LMFDB - Embedded newform 418.2.n.d.159.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [418,2,Mod(49,418)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(418, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([12, 20]))

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

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

chi := DirichletCharacter("418.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 418 = 2 \cdot 11 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	418.n (of order $15$, degree $8$, 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:	$3.33774680449$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$8$ over $\Q(\zeta_{15})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			159.2
Character	$\chi$	$=$	418.159
Dual form			418.2.n.d.163.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.669131 + 0.743145i) q^{2} +(-0.165199 + 1.57177i) q^{3} +(-0.104528 - 0.994522i) q^{4} +(1.30393 - 0.277159i) q^{5} +(-1.05751 - 1.17448i) q^{6} +(1.29335 - 0.939674i) q^{7} +(0.809017 + 0.587785i) q^{8} +(0.491287 + 0.104426i) q^{9} +O(q^{10})$	\(q+(-0.669131 + 0.743145i) q^{2} +(-0.165199 + 1.57177i) q^{3} +(-0.104528 - 0.994522i) q^{4} +(1.30393 - 0.277159i) q^{5} +(-1.05751 - 1.17448i) q^{6} +(1.29335 - 0.939674i) q^{7} +(0.809017 + 0.587785i) q^{8} +(0.491287 + 0.104426i) q^{9} +(-0.666530 + 1.15446i) q^{10} +(2.46994 - 2.21345i) q^{11} +1.58042 q^{12} +(-0.0480521 - 0.0102138i) q^{13} +(-0.167106 + 1.58991i) q^{14} +(0.220220 + 2.09526i) q^{15} +(-0.978148 + 0.207912i) q^{16} +(1.14981 - 0.244399i) q^{17} +(-0.406339 + 0.295223i) q^{18} +(4.12476 - 1.40939i) q^{19} +(-0.411938 - 1.26782i) q^{20} +(1.26329 + 2.18808i) q^{21} +(-0.00779852 + 3.31662i) q^{22} +(0.631190 - 1.09325i) q^{23} +(-1.05751 + 1.17448i) q^{24} +(-2.94431 + 1.31089i) q^{25} +(0.0397435 - 0.0288753i) q^{26} +(-1.71043 + 5.26415i) q^{27} +(-1.06972 - 1.18804i) q^{28} +(0.277322 + 2.63854i) q^{29} +(-1.70444 - 1.23835i) q^{30} +(0.134757 + 0.414740i) q^{31} +(0.500000 - 0.866025i) q^{32} +(3.07100 + 4.24783i) q^{33} +(-0.587747 + 1.01801i) q^{34} +(1.42600 - 1.58373i) q^{35} +(0.0525007 - 0.499511i) q^{36} +(-8.35232 + 6.06831i) q^{37} +(-1.71262 + 4.00836i) q^{38} +(0.0239919 - 0.0738394i) q^{39} +(1.21781 + 0.542204i) q^{40} +(0.285630 - 2.71759i) q^{41} +(-2.47136 - 0.525304i) q^{42} +(0.0915645 + 0.158594i) q^{43} +(-2.45951 - 2.22504i) q^{44} +0.669546 q^{45} +(0.390097 + 1.20059i) q^{46} +(1.74431 - 0.776618i) q^{47} +(-0.165199 - 1.57177i) q^{48} +(-1.37335 + 4.22674i) q^{49} +(0.995946 - 3.06521i) q^{50} +(0.194191 + 1.84760i) q^{51} +(-0.00513503 + 0.0488565i) q^{52} +(-3.81069 - 0.809986i) q^{53} +(-2.76753 - 4.79350i) q^{54} +(2.60716 - 3.57075i) q^{55} +1.59867 q^{56} +(1.53383 + 6.71598i) q^{57} +(-2.14638 - 1.55944i) q^{58} +(0.583453 + 0.259770i) q^{59} +(2.06076 - 0.438028i) q^{60} +(1.87982 + 2.08775i) q^{61} +(-0.398382 - 0.177371i) q^{62} +(0.733533 - 0.326590i) q^{63} +(0.309017 + 0.951057i) q^{64} -0.0654874 q^{65} +(-5.21165 - 0.560160i) q^{66} +(1.93312 - 3.34825i) q^{67} +(-0.363248 - 1.11796i) q^{68} +(1.61406 + 1.17269i) q^{69} +(0.222763 + 2.11945i) q^{70} +(5.77785 - 1.22812i) q^{71} +(0.336079 + 0.373254i) q^{72} +(-2.99352 - 1.33280i) q^{73} +(1.07916 - 10.2675i) q^{74} +(-1.57402 - 4.84433i) q^{75} +(-1.83283 - 3.95484i) q^{76} +(1.11458 - 5.18371i) q^{77} +(0.0388197 + 0.0672376i) q^{78} +(4.61047 - 5.12044i) q^{79} +(-1.21781 + 0.542204i) q^{80} +(-6.61493 - 2.94516i) q^{81} +(1.82844 + 2.03069i) q^{82} +(4.45649 - 13.7157i) q^{83} +(2.04404 - 1.48508i) q^{84} +(1.43153 - 0.637359i) q^{85} +(-0.179127 - 0.0380747i) q^{86} -4.19298 q^{87} +(3.29926 - 0.338925i) q^{88} +(6.41502 - 11.1111i) q^{89} +(-0.448014 + 0.497570i) q^{90} +(-0.0717459 + 0.0319433i) q^{91} +(-1.15324 - 0.513456i) q^{92} +(-0.674136 + 0.143292i) q^{93} +(-0.590033 + 1.81594i) q^{94} +(4.98777 - 2.98096i) q^{95} +(1.27859 + 0.928949i) q^{96} +(-7.71839 + 8.57214i) q^{97} +(-2.22213 - 3.84884i) q^{98} +(1.44459 - 0.829514i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q - 8 q^{2} - 6 q^{3} + 8 q^{4} - 7 q^{5} - 4 q^{6} + 22 q^{7} + 16 q^{8} + 14 q^{9}+O(q^{10}) $ 64 * q - 8 * q^2 - 6 * q^3 + 8 * q^4 - 7 * q^5 - 4 * q^6 + 22 * q^7 + 16 * q^8 + 14 * q^9	\( 64 q - 8 q^{2} - 6 q^{3} + 8 q^{4} - 7 q^{5} - 4 q^{6} + 22 q^{7} + 16 q^{8} + 14 q^{9} - 8 q^{10} - 6 q^{11} - 8 q^{12} + 9 q^{13} + 11 q^{14} + 9 q^{15} + 8 q^{16} - 2 q^{17} - 12 q^{18} + 4 q^{19} + 14 q^{20} - 36 q^{21} + 7 q^{22} + 8 q^{23} - 4 q^{24} + 31 q^{25} - 12 q^{26} + 54 q^{27} + 9 q^{28} + 18 q^{29} + 18 q^{30} + 20 q^{31} + 32 q^{32} + 10 q^{33} + 2 q^{34} - 16 q^{35} - 6 q^{36} + 18 q^{37} - 31 q^{38} + 2 q^{39} - 3 q^{40} + 16 q^{41} + 6 q^{42} + 42 q^{43} - 2 q^{44} - 8 q^{45} - 24 q^{46} - 34 q^{47} - 6 q^{48} - 10 q^{49} - 58 q^{50} - 40 q^{51} - 6 q^{52} + 15 q^{53} - 28 q^{54} + 49 q^{55} + 8 q^{56} + 8 q^{57} + 36 q^{58} - 7 q^{59} + 4 q^{60} - 15 q^{61} - 37 q^{63} - 16 q^{64} - 48 q^{65} - 10 q^{66} - 14 q^{67} + 4 q^{68} - 30 q^{69} - 19 q^{70} - 4 q^{71} - 14 q^{72} + 8 q^{73} + 9 q^{74} - 96 q^{75} - 10 q^{76} - 58 q^{77} + 46 q^{78} + 12 q^{79} + 3 q^{80} - 8 q^{81} + 4 q^{82} - 6 q^{83} - 48 q^{84} + 18 q^{85} + 3 q^{86} - 244 q^{87} + 6 q^{88} - 4 q^{89} - 9 q^{90} - 33 q^{91} + 8 q^{92} + 3 q^{93} + 62 q^{94} - 49 q^{95} - 12 q^{96} - 15 q^{97} - 4 q^{99}+O(q^{100}) \) 64 * q - 8 * q^2 - 6 * q^3 + 8 * q^4 - 7 * q^5 - 4 * q^6 + 22 * q^7 + 16 * q^8 + 14 * q^9 - 8 * q^10 - 6 * q^11 - 8 * q^12 + 9 * q^13 + 11 * q^14 + 9 * q^15 + 8 * q^16 - 2 * q^17 - 12 * q^18 + 4 * q^19 + 14 * q^20 - 36 * q^21 + 7 * q^22 + 8 * q^23 - 4 * q^24 + 31 * q^25 - 12 * q^26 + 54 * q^27 + 9 * q^28 + 18 * q^29 + 18 * q^30 + 20 * q^31 + 32 * q^32 + 10 * q^33 + 2 * q^34 - 16 * q^35 - 6 * q^36 + 18 * q^37 - 31 * q^38 + 2 * q^39 - 3 * q^40 + 16 * q^41 + 6 * q^42 + 42 * q^43 - 2 * q^44 - 8 * q^45 - 24 * q^46 - 34 * q^47 - 6 * q^48 - 10 * q^49 - 58 * q^50 - 40 * q^51 - 6 * q^52 + 15 * q^53 - 28 * q^54 + 49 * q^55 + 8 * q^56 + 8 * q^57 + 36 * q^58 - 7 * q^59 + 4 * q^60 - 15 * q^61 - 37 * q^63 - 16 * q^64 - 48 * q^65 - 10 * q^66 - 14 * q^67 + 4 * q^68 - 30 * q^69 - 19 * q^70 - 4 * q^71 - 14 * q^72 + 8 * q^73 + 9 * q^74 - 96 * q^75 - 10 * q^76 - 58 * q^77 + 46 * q^78 + 12 * q^79 + 3 * q^80 - 8 * q^81 + 4 * q^82 - 6 * q^83 - 48 * q^84 + 18 * q^85 + 3 * q^86 - 244 * q^87 + 6 * q^88 - 4 * q^89 - 9 * q^90 - 33 * q^91 + 8 * q^92 + 3 * q^93 + 62 * q^94 - 49 * q^95 - 12 * q^96 - 15 * q^97 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/418\mathbb{Z}\right)^\times$.

$n$	$287$	$343$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{5}\right)$

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 $

$2$	−0.669131	+	0.743145i	−0.473147	+	0.525483i
$2$	−0.669131	+	0.743145i	−0.473147	+	0.525483i
$3$	−0.165199	+	1.57177i	−0.0953778	+	0.907459i	0.837299	+	0.546746i	$0.184134\pi$
$3$	−0.165199	+	1.57177i	−0.0953778	+	0.907459i	−0.932677	+	0.360714i	$0.882533\pi$
$4$	−0.104528	−	0.994522i	−0.0522642	−	0.497261i
$5$	1.30393	−	0.277159i	0.583135	−	0.123949i	0.0931074	−	0.995656i	$-0.470320\pi$
$5$	1.30393	−	0.277159i	0.583135	−	0.123949i	0.490028	+	0.871707i	$0.336987\pi$
$6$	−1.05751	−	1.17448i	−0.431726	−	0.479481i
$7$	1.29335	−	0.939674i	0.488840	−	0.355163i	−0.315898	−	0.948793i	$-0.602306\pi$
$7$	1.29335	−	0.939674i	0.488840	−	0.355163i	0.804738	+	0.593630i	$0.202306\pi$
$8$	0.809017	+	0.587785i	0.286031	+	0.207813i
$9$	0.491287	+	0.104426i	0.163762	+	0.0348088i
$10$	−0.666530	+	1.15446i	−0.210775	+	0.365074i
$11$	2.46994	−	2.21345i	0.744716	−	0.667381i
$11$	2.46994	−	2.21345i	0.744716	−	0.667381i
$12$	1.58042			0.456229
$13$	−0.0480521	−	0.0102138i	−0.0133273	−	0.00283280i	0.201243	−	0.979541i	$-0.435502\pi$
$13$	−0.0480521	−	0.0102138i	−0.0133273	−	0.00283280i	−0.214570	+	0.976709i	$0.568835\pi$
$14$	−0.167106	+	1.58991i	−0.0446611	+	0.424922i
$15$	0.220220	+	2.09526i	0.0568607	+	0.540993i
$16$	−0.978148	+	0.207912i	−0.244537	+	0.0519779i
$17$	1.14981	−	0.244399i	0.278869	−	0.0592755i	−0.0663538	−	0.997796i	$-0.521137\pi$
$17$	1.14981	−	0.244399i	0.278869	−	0.0592755i	0.345223	+	0.938521i	$0.387803\pi$
$18$	−0.406339	+	0.295223i	−0.0957750	+	0.0695846i
$19$	4.12476	−	1.40939i	0.946284	−	0.323337i
$19$	4.12476	−	1.40939i	0.946284	−	0.323337i
$20$	−0.411938	−	1.26782i	−0.0921122	−	0.283492i
$21$	1.26329	+	2.18808i	0.275672	+	0.477477i
$22$	−0.00779852	+	3.31662i	−0.00166265	+	0.707105i
$23$	0.631190	−	1.09325i	0.131612	−	0.227959i	−0.792686	−	0.609630i	$-0.791318\pi$
$23$	0.631190	−	1.09325i	0.131612	−	0.227959i	0.924298	+	0.381671i	$0.124651\pi$
$24$	−1.05751	+	1.17448i	−0.215863	+	0.239740i
$25$	−2.94431	+	1.31089i	−0.588862	+	0.262178i
$26$	0.0397435	−	0.0288753i	0.00779434	−	0.00566292i
$27$	−1.71043	+	5.26415i	−0.329172	+	1.01309i
$28$	−1.06972	−	1.18804i	−0.202158	−	0.224519i
$29$	0.277322	+	2.63854i	0.0514974	+	0.489965i	0.989625	+	0.143675i	$0.0458920\pi$
$29$	0.277322	+	2.63854i	0.0514974	+	0.489965i	−0.938128	+	0.346290i	$0.887441\pi$
$30$	−1.70444	−	1.23835i	−0.311186	−	0.226090i
$31$	0.134757	+	0.414740i	0.0242031	+	0.0744896i	0.962429	−	0.271535i	$-0.0875313\pi$
$31$	0.134757	+	0.414740i	0.0242031	+	0.0744896i	−0.938225	+	0.346025i	$0.887531\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$	3.07100	+	4.24783i	0.534592	+	0.739453i
$34$	−0.587747	+	1.01801i	−0.100798	+	0.174587i
$35$	1.42600	−	1.58373i	0.241038	−	0.267700i
$36$	0.0525007	−	0.499511i	0.00875012	−	0.0832519i
$37$	−8.35232	+	6.06831i	−1.37311	+	0.997625i	−0.375626	+	0.926771i	$0.622572\pi$
$37$	−8.35232	+	6.06831i	−1.37311	+	0.997625i	−0.997487	+	0.0708532i	$0.977428\pi$
$38$	−1.71262	+	4.00836i	−0.277823	+	0.650242i
$39$	0.0239919	−	0.0738394i	0.00384177	−	0.0118238i
$40$	1.21781	+	0.542204i	0.192553	+	0.0857301i
$41$	0.285630	−	2.71759i	0.0446080	−	0.424417i	−0.949314	−	0.314329i	$-0.898220\pi$
$41$	0.285630	−	2.71759i	0.0446080	−	0.424417i	0.993922	−	0.110087i	$-0.0351130\pi$
$42$	−2.47136	−	0.525304i	−0.381339	−	0.0810562i
$43$	0.0915645	+	0.158594i	0.0139635	+	0.0241854i	0.872923	−	0.487859i	$-0.162222\pi$
$43$	0.0915645	+	0.158594i	0.0139635	+	0.0241854i	−0.858959	+	0.512044i	$0.828888\pi$
$44$	−2.45951	−	2.22504i	−0.370785	−	0.335438i
$45$	0.669546			0.0998101
$46$	0.390097	+	1.20059i	0.0575166	+	0.177018i
$47$	1.74431	−	0.776618i	0.254434	−	0.113281i	−0.275556	−	0.961285i	$-0.588862\pi$
$47$	1.74431	−	0.776618i	0.254434	−	0.113281i	0.529991	+	0.848004i	$0.322195\pi$
$48$	−0.165199	−	1.57177i	−0.0238445	−	0.226865i
$49$	−1.37335	+	4.22674i	−0.196193	+	0.603820i
$50$	0.995946	−	3.06521i	0.140848	−	0.433486i
$51$	0.194191	+	1.84760i	0.0271922	+	0.258716i
$52$	−0.00513503	+	0.0488565i	−0.000712100	+	0.00677518i
$53$	−3.81069	−	0.809986i	−0.523438	−	0.111260i	−0.0613878	−	0.998114i	$-0.519553\pi$
$53$	−3.81069	−	0.809986i	−0.523438	−	0.111260i	−0.462050	+	0.886854i	$0.652886\pi$
$54$	−2.76753	−	4.79350i	−0.376613	−	0.652313i
$55$	2.60716	−	3.57075i	0.351549	−	0.481480i
$56$	1.59867			0.213631
$57$	1.53383	+	6.71598i	0.203160	+	0.889553i
$58$	−2.14638	−	1.55944i	−0.281834	−	0.204764i
$59$	0.583453	+	0.259770i	0.0759591	+	0.0338192i	0.444365	−	0.895846i	$-0.353429\pi$
$59$	0.583453	+	0.259770i	0.0759591	+	0.0338192i	−0.368405	+	0.929665i	$0.620096\pi$
$60$	2.06076	−	0.438028i	0.266043	−	0.0565492i
$61$	1.87982	+	2.08775i	0.240686	+	0.267309i	0.851370	−	0.524565i	$-0.175772\pi$
$61$	1.87982	+	2.08775i	0.240686	+	0.267309i	−0.610684	+	0.791874i	$0.709106\pi$
$62$	−0.398382	−	0.177371i	−0.0505946	−	0.0225262i
$63$	0.733533	−	0.326590i	0.0924164	−	0.0411464i
$64$	0.309017	+	0.951057i	0.0386271	+	0.118882i
$65$	−0.0654874			−0.00812272
$66$	−5.21165	−	0.560160i	−0.641510	−	0.0689509i
$67$	1.93312	−	3.34825i	0.236168	−	0.409054i	−0.723444	−	0.690383i	$-0.757442\pi$
$67$	1.93312	−	3.34825i	0.236168	−	0.409054i	0.959611	+	0.281329i	$0.0907752\pi$
$68$	−0.363248	−	1.11796i	−0.0440503	−	0.135573i
$69$	1.61406	+	1.17269i	0.194311	+	0.141175i
$70$	0.222763	+	2.11945i	0.0266253	+	0.253322i
$71$	5.77785	−	1.22812i	0.685705	−	0.145751i	0.148131	−	0.988968i	$-0.452674\pi$
$71$	5.77785	−	1.22812i	0.685705	−	0.145751i	0.537574	+	0.843217i	$0.319341\pi$
$72$	0.336079	+	0.373254i	0.0396073	+	0.0439884i
$73$	−2.99352	−	1.33280i	−0.350365	−	0.155992i	0.224006	−	0.974588i	$-0.428086\pi$
$73$	−2.99352	−	1.33280i	−0.350365	−	0.155992i	−0.574371	+	0.818595i	$0.694753\pi$
$74$	1.07916	−	10.2675i	0.125449	−	1.19357i
$75$	−1.57402	−	4.84433i	−0.181752	−	0.559375i
$76$	−1.83283	−	3.95484i	−0.210240	−	0.453651i
$77$	1.11458	−	5.18371i	0.127018	−	0.590739i
$78$	0.0388197	+	0.0672376i	0.00439546	+	0.00761316i
$79$	4.61047	−	5.12044i	0.518718	−	0.576095i	−0.425691	−	0.904869i	$-0.639969\pi$
$79$	4.61047	−	5.12044i	0.518718	−	0.576095i	0.944409	+	0.328774i	$0.106635\pi$
$80$	−1.21781	+	0.542204i	−0.136155	+	0.0606203i
$81$	−6.61493	−	2.94516i	−0.734992	−	0.327240i
$82$	1.82844	+	2.03069i	0.201917	+	0.224252i
$83$	4.45649	−	13.7157i	0.489163	−	1.50549i	−0.336697	−	0.941613i	$-0.609310\pi$
$83$	4.45649	−	13.7157i	0.489163	−	1.50549i	0.825860	−	0.563876i	$-0.190690\pi$
$84$	2.04404	−	1.48508i	0.223023	−	0.162036i
$85$	1.43153	−	0.637359i	0.155271	−	0.0691312i
$86$	−0.179127	−	0.0380747i	−0.0193158	−	0.00410570i
$87$	−4.19298			−0.449535
$88$	3.29926	−	0.338925i	0.351703	−	0.0361295i
$89$	6.41502	−	11.1111i	0.679990	−	1.17778i	−0.294993	−	0.955499i	$-0.595317\pi$
$89$	6.41502	−	11.1111i	0.679990	−	1.17778i	0.974983	−	0.222278i	$-0.0713494\pi$
$90$	−0.448014	+	0.497570i	−0.0472248	+	0.0524485i
$91$	−0.0717459	+	0.0319433i	−0.00752101	+	0.00334857i
$92$	−1.15324	−	0.513456i	−0.120234	−	0.0535315i
$93$	−0.674136	+	0.143292i	−0.0699047	+	0.0148587i
$94$	−0.590033	+	1.81594i	−0.0608573	+	0.187299i
$95$	4.98777	−	2.98096i	0.511734	−	0.305840i
$96$	1.27859	+	0.928949i	0.130495	+	0.0948105i
$97$	−7.71839	+	8.57214i	−0.783684	+	0.870369i	−0.994236	−	0.107214i	$-0.965807\pi$
$97$	−7.71839	+	8.57214i	−0.783684	+	0.870369i	0.210552	+	0.977583i	$0.432474\pi$
$98$	−2.22213	−	3.84884i	−0.224469	−	0.388792i
$99$	1.44459	−	0.829514i	0.145187	−	0.0833693i
$100$	1.61148	+	2.79116i	0.161148	+	0.279116i
$101$	−8.82799	−	1.87645i	−0.878418	−	0.186713i	−0.253435	−	0.967352i	$-0.581561\pi$
$101$	−8.82799	−	1.87645i	−0.878418	−	0.186713i	−0.624982	+	0.780639i	$0.714894\pi$
$102$	−1.50298	−	1.09198i	−0.148817	−	0.108122i
$103$	−9.46847	+	6.87925i	−0.932957	+	0.677833i	−0.946715	−	0.322073i	$-0.895620\pi$
$103$	−9.46847	+	6.87925i	−0.932957	+	0.677833i	0.0137584	+	0.999905i	$0.495620\pi$
$104$	−0.0328715	−	0.0365075i	−0.00322331	−	0.00357985i
$105$	2.25368	+	2.50297i	0.219937	+	0.244265i
$106$	3.15178	−	2.28990i	0.306128	−	0.222415i
$107$	−3.68557	−	2.67772i	−0.356297	−	0.258865i	0.395209	−	0.918591i	$-0.370672\pi$
$107$	−3.68557	−	2.67772i	−0.356297	−	0.258865i	−0.751506	+	0.659726i	$0.770672\pi$
$108$	5.41410	+	1.15080i	0.520972	+	0.110736i
$109$	4.40594	+	7.63131i	0.422013	+	0.730947i	0.996136	−	0.0878214i	$-0.0279905\pi$
$109$	4.40594	+	7.63131i	0.422013	+	0.730947i	−0.574124	+	0.818769i	$0.694657\pi$
$110$	0.909061	+	4.32679i	0.0866755	+	0.412544i
$111$	−8.15817	−	14.1304i	−0.774339	−	1.34119i
$112$	−1.06972	+	1.18804i	−0.101079	+	0.112259i
$113$	−7.55430	−	5.48852i	−0.710648	−	0.516316i	0.172734	−	0.984968i	$-0.444740\pi$
$113$	−7.55430	−	5.48852i	−0.710648	−	0.516316i	−0.883383	+	0.468652i	$0.844740\pi$
$114$	−6.01728	−	3.35401i	−0.563570	−	0.314132i
$115$	0.520022	−	1.60046i	0.0484923	−	0.149244i
$116$	2.59510	−	0.551606i	0.240949	−	0.0512153i
$117$	−0.0225408	−	0.0100358i	−0.00208390	−	0.000927811i
$118$	−0.583453	+	0.259770i	−0.0537112	+	0.0239138i
$119$	1.25745	−	1.39654i	0.115270	−	0.128020i
$120$	−1.05340	+	1.82454i	−0.0961618	+	0.166557i
$121$	1.20125	−	10.9342i	0.109204	−	0.994019i
$122$	−2.80934			−0.254346
$123$	4.22423	+	0.897888i	0.380886	+	0.0809598i
$124$	0.398382	−	0.177371i	0.0357758	−	0.0159284i
$125$	−8.86819	+	6.44312i	−0.793195	+	0.576290i
$126$	−0.248126	+	0.763652i	−0.0221048	+	0.0680315i
$127$	8.54379	+	9.48884i	0.758139	+	0.841999i	0.991461	−	0.130401i	$-0.0416264\pi$
$127$	8.54379	+	9.48884i	0.758139	+	0.841999i	−0.233322	+	0.972399i	$0.574960\pi$
$128$	−0.913545	−	0.406737i	−0.0807468	−	0.0359508i
$129$	−0.264400	+	0.117718i	−0.0232791	+	0.0103645i
$130$	0.0438196	−	0.0486667i	0.00384324	−	0.00426835i
$131$	−3.81305	−	6.60439i	−0.333147	−	0.577028i	0.649980	−	0.759952i	$-0.274777\pi$
$131$	−3.81305	−	6.60439i	−0.333147	−	0.577028i	−0.983127	+	0.182923i	$0.941444\pi$
$132$	3.90356	−	3.49819i	0.339761	−	0.304479i
$133$	4.01039	−	5.69876i	0.347745	−	0.494145i
$134$	1.19473	+	3.67700i	0.103209	+	0.317645i
$135$	−0.771270	+	7.33814i	−0.0663804	+	0.631567i
$136$	1.07387	+	0.478117i	0.0920834	+	0.0409982i
$137$	−5.21615	−	5.79312i	−0.445646	−	0.494940i	0.477907	−	0.878410i	$-0.341395\pi$
$137$	−5.21615	−	5.79312i	−0.445646	−	0.494940i	−0.923553	+	0.383470i	$0.874729\pi$
$138$	−1.95150	+	0.414803i	−0.166122	+	0.0353104i
$139$	−0.381595	−	3.63063i	−0.0323665	−	0.307946i	−0.998714	−	0.0507051i	$-0.983853\pi$
$139$	−0.381595	−	3.63063i	−0.0323665	−	0.307946i	0.966347	−	0.257241i	$-0.0828135\pi$
$140$	−1.72411	−	1.25264i	−0.145714	−	0.105868i
$141$	0.932502	+	2.86995i	0.0785309	+	0.241693i
$142$	−2.95347	+	5.11555i	−0.247849	+	0.429288i
$143$	−0.141294	+	0.0811337i	−0.0118156	+	0.00678474i
$144$	−0.502263			−0.0418552
$145$	1.09290	+	3.36361i	0.0907607	+	0.279333i
$146$	2.99352	−	1.33280i	0.247745	−	0.110303i
$147$	−6.41657	−	2.85684i	−0.529230	−	0.235628i
$148$	6.90813	+	7.67225i	0.567844	+	0.630655i
$149$	15.7763	−	3.35335i	1.29244	−	0.274717i	0.490145	−	0.871641i	$-0.336944\pi$
$149$	15.7763	−	3.35335i	1.29244	−	0.274717i	0.802298	+	0.596923i	$0.203610\pi$
$150$	4.65326	+	2.07176i	0.379937	+	0.169159i
$151$	−17.8195	−	12.9466i	−1.45013	−	1.05358i	−0.985802	−	0.167914i	$-0.946297\pi$
$151$	−17.8195	−	12.9466i	−1.45013	−	1.05358i	−0.464325	−	0.885665i	$-0.653703\pi$
$152$	4.16542	+	1.28425i	0.337860	+	0.104166i
$153$	0.590407			0.0477316
$154$	3.10645	+	4.29687i	0.250325	+	0.346252i
$155$	0.290663	+	0.503443i	0.0233466	+	0.0404375i
$156$	−0.0759427	−	0.0161421i	−0.00608028	−	0.00129240i
$157$	−1.95882	+	18.6369i	−0.156331	+	1.48739i	0.582134	+	0.813093i	$0.302218\pi$
$157$	−1.95882	+	18.6369i	−0.156331	+	1.48739i	−0.738464	+	0.674293i	$0.764449\pi$
$158$	0.720225	+	6.85249i	0.0572981	+	0.545155i
$159$	1.90263	−	5.85569i	0.150888	−	0.464387i
$160$	0.411938	−	1.26782i	0.0325666	−	0.100230i
$161$	−0.210952	−	2.00707i	−0.0166253	−	0.158179i
$162$	6.61493	−	2.94516i	0.519718	−	0.231393i
$163$	1.84659	+	5.68322i	0.144636	+	0.445144i	0.996964	−	0.0778635i	$-0.0248098\pi$
$163$	1.84659	+	5.68322i	0.144636	+	0.445144i	−0.852328	+	0.523008i	$0.824810\pi$
$164$	−2.73256			−0.213377
$165$	5.18169	+	4.68772i	0.403394	+	0.364939i
$166$	7.21075	+	12.4894i	0.559662	+	0.969364i
$167$	−19.2387	−	4.08932i	−1.48874	−	0.316441i	−0.609485	−	0.792797i	$-0.708624\pi$
$167$	−19.2387	−	4.08932i	−1.48874	−	0.316441i	−0.879252	+	0.476356i	$0.841957\pi$
$168$	−0.264099	+	2.51273i	−0.0203757	+	0.193862i
$169$	−11.8739	−	5.28659i	−0.913376	−	0.406661i
$170$	−0.484231	+	1.49031i	−0.0371388	+	0.114302i
$171$	2.17362	−	0.261683i	0.166221	−	0.0200114i
$172$	0.148155	−	0.107641i	0.0112967	−	0.00820752i
$173$	−2.22908	+	21.2083i	−0.169474	+	1.61244i	0.497573	+	0.867422i	$0.334225\pi$
$173$	−2.22908	+	21.2083i	−0.169474	+	1.61244i	−0.667047	+	0.745015i	$0.732442\pi$
$174$	2.80565	−	3.11599i	0.212696	−	0.236223i
$175$	−2.57622	+	4.46214i	−0.194744	+	0.337306i
$176$	−1.95577	+	2.67861i	−0.147421	+	0.201908i
$177$	−0.504684	+	0.874138i	−0.0379343	+	0.0657042i
$178$	3.96470	+	12.2021i	0.297167	+	0.914585i
$179$	11.0800	+	8.05011i	0.828160	+	0.601694i	0.919038	−	0.394168i	$-0.128967\pi$
$179$	11.0800	+	8.05011i	0.828160	+	0.601694i	−0.0908779	+	0.995862i	$0.528967\pi$
$180$	−0.0699866	−	0.665878i	−0.00521650	−	0.0496316i
$181$	−12.8382	−	14.2582i	−0.954255	−	1.05981i	−0.998152	−	0.0607712i	$-0.980644\pi$
$181$	−12.8382	−	14.2582i	−0.954255	−	1.05981i	0.0438970	−	0.999036i	$-0.486023\pi$
$182$	0.0242688	−	0.0746918i	0.00179893	−	0.00553653i
$183$	−3.59199	+	2.60974i	−0.265528	+	0.192917i
$184$	1.15324	−	0.513456i	0.0850180	−	0.0378525i
$185$	−9.20895	+	10.2276i	−0.677055	+	0.751946i
$186$	0.344598	−	0.596862i	0.0252672	−	0.0437640i
$187$	2.29899	−	3.14870i	0.168119	−	0.230256i
$188$	−0.954694	−	1.65358i	−0.0696282	−	0.120600i
$189$	2.73441	+	8.41564i	0.198899	+	0.612147i
$190$	−1.12218	+	5.70129i	−0.0814116	+	0.413615i
$191$	−1.35440	+	0.984031i	−0.0980012	+	0.0712020i	−0.635707	−	0.771931i	$-0.719291\pi$
$191$	−1.35440	+	0.984031i	−0.0980012	+	0.0712020i	0.537706	+	0.843133i	$0.319291\pi$
$192$	−1.54589	+	0.328588i	−0.111565	+	0.0237138i
$193$	19.9751	−	4.24583i	1.43784	−	0.305622i	0.577936	−	0.816082i	$-0.303858\pi$
$193$	19.9751	−	4.24583i	1.43784	−	0.305622i	0.859901	+	0.510461i	$0.170525\pi$
$194$	−1.20573	−	11.4718i	−0.0865664	−	0.823625i
$195$	0.0108185	−	0.102931i	0.000774727	−	0.00737103i
$196$	4.34714	+	0.924013i	0.310510	+	0.0660009i
$197$	9.62811			0.685975			0.342987	−	0.939340i	$-0.388561\pi$
$197$	9.62811			0.685975			0.342987	+	0.939340i	$0.388561\pi$
$198$	−0.350173	+	1.62860i	−0.0248857	+	0.115739i
$199$	−1.99571	+	3.45667i	−0.141472	+	0.245037i	−0.928051	−	0.372453i	$-0.878517\pi$
$199$	−1.99571	+	3.45667i	−0.141472	+	0.245037i	0.786579	+	0.617490i	$0.211850\pi$
$200$	−3.15252	−	0.670089i	−0.222917	−	0.0473825i
$201$	4.94332	+	3.59153i	0.348675	+	0.253327i
$202$	7.30155	−	5.30489i	0.513735	−	0.373251i
$203$	2.83804	+	3.15197i	0.199192	+	0.221225i
$204$	1.81718	−	0.386254i	0.127228	−	0.0270432i
$205$	−0.380763	−	3.62271i	−0.0265936	−	0.253021i
$206$	1.22337	−	11.6396i	0.0852361	−	0.810967i
$207$	0.424259	−	0.471188i	0.0294881	−	0.0327498i
$208$	0.0491256			0.00340625
$209$	7.06829	−	12.6111i	0.488924	−	0.872326i
$210$	−3.36807			−0.232419
$211$	−10.1093	+	11.2275i	−0.695954	+	0.772935i	−0.982727	−	0.185063i	$-0.940751\pi$
$211$	−10.1093	+	11.2275i	−0.695954	+	0.772935i	0.286772	+	0.957999i	$0.407418\pi$
$212$	−0.407224	+	3.87448i	−0.0279683	+	0.266100i
$213$	0.975821	+	9.28431i	0.0668621	+	0.636151i
$214$	4.45606	−	0.947166i	0.304610	−	0.0647469i
$215$	0.163350	+	0.181418i	0.0111403	+	0.0123726i
$216$	−4.47796	+	3.25342i	−0.304686	+	0.221368i
$217$	0.564009	+	0.409777i	0.0382874	+	0.0278174i
$218$	−8.61932	−	1.83209i	−0.583774	−	0.124085i
$219$	2.58937	−	4.48493i	0.174974	−	0.303063i
$220$	−3.82372	−	2.21963i	−0.257795	−	0.149647i
$221$	−0.0577469			−0.00388448
$222$	15.9598	+	3.39236i	1.07115	+	0.227680i
$223$	−0.354322	+	3.37115i	−0.0237271	+	0.225749i	0.976232	+	0.216727i	$0.0695383\pi$
$223$	−0.354322	+	3.37115i	−0.0237271	+	0.225749i	−0.999959	+	0.00902128i	$0.997128\pi$
$224$	−0.167106	−	1.58991i	−0.0111653	−	0.106230i
$225$	−1.58339	+	0.336561i	−0.105560	+	0.0224374i
$226$	9.13357	−	1.94140i	0.607556	−	0.129140i
$227$	10.9452	−	7.95212i	0.726456	−	0.527801i	−0.161985	−	0.986793i	$-0.551789\pi$
$227$	10.9452	−	7.95212i	0.726456	−	0.527801i	0.888440	+	0.458992i	$0.151789\pi$
$228$	6.51886	−	2.22744i	0.431722	−	0.147516i
$229$	6.35506	+	19.5589i	0.419954	+	1.29249i	0.907744	+	0.419525i	$0.137803\pi$
$229$	6.35506	+	19.5589i	0.419954	+	1.29249i	−0.487789	+	0.872961i	$0.662197\pi$
$230$	0.841414	+	1.45737i	0.0554812	+	0.0960962i
$231$	7.96345	+	2.60820i	0.523957	+	0.171607i
$232$	−1.32654	+	2.29763i	−0.0870915	+	0.150847i
$233$	−8.41148	+	9.34189i	−0.551054	+	0.612008i	−0.952746	−	0.303767i	$-0.901756\pi$
$233$	−8.41148	+	9.34189i	−0.551054	+	0.612008i	0.401692	+	0.915775i	$0.368422\pi$
$234$	0.0225408	−	0.0100358i	0.00147354	−	0.000656061i
$235$	2.05921	−	1.49611i	0.134328	−	0.0975952i
$236$	0.197360	−	0.607410i	0.0128470	−	0.0395390i
$237$	7.28649	+	8.09246i	0.473308	+	0.525662i
$238$	0.196433	+	1.86893i	0.0127328	+	0.121145i
$239$	−14.6189	−	10.6212i	−0.945616	−	0.687030i	0.00415001	−	0.999991i	$-0.498679\pi$
$239$	−14.6189	−	10.6212i	−0.945616	−	0.687030i	−0.949766	+	0.312961i	$0.898679\pi$
$240$	−0.651037	−	2.00369i	−0.0420242	−	0.129337i
$241$	2.86847	−	4.96834i	0.184775	−	0.320039i	−0.758726	−	0.651410i	$-0.774178\pi$
$241$	2.86847	−	4.96834i	0.184775	−	0.320039i	0.943501	+	0.331371i	$0.107511\pi$
$242$	7.32191	+	8.20912i	0.470670	+	0.527702i
$243$	−2.58071	+	4.46992i	−0.165552	+	0.286745i
$244$	1.87982	−	2.08775i	0.120343	−	0.133654i
$245$	−0.619275	+	5.89201i	−0.0395640	+	0.376427i
$246$	−3.49382	+	2.53841i	−0.222758	+	0.161843i
$247$	−0.212599	+	0.0255949i	−0.0135273	+	0.00162856i
$248$	−0.134757	+	0.414740i	−0.00855710	+	0.0263360i
$249$	20.8216	+	9.27037i	1.31951	+	0.587486i
$250$	1.14581	−	10.9016i	0.0724673	−	0.689480i
$251$	−14.1377	−	3.00506i	−0.892363	−	0.189678i	−0.261160	−	0.965295i	$-0.584105\pi$
$251$	−14.1377	−	3.00506i	−0.892363	−	0.189678i	−0.631203	+	0.775618i	$0.717438\pi$
$252$	−0.401476	−	0.695376i	−0.0252906	−	0.0438046i
$253$	−0.860861	−	4.09738i	−0.0541219	−	0.257600i
$254$	−12.7685			−0.801167
$255$	0.765290	+	2.35532i	0.0479243	+	0.147496i
$256$	0.913545	−	0.406737i	0.0570966	−	0.0254210i
$257$	−1.42042	−	13.5144i	−0.0886035	−	0.843006i	−0.945084	−	0.326827i	$-0.894021\pi$
$257$	−1.42042	−	13.5144i	−0.0886035	−	0.843006i	0.856481	−	0.516179i	$-0.172646\pi$
$258$	0.0894361	−	0.275256i	0.00556805	−	0.0171367i
$259$	−5.10024	+	15.6969i	−0.316913	+	0.975359i
$260$	0.00684530	+	0.0651287i	0.000424528	+	0.00403911i
$261$	−0.139288	+	1.32524i	−0.00862174	+	0.0820304i
$262$	7.45945	+	1.58555i	0.460846	+	0.0979559i
$263$	3.89835	+	6.75214i	0.240383	+	0.416355i	0.960823	−	0.277162i	$-0.0893938\pi$
$263$	3.89835	+	6.75214i	0.240383	+	0.416355i	−0.720441	+	0.693517i	$0.756060\pi$
$264$	−0.0123250	+	5.24166i	−0.000758549	+	0.322602i
$265$	−5.19336			−0.319026
$266$	1.55154	+	6.79351i	0.0951307	+	0.416537i
$267$	16.4043	+	11.9185i	1.00393	+	0.729397i
$268$	−3.53198	−	1.57254i	−0.215750	−	0.0960580i
$269$	6.02804	−	1.28130i	0.367536	−	0.0781222i	−0.0204415	−	0.999791i	$-0.506507\pi$
$269$	6.02804	−	1.28130i	0.367536	−	0.0781222i	0.387977	+	0.921669i	$0.373174\pi$
$270$	−4.93722	−	5.48334i	−0.300470	−	0.333706i
$271$	2.66586	+	1.18692i	0.161940	+	0.0721002i	0.486106	−	0.873900i	$-0.338417\pi$
$271$	2.66586	+	1.18692i	0.161940	+	0.0721002i	−0.324166	+	0.946000i	$0.605084\pi$
$272$	−1.07387	+	0.478117i	−0.0651128	+	0.0289901i
$273$	−0.0383550	−	0.118045i	−0.00232135	−	0.00714439i
$274$	7.79542			0.470938
$275$	−4.37069	+	9.75493i	−0.263562	+	0.588244i
$276$	0.997547	−	1.72780i	0.0600453	−	0.104001i
$277$	2.72366	+	8.38256i	0.163649	+	0.503659i	0.998934	−	0.0461575i	$-0.0146976\pi$
$277$	2.72366	+	8.38256i	0.163649	+	0.503659i	−0.835285	+	0.549817i	$0.814698\pi$
$278$	2.95342	+	2.14579i	0.177135	+	0.128696i
$279$	0.0228947	+	0.217829i	0.00137067	+	0.0130411i
$280$	2.08455	−	0.443085i	0.124576	−	0.0264794i
$281$	−5.17512	−	5.74755i	−0.308722	−	0.342870i	0.568740	−	0.822518i	$-0.307431\pi$
$281$	−5.17512	−	5.74755i	−0.308722	−	0.342870i	−0.877461	+	0.479647i	$0.840765\pi$
$282$	−2.75675	−	1.22739i	−0.164162	−	0.0730897i
$283$	0.826827	−	7.86674i	0.0491498	−	0.467629i	−0.942071	−	0.335413i	$-0.891124\pi$
$283$	0.826827	−	7.86674i	0.0491498	−	0.467629i	0.991221	−	0.132216i	$-0.0422092\pi$
$284$	−1.82534	−	5.61783i	−0.108314	−	0.333357i
$285$	3.86140	+	8.33205i	0.228729	+	0.493548i
$286$	0.0342500	−	0.159291i	0.00202524	−	0.00941906i
$287$	−2.18423	−	3.78320i	−0.128931	−	0.223315i
$288$	0.336079	−	0.373254i	0.0198037	−	0.0219942i
$289$	−14.2679	+	6.35250i	−0.839291	+	0.373676i
$290$	−3.23095	−	1.43851i	−0.189728	−	0.0844722i
$291$	−12.1983	−	13.5476i	−0.715078	−	0.794175i
$292$	−1.01259	+	3.11643i	−0.0592574	+	0.182375i
$293$	−1.57902	+	1.14723i	−0.0922476	+	0.0670218i	−0.632953	−	0.774190i	$-0.718157\pi$
$293$	−1.57902	+	1.14723i	−0.0922476	+	0.0670218i	0.540705	+	0.841212i	$0.318157\pi$
$294$	6.41657	−	2.85684i	0.374222	−	0.166614i
$295$	0.832780	+	0.177013i	0.0484863	+	0.0103061i
$296$	−10.3240			−0.600072
$297$	7.42730	+	16.7881i	0.430976	+	0.974145i
$298$	−8.06437	+	13.9679i	−0.467156	+	0.809138i
$299$	−0.0414963	+	0.0460863i	−0.00239979	+	0.00266524i
$300$	−4.65326	+	2.07176i	−0.268656	+	0.119613i
$301$	0.267452	+	0.119077i	0.0154157	+	0.00686350i
$302$	21.5447	−	4.57947i	1.23976	−	0.263519i
$303$	4.40771	−	13.5655i	0.253216	−	0.779320i
$304$	−3.74159	+	2.23618i	−0.214595	+	0.128254i
$305$	3.02979	+	2.20127i	0.173485	+	0.126044i
$306$	−0.395059	+	0.438758i	−0.0225840	+	0.0250821i
$307$	−12.4165	−	21.5060i	−0.708647	−	1.22741i	−0.965359	−	0.260925i	$-0.915973\pi$
$307$	−12.4165	−	21.5060i	−0.708647	−	1.22741i	0.256712	−	0.966488i	$-0.417361\pi$
$308$	−5.27182	−	0.566627i	−0.300390	−	0.0322865i
$309$	−9.24838	−	16.0187i	−0.526122	−	0.911270i
$310$	−0.568623	−	0.120864i	−0.0322956	−	0.00686464i
$311$	−21.6322	−	15.7167i	−1.22665	−	0.891215i	−0.230017	−	0.973187i	$-0.573878\pi$
$311$	−21.6322	−	15.7167i	−1.22665	−	0.891215i	−0.996635	+	0.0819721i	$0.973878\pi$
$312$	0.0628115	−	0.0456352i	0.00355600	−	0.00258359i
$313$	−8.64708	−	9.60355i	−0.488762	−	0.542825i	0.447428	−	0.894320i	$-0.352340\pi$
$313$	−8.64708	−	9.60355i	−0.488762	−	0.542825i	−0.936190	+	0.351495i	$0.885673\pi$
$314$	−12.5392	−	13.9262i	−0.707628	−	0.785901i
$315$	0.865958	−	0.629155i	0.0487912	−	0.0354489i
$316$	−5.57432	−	4.04998i	−0.313580	−	0.227829i
$317$	7.12289	+	1.51402i	0.400061	+	0.0850357i	0.403549	−	0.914958i	$-0.367777\pi$
$317$	7.12289	+	1.51402i	0.400061	+	0.0850357i	−0.00348707	+	0.999994i	$0.501110\pi$
$318$	3.07852	+	5.33215i	0.172635	+	0.299012i
$319$	6.52526	+	5.90321i	0.365344	+	0.330516i
$320$	0.666530	+	1.15446i	0.0372602	+	0.0645365i
$321$	4.81761	−	5.35049i	0.268893	−	0.298635i
$322$	1.63270	+	1.18622i	0.0909867	+	0.0661057i
$323$	4.39822	−	2.62862i	0.244724	−	0.146260i
$324$	−2.23757	+	6.88655i	−0.124310	+	0.382586i
$325$	0.154870	−	0.0329186i	0.00859062	−	0.00182599i
$326$	−5.45907	−	2.43053i	−0.302350	−	0.134615i
$327$	−12.7225	+	5.66442i	−0.703555	+	0.313243i
$328$	1.82844	−	2.03069i	0.100959	−	0.112126i
$329$	1.52624	−	2.64352i	0.0841443	−	0.145742i
$330$	−6.95088	+	0.714047i	−0.382634	+	0.0393070i
$331$	−3.10431			−0.170628			−0.0853142	−	0.996354i	$-0.527189\pi$
$331$	−3.10431			−0.170628			−0.0853142	+	0.996354i	$0.527189\pi$
$332$	−14.1063	−	2.99840i	−0.774186	−	0.164558i
$333$	−4.73708	+	2.10908i	−0.259590	+	0.115577i
$334$	15.9122	−	11.5609i	0.870676	−	0.632583i
$335$	1.59265	−	4.90167i	0.0870157	−	0.267807i
$336$	−1.69061	−	1.87761i	−0.0922302	−	0.102432i
$337$	−17.4845	−	7.78461i	−0.952443	−	0.424055i	−0.129121	−	0.991629i	$-0.541215\pi$
$337$	−17.4845	−	7.78461i	−0.952443	−	0.424055i	−0.823322	+	0.567574i	$0.807882\pi$
$338$	11.8739	−	5.28659i	0.645854	−	0.287553i
$339$	9.87463	−	10.9669i	0.536316	−	0.595639i
$340$	−0.783503	−	1.35707i	−0.0424914	−	0.0735973i
$341$	1.25085	+	0.726106i	0.0677374	+	0.0393209i
$342$	−1.25996	+	1.79041i	−0.0681311	+	0.0968144i
$343$	5.65364	+	17.4001i	0.305268	+	0.939519i
$344$	−0.0191422	+	0.182126i	−0.00103208	+	0.00981957i
$345$	2.42965	+	1.08175i	0.130808	+	0.0582394i
$346$	−14.2693	−	15.8477i	−0.767122	−	0.851975i
$347$	32.1789	−	6.83983i	1.72745	−	0.367181i	0.766147	−	0.642665i	$-0.222171\pi$
$347$	32.1789	−	6.83983i	1.72745	−	0.367181i	0.961306	+	0.275484i	$0.0888380\pi$
$348$	0.438286	+	4.17001i	0.0234946	+	0.223536i
$349$	−16.5141	−	11.9982i	−0.883978	−	0.642248i	0.0503229	−	0.998733i	$-0.483975\pi$
$349$	−16.5141	−	11.9982i	−0.883978	−	0.642248i	−0.934301	+	0.356485i	$0.883975\pi$
$350$	−1.59219	−	4.90025i	−0.0851061	−	0.261930i
$351$	0.135957	−	0.235484i	0.00725683	−	0.0125692i
$352$	−0.681935	−	3.24576i	−0.0363473	−	0.173000i
$353$	−15.8224			−0.842141			−0.421070	−	0.907028i	$-0.638345\pi$
$353$	−15.8224			−0.842141			−0.421070	+	0.907028i	$0.638345\pi$
$354$	−0.311912	−	0.959965i	−0.0165779	−	0.0510216i
$355$	7.19353	−	3.20277i	0.381793	−	0.169985i
$356$	−11.7208	−	5.21844i	−0.621202	−	0.276577i
$357$	1.98730	+	2.20712i	0.105179	+	0.116813i
$358$	−13.3964	+	2.84749i	−0.708021	+	0.150495i
$359$	−2.18194	−	0.971461i	−0.115158	−	0.0512717i	0.348349	−	0.937365i	$-0.386742\pi$
$359$	−2.18194	−	0.971461i	−0.115158	−	0.0512717i	−0.463507	+	0.886093i	$0.653409\pi$
$360$	0.541674	+	0.393549i	0.0285487	+	0.0207419i
$361$	15.0272	−	11.6268i	0.790907	−	0.611937i
$362$	19.1864			1.00841
$363$	16.9876	+	3.69440i	0.891616	+	0.193906i
$364$	0.0392678	+	0.0680138i	0.00205819	+	0.00356489i
$365$	−4.27273	−	0.908197i	−0.223645	−	0.0475372i
$366$	0.464101	−	4.41563i	0.0242590	−	0.230809i
$367$	−1.17399	−	11.1698i	−0.0612820	−	0.583059i	−0.981474	−	0.191593i	$-0.938635\pi$
$367$	−1.17399	−	11.1698i	−0.0612820	−	0.583059i	0.920193	−	0.391466i	$-0.128032\pi$
$368$	−0.390097	+	1.20059i	−0.0203352	+	0.0625853i
$369$	0.424114	−	1.30529i	0.0220785	−	0.0679507i
$370$	−1.43858	−	13.6872i	−0.0747882	−	0.711562i
$371$	−5.68967	+	2.53321i	−0.295393	+	0.131517i
$372$	0.212974	+	0.655465i	0.0110422	+	0.0339843i
$373$	−4.82873			−0.250022			−0.125011	−	0.992155i	$-0.539897\pi$
$373$	−4.82873			−0.250022			−0.125011	+	0.992155i	$0.539897\pi$
$374$	0.801611	+	3.81538i	0.0414503	+	0.197288i
$375$	−8.66205	−	15.0031i	−0.447307	−	0.774758i
$376$	1.86766	+	0.396984i	0.0963174	+	0.0204729i
$377$	0.0136236	−	0.129620i	0.000701652	−	0.00667577i
$378$	−8.08371	−	3.59910i	−0.415781	−	0.185118i
$379$	−3.54053	+	10.8966i	−0.181865	+	0.559722i	−0.999880	−	0.0154740i	$-0.995074\pi$
$379$	−3.54053	+	10.8966i	−0.181865	+	0.559722i	0.818016	+	0.575196i	$0.195074\pi$
$380$	−3.48599	−	4.64885i	−0.178828	−	0.238481i
$381$	−16.3257	+	11.8613i	−0.836389	+	0.607672i
$382$	0.174995	−	1.66496i	0.00895351	−	0.0851869i
$383$	15.8187	−	17.5684i	0.808298	−	0.897706i	−0.188131	−	0.982144i	$-0.560243\pi$
$383$	15.8187	−	17.5684i	0.808298	−	0.897706i	0.996429	+	0.0844382i	$0.0269096\pi$
$384$	0.790212	−	1.36869i	0.0403253	−	0.0698455i
$385$	0.0166196	−	7.06811i	0.000847013	−	0.360224i
$386$	−10.2107	+	17.6854i	−0.519709	+	0.900162i
$387$	0.0284230	+	0.0874771i	0.00144482	+	0.00444671i
$388$	9.33197	+	6.78007i	0.473759	+	0.344206i
$389$	1.21315	+	11.5423i	0.0615091	+	0.585220i	0.981256	+	0.192708i	$0.0617271\pi$
$389$	1.21315	+	11.5423i	0.0615091	+	0.585220i	−0.919747	+	0.392512i	$0.871606\pi$
$390$	0.0692536	+	0.0769139i	0.00350679	+	0.00389469i
$391$	0.458557	−	1.41129i	0.0231902	−	0.0713721i
$392$	−3.59548	+	2.61227i	−0.181599	+	0.131940i
$393$	11.0105	−	4.90218i	0.555405	−	0.247282i
$394$	−6.44247	+	7.15508i	−0.324567	+	0.360468i
$395$	4.59255	−	7.95453i	0.231076	−	0.400236i
$396$	−0.975971	−	1.34997i	−0.0490444	−	0.0678387i
$397$	0.785197	+	1.36000i	0.0394079	+	0.0682565i	0.885057	−	0.465483i	$-0.154119\pi$
$397$	0.785197	+	1.36000i	0.0394079	+	0.0682565i	−0.845649	+	0.533740i	$0.820786\pi$
$398$	−1.23342	−	3.79607i	−0.0618256	−	0.190280i
$399$	8.29461	+	7.24482i	0.415250	+	0.362694i
$400$	2.60742	−	1.89440i	0.130371	−	0.0947201i
$401$	21.9843	−	4.67291i	1.09784	−	0.233354i	0.376836	−	0.926280i	$-0.377012\pi$
$401$	21.9843	−	4.67291i	1.09784	−	0.233354i	0.721009	+	0.692926i	$0.243679\pi$
$402$	−5.97676	+	1.27040i	−0.298094	+	0.0633617i
$403$	−0.00223930	−	0.0213055i	−0.000111548	−	0.00106130i
$404$	−0.943392	+	8.97577i	−0.0469355	+	0.446561i
$405$	−9.44168	−	2.00689i	−0.469161	−	0.0997232i
$406$	−4.24139			−0.210497
$407$	−7.19783	+	33.4759i	−0.356783	+	1.65934i
$408$	−0.928890	+	1.60888i	−0.0459869	+	0.0796516i
$409$	18.3335	+	3.89690i	0.906533	+	0.192690i	0.637508	−	0.770444i	$-0.279965\pi$
$409$	18.3335	+	3.89690i	0.906533	+	0.192690i	0.269025	+	0.963133i	$0.413299\pi$
$410$	2.94698	+	2.14111i	0.145541	+	0.105742i
$411$	9.96713	−	7.24155i	0.491642	−	0.357199i
$412$	7.83129	+	8.69753i	0.385820	+	0.428496i
$413$	0.998709	−	0.212282i	0.0491432	−	0.0104457i
$414$	0.0662758	+	0.630573i	0.00325728	+	0.0309909i
$415$	2.00953	−	19.1194i	0.0986440	−	0.938535i
$416$	−0.0328715	+	0.0365075i	−0.00161166	+	0.00178993i
$417$	5.76954			0.282536
$418$	4.64224	+	13.6912i	0.227060	+	0.669660i
$419$	21.3099			1.04106			0.520528	−	0.853845i	$-0.325735\pi$
$419$	21.3099			1.04106			0.520528	+	0.853845i	$0.325735\pi$
$420$	2.25368	−	2.50297i	0.109968	−	0.122132i
$421$	3.59234	−	34.1788i	0.175080	−	1.66577i	−0.455942	−	0.890010i	$-0.650697\pi$
$421$	3.59234	−	34.1788i	0.175080	−	1.66577i	0.631022	−	0.775765i	$-0.282636\pi$
$422$	−1.57923	−	15.0254i	−0.0768757	−	0.731424i
$423$	0.938057	−	0.199390i	0.0456099	−	0.00969468i
$424$	−2.60681	−	2.89516i	−0.126598	−	0.140601i
$425$	−3.06501	+	2.22686i	−0.148675	+	0.108019i
$426$	−7.55254	−	5.48724i	−0.365922	−	0.265858i
$427$	4.39306	+	0.933775i	0.212595	+	0.0451885i
$428$	−2.27781	+	3.94528i	−0.110102	+	0.190702i
$429$	−0.104181	−	0.235484i	−0.00502993	−	0.0113693i
$430$	−0.244122			−0.0117726
$431$	−14.5568	−	3.09414i	−0.701176	−	0.149040i	−0.156490	−	0.987680i	$-0.550018\pi$
$431$	−14.5568	−	3.09414i	−0.701176	−	0.149040i	−0.544686	+	0.838640i	$0.683351\pi$
$432$	0.578571	−	5.50474i	0.0278365	−	0.264847i
$433$	0.147241	+	1.40090i	0.00707593	+	0.0673230i	0.997490	−	0.0708071i	$-0.0225575\pi$
$433$	0.147241	+	1.40090i	0.00707593	+	0.0673230i	−0.990414	+	0.138130i	$0.955891\pi$
$434$	−0.681919	+	0.144946i	−0.0327332	+	0.00695765i
$435$	−5.46736	+	1.16212i	−0.262140	+	0.0557195i
$436$	7.12896	−	5.17949i	0.341415	−	0.248053i
$437$	1.06268	−	5.39899i	0.0508350	−	0.258269i
$438$	1.60032	+	4.92528i	0.0764663	+	0.235339i
$439$	−10.7387	−	18.6000i	−0.512531	−	0.887729i	−0.999894	−	0.0145303i	$-0.995375\pi$
$439$	−10.7387	−	18.6000i	−0.512531	−	0.887729i	0.487364	−	0.873199i	$-0.337959\pi$
$440$	4.20807	−	1.35635i	0.200612	−	0.0646616i
$441$	−1.11609	+	1.93313i	−0.0531472	+	0.0920537i
$442$	0.0386402	−	0.0429143i	0.00183793	−	0.00204123i
$443$	19.4224	−	8.64740i	0.922785	−	0.410850i	0.110344	−	0.993893i	$-0.464805\pi$
$443$	19.4224	−	8.64740i	0.922785	−	0.410850i	0.812441	+	0.583043i	$0.198138\pi$
$444$	−13.2002	+	9.59050i	−0.626454	+	0.455145i
$445$	5.28518	−	16.2661i	0.250542	−	0.771088i
$446$	−2.26816	−	2.51905i	−0.107401	−	0.119280i
$447$	2.66445	+	25.3506i	0.126024	+	1.19904i
$448$	1.29335	+	0.939674i	0.0611051	+	0.0443954i
$449$	5.70480	+	17.5576i	0.269226	+	0.828593i	0.990690	+	0.136141i	$0.0434699\pi$
$449$	5.70480	+	17.5576i	0.269226	+	0.828593i	−0.721463	+	0.692453i	$0.756530\pi$
$450$	0.809384	−	1.40189i	0.0381547	−	0.0660859i
$451$	−5.30977	−	7.34453i	−0.250027	−	0.345840i
$452$	−4.66881	+	8.08662i	−0.219602	+	0.380363i
$453$	23.2928	−	25.8692i	1.09439	−	1.21544i
$454$	−1.41416	+	13.4548i	−0.0663699	+	0.631467i
$455$	−0.0846982	+	0.0615368i	−0.00397071	+	0.00288489i
$456$	−2.70666	+	6.33490i	−0.126751	+	0.296659i
$457$	−0.0380440	+	0.117087i	−0.00177962	+	0.00547712i	−0.951942	−	0.306277i	$-0.900917\pi$
$457$	−0.0380440	+	0.117087i	−0.00177962	+	0.00547712i	0.950163	+	0.311754i	$0.100917\pi$
$458$	−18.7874	−	8.36471i	−0.877880	−	0.390857i
$459$	−0.680107	+	6.47079i	−0.0317447	+	0.302031i
$460$	−1.64605	−	0.349880i	−0.0767477	−	0.0163132i
$461$	−0.564063	−	0.976986i	−0.0262710	−	0.0455028i	0.852591	−	0.522579i	$-0.175030\pi$
$461$	−0.564063	−	0.976986i	−0.0262710	−	0.0455028i	−0.878862	+	0.477076i	$0.841697\pi$
$462$	−7.26686	+	4.17277i	−0.338085	+	0.194135i
$463$	−17.5630			−0.816220			−0.408110	−	0.912933i	$-0.633812\pi$
$463$	−17.5630			−0.816220			−0.408110	+	0.912933i	$0.633812\pi$
$464$	−0.819846	−	2.52323i	−0.0380604	−	0.117138i
$465$	−0.839312	+	0.373686i	−0.0389221	+	0.0173293i
$466$	−1.31400	−	12.5019i	−0.0608700	−	0.579139i
$467$	−12.7396	+	39.2084i	−0.589518	+	1.81435i	−0.00920256	+	0.999958i	$0.502929\pi$
$467$	−12.7396	+	39.2084i	−0.589518	+	1.81435i	−0.580315	+	0.814392i	$0.697071\pi$
$468$	−0.00762468	+	0.0234663i	−0.000352451	+	0.00108473i
$469$	−0.646072	−	6.14696i	−0.0298328	−	0.283840i
$470$	−0.266059	+	2.53139i	−0.0122724	+	0.116764i
$471$	−28.9692	−	6.15760i	−1.33483	−	0.283727i
$472$	0.319335	+	0.553104i	0.0146986	+	0.0254587i
$473$	0.577201	+	0.189045i	0.0265397	+	0.00869232i
$474$	−10.8895			−0.500171
$475$	−10.2970	+	9.55680i	−0.472459	+	0.438496i
$476$	−1.52033	−	1.10458i	−0.0696841	−	0.0506284i
$477$	−1.78756	−	0.795871i	−0.0818466	−	0.0364404i
$478$	17.6750	−	3.75695i	0.808438	−	0.171839i
$479$	6.06470	+	6.73553i	0.277103	+	0.307754i	0.865591	−	0.500752i	$-0.166943\pi$
$479$	6.06470	+	6.73553i	0.277103	+	0.307754i	−0.588488	+	0.808506i	$0.700276\pi$
$480$	1.92466	+	0.856912i	0.0878482	+	0.0391125i
$481$	0.463327	−	0.206287i	0.0211259	−	0.00940586i
$482$	1.77281	+	5.45616i	0.0807494	+	0.248521i
$483$	3.18949			0.145127
$484$	−10.9999	−	0.0517294i	−0.499994	−	0.00235133i
$485$	−7.68839	+	13.3167i	−0.349112	+	0.604680i
$486$	−1.59496	−	4.90880i	−0.0723491	−	0.222668i
$487$	11.2341	+	8.16204i	0.509065	+	0.369857i	0.812469	−	0.583005i	$-0.198123\pi$
$487$	11.2341	+	8.16204i	0.509065	+	0.369857i	−0.303404	+	0.952862i	$0.598123\pi$
$488$	0.293656	+	2.79395i	0.0132932	+	0.126476i
$489$	−9.23775	+	1.96354i	−0.417745	+	0.0887945i
$490$	−3.96424	−	4.40273i	−0.179086	−	0.198895i
$491$	10.8187	+	4.81678i	0.488239	+	0.217378i	0.636065	−	0.771635i	$-0.280561\pi$
$491$	10.8187	+	4.81678i	0.488239	+	0.217378i	−0.147826	+	0.989013i	$0.547228\pi$
$492$	0.451417	−	4.29495i	0.0203514	−	0.193631i
$493$	0.963724	+	2.96604i	0.0434040	+	0.133584i
$494$	0.123235	−	0.175118i	0.00554463	−	0.00787892i
$495$	1.65374	−	1.48201i	0.0743302	−	0.0666114i
$496$	−0.218042	−	0.377660i	−0.00979037	−	0.0169574i
$497$	6.31875	−	7.01769i	0.283435	−	0.314786i
$498$	−20.8216	+	9.27037i	−0.933037	+	0.415415i
$499$	28.3222	+	12.6099i	1.26788	+	0.564496i	0.926806	−	0.375541i	$-0.122543\pi$
$499$	28.3222	+	12.6099i	1.26788	+	0.564496i	0.341072	+	0.940037i	$0.389210\pi$
$500$	7.33480	+	8.14612i	0.328022	+	0.364306i
$501$	9.60567	−	29.5632i	0.429150	−	1.32079i
$502$	11.6932	−	8.49557i	0.521891	−	0.379176i
$503$	−28.0699	+	12.4975i	−1.25158	+	0.557237i	−0.922109	−	0.386930i	$-0.873535\pi$
$503$	−28.0699	+	12.4975i	−1.25158	+	0.557237i	−0.329466	+	0.944167i	$0.606869\pi$
$504$	0.785405	+	0.166943i	0.0349847	+	0.00743623i
$505$	−12.0312			−0.535379
$506$	3.62098	+	2.10194i	0.160972	+	0.0934426i
$507$	10.2708	−	17.7896i	0.456144	−	0.790065i
$508$	8.54379	−	9.48884i	0.379069	−	0.420999i
$509$	0.577934	−	0.257313i	0.0256165	−	0.0114052i	−0.393888	−	0.919158i	$-0.628870\pi$
$509$	0.577934	−	0.257313i	0.0256165	−	0.0114052i	0.419505	+	0.907753i	$0.362204\pi$
$510$	−2.26242	−	1.00730i	−0.100182	−	0.0446038i
$511$	−5.12406	+	1.08915i	−0.226675	+	0.0481813i
$512$	−0.309017	+	0.951057i	−0.0136568	+	0.0420312i
$513$	0.364161	+	24.1240i	0.0160781	+	1.06510i
$514$	10.9936	+	7.98732i	0.484907	+	0.352306i
$515$	−10.4396	+	11.5943i	−0.460023	+	0.510907i
$516$	0.144711	+	0.250646i	0.00637053	+	0.0110341i
$517$	2.58935	−	5.77916i	0.113879	−	0.254167i
$518$	−8.25235	−	14.2935i	−0.362588	−	0.628020i
$519$	−32.9662	−	7.00719i	−1.44706	−	0.307581i
$520$	−0.0529805	−	0.0384926i	−0.00232335	−	0.00168801i
$521$	−14.5812	+	10.5938i	−0.638812	+	0.464124i	−0.859442	−	0.511233i	$-0.829189\pi$
$521$	−14.5812	+	10.5938i	−0.638812	+	0.464124i	0.220630	+	0.975358i	$0.429189\pi$
$522$	−0.891644	−	0.990271i	−0.0390262	−	0.0433430i
$523$	8.92122	+	9.90802i	0.390098	+	0.433247i	0.905920	−	0.423448i	$-0.139180\pi$
$523$	8.92122	+	9.90802i	0.390098	+	0.433247i	−0.515823	+	0.856695i	$0.672514\pi$
$524$	−6.16964	+	4.48251i	−0.269522	+	0.195819i
$525$	−6.58784	−	4.78635i	−0.287517	−	0.208893i
$526$	−7.62632	−	1.62102i	−0.332523	−	0.0706800i
$527$	0.256307	+	0.443937i	0.0111649	+	0.0193382i
$528$	−3.88706	−	3.51651i	−0.169163	−	0.153037i
$529$	10.7032	+	18.5385i	0.465356	+	0.806021i
$530$	3.47504	−	3.85942i	0.150946	−	0.167642i
$531$	0.259516	+	0.188549i	0.0112620	+	0.00818235i
$532$	−6.08674	−	3.39273i	−0.263894	−	0.147094i
$533$	−0.0414821	+	0.127669i	−0.00179679	+	0.00552995i
$534$	−19.8338	+	4.21580i	−0.858292	+	0.182436i
$535$	−5.54788	−	2.47007i	−0.239856	−	0.106791i
$536$	3.53198	−	1.57254i	0.152558	−	0.0679233i
$537$	−14.4833	+	16.0853i	−0.625001	+	0.694134i
$538$	−3.08135	+	5.33706i	−0.132847	+	0.230097i
$539$	5.96359	+	13.4797i	0.256870	+	0.580610i
$540$	7.37856			0.317523
$541$	−21.0585	−	4.47612i	−0.905374	−	0.192443i	−0.268381	−	0.963313i	$-0.586489\pi$
$541$	−21.0585	−	4.47612i	−0.905374	−	0.192443i	−0.636993	+	0.770869i	$0.719822\pi$
$542$	−2.66586	+	1.18692i	−0.114509	+	0.0509825i
$543$	24.5315	−	17.8232i	1.05275	−	0.764865i
$544$	0.363248	−	1.11796i	0.0155741	−	0.0479322i
$545$	7.86012	+	8.72955i	0.336691	+	0.373933i
$546$	0.113389	+	0.0504840i	0.00485259	+	0.00216051i
$547$	33.5633	−	14.9433i	1.43506	−	0.638931i	0.465785	−	0.884898i	$-0.345772\pi$
$547$	33.5633	−	14.9433i	1.43506	−	0.638931i	0.969278	+	0.245967i	$0.0791055\pi$
$548$	−5.21615	+	5.79312i	−0.222823	+	0.247470i
$549$	0.705514	+	1.22199i	0.0301106	+	0.0521531i
$550$	−4.32476	−	9.77537i	−0.184409	−	0.416823i
$551$	4.86263	+	10.4925i	0.207155	+	0.446995i
$552$	0.616518	+	1.89745i	0.0262407	+	0.0807607i
$553$	1.15140	−	10.9549i	0.0489626	−	0.465848i
$554$	−8.05194	−	3.58495i	−0.342094	−	0.152310i
$555$	−14.5540	−	16.1639i	−0.617784	−	0.686119i
$556$	−3.57086	+	0.759009i	−0.151438	+	0.0321892i
$557$	1.73060	+	16.4656i	0.0733278	+	0.697668i	0.968001	+	0.250946i	$0.0807418\pi$
$557$	1.73060	+	16.4656i	0.0733278	+	0.697668i	−0.894673	+	0.446721i	$0.852592\pi$
$558$	−0.177198	−	0.128742i	−0.00750138	−	0.00545007i
$559$	−0.00278002	−	0.00855602i	−0.000117582	−	0.000361881i
$560$	−1.06556	+	1.84561i	−0.0450282	+	0.0779911i
$561$	4.56922	+	4.13364i	0.192913	+	0.174522i
$562$	7.73409			0.326243
$563$	6.59781	+	20.3060i	0.278064	+	0.855794i	0.988392	+	0.151923i	$0.0485467\pi$
$563$	6.59781	+	20.3060i	0.278064	+	0.855794i	−0.710328	+	0.703871i	$0.751453\pi$
$564$	2.75675	−	1.22739i	0.116080	−	0.0516822i
$565$	−11.3715	−	5.06290i	−0.478401	−	0.212998i
$566$	5.29287	+	5.87833i	0.222476	+	0.247085i
$567$	−11.3229	+	2.40676i	−0.475518	+	0.101074i
$568$	5.39625	+	2.40257i	0.226422	+	0.100809i
$569$	13.2755	+	9.64524i	0.556539	+	0.404349i	0.830191	−	0.557480i	$-0.188231\pi$
$569$	13.2755	+	9.64524i	0.556539	+	0.404349i	−0.273652	+	0.961829i	$0.588231\pi$
$570$	−8.77570	−	2.70565i	−0.367574	−	0.113327i
$571$	8.06834			0.337649			0.168825	−	0.985646i	$-0.446003\pi$
$571$	8.06834			0.337649			0.168825	+	0.985646i	$0.446003\pi$
$572$	0.0954584	+	0.132039i	0.00399132	+	0.00552083i
$573$	−1.32292	−	2.29136i	−0.0552658	−	0.0957231i
$574$	4.27300	+	0.908254i	0.178352	+	0.0379098i
$575$	−0.425283	+	4.04630i	−0.0177355	+	0.168742i
$576$	0.0525007	+	0.499511i	0.00218753	+	0.0208130i
$577$	6.78823	−	20.8920i	0.282598	−	0.869746i	−0.704511	−	0.709693i	$-0.748834\pi$
$577$	6.78823	−	20.8920i	0.282598	−	0.869746i	0.987108	−	0.160053i	$-0.0511665\pi$
$578$	4.82629	−	14.8538i	0.200747	−	0.617837i
$579$	3.37359	+	32.0975i	0.140201	+	1.33393i
$580$	3.23095	−	1.43851i	0.134158	−	0.0597309i
$581$	−7.12445	−	21.9268i	−0.295572	−	0.909676i
$582$	18.2301			0.755662
$583$	−11.2050	+	6.43415i	−0.464066	+	0.266475i
$584$	−1.63841	−	2.83780i	−0.0677977	−	0.117429i
$585$	−0.0321731	−	0.00683861i	−0.00133019	−	0.000282742i
$586$	0.204017	−	1.94109i	0.00842785	−	0.0801856i
$587$	24.6314	+	10.9666i	1.01665	+	0.452640i	0.846279	−	0.532741i	$-0.178838\pi$
$587$	24.6314	+	10.9666i	1.01665	+	0.452640i	0.170367	+	0.985381i	$0.445505\pi$
$588$	−2.17048	+	6.68004i	−0.0895089	+	0.275480i
$589$	1.14037	+	1.52078i	0.0469882	+	0.0626625i
$590$	−0.688784	+	0.500431i	−0.0283568	+	0.0206024i
$591$	−1.59056	+	15.1331i	−0.0654268	+	0.622494i
$592$	6.90813	−	7.67225i	0.283922	−	0.315328i
$593$	−8.50480	+	14.7307i	−0.349250	+	0.604919i	−0.986116	−	0.166055i	$-0.946897\pi$
$593$	−8.50480	+	14.7307i	−0.349250	+	0.604919i	0.636866	+	0.770974i	$0.280230\pi$
$594$	−17.4458	−	5.71388i	−0.715811	−	0.234443i
$595$	1.25256	−	2.16950i	0.0513500	−	0.0889408i
$596$	−4.98405	−	15.3393i	−0.204155	−	0.628324i
$597$	−5.10339	−	3.70783i	−0.208868	−	0.151751i
$598$	−0.00648235	−	0.0616755i	−0.000265083	−	0.00252210i
$599$	10.0731	+	11.1874i	0.411578	+	0.457103i	0.912916	−	0.408148i	$-0.133825\pi$
$599$	10.0731	+	11.1874i	0.411578	+	0.457103i	−0.501338	+	0.865251i	$0.667159\pi$
$600$	1.57402	−	4.84433i	0.0642590	−	0.197769i
$601$	1.64097	−	1.19223i	0.0669366	−	0.0486323i	−0.553814	−	0.832641i	$-0.686828\pi$
$601$	1.64097	−	1.19223i	0.0669366	−	0.0486323i	0.620750	+	0.784008i	$0.286828\pi$
$602$	−0.267452	+	0.119077i	−0.0109005	+	0.00485323i
$603$	1.29936	−	1.44309i	0.0529140	−	0.0587670i
$604$	−11.0130	+	19.0751i	−0.448114	+	0.776156i
$605$	−1.46417	−	14.5904i	−0.0595271	−	0.593183i
$606$	7.13183	+	12.3527i	0.289711	+	0.501794i
$607$	−2.33065	−	7.17299i	−0.0945980	−	0.291143i	0.892551	−	0.450947i	$-0.148914\pi$
$607$	−2.33065	−	7.17299i	−0.0945980	−	0.291143i	−0.987149	+	0.159804i	$0.948914\pi$
$608$	0.841809	−	4.27684i	0.0341399	−	0.173449i
$609$	−5.42300	+	3.94004i	−0.219751	+	0.159658i
$610$	−3.66318	+	0.778634i	−0.148318	+	0.0315260i
$611$	−0.0917501	+	0.0195021i	−0.00371181	+	0.000788970i
$612$	−0.0617143	−	0.587173i	−0.00249465	−	0.0237351i
$613$	−3.18469	+	30.3003i	−0.128628	+	1.22382i	0.719677	+	0.694309i	$0.244290\pi$
$613$	−3.18469	+	30.3003i	−0.128628	+	1.22382i	−0.848305	+	0.529508i	$0.822377\pi$
$614$	24.2903	+	5.16307i	0.980278	+	0.208365i
$615$	5.75696			0.232143
$616$	3.94862	−	3.53858i	0.159095	−	0.142573i
$617$	11.0566	−	19.1505i	0.445120	−	0.770971i	−0.552940	−	0.833221i	$-0.686494\pi$
$617$	11.0566	−	19.1505i	0.445120	−	0.770971i	0.998061	+	0.0622500i	$0.0198276\pi$
$618$	18.0926	+	3.84569i	0.727790	+	0.154696i
$619$	39.8778	+	28.9729i	1.60282	+	1.16452i	0.881820	+	0.471587i	$0.156319\pi$
$619$	39.8778	+	28.9729i	1.60282	+	1.16452i	0.721003	+	0.692932i	$0.243681\pi$
$620$	0.470303	−	0.341695i	0.0188878	−	0.0137228i
$621$	4.67544	+	5.19261i	0.187619	+	0.208372i
$622$	26.1546	−	5.55933i	1.04870	−	0.222909i
$623$	−2.14398	−	20.3986i	−0.0858968	−	0.817253i
$624$	−0.00811552	+	0.0772140i	−0.000324881	+	0.00309103i
$625$	1.00514	−	1.11632i	0.0402057	−	0.0446529i
$626$	12.9229			0.516501
$627$	18.6540	+	13.1930i	0.744968	+	0.526879i
$628$	18.7396			0.747789
$629$	−8.12047	+	9.01869i	−0.323784	+	0.359599i
$630$	−0.111885	+	1.06452i	−0.00445762	+	0.0424115i
$631$	3.15717	+	30.0385i	0.125685	+	1.19581i	0.857563	+	0.514378i	$0.171977\pi$
$631$	3.15717	+	30.0385i	0.125685	+	1.19581i	−0.731878	+	0.681435i	$0.761356\pi$
$632$	6.73966	−	1.43256i	0.268089	−	0.0569842i
$633$	−15.9770	−	17.7443i	−0.635029	−	0.705271i
$634$	−5.89128	+	4.28027i	−0.233973	+	0.169991i
$635$	13.7704	+	10.0048i	0.546462	+	0.397028i
$636$	−6.02250	−	1.28012i	−0.238807	−	0.0507601i
$637$	0.109164	−	0.189077i	0.00432522	−	0.00749149i
$638$	−8.75319	+	0.899194i	−0.346542	+	0.0355994i
$639$	2.96683			0.117366
$640$	−1.30393	−	0.277159i	−0.0515423	−	0.0109557i
$641$	−0.134102	+	1.27589i	−0.00529670	+	0.0503947i	−0.996851	−	0.0792975i	$-0.974732\pi$
$641$	−0.134102	+	1.27589i	−0.00529670	+	0.0503947i	0.991554	+	0.129692i	$0.0413989\pi$
$642$	0.752584	+	7.16036i	0.0297021	+	0.282597i
$643$	−32.5426	+	6.91714i	−1.28335	+	0.272785i	−0.798598	−	0.601864i	$-0.794425\pi$
$643$	−32.5426	+	6.91714i	−1.28335	+	0.272785i	−0.484756	+	0.874650i	$0.661092\pi$
$644$	−1.97403	+	0.419592i	−0.0777875	+	0.0165342i
$645$	−0.312132	+	0.226777i	−0.0122902	+	0.00892934i
$646$	−0.989542	+	5.02740i	−0.0389330	+	0.197801i
$647$	9.19986	+	28.3143i	0.361684	+	1.11315i	0.952032	+	0.305999i	$0.0989905\pi$
$647$	9.19986	+	28.3143i	0.361684	+	1.11315i	−0.590348	+	0.807149i	$0.701009\pi$
$648$	−3.62047	−	6.27084i	−0.142226	−	0.246342i
$649$	2.01609	−	0.649829i	0.0791383	−	0.0255080i
$650$	−0.0791648	+	0.137117i	−0.00310510	+	0.00537819i
$651$	−0.737246	+	0.818795i	−0.0288950	+	0.0320911i
$652$	5.45907	−	2.43053i	0.213794	−	0.0951870i
$653$	22.4378	−	16.3020i	0.878059	−	0.637947i	−0.0546786	−	0.998504i	$-0.517413\pi$
$653$	22.4378	−	16.3020i	0.878059	−	0.637947i	0.932737	+	0.360557i	$0.117413\pi$
$654$	4.30353	−	13.2449i	0.168281	−	0.517916i
$655$	−6.80241	−	7.55484i	−0.265792	−	0.295192i
$656$	0.285630	+	2.71759i	0.0111520	+	0.106104i
$657$	−1.33150	−	0.967389i	−0.0519466	−	0.0377414i
$658$	0.943268	+	2.90308i	0.0367724	+	0.113174i
$659$	9.00307	−	15.5938i	0.350710	−	0.607447i	−0.635664	−	0.771966i	$-0.719274\pi$
$659$	9.00307	−	15.5938i	0.350710	−	0.607447i	0.986374	+	0.164519i	$0.0526070\pi$
$660$	4.12041	−	5.64330i	0.160387	−	0.219665i
$661$	12.0915	−	20.9431i	0.470306	−	0.814594i	−0.529117	−	0.848549i	$-0.677477\pi$
$661$	12.0915	−	20.9431i	0.470306	−	0.814594i	0.999423	+	0.0339549i	$0.0108102\pi$
$662$	2.07719	−	2.30695i	0.0807323	−	0.0896623i
$663$	0.00953975	−	0.0907646i	0.000370493	−	0.00352501i
$664$	11.6672	−	8.47674i	0.452776	−	0.328961i
$665$	3.64980	−	8.54230i	0.141533	−	0.331256i
$666$	1.60237	−	4.93158i	0.0620905	−	0.191095i
$667$	3.05964	+	1.36224i	0.118470	+	0.0527461i
$668$	−2.05592	+	19.5608i	−0.0795460	+	0.756830i
$669$	−5.24012	−	1.11382i	−0.202595	−	0.0430628i
$670$	2.57696	+	4.46342i	0.0995566	+	0.172437i
$671$	9.26418	+	0.995734i	0.357640	+	0.0384399i
$672$	2.52657			0.0974647
$673$	−10.0029	−	30.7858i	−0.385584	−	1.18671i	−0.936056	−	0.351852i	$-0.885552\pi$
$673$	−10.0029	−	30.7858i	−0.385584	−	1.18671i	0.550471	−	0.834854i	$-0.314448\pi$
$674$	17.4845	−	7.78461i	0.673479	−	0.299852i
$675$	−1.86471	−	17.7415i	−0.0717726	−	0.682870i
$676$	−4.01648	+	12.3614i	−0.154480	+	0.475440i
$677$	−7.14731	+	21.9972i	−0.274693	+	0.845419i	0.714607	+	0.699526i	$0.246606\pi$
$677$	−7.14731	+	21.9972i	−0.274693	+	0.845419i	−0.989300	+	0.145893i	$0.953394\pi$
$678$	1.54257	+	14.6766i	0.0592420	+	0.563650i
$679$	−1.92756	+	18.3395i	−0.0739731	+	0.703807i
$680$	1.53276	+	0.325799i	0.0587788	+	0.0124938i
$681$	10.6907	+	18.5169i	0.409670	+	0.709569i
$682$	−1.37659	+	0.443704i	−0.0527122	+	0.0169903i
$683$	28.9188			1.10655			0.553273	−	0.833000i	$-0.313379\pi$
$683$	28.9188			1.10655			0.553273	+	0.833000i	$0.313379\pi$
$684$	−0.487454	−	2.13436i	−0.0186383	−	0.0816091i
$685$	−8.40711	−	6.10812i	−0.321219	−	0.233379i
$686$	−16.7138	−	7.44148i	−0.638137	−	0.284117i
$687$	−31.7918	+	6.75756i	−1.21293	+	0.257817i
$688$	−0.122537	−	0.136091i	−0.00467169	−	0.00518844i
$689$	0.174838	+	0.0778431i	0.00666082	+	0.00296559i
$690$	−2.42965	+	1.08175i	−0.0924951	+	0.0411815i
$691$	−7.92796	−	24.3997i	−0.301594	−	0.928210i	−0.980926	−	0.194380i	$-0.937731\pi$
$691$	−7.92796	−	24.3997i	−0.301594	−	0.928210i	0.679333	−	0.733831i	$-0.262269\pi$
$692$	21.3251			0.810659
$693$	1.08889	−	2.43030i	0.0413636	−	0.0923194i
$694$	−16.4489	+	28.4903i	−0.624391	+	1.08148i
$695$	−1.50384	−	4.62833i	−0.0570437	−	0.175563i
$696$	−3.39219	−	2.46457i	−0.128581	−	0.0934194i
$697$	−0.335757	−	3.19452i	−0.0127177	−	0.121001i
$698$	19.9665	−	4.24400i	0.755741	−	0.160638i
$699$	−13.2937	−	14.7641i	−0.502814	−	0.558431i
$700$	4.70698	+	2.09568i	0.177907	+	0.0792093i
$701$	−1.82044	+	17.3203i	−0.0687570	+	0.654180i	0.904816	+	0.425803i	$0.140008\pi$
$701$	−1.82044	+	17.3203i	−0.0687570	+	0.654180i	−0.973573	+	0.228376i	$0.926658\pi$
$702$	0.0840258	+	0.258605i	0.00317135	+	0.00976041i
$703$	−25.8986	+	36.8020i	−0.976786	+	1.38801i
$704$	2.86837	+	1.66506i	0.108106	+	0.0627544i
$705$	2.01135	+	3.48376i	0.0757518	+	0.131206i
$706$	10.5872	−	11.7583i	0.398456	−	0.442531i
$707$	−13.1809	+	5.86853i	−0.495720	+	0.220709i
$708$	0.922103	+	0.410547i	0.0346548	+	0.0154293i
$709$	−28.2506	−	31.3755i	−1.06098	−	1.17833i	−0.983420	−	0.181344i	$-0.941955\pi$
$709$	−28.2506	−	31.3755i	−1.06098	−	1.17833i	−0.0775555	−	0.996988i	$-0.524712\pi$
$710$	−2.43329	+	7.48890i	−0.0913198	+	0.281053i
$711$	2.79977	−	2.03415i	0.105000	−	0.0762867i
$712$	11.7208	−	5.21844i	0.439256	−	0.195569i
$713$	0.538473	+	0.114456i	0.0201660	+	0.00428641i
$714$	−2.96997			−0.111148
$715$	−0.161750	+	0.144953i	−0.00604912	+	0.00542095i
$716$	6.84784	−	11.8608i	0.255916	−	0.443259i
$717$	19.1091	−	21.2228i	0.713643	−	0.792580i
$718$	2.18194	−	0.971461i	0.0814291	−	0.0362546i
$719$	24.2545	+	10.7988i	0.904540	+	0.402727i	0.805664	−	0.592372i	$-0.201809\pi$
$719$	24.2545	+	10.7988i	0.904540	+	0.402727i	0.0988761	+	0.995100i	$0.468475\pi$
$720$	−0.654915	+	0.139206i	−0.0244072	+	0.00518792i
$721$	−5.78180	+	17.7946i	−0.215326	+	0.662704i
$722$	−1.41478	+	18.9473i	−0.0526528	+	0.705144i
$723$	7.33520	+	5.32933i	0.272799	+	0.198200i
$724$	−12.8382	+	14.2582i	−0.477127	+	0.529904i
$725$	−4.27537	−	7.40515i	−0.158783	−	0.275020i
$726$	−14.1124	+	10.1522i	−0.523760	+	0.376783i
$727$	−19.8672	−	34.4109i	−0.736832	−	1.27623i	−0.953915	−	0.300077i	$-0.902988\pi$
$727$	−19.8672	−	34.4109i	−0.736832	−	1.27623i	0.217083	−	0.976153i	$-0.430346\pi$
$728$	−0.0768194	−	0.0163285i	−0.00284712	−	0.000605174i
$729$	−24.1735	−	17.5631i	−0.895314	−	0.650483i
$730$	3.53394	−	2.56756i	0.130797	−	0.0950295i
$731$	0.144042	+	0.159975i	0.00532758	+	0.00591688i
$732$	2.97091	+	3.29953i	0.109808	+	0.121954i
$733$	28.9489	−	21.0326i	1.06925	−	0.776858i	0.0934752	−	0.995622i	$-0.470202\pi$
$733$	28.9489	−	21.0326i	1.06925	−	0.776858i	0.975778	+	0.218764i	$0.0702024\pi$
$734$	9.08634	+	6.60161i	0.335383	+	0.243670i
$735$	−9.15855	−	1.94671i	−0.337818	−	0.0718055i
$736$	−0.631190	−	1.09325i	−0.0232660	−	0.0402978i
$737$	−2.63652	−	12.5489i	−0.0971174	−	0.462243i
$738$	0.686232	+	1.18859i	0.0252605	+	0.0437525i
$739$	6.03663	−	6.70436i	0.222061	−	0.246624i	−0.621812	−	0.783166i	$-0.713603\pi$
$739$	6.03663	−	6.70436i	0.222061	−	0.246624i	0.843873	+	0.536543i	$0.180270\pi$
$740$	11.1341	+	8.08943i	0.409299	+	0.297373i
$741$	−0.00510803	−	0.338383i	−0.000187648	−	0.0124308i
$742$	1.92460	−	5.92330i	0.0706541	−	0.217451i
$743$	−28.1573	+	5.98502i	−1.03299	+	0.219569i	−0.693059	−	0.720880i	$-0.743738\pi$
$743$	−28.1573	+	5.98502i	−1.03299	+	0.219569i	−0.339933	+	0.940450i	$0.610404\pi$
$744$	−0.629613	−	0.280322i	−0.0230827	−	0.0102771i
$745$	19.6418	−	8.74507i	0.719618	−	0.320395i
$746$	3.23105	−	3.58845i	0.118297	−	0.131382i
$747$	3.62169	−	6.27295i	0.132511	−	0.229515i
$748$	−3.37176	−	1.95727i	−0.123284	−	0.0715649i
$749$	−7.28292			−0.266112
$750$	16.9455	+	3.60188i	0.618763	+	0.131522i
$751$	−18.4130	+	8.19801i	−0.671901	+	0.299150i	−0.714186	−	0.699956i	$-0.753203\pi$
$751$	−18.4130	+	8.19801i	−0.671901	+	0.299150i	0.0422851	+	0.999106i	$0.486536\pi$
$752$	−1.54473	+	1.12231i	−0.0563304	+	0.0409264i
$753$	7.05878	−	21.7247i	0.257236	−	0.791692i
$754$	0.0872105	+	0.0968571i	0.00317602	+	0.00352733i
$755$	−26.8236	−	11.9426i	−0.976210	−	0.434637i
$756$	8.08371	−	3.59910i	0.294002	−	0.130898i
$757$	5.37344	−	5.96781i	0.195301	−	0.216904i	−0.637538	−	0.770419i	$-0.720047\pi$
$757$	5.37344	−	5.96781i	0.195301	−	0.216904i	0.832839	+	0.553515i	$0.186714\pi$
$758$	−5.72870	−	9.92239i	−0.208076	−	0.360398i
$759$	6.58234	−	0.676187i	0.238924	−	0.0245440i
$760$	5.78735	+	0.520088i	0.209929	+	0.0188656i
$761$	−4.39712	−	13.5329i	−0.159395	−	0.490569i	0.839184	−	0.543847i	$-0.183033\pi$
$761$	−4.39712	−	13.5329i	−0.159395	−	0.490569i	−0.998580	+	0.0532785i	$0.983033\pi$
$762$	2.10935	−	20.0691i	0.0764135	−	0.727026i
$763$	12.8694	+	5.72981i	0.465902	+	0.207433i
$764$	1.12021	+	1.24412i	0.0405279	+	0.0450108i
$765$	0.769849	−	0.163637i	0.0278340	−	0.00591629i
$766$	2.47112	+	23.5112i	0.0892853	+	0.849493i
$767$	−0.0253829	−	0.0184418i	−0.000916524	−	0.000665894i
$768$	0.488378	+	1.50307i	0.0176228	+	0.0542374i
$769$	−15.1798	+	26.2921i	−0.547396	+	0.948118i	0.451056	+	0.892496i	$0.351048\pi$
$769$	−15.1798	+	26.2921i	−0.547396	+	0.948118i	−0.998452	+	0.0556222i	$0.982286\pi$
$770$	5.24151	+	4.74184i	0.188891	+	0.170884i
$771$	21.4761			0.773444
$772$	−6.31054	−	19.4218i	−0.227121	−	0.699007i
$773$	28.5679	−	12.7192i	1.02752	−	0.457479i	0.177435	−	0.984132i	$-0.443220\pi$
$773$	28.5679	−	12.7192i	1.02752	−	0.457479i	0.850080	+	0.526653i	$0.176553\pi$
$774$	−0.0840269	−	0.0374112i	−0.00302028	−	0.00134472i
$775$	−0.940447	−	1.04447i	−0.0337819	−	0.0375186i
$776$	−11.2829	+	2.39825i	−0.405032	+	0.0860922i
$777$	−23.8293	−	10.6095i	−0.854872	−	0.380613i
$778$	−9.38939	−	6.82179i	−0.336626	−	0.244573i
$779$	−2.65200	−	11.6120i	−0.0950176	−	0.416042i
$780$	−0.103498			−0.00370582
$781$	11.5526	−	15.8224i	0.413384	−	0.566170i
$782$	0.741960	+	1.28511i	0.0265324	+	0.0459555i
$783$	−14.3640	−	3.05317i	−0.513328	−	0.109111i
$784$	0.464551	−	4.41991i	0.0165911	−	0.157854i
$785$	2.61122	+	24.8441i	0.0931984	+	0.886724i
$786$	−3.72441	+	11.4626i	−0.132845	+	0.408856i
$787$	−12.9529	+	39.8650i	−0.461722	+	1.42103i	0.401337	+	0.915930i	$0.368546\pi$
$787$	−12.9529	+	39.8650i	−0.461722	+	1.42103i	−0.863059	+	0.505103i	$0.831454\pi$
$788$	−1.00641	−	9.57537i	−0.0358519	−	0.341108i
$789$	−11.2568	+	5.01184i	−0.400752	+	0.178426i
$790$	2.83835	+	8.73554i	0.100984	+	0.310797i
$791$	−14.9278			−0.530770
$792$	1.65628	+	0.178020i	0.0588532	+	0.00632567i
$793$	−0.0690054	−	0.119521i	−0.00245045	−	0.00424431i
$794$	−1.53608	−	0.326503i	−0.0545134	−	0.0115872i
$795$	0.857939	−	8.16274i	0.0304280	−	0.289503i
$796$	3.64635	+	1.62346i	0.129241	+	0.0575419i
$797$	−15.4757	+	47.6292i	−0.548176	+	1.68711i	0.165140	+	0.986270i	$0.447192\pi$
$797$	−15.4757	+	47.6292i	−0.548176	+	1.68711i	−0.713316	+	0.700842i	$0.752808\pi$
$798$	−10.9341	+	1.31637i	−0.387064	+	0.0465989i
$799$	1.81582	−	1.31927i	0.0642391	−	0.0466724i
$800$	−0.336890	+	3.20529i	−0.0119109	+	0.113324i
$801$	4.31191	−	4.78886i	0.152354	−	0.169206i
$802$	−11.2377	+	19.4643i	−0.396818	+	0.687309i
$803$	−10.3439	+	3.33407i	−0.365029	+	0.117657i
$804$	3.05514	−	5.29166i	0.107746	−	0.186622i
$805$	−0.831344	−	2.55861i	−0.0293010	−	0.0901792i
$806$	0.0173315	+	0.0125921i	0.000610476	+	0.000443536i
$807$	1.01807	+	9.68633i	0.0358379	+	0.340975i
$808$	−6.03905	−	6.70704i	−0.212453	−	0.235953i
$809$	−1.00237	+	3.08498i	−0.0352415	+	0.108462i	−0.967130	−	0.254283i	$-0.918160\pi$
$809$	−1.00237	+	3.08498i	−0.0352415	+	0.108462i	0.931888	+	0.362745i	$0.118160\pi$
$810$	7.80913	−	5.67367i	0.274385	−	0.199352i
$811$	−50.5623	+	22.5118i	−1.77548	+	0.790495i	−0.791751	+	0.610845i	$0.790830\pi$
$811$	−50.5623	+	22.5118i	−1.77548	+	0.790495i	−0.983730	+	0.179651i	$0.942503\pi$
$812$	2.83804	−	3.15197i	0.0995958	−	0.110612i
$813$	−2.30596	+	3.99404i	−0.0808735	+	0.140077i
$814$	−20.0611	−	27.7488i	−0.703142	−	0.972593i
$815$	3.98298	+	6.89872i	0.139518	+	0.241652i
$816$	−0.574085	−	1.76685i	−0.0200970	−	0.0618522i
$817$	0.601203	+	0.525113i	0.0210334	+	0.0183714i
$818$	−15.1635	+	11.0169i	−0.530178	+	0.385197i
$819$	−0.0385835	+	0.00820118i	−0.00134822	+	0.000286572i
$820$	−3.56307	+	0.757353i	−0.124428	+	0.0264479i
$821$	1.86535	+	17.7476i	0.0651012	+	0.619397i	0.977622	+	0.210367i	$0.0674660\pi$
$821$	1.86535	+	17.7476i	0.0651012	+	0.619397i	−0.912521	+	0.409030i	$0.865867\pi$
$822$	−1.28780	+	12.2526i	−0.0449171	+	0.427357i
$823$	42.8981	+	9.11826i	1.49533	+	0.317843i	0.881723	−	0.471767i	$-0.156384\pi$
$823$	42.8981	+	9.11826i	1.49533	+	0.317843i	0.613609	+	0.789610i	$0.289717\pi$
$824$	−11.7037			−0.407717
$825$	−14.6104	−	8.48120i	−0.508670	−	0.295277i
$826$	−0.510510	+	0.884230i	−0.0177629	+	0.0307663i
$827$	−1.46047	−	0.310432i	−0.0507854	−	0.0107948i	0.182449	−	0.983215i	$-0.441598\pi$
$827$	−1.46047	−	0.310432i	−0.0507854	−	0.0107948i	−0.233234	+	0.972421i	$0.574931\pi$
$828$	−0.512954	−	0.372683i	−0.0178264	−	0.0129516i
$829$	3.63085	−	2.63796i	0.126104	−	0.0916203i	−0.522945	−	0.852366i	$-0.675167\pi$
$829$	3.63085	−	2.63796i	0.126104	−	0.0916203i	0.649050	+	0.760746i	$0.275167\pi$
$830$	12.8638	+	14.2867i	0.446511	+	0.495900i
$831$	−13.6254	+	2.89616i	−0.472659	+	0.100467i
$832$	−0.00513503	−	0.0488565i	−0.000178025	−	0.00169380i
$833$	−0.546078	+	5.19558i	−0.0189205	+	0.180016i
$834$	−3.86058	+	4.28761i	−0.133681	+	0.148468i
$835$	−26.2193			−0.907358
$836$	−13.2808	−	5.71136i	−0.459327	−	0.197531i
$837$	−2.41375			−0.0834314
$838$	−14.2591	+	15.8363i	−0.492572	+	0.547057i
$839$	2.82493	−	26.8775i	0.0975276	−	0.927913i	−0.830906	−	0.556413i	$-0.812177\pi$
$839$	2.82493	−	26.8775i	0.0975276	−	0.927913i	0.928433	−	0.371499i	$-0.121156\pi$
$840$	0.352060	+	3.34962i	0.0121472	+	0.115573i
$841$	21.4813	−	4.56599i	0.740734	−	0.157448i
$842$	22.9961	+	25.5397i	0.792497	+	0.880158i
$843$	9.88873	−	7.18458i	0.340586	−	0.247450i
$844$	12.2227	+	8.88034i	0.420724	+	0.305674i
$845$	−16.9479	−	3.60240i	−0.583027	−	0.123926i
$846$	−0.479507	+	0.830530i	−0.0164858	+	0.0285542i
$847$	−8.72096	−	15.2705i	−0.299656	−	0.524702i
$848$	3.89582			0.133783
$849$	12.2281	+	2.59916i	0.419666	+	0.0892029i
$850$	0.396013	−	3.76781i	0.0135831	−	0.129235i
$851$	1.36230	+	12.9614i	0.0466992	+	0.444313i
$852$	9.13145	−	1.94095i	0.312838	−	0.0664958i
$853$	−21.6576	+	4.60346i	−0.741541	+	0.157619i	−0.563167	−	0.826343i	$-0.690417\pi$
$853$	−21.6576	+	4.60346i	−0.741541	+	0.157619i	−0.178374	+	0.983963i	$0.557084\pi$
$854$	−3.63346	+	2.63987i	−0.124335	+	0.0903343i
$855$	2.76172	−	0.943653i	0.0944487	−	0.0322723i
$856$	−1.40776	−	4.33265i	−0.0481163	−	0.148087i
$857$	−24.1875	−	41.8939i	−0.826229	−	1.43107i	−0.900977	−	0.433868i	$-0.857149\pi$
$857$	−24.1875	−	41.8939i	−0.826229	−	1.43107i	0.0747480	−	0.997202i	$-0.476185\pi$
$858$	0.244710	+	0.0801476i	0.00835425	+	0.00273619i
$859$	−10.8618	+	18.8131i	−0.370599	+	0.641896i	−0.989658	−	0.143449i	$-0.954181\pi$
$859$	−10.8618	+	18.8131i	−0.370599	+	0.641896i	0.619059	+	0.785345i	$0.287514\pi$
$860$	0.163350	−	0.181418i	0.00557017	−	0.00618630i
$861$	6.30713	−	2.80812i	0.214947	−	0.0957003i
$862$	12.0398	−	8.74743i	0.410077	−	0.297938i
$863$	−14.0504	+	43.2426i	−0.478280	+	1.47199i	0.363202	+	0.931710i	$0.381683\pi$
$863$	−14.0504	+	43.2426i	−0.478280	+	1.47199i	−0.841482	+	0.540285i	$0.818317\pi$
$864$	3.70368	+	4.11335i	0.126002	+	0.139939i
$865$	2.97150	+	28.2719i	0.101034	+	0.961275i
$866$	−1.13959	−	0.827964i	−0.0387250	−	0.0281354i
$867$	−7.62759	−	23.4753i	−0.259046	−	0.797263i
$868$	0.348577	−	0.603753i	0.0118315	−	0.0204927i
$869$	0.0537336	−	22.8523i	0.00182279	−	0.775210i
$870$	2.79475	−	4.84065i	0.0947509	−	0.164113i
$871$	−0.127089	+	0.141146i	−0.00430624	+	0.00478256i
$872$	−0.921092	+	8.76361i	−0.0311921	+	0.296773i
$873$	−4.68710	+	3.40538i	−0.158634	+	0.115255i
$874$	3.30116	+	4.40236i	0.111663	+	0.148912i
$875$	−5.41525	+	16.6664i	−0.183069	+	0.563428i
$876$	−4.73102	−	2.10639i	−0.159846	−	0.0711682i
$877$	0.548852	−	5.22198i	0.0185334	−	0.176334i	−0.981339	−	0.192284i	$-0.938411\pi$
$877$	0.548852	−	5.22198i	0.0185334	−	0.176334i	0.999873	+	0.0159500i	$0.00507726\pi$
$878$	21.0081	+	4.46541i	0.708989	+	0.150700i
$879$	−1.54232	−	2.67138i	−0.0520212	−	0.0901033i
$880$	−1.80778	+	4.03478i	−0.0609403	+	0.136013i
$881$	−2.93482			−0.0988766			−0.0494383	−	0.998777i	$-0.515743\pi$
$881$	−2.93482			−0.0988766			−0.0494383	+	0.998777i	$0.515743\pi$
$882$	−0.689783	−	2.12293i	−0.0232262	−	0.0714829i
$883$	7.70147	−	3.42891i	0.259175	−	0.115392i	−0.273036	−	0.962004i	$-0.588028\pi$
$883$	7.70147	−	3.42891i	0.259175	−	0.115392i	0.532211	+	0.846612i	$0.321361\pi$
$884$	0.00603620	+	0.0574306i	0.000203019	+	0.00193160i
$885$	−0.415797	+	1.27969i	−0.0139769	+	0.0430164i
$886$	−6.56984	+	20.2199i	−0.220718	+	0.679300i
$887$	−6.13766	−	58.3959i	−0.206082	−	1.96074i	−0.270213	−	0.962801i	$-0.587094\pi$
$887$	−6.13766	−	58.3959i	−0.206082	−	1.96074i	0.0641308	−	0.997942i	$-0.479573\pi$
$888$	1.70552	−	16.2270i	0.0572336	−	0.544541i
$889$	19.9665	+	4.24402i	0.669656	+	0.142340i
$890$	8.55160	+	14.8118i	0.286650	+	0.496493i
$891$	−22.8575	+	7.36747i	−0.765754	+	0.246820i
$892$	3.38972			0.113496
$893$	6.10030	−	5.66178i	0.204139	−	0.189464i
$894$	−20.6220	−	14.9828i	−0.689704	−	0.501099i
$895$	16.6787	+	7.42585i	0.557509	+	0.248219i
$896$	−1.56373	+	0.332382i	−0.0522407	+	0.0111041i
$897$	−0.0655817	−	0.0728358i	−0.00218971	−	0.00243192i
$898$	−16.8651	−	7.50882i	−0.562795	−	0.250573i
$899$	−1.05694	+	0.470579i	−0.0352509	+	0.0156947i
$900$	0.500227	+	1.53954i	0.0166742	+	0.0513180i
$901$	−4.57951			−0.152566
$902$	9.01098	+	0.968520i	0.300033	+	0.0322482i
$903$	−0.231344	+	0.400700i	−0.00769866	+	0.0133345i
$904$	−2.88548	−	8.88061i	−0.0959698	−	0.295365i
$905$	−20.6919	−	15.0335i	−0.687822	−	0.499732i
$906$	3.63869	+	34.6198i	0.120887	+	1.15017i
$907$	2.77112	−	0.589019i	0.0920134	−	0.0195581i	−0.161675	−	0.986844i	$-0.551690\pi$
$907$	2.77112	−	0.589019i	0.0920134	−	0.0195581i	0.253688	+	0.967286i	$0.418356\pi$
$908$	−9.05264	−	10.0540i	−0.300422	−	0.333653i
$909$	−4.14113	−	1.84375i	−0.137352	−	0.0611533i
$910$	0.0109434	−	0.104119i	0.000362769	−	0.00345152i
$911$	−12.5529	−	38.6339i	−0.415896	−	1.28000i	−0.911447	−	0.411418i	$-0.865034\pi$
$911$	−12.5529	−	38.6339i	−0.415896	−	1.28000i	0.495551	−	0.868579i	$-0.334966\pi$
$912$	−2.89664	−	6.25032i	−0.0959173	−	0.206969i
$913$	−19.3517	−	43.7411i	−0.640448	−	1.44762i
$914$	−0.0615565	−	0.106619i	−0.00203611	−	0.00352664i
$915$	−3.96040	+	4.39847i	−0.130927	+	0.145409i
$916$	18.7874	−	8.36471i	0.620755	−	0.276378i
$917$	−11.1376	−	4.95877i	−0.367795	−	0.163753i
$918$	−4.35365	−	4.83522i	−0.143692	−	0.159586i
$919$	−10.5283	+	32.4027i	−0.347296	+	1.06887i	0.613048	+	0.790046i	$0.289943\pi$
$919$	−10.5283	+	32.4027i	−0.347296	+	1.06887i	−0.960343	+	0.278820i	$0.910057\pi$
$920$	1.36144	−	0.989141i	0.0448852	−	0.0326110i
$921$	35.8536	−	15.9630i	1.18142	−	0.526000i
$922$	1.10347	+	0.234551i	0.0363410	+	0.00772451i
$923$	−0.290182			−0.00955145
$924$	1.76150	−	8.19246i	0.0579493	−	0.269512i
$925$	16.6369	−	28.8160i	0.547019	−	0.947464i
$926$	11.7519	−	13.0518i	0.386192	−	0.428909i
$927$	−5.37011	+	2.39093i	−0.176378	+	0.0785284i
$928$	2.42371	+	1.07910i	0.0795620	+	0.0354233i
$929$	32.5655	−	6.92201i	1.06844	−	0.227104i	0.360055	−	0.932931i	$-0.382758\pi$
$929$	32.5655	−	6.92201i	1.06844	−	0.227104i	0.708384	+	0.705827i	$0.249424\pi$
$930$	0.283907	−	0.873775i	0.00930966	−	0.0286522i
$931$	0.292396	+	19.3699i	0.00958288	+	0.634822i
$932$	10.1700	+	7.38891i	0.333128	+	0.242032i
$933$	28.2767	−	31.4044i	0.925736	−	1.02813i
$934$	−20.6131	−	35.7029i	−0.674481	−	1.16824i
$935$	2.12504	−	4.74287i	0.0694961	−	0.155108i
$936$	−0.0123370	−	0.0213683i	−0.000403247	−	0.000698444i
$937$	−44.9961	−	9.56423i	−1.46996	−	0.312450i	−0.597790	−	0.801653i	$-0.703954\pi$
$937$	−44.9961	−	9.56423i	−1.46996	−	0.312450i	−0.872170	+	0.489203i	$0.837288\pi$
$938$	5.00039	+	3.63300i	0.163269	+	0.118622i
$939$	16.5230	−	12.0047i	0.539209	−	0.391758i
$940$	−1.70316	−	1.89155i	−0.0555509	−	0.0616955i
$941$	19.4382	+	21.5884i	0.633669	+	0.703761i	0.971391	−	0.237485i	$-0.0763231\pi$
$941$	19.4382	+	21.5884i	0.633669	+	0.703761i	−0.337722	+	0.941246i	$0.609656\pi$
$942$	23.9602	−	17.4081i	0.780665	−	0.567186i
$943$	−2.79073	−	2.02758i	−0.0908786	−	0.0660272i
$944$	−0.624713	−	0.132787i	−0.0203327	−	0.00432184i
$945$	5.89794	+	10.2155i	0.191860	+	0.332311i
$946$	−0.526711	+	0.302448i	−0.0171248	+	0.00983342i
$947$	8.80863	+	15.2570i	0.286242	+	0.495786i	0.972910	−	0.231186i	$-0.0742605\pi$
$947$	8.80863	+	15.2570i	0.286242	+	0.495786i	−0.686668	+	0.726972i	$0.740927\pi$
$948$	7.28649	−	8.09246i	0.236654	−	0.262831i
$949$	0.130232	+	0.0946190i	0.00422751	+	0.00307146i
$950$	−0.212044	−	14.0469i	−0.00687960	−	0.455742i
$951$	−3.55638	+	10.9454i	−0.115323	+	0.354929i
$952$	1.83816	−	0.390713i	0.0595752	−	0.0126631i
$953$	−41.9520	−	18.6782i	−1.35896	−	0.605047i	−0.407608	−	0.913157i	$-0.633637\pi$
$953$	−41.9520	−	18.6782i	−1.35896	−	0.605047i	−0.951351	+	0.308110i	$0.900304\pi$
$954$	1.78756	−	0.795871i	0.0578743	−	0.0257673i
$955$	−1.49331	+	1.65849i	−0.0483225	+	0.0536676i
$956$	−9.03496	+	15.6490i	−0.292211	+	0.506125i
$957$	−10.3564	+	9.28097i	−0.334776	+	0.300011i
$958$	−9.06355			−0.292830
$959$	−12.1900	−	2.59106i	−0.393634	−	0.0836695i
$960$	−1.92466	+	0.856912i	−0.0621180	+	0.0276567i
$961$	24.9257	−	18.1096i	0.804054	−	0.584179i
$962$	−0.156726	+	0.482352i	−0.00505304	+	0.0155516i
$963$	−1.53105	−	1.70040i	−0.0493373	−	0.0547946i
$964$	−5.24096	−	2.33343i	−0.168800	−	0.0751546i
$965$	24.8693	−	11.0725i	0.800571	−	0.356437i
$966$	−2.13419	+	2.37026i	−0.0686664	+	0.0762617i
$967$	−4.91597	−	8.51471i	−0.158087	−	0.273815i	0.776092	−	0.630620i	$-0.217199\pi$
$967$	−4.91597	−	8.51471i	−0.158087	−	0.273815i	−0.934179	+	0.356805i	$0.883866\pi$
$968$	7.39880	−	8.13989i	0.237806	−	0.261626i
$969$	3.40499	+	7.34722i	0.109384	+	0.236027i
$970$	−4.75169	−	14.6242i	−0.152568	−	0.469555i
$971$	4.58923	−	43.6637i	0.147276	−	1.40123i	−0.632202	−	0.774803i	$-0.717849\pi$
$971$	4.58923	−	43.6637i	0.147276	−	1.40123i	0.779478	−	0.626430i	$-0.215485\pi$
$972$	4.71519	+	2.09934i	0.151240	+	0.0673362i
$973$	−3.90515	−	4.33711i	−0.125193	−	0.139041i
$974$	−13.5826	+	2.88708i	−0.435216	+	0.0925080i
$975$	0.0261559	+	0.248857i	0.000837659	+	0.00796980i
$976$	−2.27281	−	1.65129i	−0.0727507	−	0.0528565i
$977$	0.750057	+	2.30844i	0.0239964	+	0.0738535i	0.962338	−	0.271857i	$-0.0876379\pi$
$977$	0.750057	+	2.30844i	0.0239964	+	0.0738535i	−0.938341	+	0.345711i	$0.887638\pi$
$978$	4.72206	−	8.17885i	0.150995	−	0.261531i
$979$	−8.74925	−	41.6432i	−0.279627	−	1.33092i
$980$	5.92446			0.189250
$981$	1.36767	+	4.20926i	0.0436664	+	0.134391i
$982$	−10.8187	+	4.81678i	−0.345237	+	0.153710i
$983$	−13.2074	−	5.88033i	−0.421252	−	0.187553i	0.185153	−	0.982710i	$-0.440722\pi$
$983$	−13.2074	−	5.88033i	−0.421252	−	0.187553i	−0.606404	+	0.795156i	$0.707389\pi$
$984$	2.88971	+	3.20935i	0.0921206	+	0.102310i
$985$	12.5544	−	2.66852i	0.400016	−	0.0850260i
$986$	−2.84905	−	1.26848i	−0.0907324	−	0.0403966i
$987$	3.90287	+	2.83560i	0.124230	+	0.0902581i
$988$	0.0476773	+	0.208759i	0.00151682	+	0.00664149i
$989$	0.231178			0.00735104
$990$	−0.00522147	+	2.22063i	−0.000165949	+	0.0705762i
$991$	30.8205	+	53.3826i	0.979045	+	1.69576i	0.665883	+	0.746056i	$0.268055\pi$
$991$	30.8205	+	53.3826i	0.979045	+	1.69576i	0.313162	+	0.949700i	$0.398612\pi$
$992$	0.426554	+	0.0906669i	0.0135431	+	0.00287868i
$993$	0.512830	−	4.87925i	0.0162742	−	0.154838i
$994$	0.987086	+	9.39150i	0.0313085	+	0.297880i
$995$	−1.64422	+	5.06039i	−0.0521253	+	0.160425i
$996$	7.04313	−	21.6765i	0.223170	−	0.686847i
$997$	−4.92434	−	46.8520i	−0.155955	−	1.48382i	−0.740281	−	0.672298i	$-0.765308\pi$
$997$	−4.92434	−	46.8520i	−0.155955	−	1.48382i	0.584326	−	0.811519i	$-0.301359\pi$
$998$	−28.3222	+	12.6099i	−0.896525	+	0.399159i
$999$	−17.6585	−	54.3473i	−0.558690	−	1.71947i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	418.2.n.d.159.2	yes	64
11.9	even	5	inner	418.2.n.d.273.7	yes	64
19.11	even	3	inner	418.2.n.d.49.7	✓	64
209.163	even	15	inner	418.2.n.d.163.2	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
418.2.n.d.49.7	✓	64	19.11	even	3	inner
418.2.n.d.159.2	yes	64	1.1	even	1	trivial
418.2.n.d.163.2	yes	64	209.163	even	15	inner
418.2.n.d.273.7	yes	64	11.9	even	5	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:	\( N \)	\(=\)	\( 418 = 2 \cdot 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	418.n (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.669131 + 0.743145i) q^{2} +(-0.165199 + 1.57177i) q^{3} +(-0.104528 - 0.994522i) q^{4} +(1.30393 - 0.277159i) q^{5} +(-1.05751 - 1.17448i) q^{6} +(1.29335 - 0.939674i) q^{7} +(0.809017 + 0.587785i) q^{8} +(0.491287 + 0.104426i) q^{9} +O(q^{10})\)	\(q+(-0.669131 + 0.743145i) q^{2} +(-0.165199 + 1.57177i) q^{3} +(-0.104528 - 0.994522i) q^{4} +(1.30393 - 0.277159i) q^{5} +(-1.05751 - 1.17448i) q^{6} +(1.29335 - 0.939674i) q^{7} +(0.809017 + 0.587785i) q^{8} +(0.491287 + 0.104426i) q^{9} +(-0.666530 + 1.15446i) q^{10} +(2.46994 - 2.21345i) q^{11} +1.58042 q^{12} +(-0.0480521 - 0.0102138i) q^{13} +(-0.167106 + 1.58991i) q^{14} +(0.220220 + 2.09526i) q^{15} +(-0.978148 + 0.207912i) q^{16} +(1.14981 - 0.244399i) q^{17} +(-0.406339 + 0.295223i) q^{18} +(4.12476 - 1.40939i) q^{19} +(-0.411938 - 1.26782i) q^{20} +(1.26329 + 2.18808i) q^{21} +(-0.00779852 + 3.31662i) q^{22} +(0.631190 - 1.09325i) q^{23} +(-1.05751 + 1.17448i) q^{24} +(-2.94431 + 1.31089i) q^{25} +(0.0397435 - 0.0288753i) q^{26} +(-1.71043 + 5.26415i) q^{27} +(-1.06972 - 1.18804i) q^{28} +(0.277322 + 2.63854i) q^{29} +(-1.70444 - 1.23835i) q^{30} +(0.134757 + 0.414740i) q^{31} +(0.500000 - 0.866025i) q^{32} +(3.07100 + 4.24783i) q^{33} +(-0.587747 + 1.01801i) q^{34} +(1.42600 - 1.58373i) q^{35} +(0.0525007 - 0.499511i) q^{36} +(-8.35232 + 6.06831i) q^{37} +(-1.71262 + 4.00836i) q^{38} +(0.0239919 - 0.0738394i) q^{39} +(1.21781 + 0.542204i) q^{40} +(0.285630 - 2.71759i) q^{41} +(-2.47136 - 0.525304i) q^{42} +(0.0915645 + 0.158594i) q^{43} +(-2.45951 - 2.22504i) q^{44} +0.669546 q^{45} +(0.390097 + 1.20059i) q^{46} +(1.74431 - 0.776618i) q^{47} +(-0.165199 - 1.57177i) q^{48} +(-1.37335 + 4.22674i) q^{49} +(0.995946 - 3.06521i) q^{50} +(0.194191 + 1.84760i) q^{51} +(-0.00513503 + 0.0488565i) q^{52} +(-3.81069 - 0.809986i) q^{53} +(-2.76753 - 4.79350i) q^{54} +(2.60716 - 3.57075i) q^{55} +1.59867 q^{56} +(1.53383 + 6.71598i) q^{57} +(-2.14638 - 1.55944i) q^{58} +(0.583453 + 0.259770i) q^{59} +(2.06076 - 0.438028i) q^{60} +(1.87982 + 2.08775i) q^{61} +(-0.398382 - 0.177371i) q^{62} +(0.733533 - 0.326590i) q^{63} +(0.309017 + 0.951057i) q^{64} -0.0654874 q^{65} +(-5.21165 - 0.560160i) q^{66} +(1.93312 - 3.34825i) q^{67} +(-0.363248 - 1.11796i) q^{68} +(1.61406 + 1.17269i) q^{69} +(0.222763 + 2.11945i) q^{70} +(5.77785 - 1.22812i) q^{71} +(0.336079 + 0.373254i) q^{72} +(-2.99352 - 1.33280i) q^{73} +(1.07916 - 10.2675i) q^{74} +(-1.57402 - 4.84433i) q^{75} +(-1.83283 - 3.95484i) q^{76} +(1.11458 - 5.18371i) q^{77} +(0.0388197 + 0.0672376i) q^{78} +(4.61047 - 5.12044i) q^{79} +(-1.21781 + 0.542204i) q^{80} +(-6.61493 - 2.94516i) q^{81} +(1.82844 + 2.03069i) q^{82} +(4.45649 - 13.7157i) q^{83} +(2.04404 - 1.48508i) q^{84} +(1.43153 - 0.637359i) q^{85} +(-0.179127 - 0.0380747i) q^{86} -4.19298 q^{87} +(3.29926 - 0.338925i) q^{88} +(6.41502 - 11.1111i) q^{89} +(-0.448014 + 0.497570i) q^{90} +(-0.0717459 + 0.0319433i) q^{91} +(-1.15324 - 0.513456i) q^{92} +(-0.674136 + 0.143292i) q^{93} +(-0.590033 + 1.81594i) q^{94} +(4.98777 - 2.98096i) q^{95} +(1.27859 + 0.928949i) q^{96} +(-7.71839 + 8.57214i) q^{97} +(-2.22213 - 3.84884i) q^{98} +(1.44459 - 0.829514i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q - 8 q^{2} - 6 q^{3} + 8 q^{4} - 7 q^{5} - 4 q^{6} + 22 q^{7} + 16 q^{8} + 14 q^{9}+O(q^{10}) \) 64 * q - 8 * q^2 - 6 * q^3 + 8 * q^4 - 7 * q^5 - 4 * q^6 + 22 * q^7 + 16 * q^8 + 14 * q^9	\( 64 q - 8 q^{2} - 6 q^{3} + 8 q^{4} - 7 q^{5} - 4 q^{6} + 22 q^{7} + 16 q^{8} + 14 q^{9} - 8 q^{10} - 6 q^{11} - 8 q^{12} + 9 q^{13} + 11 q^{14} + 9 q^{15} + 8 q^{16} - 2 q^{17} - 12 q^{18} + 4 q^{19} + 14 q^{20} - 36 q^{21} + 7 q^{22} + 8 q^{23} - 4 q^{24} + 31 q^{25} - 12 q^{26} + 54 q^{27} + 9 q^{28} + 18 q^{29} + 18 q^{30} + 20 q^{31} + 32 q^{32} + 10 q^{33} + 2 q^{34} - 16 q^{35} - 6 q^{36} + 18 q^{37} - 31 q^{38} + 2 q^{39} - 3 q^{40} + 16 q^{41} + 6 q^{42} + 42 q^{43} - 2 q^{44} - 8 q^{45} - 24 q^{46} - 34 q^{47} - 6 q^{48} - 10 q^{49} - 58 q^{50} - 40 q^{51} - 6 q^{52} + 15 q^{53} - 28 q^{54} + 49 q^{55} + 8 q^{56} + 8 q^{57} + 36 q^{58} - 7 q^{59} + 4 q^{60} - 15 q^{61} - 37 q^{63} - 16 q^{64} - 48 q^{65} - 10 q^{66} - 14 q^{67} + 4 q^{68} - 30 q^{69} - 19 q^{70} - 4 q^{71} - 14 q^{72} + 8 q^{73} + 9 q^{74} - 96 q^{75} - 10 q^{76} - 58 q^{77} + 46 q^{78} + 12 q^{79} + 3 q^{80} - 8 q^{81} + 4 q^{82} - 6 q^{83} - 48 q^{84} + 18 q^{85} + 3 q^{86} - 244 q^{87} + 6 q^{88} - 4 q^{89} - 9 q^{90} - 33 q^{91} + 8 q^{92} + 3 q^{93} + 62 q^{94} - 49 q^{95} - 12 q^{96} - 15 q^{97} - 4 q^{99}+O(q^{100}) \) 64 * q - 8 * q^2 - 6 * q^3 + 8 * q^4 - 7 * q^5 - 4 * q^6 + 22 * q^7 + 16 * q^8 + 14 * q^9 - 8 * q^10 - 6 * q^11 - 8 * q^12 + 9 * q^13 + 11 * q^14 + 9 * q^15 + 8 * q^16 - 2 * q^17 - 12 * q^18 + 4 * q^19 + 14 * q^20 - 36 * q^21 + 7 * q^22 + 8 * q^23 - 4 * q^24 + 31 * q^25 - 12 * q^26 + 54 * q^27 + 9 * q^28 + 18 * q^29 + 18 * q^30 + 20 * q^31 + 32 * q^32 + 10 * q^33 + 2 * q^34 - 16 * q^35 - 6 * q^36 + 18 * q^37 - 31 * q^38 + 2 * q^39 - 3 * q^40 + 16 * q^41 + 6 * q^42 + 42 * q^43 - 2 * q^44 - 8 * q^45 - 24 * q^46 - 34 * q^47 - 6 * q^48 - 10 * q^49 - 58 * q^50 - 40 * q^51 - 6 * q^52 + 15 * q^53 - 28 * q^54 + 49 * q^55 + 8 * q^56 + 8 * q^57 + 36 * q^58 - 7 * q^59 + 4 * q^60 - 15 * q^61 - 37 * q^63 - 16 * q^64 - 48 * q^65 - 10 * q^66 - 14 * q^67 + 4 * q^68 - 30 * q^69 - 19 * q^70 - 4 * q^71 - 14 * q^72 + 8 * q^73 + 9 * q^74 - 96 * q^75 - 10 * q^76 - 58 * q^77 + 46 * q^78 + 12 * q^79 + 3 * q^80 - 8 * q^81 + 4 * q^82 - 6 * q^83 - 48 * q^84 + 18 * q^85 + 3 * q^86 - 244 * q^87 + 6 * q^88 - 4 * q^89 - 9 * q^90 - 33 * q^91 + 8 * q^92 + 3 * q^93 + 62 * q^94 - 49 * q^95 - 12 * q^96 - 15 * q^97 - 4 * q^99

Introduction

L-functions

Modular forms

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