LMFDB - Embedded newform 637.2.bb.b.227.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [637,2,Mod(227,637)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(637, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([2, 5]))

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

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

chi := DirichletCharacter("637.227");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 637 = 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	637.bb (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:	$5.08647060876$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 91)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			227.6
Character	$\chi$	$=$	637.227
Dual form			637.2.bb.b.362.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.595687 - 0.595687i) q^{2} +(1.24122 - 0.716618i) q^{3} +1.29031i q^{4} +(0.370805 - 1.38386i) q^{5} +(0.312498 - 1.16626i) q^{6} +(1.96000 + 1.96000i) q^{8} +(-0.472916 + 0.819114i) q^{9} +O(q^{10})$	\(q+(0.595687 - 0.595687i) q^{2} +(1.24122 - 0.716618i) q^{3} +1.29031i q^{4} +(0.370805 - 1.38386i) q^{5} +(0.312498 - 1.16626i) q^{6} +(1.96000 + 1.96000i) q^{8} +(-0.472916 + 0.819114i) q^{9} +(-0.603466 - 1.04523i) q^{10} +(1.25630 - 4.68859i) q^{11} +(0.924663 + 1.60156i) q^{12} +(-1.04975 - 3.44935i) q^{13} +(-0.531452 - 1.98341i) q^{15} -0.245542 q^{16} +2.98303 q^{17} +(0.206226 + 0.769645i) q^{18} +(6.06542 - 1.62522i) q^{19} +(1.78562 + 0.478455i) q^{20} +(-2.04457 - 3.54129i) q^{22} +1.18059i q^{23} +(3.83736 + 1.02822i) q^{24} +(2.55254 + 1.47371i) q^{25} +(-2.68005 - 1.42941i) q^{26} +5.65531i q^{27} +(-2.77911 + 4.81356i) q^{29} +(-1.49807 - 0.864909i) q^{30} +(6.54786 - 1.75449i) q^{31} +(-4.06626 + 4.06626i) q^{32} +(-1.80058 - 6.71986i) q^{33} +(1.77695 - 1.77695i) q^{34} +(-1.05692 - 0.610210i) q^{36} +(-3.95429 - 3.95429i) q^{37} +(2.64497 - 4.58121i) q^{38} +(-3.77484 - 3.52914i) q^{39} +(3.43915 - 1.98559i) q^{40} +(-4.71621 + 1.26371i) q^{41} +(-2.90941 + 1.67975i) q^{43} +(6.04975 + 1.62103i) q^{44} +(0.958183 + 0.958183i) q^{45} +(0.703262 + 0.703262i) q^{46} +(-5.63925 - 1.51103i) q^{47} +(-0.304771 + 0.175960i) q^{48} +(2.39839 - 0.642646i) q^{50} +(3.70259 - 2.13769i) q^{51} +(4.45075 - 1.35450i) q^{52} +(-2.89658 + 5.01702i) q^{53} +(3.36879 + 3.36879i) q^{54} +(-6.02252 - 3.47711i) q^{55} +(6.36385 - 6.36385i) q^{57} +(1.21190 + 4.52285i) q^{58} +(-7.87514 + 7.87514i) q^{59} +(2.55922 - 0.685740i) q^{60} +(-7.95118 - 4.59062i) q^{61} +(2.85534 - 4.94560i) q^{62} +4.35335i q^{64} +(-5.16269 + 0.173669i) q^{65} +(-5.07551 - 2.93035i) q^{66} +(1.89769 + 0.508485i) q^{67} +3.84905i q^{68} +(0.846033 + 1.46537i) q^{69} +(-3.19094 - 0.855010i) q^{71} +(-2.53237 + 0.678548i) q^{72} +(0.129211 + 0.482220i) q^{73} -4.71103 q^{74} +4.22436 q^{75} +(2.09705 + 7.82630i) q^{76} +(-4.35088 + 0.146360i) q^{78} +(3.47711 + 6.02254i) q^{79} +(-0.0910481 + 0.339796i) q^{80} +(2.63395 + 4.56214i) q^{81} +(-2.05661 + 3.56216i) q^{82} +(-3.22886 - 3.22886i) q^{83} +(1.10612 - 4.12811i) q^{85} +(-0.732493 + 2.73370i) q^{86} +7.96625i q^{87} +(11.6520 - 6.72727i) q^{88} +(0.173853 - 0.173853i) q^{89} +1.14155 q^{90} -1.52333 q^{92} +(6.87003 - 6.87003i) q^{93} +(-4.25933 + 2.45913i) q^{94} -8.99636i q^{95} +(-2.13316 + 7.96108i) q^{96} +(-2.43374 + 9.08284i) q^{97} +(3.24636 + 3.24636i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 4 q^{2} - 16 q^{8} + 8 q^{9}+O(q^{10}) $ 32 * q + 4 * q^2 - 16 * q^8 + 8 * q^9	$ 32 q + 4 q^{2} - 16 q^{8} + 8 q^{9} - 16 q^{11} - 8 q^{15} - 24 q^{16} + 68 q^{18} + 4 q^{22} + 4 q^{29} - 12 q^{30} - 68 q^{32} - 8 q^{37} - 48 q^{43} + 60 q^{44} + 24 q^{46} - 44 q^{50} - 12 q^{51} - 36 q^{53} - 92 q^{57} - 28 q^{58} - 104 q^{60} - 32 q^{65} - 8 q^{67} + 84 q^{71} + 124 q^{72} + 48 q^{74} + 148 q^{78} + 40 q^{79} + 28 q^{81} + 36 q^{85} - 60 q^{86} + 228 q^{88} + 24 q^{92} - 84 q^{93} - 60 q^{99}+O(q^{100}) $ 32 * q + 4 * q^2 - 16 * q^8 + 8 * q^9 - 16 * q^11 - 8 * q^15 - 24 * q^16 + 68 * q^18 + 4 * q^22 + 4 * q^29 - 12 * q^30 - 68 * q^32 - 8 * q^37 - 48 * q^43 + 60 * q^44 + 24 * q^46 - 44 * q^50 - 12 * q^51 - 36 * q^53 - 92 * q^57 - 28 * q^58 - 104 * q^60 - 32 * q^65 - 8 * q^67 + 84 * q^71 + 124 * q^72 + 48 * q^74 + 148 * q^78 + 40 * q^79 + 28 * q^81 + 36 * q^85 - 60 * q^86 + 228 * q^88 + 24 * q^92 - 84 * q^93 - 60 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/637\mathbb{Z}\right)^\times$.

$n$	$197$	$248$
$\chi(n)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$	0.595687	−	0.595687i	0.421214	−	0.421214i	−0.464408	−	0.885622i	$-0.653733\pi$
$2$	0.595687	−	0.595687i	0.421214	−	0.421214i	0.885622	+	0.464408i	$0.153733\pi$
$3$	1.24122	−	0.716618i	0.716618	−	0.413740i	−0.0968883	−	0.995295i	$-0.530889\pi$
$3$	1.24122	−	0.716618i	0.716618	−	0.413740i	0.813507	+	0.581555i	$0.197556\pi$
$4$			1.29031i			0.645157i
$5$	0.370805	−	1.38386i	0.165829	−	0.618883i	−0.832104	−	0.554620i	$-0.812864\pi$
$5$	0.370805	−	1.38386i	0.165829	−	0.618883i	0.997933	−	0.0642629i	$-0.0204696\pi$
$6$	0.312498	−	1.16626i	0.127577	−	0.476123i
$7$		0			0
$7$		0			0
$8$	1.96000	+	1.96000i	0.692963	+	0.692963i
$9$	−0.472916	+	0.819114i	−0.157639	+	0.273038i
$10$	−0.603466	−	1.04523i	−0.190833	−	0.330532i
$11$	1.25630	−	4.68859i	0.378790	−	1.41366i	−0.468938	−	0.883231i	$-0.655363\pi$
$11$	1.25630	−	4.68859i	0.378790	−	1.41366i	0.847728	−	0.530431i	$-0.177970\pi$
$12$	0.924663	+	1.60156i	0.266927	+	0.462332i
$13$	−1.04975	−	3.44935i	−0.291147	−	0.956678i
$13$	−1.04975	−	3.44935i	−0.291147	−	0.956678i
$14$		0			0
$15$	−0.531452	−	1.98341i	−0.137220	−	0.512113i
$16$	−0.245542			−0.0613854
$17$	2.98303			0.723491			0.361745	−	0.932277i	$-0.382181\pi$
$17$	2.98303			0.723491			0.361745	+	0.932277i	$0.382181\pi$
$18$	0.206226	+	0.769645i	0.0486079	+	0.181407i
$19$	6.06542	−	1.62522i	1.39150	−	0.372852i	0.516217	−	0.856458i	$-0.327340\pi$
$19$	6.06542	−	1.62522i	1.39150	−	0.372852i	0.875286	+	0.483606i	$0.160673\pi$
$20$	1.78562	+	0.478455i	0.399277	+	0.106986i
$21$		0			0
$22$	−2.04457	−	3.54129i	−0.435903	−	0.755006i
$23$			1.18059i			0.246170i	0.992396	+	0.123085i	$0.0392788\pi$
$23$			1.18059i			0.246170i	−0.992396	+	0.123085i	$0.960721\pi$
$24$	3.83736	+	1.02822i	0.783297	+	0.209884i
$25$	2.55254	+	1.47371i	0.510509	+	0.294742i
$26$	−2.68005	−	1.42941i	−0.525602	−	0.280331i
$27$			5.65531i			1.08837i
$28$		0			0
$29$	−2.77911	+	4.81356i	−0.516068	+	0.893856i	0.483758	+	0.875202i	$0.339271\pi$
$29$	−2.77911	+	4.81356i	−0.516068	+	0.893856i	−0.999826	+	0.0186541i	$0.994062\pi$
$30$	−1.49807	−	0.864909i	−0.273508	−	0.157910i
$31$	6.54786	−	1.75449i	1.17603	−	0.315116i	0.382680	−	0.923881i	$-0.375001\pi$
$31$	6.54786	−	1.75449i	1.17603	−	0.315116i	0.793351	+	0.608765i	$0.208335\pi$
$32$	−4.06626	+	4.06626i	−0.718820	+	0.718820i
$33$	−1.80058	−	6.71986i	−0.313441	−	1.16978i
$34$	1.77695	−	1.77695i	0.304744	−	0.304744i
$35$		0			0
$36$	−1.05692	−	0.610210i	−0.176153	−	0.101702i
$37$	−3.95429	−	3.95429i	−0.650081	−	0.650081i	0.302932	−	0.953012i	$-0.402035\pi$
$37$	−3.95429	−	3.95429i	−0.650081	−	0.650081i	−0.953012	+	0.302932i	$0.902035\pi$
$38$	2.64497	−	4.58121i	0.429070	−	0.743171i
$39$	−3.77484	−	3.52914i	−0.604458	−	0.565114i
$40$	3.43915	−	1.98559i	0.543777	−	0.313950i
$41$	−4.71621	+	1.26371i	−0.736549	+	0.197358i	−0.607544	−	0.794286i	$-0.707845\pi$
$41$	−4.71621	+	1.26371i	−0.736549	+	0.197358i	−0.129005	+	0.991644i	$0.541178\pi$
$42$		0			0
$43$	−2.90941	+	1.67975i	−0.443681	+	0.256159i	−0.705158	−	0.709050i	$-0.749124\pi$
$43$	−2.90941	+	1.67975i	−0.443681	+	0.256159i	0.261477	+	0.965210i	$0.415790\pi$
$44$	6.04975	+	1.62103i	0.912035	+	0.244379i
$45$	0.958183	+	0.958183i	0.142838	+	0.142838i
$46$	0.703262	+	0.703262i	0.103690	+	0.103690i
$47$	−5.63925	−	1.51103i	−0.822570	−	0.220407i	−0.177100	−	0.984193i	$-0.556672\pi$
$47$	−5.63925	−	1.51103i	−0.822570	−	0.220407i	−0.645470	+	0.763786i	$0.723338\pi$
$48$	−0.304771	+	0.175960i	−0.0439899	+	0.0253976i
$49$		0			0
$50$	2.39839	−	0.642646i	0.339183	−	0.0908839i
$51$	3.70259	−	2.13769i	0.518467	−	0.299337i
$52$	4.45075	−	1.35450i	0.617208	−	0.187836i
$53$	−2.89658	+	5.01702i	−0.397875	+	0.689141i	−0.993464	−	0.114149i	$-0.963586\pi$
$53$	−2.89658	+	5.01702i	−0.397875	+	0.689141i	0.595588	+	0.803290i	$0.296919\pi$
$54$	3.36879	+	3.36879i	0.458435	+	0.458435i
$55$	−6.02252	−	3.47711i	−0.812077	−	0.468853i
$56$		0			0
$57$	6.36385	−	6.36385i	0.842913	−	0.842913i
$58$	1.21190	+	4.52285i	0.159130	+	0.593880i
$59$	−7.87514	+	7.87514i	−1.02526	+	1.02526i	−0.0255833	+	0.999673i	$0.508144\pi$
$59$	−7.87514	+	7.87514i	−1.02526	+	1.02526i	−0.999673	+	0.0255833i	$0.991856\pi$
$60$	2.55922	−	0.685740i	0.330393	−	0.0885287i
$61$	−7.95118	−	4.59062i	−1.01804	−	0.587768i	−0.104508	−	0.994524i	$-0.533327\pi$
$61$	−7.95118	−	4.59062i	−1.01804	−	0.587768i	−0.913537	+	0.406756i	$0.866660\pi$
$62$	2.85534	−	4.94560i	0.362629	−	0.628092i
$63$		0			0
$64$			4.35335i			0.544169i
$65$	−5.16269	+	0.173669i	−0.640352	+	0.0215410i
$66$	−5.07551	−	2.93035i	−0.624752	−	0.360701i
$67$	1.89769	+	0.508485i	0.231840	+	0.0621214i	0.372869	−	0.927884i	$-0.378374\pi$
$67$	1.89769	+	0.508485i	0.231840	+	0.0621214i	−0.141028	+	0.990006i	$0.545041\pi$
$68$			3.84905i			0.466765i
$69$	0.846033	+	1.46537i	0.101850	+	0.176410i
$70$		0			0
$71$	−3.19094	−	0.855010i	−0.378695	−	0.101471i	0.0644501	−	0.997921i	$-0.479471\pi$
$71$	−3.19094	−	0.855010i	−0.378695	−	0.101471i	−0.443145	+	0.896450i	$0.646137\pi$
$72$	−2.53237	+	0.678548i	−0.298443	+	0.0799676i
$73$	0.129211	+	0.482220i	0.0151230	+	0.0564396i	0.973075	−	0.230489i	$-0.0740325\pi$
$73$	0.129211	+	0.482220i	0.0151230	+	0.0564396i	−0.957952	+	0.286928i	$0.907366\pi$
$74$	−4.71103			−0.547646
$75$	4.22436			0.487787
$76$	2.09705	+	7.82630i	0.240548	+	0.897738i
$77$		0			0
$78$	−4.35088	+	0.146360i	−0.492640	+	0.0165720i
$79$	3.47711	+	6.02254i	0.391206	+	0.677588i	0.992609	−	0.121357i	$-0.0387247\pi$
$79$	3.47711	+	6.02254i	0.391206	+	0.677588i	−0.601403	+	0.798946i	$0.705391\pi$
$80$	−0.0910481	+	0.339796i	−0.0101795	+	0.0379904i
$81$	2.63395	+	4.56214i	0.292662	+	0.506905i
$82$	−2.05661	+	3.56216i	−0.227115	+	0.393374i
$83$	−3.22886	−	3.22886i	−0.354413	−	0.354413i	0.507335	−	0.861749i	$-0.330631\pi$
$83$	−3.22886	−	3.22886i	−0.354413	−	0.354413i	−0.861749	+	0.507335i	$0.830631\pi$
$84$		0			0
$85$	1.10612	−	4.12811i	0.119976	−	0.447756i
$86$	−0.732493	+	2.73370i	−0.0789867	+	0.294783i
$87$			7.96625i			0.854072i
$88$	11.6520	−	6.72727i	1.24210	−	0.717129i
$89$	0.173853	−	0.173853i	0.0184284	−	0.0184284i	−0.697833	−	0.716261i	$-0.745852\pi$
$89$	0.173853	−	0.173853i	0.0184284	−	0.0184284i	0.716261	+	0.697833i	$0.245852\pi$
$90$	1.14155			0.120330
$91$		0			0
$92$	−1.52333			−0.158819
$93$	6.87003	−	6.87003i	0.712389	−	0.712389i
$94$	−4.25933	+	2.45913i	−0.439316	+	0.253639i
$95$		−	8.99636i		−	0.923007i
$96$	−2.13316	+	7.96108i	−0.217715	+	0.812524i
$97$	−2.43374	+	9.08284i	−0.247109	+	0.922223i	0.725203	+	0.688535i	$0.241746\pi$
$97$	−2.43374	+	9.08284i	−0.247109	+	0.922223i	−0.972312	+	0.233688i	$0.924921\pi$
$98$		0			0
$99$	3.24636	+	3.24636i	0.326272	+	0.326272i
$100$	−1.90155	+	3.29359i	−0.190155	+	0.329359i
$101$	−7.14344	−	12.3728i	−0.710799	−	1.23114i	−0.964558	−	0.263872i	$-0.915000\pi$
$101$	−7.14344	−	12.3728i	−0.710799	−	1.23114i	0.253759	−	0.967267i	$-0.418333\pi$
$102$	0.932190	−	3.47898i	0.0923006	−	0.344470i
$103$	−3.72565	−	6.45301i	−0.367099	−	0.635834i	0.622012	−	0.783008i	$-0.286316\pi$
$103$	−3.72565	−	6.45301i	−0.367099	−	0.635834i	−0.989111	+	0.147174i	$0.952982\pi$
$104$	4.70322	−	8.81822i	0.461189	−	0.864698i
$105$		0			0
$106$	1.26312	+	4.71402i	0.122685	+	0.457866i
$107$	−4.68264			−0.452688			−0.226344	−	0.974047i	$-0.572677\pi$
$107$	−4.68264			−0.452688			−0.226344	+	0.974047i	$0.572677\pi$
$108$	−7.29713			−0.702167
$109$	−1.11342	−	4.15534i	−0.106646	−	0.398009i	0.891880	−	0.452271i	$-0.149386\pi$
$109$	−1.11342	−	4.15534i	−0.106646	−	0.398009i	−0.998527	+	0.0542619i	$0.982719\pi$
$110$	−5.65880	+	1.51627i	−0.539546	+	0.144571i
$111$	−7.74185	−	2.07442i	−0.734824	−	0.196895i
$112$		0			0
$113$	2.02372	+	3.50518i	0.190375	+	0.329740i	0.945375	−	0.325986i	$-0.105696\pi$
$113$	2.02372	+	3.50518i	0.190375	+	0.329740i	−0.754999	+	0.655725i	$0.772363\pi$
$114$		−	7.58172i		−	0.710094i
$115$	1.63378	+	0.437769i	0.152351	+	0.0408222i
$116$	−6.21101	−	3.58593i	−0.576678	−	0.332945i
$117$	3.32186	+	0.771391i	0.307106	+	0.0713151i
$118$			9.38223i			0.863705i
$119$		0			0
$120$	2.84582	−	4.92911i	0.259787	−	0.449964i
$121$	−10.8783	−	6.28058i	−0.988935	−	0.570962i
$122$	−7.47099	+	2.00184i	−0.676391	+	0.181238i
$123$	−4.94826	+	4.94826i	−0.446170	+	0.446170i
$124$	2.26385	+	8.44880i	0.203300	+	0.758725i
$125$	8.05121	−	8.05121i	0.720122	−	0.720122i
$126$		0			0
$127$	10.6871	+	6.17021i	0.948328	+	0.547518i	0.892561	−	0.450926i	$-0.148906\pi$
$127$	10.6871	+	6.17021i	0.948328	+	0.547518i	0.0557671	+	0.998444i	$0.482240\pi$
$128$	−5.53929	−	5.53929i	−0.489608	−	0.489608i
$129$	−2.40748	+	4.16987i	−0.211967	+	0.367137i
$130$	−2.97189	+	3.17880i	−0.260652	+	0.278799i
$131$	−5.81415	+	3.35680i	−0.507985	+	0.293285i	−0.732005	−	0.681299i	$-0.761415\pi$
$131$	−5.81415	+	3.35680i	−0.507985	+	0.293285i	0.224020	+	0.974584i	$0.428082\pi$
$132$	8.67073	−	2.32332i	0.754690	−	0.202219i
$133$		0			0
$134$	1.43333	−	0.827533i	0.123821	−	0.0714879i
$135$	7.82618	+	2.09702i	0.673571	+	0.180483i
$136$	5.84673	+	5.84673i	0.501353	+	0.501353i
$137$	15.4812	+	15.4812i	1.32265	+	1.32265i	0.911623	+	0.411027i	$0.134830\pi$
$137$	15.4812	+	15.4812i	1.32265	+	1.32265i	0.411027	+	0.911623i	$0.365170\pi$
$138$	1.37687	+	0.368932i	0.117207	+	0.0314056i
$139$	−3.49682	+	2.01889i	−0.296597	+	0.171240i	−0.640913	−	0.767614i	$-0.721444\pi$
$139$	−3.49682	+	2.01889i	−0.296597	+	0.171240i	0.344316	+	0.938854i	$0.388111\pi$
$140$		0			0
$141$	−8.08239	+	2.16567i	−0.680660	+	0.182382i
$142$	−2.41012	+	1.39148i	−0.202253	+	0.116771i
$143$	−17.4914	+	0.588397i	−1.46270	+	0.0492042i
$144$	0.116121	−	0.201127i	0.00967671	−	0.0167606i
$145$	5.63081	+	5.63081i	0.467613	+	0.467613i
$146$	0.364221	+	0.210283i	0.0301432	+	0.0174032i
$147$		0			0
$148$	5.10227	−	5.10227i	0.419404	−	0.419404i
$149$	0.734196	+	2.74006i	0.0601477	+	0.224474i	0.989457	−	0.144829i	$-0.0462631\pi$
$149$	0.734196	+	2.74006i	0.0601477	+	0.224474i	−0.929309	+	0.369303i	$0.879596\pi$
$150$	2.51639	−	2.51639i	0.205463	−	0.205463i
$151$	−16.1720	+	4.33327i	−1.31606	+	0.352636i	−0.847499	−	0.530796i	$-0.821893\pi$
$151$	−16.1720	+	4.33327i	−1.31606	+	0.352636i	−0.468558	+	0.883433i	$0.655226\pi$
$152$	15.0736	+	8.70277i	1.22263	+	0.705888i
$153$	−1.41072	+	2.44344i	−0.114050	+	0.197541i
$154$		0			0
$155$		−	9.71192i		−	0.780080i
$156$	4.55370	−	4.87073i	0.364587	−	0.389970i
$157$	2.48434	+	1.43433i	0.198272	+	0.114472i	0.595849	−	0.803096i	$-0.296816\pi$
$157$	2.48434	+	1.43433i	0.198272	+	0.114472i	−0.397577	+	0.917569i	$0.630149\pi$
$158$	5.65882	+	1.51628i	0.450191	+	0.120628i
$159$			8.30296i			0.658468i
$160$	4.11936	+	7.13494i	0.325664	+	0.564067i
$161$		0			0
$162$	4.28662	+	1.14860i	0.336789	+	0.0902422i
$163$	23.2781	−	6.23736i	1.82328	−	0.488548i	0.826099	−	0.563525i	$-0.190555\pi$
$163$	23.2781	−	6.23736i	1.82328	−	0.488548i	0.997185	+	0.0749773i	$0.0238884\pi$
$164$	−1.63058	−	6.08540i	−0.127327	−	0.475190i
$165$	−9.96703			−0.775933
$166$	−3.84678			−0.298568
$167$	2.53997	+	9.47931i	0.196549	+	0.733531i	0.991860	+	0.127330i	$0.0406408\pi$
$167$	2.53997	+	9.47931i	0.196549	+	0.733531i	−0.795311	+	0.606201i	$0.792693\pi$
$168$		0			0
$169$	−10.7961	+	7.24189i	−0.830466	+	0.557069i
$170$	−1.80016	−	3.11796i	−0.138066	−	0.239137i
$171$	−1.53719	+	5.73687i	−0.117552	+	0.438709i
$172$	−2.16740	−	3.75405i	−0.165263	−	0.286244i
$173$	−2.61883	+	4.53595i	−0.199106	+	0.344862i	−0.948239	−	0.317558i	$-0.897137\pi$
$173$	−2.61883	+	4.53595i	−0.199106	+	0.344862i	0.749133	+	0.662420i	$0.230471\pi$
$174$	4.74539	+	4.74539i	0.359747	+	0.359747i
$175$		0			0
$176$	−0.308475	+	1.15124i	−0.0232522	+	0.0867783i
$177$	−4.13131	+	15.4183i	−0.310528	+	1.15891i
$178$		−	0.207124i		−	0.0155246i
$179$	19.5491	−	11.2867i	1.46117	−	0.843605i	0.462101	−	0.886827i	$-0.347096\pi$
$179$	19.5491	−	11.2867i	1.46117	−	0.843605i	0.999065	+	0.0432226i	$0.0137625\pi$
$180$	−1.23636	+	1.23636i	−0.0921527	+	0.0921527i
$181$	22.4803			1.67095			0.835474	−	0.549530i	$-0.185193\pi$
$181$	22.4803			1.67095			0.835474	+	0.549530i	$0.185193\pi$
$182$		0			0
$183$	−13.1589			−0.972733
$184$	−2.31395	+	2.31395i	−0.170587	+	0.170587i
$185$	−6.93846	+	4.00592i	−0.510126	+	0.294521i
$186$		−	8.18477i		−	0.600136i
$187$	3.74759	−	13.9862i	0.274051	−	1.02277i
$188$	1.94971	−	7.27641i	0.142197	−	0.530687i
$189$		0			0
$190$	−5.35901	−	5.35901i	−0.388783	−	0.388783i
$191$	−12.3354	+	21.3655i	−0.892557	+	1.54595i	−0.0557571	+	0.998444i	$0.517757\pi$
$191$	−12.3354	+	21.3655i	−0.892557	+	1.54595i	−0.836800	+	0.547509i	$0.815576\pi$
$192$	3.11969	+	5.40346i	0.225144	+	0.389961i
$193$	−0.890112	+	3.32194i	−0.0640717	+	0.239119i	−0.990534	−	0.137269i	$-0.956167\pi$
$193$	−0.890112	+	3.32194i	−0.0640717	+	0.239119i	0.926462	+	0.376388i	$0.122834\pi$
$194$	3.96078	+	6.86027i	0.284367	+	0.492539i
$195$	−6.28357	+	3.91524i	−0.449976	+	0.280376i
$196$		0			0
$197$	−1.03338	−	3.85664i	−0.0736255	−	0.274774i	0.919293	−	0.393575i	$-0.128762\pi$
$197$	−1.03338	−	3.85664i	−0.0736255	−	0.274774i	−0.992918	+	0.118801i	$0.962095\pi$
$198$	3.86763			0.274861
$199$	−1.02310			−0.0725257			−0.0362628	−	0.999342i	$-0.511545\pi$
$199$	−1.02310			−0.0725257			−0.0362628	+	0.999342i	$0.511545\pi$
$200$	2.11451	+	7.89145i	0.149518	+	0.558010i
$201$	2.71984	−	0.728780i	0.191843	−	0.0514042i
$202$	−11.6256	−	3.11506i	−0.817972	−	0.219175i
$203$		0			0
$204$	2.75830	+	4.77751i	0.193119	+	0.334493i
$205$			6.99518i			0.488565i
$206$	−6.06329	−	1.62465i	−0.422450	−	0.113195i
$207$	−0.967039	−	0.558320i	−0.0672139	−	0.0388059i
$208$	0.257757	+	0.846960i	0.0178722	+	0.0587261i
$209$		−	30.4800i		−	2.10835i
$210$		0			0
$211$	2.70061	−	4.67759i	0.185918	−	0.322019i	−0.757968	−	0.652292i	$-0.773808\pi$
$211$	2.70061	−	4.67759i	0.185918	−	0.322019i	0.943885	+	0.330273i	$0.107141\pi$
$212$	−6.47353	−	3.73750i	−0.444604	−	0.256692i
$213$	−4.57337	+	1.22543i	−0.313362	+	0.0839652i
$214$	−2.78939	+	2.78939i	−0.190678	+	0.190678i
$215$	1.24572	+	4.64909i	0.0849573	+	0.317065i
$216$	−11.0844	+	11.0844i	−0.754197	+	0.754197i
$217$		0			0
$218$	−3.13853	−	1.81203i	−0.212568	−	0.122726i
$219$	0.505947	+	0.505947i	0.0341887	+	0.0341887i
$220$	4.48656	−	7.77095i	0.302484	−	0.523917i
$221$	−3.13142	−	10.2895i	−0.210642	−	0.692148i
$222$	−5.84742	+	3.37601i	−0.392453	+	0.226583i
$223$	−16.6138	+	4.45165i	−1.11254	+	0.298105i	−0.767862	−	0.640616i	$-0.778679\pi$
$223$	−16.6138	+	4.45165i	−1.11254	+	0.298105i	−0.344680	+	0.938720i	$0.612013\pi$
$224$		0			0
$225$	−2.41428	+	1.39388i	−0.160952	+	0.0929256i
$226$	3.29349	+	0.882488i	0.219080	+	0.0587022i
$227$	−7.04460	−	7.04460i	−0.467566	−	0.467566i	0.433559	−	0.901125i	$-0.357258\pi$
$227$	−7.04460	−	7.04460i	−0.467566	−	0.467566i	−0.901125	+	0.433559i	$0.857258\pi$
$228$	8.21137	+	8.21137i	0.543811	+	0.543811i
$229$	4.02820	+	1.07935i	0.266191	+	0.0713257i	0.389446	−	0.921049i	$-0.372667\pi$
$229$	4.02820	+	1.07935i	0.266191	+	0.0713257i	−0.123255	+	0.992375i	$0.539333\pi$
$230$	1.23399	−	0.712446i	0.0813671	−	0.0469773i
$231$		0			0
$232$	−14.8816	+	3.98752i	−0.977026	+	0.261793i
$233$	5.47860	−	3.16307i	0.358915	−	0.207220i	−0.309690	−	0.950838i	$-0.600225\pi$
$233$	5.47860	−	3.16307i	0.358915	−	0.207220i	0.668605	+	0.743618i	$0.266892\pi$
$234$	2.43829	−	1.51928i	0.159396	−	0.0993183i
$235$	−4.18213	+	7.24366i	−0.272812	+	0.472524i
$236$	−10.1614	−	10.1614i	−0.661451	−	0.661451i
$237$	8.63172	+	4.98353i	0.560691	+	0.323715i
$238$		0			0
$239$	7.84175	−	7.84175i	0.507241	−	0.507241i	−0.406438	−	0.913679i	$-0.633229\pi$
$239$	7.84175	−	7.84175i	0.507241	−	0.507241i	0.913679	+	0.406438i	$0.133229\pi$
$240$	0.130494	+	0.487009i	0.00842332	+	0.0314363i
$241$	9.88706	−	9.88706i	0.636882	−	0.636882i	−0.312903	−	0.949785i	$-0.601302\pi$
$241$	9.88706	−	9.88706i	0.636882	−	0.636882i	0.949785	+	0.312903i	$0.101302\pi$
$242$	−10.2213	+	2.73879i	−0.657050	+	0.176056i
$243$	−8.15430	−	4.70789i	−0.523099	−	0.302011i
$244$	5.92334	−	10.2595i	0.379203	−	0.656799i
$245$		0			0
$246$			5.89523i			0.375866i
$247$	−11.9731	−	19.2157i	−0.761832	−	1.22267i
$248$	16.2726	+	9.39498i	1.03331	+	0.596582i
$249$	−6.32158	−	1.69386i	−0.400614	−	0.107344i
$250$		−	9.59199i		−	0.606651i
$251$	−13.1784	−	22.8256i	−0.831813	−	1.44074i	−0.896599	−	0.442843i	$-0.853970\pi$
$251$	−13.1784	−	22.8256i	−0.831813	−	1.44074i	0.0647865	−	0.997899i	$-0.479363\pi$
$252$		0			0
$253$	5.53531	+	1.48318i	0.348002	+	0.0932468i
$254$	10.0417	−	2.69066i	0.630071	−	0.168827i
$255$	−1.58534	−	5.91655i	−0.0992776	−	0.370509i
$256$	−15.3061			−0.956629
$257$	−10.7805			−0.672469			−0.336234	−	0.941778i	$-0.609153\pi$
$257$	−10.7805			−0.672469			−0.336234	+	0.941778i	$0.609153\pi$
$258$	1.04984	+	3.91804i	0.0653599	+	0.243927i
$259$		0			0
$260$	−0.224087	−	6.66149i	−0.0138973	−	0.413128i
$261$	−2.62857	−	4.55282i	−0.162704	−	0.281812i
$262$	−1.46381	+	5.46301i	−0.0904345	+	0.337506i
$263$	7.74562	+	13.4158i	0.477616	+	0.827254i	0.999671	−	0.0256573i	$-0.00816786\pi$
$263$	7.74562	+	13.4158i	0.477616	+	0.827254i	−0.522055	+	0.852912i	$0.674835\pi$
$264$	9.64177	−	16.7000i	0.593410	−	1.02782i
$265$	5.86881	+	5.86881i	0.360518	+	0.360518i
$266$		0			0
$267$	0.0912034	−	0.340376i	0.00558156	−	0.0208307i
$268$	−0.656106	+	2.44862i	−0.0400781	+	0.149573i
$269$		−	26.1336i		−	1.59339i	−0.604379	−	0.796697i	$-0.706579\pi$
$269$		−	26.1336i		−	1.59339i	0.604379	−	0.796697i	$-0.293421\pi$
$270$	5.91112	−	3.41279i	0.359739	−	0.207696i
$271$	4.65441	−	4.65441i	0.282735	−	0.282735i	−0.551464	−	0.834199i	$-0.685930\pi$
$271$	4.65441	−	4.65441i	0.282735	−	0.282735i	0.834199	+	0.551464i	$0.185930\pi$
$272$	−0.732458			−0.0444118
$273$		0			0
$274$	18.4439			1.11424
$275$	10.1164	−	10.1164i	0.610042	−	0.610042i
$276$	−1.89079	+	1.09165i	−0.113812	+	0.0657096i
$277$		−	29.1771i		−	1.75308i	−0.481329	−	0.876540i	$-0.659846\pi$
$277$		−	29.1771i		−	1.75308i	0.481329	−	0.876540i	$-0.340154\pi$
$278$	−0.880384	+	3.28564i	−0.0528019	+	0.197059i
$279$	−1.65946	+	6.19317i	−0.0993490	+	0.370776i
$280$		0			0
$281$	8.85369	+	8.85369i	0.528167	+	0.528167i	0.920025	−	0.391859i	$-0.128168\pi$
$281$	8.85369	+	8.85369i	0.528167	+	0.528167i	−0.391859	+	0.920025i	$0.628168\pi$
$282$	−3.52451	+	6.10463i	−0.209882	+	0.363526i
$283$	15.9706	+	27.6618i	0.949351	+	1.64432i	0.746795	+	0.665054i	$0.231591\pi$
$283$	15.9706	+	27.6618i	0.949351	+	1.64432i	0.202556	+	0.979271i	$0.435075\pi$
$284$	1.10323	−	4.11732i	0.0654648	−	0.244318i
$285$	−6.44696	−	11.1665i	−0.381885	−	0.661444i
$286$	−10.0689	+	10.7699i	−0.595386	+	0.636837i
$287$		0			0
$288$	−1.40773	−	5.25373i	−0.0829514	−	0.309579i
$289$	−8.10154			−0.476561
$290$	6.70839			0.393930
$291$	3.48813	+	13.0179i	0.204478	+	0.763121i
$292$	−0.622216	+	0.166722i	−0.0364124	+	0.00975668i
$293$	12.4822	+	3.34459i	0.729218	+	0.195393i	0.604281	−	0.796771i	$-0.293460\pi$
$293$	12.4822	+	3.34459i	0.729218	+	0.195393i	0.124937	+	0.992165i	$0.460127\pi$
$294$		0			0
$295$	7.97798	+	13.8183i	0.464496	+	0.804531i
$296$		−	15.5008i		−	0.900964i
$297$	26.5154	+	7.10479i	1.53858	+	0.412262i
$298$	2.06957	+	1.19486i	0.119887	+	0.0692167i
$299$	4.07227	−	1.23932i	0.235506	−	0.0716718i
$300$			5.45075i			0.314699i
$301$		0			0
$302$	−7.05216	+	12.2147i	−0.405806	+	0.702877i
$303$	−17.7332	−	10.2382i	−1.01874	−	0.588171i
$304$	−1.48931	+	0.399060i	−0.0854180	+	0.0228877i
$305$	−9.30113	+	9.30113i	−0.532581	+	0.532581i
$306$	0.615177	+	2.29587i	0.0351674	+	0.131246i
$307$	−5.42520	+	5.42520i	−0.309632	+	0.309632i	−0.844767	−	0.535135i	$-0.820261\pi$
$307$	−5.42520	+	5.42520i	−0.309632	+	0.309632i	0.535135	+	0.844767i	$0.320261\pi$
$308$		0			0
$309$	−9.24869	−	5.33974i	−0.526140	−	0.303767i
$310$	−5.78526	−	5.78526i	−0.328581	−	0.328581i
$311$	0.241688	−	0.418616i	0.0137049	−	0.0237375i	−0.859092	−	0.511822i	$-0.828971\pi$
$311$	0.241688	−	0.418616i	0.0137049	−	0.0237375i	0.872797	+	0.488084i	$0.162304\pi$
$312$	−0.481571	−	14.3158i	−0.0272636	−	0.810470i
$313$	0.385666	−	0.222664i	0.0217991	−	0.0125857i	−0.489061	−	0.872250i	$-0.662660\pi$
$313$	0.385666	−	0.222664i	0.0217991	−	0.0125857i	0.510860	+	0.859664i	$0.329327\pi$
$314$	2.33430	−	0.625474i	0.131732	−	0.0352976i
$315$		0			0
$316$	−7.77097	+	4.48657i	−0.437151	+	0.252389i
$317$	23.9858	+	6.42697i	1.34718	+	0.360975i	0.859091	−	0.511822i	$-0.171029\pi$
$317$	23.9858	+	6.42697i	1.34718	+	0.360975i	0.488084	+	0.872797i	$0.337696\pi$
$318$	4.94596	+	4.94596i	0.277356	+	0.277356i
$319$	19.0774	+	19.0774i	1.06813	+	1.06813i
$320$	6.02444	+	1.61424i	0.336777	+	0.0902390i
$321$	−5.81218	+	3.35567i	−0.324404	+	0.187295i
$322$		0			0
$323$	18.0933	−	4.84809i	1.00674	−	0.269755i
$324$	−5.88660	+	3.39863i	−0.327033	+	0.188813i
$325$	2.40383	−	10.3516i	0.133340	−	0.574206i
$326$	10.1510	−	17.5820i	0.562210	−	0.973776i
$327$	−4.35979	−	4.35979i	−0.241097	−	0.241097i
$328$	−11.7206	−	6.76690i	−0.647163	−	0.373640i
$329$		0			0
$330$	−5.93723	+	5.93723i	−0.326834	+	0.326834i
$331$	3.85370	+	14.3822i	0.211819	+	0.790518i	0.987262	+	0.159101i	$0.0508596\pi$
$331$	3.85370	+	14.3822i	0.211819	+	0.790518i	−0.775444	+	0.631417i	$0.782474\pi$
$332$	4.16624	−	4.16624i	0.228652	−	0.228652i
$333$	5.10906	−	1.36897i	0.279975	−	0.0750190i
$334$	7.15973	+	4.13367i	0.391763	+	0.226184i
$335$	1.40735	−	2.43760i	0.0768917	−	0.133180i
$336$		0			0
$337$		−	7.23643i		−	0.394194i	−0.980384	−	0.197097i	$-0.936849\pi$
$337$		−	7.23643i		−	0.394194i	0.980384	−	0.197097i	$-0.0631513\pi$
$338$	−2.11717	+	10.7450i	−0.115159	+	0.584449i
$339$	5.02375	+	2.90046i	0.272853	+	0.157532i
$340$	5.32656	+	1.42725i	0.288873	+	0.0774033i
$341$		−	32.9044i		−	1.78187i
$342$	2.50169	+	4.33306i	0.135276	+	0.234305i
$343$		0			0
$344$	−8.99474	−	2.41013i	−0.484964	−	0.129946i
$345$	2.34159	−	0.627427i	0.126067	−	0.0337795i
$346$	1.14200	+	4.26201i	0.0613944	+	0.229127i
$347$	−12.5681			−0.674691			−0.337345	−	0.941381i	$-0.609529\pi$
$347$	−12.5681			−0.674691			−0.337345	+	0.941381i	$0.609529\pi$
$348$	−10.2790			−0.551011
$349$	−4.81774	−	17.9800i	−0.257888	−	0.962450i	−0.966461	−	0.256813i	$-0.917328\pi$
$349$	−4.81774	−	17.9800i	−0.257888	−	0.962450i	0.708574	−	0.705637i	$-0.249339\pi$
$350$		0			0
$351$	19.5072	−	5.93665i	1.04122	−	0.316875i
$352$	13.9566	+	24.1735i	0.743887	+	1.28845i
$353$	1.61994	−	6.04570i	0.0862207	−	0.321780i	−0.909322	−	0.416093i	$-0.863399\pi$
$353$	1.61994	−	6.04570i	0.0862207	−	0.321780i	0.995543	+	0.0943134i	$0.0300656\pi$
$354$	6.72348	+	11.6454i	0.357349	+	0.618947i
$355$	−2.36643	+	4.09878i	−0.125597	+	0.217541i
$356$	0.224325	+	0.224325i	0.0118892	+	0.0118892i
$357$		0			0
$358$	4.92181	−	18.3684i	0.260126	−	0.970802i
$359$	−0.609768	+	2.27568i	−0.0321823	+	0.120106i	−0.980148	−	0.198265i	$-0.936469\pi$
$359$	−0.609768	+	2.27568i	−0.0321823	+	0.120106i	0.947966	+	0.318371i	$0.103136\pi$
$360$			3.75607i			0.197962i
$361$	17.6935	−	10.2153i	0.931236	−	0.537649i
$362$	13.3912	−	13.3912i	0.703827	−	0.703827i
$363$	−18.0031			−0.944918
$364$		0			0
$365$	0.715239			0.0374373
$366$	−7.83857	+	7.83857i	−0.409729	+	0.409729i
$367$	16.7399	−	9.66481i	0.873818	−	0.504499i	0.00520293	−	0.999986i	$-0.498344\pi$
$367$	16.7399	−	9.66481i	0.873818	−	0.504499i	0.868615	+	0.495487i	$0.165011\pi$
$368$		−	0.289884i		−	0.0151113i
$369$	1.19525	−	4.46074i	0.0622224	−	0.232217i
$370$	−1.74687	+	6.51943i	−0.0908157	+	0.338929i
$371$		0			0
$372$	8.86450	+	8.86450i	0.459603	+	0.459603i
$373$	4.17375	−	7.22914i	0.216108	−	0.374311i	−0.737507	−	0.675340i	$-0.763997\pi$
$373$	4.17375	−	7.22914i	0.216108	−	0.374311i	0.953615	+	0.301029i	$0.0973302\pi$
$374$	−6.09900	−	10.5638i	−0.315372	−	0.546240i
$375$	4.22367	−	15.7630i	0.218110	−	0.813996i
$376$	−8.09130	−	14.0145i	−0.417277	−	0.722745i
$377$	19.5210	+	4.53311i	1.00538	+	0.233467i
$378$		0			0
$379$	−4.99923	−	18.6574i	−0.256793	−	0.958365i	−0.967084	−	0.254457i	$-0.918103\pi$
$379$	−4.99923	−	18.6574i	−0.256793	−	0.958365i	0.710291	−	0.703908i	$-0.248563\pi$
$380$	11.6081			0.595485
$381$	17.6867			0.906120
$382$	5.37912	+	20.0752i	0.275220	+	1.02713i
$383$	−22.7295	+	6.09034i	−1.16142	+	0.311202i	−0.787533	−	0.616272i	$-0.788642\pi$
$383$	−22.7295	+	6.09034i	−1.16142	+	0.311202i	−0.373888	+	0.927474i	$0.621976\pi$
$384$	−10.8450	−	2.90592i	−0.553433	−	0.148292i
$385$		0			0
$386$	1.44861	+	2.50906i	0.0737323	+	0.127708i
$387$		−	3.17752i		−	0.161522i
$388$	−11.7197	−	3.14029i	−0.594979	−	0.159424i
$389$	−24.2127	−	13.9792i	−1.22763	−	0.708775i	−0.261100	−	0.965312i	$-0.584085\pi$
$389$	−24.2127	−	13.9792i	−1.22763	−	0.708775i	−0.966535	+	0.256536i	$0.917419\pi$
$390$	−1.41079	+	6.07530i	−0.0714379	+	0.307635i
$391$			3.52174i			0.178102i
$392$		0			0
$393$	−4.81109	+	8.33305i	−0.242687	+	0.420347i
$394$	−2.91292	−	1.68177i	−0.146751	−	0.0847266i
$395$	9.62371	−	2.57866i	0.484221	−	0.129747i
$396$	−4.18883	+	4.18883i	−0.210497	+	0.210497i
$397$	3.10484	+	11.5874i	0.155827	+	0.581556i	0.999033	+	0.0439649i	$0.0139990\pi$
$397$	3.10484	+	11.5874i	0.155827	+	0.581556i	−0.843206	+	0.537591i	$0.819334\pi$
$398$	−0.609447	+	0.609447i	−0.0305488	+	0.0305488i
$399$		0			0
$400$	−0.626756	−	0.361858i	−0.0313378	−	0.0180929i
$401$	−14.0001	−	14.0001i	−0.699134	−	0.699134i	0.265090	−	0.964224i	$-0.414598\pi$
$401$	−14.0001	−	14.0001i	−0.699134	−	0.699134i	−0.964224	+	0.265090i	$0.914598\pi$
$402$	1.18605	−	2.05430i	0.0591548	−	0.102459i
$403$	−12.9255	−	20.7441i	−0.643863	−	1.03334i
$404$	15.9648	−	9.21728i	0.794279	−	0.458577i
$405$	7.29007	−	1.95337i	0.362246	−	0.0970636i
$406$		0			0
$407$	−23.5078	+	13.5722i	−1.16524	+	0.672751i
$408$	11.4469	+	3.06720i	0.566708	+	0.151849i
$409$	−12.5877	−	12.5877i	−0.622424	−	0.622424i	0.323727	−	0.946151i	$-0.395064\pi$
$409$	−12.5877	−	12.5877i	−0.622424	−	0.622424i	−0.946151	+	0.323727i	$0.895064\pi$
$410$	4.16694	+	4.16694i	0.205790	+	0.205790i
$411$	30.3097	+	8.12147i	1.49507	+	0.400602i
$412$	8.32642	−	4.80726i	0.410213	−	0.236837i
$413$		0			0
$414$	−0.908636	+	0.243468i	−0.0446570	+	0.0119658i
$415$	−5.66558	+	3.27102i	−0.278112	+	0.160568i
$416$	18.2945	+	9.75742i	0.896962	+	0.478397i
$417$	−2.89355	+	5.01178i	−0.141698	+	0.245428i
$418$	−18.1565	−	18.1565i	−0.888066	−	0.888066i
$419$	8.03474	+	4.63886i	0.392523	+	0.226623i	0.683253	−	0.730182i	$-0.260565\pi$
$419$	8.03474	+	4.63886i	0.392523	+	0.226623i	−0.290730	+	0.956805i	$0.593898\pi$
$420$		0			0
$421$	−13.2205	+	13.2205i	−0.644329	+	0.644329i	−0.951617	−	0.307288i	$-0.900579\pi$
$421$	−13.2205	+	13.2205i	−0.644329	+	0.644329i	0.307288	+	0.951617i	$0.400579\pi$
$422$	−1.17766	−	4.39510i	−0.0573277	−	0.213950i
$423$	3.90460	−	3.90460i	0.189848	−	0.189848i
$424$	−15.5106	+	4.15606i	−0.753262	+	0.201836i
$425$	7.61431	+	4.39612i	0.369348	+	0.213243i
$426$	−1.99432	+	3.45427i	−0.0966253	+	0.167360i
$427$		0			0
$428$		−	6.04208i		−	0.292055i
$429$	−21.2890	+	13.2650i	−1.02784	+	0.640440i
$430$	3.51146	+	2.02734i	0.169338	+	0.0977671i
$431$	−5.72637	−	1.53438i	−0.275830	−	0.0739083i	0.118252	−	0.992984i	$-0.462271\pi$
$431$	−5.72637	−	1.53438i	−0.275830	−	0.0739083i	−0.394082	+	0.919075i	$0.628937\pi$
$432$		−	1.38861i		−	0.0668098i
$433$	6.32385	+	10.9532i	0.303905	+	0.526379i	0.977017	−	0.213162i	$-0.0683762\pi$
$433$	6.32385	+	10.9532i	0.303905	+	0.526379i	−0.673112	+	0.739541i	$0.735043\pi$
$434$		0			0
$435$	11.0242	+	2.95393i	0.528570	+	0.141630i
$436$	5.36170	−	1.43666i	0.256779	−	0.0688036i
$437$	1.91873	+	7.16078i	0.0917851	+	0.342547i
$438$	0.602771			0.0288015
$439$	25.7575			1.22934			0.614670	−	0.788784i	$-0.289289\pi$
$439$	25.7575			1.22934			0.614670	+	0.788784i	$0.289289\pi$
$440$	−4.98901	−	18.6192i	−0.237842	−	0.887638i
$441$		0			0
$442$	−7.99468	−	4.26398i	−0.380268	−	0.202817i
$443$	−8.62206	−	14.9338i	−0.409647	−	0.709529i	0.585203	−	0.810886i	$-0.301015\pi$
$443$	−8.62206	−	14.9338i	−0.409647	−	0.709529i	−0.994850	+	0.101358i	$0.967681\pi$
$444$	2.67666	−	9.98942i	0.127029	−	0.474077i
$445$	−0.176123	−	0.305054i	−0.00834904	−	0.0144610i
$446$	−7.24482	+	12.5484i	−0.343052	+	0.594184i
$447$	2.87487	+	2.87487i	0.135977	+	0.135977i
$448$		0			0
$449$	−1.50842	+	5.62952i	−0.0711870	+	0.265673i	−0.992342	−	0.123523i	$-0.960581\pi$
$449$	−1.50842	+	5.62952i	−0.0711870	+	0.265673i	0.921155	+	0.389197i	$0.127247\pi$
$450$	−0.607835	+	2.26847i	−0.0286536	+	0.106937i
$451$			23.7000i			1.11599i
$452$	−4.52278	+	2.61123i	−0.212734	+	0.122822i
$453$	−16.9677	+	16.9677i	−0.797211	+	0.797211i
$454$	−8.39274			−0.393891
$455$		0			0
$456$	24.9463			1.16822
$457$	15.7010	−	15.7010i	0.734462	−	0.734462i	−0.237038	−	0.971500i	$-0.576177\pi$
$457$	15.7010	−	15.7010i	0.734462	−	0.734462i	0.971500	+	0.237038i	$0.0761766\pi$
$458$	3.04250	−	1.75659i	0.142167	−	0.0820801i
$459$			16.8700i			0.787422i
$460$	−0.564860	+	2.10809i	−0.0263367	+	0.0982901i
$461$	5.52093	−	20.6044i	0.257135	−	0.959642i	−0.709755	−	0.704449i	$-0.751194\pi$
$461$	5.52093	−	20.6044i	0.257135	−	0.959642i	0.966890	−	0.255193i	$-0.0821390\pi$
$462$		0			0
$463$	−5.14657	−	5.14657i	−0.239181	−	0.239181i	0.577330	−	0.816511i	$-0.304095\pi$
$463$	−5.14657	−	5.14657i	−0.239181	−	0.239181i	−0.816511	+	0.577330i	$0.804095\pi$
$464$	0.682387	−	1.18193i	0.0316790	−	0.0548697i
$465$	−6.95974	−	12.0546i	−0.322750	−	0.559020i
$466$	1.37933	−	5.14772i	0.0638962	−	0.238464i
$467$	14.2554	+	24.6911i	0.659661	+	1.14257i	0.980703	+	0.195502i	$0.0626336\pi$
$467$	14.2554	+	24.6911i	0.659661	+	1.14257i	−0.321042	+	0.947065i	$0.604033\pi$
$468$	−0.995337	+	4.28624i	−0.0460095	+	0.198131i
$469$		0			0
$470$	1.82371	+	6.80619i	0.0841216	+	0.313946i
$471$	4.11148			0.189447
$472$	−30.8705			−1.42093
$473$	4.22055	+	15.7513i	0.194061	+	0.724245i
$474$	8.11042	−	2.17318i	0.372524	−	0.0998175i
$475$	17.8774	+	4.79022i	0.820270	+	0.219791i
$476$		0			0
$477$	−2.73967	−	4.74526i	−0.125441	−	0.217270i
$478$		−	9.34246i		−	0.427314i
$479$	−31.8012	−	8.52110i	−1.45303	−	0.389339i	−0.555955	−	0.831212i	$-0.687648\pi$
$479$	−31.8012	−	8.52110i	−1.45303	−	0.389339i	−0.897078	+	0.441873i	$0.854314\pi$
$480$	10.2261	+	5.90402i	0.466754	+	0.269480i
$481$	−9.48873	+	17.7907i	−0.432649	+	0.811187i
$482$		−	11.7792i		−	0.536527i
$483$		0			0
$484$	8.10392	−	14.0364i	0.368360	−	0.638018i
$485$	11.6670	+	6.73593i	0.529770	+	0.305863i
$486$	−7.66184	+	2.05298i	−0.347548	+	0.0931252i
$487$	−10.0228	+	10.0228i	−0.454174	+	0.454174i	−0.896737	−	0.442563i	$-0.854069\pi$
$487$	−10.0228	+	10.0228i	−0.454174	+	0.454174i	0.442563	+	0.896737i	$0.354069\pi$
$488$	−6.58670	−	24.5819i	−0.298166	−	1.11277i
$489$	24.4235	−	24.4235i	1.10447	−	1.10447i
$490$		0			0
$491$	−25.7788	−	14.8834i	−1.16338	−	0.671678i	−0.211269	−	0.977428i	$-0.567759\pi$
$491$	−25.7788	−	14.8834i	−1.16338	−	0.671678i	−0.952112	+	0.305750i	$0.901093\pi$
$492$	−6.38481	−	6.38481i	−0.287850	−	0.287850i
$493$	−8.29017	+	14.3590i	−0.373370	+	0.646696i
$494$	−18.5788	−	4.31430i	−0.835898	−	0.194110i
$495$	5.69629	−	3.28876i	0.256029	−	0.147819i
$496$	−1.60777	+	0.430801i	−0.0721911	+	0.0193435i
$497$		0			0
$498$	−4.77470	+	2.75667i	−0.213959	+	0.123529i
$499$	−17.8531	−	4.78371i	−0.799213	−	0.214148i	−0.163974	−	0.986465i	$-0.552431\pi$
$499$	−17.8531	−	4.78371i	−0.799213	−	0.214148i	−0.635238	+	0.772316i	$0.719098\pi$
$500$	10.3886	+	10.3886i	0.464592	+	0.464592i
$501$	9.94572	+	9.94572i	0.444342	+	0.444342i
$502$	−21.4471	−	5.74674i	−0.957232	−	0.256490i
$503$	−5.05931	+	2.92099i	−0.225583	+	0.130241i	−0.608533	−	0.793529i	$-0.708242\pi$
$503$	−5.05931	+	2.92099i	−0.225583	+	0.130241i	0.382949	+	0.923769i	$0.374908\pi$
$504$		0			0
$505$	−19.7711	+	5.29765i	−0.879802	+	0.235742i
$506$	4.18082	−	2.41380i	0.185860	−	0.107306i
$507$	−8.21061	+	16.7254i	−0.364646	+	0.742803i
$508$	−7.96151	+	13.7897i	−0.353235	+	0.611821i
$509$	20.7371	+	20.7371i	0.919156	+	0.919156i	0.996968	−	0.0778117i	$-0.0247933\pi$
$509$	20.7371	+	20.7371i	0.919156	+	0.919156i	−0.0778117	+	0.996968i	$0.524793\pi$
$510$	−4.46878	−	2.58005i	−0.197881	−	0.114246i
$511$		0			0
$512$	1.96096	−	1.96096i	0.0866629	−	0.0866629i
$513$	9.19115	+	34.3018i	0.405799	+	1.51446i
$514$	−6.42180	+	6.42180i	−0.283253	+	0.283253i
$515$	−10.3116	+	2.76298i	−0.454382	+	0.121751i
$516$	−5.38045	−	3.10640i	−0.236861	−	0.136752i
$517$	−14.1692	+	24.5418i	−0.623162	+	1.07935i
$518$		0			0
$519$			7.50681i			0.329513i
$520$	−10.4592	−	9.77846i	−0.458668	−	0.428814i
$521$	−35.5182	−	20.5064i	−1.55608	−	0.898402i	−0.997626	−	0.0688659i	$-0.978062\pi$
$521$	−35.5182	−	20.5064i	−1.55608	−	0.898402i	−0.558453	−	0.829536i	$-0.688605\pi$
$522$	−4.27786	−	1.14625i	−0.187237	−	0.0501699i
$523$			44.3762i			1.94043i	0.242237	+	0.970217i	$0.422119\pi$
$523$			44.3762i			1.94043i	−0.242237	+	0.970217i	$0.577881\pi$
$524$	−4.33133	−	7.50208i	−0.189215	−	0.327730i
$525$		0			0
$526$	12.6056	+	3.37766i	0.549630	+	0.147273i
$527$	19.5325	−	5.23370i	0.850847	−	0.227984i
$528$	0.442118	+	1.65000i	0.0192407	+	0.0718072i
$529$	21.6062			0.939400
$530$	6.99194			0.303710
$531$	−2.72636	−	10.1749i	−0.118314	−	0.441554i
$532$		0			0
$533$	9.30979	+	14.9413i	0.403252	+	0.647180i
$534$	−0.148429	−	0.257086i	−0.00642314	−	0.0111252i
$535$	−1.73635	+	6.48014i	−0.0750688	+	0.280161i
$536$	2.72284	+	4.71610i	0.117609	+	0.203705i
$537$	16.1765	−	28.0185i	0.698066	−	1.20909i
$538$	−15.5674	−	15.5674i	−0.671160	−	0.671160i
$539$		0			0
$540$	−2.70581	+	10.0982i	−0.116440	+	0.434559i
$541$	−1.77523	+	6.62524i	−0.0763230	+	0.284841i	−0.993530	−	0.113570i	$-0.963772\pi$
$541$	−1.77523	+	6.62524i	−0.0763230	+	0.284841i	0.917207	+	0.398411i	$0.130438\pi$
$542$		−	5.54514i		−	0.238184i
$543$	27.9030	−	16.1098i	1.19743	−	0.691338i
$544$	−12.1298	+	12.1298i	−0.520059	+	0.520059i
$545$	−6.16329			−0.264006
$546$		0			0
$547$	−16.7670			−0.716904			−0.358452	−	0.933548i	$-0.616695\pi$
$547$	−16.7670			−0.716904			−0.358452	+	0.933548i	$0.616695\pi$
$548$	−19.9756	+	19.9756i	−0.853317	+	0.853317i
$549$	7.52048	−	4.34195i	0.320966	−	0.185310i
$550$		−	12.0524i		−	0.513916i
$551$	−9.03336	+	33.7129i	−0.384834	+	1.43622i
$552$	−1.21390	+	4.53035i	−0.0516672	+	0.192824i
$553$		0			0
$554$	−17.3804	−	17.3804i	−0.738422	−	0.738422i
$555$	−5.74144	+	9.94446i	−0.243710	+	0.422119i
$556$	−2.60501	−	4.51200i	−0.110477	−	0.191352i
$557$	10.1967	−	38.0545i	0.432046	−	1.61242i	−0.315991	−	0.948762i	$-0.602337\pi$
$557$	10.1967	−	38.0545i	0.432046	−	1.61242i	0.748037	−	0.663657i	$-0.230996\pi$
$558$	2.70068	+	4.67771i	0.114329	+	0.198023i
$559$	8.84819	+	8.27227i	0.374238	+	0.349880i
$560$		0			0
$561$	−5.37118	−	20.0455i	−0.226772	−	0.846323i
$562$	10.5480			0.444943
$563$	−2.11172			−0.0889983			−0.0444991	−	0.999009i	$-0.514169\pi$
$563$	−2.11172			−0.0889983			−0.0444991	+	0.999009i	$0.514169\pi$
$564$	−2.79440	−	10.4288i	−0.117665	−	0.439133i
$565$	5.60110	−	1.50081i	0.235640	−	0.0631395i
$566$	25.9912	+	6.96433i	1.09249	+	0.292733i
$567$		0			0
$568$	−4.57841	−	7.93005i	−0.192106	−	0.332737i
$569$		−	36.4252i		−	1.52702i	−0.645794	−	0.763512i	$-0.723474\pi$
$569$		−	36.4252i		−	1.52702i	0.645794	−	0.763512i	$-0.276526\pi$
$570$	−10.4921	−	2.81134i	−0.439465	−	0.117754i
$571$	13.1672	+	7.60209i	0.551030	+	0.318138i	0.749537	−	0.661962i	$-0.230276\pi$
$571$	13.1672	+	7.60209i	0.551030	+	0.318138i	−0.198507	+	0.980099i	$0.563609\pi$
$572$	−0.759217	−	22.5694i	−0.0317445	−	0.943674i
$573$			35.3590i			1.47715i
$574$		0			0
$575$	−1.73985	+	3.01351i	−0.0725568	+	0.125672i
$576$	−3.56589	−	2.05877i	−0.148579	−	0.0857820i
$577$	10.9379	−	2.93081i	0.455352	−	0.122011i	−0.0238508	−	0.999716i	$-0.507593\pi$
$577$	10.9379	−	2.93081i	0.455352	−	0.122011i	0.479202	+	0.877704i	$0.340926\pi$
$578$	−4.82598	+	4.82598i	−0.200734	+	0.200734i
$579$	1.27574	+	4.76113i	0.0530180	+	0.197866i
$580$	−7.26551	+	7.26551i	−0.301684	+	0.301684i
$581$		0			0
$582$	9.83240	+	5.67674i	0.407566	+	0.235308i
$583$	19.8838	+	19.8838i	0.823501	+	0.823501i
$584$	−0.691898	+	1.19840i	−0.0286309	+	0.0495902i
$585$	2.29926	−	4.31096i	0.0950628	−	0.178236i
$586$	9.42781	−	5.44315i	0.389459	−	0.224854i
$587$	3.32195	−	0.890113i	0.137111	−	0.0367389i	−0.189611	−	0.981859i	$-0.560723\pi$
$587$	3.32195	−	0.890113i	0.137111	−	0.0367389i	0.326722	+	0.945120i	$0.394056\pi$
$588$		0			0
$589$	36.8641	−	21.2835i	1.51896	−	0.876971i
$590$	12.9837	+	3.47898i	0.534532	+	0.143227i
$591$	−4.04639	−	4.04639i	−0.166446	−	0.166446i
$592$	0.970942	+	0.970942i	0.0399055	+	0.0399055i
$593$	−44.9445	−	12.0428i	−1.84565	−	0.494540i	−0.846374	−	0.532589i	$-0.821219\pi$
$593$	−44.9445	−	12.0428i	−1.84565	−	0.494540i	−0.999276	+	0.0380481i	$0.987886\pi$
$594$	20.0271	−	11.5627i	0.821722	−	0.474422i
$595$		0			0
$596$	−3.53554	+	0.947344i	−0.144821	+	0.0388047i
$597$	−1.26989	+	0.733173i	−0.0519732	+	0.0300068i
$598$	1.68755	−	3.16405i	0.0690091	−	0.129388i
$599$	−3.80885	+	6.59712i	−0.155625	+	0.269551i	−0.933287	−	0.359133i	$-0.883073\pi$
$599$	−3.80885	+	6.59712i	−0.155625	+	0.269551i	0.777661	+	0.628684i	$0.216406\pi$
$600$	8.27973	+	8.27973i	0.338018	+	0.338018i
$601$	32.3774	+	18.6931i	1.32070	+	0.762508i	0.983841	−	0.179045i	$-0.0573009\pi$
$601$	32.3774	+	18.6931i	1.32070	+	0.762508i	0.336863	+	0.941554i	$0.390634\pi$
$602$		0			0
$603$	−1.31396	+	1.31396i	−0.0535085	+	0.0535085i
$604$	−5.59128	−	20.8669i	−0.227506	−	0.849064i
$605$	−12.7252	+	12.7252i	−0.517353	+	0.517353i
$606$	−16.6622	+	4.46462i	−0.676855	+	0.181363i
$607$	−16.4375	−	9.49020i	−0.667178	−	0.385195i	0.127829	−	0.991796i	$-0.459199\pi$
$607$	−16.4375	−	9.49020i	−0.667178	−	0.385195i	−0.795006	+	0.606601i	$0.792533\pi$
$608$	−18.0550	+	31.2722i	−0.732226	+	1.26825i
$609$		0			0
$610$			11.0811i			0.448661i
$611$	0.707701	+	21.0380i	0.0286305	+	0.851105i
$612$	−3.15281	−	1.82027i	−0.127445	−	0.0735802i
$613$	4.24543	+	1.13756i	0.171471	+	0.0459456i	0.343533	−	0.939141i	$-0.388376\pi$
$613$	4.24543	+	1.13756i	0.171471	+	0.0459456i	−0.172062	+	0.985086i	$0.555043\pi$
$614$			6.46343i			0.260843i
$615$	5.01288	+	8.68256i	0.202139	+	0.350115i
$616$		0			0
$617$	23.9468	+	6.41652i	0.964061	+	0.258319i	0.706318	−	0.707894i	$-0.250355\pi$
$617$	23.9468	+	6.41652i	0.964061	+	0.258319i	0.257743	+	0.966214i	$0.417021\pi$
$618$	−8.69013	+	2.32851i	−0.349568	+	0.0936666i
$619$	6.30966	+	23.5480i	0.253607	+	0.946473i	0.968860	+	0.247608i	$0.0796445\pi$
$619$	6.30966	+	23.5480i	0.253607	+	0.946473i	−0.715254	+	0.698865i	$0.753689\pi$
$620$	12.5314			0.503275
$621$	−6.67661			−0.267923
$622$	−0.105394	−	0.393334i	−0.00422590	−	0.0157713i
$623$		0			0
$624$	0.926879	+	0.866550i	0.0371049	+	0.0346898i
$625$	−0.787786	−	1.36449i	−0.0315115	−	0.0545794i
$626$	0.0970978	−	0.362374i	0.00388081	−	0.0144834i
$627$	−21.8426	−	37.8324i	−0.872307	−	1.51088i
$628$	−1.85074	+	3.20558i	−0.0738527	+	0.127917i
$629$	−11.7957	−	11.7957i	−0.470327	−	0.470327i
$630$		0			0
$631$	0.701056	−	2.61638i	0.0279086	−	0.104156i	−0.950567	−	0.310521i	$-0.899497\pi$
$631$	0.701056	−	2.61638i	0.0279086	−	0.104156i	0.978475	+	0.206364i	$0.0661633\pi$
$632$	−4.98902	+	18.6193i	−0.198453	+	0.740635i
$633$		−	7.74123i		−	0.307686i
$634$	18.1165	−	10.4595i	0.719497	−	0.415402i
$635$	12.5016	−	12.5016i	0.496110	−	0.496110i
$636$	−10.7134			−0.424815
$637$		0			0
$638$	22.7283			0.899822
$639$	2.20940	−	2.20940i	0.0874024	−	0.0874024i
$640$	−9.71961	+	5.61162i	−0.384202	+	0.221819i
$641$			3.13043i			0.123645i	0.998087	+	0.0618223i	$0.0196912\pi$
$641$			3.13043i			0.123645i	−0.998087	+	0.0618223i	$0.980309\pi$
$642$	−1.46331	+	5.46117i	−0.0577524	+	0.215535i
$643$	−0.747638	+	2.79022i	−0.0294840	+	0.110036i	−0.979100	−	0.203381i	$-0.934807\pi$
$643$	−0.747638	+	2.79022i	−0.0294840	+	0.110036i	0.949616	+	0.313417i	$0.101474\pi$
$644$		0			0
$645$	4.87783	+	4.87783i	0.192064	+	0.192064i
$646$	7.89001	−	13.6659i	0.310428	−	0.537677i
$647$	8.86801	+	15.3598i	0.348637	+	0.603857i	0.986008	−	0.166700i	$-0.0533112\pi$
$647$	8.86801	+	15.3598i	0.348637	+	0.603857i	−0.637370	+	0.770558i	$0.719978\pi$
$648$	−3.77924	+	14.1043i	−0.148463	+	0.554070i
$649$	27.0297	+	46.8169i	1.06101	+	1.83772i
$650$	−4.73441	−	7.59827i	−0.185699	−	0.298029i
$651$		0			0
$652$	8.04815	+	30.0361i	0.315190	+	1.17631i
$653$	−22.1955			−0.868579			−0.434289	−	0.900773i	$-0.643000\pi$
$653$	−22.1955			−0.868579			−0.434289	+	0.900773i	$0.643000\pi$
$654$	−5.19414			−0.203107
$655$	2.48944	+	9.29071i	0.0972704	+	0.363018i
$656$	1.15803	−	0.310292i	0.0452133	−	0.0121149i
$657$	−0.456099	−	0.122211i	−0.0177941	−	0.00476792i
$658$		0			0
$659$	14.4500	+	25.0282i	0.562893	+	0.974960i	0.997242	+	0.0742153i	$0.0236452\pi$
$659$	14.4500	+	25.0282i	0.562893	+	0.974960i	−0.434349	+	0.900745i	$0.643021\pi$
$660$		−	12.8606i		−	0.500599i
$661$	−3.74678	−	1.00395i	−0.145733	−	0.0390490i	0.185215	−	0.982698i	$-0.440702\pi$
$661$	−3.74678	−	1.00395i	−0.145733	−	0.0390490i	−0.330948	+	0.943649i	$0.607368\pi$
$662$	10.8629	+	6.27169i	0.422198	+	0.243756i
$663$	−11.2604	−	10.5275i	−0.437319	−	0.408855i
$664$		−	12.6571i		−	0.491191i
$665$		0			0
$666$	2.22792	−	3.85887i	0.0863302	−	0.149528i
$667$	−5.68285	−	3.28099i	−0.220041	−	0.127041i
$668$	−12.2313	+	3.27737i	−0.473243	+	0.126805i
$669$	−17.4312	+	17.4312i	−0.673930	+	0.673930i
$670$	−0.613707	−	2.29039i	−0.0237096	−	0.0884853i
$671$	−31.5126	+	31.5126i	−1.21653	+	1.21653i
$672$		0			0
$673$	14.8015	+	8.54566i	0.570557	+	0.329411i	0.757372	−	0.652984i	$-0.226483\pi$
$673$	14.8015	+	8.54566i	0.570557	+	0.329411i	−0.186815	+	0.982395i	$0.559816\pi$
$674$	−4.31065	−	4.31065i	−0.166040	−	0.166040i
$675$	−8.33430	+	14.4354i	−0.320787	+	0.555620i
$676$	−9.34432	−	13.9303i	−0.359397	−	0.535782i
$677$	−26.4773	+	15.2867i	−1.01760	+	0.587514i	−0.913409	−	0.407043i	$-0.866560\pi$
$677$	−26.4773	+	15.2867i	−1.01760	+	0.587514i	−0.104195	+	0.994557i	$0.533227\pi$
$678$	4.72035	−	1.26481i	0.181284	−	0.0485749i
$679$		0			0
$680$	10.2591	−	5.92308i	0.393417	−	0.227140i
$681$	−13.7922	−	3.69560i	−0.528517	−	0.141616i
$682$	−19.6007	−	19.6007i	−0.750550	−	0.750550i
$683$	4.48109	+	4.48109i	0.171464	+	0.171464i	0.787622	−	0.616158i	$-0.211312\pi$
$683$	4.48109	+	4.48109i	0.171464	+	0.171464i	−0.616158	+	0.787622i	$0.711312\pi$
$684$	−7.40236	−	1.98346i	−0.283036	−	0.0758394i
$685$	27.1644	−	15.6834i	1.03790	−	0.599231i
$686$		0			0
$687$	5.77337	−	1.54697i	0.220268	−	0.0590206i
$688$	0.714381	−	0.412448i	0.0272355	−	0.0157244i
$689$	20.3461	+	4.72472i	0.775126	+	0.179997i
$690$	1.02110	−	1.76860i	0.0388728	−	0.0673296i
$691$	−3.37284	−	3.37284i	−0.128309	−	0.128309i	0.640036	−	0.768345i	$-0.278919\pi$
$691$	−3.37284	−	3.37284i	−0.128309	−	0.128309i	−0.768345	+	0.640036i	$0.778919\pi$
$692$	−5.85280	−	3.37912i	−0.222490	−	0.128455i
$693$		0			0
$694$	−7.48665	+	7.48665i	−0.284189	+	0.284189i
$695$	1.49723	+	5.58774i	0.0567932	+	0.211955i
$696$	−15.6138	+	15.6138i	−0.591840	+	0.591840i
$697$	−14.0686	+	3.76967i	−0.532886	+	0.142786i
$698$	−13.5803	−	7.84061i	−0.514023	−	0.296771i
$699$	4.53343	−	7.85213i	0.171470	−	0.296995i
$700$		0			0
$701$		−	29.4647i		−	1.11287i	−0.830892	−	0.556433i	$-0.812169\pi$
$701$		−	29.4647i		−	1.11287i	0.830892	−	0.556433i	$-0.187831\pi$
$702$	8.08378	−	15.1565i	0.305103	−	0.572047i
$703$	−30.4110	−	17.5578i	−1.14697	−	0.662205i
$704$	20.4111	+	5.46913i	0.769271	+	0.206126i
$705$			11.9880i			0.451493i
$706$	−2.63637	−	4.56632i	−0.0992209	−	0.171856i
$707$		0			0
$708$	−19.8944	−	5.33069i	−0.747677	−	0.200340i
$709$	16.1912	−	4.33842i	0.608073	−	0.162933i	0.0583730	−	0.998295i	$-0.481409\pi$
$709$	16.1912	−	4.33842i	0.608073	−	0.162933i	0.549700	+	0.835362i	$0.314742\pi$
$710$	1.03194	+	3.85124i	0.0387279	+	0.144535i
$711$	−6.57753			−0.246677
$712$	0.681502			0.0255404
$713$	2.07134	+	7.73035i	0.0775723	+	0.289504i
$714$		0			0
$715$	−5.67164	+	24.4239i	−0.212107	+	0.913402i
$716$	14.5633	+	25.2245i	0.544258	+	0.942682i
$717$	4.11379	−	15.3529i	0.153632	−	0.573364i
$718$	0.992364	+	1.71882i	0.0370347	+	0.0641460i
$719$	−8.96395	+	15.5260i	−0.334299	+	0.579023i	−0.983350	−	0.181722i	$-0.941833\pi$
$719$	−8.96395	+	15.5260i	−0.334299	+	0.579023i	0.649051	+	0.760745i	$0.275166\pi$
$720$	−0.235274	−	0.235274i	−0.00876814	−	0.00876814i
$721$		0			0
$722$	4.45463	−	16.6249i	0.165784	−	0.618715i
$723$	5.18676	−	19.3573i	0.192898	−	0.719904i
$724$			29.0067i			1.07802i
$725$	−14.1876	+	8.19122i	−0.526914	+	0.304214i
$726$	−10.7242	+	10.7242i	−0.398013	+	0.398013i
$727$	−32.6548			−1.21110			−0.605549	−	0.795808i	$-0.707046\pi$
$727$	−32.6548			−1.21110			−0.605549	+	0.795808i	$0.707046\pi$
$728$		0			0
$729$	−29.2988			−1.08514
$730$	0.426059	−	0.426059i	0.0157691	−	0.0157691i
$731$	−8.67885	+	5.01074i	−0.320999	+	0.185329i
$732$		−	16.9791i		−	0.627566i
$733$	9.18149	−	34.2658i	0.339126	−	1.26564i	−0.560200	−	0.828358i	$-0.689276\pi$
$733$	9.18149	−	34.2658i	0.339126	−	1.26564i	0.899326	−	0.437279i	$-0.144058\pi$
$734$	4.21456	−	15.7290i	0.155562	−	0.580567i
$735$		0			0
$736$	−4.80059	−	4.80059i	−0.176952	−	0.176952i
$737$	4.76816	−	8.25869i	0.175637	−	0.304213i
$738$	−1.94521	−	3.36920i	−0.0716041	−	0.124022i
$739$	−3.71731	+	13.8732i	−0.136743	+	0.510333i	0.863241	+	0.504791i	$0.168431\pi$
$739$	−3.71731	+	13.8732i	−0.136743	+	0.510333i	−0.999985	+	0.00554159i	$0.998236\pi$
$740$	−5.16890	−	8.95280i	−0.190013	−	0.329112i
$741$	−28.6316	−	15.2707i	−1.05181	−	0.560984i
$742$		0			0
$743$	6.76509	+	25.2477i	0.248187	+	0.926247i	0.971755	+	0.235993i	$0.0758344\pi$
$743$	6.76509	+	25.2477i	0.248187	+	0.926247i	−0.723568	+	0.690254i	$0.757499\pi$
$744$	26.9305			0.987319
$745$	4.06411			0.148897
$746$	−1.82006	−	6.79255i	−0.0666370	−	0.248693i
$747$	4.17178	−	1.11783i	0.152638	−	0.0408991i
$748$	18.0466	+	4.83557i	0.659849	+	0.176806i
$749$		0			0
$750$	−6.87380	−	11.9058i	−0.250996	−	0.434737i
$751$		−	11.8816i		−	0.433565i	−0.976220	−	0.216783i	$-0.930444\pi$
$751$		−	11.8816i		−	0.433565i	0.976220	−	0.216783i	$-0.0695563\pi$
$752$	1.38467	+	0.371022i	0.0504938	+	0.0135298i
$753$	−32.7146	−	18.8878i	−1.19218	−	0.688308i
$754$	14.3287	−	8.92810i	0.521822	−	0.325142i
$755$			23.9866i			0.872963i
$756$		0			0
$757$	21.1088	−	36.5615i	0.767212	−	1.32885i	−0.171857	−	0.985122i	$-0.554977\pi$
$757$	21.1088	−	36.5615i	0.767212	−	1.32885i	0.939069	−	0.343729i	$-0.111690\pi$
$758$	−14.0919	−	8.13598i	−0.511842	−	0.295512i
$759$	7.93340	−	2.12575i	0.287964	−	0.0771598i
$760$	17.6328	−	17.6328i	0.639610	−	0.639610i
$761$	−7.45021	−	27.8046i	−0.270070	−	1.00792i	−0.959074	−	0.283157i	$-0.908618\pi$
$761$	−7.45021	−	27.8046i	−0.270070	−	1.00792i	0.689003	−	0.724758i	$-0.258048\pi$
$762$	10.5358	−	10.5358i	0.381670	−	0.381670i
$763$		0			0
$764$	−27.5682	−	15.9165i	−0.997383	−	0.575840i
$765$	2.85829	+	2.85829i	0.103342	+	0.103342i
$766$	−9.91170	+	17.1676i	−0.358124	+	0.620290i
$767$	35.4310	+	18.8972i	1.27934	+	0.682340i
$768$	−18.9982	+	10.9686i	−0.685538	+	0.395795i
$769$	33.9039	−	9.08451i	1.22260	−	0.327596i	0.410909	−	0.911676i	$-0.365211\pi$
$769$	33.9039	−	9.08451i	1.22260	−	0.327596i	0.811696	+	0.584081i	$0.198545\pi$
$770$		0			0
$771$	−13.3810	+	7.72550i	−0.481903	+	0.278227i
$772$	−4.28635	−	1.14852i	−0.154269	−	0.0413363i
$773$	21.4888	+	21.4888i	0.772897	+	0.772897i	0.978612	−	0.205715i	$-0.0659518\pi$
$773$	21.4888	+	21.4888i	0.772897	+	0.772897i	−0.205715	+	0.978612i	$0.565952\pi$
$774$	−1.89281	−	1.89281i	−0.0680355	−	0.0680355i
$775$	19.2993	+	5.17124i	0.693252	+	0.185756i
$776$	−22.5725	+	13.0322i	−0.810304	+	0.467829i
$777$		0			0
$778$	−22.7505	+	6.09597i	−0.815643	+	0.218551i
$779$	−26.5520	+	15.3298i	−0.951324	+	0.549247i
$780$	−5.05189	−	8.10779i	−0.180887	−	0.290305i
$781$	−8.01758	+	13.8868i	−0.286891	+	0.496911i
$782$	2.09785	+	2.09785i	0.0750190	+	0.0750190i
$783$	−27.2222	−	15.7167i	−0.972842	−	0.561670i
$784$		0			0
$785$	2.90613	−	2.90613i	0.103724	−	0.103724i
$786$	2.09799	+	7.82979i	0.0748327	+	0.279279i
$787$	7.18350	−	7.18350i	0.256064	−	0.256064i	−0.567387	−	0.823451i	$-0.692046\pi$
$787$	7.18350	−	7.18350i	0.256064	−	0.256064i	0.823451	+	0.567387i	$0.192046\pi$
$788$	4.97628	−	1.33339i	0.177272	−	0.0475000i
$789$	19.2280	+	11.1013i	0.684536	+	0.395217i
$790$	4.19664	−	7.26879i	0.149310	−	0.258612i
$791$		0			0
$792$			12.7257i			0.452189i
$793$	−7.48793	+	32.2454i	−0.265904	+	1.14507i
$794$	8.75199	+	5.05296i	0.310596	+	0.179323i
$795$	11.4902	+	3.07878i	0.407514	+	0.109193i
$796$		−	1.32012i		−	0.0467905i
$797$	18.3972	+	31.8649i	0.651662	+	1.12871i	0.982719	+	0.185101i	$0.0592613\pi$
$797$	18.3972	+	31.8649i	0.651662	+	1.12871i	−0.331057	+	0.943611i	$0.607405\pi$
$798$		0			0
$799$	−16.8221	−	4.50746i	−0.595122	−	0.159462i
$800$	−16.3718	+	4.38681i	−0.578831	+	0.155097i
$801$	0.0601876	+	0.224623i	0.00212662	+	0.00793667i
$802$	−16.6794			−0.588970
$803$	2.42326			0.0855150
$804$	0.940356	+	3.50946i	0.0331638	+	0.123769i
$805$		0			0
$806$	−20.0565	−	4.65746i	−0.706460	−	0.164052i
$807$	−18.7278	−	32.4375i	−0.659250	−	1.14186i
$808$	10.2495	−	38.2518i	0.360577	−	1.34569i
$809$	9.38058	+	16.2476i	0.329804	+	0.571237i	0.982473	−	0.186407i	$-0.0596841\pi$
$809$	9.38058	+	16.2476i	0.329804	+	0.571237i	−0.652669	+	0.757643i	$0.726351\pi$
$810$	3.17900	−	5.50619i	0.111699	−	0.193468i
$811$	−3.85841	−	3.85841i	−0.135487	−	0.135487i	0.636111	−	0.771598i	$-0.280542\pi$
$811$	−3.85841	−	3.85841i	−0.135487	−	0.135487i	−0.771598	+	0.636111i	$0.780542\pi$
$812$		0			0
$813$	2.44171	−	9.11258i	0.0856344	−	0.319592i
$814$	−5.91848	+	22.0881i	−0.207443	+	0.774187i
$815$		−	34.5266i		−	1.20941i
$816$	−0.909141	+	0.524893i	−0.0318263	+	0.0183749i
$817$	−14.9168	+	14.9168i	−0.521874	+	0.521874i
$818$	−14.9967			−0.524347
$819$		0			0
$820$	−9.02599			−0.315201
$821$	−1.46218	+	1.46218i	−0.0510305	+	0.0510305i	−0.732162	−	0.681131i	$-0.761488\pi$
$821$	−1.46218	+	1.46218i	−0.0510305	+	0.0510305i	0.681131	+	0.732162i	$0.261488\pi$
$822$	22.8929	−	13.2173i	0.798483	−	0.461005i
$823$		−	27.1096i		−	0.944983i	−0.881335	−	0.472491i	$-0.843355\pi$
$823$		−	27.1096i		−	0.944983i	0.881335	−	0.472491i	$-0.156645\pi$
$824$	5.34562	−	19.9501i	0.186224	−	0.694996i
$825$	5.30707	−	19.8063i	0.184769	−	0.689566i
$826$		0			0
$827$	−18.8233	−	18.8233i	−0.654550	−	0.654550i	0.299535	−	0.954085i	$-0.403168\pi$
$827$	−18.8233	−	18.8233i	−0.654550	−	0.654550i	−0.954085	+	0.299535i	$0.903168\pi$
$828$	0.720409	−	1.24778i	0.0250359	−	0.0433635i
$829$	−2.50749	−	4.34310i	−0.0870887	−	0.150842i	0.819191	−	0.573521i	$-0.194423\pi$
$829$	−2.50749	−	4.34310i	−0.0870887	−	0.150842i	−0.906279	+	0.422679i	$0.861090\pi$
$830$	−1.42641	+	5.32342i	−0.0495112	+	0.184778i
$831$	−20.9088	−	36.2152i	−0.725319	−	1.25629i
$832$	15.0162	−	4.56991i	0.520594	−	0.158433i
$833$		0			0
$834$	1.26180	+	4.70910i	0.0436925	+	0.163063i
$835$	14.0599			0.486564
$836$	39.3288			1.36022
$837$	9.92221	+	37.0302i	0.342962	+	1.27995i
$838$	7.54949	−	2.02288i	0.260793	−	0.0698792i
$839$	−1.91166	−	0.512227i	−0.0659978	−	0.0176840i	0.225669	−	0.974204i	$-0.427543\pi$
$839$	−1.91166	−	0.512227i	−0.0659978	−	0.0176840i	−0.291667	+	0.956520i	$0.594210\pi$
$840$		0			0
$841$	−0.946916	−	1.64011i	−0.0326523	−	0.0565554i
$842$			15.7506i			0.542801i
$843$	17.3341	+	4.64466i	0.597018	+	0.159970i
$844$	6.03557	+	3.48464i	0.207753	+	0.119946i
$845$	6.01856	+	17.6256i	0.207045	+	0.606340i
$846$		−	4.65184i		−	0.159934i
$847$		0			0
$848$	0.711230	−	1.23189i	0.0244238	−	0.0423032i
$849$	39.6459	+	22.8896i	1.36065	+	0.785569i
$850$	7.15446	−	1.91703i	0.245396	−	0.0657536i
$851$	4.66839	−	4.66839i	0.160030	−	0.160030i
$852$	−1.58119	−	5.90109i	−0.0541708	−	0.202168i
$853$	0.494551	−	0.494551i	0.0169331	−	0.0169331i	−0.698590	−	0.715523i	$-0.746189\pi$
$853$	0.494551	−	0.494551i	0.0169331	−	0.0169331i	0.715523	+	0.698590i	$0.246189\pi$
$854$		0			0
$855$	7.36904	+	4.25452i	0.252016	+	0.145502i
$856$	−9.17796	−	9.17796i	−0.313696	−	0.313696i
$857$	7.68803	−	13.3161i	0.262618	−	0.454868i	−0.704319	−	0.709884i	$-0.748747\pi$
$857$	7.68803	−	13.3161i	0.262618	−	0.454868i	0.966937	+	0.255016i	$0.0820807\pi$
$858$	−4.77980	+	20.5834i	−0.163180	+	0.702704i
$859$	28.7090	−	16.5752i	0.979540	−	0.565538i	0.0774086	−	0.996999i	$-0.475335\pi$
$859$	28.7090	−	16.5752i	0.979540	−	0.565538i	0.902131	+	0.431462i	$0.142002\pi$
$860$	−5.99879	+	1.60737i	−0.204557	+	0.0548109i
$861$		0			0
$862$	−4.32513	+	2.49712i	−0.147315	+	0.0850521i
$863$	−25.5198	−	6.83800i	−0.868703	−	0.232768i	−0.203176	−	0.979142i	$-0.565126\pi$
$863$	−25.5198	−	6.83800i	−0.868703	−	0.232768i	−0.665527	+	0.746374i	$0.731793\pi$
$864$	−22.9960	−	22.9960i	−0.782339	−	0.782339i
$865$	5.30606	+	5.30606i	0.180412	+	0.180412i
$866$	10.2917	+	2.75766i	0.349727	+	0.0937091i
$867$	−10.0558	+	5.80571i	−0.341513	+	0.197172i
$868$		0			0
$869$	32.6055	−	8.73662i	1.10607	−	0.296370i
$870$	8.32659	−	4.80736i	0.282298	−	0.162985i
$871$	−0.238152	−	7.07959i	−0.00806948	−	0.239883i
$872$	5.96215	−	10.3268i	0.201904	−	0.349708i
$873$	−6.28893	−	6.28893i	−0.212848	−	0.212848i
$874$	5.40854	+	3.12262i	0.182947	+	0.105624i
$875$		0			0
$876$	−0.652830	+	0.652830i	−0.0220571	+	0.0220571i
$877$	3.73595	+	13.9428i	0.126154	+	0.470813i	0.999878	−	0.0156084i	$-0.00496851\pi$
$877$	3.73595	+	13.9428i	0.126154	+	0.470813i	−0.873724	+	0.486422i	$0.838302\pi$
$878$	15.3434	−	15.3434i	0.517815	−	0.517815i
$879$	17.8899	−	4.79360i	0.603413	−	0.161684i
$880$	1.47878	+	0.853774i	0.0498497	+	0.0287807i
$881$	2.13690	−	3.70122i	0.0719941	−	0.124697i	−0.827781	−	0.561051i	$-0.810397\pi$
$881$	2.13690	−	3.70122i	0.0719941	−	0.124697i	0.899775	+	0.436354i	$0.143730\pi$
$882$		0			0
$883$			32.6002i			1.09708i	0.836123	+	0.548542i	$0.184817\pi$
$883$			32.6002i			1.09708i	−0.836123	+	0.548542i	$0.815183\pi$
$884$	13.2767	−	4.04052i	0.446544	−	0.135897i
$885$	19.8049	+	11.4343i	0.665733	+	0.384361i
$886$	−14.0319	−	3.75985i	−0.471412	−	0.126315i
$887$		−	17.7914i		−	0.597377i	−0.954351	−	0.298688i	$-0.903451\pi$
$887$		−	17.7914i		−	0.597377i	0.954351	−	0.298688i	$-0.0965491\pi$
$888$	−11.1081	−	19.2399i	−0.372765	−	0.645648i
$889$		0			0
$890$	−0.286631	−	0.0768025i	−0.00960789	−	0.00257443i
$891$	24.6990	−	6.61809i	0.827449	−	0.221714i
$892$	−5.74403	−	21.4370i	−0.192324	−	0.717764i
$893$	−36.6602			−1.22679
$894$	3.42505			0.114551
$895$	−8.37031	−	31.2384i	−0.279789	−	1.04418i
$896$		0			0
$897$	4.16647	−	4.45654i	0.139114	−	0.148799i
$898$	2.45488	+	4.25198i	0.0819204	+	0.141890i
$899$	−9.75187	+	36.3945i	−0.325243	+	1.21382i
$900$	−1.79855	−	3.11518i	−0.0599516	−	0.103839i
$901$	−8.64057	+	14.9659i	−0.287859	+	0.498587i
$902$	14.1178	+	14.1178i	0.470070	+	0.470070i
$903$		0			0
$904$	−2.90366	+	10.8366i	−0.0965744	+	0.360421i
$905$	8.33582	−	31.1097i	0.277092	−	1.03412i
$906$			20.2148i			0.671593i
$907$	−28.0724	+	16.2076i	−0.932129	+	0.538165i	−0.887484	−	0.460838i	$-0.847549\pi$
$907$	−28.0724	+	16.2076i	−0.932129	+	0.538165i	−0.0446448	+	0.999003i	$0.514216\pi$
$908$	9.08975	−	9.08975i	0.301654	−	0.301654i
$909$	13.5130			0.448197
$910$		0			0
$911$	−15.2599			−0.505585			−0.252792	−	0.967521i	$-0.581349\pi$
$911$	−15.2599			−0.505585			−0.252792	+	0.967521i	$0.581349\pi$
$912$	−1.56259	+	1.56259i	−0.0517425	+	0.0517425i
$913$	−19.1952	+	11.0824i	−0.635269	+	0.366773i
$914$		−	18.7058i		−	0.618732i
$915$	−4.87938	+	18.2101i	−0.161307	+	0.602008i
$916$	−1.39271	+	5.19765i	−0.0460163	+	0.171735i
$917$		0			0
$918$	10.0492	+	10.0492i	0.331673	+	0.331673i
$919$	−6.10555	+	10.5751i	−0.201404	+	0.348841i	−0.948981	−	0.315334i	$-0.897884\pi$
$919$	−6.10555	+	10.5751i	−0.201404	+	0.348841i	0.747577	+	0.664175i	$0.231217\pi$
$920$	2.34417	+	4.06022i	0.0772851	+	0.133862i
$921$	−2.84606	+	10.6217i	−0.0937810	+	0.349995i
$922$	−8.98501	−	15.5625i	−0.295906	−	0.512523i
$923$	0.400449	+	11.9042i	0.0131809	+	0.391832i
$924$		0			0
$925$	−4.26601	−	15.9210i	−0.140266	−	0.523478i
$926$	−6.13149			−0.201493
$927$	7.04767			0.231476
$928$	−8.27260	−	30.8738i	−0.271561	−	1.01348i
$929$	35.1894	−	9.42897i	1.15453	−	0.309354i	0.369749	−	0.929132i	$-0.379444\pi$
$929$	35.1894	−	9.42897i	1.15453	−	0.309354i	0.784778	+	0.619777i	$0.212777\pi$
$930$	−11.3266	−	3.03496i	−0.371414	−	0.0995201i
$931$		0			0
$932$	4.08135	+	7.06911i	0.133689	+	0.231556i
$933$		−	0.692792i		−	0.0226810i
$934$	23.1999	+	6.21639i	0.759124	+	0.203407i
$935$	−17.9654	−	10.3723i	−0.587530	−	0.339211i
$936$	4.99890	+	8.02275i	0.163394	+	0.262232i
$937$		−	37.8200i		−	1.23553i	−0.786365	−	0.617763i	$-0.788039\pi$
$937$		−	37.8200i		−	1.23553i	0.786365	−	0.617763i	$-0.211961\pi$
$938$		0			0
$939$	0.319131	−	0.552750i	0.0104144	−	0.0180383i
$940$	−9.34660	−	5.39626i	−0.304853	−	0.176007i
$941$	23.9882	−	6.42761i	0.781992	−	0.209534i	0.154329	−	0.988019i	$-0.450678\pi$
$941$	23.9882	−	6.42761i	0.781992	−	0.209534i	0.627663	+	0.778485i	$0.284012\pi$
$942$	2.44916	−	2.44916i	0.0797978	−	0.0797978i
$943$	−1.49192	−	5.56792i	−0.0485836	−	0.181316i
$944$	1.93368	−	1.93368i	0.0629358	−	0.0629358i
$945$		0			0
$946$	11.8970	+	6.86871i	0.386804	+	0.223321i
$947$	17.8082	+	17.8082i	0.578690	+	0.578690i	0.934542	−	0.355852i	$-0.115809\pi$
$947$	17.8082	+	17.8082i	0.578690	+	0.578690i	−0.355852	+	0.934542i	$0.615809\pi$
$948$	−6.43032	+	11.1376i	−0.208847	+	0.361734i
$949$	1.52771	−	0.951902i	0.0495915	−	0.0309000i
$950$	13.5028	−	7.79583i	0.438088	−	0.252930i
$951$	34.3773	−	9.21137i	1.11476	−	0.298699i
$952$		0			0
$953$	15.6650	−	9.04419i	0.507439	−	0.292970i	−0.224341	−	0.974511i	$-0.572023\pi$
$953$	15.6650	−	9.04419i	0.507439	−	0.292970i	0.731780	+	0.681541i	$0.238690\pi$
$954$	−4.45867	−	1.19470i	−0.144355	−	0.0386798i
$955$	24.9929	+	24.9929i	0.808752	+	0.808752i
$956$	10.1183	+	10.1183i	0.327250	+	0.327250i
$957$	37.3505	+	10.0080i	1.20737	+	0.323514i
$958$	−24.0194	+	13.8676i	−0.776033	+	0.448043i
$959$		0			0
$960$	8.63446	−	2.31360i	0.278676	−	0.0746710i
$961$	12.9494	−	7.47636i	0.417724	−	0.241173i
$962$	4.94539	+	16.2500i	0.159446	+	0.523921i
$963$	2.21449	−	3.83562i	0.0713611	−	0.123601i
$964$	12.7574	+	12.7574i	0.410889	+	0.410889i
$965$	4.26706	+	2.46359i	0.137361	+	0.0793057i
$966$		0			0
$967$	−2.32489	+	2.32489i	−0.0747635	+	0.0747635i	−0.743500	−	0.668736i	$-0.766836\pi$
$967$	−2.32489	+	2.32489i	−0.0747635	+	0.0747635i	0.668736	+	0.743500i	$0.266836\pi$
$968$	−9.01148	−	33.6313i	−0.289640	−	1.08095i
$969$	18.9836	−	18.9836i	0.609840	−	0.609840i
$970$	10.9624	−	2.93736i	0.351980	−	0.0943128i
$971$	−12.8317	−	7.40841i	−0.411790	−	0.237747i	0.279768	−	0.960068i	$-0.409742\pi$
$971$	−12.8317	−	7.40841i	−0.411790	−	0.237747i	−0.691559	+	0.722320i	$0.743076\pi$
$972$	6.07466	−	10.5216i	0.194845	−	0.337481i
$973$		0			0
$974$			11.9408i			0.382609i
$975$	−4.43450	−	14.5713i	−0.142018	−	0.466655i
$976$	1.95235	+	1.12719i	0.0624931	+	0.0360804i
$977$	18.2064	+	4.87838i	0.582474	+	0.156073i	0.538011	−	0.842938i	$-0.319176\pi$
$977$	18.2064	+	4.87838i	0.582474	+	0.156073i	0.0444625	+	0.999011i	$0.485842\pi$
$978$		−	29.0975i		−	0.930435i
$979$	−0.596712	−	1.03354i	−0.0190710	−	0.0330320i
$980$		0			0
$981$	3.93025	+	1.05311i	0.125483	+	0.0336231i
$982$	−24.2219	+	6.49024i	−0.772952	+	0.207112i
$983$	−1.25862	−	4.69722i	−0.0401436	−	0.149818i	0.942945	−	0.332949i	$-0.108044\pi$
$983$	−1.25862	−	4.69722i	−0.0401436	−	0.149818i	−0.983089	+	0.183131i	$0.941377\pi$
$984$	−19.3971			−0.618358
$985$	−5.72024			−0.182262
$986$	3.61512	+	13.4918i	0.115129	+	0.429666i
$987$		0			0
$988$	24.7943	−	15.4491i	0.788812	−	0.491501i
$989$	−1.98310	−	3.43482i	−0.0630588	−	0.109221i
$990$	1.43414	−	5.35228i	0.0455799	−	0.170106i
$991$	8.04617	+	13.9364i	0.255595	+	0.442703i	0.965057	−	0.262040i	$-0.0843953\pi$
$991$	8.04617	+	13.9364i	0.255595	+	0.442703i	−0.709462	+	0.704744i	$0.751062\pi$
$992$	−19.4911	+	33.7595i	−0.618842	+	1.07187i
$993$	15.0898	+	15.0898i	0.478862	+	0.478862i
$994$		0			0
$995$	−0.379371	+	1.41583i	−0.0120269	+	0.0448849i
$996$	2.18562	−	8.15683i	0.0692539	−	0.258459i
$997$		−	25.6075i		−	0.810999i	−0.914095	−	0.405500i	$-0.867098\pi$
$997$		−	25.6075i		−	0.810999i	0.914095	−	0.405500i	$-0.132902\pi$
$998$	−13.4844	+	7.78523i	−0.426842	+	0.246437i
$999$	22.3627	−	22.3627i	0.707525	−	0.707525i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	637.2.bb.b.227.6		32
7.2	even	3		637.2.x.b.19.4		32
7.3	odd	6		91.2.bc.a.6.6	yes	32
7.4	even	3		91.2.bc.a.6.5	✓	32
7.5	odd	6		637.2.x.b.19.3		32
7.6	odd	2	inner	637.2.bb.b.227.5		32
13.11	odd	12		637.2.x.b.570.4		32
21.11	odd	6		819.2.fm.g.370.3		32
21.17	even	6		819.2.fm.g.370.4		32
91.11	odd	12		91.2.bc.a.76.6	yes	32
91.24	even	12		91.2.bc.a.76.5	yes	32
91.37	odd	12	inner	637.2.bb.b.362.5		32
91.76	even	12		637.2.x.b.570.3		32
91.89	even	12	inner	637.2.bb.b.362.6		32
273.11	even	12		819.2.fm.g.622.4		32
273.206	odd	12		819.2.fm.g.622.3		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.bc.a.6.5	✓	32	7.4	even	3
91.2.bc.a.6.6	yes	32	7.3	odd	6
91.2.bc.a.76.5	yes	32	91.24	even	12
91.2.bc.a.76.6	yes	32	91.11	odd	12
637.2.x.b.19.3		32	7.5	odd	6
637.2.x.b.19.4		32	7.2	even	3
637.2.x.b.570.3		32	91.76	even	12
637.2.x.b.570.4		32	13.11	odd	12
637.2.bb.b.227.5		32	7.6	odd	2	inner
637.2.bb.b.227.6		32	1.1	even	1	trivial
637.2.bb.b.362.5		32	91.37	odd	12	inner
637.2.bb.b.362.6		32	91.89	even	12	inner
819.2.fm.g.370.3		32	21.11	odd	6
819.2.fm.g.370.4		32	21.17	even	6
819.2.fm.g.622.3		32	273.206	odd	12
819.2.fm.g.622.4		32	273.11	even	12

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:	\( N \)	\(=\)	\( 637 = 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	637.bb (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.595687 - 0.595687i) q^{2} +(1.24122 - 0.716618i) q^{3} +1.29031i q^{4} +(0.370805 - 1.38386i) q^{5} +(0.312498 - 1.16626i) q^{6} +(1.96000 + 1.96000i) q^{8} +(-0.472916 + 0.819114i) q^{9} +O(q^{10})\)	\(q+(0.595687 - 0.595687i) q^{2} +(1.24122 - 0.716618i) q^{3} +1.29031i q^{4} +(0.370805 - 1.38386i) q^{5} +(0.312498 - 1.16626i) q^{6} +(1.96000 + 1.96000i) q^{8} +(-0.472916 + 0.819114i) q^{9} +(-0.603466 - 1.04523i) q^{10} +(1.25630 - 4.68859i) q^{11} +(0.924663 + 1.60156i) q^{12} +(-1.04975 - 3.44935i) q^{13} +(-0.531452 - 1.98341i) q^{15} -0.245542 q^{16} +2.98303 q^{17} +(0.206226 + 0.769645i) q^{18} +(6.06542 - 1.62522i) q^{19} +(1.78562 + 0.478455i) q^{20} +(-2.04457 - 3.54129i) q^{22} +1.18059i q^{23} +(3.83736 + 1.02822i) q^{24} +(2.55254 + 1.47371i) q^{25} +(-2.68005 - 1.42941i) q^{26} +5.65531i q^{27} +(-2.77911 + 4.81356i) q^{29} +(-1.49807 - 0.864909i) q^{30} +(6.54786 - 1.75449i) q^{31} +(-4.06626 + 4.06626i) q^{32} +(-1.80058 - 6.71986i) q^{33} +(1.77695 - 1.77695i) q^{34} +(-1.05692 - 0.610210i) q^{36} +(-3.95429 - 3.95429i) q^{37} +(2.64497 - 4.58121i) q^{38} +(-3.77484 - 3.52914i) q^{39} +(3.43915 - 1.98559i) q^{40} +(-4.71621 + 1.26371i) q^{41} +(-2.90941 + 1.67975i) q^{43} +(6.04975 + 1.62103i) q^{44} +(0.958183 + 0.958183i) q^{45} +(0.703262 + 0.703262i) q^{46} +(-5.63925 - 1.51103i) q^{47} +(-0.304771 + 0.175960i) q^{48} +(2.39839 - 0.642646i) q^{50} +(3.70259 - 2.13769i) q^{51} +(4.45075 - 1.35450i) q^{52} +(-2.89658 + 5.01702i) q^{53} +(3.36879 + 3.36879i) q^{54} +(-6.02252 - 3.47711i) q^{55} +(6.36385 - 6.36385i) q^{57} +(1.21190 + 4.52285i) q^{58} +(-7.87514 + 7.87514i) q^{59} +(2.55922 - 0.685740i) q^{60} +(-7.95118 - 4.59062i) q^{61} +(2.85534 - 4.94560i) q^{62} +4.35335i q^{64} +(-5.16269 + 0.173669i) q^{65} +(-5.07551 - 2.93035i) q^{66} +(1.89769 + 0.508485i) q^{67} +3.84905i q^{68} +(0.846033 + 1.46537i) q^{69} +(-3.19094 - 0.855010i) q^{71} +(-2.53237 + 0.678548i) q^{72} +(0.129211 + 0.482220i) q^{73} -4.71103 q^{74} +4.22436 q^{75} +(2.09705 + 7.82630i) q^{76} +(-4.35088 + 0.146360i) q^{78} +(3.47711 + 6.02254i) q^{79} +(-0.0910481 + 0.339796i) q^{80} +(2.63395 + 4.56214i) q^{81} +(-2.05661 + 3.56216i) q^{82} +(-3.22886 - 3.22886i) q^{83} +(1.10612 - 4.12811i) q^{85} +(-0.732493 + 2.73370i) q^{86} +7.96625i q^{87} +(11.6520 - 6.72727i) q^{88} +(0.173853 - 0.173853i) q^{89} +1.14155 q^{90} -1.52333 q^{92} +(6.87003 - 6.87003i) q^{93} +(-4.25933 + 2.45913i) q^{94} -8.99636i q^{95} +(-2.13316 + 7.96108i) q^{96} +(-2.43374 + 9.08284i) q^{97} +(3.24636 + 3.24636i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 4 q^{2} - 16 q^{8} + 8 q^{9}+O(q^{10}) \) 32 * q + 4 * q^2 - 16 * q^8 + 8 * q^9	\( 32 q + 4 q^{2} - 16 q^{8} + 8 q^{9} - 16 q^{11} - 8 q^{15} - 24 q^{16} + 68 q^{18} + 4 q^{22} + 4 q^{29} - 12 q^{30} - 68 q^{32} - 8 q^{37} - 48 q^{43} + 60 q^{44} + 24 q^{46} - 44 q^{50} - 12 q^{51} - 36 q^{53} - 92 q^{57} - 28 q^{58} - 104 q^{60} - 32 q^{65} - 8 q^{67} + 84 q^{71} + 124 q^{72} + 48 q^{74} + 148 q^{78} + 40 q^{79} + 28 q^{81} + 36 q^{85} - 60 q^{86} + 228 q^{88} + 24 q^{92} - 84 q^{93} - 60 q^{99}+O(q^{100}) \) 32 * q + 4 * q^2 - 16 * q^8 + 8 * q^9 - 16 * q^11 - 8 * q^15 - 24 * q^16 + 68 * q^18 + 4 * q^22 + 4 * q^29 - 12 * q^30 - 68 * q^32 - 8 * q^37 - 48 * q^43 + 60 * q^44 + 24 * q^46 - 44 * q^50 - 12 * q^51 - 36 * q^53 - 92 * q^57 - 28 * q^58 - 104 * q^60 - 32 * q^65 - 8 * q^67 + 84 * q^71 + 124 * q^72 + 48 * q^74 + 148 * q^78 + 40 * q^79 + 28 * q^81 + 36 * q^85 - 60 * q^86 + 228 * q^88 + 24 * q^92 - 84 * q^93 - 60 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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