LMFDB - Embedded newform 1110.2.o.b.253.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1110,2,Mod(253,1110)]

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([0, 3, 1]))

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

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

chi := DirichletCharacter("1110.253");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1110 = 2 \cdot 3 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1110.o (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			253.2
Character	$\chi$	$=$	1110.253
Dual form			1110.2.o.b.487.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +(-0.707107 + 0.707107i) q^{3} +1.00000 q^{4} +(-1.17802 + 1.90060i) q^{5} +(-0.707107 + 0.707107i) q^{6} +(-2.67041 + 2.67041i) q^{7} +1.00000 q^{8} -1.00000i q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +(-0.707107 + 0.707107i) q^{3} +1.00000 q^{4} +(-1.17802 + 1.90060i) q^{5} +(-0.707107 + 0.707107i) q^{6} +(-2.67041 + 2.67041i) q^{7} +1.00000 q^{8} -1.00000i q^{9} +(-1.17802 + 1.90060i) q^{10} -2.74868i q^{11} +(-0.707107 + 0.707107i) q^{12} -3.42928 q^{13} +(-2.67041 + 2.67041i) q^{14} +(-0.510937 - 2.17691i) q^{15} +1.00000 q^{16} -0.534649i q^{17} -1.00000i q^{18} +(-1.10003 - 1.10003i) q^{19} +(-1.17802 + 1.90060i) q^{20} -3.77653i q^{21} -2.74868i q^{22} +2.91366 q^{23} +(-0.707107 + 0.707107i) q^{24} +(-2.22453 - 4.47789i) q^{25} -3.42928 q^{26} +(0.707107 + 0.707107i) q^{27} +(-2.67041 + 2.67041i) q^{28} +(-6.34828 + 6.34828i) q^{29} +(-0.510937 - 2.17691i) q^{30} +(-3.92620 - 3.92620i) q^{31} +1.00000 q^{32} +(1.94361 + 1.94361i) q^{33} -0.534649i q^{34} +(-1.92957 - 8.22118i) q^{35} -1.00000i q^{36} +(0.429296 - 6.06759i) q^{37} +(-1.10003 - 1.10003i) q^{38} +(2.42487 - 2.42487i) q^{39} +(-1.17802 + 1.90060i) q^{40} -9.62252i q^{41} -3.77653i q^{42} +1.95296 q^{43} -2.74868i q^{44} +(1.90060 + 1.17802i) q^{45} +2.91366 q^{46} +(-9.10685 + 9.10685i) q^{47} +(-0.707107 + 0.707107i) q^{48} -7.26220i q^{49} +(-2.22453 - 4.47789i) q^{50} +(0.378054 + 0.378054i) q^{51} -3.42928 q^{52} +(8.83246 + 8.83246i) q^{53} +(0.707107 + 0.707107i) q^{54} +(5.22412 + 3.23800i) q^{55} +(-2.67041 + 2.67041i) q^{56} +1.55567 q^{57} +(-6.34828 + 6.34828i) q^{58} +(-8.17158 - 8.17158i) q^{59} +(-0.510937 - 2.17691i) q^{60} +(3.52447 + 3.52447i) q^{61} +(-3.92620 - 3.92620i) q^{62} +(2.67041 + 2.67041i) q^{63} +1.00000 q^{64} +(4.03977 - 6.51767i) q^{65} +(1.94361 + 1.94361i) q^{66} +(5.36985 + 5.36985i) q^{67} -0.534649i q^{68} +(-2.06027 + 2.06027i) q^{69} +(-1.92957 - 8.22118i) q^{70} -15.0364 q^{71} -1.00000i q^{72} +(-7.28489 + 7.28489i) q^{73} +(0.429296 - 6.06759i) q^{74} +(4.73932 + 1.59337i) q^{75} +(-1.10003 - 1.10003i) q^{76} +(7.34010 + 7.34010i) q^{77} +(2.42487 - 2.42487i) q^{78} +(4.60304 + 4.60304i) q^{79} +(-1.17802 + 1.90060i) q^{80} -1.00000 q^{81} -9.62252i q^{82} +(-10.9528 - 10.9528i) q^{83} -3.77653i q^{84} +(1.01615 + 0.629829i) q^{85} +1.95296 q^{86} -8.97783i q^{87} -2.74868i q^{88} +(-9.99204 + 9.99204i) q^{89} +(1.90060 + 1.17802i) q^{90} +(9.15759 - 9.15759i) q^{91} +2.91366 q^{92} +5.55248 q^{93} +(-9.10685 + 9.10685i) q^{94} +(3.38656 - 0.794851i) q^{95} +(-0.707107 + 0.707107i) q^{96} +14.3863i q^{97} -7.26220i q^{98} -2.74868 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 40 q^{2} + 40 q^{4} - 4 q^{7} + 40 q^{8}+O(q^{10}) $ 40 * q + 40 * q^2 + 40 * q^4 - 4 * q^7 + 40 * q^8	$ 40 q + 40 q^{2} + 40 q^{4} - 4 q^{7} + 40 q^{8} + 8 q^{13} - 4 q^{14} + 40 q^{16} - 4 q^{19} - 8 q^{25} + 8 q^{26} - 4 q^{28} + 28 q^{31} + 40 q^{32} - 4 q^{33} + 12 q^{35} + 8 q^{37} - 4 q^{38} - 4 q^{39} - 16 q^{47} - 8 q^{50} + 16 q^{51} + 8 q^{52} + 20 q^{53} - 8 q^{55} - 4 q^{56} - 8 q^{57} + 4 q^{59} - 8 q^{61} + 28 q^{62} + 4 q^{63} + 40 q^{64} + 4 q^{65} - 4 q^{66} - 16 q^{67} + 8 q^{69} + 12 q^{70} + 40 q^{71} - 8 q^{73} + 8 q^{74} + 16 q^{75} - 4 q^{76} + 24 q^{77} - 4 q^{78} + 12 q^{79} - 40 q^{81} - 8 q^{83} + 8 q^{85} - 12 q^{89} - 24 q^{91} - 8 q^{93} - 16 q^{94} + 28 q^{95} - 8 q^{99}+O(q^{100}) $ 40 * q + 40 * q^2 + 40 * q^4 - 4 * q^7 + 40 * q^8 + 8 * q^13 - 4 * q^14 + 40 * q^16 - 4 * q^19 - 8 * q^25 + 8 * q^26 - 4 * q^28 + 28 * q^31 + 40 * q^32 - 4 * q^33 + 12 * q^35 + 8 * q^37 - 4 * q^38 - 4 * q^39 - 16 * q^47 - 8 * q^50 + 16 * q^51 + 8 * q^52 + 20 * q^53 - 8 * q^55 - 4 * q^56 - 8 * q^57 + 4 * q^59 - 8 * q^61 + 28 * q^62 + 4 * q^63 + 40 * q^64 + 4 * q^65 - 4 * q^66 - 16 * q^67 + 8 * q^69 + 12 * q^70 + 40 * q^71 - 8 * q^73 + 8 * q^74 + 16 * q^75 - 4 * q^76 + 24 * q^77 - 4 * q^78 + 12 * q^79 - 40 * q^81 - 8 * q^83 + 8 * q^85 - 12 * q^89 - 24 * q^91 - 8 * q^93 - 16 * q^94 + 28 * q^95 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	1.00000			0.707107
$2$	1.00000			0.707107
$3$	−0.707107	+	0.707107i	−0.408248	+	0.408248i
$3$	−0.707107	+	0.707107i	−0.408248	+	0.408248i
$4$	1.00000			0.500000
$5$	−1.17802	+	1.90060i	−0.526827	+	0.849972i
$5$	−1.17802	+	1.90060i	−0.526827	+	0.849972i
$6$	−0.707107	+	0.707107i	−0.288675	+	0.288675i
$7$	−2.67041	+	2.67041i	−1.00932	+	1.00932i	−0.00936469	+	0.999956i	$0.502981\pi$
$7$	−2.67041	+	2.67041i	−1.00932	+	1.00932i	−0.999956	+	0.00936469i	$0.997019\pi$
$8$	1.00000			0.353553
$9$		−	1.00000i		−	0.333333i
$10$	−1.17802	+	1.90060i	−0.372523	+	0.601021i
$11$		−	2.74868i		−	0.828757i	−0.910105	−	0.414378i	$-0.863999\pi$
$11$		−	2.74868i		−	0.828757i	0.910105	−	0.414378i	$-0.136001\pi$
$12$	−0.707107	+	0.707107i	−0.204124	+	0.204124i
$13$	−3.42928			−0.951111			−0.475556	−	0.879686i	$-0.657753\pi$
$13$	−3.42928			−0.951111			−0.475556	+	0.879686i	$0.657753\pi$
$14$	−2.67041	+	2.67041i	−0.713698	+	0.713698i
$15$	−0.510937	−	2.17691i	−0.131923	−	0.562076i
$16$	1.00000			0.250000
$17$		−	0.534649i		−	0.129672i	−0.997896	−	0.0648358i	$-0.979348\pi$
$17$		−	0.534649i		−	0.129672i	0.997896	−	0.0648358i	$-0.0206524\pi$
$18$		−	1.00000i		−	0.235702i
$19$	−1.10003	−	1.10003i	−0.252364	−	0.252364i	0.569575	−	0.821939i	$-0.307108\pi$
$19$	−1.10003	−	1.10003i	−0.252364	−	0.252364i	−0.821939	+	0.569575i	$0.807108\pi$
$20$	−1.17802	+	1.90060i	−0.263414	+	0.424986i
$21$		−	3.77653i		−	0.824107i
$22$		−	2.74868i		−	0.586020i
$23$	2.91366			0.607540			0.303770	−	0.952745i	$-0.401754\pi$
$23$	2.91366			0.607540			0.303770	+	0.952745i	$0.401754\pi$
$24$	−0.707107	+	0.707107i	−0.144338	+	0.144338i
$25$	−2.22453	−	4.47789i	−0.444906	−	0.895577i
$26$	−3.42928			−0.672537
$27$	0.707107	+	0.707107i	0.136083	+	0.136083i
$28$	−2.67041	+	2.67041i	−0.504660	+	0.504660i
$29$	−6.34828	+	6.34828i	−1.17885	+	1.17885i	−0.198808	+	0.980039i	$0.563707\pi$
$29$	−6.34828	+	6.34828i	−1.17885	+	1.17885i	−0.980039	+	0.198808i	$0.936293\pi$
$30$	−0.510937	−	2.17691i	−0.0932839	−	0.397448i
$31$	−3.92620	−	3.92620i	−0.705166	−	0.705166i	0.260349	−	0.965515i	$-0.416162\pi$
$31$	−3.92620	−	3.92620i	−0.705166	−	0.705166i	−0.965515	+	0.260349i	$0.916162\pi$
$32$	1.00000			0.176777
$33$	1.94361	+	1.94361i	0.338339	+	0.338339i
$34$		−	0.534649i		−	0.0916916i
$35$	−1.92957	−	8.22118i	−0.326157	−	1.38963i
$36$		−	1.00000i		−	0.166667i
$37$	0.429296	−	6.06759i	0.0705758	−	0.997506i
$37$	0.429296	−	6.06759i	0.0705758	−	0.997506i
$38$	−1.10003	−	1.10003i	−0.178448	−	0.178448i
$39$	2.42487	−	2.42487i	0.388289	−	0.388289i
$40$	−1.17802	+	1.90060i	−0.186262	+	0.300511i
$41$		−	9.62252i		−	1.50279i	−0.659855	−	0.751393i	$-0.729382\pi$
$41$		−	9.62252i		−	1.50279i	0.659855	−	0.751393i	$-0.270618\pi$
$42$		−	3.77653i		−	0.582732i
$43$	1.95296			0.297824			0.148912	−	0.988850i	$-0.452423\pi$
$43$	1.95296			0.297824			0.148912	+	0.988850i	$0.452423\pi$
$44$		−	2.74868i		−	0.414378i
$45$	1.90060	+	1.17802i	0.283324	+	0.175609i
$46$	2.91366			0.429596
$47$	−9.10685	+	9.10685i	−1.32837	+	1.32837i	−0.421580	+	0.906791i	$0.638524\pi$
$47$	−9.10685	+	9.10685i	−1.32837	+	1.32837i	−0.906791	+	0.421580i	$0.861476\pi$
$48$	−0.707107	+	0.707107i	−0.102062	+	0.102062i
$49$		−	7.26220i		−	1.03746i
$50$	−2.22453	−	4.47789i	−0.314596	−	0.633269i
$51$	0.378054	+	0.378054i	0.0529382	+	0.0529382i
$52$	−3.42928			−0.475556
$53$	8.83246	+	8.83246i	1.21323	+	1.21323i	0.969958	+	0.243273i	$0.0782212\pi$
$53$	8.83246	+	8.83246i	1.21323	+	1.21323i	0.243273	+	0.969958i	$0.421779\pi$
$54$	0.707107	+	0.707107i	0.0962250	+	0.0962250i
$55$	5.22412	+	3.23800i	0.704420	+	0.436612i
$56$	−2.67041	+	2.67041i	−0.356849	+	0.356849i
$57$	1.55567			0.206054
$58$	−6.34828	+	6.34828i	−0.833570	+	0.833570i
$59$	−8.17158	−	8.17158i	−1.06385	−	1.06385i	−0.997818	−	0.0660316i	$-0.978966\pi$
$59$	−8.17158	−	8.17158i	−1.06385	−	1.06385i	−0.0660316	−	0.997818i	$-0.521034\pi$
$60$	−0.510937	−	2.17691i	−0.0659616	−	0.281038i
$61$	3.52447	+	3.52447i	0.451262	+	0.451262i	0.895773	−	0.444511i	$-0.146623\pi$
$61$	3.52447	+	3.52447i	0.451262	+	0.451262i	−0.444511	+	0.895773i	$0.646623\pi$
$62$	−3.92620	−	3.92620i	−0.498628	−	0.498628i
$63$	2.67041	+	2.67041i	0.336440	+	0.336440i
$64$	1.00000			0.125000
$65$	4.03977	−	6.51767i	0.501071	−	0.808418i
$66$	1.94361	+	1.94361i	0.239241	+	0.239241i
$67$	5.36985	+	5.36985i	0.656032	+	0.656032i	0.954439	−	0.298407i	$-0.0964552\pi$
$67$	5.36985	+	5.36985i	0.656032	+	0.656032i	−0.298407	+	0.954439i	$0.596455\pi$
$68$		−	0.534649i		−	0.0648358i
$69$	−2.06027	+	2.06027i	−0.248027	+	0.248027i
$70$	−1.92957	−	8.22118i	−0.230628	−	0.982619i
$71$	−15.0364			−1.78449			−0.892245	−	0.451551i	$-0.850871\pi$
$71$	−15.0364			−1.78449			−0.892245	+	0.451551i	$0.850871\pi$
$72$		−	1.00000i		−	0.117851i
$73$	−7.28489	+	7.28489i	−0.852632	+	0.852632i	−0.990457	−	0.137825i	$-0.955989\pi$
$73$	−7.28489	+	7.28489i	−0.852632	+	0.852632i	0.137825	+	0.990457i	$0.455989\pi$
$74$	0.429296	−	6.06759i	0.0499046	−	0.705344i
$75$	4.73932	+	1.59337i	0.547250	+	0.183986i
$76$	−1.10003	−	1.10003i	−0.126182	−	0.126182i
$77$	7.34010	+	7.34010i	0.836482	+	0.836482i
$78$	2.42487	−	2.42487i	0.274562	−	0.274562i
$79$	4.60304	+	4.60304i	0.517882	+	0.517882i	0.916930	−	0.399048i	$-0.130659\pi$
$79$	4.60304	+	4.60304i	0.517882	+	0.517882i	−0.399048	+	0.916930i	$0.630659\pi$
$80$	−1.17802	+	1.90060i	−0.131707	+	0.212493i
$81$	−1.00000			−0.111111
$82$		−	9.62252i		−	1.06263i
$83$	−10.9528	−	10.9528i	−1.20223	−	1.20223i	−0.973488	−	0.228739i	$-0.926540\pi$
$83$	−10.9528	−	10.9528i	−1.20223	−	1.20223i	−0.228739	−	0.973488i	$-0.573460\pi$
$84$		−	3.77653i		−	0.412054i
$85$	1.01615	+	0.629829i	0.110217	+	0.0683145i
$86$	1.95296			0.210594
$87$		−	8.97783i		−	0.962524i
$88$		−	2.74868i		−	0.293010i
$89$	−9.99204	+	9.99204i	−1.05915	+	1.05915i	−0.0610170	+	0.998137i	$0.519434\pi$
$89$	−9.99204	+	9.99204i	−1.05915	+	1.05915i	−0.998137	+	0.0610170i	$0.980566\pi$
$90$	1.90060	+	1.17802i	0.200340	+	0.124174i
$91$	9.15759	−	9.15759i	0.959976	−	0.959976i
$92$	2.91366			0.303770
$93$	5.55248			0.575765
$94$	−9.10685	+	9.10685i	−0.939300	+	0.939300i
$95$	3.38656	−	0.794851i	0.347454	−	0.0815500i
$96$	−0.707107	+	0.707107i	−0.0721688	+	0.0721688i
$97$			14.3863i			1.46070i	0.683071	+	0.730352i	$0.260644\pi$
$97$			14.3863i			1.46070i	−0.683071	+	0.730352i	$0.739356\pi$
$98$		−	7.26220i		−	0.733593i
$99$	−2.74868			−0.276252
$100$	−2.22453	−	4.47789i	−0.222453	−	0.447789i
$101$			6.04894i			0.601892i	0.953641	+	0.300946i	$0.0973025\pi$
$101$			6.04894i			0.601892i	−0.953641	+	0.300946i	$0.902698\pi$
$102$	0.378054	+	0.378054i	0.0374329	+	0.0374329i
$103$		−	3.18651i		−	0.313976i	−0.987601	−	0.156988i	$-0.949822\pi$
$103$		−	3.18651i		−	0.313976i	0.987601	−	0.156988i	$-0.0501784\pi$
$104$	−3.42928			−0.336269
$105$	7.17766	+	4.44884i	0.700468	+	0.434162i
$106$	8.83246	+	8.83246i	0.857884	+	0.857884i
$107$	−14.0401	+	14.0401i	−1.35731	+	1.35731i	−0.480087	+	0.877221i	$0.659395\pi$
$107$	−14.0401	+	14.0401i	−1.35731	+	1.35731i	−0.877221	+	0.480087i	$0.840605\pi$
$108$	0.707107	+	0.707107i	0.0680414	+	0.0680414i
$109$	12.8170	+	12.8170i	1.22764	+	1.22764i	0.964853	+	0.262792i	$0.0846433\pi$
$109$	12.8170	+	12.8170i	1.22764	+	1.22764i	0.262792	+	0.964853i	$0.415357\pi$
$110$	5.22412	+	3.23800i	0.498100	+	0.308731i
$111$	3.98688	+	4.59400i	0.378418	+	0.436043i
$112$	−2.67041	+	2.67041i	−0.252330	+	0.252330i
$113$		−	5.27748i		−	0.496463i	−0.968701	−	0.248232i	$-0.920151\pi$
$113$		−	5.27748i		−	0.496463i	0.968701	−	0.248232i	$-0.0798494\pi$
$114$	1.55567			0.145702
$115$	−3.43236	+	5.53769i	−0.320069	+	0.516393i
$116$	−6.34828	+	6.34828i	−0.589423	+	0.589423i
$117$			3.42928i			0.317037i
$118$	−8.17158	−	8.17158i	−0.752255	−	0.752255i
$119$	1.42773	+	1.42773i	0.130880	+	0.130880i
$120$	−0.510937	−	2.17691i	−0.0466419	−	0.198724i
$121$	3.44478			0.313162
$122$	3.52447	+	3.52447i	0.319091	+	0.319091i
$123$	6.80415	+	6.80415i	0.613510	+	0.613510i
$124$	−3.92620	−	3.92620i	−0.352583	−	0.352583i
$125$	11.1312	+	1.04712i	0.995604	+	0.0936574i
$126$	2.67041	+	2.67041i	0.237899	+	0.237899i
$127$	4.97900	−	4.97900i	0.441814	−	0.441814i	−0.450807	−	0.892621i	$-0.648864\pi$
$127$	4.97900	−	4.97900i	0.441814	−	0.441814i	0.892621	+	0.450807i	$0.148864\pi$
$128$	1.00000			0.0883883
$129$	−1.38095	+	1.38095i	−0.121586	+	0.121586i
$130$	4.03977	−	6.51767i	0.354311	−	0.571638i
$131$	−3.39312	−	3.39312i	−0.296458	−	0.296458i	0.543167	−	0.839625i	$-0.317225\pi$
$131$	−3.39312	−	3.39312i	−0.296458	−	0.296458i	−0.839625	+	0.543167i	$0.817225\pi$
$132$	1.94361	+	1.94361i	0.169169	+	0.169169i
$133$	5.87505			0.509432
$134$	5.36985	+	5.36985i	0.463885	+	0.463885i
$135$	−2.17691	+	0.510937i	−0.187359	+	0.0439744i
$136$		−	0.534649i		−	0.0458458i
$137$	7.71617	−	7.71617i	0.659237	−	0.659237i	−0.295963	−	0.955200i	$-0.595640\pi$
$137$	7.71617	−	7.71617i	0.659237	−	0.659237i	0.955200	+	0.295963i	$0.0956404\pi$
$138$	−2.06027	+	2.06027i	−0.175382	+	0.175382i
$139$	1.56682			0.132896			0.0664480	−	0.997790i	$-0.478833\pi$
$139$	1.56682			0.132896			0.0664480	+	0.997790i	$0.478833\pi$
$140$	−1.92957	−	8.22118i	−0.163078	−	0.694816i
$141$		−	12.8790i		−	1.08461i
$142$	−15.0364			−1.26183
$143$			9.42598i			0.788240i
$144$		−	1.00000i		−	0.0833333i
$145$	−4.58710	−	19.5439i	−0.380938	−	1.62304i
$146$	−7.28489	+	7.28489i	−0.602902	+	0.602902i
$147$	5.13515	+	5.13515i	0.423540	+	0.423540i
$148$	0.429296	−	6.06759i	0.0352879	−	0.498753i
$149$			9.53201i			0.780893i	0.920626	+	0.390446i	$0.127679\pi$
$149$			9.53201i			0.780893i	−0.920626	+	0.390446i	$0.872321\pi$
$150$	4.73932	+	1.59337i	0.386964	+	0.130098i
$151$		−	17.4581i		−	1.42072i	−0.703840	−	0.710359i	$-0.748533\pi$
$151$		−	17.4581i		−	1.42072i	0.703840	−	0.710359i	$-0.251467\pi$
$152$	−1.10003	−	1.10003i	−0.0892240	−	0.0892240i
$153$	−0.534649			−0.0432238
$154$	7.34010	+	7.34010i	0.591482	+	0.591482i
$155$	12.0873	−	2.83697i	0.970872	−	0.227871i
$156$	2.42487	−	2.42487i	0.194145	−	0.194145i
$157$	7.38980	−	7.38980i	0.589771	−	0.589771i	−0.347799	−	0.937569i	$-0.613071\pi$
$157$	7.38980	−	7.38980i	0.589771	−	0.589771i	0.937569	+	0.347799i	$0.113071\pi$
$158$	4.60304	+	4.60304i	0.366198	+	0.366198i
$159$	−12.4910			−0.990599
$160$	−1.17802	+	1.90060i	−0.0931308	+	0.150255i
$161$	−7.78068	+	7.78068i	−0.613203	+	0.613203i
$162$	−1.00000			−0.0785674
$163$			11.7022i			0.916586i	0.888801	+	0.458293i	$0.151539\pi$
$163$			11.7022i			0.916586i	−0.888801	+	0.458293i	$0.848461\pi$
$164$		−	9.62252i		−	0.751393i
$165$	−5.98362	+	1.40440i	−0.465824	+	0.109332i
$166$	−10.9528	−	10.9528i	−0.850103	−	0.850103i
$167$			1.27852i			0.0989345i	0.998776	+	0.0494673i	$0.0157523\pi$
$167$			1.27852i			0.0989345i	−0.998776	+	0.0494673i	$0.984248\pi$
$168$		−	3.77653i		−	0.291366i
$169$	−1.24004			−0.0953877
$170$	1.01615	+	0.629829i	0.0779353	+	0.0483057i
$171$	−1.10003	+	1.10003i	−0.0841212	+	0.0841212i
$172$	1.95296			0.148912
$173$	8.86215	−	8.86215i	0.673777	−	0.673777i	−0.284808	−	0.958585i	$-0.591930\pi$
$173$	8.86215	−	8.86215i	0.673777	−	0.673777i	0.958585	+	0.284808i	$0.0919297\pi$
$174$		−	8.97783i		−	0.680607i
$175$	17.8982	+	6.01740i	1.35298	+	0.454872i
$176$		−	2.74868i		−	0.207189i
$177$	11.5564			0.868629
$178$	−9.99204	+	9.99204i	−0.748935	+	0.748935i
$179$	−5.78220	+	5.78220i	−0.432182	+	0.432182i	−0.889370	−	0.457188i	$-0.848857\pi$
$179$	−5.78220	+	5.78220i	−0.432182	+	0.432182i	0.457188	+	0.889370i	$0.348857\pi$
$180$	1.90060	+	1.17802i	0.141662	+	0.0878046i
$181$	−6.35842			−0.472618			−0.236309	−	0.971678i	$-0.575938\pi$
$181$	−6.35842			−0.472618			−0.236309	+	0.971678i	$0.575938\pi$
$182$	9.15759	−	9.15759i	0.678806	−	0.678806i
$183$	−4.98435			−0.368454
$184$	2.91366			0.214798
$185$	11.0263	+	7.96368i	0.810672	+	0.585501i
$186$	5.55248			0.407128
$187$	−1.46958			−0.107466
$188$	−9.10685	+	9.10685i	−0.664186	+	0.664186i
$189$	−3.77653			−0.274702
$190$	3.38656	−	0.794851i	0.245687	−	0.0576646i
$191$	12.2425	−	12.2425i	0.885835	−	0.885835i	−0.108285	−	0.994120i	$-0.534536\pi$
$191$	12.2425	−	12.2425i	0.885835	−	0.885835i	0.994120	+	0.108285i	$0.0345358\pi$
$192$	−0.707107	+	0.707107i	−0.0510310	+	0.0510310i
$193$	−7.16959			−0.516078			−0.258039	−	0.966134i	$-0.583076\pi$
$193$	−7.16959			−0.516078			−0.258039	+	0.966134i	$0.583076\pi$
$194$			14.3863i			1.03287i
$195$	1.75215	+	7.46524i	0.125474	+	0.534597i
$196$		−	7.26220i		−	0.518729i
$197$	−12.4994	+	12.4994i	−0.890546	+	0.890546i	−0.994574	−	0.104028i	$-0.966827\pi$
$197$	−12.4994	+	12.4994i	−0.890546	+	0.890546i	0.104028	+	0.994574i	$0.466827\pi$
$198$	−2.74868			−0.195340
$199$	−9.53384	+	9.53384i	−0.675836	+	0.675836i	−0.959055	−	0.283219i	$-0.908598\pi$
$199$	−9.53384	+	9.53384i	−0.675836	+	0.675836i	0.283219	+	0.959055i	$0.408598\pi$
$200$	−2.22453	−	4.47789i	−0.157298	−	0.316634i
$201$	−7.59412			−0.535648
$202$			6.04894i			0.425602i
$203$		−	33.9051i		−	2.37967i
$204$	0.378054	+	0.378054i	0.0264691	+	0.0264691i
$205$	18.2885	+	11.3355i	1.27733	+	0.791709i
$206$		−	3.18651i		−	0.222014i
$207$		−	2.91366i		−	0.202513i
$208$	−3.42928			−0.237778
$209$	−3.02362	+	3.02362i	−0.209148	+	0.209148i
$210$	7.17766	+	4.44884i	0.495306	+	0.306999i
$211$	6.93916			0.477712			0.238856	−	0.971055i	$-0.423228\pi$
$211$	6.93916			0.477712			0.238856	+	0.971055i	$0.423228\pi$
$212$	8.83246	+	8.83246i	0.606616	+	0.606616i
$213$	10.6323	−	10.6323i	0.728515	−	0.728515i
$214$	−14.0401	+	14.0401i	−0.959762	+	0.959762i
$215$	−2.30064	+	3.71180i	−0.156902	+	0.253142i
$216$	0.707107	+	0.707107i	0.0481125	+	0.0481125i
$217$	20.9691			1.42348
$218$	12.8170	+	12.8170i	0.868076	+	0.868076i
$219$		−	10.3024i		−	0.696171i
$220$	5.22412	+	3.23800i	0.352210	+	0.218306i
$221$			1.83346i			0.123332i
$222$	3.98688	+	4.59400i	0.267582	+	0.308329i
$223$	0.721579	+	0.721579i	0.0483205	+	0.0483205i	0.730854	−	0.682534i	$-0.239122\pi$
$223$	0.721579	+	0.721579i	0.0483205	+	0.0483205i	−0.682534	+	0.730854i	$0.739122\pi$
$224$	−2.67041	+	2.67041i	−0.178424	+	0.178424i
$225$	−4.47789	+	2.22453i	−0.298526	+	0.148302i
$226$		−	5.27748i		−	0.351053i
$227$			1.19506i			0.0793187i	0.999213	+	0.0396594i	$0.0126273\pi$
$227$			1.19506i			0.0793187i	−0.999213	+	0.0396594i	$0.987373\pi$
$228$	1.55567			0.103027
$229$		−	13.9339i		−	0.920781i	−0.887717	−	0.460390i	$-0.847709\pi$
$229$		−	13.9339i		−	0.920781i	0.887717	−	0.460390i	$-0.152291\pi$
$230$	−3.43236	+	5.53769i	−0.226323	+	0.365145i
$231$	−10.3805			−0.682984
$232$	−6.34828	+	6.34828i	−0.416785	+	0.416785i
$233$	−3.59105	+	3.59105i	−0.235258	+	0.235258i	−0.814883	−	0.579625i	$-0.803199\pi$
$233$	−3.59105	+	3.59105i	−0.235258	+	0.235258i	0.579625	+	0.814883i	$0.303199\pi$
$234$			3.42928i			0.224179i
$235$	−6.58037	−	28.0365i	−0.429256	−	1.82890i
$236$	−8.17158	−	8.17158i	−0.531925	−	0.531925i
$237$	−6.50968			−0.422849
$238$	1.42773	+	1.42773i	0.0925463	+	0.0925463i
$239$	2.73603	+	2.73603i	0.176979	+	0.176979i	0.790037	−	0.613059i	$-0.210061\pi$
$239$	2.73603	+	2.73603i	0.176979	+	0.176979i	−0.613059	+	0.790037i	$0.710061\pi$
$240$	−0.510937	−	2.17691i	−0.0329808	−	0.140519i
$241$	2.73812	−	2.73812i	0.176378	−	0.176378i	−0.613397	−	0.789775i	$-0.710197\pi$
$241$	2.73812	−	2.73812i	0.176378	−	0.176378i	0.789775	+	0.613397i	$0.210197\pi$
$242$	3.44478			0.221439
$243$	0.707107	−	0.707107i	0.0453609	−	0.0453609i
$244$	3.52447	+	3.52447i	0.225631	+	0.225631i
$245$	13.8025	+	8.55503i	0.881810	+	0.546561i
$246$	6.80415	+	6.80415i	0.433817	+	0.433817i
$247$	3.77230	+	3.77230i	0.240026	+	0.240026i
$248$	−3.92620	−	3.92620i	−0.249314	−	0.249314i
$249$	15.4896			0.981614
$250$	11.1312	+	1.04712i	0.703999	+	0.0662258i
$251$	7.76206	+	7.76206i	0.489937	+	0.489937i	0.908286	−	0.418349i	$-0.137391\pi$
$251$	7.76206	+	7.76206i	0.489937	+	0.489937i	−0.418349	+	0.908286i	$0.637391\pi$
$252$	2.67041	+	2.67041i	0.168220	+	0.168220i
$253$		−	8.00871i		−	0.503503i
$254$	4.97900	−	4.97900i	0.312410	−	0.312410i
$255$	−1.16388	+	0.273172i	−0.0728853	+	0.0171067i
$256$	1.00000			0.0625000
$257$			12.5524i			0.782998i	0.920178	+	0.391499i	$0.128043\pi$
$257$			12.5524i			0.782998i	−0.920178	+	0.391499i	$0.871957\pi$
$258$	−1.38095	+	1.38095i	−0.0859745	+	0.0859745i
$259$	15.0566	+	17.3494i	0.935570	+	1.07804i
$260$	4.03977	−	6.51767i	0.250536	−	0.404209i
$261$	6.34828	+	6.34828i	0.392949	+	0.392949i
$262$	−3.39312	−	3.39312i	−0.209628	−	0.209628i
$263$	−11.9084	+	11.9084i	−0.734302	+	0.734302i	−0.971469	−	0.237167i	$-0.923781\pi$
$263$	−11.9084	+	11.9084i	−0.734302	+	0.734302i	0.237167	+	0.971469i	$0.423781\pi$
$264$	1.94361	+	1.94361i	0.119621	+	0.119621i
$265$	−27.1918	+	6.38210i	−1.67038	+	0.392049i
$266$	5.87505			0.360223
$267$		−	14.1309i		−	0.864795i
$268$	5.36985	+	5.36985i	0.328016	+	0.328016i
$269$			29.2737i			1.78485i	0.451195	+	0.892425i	$0.350998\pi$
$269$			29.2737i			1.78485i	−0.451195	+	0.892425i	$0.649002\pi$
$270$	−2.17691	+	0.510937i	−0.132483	+	0.0310946i
$271$	−6.00684			−0.364890			−0.182445	−	0.983216i	$-0.558401\pi$
$271$	−6.00684			−0.364890			−0.182445	+	0.983216i	$0.558401\pi$
$272$		−	0.534649i		−	0.0324179i
$273$			12.9508i			0.783817i
$274$	7.71617	−	7.71617i	0.466151	−	0.466151i
$275$	−12.3083	+	6.11451i	−0.742216	+	0.368719i
$276$	−2.06027	+	2.06027i	−0.124014	+	0.124014i
$277$	9.15050			0.549800			0.274900	−	0.961473i	$-0.411355\pi$
$277$	9.15050			0.549800			0.274900	+	0.961473i	$0.411355\pi$
$278$	1.56682			0.0939716
$279$	−3.92620	+	3.92620i	−0.235055	+	0.235055i
$280$	−1.92957	−	8.22118i	−0.115314	−	0.491309i
$281$	8.67829	−	8.67829i	0.517703	−	0.517703i	−0.399172	−	0.916876i	$-0.630703\pi$
$281$	8.67829	−	8.67829i	0.517703	−	0.517703i	0.916876	+	0.399172i	$0.130703\pi$
$282$		−	12.8790i		−	0.766936i
$283$			1.62977i			0.0968799i	0.998826	+	0.0484400i	$0.0154250\pi$
$283$			1.62977i			0.0968799i	−0.998826	+	0.0484400i	$0.984575\pi$
$284$	−15.0364			−0.892245
$285$	−1.83262	+	2.95671i	−0.108555	+	0.175140i
$286$			9.42598i			0.557370i
$287$	25.6961	+	25.6961i	1.51679	+	1.51679i
$288$		−	1.00000i		−	0.0589256i
$289$	16.7141			0.983185
$290$	−4.58710	−	19.5439i	−0.269364	−	1.14766i
$291$	−10.1726	−	10.1726i	−0.596330	−	0.596330i
$292$	−7.28489	+	7.28489i	−0.426316	+	0.426316i
$293$	−3.21641	−	3.21641i	−0.187905	−	0.187905i	0.606885	−	0.794790i	$-0.292419\pi$
$293$	−3.21641	−	3.21641i	−0.187905	−	0.187905i	−0.794790	+	0.606885i	$0.792419\pi$
$294$	5.13515	+	5.13515i	0.299488	+	0.299488i
$295$	25.1572	−	5.90457i	1.46471	−	0.343777i
$296$	0.429296	−	6.06759i	0.0249523	−	0.352672i
$297$	1.94361	−	1.94361i	0.112780	−	0.112780i
$298$			9.53201i			0.552175i
$299$	−9.99176			−0.577838
$300$	4.73932	+	1.59337i	0.273625	+	0.0919930i
$301$	−5.21522	+	5.21522i	−0.300600	+	0.300600i
$302$		−	17.4581i		−	1.00460i
$303$	−4.27725	−	4.27725i	−0.245722	−	0.245722i
$304$	−1.10003	−	1.10003i	−0.0630909	−	0.0630909i
$305$	−10.8505	+	2.54669i	−0.621298	+	0.145823i
$306$	−0.534649			−0.0305639
$307$	−0.565223	−	0.565223i	−0.0322590	−	0.0322590i	0.690793	−	0.723052i	$-0.257261\pi$
$307$	−0.565223	−	0.565223i	−0.0322590	−	0.0322590i	−0.723052	+	0.690793i	$0.757261\pi$
$308$	7.34010	+	7.34010i	0.418241	+	0.418241i
$309$	2.25320	+	2.25320i	0.128180	+	0.128180i
$310$	12.0873	−	2.83697i	0.686510	−	0.161129i
$311$	−20.7503	−	20.7503i	−1.17664	−	1.17664i	−0.980595	−	0.196045i	$-0.937190\pi$
$311$	−20.7503	−	20.7503i	−1.17664	−	1.17664i	−0.196045	−	0.980595i	$-0.562810\pi$
$312$	2.42487	−	2.42487i	0.137281	−	0.137281i
$313$	10.7676			0.608618			0.304309	−	0.952573i	$-0.401574\pi$
$313$	10.7676			0.608618			0.304309	+	0.952573i	$0.401574\pi$
$314$	7.38980	−	7.38980i	0.417031	−	0.417031i
$315$	−8.22118	+	1.92957i	−0.463211	+	0.108719i
$316$	4.60304	+	4.60304i	0.258941	+	0.258941i
$317$	−0.491641	−	0.491641i	−0.0276133	−	0.0276133i	0.693165	−	0.720779i	$-0.256216\pi$
$317$	−0.491641	−	0.491641i	−0.0276133	−	0.0276133i	−0.720779	+	0.693165i	$0.756216\pi$
$318$	−12.4910			−0.700459
$319$	17.4494	+	17.4494i	0.976977	+	0.976977i
$320$	−1.17802	+	1.90060i	−0.0658534	+	0.106247i
$321$		−	19.8557i		−	1.10824i
$322$	−7.78068	+	7.78068i	−0.433600	+	0.433600i
$323$	−0.588129	+	0.588129i	−0.0327244	+	0.0327244i
$324$	−1.00000			−0.0555556
$325$	7.62853	+	15.3559i	0.423155	+	0.851794i
$326$			11.7022i			0.648124i
$327$	−18.1260			−1.00237
$328$		−	9.62252i		−	0.531315i
$329$		−	48.6381i		−	2.68151i
$330$	−5.98362	+	1.40440i	−0.329388	+	0.0773096i
$331$	−4.01488	+	4.01488i	−0.220678	+	0.220678i	−0.808784	−	0.588106i	$-0.799874\pi$
$331$	−4.01488	+	4.01488i	−0.220678	+	0.220678i	0.588106	+	0.808784i	$0.299874\pi$
$332$	−10.9528	−	10.9528i	−0.601113	−	0.601113i
$333$	−6.06759	−	0.429296i	−0.332502	−	0.0235253i
$334$			1.27852i			0.0699573i
$335$	−16.5317	+	3.88011i	−0.903224	+	0.211993i
$336$		−	3.77653i		−	0.206027i
$337$	−6.16129	−	6.16129i	−0.335627	−	0.335627i	0.519092	−	0.854719i	$-0.326270\pi$
$337$	−6.16129	−	6.16129i	−0.335627	−	0.335627i	−0.854719	+	0.519092i	$0.826270\pi$
$338$	−1.24004			−0.0674493
$339$	3.73174	+	3.73174i	0.202680	+	0.202680i
$340$	1.01615	+	0.629829i	0.0551086	+	0.0341573i
$341$	−10.7918	+	10.7918i	−0.584411	+	0.584411i
$342$	−1.10003	+	1.10003i	−0.0594827	+	0.0594827i
$343$	0.700181	+	0.700181i	0.0378062	+	0.0378062i
$344$	1.95296			0.105297
$345$	−1.48870	−	6.34278i	−0.0801487	−	0.341484i
$346$	8.86215	−	8.86215i	0.476432	−	0.476432i
$347$	3.72173			0.199793			0.0998964	−	0.994998i	$-0.468149\pi$
$347$	3.72173			0.199793			0.0998964	+	0.994998i	$0.468149\pi$
$348$		−	8.97783i		−	0.481262i
$349$			8.05700i			0.431281i	0.976473	+	0.215641i	$0.0691840\pi$
$349$			8.05700i			0.431281i	−0.976473	+	0.215641i	$0.930816\pi$
$350$	17.8982	+	6.01740i	0.956700	+	0.321643i
$351$	−2.42487	−	2.42487i	−0.129430	−	0.129430i
$352$		−	2.74868i		−	0.146505i
$353$			18.4416i			0.981549i	0.871287	+	0.490774i	$0.163286\pi$
$353$			18.4416i			0.981549i	−0.871287	+	0.490774i	$0.836714\pi$
$354$	11.5564			0.614214
$355$	17.7132	−	28.5781i	0.940118	−	1.51677i
$356$	−9.99204	+	9.99204i	−0.529577	+	0.529577i
$357$	−2.01912			−0.106863
$358$	−5.78220	+	5.78220i	−0.305599	+	0.305599i
$359$		−	18.1393i		−	0.957357i	−0.877990	−	0.478678i	$-0.841116\pi$
$359$		−	18.1393i		−	0.957357i	0.877990	−	0.478678i	$-0.158884\pi$
$360$	1.90060	+	1.17802i	0.100170	+	0.0620872i
$361$		−	16.5799i		−	0.872625i
$362$	−6.35842			−0.334191
$363$	−2.43583	+	2.43583i	−0.127848	+	0.127848i
$364$	9.15759	−	9.15759i	0.479988	−	0.479988i
$365$	−5.26387	−	22.4274i	−0.275524	−	1.17390i
$366$	−4.98435			−0.260536
$367$	0.674373	−	0.674373i	0.0352020	−	0.0352020i	−0.689287	−	0.724489i	$-0.742076\pi$
$367$	0.674373	−	0.674373i	0.0352020	−	0.0352020i	0.724489	+	0.689287i	$0.242076\pi$
$368$	2.91366			0.151885
$369$	−9.62252			−0.500929
$370$	11.0263	+	7.96368i	0.573231	+	0.414012i
$371$	−47.1726			−2.44908
$372$	5.55248			0.287883
$373$	−14.1566	+	14.1566i	−0.733002	+	0.733002i	−0.971213	−	0.238212i	$-0.923439\pi$
$373$	−14.1566	+	14.1566i	−0.733002	+	0.733002i	0.238212	+	0.971213i	$0.423439\pi$
$374$	−1.46958			−0.0759901
$375$	−8.61137	+	7.13052i	−0.444689	+	0.368218i
$376$	−9.10685	+	9.10685i	−0.469650	+	0.469650i
$377$	21.7700	−	21.7700i	1.12121	−	1.12121i
$378$	−3.77653			−0.194244
$379$		−	30.7418i		−	1.57910i	−0.613687	−	0.789549i	$-0.710314\pi$
$379$		−	30.7418i		−	1.57910i	0.613687	−	0.789549i	$-0.289686\pi$
$380$	3.38656	−	0.794851i	0.173727	−	0.0407750i
$381$			7.04136i			0.360740i
$382$	12.2425	−	12.2425i	0.626380	−	0.626380i
$383$	−9.32059			−0.476260			−0.238130	−	0.971233i	$-0.576534\pi$
$383$	−9.32059			−0.476260			−0.238130	+	0.971233i	$0.576534\pi$
$384$	−0.707107	+	0.707107i	−0.0360844	+	0.0360844i
$385$	−22.5973	+	5.30376i	−1.15167	+	0.270305i
$386$	−7.16959			−0.364922
$387$		−	1.95296i		−	0.0992748i
$388$			14.3863i			0.730352i
$389$	−14.1117	−	14.1117i	−0.715491	−	0.715491i	0.252187	−	0.967678i	$-0.418850\pi$
$389$	−14.1117	−	14.1117i	−0.715491	−	0.715491i	−0.967678	+	0.252187i	$0.918850\pi$
$390$	1.75215	+	7.46524i	0.0887233	+	0.378017i
$391$		−	1.55779i		−	0.0787807i
$392$		−	7.26220i		−	0.366796i
$393$	4.79860			0.242057
$394$	−12.4994	+	12.4994i	−0.629711	+	0.629711i
$395$	−14.1710	+	3.32603i	−0.713020	+	0.167351i
$396$	−2.74868			−0.138126
$397$	14.4178	+	14.4178i	0.723611	+	0.723611i	0.969339	−	0.245728i	$-0.0790271\pi$
$397$	14.4178	+	14.4178i	0.723611	+	0.723611i	−0.245728	+	0.969339i	$0.579027\pi$
$398$	−9.53384	+	9.53384i	−0.477888	+	0.477888i
$399$	−4.15429	+	4.15429i	−0.207975	+	0.207975i
$400$	−2.22453	−	4.47789i	−0.111226	−	0.223894i
$401$	14.7403	+	14.7403i	0.736096	+	0.736096i	0.971820	−	0.235724i	$-0.0757463\pi$
$401$	14.7403	+	14.7403i	0.736096	+	0.736096i	−0.235724	+	0.971820i	$0.575746\pi$
$402$	−7.59412			−0.378760
$403$	13.4640	+	13.4640i	0.670691	+	0.670691i
$404$			6.04894i			0.300946i
$405$	1.17802	−	1.90060i	0.0585364	−	0.0944414i
$406$		−	33.9051i		−	1.68268i
$407$	−16.6778	−	1.17999i	−0.826690	−	0.0584901i
$408$	0.378054	+	0.378054i	0.0187165	+	0.0187165i
$409$	10.9943	−	10.9943i	0.543634	−	0.543634i	−0.380958	−	0.924592i	$-0.624406\pi$
$409$	10.9943	−	10.9943i	0.543634	−	0.543634i	0.924592	+	0.380958i	$0.124406\pi$
$410$	18.2885	+	11.3355i	0.903206	+	0.559823i
$411$			10.9123i			0.538265i
$412$		−	3.18651i		−	0.156988i
$413$	43.6430			2.14753
$414$		−	2.91366i		−	0.143199i
$415$	33.7195	−	7.91421i	1.65523	−	0.388493i
$416$	−3.42928			−0.168134
$417$	−1.10791	+	1.10791i	−0.0542545	+	0.0542545i
$418$	−3.02362	+	3.02362i	−0.147890	+	0.147890i
$419$			15.2679i			0.745886i	0.927854	+	0.372943i	$0.121651\pi$
$419$			15.2679i			0.745886i	−0.927854	+	0.372943i	$0.878349\pi$
$420$	7.17766	+	4.44884i	0.350234	+	0.217081i
$421$	10.9789	+	10.9789i	0.535077	+	0.535077i	0.922079	−	0.387002i	$-0.126489\pi$
$421$	10.9789	+	10.9789i	0.535077	+	0.535077i	−0.387002	+	0.922079i	$0.626489\pi$
$422$	6.93916			0.337793
$423$	9.10685	+	9.10685i	0.442790	+	0.442790i
$424$	8.83246	+	8.83246i	0.428942	+	0.428942i
$425$	−2.39410	+	1.18934i	−0.116131	+	0.0576916i
$426$	10.6323	−	10.6323i	0.515138	−	0.515138i
$427$	−18.8236			−0.910937
$428$	−14.0401	+	14.0401i	−0.678654	+	0.678654i
$429$	−6.66517	−	6.66517i	−0.321798	−	0.321798i
$430$	−2.30064	+	3.71180i	−0.110947	+	0.178999i
$431$	−16.5186	−	16.5186i	−0.795675	−	0.795675i	0.186735	−	0.982410i	$-0.440209\pi$
$431$	−16.5186	−	16.5186i	−0.795675	−	0.795675i	−0.982410	+	0.186735i	$0.940209\pi$
$432$	0.707107	+	0.707107i	0.0340207	+	0.0340207i
$433$	−16.8050	−	16.8050i	−0.807598	−	0.807598i	0.176672	−	0.984270i	$-0.443467\pi$
$433$	−16.8050	−	16.8050i	−0.807598	−	0.807598i	−0.984270	+	0.176672i	$0.943467\pi$
$434$	20.9691			1.00655
$435$	17.0632	+	10.5761i	0.818119	+	0.507084i
$436$	12.8170	+	12.8170i	0.613822	+	0.613822i
$437$	−3.20511	−	3.20511i	−0.153321	−	0.153321i
$438$		−	10.3024i		−	0.492267i
$439$	−3.01200	+	3.01200i	−0.143755	+	0.143755i	−0.775322	−	0.631567i	$-0.782412\pi$
$439$	−3.01200	+	3.01200i	−0.143755	+	0.143755i	0.631567	+	0.775322i	$0.282412\pi$
$440$	5.22412	+	3.23800i	0.249050	+	0.154366i
$441$	−7.26220			−0.345819
$442$			1.83346i			0.0872089i
$443$	−10.7717	+	10.7717i	−0.511777	+	0.511777i	−0.915071	−	0.403294i	$-0.867865\pi$
$443$	−10.7717	+	10.7717i	−0.511777	+	0.511777i	0.403294	+	0.915071i	$0.367865\pi$
$444$	3.98688	+	4.59400i	0.189209	+	0.218021i
$445$	−7.21998	−	30.7617i	−0.342260	−	1.45824i
$446$	0.721579	+	0.721579i	0.0341678	+	0.0341678i
$447$	−6.74015	−	6.74015i	−0.318798	−	0.318798i
$448$	−2.67041	+	2.67041i	−0.126165	+	0.126165i
$449$	6.33208	+	6.33208i	0.298829	+	0.298829i	0.840555	−	0.541726i	$-0.182229\pi$
$449$	6.33208	+	6.33208i	0.298829	+	0.298829i	−0.541726	+	0.840555i	$0.682229\pi$
$450$	−4.47789	+	2.22453i	−0.211090	+	0.104865i
$451$	−26.4492			−1.24544
$452$		−	5.27748i		−	0.248232i
$453$	12.3447	+	12.3447i	0.580005	+	0.580005i
$454$			1.19506i			0.0560868i
$455$	6.61703	+	28.1927i	0.310211	+	1.32170i
$456$	1.55567			0.0728511
$457$		−	34.7548i		−	1.62576i	−0.582429	−	0.812882i	$-0.697898\pi$
$457$		−	34.7548i		−	1.62576i	0.582429	−	0.812882i	$-0.302102\pi$
$458$		−	13.9339i		−	0.651090i
$459$	0.378054	−	0.378054i	0.0176461	−	0.0176461i
$460$	−3.43236	+	5.53769i	−0.160035	+	0.258196i
$461$	−9.43804	+	9.43804i	−0.439573	+	0.439573i	−0.891868	−	0.452295i	$-0.850605\pi$
$461$	−9.43804	+	9.43804i	−0.439573	+	0.439573i	0.452295	+	0.891868i	$0.350605\pi$
$462$	−10.3805			−0.482943
$463$	−26.8196			−1.24641			−0.623206	−	0.782058i	$-0.714170\pi$
$463$	−26.8196			−1.24641			−0.623206	+	0.782058i	$0.714170\pi$
$464$	−6.34828	+	6.34828i	−0.294712	+	0.294712i
$465$	−6.54095	+	10.5530i	−0.303329	+	0.489385i
$466$	−3.59105	+	3.59105i	−0.166352	+	0.166352i
$467$		−	30.6261i		−	1.41721i	−0.705606	−	0.708604i	$-0.749325\pi$
$467$		−	30.6261i		−	1.41721i	0.705606	−	0.708604i	$-0.250675\pi$
$468$			3.42928i			0.158519i
$469$	−28.6794			−1.32429
$470$	−6.58037	−	28.0365i	−0.303530	−	1.29323i
$471$			10.4508i			0.481546i
$472$	−8.17158	−	8.17158i	−0.376127	−	0.376127i
$473$		−	5.36807i		−	0.246824i
$474$	−6.50968			−0.298999
$475$	−2.47876	+	7.37284i	−0.113733	+	0.338289i
$476$	1.42773	+	1.42773i	0.0654401	+	0.0654401i
$477$	8.83246	−	8.83246i	0.404410	−	0.404410i
$478$	2.73603	+	2.73603i	0.125143	+	0.125143i
$479$	−28.4708	−	28.4708i	−1.30087	−	1.30087i	−0.927808	−	0.373058i	$-0.878309\pi$
$479$	−28.4708	−	28.4708i	−1.30087	−	1.30087i	−0.373058	−	0.927808i	$-0.621691\pi$
$480$	−0.510937	−	2.17691i	−0.0233210	−	0.0993620i
$481$	−1.47217	+	20.8075i	−0.0671254	+	0.948739i
$482$	2.73812	−	2.73812i	0.124718	−	0.124718i
$483$		−	11.0035i		−	0.500678i
$484$	3.44478			0.156581
$485$	−27.3425	−	16.9473i	−1.24156	−	0.769539i
$486$	0.707107	−	0.707107i	0.0320750	−	0.0320750i
$487$			25.3425i			1.14838i	0.818723	+	0.574188i	$0.194682\pi$
$487$			25.3425i			1.14838i	−0.818723	+	0.574188i	$0.805318\pi$
$488$	3.52447	+	3.52447i	0.159545	+	0.159545i
$489$	−8.27469	−	8.27469i	−0.374194	−	0.374194i
$490$	13.8025	+	8.55503i	0.623534	+	0.386477i
$491$	23.3602			1.05423			0.527115	−	0.849794i	$-0.323274\pi$
$491$	23.3602			1.05423			0.527115	+	0.849794i	$0.323274\pi$
$492$	6.80415	+	6.80415i	0.306755	+	0.306755i
$493$	3.39410	+	3.39410i	0.152863	+	0.152863i
$494$	3.77230	+	3.77230i	0.169724	+	0.169724i
$495$	3.23800	−	5.22412i	0.145537	−	0.234807i
$496$	−3.92620	−	3.92620i	−0.176291	−	0.176291i
$497$	40.1533	−	40.1533i	1.80112	−	1.80112i
$498$	15.4896			0.694106
$499$	9.86951	−	9.86951i	0.441820	−	0.441820i	−0.450803	−	0.892623i	$-0.648862\pi$
$499$	9.86951	−	9.86951i	0.441820	−	0.441820i	0.892623	+	0.450803i	$0.148862\pi$
$500$	11.1312	+	1.04712i	0.497802	+	0.0468287i
$501$	−0.904047	−	0.904047i	−0.0403898	−	0.0403898i
$502$	7.76206	+	7.76206i	0.346438	+	0.346438i
$503$	−2.37206			−0.105765			−0.0528825	−	0.998601i	$-0.516841\pi$
$503$	−2.37206			−0.105765			−0.0528825	+	0.998601i	$0.516841\pi$
$504$	2.67041	+	2.67041i	0.118950	+	0.118950i
$505$	−11.4966	−	7.12579i	−0.511592	−	0.317093i
$506$		−	8.00871i		−	0.356031i
$507$	0.876840	−	0.876840i	0.0389418	−	0.0389418i
$508$	4.97900	−	4.97900i	0.220907	−	0.220907i
$509$	21.6650			0.960285			0.480142	−	0.877191i	$-0.340585\pi$
$509$	21.6650			0.960285			0.480142	+	0.877191i	$0.340585\pi$
$510$	−1.16388	+	0.273172i	−0.0515377	+	0.0120963i
$511$		−	38.9073i		−	1.72116i
$512$	1.00000			0.0441942
$513$		−	1.55567i		−	0.0686847i
$514$			12.5524i			0.553663i
$515$	6.05626	+	3.75377i	0.266871	+	0.165411i
$516$	−1.38095	+	1.38095i	−0.0607931	+	0.0607931i
$517$	25.0318	+	25.0318i	1.10090	+	1.10090i
$518$	15.0566	+	17.3494i	0.661548	+	0.762288i
$519$			12.5330i			0.550137i
$520$	4.03977	−	6.51767i	0.177156	−	0.285819i
$521$			36.2439i			1.58788i	0.607999	+	0.793938i	$0.291973\pi$
$521$			36.2439i			1.58788i	−0.607999	+	0.793938i	$0.708027\pi$
$522$	6.34828	+	6.34828i	0.277857	+	0.277857i
$523$	22.6025			0.988339			0.494170	−	0.869366i	$-0.335472\pi$
$523$	22.6025			0.988339			0.494170	+	0.869366i	$0.335472\pi$
$524$	−3.39312	−	3.39312i	−0.148229	−	0.148229i
$525$	−16.9109	+	8.40100i	−0.738052	+	0.366650i
$526$	−11.9084	+	11.9084i	−0.519230	+	0.519230i
$527$	−2.09914	+	2.09914i	−0.0914399	+	0.0914399i
$528$	1.94361	+	1.94361i	0.0845846	+	0.0845846i
$529$	−14.5106			−0.630895
$530$	−27.1918	+	6.38210i	−1.18113	+	0.277221i
$531$	−8.17158	+	8.17158i	−0.354616	+	0.354616i
$532$	5.87505			0.254716
$533$			32.9983i			1.42932i
$534$		−	14.1309i		−	0.611503i
$535$	−10.1450	−	43.2241i	−0.438607	−	1.86874i
$536$	5.36985	+	5.36985i	0.231942	+	0.231942i
$537$		−	8.17727i		−	0.352875i
$538$			29.2737i			1.26208i
$539$	−19.9614			−0.859800
$540$	−2.17691	+	0.510937i	−0.0936794	+	0.0219872i
$541$	15.3087	−	15.3087i	0.658172	−	0.658172i	−0.296775	−	0.954947i	$-0.595911\pi$
$541$	15.3087	−	15.3087i	0.658172	−	0.658172i	0.954947	+	0.296775i	$0.0959112\pi$
$542$	−6.00684			−0.258016
$543$	4.49608	−	4.49608i	0.192945	−	0.192945i
$544$		−	0.534649i		−	0.0229229i
$545$	−39.4586	+	9.26122i	−1.69022	+	0.396707i
$546$			12.9508i			0.554243i
$547$	−20.4617			−0.874879			−0.437439	−	0.899248i	$-0.644115\pi$
$547$	−20.4617			−0.874879			−0.437439	+	0.899248i	$0.644115\pi$
$548$	7.71617	−	7.71617i	0.329618	−	0.329618i
$549$	3.52447	−	3.52447i	0.150421	−	0.150421i
$550$	−12.3083	+	6.11451i	−0.524826	+	0.260723i
$551$	13.9666			0.594996
$552$	−2.06027	+	2.06027i	−0.0876909	+	0.0876909i
$553$	−24.5840			−1.04542
$554$	9.15050			0.388767
$555$	−13.4280	+	2.16562i	−0.569985	+	0.0919254i
$556$	1.56682			0.0664480
$557$	−22.9203			−0.971162			−0.485581	−	0.874192i	$-0.661392\pi$
$557$	−22.9203			−0.971162			−0.485581	+	0.874192i	$0.661392\pi$
$558$	−3.92620	+	3.92620i	−0.166209	+	0.166209i
$559$	−6.69726			−0.283264
$560$	−1.92957	−	8.22118i	−0.0815392	−	0.347408i
$561$	1.03915	−	1.03915i	0.0438729	−	0.0438729i
$562$	8.67829	−	8.67829i	0.366072	−	0.366072i
$563$	−7.83533			−0.330220			−0.165110	−	0.986275i	$-0.552798\pi$
$563$	−7.83533			−0.330220			−0.165110	+	0.986275i	$0.552798\pi$
$564$		−	12.8790i		−	0.542305i
$565$	10.0304	+	6.21699i	0.421980	+	0.261551i
$566$			1.62977i			0.0685044i
$567$	2.67041	−	2.67041i	0.112147	−	0.112147i
$568$	−15.0364			−0.630913
$569$	−17.1922	+	17.1922i	−0.720735	+	0.720735i	−0.968755	−	0.248020i	$-0.920220\pi$
$569$	−17.1922	+	17.1922i	−0.720735	+	0.720735i	0.248020	+	0.968755i	$0.420220\pi$
$570$	−1.83262	+	2.95671i	−0.0767599	+	0.123843i
$571$	−7.23109			−0.302612			−0.151306	−	0.988487i	$-0.548348\pi$
$571$	−7.23109			−0.302612			−0.151306	+	0.988487i	$0.548348\pi$
$572$			9.42598i			0.394120i
$573$			17.3135i			0.723281i
$574$	25.6961	+	25.6961i	1.07253	+	1.07253i
$575$	−6.48152	−	13.0470i	−0.270298	−	0.544100i
$576$		−	1.00000i		−	0.0416667i
$577$			12.3162i			0.512731i	0.966580	+	0.256366i	$0.0825251\pi$
$577$			12.3162i			0.512731i	−0.966580	+	0.256366i	$0.917475\pi$
$578$	16.7141			0.695217
$579$	5.06966	−	5.06966i	0.210688	−	0.210688i
$580$	−4.58710	−	19.5439i	−0.190469	−	0.811518i
$581$	58.4970			2.42687
$582$	−10.1726	−	10.1726i	−0.421669	−	0.421669i
$583$	24.2776	−	24.2776i	1.00547	−	1.00547i
$584$	−7.28489	+	7.28489i	−0.301451	+	0.301451i
$585$	−6.51767	−	4.03977i	−0.269473	−	0.167024i
$586$	−3.21641	−	3.21641i	−0.132869	−	0.132869i
$587$	20.5928			0.849956			0.424978	−	0.905204i	$-0.360282\pi$
$587$	20.5928			0.849956			0.424978	+	0.905204i	$0.360282\pi$
$588$	5.13515	+	5.13515i	0.211770	+	0.211770i
$589$			8.63785i			0.355916i
$590$	25.1572	−	5.90457i	1.03570	−	0.243087i
$591$		−	17.6768i		−	0.727128i
$592$	0.429296	−	6.06759i	0.0176439	−	0.249377i
$593$	13.1364	+	13.1364i	0.539449	+	0.539449i	0.923367	−	0.383918i	$-0.125426\pi$
$593$	13.1364	+	13.1364i	0.539449	+	0.539449i	−0.383918	+	0.923367i	$0.625426\pi$
$594$	1.94361	−	1.94361i	0.0797472	−	0.0797472i
$595$	−4.39545	+	1.03164i	−0.180196	+	0.0422932i
$596$			9.53201i			0.390446i
$597$		−	13.4829i		−	0.551818i
$598$	−9.99176			−0.408594
$599$			25.2096i			1.03003i	0.857180	+	0.515017i	$0.172214\pi$
$599$			25.2096i			1.03003i	−0.857180	+	0.515017i	$0.827786\pi$
$600$	4.73932	+	1.59337i	0.193482	+	0.0650489i
$601$	−30.5288			−1.24529			−0.622647	−	0.782502i	$-0.713943\pi$
$601$	−30.5288			−1.24529			−0.622647	+	0.782502i	$0.713943\pi$
$602$	−5.21522	+	5.21522i	−0.212557	+	0.212557i
$603$	5.36985	−	5.36985i	0.218677	−	0.218677i
$604$		−	17.4581i		−	0.710359i
$605$	−4.05803	+	6.54714i	−0.164982	+	0.266179i
$606$	−4.27725	−	4.27725i	−0.173751	−	0.173751i
$607$	13.8699			0.562963			0.281482	−	0.959567i	$-0.409174\pi$
$607$	13.8699			0.562963			0.281482	+	0.959567i	$0.409174\pi$
$608$	−1.10003	−	1.10003i	−0.0446120	−	0.0446120i
$609$	23.9745	+	23.9745i	0.971495	+	0.971495i
$610$	−10.8505	+	2.54669i	−0.439324	+	0.103112i
$611$	31.2300	−	31.2300i	1.26343	−	1.26343i
$612$	−0.534649			−0.0216119
$613$	−16.6052	+	16.6052i	−0.670679	+	0.670679i	−0.957873	−	0.287193i	$-0.907278\pi$
$613$	−16.6052	+	16.6052i	−0.670679	+	0.670679i	0.287193	+	0.957873i	$0.407278\pi$
$614$	−0.565223	−	0.565223i	−0.0228106	−	0.0228106i
$615$	−20.9474	+	4.91650i	−0.844680	+	0.198252i
$616$	7.34010	+	7.34010i	0.295741	+	0.295741i
$617$	17.4344	+	17.4344i	0.701884	+	0.701884i	0.964815	−	0.262931i	$-0.0846891\pi$
$617$	17.4344	+	17.4344i	0.701884	+	0.701884i	−0.262931	+	0.964815i	$0.584689\pi$
$618$	2.25320	+	2.25320i	0.0906370	+	0.0906370i
$619$	4.16120			0.167253			0.0836263	−	0.996497i	$-0.473350\pi$
$619$	4.16120			0.167253			0.0836263	+	0.996497i	$0.473350\pi$
$620$	12.0873	−	2.83697i	0.485436	−	0.113935i
$621$	2.06027	+	2.06027i	0.0826758	+	0.0826758i
$622$	−20.7503	−	20.7503i	−0.832010	−	0.832010i
$623$		−	53.3657i		−	2.13805i
$624$	2.42487	−	2.42487i	0.0970724	−	0.0970724i
$625$	−15.1029	+	19.9224i	−0.604118	+	0.796895i
$626$	10.7676			0.430358
$627$		−	4.27604i		−	0.170769i
$628$	7.38980	−	7.38980i	0.294885	−	0.294885i
$629$	−3.24404	−	0.229523i	−0.129348	−	0.00915167i
$630$	−8.22118	+	1.92957i	−0.327540	+	0.0768759i
$631$	−24.5515	−	24.5515i	−0.977381	−	0.977381i	0.0223684	−	0.999750i	$-0.492879\pi$
$631$	−24.5515	−	24.5515i	−0.977381	−	0.977381i	−0.999750	+	0.0223684i	$0.992879\pi$
$632$	4.60304	+	4.60304i	0.183099	+	0.183099i
$633$	−4.90673	+	4.90673i	−0.195025	+	0.195025i
$634$	−0.491641	−	0.491641i	−0.0195255	−	0.0195255i
$635$	3.59769	+	15.3284i	0.142770	+	0.608290i
$636$	−12.4910			−0.495300
$637$			24.9041i			0.986737i
$638$	17.4494	+	17.4494i	0.690827	+	0.690827i
$639$			15.0364i			0.594830i
$640$	−1.17802	+	1.90060i	−0.0465654	+	0.0751276i
$641$	24.1766			0.954918			0.477459	−	0.878654i	$-0.341558\pi$
$641$	24.1766			0.954918			0.477459	+	0.878654i	$0.341558\pi$
$642$		−	19.8557i		−	0.783642i
$643$			34.5674i			1.36320i	0.731723	+	0.681602i	$0.238717\pi$
$643$			34.5674i			1.36320i	−0.731723	+	0.681602i	$0.761283\pi$
$644$	−7.78068	+	7.78068i	−0.306602	+	0.306602i
$645$	−0.997841	−	4.25143i	−0.0392900	−	0.167400i
$646$	−0.588129	+	0.588129i	−0.0231396	+	0.0231396i
$647$	8.23154			0.323615			0.161808	−	0.986822i	$-0.448268\pi$
$647$	8.23154			0.323615			0.161808	+	0.986822i	$0.448268\pi$
$648$	−1.00000			−0.0392837
$649$	−22.4610	+	22.4610i	−0.881672	+	0.881672i
$650$	7.62853	+	15.3559i	0.299216	+	0.602309i
$651$	−14.8274	+	14.8274i	−0.581132	+	0.581132i
$652$			11.7022i			0.458293i
$653$		−	37.1465i		−	1.45366i	−0.686820	−	0.726828i	$-0.740994\pi$
$653$		−	37.1465i		−	1.45366i	0.686820	−	0.726828i	$-0.259006\pi$
$654$	−18.1260			−0.708781
$655$	10.4461	−	2.45178i	0.408164	−	0.0957990i
$656$		−	9.62252i		−	0.375696i
$657$	7.28489	+	7.28489i	0.284211	+	0.284211i
$658$		−	48.6381i		−	1.89611i
$659$	−32.8070			−1.27798			−0.638990	−	0.769215i	$-0.720647\pi$
$659$	−32.8070			−1.27798			−0.638990	+	0.769215i	$0.720647\pi$
$660$	−5.98362	+	1.40440i	−0.232912	+	0.0546662i
$661$	−5.94634	−	5.94634i	−0.231286	−	0.231286i	0.581943	−	0.813229i	$-0.302292\pi$
$661$	−5.94634	−	5.94634i	−0.231286	−	0.231286i	−0.813229	+	0.581943i	$0.802292\pi$
$662$	−4.01488	+	4.01488i	−0.156043	+	0.156043i
$663$	−1.29645	−	1.29645i	−0.0503501	−	0.0503501i
$664$	−10.9528	−	10.9528i	−0.425051	−	0.425051i
$665$	−6.92094	+	11.1661i	−0.268383	+	0.433003i
$666$	−6.06759	−	0.429296i	−0.235115	−	0.0166349i
$667$	−18.4967	+	18.4967i	−0.716197	+	0.716197i
$668$			1.27852i			0.0494673i
$669$	−1.02047			−0.0394536
$670$	−16.5317	+	3.88011i	−0.638676	+	0.149902i
$671$	9.68762	−	9.68762i	0.373987	−	0.373987i
$672$		−	3.77653i		−	0.145683i
$673$	−3.48219	−	3.48219i	−0.134229	−	0.134229i	0.636800	−	0.771029i	$-0.280258\pi$
$673$	−3.48219	−	3.48219i	−0.134229	−	0.134229i	−0.771029	+	0.636800i	$0.780258\pi$
$674$	−6.16129	−	6.16129i	−0.237324	−	0.237324i
$675$	1.59337	−	4.73932i	0.0613287	−	0.182417i
$676$	−1.24004			−0.0476938
$677$	−27.3326	−	27.3326i	−1.05048	−	1.05048i	−0.998656	−	0.0518189i	$-0.983498\pi$
$677$	−27.3326	−	27.3326i	−1.05048	−	1.05048i	−0.0518189	−	0.998656i	$-0.516502\pi$
$678$	3.73174	+	3.73174i	0.143317	+	0.143317i
$679$	−38.4172	−	38.4172i	−1.47432	−	1.47432i
$680$	1.01615	+	0.629829i	0.0389677	+	0.0241528i
$681$	−0.845033	−	0.845033i	−0.0323817	−	0.0323817i
$682$	−10.7918	+	10.7918i	−0.413241	+	0.413241i
$683$	29.9135			1.14461			0.572304	−	0.820041i	$-0.306050\pi$
$683$	29.9135			1.14461			0.572304	+	0.820041i	$0.306050\pi$
$684$	−1.10003	+	1.10003i	−0.0420606	+	0.0420606i
$685$	5.57550	+	23.7551i	0.213029	+	0.907637i
$686$	0.700181	+	0.700181i	0.0267330	+	0.0267330i
$687$	9.85278	+	9.85278i	0.375907	+	0.375907i
$688$	1.95296			0.0744561
$689$	−30.2890	−	30.2890i	−1.15392	−	1.15392i
$690$	−1.48870	−	6.34278i	−0.0566737	−	0.241466i
$691$		−	12.3285i		−	0.468998i	−0.972116	−	0.234499i	$-0.924655\pi$
$691$		−	12.3285i		−	0.468998i	0.972116	−	0.234499i	$-0.0753450\pi$
$692$	8.86215	−	8.86215i	0.336889	−	0.336889i
$693$	7.34010	−	7.34010i	0.278827	−	0.278827i
$694$	3.72173			0.141275
$695$	−1.84575	+	2.97789i	−0.0700132	+	0.112958i
$696$		−	8.97783i		−	0.340304i
$697$	−5.14468			−0.194869
$698$			8.05700i			0.304962i
$699$		−	5.07851i		−	0.192087i
$700$	17.8982	+	6.01740i	0.676489	+	0.227436i
$701$	−12.1525	+	12.1525i	−0.458994	+	0.458994i	−0.898325	−	0.439331i	$-0.855215\pi$
$701$	−12.1525	+	12.1525i	−0.458994	+	0.458994i	0.439331	+	0.898325i	$0.355215\pi$
$702$	−2.42487	−	2.42487i	−0.0915207	−	0.0915207i
$703$	−7.14676	+	6.20228i	−0.269545	+	0.233924i
$704$		−	2.74868i		−	0.103595i
$705$	24.4778	+	15.1718i	0.921889	+	0.571403i
$706$			18.4416i			0.694060i
$707$	−16.1532	−	16.1532i	−0.607503	−	0.607503i
$708$	11.5564			0.434315
$709$	12.7149	+	12.7149i	0.477517	+	0.477517i	0.904337	−	0.426820i	$-0.140366\pi$
$709$	12.7149	+	12.7149i	0.477517	+	0.477517i	−0.426820	+	0.904337i	$0.640366\pi$
$710$	17.7132	−	28.5781i	0.664764	−	1.07252i
$711$	4.60304	−	4.60304i	0.172627	−	0.172627i
$712$	−9.99204	+	9.99204i	−0.374467	+	0.374467i
$713$	−11.4396	−	11.4396i	−0.428417	−	0.428417i
$714$	−2.01912			−0.0755637
$715$	−17.9150	−	11.1040i	−0.669982	−	0.415266i
$716$	−5.78220	+	5.78220i	−0.216091	+	0.216091i
$717$	−3.86933			−0.144503
$718$		−	18.1393i		−	0.676954i
$719$			6.10088i			0.227524i	0.993508	+	0.113762i	$0.0362902\pi$
$719$			6.10088i			0.227524i	−0.993508	+	0.113762i	$0.963710\pi$
$720$	1.90060	+	1.17802i	0.0708310	+	0.0439023i
$721$	8.50928	+	8.50928i	0.316902	+	0.316902i
$722$		−	16.5799i		−	0.617039i
$723$			3.87229i			0.144012i
$724$	−6.35842			−0.236309
$725$	42.5488	+	14.3050i	1.58022	+	0.531273i
$726$	−2.43583	+	2.43583i	−0.0904021	+	0.0904021i
$727$	33.5779			1.24534			0.622668	−	0.782486i	$-0.286049\pi$
$727$	33.5779			1.24534			0.622668	+	0.782486i	$0.286049\pi$
$728$	9.15759	−	9.15759i	0.339403	−	0.339403i
$729$			1.00000i			0.0370370i
$730$	−5.26387	−	22.4274i	−0.194825	−	0.830075i
$731$		−	1.04415i		−	0.0386193i
$732$	−4.98435			−0.184227
$733$	26.0037	−	26.0037i	0.960467	−	0.960467i	−0.0387805	−	0.999248i	$-0.512347\pi$
$733$	26.0037	−	26.0037i	0.960467	−	0.960467i	0.999248	+	0.0387805i	$0.0123473\pi$
$734$	0.674373	−	0.674373i	0.0248916	−	0.0248916i
$735$	−15.8092	+	3.71052i	−0.583130	+	0.136865i
$736$	2.91366			0.107399
$737$	14.7600	−	14.7600i	0.543691	−	0.543691i
$738$	−9.62252			−0.354210
$739$	−37.1311			−1.36589			−0.682945	−	0.730470i	$-0.739301\pi$
$739$	−37.1311			−1.36589			−0.682945	+	0.730470i	$0.739301\pi$
$740$	11.0263	+	7.96368i	0.405336	+	0.292751i
$741$	−5.33484			−0.195980
$742$	−47.1726			−1.73176
$743$	1.00487	−	1.00487i	0.0368651	−	0.0368651i	−0.688434	−	0.725299i	$-0.741701\pi$
$743$	1.00487	−	1.00487i	0.0368651	−	0.0368651i	0.725299	+	0.688434i	$0.241701\pi$
$744$	5.55248			0.203564
$745$	−18.1165	−	11.2289i	−0.663737	−	0.411396i
$746$	−14.1566	+	14.1566i	−0.518311	+	0.518311i
$747$	−10.9528	+	10.9528i	−0.400742	+	0.400742i
$748$	−1.46958			−0.0537331
$749$		−	74.9857i		−	2.73992i
$750$	−8.61137	+	7.13052i	−0.314443	+	0.260370i
$751$			14.6004i			0.532777i	0.963866	+	0.266388i	$0.0858304\pi$
$751$			14.6004i			0.532777i	−0.963866	+	0.266388i	$0.914170\pi$
$752$	−9.10685	+	9.10685i	−0.332093	+	0.332093i
$753$	−10.9772			−0.400032
$754$	21.7700	−	21.7700i	0.792818	−	0.792818i
$755$	33.1807	+	20.5660i	1.20757	+	0.748473i
$756$	−3.77653			−0.137351
$757$			23.5268i			0.855096i	0.903993	+	0.427548i	$0.140622\pi$
$757$			23.5268i			0.855096i	−0.903993	+	0.427548i	$0.859378\pi$
$758$		−	30.7418i		−	1.11659i
$759$	5.66301	+	5.66301i	0.205554	+	0.205554i
$760$	3.38656	−	0.794851i	0.122844	−	0.0288323i
$761$		−	36.6320i		−	1.32791i	−0.747773	−	0.663954i	$-0.768877\pi$
$761$		−	36.6320i		−	1.32791i	0.747773	−	0.663954i	$-0.231123\pi$
$762$			7.04136i			0.255082i
$763$	−68.4533			−2.47817
$764$	12.2425	−	12.2425i	0.442918	−	0.442918i
$765$	0.629829	−	1.01615i	0.0227715	−	0.0367391i
$766$	−9.32059			−0.336767
$767$	28.0226	+	28.0226i	1.01184	+	1.01184i
$768$	−0.707107	+	0.707107i	−0.0255155	+	0.0255155i
$769$	29.7982	−	29.7982i	1.07455	−	1.07455i	0.0775648	−	0.996987i	$-0.475286\pi$
$769$	29.7982	−	29.7982i	1.07455	−	1.07455i	0.996987	−	0.0775648i	$-0.0247145\pi$
$770$	−22.5973	+	5.30376i	−0.814352	+	0.191134i
$771$	−8.87590	−	8.87590i	−0.319658	−	0.319658i
$772$	−7.16959			−0.258039
$773$	27.1868	+	27.1868i	0.977841	+	0.977841i	0.999760	−	0.0219190i	$-0.00697761\pi$
$773$	27.1868	+	27.1868i	0.977841	+	0.977841i	−0.0219190	+	0.999760i	$0.506978\pi$
$774$		−	1.95296i		−	0.0701979i
$775$	−8.84713	+	26.3150i	−0.317798	+	0.945263i
$776$			14.3863i			0.516437i
$777$	−22.9145	−	1.62125i	−0.822052	−	0.0581620i
$778$	−14.1117	−	14.1117i	−0.505928	−	0.505928i
$779$	−10.5850	+	10.5850i	−0.379248	+	0.379248i
$780$	1.75215	+	7.46524i	0.0627369	+	0.267298i
$781$			41.3301i			1.47891i
$782$		−	1.55779i		−	0.0557064i
$783$	−8.97783			−0.320841
$784$		−	7.26220i		−	0.259364i
$785$	5.33968	+	22.7504i	0.190581	+	0.811996i
$786$	4.79860			0.171160
$787$	−23.5700	+	23.5700i	−0.840179	+	0.840179i	−0.988882	−	0.148703i	$-0.952490\pi$
$787$	−23.5700	+	23.5700i	−0.840179	+	0.840179i	0.148703	+	0.988882i	$0.452490\pi$
$788$	−12.4994	+	12.4994i	−0.445273	+	0.445273i
$789$		−	16.8410i		−	0.599555i
$790$	−14.1710	+	3.32603i	−0.504181	+	0.118335i
$791$	14.0930	+	14.0930i	0.501091	+	0.501091i
$792$	−2.74868			−0.0976699
$793$	−12.0864	−	12.0864i	−0.429200	−	0.429200i
$794$	14.4178	+	14.4178i	0.511670	+	0.511670i
$795$	14.7146	−	23.7403i	0.521875	−	0.841982i
$796$	−9.53384	+	9.53384i	−0.337918	+	0.337918i
$797$	4.21520			0.149310			0.0746551	−	0.997209i	$-0.476214\pi$
$797$	4.21520			0.149310			0.0746551	+	0.997209i	$0.476214\pi$
$798$	−4.15429	+	4.15429i	−0.147060	+	0.147060i
$799$	4.86897	+	4.86897i	0.172252	+	0.172252i
$800$	−2.22453	−	4.47789i	−0.0786489	−	0.158317i
$801$	9.99204	+	9.99204i	0.353051	+	0.353051i
$802$	14.7403	+	14.7403i	0.520498	+	0.520498i
$803$	20.0238	+	20.0238i	0.706625	+	0.706625i
$804$	−7.59412			−0.267824
$805$	−5.62211	−	23.9537i	−0.198153	−	0.844258i
$806$	13.4640	+	13.4640i	0.474250	+	0.474250i
$807$	−20.6996	−	20.6996i	−0.728662	−	0.728662i
$808$			6.04894i			0.212801i
$809$	25.7274	−	25.7274i	0.904528	−	0.904528i	−0.0912957	−	0.995824i	$-0.529101\pi$
$809$	25.7274	−	25.7274i	0.904528	−	0.904528i	0.995824	+	0.0912957i	$0.0291008\pi$
$810$	1.17802	−	1.90060i	0.0413915	−	0.0667801i
$811$	49.0516			1.72244			0.861218	−	0.508236i	$-0.169702\pi$
$811$	49.0516			1.72244			0.861218	+	0.508236i	$0.169702\pi$
$812$		−	33.9051i		−	1.18983i
$813$	4.24748	−	4.24748i	0.148966	−	0.148966i
$814$	−16.6778	−	1.17999i	−0.584558	−	0.0413588i
$815$	−22.2411	−	13.7854i	−0.779072	−	0.482882i
$816$	0.378054	+	0.378054i	0.0132345	+	0.0132345i
$817$	−2.14832	−	2.14832i	−0.0751600	−	0.0751600i
$818$	10.9943	−	10.9943i	0.384407	−	0.384407i
$819$	−9.15759	−	9.15759i	−0.319992	−	0.319992i
$820$	18.2885	+	11.3355i	0.638663	+	0.395854i
$821$	2.90960			0.101546			0.0507728	−	0.998710i	$-0.483832\pi$
$821$	2.90960			0.101546			0.0507728	+	0.998710i	$0.483832\pi$
$822$			10.9123i			0.380611i
$823$	−30.1945	−	30.1945i	−1.05252	−	1.05252i	−0.998542	−	0.0539732i	$-0.982811\pi$
$823$	−30.1945	−	30.1945i	−1.05252	−	1.05252i	−0.0539732	−	0.998542i	$-0.517189\pi$
$824$		−	3.18651i		−	0.111007i
$825$	4.37964	−	13.0269i	0.152480	−	0.453537i
$826$	43.6430			1.51853
$827$			49.2078i			1.71112i	0.517703	+	0.855561i	$0.326787\pi$
$827$			49.2078i			1.71112i	−0.517703	+	0.855561i	$0.673213\pi$
$828$		−	2.91366i		−	0.101257i
$829$	−10.5621	+	10.5621i	−0.366838	+	0.366838i	−0.866323	−	0.499485i	$-0.833523\pi$
$829$	−10.5621	+	10.5621i	−0.366838	+	0.366838i	0.499485	+	0.866323i	$0.333523\pi$
$830$	33.7195	−	7.91421i	1.17042	−	0.274706i
$831$	−6.47038	+	6.47038i	−0.224455	+	0.224455i
$832$	−3.42928			−0.118889
$833$	−3.88273			−0.134529
$834$	−1.10791	+	1.10791i	−0.0383638	+	0.0383638i
$835$	−2.42994	−	1.50612i	−0.0840916	−	0.0521214i
$836$	−3.02362	+	3.02362i	−0.104574	+	0.104574i
$837$		−	5.55248i		−	0.191922i
$838$			15.2679i			0.527421i
$839$	−6.68559			−0.230812			−0.115406	−	0.993318i	$-0.536817\pi$
$839$	−6.68559			−0.230812			−0.115406	+	0.993318i	$0.536817\pi$
$840$	7.17766	+	4.44884i	0.247653	+	0.153500i
$841$		−	51.6013i		−	1.77936i
$842$	10.9789	+	10.9789i	0.378357	+	0.378357i
$843$			12.2730i			0.422703i
$844$	6.93916			0.238856
$845$	1.46079	−	2.35681i	0.0502528	−	0.0810769i
$846$	9.10685	+	9.10685i	0.313100	+	0.313100i
$847$	−9.19899	+	9.19899i	−0.316081	+	0.316081i
$848$	8.83246	+	8.83246i	0.303308	+	0.303308i
$849$	−1.15242	−	1.15242i	−0.0395511	−	0.0395511i
$850$	−2.39410	+	1.18934i	−0.0821169	+	0.0407941i
$851$	1.25082	−	17.6789i	0.0428776	−	0.606026i
$852$	10.6323	−	10.6323i	0.364258	−	0.364258i
$853$			24.9425i			0.854016i	0.904248	+	0.427008i	$0.140432\pi$
$853$			24.9425i			0.854016i	−0.904248	+	0.427008i	$0.859568\pi$
$854$	−18.8236			−0.644129
$855$	−0.794851	−	3.38656i	−0.0271833	−	0.115818i
$856$	−14.0401	+	14.0401i	−0.479881	+	0.479881i
$857$		−	23.2261i		−	0.793387i	−0.917951	−	0.396694i	$-0.870157\pi$
$857$		−	23.2261i		−	0.793387i	0.917951	−	0.396694i	$-0.129843\pi$
$858$	−6.66517	−	6.66517i	−0.227545	−	0.227545i
$859$	38.4729	+	38.4729i	1.31268	+	1.31268i	0.919434	+	0.393244i	$0.128647\pi$
$859$	38.4729	+	38.4729i	1.31268	+	1.31268i	0.393244	+	0.919434i	$0.371353\pi$
$860$	−2.30064	+	3.71180i	−0.0784510	+	0.126571i
$861$	−36.3398			−1.23846
$862$	−16.5186	−	16.5186i	−0.562627	−	0.562627i
$863$	−16.3264	−	16.3264i	−0.555757	−	0.555757i	0.372340	−	0.928096i	$-0.378556\pi$
$863$	−16.3264	−	16.3264i	−0.555757	−	0.555757i	−0.928096	+	0.372340i	$0.878556\pi$
$864$	0.707107	+	0.707107i	0.0240563	+	0.0240563i
$865$	6.40356	+	27.2832i	0.217728	+	0.927656i
$866$	−16.8050	−	16.8050i	−0.571058	−	0.571058i
$867$	−11.8187	+	11.8187i	−0.401384	+	0.401384i
$868$	20.9691			0.711739
$869$	12.6523	−	12.6523i	0.429198	−	0.429198i
$870$	17.0632	+	10.5761i	0.578497	+	0.358563i
$871$	−18.4147	−	18.4147i	−0.623959	−	0.623959i
$872$	12.8170	+	12.8170i	0.434038	+	0.434038i
$873$	14.3863			0.486901
$874$	−3.20511	−	3.20511i	−0.108414	−	0.108414i
$875$	−32.5211	+	26.9286i	−1.09941	+	0.910354i
$876$		−	10.3024i		−	0.348086i
$877$	17.1008	−	17.1008i	0.577454	−	0.577454i	−0.356747	−	0.934201i	$-0.616114\pi$
$877$	17.1008	−	17.1008i	0.577454	−	0.577454i	0.934201	+	0.356747i	$0.116114\pi$
$878$	−3.01200	+	3.01200i	−0.101650	+	0.101650i
$879$	4.54869			0.153423
$880$	5.22412	+	3.23800i	0.176105	+	0.109153i
$881$			19.4242i			0.654419i	0.944952	+	0.327209i	$0.106108\pi$
$881$			19.4242i			0.654419i	−0.944952	+	0.327209i	$0.893892\pi$
$882$	−7.26220			−0.244531
$883$		−	51.0527i		−	1.71806i	−0.511926	−	0.859029i	$-0.671068\pi$
$883$		−	51.0527i		−	1.71806i	0.511926	−	0.859029i	$-0.328932\pi$
$884$			1.83346i			0.0616660i
$885$	−13.6136	+	21.9640i	−0.457618	+	0.738311i
$886$	−10.7717	+	10.7717i	−0.361881	+	0.361881i
$887$	−6.64936	−	6.64936i	−0.223264	−	0.223264i	0.586608	−	0.809871i	$-0.300463\pi$
$887$	−6.64936	−	6.64936i	−0.223264	−	0.223264i	−0.809871	+	0.586608i	$0.800463\pi$
$888$	3.98688	+	4.59400i	0.133791	+	0.154164i
$889$			26.5919i			0.891865i
$890$	−7.21998	−	30.7617i	−0.242014	−	1.03113i
$891$			2.74868i			0.0920841i
$892$	0.721579	+	0.721579i	0.0241603	+	0.0241603i
$893$	20.0356			0.670465
$894$	−6.74015	−	6.74015i	−0.225424	−	0.225424i
$895$	−4.17807	−	17.8012i	−0.139657	−	0.595028i
$896$	−2.67041	+	2.67041i	−0.0892122	+	0.0892122i
$897$	7.06524	−	7.06524i	0.235902	−	0.235902i
$898$	6.33208	+	6.33208i	0.211304	+	0.211304i
$899$	49.8492			1.66256
$900$	−4.47789	+	2.22453i	−0.149263	+	0.0741509i
$901$	4.72227	−	4.72227i	0.157322	−	0.157322i
$902$	−26.4492			−0.880662
$903$		−	7.37544i		−	0.245439i
$904$		−	5.27748i		−	0.175526i
$905$	7.49036	−	12.0848i	0.248988	−	0.401712i
$906$	12.3447	+	12.3447i	0.410126	+	0.410126i
$907$			22.6816i			0.753129i	0.926390	+	0.376565i	$0.122895\pi$
$907$			22.6816i			0.753129i	−0.926390	+	0.376565i	$0.877105\pi$
$908$			1.19506i			0.0396594i
$909$	6.04894			0.200631
$910$	6.61703	+	28.1927i	0.219353	+	0.934580i
$911$	23.5154	−	23.5154i	0.779099	−	0.779099i	−0.200578	−	0.979678i	$-0.564282\pi$
$911$	23.5154	−	23.5154i	0.779099	−	0.779099i	0.979678	+	0.200578i	$0.0642821\pi$
$912$	1.55567			0.0515135
$913$	−30.1057	+	30.1057i	−0.996354	+	0.996354i
$914$		−	34.7548i		−	1.14959i
$915$	5.87168	−	9.47324i	0.194112	−	0.313176i
$916$		−	13.9339i		−	0.460390i
$917$	18.1221			0.598443
$918$	0.378054	−	0.378054i	0.0124776	−	0.0124776i
$919$	−13.6406	+	13.6406i	−0.449963	+	0.449963i	−0.895342	−	0.445379i	$-0.853069\pi$
$919$	−13.6406	+	13.6406i	−0.449963	+	0.449963i	0.445379	+	0.895342i	$0.353069\pi$
$920$	−3.43236	+	5.53769i	−0.113161	+	0.182572i
$921$	0.799346			0.0263394
$922$	−9.43804	+	9.43804i	−0.310825	+	0.310825i
$923$	51.5640			1.69725
$924$	−10.3805			−0.341492
$925$	−28.1250	+	11.5752i	−0.924744	+	0.380590i
$926$	−26.8196			−0.881346
$927$	−3.18651			−0.104659
$928$	−6.34828	+	6.34828i	−0.208393	+	0.208393i
$929$	−17.2093			−0.564617			−0.282309	−	0.959324i	$-0.591100\pi$
$929$	−17.2093			−0.564617			−0.282309	+	0.959324i	$0.591100\pi$
$930$	−6.54095	+	10.5530i	−0.214486	+	0.346047i
$931$	−7.98862	+	7.98862i	−0.261816	+	0.261816i
$932$	−3.59105	+	3.59105i	−0.117629	+	0.117629i
$933$	29.3453			0.960723
$934$		−	30.6261i		−	1.00212i
$935$	1.73119	−	2.79307i	0.0566161	−	0.0913433i
$936$			3.42928i			0.112090i
$937$	27.7679	−	27.7679i	0.907137	−	0.907137i	−0.0889033	−	0.996040i	$-0.528336\pi$
$937$	27.7679	−	27.7679i	0.907137	−	0.907137i	0.996040	+	0.0889033i	$0.0283362\pi$
$938$	−28.6794			−0.936417
$939$	−7.61381	+	7.61381i	−0.248467	+	0.248467i
$940$	−6.58037	−	28.0365i	−0.214628	−	0.914451i
$941$	−30.3798			−0.990352			−0.495176	−	0.868793i	$-0.664896\pi$
$941$	−30.3798			−0.990352			−0.495176	+	0.868793i	$0.664896\pi$
$942$			10.4508i			0.340504i
$943$		−	28.0368i		−	0.913003i
$944$	−8.17158	−	8.17158i	−0.265962	−	0.265962i
$945$	4.44884	−	7.17766i	0.144721	−	0.233489i
$946$		−	5.36807i		−	0.174531i
$947$			40.0733i			1.30221i	0.758989	+	0.651103i	$0.225694\pi$
$947$			40.0733i			1.30221i	−0.758989	+	0.651103i	$0.774306\pi$
$948$	−6.50968			−0.211425
$949$	24.9819	−	24.9819i	0.810948	−	0.810948i
$950$	−2.47876	+	7.37284i	−0.0804215	+	0.239207i
$951$	0.695285			0.0225462
$952$	1.42773	+	1.42773i	0.0462731	+	0.0462731i
$953$	25.8258	−	25.8258i	0.836578	−	0.836578i	−0.151829	−	0.988407i	$-0.548516\pi$
$953$	25.8258	−	25.8258i	0.836578	−	0.836578i	0.988407	+	0.151829i	$0.0485162\pi$
$954$	8.83246	−	8.83246i	0.285961	−	0.285961i
$955$	8.84610	+	37.6899i	0.286253	+	1.21962i
$956$	2.73603	+	2.73603i	0.0884895	+	0.0884895i
$957$	−24.6771			−0.797698
$958$	−28.4708	−	28.4708i	−0.919851	−	0.919851i
$959$			41.2107i			1.33076i
$960$	−0.510937	−	2.17691i	−0.0164904	−	0.0702595i
$961$		−	0.169953i		−	0.00548236i
$962$	−1.47217	+	20.8075i	−0.0474648	+	0.670860i
$963$	14.0401	+	14.0401i	0.452436	+	0.452436i
$964$	2.73812	−	2.73812i	0.0881890	−	0.0881890i
$965$	8.44593	−	13.6265i	0.271884	−	0.438652i
$966$		−	11.0035i		−	0.354033i
$967$		−	43.2675i		−	1.39139i	−0.718338	−	0.695694i	$-0.755097\pi$
$967$		−	43.2675i		−	1.39139i	0.718338	−	0.695694i	$-0.244903\pi$
$968$	3.44478			0.110720
$969$		−	0.831740i		−	0.0267193i
$970$	−27.3425	−	16.9473i	−0.877914	−	0.544146i
$971$	28.1554			0.903551			0.451775	−	0.892132i	$-0.350791\pi$
$971$	28.1554			0.903551			0.451775	+	0.892132i	$0.350791\pi$
$972$	0.707107	−	0.707107i	0.0226805	−	0.0226805i
$973$	−4.18406	+	4.18406i	−0.134135	+	0.134135i
$974$			25.3425i			0.812025i
$975$	−16.2525	−	5.46410i	−0.520495	−	0.174991i
$976$	3.52447	+	3.52447i	0.112816	+	0.112816i
$977$	−51.7752			−1.65644			−0.828218	−	0.560406i	$-0.810645\pi$
$977$	−51.7752			−1.65644			−0.828218	+	0.560406i	$0.810645\pi$
$978$	−8.27469	−	8.27469i	−0.264595	−	0.264595i
$979$	27.4649	+	27.4649i	0.877781	+	0.877781i
$980$	13.8025	+	8.55503i	0.440905	+	0.273280i
$981$	12.8170	−	12.8170i	0.409215	−	0.409215i
$982$	23.3602			0.745452
$983$	8.76162	−	8.76162i	0.279452	−	0.279452i	−0.553438	−	0.832890i	$-0.686684\pi$
$983$	8.76162	−	8.76162i	0.279452	−	0.279452i	0.832890	+	0.553438i	$0.186684\pi$
$984$	6.80415	+	6.80415i	0.216908	+	0.216908i
$985$	−9.03175	−	38.4809i	−0.287775	−	1.22610i
$986$	3.39410	+	3.39410i	0.108090	+	0.108090i
$987$	34.3923	+	34.3923i	1.09472	+	1.09472i
$988$	3.77230	+	3.77230i	0.120013	+	0.120013i
$989$	5.69028			0.180940
$990$	3.23800	−	5.22412i	0.102910	−	0.166033i
$991$	22.3850	+	22.3850i	0.711083	+	0.711083i	0.966762	−	0.255679i	$-0.0822989\pi$
$991$	22.3850	+	22.3850i	0.711083	+	0.711083i	−0.255679	+	0.966762i	$0.582299\pi$
$992$	−3.92620	−	3.92620i	−0.124657	−	0.124657i
$993$		−	5.67790i		−	0.180183i
$994$	40.1533	−	40.1533i	1.27359	−	1.27359i
$995$	−6.88890	−	29.3510i	−0.218393	−	0.930491i
$996$	15.4896			0.490807
$997$			17.3884i			0.550697i	0.961344	+	0.275349i	$0.0887933\pi$
$997$			17.3884i			0.550697i	−0.961344	+	0.275349i	$0.911207\pi$
$998$	9.86951	−	9.86951i	0.312414	−	0.312414i
$999$	4.59400	−	3.98688i	0.145348	−	0.126139i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1110.2.o.b.253.2	yes	40
5.2	odd	4		1110.2.l.b.697.19	yes	40
37.6	odd	4		1110.2.l.b.43.19	✓	40
185.117	even	4	inner	1110.2.o.b.487.2	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1110.2.l.b.43.19	✓	40	37.6	odd	4
1110.2.l.b.697.19	yes	40	5.2	odd	4
1110.2.o.b.253.2	yes	40	1.1	even	1	trivial
1110.2.o.b.487.2	yes	40	185.117	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.o (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +(-0.707107 + 0.707107i) q^{3} +1.00000 q^{4} +(-1.17802 + 1.90060i) q^{5} +(-0.707107 + 0.707107i) q^{6} +(-2.67041 + 2.67041i) q^{7} +1.00000 q^{8} -1.00000i q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +(-0.707107 + 0.707107i) q^{3} +1.00000 q^{4} +(-1.17802 + 1.90060i) q^{5} +(-0.707107 + 0.707107i) q^{6} +(-2.67041 + 2.67041i) q^{7} +1.00000 q^{8} -1.00000i q^{9} +(-1.17802 + 1.90060i) q^{10} -2.74868i q^{11} +(-0.707107 + 0.707107i) q^{12} -3.42928 q^{13} +(-2.67041 + 2.67041i) q^{14} +(-0.510937 - 2.17691i) q^{15} +1.00000 q^{16} -0.534649i q^{17} -1.00000i q^{18} +(-1.10003 - 1.10003i) q^{19} +(-1.17802 + 1.90060i) q^{20} -3.77653i q^{21} -2.74868i q^{22} +2.91366 q^{23} +(-0.707107 + 0.707107i) q^{24} +(-2.22453 - 4.47789i) q^{25} -3.42928 q^{26} +(0.707107 + 0.707107i) q^{27} +(-2.67041 + 2.67041i) q^{28} +(-6.34828 + 6.34828i) q^{29} +(-0.510937 - 2.17691i) q^{30} +(-3.92620 - 3.92620i) q^{31} +1.00000 q^{32} +(1.94361 + 1.94361i) q^{33} -0.534649i q^{34} +(-1.92957 - 8.22118i) q^{35} -1.00000i q^{36} +(0.429296 - 6.06759i) q^{37} +(-1.10003 - 1.10003i) q^{38} +(2.42487 - 2.42487i) q^{39} +(-1.17802 + 1.90060i) q^{40} -9.62252i q^{41} -3.77653i q^{42} +1.95296 q^{43} -2.74868i q^{44} +(1.90060 + 1.17802i) q^{45} +2.91366 q^{46} +(-9.10685 + 9.10685i) q^{47} +(-0.707107 + 0.707107i) q^{48} -7.26220i q^{49} +(-2.22453 - 4.47789i) q^{50} +(0.378054 + 0.378054i) q^{51} -3.42928 q^{52} +(8.83246 + 8.83246i) q^{53} +(0.707107 + 0.707107i) q^{54} +(5.22412 + 3.23800i) q^{55} +(-2.67041 + 2.67041i) q^{56} +1.55567 q^{57} +(-6.34828 + 6.34828i) q^{58} +(-8.17158 - 8.17158i) q^{59} +(-0.510937 - 2.17691i) q^{60} +(3.52447 + 3.52447i) q^{61} +(-3.92620 - 3.92620i) q^{62} +(2.67041 + 2.67041i) q^{63} +1.00000 q^{64} +(4.03977 - 6.51767i) q^{65} +(1.94361 + 1.94361i) q^{66} +(5.36985 + 5.36985i) q^{67} -0.534649i q^{68} +(-2.06027 + 2.06027i) q^{69} +(-1.92957 - 8.22118i) q^{70} -15.0364 q^{71} -1.00000i q^{72} +(-7.28489 + 7.28489i) q^{73} +(0.429296 - 6.06759i) q^{74} +(4.73932 + 1.59337i) q^{75} +(-1.10003 - 1.10003i) q^{76} +(7.34010 + 7.34010i) q^{77} +(2.42487 - 2.42487i) q^{78} +(4.60304 + 4.60304i) q^{79} +(-1.17802 + 1.90060i) q^{80} -1.00000 q^{81} -9.62252i q^{82} +(-10.9528 - 10.9528i) q^{83} -3.77653i q^{84} +(1.01615 + 0.629829i) q^{85} +1.95296 q^{86} -8.97783i q^{87} -2.74868i q^{88} +(-9.99204 + 9.99204i) q^{89} +(1.90060 + 1.17802i) q^{90} +(9.15759 - 9.15759i) q^{91} +2.91366 q^{92} +5.55248 q^{93} +(-9.10685 + 9.10685i) q^{94} +(3.38656 - 0.794851i) q^{95} +(-0.707107 + 0.707107i) q^{96} +14.3863i q^{97} -7.26220i q^{98} -2.74868 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 40 q^{2} + 40 q^{4} - 4 q^{7} + 40 q^{8}+O(q^{10}) \) 40 * q + 40 * q^2 + 40 * q^4 - 4 * q^7 + 40 * q^8	\( 40 q + 40 q^{2} + 40 q^{4} - 4 q^{7} + 40 q^{8} + 8 q^{13} - 4 q^{14} + 40 q^{16} - 4 q^{19} - 8 q^{25} + 8 q^{26} - 4 q^{28} + 28 q^{31} + 40 q^{32} - 4 q^{33} + 12 q^{35} + 8 q^{37} - 4 q^{38} - 4 q^{39} - 16 q^{47} - 8 q^{50} + 16 q^{51} + 8 q^{52} + 20 q^{53} - 8 q^{55} - 4 q^{56} - 8 q^{57} + 4 q^{59} - 8 q^{61} + 28 q^{62} + 4 q^{63} + 40 q^{64} + 4 q^{65} - 4 q^{66} - 16 q^{67} + 8 q^{69} + 12 q^{70} + 40 q^{71} - 8 q^{73} + 8 q^{74} + 16 q^{75} - 4 q^{76} + 24 q^{77} - 4 q^{78} + 12 q^{79} - 40 q^{81} - 8 q^{83} + 8 q^{85} - 12 q^{89} - 24 q^{91} - 8 q^{93} - 16 q^{94} + 28 q^{95} - 8 q^{99}+O(q^{100}) \) 40 * q + 40 * q^2 + 40 * q^4 - 4 * q^7 + 40 * q^8 + 8 * q^13 - 4 * q^14 + 40 * q^16 - 4 * q^19 - 8 * q^25 + 8 * q^26 - 4 * q^28 + 28 * q^31 + 40 * q^32 - 4 * q^33 + 12 * q^35 + 8 * q^37 - 4 * q^38 - 4 * q^39 - 16 * q^47 - 8 * q^50 + 16 * q^51 + 8 * q^52 + 20 * q^53 - 8 * q^55 - 4 * q^56 - 8 * q^57 + 4 * q^59 - 8 * q^61 + 28 * q^62 + 4 * q^63 + 40 * q^64 + 4 * q^65 - 4 * q^66 - 16 * q^67 + 8 * q^69 + 12 * q^70 + 40 * q^71 - 8 * q^73 + 8 * q^74 + 16 * q^75 - 4 * q^76 + 24 * q^77 - 4 * q^78 + 12 * q^79 - 40 * q^81 - 8 * q^83 + 8 * q^85 - 12 * q^89 - 24 * q^91 - 8 * q^93 - 16 * q^94 + 28 * q^95 - 8 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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