LMFDB - Embedded newform 784.2.x.j.373.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [784,2,Mod(165,784)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(784, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 3, 8]))

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

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

chi := DirichletCharacter("784.165");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 784 = 2^{4} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	784.x (of order $12$, degree $4$, 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:	$6.26027151847$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{12})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 2 x^{15} + 4 x^{14} + 4 x^{13} - 13 x^{12} + 32 x^{11} - 4 x^{10} - 34 x^{9} + 121 x^{8} + \cdots + 256 $ x^16 - 2x^15 + 4x^14 + 4x^13 - 13x^12 + 32x^11 - 4x^10 - 34x^9 + 121x^8 - 68x^7 - 16x^6 + 256x^5 - 208x^4 + 128x^3 + 256x^2 - 256*x + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 112)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			373.4
Root			$0.250645 + 1.39183i$ of defining polynomial
Character	$\chi$	$=$	784.373
Dual form			784.2.x.j.557.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.25323 + 0.655294i) q^{2} +(2.01092 + 0.538823i) q^{3} +(1.14118 + 1.64247i) q^{4} +(0.483385 - 0.129523i) q^{5} +(2.16706 + 1.99301i) q^{6} +(0.353863 + 2.80620i) q^{8} +(1.15537 + 0.667056i) q^{9} +O(q^{10})$	\(q+(1.25323 + 0.655294i) q^{2} +(2.01092 + 0.538823i) q^{3} +(1.14118 + 1.64247i) q^{4} +(0.483385 - 0.129523i) q^{5} +(2.16706 + 1.99301i) q^{6} +(0.353863 + 2.80620i) q^{8} +(1.15537 + 0.667056i) q^{9} +(0.690669 + 0.154437i) q^{10} +(0.122293 - 0.456405i) q^{11} +(1.40982 + 3.91776i) q^{12} +(3.17982 - 3.17982i) q^{13} +1.04184 q^{15} +(-1.39542 + 3.74871i) q^{16} +(0.646137 + 1.11914i) q^{17} +(1.01083 + 1.59309i) q^{18} +(-0.963437 - 3.59560i) q^{19} +(0.764367 + 0.646137i) q^{20} +(0.452341 - 0.491843i) q^{22} +(-2.26039 - 1.30504i) q^{23} +(-0.800460 + 5.83371i) q^{24} +(-4.11324 + 2.37478i) q^{25} +(6.06876 - 1.90133i) q^{26} +(-2.45234 - 2.45234i) q^{27} +(-6.98602 + 6.98602i) q^{29} +(1.30566 + 0.682709i) q^{30} +(4.17982 + 7.23966i) q^{31} +(-4.20529 + 3.78359i) q^{32} +(0.491843 - 0.851898i) q^{33} +(0.0763926 + 1.82596i) q^{34} +(0.222871 + 2.65890i) q^{36} +(4.53539 - 1.21525i) q^{37} +(1.14876 - 5.13745i) q^{38} +(8.10770 - 4.68099i) q^{39} +(0.534519 + 1.31064i) q^{40} -9.93254i q^{41} +(-7.61241 - 7.61241i) q^{43} +(0.889190 - 0.319977i) q^{44} +(0.644890 + 0.172798i) q^{45} +(-1.97761 - 3.11673i) q^{46} +(-2.29805 + 3.98033i) q^{47} +(-4.82596 + 6.78645i) q^{48} +(-6.71102 + 0.280770i) q^{50} +(0.696308 + 2.59866i) q^{51} +(8.85150 + 1.59401i) q^{52} +(-1.44367 + 5.38786i) q^{53} +(-1.46635 - 4.68036i) q^{54} -0.236459i q^{55} -7.74956i q^{57} +(-13.3330 + 4.17721i) q^{58} +(2.34099 - 8.73669i) q^{59} +(1.18892 + 1.71119i) q^{60} +(-1.59362 - 5.94749i) q^{61} +(0.494178 + 11.8120i) q^{62} +(-7.74956 + 1.98602i) q^{64} +(1.12522 - 1.94894i) q^{65} +(1.17464 - 0.745323i) q^{66} +(13.6221 + 3.65002i) q^{67} +(-1.10080 + 2.33840i) q^{68} +(-3.84227 - 3.84227i) q^{69} -7.62395i q^{71} +(-1.46305 + 3.47826i) q^{72} +(0.482023 - 0.278296i) q^{73} +(6.48024 + 1.44902i) q^{74} +(-9.55097 + 2.55917i) q^{75} +(4.80620 - 5.68564i) q^{76} +(13.2283 - 0.553431i) q^{78} +(0.744616 - 1.28971i) q^{79} +(-0.188981 + 1.99281i) q^{80} +(-5.61124 - 9.71895i) q^{81} +(6.50873 - 12.4478i) q^{82} +(-1.47209 + 1.47209i) q^{83} +(0.457288 + 0.457288i) q^{85} +(-4.55175 - 14.5285i) q^{86} +(-17.8125 + 10.2841i) q^{87} +(1.32404 + 0.181675i) q^{88} +(10.6453 + 6.14609i) q^{89} +(0.694964 + 0.639148i) q^{90} +(-0.436028 - 5.20190i) q^{92} +(4.50437 + 16.8105i) q^{93} +(-5.48827 + 3.48239i) q^{94} +(-0.931423 - 1.61327i) q^{95} +(-10.4952 + 5.34258i) q^{96} -5.50078 q^{97} +(0.445742 - 0.445742i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 2 q^{2} - 4 q^{4} - 4 q^{5} + 32 q^{6} - 8 q^{8}+O(q^{10}) $ 16 * q - 2 * q^2 - 4 * q^4 - 4 * q^5 + 32 * q^6 - 8 * q^8	$ 16 q - 2 q^{2} - 4 q^{4} - 4 q^{5} + 32 q^{6} - 8 q^{8} + 12 q^{10} - 12 q^{12} - 16 q^{15} - 8 q^{16} + 24 q^{17} - 6 q^{18} - 12 q^{19} + 16 q^{20} - 8 q^{22} + 8 q^{26} - 24 q^{27} - 32 q^{29} - 20 q^{30} + 16 q^{31} + 28 q^{32} - 24 q^{33} + 24 q^{34} + 48 q^{36} - 16 q^{37} - 16 q^{38} + 28 q^{40} - 64 q^{43} + 32 q^{44} - 8 q^{45} - 20 q^{46} + 24 q^{47} - 40 q^{48} - 28 q^{50} - 8 q^{51} + 32 q^{52} + 8 q^{53} - 16 q^{54} - 12 q^{58} - 28 q^{59} + 28 q^{60} + 28 q^{61} - 40 q^{62} - 64 q^{64} + 48 q^{65} - 16 q^{66} + 28 q^{68} - 88 q^{69} - 44 q^{72} + 4 q^{74} + 28 q^{75} + 48 q^{76} + 24 q^{78} + 24 q^{79} - 12 q^{80} - 40 q^{81} + 4 q^{82} - 80 q^{85} + 40 q^{88} + 32 q^{90} + 72 q^{92} - 16 q^{93} + 28 q^{94} - 16 q^{95} + 8 q^{96} + 64 q^{97} + 96 q^{99}+O(q^{100}) $ 16 * q - 2 * q^2 - 4 * q^4 - 4 * q^5 + 32 * q^6 - 8 * q^8 + 12 * q^10 - 12 * q^12 - 16 * q^15 - 8 * q^16 + 24 * q^17 - 6 * q^18 - 12 * q^19 + 16 * q^20 - 8 * q^22 + 8 * q^26 - 24 * q^27 - 32 * q^29 - 20 * q^30 + 16 * q^31 + 28 * q^32 - 24 * q^33 + 24 * q^34 + 48 * q^36 - 16 * q^37 - 16 * q^38 + 28 * q^40 - 64 * q^43 + 32 * q^44 - 8 * q^45 - 20 * q^46 + 24 * q^47 - 40 * q^48 - 28 * q^50 - 8 * q^51 + 32 * q^52 + 8 * q^53 - 16 * q^54 - 12 * q^58 - 28 * q^59 + 28 * q^60 + 28 * q^61 - 40 * q^62 - 64 * q^64 + 48 * q^65 - 16 * q^66 + 28 * q^68 - 88 * q^69 - 44 * q^72 + 4 * q^74 + 28 * q^75 + 48 * q^76 + 24 * q^78 + 24 * q^79 - 12 * q^80 - 40 * q^81 + 4 * q^82 - 80 * q^85 + 40 * q^88 + 32 * q^90 + 72 * q^92 - 16 * q^93 + 28 * q^94 - 16 * q^95 + 8 * q^96 + 64 * q^97 + 96 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/784\mathbb{Z}\right)^\times$.

$n$	$197$	$687$	$689$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	1.25323	+	0.655294i	0.886169	+	0.463363i
$2$	1.25323	+	0.655294i	0.886169	+	0.463363i
$3$	2.01092	+	0.538823i	1.16100	+	0.311090i	0.787366	−	0.616486i	$-0.211444\pi$
$3$	2.01092	+	0.538823i	1.16100	+	0.311090i	0.373636	+	0.927575i	$0.378111\pi$
$4$	1.14118	+	1.64247i	0.570590	+	0.821235i
$5$	0.483385	−	0.129523i	0.216177	−	0.0579243i	−0.149105	−	0.988821i	$-0.547639\pi$
$5$	0.483385	−	0.129523i	0.216177	−	0.0579243i	0.365282	+	0.930897i	$0.380973\pi$
$6$	2.16706	+	1.99301i	0.884697	+	0.813643i
$7$		0			0
$7$		0			0
$8$	0.353863	+	2.80620i	0.125109	+	0.992143i
$9$	1.15537	+	0.667056i	0.385125	+	0.222352i
$10$	0.690669	+	0.154437i	0.218409	+	0.0488374i
$11$	0.122293	−	0.456405i	0.0368728	−	0.137611i	−0.945036	−	0.326967i	$-0.893973\pi$
$11$	0.122293	−	0.456405i	0.0368728	−	0.137611i	0.981909	+	0.189356i	$0.0606400\pi$
$12$	1.40982	+	3.91776i	0.406979	+	1.13096i
$13$	3.17982	−	3.17982i	0.881923	−	0.881923i	−0.111807	−	0.993730i	$-0.535664\pi$
$13$	3.17982	−	3.17982i	0.881923	−	0.881923i	0.993730	+	0.111807i	$0.0356639\pi$
$14$		0			0
$15$	1.04184			0.269001
$16$	−1.39542	+	3.74871i	−0.348854	+	0.937177i
$17$	0.646137	+	1.11914i	0.156711	+	0.271432i	0.933681	−	0.358106i	$-0.116577\pi$
$17$	0.646137	+	1.11914i	0.156711	+	0.271432i	−0.776970	+	0.629538i	$0.783244\pi$
$18$	1.01083	+	1.59309i	0.238256	+	0.375494i
$19$	−0.963437	−	3.59560i	−0.221028	−	0.824886i	−0.983957	−	0.178405i	$-0.942906\pi$
$19$	−0.963437	−	3.59560i	−0.221028	−	0.824886i	0.762930	−	0.646482i	$-0.223760\pi$
$20$	0.764367	+	0.646137i	0.170918	+	0.144481i
$21$		0			0
$22$	0.452341	−	0.491843i	0.0964395	−	0.104861i
$23$	−2.26039	−	1.30504i	−0.471324	−	0.272119i	0.245470	−	0.969404i	$-0.421058\pi$
$23$	−2.26039	−	1.30504i	−0.471324	−	0.272119i	−0.716794	+	0.697285i	$0.754391\pi$
$24$	−0.800460	+	5.83371i	−0.163393	+	1.19080i
$25$	−4.11324	+	2.37478i	−0.822648	+	0.474956i
$26$	6.06876	−	1.90133i	1.19018	−	0.372882i
$27$	−2.45234	−	2.45234i	−0.471953	−	0.471953i
$28$		0			0
$29$	−6.98602	+	6.98602i	−1.29727	+	1.29727i	−0.367084	+	0.930188i	$0.619644\pi$
$29$	−6.98602	+	6.98602i	−1.29727	+	1.29727i	−0.930188	+	0.367084i	$0.880356\pi$
$30$	1.30566	+	0.682709i	0.238380	+	0.124645i
$31$	4.17982	+	7.23966i	0.750717	+	1.30028i	0.947475	+	0.319829i	$0.103625\pi$
$31$	4.17982	+	7.23966i	0.750717	+	1.30028i	−0.196758	+	0.980452i	$0.563041\pi$
$32$	−4.20529	+	3.78359i	−0.743396	+	0.668851i
$33$	0.491843	−	0.851898i	0.0856189	−	0.148296i
$34$	0.0763926	+	1.82596i	0.0131012	+	0.313149i
$35$		0			0
$36$	0.222871	+	2.65890i	0.0371452	+	0.443150i
$37$	4.53539	−	1.21525i	0.745613	−	0.199786i	0.134042	−	0.990976i	$-0.457204\pi$
$37$	4.53539	−	1.21525i	0.745613	−	0.199786i	0.611571	+	0.791189i	$0.290538\pi$
$38$	1.14876	−	5.13745i	0.186354	−	0.833404i
$39$	8.10770	−	4.68099i	1.29827	−	0.749558i
$40$	0.534519	+	1.31064i	0.0845149	+	0.207231i
$41$		−	9.93254i		−	1.55120i	−0.631223	−	0.775601i	$-0.717447\pi$
$41$		−	9.93254i		−	1.55120i	0.631223	−	0.775601i	$-0.282553\pi$
$42$		0			0
$43$	−7.61241	−	7.61241i	−1.16088	−	1.16088i	−0.984283	−	0.176598i	$-0.943491\pi$
$43$	−7.61241	−	7.61241i	−1.16088	−	1.16088i	−0.176598	−	0.984283i	$-0.556509\pi$
$44$	0.889190	−	0.319977i	0.134051	−	0.0482384i
$45$	0.644890	+	0.172798i	0.0961345	+	0.0257592i
$46$	−1.97761	−	3.11673i	−0.291583	−	0.459537i
$47$	−2.29805	+	3.98033i	−0.335205	+	0.580591i	−0.983524	−	0.180777i	$-0.942139\pi$
$47$	−2.29805	+	3.98033i	−0.335205	+	0.580591i	0.648319	+	0.761368i	$0.275472\pi$
$48$	−4.82596	+	6.78645i	−0.696567	+	0.979540i
$49$		0			0
$50$	−6.71102	+	0.280770i	−0.949082	+	0.0397068i
$51$	0.696308	+	2.59866i	0.0975026	+	0.363885i
$52$	8.85150	+	1.59401i	1.22748	+	0.221050i
$53$	−1.44367	+	5.38786i	−0.198304	+	0.740079i	0.793083	+	0.609113i	$0.208474\pi$
$53$	−1.44367	+	5.38786i	−0.198304	+	0.740079i	−0.991387	+	0.130966i	$0.958192\pi$
$54$	−1.46635	−	4.68036i	−0.199545	−	0.636916i
$55$		−	0.236459i		−	0.0318842i
$56$		0			0
$57$		−	7.74956i		−	1.02645i
$58$	−13.3330	+	4.17721i	−1.75071	+	0.548494i
$59$	2.34099	−	8.73669i	0.304771	−	1.13742i	−0.628372	−	0.777913i	$-0.716278\pi$
$59$	2.34099	−	8.73669i	0.304771	−	1.13742i	0.933142	−	0.359507i	$-0.117055\pi$
$60$	1.18892	+	1.71119i	0.153489	+	0.220913i
$61$	−1.59362	−	5.94749i	−0.204043	−	0.761498i	−0.989739	−	0.142886i	$-0.954362\pi$
$61$	−1.59362	−	5.94749i	−0.204043	−	0.761498i	0.785697	−	0.618612i	$-0.212305\pi$
$62$	0.494178	+	11.8120i	0.0627607	+	1.50012i
$63$		0			0
$64$	−7.74956	+	1.98602i	−0.968695	+	0.248253i
$65$	1.12522	−	1.94894i	0.139566	−	0.241736i
$66$	1.17464	−	0.745323i	0.144588	−	0.0917430i
$67$	13.6221	+	3.65002i	1.66420	+	0.445921i	0.963538	−	0.267572i	$-0.0862213\pi$
$67$	13.6221	+	3.65002i	1.66420	+	0.445921i	0.700662	+	0.713493i	$0.252888\pi$
$68$	−1.10080	+	2.33840i	−0.133492	+	0.283573i
$69$	−3.84227	−	3.84227i	−0.462555	−	0.462555i
$70$		0			0
$71$		−	7.62395i		−	0.904797i	−0.891816	−	0.452398i	$-0.850569\pi$
$71$		−	7.62395i		−	0.904797i	0.891816	−	0.452398i	$-0.149431\pi$
$72$	−1.46305	+	3.47826i	−0.172422	+	0.409917i
$73$	0.482023	−	0.278296i	0.0564166	−	0.0325721i	−0.471526	−	0.881852i	$-0.656297\pi$
$73$	0.482023	−	0.278296i	0.0564166	−	0.0325721i	0.527943	+	0.849280i	$0.322963\pi$
$74$	6.48024	+	1.44902i	0.753312	+	0.168445i
$75$	−9.55097	+	2.55917i	−1.10285	+	0.295508i
$76$	4.80620	−	5.68564i	0.551309	−	0.652188i
$77$		0			0
$78$	13.2283	−	0.553431i	1.49780	−	0.0626638i
$79$	0.744616	−	1.28971i	0.0837758	−	0.145104i	−0.821093	−	0.570794i	$-0.806635\pi$
$79$	0.744616	−	1.28971i	0.0837758	−	0.145104i	0.904869	+	0.425690i	$0.139969\pi$
$80$	−0.188981	+	1.99281i	−0.0211287	+	0.222803i
$81$	−5.61124	−	9.71895i	−0.623471	−	1.07988i
$82$	6.50873	−	12.4478i	0.718769	−	1.37463i
$83$	−1.47209	+	1.47209i	−0.161583	+	0.161583i	−0.783268	−	0.621685i	$-0.786449\pi$
$83$	−1.47209	+	1.47209i	−0.161583	+	0.161583i	0.621685	+	0.783268i	$0.286449\pi$
$84$		0			0
$85$	0.457288	+	0.457288i	0.0495998	+	0.0495998i
$86$	−4.55175	−	14.5285i	−0.490828	−	1.56665i
$87$	−17.8125	+	10.2841i	−1.90970	+	1.10257i
$88$	1.32404	+	0.181675i	0.141143	+	0.0193667i
$89$	10.6453	+	6.14609i	1.12840	+	0.651484i	0.943533	−	0.331279i	$-0.107480\pi$
$89$	10.6453	+	6.14609i	1.12840	+	0.651484i	0.184871	+	0.982763i	$0.440813\pi$
$90$	0.694964	+	0.639148i	0.0732556	+	0.0673721i
$91$		0			0
$92$	−0.436028	−	5.20190i	−0.0454591	−	0.542336i
$93$	4.50437	+	16.8105i	0.467081	+	1.74317i
$94$	−5.48827	+	3.48239i	−0.566072	+	0.359181i
$95$	−0.931423	−	1.61327i	−0.0955620	−	0.165518i
$96$	−10.4952	+	5.34258i	−1.07116	+	0.545275i
$97$	−5.50078			−0.558519			−0.279260	−	0.960216i	$-0.590089\pi$
$97$	−5.50078			−0.558519			−0.279260	+	0.960216i	$0.590089\pi$
$98$		0			0
$99$	0.445742	−	0.445742i	0.0447988	−	0.0447988i
$100$	−8.59446	−	4.04582i	−0.859446	−	0.404582i
$101$	−2.57268	+	9.60136i	−0.255991	+	0.955371i	0.711546	+	0.702640i	$0.247996\pi$
$101$	−2.57268	+	9.60136i	−0.255991	+	0.955371i	−0.967537	+	0.252731i	$0.918671\pi$
$102$	−0.830248	+	3.71300i	−0.0822068	+	0.367642i
$103$	−12.6446	−	7.30038i	−1.24591	−	0.719328i	−0.275621	−	0.961266i	$-0.588884\pi$
$103$	−12.6446	−	7.30038i	−1.24591	−	0.719328i	−0.970292	+	0.241938i	$0.922217\pi$
$104$	10.0484	+	7.79800i	0.985330	+	0.764657i
$105$		0			0
$106$	−5.33988	+	5.80620i	−0.518655	+	0.563948i
$107$	−1.42318	+	0.381339i	−0.137584	+	0.0368654i	−0.326954	−	0.945040i	$-0.606022\pi$
$107$	−1.42318	+	0.381339i	−0.137584	+	0.0368654i	0.189370	+	0.981906i	$0.439355\pi$
$108$	1.22933	−	6.82646i	0.118293	−	0.656876i
$109$	5.91732	+	1.58554i	0.566776	+	0.151867i	0.530818	−	0.847486i	$-0.321885\pi$
$109$	5.91732	+	1.58554i	0.566776	+	0.151867i	0.0359585	+	0.999353i	$0.488552\pi$
$110$	0.154950	−	0.296338i	0.0147739	−	0.0282548i
$111$	9.77509			0.927810
$112$		0			0
$113$	17.6379			1.65924			0.829619	−	0.558331i	$-0.188558\pi$
$113$	17.6379			1.65924			0.829619	+	0.558331i	$0.188558\pi$
$114$	5.07824	−	9.71200i	0.475621	−	0.909612i
$115$	−1.26167	−	0.338064i	−0.117651	−	0.0315246i
$116$	−19.4466	−	3.50202i	−1.80558	−	0.325155i
$117$	5.79500	−	1.55276i	0.535748	−	0.143553i
$118$	8.65890	−	9.41506i	0.797116	−	0.866727i
$119$		0			0
$120$	0.368667	+	2.92361i	0.0336546	+	0.266888i
$121$	9.33293	+	5.38837i	0.848448	+	0.489852i
$122$	1.90017	−	8.49787i	0.172033	−	0.769361i
$123$	5.35188	−	19.9735i	0.482563	−	1.80095i
$124$	−7.12100	+	15.1270i	−0.639484	+	1.35844i
$125$	−3.45001	+	3.45001i	−0.308578	+	0.308578i
$126$		0			0
$127$	7.75122			0.687809			0.343905	−	0.939005i	$-0.388250\pi$
$127$	7.75122			0.687809			0.343905	+	0.939005i	$0.388250\pi$
$128$	−11.0134	−	2.58929i	−0.973459	−	0.228863i
$129$	−11.2062	−	19.4097i	−0.986648	−	1.70892i
$130$	2.68729	−	1.70512i	0.235691	−	0.149549i
$131$	−0.554991	−	2.07126i	−0.0484898	−	0.180966i	0.937434	−	0.348164i	$-0.113195\pi$
$131$	−0.554991	−	2.07126i	−0.0484898	−	0.180966i	−0.985923	+	0.167198i	$0.946528\pi$
$132$	1.96050	−	0.164331i	0.170639	−	0.0143031i
$133$		0			0
$134$	14.6798	+	13.5008i	1.26814	+	1.16629i
$135$	−1.50306	−	0.867792i	−0.129363	−	0.0746877i
$136$	−2.91190	+	2.20922i	−0.249693	+	0.189439i
$137$	−5.17194	+	2.98602i	−0.441869	+	0.255113i	−0.704390	−	0.709813i	$-0.748779\pi$
$137$	−5.17194	+	2.98602i	−0.441869	+	0.255113i	0.262521	+	0.964926i	$0.415446\pi$
$138$	−2.29744	−	7.33307i	−0.195571	−	0.624232i
$139$	−9.10343	−	9.10343i	−0.772142	−	0.772142i	0.206338	−	0.978481i	$-0.433845\pi$
$139$	−9.10343	−	9.10343i	−0.772142	−	0.772142i	−0.978481	+	0.206338i	$0.933845\pi$
$140$		0			0
$141$	−6.76588	+	6.76588i	−0.569790	+	0.569790i
$142$	4.99593	−	9.55458i	0.419249	−	0.801803i
$143$	−1.06241	−	1.84016i	−0.0888436	−	0.153882i
$144$	−4.11283	+	3.40034i	−0.342736	+	0.283362i
$145$	−2.47209	+	4.28179i	−0.205296	+	0.355583i
$146$	0.786453	−	0.0329029i	0.0650873	−	0.00272306i
$147$		0			0
$148$	7.17171	+	6.06241i	0.589511	+	0.498327i
$149$	4.28543	−	1.14828i	0.351076	−	0.0940706i	−0.0789711	−	0.996877i	$-0.525163\pi$
$149$	4.28543	−	1.14828i	0.351076	−	0.0940706i	0.430047	+	0.902806i	$0.358497\pi$
$150$	−13.6466	−	3.05145i	−1.11424	−	0.249150i
$151$	−10.4144	+	6.01276i	−0.847513	+	0.489312i	−0.859811	−	0.510613i	$-0.829419\pi$
$151$	−10.4144	+	6.01276i	−0.847513	+	0.489312i	0.0122982	+	0.999924i	$0.496085\pi$
$152$	9.74905	−	3.97595i	0.790753	−	0.322492i
$153$			1.72404i			0.139380i
$154$		0			0
$155$	2.95816	+	2.95816i	0.237605	+	0.237605i
$156$	16.9407	+	7.97482i	1.35634	+	0.638496i
$157$	11.4183	+	3.05954i	0.911283	+	0.244178i	0.683856	−	0.729617i	$-0.260302\pi$
$157$	11.4183	+	3.05954i	0.911283	+	0.244178i	0.227428	+	0.973795i	$0.426968\pi$
$158$	1.77832	−	1.12837i	0.141475	−	0.0897680i
$159$	−5.80620	+	10.0566i	−0.460462	+	0.797543i
$160$	−1.54271	+	2.37361i	−0.121962	+	0.187651i
$161$		0			0
$162$	−0.663415	−	15.8571i	−0.0521228	−	1.24585i
$163$	−0.336253	−	1.25491i	−0.0263374	−	0.0982925i	0.951506	−	0.307630i	$-0.0995359\pi$
$163$	−0.336253	−	1.25491i	−0.0263374	−	0.0982925i	−0.977843	+	0.209338i	$0.932869\pi$
$164$	16.3139	−	11.3348i	1.27390	−	0.885101i
$165$	0.127410	−	0.475500i	0.00991884	−	0.0370176i
$166$	−2.80953	+	0.880220i	−0.218062	+	0.0683183i
$167$			13.0690i			1.01131i	0.862736	+	0.505655i	$0.168749\pi$
$167$			13.0690i			1.01131i	−0.862736	+	0.505655i	$0.831251\pi$
$168$		0			0
$169$		−	7.22248i		−	0.555575i
$170$	0.273430	+	0.872745i	0.0209711	+	0.0669365i
$171$	1.28533	−	4.79693i	0.0982918	−	0.366830i
$172$	3.81602	−	21.1903i	0.290969	−	1.61574i
$173$	1.39402	+	5.20256i	0.105986	+	0.395543i	0.998455	−	0.0555642i	$-0.0176957\pi$
$173$	1.39402	+	5.20256i	0.105986	+	0.395543i	−0.892470	+	0.451108i	$0.851029\pi$
$174$	−29.0623	+	1.21588i	−2.20321	+	0.0921758i
$175$		0			0
$176$	1.54028	+	1.09532i	0.116103	+	0.0825626i
$177$	9.41506	−	16.3074i	0.707679	−	1.22574i
$178$	9.31358	+	14.6783i	0.698082	+	1.10018i
$179$	−12.0632	−	3.23233i	−0.901649	−	0.241596i	−0.221924	−	0.975064i	$-0.571234\pi$
$179$	−12.0632	−	3.23233i	−0.901649	−	0.241596i	−0.679724	+	0.733468i	$0.737900\pi$
$180$	0.452121	+	1.25641i	0.0336991	+	0.0936470i
$181$	1.37018	+	1.37018i	0.101844	+	0.101844i	0.756193	−	0.654349i	$-0.227057\pi$
$181$	1.37018	+	1.37018i	0.101844	+	0.101844i	−0.654349	+	0.756193i	$0.727057\pi$
$182$		0			0
$183$		−	12.8186i		−	0.947576i
$184$	2.86233	−	6.80492i	0.211014	−	0.501665i
$185$	2.03494	−	1.17487i	0.149612	−	0.0863783i
$186$	−5.37082	+	24.0192i	−0.393807	+	1.76117i
$187$	0.589801	−	0.158037i	0.0431305	−	0.0115568i
$188$	−9.16007	+	0.767805i	−0.668067	+	0.0559979i
$189$		0			0
$190$	−0.110122	−	2.63216i	−0.00798908	−	0.190957i
$191$	0.707725	−	1.22582i	0.0512092	−	0.0886970i	−0.839285	−	0.543692i	$-0.817026\pi$
$191$	0.707725	−	1.22582i	0.0512092	−	0.0886970i	0.890494	+	0.454995i	$0.150359\pi$
$192$	−16.6538	−	0.181922i	−1.20189	−	0.0131291i
$193$	5.48485	+	9.50005i	0.394808	+	0.683828i	0.993077	−	0.117468i	$-0.0374776\pi$
$193$	5.48485	+	9.50005i	0.394808	+	0.683828i	−0.598268	+	0.801296i	$0.704144\pi$
$194$	−6.89375	−	3.60463i	−0.494942	−	0.258797i
$195$	3.31285	−	3.31285i	0.237238	−	0.237238i
$196$		0			0
$197$	8.92787	+	8.92787i	0.636084	+	0.636084i	0.949587	−	0.313503i	$-0.101503\pi$
$197$	8.92787	+	8.92787i	0.636084	+	0.636084i	−0.313503	+	0.949587i	$0.601503\pi$
$198$	0.850711	−	0.266526i	0.0604574	−	0.0189412i
$199$	−7.58080	+	4.37678i	−0.537388	+	0.310261i	−0.744020	−	0.668157i	$-0.767083\pi$
$199$	−7.58080	+	4.37678i	−0.537388	+	0.310261i	0.206631	+	0.978419i	$0.433750\pi$
$200$	−8.11964	−	10.7022i	−0.574145	−	0.756763i
$201$	25.4261	+	14.6798i	1.79342	+	1.03543i
$202$	−9.51587	+	10.3469i	−0.669535	+	0.728003i
$203$		0			0
$204$	−3.47360	+	4.10920i	−0.243201	+	0.287701i
$205$	−1.28649	−	4.80125i	−0.0898524	−	0.335334i
$206$	−11.0628	−	17.4350i	−0.770779	−	1.21476i
$207$	−1.74106	−	3.01561i	−0.121012	−	0.209600i
$208$	7.48304	+	16.3574i	0.518855	+	1.13418i
$209$	−1.75887			−0.121664
$210$		0			0
$211$	−9.88837	+	9.88837i	−0.680743	+	0.680743i	−0.960168	−	0.279424i	$-0.909856\pi$
$211$	−9.88837	+	9.88837i	−0.680743	+	0.680743i	0.279424	+	0.960168i	$0.409856\pi$
$212$	−10.4969	+	3.77733i	−0.720929	+	0.259428i
$213$	4.10796	−	15.3311i	0.281473	−	1.05047i
$214$	−2.03346	−	0.454692i	−0.139004	−	0.0310821i
$215$	−4.66571	−	2.69375i	−0.318199	−	0.183712i
$216$	6.01398	−	7.74956i	0.409199	−	0.527291i
$217$		0			0
$218$	6.37678	+	5.86463i	0.431890	+	0.397203i
$219$	1.11926	−	0.299905i	0.0756327	−	0.0202657i
$220$	0.388377	−	0.269843i	0.0261844	−	0.0181928i
$221$	5.61327	+	1.50407i	0.377589	+	0.101175i
$222$	12.2504	+	6.40555i	0.822196	+	0.429913i
$223$	−6.12483			−0.410149			−0.205074	−	0.978746i	$-0.565744\pi$
$223$	−6.12483			−0.410149			−0.205074	+	0.978746i	$0.565744\pi$
$224$		0			0
$225$	−6.33645			−0.422430
$226$	22.1044	+	11.5580i	1.47036	+	0.768829i
$227$	−7.56121	−	2.02602i	−0.501855	−	0.134472i	−0.000994262	−	1.00000i	$-0.500316\pi$
$227$	−7.56121	−	2.02602i	−0.501855	−	0.134472i	−0.500861	+	0.865528i	$0.666983\pi$
$228$	12.7284	−	8.84365i	0.842961	−	0.585685i
$229$	17.4745	−	4.68228i	1.15475	−	0.309414i	0.369882	−	0.929079i	$-0.379398\pi$
$229$	17.4745	−	4.68228i	1.15475	−	0.309414i	0.784866	+	0.619665i	$0.212732\pi$
$230$	−1.35964	−	1.25044i	−0.0896517	−	0.0824514i
$231$		0			0
$232$	−22.0763	−	17.1321i	−1.44938	−	1.12478i
$233$	−21.3351	−	12.3178i	−1.39771	−	0.806966i	−0.403554	−	0.914956i	$-0.632225\pi$
$233$	−21.3351	−	12.3178i	−1.39771	−	0.806966i	−0.994152	+	0.107990i	$0.965559\pi$
$234$	8.27999	+	1.85145i	0.541280	+	0.121033i
$235$	−0.595299	+	2.22169i	−0.0388330	+	0.144927i
$236$	17.0212	−	6.12513i	1.10799	−	0.398712i
$237$	2.19229	−	2.19229i	0.142404	−	0.142404i
$238$		0			0
$239$	−10.8844			−0.704052			−0.352026	−	0.935990i	$-0.614507\pi$
$239$	−10.8844			−0.704052			−0.352026	+	0.935990i	$0.614507\pi$
$240$	−1.45380	+	3.90554i	−0.0938421	+	0.252102i
$241$	−7.57634	−	13.1226i	−0.488035	−	0.845302i	0.511870	−	0.859063i	$-0.328953\pi$
$241$	−7.57634	−	13.1226i	−0.488035	−	0.845302i	−0.999905	+	0.0137611i	$0.995620\pi$
$242$	8.16536	+	12.8687i	0.524889	+	0.827231i
$243$	−3.35408	−	12.5176i	−0.215164	−	0.803003i
$244$	7.94996	−	9.40463i	0.508944	−	0.602070i
$245$		0			0
$246$	19.7957	−	21.5244i	1.26213	−	1.37234i
$247$	−14.4969	−	8.36979i	−0.922415	−	0.532557i
$248$	−18.8369	+	14.2913i	−1.19614	+	0.907496i
$249$	−3.75345	+	2.16706i	−0.237865	+	0.137332i
$250$	−6.58443	+	2.06289i	−0.416436	+	0.130469i
$251$	0.848041	+	0.848041i	0.0535279	+	0.0535279i	0.733364	−	0.679836i	$-0.237949\pi$
$251$	0.848041	+	0.848041i	0.0535279	+	0.0535279i	−0.679836	+	0.733364i	$0.737949\pi$
$252$		0			0
$253$	−0.872056	+	0.872056i	−0.0548257	+	0.0548257i
$254$	9.71407	+	5.07932i	0.609515	+	0.318705i
$255$	0.673170	+	1.16596i	0.0421555	+	0.0730155i
$256$	−12.1056	−	10.4620i	−0.756602	−	0.653876i
$257$	−5.82596	+	10.0909i	−0.363413	+	0.629450i	−0.988520	−	0.151089i	$-0.951722\pi$
$257$	−5.82596	+	10.0909i	−0.363413	+	0.629450i	0.625107	+	0.780539i	$0.285055\pi$
$258$	−1.32490	−	31.6681i	−0.0824848	−	1.97157i
$259$		0			0
$260$	4.48515	−	0.375949i	0.278157	−	0.0233154i
$261$	−12.7315	+	3.41141i	−0.788062	+	0.211161i
$262$	0.661748	−	2.95945i	0.0408829	−	0.182835i
$263$	−15.7448	+	9.09027i	−0.970867	+	0.560530i	−0.899500	−	0.436920i	$-0.856069\pi$
$263$	−15.7448	+	9.09027i	−0.970867	+	0.560530i	−0.0713665	+	0.997450i	$0.522736\pi$
$264$	2.56464	+	1.07876i	0.157843	+	0.0663930i
$265$			2.79140i			0.171474i
$266$		0			0
$267$	18.0952	+	18.0952i	1.10741	+	1.10741i
$268$	9.55018	+	26.5392i	0.583370	+	1.62114i
$269$	30.6750	+	8.21935i	1.87029	+	0.501143i	0.999962	+	0.00866872i	$0.00275937\pi$
$269$	30.6750	+	8.21935i	1.87029	+	0.501143i	0.870327	+	0.492474i	$0.163907\pi$
$270$	−1.31502	−	2.07249i	−0.0800298	−	0.126128i
$271$	11.1066	−	19.2372i	0.674677	−	1.16857i	−0.301886	−	0.953344i	$-0.597616\pi$
$271$	11.1066	−	19.2372i	0.674677	−	1.16857i	0.976563	−	0.215231i	$-0.0690504\pi$
$272$	−5.09697	+	0.860511i	−0.309049	+	0.0521761i
$273$		0			0
$274$	−8.43836	+	0.353036i	−0.509780	+	0.0213277i
$275$	0.580840	+	2.16772i	0.0350260	+	0.130719i
$276$	1.92609	−	10.6955i	0.115937	−	0.643795i
$277$	−2.98921	+	11.1559i	−0.179604	+	0.670291i	0.816117	+	0.577886i	$0.196122\pi$
$277$	−2.98921	+	11.1559i	−0.179604	+	0.670291i	−0.995721	+	0.0924053i	$0.970544\pi$
$278$	−5.44328	−	17.3741i	−0.326466	−	1.04203i
$279$			11.1527i			0.667694i
$280$		0			0
$281$			26.7783i			1.59746i	0.601690	+	0.798730i	$0.294494\pi$
$281$			26.7783i			1.59746i	−0.601690	+	0.798730i	$0.705506\pi$
$282$	−12.9128	+	4.04557i	−0.768949	+	0.240910i
$283$	4.30009	−	16.0481i	0.255614	−	0.953963i	−0.712135	−	0.702043i	$-0.752271\pi$
$283$	4.30009	−	16.0481i	0.255614	−	0.953963i	0.967748	−	0.251920i	$-0.0810619\pi$
$284$	12.5221	−	8.70030i	0.743051	−	0.516268i
$285$	−1.00374	−	3.74603i	−0.0594567	−	0.221895i
$286$	−0.125609	−	3.00234i	−0.00742741	−	0.177532i
$287$		0			0
$288$	−7.38255	+	1.56631i	−0.435021	+	0.0922955i
$289$	7.66501	−	13.2762i	0.450883	−	0.780952i
$290$	−5.90393	+	3.74613i	−0.346691	+	0.219980i
$291$	−11.0616	−	2.96395i	−0.648442	−	0.173750i
$292$	1.00717	+	0.474123i	0.0589401	+	0.0277459i
$293$	15.2256	+	15.2256i	0.889492	+	0.889492i	0.994474	−	0.104983i	$-0.0334787\pi$
$293$	15.2256	+	15.2256i	0.889492	+	0.889492i	−0.104983	+	0.994474i	$0.533479\pi$
$294$		0			0
$295$		−	4.52640i		−	0.263537i
$296$	5.01515	+	12.2972i	0.291500	+	0.714760i
$297$	−1.41917	+	0.819356i	−0.0823484	+	0.0475439i
$298$	6.12310	+	1.36916i	0.354702	+	0.0793132i
$299$	−11.3374	+	3.03785i	−0.655659	+	0.175683i
$300$	−15.1027	−	12.7667i	−0.871957	−	0.737086i
$301$		0			0
$302$	−16.9918	+	0.710887i	−0.977768	+	0.0409069i
$303$	−10.3469	+	17.9213i	−0.594412	+	1.02955i
$304$	14.8232	+	1.40571i	0.850171	+	0.0806229i
$305$	−1.54067	−	2.66852i	−0.0882185	−	0.152799i
$306$	−1.12975	+	2.16062i	−0.0645836	+	0.123514i
$307$	13.7596	−	13.7596i	0.785302	−	0.785302i	−0.195418	−	0.980720i	$-0.562606\pi$
$307$	13.7596	−	13.7596i	0.785302	−	0.785302i	0.980720	+	0.195418i	$0.0626064\pi$
$308$		0			0
$309$	−21.4937	−	21.4937i	−1.22273	−	1.22273i
$310$	1.76880	+	5.64573i	0.100461	+	0.320656i
$311$	−9.07434	+	5.23907i	−0.514558	+	0.297080i	−0.734705	−	0.678386i	$-0.762680\pi$
$311$	−9.07434	+	5.23907i	−0.514558	+	0.297080i	0.220147	+	0.975467i	$0.429346\pi$
$312$	16.0048	+	21.0954i	0.906094	+	1.19429i
$313$	−28.4453	−	16.4229i	−1.60782	−	0.928276i	−0.989857	−	0.142070i	$-0.954624\pi$
$313$	−28.4453	−	16.4229i	−1.60782	−	0.928276i	−0.617964	−	0.786206i	$-0.712042\pi$
$314$	12.3049	+	11.3167i	0.694408	+	0.638637i
$315$		0			0
$316$	2.96806	−	0.248785i	0.166966	−	0.0139952i
$317$	2.17572	+	8.11991i	0.122201	+	0.456059i	0.999724	−	0.0234738i	$-0.00747264\pi$
$317$	2.17572	+	8.11991i	0.122201	+	0.456059i	−0.877524	+	0.479533i	$0.840806\pi$
$318$	−13.8666	+	8.79853i	−0.777599	+	0.493397i
$319$	2.33411	+	4.04280i	0.130685	+	0.226353i
$320$	−3.48879	+	1.96376i	−0.195029	+	0.109777i
$321$	−3.06736			−0.171203
$322$		0			0
$323$	3.40147	−	3.40147i	0.189263	−	0.189263i
$324$	9.55966	−	20.3074i	0.531092	−	1.12819i
$325$	−5.52799	+	20.6307i	−0.306638	+	1.14439i
$326$	0.400934	−	1.79304i	0.0222057	−	0.0993075i
$327$	11.0449	+	6.37678i	0.610784	+	0.352636i
$328$	27.8727	−	3.51476i	1.53901	−	0.194070i
$329$		0			0
$330$	0.471266	−	0.512421i	0.0259423	−	0.0282078i
$331$	0.491271	−	0.131636i	0.0270027	−	0.00723535i	−0.245292	−	0.969449i	$-0.578884\pi$
$331$	0.491271	−	0.131636i	0.0270027	−	0.00723535i	0.272295	+	0.962214i	$0.412217\pi$
$332$	−4.09779	−	0.737945i	−0.224895	−	0.0405000i
$333$	6.05071	+	1.62128i	0.331577	+	0.0888458i
$334$	−8.56404	+	16.3785i	−0.468604	+	0.896192i
$335$	7.05747			0.385591
$336$		0			0
$337$	27.0287			1.47235			0.736174	−	0.676792i	$-0.236630\pi$
$337$	27.0287			1.47235			0.736174	+	0.676792i	$0.236630\pi$
$338$	4.73285	−	9.05144i	0.257433	−	0.492334i
$339$	35.4684	+	9.50373i	1.92638	+	0.516172i
$340$	−0.229234	+	1.27293i	−0.0124319	+	0.0690343i
$341$	3.81538	−	1.02233i	0.206614	−	0.0553622i
$342$	4.75422	−	5.16939i	0.257079	−	0.279529i
$343$		0			0
$344$	18.6682	−	24.0557i	1.00652	−	1.29700i
$345$	−2.35496	−	1.35964i	−0.126787	−	0.0732003i
$346$	−1.66217	+	7.43351i	−0.0893590	+	0.399628i
$347$	0.935173	−	3.49011i	0.0502027	−	0.187359i	−0.936271	−	0.351278i	$-0.885747\pi$
$347$	0.935173	−	3.49011i	0.0502027	−	0.187359i	0.986474	+	0.163919i	$0.0524137\pi$
$348$	−37.2186	−	17.5206i	−1.99513	−	0.939201i
$349$	−2.82678	+	2.82678i	−0.151314	+	0.151314i	−0.778705	−	0.627391i	$-0.784123\pi$
$349$	−2.82678	+	2.82678i	−0.151314	+	0.151314i	0.627391	+	0.778705i	$0.284123\pi$
$350$		0			0
$351$	−15.5960			−0.832453
$352$	1.21257	+	2.38202i	0.0646303	+	0.126962i
$353$	−0.424483	−	0.735225i	−0.0225929	−	0.0391321i	0.854508	−	0.519438i	$-0.173859\pi$
$353$	−0.424483	−	0.735225i	−0.0225929	−	0.0391321i	−0.877101	+	0.480306i	$0.840525\pi$
$354$	22.4854	−	14.2673i	1.19508	−	0.758297i
$355$	−0.987475	−	3.68531i	−0.0524097	−	0.195596i
$356$	2.05348	+	24.4984i	0.108834	+	1.29841i
$357$		0			0
$358$	−12.9999	−	11.9558i	−0.687066	−	0.631885i
$359$	−24.8695	−	14.3584i	−1.31256	−	0.757808i	−0.330043	−	0.943966i	$-0.607063\pi$
$359$	−24.8695	−	14.3584i	−1.31256	−	0.757808i	−0.982520	+	0.186158i	$0.940396\pi$
$360$	−0.256703	+	1.87084i	−0.0135295	+	0.0986019i
$361$	4.45438	−	2.57174i	0.234441	−	0.135355i
$362$	0.819280	+	2.61502i	0.0430604	+	0.137442i
$363$	15.8644	+	15.8644i	0.832663	+	0.832663i
$364$		0			0
$365$	0.196957	−	0.196957i	0.0103092	−	0.0103092i
$366$	8.39993	−	16.0646i	0.439072	−	0.839713i
$367$	10.6496	+	18.4456i	0.555903	+	0.962853i	0.997833	+	0.0658029i	$0.0209609\pi$
$367$	10.6496	+	18.4456i	0.555903	+	0.962853i	−0.441929	+	0.897050i	$0.645706\pi$
$368$	8.04639	−	6.65247i	0.419447	−	0.346784i
$369$	6.62556	−	11.4758i	0.344913	−	0.597407i
$370$	3.32013	−	0.138905i	0.172606	−	0.00722131i
$371$		0			0
$372$	−22.4705	+	26.5821i	−1.16504	+	1.37822i
$373$	−7.62531	+	2.04320i	−0.394824	+	0.105793i	−0.450768	−	0.892641i	$-0.648850\pi$
$373$	−7.62531	+	2.04320i	−0.394824	+	0.105793i	0.0559442	+	0.998434i	$0.482183\pi$
$374$	0.842717	+	0.188436i	0.0435759	+	0.00974381i
$375$	−8.79661	+	5.07873i	−0.454255	+	0.262264i
$376$	−11.9828	−	5.04030i	−0.617967	−	0.259934i
$377$			44.4286i			2.28819i
$378$		0			0
$379$	12.0442	+	12.0442i	0.618668	+	0.618668i	0.945190	−	0.326522i	$-0.105877\pi$
$379$	12.0442	+	12.0442i	0.618668	+	0.618668i	−0.326522	+	0.945190i	$0.605877\pi$
$380$	1.58683	−	3.37087i	0.0814026	−	0.172922i
$381$	15.5870	+	4.17653i	0.798548	+	0.213970i
$382$	1.69021	−	1.07246i	0.0864789	−	0.0548720i
$383$	−0.0426634	+	0.0738952i	−0.00218000	+	0.00377587i	−0.867113	−	0.498111i	$-0.834027\pi$
$383$	−0.0426634	+	0.0738952i	−0.00218000	+	0.00377587i	0.864933	+	0.501887i	$0.167361\pi$
$384$	−20.7519	−	11.1411i	−1.05899	−	0.568544i
$385$		0			0
$386$	0.648472	+	15.5000i	0.0330064	+	0.788927i
$387$	−3.71728	−	13.8731i	−0.188960	−	0.705209i
$388$	−6.27738	−	9.03486i	−0.318686	−	0.458676i
$389$	0.192925	−	0.720006i	0.00978169	−	0.0365058i	−0.960863	−	0.277026i	$-0.910651\pi$
$389$	0.192925	−	0.720006i	0.00978169	−	0.0365058i	0.970644	+	0.240520i	$0.0773179\pi$
$390$	6.32266	−	1.98088i	0.320160	−	0.100306i
$391$		−	3.37293i		−	0.170576i
$392$		0			0
$393$		−	4.46416i		−	0.225187i
$394$	5.33831	+	17.0391i	0.268940	+	0.858416i
$395$	0.192889	−	0.719873i	0.00970532	−	0.0362207i
$396$	1.24079	+	0.223446i	0.0623521	+	0.0112286i
$397$	5.54245	+	20.6847i	0.278167	+	1.03813i	0.953689	+	0.300795i	$0.0972519\pi$
$397$	5.54245	+	20.6847i	0.278167	+	1.03813i	−0.675522	+	0.737340i	$0.736081\pi$
$398$	−12.3686	+	0.517465i	−0.619980	+	0.0259382i
$399$		0			0
$400$	−3.16268	−	18.7332i	−0.158134	−	0.936658i
$401$	−17.1809	+	29.7583i	−0.857975	+	1.48606i	0.0158823	+	0.999874i	$0.494944\pi$
$401$	−17.1809	+	29.7583i	−0.857975	+	1.48606i	−0.873857	+	0.486182i	$0.838389\pi$
$402$	22.2452	+	35.0587i	1.10949	+	1.74857i
$403$	36.3118	+	9.72973i	1.80882	+	0.484672i
$404$	−18.7058	+	6.73134i	−0.930650	+	0.334897i
$405$	−3.97122	−	3.97122i	−0.197331	−	0.197331i
$406$		0			0
$407$		−	2.21859i		−	0.109971i
$408$	−7.04596	+	2.87355i	−0.348827	+	0.142262i
$409$	−13.3958	+	7.73408i	−0.662380	+	0.382425i	−0.793183	−	0.608983i	$-0.791578\pi$
$409$	−13.3958	+	7.73408i	−0.662380	+	0.382425i	0.130803	+	0.991408i	$0.458244\pi$
$410$	1.53396	−	6.86010i	0.0757567	−	0.338796i
$411$	−12.0093	+	3.21788i	−0.592374	+	0.158726i
$412$	−2.43914	−	29.0995i	−0.120168	−	1.43363i
$413$		0			0
$414$	−0.205845	−	4.92017i	−0.0101168	−	0.241813i
$415$	−0.520919	+	0.902257i	−0.0255709	+	0.0442901i
$416$	−1.34090	+	25.4032i	−0.0657433	+	1.24549i
$417$	−13.4011	−	23.2114i	−0.656254	−	1.13666i
$418$	−2.20427	−	1.15258i	−0.107814	−	0.0563744i
$419$	−26.1914	+	26.1914i	−1.27953	+	1.27953i	−0.338602	+	0.940930i	$0.609954\pi$
$419$	−26.1914	+	26.1914i	−1.27953	+	1.27953i	−0.940930	+	0.338602i	$0.890046\pi$
$420$		0			0
$421$	20.3620	+	20.3620i	0.992382	+	0.992382i	0.999971	−	0.00758948i	$-0.00241583\pi$
$421$	20.3620	+	20.3620i	0.992382	+	0.992382i	−0.00758948	+	0.999971i	$0.502416\pi$
$422$	−18.8722	+	5.91263i	−0.918685	+	0.287822i
$423$	−5.31021	+	3.06585i	−0.258191	+	0.149067i
$424$	−15.6303	−	2.14468i	−0.759074	−	0.104155i
$425$	−5.31544	−	3.06887i	−0.257837	−	0.148862i
$426$	15.1946	−	16.5215i	0.736182	−	0.800471i
$427$		0			0
$428$	−2.25044	−	1.90235i	−0.108779	−	0.0919534i
$429$	−1.14491	−	4.27285i	−0.0552766	−	0.206295i
$430$	−4.08202	−	6.43330i	−0.196852	−	0.310241i
$431$	12.6089	+	21.8392i	0.607347	+	1.05196i	0.991676	+	0.128760i	$0.0410997\pi$
$431$	12.6089	+	21.8392i	0.607347	+	1.05196i	−0.384329	+	0.923196i	$0.625567\pi$
$432$	12.6151	−	5.77108i	0.606947	−	0.277661i
$433$	−11.8077			−0.567442			−0.283721	−	0.958907i	$-0.591569\pi$
$433$	−11.8077			−0.567442			−0.283721	+	0.958907i	$0.591569\pi$
$434$		0			0
$435$	−7.27830	+	7.27830i	−0.348968	+	0.348968i
$436$	4.14852	+	11.5284i	0.198678	+	0.552110i
$437$	−2.51464	+	9.38477i	−0.120292	+	0.448934i
$438$	1.59922	+	0.357594i	0.0764137	+	0.0170865i
$439$	23.7665	+	13.7216i	1.13431	+	0.654897i	0.945016	−	0.327023i	$-0.106046\pi$
$439$	23.7665	+	13.7216i	1.13431	+	0.654897i	0.189298	+	0.981920i	$0.439379\pi$
$440$	0.663553	−	0.0836741i	0.0316337	−	0.00398901i
$441$		0			0
$442$	6.04912	+	5.56329i	0.287727	+	0.264619i
$443$	27.9419	−	7.48700i	1.32756	−	0.355718i	0.475753	−	0.879579i	$-0.342175\pi$
$443$	27.9419	−	7.48700i	1.32756	−	0.355718i	0.851804	+	0.523861i	$0.175509\pi$
$444$	11.1551	+	16.0553i	0.529399	+	0.761950i
$445$	5.94186	+	1.59212i	0.281671	+	0.0754736i
$446$	−7.67583	−	4.01356i	−0.363461	−	0.190048i
$447$	9.23636			0.436865
$448$		0			0
$449$	−24.2497			−1.14441			−0.572206	−	0.820110i	$-0.693912\pi$
$449$	−24.2497			−1.14441			−0.572206	+	0.820110i	$0.693912\pi$
$450$	−7.94104	−	4.15223i	−0.374344	−	0.195738i
$451$	−4.53326	−	1.21468i	−0.213463	−	0.0571972i
$452$	20.1281	+	28.9698i	0.946744	+	1.36262i
$453$	−24.1823	+	6.47963i	−1.13618	+	0.304440i
$454$	−8.14831	−	7.49389i	−0.382419	−	0.351705i
$455$		0			0
$456$	21.7469	−	2.74228i	1.01839	−	0.128419i
$457$	11.7825	+	6.80265i	0.551164	+	0.318215i	0.749591	−	0.661901i	$-0.230250\pi$
$457$	11.7825	+	6.80265i	0.551164	+	0.318215i	−0.198427	+	0.980116i	$0.563583\pi$
$458$	24.9679	+	5.58295i	1.16667	+	0.260874i
$459$	1.15997	−	4.32907i	0.0541428	−	0.202064i
$460$	−0.884534	−	2.45805i	−0.0412416	−	0.114607i
$461$	28.1748	−	28.1748i	1.31223	−	1.31223i	0.392462	−	0.919768i	$-0.371624\pi$
$461$	28.1748	−	28.1748i	1.31223	−	1.31223i	0.919768	−	0.392462i	$-0.128376\pi$
$462$		0			0
$463$	−29.2805			−1.36078			−0.680391	−	0.732849i	$-0.738190\pi$
$463$	−29.2805			−1.36078			−0.680391	+	0.732849i	$0.738190\pi$
$464$	−16.4401	−	35.9370i	−0.763215	−	1.66833i
$465$	4.35469	+	7.54254i	0.201944	+	0.349777i
$466$	−18.6660	−	29.4178i	−0.864685	−	1.36275i
$467$	8.13184	+	30.3485i	0.376297	+	1.40436i	0.851441	+	0.524451i	$0.175729\pi$
$467$	8.13184	+	30.3485i	0.376297	+	1.40436i	−0.475144	+	0.879908i	$0.657604\pi$
$468$	9.16350	+	7.74612i	0.423583	+	0.358065i
$469$		0			0
$470$	−2.20190	+	2.39419i	−0.101566	+	0.110436i
$471$	21.3128	+	12.3049i	0.982041	+	0.566982i
$472$	25.3453	+	3.47770i	1.16661	+	0.160074i
$473$	−4.40529	+	2.54339i	−0.202555	+	0.116945i
$474$	4.18404	−	1.31085i	0.192179	−	0.0602094i
$475$	12.5016	+	12.5016i	0.573613	+	0.573613i
$476$		0			0
$477$	−5.26198	+	5.26198i	−0.240930	+	0.240930i
$478$	−13.6407	−	7.13247i	−0.623909	−	0.326231i
$479$	−16.8012	−	29.1005i	−0.767665	−	1.32963i	−0.938826	−	0.344391i	$-0.888085\pi$
$479$	−16.8012	−	29.1005i	−0.767665	−	1.32963i	0.171162	−	0.985243i	$-0.445248\pi$
$480$	−4.38122	+	3.94189i	−0.199975	+	0.179922i
$481$	10.5574	−	18.2860i	0.481377	−	0.833769i
$482$	−0.895749	−	21.4104i	−0.0408002	−	0.975217i
$483$		0			0
$484$	1.80032	+	21.4782i	0.0818326	+	0.976280i
$485$	−2.65900	+	0.712476i	−0.120739	+	0.0323519i
$486$	3.99926	−	17.8853i	0.181410	−	0.811295i
$487$	11.1651	−	6.44618i	0.505939	−	0.292104i	−0.225224	−	0.974307i	$-0.572311\pi$
$487$	11.1651	−	6.44618i	0.505939	−	0.292104i	0.731163	+	0.682203i	$0.238978\pi$
$488$	16.1259	−	6.57663i	0.729987	−	0.297710i
$489$		−	2.70471i		−	0.122311i
$490$		0			0
$491$	5.46128	+	5.46128i	0.246464	+	0.246464i	0.819518	−	0.573054i	$-0.194241\pi$
$491$	5.46128	+	5.46128i	0.246464	+	0.246464i	−0.573054	+	0.819518i	$0.694241\pi$
$492$	38.9133	−	14.0031i	1.75435	−	0.631306i
$493$	−12.3323	−	3.30443i	−0.555418	−	0.148824i
$494$	−12.6833	−	19.9890i	−0.570649	−	0.899348i
$495$	0.157732	−	0.273199i	0.00708951	−	0.0122794i
$496$	−32.9719	+	5.56658i	−1.48048	+	0.249947i
$497$		0			0
$498$	−6.12400	+	0.256210i	−0.274423	+	0.0114811i
$499$	5.80620	+	21.6691i	0.259921	+	0.970040i	0.965286	+	0.261195i	$0.0841166\pi$
$499$	5.80620	+	21.6691i	0.259921	+	0.970040i	−0.705365	+	0.708845i	$0.749217\pi$
$500$	−9.60361	−	1.72945i	−0.429487	−	0.0773435i
$501$	−7.04189	+	26.2807i	−0.314608	+	1.17413i
$502$	0.507076	+	1.61851i	0.0226319	+	0.0722376i
$503$			2.46825i			0.110054i	0.998485	+	0.0550269i	$0.0175245\pi$
$503$			2.46825i			0.110054i	−0.998485	+	0.0550269i	$0.982476\pi$
$504$		0			0
$505$			4.97438i			0.221357i
$506$	−1.66434	+	0.521435i	−0.0739890	+	0.0231806i
$507$	3.89164	−	14.5238i	0.172834	−	0.645025i
$508$	8.84553	+	12.7311i	0.392457	+	0.564853i
$509$	−4.90288	−	18.2978i	−0.217316	−	0.811036i	−0.985338	−	0.170612i	$-0.945425\pi$
$509$	−4.90288	−	18.2978i	−0.217316	−	0.811036i	0.768022	−	0.640424i	$-0.221241\pi$
$510$	0.0795886	+	1.90235i	0.00352424	+	0.0842374i
$511$		0			0
$512$	−8.31546	−	21.0441i	−0.367495	−	0.930025i
$513$	−6.45495	+	11.1803i	−0.284993	+	0.493623i
$514$	−13.9137	+	8.82846i	−0.613709	+	0.389407i
$515$	−7.05780	−	1.89113i	−0.311004	−	0.0833332i
$516$	19.0915	−	40.5557i	0.840457	−	1.78537i
$517$	1.53561	+	1.53561i	0.0675360	+	0.0675360i
$518$		0			0
$519$			11.2130i			0.492198i
$520$	5.86729	+	2.46794i	0.257297	+	0.108226i
$521$	−11.2226	+	6.47937i	−0.491671	+	0.283867i	−0.725268	−	0.688467i	$-0.758284\pi$
$521$	−11.2226	+	6.47937i	−0.491671	+	0.283867i	0.233596	+	0.972334i	$0.424951\pi$
$522$	−18.1910	−	4.06762i	−0.796200	−	0.178035i
$523$	25.9051	−	6.94125i	1.13275	−	0.303520i	0.356718	−	0.934212i	$-0.383896\pi$
$523$	25.9051	−	6.94125i	1.13275	−	0.303520i	0.776033	+	0.630693i	$0.217229\pi$
$524$	2.76863	−	3.27523i	0.120948	−	0.143079i
$525$		0			0
$526$	−25.6887	+	1.07474i	−1.12008	+	0.0468609i
$527$	−5.40147	+	9.35562i	−0.235292	+	0.407537i
$528$	2.50719	+	3.03253i	0.109111	+	0.131974i
$529$	−8.09376	−	14.0188i	−0.351903	−	0.609513i
$530$	−1.82919	+	3.49827i	−0.0794548	+	0.151955i
$531$	8.53258	−	8.53258i	0.370282	−	0.370282i
$532$		0			0
$533$	−31.5837	−	31.5837i	−1.36804	−	1.36804i
$534$	10.8198	+	34.5352i	0.468219	+	1.49448i
$535$	−0.638550	+	0.368667i	−0.0276069	+	0.0159389i
$536$	−5.42236	+	39.5179i	−0.234210	+	1.70691i
$537$	−22.5165	−	12.9999i	−0.971658	−	0.560987i
$538$	33.0568	+	30.4019i	1.42518	+	1.31072i
$539$		0			0
$540$	−0.289940	−	3.45904i	−0.0124770	−	0.148853i
$541$	−4.11365	−	15.3523i	−0.176860	−	0.660049i	−0.996227	−	0.0867808i	$-0.972342\pi$
$541$	−4.11365	−	15.3523i	−0.176860	−	0.660049i	0.819368	−	0.573268i	$-0.194325\pi$
$542$	26.5251	−	16.8306i	1.13935	−	0.722934i
$543$	2.01703	+	3.49359i	0.0865589	+	0.149924i
$544$	−6.95157	−	2.26159i	−0.298046	−	0.0969650i
$545$	3.06571			0.131321
$546$		0			0
$547$	19.2062	−	19.2062i	0.821196	−	0.821196i	−0.165083	−	0.986280i	$-0.552789\pi$
$547$	19.2062	−	19.2062i	0.821196	−	0.821196i	0.986280	+	0.165083i	$0.0527893\pi$
$548$	−10.8066	−	5.08717i	−0.461634	−	0.217313i
$549$	2.12607	−	7.93461i	0.0907386	−	0.338641i
$550$	−0.692569	+	3.09728i	−0.0295313	+	0.132069i
$551$	31.8495	+	18.3883i	1.35683	+	0.783369i
$552$	9.42255	−	12.1418i	0.401051	−	0.516790i
$553$		0			0
$554$	−11.0565	+	12.0221i	−0.469748	+	0.510769i
$555$	4.72513	−	1.26610i	0.200571	−	0.0537428i
$556$	4.56346	−	25.3408i	0.193534	−	1.07469i
$557$	−5.74906	−	1.54045i	−0.243595	−	0.0652712i	0.134956	−	0.990852i	$-0.456911\pi$
$557$	−5.74906	−	1.54045i	−0.243595	−	0.0652712i	−0.378551	+	0.925580i	$0.623577\pi$
$558$	−7.30829	+	13.9769i	−0.309384	+	0.591689i
$559$	−48.4121			−2.04762
$560$		0			0
$561$	1.27119			0.0536698
$562$	−17.5476	+	33.5594i	−0.740203	+	1.41562i
$563$	15.6431	+	4.19155i	0.659276	+	0.176653i	0.572919	−	0.819612i	$-0.305811\pi$
$563$	15.6431	+	4.19155i	0.659276	+	0.176653i	0.0863570	+	0.996264i	$0.472477\pi$
$564$	−18.8338	−	3.39167i	−0.793047	−	0.142815i
$565$	8.52592	−	2.28451i	0.358688	−	0.0961102i
$566$	15.9053	−	17.2942i	0.668548	−	0.726930i
$567$		0			0
$568$	21.3944	−	2.69783i	0.897688	−	0.113199i
$569$	13.0326	+	7.52436i	0.546354	+	0.315437i	0.747650	−	0.664093i	$-0.231182\pi$
$569$	13.0326	+	7.52436i	0.546354	+	0.315437i	−0.201296	+	0.979530i	$0.564515\pi$
$570$	1.19682	−	5.35239i	0.0501294	−	0.224187i
$571$	−4.59003	+	17.1302i	−0.192087	+	0.716877i	0.800915	+	0.598778i	$0.204347\pi$
$571$	−4.59003	+	17.1302i	−0.192087	+	0.716877i	−0.993002	+	0.118099i	$0.962320\pi$
$572$	1.80999	−	3.84493i	0.0756797	−	0.160765i
$573$	2.08367	−	2.08367i	0.0870467	−	0.0870467i
$574$		0			0
$575$	12.3967			0.516978
$576$	−10.2784	−	2.87479i	−0.428268	−	0.119783i
$577$	−23.1600	−	40.1142i	−0.964162	−	1.66998i	−0.711850	−	0.702332i	$-0.752142\pi$
$577$	−23.1600	−	40.1142i	−0.964162	−	1.66998i	−0.252313	−	0.967646i	$-0.581191\pi$
$578$	18.3058	−	11.6153i	0.761423	−	0.483133i
$579$	5.91073	+	22.0592i	0.245642	+	0.916747i
$580$	−9.85381	+	0.825955i	−0.409157	+	0.0342959i
$581$		0			0
$582$	−11.9205	−	10.9631i	−0.494120	−	0.454436i
$583$	2.28249	+	1.31780i	0.0945312	+	0.0545776i
$584$	0.951527	+	1.25418i	0.0393745	+	0.0518982i
$585$	2.60010	−	1.50117i	0.107501	−	0.0620656i
$586$	9.10399	+	29.0585i	0.376082	+	1.20040i
$587$	−4.90812	−	4.90812i	−0.202580	−	0.202580i	0.598525	−	0.801104i	$-0.295754\pi$
$587$	−4.90812	−	4.90812i	−0.202580	−	0.202580i	−0.801104	+	0.598525i	$0.795754\pi$
$588$		0			0
$589$	22.0039	−	22.0039i	0.906654	−	0.906654i
$590$	2.96612	−	5.67263i	0.122113	−	0.233538i
$591$	13.1427	+	22.7637i	0.540616	+	0.936375i
$592$	−1.77312	+	18.6976i	−0.0728749	+	0.768468i
$593$	−12.0345	+	20.8443i	−0.494196	+	0.855972i	−0.999978	−	0.00668902i	$-0.997871\pi$
$593$	−12.0345	+	20.8443i	−0.494196	+	0.855972i	0.505782	+	0.862662i	$0.331204\pi$
$594$	−2.31546	+	0.0968722i	−0.0950046	+	0.00397471i
$595$		0			0
$596$	6.77646	+	5.72830i	0.277575	+	0.234640i
$597$	−17.6027	+	4.71662i	−0.720429	+	0.193038i
$598$	−16.1991	−	3.62220i	−0.662430	−	0.148123i
$599$	−5.33990	+	3.08299i	−0.218182	+	0.125968i	−0.605108	−	0.796143i	$-0.706870\pi$
$599$	−5.33990	+	3.08299i	−0.218182	+	0.125968i	0.386926	+	0.922111i	$0.373537\pi$
$600$	−10.5613	−	25.8964i	−0.431163	−	1.05721i
$601$		−	16.2922i		−	0.664572i	−0.943179	−	0.332286i	$-0.892180\pi$
$601$		−	16.2922i		−	0.664572i	0.943179	−	0.332286i	$-0.107820\pi$
$602$		0			0
$603$	13.3038	+	13.3038i	0.541773	+	0.541773i
$604$	−21.7605	−	10.2437i	−0.885422	−	0.416811i
$605$	5.20932	+	1.39583i	0.211789	+	0.0567487i
$606$	−24.7108	+	15.6793i	−1.00381	+	0.636929i
$607$	17.4917	−	30.2966i	0.709968	−	1.22970i	−0.254900	−	0.966967i	$-0.582043\pi$
$607$	17.4917	−	30.2966i	0.709968	−	1.22970i	0.964868	−	0.262733i	$-0.0846240\pi$
$608$	17.6558	+	11.4753i	0.716037	+	0.465383i
$609$		0			0
$610$	−0.182153	−	4.35386i	−0.00737515	−	0.176283i
$611$	5.34937	+	19.9641i	0.216412	+	0.807661i
$612$	−2.83168	+	1.96744i	−0.114464	+	0.0795290i
$613$	5.53096	−	20.6418i	0.223393	−	0.833715i	−0.759649	−	0.650334i	$-0.774629\pi$
$613$	5.53096	−	20.6418i	0.223393	−	0.833715i	0.983042	−	0.183381i	$-0.0587042\pi$
$614$	26.2605	−	8.22739i	1.05979	−	0.332030i
$615$		−	10.3481i		−	0.417275i
$616$		0			0
$617$			2.21451i			0.0891526i	0.999006	+	0.0445763i	$0.0141938\pi$
$617$			2.21451i			0.0891526i	−0.999006	+	0.0445763i	$0.985806\pi$
$618$	−12.8519	−	41.0212i	−0.516979	−	1.65012i
$619$	0.725777	−	2.70864i	0.0291714	−	0.108869i	−0.949805	−	0.312842i	$-0.898719\pi$
$619$	0.725777	−	2.70864i	0.0291714	−	0.108869i	0.978977	+	0.203973i	$0.0653855\pi$
$620$	−1.48290	+	8.23449i	−0.0595546	+	0.330705i
$621$	2.34285	+	8.74364i	0.0940154	+	0.350870i
$622$	−14.8054	+	0.619414i	−0.593642	+	0.0248362i
$623$		0			0
$624$	6.23403	+	36.9253i	0.249561	+	1.47820i
$625$	10.6531	−	18.4517i	0.426123	−	0.738067i
$626$	−24.8867	−	39.2217i	−0.994672	−	1.56761i
$627$	−3.53694	−	0.947720i	−0.141252	−	0.0378483i
$628$	8.00519	+	22.2458i	0.319442	+	0.887703i
$629$	4.29052	+	4.29052i	0.171074	+	0.171074i
$630$		0			0
$631$		−	24.6123i		−	0.979801i	−0.871778	−	0.489900i	$-0.837033\pi$
$631$		−	24.6123i		−	0.979801i	0.871778	−	0.489900i	$-0.162967\pi$
$632$	3.88269	+	1.63316i	0.154445	+	0.0649637i
$633$	−25.2128	+	14.5566i	−1.00212	+	0.578573i
$634$	−2.59424	+	11.6019i	−0.103030	+	0.460769i
$635$	3.74682	−	1.00396i	0.148688	−	0.0398409i
$636$	−23.1437	+	1.93992i	−0.917706	+	0.0769229i
$637$		0			0
$638$	0.275961	+	6.59609i	0.0109254	+	0.261142i
$639$	5.08560	−	8.80852i	0.201183	−	0.348460i
$640$	−5.65910	+	0.174862i	−0.223696	+	0.00691202i
$641$	11.7655	+	20.3784i	0.464709	+	0.804899i	0.999188	−	0.0402822i	$-0.0128257\pi$
$641$	11.7655	+	20.3784i	0.464709	+	0.804899i	−0.534480	+	0.845181i	$0.679492\pi$
$642$	−3.84411	−	2.01002i	−0.151715	−	0.0793293i
$643$	8.79484	−	8.79484i	0.346835	−	0.346835i	−0.512095	−	0.858929i	$-0.671130\pi$
$643$	8.79484	−	8.79484i	0.346835	−	0.346835i	0.858929	+	0.512095i	$0.171130\pi$
$644$		0			0
$645$	−7.93089	−	7.93089i	−0.312278	−	0.312278i
$646$	6.49180	−	2.03387i	0.255416	−	0.0800215i
$647$	18.3033	−	10.5674i	0.719577	−	0.415448i	−0.0950202	−	0.995475i	$-0.530292\pi$
$647$	18.3033	−	10.5674i	0.719577	−	0.415448i	0.814597	+	0.580028i	$0.196958\pi$
$648$	25.2878	−	19.1855i	0.993397	−	0.753676i
$649$	−3.70118	−	2.13688i	−0.145284	−	0.0838798i
$650$	−20.4470	+	22.2326i	−0.801999	+	0.872036i
$651$		0			0
$652$	1.67743	−	1.98437i	0.0656934	−	0.0777139i
$653$	2.44159	+	9.11215i	0.0955470	+	0.356586i	0.997102	−	0.0760787i	$-0.0242400\pi$
$653$	2.44159	+	9.11215i	0.0955470	+	0.356586i	−0.901555	+	0.432665i	$0.857573\pi$
$654$	9.66316	+	15.2292i	0.377859	+	0.595510i
$655$	−0.536549	−	0.929331i	−0.0209647	−	0.0363120i
$656$	37.2342	+	13.8600i	1.45375	+	0.541143i
$657$	0.742557			0.0289699
$658$		0			0
$659$	−2.68220	+	2.68220i	−0.104484	+	0.104484i	−0.757416	−	0.652932i	$-0.773539\pi$
$659$	−2.68220	+	2.68220i	−0.104484	+	0.104484i	0.652932	+	0.757416i	$0.273539\pi$
$660$	0.926392	−	0.333364i	0.0360597	−	0.0129762i
$661$	0.212553	−	0.793258i	0.00826735	−	0.0308542i	−0.961669	−	0.274213i	$-0.911583\pi$
$661$	0.212553	−	0.793258i	0.00826735	−	0.0308542i	0.969936	+	0.243359i	$0.0782493\pi$
$662$	0.701937	+	0.156957i	0.0272815	+	0.00610030i
$663$	10.4774	+	6.04912i	0.406908	+	0.234928i
$664$	−4.65191	−	3.61007i	−0.180529	−	0.140098i
$665$		0			0
$666$	6.52053	+	5.99684i	0.252665	+	0.232373i
$667$	24.9081	−	6.67412i	0.964447	−	0.258423i
$668$	−21.4655	+	14.9141i	−0.830524	+	0.577044i
$669$	−12.3165	−	3.30020i	−0.476184	−	0.127593i
$670$	8.84464	+	4.62472i	0.341698	+	0.178668i
$671$	−2.90935			−0.112314
$672$		0			0
$673$	−7.60472			−0.293140			−0.146570	−	0.989200i	$-0.546823\pi$
$673$	−7.60472			−0.293140			−0.146570	+	0.989200i	$0.546823\pi$
$674$	33.8733	+	17.7118i	1.30475	+	0.682232i
$675$	15.9108	+	4.26330i	0.612409	+	0.164094i
$676$	11.8627	−	8.24215i	0.456258	−	0.317006i
$677$	−28.9188	+	7.74876i	−1.11144	+	0.297809i	−0.767414	−	0.641152i	$-0.778457\pi$
$677$	−28.9188	+	7.74876i	−1.11144	+	0.297809i	−0.344024	+	0.938961i	$0.611790\pi$
$678$	38.2224	+	35.1526i	1.46792	+	1.35003i
$679$		0			0
$680$	−1.12143	+	1.44506i	−0.0430047	+	0.0554155i
$681$	−14.1133	−	8.14831i	−0.540822	−	0.312244i
$682$	5.45148	+	1.21898i	0.208748	+	0.0466772i
$683$	2.15611	−	8.04672i	0.0825013	−	0.307899i	−0.912328	−	0.409460i	$-0.865717\pi$
$683$	2.15611	−	8.04672i	0.0825013	−	0.307899i	0.994829	+	0.101561i	$0.0323837\pi$
$684$	9.34561	−	3.36304i	0.357338	−	0.128589i
$685$	−2.11328	+	2.11328i	−0.0807444	+	0.0807444i
$686$		0			0
$687$	37.6627			1.43692
$688$	39.1592	−	17.9142i	1.49293	−	0.682973i
$689$	12.5418	+	21.7230i	0.477804	+	0.827581i
$690$	−2.06035	−	3.24713i	−0.0784361	−	0.123616i
$691$	−4.38774	−	16.3753i	−0.166918	−	0.622945i	−0.997788	−	0.0664786i	$-0.978824\pi$
$691$	−4.38774	−	16.3753i	−0.166918	−	0.622945i	0.830870	−	0.556466i	$-0.187843\pi$
$692$	−6.95422	+	8.22670i	−0.264360	+	0.312732i
$693$		0			0
$694$	3.45904	−	3.76111i	0.131303	−	0.142770i
$695$	−5.57956	−	3.22136i	−0.211645	−	0.122193i
$696$	−35.1624	−	46.3464i	−1.33283	−	1.75676i
$697$	11.1159	−	6.41779i	0.421046	−	0.243091i
$698$	−5.39498	+	1.69024i	−0.204203	+	0.0639765i
$699$	−36.2659	−	36.2659i	−1.37170	−	1.37170i
$700$		0			0
$701$	−12.6791	+	12.6791i	−0.478882	+	0.478882i	−0.904774	−	0.425892i	$-0.859960\pi$
$701$	−12.6791	+	12.6791i	−0.478882	+	0.478882i	0.425892	+	0.904774i	$0.359960\pi$
$702$	−19.5454	−	10.2200i	−0.737694	−	0.385728i
$703$	−8.73912	−	15.1366i	−0.329602	−	0.570888i
$704$	−0.0412897	+	3.77982i	−0.00155616	+	0.142457i
$705$	−2.39419	+	4.14686i	−0.0901704	+	0.156180i
$706$	−0.0501864	−	1.19957i	−0.00188879	−	0.0451464i
$707$		0			0
$708$	37.5286	−	3.14568i	1.41041	−	0.118222i
$709$	15.4700	−	4.14517i	0.580987	−	0.155675i	0.0436562	−	0.999047i	$-0.486099\pi$
$709$	15.4700	−	4.14517i	0.580987	−	0.155675i	0.537331	+	0.843372i	$0.319433\pi$
$710$	1.17742	−	5.26563i	0.0441879	−	0.197616i
$711$	1.72062	−	0.993401i	0.0645283	−	0.0372554i
$712$	−13.4802	+	32.0479i	−0.505192	+	1.20104i
$713$		−	21.8193i		−	0.817138i
$714$		0			0
$715$	−0.751898	−	0.751898i	−0.0281194	−	0.0281194i
$716$	−8.45731	−	23.5022i	−0.316065	−	0.878318i
$717$	−21.8876	−	5.86476i	−0.817406	−	0.219023i
$718$	−21.7583	−	34.2913i	−0.812012	−	1.27974i
$719$	−0.669732	+	1.16001i	−0.0249768	+	0.0432611i	−0.878244	−	0.478213i	$-0.841285\pi$
$719$	−0.669732	+	1.16001i	−0.0249768	+	0.0432611i	0.853267	+	0.521475i	$0.174618\pi$
$720$	−1.54766	+	2.17638i	−0.0576778	+	0.0811089i
$721$		0			0
$722$	7.26762	−	0.304056i	0.270473	−	0.0113158i
$723$	−8.16462	−	30.4708i	−0.303645	−	1.13322i
$724$	−0.686856	+	3.81409i	−0.0255268	+	0.141750i
$725$	12.1449	−	45.3255i	0.451051	−	1.68335i
$726$	9.48590	+	30.2775i	0.352055	+	1.12370i
$727$			3.87352i			0.143661i	0.997417	+	0.0718304i	$0.0228840\pi$
$727$			3.87352i			0.143661i	−0.997417	+	0.0718304i	$0.977116\pi$
$728$		0			0
$729$			6.68839i			0.247718i
$730$	0.375898	−	0.117768i	0.0139126	−	0.00435880i
$731$	3.60071	−	13.4380i	0.133177	−	0.497024i
$732$	21.0541	−	14.6283i	0.778183	−	0.540678i
$733$	−11.0490	−	41.2353i	−0.408103	−	1.52306i	−0.798261	−	0.602312i	$-0.794246\pi$
$733$	−11.0490	−	41.2353i	−0.408103	−	1.52306i	0.390158	−	0.920748i	$-0.372420\pi$
$734$	1.25910	+	30.0952i	0.0464741	+	1.11083i
$735$		0			0
$736$	14.4433	−	3.06434i	0.532387	−	0.112953i
$737$	3.33178	−	5.77081i	0.122728	−	0.212570i
$738$	15.8234	−	10.0402i	0.582467	−	0.369583i
$739$	−26.0274	−	6.97402i	−0.957434	−	0.256544i	−0.253920	−	0.967225i	$-0.581720\pi$
$739$	−26.0274	−	6.97402i	−0.957434	−	0.256544i	−0.703514	+	0.710682i	$0.748387\pi$
$740$	4.25192	+	2.00158i	0.156304	+	0.0735797i
$741$	−24.6422	−	24.6422i	−0.905254	−	0.905254i
$742$		0			0
$743$			13.4783i			0.494470i	0.968956	+	0.247235i	$0.0795219\pi$
$743$			13.4783i			0.494470i	−0.968956	+	0.247235i	$0.920478\pi$
$744$	−45.5798	+	18.5888i	−1.67104	+	0.681498i
$745$	1.92279	−	1.11012i	0.0704455	−	0.0406717i
$746$	−10.8952	−	2.43622i	−0.398901	−	0.0891964i
$747$	−2.68279	+	0.718850i	−0.0981580	+	0.0263014i
$748$	0.932639	+	0.788382i	0.0341007	+	0.0288261i
$749$		0			0
$750$	−14.3523	+	0.600456i	−0.524070	+	0.0219256i
$751$	17.8616	−	30.9372i	0.651780	−	1.12892i	−0.330911	−	0.943662i	$-0.607356\pi$
$751$	17.8616	−	30.9372i	0.651780	−	1.12892i	0.982691	−	0.185254i	$-0.0593108\pi$
$752$	−11.7144	−	14.1689i	−0.427180	−	0.516688i
$753$	1.24839	+	2.16228i	0.0454940	+	0.0787980i
$754$	−29.1138	+	55.6793i	−1.06026	+	2.02772i
$755$	−4.25538	+	4.25538i	−0.154869	+	0.154869i
$756$		0			0
$757$	10.1603	+	10.1603i	0.369284	+	0.369284i	0.867216	−	0.497932i	$-0.165907\pi$
$757$	10.1603	+	10.1603i	0.369284	+	0.369284i	−0.497932	+	0.867216i	$0.665907\pi$
$758$	7.20167	+	22.9866i	0.261576	+	0.834911i
$759$	−2.22351	+	1.28375i	−0.0807085	+	0.0465971i
$760$	4.19757	−	3.18464i	0.152262	−	0.115519i
$761$	−19.1505	−	11.0565i	−0.694205	−	0.400799i	0.110980	−	0.993823i	$-0.464601\pi$
$761$	−19.1505	−	11.0565i	−0.694205	−	0.400799i	−0.805185	+	0.593023i	$0.797934\pi$
$762$	16.7973	+	15.4483i	0.608503	+	0.559631i
$763$		0			0
$764$	2.82101	−	0.236459i	0.102061	−	0.00855480i
$765$	0.223302	+	0.833375i	0.00807351	+	0.0301307i
$766$	−0.101890	+	0.0646507i	−0.00368144	+	0.00233593i
$767$	−20.3372	−	35.2250i	−0.734332	−	1.27190i
$768$	−18.7062	−	27.5610i	−0.675002	−	0.994523i
$769$	−18.2859			−0.659405			−0.329702	−	0.944085i	$-0.606948\pi$
$769$	−18.2859			−0.659405			−0.329702	+	0.944085i	$0.606948\pi$
$770$		0			0
$771$	−17.1527	+	17.1527i	−0.617739	+	0.617739i
$772$	−9.34434	+	19.8500i	−0.336310	+	0.714416i
$773$	−3.34971	+	12.5013i	−0.120481	+	0.449640i	−0.999638	−	0.0268907i	$-0.991439\pi$
$773$	−3.34971	+	12.5013i	−0.120481	+	0.449640i	0.879158	+	0.476531i	$0.158106\pi$
$774$	4.43233	−	19.8221i	0.159317	−	0.712491i
$775$	−34.3852	−	19.8523i	−1.23515	−	0.713116i
$776$	−1.94652	−	15.4363i	−0.0698760	−	0.554131i
$777$		0			0
$778$	0.713596	−	0.775912i	0.0255836	−	0.0278178i
$779$	−35.7134	+	9.56938i	−1.27957	+	0.342859i
$780$	9.22182	+	1.66070i	0.330194	+	0.0594626i
$781$	−3.47961	−	0.932359i	−0.124510	−	0.0333624i
$782$	2.21026	−	4.22706i	0.0790388	−	0.151160i
$783$	34.2642			1.22450
$784$		0			0
$785$	5.91574			0.211142
$786$	2.92534	−	5.59463i	0.104343	−	0.199554i
$787$	−33.0828	−	8.86450i	−1.17927	−	0.315985i	−0.384635	−	0.923069i	$-0.625673\pi$
$787$	−33.0828	−	8.86450i	−1.17927	−	0.315985i	−0.794638	+	0.607083i	$0.792339\pi$
$788$	−4.47545	+	24.8521i	−0.159431	+	0.885318i
$789$	−36.5595	+	9.79610i	−1.30155	+	0.348750i
$790$	0.713463	−	0.775769i	0.0253839	−	0.0276006i
$791$		0			0
$792$	1.40858	+	1.09311i	0.0500516	+	0.0388421i
$793$	−23.9794	−	13.8445i	−0.851532	−	0.491632i
$794$	−6.60858	+	29.5546i	−0.234530	+	1.04886i
$795$	−1.50407	+	5.61327i	−0.0533439	+	0.199082i
$796$	−15.8398	−	7.45654i	−0.561426	−	0.264290i
$797$	−12.6836	+	12.6836i	−0.449277	+	0.449277i	−0.895114	−	0.445837i	$-0.852906\pi$
$797$	−12.6836	+	12.6836i	−0.449277	+	0.449277i	0.445837	+	0.895114i	$0.352906\pi$
$798$		0			0
$799$	−5.93942			−0.210121
$800$	8.31215	−	25.5495i	0.293879	−	0.903310i
$801$	8.19957	+	14.2021i	0.289718	+	0.501805i
$802$	−41.0321	+	26.0354i	−1.44889	+	0.919343i
$803$	−0.0680676	−	0.254032i	−0.00240205	−	0.00896459i
$804$	4.90468	+	58.5139i	0.172975	+	2.06363i
$805$		0			0
$806$	39.1313	+	35.9885i	1.37834	+	1.26764i
$807$	57.2561	+	33.0568i	2.01551	+	1.16366i
$808$	−27.8538	−	3.82189i	−0.979892	−	0.134454i
$809$	7.52353	−	4.34371i	0.264513	−	0.152717i	−0.361878	−	0.932225i	$-0.617864\pi$
$809$	7.52353	−	4.34371i	0.264513	−	0.152717i	0.626392	+	0.779509i	$0.284531\pi$
$810$	−2.37454	−	7.57917i	−0.0834329	−	0.266305i
$811$	2.41161	+	2.41161i	0.0846830	+	0.0846830i	0.748179	−	0.663496i	$-0.230928\pi$
$811$	2.41161	+	2.41161i	0.0846830	+	0.0846830i	−0.663496	+	0.748179i	$0.730928\pi$
$812$		0			0
$813$	32.6998	−	32.6998i	1.14683	−	1.14683i
$814$	1.45383	−	2.78041i	0.0509567	−	0.0974533i
$815$	−0.325080	−	0.563055i	−0.0113871	−	0.0197229i
$816$	−10.7132	−	1.01595i	−0.375038	−	0.0355654i
$817$	−20.0371	+	34.7052i	−0.701008	+	1.21418i
$818$	−21.8561	+	0.914397i	−0.764182	+	0.0319711i
$819$		0			0
$820$	6.41779	−	7.59211i	0.224119	−	0.265128i
$821$	9.05181	−	2.42543i	0.315910	−	0.0846479i	−0.0973798	−	0.995247i	$-0.531046\pi$
$821$	9.05181	−	2.42543i	0.315910	−	0.0846479i	0.413290	+	0.910599i	$0.364379\pi$
$822$	−17.1591	−	3.83686i	−0.598491	−	0.133826i
$823$	−8.76954	+	5.06310i	−0.305687	+	0.176488i	−0.644995	−	0.764187i	$-0.723140\pi$
$823$	−8.76954	+	5.06310i	−0.305687	+	0.176488i	0.339308	+	0.940675i	$0.389807\pi$
$824$	16.0119	−	38.0668i	0.557801	−	1.32612i
$825$			4.67208i			0.162661i
$826$		0			0
$827$	2.96806	+	2.96806i	0.103209	+	0.103209i	0.756826	−	0.653617i	$-0.226749\pi$
$827$	2.96806	+	2.96806i	0.103209	+	0.103209i	−0.653617	+	0.756826i	$0.726749\pi$
$828$	2.96618	−	6.30100i	0.103082	−	0.218975i
$829$	−41.8251	−	11.2070i	−1.45265	−	0.389235i	−0.555702	−	0.831381i	$-0.687551\pi$
$829$	−41.8251	−	11.2070i	−1.45265	−	0.389235i	−0.896943	+	0.442146i	$0.854217\pi$
$830$	−1.24408	+	0.789383i	−0.0431825	+	0.0273999i
$831$	−12.0221	+	20.8229i	−0.417042	+	0.722337i
$832$	−18.3270	+	30.9574i	−0.635375	+	1.07325i
$833$		0			0
$834$	−1.58441	−	37.8709i	−0.0548635	−	1.31136i
$835$	1.69273	+	6.31737i	0.0585795	+	0.218622i
$836$	−2.00719	−	2.88889i	−0.0694200	−	0.0999144i
$837$	7.50377	−	28.0044i	0.259368	−	0.967975i
$838$	−49.9869	+	15.6608i	−1.72677	+	0.540994i
$839$		−	51.7749i		−	1.78747i	−0.448598	−	0.893734i	$-0.648076\pi$
$839$		−	51.7749i		−	1.78747i	0.448598	−	0.893734i	$-0.351924\pi$
$840$		0			0
$841$		−	68.6090i		−	2.36583i
$842$	12.1752	+	38.8613i	0.419585	+	1.33925i
$843$	−14.4288	+	53.8489i	−0.496953	+	1.85465i
$844$	−27.5258	−	4.95694i	−0.947476	−	0.170625i
$845$	−0.935475	−	3.49124i	−0.0321813	−	0.120102i
$846$	−8.66396	+	0.362475i	−0.297873	+	0.0124621i
$847$		0			0
$848$	−18.1830	−	12.9302i	−0.624406	−	0.444025i
$849$	17.2942	−	29.9545i	0.593536	−	1.02803i
$850$	−4.65046	−	7.32918i	−0.159510	−	0.251389i
$851$	−11.8377	−	3.17190i	−0.405791	−	0.108731i
$852$	29.8688	−	10.7484i	1.02329	−	0.368233i
$853$	5.56576	+	5.56576i	0.190568	+	0.190568i	0.795941	−	0.605374i	$-0.206976\pi$
$853$	5.56576	+	5.56576i	0.190568	+	0.190568i	−0.605374	+	0.795941i	$0.706976\pi$
$854$		0			0
$855$		−	2.48524i		−	0.0849936i
$856$	−1.57372	−	3.85878i	−0.0537888	−	0.131890i
$857$	28.0770	−	16.2103i	0.959093	−	0.553733i	0.0631996	−	0.998001i	$-0.479870\pi$
$857$	28.0770	−	16.2103i	0.959093	−	0.553733i	0.895894	+	0.444268i	$0.146536\pi$
$858$	1.36514	−	6.10512i	0.0466051	−	0.208425i
$859$	10.4855	−	2.80958i	0.357761	−	0.0958618i	−0.0754617	−	0.997149i	$-0.524043\pi$
$859$	10.4855	−	2.80958i	0.357761	−	0.0958618i	0.433223	+	0.901287i	$0.357376\pi$
$860$	−0.900012	−	10.7373i	−0.0306902	−	0.366140i
$861$		0			0
$862$	1.49074	+	35.6321i	0.0507748	+	1.21363i
$863$	16.5015	−	28.5814i	0.561716	−	0.972921i	−0.435631	−	0.900126i	$-0.643475\pi$
$863$	16.5015	−	28.5814i	0.561716	−	0.972921i	0.997347	−	0.0727955i	$-0.0231921\pi$
$864$	19.5915	+	1.03413i	0.666515	+	0.0351819i
$865$	1.34770	+	2.33428i	0.0458232	+	0.0793681i
$866$	−14.7978	−	7.73752i	−0.502850	−	0.262932i
$867$	22.5672	−	22.5672i	0.766423	−	0.766423i
$868$		0			0
$869$	−0.497570	−	0.497570i	−0.0168789	−	0.0168789i
$870$	−13.8908	+	4.35197i	−0.470943	+	0.147546i
$871$	54.9221	−	31.7093i	1.86096	−	1.07443i
$872$	−2.35543	+	17.1663i	−0.0797650	+	0.581323i
$873$	−6.35546	−	3.66933i	−0.215100	−	0.124188i
$874$	−9.30121	+	10.1135i	−0.314618	+	0.342093i
$875$		0			0
$876$	1.76986	+	1.49611i	0.0597981	+	0.0505488i
$877$	−12.3637	−	46.1420i	−0.417493	−	1.55810i	−0.779789	−	0.626042i	$-0.784674\pi$
$877$	−12.3637	−	46.1420i	−0.417493	−	1.55810i	0.362296	−	0.932063i	$-0.381993\pi$
$878$	20.7933	+	32.7704i	0.701739	+	1.10595i
$879$	22.4136	+	38.8214i	0.755990	+	1.30941i
$880$	0.886417	+	0.329959i	0.0298811	+	0.0111229i
$881$	46.9509			1.58181			0.790907	−	0.611936i	$-0.209609\pi$
$881$	46.9509			1.58181			0.790907	+	0.611936i	$0.209609\pi$
$882$		0			0
$883$	13.8628	−	13.8628i	0.466522	−	0.466522i	−0.434264	−	0.900786i	$-0.642991\pi$
$883$	13.8628	−	13.8628i	0.466522	−	0.466522i	0.900786	+	0.434264i	$0.142991\pi$
$884$	3.93536	+	10.9360i	0.132360	+	0.367819i
$885$	2.43893	−	9.10221i	0.0819837	−	0.305967i
$886$	39.9238	+	8.92718i	1.34127	+	0.299914i
$887$	−6.75025	−	3.89726i	−0.226651	−	0.130857i	0.382375	−	0.924007i	$-0.375106\pi$
$887$	−6.75025	−	3.89726i	−0.226651	−	0.130857i	−0.609026	+	0.793150i	$0.708440\pi$
$888$	3.45904	+	27.4309i	0.116078	+	0.920520i
$889$		0			0
$890$	6.40322	+	5.88895i	0.214637	+	0.197398i
$891$	−5.12200	+	1.37244i	−0.171593	+	0.0459783i
$892$	−6.98953	−	10.0598i	−0.234027	−	0.336829i
$893$	16.5257	+	4.42805i	0.553011	+	0.148179i
$894$	11.5753	+	6.05253i	0.387136	+	0.202427i
$895$	−6.24985			−0.208910
$896$		0			0
$897$	−24.4354			−0.815875
$898$	−30.3904	−	15.8907i	−1.01414	−	0.530278i
$899$	−79.7767	−	21.3761i	−2.66070	−	0.712933i
$900$	−7.23103	−	10.4074i	−0.241034	−	0.346914i
$901$	−6.96259	+	1.86562i	−0.231958	+	0.0621528i
$902$	−4.88525	−	4.49290i	−0.162661	−	0.149597i
$903$		0			0
$904$	6.24141	+	49.4956i	0.207586	+	1.64620i
$905$	0.839792	+	0.484854i	0.0279156	+	0.0161171i
$906$	−34.5521	−	7.72604i	−1.14792	−	0.256680i
$907$	−2.48814	+	9.28586i	−0.0826173	+	0.308332i	−0.994852	−	0.101335i	$-0.967689\pi$
$907$	−2.48814	+	9.28586i	−0.0826173	+	0.308332i	0.912235	+	0.409667i	$0.134355\pi$
$908$	−5.30102	−	14.7311i	−0.175921	−	0.488869i
$909$	−9.37705	+	9.37705i	−0.311017	+	0.311017i
$910$		0			0
$911$	−6.36372			−0.210839			−0.105420	−	0.994428i	$-0.533619\pi$
$911$	−6.36372			−0.210839			−0.105420	+	0.994428i	$0.533619\pi$
$912$	29.0508	+	10.8139i	0.961970	+	0.358083i
$913$	0.491843	+	0.851898i	0.0162776	+	0.0281937i
$914$	10.3085	+	16.2463i	0.340975	+	0.537381i
$915$	−1.66030	−	6.19631i	−0.0548877	−	0.204844i
$916$	27.6321	+	23.3580i	0.912989	+	0.771771i
$917$		0			0
$918$	4.29052	−	4.66521i	0.141608	−	0.153975i
$919$	−14.5846	−	8.42040i	−0.481100	−	0.277763i	0.239775	−	0.970829i	$-0.422926\pi$
$919$	−14.5846	−	8.42040i	−0.481100	−	0.277763i	−0.720875	+	0.693065i	$0.756260\pi$
$920$	0.502218	−	3.66013i	0.0165576	−	0.120671i
$921$	35.0834	−	20.2554i	1.15604	−	0.667438i
$922$	53.7723	−	16.8468i	1.77090	−	0.554819i
$923$	−24.2428	−	24.2428i	−0.797961	−	0.797961i
$924$		0			0
$925$	−15.7692	+	15.7692i	−0.518487	+	0.518487i
$926$	−36.6953	−	19.1874i	−1.20588	−	0.630536i
$927$	−9.73953	−	16.8694i	−0.319888	−	0.554062i
$928$	2.94595	−	55.8105i	0.0967056	−	1.83207i
$929$	10.8991	−	18.8778i	0.357587	−	0.619360i	−0.629970	−	0.776620i	$-0.716933\pi$
$929$	10.8991	−	18.8778i	0.357587	−	0.619360i	0.987557	+	0.157260i	$0.0502661\pi$
$930$	0.514853	+	12.3062i	0.0168827	+	0.403535i
$931$		0			0
$932$	−4.11552	−	49.0990i	−0.134808	−	1.60829i
$933$	−21.0707	+	5.64587i	−0.689822	+	0.184837i
$934$	−9.69607	+	43.3624i	−0.317265	+	1.41886i
$935$	0.264632	−	0.152785i	0.00865438	−	0.00499661i
$936$	6.40801	+	15.7125i	0.209452	+	0.513578i
$937$		−	21.3450i		−	0.697310i	−0.937251	−	0.348655i	$-0.886639\pi$
$937$		−	21.3450i		−	0.697310i	0.937251	−	0.348655i	$-0.113361\pi$
$938$		0			0
$939$	−48.3520	−	48.3520i	−1.57791	−	1.57791i
$940$	−4.32839	+	1.55758i	−0.141177	+	0.0508027i
$941$	50.3151	+	13.4819i	1.64022	+	0.439497i	0.956853	−	0.290574i	$-0.0938462\pi$
$941$	50.3151	+	13.4819i	1.64022	+	0.439497i	0.683372	+	0.730071i	$0.260513\pi$
$942$	18.6465	+	29.3871i	0.607536	+	0.957483i
$943$	−12.9623	+	22.4514i	−0.422112	+	0.731119i
$944$	29.4846	+	20.9670i	0.959643	+	0.682418i
$945$		0			0
$946$	−7.18752	+	0.300705i	−0.233686	+	0.00977675i
$947$	0.564067	+	2.10513i	0.0183297	+	0.0684074i	0.974485	−	0.224453i	$-0.0720595\pi$
$947$	0.564067	+	2.10513i	0.0183297	+	0.0684074i	−0.956155	+	0.292860i	$0.905393\pi$
$948$	6.10256	+	1.09897i	0.198202	+	0.0356929i
$949$	0.647815	−	2.41768i	0.0210290	−	0.0784812i
$950$	7.47518	+	23.8596i	0.242527	+	0.774109i
$951$			17.5008i			0.567502i
$952$		0			0
$953$		−	7.31316i		−	0.236897i	−0.992960	−	0.118448i	$-0.962208\pi$
$953$		−	7.31316i		−	0.236897i	0.992960	−	0.118448i	$-0.0377920\pi$
$954$	−10.0426	+	3.14634i	−0.325142	+	0.101867i
$955$	0.183333	−	0.684208i	0.00593252	−	0.0221405i
$956$	−12.4210	−	17.8773i	−0.401725	−	0.578192i
$957$	2.51535	+	9.38740i	0.0813096	+	0.303452i
$958$	−1.98640	−	47.4793i	−0.0641775	−	1.53399i
$959$		0			0
$960$	−8.07378	+	2.06911i	−0.260580	+	0.0667803i
$961$	−19.4418	+	33.6741i	−0.627153	+	1.08626i
$962$	25.2136	−	15.9984i	0.812919	−	0.515808i
$963$	−1.89868	−	0.508749i	−0.0611840	−	0.0163942i
$964$	12.9075	−	27.4192i	0.415723	−	0.883112i
$965$	3.88177	+	3.88177i	0.124959	+	0.124959i
$966$		0			0
$967$			42.1882i			1.35668i	0.734748	+	0.678341i	$0.237301\pi$
$967$			42.1882i			1.35668i	−0.734748	+	0.678341i	$0.762699\pi$
$968$	−11.8183	+	28.0968i	−0.379854	+	0.903067i
$969$	8.67287	−	5.00728i	0.278613	−	0.160857i
$970$	−3.79922	−	0.849526i	−0.121986	−	0.0272766i
$971$	57.7769	−	15.4813i	1.85415	−	0.496818i	0.854408	−	0.519603i	$-0.173920\pi$
$971$	57.7769	−	15.4813i	1.85415	−	0.496818i	0.999740	+	0.0227850i	$0.00725333\pi$
$972$	16.7321	−	19.7938i	0.536684	−	0.634886i
$973$		0			0
$974$	18.2166	−	0.762130i	0.583698	−	0.0244202i
$975$	−22.2326	+	38.5080i	−0.712014	+	1.23324i
$976$	24.5192	+	2.32519i	0.784839	+	0.0744274i
$977$	3.53396	+	6.12099i	0.113061	+	0.195828i	0.917003	−	0.398880i	$-0.130601\pi$
$977$	3.53396	+	6.12099i	0.113061	+	0.195828i	−0.803942	+	0.594708i	$0.797268\pi$
$978$	1.77238	−	3.38963i	0.0566744	−	0.108388i
$979$	4.10696	−	4.10696i	0.131259	−	0.131259i
$980$		0			0
$981$	5.77907	+	5.77907i	0.184512	+	0.184512i
$982$	3.26550	+	10.4230i	0.104206	+	0.332611i
$983$	−36.6563	+	21.1635i	−1.16915	+	0.675011i	−0.953480	−	0.301455i	$-0.902528\pi$
$983$	−36.6563	+	21.1635i	−1.16915	+	0.675011i	−0.215673	+	0.976466i	$0.569194\pi$
$984$	57.9436	+	7.95060i	1.84717	+	0.253456i
$985$	5.47196	+	3.15924i	0.174351	+	0.100662i
$986$	−13.2898	−	12.2225i	−0.423235	−	0.389243i
$987$		0			0
$988$	−2.79644	−	33.3621i	−0.0889667	−	1.06139i
$989$	7.27254	+	27.1415i	0.231253	+	0.863049i
$990$	0.376700	−	0.239021i	0.0119723	−	0.00759660i
$991$	−8.73586	−	15.1310i	−0.277504	−	0.480651i	0.693260	−	0.720688i	$-0.256174\pi$
$991$	−8.73586	−	15.1310i	−0.277504	−	0.480651i	−0.970764	+	0.240037i	$0.922840\pi$
$992$	−44.9692	−	14.6301i	−1.42777	−	0.464506i
$993$	1.05883			0.0336010
$994$		0			0
$995$	−3.09755	+	3.09755i	−0.0981991	+	0.0981991i
$996$	−7.84269	−	3.69193i	−0.248505	−	0.116983i
$997$	1.28037	−	4.77839i	0.0405496	−	0.151333i	−0.942683	−	0.333690i	$-0.891706\pi$
$997$	1.28037	−	4.77839i	0.0405496	−	0.151333i	0.983232	+	0.182357i	$0.0583727\pi$
$998$	−6.92307	+	30.9611i	−0.219146	+	0.980057i
$999$	−14.1025	−	8.14210i	−0.446184	−	0.257605i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	784.2.x.j.373.4		16
7.2	even	3		784.2.m.g.197.2		8
7.3	odd	6		784.2.x.k.165.1		16
7.4	even	3	inner	784.2.x.j.165.1		16
7.5	odd	6		112.2.m.c.85.2	yes	8
7.6	odd	2		784.2.x.k.373.4		16
16.13	even	4	inner	784.2.x.j.765.1		16
28.19	even	6		448.2.m.c.113.1		8
56.5	odd	6		896.2.m.e.225.1		8
56.19	even	6		896.2.m.f.225.4		8
112.5	odd	12		896.2.m.e.673.1		8
112.13	odd	4		784.2.x.k.765.1		16
112.19	even	12		448.2.m.c.337.1		8
112.45	odd	12		784.2.x.k.557.4		16
112.61	odd	12		112.2.m.c.29.2	✓	8
112.75	even	12		896.2.m.f.673.4		8
112.93	even	12		784.2.m.g.589.2		8
112.109	even	12	inner	784.2.x.j.557.4		16
224.19	even	24		7168.2.a.bd.1.7		8
224.61	odd	24		7168.2.a.bc.1.7		8
224.131	even	24		7168.2.a.bd.1.2		8
224.173	odd	24		7168.2.a.bc.1.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
112.2.m.c.29.2	✓	8	112.61	odd	12
112.2.m.c.85.2	yes	8	7.5	odd	6
448.2.m.c.113.1		8	28.19	even	6
448.2.m.c.337.1		8	112.19	even	12
784.2.m.g.197.2		8	7.2	even	3
784.2.m.g.589.2		8	112.93	even	12
784.2.x.j.165.1		16	7.4	even	3	inner
784.2.x.j.373.4		16	1.1	even	1	trivial
784.2.x.j.557.4		16	112.109	even	12	inner
784.2.x.j.765.1		16	16.13	even	4	inner
784.2.x.k.165.1		16	7.3	odd	6
784.2.x.k.373.4		16	7.6	odd	2
784.2.x.k.557.4		16	112.45	odd	12
784.2.x.k.765.1		16	112.13	odd	4
896.2.m.e.225.1		8	56.5	odd	6
896.2.m.e.673.1		8	112.5	odd	12
896.2.m.f.225.4		8	56.19	even	6
896.2.m.f.673.4		8	112.75	even	12
7168.2.a.bc.1.2		8	224.173	odd	24
7168.2.a.bc.1.7		8	224.61	odd	24
7168.2.a.bd.1.2		8	224.131	even	24
7168.2.a.bd.1.7		8	224.19	even	24

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 784 = 2^{4} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	784.x (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.25323 + 0.655294i) q^{2} +(2.01092 + 0.538823i) q^{3} +(1.14118 + 1.64247i) q^{4} +(0.483385 - 0.129523i) q^{5} +(2.16706 + 1.99301i) q^{6} +(0.353863 + 2.80620i) q^{8} +(1.15537 + 0.667056i) q^{9} +O(q^{10})\)	\(q+(1.25323 + 0.655294i) q^{2} +(2.01092 + 0.538823i) q^{3} +(1.14118 + 1.64247i) q^{4} +(0.483385 - 0.129523i) q^{5} +(2.16706 + 1.99301i) q^{6} +(0.353863 + 2.80620i) q^{8} +(1.15537 + 0.667056i) q^{9} +(0.690669 + 0.154437i) q^{10} +(0.122293 - 0.456405i) q^{11} +(1.40982 + 3.91776i) q^{12} +(3.17982 - 3.17982i) q^{13} +1.04184 q^{15} +(-1.39542 + 3.74871i) q^{16} +(0.646137 + 1.11914i) q^{17} +(1.01083 + 1.59309i) q^{18} +(-0.963437 - 3.59560i) q^{19} +(0.764367 + 0.646137i) q^{20} +(0.452341 - 0.491843i) q^{22} +(-2.26039 - 1.30504i) q^{23} +(-0.800460 + 5.83371i) q^{24} +(-4.11324 + 2.37478i) q^{25} +(6.06876 - 1.90133i) q^{26} +(-2.45234 - 2.45234i) q^{27} +(-6.98602 + 6.98602i) q^{29} +(1.30566 + 0.682709i) q^{30} +(4.17982 + 7.23966i) q^{31} +(-4.20529 + 3.78359i) q^{32} +(0.491843 - 0.851898i) q^{33} +(0.0763926 + 1.82596i) q^{34} +(0.222871 + 2.65890i) q^{36} +(4.53539 - 1.21525i) q^{37} +(1.14876 - 5.13745i) q^{38} +(8.10770 - 4.68099i) q^{39} +(0.534519 + 1.31064i) q^{40} -9.93254i q^{41} +(-7.61241 - 7.61241i) q^{43} +(0.889190 - 0.319977i) q^{44} +(0.644890 + 0.172798i) q^{45} +(-1.97761 - 3.11673i) q^{46} +(-2.29805 + 3.98033i) q^{47} +(-4.82596 + 6.78645i) q^{48} +(-6.71102 + 0.280770i) q^{50} +(0.696308 + 2.59866i) q^{51} +(8.85150 + 1.59401i) q^{52} +(-1.44367 + 5.38786i) q^{53} +(-1.46635 - 4.68036i) q^{54} -0.236459i q^{55} -7.74956i q^{57} +(-13.3330 + 4.17721i) q^{58} +(2.34099 - 8.73669i) q^{59} +(1.18892 + 1.71119i) q^{60} +(-1.59362 - 5.94749i) q^{61} +(0.494178 + 11.8120i) q^{62} +(-7.74956 + 1.98602i) q^{64} +(1.12522 - 1.94894i) q^{65} +(1.17464 - 0.745323i) q^{66} +(13.6221 + 3.65002i) q^{67} +(-1.10080 + 2.33840i) q^{68} +(-3.84227 - 3.84227i) q^{69} -7.62395i q^{71} +(-1.46305 + 3.47826i) q^{72} +(0.482023 - 0.278296i) q^{73} +(6.48024 + 1.44902i) q^{74} +(-9.55097 + 2.55917i) q^{75} +(4.80620 - 5.68564i) q^{76} +(13.2283 - 0.553431i) q^{78} +(0.744616 - 1.28971i) q^{79} +(-0.188981 + 1.99281i) q^{80} +(-5.61124 - 9.71895i) q^{81} +(6.50873 - 12.4478i) q^{82} +(-1.47209 + 1.47209i) q^{83} +(0.457288 + 0.457288i) q^{85} +(-4.55175 - 14.5285i) q^{86} +(-17.8125 + 10.2841i) q^{87} +(1.32404 + 0.181675i) q^{88} +(10.6453 + 6.14609i) q^{89} +(0.694964 + 0.639148i) q^{90} +(-0.436028 - 5.20190i) q^{92} +(4.50437 + 16.8105i) q^{93} +(-5.48827 + 3.48239i) q^{94} +(-0.931423 - 1.61327i) q^{95} +(-10.4952 + 5.34258i) q^{96} -5.50078 q^{97} +(0.445742 - 0.445742i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 2 q^{2} - 4 q^{4} - 4 q^{5} + 32 q^{6} - 8 q^{8}+O(q^{10}) \) 16 * q - 2 * q^2 - 4 * q^4 - 4 * q^5 + 32 * q^6 - 8 * q^8	\( 16 q - 2 q^{2} - 4 q^{4} - 4 q^{5} + 32 q^{6} - 8 q^{8} + 12 q^{10} - 12 q^{12} - 16 q^{15} - 8 q^{16} + 24 q^{17} - 6 q^{18} - 12 q^{19} + 16 q^{20} - 8 q^{22} + 8 q^{26} - 24 q^{27} - 32 q^{29} - 20 q^{30} + 16 q^{31} + 28 q^{32} - 24 q^{33} + 24 q^{34} + 48 q^{36} - 16 q^{37} - 16 q^{38} + 28 q^{40} - 64 q^{43} + 32 q^{44} - 8 q^{45} - 20 q^{46} + 24 q^{47} - 40 q^{48} - 28 q^{50} - 8 q^{51} + 32 q^{52} + 8 q^{53} - 16 q^{54} - 12 q^{58} - 28 q^{59} + 28 q^{60} + 28 q^{61} - 40 q^{62} - 64 q^{64} + 48 q^{65} - 16 q^{66} + 28 q^{68} - 88 q^{69} - 44 q^{72} + 4 q^{74} + 28 q^{75} + 48 q^{76} + 24 q^{78} + 24 q^{79} - 12 q^{80} - 40 q^{81} + 4 q^{82} - 80 q^{85} + 40 q^{88} + 32 q^{90} + 72 q^{92} - 16 q^{93} + 28 q^{94} - 16 q^{95} + 8 q^{96} + 64 q^{97} + 96 q^{99}+O(q^{100}) \) 16 * q - 2 * q^2 - 4 * q^4 - 4 * q^5 + 32 * q^6 - 8 * q^8 + 12 * q^10 - 12 * q^12 - 16 * q^15 - 8 * q^16 + 24 * q^17 - 6 * q^18 - 12 * q^19 + 16 * q^20 - 8 * q^22 + 8 * q^26 - 24 * q^27 - 32 * q^29 - 20 * q^30 + 16 * q^31 + 28 * q^32 - 24 * q^33 + 24 * q^34 + 48 * q^36 - 16 * q^37 - 16 * q^38 + 28 * q^40 - 64 * q^43 + 32 * q^44 - 8 * q^45 - 20 * q^46 + 24 * q^47 - 40 * q^48 - 28 * q^50 - 8 * q^51 + 32 * q^52 + 8 * q^53 - 16 * q^54 - 12 * q^58 - 28 * q^59 + 28 * q^60 + 28 * q^61 - 40 * q^62 - 64 * q^64 + 48 * q^65 - 16 * q^66 + 28 * q^68 - 88 * q^69 - 44 * q^72 + 4 * q^74 + 28 * q^75 + 48 * q^76 + 24 * q^78 + 24 * q^79 - 12 * q^80 - 40 * q^81 + 4 * q^82 - 80 * q^85 + 40 * q^88 + 32 * q^90 + 72 * q^92 - 16 * q^93 + 28 * q^94 - 16 * q^95 + 8 * q^96 + 64 * q^97 + 96 * q^99

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