LMFDB - Embedded newform 1110.2.u.f.191.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1110,2,Mod(191,1110)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1110, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 0, 3]))

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

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

chi := DirichletCharacter("1110.191");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1110 = 2 \cdot 3 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1110.u (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$8.86339462436$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$20$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			191.20
Character	$\chi$	$=$	1110.191
Dual form			1110.2.u.f.401.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 + 0.707107i) q^{2} +(0.407565 + 1.68342i) q^{3} +1.00000i q^{4} +(-0.707107 + 0.707107i) q^{5} +(-0.902163 + 1.47855i) q^{6} +2.94059 q^{7} +(-0.707107 + 0.707107i) q^{8} +(-2.66778 + 1.37220i) q^{9} +O(q^{10})$	\(q+(0.707107 + 0.707107i) q^{2} +(0.407565 + 1.68342i) q^{3} +1.00000i q^{4} +(-0.707107 + 0.707107i) q^{5} +(-0.902163 + 1.47855i) q^{6} +2.94059 q^{7} +(-0.707107 + 0.707107i) q^{8} +(-2.66778 + 1.37220i) q^{9} -1.00000 q^{10} +5.04186 q^{11} +(-1.68342 + 0.407565i) q^{12} +(2.73495 + 2.73495i) q^{13} +(2.07931 + 2.07931i) q^{14} +(-1.47855 - 0.902163i) q^{15} -1.00000 q^{16} +(5.09995 - 5.09995i) q^{17} +(-2.85670 - 0.916111i) q^{18} +(2.15857 + 2.15857i) q^{19} +(-0.707107 - 0.707107i) q^{20} +(1.19848 + 4.95024i) q^{21} +(3.56513 + 3.56513i) q^{22} +(-3.53316 + 3.53316i) q^{23} +(-1.47855 - 0.902163i) q^{24} -1.00000i q^{25} +3.86781i q^{26} +(-3.39729 - 3.93172i) q^{27} +2.94059i q^{28} +(-4.90114 - 4.90114i) q^{29} +(-0.407565 - 1.68342i) q^{30} +(-4.78496 + 4.78496i) q^{31} +(-0.707107 - 0.707107i) q^{32} +(2.05489 + 8.48754i) q^{33} +7.21242 q^{34} +(-2.07931 + 2.07931i) q^{35} +(-1.37220 - 2.66778i) q^{36} +(-5.76694 - 1.93453i) q^{37} +3.05268i q^{38} +(-3.48939 + 5.71874i) q^{39} -1.00000i q^{40} -5.08085 q^{41} +(-2.65289 + 4.34780i) q^{42} +(-1.16646 - 1.16646i) q^{43} +5.04186i q^{44} +(0.916111 - 2.85670i) q^{45} -4.99664 q^{46} -6.36311i q^{47} +(-0.407565 - 1.68342i) q^{48} +1.64707 q^{49} +(0.707107 - 0.707107i) q^{50} +(10.6639 + 6.50678i) q^{51} +(-2.73495 + 2.73495i) q^{52} -3.67782i q^{53} +(0.377904 - 5.18239i) q^{54} +(-3.56513 + 3.56513i) q^{55} +(-2.07931 + 2.07931i) q^{56} +(-2.75401 + 4.51353i) q^{57} -6.93126i q^{58} +(6.34723 - 6.34723i) q^{59} +(0.902163 - 1.47855i) q^{60} +(3.36135 - 3.36135i) q^{61} -6.76696 q^{62} +(-7.84485 + 4.03509i) q^{63} -1.00000i q^{64} -3.86781 q^{65} +(-4.54858 + 7.45462i) q^{66} +11.8418i q^{67} +(5.09995 + 5.09995i) q^{68} +(-7.38777 - 4.50778i) q^{69} -2.94059 q^{70} -6.94832i q^{71} +(0.916111 - 2.85670i) q^{72} -8.41023i q^{73} +(-2.70992 - 5.44576i) q^{74} +(1.68342 - 0.407565i) q^{75} +(-2.15857 + 2.15857i) q^{76} +14.8260 q^{77} +(-6.51113 + 1.57638i) q^{78} +(10.3416 + 10.3416i) q^{79} +(0.707107 - 0.707107i) q^{80} +(5.23411 - 7.32148i) q^{81} +(-3.59270 - 3.59270i) q^{82} -4.78277i q^{83} +(-4.95024 + 1.19848i) q^{84} +7.21242i q^{85} -1.64962i q^{86} +(6.25312 - 10.2482i) q^{87} +(-3.56513 + 3.56513i) q^{88} +(2.54048 + 2.54048i) q^{89} +(2.66778 - 1.37220i) q^{90} +(8.04238 + 8.04238i) q^{91} +(-3.53316 - 3.53316i) q^{92} +(-10.0053 - 6.10490i) q^{93} +(4.49940 - 4.49940i) q^{94} -3.05268 q^{95} +(0.902163 - 1.47855i) q^{96} +(-9.97547 - 9.97547i) q^{97} +(1.16465 + 1.16465i) q^{98} +(-13.4506 + 6.91846i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 24 q^{7} - 8 q^{9}+O(q^{10}) $ 40 * q + 24 * q^7 - 8 * q^9	$ 40 q + 24 q^{7} - 8 q^{9} - 40 q^{10} + 16 q^{13} - 40 q^{16} + 8 q^{18} + 16 q^{19} - 16 q^{22} - 8 q^{31} + 24 q^{33} + 24 q^{34} + 32 q^{37} + 16 q^{39} + 12 q^{42} + 32 q^{43} + 8 q^{45} - 56 q^{46} - 32 q^{49} - 44 q^{51} - 16 q^{52} - 24 q^{54} + 16 q^{55} + 8 q^{57} - 72 q^{61} + 24 q^{63} - 28 q^{66} + 16 q^{69} - 24 q^{70} + 8 q^{72} - 16 q^{76} - 48 q^{79} + 120 q^{81} - 24 q^{82} - 24 q^{84} + 20 q^{87} + 16 q^{88} + 8 q^{90} - 92 q^{93} - 8 q^{94} - 40 q^{97}+O(q^{100}) $ 40 * q + 24 * q^7 - 8 * q^9 - 40 * q^10 + 16 * q^13 - 40 * q^16 + 8 * q^18 + 16 * q^19 - 16 * q^22 - 8 * q^31 + 24 * q^33 + 24 * q^34 + 32 * q^37 + 16 * q^39 + 12 * q^42 + 32 * q^43 + 8 * q^45 - 56 * q^46 - 32 * q^49 - 44 * q^51 - 16 * q^52 - 24 * q^54 + 16 * q^55 + 8 * q^57 - 72 * q^61 + 24 * q^63 - 28 * q^66 + 16 * q^69 - 24 * q^70 + 8 * q^72 - 16 * q^76 - 48 * q^79 + 120 * q^81 - 24 * q^82 - 24 * q^84 + 20 * q^87 + 16 * q^88 + 8 * q^90 - 92 * q^93 - 8 * q^94 - 40 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$371$	$631$	$667$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$	$1$

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 $

$2$	0.707107	+	0.707107i	0.500000	+	0.500000i
$2$	0.707107	+	0.707107i	0.500000	+	0.500000i
$3$	0.407565	+	1.68342i	0.235308	+	0.971921i
$3$	0.407565	+	1.68342i	0.235308	+	0.971921i
$4$			1.00000i			0.500000i
$5$	−0.707107	+	0.707107i	−0.316228	+	0.316228i
$5$	−0.707107	+	0.707107i	−0.316228	+	0.316228i
$6$	−0.902163	+	1.47855i	−0.368306	+	0.603614i
$7$	2.94059			1.11144			0.555719	−	0.831370i	$-0.312443\pi$
$7$	2.94059			1.11144			0.555719	+	0.831370i	$0.312443\pi$
$8$	−0.707107	+	0.707107i	−0.250000	+	0.250000i
$9$	−2.66778	+	1.37220i	−0.889260	+	0.457401i
$10$	−1.00000			−0.316228
$11$	5.04186			1.52018			0.760088	−	0.649820i	$-0.225156\pi$
$11$	5.04186			1.52018			0.760088	+	0.649820i	$0.225156\pi$
$12$	−1.68342	+	0.407565i	−0.485960	+	0.117654i
$13$	2.73495	+	2.73495i	0.758540	+	0.758540i	0.976057	−	0.217517i	$-0.0697957\pi$
$13$	2.73495	+	2.73495i	0.758540	+	0.758540i	−0.217517	+	0.976057i	$0.569796\pi$
$14$	2.07931	+	2.07931i	0.555719	+	0.555719i
$15$	−1.47855	−	0.902163i	−0.381759	−	0.232937i
$16$	−1.00000			−0.250000
$17$	5.09995	−	5.09995i	1.23692	−	1.23692i	0.275666	−	0.961254i	$-0.411102\pi$
$17$	5.09995	−	5.09995i	1.23692	−	1.23692i	0.961254	−	0.275666i	$-0.0888983\pi$
$18$	−2.85670	−	0.916111i	−0.673331	−	0.215929i
$19$	2.15857	+	2.15857i	0.495210	+	0.495210i	0.909943	−	0.414733i	$-0.136125\pi$
$19$	2.15857	+	2.15857i	0.495210	+	0.495210i	−0.414733	+	0.909943i	$0.636125\pi$
$20$	−0.707107	−	0.707107i	−0.158114	−	0.158114i
$21$	1.19848	+	4.95024i	0.261530	+	1.08023i
$22$	3.56513	+	3.56513i	0.760088	+	0.760088i
$23$	−3.53316	+	3.53316i	−0.736714	+	0.736714i	−0.971941	−	0.235227i	$-0.924417\pi$
$23$	−3.53316	+	3.53316i	−0.736714	+	0.736714i	0.235227	+	0.971941i	$0.424417\pi$
$24$	−1.47855	−	0.902163i	−0.301807	−	0.184153i
$25$		−	1.00000i		−	0.200000i
$26$			3.86781i			0.758540i
$27$	−3.39729	−	3.93172i	−0.653808	−	0.756661i
$28$			2.94059i			0.555719i
$29$	−4.90114	−	4.90114i	−0.910119	−	0.910119i	0.0861625	−	0.996281i	$-0.472540\pi$
$29$	−4.90114	−	4.90114i	−0.910119	−	0.910119i	−0.996281	+	0.0861625i	$0.972540\pi$
$30$	−0.407565	−	1.68342i	−0.0744109	−	0.307348i
$31$	−4.78496	+	4.78496i	−0.859405	+	0.859405i	−0.991268	−	0.131863i	$-0.957904\pi$
$31$	−4.78496	+	4.78496i	−0.859405	+	0.859405i	0.131863	+	0.991268i	$0.457904\pi$
$32$	−0.707107	−	0.707107i	−0.125000	−	0.125000i
$33$	2.05489	+	8.48754i	0.357710	+	1.47749i
$34$	7.21242			1.23692
$35$	−2.07931	+	2.07931i	−0.351468	+	0.351468i
$36$	−1.37220	−	2.66778i	−0.228701	−	0.444630i
$37$	−5.76694	−	1.93453i	−0.948079	−	0.318035i
$37$	−5.76694	−	1.93453i	−0.948079	−	0.318035i
$38$			3.05268i			0.495210i
$39$	−3.48939	+	5.71874i	−0.558750	+	0.915731i
$40$		−	1.00000i		−	0.158114i
$41$	−5.08085			−0.793495			−0.396748	−	0.917928i	$-0.629861\pi$
$41$	−5.08085			−0.793495			−0.396748	+	0.917928i	$0.629861\pi$
$42$	−2.65289	+	4.34780i	−0.409350	+	0.670880i
$43$	−1.16646	−	1.16646i	−0.177884	−	0.177884i	0.612549	−	0.790433i	$-0.290144\pi$
$43$	−1.16646	−	1.16646i	−0.177884	−	0.177884i	−0.790433	+	0.612549i	$0.790144\pi$
$44$			5.04186i			0.760088i
$45$	0.916111	−	2.85670i	0.136566	−	0.425852i
$46$	−4.99664			−0.736714
$47$		−	6.36311i		−	0.928155i	−0.885795	−	0.464077i	$-0.846386\pi$
$47$		−	6.36311i		−	0.928155i	0.885795	−	0.464077i	$-0.153614\pi$
$48$	−0.407565	−	1.68342i	−0.0588270	−	0.242980i
$49$	1.64707			0.235295
$50$	0.707107	−	0.707107i	0.100000	−	0.100000i
$51$	10.6639	+	6.50678i	1.49324	+	0.911131i
$52$	−2.73495	+	2.73495i	−0.379270	+	0.379270i
$53$		−	3.67782i		−	0.505187i	−0.967572	−	0.252594i	$-0.918716\pi$
$53$		−	3.67782i		−	0.505187i	0.967572	−	0.252594i	$-0.0812836\pi$
$54$	0.377904	−	5.18239i	0.0514263	−	0.705234i
$55$	−3.56513	+	3.56513i	−0.480722	+	0.480722i
$56$	−2.07931	+	2.07931i	−0.277860	+	0.277860i
$57$	−2.75401	+	4.51353i	−0.364778	+	0.597831i
$58$		−	6.93126i		−	0.910119i
$59$	6.34723	−	6.34723i	0.826338	−	0.826338i	−0.160670	−	0.987008i	$-0.551365\pi$
$59$	6.34723	−	6.34723i	0.826338	−	0.826338i	0.987008	+	0.160670i	$0.0513654\pi$
$60$	0.902163	−	1.47855i	0.116469	−	0.190880i
$61$	3.36135	−	3.36135i	0.430376	−	0.430376i	−0.458380	−	0.888756i	$-0.651570\pi$
$61$	3.36135	−	3.36135i	0.430376	−	0.430376i	0.888756	+	0.458380i	$0.151570\pi$
$62$	−6.76696			−0.859405
$63$	−7.84485	+	4.03509i	−0.988358	+	0.508374i
$64$		−	1.00000i		−	0.125000i
$65$	−3.86781			−0.479743
$66$	−4.54858	+	7.45462i	−0.559891	+	0.917601i
$67$			11.8418i			1.44670i	0.690481	+	0.723350i	$0.257399\pi$
$67$			11.8418i			1.44670i	−0.690481	+	0.723350i	$0.742601\pi$
$68$	5.09995	+	5.09995i	0.618460	+	0.618460i
$69$	−7.38777	−	4.50778i	−0.889382	−	0.542673i
$70$	−2.94059			−0.351468
$71$		−	6.94832i		−	0.824613i	−0.911045	−	0.412307i	$-0.864723\pi$
$71$		−	6.94832i		−	0.824613i	0.911045	−	0.412307i	$-0.135277\pi$
$72$	0.916111	−	2.85670i	0.107965	−	0.336665i
$73$		−	8.41023i		−	0.984342i	−0.870498	−	0.492171i	$-0.836203\pi$
$73$		−	8.41023i		−	0.984342i	0.870498	−	0.492171i	$-0.163797\pi$
$74$	−2.70992	−	5.44576i	−0.315022	−	0.633057i
$75$	1.68342	−	0.407565i	0.194384	−	0.0470616i
$76$	−2.15857	+	2.15857i	−0.247605	+	0.247605i
$77$	14.8260			1.68958
$78$	−6.51113	+	1.57638i	−0.737240	+	0.178490i
$79$	10.3416	+	10.3416i	1.16352	+	1.16352i	0.983699	+	0.179824i	$0.0575530\pi$
$79$	10.3416	+	10.3416i	1.16352	+	1.16352i	0.179824	+	0.983699i	$0.442447\pi$
$80$	0.707107	−	0.707107i	0.0790569	−	0.0790569i
$81$	5.23411	−	7.32148i	0.581568	−	0.813498i
$82$	−3.59270	−	3.59270i	−0.396748	−	0.396748i
$83$		−	4.78277i		−	0.524977i	−0.964935	−	0.262488i	$-0.915457\pi$
$83$		−	4.78277i		−	0.524977i	0.964935	−	0.262488i	$-0.0845431\pi$
$84$	−4.95024	+	1.19848i	−0.540115	+	0.130765i
$85$			7.21242i			0.782297i
$86$		−	1.64962i		−	0.177884i
$87$	6.25312	−	10.2482i	0.670405	−	1.09872i
$88$	−3.56513	+	3.56513i	−0.380044	+	0.380044i
$89$	2.54048	+	2.54048i	0.269290	+	0.269290i	0.828814	−	0.559524i	$-0.189016\pi$
$89$	2.54048	+	2.54048i	0.269290	+	0.269290i	−0.559524	+	0.828814i	$0.689016\pi$
$90$	2.66778	−	1.37220i	0.281209	−	0.144643i
$91$	8.04238	+	8.04238i	0.843070	+	0.843070i
$92$	−3.53316	−	3.53316i	−0.368357	−	0.368357i
$93$	−10.0053	−	6.10490i	−1.03750	−	0.633049i
$94$	4.49940	−	4.49940i	0.464077	−	0.464077i
$95$	−3.05268			−0.313198
$96$	0.902163	−	1.47855i	0.0920766	−	0.150904i
$97$	−9.97547	−	9.97547i	−1.01286	−	1.01286i	−0.999916	−	0.0129388i	$-0.995881\pi$
$97$	−9.97547	−	9.97547i	−1.01286	−	1.01286i	−0.0129388	−	0.999916i	$-0.504119\pi$
$98$	1.16465	+	1.16465i	0.117648	+	0.117648i
$99$	−13.4506	+	6.91846i	−1.35183	+	0.695331i
$100$	1.00000			0.100000
$101$	−6.77892			−0.674528			−0.337264	−	0.941410i	$-0.609501\pi$
$101$	−6.77892			−0.674528			−0.337264	+	0.941410i	$0.609501\pi$
$102$	2.93953	+	12.1415i	0.291057	+	1.20219i
$103$	−12.2231	+	12.2231i	−1.20438	+	1.20438i	−0.231556	+	0.972822i	$0.574382\pi$
$103$	−12.2231	+	12.2231i	−1.20438	+	1.20438i	−0.972822	+	0.231556i	$0.925618\pi$
$104$	−3.86781			−0.379270
$105$	−4.34780	−	2.65289i	−0.424302	−	0.258896i
$106$	2.60061	−	2.60061i	0.252594	−	0.252594i
$107$		−	5.25370i		−	0.507894i	−0.967218	−	0.253947i	$-0.918271\pi$
$107$		−	5.25370i		−	0.507894i	0.967218	−	0.253947i	$-0.0817289\pi$
$108$	3.93172	−	3.39729i	0.378330	−	0.326904i
$109$	3.81502	+	3.81502i	0.365413	+	0.365413i	0.865801	−	0.500388i	$-0.166809\pi$
$109$	3.81502	+	3.81502i	0.365413	+	0.365413i	−0.500388	+	0.865801i	$0.666809\pi$
$110$	−5.04186			−0.480722
$111$	0.906215	−	10.4966i	0.0860141	−	0.996294i
$112$	−2.94059			−0.277860
$113$	10.1862	+	10.1862i	0.958236	+	0.958236i	0.999162	−	0.0409259i	$-0.0130307\pi$
$113$	10.1862	+	10.1862i	0.958236	+	0.958236i	−0.0409259	+	0.999162i	$0.513031\pi$
$114$	−5.13893	+	1.24417i	−0.481305	+	0.116527i
$115$		−	4.99664i		−	0.465939i
$116$	4.90114	−	4.90114i	0.455059	−	0.455059i
$117$	−11.0492	−	3.54334i	−1.02150	−	0.327582i
$118$	8.97633			0.826338
$119$	14.9969	−	14.9969i	1.37476	−	1.37476i
$120$	1.68342	−	0.407565i	0.153674	−	0.0372055i
$121$	14.4203			1.31094
$122$	4.75366			0.430376
$123$	−2.07078	−	8.55319i	−0.186716	−	0.771215i
$124$	−4.78496	−	4.78496i	−0.429702	−	0.429702i
$125$	0.707107	+	0.707107i	0.0632456	+	0.0632456i
$126$	−8.40039	−	2.69391i	−0.748366	−	0.239992i
$127$	−2.94575			−0.261393			−0.130696	−	0.991422i	$-0.541721\pi$
$127$	−2.94575			−0.261393			−0.130696	+	0.991422i	$0.541721\pi$
$128$	0.707107	−	0.707107i	0.0625000	−	0.0625000i
$129$	1.48823	−	2.43905i	0.131031	−	0.214746i
$130$	−2.73495	−	2.73495i	−0.239871	−	0.239871i
$131$	8.10221	+	8.10221i	0.707893	+	0.707893i	0.966092	−	0.258198i	$-0.0831289\pi$
$131$	8.10221	+	8.10221i	0.707893	+	0.707893i	−0.258198	+	0.966092i	$0.583129\pi$
$132$	−8.48754	+	2.05489i	−0.738746	+	0.178855i
$133$	6.34747	+	6.34747i	0.550395	+	0.550395i
$134$	−8.37338	+	8.37338i	−0.723350	+	0.723350i
$135$	5.18239	+	0.377904i	0.446029	+	0.0325248i
$136$			7.21242i			0.618460i
$137$			9.24078i			0.789493i	0.918790	+	0.394747i	$0.129168\pi$
$137$			9.24078i			0.789493i	−0.918790	+	0.394747i	$0.870832\pi$
$138$	−2.03646	−	8.41142i	−0.173355	−	0.716028i
$139$		−	1.68616i		−	0.143019i	−0.997440	−	0.0715093i	$-0.977218\pi$
$139$		−	1.68616i		−	0.143019i	0.997440	−	0.0715093i	$-0.0227816\pi$
$140$	−2.07931	−	2.07931i	−0.175734	−	0.175734i
$141$	10.7118	−	2.59338i	0.902093	−	0.218402i
$142$	4.91320	−	4.91320i	0.412307	−	0.412307i
$143$	13.7892	+	13.7892i	1.15311	+	1.15311i
$144$	2.66778	−	1.37220i	0.222315	−	0.114350i
$145$	6.93126			0.575610
$146$	5.94693	−	5.94693i	0.492171	−	0.492171i
$147$	0.671288	+	2.77270i	0.0553669	+	0.228689i
$148$	1.93453	−	5.76694i	0.159017	−	0.474040i
$149$		−	10.7664i		−	0.882014i	−0.897504	−	0.441007i	$-0.854621\pi$
$149$		−	10.7664i		−	0.882014i	0.897504	−	0.441007i	$-0.145379\pi$
$150$	1.47855	+	0.902163i	0.120723	+	0.0736613i
$151$		−	0.235522i		−	0.0191665i	−0.999954	−	0.00958325i	$-0.996950\pi$
$151$		−	0.235522i		−	0.0191665i	0.999954	−	0.00958325i	$-0.00305049\pi$
$152$	−3.05268			−0.247605
$153$	−6.60738	+	20.6037i	−0.534175	+	1.66571i
$154$	10.4836	+	10.4836i	0.844791	+	0.844791i
$155$		−	6.76696i		−	0.543535i
$156$	−5.71874	−	3.48939i	−0.457865	−	0.279375i
$157$	−4.03882			−0.322333			−0.161167	−	0.986927i	$-0.551526\pi$
$157$	−4.03882			−0.322333			−0.161167	+	0.986927i	$0.551526\pi$
$158$			14.6253i			1.16352i
$159$	6.19130	−	1.49895i	0.491002	−	0.118875i
$160$	1.00000			0.0790569
$161$	−10.3896	+	10.3896i	−0.818812	+	0.818812i
$162$	8.87814	−	1.47599i	0.697533	−	0.115965i
$163$	13.2705	−	13.2705i	1.03942	−	1.03942i	0.0402341	−	0.999190i	$-0.487190\pi$
$163$	13.2705	−	13.2705i	1.03942	−	1.03942i	0.999190	−	0.0402341i	$-0.0128104\pi$
$164$		−	5.08085i		−	0.396748i
$165$	−7.45462	−	4.54858i	−0.580342	−	0.354106i
$166$	3.38193	−	3.38193i	0.262488	−	0.262488i
$167$	−4.49594	+	4.49594i	−0.347906	+	0.347906i	−0.859329	−	0.511423i	$-0.829119\pi$
$167$	−4.49594	+	4.49594i	−0.347906	+	0.347906i	0.511423	+	0.859329i	$0.329119\pi$
$168$	−4.34780	−	2.65289i	−0.335440	−	0.204675i
$169$			1.95994i			0.150765i
$170$	−5.09995	+	5.09995i	−0.391148	+	0.391148i
$171$	−8.72059	−	2.79659i	−0.666880	−	0.213861i
$172$	1.16646	−	1.16646i	0.0889418	−	0.0889418i
$173$	−5.43932			−0.413544			−0.206772	−	0.978389i	$-0.566296\pi$
$173$	−5.43932			−0.413544			−0.206772	+	0.978389i	$0.566296\pi$
$174$	11.6682	−	2.82494i	0.884563	−	0.214158i
$175$		−	2.94059i		−	0.222288i
$176$	−5.04186			−0.380044
$177$	13.2719	+	8.09811i	0.997580	+	0.608692i
$178$			3.59278i			0.269290i
$179$	−12.7331	−	12.7331i	−0.951720	−	0.951720i	0.0471669	−	0.998887i	$-0.484981\pi$
$179$	−12.7331	−	12.7331i	−0.951720	−	0.951720i	−0.998887	+	0.0471669i	$0.984981\pi$
$180$	2.85670	+	0.916111i	0.212926	+	0.0682829i
$181$	−7.21334			−0.536164			−0.268082	−	0.963396i	$-0.586390\pi$
$181$	−7.21334			−0.536164			−0.268082	+	0.963396i	$0.586390\pi$
$182$			11.3736i			0.843070i
$183$	7.02851	+	4.28858i	0.519563	+	0.317021i
$184$		−	4.99664i		−	0.368357i
$185$	5.44576	−	2.70992i	0.400380	−	0.199237i
$186$	−2.75798	−	11.3916i	−0.202225	−	0.835273i
$187$	25.7132	−	25.7132i	1.88034	−	1.88034i
$188$	6.36311			0.464077
$189$	−9.99002	−	11.5616i	−0.726667	−	0.840982i
$190$	−2.15857	−	2.15857i	−0.156599	−	0.156599i
$191$	5.75487	−	5.75487i	0.416408	−	0.416408i	−0.467556	−	0.883964i	$-0.654865\pi$
$191$	5.75487	−	5.75487i	0.416408	−	0.416408i	0.883964	+	0.467556i	$0.154865\pi$
$192$	1.68342	−	0.407565i	0.121490	−	0.0294135i
$193$	14.0840	+	14.0840i	1.01379	+	1.01379i	0.999904	+	0.0138841i	$0.00441958\pi$
$193$	14.0840	+	14.0840i	1.01379	+	1.01379i	0.0138841	+	0.999904i	$0.495580\pi$
$194$		−	14.1074i		−	1.01286i
$195$	−1.57638	−	6.51113i	−0.112887	−	0.466272i
$196$			1.64707i			0.117648i
$197$			8.93292i			0.636445i	0.948016	+	0.318222i	$0.103086\pi$
$197$			8.93292i			0.636445i	−0.948016	+	0.318222i	$0.896914\pi$
$198$	−14.4031	−	4.61890i	−1.02358	−	0.328251i
$199$	11.9763	−	11.9763i	0.848977	−	0.848977i	−0.141028	−	0.990006i	$-0.545041\pi$
$199$	11.9763	−	11.9763i	0.848977	−	0.848977i	0.990006	+	0.141028i	$0.0450409\pi$
$200$	0.707107	+	0.707107i	0.0500000	+	0.0500000i
$201$	−19.9346	+	4.82629i	−1.40608	+	0.340420i
$202$	−4.79342	−	4.79342i	−0.337264	−	0.337264i
$203$	−14.4122	−	14.4122i	−1.01154	−	1.01154i
$204$	−6.50678	+	10.6639i	−0.455565	+	0.746622i
$205$	3.59270	−	3.59270i	0.250925	−	0.250925i
$206$	−17.2861			−1.20438
$207$	4.57748	−	14.2739i	0.318157	−	0.992105i
$208$	−2.73495	−	2.73495i	−0.189635	−	0.189635i
$209$	10.8832	+	10.8832i	0.752806	+	0.752806i
$210$	−1.19848	−	4.95024i	−0.0827031	−	0.341599i
$211$	−7.08120			−0.487490			−0.243745	−	0.969839i	$-0.578376\pi$
$211$	−7.08120			−0.487490			−0.243745	+	0.969839i	$0.578376\pi$
$212$	3.67782			0.252594
$213$	11.6969	−	2.83189i	0.801459	−	0.194038i
$214$	3.71492	−	3.71492i	0.253947	−	0.253947i
$215$	1.64962			0.112503
$216$	5.18239	+	0.377904i	0.352617	+	0.0257131i
$217$	−14.0706	+	14.0706i	−0.955175	+	0.955175i
$218$			5.39525i			0.365413i
$219$	14.1579	−	3.42772i	0.956703	−	0.231624i
$220$	−3.56513	−	3.56513i	−0.240361	−	0.240361i
$221$	27.8962			1.87650
$222$	8.06301	−	6.78143i	0.541154	−	0.455140i
$223$	−22.6024			−1.51357			−0.756786	−	0.653663i	$-0.773231\pi$
$223$	−22.6024			−1.51357			−0.756786	+	0.653663i	$0.773231\pi$
$224$	−2.07931	−	2.07931i	−0.138930	−	0.138930i
$225$	1.37220	+	2.66778i	0.0914803	+	0.177852i
$226$			14.4055i			0.958236i
$227$	−7.28245	+	7.28245i	−0.483353	+	0.483353i	−0.906201	−	0.422848i	$-0.861031\pi$
$227$	−7.28245	+	7.28245i	−0.483353	+	0.483353i	0.422848	+	0.906201i	$0.361031\pi$
$228$	−4.51353	−	2.75401i	−0.298916	−	0.182389i
$229$	17.0508			1.12675			0.563376	−	0.826201i	$-0.309502\pi$
$229$	17.0508			1.12675			0.563376	+	0.826201i	$0.309502\pi$
$230$	3.53316	−	3.53316i	0.232969	−	0.232969i
$231$	6.04258	+	24.9584i	0.397572	+	1.64214i
$232$	6.93126			0.455059
$233$	−20.4845			−1.34198			−0.670992	−	0.741465i	$-0.734132\pi$
$233$	−20.4845			−1.34198			−0.670992	+	0.741465i	$0.734132\pi$
$234$	−5.30742	−	10.3185i	−0.346957	−	0.674539i
$235$	4.49940	+	4.49940i	0.293508	+	0.293508i
$236$	6.34723	+	6.34723i	0.413169	+	0.413169i
$237$	−13.1944	+	21.6241i	−0.857066	+	1.40464i
$238$	21.2088			1.37476
$239$	9.56079	−	9.56079i	0.618436	−	0.618436i	−0.326694	−	0.945130i	$-0.605935\pi$
$239$	9.56079	−	9.56079i	0.618436	−	0.618436i	0.945130	+	0.326694i	$0.105935\pi$
$240$	1.47855	+	0.902163i	0.0954398	+	0.0582344i
$241$	11.7075	+	11.7075i	0.754147	+	0.754147i	0.975250	−	0.221103i	$-0.0709657\pi$
$241$	11.7075	+	11.7075i	0.754147	+	0.754147i	−0.221103	+	0.975250i	$0.570966\pi$
$242$	10.1967	+	10.1967i	0.655469	+	0.655469i
$243$	14.4583	+	5.82721i	0.927503	+	0.373815i
$244$	3.36135	+	3.36135i	0.215188	+	0.215188i
$245$	−1.16465	+	1.16465i	−0.0744070	+	0.0744070i
$246$	4.58375	−	7.51228i	0.292250	−	0.478965i
$247$			11.8072i			0.751272i
$248$		−	6.76696i		−	0.429702i
$249$	8.05139	−	1.94929i	0.510236	−	0.123531i
$250$			1.00000i			0.0632456i
$251$	−13.4030	−	13.4030i	−0.845990	−	0.845990i	0.143640	−	0.989630i	$-0.454119\pi$
$251$	−13.4030	−	13.4030i	−0.845990	−	0.845990i	−0.989630	+	0.143640i	$0.954119\pi$
$252$	−4.03509	−	7.84485i	−0.254187	−	0.494179i
$253$	−17.8137	+	17.8137i	−1.11994	+	1.11994i
$254$	−2.08296	−	2.08296i	−0.130696	−	0.130696i
$255$	−12.1415	+	2.93953i	−0.760330	+	0.184081i
$256$	1.00000			0.0625000
$257$	−9.68366	+	9.68366i	−0.604050	+	0.604050i	−0.941385	−	0.337335i	$-0.890475\pi$
$257$	−9.68366	+	9.68366i	−0.604050	+	0.604050i	0.337335	+	0.941385i	$0.390475\pi$
$258$	2.77700	−	0.672330i	0.172889	−	0.0418574i
$259$	−16.9582	−	5.68866i	−1.05373	−	0.353476i
$260$		−	3.86781i		−	0.239871i
$261$	19.8005	+	6.34980i	1.22562	+	0.393043i
$262$			11.4583i			0.707893i
$263$	5.52569			0.340728			0.170364	−	0.985381i	$-0.445506\pi$
$263$	5.52569			0.340728			0.170364	+	0.985381i	$0.445506\pi$
$264$	−7.45462	−	4.54858i	−0.458800	−	0.279945i
$265$	2.60061	+	2.60061i	0.159754	+	0.159754i
$266$			8.97667i			0.550395i
$267$	−3.24127	+	5.31209i	−0.198363	+	0.325095i
$268$	−11.8418			−0.723350
$269$		−	7.47216i		−	0.455586i	−0.973710	−	0.227793i	$-0.926849\pi$
$269$		−	7.47216i		−	0.455586i	0.973710	−	0.227793i	$-0.0731509\pi$
$270$	3.39729	+	3.93172i	0.206752	+	0.239277i
$271$	13.0280			0.791397			0.395698	−	0.918380i	$-0.370503\pi$
$271$	13.0280			0.791397			0.395698	+	0.918380i	$0.370503\pi$
$272$	−5.09995	+	5.09995i	−0.309230	+	0.309230i
$273$	−10.2609	+	16.8165i	−0.621016	+	1.01778i
$274$	−6.53422	+	6.53422i	−0.394747	+	0.394747i
$275$		−	5.04186i		−	0.304035i
$276$	4.50778	−	7.38777i	0.271337	−	0.444691i
$277$	10.6534	−	10.6534i	0.640103	−	0.640103i	−0.310478	−	0.950581i	$-0.600489\pi$
$277$	10.6534	−	10.6534i	0.640103	−	0.640103i	0.950581	+	0.310478i	$0.100489\pi$
$278$	1.19230	−	1.19230i	0.0715093	−	0.0715093i
$279$	6.19929	−	19.3312i	0.371142	−	1.15733i
$280$		−	2.94059i		−	0.175734i
$281$	−4.38187	+	4.38187i	−0.261400	+	0.261400i	−0.825623	−	0.564222i	$-0.809176\pi$
$281$	−4.38187	+	4.38187i	−0.261400	+	0.261400i	0.564222	+	0.825623i	$0.309176\pi$
$282$	9.40816	+	5.74056i	0.560248	+	0.341845i
$283$	22.2583	−	22.2583i	1.32312	−	1.32312i	0.411879	−	0.911238i	$-0.364872\pi$
$283$	22.2583	−	22.2583i	1.32312	−	1.32312i	0.911238	−	0.411879i	$-0.135128\pi$
$284$	6.94832			0.412307
$285$	−1.24417	−	5.13893i	−0.0736980	−	0.304404i
$286$			19.5009i			1.15311i
$287$	−14.9407			−0.881921
$288$	2.85670	+	0.916111i	0.168333	+	0.0539824i
$289$		−	35.0190i		−	2.05994i
$290$	4.90114	+	4.90114i	0.287805	+	0.287805i
$291$	12.7272	−	20.8585i	0.746082	−	1.22275i
$292$	8.41023			0.492171
$293$			31.5604i			1.84378i	0.387455	+	0.921888i	$0.373354\pi$
$293$			31.5604i			1.84378i	−0.387455	+	0.921888i	$0.626646\pi$
$294$	−1.48592	+	2.43527i	−0.0866608	+	0.142028i
$295$			8.97633i			0.522622i
$296$	5.44576	−	2.70992i	0.316528	−	0.157511i
$297$	−17.1286	−	19.8232i	−0.993904	−	1.15026i
$298$	7.61296	−	7.61296i	0.441007	−	0.441007i
$299$	−19.3260			−1.11765
$300$	0.407565	+	1.68342i	0.0235308	+	0.0971921i
$301$	−3.43008	−	3.43008i	−0.197707	−	0.197707i
$302$	0.166539	−	0.166539i	0.00958325	−	0.00958325i
$303$	−2.76285	−	11.4117i	−0.158722	−	0.655588i
$304$	−2.15857	−	2.15857i	−0.123802	−	0.123802i
$305$			4.75366i			0.272194i
$306$	−19.2412	+	9.89691i	−1.09994	+	0.565769i
$307$		−	13.2263i		−	0.754866i	−0.926037	−	0.377433i	$-0.876807\pi$
$307$		−	13.2263i		−	0.754866i	0.926037	−	0.377433i	$-0.123193\pi$
$308$			14.8260i			0.844791i
$309$	−25.5583	−	15.5948i	−1.45396	−	0.887160i
$310$	4.78496	−	4.78496i	0.271768	−	0.271768i
$311$	18.1637	+	18.1637i	1.02997	+	1.02997i	0.999537	+	0.0304335i	$0.00968878\pi$
$311$	18.1637	+	18.1637i	1.02997	+	1.02997i	0.0304335	+	0.999537i	$0.490311\pi$
$312$	−1.57638	−	6.51113i	−0.0892452	−	0.368620i
$313$	3.85608	+	3.85608i	0.217958	+	0.217958i	0.807638	−	0.589679i	$-0.200746\pi$
$313$	3.85608	+	3.85608i	0.217958	+	0.217958i	−0.589679	+	0.807638i	$0.700746\pi$
$314$	−2.85588	−	2.85588i	−0.161167	−	0.161167i
$315$	2.69391	−	8.40039i	0.151784	−	0.473308i
$316$	−10.3416	+	10.3416i	−0.581762	+	0.581762i
$317$	−15.4121			−0.865628			−0.432814	−	0.901483i	$-0.642479\pi$
$317$	−15.4121			−0.865628			−0.432814	+	0.901483i	$0.642479\pi$
$318$	5.43783	+	3.31799i	0.304938	+	0.186064i
$319$	−24.7108	−	24.7108i	−1.38354	−	1.38354i
$320$	0.707107	+	0.707107i	0.0395285	+	0.0395285i
$321$	8.84416	−	2.14122i	0.493633	−	0.119511i
$322$	−14.6931			−0.818812
$323$	22.0172			1.22507
$324$	7.32148	+	5.23411i	0.406749	+	0.290784i
$325$	2.73495	−	2.73495i	0.151708	−	0.151708i
$326$	18.7673			1.03942
$327$	−4.86740	+	7.97714i	−0.269168	+	0.441137i
$328$	3.59270	−	3.59270i	0.198374	−	0.198374i
$329$		−	18.7113i		−	1.03159i
$330$	−2.05489	−	8.48754i	−0.113118	−	0.467224i
$331$	−23.1704	−	23.1704i	−1.27356	−	1.27356i	−0.944207	−	0.329352i	$-0.893170\pi$
$331$	−23.1704	−	23.1704i	−1.27356	−	1.27356i	−0.329352	−	0.944207i	$-0.606830\pi$
$332$	4.78277			0.262488
$333$	18.0395	−	2.75252i	0.988559	−	0.150837i
$334$	−6.35822			−0.347906
$335$	−8.37338	−	8.37338i	−0.457487	−	0.457487i
$336$	−1.19848	−	4.95024i	−0.0653826	−	0.270058i
$337$		−	24.7651i		−	1.34904i	−0.738256	−	0.674521i	$-0.764350\pi$
$337$		−	24.7651i		−	1.34904i	0.738256	−	0.674521i	$-0.235650\pi$
$338$	−1.38589	+	1.38589i	−0.0753823	+	0.0753823i
$339$	−12.9961	+	21.2991i	−0.705849	+	1.15681i
$340$	−7.21242			−0.391148
$341$	−24.1251	+	24.1251i	−1.30645	+	1.30645i
$342$	−4.18890	−	8.14387i	−0.226510	−	0.440370i
$343$	−15.7408			−0.849922
$344$	1.64962			0.0889418
$345$	8.41142	−	2.03646i	0.452856	−	0.109639i
$346$	−3.84618	−	3.84618i	−0.206772	−	0.206772i
$347$	−21.0637	−	21.0637i	−1.13076	−	1.13076i	−0.990051	−	0.140710i	$-0.955061\pi$
$347$	−21.0637	−	21.0637i	−1.13076	−	1.13076i	−0.140710	−	0.990051i	$-0.544939\pi$
$348$	10.2482	+	6.25312i	0.549361	+	0.335203i
$349$	8.99401			0.481438			0.240719	−	0.970595i	$-0.422617\pi$
$349$	8.99401			0.481438			0.240719	+	0.970595i	$0.422617\pi$
$350$	2.07931	−	2.07931i	0.111144	−	0.111144i
$351$	1.46166	−	20.0445i	0.0780177	−	1.06990i
$352$	−3.56513	−	3.56513i	−0.190022	−	0.190022i
$353$	20.7328	+	20.7328i	1.10349	+	1.10349i	0.993986	+	0.109508i	$0.0349276\pi$
$353$	20.7328	+	20.7328i	1.10349	+	1.10349i	0.109508	+	0.993986i	$0.465072\pi$
$354$	3.65844	+	15.1109i	0.194444	+	0.803136i
$355$	4.91320	+	4.91320i	0.260766	+	0.260766i
$356$	−2.54048	+	2.54048i	−0.134645	+	0.134645i
$357$	31.3582	+	19.1338i	1.65965	+	1.01267i
$358$		−	18.0074i		−	0.951720i
$359$		−	16.8615i		−	0.889914i	−0.895552	−	0.444957i	$-0.853219\pi$
$359$		−	16.8615i		−	0.889914i	0.895552	−	0.444957i	$-0.146781\pi$
$360$	1.37220	+	2.66778i	0.0723215	+	0.140604i
$361$		−	9.68116i		−	0.509535i
$362$	−5.10060	−	5.10060i	−0.268082	−	0.268082i
$363$	5.87722	+	24.2754i	0.308474	+	1.27413i
$364$	−8.04238	+	8.04238i	−0.421535	+	0.421535i
$365$	5.94693	+	5.94693i	0.311276	+	0.311276i
$366$	1.93743	+	8.00239i	0.101271	+	0.418292i
$367$	27.0099			1.40991			0.704953	−	0.709254i	$-0.250968\pi$
$367$	27.0099			1.40991			0.704953	+	0.709254i	$0.250968\pi$
$368$	3.53316	−	3.53316i	0.184179	−	0.184179i
$369$	13.5546	−	6.97196i	0.705624	−	0.362946i
$370$	5.76694	+	1.93453i	0.299809	+	0.100571i
$371$		−	10.8150i		−	0.561485i
$372$	6.10490	−	10.0053i	0.316524	−	0.518749i
$373$			13.8202i			0.715583i	0.933802	+	0.357791i	$0.116470\pi$
$373$			13.8202i			0.715583i	−0.933802	+	0.357791i	$0.883530\pi$
$374$	36.3640			1.88034
$375$	−0.902163	+	1.47855i	−0.0465875	+	0.0763519i
$376$	4.49940	+	4.49940i	0.232039	+	0.232039i
$377$		−	26.8088i		−	1.38072i
$378$	1.11126	−	15.2393i	0.0571571	−	0.783824i
$379$	33.0063			1.69542			0.847709	−	0.530462i	$-0.177982\pi$
$379$	33.0063			1.69542			0.847709	+	0.530462i	$0.177982\pi$
$380$		−	3.05268i		−	0.156599i
$381$	−1.20058	−	4.95892i	−0.0615078	−	0.254053i
$382$	8.13862			0.416408
$383$	13.5981	−	13.5981i	0.694829	−	0.694829i	−0.268461	−	0.963290i	$-0.586515\pi$
$383$	13.5981	−	13.5981i	0.694829	−	0.694829i	0.963290	+	0.268461i	$0.0865151\pi$
$384$	1.47855	+	0.902163i	0.0754518	+	0.0460383i
$385$	−10.4836	+	10.4836i	−0.534293	+	0.534293i
$386$			19.9178i			1.01379i
$387$	4.71248	+	1.51124i	0.239549	+	0.0768206i
$388$	9.97547	−	9.97547i	0.506428	−	0.506428i
$389$	−18.9299	+	18.9299i	−0.959785	+	0.959785i	−0.999222	−	0.0394374i	$-0.987443\pi$
$389$	−18.9299	+	18.9299i	−0.959785	+	0.959785i	0.0394374	+	0.999222i	$0.487443\pi$
$390$	3.48939	−	5.71874i	0.176692	−	0.289580i
$391$			36.0378i			1.82251i
$392$	−1.16465	+	1.16465i	−0.0588239	+	0.0588239i
$393$	−10.3372	+	16.9416i	−0.521443	+	0.854589i
$394$	−6.31653	+	6.31653i	−0.318222	+	0.318222i
$395$	−14.6253			−0.735877
$396$	−6.91846	−	13.4506i	−0.347665	−	0.675916i
$397$		−	3.30397i		−	0.165821i	−0.996557	−	0.0829107i	$-0.973578\pi$
$397$		−	3.30397i		−	0.165821i	0.996557	−	0.0829107i	$-0.0264216\pi$
$398$	16.9370			0.848977
$399$	−8.09842	+	13.2724i	−0.405428	+	0.664453i
$400$			1.00000i			0.0500000i
$401$	2.19308	+	2.19308i	0.109517	+	0.109517i	0.759742	−	0.650225i	$-0.225325\pi$
$401$	2.19308	+	2.19308i	0.109517	+	0.109517i	−0.650225	+	0.759742i	$0.725325\pi$
$402$	−17.5086	−	10.6832i	−0.873249	−	0.532829i
$403$	−26.1733			−1.30378
$404$		−	6.77892i		−	0.337264i
$405$	1.47599	+	8.87814i	0.0733427	+	0.441159i
$406$		−	20.3820i		−	1.01154i
$407$	−29.0761	−	9.75362i	−1.44125	−	0.483469i
$408$	−12.1415	+	2.93953i	−0.601094	+	0.145528i
$409$	−3.00244	+	3.00244i	−0.148461	+	0.148461i	−0.777430	−	0.628969i	$-0.783477\pi$
$409$	−3.00244	+	3.00244i	−0.148461	+	0.148461i	0.628969	+	0.777430i	$0.283477\pi$
$410$	5.08085			0.250925
$411$	−15.5561	+	3.76622i	−0.767325	+	0.185774i
$412$	−12.2231	−	12.2231i	−0.602189	−	0.602189i
$413$	18.6646	−	18.6646i	0.918424	−	0.918424i
$414$	13.3299	−	6.85641i	0.655131	−	0.336974i
$415$	3.38193	+	3.38193i	0.166012	+	0.166012i
$416$		−	3.86781i		−	0.189635i
$417$	2.83852	−	0.687222i	0.139003	−	0.0336534i
$418$			15.3912i			0.752806i
$419$		−	0.755205i		−	0.0368942i	−0.999830	−	0.0184471i	$-0.994128\pi$
$419$		−	0.755205i		−	0.0368942i	0.999830	−	0.0184471i	$-0.00587223\pi$
$420$	2.65289	−	4.34780i	0.129448	−	0.212151i
$421$	9.82974	−	9.82974i	0.479072	−	0.479072i	−0.425763	−	0.904835i	$-0.639994\pi$
$421$	9.82974	−	9.82974i	0.479072	−	0.479072i	0.904835	+	0.425763i	$0.139994\pi$
$422$	−5.00716	−	5.00716i	−0.243745	−	0.243745i
$423$	8.73149	+	16.9754i	0.424539	+	0.825371i
$424$	2.60061	+	2.60061i	0.126297	+	0.126297i
$425$	−5.09995	−	5.09995i	−0.247384	−	0.247384i
$426$	10.2734	+	6.26851i	0.497748	+	0.303710i
$427$	9.88434	−	9.88434i	0.478337	−	0.478337i
$428$	5.25370			0.253947
$429$	−17.5930	+	28.8330i	−0.849399	+	1.39207i
$430$	1.16646	+	1.16646i	0.0562517	+	0.0562517i
$431$	−13.5698	−	13.5698i	−0.653634	−	0.653634i	0.300232	−	0.953866i	$-0.402936\pi$
$431$	−13.5698	−	13.5698i	−0.653634	−	0.653634i	−0.953866	+	0.300232i	$0.902936\pi$
$432$	3.39729	+	3.93172i	0.163452	+	0.189165i
$433$	−38.7114			−1.86035			−0.930175	−	0.367117i	$-0.880345\pi$
$433$	−38.7114			−1.86035			−0.930175	+	0.367117i	$0.880345\pi$
$434$	−19.8989			−0.955175
$435$	2.82494	+	11.6682i	0.135445	+	0.559447i
$436$	−3.81502	+	3.81502i	−0.182706	+	0.182706i
$437$	−15.2531			−0.729656
$438$	12.4349	+	7.58739i	0.594163	+	0.362540i
$439$	−15.4857	+	15.4857i	−0.739093	+	0.739093i	−0.972403	−	0.233309i	$-0.925044\pi$
$439$	−15.4857	+	15.4857i	−0.739093	+	0.739093i	0.233309	+	0.972403i	$0.425044\pi$
$440$		−	5.04186i		−	0.240361i
$441$	−4.39402	+	2.26011i	−0.209239	+	0.107624i
$442$	19.7256	+	19.7256i	0.938252	+	0.938252i
$443$	18.6178			0.884560			0.442280	−	0.896877i	$-0.354170\pi$
$443$	18.6178			0.884560			0.442280	+	0.896877i	$0.354170\pi$
$444$	10.4966	+	0.906215i	0.498147	+	0.0430070i
$445$	−3.59278			−0.170314
$446$	−15.9823	−	15.9823i	−0.756786	−	0.756786i
$447$	18.1243	−	4.38799i	0.857248	−	0.207545i
$448$		−	2.94059i		−	0.138930i
$449$	24.6246	−	24.6246i	1.16211	−	1.16211i	0.178093	−	0.984014i	$-0.443007\pi$
$449$	24.6246	−	24.6246i	1.16211	−	1.16211i	0.984014	−	0.178093i	$-0.0569928\pi$
$450$	−0.916111	+	2.85670i	−0.0431859	+	0.134666i
$451$	−25.6169			−1.20625
$452$	−10.1862	+	10.1862i	−0.479118	+	0.479118i
$453$	0.396482	−	0.0959906i	0.0186283	−	0.00451003i
$454$	−10.2989			−0.483353
$455$	−11.3736			−0.533204
$456$	−1.24417	−	5.13893i	−0.0582634	−	0.240652i
$457$	3.74947	+	3.74947i	0.175393	+	0.175393i	0.789344	−	0.613951i	$-0.210421\pi$
$457$	3.74947	+	3.74947i	0.175393	+	0.175393i	−0.613951	+	0.789344i	$0.710421\pi$
$458$	12.0568	+	12.0568i	0.563376	+	0.563376i
$459$	−37.3776	−	2.72560i	−1.74464	−	0.127220i
$460$	4.99664			0.232969
$461$	−10.6793	+	10.6793i	−0.497386	+	0.497386i	−0.910623	−	0.413237i	$-0.864398\pi$
$461$	−10.6793	+	10.6793i	−0.497386	+	0.497386i	0.413237	+	0.910623i	$0.364398\pi$
$462$	−13.3755	+	21.9210i	−0.622284	+	1.01986i
$463$	22.6531	+	22.6531i	1.05278	+	1.05278i	0.998527	+	0.0542528i	$0.0172777\pi$
$463$	22.6531	+	22.6531i	1.05278	+	1.05278i	0.0542528	+	0.998527i	$0.482722\pi$
$464$	4.90114	+	4.90114i	0.227530	+	0.227530i
$465$	11.3916	−	2.75798i	0.528273	−	0.127898i
$466$	−14.4847	−	14.4847i	−0.670992	−	0.670992i
$467$	−14.0867	+	14.0867i	−0.651855	+	0.651855i	−0.953440	−	0.301584i	$-0.902485\pi$
$467$	−14.0867	+	14.0867i	−0.651855	+	0.651855i	0.301584	+	0.953440i	$0.402485\pi$
$468$	3.54334	−	11.0492i	0.163791	−	0.510748i
$469$			34.8217i			1.60792i
$470$			6.36311i			0.293508i
$471$	−1.64608	−	6.79902i	−0.0758475	−	0.313282i
$472$			8.97633i			0.413169i
$473$	−5.88113	−	5.88113i	−0.270414	−	0.270414i
$474$	−24.6204	+	5.96075i	−1.13085	+	0.273786i
$475$	2.15857	−	2.15857i	0.0990419	−	0.0990419i
$476$	14.9969	+	14.9969i	0.687380	+	0.687380i
$477$	5.04672	+	9.81162i	0.231073	+	0.449243i
$478$	13.5210			0.618436
$479$	−15.9366	+	15.9366i	−0.728163	+	0.728163i	−0.970254	−	0.242090i	$-0.922167\pi$
$479$	−15.9366	+	15.9366i	−0.728163	+	0.728163i	0.242090	+	0.970254i	$0.422167\pi$
$480$	0.407565	+	1.68342i	0.0186027	+	0.0768371i
$481$	−10.4815	−	21.0632i	−0.477914	−	0.960397i
$482$			16.5569i			0.754147i
$483$	−21.7244	−	13.2555i	−0.988494	−	0.603148i
$484$			14.4203i			0.655469i
$485$	14.1074			0.640586
$486$	6.10313	+	14.3440i	0.276844	+	0.650659i
$487$	20.3283	+	20.3283i	0.921163	+	0.921163i	0.997112	−	0.0759486i	$-0.0241985\pi$
$487$	20.3283	+	20.3283i	0.921163	+	0.921163i	−0.0759486	+	0.997112i	$0.524198\pi$
$488$			4.75366i			0.215188i
$489$	27.7483	+	16.9312i	1.25482	+	0.765653i
$490$	−1.64707			−0.0744070
$491$		−	12.3716i		−	0.558323i	−0.960244	−	0.279161i	$-0.909944\pi$
$491$		−	12.3716i		−	0.558323i	0.960244	−	0.279161i	$-0.0900564\pi$
$492$	8.55319	−	2.07078i	0.385607	−	0.0933579i
$493$	−49.9911			−2.25149
$494$	−8.34893	+	8.34893i	−0.375636	+	0.375636i
$495$	4.61890	−	14.4031i	0.207604	−	0.647370i
$496$	4.78496	−	4.78496i	0.214851	−	0.214851i
$497$		−	20.4321i		−	0.916507i
$498$	7.07154	+	4.31483i	0.316884	+	0.193352i
$499$	−7.11986	+	7.11986i	−0.318729	+	0.318729i	−0.848279	−	0.529550i	$-0.822361\pi$
$499$	−7.11986	+	7.11986i	−0.318729	+	0.318729i	0.529550	+	0.848279i	$0.322361\pi$
$500$	−0.707107	+	0.707107i	−0.0316228	+	0.0316228i
$501$	−9.40093	−	5.73615i	−0.420002	−	0.256272i
$502$		−	18.9547i		−	0.845990i
$503$	−25.7243	+	25.7243i	−1.14699	+	1.14699i	−0.159847	+	0.987142i	$0.551100\pi$
$503$	−25.7243	+	25.7243i	−1.14699	+	1.14699i	−0.987142	+	0.159847i	$0.948900\pi$
$504$	2.69391	−	8.40039i	0.119996	−	0.374183i
$505$	4.79342	−	4.79342i	0.213304	−	0.213304i
$506$	−25.1923			−1.11994
$507$	−3.29939	+	0.798803i	−0.146531	+	0.0354761i
$508$		−	2.94575i		−	0.130696i
$509$	−11.3133			−0.501452			−0.250726	−	0.968058i	$-0.580669\pi$
$509$	−11.3133			−0.501452			−0.250726	+	0.968058i	$0.580669\pi$
$510$	−10.6639	−	6.50678i	−0.472205	−	0.288125i
$511$		−	24.7310i		−	1.09404i
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$	1.15362	−	15.8202i	0.0509336	−	0.698478i
$514$	−13.6948			−0.604050
$515$		−	17.2861i		−	0.761715i
$516$	2.43905	+	1.48823i	0.107373	+	0.0655157i
$517$		−	32.0819i		−	1.41096i
$518$	−7.96877	−	16.0138i	−0.350128	−	0.703604i
$519$	−2.21688	−	9.15664i	−0.0973102	−	0.401932i
$520$	2.73495	−	2.73495i	0.119936	−	0.119936i
$521$	10.1529			0.444808			0.222404	−	0.974955i	$-0.428610\pi$
$521$	10.1529			0.444808			0.222404	+	0.974955i	$0.428610\pi$
$522$	9.51110	+	18.4911i	0.416290	+	0.809332i
$523$	2.65486	+	2.65486i	0.116089	+	0.116089i	0.762765	−	0.646676i	$-0.223841\pi$
$523$	2.65486	+	2.65486i	0.116089	+	0.116089i	−0.646676	+	0.762765i	$0.723841\pi$
$524$	−8.10221	+	8.10221i	−0.353947	+	0.353947i
$525$	4.95024	−	1.19848i	0.216046	−	0.0523061i
$526$	3.90725	+	3.90725i	0.170364	+	0.170364i
$527$			48.8061i			2.12603i
$528$	−2.05489	−	8.48754i	−0.0894274	−	0.369373i
$529$		−	1.96639i		−	0.0854951i
$530$			3.67782i			0.159754i
$531$	−8.22332	+	25.6427i	−0.356862	+	1.11280i
$532$	−6.34747	+	6.34747i	−0.275198	+	0.275198i
$533$	−13.8959	−	13.8959i	−0.601898	−	0.601898i
$534$	−6.04814	+	1.46429i	−0.261729	+	0.0633661i
$535$	3.71492	+	3.71492i	0.160610	+	0.160610i
$536$	−8.37338	−	8.37338i	−0.361675	−	0.361675i
$537$	16.2456	−	26.6248i	0.701049	−	1.14894i
$538$	5.28362	−	5.28362i	0.227793	−	0.227793i
$539$	8.30428			0.357691
$540$	−0.377904	+	5.18239i	−0.0162624	+	0.223015i
$541$	22.4646	+	22.4646i	0.965827	+	0.965827i	0.999435	−	0.0336082i	$-0.0106998\pi$
$541$	22.4646	+	22.4646i	0.965827	+	0.965827i	−0.0336082	+	0.999435i	$0.510700\pi$
$542$	9.21221	+	9.21221i	0.395698	+	0.395698i
$543$	−2.93991	−	12.1431i	−0.126164	−	0.521108i
$544$	−7.21242			−0.309230
$545$	−5.39525			−0.231107
$546$	−19.1466	+	4.63550i	−0.819397	+	0.198381i
$547$	−6.90611	+	6.90611i	−0.295284	+	0.295284i	−0.839163	−	0.543879i	$-0.816955\pi$
$547$	−6.90611	+	6.90611i	−0.295284	+	0.295284i	0.543879	+	0.839163i	$0.316955\pi$
$548$	−9.24078			−0.394747
$549$	−4.35488	+	13.5798i	−0.185862	+	0.579571i
$550$	3.56513	−	3.56513i	0.152018	−	0.152018i
$551$		−	21.1589i		−	0.901399i
$552$	8.41142	−	2.03646i	0.358014	−	0.0866773i
$553$	30.4105	+	30.4105i	1.29318	+	1.29318i
$554$	15.0662			0.640103
$555$	6.78143	+	8.06301i	0.287856	+	0.342256i
$556$	1.68616			0.0715093
$557$	−21.3749	−	21.3749i	−0.905684	−	0.905684i	0.0902368	−	0.995920i	$-0.471238\pi$
$557$	−21.3749	−	21.3749i	−0.905684	−	0.905684i	−0.995920	+	0.0902368i	$0.971238\pi$
$558$	18.0528	−	9.28565i	0.764234	−	0.393093i
$559$		−	6.38043i		−	0.269863i
$560$	2.07931	−	2.07931i	0.0878669	−	0.0878669i
$561$	53.7658	+	32.8062i	2.27000	+	1.38508i
$562$	−6.19690			−0.261400
$563$	−9.50445	+	9.50445i	−0.400565	+	0.400565i	−0.878432	−	0.477867i	$-0.841410\pi$
$563$	−9.50445	+	9.50445i	−0.400565	+	0.400565i	0.477867	+	0.878432i	$0.341410\pi$
$564$	2.59338	+	10.7118i	0.109201	+	0.451047i
$565$	−14.4055			−0.606042
$566$	31.4780			1.32312
$567$	15.3914	−	21.5295i	0.646377	−	0.904153i
$568$	4.91320	+	4.91320i	0.206153	+	0.206153i
$569$	12.0277	+	12.0277i	0.504225	+	0.504225i	0.912748	−	0.408523i	$-0.133956\pi$
$569$	12.0277	+	12.0277i	0.504225	+	0.504225i	−0.408523	+	0.912748i	$0.633956\pi$
$570$	2.75401	−	4.51353i	0.115353	−	0.189051i
$571$	−31.2211			−1.30656			−0.653281	−	0.757115i	$-0.726608\pi$
$571$	−31.2211			−1.30656			−0.653281	+	0.757115i	$0.726608\pi$
$572$	−13.7892	+	13.7892i	−0.576557	+	0.576557i
$573$	12.0333	+	7.34236i	0.502700	+	0.306731i
$574$	−10.5647	−	10.5647i	−0.440961	−	0.440961i
$575$	3.53316	+	3.53316i	0.147343	+	0.147343i
$576$	1.37220	+	2.66778i	0.0571752	+	0.111158i
$577$	−2.77944	−	2.77944i	−0.115710	−	0.115710i	0.646881	−	0.762591i	$-0.276073\pi$
$577$	−2.77944	−	2.77944i	−0.115710	−	0.115710i	−0.762591	+	0.646881i	$0.776073\pi$
$578$	24.7621	−	24.7621i	1.02997	−	1.02997i
$579$	−17.9691	+	29.4494i	−0.746769	+	1.22387i
$580$			6.93126i			0.287805i
$581$		−	14.0642i		−	0.583479i
$582$	23.7487	−	5.74970i	0.984415	−	0.238333i
$583$		−	18.5430i		−	0.767974i
$584$	5.94693	+	5.94693i	0.246086	+	0.246086i
$585$	10.3185	−	5.30742i	0.426616	−	0.219435i
$586$	−22.3166	+	22.3166i	−0.921888	+	0.921888i
$587$	29.9015	+	29.9015i	1.23417	+	1.23417i	0.962348	+	0.271821i	$0.0876258\pi$
$587$	29.9015	+	29.9015i	1.23417	+	1.23417i	0.271821	+	0.962348i	$0.412374\pi$
$588$	−2.77270	+	0.671288i	−0.114344	+	0.0276834i
$589$	−20.6573			−0.851171
$590$	−6.34723	+	6.34723i	−0.261311	+	0.261311i
$591$	−15.0378	+	3.64075i	−0.618574	+	0.149760i
$592$	5.76694	+	1.93453i	0.237020	+	0.0795087i
$593$			6.19193i			0.254272i	0.991885	+	0.127136i	$0.0405785\pi$
$593$			6.19193i			0.254272i	−0.991885	+	0.127136i	$0.959422\pi$
$594$	1.90534	−	26.1289i	0.0781770	−	1.07208i
$595$			21.2088i			0.869474i
$596$	10.7664			0.441007
$597$	25.0422	+	15.2800i	1.02491	+	0.625367i
$598$	−13.6656	−	13.6656i	−0.558827	−	0.558827i
$599$		−	15.6084i		−	0.637742i	−0.947798	−	0.318871i	$-0.896696\pi$
$599$		−	15.6084i		−	0.637742i	0.947798	−	0.318871i	$-0.103304\pi$
$600$	−0.902163	+	1.47855i	−0.0368306	+	0.0603614i
$601$	−28.4419			−1.16017			−0.580084	−	0.814557i	$-0.696980\pi$
$601$	−28.4419			−1.16017			−0.580084	+	0.814557i	$0.696980\pi$
$602$		−	4.85087i		−	0.197707i
$603$	−16.2493	−	31.5912i	−0.661723	−	1.28649i
$604$	0.235522			0.00958325
$605$	−10.1967	+	10.1967i	−0.414555	+	0.414555i
$606$	6.11569	−	10.0230i	0.248433	−	0.407155i
$607$	−1.73952	+	1.73952i	−0.0706049	+	0.0706049i	−0.741527	−	0.670923i	$-0.765898\pi$
$607$	−1.73952	+	1.73952i	−0.0706049	+	0.0706049i	0.670923	+	0.741527i	$0.265898\pi$
$608$		−	3.05268i		−	0.123802i
$609$	18.3879	−	30.1357i	0.745114	−	1.22116i
$610$	−3.36135	+	3.36135i	−0.136097	+	0.136097i
$611$	17.4028	−	17.4028i	0.704042	−	0.704042i
$612$	−20.6037	−	6.60738i	−0.832856	−	0.267087i
$613$			33.5967i			1.35696i	0.734621	+	0.678478i	$0.237360\pi$
$613$			33.5967i			1.35696i	−0.734621	+	0.678478i	$0.762640\pi$
$614$	9.35242	−	9.35242i	0.377433	−	0.377433i
$615$	7.51228	+	4.58375i	0.302924	+	0.184835i
$616$	−10.4836	+	10.4836i	−0.422396	+	0.422396i
$617$	8.73035			0.351471			0.175735	−	0.984437i	$-0.443770\pi$
$617$	8.73035			0.351471			0.175735	+	0.984437i	$0.443770\pi$
$618$	−7.04520	−	29.0996i	−0.283400	−	1.17056i
$619$			26.1517i			1.05113i	0.850755	+	0.525563i	$0.176145\pi$
$619$			26.1517i			1.05113i	−0.850755	+	0.525563i	$0.823855\pi$
$620$	6.76696			0.271768
$621$	25.8945	+	1.88825i	1.03911	+	0.0757729i
$622$			25.6874i			1.02997i
$623$	7.47050	+	7.47050i	0.299299	+	0.299299i
$624$	3.48939	−	5.71874i	0.139688	−	0.228933i
$625$	−1.00000			−0.0400000
$626$			5.45331i			0.217958i
$627$	−13.8853	+	22.7566i	−0.554527	+	0.908809i
$628$		−	4.03882i		−	0.161167i
$629$	−39.2771	+	19.5451i	−1.56608	+	0.779314i
$630$	7.84485	−	4.03509i	0.312546	−	0.160762i
$631$	28.8630	−	28.8630i	1.14902	−	1.14902i	0.162272	−	0.986746i	$-0.448118\pi$
$631$	28.8630	−	28.8630i	1.14902	−	1.14902i	0.986746	−	0.162272i	$-0.0518823\pi$
$632$	−14.6253			−0.581762
$633$	−2.88605	−	11.9206i	−0.114710	−	0.473802i
$634$	−10.8980	−	10.8980i	−0.432814	−	0.432814i
$635$	2.08296	−	2.08296i	0.0826597	−	0.0826597i
$636$	1.49895	+	6.19130i	0.0594373	+	0.245501i
$637$	4.50465	+	4.50465i	0.178481	+	0.178481i
$638$		−	34.9464i		−	1.38354i
$639$	9.53451	+	18.5366i	0.377179	+	0.733296i
$640$			1.00000i			0.0395285i
$641$			19.6409i			0.775768i	0.921708	+	0.387884i	$0.126794\pi$
$641$			19.6409i			0.775768i	−0.921708	+	0.387884i	$0.873206\pi$
$642$	7.76784	+	4.73969i	0.306572	+	0.187061i
$643$	5.52053	−	5.52053i	0.217709	−	0.217709i	−0.589824	−	0.807532i	$-0.700803\pi$
$643$	5.52053	−	5.52053i	0.217709	−	0.217709i	0.807532	+	0.589824i	$0.200803\pi$
$644$	−10.3896	−	10.3896i	−0.409406	−	0.409406i
$645$	0.672330	+	2.77700i	0.0264730	+	0.109344i
$646$	15.5685	+	15.5685i	0.612534	+	0.612534i
$647$	18.7666	+	18.7666i	0.737790	+	0.737790i	0.972150	−	0.234360i	$-0.0752994\pi$
$647$	18.7666	+	18.7666i	0.737790	+	0.737790i	−0.234360	+	0.972150i	$0.575299\pi$
$648$	1.47599	+	8.87814i	0.0579825	+	0.348766i
$649$	32.0018	−	32.0018i	1.25618	−	1.25618i
$650$	3.86781			0.151708
$651$	−29.4214	−	17.9520i	−1.15312	−	0.703595i
$652$	13.2705	+	13.2705i	0.519712	+	0.519712i
$653$	−13.3928	−	13.3928i	−0.524101	−	0.524101i	0.394706	−	0.918807i	$-0.370846\pi$
$653$	−13.3928	−	13.3928i	−0.524101	−	0.524101i	−0.918807	+	0.394706i	$0.870846\pi$
$654$	−9.08246	+	2.19892i	−0.355152	+	0.0859845i
$655$	−11.4583			−0.447711
$656$	5.08085			0.198374
$657$	11.5405	+	22.4366i	0.450240	+	0.875337i
$658$	13.2309	−	13.2309i	0.515794	−	0.515794i
$659$	24.4864			0.953854			0.476927	−	0.878943i	$-0.341751\pi$
$659$	24.4864			0.953854			0.476927	+	0.878943i	$0.341751\pi$
$660$	4.54858	−	7.45462i	0.177053	−	0.290171i
$661$	2.59300	−	2.59300i	0.100856	−	0.100856i	−0.654878	−	0.755734i	$-0.727280\pi$
$661$	2.59300	−	2.59300i	0.100856	−	0.100856i	0.755734	+	0.654878i	$0.227280\pi$
$662$		−	32.7679i		−	1.27356i
$663$	11.3695	+	46.9610i	0.441556	+	1.82381i
$664$	3.38193	+	3.38193i	0.131244	+	0.131244i
$665$	−8.97667			−0.348100
$666$	14.7022	+	10.8095i	0.569698	+	0.418861i
$667$	34.6330			1.34099
$668$	−4.49594	−	4.49594i	−0.173953	−	0.173953i
$669$	−9.21197	−	38.0493i	−0.356155	−	1.47107i
$670$		−	11.8418i		−	0.457487i
$671$	16.9474	−	16.9474i	0.654248	−	0.654248i
$672$	2.65289	−	4.34780i	0.102337	−	0.167720i
$673$	−29.4109			−1.13371			−0.566853	−	0.823819i	$-0.691839\pi$
$673$	−29.4109			−1.13371			−0.566853	+	0.823819i	$0.691839\pi$
$674$	17.5116	−	17.5116i	0.674521	−	0.674521i
$675$	−3.93172	+	3.39729i	−0.151332	+	0.130762i
$676$	−1.95994			−0.0753823
$677$	−31.4706			−1.20951			−0.604756	−	0.796410i	$-0.706730\pi$
$677$	−31.4706			−1.20951			−0.604756	+	0.796410i	$0.706730\pi$
$678$	−24.2504	+	5.87116i	−0.931330	+	0.225481i
$679$	−29.3338	−	29.3338i	−1.12573	−	1.12573i
$680$	−5.09995	−	5.09995i	−0.195574	−	0.195574i
$681$	−15.2275	−	9.29132i	−0.583518	−	0.356044i
$682$	−34.1180			−1.30645
$683$	−4.09829	+	4.09829i	−0.156817	+	0.156817i	−0.781154	−	0.624338i	$-0.785369\pi$
$683$	−4.09829	+	4.09829i	−0.156817	+	0.156817i	0.624338	+	0.781154i	$0.285369\pi$
$684$	2.79659	−	8.72059i	0.106930	−	0.333440i
$685$	−6.53422	−	6.53422i	−0.249660	−	0.249660i
$686$	−11.1304	−	11.1304i	−0.424961	−	0.424961i
$687$	6.94933	+	28.7037i	0.265134	+	1.09511i
$688$	1.16646	+	1.16646i	0.0444709	+	0.0444709i
$689$	10.0587	−	10.0587i	0.383205	−	0.383205i
$690$	7.38777	+	4.50778i	0.281247	+	0.171608i
$691$		−	17.6928i		−	0.673064i	−0.941672	−	0.336532i	$-0.890746\pi$
$691$		−	17.6928i		−	0.673064i	0.941672	−	0.336532i	$-0.109254\pi$
$692$		−	5.43932i		−	0.206772i
$693$	−39.5526	+	20.3443i	−1.50248	+	0.772818i
$694$		−	29.7886i		−	1.13076i
$695$	1.19230	+	1.19230i	0.0452264	+	0.0452264i
$696$	2.82494	+	11.6682i	0.107079	+	0.442282i
$697$	−25.9121	+	25.9121i	−0.981490	+	0.981490i
$698$	6.35972	+	6.35972i	0.240719	+	0.240719i
$699$	−8.34877	−	34.4839i	−0.315780	−	1.30430i
$700$	2.94059			0.111144
$701$	−18.5106	+	18.5106i	−0.699135	+	0.699135i	−0.964224	−	0.265089i	$-0.914599\pi$
$701$	−18.5106	+	18.5106i	−0.699135	+	0.699135i	0.265089	+	0.964224i	$0.414599\pi$
$702$	15.2072	−	13.1400i	0.573957	−	0.495939i
$703$	−8.27252	−	16.6242i	−0.312004	−	0.626992i
$704$		−	5.04186i		−	0.190022i
$705$	−5.74056	+	9.40816i	−0.216202	+	0.354332i
$706$			29.3206i			1.10349i
$707$	−19.9340			−0.749696
$708$	−8.09811	+	13.2719i	−0.304346	+	0.498790i
$709$	31.3200	+	31.3200i	1.17625	+	1.17625i	0.980693	+	0.195555i	$0.0626509\pi$
$709$	31.3200	+	31.3200i	1.17625	+	1.17625i	0.195555	+	0.980693i	$0.437349\pi$
$710$			6.94832i			0.260766i
$711$	−41.7800	−	13.3984i	−1.56687	−	0.502478i
$712$	−3.59278			−0.134645
$713$		−	33.8120i		−	1.26627i
$714$	8.64396	+	35.7032i	0.323492	+	1.33616i
$715$	−19.5009			−0.729293
$716$	12.7331	−	12.7331i	0.475860	−	0.475860i
$717$	19.9914	+	12.1981i	0.746594	+	0.455548i
$718$	11.9229	−	11.9229i	0.444957	−	0.444957i
$719$		−	13.6556i		−	0.509267i	−0.967038	−	0.254633i	$-0.918045\pi$
$719$		−	13.6556i		−	0.509267i	0.967038	−	0.254633i	$-0.0819548\pi$
$720$	−0.916111	+	2.85670i	−0.0341414	+	0.106463i
$721$	−35.9431	+	35.9431i	−1.33859	+	1.33859i
$722$	6.84561	−	6.84561i	0.254767	−	0.254767i
$723$	−14.9370	+	24.4802i	−0.555515	+	0.910429i
$724$		−	7.21334i		−	0.268082i
$725$	−4.90114	+	4.90114i	−0.182024	+	0.182024i
$726$	−13.0095	+	21.3211i	−0.482827	+	0.791301i
$727$	−17.5342	+	17.5342i	−0.650307	+	0.650307i	−0.953067	−	0.302760i	$-0.902092\pi$
$727$	−17.5342	+	17.5342i	−0.650307	+	0.650307i	0.302760	+	0.953067i	$0.402092\pi$
$728$	−11.3736			−0.421535
$729$	−3.91690	+	26.7144i	−0.145070	+	0.989421i
$730$			8.41023i			0.311276i
$731$	−11.8978			−0.440055
$732$	−4.28858	+	7.02851i	−0.158510	+	0.259781i
$733$		−	3.17234i		−	0.117173i	−0.998282	−	0.0585865i	$-0.981341\pi$
$733$		−	3.17234i		−	0.117173i	0.998282	−	0.0585865i	$-0.0186594\pi$
$734$	19.0989	+	19.0989i	0.704953	+	0.704953i
$735$	−2.43527	−	1.48592i	−0.0898262	−	0.0548091i
$736$	4.99664			0.184179
$737$			59.7044i			2.19924i
$738$	14.5145	+	4.65462i	0.534285	+	0.171339i
$739$			34.7344i			1.27773i	0.769321	+	0.638863i	$0.220595\pi$
$739$			34.7344i			1.27773i	−0.769321	+	0.638863i	$0.779405\pi$
$740$	2.70992	+	5.44576i	0.0996187	+	0.200190i
$741$	−19.8764	+	4.81219i	−0.730177	+	0.176780i
$742$	7.64733	−	7.64733i	0.280742	−	0.280742i
$743$	−29.6412			−1.08743			−0.543715	−	0.839270i	$-0.682983\pi$
$743$	−29.6412			−1.08743			−0.543715	+	0.839270i	$0.682983\pi$
$744$	11.3916	−	2.75798i	0.417637	−	0.101112i
$745$	7.61296	+	7.61296i	0.278917	+	0.278917i
$746$	−9.77235	+	9.77235i	−0.357791	+	0.357791i
$747$	6.56293	+	12.7594i	0.240125	+	0.466841i
$748$	25.7132	+	25.7132i	0.940168	+	0.940168i
$749$		−	15.4490i		−	0.564493i
$750$	−1.68342	+	0.407565i	−0.0614697	+	0.0148822i
$751$		−	6.88875i		−	0.251374i	−0.992070	−	0.125687i	$-0.959886\pi$
$751$		−	6.88875i		−	0.251374i	0.992070	−	0.125687i	$-0.0401135\pi$
$752$			6.36311i			0.232039i
$753$	17.1002	−	28.0254i	0.623167	−	1.02130i
$754$	18.9567	−	18.9567i	0.690361	−	0.690361i
$755$	0.166539	+	0.166539i	0.00606098	+	0.00606098i
$756$	11.5616	−	9.99002i	0.420491	−	0.363334i
$757$	−7.13072	−	7.13072i	−0.259170	−	0.259170i	0.565546	−	0.824717i	$-0.308665\pi$
$757$	−7.13072	−	7.13072i	−0.259170	−	0.259170i	−0.824717	+	0.565546i	$0.808665\pi$
$758$	23.3389	+	23.3389i	0.847709	+	0.847709i
$759$	−37.2480	−	22.7276i	−1.35202	−	0.824959i
$760$	2.15857	−	2.15857i	0.0782995	−	0.0782995i
$761$	28.7364			1.04169			0.520847	−	0.853650i	$-0.325616\pi$
$761$	28.7364			1.04169			0.520847	+	0.853650i	$0.325616\pi$
$762$	2.65754	−	4.35543i	0.0962727	−	0.157780i
$763$	11.2184	+	11.2184i	0.406134	+	0.406134i
$764$	5.75487	+	5.75487i	0.208204	+	0.208204i
$765$	−9.89691	−	19.2412i	−0.357824	−	0.695665i
$766$	19.2306			0.694829
$767$	34.7187			1.25362
$768$	0.407565	+	1.68342i	0.0147067	+	0.0607451i
$769$	−7.54661	+	7.54661i	−0.272138	+	0.272138i	−0.829960	−	0.557823i	$-0.811637\pi$
$769$	−7.54661	+	7.54661i	−0.272138	+	0.272138i	0.557823	+	0.829960i	$0.311637\pi$
$770$	−14.8260			−0.534293
$771$	−20.2483	−	12.3549i	−0.729226	−	0.444951i
$772$	−14.0840	+	14.0840i	−0.506894	+	0.506894i
$773$		−	13.7839i		−	0.495772i	−0.968789	−	0.247886i	$-0.920264\pi$
$773$		−	13.7839i		−	0.495772i	0.968789	−	0.247886i	$-0.0797359\pi$
$774$	2.26362	+	4.40084i	0.0813642	+	0.158185i
$775$	4.78496	+	4.78496i	0.171881	+	0.171881i
$776$	14.1074			0.506428
$777$	2.66481	−	30.8662i	0.0955994	−	1.10732i
$778$	−26.7709			−0.959785
$779$	−10.9674	−	10.9674i	−0.392947	−	0.392947i
$780$	6.51113	−	1.57638i	0.233136	−	0.0564436i
$781$		−	35.0324i		−	1.25356i
$782$	−25.4826	+	25.4826i	−0.911256	+	0.911256i
$783$	−2.61935	+	35.9205i	−0.0936080	+	1.28369i
$784$	−1.64707			−0.0588239
$785$	2.85588	−	2.85588i	0.101931	−	0.101931i
$786$	−19.2890	+	4.66999i	−0.688016	+	0.166573i
$787$	−52.8045			−1.88228			−0.941139	−	0.338019i	$-0.890243\pi$
$787$	−52.8045			−1.88228			−0.941139	+	0.338019i	$0.890243\pi$
$788$	−8.93292			−0.318222
$789$	2.25208	+	9.30203i	0.0801761	+	0.331161i
$790$	−10.3416	−	10.3416i	−0.367938	−	0.367938i
$791$	29.9534	+	29.9534i	1.06502	+	1.06502i
$792$	4.61890	−	14.4031i	0.164125	−	0.511791i
$793$	18.3863			0.652915
$794$	2.33626	−	2.33626i	0.0829107	−	0.0829107i
$795$	−3.31799	+	5.43783i	−0.117677	+	0.192860i
$796$	11.9763	+	11.9763i	0.424489	+	0.424489i
$797$	−9.22136	−	9.22136i	−0.326637	−	0.326637i	0.524669	−	0.851306i	$-0.324189\pi$
$797$	−9.22136	−	9.22136i	−0.326637	−	0.326637i	−0.851306	+	0.524669i	$0.824189\pi$
$798$	−15.1115	+	3.65858i	−0.534940	+	0.129512i
$799$	−32.4515	−	32.4515i	−1.14805	−	1.14805i
$800$	−0.707107	+	0.707107i	−0.0250000	+	0.0250000i
$801$	−10.2635	−	3.29138i	−0.362643	−	0.116295i
$802$			3.10148i			0.109517i
$803$		−	42.4031i		−	1.49637i
$804$	−4.82629	−	19.9346i	−0.170210	−	0.703039i
$805$		−	14.6931i		−	0.517862i
$806$	−18.5073	−	18.5073i	−0.651892	−	0.651892i
$807$	12.5788	−	3.04539i	0.442793	−	0.107203i
$808$	4.79342	−	4.79342i	0.168632	−	0.168632i
$809$	32.0051	+	32.0051i	1.12524	+	1.12524i	0.990941	+	0.134297i	$0.0428776\pi$
$809$	32.0051	+	32.0051i	1.12524	+	1.12524i	0.134297	+	0.990941i	$0.457122\pi$
$810$	−5.23411	+	7.32148i	−0.183908	+	0.257251i
$811$	51.5438			1.80995			0.904973	−	0.425469i	$-0.139891\pi$
$811$	51.5438			1.80995			0.904973	+	0.425469i	$0.139891\pi$
$812$	14.4122	−	14.4122i	0.505770	−	0.505770i
$813$	5.30978	+	21.9316i	0.186222	+	0.769175i
$814$	−13.6630	−	27.4567i	−0.478889	−	0.962358i
$815$			18.7673i			0.657390i
$816$	−10.6639	−	6.50678i	−0.373311	−	0.227783i
$817$		−	5.03577i		−	0.176179i
$818$	−4.24609			−0.148461
$819$	−32.4911	−	10.4195i	−1.13533	−	0.364087i
$820$	3.59270	+	3.59270i	0.125463	+	0.125463i
$821$		−	5.25710i		−	0.183474i	−0.995783	−	0.0917371i	$-0.970758\pi$
$821$		−	5.25710i		−	0.183474i	0.995783	−	0.0917371i	$-0.0292419\pi$
$822$	−13.6629	−	8.33669i	−0.476550	−	0.290776i
$823$	−53.8316			−1.87645			−0.938225	−	0.346025i	$-0.887531\pi$
$823$	−53.8316			−1.87645			−0.938225	+	0.346025i	$0.887531\pi$
$824$		−	17.2861i		−	0.602189i
$825$	8.48754	−	2.05489i	0.295498	−	0.0715419i
$826$	26.3957			0.918424
$827$	−1.49030	+	1.49030i	−0.0518227	+	0.0518227i	−0.732543	−	0.680721i	$-0.761667\pi$
$827$	−1.49030	+	1.49030i	−0.0518227	+	0.0518227i	0.680721	+	0.732543i	$0.261667\pi$
$828$	14.2739	+	4.57748i	0.496052	+	0.159078i
$829$	−1.55844	+	1.55844i	−0.0541267	+	0.0541267i	−0.733652	−	0.679525i	$-0.762186\pi$
$829$	−1.55844	+	1.55844i	−0.0541267	+	0.0541267i	0.679525	+	0.733652i	$0.262186\pi$
$830$			4.78277i			0.166012i
$831$	22.2761	+	13.5922i	0.772751	+	0.471508i
$832$	2.73495	−	2.73495i	0.0948174	−	0.0948174i
$833$	8.39996	−	8.39996i	0.291042	−	0.291042i
$834$	2.49307	+	1.52119i	0.0863281	+	0.0526747i
$835$		−	6.35822i		−	0.220035i
$836$	−10.8832	+	10.8832i	−0.376403	+	0.376403i
$837$	35.0690	+	2.55726i	1.21216	+	0.0883919i
$838$	0.534011	−	0.534011i	0.0184471	−	0.0184471i
$839$	−27.0439			−0.933660			−0.466830	−	0.884347i	$-0.654604\pi$
$839$	−27.0439			−0.933660			−0.466830	+	0.884347i	$0.654604\pi$
$840$	4.95024	−	1.19848i	0.170799	−	0.0413516i
$841$			19.0423i			0.656632i
$842$	13.9013			0.479072
$843$	−9.16241	−	5.59061i	−0.315570	−	0.192551i
$844$		−	7.08120i		−	0.243745i
$845$	−1.38589	−	1.38589i	−0.0476759	−	0.0476759i
$846$	−5.82932	+	18.1775i	−0.200416	+	0.624955i
$847$	42.4042			1.45703
$848$			3.67782i			0.126297i
$849$	46.5417	+	28.3983i	1.59731	+	0.974626i
$850$		−	7.21242i		−	0.247384i
$851$	27.2105	−	13.5405i	0.932764	−	0.464162i
$852$	2.83189	+	11.6969i	0.0970190	+	0.400729i
$853$	−38.6269	+	38.6269i	−1.32256	+	1.32256i	−0.410865	+	0.911696i	$0.634773\pi$
$853$	−38.6269	+	38.6269i	−1.32256	+	1.32256i	−0.911696	+	0.410865i	$0.865227\pi$
$854$	13.9786			0.478337
$855$	8.14387	−	4.18890i	0.278515	−	0.143257i
$856$	3.71492	+	3.71492i	0.126973	+	0.126973i
$857$	−40.4243	+	40.4243i	−1.38087	+	1.38087i	−0.537788	+	0.843080i	$0.680740\pi$
$857$	−40.4243	+	40.4243i	−1.38087	+	1.38087i	−0.843080	+	0.537788i	$0.819260\pi$
$858$	−32.8282	+	7.94790i	−1.12074	+	0.271337i
$859$	−14.0135	−	14.0135i	−0.478136	−	0.478136i	0.426399	−	0.904535i	$-0.359782\pi$
$859$	−14.0135	−	14.0135i	−0.478136	−	0.478136i	−0.904535	+	0.426399i	$0.859782\pi$
$860$			1.64962i			0.0562517i
$861$	−6.08931	−	25.1514i	−0.207523	−	0.857158i
$862$		−	19.1906i		−	0.653634i
$863$		−	24.9254i		−	0.848470i	−0.905552	−	0.424235i	$-0.860543\pi$
$863$		−	24.9254i		−	0.848470i	0.905552	−	0.424235i	$-0.139457\pi$
$864$	−0.377904	+	5.18239i	−0.0128566	+	0.176309i
$865$	3.84618	−	3.84618i	0.130774	−	0.130774i
$866$	−27.3731	−	27.3731i	−0.930175	−	0.930175i
$867$	58.9515	−	14.2725i	2.00210	−	0.484720i
$868$	−14.0706	−	14.0706i	−0.477588	−	0.477588i
$869$	52.1410	+	52.1410i	1.76876	+	1.76876i
$870$	−6.25312	+	10.2482i	−0.212001	+	0.347446i
$871$	−32.3866	+	32.3866i	−1.09738	+	1.09738i
$872$	−5.39525			−0.182706
$873$	40.3007	+	12.9240i	1.36397	+	0.437411i
$874$	−10.7856	−	10.7856i	−0.364828	−	0.364828i
$875$	2.07931	+	2.07931i	0.0702935	+	0.0702935i
$876$	3.42772	+	14.1579i	0.115812	+	0.478351i
$877$	−47.8066			−1.61431			−0.807156	−	0.590338i	$-0.798995\pi$
$877$	−47.8066			−1.61431			−0.807156	+	0.590338i	$0.798995\pi$
$878$	−21.9001			−0.739093
$879$	−53.1293	+	12.8629i	−1.79201	+	0.433855i
$880$	3.56513	−	3.56513i	0.120181	−	0.120181i
$881$	−26.9205			−0.906974			−0.453487	−	0.891263i	$-0.649820\pi$
$881$	−26.9205			−0.906974			−0.453487	+	0.891263i	$0.649820\pi$
$882$	−4.70518	−	1.50890i	−0.158432	−	0.0508072i
$883$	32.1101	−	32.1101i	1.08059	−	1.08059i	0.0841371	−	0.996454i	$-0.473187\pi$
$883$	32.1101	−	32.1101i	1.08059	−	1.08059i	0.996454	−	0.0841371i	$-0.0268134\pi$
$884$			27.8962i			0.938252i
$885$	−15.1109	+	3.65844i	−0.507948	+	0.122977i
$886$	13.1648	+	13.1648i	0.442280	+	0.442280i
$887$	44.0504			1.47907			0.739534	−	0.673119i	$-0.235046\pi$
$887$	44.0504			1.47907			0.739534	+	0.673119i	$0.235046\pi$
$888$	6.78143	+	8.06301i	0.227570	+	0.270577i
$889$	−8.66223			−0.290522
$890$	−2.54048	−	2.54048i	−0.0851570	−	0.0851570i
$891$	26.3896	−	36.9138i	0.884086	−	1.23666i
$892$		−	22.6024i		−	0.756786i
$893$	13.7352	−	13.7352i	0.459631	−	0.459631i
$894$	15.9186	+	9.71300i	0.532396	+	0.324851i
$895$	18.0074			0.601921
$896$	2.07931	−	2.07931i	0.0694649	−	0.0694649i
$897$	−7.87662	−	32.5338i	−0.262993	−	1.08627i
$898$	34.8244			1.16211
$899$	46.9035			1.56432
$900$	−2.66778	+	1.37220i	−0.0889260	+	0.0457401i
$901$	−18.7567	−	18.7567i	−0.624876	−	0.624876i
$902$	−18.1139	−	18.1139i	−0.603127	−	0.603127i
$903$	4.37627	−	7.17224i	0.145633	−	0.238677i
$904$	−14.4055			−0.479118
$905$	5.10060	−	5.10060i	0.169550	−	0.169550i
$906$	0.348230	+	0.212479i	0.0115692	+	0.00705915i
$907$	21.1653	+	21.1653i	0.702782	+	0.702782i	0.965007	−	0.262225i	$-0.0844562\pi$
$907$	21.1653	+	21.1653i	0.702782	+	0.702782i	−0.262225	+	0.965007i	$0.584456\pi$
$908$	−7.28245	−	7.28245i	−0.241677	−	0.241677i
$909$	18.0847	−	9.30206i	0.599831	−	0.308530i
$910$	−8.04238	−	8.04238i	−0.266602	−	0.266602i
$911$	20.5547	−	20.5547i	0.681008	−	0.681008i	−0.279220	−	0.960227i	$-0.590076\pi$
$911$	20.5547	−	20.5547i	0.681008	−	0.681008i	0.960227	+	0.279220i	$0.0900758\pi$
$912$	2.75401	−	4.51353i	0.0911945	−	0.149458i
$913$		−	24.1140i		−	0.798057i
$914$			5.30255i			0.175393i
$915$	−8.00239	+	1.93743i	−0.264551	+	0.0640494i
$916$			17.0508i			0.563376i
$917$	23.8253	+	23.8253i	0.786780	+	0.786780i
$918$	−24.5026	−	28.3572i	−0.808708	−	0.935928i
$919$	24.6949	−	24.6949i	0.814608	−	0.814608i	−0.170713	−	0.985321i	$-0.554607\pi$
$919$	24.6949	−	24.6949i	0.814608	−	0.814608i	0.985321	+	0.170713i	$0.0546070\pi$
$920$	3.53316	+	3.53316i	0.116485	+	0.116485i
$921$	22.2654	−	5.39059i	0.733670	−	0.177626i
$922$	−15.1029			−0.497386
$923$	19.0033	−	19.0033i	0.625502	−	0.625502i
$924$	−24.9584	+	6.04258i	−0.821070	+	0.198786i
$925$	−1.93453	+	5.76694i	−0.0636070	+	0.189616i
$926$			32.0364i			1.05278i
$927$	15.8360	−	49.3811i	0.520121	−	1.62189i
$928$			6.93126i			0.227530i
$929$	23.7969			0.780752			0.390376	−	0.920655i	$-0.372345\pi$
$929$	23.7969			0.780752			0.390376	+	0.920655i	$0.372345\pi$
$930$	10.0053	+	6.10490i	0.328086	+	0.200188i
$931$	3.55531	+	3.55531i	0.116521	+	0.116521i
$932$		−	20.4845i		−	0.670992i
$933$	−23.1742	+	37.9800i	−0.758689	+	1.24341i
$934$	−19.9216			−0.651855
$935$			36.3640i			1.18923i
$936$	10.3185	−	5.30742i	0.337270	−	0.173479i
$937$	34.2005			1.11728			0.558640	−	0.829410i	$-0.311323\pi$
$937$	34.2005			1.11728			0.558640	+	0.829410i	$0.311323\pi$
$938$	−24.6227	+	24.6227i	−0.803959	+	0.803959i
$939$	−4.91978	+	8.06298i	−0.160551	+	0.263126i
$940$	−4.49940	+	4.49940i	−0.146754	+	0.146754i
$941$		−	1.15354i		−	0.0376044i	−0.999823	−	0.0188022i	$-0.994015\pi$
$941$		−	1.15354i		−	0.0376044i	0.999823	−	0.0188022i	$-0.00598528\pi$
$942$	3.64368	−	5.97159i	0.118717	−	0.194565i
$943$	17.9514	−	17.9514i	0.584579	−	0.584579i
$944$	−6.34723	+	6.34723i	−0.206585	+	0.206585i
$945$	15.2393	+	1.11126i	0.495734	+	0.0361493i
$946$		−	8.31717i		−	0.270414i
$947$	18.6642	−	18.6642i	0.606505	−	0.606505i	−0.335526	−	0.942031i	$-0.608914\pi$
$947$	18.6642	−	18.6642i	0.606505	−	0.606505i	0.942031	+	0.335526i	$0.108914\pi$
$948$	−21.6241	−	13.1944i	−0.702319	−	0.428533i
$949$	23.0016	−	23.0016i	0.746663	−	0.746663i
$950$	3.05268			0.0990419
$951$	−6.28142	−	25.9449i	−0.203689	−	0.841322i
$952$			21.2088i			0.687380i
$953$	45.3751			1.46984			0.734921	−	0.678153i	$-0.237219\pi$
$953$	45.3751			1.46984			0.734921	+	0.678153i	$0.237219\pi$
$954$	−3.36929	+	10.5064i	−0.109085	+	0.340158i
$955$			8.13862i			0.263360i
$956$	9.56079	+	9.56079i	0.309218	+	0.309218i
$957$	31.5273	−	51.6699i	1.01913	−	1.67025i
$958$	−22.5378			−0.728163
$959$			27.1734i			0.877473i
$960$	−0.902163	+	1.47855i	−0.0291172	+	0.0477199i
$961$		−	14.7917i		−	0.477153i
$962$	7.48239	−	22.3054i	0.241242	−	0.719155i
$963$	7.20914	+	14.0157i	0.232311	+	0.451650i
$964$	−11.7075	+	11.7075i	−0.377074	+	0.377074i
$965$	−19.9178			−0.641176
$966$	−5.98838	−	24.7345i	−0.192673	−	0.795821i
$967$	−39.0460	−	39.0460i	−1.25563	−	1.25563i	−0.953156	−	0.302478i	$-0.902186\pi$
$967$	−39.0460	−	39.0460i	−1.25563	−	1.25563i	−0.302478	−	0.953156i	$-0.597814\pi$
$968$	−10.1967	+	10.1967i	−0.327734	+	0.327734i
$969$	8.97344	+	37.0641i	0.288268	+	1.19067i
$970$	9.97547	+	9.97547i	0.320293	+	0.320293i
$971$			8.34707i			0.267870i	0.990990	+	0.133935i	$0.0427614\pi$
$971$			8.34707i			0.267870i	−0.990990	+	0.133935i	$0.957239\pi$
$972$	−5.82721	+	14.4583i	−0.186908	+	0.463752i
$973$		−	4.95832i		−	0.158956i
$974$			28.7486i			0.921163i
$975$	5.71874	+	3.48939i	0.183146	+	0.111750i
$976$	−3.36135	+	3.36135i	−0.107594	+	0.107594i
$977$	16.1384	+	16.1384i	0.516312	+	0.516312i	0.916453	−	0.400142i	$-0.131039\pi$
$977$	16.1384	+	16.1384i	0.516312	+	0.516312i	−0.400142	+	0.916453i	$0.631039\pi$
$978$	7.64890	+	31.5932i	0.244585	+	1.01024i
$979$	12.8087	+	12.8087i	0.409369	+	0.409369i
$980$	−1.16465	−	1.16465i	−0.0372035	−	0.0372035i
$981$	−15.4126	−	4.94265i	−0.492087	−	0.157807i
$982$	8.74804	−	8.74804i	0.279161	−	0.279161i
$983$	−14.0276			−0.447410			−0.223705	−	0.974657i	$-0.571815\pi$
$983$	−14.0276			−0.447410			−0.223705	+	0.974657i	$0.571815\pi$
$984$	7.51228	+	4.58375i	0.239483	+	0.146125i
$985$	−6.31653	−	6.31653i	−0.201261	−	0.201261i
$986$	−35.3491	−	35.3491i	−1.12574	−	1.12574i
$987$	31.4989	−	7.62607i	1.00262	−	0.242741i
$988$	−11.8072			−0.375636
$989$	8.24258			0.262099
$990$	13.4506	−	6.91846i	0.427487	−	0.219883i
$991$	−4.77484	+	4.77484i	−0.151678	+	0.151678i	−0.778867	−	0.627189i	$-0.784205\pi$
$991$	−4.77484	+	4.77484i	−0.151678	+	0.151678i	0.627189	+	0.778867i	$0.284205\pi$
$992$	6.76696			0.214851
$993$	29.5619	−	48.4488i	0.938120	−	1.53748i
$994$	14.4477	−	14.4477i	0.458253	−	0.458253i
$995$			16.9370i			0.536940i
$996$	1.94929	+	8.05139i	0.0617656	+	0.255118i
$997$	−30.6953	−	30.6953i	−0.972131	−	0.972131i	0.0274909	−	0.999622i	$-0.491248\pi$
$997$	−30.6953	−	30.6953i	−0.972131	−	0.972131i	−0.999622	+	0.0274909i	$0.991248\pi$
$998$	−10.0690			−0.318729
$999$	11.9859	+	29.2462i	0.379217	+	0.925308i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1110.2.u.f.191.20	yes	40
3.2	odd	2	inner	1110.2.u.f.191.6	✓	40
37.31	odd	4	inner	1110.2.u.f.401.6	yes	40
111.68	even	4	inner	1110.2.u.f.401.20	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1110.2.u.f.191.6	✓	40	3.2	odd	2	inner
1110.2.u.f.191.20	yes	40	1.1	even	1	trivial
1110.2.u.f.401.6	yes	40	37.31	odd	4	inner
1110.2.u.f.401.20	yes	40	111.68	even	4	inner

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.u (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 + 0.707107i) q^{2} +(0.407565 + 1.68342i) q^{3} +1.00000i q^{4} +(-0.707107 + 0.707107i) q^{5} +(-0.902163 + 1.47855i) q^{6} +2.94059 q^{7} +(-0.707107 + 0.707107i) q^{8} +(-2.66778 + 1.37220i) q^{9} +O(q^{10})\)	\(q+(0.707107 + 0.707107i) q^{2} +(0.407565 + 1.68342i) q^{3} +1.00000i q^{4} +(-0.707107 + 0.707107i) q^{5} +(-0.902163 + 1.47855i) q^{6} +2.94059 q^{7} +(-0.707107 + 0.707107i) q^{8} +(-2.66778 + 1.37220i) q^{9} -1.00000 q^{10} +5.04186 q^{11} +(-1.68342 + 0.407565i) q^{12} +(2.73495 + 2.73495i) q^{13} +(2.07931 + 2.07931i) q^{14} +(-1.47855 - 0.902163i) q^{15} -1.00000 q^{16} +(5.09995 - 5.09995i) q^{17} +(-2.85670 - 0.916111i) q^{18} +(2.15857 + 2.15857i) q^{19} +(-0.707107 - 0.707107i) q^{20} +(1.19848 + 4.95024i) q^{21} +(3.56513 + 3.56513i) q^{22} +(-3.53316 + 3.53316i) q^{23} +(-1.47855 - 0.902163i) q^{24} -1.00000i q^{25} +3.86781i q^{26} +(-3.39729 - 3.93172i) q^{27} +2.94059i q^{28} +(-4.90114 - 4.90114i) q^{29} +(-0.407565 - 1.68342i) q^{30} +(-4.78496 + 4.78496i) q^{31} +(-0.707107 - 0.707107i) q^{32} +(2.05489 + 8.48754i) q^{33} +7.21242 q^{34} +(-2.07931 + 2.07931i) q^{35} +(-1.37220 - 2.66778i) q^{36} +(-5.76694 - 1.93453i) q^{37} +3.05268i q^{38} +(-3.48939 + 5.71874i) q^{39} -1.00000i q^{40} -5.08085 q^{41} +(-2.65289 + 4.34780i) q^{42} +(-1.16646 - 1.16646i) q^{43} +5.04186i q^{44} +(0.916111 - 2.85670i) q^{45} -4.99664 q^{46} -6.36311i q^{47} +(-0.407565 - 1.68342i) q^{48} +1.64707 q^{49} +(0.707107 - 0.707107i) q^{50} +(10.6639 + 6.50678i) q^{51} +(-2.73495 + 2.73495i) q^{52} -3.67782i q^{53} +(0.377904 - 5.18239i) q^{54} +(-3.56513 + 3.56513i) q^{55} +(-2.07931 + 2.07931i) q^{56} +(-2.75401 + 4.51353i) q^{57} -6.93126i q^{58} +(6.34723 - 6.34723i) q^{59} +(0.902163 - 1.47855i) q^{60} +(3.36135 - 3.36135i) q^{61} -6.76696 q^{62} +(-7.84485 + 4.03509i) q^{63} -1.00000i q^{64} -3.86781 q^{65} +(-4.54858 + 7.45462i) q^{66} +11.8418i q^{67} +(5.09995 + 5.09995i) q^{68} +(-7.38777 - 4.50778i) q^{69} -2.94059 q^{70} -6.94832i q^{71} +(0.916111 - 2.85670i) q^{72} -8.41023i q^{73} +(-2.70992 - 5.44576i) q^{74} +(1.68342 - 0.407565i) q^{75} +(-2.15857 + 2.15857i) q^{76} +14.8260 q^{77} +(-6.51113 + 1.57638i) q^{78} +(10.3416 + 10.3416i) q^{79} +(0.707107 - 0.707107i) q^{80} +(5.23411 - 7.32148i) q^{81} +(-3.59270 - 3.59270i) q^{82} -4.78277i q^{83} +(-4.95024 + 1.19848i) q^{84} +7.21242i q^{85} -1.64962i q^{86} +(6.25312 - 10.2482i) q^{87} +(-3.56513 + 3.56513i) q^{88} +(2.54048 + 2.54048i) q^{89} +(2.66778 - 1.37220i) q^{90} +(8.04238 + 8.04238i) q^{91} +(-3.53316 - 3.53316i) q^{92} +(-10.0053 - 6.10490i) q^{93} +(4.49940 - 4.49940i) q^{94} -3.05268 q^{95} +(0.902163 - 1.47855i) q^{96} +(-9.97547 - 9.97547i) q^{97} +(1.16465 + 1.16465i) q^{98} +(-13.4506 + 6.91846i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 24 q^{7} - 8 q^{9}+O(q^{10}) \) 40 * q + 24 * q^7 - 8 * q^9	\( 40 q + 24 q^{7} - 8 q^{9} - 40 q^{10} + 16 q^{13} - 40 q^{16} + 8 q^{18} + 16 q^{19} - 16 q^{22} - 8 q^{31} + 24 q^{33} + 24 q^{34} + 32 q^{37} + 16 q^{39} + 12 q^{42} + 32 q^{43} + 8 q^{45} - 56 q^{46} - 32 q^{49} - 44 q^{51} - 16 q^{52} - 24 q^{54} + 16 q^{55} + 8 q^{57} - 72 q^{61} + 24 q^{63} - 28 q^{66} + 16 q^{69} - 24 q^{70} + 8 q^{72} - 16 q^{76} - 48 q^{79} + 120 q^{81} - 24 q^{82} - 24 q^{84} + 20 q^{87} + 16 q^{88} + 8 q^{90} - 92 q^{93} - 8 q^{94} - 40 q^{97}+O(q^{100}) \) 40 * q + 24 * q^7 - 8 * q^9 - 40 * q^10 + 16 * q^13 - 40 * q^16 + 8 * q^18 + 16 * q^19 - 16 * q^22 - 8 * q^31 + 24 * q^33 + 24 * q^34 + 32 * q^37 + 16 * q^39 + 12 * q^42 + 32 * q^43 + 8 * q^45 - 56 * q^46 - 32 * q^49 - 44 * q^51 - 16 * q^52 - 24 * q^54 + 16 * q^55 + 8 * q^57 - 72 * q^61 + 24 * q^63 - 28 * q^66 + 16 * q^69 - 24 * q^70 + 8 * q^72 - 16 * q^76 - 48 * q^79 + 120 * q^81 - 24 * q^82 - 24 * q^84 + 20 * q^87 + 16 * q^88 + 8 * q^90 - 92 * q^93 - 8 * q^94 - 40 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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