LMFDB - Embedded newform 804.2.s.b.5.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [804,2,Mod(5,804)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(804, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 11, 5]))

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

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

chi := DirichletCharacter("804.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 804 = 2^{2} \cdot 3 \cdot 67 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	804.s (of order $22$, degree $10$, 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:	$6.41997232251$
Analytic rank:	$0$
Dimension:	$200$
Relative dimension:	$20$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			5.20
Character	$\chi$	$=$	804.5
Dual form			804.2.s.b.161.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.64768 - 0.533989i) q^{3} +(2.22357 - 0.652900i) q^{5} +(2.01808 + 1.74867i) q^{7} +(2.42971 - 1.75969i) q^{9} +O(q^{10})$	\(q+(1.64768 - 0.533989i) q^{3} +(2.22357 - 0.652900i) q^{5} +(2.01808 + 1.74867i) q^{7} +(2.42971 - 1.75969i) q^{9} +(0.819238 - 0.240550i) q^{11} +(1.65269 + 2.57164i) q^{13} +(3.31510 - 2.26314i) q^{15} +(-5.09528 - 0.732591i) q^{17} +(0.289069 + 0.333603i) q^{19} +(4.25892 + 1.80362i) q^{21} +(-7.43322 + 3.39464i) q^{23} +(0.311737 - 0.200341i) q^{25} +(3.06373 - 4.19685i) q^{27} -2.95311i q^{29} +(-0.121792 + 0.189512i) q^{31} +(1.22139 - 0.833814i) q^{33} +(5.62905 + 2.57070i) q^{35} +1.16503 q^{37} +(4.09634 + 3.35472i) q^{39} +(0.236280 - 1.64336i) q^{41} +(0.275166 + 0.0395630i) q^{43} +(4.25374 - 5.49916i) q^{45} +(-9.50691 + 4.34166i) q^{47} +(0.0185697 + 0.129155i) q^{49} +(-8.78660 + 1.51375i) q^{51} +(-0.673384 - 4.68349i) q^{53} +(1.66458 - 1.06976i) q^{55} +(0.654435 + 0.395313i) q^{57} +(5.71278 - 8.88926i) q^{59} +(0.773829 - 2.63542i) q^{61} +(7.98046 + 0.697581i) q^{63} +(5.35390 + 4.63918i) q^{65} +(-4.57523 - 6.78728i) q^{67} +(-10.4349 + 9.56254i) q^{69} +(9.96884 - 1.43330i) q^{71} +(-9.73985 - 2.85988i) q^{73} +(0.406664 - 0.496563i) q^{75} +(2.07393 + 0.947131i) q^{77} +(4.58257 + 7.13062i) q^{79} +(2.80699 - 8.55107i) q^{81} +(2.86539 + 9.75864i) q^{83} +(-11.8080 + 1.69774i) q^{85} +(-1.57693 - 4.86579i) q^{87} +(1.51223 + 0.690613i) q^{89} +(-1.16170 + 8.07977i) q^{91} +(-0.0994770 + 0.377291i) q^{93} +(0.860576 + 0.553059i) q^{95} -10.4721i q^{97} +(1.56722 - 2.02607i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 200 q - 10 q^{9}+O(q^{10}) $ 200 * q - 10 * q^9	$ 200 q - 10 q^{9} + 2 q^{15} + 6 q^{19} - 10 q^{21} - 20 q^{25} - 44 q^{31} - 5 q^{33} + 78 q^{39} - 22 q^{43} - 22 q^{45} - 16 q^{49} + 36 q^{55} + 66 q^{57} + 176 q^{61} + 132 q^{63} + 46 q^{67} - 26 q^{73} - 165 q^{75} - 44 q^{79} + 42 q^{81} - 66 q^{87} - 20 q^{91} + 84 q^{93} - 55 q^{99}+O(q^{100}) $ 200 * q - 10 * q^9 + 2 * q^15 + 6 * q^19 - 10 * q^21 - 20 * q^25 - 44 * q^31 - 5 * q^33 + 78 * q^39 - 22 * q^43 - 22 * q^45 - 16 * q^49 + 36 * q^55 + 66 * q^57 + 176 * q^61 + 132 * q^63 + 46 * q^67 - 26 * q^73 - 165 * q^75 - 44 * q^79 + 42 * q^81 - 66 * q^87 - 20 * q^91 + 84 * q^93 - 55 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/804\mathbb{Z}\right)^\times$.

$n$	$269$	$337$	$403$
$\chi(n)$	$-1$	$e\left(\frac{5}{22}\right)$	$1$

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			0
$2$		0			0
$3$	1.64768	−	0.533989i	0.951290	−	0.308299i
$3$	1.64768	−	0.533989i	0.951290	−	0.308299i
$4$		0			0
$5$	2.22357	−	0.652900i	0.994413	−	0.291986i	0.256251	−	0.966610i	$-0.417512\pi$
$5$	2.22357	−	0.652900i	0.994413	−	0.291986i	0.738161	+	0.674624i	$0.235694\pi$
$6$		0			0
$7$	2.01808	+	1.74867i	0.762761	+	0.660936i	0.946742	−	0.321994i	$-0.104353\pi$
$7$	2.01808	+	1.74867i	0.762761	+	0.660936i	−0.183981	+	0.982930i	$0.558898\pi$
$8$		0			0
$9$	2.42971	−	1.75969i	0.809903	−	0.586563i
$10$		0			0
$11$	0.819238	−	0.240550i	0.247010	−	0.0725286i	−0.155884	−	0.987775i	$-0.549823\pi$
$11$	0.819238	−	0.240550i	0.247010	−	0.0725286i	0.402894	+	0.915247i	$0.368004\pi$
$12$		0			0
$13$	1.65269	+	2.57164i	0.458374	+	0.713244i	0.991111	−	0.133037i	$-0.0424729\pi$
$13$	1.65269	+	2.57164i	0.458374	+	0.713244i	−0.532737	+	0.846281i	$0.678837\pi$
$14$		0			0
$15$	3.31510	−	2.26314i	0.855955	−	0.584340i
$16$		0			0
$17$	−5.09528	−	0.732591i	−1.23579	−	0.177679i	−0.506714	−	0.862114i	$-0.669140\pi$
$17$	−5.09528	−	0.732591i	−1.23579	−	0.177679i	−0.729074	+	0.684435i	$0.760049\pi$
$18$		0			0
$19$	0.289069	+	0.333603i	0.0663170	+	0.0765339i	0.787939	−	0.615754i	$-0.211148\pi$
$19$	0.289069	+	0.333603i	0.0663170	+	0.0765339i	−0.721622	+	0.692288i	$0.756603\pi$
$20$		0			0
$21$	4.25892	+	1.80362i	0.929372	+	0.393583i
$22$		0			0
$23$	−7.43322	+	3.39464i	−1.54993	+	0.707830i	−0.992483	−	0.122381i	$-0.960947\pi$
$23$	−7.43322	+	3.39464i	−1.54993	+	0.707830i	−0.557449	+	0.830211i	$0.688220\pi$
$24$		0			0
$25$	0.311737	−	0.200341i	0.0623475	−	0.0400683i
$26$		0			0
$27$	3.06373	−	4.19685i	0.589616	−	0.807684i
$28$		0			0
$29$		−	2.95311i		−	0.548379i	−0.961676	−	0.274189i	$-0.911590\pi$
$29$		−	2.95311i		−	0.548379i	0.961676	−	0.274189i	$-0.0884095\pi$
$30$		0			0
$31$	−0.121792	+	0.189512i	−0.0218745	+	0.0340374i	−0.852019	−	0.523511i	$-0.824622\pi$
$31$	−0.121792	+	0.189512i	−0.0218745	+	0.0340374i	0.830144	+	0.557549i	$0.188258\pi$
$32$		0			0
$33$	1.22139	−	0.833814i	0.212617	−	0.145148i
$34$		0			0
$35$	5.62905	+	2.57070i	0.951483	+	0.434528i
$36$		0			0
$37$	1.16503			0.191530			0.0957649	−	0.995404i	$-0.469470\pi$
$37$	1.16503			0.191530			0.0957649	+	0.995404i	$0.469470\pi$
$38$		0			0
$39$	4.09634	+	3.35472i	0.655939	+	0.537185i
$40$		0			0
$41$	0.236280	−	1.64336i	0.0369007	−	0.256650i	−0.963018	−	0.269439i	$-0.913162\pi$
$41$	0.236280	−	1.64336i	0.0369007	−	0.256650i	0.999918	+	0.0127888i	$0.00407091\pi$
$42$		0			0
$43$	0.275166	+	0.0395630i	0.0419625	+	0.00603330i	0.163264	−	0.986582i	$-0.447798\pi$
$43$	0.275166	+	0.0395630i	0.0419625	+	0.00603330i	−0.121302	+	0.992616i	$0.538707\pi$
$44$		0			0
$45$	4.25374	−	5.49916i	0.634110	−	0.819766i
$46$		0			0
$47$	−9.50691	+	4.34166i	−1.38673	+	0.633296i	−0.962256	−	0.272146i	$-0.912267\pi$
$47$	−9.50691	+	4.34166i	−1.38673	+	0.633296i	−0.424469	+	0.905442i	$0.639539\pi$
$48$		0			0
$49$	0.0185697	+	0.129155i	0.00265282	+	0.0184508i
$50$		0			0
$51$	−8.78660	+	1.51375i	−1.23037	+	0.211967i
$52$		0			0
$53$	−0.673384	−	4.68349i	−0.0924965	−	0.643327i	−0.982346	−	0.187073i	$-0.940100\pi$
$53$	−0.673384	−	4.68349i	−0.0924965	−	0.643327i	0.889850	−	0.456254i	$-0.150809\pi$
$54$		0			0
$55$	1.66458	−	1.06976i	0.224452	−	0.144247i
$56$		0			0
$57$	0.654435	+	0.395313i	0.0866820	+	0.0523604i
$58$		0			0
$59$	5.71278	−	8.88926i	0.743741	−	1.15728i	−0.238770	−	0.971076i	$-0.576744\pi$
$59$	5.71278	−	8.88926i	0.743741	−	1.15728i	0.982511	−	0.186207i	$-0.0596195\pi$
$60$		0			0
$61$	0.773829	−	2.63542i	0.0990787	−	0.337431i	−0.895004	−	0.446058i	$-0.852827\pi$
$61$	0.773829	−	2.63542i	0.0990787	−	0.337431i	0.994083	+	0.108627i	$0.0346456\pi$
$62$		0			0
$63$	7.98046	+	0.697581i	1.00544	+	0.0878870i
$64$		0			0
$65$	5.35390	+	4.63918i	0.664070	+	0.575420i
$66$		0			0
$67$	−4.57523	−	6.78728i	−0.558954	−	0.829199i
$67$	−4.57523	−	6.78728i	−0.558954	−	0.829199i
$68$		0			0
$69$	−10.4349	+	9.56254i	−1.25621	+	1.15119i
$70$		0			0
$71$	9.96884	−	1.43330i	1.18308	−	0.170102i	0.477437	−	0.878666i	$-0.341566\pi$
$71$	9.96884	−	1.43330i	1.18308	−	0.170102i	0.705646	+	0.708564i	$0.250657\pi$
$72$		0			0
$73$	−9.73985	−	2.85988i	−1.13996	−	0.334723i	−0.343347	−	0.939209i	$-0.611561\pi$
$73$	−9.73985	−	2.85988i	−1.13996	−	0.334723i	−0.796616	+	0.604485i	$0.793379\pi$
$74$		0			0
$75$	0.406664	−	0.496563i	0.0469575	−	0.0573382i
$76$		0			0
$77$	2.07393	+	0.947131i	0.236346	+	0.107936i
$78$		0			0
$79$	4.58257	+	7.13062i	0.515580	+	0.802258i	0.997251	−	0.0740942i	$-0.0236065\pi$
$79$	4.58257	+	7.13062i	0.515580	+	0.802258i	−0.481672	+	0.876352i	$0.659970\pi$
$80$		0			0
$81$	2.80699	−	8.55107i	0.311887	−	0.950119i
$82$		0			0
$83$	2.86539	+	9.75864i	0.314518	+	1.07115i	0.953366	+	0.301817i	$0.0975931\pi$
$83$	2.86539	+	9.75864i	0.314518	+	1.07115i	−0.638848	+	0.769333i	$0.720589\pi$
$84$		0			0
$85$	−11.8080	+	1.69774i	−1.28076	+	0.184146i
$86$		0			0
$87$	−1.57693	−	4.86579i	−0.169065	−	0.521667i
$88$		0			0
$89$	1.51223	+	0.690613i	0.160296	+	0.0732049i	0.493947	−	0.869492i	$-0.335553\pi$
$89$	1.51223	+	0.690613i	0.160296	+	0.0732049i	−0.333651	+	0.942697i	$0.608281\pi$
$90$		0			0
$91$	−1.16170	+	8.07977i	−0.121779	+	0.846990i
$92$		0			0
$93$	−0.0994770	+	0.377291i	−0.0103153	+	0.0391233i
$94$		0			0
$95$	0.860576	+	0.553059i	0.0882933	+	0.0567426i
$96$		0			0
$97$		−	10.4721i		−	1.06328i	−0.846971	−	0.531640i	$-0.821576\pi$
$97$		−	10.4721i		−	1.06328i	0.846971	−	0.531640i	$-0.178424\pi$
$98$		0			0
$99$	1.56722	−	2.02607i	0.157511	−	0.203628i
$100$		0			0
$101$	1.06665	+	1.23098i	0.106136	+	0.122487i	0.806332	−	0.591463i	$-0.201450\pi$
$101$	1.06665	+	1.23098i	0.106136	+	0.122487i	−0.700196	+	0.713951i	$0.746904\pi$
$102$		0			0
$103$	4.52340	+	2.90702i	0.445704	+	0.286437i	0.744178	−	0.667981i	$-0.232841\pi$
$103$	4.52340	+	2.90702i	0.445704	+	0.286437i	−0.298474	+	0.954418i	$0.596478\pi$
$104$		0			0
$105$	10.6476	+	1.22984i	1.03910	+	0.120020i
$106$		0			0
$107$	1.96542	−	6.69362i	0.190005	−	0.647097i	−0.808293	−	0.588780i	$-0.799608\pi$
$107$	1.96542	−	6.69362i	0.190005	−	0.647097i	0.998298	−	0.0583167i	$-0.0185733\pi$
$108$		0			0
$109$	−0.811372	−	1.26252i	−0.0777153	−	0.120927i	0.800220	−	0.599706i	$-0.204716\pi$
$109$	−0.811372	−	1.26252i	−0.0777153	−	0.120927i	−0.877936	+	0.478779i	$0.841080\pi$
$110$		0			0
$111$	1.91960	−	0.622114i	0.182200	−	0.0590484i
$112$		0			0
$113$	−11.7027	−	3.43621i	−1.10089	−	0.323251i	−0.319686	−	0.947524i	$-0.603577\pi$
$113$	−11.7027	−	3.43621i	−1.10089	−	0.323251i	−0.781207	+	0.624272i	$0.785396\pi$
$114$		0			0
$115$	−14.3119	+	12.4014i	−1.33460	+	1.15643i
$116$		0			0
$117$	8.54084	+	3.34011i	0.789601	+	0.308793i
$118$		0			0
$119$	−9.00160	−	10.3884i	−0.825175	−	0.952303i
$120$		0			0
$121$	−8.64050	+	5.55291i	−0.785500	+	0.504810i
$122$		0			0
$123$	−0.488224	−	2.83391i	−0.0440217	−	0.255525i
$124$		0			0
$125$	−7.02566	+	8.10804i	−0.628394	+	0.725205i
$126$		0			0
$127$	−2.32037	+	2.67785i	−0.205900	+	0.237621i	−0.849302	−	0.527907i	$-0.822977\pi$
$127$	−2.32037	+	2.67785i	−0.205900	+	0.237621i	0.643402	+	0.765528i	$0.277522\pi$
$128$		0			0
$129$	0.474513	−	0.0817488i	0.0417785	−	0.00719758i
$130$		0			0
$131$	8.34179	−	3.80957i	0.728826	−	0.332844i	−0.0162095	−	0.999869i	$-0.505160\pi$
$131$	8.34179	−	3.80957i	0.728826	−	0.332844i	0.745035	+	0.667025i	$0.232433\pi$
$132$		0			0
$133$			1.17872i			0.102208i
$134$		0			0
$135$	4.07232	−	11.3323i	0.350489	−	0.975331i
$136$		0			0
$137$	7.44112	+	16.2938i	0.635738	+	1.39207i	0.903500	+	0.428587i	$0.140989\pi$
$137$	7.44112	+	16.2938i	0.635738	+	1.39207i	−0.267762	+	0.963485i	$0.586284\pi$
$138$		0			0
$139$	6.55050	+	22.3090i	0.555606	+	1.89222i	0.437493	+	0.899222i	$0.355866\pi$
$139$	6.55050	+	22.3090i	0.555606	+	1.89222i	0.118113	+	0.993000i	$0.462315\pi$
$140$		0			0
$141$	−13.3460	+	12.2303i	−1.12393	+	1.02997i
$142$		0			0
$143$	1.97255	+	1.70923i	0.164953	+	0.142933i
$144$		0			0
$145$	−1.92809	−	6.56646i	−0.160119	−	0.545315i
$146$		0			0
$147$	0.0995647	+	0.202891i	0.00821196	+	0.0167342i
$148$		0			0
$149$	12.0237	−	10.4186i	0.985021	−	0.853526i	−0.00419440	−	0.999991i	$-0.501335\pi$
$149$	12.0237	−	10.4186i	0.985021	−	0.853526i	0.989216	+	0.146465i	$0.0467897\pi$
$150$		0			0
$151$	−0.672096	+	4.67453i	−0.0546944	+	0.380408i	0.944028	+	0.329867i	$0.107004\pi$
$151$	−0.672096	+	4.67453i	−0.0546944	+	0.380408i	−0.998722	+	0.0505414i	$0.983905\pi$
$152$		0			0
$153$	−13.6692	+	7.18613i	−1.10509	+	0.580964i
$154$		0			0
$155$	−0.147081	+	0.500912i	−0.0118138	+	0.0402342i
$156$		0			0
$157$	−1.57775	−	3.45479i	−0.125918	−	0.275722i	0.836165	−	0.548477i	$-0.184792\pi$
$157$	−1.57775	−	3.45479i	−0.125918	−	0.275722i	−0.962083	+	0.272755i	$0.912065\pi$
$158$		0			0
$159$	−3.61046	−	7.35732i	−0.286328	−	0.583474i
$160$		0			0
$161$	−20.9369	−	6.14763i	−1.65006	−	0.484501i
$162$		0			0
$163$	−15.9465			−1.24903			−0.624513	−	0.781014i	$-0.714703\pi$
$163$	−15.9465			−1.24903			−0.624513	+	0.781014i	$0.714703\pi$
$164$		0			0
$165$	2.17146	−	2.65150i	0.169048	−	0.206419i
$166$		0			0
$167$	5.28474	−	4.57925i	0.408945	−	0.354353i	−0.425964	−	0.904740i	$-0.640065\pi$
$167$	5.28474	−	4.57925i	0.408945	−	0.354353i	0.834910	+	0.550387i	$0.185520\pi$
$168$		0			0
$169$	1.51847	−	3.32498i	0.116805	−	0.255767i
$170$		0			0
$171$	1.28939	+	0.301888i	0.0986023	+	0.0230860i
$172$		0			0
$173$	6.87305	−	10.6947i	0.522549	−	0.813102i	−0.475220	−	0.879867i	$-0.657632\pi$
$173$	6.87305	−	10.6947i	0.522549	−	0.813102i	0.997769	+	0.0667654i	$0.0212679\pi$
$174$		0			0
$175$	0.979441	+	0.140822i	0.0740388	+	0.0106452i
$176$		0			0
$177$	4.66607	−	17.6972i	0.350724	−	1.33021i
$178$		0			0
$179$	−9.73917	+	21.3258i	−0.727940	+	1.59397i	0.0744916	+	0.997222i	$0.476267\pi$
$179$	−9.73917	+	21.3258i	−0.727940	+	1.59397i	−0.802431	+	0.596744i	$0.796461\pi$
$180$		0			0
$181$	−7.21188	−	15.7918i	−0.536055	−	1.17380i	−0.962996	−	0.269517i	$-0.913136\pi$
$181$	−7.21188	−	15.7918i	−0.536055	−	1.17380i	0.426940	−	0.904280i	$-0.359591\pi$
$182$		0			0
$183$	−0.132262	−	4.75555i	−0.00977712	−	0.351540i
$184$		0			0
$185$	2.59053	−	0.760648i	0.190460	−	0.0559240i
$186$		0			0
$187$	−4.35047	+	0.625504i	−0.318138	+	0.0457414i
$188$		0			0
$189$	13.5218	−	3.11209i	0.983563	−	0.226371i
$190$		0			0
$191$	−6.82175	+	14.9376i	−0.493605	+	1.08084i	0.484891	+	0.874575i	$0.338859\pi$
$191$	−6.82175	+	14.9376i	−0.493605	+	1.08084i	−0.978495	+	0.206269i	$0.933868\pi$
$192$		0			0
$193$	−15.3945	−	9.89347i	−1.10812	−	0.712148i	−0.147240	−	0.989101i	$-0.547039\pi$
$193$	−15.3945	−	9.89347i	−1.10812	−	0.712148i	−0.960883	+	0.276953i	$0.910675\pi$
$194$		0			0
$195$	11.2988	+	4.78497i	0.809124	+	0.342659i
$196$		0			0
$197$	−0.451957	−	3.14343i	−0.0322006	−	0.223960i	0.967366	−	0.253381i	$-0.0815427\pi$
$197$	−0.451957	−	3.14343i	−0.0322006	−	0.223960i	−0.999567	+	0.0294210i	$0.990634\pi$
$198$		0			0
$199$	−3.07432	+	3.54796i	−0.217933	+	0.251508i	−0.854180	−	0.519977i	$-0.825940\pi$
$199$	−3.07432	+	3.54796i	−0.217933	+	0.251508i	0.636247	+	0.771485i	$0.280486\pi$
$200$		0			0
$201$	−11.1629	−	8.74016i	−0.787368	−	0.616483i
$202$		0			0
$203$	5.16402	−	5.95960i	0.362443	−	0.418282i
$204$		0			0
$205$	−0.547566	−	3.80840i	−0.0382437	−	0.265991i
$206$		0			0
$207$	−12.0871	+	21.3281i	−0.840108	+	1.48241i
$208$		0			0
$209$	0.317065	+	0.203765i	0.0219318	+	0.0140947i
$210$		0			0
$211$	−8.80239	+	19.2745i	−0.605981	+	1.32691i	0.319307	+	0.947651i	$0.396550\pi$
$211$	−8.80239	+	19.2745i	−0.605981	+	1.32691i	−0.925289	+	0.379263i	$0.876178\pi$
$212$		0			0
$213$	15.6601	−	7.68488i	1.07301	−	0.526559i
$214$		0			0
$215$	0.637684	−	0.0916851i	0.0434897	−	0.00625287i
$216$		0			0
$217$	−0.577180	+	0.169475i	−0.0391815	+	0.0115047i
$218$		0			0
$219$	−17.5753	+	0.488809i	−1.18763	+	0.0330306i
$220$		0			0
$221$	−6.53697	−	14.3140i	−0.439724	−	0.962861i
$222$		0			0
$223$	0.563061	−	1.23293i	0.0377053	−	0.0825632i	−0.889842	−	0.456269i	$-0.849186\pi$
$223$	0.563061	−	1.23293i	0.0377053	−	0.0825632i	0.927547	+	0.373705i	$0.121913\pi$
$224$		0			0
$225$	0.404893	−	1.03533i	0.0269929	−	0.0690222i
$226$		0			0
$227$	−4.27145	−	0.614142i	−0.283506	−	0.0407621i	−0.000905286	−	1.00000i	$-0.500288\pi$
$227$	−4.27145	−	0.614142i	−0.283506	−	0.0407621i	−0.282601	+	0.959238i	$0.591197\pi$
$228$		0			0
$229$	−2.29606	+	3.57274i	−0.151728	+	0.236093i	−0.908794	−	0.417245i	$-0.862996\pi$
$229$	−2.29606	+	3.57274i	−0.151728	+	0.236093i	0.757066	+	0.653338i	$0.226632\pi$
$230$		0			0
$231$	3.92293	+	0.453115i	0.258110	+	0.0298128i
$232$		0			0
$233$	−9.12364	+	19.9780i	−0.597710	+	1.30880i	0.332960	+	0.942941i	$0.391953\pi$
$233$	−9.12364	+	19.9780i	−0.597710	+	1.30880i	−0.930670	+	0.365860i	$0.880775\pi$
$234$		0			0
$235$	−18.3047	+	15.8611i	−1.19406	+	1.03466i
$236$		0			0
$237$	11.3583	+	9.30195i	0.737801	+	0.604227i
$238$		0			0
$239$	22.7021			1.46848			0.734239	−	0.678891i	$-0.237539\pi$
$239$	22.7021			1.46848			0.734239	+	0.678891i	$0.237539\pi$
$240$		0			0
$241$	−15.9742	−	4.69045i	−1.02899	−	0.302139i	−0.276690	−	0.960959i	$-0.589237\pi$
$241$	−15.9742	−	4.69045i	−1.02899	−	0.302139i	−0.752300	+	0.658821i	$0.771056\pi$
$242$		0			0
$243$	0.0588374	−	15.5883i	0.00377442	−	0.999993i
$244$		0			0
$245$	0.125617	+	0.275063i	0.00802537	+	0.0175731i
$246$		0			0
$247$	−0.380165	+	1.29472i	−0.0241893	+	0.0823813i
$248$		0			0
$249$	9.93227	+	14.5490i	0.629432	+	0.922008i
$250$		0			0
$251$	−1.96791	+	13.6871i	−0.124214	+	0.863924i	0.828486	+	0.560010i	$0.189203\pi$
$251$	−1.96791	+	13.6871i	−0.124214	+	0.863924i	−0.952699	+	0.303914i	$0.901706\pi$
$252$		0			0
$253$	−5.27299	+	4.56908i	−0.331510	+	0.287255i
$254$		0			0
$255$	−18.5493	+	9.10271i	−1.16160	+	0.570034i
$256$		0			0
$257$	−1.64284	−	5.59501i	−0.102478	−	0.349007i	0.892252	−	0.451537i	$-0.149124\pi$
$257$	−1.64284	−	5.59501i	−0.102478	−	0.349007i	−0.994730	+	0.102530i	$0.967306\pi$
$258$		0			0
$259$	2.35112	+	2.03726i	0.146091	+	0.126589i
$260$		0			0
$261$	−5.19656	−	7.17520i	−0.321659	−	0.444134i
$262$		0			0
$263$	−5.40171	−	18.3965i	−0.333084	−	1.13438i	−0.940443	−	0.339951i	$-0.889589\pi$
$263$	−5.40171	−	18.3965i	−0.333084	−	1.13438i	0.607359	−	0.794427i	$-0.292229\pi$
$264$		0			0
$265$	−4.55517	−	9.97444i	−0.279822	−	0.612725i
$266$		0			0
$267$	2.86046	+	0.330395i	0.175057	+	0.0202198i
$268$		0			0
$269$			17.8647i			1.08923i	0.838687	+	0.544614i	$0.183324\pi$
$269$			17.8647i			1.08923i	−0.838687	+	0.544614i	$0.816676\pi$
$270$		0			0
$271$	3.89142	−	1.77715i	0.236387	−	0.107954i	−0.293700	−	0.955898i	$-0.594887\pi$
$271$	3.89142	−	1.77715i	0.236387	−	0.107954i	0.530087	+	0.847943i	$0.322159\pi$
$272$		0			0
$273$	2.40041	+	13.9332i	0.145279	+	0.843277i
$274$		0			0
$275$	0.207195	−	0.239116i	0.0124943	−	0.0144192i
$276$		0			0
$277$	16.5491	−	19.0987i	0.994342	−	1.14753i	0.00528681	−	0.999986i	$-0.498317\pi$
$277$	16.5491	−	19.0987i	0.994342	−	1.14753i	0.989055	−	0.147546i	$-0.0471374\pi$
$278$		0			0
$279$	0.0375631	+	0.674775i	0.00224884	+	0.0403977i
$280$		0			0
$281$	6.23786	−	4.00883i	0.372120	−	0.239147i	−0.341192	−	0.939994i	$-0.610831\pi$
$281$	6.23786	−	4.00883i	0.372120	−	0.239147i	0.713312	+	0.700847i	$0.247194\pi$
$282$		0			0
$283$	13.1467	+	15.1721i	0.781489	+	0.901886i	0.997216	−	0.0745676i	$-0.0237576\pi$
$283$	13.1467	+	15.1721i	0.781489	+	0.901886i	−0.215727	+	0.976454i	$0.569212\pi$
$284$		0			0
$285$	1.71328	+	0.451726i	0.101486	+	0.0267580i
$286$		0			0
$287$	3.35053	−	2.90325i	0.197776	−	0.171374i
$288$		0			0
$289$	9.11383	+	2.67606i	0.536108	+	0.157415i
$290$		0			0
$291$	−5.59199	−	17.2547i	−0.327808	−	1.01149i
$292$		0			0
$293$	7.63596	+	11.8818i	0.446098	+	0.694141i	0.989371	−	0.145415i	$-0.0464516\pi$
$293$	7.63596	+	11.8818i	0.446098	+	0.694141i	−0.543273	+	0.839556i	$0.682815\pi$
$294$		0			0
$295$	6.89899	−	23.4958i	0.401675	−	1.36798i
$296$		0			0
$297$	1.50038	−	4.17520i	0.0870606	−	0.242270i
$298$		0			0
$299$	−21.0146	−	13.5052i	−1.21530	−	0.781029i
$300$		0			0
$301$	0.486124	+	0.561017i	0.0280197	+	0.0323365i
$302$		0			0
$303$	2.41484	+	1.45869i	0.138729	+	0.0837994i
$304$		0			0
$305$		−	6.36529i		−	0.364475i
$306$		0			0
$307$	10.6764	+	6.86130i	0.609333	+	0.391595i	0.808607	−	0.588349i	$-0.200222\pi$
$307$	10.6764	+	6.86130i	0.609333	+	0.391595i	−0.199274	+	0.979944i	$0.563858\pi$
$308$		0			0
$309$	9.00545	+	2.37439i	0.512302	+	0.135074i
$310$		0			0
$311$	−3.43808	+	23.9124i	−0.194956	+	1.35595i	0.623700	+	0.781664i	$0.285629\pi$
$311$	−3.43808	+	23.9124i	−0.194956	+	1.35595i	−0.818656	+	0.574284i	$0.805281\pi$
$312$		0			0
$313$	−10.0420	−	4.58604i	−0.567609	−	0.259218i	0.110874	−	0.993834i	$-0.464635\pi$
$313$	−10.0420	−	4.58604i	−0.567609	−	0.259218i	−0.678483	+	0.734616i	$0.737362\pi$
$314$		0			0
$315$	18.2006	−	3.65932i	1.02549	−	0.206179i
$316$		0			0
$317$	15.0821	−	2.16848i	0.847095	−	0.121794i	0.294920	−	0.955522i	$-0.404707\pi$
$317$	15.0821	−	2.16848i	0.847095	−	0.121794i	0.552175	+	0.833728i	$0.313798\pi$
$318$		0			0
$319$	−0.710371	−	2.41930i	−0.0397731	−	0.135455i
$320$		0			0
$321$	−0.335929	−	12.0785i	−0.0187497	−	0.674154i
$322$		0			0
$323$	−1.22849	−	1.91157i	−0.0683552	−	0.106363i
$324$		0			0
$325$	1.03041	+	0.470573i	0.0571569	+	0.0261027i
$326$		0			0
$327$	−2.01105	−	1.64697i	−0.111212	−	0.0910774i
$328$		0			0
$329$	−26.7778	−	7.86267i	−1.47631	−	0.433483i
$330$		0			0
$331$	20.5531	−	2.95508i	1.12970	−	0.162426i	0.447982	−	0.894043i	$-0.352143\pi$
$331$	20.5531	−	2.95508i	1.12970	−	0.162426i	0.681716	+	0.731617i	$0.261234\pi$
$332$		0			0
$333$	2.83069	−	2.05009i	0.155121	−	0.112344i
$334$		0			0
$335$	−14.6048	−	12.1049i	−0.797945	−	0.661359i
$336$		0			0
$337$	10.1591	+	8.80291i	0.553401	+	0.479525i	0.886091	−	0.463511i	$-0.153411\pi$
$337$	10.1591	+	8.80291i	0.553401	+	0.479525i	−0.332690	+	0.943036i	$0.607956\pi$
$338$		0			0
$339$	−21.1171	+	0.587315i	−1.14693	+	0.0318986i
$340$		0			0
$341$	−0.0541895	+	0.184553i	−0.00293453	+	0.00999408i
$342$		0			0
$343$	9.91732	−	15.4317i	0.535485	−	0.833231i
$344$		0			0
$345$	−16.9593	+	28.0759i	−0.913060	+	1.51156i
$346$		0			0
$347$	−6.56322	+	4.21793i	−0.352332	+	0.226430i	−0.704820	−	0.709386i	$-0.748972\pi$
$347$	−6.56322	+	4.21793i	−0.352332	+	0.226430i	0.352488	+	0.935816i	$0.385336\pi$
$348$		0			0
$349$	−4.40747	−	30.6546i	−0.235926	−	1.64090i	−0.671682	−	0.740840i	$-0.734428\pi$
$349$	−4.40747	−	30.6546i	−0.235926	−	1.64090i	0.435755	−	0.900065i	$-0.356481\pi$
$350$		0			0
$351$	15.8562	+	0.942720i	0.846340	+	0.0503187i
$352$		0			0
$353$	1.80519	+	12.5554i	0.0960806	+	0.668255i	0.979762	+	0.200166i	$0.0641482\pi$
$353$	1.80519	+	12.5554i	0.0960806	+	0.668255i	−0.883681	+	0.468089i	$0.844943\pi$
$354$		0			0
$355$	21.2307	−	9.69571i	1.12681	−	0.514595i
$356$		0			0
$357$	−20.3791	−	12.3100i	−1.07857	−	0.651515i
$358$		0			0
$359$	−2.24774	−	0.323176i	−0.118631	−	0.0170566i	0.0827435	−	0.996571i	$-0.473632\pi$
$359$	−2.24774	−	0.323176i	−0.118631	−	0.0170566i	−0.201375	+	0.979514i	$0.564541\pi$
$360$		0			0
$361$	2.67625	−	18.6137i	0.140855	−	0.979670i
$362$		0			0
$363$	−11.2716	+	13.7634i	−0.591606	+	0.722390i
$364$		0			0
$365$	−23.5245			−1.23133
$366$		0			0
$367$	19.6118	+	8.95640i	1.02373	+	0.467520i	0.855267	−	0.518188i	$-0.173393\pi$
$367$	19.6118	+	8.95640i	1.02373	+	0.467520i	0.168460	+	0.985708i	$0.446121\pi$
$368$		0			0
$369$	−2.31772	−	4.40867i	−0.120655	−	0.229506i
$370$		0			0
$371$	6.83095	−	10.6292i	0.354645	−	0.551839i
$372$		0			0
$373$			35.5582i			1.84113i	0.390587	+	0.920566i	$0.372272\pi$
$373$			35.5582i			1.84113i	−0.390587	+	0.920566i	$0.627728\pi$
$374$		0			0
$375$	−7.24644	+	17.1111i	−0.374205	+	0.883613i
$376$		0			0
$377$	7.59433	−	4.88058i	0.391128	−	0.251363i
$378$		0			0
$379$	6.58430	−	3.00695i	0.338213	−	0.154457i	−0.239067	−	0.971003i	$-0.576842\pi$
$379$	6.58430	−	3.00695i	0.338213	−	0.154457i	0.577280	+	0.816546i	$0.304114\pi$
$380$		0			0
$381$	−2.39329	+	5.65130i	−0.122612	+	0.289525i
$382$		0			0
$383$	−10.0397	−	11.5864i	−0.513003	−	0.592037i	0.438862	−	0.898554i	$-0.355382\pi$
$383$	−10.0397	−	11.5864i	−0.513003	−	0.592037i	−0.951865	+	0.306517i	$0.900836\pi$
$384$		0			0
$385$	5.22992	+	0.751948i	0.266541	+	0.0383228i
$386$		0			0
$387$	0.738193	−	0.388081i	0.0375245	−	0.0197273i
$388$		0			0
$389$	0.293311	+	0.456400i	0.0148714	+	0.0231404i	0.848610	−	0.529019i	$-0.177440\pi$
$389$	0.293311	+	0.456400i	0.0148714	+	0.0231404i	−0.833738	+	0.552160i	$0.813804\pi$
$390$		0			0
$391$	40.3612	−	11.8511i	2.04115	−	0.599337i
$392$		0			0
$393$	11.7104	−	10.7314i	0.590709	−	0.541327i
$394$		0			0
$395$	14.8453	+	12.8635i	0.746947	+	0.647233i
$396$		0			0
$397$	30.3256	−	8.90441i	1.52200	−	0.446900i	0.589410	−	0.807834i	$-0.299360\pi$
$397$	30.3256	−	8.90441i	1.52200	−	0.446900i	0.932591	+	0.360935i	$0.117542\pi$
$398$		0			0
$399$	0.629426	+	1.94216i	0.0315107	+	0.0972297i
$400$		0			0
$401$	36.7151			1.83346			0.916732	−	0.399504i	$-0.130818\pi$
$401$	36.7151			1.83346			0.916732	+	0.399504i	$0.130818\pi$
$402$		0			0
$403$	−0.688641			−0.0343036
$404$		0			0
$405$	0.658545	−	20.8466i	0.0327233	−	1.03588i
$406$		0			0
$407$	0.954437	−	0.280248i	0.0473097	−	0.0138914i
$408$		0			0
$409$	0.203823	+	0.176614i	0.0100784	+	0.00873298i	0.659885	−	0.751366i	$-0.270605\pi$
$409$	0.203823	+	0.176614i	0.0100784	+	0.00873298i	−0.649807	+	0.760099i	$0.725150\pi$
$410$		0			0
$411$	20.9613	+	22.8735i	1.03395	+	1.12827i
$412$		0			0
$413$	27.0732	−	7.94942i	1.33219	−	0.391165i
$414$		0			0
$415$	12.7428	+	19.8282i	0.625521	+	0.973330i
$416$		0			0
$417$	22.7059	+	33.2602i	1.11191	+	1.62876i
$418$		0			0
$419$	20.6344	+	2.96678i	1.00806	+	0.144937i	0.626511	−	0.779413i	$-0.284483\pi$
$419$	20.6344	+	2.96678i	1.00806	+	0.144937i	0.381547	+	0.924350i	$0.375392\pi$
$420$		0			0
$421$	−7.46031	−	8.60966i	−0.363593	−	0.419609i	0.544247	−	0.838925i	$-0.316815\pi$
$421$	−7.46031	−	8.60966i	−0.363593	−	0.419609i	−0.907840	+	0.419316i	$0.862270\pi$
$422$		0			0
$423$	−15.4591	+	27.2782i	−0.751645	+	1.32631i
$424$		0			0
$425$	−1.73516	+	0.792420i	−0.0841675	+	0.0384380i
$426$		0			0
$427$	6.17013	−	3.96530i	0.298594	−	0.191894i
$428$		0			0
$429$	4.16285	+	1.76294i	0.200984	+	0.0851156i
$430$		0			0
$431$		−	33.4433i		−	1.61091i	−0.592657	−	0.805455i	$-0.701921\pi$
$431$		−	33.4433i		−	1.61091i	0.592657	−	0.805455i	$-0.298079\pi$
$432$		0			0
$433$	−15.3658	+	23.9097i	−0.738434	+	1.14903i	0.245310	+	0.969445i	$0.421110\pi$
$433$	−15.3658	+	23.9097i	−0.738434	+	1.14903i	−0.983743	+	0.179580i	$0.942526\pi$
$434$		0			0
$435$	−6.68329	−	9.78986i	−0.320439	−	0.469388i
$436$		0			0
$437$	−3.28117	−	1.49846i	−0.156960	−	0.0716812i
$438$		0			0
$439$	33.0398			1.57690			0.788451	−	0.615097i	$-0.210883\pi$
$439$	33.0398			1.57690			0.788451	+	0.615097i	$0.210883\pi$
$440$		0			0
$441$	0.272393	+	0.281133i	0.0129711	+	0.0133873i
$442$		0			0
$443$	2.63553	−	18.3305i	0.125218	−	0.870908i	−0.826282	−	0.563257i	$-0.809548\pi$
$443$	2.63553	−	18.3305i	0.125218	−	0.870908i	0.951499	−	0.307651i	$-0.0995429\pi$
$444$		0			0
$445$	3.81346	+	0.548293i	0.180775	+	0.0259916i
$446$		0			0
$447$	14.2478	−	23.5871i	0.673899	−	1.11563i
$448$		0			0
$449$	0.0867474	−	0.0396162i	0.00409386	−	0.00186960i	−0.413367	−	0.910564i	$-0.635647\pi$
$449$	0.0867474	−	0.0396162i	0.00409386	−	0.00186960i	0.417461	+	0.908695i	$0.362920\pi$
$450$		0			0
$451$	−0.201741	−	1.40314i	−0.00949963	−	0.0660714i
$452$		0			0
$453$	1.38875	+	8.06103i	0.0652492	+	0.378740i
$454$		0			0
$455$	2.69217	+	18.7244i	0.126211	+	0.877816i
$456$		0			0
$457$	21.0770	−	13.5453i	0.985939	−	0.633625i	0.0548801	−	0.998493i	$-0.482522\pi$
$457$	21.0770	−	13.5453i	0.985939	−	0.633625i	0.931059	+	0.364868i	$0.118886\pi$
$458$		0			0
$459$	−18.6852	+	19.1397i	−0.872149	+	0.893363i
$460$		0			0
$461$	−8.20038	+	12.7600i	−0.381930	+	0.594295i	−0.977992	−	0.208644i	$-0.933095\pi$
$461$	−8.20038	+	12.7600i	−0.381930	+	0.594295i	0.596062	+	0.802939i	$0.296731\pi$
$462$		0			0
$463$	−4.69457	+	15.9882i	−0.218175	+	0.743037i	0.775560	+	0.631274i	$0.217468\pi$
$463$	−4.69457	+	15.9882i	−0.218175	+	0.743037i	−0.993735	+	0.111762i	$0.964350\pi$
$464$		0			0
$465$	0.0251390	+	0.903884i	0.00116579	+	0.0419166i
$466$		0			0
$467$	−21.7502	−	18.8467i	−1.00648	−	0.872119i	−0.0146757	−	0.999892i	$-0.504672\pi$
$467$	−21.7502	−	18.8467i	−1.00648	−	0.872119i	−0.991803	+	0.127773i	$0.959217\pi$
$468$		0			0
$469$	2.63557	−	21.6978i	0.121699	−	1.00191i
$470$		0			0
$471$	−4.44445	−	4.84989i	−0.204789	−	0.223471i
$472$		0			0
$473$	0.234944	−	0.0337798i	0.0108027	−	0.00155320i
$474$		0			0
$475$	0.156948	+	0.0460842i	0.00720128	+	0.00211449i
$476$		0			0
$477$	−9.87762	−	10.1946i	−0.452265	−	0.466778i
$478$		0			0
$479$	13.2034	+	6.02980i	0.603279	+	0.275509i	0.693550	−	0.720409i	$-0.256046\pi$
$479$	13.2034	+	6.02980i	0.603279	+	0.275509i	−0.0902702	+	0.995917i	$0.528773\pi$
$480$		0			0
$481$	1.92543	+	2.99603i	0.0877922	+	0.136607i
$482$		0			0
$483$	−37.7801	+	1.05075i	−1.71905	+	0.0478107i
$484$		0			0
$485$	−6.83723	−	23.2855i	−0.310463	−	1.05734i
$486$		0			0
$487$	22.7140	−	3.26578i	1.02927	−	0.147986i	0.393067	−	0.919510i	$-0.371414\pi$
$487$	22.7140	−	3.26578i	1.02927	−	0.147986i	0.636201	+	0.771523i	$0.280505\pi$
$488$		0			0
$489$	−26.2748	+	8.51526i	−1.18819	+	0.385073i
$490$		0			0
$491$	−13.3009	−	6.07431i	−0.600261	−	0.274130i	0.0920211	−	0.995757i	$-0.470667\pi$
$491$	−13.3009	−	6.07431i	−0.600261	−	0.274130i	−0.692282	+	0.721627i	$0.743395\pi$
$492$		0			0
$493$	−2.16342	+	15.0469i	−0.0974356	+	0.677680i
$494$		0			0
$495$	2.16200	−	5.52836i	0.0971748	−	0.248481i
$496$		0			0
$497$	22.6242	+	14.5397i	1.01484	+	0.652196i
$498$		0			0
$499$			9.86407i			0.441576i	0.975322	+	0.220788i	$0.0708629\pi$
$499$			9.86407i			0.441576i	−0.975322	+	0.220788i	$0.929137\pi$
$500$		0			0
$501$	6.26230	−	10.3671i	0.279779	−	0.463170i
$502$		0			0
$503$	25.6829	+	29.6397i	1.14515	+	1.32157i	0.939345	+	0.342974i	$0.111434\pi$
$503$	25.6829	+	29.6397i	1.14515	+	1.32157i	0.205801	+	0.978594i	$0.434020\pi$
$504$		0			0
$505$	3.17549	+	2.04077i	0.141308	+	0.0908129i
$506$		0			0
$507$	0.726446	−	6.28935i	0.0322626	−	0.279320i
$508$		0			0
$509$	−4.71240	+	16.0490i	−0.208873	+	0.711358i	0.786697	+	0.617339i	$0.211789\pi$
$509$	−4.71240	+	16.0490i	−0.208873	+	0.711358i	−0.995570	+	0.0940184i	$0.970029\pi$
$510$		0			0
$511$	−14.6548	−	22.8033i	−0.648289	−	1.00876i
$512$		0			0
$513$	2.28571	−	0.191107i	0.100917	−	0.00843756i
$514$		0			0
$515$	11.9561	+	3.51063i	0.526849	+	0.154697i
$516$		0			0
$517$	−6.74404	+	5.84374i	−0.296602	+	0.257007i
$518$		0			0
$519$	5.61376	−	21.2916i	0.246417	−	0.934596i
$520$		0			0
$521$	12.8160	+	14.7905i	0.561481	+	0.647983i	0.963519	−	0.267639i	$-0.0862436\pi$
$521$	12.8160	+	14.7905i	0.561481	+	0.647983i	−0.402038	+	0.915623i	$0.631698\pi$
$522$		0			0
$523$	−25.6769	+	16.5016i	−1.12277	+	0.721563i	−0.964040	−	0.265759i	$-0.914378\pi$
$523$	−25.6769	+	16.5016i	−1.12277	+	0.721563i	−0.158734	+	0.987321i	$0.550741\pi$
$524$		0			0
$525$	1.68900	−	0.290981i	0.0737142	−	0.0126994i
$526$		0			0
$527$	0.759399	−	0.876394i	0.0330800	−	0.0381763i
$528$		0			0
$529$	28.6673	−	33.0839i	1.24641	−	1.43843i
$530$		0			0
$531$	−1.76193	−	31.6510i	−0.0764614	−	1.37354i
$532$		0			0
$533$	4.61663	−	2.10834i	0.199968	−	0.0913225i
$534$		0			0
$535$		−	16.1670i		−	0.698960i
$536$		0			0
$537$	−4.65930	+	40.3388i	−0.201063	+	1.74075i
$538$		0			0
$539$	0.0462814	+	0.101342i	0.00199348	+	0.00436511i
$540$		0			0
$541$	12.3523	+	42.0681i	0.531067	+	1.80865i	0.586198	+	0.810168i	$0.300624\pi$
$541$	12.3523	+	42.0681i	0.531067	+	1.80865i	−0.0551315	+	0.998479i	$0.517558\pi$
$542$		0			0
$543$	−20.3156	−	22.1688i	−0.871824	−	0.951355i
$544$		0			0
$545$	−2.62845	−	2.27756i	−0.112590	−	0.0975600i
$546$		0			0
$547$	−12.2118	−	41.5897i	−0.522141	−	1.77825i	−0.621743	−	0.783221i	$-0.713575\pi$
$547$	−12.2118	−	41.5897i	−0.522141	−	1.77825i	0.0996027	−	0.995027i	$-0.468243\pi$
$548$		0			0
$549$	−2.75734	−	7.76501i	−0.117680	−	0.331402i
$550$		0			0
$551$	0.985168	−	0.853653i	0.0419696	−	0.0363668i
$552$		0			0
$553$	−3.22114	+	22.4036i	−0.136977	+	0.952696i
$554$		0			0
$555$	3.86219	−	2.63662i	0.163941	−	0.111918i
$556$		0			0
$557$	2.56898	−	8.74915i	0.108851	−	0.370713i	−0.886993	−	0.461782i	$-0.847210\pi$
$557$	2.56898	−	8.74915i	0.108851	−	0.370713i	0.995845	+	0.0910688i	$0.0290283\pi$
$558$		0			0
$559$	0.353023	+	0.773014i	0.0149313	+	0.0326950i
$560$		0			0
$561$	−6.83418	+	3.35374i	−0.288540	+	0.141595i
$562$		0			0
$563$	14.3375	+	4.20987i	0.604253	+	0.177425i	0.569528	−	0.821972i	$-0.307126\pi$
$563$	14.3375	+	4.20987i	0.604253	+	0.177425i	0.0347256	+	0.999397i	$0.488944\pi$
$564$		0			0
$565$	−28.2652			−1.18913
$566$		0			0
$567$	20.6177	−	12.3482i	0.865863	−	0.518576i
$568$		0			0
$569$	10.7257	−	9.29384i	0.449643	−	0.389618i	−0.400392	−	0.916344i	$-0.631126\pi$
$569$	10.7257	−	9.29384i	0.449643	−	0.389618i	0.850035	+	0.526726i	$0.176581\pi$
$570$		0			0
$571$	4.24451	−	9.29417i	0.177627	−	0.388949i	−0.799787	−	0.600285i	$-0.795054\pi$
$571$	4.24451	−	9.29417i	0.177627	−	0.388949i	0.977414	+	0.211336i	$0.0677813\pi$
$572$		0			0
$573$	−3.26358	+	28.2551i	−0.136338	+	1.18037i
$574$		0			0
$575$	−1.63712	+	2.54742i	−0.0682728	+	0.106235i
$576$		0			0
$577$	22.1115	+	3.17915i	0.920514	+	0.132350i	0.586251	−	0.810130i	$-0.300603\pi$
$577$	22.1115	+	3.17915i	0.920514	+	0.132350i	0.334263	+	0.942480i	$0.391512\pi$
$578$		0			0
$579$	−30.6483	−	8.08077i	−1.27370	−	0.335825i
$580$		0			0
$581$	−11.2821	+	24.7043i	−0.468059	+	1.02491i
$582$		0			0
$583$	−1.67828	−	3.67491i	−0.0695071	−	0.152199i
$584$		0			0
$585$	21.1720	+	1.85067i	0.875353	+	0.0765156i
$586$		0			0
$587$	−38.0598	+	11.1754i	−1.57090	+	0.461257i	−0.947262	−	0.320460i	$-0.896163\pi$
$587$	−38.0598	+	11.1754i	−1.57090	+	0.461257i	−0.623634	+	0.781717i	$0.714344\pi$
$588$		0			0
$589$	−0.0984282	+	0.0141518i	−0.00405566	+	0.000583116i
$590$		0			0
$591$	−2.42324	−	4.93804i	−0.0996788	−	0.203124i
$592$		0			0
$593$	4.07433	−	8.92153i	0.167313	−	0.366363i	−0.807340	−	0.590086i	$-0.799094\pi$
$593$	4.07433	−	8.92153i	0.167313	−	0.366363i	0.974653	+	0.223723i	$0.0718210\pi$
$594$		0			0
$595$	−26.7983	−	17.2222i	−1.09862	−	0.706043i
$596$		0			0
$597$	−3.17093	+	7.48756i	−0.129778	+	0.306445i
$598$		0			0
$599$	−5.18426	−	36.0573i	−0.211823	−	1.47326i	−0.767063	−	0.641572i	$-0.778282\pi$
$599$	−5.18426	−	36.0573i	−0.211823	−	1.47326i	0.555239	−	0.831691i	$-0.312627\pi$
$600$		0			0
$601$	24.1318	−	27.8496i	0.984356	−	1.13601i	−0.00634899	−	0.999980i	$-0.502021\pi$
$601$	24.1318	−	27.8496i	0.984356	−	1.13601i	0.990705	−	0.136028i	$-0.0434336\pi$
$602$		0			0
$603$	−23.0600	−	8.44015i	−0.939076	−	0.343709i
$604$		0			0
$605$	−15.5873	+	17.9887i	−0.633714	+	0.731345i
$606$		0			0
$607$	−2.89566	−	20.1398i	−0.117531	−	0.817448i	−0.960260	−	0.279109i	$-0.909961\pi$
$607$	−2.89566	−	20.1398i	−0.117531	−	0.817448i	0.842728	−	0.538339i	$-0.180948\pi$
$608$		0			0
$609$	5.32630	−	12.5771i	0.215833	−	0.509648i
$610$		0			0
$611$	−26.8772	−	17.2729i	−1.08733	−	0.698787i
$612$		0			0
$613$	−12.0272	+	26.3359i	−0.485775	+	1.06370i	0.495060	+	0.868859i	$0.335146\pi$
$613$	−12.0272	+	26.3359i	−0.485775	+	1.06370i	−0.980835	+	0.194840i	$0.937581\pi$
$614$		0			0
$615$	−2.93586	−	5.98264i	−0.118385	−	0.241244i
$616$		0			0
$617$	−47.8677	+	6.88234i	−1.92708	+	0.277073i	−0.996117	−	0.0880352i	$-0.971941\pi$
$617$	−47.8677	+	6.88234i	−1.92708	+	0.277073i	−0.930965	+	0.365108i	$0.881032\pi$
$618$		0			0
$619$	−11.6821	+	3.43018i	−0.469544	+	0.137871i	−0.507941	−	0.861392i	$-0.669593\pi$
$619$	−11.6821	+	3.43018i	−0.469544	+	0.137871i	0.0383967	+	0.999263i	$0.487775\pi$
$620$		0			0
$621$	−8.52662	+	41.5963i	−0.342162	+	1.66920i
$622$		0			0
$623$	1.84414	+	4.03811i	0.0738840	+	0.161783i
$624$		0			0
$625$	−11.0980	+	24.3013i	−0.443921	+	0.972051i
$626$		0			0
$627$	0.631230	+	0.166431i	0.0252089	+	0.00664661i
$628$		0			0
$629$	−5.93616	−	0.853490i	−0.236690	−	0.0340309i
$630$		0			0
$631$	−1.12766	+	1.75467i	−0.0448914	+	0.0698524i	−0.862974	−	0.505248i	$-0.831401\pi$
$631$	−1.12766	+	1.75467i	−0.0448914	+	0.0698524i	0.818082	+	0.575101i	$0.195037\pi$
$632$		0			0
$633$	−4.21113	+	36.4587i	−0.167377	+	1.44910i
$634$		0			0
$635$	−3.41115	+	7.46937i	−0.135367	+	0.296413i
$636$		0			0
$637$	−0.301451	+	0.261209i	−0.0119439	+	0.0103495i
$638$		0			0
$639$	21.6992	−	21.0246i	0.858408	−	0.831719i
$640$		0			0
$641$	−32.2874			−1.27528			−0.637639	−	0.770336i	$-0.720089\pi$
$641$	−32.2874			−1.27528			−0.637639	+	0.770336i	$0.720089\pi$
$642$		0			0
$643$	−27.9797	−	8.21557i	−1.10341	−	0.323991i	−0.321204	−	0.947010i	$-0.604088\pi$
$643$	−27.9797	−	8.21557i	−1.10341	−	0.323991i	−0.782206	+	0.623019i	$0.785906\pi$
$644$		0			0
$645$	1.00174	−	0.491584i	0.0394435	−	0.0193561i
$646$		0			0
$647$	−10.4040	−	22.7815i	−0.409023	−	0.895635i	−0.996275	−	0.0862309i	$-0.972518\pi$
$647$	−10.4040	−	22.7815i	−0.409023	−	0.895635i	0.587253	−	0.809404i	$-0.300210\pi$
$648$		0			0
$649$	2.54182	−	8.65663i	0.0997750	−	0.339802i
$650$		0			0
$651$	−0.860511	+	0.587449i	−0.0337261	+	0.0230240i
$652$		0			0
$653$	3.38879	−	23.5696i	0.132614	−	0.922348i	−0.809516	−	0.587098i	$-0.800270\pi$
$653$	3.38879	−	23.5696i	0.132614	−	0.922348i	0.942129	−	0.335250i	$-0.108821\pi$
$654$		0			0
$655$	16.0613	−	13.9172i	0.627568	−	0.543791i
$656$		0			0
$657$	−28.6975	+	10.1904i	−1.11960	+	0.397567i
$658$		0			0
$659$	5.05336	+	17.2102i	0.196851	+	0.670413i	0.997460	+	0.0712260i	$0.0226911\pi$
$659$	5.05336	+	17.2102i	0.196851	+	0.670413i	−0.800609	+	0.599187i	$0.795491\pi$
$660$		0			0
$661$	−3.39807	−	2.94445i	−0.132170	−	0.114526i	0.586267	−	0.810118i	$-0.300597\pi$
$661$	−3.39807	−	2.94445i	−0.132170	−	0.114526i	−0.718437	+	0.695592i	$0.755142\pi$
$662$		0			0
$663$	−18.4143	−	20.0942i	−0.715154	−	0.780393i
$664$		0			0
$665$	0.769589	+	2.62098i	0.0298434	+	0.101637i
$666$		0			0
$667$	10.0247	+	21.9511i	0.388159	+	0.849950i
$668$		0			0
$669$	0.269373	−	2.33215i	0.0104146	−	0.0901660i
$670$		0			0
$671$		−	2.34518i		−	0.0905347i
$672$		0			0
$673$	−6.05052	+	2.76318i	−0.233230	+	0.106513i	−0.528602	−	0.848870i	$-0.677284\pi$
$673$	−6.05052	+	2.76318i	−0.233230	+	0.106513i	0.295372	+	0.955382i	$0.404556\pi$
$674$		0			0
$675$	0.114278	−	1.92211i	0.00439855	−	0.0739819i
$676$		0			0
$677$	17.5361	−	20.2377i	0.673967	−	0.777800i	−0.311024	−	0.950402i	$-0.600672\pi$
$677$	17.5361	−	20.2377i	0.673967	−	0.777800i	0.984992	+	0.172602i	$0.0552176\pi$
$678$		0			0
$679$	18.3123	−	21.1335i	0.702760	−	0.811028i
$680$		0			0
$681$	−7.36594	+	1.26900i	−0.282264	+	0.0486282i
$682$		0			0
$683$	−35.1796	+	22.6085i	−1.34611	+	0.865092i	−0.997395	−	0.0721370i	$-0.977018\pi$
$683$	−35.1796	+	22.6085i	−1.34611	+	0.865092i	−0.348715	+	0.937229i	$0.613382\pi$
$684$		0			0
$685$	27.1841	+	31.3721i	1.03865	+	1.19867i
$686$		0			0
$687$	−1.87537	+	7.11280i	−0.0715498	+	0.271370i
$688$		0			0
$689$	10.9313	−	9.47206i	0.416451	−	0.360857i
$690$		0			0
$691$	−29.0762	−	8.53754i	−1.10611	−	0.324783i	−0.322833	−	0.946456i	$-0.604635\pi$
$691$	−29.0762	−	8.53754i	−1.10611	−	0.324783i	−0.783277	+	0.621673i	$0.786453\pi$
$692$		0			0
$693$	6.70570	−	1.34821i	0.254728	−	0.0512144i
$694$		0			0
$695$	29.1311	+	45.3288i	1.10500	+	1.71942i
$696$		0			0
$697$	−2.40782	+	8.20030i	−0.0912028	+	0.310608i
$698$		0			0
$699$	−4.36482	+	37.7893i	−0.165093	+	1.42932i
$700$		0			0
$701$	7.64757	+	4.91479i	0.288845	+	0.185629i	0.677037	−	0.735949i	$-0.263264\pi$
$701$	7.64757	+	4.91479i	0.288845	+	0.185629i	−0.388192	+	0.921579i	$0.626900\pi$
$702$		0			0
$703$	0.336774	+	0.388658i	0.0127017	+	0.0146585i
$704$		0			0
$705$	−21.6906	+	35.9085i	−0.816915	+	1.35239i
$706$		0			0
$707$			4.34945i			0.163578i
$708$		0			0
$709$	−20.8810	−	13.4194i	−0.784204	−	0.503977i	0.0862225	−	0.996276i	$-0.472520\pi$
$709$	−20.8810	−	13.4194i	−0.784204	−	0.503977i	−0.870426	+	0.492299i	$0.836157\pi$
$710$		0			0
$711$	23.6820	+	9.26144i	0.888145	+	0.347331i
$712$		0			0
$713$	0.261982	−	1.82212i	0.00981129	−	0.0682390i
$714$		0			0
$715$	5.50208	+	2.51271i	0.205766	+	0.0939702i
$716$		0			0
$717$	37.4059	−	12.1227i	1.39695	−	0.452730i
$718$		0			0
$719$	34.6967	−	4.98863i	1.29397	−	0.186044i	0.539278	−	0.842128i	$-0.318697\pi$
$719$	34.6967	−	4.98863i	1.29397	−	0.186044i	0.754689	+	0.656083i	$0.227788\pi$
$720$		0			0
$721$	4.04515	+	13.7765i	0.150649	+	0.513065i
$722$		0			0
$723$	−28.8251	+	0.801689i	−1.07202	+	0.0298151i
$724$		0			0
$725$	−0.591630	−	0.920595i	−0.0219726	−	0.0341900i
$726$		0			0
$727$	−32.5087	−	14.8462i	−1.20568	−	0.550616i	−0.291754	−	0.956493i	$-0.594239\pi$
$727$	−32.5087	−	14.8462i	−1.20568	−	0.550616i	−0.913928	+	0.405877i	$0.866966\pi$
$728$		0			0
$729$	−8.22707	−	25.7161i	−0.304706	−	0.952446i
$730$		0			0
$731$	−1.37307	−	0.403169i	−0.0507847	−	0.0149117i
$732$		0			0
$733$	−39.4566	+	5.67300i	−1.45736	+	0.209537i	−0.824999	−	0.565135i	$-0.808824\pi$
$733$	−39.4566	+	5.67300i	−1.45736	+	0.209537i	−0.632363	+	0.774672i	$0.717915\pi$
$734$		0			0
$735$	0.353857	+	0.386137i	0.0130522	+	0.0142429i
$736$		0			0
$737$	−5.38089	−	4.45983i	−0.198208	−	0.164280i
$738$		0			0
$739$	−16.8403	−	14.5922i	−0.619480	−	0.536782i	0.287595	−	0.957752i	$-0.407144\pi$
$739$	−16.8403	−	14.5922i	−0.619480	−	0.536782i	−0.907075	+	0.420970i	$0.861690\pi$
$740$		0			0
$741$	0.0649776	+	2.33630i	0.00238701	+	0.0858260i
$742$		0			0
$743$	3.18990	−	10.8638i	0.117026	−	0.398554i	−0.880058	−	0.474866i	$-0.842496\pi$
$743$	3.18990	−	10.8638i	0.117026	−	0.398554i	0.997084	+	0.0763124i	$0.0243146\pi$
$744$		0			0
$745$	19.9333	−	31.0169i	0.730300	−	1.13637i
$746$		0			0
$747$	24.1343	+	18.6685i	0.883026	+	0.683043i
$748$		0			0
$749$	15.6713	−	10.0713i	0.572618	−	0.367999i
$750$		0			0
$751$	3.83220	+	26.6535i	0.139839	+	0.972600i	0.932044	+	0.362345i	$0.118024\pi$
$751$	3.83220	+	26.6535i	0.139839	+	0.972600i	−0.792205	+	0.610255i	$0.791067\pi$
$752$		0			0
$753$	4.06629	+	23.6029i	0.148184	+	0.860137i
$754$		0			0
$755$	1.55755	+	10.8330i	0.0566850	+	0.394253i
$756$		0			0
$757$	16.5988	−	7.58043i	0.603295	−	0.275515i	−0.0902614	−	0.995918i	$-0.528770\pi$
$757$	16.5988	−	7.58043i	0.603295	−	0.275515i	0.693556	+	0.720403i	$0.256043\pi$
$758$		0			0
$759$	−6.24838	+	10.3441i	−0.226802	+	0.375467i
$760$		0			0
$761$	18.3174	+	2.63364i	0.664004	+	0.0954693i	0.466072	−	0.884747i	$-0.345669\pi$
$761$	18.3174	+	2.63364i	0.664004	+	0.0954693i	0.197931	+	0.980216i	$0.436578\pi$
$762$		0			0
$763$	0.570323	−	3.96668i	0.0206471	−	0.143604i
$764$		0			0
$765$	−25.7026	+	24.9035i	−0.929281	+	0.900389i
$766$		0			0
$767$	32.3014			1.16634
$768$		0			0
$769$	1.33843	+	0.611241i	0.0482651	+	0.0220419i	0.439401	−	0.898291i	$-0.355191\pi$
$769$	1.33843	+	0.611241i	0.0482651	+	0.0220419i	−0.391136	+	0.920333i	$0.627918\pi$
$770$		0			0
$771$	−5.69456	−	8.34153i	−0.205084	−	0.300413i
$772$		0			0
$773$	−17.7219	+	27.5759i	−0.637413	+	0.991835i	0.360832	+	0.932631i	$0.382493\pi$
$773$	−17.7219	+	27.5759i	−0.637413	+	0.991835i	−0.998246	+	0.0592040i	$0.981144\pi$
$774$		0			0
$775$			0.0834780i			0.00299862i
$776$		0			0
$777$	4.96177	+	2.10128i	0.178002	+	0.0753829i
$778$		0			0
$779$	0.616532	−	0.396221i	0.0220896	−	0.0141961i
$780$		0			0
$781$	7.82207	−	3.57222i	0.279896	−	0.127824i
$782$		0			0
$783$	−12.3938	−	9.04754i	−0.442917	−	0.323333i
$784$		0			0
$785$	−5.76387	−	6.65186i	−0.205721	−	0.237415i
$786$		0			0
$787$	−33.0371	−	4.75002i	−1.17765	−	0.169320i	−0.474428	−	0.880294i	$-0.657345\pi$
$787$	−33.0371	−	4.75002i	−1.17765	−	0.169320i	−0.703218	+	0.710974i	$0.748254\pi$
$788$		0			0
$789$	−18.7239	−	27.4272i	−0.666587	−	0.976433i
$790$		0			0
$791$	−17.6080	−	27.3986i	−0.626070	−	0.974183i
$792$		0			0
$793$	8.05624	−	2.36553i	0.286086	−	0.0840023i
$794$		0			0
$795$	−12.8317	−	14.0023i	−0.455094	−	0.496610i
$796$		0			0
$797$	38.5423	+	33.3971i	1.36524	+	1.18299i	0.963651	+	0.267165i	$0.0860869\pi$
$797$	38.5423	+	33.3971i	1.36524	+	1.18299i	0.401588	+	0.915821i	$0.368459\pi$
$798$		0			0
$799$	51.6210	−	15.1573i	1.82622	−	0.536227i
$800$		0			0
$801$	4.88955	−	0.983069i	0.172764	−	0.0347350i
$802$		0			0
$803$	−8.66720			−0.305859
$804$		0			0
$805$	−50.5685			−1.78231
$806$		0			0
$807$	9.53955	+	29.4353i	0.335808	+	1.03617i
$808$		0			0
$809$	−32.8857	+	9.65612i	−1.15620	+	0.339491i	−0.802955	−	0.596040i	$-0.796740\pi$
$809$	−32.8857	+	9.65612i	−1.15620	+	0.339491i	−0.353245	+	0.935531i	$0.614922\pi$
$810$		0			0
$811$	12.7758	+	11.0703i	0.448618	+	0.388730i	0.849661	−	0.527330i	$-0.176807\pi$
$811$	12.7758	+	11.0703i	0.448618	+	0.388730i	−0.401043	+	0.916059i	$0.631352\pi$
$812$		0			0
$813$	5.46284	−	5.00616i	0.191590	−	0.175574i
$814$		0			0
$815$	−35.4582	+	10.4115i	−1.24205	+	0.364698i
$816$		0			0
$817$	0.0663438	+	0.103233i	0.00232107	+	0.00361166i
$818$		0			0
$819$	11.3953	+	21.6757i	0.398184	+	0.757411i
$820$		0			0
$821$	21.1471	+	3.04049i	0.738037	+	0.106114i	0.501073	−	0.865405i	$-0.332939\pi$
$821$	21.1471	+	3.04049i	0.738037	+	0.106114i	0.236964	+	0.971518i	$0.423848\pi$
$822$		0			0
$823$	−3.89496	−	4.49502i	−0.135770	−	0.156687i	0.683793	−	0.729676i	$-0.260329\pi$
$823$	−3.89496	−	4.49502i	−0.135770	−	0.156687i	−0.819563	+	0.572989i	$0.805784\pi$
$824$		0			0
$825$	0.213706	−	0.504627i	0.00744029	−	0.0175688i
$826$		0			0
$827$	50.0100	−	22.8388i	1.73902	−	0.794183i	0.747493	−	0.664269i	$-0.231257\pi$
$827$	50.0100	−	22.8388i	1.73902	−	0.794183i	0.991525	−	0.129914i	$-0.0414701\pi$
$828$		0			0
$829$	−23.7129	+	15.2394i	−0.823583	+	0.529285i	−0.883233	−	0.468935i	$-0.844638\pi$
$829$	−23.7129	+	15.2394i	−0.823583	+	0.529285i	0.0596497	+	0.998219i	$0.481002\pi$
$830$		0			0
$831$	17.0692	−	40.3057i	0.592124	−	1.39819i
$832$		0			0
$833$		−	0.671687i		−	0.0232726i
$834$		0			0
$835$	8.76122	−	13.6327i	0.303194	−	0.471780i
$836$		0			0
$837$	0.422215	+	1.09176i	0.0145939	+	0.0377366i
$838$		0			0
$839$	−36.3792	−	16.6138i	−1.25595	−	0.573573i	−0.327438	−	0.944873i	$-0.606185\pi$
$839$	−36.3792	−	16.6138i	−1.25595	−	0.573573i	−0.928513	+	0.371299i	$0.878912\pi$
$840$		0			0
$841$	20.2791			0.699281
$842$		0			0
$843$	8.13734	−	9.93623i	0.280265	−	0.342222i
$844$		0			0
$845$	1.20554	−	8.38474i	0.0414719	−	0.288444i
$846$		0			0
$847$	−27.1474	−	3.90321i	−0.932796	−	0.134116i
$848$		0			0
$849$	29.7633	+	17.9786i	1.02147	+	0.617023i
$850$		0			0
$851$	−8.65992	+	3.95485i	−0.296858	+	0.135571i
$852$		0			0
$853$	4.40957	+	30.6692i	0.150981	+	1.05009i	0.914580	+	0.404404i	$0.132521\pi$
$853$	4.40957	+	30.6692i	0.150981	+	1.05009i	−0.763600	+	0.645690i	$0.776570\pi$
$854$		0			0
$855$	3.06416	−	0.170574i	0.104792	−	0.00583352i
$856$		0			0
$857$	−3.57622	−	24.8731i	−0.122161	−	0.849650i	−0.955100	−	0.296284i	$-0.904252\pi$
$857$	−3.57622	−	24.8731i	−0.122161	−	0.849650i	0.832939	−	0.553365i	$-0.186657\pi$
$858$		0			0
$859$	17.7223	−	11.3894i	0.604678	−	0.388603i	−0.202180	−	0.979348i	$-0.564803\pi$
$859$	17.7223	−	11.3894i	0.604678	−	0.388603i	0.806858	+	0.590746i	$0.201166\pi$
$860$		0			0
$861$	3.97030	−	6.57278i	0.135308	−	0.224000i
$862$		0			0
$863$	−3.99182	+	6.21139i	−0.135883	+	0.211438i	−0.902526	−	0.430636i	$-0.858289\pi$
$863$	−3.99182	+	6.21139i	−0.135883	+	0.211438i	0.766643	+	0.642074i	$0.221926\pi$
$864$		0			0
$865$	8.30019	−	28.2678i	0.282215	−	0.961136i
$866$		0			0
$867$	16.4457	−	0.457391i	0.558524	−	0.0155338i
$868$		0			0
$869$	5.46949	+	4.73934i	0.185540	+	0.160771i
$870$		0			0
$871$	9.89299	−	22.9831i	0.335211	−	0.778753i
$872$		0			0
$873$	−18.4276	−	25.4441i	−0.623681	−	0.861154i
$874$		0			0
$875$	−28.3566	+	4.07707i	−0.958629	+	0.137830i
$876$		0			0
$877$	26.5852	+	7.80612i	0.897719	+	0.263594i	0.697863	−	0.716231i	$-0.254134\pi$
$877$	26.5852	+	7.80612i	0.897719	+	0.263594i	0.199856	+	0.979825i	$0.435953\pi$
$878$		0			0
$879$	18.9264	+	15.4999i	0.638371	+	0.522798i
$880$		0			0
$881$	17.1277	+	7.82197i	0.577048	+	0.263529i	0.682488	−	0.730897i	$-0.260898\pi$
$881$	17.1277	+	7.82197i	0.577048	+	0.263529i	−0.105440	+	0.994426i	$0.533625\pi$
$882$		0			0
$883$	3.41903	+	5.32011i	0.115059	+	0.179036i	0.894007	−	0.448053i	$-0.147883\pi$
$883$	3.41903	+	5.32011i	0.115059	+	0.179036i	−0.778947	+	0.627089i	$0.784246\pi$
$884$		0			0
$885$	−1.17917	−	42.3976i	−0.0396374	−	1.42518i
$886$		0			0
$887$	1.40322	+	4.77894i	0.0471156	+	0.160461i	0.979691	−	0.200515i	$-0.0642617\pi$
$887$	1.40322	+	4.77894i	0.0471156	+	0.160461i	−0.932575	+	0.360976i	$0.882443\pi$
$888$		0			0
$889$	−9.36537	+	1.34654i	−0.314104	+	0.0451614i
$890$		0			0
$891$	0.242630	−	7.68059i	0.00812839	−	0.257309i
$892$		0			0
$893$	−4.19655	−	1.91650i	−0.140432	−	0.0641332i
$894$		0			0
$895$	−7.73214	+	53.7782i	−0.258457	+	1.79761i
$896$		0			0
$897$	−41.8370	−	11.0308i	−1.39690	−	0.368307i
$898$		0			0
$899$	0.559650	+	0.359665i	0.0186654	+	0.0119955i
$900$		0			0
$901$			24.3570i			0.811450i
$902$		0			0
$903$	1.10055	+	0.664792i	0.0366242	+	0.0221229i
$904$		0			0
$905$	−26.3466	−	30.4057i	−0.875792	−	1.01072i
$906$		0			0
$907$	−33.5358	−	21.5521i	−1.11354	−	0.715627i	−0.151476	−	0.988461i	$-0.548403\pi$
$907$	−33.5358	−	21.5521i	−1.11354	−	0.715627i	−0.962061	+	0.272834i	$0.912039\pi$
$908$		0			0
$909$	4.75781	+	1.11396i	0.157807	+	0.0369476i
$910$		0			0
$911$	0.736874	−	2.50956i	0.0244137	−	0.0831455i	−0.946385	−	0.323041i	$-0.895295\pi$
$911$	0.736874	−	2.50956i	0.0244137	−	0.0831455i	0.970799	+	0.239895i	$0.0771131\pi$
$912$		0			0
$913$	4.69488	+	7.30538i	0.155378	+	0.241773i
$914$		0			0
$915$	−3.39900	−	10.4880i	−0.112367	−	0.346721i
$916$		0			0
$917$	23.4961	+	6.89907i	0.775908	+	0.227827i
$918$		0			0
$919$	−28.4369	+	24.6408i	−0.938048	+	0.812823i	−0.982514	−	0.186188i	$-0.940387\pi$
$919$	−28.4369	+	24.6408i	−0.938048	+	0.812823i	0.0444661	+	0.999011i	$0.485841\pi$
$920$		0			0
$921$	21.2551	+	5.60416i	0.700381	+	0.184663i
$922$		0			0
$923$	20.1613	+	23.2674i	0.663619	+	0.765857i
$924$		0			0
$925$	0.363183	−	0.233404i	0.0119414	−	0.00767427i
$926$		0			0
$927$	16.1060	−	0.896581i	0.528991	−	0.0294476i
$928$		0			0
$929$	−17.4505	+	20.1390i	−0.572534	+	0.660739i	−0.965983	−	0.258607i	$-0.916736\pi$
$929$	−17.4505	+	20.1390i	−0.572534	+	0.660739i	0.393449	+	0.919347i	$0.371282\pi$
$930$		0			0
$931$	−0.0377188	+	0.0435298i	−0.00123618	+	0.00142663i
$932$		0			0
$933$	7.10410	+	41.2359i	0.232578	+	1.35000i
$934$		0			0
$935$	−9.26521	+	4.23128i	−0.303005	+	0.138378i
$936$		0			0
$937$		−	29.7428i		−	0.971655i	−0.874055	−	0.485828i	$-0.838518\pi$
$937$		−	29.7428i		−	0.971655i	0.874055	−	0.485828i	$-0.161482\pi$
$938$		0			0
$939$	−18.9950	−	2.19400i	−0.619878	−	0.0715985i
$940$		0			0
$941$	6.57019	+	14.3867i	0.214182	+	0.468993i	0.985978	−	0.166877i	$-0.0533684\pi$
$941$	6.57019	+	14.3867i	0.214182	+	0.468993i	−0.771796	+	0.635871i	$0.780641\pi$
$942$		0			0
$943$	3.82230	+	13.0175i	0.124471	+	0.423910i
$944$		0			0
$945$	28.0348	−	15.7483i	0.911971	−	0.512293i
$946$		0			0
$947$	−8.40576	−	7.28364i	−0.273151	−	0.236686i	0.507503	−	0.861650i	$-0.330568\pi$
$947$	−8.40576	−	7.28364i	−0.273151	−	0.236686i	−0.780654	+	0.624963i	$0.785114\pi$
$948$		0			0
$949$	−8.74239	−	29.7739i	−0.283790	−	0.966500i
$950$		0			0
$951$	23.6926	−	11.6266i	0.768284	−	0.377020i
$952$		0			0
$953$	35.5845	−	30.8341i	1.15269	−	0.998815i	0.152750	−	0.988265i	$-0.451187\pi$
$953$	35.5845	−	30.8341i	1.15269	−	0.998815i	0.999944	−	0.0105502i	$-0.00335829\pi$
$954$		0			0
$955$	−5.41594	+	37.6687i	−0.175256	+	1.21893i
$956$		0			0
$957$	−2.46235	−	3.60691i	−0.0795963	−	0.116595i
$958$		0			0
$959$	−13.4757	+	45.8942i	−0.435155	+	1.48200i
$960$		0			0
$961$	12.8568	+	28.1524i	0.414735	+	0.908143i
$962$		0			0
$963$	−7.00328	−	19.7221i	−0.225678	−	0.635536i
$964$		0			0
$965$	−40.6904	−	11.9478i	−1.30987	−	0.384612i
$966$		0			0
$967$	3.70365			0.119101			0.0595506	−	0.998225i	$-0.481033\pi$
$967$	3.70365			0.119101			0.0595506	+	0.998225i	$0.481033\pi$
$968$		0			0
$969$	−3.04493	−	2.49366i	−0.0978171	−	0.0801080i
$970$		0			0
$971$	−7.10228	+	6.15416i	−0.227923	+	0.197496i	−0.761334	−	0.648360i	$-0.775455\pi$
$971$	−7.10228	+	6.15416i	−0.227923	+	0.197496i	0.533411	+	0.845856i	$0.320910\pi$
$972$		0			0
$973$	−25.7917	+	56.4759i	−0.826843	+	1.81053i
$974$		0			0
$975$	1.94907	+	0.225126i	0.0624202	+	0.00720980i
$976$		0			0
$977$	8.66680	−	13.4858i	0.277276	−	0.431449i	−0.674486	−	0.738288i	$-0.735635\pi$
$977$	8.66680	−	13.4858i	0.277276	−	0.431449i	0.951762	+	0.306838i	$0.0992711\pi$
$978$		0			0
$979$	1.40501	+	0.202009i	0.0449042	+	0.00645625i
$980$		0			0
$981$	−4.19304	−	1.63979i	−0.133873	−	0.0523546i
$982$		0			0
$983$	18.1074	−	39.6497i	0.577537	−	1.26463i	−0.365149	−	0.930949i	$-0.618982\pi$
$983$	18.1074	−	39.6497i	0.577537	−	1.26463i	0.942686	−	0.333681i	$-0.108291\pi$
$984$		0			0
$985$	−3.05731	−	6.69457i	−0.0974140	−	0.213307i
$986$		0			0
$987$	−48.3199	+	1.34388i	−1.53804	+	0.0427763i
$988$		0			0
$989$	−2.17967	+	0.640010i	−0.0693096	+	0.0203511i
$990$		0			0
$991$	−20.2861	+	2.91669i	−0.644408	+	0.0926519i	−0.456768	−	0.889586i	$-0.650993\pi$
$991$	−20.2861	+	2.91669i	−0.644408	+	0.0926519i	−0.187640	+	0.982238i	$0.560084\pi$
$992$		0			0
$993$	32.2869	−	15.8442i	1.02459	−	0.502799i
$994$		0			0
$995$	−4.51952	+	9.89637i	−0.143279	+	0.313736i
$996$		0			0
$997$	−38.3251	−	24.6301i	−1.21377	−	0.780042i	−0.232484	−	0.972600i	$-0.574685\pi$
$997$	−38.3251	−	24.6301i	−1.21377	−	0.780042i	−0.981286	+	0.192558i	$0.938322\pi$
$998$		0			0
$999$	3.56934	−	4.88945i	0.112929	−	0.154695i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	804.2.s.b.5.20	yes	200
3.2	odd	2	inner	804.2.s.b.5.17	✓	200
67.27	odd	22	inner	804.2.s.b.161.17	yes	200
201.161	even	22	inner	804.2.s.b.161.20	yes	200

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
804.2.s.b.5.17	✓	200	3.2	odd	2	inner
804.2.s.b.5.20	yes	200	1.1	even	1	trivial
804.2.s.b.161.17	yes	200	67.27	odd	22	inner
804.2.s.b.161.20	yes	200	201.161	even	22	inner

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:	\( N \)	\(=\)	\( 804 = 2^{2} \cdot 3 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	804.s (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(1.64768 - 0.533989i) q^{3} +(2.22357 - 0.652900i) q^{5} +(2.01808 + 1.74867i) q^{7} +(2.42971 - 1.75969i) q^{9} +O(q^{10})\)	\(q+(1.64768 - 0.533989i) q^{3} +(2.22357 - 0.652900i) q^{5} +(2.01808 + 1.74867i) q^{7} +(2.42971 - 1.75969i) q^{9} +(0.819238 - 0.240550i) q^{11} +(1.65269 + 2.57164i) q^{13} +(3.31510 - 2.26314i) q^{15} +(-5.09528 - 0.732591i) q^{17} +(0.289069 + 0.333603i) q^{19} +(4.25892 + 1.80362i) q^{21} +(-7.43322 + 3.39464i) q^{23} +(0.311737 - 0.200341i) q^{25} +(3.06373 - 4.19685i) q^{27} -2.95311i q^{29} +(-0.121792 + 0.189512i) q^{31} +(1.22139 - 0.833814i) q^{33} +(5.62905 + 2.57070i) q^{35} +1.16503 q^{37} +(4.09634 + 3.35472i) q^{39} +(0.236280 - 1.64336i) q^{41} +(0.275166 + 0.0395630i) q^{43} +(4.25374 - 5.49916i) q^{45} +(-9.50691 + 4.34166i) q^{47} +(0.0185697 + 0.129155i) q^{49} +(-8.78660 + 1.51375i) q^{51} +(-0.673384 - 4.68349i) q^{53} +(1.66458 - 1.06976i) q^{55} +(0.654435 + 0.395313i) q^{57} +(5.71278 - 8.88926i) q^{59} +(0.773829 - 2.63542i) q^{61} +(7.98046 + 0.697581i) q^{63} +(5.35390 + 4.63918i) q^{65} +(-4.57523 - 6.78728i) q^{67} +(-10.4349 + 9.56254i) q^{69} +(9.96884 - 1.43330i) q^{71} +(-9.73985 - 2.85988i) q^{73} +(0.406664 - 0.496563i) q^{75} +(2.07393 + 0.947131i) q^{77} +(4.58257 + 7.13062i) q^{79} +(2.80699 - 8.55107i) q^{81} +(2.86539 + 9.75864i) q^{83} +(-11.8080 + 1.69774i) q^{85} +(-1.57693 - 4.86579i) q^{87} +(1.51223 + 0.690613i) q^{89} +(-1.16170 + 8.07977i) q^{91} +(-0.0994770 + 0.377291i) q^{93} +(0.860576 + 0.553059i) q^{95} -10.4721i q^{97} +(1.56722 - 2.02607i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 200 q - 10 q^{9}+O(q^{10}) \) 200 * q - 10 * q^9	\( 200 q - 10 q^{9} + 2 q^{15} + 6 q^{19} - 10 q^{21} - 20 q^{25} - 44 q^{31} - 5 q^{33} + 78 q^{39} - 22 q^{43} - 22 q^{45} - 16 q^{49} + 36 q^{55} + 66 q^{57} + 176 q^{61} + 132 q^{63} + 46 q^{67} - 26 q^{73} - 165 q^{75} - 44 q^{79} + 42 q^{81} - 66 q^{87} - 20 q^{91} + 84 q^{93} - 55 q^{99}+O(q^{100}) \) 200 * q - 10 * q^9 + 2 * q^15 + 6 * q^19 - 10 * q^21 - 20 * q^25 - 44 * q^31 - 5 * q^33 + 78 * q^39 - 22 * q^43 - 22 * q^45 - 16 * q^49 + 36 * q^55 + 66 * q^57 + 176 * q^61 + 132 * q^63 + 46 * q^67 - 26 * q^73 - 165 * q^75 - 44 * q^79 + 42 * q^81 - 66 * q^87 - 20 * q^91 + 84 * q^93 - 55 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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