LMFDB - Embedded newform 784.2.x.m.557.2

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:	$24$
Relative dimension:	$6$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 112)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			557.2
Character	$\chi$	$=$	784.557
Dual form			784.2.x.m.373.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.02649 - 0.972785i) q^{2} +(0.862219 - 0.231031i) q^{3} +(0.107378 + 1.99712i) q^{4} +(-3.20004 - 0.857449i) q^{5} +(-1.10981 - 0.601602i) q^{6} +(1.83254 - 2.15448i) q^{8} +(-1.90803 + 1.10160i) q^{9} +O(q^{10})$	\(q+(-1.02649 - 0.972785i) q^{2} +(0.862219 - 0.231031i) q^{3} +(0.107378 + 1.99712i) q^{4} +(-3.20004 - 0.857449i) q^{5} +(-1.10981 - 0.601602i) q^{6} +(1.83254 - 2.15448i) q^{8} +(-1.90803 + 1.10160i) q^{9} +(2.45071 + 3.99312i) q^{10} +(-0.799070 - 2.98217i) q^{11} +(0.553978 + 1.69714i) q^{12} +(4.03390 + 4.03390i) q^{13} -2.95723 q^{15} +(-3.97694 + 0.428891i) q^{16} +(0.173966 - 0.301317i) q^{17} +(3.03020 + 0.725317i) q^{18} +(-1.56048 + 5.82380i) q^{19} +(1.36881 - 6.48293i) q^{20} +(-2.08077 + 3.83850i) q^{22} +(5.40216 - 3.11894i) q^{23} +(1.08230 - 2.28101i) q^{24} +(5.17494 + 2.98775i) q^{25} +(-0.216653 - 8.06488i) q^{26} +(-3.28420 + 3.28420i) q^{27} +(1.21961 + 1.21961i) q^{29} +(3.03558 + 2.87675i) q^{30} +(-0.631188 + 1.09325i) q^{31} +(4.49952 + 3.42846i) q^{32} +(-1.37795 - 2.38667i) q^{33} +(-0.471692 + 0.140069i) q^{34} +(-2.40491 - 3.69227i) q^{36} +(8.77373 + 2.35091i) q^{37} +(7.26713 - 4.46008i) q^{38} +(4.41005 + 2.54615i) q^{39} +(-7.71157 + 5.32312i) q^{40} +2.68519i q^{41} +(4.05478 - 4.05478i) q^{43} +(5.86993 - 1.91605i) q^{44} +(7.05035 - 1.88914i) q^{45} +(-8.57934 - 2.05357i) q^{46} +(2.32249 + 4.02267i) q^{47} +(-3.32990 + 1.28859i) q^{48} +(-2.40560 - 8.10101i) q^{50} +(0.0803829 - 0.299993i) q^{51} +(-7.62301 + 8.48931i) q^{52} +(3.08965 + 11.5307i) q^{53} +(6.56603 - 0.176388i) q^{54} +10.2282i q^{55} +5.38191i q^{57} +(-0.0655030 - 2.43834i) q^{58} +(1.89519 + 7.07295i) q^{59} +(-0.317541 - 5.90594i) q^{60} +(0.00195333 - 0.00728993i) q^{61} +(1.71141 - 0.508203i) q^{62} +(-1.28358 - 7.89636i) q^{64} +(-9.44979 - 16.3675i) q^{65} +(-0.907267 + 3.79035i) q^{66} +(-4.12554 + 1.10544i) q^{67} +(0.620446 + 0.315075i) q^{68} +(3.93727 - 3.93727i) q^{69} +0.828913i q^{71} +(-1.12317 + 6.12955i) q^{72} +(-5.41415 - 3.12586i) q^{73} +(-6.71924 - 10.9481i) q^{74} +(5.15219 + 1.38052i) q^{75} +(-11.7984 - 2.49112i) q^{76} +(-2.05004 - 6.90364i) q^{78} +(0.377945 + 0.654620i) q^{79} +(13.0941 + 2.03756i) q^{80} +(1.23186 - 2.13364i) q^{81} +(2.61211 - 2.75633i) q^{82} +(3.66586 + 3.66586i) q^{83} +(-0.815062 + 0.815062i) q^{85} +(-8.10663 + 0.217775i) q^{86} +(1.33334 + 0.769803i) q^{87} +(-7.88935 - 3.74337i) q^{88} +(-5.40799 + 3.12231i) q^{89} +(-9.07486 - 4.91929i) q^{90} +(6.80895 + 10.4538i) q^{92} +(-0.291648 + 1.08844i) q^{93} +(1.52917 - 6.38853i) q^{94} +(9.98723 - 17.2984i) q^{95} +(4.67165 + 1.91655i) q^{96} -2.18393 q^{97} +(4.80981 + 4.80981i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 2 q^{2} + 4 q^{3} + 6 q^{4} + 4 q^{5} - 8 q^{6} - 8 q^{8}+O(q^{10}) $ 24 * q - 2 * q^2 + 4 * q^3 + 6 * q^4 + 4 * q^5 - 8 * q^6 - 8 * q^8	$ 24 q - 2 q^{2} + 4 q^{3} + 6 q^{4} + 4 q^{5} - 8 q^{6} - 8 q^{8} - 4 q^{10} + 8 q^{12} - 48 q^{15} - 10 q^{16} - 8 q^{17} + 40 q^{20} + 28 q^{22} - 8 q^{24} - 20 q^{26} - 8 q^{27} - 8 q^{29} + 28 q^{30} - 8 q^{31} - 12 q^{32} - 16 q^{34} - 32 q^{36} + 20 q^{37} + 16 q^{38} - 8 q^{40} + 32 q^{43} - 14 q^{44} + 40 q^{45} + 28 q^{46} + 16 q^{47} - 32 q^{48} + 88 q^{50} + 16 q^{51} - 16 q^{52} - 4 q^{53} + 64 q^{54} - 14 q^{58} - 16 q^{59} - 60 q^{60} - 20 q^{61} - 16 q^{62} - 36 q^{64} - 32 q^{65} + 12 q^{66} - 24 q^{67} - 28 q^{68} + 8 q^{69} - 6 q^{72} + 38 q^{74} - 40 q^{75} - 96 q^{76} - 152 q^{78} - 24 q^{79} + 24 q^{80} + 44 q^{81} - 16 q^{82} + 40 q^{83} - 16 q^{85} - 38 q^{86} + 14 q^{88} + 80 q^{90} + 64 q^{92} + 48 q^{93} - 24 q^{94} - 16 q^{96} - 96 q^{97} + 64 q^{99}+O(q^{100}) $ 24 * q - 2 * q^2 + 4 * q^3 + 6 * q^4 + 4 * q^5 - 8 * q^6 - 8 * q^8 - 4 * q^10 + 8 * q^12 - 48 * q^15 - 10 * q^16 - 8 * q^17 + 40 * q^20 + 28 * q^22 - 8 * q^24 - 20 * q^26 - 8 * q^27 - 8 * q^29 + 28 * q^30 - 8 * q^31 - 12 * q^32 - 16 * q^34 - 32 * q^36 + 20 * q^37 + 16 * q^38 - 8 * q^40 + 32 * q^43 - 14 * q^44 + 40 * q^45 + 28 * q^46 + 16 * q^47 - 32 * q^48 + 88 * q^50 + 16 * q^51 - 16 * q^52 - 4 * q^53 + 64 * q^54 - 14 * q^58 - 16 * q^59 - 60 * q^60 - 20 * q^61 - 16 * q^62 - 36 * q^64 - 32 * q^65 + 12 * q^66 - 24 * q^67 - 28 * q^68 + 8 * q^69 - 6 * q^72 + 38 * q^74 - 40 * q^75 - 96 * q^76 - 152 * q^78 - 24 * q^79 + 24 * q^80 + 44 * q^81 - 16 * q^82 + 40 * q^83 - 16 * q^85 - 38 * q^86 + 14 * q^88 + 80 * q^90 + 64 * q^92 + 48 * q^93 - 24 * q^94 - 16 * q^96 - 96 * q^97 + 64 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$197$	$687$	$689$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−1.02649	−	0.972785i	−0.725840	−	0.687863i
$2$	−1.02649	−	0.972785i	−0.725840	−	0.687863i
$3$	0.862219	−	0.231031i	0.497802	−	0.133386i	−0.00117766	−	0.999999i	$-0.500375\pi$
$3$	0.862219	−	0.231031i	0.497802	−	0.133386i	0.498980	+	0.866614i	$0.333708\pi$
$4$	0.107378	+	1.99712i	0.0536888	+	0.998558i
$5$	−3.20004	−	0.857449i	−1.43110	−	0.383463i	−0.541694	−	0.840576i	$-0.682217\pi$
$5$	−3.20004	−	0.857449i	−1.43110	−	0.383463i	−0.889409	+	0.457113i	$0.848884\pi$
$6$	−1.10981	−	0.601602i	−0.453076	−	0.245603i
$7$		0			0
$7$		0			0
$8$	1.83254	−	2.15448i	0.647902	−	0.761724i
$9$	−1.90803	+	1.10160i	−0.636010	+	0.367201i
$10$	2.45071	+	3.99312i	0.774983	+	1.26274i
$11$	−0.799070	−	2.98217i	−0.240929	−	0.899158i	−0.975386	−	0.220503i	$-0.929230\pi$
$11$	−0.799070	−	2.98217i	−0.240929	−	0.899158i	0.734458	−	0.678654i	$-0.237437\pi$
$12$	0.553978	+	1.69714i	0.159920	+	0.489923i
$13$	4.03390	+	4.03390i	1.11880	+	1.11880i	0.991918	+	0.126884i	$0.0404976\pi$
$13$	4.03390	+	4.03390i	1.11880	+	1.11880i	0.126884	+	0.991918i	$0.459502\pi$
$14$		0			0
$15$	−2.95723			−0.763555
$16$	−3.97694	+	0.428891i	−0.994235	+	0.107223i
$17$	0.173966	−	0.301317i	0.0421929	−	0.0730802i	−0.844158	−	0.536095i	$-0.819899\pi$
$17$	0.173966	−	0.301317i	0.0421929	−	0.0730802i	0.886351	+	0.463015i	$0.153232\pi$
$18$	3.03020	+	0.725317i	0.714226	+	0.170959i
$19$	−1.56048	+	5.82380i	−0.357999	+	1.33607i	0.518669	+	0.854975i	$0.326428\pi$
$19$	−1.56048	+	5.82380i	−0.357999	+	1.33607i	−0.876668	+	0.481096i	$0.840239\pi$
$20$	1.36881	−	6.48293i	0.306076	−	1.44963i
$21$		0			0
$22$	−2.08077	+	3.83850i	−0.443622	+	0.818371i
$23$	5.40216	−	3.11894i	1.12643	−	0.650344i	0.183394	−	0.983040i	$-0.441292\pi$
$23$	5.40216	−	3.11894i	1.12643	−	0.650344i	0.943034	+	0.332696i	$0.107958\pi$
$24$	1.08230	−	2.28101i	0.220924	−	0.465609i
$25$	5.17494	+	2.98775i	1.03499	+	0.597550i
$26$	−0.216653	−	8.06488i	−0.0424892	−	1.58165i
$27$	−3.28420	+	3.28420i	−0.632044	+	0.632044i
$28$		0			0
$29$	1.21961	+	1.21961i	0.226476	+	0.226476i	0.811219	−	0.584743i	$-0.198805\pi$
$29$	1.21961	+	1.21961i	0.226476	+	0.226476i	−0.584743	+	0.811219i	$0.698805\pi$
$30$	3.03558	+	2.87675i	0.554219	+	0.525221i
$31$	−0.631188	+	1.09325i	−0.113365	+	0.196353i	−0.917125	−	0.398600i	$-0.869496\pi$
$31$	−0.631188	+	1.09325i	−0.113365	+	0.196353i	0.803760	+	0.594953i	$0.202830\pi$
$32$	4.49952	+	3.42846i	0.795411	+	0.606071i
$33$	−1.37795	−	2.38667i	−0.239869	−	0.415466i
$34$	−0.471692	+	0.140069i	−0.0808945	+	0.0240216i
$35$		0			0
$36$	−2.40491	−	3.69227i	−0.400818	−	0.615378i
$37$	8.77373	+	2.35091i	1.44239	+	0.386488i	0.893371	−	0.449321i	$-0.148334\pi$
$37$	8.77373	+	2.35091i	1.44239	+	0.386488i	0.549021	+	0.835808i	$0.315001\pi$
$38$	7.26713	−	4.46008i	1.17888	−	0.723520i
$39$	4.41005	+	2.54615i	0.706174	+	0.407710i
$40$	−7.71157	+	5.32312i	−1.21931	+	0.841660i
$41$			2.68519i			0.419356i	0.977770	+	0.209678i	$0.0672416\pi$
$41$			2.68519i			0.419356i	−0.977770	+	0.209678i	$0.932758\pi$
$42$		0			0
$43$	4.05478	−	4.05478i	0.618348	−	0.618348i	−0.326760	−	0.945107i	$-0.605957\pi$
$43$	4.05478	−	4.05478i	0.618348	−	0.618348i	0.945107	+	0.326760i	$0.105957\pi$
$44$	5.86993	−	1.91605i	0.884926	−	0.288856i
$45$	7.05035	−	1.88914i	1.05100	−	0.281616i
$46$	−8.57934	−	2.05357i	−1.26495	−	0.302783i
$47$	2.32249	+	4.02267i	0.338770	+	0.586767i	0.984202	−	0.177051i	$-0.0566558\pi$
$47$	2.32249	+	4.02267i	0.338770	+	0.586767i	−0.645432	+	0.763818i	$0.723323\pi$
$48$	−3.32990	+	1.28859i	−0.480630	+	0.185992i
$49$		0			0
$50$	−2.40560	−	8.10101i	−0.340203	−	1.14566i
$51$	0.0803829	−	0.299993i	0.0112559	−	0.0420074i
$52$	−7.62301	+	8.48931i	−1.05712	+	1.17726i
$53$	3.08965	+	11.5307i	0.424396	+	1.58387i	0.765238	+	0.643747i	$0.222621\pi$
$53$	3.08965	+	11.5307i	0.424396	+	1.58387i	−0.340842	+	0.940120i	$0.610712\pi$
$54$	6.56603	−	0.176388i	0.893523	−	0.0240034i
$55$			10.2282i			1.37917i
$56$		0			0
$57$			5.38191i			0.712851i
$58$	−0.0655030	−	2.43834i	−0.00860096	−	0.320170i
$59$	1.89519	+	7.07295i	0.246733	+	0.920820i	0.972504	+	0.232884i	$0.0748163\pi$
$59$	1.89519	+	7.07295i	0.246733	+	0.920820i	−0.725771	+	0.687936i	$0.758517\pi$
$60$	−0.317541	−	5.90594i	−0.0409943	−	0.762453i
$61$	0.00195333	−	0.00728993i	0.000250098	−	0.000933379i	−0.965801	−	0.259286i	$-0.916513\pi$
$61$	0.00195333	−	0.00728993i	0.000250098	−	0.000933379i	0.966051	+	0.258352i	$0.0831795\pi$
$62$	1.71141	−	0.508203i	0.217349	−	0.0645419i
$63$		0			0
$64$	−1.28358	−	7.89636i	−0.160447	−	0.987044i
$65$	−9.44979	−	16.3675i	−1.17210	−	2.03014i
$66$	−0.907267	+	3.79035i	−0.111677	+	0.466560i
$67$	−4.12554	+	1.10544i	−0.504015	+	0.135050i	−0.501863	−	0.864947i	$-0.667352\pi$
$67$	−4.12554	+	1.10544i	−0.504015	+	0.135050i	−0.00215224	+	0.999998i	$0.500685\pi$
$68$	0.620446	+	0.315075i	0.0752401	+	0.0382084i
$69$	3.93727	−	3.93727i	0.473992	−	0.473992i
$70$		0			0
$71$			0.828913i			0.0983739i	0.998790	+	0.0491869i	$0.0156630\pi$
$71$			0.828913i			0.0983739i	−0.998790	+	0.0491869i	$0.984337\pi$
$72$	−1.12317	+	6.12955i	−0.132366	+	0.722374i
$73$	−5.41415	−	3.12586i	−0.633679	−	0.365855i	0.148497	−	0.988913i	$-0.452557\pi$
$73$	−5.41415	−	3.12586i	−0.633679	−	0.365855i	−0.782175	+	0.623058i	$0.785890\pi$
$74$	−6.71924	−	10.9481i	−0.781096	−	1.27270i
$75$	5.15219	+	1.38052i	0.594923	+	0.159409i
$76$	−11.7984	−	2.49112i	−1.35337	−	0.285751i
$77$		0			0
$78$	−2.05004	−	6.90364i	−0.232121	−	0.781683i
$79$	0.377945	+	0.654620i	0.0425222	+	0.0736506i	0.886503	−	0.462722i	$-0.153127\pi$
$79$	0.377945	+	0.654620i	0.0425222	+	0.0736506i	−0.843981	+	0.536373i	$0.819794\pi$
$80$	13.0941	+	2.03756i	1.46397	+	0.227806i
$81$	1.23186	−	2.13364i	0.136873	−	0.237072i
$82$	2.61211	−	2.75633i	0.288460	−	0.304386i
$83$	3.66586	+	3.66586i	0.402380	+	0.402380i	0.879071	−	0.476691i	$-0.158164\pi$
$83$	3.66586	+	3.66586i	0.402380	+	0.402380i	−0.476691	+	0.879071i	$0.658164\pi$
$84$		0			0
$85$	−0.815062	+	0.815062i	−0.0884059	+	0.0884059i
$86$	−8.10663	+	0.217775i	−0.874160	+	0.0234832i
$87$	1.33334	+	0.769803i	0.142949	+	0.0825315i
$88$	−7.88935	−	3.74337i	−0.841008	−	0.399044i
$89$	−5.40799	+	3.12231i	−0.573246	+	0.330964i	−0.758445	−	0.651737i	$-0.774040\pi$
$89$	−5.40799	+	3.12231i	−0.573246	+	0.330964i	0.185199	+	0.982701i	$0.440707\pi$
$90$	−9.07486	−	4.91929i	−0.956574	−	0.518539i
$91$		0			0
$92$	6.80895	+	10.4538i	0.709882	+	1.08989i
$93$	−0.291648	+	1.08844i	−0.0302424	+	0.112866i
$94$	1.52917	−	6.38853i	0.157722	−	0.658926i
$95$	9.98723	−	17.2984i	1.02467	−	1.77478i
$96$	4.67165	+	1.91655i	0.476798	+	0.195607i
$97$	−2.18393			−0.221745			−0.110872	−	0.993835i	$-0.535365\pi$
$97$	−2.18393			−0.221745			−0.110872	+	0.993835i	$0.535365\pi$
$98$		0			0
$99$	4.80981	+	4.80981i	0.483404	+	0.483404i
$100$	−5.41121	+	10.6558i	−0.541121	+	1.06558i
$101$	1.73981	+	6.49307i	0.173118	+	0.646084i	0.996865	+	0.0791265i	$0.0252131\pi$
$101$	1.73981	+	6.49307i	0.173118	+	0.646084i	−0.823747	+	0.566958i	$0.808120\pi$
$102$	−0.374341	+	0.229745i	−0.0370653	+	0.0227482i
$103$	13.6190	−	7.86295i	1.34192	−	0.774760i	0.354834	−	0.934929i	$-0.384538\pi$
$103$	13.6190	−	7.86295i	1.34192	−	0.774760i	0.987089	+	0.160170i	$0.0512042\pi$
$104$	16.0832	−	1.29867i	1.57709	−	0.127345i
$105$		0			0
$106$	8.04542	−	14.8418i	0.781440	−	1.44156i
$107$	9.12614	+	2.44534i	0.882257	+	0.236400i	0.671381	−	0.741113i	$-0.265702\pi$
$107$	9.12614	+	2.44534i	0.882257	+	0.236400i	0.210876	+	0.977513i	$0.432368\pi$
$108$	−6.91157	−	6.20627i	−0.665066	−	0.597199i
$109$	1.10991	−	0.297398i	0.106310	−	0.0284856i	−0.205272	−	0.978705i	$-0.565808\pi$
$109$	1.10991	−	0.297398i	0.106310	−	0.0284856i	0.311582	+	0.950219i	$0.399141\pi$
$110$	9.94987	−	10.4992i	0.948683	−	1.00106i
$111$	8.10800			0.769578
$112$		0			0
$113$	−18.5170			−1.74193			−0.870966	−	0.491343i	$-0.836506\pi$
$113$	−18.5170			−1.74193			−0.870966	+	0.491343i	$0.836506\pi$
$114$	5.23544	−	5.52449i	0.490344	−	0.517416i
$115$	−19.9615	+	5.34866i	−1.86142	+	0.498765i
$116$	−2.30474	+	2.56666i	−0.213990	+	0.238308i
$117$	−12.1405	−	3.25305i	−1.12239	−	0.300745i
$118$	4.93506	−	9.10396i	0.454309	−	0.838087i
$119$		0			0
$120$	−5.41926	+	6.37131i	−0.494708	+	0.581618i
$121$	1.27146	−	0.734080i	0.115588	−	0.0667345i
$122$	−0.00909661	+	0.00558289i	−0.000823569	+	0.000505451i
$123$	0.620361	+	2.31522i	0.0559361	+	0.208756i
$124$	−2.25112	−	1.14316i	−0.202157	−	0.102659i
$125$	−2.28520	−	2.28520i	−0.204395	−	0.204395i
$126$		0			0
$127$	13.7063			1.21624			0.608121	−	0.793845i	$-0.291924\pi$
$127$	13.7063			1.21624			0.608121	+	0.793845i	$0.291924\pi$
$128$	−6.36387	+	9.35420i	−0.562492	+	0.826803i
$129$	2.55933	−	4.43288i	0.225336	−	0.390294i
$130$	−6.22193	+	25.9938i	−0.545699	+	2.27980i
$131$	1.29180	−	4.82105i	0.112865	−	0.421217i	−0.886254	−	0.463200i	$-0.846701\pi$
$131$	1.29180	−	4.82105i	0.112865	−	0.421217i	0.999118	+	0.0419836i	$0.0133677\pi$
$132$	4.61850	−	3.00819i	0.401989	−	0.261829i
$133$		0			0
$134$	5.31019	+	2.87854i	0.458731	+	0.248668i
$135$	13.3256	−	7.69355i	1.14689	−	0.662155i
$136$	−0.330383	−	0.926983i	−0.0283301	−	0.0794881i
$137$	−13.5567	−	7.82698i	−1.15823	−	0.668704i	−0.207350	−	0.978267i	$-0.566484\pi$
$137$	−13.5567	−	7.82698i	−1.15823	−	0.668704i	−0.950879	+	0.309563i	$0.899817\pi$
$138$	−7.87170	+	0.211464i	−0.670084	+	0.0180010i
$139$	−1.52569	+	1.52569i	−0.129408	+	0.129408i	−0.768844	−	0.639436i	$-0.779168\pi$
$139$	−1.52569	+	1.52569i	−0.129408	+	0.129408i	0.639436	+	0.768844i	$0.279168\pi$
$140$		0			0
$141$	2.93185	+	2.93185i	0.246907	+	0.246907i
$142$	0.806354	−	0.850874i	0.0676678	−	0.0714037i
$143$	8.80639	−	15.2531i	0.736428	−	1.27553i
$144$	7.11566	−	5.19934i	0.592971	−	0.433278i
$145$	−2.85705	−	4.94856i	−0.237265	−	0.410955i
$146$	2.51680	+	8.47549i	0.208292	+	0.701436i
$147$		0			0
$148$	−3.75294	+	17.7746i	−0.308490	+	1.46106i
$149$	−12.6192	−	3.38130i	−1.03380	−	0.277007i	−0.298260	−	0.954485i	$-0.596406\pi$
$149$	−12.6192	−	3.38130i	−1.03380	−	0.277007i	−0.735543	+	0.677478i	$0.763073\pi$
$150$	−3.94573	−	6.42907i	−0.322168	−	0.524931i
$151$	−10.1555	−	5.86330i	−0.826445	−	0.477149i	0.0261886	−	0.999657i	$-0.491663\pi$
$151$	−10.1555	−	5.86330i	−0.826445	−	0.477149i	−0.852634	+	0.522508i	$0.824996\pi$
$152$	9.68762	+	14.0344i	0.785770	+	1.13834i
$153$			0.766564i			0.0619730i
$154$		0			0
$155$	2.95723	−	2.95723i	0.237531	−	0.237531i
$156$	−4.61141	+	9.08079i	−0.369208	+	0.727045i
$157$	−14.1818	+	3.80001i	−1.13183	+	0.303274i	−0.775663	−	0.631147i	$-0.782585\pi$
$157$	−14.1818	+	3.80001i	−1.13183	+	0.303274i	−0.356171	+	0.934421i	$0.615918\pi$
$158$	0.248847	−	1.03962i	0.0197972	−	0.0827080i
$159$	5.32791	+	9.22821i	0.422530	+	0.731844i
$160$	−11.4589	−	14.8293i	−0.905909	−	1.17236i
$161$		0			0
$162$	−3.34007	+	0.991836i	−0.262421	+	0.0779260i
$163$	−5.73029	+	21.3857i	−0.448831	+	1.67506i	0.256788	+	0.966468i	$0.417336\pi$
$163$	−5.73029	+	21.3857i	−0.448831	+	1.67506i	−0.705619	+	0.708592i	$0.749331\pi$
$164$	−5.36263	+	0.288329i	−0.418751	+	0.0225147i
$165$	2.36304	+	8.81897i	0.183962	+	0.686556i
$166$	−0.196887	−	7.32908i	−0.0152814	−	0.568847i
$167$		−	2.12023i		−	0.164068i	−0.996630	−	0.0820341i	$-0.973858\pi$
$167$		−	2.12023i		−	0.164068i	0.996630	−	0.0820341i	$-0.0261416\pi$
$168$		0			0
$169$			19.5446i			1.50343i
$170$	1.62954	−	0.0437755i	0.124980	−	0.00335743i
$171$	−3.43806	−	12.8310i	−0.262915	−	0.981213i
$172$	8.53325	+	7.66247i	0.650654	+	0.584258i
$173$	−0.778368	+	2.90491i	−0.0591782	+	0.220856i	−0.989182	−	0.146694i	$-0.953137\pi$
$173$	−0.778368	+	2.90491i	−0.0591782	+	0.220856i	0.930004	+	0.367550i	$0.119803\pi$
$174$	−0.619810	−	2.08725i	−0.0469876	−	0.158234i
$175$		0			0
$176$	4.45688	+	11.5172i	0.335950	+	0.868141i
$177$	3.26814	+	5.66059i	0.245648	+	0.425476i
$178$	8.58860	+	2.05579i	0.643743	+	0.154088i
$179$	−1.93855	+	0.519432i	−0.144894	+	0.0388242i	−0.330537	−	0.943793i	$-0.607230\pi$
$179$	−1.93855	+	0.519432i	−0.144894	+	0.0388242i	0.185643	+	0.982617i	$0.440563\pi$
$180$	4.52987	+	13.8775i	0.337637	+	1.03437i
$181$	−14.3191	+	14.3191i	−1.06433	+	1.06433i	−0.0665470	+	0.997783i	$0.521198\pi$
$181$	−14.3191	+	14.3191i	−1.06433	+	1.06433i	−0.997783	+	0.0665470i	$0.978802\pi$
$182$		0			0
$183$		−	0.00673679i		−	0.000497998i
$184$	3.17999	−	17.3544i	0.234432	−	1.27939i
$185$	−26.0605	−	15.0461i	−1.91601	−	1.10621i
$186$	1.35820	−	0.833570i	0.0995878	−	0.0611203i
$187$	−1.03759	−	0.278021i	−0.0758761	−	0.0203309i
$188$	−7.78435	+	5.07022i	−0.567732	+	0.369784i
$189$		0			0
$190$	−27.0794	+	8.04125i	−1.96455	+	0.583374i
$191$	−3.11139	−	5.38909i	−0.225133	−	0.389941i	0.731227	−	0.682135i	$-0.238948\pi$
$191$	−3.11139	−	5.38909i	−0.225133	−	0.389941i	−0.956359	+	0.292194i	$0.905615\pi$
$192$	−2.93103	−	6.51184i	−0.211529	−	0.469951i
$193$	−0.788091	+	1.36501i	−0.0567280	+	0.0982558i	−0.892995	−	0.450067i	$-0.851400\pi$
$193$	−0.788091	+	1.36501i	−0.0567280	+	0.0982558i	0.836267	+	0.548323i	$0.184733\pi$
$194$	2.24179	+	2.12450i	0.160951	+	0.152530i
$195$	−11.9292	−	11.9292i	−0.854266	−	0.854266i
$196$		0			0
$197$	10.7183	−	10.7183i	0.763648	−	0.763648i	−0.213332	−	0.976980i	$-0.568432\pi$
$197$	10.7183	−	10.7183i	0.763648	−	0.763648i	0.976980	+	0.213332i	$0.0684315\pi$
$198$	−0.258326	−	9.61615i	−0.0183584	−	0.683390i
$199$	22.1151	+	12.7681i	1.56769	+	0.905109i	0.996437	+	0.0843377i	$0.0268774\pi$
$199$	22.1151	+	12.7681i	1.56769	+	0.905109i	0.571257	+	0.820771i	$0.306456\pi$
$200$	15.9203	−	5.67412i	1.12574	−	0.401221i
$201$	−3.30173	+	1.90625i	−0.232886	+	0.134457i
$202$	4.53045	−	8.35755i	0.318762	−	0.588035i
$203$		0			0
$204$	0.607752	+	0.128321i	0.0425511	+	0.00898429i
$205$	2.30241	−	8.59272i	0.160808	−	0.600142i
$206$	−21.6288	−	5.17713i	−1.50695	−	0.360707i
$207$	−6.87166	+	11.9021i	−0.477613	+	0.827250i
$208$	−17.7727	−	14.3125i	−1.23231	−	0.992391i
$209$	18.6145			1.28759
$210$		0			0
$211$	9.19881	+	9.19881i	0.633272	+	0.633272i	0.948887	−	0.315615i	$-0.102211\pi$
$211$	9.19881	+	9.19881i	0.633272	+	0.633272i	−0.315615	+	0.948887i	$0.602211\pi$
$212$	−22.6964	+	7.40853i	−1.55880	+	0.508820i
$213$	0.191504	+	0.714704i	0.0131217	+	0.0489707i
$214$	−6.98913	−	11.3879i	−0.477767	−	0.778461i
$215$	−16.4522	+	9.49870i	−1.12203	+	0.647806i
$216$	1.05731	+	13.0942i	0.0719409	+	0.890946i
$217$		0			0
$218$	−1.42862	−	0.774422i	−0.0967580	−	0.0524505i
$219$	−5.39036	−	1.44434i	−0.364246	−	0.0975995i
$220$	−20.4270	+	1.09828i	−1.37719	+	0.0740462i
$221$	1.91724	−	0.513724i	0.128968	−	0.0345568i
$222$	−8.32281	−	7.88735i	−0.558591	−	0.529364i
$223$	−12.7530			−0.854003			−0.427001	−	0.904251i	$-0.640430\pi$
$223$	−12.7530			−0.854003			−0.427001	+	0.904251i	$0.640430\pi$
$224$		0			0
$225$	−13.1652			−0.877683
$226$	19.0076	+	18.0131i	1.26436	+	1.19821i
$227$	−16.7271	+	4.48200i	−1.11021	+	0.297481i	−0.766917	−	0.641746i	$-0.778210\pi$
$227$	−16.7271	+	4.48200i	−1.11021	+	0.297481i	−0.343296	+	0.939227i	$0.611544\pi$
$228$	−10.7483	+	0.577896i	−0.711823	+	0.0382721i
$229$	−13.5673	−	3.63534i	−0.896551	−	0.240230i	−0.219016	−	0.975721i	$-0.570285\pi$
$229$	−13.5673	−	3.63534i	−0.896551	−	0.240230i	−0.677534	+	0.735491i	$0.736951\pi$
$230$	25.6934	+	13.9279i	1.69417	+	0.918376i
$231$		0			0
$232$	4.86261	−	0.392640i	0.319246	−	0.0257781i
$233$	−15.8606	+	9.15715i	−1.03907	+	0.599905i	−0.919568	−	0.392930i	$-0.871461\pi$
$233$	−15.8606	+	9.15715i	−1.03907	+	0.599905i	−0.119497	+	0.992835i	$0.538128\pi$
$234$	9.29767	+	15.1494i	0.607808	+	0.990346i
$235$	−3.98283	−	14.8641i	−0.259811	−	0.969629i
$236$	−13.9220	+	4.54439i	−0.906245	+	0.295815i
$237$	0.477109	+	0.477109i	0.0309916	+	0.0309916i
$238$		0			0
$239$	−18.3443			−1.18660			−0.593298	−	0.804983i	$-0.702174\pi$
$239$	−18.3443			−1.18660			−0.593298	+	0.804983i	$0.702174\pi$
$240$	11.7607	−	1.26833i	0.759153	−	0.0818704i
$241$	12.7073	−	22.0098i	0.818552	−	1.41777i	−0.0881977	−	0.996103i	$-0.528111\pi$
$241$	12.7073	−	22.0098i	0.818552	−	1.41777i	0.906749	−	0.421670i	$-0.138556\pi$
$242$	−2.01925	−	0.483333i	−0.129802	−	0.0310698i
$243$	4.17550	−	15.5832i	0.267858	−	0.999660i
$244$	0.0147686	+	0.00311825i	0.000945461	+	0.000199626i
$245$		0			0
$246$	1.61542	−	2.98004i	0.102995	−	0.190000i
$247$	−29.7874	+	17.1978i	−1.89533	+	1.09427i
$248$	1.19871	+	3.36331i	0.0761180	+	0.213570i
$249$	4.00770	+	2.31385i	0.253978	+	0.146634i
$250$	0.122734	+	4.56876i	0.00776238	+	0.288954i
$251$	10.9301	−	10.9301i	0.689903	−	0.689903i	−0.272307	−	0.962210i	$-0.587787\pi$
$251$	10.9301	−	10.9301i	0.689903	−	0.689903i	0.962210	+	0.272307i	$0.0877867\pi$
$252$		0			0
$253$	−13.6179	−	13.6179i	−0.856150	−	0.856150i
$254$	−14.0695	−	13.3333i	−0.882797	−	0.836608i
$255$	−0.514457	+	0.891066i	−0.0322166	+	0.0558007i
$256$	15.6321	−	3.41134i	0.977007	−	0.213209i
$257$	1.14826	+	1.98884i	0.0716265	+	0.124061i	0.899614	−	0.436685i	$-0.143848\pi$
$257$	1.14826	+	1.98884i	0.0716265	+	0.124061i	−0.827988	+	0.560746i	$0.810514\pi$
$258$	−6.93937	+	2.06065i	−0.432027	+	0.128290i
$259$		0			0
$260$	31.6731	−	20.6298i	1.96428	−	1.27941i
$261$	−3.67058	−	0.983528i	−0.227203	−	0.0608789i
$262$	−6.01586	+	3.69213i	−0.371661	+	0.228101i
$263$	10.2631	+	5.92538i	0.632848	+	0.365375i	0.781854	−	0.623462i	$-0.214274\pi$
$263$	10.2631	+	5.92538i	0.632848	+	0.365375i	−0.149007	+	0.988836i	$0.547608\pi$
$264$	−7.66718	−	1.40492i	−0.471882	−	0.0864668i
$265$		−	39.5481i		−	2.42942i
$266$		0			0
$267$	−3.94152	+	3.94152i	−0.241217	+	0.241217i
$268$	−2.65067	−	8.12048i	−0.161916	−	0.496037i
$269$	7.79715	−	2.08924i	0.475401	−	0.127383i	−0.0131596	−	0.999913i	$-0.504189\pi$
$269$	7.79715	−	2.08924i	0.475401	−	0.127383i	0.488560	+	0.872530i	$0.337522\pi$
$270$	−21.1628	−	5.06559i	−1.28793	−	0.308282i
$271$	13.0617	+	22.6235i	0.793441	+	1.37428i	0.923825	+	0.382816i	$0.125046\pi$
$271$	13.0617	+	22.6235i	0.793441	+	1.37428i	−0.130384	+	0.991464i	$0.541621\pi$
$272$	−0.562619	+	1.27293i	−0.0341138	+	0.0771829i
$273$		0			0
$274$	6.30192	+	21.2221i	0.380713	+	1.28208i
$275$	4.77484	−	17.8199i	0.287934	−	1.07458i
$276$	8.28596	+	7.44041i	0.498756	+	0.447860i
$277$	0.725732	+	2.70847i	0.0436050	+	0.162736i	0.984295	−	0.176531i	$-0.0564876\pi$
$277$	0.725732	+	2.70847i	0.0436050	+	0.162736i	−0.940690	+	0.339267i	$0.889821\pi$
$278$	3.05029	−	0.0819422i	0.182944	−	0.00491456i
$279$		−	2.78127i		−	0.166510i
$280$		0			0
$281$		−	6.52475i		−	0.389234i	−0.980879	−	0.194617i	$-0.937654\pi$
$281$		−	6.52475i		−	0.389234i	0.980879	−	0.194617i	$-0.0623464\pi$
$282$	−0.157464	−	5.86159i	−0.00937687	−	0.349053i
$283$	5.10891	+	19.0667i	0.303693	+	1.13340i	0.934064	+	0.357104i	$0.116236\pi$
$283$	5.10891	+	19.0667i	0.303693	+	1.13340i	−0.630371	+	0.776294i	$0.717097\pi$
$284$	−1.65544	+	0.0890066i	−0.0982320	+	0.00528157i
$285$	4.61471	−	17.2223i	0.273352	−	1.02016i
$286$	−23.8777	+	7.09050i	−1.41192	+	0.419270i
$287$		0			0
$288$	−12.3620	−	1.58492i	−0.728439	−	0.0933921i
$289$	8.43947	+	14.6176i	0.496440	+	0.859858i
$290$	−1.88114	+	7.85896i	−0.110464	+	0.461494i
$291$	−1.88303	+	0.504556i	−0.110385	+	0.0295776i
$292$	5.66135	−	11.1483i	0.331306	−	0.652407i
$293$	2.57087	−	2.57087i	0.150192	−	0.150192i	−0.628012	−	0.778204i	$-0.716131\pi$
$293$	2.57087	−	2.57087i	0.150192	−	0.150192i	0.778204	+	0.628012i	$0.216131\pi$
$294$		0			0
$295$		−	24.2588i		−	1.41240i
$296$	21.1432	−	14.5947i	1.22892	−	0.848299i
$297$	12.4183	+	7.16973i	0.720585	+	0.416030i
$298$	9.66422	+	15.7466i	0.559833	+	0.912178i
$299$	34.3732	+	9.21028i	1.98785	+	0.532644i
$300$	−2.20384	+	10.4378i	−0.127239	+	0.602624i
$301$		0			0
$302$	4.72086	+	15.8978i	0.271655	+	0.914815i
$303$	3.00020	+	5.19649i	0.172357	+	0.298531i
$304$	3.70817	−	23.8302i	0.212678	−	1.36675i
$305$	−0.0125015	+	0.0216532i	−0.000715833	+	0.00123986i
$306$	0.745702	−	0.786873i	0.0426289	−	0.0449825i
$307$	−18.8253	−	18.8253i	−1.07441	−	1.07441i	−0.996999	−	0.0774148i	$-0.975333\pi$
$307$	−18.8253	−	18.8253i	−1.07441	−	1.07441i	−0.0774148	−	0.996999i	$-0.524667\pi$
$308$		0			0
$309$	9.92600	−	9.92600i	0.564670	−	0.564670i
$310$	−5.91234	+	0.158828i	−0.335798	+	0.00902080i
$311$	20.6909	+	11.9459i	1.17327	+	0.677389i	0.954449	−	0.298375i	$-0.0964446\pi$
$311$	20.6909	+	11.9459i	1.17327	+	0.677389i	0.218824	+	0.975764i	$0.429778\pi$
$312$	13.5672	−	4.83546i	0.768093	−	0.273754i
$313$	15.6650	−	9.04419i	0.885438	−	0.511208i	0.0129904	−	0.999916i	$-0.495865\pi$
$313$	15.6650	−	9.04419i	0.885438	−	0.511208i	0.872448	+	0.488708i	$0.162532\pi$
$314$	18.2542	+	9.89520i	1.03014	+	0.558418i
$315$		0			0
$316$	−1.26677	+	0.825092i	−0.0712614	+	0.0464150i
$317$	−1.96360	+	7.32824i	−0.110287	+	0.411595i	−0.998891	−	0.0470789i	$-0.985009\pi$
$317$	−1.96360	+	7.32824i	−0.110287	+	0.411595i	0.888605	+	0.458674i	$0.151675\pi$
$318$	3.50800	−	14.6556i	0.196719	−	0.821845i
$319$	2.66253	−	4.61164i	0.149073	−	0.258202i
$320$	−2.66322	+	26.3693i	−0.148878	+	1.47409i
$321$	8.43367			0.470722
$322$		0			0
$323$	1.48334	+	1.48334i	0.0825354	+	0.0825354i
$324$	4.39341	+	2.23106i	0.244078	+	0.123948i
$325$	8.82288	+	32.9274i	0.489405	+	1.82649i
$326$	26.6858	−	16.3780i	1.47799	−	0.907092i
$327$	0.888273	−	0.512845i	0.0491216	−	0.0283604i
$328$	5.78519	+	4.92072i	0.319434	+	0.271701i
$329$		0			0
$330$	6.15332	−	11.3513i	0.338729	−	0.624871i
$331$	30.5393	+	8.18298i	1.67859	+	0.449777i	0.967407	−	0.253228i	$-0.0814922\pi$
$331$	30.5393	+	8.18298i	1.67859	+	0.449777i	0.711185	+	0.703005i	$0.248159\pi$
$332$	−6.92751	+	7.71478i	−0.380197	+	0.423403i
$333$	−19.3303	+	5.17954i	−1.05929	+	0.283837i
$334$	−2.06253	+	2.17640i	−0.112856	+	0.119087i
$335$	14.1498			0.773084
$336$		0			0
$337$	11.5086			0.626914			0.313457	−	0.949602i	$-0.398513\pi$
$337$	11.5086			0.626914			0.313457	+	0.949602i	$0.398513\pi$
$338$	19.0127	−	20.0624i	1.03416	−	1.09125i
$339$	−15.9657	+	4.27799i	−0.867137	+	0.232349i
$340$	−1.71529	−	1.54025i	−0.0930248	−	0.0835320i
$341$	3.76462	+	1.00873i	0.203865	+	0.0546256i
$342$	−8.95268	+	16.5155i	−0.484106	+	0.893053i
$343$		0			0
$344$	−1.30539	−	16.1665i	−0.0703820	−	0.871639i
$345$	−15.9755	+	9.22343i	−0.860089	+	0.496573i
$346$	3.62484	−	2.22469i	0.194873	−	0.119600i
$347$	4.50907	+	16.8281i	0.242060	+	0.903379i	0.974839	+	0.222912i	$0.0715563\pi$
$347$	4.50907	+	16.8281i	0.242060	+	0.903379i	−0.732779	+	0.680467i	$0.761777\pi$
$348$	−1.39421	+	2.74549i	−0.0747378	+	0.147174i
$349$	−0.251501	−	0.251501i	−0.0134625	−	0.0134625i	0.700343	−	0.713806i	$-0.253030\pi$
$349$	−0.251501	−	0.251501i	−0.0134625	−	0.0134625i	−0.713806	+	0.700343i	$0.753030\pi$
$350$		0			0
$351$	−26.4962			−1.41426
$352$	6.62880	−	16.1579i	0.353316	−	0.861219i
$353$	8.34440	−	14.4529i	0.444128	−	0.769251i	−0.553863	−	0.832608i	$-0.686847\pi$
$353$	8.34440	−	14.4529i	0.444128	−	0.769251i	0.997991	+	0.0633560i	$0.0201804\pi$
$354$	2.15181	−	8.98975i	0.114367	−	0.477800i
$355$	0.710751	−	2.65256i	0.0377227	−	0.140783i
$356$	−6.81630	−	10.4651i	−0.361263	−	0.554650i
$357$		0			0
$358$	2.49520	+	1.35260i	0.131876	+	0.0714869i
$359$	15.5695	−	8.98907i	0.821728	−	0.474425i	−0.0292842	−	0.999571i	$-0.509323\pi$
$359$	15.5695	−	8.98907i	0.821728	−	0.474425i	0.851012	+	0.525146i	$0.175989\pi$
$360$	8.84996	−	18.6518i	0.466434	−	0.983034i
$361$	−15.0271	−	8.67588i	−0.790898	−	0.456625i
$362$	28.6279	−	0.769052i	1.50465	−	0.0404205i
$363$	0.926684	−	0.926684i	0.0486383	−	0.0486383i
$364$		0			0
$365$	14.6453	+	14.6453i	0.766568	+	0.766568i
$366$	−0.00655345	+	0.00691527i	−0.000342554	+	0.000361467i
$367$	10.8135	−	18.7296i	0.564461	−	0.977675i	−0.432639	−	0.901567i	$-0.642418\pi$
$367$	10.8135	−	18.7296i	0.564461	−	0.977675i	0.997100	−	0.0761073i	$-0.0242492\pi$
$368$	−20.1464	+	14.7208i	−1.05020	+	0.767373i
$369$	−2.95801	−	5.12342i	−0.153988	−	0.266715i
$370$	12.1144	+	40.7960i	0.629797	+	2.12088i
$371$		0			0
$372$	−2.20506	−	0.465580i	−0.114327	−	0.0241392i
$373$	16.5459	+	4.43346i	0.856715	+	0.229556i	0.660334	−	0.750972i	$-0.270415\pi$
$373$	16.5459	+	4.43346i	0.856715	+	0.229556i	0.196380	+	0.980528i	$0.437081\pi$
$374$	0.794624	+	1.29474i	0.0410890	+	0.0669494i
$375$	−2.49830	−	1.44239i	−0.129011	−	0.0744848i
$376$	12.9228	+	2.36795i	0.666444	+	0.122118i
$377$			9.83956i			0.506763i
$378$		0			0
$379$	4.34251	−	4.34251i	0.223060	−	0.223060i	−0.586726	−	0.809786i	$-0.699583\pi$
$379$	4.34251	−	4.34251i	0.223060	−	0.223060i	0.809786	+	0.586726i	$0.199583\pi$
$380$	35.6193	+	18.0882i	1.82723	+	0.927904i
$381$	11.8179	−	3.16659i	0.605448	−	0.162229i
$382$	−2.04860	+	8.55859i	−0.104816	+	0.437895i
$383$	−16.4121	−	28.4266i	−0.838619	−	1.45253i	−0.891049	−	0.453907i	$-0.850030\pi$
$383$	−16.4121	−	28.4266i	−0.838619	−	1.45253i	0.0524297	−	0.998625i	$-0.483303\pi$
$384$	−3.32594	+	9.53562i	−0.169726	+	0.486612i
$385$		0			0
$386$	2.13684	−	0.634534i	0.108762	−	0.0322969i
$387$	−3.26989	+	12.2034i	−0.166218	+	0.620333i
$388$	−0.234505	−	4.36157i	−0.0119052	−	0.221425i
$389$	0.0860114	+	0.320999i	0.00436095	+	0.0162753i	0.968072	−	0.250672i	$-0.0806516\pi$
$389$	0.0860114	+	0.320999i	0.00436095	+	0.0162753i	−0.963711	+	0.266948i	$0.913985\pi$
$390$	0.640694	+	23.8498i	0.0324428	+	1.20768i
$391$		−	2.17035i		−	0.109759i
$392$		0			0
$393$		−	4.45524i		−	0.224737i
$394$	−21.4289	+	0.575660i	−1.07957	+	0.0290014i
$395$	−0.648138	−	2.41888i	−0.0326114	−	0.121707i
$396$	−9.08928	+	10.1222i	−0.456754	+	0.508660i
$397$	−0.724669	+	2.70450i	−0.0363701	+	0.135735i	−0.981724	−	0.190312i	$-0.939050\pi$
$397$	−0.724669	+	2.70450i	−0.0363701	+	0.135735i	0.945354	+	0.326047i	$0.105717\pi$
$398$	−10.2803	−	34.6196i	−0.515305	−	1.73532i
$399$		0			0
$400$	−21.8618	−	9.66262i	−1.09309	−	0.483131i
$401$	2.57522	+	4.46041i	0.128600	+	0.222742i	0.923134	−	0.384477i	$-0.125618\pi$
$401$	2.57522	+	4.46041i	0.128600	+	0.222742i	−0.794534	+	0.607219i	$0.792285\pi$
$402$	5.24358	+	1.25512i	0.261526	+	0.0625995i
$403$	−6.95620	+	1.86391i	−0.346513	+	0.0928479i
$404$	−12.7806	+	4.17181i	−0.635858	+	0.207556i
$405$	−5.77150	+	5.77150i	−0.286788	+	0.286788i
$406$		0			0
$407$		−	28.0433i		−	1.39005i
$408$	−0.499024	−	0.722933i	−0.0247054	−	0.0357905i
$409$	0.0631364	+	0.0364518i	0.00312189	+	0.00180243i	0.501560	−	0.865123i	$-0.332760\pi$
$409$	0.0631364	+	0.0364518i	0.00312189	+	0.00180243i	−0.498438	+	0.866925i	$0.666093\pi$
$410$	−10.7223	+	6.58062i	−0.529536	+	0.324994i
$411$	−13.4971	−	3.61654i	−0.665764	−	0.178391i
$412$	17.1656	+	26.3545i	0.845688	+	1.29839i
$413$		0			0
$414$	18.6319	−	5.53274i	0.915706	−	0.271919i
$415$	−8.58762	−	14.8742i	−0.421550	−	0.730146i
$416$	4.32057	+	31.9806i	0.211833	+	1.56798i
$417$	−0.962999	+	1.66796i	−0.0471583	+	0.0816805i
$418$	−19.1077	−	18.1079i	−0.934586	−	0.885686i
$419$	13.7426	+	13.7426i	0.671370	+	0.671370i	0.958032	−	0.286662i	$-0.0925456\pi$
$419$	13.7426	+	13.7426i	0.671370	+	0.671370i	−0.286662	+	0.958032i	$0.592546\pi$
$420$		0			0
$421$	3.88097	−	3.88097i	0.189147	−	0.189147i	−0.606180	−	0.795327i	$-0.707299\pi$
$421$	3.88097	−	3.88097i	0.189147	−	0.189147i	0.795327	+	0.606180i	$0.207299\pi$
$422$	−0.494051	−	18.3910i	−0.0240500	−	0.895259i
$423$	−8.86276	−	5.11692i	−0.430922	−	0.248793i
$424$	30.5047	+	14.4740i	1.48144	+	0.702917i
$425$	1.80052	−	1.03953i	0.0873382	−	0.0504247i
$426$	0.498676	−	0.919932i	0.0241609	−	0.0445708i
$427$		0			0
$428$	−3.90369	+	18.4885i	−0.188692	+	0.893676i
$429$	4.06910	−	15.1861i	0.196458	−	0.733191i
$430$	26.1283	+	6.25414i	1.26002	+	0.301601i
$431$	16.9017	−	29.2746i	0.814125	−	1.41011i	−0.0958298	−	0.995398i	$-0.530550\pi$
$431$	16.9017	−	29.2746i	0.814125	−	1.41011i	0.909955	−	0.414708i	$-0.136116\pi$
$432$	11.6525	−	14.4696i	0.560631	−	0.696170i
$433$	−18.6931			−0.898334			−0.449167	−	0.893448i	$-0.648279\pi$
$433$	−18.6931			−0.898334			−0.449167	+	0.893448i	$0.648279\pi$
$434$		0			0
$435$	−3.60667	−	3.60667i	−0.172927	−	0.172927i
$436$	0.713117	+	2.18467i	0.0341521	+	0.104627i
$437$	9.73410	+	36.3281i	0.465645	+	1.73781i
$438$	4.12813	+	6.72627i	0.197250	+	0.321393i
$439$	−5.22336	+	3.01571i	−0.249298	+	0.143932i	−0.619443	−	0.785042i	$-0.712641\pi$
$439$	−5.22336	+	3.01571i	−0.249298	+	0.143932i	0.370145	+	0.928974i	$0.379308\pi$
$440$	22.0365	+	18.7437i	1.05055	+	0.893569i
$441$		0			0
$442$	−2.46778	−	1.33773i	−0.117380	−	0.0636294i
$443$	−34.0356	−	9.11980i	−1.61708	−	0.433295i	−0.666937	−	0.745114i	$-0.732395\pi$
$443$	−34.0356	−	9.11980i	−1.61708	−	0.433295i	−0.950141	+	0.311819i	$0.899062\pi$
$444$	0.870617	+	16.1926i	0.0413177	+	0.768468i
$445$	19.9830	−	5.35444i	0.947287	−	0.253825i
$446$	13.0909	+	12.4059i	0.619870	+	0.587437i
$447$	−11.6617			−0.551578
$448$		0			0
$449$	21.9883			1.03769			0.518846	−	0.854868i	$-0.326362\pi$
$449$	21.9883			1.03769			0.518846	+	0.854868i	$0.326362\pi$
$450$	13.5140	+	12.8070i	0.637058	+	0.603726i
$451$	8.00769	−	2.14565i	0.377067	−	0.101035i
$452$	−1.98831	−	36.9806i	−0.0935222	−	1.73942i
$453$	−10.1109	−	2.70921i	−0.475051	−	0.127290i
$454$	21.5302	+	11.6711i	1.01046	+	0.547751i
$455$		0			0
$456$	11.5952	+	9.86257i	0.542996	+	0.461857i
$457$	23.1559	−	13.3691i	1.08319	−	0.625378i	0.151432	−	0.988468i	$-0.451611\pi$
$457$	23.1559	−	13.3691i	1.08319	−	0.625378i	0.931754	+	0.363090i	$0.118278\pi$
$458$	10.3903	+	16.9297i	0.485507	+	0.791073i
$459$	0.418248	+	1.56092i	0.0195222	+	0.0728577i
$460$	−12.8253	−	39.2911i	−0.597983	−	1.83195i
$461$	−23.5563	−	23.5563i	−1.09713	−	1.09713i	−0.994745	−	0.102381i	$-0.967354\pi$
$461$	−23.5563	−	23.5563i	−1.09713	−	1.09713i	−0.102381	−	0.994745i	$-0.532646\pi$
$462$		0			0
$463$	−9.83629			−0.457131			−0.228566	−	0.973529i	$-0.573404\pi$
$463$	−9.83629			−0.457131			−0.228566	+	0.973529i	$0.573404\pi$
$464$	−5.37340	−	4.32724i	−0.249454	−	0.200887i
$465$	1.86657	−	3.23299i	0.0865601	−	0.149927i
$466$	25.1888	+	6.02925i	1.16685	+	0.279300i
$467$	−0.719583	+	2.68552i	−0.0332983	+	0.124271i	−0.980574	−	0.196147i	$-0.937157\pi$
$467$	−0.719583	+	2.68552i	−0.0332983	+	0.124271i	0.947276	+	0.320419i	$0.103824\pi$
$468$	5.19309	−	24.5954i	0.240051	−	1.13692i
$469$		0			0
$470$	−10.3713	+	19.1324i	−0.478391	+	0.882511i
$471$	−11.3499	+	6.55288i	−0.522977	+	0.301941i
$472$	18.7116	+	8.87833i	0.861270	+	0.408658i
$473$	−15.3321	−	8.85198i	−0.704970	−	0.407014i
$474$	−0.0256246	−	0.953874i	−0.00117698	−	0.0438129i
$475$	−25.4755	+	25.4755i	−1.16889	+	1.16889i
$476$		0			0
$477$	−18.5974	−	18.5974i	−0.851517	−	0.851517i
$478$	18.8303	+	17.8451i	0.861279	+	0.816216i
$479$	1.89344	−	3.27954i	0.0865136	−	0.149846i	−0.819522	−	0.573048i	$-0.805761\pi$
$479$	1.89344	−	3.27954i	0.0865136	−	0.149846i	0.906035	+	0.423202i	$0.139094\pi$
$480$	−13.3061	−	10.1387i	−0.607339	−	0.462768i
$481$	25.9090	+	44.8756i	1.18135	+	2.04615i
$482$	−34.4548	+	10.2314i	−1.56937	+	0.466026i
$483$		0			0
$484$	1.60257	+	2.46044i	0.0728440	+	0.111838i
$485$	6.98868	+	1.87261i	0.317340	+	0.0850309i
$486$	−19.4452	+	11.9342i	−0.882052	+	0.541344i
$487$	14.5665	+	8.40999i	0.660073	+	0.381093i	0.792305	−	0.610126i	$-0.208881\pi$
$487$	14.5665	+	8.40999i	0.660073	+	0.381093i	−0.132232	+	0.991219i	$0.542214\pi$
$488$	−0.0121264	−	0.0175675i	−0.000548939	−	0.000795244i
$489$			19.7630i			0.893716i
$490$		0			0
$491$	−6.41618	+	6.41618i	−0.289558	+	0.289558i	−0.836906	−	0.547347i	$-0.815638\pi$
$491$	−6.41618	+	6.41618i	−0.289558	+	0.289558i	0.547347	+	0.836906i	$0.315638\pi$
$492$	−4.55715	+	1.48754i	−0.205452	+	0.0670633i
$493$	0.579660	−	0.155319i	0.0261066	−	0.00699524i
$494$	47.3064	+	11.3234i	2.12841	+	0.509462i
$495$	−11.2674	−	19.5158i	−0.506434	−	0.877169i
$496$	2.04131	−	4.61850i	0.0916576	−	0.207377i
$497$		0			0
$498$	−1.86300	−	6.27378i	−0.0834831	−	0.281135i
$499$	−1.71776	+	6.41078i	−0.0768977	+	0.286986i	−0.993657	−	0.112454i	$-0.964129\pi$
$499$	−1.71776	+	6.41078i	−0.0768977	+	0.286986i	0.916759	+	0.399440i	$0.130796\pi$
$500$	4.31843	−	4.80919i	0.193126	−	0.215074i
$501$	−0.489838	−	1.82810i	−0.0218843	−	0.0816735i
$502$	−21.8524	+	0.587036i	−0.975318	+	0.0262007i
$503$			4.37360i			0.195009i	0.995235	+	0.0975045i	$0.0310860\pi$
$503$			4.37360i			0.195009i	−0.995235	+	0.0975045i	$0.968914\pi$
$504$		0			0
$505$		−	22.2699i		−	0.990998i
$506$	0.731392	+	27.2260i	0.0325143	+	1.21034i
$507$	4.51541	+	16.8518i	0.200537	+	0.748413i
$508$	1.47175	+	27.3732i	0.0652985	+	1.21449i
$509$	−0.708694	+	2.64488i	−0.0314123	+	0.117232i	−0.979852	−	0.199726i	$-0.935995\pi$
$509$	−0.708694	+	2.64488i	−0.0314123	+	0.117232i	0.948440	+	0.316958i	$0.102661\pi$
$510$	1.39490	−	0.414217i	0.0617674	−	0.0183418i
$511$		0			0
$512$	−19.3648	−	11.7050i	−0.855810	−	0.517291i
$513$	−14.0016	−	24.2515i	−0.618185	−	1.07073i
$514$	0.756037	−	3.15855i	0.0333474	−	0.139317i
$515$	−50.3236	+	13.4842i	−2.21752	+	0.594183i
$516$	9.12779	+	4.63528i	0.401829	+	0.204057i
$517$	10.1404	−	10.1404i	0.445976	−	0.445976i
$518$		0			0
$519$			2.68449i			0.117836i
$520$	−52.5806	−	9.63477i	−2.30581	−	0.422512i
$521$	−30.5966	−	17.6650i	−1.34046	−	0.773917i	−0.353588	−	0.935401i	$-0.615038\pi$
$521$	−30.5966	−	17.6650i	−1.34046	−	0.773917i	−0.986875	+	0.161485i	$0.948372\pi$
$522$	2.81106	+	4.58027i	0.123037	+	0.200473i
$523$	−31.9451	−	8.55965i	−1.39686	−	0.374287i	−0.519644	−	0.854383i	$-0.673935\pi$
$523$	−31.9451	−	8.55965i	−1.39686	−	0.374287i	−0.877216	+	0.480096i	$0.840602\pi$
$524$	9.76690	+	2.06219i	0.426669	+	0.0900873i
$525$		0			0
$526$	−4.77084	−	16.0661i	−0.208019	−	0.700516i
$527$	0.219610	+	0.380376i	0.00956636	+	0.0165694i
$528$	6.50363	+	8.90066i	0.283034	+	0.387352i
$529$	7.95555	−	13.7794i	0.345893	−	0.599105i
$530$	−38.4718	+	40.5958i	−1.67111	+	1.76337i
$531$	−11.4077	−	11.4077i	−0.495051	−	0.495051i
$532$		0			0
$533$	−10.8318	+	10.8318i	−0.469176	+	0.469176i
$534$	7.88020	−	0.211692i	0.341010	−	0.00916080i
$535$	−27.1073	−	15.6504i	−1.17195	−	0.676626i
$536$	−5.17859	+	10.9142i	−0.223681	+	0.471420i
$537$	−1.55145	+	0.895728i	−0.0669499	+	0.0386535i
$538$	−10.0361	−	5.44036i	−0.432687	−	0.234551i
$539$		0			0
$540$	16.7958	+	25.7867i	0.722775	+	1.10968i
$541$	−1.87835	+	7.01011i	−0.0807567	+	0.301388i	−0.994477	−	0.104956i	$-0.966530\pi$
$541$	−1.87835	+	7.01011i	−0.0807567	+	0.301388i	0.913720	+	0.406344i	$0.133197\pi$
$542$	8.60007	−	35.9291i	0.369405	−	1.54329i
$543$	−9.03804	+	15.6543i	−0.387859	+	0.671792i
$544$	1.81582	−	0.759351i	0.0778525	−	0.0325569i
$545$	−3.80675			−0.163063
$546$		0			0
$547$	16.8157	+	16.8157i	0.718989	+	0.718989i	0.968398	−	0.249409i	$-0.0802365\pi$
$547$	16.8157	+	16.8157i	0.718989	+	0.718989i	−0.249409	+	0.968398i	$0.580236\pi$
$548$	14.1757	−	27.9148i	0.605555	−	1.19246i
$549$	0.00430358	+	0.0160612i	0.000183672	+	0.000685475i
$550$	−22.2363	+	13.6472i	−0.948160	+	0.581917i
$551$	−9.00595	+	5.19959i	−0.383666	+	0.221510i
$552$	−1.26756	−	15.6980i	−0.0539510	−	0.668151i
$553$		0			0
$554$	1.88980	−	3.48621i	0.0802899	−	0.148115i
$555$	−25.9460	−	6.95220i	−1.10135	−	0.295105i
$556$	−3.21081	−	2.88316i	−0.136169	−	0.122273i
$557$	15.1457	−	4.05828i	0.641744	−	0.171955i	0.0767505	−	0.997050i	$-0.475546\pi$
$557$	15.1457	−	4.05828i	0.641744	−	0.171955i	0.564993	+	0.825096i	$0.308879\pi$
$558$	−2.70558	+	2.85496i	−0.114536	+	0.120860i
$559$	32.7131			1.38362
$560$		0			0
$561$	−0.958861			−0.0404831
$562$	−6.34718	+	6.69761i	−0.267740	+	0.282522i
$563$	30.3335	−	8.12783i	1.27840	−	0.342547i	0.445159	−	0.895451i	$-0.353147\pi$
$563$	30.3335	−	8.12783i	1.27840	−	0.342547i	0.833245	+	0.552904i	$0.186480\pi$
$564$	−5.54044	+	6.17007i	−0.233294	+	0.259807i
$565$	59.2552	+	15.8774i	2.49288	+	0.667966i
$566$	13.3036	−	24.5417i	0.559190	−	1.03157i
$567$		0			0
$568$	1.78588	+	1.51902i	0.0749338	+	0.0637366i
$569$	−0.274678	+	0.158585i	−0.0115151	+	0.00664825i	−0.505746	−	0.862682i	$-0.668783\pi$
$569$	−0.274678	+	0.158585i	−0.0115151	+	0.00664825i	0.494231	+	0.869330i	$0.335450\pi$
$570$	−21.4906	+	13.1895i	−0.900143	+	0.552447i
$571$	−2.85631	−	10.6599i	−0.119533	−	0.446102i	0.880053	−	0.474875i	$-0.157507\pi$
$571$	−2.85631	−	10.6599i	−0.119533	−	0.446102i	−0.999586	+	0.0287727i	$0.990840\pi$
$572$	31.4079	+	15.9495i	1.31323	+	0.666884i
$573$	−3.92775	−	3.92775i	−0.164084	−	0.164084i
$574$		0			0
$575$	37.2744			1.55445
$576$	11.1477	+	13.6525i	0.464489	+	0.568854i
$577$	−5.13494	+	8.89397i	−0.213770	+	0.370261i	−0.952891	−	0.303312i	$-0.901908\pi$
$577$	−5.13494	+	8.89397i	−0.213770	+	0.370261i	0.739121	+	0.673572i	$0.235241\pi$
$578$	5.55672	−	23.2147i	0.231129	−	0.965602i
$579$	−0.364147	+	1.35901i	−0.0151334	+	0.0564787i
$580$	9.57606	−	6.23723i	0.397624	−	0.258987i
$581$		0			0
$582$	2.42374	+	1.31386i	0.100467	+	0.0544612i
$583$	31.9177	−	18.4277i	1.32190	−	0.763198i
$584$	−16.6563	+	5.93642i	−0.689242	+	0.245651i
$585$	36.0610	+	20.8198i	1.49094	+	0.860793i
$586$	−5.13989	+	0.138077i	−0.212327	+	0.00570390i
$587$	27.9965	−	27.9965i	1.15554	−	1.15554i	0.170113	−	0.985425i	$-0.445587\pi$
$587$	27.9965	−	27.9965i	1.15554	−	1.15554i	0.985425	−	0.170113i	$-0.0544133\pi$
$588$		0			0
$589$	−5.38191	−	5.38191i	−0.221758	−	0.221758i
$590$	−23.5986	+	24.9015i	−0.971539	+	1.02518i
$591$	6.76527	−	11.7178i	0.278286	−	0.482005i
$592$	−35.9009	−	5.58647i	−1.47552	−	0.229603i
$593$	−17.2951	−	29.9560i	−0.710225	−	1.23015i	−0.964772	−	0.263086i	$-0.915260\pi$
$593$	−17.2951	−	29.9560i	−0.710225	−	1.23015i	0.254547	−	0.967060i	$-0.418074\pi$
$594$	−5.77273	−	19.4401i	−0.236858	−	0.797635i
$595$		0			0
$596$	5.39783	−	25.5650i	0.221104	−	1.04718i
$597$	22.0178	+	5.89966i	0.901130	+	0.241457i
$598$	−26.3243	−	42.8921i	−1.07648	−	1.75399i
$599$	12.1993	+	7.04329i	0.498452	+	0.287781i	0.728074	−	0.685499i	$-0.240416\pi$
$599$	12.1993	+	7.04329i	0.498452	+	0.287781i	−0.229622	+	0.973280i	$0.573749\pi$
$600$	12.4159	−	8.57042i	0.506878	−	0.349886i
$601$		−	7.07501i		−	0.288595i	−0.989534	−	0.144298i	$-0.953908\pi$
$601$		−	7.07501i		−	0.288595i	0.989534	−	0.144298i	$-0.0460923\pi$
$602$		0			0
$603$	6.65391	−	6.65391i	0.270968	−	0.270968i
$604$	10.6192	−	20.9114i	0.432090	−	0.850871i
$605$	−4.69817	+	1.25887i	−0.191008	+	0.0511804i
$606$	1.97539	−	8.25271i	0.0802447	−	0.335244i
$607$	2.99647	+	5.19003i	0.121623	+	0.210657i	0.920408	−	0.390960i	$-0.127857\pi$
$607$	2.99647	+	5.19003i	0.121623	+	0.210657i	−0.798785	+	0.601617i	$0.794523\pi$
$608$	−26.9881	+	20.8543i	−1.09451	+	0.845752i
$609$		0			0
$610$	0.0338966	−	0.0100656i	0.00137243	−	0.000407545i
$611$	−6.85835	+	25.5957i	−0.277459	+	1.03549i
$612$	−1.53092	+	0.0823117i	−0.0618836	+	0.00332725i
$613$	−4.50820	−	16.8248i	−0.182084	−	0.679549i	−0.995236	−	0.0974963i	$-0.968917\pi$
$613$	−4.50820	−	16.8248i	−0.182084	−	0.679549i	0.813151	−	0.582052i	$-0.197750\pi$
$614$	1.01107	+	37.6369i	0.0408034	+	1.51890i
$615$		−	7.94074i		−	0.320201i
$616$		0			0
$617$			40.3690i			1.62519i	0.582827	+	0.812596i	$0.301947\pi$
$617$			40.3690i			1.62519i	−0.582827	+	0.812596i	$0.698053\pi$
$618$	−19.8448	+	0.533107i	−0.798276	+	0.0214447i
$619$	−11.3239	−	42.2614i	−0.455147	−	1.69863i	−0.687656	−	0.726036i	$-0.741360\pi$
$619$	−11.3239	−	42.2614i	−0.455147	−	1.69863i	0.232510	−	0.972594i	$-0.425306\pi$
$620$	6.22348	+	5.58840i	0.249941	+	0.224435i
$621$	−7.49855	+	27.9850i	−0.300907	+	1.12300i
$622$	−9.61828	−	32.3902i	−0.385658	−	1.29873i
$623$		0			0
$624$	−18.6305	−	8.23444i	−0.745819	−	0.329641i
$625$	−9.58545	−	16.6025i	−0.383418	−	0.664099i
$626$	−24.8781	−	5.95488i	−0.994328	−	0.238005i
$627$	16.0498	−	4.30052i	0.640966	−	0.171746i
$628$	−9.11188	−	27.9147i	−0.363603	−	1.11392i
$629$	2.23470	−	2.23470i	0.0891033	−	0.0891033i
$630$		0			0
$631$			23.7329i			0.944792i	0.881386	+	0.472396i	$0.156611\pi$
$631$			23.7329i			0.944792i	−0.881386	+	0.472396i	$0.843389\pi$
$632$	2.10297	+	0.385344i	0.0836516	+	0.0153281i
$633$	10.0566	+	5.80618i	0.399714	+	0.230775i
$634$	9.14443	−	5.61224i	0.363172	−	0.222890i
$635$	−43.8609	−	11.7525i	−1.74057	−	0.466384i
$636$	−17.8577	+	11.6313i	−0.708104	+	0.461213i
$637$		0			0
$638$	−7.21920	+	2.14374i	−0.285811	+	0.0848717i
$639$	−0.913132	−	1.58159i	−0.0361230	−	0.0625668i
$640$	28.3854	−	24.4772i	1.12203	−	0.967545i
$641$	7.49413	−	12.9802i	0.296000	−	0.512687i	−0.679217	−	0.733938i	$-0.737680\pi$
$641$	7.49413	−	12.9802i	0.296000	−	0.512687i	0.975217	+	0.221250i	$0.0710138\pi$
$642$	−8.65711	−	8.20415i	−0.341669	−	0.323792i
$643$	11.8452	+	11.8452i	0.467130	+	0.467130i	0.900983	−	0.433854i	$-0.142847\pi$
$643$	11.8452	+	11.8452i	0.467130	+	0.467130i	−0.433854	+	0.900983i	$0.642847\pi$
$644$		0			0
$645$	−11.9909	+	11.9909i	−0.472142	+	0.472142i
$646$	−0.0796675	−	2.96561i	−0.00313448	−	0.116681i
$647$	3.57210	+	2.06235i	0.140434	+	0.0810795i	0.568571	−	0.822634i	$-0.307497\pi$
$647$	3.57210	+	2.06235i	0.140434	+	0.0810795i	−0.428137	+	0.903714i	$0.640830\pi$
$648$	−2.33946	−	6.56401i	−0.0919027	−	0.257859i
$649$	19.5784	−	11.3036i	0.768518	−	0.443704i
$650$	22.9747	−	42.3826i	0.901142	−	1.66238i
$651$		0			0
$652$	−43.3251	−	9.14770i	−1.69674	−	0.358252i
$653$	−9.31592	+	34.7675i	−0.364560	+	1.36056i	0.503456	+	0.864021i	$0.332062\pi$
$653$	−9.31592	+	34.7675i	−0.364560	+	1.36056i	−0.868016	+	0.496536i	$0.834605\pi$
$654$	−1.41069	−	0.337667i	−0.0551625	−	0.0132038i
$655$	−8.26760	+	14.3199i	−0.323042	+	0.559525i
$656$	−1.15165	−	10.6788i	−0.0449645	−	0.416939i
$657$	13.7738			0.537368
$658$		0			0
$659$	7.38409	+	7.38409i	0.287643	+	0.287643i	0.836148	−	0.548504i	$-0.184803\pi$
$659$	7.38409	+	7.38409i	0.287643	+	0.287643i	−0.548504	+	0.836148i	$0.684803\pi$
$660$	−17.3588	+	5.66622i	−0.675689	+	0.220557i
$661$	−5.15817	−	19.2505i	−0.200629	−	0.748759i	−0.990737	−	0.135792i	$-0.956642\pi$
$661$	−5.15817	−	19.2505i	−0.200629	−	0.748759i	0.790108	−	0.612968i	$-0.210024\pi$
$662$	−23.3881	−	38.1080i	−0.909004	−	1.48111i
$663$	1.53440	−	0.885884i	0.0595910	−	0.0344049i
$664$	14.6159	−	1.18018i	0.567206	−	0.0458000i
$665$		0			0
$666$	24.8810	+	13.4875i	0.964120	+	0.522629i
$667$	10.3924	+	2.78464i	0.402396	+	0.107822i
$668$	4.23434	−	0.227665i	0.163832	−	0.00880862i
$669$	−10.9959	+	2.94633i	−0.425124	+	0.113912i
$670$	−14.5246	−	13.7647i	−0.561136	−	0.531776i
$671$	−0.0233006			−0.000899511
$672$		0			0
$673$	−35.0089			−1.34949			−0.674746	−	0.738050i	$-0.735747\pi$
$673$	−35.0089			−1.34949			−0.674746	+	0.738050i	$0.735747\pi$
$674$	−11.8135	−	11.1954i	−0.455040	−	0.431231i
$675$	−26.8079	+	7.18315i	−1.03184	+	0.276480i
$676$	−39.0329	+	2.09866i	−1.50127	+	0.0807175i
$677$	15.4169	+	4.13095i	0.592521	+	0.158765i	0.542605	−	0.839988i	$-0.317438\pi$
$677$	15.4169	+	4.13095i	0.592521	+	0.158765i	0.0499158	+	0.998753i	$0.484105\pi$
$678$	20.5502	+	11.1399i	0.789228	+	0.427824i
$679$		0			0
$680$	0.262400	+	3.24967i	0.0100626	+	0.124619i
$681$	−13.3869	+	7.72893i	−0.512987	+	0.296173i
$682$	−2.88308	−	4.69761i	−0.110399	−	0.179881i
$683$	12.2351	+	45.6621i	0.468164	+	1.74721i	0.646180	+	0.763185i	$0.276366\pi$
$683$	12.2351	+	45.6621i	0.468164	+	1.74721i	−0.178016	+	0.984028i	$0.556968\pi$
$684$	25.2559	−	8.24397i	0.965682	−	0.315216i
$685$	36.6709	+	36.6709i	1.40112	+	1.40112i
$686$		0			0
$687$	−12.5378			−0.478348
$688$	−14.3866	+	17.8647i	−0.548482	+	0.681084i
$689$	−34.0504	+	58.9771i	−1.29722	+	2.24685i
$690$	25.3711	+	6.07289i	0.965862	+	0.231191i
$691$	1.84367	−	6.88067i	0.0701365	−	0.261753i	−0.921950	−	0.387309i	$-0.873405\pi$
$691$	1.84367	−	6.88067i	0.0701365	−	0.261753i	0.992087	+	0.125556i	$0.0400714\pi$
$692$	−5.88502	−	1.24257i	−0.223715	−	0.0472354i
$693$		0			0
$694$	11.7416	−	21.6603i	0.445704	−	0.822213i
$695$	6.19049	−	3.57408i	0.234819	−	0.135573i
$696$	4.10192	−	1.46195i	0.155483	−	0.0554153i
$697$	0.809094	+	0.467131i	0.0306466	+	0.0176938i
$698$	0.0135076	+	0.502820i	0.000511272	+	0.0190320i
$699$	−11.5598	+	11.5598i	−0.437230	+	0.437230i
$700$		0			0
$701$	1.77330	+	1.77330i	0.0669766	+	0.0669766i	0.739802	−	0.672825i	$-0.234919\pi$
$701$	1.77330	+	1.77330i	0.0669766	+	0.0669766i	−0.672825	+	0.739802i	$0.734919\pi$
$702$	27.1982	+	25.7751i	1.02653	+	0.972820i
$703$	−27.3825	+	47.4279i	−1.03275	+	1.78878i
$704$	−22.5226	+	10.1376i	−0.848852	+	0.382075i
$705$	−6.86815	−	11.8960i	−0.258669	−	0.448028i
$706$	−22.6251	+	6.71852i	−0.851505	+	0.252855i
$707$		0			0
$708$	−10.9539	+	7.13467i	−0.411673	+	0.268137i
$709$	12.0863	+	3.23852i	0.453912	+	0.121625i	0.478529	−	0.878072i	$-0.341170\pi$
$709$	12.0863	+	3.23852i	0.453912	+	0.121625i	−0.0246175	+	0.999697i	$0.507837\pi$
$710$	−3.30995	+	2.03143i	−0.124220	+	0.0762381i
$711$	−1.44226	−	0.832691i	−0.0540891	−	0.0312283i
$712$	−3.18343	+	17.3732i	−0.119304	+	0.651087i
$713$			7.87454i			0.294904i
$714$		0			0
$715$	−41.2596	+	41.2596i	−1.54302	+	1.54302i
$716$	−1.24552	−	3.81573i	−0.0465474	−	0.142600i
$717$	−15.8168	+	4.23810i	−0.590690	+	0.158275i
$718$	−24.7264	−	5.91858i	−0.922782	−	0.220880i
$719$	−5.91286	−	10.2414i	−0.220512	−	0.381939i	0.734451	−	0.678661i	$-0.237440\pi$
$719$	−5.91286	−	10.2414i	−0.220512	−	0.381939i	−0.954964	+	0.296723i	$0.904106\pi$
$720$	−27.2286	+	10.5368i	−1.01475	+	0.392684i
$721$		0			0
$722$	6.98542	+	23.5238i	0.259970	+	0.875467i
$723$	5.87157	−	21.9130i	0.218366	−	0.814953i
$724$	−30.1344	−	27.0593i	−1.11994	−	1.00565i
$725$	2.66751	+	9.95529i	0.0990689	+	0.369730i
$726$	−1.85270	+	0.0497705i	−0.0687602	+	0.00184716i
$727$		−	27.7703i		−	1.02994i	−0.857207	−	0.514972i	$-0.827802\pi$
$727$		−	27.7703i		−	1.02994i	0.857207	−	0.514972i	$-0.172198\pi$
$728$		0			0
$729$		−	7.00960i		−	0.259615i
$730$	−0.786570	−	29.2800i	−0.0291123	−	1.08370i
$731$	−0.516383	−	1.92717i	−0.0190991	−	0.0712789i
$732$	0.0134541		0.000723380i	0.000497280		2.67369e-5i
$733$	−13.1208	+	48.9673i	−0.484626	+	1.80865i	0.0971120	+	0.995273i	$0.469039\pi$
$733$	−13.1208	+	48.9673i	−0.484626	+	1.80865i	−0.581738	+	0.813376i	$0.697627\pi$
$734$	−29.3198	+	8.70654i	−1.08221	+	0.321364i
$735$		0			0
$736$	35.0003	+	4.48733i	1.29013	+	0.165405i
$737$	6.59319	+	11.4197i	0.242863	+	0.420651i
$738$	−1.94761	+	8.13667i	−0.0716926	+	0.299515i
$739$	13.8089	−	3.70009i	0.507970	−	0.136110i	0.00427340	−	0.999991i	$-0.498640\pi$
$739$	13.8089	−	3.70009i	0.507970	−	0.136110i	0.503696	+	0.863881i	$0.331973\pi$
$740$	27.2504	−	53.6615i	1.00174	−	1.97264i
$741$	−21.7101	+	21.7101i	−0.797539	+	0.797539i
$742$		0			0
$743$			31.4037i			1.15209i	0.817418	+	0.576045i	$0.195405\pi$
$743$			31.4037i			1.15209i	−0.817418	+	0.576045i	$0.804595\pi$
$744$	1.81057	+	2.62297i	0.0663789	+	0.0961627i
$745$	37.4826	+	21.6406i	1.37326	+	0.792850i
$746$	−12.6715	−	20.6465i	−0.463935	−	0.755923i
$747$	−11.0329	−	2.95625i	−0.403672	−	0.108164i
$748$	0.443827	−	2.10204i	0.0162279	−	0.0768582i
$749$		0			0
$750$	1.16135	+	3.91091i	0.0424064	+	0.142806i
$751$	−6.32654	−	10.9579i	−0.230859	−	0.399859i	0.727202	−	0.686423i	$-0.240820\pi$
$751$	−6.32654	−	10.9579i	−0.230859	−	0.399859i	−0.958061	+	0.286564i	$0.907487\pi$
$752$	−10.9617	−	15.0018i	−0.399732	−	0.547060i
$753$	6.89896	−	11.9493i	0.251412	−	0.435458i
$754$	9.57178	−	10.1002i	0.348584	−	0.367829i
$755$	27.4707	+	27.4707i	0.999760	+	0.999760i
$756$		0			0
$757$	19.6555	−	19.6555i	0.714391	−	0.714391i	−0.253060	−	0.967451i	$-0.581437\pi$
$757$	19.6555	−	19.6555i	0.714391	−	0.714391i	0.967451	+	0.253060i	$0.0814370\pi$
$758$	−8.68189	+	0.233228i	−0.315340	+	0.00847122i
$759$	−14.8878	−	8.59545i	−0.540391	−	0.311995i
$760$	−18.9670	−	53.2173i	−0.688006	−	1.93039i
$761$	10.6308	−	6.13772i	0.385368	−	0.222492i	−0.294783	−	0.955564i	$-0.595248\pi$
$761$	10.6308	−	6.13772i	0.385368	−	0.222492i	0.680151	+	0.733072i	$0.261914\pi$
$762$	−15.2114	−	8.24576i	−0.551050	−	0.298713i
$763$		0			0
$764$	10.4285	−	6.79248i	0.377292	−	0.245743i
$765$	0.657290	−	2.45304i	0.0237644	−	0.0886898i
$766$	−10.8061	+	45.1452i	−0.390439	+	1.63116i
$767$	−20.8866	+	36.1766i	−0.754170	+	1.30626i
$768$	12.6902	−	6.55282i	0.457917	−	0.236455i
$769$	−44.0633			−1.58896			−0.794481	−	0.607289i	$-0.792257\pi$
$769$	−44.0633			−1.58896			−0.794481	+	0.607289i	$0.792257\pi$
$770$		0			0
$771$	1.44954	+	1.44954i	0.0522037	+	0.0522037i
$772$	−2.81071	−	1.42734i	−0.101160	−	0.0513710i
$773$	−11.3171	−	42.2358i	−0.407046	−	1.51912i	−0.800251	−	0.599666i	$-0.795300\pi$
$773$	−11.3171	−	42.2358i	−0.407046	−	1.51912i	0.393205	−	0.919451i	$-0.371366\pi$
$774$	15.2278	−	9.34580i	0.547352	−	0.335928i
$775$	−6.53271	+	3.77166i	−0.234662	+	0.135482i
$776$	−4.00215	+	4.70524i	−0.143669	+	0.168908i
$777$		0			0
$778$	0.223973	−	0.413174i	0.00802982	−	0.0148130i
$779$	−15.6380	−	4.19019i	−0.560290	−	0.150129i
$780$	22.5430	−	25.1049i	0.807170	−	0.898899i
$781$	2.47196	−	0.662359i	0.0884536	−	0.0237011i
$782$	−2.11129	+	2.22785i	−0.0754995	+	0.0796679i
$783$	−8.01088			−0.286286
$784$		0			0
$785$	48.6408			1.73607
$786$	−4.33399	+	4.57327i	−0.154588	+	0.163123i
$787$	18.3040	−	4.90453i	0.652465	−	0.174828i	0.0826221	−	0.996581i	$-0.473671\pi$
$787$	18.3040	−	4.90453i	0.652465	−	0.174828i	0.569843	+	0.821753i	$0.307004\pi$
$788$	22.5566	+	20.2548i	0.803546	+	0.721547i
$789$	10.2179	+	2.73789i	0.363769	+	0.0974715i
$790$	−1.68774	+	3.11347i	−0.0600473	+	0.110772i
$791$		0			0
$792$	19.1768	−	1.54847i	0.681419	−	0.0550223i
$793$	0.0372863	−	0.0215273i	0.00132408	−	0.000764456i
$794$	3.37477	−	2.07121i	0.119766	−	0.0735044i
$795$	−9.13682	−	34.0991i	−0.324050	−	1.20937i
$796$	−23.1248	+	45.5373i	−0.819636	+	1.61403i
$797$	16.1055	+	16.1055i	0.570485	+	0.570485i	0.932264	−	0.361779i	$-0.117831\pi$
$797$	16.1055	+	16.1055i	0.570485	+	0.570485i	−0.361779	+	0.932264i	$0.617831\pi$
$798$		0			0
$799$	1.61613			0.0571747
$800$	13.0414	+	31.1855i	0.461082	+	1.10257i
$801$	6.87908	−	11.9149i	0.243060	−	0.420993i
$802$	1.69558	−	7.08371i	0.0598728	−	0.250135i
$803$	−4.99557	+	18.6437i	−0.176290	+	0.657922i
$804$	−4.16154	−	6.38924i	−0.146766	−	0.225331i
$805$		0			0
$806$	8.95368	+	4.85360i	0.315380	+	0.170961i
$807$	6.24017	−	3.60276i	0.219664	−	0.126823i
$808$	17.1775	+	8.15043i	0.604301	+	0.286731i
$809$	−32.5667	−	18.8024i	−1.14498	−	0.661056i	−0.197323	−	0.980339i	$-0.563225\pi$
$809$	−32.5667	−	18.8024i	−1.14498	−	0.661056i	−0.947660	+	0.319282i	$0.896558\pi$
$810$	11.5388	−	0.309976i	0.405433	−	0.0108915i
$811$	−7.00106	+	7.00106i	−0.245841	+	0.245841i	−0.819261	−	0.573421i	$-0.805616\pi$
$811$	−7.00106	+	7.00106i	−0.245841	+	0.245841i	0.573421	+	0.819261i	$0.305616\pi$
$812$		0			0
$813$	16.4887	+	16.4887i	0.578286	+	0.578286i
$814$	−27.2801	+	28.7862i	−0.956166	+	1.00896i
$815$	36.6744	−	63.5218i	1.28465	−	2.22507i
$816$	−0.191014	+	1.22753i	−0.00668682	+	0.0429721i
$817$	17.2868	+	29.9416i	0.604789	+	1.04752i
$818$	−0.0293493	−	0.0988357i	−0.00102617	−	0.00345571i
$819$		0			0
$820$	17.4079	+	3.67552i	0.607910	+	0.128355i
$821$	−0.972462	−	0.260570i	−0.0339392	−	0.00909397i	0.241810	−	0.970324i	$-0.422259\pi$
$821$	−0.972462	−	0.260570i	−0.0339392	−	0.00909397i	−0.275749	+	0.961230i	$0.588926\pi$
$822$	10.3366	+	16.8422i	0.360530	+	0.587438i
$823$	−10.4164	−	6.01390i	−0.363092	−	0.209631i	0.307344	−	0.951598i	$-0.400560\pi$
$823$	−10.4164	−	6.01390i	−0.363092	−	0.209631i	−0.670436	+	0.741967i	$0.733893\pi$
$824$	8.01687	−	43.7511i	0.279281	−	1.52414i
$825$		−	16.4678i		−	0.573336i
$826$		0			0
$827$	16.1838	−	16.1838i	0.562764	−	0.562764i	−0.367328	−	0.930092i	$-0.619727\pi$
$827$	16.1838	−	16.1838i	0.562764	−	0.562764i	0.930092	+	0.367328i	$0.119727\pi$
$828$	−24.5076	−	12.4455i	−0.851700	−	0.432510i
$829$	4.52931	−	1.21363i	0.157310	−	0.0421510i	−0.179305	−	0.983794i	$-0.557385\pi$
$829$	4.52931	−	1.21363i	0.157310	−	0.0421510i	0.336614	+	0.941643i	$0.390718\pi$
$830$	−5.65426	+	23.6222i	−0.196262	+	0.819938i
$831$	1.25148	+	2.16763i	0.0434134	+	0.0751941i
$832$	26.6753	−	37.0309i	0.924798	−	1.28382i
$833$		0			0
$834$	2.61108	−	0.775362i	0.0904144	−	0.0268486i
$835$	−1.81799	+	6.78482i	−0.0629141	+	0.234798i
$836$	1.99878	+	37.1753i	0.0691292	+	1.28573i
$837$	−1.51750	−	5.66339i	−0.0524525	−	0.195756i
$838$	−0.738090	−	27.4753i	−0.0254969	−	0.949118i
$839$			47.4324i			1.63755i	0.574116	+	0.818774i	$0.305346\pi$
$839$			47.4324i			1.63755i	−0.574116	+	0.818774i	$0.694654\pi$
$840$		0			0
$841$		−	26.0251i		−	0.897417i
$842$	−7.75914	+	0.208440i	−0.267398	+	0.00718331i
$843$	−1.50742	−	5.62576i	−0.0519182	−	0.193762i
$844$	−17.3833	+	19.3588i	−0.598359	+	0.666358i
$845$	16.7585	−	62.5437i	0.576511	−	2.15157i
$846$	4.11990	+	13.8740i	0.141645	+	0.477000i
$847$		0			0
$848$	−17.2328	−	44.5319i	−0.591776	−	1.52923i
$849$	8.80999	+	15.2594i	0.302358	+	0.523700i
$850$	−2.85947	−	0.684449i	−0.0980789	−	0.0234764i
$851$	54.7294	−	14.6647i	1.87610	−	0.502700i
$852$	−1.40678	+	0.459200i	−0.0481956	+	0.0157319i
$853$	−3.99601	+	3.99601i	−0.136821	+	0.136821i	−0.772200	−	0.635379i	$-0.780844\pi$
$853$	−3.99601	+	3.99601i	−0.136821	+	0.136821i	0.635379	+	0.772200i	$0.280844\pi$
$854$		0			0
$855$			44.0078i			1.50503i
$856$	21.9925	−	15.1809i	0.751687	−	0.518872i
$857$	−9.68683	−	5.59270i	−0.330896	−	0.191043i	0.325343	−	0.945596i	$-0.394520\pi$
$857$	−9.68683	−	5.59270i	−0.330896	−	0.191043i	−0.656239	+	0.754553i	$0.727854\pi$
$858$	−18.9497	+	11.6300i	−0.646932	+	0.397043i
$859$	20.5870	+	5.51627i	0.702420	+	0.188213i	0.592314	−	0.805707i	$-0.298214\pi$
$859$	20.5870	+	5.51627i	0.702420	+	0.188213i	0.110106	+	0.993920i	$0.464881\pi$
$860$	−20.7366	−	31.8371i	−0.707112	−	1.08563i
$861$		0			0
$862$	−45.8273	+	13.6084i	−1.56088	+	0.463505i
$863$	−14.8376	−	25.6994i	−0.505076	−	0.874818i	−0.999983	−	0.00587153i	$-0.998131\pi$
$863$	−14.8376	−	25.6994i	−0.505076	−	0.874818i	0.494906	−	0.868946i	$-0.335202\pi$
$864$	−26.0371	+	3.51759i	−0.885799	+	0.119671i
$865$	4.98163	−	8.62843i	0.169380	−	0.293375i
$866$	19.1884	+	18.1844i	0.652047	+	0.617931i
$867$	10.6538	+	10.6538i	0.361821	+	0.361821i
$868$		0			0
$869$	1.65018	−	1.65018i	0.0559787	−	0.0559787i
$870$	0.193708	+	7.21074i	0.00656731	+	0.244467i
$871$	−21.1012	−	12.1828i	−0.714987	−	0.412798i
$872$	1.39321	−	2.93626i	0.0471800	−	0.0994345i
$873$	4.16701	−	2.40583i	0.141032	−	0.0814249i
$874$	25.3475	−	46.7598i	0.857392	−	1.58167i
$875$		0			0
$876$	2.30571	−	10.9203i	0.0779028	−	0.368961i
$877$	1.04356	−	3.89460i	0.0352384	−	0.131511i	−0.946066	−	0.323974i	$-0.894981\pi$
$877$	1.04356	−	3.89460i	0.0352384	−	0.131511i	0.981304	+	0.192463i	$0.0616475\pi$
$878$	8.29539	+	1.98560i	0.279956	+	0.0670109i
$879$	1.62270	−	2.81060i	0.0547324	−	0.0947993i
$880$	−4.38679	−	40.6771i	−0.147879	−	1.37122i
$881$	23.4719			0.790789			0.395394	−	0.918511i	$-0.370608\pi$
$881$	23.4719			0.790789			0.395394	+	0.918511i	$0.370608\pi$
$882$		0			0
$883$	−22.0401	−	22.0401i	−0.741710	−	0.741710i	0.231197	−	0.972907i	$-0.425736\pi$
$883$	−22.0401	−	22.0401i	−0.741710	−	0.741710i	−0.972907	+	0.231197i	$0.925736\pi$
$884$	1.23183	+	3.77379i	0.0414311	+	0.126926i
$885$	−5.60453	−	20.9164i	−0.188394	−	0.703097i
$886$	26.0657	+	42.4707i	0.875693	+	1.42683i
$887$	16.1626	−	9.33146i	0.542686	−	0.313320i	−0.203481	−	0.979079i	$-0.565225\pi$
$887$	16.1626	−	9.33146i	0.542686	−	0.313320i	0.746167	+	0.665759i	$0.231892\pi$
$888$	14.8583	−	17.4685i	0.498611	−	0.586206i
$889$		0			0
$890$	−25.7212	−	13.9429i	−0.862176	−	0.467367i
$891$	−7.34723	−	1.96868i	−0.246141	−	0.0659534i
$892$	−1.36938	−	25.4692i	−0.0458504	−	0.852771i
$893$	−27.0514	+	7.24841i	−0.905242	+	0.242559i
$894$	11.9706	+	11.3443i	0.400358	+	0.379410i
$895$	6.64882			0.222246
$896$		0			0
$897$	31.7651			1.06061
$898$	−22.5708	−	21.3899i	−0.753199	−	0.713790i
$899$	−2.10314	+	0.563535i	−0.0701437	+	0.0187949i
$900$	−1.41365	−	26.2925i	−0.0471217	−	0.876417i
$901$	4.01190	+	1.07499i	0.133656	+	0.0358130i
$902$	−10.3071	−	5.58726i	−0.343189	−	0.186035i
$903$		0			0
$904$	−33.9332	+	39.8945i	−1.12860	+	1.32687i
$905$	58.0996	−	33.5438i	1.93130	−	1.11504i
$906$	7.74329	+	12.6167i	0.257254	+	0.419162i
$907$	−1.07993	−	4.03036i	−0.0358585	−	0.133826i	0.945676	−	0.325110i	$-0.105401\pi$
$907$	−1.07993	−	4.03036i	−0.0358585	−	0.133826i	−0.981535	+	0.191284i	$0.938735\pi$
$908$	−10.7472	−	32.9246i	−0.356658	−	1.09264i
$909$	−10.4724	−	10.4724i	−0.347347	−	0.347347i
$910$		0			0
$911$	−26.5648			−0.880132			−0.440066	−	0.897965i	$-0.645045\pi$
$911$	−26.5648			−0.880132			−0.440066	+	0.897965i	$0.645045\pi$
$912$	−2.30825	−	21.4035i	−0.0764338	−	0.708742i
$913$	8.00293	−	13.8615i	0.264858	−	0.458748i
$914$	−36.7746	−	8.80245i	−1.21639	−	0.291159i
$915$	−0.00577645	+	0.0215580i	−0.000190964	+	0.000712686i
$916$	5.80337	−	27.4858i	0.191749	−	0.908155i
$917$		0			0
$918$	1.08911	−	2.00914i	0.0359461	−	0.0663116i
$919$	−19.0369	+	10.9909i	−0.627969	+	0.362558i	−0.779965	−	0.625823i	$-0.784763\pi$
$919$	−19.0369	+	10.9909i	−0.627969	+	0.362558i	0.151996	+	0.988381i	$0.451430\pi$
$920$	−25.0567	+	52.8083i	−0.826094	+	1.74104i
$921$	−20.5807	−	11.8823i	−0.678157	−	0.391534i
$922$	1.26517	+	47.0956i	0.0416660	+	1.55101i
$923$	−3.34375	+	3.34375i	−0.110061	+	0.110061i
$924$		0			0
$925$	38.3795	+	38.3795i	1.26191	+	1.26191i
$926$	10.0969	+	9.56859i	0.331804	+	0.314444i
$927$	−17.3237	+	30.0055i	−0.568985	+	0.985510i
$928$	1.30628	+	9.66904i	0.0428808	+	0.317402i
$929$	7.02800	+	12.1729i	0.230581	+	0.399379i	0.957979	−	0.286837i	$-0.0926039\pi$
$929$	7.02800	+	12.1729i	0.230581	+	0.399379i	−0.727398	+	0.686216i	$0.759271\pi$
$930$	−5.06103	+	1.50288i	−0.165958	+	0.0492812i
$931$		0			0
$932$	−19.9910	−	30.6923i	−0.654825	−	1.00536i
$933$	20.5999	+	5.51974i	0.674412	+	0.180708i
$934$	3.35108	−	2.05667i	0.109651	−	0.0672962i
$935$	3.08194	+	1.77936i	0.100790	+	0.0581913i
$936$	−29.2567	+	20.1952i	−0.956285	+	0.660102i
$937$			57.9965i			1.89466i	0.320256	+	0.947331i	$0.396231\pi$
$937$			57.9965i			1.89466i	−0.320256	+	0.947331i	$0.603769\pi$
$938$		0			0
$939$	11.4172	−	11.4172i	0.372585	−	0.372585i
$940$	29.2577	−	9.55025i	0.954282	−	0.311495i
$941$	−21.1286	+	5.66139i	−0.688773	+	0.184556i	−0.586196	−	0.810169i	$-0.699375\pi$
$941$	−21.1286	+	5.66139i	−0.688773	+	0.184556i	−0.102576	+	0.994725i	$0.532709\pi$
$942$	18.0252	+	4.31455i	0.587292	+	0.140576i
$943$	8.37494	+	14.5058i	0.272726	+	0.472375i
$944$	−10.5706	−	27.3159i	−0.344043	−	0.889056i
$945$		0			0
$946$	7.12720	+	24.0013i	0.231725	+	0.780350i
$947$	6.93379	−	25.8773i	0.225318	−	0.840898i	−0.756959	−	0.653463i	$-0.773316\pi$
$947$	6.93379	−	25.8773i	0.225318	−	0.840898i	0.982277	−	0.187436i	$-0.0600177\pi$
$948$	−0.901611	+	1.00407i	−0.0292830	+	0.0326108i
$949$	−9.23073	−	34.4495i	−0.299642	−	1.11828i
$950$	50.9325	−	1.36824i	1.65247	−	0.0443915i
$951$			6.77220i			0.219604i
$952$		0			0
$953$			20.2198i			0.654983i	0.944854	+	0.327491i	$0.106203\pi$
$953$			20.2198i			0.654983i	−0.944854	+	0.327491i	$0.893797\pi$
$954$	0.998833	+	37.1814i	0.0323384	+	1.20379i
$955$	5.33572	+	19.9132i	0.172660	+	0.644376i
$956$	−1.96977	−	36.6357i	−0.0637069	−	1.18488i
$957$	1.23025	−	4.59136i	0.0397684	−	0.148418i
$958$	−5.13389	+	1.52451i	−0.165869	+	0.0492547i
$959$		0			0
$960$	3.79584	+	23.3514i	0.122510	+	0.753662i
$961$	14.7032	+	25.4667i	0.474297	+	0.821506i
$962$	17.0590	−	71.2684i	0.550004	−	2.29779i
$963$	−20.1067	+	5.38758i	−0.647931	+	0.173612i
$964$	45.3205	+	23.0147i	1.45968	+	0.741253i
$965$	3.69236	−	3.69236i	0.118861	−	0.118861i
$966$		0			0
$967$		−	33.3933i		−	1.07385i	−0.843628	−	0.536927i	$-0.819585\pi$
$967$		−	33.3933i		−	1.07385i	0.843628	−	0.536927i	$-0.180415\pi$
$968$	0.748449	−	4.08458i	0.0240561	−	0.131283i
$969$	1.62166	+	0.936267i	0.0520953	+	0.0300772i
$970$	−5.35219	−	8.72071i	−0.171848	−	0.280005i
$971$	10.2753	+	2.75325i	0.329749	+	0.0883560i	0.419895	−	0.907573i	$-0.362067\pi$
$971$	10.2753	+	2.75325i	0.329749	+	0.0883560i	−0.0901463	+	0.995929i	$0.528733\pi$
$972$	31.5697	+	6.66567i	1.01260	+	0.213801i
$973$		0			0
$974$	−6.77134	−	22.8029i	−0.216968	−	0.730653i
$975$	15.2145	+	26.3523i	0.487254	+	0.843949i
$976$	−0.00464169	+	0.0298294i	−0.000148577	+	0.000954815i
$977$	−14.1382	+	24.4881i	−0.452321	+	0.783442i	−0.998530	−	0.0542066i	$-0.982737\pi$
$977$	−14.1382	+	24.4881i	−0.452321	+	0.783442i	0.546209	+	0.837649i	$0.316070\pi$
$978$	19.2252	−	20.2866i	0.614754	−	0.648695i
$979$	13.6326	+	13.6326i	0.435700	+	0.435700i
$980$		0			0
$981$	−1.79012	+	1.79012i	−0.0571541	+	0.0571541i
$982$	12.8277	−	0.344601i	0.409350	−	0.0109967i
$983$	1.68335	+	0.971882i	0.0536905	+	0.0309982i	0.526605	−	0.850110i	$-0.323465\pi$
$983$	1.68335	+	0.971882i	0.0536905	+	0.0309982i	−0.472914	+	0.881108i	$0.656798\pi$
$984$	6.12494	+	2.90618i	0.195256	+	0.0926457i
$985$	−43.4895	+	25.1087i	−1.38569	+	0.800028i
$986$	−0.746110	−	0.404450i	−0.0237610	−	0.0128803i
$987$		0			0
$988$	−37.5445	−	57.6423i	−1.19445	−	1.83385i
$989$	9.25795	−	34.5512i	0.294386	−	1.09866i
$990$	−7.41871	+	30.9936i	−0.235782	+	0.985042i
$991$	4.30271	−	7.45251i	0.136680	−	0.236737i	−0.789558	−	0.613676i	$-0.789690\pi$
$991$	4.30271	−	7.45251i	0.136680	−	0.236737i	0.926238	+	0.376939i	$0.123023\pi$
$992$	−6.58820	+	2.75510i	−0.209176	+	0.0874745i
$993$	28.2221			0.895600
$994$		0			0
$995$	−59.8211	−	59.8211i	−1.89646	−	1.89646i
$996$	−4.19068	+	8.25229i	−0.132787	+	0.261484i
$997$	−2.84895	−	10.6324i	−0.0902272	−	0.336732i	0.906025	−	0.423223i	$-0.139101\pi$
$997$	−2.84895	−	10.6324i	−0.0902272	−	0.336732i	−0.996253	+	0.0864907i	$0.972435\pi$
$998$	7.99959	−	4.90961i	0.253223	−	0.155411i
$999$	−36.5355	+	21.0938i	−1.15593	+	0.667378i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	784.2.x.m.557.2		24
7.2	even	3	inner	784.2.x.m.765.3		24
7.3	odd	6		112.2.m.d.29.6	✓	12
7.4	even	3		784.2.m.h.589.6		12
7.5	odd	6		784.2.x.l.765.3		24
7.6	odd	2		784.2.x.l.557.2		24
16.5	even	4	inner	784.2.x.m.165.3		24
28.3	even	6		448.2.m.d.337.3		12
56.3	even	6		896.2.m.h.673.4		12
56.45	odd	6		896.2.m.g.673.3		12
112.3	even	12		896.2.m.h.225.4		12
112.5	odd	12		784.2.x.l.373.2		24
112.37	even	12	inner	784.2.x.m.373.2		24
112.45	odd	12		896.2.m.g.225.3		12
112.53	even	12		784.2.m.h.197.6		12
112.59	even	12		448.2.m.d.113.3		12
112.69	odd	4		784.2.x.l.165.3		24
112.101	odd	12		112.2.m.d.85.6	yes	12
224.59	even	24		7168.2.a.bi.1.9		12
224.101	odd	24		7168.2.a.bj.1.4		12
224.171	even	24		7168.2.a.bi.1.4		12
224.213	odd	24		7168.2.a.bj.1.9		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
112.2.m.d.29.6	✓	12	7.3	odd	6
112.2.m.d.85.6	yes	12	112.101	odd	12
448.2.m.d.113.3		12	112.59	even	12
448.2.m.d.337.3		12	28.3	even	6
784.2.m.h.197.6		12	112.53	even	12
784.2.m.h.589.6		12	7.4	even	3
784.2.x.l.165.3		24	112.69	odd	4
784.2.x.l.373.2		24	112.5	odd	12
784.2.x.l.557.2		24	7.6	odd	2
784.2.x.l.765.3		24	7.5	odd	6
784.2.x.m.165.3		24	16.5	even	4	inner
784.2.x.m.373.2		24	112.37	even	12	inner
784.2.x.m.557.2		24	1.1	even	1	trivial
784.2.x.m.765.3		24	7.2	even	3	inner
896.2.m.g.225.3		12	112.45	odd	12
896.2.m.g.673.3		12	56.45	odd	6
896.2.m.h.225.4		12	112.3	even	12
896.2.m.h.673.4		12	56.3	even	6
7168.2.a.bi.1.4		12	224.171	even	24
7168.2.a.bi.1.9		12	224.59	even	24
7168.2.a.bj.1.4		12	224.101	odd	24
7168.2.a.bj.1.9		12	224.213	odd	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)

\(f(q)\)	\(=\)	\(q+(-1.02649 - 0.972785i) q^{2} +(0.862219 - 0.231031i) q^{3} +(0.107378 + 1.99712i) q^{4} +(-3.20004 - 0.857449i) q^{5} +(-1.10981 - 0.601602i) q^{6} +(1.83254 - 2.15448i) q^{8} +(-1.90803 + 1.10160i) q^{9} +O(q^{10})\)	\(q+(-1.02649 - 0.972785i) q^{2} +(0.862219 - 0.231031i) q^{3} +(0.107378 + 1.99712i) q^{4} +(-3.20004 - 0.857449i) q^{5} +(-1.10981 - 0.601602i) q^{6} +(1.83254 - 2.15448i) q^{8} +(-1.90803 + 1.10160i) q^{9} +(2.45071 + 3.99312i) q^{10} +(-0.799070 - 2.98217i) q^{11} +(0.553978 + 1.69714i) q^{12} +(4.03390 + 4.03390i) q^{13} -2.95723 q^{15} +(-3.97694 + 0.428891i) q^{16} +(0.173966 - 0.301317i) q^{17} +(3.03020 + 0.725317i) q^{18} +(-1.56048 + 5.82380i) q^{19} +(1.36881 - 6.48293i) q^{20} +(-2.08077 + 3.83850i) q^{22} +(5.40216 - 3.11894i) q^{23} +(1.08230 - 2.28101i) q^{24} +(5.17494 + 2.98775i) q^{25} +(-0.216653 - 8.06488i) q^{26} +(-3.28420 + 3.28420i) q^{27} +(1.21961 + 1.21961i) q^{29} +(3.03558 + 2.87675i) q^{30} +(-0.631188 + 1.09325i) q^{31} +(4.49952 + 3.42846i) q^{32} +(-1.37795 - 2.38667i) q^{33} +(-0.471692 + 0.140069i) q^{34} +(-2.40491 - 3.69227i) q^{36} +(8.77373 + 2.35091i) q^{37} +(7.26713 - 4.46008i) q^{38} +(4.41005 + 2.54615i) q^{39} +(-7.71157 + 5.32312i) q^{40} +2.68519i q^{41} +(4.05478 - 4.05478i) q^{43} +(5.86993 - 1.91605i) q^{44} +(7.05035 - 1.88914i) q^{45} +(-8.57934 - 2.05357i) q^{46} +(2.32249 + 4.02267i) q^{47} +(-3.32990 + 1.28859i) q^{48} +(-2.40560 - 8.10101i) q^{50} +(0.0803829 - 0.299993i) q^{51} +(-7.62301 + 8.48931i) q^{52} +(3.08965 + 11.5307i) q^{53} +(6.56603 - 0.176388i) q^{54} +10.2282i q^{55} +5.38191i q^{57} +(-0.0655030 - 2.43834i) q^{58} +(1.89519 + 7.07295i) q^{59} +(-0.317541 - 5.90594i) q^{60} +(0.00195333 - 0.00728993i) q^{61} +(1.71141 - 0.508203i) q^{62} +(-1.28358 - 7.89636i) q^{64} +(-9.44979 - 16.3675i) q^{65} +(-0.907267 + 3.79035i) q^{66} +(-4.12554 + 1.10544i) q^{67} +(0.620446 + 0.315075i) q^{68} +(3.93727 - 3.93727i) q^{69} +0.828913i q^{71} +(-1.12317 + 6.12955i) q^{72} +(-5.41415 - 3.12586i) q^{73} +(-6.71924 - 10.9481i) q^{74} +(5.15219 + 1.38052i) q^{75} +(-11.7984 - 2.49112i) q^{76} +(-2.05004 - 6.90364i) q^{78} +(0.377945 + 0.654620i) q^{79} +(13.0941 + 2.03756i) q^{80} +(1.23186 - 2.13364i) q^{81} +(2.61211 - 2.75633i) q^{82} +(3.66586 + 3.66586i) q^{83} +(-0.815062 + 0.815062i) q^{85} +(-8.10663 + 0.217775i) q^{86} +(1.33334 + 0.769803i) q^{87} +(-7.88935 - 3.74337i) q^{88} +(-5.40799 + 3.12231i) q^{89} +(-9.07486 - 4.91929i) q^{90} +(6.80895 + 10.4538i) q^{92} +(-0.291648 + 1.08844i) q^{93} +(1.52917 - 6.38853i) q^{94} +(9.98723 - 17.2984i) q^{95} +(4.67165 + 1.91655i) q^{96} -2.18393 q^{97} +(4.80981 + 4.80981i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 2 q^{2} + 4 q^{3} + 6 q^{4} + 4 q^{5} - 8 q^{6} - 8 q^{8}+O(q^{10}) \) 24 * q - 2 * q^2 + 4 * q^3 + 6 * q^4 + 4 * q^5 - 8 * q^6 - 8 * q^8	\( 24 q - 2 q^{2} + 4 q^{3} + 6 q^{4} + 4 q^{5} - 8 q^{6} - 8 q^{8} - 4 q^{10} + 8 q^{12} - 48 q^{15} - 10 q^{16} - 8 q^{17} + 40 q^{20} + 28 q^{22} - 8 q^{24} - 20 q^{26} - 8 q^{27} - 8 q^{29} + 28 q^{30} - 8 q^{31} - 12 q^{32} - 16 q^{34} - 32 q^{36} + 20 q^{37} + 16 q^{38} - 8 q^{40} + 32 q^{43} - 14 q^{44} + 40 q^{45} + 28 q^{46} + 16 q^{47} - 32 q^{48} + 88 q^{50} + 16 q^{51} - 16 q^{52} - 4 q^{53} + 64 q^{54} - 14 q^{58} - 16 q^{59} - 60 q^{60} - 20 q^{61} - 16 q^{62} - 36 q^{64} - 32 q^{65} + 12 q^{66} - 24 q^{67} - 28 q^{68} + 8 q^{69} - 6 q^{72} + 38 q^{74} - 40 q^{75} - 96 q^{76} - 152 q^{78} - 24 q^{79} + 24 q^{80} + 44 q^{81} - 16 q^{82} + 40 q^{83} - 16 q^{85} - 38 q^{86} + 14 q^{88} + 80 q^{90} + 64 q^{92} + 48 q^{93} - 24 q^{94} - 16 q^{96} - 96 q^{97} + 64 q^{99}+O(q^{100}) \) 24 * q - 2 * q^2 + 4 * q^3 + 6 * q^4 + 4 * q^5 - 8 * q^6 - 8 * q^8 - 4 * q^10 + 8 * q^12 - 48 * q^15 - 10 * q^16 - 8 * q^17 + 40 * q^20 + 28 * q^22 - 8 * q^24 - 20 * q^26 - 8 * q^27 - 8 * q^29 + 28 * q^30 - 8 * q^31 - 12 * q^32 - 16 * q^34 - 32 * q^36 + 20 * q^37 + 16 * q^38 - 8 * q^40 + 32 * q^43 - 14 * q^44 + 40 * q^45 + 28 * q^46 + 16 * q^47 - 32 * q^48 + 88 * q^50 + 16 * q^51 - 16 * q^52 - 4 * q^53 + 64 * q^54 - 14 * q^58 - 16 * q^59 - 60 * q^60 - 20 * q^61 - 16 * q^62 - 36 * q^64 - 32 * q^65 + 12 * q^66 - 24 * q^67 - 28 * q^68 + 8 * q^69 - 6 * q^72 + 38 * q^74 - 40 * q^75 - 96 * q^76 - 152 * q^78 - 24 * q^79 + 24 * q^80 + 44 * q^81 - 16 * q^82 + 40 * q^83 - 16 * q^85 - 38 * q^86 + 14 * q^88 + 80 * q^90 + 64 * q^92 + 48 * q^93 - 24 * q^94 - 16 * q^96 - 96 * q^97 + 64 * q^99

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