LMFDB - Embedded newform 225.2.q.a.121.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [225,2,Mod(16,225)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(225, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([20, 6]))

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

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

chi := DirichletCharacter("225.16");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 225 = 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	225.q (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:	$1.79663404548$
Analytic rank:	$0$
Dimension:	$224$
Relative dimension:	$28$ over $\Q(\zeta_{15})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			121.20
Character	$\chi$	$=$	225.121
Dual form			225.2.q.a.106.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.37843 - 0.292995i) q^{2} +(1.63456 + 0.572891i) q^{3} +(-0.0128554 + 0.00572357i) q^{4} +(1.56242 + 1.59963i) q^{5} +(2.42099 + 0.310774i) q^{6} +(-2.48652 - 4.30678i) q^{7} +(-2.29622 + 1.66830i) q^{8} +(2.34359 + 1.87285i) q^{9} +O(q^{10})$	\(q+(1.37843 - 0.292995i) q^{2} +(1.63456 + 0.572891i) q^{3} +(-0.0128554 + 0.00572357i) q^{4} +(1.56242 + 1.59963i) q^{5} +(2.42099 + 0.310774i) q^{6} +(-2.48652 - 4.30678i) q^{7} +(-2.29622 + 1.66830i) q^{8} +(2.34359 + 1.87285i) q^{9} +(2.62239 + 1.74721i) q^{10} +(3.07362 - 0.653319i) q^{11} +(-0.0242919 + 0.00199082i) q^{12} +(-1.44657 - 0.307478i) q^{13} +(-4.68937 - 5.20807i) q^{14} +(1.63747 + 3.50980i) q^{15} +(-2.65756 + 2.95152i) q^{16} +(-2.39081 + 1.73703i) q^{17} +(3.77922 + 1.89494i) q^{18} +(-1.51211 + 1.09861i) q^{19} +(-0.0292411 - 0.0116212i) q^{20} +(-1.59706 - 8.46420i) q^{21} +(4.04537 - 1.80111i) q^{22} +(-4.45542 - 4.94825i) q^{23} +(-4.70908 + 1.41146i) q^{24} +(-0.117657 + 4.99862i) q^{25} -2.08409 q^{26} +(2.75781 + 4.40392i) q^{27} +(0.0566152 + 0.0411334i) q^{28} +(0.427253 - 4.06504i) q^{29} +(3.28549 + 4.35826i) q^{30} +(-0.681027 - 6.47954i) q^{31} +(0.0398007 - 0.0689368i) q^{32} +(5.39831 + 0.692961i) q^{33} +(-2.78664 + 3.09487i) q^{34} +(3.00427 - 10.7065i) q^{35} +(-0.0408471 - 0.0106625i) q^{36} +(1.50355 + 4.62746i) q^{37} +(-1.76246 + 1.95741i) q^{38} +(-2.18836 - 1.33132i) q^{39} +(-6.25636 - 1.06652i) q^{40} +(2.38999 + 0.508007i) q^{41} +(-4.68141 - 11.1994i) q^{42} +(-1.92193 - 3.32888i) q^{43} +(-0.0357732 + 0.0259908i) q^{44} +(0.665807 + 6.67508i) q^{45} +(-7.59132 - 5.51542i) q^{46} +(-0.175217 + 1.66708i) q^{47} +(-6.03484 + 3.30195i) q^{48} +(-8.86554 + 15.3556i) q^{49} +(1.30239 + 6.92474i) q^{50} +(-4.90306 + 1.46960i) q^{51} +(0.0203561 - 0.00432682i) q^{52} +(0.228304 + 0.165873i) q^{53} +(5.09178 + 5.26249i) q^{54} +(5.84738 + 3.89591i) q^{55} +(12.8946 + 5.74105i) q^{56} +(-3.10103 + 0.929477i) q^{57} +(-0.602097 - 5.72857i) q^{58} +(2.95891 + 0.628937i) q^{59} +(-0.0411388 - 0.0357476i) q^{60} +(7.58789 - 1.61286i) q^{61} +(-2.83723 - 8.73208i) q^{62} +(2.23857 - 14.7502i) q^{63} +(2.48928 - 7.66123i) q^{64} +(-1.76831 - 2.79440i) q^{65} +(7.64425 - 0.626479i) q^{66} +(1.19291 + 11.3498i) q^{67} +(0.0207927 - 0.0360141i) q^{68} +(-4.44786 - 10.6407i) q^{69} +(1.00422 - 15.6385i) q^{70} +(13.0547 + 9.48483i) q^{71} +(-8.50590 - 0.390666i) q^{72} +(-2.03962 + 6.27730i) q^{73} +(3.42837 + 5.93811i) q^{74} +(-3.05598 + 8.10315i) q^{75} +(0.0131507 - 0.0227777i) q^{76} +(-10.4563 - 11.6129i) q^{77} +(-3.40658 - 1.19396i) q^{78} +(-0.847007 + 8.05873i) q^{79} +(-8.87358 + 0.360405i) q^{80} +(1.98484 + 8.77841i) q^{81} +3.44328 q^{82} +(-8.79712 - 3.91673i) q^{83} +(0.0689762 + 0.0996694i) q^{84} +(-6.51407 - 1.11045i) q^{85} +(-3.62460 - 4.02553i) q^{86} +(3.02720 - 6.39979i) q^{87} +(-5.96780 + 6.62791i) q^{88} +(0.845142 - 2.60108i) q^{89} +(2.87354 + 9.00608i) q^{90} +(2.27269 + 6.99461i) q^{91} +(0.0855977 + 0.0381106i) q^{92} +(2.59889 - 10.9814i) q^{93} +(0.246921 + 2.34930i) q^{94} +(-4.11994 - 0.702323i) q^{95} +(0.104550 - 0.0898801i) q^{96} +(1.02725 - 9.77359i) q^{97} +(-7.72146 + 23.7642i) q^{98} +(8.42689 + 4.22533i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 224 q - 3 q^{2} - 8 q^{3} + 23 q^{4} - 8 q^{5} - 10 q^{6} - 8 q^{7} - 20 q^{8} - 8 q^{9}+O(q^{10}) $ 224 * q - 3 * q^2 - 8 * q^3 + 23 * q^4 - 8 * q^5 - 10 * q^6 - 8 * q^7 - 20 * q^8 - 8 * q^9	\( 224 q - 3 q^{2} - 8 q^{3} + 23 q^{4} - 8 q^{5} - 10 q^{6} - 8 q^{7} - 20 q^{8} - 8 q^{9} - 20 q^{10} - 11 q^{11} - 4 q^{12} - 3 q^{13} + q^{14} - 48 q^{15} + 23 q^{16} - 24 q^{17} - 12 q^{19} + q^{20} + 15 q^{21} - 11 q^{22} + q^{23} - 30 q^{24} - 16 q^{25} - 136 q^{26} + 7 q^{27} + 4 q^{28} - 15 q^{29} - 24 q^{30} + 3 q^{31} + 12 q^{32} - 5 q^{33} + q^{34} + 14 q^{35} + 38 q^{36} - 24 q^{37} + 55 q^{38} + 20 q^{39} + q^{40} - 19 q^{41} - 38 q^{42} - 8 q^{43} + 4 q^{44} - 38 q^{45} - 20 q^{46} - 10 q^{47} - 25 q^{48} - 72 q^{49} - 3 q^{50} - 26 q^{51} - 25 q^{52} - 12 q^{53} + 53 q^{54} - 20 q^{55} - 60 q^{56} + 38 q^{57} - 23 q^{58} - 30 q^{59} - 33 q^{60} - 3 q^{61} - 44 q^{62} + 46 q^{63} - 44 q^{64} + 51 q^{65} - 134 q^{66} - 12 q^{67} - 156 q^{68} + 4 q^{69} - 16 q^{70} + 42 q^{71} + 74 q^{72} - 12 q^{73} + 90 q^{74} + 67 q^{75} - 8 q^{76} + 31 q^{77} - 92 q^{78} - 15 q^{79} + 298 q^{80} - 104 q^{81} + 8 q^{82} + 59 q^{83} + 115 q^{84} - 11 q^{85} + 9 q^{86} - 59 q^{87} - 23 q^{88} + 106 q^{89} + 107 q^{90} + 30 q^{91} + 11 q^{92} + 32 q^{93} + 25 q^{94} + 7 q^{95} + 35 q^{96} - 21 q^{97} + 146 q^{98} - 20 q^{99}+O(q^{100}) \) 224 * q - 3 * q^2 - 8 * q^3 + 23 * q^4 - 8 * q^5 - 10 * q^6 - 8 * q^7 - 20 * q^8 - 8 * q^9 - 20 * q^10 - 11 * q^11 - 4 * q^12 - 3 * q^13 + q^14 - 48 * q^15 + 23 * q^16 - 24 * q^17 - 12 * q^19 + q^20 + 15 * q^21 - 11 * q^22 + q^23 - 30 * q^24 - 16 * q^25 - 136 * q^26 + 7 * q^27 + 4 * q^28 - 15 * q^29 - 24 * q^30 + 3 * q^31 + 12 * q^32 - 5 * q^33 + q^34 + 14 * q^35 + 38 * q^36 - 24 * q^37 + 55 * q^38 + 20 * q^39 + q^40 - 19 * q^41 - 38 * q^42 - 8 * q^43 + 4 * q^44 - 38 * q^45 - 20 * q^46 - 10 * q^47 - 25 * q^48 - 72 * q^49 - 3 * q^50 - 26 * q^51 - 25 * q^52 - 12 * q^53 + 53 * q^54 - 20 * q^55 - 60 * q^56 + 38 * q^57 - 23 * q^58 - 30 * q^59 - 33 * q^60 - 3 * q^61 - 44 * q^62 + 46 * q^63 - 44 * q^64 + 51 * q^65 - 134 * q^66 - 12 * q^67 - 156 * q^68 + 4 * q^69 - 16 * q^70 + 42 * q^71 + 74 * q^72 - 12 * q^73 + 90 * q^74 + 67 * q^75 - 8 * q^76 + 31 * q^77 - 92 * q^78 - 15 * q^79 + 298 * q^80 - 104 * q^81 + 8 * q^82 + 59 * q^83 + 115 * q^84 - 11 * q^85 + 9 * q^86 - 59 * q^87 - 23 * q^88 + 106 * q^89 + 107 * q^90 + 30 * q^91 + 11 * q^92 + 32 * q^93 + 25 * q^94 + 7 * q^95 + 35 * q^96 - 21 * q^97 + 146 * q^98 - 20 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/225\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{3}{5}\right)$

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 $

$2$	1.37843	−	0.292995i	0.974700	−	0.207179i	0.307082	−	0.951683i	$-0.400647\pi$
$2$	1.37843	−	0.292995i	0.974700	−	0.207179i	0.667618	+	0.744504i	$0.267314\pi$
$3$	1.63456	+	0.572891i	0.943715	+	0.330759i
$3$	1.63456	+	0.572891i	0.943715	+	0.330759i
$4$	−0.0128554	+	0.00572357i	−0.00642768	+	0.00286179i
$5$	1.56242	+	1.59963i	0.698738	+	0.715378i
$5$	1.56242	+	1.59963i	0.698738	+	0.715378i
$6$	2.42099	+	0.310774i	0.988366	+	0.126873i
$7$	−2.48652	−	4.30678i	−0.939815	−	1.62781i	−0.765813	−	0.643063i	$-0.777663\pi$
$7$	−2.48652	−	4.30678i	−0.939815	−	1.62781i	−0.174002	−	0.984745i	$-0.555670\pi$
$8$	−2.29622	+	1.66830i	−0.811838	+	0.589835i
$9$	2.34359	+	1.87285i	0.781197	+	0.624284i
$10$	2.62239	+	1.74721i	0.829271	+	0.552515i
$11$	3.07362	−	0.653319i	0.926732	−	0.196983i	0.280263	−	0.959923i	$-0.409578\pi$
$11$	3.07362	−	0.653319i	0.926732	−	0.196983i	0.646469	+	0.762940i	$0.276245\pi$
$12$	−0.0242919	+	0.00199082i	−0.00701246	+	0.000574701i
$13$	−1.44657	−	0.307478i	−0.401207	−	0.0852791i	0.00288893	−	0.999996i	$-0.499080\pi$
$13$	−1.44657	−	0.307478i	−0.401207	−	0.0852791i	−0.404096	+	0.914717i	$0.632414\pi$
$14$	−4.68937	−	5.20807i	−1.25329	−	1.39192i
$15$	1.63747	+	3.50980i	0.422792	+	0.906227i
$16$	−2.65756	+	2.95152i	−0.664389	+	0.737879i
$17$	−2.39081	+	1.73703i	−0.579857	+	0.421291i	−0.838672	−	0.544636i	$-0.816668\pi$
$17$	−2.39081	+	1.73703i	−0.579857	+	0.421291i	0.258816	+	0.965927i	$0.416668\pi$
$18$	3.77922	+	1.89494i	0.890772	+	0.446643i
$19$	−1.51211	+	1.09861i	−0.346902	+	0.252039i	−0.747568	−	0.664185i	$-0.768779\pi$
$19$	−1.51211	+	1.09861i	−0.346902	+	0.252039i	0.400666	+	0.916224i	$0.368779\pi$
$20$	−0.0292411	−	0.0116212i	−0.00653852	−	0.00259858i
$21$	−1.59706	−	8.46420i	−0.348506	−	1.84704i
$22$	4.04537	−	1.80111i	0.862476	−	0.383999i
$23$	−4.45542	−	4.94825i	−0.929020	−	1.03178i	−0.999413	−	0.0342618i	$-0.989092\pi$
$23$	−4.45542	−	4.94825i	−0.929020	−	1.03178i	0.0703930	−	0.997519i	$-0.477575\pi$
$24$	−4.70908	+	1.41146i	−0.961237	+	0.288114i
$25$	−0.117657	+	4.99862i	−0.0235313	+	0.999723i
$26$	−2.08409			−0.408725
$27$	2.75781	+	4.40392i	0.530740	+	0.847535i
$28$	0.0566152	+	0.0411334i	0.0106993	+	0.00777347i
$29$	0.427253	−	4.06504i	0.0793388	−	0.754859i	−0.880451	−	0.474138i	$-0.842760\pi$
$29$	0.427253	−	4.06504i	0.0793388	−	0.754859i	0.959789	−	0.280721i	$-0.0905735\pi$
$30$	3.28549	+	4.35826i	0.599847	+	0.795706i
$31$	−0.681027	−	6.47954i	−0.122316	−	1.16376i	−0.867687	−	0.497110i	$-0.834394\pi$
$31$	−0.681027	−	6.47954i	−0.122316	−	1.16376i	0.745371	−	0.666649i	$-0.232272\pi$
$32$	0.0398007	−	0.0689368i	0.00703584	−	0.0121864i
$33$	5.39831	+	0.692961i	0.939725	+	0.120629i
$34$	−2.78664	+	3.09487i	−0.477904	+	0.530766i
$35$	3.00427	−	10.7065i	0.507814	−	1.80973i
$36$	−0.0408471	−	0.0106625i	−0.00680785	−	0.00177708i
$37$	1.50355	+	4.62746i	0.247182	+	0.760749i	0.995270	+	0.0971489i	$0.0309723\pi$
$37$	1.50355	+	4.62746i	0.247182	+	0.760749i	−0.748088	+	0.663600i	$0.769028\pi$
$38$	−1.76246	+	1.95741i	−0.285908	+	0.317533i
$39$	−2.18836	−	1.33132i	−0.350418	−	0.213182i
$40$	−6.25636	−	1.06652i	−0.989217	−	0.168631i
$41$	2.38999	+	0.508007i	0.373253	+	0.0793374i	0.390719	−	0.920510i	$-0.372226\pi$
$41$	2.38999	+	0.508007i	0.373253	+	0.0793374i	−0.0174658	+	0.999847i	$0.505560\pi$
$42$	−4.68141	−	11.1994i	−0.722357	−	1.72811i
$43$	−1.92193	−	3.32888i	−0.293091	−	0.507649i	0.681448	−	0.731867i	$-0.261351\pi$
$43$	−1.92193	−	3.32888i	−0.293091	−	0.507649i	−0.974539	+	0.224218i	$0.928017\pi$
$44$	−0.0357732	+	0.0259908i	−0.00539301	+	0.00391825i
$45$	0.665807	+	6.67508i	0.0992527	+	0.995062i
$46$	−7.59132	−	5.51542i	−1.11928	−	0.813204i
$47$	−0.175217	+	1.66708i	−0.0255581	+	0.243169i	0.974283	+	0.225329i	$0.0723456\pi$
$47$	−0.175217	+	1.66708i	−0.0255581	+	0.243169i	−0.999841	+	0.0178399i	$0.994321\pi$
$48$	−6.03484	+	3.30195i	−0.871055	+	0.476595i
$49$	−8.86554	+	15.3556i	−1.26651	+	2.19365i
$50$	1.30239	+	6.92474i	0.184186	+	0.979306i
$51$	−4.90306	+	1.46960i	−0.686565	+	0.205786i
$52$	0.0203561	−	0.00432682i	0.00282288	−	0.000600021i
$53$	0.228304	+	0.165873i	0.0313600	+	0.0227844i	0.603355	−	0.797473i	$-0.293830\pi$
$53$	0.228304	+	0.165873i	0.0313600	+	0.0227844i	−0.571995	+	0.820257i	$0.693830\pi$
$54$	5.09178	+	5.26249i	0.692904	+	0.716134i
$55$	5.84738	+	3.89591i	0.788460	+	0.525324i
$56$	12.8946	+	5.74105i	1.72312	+	0.767181i
$57$	−3.10103	+	0.929477i	−0.410741	+	0.123112i
$58$	−0.602097	−	5.72857i	−0.0790592	−	0.752198i
$59$	2.95891	+	0.628937i	0.385218	+	0.0818806i	0.396450	−	0.918056i	$-0.370242\pi$
$59$	2.95891	+	0.628937i	0.385218	+	0.0818806i	−0.0112321	+	0.999937i	$0.503575\pi$
$60$	−0.0411388	−	0.0357476i	−0.00531100	−	0.00461499i
$61$	7.58789	−	1.61286i	0.971530	−	0.206505i	0.305304	−	0.952255i	$-0.401242\pi$
$61$	7.58789	−	1.61286i	0.971530	−	0.206505i	0.666226	+	0.745750i	$0.267909\pi$
$62$	−2.83723	−	8.73208i	−0.360328	−	1.10898i
$63$	2.23857	−	14.7502i	0.282034	−	1.85835i
$64$	2.48928	−	7.66123i	0.311161	−	0.957654i
$65$	−1.76831	−	2.79440i	−0.219332	−	0.346602i
$66$	7.64425	−	0.626479i	0.940943	−	0.0771142i
$67$	1.19291	+	11.3498i	0.145738	+	1.38660i	0.785896	+	0.618358i	$0.212202\pi$
$67$	1.19291	+	11.3498i	0.145738	+	1.38660i	−0.640158	+	0.768243i	$0.721131\pi$
$68$	0.0207927	−	0.0360141i	0.00252149	−	0.00436735i
$69$	−4.44786	−	10.6407i	−0.535460	−	1.28099i
$70$	1.00422	−	15.6385i	0.120027	−	1.86916i
$71$	13.0547	+	9.48483i	1.54931	+	1.12564i	0.944138	+	0.329550i	$0.106897\pi$
$71$	13.0547	+	9.48483i	1.54931	+	1.12564i	0.605175	+	0.796092i	$0.293103\pi$
$72$	−8.50590	−	0.390666i	−1.00243	−	0.0460404i
$73$	−2.03962	+	6.27730i	−0.238719	+	0.734703i	0.757887	+	0.652386i	$0.226232\pi$
$73$	−2.03962	+	6.27730i	−0.238719	+	0.734703i	−0.996606	+	0.0823167i	$0.973768\pi$
$74$	3.42837	+	5.93811i	0.398540	+	0.690291i
$75$	−3.05598	+	8.10315i	−0.352874	+	0.935671i
$76$	0.0131507	−	0.0227777i	0.00150849	−	0.00261278i
$77$	−10.4563	−	11.6129i	−1.19161	−	1.32341i
$78$	−3.40658	−	1.19396i	−0.385720	−	0.135189i
$79$	−0.847007	+	8.05873i	−0.0952957	+	0.906678i	0.837540	+	0.546376i	$0.183993\pi$
$79$	−0.847007	+	8.05873i	−0.0952957	+	0.906678i	−0.932836	+	0.360302i	$0.882674\pi$
$80$	−8.87358	+	0.360405i	−0.992097	+	0.0402944i
$81$	1.98484	+	8.77841i	0.220538	+	0.975378i
$82$	3.44328			0.380247
$83$	−8.79712	−	3.91673i	−0.965609	−	0.429917i	−0.137511	−	0.990500i	$-0.543910\pi$
$83$	−8.79712	−	3.91673i	−0.965609	−	0.429917i	−0.828098	+	0.560583i	$0.810577\pi$
$84$	0.0689762	+	0.0996694i	0.00752592	+	0.0108748i
$85$	−6.51407	−	1.11045i	−0.706550	−	0.120445i
$86$	−3.62460	−	4.02553i	−0.390851	−	0.434084i
$87$	3.02720	−	6.39979i	0.324549	−	0.686130i
$88$	−5.96780	+	6.62791i	−0.636169	+	0.706537i
$89$	0.845142	−	2.60108i	0.0895849	−	0.275714i	−0.896220	−	0.443610i	$-0.853697\pi$
$89$	0.845142	−	2.60108i	0.0895849	−	0.275714i	0.985805	+	0.167896i	$0.0536974\pi$
$90$	2.87354	+	9.00608i	0.302898	+	0.949325i
$91$	2.27269	+	6.99461i	0.238242	+	0.733234i
$92$	0.0855977	+	0.0381106i	0.00892418	+	0.00397330i
$93$	2.59889	−	10.9814i	0.269492	−	1.13871i
$94$	0.246921	+	2.34930i	0.0254680	+	0.242312i
$95$	−4.11994	−	0.702323i	−0.422697	−	0.0720569i
$96$	0.104550	−	0.0898801i	0.0106706	−	0.00917335i
$97$	1.02725	−	9.77359i	0.104301	−	0.992358i	−0.809755	−	0.586769i	$-0.800400\pi$
$97$	1.02725	−	9.77359i	0.104301	−	0.992358i	0.914056	−	0.405589i	$-0.132934\pi$
$98$	−7.72146	+	23.7642i	−0.779985	+	2.40055i
$99$	8.42689	+	4.22533i	0.846934	+	0.424662i
$100$	−0.0270974	−	0.0649324i	−0.00270974	−	0.00649324i
$101$	−3.76987	−	6.52961i	−0.375116	−	0.649720i	0.615228	−	0.788349i	$-0.289064\pi$
$101$	−3.76987	−	6.52961i	−0.375116	−	0.649720i	−0.990344	+	0.138629i	$0.955731\pi$
$102$	−6.32795	+	3.46232i	−0.626561	+	0.342821i
$103$	0.282302	−	0.125689i	0.0278161	−	0.0123845i	−0.392781	−	0.919632i	$-0.628487\pi$
$103$	0.282302	−	0.125689i	0.0278161	−	0.0123845i	0.420598	+	0.907247i	$0.361820\pi$
$104$	3.83462	−	1.70728i	0.376016	−	0.167413i
$105$	11.0443	−	15.7794i	1.07782	−	1.53991i
$106$	0.363303	+	0.161753i	0.0352871	+	0.0157108i
$107$	10.6092			1.02563			0.512814	−	0.858500i	$-0.328603\pi$
$107$	10.6092			1.02563			0.512814	+	0.858500i	$0.328603\pi$
$108$	−0.0606587	−	0.0408294i	−0.00583689	−	0.00392881i
$109$	2.72546	+	8.38810i	0.261052	+	0.803434i	0.992577	+	0.121620i	$0.0388088\pi$
$109$	2.72546	+	8.38810i	0.261052	+	0.803434i	−0.731525	+	0.681814i	$0.761191\pi$
$110$	9.20171	+	3.65700i	0.877349	+	0.348682i
$111$	−0.193379	+	8.42524i	−0.0183547	+	0.799688i
$112$	19.3196	+	4.10651i	1.82553	+	0.388028i
$113$	8.58747	+	1.82532i	0.807841	+	0.171712i	0.593277	−	0.804998i	$-0.297834\pi$
$113$	8.58747	+	1.82532i	0.807841	+	0.171712i	0.214564	+	0.976710i	$0.431167\pi$
$114$	−4.00223	+	2.18981i	−0.374843	+	0.205094i
$115$	0.954121	−	14.8583i	0.0889723	−	1.38554i
$116$	0.0177741	+	0.0547029i	0.00165028	+	0.00507904i
$117$	−2.81431	−	3.42982i	−0.260183	−	0.317087i
$118$	4.26294			0.392436
$119$	13.4258	+	5.97754i	1.23074	+	0.547960i
$120$	−9.61541	−	5.32750i	−0.877763	−	0.486332i
$121$	−1.02866	+	0.457990i	−0.0935148	+	0.0416355i
$122$	9.98685	−	4.44643i	0.904167	−	0.402561i
$123$	3.61555	+	2.19957i	0.326003	+	0.198329i
$124$	0.0458410	+	0.0793989i	0.00411664	+	0.00713023i
$125$	−8.17978	+	7.62175i	−0.731622	+	0.681710i
$126$	−1.23601	−	20.9881i	−0.110113	−	1.86977i
$127$	2.46680	−	7.59204i	0.218894	−	0.673685i	−0.779961	−	0.625829i	$-0.784761\pi$
$127$	2.46680	−	7.59204i	0.218894	−	0.673685i	0.998854	−	0.0478565i	$-0.0152390\pi$
$128$	1.16997	−	11.1315i	0.103412	−	0.983897i
$129$	−1.23443	−	6.54232i	−0.108685	−	0.576019i
$130$	−3.25624	−	3.33379i	−0.285591	−	0.292393i
$131$	−1.14556	−	10.8993i	−0.100088	−	0.952277i	−0.923180	−	0.384368i	$-0.874419\pi$
$131$	−1.14556	−	10.8993i	−0.100088	−	0.952277i	0.823091	−	0.567909i	$-0.192247\pi$
$132$	−0.0733634	+	0.0219894i	−0.00638547	+	0.00191393i
$133$	8.49137	+	3.78060i	0.736295	+	0.327820i
$134$	4.96980	+	15.2955i	0.429325	+	1.32133i
$135$	−2.73579	+	11.2923i	−0.235459	+	0.971884i
$136$	2.59195	−	7.97720i	0.222258	−	0.684039i
$137$	−4.60452	+	5.11383i	−0.393390	+	0.436904i	−0.907007	−	0.421115i	$-0.861639\pi$
$137$	−4.60452	+	5.11383i	−0.393390	+	0.436904i	0.513617	+	0.858020i	$0.328305\pi$
$138$	−9.24876	−	13.3643i	−0.787307	−	1.13764i
$139$	5.05979	+	5.61946i	0.429166	+	0.476637i	0.918478	−	0.395472i	$-0.129419\pi$
$139$	5.05979	+	5.61946i	0.429166	+	0.476637i	−0.489313	+	0.872109i	$0.662752\pi$
$140$	0.0226587	+	0.154831i	0.00191501	+	0.0130856i
$141$	−1.24146	+	2.62457i	−0.104550	+	0.221028i
$142$	20.7741	+	9.24924i	1.74333	+	0.776179i
$143$	−4.64710			−0.388610
$144$	−11.7560	+	1.93994i	−0.979666	+	0.161661i
$145$	7.17012	−	5.66787i	0.595446	−	0.470691i
$146$	−0.972262	+	9.25045i	−0.0804649	+	0.765573i
$147$	−23.2884	+	20.0207i	−1.92079	+	1.65128i
$148$	−0.0458143	−	0.0508819i	−0.00376591	−	0.00418247i
$149$	7.49125	−	12.9752i	0.613707	−	1.06297i	−0.376903	−	0.926253i	$-0.623011\pi$
$149$	7.49125	−	12.9752i	0.613707	−	1.06297i	0.990610	−	0.136719i	$-0.0436558\pi$
$150$	−1.83828	+	12.0650i	−0.150095	+	0.985107i
$151$	2.80456	+	4.85765i	0.228232	+	0.395310i	0.957284	−	0.289149i	$-0.0933722\pi$
$151$	2.80456	+	4.85765i	0.228232	+	0.395310i	−0.729052	+	0.684458i	$0.760039\pi$
$152$	1.63932	−	5.04532i	0.132967	−	0.409230i
$153$	−8.85628	−	0.406758i	−0.715987	−	0.0328845i
$154$	−17.8159	−	12.9440i	−1.43564	−	1.04306i
$155$	9.30084	−	11.2132i	0.747061	−	0.900665i
$156$	0.0357521	+	0.00458936i	0.00286246	+	0.000367443i
$157$	7.68556	−	13.3118i	0.613374	−	1.06240i	−0.377293	−	0.926094i	$-0.623145\pi$
$157$	7.68556	−	13.3118i	0.613374	−	1.06240i	0.990667	−	0.136302i	$-0.0435216\pi$
$158$	1.19363	+	11.3566i	0.0949599	+	0.903483i
$159$	0.278151	+	0.401923i	0.0220588	+	0.0318746i
$160$	0.172459	−	0.0440421i	0.0136341	−	0.00348183i
$161$	−10.2325	+	31.4924i	−0.806434	+	2.48195i
$162$	5.30801	+	11.5189i	0.417036	+	0.905011i
$163$	−6.69457	−	20.6038i	−0.524359	−	1.61381i	−0.765580	−	0.643341i	$-0.777548\pi$
$163$	−6.69457	−	20.6038i	−0.524359	−	1.61381i	0.241221	−	0.970470i	$-0.422452\pi$
$164$	−0.0336317	+	0.00714865i	−0.00262620	+	0.000558215i
$165$	7.32597	+	9.71802i	0.570326	+	0.756547i
$166$	−13.2738	−	2.82144i	−1.03025	−	0.218986i
$167$	1.72511	+	16.4133i	0.133493	+	1.27010i	0.832113	+	0.554607i	$0.187131\pi$
$167$	1.72511	+	16.4133i	0.133493	+	1.27010i	−0.698620	+	0.715493i	$0.746202\pi$
$168$	17.7881	+	16.7713i	1.37238	+	1.29394i
$169$	−9.87806	−	4.39800i	−0.759851	−	0.338307i
$170$	−9.30457	+	0.377909i	−0.713628	+	0.0289843i
$171$	−5.60131	−	0.257262i	−0.428343	−	0.0196733i
$172$	0.0437602	+	0.0317936i	0.00333668	+	0.00242424i
$173$	−11.8161	+	2.51159i	−0.898360	+	0.190952i	−0.633873	−	0.773437i	$-0.718536\pi$
$173$	−11.8161	+	2.51159i	−0.898360	+	0.190952i	−0.264487	+	0.964389i	$0.585203\pi$
$174$	2.29768	−	9.70865i	0.174187	−	0.736011i
$175$	21.8205	−	11.9224i	1.64947	−	0.901251i
$176$	−6.24005	+	10.8081i	−0.470362	+	0.814690i
$177$	4.47622	+	2.72317i	0.336453	+	0.204686i
$178$	0.402869	−	3.83304i	0.0301963	−	0.287299i
$179$	−10.7597	−	7.81740i	−0.804220	−	0.584300i	0.107929	−	0.994159i	$-0.465578\pi$
$179$	−10.7597	−	7.81740i	−0.804220	−	0.584300i	−0.912149	+	0.409859i	$0.865578\pi$
$180$	−0.0467645	−	0.0819997i	−0.00348562	−	0.00611190i
$181$	−16.9365	+	12.3051i	−1.25888	+	0.914629i	−0.998702	−	0.0509324i	$-0.983781\pi$
$181$	−16.9365	+	12.3051i	−1.25888	+	0.914629i	−0.260176	+	0.965561i	$0.583781\pi$
$182$	5.18214	+	8.97573i	0.384126	+	0.665325i
$183$	13.3269	+	1.71072i	0.985151	+	0.126460i
$184$	18.4858	+	3.92929i	1.36279	+	0.289671i
$185$	−5.05305	+	9.63518i	−0.371507	+	0.708393i
$186$	0.364909	−	15.8986i	0.0267564	−	1.16574i
$187$	−6.21362	+	6.90092i	−0.454385	+	0.504646i
$188$	−0.00728918	−	0.0224338i	−0.000531618	−	0.00163615i
$189$	12.1094	−	22.8277i	0.880826	−	1.66047i
$190$	−5.88484	+	0.239016i	−0.426931	+	0.0173400i
$191$	−3.24560	+	3.60461i	−0.234844	+	0.260820i	−0.849035	−	0.528337i	$-0.822816\pi$
$191$	−3.24560	+	3.60461i	−0.234844	+	0.260820i	0.614191	+	0.789157i	$0.289482\pi$
$192$	8.45794	−	11.0967i	0.610399	−	0.800833i
$193$	1.77174	−	3.06874i	0.127533	−	0.220893i	−0.795187	−	0.606364i	$-0.792628\pi$
$193$	1.77174	−	3.06874i	0.127533	−	0.220893i	0.922720	+	0.385471i	$0.125961\pi$
$194$	−1.44762	−	13.7732i	−0.103933	−	0.988860i
$195$	−1.28952	−	5.58067i	−0.0923447	−	0.399640i
$196$	0.0260810	−	0.248144i	0.00186293	−	0.0177246i
$197$	−17.3425	−	12.6000i	−1.23560	−	0.897715i	−0.238302	−	0.971191i	$-0.576591\pi$
$197$	−17.3425	−	12.6000i	−1.23560	−	0.897715i	−0.997297	+	0.0734759i	$0.976591\pi$
$198$	12.8539	+	3.35531i	0.913488	+	0.238451i
$199$	18.9405			1.34265			0.671327	−	0.741162i	$-0.265725\pi$
$199$	18.9405			1.34265			0.671327	+	0.741162i	$0.265725\pi$
$200$	−8.06905	−	11.6742i	−0.570568	−	0.825493i
$201$	−4.55232	+	19.2354i	−0.321096	+	1.35676i
$202$	−7.10967	−	7.89608i	−0.500234	−	0.555566i
$203$	−18.5696	+	8.26771i	−1.30333	+	0.580279i
$204$	0.0546191	−	0.0469553i	0.00382410	−	0.00328753i
$205$	2.92155	+	4.61683i	0.204050	+	0.322453i
$206$	0.352309	−	0.255967i	0.0245465	−	0.0178341i
$207$	−1.17435	−	19.9410i	−0.0816229	−	1.38600i
$208$	4.75188	−	3.45244i	0.329483	−	0.239384i
$209$	−3.92991	+	4.36461i	−0.271838	+	0.301907i
$210$	10.6006	−	24.9868i	0.731512	−	1.72425i
$211$	−15.1945	−	16.8753i	−1.04604	−	1.16174i	−0.986541	−	0.163512i	$-0.947718\pi$
$211$	−15.1945	−	16.8753i	−1.04604	−	1.16174i	−0.0594945	−	0.998229i	$-0.518949\pi$
$212$	−0.00388432		0.000825637i	−0.000266776		5.67050e-5i
$213$	15.9050	+	22.9825i	1.08979	+	1.57473i
$214$	14.6241	−	3.10844i	0.999680	−	0.212489i
$215$	2.32212	−	8.27551i	0.158367	−	0.564385i
$216$	−13.6796	−	5.51152i	−0.930780	−	0.375012i
$217$	−26.2125	+	19.0445i	−1.77942	+	1.29283i
$218$	6.21454	+	10.7639i	0.420902	+	0.729023i
$219$	−6.93010	+	9.09217i	−0.468293	+	0.614392i
$220$	−0.0974686	−	0.0166154i	−0.00657133	−	0.00112021i
$221$	3.99258	−	1.77761i	0.268570	−	0.119575i
$222$	2.20200	+	11.6703i	0.147788	+	0.783259i
$223$	−21.0904	+	4.48289i	−1.41231	+	0.300197i	−0.850024	−	0.526743i	$-0.823413\pi$
$223$	−21.0904	+	4.48289i	−1.41231	+	0.300197i	−0.562290	+	0.826940i	$0.690080\pi$
$224$	−0.395861			−0.0264496
$225$	−9.63741	+	11.4944i	−0.642494	+	0.766291i
$226$	12.3721			0.822978
$227$	2.12348	−	0.451359i	0.140940	−	0.0299578i	−0.136901	−	0.990585i	$-0.543714\pi$
$227$	2.12348	−	0.451359i	0.140940	−	0.0299578i	0.277842	+	0.960627i	$0.410381\pi$
$228$	0.0345449	−	0.0296977i	0.00228779	−	0.00196678i
$229$	−17.6347	+	7.85147i	−1.16533	+	0.518840i	−0.895933	−	0.444189i	$-0.853492\pi$
$229$	−17.6347	+	7.85147i	−1.16533	+	0.518840i	−0.269400	+	0.963028i	$0.586825\pi$
$230$	−3.03822	−	20.7608i	−0.200334	−	1.36892i
$231$	−10.4386	−	24.9724i	−0.686808	−	1.64306i
$232$	5.80065	+	10.0470i	0.380832	+	0.659620i
$233$	21.4951	−	15.6171i	1.40819	−	1.02311i	0.414606	−	0.910001i	$-0.363920\pi$
$233$	21.4951	−	15.6171i	1.40819	−	1.02311i	0.993583	−	0.113108i	$-0.0360805\pi$
$234$	−4.88427	−	3.90320i	−0.319294	−	0.255160i
$235$	−2.94048	+	2.32440i	−0.191816	+	0.151627i
$236$	−0.0416377	+	0.00885036i	−0.00271038	+	0.000576109i
$237$	−6.00126	+	12.6873i	−0.389824	+	0.824126i
$238$	20.2579	+	4.30596i	1.31313	+	0.279114i
$239$	−4.94130	−	5.48787i	−0.319626	−	0.354981i	0.561825	−	0.827256i	$-0.310099\pi$
$239$	−4.94130	−	5.48787i	−0.319626	−	0.354981i	−0.881451	+	0.472275i	$0.843433\pi$
$240$	−14.7109	−	4.49449i	−0.949584	−	0.290118i
$241$	−9.43354	+	10.4770i	−0.607668	+	0.674883i	−0.965950	−	0.258730i	$-0.916696\pi$
$241$	−9.43354	+	10.4770i	−0.607668	+	0.674883i	0.358282	+	0.933613i	$0.383363\pi$
$242$	−1.28376	+	0.932703i	−0.0825229	+	0.0599564i
$243$	−1.78472	+	15.4860i	−0.114490	+	0.993424i
$244$	−0.0883137	+	0.0641637i	−0.00565371	+	0.00410766i
$245$	−38.4150	+	9.81031i	−2.45425	+	0.626757i
$246$	5.62826	+	1.97263i	0.358845	+	0.125770i
$247$	2.52518	−	1.12428i	0.160673	−	0.0715363i
$248$	12.3736	+	13.7423i	0.785727	+	0.872638i
$249$	−12.1356	−	11.4419i	−0.769061	−	0.725103i
$250$	−9.04216	+	12.9027i	−0.571876	+	0.816040i
$251$	23.6990			1.49587			0.747934	−	0.663773i	$-0.231046\pi$
$251$	23.6990			1.49587			0.747934	+	0.663773i	$0.231046\pi$
$252$	0.0556462	+	0.202432i	0.00350538	+	0.0127520i
$253$	−16.9271	−	12.2982i	−1.06420	−	0.773184i
$254$	1.17590	−	11.1879i	0.0737822	−	0.701991i
$255$	−10.0115	−	5.54695i	−0.626943	−	0.347363i
$256$	0.0353003	+	0.335860i	0.00220627	+	0.0209912i
$257$	−3.54893	+	6.14694i	−0.221376	+	0.383435i	−0.955226	−	0.295877i	$-0.904388\pi$
$257$	−3.54893	+	6.14694i	−0.221376	+	0.383435i	0.733850	+	0.679312i	$0.237722\pi$
$258$	−3.61845	−	8.65648i	−0.225275	−	0.538929i
$259$	16.1908	−	17.9817i	1.00605	−	1.11733i
$260$	0.0387261	+	0.0258019i	0.00240169	+	0.00160017i
$261$	8.61452	−	8.72661i	0.533226	−	0.540163i
$262$	−4.77253	−	14.6883i	−0.294848	−	0.907449i
$263$	9.89329	−	10.9876i	0.610047	−	0.677525i	−0.356418	−	0.934327i	$-0.616002\pi$
$263$	9.89329	−	10.9876i	0.610047	−	0.677525i	0.966464	+	0.256801i	$0.0826686\pi$
$264$	−13.5518	+	7.41484i	−0.834056	+	0.456352i
$265$	0.0913727	+	0.624367i	0.00561298	+	0.0383546i
$266$	12.8125	+	2.72338i	0.785584	+	0.166981i
$267$	2.87157	−	3.76746i	0.175737	−	0.230565i
$268$	−0.0802969	−	0.139078i	−0.00490491	−	0.00849556i
$269$	5.30527	−	3.85450i	0.323468	−	0.235013i	−0.414186	−	0.910192i	$-0.635934\pi$
$269$	5.30527	−	3.85450i	0.323468	−	0.235013i	0.737654	+	0.675179i	$0.235934\pi$
$270$	−0.462525	+	16.3672i	−0.0281484	+	0.996078i
$271$	−4.15808	−	3.02102i	−0.252585	−	0.183514i	0.454286	−	0.890856i	$-0.349894\pi$
$271$	−4.15808	−	3.02102i	−0.252585	−	0.183514i	−0.706872	+	0.707342i	$0.749894\pi$
$272$	1.22686	−	11.6728i	0.0743891	−	0.707765i
$273$	−0.292301	+	12.7351i	−0.0176908	+	0.770765i
$274$	−4.84870	+	8.39819i	−0.292920	+	0.507353i
$275$	2.90406	+	15.4407i	0.175121	+	0.931111i
$276$	0.118082	+	0.111332i	0.00710768	+	0.00670141i
$277$	5.58097	−	1.18627i	0.335328	−	0.0712762i	−0.0371705	−	0.999309i	$-0.511834\pi$
$277$	5.58097	−	1.18627i	0.335328	−	0.0712762i	0.372499	+	0.928033i	$0.378501\pi$
$278$	8.62106	+	6.26357i	0.517057	+	0.375664i
$279$	10.5392	−	16.4609i	0.630964	−	0.985486i
$280$	10.9633	+	29.5966i	0.655182	+	1.76874i
$281$	4.74099	+	2.11083i	0.282824	+	0.125921i	0.543246	−	0.839574i	$-0.317195\pi$
$281$	4.74099	+	2.11083i	0.282824	+	0.125921i	−0.260422	+	0.965495i	$0.583862\pi$
$282$	−0.942284	+	3.98154i	−0.0561122	+	0.237097i
$283$	−0.634300	−	6.03496i	−0.0377052	−	0.358741i	−0.997065	−	0.0765564i	$-0.975607\pi$
$283$	−0.634300	−	6.03496i	−0.0377052	−	0.358741i	0.959360	−	0.282185i	$-0.0910592\pi$
$284$	−0.222111	−	0.0472110i	−0.0131798	−	0.00280146i
$285$	−6.33194	−	3.50827i	−0.375072	−	0.207812i
$286$	−6.40572	+	1.36158i	−0.378778	+	0.0805118i
$287$	−3.75487	−	11.5563i	−0.221643	−	0.682147i
$288$	0.222385	−	0.0870189i	0.0131042	−	0.00512764i
$289$	−2.55457	+	7.86216i	−0.150269	+	0.462480i
$290$	8.22288	−	9.91360i	0.482864	−	0.582146i
$291$	7.27830	−	15.3870i	0.426661	−	0.902005i
$292$	−0.00970857	−	0.0923709i	−0.000568151	−	0.00540560i
$293$	−2.94596	+	5.10256i	−0.172105	+	0.298094i	−0.939156	−	0.343492i	$-0.888390\pi$
$293$	−2.94596	+	5.10256i	−0.172105	+	0.298094i	0.767051	+	0.641587i	$0.221723\pi$
$294$	−26.2355	+	34.4205i	−1.53009	+	2.00745i
$295$	3.61701	+	5.71584i	0.210591	+	0.332789i
$296$	−11.1725	−	8.11730i	−0.649388	−	0.471808i
$297$	11.3536	+	11.7343i	0.658804	+	0.680891i
$298$	6.52452	−	20.0804i	0.377955	−	1.16323i
$299$	4.92361	+	8.52794i	0.284740	+	0.493184i
$300$	−0.00709325	−	0.121660i	−0.000409529	−	0.00702404i
$301$	−9.55782	+	16.5546i	−0.550904	+	0.954193i
$302$	5.28917	+	5.87422i	0.304358	+	0.338024i
$303$	−2.42134	−	12.8328i	−0.139102	−	0.737224i
$304$	0.775948	−	7.38265i	0.0445036	−	0.423424i
$305$	14.4355	+	9.61788i	0.826574	+	0.550718i
$306$	−12.3270	+	2.03416i	−0.704686	+	0.116285i
$307$	−31.9044			−1.82088			−0.910439	−	0.413643i	$-0.864256\pi$
$307$	−31.9044			−1.82088			−0.910439	+	0.413643i	$0.864256\pi$
$308$	0.200887	+	0.0894407i	0.0114466	+	0.00509636i
$309$	0.533447	−	0.0437182i	0.0303467	−	0.00248704i
$310$	9.53518	−	18.1817i	0.541562	−	1.03265i
$311$	−10.7404	−	11.9285i	−0.609035	−	0.676402i	0.357211	−	0.934024i	$-0.383728\pi$
$311$	−10.7404	−	11.9285i	−0.609035	−	0.676402i	−0.966246	+	0.257622i	$0.917061\pi$
$312$	7.24602	−	0.593842i	0.410225	−	0.0336197i
$313$	−2.98176	+	3.31158i	−0.168539	+	0.187181i	−0.821497	−	0.570212i	$-0.806861\pi$
$313$	−2.98176	+	3.31158i	−0.168539	+	0.187181i	0.652958	+	0.757394i	$0.273528\pi$
$314$	6.69375	−	20.6012i	0.377750	−	1.16260i
$315$	27.0925	−	19.4652i	1.52649	−	1.09674i
$316$	−0.0352362	−	0.108446i	−0.00198219	−	0.00610055i
$317$	13.3281	+	5.93403i	0.748578	+	0.333288i	0.745321	−	0.666706i	$-0.232296\pi$
$317$	13.3281	+	5.93403i	0.748578	+	0.333288i	0.00325753	+	0.999995i	$0.498963\pi$
$318$	0.501174	+	0.472528i	0.0281045	+	0.0264980i
$319$	−1.34255	−	12.7735i	−0.0751685	−	0.715180i
$320$	16.1445	−	7.98815i	0.902504	−	0.446551i
$321$	17.3414	+	6.07791i	0.967901	+	0.339236i
$322$	−4.87771	+	46.4083i	−0.271824	+	2.58623i
$323$	1.70685	−	5.25315i	0.0949718	−	0.292293i
$324$	−0.0757597	−	0.101489i	−0.00420887	−	0.00563828i
$325$	1.70716	−	7.19468i	0.0946965	−	0.399089i
$326$	−15.2648	−	26.4395i	−0.845440	−	1.46435i
$327$	−0.350534	+	15.2723i	−0.0193846	+	0.844558i
$328$	−6.33546	+	2.82073i	−0.349817	+	0.155749i
$329$	7.61542	−	3.39060i	0.419852	−	0.186930i
$330$	12.9457	+	11.2492i	0.712638	+	0.619247i
$331$	21.5518	+	9.59549i	1.18459	+	0.527416i	0.901963	−	0.431813i	$-0.142126\pi$
$331$	21.5518	+	9.59549i	1.18459	+	0.527416i	0.282632	+	0.959228i	$0.408793\pi$
$332$	0.135508			0.00743696
$333$	−5.14283	+	13.6608i	−0.281826	+	0.748607i
$334$	7.18697	+	22.1192i	0.393253	+	1.21031i
$335$	−16.2917	+	19.6415i	−0.890112	+	1.07313i
$336$	29.2265	+	17.7804i	1.59444	+	0.969998i
$337$	8.15060	+	1.73246i	0.443991	+	0.0943733i	0.424482	−	0.905436i	$-0.360456\pi$
$337$	8.15060	+	1.73246i	0.443991	+	0.0943733i	0.0195094	+	0.999810i	$0.493790\pi$
$338$	−14.9049	−	3.16813i	−0.810717	−	0.172323i
$339$	12.9910	+	7.90329i	0.705577	+	0.429248i
$340$	0.0900964	−	0.0230085i	0.00488616	−	0.00124781i
$341$	−6.32643	−	19.4707i	−0.342595	−	1.05440i
$342$	−7.79642	+	1.28654i	−0.421582	+	0.0695681i
$343$	53.3661			2.88150
$344$	9.96677	+	4.43749i	0.537372	+	0.239253i
$345$	10.0718	−	23.7402i	0.542246	−	1.27813i
$346$	−15.5518	+	6.92411i	−0.836071	+	0.372243i
$347$	13.7816	−	6.13595i	0.739833	−	0.329395i	−0.00198319	−	0.999998i	$-0.500631\pi$
$347$	13.7816	−	6.13595i	0.739833	−	0.329395i	0.741816	+	0.670603i	$0.233965\pi$
$348$	−0.00228600	+	0.0995979i	−0.000122543	+	0.00533901i
$349$	−3.03867	−	5.26314i	−0.162656	−	0.281729i	0.773164	−	0.634206i	$-0.218673\pi$
$349$	−3.03867	−	5.26314i	−0.162656	−	0.281729i	−0.935821	+	0.352477i	$0.885340\pi$
$350$	26.5849	−	22.8276i	1.42102	−	1.22019i
$351$	−2.63526	−	7.21855i	−0.140660	−	0.385298i
$352$	0.0772947	−	0.237888i	0.00411982	−	0.0126795i
$353$	2.43564	−	23.1735i	0.129636	−	1.23340i	−0.715408	−	0.698707i	$-0.753759\pi$
$353$	2.43564	−	23.1735i	0.129636	−	1.23340i	0.845044	−	0.534697i	$-0.179574\pi$
$354$	6.96805	+	2.44220i	0.370348	+	0.129802i
$355$	5.22481	+	35.7021i	0.277304	+	1.89487i
$356$	0.00402287	+	0.0382750i	0.000213212	+	0.00202857i
$357$	18.5208	+	17.4622i	0.980224	+	0.924196i
$358$	−17.1220	−	7.62322i	−0.904928	−	0.402900i
$359$	1.23779	+	3.80952i	0.0653279	+	0.201059i	0.978392	−	0.206756i	$-0.0662908\pi$
$359$	1.23779	+	3.80952i	0.0653279	+	0.201059i	−0.913065	+	0.407815i	$0.866291\pi$
$360$	−12.6649	−	14.2167i	−0.667499	−	0.749287i
$361$	−4.79179	+	14.7476i	−0.252200	+	0.776191i
$362$	−19.7405	+	21.9240i	−1.03754	+	1.15230i
$363$	−1.94379	+	0.159302i	−0.102023	+	0.00836119i
$364$	−0.0692504	−	0.0769103i	−0.00362970	−	0.00403120i
$365$	−13.2281	+	6.54517i	−0.692392	+	0.342590i
$366$	18.8715	−	1.54660i	0.986427	−	0.0808418i
$367$	−20.9787	−	9.34033i	−1.09508	−	0.487561i	−0.221955	−	0.975057i	$-0.571244\pi$
$367$	−20.9787	−	9.34033i	−1.09508	−	0.487561i	−0.873125	+	0.487496i	$0.837910\pi$
$368$	26.4454			1.37856
$369$	4.64973	+	5.66665i	0.242055	+	0.294994i
$370$	−4.14223	+	14.7620i	−0.215344	+	0.767439i
$371$	0.146694	−	1.39570i	0.00761598	−	0.0724612i
$372$	0.0294430	+	0.156044i	0.00152655	+	0.00809052i
$373$	13.6711	+	15.1833i	0.707864	+	0.786163i	0.984607	−	0.174781i	$-0.0559217\pi$
$373$	13.6711	+	15.1833i	0.707864	+	0.786163i	−0.276743	+	0.960944i	$0.589255\pi$
$374$	−6.54313	+	11.3330i	−0.338337	+	0.586017i
$375$	−17.7368	+	7.77211i	−0.915925	+	0.401350i
$376$	−2.37886	−	4.12031i	−0.122680	−	0.212489i
$377$	−1.86796	+	5.74900i	−0.0962050	+	0.296088i
$378$	10.0035	−	35.0144i	0.514527	−	1.80095i
$379$	2.11954	+	1.53993i	0.108873	+	0.0791011i	0.640890	−	0.767633i	$-0.278566\pi$
$379$	2.11954	+	1.53993i	0.108873	+	0.0791011i	−0.532016	+	0.846734i	$0.678566\pi$
$380$	0.0569831	−	0.0145521i	0.00292317	−	0.000746509i
$381$	8.38156	−	10.9965i	0.429400	−	0.563366i
$382$	−3.41772	+	5.91966i	−0.174866	+	0.302876i
$383$	1.15470	+	10.9862i	0.0590023	+	0.561369i	0.983592	+	0.180405i	$0.0577410\pi$
$383$	1.15470	+	10.9862i	0.0590023	+	0.561369i	−0.924590	+	0.380964i	$0.875592\pi$
$384$	8.28954	−	17.5249i	0.423024	−	0.894314i
$385$	2.23920	−	34.8706i	0.114120	−	1.77717i
$386$	1.54310	−	4.74917i	0.0785417	−	0.241727i
$387$	1.73028	−	11.4010i	0.0879553	−	0.579547i
$388$	0.0427342	+	0.131522i	0.00216950	+	0.00667704i
$389$	12.2582	−	2.60556i	0.621515	−	0.132107i	0.113617	−	0.993525i	$-0.463756\pi$
$389$	12.2582	−	2.60556i	0.621515	−	0.132107i	0.507897	+	0.861418i	$0.330423\pi$
$390$	−3.41263	−	7.31476i	−0.172805	−	0.370397i
$391$	19.2473	+	4.09114i	0.973378	+	0.206898i
$392$	−5.26050	−	50.0503i	−0.265695	−	2.52792i
$393$	4.37162	−	18.4719i	0.220519	−	0.931784i
$394$	−27.5972	−	12.2871i	−1.39033	−	0.619013i
$395$	−14.2144	+	11.2363i	−0.715204	+	0.565358i
$396$	−0.132515	−	0.00608624i	−0.00665911	−	0.000305845i
$397$	25.5180	+	18.5399i	1.28071	+	0.930493i	0.999574	−	0.0291737i	$-0.00928761\pi$
$397$	25.5180	+	18.5399i	1.28071	+	0.930493i	0.281140	+	0.959667i	$0.409288\pi$
$398$	26.1082	−	5.54946i	1.30868	−	0.278170i
$399$	11.7138	+	11.0443i	0.586424	+	0.552905i
$400$	−14.4408	−	13.6314i	−0.722041	−	0.681569i
$401$	4.83754	−	8.37886i	0.241575	−	0.418420i	−0.719588	−	0.694401i	$-0.755669\pi$
$401$	4.83754	−	8.37886i	0.241575	−	0.418420i	0.961163	+	0.275981i	$0.0890026\pi$
$402$	−0.639189	+	27.8486i	−0.0318798	+	1.38896i
$403$	−1.00716	+	9.58252i	−0.0501704	+	0.477339i
$404$	0.0858357	+	0.0623633i	0.00427049	+	0.00310269i
$405$	−10.9411	+	16.8906i	−0.543666	+	0.839302i
$406$	−23.1745	+	16.8373i	−1.15013	+	0.835621i
$407$	7.64456	+	13.2408i	0.378927	+	0.656320i
$408$	8.80677	−	11.5543i	0.436000	−	0.572025i
$409$	−10.5677	−	2.24623i	−0.522539	−	0.111069i	−0.0609119	−	0.998143i	$-0.519401\pi$
$409$	−10.5677	−	2.24623i	−0.522539	−	0.111069i	−0.461627	+	0.887074i	$0.652734\pi$
$410$	5.37987	+	5.50799i	0.265693	+	0.272020i
$411$	−10.4560	+	5.72100i	−0.515759	+	0.282196i
$412$	−0.00290970	+	0.00323155i	−0.000143351	+	0.000159207i
$413$	−4.64870	−	14.3072i	−0.228748	−	0.704013i
$414$	−7.46139	−	27.1433i	−0.366707	−	1.33402i
$415$	−7.47951	−	20.1918i	−0.367154	−	0.991175i
$416$	−0.0787712	+	0.0874842i	−0.00386207	+	0.00428927i
$417$	5.05120	+	12.0841i	0.247358	+	0.591760i
$418$	−4.13832	+	7.16778i	−0.202412	+	0.350588i
$419$	4.02027	+	38.2503i	0.196403	+	1.86865i	0.438954	+	0.898510i	$0.355349\pi$
$419$	4.02027	+	38.2503i	0.196403	+	1.86865i	−0.242551	+	0.970139i	$0.577984\pi$
$420$	−0.0516644	+	0.266063i	−0.00252097	+	0.0129825i
$421$	0.651732	−	6.20082i	0.0317635	−	0.302209i	−0.967094	−	0.254420i	$-0.918116\pi$
$421$	0.651732	−	6.20082i	0.0317635	−	0.302209i	0.998857	−	0.0477898i	$-0.0152178\pi$
$422$	−25.8891	−	18.8095i	−1.26026	−	0.915632i
$423$	−3.53283	+	3.57880i	−0.171772	+	0.174007i
$424$	−0.800965			−0.0388983
$425$	−8.40143	−	12.1551i	−0.407529	−	0.589610i
$426$	28.6578	+	27.0198i	1.38848	+	1.30911i
$427$	−25.8136	−	28.6689i	−1.24921	−	1.38739i
$428$	−0.136385	+	0.0607224i	−0.00659241	+	0.00293513i
$429$	−7.59598	−	2.66228i	−0.366737	−	0.128536i
$430$	0.776202	−	12.0876i	0.0374318	−	0.582916i
$431$	−5.18988	+	3.77067i	−0.249988	+	0.181627i	−0.705721	−	0.708489i	$-0.749377\pi$
$431$	−5.18988	+	3.77067i	−0.249988	+	0.181627i	0.455734	+	0.890116i	$0.349377\pi$
$432$	−20.3273	−	3.56395i	−0.977996	−	0.171471i
$433$	−12.6872	+	9.21781i	−0.609709	+	0.442980i	−0.849312	−	0.527891i	$-0.822983\pi$
$433$	−12.6872	+	9.21781i	−0.609709	+	0.442980i	0.239603	+	0.970871i	$0.422983\pi$
$434$	−30.5523	+	33.9318i	−1.46656	+	1.62878i
$435$	14.9671	−	5.15679i	0.717617	−	0.247249i
$436$	−0.0830466	−	0.0922326i	−0.00397721	−	0.00441714i
$437$	12.1733	+	2.58752i	0.582328	+	0.123778i
$438$	−6.88872	+	14.5634i	−0.329156	+	0.695868i
$439$	−15.2390	+	3.23916i	−0.727320	+	0.154597i	−0.556668	−	0.830735i	$-0.687921\pi$
$439$	−15.2390	+	3.23916i	−0.727320	+	0.154597i	−0.170652	+	0.985331i	$0.554587\pi$
$440$	−19.9265	+	0.809322i	−0.949957	+	0.0385829i
$441$	−49.5359	+	19.3833i	−2.35885	+	0.923016i
$442$	4.98267	−	3.62012i	0.237002	−	0.172192i
$443$	−0.149149	−	0.258333i	−0.00708627	−	0.0122738i	0.862461	−	0.506124i	$-0.168922\pi$
$443$	−0.149149	−	0.258333i	−0.00708627	−	0.0122738i	−0.869547	+	0.493851i	$0.835589\pi$
$444$	−0.0457365	−	0.109416i	−0.00217056	−	0.00519266i
$445$	5.48125	−	2.71207i	0.259836	−	0.128565i
$446$	−27.7582	+	12.3588i	−1.31439	+	0.585204i
$447$	19.6783	−	16.9172i	0.930752	−	0.800154i
$448$	−39.1848	+	8.32900i	−1.85131	+	0.393508i
$449$	−0.00271457			−0.000128108			−6.40542e−5	−	1.00000i	$-0.500020\pi$
$449$	−0.00271457			−0.000128108			−6.40542e−5		1.00000i	$0.500020\pi$
$450$	−9.91675	+	18.6679i	−0.467480	+	0.880015i
$451$	7.67781			0.361534
$452$	−0.120842	+	0.0256858i	−0.00568394	+	0.00120816i
$453$	1.80133	+	9.54684i	0.0846340	+	0.448550i
$454$	2.79483	−	1.24434i	0.131168	−	0.0583997i
$455$	−7.63791	+	14.5640i	−0.358071	+	0.682772i
$456$	5.57000	−	7.30774i	0.260839	−	0.342216i
$457$	1.96454	+	3.40268i	0.0918972	+	0.159171i	0.908309	−	0.418299i	$-0.137374\pi$
$457$	1.96454	+	3.40268i	0.0918972	+	0.159171i	−0.816412	+	0.577470i	$0.804040\pi$
$458$	−22.0078	+	15.9896i	−1.02836	+	0.747146i
$459$	−14.2431	−	5.73855i	−0.664812	−	0.267853i
$460$	0.0727771	+	0.196470i	0.00339325	+	0.00916045i
$461$	−7.58196	+	1.61160i	−0.353127	+	0.0750595i	−0.381060	−	0.924550i	$-0.624441\pi$
$461$	−7.58196	+	1.61160i	−0.353127	+	0.0750595i	0.0279328	+	0.999610i	$0.491108\pi$
$462$	−21.7057	−	31.3643i	−1.00984	−	1.45920i
$463$	−25.2334	−	5.36353i	−1.17270	−	0.249264i	−0.419933	−	0.907555i	$-0.637946\pi$
$463$	−25.2334	−	5.36353i	−1.17270	−	0.249264i	−0.752764	+	0.658291i	$0.771280\pi$
$464$	10.8626	+	12.0641i	0.504283	+	0.560063i
$465$	21.6267	−	13.0003i	1.00292	−	0.602874i
$466$	25.0538	−	27.8251i	1.16060	−	1.28897i
$467$	15.4805	−	11.2472i	0.716350	−	0.520459i	−0.168866	−	0.985639i	$-0.554011\pi$
$467$	15.4805	−	11.2472i	0.716350	−	0.520459i	0.885216	+	0.465180i	$0.154011\pi$
$468$	0.0558098	+	0.0279836i	0.00257981	+	0.00129354i
$469$	45.9149	−	33.3591i	2.12015	−	1.54038i
$470$	−3.37222	+	4.06559i	−0.155549	+	0.187532i
$471$	20.1887	−	17.3560i	0.930248	−	0.799720i
$472$	−7.84359	+	3.49219i	−0.361030	+	0.160741i
$473$	−8.08211	−	8.97609i	−0.371616	−	0.412721i
$474$	−4.55504	+	19.2469i	−0.209220	+	0.884039i
$475$	−5.31363	−	7.68772i	−0.243806	−	0.352737i
$476$	−0.206806			−0.00947893
$477$	0.224397	+	0.816319i	0.0102744	+	0.0373767i
$478$	−8.41917	−	6.11689i	−0.385084	−	0.279780i
$479$	1.14191	−	10.8645i	0.0521750	−	0.496412i	−0.936964	−	0.349427i	$-0.886376\pi$
$479$	1.14191	−	10.8645i	0.0521750	−	0.496412i	0.989139	−	0.146985i	$-0.0469570\pi$
$480$	0.307127	+	0.0268108i	0.0140184	+	0.00122374i
$481$	−0.752153	−	7.15626i	−0.0342952	−	0.326297i
$482$	−9.93380	+	17.2059i	−0.452472	+	0.783705i
$483$	−34.7674	+	45.6142i	−1.58197	+	2.07552i
$484$	0.0106025	−	0.0117753i	0.000481931	−	0.000535239i
$485$	17.2392	−	13.6273i	0.782790	−	0.618783i
$486$	2.07719	+	21.8693i	0.0942234	+	0.992011i
$487$	−8.95137	−	27.5495i	−0.405625	−	1.24839i	−0.920372	−	0.391044i	$-0.872114\pi$
$487$	−8.95137	−	27.5495i	−0.405625	−	1.24839i	0.514746	−	0.857343i	$-0.327886\pi$
$488$	−14.7328	+	16.3624i	−0.666921	+	0.740691i
$489$	0.861019	−	37.5134i	0.0389366	−	1.69641i
$490$	−50.0782	+	24.7783i	−2.26230	+	1.11937i
$491$	23.9463	+	5.08995i	1.08068	+	0.229706i	0.713650	−	0.700502i	$-0.247041\pi$
$491$	23.9463	+	5.08995i	1.08068	+	0.229706i	0.367032	+	0.930208i	$0.380374\pi$
$492$	−0.0590686	−	0.00758241i	−0.00266302	−	0.000341841i
$493$	6.03959	+	10.4609i	0.272010	+	0.471134i
$494$	3.15138	−	2.28961i	0.141787	−	0.103015i
$495$	6.40740	+	20.0817i	0.287991	+	0.902605i
$496$	20.9343	+	15.2097i	0.939980	+	0.682935i
$497$	8.38817	−	79.8081i	0.376261	−	3.57988i
$498$	−20.0805	−	12.2163i	−0.899831	−	0.547425i
$499$	12.7554	−	22.0929i	0.571008	−	0.989016i	−0.425454	−	0.904980i	$-0.639886\pi$
$499$	12.7554	−	22.0929i	0.571008	−	0.989016i	0.996463	−	0.0840358i	$-0.0267810\pi$
$500$	0.0615304	−	0.144798i	0.00275172	−	0.00647556i
$501$	−6.58324	+	27.8169i	−0.294117	+	1.24277i
$502$	32.6675	−	6.94370i	1.45802	−	0.309912i
$503$	−8.07131	−	5.86415i	−0.359882	−	0.261470i	0.393121	−	0.919487i	$-0.371395\pi$
$503$	−8.07131	−	5.86415i	−0.359882	−	0.261470i	−0.753003	+	0.658017i	$0.771395\pi$
$504$	19.4676	+	37.6044i	0.867154	+	1.67503i
$505$	4.55484	−	16.2324i	0.202688	−	0.722334i
$506$	−26.9362	−	11.9928i	−1.19746	−	0.533144i
$507$	−13.6267	−	12.8479i	−0.605185	−	0.570593i
$508$	0.0117420	+	0.111717i	0.000520966	+	0.00495666i
$509$	−24.2676	−	5.15824i	−1.07564	−	0.228635i	−0.364158	−	0.931337i	$-0.618643\pi$
$509$	−24.2676	−	5.15824i	−1.07564	−	0.228635i	−0.711484	+	0.702702i	$0.751977\pi$
$510$	−15.4254	−	4.71279i	−0.683048	−	0.208686i
$511$	32.1065	−	6.82444i	1.42031	−	0.301896i
$512$	7.06462	+	21.7427i	0.312215	+	0.960899i
$513$	−9.00831	−	3.62945i	−0.397727	−	0.160244i
$514$	−3.09095	+	9.51297i	−0.136336	+	0.419599i
$515$	0.642132	+	0.255200i	0.0282957	+	0.0112455i
$516$	0.0533145	+	0.0770385i	0.00234704	+	0.00339143i
$517$	0.550583	+	5.23845i	0.0242146	+	0.230387i
$518$	17.0494	−	29.5304i	0.749108	−	1.29749i
$519$	−20.7530	−	2.66398i	−0.910955	−	0.116936i
$520$	8.72234	+	3.46649i	0.382500	+	0.152016i
$521$	1.27373	+	0.925421i	0.0558033	+	0.0405434i	0.615337	−	0.788264i	$-0.289020\pi$
$521$	1.27373	+	0.925421i	0.0558033	+	0.0405434i	−0.559534	+	0.828807i	$0.689020\pi$
$522$	9.31770	−	14.5531i	0.407825	−	0.636971i
$523$	−1.55314	+	4.78007i	−0.0679141	+	0.209018i	−0.979254	−	0.202637i	$-0.935049\pi$
$523$	−1.55314	+	4.78007i	−0.0679141	+	0.209018i	0.911340	+	0.411655i	$0.135049\pi$
$524$	0.0771096	+	0.133558i	0.00336855	+	0.00583450i
$525$	42.4972	−	6.98720i	1.85473	−	0.304947i
$526$	10.4179	−	18.0444i	0.454244	−	0.786773i
$527$	12.8833	+	14.3084i	0.561207	+	0.623283i
$528$	−16.3916	+	14.0916i	−0.713353	+	0.613259i
$529$	−2.23021	+	21.2191i	−0.0969659	+	0.922569i
$530$	0.308888	+	0.833878i	0.0134172	+	0.0362213i
$531$	5.75658	+	7.01558i	0.249814	+	0.304450i
$532$	−0.130798			−0.00567082
$533$	−3.30109	−	1.46974i	−0.142986	−	0.0636614i
$534$	2.85443	−	6.03455i	0.123523	−	0.261140i
$535$	16.5761	+	16.9708i	0.716645	+	0.733712i
$536$	−21.6742	−	24.0716i	−0.936181	−	1.03973i
$537$	−13.1089	−	18.9422i	−0.565692	−	0.817415i
$538$	6.18362	−	6.86760i	0.266595	−	0.296083i
$539$	−17.2173	+	52.9893i	−0.741600	+	2.28241i
$540$	−0.0294626	−	0.160825i	−0.00126787	−	0.00692079i
$541$	−5.34859	−	16.4613i	−0.229954	−	0.707725i	−0.997751	−	0.0670319i	$-0.978647\pi$
$541$	−5.34859	−	16.4613i	−0.229954	−	0.707725i	0.767797	−	0.640693i	$-0.221353\pi$
$542$	−6.61679	−	2.94598i	−0.284215	−	0.126541i
$543$	−34.7332	+	10.4107i	−1.49054	+	0.446764i
$544$	0.0245891	+	0.233950i	0.00105425	+	0.0100305i
$545$	−9.15956	+	17.4655i	−0.392352	+	0.748140i
$546$	3.32842	+	17.6402i	0.142443	+	0.754930i
$547$	−1.44601	+	13.7578i	−0.0618268	+	0.588243i	0.919121	+	0.393974i	$0.128900\pi$
$547$	−1.44601	+	13.7578i	−0.0618268	+	0.588243i	−0.980948	+	0.194269i	$0.937767\pi$
$548$	0.0299233	−	0.0920944i	0.00127826	−	0.00393408i
$549$	20.8036	+	10.4311i	0.887874	+	0.445190i
$550$	8.52712	+	20.4332i	0.363597	+	0.871273i
$551$	3.81985	+	6.61617i	0.162731	+	0.281858i
$552$	27.9652	+	17.0130i	1.19028	+	0.724123i
$553$	36.8132	−	16.3903i	1.56546	−	0.696987i
$554$	7.34543	−	3.27040i	0.312078	−	0.138946i
$555$	−13.7794	+	12.8545i	−0.584904	+	0.545642i
$556$	−0.0972088	−	0.0432801i	−0.00412257	−	0.00183549i
$557$	18.9380			0.802431			0.401215	−	0.915984i	$-0.368588\pi$
$557$	18.9380			0.802431			0.401215	+	0.915984i	$0.368588\pi$
$558$	9.70461	−	25.7781i	0.410829	−	1.09128i
$559$	1.75665	+	5.40641i	0.0742984	+	0.228667i
$560$	23.6165	+	37.3204i	0.997979	+	1.57707i
$561$	−14.1100	+	7.72027i	−0.595726	+	0.325950i
$562$	7.15361	+	1.52055i	0.301757	+	0.0641404i
$563$	12.2407	+	2.60183i	0.515882	+	0.109654i	0.458494	−	0.888698i	$-0.348389\pi$
$563$	12.2407	+	2.60183i	0.515882	+	0.109654i	0.0573888	+	0.998352i	$0.481723\pi$
$564$	0.000937494	−	0.0408453i	3.94756e−5	−	0.00171990i
$565$	10.4974	+	16.5887i	0.441630	+	0.697893i
$566$	−2.64256	−	8.13296i	−0.111075	−	0.341854i
$567$	32.8713	−	30.3759i	1.38046	−	1.27567i
$568$	−45.8002			−1.92173
$569$	2.72817	+	1.21466i	0.114371	+	0.0509213i	0.463124	−	0.886293i	$-0.346728\pi$
$569$	2.72817	+	1.21466i	0.114371	+	0.0509213i	−0.348753	+	0.937215i	$0.613395\pi$
$570$	−9.75607	−	2.98069i	−0.408637	−	0.124847i
$571$	−11.1866	+	4.98059i	−0.468144	+	0.208431i	−0.627231	−	0.778834i	$-0.715812\pi$
$571$	−11.1866	+	4.98059i	−0.468144	+	0.208431i	0.159087	+	0.987265i	$0.449145\pi$
$572$	0.0597401	−	0.0265980i	0.00249786	−	0.00111212i
$573$	−7.37019	+	4.03258i	−0.307894	+	0.168463i
$574$	−8.56178	−	14.8294i	−0.357362	−	0.618969i
$575$	25.2586	−	21.6888i	1.05336	−	0.904484i
$576$	20.1822	−	13.2927i	0.840926	−	0.553864i
$577$	9.05957	−	27.8825i	0.377155	−	1.16076i	−0.564859	−	0.825188i	$-0.691069\pi$
$577$	9.05957	−	27.8825i	0.377155	−	1.16076i	0.942013	−	0.335575i	$-0.108931\pi$
$578$	−1.21773	+	11.5860i	−0.0506510	+	0.481912i
$579$	4.65408	−	4.00104i	0.193417	−	0.166278i
$580$	−0.0597340	+	0.113901i	−0.00248032	+	0.00472949i
$581$	5.00572	+	47.6262i	0.207672	+	1.97587i
$582$	5.52433	−	23.3425i	0.228991	−	0.967579i
$583$	0.810090	+	0.360675i	0.0335505	+	0.0149376i
$584$	−5.78903	−	17.8168i	−0.239552	−	0.737265i
$585$	1.08930	−	9.86070i	0.0450372	−	0.407690i
$586$	−2.56579	+	7.89669i	−0.105992	+	0.326209i
$587$	−22.0289	+	24.4656i	−0.909230	+	1.00980i	0.0906726	+	0.995881i	$0.471098\pi$
$587$	−22.0289	+	24.4656i	−0.909230	+	1.00980i	−0.999903	+	0.0139220i	$0.995568\pi$
$588$	0.184790	−	0.390665i	0.00762063	−	0.0161108i
$589$	8.14829	+	9.04960i	0.335745	+	0.372882i
$590$	6.66053	+	6.81915i	0.274210	+	0.280740i
$591$	−21.1289	−	30.5309i	−0.869126	−	1.25587i
$592$	−17.6538	−	7.85997i	−0.725566	−	0.323043i
$593$	4.25001			0.174527			0.0872635	−	0.996185i	$-0.472188\pi$
$593$	4.25001			0.174527			0.0872635	+	0.996185i	$0.472188\pi$
$594$	19.0883	+	12.8484i	0.783203	+	0.527174i
$595$	11.4149	+	30.8158i	0.467965	+	1.26332i
$596$	−0.0220380	+	0.209678i	−0.000902713	+	0.00858874i
$597$	30.9594	+	10.8508i	1.26708	+	0.444094i
$598$	9.28552	+	10.3126i	0.379713	+	0.421714i
$599$	5.93409	−	10.2782i	0.242460	−	0.419954i	−0.718954	−	0.695058i	$-0.755379\pi$
$599$	5.93409	−	10.2782i	0.242460	−	0.419954i	0.961415	+	0.275104i	$0.0887122\pi$
$600$	−6.50130	−	23.7050i	−0.265415	−	0.967751i
$601$	−1.60271	−	2.77598i	−0.0653759	−	0.113234i	0.831485	−	0.555548i	$-0.187491\pi$
$601$	−1.60271	−	2.77598i	−0.0653759	−	0.113234i	−0.896861	+	0.442313i	$0.854158\pi$
$602$	−8.32440	+	25.6199i	−0.339277	+	1.04419i
$603$	−18.4608	+	28.8335i	−0.751784	+	1.17419i
$604$	−0.0638567	−	0.0463946i	−0.00259829	−	0.00188777i
$605$	−2.33982	−	0.929908i	−0.0951274	−	0.0378061i
$606$	−7.09760	−	16.9797i	−0.288320	−	0.689753i
$607$	20.6184	−	35.7121i	0.836876	−	1.44951i	−0.0556185	−	0.998452i	$-0.517713\pi$
$607$	20.6184	−	35.7121i	0.836876	−	1.44951i	0.892494	−	0.451059i	$-0.148954\pi$
$608$	0.0155518	+	0.147966i	0.000630710	+	0.00600080i
$609$	−35.0896	+	2.87574i	−1.42190	+	0.116531i
$610$	22.7164	+	9.02809i	0.919759	+	0.365537i
$611$	0.766055	−	2.35768i	0.0309913	−	0.0953813i
$612$	0.116179	−	0.0454605i	0.00469624	−	0.00183763i
$613$	1.02258	+	3.14717i	0.0413015	+	0.127113i	0.969581	−	0.244770i	$-0.0787123\pi$
$613$	1.02258	+	3.14717i	0.0413015	+	0.127113i	−0.928280	+	0.371883i	$0.878712\pi$
$614$	−43.9781	+	9.34783i	−1.77481	+	0.377248i
$615$	2.13052	+	9.22022i	0.0859107	+	0.371795i
$616$	43.3839	+	9.22154i	1.74799	+	0.371547i
$617$	2.80281	+	26.6670i	0.112837	+	1.07357i	0.893637	+	0.448790i	$0.148145\pi$
$617$	2.80281	+	26.6670i	0.112837	+	1.07357i	−0.780800	+	0.624781i	$0.785188\pi$
$618$	0.722512	−	0.216560i	0.0290637	−	0.00871132i
$619$	−28.6686	−	12.7641i	−1.15229	−	0.513032i	−0.260495	−	0.965475i	$-0.583886\pi$
$619$	−28.6686	−	12.7641i	−1.15229	−	0.513032i	−0.891793	+	0.452444i	$0.850552\pi$
$620$	−0.0553861	+	0.197384i	−0.00222436	+	0.00792711i
$621$	9.50449	−	33.2676i	0.381402	−	1.33498i
$622$	−18.3000	−	13.2957i	−0.733763	−	0.533110i
$623$	−13.3037	+	2.82780i	−0.533003	+	0.113293i
$624$	9.74511	−	2.92092i	0.390117	−	0.116930i
$625$	−24.9723	−	1.17624i	−0.998893	−	0.0470496i
$626$	−3.13988	+	5.43843i	−0.125495	+	0.217363i
$627$	−8.92414	+	4.88282i	−0.356396	+	0.195001i
$628$	−0.0226097	+	0.215116i	−0.000902223	+	0.00858408i
$629$	−11.6327	−	8.45166i	−0.463827	−	0.336990i
$630$	31.6421	−	34.7695i	1.26065	−	1.38525i
$631$	0.499112	−	0.362626i	0.0198693	−	0.0144359i	−0.577806	−	0.816174i	$-0.696091\pi$
$631$	0.499112	−	0.362626i	0.0198693	−	0.0144359i	0.597676	+	0.801738i	$0.296091\pi$
$632$	−11.4995	−	19.9177i	−0.457426	−	0.792285i
$633$	−15.1688	−	36.2885i	−0.602904	−	1.44234i
$634$	20.1105	+	4.27462i	0.798690	+	0.169767i
$635$	15.9987	−	7.91602i	0.634889	−	0.314138i
$636$	−0.00587616	−	0.00357485i	−0.000233005	−	0.000141752i
$637$	17.5462	−	19.4870i	0.695204	−	0.772102i
$638$	−5.59320	−	17.2141i	−0.221437	−	0.681513i
$639$	12.8313	+	46.6782i	0.507599	+	1.84656i
$640$	19.6343	−	15.5206i	0.776116	−	0.613507i
$641$	5.70725	−	6.33855i	0.225423	−	0.250358i	−0.619815	−	0.784748i	$-0.712792\pi$
$641$	5.70725	−	6.33855i	0.225423	−	0.250358i	0.845238	+	0.534391i	$0.179459\pi$
$642$	25.6847	+	3.29705i	1.01370	+	0.130124i
$643$	−9.71503	+	16.8269i	−0.383124	+	0.663589i	−0.991507	−	0.130054i	$-0.958485\pi$
$643$	−9.71503	+	16.8269i	−0.383124	+	0.663589i	0.608383	+	0.793643i	$0.291818\pi$
$644$	−0.0487066	−	0.463413i	−0.00191931	−	0.0182610i
$645$	8.53661	−	12.1965i	0.336129	−	0.480237i
$646$	0.813635	−	7.74122i	0.0320120	−	0.304574i
$647$	23.3550	+	16.9684i	0.918180	+	0.667097i	0.943070	−	0.332593i	$-0.107924\pi$
$647$	23.3550	+	16.9684i	0.918180	+	0.667097i	−0.0248902	+	0.999690i	$0.507924\pi$
$648$	−19.2027	−	16.8459i	−0.754353	−	0.661768i
$649$	9.50548			0.373123
$650$	0.245207	−	10.4176i	0.00961782	−	0.408611i
$651$	−53.7565	+	16.1125i	−2.10688	+	0.631500i
$652$	0.203988	+	0.226552i	0.00798879	+	0.00887245i
$653$	12.0328	−	5.35734i	0.470879	−	0.209649i	−0.157557	−	0.987510i	$-0.550362\pi$
$653$	12.0328	−	5.35734i	0.470879	−	0.209649i	0.628436	+	0.777861i	$0.283695\pi$
$654$	3.99151	+	21.1545i	0.156081	+	0.827207i
$655$	15.6450	−	18.8618i	0.611303	−	0.736993i
$656$	−7.85092	+	5.70403i	−0.306527	+	0.222705i
$657$	−16.5365	+	10.8915i	−0.645150	+	0.424919i
$658$	9.50393	−	6.90501i	0.370502	−	0.269185i
$659$	1.16065	−	1.28904i	0.0452126	−	0.0502137i	−0.720114	−	0.693855i	$-0.755911\pi$
$659$	1.16065	−	1.28904i	0.0452126	−	0.0502137i	0.765327	+	0.643642i	$0.222577\pi$
$660$	−0.149800	−	0.0829979i	−0.00583095	−	0.00323069i
$661$	3.99118	+	4.43266i	0.155239	+	0.172410i	0.815747	−	0.578408i	$-0.196326\pi$
$661$	3.99118	+	4.43266i	0.155239	+	0.172410i	−0.660508	+	0.750819i	$0.729659\pi$
$662$	32.5192	+	6.91217i	1.26389	+	0.268649i
$663$	7.54449	−	0.618303i	0.293004	−	0.0240129i
$664$	26.7345	−	5.68259i	1.03750	−	0.220527i
$665$	7.21955	+	19.4900i	0.279962	+	0.755789i
$666$	−3.08651	+	20.3373i	−0.119600	+	0.788056i
$667$	−22.0184	+	15.9973i	−0.852556	+	0.619418i
$668$	−0.116120	−	0.201125i	−0.00449280	−	0.00778176i
$669$	−37.0417	−	4.75491i	−1.43212	−	0.183835i
$670$	−16.7022	+	31.8479i	−0.645263	+	1.23039i
$671$	22.2686	−	9.91462i	0.859670	−	0.382750i
$672$	−0.647059	−	0.226785i	−0.0249609	−	0.00874842i
$673$	36.5259	−	7.76382i	1.40797	−	0.299273i	0.559638	−	0.828737i	$-0.310940\pi$
$673$	36.5259	−	7.76382i	1.40797	−	0.299273i	0.848332	+	0.529464i	$0.177607\pi$
$674$	11.7427			0.452311
$675$	−22.3380	+	13.2671i	−0.859789	+	0.510650i
$676$	0.152158			0.00585224
$677$	−18.1401	+	3.85579i	−0.697180	+	0.148190i	−0.542851	−	0.839829i	$-0.682655\pi$
$677$	−18.1401	+	3.85579i	−0.697180	+	0.148190i	−0.154329	+	0.988019i	$0.549322\pi$
$678$	20.2229	+	7.08785i	0.776657	+	0.272207i
$679$	−44.6469	+	19.8781i	−1.71339	+	0.762851i
$680$	16.8103	−	8.31761i	0.644647	−	0.318966i
$681$	3.72954	+	0.478747i	0.142916	+	0.0183456i
$682$	−14.4254	−	24.9855i	−0.552377	−	0.956745i
$683$	23.3543	−	16.9679i	0.893628	−	0.649259i	−0.0431936	−	0.999067i	$-0.513753\pi$
$683$	23.3543	−	16.9679i	0.893628	−	0.649259i	0.936821	+	0.349808i	$0.113753\pi$
$684$	0.0734793	−	0.0287523i	0.00280955	−	0.00109937i
$685$	−15.3745	+	0.624441i	−0.587429	+	0.0238587i
$686$	73.5617	−	15.6360i	2.80860	−	0.596986i
$687$	−33.3230	+	2.73096i	−1.27135	+	0.104193i
$688$	14.9329	+	3.17408i	0.569311	+	0.121011i
$689$	−0.279256	−	0.310146i	−0.0106388	−	0.0118156i
$690$	6.92749	−	35.6753i	0.263725	−	1.35814i
$691$	−22.4462	+	24.9290i	−0.853894	+	0.948345i	−0.999157	−	0.0410478i	$-0.986930\pi$
$691$	−22.4462	+	24.9290i	−0.853894	+	0.948345i	0.145263	+	0.989393i	$0.453597\pi$
$692$	0.137525	−	0.0999175i	0.00522790	−	0.00379829i
$693$	−2.75605	−	46.7991i	−0.104694	−	1.77775i
$694$	17.1992	−	12.4959i	0.652872	−	0.474339i
$695$	−1.08355	+	16.8738i	−0.0411012	+	0.640060i
$696$	3.72568	+	19.7456i	0.141222	+	0.748457i
$697$	−6.59642	+	2.93692i	−0.249857	+	0.111244i
$698$	−5.73069	−	6.36457i	−0.216910	−	0.240903i
$699$	44.0819	−	13.2128i	1.66733	−	0.499753i
$700$	−0.212271	+	0.278158i	−0.00802309	+	0.0105134i
$701$	−29.9242			−1.13022			−0.565110	−	0.825015i	$-0.691166\pi$
$701$	−29.9242			−1.13022			−0.565110	+	0.825015i	$0.691166\pi$
$702$	−5.74753	−	9.17818i	−0.216927	−	0.346408i
$703$	−7.35732	−	5.34540i	−0.277486	−	0.201606i
$704$	2.64590	−	25.1740i	0.0997210	−	0.948782i
$705$	−6.13803	+	2.11481i	−0.231172	+	0.0796483i
$706$	−3.43237	−	32.6569i	−0.129179	−	1.22906i
$707$	−18.7477	+	32.4720i	−0.705080	+	1.22123i
$708$	−0.0731296	−	0.00938738i	−0.00274838	−	0.000352799i
$709$	−14.3766	+	15.9668i	−0.539923	+	0.599645i	−0.949940	−	0.312433i	$-0.898856\pi$
$709$	−14.3766	+	15.9668i	−0.539923	+	0.599645i	0.410017	+	0.912078i	$0.365523\pi$
$710$	17.6626	+	47.6822i	0.662866	+	1.78948i
$711$	−17.0779	+	17.3001i	−0.640470	+	0.648803i
$712$	2.39876	+	7.38262i	0.0898973	+	0.276675i
$713$	−29.0281	+	32.2390i	−1.08711	+	1.20736i
$714$	30.6460	+	18.6439i	1.14690	+	0.697732i
$715$	−7.26074	−	7.43366i	−0.271536	−	0.278003i
$716$	0.183064	+	0.0389114i	0.00684140	+	0.00145419i
$717$	−4.93291	−	11.8011i	−0.184223	−	0.440720i
$718$	2.82238	+	4.88851i	0.105330	+	0.182437i
$719$	1.84892	−	1.34332i	0.0689531	−	0.0500973i	−0.552775	−	0.833331i	$-0.686431\pi$
$719$	1.84892	−	1.34332i	0.0689531	−	0.0500973i	0.621728	+	0.783233i	$0.286431\pi$
$720$	−21.4710	−	15.7743i	−0.800178	−	0.587872i
$721$	−1.24326	−	0.903284i	−0.0463016	−	0.0336401i
$722$	−2.28419	+	21.7326i	−0.0850087	+	0.808804i
$723$	−21.4219	+	11.7209i	−0.796689	+	0.435906i
$724$	0.147295	−	0.255123i	0.00547419	−	0.00948158i
$725$	20.2693	+	2.61395i	0.752783	+	0.0970797i
$726$	−2.63272	+	0.789109i	−0.0977092	+	0.0292866i
$727$	−45.5201	+	9.67560i	−1.68825	+	0.358848i	−0.949168	−	0.314770i	$-0.898073\pi$
$727$	−45.5201	+	9.67560i	−1.68825	+	0.358848i	−0.739080	+	0.673618i	$0.764739\pi$
$728$	−16.8877	−	12.2697i	−0.625901	−	0.454744i
$729$	−11.7890	+	24.2903i	−0.436630	+	0.899641i
$730$	−16.3164	+	12.8979i	−0.603898	+	0.477372i
$731$	10.3773	+	4.62028i	0.383819	+	0.170887i
$732$	−0.181113	+	0.0542854i	−0.00669413	+	0.00200645i
$733$	3.61620	+	34.4059i	0.133568	+	1.27081i	0.831855	+	0.554993i	$0.187279\pi$
$733$	3.61620	+	34.4059i	0.133568	+	1.27081i	−0.698288	+	0.715817i	$0.746054\pi$
$734$	−31.6545	−	6.72837i	−1.16839	−	0.248348i
$735$	−68.4120	−	5.97207i	−2.52342	−	0.220283i
$736$	−0.518446	+	0.110199i	−0.0191102	+	0.00406199i
$737$	11.0816	+	34.1057i	0.408197	+	1.25630i
$738$	8.06965	+	6.44876i	0.297048	+	0.237382i
$739$	2.02765	−	6.24048i	0.0745885	−	0.229560i	−0.906811	−	0.421538i	$-0.861490\pi$
$739$	2.02765	−	6.24048i	0.0745885	−	0.229560i	0.981399	+	0.191978i	$0.0614904\pi$
$740$	0.00981105	−	0.152785i	0.000360661	−	0.00561650i
$741$	4.77165	−	0.391057i	0.175291	−	0.0143658i
$742$	−0.206726	−	1.96686i	−0.00758914	−	0.0722058i
$743$	−3.23803	+	5.60843i	−0.118792	+	0.205753i	−0.919289	−	0.393583i	$-0.871235\pi$
$743$	−3.23803	+	5.60843i	−0.118792	+	0.205753i	0.800497	+	0.599336i	$0.204569\pi$
$744$	12.3526	+	29.5514i	0.452870	+	1.08341i
$745$	32.4601	−	8.28956i	1.18925	−	0.303706i
$746$	23.2934	+	16.9236i	0.852832	+	0.619619i
$747$	−13.2814	−	25.6549i	−0.485941	−	0.938665i
$748$	0.0403803	−	0.124278i	0.00147645	−	0.00454405i
$749$	−26.3799	−	45.6914i	−0.963901	−	1.66953i
$750$	−22.1718	+	15.9101i	−0.809601	+	0.580956i
$751$	24.7422	−	42.8547i	0.902855	−	1.56379i	0.0790844	−	0.996868i	$-0.474800\pi$
$751$	24.7422	−	42.8547i	0.902855	−	1.56379i	0.823771	−	0.566923i	$-0.191866\pi$
$752$	−4.45477	−	4.94752i	−0.162449	−	0.180417i
$753$	38.7375	+	13.5769i	1.41167	+	0.494771i
$754$	−0.890435	+	8.47192i	−0.0324277	+	0.308529i
$755$	−3.38854	+	12.0760i	−0.123321	+	0.439490i
$756$	−0.0250141	+	0.362767i	−0.000909756	+	0.0131937i
$757$	6.28412			0.228400			0.114200	−	0.993458i	$-0.463569\pi$
$757$	6.28412			0.228400			0.114200	+	0.993458i	$0.463569\pi$
$758$	3.37284	+	1.50168i	0.122507	+	0.0545436i
$759$	−20.6228	−	29.7996i	−0.748561	−	1.08166i
$760$	10.6320	−	5.26062i	0.385663	−	0.190823i
$761$	−5.24853	−	5.82909i	−0.190259	−	0.211304i	0.640467	−	0.767986i	$-0.278741\pi$
$761$	−5.24853	−	5.82909i	−0.190259	−	0.211304i	−0.830726	+	0.556682i	$0.812074\pi$
$762$	8.33152	−	17.6137i	0.301819	−	0.638076i
$763$	29.3488	−	32.5951i	1.06250	−	1.18002i
$764$	0.0210921	−	0.0649149i	0.000763087	−	0.00234854i
$765$	−13.1866	−	14.8023i	−0.476763	−	0.535179i
$766$	4.81058	+	14.8054i	0.173813	+	0.534943i
$767$	−4.08690	−	1.81960i	−0.147569	−	0.0657021i
$768$	−0.134711	+	0.569207i	−0.00486095	+	0.0205395i
$769$	1.70445	+	16.2167i	0.0614639	+	0.584790i	0.981300	+	0.192486i	$0.0616551\pi$
$769$	1.70445	+	16.2167i	0.0614639	+	0.584790i	−0.919836	+	0.392304i	$0.871678\pi$
$770$	−7.13033	−	48.7229i	−0.256959	−	1.75585i
$771$	−9.32248	+	8.01440i	−0.335741	+	0.288632i
$772$	−0.00521217	+	0.0495905i	−0.000187590	+	0.00178480i
$773$	5.02215	−	15.4566i	0.180634	−	0.555934i	−0.819212	−	0.573491i	$-0.805589\pi$
$773$	5.02215	−	15.4566i	0.180634	−	0.555934i	0.999846	+	0.0175566i	$0.00558874\pi$
$774$	−0.955363	−	16.2225i	−0.0343398	−	0.583107i
$775$	32.4689	−	2.64183i	1.16632	−	0.0948974i
$776$	13.9465	+	24.1561i	0.500652	+	0.867154i
$777$	36.7664	−	20.1167i	1.31899	−	0.721681i
$778$	16.1337	−	7.18318i	0.578421	−	0.257530i
$779$	−4.17203	+	1.85751i	−0.149478	+	0.0665521i
$780$	0.0485186	+	0.0643607i	0.00173725	+	0.00230448i
$781$	46.3220	+	20.6239i	1.65753	+	0.737981i
$782$	27.7298			0.991617
$783$	19.0804	−	9.32900i	0.681877	−	0.333391i
$784$	−21.7615	−	66.9751i	−0.777198	−	2.39197i
$785$	33.3021	−	8.50458i	1.18860	−	0.303541i
$786$	0.613817	−	26.7432i	0.0218941	−	0.953897i
$787$	2.67825	+	0.569279i	0.0954692	+	0.0202926i	0.255399	−	0.966836i	$-0.417793\pi$
$787$	2.67825	+	0.569279i	0.0954692	+	0.0202926i	−0.159929	+	0.987128i	$0.551127\pi$
$788$	0.295061	+	0.0627171i	0.0105111	+	0.00223420i
$789$	22.4659	−	12.2922i	0.799808	−	0.437613i
$790$	−16.3015	+	19.6532i	−0.579980	+	0.699230i
$791$	−13.4916	−	41.5230i	−0.479707	−	1.47639i
$792$	−26.3992	+	4.35631i	−0.938054	+	0.154795i
$793$	−11.4723			−0.407395
$794$	40.6071	+	18.0794i	1.44109	+	0.641615i
$795$	−0.208340	+	1.07291i	−0.00738906	+	0.0380523i
$796$	−0.243486	+	0.108407i	−0.00863014	+	0.00384239i
$797$	−8.63501	+	3.84456i	−0.305868	+	0.136181i	−0.553931	−	0.832563i	$-0.686873\pi$
$797$	−8.63501	+	3.84456i	−0.305868	+	0.136181i	0.248063	+	0.968744i	$0.420206\pi$
$798$	19.3826	+	11.7917i	0.686138	+	0.417422i
$799$	−2.47685	−	4.29003i	−0.0876246	−	0.151770i
$800$	0.339906	+	0.207059i	0.0120175	+	0.00732065i
$801$	6.85211	−	4.51304i	0.242107	−	0.159461i
$802$	4.21326	−	12.9671i	0.148775	−	0.457884i
$803$	−2.16794	+	20.6266i	−0.0765050	+	0.727897i
$804$	−0.0515736	−	0.273333i	−0.00181886	−	0.00963973i
$805$	−66.3639	+	32.8363i	−2.33902	+	1.15733i
$806$	1.41932	+	13.5040i	0.0499936	+	0.475657i
$807$	10.8800	−	3.26109i	0.382994	−	0.114796i
$808$	19.5498	+	8.70415i	0.687761	+	0.306211i
$809$	9.23232	+	28.4142i	0.324591	+	0.998989i	0.971625	+	0.236528i	$0.0760094\pi$
$809$	9.23232	+	28.4142i	0.324591	+	0.998989i	−0.647034	+	0.762462i	$0.723991\pi$
$810$	−10.1327	+	26.4883i	−0.356026	+	0.930704i
$811$	0.848346	−	2.61094i	0.0297894	−	0.0916825i	−0.935056	−	0.354499i	$-0.884651\pi$
$811$	0.848346	−	2.61094i	0.0297894	−	0.0916825i	0.964846	+	0.262817i	$0.0846514\pi$
$812$	0.191398	−	0.212569i	0.00671674	−	0.00745970i
$813$	−5.06593	−	7.32018i	−0.177670	−	0.256730i
$814$	14.4170	+	16.0117i	0.505316	+	0.561210i
$815$	22.4987	−	42.9007i	0.788095	−	1.50275i
$816$	8.69260	−	18.3770i	0.304302	−	0.643324i
$817$	6.56332	+	2.92218i	0.229621	+	0.102234i
$818$	−15.2250			−0.532330
$819$	−7.77363	+	20.6489i	−0.271633	+	0.721532i
$820$	−0.0639823	−	0.0426292i	−0.00223436	−	0.00148868i
$821$	3.01248	−	28.6618i	0.105136	−	1.00030i	−0.807037	−	0.590500i	$-0.798930\pi$
$821$	3.01248	−	28.6618i	0.105136	−	1.00030i	0.912174	−	0.409804i	$-0.134403\pi$
$822$	−12.7367	+	10.9496i	−0.444245	+	0.381911i
$823$	18.5365	+	20.5868i	0.646140	+	0.717611i	0.973856	−	0.227165i	$-0.0729456\pi$
$823$	18.5365	+	20.5868i	0.646140	+	0.717611i	−0.327716	+	0.944776i	$0.606279\pi$
$824$	−0.438542	+	0.759576i	−0.0152773	+	0.0264611i
$825$	−4.09899	+	26.9026i	−0.142709	+	0.936627i
$826$	−10.5999	−	18.3595i	−0.368817	−	0.638810i
$827$	−5.96739	+	18.3657i	−0.207506	+	0.638639i	0.792095	+	0.610398i	$0.208991\pi$
$827$	−5.96739	+	18.3657i	−0.207506	+	0.638639i	−0.999601	+	0.0282408i	$0.991009\pi$
$828$	0.129231	+	0.249627i	0.00449107	+	0.00867515i
$829$	−0.588767	−	0.427764i	−0.0204487	−	0.0148569i	0.577514	−	0.816381i	$-0.304023\pi$
$829$	−0.588767	−	0.427764i	−0.0204487	−	0.0148569i	−0.597963	+	0.801524i	$0.704023\pi$
$830$	−16.2261	−	25.6416i	−0.563216	−	0.890032i
$831$	9.80206	+	1.25825i	0.340030	+	0.0436483i
$832$	−5.95659	+	10.3171i	−0.206508	+	0.357682i
$833$	−5.47718	−	52.1119i	−0.189773	−	1.80557i
$834$	10.5033	+	15.1771i	0.363700	+	0.525541i
$835$	−23.5599	+	28.4041i	−0.815325	+	0.982964i
$836$	0.0255393	−	0.0786018i	0.000883294	−	0.00271850i
$837$	26.6572	−	20.8685i	0.921408	−	0.721321i
$838$	16.7488	+	51.5476i	0.578579	+	1.78068i
$839$	1.66285	−	0.353450i	0.0574081	−	0.0122025i	−0.179118	−	0.983828i	$-0.557324\pi$
$839$	1.66285	−	0.353450i	0.0574081	−	0.0122025i	0.236526	+	0.971625i	$0.423991\pi$
$840$	0.964539	+	54.6583i	0.0332797	+	1.88589i
$841$	12.0243	+	2.55584i	0.414631	+	0.0881325i
$842$	−0.918440	−	8.73838i	−0.0316515	−	0.301144i
$843$	6.54018	+	6.16635i	0.225256	+	0.212380i
$844$	0.291918	+	0.129970i	0.0100482	+	0.00447376i
$845$	−8.39855	−	22.6728i	−0.288919	−	0.779969i
$846$	−3.82121	+	5.96824i	−0.131376	+	0.205192i
$847$	4.53025	+	3.29142i	0.155661	+	0.113094i
$848$	−1.09631	+	0.233028i	−0.0376474	+	0.00800220i
$849$	2.42057	−	10.2279i	0.0830739	−	0.351021i
$850$	−15.1422	−	14.2934i	−0.519373	−	0.490261i
$851$	16.1988	−	28.0572i	0.555289	−	0.961789i
$852$	−0.336007	−	0.204415i	−0.0115114	−	0.00700313i
$853$	−3.19910	+	30.4374i	−0.109535	+	1.04216i	0.792316	+	0.610111i	$0.208875\pi$
$853$	−3.19910	+	30.4374i	−0.109535	+	1.04216i	−0.901851	+	0.432047i	$0.857792\pi$
$854$	−43.9823	−	31.9550i	−1.50504	−	1.09348i
$855$	−8.34010	−	9.36200i	−0.285225	−	0.320174i
$856$	−24.3611	+	17.6994i	−0.832644	+	0.604951i
$857$	11.3582	+	19.6730i	0.387989	+	0.672017i	0.992179	−	0.124824i	$-0.0398365\pi$
$857$	11.3582	+	19.6730i	0.387989	+	0.672017i	−0.604190	+	0.796840i	$0.706503\pi$
$858$	−11.2506	−	1.44420i	−0.384089	−	0.0493040i
$859$	28.1463	+	5.98269i	0.960341	+	0.204127i	0.661307	−	0.750116i	$-0.270002\pi$
$859$	28.1463	+	5.98269i	0.960341	+	0.204127i	0.299034	+	0.954242i	$0.403336\pi$
$860$	0.0175138	+	0.119675i	0.000597216	+	0.00408090i
$861$	0.482931	−	21.0406i	0.0164582	−	0.717063i
$862$	−6.04913	+	6.71824i	−0.206034	+	0.228824i
$863$	4.01032	+	12.3425i	0.136513	+	0.420143i	0.995822	−	0.0913127i	$-0.0291063\pi$
$863$	4.01032	+	12.3425i	0.136513	+	0.420143i	−0.859309	+	0.511456i	$0.829106\pi$
$864$	0.413355	−	0.0148354i	0.0140626	−	0.000504712i
$865$	−22.4794	−	14.9772i	−0.764321	−	0.509241i
$866$	−14.7877	+	16.4234i	−0.502508	+	0.558091i
$867$	−8.67977	+	11.3877i	−0.294781	+	0.386747i
$868$	0.227969	−	0.394853i	0.00773776	−	0.0134022i
$869$	2.66154	+	25.3229i	0.0902866	+	0.859020i
$870$	19.1202	−	11.4936i	0.648237	−	0.389669i
$871$	1.76419	−	16.7851i	0.0597772	−	0.568742i
$872$	−20.2522	−	14.7141i	−0.685825	−	0.498281i
$873$	20.7119	−	20.9814i	0.700993	−	0.710113i
$874$	17.5382			0.593239
$875$	53.1644	+	16.2769i	1.79728	+	0.550258i
$876$	0.0370492	−	0.156548i	0.00125178	−	0.00528927i
$877$	−1.36259	−	1.51331i	−0.0460114	−	0.0511009i	0.719700	−	0.694285i	$-0.244279\pi$
$877$	−1.36259	−	1.51331i	−0.0460114	−	0.0511009i	−0.765711	+	0.643185i	$0.777613\pi$
$878$	−20.0570	+	8.92994i	−0.676890	+	0.301371i
$879$	−7.73857	+	6.65273i	−0.261015	+	0.224391i
$880$	−27.0386	+	6.90503i	−0.911471	+	0.232768i
$881$	41.9767	−	30.4979i	1.41423	−	1.02750i	0.421540	−	0.906810i	$-0.361490\pi$
$881$	41.9767	−	30.4979i	1.41423	−	1.02750i	0.992690	−	0.120689i	$-0.0385104\pi$
$882$	−62.6028	+	41.2324i	−2.10795	+	1.38837i
$883$	−3.04267	+	2.21063i	−0.102394	+	0.0743937i	−0.637804	−	0.770199i	$-0.720157\pi$
$883$	−3.04267	+	2.21063i	−0.102394	+	0.0743937i	0.535410	+	0.844592i	$0.320157\pi$
$884$	−0.0411517	+	0.0457036i	−0.00138408	+	0.00153718i
$885$	2.63768	+	11.4151i	0.0886646	+	0.383713i
$886$	−0.281282	−	0.312395i	−0.00944986	−	0.0104951i
$887$	−50.1206	−	10.6535i	−1.68288	−	0.357708i	−0.735430	−	0.677600i	$-0.763020\pi$
$887$	−50.1206	−	10.6535i	−1.68288	−	0.357708i	−0.947454	+	0.319892i	$0.896353\pi$
$888$	−13.6118	−	19.6689i	−0.456783	−	0.660044i
$889$	−38.8310	+	8.25378i	−1.30235	+	0.276823i
$890$	6.76092	−	5.34440i	0.226626	−	0.179145i
$891$	11.8358	+	25.6848i	0.396513	+	0.860472i
$892$	0.245466	−	0.178341i	0.00821880	−	0.00597131i
$893$	−1.56653	−	2.71331i	−0.0524219	−	0.0907973i
$894$	22.1686	−	29.0848i	0.741429	−	0.972743i
$895$	−4.30629	−	29.4257i	−0.143943	−	0.983593i
$896$	−50.8501	+	22.6399i	−1.69878	+	0.756347i
$897$	3.16237	+	16.7602i	0.105588	+	0.559605i
$898$	−0.00374185		0.000795355i	−0.000124867		2.65414e-5i
$899$	−26.6305			−0.888178
$900$	0.0581035	−	0.202924i	0.00193678	−	0.00676415i
$901$	−0.833958			−0.0277832
$902$	10.5834	−	2.24956i	0.352387	−	0.0749022i
$903$	−25.1069	+	21.5840i	−0.835504	+	0.718271i
$904$	−22.7640	+	10.1352i	−0.757118	+	0.337091i
$905$	−46.1456	−	7.86641i	−1.53393	−	0.261488i
$906$	5.28020	+	12.6319i	0.175423	+	0.419667i
$907$	16.7448	+	29.0028i	0.556002	+	0.963023i	0.997825	+	0.0659210i	$0.0209985\pi$
$907$	16.7448	+	29.0028i	0.556002	+	0.963023i	−0.441823	+	0.897102i	$0.645668\pi$
$908$	−0.0247147	+	0.0179563i	−0.000820185	+	0.000595900i
$909$	3.39396	−	22.3631i	0.112570	−	0.741739i
$910$	−6.26117	+	22.3134i	−0.207556	+	0.739683i
$911$	−33.2706	+	7.07188i	−1.10230	+	0.234302i	−0.722916	−	0.690936i	$-0.757199\pi$
$911$	−33.2706	+	7.07188i	−1.10230	+	0.234302i	−0.379387	+	0.925238i	$0.623865\pi$
$912$	5.49779	−	11.6229i	0.182050	−	0.384872i
$913$	−29.5979	−	6.29123i	−0.979548	−	0.208209i
$914$	3.70495	+	4.11477i	0.122549	+	0.136104i
$915$	18.0857	+	23.9910i	0.597895	+	0.793118i
$916$	0.181762	−	0.201867i	0.00600558	−	0.00666987i
$917$	−44.0924	+	32.0350i	−1.45606	+	1.05789i
$918$	−21.3146	−	3.73706i	−0.703486	−	0.123341i
$919$	−28.2156	+	20.4998i	−0.930745	+	0.676226i	−0.946175	−	0.323655i	$-0.895088\pi$
$919$	−28.2156	+	20.4998i	−0.930745	+	0.676226i	0.0154297	+	0.999881i	$0.495088\pi$
$920$	22.5973	+	35.7098i	0.745012	+	1.17732i
$921$	−52.1497	−	18.2777i	−1.71839	−	0.602271i
$922$	−9.97905	+	4.44296i	−0.328642	+	0.146321i
$923$	−15.9683	−	17.7345i	−0.525601	−	0.583739i
$924$	0.277123	+	0.261283i	0.00911667	+	0.00859557i
$925$	−23.3078	+	6.97123i	−0.766355	+	0.229212i
$926$	−36.3541			−1.19467
$927$	0.896998	+	0.234147i	0.0294613	+	0.00769039i
$928$	−0.263226	−	0.191245i	−0.00864081	−	0.00627792i
$929$	4.27446	−	40.6688i	0.140240	−	1.33430i	−0.667434	−	0.744669i	$-0.732607\pi$
$929$	4.27446	−	40.6688i	0.140240	−	1.33430i	0.807674	−	0.589629i	$-0.200726\pi$
$930$	26.0020	−	24.2566i	0.852640	−	0.795405i
$931$	−3.46414	−	32.9591i	−0.113533	−	1.08019i
$932$	−0.186941	+	0.323792i	−0.00612346	+	0.0106061i
$933$	−10.7222	−	25.6510i	−0.351030	−	0.839774i
$934$	18.0434	−	20.0392i	0.590398	−	0.655704i
$935$	−20.7473	+	0.842660i	−0.678508	+	0.0275579i
$936$	12.1843	+	3.18051i	0.398256	+	0.103958i
$937$	9.99024	+	30.7468i	0.326367	+	1.00445i	0.970820	+	0.239810i	$0.0770852\pi$
$937$	9.99024	+	30.7468i	0.326367	+	1.00445i	−0.644453	+	0.764644i	$0.722915\pi$
$938$	53.5167	−	59.4363i	1.74738	−	1.94066i
$939$	−6.77104	+	3.70476i	−0.220965	+	0.120900i
$940$	0.0244970	−	0.0467111i	0.000799005	−	0.00152355i
$941$	−6.59671	−	1.40217i	−0.215047	−	0.0457096i	0.0991284	−	0.995075i	$-0.468395\pi$
$941$	−6.59671	−	1.40217i	−0.215047	−	0.0457096i	−0.314175	+	0.949365i	$0.601728\pi$
$942$	22.7436	−	29.8392i	0.741027	−	0.972215i
$943$	−8.13465	−	14.0896i	−0.264901	−	0.458822i
$944$	−9.71980	+	7.06185i	−0.316353	+	0.229844i
$945$	55.4359	−	16.2960i	1.80333	−	0.530109i
$946$	−13.7706	−	10.0049i	−0.447721	−	0.325288i
$947$	−5.50695	+	52.3951i	−0.178952	+	1.70261i	0.424676	+	0.905345i	$0.360388\pi$
$947$	−5.50695	+	52.3951i	−0.178952	+	1.70261i	−0.603628	+	0.797266i	$0.706279\pi$
$948$	0.00453189	−	0.197448i	0.000147189	−	0.00641281i
$949$	4.88059	−	8.45343i	0.158431	−	0.274410i
$950$	−9.57696	−	9.04015i	−0.310718	−	0.293301i
$951$	18.3860	+	17.3351i	0.596207	+	0.562128i
$952$	−40.8009	+	8.67251i	−1.32237	+	0.281078i
$953$	35.1915	+	25.5681i	1.13996	+	0.828232i	0.987114	−	0.160017i	$-0.0511551\pi$
$953$	35.1915	+	25.5681i	1.13996	+	0.828232i	0.152849	+	0.988249i	$0.451155\pi$
$954$	0.548494	+	1.05949i	0.0177581	+	0.0343024i
$955$	−10.8371	+	0.440152i	−0.350679	+	0.0142430i
$956$	0.0949323	+	0.0422666i	0.00307033	+	0.00136700i
$957$	5.12335	−	21.6483i	0.165615	−	0.699789i
$958$	−1.60921	−	15.3106i	−0.0519912	−	0.494663i
$959$	33.4734	+	7.11498i	1.08091	+	0.229755i
$960$	30.9655	−	3.80811i	0.999408	−	0.122906i
$961$	−11.1981	+	2.38022i	−0.361227	+	0.0767813i
$962$	−3.13354	−	9.64405i	−0.101029	−	0.310937i
$963$	24.8636	+	19.8694i	0.801218	+	0.640284i
$964$	0.0613056	−	0.188679i	0.00197452	−	0.00607695i
$965$	7.67708	−	1.96055i	0.247134	−	0.0631122i
$966$	−34.5598	+	73.0629i	−1.11194	+	2.35076i
$967$	1.16620	+	11.0956i	0.0375024	+	0.356812i	0.997140	+	0.0755731i	$0.0240786\pi$
$967$	1.16620	+	11.0956i	0.0375024	+	0.356812i	−0.959638	+	0.281239i	$0.909255\pi$
$968$	1.59797	−	2.76777i	0.0513608	−	0.0889595i
$969$	5.79944	−	7.60876i	0.186305	−	0.244429i
$970$	19.7703	−	23.8353i	0.634787	−	0.765306i
$971$	−36.1891	−	26.2929i	−1.16136	−	0.843781i	−0.171415	−	0.985199i	$-0.554834\pi$
$971$	−36.1891	−	26.2929i	−1.16136	−	0.843781i	−0.989950	+	0.141418i	$0.954834\pi$
$972$	−0.0656918	−	0.209292i	−0.00210706	−	0.00671306i
$973$	11.6205	−	35.7643i	0.372537	−	1.14655i
$974$	−20.4108	−	35.3525i	−0.654003	−	1.13277i
$975$	6.91224	−	10.7821i	0.221369	−	0.345305i
$976$	−15.4049	+	26.6820i	−0.493098	+	0.854071i
$977$	−16.3372	−	18.1442i	−0.522672	−	0.580486i	0.422786	−	0.906229i	$-0.361052\pi$
$977$	−16.3372	−	18.1442i	−0.522672	−	0.580486i	−0.945458	+	0.325743i	$0.894385\pi$
$978$	−9.80439	−	51.9620i	−0.313510	−	1.66156i
$979$	0.898314	−	8.54689i	0.0287103	−	0.273160i
$980$	0.437689	−	0.345986i	0.0139815	−	0.0110521i
$981$	−9.32231	+	24.7627i	−0.297639	+	0.790611i
$982$	34.4998			1.10093
$983$	25.2361	+	11.2358i	0.804907	+	0.358368i	0.767595	−	0.640936i	$-0.221454\pi$
$983$	25.2361	+	11.2358i	0.804907	+	0.358368i	0.0373129	+	0.999304i	$0.488120\pi$
$984$	−11.9717	+	0.981129i	−0.381643	+	0.0312772i
$985$	−6.94085	−	47.4282i	−0.221154	−	1.51119i
$986$	11.3902	+	12.6501i	0.362737	+	0.402860i
$987$	14.3903	−	1.17935i	0.458049	−	0.0375391i
$988$	−0.0260271	+	0.0289061i	−0.000828033	+	0.000919624i
$989$	−7.90911	+	24.3417i	−0.251495	+	0.774023i
$990$	14.7160	+	25.8040i	0.467706	+	0.820104i
$991$	−10.4706	−	32.2253i	−0.332610	−	1.02367i	−0.967887	−	0.251385i	$-0.919114\pi$
$991$	−10.4706	−	32.2253i	−0.332610	−	1.02367i	0.635277	−	0.772284i	$-0.280886\pi$
$992$	−0.473784	−	0.210942i	−0.0150427	−	0.00669743i
$993$	29.7306	+	28.0313i	0.943473	+	0.889545i
$994$	−11.8209	−	112.468i	−0.374935	−	3.56726i
$995$	29.5930	+	30.2978i	0.938162	+	0.960505i
$996$	0.221496	+	0.0776312i	0.00701837	+	0.00245984i
$997$	−1.53221	+	14.5780i	−0.0485255	+	0.461689i	0.943097	+	0.332518i	$0.107898\pi$
$997$	−1.53221	+	14.5780i	−0.0485255	+	0.461689i	−0.991622	+	0.129171i	$0.958768\pi$
$998$	11.1093	−	34.1909i	0.351659	−	1.08229i
$999$	−16.2324	+	19.3831i	−0.513571	+	0.613256i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	225.2.q.a.121.20	yes	224
3.2	odd	2		675.2.r.a.496.9		224
9.2	odd	6		675.2.r.a.46.20		224
9.7	even	3	inner	225.2.q.a.196.9	yes	224
25.6	even	5	inner	225.2.q.a.31.9	✓	224
75.56	odd	10		675.2.r.a.631.20		224
225.56	odd	30		675.2.r.a.181.9		224
225.106	even	15	inner	225.2.q.a.106.20	yes	224

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
225.2.q.a.31.9	✓	224	25.6	even	5	inner
225.2.q.a.106.20	yes	224	225.106	even	15	inner
225.2.q.a.121.20	yes	224	1.1	even	1	trivial
225.2.q.a.196.9	yes	224	9.7	even	3	inner
675.2.r.a.46.20		224	9.2	odd	6
675.2.r.a.181.9		224	225.56	odd	30
675.2.r.a.496.9		224	3.2	odd	2
675.2.r.a.631.20		224	75.56	odd	10

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:	\( N \)	\(=\)	\( 225 = 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	225.q (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(1.37843 - 0.292995i) q^{2} +(1.63456 + 0.572891i) q^{3} +(-0.0128554 + 0.00572357i) q^{4} +(1.56242 + 1.59963i) q^{5} +(2.42099 + 0.310774i) q^{6} +(-2.48652 - 4.30678i) q^{7} +(-2.29622 + 1.66830i) q^{8} +(2.34359 + 1.87285i) q^{9} +O(q^{10})\)	\(q+(1.37843 - 0.292995i) q^{2} +(1.63456 + 0.572891i) q^{3} +(-0.0128554 + 0.00572357i) q^{4} +(1.56242 + 1.59963i) q^{5} +(2.42099 + 0.310774i) q^{6} +(-2.48652 - 4.30678i) q^{7} +(-2.29622 + 1.66830i) q^{8} +(2.34359 + 1.87285i) q^{9} +(2.62239 + 1.74721i) q^{10} +(3.07362 - 0.653319i) q^{11} +(-0.0242919 + 0.00199082i) q^{12} +(-1.44657 - 0.307478i) q^{13} +(-4.68937 - 5.20807i) q^{14} +(1.63747 + 3.50980i) q^{15} +(-2.65756 + 2.95152i) q^{16} +(-2.39081 + 1.73703i) q^{17} +(3.77922 + 1.89494i) q^{18} +(-1.51211 + 1.09861i) q^{19} +(-0.0292411 - 0.0116212i) q^{20} +(-1.59706 - 8.46420i) q^{21} +(4.04537 - 1.80111i) q^{22} +(-4.45542 - 4.94825i) q^{23} +(-4.70908 + 1.41146i) q^{24} +(-0.117657 + 4.99862i) q^{25} -2.08409 q^{26} +(2.75781 + 4.40392i) q^{27} +(0.0566152 + 0.0411334i) q^{28} +(0.427253 - 4.06504i) q^{29} +(3.28549 + 4.35826i) q^{30} +(-0.681027 - 6.47954i) q^{31} +(0.0398007 - 0.0689368i) q^{32} +(5.39831 + 0.692961i) q^{33} +(-2.78664 + 3.09487i) q^{34} +(3.00427 - 10.7065i) q^{35} +(-0.0408471 - 0.0106625i) q^{36} +(1.50355 + 4.62746i) q^{37} +(-1.76246 + 1.95741i) q^{38} +(-2.18836 - 1.33132i) q^{39} +(-6.25636 - 1.06652i) q^{40} +(2.38999 + 0.508007i) q^{41} +(-4.68141 - 11.1994i) q^{42} +(-1.92193 - 3.32888i) q^{43} +(-0.0357732 + 0.0259908i) q^{44} +(0.665807 + 6.67508i) q^{45} +(-7.59132 - 5.51542i) q^{46} +(-0.175217 + 1.66708i) q^{47} +(-6.03484 + 3.30195i) q^{48} +(-8.86554 + 15.3556i) q^{49} +(1.30239 + 6.92474i) q^{50} +(-4.90306 + 1.46960i) q^{51} +(0.0203561 - 0.00432682i) q^{52} +(0.228304 + 0.165873i) q^{53} +(5.09178 + 5.26249i) q^{54} +(5.84738 + 3.89591i) q^{55} +(12.8946 + 5.74105i) q^{56} +(-3.10103 + 0.929477i) q^{57} +(-0.602097 - 5.72857i) q^{58} +(2.95891 + 0.628937i) q^{59} +(-0.0411388 - 0.0357476i) q^{60} +(7.58789 - 1.61286i) q^{61} +(-2.83723 - 8.73208i) q^{62} +(2.23857 - 14.7502i) q^{63} +(2.48928 - 7.66123i) q^{64} +(-1.76831 - 2.79440i) q^{65} +(7.64425 - 0.626479i) q^{66} +(1.19291 + 11.3498i) q^{67} +(0.0207927 - 0.0360141i) q^{68} +(-4.44786 - 10.6407i) q^{69} +(1.00422 - 15.6385i) q^{70} +(13.0547 + 9.48483i) q^{71} +(-8.50590 - 0.390666i) q^{72} +(-2.03962 + 6.27730i) q^{73} +(3.42837 + 5.93811i) q^{74} +(-3.05598 + 8.10315i) q^{75} +(0.0131507 - 0.0227777i) q^{76} +(-10.4563 - 11.6129i) q^{77} +(-3.40658 - 1.19396i) q^{78} +(-0.847007 + 8.05873i) q^{79} +(-8.87358 + 0.360405i) q^{80} +(1.98484 + 8.77841i) q^{81} +3.44328 q^{82} +(-8.79712 - 3.91673i) q^{83} +(0.0689762 + 0.0996694i) q^{84} +(-6.51407 - 1.11045i) q^{85} +(-3.62460 - 4.02553i) q^{86} +(3.02720 - 6.39979i) q^{87} +(-5.96780 + 6.62791i) q^{88} +(0.845142 - 2.60108i) q^{89} +(2.87354 + 9.00608i) q^{90} +(2.27269 + 6.99461i) q^{91} +(0.0855977 + 0.0381106i) q^{92} +(2.59889 - 10.9814i) q^{93} +(0.246921 + 2.34930i) q^{94} +(-4.11994 - 0.702323i) q^{95} +(0.104550 - 0.0898801i) q^{96} +(1.02725 - 9.77359i) q^{97} +(-7.72146 + 23.7642i) q^{98} +(8.42689 + 4.22533i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 224 q - 3 q^{2} - 8 q^{3} + 23 q^{4} - 8 q^{5} - 10 q^{6} - 8 q^{7} - 20 q^{8} - 8 q^{9}+O(q^{10}) \) 224 * q - 3 * q^2 - 8 * q^3 + 23 * q^4 - 8 * q^5 - 10 * q^6 - 8 * q^7 - 20 * q^8 - 8 * q^9	\( 224 q - 3 q^{2} - 8 q^{3} + 23 q^{4} - 8 q^{5} - 10 q^{6} - 8 q^{7} - 20 q^{8} - 8 q^{9} - 20 q^{10} - 11 q^{11} - 4 q^{12} - 3 q^{13} + q^{14} - 48 q^{15} + 23 q^{16} - 24 q^{17} - 12 q^{19} + q^{20} + 15 q^{21} - 11 q^{22} + q^{23} - 30 q^{24} - 16 q^{25} - 136 q^{26} + 7 q^{27} + 4 q^{28} - 15 q^{29} - 24 q^{30} + 3 q^{31} + 12 q^{32} - 5 q^{33} + q^{34} + 14 q^{35} + 38 q^{36} - 24 q^{37} + 55 q^{38} + 20 q^{39} + q^{40} - 19 q^{41} - 38 q^{42} - 8 q^{43} + 4 q^{44} - 38 q^{45} - 20 q^{46} - 10 q^{47} - 25 q^{48} - 72 q^{49} - 3 q^{50} - 26 q^{51} - 25 q^{52} - 12 q^{53} + 53 q^{54} - 20 q^{55} - 60 q^{56} + 38 q^{57} - 23 q^{58} - 30 q^{59} - 33 q^{60} - 3 q^{61} - 44 q^{62} + 46 q^{63} - 44 q^{64} + 51 q^{65} - 134 q^{66} - 12 q^{67} - 156 q^{68} + 4 q^{69} - 16 q^{70} + 42 q^{71} + 74 q^{72} - 12 q^{73} + 90 q^{74} + 67 q^{75} - 8 q^{76} + 31 q^{77} - 92 q^{78} - 15 q^{79} + 298 q^{80} - 104 q^{81} + 8 q^{82} + 59 q^{83} + 115 q^{84} - 11 q^{85} + 9 q^{86} - 59 q^{87} - 23 q^{88} + 106 q^{89} + 107 q^{90} + 30 q^{91} + 11 q^{92} + 32 q^{93} + 25 q^{94} + 7 q^{95} + 35 q^{96} - 21 q^{97} + 146 q^{98} - 20 q^{99}+O(q^{100}) \) 224 * q - 3 * q^2 - 8 * q^3 + 23 * q^4 - 8 * q^5 - 10 * q^6 - 8 * q^7 - 20 * q^8 - 8 * q^9 - 20 * q^10 - 11 * q^11 - 4 * q^12 - 3 * q^13 + q^14 - 48 * q^15 + 23 * q^16 - 24 * q^17 - 12 * q^19 + q^20 + 15 * q^21 - 11 * q^22 + q^23 - 30 * q^24 - 16 * q^25 - 136 * q^26 + 7 * q^27 + 4 * q^28 - 15 * q^29 - 24 * q^30 + 3 * q^31 + 12 * q^32 - 5 * q^33 + q^34 + 14 * q^35 + 38 * q^36 - 24 * q^37 + 55 * q^38 + 20 * q^39 + q^40 - 19 * q^41 - 38 * q^42 - 8 * q^43 + 4 * q^44 - 38 * q^45 - 20 * q^46 - 10 * q^47 - 25 * q^48 - 72 * q^49 - 3 * q^50 - 26 * q^51 - 25 * q^52 - 12 * q^53 + 53 * q^54 - 20 * q^55 - 60 * q^56 + 38 * q^57 - 23 * q^58 - 30 * q^59 - 33 * q^60 - 3 * q^61 - 44 * q^62 + 46 * q^63 - 44 * q^64 + 51 * q^65 - 134 * q^66 - 12 * q^67 - 156 * q^68 + 4 * q^69 - 16 * q^70 + 42 * q^71 + 74 * q^72 - 12 * q^73 + 90 * q^74 + 67 * q^75 - 8 * q^76 + 31 * q^77 - 92 * q^78 - 15 * q^79 + 298 * q^80 - 104 * q^81 + 8 * q^82 + 59 * q^83 + 115 * q^84 - 11 * q^85 + 9 * q^86 - 59 * q^87 - 23 * q^88 + 106 * q^89 + 107 * q^90 + 30 * q^91 + 11 * q^92 + 32 * q^93 + 25 * q^94 + 7 * q^95 + 35 * q^96 - 21 * q^97 + 146 * q^98 - 20 * q^99

Introduction

L-functions

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