LMFDB - Embedded newform 1110.2.e.d.739.3

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			739.3
Root			$-1.28817 + 1.28817i$ of defining polynomial
Character	$\chi$	$=$	1110.739
Dual form			1110.2.e.d.739.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.00000 q^{2} -1.00000i q^{3} +1.00000 q^{4} +(-1.28817 - 1.82773i) q^{5} -1.00000i q^{6} +1.25548i q^{7} +1.00000 q^{8} -1.00000 q^{9} +(-1.28817 - 1.82773i) q^{10} -5.46829 q^{11} -1.00000i q^{12} -4.70887 q^{13} +1.25548i q^{14} +(-1.82773 + 1.28817i) q^{15} +1.00000 q^{16} -1.19309 q^{17} -1.00000 q^{18} -1.22179i q^{19} +(-1.28817 - 1.82773i) q^{20} +1.25548 q^{21} -5.46829 q^{22} -1.91577 q^{23} -1.00000i q^{24} +(-1.68122 + 4.70887i) q^{25} -4.70887 q^{26} +1.00000i q^{27} +1.25548i q^{28} -5.08822i q^{29} +(-1.82773 + 1.28817i) q^{30} -3.43275i q^{31} +1.00000 q^{32} +5.46829i q^{33} -1.19309 q^{34} +(2.29468 - 1.61728i) q^{35} -1.00000 q^{36} +(4.58473 + 3.99753i) q^{37} -1.22179i q^{38} +4.70887i q^{39} +(-1.28817 - 1.82773i) q^{40} -4.46326 q^{41} +1.25548 q^{42} -1.34271 q^{43} -5.46829 q^{44} +(1.28817 + 1.82773i) q^{45} -1.91577 q^{46} -1.90301i q^{47} -1.00000i q^{48} +5.42377 q^{49} +(-1.68122 + 4.70887i) q^{50} +1.19309i q^{51} -4.70887 q^{52} +1.11671i q^{53} +1.00000i q^{54} +(7.04410 + 9.99458i) q^{55} +1.25548i q^{56} -1.22179 q^{57} -5.08822i q^{58} -8.99577i q^{59} +(-1.82773 + 1.28817i) q^{60} -6.21190i q^{61} -3.43275i q^{62} -1.25548i q^{63} +1.00000 q^{64} +(6.06585 + 8.60657i) q^{65} +5.46829i q^{66} -4.21117i q^{67} -1.19309 q^{68} +1.91577i q^{69} +(2.29468 - 1.61728i) q^{70} -12.4170 q^{71} -1.00000 q^{72} +10.2834i q^{73} +(4.58473 + 3.99753i) q^{74} +(4.70887 + 1.68122i) q^{75} -1.22179i q^{76} -6.86533i q^{77} +4.70887i q^{78} +1.00691i q^{79} +(-1.28817 - 1.82773i) q^{80} +1.00000 q^{81} -4.46326 q^{82} +0.754493i q^{83} +1.25548 q^{84} +(1.53691 + 2.18065i) q^{85} -1.34271 q^{86} -5.08822 q^{87} -5.46829 q^{88} -11.4743i q^{89} +(1.28817 + 1.82773i) q^{90} -5.91190i q^{91} -1.91577 q^{92} -3.43275 q^{93} -1.90301i q^{94} +(-2.23311 + 1.57388i) q^{95} -1.00000i q^{96} -16.6814 q^{97} +5.42377 q^{98} +5.46829 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 16 q^{2} + 16 q^{4} + 2 q^{5} + 16 q^{8} - 16 q^{9} + 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}+ \cdots - 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

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
$5$	−1.28817	−	1.82773i	−0.576089	−	0.817387i
$5$	−1.28817	−	1.82773i	−0.576089	−	0.817387i
$6$		−	1.00000i		−	0.408248i
$7$			1.25548i			0.474527i	0.971445	+	0.237263i	$0.0762505\pi$
$7$			1.25548i			0.474527i	−0.971445	+	0.237263i	$0.923750\pi$
$8$	1.00000			0.353553
$9$	−1.00000			−0.333333
$10$	−1.28817	−	1.82773i	−0.407356	−	0.577980i
$11$	−5.46829			−1.64875			−0.824376	−	0.566043i	$-0.808474\pi$
$11$	−5.46829			−1.64875			−0.824376	+	0.566043i	$0.808474\pi$
$12$		−	1.00000i		−	0.288675i
$13$	−4.70887			−1.30601			−0.653003	−	0.757355i	$-0.726491\pi$
$13$	−4.70887			−1.30601			−0.653003	+	0.757355i	$0.726491\pi$
$14$			1.25548i			0.335541i
$15$	−1.82773	+	1.28817i	−0.471919	+	0.332605i
$16$	1.00000			0.250000
$17$	−1.19309			−0.289367			−0.144684	−	0.989478i	$-0.546216\pi$
$17$	−1.19309			−0.289367			−0.144684	+	0.989478i	$0.546216\pi$
$18$	−1.00000			−0.235702
$19$		−	1.22179i		−	0.280298i	−0.990130	−	0.140149i	$-0.955242\pi$
$19$		−	1.22179i		−	0.280298i	0.990130	−	0.140149i	$-0.0447582\pi$
$20$	−1.28817	−	1.82773i	−0.288044	−	0.408694i
$21$	1.25548			0.273968
$22$	−5.46829			−1.16584
$23$	−1.91577			−0.399466			−0.199733	−	0.979850i	$-0.564007\pi$
$23$	−1.91577			−0.399466			−0.199733	+	0.979850i	$0.564007\pi$
$24$		−	1.00000i		−	0.204124i
$25$	−1.68122	+	4.70887i	−0.336244	+	0.941775i
$26$	−4.70887			−0.923486
$27$			1.00000i			0.192450i
$28$			1.25548i			0.237263i
$29$		−	5.08822i		−	0.944858i	−0.881369	−	0.472429i	$-0.843377\pi$
$29$		−	5.08822i		−	0.944858i	0.881369	−	0.472429i	$-0.156623\pi$
$30$	−1.82773	+	1.28817i	−0.333697	+	0.235187i
$31$		−	3.43275i		−	0.616540i	−0.951299	−	0.308270i	$-0.900250\pi$
$31$		−	3.43275i		−	0.616540i	0.951299	−	0.308270i	$-0.0997501\pi$
$32$	1.00000			0.176777
$33$			5.46829i			0.951907i
$34$	−1.19309			−0.204613
$35$	2.29468	−	1.61728i	0.387872	−	0.273370i
$36$	−1.00000			−0.166667
$37$	4.58473	+	3.99753i	0.753725	+	0.657190i
$37$	4.58473	+	3.99753i	0.753725	+	0.657190i
$38$		−	1.22179i		−	0.198201i
$39$			4.70887i			0.754023i
$40$	−1.28817	−	1.82773i	−0.203678	−	0.288990i
$41$	−4.46326			−0.697043			−0.348522	−	0.937301i	$-0.613316\pi$
$41$	−4.46326			−0.697043			−0.348522	+	0.937301i	$0.613316\pi$
$42$	1.25548			0.193725
$43$	−1.34271			−0.204761			−0.102380	−	0.994745i	$-0.532646\pi$
$43$	−1.34271			−0.204761			−0.102380	+	0.994745i	$0.532646\pi$
$44$	−5.46829			−0.824376
$45$	1.28817	+	1.82773i	0.192030	+	0.272462i
$46$	−1.91577			−0.282465
$47$		−	1.90301i		−	0.277583i	−0.990322	−	0.138791i	$-0.955678\pi$
$47$		−	1.90301i		−	0.277583i	0.990322	−	0.138791i	$-0.0443217\pi$
$48$		−	1.00000i		−	0.144338i
$49$	5.42377			0.774824
$50$	−1.68122	+	4.70887i	−0.237760	+	0.665935i
$51$			1.19309i			0.167066i
$52$	−4.70887			−0.653003
$53$			1.11671i			0.153392i	0.997055	+	0.0766959i	$0.0244370\pi$
$53$			1.11671i			0.153392i	−0.997055	+	0.0766959i	$0.975563\pi$
$54$			1.00000i			0.136083i
$55$	7.04410	+	9.99458i	0.949827	+	1.34767i
$56$			1.25548i			0.167771i
$57$	−1.22179			−0.161830
$58$		−	5.08822i		−	0.668116i
$59$		−	8.99577i		−	1.17115i	−0.810618	−	0.585575i	$-0.800869\pi$
$59$		−	8.99577i		−	1.17115i	0.810618	−	0.585575i	$-0.199131\pi$
$60$	−1.82773	+	1.28817i	−0.235959	+	0.166302i
$61$		−	6.21190i		−	0.795352i	−0.917526	−	0.397676i	$-0.869817\pi$
$61$		−	6.21190i		−	0.795352i	0.917526	−	0.397676i	$-0.130183\pi$
$62$		−	3.43275i		−	0.435960i
$63$		−	1.25548i		−	0.158176i
$64$	1.00000			0.125000
$65$	6.06585	+	8.60657i	0.752376	+	1.06751i
$66$			5.46829i			0.673100i
$67$		−	4.21117i		−	0.514476i	−0.966348	−	0.257238i	$-0.917188\pi$
$67$		−	4.21117i		−	0.514476i	0.966348	−	0.257238i	$-0.0828125\pi$
$68$	−1.19309			−0.144684
$69$			1.91577i			0.230632i
$70$	2.29468	−	1.61728i	0.274267	−	0.193301i
$71$	−12.4170			−1.47363			−0.736815	−	0.676094i	$-0.763671\pi$
$71$	−12.4170			−1.47363			−0.736815	+	0.676094i	$0.763671\pi$
$72$	−1.00000			−0.117851
$73$			10.2834i			1.20359i	0.798652	+	0.601793i	$0.205547\pi$
$73$			10.2834i			1.20359i	−0.798652	+	0.601793i	$0.794453\pi$
$74$	4.58473	+	3.99753i	0.532964	+	0.464703i
$75$	4.70887	+	1.68122i	0.543734	+	0.194130i
$76$		−	1.22179i		−	0.140149i
$77$		−	6.86533i		−	0.782377i
$78$			4.70887i			0.533175i
$79$			1.00691i			0.113286i	0.998394	+	0.0566431i	$0.0180397\pi$
$79$			1.00691i			0.113286i	−0.998394	+	0.0566431i	$0.981960\pi$
$80$	−1.28817	−	1.82773i	−0.144022	−	0.204347i
$81$	1.00000			0.111111
$82$	−4.46326			−0.492884
$83$			0.754493i			0.0828164i	0.999142	+	0.0414082i	$0.0131844\pi$
$83$			0.754493i			0.0828164i	−0.999142	+	0.0414082i	$0.986816\pi$
$84$	1.25548			0.136984
$85$	1.53691	+	2.18065i	0.166701	+	0.236525i
$86$	−1.34271			−0.144788
$87$	−5.08822			−0.545514
$88$	−5.46829			−0.582922
$89$		−	11.4743i		−	1.21627i	−0.793832	−	0.608137i	$-0.791917\pi$
$89$		−	11.4743i		−	1.21627i	0.793832	−	0.608137i	$-0.208083\pi$
$90$	1.28817	+	1.82773i	0.135785	+	0.192660i
$91$		−	5.91190i		−	0.619735i
$92$	−1.91577			−0.199733
$93$	−3.43275			−0.355960
$94$		−	1.90301i		−	0.196281i
$95$	−2.23311	+	1.57388i	−0.229112	+	0.161477i
$96$		−	1.00000i		−	0.102062i
$97$	−16.6814			−1.69374			−0.846868	−	0.531803i	$-0.821515\pi$
$97$	−16.6814			−1.69374			−0.846868	+	0.531803i	$0.821515\pi$
$98$	5.42377			0.547883
$99$	5.46829			0.549584
$100$	−1.68122	+	4.70887i	−0.168122	+	0.470887i
$101$	3.26214			0.324595			0.162298	−	0.986742i	$-0.448110\pi$
$101$	3.26214			0.324595			0.162298	+	0.986742i	$0.448110\pi$
$102$			1.19309i			0.118134i
$103$	−5.19330			−0.511711			−0.255856	−	0.966715i	$-0.582357\pi$
$103$	−5.19330			−0.511711			−0.255856	+	0.966715i	$0.582357\pi$
$104$	−4.70887			−0.461743
$105$	−1.61728	−	2.29468i	−0.157830	−	0.223938i
$106$			1.11671i			0.108464i
$107$			8.65950i			0.837146i	0.908183	+	0.418573i	$0.137470\pi$
$107$			8.65950i			0.837146i	−0.908183	+	0.418573i	$0.862530\pi$
$108$			1.00000i			0.0962250i
$109$			2.54677i			0.243936i	0.992534	+	0.121968i	$0.0389205\pi$
$109$			2.54677i			0.243936i	−0.992534	+	0.121968i	$0.961079\pi$
$110$	7.04410	+	9.99458i	0.671629	+	0.952945i
$111$	3.99753	−	4.58473i	0.379429	−	0.435164i
$112$			1.25548i			0.118632i
$113$	4.72781			0.444755			0.222378	−	0.974961i	$-0.428618\pi$
$113$	4.72781			0.444755			0.222378	+	0.974961i	$0.428618\pi$
$114$	−1.22179			−0.114431
$115$	2.46784	+	3.50152i	0.230128	+	0.326518i
$116$		−	5.08822i		−	0.472429i
$117$	4.70887			0.435336
$118$		−	8.99577i		−	0.828128i
$119$		−	1.49790i		−	0.137312i
$120$	−1.82773	+	1.28817i	−0.166848	+	0.117594i
$121$	18.9022			1.71838
$122$		−	6.21190i		−	0.562399i
$123$			4.46326i			0.402438i
$124$		−	3.43275i		−	0.308270i
$125$	10.7723	−	2.99303i	0.963501	−	0.267704i
$126$		−	1.25548i		−	0.111847i
$127$		−	8.05067i		−	0.714381i	−0.934031	−	0.357191i	$-0.883735\pi$
$127$		−	8.05067i		−	0.714381i	0.934031	−	0.357191i	$-0.116265\pi$
$128$	1.00000			0.0883883
$129$			1.34271i			0.118219i
$130$	6.06585	+	8.60657i	0.532010	+	0.754846i
$131$		−	12.9999i		−	1.13581i	−0.823094	−	0.567905i	$-0.807754\pi$
$131$		−	12.9999i		−	1.13581i	0.823094	−	0.567905i	$-0.192246\pi$
$132$			5.46829i			0.475954i
$133$	1.53393			0.133009
$134$		−	4.21117i		−	0.363790i
$135$	1.82773	−	1.28817i	0.157306	−	0.110868i
$136$	−1.19309			−0.102307
$137$		−	13.5487i		−	1.15754i	−0.815490	−	0.578772i	$-0.803532\pi$
$137$		−	13.5487i		−	1.15754i	0.815490	−	0.578772i	$-0.196468\pi$
$138$			1.91577i			0.163081i
$139$	15.3257			1.29991			0.649955	−	0.759972i	$-0.274788\pi$
$139$	15.3257			1.29991			0.649955	+	0.759972i	$0.274788\pi$
$140$	2.29468	−	1.61728i	0.193936	−	0.136685i
$141$	−1.90301			−0.160262
$142$	−12.4170			−1.04201
$143$	25.7495			2.15328
$144$	−1.00000			−0.0833333
$145$	−9.29991	+	6.55451i	−0.772315	+	0.544322i
$146$			10.2834i			0.851064i
$147$		−	5.42377i		−	0.447345i
$148$	4.58473	+	3.99753i	0.376863	+	0.328595i
$149$	13.4684			1.10337			0.551686	−	0.834052i	$-0.313985\pi$
$149$	13.4684			1.10337			0.551686	+	0.834052i	$0.313985\pi$
$150$	4.70887	+	1.68122i	0.384478	+	0.137271i
$151$	−10.3930			−0.845767			−0.422883	−	0.906184i	$-0.638982\pi$
$151$	−10.3930			−0.845767			−0.422883	+	0.906184i	$0.638982\pi$
$152$		−	1.22179i		−	0.0991003i
$153$	1.19309			0.0964557
$154$		−	6.86533i		−	0.553224i
$155$	−6.27415	+	4.42198i	−0.503952	+	0.355182i
$156$			4.70887i			0.377012i
$157$		−	14.2297i		−	1.13565i	−0.823148	−	0.567827i	$-0.807784\pi$
$157$		−	14.2297i		−	1.13565i	0.823148	−	0.567827i	$-0.192216\pi$
$158$			1.00691i			0.0801054i
$159$	1.11671			0.0885608
$160$	−1.28817	−	1.82773i	−0.101839	−	0.144495i
$161$		−	2.40521i		−	0.189557i
$162$	1.00000			0.0785674
$163$	−0.455364			−0.0356669			−0.0178334	−	0.999841i	$-0.505677\pi$
$163$	−0.455364			−0.0356669			−0.0178334	+	0.999841i	$0.505677\pi$
$164$	−4.46326			−0.348522
$165$	9.99458	−	7.04410i	0.778077	−	0.548383i
$166$			0.754493i			0.0585600i
$167$	−0.755752			−0.0584819			−0.0292409	−	0.999572i	$-0.509309\pi$
$167$	−0.755752			−0.0584819			−0.0292409	+	0.999572i	$0.509309\pi$
$168$	1.25548			0.0968624
$169$	9.17350			0.705654
$170$	1.53691	+	2.18065i	0.117875	+	0.167248i
$171$			1.22179i			0.0934327i
$172$	−1.34271			−0.102380
$173$		−	4.41375i		−	0.335571i	−0.985823	−	0.167786i	$-0.946338\pi$
$173$		−	4.41375i		−	0.335571i	0.985823	−	0.167786i	$-0.0536617\pi$
$174$	−5.08822			−0.385737
$175$	−5.91190	−	2.11074i	−0.446898	−	0.159557i
$176$	−5.46829			−0.412188
$177$	−8.99577			−0.676164
$178$		−	11.4743i		−	0.860036i
$179$			12.6883i			0.948368i	0.880426	+	0.474184i	$0.157257\pi$
$179$			12.6883i			0.948368i	−0.880426	+	0.474184i	$0.842743\pi$
$180$	1.28817	+	1.82773i	0.0960148	+	0.136231i
$181$	13.2444			0.984445			0.492223	−	0.870469i	$-0.336185\pi$
$181$	13.2444			0.984445			0.492223	+	0.870469i	$0.336185\pi$
$182$		−	5.91190i		−	0.438219i
$183$	−6.21190			−0.459197
$184$	−1.91577			−0.141233
$185$	1.40049	−	13.5292i	0.102966	−	0.994685i
$186$	−3.43275			−0.251702
$187$	6.52417			0.477094
$188$		−	1.90301i		−	0.138791i
$189$	−1.25548			−0.0913227
$190$	−2.23311	+	1.57388i	−0.162007	+	0.114181i
$191$		−	7.03990i		−	0.509389i	−0.967022	−	0.254695i	$-0.918025\pi$
$191$		−	7.03990i		−	0.509389i	0.967022	−	0.254695i	$-0.0819749\pi$
$192$		−	1.00000i		−	0.0721688i
$193$	0.635749			0.0457622			0.0228811	−	0.999738i	$-0.492716\pi$
$193$	0.635749			0.0457622			0.0228811	+	0.999738i	$0.492716\pi$
$194$	−16.6814			−1.19765
$195$	8.60657	−	6.06585i	0.616329	−	0.434384i
$196$	5.42377			0.387412
$197$		−	5.18937i		−	0.369727i	−0.982764	−	0.184864i	$-0.940816\pi$
$197$		−	5.18937i		−	0.369727i	0.982764	−	0.184864i	$-0.0591843\pi$
$198$	5.46829			0.388614
$199$			23.8852i			1.69318i	0.532247	+	0.846589i	$0.321348\pi$
$199$			23.8852i			1.69318i	−0.532247	+	0.846589i	$0.678652\pi$
$200$	−1.68122	+	4.70887i	−0.118880	+	0.332968i
$201$	−4.21117			−0.297033
$202$	3.26214			0.229523
$203$	6.38816			0.448361
$204$			1.19309i			0.0835331i
$205$	5.74945	+	8.15764i	0.401559	+	0.569754i
$206$	−5.19330			−0.361834
$207$	1.91577			0.133155
$208$	−4.70887			−0.326502
$209$			6.68111i			0.462142i
$210$	−1.61728	−	2.29468i	−0.111603	−	0.158348i
$211$	−26.6260			−1.83301			−0.916505	−	0.400022i	$-0.869002\pi$
$211$	−26.6260			−1.83301			−0.916505	+	0.400022i	$0.869002\pi$
$212$			1.11671i			0.0766959i
$213$			12.4170i			0.850801i
$214$			8.65950i			0.591952i
$215$	1.72964	+	2.45411i	0.117960	+	0.167369i
$216$			1.00000i			0.0680414i
$217$	4.30975			0.292565
$218$			2.54677i			0.172489i
$219$	10.2834			0.694891
$220$	7.04410	+	9.99458i	0.474913	+	0.673834i
$221$	5.61812			0.377915
$222$	3.99753	−	4.58473i	0.268297	−	0.307707i
$223$			20.0982i			1.34588i	0.739698	+	0.672938i	$0.234968\pi$
$223$			20.0982i			1.34588i	−0.739698	+	0.672938i	$0.765032\pi$
$224$			1.25548i			0.0838853i
$225$	1.68122	−	4.70887i	0.112081	−	0.313925i
$226$	4.72781			0.314489
$227$	−15.1621			−1.00635			−0.503173	−	0.864186i	$-0.667834\pi$
$227$	−15.1621			−1.00635			−0.503173	+	0.864186i	$0.667834\pi$
$228$	−1.22179			−0.0809151
$229$	−2.54527			−0.168196			−0.0840980	−	0.996457i	$-0.526801\pi$
$229$	−2.54527			−0.168196			−0.0840980	+	0.996457i	$0.526801\pi$
$230$	2.46784	+	3.50152i	0.162725	+	0.230883i
$231$	−6.86533			−0.451705
$232$		−	5.08822i		−	0.334058i
$233$			13.9212i			0.912008i	0.889978	+	0.456004i	$0.150720\pi$
$233$			13.9212i			0.912008i	−0.889978	+	0.456004i	$0.849280\pi$
$234$	4.70887			0.307829
$235$	−3.47820	+	2.45141i	−0.226892	+	0.159912i
$236$		−	8.99577i		−	0.585575i
$237$	1.00691			0.0654058
$238$		−	1.49790i		−	0.0970945i
$239$			28.8753i			1.86779i	0.357546	+	0.933895i	$0.383613\pi$
$239$			28.8753i			1.86779i	−0.357546	+	0.933895i	$0.616387\pi$
$240$	−1.82773	+	1.28817i	−0.117980	+	0.0831512i
$241$		−	6.84853i		−	0.441152i	−0.975370	−	0.220576i	$-0.929206\pi$
$241$		−	6.84853i		−	0.441152i	0.975370	−	0.220576i	$-0.0707938\pi$
$242$	18.9022			1.21508
$243$		−	1.00000i		−	0.0641500i
$244$		−	6.21190i		−	0.397676i
$245$	−6.98676	−	9.91321i	−0.446367	−	0.633331i
$246$			4.46326i			0.284567i
$247$			5.75326i			0.366071i
$248$		−	3.43275i		−	0.217980i
$249$	0.754493			0.0478141
$250$	10.7723	−	2.99303i	0.681298	−	0.189296i
$251$		−	18.7459i		−	1.18323i	−0.806221	−	0.591615i	$-0.798491\pi$
$251$		−	18.7459i		−	1.18323i	0.806221	−	0.591615i	$-0.201509\pi$
$252$		−	1.25548i		−	0.0790878i
$253$	10.4760			0.658620
$254$		−	8.05067i		−	0.505144i
$255$	2.18065	−	1.53691i	0.136558	−	0.0962449i
$256$	1.00000			0.0625000
$257$	−17.3509			−1.08232			−0.541158	−	0.840921i	$-0.682014\pi$
$257$	−17.3509			−1.08232			−0.541158	+	0.840921i	$0.682014\pi$
$258$			1.34271i			0.0835933i
$259$	−5.01882	+	5.75604i	−0.311854	+	0.357663i
$260$	6.06585	+	8.60657i	0.376188	+	0.533757i
$261$			5.08822i			0.314953i
$262$		−	12.9999i		−	0.803139i
$263$		−	31.3436i		−	1.93273i	−0.257176	−	0.966364i	$-0.582792\pi$
$263$		−	31.3436i		−	1.93273i	0.257176	−	0.966364i	$-0.417208\pi$
$264$			5.46829i			0.336550i
$265$	2.04105	−	1.43851i	0.125380	−	0.0883672i
$266$	1.53393			0.0940516
$267$	−11.4743			−0.702217
$268$		−	4.21117i		−	0.257238i
$269$	20.8503			1.27126			0.635631	−	0.771993i	$-0.280740\pi$
$269$	20.8503			1.27126			0.635631	+	0.771993i	$0.280740\pi$
$270$	1.82773	−	1.28817i	0.111232	−	0.0783957i
$271$	−0.977182			−0.0593596			−0.0296798	−	0.999559i	$-0.509449\pi$
$271$	−0.977182			−0.0593596			−0.0296798	+	0.999559i	$0.509449\pi$
$272$	−1.19309			−0.0723418
$273$	−5.91190			−0.357804
$274$		−	13.5487i		−	0.818507i
$275$	9.19339	−	25.7495i	0.554383	−	1.55275i
$276$			1.91577i			0.115316i
$277$	28.0775			1.68701			0.843506	−	0.537120i	$-0.180488\pi$
$277$	28.0775			1.68701			0.843506	+	0.537120i	$0.180488\pi$
$278$	15.3257			0.919176
$279$			3.43275i			0.205513i
$280$	2.29468	−	1.61728i	0.137134	−	0.0966507i
$281$			20.9112i			1.24746i	0.781640	+	0.623730i	$0.214383\pi$
$281$			20.9112i			1.24746i	−0.781640	+	0.623730i	$0.785617\pi$
$282$	−1.90301			−0.113323
$283$	11.7273			0.697116			0.348558	−	0.937287i	$-0.386671\pi$
$283$	11.7273			0.697116			0.348558	+	0.937287i	$0.386671\pi$
$284$	−12.4170			−0.736815
$285$	1.57388	+	2.23311i	0.0932285	+	0.132278i
$286$	25.7495			1.52260
$287$		−	5.60353i		−	0.330766i
$288$	−1.00000			−0.0589256
$289$	−15.5765			−0.916267
$290$	−9.29991	+	6.55451i	−0.546109	+	0.384894i
$291$			16.6814i			0.977879i
$292$			10.2834i			0.601793i
$293$		−	19.0944i		−	1.11550i	−0.830007	−	0.557752i	$-0.811664\pi$
$293$		−	19.0944i		−	1.11550i	0.830007	−	0.557752i	$-0.188336\pi$
$294$		−	5.42377i		−	0.316321i
$295$	−16.4419	+	11.5881i	−0.957283	+	0.674686i
$296$	4.58473	+	3.99753i	0.266482	+	0.232352i
$297$		−	5.46829i		−	0.317302i
$298$	13.4684			0.780202
$299$	9.02113			0.521705
$300$	4.70887	+	1.68122i	0.271867	+	0.0970652i
$301$		−	1.68574i		−	0.0971645i
$302$	−10.3930			−0.598048
$303$		−	3.26214i		−	0.187405i
$304$		−	1.22179i		−	0.0700745i
$305$	−11.3537	+	8.00200i	−0.650111	+	0.458193i
$306$	1.19309			0.0682045
$307$		−	31.2854i		−	1.78555i	−0.450500	−	0.892777i	$-0.648754\pi$
$307$		−	31.2854i		−	1.78555i	0.450500	−	0.892777i	$-0.351246\pi$
$308$		−	6.86533i		−	0.391188i
$309$			5.19330i			0.295437i
$310$	−6.27415	+	4.42198i	−0.356348	+	0.251151i
$311$		−	7.52409i		−	0.426652i	−0.976981	−	0.213326i	$-0.931570\pi$
$311$		−	7.52409i		−	0.426652i	0.976981	−	0.213326i	$-0.0684296\pi$
$312$			4.70887i			0.266588i
$313$	0.0900227			0.00508838			0.00254419	−	0.999997i	$-0.499190\pi$
$313$	0.0900227			0.00508838			0.00254419	+	0.999997i	$0.499190\pi$
$314$		−	14.2297i		−	0.803029i
$315$	−2.29468	+	1.61728i	−0.129291	+	0.0911232i
$316$			1.00691i			0.0566431i
$317$		−	7.86659i		−	0.441832i	−0.975293	−	0.220916i	$-0.929095\pi$
$317$		−	7.86659i		−	0.441832i	0.975293	−	0.220916i	$-0.0709046\pi$
$318$	1.11671			0.0626219
$319$			27.8239i			1.55784i
$320$	−1.28817	−	1.82773i	−0.0720111	−	0.102173i
$321$	8.65950			0.483326
$322$		−	2.40521i		−	0.134037i
$323$			1.45771i			0.0811090i
$324$	1.00000			0.0555556
$325$	7.91665	−	22.1735i	0.439137	−	1.22996i
$326$	−0.455364			−0.0252203
$327$	2.54677			0.140836
$328$	−4.46326			−0.246442
$329$	2.38919			0.131720
$330$	9.99458	−	7.04410i	0.550183	−	0.387765i
$331$			21.5849i			1.18641i	0.805051	+	0.593205i	$0.202138\pi$
$331$			21.5849i			1.18641i	−0.805051	+	0.593205i	$0.797862\pi$
$332$			0.754493i			0.0414082i
$333$	−4.58473	−	3.99753i	−0.251242	−	0.219063i
$334$	−0.755752			−0.0413529
$335$	−7.69690	+	5.42472i	−0.420526	+	0.296384i
$336$	1.25548			0.0684921
$337$		−	24.3782i		−	1.32796i	−0.747748	−	0.663982i	$-0.768865\pi$
$337$		−	24.3782i		−	1.32796i	0.747748	−	0.663982i	$-0.231135\pi$
$338$	9.17350			0.498973
$339$		−	4.72781i		−	0.256779i
$340$	1.53691	+	2.18065i	0.0833505	+	0.118262i
$341$			18.7713i			1.01652i
$342$			1.22179i			0.0660669i
$343$			15.5978i			0.842202i
$344$	−1.34271			−0.0723939
$345$	3.50152	−	2.46784i	0.188515	−	0.132864i
$346$		−	4.41375i		−	0.237285i
$347$	−25.4950			−1.36864			−0.684321	−	0.729181i	$-0.739901\pi$
$347$	−25.4950			−1.36864			−0.684321	+	0.729181i	$0.739901\pi$
$348$	−5.08822			−0.272757
$349$	2.69761			0.144400			0.0721999	−	0.997390i	$-0.476998\pi$
$349$	2.69761			0.144400			0.0721999	+	0.997390i	$0.476998\pi$
$350$	−5.91190	−	2.11074i	−0.316004	−	0.112824i
$351$		−	4.70887i		−	0.251341i
$352$	−5.46829			−0.291461
$353$	21.7179			1.15592			0.577962	−	0.816063i	$-0.303848\pi$
$353$	21.7179			1.15592			0.577962	+	0.816063i	$0.303848\pi$
$354$	−8.99577			−0.478120
$355$	15.9953	+	22.6950i	0.848942	+	1.20453i
$356$		−	11.4743i		−	0.608137i
$357$	−1.49790			−0.0792774
$358$			12.6883i			0.670597i
$359$	−20.3716			−1.07517			−0.537585	−	0.843210i	$-0.680663\pi$
$359$	−20.3716			−1.07517			−0.537585	+	0.843210i	$0.680663\pi$
$360$	1.28817	+	1.82773i	0.0678927	+	0.0963300i
$361$	17.5072			0.921433
$362$	13.2444			0.696108
$363$		−	18.9022i		−	0.992108i
$364$		−	5.91190i		−	0.309868i
$365$	18.7954	−	13.2469i	0.983796	−	0.693372i
$366$	−6.21190			−0.324701
$367$			31.0972i			1.62326i	0.584172	+	0.811630i	$0.301419\pi$
$367$			31.0972i			1.62326i	−0.584172	+	0.811630i	$0.698581\pi$
$368$	−1.91577			−0.0998665
$369$	4.46326			0.232348
$370$	1.40049	−	13.5292i	0.0728078	−	0.703348i
$371$	−1.40201			−0.0727885
$372$	−3.43275			−0.177980
$373$			33.4131i			1.73006i	0.501716	+	0.865032i	$0.332702\pi$
$373$			33.4131i			1.73006i	−0.501716	+	0.865032i	$0.667298\pi$
$374$	6.52417			0.337357
$375$	−2.99303	−	10.7723i	−0.154559	−	0.556278i
$376$		−	1.90301i		−	0.0981403i
$377$			23.9598i			1.23399i
$378$	−1.25548			−0.0645749
$379$	−24.6191			−1.26460			−0.632298	−	0.774725i	$-0.717888\pi$
$379$	−24.6191			−1.26460			−0.632298	+	0.774725i	$0.717888\pi$
$380$	−2.23311	+	1.57388i	−0.114556	+	0.0807383i
$381$	−8.05067			−0.412448
$382$		−	7.03990i		−	0.360192i
$383$	−17.5596			−0.897252			−0.448626	−	0.893720i	$-0.648086\pi$
$383$	−17.5596			−0.897252			−0.448626	+	0.893720i	$0.648086\pi$
$384$		−	1.00000i		−	0.0510310i
$385$	−12.5480	+	8.84373i	−0.639505	+	0.450718i
$386$	0.635749			0.0323587
$387$	1.34271			0.0682536
$388$	−16.6814			−0.846868
$389$		−	19.6417i		−	0.995875i	−0.867213	−	0.497937i	$-0.834091\pi$
$389$		−	19.6417i		−	0.995875i	0.867213	−	0.497937i	$-0.165909\pi$
$390$	8.60657	−	6.06585i	0.435811	−	0.307156i
$391$	2.28569			0.115592
$392$	5.42377			0.273942
$393$	−12.9999			−0.655760
$394$		−	5.18937i		−	0.261437i
$395$	1.84036	−	1.29707i	0.0925987	−	0.0652629i
$396$	5.46829			0.274792
$397$			4.31480i			0.216554i	0.994121	+	0.108277i	$0.0345333\pi$
$397$			4.31480i			0.216554i	−0.994121	+	0.108277i	$0.965467\pi$
$398$			23.8852i			1.19726i
$399$		−	1.53393i		−	0.0767928i
$400$	−1.68122	+	4.70887i	−0.0840610	+	0.235444i
$401$			9.64980i			0.481888i	0.970539	+	0.240944i	$0.0774570\pi$
$401$			9.64980i			0.481888i	−0.970539	+	0.240944i	$0.922543\pi$
$402$	−4.21117			−0.210034
$403$			16.1644i			0.805206i
$404$	3.26214			0.162298
$405$	−1.28817	−	1.82773i	−0.0640098	−	0.0908208i
$406$	6.38816			0.317039
$407$	−25.0706	−	21.8596i	−1.24271	−	1.08354i
$408$			1.19309i			0.0590668i
$409$		−	25.5235i		−	1.26206i	−0.775760	−	0.631029i	$-0.782633\pi$
$409$		−	25.5235i		−	1.26206i	0.775760	−	0.631029i	$-0.217367\pi$
$410$	5.74945	+	8.15764i	0.283945	+	0.402877i
$411$	−13.5487			−0.668308
$412$	−5.19330			−0.255856
$413$	11.2940			0.555742
$414$	1.91577			0.0941550
$415$	1.37901	−	0.971918i	0.0676930	−	0.0477096i
$416$	−4.70887			−0.230872
$417$		−	15.3257i		−	0.750504i
$418$			6.68111i			0.326784i
$419$	−22.0969			−1.07950			−0.539751	−	0.841824i	$-0.681482\pi$
$419$	−22.0969			−1.07950			−0.539751	+	0.841824i	$0.681482\pi$
$420$	−1.61728	−	2.29468i	−0.0789150	−	0.111969i
$421$		−	8.20101i		−	0.399693i	−0.979827	−	0.199846i	$-0.935956\pi$
$421$		−	8.20101i		−	0.399693i	0.979827	−	0.199846i	$-0.0640443\pi$
$422$	−26.6260			−1.29613
$423$			1.90301i			0.0925275i
$424$			1.11671i			0.0542322i
$425$	2.00585	−	5.61812i	0.0972979	−	0.272519i
$426$			12.4170i			0.601607i
$427$	7.79891			0.377416
$428$			8.65950i			0.418573i
$429$		−	25.7495i		−	1.24320i
$430$	1.72964	+	2.45411i	0.0834106	+	0.118348i
$431$			9.83076i			0.473531i	0.971567	+	0.236765i	$0.0760873\pi$
$431$			9.83076i			0.473531i	−0.971567	+	0.236765i	$0.923913\pi$
$432$			1.00000i			0.0481125i
$433$		−	1.61024i		−	0.0773832i	−0.999251	−	0.0386916i	$-0.987681\pi$
$433$		−	1.61024i		−	0.0773832i	0.999251	−	0.0386916i	$-0.0123190\pi$
$434$	4.30975			0.206875
$435$	6.55451	+	9.29991i	0.314265	+	0.445896i
$436$			2.54677i			0.121968i
$437$			2.34067i			0.111970i
$438$	10.2834			0.491362
$439$			32.2443i			1.53894i	0.638684	+	0.769469i	$0.279479\pi$
$439$			32.2443i			1.53894i	−0.638684	+	0.769469i	$0.720521\pi$
$440$	7.04410	+	9.99458i	0.335815	+	0.476473i
$441$	−5.42377			−0.258275
$442$	5.61812			0.267226
$443$		−	19.0730i		−	0.906186i	−0.891463	−	0.453093i	$-0.850321\pi$
$443$		−	19.0730i		−	0.906186i	0.891463	−	0.453093i	$-0.149679\pi$
$444$	3.99753	−	4.58473i	0.189714	−	0.217582i
$445$	−20.9720	+	14.7809i	−0.994168	+	0.700682i
$446$			20.0982i			0.951679i
$447$		−	13.4684i		−	0.637032i
$448$			1.25548i			0.0593159i
$449$			30.6914i			1.44841i	0.689582	+	0.724207i	$0.257794\pi$
$449$			30.6914i			1.44841i	−0.689582	+	0.724207i	$0.742206\pi$
$450$	1.68122	−	4.70887i	0.0792534	−	0.221978i
$451$	24.4064			1.14925
$452$	4.72781			0.222378
$453$			10.3930i			0.488304i
$454$	−15.1621			−0.711593
$455$	−10.8054	+	7.61555i	−0.506564	+	0.357022i
$456$	−1.22179			−0.0572156
$457$	−22.4560			−1.05045			−0.525223	−	0.850965i	$-0.676018\pi$
$457$	−22.4560			−1.05045			−0.525223	+	0.850965i	$0.676018\pi$
$458$	−2.54527			−0.118932
$459$		−	1.19309i		−	0.0556887i
$460$	2.46784	+	3.50152i	0.115064	+	0.163259i
$461$		−	7.37800i		−	0.343628i	−0.985129	−	0.171814i	$-0.945037\pi$
$461$		−	7.37800i		−	0.343628i	0.985129	−	0.171814i	$-0.0549628\pi$
$462$	−6.86533			−0.319404
$463$	6.16145			0.286347			0.143173	−	0.989698i	$-0.454269\pi$
$463$	6.16145			0.286347			0.143173	+	0.989698i	$0.454269\pi$
$464$		−	5.08822i		−	0.236215i
$465$	4.42198	+	6.27415i	0.205064	+	0.290957i
$466$			13.9212i			0.644887i
$467$	−5.37297			−0.248631			−0.124316	−	0.992243i	$-0.539674\pi$
$467$	−5.37297			−0.248631			−0.124316	+	0.992243i	$0.539674\pi$
$468$	4.70887			0.217668
$469$	5.28704			0.244133
$470$	−3.47820	+	2.45141i	−0.160437	+	0.113075i
$471$	−14.2297			−0.655670
$472$		−	8.99577i		−	0.414064i
$473$	7.34231			0.337600
$474$	1.00691			0.0462489
$475$	5.75326	+	2.05410i	0.263978	+	0.0942485i
$476$		−	1.49790i		−	0.0686562i
$477$		−	1.11671i		−	0.0511306i
$478$			28.8753i			1.32073i
$479$		−	21.5810i		−	0.986062i	−0.870012	−	0.493031i	$-0.835889\pi$
$479$		−	21.5810i		−	0.986062i	0.870012	−	0.493031i	$-0.164111\pi$
$480$	−1.82773	+	1.28817i	−0.0834242	+	0.0587968i
$481$	−21.5889	−	18.8239i	−0.984370	−	0.858294i
$482$		−	6.84853i		−	0.311942i
$483$	−2.40521			−0.109441
$484$	18.9022			0.859191
$485$	21.4885	+	30.4891i	0.975742	+	1.38444i
$486$		−	1.00000i		−	0.0453609i
$487$	0.346315			0.0156930			0.00784652	−	0.999969i	$-0.497502\pi$
$487$	0.346315			0.0156930			0.00784652	+	0.999969i	$0.497502\pi$
$488$		−	6.21190i		−	0.281199i
$489$			0.455364i			0.0205923i
$490$	−6.98676	−	9.91321i	−0.315629	−	0.447833i
$491$	10.6278			0.479624			0.239812	−	0.970819i	$-0.422914\pi$
$491$	10.6278			0.479624			0.239812	+	0.970819i	$0.422914\pi$
$492$			4.46326i			0.201219i
$493$			6.07071i			0.273411i
$494$			5.75326i			0.258851i
$495$	−7.04410	−	9.99458i	−0.316609	−	0.449223i
$496$		−	3.43275i		−	0.154135i
$497$		−	15.5893i		−	0.699277i
$498$	0.754493			0.0338096
$499$		−	12.0121i		−	0.537736i	−0.963177	−	0.268868i	$-0.913350\pi$
$499$		−	12.0121i		−	0.537736i	0.963177	−	0.268868i	$-0.0866496\pi$
$500$	10.7723	−	2.99303i	0.481751	−	0.133852i
$501$			0.755752i			0.0337645i
$502$		−	18.7459i		−	0.836669i
$503$	4.15447			0.185239			0.0926194	−	0.995702i	$-0.470476\pi$
$503$	4.15447			0.185239			0.0926194	+	0.995702i	$0.470476\pi$
$504$		−	1.25548i		−	0.0559235i
$505$	−4.20220	−	5.96232i	−0.186996	−	0.265320i
$506$	10.4760			0.465715
$507$		−	9.17350i		−	0.407410i
$508$		−	8.05067i		−	0.357191i
$509$	−8.30223			−0.367990			−0.183995	−	0.982927i	$-0.558903\pi$
$509$	−8.30223			−0.367990			−0.183995	+	0.982927i	$0.558903\pi$
$510$	2.18065	−	1.53691i	0.0965609	−	0.0680554i
$511$	−12.9107			−0.571134
$512$	1.00000			0.0441942
$513$	1.22179			0.0539434
$514$	−17.3509			−0.765313
$515$	6.68987	+	9.49197i	0.294791	+	0.418266i
$516$			1.34271i			0.0591094i
$517$			10.4062i			0.457665i
$518$	−5.01882	+	5.75604i	−0.220514	+	0.252906i
$519$	−4.41375			−0.193742
$520$	6.06585	+	8.60657i	0.266005	+	0.377423i
$521$	14.0992			0.617698			0.308849	−	0.951111i	$-0.400056\pi$
$521$	14.0992			0.617698			0.308849	+	0.951111i	$0.400056\pi$
$522$			5.08822i			0.222705i
$523$	−29.0802			−1.27159			−0.635794	−	0.771858i	$-0.719327\pi$
$523$	−29.0802			−1.27159			−0.635794	+	0.771858i	$0.719327\pi$
$524$		−	12.9999i		−	0.567905i
$525$	−2.11074	+	5.91190i	−0.0921201	+	0.258016i
$526$		−	31.3436i		−	1.36665i
$527$			4.09558i			0.178406i
$528$			5.46829i			0.237977i
$529$	−19.3298			−0.840427
$530$	2.04105	−	1.43851i	0.0886574	−	0.0624851i
$531$			8.99577i			0.390383i
$532$	1.53393			0.0665045
$533$	21.0169			0.910344
$534$	−11.4743			−0.496542
$535$	15.8273	−	11.1549i	0.684272	−	0.482270i
$536$		−	4.21117i		−	0.181895i
$537$	12.6883			0.547540
$538$	20.8503			0.898918
$539$	−29.6587			−1.27749
$540$	1.82773	−	1.28817i	0.0786531	−	0.0554342i
$541$			10.2446i			0.440450i	0.975449	+	0.220225i	$0.0706791\pi$
$541$			10.2446i			0.440450i	−0.975449	+	0.220225i	$0.929321\pi$
$542$	−0.977182			−0.0419736
$543$		−	13.2444i		−	0.568370i
$544$	−1.19309			−0.0511533
$545$	4.65481	−	3.28068i	0.199390	−	0.140529i
$546$	−5.91190			−0.253006
$547$	−36.6360			−1.56644			−0.783220	−	0.621744i	$-0.786424\pi$
$547$	−36.6360			−1.56644			−0.783220	+	0.621744i	$0.786424\pi$
$548$		−	13.5487i		−	0.578772i
$549$			6.21190i			0.265117i
$550$	9.19339	−	25.7495i	0.392008	−	1.09796i
$551$	−6.21674			−0.264842
$552$			1.91577i			0.0815406i
$553$	−1.26415			−0.0537573
$554$	28.0775			1.19290
$555$	−13.5292	−	1.40049i	−0.574282	−	0.0594474i
$556$	15.3257			0.649955
$557$	3.19892			0.135543			0.0677714	−	0.997701i	$-0.478411\pi$
$557$	3.19892			0.135543			0.0677714	+	0.997701i	$0.478411\pi$
$558$			3.43275i			0.145320i
$559$	6.32264			0.267419
$560$	2.29468	−	1.61728i	0.0969680	−	0.0683424i
$561$		−	6.52417i		−	0.275451i
$562$			20.9112i			0.882087i
$563$	−43.0080			−1.81257			−0.906285	−	0.422668i	$-0.861094\pi$
$563$	−43.0080			−1.81257			−0.906285	+	0.422668i	$0.861094\pi$
$564$	−1.90301			−0.0801312
$565$	−6.09024	−	8.64118i	−0.256218	−	0.363537i
$566$	11.7273			0.492936
$567$			1.25548i			0.0527252i
$568$	−12.4170			−0.521007
$569$			19.8692i			0.832960i	0.909145	+	0.416480i	$0.136736\pi$
$569$			19.8692i			0.832960i	−0.909145	+	0.416480i	$0.863264\pi$
$570$	1.57388	+	2.23311i	0.0659225	+	0.0935346i
$571$	−16.6100			−0.695105			−0.347553	−	0.937660i	$-0.612987\pi$
$571$	−16.6100			−0.695105			−0.347553	+	0.937660i	$0.612987\pi$
$572$	25.7495			1.07664
$573$	−7.03990			−0.294096
$574$		−	5.60353i		−	0.233887i
$575$	3.22083	−	9.02113i	0.134318	−	0.376207i
$576$	−1.00000			−0.0416667
$577$	36.4851			1.51890			0.759448	−	0.650568i	$-0.225469\pi$
$577$	36.4851			1.51890			0.759448	+	0.650568i	$0.225469\pi$
$578$	−15.5765			−0.647898
$579$		−	0.635749i		−	0.0264208i
$580$	−9.29991	+	6.55451i	−0.386158	+	0.272161i
$581$	−0.947251			−0.0392986
$582$			16.6814i			0.691465i
$583$		−	6.10649i		−	0.252905i
$584$			10.2834i			0.425532i
$585$	−6.06585	−	8.60657i	−0.250792	−	0.355838i
$586$		−	19.0944i		−	0.788781i
$587$	−14.3652			−0.592917			−0.296458	−	0.955046i	$-0.595806\pi$
$587$	−14.3652			−0.592917			−0.296458	+	0.955046i	$0.595806\pi$
$588$		−	5.42377i		−	0.223673i
$589$	−4.19411			−0.172815
$590$	−16.4419	+	11.5881i	−0.676901	+	0.477075i
$591$	−5.18937			−0.213462
$592$	4.58473	+	3.99753i	0.188431	+	0.164297i
$593$			19.6724i			0.807850i	0.914792	+	0.403925i	$0.132354\pi$
$593$			19.6724i			0.807850i	−0.914792	+	0.403925i	$0.867646\pi$
$594$		−	5.46829i		−	0.224367i
$595$	−2.73777	+	1.92956i	−0.112237	+	0.0791041i
$596$	13.4684			0.551686
$597$	23.8852			0.977557
$598$	9.02113			0.368901
$599$	32.9039			1.34442			0.672208	−	0.740362i	$-0.265346\pi$
$599$	32.9039			1.34442			0.672208	+	0.740362i	$0.265346\pi$
$600$	4.70887	+	1.68122i	0.192239	+	0.0686355i
$601$	43.6508			1.78055			0.890276	−	0.455422i	$-0.150512\pi$
$601$	43.6508			1.78055			0.890276	+	0.455422i	$0.150512\pi$
$602$		−	1.68574i		−	0.0687057i
$603$			4.21117i			0.171492i
$604$	−10.3930			−0.422883
$605$	−24.3493	−	34.5482i	−0.989940	−	1.40458i
$606$		−	3.26214i		−	0.132515i
$607$	−15.4852			−0.628523			−0.314262	−	0.949336i	$-0.601757\pi$
$607$	−15.4852			−0.628523			−0.314262	+	0.949336i	$0.601757\pi$
$608$		−	1.22179i		−	0.0495502i
$609$		−	6.38816i		−	0.258861i
$610$	−11.3537	+	8.00200i	−0.459698	+	0.323992i
$611$			8.96104i			0.362525i
$612$	1.19309			0.0482278
$613$		−	47.5322i		−	1.91981i	−0.280329	−	0.959904i	$-0.590444\pi$
$613$		−	47.5322i		−	1.91981i	0.280329	−	0.959904i	$-0.409556\pi$
$614$		−	31.2854i		−	1.26258i
$615$	8.15764	−	5.74945i	0.328948	−	0.231840i
$616$		−	6.86533i		−	0.276612i
$617$			31.3888i			1.26367i	0.775105	+	0.631833i	$0.217697\pi$
$617$			31.3888i			1.26367i	−0.775105	+	0.631833i	$0.782303\pi$
$618$			5.19330i			0.208905i
$619$	8.12905			0.326734			0.163367	−	0.986565i	$-0.447765\pi$
$619$	8.12905			0.326734			0.163367	+	0.986565i	$0.447765\pi$
$620$	−6.27415	+	4.42198i	−0.251976	+	0.177591i
$621$		−	1.91577i		−	0.0768772i
$622$		−	7.52409i		−	0.301688i
$623$	14.4058			0.577155
$624$			4.70887i			0.188506i
$625$	−19.3470	−	15.8333i	−0.773880	−	0.633332i
$626$	0.0900227			0.00359803
$627$	6.68111			0.266818
$628$		−	14.2297i		−	0.567827i
$629$	−5.47000	−	4.76941i	−0.218103	−	0.190169i
$630$	−2.29468	+	1.61728i	−0.0914224	+	0.0644338i
$631$		−	37.9315i		−	1.51003i	−0.655709	−	0.755014i	$-0.727630\pi$
$631$		−	37.9315i		−	1.51003i	0.655709	−	0.755014i	$-0.272370\pi$
$632$			1.00691i			0.0400527i
$633$			26.6260i			1.05829i
$634$		−	7.86659i		−	0.312422i
$635$	−14.7145	+	10.3707i	−0.583926	+	0.411547i
$636$	1.11671			0.0442804
$637$	−25.5399			−1.01193
$638$			27.8239i			1.10156i
$639$	12.4170			0.491210
$640$	−1.28817	−	1.82773i	−0.0509195	−	0.0722475i
$641$	−36.9793			−1.46059			−0.730296	−	0.683130i	$-0.760618\pi$
$641$	−36.9793			−1.46059			−0.730296	+	0.683130i	$0.760618\pi$
$642$	8.65950			0.341763
$643$	8.44944			0.333213			0.166607	−	0.986023i	$-0.446719\pi$
$643$	8.44944			0.333213			0.166607	+	0.986023i	$0.446719\pi$
$644$		−	2.40521i		−	0.0947786i
$645$	2.45411	−	1.72964i	0.0966305	−	0.0681045i
$646$			1.45771i			0.0573527i
$647$	−4.22924			−0.166269			−0.0831343	−	0.996538i	$-0.526493\pi$
$647$	−4.22924			−0.166269			−0.0831343	+	0.996538i	$0.526493\pi$
$648$	1.00000			0.0392837
$649$			49.1915i			1.93093i
$650$	7.91665	−	22.1735i	0.310517	−	0.869716i
$651$		−	4.30975i		−	0.168912i
$652$	−0.455364			−0.0178334
$653$	−40.2219			−1.57400			−0.787002	−	0.616951i	$-0.788368\pi$
$653$	−40.2219			−1.57400			−0.787002	+	0.616951i	$0.788368\pi$
$654$	2.54677			0.0995864
$655$	−23.7604	+	16.7462i	−0.928397	+	0.654327i
$656$	−4.46326			−0.174261
$657$		−	10.2834i		−	0.401195i
$658$	2.38919			0.0931404
$659$	20.4172			0.795341			0.397670	−	0.917528i	$-0.369819\pi$
$659$	20.4172			0.795341			0.397670	+	0.917528i	$0.369819\pi$
$660$	9.99458	−	7.04410i	0.389038	−	0.274191i
$661$		−	49.8075i		−	1.93729i	−0.248454	−	0.968644i	$-0.579923\pi$
$661$		−	49.8075i		−	1.93729i	0.248454	−	0.968644i	$-0.420077\pi$
$662$			21.5849i			0.838919i
$663$		−	5.61812i		−	0.218190i
$664$			0.754493i			0.0292800i
$665$	−1.97597	−	2.80362i	−0.0766250	−	0.108720i
$666$	−4.58473	−	3.99753i	−0.177655	−	0.154901i
$667$			9.74786i			0.377439i
$668$	−0.755752			−0.0292409
$669$	20.0982			0.777042
$670$	−7.69690	+	5.42472i	−0.297357	+	0.209575i
$671$			33.9685i			1.31134i
$672$	1.25548			0.0484312
$673$		−	30.7799i		−	1.18648i	−0.805026	−	0.593239i	$-0.797849\pi$
$673$		−	30.7799i		−	1.18648i	0.805026	−	0.593239i	$-0.202151\pi$
$674$		−	24.3782i		−	0.939013i
$675$	−4.70887	−	1.68122i	−0.181245	−	0.0647102i
$676$	9.17350			0.352827
$677$			36.8784i			1.41735i	0.705533	+	0.708677i	$0.250708\pi$
$677$			36.8784i			1.41735i	−0.705533	+	0.708677i	$0.749292\pi$
$678$		−	4.72781i		−	0.181571i
$679$		−	20.9431i		−	0.803723i
$680$	1.53691	+	2.18065i	0.0589377	+	0.0836242i
$681$			15.1621i			0.581014i
$682$			18.7713i			0.718789i
$683$	−22.1763			−0.848552			−0.424276	−	0.905533i	$-0.639471\pi$
$683$	−22.1763			−0.848552			−0.424276	+	0.905533i	$0.639471\pi$
$684$			1.22179i			0.0467164i
$685$	−24.7634	+	17.4531i	−0.946161	+	0.666848i
$686$			15.5978i			0.595527i
$687$			2.54527i			0.0971080i
$688$	−1.34271			−0.0511902
$689$		−	5.25844i		−	0.200331i
$690$	3.50152	−	2.46784i	0.133301	−	0.0939492i
$691$	15.0935			0.574185			0.287093	−	0.957903i	$-0.407311\pi$
$691$	15.0935			0.574185			0.287093	+	0.957903i	$0.407311\pi$
$692$		−	4.41375i		−	0.167786i
$693$			6.86533i			0.260792i
$694$	−25.4950			−0.967776
$695$	−19.7422	−	28.0113i	−0.748864	−	1.06253i
$696$	−5.08822			−0.192868
$697$	5.32507			0.201701
$698$	2.69761			0.102106
$699$	13.9212			0.526548
$700$	−5.91190	−	2.11074i	−0.223449	−	0.0797784i
$701$			31.2390i			1.17988i	0.807447	+	0.589941i	$0.200849\pi$
$701$			31.2390i			1.17988i	−0.807447	+	0.589941i	$0.799151\pi$
$702$		−	4.70887i		−	0.177725i
$703$	4.88414	−	5.60159i	0.184209	−	0.211268i
$704$	−5.46829			−0.206094
$705$	2.45141	+	3.47820i	0.0923253	+	0.130996i
$706$	21.7179			0.817362
$707$			4.09555i			0.154029i
$708$	−8.99577			−0.338082
$709$		−	23.2007i		−	0.871322i	−0.900111	−	0.435661i	$-0.856515\pi$
$709$		−	23.2007i		−	0.871322i	0.900111	−	0.435661i	$-0.143485\pi$
$710$	15.9953	+	22.6950i	0.600293	+	0.851729i
$711$		−	1.00691i		−	0.0377621i
$712$		−	11.4743i		−	0.430018i
$713$			6.57636i			0.246287i
$714$	−1.49790			−0.0560576
$715$	−33.1698	−	47.0632i	−1.24048	−	1.76006i
$716$			12.6883i			0.474184i
$717$	28.8753			1.07837
$718$	−20.3716			−0.760260
$719$	41.3863			1.54345			0.771724	−	0.635958i	$-0.219395\pi$
$719$	41.3863			1.54345			0.771724	+	0.635958i	$0.219395\pi$
$720$	1.28817	+	1.82773i	0.0480074	+	0.0681156i
$721$		−	6.52009i		−	0.242821i
$722$	17.5072			0.651552
$723$	−6.84853			−0.254699
$724$	13.2444			0.492223
$725$	23.9598	+	8.55441i	0.889844	+	0.317703i
$726$		−	18.9022i		−	0.701526i
$727$	8.02093			0.297480			0.148740	−	0.988876i	$-0.452478\pi$
$727$	8.02093			0.297480			0.148740	+	0.988876i	$0.452478\pi$
$728$		−	5.91190i		−	0.219110i
$729$	−1.00000			−0.0370370
$730$	18.7954	−	13.2469i	0.695649	−	0.490288i
$731$	1.60197			0.0592510
$732$	−6.21190			−0.229598
$733$		−	43.5044i		−	1.60687i	−0.595391	−	0.803436i	$-0.703003\pi$
$733$		−	43.5044i		−	1.60687i	0.595391	−	0.803436i	$-0.296997\pi$
$734$			31.0972i			1.14782i
$735$	−9.91321	+	6.98676i	−0.365654	+	0.257710i
$736$	−1.91577			−0.0706163
$737$			23.0279i			0.848244i
$738$	4.46326			0.164295
$739$	−40.4960			−1.48967			−0.744834	−	0.667249i	$-0.767472\pi$
$739$	−40.4960			−1.48967			−0.744834	+	0.667249i	$0.767472\pi$
$740$	1.40049	−	13.5292i	0.0514829	−	0.497342i
$741$	5.75326			0.211351
$742$	−1.40201			−0.0514692
$743$			33.7617i			1.23860i	0.785156	+	0.619298i	$0.212583\pi$
$743$			33.7617i			1.23860i	−0.785156	+	0.619298i	$0.787417\pi$
$744$	−3.43275			−0.125851
$745$	−17.3496	−	24.6166i	−0.635640	−	0.901882i
$746$			33.4131i			1.22334i
$747$		−	0.754493i		−	0.0276055i
$748$	6.52417			0.238547
$749$	−10.8718			−0.397248
$750$	−2.99303	−	10.7723i	−0.109290	−	0.393348i
$751$	−16.9597			−0.618867			−0.309434	−	0.950921i	$-0.600139\pi$
$751$	−16.9597			−0.618867			−0.309434	+	0.950921i	$0.600139\pi$
$752$		−	1.90301i		−	0.0693956i
$753$	−18.7459			−0.683138
$754$			23.9598i			0.872564i
$755$	13.3879	+	18.9956i	0.487237	+	0.691319i
$756$	−1.25548			−0.0456614
$757$	−10.2892			−0.373969			−0.186984	−	0.982363i	$-0.559871\pi$
$757$	−10.2892			−0.373969			−0.186984	+	0.982363i	$0.559871\pi$
$758$	−24.6191			−0.894204
$759$		−	10.4760i		−	0.380254i
$760$	−2.23311	+	1.57388i	−0.0810034	+	0.0570906i
$761$	−30.3977			−1.10192			−0.550959	−	0.834533i	$-0.685738\pi$
$761$	−30.3977			−1.10192			−0.550959	+	0.834533i	$0.685738\pi$
$762$	−8.05067			−0.291645
$763$	−3.19741			−0.115754
$764$		−	7.03990i		−	0.254695i
$765$	−1.53691	−	2.18065i	−0.0555670	−	0.0788416i
$766$	−17.5596			−0.634453
$767$			42.3600i			1.52953i
$768$		−	1.00000i		−	0.0360844i
$769$			46.4643i			1.67554i	0.546019	+	0.837772i	$0.316142\pi$
$769$			46.4643i			1.67554i	−0.546019	+	0.837772i	$0.683858\pi$
$770$	−12.5480	+	8.84373i	−0.452198	+	0.318706i
$771$			17.3509i			0.624876i
$772$	0.635749			0.0228811
$773$			30.6420i			1.10212i	0.834467	+	0.551058i	$0.185776\pi$
$773$			30.6420i			1.10212i	−0.834467	+	0.551058i	$0.814224\pi$
$774$	1.34271			0.0482626
$775$	16.1644	+	5.77121i	0.580642	+	0.207308i
$776$	−16.6814			−0.598826
$777$	5.75604	+	5.01882i	0.206497	+	0.180049i
$778$		−	19.6417i		−	0.704190i
$779$			5.45317i			0.195380i
$780$	8.60657	−	6.06585i	0.308165	−	0.217192i
$781$	67.8999			2.42965
$782$	2.28569			0.0817361
$783$	5.08822			0.181838
$784$	5.42377			0.193706
$785$	−26.0081	+	18.3303i	−0.928270	+	0.654238i
$786$	−12.9999			−0.463693
$787$		−	8.65409i		−	0.308485i	−0.988033	−	0.154243i	$-0.950706\pi$
$787$		−	8.65409i		−	0.308485i	0.988033	−	0.154243i	$-0.0492937\pi$
$788$		−	5.18937i		−	0.184864i
$789$	−31.3436			−1.11586
$790$	1.84036	−	1.29707i	0.0654772	−	0.0461478i
$791$			5.93567i			0.211048i
$792$	5.46829			0.194307
$793$			29.2511i			1.03874i
$794$			4.31480i			0.153127i
$795$	−1.43851	−	2.04105i	−0.0510188	−	0.0723884i
$796$			23.8852i			0.846589i
$797$	25.1436			0.890634			0.445317	−	0.895373i	$-0.353091\pi$
$797$	25.1436			0.890634			0.445317	+	0.895373i	$0.353091\pi$
$798$		−	1.53393i		−	0.0543007i
$799$			2.27046i			0.0803232i
$800$	−1.68122	+	4.70887i	−0.0594401	+	0.166484i
$801$			11.4743i			0.405425i
$802$			9.64980i			0.340746i
$803$		−	56.2328i		−	1.98441i
$804$	−4.21117			−0.148517
$805$	−4.39609	+	3.09833i	−0.154942	+	0.109202i
$806$			16.1644i			0.569367i
$807$		−	20.8503i		−	0.733964i
$808$	3.26214			0.114762
$809$			54.4206i			1.91333i	0.291199	+	0.956663i	$0.405946\pi$
$809$			54.4206i			1.91333i	−0.291199	+	0.956663i	$0.594054\pi$
$810$	−1.28817	−	1.82773i	−0.0452618	−	0.0642200i
$811$	32.8378			1.15309			0.576546	−	0.817065i	$-0.304400\pi$
$811$	32.8378			1.15309			0.576546	+	0.817065i	$0.304400\pi$
$812$	6.38816			0.224180
$813$			0.977182i			0.0342713i
$814$	−25.0706	−	21.8596i	−0.878726	−	0.766180i
$815$	0.586588	+	0.832284i	0.0205473	+	0.0291536i
$816$			1.19309i			0.0417665i
$817$			1.64051i			0.0573941i
$818$		−	25.5235i		−	0.892409i
$819$			5.91190i			0.206578i
$820$	5.74945	+	8.15764i	0.200779	+	0.284877i
$821$	25.1041			0.876138			0.438069	−	0.898941i	$-0.355663\pi$
$821$	25.1041			0.876138			0.438069	+	0.898941i	$0.355663\pi$
$822$	−13.5487			−0.472565
$823$		−	11.1202i		−	0.387627i	−0.981038	−	0.193814i	$-0.937914\pi$
$823$		−	11.1202i		−	0.387627i	0.981038	−	0.193814i	$-0.0620857\pi$
$824$	−5.19330			−0.180917
$825$	−25.7495	−	9.19339i	−0.896482	−	0.320073i
$826$	11.2940			0.392969
$827$	−7.01483			−0.243930			−0.121965	−	0.992534i	$-0.538920\pi$
$827$	−7.01483			−0.243930			−0.121965	+	0.992534i	$0.538920\pi$
$828$	1.91577			0.0665776
$829$		−	12.5028i		−	0.434240i	−0.976145	−	0.217120i	$-0.930334\pi$
$829$		−	12.5028i		−	0.434240i	0.976145	−	0.217120i	$-0.0696662\pi$
$830$	1.37901	−	0.971918i	0.0478662	−	0.0337358i
$831$		−	28.0775i		−	0.973997i
$832$	−4.70887			−0.163251
$833$	−6.47105			−0.224209
$834$		−	15.3257i		−	0.530686i
$835$	0.973540	+	1.38131i	0.0336907	+	0.0478023i
$836$			6.68111i			0.231071i
$837$	3.43275			0.118653
$838$	−22.0969			−0.763324
$839$	44.6267			1.54069			0.770343	−	0.637630i	$-0.220085\pi$
$839$	44.6267			1.54069			0.770343	+	0.637630i	$0.220085\pi$
$840$	−1.61728	−	2.29468i	−0.0558013	−	0.0791741i
$841$	3.11004			0.107243
$842$		−	8.20101i		−	0.282626i
$843$	20.9112			0.720221
$844$	−26.6260			−0.916505
$845$	−11.8171	−	16.7667i	−0.406519	−	0.576793i
$846$			1.90301i			0.0654268i
$847$			23.7313i			0.815418i
$848$			1.11671i			0.0383479i
$849$		−	11.7273i		−	0.402480i
$850$	2.00585	−	5.61812i	0.0688000	−	0.192700i
$851$	−8.78330	−	7.65835i	−0.301088	−	0.262525i
$852$			12.4170i			0.425401i
$853$	−3.59757			−0.123178			−0.0615892	−	0.998102i	$-0.519617\pi$
$853$	−3.59757			−0.123178			−0.0615892	+	0.998102i	$0.519617\pi$
$854$	7.79891			0.266873
$855$	2.23311	−	1.57388i	0.0763707	−	0.0538255i
$856$			8.65950i			0.295976i
$857$	−7.66263			−0.261750			−0.130875	−	0.991399i	$-0.541779\pi$
$857$	−7.66263			−0.261750			−0.130875	+	0.991399i	$0.541779\pi$
$858$		−	25.7495i		−	0.879073i
$859$		−	56.3900i		−	1.92400i	−0.273046	−	0.962001i	$-0.588031\pi$
$859$		−	56.3900i		−	1.92400i	0.273046	−	0.962001i	$-0.411969\pi$
$860$	1.72964	+	2.45411i	0.0589802	+	0.0836844i
$861$	−5.60353			−0.190968
$862$			9.83076i			0.334837i
$863$		−	12.7800i		−	0.435037i	−0.976056	−	0.217518i	$-0.930204\pi$
$863$		−	12.7800i		−	0.435037i	0.976056	−	0.217518i	$-0.0697962\pi$
$864$			1.00000i			0.0340207i
$865$	−8.06716	+	5.68568i	−0.274292	+	0.193319i
$866$		−	1.61024i		−	0.0547182i
$867$			15.5765i			0.529007i
$868$	4.30975			0.146282
$869$		−	5.50607i		−	0.186781i
$870$	6.55451	+	9.29991i	0.222219	+	0.315296i
$871$			19.8299i			0.671910i
$872$			2.54677i			0.0862444i
$873$	16.6814			0.564579
$874$			2.34067i			0.0791744i
$875$	3.75768	+	13.5244i	0.127033	+	0.457207i
$876$	10.2834			0.347445
$877$			40.4607i			1.36626i	0.730297	+	0.683130i	$0.239382\pi$
$877$			40.4607i			1.36626i	−0.730297	+	0.683130i	$0.760618\pi$
$878$			32.2443i			1.08819i
$879$	−19.0944			−0.644037
$880$	7.04410	+	9.99458i	0.237457	+	0.336917i
$881$	−48.2664			−1.62614			−0.813069	−	0.582168i	$-0.802205\pi$
$881$	−48.2664			−1.62614			−0.813069	+	0.582168i	$0.802205\pi$
$882$	−5.42377			−0.182628
$883$	7.33442			0.246823			0.123411	−	0.992356i	$-0.460617\pi$
$883$	7.33442			0.246823			0.123411	+	0.992356i	$0.460617\pi$
$884$	5.61812			0.188958
$885$	11.5881	+	16.4419i	0.389530	+	0.552687i
$886$		−	19.0730i		−	0.640770i
$887$		−	28.5353i		−	0.958120i	−0.877782	−	0.479060i	$-0.840978\pi$
$887$		−	28.5353i		−	0.958120i	0.877782	−	0.479060i	$-0.159022\pi$
$888$	3.99753	−	4.58473i	0.134148	−	0.153854i
$889$	10.1075			0.338993
$890$	−20.9720	+	14.7809i	−0.702983	+	0.495457i
$891$	−5.46829			−0.183195
$892$			20.0982i			0.672938i
$893$	−2.32508			−0.0778059
$894$		−	13.4684i		−	0.450450i
$895$	23.1908	−	16.3447i	0.775184	−	0.546344i
$896$			1.25548i			0.0419426i
$897$		−	9.02113i		−	0.301207i
$898$			30.6914i			1.02418i
$899$	−17.4666			−0.582543
$900$	1.68122	−	4.70887i	0.0560406	−	0.156962i
$901$		−	1.33233i		−	0.0443865i
$902$	24.4064			0.812643
$903$	−1.68574			−0.0560980
$904$	4.72781			0.157245
$905$	−17.0610	−	24.2072i	−0.567128	−	0.804673i
$906$			10.3930i			0.345283i
$907$	31.6207			1.04995			0.524974	−	0.851118i	$-0.324075\pi$
$907$	31.6207			1.04995			0.524974	+	0.851118i	$0.324075\pi$
$908$	−15.1621			−0.503173
$909$	−3.26214			−0.108198
$910$	−10.8054	+	7.61555i	−0.358195	+	0.252453i
$911$		−	2.67057i		−	0.0884800i	−0.999021	−	0.0442400i	$-0.985913\pi$
$911$		−	2.67057i		−	0.0884800i	0.999021	−	0.0442400i	$-0.0140866\pi$
$912$	−1.22179			−0.0404575
$913$		−	4.12579i		−	0.136544i
$914$	−22.4560			−0.742777
$915$	8.00200	+	11.3537i	0.264538	+	0.375342i
$916$	−2.54527			−0.0840980
$917$	16.3212			0.538972
$918$		−	1.19309i		−	0.0393779i
$919$			40.0514i			1.32117i	0.750750	+	0.660587i	$0.229692\pi$
$919$			40.0514i			1.32117i	−0.750750	+	0.660587i	$0.770308\pi$
$920$	2.46784	+	3.50152i	0.0813624	+	0.115442i
$921$	−31.2854			−1.03089
$922$		−	7.37800i		−	0.242981i
$923$	58.4703			1.92457
$924$	−6.86533			−0.225853
$925$	−26.5318	+	14.8682i	−0.872360	+	0.488864i
$926$	6.16145			0.202478
$927$	5.19330			0.170570
$928$		−	5.08822i		−	0.167029i
$929$	47.8279			1.56918			0.784592	−	0.620013i	$-0.212873\pi$
$929$	47.8279			1.56918			0.784592	+	0.620013i	$0.212873\pi$
$930$	4.42198	+	6.27415i	0.145002	+	0.205738i
$931$		−	6.62671i		−	0.217182i
$932$			13.9212i			0.456004i
$933$	−7.52409			−0.246328
$934$	−5.37297			−0.175809
$935$	−8.40426	−	11.9244i	−0.274849	−	0.389971i
$936$	4.70887			0.153914
$937$		−	44.7707i		−	1.46260i	−0.682058	−	0.731298i	$-0.738915\pi$
$937$		−	44.7707i		−	1.46260i	0.682058	−	0.731298i	$-0.261085\pi$
$938$	5.28704			0.172628
$939$		−	0.0900227i		−	0.00293778i
$940$	−3.47820	+	2.45141i	−0.113446	+	0.0799561i
$941$	38.1052			1.24219			0.621097	−	0.783734i	$-0.286687\pi$
$941$	38.1052			1.24219			0.621097	+	0.783734i	$0.286687\pi$
$942$	−14.2297			−0.463629
$943$	8.55058			0.278445
$944$		−	8.99577i		−	0.292787i
$945$	1.61728	+	2.29468i	0.0526100	+	0.0746460i
$946$	7.34231			0.238719
$947$	−53.7661			−1.74716			−0.873582	−	0.486678i	$-0.838209\pi$
$947$	−53.7661			−1.74716			−0.873582	+	0.486678i	$0.838209\pi$
$948$	1.00691			0.0327029
$949$		−	48.4234i		−	1.57189i
$950$	5.75326	+	2.05410i	0.186660	+	0.0666438i
$951$	−7.86659			−0.255092
$952$		−	1.49790i		−	0.0485473i
$953$		−	12.7882i		−	0.414252i	−0.978314	−	0.207126i	$-0.933589\pi$
$953$		−	12.7882i		−	0.414252i	0.978314	−	0.207126i	$-0.0664109\pi$
$954$		−	1.11671i		−	0.0361548i
$955$	−12.8671	+	9.06861i	−0.416368	+	0.293453i
$956$			28.8753i			0.933895i
$957$	27.8239			0.899417
$958$		−	21.5810i		−	0.697251i
$959$	17.0101			0.549286
$960$	−1.82773	+	1.28817i	−0.0589898	+	0.0415756i
$961$	19.2162			0.619878
$962$	−21.5889	−	18.8239i	−0.696055	−	0.606906i
$963$		−	8.65950i		−	0.279049i
$964$		−	6.84853i		−	0.220576i
$965$	−0.818954	−	1.16198i	−0.0263631	−	0.0374054i
$966$	−2.40521			−0.0773864
$967$	49.4979			1.59175			0.795873	−	0.605463i	$-0.207012\pi$
$967$	49.4979			1.59175			0.795873	+	0.605463i	$0.207012\pi$
$968$	18.9022			0.607540
$969$	1.45771			0.0468283
$970$	21.4885	+	30.4891i	0.689954	+	0.978946i
$971$	−22.7751			−0.730887			−0.365444	−	0.930834i	$-0.619083\pi$
$971$	−22.7751			−0.730887			−0.365444	+	0.930834i	$0.619083\pi$
$972$		−	1.00000i		−	0.0320750i
$973$			19.2411i			0.616843i
$974$	0.346315			0.0110967
$975$	−22.1735	−	7.91665i	−0.710120	−	0.253536i
$976$		−	6.21190i		−	0.198838i
$977$	−7.08386			−0.226633			−0.113316	−	0.993559i	$-0.536147\pi$
$977$	−7.08386			−0.226633			−0.113316	+	0.993559i	$0.536147\pi$
$978$			0.455364i			0.0145609i
$979$			62.7449i			2.00534i
$980$	−6.98676	−	9.91321i	−0.223184	−	0.316666i
$981$		−	2.54677i		−	0.0813120i
$982$	10.6278			0.339146
$983$		−	50.8277i		−	1.62115i	−0.585634	−	0.810576i	$-0.699154\pi$
$983$		−	50.8277i		−	1.62115i	0.585634	−	0.810576i	$-0.300846\pi$
$984$			4.46326i			0.142283i
$985$	−9.48478	+	6.68481i	−0.302210	+	0.212996i
$986$			6.07071i			0.193331i
$987$		−	2.38919i		−	0.0760488i
$988$			5.75326i			0.183036i
$989$	2.57232			0.0817949
$990$	−7.04410	−	9.99458i	−0.223876	−	0.317648i
$991$		−	42.8852i		−	1.36229i	−0.732146	−	0.681147i	$-0.761481\pi$
$991$		−	42.8852i		−	1.36229i	0.732146	−	0.681147i	$-0.238519\pi$
$992$		−	3.43275i		−	0.108990i
$993$	21.5849			0.684975
$994$		−	15.5893i		−	0.494464i
$995$	43.6558	−	30.7683i	1.38398	−	0.975421i
$996$	0.754493			0.0239070
$997$	−6.15244			−0.194850			−0.0974248	−	0.995243i	$-0.531061\pi$
$997$	−6.15244			−0.194850			−0.0974248	+	0.995243i	$0.531061\pi$
$998$		−	12.0121i		−	0.380237i
$999$	−3.99753	+	4.58473i	−0.126476	+	0.145055i

Twists

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

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

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.00000i q^{3} +1.00000 q^{4} +(-1.28817 - 1.82773i) q^{5} -1.00000i q^{6} +1.25548i q^{7} +1.00000 q^{8} -1.00000 q^{9} +(-1.28817 - 1.82773i) q^{10} -5.46829 q^{11} -1.00000i q^{12} -4.70887 q^{13} +1.25548i q^{14} +(-1.82773 + 1.28817i) q^{15} +1.00000 q^{16} -1.19309 q^{17} -1.00000 q^{18} -1.22179i q^{19} +(-1.28817 - 1.82773i) q^{20} +1.25548 q^{21} -5.46829 q^{22} -1.91577 q^{23} -1.00000i q^{24} +(-1.68122 + 4.70887i) q^{25} -4.70887 q^{26} +1.00000i q^{27} +1.25548i q^{28} -5.08822i q^{29} +(-1.82773 + 1.28817i) q^{30} -3.43275i q^{31} +1.00000 q^{32} +5.46829i q^{33} -1.19309 q^{34} +(2.29468 - 1.61728i) q^{35} -1.00000 q^{36} +(4.58473 + 3.99753i) q^{37} -1.22179i q^{38} +4.70887i q^{39} +(-1.28817 - 1.82773i) q^{40} -4.46326 q^{41} +1.25548 q^{42} -1.34271 q^{43} -5.46829 q^{44} +(1.28817 + 1.82773i) q^{45} -1.91577 q^{46} -1.90301i q^{47} -1.00000i q^{48} +5.42377 q^{49} +(-1.68122 + 4.70887i) q^{50} +1.19309i q^{51} -4.70887 q^{52} +1.11671i q^{53} +1.00000i q^{54} +(7.04410 + 9.99458i) q^{55} +1.25548i q^{56} -1.22179 q^{57} -5.08822i q^{58} -8.99577i q^{59} +(-1.82773 + 1.28817i) q^{60} -6.21190i q^{61} -3.43275i q^{62} -1.25548i q^{63} +1.00000 q^{64} +(6.06585 + 8.60657i) q^{65} +5.46829i q^{66} -4.21117i q^{67} -1.19309 q^{68} +1.91577i q^{69} +(2.29468 - 1.61728i) q^{70} -12.4170 q^{71} -1.00000 q^{72} +10.2834i q^{73} +(4.58473 + 3.99753i) q^{74} +(4.70887 + 1.68122i) q^{75} -1.22179i q^{76} -6.86533i q^{77} +4.70887i q^{78} +1.00691i q^{79} +(-1.28817 - 1.82773i) q^{80} +1.00000 q^{81} -4.46326 q^{82} +0.754493i q^{83} +1.25548 q^{84} +(1.53691 + 2.18065i) q^{85} -1.34271 q^{86} -5.08822 q^{87} -5.46829 q^{88} -11.4743i q^{89} +(1.28817 + 1.82773i) q^{90} -5.91190i q^{91} -1.91577 q^{92} -3.43275 q^{93} -1.90301i q^{94} +(-2.23311 + 1.57388i) q^{95} -1.00000i q^{96} -16.6814 q^{97} +5.42377 q^{98} +5.46829 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 16 q^{2} + 16 q^{4} + 2 q^{5} + 16 q^{8} - 16 q^{9} + 2 q^{10} + 2 q^{11} - 6 q^{15} + 16 q^{16} + 38 q^{17} - 16 q^{18} + 2 q^{20} + 6 q^{21} + 2 q^{22} + 20 q^{23} - 4 q^{25} - 6 q^{30} + 16 q^{32}+ \cdots - 2 q^{99}+O(q^{100}) \) 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

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Database

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