LMFDB - Embedded newform 374.2.g.b.69.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [374,2,Mod(69,374)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("374.69"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(374, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([8, 0])) N = Newforms(chi, 2, names="a")

Level:	$N$	$=$	$374 = 2 \cdot 11 \cdot 17$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	374.g (of order $5$ , degree $4$ , minimal)

Newform invariants

comment:select newform

sage:traces = [4,-1,-2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$2.98640503560$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{10})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$x^{4} - x^{3} + x^{2} - x + 1$ x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$1$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			69.1
Root			$0.809017 + 0.587785i$ of defining polynomial
Character	$\chi$	$=$	374.69
Dual form			374.2.g.b.103.1

$q$ -expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.809017 + 0.587785i) q^{2} +(-0.500000 - 1.53884i) q^{3} +(0.309017 - 0.951057i) q^{4} +(-0.809017 - 0.587785i) q^{5} +(1.30902 + 0.951057i) q^{6} +(-0.118034 + 0.363271i) q^{7} +(0.309017 + 0.951057i) q^{8} +(0.309017 - 0.224514i) q^{9} +1.00000 q^{10} +(0.309017 - 3.30220i) q^{11} -1.61803 q^{12} +(-2.11803 + 1.53884i) q^{13} +(-0.118034 - 0.363271i) q^{14} +(-0.500000 + 1.53884i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(-0.809017 - 0.587785i) q^{17} +(-0.118034 + 0.363271i) q^{18} +(-0.927051 - 2.85317i) q^{19} +(-0.809017 + 0.587785i) q^{20} +0.618034 q^{21} +(1.69098 + 2.85317i) q^{22} -8.47214 q^{23} +(1.30902 - 0.951057i) q^{24} +(-1.23607 - 3.80423i) q^{25} +(0.809017 - 2.48990i) q^{26} +(-4.42705 - 3.21644i) q^{27} +(0.309017 + 0.224514i) q^{28} +(-1.16312 + 3.57971i) q^{29} +(-0.500000 - 1.53884i) q^{30} +(-2.61803 + 1.90211i) q^{31} +1.00000 q^{32} +(-5.23607 + 1.17557i) q^{33} +1.00000 q^{34} +(0.309017 - 0.224514i) q^{35} +(-0.118034 - 0.363271i) q^{36} +(-0.309017 + 0.951057i) q^{37} +(2.42705 + 1.76336i) q^{38} +(3.42705 + 2.48990i) q^{39} +(0.309017 - 0.951057i) q^{40} +(-2.30902 - 7.10642i) q^{41} +(-0.500000 + 0.363271i) q^{42} +10.9443 q^{43} +(-3.04508 - 1.31433i) q^{44} -0.381966 q^{45} +(6.85410 - 4.97980i) q^{46} +(-2.69098 - 8.28199i) q^{47} +(-0.500000 + 1.53884i) q^{48} +(5.54508 + 4.02874i) q^{49} +(3.23607 + 2.35114i) q^{50} +(-0.500000 + 1.53884i) q^{51} +(0.809017 + 2.48990i) q^{52} +(-1.42705 + 1.03681i) q^{53} +5.47214 q^{54} +(-2.19098 + 2.48990i) q^{55} -0.381966 q^{56} +(-3.92705 + 2.85317i) q^{57} +(-1.16312 - 3.57971i) q^{58} +(3.85410 - 11.8617i) q^{59} +(1.30902 + 0.951057i) q^{60} +(3.35410 + 2.43690i) q^{61} +(1.00000 - 3.07768i) q^{62} +(0.0450850 + 0.138757i) q^{63} +(-0.809017 + 0.587785i) q^{64} +2.61803 q^{65} +(3.54508 - 4.02874i) q^{66} +7.94427 q^{67} +(-0.809017 + 0.587785i) q^{68} +(4.23607 + 13.0373i) q^{69} +(-0.118034 + 0.363271i) q^{70} +(-2.92705 - 2.12663i) q^{71} +(0.309017 + 0.224514i) q^{72} +(-4.39919 + 13.5393i) q^{73} +(-0.309017 - 0.951057i) q^{74} +(-5.23607 + 3.80423i) q^{75} -3.00000 q^{76} +(1.16312 + 0.502029i) q^{77} -4.23607 q^{78} +(4.42705 - 3.21644i) q^{79} +(0.309017 + 0.951057i) q^{80} +(-2.38197 + 7.33094i) q^{81} +(6.04508 + 4.39201i) q^{82} +(7.97214 + 5.79210i) q^{83} +(0.190983 - 0.587785i) q^{84} +(0.309017 + 0.951057i) q^{85} +(-8.85410 + 6.43288i) q^{86} +6.09017 q^{87} +(3.23607 - 0.726543i) q^{88} -7.18034 q^{89} +(0.309017 - 0.224514i) q^{90} +(-0.309017 - 0.951057i) q^{91} +(-2.61803 + 8.05748i) q^{92} +(4.23607 + 3.07768i) q^{93} +(7.04508 + 5.11855i) q^{94} +(-0.927051 + 2.85317i) q^{95} +(-0.500000 - 1.53884i) q^{96} +(2.69098 - 1.95511i) q^{97} -6.85410 q^{98} +(-0.645898 - 1.08981i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$4 q - q^{2} - 2 q^{3} - q^{4} - q^{5} + 3 q^{6} + 4 q^{7} - q^{8} - q^{9} + 4 q^{10} - q^{11} - 2 q^{12} - 4 q^{13} + 4 q^{14} - 2 q^{15} - q^{16} - q^{17} + 4 q^{18} + 3 q^{19} - q^{20} - 2 q^{21}+ \cdots - 16 q^{99}+O(q^{100})$ 4 * q - q^2 - 2 * q^3 - q^4 - q^5 + 3 * q^6 + 4 * q^7 - q^8 - q^9 + 4 * q^10 - q^11 - 2 * q^12 - 4 * q^13 + 4 * q^14 - 2 * q^15 - q^16 - q^17 + 4 * q^18 + 3 * q^19 - q^20 - 2 * q^21 + 9 * q^22 - 16 * q^23 + 3 * q^24 + 4 * q^25 + q^26 - 11 * q^27 - q^28 + 11 * q^29 - 2 * q^30 - 6 * q^31 + 4 * q^32 - 12 * q^33 + 4 * q^34 - q^35 + 4 * q^36 + q^37 + 3 * q^38 + 7 * q^39 - q^40 - 7 * q^41 - 2 * q^42 + 8 * q^43 - q^44 - 6 * q^45 + 14 * q^46 - 13 * q^47 - 2 * q^48 + 11 * q^49 + 4 * q^50 - 2 * q^51 + q^52 + q^53 + 4 * q^54 - 11 * q^55 - 6 * q^56 - 9 * q^57 + 11 * q^58 + 2 * q^59 + 3 * q^60 + 4 * q^62 - 11 * q^63 - q^64 + 6 * q^65 + 3 * q^66 - 4 * q^67 - q^68 + 8 * q^69 + 4 * q^70 - 5 * q^71 - q^72 + 7 * q^73 + q^74 - 12 * q^75 - 12 * q^76 - 11 * q^77 - 8 * q^78 + 11 * q^79 - q^80 - 14 * q^81 + 13 * q^82 + 14 * q^83 + 3 * q^84 - q^85 - 22 * q^86 + 2 * q^87 + 4 * q^88 + 16 * q^89 - q^90 + q^91 - 6 * q^92 + 8 * q^93 + 17 * q^94 + 3 * q^95 - 2 * q^96 + 13 * q^97 - 14 * q^98 - 16 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/374\mathbb{Z}\right)^\times$ .

$n$	$35$	$309$
$\chi(n)$	$e\left(\frac{4}{5}\right)$	$1$

Coefficient data

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

Display

a_p

with

p

up to: 50 250 1000 (See

a_n

instead) (See

a_n

instead) (See

a_n

instead) Display

a_n

with

n

up to: 50 250 1000 (See only

a_p

) (See only

a_p

) (See only

a_p

)

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

$2$	−0.809017	+	0.587785i	−0.572061	+	0.415627i
$2$	−0.809017	+	0.587785i	−0.572061	+	0.415627i
$3$	−0.500000	−	1.53884i	−0.288675	−	0.888451i	−0.985273	−	0.170989i	$-0.945304\pi$
$3$	−0.500000	−	1.53884i	−0.288675	−	0.888451i	0.696598	−	0.717462i	$-0.254696\pi$
$4$	0.309017	−	0.951057i	0.154508	−	0.475528i
$5$	−0.809017	−	0.587785i	−0.361803	−	0.262866i	0.392000	−	0.919965i	$-0.371783\pi$
$5$	−0.809017	−	0.587785i	−0.361803	−	0.262866i	−0.753804	+	0.657099i	$0.771783\pi$
$6$	1.30902	+	0.951057i	0.534404	+	0.388267i
$7$	−0.118034	+	0.363271i	−0.0446127	+	0.137304i	−0.970882	−	0.239559i	$-0.922997\pi$
$7$	−0.118034	+	0.363271i	−0.0446127	+	0.137304i	0.926269	+	0.376863i	$0.122997\pi$
$8$	0.309017	+	0.951057i	0.109254	+	0.336249i
$9$	0.309017	−	0.224514i	0.103006	−	0.0748380i
$10$	1.00000			0.316228
$11$	0.309017	−	3.30220i	0.0931721	−	0.995650i
$11$	0.309017	−	3.30220i	0.0931721	−	0.995650i
$12$	−1.61803			−0.467086
$13$	−2.11803	+	1.53884i	−0.587437	+	0.426798i	−0.841398	−	0.540417i	$-0.818267\pi$
$13$	−2.11803	+	1.53884i	−0.587437	+	0.426798i	0.253961	+	0.967215i	$0.418267\pi$
$14$	−0.118034	−	0.363271i	−0.0315459	−	0.0970883i
$15$	−0.500000	+	1.53884i	−0.129099	+	0.397327i
$16$	−0.809017	−	0.587785i	−0.202254	−	0.146946i
$17$	−0.809017	−	0.587785i	−0.196215	−	0.142559i
$17$	−0.809017	−	0.587785i	−0.196215	−	0.142559i
$18$	−0.118034	+	0.363271i	−0.0278209	+	0.0856239i
$19$	−0.927051	−	2.85317i	−0.212680	−	0.654562i	−0.999310	−	0.0371374i	$-0.988176\pi$
$19$	−0.927051	−	2.85317i	−0.212680	−	0.654562i	0.786630	−	0.617425i	$-0.211824\pi$
$20$	−0.809017	+	0.587785i	−0.180902	+	0.131433i
$21$	0.618034			0.134866
$22$	1.69098	+	2.85317i	0.360519	+	0.608298i
$23$	−8.47214			−1.76656			−0.883281	−	0.468844i	$-0.844671\pi$
$23$	−8.47214			−1.76656			−0.883281	+	0.468844i	$0.844671\pi$
$24$	1.30902	−	0.951057i	0.267202	−	0.194134i
$25$	−1.23607	−	3.80423i	−0.247214	−	0.760845i
$26$	0.809017	−	2.48990i	0.158661	−	0.488309i
$27$	−4.42705	−	3.21644i	−0.851986	−	0.619004i
$28$	0.309017	+	0.224514i	0.0583987	+	0.0424292i
$29$	−1.16312	+	3.57971i	−0.215986	+	0.664736i	0.783096	+	0.621900i	$0.213639\pi$
$29$	−1.16312	+	3.57971i	−0.215986	+	0.664736i	−0.999082	+	0.0428355i	$0.986361\pi$
$30$	−0.500000	−	1.53884i	−0.0912871	−	0.280953i
$31$	−2.61803	+	1.90211i	−0.470213	+	0.341630i	−0.797524	−	0.603287i	$-0.793857\pi$
$31$	−2.61803	+	1.90211i	−0.470213	+	0.341630i	0.327311	+	0.944917i	$0.393857\pi$
$32$	1.00000			0.176777
$33$	−5.23607	+	1.17557i	−0.911482	+	0.204641i
$34$	1.00000			0.171499
$35$	0.309017	−	0.224514i	0.0522334	−	0.0379498i
$36$	−0.118034	−	0.363271i	−0.0196723	−	0.0605452i
$37$	−0.309017	+	0.951057i	−0.0508021	+	0.156353i	−0.973239	−	0.229795i	$-0.926194\pi$
$37$	−0.309017	+	0.951057i	−0.0508021	+	0.156353i	0.922437	+	0.386148i	$0.126194\pi$
$38$	2.42705	+	1.76336i	0.393720	+	0.286054i
$39$	3.42705	+	2.48990i	0.548767	+	0.398703i
$40$	0.309017	−	0.951057i	0.0488599	−	0.150375i
$41$	−2.30902	−	7.10642i	−0.360608	−	1.10984i	−0.952686	−	0.303956i	$-0.901692\pi$
$41$	−2.30902	−	7.10642i	−0.360608	−	1.10984i	0.592078	−	0.805881i	$-0.298308\pi$
$42$	−0.500000	+	0.363271i	−0.0771517	+	0.0560540i
$43$	10.9443			1.66899			0.834493	−	0.551019i	$-0.185761\pi$
$43$	10.9443			1.66899			0.834493	+	0.551019i	$0.185761\pi$
$44$	−3.04508	−	1.31433i	−0.459064	−	0.198142i
$45$	−0.381966			−0.0569401
$46$	6.85410	−	4.97980i	1.01058	−	0.734231i
$47$	−2.69098	−	8.28199i	−0.392520	−	1.20805i	−0.930876	−	0.365335i	$-0.880954\pi$
$47$	−2.69098	−	8.28199i	−0.392520	−	1.20805i	0.538356	−	0.842718i	$-0.319046\pi$
$48$	−0.500000	+	1.53884i	−0.0721688	+	0.222113i
$49$	5.54508	+	4.02874i	0.792155	+	0.575534i
$50$	3.23607	+	2.35114i	0.457649	+	0.332502i
$51$	−0.500000	+	1.53884i	−0.0700140	+	0.215481i
$52$	0.809017	+	2.48990i	0.112190	+	0.345287i
$53$	−1.42705	+	1.03681i	−0.196021	+	0.142417i	−0.681466	−	0.731850i	$-0.738657\pi$
$53$	−1.42705	+	1.03681i	−0.196021	+	0.142417i	0.485446	+	0.874267i	$0.338657\pi$
$54$	5.47214			0.744663
$55$	−2.19098	+	2.48990i	−0.295432	+	0.335738i
$56$	−0.381966			−0.0510424
$57$	−3.92705	+	2.85317i	−0.520151	+	0.377912i
$58$	−1.16312	−	3.57971i	−0.152725	−	0.470039i
$59$	3.85410	−	11.8617i	0.501761	−	1.54426i	−0.304387	−	0.952549i	$-0.598451\pi$
$59$	3.85410	−	11.8617i	0.501761	−	1.54426i	0.806148	−	0.591714i	$-0.201549\pi$
$60$	1.30902	+	0.951057i	0.168993	+	0.122781i
$61$	3.35410	+	2.43690i	0.429449	+	0.312013i	0.781428	−	0.623995i	$-0.214491\pi$
$61$	3.35410	+	2.43690i	0.429449	+	0.312013i	−0.351980	+	0.936008i	$0.614491\pi$
$62$	1.00000	−	3.07768i	0.127000	−	0.390866i
$63$	0.0450850	+	0.138757i	0.00568017	+	0.0174818i
$64$	−0.809017	+	0.587785i	−0.101127	+	0.0734732i
$65$	2.61803			0.324727
$66$	3.54508	−	4.02874i	0.436370	−	0.495904i
$67$	7.94427			0.970547			0.485274	−	0.874362i	$-0.338720\pi$
$67$	7.94427			0.970547			0.485274	+	0.874362i	$0.338720\pi$
$68$	−0.809017	+	0.587785i	−0.0981077	+	0.0712794i
$69$	4.23607	+	13.0373i	0.509963	+	1.56950i
$70$	−0.118034	+	0.363271i	−0.0141078	+	0.0434192i
$71$	−2.92705	−	2.12663i	−0.347377	−	0.252384i	0.400391	−	0.916344i	$-0.368874\pi$
$71$	−2.92705	−	2.12663i	−0.347377	−	0.252384i	−0.747768	+	0.663960i	$0.768874\pi$
$72$	0.309017	+	0.224514i	0.0364180	+	0.0264592i
$73$	−4.39919	+	13.5393i	−0.514886	+	1.58466i	0.268604	+	0.963251i	$0.413438\pi$
$73$	−4.39919	+	13.5393i	−0.514886	+	1.58466i	−0.783490	+	0.621405i	$0.786562\pi$
$74$	−0.309017	−	0.951057i	−0.0359225	−	0.110558i
$75$	−5.23607	+	3.80423i	−0.604609	+	0.439274i
$76$	−3.00000			−0.344124
$77$	1.16312	+	0.502029i	0.132550	+	0.0572115i
$78$	−4.23607			−0.479640
$79$	4.42705	−	3.21644i	0.498082	−	0.361878i	−0.310202	−	0.950671i	$-0.600397\pi$
$79$	4.42705	−	3.21644i	0.498082	−	0.361878i	0.808284	+	0.588793i	$0.200397\pi$
$80$	0.309017	+	0.951057i	0.0345492	+	0.106331i
$81$	−2.38197	+	7.33094i	−0.264663	+	0.814549i
$82$	6.04508	+	4.39201i	0.667568	+	0.485017i
$83$	7.97214	+	5.79210i	0.875056	+	0.635765i	0.931939	−	0.362616i	$-0.118116\pi$
$83$	7.97214	+	5.79210i	0.875056	+	0.635765i	−0.0568831	+	0.998381i	$0.518116\pi$
$84$	0.190983	−	0.587785i	0.0208380	−	0.0641326i
$85$	0.309017	+	0.951057i	0.0335176	+	0.103157i
$86$	−8.85410	+	6.43288i	−0.954762	+	0.693675i
$87$	6.09017			0.652935
$88$	3.23607	−	0.726543i	0.344966	−	0.0774497i
$89$	−7.18034			−0.761115			−0.380557	−	0.924757i	$-0.624268\pi$
$89$	−7.18034			−0.761115			−0.380557	+	0.924757i	$0.624268\pi$
$90$	0.309017	−	0.224514i	0.0325733	−	0.0236659i
$91$	−0.309017	−	0.951057i	−0.0323938	−	0.0996978i
$92$	−2.61803	+	8.05748i	−0.272949	+	0.840050i
$93$	4.23607	+	3.07768i	0.439260	+	0.319141i
$94$	7.04508	+	5.11855i	0.726645	+	0.527939i
$95$	−0.927051	+	2.85317i	−0.0951134	+	0.292729i
$96$	−0.500000	−	1.53884i	−0.0510310	−	0.157057i
$97$	2.69098	−	1.95511i	0.273228	−	0.198512i	−0.442730	−	0.896655i	$-0.645990\pi$
$97$	2.69098	−	1.95511i	0.273228	−	0.198512i	0.715958	+	0.698143i	$0.245990\pi$
$98$	−6.85410			−0.692369
$99$	−0.645898	−	1.08981i	−0.0649152	−	0.109530i
$100$	−4.00000			−0.400000
$101$	4.97214	−	3.61247i	0.494746	−	0.359454i	−0.312261	−	0.949997i	$-0.601086\pi$
$101$	4.97214	−	3.61247i	0.494746	−	0.359454i	0.807007	+	0.590542i	$0.201086\pi$
$102$	−0.500000	−	1.53884i	−0.0495074	−	0.152368i
$103$	−1.35410	+	4.16750i	−0.133424	+	0.410636i	−0.995341	−	0.0964122i	$-0.969263\pi$
$103$	−1.35410	+	4.16750i	−0.133424	+	0.410636i	0.861918	+	0.507048i	$0.169263\pi$
$104$	−2.11803	−	1.53884i	−0.207690	−	0.150896i
$105$	−0.500000	−	0.363271i	−0.0487950	−	0.0354516i
$106$	0.545085	−	1.67760i	0.0529433	−	0.162943i
$107$	−1.61803	−	4.97980i	−0.156421	−	0.481415i	0.841881	−	0.539663i	$-0.181448\pi$
$107$	−1.61803	−	4.97980i	−0.156421	−	0.481415i	−0.998302	+	0.0582483i	$0.981448\pi$
$108$	−4.42705	+	3.21644i	−0.425993	+	0.309502i
$109$	17.3262			1.65955			0.829776	−	0.558096i	$-0.188468\pi$
$109$	17.3262			1.65955			0.829776	+	0.558096i	$0.188468\pi$
$110$	0.309017	−	3.30220i	0.0294636	−	0.314852i
$111$	1.61803			0.153577
$112$	0.309017	−	0.224514i	0.0291994	−	0.0212146i
$113$	−1.59017	−	4.89404i	−0.149591	−	0.460393i	0.847982	−	0.530025i	$-0.177817\pi$
$113$	−1.59017	−	4.89404i	−0.149591	−	0.460393i	−0.997573	+	0.0696323i	$0.977817\pi$
$114$	1.50000	−	4.61653i	0.140488	−	0.432377i
$115$	6.85410	+	4.97980i	0.639148	+	0.464368i
$116$	3.04508	+	2.21238i	0.282729	+	0.205415i
$117$	−0.309017	+	0.951057i	−0.0285686	+	0.0879252i
$118$	3.85410	+	11.8617i	0.354799	+	1.09196i
$119$	0.309017	−	0.224514i	0.0283275	−	0.0205812i
$120$	−1.61803			−0.147706
$121$	−10.8090	−	2.04087i	−0.982638	−	0.185534i
$122$	−4.14590			−0.375352
$123$	−9.78115	+	7.10642i	−0.881937	+	0.640765i
$124$	1.00000	+	3.07768i	0.0898027	+	0.276384i
$125$	−2.78115	+	8.55951i	−0.248754	+	0.765586i
$126$	−0.118034	−	0.0857567i	−0.0105153	−	0.00763982i
$127$	−7.23607	−	5.25731i	−0.642097	−	0.466511i	0.218473	−	0.975843i	$-0.429892\pi$
$127$	−7.23607	−	5.25731i	−0.642097	−	0.466511i	−0.860570	+	0.509332i	$0.829892\pi$
$128$	0.309017	−	0.951057i	0.0273135	−	0.0840623i
$129$	−5.47214	−	16.8415i	−0.481795	−	1.48281i
$130$	−2.11803	+	1.53884i	−0.185764	+	0.134965i
$131$	2.32624			0.203244			0.101622	−	0.994823i	$-0.467597\pi$
$131$	2.32624			0.203244			0.101622	+	0.994823i	$0.467597\pi$
$132$	−0.500000	+	5.34307i	−0.0435194	+	0.465054i
$133$	1.14590			0.0993620
$134$	−6.42705	+	4.66953i	−0.555213	+	0.403386i
$135$	1.69098	+	5.20431i	0.145537	+	0.447916i
$136$	0.309017	−	0.951057i	0.0264980	−	0.0815524i
$137$	15.0902	+	10.9637i	1.28924	+	0.936688i	0.999790	−	0.0205051i	$-0.00652745\pi$
$137$	15.0902	+	10.9637i	1.28924	+	0.936688i	0.289450	+	0.957193i	$0.406527\pi$
$138$	−11.0902	−	8.05748i	−0.944058	−	0.685898i
$139$	4.30902	−	13.2618i	0.365486	−	1.12485i	−0.584190	−	0.811617i	$-0.698588\pi$
$139$	4.30902	−	13.2618i	0.365486	−	1.12485i	0.949676	−	0.313234i	$-0.101412\pi$
$140$	−0.118034	−	0.363271i	−0.00997569	−	0.0307020i
$141$	−11.3992	+	8.28199i	−0.959985	+	0.697470i
$142$	3.61803			0.303619
$143$	4.42705	+	7.46969i	0.370209	+	0.624647i
$144$	−0.381966			−0.0318305
$145$	3.04508	−	2.21238i	0.252881	−	0.183728i
$146$	−4.39919	−	13.5393i	−0.364079	−	1.12052i
$147$	3.42705	−	10.5474i	0.282658	−	0.869933i
$148$	0.809017	+	0.587785i	0.0665008	+	0.0483157i
$149$	6.16312	+	4.47777i	0.504902	+	0.366833i	0.810886	−	0.585204i	$-0.198985\pi$
$149$	6.16312	+	4.47777i	0.504902	+	0.366833i	−0.305984	+	0.952037i	$0.598985\pi$
$150$	2.00000	−	6.15537i	0.163299	−	0.502584i
$151$	−7.07295	−	21.7683i	−0.575588	−	1.77148i	−0.634167	−	0.773196i	$-0.718657\pi$
$151$	−7.07295	−	21.7683i	−0.575588	−	1.77148i	0.0585784	−	0.998283i	$-0.481343\pi$
$152$	2.42705	−	1.76336i	0.196860	−	0.143027i
$153$	−0.381966			−0.0308801
$154$	−1.23607	+	0.277515i	−0.0996052	+	0.0223628i
$155$	3.23607			0.259927
$156$	3.42705	−	2.48990i	0.274384	−	0.199351i
$157$	1.24671	+	3.83698i	0.0994984	+	0.306225i	0.988400	−	0.151874i	$-0.0485307\pi$
$157$	1.24671	+	3.83698i	0.0994984	+	0.306225i	−0.888902	+	0.458098i	$0.848531\pi$
$158$	−1.69098	+	5.20431i	−0.134527	+	0.414033i
$159$	2.30902	+	1.67760i	0.183117	+	0.133042i
$160$	−0.809017	−	0.587785i	−0.0639584	−	0.0464685i
$161$	1.00000	−	3.07768i	0.0788110	−	0.242555i
$162$	−2.38197	−	7.33094i	−0.187145	−	0.575973i
$163$	3.57295	−	2.59590i	0.279855	−	0.203327i	−0.438999	−	0.898487i	$-0.644667\pi$
$163$	3.57295	−	2.59590i	0.279855	−	0.203327i	0.718854	+	0.695161i	$0.244667\pi$
$164$	−7.47214			−0.583476
$165$	4.92705	+	2.12663i	0.383570	+	0.165558i
$166$	−9.85410			−0.764827
$167$	8.42705	−	6.12261i	0.652105	−	0.473782i	−0.211883	−	0.977295i	$-0.567959\pi$
$167$	8.42705	−	6.12261i	0.652105	−	0.473782i	0.863988	+	0.503513i	$0.167959\pi$
$168$	0.190983	+	0.587785i	0.0147347	+	0.0453486i
$169$	−1.89919	+	5.84510i	−0.146091	+	0.449623i
$170$	−0.809017	−	0.587785i	−0.0620488	−	0.0450811i
$171$	−0.927051	−	0.673542i	−0.0708934	−	0.0515070i
$172$	3.38197	−	10.4086i	0.257872	−	0.793650i
$173$	−6.59017	−	20.2825i	−0.501041	−	1.54205i	−0.807325	−	0.590107i	$-0.799086\pi$
$173$	−6.59017	−	20.2825i	−0.501041	−	1.54205i	0.306284	−	0.951940i	$-0.400914\pi$
$174$	−4.92705	+	3.57971i	−0.373519	+	0.271377i
$175$	1.52786			0.115496
$176$	−2.19098	+	2.48990i	−0.165152	+	0.187683i
$177$	−20.1803			−1.51685
$178$	5.80902	−	4.22050i	0.435404	−	0.316340i
$179$	0.663119	+	2.04087i	0.0495638	+	0.152542i	0.972775	−	0.231751i	$-0.0744454\pi$
$179$	0.663119	+	2.04087i	0.0495638	+	0.152542i	−0.923211	+	0.384293i	$0.874445\pi$
$180$	−0.118034	+	0.363271i	−0.00879773	+	0.0270766i
$181$	−6.30902	−	4.58377i	−0.468946	−	0.340709i	0.328085	−	0.944648i	$-0.393597\pi$
$181$	−6.30902	−	4.58377i	−0.468946	−	0.340709i	−0.797030	+	0.603939i	$0.793597\pi$
$182$	0.809017	+	0.587785i	0.0599683	+	0.0435695i
$183$	2.07295	−	6.37988i	0.153237	−	0.471614i
$184$	−2.61803	−	8.05748i	−0.193004	−	0.594005i
$185$	0.809017	−	0.587785i	0.0594801	−	0.0432148i
$186$	−5.23607			−0.383927
$187$	−2.19098	+	2.48990i	−0.160221	+	0.182079i
$188$	−8.70820			−0.635111
$189$	1.69098	−	1.22857i	0.123001	−	0.0893654i
$190$	−0.927051	−	2.85317i	−0.0672553	−	0.206991i
$191$	6.19098	−	19.0539i	0.447964	−	1.37869i	−0.431237	−	0.902239i	$-0.641923\pi$
$191$	6.19098	−	19.0539i	0.447964	−	1.37869i	0.879200	−	0.476452i	$-0.158077\pi$
$192$	1.30902	+	0.951057i	0.0944702	+	0.0686366i
$193$	9.54508	+	6.93491i	0.687070	+	0.499186i	0.875696	−	0.482863i	$-0.160403\pi$
$193$	9.54508	+	6.93491i	0.687070	+	0.499186i	−0.188625	+	0.982049i	$0.560403\pi$
$194$	−1.02786	+	3.16344i	−0.0737963	+	0.227122i
$195$	−1.30902	−	4.02874i	−0.0937407	−	0.288504i
$196$	5.54508	−	4.02874i	0.396077	−	0.287767i
$197$	−8.52786			−0.607585			−0.303793	−	0.952738i	$-0.598253\pi$
$197$	−8.52786			−0.607585			−0.303793	+	0.952738i	$0.598253\pi$
$198$	1.16312	+	0.502029i	0.0826593	+	0.0356776i
$199$	−3.09017			−0.219056			−0.109528	−	0.993984i	$-0.534934\pi$
$199$	−3.09017			−0.219056			−0.109528	+	0.993984i	$0.534934\pi$
$200$	3.23607	−	2.35114i	0.228825	−	0.166251i
$201$	−3.97214	−	12.2250i	−0.280173	−	0.862283i
$202$	−1.89919	+	5.84510i	−0.133626	+	0.411260i
$203$	−1.16312	−	0.845055i	−0.0816349	−	0.0593113i
$204$	1.30902	+	0.951057i	0.0916495	+	0.0665873i
$205$	−2.30902	+	7.10642i	−0.161269	+	0.496334i
$206$	−1.35410	−	4.16750i	−0.0943448	−	0.290363i
$207$	−2.61803	+	1.90211i	−0.181966	+	0.132206i
$208$	2.61803			0.181528
$209$	−9.70820	+	2.17963i	−0.671531	+	0.150768i
$210$	0.618034			0.0426484
$211$	15.1631	−	11.0167i	1.04387	−	0.758418i	0.0728345	−	0.997344i	$-0.476796\pi$
$211$	15.1631	−	11.0167i	1.04387	−	0.758418i	0.971038	+	0.238927i	$0.0767955\pi$
$212$	0.545085	+	1.67760i	0.0374366	+	0.115218i
$213$	−1.80902	+	5.56758i	−0.123952	+	0.381484i
$214$	4.23607	+	3.07768i	0.289572	+	0.210386i
$215$	−8.85410	−	6.43288i	−0.603845	−	0.438719i
$216$	1.69098	−	5.20431i	0.115057	−	0.354108i
$217$	−0.381966	−	1.17557i	−0.0259295	−	0.0798029i
$218$	−14.0172	+	10.1841i	−0.949366	+	0.689755i
$219$	23.0344			1.55652
$220$	1.69098	+	2.85317i	0.114006	+	0.192361i
$221$	2.61803			0.176108
$222$	−1.30902	+	0.951057i	−0.0878555	+	0.0638307i
$223$	2.02786	+	6.24112i	0.135796	+	0.417937i	0.995713	−	0.0924971i	$-0.0294849\pi$
$223$	2.02786	+	6.24112i	0.135796	+	0.417937i	−0.859917	+	0.510434i	$0.829485\pi$
$224$	−0.118034	+	0.363271i	−0.00788648	+	0.0242721i
$225$	−1.23607	−	0.898056i	−0.0824045	−	0.0598704i
$226$	4.16312	+	3.02468i	0.276927	+	0.201199i
$227$	−5.68034	+	17.4823i	−0.377017	+	1.16034i	0.565090	+	0.825029i	$0.308841\pi$
$227$	−5.68034	+	17.4823i	−0.377017	+	1.16034i	−0.942107	+	0.335311i	$0.891159\pi$
$228$	1.50000	+	4.61653i	0.0993399	+	0.305737i
$229$	13.6631	−	9.92684i	0.902884	−	0.655984i	−0.0363209	−	0.999340i	$-0.511564\pi$
$229$	13.6631	−	9.92684i	0.902884	−	0.655984i	0.939205	+	0.343356i	$0.111564\pi$
$230$	−8.47214			−0.558636
$231$	0.190983	−	2.04087i	0.0125658	−	0.134279i
$232$	−3.76393			−0.247114
$233$	−12.5172	+	9.09429i	−0.820030	+	0.595787i	−0.916721	−	0.399528i	$-0.869174\pi$
$233$	−12.5172	+	9.09429i	−0.820030	+	0.595787i	0.0966908	+	0.995314i	$0.469174\pi$
$234$	−0.309017	−	0.951057i	−0.0202011	−	0.0621725i
$235$	−2.69098	+	8.28199i	−0.175540	+	0.540258i
$236$	−10.0902	−	7.33094i	−0.656814	−	0.477203i
$237$	−7.16312	−	5.20431i	−0.465295	−	0.338056i
$238$	−0.118034	+	0.363271i	−0.00765101	+	0.0235474i
$239$	9.10739	+	28.0297i	0.589108	+	1.81309i	0.582106	+	0.813113i	$0.302229\pi$
$239$	9.10739	+	28.0297i	0.589108	+	1.81309i	0.00700219	+	0.999975i	$0.497771\pi$
$240$	1.30902	−	0.951057i	0.0844967	−	0.0613904i
$241$	−12.8541			−0.828005			−0.414003	−	0.910276i	$-0.635870\pi$
$241$	−12.8541			−0.828005			−0.414003	+	0.910276i	$0.635870\pi$
$242$	9.94427	−	4.70228i	0.639242	−	0.302274i
$243$	−3.94427			−0.253025
$244$	3.35410	−	2.43690i	0.214724	−	0.156006i
$245$	−2.11803	−	6.51864i	−0.135316	−	0.416461i
$246$	3.73607	−	11.4984i	0.238203	−	0.733113i
$247$	6.35410	+	4.61653i	0.404302	+	0.293742i
$248$	−2.61803	−	1.90211i	−0.166245	−	0.120784i
$249$	4.92705	−	15.1639i	0.312239	−	0.960973i
$250$	−2.78115	−	8.55951i	−0.175896	−	0.541351i
$251$	1.61803	−	1.17557i	0.102129	−	0.0742014i	−0.535548	−	0.844504i	$-0.679895\pi$
$251$	1.61803	−	1.17557i	0.102129	−	0.0742014i	0.637678	+	0.770303i	$0.279895\pi$
$252$	0.145898			0.00919071
$253$	−2.61803	+	27.9767i	−0.164594	+	1.75888i
$254$	8.94427			0.561214
$255$	1.30902	−	0.951057i	0.0819738	−	0.0595575i
$256$	0.309017	+	0.951057i	0.0193136	+	0.0594410i
$257$	6.20820	−	19.1069i	0.387257	−	1.19185i	−0.547572	−	0.836758i	$-0.684448\pi$
$257$	6.20820	−	19.1069i	0.387257	−	1.19185i	0.934830	−	0.355097i	$-0.115552\pi$
$258$	14.3262	+	10.4086i	0.891913	+	0.648012i
$259$	−0.309017	−	0.224514i	−0.0192014	−	0.0139506i
$260$	0.809017	−	2.48990i	0.0501731	−	0.154417i
$261$	0.444272	+	1.36733i	0.0274997	+	0.0846355i
$262$	−1.88197	+	1.36733i	−0.116268	+	0.0844738i
$263$	−9.61803			−0.593073			−0.296537	−	0.955021i	$-0.595832\pi$
$263$	−9.61803			−0.593073			−0.296537	+	0.955021i	$0.595832\pi$
$264$	−2.73607	−	4.61653i	−0.168393	−	0.284127i
$265$	1.76393			0.108357
$266$	−0.927051	+	0.673542i	−0.0568411	+	0.0412975i
$267$	3.59017	+	11.0494i	0.219715	+	0.676213i
$268$	2.45492	−	7.55545i	0.149958	−	0.461523i
$269$	−10.2082	−	7.41669i	−0.622405	−	0.452204i	0.231356	−	0.972869i	$-0.425684\pi$
$269$	−10.2082	−	7.41669i	−0.622405	−	0.452204i	−0.853761	+	0.520665i	$0.825684\pi$
$270$	−4.42705	−	3.21644i	−0.269422	−	0.195746i
$271$	−4.01722	+	12.3637i	−0.244029	+	0.751043i	0.751766	+	0.659430i	$0.229202\pi$
$271$	−4.01722	+	12.3637i	−0.244029	+	0.751043i	−0.995795	+	0.0916133i	$0.970798\pi$
$272$	0.309017	+	0.951057i	0.0187369	+	0.0576663i
$273$	−1.30902	+	0.951057i	−0.0792253	+	0.0575606i
$274$	−18.6525			−1.12684
$275$	−12.9443	+	2.90617i	−0.780569	+	0.175249i
$276$	13.7082			0.825137
$277$	−7.73607	+	5.62058i	−0.464815	+	0.337708i	−0.795417	−	0.606062i	$-0.792748\pi$
$277$	−7.73607	+	5.62058i	−0.464815	+	0.337708i	0.330602	+	0.943770i	$0.392748\pi$
$278$	4.30902	+	13.2618i	0.258438	+	0.795389i
$279$	−0.381966	+	1.17557i	−0.0228677	+	0.0703796i
$280$	0.309017	+	0.224514i	0.0184673	+	0.0134173i
$281$	9.42705	+	6.84915i	0.562371	+	0.408586i	0.832326	−	0.554287i	$-0.187009\pi$
$281$	9.42705	+	6.84915i	0.562371	+	0.408586i	−0.269955	+	0.962873i	$0.587009\pi$
$282$	4.35410	−	13.4005i	0.259283	−	0.797991i
$283$	−2.19098	−	6.74315i	−0.130240	−	0.400839i	0.864579	−	0.502497i	$-0.167585\pi$
$283$	−2.19098	−	6.74315i	−0.130240	−	0.400839i	−0.994819	+	0.101658i	$0.967585\pi$
$284$	−2.92705	+	2.12663i	−0.173689	+	0.126192i
$285$	4.85410			0.287532
$286$	−7.97214	−	3.44095i	−0.471402	−	0.203468i
$287$	2.85410			0.168472
$288$	0.309017	−	0.224514i	0.0182090	−	0.0132296i
$289$	0.309017	+	0.951057i	0.0181775	+	0.0559445i
$290$	−1.16312	+	3.57971i	−0.0683007	+	0.210208i
$291$	−4.35410	−	3.16344i	−0.255242	−	0.185444i
$292$	11.5172	+	8.36775i	0.673994	+	0.489686i
$293$	−4.24671	+	13.0700i	−0.248096	+	0.763559i	0.747016	+	0.664806i	$0.231486\pi$
$293$	−4.24671	+	13.0700i	−0.248096	+	0.763559i	−0.995112	+	0.0987538i	$0.968514\pi$
$294$	3.42705	+	10.5474i	0.199870	+	0.615136i
$295$	−10.0902	+	7.33094i	−0.587472	+	0.426824i
$296$	−1.00000			−0.0581238
$297$	−11.9894	+	13.6251i	−0.695693	+	0.790606i
$298$	−7.61803			−0.441301
$299$	17.9443	−	13.0373i	1.03774	−	0.753965i
$300$	2.00000	+	6.15537i	0.115470	+	0.355380i
$301$	−1.29180	+	3.97574i	−0.0744579	+	0.229158i
$302$	18.5172	+	13.4535i	1.06555	+	0.774165i
$303$	−8.04508	−	5.84510i	−0.462178	−	0.335792i
$304$	−0.927051	+	2.85317i	−0.0531700	+	0.163640i
$305$	−1.28115	−	3.94298i	−0.0733586	−	0.225775i
$306$	0.309017	−	0.224514i	0.0176653	−	0.0128346i
$307$	−11.7639			−0.671403			−0.335702	−	0.941968i	$-0.608973\pi$
$307$	−11.7639			−0.671403			−0.335702	+	0.941968i	$0.608973\pi$
$308$	0.836881	−	0.951057i	0.0476857	−	0.0541915i
$309$	7.09017			0.403346
$310$	−2.61803	+	1.90211i	−0.148694	+	0.108033i
$311$	9.96149	+	30.6583i	0.564864	+	1.73847i	0.668354	+	0.743843i	$0.266999\pi$
$311$	9.96149	+	30.6583i	0.564864	+	1.73847i	−0.103489	+	0.994631i	$0.533001\pi$
$312$	−1.30902	+	4.02874i	−0.0741085	+	0.228082i
$313$	−10.9721	−	7.97172i	−0.620182	−	0.450588i	0.232803	−	0.972524i	$-0.425210\pi$
$313$	−10.9721	−	7.97172i	−0.620182	−	0.450588i	−0.852985	+	0.521935i	$0.825210\pi$
$314$	−3.26393	−	2.37139i	−0.184194	−	0.133825i
$315$	0.0450850	−	0.138757i	0.00254025	−	0.00781809i
$316$	−1.69098	−	5.20431i	−0.0951252	−	0.292765i
$317$	17.0172	−	12.3637i	0.955782	−	0.694417i	0.00361496	−	0.999993i	$-0.498849\pi$
$317$	17.0172	−	12.3637i	0.955782	−	0.694417i	0.952167	+	0.305577i	$0.0988493\pi$
$318$	−2.85410			−0.160050
$319$	11.4615	+	4.94704i	0.641720	+	0.276981i
$320$	1.00000			0.0559017
$321$	−6.85410	+	4.97980i	−0.382559	+	0.277945i
$322$	1.00000	+	3.07768i	0.0557278	+	0.171513i
$323$	−0.927051	+	2.85317i	−0.0515825	+	0.158755i
$324$	6.23607	+	4.53077i	0.346448	+	0.251709i
$325$	8.47214	+	6.15537i	0.469950	+	0.341438i
$326$	−1.36475	+	4.20025i	−0.0755862	+	0.232631i
$327$	−8.66312	−	26.6623i	−0.479072	−	1.47443i
$328$	6.04508	−	4.39201i	0.333784	−	0.242508i
$329$	3.32624			0.183381
$330$	−5.23607	+	1.17557i	−0.288236	+	0.0647130i
$331$	8.41641			0.462608			0.231304	−	0.972882i	$-0.425701\pi$
$331$	8.41641			0.462608			0.231304	+	0.972882i	$0.425701\pi$
$332$	7.97214	−	5.79210i	0.437528	−	0.317883i
$333$	0.118034	+	0.363271i	0.00646822	+	0.0199071i
$334$	−3.21885	+	9.90659i	−0.176127	+	0.542065i
$335$	−6.42705	−	4.66953i	−0.351147	−	0.255123i
$336$	−0.500000	−	0.363271i	−0.0272772	−	0.0198181i
$337$	2.60081	−	8.00448i	0.141675	−	0.436032i	−0.854893	−	0.518804i	$-0.826377\pi$
$337$	2.60081	−	8.00448i	0.141675	−	0.436032i	0.996568	+	0.0827723i	$0.0263774\pi$
$338$	−1.89919	−	5.84510i	−0.103302	−	0.317931i
$339$	−6.73607	+	4.89404i	−0.365853	+	0.265808i
$340$	1.00000			0.0542326
$341$	5.47214	+	9.23305i	0.296333	+	0.499998i
$342$	1.14590			0.0619631
$343$	−4.28115	+	3.11044i	−0.231161	+	0.167948i
$344$	3.38197	+	10.4086i	0.182343	+	0.561195i
$345$	4.23607	−	13.0373i	0.228062	−	0.701903i
$346$	17.2533	+	12.5352i	0.927543	+	0.673899i
$347$	10.5172	+	7.64121i	0.564594	+	0.410202i	0.833137	−	0.553066i	$-0.186542\pi$
$347$	10.5172	+	7.64121i	0.564594	+	0.410202i	−0.268543	+	0.963268i	$0.586542\pi$
$348$	1.88197	−	5.79210i	0.100884	−	0.310489i
$349$	−0.118034	−	0.363271i	−0.00631821	−	0.0194455i	0.947848	−	0.318724i	$-0.103254\pi$
$349$	−0.118034	−	0.363271i	−0.00631821	−	0.0194455i	−0.954166	+	0.299278i	$0.903254\pi$
$350$	−1.23607	+	0.898056i	−0.0660706	+	0.0480031i
$351$	14.3262			0.764678
$352$	0.309017	−	3.30220i	0.0164707	−	0.176008i
$353$	3.81966			0.203300			0.101650	−	0.994820i	$-0.467588\pi$
$353$	3.81966			0.203300			0.101650	+	0.994820i	$0.467588\pi$
$354$	16.3262	−	11.8617i	0.867730	−	0.630443i
$355$	1.11803	+	3.44095i	0.0593391	+	0.182627i
$356$	−2.21885	+	6.82891i	−0.117599	+	0.361931i
$357$	−0.500000	−	0.363271i	−0.0264628	−	0.0192264i
$358$	−1.73607	−	1.26133i	−0.0917540	−	0.0666632i
$359$	−5.12868	+	15.7844i	−0.270681	+	0.833071i	0.719649	+	0.694338i	$0.244303\pi$
$359$	−5.12868	+	15.7844i	−0.270681	+	0.833071i	−0.990330	+	0.138733i	$0.955697\pi$
$360$	−0.118034	−	0.363271i	−0.00622094	−	0.0191461i
$361$	8.09017	−	5.87785i	0.425798	−	0.309361i
$362$	7.79837			0.409873
$363$	2.26393	+	17.6538i	0.118826	+	0.926584i
$364$	−1.00000			−0.0524142
$365$	11.5172	−	8.36775i	0.602839	−	0.437988i
$366$	2.07295	+	6.37988i	0.108355	+	0.333482i
$367$	6.26393	−	19.2784i	0.326975	−	1.00632i	−0.643567	−	0.765390i	$-0.722546\pi$
$367$	6.26393	−	19.2784i	0.326975	−	1.00632i	0.970541	−	0.240934i	$-0.0774539\pi$
$368$	6.85410	+	4.97980i	0.357295	+	0.259590i
$369$	−2.30902	−	1.67760i	−0.120203	−	0.0873323i
$370$	−0.309017	+	0.951057i	−0.0160650	+	0.0494431i
$371$	−0.208204	−	0.640786i	−0.0108094	−	0.0332679i
$372$	4.23607	−	3.07768i	0.219630	−	0.159570i
$373$	6.56231			0.339783			0.169892	−	0.985463i	$-0.445658\pi$
$373$	6.56231			0.339783			0.169892	+	0.985463i	$0.445658\pi$
$374$	0.309017	−	3.30220i	0.0159789	−	0.170753i
$375$	14.5623			0.751994
$376$	7.04508	−	5.11855i	0.363323	−	0.263969i
$377$	−3.04508	−	9.37181i	−0.156830	−	0.482673i
$378$	−0.645898	+	1.98787i	−0.0332214	+	0.102245i
$379$	−16.2984	−	11.8415i	−0.837191	−	0.608255i	0.0843934	−	0.996433i	$-0.473105\pi$
$379$	−16.2984	−	11.8415i	−0.837191	−	0.608255i	−0.921585	+	0.388177i	$0.873105\pi$
$380$	2.42705	+	1.76336i	0.124505	+	0.0904582i
$381$	−4.47214	+	13.7638i	−0.229114	+	0.705142i
$382$	6.19098	+	19.0539i	0.316758	+	0.974882i
$383$	−24.8435	+	18.0498i	−1.26944	+	0.922303i	−0.999180	−	0.0404838i	$-0.987110\pi$
$383$	−24.8435	+	18.0498i	−1.26944	+	0.922303i	−0.270261	+	0.962787i	$0.587110\pi$
$384$	−1.61803			−0.0825700
$385$	−0.645898	−	1.08981i	−0.0329180	−	0.0555421i
$386$	−11.7984			−0.600521
$387$	3.38197	−	2.45714i	0.171915	−	0.124904i
$388$	−1.02786	−	3.16344i	−0.0521819	−	0.160599i
$389$	6.20820	−	19.1069i	0.314768	−	0.968758i	−0.661081	−	0.750314i	$-0.729902\pi$
$389$	6.20820	−	19.1069i	0.314768	−	0.968758i	0.975850	−	0.218443i	$-0.0700979\pi$
$390$	3.42705	+	2.48990i	0.173535	+	0.126081i
$391$	6.85410	+	4.97980i	0.346627	+	0.251839i
$392$	−2.11803	+	6.51864i	−0.106977	+	0.329241i
$393$	−1.16312	−	3.57971i	−0.0586716	−	0.180573i
$394$	6.89919	−	5.01255i	0.347576	−	0.252529i
$395$	−5.47214			−0.275333
$396$	−1.23607	+	0.277515i	−0.0621148	+	0.0139456i
$397$	4.41641			0.221653			0.110827	−	0.993840i	$-0.464650\pi$
$397$	4.41641			0.221653			0.110827	+	0.993840i	$0.464650\pi$
$398$	2.50000	−	1.81636i	0.125314	−	0.0910457i
$399$	−0.572949	−	1.76336i	−0.0286833	−	0.0882782i
$400$	−1.23607	+	3.80423i	−0.0618034	+	0.190211i
$401$	9.01722	+	6.55139i	0.450299	+	0.327161i	0.789714	−	0.613476i	$-0.210229\pi$
$401$	9.01722	+	6.55139i	0.450299	+	0.327161i	−0.339415	+	0.940637i	$0.610229\pi$
$402$	10.3992	+	7.55545i	0.518664	+	0.376832i
$403$	2.61803	−	8.05748i	0.130414	−	0.401372i
$404$	−1.89919	−	5.84510i	−0.0944881	−	0.290804i
$405$	6.23607	−	4.53077i	0.309873	−	0.225136i
$406$	1.43769			0.0713516
$407$	3.04508	+	1.31433i	0.150939	+	0.0651488i
$408$	−1.61803			−0.0801046
$409$	−10.7812	+	7.83297i	−0.533094	+	0.387315i	−0.821514	−	0.570189i	$-0.806870\pi$
$409$	−10.7812	+	7.83297i	−0.533094	+	0.387315i	0.288420	+	0.957504i	$0.406870\pi$
$410$	−2.30902	−	7.10642i	−0.114034	−	0.350961i
$411$	9.32624	−	28.7032i	0.460029	−	1.41582i
$412$	3.54508	+	2.57565i	0.174654	+	0.126893i
$413$	3.85410	+	2.80017i	0.189648	+	0.137787i
$414$	1.00000	−	3.07768i	0.0491473	−	0.151260i
$415$	−3.04508	−	9.37181i	−0.149477	−	0.460044i
$416$	−2.11803	+	1.53884i	−0.103845	+	0.0754479i
$417$	−22.5623			−1.10488
$418$	6.57295	−	7.46969i	0.321493	−	0.365355i
$419$	−9.65248			−0.471554			−0.235777	−	0.971807i	$-0.575764\pi$
$419$	−9.65248			−0.471554			−0.235777	+	0.971807i	$0.575764\pi$
$420$	−0.500000	+	0.363271i	−0.0243975	+	0.0177258i
$421$	7.96149	+	24.5030i	0.388019	+	1.19420i	0.934266	+	0.356577i	$0.116056\pi$
$421$	7.96149	+	24.5030i	0.388019	+	1.19420i	−0.546247	+	0.837624i	$0.683944\pi$
$422$	−5.79180	+	17.8253i	−0.281940	+	0.867723i
$423$	−2.69098	−	1.95511i	−0.130840	−	0.0950609i
$424$	−1.42705	−	1.03681i	−0.0693037	−	0.0503521i
$425$	−1.23607	+	3.80423i	−0.0599581	+	0.184532i
$426$	−1.80902	−	5.56758i	−0.0876472	−	0.269750i
$427$	−1.28115	+	0.930812i	−0.0619993	+	0.0450452i
$428$	−5.23607			−0.253095
$429$	9.28115	−	10.5474i	0.448098	−	0.509232i
$430$	10.9443			0.527780
$431$	24.8885	−	18.0826i	1.19884	−	0.871007i	0.204669	−	0.978831i	$-0.434388\pi$
$431$	24.8885	−	18.0826i	1.19884	−	0.871007i	0.994170	+	0.107824i	$0.0343882\pi$
$432$	1.69098	+	5.20431i	0.0813575	+	0.250393i
$433$	6.60081	−	20.3152i	0.317215	−	0.976287i	−0.657618	−	0.753351i	$-0.728436\pi$
$433$	6.60081	−	20.3152i	0.317215	−	0.976287i	0.974833	−	0.222936i	$-0.0715640\pi$
$434$	1.00000	+	0.726543i	0.0480015	+	0.0348752i
$435$	−4.92705	−	3.57971i	−0.236234	−	0.171634i
$436$	5.35410	−	16.4782i	0.256415	−	0.789164i
$437$	7.85410	+	24.1724i	0.375713	+	1.15632i
$438$	−18.6353	+	13.5393i	−0.890427	+	0.646933i
$439$	−37.2705			−1.77882			−0.889412	−	0.457106i	$-0.848886\pi$
$439$	−37.2705			−1.77882			−0.889412	+	0.457106i	$0.848886\pi$
$440$	−3.04508	−	1.31433i	−0.145169	−	0.0626581i
$441$	2.61803			0.124668
$442$	−2.11803	+	1.53884i	−0.100745	+	0.0731952i
$443$	6.75329	+	20.7845i	0.320858	+	0.987501i	0.973275	+	0.229641i	$0.0737551\pi$
$443$	6.75329	+	20.7845i	0.320858	+	0.987501i	−0.652417	+	0.757860i	$0.726245\pi$
$444$	0.500000	−	1.53884i	0.0237289	−	0.0730302i
$445$	5.80902	+	4.22050i	0.275374	+	0.200071i
$446$	−5.30902	−	3.85723i	−0.251389	−	0.182645i
$447$	3.80902	−	11.7229i	0.180160	−	0.554476i
$448$	−0.118034	−	0.363271i	−0.00557658	−	0.0171630i
$449$	8.82624	−	6.41264i	0.416536	−	0.302631i	−0.359707	−	0.933065i	$-0.617123\pi$
$449$	8.82624	−	6.41264i	0.416536	−	0.302631i	0.776243	+	0.630434i	$0.217123\pi$
$450$	1.52786			0.0720242
$451$	−24.1803	+	5.42882i	−1.13861	+	0.255633i
$452$	−5.14590			−0.242043
$453$	−29.9615	+	21.7683i	−1.40771	+	1.02276i
$454$	−5.68034	−	17.4823i	−0.266592	−	0.820484i
$455$	−0.309017	+	0.951057i	−0.0144869	+	0.0445862i
$456$	−3.92705	−	2.85317i	−0.183901	−	0.133612i
$457$	−0.618034	−	0.449028i	−0.0289104	−	0.0210046i	0.573236	−	0.819390i	$-0.305688\pi$
$457$	−0.618034	−	0.449028i	−0.0289104	−	0.0210046i	−0.602147	+	0.798386i	$0.705688\pi$
$458$	−5.21885	+	16.0620i	−0.243861	+	0.750526i
$459$	1.69098	+	5.20431i	0.0789283	+	0.242916i
$460$	6.85410	−	4.97980i	0.319574	−	0.232184i
$461$	26.8328			1.24973			0.624864	−	0.780733i	$-0.285154\pi$
$461$	26.8328			1.24973			0.624864	+	0.780733i	$0.285154\pi$
$462$	1.04508	+	1.76336i	0.0486218	+	0.0820387i
$463$	−26.5066			−1.23187			−0.615933	−	0.787799i	$-0.711221\pi$
$463$	−26.5066			−1.23187			−0.615933	+	0.787799i	$0.711221\pi$
$464$	3.04508	−	2.21238i	0.141365	−	0.102707i
$465$	−1.61803	−	4.97980i	−0.0750345	−	0.230933i
$466$	4.78115	−	14.7149i	0.221483	−	0.681653i
$467$	−28.9894	−	21.0620i	−1.34147	−	0.974633i	−0.999389	−	0.0349619i	$-0.988869\pi$
$467$	−28.9894	−	21.0620i	−1.34147	−	0.974633i	−0.342079	−	0.939671i	$-0.611131\pi$
$468$	0.809017	+	0.587785i	0.0373968	+	0.0271704i
$469$	−0.937694	+	2.88593i	−0.0432987	+	0.133260i
$470$	−2.69098	−	8.28199i	−0.124126	−	0.382020i
$471$	5.28115	−	3.83698i	0.243343	−	0.176799i
$472$	12.4721			0.574077
$473$	3.38197	−	36.1401i	0.155503	−	1.66173i
$474$	8.85410			0.406682
$475$	−9.70820	+	7.05342i	−0.445443	+	0.323633i
$476$	−0.118034	−	0.363271i	−0.00541008	−	0.0166505i
$477$	−0.208204	+	0.640786i	−0.00953300	+	0.0293396i
$478$	−23.8435	−	17.3233i	−1.09057	−	0.792349i
$479$	−1.70820	−	1.24108i	−0.0780498	−	0.0567065i	0.548076	−	0.836428i	$-0.315360\pi$
$479$	−1.70820	−	1.24108i	−0.0780498	−	0.0567065i	−0.626126	+	0.779722i	$0.715360\pi$
$480$	−0.500000	+	1.53884i	−0.0228218	+	0.0702382i
$481$	−0.809017	−	2.48990i	−0.0368880	−	0.113530i
$482$	10.3992	−	7.55545i	0.473670	−	0.344141i
$483$	−5.23607			−0.238249
$484$	−5.28115	+	9.64932i	−0.240052	+	0.438606i
$485$	−3.32624			−0.151037
$486$	3.19098	−	2.31838i	0.144746	−	0.105164i
$487$	−12.1631	−	37.4342i	−0.551164	−	1.69631i	−0.705866	−	0.708346i	$-0.749442\pi$
$487$	−12.1631	−	37.4342i	−0.551164	−	1.69631i	0.154702	−	0.987961i	$-0.450558\pi$
$488$	−1.28115	+	3.94298i	−0.0579951	+	0.178490i
$489$	−5.78115	−	4.20025i	−0.261433	−	0.189942i
$490$	5.54508	+	4.02874i	0.250501	+	0.182000i
$491$	−6.06231	+	18.6579i	−0.273588	+	0.842017i	0.716001	+	0.698099i	$0.245970\pi$
$491$	−6.06231	+	18.6579i	−0.273588	+	0.842017i	−0.989590	+	0.143919i	$0.954030\pi$
$492$	3.73607	+	11.4984i	0.168435	+	0.518389i
$493$	3.04508	−	2.21238i	0.137144	−	0.0996408i
$494$	−7.85410			−0.353373
$495$	−0.118034	+	1.26133i	−0.00530523	+	0.0566924i
$496$	3.23607			0.145304
$497$	1.11803	−	0.812299i	0.0501507	−	0.0364366i
$498$	4.92705	+	15.1639i	0.220786	+	0.679511i
$499$	−5.47214	+	16.8415i	−0.244966	+	0.753929i	0.750676	+	0.660671i	$0.229728\pi$
$499$	−5.47214	+	16.8415i	−0.244966	+	0.753929i	−0.995642	+	0.0932581i	$0.970272\pi$
$500$	7.28115	+	5.29007i	0.325623	+	0.236579i
$501$	−13.6353	−	9.90659i	−0.609178	−	0.442594i
$502$	−0.618034	+	1.90211i	−0.0275842	+	0.0848955i
$503$	3.76393	+	11.5842i	0.167825	+	0.516514i	0.999233	−	0.0391489i	$-0.0124647\pi$
$503$	3.76393	+	11.5842i	0.167825	+	0.516514i	−0.831408	+	0.555663i	$0.812465\pi$
$504$	−0.118034	+	0.0857567i	−0.00525765	+	0.00381991i
$505$	−6.14590			−0.273489
$506$	−14.3262	−	24.1724i	−0.636879	−	1.07460i
$507$	9.94427			0.441641
$508$	−7.23607	+	5.25731i	−0.321049	+	0.233255i
$509$	−9.48936	−	29.2052i	−0.420608	−	1.29450i	−0.907137	−	0.420835i	$-0.861737\pi$
$509$	−9.48936	−	29.2052i	−0.420608	−	1.29450i	0.486529	−	0.873664i	$-0.338263\pi$
$510$	−0.500000	+	1.53884i	−0.0221404	+	0.0681411i
$511$	−4.39919	−	3.19620i	−0.194609	−	0.141391i
$512$	−0.809017	−	0.587785i	−0.0357538	−	0.0259767i
$513$	−5.07295	+	15.6129i	−0.223976	+	0.689328i
$514$	6.20820	+	19.1069i	0.273832	+	0.842769i
$515$	3.54508	−	2.57565i	0.156215	−	0.113497i
$516$	−17.7082			−0.779560
$517$	−28.1803	+	6.32688i	−1.23937	+	0.278256i
$518$	0.381966			0.0167826
$519$	−27.9164	+	20.2825i	−1.22539	+	0.890301i
$520$	0.809017	+	2.48990i	0.0354777	+	0.109189i
$521$	−12.7254	+	39.1648i	−0.557511	+	1.71584i	0.131707	+	0.991289i	$0.457954\pi$
$521$	−12.7254	+	39.1648i	−0.557511	+	1.71584i	−0.689218	+	0.724554i	$0.742046\pi$
$522$	−1.16312	−	0.845055i	−0.0509083	−	0.0369871i
$523$	−1.82624	−	1.32684i	−0.0798558	−	0.0580186i	0.547141	−	0.837040i	$-0.315716\pi$
$523$	−1.82624	−	1.32684i	−0.0798558	−	0.0580186i	−0.626997	+	0.779022i	$0.715716\pi$
$524$	0.718847	−	2.21238i	0.0314030	−	0.0966484i
$525$	−0.763932	−	2.35114i	−0.0333407	−	0.102612i
$526$	7.78115	−	5.65334i	0.339274	−	0.246497i
$527$	3.23607			0.140965
$528$	4.92705	+	2.12663i	0.214422	+	0.0925496i
$529$	48.7771			2.12074
$530$	−1.42705	+	1.03681i	−0.0619871	+	0.0450363i
$531$	−1.47214	−	4.53077i	−0.0638853	−	0.196619i
$532$	0.354102	−	1.08981i	0.0153523	−	0.0472494i
$533$	15.8262	+	11.4984i	0.685510	+	0.498053i
$534$	−9.39919	−	6.82891i	−0.406743	−	0.295516i
$535$	−1.61803	+	4.97980i	−0.0699537	+	0.215295i
$536$	2.45492	+	7.55545i	0.106036	+	0.326346i
$537$	2.80902	−	2.04087i	0.121218	−	0.0880701i
$538$	12.6180			0.544002
$539$	15.0172	−	17.0660i	0.646837	−	0.735085i
$540$	5.47214			0.235483
$541$	18.4615	−	13.4131i	0.793722	−	0.576672i	−0.115344	−	0.993326i	$-0.536797\pi$
$541$	18.4615	−	13.4131i	0.793722	−	0.576672i	0.909066	+	0.416653i	$0.136797\pi$
$542$	−4.01722	−	12.3637i	−0.172554	−	0.531068i
$543$	−3.89919	+	12.0005i	−0.167330	+	0.514989i
$544$	−0.809017	−	0.587785i	−0.0346863	−	0.0252011i
$545$	−14.0172	−	10.1841i	−0.600432	−	0.436239i
$546$	0.500000	−	1.53884i	0.0213980	−	0.0658563i
$547$	13.3647	+	41.1325i	0.571435	+	1.75870i	0.648009	+	0.761633i	$0.275602\pi$
$547$	13.3647	+	41.1325i	0.571435	+	1.75870i	−0.0765735	+	0.997064i	$0.524398\pi$
$548$	15.0902	−	10.9637i	0.644620	−	0.468344i
$549$	1.58359			0.0675861
$550$	8.76393	−	9.95959i	0.373695	−	0.424678i
$551$	11.2918			0.481047
$552$	−11.0902	+	8.05748i	−0.472029	+	0.342949i
$553$	0.645898	+	1.98787i	0.0274664	+	0.0845328i
$554$	2.95492	−	9.09429i	0.125542	−	0.386379i
$555$	−1.30902	−	0.951057i	−0.0555647	−	0.0403701i
$556$	−11.2812	−	8.19624i	−0.478427	−	0.347598i
$557$	1.48936	−	4.58377i	0.0631061	−	0.194221i	−0.914533	−	0.404512i	$-0.867441\pi$
$557$	1.48936	−	4.58377i	0.0631061	−	0.194221i	0.977639	+	0.210292i	$0.0674413\pi$
$558$	−0.381966	−	1.17557i	−0.0161699	−	0.0497659i
$559$	−23.1803	+	16.8415i	−0.980424	+	0.712320i
$560$	−0.381966			−0.0161410
$561$	4.92705	+	2.12663i	0.208020	+	0.0897863i
$562$	−11.6525			−0.491530
$563$	1.85410	−	1.34708i	0.0781411	−	0.0567728i	−0.548029	−	0.836459i	$-0.684622\pi$
$563$	1.85410	−	1.34708i	0.0781411	−	0.0567728i	0.626170	+	0.779687i	$0.284622\pi$
$564$	4.35410	+	13.4005i	0.183341	+	0.564265i
$565$	−1.59017	+	4.89404i	−0.0668990	+	0.205894i
$566$	5.73607	+	4.16750i	0.241105	+	0.175173i
$567$	−2.38197	−	1.73060i	−0.100033	−	0.0726784i
$568$	1.11803	−	3.44095i	0.0469117	−	0.144379i
$569$	−2.29837	−	7.07367i	−0.0963528	−	0.296544i	0.891251	−	0.453510i	$-0.149828\pi$
$569$	−2.29837	−	7.07367i	−0.0963528	−	0.296544i	−0.987604	+	0.156967i	$0.949828\pi$
$570$	−3.92705	+	2.85317i	−0.164486	+	0.119506i
$571$	−5.70820			−0.238881			−0.119440	−	0.992841i	$-0.538110\pi$
$571$	−5.70820			−0.238881			−0.119440	+	0.992841i	$0.538110\pi$
$572$	8.47214	−	1.90211i	0.354238	−	0.0795313i
$573$	−32.4164			−1.35421
$574$	−2.30902	+	1.67760i	−0.0963765	+	0.0700216i
$575$	10.4721	+	32.2299i	0.436718	+	1.34408i
$576$	−0.118034	+	0.363271i	−0.00491808	+	0.0151363i
$577$	−36.1246	−	26.2461i	−1.50389	−	1.09264i	−0.968801	−	0.247841i	$-0.920279\pi$
$577$	−36.1246	−	26.2461i	−1.50389	−	1.09264i	−0.535086	−	0.844797i	$-0.679721\pi$
$578$	−0.809017	−	0.587785i	−0.0336507	−	0.0244486i
$579$	5.89919	−	18.1558i	0.245162	−	0.754531i
$580$	−1.16312	−	3.57971i	−0.0482959	−	0.148639i
$581$	−3.04508	+	2.21238i	−0.126331	+	0.0917851i
$582$	5.38197			0.223090
$583$	2.98278	+	5.03280i	0.123534	+	0.208437i
$584$	−14.2361			−0.589093
$585$	0.809017	−	0.587785i	0.0334487	−	0.0243019i
$586$	−4.24671	−	13.0700i	−0.175430	−	0.539918i
$587$	10.0729	−	31.0013i	0.415755	−	1.27956i	−0.495819	−	0.868426i	$-0.665132\pi$
$587$	10.0729	−	31.0013i	0.415755	−	1.27956i	0.911574	−	0.411137i	$-0.134868\pi$
$588$	−8.97214	−	6.51864i	−0.370005	−	0.268824i
$589$	7.85410	+	5.70634i	0.323623	+	0.235126i
$590$	3.85410	−	11.8617i	0.158671	−	0.488339i
$591$	4.26393	+	13.1230i	0.175395	+	0.539809i
$592$	0.809017	−	0.587785i	0.0332504	−	0.0241578i
$593$	7.76393			0.318826			0.159413	−	0.987212i	$-0.449040\pi$
$593$	7.76393			0.318826			0.159413	+	0.987212i	$0.449040\pi$
$594$	1.69098	−	18.0701i	0.0693819	−	0.741424i
$595$	−0.381966			−0.0156591
$596$	6.16312	−	4.47777i	0.252451	−	0.183417i
$597$	1.54508	+	4.75528i	0.0632361	+	0.194621i
$598$	−6.85410	+	21.0948i	−0.280285	+	0.862629i
$599$	−14.3541	−	10.4289i	−0.586493	−	0.426112i	0.254566	−	0.967055i	$-0.418067\pi$
$599$	−14.3541	−	10.4289i	−0.586493	−	0.426112i	−0.841059	+	0.540943i	$0.818067\pi$
$600$	−5.23607	−	3.80423i	−0.213762	−	0.155307i
$601$	7.76393	−	23.8949i	0.316697	−	0.974694i	−0.658353	−	0.752710i	$-0.728746\pi$
$601$	7.76393	−	23.8949i	0.316697	−	0.974694i	0.975050	−	0.221985i	$-0.0712535\pi$
$602$	−1.29180	−	3.97574i	−0.0526497	−	0.162039i
$603$	2.45492	−	1.78360i	0.0999719	−	0.0726338i
$604$	−22.8885			−0.931322
$605$	7.54508	+	8.00448i	0.306751	+	0.325428i
$606$	9.94427			0.403958
$607$	21.9443	−	15.9434i	0.890691	−	0.647125i	−0.0453674	−	0.998970i	$-0.514446\pi$
$607$	21.9443	−	15.9434i	0.890691	−	0.647125i	0.936058	+	0.351846i	$0.114446\pi$
$608$	−0.927051	−	2.85317i	−0.0375969	−	0.115711i
$609$	−0.718847	+	2.21238i	−0.0291292	+	0.0896503i
$610$	3.35410	+	2.43690i	0.135804	+	0.0986671i
$611$	18.4443	+	13.4005i	0.746175	+	0.542128i
$612$	−0.118034	+	0.363271i	−0.00477124	+	0.0146844i
$613$	6.79837	+	20.9232i	0.274584	+	0.845082i	0.989329	+	0.145697i	$0.0465425\pi$
$613$	6.79837	+	20.9232i	0.274584	+	0.845082i	−0.714745	+	0.699385i	$0.753457\pi$
$614$	9.51722	−	6.91467i	0.384084	−	0.279053i
$615$	12.0902			0.487523
$616$	−0.118034	+	1.26133i	−0.00475572	+	0.0508203i
$617$	46.0689			1.85466			0.927332	−	0.374240i	$-0.122097\pi$
$617$	46.0689			1.85466			0.927332	+	0.374240i	$0.122097\pi$
$618$	−5.73607	+	4.16750i	−0.230738	+	0.167641i
$619$	−8.19098	−	25.2093i	−0.329223	−	1.01325i	−0.969498	−	0.245099i	$-0.921179\pi$
$619$	−8.19098	−	25.2093i	−0.329223	−	1.01325i	0.640275	−	0.768146i	$-0.278821\pi$
$620$	1.00000	−	3.07768i	0.0401610	−	0.123603i
$621$	37.5066	+	27.2501i	1.50509	+	1.09351i
$622$	−26.0795	−	18.9479i	−1.04569	−	0.759741i
$623$	0.847524	−	2.60841i	0.0339553	−	0.104504i
$624$	−1.30902	−	4.02874i	−0.0524026	−	0.161279i
$625$	−8.89919	+	6.46564i	−0.355967	+	0.258626i
$626$	13.5623			0.542059
$627$	8.20820	+	13.8496i	0.327804	+	0.553099i
$628$	4.03444			0.160992
$629$	0.809017	−	0.587785i	0.0322576	−	0.0234365i
$630$	0.0450850	+	0.138757i	0.00179623	+	0.00552822i
$631$	−0.420473	+	1.29408i	−0.0167388	+	0.0515166i	−0.959077	−	0.283145i	$-0.908622\pi$
$631$	−0.420473	+	1.29408i	−0.0167388	+	0.0515166i	0.942338	+	0.334662i	$0.108622\pi$
$632$	4.42705	+	3.21644i	0.176099	+	0.127943i
$633$	−24.5344	−	17.8253i	−0.975157	−	0.708493i
$634$	−6.50000	+	20.0049i	−0.258148	+	0.794498i
$635$	2.76393	+	8.50651i	0.109683	+	0.337570i
$636$	2.30902	−	1.67760i	0.0915585	−	0.0665211i
$637$	−17.9443			−0.710978
$638$	−12.1803	+	2.73466i	−0.482224	+	0.108266i
$639$	−1.38197			−0.0546697
$640$	−0.809017	+	0.587785i	−0.0319792	+	0.0232343i
$641$	−11.1631	−	34.3565i	−0.440917	−	1.35700i	−0.886900	−	0.461961i	$-0.847146\pi$
$641$	−11.1631	−	34.3565i	−0.440917	−	1.35700i	0.445984	−	0.895041i	$-0.352854\pi$
$642$	2.61803	−	8.05748i	0.103326	−	0.318003i
$643$	4.32624	+	3.14320i	0.170610	+	0.123956i	0.669814	−	0.742529i	$-0.266374\pi$
$643$	4.32624	+	3.14320i	0.170610	+	0.123956i	−0.499203	+	0.866485i	$0.666374\pi$
$644$	−2.61803	−	1.90211i	−0.103165	−	0.0749538i
$645$	−5.47214	+	16.8415i	−0.215465	+	0.663134i
$646$	−0.927051	−	2.85317i	−0.0364743	−	0.112256i
$647$	−9.94427	+	7.22494i	−0.390950	+	0.284042i	−0.765845	−	0.643026i	$-0.777679\pi$
$647$	−9.94427	+	7.22494i	−0.390950	+	0.284042i	0.374895	+	0.927067i	$0.377679\pi$
$648$	−7.70820			−0.302807
$649$	−37.9787	−	16.3925i	−1.49079	−	0.643461i
$650$	−10.4721			−0.410751
$651$	−1.61803	+	1.17557i	−0.0634158	+	0.0460742i
$652$	−1.36475	−	4.20025i	−0.0534475	−	0.164495i
$653$	10.7361	−	33.0422i	0.420135	−	1.29304i	−0.487442	−	0.873155i	$-0.662070\pi$
$653$	10.7361	−	33.0422i	0.420135	−	1.29304i	0.907577	−	0.419887i	$-0.137930\pi$
$654$	22.6803	+	16.4782i	0.886871	+	0.644350i
$655$	−1.88197	−	1.36733i	−0.0735345	−	0.0534259i
$656$	−2.30902	+	7.10642i	−0.0901520	+	0.277459i
$657$	1.68034	+	5.17155i	0.0655563	+	0.201762i
$658$	−2.69098	+	1.95511i	−0.104905	+	0.0762183i
$659$	−29.9787			−1.16780			−0.583902	−	0.811824i	$-0.698475\pi$
$659$	−29.9787			−1.16780			−0.583902	+	0.811824i	$0.698475\pi$
$660$	3.54508	−	4.02874i	0.137992	−	0.156818i
$661$	5.12461			0.199324			0.0996621	−	0.995021i	$-0.468224\pi$
$661$	5.12461			0.199324			0.0996621	+	0.995021i	$0.468224\pi$
$662$	−6.80902	+	4.94704i	−0.264640	+	0.192272i
$663$	−1.30902	−	4.02874i	−0.0508380	−	0.156463i
$664$	−3.04508	+	9.37181i	−0.118172	+	0.363697i
$665$	−0.927051	−	0.673542i	−0.0359495	−	0.0261188i
$666$	−0.309017	−	0.224514i	−0.0119742	−	0.00869974i
$667$	9.85410	−	30.3278i	0.381552	−	1.17430i
$668$	−3.21885	−	9.90659i	−0.124541	−	0.383298i
$669$	8.59017	−	6.24112i	0.332115	−	0.241296i
$670$	7.94427			0.306914
$671$	9.08359	−	10.3229i	0.350668	−	0.398510i
$672$	0.618034			0.0238412
$673$	−10.6631	+	7.74721i	−0.411033	+	0.298633i	−0.774020	−	0.633161i	$-0.781757\pi$
$673$	−10.6631	+	7.74721i	−0.411033	+	0.298633i	0.362987	+	0.931794i	$0.381757\pi$
$674$	2.60081	+	8.00448i	0.100180	+	0.308321i
$675$	−6.76393	+	20.8172i	−0.260344	+	0.801256i
$676$	4.97214	+	3.61247i	0.191236	+	0.138941i
$677$	8.11803	+	5.89810i	0.312001	+	0.226682i	0.732755	−	0.680493i	$-0.238234\pi$
$677$	8.11803	+	5.89810i	0.312001	+	0.226682i	−0.420753	+	0.907175i	$0.638234\pi$
$678$	2.57295	−	7.91872i	0.0988135	−	0.304117i
$679$	0.392609	+	1.20833i	0.0150670	+	0.0463713i
$680$	−0.809017	+	0.587785i	−0.0310244	+	0.0225405i
$681$	29.7426			1.13974
$682$	−9.85410	−	4.25325i	−0.377333	−	0.162866i
$683$	−11.4508			−0.438155			−0.219077	−	0.975708i	$-0.570305\pi$
$683$	−11.4508			−0.438155			−0.219077	+	0.975708i	$0.570305\pi$
$684$	−0.927051	+	0.673542i	−0.0354467	+	0.0257535i
$685$	−5.76393	−	17.7396i	−0.220229	−	0.677794i
$686$	1.63525	−	5.03280i	0.0624343	−	0.192153i
$687$	−22.1074	−	16.0620i	−0.843450	−	0.612802i
$688$	−8.85410	−	6.43288i	−0.337559	−	0.245251i
$689$	1.42705	−	4.39201i	0.0543663	−	0.167322i
$690$	4.23607	+	13.0373i	0.161264	+	0.496321i
$691$	−13.1353	+	9.54332i	−0.499689	+	0.363045i	−0.808898	−	0.587949i	$-0.799936\pi$
$691$	−13.1353	+	9.54332i	−0.499689	+	0.363045i	0.309209	+	0.950994i	$0.399936\pi$
$692$	−21.3262			−0.810702
$693$	0.472136	−	0.106001i	0.0179350	−	0.00402665i
$694$	−13.0000			−0.493473
$695$	−11.2812	+	8.19624i	−0.427919	+	0.310901i
$696$	1.88197	+	5.79210i	0.0713357	+	0.219549i
$697$	−2.30902	+	7.10642i	−0.0874603	+	0.269175i
$698$	0.309017	+	0.224514i	0.0116965	+	0.00849798i
$699$	20.2533	+	14.7149i	0.766050	+	0.556568i
$700$	0.472136	−	1.45309i	0.0178451	−	0.0549215i
$701$	−1.53851	−	4.73504i	−0.0581086	−	0.178840i	0.917789	−	0.397068i	$-0.129972\pi$
$701$	−1.53851	−	4.73504i	−0.0581086	−	0.178840i	−0.975898	+	0.218228i	$0.929972\pi$
$702$	−11.5902	+	8.42075i	−0.437443	+	0.317821i
$703$	3.00000			0.113147
$704$	1.69098	+	2.85317i	0.0637313	+	0.107533i
$705$	14.0902			0.530667
$706$	−3.09017	+	2.24514i	−0.116300	+	0.0844970i
$707$	0.725425	+	2.23263i	0.0272824	+	0.0839666i
$708$	−6.23607	+	19.1926i	−0.234366	+	0.721304i
$709$	20.8435	+	15.1437i	0.782793	+	0.568732i	0.905816	−	0.423672i	$-0.139259\pi$
$709$	20.8435	+	15.1437i	0.782793	+	0.568732i	−0.123023	+	0.992404i	$0.539259\pi$
$710$	−2.92705	−	2.12663i	−0.109850	−	0.0798109i
$711$	0.645898	−	1.98787i	0.0242231	−	0.0745509i
$712$	−2.21885	−	6.82891i	−0.0831548	−	0.255924i
$713$	22.1803	−	16.1150i	0.830660	−	0.603510i
$714$	0.618034			0.0231293
$715$	0.809017	−	8.64527i	0.0302555	−	0.323315i
$716$	2.14590			0.0801960
$717$	38.5795	−	28.0297i	1.44078	−	1.04679i
$718$	−5.12868	−	15.7844i	−0.191401	−	0.589070i
$719$	14.7148	−	45.2874i	0.548769	−	1.68894i	−0.163088	−	0.986612i	$-0.552145\pi$
$719$	14.7148	−	45.2874i	0.548769	−	1.68894i	0.711856	−	0.702325i	$-0.247855\pi$
$720$	0.309017	+	0.224514i	0.0115164	+	0.00836714i
$721$	−1.35410	−	0.983813i	−0.0504294	−	0.0366391i
$722$	−3.09017	+	9.51057i	−0.115004	+	0.353947i
$723$	6.42705	+	19.7804i	0.239025	+	0.735642i
$724$	−6.30902	+	4.58377i	−0.234473	+	0.170354i
$725$	15.0557			0.559156
$726$	−12.2082	−	12.9515i	−0.453089	−	0.480676i
$727$	36.1246			1.33979			0.669894	−	0.742457i	$-0.266340\pi$
$727$	36.1246			1.33979			0.669894	+	0.742457i	$0.266340\pi$
$728$	0.809017	−	0.587785i	0.0299842	−	0.0217848i
$729$	9.11803	+	28.0624i	0.337705	+	1.03935i
$730$	−4.39919	+	13.5393i	−0.162821	+	0.501112i
$731$	−8.85410	−	6.43288i	−0.327481	−	0.237929i
$732$	−5.42705	−	3.94298i	−0.200590	−	0.145737i
$733$	2.59017	−	7.97172i	0.0956701	−	0.294442i	−0.891758	−	0.452513i	$-0.850527\pi$
$733$	2.59017	−	7.97172i	0.0956701	−	0.294442i	0.987428	+	0.158071i	$0.0505275\pi$
$734$	6.26393	+	19.2784i	0.231206	+	0.711579i
$735$	−8.97214	+	6.51864i	−0.330942	+	0.240444i
$736$	−8.47214			−0.312287
$737$	2.45492	−	26.2336i	0.0904280	−	0.966325i
$738$	2.85410			0.105061
$739$	−37.9787	+	27.5932i	−1.39707	+	1.01503i	−0.402022	+	0.915630i	$0.631692\pi$
$739$	−37.9787	+	27.5932i	−1.39707	+	1.01503i	−0.995048	+	0.0994005i	$0.968308\pi$
$740$	−0.309017	−	0.951057i	−0.0113597	−	0.0349615i
$741$	3.92705	−	12.0862i	0.144264	−	0.443998i
$742$	0.545085	+	0.396027i	0.0200107	+	0.0145386i
$743$	38.8156	+	28.2012i	1.42401	+	1.03460i	0.991094	+	0.133165i	$0.0425140\pi$
$743$	38.8156	+	28.2012i	1.42401	+	1.03460i	0.432912	+	0.901436i	$0.357486\pi$
$744$	−1.61803	+	4.97980i	−0.0593200	+	0.182568i
$745$	−2.35410	−	7.24518i	−0.0862476	−	0.265443i
$746$	−5.30902	+	3.85723i	−0.194377	+	0.141223i
$747$	3.76393			0.137715
$748$	1.69098	+	2.85317i	0.0618285	+	0.104322i
$749$	2.00000			0.0730784
$750$	−11.7812	+	8.55951i	−0.430187	+	0.312549i
$751$	−2.30902	−	7.10642i	−0.0842572	−	0.259317i	0.900048	−	0.435790i	$-0.143531\pi$
$751$	−2.30902	−	7.10642i	−0.0842572	−	0.259317i	−0.984305	+	0.176473i	$0.943531\pi$
$752$	−2.69098	+	8.28199i	−0.0981301	+	0.302013i
$753$	−2.61803	−	1.90211i	−0.0954065	−	0.0693169i
$754$	7.97214	+	5.79210i	0.290328	+	0.210936i
$755$	−7.07295	+	21.7683i	−0.257411	+	0.792230i
$756$	−0.645898	−	1.98787i	−0.0234911	−	0.0722981i
$757$	33.2254	−	24.1397i	1.20760	−	0.877372i	0.212588	−	0.977142i	$-0.431811\pi$
$757$	33.2254	−	24.1397i	1.20760	−	0.877372i	0.995011	+	0.0997702i	$0.0318108\pi$
$758$	20.1459			0.731732
$759$	44.3607	−	9.95959i	1.61019	−	0.361510i
$760$	−3.00000			−0.108821
$761$	−11.5623	+	8.40051i	−0.419133	+	0.304518i	−0.777289	−	0.629144i	$-0.783406\pi$
$761$	−11.5623	+	8.40051i	−0.419133	+	0.304518i	0.358156	+	0.933662i	$0.383406\pi$
$762$	−4.47214	−	13.7638i	−0.162008	−	0.498611i
$763$	−2.04508	+	6.29412i	−0.0740370	+	0.227863i
$764$	−16.2082	−	11.7759i	−0.586392	−	0.426039i
$765$	0.309017	+	0.224514i	0.0111725	+	0.00811732i
$766$	9.48936	−	29.2052i	0.342864	−	1.05523i
$767$	10.0902	+	31.0543i	0.364335	+	1.12131i
$768$	1.30902	−	0.951057i	0.0472351	−	0.0343183i
$769$	38.4164			1.38533			0.692666	−	0.721259i	$-0.256436\pi$
$769$	38.4164			1.38533			0.692666	+	0.721259i	$0.256436\pi$
$770$	1.16312	+	0.502029i	0.0419159	+	0.0180919i
$771$	−32.5066			−1.17070
$772$	9.54508	−	6.93491i	0.343535	−	0.249593i
$773$	8.98936	+	27.6664i	0.323325	+	0.995091i	0.972191	+	0.234189i	$0.0752434\pi$
$773$	8.98936	+	27.6664i	0.323325	+	0.995091i	−0.648866	+	0.760902i	$0.724757\pi$
$774$	−1.29180	+	3.97574i	−0.0464327	+	0.142905i
$775$	10.4721	+	7.60845i	0.376170	+	0.273304i
$776$	2.69098	+	1.95511i	0.0966007	+	0.0701845i
$777$	−0.190983	+	0.587785i	−0.00685148	+	0.0210867i
$778$	6.20820	+	19.1069i	0.222575	+	0.685015i
$779$	−18.1353	+	13.1760i	−0.649763	+	0.472080i
$780$	−4.23607			−0.151676
$781$	−7.92705	+	9.00854i	−0.283652	+	0.322351i
$782$	−8.47214			−0.302963
$783$	16.6631	−	12.1065i	0.595491	−	0.432650i
$784$	−2.11803	−	6.51864i	−0.0756441	−	0.232809i
$785$	1.24671	−	3.83698i	0.0444970	−	0.136948i
$786$	3.04508	+	2.21238i	0.108615	+	0.0789131i
$787$	−39.3156	−	28.5645i	−1.40145	−	1.01821i	−0.994497	−	0.104763i	$-0.966591\pi$
$787$	−39.3156	−	28.5645i	−1.40145	−	1.01821i	−0.406952	−	0.913449i	$-0.633409\pi$
$788$	−2.63525	+	8.11048i	−0.0938771	+	0.288924i
$789$	4.80902	+	14.8006i	0.171206	+	0.526916i
$790$	4.42705	−	3.21644i	0.157507	−	0.114436i
$791$	1.96556			0.0698872
$792$	0.836881	−	0.951057i	0.0297373	−	0.0337943i
$793$	−10.8541			−0.385440
$794$	−3.57295	+	2.59590i	−0.126799	+	0.0921250i
$795$	−0.881966	−	2.71441i	−0.0312801	−	0.0962703i
$796$	−0.954915	+	2.93893i	−0.0338461	+	0.104167i
$797$	−39.0344	−	28.3602i	−1.38267	−	1.00457i	−0.996625	−	0.0820896i	$-0.973841\pi$
$797$	−39.0344	−	28.3602i	−1.38267	−	1.00457i	−0.386046	−	0.922480i	$-0.626159\pi$
$798$	1.50000	+	1.08981i	0.0530994	+	0.0385790i
$799$	−2.69098	+	8.28199i	−0.0952001	+	0.292996i
$800$	−1.23607	−	3.80423i	−0.0437016	−	0.134500i
$801$	−2.21885	+	1.61209i	−0.0783991	+	0.0569603i
$802$	−11.1459			−0.393575
$803$	43.3500	+	18.7109i	1.52979	+	0.660292i
$804$	−12.8541			−0.453329
$805$	−2.61803	+	1.90211i	−0.0922736	+	0.0670407i
$806$	2.61803	+	8.05748i	0.0922163	+	0.283813i
$807$	−6.30902	+	19.4172i	−0.222088	+	0.683516i
$808$	4.97214	+	3.61247i	0.174919	+	0.127086i
$809$	−4.71885	−	3.42844i	−0.165906	−	0.120538i	0.501734	−	0.865022i	$-0.332696\pi$
$809$	−4.71885	−	3.42844i	−0.165906	−	0.120538i	−0.667640	+	0.744484i	$0.732696\pi$
$810$	−2.38197	+	7.33094i	−0.0836938	+	0.257583i
$811$	7.82624	+	24.0867i	0.274816	+	0.845798i	0.989268	+	0.146113i	$0.0466763\pi$
$811$	7.82624	+	24.0867i	0.274816	+	0.845798i	−0.714452	+	0.699685i	$0.753324\pi$
$812$	−1.16312	+	0.845055i	−0.0408175	+	0.0296556i
$813$	21.0344			0.737710
$814$	−3.23607	+	0.726543i	−0.113424	+	0.0254653i
$815$	−4.41641			−0.154700
$816$	1.30902	−	0.951057i	0.0458248	−	0.0332936i
$817$	−10.1459	−	31.2259i	−0.354960	−	1.09245i
$818$	4.11803	−	12.6740i	0.143984	−	0.443136i
$819$	−0.309017	−	0.224514i	−0.0107979	−	0.00784515i
$820$	6.04508	+	4.39201i	0.211104	+	0.153376i
$821$	−6.34752	+	19.5357i	−0.221530	+	0.681800i	0.777095	+	0.629383i	$0.216692\pi$
$821$	−6.34752	+	19.5357i	−0.221530	+	0.681800i	−0.998625	+	0.0524165i	$0.983308\pi$
$822$	9.32624	+	28.7032i	0.325290	+	1.00114i
$823$	−7.95492	+	5.77958i	−0.277291	+	0.201464i	−0.717735	−	0.696316i	$-0.754821\pi$
$823$	−7.95492	+	5.77958i	−0.277291	+	0.201464i	0.440444	+	0.897780i	$0.354821\pi$
$824$	−4.38197			−0.152653
$825$	10.9443	+	18.4661i	0.381031	+	0.642907i
$826$	−4.76393			−0.165758
$827$	−42.6525	+	30.9888i	−1.48317	+	1.07759i	−0.506654	+	0.862149i	$0.669118\pi$
$827$	−42.6525	+	30.9888i	−1.48317	+	1.07759i	−0.976517	+	0.215438i	$0.930882\pi$
$828$	1.00000	+	3.07768i	0.0347524	+	0.106957i
$829$	−15.3820	+	47.3408i	−0.534238	+	1.64421i	0.211053	+	0.977475i	$0.432311\pi$
$829$	−15.3820	+	47.3408i	−0.534238	+	1.64421i	−0.745290	+	0.666740i	$0.767689\pi$
$830$	7.97214	+	5.79210i	0.276717	+	0.201047i
$831$	12.5172	+	9.09429i	0.434218	+	0.315478i
$832$	0.809017	−	2.48990i	0.0280476	−	0.0863217i
$833$	−2.11803	−	6.51864i	−0.0733855	−	0.225857i
$834$	18.2533	−	13.2618i	0.632060	−	0.459218i
$835$	−10.4164			−0.360475
$836$	−0.927051	+	9.90659i	−0.0320627	+	0.342627i
$837$	17.7082			0.612085
$838$	7.80902	−	5.67358i	0.269758	−	0.195991i
$839$	3.52786	+	10.8576i	0.121795	+	0.374848i	0.993304	−	0.115533i	$-0.0368577\pi$
$839$	3.52786	+	10.8576i	0.121795	+	0.374848i	−0.871508	+	0.490381i	$0.836858\pi$
$840$	0.190983	−	0.587785i	0.00658954	−	0.0202805i
$841$	12.0000	+	8.71851i	0.413793	+	0.300638i
$842$	−20.8435	−	15.1437i	−0.718313	−	0.521885i
$843$	5.82624	−	17.9313i	0.200666	−	0.617587i
$844$	−5.79180	−	17.8253i	−0.199362	−	0.613573i
$845$	4.97214	−	3.61247i	0.171047	−	0.124273i
$846$	3.32624			0.114358
$847$	2.01722	−	3.68571i	0.0693125	−	0.126643i
$848$	1.76393			0.0605737
$849$	−9.28115	+	6.74315i	−0.318528	+	0.231424i
$850$	−1.23607	−	3.80423i	−0.0423968	−	0.130484i
$851$	2.61803	−	8.05748i	0.0897450	−	0.276207i
$852$	4.73607	+	3.44095i	0.162255	+	0.117885i
$853$	−13.7533	−	9.99235i	−0.470904	−	0.342132i	0.326890	−	0.945062i	$-0.393999\pi$
$853$	−13.7533	−	9.99235i	−0.470904	−	0.342132i	−0.797793	+	0.602931i	$0.793999\pi$
$854$	0.489357	−	1.50609i	0.0167454	−	0.0515372i
$855$	0.354102	+	1.08981i	0.0121100	+	0.0372708i
$856$	4.23607	−	3.07768i	0.144786	−	0.105193i
$857$	36.3607			1.24206			0.621029	−	0.783788i	$-0.286715\pi$
$857$	36.3607			1.24206			0.621029	+	0.783788i	$0.286715\pi$
$858$	−1.30902	+	13.9883i	−0.0446891	+	0.477554i
$859$	29.5410			1.00793			0.503963	−	0.863725i	$-0.331875\pi$
$859$	29.5410			1.00793			0.503963	+	0.863725i	$0.331875\pi$
$860$	−8.85410	+	6.43288i	−0.301922	+	0.219359i
$861$	−1.42705	−	4.39201i	−0.0486338	−	0.149679i
$862$	−9.50658	+	29.2582i	−0.323795	+	0.996540i
$863$	13.1074	+	9.52308i	0.446181	+	0.324169i	0.788086	−	0.615565i	$-0.211072\pi$
$863$	13.1074	+	9.52308i	0.446181	+	0.324169i	−0.341905	+	0.939734i	$0.611072\pi$
$864$	−4.42705	−	3.21644i	−0.150611	−	0.109426i
$865$	−6.59017	+	20.2825i	−0.224073	+	0.689624i
$866$	6.60081	+	20.3152i	0.224305	+	0.690339i
$867$	1.30902	−	0.951057i	0.0444565	−	0.0322996i
$868$	−1.23607			−0.0419549
$869$	−9.25329	−	15.6129i	−0.313896	−	0.529632i
$870$	6.09017			0.206476
$871$	−16.8262	+	12.2250i	−0.570135	+	0.414228i
$872$	5.35410	+	16.4782i	0.181313	+	0.558023i
$873$	0.392609	−	1.20833i	0.0132878	−	0.0408957i
$874$	−20.5623	−	14.9394i	−0.695530	−	0.505332i
$875$	−2.78115	−	2.02063i	−0.0940201	−	0.0683096i
$876$	7.11803	−	21.9071i	0.240496	−	0.740171i
$877$	6.69756	+	20.6130i	0.226161	+	0.696051i	0.998172	+	0.0604417i	$0.0192509\pi$
$877$	6.69756	+	20.6130i	0.226161	+	0.696051i	−0.772011	+	0.635609i	$0.780749\pi$
$878$	30.1525	−	21.9071i	1.01760	−	0.739327i
$879$	22.2361			0.750004
$880$	3.23607	−	0.726543i	0.109088	−	0.0244917i
$881$	−29.3607			−0.989186			−0.494593	−	0.869125i	$-0.664683\pi$
$881$	−29.3607			−0.989186			−0.494593	+	0.869125i	$0.664683\pi$
$882$	−2.11803	+	1.53884i	−0.0713179	+	0.0518155i
$883$	1.41641	+	4.35926i	0.0476659	+	0.146701i	0.972057	−	0.234746i	$-0.0754259\pi$
$883$	1.41641	+	4.35926i	0.0476659	+	0.146701i	−0.924391	+	0.381447i	$0.875426\pi$
$884$	0.809017	−	2.48990i	0.0272102	−	0.0837443i
$885$	16.3262	+	11.8617i	0.548800	+	0.398727i
$886$	−17.6803	−	12.8455i	−0.593983	−	0.431554i
$887$	−3.41641	+	10.5146i	−0.114712	+	0.353046i	−0.991887	−	0.127124i	$-0.959425\pi$
$887$	−3.41641	+	10.5146i	−0.114712	+	0.353046i	0.877175	+	0.480171i	$0.159425\pi$
$888$	0.500000	+	1.53884i	0.0167789	+	0.0516401i
$889$	2.76393	−	2.00811i	0.0926993	−	0.0673500i
$890$	−7.18034			−0.240686
$891$	23.4721	+	10.1311i	0.786346	+	0.339405i
$892$	6.56231			0.219722
$893$	−21.1353	+	15.3557i	−0.707264	+	0.513858i
$894$	3.80902	+	11.7229i	0.127393	+	0.392074i
$895$	0.663119	−	2.04087i	0.0221656	−	0.0682188i
$896$	0.309017	+	0.224514i	0.0103235	+	0.00750049i
$897$	−29.0344	−	21.0948i	−0.969432	−	0.704333i
$898$	−3.37132	+	10.3759i	−0.112503	+	0.346247i
$899$	−3.76393	−	11.5842i	−0.125534	−	0.386354i
$900$	−1.23607	+	0.898056i	−0.0412023	+	0.0299352i
$901$	1.76393			0.0587651
$902$	16.3713	−	18.6049i	0.545105	−	0.619474i
$903$	6.76393			0.225090
$904$	4.16312	−	3.02468i	0.138463	−	0.100599i
$905$	2.40983	+	7.41669i	0.0801055	+	0.246539i
$906$	11.4443	−	35.2218i	0.380210	−	1.17017i
$907$	−17.4271	−	12.6615i	−0.578656	−	0.420418i	0.259583	−	0.965721i	$-0.416415\pi$
$907$	−17.4271	−	12.6615i	−0.578656	−	0.420418i	−0.838239	+	0.545303i	$0.816415\pi$
$908$	14.8713	+	10.8046i	0.493522	+	0.358565i
$909$	0.725425	−	2.23263i	0.0240608	−	0.0740516i
$910$	−0.309017	−	0.951057i	−0.0102438	−	0.0315272i
$911$	12.8713	−	9.35156i	0.426446	−	0.309831i	−0.353780	−	0.935329i	$-0.615104\pi$
$911$	12.8713	−	9.35156i	0.426446	−	0.309831i	0.780226	+	0.625497i	$0.215104\pi$
$912$	4.85410			0.160735
$913$	21.5902	−	24.5357i	0.714530	−	0.812014i
$914$	0.763932			0.0252686
$915$	−5.42705	+	3.94298i	−0.179413	+	0.130351i
$916$	−5.21885	−	16.0620i	−0.172436	−	0.530702i
$917$	−0.274575	+	0.845055i	−0.00906727	+	0.0279062i
$918$	−4.42705	−	3.21644i	−0.146114	−	0.106158i
$919$	−38.6976	−	28.1154i	−1.27651	−	0.927442i	−0.277073	−	0.960849i	$-0.589364\pi$
$919$	−38.6976	−	28.1154i	−1.27651	−	0.927442i	−0.999442	+	0.0334066i	$0.989364\pi$
$920$	−2.61803	+	8.05748i	−0.0863140	+	0.265647i
$921$	5.88197	+	18.1028i	0.193817	+	0.596509i
$922$	−21.7082	+	15.7719i	−0.714922	+	0.519421i
$923$	9.47214			0.311779
$924$	−1.88197	−	0.812299i	−0.0619121	−	0.0267227i
$925$	4.00000			0.131519
$926$	21.4443	−	15.5802i	0.704702	−	0.511996i
$927$	0.517221	+	1.59184i	0.0169878	+	0.0522830i
$928$	−1.16312	+	3.57971i	−0.0381813	+	0.117510i
$929$	−22.0451	−	16.0167i	−0.723276	−	0.525491i	0.164153	−	0.986435i	$-0.447511\pi$
$929$	−22.0451	−	16.0167i	−0.723276	−	0.525491i	−0.887429	+	0.460944i	$0.847511\pi$
$930$	4.23607	+	3.07768i	0.138906	+	0.100921i
$931$	6.35410	−	19.5559i	0.208247	−	0.640919i
$932$	4.78115	+	14.7149i	0.156612	+	0.482002i
$933$	42.1976	−	30.6583i	1.38149	−	1.00371i
$934$	35.8328			1.17249
$935$	3.23607	−	0.726543i	0.105831	−	0.0237605i
$936$	−1.00000			−0.0326860
$937$	−17.2082	+	12.5025i	−0.562168	+	0.408439i	−0.832252	−	0.554398i	$-0.812949\pi$
$937$	−17.2082	+	12.5025i	−0.562168	+	0.408439i	0.270084	+	0.962837i	$0.412949\pi$
$938$	−0.937694	−	2.88593i	−0.0306168	−	0.0942288i
$939$	−6.78115	+	20.8702i	−0.221295	+	0.681075i
$940$	7.04508	+	5.11855i	0.229785	+	0.166949i
$941$	−2.42705	−	1.76336i	−0.0791196	−	0.0574838i	0.547522	−	0.836791i	$-0.315571\pi$
$941$	−2.42705	−	1.76336i	−0.0791196	−	0.0574838i	−0.626642	+	0.779307i	$0.715571\pi$
$942$	−2.01722	+	6.20837i	−0.0657246	+	0.202280i
$943$	19.5623	+	60.2066i	0.637036	+	1.96060i
$944$	−10.0902	+	7.33094i	−0.328407	+	0.238602i
$945$	−2.09017			−0.0679932
$946$	18.5066	+	31.2259i	0.601701	+	1.01524i
$947$	43.8885			1.42619			0.713093	−	0.701069i	$-0.247294\pi$
$947$	43.8885			1.42619			0.713093	+	0.701069i	$0.247294\pi$
$948$	−7.16312	+	5.20431i	−0.232647	+	0.169028i
$949$	−11.5172	−	35.4464i	−0.373865	−	1.15064i
$950$	3.70820	−	11.4127i	0.120310	−	0.370276i
$951$	−27.5344	−	20.0049i	−0.892865	−	0.648705i
$952$	0.309017	+	0.224514i	0.0100153	+	0.00727654i
$953$	−0.184405	+	0.567541i	−0.00597347	+	0.0183845i	−0.953999	−	0.299810i	$-0.903077\pi$
$953$	−0.184405	+	0.567541i	−0.00597347	+	0.0183845i	0.948025	+	0.318195i	$0.103077\pi$
$954$	−0.208204	−	0.640786i	−0.00674085	−	0.0207462i
$955$	−16.2082	+	11.7759i	−0.524485	+	0.381061i
$956$	29.4721			0.953197
$957$	1.88197	−	20.1109i	0.0608353	−	0.650094i
$958$	2.11146			0.0682181
$959$	−5.76393	+	4.18774i	−0.186127	+	0.135229i
$960$	−0.500000	−	1.53884i	−0.0161374	−	0.0496659i
$961$	−6.34346	+	19.5232i	−0.204628	+	0.629779i
$962$	2.11803	+	1.53884i	0.0682882	+	0.0496142i
$963$	−1.61803	−	1.17557i	−0.0521404	−	0.0378822i
$964$	−3.97214	+	12.2250i	−0.127934	+	0.393740i
$965$	−3.64590	−	11.2209i	−0.117366	−	0.361214i
$966$	4.23607	−	3.07768i	0.136293	−	0.0990228i
$967$	36.2918			1.16707			0.583533	−	0.812090i	$-0.301670\pi$
$967$	36.2918			1.16707			0.583533	+	0.812090i	$0.301670\pi$
$968$	−1.39919	−	10.9106i	−0.0449716	−	0.350682i
$969$	4.85410			0.155936
$970$	2.69098	−	1.95511i	0.0864023	−	0.0627749i
$971$	7.63525	+	23.4989i	0.245027	+	0.754116i	0.995632	+	0.0933644i	$0.0297621\pi$
$971$	7.63525	+	23.4989i	0.245027	+	0.754116i	−0.750605	+	0.660751i	$0.770238\pi$
$972$	−1.21885	+	3.75123i	−0.0390945	+	0.120321i
$973$	4.30902	+	3.13068i	0.138141	+	0.100365i
$974$	31.8435	+	23.1356i	1.02033	+	0.741313i
$975$	5.23607	−	16.1150i	0.167688	−	0.516092i
$976$	−1.28115	−	3.94298i	−0.0410087	−	0.126212i
$977$	13.6074	−	9.88635i	0.435339	−	0.316292i	−0.348441	−	0.937331i	$-0.613289\pi$
$977$	13.6074	−	9.88635i	0.435339	−	0.316292i	0.783780	+	0.621038i	$0.213289\pi$
$978$	7.14590			0.228501
$979$	−2.21885	+	23.7109i	−0.0709147	+	0.757804i
$980$	−6.85410			−0.218946
$981$	5.35410	−	3.88998i	0.170943	−	0.124198i
$982$	−6.06231	−	18.6579i	−0.193456	−	0.595396i
$983$	−17.5729	+	54.0840i	−0.560490	+	1.72501i	0.120495	+	0.992714i	$0.461552\pi$
$983$	−17.5729	+	54.0840i	−0.560490	+	1.72501i	−0.680985	+	0.732297i	$0.738448\pi$
$984$	−9.78115	−	7.10642i	−0.311812	−	0.226545i
$985$	6.89919	+	5.01255i	0.219826	+	0.159713i
$986$	−1.16312	+	3.57971i	−0.0370413	+	0.114001i
$987$	−1.66312	−	5.11855i	−0.0529377	−	0.162925i
$988$	6.35410	−	4.61653i	0.202151	−	0.146871i
$989$	−92.7214			−2.94837
$990$	−0.645898	−	1.08981i	−0.0205280	−	0.0346366i
$991$	39.6525			1.25960			0.629801	−	0.776756i	$-0.283136\pi$
$991$	39.6525			1.25960			0.629801	+	0.776756i	$0.283136\pi$
$992$	−2.61803	+	1.90211i	−0.0831227	+	0.0603921i
$993$	−4.20820	−	12.9515i	−0.133543	−	0.411004i
$994$	−0.427051	+	1.31433i	−0.0135452	+	0.0416879i
$995$	2.50000	+	1.81636i	0.0792553	+	0.0575824i
$996$	−12.8992	−	9.37181i	−0.408726	−	0.296957i
$997$	1.70163	−	5.23707i	0.0538910	−	0.165860i	−0.920488	−	0.390770i	$-0.872209\pi$
$997$	1.70163	−	5.23707i	0.0538910	−	0.165860i	0.974380	+	0.224910i	$0.0722089\pi$
$998$	−5.47214	−	16.8415i	−0.173217	−	0.533108i
$999$	4.42705	−	3.21644i	0.140066	−	0.101764i

Display

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Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	374.2.g.b.69.1	✓	4
11.2	odd	10		4114.2.a.g.1.1		2
11.4	even	5	inner	374.2.g.b.103.1	yes	4
11.9	even	5		4114.2.a.l.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
374.2.g.b.69.1	✓	4	1.1	even	1	trivial
374.2.g.b.103.1	yes	4	11.4	even	5	inner
4114.2.a.g.1.1		2	11.2	odd	10
4114.2.a.l.1.1		2	11.9	even	5

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Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

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Fields

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Groups

Database

Properties

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Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	374.2.g.b.69.1

Level	$374$
Weight	$2$
Character	374.69
Analytic conductor	$2.986$
Analytic rank	$0$
Dimension	$4$
Inner twists	$2$