LMFDB - Embedded newform 520.2.ca.a.101.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [520,2,Mod(101,520)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(520, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 0, 5]))

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

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

chi := DirichletCharacter("520.101");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 520 = 2^{3} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	520.ca (of order $6$, 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:	$4.15222090511$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$28$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			101.13
Character	$\chi$	$=$	520.101
Dual form			520.2.ca.a.381.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.137476 + 1.40752i) q^{2} +(-1.00895 + 0.582519i) q^{3} +(-1.96220 - 0.386999i) q^{4} -1.00000 q^{5} +(-0.681198 - 1.50020i) q^{6} +(0.786953 + 0.454347i) q^{7} +(0.814463 - 2.70863i) q^{8} +(-0.821344 + 1.42261i) q^{9} +(0.137476 - 1.40752i) q^{10} +(-2.01803 - 3.49532i) q^{11} +(2.20520 - 0.752555i) q^{12} +(-1.21154 - 3.39590i) q^{13} +(-0.747688 + 1.04519i) q^{14} +(1.00895 - 0.582519i) q^{15} +(3.70046 + 1.51874i) q^{16} +(1.41984 - 2.45923i) q^{17} +(-1.88943 - 1.35163i) q^{18} +(-0.810340 + 1.40355i) q^{19} +(1.96220 + 0.386999i) q^{20} -1.05866 q^{21} +(5.19715 - 2.35988i) q^{22} +(-0.494250 - 0.856067i) q^{23} +(0.756071 + 3.20731i) q^{24} +1.00000 q^{25} +(4.94635 - 1.23841i) q^{26} -5.40891i q^{27} +(-1.36833 - 1.19607i) q^{28} +(7.87290 - 4.54542i) q^{29} +(0.681198 + 1.50020i) q^{30} +3.84896i q^{31} +(-2.64637 + 4.99967i) q^{32} +(4.07218 + 2.35108i) q^{33} +(3.26621 + 2.33653i) q^{34} +(-0.786953 - 0.454347i) q^{35} +(2.16219 - 2.47359i) q^{36} +(0.538020 + 0.931878i) q^{37} +(-1.86412 - 1.33352i) q^{38} +(3.20056 + 2.72056i) q^{39} +(-0.814463 + 2.70863i) q^{40} +(7.68661 - 4.43786i) q^{41} +(0.145541 - 1.49009i) q^{42} +(-9.23470 - 5.33166i) q^{43} +(2.60708 + 7.63950i) q^{44} +(0.821344 - 1.42261i) q^{45} +(1.27288 - 0.577977i) q^{46} -11.5567i q^{47} +(-4.61828 + 0.623254i) q^{48} +(-3.08714 - 5.34708i) q^{49} +(-0.137476 + 1.40752i) q^{50} +3.30832i q^{51} +(1.06307 + 7.13231i) q^{52} +10.1285i q^{53} +(7.61312 + 0.743594i) q^{54} +(2.01803 + 3.49532i) q^{55} +(1.87160 - 1.76151i) q^{56} -1.88815i q^{57} +(5.31542 + 11.7061i) q^{58} +(-4.67358 + 8.09488i) q^{59} +(-2.20520 + 0.752555i) q^{60} +(-0.159169 - 0.0918962i) q^{61} +(-5.41748 - 0.529140i) q^{62} +(-1.29272 + 0.746351i) q^{63} +(-6.67330 - 4.41215i) q^{64} +(1.21154 + 3.39590i) q^{65} +(-3.86900 + 5.40844i) q^{66} +(-5.74510 - 9.95080i) q^{67} +(-3.73772 + 4.27602i) q^{68} +(0.997350 + 0.575820i) q^{69} +(0.747688 - 1.04519i) q^{70} +(4.27599 + 2.46874i) q^{71} +(3.18436 + 3.38337i) q^{72} -5.44599i q^{73} +(-1.38560 + 0.629161i) q^{74} +(-1.00895 + 0.582519i) q^{75} +(2.13322 - 2.44045i) q^{76} -3.66754i q^{77} +(-4.26923 + 4.13083i) q^{78} -14.8307 q^{79} +(-3.70046 - 1.51874i) q^{80} +(0.686757 + 1.18950i) q^{81} +(5.18964 + 11.4291i) q^{82} -14.8263 q^{83} +(2.07731 + 0.409702i) q^{84} +(-1.41984 + 2.45923i) q^{85} +(8.77394 - 12.2650i) q^{86} +(-5.29559 + 9.17223i) q^{87} +(-11.1111 + 2.61926i) q^{88} +(-2.39372 + 1.38202i) q^{89} +(1.88943 + 1.35163i) q^{90} +(0.589495 - 3.22288i) q^{91} +(0.638521 + 1.87105i) q^{92} +(-2.24209 - 3.88342i) q^{93} +(16.2662 + 1.58876i) q^{94} +(0.810340 - 1.40355i) q^{95} +(-0.242336 - 6.58599i) q^{96} +(-9.80772 - 5.66249i) q^{97} +(7.95050 - 3.61010i) q^{98} +6.62997 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 6 q^{4} - 56 q^{5} - 5 q^{6} + 28 q^{9} + 8 q^{11} + 6 q^{12} - 4 q^{14} - 10 q^{16} - 18 q^{18} + 16 q^{19} + 6 q^{20} - 6 q^{22} + 12 q^{23} + 2 q^{24} + 56 q^{25} + 11 q^{26} + 6 q^{28} + 5 q^{30}+ \cdots + 48 q^{99}+O(q^{100}) $ 56 * q - 6 * q^4 - 56 * q^5 - 5 * q^6 + 28 * q^9 + 8 * q^11 + 6 * q^12 - 4 * q^14 - 10 * q^16 - 18 * q^18 + 16 * q^19 + 6 * q^20 - 6 * q^22 + 12 * q^23 + 2 * q^24 + 56 * q^25 + 11 * q^26 + 6 * q^28 + 5 * q^30 + 16 * q^34 - 21 * q^36 - 4 * q^37 - 24 * q^39 + 29 * q^42 - 24 * q^44 - 28 * q^45 - 11 * q^46 + 3 * q^48 + 20 * q^49 + 18 * q^52 - 49 * q^54 - 8 * q^55 + 61 * q^56 - 47 * q^58 + 16 * q^59 - 6 * q^60 - 2 * q^62 - 30 * q^64 + 14 * q^66 + 36 * q^67 + 33 * q^68 + 4 * q^70 - 51 * q^72 - 2 * q^74 - 48 * q^76 - 35 * q^78 + 10 * q^80 - 28 * q^81 - 21 * q^82 - 40 * q^83 - 61 * q^84 + 28 * q^86 - 36 * q^87 + 41 * q^88 + 18 * q^90 - 16 * q^91 - 18 * q^92 - 41 * q^94 - 16 * q^95 + 48 * q^96 + 24 * q^97 + 28 * q^98 + 48 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/520\mathbb{Z}\right)^\times$.

$n$	$41$	$261$	$391$	$417$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$	$1$	$1$

Coefficient data

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

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

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

$2$	−0.137476	+	1.40752i	−0.0972102	+	0.995264i
$2$	−0.137476	+	1.40752i	−0.0972102	+	0.995264i
$3$	−1.00895	+	0.582519i	−0.582519	+	0.336317i	−0.762134	−	0.647420i	$-0.775848\pi$
$3$	−1.00895	+	0.582519i	−0.582519	+	0.336317i	0.179615	+	0.983737i	$0.442515\pi$
$4$	−1.96220	−	0.386999i	−0.981100	−	0.193500i
$5$	−1.00000			−0.447214
$5$	−1.00000			−0.447214
$6$	−0.681198	−	1.50020i	−0.278098	−	0.612453i
$7$	0.786953	+	0.454347i	0.297440	+	0.171727i	0.641292	−	0.767297i	$-0.278399\pi$
$7$	0.786953	+	0.454347i	0.297440	+	0.171727i	−0.343852	+	0.939024i	$0.611732\pi$
$8$	0.814463	−	2.70863i	0.287956	−	0.957644i
$9$	−0.821344	+	1.42261i	−0.273781	+	0.474203i
$10$	0.137476	−	1.40752i	0.0434737	−	0.445096i
$11$	−2.01803	−	3.49532i	−0.608458	−	1.05388i	−0.991495	−	0.130147i	$-0.958455\pi$
$11$	−2.01803	−	3.49532i	−0.608458	−	1.05388i	0.383037	−	0.923733i	$-0.374878\pi$
$12$	2.20520	−	0.752555i	0.636587	−	0.217244i
$13$	−1.21154	−	3.39590i	−0.336021	−	0.941855i
$13$	−1.21154	−	3.39590i	−0.336021	−	0.941855i
$14$	−0.747688	+	1.04519i	−0.199828	+	0.279338i
$15$	1.00895	−	0.582519i	0.260510	−	0.150406i
$16$	3.70046	+	1.51874i	0.925116	+	0.379685i
$17$	1.41984	−	2.45923i	0.344361	−	0.596450i	−0.640877	−	0.767644i	$-0.721429\pi$
$17$	1.41984	−	2.45923i	0.344361	−	0.596450i	0.985237	+	0.171194i	$0.0547623\pi$
$18$	−1.88943	−	1.35163i	−0.445343	−	0.318582i
$19$	−0.810340	+	1.40355i	−0.185905	+	0.321996i	−0.943881	−	0.330286i	$-0.892855\pi$
$19$	−0.810340	+	1.40355i	−0.185905	+	0.321996i	0.757976	+	0.652282i	$0.226188\pi$
$20$	1.96220	+	0.386999i	0.438761	+	0.0865356i
$21$	−1.05866			−0.231019
$22$	5.19715	−	2.35988i	1.10804	−	0.503128i
$23$	−0.494250	−	0.856067i	−0.103058	−	0.178502i	0.809885	−	0.586589i	$-0.199530\pi$
$23$	−0.494250	−	0.856067i	−0.103058	−	0.178502i	−0.912943	+	0.408087i	$0.866196\pi$
$24$	0.756071	+	3.20731i	0.154332	+	0.654690i
$25$	1.00000			0.200000
$26$	4.94635	−	1.23841i	0.970058	−	0.242872i
$27$		−	5.40891i		−	1.04094i
$28$	−1.36833	−	1.19607i	−0.258589	−	0.226036i
$29$	7.87290	−	4.54542i	1.46196	−	0.844064i	0.462859	−	0.886432i	$-0.346823\pi$
$29$	7.87290	−	4.54542i	1.46196	−	0.844064i	0.999102	+	0.0423678i	$0.0134901\pi$
$30$	0.681198	+	1.50020i	0.124369	+	0.273897i
$31$			3.84896i			0.691294i	0.938365	+	0.345647i	$0.112341\pi$
$31$			3.84896i			0.691294i	−0.938365	+	0.345647i	$0.887659\pi$
$32$	−2.64637	+	4.99967i	−0.467817	+	0.883825i
$33$	4.07218	+	2.35108i	0.708876	+	0.409270i
$34$	3.26621	+	2.33653i	0.560150	+	0.400711i
$35$	−0.786953	−	0.454347i	−0.133019	−	0.0767987i
$36$	2.16219	−	2.47359i	0.360365	−	0.412264i
$37$	0.538020	+	0.931878i	0.0884500	+	0.153200i	0.906856	−	0.421440i	$-0.138475\pi$
$37$	0.538020	+	0.931878i	0.0884500	+	0.153200i	−0.818406	+	0.574640i	$0.805142\pi$
$38$	−1.86412	−	1.33352i	−0.302400	−	0.216326i
$39$	3.20056	+	2.72056i	0.512500	+	0.435638i
$40$	−0.814463	+	2.70863i	−0.128778	+	0.428271i
$41$	7.68661	−	4.43786i	1.20045	−	0.693078i	0.239792	−	0.970824i	$-0.422921\pi$
$41$	7.68661	−	4.43786i	1.20045	−	0.693078i	0.960654	+	0.277747i	$0.0895875\pi$
$42$	0.145541	−	1.49009i	0.0224574	−	0.229925i
$43$	−9.23470	−	5.33166i	−1.40828	−	0.813070i	−0.413056	−	0.910706i	$-0.635539\pi$
$43$	−9.23470	−	5.33166i	−1.40828	−	0.813070i	−0.995222	+	0.0976356i	$0.968872\pi$
$44$	2.60708	+	7.63950i	0.393033	+	1.15170i
$45$	0.821344	−	1.42261i	0.122439	−	0.212070i
$46$	1.27288	−	0.577977i	0.187675	−	0.0852180i
$47$		−	11.5567i		−	1.68571i	−0.538138	−	0.842857i	$-0.680872\pi$
$47$		−	11.5567i		−	1.68571i	0.538138	−	0.842857i	$-0.319128\pi$
$48$	−4.61828	+	0.623254i	−0.666592	+	0.0899589i
$49$	−3.08714	−	5.34708i	−0.441020	−	0.763868i
$50$	−0.137476	+	1.40752i	−0.0194420	+	0.199053i
$51$			3.30832i			0.463258i
$52$	1.06307	+	7.13231i	0.147422	+	0.989074i
$53$			10.1285i			1.39126i	0.718399	+	0.695631i	$0.244875\pi$
$53$			10.1285i			1.39126i	−0.718399	+	0.695631i	$0.755125\pi$
$54$	7.61312	+	0.743594i	1.03601	+	0.101190i
$55$	2.01803	+	3.49532i	0.272111	+	0.471309i
$56$	1.87160	−	1.76151i	0.250103	−	0.235392i
$57$		−	1.88815i		−	0.250092i
$58$	5.31542	+	11.7061i	0.697949	+	1.53709i
$59$	−4.67358	+	8.09488i	−0.608449	+	1.05386i	0.383048	+	0.923729i	$0.374875\pi$
$59$	−4.67358	+	8.09488i	−0.608449	+	1.05386i	−0.991496	+	0.130135i	$0.958459\pi$
$60$	−2.20520	+	0.752555i	−0.284690	+	0.0971545i
$61$	−0.159169	−	0.0918962i	−0.0203795	−	0.0117661i	0.489776	−	0.871849i	$-0.337079\pi$
$61$	−0.159169	−	0.0918962i	−0.0203795	−	0.0117661i	−0.510155	+	0.860082i	$0.670412\pi$
$62$	−5.41748	−	0.529140i	−0.688020	−	0.0672008i
$63$	−1.29272	+	0.746351i	−0.162867	+	0.0940313i
$64$	−6.67330	−	4.41215i	−0.834163	−	0.551519i
$65$	1.21154	+	3.39590i	0.150273	+	0.421210i
$66$	−3.86900	+	5.40844i	−0.476241	+	0.665733i
$67$	−5.74510	−	9.95080i	−0.701875	−	1.21568i	−0.967807	−	0.251692i	$-0.919013\pi$
$67$	−5.74510	−	9.95080i	−0.701875	−	1.21568i	0.265932	−	0.963992i	$-0.414320\pi$
$68$	−3.73772	+	4.27602i	−0.453265	+	0.518544i
$69$	0.997350	+	0.575820i	0.120067	+	0.0693206i
$70$	0.747688	−	1.04519i	0.0893658	−	0.124924i
$71$	4.27599	+	2.46874i	0.507467	+	0.292986i	0.731792	−	0.681528i	$-0.238684\pi$
$71$	4.27599	+	2.46874i	0.507467	+	0.292986i	−0.224325	+	0.974514i	$0.572018\pi$
$72$	3.18436	+	3.38337i	0.375281	+	0.398735i
$73$		−	5.44599i		−	0.637405i	−0.947855	−	0.318703i	$-0.896753\pi$
$73$		−	5.44599i		−	0.637405i	0.947855	−	0.318703i	$-0.103247\pi$
$74$	−1.38560	+	0.629161i	−0.161073	+	0.0731385i
$75$	−1.00895	+	0.582519i	−0.116504	+	0.0672635i
$76$	2.13322	−	2.44045i	0.244697	−	0.279938i
$77$		−	3.66754i		−	0.417955i
$78$	−4.26923	+	4.13083i	−0.483395	+	0.467725i
$79$	−14.8307			−1.66859			−0.834294	−	0.551320i	$-0.814124\pi$
$79$	−14.8307			−1.66859			−0.834294	+	0.551320i	$0.814124\pi$
$80$	−3.70046	−	1.51874i	−0.413724	−	0.169800i
$81$	0.686757	+	1.18950i	0.0763064	+	0.132167i
$82$	5.18964	+	11.4291i	0.573100	+	1.26213i
$83$	−14.8263			−1.62740			−0.813701	−	0.581284i	$-0.802551\pi$
$83$	−14.8263			−1.62740			−0.813701	+	0.581284i	$0.802551\pi$
$84$	2.07731	+	0.409702i	0.226653	+	0.0447021i
$85$	−1.41984	+	2.45923i	−0.154003	+	0.266741i
$86$	8.77394	−	12.2650i	0.946118	−	1.32257i
$87$	−5.29559	+	9.17223i	−0.567747	+	0.983366i
$88$	−11.1111	+	2.61926i	−1.18445	+	0.279215i
$89$	−2.39372	+	1.38202i	−0.253734	+	0.146494i	−0.621473	−	0.783436i	$-0.713465\pi$
$89$	−2.39372	+	1.38202i	−0.253734	+	0.146494i	0.367739	+	0.929929i	$0.380132\pi$
$90$	1.88943	+	1.35163i	0.199163	+	0.142474i
$91$	0.589495	−	3.22288i	0.0617959	−	0.337849i
$92$	0.638521	+	1.87105i	0.0665705	+	0.195070i
$93$	−2.24209	−	3.88342i	−0.232494	−	0.402692i
$94$	16.2662	+	1.58876i	1.67773	+	0.163869i
$95$	0.810340	−	1.40355i	0.0831391	−	0.144001i
$96$	−0.242336	−	6.58599i	−0.0247333	−	0.672180i
$97$	−9.80772	−	5.66249i	−0.995823	−	0.574939i	−0.0888131	−	0.996048i	$-0.528307\pi$
$97$	−9.80772	−	5.66249i	−0.995823	−	0.574939i	−0.907010	+	0.421110i	$0.861641\pi$
$98$	7.95050	−	3.61010i	0.803122	−	0.364675i
$99$	6.62997			0.666337
$100$	−1.96220	−	0.386999i	−0.196220	−	0.0386999i
$101$	15.2516	−	8.80549i	1.51759	−	0.876179i	0.517801	−	0.855501i	$-0.326751\pi$
$101$	15.2516	−	8.80549i	1.51759	−	0.876179i	0.999786	−	0.0206778i	$-0.00658243\pi$
$102$	−4.65652	−	0.454815i	−0.461064	−	0.0450334i
$103$	−4.00462			−0.394587			−0.197293	−	0.980344i	$-0.563215\pi$
$103$	−4.00462			−0.394587			−0.197293	+	0.980344i	$0.563215\pi$
$104$	−10.1850	+	0.515771i	−0.998720	+	0.0505755i
$105$	1.05866			0.103315
$106$	−14.2561	−	1.39243i	−1.38467	−	0.135245i
$107$	10.4667	−	6.04294i	1.01185	−	0.584193i	0.100118	−	0.994976i	$-0.468078\pi$
$107$	10.4667	−	6.04294i	1.01185	−	0.584193i	0.911733	+	0.410783i	$0.134745\pi$
$108$	−2.09324	+	10.6134i	−0.201422	+	1.02127i
$109$	−4.69338			−0.449544			−0.224772	−	0.974411i	$-0.572164\pi$
$109$	−4.69338			−0.449544			−0.224772	+	0.974411i	$0.572164\pi$
$110$	−5.19715	+	2.35988i	−0.495529	+	0.225006i
$111$	−1.08567	−	0.626814i	−0.103048	−	0.0594945i
$112$	2.22205	+	2.87647i	0.209964	+	0.271801i
$113$	5.70070	−	9.87391i	0.536277	−	0.928859i	−0.462823	−	0.886450i	$-0.653164\pi$
$113$	5.70070	−	9.87391i	0.536277	−	0.928859i	0.999100	−	0.0424084i	$-0.0135031\pi$
$114$	2.65761	+	0.259576i	0.248908	+	0.0243115i
$115$	0.494250	+	0.856067i	0.0460891	+	0.0798286i
$116$	−17.2073	+	5.87223i	−1.59766	+	0.545222i
$117$	5.82614	+	1.06566i	0.538627	+	0.0985200i
$118$	−10.7512	−	7.69099i	−0.989725	−	0.708013i
$119$	2.23469	−	1.29020i	0.204853	−	0.118272i
$120$	−0.756071	−	3.20731i	−0.0690195	−	0.292786i
$121$	−2.64485	+	4.58102i	−0.240441	+	0.416457i
$122$	0.151227	−	0.211399i	0.0136915	−	0.0191392i
$123$	−5.17028	+	8.95518i	−0.466188	+	0.807462i
$124$	1.48955	−	7.55244i	0.133765	−	0.678229i
$125$	−1.00000			−0.0894427
$126$	−0.872783	−	1.92212i	−0.0777537	−	0.171237i
$127$	5.13384	+	8.89208i	0.455555	+	0.789044i	0.998720	−	0.0505816i	$-0.0161075\pi$
$127$	5.13384	+	8.89208i	0.455555	+	0.789044i	−0.543165	+	0.839626i	$0.682774\pi$
$128$	7.12759	−	8.78621i	0.629996	−	0.776599i
$129$	12.4232			1.09380
$130$	−4.94635	+	1.23841i	−0.433823	+	0.108615i
$131$			5.02397i			0.438946i	0.975619	+	0.219473i	$0.0704339\pi$
$131$			5.02397i			0.438946i	−0.975619	+	0.219473i	$0.929566\pi$
$132$	−7.08057	−	6.18921i	−0.616285	−	0.538702i
$133$	−1.27540	+	0.736352i	−0.110591	+	0.0638498i
$134$	14.7957	−	6.71832i	1.27816	−	0.580374i
$135$			5.40891i			0.465524i
$136$	−5.50472	−	5.84875i	−0.472026	−	0.501526i
$137$	−18.9228	−	10.9251i	−1.61668	−	0.933393i	−0.987770	−	0.155918i	$-0.950166\pi$
$137$	−18.9228	−	10.9251i	−1.61668	−	0.933393i	−0.628914	−	0.777475i	$-0.716500\pi$
$138$	−0.947588	+	1.32462i	−0.0806640	+	0.112760i
$139$	1.79457	+	1.03610i	0.152214	+	0.0878807i	0.574172	−	0.818734i	$-0.305324\pi$
$139$	1.79457	+	1.03610i	0.152214	+	0.0878807i	−0.421959	+	0.906615i	$0.638657\pi$
$140$	1.36833	+	1.19607i	0.115645	+	0.101086i
$141$	6.73198	+	11.6601i	0.566935	+	0.981960i
$142$	−4.06264	+	5.67913i	−0.340929	+	0.476582i
$143$	−9.42486	+	11.0877i	−0.788147	+	0.927204i
$144$	−5.19993	+	4.01691i	−0.433327	+	0.334742i
$145$	−7.87290	+	4.54542i	−0.653809	+	0.377477i
$146$	7.66532	+	0.748693i	0.634386	+	0.0619623i
$147$	6.22955	+	3.59663i	0.513804	+	0.296645i
$148$	−0.695067	−	2.03675i	−0.0571342	−	0.167419i
$149$	−1.07638	+	1.86435i	−0.0881809	+	0.152734i	−0.906742	−	0.421685i	$-0.861439\pi$
$149$	−1.07638	+	1.86435i	−0.0881809	+	0.152734i	0.818561	+	0.574419i	$0.194772\pi$
$150$	−0.681198	−	1.50020i	−0.0556196	−	0.122491i
$151$			7.39857i			0.602087i	0.953610	+	0.301043i	$0.0973349\pi$
$151$			7.39857i			0.602087i	−0.953610	+	0.301043i	$0.902665\pi$
$152$	3.14170	+	3.33805i	0.254825	+	0.270751i
$153$	2.33235	+	4.03974i	0.188559	+	0.326594i
$154$	5.16212	+	0.504198i	0.415975	+	0.0406295i
$155$		−	3.84896i		−	0.309156i
$156$	−5.22730	−	6.57690i	−0.418519	−	0.526574i
$157$			7.81527i			0.623726i	0.950127	+	0.311863i	$0.100953\pi$
$157$			7.81527i			0.623726i	−0.950127	+	0.311863i	$0.899047\pi$
$158$	2.03887	−	20.8745i	0.162204	−	1.66068i
$159$	−5.90006	−	10.2192i	−0.467906	−	0.810436i
$160$	2.64637	−	4.99967i	0.209214	−	0.395259i
$161$		−	0.898245i		−	0.0707916i
$162$	−1.76865	+	0.803094i	−0.138958	+	0.0630970i
$163$	3.49430	−	6.05231i	0.273695	−	0.474054i	−0.696110	−	0.717935i	$-0.745087\pi$
$163$	3.49430	−	6.05231i	0.273695	−	0.474054i	0.969805	+	0.243881i	$0.0784208\pi$
$164$	−16.8001	+	5.73327i	−1.31187	+	0.447693i
$165$	−4.07218	−	2.35108i	−0.317019	−	0.183031i
$166$	2.03826	−	20.8683i	0.158200	−	1.61969i
$167$	6.37387	−	3.67996i	0.493225	−	0.284763i	−0.232686	−	0.972552i	$-0.574752\pi$
$167$	6.37387	−	3.67996i	0.493225	−	0.284763i	0.725911	+	0.687788i	$0.241418\pi$
$168$	−0.862242	+	2.86752i	−0.0665234	+	0.221234i
$169$	−10.0643	+	8.22855i	−0.774180	+	0.632965i
$170$	−3.26621	−	2.33653i	−0.250507	−	0.179203i
$171$	−1.33114	−	2.30559i	−0.101794	−	0.176313i
$172$	16.0570	+	14.0356i	1.22433	+	1.07020i
$173$	11.6569	+	6.73009i	0.886255	+	0.511679i	0.872716	−	0.488229i	$-0.162357\pi$
$173$	11.6569	+	6.73009i	0.886255	+	0.511679i	0.0135391	+	0.999908i	$0.495690\pi$
$174$	−12.1820	−	8.71458i	−0.923518	−	0.660651i
$175$	0.786953	+	0.454347i	0.0594880	+	0.0343454i
$176$	−2.15914	−	15.9992i	−0.162752	−	1.20598i
$177$		−	10.8898i		−	0.818527i
$178$	−1.61613	−	3.55920i	−0.121134	−	0.266773i
$179$	5.65198	−	3.26317i	0.422449	−	0.243901i	−0.273676	−	0.961822i	$-0.588239\pi$
$179$	5.65198	−	3.26317i	0.422449	−	0.243901i	0.696125	+	0.717921i	$0.254906\pi$
$180$	−2.16219	+	2.47359i	−0.161160	+	0.184370i
$181$			11.3825i			0.846055i	0.906117	+	0.423028i	$0.139033\pi$
$181$			11.3825i			0.846055i	−0.906117	+	0.423028i	$0.860967\pi$
$182$	4.45521	+	1.27279i	0.330242	+	0.0943456i
$183$	0.214125			0.0158286
$184$	−2.72131	+	0.641505i	−0.200618	+	0.0472923i
$185$	−0.538020	−	0.931878i	−0.0395560	−	0.0685131i
$186$	5.77421	−	2.62190i	0.423385	−	0.192247i
$187$	−11.4611			−0.838116
$188$	−4.47242	+	22.6765i	−0.326185	+	1.65385i
$189$	2.45752	−	4.25655i	0.178758	−	0.309619i
$190$	1.86412	+	1.33352i	0.135237	+	0.0967438i
$191$	−5.34414	+	9.25631i	−0.386688	+	0.669763i	−0.992002	−	0.126224i	$-0.959714\pi$
$191$	−5.34414	+	9.25631i	−0.386688	+	0.669763i	0.605314	+	0.795987i	$0.293048\pi$
$192$	9.30320	+	0.564324i	0.671401	+	0.0407266i
$193$	−11.5999	+	6.69719i	−0.834977	+	0.482074i	−0.855554	−	0.517714i	$-0.826783\pi$
$193$	−11.5999	+	6.69719i	−0.834977	+	0.482074i	0.0205769	+	0.999788i	$0.493450\pi$
$194$	9.31837	−	13.0261i	0.669020	−	0.935217i
$195$	−3.20056	−	2.72056i	−0.229197	−	0.194823i
$196$	3.98827	+	11.6868i	0.284876	+	0.834769i
$197$	5.72584	+	9.91745i	0.407950	+	0.706589i	0.994660	−	0.103208i	$-0.0329106\pi$
$197$	5.72584	+	9.91745i	0.407950	+	0.706589i	−0.586710	+	0.809797i	$0.699577\pi$
$198$	−0.911462	+	9.33179i	−0.0647748	+	0.663181i
$199$	4.98119	−	8.62768i	0.353108	−	0.611600i	−0.633685	−	0.773591i	$-0.718458\pi$
$199$	4.98119	−	8.62768i	0.353108	−	0.611600i	0.986792	+	0.161991i	$0.0517916\pi$
$200$	0.814463	−	2.70863i	0.0575912	−	0.191529i
$201$	11.5931	+	6.69325i	0.817711	+	0.472106i
$202$	10.2971	+	22.6774i	0.724505	+	1.59557i
$203$	8.26080			0.579795
$204$	1.28032	−	6.49160i	0.0896402	−	0.454503i
$205$	−7.68661	+	4.43786i	−0.536856	+	0.309954i
$206$	0.550539	−	5.63656i	0.0383578	−	0.392718i
$207$	1.62380			0.112862
$208$	0.674236	−	14.4064i	0.0467498	−	0.998907i
$209$	6.54115			0.452461
$210$	−0.145541	+	1.49009i	−0.0100433	+	0.102826i
$211$	−3.72205	+	2.14892i	−0.256236	+	0.147938i	−0.622616	−	0.782527i	$-0.713930\pi$
$211$	−3.72205	+	2.14892i	−0.256236	+	0.147938i	0.366380	+	0.930465i	$0.380597\pi$
$212$	3.91974	−	19.8742i	0.269209	−	1.36497i
$213$	−5.75236			−0.394145
$214$	7.06661	+	15.5628i	0.483064	+	1.06385i
$215$	9.23470	+	5.33166i	0.629801	+	0.363616i
$216$	−14.6507	−	4.40535i	−0.996854	−	0.299746i
$217$	−1.74877	+	3.02895i	−0.118714	+	0.205619i
$218$	0.645226	−	6.60600i	0.0437002	−	0.447415i
$219$	3.17239	+	5.49474i	0.214370	+	0.371300i
$220$	−2.60708	−	7.63950i	−0.175770	−	0.515055i
$221$	−10.0715	−	1.84217i	−0.677482	−	0.123918i
$222$	1.03150	−	1.44193i	0.0692300	−	0.0967760i
$223$	6.29404	−	3.63386i	0.421480	−	0.243342i	−0.274230	−	0.961664i	$-0.588423\pi$
$223$	6.29404	−	3.63386i	0.421480	−	0.243342i	0.695710	+	0.718322i	$0.255090\pi$
$224$	−4.35416	+	2.73213i	−0.290924	+	0.182548i
$225$	−0.821344	+	1.42261i	−0.0547563	+	0.0948406i
$226$	13.1140	+	9.38125i	0.872328	+	0.624032i
$227$	−1.11578	+	1.93259i	−0.0740568	+	0.128270i	−0.900676	−	0.434492i	$-0.856928\pi$
$227$	−1.11578	+	1.93259i	−0.0740568	+	0.128270i	0.826619	+	0.562762i	$0.190261\pi$
$228$	−0.730714	+	3.70494i	−0.0483927	+	0.245365i
$229$	5.95549			0.393550			0.196775	−	0.980449i	$-0.436953\pi$
$229$	5.95549			0.393550			0.196775	+	0.980449i	$0.436953\pi$
$230$	−1.27288	+	0.577977i	−0.0839309	+	0.0381106i
$231$	2.13641	+	3.70037i	0.140565	+	0.243466i
$232$	−5.89966	−	25.0268i	−0.387332	−	1.64309i
$233$	0.994961			0.0651821			0.0325910	−	0.999469i	$-0.489624\pi$
$233$	0.994961			0.0651821			0.0325910	+	0.999469i	$0.489624\pi$
$234$	−2.30088	+	8.05388i	−0.150413	+	0.526498i
$235$			11.5567i			0.753874i
$236$	12.3032	−	14.0751i	0.800871	−	0.916212i
$237$	14.9635	−	8.63918i	0.971983	−	0.561175i
$238$	1.50876	+	3.32273i	0.0977982	+	0.215380i
$239$			2.10697i			0.136288i	0.997675	+	0.0681442i	$0.0217078\pi$
$239$			2.10697i			0.136288i	−0.997675	+	0.0681442i	$0.978292\pi$
$240$	4.61828	−	0.623254i	0.298109	−	0.0402308i
$241$	12.4843	+	7.20780i	0.804183	+	0.464295i	0.844932	−	0.534874i	$-0.179641\pi$
$241$	12.4843	+	7.20780i	0.804183	+	0.464295i	−0.0407487	+	0.999169i	$0.512974\pi$
$242$	−6.08426	−	4.35245i	−0.391111	−	0.279786i
$243$	12.6669	+	7.31326i	0.812584	+	0.469146i
$244$	0.276758	+	0.241917i	0.0177176	+	0.0154872i
$245$	3.08714	+	5.34708i	0.197230	+	0.341612i
$246$	−11.8938	−	8.50837i	−0.758319	−	0.542474i
$247$	5.74808	+	1.05138i	0.365742	+	0.0668977i
$248$	10.4254	+	3.13484i	0.662014	+	0.199062i
$249$	14.9591	−	8.63662i	0.947992	−	0.547324i
$250$	0.137476	−	1.40752i	0.00869474	−	0.0890191i
$251$	−2.37866	−	1.37332i	−0.150139	−	0.0866830i	0.423048	−	0.906107i	$-0.360960\pi$
$251$	−2.37866	−	1.37332i	−0.150139	−	0.0866830i	−0.573188	+	0.819424i	$0.694293\pi$
$252$	2.82541	−	0.964209i	0.177984	−	0.0607395i
$253$	−1.99482	+	3.45513i	−0.125413	+	0.217222i
$254$	−13.2215	+	6.00352i	−0.829592	+	0.376694i
$255$		−	3.30832i		−	0.207175i
$256$	11.3869	+	11.2401i	0.711679	+	0.702505i
$257$	−3.27795	−	5.67758i	−0.204473	−	0.354158i	0.745492	−	0.666515i	$-0.232215\pi$
$257$	−3.27795	−	5.67758i	−0.204473	−	0.354158i	−0.949965	+	0.312357i	$0.898881\pi$
$258$	−1.70789	+	17.4858i	−0.106328	+	1.08862i
$259$			0.977792i			0.0607570i
$260$	−1.06307	−	7.13231i	−0.0659290	−	0.442327i
$261$			14.9334i			0.924356i
$262$	−7.07132	−	0.690675i	−0.436868	−	0.0426701i
$263$	0.410453	+	0.710926i	0.0253096	+	0.0438376i	0.878403	−	0.477921i	$-0.158609\pi$
$263$	0.410453	+	0.710926i	0.0253096	+	0.0438376i	−0.853093	+	0.521759i	$0.825276\pi$
$264$	9.68482	−	9.11515i	0.596060	−	0.560999i
$265$		−	10.1285i		−	0.622191i
$266$	−0.861090	−	1.89637i	−0.0527968	−	0.116274i
$267$	1.61010	−	2.78878i	0.0985367	−	0.170670i
$268$	7.42208	+	21.7488i	0.453376	+	1.32852i
$269$	−15.4691	−	8.93107i	−0.943166	−	0.544537i	−0.0522145	−	0.998636i	$-0.516628\pi$
$269$	−15.4691	−	8.93107i	−0.943166	−	0.544537i	−0.890951	+	0.454099i	$0.849961\pi$
$270$	−7.61312	−	0.743594i	−0.463320	−	0.0452537i
$271$	8.02412	−	4.63273i	0.487431	−	0.281418i	−0.236077	−	0.971734i	$-0.575862\pi$
$271$	8.02412	−	4.63273i	0.487431	−	0.281418i	0.723508	+	0.690316i	$0.242529\pi$
$272$	8.98898	−	6.94392i	0.545037	−	0.421037i
$273$	1.28261	+	3.59512i	0.0776273	+	0.217587i
$274$	17.9787	−	25.1322i	1.08613	−	1.51829i
$275$	−2.01803	−	3.49532i	−0.121692	−	0.210776i
$276$	−1.73416	−	1.51585i	−0.104384	−	0.0912434i
$277$	5.69939	+	3.29054i	0.342443	+	0.197710i	0.661352	−	0.750076i	$-0.269983\pi$
$277$	5.69939	+	3.29054i	0.342443	+	0.197710i	−0.318909	+	0.947785i	$0.603316\pi$
$278$	−1.70503	+	2.38345i	−0.102261	+	0.142950i
$279$	−5.47557	−	3.16132i	−0.327814	−	0.189263i
$280$	−1.87160	+	1.76151i	−0.111849	+	0.105270i
$281$		−	0.628207i		−	0.0374757i	−0.999824	−	0.0187378i	$-0.994035\pi$
$281$		−	0.628207i		−	0.0374757i	0.999824	−	0.0187378i	$-0.00596479\pi$
$282$	−17.3373	+	7.87238i	−1.03242	+	0.468793i
$283$	−3.25394	+	1.87866i	−0.193427	+	0.111675i	−0.593586	−	0.804771i	$-0.702288\pi$
$283$	−3.25394	+	1.87866i	−0.193427	+	0.111675i	0.400159	+	0.916446i	$0.368955\pi$
$284$	−7.43495	−	6.49897i	−0.441183	−	0.385643i
$285$			1.88815i			0.111845i
$286$	−14.3105	−	14.7899i	−0.846197	−	0.874548i
$287$	8.06532			0.476081
$288$	−4.93899	−	7.87121i	−0.291033	−	0.463815i
$289$	4.46813	+	7.73903i	0.262831	+	0.455237i
$290$	−5.31542	−	11.7061i	−0.312132	−	0.687407i
$291$	13.1940			0.773447
$292$	−2.10759	+	10.6861i	−0.123338	+	0.625358i
$293$	10.2140	−	17.6911i	0.596707	−	1.03353i	−0.396597	−	0.917993i	$-0.629809\pi$
$293$	10.2140	−	17.6911i	0.596707	−	1.03353i	0.993304	−	0.115534i	$-0.0368579\pi$
$294$	−5.91873	+	8.27373i	−0.345187	+	0.482534i
$295$	4.67358	−	8.09488i	0.272107	−	0.471302i
$296$	2.96231	−	0.698315i	0.172181	−	0.0405887i
$297$	−18.9059	+	10.9153i	−1.09703	+	0.633370i
$298$	−2.47613	−	1.77133i	−0.143438	−	0.102611i
$299$	−2.30832	+	2.71559i	−0.133493	+	0.157046i
$300$	2.20520	−	0.752555i	0.127317	−	0.0434488i
$301$	−4.84485	−	8.39152i	−0.279252	−	0.483679i
$302$	−10.4136	−	1.01713i	−0.599235	−	0.0585290i
$303$	−10.2587	+	17.7686i	−0.589349	+	1.02078i
$304$	−5.13026	+	3.96309i	−0.294241	+	0.227299i
$305$	0.159169	+	0.0918962i	0.00911399	+	0.00526196i
$306$	−6.00664	+	2.72745i	−0.343377	+	0.155918i
$307$	29.0460			1.65774			0.828870	−	0.559441i	$-0.188984\pi$
$307$	29.0460			1.65774			0.828870	+	0.559441i	$0.188984\pi$
$308$	−1.41933	+	7.19644i	−0.0808741	+	0.410056i
$309$	4.04047	−	2.33277i	0.229854	−	0.132706i
$310$	5.41748	+	0.529140i	0.307692	+	0.0300531i
$311$	29.6373			1.68057			0.840287	−	0.542141i	$-0.182386\pi$
$311$	29.6373			1.68057			0.840287	+	0.542141i	$0.182386\pi$
$312$	9.97572	−	6.45333i	0.564764	−	0.365348i
$313$	21.2962			1.20373			0.601867	−	0.798597i	$-0.294424\pi$
$313$	21.2962			1.20373			0.601867	+	0.798597i	$0.294424\pi$
$314$	−11.0001	−	1.07441i	−0.620772	−	0.0606326i
$315$	1.29272	−	0.746351i	0.0728364	−	0.0420521i
$316$	29.1009	+	5.73948i	1.63705	+	0.322871i
$317$	−13.7154			−0.770334			−0.385167	−	0.922847i	$-0.625856\pi$
$317$	−13.7154			−0.770334			−0.385167	+	0.922847i	$0.625856\pi$
$318$	15.1948	−	6.89954i	0.852083	−	0.386907i
$319$	−31.7754	−	18.3456i	−1.77908	−	1.02715i
$320$	6.67330	+	4.41215i	0.373049	+	0.246647i
$321$	−7.04025	+	12.1941i	−0.392948	+	0.680607i
$322$	1.26429	+	0.123487i	0.0704564	+	0.00688167i
$323$	2.30110	+	3.98562i	0.128037	+	0.221766i
$324$	−0.887221	−	2.59981i	−0.0492900	−	0.144434i
$325$	−1.21154	−	3.39590i	−0.0672042	−	0.188371i
$326$	8.03834	+	5.75034i	0.445203	+	0.318482i
$327$	4.73539	−	2.73398i	0.261868	−	0.151189i
$328$	−5.76006	−	24.4346i	−0.318046	−	1.34918i
$329$	5.25074	−	9.09455i	0.289483	−	0.501399i
$330$	3.86900	−	5.40844i	0.212982	−	0.297725i
$331$	−11.7962	+	20.4317i	−0.648380	+	1.12303i	0.335130	+	0.942172i	$0.391220\pi$
$331$	−11.7962	+	20.4317i	−0.648380	+	1.12303i	−0.983510	+	0.180855i	$0.942113\pi$
$332$	29.0923	+	5.73778i	1.59664	+	0.314902i
$333$	−1.76760			−0.0968638
$334$	4.30334	+	9.47723i	0.235468	+	0.518571i
$335$	5.74510	+	9.95080i	0.313888	+	0.543670i
$336$	−3.91754	−	1.60783i	−0.213720	−	0.0877145i
$337$	10.2973			0.560931			0.280465	−	0.959864i	$-0.409511\pi$
$337$	10.2973			0.560931			0.280465	+	0.959864i	$0.409511\pi$
$338$	−10.1982	−	15.2969i	−0.554710	−	0.832044i
$339$			13.2831i			0.721437i
$340$	3.73772	−	4.27602i	0.202706	−	0.231900i
$341$	13.4534	−	7.76731i	0.728541	−	0.420623i
$342$	3.42816	−	1.55663i	0.185374	−	0.0841729i
$343$		−	11.9714i		−	0.646394i
$344$	−21.9628	+	20.6709i	−1.18415	+	1.11450i
$345$	−0.997350	−	0.575820i	−0.0536955	−	0.0310011i
$346$	−11.0752	+	15.4820i	−0.595409	+	0.832317i
$347$	−8.66358	−	5.00192i	−0.465085	−	0.268517i	0.249095	−	0.968479i	$-0.419867\pi$
$347$	−8.66358	−	5.00192i	−0.465085	−	0.268517i	−0.714180	+	0.699962i	$0.753200\pi$
$348$	13.9407	−	15.9484i	0.747297	−	0.854922i
$349$	−10.9211	−	18.9158i	−0.584591	−	1.01254i	−0.994926	−	0.100607i	$-0.967922\pi$
$349$	−10.9211	−	18.9158i	−0.584591	−	1.01254i	0.410335	−	0.911935i	$-0.365412\pi$
$350$	−0.747688	+	1.04519i	−0.0399656	+	0.0558676i
$351$	−18.3681	+	6.55311i	−0.980418	+	0.349779i
$352$	22.8159	−	0.839527i	1.21609	−	0.0447469i
$353$	4.63051	−	2.67343i	0.246457	−	0.142292i	−0.371684	−	0.928359i	$-0.621219\pi$
$353$	4.63051	−	2.67343i	0.246457	−	0.142292i	0.618141	+	0.786067i	$0.287886\pi$
$354$	15.3276	+	1.49709i	0.814651	+	0.0795692i
$355$	−4.27599	−	2.46874i	−0.226946	−	0.131027i
$356$	5.23181	−	1.78543i	0.277285	−	0.0946274i
$357$	−1.50313	+	2.60349i	−0.0795540	+	0.137792i
$358$	3.81596	+	8.40386i	0.201680	+	0.444158i
$359$		−	15.3255i		−	0.808851i	−0.914571	−	0.404426i	$-0.867471\pi$
$359$		−	15.3255i		−	0.808851i	0.914571	−	0.404426i	$-0.132529\pi$
$360$	−3.18436	−	3.38337i	−0.167831	−	0.178320i
$361$	8.18670	+	14.1798i	0.430879	+	0.746304i
$362$	−16.0211	−	1.56482i	−0.842048	−	0.0822452i
$363$		−	6.16271i		−	0.323458i
$364$	−2.40396	+	6.09580i	−0.126002	+	0.319507i
$365$			5.44599i			0.285056i
$366$	−0.0294371	+	0.301385i	−0.00153870	+	0.0157536i
$367$	−17.4724	−	30.2631i	−0.912053	−	1.57972i	−0.811159	−	0.584826i	$-0.801163\pi$
$367$	−17.4724	−	30.2631i	−0.912053	−	1.57972i	−0.100895	−	0.994897i	$-0.532170\pi$
$368$	−0.528813	−	3.91848i	−0.0275663	−	0.204265i
$369$			14.5800i			0.759007i
$370$	1.38560	−	0.629161i	0.0720338	−	0.0327085i
$371$	−4.60187	+	7.97068i	−0.238917	+	0.413817i
$372$	2.89656	+	8.48774i	0.150179	+	0.440069i
$373$	13.8440	+	7.99284i	0.716815	+	0.413854i	0.813579	−	0.581454i	$-0.197516\pi$
$373$	13.8440	+	7.99284i	0.716815	+	0.413854i	−0.0967640	+	0.995307i	$0.530849\pi$
$374$	1.57562	−	16.1316i	0.0814734	−	0.834146i
$375$	1.00895	−	0.582519i	0.0521021	−	0.0300811i
$376$	−31.3027	−	9.41248i	−1.61431	−	0.485412i
$377$	−24.9742	−	21.2287i	−1.28623	−	1.09333i
$378$	5.65331	+	4.04417i	0.290775	+	0.208010i
$379$	0.360892	+	0.625083i	0.0185378	+	0.0321084i	0.875145	−	0.483860i	$-0.160766\pi$
$379$	0.360892	+	0.625083i	0.0185378	+	0.0321084i	−0.856608	+	0.515968i	$0.827432\pi$
$380$	−2.13322	+	2.44045i	−0.109432	+	0.125192i
$381$	−10.3596	−	5.98112i	−0.530739	−	0.306422i
$382$	−12.2937	−	8.79447i	−0.629001	−	0.449964i
$383$	−29.8976	−	17.2614i	−1.52769	−	0.882015i	−0.999458	−	0.0329171i	$-0.989520\pi$
$383$	−29.8976	−	17.2614i	−1.52769	−	0.882015i	−0.528236	−	0.849098i	$-0.677146\pi$
$384$	−2.07326	+	13.0168i	−0.105801	+	0.664262i
$385$			3.66754i			0.186915i
$386$	−7.83169	−	17.2477i	−0.398623	−	0.877885i
$387$	15.1697	−	8.75825i	0.771121	−	0.445207i
$388$	17.0533	+	14.9065i	0.865752	+	0.756764i
$389$		−	28.3941i		−	1.43964i	−0.694163	−	0.719818i	$-0.744225\pi$
$389$		−	28.3941i		−	1.43964i	0.694163	−	0.719818i	$-0.255775\pi$
$390$	4.26923	−	4.13083i	0.216181	−	0.209173i
$391$	−2.80702			−0.141957
$392$	−16.9976	+	4.00690i	−0.858508	+	0.202379i
$393$	−2.92656	−	5.06895i	−0.147625	−	0.255695i
$394$	−14.7461	+	6.69580i	−0.742900	+	0.337330i
$395$	14.8307			0.746215
$396$	−13.0093	−	2.56579i	−0.653744	−	0.128936i
$397$	−19.2805	+	33.3949i	−0.967662	+	1.67604i	−0.265378	+	0.964145i	$0.585497\pi$
$397$	−19.2805	+	33.3949i	−0.967662	+	1.67604i	−0.702285	+	0.711896i	$0.747837\pi$
$398$	11.4588	+	8.19721i	0.574378	+	0.410889i
$399$	0.857877	−	1.48589i	0.0429476	−	0.0743874i
$400$	3.70046	+	1.51874i	0.185023	+	0.0759370i
$401$	−24.7230	+	14.2738i	−1.23461	+	0.712802i	−0.967987	−	0.251000i	$-0.919241\pi$
$401$	−24.7230	+	14.2738i	−1.23461	+	0.712802i	−0.266622	+	0.963801i	$0.585907\pi$
$402$	−11.0146	+	15.3972i	−0.549360	+	0.767945i
$403$	13.0707	−	4.66317i	0.651099	−	0.232289i
$404$	−33.3343	+	11.3758i	−1.65845	+	0.565967i
$405$	−0.686757	−	1.18950i	−0.0341252	−	0.0591067i
$406$	−1.13566	+	11.6272i	−0.0563619	+	0.577049i
$407$	2.17148	−	3.76111i	0.107636	−	0.186431i
$408$	8.96101	+	2.69451i	0.443636	+	0.133398i
$409$	16.0645	+	9.27487i	0.794341	+	0.458613i	0.841488	−	0.540275i	$-0.181680\pi$
$409$	16.0645	+	9.27487i	0.794341	+	0.458613i	−0.0471479	+	0.998888i	$0.515013\pi$
$410$	−5.18964	−	11.4291i	−0.256298	−	0.564444i
$411$	25.4563			1.25567
$412$	7.85786	+	1.54978i	0.387129	+	0.0763524i
$413$	−7.35578	+	4.24686i	−0.361954	+	0.208974i
$414$	−0.223233	+	2.28552i	−0.0109713	+	0.112327i
$415$	14.8263			0.727796
$416$	20.1846	+	2.92954i	0.989631	+	0.143632i
$417$	−2.41419			−0.118223
$418$	−0.899251	+	9.20677i	−0.0439838	+	0.450318i
$419$	−14.6025	+	8.43073i	−0.713377	+	0.411868i	−0.812310	−	0.583226i	$-0.801790\pi$
$419$	−14.6025	+	8.43073i	−0.713377	+	0.411868i	0.0989333	+	0.995094i	$0.468457\pi$
$420$	−2.07731	−	0.409702i	−0.101362	−	0.0199914i
$421$	−27.8277			−1.35624			−0.678120	−	0.734951i	$-0.737205\pi$
$421$	−27.8277			−1.35624			−0.678120	+	0.734951i	$0.737205\pi$
$422$	−2.51295	−	5.53426i	−0.122329	−	0.269404i
$423$	16.4406	+	9.49200i	0.799371	+	0.461517i
$424$	27.4344	+	8.24932i	1.33233	+	0.400622i
$425$	1.41984	−	2.45923i	0.0688721	−	0.119290i
$426$	0.790811	−	8.09653i	0.0383149	−	0.392278i
$427$	−0.0835056	−	0.144636i	−0.00404112	−	0.00699943i
$428$	−22.8763	+	7.80686i	−1.10577	+	0.377359i
$429$	3.05042	−	16.6772i	0.147275	−	0.805181i
$430$	−8.77394	+	12.2650i	−0.423117	+	0.591471i
$431$	7.01128	−	4.04796i	0.337721	−	0.194984i	−0.321543	−	0.946895i	$-0.604201\pi$
$431$	7.01128	−	4.04796i	0.337721	−	0.194984i	0.659264	+	0.751912i	$0.270868\pi$
$432$	8.21472	−	20.0155i	0.395231	−	0.962994i
$433$	−4.48649	+	7.77083i	−0.215607	+	0.373442i	−0.953460	−	0.301519i	$-0.902506\pi$
$433$	−4.48649	+	7.77083i	−0.215607	+	0.373442i	0.737853	+	0.674961i	$0.235840\pi$
$434$	−4.02288	−	2.87782i	−0.193105	−	0.138140i
$435$	5.29559	−	9.17223i	0.253904	−	0.439775i
$436$	9.20935	+	1.81633i	0.441048	+	0.0869865i
$437$	1.60204			0.0766361
$438$	−8.17007	+	3.70980i	−0.390381	+	0.177261i
$439$	3.21962	+	5.57654i	0.153664	+	0.266154i	0.932572	−	0.360985i	$-0.117559\pi$
$439$	3.21962	+	5.57654i	0.153664	+	0.266154i	−0.778908	+	0.627139i	$0.784226\pi$
$440$	11.1111	−	2.61926i	0.529702	−	0.124869i
$441$	10.1424			0.482972
$442$	3.97748	−	13.9225i	0.189189	−	0.662227i
$443$			10.0241i			0.476260i	0.971233	+	0.238130i	$0.0765344\pi$
$443$			10.0241i			0.476260i	−0.971233	+	0.238130i	$0.923466\pi$
$444$	1.88773	+	1.65009i	0.0895878	+	0.0783097i
$445$	2.39372	−	1.38202i	0.113473	−	0.0655139i
$446$	4.24944	+	9.35853i	0.201217	+	0.443139i
$447$		−	2.50806i		−	0.118627i
$448$	−3.24692	−	6.50415i	−0.153403	−	0.307292i
$449$	−35.4627	−	20.4744i	−1.67359	−	0.966247i	−0.965603	−	0.260020i	$-0.916271\pi$
$449$	−35.4627	−	20.4744i	−1.67359	−	0.966247i	−0.707985	−	0.706227i	$-0.750396\pi$
$450$	−1.88943	−	1.35163i	−0.0890686	−	0.0637164i
$451$	−31.0235	−	17.9114i	−1.46084	−	0.843417i
$452$	−15.0071	+	17.1684i	−0.705875	+	0.807534i
$453$	−4.30980	−	7.46480i	−0.202492	−	0.350727i
$454$	−2.56675	−	1.83616i	−0.120464	−	0.0861753i
$455$	−0.589495	+	3.22288i	−0.0276360	+	0.151091i
$456$	−5.11430	−	1.53783i	−0.239499	−	0.0720155i
$457$	−17.0300	+	9.83229i	−0.796631	+	0.459935i	−0.842292	−	0.539022i	$-0.818794\pi$
$457$	−17.0300	+	9.83229i	−0.796631	+	0.459935i	0.0456608	+	0.998957i	$0.485461\pi$
$458$	−0.818736	+	8.38244i	−0.0382570	+	0.391686i
$459$	−13.3017	−	7.67976i	−0.620872	−	0.358460i
$460$	−0.638521	−	1.87105i	−0.0297712	−	0.0872381i
$461$	9.15438	−	15.8559i	0.426362	−	0.738481i	−0.570185	−	0.821517i	$-0.693128\pi$
$461$	9.15438	−	15.8559i	0.426362	−	0.738481i	0.996547	+	0.0830360i	$0.0264617\pi$
$462$	−5.50203	+	2.49832i	−0.255978	+	0.116232i
$463$		−	34.7475i		−	1.61485i	−0.589968	−	0.807426i	$-0.700860\pi$
$463$		−	34.7475i		−	1.61485i	0.589968	−	0.807426i	$-0.299140\pi$
$464$	36.0367	−	4.86328i	1.67296	−	0.225772i
$465$	2.24209	+	3.88342i	0.103975	+	0.180089i
$466$	−0.136783	+	1.40042i	−0.00633636	+	0.0648733i
$467$			12.6309i			0.584489i	0.956344	+	0.292245i	$0.0944021\pi$
$467$			12.6309i			0.584489i	−0.956344	+	0.292245i	$0.905598\pi$
$468$	−11.0196	−	4.34574i	−0.509383	−	0.200882i
$469$		−	10.4411i		−	0.482124i
$470$	−16.2662	−	1.58876i	−0.750304	−	0.0732842i
$471$	−4.55254	−	7.88523i	−0.209770	−	0.363332i
$472$	18.1195	+	19.2520i	0.834020	+	0.886144i
$473$			43.0377i			1.97887i
$474$	10.1027	+	22.2490i	0.464030	+	1.02193i
$475$	−0.810340	+	1.40355i	−0.0371810	+	0.0643993i
$476$	−4.88421	+	1.66680i	−0.223867	+	0.0763978i
$477$	−14.4090	−	8.31901i	−0.659741	−	0.380901i
$478$	−2.96559	−	0.289657i	−0.135643	−	0.0132486i
$479$	1.01749	−	0.587451i	0.0464905	−	0.0268413i	−0.476575	−	0.879134i	$-0.658122\pi$
$479$	1.01749	−	0.587451i	0.0464905	−	0.0268413i	0.523065	+	0.852293i	$0.324788\pi$
$480$	0.242336	+	6.58599i	0.0110611	+	0.300608i
$481$	2.51274	−	2.95607i	0.114571	−	0.134785i
$482$	−11.8614	+	16.5809i	−0.540271	+	0.755240i
$483$	0.523245	+	0.906286i	0.0238085	+	0.0412375i
$484$	6.96259	−	7.96533i	0.316481	−	0.362060i
$485$	9.80772	+	5.66249i	0.445345	+	0.257120i
$486$	−12.0349	+	16.8235i	−0.545915	+	0.763130i
$487$	12.8997	+	7.44763i	0.584540	+	0.337484i	0.762936	−	0.646475i	$-0.223757\pi$
$487$	12.8997	+	7.44763i	0.584540	+	0.337484i	−0.178396	+	0.983959i	$0.557091\pi$
$488$	−0.378550	+	0.356283i	−0.0171361	+	0.0161282i
$489$			8.14199i			0.368194i
$490$	−7.95050	+	3.61010i	−0.359167	+	0.163088i
$491$	29.0986	−	16.8001i	1.31320	−	0.758178i	0.330578	−	0.943779i	$-0.392756\pi$
$491$	29.0986	−	16.8001i	1.31320	−	0.758178i	0.982625	+	0.185600i	$0.0594230\pi$
$492$	13.6108	−	15.5710i	0.613621	−	0.701994i
$493$		−	25.8150i		−	1.16265i
$494$	−2.27006	+	7.94598i	−0.102135	+	0.357506i
$495$	−6.62997			−0.297995
$496$	−5.84557	+	14.2429i	−0.262474	+	0.639527i
$497$	2.24333	+	3.88557i	0.100627	+	0.174292i
$498$	10.0997	+	22.2424i	0.452577	+	0.996708i
$499$	−17.4987			−0.783349			−0.391674	−	0.920104i	$-0.628104\pi$
$499$	−17.4987			−0.783349			−0.391674	+	0.920104i	$0.628104\pi$
$500$	1.96220	+	0.386999i	0.0877523	+	0.0173071i
$501$	−4.28729	+	7.42580i	−0.191542	+	0.331760i
$502$	2.25997	−	3.15920i	0.100868	−	0.141002i
$503$	−7.33267	+	12.7006i	−0.326948	+	0.566290i	−0.981905	−	0.189376i	$-0.939353\pi$
$503$	−7.33267	+	12.7006i	−0.326948	+	0.566290i	0.654957	+	0.755666i	$0.272687\pi$
$504$	0.968714	+	4.10936i	0.0431500	+	0.183045i
$505$	−15.2516	+	8.80549i	−0.678685	+	0.391839i
$506$	−4.58891	−	3.28274i	−0.204002	−	0.145935i
$507$	5.36115	−	14.1649i	0.238097	−	0.629084i
$508$	−6.63241	−	19.4348i	−0.294265	−	0.862282i
$509$	17.8928	+	30.9912i	0.793084	+	1.37366i	0.924048	+	0.382275i	$0.124859\pi$
$509$	17.8928	+	30.9912i	0.793084	+	1.37366i	−0.130964	+	0.991387i	$0.541807\pi$
$510$	4.65652	+	0.454815i	0.206194	+	0.0201395i
$511$	2.47437	−	4.28574i	0.109460	−	0.189590i
$512$	−17.3860	+	14.4819i	−0.768360	+	0.640017i
$513$	7.59167	+	4.38305i	0.335180	+	0.193516i
$514$	8.44192	−	3.83324i	0.372357	−	0.169077i
$515$	4.00462			0.176465
$516$	−24.3767	−	4.80775i	−1.07313	−	0.211649i
$517$	−40.3943	+	23.3217i	−1.77654	+	1.02569i
$518$	−1.37626	−	0.134423i	−0.0604693	−	0.00590620i
$519$	−15.6816			−0.688347
$520$	10.1850	−	0.515771i	0.446641	−	0.0226180i
$521$	33.7099			1.47686			0.738428	−	0.674332i	$-0.235568\pi$
$521$	33.7099			1.47686			0.738428	+	0.674332i	$0.235568\pi$
$522$	−21.0190	−	2.05299i	−0.919978	−	0.0898568i
$523$	3.92771	−	2.26767i	0.171747	−	0.0991581i	−0.411662	−	0.911336i	$-0.635052\pi$
$523$	3.92771	−	2.26767i	0.171747	−	0.0991581i	0.583409	+	0.812178i	$0.301718\pi$
$524$	1.94427	−	9.85804i	0.0849360	−	0.430651i
$525$	−1.05866			−0.0462039
$526$	−1.05707	+	0.479984i	−0.0460903	+	0.0209283i
$527$	9.46548	+	5.46490i	0.412323	+	0.238055i
$528$	11.4983	+	14.8847i	0.500399	+	0.647771i
$529$	11.0114	−	19.0724i	0.478758	−	0.829233i
$530$	14.2561	+	1.39243i	0.619244	+	0.0604833i
$531$	−7.67724	−	13.2974i	−0.333164	−	0.577056i
$532$	2.78755	−	0.951292i	0.120856	−	0.0412437i
$533$	−24.3832	−	20.7263i	−1.05615	−	0.897757i
$534$	3.70390	+	2.64963i	0.160283	+	0.114661i
$535$	−10.4667	+	6.04294i	−0.452514	+	0.261259i
$536$	−31.6322	+	7.45676i	−1.36630	+	0.322083i
$537$	−3.80172	+	6.58477i	−0.164056	+	0.284154i
$538$	14.6972	−	20.5452i	0.633643	−	0.885764i
$539$	−12.4598	+	21.5811i	−0.536683	+	0.929563i
$540$	2.09324	−	10.6134i	0.0900788	−	0.456726i
$541$	−28.0708			−1.20686			−0.603430	−	0.797416i	$-0.706200\pi$
$541$	−28.0708			−1.20686			−0.603430	+	0.797416i	$0.706200\pi$
$542$	5.41752	+	11.9310i	0.232702	+	0.512479i
$543$	−6.63052	−	11.4844i	−0.284543	−	0.492843i
$544$	8.53791	+	13.6067i	0.366060	+	0.583385i
$545$	4.69338			0.201042
$546$	−5.23652	+	1.31106i	−0.224102	+	0.0561080i
$547$		−	8.48845i		−	0.362940i	−0.983396	−	0.181470i	$-0.941914\pi$
$547$		−	8.48845i		−	0.362940i	0.983396	−	0.181470i	$-0.0580855\pi$
$548$	32.9023	+	28.7603i	1.40552	+	1.22858i
$549$	0.261465	−	0.150957i	0.0111590	−	0.00644268i
$550$	5.19715	−	2.35988i	0.221607	−	0.100626i
$551$			14.7334i			0.627662i
$552$	2.37199	−	2.23246i	0.100958	−	0.0950199i
$553$	−11.6711	−	6.73830i	−0.496305	−	0.286542i
$554$	−5.41502	+	7.56961i	−0.230062	+	0.321602i
$555$	1.08567	+	0.626814i	0.0460843	+	0.0266068i
$556$	−3.12035	−	2.72753i	−0.132332	−	0.115673i
$557$	−6.60522	−	11.4406i	−0.279872	−	0.484753i	0.691481	−	0.722395i	$-0.256959\pi$
$557$	−6.60522	−	11.4406i	−0.279872	−	0.484753i	−0.971353	+	0.237642i	$0.923625\pi$
$558$	5.20237	−	7.27235i	0.220234	−	0.307863i
$559$	−6.91759	+	37.8197i	−0.292583	+	1.59960i
$560$	−2.22205	−	2.87647i	−0.0938989	−	0.121553i
$561$	11.5637	−	6.67628i	0.488218	−	0.281873i
$562$	0.884211	+	0.0863633i	0.0372982	+	0.00364302i
$563$	13.6293	+	7.86886i	0.574405	+	0.331633i	0.758907	−	0.651199i	$-0.225734\pi$
$563$	13.6293	+	7.86886i	0.574405	+	0.331633i	−0.184502	+	0.982832i	$0.559067\pi$
$564$	−8.69703	−	25.4848i	−0.366211	−	1.07310i
$565$	−5.70070	+	9.87391i	−0.239830	+	0.415398i
$566$	−2.19691	−	4.83824i	−0.0923430	−	0.203366i
$567$			1.24811i			0.0524155i
$568$	10.1695	−	9.57135i	0.426704	−	0.401605i
$569$	17.8062	+	30.8412i	0.746475	+	1.29293i	0.949503	+	0.313759i	$0.101588\pi$
$569$	17.8062	+	30.8412i	0.746475	+	1.29293i	−0.203028	+	0.979173i	$0.565078\pi$
$570$	−2.65761	−	0.259576i	−0.111315	−	0.0108724i
$571$			22.5745i			0.944715i	0.881407	+	0.472357i	$0.156597\pi$
$571$			22.5745i			0.944715i	−0.881407	+	0.472357i	$0.843403\pi$
$572$	22.7844	−	18.1090i	0.952665	−	0.757174i
$573$		−	12.4522i		−	0.520200i
$574$	−1.10879	+	11.3521i	−0.0462799	+	0.473826i
$575$	−0.494250	−	0.856067i	−0.0206117	−	0.0357005i
$576$	11.7578	−	5.86961i	0.489910	−	0.244567i
$577$			5.11683i			0.213016i	0.994312	+	0.106508i	$0.0339670\pi$
$577$			5.11683i			0.213016i	−0.994312	+	0.106508i	$0.966033\pi$
$578$	−11.5071	+	5.22504i	−0.478631	+	0.217333i
$579$	7.80247	−	13.5143i	0.324260	−	0.561634i
$580$	17.2073	−	5.87223i	0.714494	−	0.243831i
$581$	−11.6676	−	6.73631i	−0.484055	−	0.279469i
$582$	−1.81386	+	18.5708i	−0.0751869	+	0.769784i
$583$	35.4025	−	20.4397i	1.46622	−	0.846524i
$584$	−14.7511	−	4.43556i	−0.610407	−	0.183545i
$585$	−5.82614	−	1.06566i	−0.240881	−	0.0440595i
$586$	23.4964	+	16.8084i	0.970626	+	0.694350i
$587$	−8.14685	−	14.1108i	−0.336256	−	0.582413i	0.647469	−	0.762092i	$-0.275828\pi$
$587$	−8.14685	−	14.1108i	−0.336256	−	0.582413i	−0.983725	+	0.179679i	$0.942494\pi$
$588$	−10.8317	−	9.46814i	−0.446693	−	0.390460i
$589$	−5.40221	−	3.11897i	−0.222594	−	0.128515i
$590$	10.7512	+	7.69099i	0.442619	+	0.316633i
$591$	−11.5542	−	6.67082i	−0.475276	−	0.274401i
$592$	0.575643	+	4.26549i	0.0236588	+	0.175311i
$593$		−	45.0181i		−	1.84867i	−0.381581	−	0.924335i	$-0.624620\pi$
$593$		−	45.0181i		−	1.84867i	0.381581	−	0.924335i	$-0.375380\pi$
$594$	−12.7644	−	28.1109i	−0.523728	−	1.15340i
$595$	−2.23469	+	1.29020i	−0.0916132	+	0.0528929i
$596$	2.83359	−	3.24168i	0.116068	−	0.132784i
$597$			11.6066i			0.475025i
$598$	−3.50489	−	3.62232i	−0.143326	−	0.148128i
$599$	17.8885			0.730903			0.365452	−	0.930830i	$-0.380915\pi$
$599$	17.8885			0.730903			0.365452	+	0.930830i	$0.380915\pi$
$600$	0.756071	+	3.20731i	0.0308665	+	0.130938i
$601$	−17.9649	−	31.1161i	−0.732803	−	1.26925i	−0.955681	−	0.294406i	$-0.904878\pi$
$601$	−17.9649	−	31.1161i	−0.732803	−	1.26925i	0.222877	−	0.974846i	$-0.428455\pi$
$602$	12.4772	−	5.66557i	0.508535	−	0.230911i
$603$	18.8748			0.768641
$604$	2.86324	−	14.5175i	0.116504	−	0.590708i
$605$	2.64485	−	4.58102i	0.107529	−	0.186245i
$606$	−23.5993	−	16.8821i	−0.958656	−	0.685788i
$607$	−4.90763	+	8.50026i	−0.199194	+	0.345015i	−0.948267	−	0.317473i	$-0.897166\pi$
$607$	−4.90763	+	8.50026i	−0.199194	+	0.345015i	0.749073	+	0.662487i	$0.230499\pi$
$608$	−4.87282	−	7.76575i	−0.197619	−	0.314943i
$609$	−8.33475	+	4.81207i	−0.337741	+	0.194995i
$610$	−0.151227	+	0.211399i	−0.00612302	+	0.00855931i
$611$	−39.2454	+	14.0014i	−1.58770	+	0.566435i
$612$	−3.01316	−	8.82940i	−0.121800	−	0.356907i
$613$	7.95475	+	13.7780i	0.321289	+	0.556489i	0.980754	−	0.195246i	$-0.0625505\pi$
$613$	7.95475	+	13.7780i	0.321289	+	0.556489i	−0.659465	+	0.751735i	$0.729217\pi$
$614$	−3.99312	+	40.8826i	−0.161149	+	1.64989i
$615$	5.17028	−	8.95518i	0.208486	−	0.361108i
$616$	−9.93398	−	2.98707i	−0.400252	−	0.120353i
$617$	−29.7504	−	17.1764i	−1.19771	−	0.691496i	−0.237663	−	0.971348i	$-0.576381\pi$
$617$	−29.7504	−	17.1764i	−1.19771	−	0.691496i	−0.960043	+	0.279852i	$0.909715\pi$
$618$	2.72794	+	6.00772i	0.109734	+	0.241666i
$619$	36.9709			1.48599			0.742994	−	0.669298i	$-0.233405\pi$
$619$	36.9709			1.48599			0.742994	+	0.669298i	$0.233405\pi$
$620$	−1.48955	+	7.55244i	−0.0598216	+	0.303313i
$621$	−4.63038	+	2.67335i	−0.185811	+	0.107278i
$622$	−4.07441	+	41.7149i	−0.163369	+	1.67262i
$623$	−2.51166			−0.100628
$624$	7.71175	+	14.9282i	0.308717	+	0.597605i
$625$	1.00000			0.0400000
$626$	−2.92772	+	29.9748i	−0.117015	+	1.19803i
$627$	−6.59970	+	3.81034i	−0.263567	+	0.152170i
$628$	3.02450	−	15.3351i	0.120691	−	0.611938i
$629$	3.05560			0.121835
$630$	0.872783	+	1.92212i	0.0347725	+	0.0765793i
$631$	22.4180	+	12.9431i	0.892448	+	0.515255i	0.874742	−	0.484588i	$-0.161030\pi$
$631$	22.4180	+	12.9431i	0.892448	+	0.515255i	0.0177056	+	0.999843i	$0.494364\pi$
$632$	−12.0791	+	40.1709i	−0.480480	+	1.59791i
$633$	2.50358	−	4.33632i	0.0995083	−	0.172353i
$634$	1.88554	−	19.3047i	0.0748843	−	0.766686i
$635$	−5.13384	−	8.89208i	−0.203730	−	0.352871i
$636$	7.62228	+	22.3355i	0.302243	+	0.885659i
$637$	−14.4180	+	16.9618i	−0.571261	+	0.672052i
$638$	30.1900	−	42.2024i	1.19523	−	1.67081i
$639$	−7.02411	+	4.05537i	−0.277870	+	0.160428i
$640$	−7.12759	+	8.78621i	−0.281743	+	0.347305i
$641$	−22.0205	+	38.1406i	−0.869757	+	1.50646i	−0.00751163	+	0.999972i	$0.502391\pi$
$641$	−22.0205	+	38.1406i	−0.869757	+	1.50646i	−0.862245	+	0.506491i	$0.830942\pi$
$642$	−16.1955	−	11.5857i	−0.639185	−	0.457249i
$643$	−3.63461	+	6.29534i	−0.143335	+	0.248264i	−0.928751	−	0.370705i	$-0.879116\pi$
$643$	−3.63461	+	6.29534i	−0.143335	+	0.248264i	0.785415	+	0.618969i	$0.212449\pi$
$644$	−0.347620	+	1.76254i	−0.0136982	+	0.0694537i
$645$	−12.4232			−0.489161
$646$	−5.92617	+	2.69091i	−0.233162	+	0.105872i
$647$	22.3305	+	38.6775i	0.877902	+	1.52057i	0.853639	+	0.520865i	$0.174391\pi$
$647$	22.3305	+	38.6775i	0.877902	+	1.52057i	0.0242628	+	0.999706i	$0.492276\pi$
$648$	3.78124	−	0.891366i	0.148541	−	0.0350162i
$649$	37.7256			1.48086
$650$	4.94635	−	1.23841i	0.194012	−	0.0485743i
$651$		−	4.07476i		−	0.159702i
$652$	−9.19877	+	10.5236i	−0.360252	+	0.412134i
$653$	28.1392	−	16.2462i	1.10117	−	0.635762i	0.164643	−	0.986353i	$-0.447353\pi$
$653$	28.1392	−	16.2462i	1.10117	−	0.635762i	0.936528	+	0.350592i	$0.114019\pi$
$654$	3.19712	+	7.04099i	0.125017	+	0.275325i
$655$		−	5.02397i		−	0.196303i
$656$	35.1840	−	4.74820i	1.37370	−	0.185386i
$657$	7.74752	+	4.47303i	0.302259	+	0.174510i
$658$	12.0789	+	8.64078i	0.470884	+	0.336853i
$659$	25.1640	+	14.5284i	0.980251	+	0.565948i	0.902346	−	0.431013i	$-0.141844\pi$
$659$	25.1640	+	14.5284i	0.980251	+	0.565948i	0.0779048	+	0.996961i	$0.475177\pi$
$660$	7.08057	+	6.18921i	0.275611	+	0.240915i
$661$	−3.00066	−	5.19730i	−0.116712	−	0.202151i	0.801751	−	0.597659i	$-0.203902\pi$
$661$	−3.00066	−	5.19730i	−0.116712	−	0.202151i	−0.918463	+	0.395507i	$0.870569\pi$
$662$	−27.1362	−	19.4123i	−1.05468	−	0.754479i
$663$	11.2348	−	4.00817i	0.436322	−	0.155664i
$664$	−12.0755	+	40.1590i	−0.468620	+	1.55847i
$665$	1.27540	−	0.736352i	0.0494578	−	0.0285545i
$666$	0.243002	−	2.48792i	0.00941615	−	0.0964050i
$667$	−7.78237	−	4.49315i	−0.301335	−	0.173976i
$668$	−13.9310	+	4.75413i	−0.539005	+	0.183943i
$669$	−4.23359	+	7.33279i	−0.163680	+	0.283502i
$670$	−14.7957	+	6.71832i	−0.571609	+	0.259551i
$671$			0.741796i			0.0286367i
$672$	2.80162	−	5.29297i	0.108075	−	0.204181i
$673$	−3.97923	−	6.89223i	−0.153388	−	0.265676i	0.779083	−	0.626921i	$-0.215685\pi$
$673$	−3.97923	−	6.89223i	−0.153388	−	0.265676i	−0.932471	+	0.361245i	$0.882352\pi$
$674$	−1.41563	+	14.4936i	−0.0545282	+	0.558274i
$675$		−	5.40891i		−	0.208189i
$676$	22.9327	−	12.2512i	0.882027	−	0.471199i
$677$		−	34.9163i		−	1.34194i	−0.741483	−	0.670972i	$-0.765877\pi$
$677$		−	34.9163i		−	1.34194i	0.741483	−	0.670972i	$-0.234123\pi$
$678$	−18.6961	−	1.82610i	−0.718020	−	0.0701310i
$679$	−5.14547	−	8.91222i	−0.197465	−	0.342020i
$680$	5.50472	+	5.84875i	0.211096	+	0.224289i
$681$		−	2.59985i		−	0.0996264i
$682$	9.08309	+	20.0036i	0.347810	+	0.765979i
$683$	8.39031	−	14.5324i	0.321046	−	0.556068i	−0.659658	−	0.751566i	$-0.729299\pi$
$683$	8.39031	−	14.5324i	0.321046	−	0.556068i	0.980704	+	0.195498i	$0.0626322\pi$
$684$	1.71969	+	5.03919i	0.0657541	+	0.192678i
$685$	18.9228	+	10.9251i	0.723003	+	0.417426i
$686$	16.8499	+	1.64578i	0.643333	+	0.0628361i
$687$	−6.00880	+	3.46918i	−0.229250	+	0.132358i
$688$	−26.0753	−	33.7547i	−0.994110	−	1.28689i
$689$	34.3956	−	12.2711i	1.31037	−	0.467493i
$690$	0.947588	−	1.32462i	0.0360740	−	0.0504276i
$691$	1.56844	+	2.71661i	0.0596661	+	0.103345i	0.894316	−	0.447437i	$-0.147663\pi$
$691$	1.56844	+	2.71661i	0.0596661	+	0.103345i	−0.834649	+	0.550782i	$0.814330\pi$
$692$	−20.2686	−	17.7170i	−0.770495	−	0.673499i
$693$	5.21747	+	3.01231i	0.198195	+	0.114428i
$694$	8.23132	−	11.5065i	0.312456	−	0.436780i
$695$	−1.79457	−	1.03610i	−0.0680721	−	0.0393014i
$696$	20.5311	+	21.8142i	0.778228	+	0.826865i
$697$		−	25.2041i		−	0.954675i
$698$	28.1257	−	12.7711i	1.06457	−	0.483393i
$699$	−1.00387	+	0.579583i	−0.0379698	+	0.0219219i
$700$	−1.36833	−	1.19607i	−0.0517179	−	0.0452072i
$701$			15.2711i			0.576782i	0.957513	+	0.288391i	$0.0931203\pi$
$701$			15.2711i			0.576782i	−0.957513	+	0.288391i	$0.906880\pi$
$702$	−6.69842	−	26.7543i	−0.252816	−	1.00978i
$703$	−1.74392			−0.0657731
$704$	−1.95499	+	32.2292i	−0.0736815	+	1.21468i
$705$	−6.73198	−	11.6601i	−0.253541	−	0.439146i
$706$	3.12631	+	6.88505i	0.117660	+	0.259122i
$707$	16.0030			0.601855
$708$	−4.21434	+	21.3680i	−0.158385	+	0.803058i
$709$	−3.41446	+	5.91402i	−0.128233	+	0.222106i	−0.922992	−	0.384819i	$-0.874264\pi$
$709$	−3.41446	+	5.91402i	−0.128233	+	0.222106i	0.794759	+	0.606925i	$0.207597\pi$
$710$	4.06264	−	5.67913i	0.152468	−	0.213134i
$711$	12.1811	−	21.0983i	0.456828	−	0.791249i
$712$	1.79377	+	7.60930i	0.0672243	+	0.285171i
$713$	3.29497	−	1.90235i	0.123398	−	0.0712436i
$714$	−3.45781	−	2.47359i	−0.129405	−	0.0925719i
$715$	9.42486	−	11.0877i	0.352470	−	0.414658i
$716$	−12.3532	+	4.21569i	−0.461660	+	0.157548i
$717$	−1.22735	−	2.12583i	−0.0458362	−	0.0793906i
$718$	21.5709	+	2.10689i	0.805020	+	0.0786286i
$719$	1.44358	−	2.50036i	0.0538366	−	0.0932477i	−0.837851	−	0.545899i	$-0.816188\pi$
$719$	1.44358	−	2.50036i	0.0538366	−	0.0932477i	0.891688	+	0.452651i	$0.149522\pi$
$720$	5.19993	−	4.01691i	0.193790	−	0.149701i
$721$	−3.15144	−	1.81949i	−0.117366	−	0.0677612i
$722$	−21.0837	+	9.57353i	−0.784655	+	0.356290i
$723$	−16.7947			−0.624602
$724$	4.40502	−	22.3348i	0.163711	−	0.830065i
$725$	7.87290	−	4.54542i	0.292392	−	0.168813i
$726$	8.67411	+	0.847224i	0.321926	+	0.0314434i
$727$	43.6301			1.61815			0.809075	−	0.587705i	$-0.199968\pi$
$727$	43.6301			1.61815			0.809075	+	0.587705i	$0.199968\pi$
$728$	−8.24944	−	4.22163i	−0.305745	−	0.156464i
$729$	−21.1610			−0.783740
$730$	−7.66532	−	0.748693i	−0.283706	−	0.0277104i
$731$	−26.2235	+	15.1402i	−0.969912	+	0.559979i
$732$	−0.420157	−	0.0828662i	−0.0155294	−	0.00306282i
$733$	−0.536145			−0.0198030			−0.00990149	−	0.999951i	$-0.503152\pi$
$733$	−0.536145			−0.0198030			−0.00990149	+	0.999951i	$0.503152\pi$
$734$	44.9979	−	20.4323i	1.66090	−	0.754169i
$735$	−6.22955	−	3.59663i	−0.229780	−	0.132664i
$736$	5.58802	−	0.205615i	0.205977	−	0.00757907i
$737$	−23.1875	+	40.1619i	−0.854123	+	1.47938i
$738$	−20.5216	−	2.00441i	−0.755412	−	0.0737832i
$739$	−25.8337	−	44.7452i	−0.950307	−	1.64598i	−0.744760	−	0.667333i	$-0.767436\pi$
$739$	−25.8337	−	44.7452i	−0.950307	−	1.64598i	−0.205547	−	0.978647i	$-0.565897\pi$
$740$	0.695067	+	2.03675i	0.0255512	+	0.0748723i
$741$	−6.41199	+	2.28757i	−0.235550	+	0.0840361i
$742$	−10.5862	−	7.57299i	−0.388632	−	0.278013i
$743$	6.05907	−	3.49821i	0.222286	−	0.128337i	−0.384722	−	0.923032i	$-0.625703\pi$
$743$	6.05907	−	3.49821i	0.222286	−	0.128337i	0.607008	+	0.794696i	$0.292369\pi$
$744$	−12.3448	+	2.91009i	−0.452583	+	0.106689i
$745$	1.07638	−	1.86435i	0.0394357	−	0.0683046i
$746$	−13.1533	+	18.3868i	−0.481575	+	0.673190i
$747$	12.1775	−	21.0921i	0.445552	−	0.771719i
$748$	22.4889	+	4.43542i	0.822276	+	0.162175i
$749$	10.9824			0.401287
$750$	0.681198	+	1.50020i	0.0248738	+	0.0547795i
$751$	−17.9187	−	31.0362i	−0.653864	−	1.13253i	−0.982177	−	0.187957i	$-0.939814\pi$
$751$	−17.9187	−	31.0362i	−0.653864	−	1.13253i	0.328313	−	0.944569i	$-0.393520\pi$
$752$	17.5516	−	42.7650i	0.640040	−	1.55948i
$753$	3.19993			0.116612
$754$	33.3130	−	32.2331i	1.21319	−	1.17386i
$755$		−	7.39857i		−	0.269261i
$756$	−6.46943	+	7.40115i	−0.235291	+	0.269177i
$757$	2.11175	−	1.21922i	0.0767528	−	0.0443133i	−0.461132	−	0.887331i	$-0.652557\pi$
$757$	2.11175	−	1.21922i	0.0767528	−	0.0443133i	0.537885	+	0.843018i	$0.319223\pi$
$758$	−0.929428	+	0.422027i	−0.0337584	+	0.0153287i
$759$		−	4.64808i		−	0.168715i
$760$	−3.14170	−	3.33805i	−0.113961	−	0.121084i
$761$	−20.1359	−	11.6254i	−0.729924	−	0.421422i	0.0884703	−	0.996079i	$-0.471802\pi$
$761$	−20.1359	−	11.6254i	−0.729924	−	0.421422i	−0.818394	+	0.574657i	$0.805135\pi$
$762$	9.84272	−	13.7590i	0.356564	−	0.498438i
$763$	−3.69346	−	2.13242i	−0.133712	−	0.0771989i
$764$	14.0685	−	16.0946i	0.508979	−	0.582281i
$765$	−2.33235	−	4.03974i	−0.0843262	−	0.146057i
$766$	28.4058	−	39.7083i	1.02634	−	1.43472i
$767$	33.1517	+	6.06377i	1.19704	+	0.218950i
$768$	−18.0364	−	4.70765i	−0.650831	−	0.169873i
$769$	−8.79396	+	5.07719i	−0.317118	+	0.183088i	−0.650107	−	0.759842i	$-0.725276\pi$
$769$	−8.79396	+	5.07719i	−0.317118	+	0.183088i	0.332989	+	0.942931i	$0.391943\pi$
$770$	−5.16212	−	0.504198i	−0.186030	−	0.0181700i
$771$	6.61459	+	3.81894i	0.238219	+	0.137536i
$772$	25.3531	−	8.65209i	0.912477	−	0.311395i
$773$	9.56785	−	16.5720i	0.344132	−	0.596054i	−0.641064	−	0.767488i	$-0.721507\pi$
$773$	9.56785	−	16.5720i	0.344132	−	0.596054i	0.985196	+	0.171434i	$0.0548400\pi$
$774$	10.2419	+	22.5557i	0.368137	+	0.810747i
$775$			3.84896i			0.138259i
$776$	−23.3256	+	21.9535i	−0.837339	+	0.788086i
$777$	−0.569582	−	0.986545i	−0.0204336	−	0.0353921i
$778$	39.9651	+	3.90350i	1.43282	+	0.139947i
$779$			14.3847i			0.515386i
$780$	5.22730	+	6.57690i	0.187167	+	0.235491i
$781$		−	19.9279i		−	0.713078i
$782$	0.385897	−	3.95092i	0.0137997	−	0.141285i
$783$	−24.5858	−	42.5838i	−0.878623	−	1.52182i
$784$	−3.30302	−	24.4752i	−0.117965	−	0.874115i
$785$		−	7.81527i		−	0.278939i
$786$	7.53695	−	3.42232i	0.268834	−	0.122070i
$787$	7.67461	−	13.2928i	0.273570	−	0.473838i	−0.696203	−	0.717845i	$-0.745129\pi$
$787$	7.67461	−	13.2928i	0.273570	−	0.473838i	0.969773	+	0.244007i	$0.0784620\pi$
$788$	−7.39721	−	21.6759i	−0.263515	−	0.772173i
$789$	−0.828256	−	0.478194i	−0.0294867	−	0.0170241i
$790$	−2.03887	+	20.8745i	−0.0725397	+	0.742681i
$791$	8.97236	−	5.18020i	0.319021	−	0.184187i
$792$	5.39986	−	17.9581i	0.191876	−	0.638114i
$793$	−0.119231	+	0.651859i	−0.00423403	+	0.0231482i
$794$	−44.3532	−	31.7287i	−1.57404	−	1.12601i
$795$	5.90006	+	10.2192i	0.209254	+	0.362438i
$796$	−13.1130	+	15.0015i	−0.464778	+	0.531715i
$797$	31.2409	+	18.0369i	1.10661	+	0.638901i	0.937949	−	0.346773i	$-0.112723\pi$
$797$	31.2409	+	18.0369i	1.10661	+	0.638901i	0.168660	+	0.985674i	$0.446056\pi$
$798$	1.97347	+	1.41175i	0.0698601	+	0.0499754i
$799$	−28.4205	−	16.4086i	−1.00544	−	0.580494i
$800$	−2.64637	+	4.99967i	−0.0935635	+	0.176765i
$801$		−	4.54045i		−	0.160429i
$802$	−16.6918	−	36.7603i	−0.589409	−	1.29805i
$803$	−19.0355	+	10.9901i	−0.671748	+	0.387834i
$804$	−20.1576	−	17.6200i	−0.710904	−	0.621410i
$805$			0.898245i			0.0316590i
$806$	4.76658	+	19.0383i	0.167896	+	0.670596i
$807$	20.8101			0.732549
$808$	−11.4289	−	48.4825i	−0.402069	−	1.70561i
$809$	10.4156	+	18.0404i	0.366194	+	0.634266i	0.988967	−	0.148136i	$-0.0473274\pi$
$809$	10.4156	+	18.0404i	0.366194	+	0.634266i	−0.622773	+	0.782402i	$0.713994\pi$
$810$	1.76865	−	0.803094i	0.0621440	−	0.0282179i
$811$	37.5696			1.31925			0.659624	−	0.751596i	$-0.270716\pi$
$811$	37.5696			1.31925			0.659624	+	0.751596i	$0.270716\pi$
$812$	−16.2094	−	3.19692i	−0.568837	−	0.112190i
$813$	−5.39730	+	9.34840i	−0.189292	+	0.327863i
$814$	4.99529	+	3.57345i	0.175085	+	0.125249i
$815$	−3.49430	+	6.05231i	−0.122400	+	0.212003i
$816$	−5.02448	+	12.2423i	−0.175892	+	0.428567i
$817$	14.9665	−	8.64091i	0.523611	−	0.302307i
$818$	−15.2630	+	21.3360i	−0.533659	+	0.745997i
$819$	4.10071	+	3.48571i	0.143291	+	0.121801i
$820$	16.8001	−	5.73327i	0.586685	−	0.200214i
$821$	−11.8999	−	20.6113i	−0.415311	−	0.719340i	0.580150	−	0.814510i	$-0.302994\pi$
$821$	−11.8999	−	20.6113i	−0.415311	−	0.719340i	−0.995461	+	0.0951699i	$0.969661\pi$
$822$	−3.49962	+	35.8301i	−0.122063	+	1.24972i
$823$	−8.43345	+	14.6072i	−0.293971	+	0.509173i	−0.974745	−	0.223320i	$-0.928310\pi$
$823$	−8.43345	+	14.6072i	−0.293971	+	0.509173i	0.680774	+	0.732494i	$0.261644\pi$
$824$	−3.26161	+	10.8470i	−0.113624	+	0.377873i
$825$	4.07218	+	2.35108i	0.141775	+	0.0818539i
$826$	−4.96628	−	10.9372i	−0.172799	−	0.380554i
$827$	−33.9126			−1.17926			−0.589628	−	0.807675i	$-0.700726\pi$
$827$	−33.9126			−1.17926			−0.589628	+	0.807675i	$0.700726\pi$
$828$	−3.18622	−	0.628408i	−0.110729	−	0.0218387i
$829$	19.0146	−	10.9781i	0.660404	−	0.381284i	−0.132027	−	0.991246i	$-0.542149\pi$
$829$	19.0146	−	10.9781i	0.660404	−	0.381284i	0.792431	+	0.609962i	$0.208815\pi$
$830$	−2.03826	+	20.8683i	−0.0707492	+	0.724349i
$831$	−7.66721			−0.265973
$832$	−6.89826	+	28.0074i	−0.239154	+	0.970982i
$833$	−17.5329			−0.607479
$834$	0.331892	−	3.39800i	0.0114925	−	0.117663i
$835$	−6.37387	+	3.67996i	−0.220577	+	0.127350i
$836$	−12.8350	−	2.53142i	−0.443909	−	0.0875509i
$837$	20.8187			0.719599
$838$	−9.85890	−	21.7122i	−0.340570	−	0.750036i
$839$	−10.2135	−	5.89678i	−0.352610	−	0.203579i	0.313224	−	0.949679i	$-0.398591\pi$
$839$	−10.2135	−	5.89678i	−0.352610	−	0.203579i	−0.665834	+	0.746100i	$0.731924\pi$
$840$	0.862242	−	2.86752i	0.0297502	−	0.0989389i
$841$	26.8217	−	46.4566i	0.924888	−	1.60195i
$842$	3.82564	−	39.1679i	0.131840	−	1.34982i
$843$	0.365942	+	0.633831i	0.0126037	+	0.0218303i
$844$	8.13503	−	2.77619i	0.280019	−	0.0955605i
$845$	10.0643	−	8.22855i	0.346224	−	0.283071i
$846$	−15.6203	+	21.8355i	−0.537038	+	0.750721i
$847$	−4.16275	+	2.40336i	−0.143034	+	0.0825806i
$848$	−15.3826	+	37.4803i	−0.528241	+	1.28708i
$849$	2.18871	−	3.79096i	0.0751164	−	0.130105i
$850$	3.26621	+	2.33653i	0.112030	+	0.0801422i
$851$	0.531833	−	0.921162i	0.0182310	−	0.0315770i
$852$	11.2873	+	2.22616i	0.386696	+	0.0762669i
$853$	−18.9735			−0.649639			−0.324819	−	0.945776i	$-0.605304\pi$
$853$	−18.9735			−0.649639			−0.324819	+	0.945776i	$0.605304\pi$
$854$	0.215057	−	0.0976515i	0.00735911	−	0.00334157i
$855$	1.33114	+	2.30559i	0.0455239	+	0.0788497i
$856$	−7.84334	−	33.2720i	−0.268080	−	1.13722i
$857$	19.7085			0.673230			0.336615	−	0.941642i	$-0.390718\pi$
$857$	19.7085			0.673230			0.336615	+	0.941642i	$0.390718\pi$
$858$	23.0540	+	6.58622i	0.787051	+	0.224850i
$859$		−	28.7367i		−	0.980484i	−0.871586	−	0.490242i	$-0.836908\pi$
$859$		−	28.7367i		−	0.980484i	0.871586	−	0.490242i	$-0.163092\pi$
$860$	−16.0570	−	14.0356i	−0.547539	−	0.478610i
$861$	−8.13753	+	4.69820i	−0.277326	+	0.160114i
$862$	4.73369	+	10.4250i	0.161230	+	0.355076i
$863$			50.3093i			1.71255i	0.516523	+	0.856274i	$0.327226\pi$
$863$			50.3093i			1.71255i	−0.516523	+	0.856274i	$0.672774\pi$
$864$	27.0427	+	14.3140i	0.920013	+	0.486972i
$865$	−11.6569	−	6.73009i	−0.396345	−	0.228830i
$866$	−10.3208	−	7.38311i	−0.350715	−	0.250888i
$867$	−9.01626	−	5.20554i	−0.306208	−	0.176790i
$868$	4.60363	−	5.26664i	0.156257	−	0.178761i
$869$	29.9288	+	51.8382i	1.01526	+	1.75849i
$870$	12.1820	+	8.71458i	0.413010	+	0.295452i
$871$	−26.8316	+	31.5656i	−0.909153	+	1.06956i
$872$	−3.82258	+	12.7126i	−0.129449	+	0.430503i
$873$	16.1110	−	9.30170i	0.545275	−	0.314815i
$874$	−0.220242	+	2.25490i	−0.00744981	+	0.0762732i
$875$	−0.786953	−	0.454347i	−0.0266039	−	0.0153597i
$876$	−4.09841	−	12.0095i	−0.138472	−	0.405763i
$877$	1.27815	−	2.21383i	0.0431602	−	0.0747556i	−0.843638	−	0.536912i	$-0.819591\pi$
$877$	1.27815	−	2.21383i	0.0431602	−	0.0747556i	0.886799	+	0.462156i	$0.152924\pi$
$878$	−8.29169	+	3.76502i	−0.279831	+	0.127063i
$879$			23.7993i			0.802732i
$880$	2.15914	+	15.9992i	0.0727847	+	0.539332i
$881$	−19.1801	−	33.2209i	−0.646194	−	1.11924i	−0.984024	−	0.178034i	$-0.943026\pi$
$881$	−19.1801	−	33.2209i	−0.646194	−	1.11924i	0.337830	−	0.941207i	$-0.390307\pi$
$882$	−1.39434	+	14.2756i	−0.0469498	+	0.480684i
$883$			34.6311i			1.16543i	0.812677	+	0.582715i	$0.198010\pi$
$883$			34.6311i			1.16543i	−0.812677	+	0.582715i	$0.801990\pi$
$884$	19.0494	+	7.51237i	0.640700	+	0.252668i
$885$			10.8898i			0.366057i
$886$	−14.1091	−	1.37807i	−0.474004	−	0.0462973i
$887$	−7.48492	−	12.9643i	−0.251319	−	0.435297i	0.712570	−	0.701601i	$-0.247531\pi$
$887$	−7.48492	−	12.9643i	−0.251319	−	0.435297i	−0.963889	+	0.266304i	$0.914198\pi$
$888$	−2.58204	+	2.43017i	−0.0866477	+	0.0815510i
$889$			9.33019i			0.312925i
$890$	1.61613	+	3.55920i	0.0541729	+	0.119305i
$891$	2.77179	−	4.80088i	0.0928584	−	0.160835i
$892$	−13.7565	+	4.69458i	−0.460601	+	0.157186i
$893$	16.2204	+	9.36483i	0.542794	+	0.313382i
$894$	3.53013	+	0.344798i	0.118065	+	0.0115318i
$895$	−5.65198	+	3.26317i	−0.188925	+	0.109076i
$896$	9.60106	−	3.67593i	0.320749	−	0.122804i
$897$	0.747101	−	4.08454i	0.0249450	−	0.136379i
$898$	33.6933	−	47.0996i	1.12436	−	1.57173i
$899$	17.4952	+	30.3025i	0.583497	+	1.01065i
$900$	2.16219	−	2.47359i	0.0720730	−	0.0824528i
$901$	24.9084	+	14.3809i	0.829819	+	0.479096i
$902$	29.4756	−	41.2037i	0.981431	−	1.37193i
$903$	9.77644	+	5.64443i	0.325339	+	0.187835i
$904$	−22.1017	−	23.4830i	−0.735092	−	0.781033i
$905$		−	11.3825i		−	0.378367i
$906$	11.0993	−	5.03989i	0.368750	−	0.167439i
$907$	−19.2725	+	11.1270i	−0.639933	+	0.369465i	−0.784589	−	0.620017i	$-0.787126\pi$
$907$	−19.2725	+	11.1270i	−0.639933	+	0.369465i	0.144656	+	0.989482i	$0.453792\pi$
$908$	2.93729	−	3.36032i	0.0974774	−	0.111516i
$909$			28.9293i			0.959526i
$910$	−4.45521	−	1.27279i	−0.147689	−	0.0421926i
$911$	−53.1442			−1.76075			−0.880374	−	0.474281i	$-0.842708\pi$
$911$	−53.1442			−1.76075			−0.880374	+	0.474281i	$0.842708\pi$
$912$	2.86761	−	6.98704i	0.0949562	−	0.231364i
$913$	29.9199	+	51.8228i	0.990205	+	1.71509i
$914$	−11.4979	−	25.3217i	−0.380316	−	0.837568i
$915$	−0.214125			−0.00707876
$916$	−11.6859	−	2.30477i	−0.386112	−	0.0761517i
$917$	−2.28263	+	3.95363i	−0.0753790	+	0.130560i
$918$	12.6380	−	17.6666i	0.417118	−	0.583085i
$919$	−15.4362	+	26.7363i	−0.509193	+	0.881948i	0.490750	+	0.871300i	$0.336723\pi$
$919$	−15.4362	+	26.7363i	−0.509193	+	0.881948i	−0.999943	+	0.0106477i	$0.996611\pi$
$920$	2.72131	−	0.641505i	0.0897190	−	0.0211498i
$921$	−29.3060	+	16.9198i	−0.965665	+	0.557527i
$922$	21.0589	+	15.0647i	0.693536	+	0.496130i
$923$	3.20308	−	17.5118i	0.105431	−	0.576409i
$924$	−2.76002	−	8.08766i	−0.0907981	−	0.266064i
$925$	0.538020	+	0.931878i	0.0176900	+	0.0306400i
$926$	48.9076	+	4.77694i	1.60720	+	0.156980i
$927$	3.28917	−	5.69701i	0.108030	−	0.187114i
$928$	1.89096	+	51.3908i	0.0620738	+	1.68699i
$929$	45.2262	+	26.1113i	1.48382	+	0.856685i	0.999831	−	0.0183871i	$-0.00585313\pi$
$929$	45.2262	+	26.1113i	1.48382	+	0.856685i	0.483992	+	0.875073i	$0.339186\pi$
$930$	−5.77421	+	2.62190i	−0.189344	+	0.0859756i
$931$	10.0065			0.327951
$932$	−1.95231	−	0.385049i	−0.0639501	−	0.0126127i
$933$	−29.9026	+	17.2643i	−0.978966	+	0.565206i
$934$	−17.7782	−	1.73645i	−0.581721	−	0.0568183i
$935$	11.4611			0.374817
$936$	7.63164	−	14.9129i	0.249448	−	0.487443i
$937$	60.8755			1.98871			0.994357	−	0.106082i	$-0.0338306\pi$
$937$	60.8755			1.98871			0.994357	+	0.106082i	$0.0338306\pi$
$938$	14.6960	+	1.43540i	0.479841	+	0.0468674i
$939$	−21.4869	+	12.4054i	−0.701197	+	0.404836i
$940$	4.47242	−	22.6765i	0.145874	−	0.739626i
$941$	38.6569			1.26018			0.630089	−	0.776523i	$-0.283019\pi$
$941$	38.6569			1.26018			0.630089	+	0.776523i	$0.283019\pi$
$942$	11.7245	−	5.32374i	0.382003	−	0.173457i
$943$	−7.59822	−	4.38683i	−0.247432	−	0.142855i
$944$	−29.5884	+	22.8569i	−0.963022	+	0.743927i
$945$	−2.45752	+	4.25655i	−0.0799432	+	0.138466i
$946$	−60.5762	−	5.91665i	−1.96950	−	0.192367i
$947$	−7.68675	−	13.3138i	−0.249786	−	0.432642i	0.713680	−	0.700471i	$-0.247027\pi$
$947$	−7.68675	−	13.3138i	−0.249786	−	0.432642i	−0.963466	+	0.267830i	$0.913694\pi$
$948$	−32.7047	+	11.1609i	−1.06220	+	0.362491i
$949$	−18.4941	+	6.59804i	−0.600343	+	0.214181i
$950$	−1.86412	−	1.33352i	−0.0604799	−	0.0432651i
$951$	13.8382	−	7.98948i	0.448734	−	0.259077i
$952$	−1.67459	−	7.10375i	−0.0542738	−	0.230234i
$953$	−22.6424	+	39.2178i	−0.733459	+	1.27039i	0.221937	+	0.975061i	$0.428762\pi$
$953$	−22.6424	+	39.2178i	−0.733459	+	1.27039i	−0.955396	+	0.295328i	$0.904571\pi$
$954$	13.6900	−	19.1372i	0.443231	−	0.619589i
$955$	5.34414	−	9.25631i	0.172932	−	0.299527i
$956$	0.815395	−	4.13429i	0.0263718	−	0.133713i
$957$	42.7465			1.38180
$958$	0.686965	+	1.51290i	0.0221948	+	0.0488796i
$959$	−9.92756	−	17.1950i	−0.320578	−	0.555257i
$960$	−9.30320	−	0.564324i	−0.300259	−	0.0182135i
$961$	16.1855			0.522112
$962$	3.81528	+	3.94311i	0.123010	+	0.127131i
$963$			19.8533i			0.639764i
$964$	−21.7072	−	18.9746i	−0.699143	−	0.611129i
$965$	11.5999	−	6.69719i	0.373413	−	0.215590i
$966$	−1.34755	+	0.611883i	−0.0433566	+	0.0196870i
$967$			33.4312i			1.07508i	0.843240	+	0.537538i	$0.180645\pi$
$967$			33.4312i			1.07508i	−0.843240	+	0.537538i	$0.819355\pi$
$968$	10.2541	+	10.8950i	0.329580	+	0.350178i
$969$	−4.64340	−	2.68087i	−0.149167	−	0.0861219i
$970$	−9.31837	+	13.0261i	−0.299195	+	0.418242i
$971$	1.69236	+	0.977085i	0.0543105	+	0.0313562i	0.526909	−	0.849921i	$-0.323351\pi$
$971$	1.69236	+	0.977085i	0.0543105	+	0.0313562i	−0.472599	+	0.881278i	$0.656684\pi$
$972$	−22.0248	−	19.2522i	−0.706447	−	0.617514i
$973$	0.941496	+	1.63072i	0.0301830	+	0.0522785i
$974$	−12.2560	+	17.1326i	−0.392709	+	0.548964i
$975$	3.20056	+	2.72056i	0.102500	+	0.0871277i
$976$	−0.449432	−	0.581795i	−0.0143860	−	0.0186228i
$977$	−4.71951	+	2.72481i	−0.150990	+	0.0871744i	−0.573592	−	0.819141i	$-0.694450\pi$
$977$	−4.71951	+	2.72481i	−0.150990	+	0.0871744i	0.422601	+	0.906316i	$0.361117\pi$
$978$	−11.4600	−	1.11933i	−0.366450	−	0.0357922i
$979$	9.66119	+	5.57789i	0.308773	+	0.178270i
$980$	−3.98827	−	11.6868i	−0.127401	−	0.373320i
$981$	3.85488	−	6.67684i	0.123077	−	0.213175i
$982$	19.6461	+	43.2664i	0.626931	+	1.38069i
$983$			22.4502i			0.716049i	0.933712	+	0.358024i	$0.116550\pi$
$983$			22.4502i			0.716049i	−0.933712	+	0.358024i	$0.883450\pi$
$984$	20.0452	+	21.2980i	0.639019	+	0.678956i
$985$	−5.72584	−	9.91745i	−0.182441	−	0.315996i
$986$	36.3350	+	3.54894i	1.15714	+	0.113021i
$987$			12.2346i			0.389432i
$988$	−10.8720	−	4.28752i	−0.345885	−	0.136404i
$989$			10.5407i			0.335175i
$990$	0.911462	−	9.33179i	0.0289682	−	0.296584i
$991$	−14.0325	−	24.3051i	−0.445758	−	0.772076i	0.552347	−	0.833615i	$-0.313733\pi$
$991$	−14.0325	−	24.3051i	−0.445758	−	0.772076i	−0.998105	+	0.0615388i	$0.980399\pi$
$992$	−19.2435	−	10.1858i	−0.610983	−	0.323399i
$993$		−	27.4861i		−	0.872246i
$994$	−5.77740	+	2.62336i	−0.183248	+	0.0832078i
$995$	−4.98119	+	8.62768i	−0.157914	+	0.273516i
$996$	−32.6951	+	11.1576i	−1.03598	+	0.353543i
$997$	−25.3938	−	14.6611i	−0.804229	−	0.464322i	0.0407187	−	0.999171i	$-0.487035\pi$
$997$	−25.3938	−	14.6611i	−0.804229	−	0.464322i	−0.844948	+	0.534849i	$0.820369\pi$
$998$	2.40565	−	24.6297i	0.0761495	−	0.779639i
$999$	5.04044	−	2.91010i	0.159472	−	0.0920715i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	520.2.ca.a.101.13	✓	56
8.5	even	2		520.2.ca.b.101.6	yes	56
13.4	even	6		520.2.ca.b.381.6	yes	56
104.69	even	6	inner	520.2.ca.a.381.13	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
520.2.ca.a.101.13	✓	56	1.1	even	1	trivial
520.2.ca.a.381.13	yes	56	104.69	even	6	inner
520.2.ca.b.101.6	yes	56	8.5	even	2
520.2.ca.b.381.6	yes	56	13.4	even	6

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:	\( N \)	\(=\)	\( 520 = 2^{3} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	520.ca (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.137476 + 1.40752i) q^{2} +(-1.00895 + 0.582519i) q^{3} +(-1.96220 - 0.386999i) q^{4} -1.00000 q^{5} +(-0.681198 - 1.50020i) q^{6} +(0.786953 + 0.454347i) q^{7} +(0.814463 - 2.70863i) q^{8} +(-0.821344 + 1.42261i) q^{9} +(0.137476 - 1.40752i) q^{10} +(-2.01803 - 3.49532i) q^{11} +(2.20520 - 0.752555i) q^{12} +(-1.21154 - 3.39590i) q^{13} +(-0.747688 + 1.04519i) q^{14} +(1.00895 - 0.582519i) q^{15} +(3.70046 + 1.51874i) q^{16} +(1.41984 - 2.45923i) q^{17} +(-1.88943 - 1.35163i) q^{18} +(-0.810340 + 1.40355i) q^{19} +(1.96220 + 0.386999i) q^{20} -1.05866 q^{21} +(5.19715 - 2.35988i) q^{22} +(-0.494250 - 0.856067i) q^{23} +(0.756071 + 3.20731i) q^{24} +1.00000 q^{25} +(4.94635 - 1.23841i) q^{26} -5.40891i q^{27} +(-1.36833 - 1.19607i) q^{28} +(7.87290 - 4.54542i) q^{29} +(0.681198 + 1.50020i) q^{30} +3.84896i q^{31} +(-2.64637 + 4.99967i) q^{32} +(4.07218 + 2.35108i) q^{33} +(3.26621 + 2.33653i) q^{34} +(-0.786953 - 0.454347i) q^{35} +(2.16219 - 2.47359i) q^{36} +(0.538020 + 0.931878i) q^{37} +(-1.86412 - 1.33352i) q^{38} +(3.20056 + 2.72056i) q^{39} +(-0.814463 + 2.70863i) q^{40} +(7.68661 - 4.43786i) q^{41} +(0.145541 - 1.49009i) q^{42} +(-9.23470 - 5.33166i) q^{43} +(2.60708 + 7.63950i) q^{44} +(0.821344 - 1.42261i) q^{45} +(1.27288 - 0.577977i) q^{46} -11.5567i q^{47} +(-4.61828 + 0.623254i) q^{48} +(-3.08714 - 5.34708i) q^{49} +(-0.137476 + 1.40752i) q^{50} +3.30832i q^{51} +(1.06307 + 7.13231i) q^{52} +10.1285i q^{53} +(7.61312 + 0.743594i) q^{54} +(2.01803 + 3.49532i) q^{55} +(1.87160 - 1.76151i) q^{56} -1.88815i q^{57} +(5.31542 + 11.7061i) q^{58} +(-4.67358 + 8.09488i) q^{59} +(-2.20520 + 0.752555i) q^{60} +(-0.159169 - 0.0918962i) q^{61} +(-5.41748 - 0.529140i) q^{62} +(-1.29272 + 0.746351i) q^{63} +(-6.67330 - 4.41215i) q^{64} +(1.21154 + 3.39590i) q^{65} +(-3.86900 + 5.40844i) q^{66} +(-5.74510 - 9.95080i) q^{67} +(-3.73772 + 4.27602i) q^{68} +(0.997350 + 0.575820i) q^{69} +(0.747688 - 1.04519i) q^{70} +(4.27599 + 2.46874i) q^{71} +(3.18436 + 3.38337i) q^{72} -5.44599i q^{73} +(-1.38560 + 0.629161i) q^{74} +(-1.00895 + 0.582519i) q^{75} +(2.13322 - 2.44045i) q^{76} -3.66754i q^{77} +(-4.26923 + 4.13083i) q^{78} -14.8307 q^{79} +(-3.70046 - 1.51874i) q^{80} +(0.686757 + 1.18950i) q^{81} +(5.18964 + 11.4291i) q^{82} -14.8263 q^{83} +(2.07731 + 0.409702i) q^{84} +(-1.41984 + 2.45923i) q^{85} +(8.77394 - 12.2650i) q^{86} +(-5.29559 + 9.17223i) q^{87} +(-11.1111 + 2.61926i) q^{88} +(-2.39372 + 1.38202i) q^{89} +(1.88943 + 1.35163i) q^{90} +(0.589495 - 3.22288i) q^{91} +(0.638521 + 1.87105i) q^{92} +(-2.24209 - 3.88342i) q^{93} +(16.2662 + 1.58876i) q^{94} +(0.810340 - 1.40355i) q^{95} +(-0.242336 - 6.58599i) q^{96} +(-9.80772 - 5.66249i) q^{97} +(7.95050 - 3.61010i) q^{98} +6.62997 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 6 q^{4} - 56 q^{5} - 5 q^{6} + 28 q^{9} + 8 q^{11} + 6 q^{12} - 4 q^{14} - 10 q^{16} - 18 q^{18} + 16 q^{19} + 6 q^{20} - 6 q^{22} + 12 q^{23} + 2 q^{24} + 56 q^{25} + 11 q^{26} + 6 q^{28} + 5 q^{30}+ \cdots + 48 q^{99}+O(q^{100}) \) 56 * q - 6 * q^4 - 56 * q^5 - 5 * q^6 + 28 * q^9 + 8 * q^11 + 6 * q^12 - 4 * q^14 - 10 * q^16 - 18 * q^18 + 16 * q^19 + 6 * q^20 - 6 * q^22 + 12 * q^23 + 2 * q^24 + 56 * q^25 + 11 * q^26 + 6 * q^28 + 5 * q^30 + 16 * q^34 - 21 * q^36 - 4 * q^37 - 24 * q^39 + 29 * q^42 - 24 * q^44 - 28 * q^45 - 11 * q^46 + 3 * q^48 + 20 * q^49 + 18 * q^52 - 49 * q^54 - 8 * q^55 + 61 * q^56 - 47 * q^58 + 16 * q^59 - 6 * q^60 - 2 * q^62 - 30 * q^64 + 14 * q^66 + 36 * q^67 + 33 * q^68 + 4 * q^70 - 51 * q^72 - 2 * q^74 - 48 * q^76 - 35 * q^78 + 10 * q^80 - 28 * q^81 - 21 * q^82 - 40 * q^83 - 61 * q^84 + 28 * q^86 - 36 * q^87 + 41 * q^88 + 18 * q^90 - 16 * q^91 - 18 * q^92 - 41 * q^94 - 16 * q^95 + 48 * q^96 + 24 * q^97 + 28 * q^98 + 48 * q^99

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