LMFDB - Embedded newform 961.2.d.c.628.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [961,2,Mod(374,961)] 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("961.374"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(961, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([8])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 961 = 31^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	961.d (of order $5$, degree $4$, not minimal)

Newform invariants

comment:select newform

sage:traces = [4,-3,6,3] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(4)] == traces)

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

Self dual:	no
Analytic conductor:	$7.67362363425$
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:	no (minimal twist has level 31)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			628.1
Root			$-0.309017 + 0.951057i$ of defining polynomial
Character	$\chi$	$=$	961.628
Dual form			961.2.d.c.531.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.190983 + 0.587785i) q^{2} +(0.381966 + 1.17557i) q^{3} +(1.30902 + 0.951057i) q^{4} +1.00000 q^{5} -0.763932 q^{6} +(3.42705 + 2.48990i) q^{7} +(-1.80902 + 1.31433i) q^{8} +(1.19098 - 0.865300i) q^{9} +(-0.190983 + 0.587785i) q^{10} +(-1.61803 - 1.17557i) q^{11} +(-0.618034 + 1.90211i) q^{12} +(0.381966 + 1.17557i) q^{13} +(-2.11803 + 1.53884i) q^{14} +(0.381966 + 1.17557i) q^{15} +(0.572949 + 1.76336i) q^{16} +(-4.23607 + 3.07768i) q^{17} +(0.281153 + 0.865300i) q^{18} +(0.690983 - 2.12663i) q^{19} +(1.30902 + 0.951057i) q^{20} +(-1.61803 + 4.97980i) q^{21} +(1.00000 - 0.726543i) q^{22} +(6.23607 - 4.53077i) q^{23} +(-2.23607 - 1.62460i) q^{24} -4.00000 q^{25} -0.763932 q^{26} +(4.47214 + 3.24920i) q^{27} +(2.11803 + 6.51864i) q^{28} +(2.23607 - 6.88191i) q^{29} -0.763932 q^{30} -5.61803 q^{32} +(0.763932 - 2.35114i) q^{33} +(-1.00000 - 3.07768i) q^{34} +(3.42705 + 2.48990i) q^{35} +2.38197 q^{36} -2.00000 q^{37} +(1.11803 + 0.812299i) q^{38} +(-1.23607 + 0.898056i) q^{39} +(-1.80902 + 1.31433i) q^{40} +(2.16312 - 6.65740i) q^{41} +(-2.61803 - 1.90211i) q^{42} +(-1.00000 + 3.07768i) q^{43} +(-1.00000 - 3.07768i) q^{44} +(1.19098 - 0.865300i) q^{45} +(1.47214 + 4.53077i) q^{46} +(-2.00000 - 6.15537i) q^{47} +(-1.85410 + 1.34708i) q^{48} +(3.38197 + 10.4086i) q^{49} +(0.763932 - 2.35114i) q^{50} +(-5.23607 - 3.80423i) q^{51} +(-0.618034 + 1.90211i) q^{52} +(1.23607 - 0.898056i) q^{53} +(-2.76393 + 2.00811i) q^{54} +(-1.61803 - 1.17557i) q^{55} -9.47214 q^{56} +2.76393 q^{57} +(3.61803 + 2.62866i) q^{58} +(-0.690983 - 2.12663i) q^{59} +(-0.618034 + 1.90211i) q^{60} -14.1803 q^{61} +6.23607 q^{63} +(-0.0729490 + 0.224514i) q^{64} +(0.381966 + 1.17557i) q^{65} +(1.23607 + 0.898056i) q^{66} +8.00000 q^{67} -8.47214 q^{68} +(7.70820 + 5.60034i) q^{69} +(-2.11803 + 1.53884i) q^{70} +(-10.6631 + 7.74721i) q^{71} +(-1.01722 + 3.13068i) q^{72} +(0.381966 + 0.277515i) q^{73} +(0.381966 - 1.17557i) q^{74} +(-1.52786 - 4.70228i) q^{75} +(2.92705 - 2.12663i) q^{76} +(-2.61803 - 8.05748i) q^{77} +(-0.291796 - 0.898056i) q^{78} +(-1.38197 + 1.00406i) q^{79} +(0.572949 + 1.76336i) q^{80} +(-0.746711 + 2.29814i) q^{81} +(3.50000 + 2.54290i) q^{82} +(0.909830 - 2.80017i) q^{83} +(-6.85410 + 4.97980i) q^{84} +(-4.23607 + 3.07768i) q^{85} +(-1.61803 - 1.17557i) q^{86} +8.94427 q^{87} +4.47214 q^{88} +(1.38197 + 1.00406i) q^{89} +(0.281153 + 0.865300i) q^{90} +(-1.61803 + 4.97980i) q^{91} +12.4721 q^{92} +4.00000 q^{94} +(0.690983 - 2.12663i) q^{95} +(-2.14590 - 6.60440i) q^{96} +(-1.57295 - 1.14281i) q^{97} -6.76393 q^{98} -2.94427 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 3 q^{2} + 6 q^{3} + 3 q^{4} + 4 q^{5} - 12 q^{6} + 7 q^{7} - 5 q^{8} + 7 q^{9} - 3 q^{10} - 2 q^{11} + 2 q^{12} + 6 q^{13} - 4 q^{14} + 6 q^{15} + 9 q^{16} - 8 q^{17} - 19 q^{18} + 5 q^{19} + 3 q^{20}+ \cdots + 24 q^{99}+O(q^{100}) $ 4 * q - 3 * q^2 + 6 * q^3 + 3 * q^4 + 4 * q^5 - 12 * q^6 + 7 * q^7 - 5 * q^8 + 7 * q^9 - 3 * q^10 - 2 * q^11 + 2 * q^12 + 6 * q^13 - 4 * q^14 + 6 * q^15 + 9 * q^16 - 8 * q^17 - 19 * q^18 + 5 * q^19 + 3 * q^20 - 2 * q^21 + 4 * q^22 + 16 * q^23 - 16 * q^25 - 12 * q^26 + 4 * q^28 - 12 * q^30 - 18 * q^32 + 12 * q^33 - 4 * q^34 + 7 * q^35 + 14 * q^36 - 8 * q^37 + 4 * q^39 - 5 * q^40 - 7 * q^41 - 6 * q^42 - 4 * q^43 - 4 * q^44 + 7 * q^45 - 12 * q^46 - 8 * q^47 + 6 * q^48 + 18 * q^49 + 12 * q^50 - 12 * q^51 + 2 * q^52 - 4 * q^53 - 20 * q^54 - 2 * q^55 - 20 * q^56 + 20 * q^57 + 10 * q^58 - 5 * q^59 + 2 * q^60 - 12 * q^61 + 16 * q^63 - 7 * q^64 + 6 * q^65 - 4 * q^66 + 32 * q^67 - 16 * q^68 + 4 * q^69 - 4 * q^70 - 27 * q^71 + 25 * q^72 + 6 * q^73 + 6 * q^74 - 24 * q^75 + 5 * q^76 - 6 * q^77 - 28 * q^78 - 10 * q^79 + 9 * q^80 - 41 * q^81 + 14 * q^82 + 26 * q^83 - 14 * q^84 - 8 * q^85 - 2 * q^86 + 10 * q^89 - 19 * q^90 - 2 * q^91 + 32 * q^92 + 16 * q^94 + 5 * q^95 - 22 * q^96 - 13 * q^97 - 36 * q^98 + 24 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/961\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{2}{5}\right)$

Coefficient data

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

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

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

$2$	−0.190983	+	0.587785i	−0.135045	+	0.415627i	−0.995597	−	0.0937362i	$-0.970119\pi$
$2$	−0.190983	+	0.587785i	−0.135045	+	0.415627i	0.860552	+	0.509363i	$0.170119\pi$
$3$	0.381966	+	1.17557i	0.220528	+	0.678716i	0.998715	+	0.0506828i	$0.0161398\pi$
$3$	0.381966	+	1.17557i	0.220528	+	0.678716i	−0.778187	+	0.628033i	$0.783860\pi$
$4$	1.30902	+	0.951057i	0.654508	+	0.475528i
$5$	1.00000			0.447214			0.223607	−	0.974679i	$-0.428217\pi$
$5$	1.00000			0.447214			0.223607	+	0.974679i	$0.428217\pi$
$6$	−0.763932			−0.311874
$7$	3.42705	+	2.48990i	1.29530	+	0.941093i	0.999898	−	0.0142789i	$-0.00454526\pi$
$7$	3.42705	+	2.48990i	1.29530	+	0.941093i	0.295405	+	0.955372i	$0.404545\pi$
$8$	−1.80902	+	1.31433i	−0.639584	+	0.464685i
$9$	1.19098	−	0.865300i	0.396994	−	0.288433i
$10$	−0.190983	+	0.587785i	−0.0603941	+	0.185874i
$11$	−1.61803	−	1.17557i	−0.487856	−	0.354448i	0.316503	−	0.948591i	$-0.397491\pi$
$11$	−1.61803	−	1.17557i	−0.487856	−	0.354448i	−0.804359	+	0.594144i	$0.797491\pi$
$12$	−0.618034	+	1.90211i	−0.178411	+	0.549093i
$13$	0.381966	+	1.17557i	0.105938	+	0.326045i	0.989950	−	0.141421i	$-0.0451671\pi$
$13$	0.381966	+	1.17557i	0.105938	+	0.326045i	−0.884011	+	0.467466i	$0.845167\pi$
$14$	−2.11803	+	1.53884i	−0.566068	+	0.411273i
$15$	0.381966	+	1.17557i	0.0986232	+	0.303531i
$16$	0.572949	+	1.76336i	0.143237	+	0.440839i
$17$	−4.23607	+	3.07768i	−1.02740	+	0.746448i	−0.967786	−	0.251774i	$-0.918986\pi$
$17$	−4.23607	+	3.07768i	−1.02740	+	0.746448i	−0.0596113	+	0.998222i	$0.518986\pi$
$18$	0.281153	+	0.865300i	0.0662684	+	0.203953i
$19$	0.690983	−	2.12663i	0.158522	−	0.487882i	−0.839978	−	0.542620i	$-0.817432\pi$
$19$	0.690983	−	2.12663i	0.158522	−	0.487882i	0.998501	+	0.0547382i	$0.0174324\pi$
$20$	1.30902	+	0.951057i	0.292705	+	0.212663i
$21$	−1.61803	+	4.97980i	−0.353084	+	1.08668i
$22$	1.00000	−	0.726543i	0.213201	−	0.154899i
$23$	6.23607	−	4.53077i	1.30031	−	0.944731i	0.300351	−	0.953829i	$-0.402896\pi$
$23$	6.23607	−	4.53077i	1.30031	−	0.944731i	0.999959	+	0.00909805i	$0.00289604\pi$
$24$	−2.23607	−	1.62460i	−0.456435	−	0.331620i
$25$	−4.00000			−0.800000
$26$	−0.763932			−0.149819
$27$	4.47214	+	3.24920i	0.860663	+	0.625308i
$28$	2.11803	+	6.51864i	0.400271	+	1.23191i
$29$	2.23607	−	6.88191i	0.415227	−	1.27794i	−0.496820	−	0.867854i	$-0.665499\pi$
$29$	2.23607	−	6.88191i	0.415227	−	1.27794i	0.912047	−	0.410085i	$-0.134501\pi$
$30$	−0.763932			−0.139474
$31$		0			0
$31$		0			0
$32$	−5.61803			−0.993137
$33$	0.763932	−	2.35114i	0.132983	−	0.409281i
$34$	−1.00000	−	3.07768i	−0.171499	−	0.527818i
$35$	3.42705	+	2.48990i	0.579277	+	0.420870i
$36$	2.38197			0.396994
$37$	−2.00000			−0.328798			−0.164399	−	0.986394i	$-0.552568\pi$
$37$	−2.00000			−0.328798			−0.164399	+	0.986394i	$0.552568\pi$
$38$	1.11803	+	0.812299i	0.181369	+	0.131772i
$39$	−1.23607	+	0.898056i	−0.197929	+	0.143804i
$40$	−1.80902	+	1.31433i	−0.286031	+	0.207813i
$41$	2.16312	−	6.65740i	0.337822	−	1.03971i	−0.627493	−	0.778623i	$-0.715919\pi$
$41$	2.16312	−	6.65740i	0.337822	−	1.03971i	0.965315	−	0.261088i	$-0.0840813\pi$
$42$	−2.61803	−	1.90211i	−0.403971	−	0.293502i
$43$	−1.00000	+	3.07768i	−0.152499	+	0.469342i	−0.997899	−	0.0647909i	$-0.979362\pi$
$43$	−1.00000	+	3.07768i	−0.152499	+	0.469342i	0.845400	+	0.534133i	$0.179362\pi$
$44$	−1.00000	−	3.07768i	−0.150756	−	0.463978i
$45$	1.19098	−	0.865300i	0.177541	−	0.128991i
$46$	1.47214	+	4.53077i	0.217055	+	0.668025i
$47$	−2.00000	−	6.15537i	−0.291730	−	0.897853i	−0.984300	−	0.176502i	$-0.943522\pi$
$47$	−2.00000	−	6.15537i	−0.291730	−	0.897853i	0.692570	−	0.721350i	$-0.256478\pi$
$48$	−1.85410	+	1.34708i	−0.267617	+	0.194435i
$49$	3.38197	+	10.4086i	0.483138	+	1.48695i
$50$	0.763932	−	2.35114i	0.108036	−	0.332502i
$51$	−5.23607	−	3.80423i	−0.733196	−	0.532698i
$52$	−0.618034	+	1.90211i	−0.0857059	+	0.263776i
$53$	1.23607	−	0.898056i	0.169787	−	0.123357i	−0.499647	−	0.866229i	$-0.666537\pi$
$53$	1.23607	−	0.898056i	0.169787	−	0.123357i	0.669434	+	0.742872i	$0.266537\pi$
$54$	−2.76393	+	2.00811i	−0.376124	+	0.273270i
$55$	−1.61803	−	1.17557i	−0.218176	−	0.158514i
$56$	−9.47214			−1.26577
$57$	2.76393			0.366092
$58$	3.61803	+	2.62866i	0.475071	+	0.345159i
$59$	−0.690983	−	2.12663i	−0.0899583	−	0.276863i	0.895949	−	0.444158i	$-0.146497\pi$
$59$	−0.690983	−	2.12663i	−0.0899583	−	0.276863i	−0.985907	+	0.167294i	$0.946497\pi$
$60$	−0.618034	+	1.90211i	−0.0797878	+	0.245562i
$61$	−14.1803			−1.81561			−0.907803	−	0.419396i	$-0.862242\pi$
$61$	−14.1803			−1.81561			−0.907803	+	0.419396i	$0.862242\pi$
$62$		0			0
$63$	6.23607			0.785671
$64$	−0.0729490	+	0.224514i	−0.00911863	+	0.0280642i
$65$	0.381966	+	1.17557i	0.0473771	+	0.145812i
$66$	1.23607	+	0.898056i	0.152149	+	0.110543i
$67$	8.00000			0.977356			0.488678	−	0.872464i	$-0.337479\pi$
$67$	8.00000			0.977356			0.488678	+	0.872464i	$0.337479\pi$
$68$	−8.47214			−1.02740
$69$	7.70820	+	5.60034i	0.927959	+	0.674201i
$70$	−2.11803	+	1.53884i	−0.253153	+	0.183927i
$71$	−10.6631	+	7.74721i	−1.26548	+	0.919425i	−0.999013	−	0.0444196i	$-0.985856\pi$
$71$	−10.6631	+	7.74721i	−1.26548	+	0.919425i	−0.266466	+	0.963844i	$0.585856\pi$
$72$	−1.01722	+	3.13068i	−0.119881	+	0.368955i
$73$	0.381966	+	0.277515i	0.0447057	+	0.0324806i	0.609914	−	0.792468i	$-0.291204\pi$
$73$	0.381966	+	0.277515i	0.0447057	+	0.0324806i	−0.565208	+	0.824948i	$0.691204\pi$
$74$	0.381966	−	1.17557i	0.0444026	−	0.136657i
$75$	−1.52786	−	4.70228i	−0.176423	−	0.542973i
$76$	2.92705	−	2.12663i	0.335756	−	0.243941i
$77$	−2.61803	−	8.05748i	−0.298353	−	0.918235i
$78$	−0.291796	−	0.898056i	−0.0330394	−	0.101685i
$79$	−1.38197	+	1.00406i	−0.155483	+	0.112965i	−0.662807	−	0.748790i	$-0.730635\pi$
$79$	−1.38197	+	1.00406i	−0.155483	+	0.112965i	0.507323	+	0.861756i	$0.330635\pi$
$80$	0.572949	+	1.76336i	0.0640576	+	0.197149i
$81$	−0.746711	+	2.29814i	−0.0829679	+	0.255349i
$82$	3.50000	+	2.54290i	0.386510	+	0.280816i
$83$	0.909830	−	2.80017i	0.0998668	−	0.307358i	−0.888625	−	0.458635i	$-0.848338\pi$
$83$	0.909830	−	2.80017i	0.0998668	−	0.307358i	0.988491	+	0.151277i	$0.0483385\pi$
$84$	−6.85410	+	4.97980i	−0.747844	+	0.543340i
$85$	−4.23607	+	3.07768i	−0.459466	+	0.333822i
$86$	−1.61803	−	1.17557i	−0.174477	−	0.126765i
$87$	8.94427			0.958927
$88$	4.47214			0.476731
$89$	1.38197	+	1.00406i	0.146488	+	0.106430i	0.658615	−	0.752480i	$-0.271142\pi$
$89$	1.38197	+	1.00406i	0.146488	+	0.106430i	−0.512127	+	0.858910i	$0.671142\pi$
$90$	0.281153	+	0.865300i	0.0296361	+	0.0912106i
$91$	−1.61803	+	4.97980i	−0.169616	+	0.522025i
$92$	12.4721			1.30031
$93$		0			0
$94$	4.00000			0.412568
$95$	0.690983	−	2.12663i	0.0708934	−	0.218187i
$96$	−2.14590	−	6.60440i	−0.219015	−	0.674058i
$97$	−1.57295	−	1.14281i	−0.159709	−	0.116035i	0.505061	−	0.863084i	$-0.331470\pi$
$97$	−1.57295	−	1.14281i	−0.159709	−	0.116035i	−0.664769	+	0.747049i	$0.731470\pi$
$98$	−6.76393			−0.683260
$99$	−2.94427			−0.295910
$100$	−5.23607	−	3.80423i	−0.523607	−	0.380423i
$101$	2.42705	−	1.76336i	0.241501	−	0.175460i	−0.460451	−	0.887685i	$-0.652312\pi$
$101$	2.42705	−	1.76336i	0.241501	−	0.175460i	0.701952	+	0.712225i	$0.252312\pi$
$102$	3.23607	−	2.35114i	0.320418	−	0.232798i
$103$	0.545085	−	1.67760i	0.0537088	−	0.165299i	−0.920604	−	0.390497i	$-0.872303\pi$
$103$	0.545085	−	1.67760i	0.0537088	−	0.165299i	0.974313	+	0.225199i	$0.0723031\pi$
$104$	−2.23607	−	1.62460i	−0.219265	−	0.159305i
$105$	−1.61803	+	4.97980i	−0.157904	+	0.485978i
$106$	0.291796	+	0.898056i	0.0283417	+	0.0872269i
$107$	−8.28115	+	6.01661i	−0.800569	+	0.581648i	−0.911081	−	0.412227i	$-0.864751\pi$
$107$	−8.28115	+	6.01661i	−0.800569	+	0.581648i	0.110512	+	0.993875i	$0.464751\pi$
$108$	2.76393	+	8.50651i	0.265959	+	0.818539i
$109$	1.21885	+	3.75123i	0.116744	+	0.359302i	0.992307	−	0.123803i	$-0.0395090\pi$
$109$	1.21885	+	3.75123i	0.116744	+	0.359302i	−0.875562	+	0.483105i	$0.839509\pi$
$110$	1.00000	−	0.726543i	0.0953463	−	0.0692731i
$111$	−0.763932	−	2.35114i	−0.0725092	−	0.223160i
$112$	−2.42705	+	7.46969i	−0.229335	+	0.705820i
$113$	4.42705	+	3.21644i	0.416462	+	0.302577i	0.776213	−	0.630471i	$-0.217138\pi$
$113$	4.42705	+	3.21644i	0.416462	+	0.302577i	−0.359751	+	0.933048i	$0.617138\pi$
$114$	−0.527864	+	1.62460i	−0.0494390	+	0.152158i
$115$	6.23607	−	4.53077i	0.581516	−	0.422496i
$116$	9.47214	−	6.88191i	0.879466	−	0.638969i
$117$	1.47214	+	1.06957i	0.136099	+	0.0988817i
$118$	1.38197			0.127220
$119$	−22.1803			−2.03327
$120$	−2.23607	−	1.62460i	−0.204124	−	0.148305i
$121$	−2.16312	−	6.65740i	−0.196647	−	0.605218i
$122$	2.70820	−	8.33499i	0.245189	−	0.754615i
$123$	8.65248			0.780167
$124$		0			0
$125$	−9.00000			−0.804984
$126$	−1.19098	+	3.66547i	−0.106101	+	0.326546i
$127$	1.09017	+	3.35520i	0.0967369	+	0.297726i	0.987702	−	0.156345i	$-0.0499713\pi$
$127$	1.09017	+	3.35520i	0.0967369	+	0.297726i	−0.890966	+	0.454071i	$0.849971\pi$
$128$	−9.20820	−	6.69015i	−0.813898	−	0.591331i
$129$	−4.00000			−0.352180
$130$	−0.763932			−0.0670013
$131$	−9.70820	−	7.05342i	−0.848210	−	0.616260i	0.0764421	−	0.997074i	$-0.475644\pi$
$131$	−9.70820	−	7.05342i	−0.848210	−	0.616260i	−0.924652	+	0.380814i	$0.875644\pi$
$132$	3.23607	−	2.35114i	0.281664	−	0.204641i
$133$	7.66312	−	5.56758i	0.664477	−	0.482771i
$134$	−1.52786	+	4.70228i	−0.131987	+	0.406215i
$135$	4.47214	+	3.24920i	0.384900	+	0.279646i
$136$	3.61803	−	11.1352i	0.310244	−	0.954832i
$137$	6.09017	+	18.7436i	0.520318	+	1.60138i	0.773392	+	0.633928i	$0.218559\pi$
$137$	6.09017	+	18.7436i	0.520318	+	1.60138i	−0.253074	+	0.967447i	$0.581441\pi$
$138$	−4.76393	+	3.46120i	−0.405533	+	0.294637i
$139$	−4.14590	−	12.7598i	−0.351650	−	1.08227i	−0.957926	−	0.287014i	$-0.907337\pi$
$139$	−4.14590	−	12.7598i	−0.351650	−	1.08227i	0.606276	−	0.795254i	$-0.292663\pi$
$140$	2.11803	+	6.51864i	0.179007	+	0.550925i
$141$	6.47214	−	4.70228i	0.545052	−	0.396004i
$142$	−2.51722	−	7.74721i	−0.211240	−	0.650131i
$143$	0.763932	−	2.35114i	0.0638832	−	0.196612i
$144$	2.20820	+	1.60435i	0.184017	+	0.133696i
$145$	2.23607	−	6.88191i	0.185695	−	0.571511i
$146$	−0.236068	+	0.171513i	−0.0195371	+	0.0141946i
$147$	−10.9443	+	7.95148i	−0.902668	+	0.655827i
$148$	−2.61803	−	1.90211i	−0.215201	−	0.156353i
$149$	10.0000			0.819232			0.409616	−	0.912258i	$-0.365663\pi$
$149$	10.0000			0.819232			0.409616	+	0.912258i	$0.365663\pi$
$150$	3.05573			0.249499
$151$	−6.61803	−	4.80828i	−0.538568	−	0.391293i	0.284985	−	0.958532i	$-0.408011\pi$
$151$	−6.61803	−	4.80828i	−0.538568	−	0.391293i	−0.823553	+	0.567239i	$0.808011\pi$
$152$	1.54508	+	4.75528i	0.125323	+	0.385704i
$153$	−2.38197	+	7.33094i	−0.192571	+	0.592671i
$154$	5.23607			0.421934
$155$		0			0
$156$	−2.47214			−0.197929
$157$	−4.60081	+	14.1598i	−0.367185	+	1.13008i	0.581417	+	0.813606i	$0.302499\pi$
$157$	−4.60081	+	14.1598i	−0.367185	+	1.13008i	−0.948602	+	0.316473i	$0.897501\pi$
$158$	−0.326238	−	1.00406i	−0.0259541	−	0.0798785i
$159$	1.52786	+	1.11006i	0.121168	+	0.0880333i
$160$	−5.61803			−0.444145
$161$	32.6525			2.57338
$162$	−1.20820	−	0.877812i	−0.0949255	−	0.0689674i
$163$	2.19098	−	1.59184i	0.171611	−	0.124683i	−0.498664	−	0.866795i	$-0.666176\pi$
$163$	2.19098	−	1.59184i	0.171611	−	0.124683i	0.670275	+	0.742112i	$0.266176\pi$
$164$	9.16312	−	6.65740i	0.715519	−	0.519855i
$165$	0.763932	−	2.35114i	0.0594720	−	0.183036i
$166$	1.47214	+	1.06957i	0.114260	+	0.0830147i
$167$	0.763932	−	2.35114i	0.0591148	−	0.181937i	−0.917139	−	0.398569i	$-0.869507\pi$
$167$	0.763932	−	2.35114i	0.0591148	−	0.181937i	0.976253	+	0.216632i	$0.0695071\pi$
$168$	−3.61803	−	11.1352i	−0.279137	−	0.859097i
$169$	9.28115	−	6.74315i	0.713935	−	0.518704i
$170$	−1.00000	−	3.07768i	−0.0766965	−	0.236048i
$171$	−1.01722	−	3.13068i	−0.0777888	−	0.239409i
$172$	−4.23607	+	3.07768i	−0.322997	+	0.234671i
$173$	−4.61803	−	14.2128i	−0.351103	−	1.08058i	−0.958235	−	0.285982i	$-0.907680\pi$
$173$	−4.61803	−	14.2128i	−0.351103	−	1.08058i	0.607132	−	0.794601i	$-0.292320\pi$
$174$	−1.70820	+	5.25731i	−0.129499	+	0.398556i
$175$	−13.7082	−	9.95959i	−1.03624	−	0.752874i
$176$	1.14590	−	3.52671i	0.0863753	−	0.265836i
$177$	2.23607	−	1.62460i	0.168073	−	0.122112i
$178$	−0.854102	+	0.620541i	−0.0640176	+	0.0465115i
$179$	9.47214	+	6.88191i	0.707981	+	0.514378i	0.882522	−	0.470272i	$-0.155844\pi$
$179$	9.47214	+	6.88191i	0.707981	+	0.514378i	−0.174541	+	0.984650i	$0.555844\pi$
$180$	2.38197			0.177541
$181$	18.1803			1.35133			0.675667	−	0.737207i	$-0.263856\pi$
$181$	18.1803			1.35133			0.675667	+	0.737207i	$0.263856\pi$
$182$	−2.61803	−	1.90211i	−0.194062	−	0.140994i
$183$	−5.41641	−	16.6700i	−0.400392	−	1.23228i
$184$	−5.32624	+	16.3925i	−0.392655	+	1.20847i
$185$	−2.00000			−0.147043
$186$		0			0
$187$	10.4721			0.765798
$188$	3.23607	−	9.95959i	0.236015	−	0.726378i
$189$	7.23607	+	22.2703i	0.526346	+	1.61993i
$190$	1.11803	+	0.812299i	0.0811107	+	0.0589304i
$191$	3.18034			0.230121			0.115061	−	0.993358i	$-0.463294\pi$
$191$	3.18034			0.230121			0.115061	+	0.993358i	$0.463294\pi$
$192$	−0.291796			−0.0210586
$193$	4.42705	+	3.21644i	0.318666	+	0.231524i	0.735606	−	0.677410i	$-0.236897\pi$
$193$	4.42705	+	3.21644i	0.318666	+	0.231524i	−0.416940	+	0.908934i	$0.636897\pi$
$194$	0.972136	−	0.706298i	0.0697953	−	0.0507092i
$195$	−1.23607	+	0.898056i	−0.0885167	+	0.0643111i
$196$	−5.47214	+	16.8415i	−0.390867	+	1.20296i
$197$	12.4721	+	9.06154i	0.888603	+	0.645608i	0.935513	−	0.353291i	$-0.114938\pi$
$197$	12.4721	+	9.06154i	0.888603	+	0.645608i	−0.0469105	+	0.998899i	$0.514938\pi$
$198$	0.562306	−	1.73060i	0.0399613	−	0.122988i
$199$	−0.326238	−	1.00406i	−0.0231264	−	0.0711757i	0.938827	−	0.344388i	$-0.111914\pi$
$199$	−0.326238	−	1.00406i	−0.0231264	−	0.0711757i	−0.961954	+	0.273213i	$0.911914\pi$
$200$	7.23607	−	5.25731i	0.511667	−	0.371748i
$201$	3.05573	+	9.40456i	0.215534	+	0.663347i
$202$	0.572949	+	1.76336i	0.0403126	+	0.124069i
$203$	24.7984	−	18.0171i	1.74050	−	1.26455i
$204$	−3.23607	−	9.95959i	−0.226570	−	0.697311i
$205$	2.16312	−	6.65740i	0.151079	−	0.464973i
$206$	0.881966	+	0.640786i	0.0614495	+	0.0446457i
$207$	3.50658	−	10.7921i	0.243724	−	0.750105i
$208$	−1.85410	+	1.34708i	−0.128559	+	0.0934035i
$209$	−3.61803	+	2.62866i	−0.250265	+	0.181828i
$210$	−2.61803	−	1.90211i	−0.180662	−	0.131258i
$211$	0.819660			0.0564277			0.0282139	−	0.999602i	$-0.491018\pi$
$211$	0.819660			0.0564277			0.0282139	+	0.999602i	$0.491018\pi$
$212$	2.47214			0.169787
$213$	−13.1803	−	9.57608i	−0.903102	−	0.656142i
$214$	−1.95492	−	6.01661i	−0.133635	−	0.411287i
$215$	−1.00000	+	3.07768i	−0.0681994	+	0.209896i
$216$	−12.3607			−0.841038
$217$		0			0
$218$	−2.43769			−0.165101
$219$	−0.180340	+	0.555029i	−0.0121862	+	0.0375054i
$220$	−1.00000	−	3.07768i	−0.0674200	−	0.207497i
$221$	−5.23607	−	3.80423i	−0.352216	−	0.255900i
$222$	1.52786			0.102544
$223$	4.00000			0.267860			0.133930	−	0.990991i	$-0.457240\pi$
$223$	4.00000			0.267860			0.133930	+	0.990991i	$0.457240\pi$
$224$	−19.2533	−	13.9883i	−1.28641	−	0.934635i
$225$	−4.76393	+	3.46120i	−0.317595	+	0.230747i
$226$	−2.73607	+	1.98787i	−0.182001	+	0.132231i
$227$	0.763932	−	2.35114i	0.0507039	−	0.156051i	−0.922499	−	0.386001i	$-0.873856\pi$
$227$	0.763932	−	2.35114i	0.0507039	−	0.156051i	0.973202	+	0.229950i	$0.0738562\pi$
$228$	3.61803	+	2.62866i	0.239610	+	0.174087i
$229$	4.14590	−	12.7598i	0.273969	−	0.843189i	−0.715522	−	0.698590i	$-0.753811\pi$
$229$	4.14590	−	12.7598i	0.273969	−	0.843189i	0.989490	−	0.144598i	$-0.0461890\pi$
$230$	1.47214	+	4.53077i	0.0970698	+	0.298750i
$231$	8.47214	−	6.15537i	0.557426	−	0.404993i
$232$	5.00000	+	15.3884i	0.328266	+	1.01030i
$233$	0.0172209	+	0.0530006i	0.00112818	+	0.00347218i	0.951619	−	0.307280i	$-0.0994189\pi$
$233$	0.0172209	+	0.0530006i	0.00112818	+	0.00347218i	−0.950491	+	0.310753i	$0.899419\pi$
$234$	−0.909830	+	0.661030i	−0.0594775	+	0.0432129i
$235$	−2.00000	−	6.15537i	−0.130466	−	0.401532i
$236$	1.11803	−	3.44095i	0.0727778	−	0.223987i
$237$	−1.70820	−	1.24108i	−0.110960	−	0.0806170i
$238$	4.23607	−	13.0373i	0.274584	−	0.845081i
$239$	−1.38197	+	1.00406i	−0.0893920	+	0.0649471i	−0.631584	−	0.775308i	$-0.717595\pi$
$239$	−1.38197	+	1.00406i	−0.0893920	+	0.0649471i	0.542192	+	0.840255i	$0.317595\pi$
$240$	−1.85410	+	1.34708i	−0.119682	+	0.0869539i
$241$	24.5623	+	17.8456i	1.58220	+	1.14953i	0.914122	+	0.405440i	$0.132882\pi$
$241$	24.5623	+	17.8456i	1.58220	+	1.14953i	0.668076	+	0.744093i	$0.267118\pi$
$242$	4.32624			0.278101
$243$	13.5967			0.872232
$244$	−18.5623	−	13.4863i	−1.18833	−	0.863372i
$245$	3.38197	+	10.4086i	0.216066	+	0.664982i
$246$	−1.65248	+	5.08580i	−0.105358	+	0.324259i
$247$	2.76393			0.175865
$248$		0			0
$249$	3.63932			0.230633
$250$	1.71885	−	5.29007i	0.108709	−	0.334573i
$251$	−7.47214	−	22.9969i	−0.471637	−	1.45155i	−0.850440	−	0.526072i	$-0.823664\pi$
$251$	−7.47214	−	22.9969i	−0.471637	−	1.45155i	0.378803	−	0.925477i	$-0.376336\pi$
$252$	8.16312	+	5.93085i	0.514228	+	0.373609i
$253$	−15.4164			−0.969221
$254$	−2.18034			−0.136807
$255$	−5.23607	−	3.80423i	−0.327895	−	0.238230i
$256$	5.30902	−	3.85723i	0.331814	−	0.241077i
$257$	12.8992	−	9.37181i	0.804629	−	0.584597i	−0.107639	−	0.994190i	$-0.534329\pi$
$257$	12.8992	−	9.37181i	0.804629	−	0.584597i	0.912269	+	0.409593i	$0.134329\pi$
$258$	0.763932	−	2.35114i	0.0475603	−	0.146376i
$259$	−6.85410	−	4.97980i	−0.425893	−	0.309430i
$260$	−0.618034	+	1.90211i	−0.0383288	+	0.117964i
$261$	−3.29180	−	10.1311i	−0.203757	−	0.627100i
$262$	6.00000	−	4.35926i	0.370681	−	0.269316i
$263$	−5.79837	−	17.8456i	−0.357543	−	1.10040i	−0.954520	−	0.298146i	$-0.903632\pi$
$263$	−5.79837	−	17.8456i	−0.357543	−	1.10040i	0.596977	−	0.802258i	$-0.296368\pi$
$264$	1.70820	+	5.25731i	0.105133	+	0.323565i
$265$	1.23607	−	0.898056i	0.0759311	−	0.0551671i
$266$	1.80902	+	5.56758i	0.110918	+	0.341370i
$267$	−0.652476	+	2.00811i	−0.0399309	+	0.122895i
$268$	10.4721	+	7.60845i	0.639688	+	0.464760i
$269$	−8.94427	+	27.5276i	−0.545342	+	1.67839i	0.174834	+	0.984598i	$0.444061\pi$
$269$	−8.94427	+	27.5276i	−0.545342	+	1.67839i	−0.720176	+	0.693792i	$0.755939\pi$
$270$	−2.76393	+	2.00811i	−0.168208	+	0.122210i
$271$	−6.61803	+	4.80828i	−0.402017	+	0.292082i	−0.770362	−	0.637607i	$-0.779924\pi$
$271$	−6.61803	+	4.80828i	−0.402017	+	0.292082i	0.368345	+	0.929689i	$0.379924\pi$
$272$	−7.85410	−	5.70634i	−0.476225	−	0.345998i
$273$	−6.47214			−0.391711
$274$	−12.1803			−0.735841
$275$	6.47214	+	4.70228i	0.390284	+	0.283558i
$276$	4.76393	+	14.6619i	0.286755	+	0.882541i
$277$	5.76393	−	17.7396i	0.346321	−	1.06587i	−0.614552	−	0.788877i	$-0.710663\pi$
$277$	5.76393	−	17.7396i	0.346321	−	1.06587i	0.960873	−	0.276990i	$-0.0893370\pi$
$278$	8.29180			0.497309
$279$		0			0
$280$	−9.47214			−0.566068
$281$	5.25329	−	16.1680i	0.313385	−	0.964500i	−0.663029	−	0.748594i	$-0.730729\pi$
$281$	5.25329	−	16.1680i	0.313385	−	0.964500i	0.976414	−	0.215906i	$-0.0692705\pi$
$282$	1.52786	+	4.70228i	0.0909830	+	0.280017i
$283$	−17.7082	−	12.8658i	−1.05264	−	0.764790i	−0.0799301	−	0.996800i	$-0.525470\pi$
$283$	−17.7082	−	12.8658i	−1.05264	−	0.764790i	−0.972713	+	0.232010i	$0.925470\pi$
$284$	−21.3262			−1.26548
$285$	2.76393			0.163721
$286$	1.23607	+	0.898056i	0.0730902	+	0.0531032i
$287$	23.9894	−	17.4293i	1.41605	−	1.02882i
$288$	−6.69098	+	4.86128i	−0.394270	+	0.286454i
$289$	3.21885	−	9.90659i	0.189344	−	0.582741i
$290$	3.61803	+	2.62866i	0.212458	+	0.154360i
$291$	0.742646	−	2.28563i	0.0435347	−	0.133986i
$292$	0.236068	+	0.726543i	0.0138148	+	0.0425177i
$293$	−6.85410	+	4.97980i	−0.400421	+	0.290923i	−0.769712	−	0.638391i	$-0.779600\pi$
$293$	−6.85410	+	4.97980i	−0.400421	+	0.290923i	0.369292	+	0.929314i	$0.379600\pi$
$294$	−2.58359	−	7.95148i	−0.150678	−	0.463740i
$295$	−0.690983	−	2.12663i	−0.0402306	−	0.123817i
$296$	3.61803	−	2.62866i	0.210294	−	0.152788i
$297$	−3.41641	−	10.5146i	−0.198240	−	0.610120i
$298$	−1.90983	+	5.87785i	−0.110633	+	0.340495i
$299$	7.70820	+	5.60034i	0.445777	+	0.323876i
$300$	2.47214	−	7.60845i	0.142729	−	0.439274i
$301$	−11.0902	+	8.05748i	−0.639227	+	0.464425i
$302$	4.09017	−	2.97168i	0.235363	−	0.171001i
$303$	3.00000	+	2.17963i	0.172345	+	0.125216i
$304$	4.14590			0.237784
$305$	−14.1803			−0.811964
$306$	−3.85410	−	2.80017i	−0.220324	−	0.160075i
$307$	−4.72542	−	14.5434i	−0.269694	−	0.830034i	−0.990575	−	0.136974i	$-0.956262\pi$
$307$	−4.72542	−	14.5434i	−0.269694	−	0.830034i	0.720880	−	0.693059i	$-0.243738\pi$
$308$	4.23607	−	13.0373i	0.241372	−	0.742868i
$309$	2.18034			0.124035
$310$		0			0
$311$	−6.81966			−0.386707			−0.193354	−	0.981129i	$-0.561936\pi$
$311$	−6.81966			−0.386707			−0.193354	+	0.981129i	$0.561936\pi$
$312$	1.05573	−	3.24920i	0.0597688	−	0.183950i
$313$	6.56231	+	20.1967i	0.370923	+	1.14159i	0.946188	+	0.323618i	$0.104899\pi$
$313$	6.56231	+	20.1967i	0.370923	+	1.14159i	−0.575265	+	0.817967i	$0.695101\pi$
$314$	−7.44427	−	5.40858i	−0.420105	−	0.305224i
$315$	6.23607			0.351363
$316$	−2.76393			−0.155483
$317$	−17.7533	−	12.8985i	−0.997124	−	0.724453i	−0.0356544	−	0.999364i	$-0.511352\pi$
$317$	−17.7533	−	12.8985i	−0.997124	−	0.724453i	−0.961470	+	0.274911i	$0.911352\pi$
$318$	−0.944272	+	0.686054i	−0.0529521	+	0.0384720i
$319$	−11.7082	+	8.50651i	−0.655534	+	0.476273i
$320$	−0.0729490	+	0.224514i	−0.00407797	+	0.0125507i
$321$	−10.2361	−	7.43694i	−0.571322	−	0.415089i
$322$	−6.23607	+	19.1926i	−0.347522	+	1.06956i
$323$	3.61803	+	11.1352i	0.201313	+	0.619577i
$324$	−3.16312	+	2.29814i	−0.175729	+	0.127674i
$325$	−1.52786	−	4.70228i	−0.0847506	−	0.260836i
$326$	0.517221	+	1.59184i	0.0286462	+	0.0881640i
$327$	−3.94427	+	2.86568i	−0.218119	+	0.158473i
$328$	4.83688	+	14.8864i	0.267072	+	0.821963i
$329$	8.47214	−	26.0746i	0.467084	−	1.43754i
$330$	1.23607	+	0.898056i	0.0680433	+	0.0494364i
$331$	0.618034	−	1.90211i	0.0339702	−	0.104550i	−0.932634	−	0.360825i	$-0.882495\pi$
$331$	0.618034	−	1.90211i	0.0339702	−	0.104550i	0.966604	+	0.256275i	$0.0824953\pi$
$332$	3.85410	−	2.80017i	0.211521	−	0.153679i
$333$	−2.38197	+	1.73060i	−0.130531	+	0.0948363i
$334$	1.23607	+	0.898056i	0.0676346	+	0.0491394i
$335$	8.00000			0.437087
$336$	−9.70820			−0.529626
$337$	15.5623	+	11.3067i	0.847733	+	0.615914i	0.924520	−	0.381134i	$-0.124466\pi$
$337$	15.5623	+	11.3067i	0.847733	+	0.615914i	−0.0767872	+	0.997048i	$0.524466\pi$
$338$	2.19098	+	6.74315i	0.119174	+	0.366779i
$339$	−2.09017	+	6.43288i	−0.113522	+	0.349386i
$340$	−8.47214			−0.459466
$341$		0			0
$342$	2.03444			0.110010
$343$	−5.16312	+	15.8904i	−0.278782	+	0.858003i
$344$	−2.23607	−	6.88191i	−0.120561	−	0.371048i
$345$	7.70820	+	5.60034i	0.414996	+	0.301512i
$346$	9.23607			0.496534
$347$	1.81966			0.0976845			0.0488422	−	0.998807i	$-0.484447\pi$
$347$	1.81966			0.0976845			0.0488422	+	0.998807i	$0.484447\pi$
$348$	11.7082	+	8.50651i	0.627626	+	0.455997i
$349$	−22.5623	+	16.3925i	−1.20773	+	0.877469i	−0.995023	−	0.0996464i	$-0.968229\pi$
$349$	−22.5623	+	16.3925i	−1.20773	+	0.877469i	−0.212710	+	0.977115i	$0.568229\pi$
$350$	8.47214	−	6.15537i	0.452855	−	0.329018i
$351$	−2.11146	+	6.49839i	−0.112701	+	0.346859i
$352$	9.09017	+	6.60440i	0.484508	+	0.352015i
$353$	−6.00000	+	18.4661i	−0.319348	+	0.982851i	0.654580	+	0.755993i	$0.272846\pi$
$353$	−6.00000	+	18.4661i	−0.319348	+	0.982851i	−0.973928	+	0.226859i	$0.927154\pi$
$354$	0.527864	+	1.62460i	0.0280557	+	0.0863464i
$355$	−10.6631	+	7.74721i	−0.565940	+	0.411179i
$356$	0.854102	+	2.62866i	0.0452673	+	0.139318i
$357$	−8.47214	−	26.0746i	−0.448393	−	1.38001i
$358$	−5.85410	+	4.25325i	−0.309399	+	0.224791i
$359$	5.48936	+	16.8945i	0.289717	+	0.891658i	0.984945	+	0.172868i	$0.0553035\pi$
$359$	5.48936	+	16.8945i	0.289717	+	0.891658i	−0.695228	+	0.718789i	$0.744697\pi$
$360$	−1.01722	+	3.13068i	−0.0536123	+	0.165002i
$361$	11.3262	+	8.22899i	0.596118	+	0.433105i
$362$	−3.47214	+	10.6861i	−0.182491	+	0.561651i
$363$	7.00000	−	5.08580i	0.367405	−	0.266935i
$364$	−6.85410	+	4.97980i	−0.359253	+	0.261012i
$365$	0.381966	+	0.277515i	0.0199930	+	0.0145258i
$366$	10.8328			0.566240
$367$	18.0000			0.939592			0.469796	−	0.882775i	$-0.344327\pi$
$367$	18.0000			0.939592			0.469796	+	0.882775i	$0.344327\pi$
$368$	11.5623	+	8.40051i	0.602727	+	0.437907i
$369$	−3.18441	−	9.80059i	−0.165774	−	0.510198i
$370$	0.381966	−	1.17557i	0.0198575	−	0.0611150i
$371$	6.47214			0.336017
$372$		0			0
$373$	19.0000			0.983783			0.491891	−	0.870657i	$-0.336306\pi$
$373$	19.0000			0.983783			0.491891	+	0.870657i	$0.336306\pi$
$374$	−2.00000	+	6.15537i	−0.103418	+	0.318286i
$375$	−3.43769	−	10.5801i	−0.177522	−	0.546356i
$376$	11.7082	+	8.50651i	0.603805	+	0.438690i
$377$	8.94427			0.460653
$378$	−14.4721			−0.744366
$379$	30.6525	+	22.2703i	1.57451	+	1.14395i	0.922667	+	0.385598i	$0.126005\pi$
$379$	30.6525	+	22.2703i	1.57451	+	1.14395i	0.651845	+	0.758352i	$0.273995\pi$
$380$	2.92705	−	2.12663i	0.150155	−	0.109094i
$381$	−3.52786	+	2.56314i	−0.180738	+	0.131314i
$382$	−0.607391	+	1.86936i	−0.0310768	+	0.0956446i
$383$	−9.61803	−	6.98791i	−0.491459	−	0.357066i	0.314286	−	0.949328i	$-0.398235\pi$
$383$	−9.61803	−	6.98791i	−0.491459	−	0.357066i	−0.805745	+	0.592263i	$0.798235\pi$
$384$	4.34752	−	13.3803i	0.221859	−	0.682811i
$385$	−2.61803	−	8.05748i	−0.133427	−	0.410647i
$386$	−2.73607	+	1.98787i	−0.139262	+	0.101180i
$387$	1.47214	+	4.53077i	0.0748329	+	0.230312i
$388$	−0.972136	−	2.99193i	−0.0493527	−	0.151892i
$389$	−14.4721	+	10.5146i	−0.733766	+	0.533113i	−0.890753	−	0.454488i	$-0.849822\pi$
$389$	−14.4721	+	10.5146i	−0.733766	+	0.533113i	0.156986	+	0.987601i	$0.449822\pi$
$390$	−0.291796	−	0.898056i	−0.0147757	−	0.0454748i
$391$	−12.4721	+	38.3853i	−0.630743	+	1.94123i
$392$	−19.7984	−	14.3844i	−0.999969	−	0.726520i
$393$	4.58359	−	14.1068i	0.231212	−	0.711596i
$394$	−7.70820	+	5.60034i	−0.388334	+	0.282141i
$395$	−1.38197	+	1.00406i	−0.0695343	+	0.0505196i
$396$	−3.85410	−	2.80017i	−0.193676	−	0.140714i
$397$	−7.00000			−0.351320			−0.175660	−	0.984451i	$-0.556206\pi$
$397$	−7.00000			−0.351320			−0.175660	+	0.984451i	$0.556206\pi$
$398$	0.652476			0.0327057
$399$	9.47214	+	6.88191i	0.474200	+	0.344526i
$400$	−2.29180	−	7.05342i	−0.114590	−	0.352671i
$401$	4.88854	−	15.0454i	0.244122	−	0.751331i	−0.751657	−	0.659554i	$-0.770745\pi$
$401$	4.88854	−	15.0454i	0.244122	−	0.751331i	0.995780	−	0.0917771i	$-0.0292547\pi$
$402$	−6.11146			−0.304812
$403$		0			0
$404$	4.85410			0.241501
$405$	−0.746711	+	2.29814i	−0.0371044	+	0.114196i
$406$	5.85410	+	18.0171i	0.290534	+	0.894172i
$407$	3.23607	+	2.35114i	0.160406	+	0.116542i
$408$	14.4721			0.716477
$409$	−26.1803			−1.29453			−0.647267	−	0.762263i	$-0.724088\pi$
$409$	−26.1803			−1.29453			−0.647267	+	0.762263i	$0.724088\pi$
$410$	3.50000	+	2.54290i	0.172853	+	0.125585i
$411$	−19.7082	+	14.3188i	−0.972134	+	0.706297i
$412$	2.30902	−	1.67760i	0.113757	−	0.0826494i
$413$	2.92705	−	9.00854i	0.144031	−	0.443281i
$414$	5.67376	+	4.12223i	0.278850	+	0.202597i
$415$	0.909830	−	2.80017i	0.0446618	−	0.137455i
$416$	−2.14590	−	6.60440i	−0.105211	−	0.323807i
$417$	13.4164	−	9.74759i	0.657004	−	0.477342i
$418$	−0.854102	−	2.62866i	−0.0417755	−	0.128572i
$419$	9.30902	+	28.6502i	0.454775	+	1.39965i	0.871399	+	0.490575i	$0.163213\pi$
$419$	9.30902	+	28.6502i	0.454775	+	1.39965i	−0.416624	+	0.909079i	$0.636787\pi$
$420$	−6.85410	+	4.97980i	−0.334446	+	0.242989i
$421$	−4.74671	−	14.6089i	−0.231341	−	0.711993i	−0.997586	−	0.0694448i	$-0.977877\pi$
$421$	−4.74671	−	14.6089i	−0.231341	−	0.711993i	0.766245	−	0.642548i	$-0.222123\pi$
$422$	−0.156541	+	0.481784i	−0.00762030	+	0.0234529i
$423$	−7.70820	−	5.60034i	−0.374786	−	0.272298i
$424$	−1.05573	+	3.24920i	−0.0512707	+	0.157795i
$425$	16.9443	−	12.3107i	0.821918	−	0.597158i
$426$	8.14590	−	5.91834i	0.394670	−	0.286745i
$427$	−48.5967	−	35.3076i	−2.35176	−	1.70865i
$428$	−16.5623			−0.800569
$429$	3.05573			0.147532
$430$	−1.61803	−	1.17557i	−0.0780285	−	0.0566910i
$431$	3.70820	+	11.4127i	0.178618	+	0.549729i	0.999780	−	0.0209654i	$-0.00667397\pi$
$431$	3.70820	+	11.4127i	0.178618	+	0.549729i	−0.821162	+	0.570695i	$0.806674\pi$
$432$	−3.16718	+	9.74759i	−0.152381	+	0.468981i
$433$	−12.1803			−0.585350			−0.292675	−	0.956212i	$-0.594545\pi$
$433$	−12.1803			−0.585350			−0.292675	+	0.956212i	$0.594545\pi$
$434$		0			0
$435$	8.94427			0.428845
$436$	−1.97214	+	6.06961i	−0.0944482	+	0.290682i
$437$	−5.32624	−	16.3925i	−0.254789	−	0.784158i
$438$	−0.291796	−	0.212002i	−0.0139426	−	0.0101299i
$439$	21.1803			1.01088			0.505441	−	0.862861i	$-0.331330\pi$
$439$	21.1803			1.01088			0.505441	+	0.862861i	$0.331330\pi$
$440$	4.47214			0.213201
$441$	13.0344	+	9.47008i	0.620688	+	0.450956i
$442$	3.23607	−	2.35114i	0.153924	−	0.111832i
$443$	−13.9894	+	10.1639i	−0.664654	+	0.482900i	−0.868232	−	0.496159i	$-0.834743\pi$
$443$	−13.9894	+	10.1639i	−0.664654	+	0.482900i	0.203577	+	0.979059i	$0.434743\pi$
$444$	1.23607	−	3.80423i	0.0586612	−	0.180541i
$445$	1.38197	+	1.00406i	0.0655115	+	0.0475969i
$446$	−0.763932	+	2.35114i	−0.0361732	+	0.111330i
$447$	3.81966	+	11.7557i	0.180664	+	0.556026i
$448$	−0.809017	+	0.587785i	−0.0382225	+	0.0277702i
$449$	9.67376	+	29.7728i	0.456533	+	1.40506i	0.869326	+	0.494239i	$0.164553\pi$
$449$	9.67376	+	29.7728i	0.456533	+	1.40506i	−0.412793	+	0.910825i	$0.635447\pi$
$450$	−1.12461	−	3.46120i	−0.0530147	−	0.163162i
$451$	−11.3262	+	8.22899i	−0.533332	+	0.387488i
$452$	2.73607	+	8.42075i	0.128694	+	0.396079i
$453$	3.12461	−	9.61657i	0.146807	−	0.451826i
$454$	1.23607	+	0.898056i	0.0580115	+	0.0421479i
$455$	−1.61803	+	4.97980i	−0.0758546	+	0.233456i
$456$	−5.00000	+	3.63271i	−0.234146	+	0.170117i
$457$	16.9443	−	12.3107i	0.792620	−	0.575872i	−0.116120	−	0.993235i	$-0.537046\pi$
$457$	16.9443	−	12.3107i	0.792620	−	0.575872i	0.908740	+	0.417363i	$0.137046\pi$
$458$	6.70820	+	4.87380i	0.313454	+	0.227738i
$459$	−28.9443			−1.35100
$460$	12.4721			0.581516
$461$	8.38197	+	6.08985i	0.390387	+	0.283633i	0.765614	−	0.643300i	$-0.222435\pi$
$461$	8.38197	+	6.08985i	0.390387	+	0.283633i	−0.375227	+	0.926933i	$0.622435\pi$
$462$	2.00000	+	6.15537i	0.0930484	+	0.286374i
$463$	−9.09017	+	27.9767i	−0.422456	+	1.30019i	0.482953	+	0.875646i	$0.339564\pi$
$463$	−9.09017	+	27.9767i	−0.422456	+	1.30019i	−0.905409	+	0.424540i	$0.860436\pi$
$464$	13.4164			0.622841
$465$		0			0
$466$	−0.0344419			−0.00159549
$467$	−2.69098	+	8.28199i	−0.124524	+	0.383245i	−0.993814	−	0.111057i	$-0.964576\pi$
$467$	−2.69098	+	8.28199i	−0.124524	+	0.383245i	0.869290	+	0.494302i	$0.164576\pi$
$468$	0.909830	+	2.80017i	0.0420569	+	0.129438i
$469$	27.4164	+	19.9192i	1.26597	+	0.919783i
$470$	4.00000			0.184506
$471$	−18.4033			−0.847977
$472$	4.04508	+	2.93893i	0.186190	+	0.135275i
$473$	5.23607	−	3.80423i	0.240755	−	0.174919i
$474$	1.05573	−	0.767031i	0.0484912	−	0.0352309i
$475$	−2.76393	+	8.50651i	−0.126818	+	0.390305i
$476$	−29.0344	−	21.0948i	−1.33079	−	0.966877i
$477$	0.695048	−	2.13914i	0.0318241	−	0.0979444i
$478$	−0.326238	−	1.00406i	−0.0149218	−	0.0459245i
$479$	−29.6976	+	21.5765i	−1.35692	+	0.985857i	−0.358282	+	0.933613i	$0.616637\pi$
$479$	−29.6976	+	21.5765i	−1.35692	+	0.985857i	−0.998634	+	0.0522438i	$0.983363\pi$
$480$	−2.14590	−	6.60440i	−0.0979464	−	0.301448i
$481$	−0.763932	−	2.35114i	−0.0348323	−	0.107203i
$482$	−15.1803	+	11.0292i	−0.691446	+	0.502365i
$483$	12.4721	+	38.3853i	0.567502	+	1.74659i
$484$	3.50000	−	10.7719i	0.159091	−	0.489631i
$485$	−1.57295	−	1.14281i	−0.0714239	−	0.0518925i
$486$	−2.59675	+	7.99197i	−0.117791	+	0.362523i
$487$	11.9443	−	8.67802i	0.541247	−	0.393239i	−0.283301	−	0.959031i	$-0.591430\pi$
$487$	11.9443	−	8.67802i	0.541247	−	0.393239i	0.824548	+	0.565792i	$0.191430\pi$
$488$	25.6525	−	18.6376i	1.16123	−	0.843685i
$489$	2.70820	+	1.96763i	0.122469	+	0.0889791i
$490$	−6.76393			−0.305563
$491$	−40.3607			−1.82145			−0.910726	−	0.413011i	$-0.864477\pi$
$491$	−40.3607			−1.82145			−0.910726	+	0.413011i	$0.864477\pi$
$492$	11.3262	+	8.22899i	0.510626	+	0.370992i
$493$	11.7082	+	36.0341i	0.527311	+	1.62290i
$494$	−0.527864	+	1.62460i	−0.0237497	+	0.0730941i
$495$	−2.94427			−0.132335
$496$		0			0
$497$	−55.8328			−2.50444
$498$	−0.695048	+	2.13914i	−0.0311459	+	0.0958571i
$499$	−10.3262	−	31.7809i	−0.462266	−	1.42271i	−0.862389	−	0.506247i	$-0.831033\pi$
$499$	−10.3262	−	31.7809i	−0.462266	−	1.42271i	0.400123	−	0.916462i	$-0.368967\pi$
$500$	−11.7812	−	8.55951i	−0.526869	−	0.382793i
$501$	3.05573			0.136520
$502$	14.9443			0.666995
$503$	1.33688	+	0.971301i	0.0596086	+	0.0433082i	0.617191	−	0.786814i	$-0.288271\pi$
$503$	1.33688	+	0.971301i	0.0596086	+	0.0433082i	−0.557582	+	0.830122i	$0.688271\pi$
$504$	−11.2812	+	8.19624i	−0.502502	+	0.365089i
$505$	2.42705	−	1.76336i	0.108002	−	0.0784683i
$506$	2.94427	−	9.06154i	0.130889	−	0.402834i
$507$	11.4721	+	8.33499i	0.509495	+	0.370170i
$508$	−1.76393	+	5.42882i	−0.0782618	+	0.240865i
$509$	−6.05573	−	18.6376i	−0.268415	−	0.826098i	−0.990887	−	0.134697i	$-0.956994\pi$
$509$	−6.05573	−	18.6376i	−0.268415	−	0.826098i	0.722471	−	0.691401i	$-0.243006\pi$
$510$	3.23607	−	2.35114i	0.143295	−	0.104110i
$511$	0.618034	+	1.90211i	0.0273402	+	0.0841445i
$512$	−5.78115	−	17.7926i	−0.255493	−	0.786327i
$513$	10.0000	−	7.26543i	0.441511	−	0.320776i
$514$	3.04508	+	9.37181i	0.134313	+	0.413373i
$515$	0.545085	−	1.67760i	0.0240193	−	0.0739238i
$516$	−5.23607	−	3.80423i	−0.230505	−	0.167472i
$517$	−4.00000	+	12.3107i	−0.175920	+	0.541425i
$518$	4.23607	−	3.07768i	0.186122	−	0.135226i
$519$	14.9443	−	10.8576i	0.655981	−	0.476598i
$520$	−2.23607	−	1.62460i	−0.0980581	−	0.0712434i
$521$	2.00000			0.0876216			0.0438108	−	0.999040i	$-0.486050\pi$
$521$	2.00000			0.0876216			0.0438108	+	0.999040i	$0.486050\pi$
$522$	6.58359			0.288156
$523$	3.47214	+	2.52265i	0.151826	+	0.110308i	0.661105	−	0.750294i	$-0.270088\pi$
$523$	3.47214	+	2.52265i	0.151826	+	0.110308i	−0.509279	+	0.860602i	$0.670088\pi$
$524$	−6.00000	−	18.4661i	−0.262111	−	0.806695i
$525$	6.47214	−	19.9192i	0.282467	−	0.869345i
$526$	11.5967			0.505642
$527$		0			0
$528$	4.58359			0.199475
$529$	11.2533	−	34.6341i	0.489273	−	1.50583i
$530$	0.291796	+	0.898056i	0.0126748	+	0.0390091i
$531$	−2.66312	−	1.93487i	−0.115570	−	0.0839662i
$532$	15.3262			0.664477
$533$	8.65248			0.374780
$534$	−1.05573	−	0.767031i	−0.0456858	−	0.0331927i
$535$	−8.28115	+	6.01661i	−0.358025	+	0.260121i
$536$	−14.4721	+	10.5146i	−0.625101	+	0.454163i
$537$	−4.47214	+	13.7638i	−0.192987	+	0.593953i
$538$	−14.4721	−	10.5146i	−0.623938	−	0.453318i
$539$	6.76393	−	20.8172i	0.291343	−	0.896662i
$540$	2.76393	+	8.50651i	0.118941	+	0.366062i
$541$	−15.6631	+	11.3799i	−0.673410	+	0.489261i	−0.871165	−	0.490990i	$-0.836635\pi$
$541$	−15.6631	+	11.3799i	−0.673410	+	0.489261i	0.197755	+	0.980252i	$0.436635\pi$
$542$	−1.56231	−	4.80828i	−0.0671068	−	0.206533i
$543$	6.94427	+	21.3723i	0.298007	+	0.917172i
$544$	23.7984	−	17.2905i	1.02035	−	0.741325i
$545$	1.21885	+	3.75123i	0.0522097	+	0.160685i
$546$	1.23607	−	3.80423i	0.0528988	−	0.162806i
$547$	−22.7533	−	16.5312i	−0.972860	−	0.706824i	−0.0167587	−	0.999860i	$-0.505335\pi$
$547$	−22.7533	−	16.5312i	−0.972860	−	0.706824i	−0.956102	+	0.293035i	$0.905335\pi$
$548$	−9.85410	+	30.3278i	−0.420946	+	1.29554i
$549$	−16.8885	+	12.2702i	−0.720785	+	0.523681i
$550$	−4.00000	+	2.90617i	−0.170561	+	0.123920i
$551$	−13.0902	−	9.51057i	−0.557660	−	0.405164i
$552$	−21.3050			−0.906799
$553$	−7.23607			−0.307709
$554$	9.32624	+	6.77591i	0.396234	+	0.287881i
$555$	−0.763932	−	2.35114i	−0.0324271	−	0.0998004i
$556$	6.70820	−	20.6457i	0.284491	−	0.875574i
$557$	−12.0000			−0.508456			−0.254228	−	0.967144i	$-0.581821\pi$
$557$	−12.0000			−0.508456			−0.254228	+	0.967144i	$0.581821\pi$
$558$		0			0
$559$	−4.00000			−0.169182
$560$	−2.42705	+	7.46969i	−0.102562	+	0.315652i
$561$	4.00000	+	12.3107i	0.168880	+	0.519760i
$562$	8.50000	+	6.17561i	0.358551	+	0.260502i
$563$	−39.5410			−1.66646			−0.833228	−	0.552930i	$-0.813510\pi$
$563$	−39.5410			−1.66646			−0.833228	+	0.552930i	$0.813510\pi$
$564$	12.9443			0.545052
$565$	4.42705	+	3.21644i	0.186247	+	0.135317i
$566$	10.9443	−	7.95148i	0.460022	−	0.334226i
$567$	−8.28115	+	6.01661i	−0.347776	+	0.252674i
$568$	9.10739	−	28.0297i	0.382138	−	1.17610i
$569$	−11.7082	−	8.50651i	−0.490833	−	0.356611i	0.314671	−	0.949201i	$-0.398106\pi$
$569$	−11.7082	−	8.50651i	−0.490833	−	0.356611i	−0.805505	+	0.592589i	$0.798106\pi$
$570$	−0.527864	+	1.62460i	−0.0221098	+	0.0680469i
$571$	1.79837	+	5.53483i	0.0752596	+	0.231625i	0.981609	−	0.190905i	$-0.0611421\pi$
$571$	1.79837	+	5.53483i	0.0752596	+	0.231625i	−0.906349	+	0.422530i	$0.861142\pi$
$572$	3.23607	−	2.35114i	0.135307	−	0.0983061i
$573$	1.21478	+	3.73871i	0.0507482	+	0.156187i
$574$	5.66312	+	17.4293i	0.236374	+	0.727484i
$575$	−24.9443	+	18.1231i	−1.04025	+	0.755784i
$576$	0.107391	+	0.330515i	0.00447462	+	0.0137715i
$577$	7.67376	−	23.6174i	0.319463	−	0.983206i	−0.654415	−	0.756135i	$-0.727085\pi$
$577$	7.67376	−	23.6174i	0.319463	−	0.983206i	0.973878	−	0.227070i	$-0.0729148\pi$
$578$	5.20820	+	3.78398i	0.216633	+	0.157393i
$579$	−2.09017	+	6.43288i	−0.0868645	+	0.267341i
$580$	9.47214	−	6.88191i	0.393309	−	0.285756i
$581$	10.0902	−	7.33094i	0.418611	−	0.304139i
$582$	1.20163	+	0.873032i	0.0498090	+	0.0361884i
$583$	−3.05573			−0.126555
$584$	−1.05573			−0.0436863
$585$	1.47214	+	1.06957i	0.0608653	+	0.0442213i
$586$	−1.61803	−	4.97980i	−0.0668404	−	0.205714i
$587$	0.763932	−	2.35114i	0.0315308	−	0.0970420i	−0.934053	−	0.357136i	$-0.883753\pi$
$587$	0.763932	−	2.35114i	0.0315308	−	0.0970420i	0.965583	+	0.260094i	$0.0837534\pi$
$588$	−21.8885			−0.902668
$589$		0			0
$590$	1.38197			0.0568946
$591$	−5.88854	+	18.1231i	−0.242222	+	0.745484i
$592$	−1.14590	−	3.52671i	−0.0470961	−	0.144947i
$593$	12.5172	+	9.09429i	0.514021	+	0.373458i	0.814347	−	0.580379i	$-0.197095\pi$
$593$	12.5172	+	9.09429i	0.514021	+	0.373458i	−0.300326	+	0.953837i	$0.597095\pi$
$594$	6.83282			0.280354
$595$	−22.1803			−0.909305
$596$	13.0902	+	9.51057i	0.536194	+	0.389568i
$597$	1.05573	−	0.767031i	0.0432081	−	0.0313925i
$598$	−4.76393	+	3.46120i	−0.194812	+	0.141539i
$599$	10.6910	−	32.9035i	0.436822	−	1.34440i	−0.454387	−	0.890805i	$-0.650141\pi$
$599$	10.6910	−	32.9035i	0.436822	−	1.34440i	0.891208	−	0.453594i	$-0.149859\pi$
$600$	8.94427	+	6.49839i	0.365148	+	0.265296i
$601$	−11.2918	+	34.7526i	−0.460602	+	1.41759i	0.403828	+	0.914835i	$0.367679\pi$
$601$	−11.2918	+	34.7526i	−0.460602	+	1.41759i	−0.864430	+	0.502752i	$0.832321\pi$
$602$	−2.61803	−	8.05748i	−0.106703	−	0.328398i
$603$	9.52786	−	6.92240i	0.388005	−	0.281902i
$604$	−4.09017	−	12.5882i	−0.166427	−	0.512209i
$605$	−2.16312	−	6.65740i	−0.0879433	−	0.270662i
$606$	−1.85410	+	1.34708i	−0.0753177	+	0.0547215i
$607$	4.18034	+	12.8658i	0.169675	+	0.522205i	0.999350	−	0.0360407i	$-0.0114746\pi$
$607$	4.18034	+	12.8658i	0.169675	+	0.522205i	−0.829676	+	0.558246i	$0.811475\pi$
$608$	−3.88197	+	11.9475i	−0.157435	+	0.484534i
$609$	30.6525	+	22.2703i	1.24210	+	0.902439i
$610$	2.70820	−	8.33499i	0.109652	−	0.337474i
$611$	6.47214	−	4.70228i	0.261835	−	0.190234i
$612$	−10.0902	+	7.33094i	−0.407871	+	0.296336i
$613$	6.56231	+	4.76779i	0.265049	+	0.192569i	0.712370	−	0.701804i	$-0.247622\pi$
$613$	6.56231	+	4.76779i	0.265049	+	0.192569i	−0.447321	+	0.894374i	$0.647622\pi$
$614$	9.45085			0.381405
$615$	8.65248			0.348902
$616$	15.3262	+	11.1352i	0.617512	+	0.448649i
$617$	7.27051	+	22.3763i	0.292700	+	0.900837i	0.983984	+	0.178255i	$0.0570451\pi$
$617$	7.27051	+	22.3763i	0.292700	+	0.900837i	−0.691285	+	0.722582i	$0.742955\pi$
$618$	−0.416408	+	1.28157i	−0.0167504	+	0.0515524i
$619$	−16.1803			−0.650343			−0.325171	−	0.945655i	$-0.605422\pi$
$619$	−16.1803			−0.650343			−0.325171	+	0.945655i	$0.605422\pi$
$620$		0			0
$621$	42.6099			1.70988
$622$	1.30244	−	4.00850i	0.0522231	−	0.160726i
$623$	2.23607	+	6.88191i	0.0895862	+	0.275718i
$624$	−2.29180	−	1.66509i	−0.0917453	−	0.0666568i
$625$	11.0000			0.440000
$626$	−13.1246			−0.524565
$627$	−4.47214	−	3.24920i	−0.178600	−	0.129760i
$628$	−19.4894	+	14.1598i	−0.777710	+	0.565039i
$629$	8.47214	−	6.15537i	0.337806	−	0.245431i
$630$	−1.19098	+	3.66547i	−0.0474499	+	0.146036i
$631$	8.38197	+	6.08985i	0.333681	+	0.242433i	0.741991	−	0.670410i	$-0.233882\pi$
$631$	8.38197	+	6.08985i	0.333681	+	0.242433i	−0.408310	+	0.912843i	$0.633882\pi$
$632$	1.18034	−	3.63271i	0.0469514	−	0.144502i
$633$	0.313082	+	0.963568i	0.0124439	+	0.0382984i
$634$	10.9721	−	7.97172i	0.435759	−	0.316598i
$635$	1.09017	+	3.35520i	0.0432621	+	0.133147i
$636$	0.944272	+	2.90617i	0.0374428	+	0.115237i
$637$	−10.9443	+	7.95148i	−0.433628	+	0.315049i
$638$	−2.76393	−	8.50651i	−0.109425	−	0.336776i
$639$	−5.99593	+	18.4536i	−0.237196	+	0.730013i
$640$	−9.20820	−	6.69015i	−0.363986	−	0.264451i
$641$	3.70820	−	11.4127i	0.146465	−	0.450774i	−0.850731	−	0.525601i	$-0.823841\pi$
$641$	3.70820	−	11.4127i	0.146465	−	0.450774i	0.997197	+	0.0748272i	$0.0238405\pi$
$642$	6.32624	−	4.59628i	0.249677	−	0.181401i
$643$	−23.0344	+	16.7355i	−0.908390	+	0.659984i	−0.940607	−	0.339497i	$-0.889743\pi$
$643$	−23.0344	+	16.7355i	−0.908390	+	0.659984i	0.0322174	+	0.999481i	$0.489743\pi$
$644$	42.7426	+	31.0543i	1.68430	+	1.22371i
$645$	−4.00000			−0.157500
$646$	−7.23607			−0.284699
$647$	−13.7082	−	9.95959i	−0.538925	−	0.391552i	0.284761	−	0.958599i	$-0.408086\pi$
$647$	−13.7082	−	9.95959i	−0.538925	−	0.391552i	−0.823686	+	0.567047i	$0.808086\pi$
$648$	−1.66970	−	5.13880i	−0.0655919	−	0.201871i
$649$	−1.38197	+	4.25325i	−0.0542469	+	0.166955i
$650$	3.05573			0.119856
$651$		0			0
$652$	4.38197			0.171611
$653$	4.72949	−	14.5559i	0.185079	−	0.569615i	−0.814870	−	0.579643i	$-0.803192\pi$
$653$	4.72949	−	14.5559i	0.185079	−	0.569615i	0.999950	+	0.0100277i	$0.00319198\pi$
$654$	−0.931116	−	2.86568i	−0.0364095	−	0.112057i
$655$	−9.70820	−	7.05342i	−0.379331	−	0.275600i
$656$	12.9787			0.506734
$657$	0.695048			0.0271164
$658$	13.7082	+	9.95959i	0.534401	+	0.388265i
$659$	4.57295	−	3.32244i	0.178137	−	0.129424i	−0.495144	−	0.868811i	$-0.664885\pi$
$659$	4.57295	−	3.32244i	0.178137	−	0.129424i	0.673281	+	0.739387i	$0.264885\pi$
$660$	3.23607	−	2.35114i	0.125964	−	0.0915180i
$661$	−14.0172	+	43.1406i	−0.545207	+	1.67797i	0.175291	+	0.984517i	$0.443913\pi$
$661$	−14.0172	+	43.1406i	−0.545207	+	1.67797i	−0.720498	+	0.693457i	$0.756087\pi$
$662$	1.00000	+	0.726543i	0.0388661	+	0.0282379i
$663$	2.47214	−	7.60845i	0.0960098	−	0.295488i
$664$	2.03444	+	6.26137i	0.0789517	+	0.242988i
$665$	7.66312	−	5.56758i	0.297163	−	0.215902i
$666$	−0.562306	−	1.73060i	−0.0217889	−	0.0670594i
$667$	−17.2361	−	53.0472i	−0.667383	−	2.05399i
$668$	3.23607	−	2.35114i	0.125207	−	0.0909684i
$669$	1.52786	+	4.70228i	0.0590706	+	0.181801i
$670$	−1.52786	+	4.70228i	−0.0590265	+	0.181665i
$671$	22.9443	+	16.6700i	0.885754	+	0.643538i
$672$	9.09017	−	27.9767i	0.350661	−	1.07922i
$673$	−38.0344	+	27.6336i	−1.46612	+	1.06520i	−0.484405	+	0.874844i	$0.660964\pi$
$673$	−38.0344	+	27.6336i	−1.46612	+	1.06520i	−0.981715	+	0.190354i	$0.939036\pi$
$674$	−9.61803	+	6.98791i	−0.370473	+	0.269164i
$675$	−17.8885	−	12.9968i	−0.688530	−	0.500247i
$676$	18.5623			0.713935
$677$	42.7214			1.64192			0.820958	−	0.570989i	$-0.193440\pi$
$677$	42.7214			1.64192			0.820958	+	0.570989i	$0.193440\pi$
$678$	−3.38197	−	2.45714i	−0.129884	−	0.0943660i
$679$	−2.54508	−	7.83297i	−0.0976714	−	0.300602i
$680$	3.61803	−	11.1352i	0.138745	−	0.427014i
$681$	3.05573			0.117096
$682$		0			0
$683$	−17.1803			−0.657387			−0.328694	−	0.944437i	$-0.606608\pi$
$683$	−17.1803			−0.657387			−0.328694	+	0.944437i	$0.606608\pi$
$684$	1.64590	−	5.06555i	0.0629325	−	0.193686i
$685$	6.09017	+	18.7436i	0.232693	+	0.716157i
$686$	−8.35410	−	6.06961i	−0.318961	−	0.231739i
$687$	16.5836			0.632704
$688$	−6.00000			−0.228748
$689$	1.52786	+	1.11006i	0.0582070	+	0.0422898i
$690$	−4.76393	+	3.46120i	−0.181360	+	0.131766i
$691$	15.5172	−	11.2739i	0.590303	−	0.428880i	−0.252121	−	0.967696i	$-0.581128\pi$
$691$	15.5172	−	11.2739i	0.590303	−	0.428880i	0.842424	+	0.538816i	$0.181128\pi$
$692$	7.47214	−	22.9969i	0.284048	−	0.874210i
$693$	−10.0902	−	7.33094i	−0.383294	−	0.278479i
$694$	−0.347524	+	1.06957i	−0.0131918	+	0.0406003i
$695$	−4.14590	−	12.7598i	−0.157263	−	0.484005i
$696$	−16.1803	+	11.7557i	−0.613314	+	0.445599i
$697$	11.3262	+	34.8586i	0.429012	+	1.32036i
$698$	−5.32624	−	16.3925i	−0.201601	−	0.620464i
$699$	−0.0557281	+	0.0404888i	−0.00210783	+	0.00153143i
$700$	−8.47214	−	26.0746i	−0.320217	−	0.985525i
$701$	2.16312	−	6.65740i	0.0816999	−	0.251446i	−0.901860	−	0.432028i	$-0.857798\pi$
$701$	2.16312	−	6.65740i	0.0816999	−	0.251446i	0.983560	+	0.180582i	$0.0577981\pi$
$702$	−3.41641	−	2.48217i	−0.128944	−	0.0936833i
$703$	−1.38197	+	4.25325i	−0.0521218	+	0.160415i
$704$	0.381966	−	0.277515i	0.0143959	−	0.0104592i
$705$	6.47214	−	4.70228i	0.243755	−	0.177098i
$706$	−9.70820	−	7.05342i	−0.365373	−	0.265459i
$707$	12.7082			0.477941
$708$	4.47214			0.168073
$709$	−27.8885	−	20.2622i	−1.04738	−	0.760963i	−0.0756645	−	0.997133i	$-0.524108\pi$
$709$	−27.8885	−	20.2622i	−1.04738	−	0.760963i	−0.971712	+	0.236170i	$0.924108\pi$
$710$	−2.51722	−	7.74721i	−0.0944696	−	0.290748i
$711$	−0.777088	+	2.39163i	−0.0291431	+	0.0896931i
$712$	−3.81966			−0.143148
$713$		0			0
$714$	16.9443			0.634123
$715$	0.763932	−	2.35114i	0.0285694	−	0.0879277i
$716$	5.85410	+	18.0171i	0.218778	+	0.673330i
$717$	−1.70820	−	1.24108i	−0.0637940	−	0.0463491i
$718$	−10.9787			−0.409722
$719$	−36.1803			−1.34930			−0.674649	−	0.738138i	$-0.735705\pi$
$719$	−36.1803			−1.34930			−0.674649	+	0.738138i	$0.735705\pi$
$720$	2.20820	+	1.60435i	0.0822949	+	0.0597907i
$721$	6.04508	−	4.39201i	0.225131	−	0.163567i
$722$	−7.00000	+	5.08580i	−0.260513	+	0.189274i
$723$	−11.5967	+	35.6911i	−0.431288	+	1.32737i
$724$	23.7984	+	17.2905i	0.884460	+	0.642598i
$725$	−8.94427	+	27.5276i	−0.332182	+	1.02235i
$726$	1.65248	+	5.08580i	0.0613291	+	0.188752i
$727$	32.1697	−	23.3727i	1.19311	−	0.866844i	0.199519	−	0.979894i	$-0.436062\pi$
$727$	32.1697	−	23.3727i	1.19311	−	0.866844i	0.993589	+	0.113050i	$0.0360621\pi$
$728$	−3.61803	−	11.1352i	−0.134093	−	0.412697i
$729$	7.43363	+	22.8784i	0.275320	+	0.847347i
$730$	−0.236068	+	0.171513i	−0.00873727	+	0.00634800i
$731$	−5.23607	−	16.1150i	−0.193663	−	0.596033i
$732$	8.76393	−	26.9726i	0.323924	−	0.996936i
$733$	4.42705	+	3.21644i	0.163517	+	0.118802i	0.666534	−	0.745474i	$-0.267777\pi$
$733$	4.42705	+	3.21644i	0.163517	+	0.118802i	−0.503018	+	0.864276i	$0.667777\pi$
$734$	−3.43769	+	10.5801i	−0.126888	+	0.390520i
$735$	−10.9443	+	7.95148i	−0.403686	+	0.293295i
$736$	−35.0344	+	25.4540i	−1.29139	+	0.938247i
$737$	−12.9443	−	9.40456i	−0.476808	−	0.346422i
$738$	6.36881			0.234439
$739$	−16.1803			−0.595203			−0.297602	−	0.954690i	$-0.596187\pi$
$739$	−16.1803			−0.595203			−0.297602	+	0.954690i	$0.596187\pi$
$740$	−2.61803	−	1.90211i	−0.0962408	−	0.0699231i
$741$	1.05573	+	3.24920i	0.0387831	+	0.119362i
$742$	−1.23607	+	3.80423i	−0.0453775	+	0.139658i
$743$	27.8197			1.02060			0.510302	−	0.859995i	$-0.329534\pi$
$743$	27.8197			1.02060			0.510302	+	0.859995i	$0.329534\pi$
$744$		0			0
$745$	10.0000			0.366372
$746$	−3.62868	+	11.1679i	−0.132855	+	0.408887i
$747$	−1.33939	−	4.12223i	−0.0490058	−	0.150824i
$748$	13.7082	+	9.95959i	0.501222	+	0.364159i
$749$	−43.3607			−1.58436
$750$	6.87539			0.251054
$751$	−36.8435	−	26.7683i	−1.34444	−	0.976791i	−0.999268	−	0.0382499i	$-0.987822\pi$
$751$	−36.8435	−	26.7683i	−1.34444	−	0.976791i	−0.345169	−	0.938541i	$-0.612178\pi$
$752$	9.70820	−	7.05342i	0.354022	−	0.257212i
$753$	24.1803	−	17.5680i	0.881181	−	0.640215i
$754$	−1.70820	+	5.25731i	−0.0622091	+	0.191460i
$755$	−6.61803	−	4.80828i	−0.240855	−	0.174991i
$756$	−11.7082	+	36.0341i	−0.425823	+	1.31055i
$757$	−7.00000	−	21.5438i	−0.254419	−	0.783022i	−0.993944	−	0.109892i	$-0.964949\pi$
$757$	−7.00000	−	21.5438i	−0.254419	−	0.783022i	0.739524	−	0.673130i	$-0.235051\pi$
$758$	−18.9443	+	13.7638i	−0.688087	+	0.499924i
$759$	−5.88854	−	18.1231i	−0.213741	−	0.657826i
$760$	1.54508	+	4.75528i	0.0560461	+	0.172492i
$761$	−1.61803	+	1.17557i	−0.0586537	+	0.0426144i	−0.616726	−	0.787178i	$-0.711541\pi$
$761$	−1.61803	+	1.17557i	−0.0586537	+	0.0426144i	0.558072	+	0.829792i	$0.311541\pi$
$762$	−0.832816	−	2.56314i	−0.0301697	−	0.0928529i
$763$	−5.16312	+	15.8904i	−0.186917	+	0.575273i
$764$	4.16312	+	3.02468i	0.150616	+	0.109429i
$765$	−2.38197	+	7.33094i	−0.0861202	+	0.265051i
$766$	5.94427	−	4.31877i	0.214775	−	0.156043i
$767$	2.23607	−	1.62460i	0.0807397	−	0.0586609i
$768$	6.56231	+	4.76779i	0.236797	+	0.172043i
$769$	−2.63932			−0.0951763			−0.0475882	−	0.998867i	$-0.515154\pi$
$769$	−2.63932			−0.0951763			−0.0475882	+	0.998867i	$0.515154\pi$
$770$	5.23607			0.188695
$771$	15.9443	+	11.5842i	0.574219	+	0.417194i
$772$	2.73607	+	8.42075i	0.0984732	+	0.303069i
$773$	9.00000	−	27.6992i	0.323708	−	0.996269i	−0.648313	−	0.761374i	$-0.724525\pi$
$773$	9.00000	−	27.6992i	0.323708	−	0.996269i	0.972021	−	0.234895i	$-0.0754748\pi$
$774$	−2.94427			−0.105830
$775$		0			0
$776$	4.34752			0.156067
$777$	3.23607	−	9.95959i	0.116093	−	0.357298i
$778$	−3.41641	−	10.5146i	−0.122484	−	0.376967i
$779$	−12.6631	−	9.20029i	−0.453703	−	0.329635i
$780$	−2.47214			−0.0885167
$781$	26.3607			0.943259
$782$	−20.1803	−	14.6619i	−0.721647	−	0.524308i
$783$	32.3607	−	23.5114i	1.15648	−	0.840229i
$784$	−16.4164	+	11.9272i	−0.586300	+	0.425972i
$785$	−4.60081	+	14.1598i	−0.164210	+	0.505387i
$786$	7.41641	+	5.38834i	0.264535	+	0.192196i
$787$	11.9443	−	36.7607i	0.425767	−	1.31038i	−0.476490	−	0.879180i	$-0.658091\pi$
$787$	11.9443	−	36.7607i	0.425767	−	1.31038i	0.902258	−	0.431197i	$-0.141909\pi$
$788$	7.70820	+	23.7234i	0.274593	+	0.845112i
$789$	18.7639	−	13.6328i	0.668014	−	0.485340i
$790$	−0.326238	−	1.00406i	−0.0116070	−	0.0357227i
$791$	7.16312	+	22.0458i	0.254691	+	0.783859i
$792$	5.32624	−	3.86974i	0.189260	−	0.137505i
$793$	−5.41641	−	16.6700i	−0.192342	−	0.591969i
$794$	1.33688	−	4.11450i	0.0474441	−	0.146018i
$795$	1.52786	+	1.11006i	0.0541878	+	0.0393697i
$796$	0.527864	−	1.62460i	0.0187096	−	0.0575824i
$797$	23.1246	−	16.8010i	0.819116	−	0.595122i	−0.0973433	−	0.995251i	$-0.531034\pi$
$797$	23.1246	−	16.8010i	0.819116	−	0.595122i	0.916459	+	0.400128i	$0.131034\pi$
$798$	−5.85410	+	4.25325i	−0.207233	+	0.150564i
$799$	27.4164	+	19.9192i	0.969923	+	0.704690i
$800$	22.4721			0.794510
$801$	2.51471			0.0888529
$802$	7.90983	+	5.74683i	0.279306	+	0.202928i
$803$	−0.291796	−	0.898056i	−0.0102973	−	0.0316917i
$804$	−4.94427	+	15.2169i	−0.174371	+	0.536659i
$805$	32.6525			1.15085
$806$		0			0
$807$	−35.7771			−1.25941
$808$	−2.07295	+	6.37988i	−0.0729261	+	0.224443i
$809$	−1.05573	−	3.24920i	−0.0371174	−	0.114236i	0.930781	−	0.365577i	$-0.119128\pi$
$809$	−1.05573	−	3.24920i	−0.0371174	−	0.114236i	−0.967899	+	0.251341i	$0.919128\pi$
$810$	−1.20820	−	0.877812i	−0.0424520	−	0.0308432i
$811$	−28.0000			−0.983213			−0.491606	−	0.870817i	$-0.663590\pi$
$811$	−28.0000			−0.983213			−0.491606	+	0.870817i	$0.663590\pi$
$812$	49.5967			1.74050
$813$	−8.18034	−	5.94336i	−0.286897	−	0.208443i
$814$	−2.00000	+	1.45309i	−0.0701000	+	0.0509306i
$815$	2.19098	−	1.59184i	0.0767468	−	0.0557598i
$816$	3.70820	−	11.4127i	0.129813	−	0.399524i
$817$	5.85410	+	4.25325i	0.204809	+	0.148803i
$818$	5.00000	−	15.3884i	0.174821	−	0.538043i
$819$	2.38197	+	7.33094i	0.0832326	+	0.256164i
$820$	9.16312	−	6.65740i	0.319990	−	0.232486i
$821$	−11.2918	−	34.7526i	−0.394086	−	1.21287i	−0.929671	−	0.368391i	$-0.879909\pi$
$821$	−11.2918	−	34.7526i	−0.394086	−	1.21287i	0.535584	−	0.844482i	$-0.320091\pi$
$822$	−4.65248	−	14.3188i	−0.162274	−	0.499427i
$823$	22.4164	−	16.2865i	0.781387	−	0.567711i	−0.124008	−	0.992281i	$-0.539575\pi$
$823$	22.4164	−	16.2865i	0.781387	−	0.567711i	0.905395	+	0.424570i	$0.139575\pi$
$824$	1.21885	+	3.75123i	0.0424605	+	0.130680i
$825$	−3.05573	+	9.40456i	−0.106387	+	0.327425i
$826$	4.73607	+	3.44095i	0.164789	+	0.119726i
$827$	15.0344	−	46.2713i	0.522799	−	1.60901i	−0.245829	−	0.969313i	$-0.579060\pi$
$827$	15.0344	−	46.2713i	0.522799	−	1.60901i	0.768628	−	0.639696i	$-0.220940\pi$
$828$	14.8541	−	10.7921i	0.516216	−	0.375053i
$829$	29.7984	−	21.6498i	1.03494	−	0.751928i	0.0656488	−	0.997843i	$-0.479088\pi$
$829$	29.7984	−	21.6498i	1.03494	−	0.751928i	0.969291	+	0.245915i	$0.0790883\pi$
$830$	1.47214	+	1.06957i	0.0510986	+	0.0371253i
$831$	23.0557			0.799794
$832$	−0.291796			−0.0101162
$833$	−46.3607	−	33.6830i	−1.60630	−	1.16705i
$834$	3.16718	+	9.74759i	0.109671	+	0.337531i
$835$	0.763932	−	2.35114i	0.0264370	−	0.0813646i
$836$	−7.23607			−0.250265
$837$		0			0
$838$	−18.6180			−0.643149
$839$	3.41641	−	10.5146i	0.117947	−	0.363005i	−0.874603	−	0.484840i	$-0.838878\pi$
$839$	3.41641	−	10.5146i	0.117947	−	0.363005i	0.992550	+	0.121835i	$0.0388778\pi$
$840$	−3.61803	−	11.1352i	−0.124834	−	0.384200i
$841$	−18.8992	−	13.7311i	−0.651696	−	0.473485i
$842$	9.49342			0.327165
$843$	21.0132			0.723732
$844$	1.07295	+	0.779543i	0.0369324	+	0.0268330i
$845$	9.28115	−	6.74315i	0.319281	−	0.231971i
$846$	4.76393	−	3.46120i	0.163787	−	0.118998i
$847$	9.16312	−	28.2012i	0.314848	−	0.969004i
$848$	2.29180	+	1.66509i	0.0787006	+	0.0571793i
$849$	8.36068	−	25.7315i	0.286938	−	0.883104i
$850$	4.00000	+	12.3107i	0.137199	+	0.422255i
$851$	−12.4721	+	9.06154i	−0.427539	+	0.310625i
$852$	−8.14590	−	25.0705i	−0.279074	−	0.858901i
$853$	11.5623	+	35.5851i	0.395886	+	1.21841i	0.928270	+	0.371908i	$0.121296\pi$
$853$	11.5623	+	35.5851i	0.395886	+	1.21841i	−0.532384	+	0.846503i	$0.678704\pi$
$854$	30.0344	−	21.8213i	1.02776	−	0.746709i
$855$	−1.01722	−	3.13068i	−0.0347882	−	0.107067i
$856$	7.07295	−	21.7683i	0.241748	−	0.744025i
$857$	−41.7984	−	30.3683i	−1.42781	−	1.03736i	−0.990420	−	0.138087i	$-0.955905\pi$
$857$	−41.7984	−	30.3683i	−1.42781	−	1.03736i	−0.437385	−	0.899274i	$-0.644095\pi$
$858$	−0.583592	+	1.79611i	−0.0199235	+	0.0613182i
$859$	−30.6525	+	22.2703i	−1.04585	+	0.759854i	−0.971419	−	0.237372i	$-0.923714\pi$
$859$	−30.6525	+	22.2703i	−1.04585	+	0.759854i	−0.0744303	+	0.997226i	$0.523714\pi$
$860$	−4.23607	+	3.07768i	−0.144449	+	0.104948i
$861$	29.6525	+	21.5438i	1.01055	+	0.734210i
$862$	−7.41641			−0.252604
$863$	−32.1803			−1.09543			−0.547716	−	0.836664i	$-0.684502\pi$
$863$	−32.1803			−1.09543			−0.547716	+	0.836664i	$0.684502\pi$
$864$	−25.1246	−	18.2541i	−0.854757	−	0.621017i
$865$	−4.61803	−	14.2128i	−0.157018	−	0.483251i
$866$	2.32624	−	7.15942i	0.0790488	−	0.243287i
$867$	12.8754			0.437271
$868$		0			0
$869$	3.41641			0.115894
$870$	−1.70820	+	5.25731i	−0.0579135	+	0.178240i
$871$	3.05573	+	9.40456i	0.103539	+	0.318661i
$872$	−7.13525	−	5.18407i	−0.241630	−	0.175555i
$873$	−2.86223			−0.0968719
$874$	10.6525			0.360325
$875$	−30.8435	−	22.4091i	−1.04270	−	0.757565i
$876$	−0.763932	+	0.555029i	−0.0258109	+	0.0187527i
$877$	29.0795	−	21.1275i	0.981946	−	0.713425i	0.0238032	−	0.999717i	$-0.492422\pi$
$877$	29.0795	−	21.1275i	0.981946	−	0.713425i	0.958143	+	0.286291i	$0.0924225\pi$
$878$	−4.04508	+	12.4495i	−0.136515	+	0.420150i
$879$	−8.47214	−	6.15537i	−0.285758	−	0.207615i
$880$	1.14590	−	3.52671i	0.0386282	−	0.118885i
$881$	7.52786	+	23.1684i	0.253620	+	0.780563i	0.994098	+	0.108482i	$0.0345991\pi$
$881$	7.52786	+	23.1684i	0.253620	+	0.780563i	−0.740478	+	0.672080i	$0.765401\pi$
$882$	−8.05573	+	5.85283i	−0.271250	+	0.197075i
$883$	12.2918	+	37.8303i	0.413652	+	1.27309i	0.913451	+	0.406948i	$0.133407\pi$
$883$	12.2918	+	37.8303i	0.413652	+	1.27309i	−0.499799	+	0.866141i	$0.666593\pi$
$884$	−3.23607	−	9.95959i	−0.108841	−	0.334977i
$885$	2.23607	−	1.62460i	0.0751646	−	0.0546103i
$886$	−3.30244	−	10.1639i	−0.110948	−	0.341462i
$887$	−9.60081	+	29.5483i	−0.322364	+	0.992134i	0.650253	+	0.759718i	$0.274663\pi$
$887$	−9.60081	+	29.5483i	−0.322364	+	0.992134i	−0.972617	+	0.232416i	$0.925337\pi$
$888$	4.47214	+	3.24920i	0.150075	+	0.109036i
$889$	−4.61803	+	14.2128i	−0.154884	+	0.476684i
$890$	−0.854102	+	0.620541i	−0.0286296	+	0.0208006i
$891$	3.90983	−	2.84066i	0.130984	−	0.0951656i
$892$	5.23607	+	3.80423i	0.175317	+	0.127375i
$893$	−14.4721			−0.484292
$894$	−7.63932			−0.255497
$895$	9.47214	+	6.88191i	0.316619	+	0.230037i
$896$	−14.8992	−	45.8550i	−0.497747	−	1.53191i
$897$	−3.63932	+	11.2007i	−0.121513	+	0.373980i
$898$	−19.3475			−0.645635
$899$		0			0
$900$	−9.52786			−0.317595
$901$	−2.47214	+	7.60845i	−0.0823588	+	0.253474i
$902$	−2.67376	−	8.22899i	−0.0890265	−	0.273996i
$903$	−13.7082	−	9.95959i	−0.456180	−	0.331435i
$904$	−12.2361			−0.406966
$905$	18.1803			0.604335
$906$	5.05573	+	3.67320i	0.167965	+	0.122034i
$907$	15.9894	−	11.6169i	0.530918	−	0.385734i	−0.289783	−	0.957092i	$-0.593583\pi$
$907$	15.9894	−	11.6169i	0.530918	−	0.385734i	0.820701	+	0.571358i	$0.193583\pi$
$908$	3.23607	−	2.35114i	0.107393	−	0.0780254i
$909$	1.36475	−	4.20025i	0.0452657	−	0.139314i
$910$	−2.61803	−	1.90211i	−0.0867870	−	0.0630544i
$911$	−1.29180	+	3.97574i	−0.0427991	+	0.131722i	−0.970173	−	0.242414i	$-0.922061\pi$
$911$	−1.29180	+	3.97574i	−0.0427991	+	0.131722i	0.927374	+	0.374136i	$0.122061\pi$
$912$	1.58359	+	4.87380i	0.0524380	+	0.161387i
$913$	−4.76393	+	3.46120i	−0.157663	+	0.114549i
$914$	4.00000	+	12.3107i	0.132308	+	0.407203i
$915$	−5.41641	−	16.6700i	−0.179061	−	0.551093i
$916$	17.5623	−	12.7598i	0.580275	−	0.421594i
$917$	−15.7082	−	48.3449i	−0.518731	−	1.59649i
$918$	5.52786	−	17.0130i	0.182447	−	0.561513i
$919$	4.47214	+	3.24920i	0.147522	+	0.107181i	0.659098	−	0.752057i	$-0.270938\pi$
$919$	4.47214	+	3.24920i	0.147522	+	0.107181i	−0.511576	+	0.859238i	$0.670938\pi$
$920$	−5.32624	+	16.3925i	−0.175601	+	0.540444i
$921$	15.2918	−	11.1101i	0.503882	−	0.366092i
$922$	−5.18034	+	3.76374i	−0.170605	+	0.123952i
$923$	−13.1803	−	9.57608i	−0.433836	−	0.315200i
$924$	16.9443			0.557426
$925$	8.00000			0.263038
$926$	−14.7082	−	10.6861i	−0.483342	−	0.351168i
$927$	−0.802439	−	2.46965i	−0.0263556	−	0.0811141i
$928$	−12.5623	+	38.6628i	−0.412378	+	1.26917i
$929$	−20.0000			−0.656179			−0.328089	−	0.944647i	$-0.606405\pi$
$929$	−20.0000			−0.656179			−0.328089	+	0.944647i	$0.606405\pi$
$930$		0			0
$931$	24.4721			0.802042
$932$	−0.0278640	+	0.0857567i	−0.000912717	+	0.00280905i
$933$	−2.60488	−	8.01699i	−0.0852799	−	0.262465i
$934$	−4.35410	−	3.16344i	−0.142471	−	0.103511i
$935$	10.4721			0.342475
$936$	−4.06888			−0.132996
$937$	−21.7984	−	15.8374i	−0.712122	−	0.517387i	0.171736	−	0.985143i	$-0.445063\pi$
$937$	−21.7984	−	15.8374i	−0.712122	−	0.517387i	−0.883857	+	0.467756i	$0.845063\pi$
$938$	−16.9443	+	12.3107i	−0.553250	+	0.401960i
$939$	−21.2361	+	15.4289i	−0.693013	+	0.503503i
$940$	3.23607	−	9.95959i	0.105549	−	0.324846i
$941$	30.7426	+	22.3358i	1.00218	+	0.728128i	0.962555	−	0.271087i	$-0.0873831\pi$
$941$	30.7426	+	22.3358i	1.00218	+	0.728128i	0.0396268	+	0.999215i	$0.487383\pi$
$942$	3.51471	−	10.8172i	0.114515	−	0.352442i
$943$	−16.6738	−	51.3166i	−0.542972	−	1.67110i
$944$	3.35410	−	2.43690i	0.109167	−	0.0793143i
$945$	7.23607	+	22.2703i	0.235389	+	0.724454i
$946$	1.23607	+	3.80423i	0.0401880	+	0.123686i
$947$	25.0344	−	18.1886i	0.813510	−	0.591050i	−0.101336	−	0.994852i	$-0.532312\pi$
$947$	25.0344	−	18.1886i	0.813510	−	0.591050i	0.914846	+	0.403803i	$0.132312\pi$
$948$	−1.05573	−	3.24920i	−0.0342885	−	0.105529i
$949$	−0.180340	+	0.555029i	−0.00585408	+	0.0180170i
$950$	−4.47214	−	3.24920i	−0.145095	−	0.105418i
$951$	8.38197	−	25.7970i	0.271804	−	0.836526i
$952$	40.1246	−	29.1522i	1.30045	−	0.944829i
$953$	−26.1246	+	18.9806i	−0.846259	+	0.614843i	−0.924112	−	0.382122i	$-0.875194\pi$
$953$	−26.1246	+	18.9806i	−0.846259	+	0.614843i	0.0778529	+	0.996965i	$0.475194\pi$
$954$	1.12461	+	0.817078i	0.0364107	+	0.0264539i
$955$	3.18034			0.102913
$956$	−2.76393			−0.0893920
$957$	−14.4721	−	10.5146i	−0.467818	−	0.339889i
$958$	−7.01064	−	21.5765i	−0.226504	−	0.697106i
$959$	−25.7984	+	79.3992i	−0.833073	+	2.56393i
$960$	−0.291796			−0.00941768
$961$		0			0
$962$	1.52786			0.0492603
$963$	−4.65654	+	14.3314i	−0.150055	+	0.461822i
$964$	15.1803	+	46.7203i	0.488926	+	1.50476i
$965$	4.42705	+	3.21644i	0.142512	+	0.103541i
$966$	−24.9443			−0.802569
$967$	15.6393			0.502927			0.251463	−	0.967867i	$-0.419088\pi$
$967$	15.6393			0.502927			0.251463	+	0.967867i	$0.419088\pi$
$968$	12.6631	+	9.20029i	0.407008	+	0.295709i
$969$	−11.7082	+	8.50651i	−0.376122	+	0.273268i
$970$	0.972136	−	0.706298i	0.0312134	−	0.0226779i
$971$	−8.65248	+	26.6296i	−0.277671	+	0.854584i	0.710829	+	0.703365i	$0.248320\pi$
$971$	−8.65248	+	26.6296i	−0.277671	+	0.854584i	−0.988500	+	0.151219i	$0.951680\pi$
$972$	17.7984	+	12.9313i	0.570883	+	0.414771i
$973$	17.5623	−	54.0512i	0.563022	−	1.73280i
$974$	2.81966	+	8.67802i	0.0903477	+	0.278062i
$975$	4.94427	−	3.59222i	0.158343	−	0.115043i
$976$	−8.12461	−	25.0050i	−0.260062	−	0.800390i
$977$	10.2746	+	31.6219i	0.328713	+	1.01167i	0.969737	+	0.244153i	$0.0785099\pi$
$977$	10.2746	+	31.6219i	0.328713	+	1.01167i	−0.641024	+	0.767521i	$0.721490\pi$
$978$	−1.67376	+	1.21606i	−0.0535210	+	0.0388853i
$979$	−1.05573	−	3.24920i	−0.0337412	−	0.103845i
$980$	−5.47214	+	16.8415i	−0.174801	+	0.537982i
$981$	4.69756	+	3.41298i	0.149982	+	0.108968i
$982$	7.70820	−	23.7234i	0.245979	−	0.757045i
$983$	−39.2148	+	28.4912i	−1.25076	+	0.908728i	−0.998266	−	0.0588707i	$-0.981250\pi$
$983$	−39.2148	+	28.4912i	−1.25076	+	0.908728i	−0.252492	+	0.967599i	$0.581250\pi$
$984$	−15.6525	+	11.3722i	−0.498983	+	0.362532i
$985$	12.4721	+	9.06154i	0.397395	+	0.288725i
$986$	−23.4164			−0.745730
$987$	33.8885			1.07868
$988$	3.61803	+	2.62866i	0.115105	+	0.0836287i
$989$	7.70820	+	23.7234i	0.245107	+	0.754361i
$990$	0.562306	−	1.73060i	0.0178713	−	0.0550021i
$991$	50.5410			1.60549			0.802744	−	0.596324i	$-0.203372\pi$
$991$	50.5410			1.60549			0.802744	+	0.596324i	$0.203372\pi$
$992$		0			0
$993$	2.47214			0.0784509
$994$	10.6631	−	32.8177i	0.338214	−	1.04091i
$995$	−0.326238	−	1.00406i	−0.0103424	−	0.0318307i
$996$	4.76393	+	3.46120i	0.150951	+	0.109672i
$997$	15.3607			0.486478			0.243239	−	0.969966i	$-0.421790\pi$
$997$	15.3607			0.486478			0.243239	+	0.969966i	$0.421790\pi$
$998$	20.6525			0.653743
$999$	−8.94427	−	6.49839i	−0.282984	−	0.205600i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	961.2.d.c.628.1		4
31.2	even	5		31.2.a.a.1.1	✓	2
31.3	odd	30		961.2.g.e.816.1		8
31.4	even	5	inner	961.2.d.c.531.1		4
31.5	even	3		961.2.g.a.448.1		8
31.6	odd	6		961.2.g.d.846.1		8
31.7	even	15		961.2.g.a.547.1		8
31.8	even	5		961.2.d.d.388.1		4
31.9	even	15		961.2.g.h.338.1		8
31.10	even	15		961.2.c.e.521.1		4
31.11	odd	30		961.2.g.d.844.1		8
31.12	odd	30		961.2.c.c.439.1		4
31.13	odd	30		961.2.g.e.732.1		8
31.14	even	15		961.2.g.h.235.1		8
31.15	odd	10		961.2.d.g.374.1		4
31.16	even	5		961.2.d.d.374.1		4
31.17	odd	30		961.2.g.e.235.1		8
31.18	even	15		961.2.g.h.732.1		8
31.19	even	15		961.2.c.e.439.1		4
31.20	even	15		961.2.g.a.844.1		8
31.21	odd	30		961.2.c.c.521.1		4
31.22	odd	30		961.2.g.e.338.1		8
31.23	odd	10		961.2.d.g.388.1		4
31.24	odd	30		961.2.g.d.547.1		8
31.25	even	3		961.2.g.a.846.1		8
31.26	odd	6		961.2.g.d.448.1		8
31.27	odd	10		961.2.d.a.531.1		4
31.28	even	15		961.2.g.h.816.1		8
31.29	odd	10		961.2.a.f.1.1		2
31.30	odd	2		961.2.d.a.628.1		4
93.2	odd	10		279.2.a.a.1.2		2
93.29	even	10		8649.2.a.c.1.2		2
124.95	odd	10		496.2.a.i.1.1		2
155.2	odd	20		775.2.b.d.249.2		4
155.33	odd	20		775.2.b.d.249.3		4
155.64	even	10		775.2.a.d.1.2		2
217.188	odd	10		1519.2.a.a.1.1		2
248.157	even	10		1984.2.a.r.1.1		2
248.219	odd	10		1984.2.a.n.1.2		2
341.219	odd	10		3751.2.a.b.1.2		2
372.95	even	10		4464.2.a.bf.1.2		2
403.64	even	10		5239.2.a.f.1.2		2
465.374	odd	10		6975.2.a.y.1.1		2
527.33	even	10		8959.2.a.b.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
31.2.a.a.1.1	✓	2	31.2	even	5
279.2.a.a.1.2		2	93.2	odd	10
496.2.a.i.1.1		2	124.95	odd	10
775.2.a.d.1.2		2	155.64	even	10
775.2.b.d.249.2		4	155.2	odd	20
775.2.b.d.249.3		4	155.33	odd	20
961.2.a.f.1.1		2	31.29	odd	10
961.2.c.c.439.1		4	31.12	odd	30
961.2.c.c.521.1		4	31.21	odd	30
961.2.c.e.439.1		4	31.19	even	15
961.2.c.e.521.1		4	31.10	even	15
961.2.d.a.531.1		4	31.27	odd	10
961.2.d.a.628.1		4	31.30	odd	2
961.2.d.c.531.1		4	31.4	even	5	inner
961.2.d.c.628.1		4	1.1	even	1	trivial
961.2.d.d.374.1		4	31.16	even	5
961.2.d.d.388.1		4	31.8	even	5
961.2.d.g.374.1		4	31.15	odd	10
961.2.d.g.388.1		4	31.23	odd	10
961.2.g.a.448.1		8	31.5	even	3
961.2.g.a.547.1		8	31.7	even	15
961.2.g.a.844.1		8	31.20	even	15
961.2.g.a.846.1		8	31.25	even	3
961.2.g.d.448.1		8	31.26	odd	6
961.2.g.d.547.1		8	31.24	odd	30
961.2.g.d.844.1		8	31.11	odd	30
961.2.g.d.846.1		8	31.6	odd	6
961.2.g.e.235.1		8	31.17	odd	30
961.2.g.e.338.1		8	31.22	odd	30
961.2.g.e.732.1		8	31.13	odd	30
961.2.g.e.816.1		8	31.3	odd	30
961.2.g.h.235.1		8	31.14	even	15
961.2.g.h.338.1		8	31.9	even	15
961.2.g.h.732.1		8	31.18	even	15
961.2.g.h.816.1		8	31.28	even	15
1519.2.a.a.1.1		2	217.188	odd	10
1984.2.a.n.1.2		2	248.219	odd	10
1984.2.a.r.1.1		2	248.157	even	10
3751.2.a.b.1.2		2	341.219	odd	10
4464.2.a.bf.1.2		2	372.95	even	10
5239.2.a.f.1.2		2	403.64	even	10
6975.2.a.y.1.1		2	465.374	odd	10
8649.2.a.c.1.2		2	93.29	even	10
8959.2.a.b.1.1		2	527.33	even	10

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 961 = 31^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	961.d (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.190983 + 0.587785i) q^{2} +(0.381966 + 1.17557i) q^{3} +(1.30902 + 0.951057i) q^{4} +1.00000 q^{5} -0.763932 q^{6} +(3.42705 + 2.48990i) q^{7} +(-1.80902 + 1.31433i) q^{8} +(1.19098 - 0.865300i) q^{9} +(-0.190983 + 0.587785i) q^{10} +(-1.61803 - 1.17557i) q^{11} +(-0.618034 + 1.90211i) q^{12} +(0.381966 + 1.17557i) q^{13} +(-2.11803 + 1.53884i) q^{14} +(0.381966 + 1.17557i) q^{15} +(0.572949 + 1.76336i) q^{16} +(-4.23607 + 3.07768i) q^{17} +(0.281153 + 0.865300i) q^{18} +(0.690983 - 2.12663i) q^{19} +(1.30902 + 0.951057i) q^{20} +(-1.61803 + 4.97980i) q^{21} +(1.00000 - 0.726543i) q^{22} +(6.23607 - 4.53077i) q^{23} +(-2.23607 - 1.62460i) q^{24} -4.00000 q^{25} -0.763932 q^{26} +(4.47214 + 3.24920i) q^{27} +(2.11803 + 6.51864i) q^{28} +(2.23607 - 6.88191i) q^{29} -0.763932 q^{30} -5.61803 q^{32} +(0.763932 - 2.35114i) q^{33} +(-1.00000 - 3.07768i) q^{34} +(3.42705 + 2.48990i) q^{35} +2.38197 q^{36} -2.00000 q^{37} +(1.11803 + 0.812299i) q^{38} +(-1.23607 + 0.898056i) q^{39} +(-1.80902 + 1.31433i) q^{40} +(2.16312 - 6.65740i) q^{41} +(-2.61803 - 1.90211i) q^{42} +(-1.00000 + 3.07768i) q^{43} +(-1.00000 - 3.07768i) q^{44} +(1.19098 - 0.865300i) q^{45} +(1.47214 + 4.53077i) q^{46} +(-2.00000 - 6.15537i) q^{47} +(-1.85410 + 1.34708i) q^{48} +(3.38197 + 10.4086i) q^{49} +(0.763932 - 2.35114i) q^{50} +(-5.23607 - 3.80423i) q^{51} +(-0.618034 + 1.90211i) q^{52} +(1.23607 - 0.898056i) q^{53} +(-2.76393 + 2.00811i) q^{54} +(-1.61803 - 1.17557i) q^{55} -9.47214 q^{56} +2.76393 q^{57} +(3.61803 + 2.62866i) q^{58} +(-0.690983 - 2.12663i) q^{59} +(-0.618034 + 1.90211i) q^{60} -14.1803 q^{61} +6.23607 q^{63} +(-0.0729490 + 0.224514i) q^{64} +(0.381966 + 1.17557i) q^{65} +(1.23607 + 0.898056i) q^{66} +8.00000 q^{67} -8.47214 q^{68} +(7.70820 + 5.60034i) q^{69} +(-2.11803 + 1.53884i) q^{70} +(-10.6631 + 7.74721i) q^{71} +(-1.01722 + 3.13068i) q^{72} +(0.381966 + 0.277515i) q^{73} +(0.381966 - 1.17557i) q^{74} +(-1.52786 - 4.70228i) q^{75} +(2.92705 - 2.12663i) q^{76} +(-2.61803 - 8.05748i) q^{77} +(-0.291796 - 0.898056i) q^{78} +(-1.38197 + 1.00406i) q^{79} +(0.572949 + 1.76336i) q^{80} +(-0.746711 + 2.29814i) q^{81} +(3.50000 + 2.54290i) q^{82} +(0.909830 - 2.80017i) q^{83} +(-6.85410 + 4.97980i) q^{84} +(-4.23607 + 3.07768i) q^{85} +(-1.61803 - 1.17557i) q^{86} +8.94427 q^{87} +4.47214 q^{88} +(1.38197 + 1.00406i) q^{89} +(0.281153 + 0.865300i) q^{90} +(-1.61803 + 4.97980i) q^{91} +12.4721 q^{92} +4.00000 q^{94} +(0.690983 - 2.12663i) q^{95} +(-2.14590 - 6.60440i) q^{96} +(-1.57295 - 1.14281i) q^{97} -6.76393 q^{98} -2.94427 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 3 q^{2} + 6 q^{3} + 3 q^{4} + 4 q^{5} - 12 q^{6} + 7 q^{7} - 5 q^{8} + 7 q^{9} - 3 q^{10} - 2 q^{11} + 2 q^{12} + 6 q^{13} - 4 q^{14} + 6 q^{15} + 9 q^{16} - 8 q^{17} - 19 q^{18} + 5 q^{19} + 3 q^{20}+ \cdots + 24 q^{99}+O(q^{100}) \) 4 * q - 3 * q^2 + 6 * q^3 + 3 * q^4 + 4 * q^5 - 12 * q^6 + 7 * q^7 - 5 * q^8 + 7 * q^9 - 3 * q^10 - 2 * q^11 + 2 * q^12 + 6 * q^13 - 4 * q^14 + 6 * q^15 + 9 * q^16 - 8 * q^17 - 19 * q^18 + 5 * q^19 + 3 * q^20 - 2 * q^21 + 4 * q^22 + 16 * q^23 - 16 * q^25 - 12 * q^26 + 4 * q^28 - 12 * q^30 - 18 * q^32 + 12 * q^33 - 4 * q^34 + 7 * q^35 + 14 * q^36 - 8 * q^37 + 4 * q^39 - 5 * q^40 - 7 * q^41 - 6 * q^42 - 4 * q^43 - 4 * q^44 + 7 * q^45 - 12 * q^46 - 8 * q^47 + 6 * q^48 + 18 * q^49 + 12 * q^50 - 12 * q^51 + 2 * q^52 - 4 * q^53 - 20 * q^54 - 2 * q^55 - 20 * q^56 + 20 * q^57 + 10 * q^58 - 5 * q^59 + 2 * q^60 - 12 * q^61 + 16 * q^63 - 7 * q^64 + 6 * q^65 - 4 * q^66 + 32 * q^67 - 16 * q^68 + 4 * q^69 - 4 * q^70 - 27 * q^71 + 25 * q^72 + 6 * q^73 + 6 * q^74 - 24 * q^75 + 5 * q^76 - 6 * q^77 - 28 * q^78 - 10 * q^79 + 9 * q^80 - 41 * q^81 + 14 * q^82 + 26 * q^83 - 14 * q^84 - 8 * q^85 - 2 * q^86 + 10 * q^89 - 19 * q^90 - 2 * q^91 + 32 * q^92 + 16 * q^94 + 5 * q^95 - 22 * q^96 - 13 * q^97 - 36 * q^98 + 24 * q^99

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