LMFDB - Embedded newform 570.2.m.b.37.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [570,2,Mod(37,570)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(570, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 1, 2]))

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

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

chi := DirichletCharacter("570.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 570 = 2 \cdot 3 \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	570.m (of order $4$, degree $2$, 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:	$4.55147291521$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 108x^{16} + 1318x^{12} + 4652x^{8} + 5057x^{4} + 256 $ x^20 + 108x^16 + 1318x^12 + 4652x^8 + 5057x^4 + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 2^{9} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			37.8
Root			$1.20277 - 1.20277i$ of defining polynomial
Character	$\chi$	$=$	570.37
Dual form			570.2.m.b.493.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 - 0.707107i) q^{2} +(-0.707107 - 0.707107i) q^{3} -1.00000i q^{4} +(0.528178 + 2.17279i) q^{5} -1.00000 q^{6} +(0.904140 + 0.904140i) q^{7} +(-0.707107 - 0.707107i) q^{8} +1.00000i q^{9} +O(q^{10})$	\(q+(0.707107 - 0.707107i) q^{2} +(-0.707107 - 0.707107i) q^{3} -1.00000i q^{4} +(0.528178 + 2.17279i) q^{5} -1.00000 q^{6} +(0.904140 + 0.904140i) q^{7} +(-0.707107 - 0.707107i) q^{8} +1.00000i q^{9} +(1.90987 + 1.16292i) q^{10} +2.66147 q^{11} +(-0.707107 + 0.707107i) q^{12} +(0.143663 + 0.143663i) q^{13} +1.27865 q^{14} +(1.16292 - 1.90987i) q^{15} -1.00000 q^{16} +(3.29524 + 3.29524i) q^{17} +(0.707107 + 0.707107i) q^{18} +(4.05688 - 1.59427i) q^{19} +(2.17279 - 0.528178i) q^{20} -1.27865i q^{21} +(1.88194 - 1.88194i) q^{22} +(1.75733 - 1.75733i) q^{23} +1.00000i q^{24} +(-4.44206 + 2.29524i) q^{25} +0.203169 q^{26} +(0.707107 - 0.707107i) q^{27} +(0.904140 - 0.904140i) q^{28} +2.17494 q^{29} +(-0.528178 - 2.17279i) q^{30} -2.62167i q^{31} +(-0.707107 + 0.707107i) q^{32} +(-1.88194 - 1.88194i) q^{33} +4.66018 q^{34} +(-1.48696 + 2.44206i) q^{35} +1.00000 q^{36} +(-0.984090 + 0.984090i) q^{37} +(1.74133 - 3.99597i) q^{38} -0.203169i q^{39} +(1.16292 - 1.90987i) q^{40} -3.74005i q^{41} +(-0.904140 - 0.904140i) q^{42} +(-2.01084 + 2.01084i) q^{43} -2.66147i q^{44} +(-2.17279 + 0.528178i) q^{45} -2.48524i q^{46} +(3.24973 + 3.24973i) q^{47} +(0.707107 + 0.707107i) q^{48} -5.36506i q^{49} +(-1.51803 + 4.76399i) q^{50} -4.66018i q^{51} +(0.143663 - 0.143663i) q^{52} +(-2.54197 - 2.54197i) q^{53} -1.00000i q^{54} +(1.40573 + 5.78282i) q^{55} -1.27865i q^{56} +(-3.99597 - 1.74133i) q^{57} +(1.53792 - 1.53792i) q^{58} +2.19877 q^{59} +(-1.90987 - 1.16292i) q^{60} -8.90579 q^{61} +(-1.85380 - 1.85380i) q^{62} +(-0.904140 + 0.904140i) q^{63} +1.00000i q^{64} +(-0.236270 + 0.388028i) q^{65} -2.66147 q^{66} +(-4.50928 + 4.50928i) q^{67} +(3.29524 - 3.29524i) q^{68} -2.48524 q^{69} +(0.675353 + 2.77824i) q^{70} +2.55729i q^{71} +(0.707107 - 0.707107i) q^{72} +(-5.25513 + 5.25513i) q^{73} +1.39171i q^{74} +(4.76399 + 1.51803i) q^{75} +(-1.59427 - 4.05688i) q^{76} +(2.40634 + 2.40634i) q^{77} +(-0.143663 - 0.143663i) q^{78} +4.22731 q^{79} +(-0.528178 - 2.17279i) q^{80} -1.00000 q^{81} +(-2.64461 - 2.64461i) q^{82} +(6.55477 - 6.55477i) q^{83} -1.27865 q^{84} +(-5.41940 + 8.90035i) q^{85} +2.84376i q^{86} +(-1.53792 - 1.53792i) q^{87} +(-1.88194 - 1.88194i) q^{88} +4.94664 q^{89} +(-1.16292 + 1.90987i) q^{90} +0.259782i q^{91} +(-1.75733 - 1.75733i) q^{92} +(-1.85380 + 1.85380i) q^{93} +4.59581 q^{94} +(5.60678 + 7.97271i) q^{95} +1.00000 q^{96} +(-11.8481 + 11.8481i) q^{97} +(-3.79367 - 3.79367i) q^{98} +2.66147i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 12 q^{5} - 20 q^{6} - 4 q^{7}+O(q^{10}) $ 20 * q + 12 * q^5 - 20 * q^6 - 4 * q^7	$ 20 q + 12 q^{5} - 20 q^{6} - 4 q^{7} - 8 q^{11} - 20 q^{16} - 12 q^{17} - 4 q^{23} - 28 q^{25} + 24 q^{26} - 4 q^{28} - 12 q^{30} + 4 q^{35} + 20 q^{36} - 12 q^{38} + 4 q^{42} - 12 q^{43} - 44 q^{47} + 64 q^{55} + 12 q^{57} - 8 q^{58} - 24 q^{62} + 4 q^{63} + 8 q^{66} - 12 q^{68} - 4 q^{73} + 4 q^{76} + 88 q^{77} - 12 q^{80} - 20 q^{81} - 8 q^{82} + 76 q^{83} - 12 q^{85} + 8 q^{87} + 4 q^{92} - 24 q^{93} - 24 q^{95} + 20 q^{96}+O(q^{100}) $ 20 * q + 12 * q^5 - 20 * q^6 - 4 * q^7 - 8 * q^11 - 20 * q^16 - 12 * q^17 - 4 * q^23 - 28 * q^25 + 24 * q^26 - 4 * q^28 - 12 * q^30 + 4 * q^35 + 20 * q^36 - 12 * q^38 + 4 * q^42 - 12 * q^43 - 44 * q^47 + 64 * q^55 + 12 * q^57 - 8 * q^58 - 24 * q^62 + 4 * q^63 + 8 * q^66 - 12 * q^68 - 4 * q^73 + 4 * q^76 + 88 * q^77 - 12 * q^80 - 20 * q^81 - 8 * q^82 + 76 * q^83 - 12 * q^85 + 8 * q^87 + 4 * q^92 - 24 * q^93 - 24 * q^95 + 20 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/570\mathbb{Z}\right)^\times$.

$n$	$191$	$211$	$457$
$\chi(n)$	$1$	$-1$	$e\left(\frac{1}{4}\right)$

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 $

$2$	0.707107	−	0.707107i	0.500000	−	0.500000i
$2$	0.707107	−	0.707107i	0.500000	−	0.500000i
$3$	−0.707107	−	0.707107i	−0.408248	−	0.408248i
$3$	−0.707107	−	0.707107i	−0.408248	−	0.408248i
$4$		−	1.00000i		−	0.500000i
$5$	0.528178	+	2.17279i	0.236208	+	0.971702i
$5$	0.528178	+	2.17279i	0.236208	+	0.971702i
$6$	−1.00000			−0.408248
$7$	0.904140	+	0.904140i	0.341733	+	0.341733i	0.857018	−	0.515286i	$-0.172314\pi$
$7$	0.904140	+	0.904140i	0.341733	+	0.341733i	−0.515286	+	0.857018i	$0.672314\pi$
$8$	−0.707107	−	0.707107i	−0.250000	−	0.250000i
$9$			1.00000i			0.333333i
$10$	1.90987	+	1.16292i	0.603955	+	0.367747i
$11$	2.66147			0.802462			0.401231	−	0.915977i	$-0.368582\pi$
$11$	2.66147			0.802462			0.401231	+	0.915977i	$0.368582\pi$
$12$	−0.707107	+	0.707107i	−0.204124	+	0.204124i
$13$	0.143663	+	0.143663i	0.0398448	+	0.0398448i	0.726748	−	0.686904i	$-0.241031\pi$
$13$	0.143663	+	0.143663i	0.0398448	+	0.0398448i	−0.686904	+	0.726748i	$0.741031\pi$
$14$	1.27865			0.341733
$15$	1.16292	−	1.90987i	0.300264	−	0.493128i
$16$	−1.00000			−0.250000
$17$	3.29524	+	3.29524i	0.799214	+	0.799214i	0.982972	−	0.183758i	$-0.0588262\pi$
$17$	3.29524	+	3.29524i	0.799214	+	0.799214i	−0.183758	+	0.982972i	$0.558826\pi$
$18$	0.707107	+	0.707107i	0.166667	+	0.166667i
$19$	4.05688	−	1.59427i	0.930713	−	0.365751i
$19$	4.05688	−	1.59427i	0.930713	−	0.365751i
$20$	2.17279	−	0.528178i	0.485851	−	0.118104i
$21$		−	1.27865i		−	0.279024i
$22$	1.88194	−	1.88194i	0.401231	−	0.401231i
$23$	1.75733	−	1.75733i	0.366428	−	0.366428i	−0.499745	−	0.866173i	$-0.666573\pi$
$23$	1.75733	−	1.75733i	0.366428	−	0.366428i	0.866173	+	0.499745i	$0.166573\pi$
$24$			1.00000i			0.204124i
$25$	−4.44206	+	2.29524i	−0.888411	+	0.459049i
$26$	0.203169			0.0398448
$27$	0.707107	−	0.707107i	0.136083	−	0.136083i
$28$	0.904140	−	0.904140i	0.170866	−	0.170866i
$29$	2.17494			0.403876			0.201938	−	0.979398i	$-0.435276\pi$
$29$	2.17494			0.403876			0.201938	+	0.979398i	$0.435276\pi$
$30$	−0.528178	−	2.17279i	−0.0964317	−	0.396696i
$31$		−	2.62167i		−	0.470865i	−0.971891	−	0.235432i	$-0.924349\pi$
$31$		−	2.62167i		−	0.470865i	0.971891	−	0.235432i	$-0.0756507\pi$
$32$	−0.707107	+	0.707107i	−0.125000	+	0.125000i
$33$	−1.88194	−	1.88194i	−0.327604	−	0.327604i
$34$	4.66018			0.799214
$35$	−1.48696	+	2.44206i	−0.251342	+	0.412783i
$36$	1.00000			0.166667
$37$	−0.984090	+	0.984090i	−0.161783	+	0.161783i	−0.783356	−	0.621573i	$-0.786494\pi$
$37$	−0.984090	+	0.984090i	−0.161783	+	0.161783i	0.621573	+	0.783356i	$0.286494\pi$
$38$	1.74133	−	3.99597i	0.282481	−	0.648232i
$39$		−	0.203169i		−	0.0325332i
$40$	1.16292	−	1.90987i	0.183874	−	0.301978i
$41$		−	3.74005i		−	0.584098i	−0.956403	−	0.292049i	$-0.905663\pi$
$41$		−	3.74005i		−	0.584098i	0.956403	−	0.292049i	$-0.0943370\pi$
$42$	−0.904140	−	0.904140i	−0.139512	−	0.139512i
$43$	−2.01084	+	2.01084i	−0.306650	+	0.306650i	−0.843609	−	0.536959i	$-0.819573\pi$
$43$	−2.01084	+	2.01084i	−0.306650	+	0.306650i	0.536959	+	0.843609i	$0.319573\pi$
$44$		−	2.66147i		−	0.401231i
$45$	−2.17279	+	0.528178i	−0.323901	+	0.0787361i
$46$		−	2.48524i		−	0.366428i
$47$	3.24973	+	3.24973i	0.474021	+	0.474021i	0.903213	−	0.429192i	$-0.141202\pi$
$47$	3.24973	+	3.24973i	0.474021	+	0.474021i	−0.429192	+	0.903213i	$0.641202\pi$
$48$	0.707107	+	0.707107i	0.102062	+	0.102062i
$49$		−	5.36506i		−	0.766437i
$50$	−1.51803	+	4.76399i	−0.214681	+	0.673730i
$51$		−	4.66018i		−	0.652555i
$52$	0.143663	−	0.143663i	0.0199224	−	0.0199224i
$53$	−2.54197	−	2.54197i	−0.349166	−	0.349166i	0.510633	−	0.859799i	$-0.329411\pi$
$53$	−2.54197	−	2.54197i	−0.349166	−	0.349166i	−0.859799	+	0.510633i	$0.829411\pi$
$54$		−	1.00000i		−	0.136083i
$55$	1.40573	+	5.78282i	0.189548	+	0.779755i
$56$		−	1.27865i		−	0.170866i
$57$	−3.99597	−	1.74133i	−0.529279	−	0.230645i
$58$	1.53792	−	1.53792i	0.201938	−	0.201938i
$59$	2.19877			0.286256			0.143128	−	0.989704i	$-0.454284\pi$
$59$	2.19877			0.286256			0.143128	+	0.989704i	$0.454284\pi$
$60$	−1.90987	−	1.16292i	−0.246564	−	0.150132i
$61$	−8.90579			−1.14027			−0.570135	−	0.821551i	$-0.693109\pi$
$61$	−8.90579			−1.14027			−0.570135	+	0.821551i	$0.693109\pi$
$62$	−1.85380	−	1.85380i	−0.235432	−	0.235432i
$63$	−0.904140	+	0.904140i	−0.113911	+	0.113911i
$64$			1.00000i			0.125000i
$65$	−0.236270	+	0.388028i	−0.0293056	+	0.0481290i
$66$	−2.66147			−0.327604
$67$	−4.50928	+	4.50928i	−0.550896	+	0.550896i	−0.926700	−	0.375803i	$-0.877367\pi$
$67$	−4.50928	+	4.50928i	−0.550896	+	0.550896i	0.375803	+	0.926700i	$0.377367\pi$
$68$	3.29524	−	3.29524i	0.399607	−	0.399607i
$69$	−2.48524			−0.299187
$70$	0.675353	+	2.77824i	0.0807202	+	0.332063i
$71$			2.55729i			0.303495i	0.988419	+	0.151748i	$0.0484901\pi$
$71$			2.55729i			0.303495i	−0.988419	+	0.151748i	$0.951510\pi$
$72$	0.707107	−	0.707107i	0.0833333	−	0.0833333i
$73$	−5.25513	+	5.25513i	−0.615066	+	0.615066i	−0.944262	−	0.329196i	$-0.893222\pi$
$73$	−5.25513	+	5.25513i	−0.615066	+	0.615066i	0.329196	+	0.944262i	$0.393222\pi$
$74$			1.39171i			0.161783i
$75$	4.76399	+	1.51803i	0.550098	+	0.175287i
$76$	−1.59427	−	4.05688i	−0.182876	−	0.465356i
$77$	2.40634	+	2.40634i	0.274228	+	0.274228i
$78$	−0.143663	−	0.143663i	−0.0162666	−	0.0162666i
$79$	4.22731			0.475610			0.237805	−	0.971313i	$-0.423572\pi$
$79$	4.22731			0.475610			0.237805	+	0.971313i	$0.423572\pi$
$80$	−0.528178	−	2.17279i	−0.0590521	−	0.242926i
$81$	−1.00000			−0.111111
$82$	−2.64461	−	2.64461i	−0.292049	−	0.292049i
$83$	6.55477	−	6.55477i	0.719479	−	0.719479i	−0.249019	−	0.968499i	$-0.580108\pi$
$83$	6.55477	−	6.55477i	0.719479	−	0.719479i	0.968499	+	0.249019i	$0.0801083\pi$
$84$	−1.27865			−0.139512
$85$	−5.41940	+	8.90035i	−0.587817	+	0.965379i
$86$			2.84376i			0.306650i
$87$	−1.53792	−	1.53792i	−0.164882	−	0.164882i
$88$	−1.88194	−	1.88194i	−0.200616	−	0.200616i
$89$	4.94664			0.524343			0.262171	−	0.965021i	$-0.415561\pi$
$89$	4.94664			0.524343			0.262171	+	0.965021i	$0.415561\pi$
$90$	−1.16292	+	1.90987i	−0.122582	+	0.201318i
$91$			0.259782i			0.0272326i
$92$	−1.75733	−	1.75733i	−0.183214	−	0.183214i
$93$	−1.85380	+	1.85380i	−0.192230	+	0.192230i
$94$	4.59581			0.474021
$95$	5.60678	+	7.97271i	0.575243	+	0.817982i
$96$	1.00000			0.102062
$97$	−11.8481	+	11.8481i	−1.20300	+	1.20300i	−0.229746	+	0.973251i	$0.573789\pi$
$97$	−11.8481	+	11.8481i	−1.20300	+	1.20300i	−0.973251	+	0.229746i	$0.926211\pi$
$98$	−3.79367	−	3.79367i	−0.383219	−	0.383219i
$99$			2.66147i			0.267487i
$100$	2.29524	+	4.44206i	0.229524	+	0.444206i
$101$	3.64684			0.362874			0.181437	−	0.983403i	$-0.441925\pi$
$101$	3.64684			0.362874			0.181437	+	0.983403i	$0.441925\pi$
$102$	−3.29524	−	3.29524i	−0.326278	−	0.326278i
$103$	−4.27174	−	4.27174i	−0.420907	−	0.420907i	0.464609	−	0.885516i	$-0.346195\pi$
$103$	−4.27174	−	4.27174i	−0.420907	−	0.420907i	−0.885516	+	0.464609i	$0.846195\pi$
$104$		−	0.203169i		−	0.0199224i
$105$	2.77824	−	0.675353i	0.271128	−	0.0659077i
$106$	−3.59488			−0.349166
$107$	−9.39155	+	9.39155i	−0.907915	+	0.907915i	−0.996104	−	0.0881885i	$-0.971892\pi$
$107$	−9.39155	+	9.39155i	−0.907915	+	0.907915i	0.0881885	+	0.996104i	$0.471892\pi$
$108$	−0.707107	−	0.707107i	−0.0680414	−	0.0680414i
$109$	−12.0254			−1.15182			−0.575912	−	0.817512i	$-0.695353\pi$
$109$	−12.0254			−1.15182			−0.575912	+	0.817512i	$0.695353\pi$
$110$	5.08307	+	3.09507i	0.484652	+	0.295103i
$111$	1.39171			0.132096
$112$	−0.904140	−	0.904140i	−0.0854332	−	0.0854332i
$113$	1.99650	+	1.99650i	0.187815	+	0.187815i	0.794751	−	0.606936i	$-0.207601\pi$
$113$	1.99650	+	1.99650i	0.187815	+	0.187815i	−0.606936	+	0.794751i	$0.707601\pi$
$114$	−4.05688	+	1.59427i	−0.379962	+	0.149317i
$115$	4.74649	+	2.89013i	0.442612	+	0.269506i
$116$		−	2.17494i		−	0.201938i
$117$	−0.143663	+	0.143663i	−0.0132816	+	0.0132816i
$118$	1.55477	−	1.55477i	0.143128	−	0.143128i
$119$			5.95872i			0.546235i
$120$	−2.17279	+	0.528178i	−0.198348	+	0.0482158i
$121$	−3.91659			−0.356054
$122$	−6.29734	+	6.29734i	−0.570135	+	0.570135i
$123$	−2.64461	+	2.64461i	−0.238457	+	0.238457i
$124$	−2.62167			−0.235432
$125$	−7.33328	−	8.43937i	−0.655909	−	0.754840i
$126$			1.27865i			0.113911i
$127$	−12.5449	+	12.5449i	−1.11318	+	1.11318i	−0.120462	+	0.992718i	$0.538438\pi$
$127$	−12.5449	+	12.5449i	−1.11318	+	1.11318i	−0.992718	+	0.120462i	$0.961562\pi$
$128$	0.707107	+	0.707107i	0.0625000	+	0.0625000i
$129$	2.84376			0.250379
$130$	0.107310	+	0.441445i	0.00941168	+	0.0387173i
$131$	20.6202			1.80159			0.900797	−	0.434240i	$-0.142983\pi$
$131$	20.6202			1.80159			0.900797	+	0.434240i	$0.142983\pi$
$132$	−1.88194	+	1.88194i	−0.163802	+	0.163802i
$133$	5.10944	+	2.22655i	0.443044	+	0.193066i
$134$			6.37709i			0.550896i
$135$	1.90987	+	1.16292i	0.164376	+	0.100088i
$136$		−	4.66018i		−	0.399607i
$137$	−2.44206	−	2.44206i	−0.208639	−	0.208639i	0.595050	−	0.803689i	$-0.297132\pi$
$137$	−2.44206	−	2.44206i	−0.208639	−	0.208639i	−0.803689	+	0.595050i	$0.797132\pi$
$138$	−1.75733	+	1.75733i	−0.149594	+	0.149594i
$139$		−	16.1995i		−	1.37402i	−0.726647	−	0.687011i	$-0.758923\pi$
$139$		−	16.1995i		−	1.37402i	0.726647	−	0.687011i	$-0.241077\pi$
$140$	2.44206	+	1.48696i	0.206391	+	0.125671i
$141$		−	4.59581i		−	0.387037i
$142$	1.80828	+	1.80828i	0.151748	+	0.151748i
$143$	0.382353	+	0.382353i	0.0319740	+	0.0319740i
$144$		−	1.00000i		−	0.0833333i
$145$	1.14876	+	4.72570i	0.0953990	+	0.392448i
$146$			7.43187i			0.615066i
$147$	−3.79367	+	3.79367i	−0.312897	+	0.312897i
$148$	0.984090	+	0.984090i	0.0808917	+	0.0808917i
$149$			2.85261i			0.233695i	0.993150	+	0.116847i	$0.0372789\pi$
$149$			2.85261i			0.233695i	−0.993150	+	0.116847i	$0.962721\pi$
$150$	4.44206	−	2.29524i	0.362692	−	0.187406i
$151$		−	18.6146i		−	1.51483i	−0.652932	−	0.757417i	$-0.726461\pi$
$151$		−	18.6146i		−	1.51483i	0.652932	−	0.757417i	$-0.273539\pi$
$152$	−3.99597	−	1.74133i	−0.324116	−	0.141240i
$153$	−3.29524	+	3.29524i	−0.266405	+	0.266405i
$154$	3.40308			0.274228
$155$	5.69634	−	1.38471i	0.457541	−	0.111222i
$156$	−0.203169			−0.0162666
$157$	−10.0694	−	10.0694i	−0.803627	−	0.803627i	0.180033	−	0.983661i	$-0.442379\pi$
$157$	−10.0694	−	10.0694i	−0.803627	−	0.803627i	−0.983661	+	0.180033i	$0.942379\pi$
$158$	2.98916	−	2.98916i	0.237805	−	0.237805i
$159$			3.59488i			0.285093i
$160$	−1.90987	−	1.16292i	−0.150989	−	0.0919368i
$161$	3.17774			0.250441
$162$	−0.707107	+	0.707107i	−0.0555556	+	0.0555556i
$163$	16.5520	−	16.5520i	1.29645	−	1.29645i	0.365735	−	0.930719i	$-0.380818\pi$
$163$	16.5520	−	16.5520i	1.29645	−	1.29645i	0.930719	−	0.365735i	$-0.119182\pi$
$164$	−3.74005			−0.292049
$165$	3.09507	−	5.08307i	0.240951	−	0.395716i
$166$		−	9.26984i		−	0.719479i
$167$	−7.05038	+	7.05038i	−0.545575	+	0.545575i	−0.925158	−	0.379583i	$-0.876068\pi$
$167$	−7.05038	+	7.05038i	−0.545575	+	0.545575i	0.379583	+	0.925158i	$0.376068\pi$
$168$	−0.904140	+	0.904140i	−0.0697559	+	0.0697559i
$169$		−	12.9587i		−	0.996825i
$170$	2.46140	+	10.1256i	0.188781	+	0.776598i
$171$	1.59427	+	4.05688i	0.121917	+	0.310238i
$172$	2.01084	+	2.01084i	0.153325	+	0.153325i
$173$	−14.7696	−	14.7696i	−1.12291	−	1.12291i	−0.991302	−	0.131609i	$-0.957986\pi$
$173$	−14.7696	−	14.7696i	−1.12291	−	1.12291i	−0.131609	−	0.991302i	$-0.542014\pi$
$174$	−2.17494			−0.164882
$175$	−6.09146	−	1.94102i	−0.460471	−	0.146727i
$176$	−2.66147			−0.200616
$177$	−1.55477	−	1.55477i	−0.116864	−	0.116864i
$178$	3.49780	−	3.49780i	0.262171	−	0.262171i
$179$	−6.48791			−0.484929			−0.242465	−	0.970160i	$-0.577956\pi$
$179$	−6.48791			−0.484929			−0.242465	+	0.970160i	$0.577956\pi$
$180$	0.528178	+	2.17279i	0.0393681	+	0.161950i
$181$		−	0.122571i		−	0.00911063i	−0.999990	−	0.00455531i	$-0.998550\pi$
$181$		−	0.122571i		−	0.00911063i	0.999990	−	0.00455531i	$-0.00145001\pi$
$182$	0.183694	+	0.183694i	0.0136163	+	0.0136163i
$183$	6.29734	+	6.29734i	0.465513	+	0.465513i
$184$	−2.48524			−0.183214
$185$	−2.65800	−	1.61845i	−0.195420	−	0.118991i
$186$			2.62167i			0.192230i
$187$	8.77018	+	8.77018i	0.641339	+	0.641339i
$188$	3.24973	−	3.24973i	0.237011	−	0.237011i
$189$	1.27865			0.0930079
$190$	9.60215	+	1.67296i	0.696613	+	0.121370i
$191$	−0.473897			−0.0342900			−0.0171450	−	0.999853i	$-0.505458\pi$
$191$	−0.473897			−0.0342900			−0.0171450	+	0.999853i	$0.505458\pi$
$192$	0.707107	−	0.707107i	0.0510310	−	0.0510310i
$193$	8.37158	+	8.37158i	0.602600	+	0.602600i	0.941002	−	0.338402i	$-0.109886\pi$
$193$	8.37158	+	8.37158i	0.602600	+	0.602600i	−0.338402	+	0.941002i	$0.609886\pi$
$194$			16.7558i			1.20300i
$195$	0.441445	−	0.107310i	0.0316125	−	0.00768460i
$196$	−5.36506			−0.383219
$197$	−9.45290	−	9.45290i	−0.673491	−	0.673491i	0.285028	−	0.958519i	$-0.407997\pi$
$197$	−9.45290	−	9.45290i	−0.673491	−	0.673491i	−0.958519	+	0.285028i	$0.907997\pi$
$198$	1.88194	+	1.88194i	0.133744	+	0.133744i
$199$			3.17530i			0.225091i	0.993647	+	0.112545i	$0.0359004\pi$
$199$			3.17530i			0.225091i	−0.993647	+	0.112545i	$0.964100\pi$
$200$	4.76399	+	1.51803i	0.336865	+	0.107341i
$201$	6.37709			0.449805
$202$	2.57871	−	2.57871i	0.181437	−	0.181437i
$203$	1.96645	+	1.96645i	0.138018	+	0.138018i
$204$	−4.66018			−0.326278
$205$	8.12635	−	1.97541i	0.567569	−	0.137969i
$206$	−6.04115			−0.420907
$207$	1.75733	+	1.75733i	0.122143	+	0.122143i
$208$	−0.143663	−	0.143663i	−0.00996120	−	0.00996120i
$209$	10.7973	−	4.24310i	0.746862	−	0.293501i
$210$	1.48696	−	2.44206i	0.102610	−	0.168518i
$211$			14.4553i			0.995142i	0.867423	+	0.497571i	$0.165775\pi$
$211$			14.4553i			0.995142i	−0.867423	+	0.497571i	$0.834225\pi$
$212$	−2.54197	+	2.54197i	−0.174583	+	0.174583i
$213$	1.80828	−	1.80828i	0.123901	−	0.123901i
$214$			13.2817i			0.907915i
$215$	−5.43122	−	3.30706i	−0.370406	−	0.225539i
$216$	−1.00000			−0.0680414
$217$	2.37035	−	2.37035i	0.160910	−	0.160910i
$218$	−8.50324	+	8.50324i	−0.575912	+	0.575912i
$219$	7.43187			0.502199
$220$	5.78282	−	1.40573i	0.389877	−	0.0947742i
$221$			0.946806i			0.0636890i
$222$	0.984090	−	0.984090i	0.0660478	−	0.0660478i
$223$	−13.3101	−	13.3101i	−0.891312	−	0.891312i	0.103335	−	0.994647i	$-0.467049\pi$
$223$	−13.3101	−	13.3101i	−0.891312	−	0.891312i	−0.994647	+	0.103335i	$0.967049\pi$
$224$	−1.27865			−0.0854332
$225$	−2.29524	−	4.44206i	−0.153016	−	0.296137i
$226$	2.82348			0.187815
$227$	21.0661	−	21.0661i	1.39820	−	1.39820i	0.593005	−	0.805199i	$-0.297942\pi$
$227$	21.0661	−	21.0661i	1.39820	−	1.39820i	0.805199	−	0.593005i	$-0.202058\pi$
$228$	−1.74133	+	3.99597i	−0.115322	+	0.264640i
$229$		−	18.2167i		−	1.20379i	−0.798574	−	0.601897i	$-0.794412\pi$
$229$		−	18.2167i		−	1.20379i	0.798574	−	0.601897i	$-0.205588\pi$
$230$	5.39990	−	1.31265i	0.356059	−	0.0865533i
$231$		−	3.40308i		−	0.223906i
$232$	−1.53792	−	1.53792i	−0.100969	−	0.100969i
$233$	−20.6479	+	20.6479i	−1.35269	+	1.35269i	−0.470045	+	0.882642i	$0.655762\pi$
$233$	−20.6479	+	20.6479i	−1.35269	+	1.35269i	−0.882642	+	0.470045i	$0.844238\pi$
$234$			0.203169i			0.0132816i
$235$	−5.34455	+	8.77741i	−0.348640	+	0.572575i
$236$		−	2.19877i		−	0.143128i
$237$	−2.98916	−	2.98916i	−0.194167	−	0.194167i
$238$	4.21345	+	4.21345i	0.273118	+	0.273118i
$239$		−	1.78480i		−	0.115449i	−0.998333	−	0.0577247i	$-0.981615\pi$
$239$		−	1.78480i		−	0.115449i	0.998333	−	0.0577247i	$-0.0183846\pi$
$240$	−1.16292	+	1.90987i	−0.0750660	+	0.123282i
$241$		−	6.17706i		−	0.397899i	−0.980010	−	0.198950i	$-0.936247\pi$
$241$		−	6.17706i		−	0.397899i	0.980010	−	0.198950i	$-0.0637530\pi$
$242$	−2.76945	+	2.76945i	−0.178027	+	0.178027i
$243$	0.707107	+	0.707107i	0.0453609	+	0.0453609i
$244$			8.90579i			0.570135i
$245$	11.6572	−	2.83371i	0.744749	−	0.181039i
$246$			3.74005i			0.238457i
$247$	0.811859	+	0.353785i	0.0516574	+	0.0225108i
$248$	−1.85380	+	1.85380i	−0.117716	+	0.117716i
$249$	−9.26984			−0.587452
$250$	−11.1529	−	0.782122i	−0.705374	−	0.0494658i
$251$	−3.89007			−0.245539			−0.122769	−	0.992435i	$-0.539178\pi$
$251$	−3.89007			−0.245539			−0.122769	+	0.992435i	$0.539178\pi$
$252$	0.904140	+	0.904140i	0.0569555	+	0.0569555i
$253$	4.67707	−	4.67707i	0.294045	−	0.294045i
$254$			17.7412i			1.11318i
$255$	10.1256	−	2.46140i	0.634090	−	0.154139i
$256$	1.00000			0.0625000
$257$	13.9017	−	13.9017i	0.867164	−	0.867164i	−0.124994	−	0.992158i	$-0.539891\pi$
$257$	13.9017	−	13.9017i	0.867164	−	0.867164i	0.992158	+	0.124994i	$0.0398911\pi$
$258$	2.01084	−	2.01084i	0.125189	−	0.125189i
$259$	−1.77951			−0.110573
$260$	0.388028	+	0.236270i	0.0240645	+	0.0146528i
$261$			2.17494i			0.134625i
$262$	14.5807	−	14.5807i	0.900797	−	0.900797i
$263$	−12.6517	+	12.6517i	−0.780135	+	0.780135i	−0.979853	−	0.199718i	$-0.935997\pi$
$263$	−12.6517	+	12.6517i	−0.780135	+	0.780135i	0.199718	+	0.979853i	$0.435997\pi$
$264$			2.66147i			0.163802i
$265$	4.18055	−	6.86578i	0.256809	−	0.421761i
$266$	5.18732	−	2.03851i	0.318055	−	0.124989i
$267$	−3.49780	−	3.49780i	−0.214062	−	0.214062i
$268$	4.50928	+	4.50928i	0.275448	+	0.275448i
$269$	23.7972			1.45094			0.725470	−	0.688254i	$-0.241623\pi$
$269$	23.7972			1.45094			0.725470	+	0.688254i	$0.241623\pi$
$270$	2.17279	−	0.528178i	0.132232	−	0.0321439i
$271$	−13.5524			−0.823249			−0.411624	−	0.911354i	$-0.635038\pi$
$271$	−13.5524			−0.823249			−0.411624	+	0.911354i	$0.635038\pi$
$272$	−3.29524	−	3.29524i	−0.199803	−	0.199803i
$273$	0.183694	−	0.183694i	0.0111176	−	0.0111176i
$274$	−3.45359			−0.208639
$275$	−11.8224	+	6.10871i	−0.712917	+	0.368369i
$276$			2.48524i			0.149594i
$277$	11.8777	+	11.8777i	0.713662	+	0.713662i	0.967299	−	0.253637i	$-0.0816270\pi$
$277$	11.8777	+	11.8777i	0.713662	+	0.713662i	−0.253637	+	0.967299i	$0.581627\pi$
$278$	−11.4548	−	11.4548i	−0.687011	−	0.687011i
$279$	2.62167			0.156955
$280$	2.77824	−	0.675353i	0.166031	−	0.0403601i
$281$			16.4158i			0.979285i	0.871923	+	0.489643i	$0.162873\pi$
$281$			16.4158i			0.979285i	−0.871923	+	0.489643i	$0.837127\pi$
$282$	−3.24973	−	3.24973i	−0.193518	−	0.193518i
$283$	15.5488	−	15.5488i	0.924283	−	0.924283i	−0.0730457	−	0.997329i	$-0.523272\pi$
$283$	15.5488	−	15.5488i	0.924283	−	0.924283i	0.997329	+	0.0730457i	$0.0232719\pi$
$284$	2.55729			0.151748
$285$	1.67296	−	9.60215i	0.0990978	−	0.568782i
$286$	0.540729			0.0319740
$287$	3.38153	−	3.38153i	0.199605	−	0.199605i
$288$	−0.707107	−	0.707107i	−0.0416667	−	0.0416667i
$289$			4.71725i			0.277485i
$290$	4.15387	+	2.52928i	0.243923	+	0.148524i
$291$	16.7558			0.982242
$292$	5.25513	+	5.25513i	0.307533	+	0.307533i
$293$	−19.2031	−	19.2031i	−1.12186	−	1.12186i	−0.991462	−	0.130398i	$-0.958375\pi$
$293$	−19.2031	−	19.2031i	−1.12186	−	1.12186i	−0.130398	−	0.991462i	$-0.541625\pi$
$294$			5.36506i			0.312897i
$295$	1.16134	+	4.77748i	0.0676161	+	0.278156i
$296$	1.39171			0.0808917
$297$	1.88194	−	1.88194i	0.109201	−	0.109201i
$298$	2.01710	+	2.01710i	0.116847	+	0.116847i
$299$	0.504924			0.0292005
$300$	1.51803	−	4.76399i	0.0876433	−	0.275049i
$301$	−3.63616			−0.209585
$302$	−13.1625	−	13.1625i	−0.757417	−	0.757417i
$303$	−2.57871	−	2.57871i	−0.148143	−	0.148143i
$304$	−4.05688	+	1.59427i	−0.232678	+	0.0914378i
$305$	−4.70384	−	19.3504i	−0.269341	−	1.10800i
$306$			4.66018i			0.266405i
$307$	−15.2483	+	15.2483i	−0.870269	+	0.870269i	−0.992501	−	0.122233i	$-0.960995\pi$
$307$	−15.2483	+	15.2483i	−0.870269	+	0.870269i	0.122233	+	0.992501i	$0.460995\pi$
$308$	2.40634	−	2.40634i	0.137114	−	0.137114i
$309$			6.04115i			0.343669i
$310$	3.04878	−	5.00705i	0.173159	−	0.284381i
$311$	0.213974			0.0121334			0.00606668	−	0.999982i	$-0.498069\pi$
$311$	0.213974			0.0121334			0.00606668	+	0.999982i	$0.498069\pi$
$312$	−0.143663	+	0.143663i	−0.00813329	+	0.00813329i
$313$	−18.2399	+	18.2399i	−1.03098	+	1.03098i	−0.0314771	+	0.999504i	$0.510021\pi$
$313$	−18.2399	+	18.2399i	−1.03098	+	1.03098i	−0.999504	+	0.0314771i	$0.989979\pi$
$314$	−14.2403			−0.803627
$315$	−2.44206	−	1.48696i	−0.137594	−	0.0837808i
$316$		−	4.22731i		−	0.237805i
$317$	12.5740	−	12.5740i	0.706226	−	0.706226i	−0.259513	−	0.965740i	$-0.583562\pi$
$317$	12.5740	−	12.5740i	0.706226	−	0.706226i	0.965740	+	0.259513i	$0.0835621\pi$
$318$	2.54197	+	2.54197i	0.142546	+	0.142546i
$319$	5.78853			0.324096
$320$	−2.17279	+	0.528178i	−0.121463	+	0.0295260i
$321$	13.2817			0.741310
$322$	2.24700	−	2.24700i	0.125220	−	0.125220i
$323$	18.6219	+	8.11490i	1.03615	+	0.451525i
$324$			1.00000i			0.0555556i
$325$	−0.967897	−	0.308417i	−0.0536893	−	0.0171079i
$326$		−	23.4081i		−	1.29645i
$327$	8.50324	+	8.50324i	0.470230	+	0.470230i
$328$	−2.64461	+	2.64461i	−0.146024	+	0.146024i
$329$			5.87641i			0.323977i
$330$	−1.40573	−	5.78282i	−0.0773828	−	0.318334i
$331$		−	12.5316i		−	0.688802i	−0.938823	−	0.344401i	$-0.888082\pi$
$331$		−	12.5316i		−	0.688802i	0.938823	−	0.344401i	$-0.111918\pi$
$332$	−6.55477	−	6.55477i	−0.359740	−	0.359740i
$333$	−0.984090	−	0.984090i	−0.0539278	−	0.0539278i
$334$			9.97075i			0.545575i
$335$	−12.1794	−	7.41603i	−0.665434	−	0.405181i
$336$			1.27865i			0.0697559i
$337$	10.1843	−	10.1843i	0.554774	−	0.554774i	−0.373041	−	0.927815i	$-0.621685\pi$
$337$	10.1843	−	10.1843i	0.554774	−	0.554774i	0.927815	+	0.373041i	$0.121685\pi$
$338$	−9.16320	−	9.16320i	−0.498412	−	0.498412i
$339$		−	2.82348i		−	0.153351i
$340$	8.90035	+	5.41940i	0.482689	+	0.293908i
$341$		−	6.97748i		−	0.377851i
$342$	3.99597	+	1.74133i	0.216077	+	0.0941603i
$343$	11.1797	−	11.1797i	0.603650	−	0.603650i
$344$	2.84376			0.153325
$345$	−1.31265	−	5.39990i	−0.0706705	−	0.290721i
$346$	−20.8873			−1.12291
$347$	3.39715	+	3.39715i	0.182369	+	0.182369i	0.792387	−	0.610019i	$-0.208838\pi$
$347$	3.39715	+	3.39715i	0.182369	+	0.182369i	−0.610019	+	0.792387i	$0.708838\pi$
$348$	−1.53792	+	1.53792i	−0.0824409	+	0.0824409i
$349$			18.4982i			0.990188i	0.868840	+	0.495094i	$0.164866\pi$
$349$			18.4982i			0.990188i	−0.868840	+	0.495094i	$0.835134\pi$
$350$	−5.67982	+	2.93481i	−0.303599	+	0.156872i
$351$	0.203169			0.0108444
$352$	−1.88194	+	1.88194i	−0.100308	+	0.100308i
$353$	−2.03694	+	2.03694i	−0.108415	+	0.108415i	−0.759234	−	0.650818i	$-0.774426\pi$
$353$	−2.03694	+	2.03694i	−0.108415	+	0.108415i	0.650818	+	0.759234i	$0.274426\pi$
$354$	−2.19877			−0.116864
$355$	−5.55647	+	1.35071i	−0.294907	+	0.0716881i
$356$		−	4.94664i		−	0.262171i
$357$	4.21345	−	4.21345i	0.223000	−	0.223000i
$358$	−4.58765	+	4.58765i	−0.242465	+	0.242465i
$359$		−	20.9321i		−	1.10475i	−0.833595	−	0.552376i	$-0.813721\pi$
$359$		−	20.9321i		−	1.10475i	0.833595	−	0.552376i	$-0.186279\pi$
$360$	1.90987	+	1.16292i	0.100659	+	0.0612912i
$361$	13.9166	−	12.9355i	0.732452	−	0.680818i
$362$	−0.0866707	−	0.0866707i	−0.00455531	−	0.00455531i
$363$	2.76945	+	2.76945i	0.145358	+	0.145358i
$364$	0.259782			0.0136163
$365$	−14.1939	−	8.64266i	−0.742945	−	0.452378i
$366$	8.90579			0.465513
$367$	20.7061	+	20.7061i	1.08085	+	1.08085i	0.996430	+	0.0844175i	$0.0269029\pi$
$367$	20.7061	+	20.7061i	1.08085	+	1.08085i	0.0844175	+	0.996430i	$0.473097\pi$
$368$	−1.75733	+	1.75733i	−0.0916070	+	0.0916070i
$369$	3.74005			0.194699
$370$	−3.02390	+	0.735072i	−0.157205	+	0.0382146i
$371$		−	4.59659i		−	0.238643i
$372$	1.85380	+	1.85380i	0.0961149	+	0.0961149i
$373$	7.00175	+	7.00175i	0.362537	+	0.362537i	0.864746	−	0.502209i	$-0.167479\pi$
$373$	7.00175	+	7.00175i	0.362537	+	0.362537i	−0.502209	+	0.864746i	$0.667479\pi$
$374$	12.4029			0.641339
$375$	−0.782122	+	11.1529i	−0.0403886	+	0.575936i
$376$		−	4.59581i		−	0.237011i
$377$	0.312458	+	0.312458i	0.0160924	+	0.0160924i
$378$	0.904140	−	0.904140i	0.0465040	−	0.0465040i
$379$	8.60331			0.441922			0.220961	−	0.975283i	$-0.429081\pi$
$379$	8.60331			0.441922			0.220961	+	0.975283i	$0.429081\pi$
$380$	7.97271	−	5.60678i	0.408991	−	0.287622i
$381$	17.7412			0.908908
$382$	−0.335096	+	0.335096i	−0.0171450	+	0.0171450i
$383$	1.41335	+	1.41335i	0.0722188	+	0.0722188i	0.742294	−	0.670075i	$-0.233738\pi$
$383$	1.41335	+	1.41335i	0.0722188	+	0.0722188i	−0.670075	+	0.742294i	$0.733738\pi$
$384$		−	1.00000i		−	0.0510310i
$385$	−3.95750	+	6.49945i	−0.201693	+	0.331243i
$386$	11.8392			0.602600
$387$	−2.01084	−	2.01084i	−0.102217	−	0.102217i
$388$	11.8481	+	11.8481i	0.601498	+	0.601498i
$389$			14.9165i			0.756295i	0.925745	+	0.378148i	$0.123439\pi$
$389$			14.9165i			0.756295i	−0.925745	+	0.378148i	$0.876561\pi$
$390$	0.236270	−	0.388028i	0.0119640	−	0.0196486i
$391$	11.5816			0.585708
$392$	−3.79367	+	3.79367i	−0.191609	+	0.191609i
$393$	−14.5807	−	14.5807i	−0.735498	−	0.735498i
$394$	−13.3684			−0.673491
$395$	2.23277	+	9.18507i	0.112343	+	0.462151i
$396$	2.66147			0.133744
$397$	−20.0161	−	20.0161i	−1.00458	−	1.00458i	−0.999989	−	0.00459066i	$-0.998539\pi$
$397$	−20.0161	−	20.0161i	−1.00458	−	1.00458i	−0.00459066	−	0.999989i	$-0.501461\pi$
$398$	2.24527	+	2.24527i	0.112545	+	0.112545i
$399$	−2.03851	−	5.18732i	−0.102053	−	0.259691i
$400$	4.44206	−	2.29524i	0.222103	−	0.114762i
$401$			9.55630i			0.477219i	0.971116	+	0.238609i	$0.0766916\pi$
$401$			9.55630i			0.477219i	−0.971116	+	0.238609i	$0.923308\pi$
$402$	4.50928	−	4.50928i	0.224903	−	0.224903i
$403$	0.376635	−	0.376635i	0.0187615	−	0.0187615i
$404$		−	3.64684i		−	0.181437i
$405$	−0.528178	−	2.17279i	−0.0262454	−	0.107967i
$406$	2.78098			0.138018
$407$	−2.61912	+	2.61912i	−0.129825	+	0.129825i
$408$	−3.29524	+	3.29524i	−0.163139	+	0.163139i
$409$	37.3114			1.84493			0.922466	−	0.386079i	$-0.126171\pi$
$409$	37.3114			1.84493			0.922466	+	0.386079i	$0.126171\pi$
$410$	4.34937	−	7.14303i	0.214800	−	0.352769i
$411$			3.45359i			0.170353i
$412$	−4.27174	+	4.27174i	−0.210454	+	0.210454i
$413$	1.98800	+	1.98800i	0.0978231	+	0.0978231i
$414$	2.48524			0.122143
$415$	17.7042	+	10.7801i	0.869067	+	0.529173i
$416$	−0.203169			−0.00996120
$417$	−11.4548	+	11.4548i	−0.560942	+	0.560942i
$418$	4.63449	−	10.6351i	0.226680	−	0.520182i
$419$		−	33.2272i		−	1.62326i	−0.584175	−	0.811628i	$-0.698582\pi$
$419$		−	33.2272i		−	1.62326i	0.584175	−	0.811628i	$-0.301418\pi$
$420$	−0.675353	−	2.77824i	−0.0329539	−	0.135564i
$421$			38.3380i			1.86848i	0.356646	+	0.934240i	$0.383920\pi$
$421$			38.3380i			1.86848i	−0.356646	+	0.934240i	$0.616080\pi$
$422$	10.2214	+	10.2214i	0.497571	+	0.497571i
$423$	−3.24973	+	3.24973i	−0.158007	+	0.158007i
$424$			3.59488i			0.174583i
$425$	−22.2010	−	7.07427i	−1.07691	−	0.343153i
$426$		−	2.55729i		−	0.123901i
$427$	−8.05208	−	8.05208i	−0.389668	−	0.389668i
$428$	9.39155	+	9.39155i	0.453958	+	0.453958i
$429$		−	0.540729i		−	0.0261066i
$430$	−6.17889	+	1.50201i	−0.297973	+	0.0724333i
$431$			21.2257i			1.02241i	0.859460	+	0.511203i	$0.170800\pi$
$431$			21.2257i			1.02241i	−0.859460	+	0.511203i	$0.829200\pi$
$432$	−0.707107	+	0.707107i	−0.0340207	+	0.0340207i
$433$	10.9862	+	10.9862i	0.527961	+	0.527961i	0.919964	−	0.392003i	$-0.128218\pi$
$433$	10.9862	+	10.9862i	0.527961	+	0.527961i	−0.392003	+	0.919964i	$0.628218\pi$
$434$		−	3.35219i		−	0.160910i
$435$	2.52928	−	4.15387i	0.121270	−	0.199163i
$436$			12.0254i			0.575912i
$437$	4.32761	−	9.93092i	0.207018	−	0.475061i
$438$	5.25513	−	5.25513i	0.251100	−	0.251100i
$439$	1.43541			0.0685084			0.0342542	−	0.999413i	$-0.489094\pi$
$439$	1.43541			0.0685084			0.0342542	+	0.999413i	$0.489094\pi$
$440$	3.09507	−	5.08307i	0.147552	−	0.242326i
$441$	5.36506			0.255479
$442$	0.669493	+	0.669493i	0.0318445	+	0.0318445i
$443$	9.49661	−	9.49661i	0.451198	−	0.451198i	−0.444554	−	0.895752i	$-0.646638\pi$
$443$	9.49661	−	9.49661i	0.451198	−	0.451198i	0.895752	+	0.444554i	$0.146638\pi$
$444$		−	1.39171i		−	0.0660478i
$445$	2.61271	+	10.7480i	0.123854	+	0.509505i
$446$	−18.8234			−0.891312
$447$	2.01710	−	2.01710i	0.0954056	−	0.0954056i
$448$	−0.904140	+	0.904140i	−0.0427166	+	0.0427166i
$449$	−17.7665			−0.838454			−0.419227	−	0.907881i	$-0.637699\pi$
$449$	−17.7665			−0.838454			−0.419227	+	0.907881i	$0.637699\pi$
$450$	−4.76399	−	1.51803i	−0.224577	−	0.0715605i
$451$		−	9.95402i		−	0.468716i
$452$	1.99650	−	1.99650i	0.0939076	−	0.0939076i
$453$	−13.1625	+	13.1625i	−0.618428	+	0.618428i
$454$		−	29.7919i		−	1.39820i
$455$	−0.564453	+	0.137211i	−0.0264620	+	0.00643256i
$456$	1.59427	+	4.05688i	0.0746586	+	0.189981i
$457$	6.74008	+	6.74008i	0.315288	+	0.315288i	0.846954	−	0.531666i	$-0.178434\pi$
$457$	6.74008	+	6.74008i	0.315288	+	0.315288i	−0.531666	+	0.846954i	$0.678434\pi$
$458$	−12.8812	−	12.8812i	−0.601897	−	0.601897i
$459$	4.66018			0.217518
$460$	2.89013	−	4.74649i	0.134753	−	0.221306i
$461$	−4.22763			−0.196900			−0.0984501	−	0.995142i	$-0.531388\pi$
$461$	−4.22763			−0.196900			−0.0984501	+	0.995142i	$0.531388\pi$
$462$	−2.40634	−	2.40634i	−0.111953	−	0.111953i
$463$	12.2736	−	12.2736i	0.570403	−	0.570403i	−0.361838	−	0.932241i	$-0.617851\pi$
$463$	12.2736	−	12.2736i	0.570403	−	0.570403i	0.932241	+	0.361838i	$0.117851\pi$
$464$	−2.17494			−0.100969
$465$	−5.00705	−	3.04878i	−0.232196	−	0.141384i
$466$			29.2005i			1.35269i
$467$	9.12358	+	9.12358i	0.422189	+	0.422189i	0.885957	−	0.463768i	$-0.153503\pi$
$467$	9.12358	+	9.12358i	0.422189	+	0.422189i	−0.463768	+	0.885957i	$0.653503\pi$
$468$	0.143663	+	0.143663i	0.00664080	+	0.00664080i
$469$	−8.15405			−0.376519
$470$	2.42740	+	9.98573i	0.111968	+	0.460608i
$471$			14.2403i			0.656159i
$472$	−1.55477	−	1.55477i	−0.0715640	−	0.0715640i
$473$	−5.35178	+	5.35178i	−0.246075	+	0.246075i
$474$	−4.22731			−0.194167
$475$	−14.3617	+	16.3934i	−0.658958	+	0.752180i
$476$	5.95872			0.273118
$477$	2.54197	−	2.54197i	0.116389	−	0.116389i
$478$	−1.26205	−	1.26205i	−0.0577247	−	0.0577247i
$479$			36.9313i			1.68744i	0.536787	+	0.843718i	$0.319638\pi$
$479$			36.9313i			1.68744i	−0.536787	+	0.843718i	$0.680362\pi$
$480$	0.528178	+	2.17279i	0.0241079	+	0.0991740i
$481$	−0.282754			−0.0128925
$482$	−4.36784	−	4.36784i	−0.198950	−	0.198950i
$483$	−2.24700	−	2.24700i	−0.102242	−	0.102242i
$484$			3.91659i			0.178027i
$485$	−32.0015	−	19.4856i	−1.45311	−	0.884797i
$486$	1.00000			0.0453609
$487$	−10.3862	+	10.3862i	−0.470642	+	0.470642i	−0.902122	−	0.431481i	$-0.857991\pi$
$487$	−10.3862	+	10.3862i	−0.470642	+	0.470642i	0.431481	+	0.902122i	$0.357991\pi$
$488$	6.29734	+	6.29734i	0.285067	+	0.285067i
$489$	−23.4081			−1.05855
$490$	6.23913	−	10.2466i	0.281855	−	0.462894i
$491$	−31.2661			−1.41102			−0.705509	−	0.708701i	$-0.749281\pi$
$491$	−31.2661			−1.41102			−0.705509	+	0.708701i	$0.749281\pi$
$492$	2.64461	+	2.64461i	0.119228	+	0.119228i
$493$	7.16696	+	7.16696i	0.322784	+	0.322784i
$494$	0.824235	−	0.323907i	0.0370841	−	0.0145733i
$495$	−5.78282	+	1.40573i	−0.259918	+	0.0631828i
$496$			2.62167i			0.117716i
$497$	−2.31215	+	2.31215i	−0.103714	+	0.103714i
$498$	−6.55477	+	6.55477i	−0.293726	+	0.293726i
$499$		−	31.8064i		−	1.42385i	−0.702256	−	0.711925i	$-0.747824\pi$
$499$		−	31.8064i		−	1.42385i	0.702256	−	0.711925i	$-0.252176\pi$
$500$	−8.43937	+	7.33328i	−0.377420	+	0.327954i
$501$	9.97075			0.445460
$502$	−2.75069	+	2.75069i	−0.122769	+	0.122769i
$503$	−30.1365	+	30.1365i	−1.34372	+	1.34372i	−0.451396	+	0.892324i	$0.649074\pi$
$503$	−30.1365	+	30.1365i	−1.34372	+	1.34372i	−0.892324	+	0.451396i	$0.850926\pi$
$504$	1.27865			0.0569555
$505$	1.92618	+	7.92383i	0.0857139	+	0.352606i
$506$		−	6.61437i		−	0.294045i
$507$	−9.16320	+	9.16320i	−0.406952	+	0.406952i
$508$	12.5449	+	12.5449i	0.556590	+	0.556590i
$509$	−39.4733			−1.74962			−0.874811	−	0.484463i	$-0.839015\pi$
$509$	−39.4733			−1.74962			−0.874811	+	0.484463i	$0.839015\pi$
$510$	5.41940	−	8.90035i	0.239975	−	0.394114i
$511$	−9.50274			−0.420377
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$	1.74133	−	3.99597i	0.0768815	−	0.176426i
$514$		−	19.6600i		−	0.867164i
$515$	7.02537	−	11.5378i	0.309575	−	0.508418i
$516$		−	2.84376i		−	0.125189i
$517$	8.64904	+	8.64904i	0.380384	+	0.380384i
$518$	−1.25830	+	1.25830i	−0.0552867	+	0.0552867i
$519$			20.8873i			0.916853i
$520$	0.441445	−	0.107310i	0.0193587	−	0.00470584i
$521$			43.0892i			1.88777i	0.330271	+	0.943886i	$0.392860\pi$
$521$			43.0892i			1.88777i	−0.330271	+	0.943886i	$0.607140\pi$
$522$	1.53792	+	1.53792i	0.0673127	+	0.0673127i
$523$	−12.0200	−	12.0200i	−0.525600	−	0.525600i	0.393658	−	0.919257i	$-0.371210\pi$
$523$	−12.0200	−	12.0200i	−0.525600	−	0.525600i	−0.919257	+	0.393658i	$0.871210\pi$
$524$		−	20.6202i		−	0.900797i
$525$	2.93481	+	5.67982i	0.128085	+	0.247888i
$526$			17.8922i			0.780135i
$527$	8.63902	−	8.63902i	0.376322	−	0.376322i
$528$	1.88194	+	1.88194i	0.0819010	+	0.0819010i
$529$			16.8236i			0.731461i
$530$	−1.89874	−	7.81093i	−0.0824759	−	0.339285i
$531$			2.19877i			0.0954187i
$532$	2.22655	−	5.10944i	0.0965330	−	0.221522i
$533$	0.537305	−	0.537305i	0.0232733	−	0.0232733i
$534$	−4.94664			−0.214062
$535$	−25.3663	−	15.4455i	−1.09668	−	0.667766i
$536$	6.37709			0.275448
$537$	4.58765	+	4.58765i	0.197972	+	0.197972i
$538$	16.8271	−	16.8271i	0.725470	−	0.725470i
$539$		−	14.2789i		−	0.615037i
$540$	1.16292	−	1.90987i	0.0500440	−	0.0821879i
$541$	−8.87532			−0.381580			−0.190790	−	0.981631i	$-0.561105\pi$
$541$	−8.87532			−0.381580			−0.190790	+	0.981631i	$0.561105\pi$
$542$	−9.58298	+	9.58298i	−0.411624	+	0.411624i
$543$	−0.0866707	+	0.0866707i	−0.00371940	+	0.00371940i
$544$	−4.66018			−0.199803
$545$	−6.35155	−	26.1287i	−0.272070	−	1.11923i
$546$		−	0.259782i		−	0.0111176i
$547$	13.9130	−	13.9130i	0.594877	−	0.594877i	−0.344068	−	0.938945i	$-0.611805\pi$
$547$	13.9130	−	13.9130i	0.594877	−	0.594877i	0.938945	+	0.344068i	$0.111805\pi$
$548$	−2.44206	+	2.44206i	−0.104319	+	0.104319i
$549$		−	8.90579i		−	0.380090i
$550$	−4.04018	+	12.6792i	−0.172274	+	0.540643i
$551$	8.82348	−	3.46745i	0.375893	−	0.147718i
$552$	1.75733	+	1.75733i	0.0747968	+	0.0747968i
$553$	3.82208	+	3.82208i	0.162531	+	0.162531i
$554$	16.7976			0.713662
$555$	0.735072	+	3.02390i	0.0312021	+	0.128358i
$556$	−16.1995			−0.687011
$557$	14.7010	+	14.7010i	0.622900	+	0.622900i	0.946272	−	0.323372i	$-0.104816\pi$
$557$	14.7010	+	14.7010i	0.622900	+	0.622900i	−0.323372	+	0.946272i	$0.604816\pi$
$558$	1.85380	−	1.85380i	0.0784775	−	0.0784775i
$559$	−0.577764			−0.0244368
$560$	1.48696	−	2.44206i	0.0628356	−	0.103196i
$561$		−	12.4029i		−	0.523651i
$562$	11.6077	+	11.6077i	0.489643	+	0.489643i
$563$	9.68060	+	9.68060i	0.407989	+	0.407989i	0.881037	−	0.473048i	$-0.156846\pi$
$563$	9.68060	+	9.68060i	0.407989	+	0.407989i	−0.473048	+	0.881037i	$0.656846\pi$
$564$	−4.59581			−0.193518
$565$	−3.28348	+	5.39250i	−0.138137	+	0.226864i
$566$		−	21.9894i		−	0.924283i
$567$	−0.904140	−	0.904140i	−0.0379703	−	0.0379703i
$568$	1.80828	−	1.80828i	0.0758738	−	0.0758738i
$569$	−36.5026			−1.53027			−0.765133	−	0.643872i	$-0.777327\pi$
$569$	−36.5026			−1.53027			−0.765133	+	0.643872i	$0.777327\pi$
$570$	−5.60678	−	7.97271i	−0.234842	−	0.333940i
$571$	−18.0651			−0.756000			−0.378000	−	0.925806i	$-0.623388\pi$
$571$	−18.0651			−0.756000			−0.378000	+	0.925806i	$0.623388\pi$
$572$	0.382353	−	0.382353i	0.0159870	−	0.0159870i
$573$	0.335096	+	0.335096i	0.0139988	+	0.0139988i
$574$		−	4.78220i		−	0.199605i
$575$	−3.77265	+	11.8396i	−0.157330	+	0.493747i
$576$	−1.00000			−0.0416667
$577$	13.7843	+	13.7843i	0.573847	+	0.573847i	0.933201	−	0.359354i	$-0.117003\pi$
$577$	13.7843	+	13.7843i	0.573847	+	0.573847i	−0.359354	+	0.933201i	$0.617003\pi$
$578$	3.33560	+	3.33560i	0.138743	+	0.138743i
$579$		−	11.8392i		−	0.492021i
$580$	4.72570	−	1.14876i	0.196224	−	0.0476995i
$581$	11.8529			0.491739
$582$	11.8481	−	11.8481i	0.491121	−	0.491121i
$583$	−6.76536	−	6.76536i	−0.280192	−	0.280192i
$584$	7.43187			0.307533
$585$	−0.388028	−	0.236270i	−0.0160430	−	0.00976854i
$586$	−27.1573			−1.12186
$587$	−12.9491	−	12.9491i	−0.534466	−	0.534466i	0.387432	−	0.921898i	$-0.373362\pi$
$587$	−12.9491	−	12.9491i	−0.534466	−	0.534466i	−0.921898	+	0.387432i	$0.873362\pi$
$588$	3.79367	+	3.79367i	0.156448	+	0.156448i
$589$	−4.17965	−	10.6358i	−0.172219	−	0.438240i
$590$	4.19938	+	2.55699i	0.172886	+	0.105270i
$591$			13.3684i			0.549903i
$592$	0.984090	−	0.984090i	0.0404458	−	0.0404458i
$593$	1.56552	−	1.56552i	0.0642881	−	0.0642881i	−0.674232	−	0.738520i	$-0.735525\pi$
$593$	1.56552	−	1.56552i	0.0642881	−	0.0642881i	0.738520	+	0.674232i	$0.235525\pi$
$594$		−	2.66147i		−	0.109201i
$595$	−12.9471	+	3.14727i	−0.530778	+	0.129025i
$596$	2.85261			0.116847
$597$	2.24527	−	2.24527i	0.0918929	−	0.0918929i
$598$	0.357035	−	0.357035i	0.0146003	−	0.0146003i
$599$	−31.2077			−1.27511			−0.637556	−	0.770404i	$-0.720054\pi$
$599$	−31.2077			−1.27511			−0.637556	+	0.770404i	$0.720054\pi$
$600$	−2.29524	−	4.44206i	−0.0937029	−	0.181346i
$601$		−	27.0296i		−	1.10256i	−0.834320	−	0.551281i	$-0.814139\pi$
$601$		−	27.0296i		−	1.10256i	0.834320	−	0.551281i	$-0.185861\pi$
$602$	−2.57115	+	2.57115i	−0.104792	+	0.104792i
$603$	−4.50928	−	4.50928i	−0.183632	−	0.183632i
$604$	−18.6146			−0.757417
$605$	−2.06866	−	8.50995i	−0.0841029	−	0.345979i
$606$	−3.64684			−0.148143
$607$	10.1961	−	10.1961i	0.413847	−	0.413847i	−0.469229	−	0.883076i	$-0.655468\pi$
$607$	10.1961	−	10.1961i	0.413847	−	0.413847i	0.883076	+	0.469229i	$0.155468\pi$
$608$	−1.74133	+	3.99597i	−0.0706202	+	0.162058i
$609$		−	2.78098i		−	0.112691i
$610$	−17.0089	−	10.3567i	−0.688672	−	0.419331i
$611$			0.933728i			0.0377746i
$612$	3.29524	+	3.29524i	0.133202	+	0.133202i
$613$	−22.4225	+	22.4225i	−0.905634	+	0.905634i	−0.995916	−	0.0902818i	$-0.971223\pi$
$613$	−22.4225	+	22.4225i	−0.905634	+	0.905634i	0.0902818	+	0.995916i	$0.471223\pi$
$614$			21.5644i			0.870269i
$615$	−7.14303	−	4.34937i	−0.288035	−	0.175384i
$616$		−	3.40308i		−	0.137114i
$617$	−1.22259	−	1.22259i	−0.0492195	−	0.0492195i	0.682069	−	0.731288i	$-0.261081\pi$
$617$	−1.22259	−	1.22259i	−0.0492195	−	0.0492195i	−0.731288	+	0.682069i	$0.761081\pi$
$618$	4.27174	+	4.27174i	0.171835	+	0.171835i
$619$		−	26.1462i		−	1.05090i	−0.850823	−	0.525452i	$-0.823896\pi$
$619$		−	26.1462i		−	1.05090i	0.850823	−	0.525452i	$-0.176104\pi$
$620$	−1.38471	−	5.69634i	−0.0556111	−	0.228770i
$621$		−	2.48524i		−	0.0997291i
$622$	0.151302	−	0.151302i	0.00606668	−	0.00606668i
$623$	4.47245	+	4.47245i	0.179185	+	0.179185i
$624$			0.203169i			0.00813329i
$625$	14.4637	−	20.3912i	0.578549	−	0.815648i
$626$			25.7952i			1.03098i
$627$	−10.6351	−	4.63449i	−0.424727	−	0.185084i
$628$	−10.0694	+	10.0694i	−0.401814	+	0.401814i
$629$	−6.48563			−0.258599
$630$	−2.77824	+	0.675353i	−0.110688	+	0.0269067i
$631$	−33.3652			−1.32825			−0.664124	−	0.747623i	$-0.731195\pi$
$631$	−33.3652			−1.32825			−0.664124	+	0.747623i	$0.731195\pi$
$632$	−2.98916	−	2.98916i	−0.118902	−	0.118902i
$633$	10.2214	−	10.2214i	0.406265	−	0.406265i
$634$		−	17.7823i		−	0.706226i
$635$	−33.8834	−	20.6315i	−1.34462	−	0.818737i
$636$	3.59488			0.142546
$637$	0.770758	−	0.770758i	0.0305386	−	0.0305386i
$638$	4.09311	−	4.09311i	0.162048	−	0.162048i
$639$	−2.55729			−0.101165
$640$	−1.16292	+	1.90987i	−0.0459684	+	0.0754944i
$641$			31.2439i			1.23406i	0.786940	+	0.617029i	$0.211664\pi$
$641$			31.2439i			1.23406i	−0.786940	+	0.617029i	$0.788336\pi$
$642$	9.39155	−	9.39155i	0.370655	−	0.370655i
$643$	−3.28874	+	3.28874i	−0.129695	+	0.129695i	−0.768975	−	0.639279i	$-0.779233\pi$
$643$	−3.28874	+	3.28874i	−0.129695	+	0.129695i	0.639279	+	0.768975i	$0.279233\pi$
$644$		−	3.17774i		−	0.125220i
$645$	1.50201	+	6.17889i	0.0591416	+	0.243294i
$646$	18.9058	−	7.42959i	0.743838	−	0.292313i
$647$	24.2688	+	24.2688i	0.954105	+	0.954105i	0.998992	−	0.0448869i	$-0.0142928\pi$
$647$	24.2688	+	24.2688i	0.954105	+	0.954105i	−0.0448869	+	0.998992i	$0.514293\pi$
$648$	0.707107	+	0.707107i	0.0277778	+	0.0277778i
$649$	5.85196			0.229710
$650$	−0.902490	+	0.466323i	−0.0353986	+	0.0182907i
$651$	−3.35219			−0.131382
$652$	−16.5520	−	16.5520i	−0.648227	−	0.648227i
$653$	0.820035	−	0.820035i	0.0320904	−	0.0320904i	−0.690879	−	0.722970i	$-0.742776\pi$
$653$	0.820035	−	0.820035i	0.0320904	−	0.0320904i	0.722970	+	0.690879i	$0.242776\pi$
$654$	12.0254			0.470230
$655$	10.8911	+	44.8034i	0.425552	+	1.75061i
$656$			3.74005i			0.146024i
$657$	−5.25513	−	5.25513i	−0.205022	−	0.205022i
$658$	4.15525	+	4.15525i	0.161989	+	0.161989i
$659$	42.2189			1.64461			0.822307	−	0.569044i	$-0.192687\pi$
$659$	42.2189			1.64461			0.822307	+	0.569044i	$0.192687\pi$
$660$	−5.08307	−	3.09507i	−0.197858	−	0.120475i
$661$			26.8163i			1.04303i	0.853241	+	0.521517i	$0.174634\pi$
$661$			26.8163i			1.04303i	−0.853241	+	0.521517i	$0.825366\pi$
$662$	−8.86121	−	8.86121i	−0.344401	−	0.344401i
$663$	0.669493	−	0.669493i	0.0260009	−	0.0260009i
$664$	−9.26984			−0.359740
$665$	−2.13913	+	12.2778i	−0.0829519	+	0.476111i
$666$	−1.39171			−0.0539278
$667$	3.82208	−	3.82208i	0.147992	−	0.147992i
$668$	7.05038	+	7.05038i	0.272788	+	0.272788i
$669$			18.8234i			0.727753i
$670$	−13.8561	+	3.36824i	−0.535307	+	0.130126i
$671$	−23.7025			−0.915023
$672$	0.904140	+	0.904140i	0.0348780	+	0.0348780i
$673$	23.1618	+	23.1618i	0.892824	+	0.892824i	0.994788	−	0.101964i	$-0.0325128\pi$
$673$	23.1618	+	23.1618i	0.892824	+	0.892824i	−0.101964	+	0.994788i	$0.532513\pi$
$674$		−	14.4028i		−	0.554774i
$675$	−1.51803	+	4.76399i	−0.0584289	+	0.183366i
$676$	−12.9587			−0.498412
$677$	18.0408	−	18.0408i	0.693364	−	0.693364i	−0.269606	−	0.962971i	$-0.586894\pi$
$677$	18.0408	−	18.0408i	0.693364	−	0.693364i	0.962971	+	0.269606i	$0.0868935\pi$
$678$	−1.99650	−	1.99650i	−0.0766753	−	0.0766753i
$679$	−21.4248			−0.822207
$680$	10.1256	−	2.46140i	0.388299	−	0.0943905i
$681$	−29.7919			−1.14163
$682$	−4.93382	−	4.93382i	−0.188926	−	0.188926i
$683$	20.2075	+	20.2075i	0.773220	+	0.773220i	0.978668	−	0.205448i	$-0.0658651\pi$
$683$	20.2075	+	20.2075i	0.773220	+	0.773220i	−0.205448	+	0.978668i	$0.565865\pi$
$684$	4.05688	−	1.59427i	0.155119	−	0.0609585i
$685$	4.01624	−	6.59592i	0.153453	−	0.252017i
$686$		−	15.8106i		−	0.603650i
$687$	−12.8812	+	12.8812i	−0.491447	+	0.491447i
$688$	2.01084	−	2.01084i	0.0766625	−	0.0766625i
$689$		−	0.730371i		−	0.0278249i
$690$	−4.74649	−	2.89013i	−0.180696	−	0.110025i
$691$	−5.06618			−0.192727			−0.0963633	−	0.995346i	$-0.530721\pi$
$691$	−5.06618			−0.192727			−0.0963633	+	0.995346i	$0.530721\pi$
$692$	−14.7696	+	14.7696i	−0.561455	+	0.561455i
$693$	−2.40634	+	2.40634i	−0.0914093	+	0.0914093i
$694$	4.80430			0.182369
$695$	35.1981	−	8.55620i	1.33514	−	0.324555i
$696$			2.17494i			0.0824409i
$697$	12.3244	−	12.3244i	0.466819	−	0.466819i
$698$	13.0802	+	13.0802i	0.495094	+	0.495094i
$699$	29.2005			1.10446
$700$	−1.94102	+	6.09146i	−0.0733637	+	0.230236i
$701$	31.7812			1.20036			0.600180	−	0.799865i	$-0.295096\pi$
$701$	31.7812			1.20036			0.600180	+	0.799865i	$0.295096\pi$
$702$	0.143663	−	0.143663i	0.00542219	−	0.00542219i
$703$	−2.42343	+	5.56124i	−0.0914014	+	0.209746i
$704$			2.66147i			0.100308i
$705$	9.98573	−	2.42740i	0.376084	−	0.0914213i
$706$			2.88067i			0.108415i
$707$	3.29726	+	3.29726i	0.124006	+	0.124006i
$708$	−1.55477	+	1.55477i	−0.0584318	+	0.0584318i
$709$			40.1995i			1.50972i	0.655884	+	0.754861i	$0.272296\pi$
$709$			40.1995i			1.50972i	−0.655884	+	0.754861i	$0.727704\pi$
$710$	−2.97392	+	4.88411i	−0.111609	+	0.183297i
$711$			4.22731i			0.158537i
$712$	−3.49780	−	3.49780i	−0.131086	−	0.131086i
$713$	−4.60712	−	4.60712i	−0.172538	−	0.172538i
$714$		−	5.95872i		−	0.223000i
$715$	−0.628823	+	1.03272i	−0.0235167	+	0.0386217i
$716$			6.48791i			0.242465i
$717$	−1.26205	+	1.26205i	−0.0471320	+	0.0471320i
$718$	−14.8012	−	14.8012i	−0.552376	−	0.552376i
$719$			9.60719i			0.358288i	0.983823	+	0.179144i	$0.0573328\pi$
$719$			9.60719i			0.358288i	−0.983823	+	0.179144i	$0.942667\pi$
$720$	2.17279	−	0.528178i	0.0809752	−	0.0196840i
$721$		−	7.72450i		−	0.287676i
$722$	0.693705	−	18.9873i	0.0258170	−	0.706635i
$723$	−4.36784	+	4.36784i	−0.162442	+	0.162442i
$724$	−0.122571			−0.00455531
$725$	−9.66121	+	4.99202i	−0.358808	+	0.185399i
$726$	3.91659			0.145358
$727$	7.58566	+	7.58566i	0.281337	+	0.281337i	0.833642	−	0.552305i	$-0.186252\pi$
$727$	7.58566	+	7.58566i	0.281337	+	0.281337i	−0.552305	+	0.833642i	$0.686252\pi$
$728$	0.183694	−	0.183694i	0.00680814	−	0.00680814i
$729$		−	1.00000i		−	0.0370370i
$730$	−16.1479	+	3.92535i	−0.597661	+	0.145284i
$731$	−13.2524			−0.490158
$732$	6.29734	−	6.29734i	0.232757	−	0.232757i
$733$	16.6371	−	16.6371i	0.614504	−	0.614504i	−0.329612	−	0.944116i	$-0.606918\pi$
$733$	16.6371	−	16.6371i	0.614504	−	0.614504i	0.944116	+	0.329612i	$0.106918\pi$
$734$	29.2828			1.08085
$735$	−10.2466	−	6.23913i	−0.377951	−	0.230134i
$736$			2.48524i			0.0916070i
$737$	−12.0013	+	12.0013i	−0.442074	+	0.442074i
$738$	2.64461	−	2.64461i	0.0973496	−	0.0973496i
$739$		−	18.7582i		−	0.690030i	−0.938597	−	0.345015i	$-0.887874\pi$
$739$		−	18.7582i		−	0.690030i	0.938597	−	0.345015i	$-0.112126\pi$
$740$	−1.61845	+	2.65800i	−0.0594954	+	0.0977099i
$741$	−0.323907	−	0.824235i	−0.0118990	−	0.0302790i
$742$	−3.25028	−	3.25028i	−0.119321	−	0.119321i
$743$	18.3052	+	18.3052i	0.671553	+	0.671553i	0.958074	−	0.286521i	$-0.0924989\pi$
$743$	18.3052	+	18.3052i	0.671553	+	0.671553i	−0.286521	+	0.958074i	$0.592499\pi$
$744$	2.62167			0.0961149
$745$	−6.19813	+	1.50669i	−0.227082	+	0.0552007i
$746$	9.90197			0.362537
$747$	6.55477	+	6.55477i	0.239826	+	0.239826i
$748$	8.77018	−	8.77018i	0.320669	−	0.320669i
$749$	−16.9826			−0.620529
$750$	7.33328	+	8.43937i	0.267774	+	0.308162i
$751$		−	32.7384i		−	1.19464i	−0.802002	−	0.597321i	$-0.796232\pi$
$751$		−	32.7384i		−	1.19464i	0.802002	−	0.597321i	$-0.203768\pi$
$752$	−3.24973	−	3.24973i	−0.118505	−	0.118505i
$753$	2.75069	+	2.75069i	0.100241	+	0.100241i
$754$	0.441882			0.0160924
$755$	40.4456	−	9.83182i	1.47197	−	0.357816i
$756$		−	1.27865i		−	0.0465040i
$757$	18.8701	+	18.8701i	0.685844	+	0.685844i	0.961311	−	0.275466i	$-0.0888322\pi$
$757$	18.8701	+	18.8701i	0.685844	+	0.685844i	−0.275466	+	0.961311i	$0.588832\pi$
$758$	6.08346	−	6.08346i	0.220961	−	0.220961i
$759$	−6.61437			−0.240086
$760$	1.67296	−	9.60215i	0.0606848	−	0.348306i
$761$	6.60459			0.239416			0.119708	−	0.992809i	$-0.461804\pi$
$761$	6.60459			0.239416			0.119708	+	0.992809i	$0.461804\pi$
$762$	12.5449	−	12.5449i	0.454454	−	0.454454i
$763$	−10.8726	−	10.8726i	−0.393616	−	0.393616i
$764$			0.473897i			0.0171450i
$765$	−8.90035	−	5.41940i	−0.321793	−	0.195939i
$766$	1.99878			0.0722188
$767$	0.315881	+	0.315881i	0.0114058	+	0.0114058i
$768$	−0.707107	−	0.707107i	−0.0255155	−	0.0255155i
$769$		−	5.37624i		−	0.193872i	−0.995291	−	0.0969360i	$-0.969096\pi$
$769$		−	5.37624i		−	0.193872i	0.995291	−	0.0969360i	$-0.0309042\pi$
$770$	1.79743	+	7.39418i	0.0647749	+	0.266468i
$771$	−19.6600			−0.708036
$772$	8.37158	−	8.37158i	0.301300	−	0.301300i
$773$	1.67948	+	1.67948i	0.0604066	+	0.0604066i	0.736665	−	0.676258i	$-0.236400\pi$
$773$	1.67948	+	1.67948i	0.0604066	+	0.0604066i	−0.676258	+	0.736665i	$0.736400\pi$
$774$	−2.84376			−0.102217
$775$	6.01736	+	11.6456i	0.216150	+	0.418322i
$776$	16.7558			0.601498
$777$	1.25830	+	1.25830i	0.0451414	+	0.0451414i
$778$	10.5475	+	10.5475i	0.378148	+	0.378148i
$779$	−5.96266	−	15.1729i	−0.213634	−	0.543627i
$780$	−0.107310	−	0.441445i	−0.00384230	−	0.0158063i
$781$			6.80615i			0.243543i
$782$	8.18945	−	8.18945i	0.292854	−	0.292854i
$783$	1.53792	−	1.53792i	0.0549606	−	0.0549606i
$784$			5.36506i			0.191609i
$785$	16.5603	−	27.1972i	0.591063	−	0.970710i
$786$	−20.6202			−0.735498
$787$	33.8233	−	33.8233i	1.20567	−	1.20567i	0.233257	−	0.972415i	$-0.425062\pi$
$787$	33.8233	−	33.8233i	1.20567	−	1.20567i	0.972415	−	0.233257i	$-0.0749383\pi$
$788$	−9.45290	+	9.45290i	−0.336745	+	0.336745i
$789$	17.8922			0.636978
$790$	8.07364	+	4.91602i	0.287247	+	0.174904i
$791$			3.61024i			0.128365i
$792$	1.88194	−	1.88194i	0.0668719	−	0.0668719i
$793$	−1.27943	−	1.27943i	−0.0454338	−	0.0454338i
$794$	−28.3071			−1.00458
$795$	−7.81093	+	1.89874i	−0.277025	+	0.0673413i
$796$	3.17530			0.112545
$797$	19.1081	−	19.1081i	0.676844	−	0.676844i	−0.282441	−	0.959285i	$-0.591144\pi$
$797$	19.1081	−	19.1081i	0.676844	−	0.676844i	0.959285	+	0.282441i	$0.0911440\pi$
$798$	−5.10944	−	2.22655i	−0.180872	−	0.0788189i
$799$			21.4173i			0.757688i
$800$	1.51803	−	4.76399i	0.0536703	−	0.168432i
$801$			4.94664i			0.174781i
$802$	6.75733	+	6.75733i	0.238609	+	0.238609i
$803$	−13.9863	+	13.9863i	−0.493568	+	0.493568i
$804$		−	6.37709i		−	0.224903i
$805$	1.67841	+	6.90457i	0.0591562	+	0.243354i
$806$		−	0.532642i		−	0.0187615i
$807$	−16.8271	−	16.8271i	−0.592344	−	0.592344i
$808$	−2.57871	−	2.57871i	−0.0907186	−	0.0907186i
$809$		−	9.60569i		−	0.337718i	−0.985640	−	0.168859i	$-0.945992\pi$
$809$		−	9.60569i		−	0.337718i	0.985640	−	0.168859i	$-0.0540082\pi$
$810$	−1.90987	−	1.16292i	−0.0671062	−	0.0408608i
$811$		−	28.5091i		−	1.00109i	−0.865711	−	0.500545i	$-0.833133\pi$
$811$		−	28.5091i		−	1.00109i	0.865711	−	0.500545i	$-0.166867\pi$
$812$	1.96645	−	1.96645i	0.0690089	−	0.0690089i
$813$	9.58298	+	9.58298i	0.336090	+	0.336090i
$814$			3.70400i			0.129825i
$815$	44.7065	+	27.2217i	1.56600	+	0.953534i
$816$			4.66018i			0.163139i
$817$	−4.95191	+	11.3636i	−0.173246	+	0.397561i
$818$	26.3832	−	26.3832i	0.922466	−	0.922466i
$819$	−0.259782			−0.00907752
$820$	−1.97541	−	8.12635i	−0.0689844	−	0.283785i
$821$	13.9024			0.485196			0.242598	−	0.970127i	$-0.422000\pi$
$821$	13.9024			0.485196			0.242598	+	0.970127i	$0.422000\pi$
$822$	2.44206	+	2.44206i	0.0851765	+	0.0851765i
$823$	21.8340	−	21.8340i	0.761085	−	0.761085i	−0.215434	−	0.976518i	$-0.569117\pi$
$823$	21.8340	−	21.8340i	0.761085	−	0.761085i	0.976518	+	0.215434i	$0.0691165\pi$
$824$			6.04115i			0.210454i
$825$	12.6792	+	4.04018i	0.441433	+	0.140661i
$826$	2.81146			0.0978231
$827$	−10.5045	+	10.5045i	−0.365278	+	0.365278i	−0.865752	−	0.500473i	$-0.833159\pi$
$827$	−10.5045	+	10.5045i	−0.365278	+	0.365278i	0.500473	+	0.865752i	$0.333159\pi$
$828$	1.75733	−	1.75733i	0.0610713	−	0.0610713i
$829$	22.5926			0.784674			0.392337	−	0.919822i	$-0.371667\pi$
$829$	22.5926			0.784674			0.392337	+	0.919822i	$0.371667\pi$
$830$	20.1414	−	4.89613i	0.699120	−	0.169947i
$831$		−	16.7976i		−	0.582703i
$832$	−0.143663	+	0.143663i	−0.00498060	+	0.00498060i
$833$	17.6792	−	17.6792i	0.612547	−	0.612547i
$834$			16.1995i			0.560942i
$835$	−19.0429	−	11.5952i	−0.659006	−	0.401267i
$836$	−4.24310	−	10.7973i	−0.146751	−	0.373431i
$837$	−1.85380	−	1.85380i	−0.0640766	−	0.0640766i
$838$	−23.4952	−	23.4952i	−0.811628	−	0.811628i
$839$	8.89881			0.307221			0.153610	−	0.988131i	$-0.450910\pi$
$839$	8.89881			0.307221			0.153610	+	0.988131i	$0.450910\pi$
$840$	−2.44206	−	1.48696i	−0.0842589	−	0.0513051i
$841$	−24.2696			−0.836884
$842$	27.1090	+	27.1090i	0.934240	+	0.934240i
$843$	11.6077	−	11.6077i	0.399792	−	0.399792i
$844$	14.4553			0.497571
$845$	28.1566	−	6.84451i	0.968617	−	0.235458i
$846$			4.59581i			0.158007i
$847$	−3.54115	−	3.54115i	−0.121675	−	0.121675i
$848$	2.54197	+	2.54197i	0.0872915	+	0.0872915i
$849$	−21.9894			−0.754674
$850$	−20.7008	+	10.6962i	−0.710030	+	0.366878i
$851$			3.45873i			0.118564i
$852$	−1.80828	−	1.80828i	−0.0619507	−	0.0619507i
$853$	−4.21663	+	4.21663i	−0.144375	+	0.144375i	−0.775600	−	0.631225i	$-0.782552\pi$
$853$	−4.21663	+	4.21663i	−0.144375	+	0.144375i	0.631225	+	0.775600i	$0.282552\pi$
$854$	−11.3874			−0.389668
$855$	−7.97271	+	5.60678i	−0.272661	+	0.191748i
$856$	13.2817			0.453958
$857$	−1.84086	+	1.84086i	−0.0628825	+	0.0628825i	−0.737849	−	0.674966i	$-0.764158\pi$
$857$	−1.84086	+	1.84086i	−0.0628825	+	0.0628825i	0.674966	+	0.737849i	$0.264158\pi$
$858$	−0.382353	−	0.382353i	−0.0130533	−	0.0130533i
$859$		−	14.0924i		−	0.480826i	−0.970671	−	0.240413i	$-0.922717\pi$
$859$		−	14.0924i		−	0.480826i	0.970671	−	0.240413i	$-0.0772829\pi$
$860$	−3.30706	+	5.43122i	−0.112770	+	0.185203i
$861$	−4.78220			−0.162977
$862$	15.0089	+	15.0089i	0.511203	+	0.511203i
$863$	2.40643	+	2.40643i	0.0819160	+	0.0819160i	0.746878	−	0.664962i	$-0.231552\pi$
$863$	2.40643	+	2.40643i	0.0819160	+	0.0819160i	−0.664962	+	0.746878i	$0.731552\pi$
$864$			1.00000i			0.0340207i
$865$	24.2903	−	39.8922i	0.825894	−	1.35638i
$866$	15.5368			0.527961
$867$	3.33560	−	3.33560i	0.113283	−	0.113283i
$868$	−2.37035	−	2.37035i	−0.0804550	−	0.0804550i
$869$	11.2509			0.381659
$870$	−1.14876	−	4.72570i	−0.0389465	−	0.160216i
$871$	−1.29563			−0.0439007
$872$	8.50324	+	8.50324i	0.287956	+	0.287956i
$873$	−11.8481	−	11.8481i	−0.400999	−	0.400999i
$874$	−3.96214	−	10.0823i	−0.134021	−	0.341039i
$875$	1.00006	−	14.2607i	0.0338081	−	0.482099i
$876$		−	7.43187i		−	0.251100i
$877$	−1.38678	+	1.38678i	−0.0468281	+	0.0468281i	−0.730133	−	0.683305i	$-0.760542\pi$
$877$	−1.38678	+	1.38678i	−0.0468281	+	0.0468281i	0.683305	+	0.730133i	$0.260542\pi$
$878$	1.01499	−	1.01499i	0.0342542	−	0.0342542i
$879$			27.1573i			0.915994i
$880$	−1.40573	−	5.78282i	−0.0473871	−	0.194939i
$881$	8.63628			0.290964			0.145482	−	0.989361i	$-0.453527\pi$
$881$	8.63628			0.290964			0.145482	+	0.989361i	$0.453527\pi$
$882$	3.79367	−	3.79367i	0.127740	−	0.127740i
$883$	−17.5459	+	17.5459i	−0.590468	+	0.590468i	−0.937758	−	0.347290i	$-0.887102\pi$
$883$	−17.5459	+	17.5459i	−0.590468	+	0.590468i	0.347290	+	0.937758i	$0.387102\pi$
$884$	0.946806			0.0318445
$885$	2.55699	−	4.19938i	0.0859524	−	0.141161i
$886$		−	13.4302i		−	0.451198i
$887$	19.8938	−	19.8938i	0.667970	−	0.667970i	−0.289276	−	0.957246i	$-0.593415\pi$
$887$	19.8938	−	19.8938i	0.667970	−	0.667970i	0.957246	+	0.289276i	$0.0934145\pi$
$888$	−0.984090	−	0.984090i	−0.0330239	−	0.0330239i
$889$	−22.6847			−0.760821
$890$	9.44746	+	5.75254i	0.316680	+	0.192825i
$891$	−2.66147			−0.0891625
$892$	−13.3101	+	13.3101i	−0.445656	+	0.445656i
$893$	18.3647	+	8.00281i	0.614551	+	0.267804i
$894$		−	2.85261i		−	0.0954056i
$895$	−3.42677	−	14.0969i	−0.114544	−	0.471207i
$896$			1.27865i			0.0427166i
$897$	−0.357035	−	0.357035i	−0.0119211	−	0.0119211i
$898$	−12.5628	+	12.5628i	−0.419227	+	0.419227i
$899$		−	5.70197i		−	0.190171i
$900$	−4.44206	+	2.29524i	−0.148069	+	0.0765081i
$901$		−	16.7528i		−	0.558116i
$902$	−7.03855	−	7.03855i	−0.234358	−	0.234358i
$903$	2.57115	+	2.57115i	0.0855626	+	0.0855626i
$904$		−	2.82348i		−	0.0939076i
$905$	0.266321	−	0.0647393i	0.00885282	−	0.00215201i
$906$			18.6146i			0.618428i
$907$	19.4964	−	19.4964i	0.647367	−	0.647367i	−0.304989	−	0.952356i	$-0.598653\pi$
$907$	19.4964	−	19.4964i	0.647367	−	0.647367i	0.952356	+	0.304989i	$0.0986528\pi$
$908$	−21.0661	−	21.0661i	−0.699102	−	0.699102i
$909$			3.64684i			0.120958i
$910$	−0.302105	+	0.496151i	−0.0100147	+	0.0164473i
$911$		−	47.2989i		−	1.56708i	−0.621341	−	0.783541i	$-0.713412\pi$
$911$		−	47.2989i		−	1.56708i	0.621341	−	0.783541i	$-0.286588\pi$
$912$	3.99597	+	1.74133i	0.132320	+	0.0576612i
$913$	17.4453	−	17.4453i	0.577355	−	0.577355i
$914$	9.53191			0.315288
$915$	−10.3567	+	17.0089i	−0.342382	+	0.562298i
$916$	−18.2167			−0.601897
$917$	18.6435	+	18.6435i	0.615664	+	0.615664i
$918$	3.29524	−	3.29524i	0.108759	−	0.108759i
$919$			42.1995i			1.39203i	0.718026	+	0.696016i	$0.245046\pi$
$919$			42.1995i			1.39203i	−0.718026	+	0.696016i	$0.754954\pi$
$920$	−1.31265	−	5.39990i	−0.0432767	−	0.178029i
$921$	21.5644			0.710571
$922$	−2.98938	+	2.98938i	−0.0984501	+	0.0984501i
$923$	−0.367387	+	0.367387i	−0.0120927	+	0.0120927i
$924$	−3.40308			−0.111953
$925$	2.11266	−	6.63011i	0.0694637	−	0.217997i
$926$		−	17.3575i		−	0.570403i
$927$	4.27174	−	4.27174i	0.140302	−	0.140302i
$928$	−1.53792	+	1.53792i	−0.0504846	+	0.0504846i
$929$			15.8786i			0.520960i	0.965479	+	0.260480i	$0.0838809\pi$
$929$			15.8786i			0.520960i	−0.965479	+	0.260480i	$0.916119\pi$
$930$	−5.69634	+	1.38471i	−0.186790	+	0.0454063i
$931$	−8.55337	−	21.7654i	−0.280325	−	0.713333i
$932$	20.6479	+	20.6479i	0.676344	+	0.676344i
$933$	−0.151302	−	0.151302i	−0.00495342	−	0.00495342i
$934$	12.9027			0.422189
$935$	−14.4236	+	23.6880i	−0.471701	+	0.774680i
$936$	0.203169			0.00664080
$937$	−7.52072	−	7.52072i	−0.245691	−	0.245691i	0.573508	−	0.819200i	$-0.305582\pi$
$937$	−7.52072	−	7.52072i	−0.245691	−	0.245691i	−0.819200	+	0.573508i	$0.805582\pi$
$938$	−5.76578	+	5.76578i	−0.188259	+	0.188259i
$939$	25.7952			0.841793
$940$	8.77741	+	5.34455i	0.286288	+	0.174320i
$941$		−	17.9276i		−	0.584422i	−0.956354	−	0.292211i	$-0.905609\pi$
$941$		−	17.9276i		−	0.584422i	0.956354	−	0.292211i	$-0.0943909\pi$
$942$	10.0694	+	10.0694i	0.328079	+	0.328079i
$943$	−6.57249	−	6.57249i	−0.214030	−	0.214030i
$944$	−2.19877			−0.0715640
$945$	0.675353	+	2.77824i	0.0219692	+	0.0903760i
$946$			7.56856i			0.246075i
$947$	−6.90093	−	6.90093i	−0.224250	−	0.224250i	0.586035	−	0.810285i	$-0.300688\pi$
$947$	−6.90093	−	6.90093i	−0.224250	−	0.224250i	−0.810285	+	0.586035i	$0.800688\pi$
$948$	−2.98916	+	2.98916i	−0.0970834	+	0.0970834i
$949$	−1.50993			−0.0490144
$950$	1.43664	+	21.7471i	0.0466107	+	0.705569i
$951$	−17.7823			−0.576632
$952$	4.21345	−	4.21345i	0.136559	−	0.136559i
$953$	42.1375	+	42.1375i	1.36497	+	1.36497i	0.867458	+	0.497511i	$0.165752\pi$
$953$	42.1375	+	42.1375i	1.36497	+	1.36497i	0.497511	+	0.867458i	$0.334248\pi$
$954$		−	3.59488i		−	0.116389i
$955$	−0.250302	−	1.02968i	−0.00809958	−	0.0333197i
$956$	−1.78480			−0.0577247
$957$	−4.09311	−	4.09311i	−0.132312	−	0.132312i
$958$	26.1144	+	26.1144i	0.843718	+	0.843718i
$959$		−	4.41592i		−	0.142598i
$960$	1.90987	+	1.16292i	0.0616409	+	0.0375330i
$961$	24.1269			0.778286
$962$	−0.199937	+	0.199937i	−0.00644623	+	0.00644623i
$963$	−9.39155	−	9.39155i	−0.302638	−	0.302638i
$964$	−6.17706			−0.198950
$965$	−13.7680	+	22.6114i	−0.443209	+	0.727887i
$966$	−3.17774			−0.102242
$967$	−9.16729	−	9.16729i	−0.294800	−	0.294800i	0.544173	−	0.838973i	$-0.316844\pi$
$967$	−9.16729	−	9.16729i	−0.294800	−	0.294800i	−0.838973	+	0.544173i	$0.816844\pi$
$968$	2.76945	+	2.76945i	0.0890135	+	0.0890135i
$969$	−7.42959	−	18.9058i	−0.238673	−	0.607341i
$970$	−36.4069	+	8.85004i	−1.16895	+	0.284158i
$971$			47.1525i			1.51319i	0.653881	+	0.756597i	$0.273140\pi$
$971$			47.1525i			1.51319i	−0.653881	+	0.756597i	$0.726860\pi$
$972$	0.707107	−	0.707107i	0.0226805	−	0.0226805i
$973$	14.6466	−	14.6466i	0.469548	−	0.469548i
$974$			14.6882i			0.470642i
$975$	0.466323	+	0.902490i	0.0149343	+	0.0289028i
$976$	8.90579			0.285067
$977$	−26.5454	+	26.5454i	−0.849262	+	0.849262i	−0.990041	−	0.140779i	$-0.955039\pi$
$977$	−26.5454	+	26.5454i	−0.849262	+	0.849262i	0.140779	+	0.990041i	$0.455039\pi$
$978$	−16.5520	+	16.5520i	−0.529275	+	0.529275i
$979$	13.1653			0.420765
$980$	−2.83371	−	11.6572i	−0.0905195	−	0.372374i
$981$		−	12.0254i		−	0.383941i
$982$	−22.1084	+	22.1084i	−0.705509	+	0.705509i
$983$	30.2846	+	30.2846i	0.965928	+	0.965928i	0.999438	−	0.0335108i	$-0.0106688\pi$
$983$	30.2846	+	30.2846i	0.965928	+	0.965928i	−0.0335108	+	0.999438i	$0.510669\pi$
$984$	3.74005			0.119228
$985$	15.5464	−	25.5320i	0.495349	−	0.813517i
$986$	10.1356			0.322784
$987$	4.15525	−	4.15525i	0.132263	−	0.132263i
$988$	0.353785	−	0.811859i	0.0112554	−	0.0258287i
$989$			7.06740i			0.224730i
$990$	−3.09507	+	5.08307i	−0.0983677	+	0.161551i
$991$		−	3.31607i		−	0.105339i	−0.998612	−	0.0526693i	$-0.983227\pi$
$991$		−	3.31607i		−	0.105339i	0.998612	−	0.0526693i	$-0.0167729\pi$
$992$	1.85380	+	1.85380i	0.0588581	+	0.0588581i
$993$	−8.86121	+	8.86121i	−0.281202	+	0.281202i
$994$			3.26988i			0.103714i
$995$	−6.89926	+	1.67712i	−0.218721	+	0.0531683i
$996$			9.26984i			0.293726i
$997$	−36.9548	−	36.9548i	−1.17037	−	1.17037i	−0.982122	−	0.188247i	$-0.939719\pi$
$997$	−36.9548	−	36.9548i	−1.17037	−	1.17037i	−0.188247	−	0.982122i	$-0.560281\pi$
$998$	−22.4905	−	22.4905i	−0.711925	−	0.711925i
$999$			1.39171i			0.0440319i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	570.2.m.b.37.8	yes	20
3.2	odd	2		1710.2.p.c.37.3		20
5.3	odd	4	inner	570.2.m.b.493.3	yes	20
15.8	even	4		1710.2.p.c.1063.8		20
19.18	odd	2	inner	570.2.m.b.37.3	✓	20
57.56	even	2		1710.2.p.c.37.8		20
95.18	even	4	inner	570.2.m.b.493.8	yes	20
285.113	odd	4		1710.2.p.c.1063.3		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.m.b.37.3	✓	20	19.18	odd	2	inner
570.2.m.b.37.8	yes	20	1.1	even	1	trivial
570.2.m.b.493.3	yes	20	5.3	odd	4	inner
570.2.m.b.493.8	yes	20	95.18	even	4	inner
1710.2.p.c.37.3		20	3.2	odd	2
1710.2.p.c.37.8		20	57.56	even	2
1710.2.p.c.1063.3		20	285.113	odd	4
1710.2.p.c.1063.8		20	15.8	even	4

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:	\( N \)	\(=\)	\( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	570.m (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 - 0.707107i) q^{2} +(-0.707107 - 0.707107i) q^{3} -1.00000i q^{4} +(0.528178 + 2.17279i) q^{5} -1.00000 q^{6} +(0.904140 + 0.904140i) q^{7} +(-0.707107 - 0.707107i) q^{8} +1.00000i q^{9} +O(q^{10})\)	\(q+(0.707107 - 0.707107i) q^{2} +(-0.707107 - 0.707107i) q^{3} -1.00000i q^{4} +(0.528178 + 2.17279i) q^{5} -1.00000 q^{6} +(0.904140 + 0.904140i) q^{7} +(-0.707107 - 0.707107i) q^{8} +1.00000i q^{9} +(1.90987 + 1.16292i) q^{10} +2.66147 q^{11} +(-0.707107 + 0.707107i) q^{12} +(0.143663 + 0.143663i) q^{13} +1.27865 q^{14} +(1.16292 - 1.90987i) q^{15} -1.00000 q^{16} +(3.29524 + 3.29524i) q^{17} +(0.707107 + 0.707107i) q^{18} +(4.05688 - 1.59427i) q^{19} +(2.17279 - 0.528178i) q^{20} -1.27865i q^{21} +(1.88194 - 1.88194i) q^{22} +(1.75733 - 1.75733i) q^{23} +1.00000i q^{24} +(-4.44206 + 2.29524i) q^{25} +0.203169 q^{26} +(0.707107 - 0.707107i) q^{27} +(0.904140 - 0.904140i) q^{28} +2.17494 q^{29} +(-0.528178 - 2.17279i) q^{30} -2.62167i q^{31} +(-0.707107 + 0.707107i) q^{32} +(-1.88194 - 1.88194i) q^{33} +4.66018 q^{34} +(-1.48696 + 2.44206i) q^{35} +1.00000 q^{36} +(-0.984090 + 0.984090i) q^{37} +(1.74133 - 3.99597i) q^{38} -0.203169i q^{39} +(1.16292 - 1.90987i) q^{40} -3.74005i q^{41} +(-0.904140 - 0.904140i) q^{42} +(-2.01084 + 2.01084i) q^{43} -2.66147i q^{44} +(-2.17279 + 0.528178i) q^{45} -2.48524i q^{46} +(3.24973 + 3.24973i) q^{47} +(0.707107 + 0.707107i) q^{48} -5.36506i q^{49} +(-1.51803 + 4.76399i) q^{50} -4.66018i q^{51} +(0.143663 - 0.143663i) q^{52} +(-2.54197 - 2.54197i) q^{53} -1.00000i q^{54} +(1.40573 + 5.78282i) q^{55} -1.27865i q^{56} +(-3.99597 - 1.74133i) q^{57} +(1.53792 - 1.53792i) q^{58} +2.19877 q^{59} +(-1.90987 - 1.16292i) q^{60} -8.90579 q^{61} +(-1.85380 - 1.85380i) q^{62} +(-0.904140 + 0.904140i) q^{63} +1.00000i q^{64} +(-0.236270 + 0.388028i) q^{65} -2.66147 q^{66} +(-4.50928 + 4.50928i) q^{67} +(3.29524 - 3.29524i) q^{68} -2.48524 q^{69} +(0.675353 + 2.77824i) q^{70} +2.55729i q^{71} +(0.707107 - 0.707107i) q^{72} +(-5.25513 + 5.25513i) q^{73} +1.39171i q^{74} +(4.76399 + 1.51803i) q^{75} +(-1.59427 - 4.05688i) q^{76} +(2.40634 + 2.40634i) q^{77} +(-0.143663 - 0.143663i) q^{78} +4.22731 q^{79} +(-0.528178 - 2.17279i) q^{80} -1.00000 q^{81} +(-2.64461 - 2.64461i) q^{82} +(6.55477 - 6.55477i) q^{83} -1.27865 q^{84} +(-5.41940 + 8.90035i) q^{85} +2.84376i q^{86} +(-1.53792 - 1.53792i) q^{87} +(-1.88194 - 1.88194i) q^{88} +4.94664 q^{89} +(-1.16292 + 1.90987i) q^{90} +0.259782i q^{91} +(-1.75733 - 1.75733i) q^{92} +(-1.85380 + 1.85380i) q^{93} +4.59581 q^{94} +(5.60678 + 7.97271i) q^{95} +1.00000 q^{96} +(-11.8481 + 11.8481i) q^{97} +(-3.79367 - 3.79367i) q^{98} +2.66147i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 12 q^{5} - 20 q^{6} - 4 q^{7}+O(q^{10}) \) 20 * q + 12 * q^5 - 20 * q^6 - 4 * q^7	\( 20 q + 12 q^{5} - 20 q^{6} - 4 q^{7} - 8 q^{11} - 20 q^{16} - 12 q^{17} - 4 q^{23} - 28 q^{25} + 24 q^{26} - 4 q^{28} - 12 q^{30} + 4 q^{35} + 20 q^{36} - 12 q^{38} + 4 q^{42} - 12 q^{43} - 44 q^{47} + 64 q^{55} + 12 q^{57} - 8 q^{58} - 24 q^{62} + 4 q^{63} + 8 q^{66} - 12 q^{68} - 4 q^{73} + 4 q^{76} + 88 q^{77} - 12 q^{80} - 20 q^{81} - 8 q^{82} + 76 q^{83} - 12 q^{85} + 8 q^{87} + 4 q^{92} - 24 q^{93} - 24 q^{95} + 20 q^{96}+O(q^{100}) \) 20 * q + 12 * q^5 - 20 * q^6 - 4 * q^7 - 8 * q^11 - 20 * q^16 - 12 * q^17 - 4 * q^23 - 28 * q^25 + 24 * q^26 - 4 * q^28 - 12 * q^30 + 4 * q^35 + 20 * q^36 - 12 * q^38 + 4 * q^42 - 12 * q^43 - 44 * q^47 + 64 * q^55 + 12 * q^57 - 8 * q^58 - 24 * q^62 + 4 * q^63 + 8 * q^66 - 12 * q^68 - 4 * q^73 + 4 * q^76 + 88 * q^77 - 12 * q^80 - 20 * q^81 - 8 * q^82 + 76 * q^83 - 12 * q^85 + 8 * q^87 + 4 * q^92 - 24 * q^93 - 24 * q^95 + 20 * q^96

Introduction

L-functions

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