LMFDB - Embedded newform 804.2.s.b.5.17

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			5.17
Character	$\chi$	$=$	804.5
Dual form			804.2.s.b.161.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.48256 - 0.895546i) q^{3} +(-2.22357 + 0.652900i) q^{5} +(2.01808 + 1.74867i) q^{7} +(1.39599 - 2.65541i) q^{9} +O(q^{10})$	\(q+(1.48256 - 0.895546i) q^{3} +(-2.22357 + 0.652900i) q^{5} +(2.01808 + 1.74867i) q^{7} +(1.39599 - 2.65541i) q^{9} +(-0.819238 + 0.240550i) q^{11} +(1.65269 + 2.57164i) q^{13} +(-2.71189 + 2.95928i) q^{15} +(5.09528 + 0.732591i) q^{17} +(0.289069 + 0.333603i) q^{19} +(4.55794 + 0.785240i) q^{21} +(7.43322 - 3.39464i) q^{23} +(0.311737 - 0.200341i) q^{25} +(-0.308390 - 5.18699i) q^{27} +2.95311i q^{29} +(-0.121792 + 0.189512i) q^{31} +(-0.999150 + 1.09030i) q^{33} +(-5.62905 - 2.57070i) q^{35} +1.16503 q^{37} +(4.75324 + 2.33256i) q^{39} +(-0.236280 + 1.64336i) q^{41} +(0.275166 + 0.0395630i) q^{43} +(-1.37038 + 6.81595i) q^{45} +(9.50691 - 4.34166i) q^{47} +(0.0185697 + 0.129155i) q^{49} +(8.21015 - 3.47695i) q^{51} +(0.673384 + 4.68349i) q^{53} +(1.66458 - 1.06976i) q^{55} +(0.727321 + 0.235714i) q^{57} +(-5.71278 + 8.88926i) q^{59} +(0.773829 - 2.63542i) q^{61} +(7.46066 - 2.91768i) q^{63} +(-5.35390 - 4.63918i) q^{65} +(-4.57523 - 6.78728i) q^{67} +(7.98017 - 11.6896i) q^{69} +(-9.96884 + 1.43330i) q^{71} +(-9.73985 - 2.85988i) q^{73} +(0.282756 - 0.576194i) q^{75} +(-2.07393 - 0.947131i) q^{77} +(4.58257 + 7.13062i) q^{79} +(-5.10240 - 7.41387i) q^{81} +(-2.86539 - 9.75864i) q^{83} +(-11.8080 + 1.69774i) q^{85} +(2.64465 + 4.37818i) q^{87} +(-1.51223 - 0.690613i) q^{89} +(-1.16170 + 8.07977i) q^{91} +(-0.0108477 + 0.390034i) q^{93} +(-0.860576 - 0.553059i) q^{95} -10.4721i q^{97} +(-0.504893 + 2.51122i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	1.48256	−	0.895546i	0.855959	−	0.517044i
$3$	1.48256	−	0.895546i	0.855959	−	0.517044i
$4$		0			0
$5$	−2.22357	+	0.652900i	−0.994413	+	0.291986i	−0.738161	−	0.674624i	$-0.764306\pi$
$5$	−2.22357	+	0.652900i	−0.994413	+	0.291986i	−0.256251	+	0.966610i	$0.582488\pi$
$6$		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
$9$	1.39599	−	2.65541i	0.465331	−	0.885136i
$10$		0			0
$11$	−0.819238	+	0.240550i	−0.247010	+	0.0725286i	−0.402894	−	0.915247i	$-0.631996\pi$
$11$	−0.819238	+	0.240550i	−0.247010	+	0.0725286i	0.155884	+	0.987775i	$0.450177\pi$
$12$		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
$15$	−2.71189	+	2.95928i	−0.700207	+	0.764083i
$16$		0			0
$17$	5.09528	+	0.732591i	1.23579	+	0.177679i	0.729074	−	0.684435i	$-0.239951\pi$
$17$	5.09528	+	0.732591i	1.23579	+	0.177679i	0.506714	+	0.862114i	$0.330860\pi$
$18$		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
$21$	4.55794	+	0.785240i	0.994625	+	0.171353i
$22$		0			0
$23$	7.43322	−	3.39464i	1.54993	−	0.707830i	0.557449	−	0.830211i	$-0.311780\pi$
$23$	7.43322	−	3.39464i	1.54993	−	0.707830i	0.992483	+	0.122381i	$0.0390529\pi$
$24$		0			0
$25$	0.311737	−	0.200341i	0.0623475	−	0.0400683i
$26$		0			0
$27$	−0.308390	−	5.18699i	−0.0593496	−	0.998237i
$28$		0			0
$29$			2.95311i			0.548379i	0.961676	+	0.274189i	$0.0884095\pi$
$29$			2.95311i			0.548379i	−0.961676	+	0.274189i	$0.911590\pi$
$30$		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
$33$	−0.999150	+	1.09030i	−0.173930	+	0.189796i
$34$		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
$39$	4.75324	+	2.33256i	0.761127	+	0.373508i
$40$		0			0
$41$	−0.236280	+	1.64336i	−0.0369007	+	0.256650i	−0.999918	−	0.0127888i	$-0.995929\pi$
$41$	−0.236280	+	1.64336i	−0.0369007	+	0.256650i	0.963018	+	0.269439i	$0.0868382\pi$
$42$		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
$45$	−1.37038	+	6.81595i	−0.204284	+	1.01606i
$46$		0			0
$47$	9.50691	−	4.34166i	1.38673	−	0.633296i	0.424469	−	0.905442i	$-0.360461\pi$
$47$	9.50691	−	4.34166i	1.38673	−	0.633296i	0.962256	+	0.272146i	$0.0877334\pi$
$48$		0			0
$49$	0.0185697	+	0.129155i	0.00265282	+	0.0184508i
$50$		0			0
$51$	8.21015	−	3.47695i	1.14965	−	0.486870i
$52$		0			0
$53$	0.673384	+	4.68349i	0.0924965	+	0.643327i	0.982346	+	0.187073i	$0.0599001\pi$
$53$	0.673384	+	4.68349i	0.0924965	+	0.643327i	−0.889850	+	0.456254i	$0.849191\pi$
$54$		0			0
$55$	1.66458	−	1.06976i	0.224452	−	0.144247i
$56$		0			0
$57$	0.727321	+	0.235714i	0.0963360	+	0.0312211i
$58$		0			0
$59$	−5.71278	+	8.88926i	−0.743741	+	1.15728i	0.238770	+	0.971076i	$0.423256\pi$
$59$	−5.71278	+	8.88926i	−0.743741	+	1.15728i	−0.982511	+	0.186207i	$0.940381\pi$
$60$		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
$63$	7.46066	−	2.91768i	0.939955	−	0.367593i
$64$		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
$69$	7.98017	−	11.6896i	0.960699	−	1.40726i
$70$		0			0
$71$	−9.96884	+	1.43330i	−1.18308	+	0.170102i	−0.705646	−	0.708564i	$-0.749343\pi$
$71$	−9.96884	+	1.43330i	−1.18308	+	0.170102i	−0.477437	+	0.878666i	$0.658434\pi$
$72$		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
$75$	0.282756	−	0.576194i	0.0326498	−	0.0665332i
$76$		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
$81$	−5.10240	−	7.41387i	−0.566933	−	0.823764i
$82$		0			0
$83$	−2.86539	−	9.75864i	−0.314518	−	1.07115i	−0.953366	−	0.301817i	$-0.902407\pi$
$83$	−2.86539	−	9.75864i	−0.314518	−	1.07115i	0.638848	−	0.769333i	$-0.279411\pi$
$84$		0			0
$85$	−11.8080	+	1.69774i	−1.28076	+	0.184146i
$86$		0			0
$87$	2.64465	+	4.37818i	0.283536	+	0.469390i
$88$		0			0
$89$	−1.51223	−	0.690613i	−0.160296	−	0.0732049i	0.333651	−	0.942697i	$-0.391719\pi$
$89$	−1.51223	−	0.690613i	−0.160296	−	0.0732049i	−0.493947	+	0.869492i	$0.664447\pi$
$90$		0			0
$91$	−1.16170	+	8.07977i	−0.121779	+	0.846990i
$92$		0			0
$93$	−0.0108477	+	0.390034i	−0.00112486	+	0.0404447i
$94$		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
$99$	−0.504893	+	2.51122i	−0.0507437	+	0.252387i
$100$		0			0
$101$	−1.06665	−	1.23098i	−0.106136	−	0.122487i	0.700196	−	0.713951i	$-0.253096\pi$
$101$	−1.06665	−	1.23098i	−0.106136	−	0.122487i	−0.806332	+	0.591463i	$0.798550\pi$
$102$		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	$0.200392\pi$
$107$	−1.96542	+	6.69362i	−0.190005	+	0.647097i	−0.998298	+	0.0583167i	$0.981427\pi$
$108$		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
$111$	1.72723	−	1.04334i	0.163942	−	0.0990292i
$112$		0			0
$113$	11.7027	+	3.43621i	1.10089	+	0.323251i	0.781207	−	0.624272i	$-0.214604\pi$
$113$	11.7027	+	3.43621i	1.10089	+	0.323251i	0.319686	+	0.947524i	$0.396423\pi$
$114$		0			0
$115$	−14.3119	+	12.4014i	−1.33460	+	1.15643i
$116$		0			0
$117$	9.13590	−	0.798579i	0.844614	−	0.0738287i
$118$		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
$123$	1.12141	+	2.64799i	0.101114	+	0.238761i
$124$		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
$129$	0.443382	−	0.187770i	0.0390376	−	0.0165322i
$130$		0			0
$131$	−8.34179	+	3.80957i	−0.728826	+	0.332844i	−0.745035	−	0.667025i	$-0.767567\pi$
$131$	−8.34179	+	3.80957i	−0.728826	+	0.332844i	0.0162095	+	0.999869i	$0.494840\pi$
$132$		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	$-0.859011\pi$
$137$	−7.44112	−	16.2938i	−0.635738	−	1.39207i	0.267762	−	0.963485i	$-0.413716\pi$
$138$		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
$141$	10.2064	−	14.9507i	0.859538	−	1.25907i
$142$		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
$147$	0.143195	+	0.174851i	0.0118106	+	0.0144215i
$148$		0			0
$149$	−12.0237	+	10.4186i	−0.985021	+	0.853526i	−0.989216	−	0.146465i	$-0.953210\pi$
$149$	−12.0237	+	10.4186i	−0.985021	+	0.853526i	0.00419440	+	0.999991i	$0.498665\pi$
$150$		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
$153$	9.05831	−	12.5074i	0.732321	−	1.01116i
$154$		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
$159$	5.19262	+	6.34053i	0.411801	+	0.502837i
$160$		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
$165$	1.50983	−	3.07670i	0.117540	−	0.239521i
$166$		0			0
$167$	−5.28474	+	4.57925i	−0.408945	+	0.354353i	−0.834910	−	0.550387i	$-0.814480\pi$
$167$	−5.28474	+	4.57925i	−0.408945	+	0.354353i	0.425964	+	0.904740i	$0.359935\pi$
$168$		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	−0.997769	−	0.0667654i	$-0.978732\pi$
$173$	−6.87305	+	10.6947i	−0.522549	+	0.813102i	0.475220	+	0.879867i	$0.342368\pi$
$174$		0			0
$175$	0.979441	+	0.140822i	0.0740388	+	0.0106452i
$176$		0			0
$177$	−0.508823	+	18.2950i	−0.0382455	+	1.37513i
$178$		0			0
$179$	9.73917	−	21.3258i	0.727940	−	1.59397i	−0.0744916	−	0.997222i	$-0.523733\pi$
$179$	9.73917	−	21.3258i	0.727940	−	1.59397i	0.802431	−	0.596744i	$-0.203539\pi$
$180$		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
$183$	−1.21289	−	4.60018i	−0.0896593	−	0.340055i
$184$		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
$189$	8.44800	−	11.0070i	0.614501	−	0.800643i
$190$		0			0
$191$	6.82175	−	14.9376i	0.493605	−	1.08084i	−0.484891	−	0.874575i	$-0.661141\pi$
$191$	6.82175	−	14.9376i	0.493605	−	1.08084i	0.978495	−	0.206269i	$-0.0661321\pi$
$192$		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
$195$	−12.0921	−	2.08322i	−0.865934	−	0.149183i
$196$		0			0
$197$	0.451957	+	3.14343i	0.0322006	+	0.223960i	0.999567	−	0.0294210i	$-0.00936636\pi$
$197$	0.451957	+	3.14343i	0.0322006	+	0.223960i	−0.967366	+	0.253381i	$0.918457\pi$
$198$		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
$201$	−12.8614	−	5.96525i	−0.907174	−	0.420757i
$202$		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
$207$	1.36258	−	24.4771i	0.0947059	−	1.70128i
$208$		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
$213$	−13.4959	+	11.0525i	−0.924721	+	0.757306i
$214$		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
$219$	−17.0011	+	4.48253i	−1.14883	+	0.302901i
$220$		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
$225$	−0.0968049	−	1.10747i	−0.00645366	−	0.0738311i
$226$		0			0
$227$	4.27145	+	0.614142i	0.283506	+	0.0407621i	0.282601	−	0.959238i	$-0.408803\pi$
$227$	4.27145	+	0.614142i	0.283506	+	0.0407621i	0.000905286		1.00000i	$0.499712\pi$
$228$		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	$-0.608047\pi$
$233$	9.12364	−	19.9780i	0.597710	−	1.30880i	0.930670	−	0.365860i	$-0.119225\pi$
$234$		0			0
$235$	−18.3047	+	15.8611i	−1.19406	+	1.03466i
$236$		0			0
$237$	13.1798	+	6.46770i	0.856117	+	0.420122i
$238$		0			0
$239$	−22.7021			−1.46848			−0.734239	−	0.678891i	$-0.762461\pi$
$239$	−22.7021			−1.46848			−0.734239	+	0.678891i	$0.762461\pi$
$240$		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
$243$	−14.2041	−	6.42211i	−0.911193	−	0.411979i
$244$		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
$249$	−12.9874	−	11.9017i	−0.823046	−	0.754241i
$250$		0			0
$251$	1.96791	−	13.6871i	0.124214	−	0.863924i	−0.828486	−	0.560010i	$-0.810797\pi$
$251$	1.96791	−	13.6871i	0.124214	−	0.863924i	0.952699	−	0.303914i	$-0.0982937\pi$
$252$		0			0
$253$	−5.27299	+	4.56908i	−0.331510	+	0.287255i
$254$		0			0
$255$	−15.9858	+	13.0917i	−1.00107	+	0.819832i
$256$		0			0
$257$	1.64284	+	5.59501i	0.102478	+	0.349007i	0.994730	−	0.102530i	$-0.0326939\pi$
$257$	1.64284	+	5.59501i	0.102478	+	0.349007i	−0.892252	+	0.451537i	$0.850876\pi$
$258$		0			0
$259$	2.35112	+	2.03726i	0.146091	+	0.126589i
$260$		0			0
$261$	7.84172	+	4.12253i	0.485390	+	0.255178i
$262$		0			0
$263$	5.40171	+	18.3965i	0.333084	+	1.13438i	0.940443	+	0.339951i	$0.110411\pi$
$263$	5.40171	+	18.3965i	0.333084	+	1.13438i	−0.607359	+	0.794427i	$0.707771\pi$
$264$		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	$-0.816676\pi$
$269$		−	17.8647i		−	1.08923i	0.838687	−	0.544614i	$-0.183324\pi$
$270$		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
$273$	5.51352	+	13.0191i	0.333693	+	0.787954i
$274$		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
$279$	0.333211	+	0.587965i	0.0199488	+	0.0352006i
$280$		0			0
$281$	−6.23786	+	4.00883i	−0.372120	+	0.239147i	−0.713312	−	0.700847i	$-0.752806\pi$
$281$	−6.23786	+	4.00883i	−0.372120	+	0.239147i	0.341192	+	0.939994i	$0.389169\pi$
$282$		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
$285$	−1.77115	−	0.0492596i	−0.104914	−	0.00291789i
$286$		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
$291$	−9.37824	−	15.5255i	−0.549762	−	0.910124i
$292$		0			0
$293$	−7.63596	−	11.8818i	−0.446098	−	0.694141i	0.543273	−	0.839556i	$-0.317185\pi$
$293$	−7.63596	−	11.8818i	−0.446098	−	0.694141i	−0.989371	+	0.145415i	$0.953548\pi$
$294$		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
$303$	−2.68379	−	0.869775i	−0.154179	−	0.0499673i
$304$		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
$309$	9.30960	+	0.258921i	0.529605	+	0.0147295i
$310$		0			0
$311$	3.43808	−	23.9124i	0.194956	−	1.35595i	−0.623700	−	0.781664i	$-0.714371\pi$
$311$	3.43808	−	23.9124i	0.194956	−	1.35595i	0.818656	−	0.574284i	$-0.194719\pi$
$312$		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
$315$	−14.6844	+	11.3587i	−0.827371	+	0.639993i
$316$		0			0
$317$	−15.0821	+	2.16848i	−0.847095	+	0.121794i	−0.552175	−	0.833728i	$-0.686202\pi$
$317$	−15.0821	+	2.16848i	−0.847095	+	0.121794i	−0.294920	+	0.955522i	$0.595293\pi$
$318$		0			0
$319$	−0.710371	−	2.41930i	−0.0397731	−	0.135455i
$320$		0			0
$321$	3.08058	+	11.6838i	0.171941	+	0.652129i
$322$		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
$327$	−2.33356	−	1.14515i	−0.129046	−	0.0633267i
$328$		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
$333$	1.62638	−	3.09363i	0.0891248	−	0.169530i
$334$		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
$339$	20.4272	−	5.38586i	1.10945	−	0.292520i
$340$		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
$345$	−10.1124	+	31.2028i	−0.544432	+	1.67990i
$346$		0			0
$347$	6.56322	−	4.21793i	0.352332	−	0.226430i	−0.352488	−	0.935816i	$-0.614664\pi$
$347$	6.56322	−	4.21793i	0.352332	−	0.226430i	0.704820	+	0.709386i	$0.251028\pi$
$348$		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
$351$	12.8294	−	9.36556i	0.684782	−	0.499897i
$352$		0			0
$353$	−1.80519	−	12.5554i	−0.0960806	−	0.668255i	−0.979762	−	0.200166i	$-0.935852\pi$
$353$	−1.80519	−	12.5554i	−0.0960806	−	0.668255i	0.883681	−	0.468089i	$-0.155057\pi$
$354$		0			0
$355$	21.2307	−	9.69571i	1.12681	−	0.514595i
$356$		0			0
$357$	22.6487	+	7.34013i	1.19870	+	0.388481i
$358$		0			0
$359$	2.24774	+	0.323176i	0.118631	+	0.0170566i	0.201375	−	0.979514i	$-0.435459\pi$
$359$	2.24774	+	0.323176i	0.118631	+	0.0170566i	−0.0827435	+	0.996571i	$0.526368\pi$
$360$		0			0
$361$	2.67625	−	18.6137i	0.140855	−	0.979670i
$362$		0			0
$363$	−7.83721	+	15.9705i	−0.411347	+	0.838235i
$364$		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
$369$	4.03395	+	2.92154i	0.209999	+	0.152089i
$370$		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
$375$	3.15487	−	18.3125i	0.162917	−	0.945653i
$376$		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
$381$	−1.04196	+	6.04809i	−0.0533813	+	0.309853i
$382$		0			0
$383$	10.0397	+	11.5864i	0.513003	+	0.592037i	0.951865	−	0.306517i	$-0.0991637\pi$
$383$	10.0397	+	11.5864i	0.513003	+	0.592037i	−0.438862	+	0.898554i	$0.644618\pi$
$384$		0			0
$385$	5.22992	+	0.751948i	0.266541	+	0.0383228i
$386$		0			0
$387$	0.489187	−	0.675450i	0.0248668	−	0.0343351i
$388$		0			0
$389$	−0.293311	−	0.456400i	−0.0148714	−	0.0231404i	0.833738	−	0.552160i	$-0.186196\pi$
$389$	−0.293311	−	0.456400i	−0.0148714	−	0.0231404i	−0.848610	+	0.529019i	$0.822560\pi$
$390$		0			0
$391$	40.3612	−	11.8511i	2.04115	−	0.599337i
$392$		0			0
$393$	−8.95560	+	13.1184i	−0.451750	+	0.661735i
$394$		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
$399$	1.05560	+	1.74753i	0.0528462	+	0.0874861i
$400$		0			0
$401$	−36.7151			−1.83346			−0.916732	−	0.399504i	$-0.869182\pi$
$401$	−36.7151			−1.83346			−0.916732	+	0.399504i	$0.869182\pi$
$402$		0			0
$403$	−0.688641			−0.0343036
$404$		0			0
$405$	16.1861	+	13.1539i	0.804293	+	0.653625i
$406$		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
$411$	−25.6238	−	17.4927i	−1.26393	−	0.862852i
$412$		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
$417$	29.6903	+	27.2082i	1.45394	+	1.33239i
$418$		0			0
$419$	−20.6344	−	2.96678i	−1.00806	−	0.144937i	−0.381547	−	0.924350i	$-0.624608\pi$
$419$	−20.6344	−	2.96678i	−1.00806	−	0.144937i	−0.626511	+	0.779413i	$0.715517\pi$
$420$		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
$423$	1.74271	−	31.3057i	0.0847334	−	1.52213i
$424$		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
$429$	−4.45513	−	0.767528i	−0.215096	−	0.0370566i
$430$		0			0
$431$			33.4433i			1.61091i	0.592657	+	0.805455i	$0.298079\pi$
$431$			33.4433i			1.61091i	−0.592657	+	0.805455i	$0.701921\pi$
$432$		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
$435$	−8.73908	−	8.00851i	−0.419007	−	0.383979i
$436$		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
$441$	0.368884	+	0.130990i	0.0175659	+	0.00623762i
$442$		0			0
$443$	−2.63553	+	18.3305i	−0.125218	+	0.870908i	0.826282	+	0.563257i	$0.190452\pi$
$443$	−2.63553	+	18.3305i	−0.125218	+	0.870908i	−0.951499	+	0.307651i	$0.900457\pi$
$444$		0			0
$445$	3.81346	+	0.548293i	0.180775	+	0.0259916i
$446$		0			0
$447$	−8.49559	+	26.2141i	−0.401828	+	1.23988i
$448$		0			0
$449$	−0.0867474	+	0.0396162i	−0.00409386	+	0.00186960i	−0.417461	−	0.908695i	$-0.637080\pi$
$449$	−0.0867474	+	0.0396162i	−0.00409386	+	0.00186960i	0.413367	+	0.910564i	$0.364353\pi$
$450$		0			0
$451$	−0.201741	−	1.40314i	−0.00949963	−	0.0660714i
$452$		0			0
$453$	3.18983	+	7.53219i	0.149871	+	0.353893i
$454$		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
$459$	2.22861	−	26.6551i	0.104023	−	1.24415i
$460$		0			0
$461$	8.20038	−	12.7600i	0.381930	−	0.594295i	−0.596062	−	0.802939i	$-0.703269\pi$
$461$	8.20038	−	12.7600i	0.381930	−	0.594295i	0.977992	+	0.208644i	$0.0669050\pi$
$462$		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
$465$	−0.230533	−	0.874352i	−0.0106907	−	0.0405471i
$466$		0			0
$467$	21.7502	+	18.8467i	1.00648	+	0.872119i	0.991803	−	0.127773i	$-0.0407830\pi$
$467$	21.7502	+	18.8467i	1.00648	+	0.872119i	0.0146757	+	0.999892i	$0.495328\pi$
$468$		0			0
$469$	2.63557	−	21.6978i	0.121699	−	1.00191i
$470$		0			0
$471$	−5.43303	−	3.70900i	−0.250341	−	0.170902i
$472$		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
$477$	13.3766	+	4.75002i	0.612474	+	0.217488i
$478$		0			0
$479$	−13.2034	−	6.02980i	−0.603279	−	0.275509i	0.0902702	−	0.995917i	$-0.471227\pi$
$479$	−13.2034	−	6.02980i	−0.603279	−	0.275509i	−0.693550	+	0.720409i	$0.743954\pi$
$480$		0			0
$481$	1.92543	+	2.99603i	0.0877922	+	0.136607i
$482$		0			0
$483$	36.5458	−	9.63570i	1.66289	−	0.438440i
$484$		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
$489$	−23.6417	+	14.2808i	−1.06912	+	0.645801i
$490$		0			0
$491$	13.3009	+	6.07431i	0.600261	+	0.274130i	0.692282	−	0.721627i	$-0.256605\pi$
$491$	13.3009	+	6.07431i	0.600261	+	0.274130i	−0.0920211	+	0.995757i	$0.529333\pi$
$492$		0			0
$493$	−2.16342	+	15.0469i	−0.0974356	+	0.677680i
$494$		0			0
$495$	−0.516909	−	5.91353i	−0.0232333	−	0.265793i
$496$		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
$501$	−3.73403	+	11.5218i	−0.166824	+	0.514754i
$502$		0			0
$503$	−25.6829	−	29.6397i	−1.14515	−	1.32157i	−0.939345	−	0.342974i	$-0.888566\pi$
$503$	−25.6829	−	29.6397i	−1.14515	−	1.32157i	−0.205801	−	0.978594i	$-0.565980\pi$
$504$		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	$-0.788211\pi$
$509$	4.71240	−	16.0490i	0.208873	−	0.711358i	0.995570	−	0.0940184i	$-0.0299713\pi$
$510$		0			0
$511$	−14.6548	−	22.8033i	−0.648289	−	1.00876i
$512$		0			0
$513$	1.64125	−	1.60228i	0.0724631	−	0.0707423i
$514$		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
$519$	−0.612166	+	22.0107i	−0.0268711	+	0.966162i
$520$		0			0
$521$	−12.8160	−	14.7905i	−0.561481	−	0.647983i	0.402038	−	0.915623i	$-0.368302\pi$
$521$	−12.8160	−	14.7905i	−0.561481	−	0.647983i	−0.963519	+	0.267639i	$0.913756\pi$
$522$		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
$525$	1.57820	−	0.668356i	0.0688782	−	0.0291695i
$526$		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
$531$	15.6296	+	27.5791i	0.678268	+	1.19683i
$532$		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
$543$	−24.8344	−	16.9538i	−1.06575	−	0.727558i
$544$		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
$549$	−5.91786	−	5.73386i	−0.252568	−	0.244715i
$550$		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
$555$	−3.15943	+	3.44765i	−0.134110	+	0.146345i
$556$		0			0
$557$	−2.56898	+	8.74915i	−0.108851	+	0.370713i	−0.995845	−	0.0910688i	$-0.970972\pi$
$557$	−2.56898	+	8.74915i	−0.108851	+	0.370713i	0.886993	+	0.461782i	$0.152790\pi$
$558$		0			0
$559$	0.353023	+	0.773014i	0.0149313	+	0.0326950i
$560$		0			0
$561$	−5.88969	+	4.82340i	−0.248663	+	0.203644i
$562$		0			0
$563$	−14.3375	−	4.20987i	−0.604253	−	0.177425i	−0.0347256	−	0.999397i	$-0.511056\pi$
$563$	−14.3375	−	4.20987i	−0.604253	−	0.177425i	−0.569528	+	0.821972i	$0.692874\pi$
$564$		0			0
$565$	−28.2652			−1.18913
$566$		0			0
$567$	2.66741	−	23.8842i	0.112021	−	1.00304i
$568$		0			0
$569$	−10.7257	+	9.29384i	−0.449643	+	0.389618i	−0.850035	−	0.526726i	$-0.823419\pi$
$569$	−10.7257	+	9.29384i	−0.449643	+	0.389618i	0.400392	+	0.916344i	$0.368874\pi$
$570$		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
$579$	−31.6835	−	0.881187i	−1.31672	−	0.0366209i
$580$		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
$585$	−19.7930	+	7.74053i	−0.818338	+	0.320032i
$586$		0			0
$587$	38.0598	−	11.1754i	1.57090	−	0.461257i	0.623634	−	0.781717i	$-0.285656\pi$
$587$	38.0598	−	11.1754i	1.57090	−	0.461257i	0.947262	+	0.320460i	$0.103837\pi$
$588$		0			0
$589$	−0.0984282	+	0.0141518i	−0.00405566	+	0.000583116i
$590$		0			0
$591$	3.48514	+	4.25559i	0.143360	+	0.175052i
$592$		0			0
$593$	−4.07433	+	8.92153i	−0.167313	+	0.366363i	−0.974653	−	0.223723i	$-0.928179\pi$
$593$	−4.07433	+	8.92153i	−0.167313	+	0.366363i	0.807340	+	0.590086i	$0.200906\pi$
$594$		0			0
$595$	−26.7983	−	17.2222i	−1.09862	−	0.706043i
$596$		0			0
$597$	−1.38052	+	8.01327i	−0.0565010	+	0.327961i
$598$		0			0
$599$	5.18426	+	36.0573i	0.211823	+	1.47326i	0.767063	+	0.641572i	$0.221718\pi$
$599$	5.18426	+	36.0573i	0.211823	+	1.47326i	−0.555239	+	0.831691i	$0.687373\pi$
$600$		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
$603$	−24.4100	+	2.67411i	−0.994053	+	0.108898i
$604$		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
$609$	−2.31890	+	13.4601i	−0.0939666	+	0.545431i
$610$		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
$615$	−4.22240	−	5.15583i	−0.170264	−	0.207903i
$616$		0			0
$617$	47.8677	−	6.88234i	1.92708	−	0.277073i	0.930965	−	0.365108i	$-0.118968\pi$
$617$	47.8677	−	6.88234i	1.92708	−	0.277073i	0.996117	+	0.0880352i	$0.0280588\pi$
$618$		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
$621$	−19.9003	−	37.5092i	−0.798571	−	1.50519i
$622$		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
$627$	−0.652550	−	0.0181489i	−0.0260603	−	0.000724796i
$628$		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
$639$	−10.1104	+	28.4722i	−0.399963	+	1.12634i
$640$		0			0
$641$	32.2874			1.27528			0.637639	−	0.770336i	$-0.279911\pi$
$641$	32.2874			1.27528			0.637639	+	0.770336i	$0.279911\pi$
$642$		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
$645$	−0.863299	+	0.707004i	−0.0339924	+	0.0278383i
$646$		0			0
$647$	10.4040	+	22.7815i	0.409023	+	0.895635i	0.996275	+	0.0862309i	$0.0274823\pi$
$647$	10.4040	+	22.7815i	0.409023	+	0.895635i	−0.587253	+	0.809404i	$0.699790\pi$
$648$		0			0
$649$	2.54182	−	8.65663i	0.0997750	−	0.339802i
$650$		0			0
$651$	−0.703933	+	0.768149i	−0.0275893	+	0.0301061i
$652$		0			0
$653$	−3.38879	+	23.5696i	−0.132614	+	0.922348i	0.809516	+	0.587098i	$0.199730\pi$
$653$	−3.38879	+	23.5696i	−0.132614	+	0.922348i	−0.942129	+	0.335250i	$0.891179\pi$
$654$		0			0
$655$	16.0613	−	13.9172i	0.627568	−	0.543791i
$656$		0			0
$657$	−21.1909	+	21.8709i	−0.826737	+	0.853266i
$658$		0			0
$659$	−5.05336	−	17.2102i	−0.196851	−	0.670413i	−0.997460	−	0.0712260i	$-0.977309\pi$
$659$	−5.05336	−	17.2102i	−0.196851	−	0.670413i	0.800609	−	0.599187i	$-0.204509\pi$
$660$		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
$663$	22.5103	+	15.3672i	0.874227	+	0.596813i
$664$		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
$675$	−1.13531	−	1.55520i	−0.0436980	−	0.0598595i
$676$		0			0
$677$	−17.5361	+	20.2377i	−0.673967	+	0.777800i	−0.984992	−	0.172602i	$-0.944782\pi$
$677$	−17.5361	+	20.2377i	−0.673967	+	0.777800i	0.311024	+	0.950402i	$0.399328\pi$
$678$		0			0
$679$	18.3123	−	21.1335i	0.702760	−	0.811028i
$680$		0			0
$681$	6.88270	−	2.91478i	0.263746	−	0.111695i
$682$		0			0
$683$	35.1796	−	22.6085i	1.34611	−	0.865092i	0.348715	−	0.937229i	$-0.386618\pi$
$683$	35.1796	−	22.6085i	1.34611	−	0.865092i	0.997395	+	0.0721370i	$0.0229819\pi$
$684$		0			0
$685$	27.1841	+	31.3721i	1.03865	+	1.19867i
$686$		0			0
$687$	−0.204504	+	7.35304i	−0.00780232	+	0.280536i
$688$		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
$693$	−5.41021	+	4.18494i	−0.205517	+	0.158973i
$694$		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	0.388192	−	0.921579i	$-0.373100\pi$
$701$	−7.64757	−	4.91479i	−0.288845	−	0.185629i	−0.677037	+	0.735949i	$0.736736\pi$
$702$		0			0
$703$	0.336774	+	0.388658i	0.0127017	+	0.0146585i
$704$		0			0
$705$	−12.9335	+	39.9077i	−0.487104	+	1.50301i
$706$		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
$711$	25.3320	−	2.21430i	0.950023	−	0.0830426i
$712$		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
$717$	−33.6574	+	20.3308i	−1.25696	+	0.759267i
$718$		0			0
$719$	−34.6967	+	4.98863i	−1.29397	+	0.186044i	−0.754689	−	0.656083i	$-0.772212\pi$
$719$	−34.6967	+	4.98863i	−1.29397	+	0.186044i	−0.539278	+	0.842128i	$0.681303\pi$
$720$		0			0
$721$	4.04515	+	13.7765i	0.150649	+	0.513065i
$722$		0			0
$723$	−27.8833	+	7.35175i	−1.03699	+	0.273414i
$724$		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
$729$	−26.8098	+	3.19923i	−0.992955	+	0.118490i
$730$		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
$735$	−0.432566	−	0.295302i	−0.0159554	−	0.0108924i
$736$		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
$741$	0.595865	+	2.25997i	0.0218897	+	0.0830220i
$742$		0			0
$743$	−3.18990	+	10.8638i	−0.117026	+	0.398554i	−0.997084	−	0.0763124i	$-0.975685\pi$
$743$	−3.18990	+	10.8638i	−0.117026	+	0.398554i	0.880058	+	0.474866i	$0.157504\pi$
$744$		0			0
$745$	19.9333	−	31.0169i	0.730300	−	1.13637i
$746$		0			0
$747$	−29.9133	−	6.01421i	−1.09447	−	0.220048i
$748$		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
$753$	−9.33990	−	22.0544i	−0.340365	−	0.803708i
$754$		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
$759$	−3.72574	+	11.4962i	−0.135236	+	0.417284i
$760$		0			0
$761$	−18.3174	−	2.63364i	−0.664004	−	0.0954693i	−0.197931	−	0.980216i	$-0.563422\pi$
$761$	−18.3174	−	2.63364i	−0.664004	−	0.0954693i	−0.466072	+	0.884747i	$0.654331\pi$
$762$		0			0
$763$	0.570323	−	3.96668i	0.0206471	−	0.143604i
$764$		0			0
$765$	−11.9758	+	33.7252i	−0.432985	+	1.21934i
$766$		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
$771$	7.44621	+	6.82372i	0.268169	+	0.245750i
$772$		0			0
$773$	17.7219	−	27.5759i	0.637413	−	0.991835i	−0.360832	−	0.932631i	$-0.617507\pi$
$773$	17.7219	−	27.5759i	0.637413	−	0.991835i	0.998246	−	0.0592040i	$-0.0188562\pi$
$774$		0			0
$775$			0.0834780i			0.00299862i
$776$		0			0
$777$	5.31014	+	0.914828i	0.190500	+	0.0328193i
$778$		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
$783$	15.3178	−	0.910709i	0.547412	−	0.0325461i
$784$		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
$789$	24.4833	+	22.4366i	0.871629	+	0.798763i
$790$		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
$795$	−15.6859	−	10.7084i	−0.556322	−	0.379787i
$796$		0			0
$797$	−38.5423	−	33.3971i	−1.36524	−	1.18299i	−0.963651	−	0.267165i	$-0.913913\pi$
$797$	−38.5423	−	33.3971i	−1.36524	−	1.18299i	−0.401588	−	0.915821i	$-0.631541\pi$
$798$		0			0
$799$	51.6210	−	15.1573i	1.82622	−	0.536227i
$800$		0			0
$801$	−3.94493	+	3.05150i	−0.139387	+	0.107820i
$802$		0			0
$803$	8.66720			0.305859
$804$		0			0
$805$	−50.5685			−1.78231
$806$		0			0
$807$	−15.9986	−	26.4855i	−0.563179	−	0.932335i
$808$		0			0
$809$	32.8857	−	9.65612i	1.15620	−	0.339491i	0.353245	−	0.935531i	$-0.385078\pi$
$809$	32.8857	−	9.65612i	1.15620	−	0.339491i	0.802955	+	0.596040i	$0.203260\pi$
$810$		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
$813$	4.17776	−	6.11969i	0.146520	−	0.214627i
$814$		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
$819$	19.8334	+	14.3641i	0.693034	+	0.501922i
$820$		0			0
$821$	−21.1471	−	3.04049i	−0.738037	−	0.106114i	−0.236964	−	0.971518i	$-0.576152\pi$
$821$	−21.1471	−	3.04049i	−0.738037	−	0.106114i	−0.501073	+	0.865405i	$0.667061\pi$
$822$		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
$825$	−0.0930407	+	0.540057i	−0.00323926	+	0.0188024i
$826$		0			0
$827$	−50.0100	+	22.8388i	−1.73902	+	0.794183i	−0.747493	+	0.664269i	$0.768743\pi$
$827$	−50.0100	+	22.8388i	−1.73902	+	0.794183i	−0.991525	+	0.129914i	$0.958530\pi$
$828$		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
$831$	7.43138	−	43.1356i	0.257792	−	1.49636i
$832$		0			0
$833$			0.671687i			0.0232726i
$834$		0			0
$835$	8.76122	−	13.6327i	0.303194	−	0.471780i
$836$		0			0
$837$	1.02056	+	0.573291i	0.0352756	+	0.0198158i
$838$		0			0
$839$	36.3792	+	16.6138i	1.25595	+	0.573573i	0.928513	−	0.371299i	$-0.121088\pi$
$839$	36.3792	+	16.6138i	1.25595	+	0.573573i	0.327438	+	0.944873i	$0.393815\pi$
$840$		0			0
$841$	20.2791			0.699281
$842$		0			0
$843$	−5.65794	+	11.5296i	−0.194870	+	0.397102i
$844$		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
$849$	33.0781	+	10.7201i	1.13524	+	0.367914i
$850$		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
$855$	−2.66996	+	1.51312i	−0.0913106	+	0.0517475i
$856$		0			0
$857$	3.57622	+	24.8731i	0.122161	+	0.849650i	0.955100	+	0.296284i	$0.0957476\pi$
$857$	3.57622	+	24.8731i	0.122161	+	0.849650i	−0.832939	+	0.553365i	$0.813343\pi$
$858$		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
$861$	−2.36738	+	7.30481i	−0.0806802	+	0.248947i
$862$		0			0
$863$	3.99182	−	6.21139i	0.135883	−	0.211438i	−0.766643	−	0.642074i	$-0.778074\pi$
$863$	3.99182	−	6.21139i	0.135883	−	0.211438i	0.902526	+	0.430636i	$0.141711\pi$
$864$		0			0
$865$	8.30019	−	28.2678i	0.282215	−	0.961136i
$866$		0			0
$867$	15.9084	−	4.19442i	0.540277	−	0.142450i
$868$		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
$873$	−27.8077	−	14.6190i	−0.941147	−	0.494777i
$874$		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
$879$	−21.9615	−	10.7772i	−0.740743	−	0.363505i
$880$		0			0
$881$	−17.1277	−	7.82197i	−0.577048	−	0.263529i	0.105440	−	0.994426i	$-0.466375\pi$
$881$	−17.1277	−	7.82197i	−0.577048	−	0.263529i	−0.682488	+	0.730897i	$0.739102\pi$
$882$		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
$885$	−10.8134	−	41.0124i	−0.363488	−	1.37862i
$886$		0			0
$887$	−1.40322	−	4.77894i	−0.0471156	−	0.160461i	0.932575	−	0.360976i	$-0.117557\pi$
$887$	−1.40322	−	4.77894i	−0.0471156	−	0.160461i	−0.979691	+	0.200515i	$0.935738\pi$
$888$		0			0
$889$	−9.36537	+	1.34654i	−0.314104	+	0.0451614i
$890$		0			0
$891$	5.96349	+	4.84635i	0.199784	+	0.162359i
$892$		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
$897$	43.2500	+	1.20288i	1.44408	+	0.0401630i
$898$		0			0
$899$	−0.559650	−	0.359665i	−0.0186654	−	0.0119955i
$900$		0			0
$901$			24.3570i			0.811450i
$902$		0			0
$903$	1.22313	+	0.396397i	0.0407031	+	0.0131913i
$904$		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	−0.970799	−	0.239895i	$-0.922887\pi$
$911$	−0.736874	+	2.50956i	−0.0244137	+	0.0831455i	0.946385	+	0.323041i	$0.104705\pi$
$912$		0			0
$913$	4.69488	+	7.30538i	0.155378	+	0.241773i
$914$		0			0
$915$	5.70041	+	9.43695i	0.188450	+	0.311976i
$916$		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
$921$	21.9730	+	0.611119i	0.724036	+	0.0201370i
$922$		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
$927$	14.0340	−	7.95331i	0.460936	−	0.261221i
$928$		0			0
$929$	17.4505	−	20.1390i	0.572534	−	0.660739i	−0.393449	−	0.919347i	$-0.628718\pi$
$929$	17.4505	−	20.1390i	0.572534	−	0.660739i	0.965983	+	0.258607i	$0.0832635\pi$
$930$		0			0
$931$	−0.0377188	+	0.0435298i	−0.00123618	+	0.00142663i
$932$		0			0
$933$	−16.3175	−	38.5306i	−0.534210	−	1.26144i
$934$		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	0.771796	−	0.635871i	$-0.219359\pi$
$941$	−6.57019	−	14.3867i	−0.214182	−	0.468993i	−0.985978	+	0.166877i	$0.946632\pi$
$942$		0			0
$943$	3.82230	+	13.0175i	0.124471	+	0.423910i
$944$		0			0
$945$	−11.5983	+	29.9906i	−0.377292	+	0.975595i
$946$		0			0
$947$	8.40576	+	7.28364i	0.273151	+	0.236686i	0.780654	−	0.624963i	$-0.214886\pi$
$947$	8.40576	+	7.28364i	0.273151	+	0.236686i	−0.507503	+	0.861650i	$0.669432\pi$
$948$		0			0
$949$	−8.74239	−	29.7739i	−0.283790	−	0.966500i
$950$		0			0
$951$	−20.4182	+	16.7216i	−0.662106	+	0.542236i
$952$		0			0
$953$	−35.5845	+	30.8341i	−1.15269	+	0.998815i	−0.152750	+	0.988265i	$0.548813\pi$
$953$	−35.5845	+	30.8341i	−1.15269	+	0.998815i	−0.999944	+	0.0105502i	$0.996642\pi$
$954$		0			0
$955$	−5.41594	+	37.6687i	−0.175256	+	1.21893i
$956$		0			0
$957$	−3.21977	−	2.95060i	−0.104080	−	0.0953793i
$958$		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
$963$	15.0306	+	14.5633i	0.484354	+	0.469295i
$964$		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
$969$	3.53322	+	1.73386i	0.113503	+	0.0556995i
$970$		0			0
$971$	7.10228	−	6.15416i	0.227923	−	0.197496i	−0.533411	−	0.845856i	$-0.679090\pi$
$971$	7.10228	−	6.15416i	0.227923	−	0.197496i	0.761334	+	0.648360i	$0.224545\pi$
$972$		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	−0.951762	−	0.306838i	$-0.900729\pi$
$977$	−8.66680	+	13.4858i	−0.277276	+	0.431449i	0.674486	+	0.738288i	$0.264365\pi$
$978$		0			0
$979$	1.40501	+	0.202009i	0.0449042	+	0.00645625i
$980$		0			0
$981$	−4.48518	+	0.392055i	−0.143201	+	0.0125173i
$982$		0			0
$983$	−18.1074	+	39.6497i	−0.577537	+	1.26463i	0.365149	+	0.930949i	$0.381018\pi$
$983$	−18.1074	+	39.6497i	−0.577537	+	1.26463i	−0.942686	+	0.333681i	$0.891709\pi$
$984$		0			0
$985$	−3.05731	−	6.69457i	−0.0974140	−	0.213307i
$986$		0			0
$987$	46.7412	−	12.3238i	1.48779	−	0.392272i
$988$		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
$993$	27.8248	−	22.7873i	0.882994	−	0.723133i
$994$		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
$999$	−0.359283	−	6.04300i	−0.0113672	−	0.191192i

Twists

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

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

\(f(q)\)	\(=\)	\(q+(1.48256 - 0.895546i) q^{3} +(-2.22357 + 0.652900i) q^{5} +(2.01808 + 1.74867i) q^{7} +(1.39599 - 2.65541i) q^{9} +O(q^{10})\)	\(q+(1.48256 - 0.895546i) q^{3} +(-2.22357 + 0.652900i) q^{5} +(2.01808 + 1.74867i) q^{7} +(1.39599 - 2.65541i) q^{9} +(-0.819238 + 0.240550i) q^{11} +(1.65269 + 2.57164i) q^{13} +(-2.71189 + 2.95928i) q^{15} +(5.09528 + 0.732591i) q^{17} +(0.289069 + 0.333603i) q^{19} +(4.55794 + 0.785240i) q^{21} +(7.43322 - 3.39464i) q^{23} +(0.311737 - 0.200341i) q^{25} +(-0.308390 - 5.18699i) q^{27} +2.95311i q^{29} +(-0.121792 + 0.189512i) q^{31} +(-0.999150 + 1.09030i) q^{33} +(-5.62905 - 2.57070i) q^{35} +1.16503 q^{37} +(4.75324 + 2.33256i) q^{39} +(-0.236280 + 1.64336i) q^{41} +(0.275166 + 0.0395630i) q^{43} +(-1.37038 + 6.81595i) q^{45} +(9.50691 - 4.34166i) q^{47} +(0.0185697 + 0.129155i) q^{49} +(8.21015 - 3.47695i) q^{51} +(0.673384 + 4.68349i) q^{53} +(1.66458 - 1.06976i) q^{55} +(0.727321 + 0.235714i) q^{57} +(-5.71278 + 8.88926i) q^{59} +(0.773829 - 2.63542i) q^{61} +(7.46066 - 2.91768i) q^{63} +(-5.35390 - 4.63918i) q^{65} +(-4.57523 - 6.78728i) q^{67} +(7.98017 - 11.6896i) q^{69} +(-9.96884 + 1.43330i) q^{71} +(-9.73985 - 2.85988i) q^{73} +(0.282756 - 0.576194i) q^{75} +(-2.07393 - 0.947131i) q^{77} +(4.58257 + 7.13062i) q^{79} +(-5.10240 - 7.41387i) q^{81} +(-2.86539 - 9.75864i) q^{83} +(-11.8080 + 1.69774i) q^{85} +(2.64465 + 4.37818i) q^{87} +(-1.51223 - 0.690613i) q^{89} +(-1.16170 + 8.07977i) q^{91} +(-0.0108477 + 0.390034i) q^{93} +(-0.860576 - 0.553059i) q^{95} -10.4721i q^{97} +(-0.504893 + 2.51122i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 200 q - 10 q^{9}+O(q^{10}) \) 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

Related objects

Downloads

Learn more