LMFDB - Embedded newform 1110.2.e.d.739.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1110,2,Mod(739,1110)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1110, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1110.739");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1110 = 2 \cdot 3 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1110.e (of order $2$, degree $1$, 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:	$8.86339462436$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 2 x^{15} + 2 x^{14} + 8 x^{13} + 138 x^{12} - 220 x^{11} + 196 x^{10} + 744 x^{9} + 4241 x^{8} + \cdots + 64 $ x^16 - 2x^15 + 2x^14 + 8x^13 + 138x^12 - 220x^11 + 196x^10 + 744x^9 + 4241x^8 - 3018x^7 + 658x^6 - 1584x^5 + 16372x^4 - 18840x^3 + 10952x^2 - 1184*x + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{6} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			739.6
Root			$0.718347 - 0.718347i$ of defining polynomial
Character	$\chi$	$=$	1110.739
Dual form			1110.2.e.d.739.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -1.00000i q^{3} +1.00000 q^{4} +(0.718347 + 2.11754i) q^{5} -1.00000i q^{6} +2.74990i q^{7} +1.00000 q^{8} -1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.00000i q^{3} +1.00000 q^{4} +(0.718347 + 2.11754i) q^{5} -1.00000i q^{6} +2.74990i q^{7} +1.00000 q^{8} -1.00000 q^{9} +(0.718347 + 2.11754i) q^{10} -0.572952 q^{11} -1.00000i q^{12} -3.04226 q^{13} +2.74990i q^{14} +(2.11754 - 0.718347i) q^{15} +1.00000 q^{16} +4.95991 q^{17} -1.00000 q^{18} +3.74447i q^{19} +(0.718347 + 2.11754i) q^{20} +2.74990 q^{21} -0.572952 q^{22} +2.98281 q^{23} -1.00000i q^{24} +(-3.96796 + 3.04226i) q^{25} -3.04226 q^{26} +1.00000i q^{27} +2.74990i q^{28} +7.36456i q^{29} +(2.11754 - 0.718347i) q^{30} +1.12948i q^{31} +1.00000 q^{32} +0.572952i q^{33} +4.95991 q^{34} +(-5.82303 + 1.97538i) q^{35} -1.00000 q^{36} +(4.94859 - 3.53716i) q^{37} +3.74447i q^{38} +3.04226i q^{39} +(0.718347 + 2.11754i) q^{40} -11.7792 q^{41} +2.74990 q^{42} +6.91360 q^{43} -0.572952 q^{44} +(-0.718347 - 2.11754i) q^{45} +2.98281 q^{46} +0.776516i q^{47} -1.00000i q^{48} -0.561961 q^{49} +(-3.96796 + 3.04226i) q^{50} -4.95991i q^{51} -3.04226 q^{52} +3.55948i q^{53} +1.00000i q^{54} +(-0.411579 - 1.21325i) q^{55} +2.74990i q^{56} +3.74447 q^{57} +7.36456i q^{58} -9.27315i q^{59} +(2.11754 - 0.718347i) q^{60} -11.2507i q^{61} +1.12948i q^{62} -2.74990i q^{63} +1.00000 q^{64} +(-2.18540 - 6.44210i) q^{65} +0.572952i q^{66} +9.09361i q^{67} +4.95991 q^{68} -2.98281i q^{69} +(-5.82303 + 1.97538i) q^{70} +6.26296 q^{71} -1.00000 q^{72} -7.83759i q^{73} +(4.94859 - 3.53716i) q^{74} +(3.04226 + 3.96796i) q^{75} +3.74447i q^{76} -1.57556i q^{77} +3.04226i q^{78} -0.716273i q^{79} +(0.718347 + 2.11754i) q^{80} +1.00000 q^{81} -11.7792 q^{82} -2.01848i q^{83} +2.74990 q^{84} +(3.56294 + 10.5028i) q^{85} +6.91360 q^{86} +7.36456 q^{87} -0.572952 q^{88} +8.33434i q^{89} +(-0.718347 - 2.11754i) q^{90} -8.36591i q^{91} +2.98281 q^{92} +1.12948 q^{93} +0.776516i q^{94} +(-7.92907 + 2.68983i) q^{95} -1.00000i q^{96} +15.6494 q^{97} -0.561961 q^{98} +0.572952 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 16 q^{2} + 16 q^{4} + 2 q^{5} + 16 q^{8} - 16 q^{9}+O(q^{10}) $ 16 * q + 16 * q^2 + 16 * q^4 + 2 * q^5 + 16 * q^8 - 16 * q^9	$ 16 q + 16 q^{2} + 16 q^{4} + 2 q^{5} + 16 q^{8} - 16 q^{9} + 2 q^{10} + 2 q^{11} - 6 q^{15} + 16 q^{16} + 38 q^{17} - 16 q^{18} + 2 q^{20} + 6 q^{21} + 2 q^{22} + 20 q^{23} - 4 q^{25} - 6 q^{30} + 16 q^{32} + 38 q^{34} + 10 q^{35} - 16 q^{36} + 4 q^{37} + 2 q^{40} - 6 q^{41} + 6 q^{42} + 2 q^{43} + 2 q^{44} - 2 q^{45} + 20 q^{46} - 18 q^{49} - 4 q^{50} - 20 q^{55} - 16 q^{57} - 6 q^{60} + 16 q^{64} + 12 q^{65} + 38 q^{68} + 10 q^{70} - 24 q^{71} - 16 q^{72} + 4 q^{74} + 2 q^{80} + 16 q^{81} - 6 q^{82} + 6 q^{84} + 2 q^{86} - 2 q^{87} + 2 q^{88} - 2 q^{90} + 20 q^{92} - 22 q^{93} - 16 q^{95} - 38 q^{97} - 18 q^{98} - 2 q^{99}+O(q^{100}) $ 16 * q + 16 * q^2 + 16 * q^4 + 2 * q^5 + 16 * q^8 - 16 * q^9 + 2 * q^10 + 2 * q^11 - 6 * q^15 + 16 * q^16 + 38 * q^17 - 16 * q^18 + 2 * q^20 + 6 * q^21 + 2 * q^22 + 20 * q^23 - 4 * q^25 - 6 * q^30 + 16 * q^32 + 38 * q^34 + 10 * q^35 - 16 * q^36 + 4 * q^37 + 2 * q^40 - 6 * q^41 + 6 * q^42 + 2 * q^43 + 2 * q^44 - 2 * q^45 + 20 * q^46 - 18 * q^49 - 4 * q^50 - 20 * q^55 - 16 * q^57 - 6 * q^60 + 16 * q^64 + 12 * q^65 + 38 * q^68 + 10 * q^70 - 24 * q^71 - 16 * q^72 + 4 * q^74 + 2 * q^80 + 16 * q^81 - 6 * q^82 + 6 * q^84 + 2 * q^86 - 2 * q^87 + 2 * q^88 - 2 * q^90 + 20 * q^92 - 22 * q^93 - 16 * q^95 - 38 * q^97 - 18 * q^98 - 2 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1110\mathbb{Z}\right)^\times$.

$n$	$371$	$631$	$667$
$\chi(n)$	$1$	$-1$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	1.00000			0.707107
$2$	1.00000			0.707107
$3$		−	1.00000i		−	0.577350i
$3$		−	1.00000i		−	0.577350i
$4$	1.00000			0.500000
$5$	0.718347	+	2.11754i	0.321254	+	0.946993i
$5$	0.718347	+	2.11754i	0.321254	+	0.946993i
$6$		−	1.00000i		−	0.408248i
$7$			2.74990i			1.03937i	0.854359	+	0.519683i	$0.173950\pi$
$7$			2.74990i			1.03937i	−0.854359	+	0.519683i	$0.826050\pi$
$8$	1.00000			0.353553
$9$	−1.00000			−0.333333
$10$	0.718347	+	2.11754i	0.227161	+	0.669625i
$11$	−0.572952			−0.172752			−0.0863758	−	0.996263i	$-0.527529\pi$
$11$	−0.572952			−0.172752			−0.0863758	+	0.996263i	$0.527529\pi$
$12$		−	1.00000i		−	0.288675i
$13$	−3.04226			−0.843770			−0.421885	−	0.906649i	$-0.638631\pi$
$13$	−3.04226			−0.843770			−0.421885	+	0.906649i	$0.638631\pi$
$14$			2.74990i			0.734942i
$15$	2.11754	−	0.718347i	0.546747	−	0.185476i
$16$	1.00000			0.250000
$17$	4.95991			1.20296			0.601478	−	0.798889i	$-0.294579\pi$
$17$	4.95991			1.20296			0.601478	+	0.798889i	$0.294579\pi$
$18$	−1.00000			−0.235702
$19$			3.74447i			0.859041i	0.903057	+	0.429520i	$0.141317\pi$
$19$			3.74447i			0.859041i	−0.903057	+	0.429520i	$0.858683\pi$
$20$	0.718347	+	2.11754i	0.160627	+	0.473496i
$21$	2.74990			0.600078
$22$	−0.572952			−0.122154
$23$	2.98281			0.621959			0.310980	−	0.950417i	$-0.399343\pi$
$23$	2.98281			0.621959			0.310980	+	0.950417i	$0.399343\pi$
$24$		−	1.00000i		−	0.204124i
$25$	−3.96796	+	3.04226i	−0.793591	+	0.608451i
$26$	−3.04226			−0.596636
$27$			1.00000i			0.192450i
$28$			2.74990i			0.519683i
$29$			7.36456i			1.36757i	0.729686	+	0.683783i	$0.239666\pi$
$29$			7.36456i			1.36757i	−0.729686	+	0.683783i	$0.760334\pi$
$30$	2.11754	−	0.718347i	0.386608	−	0.131152i
$31$			1.12948i			0.202861i	0.994843	+	0.101431i	$0.0323420\pi$
$31$			1.12948i			0.202861i	−0.994843	+	0.101431i	$0.967658\pi$
$32$	1.00000			0.176777
$33$			0.572952i			0.0997382i
$34$	4.95991			0.850618
$35$	−5.82303	+	1.97538i	−0.984272	+	0.333901i
$36$	−1.00000			−0.166667
$37$	4.94859	−	3.53716i	0.813542	−	0.581506i
$37$	4.94859	−	3.53716i	0.813542	−	0.581506i
$38$			3.74447i			0.607433i
$39$			3.04226i			0.487151i
$40$	0.718347	+	2.11754i	0.113581	+	0.334813i
$41$	−11.7792			−1.83960			−0.919800	−	0.392388i	$-0.871649\pi$
$41$	−11.7792			−1.83960			−0.919800	+	0.392388i	$0.871649\pi$
$42$	2.74990			0.424319
$43$	6.91360			1.05431			0.527157	−	0.849768i	$-0.323258\pi$
$43$	6.91360			1.05431			0.527157	+	0.849768i	$0.323258\pi$
$44$	−0.572952			−0.0863758
$45$	−0.718347	−	2.11754i	−0.107085	−	0.315664i
$46$	2.98281			0.439792
$47$			0.776516i			0.113266i	0.998395	+	0.0566332i	$0.0180366\pi$
$47$			0.776516i			0.113266i	−0.998395	+	0.0566332i	$0.981963\pi$
$48$		−	1.00000i		−	0.144338i
$49$	−0.561961			−0.0802801
$50$	−3.96796	+	3.04226i	−0.561154	+	0.430240i
$51$		−	4.95991i		−	0.694527i
$52$	−3.04226			−0.421885
$53$			3.55948i			0.488932i	0.969658	+	0.244466i	$0.0786127\pi$
$53$			3.55948i			0.488932i	−0.969658	+	0.244466i	$0.921387\pi$
$54$			1.00000i			0.136083i
$55$	−0.411579	−	1.21325i	−0.0554972	−	0.163595i
$56$			2.74990i			0.367471i
$57$	3.74447			0.495967
$58$			7.36456i			0.967015i
$59$		−	9.27315i		−	1.20726i	−0.797264	−	0.603631i	$-0.793720\pi$
$59$		−	9.27315i		−	1.20726i	0.797264	−	0.603631i	$-0.206280\pi$
$60$	2.11754	−	0.718347i	0.273373	−	0.0927382i
$61$		−	11.2507i		−	1.44051i	−0.693711	−	0.720254i	$-0.744025\pi$
$61$		−	11.2507i		−	1.44051i	0.693711	−	0.720254i	$-0.255975\pi$
$62$			1.12948i			0.143444i
$63$		−	2.74990i		−	0.346455i
$64$	1.00000			0.125000
$65$	−2.18540	−	6.44210i	−0.271065	−	0.799045i
$66$			0.572952i			0.0705256i
$67$			9.09361i			1.11096i	0.831529	+	0.555481i	$0.187466\pi$
$67$			9.09361i			1.11096i	−0.831529	+	0.555481i	$0.812534\pi$
$68$	4.95991			0.601478
$69$		−	2.98281i		−	0.359088i
$70$	−5.82303	+	1.97538i	−0.695985	+	0.236103i
$71$	6.26296			0.743277			0.371638	−	0.928378i	$-0.378796\pi$
$71$	6.26296			0.743277			0.371638	+	0.928378i	$0.378796\pi$
$72$	−1.00000			−0.117851
$73$		−	7.83759i		−	0.917320i	−0.888612	−	0.458660i	$-0.848330\pi$
$73$		−	7.83759i		−	0.917320i	0.888612	−	0.458660i	$-0.151670\pi$
$74$	4.94859	−	3.53716i	0.575261	−	0.411187i
$75$	3.04226	+	3.96796i	0.351290	+	0.458180i
$76$			3.74447i			0.429520i
$77$		−	1.57556i		−	0.179552i
$78$			3.04226i			0.344468i
$79$		−	0.716273i		−	0.0805870i	−0.999188	−	0.0402935i	$-0.987171\pi$
$79$		−	0.716273i		−	0.0805870i	0.999188	−	0.0402935i	$-0.0128293\pi$
$80$	0.718347	+	2.11754i	0.0803136	+	0.236748i
$81$	1.00000			0.111111
$82$	−11.7792			−1.30079
$83$		−	2.01848i		−	0.221557i	−0.993845	−	0.110779i	$-0.964666\pi$
$83$		−	2.01848i		−	0.221557i	0.993845	−	0.110779i	$-0.0353345\pi$
$84$	2.74990			0.300039
$85$	3.56294	+	10.5028i	0.386455	+	1.13919i
$86$	6.91360			0.745513
$87$	7.36456			0.789564
$88$	−0.572952			−0.0610769
$89$			8.33434i			0.883439i	0.897153	+	0.441719i	$0.145631\pi$
$89$			8.33434i			0.883439i	−0.897153	+	0.441719i	$0.854369\pi$
$90$	−0.718347	−	2.11754i	−0.0757204	−	0.223208i
$91$		−	8.36591i		−	0.876986i
$92$	2.98281			0.310980
$93$	1.12948			0.117122
$94$			0.776516i			0.0800915i
$95$	−7.92907	+	2.68983i	−0.813505	+	0.275971i
$96$		−	1.00000i		−	0.102062i
$97$	15.6494			1.58896			0.794478	−	0.607293i	$-0.207745\pi$
$97$	15.6494			1.58896			0.794478	+	0.607293i	$0.207745\pi$
$98$	−0.561961			−0.0567666
$99$	0.572952			0.0575839
$100$	−3.96796	+	3.04226i	−0.396796	+	0.304226i
$101$	−3.53653			−0.351898			−0.175949	−	0.984399i	$-0.556299\pi$
$101$	−3.53653			−0.351898			−0.175949	+	0.984399i	$0.556299\pi$
$102$		−	4.95991i		−	0.491105i
$103$	14.6685			1.44533			0.722666	−	0.691198i	$-0.242917\pi$
$103$	14.6685			1.44533			0.722666	+	0.691198i	$0.242917\pi$
$104$	−3.04226			−0.298318
$105$	1.97538	+	5.82303i	0.192778	+	0.568269i
$106$			3.55948i			0.345727i
$107$		−	12.8769i		−	1.24486i	−0.782676	−	0.622430i	$-0.786146\pi$
$107$		−	12.8769i		−	1.24486i	0.782676	−	0.622430i	$-0.213854\pi$
$108$			1.00000i			0.0962250i
$109$		−	11.7065i		−	1.12128i	−0.828060	−	0.560639i	$-0.810555\pi$
$109$		−	11.7065i		−	1.12128i	0.828060	−	0.560639i	$-0.189445\pi$
$110$	−0.411579	−	1.21325i	−0.0392425	−	0.115679i
$111$	−3.53716	−	4.94859i	−0.335732	−	0.469699i
$112$			2.74990i			0.259841i
$113$	−8.18232			−0.769728			−0.384864	−	0.922973i	$-0.625752\pi$
$113$	−8.18232			−0.769728			−0.384864	+	0.922973i	$0.625752\pi$
$114$	3.74447			0.350702
$115$	2.14269	+	6.31622i	0.199807	+	0.588991i
$116$			7.36456i			0.683783i
$117$	3.04226			0.281257
$118$		−	9.27315i		−	0.853663i
$119$			13.6393i			1.25031i
$120$	2.11754	−	0.718347i	0.193304	−	0.0655758i
$121$	−10.6717			−0.970157
$122$		−	11.2507i		−	1.01859i
$123$			11.7792i			1.06209i
$124$			1.12948i			0.101431i
$125$	−9.29247	−	6.21691i	−0.831144	−	0.556057i
$126$		−	2.74990i		−	0.244981i
$127$		−	9.55633i		−	0.847987i	−0.905665	−	0.423994i	$-0.860628\pi$
$127$		−	9.55633i		−	0.847987i	0.905665	−	0.423994i	$-0.139372\pi$
$128$	1.00000			0.0883883
$129$		−	6.91360i		−	0.608709i
$130$	−2.18540	−	6.44210i	−0.191672	−	0.565010i
$131$		−	6.83587i		−	0.597253i	−0.954370	−	0.298627i	$-0.903472\pi$
$131$		−	6.83587i		−	0.597253i	0.954370	−	0.298627i	$-0.0965285\pi$
$132$			0.572952i			0.0498691i
$133$	−10.2969			−0.892857
$134$			9.09361i			0.785568i
$135$	−2.11754	+	0.718347i	−0.182249	+	0.0618255i
$136$	4.95991			0.425309
$137$		−	2.98494i		−	0.255021i	−0.991837	−	0.127510i	$-0.959301\pi$
$137$		−	2.98494i		−	0.255021i	0.991837	−	0.127510i	$-0.0406987\pi$
$138$		−	2.98281i		−	0.253914i
$139$	−2.69497			−0.228584			−0.114292	−	0.993447i	$-0.536460\pi$
$139$	−2.69497			−0.228584			−0.114292	+	0.993447i	$0.536460\pi$
$140$	−5.82303	+	1.97538i	−0.492136	+	0.166950i
$141$	0.776516			0.0653944
$142$	6.26296			0.525576
$143$	1.74307			0.145763
$144$	−1.00000			−0.0833333
$145$	−15.5948	+	5.29031i	−1.29507	+	0.439336i
$146$		−	7.83759i		−	0.648643i
$147$			0.561961i			0.0463498i
$148$	4.94859	−	3.53716i	0.406771	−	0.290753i
$149$	−21.7045			−1.77810			−0.889049	−	0.457811i	$-0.848634\pi$
$149$	−21.7045			−1.77810			−0.889049	+	0.457811i	$0.848634\pi$
$150$	3.04226	+	3.96796i	0.248399	+	0.323982i
$151$	10.8407			0.882201			0.441100	−	0.897458i	$-0.354588\pi$
$151$	10.8407			0.882201			0.441100	+	0.897458i	$0.354588\pi$
$152$			3.74447i			0.303717i
$153$	−4.95991			−0.400985
$154$		−	1.57556i		−	0.126962i
$155$	−2.39173	+	0.811360i	−0.192108	+	0.0651700i
$156$			3.04226i			0.243576i
$157$		−	19.6615i		−	1.56916i	−0.620028	−	0.784579i	$-0.712879\pi$
$157$		−	19.6615i		−	1.56916i	0.620028	−	0.784579i	$-0.287121\pi$
$158$		−	0.716273i		−	0.0569836i
$159$	3.55948			0.282285
$160$	0.718347	+	2.11754i	0.0567903	+	0.167406i
$161$			8.20244i			0.646443i
$162$	1.00000			0.0785674
$163$	−4.07237			−0.318973			−0.159486	−	0.987200i	$-0.550984\pi$
$163$	−4.07237			−0.318973			−0.159486	+	0.987200i	$0.550984\pi$
$164$	−11.7792			−0.919800
$165$	−1.21325	+	0.411579i	−0.0944514	+	0.0320413i
$166$		−	2.01848i		−	0.156665i
$167$	8.82919			0.683223			0.341611	−	0.939841i	$-0.389027\pi$
$167$	8.82919			0.683223			0.341611	+	0.939841i	$0.389027\pi$
$168$	2.74990			0.212160
$169$	−3.74467			−0.288052
$170$	3.56294	+	10.5028i	0.273265	+	0.805529i
$171$		−	3.74447i		−	0.286347i
$172$	6.91360			0.527157
$173$			6.89548i			0.524253i	0.965033	+	0.262127i	$0.0844238\pi$
$173$			6.89548i			0.524253i	−0.965033	+	0.262127i	$0.915576\pi$
$174$	7.36456			0.558306
$175$	−8.36591	−	10.9115i	−0.632403	−	0.824831i
$176$	−0.572952			−0.0431879
$177$	−9.27315			−0.697013
$178$			8.33434i			0.624685i
$179$			6.95856i			0.520107i	0.965594	+	0.260054i	$0.0837403\pi$
$179$			6.95856i			0.520107i	−0.965594	+	0.260054i	$0.916260\pi$
$180$	−0.718347	−	2.11754i	−0.0535424	−	0.157832i
$181$	10.3719			0.770940			0.385470	−	0.922720i	$-0.374039\pi$
$181$	10.3719			0.770940			0.385470	+	0.922720i	$0.374039\pi$
$182$		−	8.36591i		−	0.620122i
$183$	−11.2507			−0.831677
$184$	2.98281			0.219896
$185$	11.0449	+	7.93792i	0.812036	+	0.583608i
$186$	1.12948			0.0828177
$187$	−2.84179			−0.207813
$188$			0.776516i			0.0566332i
$189$	−2.74990			−0.200026
$190$	−7.92907	+	2.68983i	−0.575235	+	0.195141i
$191$		−	9.49717i		−	0.687191i	−0.939118	−	0.343596i	$-0.888355\pi$
$191$		−	9.49717i		−	0.687191i	0.939118	−	0.343596i	$-0.111645\pi$
$192$		−	1.00000i		−	0.0721688i
$193$	−17.0877			−1.23000			−0.615001	−	0.788526i	$-0.710844\pi$
$193$	−17.0877			−1.23000			−0.615001	+	0.788526i	$0.710844\pi$
$194$	15.6494			1.12356
$195$	−6.44210	+	2.18540i	−0.461329	+	0.156499i
$196$	−0.561961			−0.0401401
$197$		−	14.9122i		−	1.06245i	−0.847232	−	0.531224i	$-0.821732\pi$
$197$		−	14.9122i		−	1.06245i	0.847232	−	0.531224i	$-0.178268\pi$
$198$	0.572952			0.0407180
$199$			25.1320i			1.78156i	0.454438	+	0.890778i	$0.349840\pi$
$199$			25.1320i			1.78156i	−0.454438	+	0.890778i	$0.650160\pi$
$200$	−3.96796	+	3.04226i	−0.280577	+	0.215120i
$201$	9.09361			0.641414
$202$	−3.53653			−0.248829
$203$	−20.2518			−1.42140
$204$		−	4.95991i		−	0.347263i
$205$	−8.46154	−	24.9429i	−0.590980	−	1.74209i
$206$	14.6685			1.02200
$207$	−2.98281			−0.207320
$208$	−3.04226			−0.210943
$209$		−	2.14540i		−	0.148401i
$210$	1.97538	+	5.82303i	0.136314	+	0.401827i
$211$	28.5808			1.96758			0.983792	−	0.179311i	$-0.0573869\pi$
$211$	28.5808			1.96758			0.983792	+	0.179311i	$0.0573869\pi$
$212$			3.55948i			0.244466i
$213$		−	6.26296i		−	0.429131i
$214$		−	12.8769i		−	0.880248i
$215$	4.96636	+	14.6398i	0.338703	+	0.998428i
$216$			1.00000i			0.0680414i
$217$	−3.10597			−0.210847
$218$		−	11.7065i		−	0.792864i
$219$	−7.83759			−0.529615
$220$	−0.411579	−	1.21325i	−0.0277486	−	0.0817973i
$221$	−15.0893			−1.01502
$222$	−3.53716	−	4.94859i	−0.237399	−	0.332127i
$223$		−	22.9412i		−	1.53625i	−0.640298	−	0.768127i	$-0.721189\pi$
$223$		−	22.9412i		−	1.53625i	0.640298	−	0.768127i	$-0.278811\pi$
$224$			2.74990i			0.183736i
$225$	3.96796	−	3.04226i	0.264530	−	0.202817i
$226$	−8.18232			−0.544280
$227$	−17.2447			−1.14457			−0.572285	−	0.820055i	$-0.693943\pi$
$227$	−17.2447			−1.14457			−0.572285	+	0.820055i	$0.693943\pi$
$228$	3.74447			0.247984
$229$	−19.2252			−1.27043			−0.635217	−	0.772334i	$-0.719089\pi$
$229$	−19.2252			−1.27043			−0.635217	+	0.772334i	$0.719089\pi$
$230$	2.14269	+	6.31622i	0.141285	+	0.416479i
$231$	−1.57556			−0.103664
$232$			7.36456i			0.483507i
$233$			25.3616i			1.66150i	0.556649	+	0.830748i	$0.312087\pi$
$233$			25.3616i			1.66150i	−0.556649	+	0.830748i	$0.687913\pi$
$234$	3.04226			0.198879
$235$	−1.64430	+	0.557808i	−0.107263	+	0.0363874i
$236$		−	9.27315i		−	0.603631i
$237$	−0.716273			−0.0465269
$238$			13.6393i			0.884103i
$239$			2.44191i			0.157954i	0.996876	+	0.0789769i	$0.0251653\pi$
$239$			2.44191i			0.157954i	−0.996876	+	0.0789769i	$0.974835\pi$
$240$	2.11754	−	0.718347i	0.136687	−	0.0463691i
$241$		−	13.2870i		−	0.855893i	−0.903804	−	0.427946i	$-0.859237\pi$
$241$		−	13.2870i		−	0.855893i	0.903804	−	0.427946i	$-0.140763\pi$
$242$	−10.6717			−0.686005
$243$		−	1.00000i		−	0.0641500i
$244$		−	11.2507i		−	0.720254i
$245$	−0.403683	−	1.18998i	−0.0257904	−	0.0760247i
$246$			11.7792i			0.751013i
$247$		−	11.3916i		−	0.724833i
$248$			1.12948i			0.0717222i
$249$	−2.01848			−0.127916
$250$	−9.29247	−	6.21691i	−0.587707	−	0.393192i
$251$			19.0323i			1.20131i	0.799509	+	0.600654i	$0.205093\pi$
$251$			19.0323i			1.20131i	−0.799509	+	0.600654i	$0.794907\pi$
$252$		−	2.74990i		−	0.173228i
$253$	−1.70901			−0.107444
$254$		−	9.55633i		−	0.599617i
$255$	10.5028	−	3.56294i	0.657712	−	0.223120i
$256$	1.00000			0.0625000
$257$	−7.10256			−0.443045			−0.221523	−	0.975155i	$-0.571103\pi$
$257$	−7.10256			−0.443045			−0.221523	+	0.975155i	$0.571103\pi$
$258$		−	6.91360i		−	0.430422i
$259$	9.72684	+	13.6081i	0.604397	+	0.845568i
$260$	−2.18540	−	6.44210i	−0.135533	−	0.399522i
$261$		−	7.36456i		−	0.455855i
$262$		−	6.83587i		−	0.422322i
$263$			10.1942i			0.628603i	0.949323	+	0.314301i	$0.101770\pi$
$263$			10.1942i			0.628603i	−0.949323	+	0.314301i	$0.898230\pi$
$264$			0.572952i			0.0352628i
$265$	−7.53734	+	2.55694i	−0.463015	+	0.157072i
$266$	−10.2969			−0.631345
$267$	8.33434			0.510053
$268$			9.09361i			0.555481i
$269$	−4.19787			−0.255949			−0.127974	−	0.991777i	$-0.540848\pi$
$269$	−4.19787			−0.255949			−0.127974	+	0.991777i	$0.540848\pi$
$270$	−2.11754	+	0.718347i	−0.128869	+	0.0437172i
$271$	21.1875			1.28705			0.643524	−	0.765426i	$-0.277472\pi$
$271$	21.1875			1.28705			0.643524	+	0.765426i	$0.277472\pi$
$272$	4.95991			0.300739
$273$	−8.36591			−0.506328
$274$		−	2.98494i		−	0.180327i
$275$	2.27345	−	1.74307i	0.137094	−	0.105111i
$276$		−	2.98281i		−	0.179544i
$277$	19.1388			1.14994			0.574968	−	0.818176i	$-0.305014\pi$
$277$	19.1388			1.14994			0.574968	+	0.818176i	$0.305014\pi$
$278$	−2.69497			−0.161634
$279$		−	1.12948i		−	0.0676204i
$280$	−5.82303	+	1.97538i	−0.347993	+	0.118052i
$281$		−	1.77696i		−	0.106004i	−0.998594	−	0.0530021i	$-0.983121\pi$
$281$		−	1.77696i		−	0.106004i	0.998594	−	0.0530021i	$-0.0168790\pi$
$282$	0.776516			0.0462408
$283$	1.11078			0.0660292			0.0330146	−	0.999455i	$-0.489489\pi$
$283$	1.11078			0.0660292			0.0330146	+	0.999455i	$0.489489\pi$
$284$	6.26296			0.371638
$285$	2.68983	+	7.92907i	0.159332	+	0.469678i
$286$	1.74307			0.103070
$287$		−	32.3916i		−	1.91202i
$288$	−1.00000			−0.0589256
$289$	7.60075			0.447103
$290$	−15.5948	+	5.29031i	−0.915756	+	0.310658i
$291$		−	15.6494i		−	0.917384i
$292$		−	7.83759i		−	0.458660i
$293$		−	24.1210i		−	1.40916i	−0.709623	−	0.704582i	$-0.751135\pi$
$293$		−	24.1210i		−	1.40916i	0.709623	−	0.704582i	$-0.248865\pi$
$294$			0.561961i			0.0327742i
$295$	19.6363	−	6.66134i	1.14327	−	0.387838i
$296$	4.94859	−	3.53716i	0.287631	−	0.205593i
$297$		−	0.572952i		−	0.0332461i
$298$	−21.7045			−1.25731
$299$	−9.07448			−0.524791
$300$	3.04226	+	3.96796i	0.175645	+	0.229090i
$301$			19.0117i			1.09582i
$302$	10.8407			0.623810
$303$			3.53653i			0.203168i
$304$			3.74447i			0.214760i
$305$	23.8239	−	8.08192i	1.36415	−	0.462770i
$306$	−4.95991			−0.283539
$307$		−	14.2638i		−	0.814080i	−0.913410	−	0.407040i	$-0.866561\pi$
$307$		−	14.2638i		−	0.814080i	0.913410	−	0.407040i	$-0.133439\pi$
$308$		−	1.57556i		−	0.0897760i
$309$		−	14.6685i		−	0.834463i
$310$	−2.39173	+	0.811360i	−0.135841	+	0.0460822i
$311$			10.5684i			0.599279i	0.954052	+	0.299640i	$0.0968665\pi$
$311$			10.5684i			0.599279i	−0.954052	+	0.299640i	$0.903134\pi$
$312$			3.04226i			0.172234i
$313$	−1.67134			−0.0944696			−0.0472348	−	0.998884i	$-0.515041\pi$
$313$	−1.67134			−0.0944696			−0.0472348	+	0.998884i	$0.515041\pi$
$314$		−	19.6615i		−	1.10956i
$315$	5.82303	−	1.97538i	0.328091	−	0.111300i
$316$		−	0.716273i		−	0.0402935i
$317$			17.0342i			0.956737i	0.878159	+	0.478369i	$0.158772\pi$
$317$			17.0342i			0.956737i	−0.878159	+	0.478369i	$0.841228\pi$
$318$	3.55948			0.199606
$319$		−	4.21954i		−	0.236249i
$320$	0.718347	+	2.11754i	0.0401568	+	0.118374i
$321$	−12.8769			−0.718720
$322$			8.20244i			0.457104i
$323$			18.5723i			1.03339i
$324$	1.00000			0.0555556
$325$	12.0715	−	9.25533i	0.669609	−	0.513393i
$326$	−4.07237			−0.225548
$327$	−11.7065			−0.647370
$328$	−11.7792			−0.650397
$329$	−2.13534			−0.117725
$330$	−1.21325	+	0.411579i	−0.0667872	+	0.0226567i
$331$			27.9880i			1.53836i	0.639031	+	0.769181i	$0.279336\pi$
$331$			27.9880i			1.53836i	−0.639031	+	0.769181i	$0.720664\pi$
$332$		−	2.01848i		−	0.110779i
$333$	−4.94859	+	3.53716i	−0.271181	+	0.193835i
$334$	8.82919			0.483112
$335$	−19.2561	+	6.53237i	−1.05207	+	0.356901i
$336$	2.74990			0.150019
$337$			2.12305i			0.115650i	0.998327	+	0.0578250i	$0.0184165\pi$
$337$			2.12305i			0.115650i	−0.998327	+	0.0578250i	$0.981583\pi$
$338$	−3.74467			−0.203683
$339$			8.18232i			0.444403i
$340$	3.56294	+	10.5028i	0.193227	+	0.569595i
$341$		−	0.647140i		−	0.0350446i
$342$		−	3.74447i		−	0.202478i
$343$			17.7040i			0.955925i
$344$	6.91360			0.372756
$345$	6.31622	−	2.14269i	0.340054	−	0.115359i
$346$			6.89548i			0.370703i
$347$	−8.84425			−0.474784			−0.237392	−	0.971414i	$-0.576293\pi$
$347$	−8.84425			−0.474784			−0.237392	+	0.971414i	$0.576293\pi$
$348$	7.36456			0.394782
$349$	29.6036			1.58464			0.792321	−	0.610104i	$-0.208872\pi$
$349$	29.6036			1.58464			0.792321	+	0.610104i	$0.208872\pi$
$350$	−8.36591	−	10.9115i	−0.447177	−	0.583244i
$351$		−	3.04226i		−	0.162384i
$352$	−0.572952			−0.0305385
$353$	7.97381			0.424403			0.212202	−	0.977226i	$-0.431937\pi$
$353$	7.97381			0.424403			0.212202	+	0.977226i	$0.431937\pi$
$354$	−9.27315			−0.492863
$355$	4.49898	+	13.2621i	0.238781	+	0.703878i
$356$			8.33434i			0.441719i
$357$	13.6393			0.721867
$358$			6.95856i			0.367771i
$359$	21.8286			1.15207			0.576034	−	0.817426i	$-0.304600\pi$
$359$	21.8286			1.15207			0.576034	+	0.817426i	$0.304600\pi$
$360$	−0.718347	−	2.11754i	−0.0378602	−	0.111604i
$361$	4.97893			0.262049
$362$	10.3719			0.545137
$363$			10.6717i			0.560120i
$364$		−	8.36591i		−	0.438493i
$365$	16.5964	−	5.63010i	0.868696	−	0.294693i
$366$	−11.2507			−0.588085
$367$		−	21.2190i		−	1.10762i	−0.832643	−	0.553811i	$-0.813173\pi$
$367$		−	21.2190i		−	1.10762i	0.832643	−	0.553811i	$-0.186827\pi$
$368$	2.98281			0.155490
$369$	11.7792			0.613200
$370$	11.0449	+	7.93792i	0.574196	+	0.412673i
$371$	−9.78822			−0.508179
$372$	1.12948			0.0585610
$373$		−	9.40573i		−	0.487010i	−0.969900	−	0.243505i	$-0.921703\pi$
$373$		−	9.40573i		−	0.487010i	0.969900	−	0.243505i	$-0.0782973\pi$
$374$	−2.84179			−0.146946
$375$	−6.21691	+	9.29247i	−0.321040	+	0.479861i
$376$			0.776516i			0.0400457i
$377$		−	22.4049i		−	1.15391i
$378$	−2.74990			−0.141440
$379$	2.49593			0.128207			0.0641036	−	0.997943i	$-0.479581\pi$
$379$	2.49593			0.128207			0.0641036	+	0.997943i	$0.479581\pi$
$380$	−7.92907	+	2.68983i	−0.406753	+	0.137985i
$381$	−9.55633			−0.489586
$382$		−	9.49717i		−	0.485918i
$383$	12.9235			0.660361			0.330181	−	0.943918i	$-0.392890\pi$
$383$	12.9235			0.660361			0.330181	+	0.943918i	$0.392890\pi$
$384$		−	1.00000i		−	0.0510310i
$385$	3.33632	−	1.13180i	0.170035	−	0.0576819i
$386$	−17.0877			−0.869743
$387$	−6.91360			−0.351438
$388$	15.6494			0.794478
$389$		−	6.16822i		−	0.312741i	−0.987698	−	0.156370i	$-0.950021\pi$
$389$		−	6.16822i		−	0.312741i	0.987698	−	0.156370i	$-0.0499794\pi$
$390$	−6.44210	+	2.18540i	−0.326209	+	0.110662i
$391$	14.7945			0.748189
$392$	−0.561961			−0.0283833
$393$	−6.83587			−0.344824
$394$		−	14.9122i		−	0.751263i
$395$	1.51674	−	0.514532i	0.0763153	−	0.0258889i
$396$	0.572952			0.0287919
$397$			11.2553i			0.564886i	0.959284	+	0.282443i	$0.0911448\pi$
$397$			11.2553i			0.564886i	−0.959284	+	0.282443i	$0.908855\pi$
$398$			25.1320i			1.25975i
$399$			10.2969i			0.515491i
$400$	−3.96796	+	3.04226i	−0.198398	+	0.152113i
$401$		−	2.01396i		−	0.100572i	−0.998735	−	0.0502862i	$-0.983987\pi$
$401$		−	2.01396i		−	0.100572i	0.998735	−	0.0502862i	$-0.0160134\pi$
$402$	9.09361			0.453548
$403$		−	3.43618i		−	0.171168i
$404$	−3.53653			−0.175949
$405$	0.718347	+	2.11754i	0.0356949	+	0.105221i
$406$	−20.2518			−1.00508
$407$	−2.83530	+	2.02662i	−0.140541	+	0.100456i
$408$		−	4.95991i		−	0.245552i
$409$		−	1.80381i		−	0.0891925i	−0.999005	−	0.0445963i	$-0.985800\pi$
$409$		−	1.80381i		−	0.0891925i	0.999005	−	0.0445963i	$-0.0142001\pi$
$410$	−8.46154	−	24.9429i	−0.417886	−	1.23184i
$411$	−2.98494			−0.147236
$412$	14.6685			0.722666
$413$	25.5003			1.25479
$414$	−2.98281			−0.146597
$415$	4.27422	−	1.44997i	0.209813	−	0.0711763i
$416$	−3.04226			−0.149159
$417$			2.69497i			0.131973i
$418$		−	2.14540i		−	0.104935i
$419$	−10.6915			−0.522314			−0.261157	−	0.965296i	$-0.584104\pi$
$419$	−10.6915			−0.522314			−0.261157	+	0.965296i	$0.584104\pi$
$420$	1.97538	+	5.82303i	0.0963888	+	0.284135i
$421$			5.37087i			0.261760i	0.991398	+	0.130880i	$0.0417803\pi$
$421$			5.37087i			0.261760i	−0.991398	+	0.130880i	$0.958220\pi$
$422$	28.5808			1.39129
$423$		−	0.776516i		−	0.0377555i
$424$			3.55948i			0.172864i
$425$	−19.6807	+	15.0893i	−0.954655	+	0.731940i
$426$		−	6.26296i		−	0.303441i
$427$	30.9384			1.49721
$428$		−	12.8769i		−	0.622430i
$429$		−	1.74307i		−	0.0841561i
$430$	4.96636	+	14.6398i	0.239499	+	0.705995i
$431$		−	15.1098i		−	0.727815i	−0.931435	−	0.363908i	$-0.881442\pi$
$431$		−	15.1098i		−	0.727815i	0.931435	−	0.363908i	$-0.118558\pi$
$432$			1.00000i			0.0481125i
$433$		−	20.4232i		−	0.981478i	−0.871307	−	0.490739i	$-0.836727\pi$
$433$		−	20.4232i		−	0.981478i	0.871307	−	0.490739i	$-0.163273\pi$
$434$	−3.10597			−0.149091
$435$	5.29031	+	15.5948i	0.253651	+	0.747712i
$436$		−	11.7065i		−	0.560639i
$437$			11.1691i			0.534288i
$438$	−7.83759			−0.374494
$439$		−	29.6845i		−	1.41676i	−0.705829	−	0.708382i	$-0.749425\pi$
$439$		−	29.6845i		−	1.41676i	0.705829	−	0.708382i	$-0.250575\pi$
$440$	−0.411579	−	1.21325i	−0.0196212	−	0.0578394i
$441$	0.561961			0.0267600
$442$	−15.0893			−0.717726
$443$			29.7068i			1.41141i	0.708504	+	0.705707i	$0.249370\pi$
$443$			29.7068i			1.41141i	−0.708504	+	0.705707i	$0.750630\pi$
$444$	−3.53716	−	4.94859i	−0.167866	−	0.234849i
$445$	−17.6483	+	5.98695i	−0.836610	+	0.283809i
$446$		−	22.9412i		−	1.08630i
$447$			21.7045i			1.02659i
$448$			2.74990i			0.129921i
$449$			1.32258i			0.0624166i	0.999513	+	0.0312083i	$0.00993553\pi$
$449$			1.32258i			0.0624166i	−0.999513	+	0.0312083i	$0.990064\pi$
$450$	3.96796	−	3.04226i	0.187051	−	0.143413i
$451$	6.74891			0.317794
$452$	−8.18232			−0.384864
$453$		−	10.8407i		−	0.509339i
$454$	−17.2447			−0.809333
$455$	17.7152	−	6.00962i	0.830499	−	0.281736i
$456$	3.74447			0.175351
$457$	23.4170			1.09540			0.547700	−	0.836675i	$-0.315504\pi$
$457$	23.4170			1.09540			0.547700	+	0.836675i	$0.315504\pi$
$458$	−19.2252			−0.898332
$459$			4.95991i			0.231509i
$460$	2.14269	+	6.31622i	0.0999036	+	0.294495i
$461$		−	31.2227i		−	1.45419i	−0.686539	−	0.727093i	$-0.740871\pi$
$461$		−	31.2227i		−	1.45419i	0.686539	−	0.727093i	$-0.259129\pi$
$462$	−1.57556			−0.0733018
$463$	−3.93552			−0.182899			−0.0914497	−	0.995810i	$-0.529150\pi$
$463$	−3.93552			−0.182899			−0.0914497	+	0.995810i	$0.529150\pi$
$464$			7.36456i			0.341891i
$465$	0.811360	+	2.39173i	0.0376259	+	0.110914i
$466$			25.3616i			1.17485i
$467$	−32.0647			−1.48378			−0.741888	−	0.670523i	$-0.766070\pi$
$467$	−32.0647			−1.48378			−0.741888	+	0.670523i	$0.766070\pi$
$468$	3.04226			0.140628
$469$	−25.0065			−1.15469
$470$	−1.64430	+	0.557808i	−0.0758461	+	0.0257298i
$471$	−19.6615			−0.905954
$472$		−	9.27315i		−	0.426832i
$473$	−3.96116			−0.182135
$474$	−0.716273			−0.0328995
$475$	−11.3916	−	14.8579i	−0.522685	−	0.681727i
$476$			13.6393i			0.625155i
$477$		−	3.55948i		−	0.162977i
$478$			2.44191i			0.111690i
$479$			15.9248i			0.727625i	0.931472	+	0.363812i	$0.118525\pi$
$479$			15.9248i			0.727625i	−0.931472	+	0.363812i	$0.881475\pi$
$480$	2.11754	−	0.718347i	0.0966521	−	0.0327879i
$481$	−15.0549	+	10.7610i	−0.686443	+	0.490657i
$482$		−	13.2870i		−	0.605208i
$483$	8.20244			0.373224
$484$	−10.6717			−0.485078
$485$	11.2417	+	33.1382i	0.510459	+	1.50473i
$486$		−	1.00000i		−	0.0453609i
$487$	31.7992			1.44096			0.720481	−	0.693475i	$-0.243921\pi$
$487$	31.7992			1.44096			0.720481	+	0.693475i	$0.243921\pi$
$488$		−	11.2507i		−	0.509296i
$489$			4.07237i			0.184159i
$490$	−0.403683	−	1.18998i	−0.0182365	−	0.0537576i
$491$	24.1758			1.09104			0.545519	−	0.838099i	$-0.316333\pi$
$491$	24.1758			1.09104			0.545519	+	0.838099i	$0.316333\pi$
$492$			11.7792i			0.531047i
$493$			36.5276i			1.64512i
$494$		−	11.3916i		−	0.512534i
$495$	0.411579	+	1.21325i	0.0184991	+	0.0545315i
$496$			1.12948i			0.0507153i
$497$			17.2225i			0.772536i
$498$	−2.01848			−0.0904505
$499$			14.7192i			0.658921i	0.944169	+	0.329460i	$0.106867\pi$
$499$			14.7192i			0.658921i	−0.944169	+	0.329460i	$0.893133\pi$
$500$	−9.29247	−	6.21691i	−0.415572	−	0.278029i
$501$		−	8.82919i		−	0.394459i
$502$			19.0323i			0.849453i
$503$	8.56976			0.382107			0.191053	−	0.981580i	$-0.438810\pi$
$503$	8.56976			0.382107			0.191053	+	0.981580i	$0.438810\pi$
$504$		−	2.74990i		−	0.122490i
$505$	−2.54046	−	7.48875i	−0.113049	−	0.333245i
$506$	−1.70901			−0.0759747
$507$			3.74467i			0.166307i
$508$		−	9.55633i		−	0.423994i
$509$	−24.3137			−1.07768			−0.538842	−	0.842407i	$-0.681138\pi$
$509$	−24.3137			−1.07768			−0.538842	+	0.842407i	$0.681138\pi$
$510$	10.5028	−	3.56294i	0.465073	−	0.157770i
$511$	21.5526			0.953431
$512$	1.00000			0.0441942
$513$	−3.74447			−0.165322
$514$	−7.10256			−0.313280
$515$	10.5371	+	31.0612i	0.464319	+	1.36872i
$516$		−	6.91360i		−	0.304354i
$517$		−	0.444907i		−	0.0195670i
$518$	9.72684	+	13.6081i	0.427373	+	0.597907i
$519$	6.89548			0.302678
$520$	−2.18540	−	6.44210i	−0.0958360	−	0.282505i
$521$	−30.0216			−1.31527			−0.657635	−	0.753336i	$-0.728443\pi$
$521$	−30.0216			−1.31527			−0.657635	+	0.753336i	$0.728443\pi$
$522$		−	7.36456i		−	0.322338i
$523$	−26.6165			−1.16386			−0.581930	−	0.813239i	$-0.697702\pi$
$523$	−26.6165			−1.16386			−0.581930	+	0.813239i	$0.697702\pi$
$524$		−	6.83587i		−	0.298627i
$525$	−10.9115	+	8.36591i	−0.476216	+	0.365118i
$526$			10.1942i			0.444489i
$527$			5.60214i			0.244033i
$528$			0.572952i			0.0249346i
$529$	−14.1028			−0.613167
$530$	−7.53734	+	2.55694i	−0.327401	+	0.111066i
$531$			9.27315i			0.402421i
$532$	−10.2969			−0.446429
$533$	35.8353			1.55220
$534$	8.33434			0.360662
$535$	27.2674	−	9.25010i	1.17887	−	0.399917i
$536$			9.09361i			0.392784i
$537$	6.95856			0.300284
$538$	−4.19787			−0.180983
$539$	0.321977			0.0138685
$540$	−2.11754	+	0.718347i	−0.0911244	+	0.0309127i
$541$			22.2550i			0.956818i	0.878137	+	0.478409i	$0.158786\pi$
$541$			22.2550i			0.956818i	−0.878137	+	0.478409i	$0.841214\pi$
$542$	21.1875			0.910081
$543$		−	10.3719i		−	0.445102i
$544$	4.95991			0.212655
$545$	24.7890	−	8.40932i	1.06184	−	0.360216i
$546$	−8.36591			−0.358028
$547$	−0.632623			−0.0270490			−0.0135245	−	0.999909i	$-0.504305\pi$
$547$	−0.632623			−0.0270490			−0.0135245	+	0.999909i	$0.504305\pi$
$548$		−	2.98494i		−	0.127510i
$549$			11.2507i			0.480169i
$550$	2.27345	−	1.74307i	0.0969402	−	0.0743247i
$551$	−27.5764			−1.17479
$552$		−	2.98281i		−	0.126957i
$553$	1.96968			0.0837593
$554$	19.1388			0.813128
$555$	7.93792	−	11.0449i	0.336946	−	0.468829i
$556$	−2.69497			−0.114292
$557$	30.0986			1.27532			0.637660	−	0.770318i	$-0.279902\pi$
$557$	30.0986			1.27532			0.637660	+	0.770318i	$0.279902\pi$
$558$		−	1.12948i		−	0.0478148i
$559$	−21.0330			−0.889599
$560$	−5.82303	+	1.97538i	−0.246068	+	0.0834752i
$561$			2.84179i			0.119981i
$562$		−	1.77696i		−	0.0749563i
$563$	19.4807			0.821014			0.410507	−	0.911857i	$-0.365352\pi$
$563$	19.4807			0.821014			0.410507	+	0.911857i	$0.365352\pi$
$564$	0.776516			0.0326972
$565$	−5.87774	−	17.3264i	−0.247278	−	0.728927i
$566$	1.11078			0.0466897
$567$			2.74990i			0.115485i
$568$	6.26296			0.262788
$569$			23.8001i			0.997751i	0.866674	+	0.498875i	$0.166253\pi$
$569$			23.8001i			0.997751i	−0.866674	+	0.498875i	$0.833747\pi$
$570$	2.68983	+	7.92907i	0.112665	+	0.332112i
$571$	−15.1243			−0.632931			−0.316466	−	0.948604i	$-0.602496\pi$
$571$	−15.1243			−0.632931			−0.316466	+	0.948604i	$0.602496\pi$
$572$	1.74307			0.0728814
$573$	−9.49717			−0.396750
$574$		−	32.3916i		−	1.35200i
$575$	−11.8357	+	9.07448i	−0.493581	+	0.378432i
$576$	−1.00000			−0.0416667
$577$	−0.516649			−0.0215084			−0.0107542	−	0.999942i	$-0.503423\pi$
$577$	−0.516649			−0.0215084			−0.0107542	+	0.999942i	$0.503423\pi$
$578$	7.60075			0.316150
$579$			17.0877i			0.710142i
$580$	−15.5948	+	5.29031i	−0.647537	+	0.219668i
$581$	5.55064			0.230279
$582$		−	15.6494i		−	0.648688i
$583$		−	2.03941i		−	0.0844639i
$584$		−	7.83759i		−	0.324322i
$585$	2.18540	+	6.44210i	0.0903550	+	0.266348i
$586$		−	24.1210i		−	0.996429i
$587$	−47.0112			−1.94036			−0.970180	−	0.242384i	$-0.922071\pi$
$587$	−47.0112			−1.94036			−0.970180	+	0.242384i	$0.922071\pi$
$588$			0.561961i			0.0231749i
$589$	−4.22932			−0.174266
$590$	19.6363	−	6.66134i	0.808413	−	0.274243i
$591$	−14.9122			−0.613404
$592$	4.94859	−	3.53716i	0.203386	−	0.145376i
$593$		−	8.43081i		−	0.346212i	−0.984903	−	0.173106i	$-0.944620\pi$
$593$		−	8.43081i		−	0.346212i	0.984903	−	0.173106i	$-0.0553803\pi$
$594$		−	0.572952i		−	0.0235085i
$595$	−28.8817	+	9.79773i	−1.18404	+	0.401668i
$596$	−21.7045			−0.889049
$597$	25.1320			1.02858
$598$	−9.07448			−0.371083
$599$	1.68965			0.0690373			0.0345186	−	0.999404i	$-0.489010\pi$
$599$	1.68965			0.0690373			0.0345186	+	0.999404i	$0.489010\pi$
$600$	3.04226	+	3.96796i	0.124200	+	0.161991i
$601$	27.1690			1.10825			0.554124	−	0.832434i	$-0.313053\pi$
$601$	27.1690			1.10825			0.554124	+	0.832434i	$0.313053\pi$
$602$			19.0117i			0.774860i
$603$		−	9.09361i		−	0.370321i
$604$	10.8407			0.441100
$605$	−7.66600	−	22.5978i	−0.311667	−	0.918732i
$606$			3.53653i			0.143662i
$607$	−15.1992			−0.616916			−0.308458	−	0.951238i	$-0.599813\pi$
$607$	−15.1992			−0.616916			−0.308458	+	0.951238i	$0.599813\pi$
$608$			3.74447i			0.151858i
$609$			20.2518i			0.820645i
$610$	23.8239	−	8.08192i	0.964600	−	0.327227i
$611$		−	2.36236i		−	0.0955709i
$612$	−4.95991			−0.200493
$613$		−	7.27288i		−	0.293749i	−0.989155	−	0.146874i	$-0.953079\pi$
$613$		−	7.27288i		−	0.293749i	0.989155	−	0.146874i	$-0.0469213\pi$
$614$		−	14.2638i		−	0.575642i
$615$	−24.9429	+	8.46154i	−1.00579	+	0.341202i
$616$		−	1.57556i		−	0.0634812i
$617$		−	9.11777i		−	0.367067i	−0.983013	−	0.183534i	$-0.941246\pi$
$617$		−	9.11777i		−	0.367067i	0.983013	−	0.183534i	$-0.0587537\pi$
$618$		−	14.6685i		−	0.590054i
$619$	−44.6848			−1.79603			−0.898016	−	0.439963i	$-0.854992\pi$
$619$	−44.6848			−1.79603			−0.898016	+	0.439963i	$0.854992\pi$
$620$	−2.39173	+	0.811360i	−0.0960540	+	0.0325850i
$621$			2.98281i			0.119696i
$622$			10.5684i			0.423755i
$623$	−22.9186			−0.918215
$624$			3.04226i			0.121788i
$625$	6.48934	−	24.1431i	0.259574	−	0.965723i
$626$	−1.67134			−0.0668001
$627$	−2.14540			−0.0856792
$628$		−	19.6615i		−	0.784579i
$629$	24.5446	−	17.5440i	0.978656	−	0.699526i
$630$	5.82303	−	1.97538i	0.231995	−	0.0787012i
$631$			37.3556i			1.48710i	0.668679	+	0.743551i	$0.266860\pi$
$631$			37.3556i			1.48710i	−0.668679	+	0.743551i	$0.733140\pi$
$632$		−	0.716273i		−	0.0284918i
$633$		−	28.5808i		−	1.13599i
$634$			17.0342i			0.676516i
$635$	20.2359	−	6.86476i	0.803038	−	0.272420i
$636$	3.55948			0.141143
$637$	1.70963			0.0677380
$638$		−	4.21954i		−	0.167053i
$639$	−6.26296			−0.247759
$640$	0.718347	+	2.11754i	0.0283952	+	0.0837031i
$641$	14.9484			0.590426			0.295213	−	0.955431i	$-0.404609\pi$
$641$	14.9484			0.590426			0.295213	+	0.955431i	$0.404609\pi$
$642$	−12.8769			−0.508212
$643$	3.91446			0.154371			0.0771857	−	0.997017i	$-0.475407\pi$
$643$	3.91446			0.154371			0.0771857	+	0.997017i	$0.475407\pi$
$644$			8.20244i			0.323221i
$645$	14.6398	−	4.96636i	0.576443	−	0.195550i
$646$			18.5723i			0.730716i
$647$	35.7399			1.40508			0.702541	−	0.711643i	$-0.252049\pi$
$647$	35.7399			1.40508			0.702541	+	0.711643i	$0.252049\pi$
$648$	1.00000			0.0392837
$649$			5.31308i			0.208556i
$650$	12.0715	−	9.25533i	0.473485	−	0.363024i
$651$			3.10597i			0.121732i
$652$	−4.07237			−0.159486
$653$	22.7292			0.889461			0.444730	−	0.895664i	$-0.353299\pi$
$653$	22.7292			0.889461			0.444730	+	0.895664i	$0.353299\pi$
$654$	−11.7065			−0.457760
$655$	14.4752	−	4.91053i	0.565594	−	0.191870i
$656$	−11.7792			−0.459900
$657$			7.83759i			0.305773i
$658$	−2.13534			−0.0832443
$659$	44.2502			1.72374			0.861871	−	0.507128i	$-0.169293\pi$
$659$	44.2502			1.72374			0.861871	+	0.507128i	$0.169293\pi$
$660$	−1.21325	+	0.411579i	−0.0472257	+	0.0160207i
$661$			10.6287i			0.413410i	0.978403	+	0.206705i	$0.0662740\pi$
$661$			10.6287i			0.413410i	−0.978403	+	0.206705i	$0.933726\pi$
$662$			27.9880i			1.08779i
$663$			15.0893i			0.586021i
$664$		−	2.01848i		−	0.0783324i
$665$	−7.39677	−	21.8042i	−0.286834	−	0.845529i
$666$	−4.94859	+	3.53716i	−0.191754	+	0.137062i
$667$			21.9671i			0.850570i
$668$	8.82919			0.341611
$669$	−22.9412			−0.886956
$670$	−19.2561	+	6.53237i	−0.743928	+	0.252367i
$671$			6.44613i			0.248850i
$672$	2.74990			0.106080
$673$			2.87396i			0.110783i	0.998465	+	0.0553916i	$0.0176407\pi$
$673$			2.87396i			0.110783i	−0.998465	+	0.0553916i	$0.982359\pi$
$674$			2.12305i			0.0817769i
$675$	−3.04226	−	3.96796i	−0.117097	−	0.152727i
$676$	−3.74467			−0.144026
$677$		−	8.34873i		−	0.320868i	−0.987047	−	0.160434i	$-0.948711\pi$
$677$		−	8.34873i		−	0.320868i	0.987047	−	0.160434i	$-0.0512893\pi$
$678$			8.18232i			0.314240i
$679$			43.0343i			1.65150i
$680$	3.56294	+	10.5028i	0.136632	+	0.402765i
$681$			17.2447i			0.660818i
$682$		−	0.647140i		−	0.0247803i
$683$	11.2525			0.430564			0.215282	−	0.976552i	$-0.430933\pi$
$683$	11.2525			0.430564			0.215282	+	0.976552i	$0.430933\pi$
$684$		−	3.74447i		−	0.143173i
$685$	6.32074	−	2.14423i	0.241503	−	0.0819266i
$686$			17.7040i			0.675941i
$687$			19.2252i			0.733485i
$688$	6.91360			0.263579
$689$		−	10.8289i		−	0.412547i
$690$	6.31622	−	2.14269i	0.240455	−	0.0815709i
$691$	−4.48310			−0.170545			−0.0852726	−	0.996358i	$-0.527176\pi$
$691$	−4.48310			−0.170545			−0.0852726	+	0.996358i	$0.527176\pi$
$692$			6.89548i			0.262127i
$693$			1.57556i			0.0598507i
$694$	−8.84425			−0.335723
$695$	−1.93592	−	5.70671i	−0.0734338	−	0.216468i
$696$	7.36456			0.279153
$697$	−58.4238			−2.21296
$698$	29.6036			1.12051
$699$	25.3616			0.959265
$700$	−8.36591	−	10.9115i	−0.316202	−	0.412416i
$701$		−	6.80397i		−	0.256983i	−0.991711	−	0.128491i	$-0.958987\pi$
$701$		−	6.80397i		−	0.256983i	0.991711	−	0.128491i	$-0.0410134\pi$
$702$		−	3.04226i		−	0.114823i
$703$	13.2448	+	18.5298i	0.499537	+	0.698866i
$704$	−0.572952			−0.0215940
$705$	0.557808	+	1.64430i	0.0210083	+	0.0619281i
$706$	7.97381			0.300098
$707$		−	9.72511i		−	0.365751i
$708$	−9.27315			−0.348506
$709$		−	16.0743i		−	0.603684i	−0.953358	−	0.301842i	$-0.902399\pi$
$709$		−	16.0743i		−	0.603684i	0.953358	−	0.301842i	$-0.0976015\pi$
$710$	4.49898	+	13.2621i	0.168844	+	0.497717i
$711$			0.716273i			0.0268623i
$712$			8.33434i			0.312343i
$713$			3.36903i			0.126171i
$714$	13.6393			0.510437
$715$	1.25213	+	3.69102i	0.0468269	+	0.138036i
$716$			6.95856i			0.260054i
$717$	2.44191			0.0911946
$718$	21.8286			0.814635
$719$	−16.2286			−0.605224			−0.302612	−	0.953114i	$-0.597859\pi$
$719$	−16.2286			−0.605224			−0.302612	+	0.953114i	$0.597859\pi$
$720$	−0.718347	−	2.11754i	−0.0267712	−	0.0789161i
$721$			40.3370i			1.50223i
$722$	4.97893			0.185297
$723$	−13.2870			−0.494150
$724$	10.3719			0.385470
$725$	−22.4049	−	29.2223i	−0.832097	−	1.08529i
$726$			10.6717i			0.396065i
$727$	1.52167			0.0564356			0.0282178	−	0.999602i	$-0.491017\pi$
$727$	1.52167			0.0564356			0.0282178	+	0.999602i	$0.491017\pi$
$728$		−	8.36591i		−	0.310061i
$729$	−1.00000			−0.0370370
$730$	16.5964	−	5.63010i	0.614260	−	0.208380i
$731$	34.2909			1.26829
$732$	−11.2507			−0.415839
$733$		−	9.58290i		−	0.353953i	−0.984215	−	0.176976i	$-0.943368\pi$
$733$		−	9.58290i		−	0.353953i	0.984215	−	0.176976i	$-0.0566316\pi$
$734$		−	21.2190i		−	0.783206i
$735$	−1.18998	+	0.403683i	−0.0438929	+	0.0148901i
$736$	2.98281			0.109948
$737$		−	5.21021i		−	0.191920i
$738$	11.7792			0.433598
$739$	−23.7057			−0.872028			−0.436014	−	0.899940i	$-0.643610\pi$
$739$	−23.7057			−0.872028			−0.436014	+	0.899940i	$0.643610\pi$
$740$	11.0449	+	7.93792i	0.406018	+	0.291804i
$741$	−11.3916			−0.418483
$742$	−9.78822			−0.359337
$743$			46.0090i			1.68791i	0.536417	+	0.843953i	$0.319777\pi$
$743$			46.0090i			1.68791i	−0.536417	+	0.843953i	$0.680223\pi$
$744$	1.12948			0.0414088
$745$	−15.5913	−	45.9601i	−0.571222	−	1.68385i
$746$		−	9.40573i		−	0.344368i
$747$			2.01848i			0.0738525i
$748$	−2.84179			−0.103906
$749$	35.4103			1.29386
$750$	−6.21691	+	9.29247i	−0.227009	+	0.339313i
$751$	29.4759			1.07559			0.537796	−	0.843075i	$-0.319257\pi$
$751$	29.4759			1.07559			0.537796	+	0.843075i	$0.319257\pi$
$752$			0.776516i			0.0283166i
$753$	19.0323			0.693575
$754$		−	22.4049i		−	0.815938i
$755$	7.78736	+	22.9555i	0.283411	+	0.835438i
$756$	−2.74990			−0.100013
$757$	16.1698			0.587702			0.293851	−	0.955851i	$-0.405063\pi$
$757$	16.1698			0.587702			0.293851	+	0.955851i	$0.405063\pi$
$758$	2.49593			0.0906562
$759$			1.70901i			0.0620331i
$760$	−7.92907	+	2.68983i	−0.287618	+	0.0975704i
$761$	43.8592			1.58989			0.794947	−	0.606678i	$-0.207498\pi$
$761$	43.8592			1.58989			0.794947	+	0.606678i	$0.207498\pi$
$762$	−9.55633			−0.346189
$763$	32.1917			1.16542
$764$		−	9.49717i		−	0.343596i
$765$	−3.56294	−	10.5028i	−0.128818	−	0.379730i
$766$	12.9235			0.466946
$767$			28.2113i			1.01865i
$768$		−	1.00000i		−	0.0360844i
$769$			28.7545i			1.03691i	0.855104	+	0.518456i	$0.173493\pi$
$769$			28.7545i			1.03691i	−0.855104	+	0.518456i	$0.826507\pi$
$770$	3.33632	−	1.13180i	0.120233	−	0.0407873i
$771$			7.10256i			0.255792i
$772$	−17.0877			−0.615001
$773$		−	46.1799i		−	1.66098i	−0.557037	−	0.830488i	$-0.688062\pi$
$773$		−	46.1799i		−	1.66098i	0.557037	−	0.830488i	$-0.311938\pi$
$774$	−6.91360			−0.248504
$775$	−3.43618	−	4.48174i	−0.123431	−	0.160989i
$776$	15.6494			0.561781
$777$	13.6081	−	9.72684i	0.488189	−	0.348949i
$778$		−	6.16822i		−	0.221141i
$779$		−	44.1068i		−	1.58029i
$780$	−6.44210	+	2.18540i	−0.230664	+	0.0782497i
$781$	−3.58838			−0.128402
$782$	14.7945			0.529050
$783$	−7.36456			−0.263188
$784$	−0.561961			−0.0200700
$785$	41.6340	−	14.1238i	1.48598	−	0.504099i
$786$	−6.83587			−0.243828
$787$		−	5.83011i		−	0.207821i	−0.994587	−	0.103910i	$-0.966864\pi$
$787$		−	5.83011i		−	0.207821i	0.994587	−	0.103910i	$-0.0331356\pi$
$788$		−	14.9122i		−	0.531224i
$789$	10.1942			0.362924
$790$	1.51674	−	0.514532i	0.0539630	−	0.0183062i
$791$		−	22.5006i		−	0.800028i
$792$	0.572952			0.0203590
$793$			34.2276i			1.21546i
$794$			11.2553i			0.399435i
$795$	2.55694	+	7.53734i	0.0906854	+	0.267322i
$796$			25.1320i			0.890778i
$797$	−36.5859			−1.29594			−0.647970	−	0.761666i	$-0.724382\pi$
$797$	−36.5859			−1.29594			−0.647970	+	0.761666i	$0.724382\pi$
$798$			10.2969i			0.364507i
$799$			3.85145i			0.136255i
$800$	−3.96796	+	3.04226i	−0.140288	+	0.107560i
$801$		−	8.33434i		−	0.294480i
$802$		−	2.01396i		−	0.0711155i
$803$			4.49056i			0.158469i
$804$	9.09361			0.320707
$805$	−17.3690	+	5.89220i	−0.612177	+	0.207673i
$806$		−	3.43618i		−	0.121034i
$807$			4.19787i			0.147772i
$808$	−3.53653			−0.124415
$809$			6.80818i			0.239363i	0.992812	+	0.119681i	$0.0381873\pi$
$809$			6.80818i			0.239363i	−0.992812	+	0.119681i	$0.961813\pi$
$810$	0.718347	+	2.11754i	0.0252401	+	0.0744028i
$811$	16.4540			0.577778			0.288889	−	0.957363i	$-0.406714\pi$
$811$	16.4540			0.577778			0.288889	+	0.957363i	$0.406714\pi$
$812$	−20.2518			−0.710700
$813$		−	21.1875i		−	0.743078i
$814$	−2.83530	+	2.02662i	−0.0993773	+	0.0710331i
$815$	−2.92537	−	8.62341i	−0.102471	−	0.302065i
$816$		−	4.95991i		−	0.173632i
$817$			25.8878i			0.905699i
$818$		−	1.80381i		−	0.0630687i
$819$			8.36591i			0.292329i
$820$	−8.46154	−	24.9429i	−0.295490	−	0.871044i
$821$	−54.6662			−1.90786			−0.953932	−	0.300023i	$-0.903006\pi$
$821$	−54.6662			−1.90786			−0.953932	+	0.300023i	$0.903006\pi$
$822$	−2.98494			−0.104112
$823$			9.56835i			0.333532i	0.985997	+	0.166766i	$0.0533324\pi$
$823$			9.56835i			0.333532i	−0.985997	+	0.166766i	$0.946668\pi$
$824$	14.6685			0.511002
$825$	−1.74307	−	2.27345i	−0.0606859	−	0.0791514i
$826$	25.5003			0.887268
$827$	47.5773			1.65443			0.827213	−	0.561889i	$-0.189925\pi$
$827$	47.5773			1.65443			0.827213	+	0.561889i	$0.189925\pi$
$828$	−2.98281			−0.103660
$829$		−	17.5677i		−	0.610150i	−0.952328	−	0.305075i	$-0.901318\pi$
$829$		−	17.5677i		−	0.610150i	0.952328	−	0.305075i	$-0.0986816\pi$
$830$	4.27422	−	1.44997i	0.148360	−	0.0503293i
$831$		−	19.1388i		−	0.663916i
$832$	−3.04226			−0.105471
$833$	−2.78728			−0.0965735
$834$			2.69497i			0.0933192i
$835$	6.34242	+	18.6962i	0.219488	+	0.647007i
$836$		−	2.14540i		−	0.0742003i
$837$	−1.12948			−0.0390406
$838$	−10.6915			−0.369332
$839$	27.6354			0.954081			0.477040	−	0.878881i	$-0.341710\pi$
$839$	27.6354			0.954081			0.477040	+	0.878881i	$0.341710\pi$
$840$	1.97538	+	5.82303i	0.0681572	+	0.200914i
$841$	−25.2368			−0.870234
$842$			5.37087i			0.185092i
$843$	−1.77696			−0.0612016
$844$	28.5808			0.983792
$845$	−2.68997	−	7.92949i	−0.0925379	−	0.272783i
$846$		−	0.776516i		−	0.0266972i
$847$		−	29.3462i		−	1.00835i
$848$			3.55948i			0.122233i
$849$		−	1.11078i		−	0.0381220i
$850$	−19.6807	+	15.0893i	−0.675043	+	0.517560i
$851$	14.7607	−	10.5507i	0.505990	−	0.361673i
$852$		−	6.26296i		−	0.214565i
$853$	−20.1704			−0.690621			−0.345310	−	0.938489i	$-0.612226\pi$
$853$	−20.1704			−0.690621			−0.345310	+	0.938489i	$0.612226\pi$
$854$	30.9384			1.05869
$855$	7.92907	−	2.68983i	0.271168	−	0.0919902i
$856$		−	12.8769i		−	0.440124i
$857$	−10.3761			−0.354440			−0.177220	−	0.984171i	$-0.556710\pi$
$857$	−10.3761			−0.354440			−0.177220	+	0.984171i	$0.556710\pi$
$858$		−	1.74307i		−	0.0595074i
$859$			3.50734i			0.119669i	0.998208	+	0.0598345i	$0.0190573\pi$
$859$			3.50734i			0.119669i	−0.998208	+	0.0598345i	$0.980943\pi$
$860$	4.96636	+	14.6398i	0.169352	+	0.499214i
$861$	−32.3916			−1.10390
$862$		−	15.1098i		−	0.514643i
$863$			15.0936i			0.513793i	0.966439	+	0.256896i	$0.0826999\pi$
$863$			15.0936i			0.513793i	−0.966439	+	0.256896i	$0.917300\pi$
$864$			1.00000i			0.0340207i
$865$	−14.6015	+	4.95334i	−0.496464	+	0.168419i
$866$		−	20.4232i		−	0.694010i
$867$		−	7.60075i		−	0.258135i
$868$	−3.10597			−0.105423
$869$			0.410390i			0.0139215i
$870$	5.29031	+	15.5948i	0.179358	+	0.528712i
$871$		−	27.6651i		−	0.937396i
$872$		−	11.7065i		−	0.396432i
$873$	−15.6494			−0.529652
$874$			11.1691i			0.377799i
$875$	17.0959	−	25.5534i	0.577947	−	0.863862i
$876$	−7.83759			−0.264807
$877$			30.3503i			1.02486i	0.858730	+	0.512429i	$0.171254\pi$
$877$			30.3503i			1.02486i	−0.858730	+	0.512429i	$0.828746\pi$
$878$		−	29.6845i		−	1.00180i
$879$	−24.1210			−0.813581
$880$	−0.411579	−	1.21325i	−0.0138743	−	0.0408986i
$881$	18.1132			0.610248			0.305124	−	0.952313i	$-0.401302\pi$
$881$	18.1132			0.610248			0.305124	+	0.952313i	$0.401302\pi$
$882$	0.561961			0.0189222
$883$	4.11110			0.138350			0.0691748	−	0.997605i	$-0.477963\pi$
$883$	4.11110			0.138350			0.0691748	+	0.997605i	$0.477963\pi$
$884$	−15.0893			−0.507509
$885$	−6.66134	−	19.6363i	−0.223919	−	0.660066i
$886$			29.7068i			0.998020i
$887$			39.7794i			1.33566i	0.744313	+	0.667831i	$0.232777\pi$
$887$			39.7794i			1.33566i	−0.744313	+	0.667831i	$0.767223\pi$
$888$	−3.53716	−	4.94859i	−0.118699	−	0.166064i
$889$	26.2790			0.881368
$890$	−17.6483	+	5.98695i	−0.591573	+	0.200683i
$891$	−0.572952			−0.0191946
$892$		−	22.9412i		−	0.768127i
$893$	−2.90764			−0.0973005
$894$			21.7045i			0.725906i
$895$	−14.7350	+	4.99866i	−0.492538	+	0.167087i
$896$			2.74990i			0.0918678i
$897$			9.07448i			0.302988i
$898$			1.32258i			0.0441352i
$899$	−8.31815			−0.277426
$900$	3.96796	−	3.04226i	0.132265	−	0.101409i
$901$			17.6547i			0.588164i
$902$	6.74891			0.224714
$903$	19.0117			0.632671
$904$	−8.18232			−0.272140
$905$	7.45065	+	21.9630i	0.247668	+	0.730075i
$906$		−	10.8407i		−	0.360157i
$907$	−46.0050			−1.52757			−0.763786	−	0.645470i	$-0.776661\pi$
$907$	−46.0050			−1.52757			−0.763786	+	0.645470i	$0.776661\pi$
$908$	−17.2447			−0.572285
$909$	3.53653			0.117299
$910$	17.7152	−	6.00962i	0.587252	−	0.199217i
$911$		−	21.2375i		−	0.703630i	−0.936070	−	0.351815i	$-0.885565\pi$
$911$		−	21.2375i		−	0.703630i	0.936070	−	0.351815i	$-0.114435\pi$
$912$	3.74447			0.123992
$913$			1.15650i			0.0382744i
$914$	23.4170			0.774564
$915$	−8.08192	−	23.8239i	−0.267180	−	0.787593i
$916$	−19.2252			−0.635217
$917$	18.7980			0.620764
$918$			4.95991i			0.163702i
$919$		−	33.8474i		−	1.11652i	−0.829665	−	0.558261i	$-0.811469\pi$
$919$		−	33.8474i		−	1.11652i	0.829665	−	0.558261i	$-0.188531\pi$
$920$	2.14269	+	6.31622i	0.0706425	+	0.208240i
$921$	−14.2638			−0.470009
$922$		−	31.2227i		−	1.02826i
$923$	−19.0535			−0.627155
$924$	−1.57556			−0.0518322
$925$	−8.87482	+	29.0902i	−0.291802	+	0.956479i
$926$	−3.93552			−0.129329
$927$	−14.6685			−0.481777
$928$			7.36456i			0.241754i
$929$	−29.3384			−0.962561			−0.481281	−	0.876567i	$-0.659828\pi$
$929$	−29.3384			−0.962561			−0.481281	+	0.876567i	$0.659828\pi$
$930$	0.811360	+	2.39173i	0.0266056	+	0.0784278i
$931$		−	2.10425i		−	0.0689639i
$932$			25.3616i			0.830748i
$933$	10.5684			0.345994
$934$	−32.0647			−1.04919
$935$	−2.04139	−	6.01762i	−0.0667607	−	0.196797i
$936$	3.04226			0.0994393
$937$			53.7694i			1.75657i	0.478136	+	0.878286i	$0.341312\pi$
$937$			53.7694i			1.75657i	−0.478136	+	0.878286i	$0.658688\pi$
$938$	−25.0065			−0.816493
$939$			1.67134i			0.0545421i
$940$	−1.64430	+	0.557808i	−0.0536313	+	0.0181937i
$941$	−53.6167			−1.74786			−0.873928	−	0.486056i	$-0.838435\pi$
$941$	−53.6167			−1.74786			−0.873928	+	0.486056i	$0.838435\pi$
$942$	−19.6615			−0.640606
$943$	−35.1351			−1.14416
$944$		−	9.27315i		−	0.301815i
$945$	−1.97538	−	5.82303i	−0.0642592	−	0.189423i
$946$	−3.96116			−0.128789
$947$	−36.6696			−1.19160			−0.595800	−	0.803133i	$-0.703165\pi$
$947$	−36.6696			−1.19160			−0.595800	+	0.803133i	$0.703165\pi$
$948$	−0.716273			−0.0232635
$949$			23.8440i			0.774007i
$950$	−11.3916	−	14.8579i	−0.369594	−	0.482054i
$951$	17.0342			0.552373
$952$			13.6393i			0.442052i
$953$		−	21.9382i		−	0.710647i	−0.934743	−	0.355324i	$-0.884371\pi$
$953$		−	21.9382i		−	0.710647i	0.934743	−	0.355324i	$-0.115629\pi$
$954$		−	3.55948i		−	0.115242i
$955$	20.1106	−	6.82226i	0.650765	−	0.220763i
$956$			2.44191i			0.0789769i
$957$	−4.21954			−0.136398
$958$			15.9248i			0.514508i
$959$	8.20830			0.265060
$960$	2.11754	−	0.718347i	0.0683433	−	0.0231845i
$961$	29.7243			0.958847
$962$	−15.0549	+	10.7610i	−0.485388	+	0.346947i
$963$			12.8769i			0.414953i
$964$		−	13.2870i		−	0.427946i
$965$	−12.2749	−	36.1840i	−0.395144	−	1.16480i
$966$	8.20244			0.263909
$967$	−34.9729			−1.12465			−0.562326	−	0.826916i	$-0.690093\pi$
$967$	−34.9729			−1.12465			−0.562326	+	0.826916i	$0.690093\pi$
$968$	−10.6717			−0.343002
$969$	18.5723			0.596627
$970$	11.2417	+	33.1382i	0.360949	+	1.06400i
$971$	37.2220			1.19451			0.597255	−	0.802052i	$-0.296258\pi$
$971$	37.2220			1.19451			0.597255	+	0.802052i	$0.296258\pi$
$972$		−	1.00000i		−	0.0320750i
$973$		−	7.41090i		−	0.237583i
$974$	31.7992			1.01891
$975$	−9.25533	−	12.0715i	−0.296408	−	0.386599i
$976$		−	11.2507i		−	0.360127i
$977$	−48.6581			−1.55671			−0.778355	−	0.627825i	$-0.783945\pi$
$977$	−48.6581			−1.55671			−0.778355	+	0.627825i	$0.783945\pi$
$978$			4.07237i			0.130220i
$979$		−	4.77518i		−	0.152615i
$980$	−0.403683	−	1.18998i	−0.0128952	−	0.0380124i
$981$			11.7065i			0.373759i
$982$	24.1758			0.771480
$983$		−	5.04447i		−	0.160894i	−0.996759	−	0.0804469i	$-0.974365\pi$
$983$		−	5.04447i		−	0.160894i	0.996759	−	0.0804469i	$-0.0256347\pi$
$984$			11.7792i			0.375507i
$985$	31.5771	−	10.7121i	1.00613	−	0.341316i
$986$			36.5276i			1.16328i
$987$			2.13534i			0.0679687i
$988$		−	11.3916i		−	0.362417i
$989$	20.6220			0.655740
$990$	0.411579	+	1.21325i	0.0130808	+	0.0385596i
$991$			31.0154i			0.985238i	0.870245	+	0.492619i	$0.163960\pi$
$991$			31.0154i			0.985238i	−0.870245	+	0.492619i	$0.836040\pi$
$992$			1.12948i			0.0358611i
$993$	27.9880			0.888174
$994$			17.2225i			0.546265i
$995$	−53.2179	+	18.0535i	−1.68712	+	0.572333i
$996$	−2.01848			−0.0639581
$997$	−57.0110			−1.80556			−0.902779	−	0.430106i	$-0.858476\pi$
$997$	−57.0110			−1.80556			−0.902779	+	0.430106i	$0.858476\pi$
$998$			14.7192i			0.465927i
$999$	3.53716	+	4.94859i	0.111911	+	0.156566i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1110.2.e.d.739.6	yes	16
3.2	odd	2		3330.2.e.e.739.5		16
5.4	even	2		1110.2.e.c.739.11	yes	16
15.14	odd	2		3330.2.e.f.739.11		16
37.36	even	2		1110.2.e.c.739.3	✓	16
111.110	odd	2		3330.2.e.f.739.12		16
185.184	even	2	inner	1110.2.e.d.739.14	yes	16
555.554	odd	2		3330.2.e.e.739.6		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1110.2.e.c.739.3	✓	16	37.36	even	2
1110.2.e.c.739.11	yes	16	5.4	even	2
1110.2.e.d.739.6	yes	16	1.1	even	1	trivial
1110.2.e.d.739.14	yes	16	185.184	even	2	inner
3330.2.e.e.739.5		16	3.2	odd	2
3330.2.e.e.739.6		16	555.554	odd	2
3330.2.e.f.739.11		16	15.14	odd	2
3330.2.e.f.739.12		16	111.110	odd	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:	\( N \)	\(=\)	\( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1110.e (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.00000i q^{3} +1.00000 q^{4} +(0.718347 + 2.11754i) q^{5} -1.00000i q^{6} +2.74990i q^{7} +1.00000 q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.00000i q^{3} +1.00000 q^{4} +(0.718347 + 2.11754i) q^{5} -1.00000i q^{6} +2.74990i q^{7} +1.00000 q^{8} -1.00000 q^{9} +(0.718347 + 2.11754i) q^{10} -0.572952 q^{11} -1.00000i q^{12} -3.04226 q^{13} +2.74990i q^{14} +(2.11754 - 0.718347i) q^{15} +1.00000 q^{16} +4.95991 q^{17} -1.00000 q^{18} +3.74447i q^{19} +(0.718347 + 2.11754i) q^{20} +2.74990 q^{21} -0.572952 q^{22} +2.98281 q^{23} -1.00000i q^{24} +(-3.96796 + 3.04226i) q^{25} -3.04226 q^{26} +1.00000i q^{27} +2.74990i q^{28} +7.36456i q^{29} +(2.11754 - 0.718347i) q^{30} +1.12948i q^{31} +1.00000 q^{32} +0.572952i q^{33} +4.95991 q^{34} +(-5.82303 + 1.97538i) q^{35} -1.00000 q^{36} +(4.94859 - 3.53716i) q^{37} +3.74447i q^{38} +3.04226i q^{39} +(0.718347 + 2.11754i) q^{40} -11.7792 q^{41} +2.74990 q^{42} +6.91360 q^{43} -0.572952 q^{44} +(-0.718347 - 2.11754i) q^{45} +2.98281 q^{46} +0.776516i q^{47} -1.00000i q^{48} -0.561961 q^{49} +(-3.96796 + 3.04226i) q^{50} -4.95991i q^{51} -3.04226 q^{52} +3.55948i q^{53} +1.00000i q^{54} +(-0.411579 - 1.21325i) q^{55} +2.74990i q^{56} +3.74447 q^{57} +7.36456i q^{58} -9.27315i q^{59} +(2.11754 - 0.718347i) q^{60} -11.2507i q^{61} +1.12948i q^{62} -2.74990i q^{63} +1.00000 q^{64} +(-2.18540 - 6.44210i) q^{65} +0.572952i q^{66} +9.09361i q^{67} +4.95991 q^{68} -2.98281i q^{69} +(-5.82303 + 1.97538i) q^{70} +6.26296 q^{71} -1.00000 q^{72} -7.83759i q^{73} +(4.94859 - 3.53716i) q^{74} +(3.04226 + 3.96796i) q^{75} +3.74447i q^{76} -1.57556i q^{77} +3.04226i q^{78} -0.716273i q^{79} +(0.718347 + 2.11754i) q^{80} +1.00000 q^{81} -11.7792 q^{82} -2.01848i q^{83} +2.74990 q^{84} +(3.56294 + 10.5028i) q^{85} +6.91360 q^{86} +7.36456 q^{87} -0.572952 q^{88} +8.33434i q^{89} +(-0.718347 - 2.11754i) q^{90} -8.36591i q^{91} +2.98281 q^{92} +1.12948 q^{93} +0.776516i q^{94} +(-7.92907 + 2.68983i) q^{95} -1.00000i q^{96} +15.6494 q^{97} -0.561961 q^{98} +0.572952 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 16 q^{2} + 16 q^{4} + 2 q^{5} + 16 q^{8} - 16 q^{9}+O(q^{10}) \) 16 * q + 16 * q^2 + 16 * q^4 + 2 * q^5 + 16 * q^8 - 16 * q^9	\( 16 q + 16 q^{2} + 16 q^{4} + 2 q^{5} + 16 q^{8} - 16 q^{9} + 2 q^{10} + 2 q^{11} - 6 q^{15} + 16 q^{16} + 38 q^{17} - 16 q^{18} + 2 q^{20} + 6 q^{21} + 2 q^{22} + 20 q^{23} - 4 q^{25} - 6 q^{30} + 16 q^{32} + 38 q^{34} + 10 q^{35} - 16 q^{36} + 4 q^{37} + 2 q^{40} - 6 q^{41} + 6 q^{42} + 2 q^{43} + 2 q^{44} - 2 q^{45} + 20 q^{46} - 18 q^{49} - 4 q^{50} - 20 q^{55} - 16 q^{57} - 6 q^{60} + 16 q^{64} + 12 q^{65} + 38 q^{68} + 10 q^{70} - 24 q^{71} - 16 q^{72} + 4 q^{74} + 2 q^{80} + 16 q^{81} - 6 q^{82} + 6 q^{84} + 2 q^{86} - 2 q^{87} + 2 q^{88} - 2 q^{90} + 20 q^{92} - 22 q^{93} - 16 q^{95} - 38 q^{97} - 18 q^{98} - 2 q^{99}+O(q^{100}) \) 16 * q + 16 * q^2 + 16 * q^4 + 2 * q^5 + 16 * q^8 - 16 * q^9 + 2 * q^10 + 2 * q^11 - 6 * q^15 + 16 * q^16 + 38 * q^17 - 16 * q^18 + 2 * q^20 + 6 * q^21 + 2 * q^22 + 20 * q^23 - 4 * q^25 - 6 * q^30 + 16 * q^32 + 38 * q^34 + 10 * q^35 - 16 * q^36 + 4 * q^37 + 2 * q^40 - 6 * q^41 + 6 * q^42 + 2 * q^43 + 2 * q^44 - 2 * q^45 + 20 * q^46 - 18 * q^49 - 4 * q^50 - 20 * q^55 - 16 * q^57 - 6 * q^60 + 16 * q^64 + 12 * q^65 + 38 * q^68 + 10 * q^70 - 24 * q^71 - 16 * q^72 + 4 * q^74 + 2 * q^80 + 16 * q^81 - 6 * q^82 + 6 * q^84 + 2 * q^86 - 2 * q^87 + 2 * q^88 - 2 * q^90 + 20 * q^92 - 22 * q^93 - 16 * q^95 - 38 * q^97 - 18 * q^98 - 2 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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