LMFDB - Embedded newform 1110.2.e.c.739.10

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			739.10
Root			$2.18974 + 2.18974i$ of defining polynomial
Character	$\chi$	$=$	1110.739
Dual form			1110.2.e.c.739.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +1.00000i q^{3} +1.00000 q^{4} +(-2.18974 - 0.452819i) q^{5} -1.00000i q^{6} +0.0776078i q^{7} -1.00000 q^{8} -1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +1.00000i q^{3} +1.00000 q^{4} +(-2.18974 - 0.452819i) q^{5} -1.00000i q^{6} +0.0776078i q^{7} -1.00000 q^{8} -1.00000 q^{9} +(2.18974 + 0.452819i) q^{10} +1.27917 q^{11} +1.00000i q^{12} -1.98311 q^{13} -0.0776078i q^{14} +(0.452819 - 2.18974i) q^{15} +1.00000 q^{16} +2.25016 q^{17} +1.00000 q^{18} +2.64058i q^{19} +(-2.18974 - 0.452819i) q^{20} -0.0776078 q^{21} -1.27917 q^{22} -7.25003 q^{23} -1.00000i q^{24} +(4.58991 + 1.98311i) q^{25} +1.98311 q^{26} -1.00000i q^{27} +0.0776078i q^{28} -5.46060i q^{29} +(-0.452819 + 2.18974i) q^{30} -6.55496i q^{31} -1.00000 q^{32} +1.27917i q^{33} -2.25016 q^{34} +(0.0351423 - 0.169941i) q^{35} -1.00000 q^{36} +(4.90774 - 3.59362i) q^{37} -2.64058i q^{38} -1.98311i q^{39} +(2.18974 + 0.452819i) q^{40} -11.0078 q^{41} +0.0776078 q^{42} +7.27593 q^{43} +1.27917 q^{44} +(2.18974 + 0.452819i) q^{45} +7.25003 q^{46} -8.23049i q^{47} +1.00000i q^{48} +6.99398 q^{49} +(-4.58991 - 1.98311i) q^{50} +2.25016i q^{51} -1.98311 q^{52} -4.77877i q^{53} +1.00000i q^{54} +(-2.80105 - 0.579233i) q^{55} -0.0776078i q^{56} -2.64058 q^{57} +5.46060i q^{58} -14.3874i q^{59} +(0.452819 - 2.18974i) q^{60} +9.19685i q^{61} +6.55496i q^{62} -0.0776078i q^{63} +1.00000 q^{64} +(4.34250 + 0.897991i) q^{65} -1.27917i q^{66} +2.98662i q^{67} +2.25016 q^{68} -7.25003i q^{69} +(-0.0351423 + 0.169941i) q^{70} +7.16641 q^{71} +1.00000 q^{72} -9.35662i q^{73} +(-4.90774 + 3.59362i) q^{74} +(-1.98311 + 4.58991i) q^{75} +2.64058i q^{76} +0.0992737i q^{77} +1.98311i q^{78} -15.9698i q^{79} +(-2.18974 - 0.452819i) q^{80} +1.00000 q^{81} +11.0078 q^{82} +3.25435i q^{83} -0.0776078 q^{84} +(-4.92727 - 1.01892i) q^{85} -7.27593 q^{86} +5.46060 q^{87} -1.27917 q^{88} +15.4591i q^{89} +(-2.18974 - 0.452819i) q^{90} -0.153905i q^{91} -7.25003 q^{92} +6.55496 q^{93} +8.23049i q^{94} +(1.19571 - 5.78219i) q^{95} -1.00000i q^{96} +11.8098 q^{97} -6.99398 q^{98} -1.27917 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	−2.18974	−	0.452819i	−0.979281	−	0.202507i
$5$	−2.18974	−	0.452819i	−0.979281	−	0.202507i
$6$		−	1.00000i		−	0.408248i
$7$			0.0776078i			0.0293330i	0.999892	+	0.0146665i	$0.00466866\pi$
$7$			0.0776078i			0.0293330i	−0.999892	+	0.0146665i	$0.995331\pi$
$8$	−1.00000			−0.353553
$9$	−1.00000			−0.333333
$10$	2.18974	+	0.452819i	0.692456	+	0.143194i
$11$	1.27917			0.385685			0.192842	−	0.981230i	$-0.438229\pi$
$11$	1.27917			0.385685			0.192842	+	0.981230i	$0.438229\pi$
$12$			1.00000i			0.288675i
$13$	−1.98311			−0.550016			−0.275008	−	0.961442i	$-0.588681\pi$
$13$	−1.98311			−0.550016			−0.275008	+	0.961442i	$0.588681\pi$
$14$		−	0.0776078i		−	0.0207416i
$15$	0.452819	−	2.18974i	0.116917	−	0.565388i
$16$	1.00000			0.250000
$17$	2.25016			0.545745			0.272872	−	0.962050i	$-0.412026\pi$
$17$	2.25016			0.545745			0.272872	+	0.962050i	$0.412026\pi$
$18$	1.00000			0.235702
$19$			2.64058i			0.605791i	0.953024	+	0.302896i	$0.0979534\pi$
$19$			2.64058i			0.605791i	−0.953024	+	0.302896i	$0.902047\pi$
$20$	−2.18974	−	0.452819i	−0.489640	−	0.101253i
$21$	−0.0776078			−0.0169354
$22$	−1.27917			−0.272720
$23$	−7.25003			−1.51174			−0.755868	−	0.654724i	$-0.772785\pi$
$23$	−7.25003			−1.51174			−0.755868	+	0.654724i	$0.772785\pi$
$24$		−	1.00000i		−	0.204124i
$25$	4.58991	+	1.98311i	0.917982	+	0.396622i
$26$	1.98311			0.388920
$27$		−	1.00000i		−	0.192450i
$28$			0.0776078i			0.0146665i
$29$		−	5.46060i		−	1.01401i	−0.861944	−	0.507004i	$-0.830753\pi$
$29$		−	5.46060i		−	1.01401i	0.861944	−	0.507004i	$-0.169247\pi$
$30$	−0.452819	+	2.18974i	−0.0826731	+	0.399790i
$31$		−	6.55496i		−	1.17730i	−0.808386	−	0.588652i	$-0.799659\pi$
$31$		−	6.55496i		−	1.17730i	0.808386	−	0.588652i	$-0.200341\pi$
$32$	−1.00000			−0.176777
$33$			1.27917i			0.222675i
$34$	−2.25016			−0.385900
$35$	0.0351423	−	0.169941i	0.00594013	−	0.0287252i
$36$	−1.00000			−0.166667
$37$	4.90774	−	3.59362i	0.806828	−	0.590787i
$37$	4.90774	−	3.59362i	0.806828	−	0.590787i
$38$		−	2.64058i		−	0.428359i
$39$		−	1.98311i		−	0.317552i
$40$	2.18974	+	0.452819i	0.346228	+	0.0715970i
$41$	−11.0078			−1.71913			−0.859565	−	0.511026i	$-0.829266\pi$
$41$	−11.0078			−1.71913			−0.859565	+	0.511026i	$0.829266\pi$
$42$	0.0776078			0.0119751
$43$	7.27593			1.10957			0.554784	−	0.831994i	$-0.312801\pi$
$43$	7.27593			1.10957			0.554784	+	0.831994i	$0.312801\pi$
$44$	1.27917			0.192842
$45$	2.18974	+	0.452819i	0.326427	+	0.0675023i
$46$	7.25003			1.06896
$47$		−	8.23049i		−	1.20054i	−0.799797	−	0.600270i	$-0.795060\pi$
$47$		−	8.23049i		−	1.20054i	0.799797	−	0.600270i	$-0.204940\pi$
$48$			1.00000i			0.144338i
$49$	6.99398			0.999140
$50$	−4.58991	−	1.98311i	−0.649111	−	0.280454i
$51$			2.25016i			0.315086i
$52$	−1.98311			−0.275008
$53$		−	4.77877i		−	0.656414i	−0.944606	−	0.328207i	$-0.893556\pi$
$53$		−	4.77877i		−	0.656414i	0.944606	−	0.328207i	$-0.106444\pi$
$54$			1.00000i			0.136083i
$55$	−2.80105	−	0.579233i	−0.377694	−	0.0781038i
$56$		−	0.0776078i		−	0.0103708i
$57$	−2.64058			−0.349754
$58$			5.46060i			0.717011i
$59$		−	14.3874i		−	1.87308i	−0.350558	−	0.936541i	$-0.614008\pi$
$59$		−	14.3874i		−	1.87308i	0.350558	−	0.936541i	$-0.385992\pi$
$60$	0.452819	−	2.18974i	0.0584587	−	0.282694i
$61$			9.19685i			1.17754i	0.808302	+	0.588768i	$0.200387\pi$
$61$			9.19685i			1.17754i	−0.808302	+	0.588768i	$0.799613\pi$
$62$			6.55496i			0.832480i
$63$		−	0.0776078i		−	0.00977766i
$64$	1.00000			0.125000
$65$	4.34250	+	0.897991i	0.538620	+	0.111382i
$66$		−	1.27917i		−	0.157455i
$67$			2.98662i			0.364874i	0.983218	+	0.182437i	$0.0583985\pi$
$67$			2.98662i			0.364874i	−0.983218	+	0.182437i	$0.941601\pi$
$68$	2.25016			0.272872
$69$		−	7.25003i		−	0.872801i
$70$	−0.0351423	+	0.169941i	−0.00420031	+	0.0203118i
$71$	7.16641			0.850496			0.425248	−	0.905077i	$-0.360187\pi$
$71$	7.16641			0.850496			0.425248	+	0.905077i	$0.360187\pi$
$72$	1.00000			0.117851
$73$		−	9.35662i		−	1.09511i	−0.836770	−	0.547555i	$-0.815559\pi$
$73$		−	9.35662i		−	1.09511i	0.836770	−	0.547555i	$-0.184441\pi$
$74$	−4.90774	+	3.59362i	−0.570513	+	0.417749i
$75$	−1.98311	+	4.58991i	−0.228990	+	0.529997i
$76$			2.64058i			0.302896i
$77$			0.0992737i			0.0113133i
$78$			1.98311i			0.224543i
$79$		−	15.9698i		−	1.79675i	−0.439232	−	0.898374i	$-0.644749\pi$
$79$		−	15.9698i		−	1.79675i	0.439232	−	0.898374i	$-0.355251\pi$
$80$	−2.18974	−	0.452819i	−0.244820	−	0.0506267i
$81$	1.00000			0.111111
$82$	11.0078			1.21561
$83$			3.25435i			0.357212i	0.983921	+	0.178606i	$0.0571587\pi$
$83$			3.25435i			0.357212i	−0.983921	+	0.178606i	$0.942841\pi$
$84$	−0.0776078			−0.00846770
$85$	−4.92727	−	1.01892i	−0.534437	−	0.110517i
$86$	−7.27593			−0.784584
$87$	5.46060			0.585437
$88$	−1.27917			−0.136360
$89$			15.4591i			1.63866i	0.573322	+	0.819330i	$0.305654\pi$
$89$			15.4591i			1.63866i	−0.573322	+	0.819330i	$0.694346\pi$
$90$	−2.18974	−	0.452819i	−0.230819	−	0.0477313i
$91$		−	0.153905i		−	0.0161336i
$92$	−7.25003			−0.755868
$93$	6.55496			0.679717
$94$			8.23049i			0.848911i
$95$	1.19571	−	5.78219i	0.122677	−	0.593240i
$96$		−	1.00000i		−	0.102062i
$97$	11.8098			1.19910			0.599552	−	0.800336i	$-0.295346\pi$
$97$	11.8098			1.19910			0.599552	+	0.800336i	$0.295346\pi$
$98$	−6.99398			−0.706498
$99$	−1.27917			−0.128562
$100$	4.58991	+	1.98311i	0.458991	+	0.198311i
$101$	4.83089			0.480691			0.240346	−	0.970687i	$-0.422739\pi$
$101$	4.83089			0.480691			0.240346	+	0.970687i	$0.422739\pi$
$102$		−	2.25016i		−	0.222799i
$103$	−1.95876			−0.193002			−0.0965010	−	0.995333i	$-0.530765\pi$
$103$	−1.95876			−0.193002			−0.0965010	+	0.995333i	$0.530765\pi$
$104$	1.98311			0.194460
$105$	0.169941	+	0.0351423i	0.0165845	+	0.00342954i
$106$			4.77877i			0.464155i
$107$		−	6.65385i		−	0.643252i	−0.946867	−	0.321626i	$-0.895771\pi$
$107$		−	6.65385i		−	0.643252i	0.946867	−	0.321626i	$-0.104229\pi$
$108$		−	1.00000i		−	0.0962250i
$109$		−	9.84106i		−	0.942603i	−0.881972	−	0.471301i	$-0.843784\pi$
$109$		−	9.84106i		−	0.942603i	0.881972	−	0.471301i	$-0.156216\pi$
$110$	2.80105	+	0.579233i	0.267070	+	0.0552277i
$111$	3.59362	+	4.90774i	0.341091	+	0.465822i
$112$			0.0776078i			0.00733325i
$113$	9.75081			0.917279			0.458640	−	0.888622i	$-0.348337\pi$
$113$	9.75081			0.917279			0.458640	+	0.888622i	$0.348337\pi$
$114$	2.64058			0.247313
$115$	15.8757	+	3.28295i	1.48041	+	0.306137i
$116$		−	5.46060i		−	0.507004i
$117$	1.98311			0.183339
$118$			14.3874i			1.32447i
$119$			0.174630i			0.0160083i
$120$	−0.452819	+	2.18974i	−0.0413366	+	0.199895i
$121$	−9.36372			−0.851247
$122$		−	9.19685i		−	0.832644i
$123$		−	11.0078i		−	0.992540i
$124$		−	6.55496i		−	0.588652i
$125$	−9.15271	−	6.42090i	−0.818643	−	0.574302i
$126$			0.0776078i			0.00691385i
$127$		−	2.70247i		−	0.239805i	−0.992786	−	0.119903i	$-0.961742\pi$
$127$		−	2.70247i		−	0.239805i	0.992786	−	0.119903i	$-0.0382583\pi$
$128$	−1.00000			−0.0883883
$129$			7.27593i			0.640610i
$130$	−4.34250	−	0.897991i	−0.380862	−	0.0787590i
$131$			5.39614i			0.471463i	0.971818	+	0.235731i	$0.0757486\pi$
$131$			5.39614i			0.471463i	−0.971818	+	0.235731i	$0.924251\pi$
$132$			1.27917i			0.111338i
$133$	−0.204930			−0.0177697
$134$		−	2.98662i		−	0.258005i
$135$	−0.452819	+	2.18974i	−0.0389725	+	0.188463i
$136$	−2.25016			−0.192950
$137$		−	16.2666i		−	1.38975i	−0.719130	−	0.694876i	$-0.755459\pi$
$137$		−	16.2666i		−	1.38975i	0.719130	−	0.694876i	$-0.244541\pi$
$138$			7.25003i			0.617163i
$139$	−9.45724			−0.802152			−0.401076	−	0.916045i	$-0.631364\pi$
$139$	−9.45724			−0.802152			−0.401076	+	0.916045i	$0.631364\pi$
$140$	0.0351423	−	0.169941i	0.00297007	−	0.0143626i
$141$	8.23049			0.693133
$142$	−7.16641			−0.601392
$143$	−2.53674			−0.212133
$144$	−1.00000			−0.0833333
$145$	−2.47266	+	11.9573i	−0.205343	+	0.992998i
$146$			9.35662i			0.774360i
$147$			6.99398i			0.576854i
$148$	4.90774	−	3.59362i	0.403414	−	0.295393i
$149$	13.0047			1.06539			0.532695	−	0.846307i	$-0.321179\pi$
$149$	13.0047			1.06539			0.532695	+	0.846307i	$0.321179\pi$
$150$	1.98311	−	4.58991i	0.161920	−	0.374765i
$151$	−20.0623			−1.63264			−0.816322	−	0.577597i	$-0.803990\pi$
$151$	−20.0623			−1.63264			−0.816322	+	0.577597i	$0.803990\pi$
$152$		−	2.64058i		−	0.214180i
$153$	−2.25016			−0.181915
$154$		−	0.0992737i		−	0.00799970i
$155$	−2.96821	+	14.3536i	−0.238412	+	1.15291i
$156$		−	1.98311i		−	0.158776i
$157$		−	13.6476i		−	1.08920i	−0.838697	−	0.544599i	$-0.816682\pi$
$157$		−	13.6476i		−	1.08920i	0.838697	−	0.544599i	$-0.183318\pi$
$158$			15.9698i			1.27049i
$159$	4.77877			0.378981
$160$	2.18974	+	0.452819i	0.173114	+	0.0357985i
$161$		−	0.562659i		−	0.0443437i
$162$	−1.00000			−0.0785674
$163$	−11.4118			−0.893840			−0.446920	−	0.894574i	$-0.647479\pi$
$163$	−11.4118			−0.893840			−0.446920	+	0.894574i	$0.647479\pi$
$164$	−11.0078			−0.859565
$165$	0.579233	−	2.80105i	0.0450933	−	0.218061i
$166$		−	3.25435i		−	0.252587i
$167$	−4.10105			−0.317348			−0.158674	−	0.987331i	$-0.550722\pi$
$167$	−4.10105			−0.317348			−0.158674	+	0.987331i	$0.550722\pi$
$168$	0.0776078			0.00598757
$169$	−9.06727			−0.697482
$170$	4.92727	+	1.01892i	0.377904	+	0.0781474i
$171$		−	2.64058i		−	0.201930i
$172$	7.27593			0.554784
$173$		−	23.3129i		−	1.77245i	−0.463259	−	0.886223i	$-0.653320\pi$
$173$		−	23.3129i		−	1.77245i	0.463259	−	0.886223i	$-0.346680\pi$
$174$	−5.46060			−0.413967
$175$	−0.153905	+	0.356213i	−0.0116341	+	0.0269272i
$176$	1.27917			0.0964212
$177$	14.3874			1.08142
$178$		−	15.4591i		−	1.15871i
$179$		−	6.40760i		−	0.478927i	−0.970905	−	0.239463i	$-0.923029\pi$
$179$		−	6.40760i		−	0.478927i	0.970905	−	0.239463i	$-0.0769715\pi$
$180$	2.18974	+	0.452819i	0.163213	+	0.0337512i
$181$	3.85705			0.286692			0.143346	−	0.989673i	$-0.454214\pi$
$181$	3.85705			0.286692			0.143346	+	0.989673i	$0.454214\pi$
$182$			0.153905i			0.0114082i
$183$	−9.19685			−0.679851
$184$	7.25003			0.534479
$185$	−12.3739	+	5.64676i	−0.909749	+	0.415158i
$186$	−6.55496			−0.480633
$187$	2.87834			0.210485
$188$		−	8.23049i		−	0.600270i
$189$	0.0776078			0.00564514
$190$	−1.19571	+	5.78219i	−0.0867457	+	0.419484i
$191$			25.6111i			1.85315i	0.376108	+	0.926576i	$0.377262\pi$
$191$			25.6111i			1.85315i	−0.376108	+	0.926576i	$0.622738\pi$
$192$			1.00000i			0.0721688i
$193$	4.02227			0.289529			0.144765	−	0.989466i	$-0.453757\pi$
$193$	4.02227			0.289529			0.144765	+	0.989466i	$0.453757\pi$
$194$	−11.8098			−0.847894
$195$	−0.897991	+	4.34250i	−0.0643065	+	0.310973i
$196$	6.99398			0.499570
$197$		−	19.2606i		−	1.37226i	−0.727479	−	0.686130i	$-0.759308\pi$
$197$		−	19.2606i		−	1.37226i	0.727479	−	0.686130i	$-0.240692\pi$
$198$	1.27917			0.0909067
$199$			2.79567i			0.198180i	0.995078	+	0.0990899i	$0.0315932\pi$
$199$			2.79567i			0.198180i	−0.995078	+	0.0990899i	$0.968407\pi$
$200$	−4.58991	−	1.98311i	−0.324556	−	0.140227i
$201$	−2.98662			−0.210660
$202$	−4.83089			−0.339900
$203$	0.423785			0.0297439
$204$			2.25016i			0.157543i
$205$	24.1042	+	4.98455i	1.68351	+	0.348136i
$206$	1.95876			0.136473
$207$	7.25003			0.503912
$208$	−1.98311			−0.137504
$209$			3.37776i			0.233644i
$210$	−0.169941	−	0.0351423i	−0.0117270	−	0.00242505i
$211$	−10.9853			−0.756257			−0.378128	−	0.925753i	$-0.623432\pi$
$211$	−10.9853			−0.756257			−0.378128	+	0.925753i	$0.623432\pi$
$212$		−	4.77877i		−	0.328207i
$213$			7.16641i			0.491034i
$214$			6.65385i			0.454848i
$215$	−15.9324	−	3.29468i	−1.08658	−	0.224695i
$216$			1.00000i			0.0680414i
$217$	0.508716			0.0345339
$218$			9.84106i			0.666521i
$219$	9.35662			0.632262
$220$	−2.80105	−	0.579233i	−0.188847	−	0.0390519i
$221$	−4.46232			−0.300168
$222$	−3.59362	−	4.90774i	−0.241188	−	0.329386i
$223$			24.5095i			1.64128i	0.571447	+	0.820639i	$0.306382\pi$
$223$			24.5095i			1.64128i	−0.571447	+	0.820639i	$0.693618\pi$
$224$		−	0.0776078i		−	0.00518539i
$225$	−4.58991	−	1.98311i	−0.305994	−	0.132207i
$226$	−9.75081			−0.648615
$227$	−2.42240			−0.160780			−0.0803901	−	0.996763i	$-0.525617\pi$
$227$	−2.42240			−0.160780			−0.0803901	+	0.996763i	$0.525617\pi$
$228$	−2.64058			−0.174877
$229$	8.80804			0.582052			0.291026	−	0.956715i	$-0.406003\pi$
$229$	8.80804			0.582052			0.291026	+	0.956715i	$0.406003\pi$
$230$	−15.8757	−	3.28295i	−1.04681	−	0.216471i
$231$	−0.0992737			−0.00653173
$232$			5.46060i			0.358506i
$233$			12.0227i			0.787636i	0.919188	+	0.393818i	$0.128846\pi$
$233$			12.0227i			0.787636i	−0.919188	+	0.393818i	$0.871154\pi$
$234$	−1.98311			−0.129640
$235$	−3.72693	+	18.0226i	−0.243118	+	1.17567i
$236$		−	14.3874i		−	0.936541i
$237$	15.9698			1.03735
$238$		−	0.174630i		−	0.0113196i
$239$			15.0286i			0.972121i	0.873925	+	0.486061i	$0.161567\pi$
$239$			15.0286i			0.972121i	−0.873925	+	0.486061i	$0.838433\pi$
$240$	0.452819	−	2.18974i	0.0292294	−	0.141347i
$241$		−	5.51284i		−	0.355113i	−0.984111	−	0.177557i	$-0.943181\pi$
$241$		−	5.51284i		−	0.355113i	0.984111	−	0.177557i	$-0.0568193\pi$
$242$	9.36372			0.601923
$243$			1.00000i			0.0641500i
$244$			9.19685i			0.588768i
$245$	−15.3150	−	3.16701i	−0.978438	−	0.202333i
$246$			11.0078i			0.701832i
$247$		−	5.23657i		−	0.333195i
$248$			6.55496i			0.416240i
$249$	−3.25435			−0.206236
$250$	9.15271	+	6.42090i	0.578868	+	0.406093i
$251$			21.6293i			1.36523i	0.730778	+	0.682615i	$0.239157\pi$
$251$			21.6293i			1.36523i	−0.730778	+	0.682615i	$0.760843\pi$
$252$		−	0.0776078i		−	0.00488883i
$253$	−9.27403			−0.583053
$254$			2.70247i			0.169568i
$255$	1.01892	−	4.92727i	0.0638071	−	0.308557i
$256$	1.00000			0.0625000
$257$	−13.3229			−0.831062			−0.415531	−	0.909579i	$-0.636404\pi$
$257$	−13.3229			−0.831062			−0.415531	+	0.909579i	$0.636404\pi$
$258$		−	7.27593i		−	0.452980i
$259$	0.278893	+	0.380879i	0.0173295	+	0.0236667i
$260$	4.34250	+	0.897991i	0.269310	+	0.0556910i
$261$			5.46060i			0.338002i
$262$		−	5.39614i		−	0.333375i
$263$			30.7985i			1.89912i	0.313589	+	0.949559i	$0.398469\pi$
$263$			30.7985i			1.89912i	−0.313589	+	0.949559i	$0.601531\pi$
$264$		−	1.27917i		−	0.0787276i
$265$	−2.16392	+	10.4643i	−0.132928	+	0.642814i
$266$	0.204930			0.0125651
$267$	−15.4591			−0.946081
$268$			2.98662i			0.182437i
$269$	−20.6738			−1.26050			−0.630252	−	0.776391i	$-0.717048\pi$
$269$	−20.6738			−1.26050			−0.630252	+	0.776391i	$0.717048\pi$
$270$	0.452819	−	2.18974i	0.0275577	−	0.133263i
$271$	−23.4840			−1.42655			−0.713276	−	0.700883i	$-0.752789\pi$
$271$	−23.4840			−1.42655			−0.713276	+	0.700883i	$0.752789\pi$
$272$	2.25016			0.136436
$273$	0.153905			0.00931475
$274$			16.2666i			0.982703i
$275$	5.87128	+	2.53674i	0.354052	+	0.152971i
$276$		−	7.25003i		−	0.436400i
$277$	28.7324			1.72636			0.863180	−	0.504896i	$-0.168469\pi$
$277$	28.7324			1.72636			0.863180	+	0.504896i	$0.168469\pi$
$278$	9.45724			0.567207
$279$			6.55496i			0.392435i
$280$	−0.0351423	+	0.169941i	−0.00210015	+	0.0101559i
$281$			15.5947i			0.930300i	0.885232	+	0.465150i	$0.154000\pi$
$281$			15.5947i			0.930300i	−0.885232	+	0.465150i	$0.846000\pi$
$282$	−8.23049			−0.490119
$283$	−2.55738			−0.152021			−0.0760103	−	0.997107i	$-0.524218\pi$
$283$	−2.55738			−0.152021			−0.0760103	+	0.997107i	$0.524218\pi$
$284$	7.16641			0.425248
$285$	5.78219	+	1.19571i	0.342507	+	0.0708276i
$286$	2.53674			0.150001
$287$		−	0.854292i		−	0.0504272i
$288$	1.00000			0.0589256
$289$	−11.9368			−0.702163
$290$	2.47266	−	11.9573i	0.145200	−	0.702155i
$291$			11.8098i			0.692303i
$292$		−	9.35662i		−	0.547555i
$293$			7.65067i			0.446957i	0.974709	+	0.223478i	$0.0717412\pi$
$293$			7.65067i			0.446957i	−0.974709	+	0.223478i	$0.928259\pi$
$294$		−	6.99398i		−	0.407897i
$295$	−6.51490	+	31.5047i	−0.379312	+	1.83427i
$296$	−4.90774	+	3.59362i	−0.285257	+	0.208875i
$297$		−	1.27917i		−	0.0742250i
$298$	−13.0047			−0.753344
$299$	14.3776			0.831479
$300$	−1.98311	+	4.58991i	−0.114495	+	0.264999i
$301$			0.564669i			0.0325470i
$302$	20.0623			1.15445
$303$			4.83089i			0.277527i
$304$			2.64058i			0.151448i
$305$	4.16451	−	20.1387i	0.238459	−	1.15314i
$306$	2.25016			0.128633
$307$		−	13.0160i		−	0.742860i	−0.928461	−	0.371430i	$-0.878868\pi$
$307$		−	13.0160i		−	0.742860i	0.928461	−	0.371430i	$-0.121132\pi$
$308$			0.0992737i			0.00565664i
$309$		−	1.95876i		−	0.111430i
$310$	2.96821	−	14.3536i	0.168583	−	0.815232i
$311$		−	15.0099i		−	0.851133i	−0.904927	−	0.425566i	$-0.860075\pi$
$311$		−	15.0099i		−	0.851133i	0.904927	−	0.425566i	$-0.139925\pi$
$312$			1.98311i			0.112272i
$313$	−8.80419			−0.497642			−0.248821	−	0.968549i	$-0.580043\pi$
$313$	−8.80419			−0.497642			−0.248821	+	0.968549i	$0.580043\pi$
$314$			13.6476i			0.770179i
$315$	−0.0351423	+	0.169941i	−0.00198004	+	0.00957508i
$316$		−	15.9698i		−	0.898374i
$317$		−	5.64539i		−	0.317076i	−0.987353	−	0.158538i	$-0.949322\pi$
$317$		−	5.64539i		−	0.317076i	0.987353	−	0.158538i	$-0.0506781\pi$
$318$	−4.77877			−0.267980
$319$		−	6.98504i		−	0.391087i
$320$	−2.18974	−	0.452819i	−0.122410	−	0.0253134i
$321$	6.65385			0.371382
$322$			0.562659i			0.0313557i
$323$			5.94174i			0.330607i
$324$	1.00000			0.0555556
$325$	−9.10230	−	3.93273i	−0.504905	−	0.218149i
$326$	11.4118			0.632040
$327$	9.84106			0.544212
$328$	11.0078			0.607804
$329$	0.638750			0.0352155
$330$	−0.579233	+	2.80105i	−0.0318857	+	0.154193i
$331$		−	20.9369i		−	1.15080i	−0.817873	−	0.575399i	$-0.804847\pi$
$331$		−	20.9369i		−	1.15080i	0.817873	−	0.575399i	$-0.195153\pi$
$332$			3.25435i			0.178606i
$333$	−4.90774	+	3.59362i	−0.268943	+	0.196929i
$334$	4.10105			0.224399
$335$	1.35240	−	6.53992i	0.0738895	−	0.357314i
$336$	−0.0776078			−0.00423385
$337$			9.66677i			0.526582i	0.964716	+	0.263291i	$0.0848080\pi$
$337$			9.66677i			0.526582i	−0.964716	+	0.263291i	$0.915192\pi$
$338$	9.06727			0.493194
$339$			9.75081i			0.529592i
$340$	−4.92727	−	1.01892i	−0.267219	−	0.0552585i
$341$		−	8.38491i		−	0.454068i
$342$			2.64058i			0.142786i
$343$			1.08604i			0.0586407i
$344$	−7.27593			−0.392292
$345$	−3.28295	+	15.8757i	−0.176748	+	0.854717i
$346$			23.3129i			1.25331i
$347$	1.94022			0.104157			0.0520783	−	0.998643i	$-0.483415\pi$
$347$	1.94022			0.104157			0.0520783	+	0.998643i	$0.483415\pi$
$348$	5.46060			0.292719
$349$	2.55258			0.136637			0.0683184	−	0.997664i	$-0.478237\pi$
$349$	2.55258			0.136637			0.0683184	+	0.997664i	$0.478237\pi$
$350$	0.153905	−	0.356213i	0.00822656	−	0.0190404i
$351$			1.98311i			0.105851i
$352$	−1.27917			−0.0681801
$353$	−13.6812			−0.728176			−0.364088	−	0.931365i	$-0.618619\pi$
$353$	−13.6812			−0.728176			−0.364088	+	0.931365i	$0.618619\pi$
$354$	−14.3874			−0.764683
$355$	−15.6926	−	3.24509i	−0.832875	−	0.172231i
$356$			15.4591i			0.819330i
$357$	−0.174630			−0.00924241
$358$			6.40760i			0.338652i
$359$	19.9763			1.05431			0.527155	−	0.849769i	$-0.323259\pi$
$359$	19.9763			1.05431			0.527155	+	0.849769i	$0.323259\pi$
$360$	−2.18974	−	0.452819i	−0.115409	−	0.0238657i
$361$	12.0273			0.633017
$362$	−3.85705			−0.202722
$363$		−	9.36372i		−	0.491468i
$364$		−	0.153905i		−	0.00806681i
$365$	−4.23686	+	20.4886i	−0.221767	+	1.07242i
$366$	9.19685			0.480727
$367$			1.86971i			0.0975979i	0.998809	+	0.0487989i	$0.0155394\pi$
$367$			1.86971i			0.0975979i	−0.998809	+	0.0487989i	$0.984461\pi$
$368$	−7.25003			−0.377934
$369$	11.0078			0.573043
$370$	12.3739	−	5.64676i	0.643290	−	0.293561i
$371$	0.370870			0.0192546
$372$	6.55496			0.339859
$373$			24.2947i			1.25793i	0.777433	+	0.628966i	$0.216522\pi$
$373$			24.2947i			1.25793i	−0.777433	+	0.628966i	$0.783478\pi$
$374$	−2.87834			−0.148836
$375$	6.42090	−	9.15271i	0.331574	−	0.472644i
$376$			8.23049i			0.424455i
$377$			10.8290i			0.557720i
$378$	−0.0776078			−0.00399171
$379$	1.89291			0.0972323			0.0486162	−	0.998818i	$-0.484519\pi$
$379$	1.89291			0.0972323			0.0486162	+	0.998818i	$0.484519\pi$
$380$	1.19571	−	5.78219i	0.0613385	−	0.296620i
$381$	2.70247			0.138452
$382$		−	25.6111i		−	1.31038i
$383$	−7.93791			−0.405608			−0.202804	−	0.979219i	$-0.565005\pi$
$383$	−7.93791			−0.405608			−0.202804	+	0.979219i	$0.565005\pi$
$384$		−	1.00000i		−	0.0510310i
$385$	0.0449530	−	0.217383i	0.00229102	−	0.0110789i
$386$	−4.02227			−0.204728
$387$	−7.27593			−0.369856
$388$	11.8098			0.599552
$389$			0.462232i			0.0234361i	0.999931	+	0.0117181i	$0.00373006\pi$
$389$			0.462232i			0.0234361i	−0.999931	+	0.0117181i	$0.996270\pi$
$390$	0.897991	−	4.34250i	0.0454715	−	0.219891i
$391$	−16.3137			−0.825021
$392$	−6.99398			−0.353249
$393$	−5.39614			−0.272199
$394$			19.2606i			0.970335i
$395$	−7.23145	+	34.9698i	−0.363854	+	1.75952i
$396$	−1.27917			−0.0642808
$397$			22.9030i			1.14947i	0.818340	+	0.574735i	$0.194895\pi$
$397$			22.9030i			1.14947i	−0.818340	+	0.574735i	$0.805105\pi$
$398$		−	2.79567i		−	0.140134i
$399$		−	0.204930i		−	0.0102593i
$400$	4.58991	+	1.98311i	0.229495	+	0.0991556i
$401$		−	12.9347i		−	0.645930i	−0.946411	−	0.322965i	$-0.895320\pi$
$401$		−	12.9347i		−	0.645930i	0.946411	−	0.322965i	$-0.104680\pi$
$402$	2.98662			0.148959
$403$			12.9992i			0.647537i
$404$	4.83089			0.240346
$405$	−2.18974	−	0.452819i	−0.108809	−	0.0225008i
$406$	−0.423785			−0.0210321
$407$	6.27784	−	4.59685i	0.311181	−	0.227857i
$408$		−	2.25016i		−	0.111400i
$409$		−	8.06217i		−	0.398649i	−0.979934	−	0.199324i	$-0.936125\pi$
$409$		−	8.06217i		−	0.398649i	0.979934	−	0.199324i	$-0.0638747\pi$
$410$	−24.1042	−	4.98455i	−1.19042	−	0.246169i
$411$	16.2666			0.802373
$412$	−1.95876			−0.0965010
$413$	1.11658			0.0549431
$414$	−7.25003			−0.356319
$415$	1.47363	−	7.12619i	0.0723379	−	0.349811i
$416$	1.98311			0.0972300
$417$		−	9.45724i		−	0.463123i
$418$		−	3.37776i		−	0.165212i
$419$	16.4216			0.802246			0.401123	−	0.916024i	$-0.368620\pi$
$419$	16.4216			0.802246			0.401123	+	0.916024i	$0.368620\pi$
$420$	0.169941	+	0.0351423i	0.00829226	+	0.00171477i
$421$		−	37.3516i		−	1.82041i	−0.414160	−	0.910204i	$-0.635925\pi$
$421$		−	37.3516i		−	1.82041i	0.414160	−	0.910204i	$-0.364075\pi$
$422$	10.9853			0.534754
$423$			8.23049i			0.400180i
$424$			4.77877i			0.232077i
$425$	10.3280	+	4.46232i	0.500984	+	0.216454i
$426$		−	7.16641i		−	0.347214i
$427$	−0.713747			−0.0345407
$428$		−	6.65385i		−	0.321626i
$429$		−	2.53674i		−	0.122475i
$430$	15.9324	+	3.29468i	0.768328	+	0.158884i
$431$		−	2.67378i		−	0.128792i	−0.997924	−	0.0643958i	$-0.979488\pi$
$431$		−	2.67378i		−	0.128792i	0.997924	−	0.0643958i	$-0.0205120\pi$
$432$		−	1.00000i		−	0.0481125i
$433$		−	29.3358i		−	1.40979i	−0.709313	−	0.704894i	$-0.750995\pi$
$433$		−	29.3358i		−	1.40979i	0.709313	−	0.704894i	$-0.249005\pi$
$434$	−0.508716			−0.0244191
$435$	−11.9573	−	2.47266i	−0.573307	−	0.118555i
$436$		−	9.84106i		−	0.471301i
$437$		−	19.1443i		−	0.915796i
$438$	−9.35662			−0.447077
$439$		−	0.994324i		−	0.0474565i	−0.999718	−	0.0237283i	$-0.992446\pi$
$439$		−	0.994324i		−	0.0474565i	0.999718	−	0.0237283i	$-0.00755365\pi$
$440$	2.80105	+	0.579233i	0.133535	+	0.0276139i
$441$	−6.99398			−0.333047
$442$	4.46232			0.212251
$443$		−	0.819642i		−	0.0389424i	−0.999810	−	0.0194712i	$-0.993802\pi$
$443$		−	0.819642i		−	0.0389424i	0.999810	−	0.0194712i	$-0.00619826\pi$
$444$	3.59362	+	4.90774i	0.170545	+	0.232911i
$445$	7.00017	−	33.8514i	0.331840	−	1.60471i
$446$		−	24.5095i		−	1.16056i
$447$			13.0047i			0.615103i
$448$			0.0776078i			0.00366662i
$449$		−	30.8073i		−	1.45389i	−0.686698	−	0.726943i	$-0.740941\pi$
$449$		−	30.8073i		−	1.45389i	0.686698	−	0.726943i	$-0.259059\pi$
$450$	4.58991	+	1.98311i	0.216370	+	0.0934848i
$451$	−14.0809			−0.663042
$452$	9.75081			0.458640
$453$		−	20.0623i		−	0.942607i
$454$	2.42240			0.113689
$455$	−0.0696911	+	0.337012i	−0.00326717	+	0.0157993i
$456$	2.64058			0.123657
$457$	−1.07040			−0.0500712			−0.0250356	−	0.999687i	$-0.507970\pi$
$457$	−1.07040			−0.0500712			−0.0250356	+	0.999687i	$0.507970\pi$
$458$	−8.80804			−0.411573
$459$		−	2.25016i		−	0.105029i
$460$	15.8757	+	3.28295i	0.740207	+	0.153068i
$461$		−	0.147990i		−	0.00689260i	−0.999994	−	0.00344630i	$-0.998903\pi$
$461$		−	0.147990i		−	0.00689260i	0.999994	−	0.00344630i	$-0.00109699\pi$
$462$	0.0992737			0.00461863
$463$	−21.1572			−0.983259			−0.491630	−	0.870804i	$-0.663599\pi$
$463$	−21.1572			−0.983259			−0.491630	+	0.870804i	$0.663599\pi$
$464$		−	5.46060i		−	0.253502i
$465$	−14.3536	−	2.96821i	−0.665634	−	0.137647i
$466$		−	12.0227i		−	0.556943i
$467$	1.39603			0.0646006			0.0323003	−	0.999478i	$-0.489717\pi$
$467$	1.39603			0.0646006			0.0323003	+	0.999478i	$0.489717\pi$
$468$	1.98311			0.0916694
$469$	−0.231785			−0.0107028
$470$	3.72693	−	18.0226i	0.171910	−	0.831322i
$471$	13.6476			0.628849
$472$			14.3874i			0.662235i
$473$	9.30716			0.427944
$474$	−15.9698			−0.733519
$475$	−5.23657	+	12.1200i	−0.240270	+	0.556106i
$476$			0.174630i			0.00800416i
$477$			4.77877i			0.218805i
$478$		−	15.0286i		−	0.687394i
$479$		−	2.07964i		−	0.0950213i	−0.998871	−	0.0475107i	$-0.984871\pi$
$479$		−	2.07964i		−	0.0950213i	0.998871	−	0.0475107i	$-0.0151288\pi$
$480$	−0.452819	+	2.18974i	−0.0206683	+	0.0999474i
$481$	−9.73260	+	7.12654i	−0.443768	+	0.324942i
$482$			5.51284i			0.251103i
$483$	0.562659			0.0256019
$484$	−9.36372			−0.425624
$485$	−25.8604	−	5.34770i	−1.17426	−	0.242827i
$486$		−	1.00000i		−	0.0453609i
$487$	−12.2739			−0.556182			−0.278091	−	0.960555i	$-0.589702\pi$
$487$	−12.2739			−0.556182			−0.278091	+	0.960555i	$0.589702\pi$
$488$		−	9.19685i		−	0.416322i
$489$		−	11.4118i		−	0.516059i
$490$	15.3150	+	3.16701i	0.691860	+	0.143071i
$491$	29.0395			1.31054			0.655268	−	0.755396i	$-0.272556\pi$
$491$	29.0395			1.31054			0.655268	+	0.755396i	$0.272556\pi$
$492$		−	11.0078i		−	0.496270i
$493$		−	12.2872i		−	0.553389i
$494$			5.23657i			0.235605i
$495$	2.80105	+	0.579233i	0.125898	+	0.0260346i
$496$		−	6.55496i		−	0.294326i
$497$			0.556169i			0.0249476i
$498$	3.25435			0.145831
$499$		−	15.4820i		−	0.693071i	−0.938037	−	0.346535i	$-0.887358\pi$
$499$		−	15.4820i		−	0.693071i	0.938037	−	0.346535i	$-0.112642\pi$
$500$	−9.15271	−	6.42090i	−0.409322	−	0.287151i
$501$		−	4.10105i		−	0.183221i
$502$		−	21.6293i		−	0.965363i
$503$	22.4782			1.00225			0.501126	−	0.865374i	$-0.332919\pi$
$503$	22.4782			1.00225			0.501126	+	0.865374i	$0.332919\pi$
$504$			0.0776078i			0.00345693i
$505$	−10.5784	−	2.18752i	−0.470732	−	0.0973433i
$506$	9.27403			0.412281
$507$		−	9.06727i		−	0.402692i
$508$		−	2.70247i		−	0.119903i
$509$	−0.125147			−0.00554705			−0.00277353	−	0.999996i	$-0.500883\pi$
$509$	−0.125147			−0.00554705			−0.00277353	+	0.999996i	$0.500883\pi$
$510$	−1.01892	+	4.92727i	−0.0451184	+	0.218183i
$511$	0.726147			0.0321229
$512$	−1.00000			−0.0441942
$513$	2.64058			0.116585
$514$	13.3229			0.587649
$515$	4.28916	+	0.886962i	0.189003	+	0.0390842i
$516$			7.27593i			0.320305i
$517$		−	10.5282i		−	0.463030i
$518$	−0.278893	−	0.380879i	−0.0122538	−	0.0167349i
$519$	23.3129			1.02332
$520$	−4.34250	−	0.897991i	−0.190431	−	0.0393795i
$521$	34.4666			1.51001			0.755005	−	0.655719i	$-0.227634\pi$
$521$	34.4666			1.51001			0.755005	+	0.655719i	$0.227634\pi$
$522$		−	5.46060i		−	0.239004i
$523$	−9.05888			−0.396117			−0.198059	−	0.980190i	$-0.563464\pi$
$523$	−9.05888			−0.396117			−0.198059	+	0.980190i	$0.563464\pi$
$524$			5.39614i			0.235731i
$525$	−0.356213	−	0.153905i	−0.0155464	−	0.00671696i
$526$		−	30.7985i		−	1.34288i
$527$		−	14.7497i		−	0.642508i
$528$			1.27917i			0.0556688i
$529$	29.5629			1.28534
$530$	2.16392	−	10.4643i	0.0939946	−	0.454538i
$531$			14.3874i			0.624361i
$532$	−0.204930			−0.00888484
$533$	21.8297			0.945550
$534$	15.4591			0.668980
$535$	−3.01299	+	14.5702i	−0.130263	+	0.629924i
$536$		−	2.98662i		−	0.129002i
$537$	6.40760			0.276508
$538$	20.6738			0.891311
$539$	8.94649			0.385353
$540$	−0.452819	+	2.18974i	−0.0194862	+	0.0942313i
$541$		−	22.5014i		−	0.967411i	−0.875231	−	0.483706i	$-0.839290\pi$
$541$		−	22.5014i		−	0.967411i	0.875231	−	0.483706i	$-0.160710\pi$
$542$	23.4840			1.00872
$543$			3.85705i			0.165522i
$544$	−2.25016			−0.0964749
$545$	−4.45622	+	21.5493i	−0.190884	+	0.923073i
$546$	−0.153905			−0.00658652
$547$	16.0103			0.684553			0.342277	−	0.939599i	$-0.388802\pi$
$547$	16.0103			0.684553			0.342277	+	0.939599i	$0.388802\pi$
$548$		−	16.2666i		−	0.694876i
$549$		−	9.19685i		−	0.392512i
$550$	−5.87128	−	2.53674i	−0.250352	−	0.108167i
$551$	14.4192			0.614277
$552$			7.25003i			0.308582i
$553$	1.23938			0.0527040
$554$	−28.7324			−1.22072
$555$	−5.64676	−	12.3739i	−0.239692	−	0.525244i
$556$	−9.45724			−0.401076
$557$	−10.5535			−0.447166			−0.223583	−	0.974685i	$-0.571775\pi$
$557$	−10.5535			−0.447166			−0.223583	+	0.974685i	$0.571775\pi$
$558$		−	6.55496i		−	0.277493i
$559$	−14.4290			−0.610281
$560$	0.0351423	−	0.169941i	0.00148503	−	0.00718131i
$561$			2.87834i			0.121524i
$562$		−	15.5947i		−	0.657822i
$563$	−6.57346			−0.277038			−0.138519	−	0.990360i	$-0.544234\pi$
$563$	−6.57346			−0.277038			−0.138519	+	0.990360i	$0.544234\pi$
$564$	8.23049			0.346566
$565$	−21.3517	−	4.41536i	−0.898274	−	0.185755i
$566$	2.55738			0.107495
$567$			0.0776078i			0.00325922i
$568$	−7.16641			−0.300696
$569$		−	11.5117i		−	0.482596i	−0.970451	−	0.241298i	$-0.922427\pi$
$569$		−	11.5117i		−	0.482596i	0.970451	−	0.241298i	$-0.0775732\pi$
$570$	−5.78219	−	1.19571i	−0.242189	−	0.0500827i
$571$	−31.3522			−1.31205			−0.656024	−	0.754740i	$-0.727763\pi$
$571$	−31.3522			−1.31205			−0.656024	+	0.754740i	$0.727763\pi$
$572$	−2.53674			−0.106066
$573$	−25.6111			−1.06992
$574$			0.854292i			0.0356574i
$575$	−33.2770	−	14.3776i	−1.38775	−	0.599588i
$576$	−1.00000			−0.0416667
$577$	20.1926			0.840631			0.420315	−	0.907378i	$-0.361919\pi$
$577$	20.1926			0.840631			0.420315	+	0.907378i	$0.361919\pi$
$578$	11.9368			0.496504
$579$			4.02227i			0.167160i
$580$	−2.47266	+	11.9573i	−0.102672	+	0.496499i
$581$	−0.252563			−0.0104781
$582$		−	11.8098i		−	0.489532i
$583$		−	6.11286i		−	0.253169i
$584$			9.35662i			0.387180i
$585$	−4.34250	−	0.897991i	−0.179540	−	0.0371274i
$586$		−	7.65067i		−	0.316046i
$587$	4.44134			0.183314			0.0916569	−	0.995791i	$-0.470784\pi$
$587$	4.44134			0.183314			0.0916569	+	0.995791i	$0.470784\pi$
$588$			6.99398i			0.288427i
$589$	17.3089			0.713201
$590$	6.51490	−	31.5047i	0.268214	−	1.29703i
$591$	19.2606			0.792275
$592$	4.90774	−	3.59362i	0.201707	−	0.147697i
$593$			11.1163i			0.456490i	0.973604	+	0.228245i	$0.0732988\pi$
$593$			11.1163i			0.456490i	−0.973604	+	0.228245i	$0.926701\pi$
$594$			1.27917i			0.0524850i
$595$	0.0790759	−	0.382394i	0.00324180	−	0.0156766i
$596$	13.0047			0.532695
$597$	−2.79567			−0.114419
$598$	−14.3776			−0.587944
$599$	−25.1544			−1.02778			−0.513890	−	0.857856i	$-0.671796\pi$
$599$	−25.1544			−1.02778			−0.513890	+	0.857856i	$0.671796\pi$
$600$	1.98311	−	4.58991i	0.0809602	−	0.187382i
$601$	−11.0884			−0.452305			−0.226153	−	0.974092i	$-0.572615\pi$
$601$	−11.0884			−0.452305			−0.226153	+	0.974092i	$0.572615\pi$
$602$		−	0.564669i		−	0.0230142i
$603$		−	2.98662i		−	0.121625i
$604$	−20.0623			−0.816322
$605$	20.5041	+	4.24007i	0.833610	+	0.172383i
$606$		−	4.83089i		−	0.196241i
$607$	−14.0598			−0.570671			−0.285335	−	0.958428i	$-0.592105\pi$
$607$	−14.0598			−0.570671			−0.285335	+	0.958428i	$0.592105\pi$
$608$		−	2.64058i		−	0.107090i
$609$			0.423785i			0.0171726i
$610$	−4.16451	+	20.1387i	−0.168616	+	0.815392i
$611$			16.3220i			0.660317i
$612$	−2.25016			−0.0909574
$613$		−	14.0624i		−	0.567976i	−0.958828	−	0.283988i	$-0.908342\pi$
$613$		−	14.0624i		−	0.567976i	0.958828	−	0.283988i	$-0.0916576\pi$
$614$			13.0160i			0.525281i
$615$	−4.98455	+	24.1042i	−0.200996	+	0.971976i
$616$		−	0.0992737i		−	0.00399985i
$617$			14.2596i			0.574070i	0.957920	+	0.287035i	$0.0926696\pi$
$617$			14.2596i			0.574070i	−0.957920	+	0.287035i	$0.907330\pi$
$618$			1.95876i			0.0787927i
$619$	40.1187			1.61251			0.806253	−	0.591570i	$-0.201492\pi$
$619$	40.1187			1.61251			0.806253	+	0.591570i	$0.201492\pi$
$620$	−2.96821	+	14.3536i	−0.119206	+	0.576456i
$621$			7.25003i			0.290934i
$622$			15.0099i			0.601842i
$623$	−1.19975			−0.0480668
$624$		−	1.98311i		−	0.0793880i
$625$	17.1345	+	18.2046i	0.685381	+	0.728184i
$626$	8.80419			0.351886
$627$	−3.37776			−0.134895
$628$		−	13.6476i		−	0.544599i
$629$	11.0432	−	8.08622i	0.440322	−	0.322419i
$630$	0.0351423	−	0.169941i	0.00140010	−	0.00677060i
$631$		−	19.0339i		−	0.757729i	−0.925452	−	0.378864i	$-0.876315\pi$
$631$		−	19.0339i		−	0.757729i	0.925452	−	0.378864i	$-0.123685\pi$
$632$			15.9698i			0.635246i
$633$		−	10.9853i		−	0.436625i
$634$			5.64539i			0.224207i
$635$	−1.22373	+	5.91770i	−0.0485623	+	0.234837i
$636$	4.77877			0.189490
$637$	−13.8698			−0.549543
$638$			6.98504i			0.276540i
$639$	−7.16641			−0.283499
$640$	2.18974	+	0.452819i	0.0865570	+	0.0178993i
$641$	15.3038			0.604464			0.302232	−	0.953234i	$-0.402268\pi$
$641$	15.3038			0.604464			0.302232	+	0.953234i	$0.402268\pi$
$642$	−6.65385			−0.262607
$643$	−23.3867			−0.922280			−0.461140	−	0.887327i	$-0.652559\pi$
$643$	−23.3867			−0.922280			−0.461140	+	0.887327i	$0.652559\pi$
$644$		−	0.562659i		−	0.0221719i
$645$	3.29468	−	15.9324i	0.129728	−	0.627337i
$646$		−	5.94174i		−	0.233775i
$647$	−45.5560			−1.79099			−0.895496	−	0.445070i	$-0.853179\pi$
$647$	−45.5560			−1.79099			−0.895496	+	0.445070i	$0.853179\pi$
$648$	−1.00000			−0.0392837
$649$		−	18.4040i		−	0.722419i
$650$	9.10230	+	3.93273i	0.357022	+	0.154254i
$651$			0.508716i			0.0199381i
$652$	−11.4118			−0.446920
$653$	38.5093			1.50698			0.753492	−	0.657457i	$-0.228368\pi$
$653$	38.5093			1.50698			0.753492	+	0.657457i	$0.228368\pi$
$654$	−9.84106			−0.384816
$655$	2.44348	−	11.8161i	0.0954745	−	0.461695i
$656$	−11.0078			−0.429783
$657$			9.35662i			0.365037i
$658$	−0.638750			−0.0249011
$659$	8.09522			0.315345			0.157673	−	0.987491i	$-0.449601\pi$
$659$	8.09522			0.315345			0.157673	+	0.987491i	$0.449601\pi$
$660$	0.579233	−	2.80105i	0.0225466	−	0.109031i
$661$		−	12.0946i		−	0.470426i	−0.971944	−	0.235213i	$-0.924421\pi$
$661$		−	12.0946i		−	0.470426i	0.971944	−	0.235213i	$-0.0755789\pi$
$662$			20.9369i			0.813736i
$663$		−	4.46232i		−	0.173302i
$664$		−	3.25435i		−	0.126293i
$665$	0.448743	+	0.0927962i	0.0174015	+	0.00359848i
$666$	4.90774	−	3.59362i	0.190171	−	0.139250i
$667$			39.5895i			1.53291i
$668$	−4.10105			−0.158674
$669$	−24.5095			−0.947592
$670$	−1.35240	+	6.53992i	−0.0522478	+	0.252659i
$671$			11.7643i			0.454158i
$672$	0.0776078			0.00299379
$673$			21.9799i			0.847261i	0.905835	+	0.423630i	$0.139244\pi$
$673$			21.9799i			0.847261i	−0.905835	+	0.423630i	$0.860756\pi$
$674$		−	9.66677i		−	0.372350i
$675$	1.98311	−	4.58991i	0.0763300	−	0.176666i
$676$	−9.06727			−0.348741
$677$		−	3.40801i		−	0.130980i	−0.997853	−	0.0654902i	$-0.979139\pi$
$677$		−	3.40801i		−	0.130980i	0.997853	−	0.0654902i	$-0.0208611\pi$
$678$		−	9.75081i		−	0.374478i
$679$			0.916532i			0.0351733i
$680$	4.92727	+	1.01892i	0.188952	+	0.0390737i
$681$		−	2.42240i		−	0.0928265i
$682$			8.38491i			0.321075i
$683$	51.8359			1.98344			0.991722	−	0.128401i	$-0.0409845\pi$
$683$	51.8359			1.98344			0.991722	+	0.128401i	$0.0409845\pi$
$684$		−	2.64058i		−	0.100965i
$685$	−7.36584	+	35.6196i	−0.281434	+	1.36096i
$686$		−	1.08604i		−	0.0414653i
$687$			8.80804i			0.336048i
$688$	7.27593			0.277392
$689$			9.47683i			0.361038i
$690$	3.28295	−	15.8757i	0.124980	−	0.604376i
$691$	−14.5439			−0.553276			−0.276638	−	0.960974i	$-0.589220\pi$
$691$	−14.5439			−0.553276			−0.276638	+	0.960974i	$0.589220\pi$
$692$		−	23.3129i		−	0.886223i
$693$		−	0.0992737i		−	0.00377109i
$694$	−1.94022			−0.0736498
$695$	20.7089	+	4.28242i	0.785533	+	0.162441i
$696$	−5.46060			−0.206983
$697$	−24.7694			−0.938206
$698$	−2.55258			−0.0966167
$699$	−12.0227			−0.454742
$700$	−0.153905	+	0.356213i	−0.00581706	+	0.0134636i
$701$		−	38.9594i		−	1.47148i	−0.677266	−	0.735738i	$-0.736835\pi$
$701$		−	38.9594i		−	1.47148i	0.677266	−	0.735738i	$-0.263165\pi$
$702$		−	1.98311i		−	0.0748477i
$703$	9.48925	+	12.9593i	0.357894	+	0.488769i
$704$	1.27917			0.0482106
$705$	−18.0226	−	3.72693i	−0.678771	−	0.140364i
$706$	13.6812			0.514898
$707$			0.374915i			0.0141001i
$708$	14.3874			0.540712
$709$			45.0682i			1.69257i	0.532730	+	0.846285i	$0.321166\pi$
$709$			45.0682i			1.69257i	−0.532730	+	0.846285i	$0.678834\pi$
$710$	15.6926	+	3.24509i	0.588931	+	0.121786i
$711$			15.9698i			0.598916i
$712$		−	15.4591i		−	0.579354i
$713$			47.5236i			1.77977i
$714$	0.174630			0.00653537
$715$	5.55480	+	1.14868i	0.207738	+	0.0429584i
$716$		−	6.40760i		−	0.239463i
$717$	−15.0286			−0.561255
$718$	−19.9763			−0.745510
$719$	−23.6652			−0.882561			−0.441281	−	0.897369i	$-0.645476\pi$
$719$	−23.6652			−0.882561			−0.441281	+	0.897369i	$0.645476\pi$
$720$	2.18974	+	0.452819i	0.0816067	+	0.0168756i
$721$		−	0.152015i		−	0.00566132i
$722$	−12.0273			−0.447610
$723$	5.51284			0.205025
$724$	3.85705			0.143346
$725$	10.8290	−	25.0636i	0.402178	−	0.930840i
$726$			9.36372i			0.347520i
$727$	−22.6866			−0.841398			−0.420699	−	0.907200i	$-0.638215\pi$
$727$	−22.6866			−0.841398			−0.420699	+	0.907200i	$0.638215\pi$
$728$			0.153905i			0.00570410i
$729$	−1.00000			−0.0370370
$730$	4.23686	−	20.4886i	0.156813	−	0.758316i
$731$	16.3720			0.605541
$732$	−9.19685			−0.339925
$733$		−	43.3855i		−	1.60248i	−0.598344	−	0.801239i	$-0.704174\pi$
$733$		−	43.3855i		−	1.60248i	0.598344	−	0.801239i	$-0.295826\pi$
$734$		−	1.86971i		−	0.0690121i
$735$	3.16701	−	15.3150i	0.116817	−	0.564902i
$736$	7.25003			0.267240
$737$			3.82040i			0.140726i
$738$	−11.0078			−0.405203
$739$	25.2371			0.928361			0.464181	−	0.885741i	$-0.346349\pi$
$739$	25.2371			0.928361			0.464181	+	0.885741i	$0.346349\pi$
$740$	−12.3739	+	5.64676i	−0.454875	+	0.207579i
$741$	5.23657			0.192370
$742$	−0.370870			−0.0136151
$743$			42.8658i			1.57259i	0.617850	+	0.786296i	$0.288004\pi$
$743$			42.8658i			1.57259i	−0.617850	+	0.786296i	$0.711996\pi$
$744$	−6.55496			−0.240316
$745$	−28.4770	−	5.88880i	−1.04332	−	0.215749i
$746$		−	24.2947i		−	0.889493i
$747$		−	3.25435i		−	0.119071i
$748$	2.87834			0.105243
$749$	0.516391			0.0188685
$750$	−6.42090	+	9.15271i	−0.234458	+	0.334210i
$751$	20.8231			0.759846			0.379923	−	0.925018i	$-0.375951\pi$
$751$	20.8231			0.759846			0.379923	+	0.925018i	$0.375951\pi$
$752$		−	8.23049i		−	0.300135i
$753$	−21.6293			−0.788216
$754$		−	10.8290i		−	0.394368i
$755$	43.9311	+	9.08458i	1.59882	+	0.330622i
$756$	0.0776078			0.00282257
$757$	24.9115			0.905425			0.452712	−	0.891657i	$-0.350456\pi$
$757$	24.9115			0.905425			0.452712	+	0.891657i	$0.350456\pi$
$758$	−1.89291			−0.0687536
$759$		−	9.27403i		−	0.336626i
$760$	−1.19571	+	5.78219i	−0.0433729	+	0.209742i
$761$	−3.17711			−0.115170			−0.0575850	−	0.998341i	$-0.518340\pi$
$761$	−3.17711			−0.115170			−0.0575850	+	0.998341i	$0.518340\pi$
$762$	−2.70247			−0.0979002
$763$	0.763743			0.0276494
$764$			25.6111i			0.926576i
$765$	4.92727	+	1.01892i	0.178146	+	0.0368390i
$766$	7.93791			0.286808
$767$			28.5319i			1.03023i
$768$			1.00000i			0.0360844i
$769$			35.5177i			1.28080i	0.768041	+	0.640400i	$0.221232\pi$
$769$			35.5177i			1.28080i	−0.768041	+	0.640400i	$0.778768\pi$
$770$	−0.0449530	+	0.217383i	−0.00161999	+	0.00783395i
$771$		−	13.3229i		−	0.479814i
$772$	4.02227			0.144765
$773$			14.8679i			0.534760i	0.963591	+	0.267380i	$0.0861580\pi$
$773$			14.8679i			0.534760i	−0.963591	+	0.267380i	$0.913842\pi$
$774$	7.27593			0.261528
$775$	12.9992	−	30.0867i	0.466945	−	1.08074i
$776$	−11.8098			−0.423947
$777$	−0.380879	+	0.278893i	−0.0136640	+	0.0100052i
$778$		−	0.462232i		−	0.0165718i
$779$		−	29.0670i		−	1.04143i
$780$	−0.897991	+	4.34250i	−0.0321532	+	0.155486i
$781$	9.16706			0.328023
$782$	16.3137			0.583378
$783$	−5.46060			−0.195146
$784$	6.99398			0.249785
$785$	−6.17990	+	29.8847i	−0.220570	+	1.06663i
$786$	5.39614			0.192474
$787$			21.1009i			0.752166i	0.926586	+	0.376083i	$0.122729\pi$
$787$			21.1009i			0.752166i	−0.926586	+	0.376083i	$0.877271\pi$
$788$		−	19.2606i		−	0.686130i
$789$	−30.7985			−1.09646
$790$	7.23145	−	34.9698i	0.257283	−	1.24417i
$791$			0.756739i			0.0269065i
$792$	1.27917			0.0454534
$793$		−	18.2384i		−	0.647664i
$794$		−	22.9030i		−	0.812798i
$795$	−10.4643	−	2.16392i	−0.371129	−	0.0767463i
$796$			2.79567i			0.0990899i
$797$	31.3634			1.11095			0.555474	−	0.831534i	$-0.312537\pi$
$797$	31.3634			1.11095			0.555474	+	0.831534i	$0.312537\pi$
$798$			0.204930i			0.00725444i
$799$		−	18.5199i		−	0.655189i
$800$	−4.58991	−	1.98311i	−0.162278	−	0.0701136i
$801$		−	15.4591i		−	0.546220i
$802$			12.9347i			0.456741i
$803$		−	11.9687i		−	0.422367i
$804$	−2.98662			−0.105330
$805$	−0.254783	+	1.23208i	−0.00897991	+	0.0434250i
$806$		−	12.9992i		−	0.457878i
$807$		−	20.6738i		−	0.727752i
$808$	−4.83089			−0.169950
$809$		−	42.7342i		−	1.50246i	−0.660043	−	0.751228i	$-0.729462\pi$
$809$		−	42.7342i		−	1.50246i	0.660043	−	0.751228i	$-0.270538\pi$
$810$	2.18974	+	0.452819i	0.0769396	+	0.0159104i
$811$	−13.6985			−0.481021			−0.240510	−	0.970647i	$-0.577315\pi$
$811$	−13.6985			−0.481021			−0.240510	+	0.970647i	$0.577315\pi$
$812$	0.423785			0.0148719
$813$		−	23.4840i		−	0.823620i
$814$	−6.27784	+	4.59685i	−0.220038	+	0.161120i
$815$	24.9888	+	5.16747i	0.875320	+	0.181009i
$816$			2.25016i			0.0787714i
$817$			19.2127i			0.672167i
$818$			8.06217i			0.281887i
$819$			0.153905i			0.00537787i
$820$	24.1042	+	4.98455i	0.841756	+	0.174068i
$821$	29.9356			1.04476			0.522381	−	0.852713i	$-0.325044\pi$
$821$	29.9356			1.04476			0.522381	+	0.852713i	$0.325044\pi$
$822$	−16.2666			−0.567364
$823$		−	40.4728i		−	1.41079i	−0.708812	−	0.705397i	$-0.750769\pi$
$823$		−	40.4728i		−	1.41079i	0.708812	−	0.705397i	$-0.249231\pi$
$824$	1.95876			0.0682365
$825$	−2.53674	+	5.87128i	−0.0883179	+	0.204412i
$826$	−1.11658			−0.0388506
$827$	−16.9793			−0.590429			−0.295214	−	0.955431i	$-0.595391\pi$
$827$	−16.9793			−0.590429			−0.295214	+	0.955431i	$0.595391\pi$
$828$	7.25003			0.251956
$829$			34.0642i			1.18310i	0.806269	+	0.591550i	$0.201484\pi$
$829$			34.0642i			1.18310i	−0.806269	+	0.591550i	$0.798516\pi$
$830$	−1.47363	+	7.12619i	−0.0511506	+	0.247354i
$831$			28.7324i			0.996715i
$832$	−1.98311			−0.0687520
$833$	15.7376			0.545275
$834$			9.45724i			0.327477i
$835$	8.98022	+	1.85703i	0.310773	+	0.0642653i
$836$			3.37776i			0.116822i
$837$	−6.55496			−0.226572
$838$	−16.4216			−0.567273
$839$	49.4631			1.70765			0.853827	−	0.520557i	$-0.174276\pi$
$839$	49.4631			1.70765			0.853827	+	0.520557i	$0.174276\pi$
$840$	−0.169941	−	0.0351423i	−0.00586351	−	0.00121252i
$841$	−0.818099			−0.0282103
$842$			37.3516i			1.28722i
$843$	−15.5947			−0.537109
$844$	−10.9853			−0.378128
$845$	19.8549	+	4.10583i	0.683031	+	0.141245i
$846$		−	8.23049i		−	0.282970i
$847$		−	0.726698i		−	0.0249696i
$848$		−	4.77877i		−	0.164104i
$849$		−	2.55738i		−	0.0877691i
$850$	−10.3280	−	4.46232i	−0.354249	−	0.153056i
$851$	−35.5813	+	26.0538i	−1.21971	+	0.893113i
$852$			7.16641i			0.245517i
$853$	12.9302			0.442722			0.221361	−	0.975192i	$-0.428950\pi$
$853$	12.9302			0.442722			0.221361	+	0.975192i	$0.428950\pi$
$854$	0.713747			0.0244239
$855$	−1.19571	+	5.78219i	−0.0408923	+	0.197747i
$856$			6.65385i			0.227424i
$857$	32.7843			1.11989			0.559945	−	0.828530i	$-0.310822\pi$
$857$	32.7843			1.11989			0.559945	+	0.828530i	$0.310822\pi$
$858$			2.53674i			0.0866029i
$859$		−	2.14358i		−	0.0731380i	−0.999331	−	0.0365690i	$-0.988357\pi$
$859$		−	2.14358i		−	0.0731380i	0.999331	−	0.0365690i	$-0.0116429\pi$
$860$	−15.9324	−	3.29468i	−0.543290	−	0.112348i
$861$	0.854292			0.0291142
$862$			2.67378i			0.0910695i
$863$		−	2.01272i		−	0.0685139i	−0.999413	−	0.0342570i	$-0.989094\pi$
$863$		−	2.01272i		−	0.0685139i	0.999413	−	0.0342570i	$-0.0109065\pi$
$864$			1.00000i			0.0340207i
$865$	−10.5565	+	51.0491i	−0.358933	+	1.73572i
$866$			29.3358i			0.996871i
$867$		−	11.9368i		−	0.405394i
$868$	0.508716			0.0172669
$869$		−	20.4282i		−	0.692978i
$870$	11.9573	+	2.47266i	0.405390	+	0.0838311i
$871$		−	5.92280i		−	0.200687i
$872$			9.84106i			0.333260i
$873$	−11.8098			−0.399701
$874$			19.1443i			0.647566i
$875$	0.498312	−	0.710322i	0.0168460	−	0.0240133i
$876$	9.35662			0.316131
$877$		−	54.9922i		−	1.85696i	−0.371387	−	0.928478i	$-0.621118\pi$
$877$		−	54.9922i		−	1.85696i	0.371387	−	0.928478i	$-0.378882\pi$
$878$			0.994324i			0.0335568i
$879$	−7.65067			−0.258051
$880$	−2.80105	−	0.579233i	−0.0944234	−	0.0195260i
$881$	−50.9762			−1.71743			−0.858716	−	0.512451i	$-0.828737\pi$
$881$	−50.9762			−1.71743			−0.858716	+	0.512451i	$0.828737\pi$
$882$	6.99398			0.235499
$883$	−33.5813			−1.13010			−0.565050	−	0.825057i	$-0.691143\pi$
$883$	−33.5813			−1.13010			−0.565050	+	0.825057i	$0.691143\pi$
$884$	−4.46232			−0.150084
$885$	−31.5047	−	6.51490i	−1.05902	−	0.218996i
$886$			0.819642i			0.0275364i
$887$			25.0279i			0.840356i	0.907442	+	0.420178i	$0.138032\pi$
$887$			25.0279i			0.840356i	−0.907442	+	0.420178i	$0.861968\pi$
$888$	−3.59362	−	4.90774i	−0.120594	−	0.164693i
$889$	0.209733			0.00703421
$890$	−7.00017	+	33.8514i	−0.234646	+	1.13470i
$891$	1.27917			0.0428539
$892$			24.5095i			0.820639i
$893$	21.7333			0.727277
$894$		−	13.0047i		−	0.434944i
$895$	−2.90149	+	14.0310i	−0.0969860	+	0.469004i
$896$		−	0.0776078i		−	0.00259269i
$897$			14.3776i			0.480055i
$898$			30.8073i			1.02805i
$899$	−35.7940			−1.19380
$900$	−4.58991	−	1.98311i	−0.152997	−	0.0661037i
$901$		−	10.7530i		−	0.358234i
$902$	14.0809			0.468842
$903$	−0.564669			−0.0187910
$904$	−9.75081			−0.324307
$905$	−8.44593	−	1.74655i	−0.280752	−	0.0580572i
$906$			20.0623i			0.666524i
$907$	−2.13539			−0.0709046			−0.0354523	−	0.999371i	$-0.511287\pi$
$907$	−2.13539			−0.0709046			−0.0354523	+	0.999371i	$0.511287\pi$
$908$	−2.42240			−0.0803901
$909$	−4.83089			−0.160230
$910$	0.0696911	−	0.337012i	0.00231024	−	0.0111718i
$911$			7.74791i			0.256700i	0.991729	+	0.128350i	$0.0409680\pi$
$911$			7.74791i			0.256700i	−0.991729	+	0.128350i	$0.959032\pi$
$912$	−2.64058			−0.0874385
$913$			4.16288i			0.137771i
$914$	1.07040			0.0354057
$915$	20.1387	+	4.16451i	0.665765	+	0.137674i
$916$	8.80804			0.291026
$917$	−0.418782			−0.0138294
$918$			2.25016i			0.0742664i
$919$		−	41.9124i		−	1.38256i	−0.722587	−	0.691281i	$-0.757047\pi$
$919$		−	41.9124i		−	1.38256i	0.722587	−	0.691281i	$-0.242953\pi$
$920$	−15.8757	−	3.28295i	−0.523405	−	0.108236i
$921$	13.0160			0.428890
$922$			0.147990i			0.00487380i
$923$	−14.2118			−0.467787
$924$	−0.0992737			−0.00326586
$925$	29.6526	−	6.76178i	0.974972	−	0.222326i
$926$	21.1572			0.695269
$927$	1.95876			0.0643340
$928$			5.46060i			0.179253i
$929$	−21.7007			−0.711976			−0.355988	−	0.934491i	$-0.615856\pi$
$929$	−21.7007			−0.711976			−0.355988	+	0.934491i	$0.615856\pi$
$930$	14.3536	+	2.96821i	0.470674	+	0.0973315i
$931$			18.4682i			0.605270i
$932$			12.0227i			0.393818i
$933$	15.0099			0.491402
$934$	−1.39603			−0.0456795
$935$	−6.30282	−	1.30337i	−0.206124	−	0.0426247i
$936$	−1.98311			−0.0648200
$937$		−	4.02508i		−	0.131493i	−0.997836	−	0.0657467i	$-0.979057\pi$
$937$		−	4.02508i		−	0.131493i	0.997836	−	0.0657467i	$-0.0209429\pi$
$938$	0.231785			0.00756805
$939$		−	8.80419i		−	0.287314i
$940$	−3.72693	+	18.0226i	−0.121559	+	0.587833i
$941$	−13.4127			−0.437241			−0.218621	−	0.975810i	$-0.570156\pi$
$941$	−13.4127			−0.437241			−0.218621	+	0.975810i	$0.570156\pi$
$942$	−13.6476			−0.444663
$943$	79.8069			2.59887
$944$		−	14.3874i		−	0.468271i
$945$	−0.169941	−	0.0351423i	−0.00552817	−	0.00114318i
$946$	−9.30716			−0.302602
$947$	−24.3967			−0.792787			−0.396394	−	0.918081i	$-0.629738\pi$
$947$	−24.3967			−0.792787			−0.396394	+	0.918081i	$0.629738\pi$
$948$	15.9698			0.518676
$949$			18.5552i			0.602328i
$950$	5.23657	−	12.1200i	0.169897	−	0.393226i
$951$	5.64539			0.183064
$952$		−	0.174630i		−	0.00565980i
$953$			32.7060i			1.05945i	0.848169	+	0.529726i	$0.177705\pi$
$953$			32.7060i			1.05945i	−0.848169	+	0.529726i	$0.822295\pi$
$954$		−	4.77877i		−	0.154718i
$955$	11.5972	−	56.0815i	0.375276	−	1.81476i
$956$			15.0286i			0.486061i
$957$	6.98504			0.225794
$958$			2.07964i			0.0671902i
$959$	1.26242			0.0407656
$960$	0.452819	−	2.18974i	0.0146147	−	0.0706735i
$961$	−11.9675			−0.386047
$962$	9.73260	−	7.12654i	0.313792	−	0.229769i
$963$			6.65385i			0.214417i
$964$		−	5.51284i		−	0.177557i
$965$	−8.80772	−	1.82136i	−0.283531	−	0.0586317i
$966$	−0.562659			−0.0181032
$967$	−56.7828			−1.82601			−0.913007	−	0.407945i	$-0.866246\pi$
$967$	−56.7828			−1.82601			−0.913007	+	0.407945i	$0.866246\pi$
$968$	9.36372			0.300961
$969$	−5.94174			−0.190876
$970$	25.8604	+	5.34770i	0.830326	+	0.171704i
$971$	30.2461			0.970643			0.485322	−	0.874336i	$-0.338703\pi$
$971$	30.2461			0.970643			0.485322	+	0.874336i	$0.338703\pi$
$972$			1.00000i			0.0320750i
$973$		−	0.733955i		−	0.0235295i
$974$	12.2739			0.393280
$975$	3.93273	−	9.10230i	0.125948	−	0.291507i
$976$			9.19685i			0.294384i
$977$	−46.3851			−1.48399			−0.741995	−	0.670405i	$-0.766120\pi$
$977$	−46.3851			−1.48399			−0.741995	+	0.670405i	$0.766120\pi$
$978$			11.4118i			0.364909i
$979$			19.7748i			0.632006i
$980$	−15.3150	−	3.16701i	−0.489219	−	0.101166i
$981$			9.84106i			0.314201i
$982$	−29.0395			−0.926689
$983$		−	54.1766i		−	1.72796i	−0.503522	−	0.863982i	$-0.667963\pi$
$983$		−	54.1766i		−	1.72796i	0.503522	−	0.863982i	$-0.332037\pi$
$984$			11.0078i			0.350916i
$985$	−8.72157	+	42.1757i	−0.277892	+	1.34383i
$986$			12.2872i			0.391305i
$987$			0.638750i			0.0203317i
$988$		−	5.23657i		−	0.166598i
$989$	−52.7507			−1.67737
$990$	−2.80105	−	0.579233i	−0.0890232	−	0.0184092i
$991$			30.8994i			0.981552i	0.871286	+	0.490776i	$0.163287\pi$
$991$			30.8994i			0.981552i	−0.871286	+	0.490776i	$0.836713\pi$
$992$			6.55496i			0.208120i
$993$	20.9369			0.664413
$994$		−	0.556169i		−	0.0176406i
$995$	1.26593	−	6.12179i	0.0401328	−	0.194074i
$996$	−3.25435			−0.103118
$997$	20.5403			0.650519			0.325260	−	0.945625i	$-0.394548\pi$
$997$	20.5403			0.650519			0.325260	+	0.945625i	$0.394548\pi$
$998$			15.4820i			0.490075i
$999$	−3.59362	−	4.90774i	−0.113697	−	0.155274i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1110.2.e.c.739.10	yes	16
3.2	odd	2		3330.2.e.f.739.14		16
5.4	even	2		1110.2.e.d.739.7	yes	16
15.14	odd	2		3330.2.e.e.739.4		16
37.36	even	2		1110.2.e.d.739.15	yes	16
111.110	odd	2		3330.2.e.e.739.3		16
185.184	even	2	inner	1110.2.e.c.739.2	✓	16
555.554	odd	2		3330.2.e.f.739.13		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1110.2.e.c.739.2	✓	16	185.184	even	2	inner
1110.2.e.c.739.10	yes	16	1.1	even	1	trivial
1110.2.e.d.739.7	yes	16	5.4	even	2
1110.2.e.d.739.15	yes	16	37.36	even	2
3330.2.e.e.739.3		16	111.110	odd	2
3330.2.e.e.739.4		16	15.14	odd	2
3330.2.e.f.739.13		16	555.554	odd	2
3330.2.e.f.739.14		16	3.2	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.00000i q^{3} +1.00000 q^{4} +(-2.18974 - 0.452819i) q^{5} -1.00000i q^{6} +0.0776078i q^{7} -1.00000 q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +1.00000i q^{3} +1.00000 q^{4} +(-2.18974 - 0.452819i) q^{5} -1.00000i q^{6} +0.0776078i q^{7} -1.00000 q^{8} -1.00000 q^{9} +(2.18974 + 0.452819i) q^{10} +1.27917 q^{11} +1.00000i q^{12} -1.98311 q^{13} -0.0776078i q^{14} +(0.452819 - 2.18974i) q^{15} +1.00000 q^{16} +2.25016 q^{17} +1.00000 q^{18} +2.64058i q^{19} +(-2.18974 - 0.452819i) q^{20} -0.0776078 q^{21} -1.27917 q^{22} -7.25003 q^{23} -1.00000i q^{24} +(4.58991 + 1.98311i) q^{25} +1.98311 q^{26} -1.00000i q^{27} +0.0776078i q^{28} -5.46060i q^{29} +(-0.452819 + 2.18974i) q^{30} -6.55496i q^{31} -1.00000 q^{32} +1.27917i q^{33} -2.25016 q^{34} +(0.0351423 - 0.169941i) q^{35} -1.00000 q^{36} +(4.90774 - 3.59362i) q^{37} -2.64058i q^{38} -1.98311i q^{39} +(2.18974 + 0.452819i) q^{40} -11.0078 q^{41} +0.0776078 q^{42} +7.27593 q^{43} +1.27917 q^{44} +(2.18974 + 0.452819i) q^{45} +7.25003 q^{46} -8.23049i q^{47} +1.00000i q^{48} +6.99398 q^{49} +(-4.58991 - 1.98311i) q^{50} +2.25016i q^{51} -1.98311 q^{52} -4.77877i q^{53} +1.00000i q^{54} +(-2.80105 - 0.579233i) q^{55} -0.0776078i q^{56} -2.64058 q^{57} +5.46060i q^{58} -14.3874i q^{59} +(0.452819 - 2.18974i) q^{60} +9.19685i q^{61} +6.55496i q^{62} -0.0776078i q^{63} +1.00000 q^{64} +(4.34250 + 0.897991i) q^{65} -1.27917i q^{66} +2.98662i q^{67} +2.25016 q^{68} -7.25003i q^{69} +(-0.0351423 + 0.169941i) q^{70} +7.16641 q^{71} +1.00000 q^{72} -9.35662i q^{73} +(-4.90774 + 3.59362i) q^{74} +(-1.98311 + 4.58991i) q^{75} +2.64058i q^{76} +0.0992737i q^{77} +1.98311i q^{78} -15.9698i q^{79} +(-2.18974 - 0.452819i) q^{80} +1.00000 q^{81} +11.0078 q^{82} +3.25435i q^{83} -0.0776078 q^{84} +(-4.92727 - 1.01892i) q^{85} -7.27593 q^{86} +5.46060 q^{87} -1.27917 q^{88} +15.4591i q^{89} +(-2.18974 - 0.452819i) q^{90} -0.153905i q^{91} -7.25003 q^{92} +6.55496 q^{93} +8.23049i q^{94} +(1.19571 - 5.78219i) q^{95} -1.00000i q^{96} +11.8098 q^{97} -6.99398 q^{98} -1.27917 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 16 q^{2} + 16 q^{4} - 2 q^{5} - 16 q^{8} - 16 q^{9}+O(q^{10}) \) 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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Representations

Groups

Database

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