LMFDB - Embedded newform 961.2.g.c.844.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [961,2,Mod(235,961)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(961, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([26]))

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

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

chi := DirichletCharacter("961.235");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$N$	$=$	$961 = 31^{2}$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	961.g (of order $15$ , degree $8$ , not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$7.67362363425$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	$\Q(\zeta_{15})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$x^{8} - x^{7} + x^{5} - x^{4} + x^{3} - x + 1$ x^8 - x^7 + x^5 - x^4 + x^3 - x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$1$
Twist minimal:	no (minimal twist has level 31)
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			844.1
Root			$0.913545 + 0.406737i$ of defining polynomial
Character	$\chi$	$=$	961.844
Dual form			961.2.g.c.846.1

$q$ -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} +(-0.978148 + 0.207912i) q^{3} +(1.30902 - 0.951057i) q^{4} +(1.30902 - 2.26728i) q^{5} +(0.309017 + 0.535233i) q^{6} +(2.74064 + 1.22021i) q^{7} +(-1.80902 - 1.31433i) q^{8} +(-1.82709 + 0.813473i) q^{9} +(-1.58268 - 0.336408i) q^{10} +(-0.0798526 - 0.759747i) q^{11} +(-1.08268 + 1.20243i) q^{12} +(-3.24803 - 3.60730i) q^{13} +(0.193806 - 1.84395i) q^{14} +(-0.809017 + 2.48990i) q^{15} +(0.572949 - 1.76336i) q^{16} +(0.0246758 - 0.234775i) q^{17} +(0.827091 + 0.918578i) q^{18} +(3.34565 - 3.71572i) q^{19} +(-0.442790 - 4.21286i) q^{20} +(-2.93444 - 0.623735i) q^{21} +(-0.431318 + 0.192035i) q^{22} +(-4.42705 - 3.21644i) q^{23} +(2.04275 + 0.909491i) q^{24} +(-0.927051 - 1.60570i) q^{25} +(-1.50000 + 2.59808i) q^{26} +(4.04508 - 2.93893i) q^{27} +(4.74803 - 1.00922i) q^{28} +(2.66312 + 8.19624i) q^{29} +1.61803 q^{30} -5.61803 q^{32} +(0.236068 + 0.726543i) q^{33} +(-0.142710 + 0.0303339i) q^{34} +(6.35410 - 4.61653i) q^{35} +(-1.61803 + 2.80252i) q^{36} +(0.118034 + 0.204441i) q^{37} +(-2.82301 - 1.25689i) q^{38} +(3.92705 + 2.85317i) q^{39} +(-5.34799 + 2.38108i) q^{40} +(-6.33070 - 1.34563i) q^{41} +(0.193806 + 1.84395i) q^{42} +(3.09007 - 3.43187i) q^{43} +(-0.827091 - 0.918578i) q^{44} +(-0.547318 + 5.20738i) q^{45} +(-1.04508 + 3.21644i) q^{46} +(-1.04508 + 3.21644i) q^{47} +(-0.193806 + 1.84395i) q^{48} +(1.33826 + 1.48629i) q^{49} +(-0.766755 + 0.851568i) q^{50} +(0.0246758 + 0.234775i) q^{51} +(-7.68247 - 1.63296i) q^{52} +(11.6095 - 5.16889i) q^{53} +(-2.50000 - 1.81636i) q^{54} +(-1.82709 - 0.813473i) q^{55} +(-3.35410 - 5.80948i) q^{56} +(-2.50000 + 4.33013i) q^{57} +(4.30902 - 3.13068i) q^{58} +(-9.26515 + 1.96937i) q^{59} +(1.30902 + 4.02874i) q^{60} +6.94427 q^{61} -6.00000 q^{63} +(-0.0729490 - 0.224514i) q^{64} +(-12.4305 + 2.64218i) q^{65} +(0.381966 - 0.277515i) q^{66} +(2.11803 - 3.66854i) q^{67} +(-0.190983 - 0.330792i) q^{68} +(4.99904 + 2.22572i) q^{69} +(-3.92705 - 2.85317i) q^{70} +(0.0823743 - 0.0366754i) q^{71} +(4.37441 + 0.929809i) q^{72} +(-0.895005 - 8.51540i) q^{73} +(0.0976248 - 0.108423i) q^{74} +(1.24064 + 1.37787i) q^{75} +(0.845653 - 8.04585i) q^{76} +(0.708204 - 2.17963i) q^{77} +(0.927051 - 2.85317i) q^{78} +(-3.24803 - 3.60730i) q^{80} +(0.669131 - 0.743145i) q^{81} +(0.418114 + 3.97809i) q^{82} +(-4.00079 - 0.850394i) q^{83} +(-4.43444 + 1.97434i) q^{84} +(-0.500000 - 0.363271i) q^{85} +(-2.60735 - 1.16087i) q^{86} +(-4.30902 - 7.46344i) q^{87} +(-0.854102 + 1.47935i) q^{88} +(-5.16312 + 3.75123i) q^{89} +(3.16535 - 0.672816i) q^{90} +(-4.50000 - 13.8496i) q^{91} -8.85410 q^{92} +2.09017 q^{94} +(-4.04508 - 12.4495i) q^{95} +(5.49527 - 1.16805i) q^{96} +(4.28115 - 3.11044i) q^{97} +(0.618034 - 1.07047i) q^{98} +(0.763932 + 1.32317i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$8 q - 6 q^{2} + q^{3} + 6 q^{4} + 6 q^{5} - 2 q^{6} + 3 q^{7} - 10 q^{8} - 2 q^{9} - 2 q^{10} - 2 q^{11} + 2 q^{12} + 6 q^{13} - 6 q^{14} - 2 q^{15} + 18 q^{16} - 3 q^{17} - 6 q^{18} + 5 q^{19} + 7 q^{20}+ \cdots + 24 q^{99}+O(q^{100})$ 8 * q - 6 * q^2 + q^3 + 6 * q^4 + 6 * q^5 - 2 * q^6 + 3 * q^7 - 10 * q^8 - 2 * q^9 - 2 * q^10 - 2 * q^11 + 2 * q^12 + 6 * q^13 - 6 * q^14 - 2 * q^15 + 18 * q^16 - 3 * q^17 - 6 * q^18 + 5 * q^19 + 7 * q^20 + 3 * q^21 - 6 * q^22 - 22 * q^23 + 5 * q^24 + 6 * q^25 - 12 * q^26 + 10 * q^27 + 6 * q^28 - 10 * q^29 + 4 * q^30 - 36 * q^32 - 16 * q^33 + 11 * q^34 + 24 * q^35 - 4 * q^36 - 8 * q^37 - 10 * q^38 + 18 * q^39 - 10 * q^40 - 8 * q^41 - 6 * q^42 + q^43 + 6 * q^44 + 8 * q^45 + 14 * q^46 + 14 * q^47 + 6 * q^48 + 2 * q^49 - 12 * q^50 - 3 * q^51 - 3 * q^52 + 21 * q^53 - 20 * q^54 - 2 * q^55 - 20 * q^57 + 30 * q^58 - 5 * q^59 + 6 * q^60 - 16 * q^61 - 48 * q^63 - 14 * q^64 - 9 * q^65 + 12 * q^66 + 8 * q^67 - 6 * q^68 + 11 * q^69 - 18 * q^70 + 7 * q^71 + 10 * q^72 + 21 * q^73 + 11 * q^74 - 9 * q^75 - 15 * q^76 - 48 * q^77 - 6 * q^78 + 6 * q^80 + q^81 - 4 * q^82 - 14 * q^83 - 9 * q^84 - 4 * q^85 - 7 * q^86 - 30 * q^87 + 20 * q^88 - 10 * q^89 + 4 * q^90 - 36 * q^91 - 44 * q^92 - 28 * q^94 - 10 * q^95 - 2 * q^96 - 6 * q^97 - 4 * q^98 + 24 * q^99

Character values

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

$n$	$3$
$\chi(n)$	$e\left(\frac{14}{15}\right)$

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	0.860552	−	0.509363i	$-0.170119\pi$
$2$	−0.190983	−	0.587785i	−0.135045	−	0.415627i	−0.995597	+	0.0937362i	$0.970119\pi$
$3$	−0.978148	+	0.207912i	−0.564734	+	0.120038i	−0.481427	−	0.876486i	$-0.659881\pi$
$3$	−0.978148	+	0.207912i	−0.564734	+	0.120038i	−0.0833066	+	0.996524i	$0.526548\pi$
$4$	1.30902	−	0.951057i	0.654508	−	0.475528i
$5$	1.30902	−	2.26728i	0.585410	−	1.01396i	−0.409414	−	0.912349i	$-0.634267\pi$
$5$	1.30902	−	2.26728i	0.585410	−	1.01396i	0.994824	−	0.101611i	$-0.0323999\pi$
$6$	0.309017	+	0.535233i	0.126156	+	0.218508i
$7$	2.74064	+	1.22021i	1.03586	+	0.461196i	0.852983	−	0.521939i	$-0.174791\pi$
$7$	2.74064	+	1.22021i	1.03586	+	0.461196i	0.182880	+	0.983135i	$0.441458\pi$
$8$	−1.80902	−	1.31433i	−0.639584	−	0.464685i
$9$	−1.82709	+	0.813473i	−0.609030	+	0.271158i
$10$	−1.58268	−	0.336408i	−0.500486	−	0.106382i
$11$	−0.0798526	−	0.759747i	−0.0240765	−	0.229072i	−0.999943	−	0.0107032i	$-0.996593\pi$
$11$	−0.0798526	−	0.759747i	−0.0240765	−	0.229072i	0.975866	−	0.218369i	$-0.0700737\pi$
$12$	−1.08268	+	1.20243i	−0.312542	+	0.347113i
$13$	−3.24803	−	3.60730i	−0.900841	−	1.00049i	−0.999985	−	0.00541216i	$-0.998277\pi$
$13$	−3.24803	−	3.60730i	−0.900841	−	1.00049i	0.0991444	−	0.995073i	$-0.468389\pi$
$14$	0.193806	−	1.84395i	0.0517969	−	0.492815i
$15$	−0.809017	+	2.48990i	−0.208887	+	0.642889i
$16$	0.572949	−	1.76336i	0.143237	−	0.440839i
$17$	0.0246758	−	0.234775i	0.00598477	−	0.0569412i	−0.991122	−	0.132956i	$-0.957553\pi$
$17$	0.0246758	−	0.234775i	0.00598477	−	0.0569412i	0.997107	+	0.0760150i	$0.0242197\pi$
$18$	0.827091	+	0.918578i	0.194947	+	0.216511i
$19$	3.34565	−	3.71572i	0.767545	−	0.852446i	−0.224995	−	0.974360i	$-0.572237\pi$
$19$	3.34565	−	3.71572i	0.767545	−	0.852446i	0.992541	+	0.121914i	$0.0389033\pi$
$20$	−0.442790	−	4.21286i	−0.0990108	−	0.942025i
$21$	−2.93444	−	0.623735i	−0.640348	−	0.136110i
$22$	−0.431318	+	0.192035i	−0.0919572	+	0.0409420i
$23$	−4.42705	−	3.21644i	−0.923104	−	0.670674i	0.0211907	−	0.999775i	$-0.493254\pi$
$23$	−4.42705	−	3.21644i	−0.923104	−	0.670674i	−0.944295	+	0.329101i	$0.893254\pi$
$24$	2.04275	+	0.909491i	0.416975	+	0.185649i
$25$	−0.927051	−	1.60570i	−0.185410	−	0.321140i
$26$	−1.50000	+	2.59808i	−0.294174	+	0.509525i
$27$	4.04508	−	2.93893i	0.778477	−	0.565597i
$28$	4.74803	−	1.00922i	0.897293	−	0.190726i
$29$	2.66312	+	8.19624i	0.494529	+	1.52200i	0.817690	+	0.575659i	$0.195254\pi$
$29$	2.66312	+	8.19624i	0.494529	+	1.52200i	−0.323161	+	0.946344i	$0.604746\pi$
$30$	1.61803			0.295411
$31$		0			0
$31$		0			0
$32$	−5.61803			−0.993137
$33$	0.236068	+	0.726543i	0.0410942	+	0.126475i
$34$	−0.142710	+	0.0303339i	−0.0244745	+	0.00520222i
$35$	6.35410	−	4.61653i	1.07404	−	0.780335i
$36$	−1.61803	+	2.80252i	−0.269672	+	0.467086i
$37$	0.118034	+	0.204441i	0.0194047	+	0.0336099i	0.875565	−	0.483101i	$-0.160490\pi$
$37$	0.118034	+	0.204441i	0.0194047	+	0.0336099i	−0.856160	+	0.516711i	$0.827156\pi$
$38$	−2.82301	−	1.25689i	−0.457953	−	0.203894i
$39$	3.92705	+	2.85317i	0.628831	+	0.456873i
$40$	−5.34799	+	2.38108i	−0.845591	+	0.376481i
$41$	−6.33070	−	1.34563i	−0.988690	−	0.210153i	−0.314940	−	0.949112i	$-0.601984\pi$
$41$	−6.33070	−	1.34563i	−0.988690	−	0.210153i	−0.673750	+	0.738959i	$0.735318\pi$
$42$	0.193806	+	1.84395i	0.0299050	+	0.284527i
$43$	3.09007	−	3.43187i	0.471231	−	0.523355i	−0.459934	−	0.887953i	$-0.652127\pi$
$43$	3.09007	−	3.43187i	0.471231	−	0.523355i	0.931165	+	0.364598i	$0.118794\pi$
$44$	−0.827091	−	0.918578i	−0.124689	−	0.138481i
$45$	−0.547318	+	5.20738i	−0.0815894	+	0.776271i
$46$	−1.04508	+	3.21644i	−0.154089	+	0.474238i
$47$	−1.04508	+	3.21644i	−0.152441	+	0.469166i	−0.997893	−	0.0648863i	$-0.979332\pi$
$47$	−1.04508	+	3.21644i	−0.152441	+	0.469166i	0.845451	+	0.534052i	$0.179332\pi$
$48$	−0.193806	+	1.84395i	−0.0279735	+	0.266151i
$49$	1.33826	+	1.48629i	0.191180	+	0.212327i
$50$	−0.766755	+	0.851568i	−0.108436	+	0.120430i
$51$	0.0246758	+	0.234775i	0.00345531	+	0.0328750i
$52$	−7.68247	−	1.63296i	−1.06537	−	0.226451i
$53$	11.6095	−	5.16889i	1.59469	−	0.710002i	0.598828	−	0.800877i	$-0.295633\pi$
$53$	11.6095	−	5.16889i	1.59469	−	0.710002i	0.995862	+	0.0908755i	$0.0289665\pi$
$54$	−2.50000	−	1.81636i	−0.340207	−	0.247175i
$55$	−1.82709	−	0.813473i	−0.246365	−	0.109689i
$56$	−3.35410	−	5.80948i	−0.448211	−	0.776324i
$57$	−2.50000	+	4.33013i	−0.331133	+	0.573539i
$58$	4.30902	−	3.13068i	0.565802	−	0.411079i
$59$	−9.26515	+	1.96937i	−1.20622	+	0.256390i	−0.766796	−	0.641890i	$-0.778150\pi$
$59$	−9.26515	+	1.96937i	−1.20622	+	0.256390i	−0.439423	+	0.898280i	$0.644817\pi$
$60$	1.30902	+	4.02874i	0.168993	+	0.520108i
$61$	6.94427			0.889123			0.444561	−	0.895748i	$-0.353360\pi$
$61$	6.94427			0.889123			0.444561	+	0.895748i	$0.353360\pi$
$62$		0			0
$63$	−6.00000			−0.755929
$64$	−0.0729490	−	0.224514i	−0.00911863	−	0.0280642i
$65$	−12.4305	+	2.64218i	−1.54181	+	0.327723i
$66$	0.381966	−	0.277515i	0.0470168	−	0.0341597i
$67$	2.11803	−	3.66854i	0.258759	−	0.448184i	−0.707151	−	0.707063i	$-0.750020\pi$
$67$	2.11803	−	3.66854i	0.258759	−	0.448184i	0.965910	+	0.258879i	$0.0833531\pi$
$68$	−0.190983	−	0.330792i	−0.0231601	−	0.0401145i
$69$	4.99904	+	2.22572i	0.601814	+	0.267945i
$70$	−3.92705	−	2.85317i	−0.469372	−	0.341019i
$71$	0.0823743	−	0.0366754i	0.00977604	−	0.00435257i	−0.401843	−	0.915709i	$-0.631630\pi$
$71$	0.0823743	−	0.0366754i	0.00977604	−	0.00435257i	0.411619	+	0.911356i	$0.364964\pi$
$72$	4.37441	+	0.929809i	0.515529	+	0.109579i
$73$	−0.895005	−	8.51540i	−0.104752	−	0.996652i	−0.913042	−	0.407867i	$-0.866273\pi$
$73$	−0.895005	−	8.51540i	−0.104752	−	0.996652i	0.808289	−	0.588786i	$-0.200394\pi$
$74$	0.0976248	−	0.108423i	0.0113487	−	0.0126040i
$75$	1.24064	+	1.37787i	0.143256	+	0.159102i
$76$	0.845653	−	8.04585i	0.0970031	−	0.922922i
$77$	0.708204	−	2.17963i	0.0807073	−	0.248392i
$78$	0.927051	−	2.85317i	0.104968	−	0.323058i
$79$		0			0		−0.994522	−	0.104528i	$-0.966667\pi$
$79$		0			0		0.994522	+	0.104528i	$0.0333333\pi$
$80$	−3.24803	−	3.60730i	−0.363141	−	0.403308i
$81$	0.669131	−	0.743145i	0.0743478	−	0.0825716i
$82$	0.418114	+	3.97809i	0.0461730	+	0.439306i
$83$	−4.00079	−	0.850394i	−0.439144	−	0.0933429i	−0.0169662	−	0.999856i	$-0.505401\pi$
$83$	−4.00079	−	0.850394i	−0.439144	−	0.0933429i	−0.422178	+	0.906513i	$0.638734\pi$
$84$	−4.43444	+	1.97434i	−0.483837	+	0.215418i
$85$	−0.500000	−	0.363271i	−0.0542326	−	0.0394023i
$86$	−2.60735	−	1.16087i	−0.281158	−	0.125180i
$87$	−4.30902	−	7.46344i	−0.461975	−	0.800164i
$88$	−0.854102	+	1.47935i	−0.0910476	+	0.157699i
$89$	−5.16312	+	3.75123i	−0.547290	+	0.397629i	−0.826785	−	0.562518i	$-0.809833\pi$
$89$	−5.16312	+	3.75123i	−0.547290	+	0.397629i	0.279496	+	0.960147i	$0.409833\pi$
$90$	3.16535	−	0.672816i	0.333657	−	0.0709211i
$91$	−4.50000	−	13.8496i	−0.471728	−	1.45183i
$92$	−8.85410			−0.923104
$93$		0			0
$94$	2.09017			0.215585
$95$	−4.04508	−	12.4495i	−0.415017	−	1.27729i
$96$	5.49527	−	1.16805i	0.560858	−	0.119214i
$97$	4.28115	−	3.11044i	0.434685	−	0.315817i	−0.348834	−	0.937184i	$-0.613422\pi$
$97$	4.28115	−	3.11044i	0.434685	−	0.315817i	0.783520	+	0.621367i	$0.213422\pi$
$98$	0.618034	−	1.07047i	0.0624309	−	0.108133i
$99$	0.763932	+	1.32317i	0.0767781	+	0.132983i
$100$	−2.74064	−	1.22021i	−0.274064	−	0.122021i
$101$	−3.85410	−	2.80017i	−0.383497	−	0.278627i	0.379288	−	0.925279i	$-0.376169\pi$
$101$	−3.85410	−	2.80017i	−0.383497	−	0.278627i	−0.762786	+	0.646651i	$0.776169\pi$
$102$	0.133284	−	0.0593421i	0.0131971	−	0.00587574i
$103$	0.142710	+	0.0303339i	0.0140616	+	0.00298889i	0.214937	−	0.976628i	$-0.431045\pi$
$103$	0.142710	+	0.0303339i	0.0140616	+	0.00298889i	−0.200876	+	0.979617i	$0.564379\pi$
$104$	1.13456	+	10.7946i	0.111253	+	1.05850i
$105$	−5.25542	+	5.83674i	−0.512876	+	0.569607i
$106$	−5.25542	−	5.83674i	−0.510452	−	0.566914i
$107$	−0.113954	+	1.08420i	−0.0110163	+	0.104813i	−0.998648	−	0.0519766i	$-0.983448\pi$
$107$	−0.113954	+	1.08420i	−0.0110163	+	0.104813i	0.987632	+	0.156790i	$0.0501146\pi$
$108$	2.50000	−	7.69421i	0.240563	−	0.740376i
$109$	−2.60081	+	8.00448i	−0.249113	+	0.766690i	0.745820	+	0.666147i	$0.232058\pi$
$109$	−2.60081	+	8.00448i	−0.249113	+	0.766690i	−0.994933	+	0.100543i	$0.967942\pi$
$110$	−0.129204	+	1.22930i	−0.0123191	+	0.117209i
$111$	−0.157960	−	0.175433i	−0.0149929	−	0.0166513i
$112$	3.72191	−	4.13360i	0.351687	−	0.390588i
$113$	0.193806	+	1.84395i	0.0182318	+	0.173464i	0.999849	−	0.0173983i	$-0.00553834\pi$
$113$	0.193806	+	1.84395i	0.0182318	+	0.173464i	−0.981617	+	0.190862i	$0.938872\pi$
$114$	3.02264	+	0.642482i	0.283096	+	0.0601740i
$115$	−13.0877	+	5.82701i	−1.22043	+	0.543371i
$116$	11.2812	+	8.19624i	1.04743	+	0.761002i
$117$	8.86889	+	3.94868i	0.819929	+	0.365056i
$118$	2.92705	+	5.06980i	0.269457	+	0.466713i
$119$	0.354102	−	0.613323i	0.0324605	−	0.0562232i
$120$	4.73607	−	3.44095i	0.432342	−	0.314115i
$121$	10.1888	−	2.16569i	0.926253	−	0.196881i
$122$	−1.32624	−	4.08174i	−0.120072	−	0.369543i
$123$	6.47214			0.583573
$124$		0			0
$125$	8.23607			0.736656
$126$	1.14590	+	3.52671i	0.102085	+	0.314184i
$127$	10.0124	−	2.12820i	0.888456	−	0.188847i	0.258994	−	0.965879i	$-0.416609\pi$
$127$	10.0124	−	2.12820i	0.888456	−	0.188847i	0.629461	+	0.777032i	$0.283276\pi$
$128$	−9.20820	+	6.69015i	−0.813898	+	0.591331i
$129$	−2.30902	+	3.99933i	−0.203298	+	0.352122i
$130$	3.92705	+	6.80185i	0.344425	+	0.596562i
$131$	0.0823743	+	0.0366754i	0.00719708	+	0.00320435i	0.410332	−	0.911936i	$-0.365413\pi$
$131$	0.0823743	+	0.0366754i	0.00719708	+	0.00320435i	−0.403135	+	0.915141i	$0.632079\pi$
$132$	1.00000	+	0.726543i	0.0870388	+	0.0632374i
$133$	13.7032	−	6.10105i	1.18822	−	0.529028i
$134$	−2.56082	−	0.544320i	−0.221221	−	0.0470221i
$135$	−1.36830	−	13.0185i	−0.117764	−	1.12045i
$136$	−0.353210	+	0.392279i	−0.0302875	+	0.0336377i
$137$	4.33070	+	4.80973i	0.369997	+	0.410923i	0.899176	−	0.437587i	$-0.144167\pi$
$137$	4.33070	+	4.80973i	0.369997	+	0.410923i	−0.529179	+	0.848510i	$0.677500\pi$
$138$	0.353512	−	3.36344i	0.0300929	−	0.286315i
$139$	−1.80902	+	5.56758i	−0.153439	+	0.472236i	−0.997999	−	0.0632239i	$-0.979862\pi$
$139$	−1.80902	+	5.56758i	−0.153439	+	0.472236i	0.844561	+	0.535460i	$0.179862\pi$
$140$	3.92705	−	12.0862i	0.331896	−	1.02147i
$141$	0.353512	−	3.36344i	0.0297711	−	0.283253i
$142$	−0.0372894	−	0.0414140i	−0.00312925	−	0.00347539i
$143$	−2.48127	+	2.75573i	−0.207494	+	0.230446i
$144$	0.387613	+	3.68789i	0.0323011	+	0.307324i
$145$	22.0693	+	4.69097i	1.83275	+	0.389564i
$146$	−4.83430	+	2.15237i	−0.400089	+	0.178131i
$147$	−1.61803	−	1.17557i	−0.133453	−	0.0969594i
$148$	0.348943	+	0.155360i	0.0286830	+	0.0127705i
$149$	8.51722	+	14.7523i	0.697758	+	1.20855i	0.969242	+	0.246109i	$0.0791522\pi$
$149$	8.51722	+	14.7523i	0.697758	+	1.20855i	−0.271484	+	0.962443i	$0.587514\pi$
$150$	0.572949	−	0.992377i	0.0467811	−	0.0810272i
$151$	−15.7812	+	11.4657i	−1.28425	+	0.933064i	−0.999673	−	0.0255888i	$-0.991854\pi$
$151$	−15.7812	+	11.4657i	−1.28425	+	0.933064i	−0.284579	+	0.958652i	$0.591854\pi$
$152$	−10.9360	+	2.32452i	−0.887029	+	0.188544i
$153$	0.145898	+	0.449028i	0.0117952	+	0.0363018i
$154$	−1.41641			−0.114137
$155$		0			0
$156$	7.85410			0.628831
$157$	3.00000	+	9.23305i	0.239426	+	0.736878i	0.996503	+	0.0835524i	$0.0266266\pi$
$157$	3.00000	+	9.23305i	0.239426	+	0.736878i	−0.757077	+	0.653325i	$0.773373\pi$
$158$		0			0
$159$	−10.2812	+	7.46969i	−0.815348	+	0.592385i
$160$	−7.35410	+	12.7377i	−0.581393	+	1.00700i
$161$	−8.20820	−	14.2170i	−0.646897	−	1.12046i
$162$	−0.564602	−	0.251377i	−0.0443593	−	0.0197500i
$163$	10.2812	+	7.46969i	0.805282	+	0.585072i	0.912459	−	0.409168i	$-0.134181\pi$
$163$	10.2812	+	7.46969i	0.805282	+	0.585072i	−0.107177	+	0.994240i	$0.534181\pi$
$164$	−9.56677	+	4.25940i	−0.747039	+	0.332603i
$165$	1.95630	+	0.415823i	0.152297	+	0.0323718i
$166$	0.264234	+	2.51402i	0.0205085	+	0.195125i
$167$	6.18014	−	6.86374i	0.478233	−	0.531132i	−0.454958	−	0.890513i	$-0.650346\pi$
$167$	6.18014	−	6.86374i	0.478233	−	0.531132i	0.933191	+	0.359381i	$0.117012\pi$
$168$	4.48866	+	4.98517i	0.346308	+	0.384614i
$169$	−1.10406	+	10.5044i	−0.0849278	+	0.808034i
$170$	−0.118034	+	0.363271i	−0.00905279	+	0.0278616i
$171$	−3.09017	+	9.51057i	−0.236311	+	0.727291i
$172$	0.781051	−	7.43120i	0.0595546	−	0.566624i
$173$	0.608795	+	0.676135i	0.0462858	+	0.0514056i	0.765843	−	0.643027i	$-0.222322\pi$
$173$	0.608795	+	0.676135i	0.0462858	+	0.0514056i	−0.719557	+	0.694433i	$0.755655\pi$
$174$	−3.56395	+	3.95817i	−0.270182	+	0.300068i
$175$	−0.581419	−	5.53184i	−0.0439512	−	0.418167i
$176$	−1.38546	−	0.294488i	−0.104433	−	0.0221978i
$177$	8.65323	−	3.85266i	0.650416	−	0.289584i
$178$	3.19098	+	2.31838i	0.239174	+	0.173770i
$179$	−18.0867	−	8.05272i	−1.35186	−	0.601889i	−0.402314	−	0.915502i	$-0.631794\pi$
$179$	−18.0867	−	8.05272i	−1.35186	−	0.601889i	−0.949551	+	0.313613i	$0.898461\pi$
$180$	4.23607	+	7.33708i	0.315738	+	0.546874i
$181$	8.50000	−	14.7224i	0.631800	−	1.09431i	−0.355383	−	0.934721i	$-0.615650\pi$
$181$	8.50000	−	14.7224i	0.631800	−	1.09431i	0.987184	−	0.159589i	$-0.0510169\pi$
$182$	−7.28115	+	5.29007i	−0.539715	+	0.392126i
$183$	−6.79252	+	1.44380i	−0.502118	+	0.106728i
$184$	3.78115	+	11.6372i	0.278750	+	0.857905i
$185$	0.618034			0.0454388
$186$		0			0
$187$	−0.180340			−0.0131878
$188$	1.69098	+	5.20431i	0.123328	+	0.379563i
$189$	14.6722	−	3.11868i	1.06725	−	0.226850i
$190$	−6.54508	+	4.75528i	−0.474830	+	0.344984i
$191$	8.04508	−	13.9345i	0.582122	−	1.00826i	−0.413106	−	0.910683i	$-0.635556\pi$
$191$	8.04508	−	13.9345i	0.582122	−	1.00826i	0.995228	−	0.0975816i	$-0.0311107\pi$
$192$	0.118034	+	0.204441i	0.00851837	+	0.0147542i
$193$	−2.17603	−	0.968833i	−0.156634	−	0.0697381i	0.326922	−	0.945051i	$-0.393989\pi$
$193$	−2.17603	−	0.968833i	−0.156634	−	0.0697381i	−0.483556	+	0.875313i	$0.660655\pi$
$194$	−2.64590	−	1.92236i	−0.189964	−	0.138017i
$195$	11.6095	−	5.16889i	0.831375	−	0.370152i
$196$	3.16535	+	0.672816i	0.226097	+	0.0480583i
$197$	1.71598	+	16.3265i	0.122259	+	1.16321i	0.867856	+	0.496816i	$0.165498\pi$
$197$	1.71598	+	16.3265i	0.122259	+	1.16321i	−0.745597	+	0.666397i	$0.767836\pi$
$198$	0.631841	−	0.701731i	0.0449030	−	0.0498698i
$199$	17.8713	+	19.8481i	1.26686	+	1.40699i	0.872925	+	0.487854i	$0.162220\pi$
$199$	17.8713	+	19.8481i	1.26686	+	1.40699i	0.393936	+	0.919138i	$0.371113\pi$
$200$	−0.433364	+	4.12319i	−0.0306435	+	0.291553i
$201$	−1.30902	+	4.02874i	−0.0923309	+	0.284165i
$202$	−0.909830	+	2.80017i	−0.0640154	+	0.197019i
$203$	−2.70249	+	25.7125i	−0.189678	+	1.80466i
$204$	0.255585	+	0.283856i	0.0178945	+	0.0198739i
$205$	−11.3379	+	12.5920i	−0.791875	+	0.879467i
$206$	−0.00942533	−	0.0896760i	−0.000656694	−	0.00624802i
$207$	10.7051	+	2.27544i	0.744057	+	0.158154i
$208$	−8.22191	+	3.66063i	−0.570087	+	0.253819i
$209$	−3.09017	−	2.24514i	−0.213752	−	0.155300i
$210$	4.43444	+	1.97434i	0.306006	+	0.136242i
$211$	4.00000	+	6.92820i	0.275371	+	0.476957i	0.970229	−	0.242190i	$-0.0778659\pi$
$211$	4.00000	+	6.92820i	0.275371	+	0.476957i	−0.694857	+	0.719148i	$0.744533\pi$
$212$	10.2812	−	17.8075i	0.706112	−	1.22302i
$213$	−0.0729490	+	0.0530006i	−0.00499838	+	0.00363154i
$214$	0.659039	−	0.140083i	0.0450510	−	0.00957588i
$215$	−3.73607	−	11.4984i	−0.254798	−	0.784187i
$216$	−11.1803			−0.760726
$217$		0			0
$218$	5.20163			0.352299
$219$	2.64590	+	8.14324i	0.178793	+	0.550269i
$220$	−3.16535	+	0.672816i	−0.213408	+	0.0453613i
$221$	−0.927051	+	0.673542i	−0.0623602	+	0.0453073i
$222$	−0.0729490	+	0.126351i	−0.00489602	+	0.00848015i
$223$	0.354102	+	0.613323i	0.0237124	+	0.0410711i	0.877638	−	0.479324i	$-0.159118\pi$
$223$	0.354102	+	0.613323i	0.0237124	+	0.0410711i	−0.853926	+	0.520395i	$0.825785\pi$
$224$	−15.3970	−	6.85518i	−1.02875	−	0.458031i
$225$	3.00000	+	2.17963i	0.200000	+	0.145309i
$226$	1.04683	−	0.466079i	0.0696341	−	0.0310031i
$227$	20.2894	+	4.31264i	1.34665	+	0.286240i	0.824137	−	0.566390i	$-0.191660\pi$
$227$	20.2894	+	4.31264i	1.34665	+	0.286240i	0.522515	+	0.852630i	$0.324994\pi$
$228$	0.845653	+	8.04585i	0.0560047	+	0.532850i
$229$	4.84187	−	5.37745i	0.319960	−	0.355352i	−0.561612	−	0.827401i	$-0.689819\pi$
$229$	4.84187	−	5.37745i	0.319960	−	0.355352i	0.881572	+	0.472049i	$0.156485\pi$
$230$	5.92455	+	6.57988i	0.390653	+	0.433864i
$231$	−0.239558	+	2.27924i	−0.0157618	+	0.149963i
$232$	5.95492	−	18.3273i	0.390959	−	1.20325i
$233$	5.80902	−	17.8783i	0.380561	−	1.17125i	−0.559088	−	0.829108i	$-0.688849\pi$
$233$	5.80902	−	17.8783i	0.380561	−	1.17125i	0.939649	−	0.342139i	$-0.111151\pi$
$234$	0.627171	−	5.96713i	0.0409994	−	0.390084i
$235$	5.92455	+	6.57988i	0.386475	+	0.429224i
$236$	−10.2553	+	11.3896i	−0.667560	+	0.741401i
$237$		0			0
$238$	−0.428129	−	0.0910017i	−0.0277515	−	0.00589877i
$239$	12.2565	−	5.45694i	0.792807	−	0.352980i	0.0299531	−	0.999551i	$-0.490464\pi$
$239$	12.2565	−	5.45694i	0.792807	−	0.352980i	0.762854	+	0.646571i	$0.223798\pi$
$240$	3.92705	+	2.85317i	0.253490	+	0.184171i
$241$	7.79059	+	3.46859i	0.501836	+	0.223432i	0.642012	−	0.766695i	$-0.278100\pi$
$241$	7.79059	+	3.46859i	0.501836	+	0.223432i	−0.140176	+	0.990127i	$0.544767\pi$
$242$	−3.21885	−	5.57521i	−0.206915	−	0.358388i
$243$	−8.00000	+	13.8564i	−0.513200	+	0.888889i
$244$	9.09017	−	6.60440i	0.581938	−	0.422803i
$245$	5.12165	−	1.08864i	0.327210	−	0.0695506i
$246$	−1.23607	−	3.80423i	−0.0788088	−	0.242549i
$247$	−24.2705			−1.54430
$248$		0			0
$249$	4.09017			0.259204
$250$	−1.57295	−	4.84104i	−0.0994820	−	0.306174i
$251$	0.923637	−	0.196325i	0.0582995	−	0.0123919i	−0.178670	−	0.983909i	$-0.557179\pi$
$251$	0.923637	−	0.196325i	0.0582995	−	0.0123919i	0.236969	+	0.971517i	$0.423846\pi$
$252$	−7.85410	+	5.70634i	−0.494762	+	0.359466i
$253$	−2.09017	+	3.62028i	−0.131408	+	0.227605i
$254$	−3.16312	−	5.47868i	−0.198472	−	0.343763i
$255$	0.564602	+	0.251377i	0.0353568	+	0.0157418i
$256$	5.30902	+	3.85723i	0.331814	+	0.241077i
$257$	1.29395	−	0.576105i	0.0807146	−	0.0359364i	−0.365982	−	0.930622i	$-0.619267\pi$
$257$	1.29395	−	0.576105i	0.0807146	−	0.0359364i	0.446697	+	0.894685i	$0.352600\pi$
$258$	2.79173	+	0.593401i	0.173806	+	0.0369435i
$259$	0.0740275	+	0.704324i	0.00459984	+	0.0437646i
$260$	−13.7589	+	15.2808i	−0.853289	+	0.947673i
$261$	−11.5332	−	12.8089i	−0.713886	−	0.792851i
$262$	0.00582517	−	0.0554228i	0.000359880	−	0.00342403i
$263$	3.33688	−	10.2699i	0.205761	−	0.633267i	−0.793920	−	0.608022i	$-0.791963\pi$
$263$	3.33688	−	10.2699i	0.205761	−	0.633267i	0.999681	−	0.0252452i	$-0.00803665\pi$
$264$	0.527864	−	1.62460i	0.0324878	−	0.0999871i
$265$	3.47772	−	33.0883i	0.213634	−	2.03260i
$266$	−6.20318	−	6.88933i	−0.380341	−	0.422412i
$267$	4.27037	−	4.74273i	0.261342	−	0.290250i
$268$	−0.716449	−	6.81655i	−0.0437641	−	0.416387i
$269$	−1.35177	−	0.287327i	−0.0824187	−	0.0175186i	0.166518	−	0.986038i	$-0.446748\pi$
$269$	−1.35177	−	0.287327i	−0.0824187	−	0.0175186i	−0.248936	+	0.968520i	$0.580081\pi$
$270$	−7.39074	+	3.29057i	−0.449786	+	0.200258i
$271$	7.73607	+	5.62058i	0.469933	+	0.341426i	0.797415	−	0.603431i	$-0.206200\pi$
$271$	7.73607	+	5.62058i	0.469933	+	0.341426i	−0.327482	+	0.944857i	$0.606200\pi$
$272$	−0.399853	−	0.178026i	−0.0242447	−	0.0107944i
$273$	7.28115	+	12.6113i	0.440675	+	0.763272i
$274$	2.00000	−	3.46410i	0.120824	−	0.209274i
$275$	−1.14590	+	0.832544i	−0.0691003	+	0.0502043i
$276$	8.66062	−	1.84087i	0.521308	−	0.110807i
$277$	−4.11803	−	12.6740i	−0.247429	−	0.761507i	−0.995228	−	0.0975818i	$-0.968889\pi$
$277$	−4.11803	−	12.6740i	−0.247429	−	0.761507i	0.747799	−	0.663925i	$-0.231111\pi$
$278$	3.61803			0.216995
$279$		0			0
$280$	−17.5623			−1.04955
$281$	5.88197	+	18.1028i	0.350889	+	1.07992i	0.958355	+	0.285579i	$0.0921859\pi$
$281$	5.88197	+	18.1028i	0.350889	+	1.07992i	−0.607466	+	0.794345i	$0.707814\pi$
$282$	−2.04449	+	0.434571i	−0.121748	+	0.0258783i
$283$	−5.30902	+	3.85723i	−0.315588	+	0.229288i	−0.734291	−	0.678835i	$-0.762485\pi$
$283$	−5.30902	+	3.85723i	−0.315588	+	0.229288i	0.418702	+	0.908124i	$0.362485\pi$
$284$	0.0729490	−	0.126351i	0.00432873	−	0.00749758i
$285$	6.54508	+	11.3364i	0.387697	+	0.671512i
$286$	2.09366	+	0.932157i	0.123801	+	0.0551196i
$287$	−15.7082	−	11.4127i	−0.927226	−	0.673669i
$288$	10.2647	−	4.57012i	0.604851	−	0.269297i
$289$	16.5740	+	3.52291i	0.974941	+	0.207230i
$290$	−1.45757	−	13.8679i	−0.0855917	−	0.814350i
$291$	−3.54090	+	3.93257i	−0.207571	+	0.230531i
$292$	−9.27020	−	10.2956i	−0.542498	−	0.602505i
$293$	0.860904	−	8.19095i	0.0502945	−	0.478520i	−0.940165	−	0.340719i	$-0.889330\pi$
$293$	0.860904	−	8.19095i	0.0502945	−	0.478520i	0.990460	−	0.137802i	$-0.0440037\pi$
$294$	−0.381966	+	1.17557i	−0.0222767	+	0.0685607i
$295$	−7.66312	+	23.5847i	−0.446164	+	1.37315i
$296$	0.0551768	−	0.524972i	0.00320709	−	0.0305134i
$297$	−2.55585	−	2.83856i	−0.148306	−	0.164710i
$298$	7.04452	−	7.82373i	0.408078	−	0.453216i
$299$	2.77652	+	26.4168i	0.160570	+	1.52772i
$300$	2.93444	+	0.623735i	0.169420	+	0.0360114i
$301$	12.6564	−	5.63497i	0.729500	−	0.324794i
$302$	9.75329	+	7.08618i	0.561239	+	0.407764i
$303$	4.35207	+	1.93767i	0.250020	+	0.111316i
$304$	−4.63525	−	8.02850i	−0.265850	−	0.460466i
$305$	9.09017	−	15.7446i	0.520502	−	0.901535i
$306$	0.236068	−	0.171513i	0.0134951	−	0.00980477i
$307$	−5.95709	+	1.26622i	−0.339989	+	0.0722669i	−0.374742	−	0.927129i	$-0.622269\pi$
$307$	−5.95709	+	1.26622i	−0.339989	+	0.0722669i	0.0347534	+	0.999396i	$0.488935\pi$
$308$	−1.14590	−	3.52671i	−0.0652936	−	0.200953i
$309$	−0.145898			−0.00829985
$310$		0			0
$311$	16.4721			0.934049			0.467025	−	0.884244i	$-0.345326\pi$
$311$	16.4721			0.934049			0.467025	+	0.884244i	$0.345326\pi$
$312$	−3.35410	−	10.3229i	−0.189889	−	0.584417i
$313$	1.20906	−	0.256993i	0.0683399	−	0.0145261i	−0.173615	−	0.984814i	$-0.555545\pi$
$313$	1.20906	−	0.256993i	0.0683399	−	0.0145261i	0.241955	+	0.970288i	$0.422211\pi$
$314$	4.85410	−	3.52671i	0.273933	−	0.199024i
$315$	−7.85410	+	13.6037i	−0.442529	+	0.766482i
$316$		0			0
$317$	23.6504	+	10.5298i	1.32834	+	0.591414i	0.943439	−	0.331546i	$-0.107570\pi$
$317$	23.6504	+	10.5298i	1.32834	+	0.591414i	0.384898	+	0.922959i	$0.374237\pi$
$318$	6.35410	+	4.61653i	0.356320	+	0.258882i
$319$	6.01441	−	2.67779i	0.336742	−	0.149927i
$320$	−0.604528	−	0.128496i	−0.0337942	−	0.00718317i
$321$	−0.113954	−	1.08420i	−0.00636028	−	0.0605140i
$322$	−6.78893	+	7.53987i	−0.378332	+	0.420181i
$323$	−0.789802	−	0.877163i	−0.0439457	−	0.0488067i
$324$	0.169131	−	1.60917i	0.00939614	−	0.0893983i
$325$	−2.78115	+	8.55951i	−0.154271	+	0.474796i
$326$	2.42705	−	7.46969i	0.134422	−	0.413708i
$327$	0.879754	−	8.37030i	0.0486505	−	0.462879i
$328$	9.68375	+	10.7549i	0.534696	+	0.593840i
$329$	−6.78893	+	7.53987i	−0.374286	+	0.415687i
$330$	−0.129204	−	1.22930i	−0.00711246	−	0.0676706i
$331$	11.0242	+	2.34327i	0.605946	+	0.128798i	0.500660	−	0.865644i	$-0.333091\pi$
$331$	11.0242	+	2.34327i	0.605946	+	0.128798i	0.105286	+	0.994442i	$0.466424\pi$
$332$	−6.04587	+	2.69180i	−0.331810	+	0.147732i
$333$	−0.381966	−	0.277515i	−0.0209316	−	0.0152077i
$334$	−5.21470	−	2.32174i	−0.285336	−	0.127040i
$335$	−5.54508	−	9.60437i	−0.302960	−	0.524743i
$336$	−2.78115	+	4.81710i	−0.151724	+	0.262794i
$337$	15.3541	−	11.1554i	0.836391	−	0.607674i	−0.0849690	−	0.996384i	$-0.527079\pi$
$337$	15.3541	−	11.1554i	0.836391	−	0.607674i	0.921360	+	0.388710i	$0.127079\pi$
$338$	6.38521	−	1.35722i	0.347310	−	0.0738230i
$339$	−0.572949	−	1.76336i	−0.0311183	−	0.0957723i
$340$	−1.00000			−0.0542326
$341$		0			0
$342$	6.18034			0.334195
$343$	−4.63525	−	14.2658i	−0.250280	−	0.770283i
$344$	−10.1006	+	2.14695i	−0.544587	+	0.115756i
$345$	11.5902	−	8.42075i	0.623994	−	0.453358i
$346$	0.281153	−	0.486971i	0.0151149	−	0.0261797i
$347$	4.06231	+	7.03612i	0.218076	+	0.377719i	0.954220	−	0.299107i	$-0.0966886\pi$
$347$	4.06231	+	7.03612i	0.218076	+	0.377719i	−0.736144	+	0.676825i	$0.763355\pi$
$348$	−12.7387	−	5.67165i	−0.682867	−	0.304032i
$349$	13.5172	+	9.82084i	0.723560	+	0.525697i	0.887520	−	0.460770i	$-0.152427\pi$
$349$	13.5172	+	9.82084i	0.723560	+	0.525697i	−0.163959	+	0.986467i	$0.552427\pi$
$350$	−3.14049	+	1.39824i	−0.167866	+	0.0747389i
$351$	−23.7401	−	5.04612i	−1.26715	−	0.269342i
$352$	0.448615	+	4.26829i	0.0239113	+	0.227500i
$353$	21.6678	−	24.0645i	1.15326	−	1.28082i	0.199619	−	0.979874i	$-0.436030\pi$
$353$	21.6678	−	24.0645i	1.15326	−	1.28082i	0.953640	−	0.300950i	$-0.0973037\pi$
$354$	−3.91716	−	4.35045i	−0.208195	−	0.231224i
$355$	0.0246758	−	0.234775i	0.00130966	−	0.0124606i
$356$	−3.19098	+	9.82084i	−0.169122	+	0.520503i
$357$	−0.218847	+	0.673542i	−0.0115826	+	0.0356476i
$358$	−1.27902	+	12.1690i	−0.0675982	+	0.643154i
$359$	−16.9466	−	18.8211i	−0.894405	−	0.993338i	0.105594	−	0.994409i	$-0.466326\pi$
$359$	−16.9466	−	18.8211i	−0.894405	−	0.993338i	−0.999999	+	0.00107162i	$0.999659\pi$
$360$	7.83432	−	8.70089i	0.412905	−	0.458577i
$361$	−0.627171	−	5.96713i	−0.0330090	−	0.314060i
$362$	−10.2770	−	2.18444i	−0.540146	−	0.114812i
$363$	−9.51586	+	4.23673i	−0.499453	+	0.222371i
$364$	−19.0623	−	13.8496i	−0.999136	−	0.725915i
$365$	−20.4784	−	9.11757i	−1.07189	−	0.477236i
$366$	2.14590	+	3.71680i	0.112168	+	0.194280i
$367$	−18.1353	+	31.4112i	−0.946653	+	1.63965i	−0.194245	+	0.980953i	$0.562226\pi$
$367$	−18.1353	+	31.4112i	−0.946653	+	1.63965i	−0.752408	+	0.658697i	$0.771108\pi$
$368$	−8.20820	+	5.96361i	−0.427882	+	0.310875i
$369$	12.6614	−	2.69127i	0.659127	−	0.140102i
$370$	−0.118034	−	0.363271i	−0.00613629	−	0.0188856i
$371$	38.1246			1.97933
$372$		0			0
$373$	−0.347524			−0.0179941			−0.00899706	−	0.999960i	$-0.502864\pi$
$373$	−0.347524			−0.0179941			−0.00899706	+	0.999960i	$0.502864\pi$
$374$	0.0344419	+	0.106001i	0.00178095	+	0.00548119i
$375$	−8.05609	+	1.71237i	−0.416015	+	0.0884267i
$376$	6.11803	−	4.44501i	0.315514	−	0.229234i
$377$	20.9164	−	36.2283i	1.07725	−	1.86585i
$378$	−4.63525	−	8.02850i	−0.238412	−	0.412941i
$379$	−16.8242	−	7.49063i	−0.864202	−	0.384768i	−0.0737395	−	0.997278i	$-0.523493\pi$
$379$	−16.8242	−	7.49063i	−0.864202	−	0.384768i	−0.790463	+	0.612510i	$0.790160\pi$
$380$	−17.1353	−	12.4495i	−0.879020	−	0.638645i
$381$	−9.35111	+	4.16338i	−0.479072	+	0.213297i
$382$	−9.72697	−	2.06753i	−0.497675	−	0.105784i
$383$	−1.76173	−	16.7618i	−0.0900204	−	0.856487i	−0.942608	−	0.333902i	$-0.891635\pi$
$383$	−1.76173	−	16.7618i	−0.0900204	−	0.856487i	0.852587	−	0.522585i	$-0.175032\pi$
$384$	7.61602	−	8.45845i	0.388653	−	0.431643i
$385$	−4.01478	−	4.45887i	−0.204612	−	0.227245i
$386$	−0.153880	+	1.46407i	−0.00783229	+	0.0745193i
$387$	−2.85410	+	8.78402i	−0.145082	+	0.446517i
$388$	2.64590	−	8.14324i	0.134325	−	0.413410i
$389$	−3.03853	+	28.9096i	−0.154059	+	1.46578i	0.595241	+	0.803547i	$0.297056\pi$
$389$	−3.03853	+	28.9096i	−0.154059	+	1.46578i	−0.749301	+	0.662230i	$0.769610\pi$
$390$	−5.25542	−	5.83674i	−0.266119	−	0.295555i
$391$	−0.864380	+	0.959992i	−0.0437136	+	0.0485489i
$392$	−0.467465	−	4.44764i	−0.0236106	−	0.224640i
$393$	−0.0881995	−	0.0187474i	−0.00444908	−	0.000945680i
$394$	9.26874	−	4.12671i	0.466952	−	0.207901i
$395$		0			0
$396$	2.25841	+	1.00551i	0.113489	+	0.0505287i
$397$	−8.14590	−	14.1091i	−0.408831	−	0.708116i	0.585928	−	0.810363i	$-0.300730\pi$
$397$	−8.14590	−	14.1091i	−0.408831	−	0.708116i	−0.994759	+	0.102247i	$0.967397\pi$
$398$	8.25329	−	14.2951i	0.413700	−	0.716549i
$399$	−12.1353	+	8.81678i	−0.607523	+	0.441391i
$400$	−3.36257	+	0.714737i	−0.168129	+	0.0357368i
$401$	9.21885	+	28.3727i	0.460367	+	1.41686i	0.864717	+	0.502260i	$0.167498\pi$
$401$	9.21885	+	28.3727i	0.460367	+	1.41686i	−0.404349	+	0.914605i	$0.632502\pi$
$402$	2.61803			0.130576
$403$		0			0
$404$	−7.70820			−0.383497
$405$	−0.809017	−	2.48990i	−0.0402004	−	0.123724i
$406$	15.6295	−	3.32216i	0.775681	−	0.164876i
$407$	0.145898	−	0.106001i	0.00723190	−	0.00525428i
$408$	0.263932	−	0.457144i	0.0130666	−	0.0226320i
$409$	−3.09017	−	5.35233i	−0.152799	−	0.264656i	0.779456	−	0.626457i	$-0.215495\pi$
$409$	−3.09017	−	5.35233i	−0.152799	−	0.264656i	−0.932255	+	0.361801i	$0.882162\pi$
$410$	9.56677	+	4.25940i	0.472469	+	0.210357i
$411$	−5.23607	−	3.80423i	−0.258276	−	0.187649i
$412$	0.215659	−	0.0960175i	0.0106247	−	0.00473044i
$413$	−27.7954	−	5.90810i	−1.36772	−	0.290719i
$414$	−0.707023	−	6.72688i	−0.0347483	−	0.330608i
$415$	−7.16519	+	7.95775i	−0.351725	+	0.390630i
$416$	18.2475	+	20.2659i	0.894659	+	0.993619i
$417$	0.611920	−	5.82203i	0.0299659	−	0.285106i
$418$	−0.729490	+	2.24514i	−0.0356805	+	0.109813i
$419$	1.38197	−	4.25325i	0.0675135	−	0.207785i	−0.911608	−	0.411060i	$-0.865159\pi$
$419$	1.38197	−	4.25325i	0.0675135	−	0.207785i	0.979122	+	0.203275i	$0.0651586\pi$
$420$	−1.32837	+	12.6386i	−0.0648178	+	0.616700i
$421$	9.87900	+	10.9717i	0.481473	+	0.534730i	0.934120	−	0.356960i	$-0.116187\pi$
$421$	9.87900	+	10.9717i	0.481473	+	0.534730i	−0.452647	+	0.891690i	$0.649520\pi$
$422$	3.30836	−	3.67431i	0.161049	−	0.178863i
$423$	−0.707023	−	6.72688i	−0.0343767	−	0.327072i
$424$	−27.7954	−	5.90810i	−1.34987	−	0.286923i
$425$	−0.399853	+	0.178026i	−0.0193957	+	0.00863554i
$426$	0.0450850	+	0.0327561i	0.00218437	+	0.00158704i
$427$	19.0317	+	8.47347i	0.921010	+	0.410060i
$428$	0.881966	+	1.52761i	0.0426314	+	0.0738398i
$429$	1.85410	−	3.21140i	0.0895169	−	0.155048i
$430$	−6.04508	+	4.39201i	−0.291520	+	0.211802i
$431$	−28.5972	+	6.07852i	−1.37748	+	0.292792i	−0.836372	−	0.548162i	$-0.815328\pi$
$431$	−28.5972	+	6.07852i	−1.37748	+	0.292792i	−0.541106	+	0.840954i	$0.681994\pi$
$432$	−2.86475	−	8.81678i	−0.137830	−	0.424197i
$433$	−0.583592			−0.0280456			−0.0140228	−	0.999902i	$-0.504464\pi$
$433$	−0.583592			−0.0280456			−0.0140228	+	0.999902i	$0.504464\pi$
$434$		0			0
$435$	−22.5623			−1.08178
$436$	4.20820	+	12.9515i	0.201536	+	0.620265i
$437$	−26.7628	+	5.68861i	−1.28024	+	0.272123i
$438$	4.28115	−	3.11044i	0.204561	−	0.148623i
$439$	−20.9164	+	36.2283i	−0.998286	+	1.72908i	−0.448455	+	0.893805i	$0.648026\pi$
$439$	−20.9164	+	36.2283i	−0.998286	+	1.72908i	−0.549831	+	0.835276i	$0.685308\pi$
$440$	2.23607	+	3.87298i	0.106600	+	0.184637i
$441$	−3.65418	−	1.62695i	−0.174009	−	0.0774736i
$442$	0.572949	+	0.416272i	0.0272524	+	0.0198000i
$443$	−37.5692	+	16.7269i	−1.78497	+	0.794718i	−0.805648	+	0.592395i	$0.798183\pi$
$443$	−37.5692	+	16.7269i	−1.78497	+	0.794718i	−0.979319	+	0.202324i	$0.935151\pi$
$444$	−0.373619	−	0.0794152i	−0.0177312	−	0.00376888i
$445$	1.74648	+	16.6167i	0.0827912	+	0.787706i
$446$	0.292875	−	0.325270i	0.0138680	−	0.0154020i
$447$	−11.3983	−	12.6591i	−0.539120	−	0.598753i
$448$	0.0740275	−	0.704324i	0.00349747	−	0.0332762i
$449$	−7.43769	+	22.8909i	−0.351006	+	1.08029i	0.607283	+	0.794486i	$0.292260\pi$
$449$	−7.43769	+	22.8909i	−0.351006	+	1.08029i	−0.958289	+	0.285801i	$0.907740\pi$
$450$	0.708204	−	2.17963i	0.0333851	−	0.102749i
$451$	−0.516817	+	4.91719i	−0.0243360	+	0.231541i
$452$	2.00739	+	2.22943i	0.0944198	+	0.104864i
$453$	13.0524	−	14.4962i	0.613258	−	0.681091i
$454$	−1.34002	−	12.7494i	−0.0628902	−	0.598361i
$455$	−37.2915	−	7.92655i	−1.74825	−	0.371603i
$456$	10.2137	−	4.54745i	0.478303	−	0.212954i
$457$	−12.7361	−	9.25330i	−0.595768	−	0.432851i	0.248606	−	0.968605i	$-0.420028\pi$
$457$	−12.7361	−	9.25330i	−0.595768	−	0.432851i	−0.844374	+	0.535754i	$0.820028\pi$
$458$	−4.08550	−	1.81898i	−0.190903	−	0.0849954i
$459$	−0.590170	−	1.02220i	−0.0275468	−	0.0477124i
$460$	−11.5902	+	20.0748i	−0.540394	+	0.935991i
$461$	8.69098	−	6.31437i	0.404779	−	0.294089i	−0.366705	−	0.930337i	$-0.619514\pi$
$461$	8.69098	−	6.31437i	0.404779	−	0.294089i	0.771485	+	0.636248i	$0.219514\pi$
$462$	1.38546	−	0.294488i	0.0644572	−	0.0137008i
$463$	9.61803	+	29.6013i	0.446988	+	1.37569i	0.880289	+	0.474438i	$0.157349\pi$
$463$	9.61803	+	29.6013i	0.446988	+	1.37569i	−0.433301	+	0.901249i	$0.642651\pi$
$464$	15.9787			0.741793
$465$		0			0
$466$	−11.6180			−0.538195
$467$	−10.1287	−	31.1729i	−0.468699	−	1.44251i	−0.854270	−	0.519830i	$-0.825995\pi$
$467$	−10.1287	−	31.1729i	−0.468699	−	1.44251i	0.385571	−	0.922678i	$-0.374005\pi$
$468$	15.3649	−	3.26592i	0.710245	−	0.150967i
$469$	10.2812	−	7.46969i	0.474740	−	0.344918i
$470$	2.73607	−	4.73901i	0.126205	−	0.218594i
$471$	−4.85410	−	8.40755i	−0.223665	−	0.387400i
$472$	19.3492	+	8.61482i	0.890619	+	0.396529i
$473$	−2.85410	−	2.07363i	−0.131232	−	0.0953454i
$474$		0			0
$475$	−9.06793	−	1.92745i	−0.416065	−	0.0884374i
$476$	−0.119779	−	1.13962i	−0.00549006	−	0.0522344i
$477$	−17.0069	+	18.8881i	−0.778692	+	0.864825i
$478$	−5.54829	−	6.16201i	−0.253773	−	0.281844i
$479$	0.934931	−	8.89527i	0.0427181	−	0.406435i	−0.952179	−	0.305541i	$-0.901163\pi$
$479$	0.934931	−	8.89527i	0.0427181	−	0.406435i	0.994897	−	0.100895i	$-0.0321705\pi$
$480$	4.54508	−	13.9883i	0.207454	−	0.638477i
$481$	0.354102	−	1.08981i	0.0161457	−	0.0496912i
$482$	0.550918	−	5.24164i	0.0250936	−	0.238750i
$483$	10.9847	+	12.1998i	0.499822	+	0.555109i
$484$	11.2776	−	12.5250i	0.512618	−	0.569320i
$485$	−1.44815	−	13.7782i	−0.0657570	−	0.625636i
$486$	9.67246	+	2.05594i	0.438751	+	0.0932595i
$487$	−20.9412	+	9.32362i	−0.948936	+	0.422493i	−0.822045	−	0.569423i	$-0.807167\pi$
$487$	−20.9412	+	9.32362i	−0.948936	+	0.422493i	−0.126891	+	0.991917i	$0.540500\pi$
$488$	−12.5623	−	9.12705i	−0.568669	−	0.413162i
$489$	−11.6095	−	5.16889i	−0.525001	−	0.233745i
$490$	−1.61803	−	2.80252i	−0.0730953	−	0.126605i
$491$	−13.7984	+	23.8995i	−0.622712	+	1.07857i	0.366267	+	0.930510i	$0.380636\pi$
$491$	−13.7984	+	23.8995i	−0.622712	+	1.07857i	−0.988979	+	0.148059i	$0.952698\pi$
$492$	8.47214	−	6.15537i	0.381953	−	0.277505i
$493$	1.98998	−	0.422984i	0.0896244	−	0.0190503i
$494$	4.63525	+	14.2658i	0.208550	+	0.641851i
$495$	4.00000			0.179787
$496$		0			0
$497$	0.270510			0.0121340
$498$	−0.781153	−	2.40414i	−0.0350043	−	0.107732i
$499$	4.05530	−	0.861981i	0.181540	−	0.0385876i	−0.116244	−	0.993221i	$-0.537086\pi$
$499$	4.05530	−	0.861981i	0.181540	−	0.0385876i	0.297785	+	0.954633i	$0.403752\pi$
$500$	10.7812	−	7.83297i	0.482148	−	0.350301i
$501$	−4.61803	+	7.99867i	−0.206319	+	0.357354i
$502$	−0.291796	−	0.505406i	−0.0130235	−	0.0225574i
$503$	12.0094	+	5.34692i	0.535472	+	0.238407i	0.656613	−	0.754228i	$-0.271989\pi$
$503$	12.0094	+	5.34692i	0.535472	+	0.238407i	−0.121141	+	0.992635i	$0.538655\pi$
$504$	10.8541	+	7.88597i	0.483480	+	0.351269i
$505$	−11.3939	+	5.07287i	−0.507020	+	0.225740i
$506$	2.52713	+	0.537159i	0.112345	+	0.0238796i
$507$	−1.10406	−	10.5044i	−0.0490331	−	0.466519i
$508$	11.0823	−	12.3082i	0.491700	−	0.546088i
$509$	1.27793	+	1.41928i	0.0566431	+	0.0629085i	0.770800	−	0.637077i	$-0.219857\pi$
$509$	1.27793	+	1.41928i	0.0566431	+	0.0629085i	−0.714157	+	0.699985i	$0.753190\pi$
$510$	0.0399263	−	0.379874i	0.00176797	−	0.0168211i
$511$	7.93769	−	24.4297i	0.351143	−	1.08071i
$512$	−5.78115	+	17.7926i	−0.255493	+	0.786327i
$513$	2.61321	−	24.8630i	0.115376	−	1.09773i
$514$	−0.585749	−	0.650540i	−0.0258363	−	0.0286941i
$515$	0.255585	−	0.283856i	0.0112624	−	0.0125082i
$516$	0.781051	+	7.43120i	0.0343838	+	0.327140i
$517$	2.52713	+	0.537159i	0.111143	+	0.0236242i
$518$	0.399853	−	0.178026i	0.0175686	−	0.00782202i
$519$	−0.736068	−	0.534785i	−0.0323098	−	0.0234744i
$520$	25.9597	+	11.5580i	1.13841	+	0.506852i
$521$	−15.5344	−	26.9064i	−0.680576	−	1.17879i	−0.974805	−	0.223058i	$-0.928396\pi$
$521$	−15.5344	−	26.9064i	−0.680576	−	1.17879i	0.294229	−	0.955735i	$-0.404937\pi$
$522$	−5.32624	+	9.22531i	−0.233123	+	0.403781i
$523$	27.6074	−	20.0579i	1.20719	−	0.877073i	0.212215	−	0.977223i	$-0.431932\pi$
$523$	27.6074	−	20.0579i	1.20719	−	0.877073i	0.994972	+	0.100150i	$0.0319324\pi$
$524$	0.142710	−	0.0303339i	0.00623431	−	0.00132514i
$525$	1.71885	+	5.29007i	0.0750166	+	0.230877i
$526$	−6.67376			−0.290990
$527$		0			0
$528$	1.41641			0.0616412
$529$	2.14590	+	6.60440i	0.0932999	+	0.287148i
$530$	−20.1130	+	4.27514i	−0.873652	+	0.185700i
$531$	15.3262	−	11.1352i	0.665102	−	0.483225i
$532$	12.1353	−	21.0189i	0.526130	−	0.911284i
$533$	15.7082	+	27.2074i	0.680398	+	1.17848i
$534$	−3.60327	−	1.60428i	−0.155929	−	0.0694240i
$535$	2.30902	+	1.67760i	0.0998275	+	0.0725289i
$536$	−8.65323	+	3.85266i	−0.373762	+	0.166410i
$537$	19.3657	+	4.11631i	0.835693	+	0.177632i
$538$	0.0892780	+	0.849423i	0.00384905	+	0.0366212i
$539$	1.02234	−	1.13542i	0.0440353	−	0.0489062i
$540$	−14.1724	−	15.7401i	−0.609884	−	0.677344i
$541$	−2.29963	+	21.8795i	−0.0988687	+	0.940672i	0.826841	+	0.562436i	$0.190136\pi$
$541$	−2.29963	+	21.8795i	−0.0988687	+	0.940672i	−0.925709	+	0.378236i	$0.876531\pi$
$542$	1.82624	−	5.62058i	0.0784436	−	0.241425i
$543$	−5.25329	+	16.1680i	−0.225440	+	0.693834i
$544$	−0.138630	+	1.31897i	−0.00594370	+	0.0565505i
$545$	14.7439	+	16.3748i	0.631560	+	0.701419i
$546$	6.02218	−	6.68830i	0.257725	−	0.286233i
$547$	2.47818	+	23.5783i	0.105959	+	1.00814i	0.910295	+	0.413961i	$0.135855\pi$
$547$	2.47818	+	23.5783i	0.105959	+	1.00814i	−0.804335	+	0.594176i	$0.797478\pi$
$548$	10.2433	+	2.17728i	0.437572	+	0.0930088i
$549$	−12.6878	+	5.64898i	−0.541503	+	0.241093i
$550$	0.708204	+	0.514540i	0.0301979	+	0.0219401i
$551$	39.3648	+	17.5264i	1.67700	+	0.746648i
$552$	−6.11803	−	10.5967i	−0.260401	−	0.451027i
$553$		0			0
$554$	−6.66312	+	4.84104i	−0.283089	+	0.205676i
$555$	−0.604528	+	0.128496i	−0.0256608	+	0.00545437i
$556$	2.92705	+	9.00854i	0.124135	+	0.382047i
$557$	−35.8885			−1.52065			−0.760323	−	0.649545i	$-0.774959\pi$
$557$	−35.8885			−1.52065			−0.760323	+	0.649545i	$0.774959\pi$
$558$		0			0
$559$	−22.4164			−0.948113
$560$	−4.50000	−	13.8496i	−0.190160	−	0.585251i
$561$	0.176399	−	0.0374948i	0.00744757	−	0.00158303i
$562$	9.51722	−	6.91467i	0.401460	−	0.291678i
$563$	4.28115	−	7.41517i	0.180429	−	0.312512i	−0.761598	−	0.648050i	$-0.775585\pi$
$563$	4.28115	−	7.41517i	0.180429	−	0.312512i	0.942027	+	0.335538i	$0.108918\pi$
$564$	−2.73607	−	4.73901i	−0.115209	−	0.199548i
$565$	4.43444	+	1.97434i	0.186558	+	0.0830612i
$566$	3.28115	+	2.38390i	0.137917	+	0.100203i
$567$	2.74064	−	1.22021i	0.115096	−	0.0512440i
$568$	−0.197220	−	0.0419204i	−0.00827517	−	0.00175894i
$569$	1.62310	+	15.4428i	0.0680440	+	0.647396i	0.974391	+	0.224861i	$0.0721929\pi$
$569$	1.62310	+	15.4428i	0.0680440	+	0.647396i	−0.906347	+	0.422535i	$0.861140\pi$
$570$	5.41338	−	6.01217i	0.226742	−	0.251822i
$571$	−4.68391	−	5.20201i	−0.196016	−	0.217698i	0.637122	−	0.770763i	$-0.280125\pi$
$571$	−4.68391	−	5.20201i	−0.196016	−	0.217698i	−0.833138	+	0.553065i	$0.813458\pi$
$572$	−0.627171	+	5.96713i	−0.0262233	+	0.249498i
$573$	−4.97214	+	15.3027i	−0.207714	+	0.639278i
$574$	−3.70820	+	11.4127i	−0.154777	+	0.476356i
$575$	−1.06054	+	10.0903i	−0.0442274	+	0.420795i
$576$	0.315921	+	0.350865i	0.0131634	+	0.0146194i
$577$	26.0819	−	28.9668i	1.08580	−	1.20590i	0.108490	−	0.994098i	$-0.465398\pi$
$577$	26.0819	−	28.9668i	1.08580	−	1.20590i	0.977311	−	0.211807i	$-0.0679349\pi$
$578$	−1.09464	−	10.4148i	−0.0455309	−	0.433197i
$579$	2.32991	+	0.495239i	0.0968279	+	0.0205814i
$580$	33.3504	−	14.8486i	1.38480	−	0.616553i
$581$	−9.92705	−	7.21242i	−0.411843	−	0.299222i
$582$	2.98776	+	1.33024i	0.123847	+	0.0551401i
$583$	−4.85410	−	8.40755i	−0.201036	−	0.348205i
$584$	−9.57295	+	16.5808i	−0.396131	+	0.686120i
$585$	20.5623	−	14.9394i	0.850147	−	0.617668i
$586$	−4.97894	+	1.05831i	−0.205678	+	0.0437182i
$587$	−11.1287	−	34.2505i	−0.459330	−	1.41367i	−0.865976	−	0.500086i	$-0.833302\pi$
$587$	−11.1287	−	34.2505i	−0.459330	−	1.41367i	0.406646	−	0.913586i	$-0.366698\pi$
$588$	−3.23607			−0.133453
$589$		0			0
$590$	15.3262			0.630971
$591$	−5.07295	−	15.6129i	−0.208673	−	0.642230i
$592$	0.428129	−	0.0910017i	0.0175960	−	0.00374015i
$593$	−4.94427	+	3.59222i	−0.203037	+	0.147515i	−0.684658	−	0.728865i	$-0.740048\pi$
$593$	−4.94427	+	3.59222i	−0.203037	+	0.147515i	0.481621	+	0.876380i	$0.340048\pi$
$594$	−1.18034	+	2.04441i	−0.0484299	+	0.0838831i
$595$	−0.927051	−	1.60570i	−0.0380054	−	0.0658273i
$596$	25.1794	+	11.2106i	1.03139	+	0.459204i
$597$	−21.6074	−	15.6987i	−0.884332	−	0.642505i
$598$	14.9971	−	6.67715i	0.613278	−	0.273049i
$599$	−29.1472	−	6.19543i	−1.19092	−	0.253138i	−0.430514	−	0.902584i	$-0.641668\pi$
$599$	−29.1472	−	6.19543i	−1.19092	−	0.253138i	−0.760408	+	0.649445i	$0.775001\pi$
$600$	−0.433364	−	4.12319i	−0.0176920	−	0.168328i
$601$	−14.7209	+	16.3492i	−0.600477	+	0.666897i	−0.964374	−	0.264542i	$-0.914779\pi$
$601$	−14.7209	+	16.3492i	−0.600477	+	0.666897i	0.363897	+	0.931439i	$0.381446\pi$
$602$	−5.72930	−	6.36303i	−0.233509	−	0.259338i
$603$	−0.885579	+	8.42572i	−0.0360636	+	0.343122i
$604$	−9.75329	+	30.0175i	−0.396856	+	1.22140i
$605$	8.42705	−	25.9358i	0.342608	−	1.05444i
$606$	0.307760	−	2.92814i	0.0125019	−	0.118948i
$607$	−17.0069	−	18.8881i	−0.690289	−	0.766643i	0.291510	−	0.956568i	$-0.405842\pi$
$607$	−17.0069	−	18.8881i	−0.690289	−	0.766643i	−0.981799	+	0.189925i	$0.939176\pi$
$608$	−18.7960	+	20.8751i	−0.762278	+	0.846596i
$609$	−2.70249	−	25.7125i	−0.109510	−	1.04192i
$610$	−10.9905	−	2.33611i	−0.444994	−	0.0945863i
$611$	14.9971	−	6.67715i	0.606719	−	0.270129i
$612$	0.618034	+	0.449028i	0.0249825	+	0.0181509i
$613$	−22.8895	−	10.1911i	−0.924500	−	0.411614i	−0.111425	−	0.993773i	$-0.535541\pi$
$613$	−22.8895	−	10.1911i	−0.924500	−	0.411614i	−0.813075	+	0.582159i	$0.802208\pi$
$614$	1.88197	+	3.25966i	0.0759500	+	0.131549i
$615$	8.47214	−	14.6742i	0.341629	−	0.591720i
$616$	−4.14590	+	3.01217i	−0.167043	+	0.121364i
$617$	13.9250	−	2.95984i	0.560598	−	0.119159i	0.0811069	−	0.996705i	$-0.474154\pi$
$617$	13.9250	−	2.95984i	0.560598	−	0.119159i	0.479491	+	0.877547i	$0.340821\pi$
$618$	0.0278640	+	0.0857567i	0.00112086	+	0.00344964i
$619$	40.0000			1.60774			0.803868	−	0.594808i	$-0.202772\pi$
$619$	40.0000			1.60774			0.803868	+	0.594808i	$0.202772\pi$
$620$		0			0
$621$	−27.3607			−1.09795
$622$	−3.14590	−	9.68208i	−0.126139	−	0.388216i
$623$	−18.7275	+	3.98066i	−0.750302	+	0.159482i
$624$	7.28115	−	5.29007i	0.291479	−	0.211772i
$625$	15.4164	−	26.7020i	0.616656	−	1.06808i
$626$	−0.381966	−	0.661585i	−0.0152664	−	0.0264422i
$627$	3.48943	+	1.55360i	0.139355	+	0.0620446i
$628$	12.7082	+	9.23305i	0.507113	+	0.368439i
$629$	0.0509101	−	0.0226667i	0.00202992	−	0.000903779i
$630$	9.49606	+	2.01845i	0.378332	+	0.0804169i
$631$	−0.912480	−	8.68167i	−0.0363253	−	0.345612i	−0.997556	−	0.0698675i	$-0.977742\pi$
$631$	−0.912480	−	8.68167i	−0.0363253	−	0.345612i	0.961231	−	0.275744i	$-0.0889243\pi$
$632$		0			0
$633$	−5.35304	−	5.94516i	−0.212764	−	0.236299i
$634$	1.67246	−	15.9124i	0.0664217	−	0.631960i
$635$	8.28115	−	25.4868i	0.328628	−	1.01141i
$636$	−6.35410	+	19.5559i	−0.251957	+	0.775442i
$637$	1.01478	−	9.65502i	0.0402072	−	0.382546i
$638$	−2.72261	−	3.02377i	−0.107789	−	0.119712i
$639$	−0.120671	+	0.134019i	−0.00477367	+	0.00530170i
$640$	3.11478	+	29.6351i	0.123122	+	1.17143i
$641$	−40.1923	−	8.54313i	−1.58750	−	0.337433i	−0.672250	−	0.740324i	$-0.734672\pi$
$641$	−40.1923	−	8.54313i	−1.58750	−	0.337433i	−0.915248	+	0.402891i	$0.868005\pi$
$642$	−0.615512	+	0.274044i	−0.0242923	+	0.0108156i
$643$	6.59017	+	4.78804i	0.259891	+	0.188822i	0.710099	−	0.704102i	$-0.248650\pi$
$643$	6.59017	+	4.78804i	0.259891	+	0.188822i	−0.450208	+	0.892924i	$0.648650\pi$
$644$	−24.2659	−	10.8039i	−0.956209	−	0.425732i
$645$	6.04508	+	10.4704i	0.238025	+	0.412271i
$646$	−0.364745	+	0.631757i	−0.0143507	+	0.0248561i
$647$	−24.1803	+	17.5680i	−0.950627	+	0.690671i	−0.950955	−	0.309329i	$-0.899896\pi$
$647$	−24.1803	+	17.5680i	−0.950627	+	0.690671i	0.000327889		1.00000i	$0.499896\pi$
$648$	−2.18720	+	0.464905i	−0.0859215	+	0.0182632i
$649$	2.23607	+	6.88191i	0.0877733	+	0.270139i
$650$	5.56231			0.218172
$651$		0			0
$652$	20.5623			0.805282
$653$	12.2533	+	37.7117i	0.479508	+	1.47577i	0.839780	+	0.542927i	$0.182684\pi$
$653$	12.2533	+	37.7117i	0.479508	+	1.47577i	−0.360272	+	0.932847i	$0.617316\pi$
$654$	−5.08796	+	1.08148i	−0.198955	+	0.0422892i
$655$	0.190983	−	0.138757i	0.00746232	−	0.00542170i
$656$	−6.00000	+	10.3923i	−0.234261	+	0.405751i
$657$	8.56231	+	14.8303i	0.334047	+	0.578587i
$658$	5.72840	+	2.55045i	0.223316	+	0.0994267i
$659$	−18.3541	−	13.3350i	−0.714974	−	0.519459i	0.169800	−	0.985478i	$-0.445688\pi$
$659$	−18.3541	−	13.3350i	−0.714974	−	0.519459i	−0.884775	+	0.466019i	$0.845688\pi$
$660$	2.95630	−	1.31623i	0.115074	−	0.0512341i
$661$	16.2549	+	3.45508i	0.632242	+	0.134387i	0.512875	−	0.858463i	$-0.328580\pi$
$661$	16.2549	+	3.45508i	0.632242	+	0.134387i	0.119367	+	0.992850i	$0.461914\pi$
$662$	−0.728099	−	6.92740i	−0.0282984	−	0.269241i
$663$	0.766755	−	0.851568i	0.0297783	−	0.0330722i
$664$	6.11980	+	6.79673i	0.237494	+	0.263764i
$665$	4.10489	−	39.0554i	0.159181	−	1.51450i
$666$	−0.0901699	+	0.277515i	−0.00349401	+	0.0107535i
$667$	14.5729	−	44.8509i	0.564267	−	1.73663i
$668$	1.56210	−	14.8624i	0.0604395	−	0.575044i
$669$	−0.473881	−	0.526298i	−0.0183213	−	0.0203479i
$670$	−4.58629	+	5.09359i	−0.177184	+	0.196783i
$671$	−0.554518	−	5.27589i	−0.0214069	−	0.203673i
$672$	16.4858	+	3.50416i	0.635954	+	0.135176i
$673$	4.03459	−	1.79631i	0.155522	−	0.0692429i	−0.327499	−	0.944851i	$-0.606206\pi$
$673$	4.03459	−	1.79631i	0.155522	−	0.0692429i	0.483021	+	0.875609i	$0.339539\pi$
$674$	−9.48936	−	6.89442i	−0.365516	−	0.265563i
$675$	−8.46903	−	3.77066i	−0.325973	−	0.145133i
$676$	8.54508	+	14.8005i	0.328657	+	0.569251i
$677$	14.3262	−	24.8138i	0.550602	−	0.953671i	−0.447629	−	0.894219i	$-0.647732\pi$
$677$	14.3262	−	24.8138i	0.550602	−	0.953671i	0.998231	−	0.0594514i	$-0.0189351\pi$
$678$	−0.927051	+	0.673542i	−0.0356032	+	0.0258672i
$679$	15.5285	−	3.30068i	0.595928	−	0.126668i
$680$	0.427051	+	1.31433i	0.0163767	+	0.0504022i
$681$	−20.7426			−0.794860
$682$		0			0
$683$	10.0557			0.384772			0.192386	−	0.981319i	$-0.438377\pi$
$683$	10.0557			0.384772			0.192386	+	0.981319i	$0.438377\pi$
$684$	5.00000	+	15.3884i	0.191180	+	0.588391i
$685$	16.5740	−	3.52291i	0.633260	−	0.134604i
$686$	−7.50000	+	5.44907i	−0.286351	+	0.208046i
$687$	−3.61803	+	6.26662i	−0.138037	+	0.239086i
$688$	−4.28115	−	7.41517i	−0.163217	−	0.282701i
$689$	−56.3538	−	25.0903i	−2.14691	−	0.955865i
$690$	−7.16312	−	5.20431i	−0.272695	−	0.198125i
$691$	3.50145	−	1.55895i	0.133201	−	0.0593051i	−0.339054	−	0.940767i	$-0.610107\pi$
$691$	3.50145	−	1.55895i	0.133201	−	0.0593051i	0.472255	+	0.881462i	$0.343440\pi$
$692$	1.43997	+	0.306074i	0.0547393	+	0.0116352i
$693$	0.479116	+	4.55848i	0.0182001	+	0.173162i
$694$	3.35990	−	3.73154i	0.127540	−	0.141647i
$695$	10.2553	+	11.3896i	0.389004	+	0.432033i
$696$	−2.01432	+	19.1649i	−0.0763525	+	0.726445i
$697$	−0.472136	+	1.45309i	−0.0178834	+	0.0550395i
$698$	3.19098	−	9.82084i	0.120780	−	0.371724i
$699$	−1.96497	+	18.6954i	−0.0743218	+	0.707125i
$700$	−6.02218	−	6.68830i	−0.227617	−	0.252794i
$701$	−20.0970	+	22.3199i	−0.759052	+	0.843013i	−0.991569	−	0.129580i	$-0.958637\pi$
$701$	−20.0970	+	22.3199i	−0.759052	+	0.843013i	0.232517	+	0.972592i	$0.425304\pi$
$702$	1.56793	+	14.9178i	0.0591776	+	0.563037i
$703$	1.15455	+	0.245406i	0.0435446	+	0.00925568i
$704$	−0.164749	+	0.0733508i	−0.00620920	+	0.00276451i
$705$	−7.16312	−	5.20431i	−0.269779	−	0.196006i
$706$	−18.2829	−	8.14008i	−0.688087	−	0.306356i
$707$	−7.14590	−	12.3771i	−0.268749	−	0.465487i
$708$	7.66312	−	13.2729i	0.287998	−	0.498827i
$709$	3.35410	−	2.43690i	0.125966	−	0.0915196i	−0.523018	−	0.852321i	$-0.675194\pi$
$709$	3.35410	−	2.43690i	0.125966	−	0.0915196i	0.648984	+	0.760802i	$0.275194\pi$
$710$	−0.142710	+	0.0303339i	−0.00535580	+	0.00113841i
$711$		0			0
$712$	14.2705			0.534810
$713$		0			0
$714$	0.437694			0.0163803
$715$	3.00000	+	9.23305i	0.112194	+	0.345297i
$716$	−31.3344	+	6.66033i	−1.17102	+	0.248908i
$717$	−10.8541	+	7.88597i	−0.405354	+	0.294507i
$718$	−7.82624	+	13.5554i	−0.292073	+	0.505885i
$719$	−20.6910	−	35.8378i	−0.771643	−	1.33653i	−0.936662	−	0.350235i	$-0.886102\pi$
$719$	−20.6910	−	35.8378i	−0.771643	−	1.33653i	0.165018	−	0.986290i	$-0.447232\pi$
$720$	8.86889	+	3.94868i	0.330524	+	0.147159i
$721$	0.354102	+	0.257270i	0.0131874	+	0.00958124i
$722$	−3.38761	+	1.50826i	−0.126074	+	0.0561317i
$723$	−8.34151	−	1.77304i	−0.310224	−	0.0659402i
$724$	−2.87522	−	27.3559i	−0.106857	−	1.01667i
$725$	10.6918	−	11.8745i	0.397085	−	0.441008i
$726$	4.30766	+	4.78414i	0.159872	+	0.177556i
$727$	2.49121	−	23.7023i	0.0923938	−	0.879068i	−0.845926	−	0.533300i	$-0.820952\pi$
$727$	2.49121	−	23.7023i	0.0923938	−	0.879068i	0.938320	−	0.345768i	$-0.112382\pi$
$728$	−10.0623	+	30.9686i	−0.372934	+	1.14777i
$729$	4.01722	−	12.3637i	0.148786	−	0.457916i
$730$	−1.44815	+	13.7782i	−0.0535984	+	0.509954i
$731$	−0.729466	−	0.810154i	−0.0269803	−	0.0299646i
$732$	−7.51840	+	8.35003i	−0.277888	+	0.308626i
$733$	−2.92097	−	27.7912i	−0.107889	−	1.02649i	−0.905797	−	0.423712i	$-0.860727\pi$
$733$	−2.92097	−	27.7912i	−0.107889	−	1.02649i	0.797908	−	0.602779i	$-0.205940\pi$
$734$	21.9266	+	4.66063i	0.809324	+	0.172027i
$735$	−4.78339	+	2.12970i	−0.176438	+	0.0785552i
$736$	24.8713	+	18.0701i	0.916769	+	0.666072i
$737$	−2.95630	−	1.31623i	−0.108897	−	0.0484839i
$738$	−4.00000	−	6.92820i	−0.147242	−	0.255031i
$739$	10.8541	−	18.7999i	0.399275	−	0.691564i	−0.594362	−	0.804198i	$-0.702595\pi$
$739$	10.8541	−	18.7999i	0.399275	−	0.691564i	0.993637	+	0.112634i	$0.0359287\pi$
$740$	0.809017	−	0.587785i	0.0297401	−	0.0216074i
$741$	23.7401	−	5.04612i	0.872116	−	0.185374i
$742$	−7.28115	−	22.4091i	−0.267300	−	0.822663i
$743$	3.43769			0.126117			0.0630584	−	0.998010i	$-0.479915\pi$
$743$	3.43769			0.126117			0.0630584	+	0.998010i	$0.479915\pi$
$744$		0			0
$745$	44.5967			1.63390
$746$	0.0663712	+	0.204270i	0.00243002	+	0.00747884i
$747$	8.00158	−	1.70079i	0.292762	−	0.0622286i
$748$	−0.236068	+	0.171513i	−0.00863150	+	0.00627115i
$749$	−1.63525	+	2.83234i	−0.0597509	+	0.103492i
$750$	2.54508	+	4.40822i	0.0929334	+	0.160965i
$751$	−36.3891	−	16.2015i	−1.32786	−	0.591200i	−0.384544	−	0.923106i	$-0.625641\pi$
$751$	−36.3891	−	16.2015i	−1.32786	−	0.591200i	−0.943312	+	0.331907i	$0.892308\pi$
$752$	5.07295	+	3.68571i	0.184991	+	0.134404i
$753$	−0.862635	+	0.384070i	−0.0314362	+	0.0139963i
$754$	−25.2891	−	5.37537i	−0.920976	−	0.195759i
$755$	5.33815	+	50.7891i	0.194275	+	1.84841i
$756$	16.2401	−	18.0365i	0.590648	−	0.655981i
$757$	−28.8560	−	32.0478i	−1.04879	−	1.16480i	−0.985996	−	0.166772i	$-0.946666\pi$
$757$	−28.8560	−	32.0478i	−1.04879	−	1.16480i	−0.0627935	−	0.998027i	$-0.520001\pi$
$758$	−1.18974	+	11.3196i	−0.0432133	+	0.411147i
$759$	1.29180	−	3.97574i	0.0468892	−	0.144310i
$760$	−9.04508	+	27.8379i	−0.328100	+	1.00979i
$761$	0.366537	−	3.48737i	0.0132870	−	0.126417i	−0.985868	−	0.167526i	$-0.946422\pi$
$761$	0.366537	−	3.48737i	0.0132870	−	0.126417i	0.999155	+	0.0411086i	$0.0130890\pi$
$762$	4.23308	+	4.70131i	0.153348	+	0.170311i
$763$	−16.8950	+	18.7638i	−0.611641	+	0.679296i
$764$	−2.72134	−	25.8918i	−0.0984546	−	0.936733i
$765$	1.20906	+	0.256993i	0.0437135	+	0.00929160i
$766$	−9.51586	+	4.23673i	−0.343822	+	0.153079i
$767$	37.1976	+	27.0256i	1.34313	+	0.975838i
$768$	−5.99496	−	2.66913i	−0.216325	−	0.0963139i
$769$	26.8713	+	46.5425i	0.969005	+	1.67837i	0.698447	+	0.715662i	$0.253875\pi$
$769$	26.8713	+	46.5425i	0.969005	+	1.67837i	0.270557	+	0.962704i	$0.412792\pi$
$770$	−1.85410	+	3.21140i	−0.0668172	+	0.115731i
$771$	−1.14590	+	0.832544i	−0.0412685	+	0.0299833i
$772$	−3.76988	+	0.801313i	−0.135681	+	0.0288399i
$773$	5.89919	+	18.1558i	0.212179	+	0.653020i	0.999342	+	0.0362746i	$0.0115491\pi$
$773$	5.89919	+	18.1558i	0.212179	+	0.653020i	−0.787163	+	0.616745i	$0.788451\pi$
$774$	5.70820			0.205177
$775$		0			0
$776$	−11.8328			−0.424773
$777$	−0.218847	−	0.673542i	−0.00785109	−	0.0241632i
$778$	17.5730	−	3.73525i	0.630021	−	0.133915i
$779$	−26.1803	+	19.0211i	−0.938008	+	0.681503i
$780$	10.2812	−	17.8075i	0.368124	−	0.637610i
$781$	−0.0344419	−	0.0596550i	−0.00123243	−	0.00213463i
$782$	0.729351	+	0.324728i	0.0260815	+	0.0116122i
$783$	34.8607	+	25.3278i	1.24582	+	0.905141i
$784$	3.38761	−	1.50826i	0.120986	−	0.0538665i
$785$	24.8610	+	5.28437i	0.887327	+	0.188607i
$786$	0.00582517	+	0.0554228i	0.000207777	+	0.00197687i
$787$	−20.9383	+	23.2543i	−0.746370	+	0.828928i	−0.990019	−	0.140936i	$-0.954989\pi$
$787$	−20.9383	+	23.2543i	−0.746370	+	0.828928i	0.243649	+	0.969863i	$0.421656\pi$
$788$	17.7737	+	19.7396i	0.633160	+	0.703196i
$789$	−1.12874	+	10.7392i	−0.0401841	+	0.382326i
$790$		0			0
$791$	−1.71885	+	5.29007i	−0.0611152	+	0.188093i
$792$	0.357112	−	3.39769i	0.0126894	−	0.120732i
$793$	−22.5552	−	25.0501i	−0.800958	−	0.889554i
$794$	−6.73740	+	7.48264i	−0.239101	+	0.265549i
$795$	3.47772	+	33.0883i	0.123342	+	1.17352i
$796$	42.2704	+	8.98486i	1.49824	+	0.318460i
$797$	−8.27282	+	3.68330i	−0.293038	+	0.130469i	−0.547990	−	0.836485i	$-0.684607\pi$
$797$	−8.27282	+	3.68330i	−0.293038	+	0.130469i	0.254952	+	0.966954i	$0.417940\pi$
$798$	7.50000	+	5.44907i	0.265497	+	0.192895i
$799$	0.729351	+	0.324728i	0.0258026	+	0.0114880i
$800$	5.20820	+	9.02087i	0.184138	+	0.318936i
$801$	6.38197	−	11.0539i	0.225496	−	0.390570i
$802$	14.9164	−	10.8374i	0.526717	−	0.382682i
$803$	−6.39808	+	1.35995i	−0.225783	+	0.0479918i
$804$	2.11803	+	6.51864i	0.0746973	+	0.229895i
$805$	−42.9787			−1.51480
$806$		0			0
$807$	1.38197			0.0486475
$808$	3.29180	+	10.1311i	0.115805	+	0.356411i
$809$	53.6009	−	11.3932i	1.88451	−	0.400564i	0.886448	−	0.462829i	$-0.153166\pi$
$809$	53.6009	−	11.3932i	1.88451	−	0.400564i	0.998060	+	0.0622647i	$0.0198323\pi$
$810$	−1.30902	+	0.951057i	−0.0459942	+	0.0334167i
$811$	−21.3885	+	37.0460i	−0.751053	+	1.30086i	0.196259	+	0.980552i	$0.437121\pi$
$811$	−21.3885	+	37.0460i	−0.751053	+	1.30086i	−0.947313	+	0.320311i	$0.896213\pi$
$812$	20.9164	+	36.2283i	0.734022	+	1.27136i
$813$	−8.73560	−	3.88934i	−0.306371	−	0.136405i
$814$	−0.0901699	−	0.0655123i	−0.00316045	−	0.00229620i
$815$	30.3941	−	13.5323i	1.06466	−	0.474017i
$816$	0.428129	+	0.0910017i	0.0149875	+	0.00318570i
$817$	−2.41358	−	22.9637i	−0.0844405	−	0.803397i
$818$	−2.55585	+	2.83856i	−0.0893633	+	0.0992479i
$819$	19.4882	+	21.6438i	0.680972	+	0.756296i
$820$	−2.86579	+	27.2662i	−0.100078	+	0.952178i
$821$	10.0344	−	30.8828i	0.350204	−	1.07782i	−0.608534	−	0.793528i	$-0.708242\pi$
$821$	10.0344	−	30.8828i	0.350204	−	1.07782i	0.958738	−	0.284290i	$-0.0917580\pi$
$822$	−1.23607	+	3.80423i	−0.0431128	+	0.132688i
$823$	−0.640196	+	6.09106i	−0.0223158	+	0.212321i	0.977682	+	0.210092i	$0.0673763\pi$
$823$	−0.640196	+	6.09106i	−0.0223158	+	0.212321i	−0.999998	+	0.00222928i	$0.999290\pi$
$824$	−0.218296	−	0.242442i	−0.00760469	−	0.00844587i
$825$	0.947762	−	1.05260i	0.0329968	−	0.0366467i
$826$	1.83576	+	17.4661i	0.0638743	+	0.607723i
$827$	2.61533	+	0.555906i	0.0909441	+	0.0193308i	0.253159	−	0.967425i	$-0.418530\pi$
$827$	2.61533	+	0.555906i	0.0909441	+	0.0193308i	−0.162215	+	0.986755i	$0.551864\pi$
$828$	16.1772	−	7.20258i	0.562198	−	0.250307i
$829$	−17.5623	−	12.7598i	−0.609964	−	0.443165i	0.239438	−	0.970912i	$-0.423037\pi$
$829$	−17.5623	−	12.7598i	−0.609964	−	0.443165i	−0.849402	+	0.527747i	$0.823037\pi$
$830$	6.04587	+	2.69180i	0.209855	+	0.0934336i
$831$	6.66312	+	11.5409i	0.231141	+	0.400348i
$832$	−0.572949	+	0.992377i	−0.0198634	+	0.0344045i
$833$	0.381966	−	0.277515i	0.0132343	−	0.00961531i
$834$	−3.53897	+	0.752232i	−0.122545	+	0.0260476i
$835$	−7.47214	−	22.9969i	−0.258584	−	0.795839i
$836$	−6.18034			−0.213752
$837$		0			0
$838$	−2.76393			−0.0954784
$839$	3.45492	+	10.6331i	0.119277	+	0.367097i	0.992815	−	0.119659i	$-0.0381802\pi$
$839$	3.45492	+	10.6331i	0.119277	+	0.367097i	−0.873538	+	0.486756i	$0.838180\pi$
$840$	17.1785	−	3.65141i	0.592716	−	0.125986i
$841$	−36.6246	+	26.6093i	−1.26292	+	0.917563i
$842$	4.56231	−	7.90215i	0.157227	−	0.272326i
$843$	−9.51722	−	16.4843i	−0.327791	−	0.567750i
$844$	11.8252	+	5.26491i	0.407040	+	0.181226i
$845$	22.3713	+	16.2537i	0.769597	+	0.559145i
$846$	−3.81893	+	1.70030i	−0.131298	+	0.0584574i
$847$	30.5664	+	6.49708i	1.05027	+	0.223242i
$848$	−2.46293	−	23.4332i	−0.0845774	−	0.804700i
$849$	4.39104	−	4.87674i	0.150700	−	0.167369i
$850$	0.181006	+	0.201028i	0.00620847	+	0.00689520i
$851$	0.135029	−	1.28472i	0.00462875	−	0.0440396i
$852$	−0.0450850	+	0.138757i	−0.00154459	+	0.00475375i
$853$	1.23607	−	3.80423i	0.0423222	−	0.130254i	−0.927663	−	0.373419i	$-0.878185\pi$
$853$	1.23607	−	3.80423i	0.0423222	−	0.130254i	0.969985	+	0.243164i	$0.0781855\pi$
$854$	1.34584	−	12.8049i	0.0460539	−	0.438173i
$855$	17.5181	+	19.4558i	0.599105	+	0.665374i
$856$	1.63114	−	1.81156i	0.0557511	−	0.0619178i
$857$	0.855078	+	8.13553i	0.0292089	+	0.277904i	0.999371	+	0.0354490i	$0.0112861\pi$
$857$	0.855078	+	8.13553i	0.0292089	+	0.277904i	−0.970163	+	0.242455i	$0.922047\pi$
$858$	−2.24171	−	0.476491i	−0.0765309	−	0.0162671i
$859$	−39.5490	+	17.6084i	−1.34940	+	0.600789i	−0.948920	−	0.315518i	$-0.897822\pi$
$859$	−39.5490	+	17.6084i	−1.34940	+	0.600789i	−0.400476	+	0.916307i	$0.631155\pi$
$860$	−15.8262	−	11.4984i	−0.539670	−	0.392093i
$861$	17.7378	+	7.89736i	0.604502	+	0.269141i
$862$	9.03444	+	15.6481i	0.307714	+	0.532977i
$863$	1.24671	−	2.15937i	0.0424385	−	0.0735057i	−0.844026	−	0.536302i	$-0.819821\pi$
$863$	1.24671	−	2.15937i	0.0424385	−	0.0735057i	0.886464	+	0.462797i	$0.153154\pi$
$864$	−22.7254	+	16.5110i	−0.773135	+	0.561715i
$865$	2.32991	−	0.495239i	0.0792195	−	0.0168386i
$866$	0.111456	+	0.343027i	0.00378744	+	0.0116565i
$867$	−16.9443			−0.575458
$868$		0			0
$869$		0			0
$870$	4.30902	+	13.2618i	0.146089	+	0.449617i
$871$	−20.1130	+	4.27514i	−0.681502	+	0.144858i
$872$	15.2254	−	11.0619i	0.515598	−	0.374604i
$873$	−5.29180	+	9.16566i	−0.179100	+	0.310211i
$874$	8.45492	+	14.6443i	0.285992	+	0.495352i
$875$	22.5721	+	10.0497i	0.763075	+	0.339743i
$876$	11.2082	+	8.14324i	0.378690	+	0.275134i
$877$	14.8833	−	6.62647i	0.502573	−	0.223760i	−0.139760	−	0.990185i	$-0.544633\pi$
$877$	14.8833	−	6.62647i	0.502573	−	0.223760i	0.642333	+	0.766425i	$0.277966\pi$
$878$	25.2891	+	5.37537i	0.853467	+	0.181410i
$879$	0.860904	+	8.19095i	0.0290376	+	0.276274i
$880$	−2.48127	+	2.75573i	−0.0836437	+	0.0928957i
$881$	10.2783	+	11.4152i	0.346285	+	0.384588i	0.890977	−	0.454048i	$-0.150020\pi$
$881$	10.2783	+	11.4152i	0.346285	+	0.384588i	−0.544693	+	0.838636i	$0.683354\pi$
$882$	−0.258409	+	2.45859i	−0.00870107	+	0.0827851i
$883$	0.309017	−	0.951057i	0.0103992	−	0.0320056i	−0.945722	−	0.324976i	$-0.894644\pi$
$883$	0.309017	−	0.951057i	0.0103992	−	0.0320056i	0.956121	+	0.292970i	$0.0946438\pi$
$884$	−0.572949	+	1.76336i	−0.0192704	+	0.0593081i
$885$	2.59214	−	24.6625i	0.0871337	−	0.829022i
$886$	17.0069	+	18.8881i	0.571358	+	0.634557i
$887$	26.1652	−	29.0594i	0.878543	−	0.975720i	−0.121315	−	0.992614i	$-0.538711\pi$
$887$	26.1652	−	29.0594i	0.878543	−	0.975720i	0.999857	+	0.0168938i	$0.00537771\pi$
$888$	0.0551768	+	0.524972i	0.00185161	+	0.0176169i
$889$	30.0372	+	6.38459i	1.00741	+	0.214132i
$890$	9.43349	−	4.20006i	0.316211	−	0.140786i
$891$	−0.618034	−	0.449028i	−0.0207049	−	0.0150430i
$892$	1.04683	+	0.466079i	0.0350505	+	0.0156055i
$893$	8.45492	+	14.6443i	0.282933	+	0.490054i
$894$	−5.26393	+	9.11740i	−0.176052	+	0.304931i
$895$	−41.9336	+	30.4666i	−1.40169	+	1.01838i
$896$	−33.3997	+	7.09933i	−1.11581	+	0.237172i
$897$	−8.20820	−	25.2623i	−0.274064	−	0.843482i
$898$	14.8754			0.496398
$899$		0			0
$900$	6.00000			0.200000
$901$	−0.927051	−	2.85317i	−0.0308845	−	0.0950529i
$902$	2.98895	−	0.635322i	0.0995213	−	0.0211539i
$903$	−11.2082	+	8.14324i	−0.372986	+	0.270990i
$904$	2.07295	−	3.59045i	0.0689453	−	0.119417i
$905$	−22.2533	−	38.5438i	−0.739724	−	1.28124i
$906$	−11.0135	−	4.90351i	−0.365898	−	0.162908i
$907$	−42.8156	−	31.1074i	−1.42167	−	1.03290i	−0.991493	−	0.130157i	$-0.958452\pi$
$907$	−42.8156	−	31.1074i	−1.42167	−	1.03290i	−0.430175	−	0.902745i	$-0.641548\pi$
$908$	30.6607	−	13.6510i	1.01751	−	0.453025i
$909$	9.31966	+	1.98095i	0.309114	+	0.0657041i
$910$	2.46293	+	23.4332i	0.0816454	+	0.776804i
$911$	−5.47372	+	6.07918i	−0.181352	+	0.201412i	−0.826966	−	0.562252i	$-0.809935\pi$
$911$	−5.47372	+	6.07918i	−0.181352	+	0.201412i	0.645614	+	0.763664i	$0.276602\pi$
$912$	6.20318	+	6.88933i	0.205408	+	0.228129i
$913$	−0.326611	+	3.10749i	−0.0108092	+	0.102843i
$914$	−3.00658	+	9.25330i	−0.0994488	+	0.306072i
$915$	−5.61803	+	17.2905i	−0.185726	+	0.571607i
$916$	1.22384	−	11.6441i	0.0404368	−	0.384731i
$917$	0.181006	+	0.201028i	0.00597736	+	0.00663853i
$918$	−0.488124	+	0.542117i	−0.0161105	+	0.0178925i
$919$	−1.03226	−	9.82129i	−0.0340511	−	0.323974i	−0.998267	−	0.0588546i	$-0.981255\pi$
$919$	−1.03226	−	9.82129i	−0.0340511	−	0.323974i	0.964215	−	0.265120i	$-0.0854115\pi$
$920$	31.3344	+	6.66033i	1.03306	+	0.219585i
$921$	5.56365	−	2.47710i	0.183328	−	0.0816231i
$922$	−5.37132	−	3.90249i	−0.176895	−	0.128522i
$923$	−0.399853	−	0.178026i	−0.0131613	−	0.00585980i
$924$	1.85410	+	3.21140i	0.0609955	+	0.105647i
$925$	0.218847	−	0.379054i	0.00719565	−	0.0124632i
$926$	15.5623	−	11.3067i	0.511409	−	0.371560i
$927$	−0.285420	+	0.0606678i	−0.00937441	+	0.00199259i
$928$	−14.9615	−	46.0467i	−0.491135	−	1.51156i
$929$	−33.5410			−1.10045			−0.550223	−	0.835018i	$-0.685457\pi$
$929$	−33.5410			−1.10045			−0.550223	+	0.835018i	$0.685457\pi$
$930$		0			0
$931$	10.0000			0.327737
$932$	−9.39919	−	28.9277i	−0.307881	−	0.947559i
$933$	−16.1122	+	3.42475i	−0.527489	+	0.112121i
$934$	−16.3885	+	11.9070i	−0.536250	+	0.389608i
$935$	−0.236068	+	0.408882i	−0.00772025	+	0.0133719i
$936$	−10.8541	−	18.7999i	−0.354777	−	0.614493i
$937$	36.9852	+	16.4669i	1.20825	+	0.537949i	0.909229	−	0.416297i	$-0.136672\pi$
$937$	36.9852	+	16.4669i	1.20825	+	0.537949i	0.299024	+	0.954246i	$0.403339\pi$
$938$	−6.35410	−	4.61653i	−0.207469	−	0.150735i
$939$	−1.12920	+	0.502754i	−0.0368502	+	0.0164068i
$940$	14.0132	+	2.97859i	0.457059	+	0.0971510i
$941$	2.98780	+	28.4270i	0.0973995	+	0.926694i	0.928690	+	0.370856i	$0.120936\pi$
$941$	2.98780	+	28.4270i	0.0973995	+	0.926694i	−0.831291	+	0.555838i	$0.812398\pi$
$942$	−4.01478	+	4.45887i	−0.130809	+	0.145278i
$943$	23.6982	+	26.3195i	0.771720	+	0.857082i
$944$	−1.83576	+	17.4661i	−0.0597489	+	0.568473i
$945$	12.1353	−	37.3485i	0.394760	−	1.21495i
$946$	−0.673762	+	2.07363i	−0.0219059	+	0.0674194i
$947$	2.30683	−	21.9480i	0.0749618	−	0.713214i	−0.890908	−	0.454184i	$-0.849931\pi$
$947$	2.30683	−	21.9480i	0.0749618	−	0.713214i	0.965869	−	0.259029i	$-0.0834026\pi$
$948$		0			0
$949$	−27.8106	+	30.8868i	−0.902771	+	1.00263i
$950$	0.598895	+	5.69810i	0.0194307	+	0.184871i
$951$	−25.3228	−	5.38253i	−0.821149	−	0.174541i
$952$	−1.44668	+	0.644105i	−0.0468873	+	0.0208756i
$953$	34.1525	+	24.8132i	1.10631	+	0.803779i	0.982078	−	0.188474i	$-0.0603542\pi$
$953$	34.1525	+	24.8132i	1.10631	+	0.803779i	0.124229	+	0.992254i	$0.460354\pi$
$954$	14.3502	+	6.38910i	0.464604	+	0.206855i
$955$	−21.0623	−	36.4810i	−0.681560	−	1.18050i
$956$	10.8541	−	18.7999i	0.351047	−	0.608031i
$957$	−5.32624	+	3.86974i	−0.172173	+	0.125091i
$958$	−5.40707	+	1.14931i	−0.174694	+	0.0371324i
$959$	6.00000	+	18.4661i	0.193750	+	0.596302i
$960$	0.618034			0.0199470
$961$		0			0
$962$	−0.708204			−0.0228334
$963$	−0.673762	−	2.07363i	−0.0217117	−	0.0668217i
$964$	13.4968	−	2.86884i	0.434704	−	0.0923992i
$965$	−5.04508	+	3.66547i	−0.162407	+	0.117996i
$966$	5.07295	−	8.78661i	0.163219	−	0.282704i
$967$	21.8262	+	37.8042i	0.701884	+	1.21570i	0.967804	+	0.251704i	$0.0809911\pi$
$967$	21.8262	+	37.8042i	0.701884	+	1.21570i	−0.265920	+	0.963995i	$0.585676\pi$
$968$	−21.2781	−	9.47363i	−0.683905	−	0.304494i
$969$	0.954915	+	0.693786i	0.0306763	+	0.0222876i
$970$	−7.82206	+	3.48260i	−0.251151	+	0.111820i
$971$	20.1130	+	4.27514i	0.645456	+	0.137196i	0.518997	−	0.854776i	$-0.326306\pi$
$971$	20.1130	+	4.27514i	0.645456	+	0.137196i	0.126459	+	0.991972i	$0.459639\pi$
$972$	2.70609	+	25.7467i	0.0867979	+	0.825827i
$973$	−11.7515	+	13.0513i	−0.376735	+	0.418407i
$974$	9.47970	+	10.5283i	0.303749	+	0.337348i
$975$	0.940756	−	8.95070i	0.0301283	−	0.286652i
$976$	3.97871	−	12.2452i	0.127356	−	0.391960i
$977$	−1.87539	+	5.77185i	−0.0599990	+	0.184658i	−0.976564	−	0.215228i	$-0.930950\pi$
$977$	−1.87539	+	5.77185i	−0.0599990	+	0.184658i	0.916565	+	0.399886i	$0.130950\pi$
$978$	−0.820977	+	7.81108i	−0.0262520	+	0.249771i
$979$	3.26227	+	3.62312i	0.104263	+	0.115795i
$980$	5.66897	−	6.29602i	0.181088	−	0.201119i
$981$	−1.75951	−	16.7406i	−0.0561768	−	0.534486i
$982$	16.6830	+	3.54609i	0.532377	+	0.113160i
$983$	−19.2159	+	8.55548i	−0.612893	+	0.272877i	−0.689616	−	0.724175i	$-0.742221\pi$
$983$	−19.2159	+	8.55548i	−0.612893	+	0.272877i	0.0767236	+	0.997052i	$0.475554\pi$
$984$	−11.7082	−	8.50651i	−0.373244	−	0.271178i
$985$	39.2630	+	17.4810i	1.25102	+	0.556992i
$986$	−0.628677	−	1.08890i	−0.0200212	−	0.0346777i
$987$	5.07295	−	8.78661i	0.161474	−	0.279681i
$988$	−31.7705	+	23.0826i	−1.01075	+	0.734356i
$989$	−24.7183	+	5.25403i	−0.785996	+	0.167069i
$990$	−0.763932	−	2.35114i	−0.0242794	−	0.0747242i
$991$	17.2705			0.548616			0.274308	−	0.961642i	$-0.411551\pi$
$991$	17.2705			0.548616			0.274308	+	0.961642i	$0.411551\pi$
$992$		0			0
$993$	−11.2705			−0.357659
$994$	−0.0516628	−	0.159002i	−0.00163864	−	0.00504323i
$995$	68.3950	−	14.5378i	2.16827	−	0.460879i
$996$	5.35410	−	3.88998i	0.169651	−	0.123259i
$997$	13.6246	−	23.5985i	0.431496	−	0.747373i	−0.565507	−	0.824744i	$-0.691319\pi$
$997$	13.6246	−	23.5985i	0.431496	−	0.747373i	0.997002	+	0.0773712i	$0.0246526\pi$
$998$	−1.28115	−	2.21902i	−0.0405542	−	0.0702419i
$999$	1.07829	+	0.480087i	0.0341157	+	0.0151893i

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

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	961.2.g.c.844.1		8
31.2	even	5		961.2.g.g.338.1		8
31.3	odd	30		961.2.a.d.1.1		2
31.4	even	5		961.2.g.g.732.1		8
31.5	even	3	inner	961.2.g.c.547.1		8
31.6	odd	6		31.2.d.a.4.1	✓	4
31.7	even	15		961.2.d.e.374.1		4
31.8	even	5	inner	961.2.g.c.448.1		8
31.9	even	15	inner	961.2.g.c.846.1		8
31.10	even	15		961.2.g.g.235.1		8
31.11	odd	30		961.2.g.f.816.1		8
31.12	odd	30		961.2.d.f.388.1		4
31.13	odd	30		961.2.c.f.439.1		4
31.14	even	15		961.2.d.b.628.1		4
31.15	odd	10		961.2.c.f.521.1		4
31.16	even	5		961.2.c.d.521.1		4
31.17	odd	30		31.2.d.a.8.1	yes	4
31.18	even	15		961.2.c.d.439.1		4
31.19	even	15		961.2.d.e.388.1		4
31.20	even	15		961.2.g.g.816.1		8
31.21	odd	30		961.2.g.f.235.1		8
31.22	odd	30		961.2.g.b.846.1		8
31.23	odd	10		961.2.g.b.448.1		8
31.24	odd	30		961.2.d.f.374.1		4
31.25	even	3		961.2.d.b.531.1		4
31.26	odd	6		961.2.g.b.547.1		8
31.27	odd	10		961.2.g.f.732.1		8
31.28	even	15		961.2.a.e.1.1		2
31.29	odd	10		961.2.g.f.338.1		8
31.30	odd	2		961.2.g.b.844.1		8
93.17	even	30		279.2.i.a.163.1		4
93.59	odd	30		8649.2.a.f.1.2		2
93.65	even	30		8649.2.a.g.1.2		2
93.68	even	6		279.2.i.a.190.1		4
124.79	even	30		496.2.n.b.225.1		4
124.99	even	6		496.2.n.b.97.1		4
155.17	even	60		775.2.bf.a.349.1		8
155.37	even	12		775.2.bf.a.624.2		8
155.48	even	60		775.2.bf.a.349.2		8
155.68	even	12		775.2.bf.a.624.1		8
155.79	odd	30		775.2.k.c.101.1		4
155.99	odd	6		775.2.k.c.376.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
31.2.d.a.4.1	✓	4	31.6	odd	6
31.2.d.a.8.1	yes	4	31.17	odd	30
279.2.i.a.163.1		4	93.17	even	30
279.2.i.a.190.1		4	93.68	even	6
496.2.n.b.97.1		4	124.99	even	6
496.2.n.b.225.1		4	124.79	even	30
775.2.k.c.101.1		4	155.79	odd	30
775.2.k.c.376.1		4	155.99	odd	6
775.2.bf.a.349.1		8	155.17	even	60
775.2.bf.a.349.2		8	155.48	even	60
775.2.bf.a.624.1		8	155.68	even	12
775.2.bf.a.624.2		8	155.37	even	12
961.2.a.d.1.1		2	31.3	odd	30
961.2.a.e.1.1		2	31.28	even	15
961.2.c.d.439.1		4	31.18	even	15
961.2.c.d.521.1		4	31.16	even	5
961.2.c.f.439.1		4	31.13	odd	30
961.2.c.f.521.1		4	31.15	odd	10
961.2.d.b.531.1		4	31.25	even	3
961.2.d.b.628.1		4	31.14	even	15
961.2.d.e.374.1		4	31.7	even	15
961.2.d.e.388.1		4	31.19	even	15
961.2.d.f.374.1		4	31.24	odd	30
961.2.d.f.388.1		4	31.12	odd	30
961.2.g.b.448.1		8	31.23	odd	10
961.2.g.b.547.1		8	31.26	odd	6
961.2.g.b.844.1		8	31.30	odd	2
961.2.g.b.846.1		8	31.22	odd	30
961.2.g.c.448.1		8	31.8	even	5	inner
961.2.g.c.547.1		8	31.5	even	3	inner
961.2.g.c.844.1		8	1.1	even	1	trivial
961.2.g.c.846.1		8	31.9	even	15	inner
961.2.g.f.235.1		8	31.21	odd	30
961.2.g.f.338.1		8	31.29	odd	10
961.2.g.f.732.1		8	31.27	odd	10
961.2.g.f.816.1		8	31.11	odd	30
961.2.g.g.235.1		8	31.10	even	15
961.2.g.g.338.1		8	31.2	even	5
961.2.g.g.732.1		8	31.4	even	5
961.2.g.g.816.1		8	31.20	even	15
8649.2.a.f.1.2		2	93.59	odd	30
8649.2.a.g.1.2		2	93.65	even	30

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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	961.2.g.c.844.1

Level	$961$
Weight	$2$
Character	961.844
Analytic conductor	$7.674$
Analytic rank	$0$
Dimension	$8$
Inner twists	$4$