LMFDB - Embedded newform 225.2.q.a.106.18

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			106.18
Character	$\chi$	$=$	225.106
Dual form			225.2.q.a.121.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.429627 + 0.0913200i) q^{2} +(0.335739 + 1.69920i) q^{3} +(-1.65085 - 0.735006i) q^{4} +(-1.76971 + 1.36679i) q^{5} +(-0.0109284 + 0.760681i) q^{6} +(-0.888066 + 1.53818i) q^{7} +(-1.35281 - 0.982874i) q^{8} +(-2.77456 + 1.14098i) q^{9} +O(q^{10})$	\(q+(0.429627 + 0.0913200i) q^{2} +(0.335739 + 1.69920i) q^{3} +(-1.65085 - 0.735006i) q^{4} +(-1.76971 + 1.36679i) q^{5} +(-0.0109284 + 0.760681i) q^{6} +(-0.888066 + 1.53818i) q^{7} +(-1.35281 - 0.982874i) q^{8} +(-2.77456 + 1.14098i) q^{9} +(-0.885131 + 0.425600i) q^{10} +(4.21184 + 0.895255i) q^{11} +(0.694667 - 3.05190i) q^{12} +(-6.27541 + 1.33388i) q^{13} +(-0.522003 + 0.579743i) q^{14} +(-2.91661 - 2.54821i) q^{15} +(1.92690 + 2.14004i) q^{16} +(0.162997 + 0.118424i) q^{17} +(-1.29622 + 0.236821i) q^{18} +(4.79916 + 3.48679i) q^{19} +(3.92613 - 0.955619i) q^{20} +(-2.91183 - 0.992576i) q^{21} +(1.72777 + 0.769251i) q^{22} +(1.83276 - 2.03549i) q^{23} +(1.21591 - 2.62868i) q^{24} +(1.26376 - 4.83765i) q^{25} -2.81790 q^{26} +(-2.87027 - 4.33146i) q^{27} +(2.59663 - 1.88657i) q^{28} +(0.0773364 + 0.735807i) q^{29} +(-1.02035 - 1.36112i) q^{30} +(-0.289472 + 2.75414i) q^{31} +(2.30458 + 3.99166i) q^{32} +(-0.107137 + 7.45733i) q^{33} +(0.0592133 + 0.0657630i) q^{34} +(-0.530743 - 3.93593i) q^{35} +(5.41901 + 0.155738i) q^{36} +(-1.36941 + 4.21461i) q^{37} +(1.74343 + 1.93628i) q^{38} +(-4.37343 - 10.2153i) q^{39} +(3.73747 - 0.109604i) q^{40} +(12.3006 - 2.61458i) q^{41} +(-1.16036 - 0.692345i) q^{42} +(-3.91700 + 6.78444i) q^{43} +(-6.29511 - 4.57366i) q^{44} +(3.35070 - 5.81144i) q^{45} +(0.973285 - 0.707133i) q^{46} +(-0.0518311 - 0.493140i) q^{47} +(-2.98942 + 3.99268i) q^{48} +(1.92268 + 3.33017i) q^{49} +(0.984721 - 1.96298i) q^{50} +(-0.146502 + 0.316724i) q^{51} +(11.3402 + 2.41043i) q^{52} +(5.99398 - 4.35488i) q^{53} +(-0.837597 - 2.12302i) q^{54} +(-8.67738 + 4.17236i) q^{55} +(2.71322 - 1.20800i) q^{56} +(-4.31349 + 9.32538i) q^{57} +(-0.0339681 + 0.323185i) q^{58} +(-9.52123 + 2.02380i) q^{59} +(2.94194 + 6.35044i) q^{60} +(-9.51841 - 2.02320i) q^{61} +(-0.375873 + 1.15682i) q^{62} +(0.708972 - 5.28102i) q^{63} +(-1.15416 - 3.55215i) q^{64} +(9.28254 - 10.9378i) q^{65} +(-0.727032 + 3.19409i) q^{66} +(-0.0149037 + 0.141799i) q^{67} +(-0.182041 - 0.315304i) q^{68} +(4.07403 + 2.43084i) q^{69} +(0.131408 - 1.73945i) q^{70} +(1.95406 - 1.41971i) q^{71} +(4.87488 + 1.18352i) q^{72} +(-0.860848 - 2.64942i) q^{73} +(-0.973212 + 1.68565i) q^{74} +(8.64444 + 0.523199i) q^{75} +(-5.35988 - 9.28359i) q^{76} +(-5.11745 + 5.68351i) q^{77} +(-0.946077 - 4.78817i) q^{78} +(-1.34516 - 12.7983i) q^{79} +(-6.33505 - 1.15358i) q^{80} +(6.39635 - 6.33140i) q^{81} +5.52343 q^{82} +(3.13799 - 1.39712i) q^{83} +(4.07744 + 3.77881i) q^{84} +(-0.450318 + 0.0132059i) q^{85} +(-2.30240 + 2.55708i) q^{86} +(-1.22432 + 0.378449i) q^{87} +(-4.81790 - 5.35082i) q^{88} +(3.29985 + 10.1559i) q^{89} +(1.97025 - 2.19076i) q^{90} +(3.52124 - 10.8373i) q^{91} +(-4.52172 + 2.01320i) q^{92} +(-4.77702 + 0.432802i) q^{93} +(0.0227655 - 0.216599i) q^{94} +(-13.2588 + 0.388827i) q^{95} +(-6.00888 + 5.25610i) q^{96} +(1.65739 + 15.7690i) q^{97} +(0.521922 + 1.60631i) q^{98} +(-12.7075 + 2.32167i) 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 $\left(\mathbb{Z}/225\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{5}\right)$

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 $

$2$	0.429627	+	0.0913200i	0.303792	+	0.0645730i	0.357286	−	0.933995i	$-0.383702\pi$
$2$	0.429627	+	0.0913200i	0.303792	+	0.0645730i	−0.0534935	+	0.998568i	$0.517036\pi$
$3$	0.335739	+	1.69920i	0.193839	+	0.981033i
$3$	0.335739	+	1.69920i	0.193839	+	0.981033i
$4$	−1.65085	−	0.735006i	−0.825426	−	0.367503i
$5$	−1.76971	+	1.36679i	−0.791439	+	0.611248i
$5$	−1.76971	+	1.36679i	−0.791439	+	0.611248i
$6$	−0.0109284	+	0.760681i	−0.00446152	+	0.310547i
$7$	−0.888066	+	1.53818i	−0.335657	+	0.581376i	−0.983611	−	0.180304i	$-0.942292\pi$
$7$	−0.888066	+	1.53818i	−0.335657	+	0.581376i	0.647953	+	0.761680i	$0.275625\pi$
$8$	−1.35281	−	0.982874i	−0.478290	−	0.347498i
$9$	−2.77456	+	1.14098i	−0.924853	+	0.380325i
$10$	−0.885131	+	0.425600i	−0.279903	+	0.134587i
$11$	4.21184	+	0.895255i	1.26992	+	0.269929i	0.793110	−	0.609078i	$-0.208460\pi$
$11$	4.21184	+	0.895255i	1.26992	+	0.269929i	0.476808	+	0.879008i	$0.341794\pi$
$12$	0.694667	−	3.05190i	0.200533	−	0.881006i
$13$	−6.27541	+	1.33388i	−1.74049	+	0.369952i	−0.965171	−	0.261622i	$-0.915743\pi$
$13$	−6.27541	+	1.33388i	−1.74049	+	0.369952i	−0.775316	+	0.631573i	$0.782409\pi$
$14$	−0.522003	+	0.579743i	−0.139511	+	0.154943i
$15$	−2.91661	−	2.54821i	−0.753066	−	0.657945i
$16$	1.92690	+	2.14004i	0.481725	+	0.535010i
$17$	0.162997	+	0.118424i	0.0395325	+	0.0287220i	0.607376	−	0.794414i	$-0.292222\pi$
$17$	0.162997	+	0.118424i	0.0395325	+	0.0287220i	−0.567844	+	0.823137i	$0.692222\pi$
$18$	−1.29622	+	0.236821i	−0.305522	+	0.0558192i
$19$	4.79916	+	3.48679i	1.10100	+	0.799925i	0.981223	−	0.192875i	$-0.0617813\pi$
$19$	4.79916	+	3.48679i	1.10100	+	0.799925i	0.119779	+	0.992801i	$0.461781\pi$
$20$	3.92613	−	0.955619i	0.877910	−	0.213683i
$21$	−2.91183	−	0.992576i	−0.635413	−	0.216598i
$22$	1.72777	+	0.769251i	0.368361	+	0.164005i
$23$	1.83276	−	2.03549i	0.382158	−	0.424429i	−0.521122	−	0.853483i	$-0.674486\pi$
$23$	1.83276	−	2.03549i	0.382158	−	0.424429i	0.903279	+	0.429054i	$0.141153\pi$
$24$	1.21591	−	2.62868i	0.248196	−	0.536578i
$25$	1.26376	−	4.83765i	0.252753	−	0.967531i
$26$	−2.81790			−0.552635
$27$	−2.87027	−	4.33146i	−0.552384	−	0.833590i
$28$	2.59663	−	1.88657i	0.490718	−	0.356527i
$29$	0.0773364	+	0.735807i	0.0143610	+	0.136636i	0.999353	−	0.0359636i	$-0.0114500\pi$
$29$	0.0773364	+	0.735807i	0.0143610	+	0.136636i	−0.984992	+	0.172599i	$0.944783\pi$
$30$	−1.02035	−	1.36112i	−0.186290	−	0.248506i
$31$	−0.289472	+	2.75414i	−0.0519906	+	0.494658i	0.937281	+	0.348573i	$0.113334\pi$
$31$	−0.289472	+	2.75414i	−0.0519906	+	0.494658i	−0.989272	+	0.146084i	$0.953333\pi$
$32$	2.30458	+	3.99166i	0.407397	+	0.705632i
$33$	−0.107137	+	7.45733i	−0.0186501	+	1.29815i
$34$	0.0592133	+	0.0657630i	0.0101550	+	0.0112783i
$35$	−0.530743	−	3.93593i	−0.0897120	−	0.665294i
$36$	5.41901	+	0.155738i	0.903168	+	0.0259563i
$37$	−1.36941	+	4.21461i	−0.225129	+	0.692877i	0.773149	+	0.634224i	$0.218680\pi$
$37$	−1.36941	+	4.21461i	−0.225129	+	0.692877i	−0.998278	+	0.0586526i	$0.981320\pi$
$38$	1.74343	+	1.93628i	0.282822	+	0.314106i
$39$	−4.37343	−	10.2153i	−0.700309	−	1.63576i
$40$	3.73747	−	0.109604i	0.590945	−	0.0173300i
$41$	12.3006	−	2.61458i	1.92103	−	0.408328i	0.921219	−	0.389045i	$-0.127195\pi$
$41$	12.3006	−	2.61458i	1.92103	−	0.408328i	0.999814	−	0.0192831i	$-0.00613837\pi$
$42$	−1.16036	−	0.692345i	−0.179047	−	0.106831i
$43$	−3.91700	+	6.78444i	−0.597336	+	1.03462i	0.395876	+	0.918304i	$0.370441\pi$
$43$	−3.91700	+	6.78444i	−0.597336	+	1.03462i	−0.993213	+	0.116313i	$0.962892\pi$
$44$	−6.29511	−	4.57366i	−0.949023	−	0.689506i
$45$	3.35070	−	5.81144i	0.499492	−	0.866318i
$46$	0.973285	−	0.707133i	0.143503	−	0.104261i
$47$	−0.0518311	−	0.493140i	−0.00756034	−	0.0719318i	0.990091	−	0.140426i	$-0.0448472\pi$
$47$	−0.0518311	−	0.493140i	−0.00756034	−	0.0719318i	−0.997652	+	0.0684942i	$0.978181\pi$
$48$	−2.98942	+	3.99268i	−0.431485	+	0.576294i
$49$	1.92268	+	3.33017i	0.274668	+	0.475739i
$50$	0.984721	−	1.96298i	0.139261	−	0.277607i
$51$	−0.146502	+	0.316724i	−0.0205143	+	0.0443502i
$52$	11.3402	+	2.41043i	1.57260	+	0.334267i
$53$	5.99398	−	4.35488i	0.823336	−	0.598189i	−0.0943302	−	0.995541i	$-0.530071\pi$
$53$	5.99398	−	4.35488i	0.823336	−	0.598189i	0.917666	+	0.397352i	$0.130071\pi$
$54$	−0.837597	−	2.12302i	−0.113982	−	0.288907i
$55$	−8.67738	+	4.17236i	−1.17006	+	0.562602i
$56$	2.71322	−	1.20800i	0.362569	−	0.161426i
$57$	−4.31349	+	9.32538i	−0.571336	+	1.23518i
$58$	−0.0339681	+	0.323185i	−0.00446023	+	0.0424362i
$59$	−9.52123	+	2.02380i	−1.23956	+	0.263476i	−0.780628	−	0.624996i	$-0.785101\pi$
$59$	−9.52123	+	2.02380i	−1.23956	+	0.263476i	−0.458931	+	0.888472i	$0.651767\pi$
$60$	2.94194	+	6.35044i	0.379803	+	0.819839i
$61$	−9.51841	−	2.02320i	−1.21871	−	0.259044i	−0.446715	−	0.894676i	$-0.647406\pi$
$61$	−9.51841	−	2.02320i	−1.21871	−	0.259044i	−0.771992	+	0.635632i	$0.780740\pi$
$62$	−0.375873	+	1.15682i	−0.0477359	+	0.146916i
$63$	0.708972	−	5.28102i	0.0893220	−	0.665346i
$64$	−1.15416	−	3.55215i	−0.144270	−	0.444019i
$65$	9.28254	−	10.9378i	1.15136	−	1.35666i
$66$	−0.727032	+	3.19409i	−0.0894915	+	0.393165i
$67$	−0.0149037	+	0.141799i	−0.00182077	+	0.0173235i	−0.995395	−	0.0958627i	$-0.969439\pi$
$67$	−0.0149037	+	0.141799i	−0.00182077	+	0.0173235i	0.993574	+	0.113186i	$0.0361057\pi$
$68$	−0.182041	−	0.315304i	−0.0220757	−	0.0382362i
$69$	4.07403	+	2.43084i	0.490456	+	0.292638i
$70$	0.131408	−	1.73945i	0.0157062	−	0.207904i
$71$	1.95406	−	1.41971i	0.231905	−	0.168489i	−0.465764	−	0.884909i	$-0.654221\pi$
$71$	1.95406	−	1.41971i	0.231905	−	0.168489i	0.697669	+	0.716420i	$0.254221\pi$
$72$	4.87488	+	1.18352i	0.574511	+	0.139479i
$73$	−0.860848	−	2.64942i	−0.100755	−	0.310091i	0.887956	−	0.459928i	$-0.152125\pi$
$73$	−0.860848	−	2.64942i	−0.100755	−	0.310091i	−0.988711	+	0.149837i	$0.952125\pi$
$74$	−0.973212	+	1.68565i	−0.113134	+	0.195953i
$75$	8.64444	+	0.523199i	0.998173	+	0.0604138i
$76$	−5.35988	−	9.28359i	−0.614821	−	1.06490i
$77$	−5.11745	+	5.68351i	−0.583188	+	0.647696i
$78$	−0.946077	−	4.78817i	−0.107122	−	0.542153i
$79$	−1.34516	−	12.7983i	−0.151342	−	1.43993i	−0.761767	−	0.647851i	$-0.775668\pi$
$79$	−1.34516	−	12.7983i	−0.151342	−	1.43993i	0.610425	−	0.792074i	$-0.290999\pi$
$80$	−6.33505	−	1.15358i	−0.708280	−	0.128975i
$81$	6.39635	−	6.33140i	0.710706	−	0.703489i
$82$	5.52343			0.609961
$83$	3.13799	−	1.39712i	0.344439	−	0.153354i	−0.227224	−	0.973842i	$-0.572965\pi$
$83$	3.13799	−	1.39712i	0.344439	−	0.153354i	0.571663	+	0.820488i	$0.306298\pi$
$84$	4.07744	+	3.77881i	0.444885	+	0.412302i
$85$	−0.450318	+	0.0132059i	−0.0488439	+	0.00143239i
$86$	−2.30240	+	2.55708i	−0.248274	+	0.275737i
$87$	−1.22432	+	0.378449i	−0.131261	+	0.0405740i
$88$	−4.81790	−	5.35082i	−0.513590	−	0.570399i
$89$	3.29985	+	10.1559i	0.349784	+	1.07652i	0.958973	+	0.283499i	$0.0914952\pi$
$89$	3.29985	+	10.1559i	0.349784	+	1.07652i	−0.609189	+	0.793025i	$0.708505\pi$
$90$	1.97025	−	2.19076i	0.207683	−	0.230927i
$91$	3.52124	−	10.8373i	0.369126	−	1.13605i
$92$	−4.52172	+	2.01320i	−0.471422	+	0.209890i
$93$	−4.77702	+	0.432802i	−0.495354	+	0.0448794i
$94$	0.0227655	−	0.216599i	0.00234808	−	0.0223405i
$95$	−13.2588	+	0.388827i	−1.36033	+	0.0398928i
$96$	−6.00888	+	5.25610i	−0.613279	+	0.536449i
$97$	1.65739	+	15.7690i	0.168283	+	1.60110i	0.674219	+	0.738531i	$0.264480\pi$
$97$	1.65739	+	15.7690i	0.168283	+	1.60110i	−0.505936	+	0.862571i	$0.668853\pi$
$98$	0.521922	+	1.60631i	0.0527221	+	0.162262i
$99$	−12.7075	+	2.32167i	−1.27715	+	0.233337i
$100$	−5.64199	+	7.05737i	−0.564199	+	0.705737i
$101$	−5.03293	+	8.71729i	−0.500795	+	0.867403i	0.499204	+	0.866484i	$0.333626\pi$
$101$	−5.03293	+	8.71729i	−0.500795	+	0.867403i	−1.00000		0.000918779i	$0.999708\pi$
$102$	−0.0918642	+	0.122694i	−0.00909592	+	0.0121486i
$103$	4.55818	+	2.02943i	0.449131	+	0.199966i	0.618822	−	0.785531i	$-0.287610\pi$
$103$	4.55818	+	2.02943i	0.449131	+	0.199966i	−0.169691	+	0.985497i	$0.554277\pi$
$104$	9.80048	+	4.36345i	0.961016	+	0.427872i
$105$	6.50974	−	2.22328i	0.635286	−	0.216970i
$106$	2.97286	−	1.32360i	0.288750	−	0.128560i
$107$	−7.10081			−0.686461			−0.343230	−	0.939251i	$-0.611521\pi$
$107$	−7.10081			−0.686461			−0.343230	+	0.939251i	$0.611521\pi$
$108$	1.55474	+	9.26026i	0.149605	+	0.891069i
$109$	0.177831	−	0.547308i	0.0170331	−	0.0524226i	−0.942179	−	0.335111i	$-0.891226\pi$
$109$	0.177831	−	0.547308i	0.0170331	−	0.0524226i	0.959212	+	0.282688i	$0.0912262\pi$
$110$	−4.10905	+	1.00014i	−0.391783	+	0.0953598i
$111$	−7.62122	−	0.911891i	−0.723374	−	0.0865529i
$112$	−5.00297	+	1.06341i	−0.472736	+	0.100483i
$113$	0.268332	−	0.0570356i	0.0252425	−	0.00536546i	−0.195273	−	0.980749i	$-0.562559\pi$
$113$	0.268332	−	0.0570356i	0.0252425	−	0.00536546i	0.220516	+	0.975383i	$0.429226\pi$
$114$	−2.70479	+	3.61252i	−0.253326	+	0.338344i
$115$	−0.461375	+	6.10724i	−0.0430234	+	0.569503i
$116$	0.413152	−	1.27155i	0.0383602	−	0.118060i
$117$	15.8896	−	10.8610i	1.46899	−	1.00410i
$118$	−4.27539			−0.393581
$119$	−0.326909	+	0.145549i	−0.0299677	+	0.0133425i
$120$	1.44105	+	6.31390i	0.131550	+	0.576378i
$121$	6.88913	+	3.06724i	0.626285	+	0.278840i
$122$	−3.90460	−	1.73844i	−0.353506	−	0.157391i
$123$	8.57248	+	20.0234i	0.772955	+	1.80545i
$124$	2.50218	−	4.33391i	0.224703	−	0.389196i
$125$	4.37556	+	10.2886i	0.391362	+	0.920237i
$126$	0.786856	−	2.20412i	0.0700987	−	0.196359i
$127$	0.765000	+	2.35443i	0.0678828	+	0.208922i	0.979244	−	0.202687i	$-0.0649672\pi$
$127$	0.765000	+	2.35443i	0.0678828	+	0.208922i	−0.911361	+	0.411608i	$0.864967\pi$
$128$	−1.13506	−	10.7993i	−0.100326	−	0.954535i
$129$	−12.8432	−	4.37796i	−1.13078	−	0.385458i
$130$	4.98686	−	3.85147i	0.437377	−	0.337797i
$131$	−0.120783	+	1.14917i	−0.0105528	+	0.100403i	−0.998530	−	0.0541935i	$-0.982741\pi$
$131$	−0.120783	+	1.14917i	−0.0105528	+	0.100403i	0.987978	+	0.154597i	$0.0494079\pi$
$132$	5.65805	−	12.2322i	0.492470	−	1.06468i
$133$	−9.62527	+	4.28545i	−0.834617	+	0.371595i
$134$	−0.0193521	+	0.0595597i	−0.00167177	+	0.00514517i
$135$	10.9998	+	3.74238i	0.946708	+	0.322092i
$136$	−0.104108	−	0.320410i	−0.00892716	−	0.0274750i
$137$	−5.64765	−	6.27235i	−0.482511	−	0.535883i	0.451905	−	0.892066i	$-0.350745\pi$
$137$	−5.64765	−	6.27235i	−0.482511	−	0.535883i	−0.934416	+	0.356183i	$0.884078\pi$
$138$	1.52833	+	1.41639i	0.130100	+	0.120571i
$139$	2.33243	−	2.59043i	0.197835	−	0.219718i	−0.636063	−	0.771638i	$-0.719438\pi$
$139$	2.33243	−	2.59043i	0.197835	−	0.219718i	0.833897	+	0.551920i	$0.186105\pi$
$140$	−2.01676	+	6.88773i	−0.170447	+	0.582120i
$141$	0.820541	−	0.253638i	0.0691020	−	0.0213601i
$142$	0.969166	−	0.431501i	0.0813306	−	0.0362107i
$143$	−27.6252			−2.31014
$144$	−7.78803	−	3.73912i	−0.649002	−	0.311593i
$145$	−1.14256	−	1.19646i	−0.0948842	−	0.0993609i
$146$	−0.127899	−	1.21687i	−0.0105850	−	0.100709i
$147$	−5.01311	+	4.38508i	−0.413475	+	0.361675i
$148$	5.35845	−	5.95116i	0.440462	−	0.489183i
$149$	6.94885	+	12.0358i	0.569272	+	0.986008i	0.996638	+	0.0819294i	$0.0261082\pi$
$149$	6.94885	+	12.0358i	0.569272	+	0.986008i	−0.427366	+	0.904079i	$0.640558\pi$
$150$	3.66610	+	1.01419i	0.299336	+	0.0828083i
$151$	2.35078	−	4.07166i	0.191303	−	0.331347i	−0.754379	−	0.656439i	$-0.772062\pi$
$151$	2.35078	−	4.07166i	0.191303	−	0.331347i	0.945682	+	0.325092i	$0.105395\pi$
$152$	−3.06527	−	9.43393i	−0.248626	−	0.765193i
$153$	−0.587363	−	0.142599i	−0.0474855	−	0.0115285i
$154$	−2.71761	+	1.97446i	−0.218991	+	0.159107i
$155$	−3.25205	−	5.26968i	−0.261211	−	0.423271i
$156$	−0.288461	+	20.0785i	−0.0230954	+	1.60757i
$157$	−4.75661	−	8.23869i	−0.379619	−	0.657519i	0.611388	−	0.791331i	$-0.290611\pi$
$157$	−4.75661	−	8.23869i	−0.379619	−	0.657519i	−0.991007	+	0.133812i	$0.957278\pi$
$158$	0.590827	−	5.62135i	0.0470037	−	0.447210i
$159$	9.41222	+	8.72286i	0.746438	+	0.691768i
$160$	−9.53421	−	3.91420i	−0.753746	−	0.309445i
$161$	1.50333	+	4.62676i	0.118479	+	0.364640i
$162$	3.32623	−	2.13603i	0.261333	−	0.167822i
$163$	2.56478	−	7.89358i	0.200889	−	0.618273i	−0.798968	−	0.601373i	$-0.794620\pi$
$163$	2.56478	−	7.89358i	0.200889	−	0.618273i	0.999857	−	0.0168995i	$-0.00537954\pi$
$164$	−22.2282	−	4.72475i	−1.73573	−	0.368941i
$165$	−10.0030	−	13.3438i	−0.778734	−	1.03881i
$166$	1.47575	−	0.313680i	0.114540	−	0.0243463i
$167$	−1.49105	+	14.1864i	−0.115381	+	1.09778i	0.771643	+	0.636056i	$0.219435\pi$
$167$	−1.49105	+	14.1864i	−0.115381	+	1.09778i	−0.887024	+	0.461723i	$0.847231\pi$
$168$	2.96357	+	4.20472i	0.228644	+	0.324402i
$169$	25.7255	−	11.4537i	1.97888	−	0.881056i
$170$	−0.194675	−	0.0354494i	−0.0149309	−	0.00271885i
$171$	−17.2939	−	4.19859i	−1.32250	−	0.321074i
$172$	11.4530	−	8.32108i	0.873282	−	0.634476i
$173$	21.1259	+	4.49046i	1.60618	+	0.341403i	0.921782	−	0.387709i	$-0.126734\pi$
$173$	21.1259	+	4.49046i	1.60618	+	0.341403i	0.684394	+	0.729113i	$0.260067\pi$
$174$	−0.560560	+	0.0507871i	−0.0424959	+	0.00385016i
$175$	6.31886	+	6.24005i	0.477661	+	0.471703i
$176$	6.19992	+	10.7386i	0.467336	+	0.809450i
$177$	−6.63549	−	15.4990i	−0.498754	−	1.16498i
$178$	0.490268	+	4.66459i	0.0367472	+	0.349626i
$179$	15.0286	−	10.9189i	1.12329	−	0.816116i	0.138583	−	0.990351i	$-0.455745\pi$
$179$	15.0286	−	10.9189i	1.12329	−	0.816116i	0.984704	+	0.174235i	$0.0557452\pi$
$180$	−9.80295	+	7.13104i	−0.730668	+	0.531516i
$181$	1.04274	+	0.757596i	0.0775063	+	0.0563116i	0.625864	−	0.779932i	$-0.284747\pi$
$181$	1.04274	+	0.757596i	0.0775063	+	0.0563116i	−0.548357	+	0.836244i	$0.684747\pi$
$182$	2.50248	−	4.33442i	0.185496	−	0.321288i
$183$	0.242120	−	16.8529i	0.0178980	−	1.24581i
$184$	−4.48001	+	0.952255i	−0.330271	+	0.0702012i
$185$	−3.33703	−	9.33034i	−0.245343	−	0.685980i
$186$	−2.09186	−	0.250294i	−0.153382	−	0.0183524i
$187$	0.580497	+	0.644707i	0.0424501	+	0.0471456i
$188$	−0.276895	+	0.852196i	−0.0201947	+	0.0621528i
$189$	9.21154	−	0.568360i	0.670041	−	0.0413421i
$190$	−5.73186	−	1.04375i	−0.415833	−	0.0757214i
$191$	−1.03713	−	1.15185i	−0.0750443	−	0.0833452i	0.704453	−	0.709750i	$-0.251192\pi$
$191$	−1.03713	−	1.15185i	−0.0750443	−	0.0833452i	−0.779498	+	0.626405i	$0.784526\pi$
$192$	5.64832	−	3.15375i	0.407632	−	0.227602i
$193$	−5.73764	−	9.93788i	−0.413004	−	0.715344i	0.582212	−	0.813037i	$-0.302187\pi$
$193$	−5.73764	−	9.93788i	−0.413004	−	0.715344i	−0.995217	+	0.0976925i	$0.968854\pi$
$194$	−0.727968	+	6.92615i	−0.0522650	+	0.497269i
$195$	21.7020	+	12.1007i	1.55411	+	0.866546i
$196$	−0.726354	−	6.91080i	−0.0518825	−	0.493629i
$197$	18.5783	−	13.4979i	1.32365	−	0.961687i	0.323770	−	0.946136i	$-0.395050\pi$
$197$	18.5783	−	13.4979i	1.32365	−	0.961687i	0.999879	−	0.0155518i	$-0.00495048\pi$
$198$	−5.67148	−	0.162994i	−0.403055	−	0.0115835i
$199$	−4.17299			−0.295816			−0.147908	−	0.989001i	$-0.547254\pi$
$199$	−4.17299			−0.295816			−0.147908	+	0.989001i	$0.547254\pi$
$200$	−6.46444	+	5.30231i	−0.457105	+	0.374930i
$201$	−0.245949	+	0.0222831i	−0.0173479	+	0.00157173i
$202$	−2.95835	+	3.28558i	−0.208148	+	0.231172i
$203$	−1.20048	−	0.534488i	−0.0842572	−	0.0375137i
$204$	0.474646	−	0.415184i	0.0332319	−	0.0290687i
$205$	−18.1950	+	21.4394i	−1.27079	+	1.49739i
$206$	1.77299	+	1.28815i	0.123530	+	0.0897497i
$207$	−2.76267	+	7.73872i	−0.192019	+	0.537878i
$208$	−14.9466	−	10.8594i	−1.03636	−	0.752962i
$209$	17.0917	+	18.9823i	1.18226	+	1.31303i
$210$	2.99979	−	0.360713i	0.207005	−	0.0248915i
$211$	1.89620	−	2.10594i	0.130540	−	0.144979i	−0.674331	−	0.738429i	$-0.735568\pi$
$211$	1.89620	−	2.10594i	0.130540	−	0.144979i	0.804871	+	0.593450i	$0.202235\pi$
$212$	−13.0960	+	2.78365i	−0.899439	+	0.191182i
$213$	3.06843	+	2.84369i	0.210245	+	0.194847i
$214$	−3.05070	−	0.648445i	−0.208541	−	0.0443268i
$215$	−2.34095	−	17.3602i	−0.159652	−	1.18396i
$216$	−0.374346	+	8.68076i	−0.0254710	+	0.590651i
$217$	−3.97928	−	2.89112i	−0.270131	−	0.196262i
$218$	0.126381	−	0.218899i	0.00855962	−	0.0148257i
$219$	4.21287	−	2.35227i	0.284679	−	0.158951i
$220$	17.3918	−	0.510028i	1.17255	−	0.0343861i
$221$	−1.18084	−	0.525742i	−0.0794316	−	0.0353652i
$222$	−3.19101	−	1.08774i	−0.214166	−	0.0730045i
$223$	20.2866	+	4.31206i	1.35849	+	0.288757i	0.828853	−	0.559466i	$-0.188994\pi$
$223$	20.2866	+	4.31206i	1.35849	+	0.288757i	0.529640	+	0.848223i	$0.322327\pi$
$224$	−8.18649			−0.546983
$225$	2.01325	+	14.8643i	0.134217	+	0.990952i
$226$	0.120491			0.00801494
$227$	1.31980	+	0.280531i	0.0875979	+	0.0186195i	0.251502	−	0.967857i	$-0.419075\pi$
$227$	1.31980	+	0.280531i	0.0875979	+	0.0186195i	−0.163904	+	0.986476i	$0.552409\pi$
$228$	13.9751	−	12.2244i	0.925527	−	0.809579i
$229$	23.4640	+	10.4468i	1.55054	+	0.690346i	0.990423	−	0.138066i	$-0.0440886\pi$
$229$	23.4640	+	10.4468i	1.55054	+	0.690346i	0.560119	+	0.828412i	$0.310755\pi$
$230$	−0.755932	+	2.58170i	−0.0498447	+	0.170232i
$231$	−11.3755	−	6.78740i	−0.748456	−	0.446578i
$232$	0.618584	−	1.07142i	0.0406120	−	0.0703421i
$233$	12.2726	+	8.91660i	0.804008	+	0.584146i	0.912087	−	0.409996i	$-0.134470\pi$
$233$	12.2726	+	8.91660i	0.804008	+	0.584146i	−0.108079	+	0.994142i	$0.534470\pi$
$234$	7.81842	−	3.21515i	0.511106	−	0.210181i
$235$	0.765745	+	0.801873i	0.0499517	+	0.0523084i
$236$	17.2056	+	3.65717i	1.11999	+	0.238062i
$237$	21.2953	−	6.58259i	1.38328	−	0.427585i
$238$	−0.153740	+	0.0326785i	−0.00996551	+	0.00211823i
$239$	9.37451	−	10.4114i	0.606387	−	0.673460i	−0.359285	−	0.933228i	$-0.616979\pi$
$239$	9.37451	−	10.4114i	0.606387	−	0.673460i	0.965671	+	0.259768i	$0.0836459\pi$
$240$	−0.166752	−	11.1518i	−0.0107638	−	0.719846i
$241$	−15.0558	−	16.7211i	−0.969827	−	1.07710i	−0.996995	−	0.0774711i	$-0.975315\pi$
$241$	−15.0558	−	16.7211i	−0.969827	−	1.07710i	0.0271676	−	0.999631i	$-0.491351\pi$
$242$	2.67966	+	1.94688i	0.172255	+	0.125150i
$243$	12.9058	+	8.74298i	0.827909	+	0.560862i
$244$	14.2264	+	10.3361i	0.910752	+	0.661700i
$245$	−7.95424	−	3.26555i	−0.508178	−	0.208628i
$246$	1.85443	+	9.38542i	0.118234	+	0.598392i
$247$	−34.7677	−	15.4796i	−2.21221	−	0.984941i
$248$	3.09857	−	3.44131i	0.196759	−	0.218523i
$249$	3.42754	+	4.86300i	0.217211	+	0.308180i
$250$	0.940308	+	4.81982i	0.0594703	+	0.304832i
$251$	0.464195			0.0292997			0.0146499	−	0.999893i	$-0.495337\pi$
$251$	0.464195			0.0292997			0.0146499	+	0.999893i	$0.495337\pi$
$252$	−5.05199	+	8.19708i	−0.318245	+	0.516368i
$253$	9.54159	−	6.93237i	0.599875	−	0.435834i
$254$	0.113658	+	1.08138i	0.00713154	+	0.0678521i
$255$	−0.173629	−	0.760747i	−0.0108731	−	0.0476398i
$256$	−0.282273	+	2.68565i	−0.0176421	+	0.167853i
$257$	−13.5014	−	23.3852i	−0.842197	−	1.45873i	−0.888034	−	0.459779i	$-0.847929\pi$
$257$	−13.5014	−	23.3852i	−0.842197	−	1.45873i	0.0458368	−	0.998949i	$-0.485405\pi$
$258$	−5.11799	−	3.05373i	−0.318632	−	0.190117i
$259$	−5.26668	−	5.84924i	−0.327256	−	0.363454i
$260$	−23.3634	+	11.2339i	−1.44894	+	0.696696i
$261$	−1.05411	−	1.95330i	−0.0652479	−	0.120906i
$262$	−0.156834	+	0.482684i	−0.00968921	+	0.0298203i
$263$	−5.71087	−	6.34256i	−0.352147	−	0.391099i	0.540881	−	0.841099i	$-0.318091\pi$
$263$	−5.71087	−	6.34256i	−0.352147	−	0.391099i	−0.893029	+	0.450000i	$0.851424\pi$
$264$	7.47455	−	9.98305i	0.460027	−	0.614414i
$265$	−4.65540	+	15.8994i	−0.285979	+	0.976692i
$266$	−4.52662	+	0.962163i	−0.277545	+	0.0589940i
$267$	−16.1490	+	9.01684i	−0.988304	+	0.551822i
$268$	0.128827	−	0.223135i	0.00786936	−	0.0136301i
$269$	0.950788	+	0.690788i	0.0579706	+	0.0421181i	0.616393	−	0.787439i	$-0.288593\pi$
$269$	0.950788	+	0.690788i	0.0579706	+	0.0421181i	−0.558423	+	0.829557i	$0.688593\pi$
$270$	4.38404	+	2.61232i	0.266804	+	0.158981i
$271$	6.66331	−	4.84118i	0.404767	−	0.294081i	−0.366713	−	0.930334i	$-0.619517\pi$
$271$	6.66331	−	4.84118i	0.404767	−	0.294081i	0.771480	+	0.636254i	$0.219517\pi$
$272$	0.0606463	+	0.577011i	0.00367722	+	0.0349864i
$273$	19.5969	+	2.34480i	1.18606	+	0.141914i
$274$	−1.85359	−	3.21051i	−0.111979	−	0.193954i
$275$	9.65371	−	19.2440i	0.582141	−	1.16046i
$276$	−4.93894	−	7.00739i	−0.297289	−	0.421795i
$277$	9.21967	+	1.95970i	0.553956	+	0.117747i	0.476380	−	0.879239i	$-0.341949\pi$
$277$	9.21967	+	1.95970i	0.553956	+	0.117747i	0.0775761	+	0.996986i	$0.475282\pi$
$278$	1.23863	−	0.899921i	0.0742884	−	0.0539737i
$279$	−2.33925	−	7.97180i	−0.140047	−	0.477259i
$280$	−3.15053	+	5.84622i	−0.188280	+	0.349378i
$281$	−13.7868	+	6.13830i	−0.822454	+	0.366180i	−0.774425	−	0.632666i	$-0.781961\pi$
$281$	−13.7868	+	6.13830i	−0.822454	+	0.366180i	−0.0480290	+	0.998846i	$0.515294\pi$
$282$	0.375689	−	0.0340377i	0.0223719	−	0.00202691i
$283$	−2.43859	+	23.2016i	−0.144959	+	1.37919i	0.644131	+	0.764915i	$0.277219\pi$
$283$	−2.43859	+	23.2016i	−0.144959	+	1.37919i	−0.789090	+	0.614278i	$0.789448\pi$
$284$	−4.26937	+	0.907482i	−0.253340	+	0.0538491i
$285$	−5.11221	−	22.3989i	−0.302821	−	1.32680i
$286$	−11.8685	−	2.52273i	−0.701801	−	0.149172i
$287$	−6.90208	+	21.2424i	−0.407417	+	1.25390i
$288$	−10.9486	−	8.44561i	−0.645152	−	0.497663i
$289$	−5.24075	−	16.1294i	−0.308279	−	0.948786i
$290$	−0.381612	−	0.618371i	−0.0224090	−	0.0363120i
$291$	−26.2383	+	8.11052i	−1.53811	+	0.475447i
$292$	−0.526207	+	5.00653i	−0.0307939	+	0.292985i
$293$	4.27487	+	7.40429i	0.249740	+	0.432563i	0.963454	−	0.267875i	$-0.0863214\pi$
$293$	4.27487	+	7.40429i	0.249740	+	0.432563i	−0.713713	+	0.700438i	$0.752988\pi$
$294$	−2.55421	+	1.42615i	−0.148965	+	0.0831748i
$295$	14.0837	−	16.5951i	0.819986	−	0.966203i
$296$	5.99498	−	4.35560i	0.348451	−	0.253164i
$297$	−8.21137	−	20.8130i	−0.476472	−	1.20770i
$298$	1.88631	+	5.80545i	0.109271	+	0.336301i
$299$	−8.78625	+	15.2182i	−0.508122	+	0.880093i
$300$	−13.8861	−	7.21744i	−0.801716	−	0.416699i
$301$	−6.95711	−	12.0501i	−0.401001	−	0.694554i
$302$	1.38178	−	1.53462i	0.0795125	−	0.0883076i
$303$	−16.5022	−	5.62522i	−0.948025	−	0.323161i
$304$	1.78562	+	16.9891i	0.102413	+	0.974391i
$305$	19.6101	−	9.42919i	1.12287	−	0.539914i
$306$	−0.239325	−	0.114902i	−0.0136813	−	0.00656853i
$307$	20.4968			1.16981			0.584907	−	0.811101i	$-0.301131\pi$
$307$	20.4968			1.16981			0.584907	+	0.811101i	$0.301131\pi$
$308$	12.6256	−	5.62127i	0.719409	−	0.320301i
$309$	−1.91805	+	8.42661i	−0.109114	+	0.479373i
$310$	−0.915941	−	2.56097i	−0.0520219	−	0.145453i
$311$	0.791719	−	0.879293i	0.0448943	−	0.0498601i	−0.720279	−	0.693684i	$-0.755986\pi$
$311$	0.791719	−	0.879293i	0.0448943	−	0.0498601i	0.765174	+	0.643824i	$0.222653\pi$
$312$	−4.12398	+	18.1179i	−0.233474	+	1.02573i
$313$	9.93394	+	11.0328i	0.561500	+	0.623609i	0.955318	−	0.295580i	$-0.0955128\pi$
$313$	9.93394	+	11.0328i	0.561500	+	0.623609i	−0.393818	+	0.919188i	$0.628846\pi$
$314$	−1.29121	−	3.97393i	−0.0728672	−	0.224262i
$315$	5.96338	+	10.3149i	0.335998	+	0.581179i
$316$	−7.18620	+	22.1168i	−0.404255	+	1.24417i
$317$	−0.319419	+	0.142214i	−0.0179404	+	0.00798756i	−0.415687	−	0.909508i	$-0.636459\pi$
$317$	−0.319419	+	0.142214i	−0.0179404	+	0.00798756i	0.397747	+	0.917495i	$0.369792\pi$
$318$	3.24717	+	4.60710i	0.182092	+	0.258353i
$319$	−0.333006	+	3.16834i	−0.0186447	+	0.177393i
$320$	6.89759	+	4.70878i	0.385587	+	0.263229i
$321$	−2.38402	−	12.0657i	−0.133063	−	0.673441i
$322$	0.223353	+	2.12506i	0.0124470	+	0.118425i
$323$	0.369327	+	1.13667i	0.0205499	+	0.0632461i
$324$	−15.2130	+	5.75085i	−0.845169	+	0.319492i
$325$	−1.47779	+	32.0440i	−0.0819731	+	1.77748i
$326$	1.82274	−	3.15708i	0.100952	−	0.174854i
$327$	0.989691	+	0.118418i	0.0547300	+	0.00654853i
$328$	−19.2102	−	8.55293i	−1.06071	−	0.472256i
$329$	0.804565	+	0.358215i	0.0443571	+	0.0197491i
$330$	−3.07901	−	6.64631i	−0.169494	−	0.365868i
$331$	−14.2383	+	6.33928i	−0.782605	+	0.348438i	−0.758838	−	0.651279i	$-0.774233\pi$
$331$	−14.2383	+	6.33928i	−0.782605	+	0.348438i	−0.0237671	+	0.999718i	$0.507566\pi$
$332$	−6.20725			−0.340667
$333$	−1.00926	−	13.2561i	−0.0553069	−	0.726432i
$334$	−1.93610	+	5.95871i	−0.105939	+	0.326046i
$335$	−0.167435	−	0.271314i	−0.00914792	−	0.0148235i
$336$	−3.48665	−	8.14402i	−0.190212	−	0.444293i
$337$	20.5449	−	4.36696i	1.11915	−	0.237883i	0.389047	−	0.921218i	$-0.372804\pi$
$337$	20.5449	−	4.36696i	1.11915	−	0.237883i	0.730106	+	0.683334i	$0.239471\pi$
$338$	12.0983	−	2.57158i	0.658061	−	0.139875i
$339$	0.187004	+	0.436800i	0.0101567	+	0.0237237i
$340$	0.753115	+	0.309186i	0.0408434	+	0.0167679i
$341$	−3.68486	+	11.3408i	−0.199547	+	0.614141i
$342$	−7.04650	−	3.38310i	−0.381031	−	0.182937i
$343$	−19.2628			−1.04009
$344$	11.9672	−	5.32814i	0.645228	−	0.287274i
$345$	−10.5323	+	1.26647i	−0.567041	+	0.0681844i
$346$	8.66620	+	3.85844i	0.465898	+	0.207431i
$347$	3.65328	+	1.62655i	0.196119	+	0.0873176i	0.502446	−	0.864609i	$-0.332434\pi$
$347$	3.65328	+	1.62655i	0.196119	+	0.0873176i	−0.306327	+	0.951926i	$0.599100\pi$
$348$	2.29933	+	0.275118i	0.123257	+	0.0147479i
$349$	−1.07056	+	1.85427i	−0.0573059	+	0.0992567i	−0.893255	−	0.449550i	$-0.851584\pi$
$349$	−1.07056	+	1.85427i	−0.0573059	+	0.0992567i	0.835949	+	0.548807i	$0.184918\pi$
$350$	2.14491	+	3.25793i	0.114650	+	0.174144i
$351$	23.7898	+	23.3531i	1.26981	+	1.24650i
$352$	6.13300	+	18.8754i	0.326890	+	1.00606i
$353$	−1.18522	−	11.2766i	−0.0630830	−	0.600194i	−0.979706	−	0.200441i	$-0.935762\pi$
$353$	−1.18522	−	11.2766i	−0.0630830	−	0.600194i	0.916623	−	0.399753i	$-0.130904\pi$
$354$	−1.43541	−	7.26474i	−0.0762914	−	0.386117i
$355$	−1.51768	+	5.18328i	−0.0805503	+	0.275100i
$356$	2.01709	−	19.1913i	0.106905	−	1.01714i
$357$	−0.357073	−	0.506617i	−0.0188983	−	0.0268130i
$358$	7.45378	−	3.31864i	0.393945	−	0.175395i
$359$	−7.26044	+	22.3453i	−0.383191	+	1.17934i	0.554593	+	0.832122i	$0.312874\pi$
$359$	−7.26044	+	22.3453i	−0.383191	+	1.17934i	−0.937784	+	0.347219i	$0.887126\pi$
$360$	−10.2448	+	4.56846i	−0.539947	+	0.240779i
$361$	5.00287	+	15.3973i	0.263309	+	0.810382i
$362$	0.378806	+	0.420706i	0.0199096	+	0.0221118i
$363$	−2.89890	+	12.7358i	−0.152153	+	0.668456i
$364$	−13.7785	+	15.3026i	−0.722190	+	0.802073i
$365$	5.14466	+	3.51211i	0.269284	+	0.183832i
$366$	1.64303	−	7.21836i	0.0858826	−	0.377310i
$367$	−18.6193	+	8.28983i	−0.971918	+	0.432726i	−0.830374	−	0.557206i	$-0.811873\pi$
$367$	−18.6193	+	8.28983i	−0.971918	+	0.432726i	−0.141544	+	0.989932i	$0.545207\pi$
$368$	7.88758			0.411168
$369$	−31.1456	+	21.2890i	−1.62138	+	1.10826i
$370$	−0.581630	−	4.31330i	−0.0302375	−	0.224238i
$371$	1.37552	+	13.0872i	0.0714135	+	0.679454i
$372$	8.20426	+	2.79665i	0.425371	+	0.144999i
$373$	−20.6426	+	22.9259i	−1.06883	+	1.18706i	−0.0872153	+	0.996189i	$0.527797\pi$
$373$	−20.6426	+	22.9259i	−1.06883	+	1.18706i	−0.981616	+	0.190868i	$0.938870\pi$
$374$	0.190522	+	0.329994i	0.00985167	+	0.0170636i
$375$	−16.0133	+	10.8892i	−0.826922	+	0.562317i
$376$	−0.414576	+	0.718068i	−0.0213801	+	0.0370315i
$377$	−1.46680	−	4.51433i	−0.0755439	−	0.232500i
$378$	4.00943	+	0.597015i	0.206223	+	0.0307071i
$379$	−26.1852	+	19.0246i	−1.34504	+	0.977230i	−0.345800	+	0.938308i	$0.612392\pi$
$379$	−26.1852	+	19.0246i	−1.34504	+	0.977230i	−0.999242	+	0.0389217i	$0.987608\pi$
$380$	22.1742	+	9.10344i	1.13751	+	0.466997i
$381$	−3.74380	+	2.09036i	−0.191801	+	0.107092i
$382$	−0.340393	−	0.589578i	−0.0174160	−	0.0301654i
$383$	3.58734	−	34.1313i	0.183304	−	1.74403i	−0.386540	−	0.922273i	$-0.626330\pi$
$383$	3.58734	−	34.1313i	0.183304	−	1.74403i	0.569844	−	0.821753i	$-0.307004\pi$
$384$	17.9691	−	5.55444i	0.916984	−	0.283449i
$385$	1.28825	−	17.0527i	0.0656555	−	0.869084i
$386$	−1.55752	−	4.79354i	−0.0792754	−	0.243985i
$387$	3.12706	−	23.2930i	0.158958	−	1.18405i
$388$	8.85423	−	27.2505i	0.449505	−	1.38344i
$389$	−4.03437	−	0.857531i	−0.204550	−	0.0434785i	0.104497	−	0.994525i	$-0.466677\pi$
$389$	−4.03437	−	0.857531i	−0.204550	−	0.0434785i	−0.309047	+	0.951047i	$0.600010\pi$
$390$	8.21871	+	7.18059i	0.416170	+	0.363603i
$391$	0.539785	−	0.114735i	0.0272981	−	0.00580239i
$392$	0.672125	−	6.39484i	0.0339474	−	0.322988i
$393$	−1.99322	+	0.180587i	−0.100545	+	0.00910942i
$394$	9.21437	−	4.10250i	0.464213	−	0.206681i
$395$	19.8732	+	20.8108i	0.999929	+	1.04711i
$396$	22.6846	+	5.50734i	1.13994	+	0.276754i
$397$	−15.7730	+	11.4597i	−0.791622	+	0.575147i	−0.908444	−	0.418006i	$-0.862729\pi$
$397$	−15.7730	+	11.4597i	−0.791622	+	0.575147i	0.116822	+	0.993153i	$0.462729\pi$
$398$	−1.79283	−	0.381078i	−0.0898664	−	0.0191017i
$399$	−10.5134	−	14.9165i	−0.526329	−	0.746757i
$400$	12.7879	−	6.61717i	0.639396	−	0.330859i
$401$	−10.5037	−	18.1930i	−0.524530	−	0.908513i	−0.999592	−	0.0285608i	$-0.990908\pi$
$401$	−10.5037	−	18.1930i	−0.524530	−	0.908513i	0.475062	−	0.879953i	$-0.342426\pi$
$402$	−0.107701	−	0.0128866i	−0.00537164	−	0.000642725i
$403$	−1.85714	−	17.6695i	−0.0925106	−	0.880179i
$404$	14.7159	−	10.6917i	0.732143	−	0.531933i
$405$	−2.66600	+	19.9472i	−0.132474	+	0.991186i
$406$	−0.466949	−	0.339258i	−0.0231743	−	0.0168371i
$407$	−9.54088	+	16.5253i	−0.472924	+	0.819128i
$408$	0.509488	−	0.284474i	0.0252234	−	0.0140836i
$409$	6.64167	−	1.41173i	0.328409	−	0.0698055i	−0.0407565	−	0.999169i	$-0.512977\pi$
$409$	6.64167	−	1.41173i	0.328409	−	0.0698055i	0.369166	+	0.929364i	$0.379643\pi$
$410$	−9.77489	+	7.54938i	−0.482747	+	0.372837i
$411$	8.76184	−	11.7024i	0.432189	−	0.577234i
$412$	−6.03323	−	6.70058i	−0.297236	−	0.330114i
$413$	5.34252	−	16.4426i	0.262888	−	0.809087i
$414$	−1.89362	+	3.07248i	−0.0930661	+	0.151004i
$415$	−3.64376	+	6.76148i	−0.178865	+	0.331908i
$416$	−19.7866	−	21.9753i	−0.970118	−	1.07743i
$417$	5.18475	+	3.09356i	0.253898	+	0.151492i
$418$	5.60960	+	9.71612i	0.274375	+	0.475231i
$419$	3.50641	−	33.3613i	0.171299	−	1.62980i	−0.484446	−	0.874821i	$-0.660979\pi$
$419$	3.50641	−	33.3613i	0.171299	−	1.62980i	0.655745	−	0.754983i	$-0.272355\pi$
$420$	−12.3807	−	1.11439i	−0.604118	−	0.0543766i
$421$	2.40764	+	22.9071i	0.117341	+	1.11643i	0.881757	+	0.471703i	$0.156361\pi$
$421$	2.40764	+	22.9071i	0.117341	+	1.11643i	−0.764416	+	0.644723i	$0.776973\pi$
$422$	1.00697	−	0.731609i	0.0490187	−	0.0356142i
$423$	0.706468	+	1.30911i	0.0343497	+	0.0636510i
$424$	−12.3890			−0.601663
$425$	0.778884	−	0.638862i	0.0377814	−	0.0309893i
$426$	1.05859	+	1.50194i	0.0512890	+	0.0727690i
$427$	11.5650	−	12.8442i	0.559670	−	0.621577i
$428$	11.7224	+	5.21914i	0.566622	+	0.252277i
$429$	−9.27486	−	46.9408i	−0.447795	−	2.26632i
$430$	0.579600	−	7.67219i	0.0279508	−	0.369986i
$431$	−15.8922	−	11.5463i	−0.765498	−	0.556167i	0.135094	−	0.990833i	$-0.456866\pi$
$431$	−15.8922	−	11.5463i	−0.765498	−	0.556167i	−0.900592	+	0.434666i	$0.856866\pi$
$432$	3.73877	−	14.4888i	0.179881	−	0.697092i
$433$	−1.24749	−	0.906354i	−0.0599505	−	0.0435566i	0.557406	−	0.830240i	$-0.311797\pi$
$433$	−1.24749	−	0.906354i	−0.0599505	−	0.0435566i	−0.617357	+	0.786683i	$0.711797\pi$
$434$	−1.44559	−	1.60549i	−0.0693904	−	0.0770659i
$435$	1.64943	−	2.34313i	0.0790841	−	0.112345i
$436$	−0.695848	+	0.772817i	−0.0333251	+	0.0370112i
$437$	15.8931	−	3.37817i	0.760268	−	0.161600i
$438$	2.02477	−	0.625877i	0.0967473	−	0.0299056i
$439$	−3.38112	−	0.718679i	−0.161372	−	0.0343007i	0.126517	−	0.991964i	$-0.459620\pi$
$439$	−3.38112	−	0.718679i	−0.161372	−	0.0343007i	−0.287889	+	0.957664i	$0.592953\pi$
$440$	15.8397	+	2.88435i	0.755130	+	0.137506i
$441$	−9.13422	−	7.04604i	−0.434963	−	0.335526i
$442$	−0.459308	−	0.333707i	−0.0218470	−	0.0158728i
$443$	−11.4007	+	19.7467i	−0.541666	+	0.938193i	0.457143	+	0.889393i	$0.348873\pi$
$443$	−11.4007	+	19.7467i	−0.541666	+	0.938193i	−0.998809	+	0.0487993i	$0.984461\pi$
$444$	11.9113	+	7.10704i	0.565283	+	0.337285i
$445$	−19.7208	−	13.4628i	−0.934855	−	0.638199i
$446$	8.32190	+	3.70515i	0.394053	+	0.175444i
$447$	−18.1182	+	15.8484i	−0.856960	+	0.749602i
$448$	6.48881	+	1.37924i	0.306567	+	0.0651629i
$449$	19.8521			0.936876			0.468438	−	0.883496i	$-0.344817\pi$
$449$	19.8521			0.936876			0.468438	+	0.883496i	$0.344817\pi$
$450$	−0.492458	+	6.56994i	−0.0232147	+	0.309710i
$451$	54.1489			2.54977
$452$	−0.484897	−	0.103068i	−0.0228076	−	0.00484791i
$453$	7.70782	+	2.62742i	0.362145	+	0.123447i
$454$	0.541401	+	0.241047i	0.0254092	+	0.0113129i
$455$	8.58069	+	23.9916i	0.402269	+	1.12475i
$456$	15.0010	−	8.37585i	0.702486	−	0.392235i
$457$	−3.84410	+	6.65818i	−0.179820	+	0.311457i	−0.941819	−	0.336122i	$-0.890885\pi$
$457$	−3.84410	+	6.65818i	−0.179820	+	0.311457i	0.761999	+	0.647578i	$0.224218\pi$
$458$	9.12674	+	6.63097i	0.426465	+	0.309845i
$459$	0.0451040	−	1.04592i	0.00210528	−	0.0488195i
$460$	5.25052	−	9.74302i	0.244807	−	0.454271i
$461$	−5.32282	−	1.13140i	−0.247908	−	0.0526945i	0.0822814	−	0.996609i	$-0.473779\pi$
$461$	−5.32282	−	1.13140i	−0.247908	−	0.0526945i	−0.330190	+	0.943915i	$0.607113\pi$
$462$	−4.26741	−	3.95486i	−0.198538	−	0.183997i
$463$	−5.77700	+	1.22794i	−0.268480	+	0.0570672i	−0.340184	−	0.940359i	$-0.610489\pi$
$463$	−5.77700	+	1.22794i	−0.268480	+	0.0570672i	0.0717044	+	0.997426i	$0.477156\pi$
$464$	−1.42564	+	1.58333i	−0.0661835	+	0.0735042i
$465$	7.86240	−	7.29512i	0.364610	−	0.338303i
$466$	4.45839	+	4.95155i	0.206531	+	0.229376i
$467$	19.9403	+	14.4875i	0.922727	+	0.670400i	0.944201	−	0.329369i	$-0.106836\pi$
$467$	19.9403	+	14.4875i	0.922727	+	0.670400i	−0.0214742	+	0.999769i	$0.506836\pi$
$468$	−34.2142	+	6.25099i	−1.58155	+	0.288952i
$469$	−0.204876	−	0.148851i	−0.00946032	−	0.00687332i
$470$	0.255757	+	0.414434i	0.0117972	+	0.0191164i
$471$	12.4022	−	10.8485i	0.571463	−	0.499871i
$472$	14.8696	+	6.62035i	0.684427	+	0.304726i
$473$	−22.5716	+	25.0683i	−1.03784	+	1.15264i
$474$	9.75015	−	0.883372i	0.447839	−	0.0405746i
$475$	22.9329	−	18.8102i	1.05223	−	0.863070i
$476$	0.646657			0.0296395
$477$	−11.6618	+	18.9218i	−0.533959	+	0.866372i
$478$	4.97831	−	3.61696i	0.227703	−	0.165436i
$479$	−1.66450	−	15.8366i	−0.0760528	−	0.723594i	−0.964405	−	0.264431i	$-0.914816\pi$
$479$	−1.66450	−	15.8366i	−0.0760528	−	0.723594i	0.888352	−	0.459163i	$-0.151851\pi$
$480$	3.45000	−	17.5147i	0.157470	−	0.799432i
$481$	2.97182	−	28.2750i	0.135504	−	1.28923i
$482$	−4.94139	−	8.55873i	−0.225074	−	0.389840i
$483$	−7.35707	+	4.10784i	−0.334758	+	0.186913i
$484$	−9.11849	−	10.1271i	−0.414477	−	0.460323i
$485$	−24.4861	−	25.6413i	−1.11186	−	1.16431i
$486$	4.74628	+	4.93478i	0.215296	+	0.223846i
$487$	9.80003	−	30.1614i	0.444082	−	1.36674i	−0.439406	−	0.898289i	$-0.644811\pi$
$487$	9.80003	−	30.1614i	0.444082	−	1.36674i	0.883488	−	0.468454i	$-0.155189\pi$
$488$	10.8880	+	12.0924i	0.492879	+	0.547397i
$489$	14.2739	+	1.70789i	0.645486	+	0.0772335i
$490$	−3.11914	−	2.12935i	−0.140908	−	0.0961942i
$491$	22.0949	−	4.69643i	0.997131	−	0.211947i	0.319689	−	0.947523i	$-0.396422\pi$
$491$	22.0949	−	4.69643i	0.997131	−	0.211947i	0.677442	+	0.735576i	$0.263088\pi$
$492$	0.565420	−	39.3564i	0.0254911	−	1.77433i
$493$	−0.0745316	+	0.129093i	−0.00335674	+	0.00581404i
$494$	−13.5235	−	9.82542i	−0.608452	−	0.442066i
$495$	19.3153	−	21.4771i	0.868159	−	0.965326i
$496$	−6.45175	+	4.68747i	−0.289692	+	0.210474i
$497$	0.448426	+	4.26649i	0.0201147	+	0.191378i
$498$	1.02847	+	2.40228i	0.0460869	+	0.107649i
$499$	9.74420	+	16.8775i	0.436210	+	0.755539i	0.997394	−	0.0721531i	$-0.0229870\pi$
$499$	9.74420	+	16.8775i	0.436210	+	0.755539i	−0.561183	+	0.827692i	$0.689654\pi$
$500$	0.338751	−	20.2009i	0.0151494	−	0.903414i
$501$	−24.6062	+	2.22934i	−1.09932	+	0.0995995i
$502$	0.199431	+	0.0423903i	0.00890102	+	0.00189197i
$503$	−14.7866	+	10.7431i	−0.659301	+	0.479010i	−0.866427	−	0.499304i	$-0.833589\pi$
$503$	−14.7866	+	10.7431i	−0.659301	+	0.479010i	0.207126	+	0.978314i	$0.433589\pi$
$504$	−6.14968	+	6.44739i	−0.273929	+	0.287189i
$505$	−3.00788	−	22.3061i	−0.133849	−	0.992607i
$506$	4.73239	−	2.10699i	0.210380	−	0.0936673i
$507$	28.0992	+	39.8673i	1.24793	+	1.77057i
$508$	0.467618	−	4.44909i	0.0207472	−	0.197396i
$509$	−22.0398	+	4.68470i	−0.976895	+	0.207645i	−0.668581	−	0.743639i	$-0.733098\pi$
$509$	−22.0398	+	4.68470i	−0.976895	+	0.207645i	−0.308314	+	0.951285i	$0.599765\pi$
$510$	−0.00512424	−	0.342693i	−0.000226905	−	0.0151747i
$511$	4.83976	+	1.02872i	0.214098	+	0.0455080i
$512$	−7.07765	+	21.7828i	−0.312791	+	0.962671i
$513$	1.32801	−	30.7954i	0.0586331	−	1.35965i
$514$	−3.66505	−	11.2799i	−0.161658	−	0.497533i
$515$	−10.8405	+	2.63857i	−0.477688	+	0.116269i
$516$	17.9844	+	16.6672i	0.791719	+	0.733732i
$517$	0.223181	−	2.12343i	0.00981550	−	0.0933883i
$518$	−1.72855	−	2.99394i	−0.0759483	−	0.131546i
$519$	−0.537382	+	37.4048i	−0.0235884	+	1.64189i
$520$	−23.3080	+	5.67315i	−1.02212	+	0.248784i
$521$	−4.02702	+	2.92580i	−0.176427	+	0.128182i	−0.672494	−	0.740103i	$-0.734777\pi$
$521$	−4.02702	+	2.92580i	−0.176427	+	0.128182i	0.496067	+	0.868284i	$0.334777\pi$
$522$	−0.274499	−	0.935452i	−0.0120145	−	0.0409436i
$523$	−0.936421	−	2.88201i	−0.0409468	−	0.126021i	0.928493	−	0.371349i	$-0.121105\pi$
$523$	−0.936421	−	2.88201i	−0.0409468	−	0.126021i	−0.969440	+	0.245327i	$0.921105\pi$
$524$	1.04404	−	1.80833i	0.0456091	−	0.0789973i
$525$	−8.48160	+	12.8320i	−0.370167	+	0.560036i
$526$	−1.87434	−	3.24645i	−0.0817251	−	0.141552i
$527$	−0.373339	+	0.414635i	−0.0162629	+	0.0180618i
$528$	−16.1654	+	14.1403i	−0.703510	+	0.615376i
$529$	1.61996	+	15.4129i	0.0704329	+	0.670124i
$530$	−3.45202	+	6.40567i	−0.149946	+	0.278245i
$531$	24.1081	−	16.4786i	1.04620	−	0.715112i
$532$	19.0397			0.825477
$533$	−73.7039	+	32.8151i	−3.19247	+	1.42138i
$534$	−7.76147	+	2.39915i	−0.335872	+	0.103821i
$535$	12.5664	−	9.70532i	0.543292	−	0.419598i
$536$	0.159532	−	0.177179i	0.00689075	−	0.00765296i
$537$	23.5990	+	21.8706i	1.01837	+	0.943787i
$538$	0.345401	+	0.383607i	0.0148913	+	0.0165385i
$539$	5.11666	+	15.7475i	0.220390	+	0.678291i
$540$	−15.4083	−	14.2630i	−0.663067	−	0.613782i
$541$	−4.84376	+	14.9075i	−0.208249	+	0.640925i	0.791315	+	0.611409i	$0.209397\pi$
$541$	−4.84376	+	14.9075i	−0.208249	+	0.640925i	−0.999564	+	0.0295168i	$0.990603\pi$
$542$	3.30483	−	1.47141i	0.141955	−	0.0632023i
$543$	−0.937217	+	2.02618i	−0.0402198	+	0.0869517i
$544$	−0.0970685	+	0.923545i	−0.00416178	+	0.0395967i
$545$	0.433346	+	1.21164i	0.0185625	+	0.0519008i
$546$	8.20522	+	2.79698i	0.351151	+	0.119700i
$547$	0.797793	+	7.59049i	0.0341112	+	0.324546i	0.998249	+	0.0591454i	$0.0188376\pi$
$547$	0.797793	+	7.59049i	0.0341112	+	0.324546i	−0.964138	+	0.265401i	$0.914496\pi$
$548$	4.71321	+	14.5058i	0.201338	+	0.619656i
$549$	28.7178	−	5.24678i	1.22565	−	0.223927i
$550$	5.90486	−	7.38618i	0.251784	−	0.314948i
$551$	−2.19446	+	3.80091i	−0.0934870	+	0.161924i
$552$	−3.12219	−	7.29272i	−0.132889	−	0.310399i
$553$	20.8807	+	9.29668i	0.887937	+	0.395335i
$554$	3.78206	+	1.68388i	0.160684	+	0.0715412i
$555$	14.7337	−	8.80283i	0.625412	−	0.373659i
$556$	−5.75449	+	2.56206i	−0.244045	+	0.108656i
$557$	17.3196			0.733856			0.366928	−	0.930249i	$-0.380410\pi$
$557$	17.3196			0.733856			0.366928	+	0.930249i	$0.380410\pi$
$558$	−0.277019	−	3.63852i	−0.0117271	−	0.154031i
$559$	15.5311	−	47.8000i	0.656898	−	2.02172i
$560$	7.40036	−	8.71995i	0.312722	−	0.368485i
$561$	−0.900590	+	1.20283i	−0.0380230	+	0.0507836i
$562$	−6.48374	+	1.37816i	−0.273500	+	0.0581343i
$563$	−25.2749	+	5.37236i	−1.06521	+	0.226418i	−0.706994	−	0.707220i	$-0.749949\pi$
$563$	−25.2749	+	5.37236i	−1.06521	+	0.226418i	−0.358218	+	0.933638i	$0.616616\pi$
$564$	−1.54102	−	0.184385i	−0.0648885	−	0.00776401i
$565$	−0.396914	+	0.467690i	−0.0166983	+	0.0196759i
$566$	−3.16645	+	9.74534i	−0.133096	+	0.409627i
$567$	4.05843	+	15.4614i	0.170438	+	0.649319i
$568$	−4.03887			−0.169467
$569$	−0.158490	+	0.0705645i	−0.00664427	+	0.00295822i	−0.410056	−	0.912060i	$-0.634491\pi$
$569$	−0.158490	+	0.0705645i	−0.00664427	+	0.00295822i	0.403412	+	0.915019i	$0.367824\pi$
$570$	−0.150875	−	10.0900i	−0.00631944	−	0.422624i
$571$	−22.4784	−	10.0080i	−0.940693	−	0.418824i	−0.121661	−	0.992572i	$-0.538822\pi$
$571$	−22.4784	−	10.0080i	−0.940693	−	0.418824i	−0.819032	+	0.573748i	$0.805489\pi$
$572$	45.6051	+	20.3047i	1.90685	+	0.848982i
$573$	1.60902	−	2.14902i	0.0672179	−	0.0897765i
$574$	−4.90518	+	8.49601i	−0.204738	+	0.354617i
$575$	−7.53082	−	11.4387i	−0.314057	−	0.477025i
$576$	7.25521	+	8.53878i	0.302300	+	0.355782i
$577$	−8.78272	−	27.0304i	−0.365629	−	1.12529i	−0.949586	−	0.313506i	$-0.898496\pi$
$577$	−8.78272	−	27.0304i	−0.365629	−	1.12529i	0.583957	−	0.811785i	$-0.301504\pi$
$578$	−0.778632	−	7.40819i	−0.0323868	−	0.308140i
$579$	14.9601	−	13.0859i	0.621720	−	0.543832i
$580$	1.00678	+	2.81497i	0.0418044	+	0.116885i
$581$	−0.637722	+	6.06752i	−0.0264572	+	0.251723i
$582$	−12.0133	+	1.08842i	−0.497968	+	0.0451163i
$583$	29.1444	−	12.9759i	1.20704	−	0.537408i
$584$	−1.43948	+	4.43027i	−0.0595661	+	0.183326i
$585$	−13.2752	+	40.9386i	−0.548864	+	1.69260i
$586$	1.16044	+	3.57146i	0.0479373	+	0.147536i
$587$	−8.62688	−	9.58112i	−0.356070	−	0.395455i	0.538323	−	0.842739i	$-0.319058\pi$
$587$	−8.62688	−	9.58112i	−0.356070	−	0.395455i	−0.894392	+	0.447284i	$0.852392\pi$
$588$	11.4990	−	3.55445i	0.474209	−	0.146583i
$589$	−10.9923	+	12.2082i	−0.452931	+	0.503031i
$590$	7.56621	−	5.84356i	0.311496	−	0.240576i
$591$	29.1731	+	27.0365i	1.20002	+	1.11213i
$592$	−11.6581	+	5.19054i	−0.479146	+	0.213330i
$593$	27.5686			1.13211			0.566053	−	0.824369i	$-0.308470\pi$
$593$	27.5686			1.13211			0.566053	+	0.824369i	$0.308470\pi$
$594$	−1.62718	−	9.69170i	−0.0667639	−	0.397655i
$595$	0.379599	−	0.704396i	0.0155621	−	0.0288774i
$596$	−2.62516	−	24.9767i	−0.107531	−	1.02309i
$597$	−1.40104	−	7.09075i	−0.0573406	−	0.290205i
$598$	−5.16454	+	5.73580i	−0.211194	+	0.234554i
$599$	−23.0932	−	39.9986i	−0.943563	−	1.63430i	−0.758604	−	0.651552i	$-0.774118\pi$
$599$	−23.0932	−	39.9986i	−0.943563	−	1.63430i	−0.184958	−	0.982746i	$-0.559215\pi$
$600$	−11.1800	−	9.20418i	−0.456423	−	0.375759i
$601$	−20.7102	+	35.8711i	−0.844787	+	1.46321i	0.0410187	+	0.999158i	$0.486940\pi$
$601$	−20.7102	+	35.8711i	−0.844787	+	1.46321i	−0.885806	+	0.464056i	$0.846394\pi$
$602$	−1.88855	−	5.81235i	−0.0769714	−	0.236894i
$603$	−0.120438	−	0.410435i	−0.00490462	−	0.0167142i
$604$	−6.87348	+	4.99388i	−0.279678	+	0.203198i
$605$	−16.3841	+	3.98787i	−0.666107	+	0.162130i
$606$	−6.57608	−	3.92372i	−0.267135	−	0.159390i
$607$	−8.40346	−	14.5552i	−0.341086	−	0.590778i	0.643549	−	0.765405i	$-0.277461\pi$
$607$	−8.40346	−	14.5552i	−0.341086	−	0.590778i	−0.984635	+	0.174627i	$0.944128\pi$
$608$	−2.85802	+	27.1922i	−0.115908	+	1.10279i
$609$	0.505154	−	2.21930i	0.0204699	−	0.0899307i
$610$	9.28611	−	2.26024i	0.375984	−	0.0915143i
$611$	0.983051	+	3.02552i	0.0397700	+	0.122399i
$612$	0.864837	+	0.667125i	0.0349590	+	0.0269669i
$613$	−6.05434	+	18.6333i	−0.244532	+	0.752593i	0.751181	+	0.660097i	$0.229485\pi$
$613$	−6.05434	+	18.6333i	−0.244532	+	0.752593i	−0.995713	+	0.0924965i	$0.970515\pi$
$614$	8.80597	+	1.87177i	0.355380	+	0.0755383i
$615$	−42.5386	−	23.7188i	−1.71532	−	0.956436i
$616$	12.5091	−	2.65889i	0.504007	−	0.107130i
$617$	0.681066	−	6.47991i	0.0274187	−	0.260871i	−0.972222	−	0.234061i	$-0.924798\pi$
$617$	0.681066	−	6.47991i	0.0274187	−	0.260871i	0.999641	−	0.0268101i	$-0.00853495\pi$
$618$	−1.59356	+	3.44514i	−0.0641026	+	0.138584i
$619$	34.1346	−	15.1977i	1.37199	−	0.610848i	0.417385	−	0.908730i	$-0.362947\pi$
$619$	34.1346	−	15.1977i	1.37199	−	0.610848i	0.954603	+	0.297882i	$0.0962801\pi$
$620$	1.49540	+	11.0897i	0.0600568	+	0.445374i
$621$	−14.0772	−	2.09613i	−0.564897	−	0.0841148i
$622$	0.420441	−	0.305468i	0.0168581	−	0.0122482i
$623$	−18.5521	−	3.94336i	−0.743273	−	0.157987i
$624$	13.4341	−	29.0433i	0.537793	−	1.16266i
$625$	−21.8058	−	12.2273i	−0.872232	−	0.489092i
$626$	3.26038	+	5.64714i	0.130311	+	0.225705i
$627$	−26.5163	+	35.4154i	−1.05896	+	1.41435i
$628$	1.79697	+	17.0970i	0.0717067	+	0.682244i
$629$	−0.722320	+	0.524796i	−0.0288008	+	0.0209250i
$630$	1.62007	+	4.97613i	0.0645451	+	0.198254i
$631$	10.2656	+	7.45836i	0.408665	+	0.296913i	0.773061	−	0.634331i	$-0.218725\pi$
$631$	10.2656	+	7.45836i	0.408665	+	0.296913i	−0.364396	+	0.931244i	$0.618725\pi$
$632$	−10.7594	+	18.6358i	−0.427986	+	0.741294i
$633$	4.21505	+	2.51498i	0.167533	+	0.0999613i
$634$	−0.150218	+	0.0319298i	−0.00596592	+	0.00126809i
$635$	−4.57184	−	3.12106i	−0.181428	−	0.123856i
$636$	−9.12682	−	21.3182i	−0.361902	−	0.845321i
$637$	−16.5076	−	18.3336i	−0.654057	−	0.726404i
$638$	−0.432401	+	1.33079i	−0.0171189	+	0.0526866i
$639$	−3.80181	+	6.16861i	−0.150397	+	0.244026i
$640$	16.7692	+	17.5603i	0.662859	+	0.694133i
$641$	5.72176	+	6.35466i	0.225996	+	0.250994i	0.845470	−	0.534024i	$-0.179321\pi$
$641$	5.72176	+	6.35466i	0.225996	+	0.250994i	−0.619474	+	0.785017i	$0.712654\pi$
$642$	0.0776007	−	5.40145i	0.00306266	−	0.213178i
$643$	4.36268	+	7.55638i	0.172047	+	0.297994i	0.939135	−	0.343547i	$-0.111629\pi$
$643$	4.36268	+	7.55638i	0.172047	+	0.297994i	−0.767088	+	0.641542i	$0.778295\pi$
$644$	0.918932	−	8.74305i	0.0362110	−	0.344524i
$645$	28.7125	−	9.80625i	1.13055	−	0.386121i
$646$	0.0548719	+	0.522071i	0.00215891	+	0.0205406i
$647$	−0.0235532	+	0.0171124i	−0.000925971	+	0.000672757i	−0.588248	−	0.808680i	$-0.700182\pi$
$647$	−0.0235532	+	0.0171124i	−0.000925971	+	0.000672757i	0.587322	+	0.809353i	$0.300182\pi$
$648$	−14.8760	+	2.27838i	−0.584385	+	0.0895032i
$649$	−41.9137			−1.64526
$650$	−3.56116	+	13.6320i	−0.139680	+	0.534691i
$651$	3.57658	−	7.73225i	0.140177	−	0.303051i
$652$	−10.0359	+	11.1460i	−0.393036	+	0.436511i
$653$	15.7626	+	7.01797i	0.616839	+	0.274634i	0.691275	−	0.722591i	$-0.257049\pi$
$653$	15.7626	+	7.01797i	0.616839	+	0.274634i	−0.0744367	+	0.997226i	$0.523716\pi$
$654$	0.414384	+	0.141254i	0.0162037	+	0.00552347i
$655$	−1.35692	−	2.19878i	−0.0530194	−	0.0859136i
$656$	29.2973	+	21.2858i	1.14387	+	0.831069i
$657$	5.41140	+	6.36876i	0.211119	+	0.248469i
$658$	0.312950	+	0.227372i	0.0122001	+	0.00886387i
$659$	−25.1350	−	27.9153i	−0.979122	−	1.08743i	−0.996158	−	0.0875707i	$-0.972090\pi$
$659$	−25.1350	−	27.9153i	−0.979122	−	1.08743i	0.0170360	−	0.999855i	$-0.494577\pi$
$660$	6.70573	+	29.3809i	0.261020	+	1.14365i
$661$	33.5406	−	37.2506i	1.30458	−	1.44888i	0.486610	−	0.873619i	$-0.338233\pi$
$661$	33.5406	−	37.2506i	1.30458	−	1.44888i	0.817969	−	0.575263i	$-0.195100\pi$
$662$	−6.69604	+	1.42329i	−0.260249	+	0.0553176i
$663$	0.496888	−	2.18299i	0.0192975	−	0.0847802i
$664$	−5.61830	−	1.19421i	−0.218032	−	0.0463442i
$665$	11.1767	−	20.7397i	0.433412	−	0.804253i
$666$	0.776946	−	5.78735i	0.0301061	−	0.224255i
$667$	1.63947	+	1.19114i	0.0634804	+	0.0461212i
$668$	12.8886	−	22.3237i	0.498676	−	0.863732i
$669$	−0.516032	+	35.9188i	−0.0199510	+	1.38870i
$670$	−0.0471580	−	0.131854i	−0.00182187	−	0.00509396i
$671$	−38.2787	−	17.0428i	−1.47773	−	0.657930i
$672$	−2.74853	−	13.9105i	−0.106027	−	0.536609i
$673$	4.67811	+	0.994364i	0.180328	+	0.0383299i	0.297191	−	0.954818i	$-0.403950\pi$
$673$	4.67811	+	0.994364i	0.180328	+	0.0383299i	−0.116862	+	0.993148i	$0.537284\pi$
$674$	9.22544			0.355351
$675$	−24.5814	+	8.41144i	−0.946140	+	0.323756i
$676$	−50.8875			−1.95721
$677$	26.6936	+	5.67390i	1.02592	+	0.218066i	0.689988	−	0.723821i	$-0.257616\pi$
$677$	26.6936	+	5.67390i	1.02592	+	0.218066i	0.335930	+	0.941887i	$0.390949\pi$
$678$	0.0404535	+	0.204738i	0.00155361	+	0.00786292i
$679$	−25.7274	−	11.4546i	−0.987327	−	0.439587i
$680$	0.622175	+	0.424741i	0.0238593	+	0.0162881i
$681$	−0.0335717	+	2.33678i	−0.00128647	+	0.0895456i
$682$	−2.61876	+	4.53583i	−0.100278	+	0.173686i
$683$	−3.32056	−	2.41252i	−0.127058	−	0.0923127i	0.522441	−	0.852675i	$-0.325021\pi$
$683$	−3.32056	−	2.41252i	−0.127058	−	0.0923127i	−0.649499	+	0.760362i	$0.725021\pi$
$684$	25.4636	+	19.6424i	0.973627	+	0.751045i
$685$	18.5677	+	3.38110i	0.709435	+	0.129185i
$686$	−8.27581	−	1.75908i	−0.315972	−	0.0671619i
$687$	−9.87348	+	43.3774i	−0.376697	+	1.65495i
$688$	−22.0666	+	4.69041i	−0.841282	+	0.178820i
$689$	−31.8058	+	35.3239i	−1.21170	+	1.34573i
$690$	−4.64062	−	0.417702i	−0.176665	−	0.0159016i
$691$	12.5662	+	13.9562i	0.478042	+	0.530920i	0.933136	−	0.359524i	$-0.117061\pi$
$691$	12.5662	+	13.9562i	0.478042	+	0.530920i	−0.455094	+	0.890444i	$0.650394\pi$
$692$	−31.5753	−	22.9408i	−1.20031	−	0.872077i
$693$	7.71393	−	21.6081i	0.293028	−	0.820824i
$694$	1.42101	+	1.03243i	0.0539409	+	0.0391903i
$695$	−0.587161	+	7.77227i	−0.0222723	+	0.294819i
$696$	2.02824	+	0.691380i	0.0768801	+	0.0262067i
$697$	2.31459	+	1.03052i	0.0876713	+	0.0390338i
$698$	−0.629274	+	0.698880i	−0.0238184	+	0.0264530i
$699$	−11.0307	+	23.8473i	−0.417218	+	0.901989i
$700$	−5.84502	−	14.9458i	−0.220921	−	0.564898i
$701$	22.5412			0.851368			0.425684	−	0.904872i	$-0.360033\pi$
$701$	22.5412			0.851368			0.425684	+	0.904872i	$0.360033\pi$
$702$	8.08813	+	12.2056i	0.305267	+	0.460671i
$703$	−21.2675	+	15.4517i	−0.802118	+	0.582773i
$704$	−1.68108	−	15.9944i	−0.0633579	−	0.602810i
$705$	−1.10545	+	1.57037i	−0.0416337	+	0.0591437i
$706$	0.520579	−	4.95298i	0.0195922	−	0.186408i
$707$	−8.93915	−	15.4831i	−0.336192	−	0.582301i
$708$	−0.437661	+	30.4637i	−0.0164483	+	1.14489i
$709$	−9.97932	−	11.0832i	−0.374781	−	0.416237i	0.526017	−	0.850474i	$-0.323685\pi$
$709$	−9.97932	−	11.0832i	−0.374781	−	0.416237i	−0.900799	+	0.434237i	$0.857018\pi$
$710$	−1.12537	+	2.08828i	−0.0422346	+	0.0783718i
$711$	18.3348	+	33.9749i	0.687609	+	1.27416i
$712$	5.51790	−	16.9823i	0.206792	−	0.636440i
$713$	5.07549	+	5.63690i	0.190078	+	0.211104i
$714$	−0.107144	−	0.250264i	−0.00400976	−	0.00936590i
$715$	48.8887	−	37.7579i	1.82833	−	1.41207i
$716$	−32.8354	+	6.97937i	−1.22712	+	0.260831i
$717$	20.8385	+	12.4336i	0.778229	+	0.464343i
$718$	−5.15985	+	8.93713i	−0.192564	+	0.333531i
$719$	−35.1450	−	25.5343i	−1.31069	−	0.952270i	−0.999998	−	0.00175887i	$-0.999440\pi$
$719$	−35.1450	−	25.5343i	−1.31069	−	0.952270i	−0.310689	−	0.950512i	$-0.600560\pi$
$720$	18.8932	−	4.02744i	0.704107	−	0.150094i
$721$	−7.16959	+	5.20901i	−0.267009	+	0.193994i
$722$	0.743291	+	7.07194i	0.0276624	+	0.263190i
$723$	23.3577	−	31.1967i	0.868683	−	1.16022i
$724$	−1.16457	−	2.01710i	−0.0432810	−	0.0749649i
$725$	3.65731	+	0.555760i	0.135829	+	0.0206404i
$726$	−2.40848	+	5.20691i	−0.0893870	+	0.193247i
$727$	15.5641	+	3.30825i	0.577241	+	0.122696i	0.487275	−	0.873249i	$-0.337991\pi$
$727$	15.5641	+	3.30825i	0.577241	+	0.122696i	0.0899657	+	0.995945i	$0.471324\pi$
$728$	−15.4152	+	11.1998i	−0.571326	+	0.415093i
$729$	−10.5231	+	24.8649i	−0.389744	+	0.920923i
$730$	1.88956	+	1.97871i	0.0699356	+	0.0732352i
$731$	−1.44190	+	0.641974i	−0.0533305	+	0.0237443i
$732$	−12.7867	+	27.6437i	−0.472611	+	1.02174i
$733$	1.63644	−	15.5697i	0.0604433	−	0.575080i	−0.921826	−	0.387604i	$-0.873303\pi$
$733$	1.63644	−	15.5697i	0.0604433	−	0.575080i	0.982269	−	0.187476i	$-0.0600306\pi$
$734$	−8.75636	+	1.86122i	−0.323203	+	0.0686990i
$735$	2.87828	−	14.6122i	0.106167	−	0.538979i
$736$	12.3487	+	2.62480i	0.455180	+	0.0967516i
$737$	−0.189718	+	0.583893i	−0.00698836	+	0.0215080i
$738$	−15.3251	+	6.30210i	−0.564124	+	0.231984i
$739$	−11.5329	−	35.4945i	−0.424243	−	1.30569i	−0.903717	−	0.428131i	$-0.859172\pi$
$739$	−11.5329	−	35.4945i	−0.424243	−	1.30569i	0.479473	−	0.877556i	$-0.340828\pi$
$740$	−1.34892	+	17.8557i	−0.0495873	+	0.656390i
$741$	14.6300	−	64.2743i	0.537447	−	2.36118i
$742$	−0.604163	+	5.74823i	−0.0221795	+	0.211024i
$743$	5.72347	+	9.91334i	0.209974	+	0.363685i	0.951706	−	0.307011i	$-0.0993288\pi$
$743$	5.72347	+	9.91334i	0.209974	+	0.363685i	−0.741732	+	0.670696i	$0.765995\pi$
$744$	6.88779	+	4.10971i	0.252518	+	0.150669i
$745$	−28.7478	−	11.8022i	−1.05324	−	0.432400i
$746$	−10.9622	+	7.96449i	−0.401354	+	0.291601i
$747$	−7.11245	+	7.45677i	−0.260231	+	0.272829i
$748$	−0.484450	−	1.49098i	−0.0177132	−	0.0545158i
$749$	6.30599	−	10.9223i	0.230416	−	0.399092i
$750$	−7.87413	+	3.21597i	−0.287523	+	0.117431i
$751$	12.6924	+	21.9839i	0.463152	+	0.802203i	0.999116	−	0.0420379i	$-0.0133850\pi$
$751$	12.6924	+	21.9839i	0.463152	+	0.802203i	−0.535964	+	0.844241i	$0.680052\pi$
$752$	0.955465	−	1.06115i	0.0348422	−	0.0386962i
$753$	0.155848	+	0.788760i	0.00567943	+	0.0287440i
$754$	−0.217926	−	2.07343i	−0.00793639	−	0.0755097i
$755$	1.40492	+	10.4187i	0.0511301	+	0.379175i
$756$	−15.6246	−	5.83226i	−0.568262	−	0.212117i
$757$	−15.8030			−0.574370			−0.287185	−	0.957875i	$-0.592719\pi$
$757$	−15.8030			−0.574370			−0.287185	+	0.957875i	$0.592719\pi$
$758$	−12.9872	+	5.78226i	−0.471716	+	0.210021i
$759$	14.9830	+	13.8856i	0.543847	+	0.504015i
$760$	18.3189	+	12.5058i	0.664495	+	0.453632i
$761$	−27.7983	+	30.8732i	−1.00769	+	1.11915i	−0.0148259	+	0.999890i	$0.504719\pi$
$761$	−27.7983	+	30.8732i	−1.00769	+	1.11915i	−0.992863	+	0.119262i	$0.961947\pi$
$762$	−1.79933	+	0.556191i	−0.0651828	+	0.0201487i
$763$	0.683930	+	0.759582i	0.0247599	+	0.0274987i
$764$	0.865533	+	2.66384i	0.0313139	+	0.0963742i
$765$	1.23437	−	0.550443i	0.0446286	−	0.0199013i
$766$	4.65808	−	14.3361i	0.168303	−	0.517984i
$767$	57.0502	−	25.4004i	2.05996	−	0.917154i
$768$	−4.65822	+	0.422038i	−0.168089	+	0.0152290i
$769$	−2.57264	+	24.4770i	−0.0927717	+	0.882664i	0.844849	+	0.535005i	$0.179690\pi$
$769$	−2.57264	+	24.4770i	−0.0927717	+	0.882664i	−0.937621	+	0.347659i	$0.886977\pi$
$770$	2.11072	−	7.20864i	0.0760650	−	0.259781i
$771$	35.2031	−	30.7930i	1.26781	−	1.10898i
$772$	2.16758	+	20.6232i	0.0780130	+	0.742244i
$773$	−17.0063	−	52.3400i	−0.611674	−	1.88254i	−0.441927	−	0.897051i	$-0.645705\pi$
$773$	−17.0063	−	52.3400i	−0.611674	−	1.88254i	−0.169747	−	0.985488i	$-0.554295\pi$
$774$	3.47059	−	9.72174i	0.124748	−	0.349441i
$775$	12.9577	+	4.88094i	0.465456	+	0.175329i
$776$	13.2568	−	22.9615i	0.475892	−	0.824270i
$777$	8.17080	−	10.9130i	0.293126	−	0.391500i
$778$	−1.65496	−	0.736836i	−0.0593333	−	0.0264169i
$779$	68.1491	+	30.3419i	2.44169	+	1.08711i
$780$	−26.9326	−	35.9275i	−0.964343	−	1.28641i
$781$	9.50121	−	4.23021i	0.339980	−	0.151369i
$782$	0.242384			0.00866763
$783$	2.96514	−	2.44695i	0.105965	−	0.0874467i
$784$	−3.42190	+	10.5315i	−0.122211	+	0.376126i
$785$	19.6784	+	8.07882i	0.702352	+	0.288345i
$786$	−0.872832	−	0.104436i	−0.0311329	−	0.00372510i
$787$	−34.8320	+	7.40376i	−1.24163	+	0.263916i	−0.781481	−	0.623929i	$-0.785536\pi$
$787$	−34.8320	+	7.40376i	−1.24163	+	0.263916i	−0.460144	+	0.887844i	$0.652202\pi$
$788$	−40.5911	+	8.62790i	−1.44600	+	0.307356i
$789$	8.85992	−	11.8334i	0.315422	−	0.421279i
$790$	6.63761	+	10.7557i	0.236156	+	0.382671i
$791$	−0.150565	+	0.463393i	−0.00535349	+	0.0164763i
$792$	19.4727	+	9.34906i	0.691932	+	0.332204i
$793$	62.4306			2.21698
$794$	−7.82298	+	3.48302i	−0.277627	+	0.123608i
$795$	−28.5792	−	2.57242i	−1.01360	−	0.0912342i
$796$	6.88899	+	3.06717i	0.244174	+	0.108713i
$797$	19.7375	+	8.78769i	0.699137	+	0.311276i	0.725350	−	0.688380i	$-0.241678\pi$
$797$	19.7375	+	8.78769i	0.699137	+	0.311276i	−0.0262126	+	0.999656i	$0.508345\pi$
$798$	−3.15467	−	7.36860i	−0.111674	−	0.260845i
$799$	0.0499513	−	0.0865182i	0.00176715	−	0.00306079i
$800$	22.2227	−	6.10427i	0.785691	−	0.215818i
$801$	−20.7433	−	24.4131i	−0.732928	−	0.862595i
$802$	−2.85129	−	8.77538i	−0.100683	−	0.309870i
$803$	−1.25385	−	11.9296i	−0.0442475	−	0.420987i
$804$	0.422403	+	0.143988i	0.0148970	+	0.00507805i
$805$	−8.98427	−	6.13331i	−0.316654	−	0.216171i
$806$	0.815701	−	7.76087i	0.0287318	−	0.273365i
$807$	−0.854570	+	1.84750i	−0.0300823	+	0.0650352i
$808$	15.3766	−	6.84610i	0.540947	−	0.240845i
$809$	−5.39556	+	16.6058i	−0.189698	+	0.583830i	−0.999998	−	0.00218564i	$-0.999304\pi$
$809$	−5.39556	+	16.6058i	−0.189698	+	0.583830i	0.810300	+	0.586016i	$0.199304\pi$
$810$	−2.96696	+	8.32641i	−0.104249	+	0.292560i
$811$	6.07813	+	18.7066i	0.213432	+	0.656876i	0.999261	+	0.0384326i	$0.0122365\pi$
$811$	6.07813	+	18.7066i	0.213432	+	0.656876i	−0.785829	+	0.618444i	$0.787764\pi$
$812$	1.58896	+	1.76472i	0.0557616	+	0.0619296i
$813$	10.4633	+	9.69693i	0.366963	+	0.340086i
$814$	−5.60811	+	6.22843i	−0.196564	+	0.218306i
$815$	6.24995	+	17.4749i	0.218926	+	0.612118i
$816$	−0.960095	+	0.296775i	−0.0336100	+	0.0103892i
$817$	−42.4542	+	18.9018i	−1.48529	+	0.661292i
$818$	2.98236			0.104276
$819$	2.59516	+	34.0863i	0.0906822	+	1.19107i
$820$	45.7953	−	22.0199i	1.59924	−	0.768967i
$821$	3.29630	+	31.3622i	0.115042	+	1.09455i	0.887921	+	0.459996i	$0.152149\pi$
$821$	3.29630	+	31.3622i	0.115042	+	1.09455i	−0.772879	+	0.634553i	$0.781184\pi$
$822$	4.83298	−	4.22751i	0.168569	−	0.147451i
$823$	16.3827	−	18.1948i	0.571064	−	0.634230i	−0.386556	−	0.922266i	$-0.626335\pi$
$823$	16.3827	−	18.1948i	0.571064	−	0.634230i	0.957620	+	0.288036i	$0.0930021\pi$
$824$	−4.17167	−	7.22555i	−0.145327	−	0.251714i
$825$	35.9406	+	9.94260i	1.25129	+	0.346157i
$826$	3.79683	−	6.57630i	0.132109	−	0.228819i
$827$	−14.6947	−	45.2257i	−0.510985	−	1.57265i	−0.790470	−	0.612501i	$-0.790164\pi$
$827$	−14.6947	−	45.2257i	−0.510985	−	1.57265i	0.279484	−	0.960150i	$-0.409836\pi$
$828$	10.2488	−	10.7449i	0.356169	−	0.373411i
$829$	−26.8175	+	19.4840i	−0.931409	+	0.676708i	−0.946337	−	0.323180i	$-0.895248\pi$
$829$	−26.8175	+	19.4840i	−0.931409	+	0.676708i	0.0149285	+	0.999889i	$0.495248\pi$
$830$	−2.18292	+	2.57216i	−0.0757701	+	0.0892811i
$831$	−0.234521	+	16.3240i	−0.00813545	+	0.566274i
$832$	11.9810	+	20.7517i	0.415366	+	0.719436i
$833$	−0.0809827	+	0.770498i	−0.00280588	+	0.0266962i
$834$	1.94500	+	1.80255i	0.0673499	+	0.0624172i
$835$	−16.7511	−	27.1439i	−0.579697	−	0.939352i
$836$	−14.2638	−	43.8995i	−0.493324	−	1.51829i
$837$	12.7603	−	6.65129i	0.441060	−	0.229902i
$838$	4.55300	−	14.0127i	0.157281	−	0.484060i
$839$	53.9961	+	11.4772i	1.86415	+	0.396238i	0.995133	−	0.0985388i	$-0.0314169\pi$
$839$	53.9961	+	11.4772i	1.86415	+	0.396238i	0.869020	+	0.494777i	$0.164750\pi$
$840$	−10.9916	−	3.39057i	−0.379248	−	0.116986i
$841$	27.8308	−	5.91563i	0.959684	−	0.203987i
$842$	−1.05749	+	10.0614i	−0.0364437	+	0.346738i
$843$	−15.0590	−	21.3657i	−0.518658	−	0.735875i
$844$	−4.67823	+	2.08288i	−0.161031	+	0.0716957i
$845$	−29.8719	+	55.4312i	−1.02762	+	1.90689i
$846$	0.183970	+	0.626942i	0.00632502	+	0.0215547i
$847$	−10.8360	+	7.87279i	−0.372328	+	0.270512i
$848$	20.8694	+	4.43593i	0.716658	+	0.152330i
$849$	−40.2429	+	3.64604i	−1.38113	+	0.125132i
$850$	0.392970	−	0.203344i	0.0134788	−	0.00697465i
$851$	6.06899	+	10.5118i	0.208042	+	0.360340i
$852$	−2.97539	−	6.94983i	−0.101935	−	0.238097i
$853$	−1.64733	−	15.6733i	−0.0564036	−	0.536644i	−0.985843	−	0.167670i	$-0.946376\pi$
$853$	−1.64733	−	15.6733i	−0.0564036	−	0.536644i	0.929440	−	0.368974i	$-0.120291\pi$
$854$	6.14158	−	4.46212i	0.210160	−	0.152690i
$855$	36.3438	−	16.2068i	1.24293	−	0.554262i
$856$	9.60604	+	6.97920i	0.328328	+	0.238544i
$857$	−14.8902	+	25.7906i	−0.508640	+	0.880990i	0.491310	+	0.870985i	$0.336518\pi$
$857$	−14.8902	+	25.7906i	−0.508640	+	0.880990i	−0.999950	+	0.0100052i	$0.996815\pi$
$858$	0.301900	−	21.0140i	0.0103067	−	0.717406i
$859$	1.52513	−	0.324175i	0.0520366	−	0.0110607i	−0.181820	−	0.983332i	$-0.558199\pi$
$859$	1.52513	−	0.324175i	0.0520366	−	0.0110607i	0.233856	+	0.972271i	$0.424865\pi$
$860$	−8.89531	+	30.3798i	−0.303328	+	1.03594i
$861$	−38.4124	−	4.59610i	−1.30909	−	0.156635i
$862$	−5.77328	−	6.41188i	−0.196639	−	0.218390i
$863$	−2.62898	+	8.09117i	−0.0894915	+	0.275427i	−0.985779	−	0.168047i	$-0.946254\pi$
$863$	−2.62898	+	8.09117i	−0.0894915	+	0.275427i	0.896287	+	0.443474i	$0.146254\pi$
$864$	10.6749	−	21.4394i	0.363168	−	0.729382i
$865$	−43.5244	+	20.9279i	−1.47987	+	0.711571i
$866$	−0.453186	−	0.503314i	−0.0153999	−	0.0171033i
$867$	25.6475	−	14.3203i	0.871034	−	0.486344i
$868$	4.44421	+	7.69760i	0.150846	+	0.261273i
$869$	5.79217	−	55.1088i	0.196486	−	1.86944i
$870$	0.922614	−	0.856047i	0.0312795	−	0.0290227i
$871$	−0.0956162	−	0.909728i	−0.00323983	−	0.0308249i
$872$	−0.778507	+	0.565618i	−0.0263636	+	0.0191543i
$873$	−22.5906	−	41.8611i	−0.764576	−	1.41678i
$874$	7.13657			0.241398
$875$	−19.7114	−	2.40654i	−0.666367	−	0.0813558i
$876$	−8.68375	+	0.786755i	−0.293397	+	0.0265820i
$877$	8.51710	−	9.45919i	0.287602	−	0.319414i	−0.581980	−	0.813203i	$-0.697722\pi$
$877$	8.51710	−	9.45919i	0.287602	−	0.319414i	0.869582	+	0.493789i	$0.164388\pi$
$878$	−1.38699	−	0.617527i	−0.0468086	−	0.0208405i
$879$	−11.1461	+	9.74976i	−0.375949	+	0.328851i
$880$	−25.6495	−	10.5302i	−0.864643	−	0.354973i
$881$	3.42753	+	2.49025i	0.115477	+	0.0838986i	0.644025	−	0.765005i	$-0.277263\pi$
$881$	3.42753	+	2.49025i	0.115477	+	0.0838986i	−0.528548	+	0.848903i	$0.677263\pi$
$882$	−3.28086	−	3.86130i	−0.110472	−	0.130017i
$883$	27.7814	+	20.1844i	0.934919	+	0.679258i	0.947192	−	0.320666i	$-0.103907\pi$
$883$	27.7814	+	20.1844i	0.934919	+	0.679258i	−0.0122733	+	0.999925i	$0.503907\pi$
$884$	1.56296	+	1.73584i	0.0525680	+	0.0583827i
$885$	32.9268	+	18.3595i	1.10682	+	0.617146i
$886$	−6.70133	+	7.44258i	−0.225136	+	0.250038i
$887$	27.4913	−	5.84345i	0.923067	−	0.196204i	0.278221	−	0.960517i	$-0.410255\pi$
$887$	27.4913	−	5.84345i	0.923067	−	0.196204i	0.644845	+	0.764313i	$0.276922\pi$
$888$	9.41379	+	8.72431i	0.315906	+	0.292769i
$889$	−4.30089	−	0.914183i	−0.144247	−	0.0306607i
$890$	−7.24316	−	7.58489i	−0.242791	−	0.254246i
$891$	32.6086	−	20.9405i	1.09243	−	0.701534i
$892$	−30.3208	−	22.0294i	−1.01522	−	0.737598i
$893$	1.47073	−	2.54738i	0.0492161	−	0.0852448i
$894$	−9.23132	+	5.15433i	−0.308742	+	0.172387i
$895$	−11.6724	+	39.8642i	−0.390165	+	1.33251i
$896$	17.6193	+	7.84461i	0.588619	+	0.262070i
$897$	−28.8087	−	9.82024i	−0.961894	−	0.327888i
$898$	8.52897	+	1.81289i	0.284615	+	0.0604969i
$899$	−2.04890			−0.0683347
$900$	7.60175	−	26.0185i	0.253392	−	0.867282i
$901$	1.49272			0.0497297
$902$	23.2638	+	4.94488i	0.774601	+	0.164647i
$903$	18.1397	−	15.8672i	0.603651	−	0.528027i
$904$	−0.419060	−	0.186578i	−0.0139377	−	0.00620548i
$905$	−2.88083	+	0.0844826i	−0.0957619	+	0.00280830i
$906$	3.07155	+	1.83269i	0.102045	+	0.0608870i
$907$	20.9176	−	36.2304i	0.694558	−	1.20301i	−0.275771	−	0.961223i	$-0.588933\pi$
$907$	20.9176	−	36.2304i	0.694558	−	1.20301i	0.970329	−	0.241787i	$-0.0777334\pi$
$908$	−1.97259	−	1.43317i	−0.0654628	−	0.0475615i
$909$	4.01795	−	29.9291i	0.133267	−	0.992685i
$910$	1.49558	+	11.0910i	0.0495780	+	0.367664i
$911$	−13.2848	−	2.82377i	−0.440144	−	0.0935556i	−0.0174911	−	0.999847i	$-0.505568\pi$
$911$	−13.2848	−	2.82377i	−0.440144	−	0.0935556i	−0.422653	+	0.906291i	$0.638901\pi$
$912$	−28.2683	+	8.73803i	−0.936058	+	0.289345i
$913$	14.4675	−	3.07516i	0.478804	−	0.101773i
$914$	−2.25955	+	2.50949i	−0.0747394	+	0.0830065i
$915$	22.6060	+	30.1558i	0.747330	+	0.996920i
$916$	−31.0570	−	34.4923i	−1.02615	−	1.13966i
$917$	−1.66036	−	1.20632i	−0.0548300	−	0.0398363i
$918$	0.114892	−	0.445237i	0.00379199	−	0.0146950i
$919$	−17.5681	−	12.7639i	−0.579517	−	0.421044i	0.259033	−	0.965868i	$-0.416596\pi$
$919$	−17.5681	−	12.7639i	−0.579517	−	0.421044i	−0.838550	+	0.544825i	$0.816596\pi$
$920$	6.62679	−	7.80846i	0.218479	−	0.257437i
$921$	6.88157	+	34.8281i	0.226755	+	1.14763i
$922$	−2.18351	−	0.972159i	−0.0719099	−	0.0320164i
$923$	−10.3688	+	11.5158i	−0.341295	+	0.379046i
$924$	13.7905	+	19.5661i	0.453676	+	0.643677i
$925$	18.6582	+	11.9510i	0.613478	+	0.392946i
$926$	−2.59409			−0.0852471
$927$	−14.9625	−	0.430010i	−0.491432	−	0.0141234i
$928$	−2.75886	+	2.00443i	−0.0905640	+	0.0657986i
$929$	−1.29341	−	12.3060i	−0.0424353	−	0.403745i	−0.995036	−	0.0995202i	$-0.968269\pi$
$929$	−1.29341	−	12.3060i	−0.0424353	−	0.403745i	0.952600	−	0.304225i	$-0.0983975\pi$
$930$	4.04409	−	2.41618i	0.132611	−	0.0792298i
$931$	−2.38440	+	22.6860i	−0.0781454	+	0.743504i
$932$	−13.7066	−	23.7404i	−0.448973	−	0.777644i
$933$	1.75991	+	1.05008i	0.0576167	+	0.0343779i
$934$	7.24389	+	8.04516i	0.237027	+	0.263246i
$935$	−1.90849	−	0.347528i	−0.0624144	−	0.0113654i
$936$	−32.1706	−	0.924558i	−1.05153	−	0.0302201i
$937$	10.4055	−	32.0249i	0.339934	−	1.04621i	−0.624307	−	0.781179i	$-0.714619\pi$
$937$	10.4055	−	32.0249i	0.339934	−	1.04621i	0.964241	−	0.265029i	$-0.0853815\pi$
$938$	−0.0744273	−	0.0826599i	−0.00243014	−	0.00269894i
$939$	−15.4117	+	20.5839i	−0.502940	+	0.671730i
$940$	−0.674749	−	1.88660i	−0.0220079	−	0.0615341i
$941$	6.56245	−	1.39489i	0.213930	−	0.0454722i	−0.0996999	−	0.995018i	$-0.531788\pi$
$941$	6.56245	−	1.39489i	0.213930	−	0.0454722i	0.313630	+	0.949545i	$0.398455\pi$
$942$	6.31900	−	3.52823i	0.205884	−	0.114956i
$943$	17.2222	−	29.8297i	0.560831	−	0.971388i
$944$	−22.6775	−	16.4761i	−0.738089	−	0.536253i
$945$	−15.5249	+	13.5961i	−0.505026	+	0.442281i
$946$	−11.9866	+	8.70876i	−0.389718	+	0.283146i
$947$	−5.03469	−	47.9018i	−0.163605	−	1.55660i	−0.700933	−	0.713227i	$-0.747233\pi$
$947$	−5.03469	−	47.9018i	−0.163605	−	1.55660i	0.537328	−	0.843373i	$-0.319434\pi$
$948$	−39.9936	−	4.78530i	−1.29893	−	0.155419i
$949$	8.93619	+	15.4779i	0.290081	+	0.502435i
$950$	11.5703	−	5.98713i	0.375391	−	0.194248i
$951$	−0.348892	−	0.495010i	−0.0113136	−	0.0160518i
$952$	0.585302	+	0.124410i	0.0189697	+	0.00403214i
$953$	−0.957332	+	0.695542i	−0.0310110	+	0.0225308i	−0.603183	−	0.797603i	$-0.706101\pi$
$953$	−0.957332	+	0.695542i	−0.0310110	+	0.0225308i	0.572172	+	0.820134i	$0.306101\pi$
$954$	−6.73818	+	7.06437i	−0.218157	+	0.228717i
$955$	3.40977	+	0.620904i	0.110338	+	0.0200920i
$956$	−23.1284	+	10.2974i	−0.748026	+	0.333043i
$957$	−5.49544	+	0.497891i	−0.177642	+	0.0160945i
$958$	0.731088	−	6.95584i	0.0236204	−	0.224733i
$959$	14.6635	−	3.11681i	0.473508	−	0.100647i
$960$	−5.68538	+	13.3013i	−0.183495	+	0.429298i
$961$	22.8211	+	4.85077i	0.736164	+	0.156477i
$962$	3.85885	−	11.8763i	0.124414	−	0.382908i
$963$	19.7016	−	8.10184i	0.634875	−	0.261078i
$964$	12.5647	+	38.6702i	0.404682	+	1.24548i
$965$	23.7370	+	9.74504i	0.764120	+	0.313704i
$966$	−3.53592	+	1.09299i	−0.113766	+	0.0351663i
$967$	2.40981	−	22.9278i	0.0774943	−	0.737309i	−0.884924	−	0.465736i	$-0.845789\pi$
$967$	2.40981	−	22.9278i	0.0774943	−	0.737309i	0.962418	−	0.271573i	$-0.0875438\pi$
$968$	−6.30498	−	10.9205i	−0.202650	−	0.350999i
$969$	−1.80743	+	1.00919i	−0.0580632	+	0.0324197i
$970$	−8.17831	−	13.2523i	−0.262590	−	0.425505i
$971$	5.11486	−	3.71616i	0.164144	−	0.119257i	−0.502681	−	0.864472i	$-0.667653\pi$
$971$	5.11486	−	3.71616i	0.164144	−	0.119257i	0.666825	+	0.745215i	$0.267653\pi$
$972$	−14.8795	−	23.9192i	−0.477259	−	0.767209i
$973$	1.91318	+	5.88817i	0.0613338	+	0.188766i
$974$	6.96469	−	12.0632i	0.223163	−	0.386530i
$975$	−54.9453	+	8.24735i	−1.75966	+	0.264127i
$976$	−14.0113	−	24.2683i	−0.448490	−	0.776808i
$977$	22.8910	−	25.4230i	0.732348	−	0.813355i	−0.255821	−	0.966724i	$-0.582346\pi$
$977$	22.8910	−	25.4230i	0.732348	−	0.813355i	0.988169	+	0.153369i	$0.0490124\pi$
$978$	5.97647	+	2.03724i	0.191106	+	0.0651439i
$979$	4.80634	+	45.7293i	0.153611	+	1.46151i
$980$	10.7311	+	11.2374i	0.342791	+	0.358964i
$981$	0.131062	+	1.72144i	0.00418448	+	0.0549613i
$982$	9.92146			0.316606
$983$	48.5545	−	21.6178i	1.54865	−	0.689502i	0.558496	−	0.829507i	$-0.311378\pi$
$983$	48.5545	−	21.6178i	1.54865	−	0.689502i	0.990151	+	0.140005i	$0.0447118\pi$
$984$	8.08352	−	35.5135i	0.257693	−	1.13213i
$985$	−14.4294	+	49.2801i	−0.459759	+	1.57019i
$986$	−0.0438095	+	0.0486554i	−0.00139518	+	0.00154950i
$987$	−0.338556	+	1.48738i	−0.0107763	+	0.0473439i
$988$	46.0187	+	51.1089i	1.46405	+	1.62599i
$989$	6.63073	+	20.4073i	0.210845	+	0.648914i
$990$	10.2597	−	7.46328i	0.326074	−	0.237199i
$991$	−13.5962	+	41.8449i	−0.431899	+	1.32925i	0.464333	+	0.885661i	$0.346294\pi$
$991$	−13.5962	+	41.8449i	−0.431899	+	1.32925i	−0.896232	+	0.443586i	$0.853706\pi$
$992$	−11.6607	+	5.19167i	−0.370227	+	0.164836i
$993$	−15.5520	−	22.0653i	−0.493529	−	0.700221i
$994$	−0.196960	+	1.87395i	−0.00624719	+	0.0594381i
$995$	7.38499	−	5.70361i	0.234120	−	0.180817i
$996$	−2.08401	−	10.5474i	−0.0660345	−	0.334206i
$997$	−1.43885	−	13.6897i	−0.0455687	−	0.433558i	−0.993393	−	0.114764i	$-0.963389\pi$
$997$	−1.43885	−	13.6897i	−0.0455687	−	0.433558i	0.947824	−	0.318794i	$-0.103278\pi$
$998$	2.64512	+	8.14084i	0.0837298	+	0.257694i
$999$	22.1860	−	6.16553i	0.701933	−	0.195069i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	225.2.q.a.106.18	yes	224
3.2	odd	2		675.2.r.a.181.11		224
9.4	even	3	inner	225.2.q.a.31.11	✓	224
9.5	odd	6		675.2.r.a.631.18		224
25.21	even	5	inner	225.2.q.a.196.11	yes	224
75.71	odd	10		675.2.r.a.46.18		224
225.121	even	15	inner	225.2.q.a.121.18	yes	224
225.221	odd	30		675.2.r.a.496.11		224

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
225.2.q.a.31.11	✓	224	9.4	even	3	inner
225.2.q.a.106.18	yes	224	1.1	even	1	trivial
225.2.q.a.121.18	yes	224	225.121	even	15	inner
225.2.q.a.196.11	yes	224	25.21	even	5	inner
675.2.r.a.46.18		224	75.71	odd	10
675.2.r.a.181.11		224	3.2	odd	2
675.2.r.a.496.11		224	225.221	odd	30
675.2.r.a.631.18		224	9.5	odd	6

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)

\(f(q)\)	\(=\)	\(q+(0.429627 + 0.0913200i) q^{2} +(0.335739 + 1.69920i) q^{3} +(-1.65085 - 0.735006i) q^{4} +(-1.76971 + 1.36679i) q^{5} +(-0.0109284 + 0.760681i) q^{6} +(-0.888066 + 1.53818i) q^{7} +(-1.35281 - 0.982874i) q^{8} +(-2.77456 + 1.14098i) q^{9} +O(q^{10})\)	\(q+(0.429627 + 0.0913200i) q^{2} +(0.335739 + 1.69920i) q^{3} +(-1.65085 - 0.735006i) q^{4} +(-1.76971 + 1.36679i) q^{5} +(-0.0109284 + 0.760681i) q^{6} +(-0.888066 + 1.53818i) q^{7} +(-1.35281 - 0.982874i) q^{8} +(-2.77456 + 1.14098i) q^{9} +(-0.885131 + 0.425600i) q^{10} +(4.21184 + 0.895255i) q^{11} +(0.694667 - 3.05190i) q^{12} +(-6.27541 + 1.33388i) q^{13} +(-0.522003 + 0.579743i) q^{14} +(-2.91661 - 2.54821i) q^{15} +(1.92690 + 2.14004i) q^{16} +(0.162997 + 0.118424i) q^{17} +(-1.29622 + 0.236821i) q^{18} +(4.79916 + 3.48679i) q^{19} +(3.92613 - 0.955619i) q^{20} +(-2.91183 - 0.992576i) q^{21} +(1.72777 + 0.769251i) q^{22} +(1.83276 - 2.03549i) q^{23} +(1.21591 - 2.62868i) q^{24} +(1.26376 - 4.83765i) q^{25} -2.81790 q^{26} +(-2.87027 - 4.33146i) q^{27} +(2.59663 - 1.88657i) q^{28} +(0.0773364 + 0.735807i) q^{29} +(-1.02035 - 1.36112i) q^{30} +(-0.289472 + 2.75414i) q^{31} +(2.30458 + 3.99166i) q^{32} +(-0.107137 + 7.45733i) q^{33} +(0.0592133 + 0.0657630i) q^{34} +(-0.530743 - 3.93593i) q^{35} +(5.41901 + 0.155738i) q^{36} +(-1.36941 + 4.21461i) q^{37} +(1.74343 + 1.93628i) q^{38} +(-4.37343 - 10.2153i) q^{39} +(3.73747 - 0.109604i) q^{40} +(12.3006 - 2.61458i) q^{41} +(-1.16036 - 0.692345i) q^{42} +(-3.91700 + 6.78444i) q^{43} +(-6.29511 - 4.57366i) q^{44} +(3.35070 - 5.81144i) q^{45} +(0.973285 - 0.707133i) q^{46} +(-0.0518311 - 0.493140i) q^{47} +(-2.98942 + 3.99268i) q^{48} +(1.92268 + 3.33017i) q^{49} +(0.984721 - 1.96298i) q^{50} +(-0.146502 + 0.316724i) q^{51} +(11.3402 + 2.41043i) q^{52} +(5.99398 - 4.35488i) q^{53} +(-0.837597 - 2.12302i) q^{54} +(-8.67738 + 4.17236i) q^{55} +(2.71322 - 1.20800i) q^{56} +(-4.31349 + 9.32538i) q^{57} +(-0.0339681 + 0.323185i) q^{58} +(-9.52123 + 2.02380i) q^{59} +(2.94194 + 6.35044i) q^{60} +(-9.51841 - 2.02320i) q^{61} +(-0.375873 + 1.15682i) q^{62} +(0.708972 - 5.28102i) q^{63} +(-1.15416 - 3.55215i) q^{64} +(9.28254 - 10.9378i) q^{65} +(-0.727032 + 3.19409i) q^{66} +(-0.0149037 + 0.141799i) q^{67} +(-0.182041 - 0.315304i) q^{68} +(4.07403 + 2.43084i) q^{69} +(0.131408 - 1.73945i) q^{70} +(1.95406 - 1.41971i) q^{71} +(4.87488 + 1.18352i) q^{72} +(-0.860848 - 2.64942i) q^{73} +(-0.973212 + 1.68565i) q^{74} +(8.64444 + 0.523199i) q^{75} +(-5.35988 - 9.28359i) q^{76} +(-5.11745 + 5.68351i) q^{77} +(-0.946077 - 4.78817i) q^{78} +(-1.34516 - 12.7983i) q^{79} +(-6.33505 - 1.15358i) q^{80} +(6.39635 - 6.33140i) q^{81} +5.52343 q^{82} +(3.13799 - 1.39712i) q^{83} +(4.07744 + 3.77881i) q^{84} +(-0.450318 + 0.0132059i) q^{85} +(-2.30240 + 2.55708i) q^{86} +(-1.22432 + 0.378449i) q^{87} +(-4.81790 - 5.35082i) q^{88} +(3.29985 + 10.1559i) q^{89} +(1.97025 - 2.19076i) q^{90} +(3.52124 - 10.8373i) q^{91} +(-4.52172 + 2.01320i) q^{92} +(-4.77702 + 0.432802i) q^{93} +(0.0227655 - 0.216599i) q^{94} +(-13.2588 + 0.388827i) q^{95} +(-6.00888 + 5.25610i) q^{96} +(1.65739 + 15.7690i) q^{97} +(0.521922 + 1.60631i) q^{98} +(-12.7075 + 2.32167i) 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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