LMFDB - Embedded newform 570.2.m.b.493.8

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			493.8
Root			$1.20277 + 1.20277i$ of defining polynomial
Character	$\chi$	$=$	570.493
Dual form			570.2.m.b.37.8

$q$-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 $\left(\mathbb{Z}/570\mathbb{Z}\right)^\times$.

$n$	$191$	$211$	$457$
$\chi(n)$	$1$	$-1$	$e\left(\frac{3}{4}\right)$

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	−0.515286	−	0.857018i	$-0.672314\pi$
$7$	0.904140	−	0.904140i	0.341733	−	0.341733i	0.857018	+	0.515286i	$0.172314\pi$
$8$	−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	−0.686904	−	0.726748i	$-0.741031\pi$
$13$	0.143663	−	0.143663i	0.0398448	−	0.0398448i	0.726748	+	0.686904i	$0.241031\pi$
$14$	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	−0.183758	−	0.982972i	$-0.558826\pi$
$17$	3.29524	−	3.29524i	0.799214	−	0.799214i	0.982972	+	0.183758i	$0.0588262\pi$
$18$	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	0.866173	−	0.499745i	$-0.166573\pi$
$23$	1.75733	+	1.75733i	0.366428	+	0.366428i	−0.499745	+	0.866173i	$0.666573\pi$
$24$		−	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	$0.0756507\pi$
$31$			2.62167i			0.470865i	−0.971891	+	0.235432i	$0.924349\pi$
$32$	−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	0.621573	−	0.783356i	$-0.286494\pi$
$37$	−0.984090	−	0.984090i	−0.161783	−	0.161783i	−0.783356	+	0.621573i	$0.786494\pi$
$38$	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	$0.0943370\pi$
$41$			3.74005i			0.584098i	−0.956403	+	0.292049i	$0.905663\pi$
$42$	−0.904140	+	0.904140i	−0.139512	+	0.139512i
$43$	−2.01084	−	2.01084i	−0.306650	−	0.306650i	0.536959	−	0.843609i	$-0.319573\pi$
$43$	−2.01084	−	2.01084i	−0.306650	−	0.306650i	−0.843609	+	0.536959i	$0.819573\pi$
$44$			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	−0.429192	−	0.903213i	$-0.641202\pi$
$47$	3.24973	−	3.24973i	0.474021	−	0.474021i	0.903213	+	0.429192i	$0.141202\pi$
$48$	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	−0.859799	−	0.510633i	$-0.829411\pi$
$53$	−2.54197	+	2.54197i	−0.349166	+	0.349166i	0.510633	+	0.859799i	$0.329411\pi$
$54$			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	0.375803	−	0.926700i	$-0.377367\pi$
$67$	−4.50928	−	4.50928i	−0.550896	−	0.550896i	−0.926700	+	0.375803i	$0.877367\pi$
$68$	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	$-0.951510\pi$
$71$		−	2.55729i		−	0.303495i	0.988419	−	0.151748i	$-0.0484901\pi$
$72$	0.707107	+	0.707107i	0.0833333	+	0.0833333i
$73$	−5.25513	−	5.25513i	−0.615066	−	0.615066i	0.329196	−	0.944262i	$-0.393222\pi$
$73$	−5.25513	−	5.25513i	−0.615066	−	0.615066i	−0.944262	+	0.329196i	$0.893222\pi$
$74$		−	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	0.968499	−	0.249019i	$-0.0801083\pi$
$83$	6.55477	+	6.55477i	0.719479	+	0.719479i	−0.249019	+	0.968499i	$0.580108\pi$
$84$	−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	−0.973251	−	0.229746i	$-0.926211\pi$
$97$	−11.8481	−	11.8481i	−1.20300	−	1.20300i	−0.229746	−	0.973251i	$-0.573789\pi$
$98$	−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	−0.885516	−	0.464609i	$-0.846195\pi$
$103$	−4.27174	+	4.27174i	−0.420907	+	0.420907i	0.464609	+	0.885516i	$0.346195\pi$
$104$			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	0.0881885	−	0.996104i	$-0.471892\pi$
$107$	−9.39155	−	9.39155i	−0.907915	−	0.907915i	−0.996104	+	0.0881885i	$0.971892\pi$
$108$	−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	−0.606936	−	0.794751i	$-0.707601\pi$
$113$	1.99650	−	1.99650i	0.187815	−	0.187815i	0.794751	+	0.606936i	$0.207601\pi$
$114$	−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	−0.992718	−	0.120462i	$-0.961562\pi$
$127$	−12.5449	−	12.5449i	−1.11318	−	1.11318i	−0.120462	−	0.992718i	$-0.538438\pi$
$128$	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	−0.803689	−	0.595050i	$-0.797132\pi$
$137$	−2.44206	+	2.44206i	−0.208639	+	0.208639i	0.595050	+	0.803689i	$0.297132\pi$
$138$	−1.75733	−	1.75733i	−0.149594	−	0.149594i
$139$			16.1995i			1.37402i	0.726647	+	0.687011i	$0.241077\pi$
$139$			16.1995i			1.37402i	−0.726647	+	0.687011i	$0.758923\pi$
$140$	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	$-0.962721\pi$
$149$		−	2.85261i		−	0.233695i	0.993150	−	0.116847i	$-0.0372789\pi$
$150$	4.44206	+	2.29524i	0.362692	+	0.187406i
$151$			18.6146i			1.51483i	0.652932	+	0.757417i	$0.273539\pi$
$151$			18.6146i			1.51483i	−0.652932	+	0.757417i	$0.726461\pi$
$152$	−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	−0.983661	−	0.180033i	$-0.942379\pi$
$157$	−10.0694	+	10.0694i	−0.803627	+	0.803627i	0.180033	+	0.983661i	$0.442379\pi$
$158$	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	0.930719	+	0.365735i	$0.119182\pi$
$163$	16.5520	+	16.5520i	1.29645	+	1.29645i	0.365735	+	0.930719i	$0.380818\pi$
$164$	−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	0.379583	−	0.925158i	$-0.376068\pi$
$167$	−7.05038	−	7.05038i	−0.545575	−	0.545575i	−0.925158	+	0.379583i	$0.876068\pi$
$168$	−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	−0.131609	+	0.991302i	$0.542014\pi$
$173$	−14.7696	+	14.7696i	−1.12291	+	1.12291i	−0.991302	+	0.131609i	$0.957986\pi$
$174$	−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	$0.00145001\pi$
$181$			0.122571i			0.00911063i	−0.999990	+	0.00455531i	$0.998550\pi$
$182$	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	−0.338402	−	0.941002i	$-0.609886\pi$
$193$	8.37158	−	8.37158i	0.602600	−	0.602600i	0.941002	+	0.338402i	$0.109886\pi$
$194$		−	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	−0.958519	−	0.285028i	$-0.907997\pi$
$197$	−9.45290	+	9.45290i	−0.673491	+	0.673491i	0.285028	+	0.958519i	$0.407997\pi$
$198$	1.88194	−	1.88194i	0.133744	−	0.133744i
$199$		−	3.17530i		−	0.225091i	−0.993647	−	0.112545i	$-0.964100\pi$
$199$		−	3.17530i		−	0.225091i	0.993647	−	0.112545i	$-0.0359004\pi$
$200$	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	$-0.834225\pi$
$211$		−	14.4553i		−	0.995142i	0.867423	−	0.497571i	$-0.165775\pi$
$212$	−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	−0.994647	−	0.103335i	$-0.967049\pi$
$223$	−13.3101	+	13.3101i	−0.891312	+	0.891312i	0.103335	+	0.994647i	$0.467049\pi$
$224$	−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	0.805199	+	0.593005i	$0.202058\pi$
$227$	21.0661	+	21.0661i	1.39820	+	1.39820i	0.593005	+	0.805199i	$0.297942\pi$
$228$	−1.74133	−	3.99597i	−0.115322	−	0.264640i
$229$			18.2167i			1.20379i	0.798574	+	0.601897i	$0.205588\pi$
$229$			18.2167i			1.20379i	−0.798574	+	0.601897i	$0.794412\pi$
$230$	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	−0.882642	−	0.470045i	$-0.844238\pi$
$233$	−20.6479	−	20.6479i	−1.35269	−	1.35269i	−0.470045	−	0.882642i	$-0.655762\pi$
$234$		−	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	$0.0183846\pi$
$239$			1.78480i			0.115449i	−0.998333	+	0.0577247i	$0.981615\pi$
$240$	−1.16292	−	1.90987i	−0.0750660	−	0.123282i
$241$			6.17706i			0.397899i	0.980010	+	0.198950i	$0.0637530\pi$
$241$			6.17706i			0.397899i	−0.980010	+	0.198950i	$0.936247\pi$
$242$	−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	0.992158	−	0.124994i	$-0.0398911\pi$
$257$	13.9017	+	13.9017i	0.867164	+	0.867164i	−0.124994	+	0.992158i	$0.539891\pi$
$258$	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	0.199718	−	0.979853i	$-0.435997\pi$
$263$	−12.6517	−	12.6517i	−0.780135	−	0.780135i	−0.979853	+	0.199718i	$0.935997\pi$
$264$		−	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	−0.253637	−	0.967299i	$-0.581627\pi$
$277$	11.8777	−	11.8777i	0.713662	−	0.713662i	0.967299	+	0.253637i	$0.0816270\pi$
$278$	−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	$-0.837127\pi$
$281$		−	16.4158i		−	0.979285i	0.871923	−	0.489643i	$-0.162873\pi$
$282$	−3.24973	+	3.24973i	−0.193518	+	0.193518i
$283$	15.5488	+	15.5488i	0.924283	+	0.924283i	0.997329	−	0.0730457i	$-0.0232719\pi$
$283$	15.5488	+	15.5488i	0.924283	+	0.924283i	−0.0730457	+	0.997329i	$0.523272\pi$
$284$	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	−0.130398	+	0.991462i	$0.541625\pi$
$293$	−19.2031	+	19.2031i	−1.12186	+	1.12186i	−0.991462	+	0.130398i	$0.958375\pi$
$294$		−	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	0.122233	−	0.992501i	$-0.460995\pi$
$307$	−15.2483	−	15.2483i	−0.870269	−	0.870269i	−0.992501	+	0.122233i	$0.960995\pi$
$308$	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	−0.999504	−	0.0314771i	$-0.989979\pi$
$313$	−18.2399	−	18.2399i	−1.03098	−	1.03098i	−0.0314771	−	0.999504i	$-0.510021\pi$
$314$	−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	0.965740	−	0.259513i	$-0.0835621\pi$
$317$	12.5740	+	12.5740i	0.706226	+	0.706226i	−0.259513	+	0.965740i	$0.583562\pi$
$318$	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	$0.111918\pi$
$331$			12.5316i			0.688802i	−0.938823	+	0.344401i	$0.888082\pi$
$332$	−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	0.927815	−	0.373041i	$-0.121685\pi$
$337$	10.1843	+	10.1843i	0.554774	+	0.554774i	−0.373041	+	0.927815i	$0.621685\pi$
$338$	−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	−0.610019	−	0.792387i	$-0.708838\pi$
$347$	3.39715	−	3.39715i	0.182369	−	0.182369i	0.792387	+	0.610019i	$0.208838\pi$
$348$	−1.53792	−	1.53792i	−0.0824409	−	0.0824409i
$349$		−	18.4982i		−	0.990188i	−0.868840	−	0.495094i	$-0.835134\pi$
$349$		−	18.4982i		−	0.990188i	0.868840	−	0.495094i	$-0.164866\pi$
$350$	−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	0.650818	−	0.759234i	$-0.274426\pi$
$353$	−2.03694	−	2.03694i	−0.108415	−	0.108415i	−0.759234	+	0.650818i	$0.774426\pi$
$354$	−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	$0.186279\pi$
$359$			20.9321i			1.10475i	−0.833595	+	0.552376i	$0.813721\pi$
$360$	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	0.0844175	−	0.996430i	$-0.473097\pi$
$367$	20.7061	−	20.7061i	1.08085	−	1.08085i	0.996430	−	0.0844175i	$-0.0269029\pi$
$368$	−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	−0.502209	−	0.864746i	$-0.667479\pi$
$373$	7.00175	−	7.00175i	0.362537	−	0.362537i	0.864746	+	0.502209i	$0.167479\pi$
$374$	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	−0.670075	−	0.742294i	$-0.733738\pi$
$383$	1.41335	−	1.41335i	0.0722188	−	0.0722188i	0.742294	+	0.670075i	$0.233738\pi$
$384$			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	$-0.876561\pi$
$389$		−	14.9165i		−	0.756295i	0.925745	−	0.378148i	$-0.123439\pi$
$390$	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	−0.00459066	+	0.999989i	$0.501461\pi$
$397$	−20.0161	+	20.0161i	−1.00458	+	1.00458i	−0.999989	+	0.00459066i	$0.998539\pi$
$398$	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	$-0.923308\pi$
$401$		−	9.55630i		−	0.477219i	0.971116	−	0.238609i	$-0.0766916\pi$
$402$	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	$0.301418\pi$
$419$			33.2272i			1.62326i	−0.584175	+	0.811628i	$0.698582\pi$
$420$	−0.675353	+	2.77824i	−0.0329539	+	0.135564i
$421$		−	38.3380i		−	1.86848i	−0.356646	−	0.934240i	$-0.616080\pi$
$421$		−	38.3380i		−	1.86848i	0.356646	−	0.934240i	$-0.383920\pi$
$422$	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	$-0.829200\pi$
$431$		−	21.2257i		−	1.02241i	0.859460	−	0.511203i	$-0.170800\pi$
$432$	−0.707107	−	0.707107i	−0.0340207	−	0.0340207i
$433$	10.9862	−	10.9862i	0.527961	−	0.527961i	−0.392003	−	0.919964i	$-0.628218\pi$
$433$	10.9862	−	10.9862i	0.527961	−	0.527961i	0.919964	+	0.392003i	$0.128218\pi$
$434$			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	0.895752	−	0.444554i	$-0.146638\pi$
$443$	9.49661	+	9.49661i	0.451198	+	0.451198i	−0.444554	+	0.895752i	$0.646638\pi$
$444$			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	−0.531666	−	0.846954i	$-0.678434\pi$
$457$	6.74008	−	6.74008i	0.315288	−	0.315288i	0.846954	+	0.531666i	$0.178434\pi$
$458$	−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	0.932241	−	0.361838i	$-0.117851\pi$
$463$	12.2736	+	12.2736i	0.570403	+	0.570403i	−0.361838	+	0.932241i	$0.617851\pi$
$464$	−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	−0.463768	−	0.885957i	$-0.653503\pi$
$467$	9.12358	−	9.12358i	0.422189	−	0.422189i	0.885957	+	0.463768i	$0.153503\pi$
$468$	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	$-0.680362\pi$
$479$		−	36.9313i		−	1.68744i	0.536787	−	0.843718i	$-0.319638\pi$
$480$	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	0.431481	−	0.902122i	$-0.357991\pi$
$487$	−10.3862	−	10.3862i	−0.470642	−	0.470642i	−0.902122	+	0.431481i	$0.857991\pi$
$488$	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	$0.252176\pi$
$499$			31.8064i			1.42385i	−0.702256	+	0.711925i	$0.747824\pi$
$500$	−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	−0.892324	−	0.451396i	$-0.850926\pi$
$503$	−30.1365	−	30.1365i	−1.34372	−	1.34372i	−0.451396	−	0.892324i	$-0.649074\pi$
$504$	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	$-0.607140\pi$
$521$		−	43.0892i		−	1.88777i	0.330271	−	0.943886i	$-0.392860\pi$
$522$	1.53792	−	1.53792i	0.0673127	−	0.0673127i
$523$	−12.0200	+	12.0200i	−0.525600	+	0.525600i	−0.919257	−	0.393658i	$-0.871210\pi$
$523$	−12.0200	+	12.0200i	−0.525600	+	0.525600i	0.393658	+	0.919257i	$0.371210\pi$
$524$			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	0.938945	−	0.344068i	$-0.111805\pi$
$547$	13.9130	+	13.9130i	0.594877	+	0.594877i	−0.344068	+	0.938945i	$0.611805\pi$
$548$	−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	−0.323372	−	0.946272i	$-0.604816\pi$
$557$	14.7010	−	14.7010i	0.622900	−	0.622900i	0.946272	+	0.323372i	$0.104816\pi$
$558$	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	−0.473048	−	0.881037i	$-0.656846\pi$
$563$	9.68060	−	9.68060i	0.407989	−	0.407989i	0.881037	+	0.473048i	$0.156846\pi$
$564$	−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	−0.359354	−	0.933201i	$-0.617003\pi$
$577$	13.7843	−	13.7843i	0.573847	−	0.573847i	0.933201	+	0.359354i	$0.117003\pi$
$578$	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	−0.921898	−	0.387432i	$-0.873362\pi$
$587$	−12.9491	+	12.9491i	−0.534466	+	0.534466i	0.387432	+	0.921898i	$0.373362\pi$
$588$	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	0.738520	−	0.674232i	$-0.235525\pi$
$593$	1.56552	+	1.56552i	0.0642881	+	0.0642881i	−0.674232	+	0.738520i	$0.735525\pi$
$594$			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	$0.185861\pi$
$601$			27.0296i			1.10256i	−0.834320	+	0.551281i	$0.814139\pi$
$602$	−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	0.883076	−	0.469229i	$-0.155468\pi$
$607$	10.1961	+	10.1961i	0.413847	+	0.413847i	−0.469229	+	0.883076i	$0.655468\pi$
$608$	−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	0.0902818	−	0.995916i	$-0.471223\pi$
$613$	−22.4225	−	22.4225i	−0.905634	−	0.905634i	−0.995916	+	0.0902818i	$0.971223\pi$
$614$		−	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	−0.731288	−	0.682069i	$-0.761081\pi$
$617$	−1.22259	+	1.22259i	−0.0492195	+	0.0492195i	0.682069	+	0.731288i	$0.261081\pi$
$618$	4.27174	−	4.27174i	0.171835	−	0.171835i
$619$			26.1462i			1.05090i	0.850823	+	0.525452i	$0.176104\pi$
$619$			26.1462i			1.05090i	−0.850823	+	0.525452i	$0.823896\pi$
$620$	−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	$-0.788336\pi$
$641$		−	31.2439i		−	1.23406i	0.786940	−	0.617029i	$-0.211664\pi$
$642$	9.39155	+	9.39155i	0.370655	+	0.370655i
$643$	−3.28874	−	3.28874i	−0.129695	−	0.129695i	0.639279	−	0.768975i	$-0.279233\pi$
$643$	−3.28874	−	3.28874i	−0.129695	−	0.129695i	−0.768975	+	0.639279i	$0.779233\pi$
$644$			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	−0.0448869	−	0.998992i	$-0.514293\pi$
$647$	24.2688	−	24.2688i	0.954105	−	0.954105i	0.998992	+	0.0448869i	$0.0142928\pi$
$648$	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	0.722970	−	0.690879i	$-0.242776\pi$
$653$	0.820035	+	0.820035i	0.0320904	+	0.0320904i	−0.690879	+	0.722970i	$0.742776\pi$
$654$	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	$-0.825366\pi$
$661$		−	26.8163i		−	1.04303i	0.853241	−	0.521517i	$-0.174634\pi$
$662$	−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	−0.101964	−	0.994788i	$-0.532513\pi$
$673$	23.1618	−	23.1618i	0.892824	−	0.892824i	0.994788	+	0.101964i	$0.0325128\pi$
$674$			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	0.962971	−	0.269606i	$-0.0868935\pi$
$677$	18.0408	+	18.0408i	0.693364	+	0.693364i	−0.269606	+	0.962971i	$0.586894\pi$
$678$	−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	−0.205448	−	0.978668i	$-0.565865\pi$
$683$	20.2075	−	20.2075i	0.773220	−	0.773220i	0.978668	+	0.205448i	$0.0658651\pi$
$684$	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	$-0.727704\pi$
$709$		−	40.1995i		−	1.50972i	0.655884	−	0.754861i	$-0.272296\pi$
$710$	−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	$-0.942667\pi$
$719$		−	9.60719i		−	0.358288i	0.983823	−	0.179144i	$-0.0573328\pi$
$720$	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	−0.552305	−	0.833642i	$-0.686252\pi$
$727$	7.58566	−	7.58566i	0.281337	−	0.281337i	0.833642	+	0.552305i	$0.186252\pi$
$728$	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	0.944116	−	0.329612i	$-0.106918\pi$
$733$	16.6371	+	16.6371i	0.614504	+	0.614504i	−0.329612	+	0.944116i	$0.606918\pi$
$734$	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	$0.112126\pi$
$739$			18.7582i			0.690030i	−0.938597	+	0.345015i	$0.887874\pi$
$740$	−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	−0.286521	−	0.958074i	$-0.592499\pi$
$743$	18.3052	−	18.3052i	0.671553	−	0.671553i	0.958074	+	0.286521i	$0.0924989\pi$
$744$	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	$0.203768\pi$
$751$			32.7384i			1.19464i	−0.802002	+	0.597321i	$0.796232\pi$
$752$	−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	−0.275466	−	0.961311i	$-0.588832\pi$
$757$	18.8701	−	18.8701i	0.685844	−	0.685844i	0.961311	+	0.275466i	$0.0888322\pi$
$758$	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	$0.0309042\pi$
$769$			5.37624i			0.193872i	−0.995291	+	0.0969360i	$0.969096\pi$
$770$	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	−0.676258	−	0.736665i	$-0.736400\pi$
$773$	1.67948	−	1.67948i	0.0604066	−	0.0604066i	0.736665	+	0.676258i	$0.236400\pi$
$774$	−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	0.972415	+	0.233257i	$0.0749383\pi$
$787$	33.8233	+	33.8233i	1.20567	+	1.20567i	0.233257	+	0.972415i	$0.425062\pi$
$788$	−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	0.959285	−	0.282441i	$-0.0911440\pi$
$797$	19.1081	+	19.1081i	0.676844	+	0.676844i	−0.282441	+	0.959285i	$0.591144\pi$
$798$	−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	$0.0540082\pi$
$809$			9.60569i			0.337718i	−0.985640	+	0.168859i	$0.945992\pi$
$810$	−1.90987	+	1.16292i	−0.0671062	+	0.0408608i
$811$			28.5091i			1.00109i	0.865711	+	0.500545i	$0.166867\pi$
$811$			28.5091i			1.00109i	−0.865711	+	0.500545i	$0.833133\pi$
$812$	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	0.976518	−	0.215434i	$-0.0691165\pi$
$823$	21.8340	+	21.8340i	0.761085	+	0.761085i	−0.215434	+	0.976518i	$0.569117\pi$
$824$		−	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	0.500473	−	0.865752i	$-0.333159\pi$
$827$	−10.5045	−	10.5045i	−0.365278	−	0.365278i	−0.865752	+	0.500473i	$0.833159\pi$
$828$	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	0.631225	−	0.775600i	$-0.282552\pi$
$853$	−4.21663	−	4.21663i	−0.144375	−	0.144375i	−0.775600	+	0.631225i	$0.782552\pi$
$854$	−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	0.674966	−	0.737849i	$-0.264158\pi$
$857$	−1.84086	−	1.84086i	−0.0628825	−	0.0628825i	−0.737849	+	0.674966i	$0.764158\pi$
$858$	−0.382353	+	0.382353i	−0.0130533	+	0.0130533i
$859$			14.0924i			0.480826i	0.970671	+	0.240413i	$0.0772829\pi$
$859$			14.0924i			0.480826i	−0.970671	+	0.240413i	$0.922717\pi$
$860$	−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	−0.664962	−	0.746878i	$-0.731552\pi$
$863$	2.40643	−	2.40643i	0.0819160	−	0.0819160i	0.746878	+	0.664962i	$0.231552\pi$
$864$		−	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	0.683305	−	0.730133i	$-0.260542\pi$
$877$	−1.38678	−	1.38678i	−0.0468281	−	0.0468281i	−0.730133	+	0.683305i	$0.760542\pi$
$878$	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	0.347290	−	0.937758i	$-0.387102\pi$
$883$	−17.5459	−	17.5459i	−0.590468	−	0.590468i	−0.937758	+	0.347290i	$0.887102\pi$
$884$	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	0.957246	−	0.289276i	$-0.0934145\pi$
$887$	19.8938	+	19.8938i	0.667970	+	0.667970i	−0.289276	+	0.957246i	$0.593415\pi$
$888$	−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	0.952356	−	0.304989i	$-0.0986528\pi$
$907$	19.4964	+	19.4964i	0.647367	+	0.647367i	−0.304989	+	0.952356i	$0.598653\pi$
$908$	−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	$0.286588\pi$
$911$			47.2989i			1.56708i	−0.621341	+	0.783541i	$0.713412\pi$
$912$	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	$-0.754954\pi$
$919$		−	42.1995i		−	1.39203i	0.718026	−	0.696016i	$-0.245046\pi$
$920$	−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	$-0.916119\pi$
$929$		−	15.8786i		−	0.520960i	0.965479	−	0.260480i	$-0.0838809\pi$
$930$	−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	−0.819200	−	0.573508i	$-0.805582\pi$
$937$	−7.52072	+	7.52072i	−0.245691	+	0.245691i	0.573508	+	0.819200i	$0.305582\pi$
$938$	−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	$0.0943909\pi$
$941$			17.9276i			0.584422i	−0.956354	+	0.292211i	$0.905609\pi$
$942$	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	−0.810285	−	0.586035i	$-0.800688\pi$
$947$	−6.90093	+	6.90093i	−0.224250	+	0.224250i	0.586035	+	0.810285i	$0.300688\pi$
$948$	−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	0.497511	−	0.867458i	$-0.334248\pi$
$953$	42.1375	−	42.1375i	1.36497	−	1.36497i	0.867458	−	0.497511i	$-0.165752\pi$
$954$			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	−0.838973	−	0.544173i	$-0.816844\pi$
$967$	−9.16729	+	9.16729i	−0.294800	+	0.294800i	0.544173	+	0.838973i	$0.316844\pi$
$968$	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	$-0.726860\pi$
$971$		−	47.1525i		−	1.51319i	0.653881	−	0.756597i	$-0.273140\pi$
$972$	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	0.140779	−	0.990041i	$-0.455039\pi$
$977$	−26.5454	−	26.5454i	−0.849262	−	0.849262i	−0.990041	+	0.140779i	$0.955039\pi$
$978$	−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	−0.0335108	−	0.999438i	$-0.510669\pi$
$983$	30.2846	−	30.2846i	0.965928	−	0.965928i	0.999438	+	0.0335108i	$0.0106688\pi$
$984$	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	$0.0167729\pi$
$991$			3.31607i			0.105339i	−0.998612	+	0.0526693i	$0.983227\pi$
$992$	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	−0.188247	+	0.982122i	$0.560281\pi$
$997$	−36.9548	+	36.9548i	−1.17037	+	1.17037i	−0.982122	+	0.188247i	$0.939719\pi$
$998$	−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.493.8	yes	20
3.2	odd	2		1710.2.p.c.1063.3		20
5.2	odd	4	inner	570.2.m.b.37.3	✓	20
15.2	even	4		1710.2.p.c.37.8		20
19.18	odd	2	inner	570.2.m.b.493.3	yes	20
57.56	even	2		1710.2.p.c.1063.8		20
95.37	even	4	inner	570.2.m.b.37.8	yes	20
285.227	odd	4		1710.2.p.c.37.3		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.m.b.37.3	✓	20	5.2	odd	4	inner
570.2.m.b.37.8	yes	20	95.37	even	4	inner
570.2.m.b.493.3	yes	20	19.18	odd	2	inner
570.2.m.b.493.8	yes	20	1.1	even	1	trivial
1710.2.p.c.37.3		20	285.227	odd	4
1710.2.p.c.37.8		20	15.2	even	4
1710.2.p.c.1063.3		20	3.2	odd	2
1710.2.p.c.1063.8		20	57.56	even	2

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

Modular forms

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