82697	−	1.81678i	0.153540	−	0.0986740i
$340$	1.02308	−	7.11567i	0.0554842	−	0.385901i
$341$	−0.511065	−	0.328442i	−0.0276757	−	0.0177861i
$342$	−3.96163	+	4.57196i	−0.214220	+	0.247223i
$343$	7.49053	+	2.19942i	0.404451	+	0.118757i
$344$	−1.71216			−0.0923135
$345$	3.99769	−	2.64924i	0.215228	−	0.142630i
$346$	22.5322			1.21134
$347$	−26.8803	−	7.89276i	−1.44301	−	0.423706i	−0.535786	−	0.844354i	$-0.679984\pi$
$347$	−26.8803	−	7.89276i	−1.44301	−	0.423706i	−0.907224	+	0.420648i	$0.861803\pi$
$348$	−0.0210385	+	0.0242797i	−0.00112778	+	0.00130153i
$349$	26.6110	+	17.1019i	1.42446	+	0.915442i	0.999950	+	0.0100173i	$0.00318865\pi$
$349$	26.6110	+	17.1019i	1.42446	+	0.915442i	0.424506	+	0.905425i	$0.360448\pi$
$350$	−0.487199	+	3.38854i	−0.0260419	+	0.181125i
$351$	−0.152240	+	0.0978389i	−0.00812599	+	0.00522226i
$352$	0.452405	+	0.990628i	0.0241132	+	0.0528006i
$353$	−2.71904	−	3.13794i	−0.144720	−	0.167016i	0.678762	−	0.734359i	$-0.262517\pi$
$353$	−2.71904	−	3.13794i	−0.144720	−	0.167016i	−0.823482	+	0.567343i	$0.807971\pi$
$354$	1.01852	+	7.08399i	0.0541339	+	0.376510i
$355$	−5.71042	+	12.5041i	−0.303078	+	0.663647i
$356$	1.27188	−	0.373457i	0.0674094	−	0.0197932i
$357$	23.6133	−	6.93349i	1.24975	−	0.366959i
$358$	6.10736	−	13.3732i	0.322784	−	0.706798i
$359$	−0.100334	−	0.697840i	−0.00529544	−	0.0368306i	0.987002	−	0.160705i	$-0.0513769\pi$
$359$	−0.100334	−	0.697840i	−0.00529544	−	0.0368306i	−0.992298	+	0.123875i	$0.960468\pi$
$360$	0.654861	+	0.755750i	0.0345142	+	0.0398315i
$361$	7.31018	+	16.0071i	0.384746	+	0.842477i
$362$	−13.5745	+	8.72377i	−0.713457	+	0.458511i
$363$	−1.39668	+	9.71409i	−0.0733065	+	0.509858i
$364$	0.521178	+	0.334940i	0.0273171	+	0.0175557i
$365$	7.52133	−	8.68008i	0.393685	−	0.454336i
$366$	6.65267	+	1.95340i	0.347741	+	0.102106i
$367$	10.8233			0.564973			0.282487	−	0.959271i	$-0.408841\pi$
$367$	10.8233			0.564973			0.282487	+	0.959271i	$0.408841\pi$
$368$	−4.58213	+	1.41565i	−0.238860	+	0.0737956i
$369$	−11.0393			−0.574684
$370$	−0.515141	−	0.151259i	−0.0267809	−	0.00786358i
$371$	−23.6103	+	27.2478i	−1.22579	+	1.41463i
$372$	0.469280	+	0.301588i	0.0243310	+	0.0156366i
$373$	−2.20376	+	15.3275i	−0.114106	+	0.793627i	0.849746	+	0.527192i	$0.176755\pi$
$373$	−2.20376	+	15.3275i	−0.114106	+	0.793627i	−0.963853	+	0.266435i	$0.914154\pi$
$374$	6.58613	−	4.23265i	0.340561	−	0.218865i
$375$	0.415415	+	0.909632i	0.0214519	+	0.0469732i
$376$	−3.65819	−	4.22177i	−0.188657	−	0.217721i
$377$	0.000827406		0.00575473i	4.26136e−5		0.000296384i
$378$	−1.42213	+	3.11402i	−0.0731463	+	0.160168i
$379$	−6.48553	+	1.90432i	−0.333139	+	0.0978186i	−0.444024	−	0.896015i	$-0.646450\pi$
$379$	−6.48553	+	1.90432i	−0.333139	+	0.0978186i	0.110885	+	0.993833i	$0.464631\pi$
$380$	5.80452	−	1.70436i	0.297766	−	0.0874319i
$381$	2.20709	−	4.83285i	0.113073	−	0.247595i
$382$	1.41696	+	9.85520i	0.0724982	+	0.504236i
$383$	20.7093	+	23.8998i	1.05820	+	1.22122i	0.974419	+	0.224739i	$0.0721530\pi$
$383$	20.7093	+	23.8998i	1.05820	+	1.22122i	0.0837775	+	0.996484i	$0.473302\pi$
$384$	−0.415415	−	0.909632i	−0.0211991	−	0.0464195i
$385$	−3.13637	+	2.01562i	−0.159844	+	0.102726i
$386$	−1.13181	+	7.87191i	−0.0576076	+	0.400670i
$387$	−1.44036	−	0.925664i	−0.0732177	−	0.0470541i
$388$	−0.460469	+	0.531410i	−0.0233768	+	0.0269782i
$389$	−16.9987	−	4.99126i	−0.861866	−	0.253067i	−0.179214	−	0.983810i	$-0.557355\pi$
$389$	−16.9987	−	4.99126i	−0.861866	−	0.253067i	−0.682652	+	0.730743i	$0.739174\pi$
$390$	0.180968			0.00916369
$391$	14.7611	+	31.1566i	0.746503	+	1.57566i
$392$	4.71958			0.238375
$393$	−7.12928	−	2.09335i	−0.359625	−	0.105595i
$394$	15.7174	−	18.1389i	0.791833	−	0.913823i
$395$	−0.181564	−	0.116684i	−0.00913546	−	0.00587101i
$396$	−0.154987	+	1.07796i	−0.00778839	+	0.0541694i
$397$	23.5956	−	15.1640i	1.18423	−	0.761057i	0.208069	−	0.978114i	$-0.433282\pi$
$397$	23.5956	−	15.1640i	1.18423	−	0.761057i	0.976159	+	0.217057i	$0.0696458\pi$
$398$	−2.47115	−	5.41106i	−0.123868	−	0.271232i
$399$	13.5622	+	15.6516i	0.678958	+	0.783559i
$400$	−0.142315	−	0.989821i	−0.00711574	−	0.0494911i
$401$	11.1450	−	24.4041i	0.556553	−	1.21868i	−0.397101	−	0.917775i	$-0.629984\pi$
$401$	11.1450	−	24.4041i	0.556553	−	1.21868i	0.953654	−	0.300906i	$-0.0972890\pi$
$402$	0.327392	−	0.0961309i	0.0163288	−	0.00479457i
$403$	0.0968611	−	0.0284410i	0.00482499	−	0.00141675i
$404$	4.86528	−	10.6535i	0.242057	−	0.530030i
$405$	0.142315	+	0.989821i	0.00707168	+	0.0491846i
$406$	0.0720229	+	0.0831188i	0.00357444	+	0.00412512i
$407$	−0.242891	−	0.531857i	−0.0120397	−	0.0263632i
$408$	−6.04764	+	3.88658i	−0.299403	+	0.192414i
$409$	1.33661	−	9.29630i	0.0660909	−	0.459672i	−0.929722	−	0.368261i	$-0.879953\pi$
$409$	1.33661	−	9.29630i	0.0660909	−	0.459672i	0.995813	−	0.0914111i	$-0.0291377\pi$
$410$	9.28686	+	5.96830i	0.458645	+	0.294753i
$411$	−12.2690	+	14.1592i	−0.605187	+	0.698424i
$412$	8.89899	+	2.61298i	0.438422	+	0.128732i
$413$	24.5006			1.20560
$414$	−4.62009	−	1.28637i	−0.227065	−	0.0632217i
$415$	5.82218			0.285799
$416$	−0.173638	−	0.0509847i	−0.00851330	−	0.00249973i
$417$	−11.7237	+	13.5298i	−0.574110	+	0.662559i
$418$	5.54238	+	3.56187i	0.271087	+	0.174217i
$419$	−4.90591	+	34.1214i	−0.239669	+	1.66694i	0.414091	+	0.910236i	$0.364100\pi$
$419$	−4.90591	+	34.1214i	−0.239669	+	1.66694i	−0.653760	+	0.756702i	$0.726809\pi$
$420$	2.87994	−	1.85082i	0.140527	−	0.0903109i
$421$	−6.63983	−	14.5392i	−0.323606	−	0.708597i	0.675994	−	0.736907i	$-0.263715\pi$
$421$	−6.63983	−	14.5392i	−0.323606	−	0.708597i	−0.999599	+	0.0283101i	$0.990987\pi$
$422$	−10.5514	−	12.1770i	−0.513635	−	0.592767i
$423$	−0.795000	−	5.52935i	−0.0386542	−	0.268846i
$424$	4.37501	−	9.57993i	0.212469	−	0.465243i
$425$	−6.89764	+	2.02533i	−0.334585	+	0.0982429i
$426$	13.1895	−	3.87278i	0.639032	−	0.187637i
$427$	9.86036	−	21.5912i	0.477176	−	1.04487i
$428$	0.629759	+	4.38007i	0.0304406	+	0.211719i
$429$	0.129061	+	0.148945i	0.00623115	+	0.00719113i
$430$	0.711257	+	1.55744i	0.0342999	+	0.0751062i
$431$	15.1382	−	9.72871i	0.729180	−	0.468615i	−0.122639	−	0.992451i	$-0.539136\pi$
$431$	15.1382	−	9.72871i	0.729180	−	0.468615i	0.851819	+	0.523836i	$0.175499\pi$
$432$	0.142315	−	0.989821i	0.00684713	−	0.0476228i
$433$	−18.2891	−	11.7537i	−0.878916	−	0.564845i	0.0215519	−	0.999768i	$-0.493139\pi$
$433$	−18.2891	−	11.7537i	−0.878916	−	0.564845i	−0.900468	+	0.434923i	$0.856776\pi$
$434$	1.25057	−	1.44324i	0.0600295	−	0.0692777i
$435$	0.0308253	+	0.00905112i	0.00147796	+	0.000433968i
$436$	−7.49699			−0.359041
$437$	−18.6894	+	22.1911i	−0.894036	+	1.06154i
$438$	−11.4854			−0.548793
$439$	−24.8840	−	7.30661i	−1.18765	−	0.348725i	−0.372531	−	0.928020i	$-0.621510\pi$
$439$	−24.8840	−	7.30661i	−1.18765	−	0.348725i	−0.815118	+	0.579294i	$0.803328\pi$
$440$	0.713171	−	0.823043i	0.0339991	−	0.0392371i
$441$	3.97036	+	2.55160i	0.189065	+	0.121505i
$442$	−0.185145	+	1.28771i	−0.00880644	+	0.0612502i
$443$	−1.64718	+	1.05858i	−0.0782598	+	0.0502945i	−0.579186	−	0.815196i	$-0.696629\pi$
$443$	−1.64718	+	1.05858i	−0.0782598	+	0.0502945i	0.500926	+	0.865490i	$0.332993\pi$
$444$	0.223032	+	0.488371i	0.0105846	+	0.0231771i
$445$	−0.868066	−	1.00180i	−0.0411503	−	0.0474899i
$446$	−2.07063	−	14.4016i	−0.0980474	−	0.681935i
$447$	−6.88025	+	15.0656i	−0.325424	+	0.712580i
$448$	−3.28472	+	0.964480i	−0.155188	+	0.0455674i
$449$	34.0772	−	10.0060i	1.60820	−	0.472211i	0.650389	−	0.759602i	$-0.274606\pi$
$449$	34.0772	−	10.0060i	1.60820	−	0.472211i	0.957813	+	0.287391i	$0.0927879\pi$
$450$	0.415415	−	0.909632i	0.0195829	−	0.0428805i
$451$	1.71095	+	11.8999i	0.0805654	+	0.560345i
$452$	2.20061	+	2.53964i	0.103508	+	0.119455i
$453$	4.71728	+	10.3294i	0.221637	+	0.485317i
$454$	−2.95834	+	1.90121i	−0.138842	+	0.0892283i
$455$	0.0881676	−	0.613219i	0.00413336	−	0.0287482i
$456$	−5.08922	−	3.27064i	−0.238325	−	0.153162i
$457$	7.21371	−	8.32506i	0.337443	−	0.389430i	−0.561514	−	0.827467i	$-0.689781\pi$
$457$	7.21371	−	8.32506i	0.337443	−	0.389430i	0.898957	+	0.438038i	$0.144326\pi$
$458$	22.9758	+	6.74630i	1.07359	+	0.315234i
$459$	−7.18884			−0.335546
$460$	3.19120	+	3.57997i	0.148791	+	0.166917i
$461$	−17.3274			−0.807019			−0.403510	−	0.914975i	$-0.632210\pi$
$461$	−17.3274			−0.807019			−0.403510	+	0.914975i	$0.632210\pi$
$462$	3.57720	+	1.05036i	0.166426	+	0.0488671i
$463$	−4.05843	+	4.68367i	−0.188611	+	0.217669i	−0.842178	−	0.539200i	$-0.818727\pi$
$463$	−4.05843	+	4.68367i	−0.188611	+	0.217669i	0.653566	+	0.756869i	$0.273272\pi$
$464$	−0.0270267	−	0.0173690i	−0.00125468	−	0.000806335i
$465$	0.0793880	−	0.552156i	0.00368153	−	0.0256056i
$466$	8.91165	−	5.72717i	0.412824	−	0.265306i
$467$	−9.79592	−	21.4501i	−0.453301	−	0.992591i	−0.988964	−	0.148159i	$-0.952665\pi$
$467$	−9.79592	−	21.4501i	−0.453301	−	0.992591i	0.535662	−	0.844432i	$-0.320062\pi$
$468$	−0.118509	−	0.136767i	−0.00547809	−	0.00632205i
$469$	−0.166239	−	1.15622i	−0.00767619	−	0.0533891i
$470$	−2.32059	+	5.08139i	−0.107041	+	0.234387i
$471$	−5.11410	+	1.50164i	−0.235645	+	0.0691917i
$472$	−6.86693	+	2.01631i	−0.316076	+	0.0928084i
$473$	−0.774589	+	1.69611i	−0.0356157	+	0.0779874i
$474$	0.0307151	+	0.213628i	0.00141079	+	0.00981228i
$475$	−3.96163	−	4.57196i	−0.181772	−	0.209776i
$476$	10.2234	+	22.3862i	0.468590	+	1.02607i
$477$	8.85980	−	5.69385i	0.405662	−	0.260703i
$478$	3.88975	−	27.0538i	0.177913	−	1.23741i
$479$	−20.8762	−	13.4163i	−0.953856	−	0.613006i	−0.0315649	−	0.999502i	$-0.510049\pi$
$479$	−20.8762	−	13.4163i	−0.953856	−	0.613006i	−0.922291	+	0.386496i	$0.873685\pi$
$480$	−0.654861	+	0.755750i	−0.0298902	+	0.0344951i
$481$	0.0932242	+	0.0273731i	0.00425066	+	0.00124811i
$482$	−24.0540			−1.09563
$483$	−6.60983	+	15.0287i	−0.300758	+	0.683828i
$484$	−9.81399			−0.446090
$485$	0.674673	+	0.198102i	0.0306353	+	0.00899535i
$486$	0.654861	−	0.755750i	0.0297051	−	0.0342815i
$487$	5.07851	+	3.26376i	0.230129	+	0.147895i	0.650624	−	0.759400i	$-0.274507\pi$
$487$	5.07851	+	3.26376i	0.230129	+	0.147895i	−0.420495	+	0.907295i	$0.638144\pi$
$488$	−0.986744	+	6.86296i	−0.0446678	+	0.310672i
$489$	−6.39970	+	4.11284i	−0.289405	+	0.185989i
$490$	−1.96058	−	4.29308i	−0.0885702	−	0.193942i
$491$	−13.2826	−	15.3290i	−0.599436	−	0.691786i	0.372231	−	0.928140i	$-0.378593\pi$
$491$	−13.2826	−	15.3290i	−0.599436	−	0.691786i	−0.971667	+	0.236354i	$0.924047\pi$
$492$	−1.57106	−	10.9269i	−0.0708288	−	0.492625i
$493$	−0.0959415	+	0.210083i	−0.00432099	+	0.00946164i
$494$	−1.05043	+	0.308435i	−0.0472613	+	0.0138772i
$495$	1.04493	−	0.306819i	0.0469660	−	0.0137905i
$496$	−0.231732	+	0.507423i	−0.0104051	+	0.0227840i
$497$	−6.69718	−	46.5799i	−0.300410	−	2.08939i
$498$	−3.81271	−	4.40011i	−0.170852	−	0.197173i
$499$	−5.48109	−	12.0019i	−0.245367	−	0.537279i	0.746375	−	0.665525i	$-0.231792\pi$
$499$	−5.48109	−	12.0019i	−0.245367	−	0.537279i	−0.991742	+	0.128246i	$0.959065\pi$
$500$	−0.841254	+	0.540641i	−0.0376220	+	0.0241782i
$501$	−1.12277	+	7.80906i	−0.0501618	+	0.348883i
$502$	−5.69183	−	3.65791i	−0.254039	−	0.163261i
$503$	15.3033	−	17.6609i	0.682339	−	0.787462i	−0.303914	−	0.952699i	$-0.598294\pi$
$503$	15.3033	−	17.6609i	0.682339	−	0.787462i	0.986254	+	0.165238i	$0.0528392\pi$
$504$	−3.28472	−	0.964480i	−0.146313	−	0.0429613i
$505$	−11.7119			−0.521171
$506$	−0.670601	+	5.17963i	−0.0298118	+	0.230263i
$507$	12.9673			0.575896
$508$	5.09776	+	1.49684i	0.226177	+	0.0664114i
$509$	−15.7305	+	18.1540i	−0.697242	+	0.804661i	−0.988377	−	0.152021i	$-0.951422\pi$
$509$	−15.7305	+	18.1540i	−0.697242	+	0.804661i	0.291135	+	0.956682i	$0.405967\pi$
$510$	6.04764	+	3.88658i	0.267794	+	0.172101i
$511$	−5.59567	+	38.9187i	−0.247538	+	1.72166i
$512$	0.841254	−	0.540641i	0.0371785	−	0.0238932i
$513$	−2.51308	−	5.50288i	−0.110955	−	0.242958i
$514$	−7.89671	−	9.11329i	−0.348309	−	0.401970i
$515$	−1.31992	−	9.18028i	−0.0581628	−	0.404531i
$516$	0.711257	−	1.55744i	0.0313114	−	0.0685623i
$517$	−5.83719	+	1.71395i	−0.256719	+	0.0753795i
$518$	1.76353	−	0.517818i	0.0774849	−	0.0227516i
$519$	−9.36020	+	20.4960i	−0.410867	+	0.899674i
$520$	0.0257545	+	0.179126i	0.00112941	+	0.00785521i
$521$	−18.8477	−	21.7514i	−0.825734	−	0.952947i	0.173759	−	0.984788i	$-0.444409\pi$
$521$	−18.8477	−	21.7514i	−0.825734	−	0.952947i	−0.999493	+	0.0318407i	$0.989863\pi$
$522$	−0.0133459	−	0.0292234i	−0.000584134	−	0.00127907i
$523$	17.7000	−	11.3751i	0.773968	−	0.497399i	−0.0930585	−	0.995661i	$-0.529664\pi$
$523$	17.7000	−	11.3751i	0.773968	−	0.497399i	0.867027	+	0.498261i	$0.166028\pi$
$524$	1.05744	−	7.35463i	0.0461943	−	0.321288i
$525$	−2.87994	−	1.85082i	−0.125691	−	0.0807765i
$526$	−14.3359	+	16.5445i	−0.625076	+	0.721376i
$527$	3.84774	+	1.12980i	0.167610	+	0.0492147i
$528$	−1.08904			−0.0473945
$529$	−22.2417	−	5.85738i	−0.967028	−	0.254669i
$530$	−10.5317			−0.457466
$531$	−6.86693	−	2.01631i	−0.298000	−	0.0875006i
$532$	−13.5622	+	15.6516i	−0.587995	+	0.678582i
$533$	−1.68063	−	1.08007i	−0.0727961	−	0.0467832i
$534$	−0.188649	+	1.31208i	−0.00816363	+	0.0567793i
$535$	3.72264	−	2.39240i	0.160944	−	0.103432i
$536$	0.141745	+	0.310378i	0.00612245	+	0.0134063i
$537$	9.62765	+	11.1109i	0.415464	+	0.479471i
$538$	3.54888	+	24.6830i	0.153003	+	1.06416i
$539$	2.13516	−	4.67535i	0.0919678	−	0.201381i
$540$	−0.959493	+	0.281733i	−0.0412900	+	0.0121238i
$541$	31.6501	−	9.29330i	1.36074	−	0.399550i	0.481718	−	0.876326i	$-0.340013\pi$
$541$	31.6501	−	9.29330i	1.36074	−	0.399550i	0.879025	+	0.476776i	$0.158195\pi$
$542$	−6.65571	+	14.5740i	−0.285887	+	0.626005i
$543$	−2.29639	−	15.9717i	−0.0985475	−	0.685413i
$544$	−4.70769	−	5.43296i	−0.201840	−	0.232936i
$545$	3.11436	+	6.81950i	0.133405	+	0.292115i
$546$	−0.521178	+	0.334940i	−0.0223043	+	0.0143341i
$547$	2.97675	−	20.7038i	0.127277	−	0.885229i	−0.821708	−	0.569908i	$-0.806979\pi$
$547$	2.97675	−	20.7038i	0.127277	−	0.885229i	0.948985	−	0.315321i	$-0.102112\pi$
$548$	−15.7612	−	10.1291i	−0.673284	−	0.432694i
$549$	−4.54050	+	5.24001i	−0.193784	+	0.223638i
$550$	−1.04493	−	0.306819i	−0.0445559	−	0.0130828i
$551$	−0.194352			−0.00827969
$552$	0.615771	−	4.75614i	0.0262089	−	0.202435i
$553$	0.738853			0.0314192
$554$	14.8084	+	4.34815i	0.629150	+	0.184735i
$555$	0.351587	−	0.405753i	0.0149240	−	0.0172233i
$556$	−15.0606	−	9.67884i	−0.638710	−	0.410474i
$557$	−0.179194	+	1.24632i	−0.00759271	+	0.0528085i	−0.993266	−	0.115860i	$-0.963038\pi$
$557$	−0.179194	+	1.24632i	−0.00759271	+	0.0528085i	0.985673	+	0.168668i	$0.0539467\pi$
$558$	−0.469280	+	0.301588i	−0.0198662	+	0.0127672i
$559$	−0.128715	−	0.281847i	−0.00544407	−	0.0119208i
$560$	2.24184	+	2.58722i	0.0947351	+	0.109330i
$561$	1.11418	+	7.74926i	0.0470405	+	0.327174i
$562$	8.39163	−	18.3751i	0.353979	−	0.775107i
$563$	18.8931	−	5.54750i	0.796248	−	0.233799i	0.141789	−	0.989897i	$-0.454715\pi$
$563$	18.8931	−	5.54750i	0.796248	−	0.233799i	0.654459	+	0.756098i	$0.272896\pi$
$564$	5.35993	−	1.57382i	0.225694	−	0.0662696i
$565$	1.39597	−	3.05675i	0.0587289	−	0.128598i
$566$	3.58914	+	24.9631i	0.150863	+	1.04928i
$567$	−2.24184	−	2.58722i	−0.0941485	−	0.108653i
$568$	5.71042	+	12.5041i	0.239604	+	0.524659i
$569$	−20.8770	+	13.4169i	−0.875211	+	0.562464i	−0.899342	−	0.437245i	$-0.855954\pi$
$569$	−20.8770	+	13.4169i	−0.875211	+	0.562464i	0.0241316	+	0.999709i	$0.492318\pi$
$570$	−0.860944	+	5.98799i	−0.0360610	+	0.250809i
$571$	16.0880	+	10.3391i	0.673260	+	0.432678i	0.832099	−	0.554626i	$-0.187139\pi$
$571$	16.0880	+	10.3391i	0.673260	+	0.432678i	−0.158839	+	0.987304i	$0.550775\pi$
$572$	−0.129061	+	0.148945i	−0.00539633	+	0.00622770i
$573$	−9.55323	−	2.80508i	−0.399092	−	0.117184i
$574$	−37.7918			−1.57740
$575$	1.93079	−	4.39000i	0.0805193	−	0.183075i
$576$	1.00000			0.0416667
$577$	1.47572	+	0.433311i	0.0614351	+	0.0180390i	0.312306	−	0.949982i	$-0.398899\pi$
$577$	1.47572	+	0.433311i	0.0614351	+	0.0180390i	−0.250871	+	0.968021i	$0.580717\pi$
$578$	−22.7102	+	26.2089i	−0.944619	+	1.09015i
$579$	−6.69037	−	4.29964i	−0.278042	−	0.178687i
$580$	−0.00457210	+	0.0317997i	−0.000189846	+	0.00132041i
$581$	−16.7675	+	10.7758i	−0.695633	+	0.447056i
$582$	−0.292102	−	0.639613i	−0.0121080	−	0.0265128i
$583$	−7.51088	−	8.66801i	−0.311069	−	0.358992i
$584$	−1.63454	−	11.3685i	−0.0676378	−	0.470431i
$585$	−0.0751770	+	0.164615i	−0.00310819	+	0.00680598i
$586$	7.95027	−	2.33441i	0.328423	−	0.0964336i
$587$	−26.4890	+	7.77787i	−1.09332	+	0.321027i	−0.778194	−	0.628024i	$-0.783864\pi$
$587$	−26.4890	+	7.77787i	−1.09332	+	0.321027i	−0.315123	+	0.949051i	$0.602046\pi$
$588$	−1.96058	+	4.29308i	−0.0808531	+	0.177044i
$589$	0.480263	+	3.34030i	0.0197889	+	0.137635i
$590$	4.68673	+	5.40878i	0.192950	+	0.222676i
$591$	9.97045	+	21.8322i	0.410129	+	0.898058i
$592$	−0.451659	+	0.290264i	−0.0185631	+	0.0119298i
$593$	−6.12772	+	42.6192i	−0.251635	+	1.75016i	0.336761	+	0.941590i	$0.390668\pi$
$593$	−6.12772	+	42.6192i	−0.251635	+	1.75016i	−0.588397	+	0.808572i	$0.700241\pi$
$594$	−0.916161	−	0.588781i	−0.0375905	−	0.0241580i
$595$	16.1162	−	18.5991i	0.660701	−	0.762490i
$596$	−15.8915	−	4.66615i	−0.650939	−	0.191133i
$597$	5.94863			0.243461
$598$	−0.577507	−	0.647862i	−0.0236160	−	0.0264931i
$599$	39.1261			1.59865			0.799324	−	0.600900i	$-0.205191\pi$
$599$	39.1261			1.59865			0.799324	+	0.600900i	$0.205191\pi$
$600$	0.959493	+	0.281733i	0.0391711	+	0.0115017i
$601$	−4.48911	+	5.18071i	−0.183115	+	0.211325i	−0.839884	−	0.542766i	$-0.817377\pi$
$601$	−4.48911	+	5.18071i	−0.183115	+	0.211325i	0.656769	+	0.754091i	$0.271922\pi$
$602$	−4.93091	−	3.16891i	−0.200969	−	0.129155i
$603$	−0.0485597	+	0.337740i	−0.00197750	+	0.0137538i
$604$	−9.55292	+	6.13929i	−0.388703	+	0.249804i
$605$	4.07688	+	8.92712i	0.165749	+	0.362939i
$606$	7.66963	+	8.85123i	0.311558	+	0.359557i
$607$	2.16680	+	15.0704i	0.0879475	+	0.611689i	0.985359	+	0.170494i	$0.0545362\pi$
$607$	2.16680	+	15.0704i	0.0879475	+	0.611689i	−0.897411	+	0.441195i	$0.854555\pi$
$608$	2.51308	−	5.50288i	0.101919	−	0.223171i
$609$	−0.105527	+	0.0309855i	−0.00427617	+	0.00125560i
$610$	6.65267	−	1.95340i	0.269359	−	0.0790909i
$611$	0.419954	−	0.919571i	0.0169895	−	0.0372019i
$612$	−1.02308	−	7.11567i	−0.0413555	−	0.287634i
$613$	−4.89353	−	5.64743i	−0.197648	−	0.228098i	0.648271	−	0.761410i	$-0.275492\pi$
$613$	−4.89353	−	5.64743i	−0.197648	−	0.228098i	−0.845918	+	0.533312i	$0.820947\pi$
$614$	−4.38851	−	9.60951i	−0.177106	−	0.387808i
$615$	−9.28686	+	5.96830i	−0.374482	+	0.240665i
$616$	−0.530580	+	3.69027i	−0.0213777	+	0.148685i
$617$	−0.895186	−	0.575301i	−0.0360388	−	0.0231608i	0.522497	−	0.852641i	$-0.325000\pi$
$617$	−0.895186	−	0.575301i	−0.0360388	−	0.0231608i	−0.558536	+	0.829480i	$0.688637\pi$
$618$	−6.07362	+	7.00934i	−0.244317	+	0.281957i
$619$	1.58397	+	0.465095i	0.0636650	+	0.0186937i	0.313410	−	0.949618i	$-0.398529\pi$
$619$	1.58397	+	0.465095i	0.0636650	+	0.0186937i	−0.249745	+	0.968312i	$0.580347\pi$
$620$	0.557834			0.0224031
$621$	3.08938	−	3.66821i	0.123973	−	0.147200i
$622$	13.1003			0.525276
$623$	4.35413	+	1.27849i	0.174445	+	0.0512216i
$624$	0.118509	−	0.136767i	0.00474416	−	0.00547505i
$625$	0.841254	+	0.540641i	0.0336501	+	0.0216256i
$626$	−4.52694	+	31.4855i	−0.180933	+	1.25842i
$627$	−5.54238	+	3.56187i	−0.221341	+	0.142247i
$628$	−2.21416	−	4.84834i	−0.0883547	−	0.193470i
$629$	2.52750	+	2.91689i	0.100778	+	0.116304i
$630$	0.487199	+	3.38854i	0.0194105	+	0.135003i
$631$	−11.4053	+	24.9741i	−0.454038	+	0.994204i	0.534769	+	0.844999i	$0.320399\pi$
$631$	−11.4053	+	24.9741i	−0.454038	+	0.994204i	−0.988806	+	0.149205i	$0.952328\pi$
$632$	−0.207083	+	0.0608050i	−0.00823731	+	0.00241869i
$633$	15.4598	−	4.53941i	0.614472	−	0.180425i
$634$	−1.88677	+	4.13146i	−0.0749333	+	0.164081i
$635$	−0.756115	−	5.25890i	−0.0300055	−	0.208693i
$636$	6.89677	+	7.95930i	0.273475	+	0.315607i
$637$	0.354804	+	0.776912i	0.0140578	+	0.0307824i
$638$	−0.0294332	+	0.0189156i	−0.00116527	+	0.000748874i
$639$	−1.95630	+	13.6064i	−0.0773901	+	0.538260i
$640$	−0.841254	−	0.540641i	−0.0332535	−	0.0213707i
$641$	−7.97161	+	9.19973i	−0.314860	+	0.363368i	−0.891016	−	0.453972i	$-0.850007\pi$
$641$	−7.97161	+	9.19973i	−0.314860	+	0.363368i	0.576156	+	0.817340i	$0.304552\pi$
$642$	−4.24587	−	1.24670i	−0.167571	−	0.0492033i
$643$	−47.0090			−1.85385			−0.926927	−	0.375241i	$-0.877560\pi$
$643$	−47.0090			−1.85385			−0.926927	+	0.375241i	$0.877560\pi$
$644$	−15.8164	−	4.40375i	−0.623252	−	0.173532i
$645$	−1.71216			−0.0674163
$646$	−41.7278	−	12.2524i	−1.64176	−	0.482063i
$647$	2.70543	−	3.12223i	0.106361	−	0.122747i	−0.700073	−	0.714072i	$-0.746849\pi$
$647$	2.70543	−	3.12223i	0.106361	−	0.122747i	0.806434	+	0.591324i	$0.201395\pi$
$648$	0.841254	+	0.540641i	0.0330476	+	0.0212384i
$649$	−1.10922	+	7.71477i	−0.0435405	+	0.302831i
$650$	0.152240	−	0.0978389i	0.00597136	−	0.00383756i
$651$	0.793310	+	1.73711i	0.0310923	+	0.0680826i
$652$	−4.98175	−	5.74924i	−0.195100	−	0.225158i
$653$	0.630345	+	4.38415i	0.0246673	+	0.171565i	0.998431	−	0.0559969i	$-0.0178337\pi$
$653$	0.630345	+	4.38415i	0.0246673	+	0.171565i	−0.973764	+	0.227562i	$0.926925\pi$
$654$	3.11436	−	6.81950i	0.121781	−	0.266664i
$655$	−7.12928	+	2.09335i	−0.278564	+	0.0817938i
$656$	10.5921	−	3.11013i	0.413554	−	0.121430i
$657$	4.77120	−	10.4475i	0.186142	−	0.407595i
$658$	−2.72159	−	18.9291i	−0.106099	−	0.737933i
$659$	−30.1856	−	34.8360i	−1.17586	−	1.35702i	−0.920772	−	0.390101i	$-0.872440\pi$
$659$	−30.1856	−	34.8360i	−1.17586	−	1.35702i	−0.255090	−	0.966917i	$-0.582105\pi$
$660$	0.452405	+	0.990628i	0.0176098	+	0.0385601i
$661$	32.2138	−	20.7025i	1.25297	−	0.805235i	0.265664	−	0.964066i	$-0.414409\pi$
$661$	32.2138	−	20.7025i	1.25297	−	0.805235i	0.987306	+	0.158831i	$0.0507725\pi$
$662$	−2.43345	+	16.9250i	−0.0945786	+	0.657808i
$663$	−1.09443	−	0.703348i	−0.0425042	−	0.0273158i
$664$	3.81271	−	4.40011i	0.147962	−	0.170757i
$665$	19.8711	+	5.83469i	0.770569	+	0.226259i
$666$	−0.536888			−0.0208040
$667$	−0.0659670	−	0.139238i	−0.00255425	−	0.00539131i
$668$	−7.88936			−0.305249
$669$	13.9603	+	4.09912i	0.539737	+	0.158481i
$670$	0.223447	−	0.257872i	0.00863252	−	0.00996245i
$671$	6.35223	+	4.08233i	0.245225	+	0.157597i
$672$	0.487199	−	3.38854i	0.0187941	−	0.130716i
$673$	−19.7175	+	12.6717i	−0.760054	+	0.488457i	−0.862360	−	0.506296i	$-0.831014\pi$
$673$	−19.7175	+	12.6717i	−0.760054	+	0.488457i	0.102306	+	0.994753i	$0.467378\pi$
$674$	15.0681	+	32.9946i	0.580402	+	1.27090i
$675$	0.654861	+	0.755750i	0.0252056	+	0.0290888i
$676$	1.84543	+	12.8353i	0.0709782	+	0.493664i
$677$	4.88077	−	10.6874i	0.187583	−	0.410750i	−0.792353	−	0.610063i	$-0.791144\pi$
$677$	4.88077	−	10.6874i	0.187583	−	0.410750i	0.979936	+	0.199314i	$0.0638713\pi$
$678$	−3.22430	+	0.946741i	−0.123829	+	0.0363594i
$679$	−2.30967	+	0.678180i	−0.0886369	+	0.0260261i
$680$	−2.98635	+	6.53920i	−0.114521	+	0.250767i
$681$	−0.500463	−	3.48080i	−0.0191778	−	0.133384i
$682$	0.397831	+	0.459121i	0.0152337	+	0.0175807i
$683$	9.80900	+	21.4787i	0.375331	+	0.821860i	0.999187	+	0.0403209i	$0.0128380\pi$
$683$	9.80900	+	21.4787i	0.375331	+	0.821860i	−0.623856	+	0.781540i	$0.714435\pi$
$684$	5.08922	−	3.27064i	0.194591	−	0.125056i
$685$	−2.66632	+	18.5447i	−0.101875	+	0.708555i
$686$	−6.56747	−	4.22065i	−0.250747	−	0.161145i
$687$	−15.6811	+	18.0970i	−0.598273	+	0.690444i
$688$	1.64281	+	0.482371i	0.0626314	+	0.0183902i
$689$	1.90590			0.0726089
$690$	−4.58213	+	1.41565i	−0.174439	+	0.0538927i
$691$	14.0727			0.535350			0.267675	−	0.963509i	$-0.413745\pi$
$691$	14.0727			0.535350			0.267675	+	0.963509i	$0.413745\pi$
$692$	−21.6195	−	6.34804i	−0.821848	−	0.241316i
$693$	−2.44146	+	2.81760i	−0.0927434	+	0.107032i
$694$	23.5678	+	15.1461i	0.894621	+	0.574938i
$695$	−2.54780	+	17.7203i	−0.0966434	+	0.672170i
$696$	0.0270267	−	0.0173690i	0.00102444	−	0.000658369i
$697$	−32.9673	−	72.1882i	−1.24872	−	2.73432i
$698$	−20.7149	−	23.9063i	−0.784072	−	0.904868i
$699$	1.50758	+	10.4855i	0.0570220	+	0.396597i
$700$	1.42213	−	3.11402i	0.0537513	−	0.117699i
$701$	2.03585	−	0.597781i	0.0768932	−	0.0225779i	−0.243060	−	0.970011i	$-0.578151\pi$
$701$	2.03585	−	0.597781i	0.0768932	−	0.0225779i	0.319953	+	0.947433i	$0.396333\pi$
$702$	0.173638	−	0.0509847i	0.00655354	−	0.00192429i
$703$	−1.34924	+	2.95443i	−0.0508877	+	0.111429i
$704$	−0.154987	−	1.07796i	−0.00584129	−	0.0406271i
$705$	−3.65819	−	4.22177i	−0.137775	−	0.159001i
$706$	1.72484	+	3.77688i	0.0649153	+	0.142145i
$707$	33.7294	−	21.6766i	1.26852	−	0.815231i
$708$	1.01852	−	7.08399i	0.0382785	−	0.266233i
$709$	29.9202	+	19.2286i	1.12368	+	0.722144i	0.964231	−	0.265063i	$-0.0853926\pi$
$709$	29.9202	+	19.2286i	1.12368	+	0.722144i	0.159447	+	0.987207i	$0.449029\pi$
$710$	9.00191	−	10.3888i	0.337836	−	0.389883i
$711$	−0.207083	−	0.0608050i	−0.00776621	−	0.00228037i
$712$	−1.32557			−0.0496780
$713$	−2.23005	+	1.47783i	−0.0835159	+	0.0553453i
$714$	−24.6102			−0.921013
$715$	0.189099	+	0.0555245i	0.00707190	+	0.00207650i
$716$	−9.62765	+	11.1109i	−0.359802	+	0.415234i
$717$	22.9931	+	14.7768i	0.858694	+	0.551849i
$718$	−0.100334	+	0.697840i	−0.00374444	+	0.0260431i
$719$	35.4395	−	22.7756i	1.32167	−	0.849387i	0.326279	−	0.945273i	$-0.394205\pi$
$719$	35.4395	−	22.7756i	1.32167	−	0.849387i	0.995392	+	0.0958865i	$0.0305686\pi$
$720$	−0.415415	−	0.909632i	−0.0154816	−	0.0339000i
$721$	20.7924	+	23.9957i	0.774348	+	0.893646i
$722$	−2.50436	−	17.4182i	−0.0932025	−	0.648238i
$723$	9.99241	−	21.8803i	0.371622	−	0.813738i
$724$	15.4824	−	4.54603i	0.575397	−	0.168952i
$725$	0.0308253	−	0.00905112i	0.00114482	−	0.000336150i
$726$	4.07688	−	8.92712i	0.151307	−	0.331316i
$727$	4.94624	+	34.4018i	0.183446	+	1.27589i	0.848539	+	0.529133i	$0.177483\pi$
$727$	4.94624	+	34.4018i	0.183446	+	1.27589i	−0.665093	+	0.746760i	$0.731608\pi$
$728$	−0.405703	−	0.468206i	−0.0150363	−	0.0173529i
$729$	0.415415	+	0.909632i	0.0153857	+	0.0336901i
$730$	−9.66213	+	6.20947i	−0.357611	+	0.229823i
$731$	1.75167	−	12.1832i	0.0647880	−	0.450611i
$732$	−5.83286	−	3.74855i	−0.215589	−	0.138550i
$733$	−18.2092	+	21.0145i	−0.672572	+	0.776190i	−0.984777	−	0.173825i	$-0.944387\pi$
$733$	−18.2092	+	21.0145i	−0.672572	+	0.776190i	0.312204	+	0.950015i	$0.398933\pi$
$734$	−10.3849	−	3.04928i	−0.383314	−	0.112551i
$735$	4.71958			0.174084
$736$	4.79536	−	0.0673656i	0.176759	−	0.00248313i
$737$	0.371596			0.0136879
$738$	10.5921	+	3.11013i	0.389902	+	0.114486i
$739$	−5.69276	+	6.56980i	−0.209412	+	0.241674i	−0.850733	−	0.525599i	$-0.823841\pi$
$739$	−5.69276	+	6.56980i	−0.209412	+	0.241674i	0.641321	+	0.767273i	$0.278387\pi$
$740$	0.451659	+	0.290264i	0.0166033	+	0.0106703i
$741$	0.155804	−	1.08364i	0.00572359	−	0.0398084i
$742$	30.3305	−	19.4922i	1.11347	−	0.715582i
$743$	−8.16712	−	17.8835i	−0.299623	−	0.656082i	0.698610	−	0.715502i	$-0.253802\pi$
$743$	−8.16712	−	17.8835i	−0.299623	−	0.656082i	−0.998233	+	0.0594201i	$0.981075\pi$
$744$	−0.365303	−	0.421583i	−0.0133927	−	0.0154560i
$745$	2.35707	+	16.3938i	0.0863563	+	0.600621i
$746$	6.43274	−	14.0857i	0.235519	−	0.515716i
$747$	5.58634	−	1.64030i	0.204393	−	0.0600153i
$748$	−7.51182	+	2.20567i	−0.274659	+	0.0806473i
$749$	−6.29307	+	13.7799i	−0.229944	+	0.503507i
$750$	−0.142315	−	0.989821i	−0.00519660	−	0.0361432i
$751$	−3.97612	−	4.58869i	−0.145091	−	0.167444i	0.678553	−	0.734552i	$-0.262608\pi$
$751$	−3.97612	−	4.58869i	−0.145091	−	0.167444i	−0.823643	+	0.567108i	$0.808062\pi$
$752$	2.32059	+	5.08139i	0.0846233	+	0.185299i
$753$	5.69183	−	3.65791i	0.207422	−	0.133302i
$754$	0.000827406	−	0.00575473i	3.01323e−5	−	0.000209575i
$755$	9.55292	+	6.13929i	0.347666	+	0.223431i
$756$	2.24184	−	2.58722i	0.0815350	−	0.0940964i
$757$	32.0770	+	9.41866i	1.16586	+	0.342327i	0.806707	−	0.590952i	$-0.201248\pi$
$757$	32.0770	+	9.41866i	1.16586	+	0.342327i	0.359152	+	0.933279i	$0.383066\pi$
$758$	6.75933			0.245510
$759$	−4.43298	−	2.76170i	−0.160907	−	0.100243i
$760$	−6.04957			−0.219441
$761$	6.21280	+	1.82424i	0.225214	+	0.0661287i	0.392392	−	0.919798i	$-0.371648\pi$
$761$	6.21280	+	1.82424i	0.225214	+	0.0661287i	−0.167179	+	0.985927i	$0.553466\pi$
$762$	−3.47926	+	4.01528i	−0.126040	+	0.145458i
$763$	−21.5909	−	13.8756i	−0.781641	−	0.502330i
$764$	1.41696	−	9.85520i	0.0512639	−	0.356549i
$765$	−6.04764	+	3.88658i	−0.218653	+	0.140520i
$766$	−13.1371	−	28.7662i	−0.474662	−	1.03936i
$767$	−0.848150	−	0.978818i	−0.0306249	−	0.0353431i
$768$	0.142315	+	0.989821i	0.00513534	+	0.0357171i
$769$	−21.3079	+	46.6579i	−0.768384	+	1.68253i	−0.0382055	+	0.999270i	$0.512164\pi$
$769$	−21.3079	+	46.6579i	−0.768384	+	1.68253i	−0.730179	+	0.683256i	$0.760563\pi$
$770$	3.57720	−	1.05036i	0.128913	−	0.0378523i
$771$	11.5702	−	3.39730i	0.416689	−	0.122351i
$772$	3.30374	−	7.23417i	0.118904	−	0.260364i
$773$	−2.72696	−	18.9664i	−0.0980819	−	0.682175i	−0.978237	−	0.207489i	$-0.933471\pi$
$773$	−2.72696	−	18.9664i	−0.0980819	−	0.682175i	0.880155	−	0.474686i	$-0.157438\pi$
$774$	1.12123	+	1.29396i	0.0403017	+	0.0465106i
$775$	−0.231732	−	0.507423i	−0.00832408	−	0.0182272i
$776$	0.591533	−	0.380155i	0.0212348	−	0.0136468i
$777$	−0.261571	+	1.81927i	−0.00938382	+	0.0652659i
$778$	14.9039	+	9.57815i	0.534330	+	0.343393i
$779$	43.7336	−	50.4713i	1.56692	−	1.80832i
$780$	−0.173638	−	0.0509847i	−0.00621724	−	0.00182554i
$781$	14.9703			0.535680
$782$	−5.38538	−	34.0532i	−0.192581	−	1.21774i
$783$	0.0321267			0.00114811
$784$	−4.52840	−	1.32966i	−0.161729	−	0.0474878i
$785$	−3.49041	+	4.02815i	−0.124578	+	0.143771i
$786$	6.25073	+	4.01710i	0.222956	+	0.143285i
$787$	6.28452	−	43.7098i	0.224019	−	1.55809i	−0.498595	−	0.866835i	$-0.666150\pi$
$787$	6.28452	−	43.7098i	0.224019	−	1.55809i	0.722614	−	0.691252i	$-0.242940\pi$
$788$	−20.1911	+	12.9760i	−0.719277	+	0.462251i
$789$	−9.09409	−	19.9133i	−0.323758	−	0.708931i
$790$	0.141335	+	0.163110i	0.00502849	+	0.00580319i
$791$	1.63719	+	11.3869i	0.0582119	+	0.404873i
$792$	0.452405	−	0.990628i	0.0160755	−	0.0352004i
$793$	−1.20392	+	0.353504i	−0.0427526	+	0.0125533i
$794$	−26.9120	+	7.90207i	−0.955070	+	0.280434i
$795$	4.37501	−	9.57993i	0.155166	−	0.339765i
$796$	0.846578	+	5.88808i	0.0300062	+	0.208697i
$797$	−13.0821	−	15.0976i	−0.463392	−	0.534783i	0.475170	−	0.879894i	$-0.342387\pi$
$797$	−13.0821	−	15.0976i	−0.463392	−	0.534783i	−0.938562	+	0.345111i	$0.887841\pi$
$798$	−8.60325	−	18.8385i	−0.304552	−	0.666876i
$799$	33.7833	−	21.7112i	1.19517	−	0.768088i
$800$	−0.142315	+	0.989821i	−0.00503159	+	0.0349955i
$801$	−1.11514	−	0.716659i	−0.0394016	−	0.0253219i
$802$	−17.5689	+	20.2756i	−0.620381	+	0.715957i
$803$	−12.0014	−	3.52393i	−0.423521	−	0.124357i
$804$	−0.341213			−0.0120337
$805$	2.56456	+	16.2165i	0.0903890	+	0.571555i
$806$	−0.100950			−0.00355582
$807$	−23.9267	−	7.02552i	−0.842260	−	0.247310i
$808$	−7.66963	+	8.85123i	−0.269817	+	0.311385i
$809$	−1.15579	−	0.742779i	−0.0406353	−	0.0261147i	0.520165	−	0.854065i	$-0.325870\pi$
$809$	−1.15579	−	0.742779i	−0.0406353	−	0.0261147i	−0.560801	+	0.827951i	$0.689507\pi$
$810$	0.142315	−	0.989821i	0.00500043	−	0.0347788i
$811$	−23.7860	+	15.2863i	−0.835239	+	0.536776i	−0.886939	−	0.461887i	$-0.847173\pi$
$811$	−23.7860	+	15.2863i	−0.835239	+	0.536776i	0.0516994	+	0.998663i	$0.483536\pi$
$812$	−0.0456882	−	0.100043i	−0.00160334	−	0.00351083i
$813$	−10.4921	−	12.1085i	−0.367973	−	0.424663i
$814$	0.0832107	+	0.578743i	0.00291653	+	0.0202849i
$815$	−3.16020	+	6.91988i	−0.110697	+	0.242393i
$816$	6.89764	−	2.02533i	0.241466	−	0.0709007i
$817$	9.93827	−	2.91814i	0.347696	−	0.102093i
$818$	−3.90153	+	8.54317i	−0.136414	+	0.298705i
$819$	−0.0881676	−	0.613219i	−0.00308083	−	0.0214276i
$820$	−7.22921	−	8.34295i	−0.252455	−	0.291349i
$821$	−10.7498	−	23.5388i	−0.375171	−	0.821509i	−0.999195	−	0.0401048i	$-0.987231\pi$
$821$	−10.7498	−	23.5388i	−0.375171	−	0.821509i	0.624025	−	0.781405i	$-0.285496\pi$
$822$	15.7612	−	10.1291i	0.549734	−	0.353293i
$823$	−4.24322	+	29.5123i	−0.147909	+	1.02873i	0.771725	+	0.635957i	$0.219394\pi$
$823$	−4.24322	+	29.5123i	−0.147909	+	1.02873i	−0.919634	+	0.392776i	$0.871515\pi$
$824$	−7.80236	−	5.01427i	−0.271808	−	0.174680i
$825$	0.713171	−	0.823043i	0.0248294	−	0.0286547i
$826$	−23.5082	−	6.90262i	−0.817954	−	0.240173i
$827$	2.53044			0.0879920			0.0439960	−	0.999032i	$-0.485991\pi$
$827$	2.53044			0.0879920			0.0439960	+	0.999032i	$0.485991\pi$
$828$	4.07053	+	2.53589i	0.141461	+	0.0881284i
$829$	17.6369			0.612555			0.306278	−	0.951942i	$-0.400916\pi$
$829$	17.6369			0.612555			0.306278	+	0.951942i	$0.400916\pi$
$830$	−5.58634	−	1.64030i	−0.193905	−	0.0569355i
$831$	−10.1069	+	11.6639i	−0.350603	+	0.404618i
$832$	0.152240	+	0.0978389i	0.00527798	+	0.00339195i
$833$	−4.82850	+	33.5830i	−0.167298	+	1.16358i
$834$	15.0606	−	9.67884i	0.521505	−	0.335151i
$835$	3.27736	+	7.17642i	0.113418	+	0.248350i
$836$	−4.31438	−	4.97906i	−0.149216	−	0.172204i
$837$	−0.0793880	−	0.552156i	−0.00274405	−	0.0190853i
$838$	14.3203	−	31.3571i	0.494686	−	1.08321i
$839$	10.2763	−	3.01739i	0.354776	−	0.104172i	−0.0994878	−	0.995039i	$-0.531720\pi$
$839$	10.2763	−	3.01739i	0.354776	−	0.104172i	0.454264	+	0.890867i	$0.349902\pi$
$840$	−3.28472	+	0.964480i	−0.113333	+	0.0332777i
$841$	−12.0466	+	26.3784i	−0.415400	+	0.909600i
$842$	2.27470	+	15.8209i	0.0783915	+	0.545225i
$843$	13.2286	+	15.2666i	0.455616	+	0.525809i
$844$	6.69336	+	14.6564i	0.230395	+	0.504495i
$845$	10.9087	−	7.01062i	0.375272	−	0.241173i
$846$	−0.795000	+	5.52935i	−0.0273327	+	0.190103i
$847$	−28.2637	−	18.1639i	−0.971151	−	0.624121i
$848$	−6.89677	+	7.95930i	−0.236836	+	0.273323i
$849$	−24.1982	−	7.10523i	−0.830479	−	0.243851i
$850$	7.18884			0.246575
$851$	−2.57457	+	0.0361678i	−0.0882552	+	0.00123982i
$852$	−13.7463			−0.470940
$853$	47.7984	+	14.0349i	1.63659	+	0.480545i	0.965407	−	0.260748i	$-0.0839692\pi$
$853$	47.7984	+	14.0349i	1.63659	+	0.480545i	0.671181	+	0.741294i	$0.265787\pi$
$854$	−15.5439	+	17.9386i	−0.531901	+	0.613846i
$855$	−5.08922	−	3.27064i	−0.174048	−	0.111854i
$856$	0.629759	−	4.38007i	0.0215247	−	0.149708i
$857$	3.13492	−	2.01469i	0.107087	−	0.0688205i	−0.486001	−	0.873958i	$-0.661545\pi$
$857$	3.13492	−	2.01469i	0.107087	−	0.0688205i	0.593088	+	0.805138i	$0.297909\pi$
$858$	−0.0818709	−	0.179272i	−0.00279503	−	0.00612026i
$859$	−29.0575	−	33.5342i	−0.991430	−	1.14417i	−0.989553	−	0.144173i	$-0.953948\pi$
$859$	−29.0575	−	33.5342i	−0.991430	−	1.14417i	−0.00187742	−	0.999998i	$-0.500598\pi$
$860$	−0.243666	−	1.69473i	−0.00830894	−	0.0577899i
$861$	15.6993	−	34.3767i	0.535031	−	1.17155i
$862$	−17.2659	+	5.06971i	−0.588078	+	0.172675i
$863$	29.6905	−	8.71792i	1.01068	−	0.296761i	0.265846	−	0.964015i	$-0.414349\pi$
$863$	29.6905	−	8.71792i	1.01068	−	0.296761i	0.744830	+	0.667254i	$0.232531\pi$
$864$	−0.415415	+	0.909632i	−0.0141327	+	0.0309463i
$865$	3.20666	+	22.3028i	0.109030	+	0.758319i
$866$	14.2368	+	16.4302i	0.483787	+	0.558320i
$867$	−14.4063	−	31.5455i	−0.489265	−	1.07134i
$868$	−1.60653	+	1.03245i	−0.0545290	+	0.0350437i
$869$	−0.0334501	+	0.232650i	−0.00113472	+	0.00789213i
$870$	−0.0270267	−	0.0173690i	−0.000916290	−	0.000588864i
$871$	−0.0404369	+	0.0466666i	−0.00137015	+	0.00158124i
$872$	7.19331	+	2.11215i	0.243596	+	0.0715263i
$873$	0.703156			0.0237982
$874$	24.1843	−	16.0268i	0.818047	−	0.542113i
$875$	−3.42339			−0.115732
$876$	11.0202	+	3.23581i	0.372337	+	0.109328i
$877$	−9.90752	+	11.4339i	−0.334553	+	0.386095i	−0.897954	−	0.440089i	$-0.854947\pi$
$877$	−9.90752	+	11.4339i	−0.334553	+	0.386095i	0.563401	+	0.826183i	$0.309493\pi$
$878$	21.8175	+	14.0213i	0.736306	+	0.473195i
$879$	−1.17921	+	8.20157i	−0.0397737	+	0.276632i
$880$	−0.916161	+	0.588781i	−0.0308838	+	0.0198478i
$881$	8.50240	+	18.6177i	0.286453	+	0.627245i	0.997083	−	0.0763210i	$-0.0243174\pi$
$881$	8.50240	+	18.6177i	0.286453	+	0.627245i	−0.710630	+	0.703566i	$0.751590\pi$
$882$	−3.09067	−	3.56682i	−0.104068	−	0.120101i
$883$	−1.10332	−	7.67375i	−0.0371296	−	0.258242i	0.962799	−	0.270220i	$-0.0870964\pi$
$883$	−1.10332	−	7.67375i	−0.0371296	−	0.258242i	−0.999928	+	0.0119776i	$0.996187\pi$
$884$	0.540435	−	1.18339i	0.0181768	−	0.0398017i
$885$	−6.86693	+	2.01631i	−0.230829	+	0.0677777i
$886$	1.87869	−	0.551634i	0.0631159	−	0.0185325i
$887$	−1.43242	+	3.13656i	−0.0480960	+	0.105315i	−0.932155	−	0.362061i	$-0.882073\pi$
$887$	−1.43242	+	3.13656i	−0.0480960	+	0.105315i	0.884059	+	0.467376i	$0.154801\pi$
$888$	−0.0764072	−	0.531424i	−0.00256406	−	0.0178334i
$889$	11.9108	+	13.7459i	0.399477	+	0.461021i
$890$	0.550663	+	1.20578i	0.0184583	+	0.0404180i
$891$	0.916161	−	0.588781i	0.0306925	−	0.0197249i
$892$	−2.07063	+	14.4016i	−0.0693300	+	0.482201i
$893$	28.4294	+	18.2705i	0.951355	+	0.611399i
$894$	10.8460	−	12.5170i	0.362745	−	0.418631i
$895$	14.1063	+	4.14198i	0.471521	+	0.138451i
$896$	3.42339			0.114367
$897$	0.829221	−	0.256187i	0.0276869	−	0.00855384i
$898$	−35.5158			−1.18518
$899$	−0.0171954	−	0.00504902i	−0.000573498	−	0.000168394i
$900$	−0.654861	+	0.755750i	−0.0218287	+	0.0251917i
$901$	63.6916	+	40.9321i	2.12188	+	1.36365i
$902$	1.71095	−	11.8999i	0.0569684	−	0.396224i
$903$	4.93091	−	3.16891i	0.164091	−	0.105455i
$904$	−1.39597	−	3.05675i	−0.0464293	−	0.101666i
$905$	−10.5668	−	12.1948i	−0.351253	−	0.405368i
$906$	−1.61607	−	11.2400i	−0.0536902	−	0.373424i
$907$	−3.42222	+	7.49362i	−0.113633	+	0.248822i	−0.957900	−	0.287100i	$-0.907309\pi$
$907$	−3.42222	+	7.49362i	−0.113633	+	0.248822i	0.844267	+	0.535922i	$0.180036\pi$
$908$	3.37414	−	0.990738i	0.111975	−	0.0328788i
$909$	−11.2374	+	3.29961i	−0.372722	+	0.109441i
$910$	−0.257360	+	0.563540i	−0.00853140	+	0.0186812i
$911$	7.82885	+	54.4508i	0.259381	+	1.80404i	0.537256	+	0.843419i	$0.319461\pi$
$911$	7.82885	+	54.4508i	0.259381	+	1.80404i	−0.277874	+	0.960617i	$0.589630\pi$
$912$	3.96163	+	4.57196i	0.131183	+	0.151393i
$913$	−2.63398	−	5.76761i	−0.0871720	−	0.190880i
$914$	−9.26694	+	5.95550i	−0.306523	+	0.196990i
$915$	−0.986744	+	6.86296i	−0.0326208	+	0.226882i
$916$	−20.1445	−	12.9461i	−0.665592	−	0.427750i
$917$	16.6575	−	19.2237i	0.550078	−	0.634824i
$918$	6.89764	+	2.02533i	0.227656	+	0.0668458i
$919$	−49.5110			−1.63322			−0.816608	−	0.577192i	$-0.804148\pi$
$919$	−49.5110			−1.63322			−0.816608	+	0.577192i	$0.804148\pi$
$920$	−2.05334	−	4.33403i	−0.0676967	−	0.142889i
$921$	10.5642			0.348101
$922$	16.6256	+	4.88170i	0.547534	+	0.160770i
$923$	−1.62906	+	1.88004i	−0.0536212	+	0.0618822i
$924$	−3.13637	−	2.01562i	−0.103179	−	0.0663092i
$925$	0.0764072	−	0.531424i	0.00251225	−	0.0174731i
$926$	5.21358	−	3.35056i	0.171329	−	0.110106i
$927$	−3.85284	−	8.43655i	−0.126544	−	0.277093i
$928$	0.0210385	+	0.0242797i	0.000690622	+	0.000797020i
$929$	−5.44957	−	37.9026i	−0.178795	−	1.24354i	−0.859557	−	0.511040i	$-0.829261\pi$
$929$	−5.44957	−	37.9026i	−0.178795	−	1.24354i	0.680763	−	0.732504i	$-0.261649\pi$
$930$	−0.231732	+	0.507423i	−0.00759881	+	0.0166391i
$931$	−27.3949	+	8.04387i	−0.897831	+	0.263627i
$932$	−10.1642	+	2.98448i	−0.332939	+	0.0977598i
$933$	−5.44208	+	11.9165i	−0.178166	+	0.390128i
$934$	3.35593	+	23.3410i	0.109809	+	0.763742i
$935$	5.12687	+	5.91673i	0.167667	+	0.193498i
$936$	0.0751770	+	0.164615i	0.00245724	+	0.00538060i
$937$	0.469254	−	0.301571i	0.0153299	−	0.00985190i	−0.532953	−	0.846145i	$-0.678918\pi$
$937$	0.469254	−	0.301571i	0.0153299	−	0.00985190i	0.548283	+	0.836293i	$0.315282\pi$
$938$	−0.166239	+	1.15622i	−0.00542788	+	0.0377518i
$939$	−26.7597	−	17.1974i	−0.873270	−	0.561216i
$940$	3.65819	−	4.22177i	0.119317	−	0.137699i
$941$	−23.2235	−	6.81903i	−0.757064	−	0.222294i	−0.119651	−	0.992816i	$-0.538177\pi$
$941$	−23.2235	−	6.81903i	−0.757064	−	0.222294i	−0.637413	+	0.770522i	$0.719996\pi$
$942$	5.33000			0.173661
$943$	51.0026	+	14.2007i	1.66087	+	0.462437i
$944$	7.15684			0.232935
$945$	−3.28472	−	0.964480i	−0.106852	−	0.0313745i
$946$	1.22106	−	1.40918i	0.0397002	−	0.0458165i
$947$	−23.1560	−	14.8814i	−0.752468	−	0.483582i	0.107325	−	0.994224i	$-0.465771\pi$
$947$	−23.1560	−	14.8814i	−0.752468	−	0.483582i	−0.859793	+	0.510642i	$0.829408\pi$
$948$	0.0307151	−	0.213628i	0.000997581	−	0.00693833i
$949$	1.74854	−	1.12372i	0.0567600	−	0.0364774i
$950$	2.51308	+	5.50288i	0.0815352	+	0.178537i
$951$	−2.97431	−	3.43254i	−0.0964486	−	0.111308i
$952$	−3.50239	−	24.3597i	−0.113513	−	0.789502i
$953$	−8.54495	+	18.7108i	−0.276798	+	0.606103i	−0.996065	−	0.0886311i	$-0.971751\pi$
$953$	−8.54495	+	18.7108i	−0.276798	+	0.606103i	0.719266	+	0.694734i	$0.244478\pi$
$954$	−10.1051	+	2.96711i	−0.327163	+	0.0960638i
$955$	−9.55323	+	2.80508i	−0.309135	+	0.0907703i
$956$	−11.3541	+	24.8620i	−0.367218	+	0.804096i
$957$	−0.00497921	−	0.0346312i	−0.000160955	−	0.00111947i
$958$	16.2507	+	18.7543i	0.525037	+	0.605925i
$959$	−26.6440	−	58.3423i	−0.860381	−	1.88397i
$960$	0.841254	−	0.540641i	0.0271513	−	0.0174491i
$961$	4.36747	−	30.3765i	0.140886	−	0.979886i
$962$	−0.0817361	−	0.0525286i	−0.00263528	−	0.00169359i
$963$	2.89783	−	3.34428i	0.0933814	−	0.107768i
$964$	23.0797	+	6.77681i	0.743346	+	0.218266i
$965$	−7.95286			−0.256011
$966$	10.5761	−	12.5577i	0.340282	−	0.404037i
$967$	−35.6075			−1.14506			−0.572530	−	0.819884i	$-0.694038\pi$
$967$	−35.6075			−1.14506			−0.572530	+	0.819884i	$0.694038\pi$
$968$	9.41645	+	2.76492i	0.302656	+	0.0888679i
$969$	28.4795	−	32.8671i	0.914893	−	1.05584i
$970$	−0.591533	−	0.380155i	−0.0189930	−	0.0122060i
$971$	3.72525	−	25.9097i	0.119549	−	0.831482i	−0.838505	−	0.544894i	$-0.816570\pi$
$971$	3.72525	−	25.9097i	0.119549	−	0.831482i	0.958054	−	0.286588i	$-0.0925211\pi$
$972$	−0.841254	+	0.540641i	−0.0269832	+	0.0173411i
$973$	−25.4597	−	55.7489i	−0.816199	−	1.78723i
$974$	−3.95329	−	4.56234i	−0.126672	−	0.146187i
$975$	0.0257545	+	0.179126i	0.000824804	+	0.00573664i
$976$	2.88029	−	6.30696i	0.0921959	−	0.201881i
$977$	35.6661	−	10.4725i	1.14106	−	0.335045i	0.344014	−	0.938965i	$-0.388213\pi$
$977$	35.6661	−	10.4725i	1.14106	−	0.335045i	0.797045	+	0.603919i	$0.206395\pi$
$978$	7.29919	−	2.14324i	0.233402	−	0.0685331i
$979$	−0.599695	+	1.31315i	−0.0191664	+	0.0419685i
$980$	0.671666	+	4.67154i	0.0214556	+	0.149227i
$981$	4.90948	+	5.66585i	0.156748	+	0.180897i
$982$	8.42591	+	18.4502i	0.268882	+	0.588768i
$983$	45.4919	−	29.2358i	1.45097	−	0.932479i	0.451780	−	0.892130i	$-0.350789\pi$
$983$	45.4919	−	29.2358i	1.45097	−	0.932479i	0.999186	−	0.0403492i	$-0.0128470\pi$
$984$	−1.57106	+	10.9269i	−0.0500835	+	0.348338i
$985$	20.1911	+	12.9760i	0.643341	+	0.413450i
$986$	0.151242	−	0.174543i	0.00481653	−	0.00555858i
$987$	18.3491	+	5.38778i	0.584058	+	0.171495i
$988$	1.09478			0.0348296
$989$	5.46385	+	6.12949i	0.173740	+	0.194907i
$990$	−1.08904			−0.0346120
$991$	−26.2546	−	7.70904i	−0.834004	−	0.244886i	−0.163268	−	0.986582i	$-0.552203\pi$
$991$	−26.2546	−	7.70904i	−0.834004	−	0.244886i	−0.670736	+	0.741696i	$0.734022\pi$
$992$	0.365303	−	0.421583i	0.0115984	−	0.0133853i
$993$	−14.3846	−	9.24444i	−0.456482	−	0.293363i
$994$	−6.69718	+	46.5799i	−0.212422	+	1.47743i
$995$	5.00431	−	3.21607i	0.158647	−	0.101956i
$996$	2.41862	+	5.29604i	0.0766369	+	0.167811i
$997$	−15.4889	−	17.8751i	−0.490537	−	0.566110i	0.455472	−	0.890250i	$-0.349471\pi$
$997$	−15.4889	−	17.8751i	−0.490537	−	0.566110i	−0.946009	+	0.324140i	$0.894925\pi$
$998$	1.87774	+	13.0599i	0.0594387	+	0.413405i
$999$	0.223032	−	0.488371i	0.00705641	−	0.0154514i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	690.2.m.d.271.2	✓	20
23.9	even	11	inner	690.2.m.d.331.2	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.2.m.d.271.2	✓	20	1.1	even	1	trivial
690.2.m.d.331.2	yes	20	23.9	even	11	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.m (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.959493 - 0.281733i) q^{2} +(0.654861 - 0.755750i) q^{3} +(0.841254 + 0.540641i) q^{4} +(0.142315 - 0.989821i) q^{5} +(-0.841254 + 0.540641i) q^{6} +(1.42213 + 3.11402i) q^{7} +(-0.654861 - 0.755750i) q^{8} +(-0.142315 - 0.989821i) q^{9} +O(q^{10})\)	\(q+(-0.959493 - 0.281733i) q^{2} +(0.654861 - 0.755750i) q^{3} +(0.841254 + 0.540641i) q^{4} +(0.142315 - 0.989821i) q^{5} +(-0.841254 + 0.540641i) q^{6} +(1.42213 + 3.11402i) q^{7} +(-0.654861 - 0.755750i) q^{8} +(-0.142315 - 0.989821i) q^{9} +(-0.415415 + 0.909632i) q^{10} +(-1.04493 + 0.306819i) q^{11} +(0.959493 - 0.281733i) q^{12} +(0.0751770 - 0.164615i) q^{13} +(-0.487199 - 3.38854i) q^{14} +(-0.654861 - 0.755750i) q^{15} +(0.415415 + 0.909632i) q^{16} +(6.04764 - 3.88658i) q^{17} +(-0.142315 + 0.989821i) q^{18} +(5.08922 + 3.27064i) q^{19} +(0.654861 - 0.755750i) q^{20} +(3.28472 + 0.964480i) q^{21} +1.08904 q^{22} +(-0.615771 + 4.75614i) q^{23} -1.00000 q^{24} +(-0.959493 - 0.281733i) q^{25} +(-0.118509 + 0.136767i) q^{26} +(-0.841254 - 0.540641i) q^{27} +(-0.487199 + 3.38854i) q^{28} +(-0.0270267 + 0.0173690i) q^{29} +(0.415415 + 0.909632i) q^{30} +(0.365303 + 0.421583i) q^{31} +(-0.142315 - 0.989821i) q^{32} +(-0.452405 + 0.990628i) q^{33} +(-6.89764 + 2.02533i) q^{34} +(3.28472 - 0.964480i) q^{35} +(0.415415 - 0.909632i) q^{36} +(0.0764072 + 0.531424i) q^{37} +(-3.96163 - 4.57196i) q^{38} +(-0.0751770 - 0.164615i) q^{39} +(-0.841254 + 0.540641i) q^{40} +(1.57106 - 10.9269i) q^{41} +(-2.87994 - 1.85082i) q^{42} +(1.12123 - 1.29396i) q^{43} +(-1.04493 - 0.306819i) q^{44} -1.00000 q^{45} +(1.93079 - 4.39000i) q^{46} +5.58621 q^{47} +(0.959493 + 0.281733i) q^{48} +(-3.09067 + 3.56682i) q^{49} +(0.841254 + 0.540641i) q^{50} +(1.02308 - 7.11567i) q^{51} +(0.152240 - 0.0978389i) q^{52} +(4.37501 + 9.57993i) q^{53} +(0.654861 + 0.755750i) q^{54} +(0.154987 + 1.07796i) q^{55} +(1.42213 - 3.11402i) q^{56} +(5.80452 - 1.70436i) q^{57} +(0.0308253 - 0.00905112i) q^{58} +(2.97306 - 6.51009i) q^{59} +(-0.142315 - 0.989821i) q^{60} +(-4.54050 - 5.24001i) q^{61} +(-0.231732 - 0.507423i) q^{62} +(2.87994 - 1.85082i) q^{63} +(-0.142315 + 0.989821i) q^{64} +(-0.152240 - 0.0978389i) q^{65} +(0.713171 - 0.823043i) q^{66} +(-0.327392 - 0.0961309i) q^{67} +7.18884 q^{68} +(3.19120 + 3.57997i) q^{69} -3.42339 q^{70} +(-13.1895 - 3.87278i) q^{71} +(-0.654861 + 0.755750i) q^{72} +(9.66213 + 6.20947i) q^{73} +(0.0764072 - 0.531424i) q^{74} +(-0.841254 + 0.540641i) q^{75} +(2.51308 + 5.50288i) q^{76} +(-2.44146 - 2.81760i) q^{77} +(0.0257545 + 0.179126i) q^{78} +(0.0896571 - 0.196322i) q^{79} +(0.959493 - 0.281733i) q^{80} +(-0.959493 + 0.281733i) q^{81} +(-4.58590 + 10.0417i) q^{82} +(0.828582 + 5.76291i) q^{83} +(2.24184 + 2.58722i) q^{84} +(-2.98635 - 6.53920i) q^{85} +(-1.44036 + 0.925664i) q^{86} +(-0.00457210 + 0.0317997i) q^{87} +(0.916161 + 0.588781i) q^{88} +(0.868066 - 1.00180i) q^{89} +(0.959493 + 0.281733i) q^{90} +0.619525 q^{91} +(-3.08938 + 3.66821i) q^{92} +0.557834 q^{93} +(-5.35993 - 1.57382i) q^{94} +(3.96163 - 4.57196i) q^{95} +(-0.841254 - 0.540641i) q^{96} +(-0.100070 + 0.695999i) q^{97} +(3.97036 - 2.55160i) q^{98} +(0.452405 + 0.990628i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 2 q^{2} + 2 q^{3} - 2 q^{4} + 2 q^{5} + 2 q^{6} + 2 q^{7} - 2 q^{8} - 2 q^{9}+O(q^{10}) \) 20 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 + 2 * q^5 + 2 * q^6 + 2 * q^7 - 2 * q^8 - 2 * q^9	\( 20 q - 2 q^{2} + 2 q^{3} - 2 q^{4} + 2 q^{5} + 2 q^{6} + 2 q^{7} - 2 q^{8} - 2 q^{9} + 2 q^{10} + 2 q^{11} + 2 q^{12} - 11 q^{13} + 2 q^{14} - 2 q^{15} - 2 q^{16} + 24 q^{17} - 2 q^{18} + 22 q^{19} + 2 q^{20} - 2 q^{21} + 2 q^{22} - 22 q^{23} - 20 q^{24} - 2 q^{25} + 11 q^{26} + 2 q^{27} + 2 q^{28} + 14 q^{29} - 2 q^{30} - 8 q^{31} - 2 q^{32} - 2 q^{33} - 9 q^{34} - 2 q^{35} - 2 q^{36} + 20 q^{37} + 11 q^{39} + 2 q^{40} - 21 q^{41} - 13 q^{42} + 34 q^{43} + 2 q^{44} - 20 q^{45} + 14 q^{47} + 2 q^{48} + 10 q^{49} - 2 q^{50} + 31 q^{51} + 2 q^{54} - 2 q^{55} + 2 q^{56} + 11 q^{57} - 19 q^{58} - 40 q^{59} - 2 q^{60} - 19 q^{61} - 8 q^{62} + 13 q^{63} - 2 q^{64} + 9 q^{66} + 18 q^{67} - 20 q^{68} - 22 q^{69} + 20 q^{70} - 85 q^{71} - 2 q^{72} + 39 q^{73} + 20 q^{74} + 2 q^{75} - 48 q^{77} - 11 q^{78} - 28 q^{79} + 2 q^{80} - 2 q^{81} + q^{82} + 49 q^{83} + 9 q^{84} - 13 q^{85} - 32 q^{86} + 8 q^{87} + 2 q^{88} + 3 q^{89} + 2 q^{90} - 34 q^{91} - 11 q^{92} - 36 q^{93} + 3 q^{94} + 2 q^{96} + 43 q^{97} + 10 q^{98} + 2 q^{99}+O(q^{100}) \) 20 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 + 2 * q^5 + 2 * q^6 + 2 * q^7 - 2 * q^8 - 2 * q^9 + 2 * q^10 + 2 * q^11 + 2 * q^12 - 11 * q^13 + 2 * q^14 - 2 * q^15 - 2 * q^16 + 24 * q^17 - 2 * q^18 + 22 * q^19 + 2 * q^20 - 2 * q^21 + 2 * q^22 - 22 * q^23 - 20 * q^24 - 2 * q^25 + 11 * q^26 + 2 * q^27 + 2 * q^28 + 14 * q^29 - 2 * q^30 - 8 * q^31 - 2 * q^32 - 2 * q^33 - 9 * q^34 - 2 * q^35 - 2 * q^36 + 20 * q^37 + 11 * q^39 + 2 * q^40 - 21 * q^41 - 13 * q^42 + 34 * q^43 + 2 * q^44 - 20 * q^45 + 14 * q^47 + 2 * q^48 + 10 * q^49 - 2 * q^50 + 31 * q^51 + 2 * q^54 - 2 * q^55 + 2 * q^56 + 11 * q^57 - 19 * q^58 - 40 * q^59 - 2 * q^60 - 19 * q^61 - 8 * q^62 + 13 * q^63 - 2 * q^64 + 9 * q^66 + 18 * q^67 - 20 * q^68 - 22 * q^69 + 20 * q^70 - 85 * q^71 - 2 * q^72 + 39 * q^73 + 20 * q^74 + 2 * q^75 - 48 * q^77 - 11 * q^78 - 28 * q^79 + 2 * q^80 - 2 * q^81 + q^82 + 49 * q^83 + 9 * q^84 - 13 * q^85 - 32 * q^86 + 8 * q^87 + 2 * q^88 + 3 * q^89 + 2 * q^90 - 34 * q^91 - 11 * q^92 - 36 * q^93 + 3 * q^94 + 2 * q^96 + 43 * q^97 + 10 * q^98 + 2 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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