LMFDB - Embedded newform 1110.2.l.b.43.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1110,2,Mod(43,1110)]

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, 3]))

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

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

chi := DirichletCharacter("1110.43");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1110 = 2 \cdot 3 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1110.l (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			43.19
Character	$\chi$	$=$	1110.43
Dual form			1110.2.l.b.697.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

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

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$		−	1.00000i		−	0.707107i
$2$		−	1.00000i		−	0.707107i
$3$	0.707107	−	0.707107i	0.408248	−	0.408248i
$3$	0.707107	−	0.707107i	0.408248	−	0.408248i
$4$	−1.00000			−0.500000
$5$	−1.90060	−	1.17802i	−0.849972	−	0.526827i
$5$	−1.90060	−	1.17802i	−0.849972	−	0.526827i
$6$	−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	$0.997019\pi$
$8$			1.00000i			0.353553i
$9$		−	1.00000i		−	0.333333i
$10$	−1.17802	+	1.90060i	−0.372523	+	0.601021i
$11$			2.74868i			0.828757i	0.910105	+	0.414378i	$0.136001\pi$
$11$			2.74868i			0.828757i	−0.910105	+	0.414378i	$0.863999\pi$
$12$	−0.707107	+	0.707107i	−0.204124	+	0.204124i
$13$		−	3.42928i		−	0.951111i	−0.879686	−	0.475556i	$-0.842247\pi$
$13$		−	3.42928i		−	0.951111i	0.879686	−	0.475556i	$-0.157753\pi$
$14$	2.67041	+	2.67041i	0.713698	+	0.713698i
$15$	−2.17691	+	0.510937i	−0.562076	+	0.131923i
$16$	1.00000			0.250000
$17$	0.534649			0.129672			0.0648358	−	0.997896i	$-0.479348\pi$
$17$	0.534649			0.129672			0.0648358	+	0.997896i	$0.479348\pi$
$18$	−1.00000			−0.235702
$19$	1.10003	−	1.10003i	0.252364	−	0.252364i	−0.569575	−	0.821939i	$-0.692892\pi$
$19$	1.10003	−	1.10003i	0.252364	−	0.252364i	0.821939	+	0.569575i	$0.192892\pi$
$20$	1.90060	+	1.17802i	0.424986	+	0.263414i
$21$			3.77653i			0.824107i
$22$	2.74868			0.586020
$23$			2.91366i			0.607540i	0.952745	+	0.303770i	$0.0982455\pi$
$23$			2.91366i			0.607540i	−0.952745	+	0.303770i	$0.901754\pi$
$24$	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	0.980039	+	0.198808i	$0.0637069\pi$
$29$	6.34828	+	6.34828i	1.17885	+	1.17885i	0.198808	+	0.980039i	$0.436293\pi$
$30$	0.510937	+	2.17691i	0.0932839	+	0.397448i
$31$	−3.92620	+	3.92620i	−0.705166	+	0.705166i	−0.965515	−	0.260349i	$-0.916162\pi$
$31$	−3.92620	+	3.92620i	−0.705166	+	0.705166i	0.260349	+	0.965515i	$0.416162\pi$
$32$		−	1.00000i		−	0.176777i
$33$	1.94361	+	1.94361i	0.338339	+	0.338339i
$34$		−	0.534649i		−	0.0916916i
$35$	8.22118	−	1.92957i	1.38963	−	0.326157i
$36$			1.00000i			0.166667i
$37$	6.06759	−	0.429296i	0.997506	−	0.0705758i
$37$	6.06759	−	0.429296i	0.997506	−	0.0705758i
$38$	−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	$0.270618\pi$
$41$			9.62252i			1.50279i	−0.659855	+	0.751393i	$0.729382\pi$
$42$	3.77653			0.582732
$43$			1.95296i			0.297824i	0.988850	+	0.148912i	$0.0475772\pi$
$43$			1.95296i			0.297824i	−0.988850	+	0.148912i	$0.952423\pi$
$44$		−	2.74868i		−	0.414378i
$45$	−1.17802	+	1.90060i	−0.175609	+	0.283324i
$46$	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
$50$	4.47789	−	2.22453i	0.633269	−	0.314596i
$51$	0.378054	−	0.378054i	0.0529382	−	0.0529382i
$52$			3.42928i			0.475556i
$53$	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
$55$	3.23800	−	5.22412i	0.436612	−	0.704420i
$56$	−2.67041	−	2.67041i	−0.356849	−	0.356849i
$57$		−	1.55567i		−	0.206054i
$58$	6.34828	−	6.34828i	0.833570	−	0.833570i
$59$	8.17158	−	8.17158i	1.06385	−	1.06385i	0.0660316	−	0.997818i	$-0.478966\pi$
$59$	8.17158	−	8.17158i	1.06385	−	1.06385i	0.997818	−	0.0660316i	$-0.0210338\pi$
$60$	2.17691	−	0.510937i	0.281038	−	0.0659616i
$61$	3.52447	−	3.52447i	0.451262	−	0.451262i	−0.444511	−	0.895773i	$-0.646623\pi$
$61$	3.52447	−	3.52447i	0.451262	−	0.451262i	0.895773	+	0.444511i	$0.146623\pi$
$62$	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	0.298407	−	0.954439i	$-0.403545\pi$
$67$	−5.36985	−	5.36985i	−0.656032	−	0.656032i	−0.954439	+	0.298407i	$0.903545\pi$
$68$	−0.534649			−0.0648358
$69$	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	$0.850871\pi$
$72$	1.00000			0.117851
$73$	7.28489	−	7.28489i	0.852632	−	0.852632i	−0.137825	−	0.990457i	$-0.544011\pi$
$73$	7.28489	−	7.28489i	0.852632	−	0.852632i	0.990457	+	0.137825i	$0.0440110\pi$
$74$	−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	$-0.869341\pi$
$79$	−4.60304	+	4.60304i	−0.517882	+	0.517882i	0.399048	+	0.916930i	$0.369341\pi$
$80$	−1.90060	−	1.17802i	−0.212493	−	0.131707i
$81$	−1.00000			−0.111111
$82$	9.62252			1.06263
$83$	−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
$87$	8.97783			0.962524
$88$	−2.74868			−0.293010
$89$	9.99204	+	9.99204i	1.05915	+	1.05915i	0.998137	+	0.0610170i	$0.0194344\pi$
$89$	9.99204	+	9.99204i	1.05915	+	1.05915i	0.0610170	+	0.998137i	$0.480566\pi$
$90$	1.90060	+	1.17802i	0.200340	+	0.124174i
$91$	9.15759	+	9.15759i	0.959976	+	0.959976i
$92$		−	2.91366i		−	0.303770i
$93$			5.55248i			0.575765i
$94$	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
$97$	−14.3863			−1.46070			−0.730352	−	0.683071i	$-0.760644\pi$
$97$	−14.3863			−1.46070			−0.730352	+	0.683071i	$0.760644\pi$
$98$	−7.26220			−0.733593
$99$	2.74868			0.276252
$100$	−2.22453	−	4.47789i	−0.222453	−	0.447789i
$101$		−	6.04894i		−	0.601892i	−0.953641	−	0.300946i	$-0.902698\pi$
$101$		−	6.04894i		−	0.601892i	0.953641	−	0.300946i	$-0.0973025\pi$
$102$	−0.378054	−	0.378054i	−0.0374329	−	0.0374329i
$103$	−3.18651			−0.313976			−0.156988	−	0.987601i	$-0.550178\pi$
$103$	−3.18651			−0.313976			−0.156988	+	0.987601i	$0.550178\pi$
$104$	3.42928			0.336269
$105$	4.44884	−	7.17766i	0.434162	−	0.700468i
$106$	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	−0.262792	+	0.964853i	$0.584643\pi$
$109$	−12.8170	+	12.8170i	−1.22764	+	1.22764i	−0.964853	+	0.262792i	$0.915357\pi$
$110$	−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
$113$	−5.27748			−0.496463			−0.248232	−	0.968701i	$-0.579849\pi$
$113$	−5.27748			−0.496463			−0.248232	+	0.968701i	$0.579849\pi$
$114$	−1.55567			−0.145702
$115$	3.43236	−	5.53769i	0.320069	−	0.516393i
$116$	−6.34828	−	6.34828i	−0.589423	−	0.589423i
$117$	−3.42928			−0.317037
$118$	−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
$125$	1.04712	−	11.1312i	0.0936574	−	0.995604i
$126$	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	$0.148864\pi$
$128$			1.00000i			0.0883883i
$129$	1.38095	+	1.38095i	0.121586	+	0.121586i
$130$	6.51767	+	4.03977i	0.571638	+	0.354311i
$131$	−3.39312	+	3.39312i	−0.296458	+	0.296458i	−0.839625	−	0.543167i	$-0.817225\pi$
$131$	−3.39312	+	3.39312i	−0.296458	+	0.296458i	0.543167	+	0.839625i	$0.317225\pi$
$132$	−1.94361	−	1.94361i	−0.169169	−	0.169169i
$133$			5.87505i			0.509432i
$134$	−5.36985	+	5.36985i	−0.463885	+	0.463885i
$135$	0.510937	+	2.17691i	0.0439744	+	0.187359i
$136$			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	$-0.521167\pi$
$139$	−1.56682			−0.132896			−0.0664480	+	0.997790i	$0.521167\pi$
$140$	−8.22118	+	1.92957i	−0.694816	+	0.163078i
$141$			12.8790i			1.08461i
$142$			15.0364i			1.26183i
$143$	9.42598			0.788240
$144$		−	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
$148$	−6.06759	+	0.429296i	−0.498753	+	0.0352879i
$149$			9.53201i			0.780893i	0.920626	+	0.390446i	$0.127679\pi$
$149$			9.53201i			0.780893i	−0.920626	+	0.390446i	$0.872321\pi$
$150$	1.59337	−	4.73932i	0.130098	−	0.386964i
$151$			17.4581i			1.42072i	0.703840	+	0.710359i	$0.251467\pi$
$151$			17.4581i			1.42072i	−0.703840	+	0.710359i	$0.748533\pi$
$152$	1.10003	+	1.10003i	0.0892240	+	0.0892240i
$153$		−	0.534649i		−	0.0432238i
$154$	−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
$162$			1.00000i			0.0785674i
$163$	11.7022			0.916586			0.458293	−	0.888801i	$-0.348461\pi$
$163$	11.7022			0.916586			0.458293	+	0.888801i	$0.348461\pi$
$164$		−	9.62252i		−	0.751393i
$165$	−1.40440	−	5.98362i	−0.109332	−	0.465824i
$166$	−10.9528	+	10.9528i	−0.850103	+	0.850103i
$167$	−1.27852			−0.0989345			−0.0494673	−	0.998776i	$-0.515752\pi$
$167$	−1.27852			−0.0989345			−0.0494673	+	0.998776i	$0.515752\pi$
$168$	−3.77653			−0.291366
$169$	1.24004			0.0953877
$170$	−0.629829	+	1.01615i	−0.0483057	+	0.0779353i
$171$	−1.10003	−	1.10003i	−0.0841212	−	0.0841212i
$172$		−	1.95296i		−	0.148912i
$173$	−8.86215	+	8.86215i	−0.673777	+	0.673777i	−0.958585	−	0.284808i	$-0.908070\pi$
$173$	−8.86215	+	8.86215i	−0.673777	+	0.673777i	0.284808	+	0.958585i	$0.408070\pi$
$174$		−	8.97783i		−	0.680607i
$175$	−17.8982	−	6.01740i	−1.35298	−	0.454872i
$176$			2.74868i			0.207189i
$177$		−	11.5564i		−	0.868629i
$178$	9.99204	−	9.99204i	0.748935	−	0.748935i
$179$	5.78220	+	5.78220i	0.432182	+	0.432182i	0.889370	−	0.457188i	$-0.151143\pi$
$179$	5.78220	+	5.78220i	0.432182	+	0.432182i	−0.457188	+	0.889370i	$0.651143\pi$
$180$	1.17802	−	1.90060i	0.0878046	−	0.141662i
$181$	−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
$183$		−	4.98435i		−	0.368454i
$184$	−2.91366			−0.214798
$185$	−12.0378	−	6.33184i	−0.885034	−	0.465526i
$186$	5.55248			0.407128
$187$			1.46958i			0.107466i
$188$	9.10685	−	9.10685i	0.664186	−	0.664186i
$189$	3.77653			0.274702
$190$	0.794851	+	3.38656i	0.0576646	+	0.245687i
$191$	12.2425	+	12.2425i	0.885835	+	0.885835i	0.994120	−	0.108285i	$-0.0345358\pi$
$191$	12.2425	+	12.2425i	0.885835	+	0.885835i	−0.108285	+	0.994120i	$0.534536\pi$
$192$	−0.707107	+	0.707107i	−0.0510310	+	0.0510310i
$193$		−	7.16959i		−	0.516078i	−0.966134	−	0.258039i	$-0.916924\pi$
$193$		−	7.16959i		−	0.516078i	0.966134	−	0.258039i	$-0.0830763\pi$
$194$			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	$0.466827\pi$
$198$		−	2.74868i		−	0.195340i
$199$	9.53384	+	9.53384i	0.675836	+	0.675836i	0.959055	−	0.283219i	$-0.0914024\pi$
$199$	9.53384	+	9.53384i	0.675836	+	0.675836i	−0.283219	+	0.959055i	$0.591402\pi$
$200$	−4.47789	+	2.22453i	−0.316634	+	0.157298i
$201$	−7.59412			−0.535648
$202$	−6.04894			−0.425602
$203$	−33.9051			−2.37967
$204$	−0.378054	+	0.378054i	−0.0264691	+	0.0264691i
$205$	11.3355	−	18.2885i	0.791709	−	1.27733i
$206$			3.18651i			0.222014i
$207$	2.91366			0.202513
$208$		−	3.42928i		−	0.237778i
$209$	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
$217$		−	20.9691i		−	1.42348i
$218$	12.8170	+	12.8170i	0.868076	+	0.868076i
$219$		−	10.3024i		−	0.696171i
$220$	−3.23800	+	5.22412i	−0.218306	+	0.352210i
$221$		−	1.83346i		−	0.123332i
$222$	−4.59400	−	3.98688i	−0.308329	−	0.267582i
$223$	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
$227$	−1.19506			−0.0793187			−0.0396594	−	0.999213i	$-0.512627\pi$
$227$	−1.19506			−0.0793187			−0.0396594	+	0.999213i	$0.512627\pi$
$228$			1.55567i			0.103027i
$229$		−	13.9339i		−	0.920781i	−0.887717	−	0.460390i	$-0.847709\pi$
$229$		−	13.9339i		−	0.920781i	0.887717	−	0.460390i	$-0.152291\pi$
$230$	−5.53769	−	3.43236i	−0.365145	−	0.226323i
$231$	−10.3805			−0.682984
$232$	−6.34828	+	6.34828i	−0.416785	+	0.416785i
$233$	3.59105	−	3.59105i	0.235258	−	0.235258i	−0.579625	−	0.814883i	$-0.696801\pi$
$233$	3.59105	−	3.59105i	0.235258	−	0.235258i	0.814883	+	0.579625i	$0.196801\pi$
$234$			3.42928i			0.224179i
$235$	28.0365	−	6.58037i	1.82890	−	0.429256i
$236$	−8.17158	+	8.17158i	−0.531925	+	0.531925i
$237$			6.50968i			0.422849i
$238$	1.42773	+	1.42773i	0.0925463	+	0.0925463i
$239$	−2.73603	+	2.73603i	−0.176979	+	0.176979i	−0.790037	−	0.613059i	$-0.789939\pi$
$239$	−2.73603	+	2.73603i	−0.176979	+	0.176979i	0.613059	+	0.790037i	$0.289939\pi$
$240$	−2.17691	+	0.510937i	−0.140519	+	0.0329808i
$241$	2.73812	+	2.73812i	0.176378	+	0.176378i	0.789775	−	0.613397i	$-0.210197\pi$
$241$	2.73812	+	2.73812i	0.176378	+	0.176378i	−0.613397	+	0.789775i	$0.710197\pi$
$242$		−	3.44478i		−	0.221439i
$243$	−0.707107	+	0.707107i	−0.0453609	+	0.0453609i
$244$	−3.52447	+	3.52447i	−0.225631	+	0.225631i
$245$	−8.55503	+	13.8025i	−0.546561	+	0.881810i
$246$	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	−0.418349	−	0.908286i	$-0.637391\pi$
$251$	7.76206	−	7.76206i	0.489937	−	0.489937i	0.908286	+	0.418349i	$0.137391\pi$
$252$	−2.67041	−	2.67041i	−0.168220	−	0.168220i
$253$	−8.00871			−0.503503
$254$	−4.97900	−	4.97900i	−0.312410	−	0.312410i
$255$	−1.16388	+	0.273172i	−0.0728853	+	0.0171067i
$256$	1.00000			0.0625000
$257$	−12.5524			−0.782998			−0.391499	−	0.920178i	$-0.628043\pi$
$257$	−12.5524			−0.782998			−0.391499	+	0.920178i	$0.628043\pi$
$258$	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	−0.237167	−	0.971469i	$-0.576219\pi$
$263$	11.9084	−	11.9084i	0.734302	−	0.734302i	0.971469	+	0.237167i	$0.0762188\pi$
$264$	−1.94361	+	1.94361i	−0.119621	+	0.119621i
$265$	−6.38210	−	27.1918i	−0.392049	−	1.67038i
$266$	5.87505			0.360223
$267$	14.1309			0.864795
$268$	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	$0.558401\pi$
$272$	0.534649			0.0324179
$273$	12.9508			0.783817
$274$	−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
$277$		−	9.15050i		−	0.549800i	−0.961473	−	0.274900i	$-0.911355\pi$
$277$		−	9.15050i		−	0.549800i	0.961473	−	0.274900i	$-0.0886448\pi$
$278$			1.56682i			0.0939716i
$279$	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	0.916876	−	0.399172i	$-0.130703\pi$
$281$	8.67829	+	8.67829i	0.517703	+	0.517703i	−0.399172	+	0.916876i	$0.630703\pi$
$282$	12.8790			0.766936
$283$	1.62977			0.0968799			0.0484400	−	0.998826i	$-0.484575\pi$
$283$	1.62977			0.0968799			0.0484400	+	0.998826i	$0.484575\pi$
$284$	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
$288$	−1.00000			−0.0589256
$289$	−16.7141			−0.983185
$290$	−19.5439	+	4.58710i	−1.14766	+	0.269364i
$291$	−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
$298$	9.53201			0.552175
$299$	9.99176			0.577838
$300$	−4.73932	−	1.59337i	−0.273625	−	0.0919930i
$301$	−5.21522	−	5.21522i	−0.300600	−	0.300600i
$302$	17.4581			1.00460
$303$	−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	0.723052	−	0.690793i	$-0.242739\pi$
$307$	0.565223	+	0.565223i	0.0322590	+	0.0322590i	−0.690793	+	0.723052i	$0.742739\pi$
$308$	7.34010	+	7.34010i	0.418241	+	0.418241i
$309$	−2.25320	+	2.25320i	−0.128180	+	0.128180i
$310$	−2.83697	−	12.0873i	−0.161129	−	0.686510i
$311$	−20.7503	+	20.7503i	−1.17664	+	1.17664i	−0.196045	+	0.980595i	$0.562810\pi$
$311$	−20.7503	+	20.7503i	−1.17664	+	1.17664i	−0.980595	+	0.196045i	$0.937190\pi$
$312$	2.42487	−	2.42487i	0.137281	−	0.137281i
$313$			10.7676i			0.608618i	0.952573	+	0.304309i	$0.0984256\pi$
$313$			10.7676i			0.608618i	−0.952573	+	0.304309i	$0.901574\pi$
$314$	−7.38980	−	7.38980i	−0.417031	−	0.417031i
$315$	−1.92957	−	8.22118i	−0.108719	−	0.463211i
$316$	4.60304	−	4.60304i	0.258941	−	0.258941i
$317$	0.491641	+	0.491641i	0.0276133	+	0.0276133i	0.720779	−	0.693165i	$-0.243784\pi$
$317$	0.491641	+	0.491641i	0.0276133	+	0.0276133i	−0.693165	+	0.720779i	$0.743784\pi$
$318$		−	12.4910i		−	0.700459i
$319$	−17.4494	+	17.4494i	−0.976977	+	0.976977i
$320$	1.90060	+	1.17802i	0.106247	+	0.0658534i
$321$			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
$325$	15.3559	−	7.62853i	0.851794	−	0.423155i
$326$		−	11.7022i		−	0.648124i
$327$			18.1260i			1.00237i
$328$	−9.62252			−0.531315
$329$		−	48.6381i		−	2.68151i
$330$	−5.98362	+	1.40440i	−0.329388	+	0.0773096i
$331$	−4.01488	−	4.01488i	−0.220678	−	0.220678i	0.588106	−	0.808784i	$-0.299874\pi$
$331$	−4.01488	−	4.01488i	−0.220678	−	0.220678i	−0.808784	+	0.588106i	$0.799874\pi$
$332$	10.9528	+	10.9528i	0.601113	+	0.601113i
$333$	−0.429296	−	6.06759i	−0.0235253	−	0.332502i
$334$			1.27852i			0.0699573i
$335$	3.88011	+	16.5317i	0.211993	+	0.903224i
$336$			3.77653i			0.206027i
$337$	6.16129	+	6.16129i	0.335627	+	0.335627i	0.854719	−	0.519092i	$-0.173730\pi$
$337$	6.16129	+	6.16129i	0.335627	+	0.335627i	−0.519092	+	0.854719i	$0.673730\pi$
$338$		−	1.24004i		−	0.0674493i
$339$	−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
$347$		−	3.72173i		−	0.199793i	−0.994998	−	0.0998964i	$-0.968149\pi$
$347$		−	3.72173i		−	0.199793i	0.994998	−	0.0998964i	$-0.0318511\pi$
$348$	−8.97783			−0.481262
$349$			8.05700i			0.431281i	0.976473	+	0.215641i	$0.0691840\pi$
$349$			8.05700i			0.431281i	−0.976473	+	0.215641i	$0.930816\pi$
$350$	−6.01740	+	17.8982i	−0.321643	+	0.956700i
$351$	−2.42487	+	2.42487i	−0.129430	+	0.129430i
$352$	2.74868			0.146505
$353$	18.4416			0.981549			0.490774	−	0.871287i	$-0.336714\pi$
$353$	18.4416			0.981549			0.490774	+	0.871287i	$0.336714\pi$
$354$	−11.5564			−0.614214
$355$	28.5781	+	17.7132i	1.51677	+	0.940118i
$356$	−9.99204	−	9.99204i	−0.529577	−	0.529577i
$357$			2.01912i			0.106863i
$358$	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
$362$			6.35842i			0.334191i
$363$	2.43583	−	2.43583i	0.127848	−	0.127848i
$364$	−9.15759	−	9.15759i	−0.479988	−	0.479988i
$365$	−22.4274	+	5.26387i	−1.17390	+	0.275524i
$366$	−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	$0.242076\pi$
$368$			2.91366i			0.151885i
$369$	9.62252			0.500929
$370$	−6.33184	+	12.0378i	−0.329177	+	0.625814i
$371$	−47.1726			−2.44908
$372$		−	5.55248i		−	0.287883i
$373$	14.1566	−	14.1566i	0.733002	−	0.733002i	−0.238212	−	0.971213i	$-0.576561\pi$
$373$	14.1566	−	14.1566i	0.733002	−	0.733002i	0.971213	+	0.238212i	$0.0765611\pi$
$374$	1.46958			0.0759901
$375$	−7.13052	−	8.61137i	−0.368218	−	0.444689i
$376$	−9.10685	−	9.10685i	−0.469650	−	0.469650i
$377$	21.7700	−	21.7700i	1.12121	−	1.12121i
$378$		−	3.77653i		−	0.194244i
$379$		−	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
$383$		−	9.32059i		−	0.476260i	−0.971233	−	0.238130i	$-0.923466\pi$
$383$		−	9.32059i		−	0.476260i	0.971233	−	0.238130i	$-0.0765344\pi$
$384$	0.707107	+	0.707107i	0.0360844	+	0.0360844i
$385$	5.30376	+	22.5973i	0.270305	+	1.15167i
$386$	−7.16959			−0.364922
$387$	1.95296			0.0992748
$388$	14.3863			0.730352
$389$	14.1117	−	14.1117i	0.715491	−	0.715491i	−0.252187	−	0.967678i	$-0.581150\pi$
$389$	14.1117	−	14.1117i	0.715491	−	0.715491i	0.967678	+	0.252187i	$0.0811500\pi$
$390$	7.46524	−	1.75215i	0.378017	−	0.0887233i
$391$			1.55779i			0.0787807i
$392$	7.26220			0.366796
$393$			4.79860i			0.242057i
$394$	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	0.245728	−	0.969339i	$-0.420973\pi$
$397$	−14.4178	−	14.4178i	−0.723611	−	0.723611i	−0.969339	+	0.245728i	$0.920973\pi$
$398$	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	−0.235724	−	0.971820i	$-0.575746\pi$
$401$	14.7403	−	14.7403i	0.736096	−	0.736096i	0.971820	+	0.235724i	$0.0757463\pi$
$402$			7.59412i			0.378760i
$403$	13.4640	+	13.4640i	0.670691	+	0.670691i
$404$			6.04894i			0.300946i
$405$	1.90060	+	1.17802i	0.0944414	+	0.0585364i
$406$			33.9051i			1.68268i
$407$	1.17999	+	16.6778i	0.0584901	+	0.826690i
$408$	0.378054	+	0.378054i	0.0187165	+	0.0187165i
$409$	−10.9943	−	10.9943i	−0.543634	−	0.543634i	0.380958	−	0.924592i	$-0.375594\pi$
$409$	−10.9943	−	10.9943i	−0.543634	−	0.543634i	−0.924592	+	0.380958i	$0.875594\pi$
$410$	−18.2885	−	11.3355i	−0.903206	−	0.559823i
$411$		−	10.9123i		−	0.538265i
$412$	3.18651			0.156988
$413$			43.6430i			2.14753i
$414$		−	2.91366i		−	0.143199i
$415$	7.91421	+	33.7195i	0.388493	+	1.65523i
$416$	−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	$0.878349\pi$
$420$	−4.44884	+	7.17766i	−0.217081	+	0.350234i
$421$	10.9789	−	10.9789i	0.535077	−	0.535077i	−0.387002	−	0.922079i	$-0.626489\pi$
$421$	10.9789	−	10.9789i	0.535077	−	0.535077i	0.922079	+	0.387002i	$0.126489\pi$
$422$		−	6.93916i		−	0.337793i
$423$	9.10685	+	9.10685i	0.442790	+	0.442790i
$424$	−8.83246	+	8.83246i	−0.428942	+	0.428942i
$425$	1.18934	+	2.39410i	0.0576916	+	0.116131i
$426$	10.6323	+	10.6323i	0.515138	+	0.515138i
$427$			18.8236i			0.910937i
$428$	14.0401	−	14.0401i	0.678654	−	0.678654i
$429$	6.66517	−	6.66517i	0.321798	−	0.321798i
$430$	−3.71180	−	2.30064i	−0.178999	−	0.110947i
$431$	−16.5186	+	16.5186i	−0.795675	+	0.795675i	−0.982410	−	0.186735i	$-0.940209\pi$
$431$	−16.5186	+	16.5186i	−0.795675	+	0.795675i	0.186735	+	0.982410i	$0.440209\pi$
$432$	−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
$438$	−10.3024			−0.492267
$439$	3.01200	+	3.01200i	0.143755	+	0.143755i	0.775322	−	0.631567i	$-0.217588\pi$
$439$	3.01200	+	3.01200i	0.143755	+	0.143755i	−0.631567	+	0.775322i	$0.717588\pi$
$440$	5.22412	+	3.23800i	0.249050	+	0.154366i
$441$	−7.26220			−0.345819
$442$	−1.83346			−0.0872089
$443$	10.7717	−	10.7717i	0.511777	−	0.511777i	−0.403294	−	0.915071i	$-0.632135\pi$
$443$	10.7717	−	10.7717i	0.511777	−	0.511777i	0.915071	+	0.403294i	$0.132135\pi$
$444$	−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	$-0.817771\pi$
$449$	−6.33208	+	6.33208i	−0.298829	+	0.298829i	0.541726	+	0.840555i	$0.317771\pi$
$450$	−2.22453	−	4.47789i	−0.104865	−	0.211090i
$451$	−26.4492			−1.24544
$452$	5.27748			0.248232
$453$	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
$457$	34.7548			1.62576			0.812882	−	0.582429i	$-0.197898\pi$
$457$	34.7548			1.62576			0.812882	+	0.582429i	$0.197898\pi$
$458$	−13.9339			−0.651090
$459$	−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	0.452295	−	0.891868i	$-0.350605\pi$
$461$	−9.43804	−	9.43804i	−0.439573	−	0.439573i	−0.891868	+	0.452295i	$0.850605\pi$
$462$			10.3805i			0.482943i
$463$		−	26.8196i		−	1.24641i	−0.782058	−	0.623206i	$-0.785830\pi$
$463$		−	26.8196i		−	1.24641i	0.782058	−	0.623206i	$-0.214170\pi$
$464$	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
$467$	30.6261			1.41721			0.708604	−	0.705606i	$-0.249325\pi$
$467$	30.6261			1.41721			0.708604	+	0.705606i	$0.249325\pi$
$468$	3.42928			0.158519
$469$	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
$473$	−5.36807			−0.246824
$474$	6.50968			0.298999
$475$	7.37284	+	2.47876i	0.338289	+	0.113733i
$476$	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	0.373058	−	0.927808i	$-0.378309\pi$
$479$	28.4708	−	28.4708i	1.30087	−	1.30087i	0.927808	−	0.373058i	$-0.121691\pi$
$480$	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
$483$	−11.0035			−0.500678
$484$	−3.44478			−0.156581
$485$	27.3425	+	16.9473i	1.24156	+	0.769539i
$486$	0.707107	+	0.707107i	0.0320750	+	0.0320750i
$487$	−25.3425			−1.14838			−0.574188	−	0.818723i	$-0.694682\pi$
$487$	−25.3425			−1.14838			−0.574188	+	0.818723i	$0.694682\pi$
$488$	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
$495$	−5.22412	−	3.23800i	−0.234807	−	0.145537i
$496$	−3.92620	+	3.92620i	−0.176291	+	0.176291i
$497$	40.1533	−	40.1533i	1.80112	−	1.80112i
$498$			15.4896i			0.694106i
$499$	−9.86951	−	9.86951i	−0.441820	−	0.441820i	0.450803	−	0.892623i	$-0.351138\pi$
$499$	−9.86951	−	9.86951i	−0.441820	−	0.441820i	−0.892623	+	0.450803i	$0.851138\pi$
$500$	−1.04712	+	11.1312i	−0.0468287	+	0.497802i
$501$	−0.904047	+	0.904047i	−0.0403898	+	0.0403898i
$502$	−7.76206	−	7.76206i	−0.346438	−	0.346438i
$503$		−	2.37206i		−	0.105765i	−0.998601	−	0.0528825i	$-0.983159\pi$
$503$		−	2.37206i		−	0.105765i	0.998601	−	0.0528825i	$-0.0168409\pi$
$504$	−2.67041	+	2.67041i	−0.118950	+	0.118950i
$505$	−7.12579	+	11.4966i	−0.317093	+	0.511592i
$506$			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	$-0.659415\pi$
$509$	−21.6650			−0.960285			−0.480142	+	0.877191i	$0.659415\pi$
$510$	0.273172	+	1.16388i	0.0120963	+	0.0515377i
$511$			38.9073i			1.72116i
$512$		−	1.00000i		−	0.0441942i
$513$	−1.55567			−0.0686847
$514$			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
$518$	17.3494	+	15.0566i	0.762288	+	0.661548i
$519$			12.5330i			0.550137i
$520$	−6.51767	−	4.03977i	−0.285819	−	0.177156i
$521$		−	36.2439i		−	1.58788i	−0.607999	−	0.793938i	$-0.708027\pi$
$521$		−	36.2439i		−	1.58788i	0.607999	−	0.793938i	$-0.291973\pi$
$522$	−6.34828	−	6.34828i	−0.277857	−	0.277857i
$523$			22.6025i			0.988339i	0.869366	+	0.494170i	$0.164528\pi$
$523$			22.6025i			0.988339i	−0.869366	+	0.494170i	$0.835472\pi$
$524$	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
$532$		−	5.87505i		−	0.254716i
$533$	32.9983			1.42932
$534$		−	14.1309i		−	0.611503i
$535$	43.2241	−	10.1450i	1.86874	−	0.438607i
$536$	5.36985	−	5.36985i	0.231942	−	0.231942i
$537$	8.17727			0.352875
$538$	29.2737			1.26208
$539$	19.9614			0.859800
$540$	−0.510937	−	2.17691i	−0.0219872	−	0.0936794i
$541$	15.3087	+	15.3087i	0.658172	+	0.658172i	0.954947	−	0.296775i	$-0.0959112\pi$
$541$	15.3087	+	15.3087i	0.658172	+	0.658172i	−0.296775	+	0.954947i	$0.595911\pi$
$542$			6.00684i			0.258016i
$543$	−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
$547$			20.4617i			0.874879i	0.899248	+	0.437439i	$0.144115\pi$
$547$			20.4617i			0.874879i	−0.899248	+	0.437439i	$0.855885\pi$
$548$	−7.71617	+	7.71617i	−0.329618	+	0.329618i
$549$	−3.52447	−	3.52447i	−0.150421	−	0.150421i
$550$	6.11451	+	12.3083i	0.260723	+	0.524826i
$551$	13.9666			0.594996
$552$	−2.06027	+	2.06027i	−0.0876909	+	0.0876909i
$553$		−	24.5840i		−	1.04542i
$554$	−9.15050			−0.388767
$555$	−12.9893	+	4.03470i	−0.551364	+	0.171263i
$556$	1.56682			0.0664480
$557$			22.9203i			0.971162i	0.874192	+	0.485581i	$0.161392\pi$
$557$			22.9203i			0.971162i	−0.874192	+	0.485581i	$0.838608\pi$
$558$	3.92620	−	3.92620i	0.166209	−	0.166209i
$559$	6.69726			0.283264
$560$	8.22118	−	1.92957i	0.347408	−	0.0815392i
$561$	1.03915	+	1.03915i	0.0438729	+	0.0438729i
$562$	8.67829	−	8.67829i	0.366072	−	0.366072i
$563$		−	7.83533i		−	0.330220i	−0.986275	−	0.165110i	$-0.947202\pi$
$563$		−	7.83533i		−	0.330220i	0.986275	−	0.165110i	$-0.0527979\pi$
$564$		−	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
$568$		−	15.0364i		−	0.630913i
$569$	17.1922	+	17.1922i	0.720735	+	0.720735i	0.968755	−	0.248020i	$-0.0797798\pi$
$569$	17.1922	+	17.1922i	0.720735	+	0.720735i	−0.248020	+	0.968755i	$0.579780\pi$
$570$	2.95671	+	1.83262i	0.123843	+	0.0767599i
$571$	−7.23109			−0.302612			−0.151306	−	0.988487i	$-0.548348\pi$
$571$	−7.23109			−0.302612			−0.151306	+	0.988487i	$0.548348\pi$
$572$	−9.42598			−0.394120
$573$	17.3135			0.723281
$574$	−25.6961	+	25.6961i	−1.07253	+	1.07253i
$575$	−13.0470	+	6.48152i	−0.544100	+	0.270298i
$576$			1.00000i			0.0416667i
$577$	−12.3162			−0.512731			−0.256366	−	0.966580i	$-0.582525\pi$
$577$	−12.3162			−0.512731			−0.256366	+	0.966580i	$0.582525\pi$
$578$			16.7141i			0.695217i
$579$	−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
$587$		−	20.5928i		−	0.849956i	−0.905204	−	0.424978i	$-0.860282\pi$
$587$		−	20.5928i		−	0.849956i	0.905204	−	0.424978i	$-0.139718\pi$
$588$	5.13515	+	5.13515i	0.211770	+	0.211770i
$589$			8.63785i			0.355916i
$590$	5.90457	+	25.1572i	0.243087	+	1.03570i
$591$			17.6768i			0.727128i
$592$	6.06759	−	0.429296i	0.249377	−	0.0176439i
$593$	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
$597$	13.4829			0.551818
$598$		−	9.99176i		−	0.408594i
$599$			25.2096i			1.03003i	0.857180	+	0.515017i	$0.172214\pi$
$599$			25.2096i			1.03003i	−0.857180	+	0.515017i	$0.827786\pi$
$600$	−1.59337	+	4.73932i	−0.0650489	+	0.193482i
$601$	−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
$605$	−6.54714	−	4.05803i	−0.266179	−	0.164982i
$606$	−4.27725	+	4.27725i	−0.173751	+	0.173751i
$607$		−	13.8699i		−	0.562963i	−0.959567	−	0.281482i	$-0.909174\pi$
$607$		−	13.8699i		−	0.562963i	0.959567	−	0.281482i	$-0.0908258\pi$
$608$	−1.10003	−	1.10003i	−0.0446120	−	0.0446120i
$609$	−23.9745	+	23.9745i	−0.971495	+	0.971495i
$610$	2.54669	+	10.8505i	0.103112	+	0.439324i
$611$	31.2300	+	31.2300i	1.26343	+	1.26343i
$612$			0.534649i			0.0216119i
$613$	16.6052	−	16.6052i	0.670679	−	0.670679i	−0.287193	−	0.957873i	$-0.592722\pi$
$613$	16.6052	−	16.6052i	0.670679	−	0.670679i	0.957873	+	0.287193i	$0.0927222\pi$
$614$	0.565223	−	0.565223i	0.0228106	−	0.0228106i
$615$	−4.91650	−	20.9474i	−0.198252	−	0.844680i
$616$	7.34010	−	7.34010i	0.295741	−	0.295741i
$617$	−17.4344	−	17.4344i	−0.701884	−	0.701884i	0.262931	−	0.964815i	$-0.415311\pi$
$617$	−17.4344	−	17.4344i	−0.701884	−	0.701884i	−0.964815	+	0.262931i	$0.915311\pi$
$618$	2.25320	+	2.25320i	0.0906370	+	0.0906370i
$619$	−4.16120			−0.167253			−0.0836263	−	0.996497i	$-0.526650\pi$
$619$	−4.16120			−0.167253			−0.0836263	+	0.996497i	$0.526650\pi$
$620$	−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
$623$	−53.3657			−2.13805
$624$	−2.42487	−	2.42487i	−0.0970724	−	0.0970724i
$625$	−15.1029	+	19.9224i	−0.604118	+	0.796895i
$626$	10.7676			0.430358
$627$	4.27604			0.170769
$628$	−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	−0.999750	−	0.0223684i	$-0.992879\pi$
$631$	−24.5515	+	24.5515i	−0.977381	+	0.977381i	0.0223684	+	0.999750i	$0.492879\pi$
$632$	−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
$635$	−15.3284	+	3.59769i	−0.608290	+	0.142770i
$636$	−12.4910			−0.495300
$637$	−24.9041			−0.986737
$638$	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	$0.341558\pi$
$642$	19.8557			0.783642
$643$	34.5674			1.36320			0.681602	−	0.731723i	$-0.261283\pi$
$643$	34.5674			1.36320			0.681602	+	0.731723i	$0.261283\pi$
$644$	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
$647$		−	8.23154i		−	0.323615i	−0.986822	−	0.161808i	$-0.948268\pi$
$647$		−	8.23154i		−	0.323615i	0.986822	−	0.161808i	$-0.0517324\pi$
$648$		−	1.00000i		−	0.0392837i
$649$	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
$652$	−11.7022			−0.458293
$653$	−37.1465			−1.45366			−0.726828	−	0.686820i	$-0.759006\pi$
$653$	−37.1465			−1.45366			−0.726828	+	0.686820i	$0.759006\pi$
$654$	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
$658$	−48.6381			−1.89611
$659$	32.8070			1.27798			0.638990	−	0.769215i	$-0.279353\pi$
$659$	32.8070			1.27798			0.638990	+	0.769215i	$0.279353\pi$
$660$	1.40440	+	5.98362i	0.0546662	+	0.232912i
$661$	−5.94634	+	5.94634i	−0.231286	+	0.231286i	−0.813229	−	0.581943i	$-0.802292\pi$
$661$	−5.94634	+	5.94634i	−0.231286	+	0.231286i	0.581943	+	0.813229i	$0.302292\pi$
$662$	−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
$668$	1.27852			0.0494673
$669$	1.02047			0.0394536
$670$	16.5317	−	3.88011i	0.638676	−	0.149902i
$671$	9.68762	+	9.68762i	0.373987	+	0.373987i
$672$	3.77653			0.145683
$673$	−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	$0.0165019\pi$
$677$	27.3326	+	27.3326i	1.05048	+	1.05048i	0.0518189	+	0.998656i	$0.483498\pi$
$678$	3.73174	+	3.73174i	0.143317	+	0.143317i
$679$	38.4172	−	38.4172i	1.47432	−	1.47432i
$680$	0.629829	−	1.01615i	0.0241528	−	0.0389677i
$681$	−0.845033	+	0.845033i	−0.0323817	+	0.0323817i
$682$	−10.7918	+	10.7918i	−0.413241	+	0.413241i
$683$			29.9135i			1.14461i	0.820041	+	0.572304i	$0.193950\pi$
$683$			29.9135i			1.14461i	−0.820041	+	0.572304i	$0.806050\pi$
$684$	1.10003	+	1.10003i	0.0420606	+	0.0420606i
$685$	−23.7551	+	5.57550i	−0.907637	+	0.213029i
$686$	0.700181	−	0.700181i	0.0267330	−	0.0267330i
$687$	−9.85278	−	9.85278i	−0.375907	−	0.375907i
$688$			1.95296i			0.0744561i
$689$	30.2890	−	30.2890i	1.15392	−	1.15392i
$690$	−6.34278	+	1.48870i	−0.241466	+	0.0566737i
$691$			12.3285i			0.468998i	0.972116	+	0.234499i	$0.0753450\pi$
$691$			12.3285i			0.468998i	−0.972116	+	0.234499i	$0.924655\pi$
$692$	8.86215	−	8.86215i	0.336889	−	0.336889i
$693$	−7.34010	+	7.34010i	−0.278827	+	0.278827i
$694$	−3.72173			−0.141275
$695$	2.97789	+	1.84575i	0.112958	+	0.0700132i
$696$			8.97783i			0.340304i
$697$			5.14468i			0.194869i
$698$	8.05700			0.304962
$699$		−	5.07851i		−	0.192087i
$700$	17.8982	+	6.01740i	0.676489	+	0.227436i
$701$	−12.1525	−	12.1525i	−0.458994	−	0.458994i	0.439331	−	0.898325i	$-0.355215\pi$
$701$	−12.1525	−	12.1525i	−0.458994	−	0.458994i	−0.898325	+	0.439331i	$0.855215\pi$
$702$	2.42487	+	2.42487i	0.0915207	+	0.0915207i
$703$	6.20228	−	7.14676i	0.233924	−	0.269545i
$704$		−	2.74868i		−	0.103595i
$705$	15.1718	−	24.4778i	0.571403	−	0.921889i
$706$		−	18.4416i		−	0.694060i
$707$	16.1532	+	16.1532i	0.607503	+	0.607503i
$708$			11.5564i			0.434315i
$709$	−12.7149	+	12.7149i	−0.477517	+	0.477517i	−0.904337	−	0.426820i	$-0.859634\pi$
$709$	−12.7149	+	12.7149i	−0.477517	+	0.477517i	0.426820	+	0.904337i	$0.359634\pi$
$710$	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
$717$			3.86933i			0.144503i
$718$	−18.1393			−0.676954
$719$			6.10088i			0.227524i	0.993508	+	0.113762i	$0.0362902\pi$
$719$			6.10088i			0.227524i	−0.993508	+	0.113762i	$0.963710\pi$
$720$	−1.17802	+	1.90060i	−0.0439023	+	0.0708310i
$721$	8.50928	−	8.50928i	0.316902	−	0.316902i
$722$	16.5799			0.617039
$723$	3.87229			0.144012
$724$	6.35842			0.236309
$725$	−14.3050	+	42.5488i	−0.531273	+	1.58022i
$726$	−2.43583	−	2.43583i	−0.0904021	−	0.0904021i
$727$		−	33.5779i		−	1.24534i	−0.782486	−	0.622668i	$-0.786049\pi$
$727$		−	33.5779i		−	1.24534i	0.782486	−	0.622668i	$-0.213951\pi$
$728$	−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
$732$			4.98435i			0.184227i
$733$	−26.0037	+	26.0037i	−0.960467	+	0.960467i	−0.999248	−	0.0387805i	$-0.987653\pi$
$733$	−26.0037	+	26.0037i	−0.960467	+	0.960467i	0.0387805	+	0.999248i	$0.487653\pi$
$734$	−0.674373	−	0.674373i	−0.0248916	−	0.0248916i
$735$	3.71052	+	15.8092i	0.136865	+	0.583130i
$736$	2.91366			0.107399
$737$	14.7600	−	14.7600i	0.543691	−	0.543691i
$738$		−	9.62252i		−	0.354210i
$739$	37.1311			1.36589			0.682945	−	0.730470i	$-0.260699\pi$
$739$	37.1311			1.36589			0.682945	+	0.730470i	$0.260699\pi$
$740$	12.0378	+	6.33184i	0.442517	+	0.232763i
$741$	−5.33484			−0.195980
$742$			47.1726i			1.73176i
$743$	−1.00487	+	1.00487i	−0.0368651	+	0.0368651i	−0.725299	−	0.688434i	$-0.758299\pi$
$743$	−1.00487	+	1.00487i	−0.0368651	+	0.0368651i	0.688434	+	0.725299i	$0.258299\pi$
$744$	−5.55248			−0.203564
$745$	11.2289	−	18.1165i	0.411396	−	0.663737i
$746$	−14.1566	−	14.1566i	−0.518311	−	0.518311i
$747$	−10.9528	+	10.9528i	−0.400742	+	0.400742i
$748$		−	1.46958i		−	0.0537331i
$749$		−	74.9857i		−	2.73992i
$750$	−8.61137	+	7.13052i	−0.314443	+	0.260370i
$751$		−	14.6004i		−	0.532777i	−0.963866	−	0.266388i	$-0.914170\pi$
$751$		−	14.6004i		−	0.532777i	0.963866	−	0.266388i	$-0.0858304\pi$
$752$	−9.10685	+	9.10685i	−0.332093	+	0.332093i
$753$		−	10.9772i		−	0.400032i
$754$	−21.7700	−	21.7700i	−0.792818	−	0.792818i
$755$	20.5660	−	33.1807i	0.748473	−	1.20757i
$756$	−3.77653			−0.137351
$757$	−23.5268			−0.855096			−0.427548	−	0.903993i	$-0.640622\pi$
$757$	−23.5268			−0.855096			−0.427548	+	0.903993i	$0.640622\pi$
$758$	−30.7418			−1.11659
$759$	−5.66301	+	5.66301i	−0.205554	+	0.205554i
$760$	−0.794851	−	3.38656i	−0.0288323	−	0.122844i
$761$			36.6320i			1.32791i	0.747773	+	0.663954i	$0.231123\pi$
$761$			36.6320i			1.32791i	−0.747773	+	0.663954i	$0.768877\pi$
$762$	−7.04136			−0.255082
$763$		−	68.4533i		−	2.47817i
$764$	−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	−0.996987	−	0.0775648i	$-0.975286\pi$
$769$	−29.7982	−	29.7982i	−1.07455	−	1.07455i	−0.0775648	−	0.996987i	$-0.524714\pi$
$770$	22.5973	−	5.30376i	0.814352	−	0.191134i
$771$	−8.87590	+	8.87590i	−0.319658	+	0.319658i
$772$			7.16959i			0.258039i
$773$	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
$775$	−26.3150	−	8.84713i	−0.945263	−	0.317798i
$776$		−	14.3863i		−	0.516437i
$777$	1.62125	+	22.9145i	0.0581620	+	0.822052i
$778$	−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
$782$	1.55779			0.0557064
$783$		−	8.97783i		−	0.320841i
$784$		−	7.26220i		−	0.259364i
$785$	−22.7504	+	5.33968i	−0.811996	+	0.190581i
$786$	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
$790$	−3.32603	−	14.1710i	−0.118335	−	0.504181i
$791$	14.0930	−	14.0930i	0.501091	−	0.501091i
$792$			2.74868i			0.0976699i
$793$	−12.0864	−	12.0864i	−0.429200	−	0.429200i
$794$	−14.4178	+	14.4178i	−0.511670	+	0.511670i
$795$	−23.7403	−	14.7146i	−0.841982	−	0.521875i
$796$	−9.53384	−	9.53384i	−0.337918	−	0.337918i
$797$		−	4.21520i		−	0.149310i	−0.997209	−	0.0746551i	$-0.976214\pi$
$797$		−	4.21520i		−	0.149310i	0.997209	−	0.0746551i	$-0.0237856\pi$
$798$	4.15429	−	4.15429i	0.147060	−	0.147060i
$799$	−4.86897	+	4.86897i	−0.172252	+	0.172252i
$800$	4.47789	−	2.22453i	0.158317	−	0.0786489i
$801$	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
$808$	6.04894			0.212801
$809$	−25.7274	−	25.7274i	−0.904528	−	0.904528i	0.0912957	−	0.995824i	$-0.470899\pi$
$809$	−25.7274	−	25.7274i	−0.904528	−	0.904528i	−0.995824	+	0.0912957i	$0.970899\pi$
$810$	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	$0.169702\pi$
$812$	33.9051			1.18983
$813$	−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
$820$	−11.3355	+	18.2885i	−0.395854	+	0.638663i
$821$	2.90960			0.101546			0.0507728	−	0.998710i	$-0.483832\pi$
$821$	2.90960			0.101546			0.0507728	+	0.998710i	$0.483832\pi$
$822$	−10.9123			−0.380611
$823$	−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
$827$	−49.2078			−1.71112			−0.855561	−	0.517703i	$-0.826787\pi$
$827$	−49.2078			−1.71112			−0.855561	+	0.517703i	$0.826787\pi$
$828$	−2.91366			−0.101257
$829$	10.5621	+	10.5621i	0.366838	+	0.366838i	0.866323	−	0.499485i	$-0.166477\pi$
$829$	10.5621	+	10.5621i	0.366838	+	0.366838i	−0.499485	+	0.866323i	$0.666477\pi$
$830$	33.7195	−	7.91421i	1.17042	−	0.274706i
$831$	−6.47038	−	6.47038i	−0.224455	−	0.224455i
$832$			3.42928i			0.118889i
$833$		−	3.88273i		−	0.134529i
$834$	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
$837$	5.55248			0.191922
$838$	15.2679			0.527421
$839$	6.68559			0.230812			0.115406	−	0.993318i	$-0.463183\pi$
$839$	6.68559			0.230812			0.115406	+	0.993318i	$0.463183\pi$
$840$	7.17766	+	4.44884i	0.247653	+	0.153500i
$841$			51.6013i			1.77936i
$842$	−10.9789	−	10.9789i	−0.378357	−	0.378357i
$843$	12.2730			0.422703
$844$	−6.93916			−0.238856
$845$	−2.35681	−	1.46079i	−0.0810769	−	0.0502528i
$846$	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
$853$	24.9425			0.854016			0.427008	−	0.904248i	$-0.359568\pi$
$853$	24.9425			0.854016			0.427008	+	0.904248i	$0.359568\pi$
$854$	18.8236			0.644129
$855$	0.794851	+	3.38656i	0.0271833	+	0.115818i
$856$	−14.0401	−	14.0401i	−0.479881	−	0.479881i
$857$	23.2261			0.793387			0.396694	−	0.917951i	$-0.370157\pi$
$857$	23.2261			0.793387			0.396694	+	0.917951i	$0.370157\pi$
$858$	−6.66517	−	6.66517i	−0.227545	−	0.227545i
$859$	−38.4729	+	38.4729i	−1.31268	+	1.31268i	−0.393244	+	0.919434i	$0.628647\pi$
$859$	−38.4729	+	38.4729i	−1.31268	+	1.31268i	−0.919434	+	0.393244i	$0.871353\pi$
$860$	−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
$865$	27.2832	−	6.40356i	0.927656	−	0.217728i
$866$	−16.8050	+	16.8050i	−0.571058	+	0.571058i
$867$	−11.8187	+	11.8187i	−0.401384	+	0.401384i
$868$			20.9691i			0.711739i
$869$	−12.6523	−	12.6523i	−0.429198	−	0.429198i
$870$	−10.5761	+	17.0632i	−0.358563	+	0.578497i
$871$	−18.4147	+	18.4147i	−0.623959	+	0.623959i
$872$	−12.8170	−	12.8170i	−0.434038	−	0.434038i
$873$			14.3863i			0.486901i
$874$	3.20511	−	3.20511i	0.108414	−	0.108414i
$875$	26.9286	+	32.5211i	0.910354	+	1.09941i
$876$			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
$880$	3.23800	−	5.22412i	0.109153	−	0.176105i
$881$		−	19.4242i		−	0.654419i	−0.944952	−	0.327209i	$-0.893892\pi$
$881$		−	19.4242i		−	0.654419i	0.944952	−	0.327209i	$-0.106108\pi$
$882$			7.26220i			0.244531i
$883$	−51.0527			−1.71806			−0.859029	−	0.511926i	$-0.828932\pi$
$883$	−51.0527			−1.71806			−0.859029	+	0.511926i	$0.828932\pi$
$884$			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	0.809871	−	0.586608i	$-0.199537\pi$
$887$	6.64936	+	6.64936i	0.223264	+	0.223264i	−0.586608	+	0.809871i	$0.699537\pi$
$888$	4.59400	+	3.98688i	0.154164	+	0.133791i
$889$			26.5919i			0.891865i
$890$	−30.7617	+	7.21998i	−1.03113	+	0.242014i
$891$		−	2.74868i		−	0.0920841i
$892$	−0.721579	−	0.721579i	−0.0241603	−	0.0241603i
$893$			20.0356i			0.670465i
$894$	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
$902$			26.4492i			0.880662i
$903$	−7.37544			−0.245439
$904$		−	5.27748i		−	0.175526i
$905$	12.0848	+	7.49036i	0.401712	+	0.248988i
$906$	12.3447	−	12.3447i	0.410126	−	0.410126i
$907$	−22.6816			−0.753129			−0.376565	−	0.926390i	$-0.622895\pi$
$907$	−22.6816			−0.753129			−0.376565	+	0.926390i	$0.622895\pi$
$908$	1.19506			0.0396594
$909$	−6.04894			−0.200631
$910$	−28.1927	+	6.61703i	−0.934580	+	0.219353i
$911$	23.5154	+	23.5154i	0.779099	+	0.779099i	0.979678	−	0.200578i	$-0.0642821\pi$
$911$	23.5154	+	23.5154i	0.779099	+	0.779099i	−0.200578	+	0.979678i	$0.564282\pi$
$912$		−	1.55567i		−	0.0515135i
$913$	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
$917$		−	18.1221i		−	0.598443i
$918$	−0.378054	+	0.378054i	−0.0124776	+	0.0124776i
$919$	13.6406	+	13.6406i	0.449963	+	0.449963i	0.895342	−	0.445379i	$-0.146931\pi$
$919$	13.6406	+	13.6406i	0.449963	+	0.449963i	−0.445379	+	0.895342i	$0.646931\pi$
$920$	5.53769	+	3.43236i	0.182572	+	0.113161i
$921$	0.799346			0.0263394
$922$	−9.43804	+	9.43804i	−0.310825	+	0.310825i
$923$			51.5640i			1.69725i
$924$	10.3805			0.341492
$925$	15.4199	+	26.2150i	0.507002	+	0.861945i
$926$	−26.8196			−0.881346
$927$			3.18651i			0.104659i
$928$	6.34828	−	6.34828i	0.208393	−	0.208393i
$929$	17.2093			0.564617			0.282309	−	0.959324i	$-0.408900\pi$
$929$	17.2093			0.564617			0.282309	+	0.959324i	$0.408900\pi$
$930$	−10.5530	−	6.54095i	−0.346047	−	0.214486i
$931$	−7.98862	−	7.98862i	−0.261816	−	0.261816i
$932$	−3.59105	+	3.59105i	−0.117629	+	0.117629i
$933$			29.3453i			0.960723i
$934$		−	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	$0.0283362\pi$
$938$		−	28.6794i		−	0.936417i
$939$	7.61381	+	7.61381i	0.248467	+	0.248467i
$940$	−28.0365	+	6.58037i	−0.914451	+	0.214628i
$941$	−30.3798			−0.990352			−0.495176	−	0.868793i	$-0.664896\pi$
$941$	−30.3798			−0.990352			−0.495176	+	0.868793i	$0.664896\pi$
$942$	−10.4508			−0.340504
$943$	−28.0368			−0.913003
$944$	8.17158	−	8.17158i	0.265962	−	0.265962i
$945$	−7.17766	−	4.44884i	−0.233489	−	0.144721i
$946$			5.36807i			0.174531i
$947$	−40.0733			−1.30221			−0.651103	−	0.758989i	$-0.725694\pi$
$947$	−40.0733			−1.30221			−0.651103	+	0.758989i	$0.725694\pi$
$948$		−	6.50968i		−	0.211425i
$949$	−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	−0.988407	−	0.151829i	$-0.951484\pi$
$953$	−25.8258	+	25.8258i	−0.836578	+	0.836578i	0.151829	+	0.988407i	$0.451484\pi$
$954$	−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
$957$			24.6771i			0.797698i
$958$	−28.4708	−	28.4708i	−0.919851	−	0.919851i
$959$			41.2107i			1.33076i
$960$	2.17691	−	0.510937i	0.0702595	−	0.0164904i
$961$			0.169953i			0.00548236i
$962$	−20.8075	+	1.47217i	−0.670860	+	0.0474648i
$963$	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
$967$	43.2675			1.39139			0.695694	−	0.718338i	$-0.255097\pi$
$967$	43.2675			1.39139			0.695694	+	0.718338i	$0.255097\pi$
$968$			3.44478i			0.110720i
$969$		−	0.831740i		−	0.0267193i
$970$	16.9473	−	27.3425i	0.544146	−	0.877914i
$971$	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
$975$	5.46410	−	16.2525i	0.174991	−	0.520495i
$976$	3.52447	−	3.52447i	0.112816	−	0.112816i
$977$			51.7752i			1.65644i	0.560406	+	0.828218i	$0.310645\pi$
$977$			51.7752i			1.65644i	−0.560406	+	0.828218i	$0.689355\pi$
$978$	−8.27469	−	8.27469i	−0.264595	−	0.264595i
$979$	−27.4649	+	27.4649i	−0.877781	+	0.877781i
$980$	8.55503	−	13.8025i	0.273280	−	0.440905i
$981$	12.8170	+	12.8170i	0.409215	+	0.409215i
$982$		−	23.3602i		−	0.745452i
$983$	−8.76162	+	8.76162i	−0.279452	+	0.279452i	−0.832890	−	0.553438i	$-0.813316\pi$
$983$	−8.76162	+	8.76162i	−0.279452	+	0.279452i	0.553438	+	0.832890i	$0.313316\pi$
$984$	−6.80415	+	6.80415i	−0.216908	+	0.216908i
$985$	38.4809	−	9.03175i	1.22610	−	0.287775i
$986$	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	−0.255679	−	0.966762i	$-0.582299\pi$
$991$	22.3850	−	22.3850i	0.711083	−	0.711083i	0.966762	+	0.255679i	$0.0822989\pi$
$992$	3.92620	+	3.92620i	0.124657	+	0.124657i
$993$	−5.67790			−0.180183
$994$	−40.1533	−	40.1533i	−1.27359	−	1.27359i
$995$	−6.88890	−	29.3510i	−0.218393	−	0.930491i
$996$	15.4896			0.490807
$997$	−17.3884			−0.550697			−0.275349	−	0.961344i	$-0.588793\pi$
$997$	−17.3884			−0.550697			−0.275349	+	0.961344i	$0.588793\pi$
$998$	−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.l.b.43.19	✓	40
5.2	odd	4		1110.2.o.b.487.2	yes	40
37.31	odd	4		1110.2.o.b.253.2	yes	40
185.142	even	4	inner	1110.2.l.b.697.19	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1110.2.l.b.43.19	✓	40	1.1	even	1	trivial
1110.2.l.b.697.19	yes	40	185.142	even	4	inner
1110.2.o.b.253.2	yes	40	37.31	odd	4
1110.2.o.b.487.2	yes	40	5.2	odd	4

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

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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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