LMFDB - Embedded newform 464.2.y.e.33.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [464,2,Mod(33,464)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(464, base_ring=CyclotomicField(14))

chi = DirichletCharacter(H, H._module([0, 0, 1]))

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

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

chi := DirichletCharacter("464.33");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 464 = 2^{4} \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	464.y (of order $14$, degree $6$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$3.70505865379$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$8$ over $\Q(\zeta_{14})$
Twist minimal:	no (minimal twist has level 232)
Sato-Tate group:	$\mathrm{SU}(2)[C_{14}]$

Embedding invariants

Embedding label			33.7
Character	$\chi$	$=$	464.33
Dual form			464.2.y.e.225.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.19841 + 2.48852i) q^{3} +(-0.882074 + 3.86462i) q^{5} +(3.53526 - 1.70249i) q^{7} +(-2.88609 + 3.61904i) q^{9} +O(q^{10})$	\(q+(1.19841 + 2.48852i) q^{3} +(-0.882074 + 3.86462i) q^{5} +(3.53526 - 1.70249i) q^{7} +(-2.88609 + 3.61904i) q^{9} +(-0.271373 + 0.216412i) q^{11} +(0.821082 + 1.02960i) q^{13} +(-10.6743 + 2.43633i) q^{15} -2.99085i q^{17} +(3.67661 - 7.63456i) q^{19} +(8.47339 + 6.75730i) q^{21} +(0.478566 + 2.09674i) q^{23} +(-9.65238 - 4.64834i) q^{25} +(-4.38638 - 1.00116i) q^{27} +(-5.29395 + 0.986986i) q^{29} +(-6.53121 - 1.49071i) q^{31} +(-0.863762 - 0.415966i) q^{33} +(3.46112 + 15.1642i) q^{35} +(0.178638 + 0.142459i) q^{37} +(-1.57820 + 3.27717i) q^{39} -2.13590i q^{41} +(6.35224 - 1.44986i) q^{43} +(-11.4405 - 14.3459i) q^{45} +(2.52882 - 2.01667i) q^{47} +(5.23518 - 6.56471i) q^{49} +(7.44280 - 3.58426i) q^{51} +(-0.144112 + 0.631397i) q^{53} +(-0.596981 - 1.23964i) q^{55} +23.4049 q^{57} -2.65805 q^{59} +(4.89841 + 10.1717i) q^{61} +(-4.04169 + 17.7078i) q^{63} +(-4.70328 + 2.26498i) q^{65} +(-2.26842 + 2.84451i) q^{67} +(-4.64426 + 3.70367i) q^{69} +(3.89410 + 4.88305i) q^{71} +(11.7893 - 2.69082i) q^{73} -29.5908i q^{75} +(-0.590933 + 1.22708i) q^{77} +(-4.78218 - 3.81366i) q^{79} +(0.324838 + 1.42321i) q^{81} +(-4.94016 - 2.37906i) q^{83} +(11.5585 + 2.63815i) q^{85} +(-8.80045 - 11.9913i) q^{87} +(-10.2826 - 2.34694i) q^{89} +(4.65564 + 2.24204i) q^{91} +(-4.11741 - 18.0395i) q^{93} +(26.2616 + 20.9430i) q^{95} +(2.77758 - 5.76770i) q^{97} -1.60669i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 2 q^{5} + 4 q^{7} + 6 q^{9}+O(q^{10}) $ 48 * q - 2 * q^5 + 4 * q^7 + 6 * q^9	$ 48 q - 2 q^{5} + 4 q^{7} + 6 q^{9} + 10 q^{13} - 14 q^{15} + 14 q^{21} - 4 q^{23} - 48 q^{25} - 4 q^{29} + 10 q^{33} - 8 q^{35} - 38 q^{45} + 14 q^{47} - 18 q^{49} + 56 q^{51} - 48 q^{53} + 28 q^{55} - 12 q^{57} + 128 q^{59} - 28 q^{61} - 42 q^{63} - 28 q^{65} + 4 q^{67} + 28 q^{69} + 14 q^{71} - 28 q^{73} + 14 q^{77} - 32 q^{81} - 80 q^{83} + 112 q^{87} + 42 q^{89} + 28 q^{91} + 6 q^{93} + 70 q^{97}+O(q^{100}) $ 48 * q - 2 * q^5 + 4 * q^7 + 6 * q^9 + 10 * q^13 - 14 * q^15 + 14 * q^21 - 4 * q^23 - 48 * q^25 - 4 * q^29 + 10 * q^33 - 8 * q^35 - 38 * q^45 + 14 * q^47 - 18 * q^49 + 56 * q^51 - 48 * q^53 + 28 * q^55 - 12 * q^57 + 128 * q^59 - 28 * q^61 - 42 * q^63 - 28 * q^65 + 4 * q^67 + 28 * q^69 + 14 * q^71 - 28 * q^73 + 14 * q^77 - 32 * q^81 - 80 * q^83 + 112 * q^87 + 42 * q^89 + 28 * q^91 + 6 * q^93 + 70 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/464\mathbb{Z}\right)^\times$.

$n$	$117$	$175$	$321$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{14}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	1.19841	+	2.48852i	0.691902	+	1.43675i	0.889718	+	0.456510i	$0.150901\pi$
$3$	1.19841	+	2.48852i	0.691902	+	1.43675i	−0.197816	+	0.980239i	$0.563385\pi$
$4$		0			0
$5$	−0.882074	+	3.86462i	−0.394475	+	1.72831i	0.254116	+	0.967174i	$0.418215\pi$
$5$	−0.882074	+	3.86462i	−0.394475	+	1.72831i	−0.648592	+	0.761136i	$0.724642\pi$
$6$		0			0
$7$	3.53526	−	1.70249i	1.33620	−	0.643482i	0.377004	−	0.926211i	$-0.376954\pi$
$7$	3.53526	−	1.70249i	1.33620	−	0.643482i	0.959200	+	0.282729i	$0.0912399\pi$
$8$		0			0
$9$	−2.88609	+	3.61904i	−0.962030	+	1.20635i
$10$		0			0
$11$	−0.271373	+	0.216412i	−0.0818219	+	0.0652508i	−0.663547	−	0.748135i	$-0.730950\pi$
$11$	−0.271373	+	0.216412i	−0.0818219	+	0.0652508i	0.581725	+	0.813386i	$0.302378\pi$
$12$		0			0
$13$	0.821082	+	1.02960i	0.227727	+	0.285561i	0.882547	−	0.470224i	$-0.155827\pi$
$13$	0.821082	+	1.02960i	0.227727	+	0.285561i	−0.654820	+	0.755785i	$0.727256\pi$
$14$		0			0
$15$	−10.6743	+	2.43633i	−2.75609	+	0.629059i
$16$		0			0
$17$		−	2.99085i		−	0.725388i	−0.931908	−	0.362694i	$-0.881857\pi$
$17$		−	2.99085i		−	0.725388i	0.931908	−	0.362694i	$-0.118143\pi$
$18$		0			0
$19$	3.67661	−	7.63456i	0.843473	−	1.75149i	0.210037	−	0.977693i	$-0.432642\pi$
$19$	3.67661	−	7.63456i	0.843473	−	1.75149i	0.633435	−	0.773796i	$-0.281644\pi$
$20$		0			0
$21$	8.47339	+	6.75730i	1.84904	+	1.47456i
$22$		0			0
$23$	0.478566	+	2.09674i	0.0997880	+	0.437200i	0.999998	+	0.00174471i	$0.000555359\pi$
$23$	0.478566	+	2.09674i	0.0997880	+	0.437200i	−0.900210	+	0.435455i	$0.856587\pi$
$24$		0			0
$25$	−9.65238	−	4.64834i	−1.93048	−	0.929668i
$26$		0			0
$27$	−4.38638	−	1.00116i	−0.844159	−	0.192674i
$28$		0			0
$29$	−5.29395	+	0.986986i	−0.983061	+	0.183279i
$29$	−5.29395	+	0.986986i	−0.983061	+	0.183279i
$30$		0			0
$31$	−6.53121	−	1.49071i	−1.17304	−	0.267739i	−0.408772	−	0.912637i	$-0.634043\pi$
$31$	−6.53121	−	1.49071i	−1.17304	−	0.267739i	−0.764269	+	0.644898i	$0.776900\pi$
$32$		0			0
$33$	−0.863762	−	0.415966i	−0.150362	−	0.0724104i
$34$		0			0
$35$	3.46112	+	15.1642i	0.585037	+	2.56321i
$36$		0			0
$37$	0.178638	+	0.142459i	0.0293679	+	0.0234201i	0.638064	−	0.769984i	$-0.279736\pi$
$37$	0.178638	+	0.142459i	0.0293679	+	0.0234201i	−0.608696	+	0.793404i	$0.708307\pi$
$38$		0			0
$39$	−1.57820	+	3.27717i	−0.252714	+	0.524767i
$40$		0			0
$41$		−	2.13590i		−	0.333572i	−0.985993	−	0.166786i	$-0.946661\pi$
$41$		−	2.13590i		−	0.333572i	0.985993	−	0.166786i	$-0.0533389\pi$
$42$		0			0
$43$	6.35224	−	1.44986i	0.968708	−	0.221101i	0.291237	−	0.956651i	$-0.405933\pi$
$43$	6.35224	−	1.44986i	0.968708	−	0.221101i	0.677471	+	0.735550i	$0.263076\pi$
$44$		0			0
$45$	−11.4405	−	14.3459i	−1.70544	−	2.13856i
$46$		0			0
$47$	2.52882	−	2.01667i	0.368866	−	0.294161i	−0.421460	−	0.906847i	$-0.638482\pi$
$47$	2.52882	−	2.01667i	0.368866	−	0.294161i	0.790326	+	0.612686i	$0.209911\pi$
$48$		0			0
$49$	5.23518	−	6.56471i	0.747883	−	0.937815i
$50$		0			0
$51$	7.44280	−	3.58426i	1.04220	−	0.501897i
$52$		0			0
$53$	−0.144112	+	0.631397i	−0.0197953	+	0.0867290i	−0.983861	−	0.178936i	$-0.942734\pi$
$53$	−0.144112	+	0.631397i	−0.0197953	+	0.0867290i	0.964065	+	0.265665i	$0.0855916\pi$
$54$		0			0
$55$	−0.596981	−	1.23964i	−0.0804968	−	0.167153i
$56$		0			0
$57$	23.4049			3.10005
$58$		0			0
$59$	−2.65805			−0.346049			−0.173024	−	0.984918i	$-0.555354\pi$
$59$	−2.65805			−0.346049			−0.173024	+	0.984918i	$0.555354\pi$
$60$		0			0
$61$	4.89841	+	10.1717i	0.627178	+	1.30235i	0.936258	+	0.351312i	$0.114264\pi$
$61$	4.89841	+	10.1717i	0.627178	+	1.30235i	−0.309081	+	0.951036i	$0.600021\pi$
$62$		0			0
$63$	−4.04169	+	17.7078i	−0.509205	+	2.23097i
$64$		0			0
$65$	−4.70328	+	2.26498i	−0.583370	+	0.280936i
$66$		0			0
$67$	−2.26842	+	2.84451i	−0.277132	+	0.347512i	−0.900845	−	0.434141i	$-0.857052\pi$
$67$	−2.26842	+	2.84451i	−0.277132	+	0.347512i	0.623713	+	0.781653i	$0.285623\pi$
$68$		0			0
$69$	−4.64426	+	3.70367i	−0.559103	+	0.445870i
$70$		0			0
$71$	3.89410	+	4.88305i	0.462145	+	0.579512i	0.957228	−	0.289334i	$-0.0934338\pi$
$71$	3.89410	+	4.88305i	0.462145	+	0.579512i	−0.495083	+	0.868846i	$0.664862\pi$
$72$		0			0
$73$	11.7893	−	2.69082i	1.37983	−	0.314937i	0.532690	−	0.846310i	$-0.321181\pi$
$73$	11.7893	−	2.69082i	1.37983	−	0.314937i	0.847138	+	0.531374i	$0.178324\pi$
$74$		0			0
$75$		−	29.5908i		−	3.41685i
$76$		0			0
$77$	−0.590933	+	1.22708i	−0.0673431	+	0.139839i
$78$		0			0
$79$	−4.78218	−	3.81366i	−0.538037	−	0.429070i	0.316400	−	0.948626i	$-0.397526\pi$
$79$	−4.78218	−	3.81366i	−0.538037	−	0.429070i	−0.854436	+	0.519556i	$0.826097\pi$
$80$		0			0
$81$	0.324838	+	1.42321i	0.0360932	+	0.158134i
$82$		0			0
$83$	−4.94016	−	2.37906i	−0.542253	−	0.261135i	0.142645	−	0.989774i	$-0.454439\pi$
$83$	−4.94016	−	2.37906i	−0.542253	−	0.261135i	−0.684898	+	0.728639i	$0.740153\pi$
$84$		0			0
$85$	11.5585	+	2.63815i	1.25370	+	0.286148i
$86$		0			0
$87$	−8.80045	−	11.9913i	−0.943507	−	1.28560i
$88$		0			0
$89$	−10.2826	−	2.34694i	−1.08996	−	0.248776i	−0.360470	−	0.932771i	$-0.617384\pi$
$89$	−10.2826	−	2.34694i	−1.08996	−	0.248776i	−0.729487	+	0.683995i	$0.760241\pi$
$90$		0			0
$91$	4.65564	+	2.24204i	0.488043	+	0.235029i
$92$		0			0
$93$	−4.11741	−	18.0395i	−0.426955	−	1.87061i
$94$		0			0
$95$	26.2616	+	20.9430i	2.69439	+	2.14870i
$96$		0			0
$97$	2.77758	−	5.76770i	0.282020	−	0.585621i	−0.711050	−	0.703141i	$-0.751780\pi$
$97$	2.77758	−	5.76770i	0.282020	−	0.585621i	0.993070	+	0.117520i	$0.0374945\pi$
$98$		0			0
$99$		−	1.60669i		−	0.161479i
$100$		0			0
$101$	13.7536	−	3.13917i	1.36853	−	0.312359i	0.525762	−	0.850631i	$-0.323780\pi$
$101$	13.7536	−	3.13917i	1.36853	−	0.312359i	0.842771	+	0.538273i	$0.180923\pi$
$102$		0			0
$103$	1.19222	+	1.49500i	0.117473	+	0.147306i	0.837091	−	0.547064i	$-0.184254\pi$
$103$	1.19222	+	1.49500i	0.117473	+	0.147306i	−0.719618	+	0.694370i	$0.755683\pi$
$104$		0			0
$105$	−33.5885	+	26.7860i	−3.27791	+	2.61404i
$106$		0			0
$107$	6.93636	−	8.69792i	0.670563	−	0.840859i	−0.323884	−	0.946097i	$-0.604989\pi$
$107$	6.93636	−	8.69792i	0.670563	−	0.840859i	0.994447	+	0.105237i	$0.0335603\pi$
$108$		0			0
$109$	−13.5539	+	6.52720i	−1.29823	+	0.625192i	−0.950009	−	0.312222i	$-0.898927\pi$
$109$	−13.5539	+	6.52720i	−1.29823	+	0.625192i	−0.348216	+	0.937414i	$0.613213\pi$
$110$		0			0
$111$	−0.140431	+	0.615269i	−0.0133291	+	0.0583988i
$112$		0			0
$113$	−1.87579	−	3.89512i	−0.176460	−	0.366422i	0.793915	−	0.608029i	$-0.208040\pi$
$113$	−1.87579	−	3.89512i	−0.176460	−	0.366422i	−0.970374	+	0.241607i	$0.922325\pi$
$114$		0			0
$115$	−8.52522			−0.794981
$116$		0			0
$117$	−6.09590			−0.563566
$118$		0			0
$119$	−5.09191	−	10.5735i	−0.466774	−	0.969267i
$120$		0			0
$121$	−2.42092	+	10.6068i	−0.220084	+	0.964250i
$122$		0			0
$123$	5.31524	−	2.55968i	0.479259	−	0.230799i
$124$		0			0
$125$	14.1206	−	17.7067i	1.26298	−	1.58373i
$126$		0			0
$127$	1.28840	−	1.02747i	0.114327	−	0.0911728i	−0.564658	−	0.825325i	$-0.690992\pi$
$127$	1.28840	−	1.02747i	0.114327	−	0.0911728i	0.678985	+	0.734153i	$0.262420\pi$
$128$		0			0
$129$	11.2206	+	14.0702i	0.987918	+	1.23881i
$130$		0			0
$131$	−10.2944	+	2.34963i	−0.899424	+	0.205288i	−0.647145	−	0.762367i	$-0.724037\pi$
$131$	−10.2944	+	2.34963i	−0.899424	+	0.205288i	−0.252279	+	0.967655i	$0.581180\pi$
$132$		0			0
$133$		−	33.2496i		−	2.88311i
$134$		0			0
$135$	7.73822	−	16.0686i	0.666000	−	1.38296i
$136$		0			0
$137$	4.77234	+	3.80582i	0.407729	+	0.325153i	0.805785	−	0.592208i	$-0.201744\pi$
$137$	4.77234	+	3.80582i	0.407729	+	0.325153i	−0.398056	+	0.917361i	$0.630315\pi$
$138$		0			0
$139$	−2.03282	−	8.90636i	−0.172421	−	0.755427i	−0.984997	−	0.172572i	$-0.944792\pi$
$139$	−2.03282	−	8.90636i	−0.172421	−	0.755427i	0.812576	−	0.582856i	$-0.198065\pi$
$140$		0			0
$141$	8.04908	+	3.87623i	0.677854	+	0.326437i
$142$		0			0
$143$	−0.445638	−	0.101714i	−0.0372661	−	0.00850575i
$144$		0			0
$145$	0.855328	−	21.3297i	0.0710312	−	1.77133i
$146$		0			0
$147$	22.6103	+	5.16065i	1.86487	+	0.425644i
$148$		0			0
$149$	9.10581	+	4.38512i	0.745977	+	0.359243i	0.767945	−	0.640515i	$-0.221279\pi$
$149$	9.10581	+	4.38512i	0.745977	+	0.359243i	−0.0219688	+	0.999759i	$0.506993\pi$
$150$		0			0
$151$	−3.78171	−	16.5688i	−0.307751	−	1.34835i	−0.858130	−	0.513432i	$-0.828374\pi$
$151$	−3.78171	−	16.5688i	−0.307751	−	1.34835i	0.550379	−	0.834915i	$-0.314483\pi$
$152$		0			0
$153$	10.8240	+	8.63187i	0.875070	+	0.697845i
$154$		0			0
$155$	11.5220	−	23.9257i	0.925471	−	1.92176i
$156$		0			0
$157$			17.9470i			1.43233i	0.697932	+	0.716164i	$0.254104\pi$
$157$			17.9470i			1.43233i	−0.697932	+	0.716164i	$0.745896\pi$
$158$		0			0
$159$	−1.74395	+	0.398045i	−0.138304	+	0.0315670i
$160$		0			0
$161$	5.26154	+	6.59776i	0.414667	+	0.519976i
$162$		0			0
$163$	−7.04064	+	5.61473i	−0.551466	+	0.439779i	−0.859161	−	0.511706i	$-0.829014\pi$
$163$	−7.04064	+	5.61473i	−0.551466	+	0.439779i	0.307695	+	0.951485i	$0.400442\pi$
$164$		0			0
$165$	2.36945	−	2.97120i	0.184462	−	0.231308i
$166$		0			0
$167$	−2.05911	+	0.991615i	−0.159339	+	0.0767335i	−0.511853	−	0.859073i	$-0.671041\pi$
$167$	−2.05911	+	0.991615i	−0.159339	+	0.0767335i	0.352515	+	0.935806i	$0.385327\pi$
$168$		0			0
$169$	2.50686	−	10.9833i	0.192836	−	0.844868i
$170$		0			0
$171$	17.0188	+	35.3398i	1.30146	+	2.70251i
$172$		0			0
$173$	−13.0060			−0.988828			−0.494414	−	0.869227i	$-0.664617\pi$
$173$	−13.0060			−0.988828			−0.494414	+	0.869227i	$0.664617\pi$
$174$		0			0
$175$	−42.0375			−3.17773
$176$		0			0
$177$	−3.18543	−	6.61462i	−0.239432	−	0.497185i
$178$		0			0
$179$	1.77801	−	7.78997i	0.132895	−	0.582249i	−0.863999	−	0.503493i	$-0.832048\pi$
$179$	1.77801	−	7.78997i	0.132895	−	0.582249i	0.996894	−	0.0787563i	$-0.0250949\pi$
$180$		0			0
$181$	−18.6684	+	8.99023i	−1.38761	+	0.668239i	−0.970608	−	0.240666i	$-0.922634\pi$
$181$	−18.6684	+	8.99023i	−1.38761	+	0.668239i	−0.417004	+	0.908905i	$0.636920\pi$
$182$		0			0
$183$	−19.4421	+	24.3796i	−1.43720	+	1.80219i
$184$		0			0
$185$	−0.708122	+	0.564708i	−0.0520622	+	0.0415182i
$186$		0			0
$187$	0.647257	+	0.811635i	0.0473322	+	0.0593526i
$188$		0			0
$189$	−17.2115	+	3.92841i	−1.25195	+	0.285750i
$190$		0			0
$191$		−	0.829838i		−	0.0600450i	−0.999549	−	0.0300225i	$-0.990442\pi$
$191$		−	0.829838i		−	0.0600450i	0.999549	−	0.0300225i	$-0.00955789\pi$
$192$		0			0
$193$	−8.66005	+	17.9828i	−0.623364	+	1.29443i	0.315102	+	0.949058i	$0.397961\pi$
$193$	−8.66005	+	17.9828i	−0.623364	+	1.29443i	−0.938466	+	0.345371i	$0.887753\pi$
$194$		0			0
$195$	−11.2729	−	8.98985i	−0.807270	−	0.643776i
$196$		0			0
$197$	−5.00645	−	21.9347i	−0.356695	−	1.56278i	−0.761368	−	0.648320i	$-0.775472\pi$
$197$	−5.00645	−	21.9347i	−0.356695	−	1.56278i	0.404674	−	0.914461i	$-0.367385\pi$
$198$		0			0
$199$	2.01486	+	0.970308i	0.142830	+	0.0687833i	0.503934	−	0.863742i	$-0.331886\pi$
$199$	2.01486	+	0.970308i	0.142830	+	0.0687833i	−0.361104	+	0.932526i	$0.617600\pi$
$200$		0			0
$201$	−9.79712	−	2.23613i	−0.691036	−	0.157724i
$202$		0			0
$203$	−17.0352	+	12.5022i	−1.19563	+	0.877480i
$204$		0			0
$205$	8.25445	+	1.88402i	0.576516	+	0.131586i
$206$		0			0
$207$	−8.96936	−	4.31942i	−0.623414	−	0.300220i
$208$		0			0
$209$	0.654482	+	2.86748i	0.0452715	+	0.198347i
$210$		0			0
$211$	7.20631	+	5.74684i	0.496103	+	0.395629i	0.839329	−	0.543624i	$-0.182948\pi$
$211$	7.20631	+	5.74684i	0.496103	+	0.395629i	−0.343226	+	0.939253i	$0.611520\pi$
$212$		0			0
$213$	−7.48485	+	15.5425i	−0.512854	+	1.06495i
$214$		0			0
$215$			25.8279i			1.76145i
$216$		0			0
$217$	−25.6275	+	5.84930i	−1.73971	+	0.397077i
$218$		0			0
$219$	20.8245	+	26.1131i	1.40719	+	1.76456i
$220$		0			0
$221$	3.07939	−	2.45573i	0.207142	−	0.165191i
$222$		0			0
$223$	13.2886	−	16.6634i	0.889871	−	1.11586i	−0.102762	−	0.994706i	$-0.532768\pi$
$223$	13.2886	−	16.6634i	0.889871	−	1.11586i	0.992633	−	0.121157i	$-0.0386604\pi$
$224$		0			0
$225$	44.6802	−	21.5168i	2.97868	−	1.43446i
$226$		0			0
$227$	−4.53810	+	19.8827i	−0.301204	+	1.31966i	0.567108	+	0.823644i	$0.308062\pi$
$227$	−4.53810	+	19.8827i	−0.301204	+	1.31966i	−0.868312	+	0.496018i	$0.834795\pi$
$228$		0			0
$229$	4.39554	+	9.12742i	0.290465	+	0.603157i	0.994229	−	0.107277i	$-0.0342130\pi$
$229$	4.39554	+	9.12742i	0.290465	+	0.603157i	−0.703764	+	0.710434i	$0.748499\pi$
$230$		0			0
$231$	−3.76181			−0.247509
$232$		0			0
$233$	2.98711			0.195692			0.0978460	−	0.995202i	$-0.468805\pi$
$233$	2.98711			0.195692			0.0978460	+	0.995202i	$0.468805\pi$
$234$		0			0
$235$	5.56304	+	11.5518i	0.362893	+	0.753554i
$236$		0			0
$237$	3.75937	−	16.4709i	0.244197	−	1.06990i
$238$		0			0
$239$	17.9304	−	8.63484i	1.15982	−	0.558541i	0.247853	−	0.968798i	$-0.420275\pi$
$239$	17.9304	−	8.63484i	1.15982	−	0.558541i	0.911970	+	0.410257i	$0.134561\pi$
$240$		0			0
$241$	−4.02175	+	5.04312i	−0.259064	+	0.324856i	−0.894305	−	0.447458i	$-0.852329\pi$
$241$	−4.02175	+	5.04312i	−0.259064	+	0.324856i	0.635241	+	0.772314i	$0.280901\pi$
$242$		0			0
$243$	−13.7052	+	10.9295i	−0.879190	+	0.701130i
$244$		0			0
$245$	20.7523	+	26.0225i	1.32581	+	1.66252i
$246$		0			0
$247$	10.8794	−	2.48315i	0.692238	−	0.157999i
$248$		0			0
$249$		−	15.1448i		−	0.959761i
$250$		0			0
$251$	−8.20982	+	17.0479i	−0.518200	+	1.07605i	0.463585	+	0.886053i	$0.346563\pi$
$251$	−8.20982	+	17.0479i	−0.518200	+	1.07605i	−0.981784	+	0.190000i	$0.939151\pi$
$252$		0			0
$253$	−0.583629	−	0.465429i	−0.0366925	−	0.0292613i
$254$		0			0
$255$	7.28671	+	31.9252i	0.456312	+	1.99923i
$256$		0			0
$257$	−0.397722	−	0.191533i	−0.0248092	−	0.0119475i	0.421438	−	0.906857i	$-0.361526\pi$
$257$	−0.397722	−	0.191533i	−0.0248092	−	0.0119475i	−0.446247	+	0.894910i	$0.647240\pi$
$258$		0			0
$259$	0.874068	+	0.199500i	0.0543120	+	0.0123964i
$260$		0			0
$261$	11.7069	−	22.0075i	0.724636	−	1.36223i
$262$		0			0
$263$	−5.56407	−	1.26996i	−0.343095	−	0.0783092i	0.0475015	−	0.998871i	$-0.484874\pi$
$263$	−5.56407	−	1.26996i	−0.343095	−	0.0783092i	−0.390597	+	0.920562i	$0.627731\pi$
$264$		0			0
$265$	−2.31299	−	1.11388i	−0.142086	−	0.0684249i
$266$		0			0
$267$	−6.48238	−	28.4012i	−0.396715	−	1.73812i
$268$		0			0
$269$	2.97231	+	2.37034i	0.181225	+	0.144522i	0.709901	−	0.704302i	$-0.248740\pi$
$269$	2.97231	+	2.37034i	0.181225	+	0.144522i	−0.528676	+	0.848824i	$0.677311\pi$
$270$		0			0
$271$	1.56733	−	3.25459i	0.0952084	−	0.197702i	−0.847925	−	0.530115i	$-0.822149\pi$
$271$	1.56733	−	3.25459i	0.0952084	−	0.197702i	0.943134	+	0.332413i	$0.107863\pi$
$272$		0			0
$273$			14.2725i			0.863813i
$274$		0			0
$275$	3.62535	−	0.827462i	0.218617	−	0.0498978i
$276$		0			0
$277$	−12.7584	−	15.9985i	−0.766578	−	0.961258i	0.233361	−	0.972390i	$-0.425028\pi$
$277$	−12.7584	−	15.9985i	−0.766578	−	0.961258i	−0.999938	+	0.0111325i	$0.996456\pi$
$278$		0			0
$279$	24.2446	−	19.3344i	1.45149	−	1.15752i
$280$		0			0
$281$	7.40379	−	9.28406i	0.441673	−	0.553841i	−0.510310	−	0.859990i	$-0.670469\pi$
$281$	7.40379	−	9.28406i	0.441673	−	0.553841i	0.951983	+	0.306150i	$0.0990408\pi$
$282$		0			0
$283$	−14.3967	+	6.93309i	−0.855795	+	0.412129i	−0.809725	−	0.586809i	$-0.800384\pi$
$283$	−14.3967	+	6.93309i	−0.855795	+	0.412129i	−0.0460699	+	0.998938i	$0.514670\pi$
$284$		0			0
$285$	−20.6448	+	90.4509i	−1.22289	+	5.35785i
$286$		0			0
$287$	−3.63636	−	7.55098i	−0.214647	−	0.445720i
$288$		0			0
$289$	8.05480			0.473812
$290$		0			0
$291$	17.6817			1.03652
$292$		0			0
$293$	6.44302	+	13.3791i	0.376405	+	0.781614i	1.00000		0.000134140i	$-4.26980e-5\pi$
$293$	6.44302	+	13.3791i	0.376405	+	0.781614i	−0.623595	+	0.781748i	$0.714328\pi$
$294$		0			0
$295$	2.34460	−	10.2724i	0.136508	−	0.598080i
$296$		0			0
$297$	1.40701	−	0.677579i	0.0816428	−	0.0393171i
$298$		0			0
$299$	−1.76587	+	2.21433i	−0.102123	+	0.128058i
$300$		0			0
$301$	19.9885	−	15.9403i	1.15212	−	0.918783i
$302$		0			0
$303$	24.2943	+	30.4641i	1.39567	+	1.75012i
$304$		0			0
$305$	−43.6304	+	9.95834i	−2.49827	+	0.570213i
$306$		0			0
$307$		−	18.3492i		−	1.04725i	−0.851950	−	0.523623i	$-0.824580\pi$
$307$		−	18.3492i		−	1.04725i	0.851950	−	0.523623i	$-0.175420\pi$
$308$		0			0
$309$	−2.29157	+	4.75849i	−0.130363	+	0.270701i
$310$		0			0
$311$	17.6888	+	14.1064i	1.00304	+	0.799900i	0.979830	−	0.199831i	$-0.0640393\pi$
$311$	17.6888	+	14.1064i	1.00304	+	0.799900i	0.0232121	+	0.999731i	$0.492611\pi$
$312$		0			0
$313$	−1.78033	−	7.80015i	−0.100630	−	0.440891i	−0.999993	−	0.00368753i	$-0.998826\pi$
$313$	−1.78033	−	7.80015i	−0.100630	−	0.440891i	0.899363	−	0.437203i	$-0.144031\pi$
$314$		0			0
$315$	−64.8689	−	31.2392i	−3.65495	−	1.76013i
$316$		0			0
$317$	−32.4897	−	7.41556i	−1.82480	−	0.416500i	−0.833995	−	0.551772i	$-0.813952\pi$
$317$	−32.4897	−	7.41556i	−1.82480	−	0.416500i	−0.990808	+	0.135272i	$0.956809\pi$
$318$		0			0
$319$	1.22304	−	1.41352i	0.0684768	−	0.0791417i
$320$		0			0
$321$	29.9576	+	6.83762i	1.67207	+	0.381638i
$322$		0			0
$323$	−22.8339	−	10.9962i	−1.27051	−	0.611845i
$324$		0			0
$325$	−3.13944	−	13.7548i	−0.174145	−	0.762979i
$326$		0			0
$327$	−32.4862	−	25.9069i	−1.79649	−	1.43265i
$328$		0			0
$329$	5.50668	−	11.4347i	0.303593	−	0.630418i
$330$		0			0
$331$		−	22.8782i		−	1.25750i	−0.777609	−	0.628749i	$-0.783568\pi$
$331$		−	22.8782i		−	1.25750i	0.777609	−	0.628749i	$-0.216432\pi$
$332$		0			0
$333$	−1.03113	+	0.235349i	−0.0565056	+	0.0128970i
$334$		0			0
$335$	−8.99203	−	11.2756i	−0.491287	−	0.616055i
$336$		0			0
$337$	3.37596	−	2.69224i	0.183900	−	0.146656i	−0.527213	−	0.849733i	$-0.676763\pi$
$337$	3.37596	−	2.69224i	0.183900	−	0.146656i	0.711113	+	0.703078i	$0.248191\pi$
$338$		0			0
$339$	7.44513	−	9.33590i	0.404364	−	0.507056i
$340$		0			0
$341$	2.09500	−	1.00890i	0.113451	−	0.0546349i
$342$		0			0
$343$	1.21940	−	5.34255i	0.0658415	−	0.288471i
$344$		0			0
$345$	−10.2167	−	21.2152i	−0.550049	−	1.14219i
$346$		0			0
$347$	8.94927			0.480422			0.240211	−	0.970721i	$-0.422783\pi$
$347$	8.94927			0.480422			0.240211	+	0.970721i	$0.422783\pi$
$348$		0			0
$349$	−13.9992			−0.749361			−0.374680	−	0.927154i	$-0.622248\pi$
$349$	−13.9992			−0.749361			−0.374680	+	0.927154i	$0.622248\pi$
$350$		0			0
$351$	−2.57077	−	5.33827i	−0.137218	−	0.284936i
$352$		0			0
$353$	−6.89228	+	30.1970i	−0.366839	+	1.60723i	0.368568	+	0.929601i	$0.379848\pi$
$353$	−6.89228	+	30.1970i	−0.366839	+	1.60723i	−0.735407	+	0.677626i	$0.763009\pi$
$354$		0			0
$355$	−22.3060	+	10.7420i	−1.18388	+	0.570127i
$356$		0			0
$357$	20.2101	−	25.3426i	1.06963	−	1.34127i
$358$		0			0
$359$	−6.91612	+	5.51542i	−0.365019	+	0.291093i	−0.788773	−	0.614684i	$-0.789283\pi$
$359$	−6.91612	+	5.51542i	−0.365019	+	0.291093i	0.423754	+	0.905777i	$0.360712\pi$
$360$		0			0
$361$	−32.9228	−	41.2839i	−1.73278	−	2.17283i
$362$		0			0
$363$	−29.2964	+	6.68671i	−1.53766	+	0.350961i
$364$		0			0
$365$			47.9345i			2.50900i
$366$		0			0
$367$	−4.51615	+	9.37789i	−0.235741	+	0.489522i	−0.984956	−	0.172805i	$-0.944717\pi$
$367$	−4.51615	+	9.37789i	−0.235741	+	0.489522i	0.749215	+	0.662327i	$0.230431\pi$
$368$		0			0
$369$	7.72992	+	6.16440i	0.402403	+	0.320906i
$370$		0			0
$371$	0.565474	+	2.47750i	0.0293580	+	0.128626i
$372$		0			0
$373$	6.38622	+	3.07544i	0.330666	+	0.159240i	0.591849	−	0.806049i	$-0.298398\pi$
$373$	6.38622	+	3.07544i	0.330666	+	0.159240i	−0.261183	+	0.965289i	$0.584113\pi$
$374$		0			0
$375$	60.9857	+	13.9196i	3.14929	+	0.718804i
$376$		0			0
$377$	−5.36297	−	4.64027i	−0.276207	−	0.238986i
$378$		0			0
$379$	23.0164	+	5.25334i	1.18227	+	0.269846i	0.768087	−	0.640346i	$-0.221209\pi$
$379$	23.0164	+	5.25334i	1.18227	+	0.269846i	0.414186	+	0.910192i	$0.364066\pi$
$380$		0			0
$381$	4.10090	+	1.97489i	0.210096	+	0.101177i
$382$		0			0
$383$	−7.11367	−	31.1670i	−0.363492	−	1.59256i	−0.744260	−	0.667890i	$-0.767198\pi$
$383$	−7.11367	−	31.1670i	−0.363492	−	1.59256i	0.380768	−	0.924670i	$-0.375660\pi$
$384$		0			0
$385$	−4.22097	−	3.36611i	−0.215120	−	0.171553i
$386$		0			0
$387$	−13.0860	+	27.1735i	−0.665201	+	1.38130i
$388$		0			0
$389$			4.55010i			0.230699i	0.993325	+	0.115350i	$0.0367989\pi$
$389$			4.55010i			0.230699i	−0.993325	+	0.115350i	$0.963201\pi$
$390$		0			0
$391$	6.27103	−	1.43132i	0.317140	−	0.0723850i
$392$		0			0
$393$	−18.1840	−	22.8020i	−0.917260	−	1.15021i
$394$		0			0
$395$	18.9566	−	15.1174i	0.953808	−	0.760637i
$396$		0			0
$397$	3.11300	−	3.90358i	0.156237	−	0.195915i	−0.697552	−	0.716534i	$-0.745727\pi$
$397$	3.11300	−	3.90358i	0.156237	−	0.195915i	0.853789	+	0.520619i	$0.174299\pi$
$398$		0			0
$399$	82.7424	−	39.8466i	4.14230	−	1.99483i
$400$		0			0
$401$	5.43917	−	23.8306i	0.271619	−	1.19004i	−0.636482	−	0.771291i	$-0.719611\pi$
$401$	5.43917	−	23.8306i	0.271619	−	1.19004i	0.908102	−	0.418750i	$-0.137532\pi$
$402$		0			0
$403$	−3.82782	−	7.94856i	−0.190677	−	0.395946i
$404$		0			0
$405$	−5.78670			−0.287543
$406$		0			0
$407$	−0.0793074			−0.00393112
$408$		0			0
$409$	−0.246731	−	0.512342i	−0.0122001	−	0.0253337i	0.894780	−	0.446508i	$-0.147332\pi$
$409$	−0.246731	−	0.512342i	−0.0122001	−	0.0253337i	−0.906980	+	0.421174i	$0.861618\pi$
$410$		0			0
$411$	−3.75164	+	16.4370i	−0.185055	+	0.810778i
$412$		0			0
$413$	−9.39691	+	4.52531i	−0.462392	+	0.222676i
$414$		0			0
$415$	13.5517	−	16.9933i	0.665228	−	0.834170i
$416$		0			0
$417$	19.7275	−	15.7322i	0.966061	−	0.770408i
$418$		0			0
$419$	−21.6536	−	27.1527i	−1.05785	−	1.32650i	−0.942882	−	0.333127i	$-0.891896\pi$
$419$	−21.6536	−	27.1527i	−1.05785	−	1.32650i	−0.114964	−	0.993370i	$-0.536675\pi$
$420$		0			0
$421$	16.7516	−	3.82343i	0.816421	−	0.186343i	0.206134	−	0.978524i	$-0.433912\pi$
$421$	16.7516	−	3.82343i	0.816421	−	0.186343i	0.610286	+	0.792181i	$0.291054\pi$
$422$		0			0
$423$			14.9722i			0.727972i
$424$		0			0
$425$	−13.9025	+	28.8688i	−0.674370	+	1.40034i
$426$		0			0
$427$	34.6344	+	27.6200i	1.67607	+	1.33662i
$428$		0			0
$429$	−0.280939	−	1.23088i	−0.0135639	−	0.0594272i
$430$		0			0
$431$	−28.1363	−	13.5497i	−1.35528	−	0.652667i	−0.391698	−	0.920094i	$-0.628112\pi$
$431$	−28.1363	−	13.5497i	−1.35528	−	0.652667i	−0.963578	+	0.267427i	$0.913827\pi$
$432$		0			0
$433$	−5.42511	−	1.23825i	−0.260714	−	0.0595063i	0.0901658	−	0.995927i	$-0.471260\pi$
$433$	−5.42511	−	1.23825i	−0.260714	−	0.0595063i	−0.350880	+	0.936420i	$0.614117\pi$
$434$		0			0
$435$	54.1044	−	23.4332i	2.59411	−	1.12353i
$436$		0			0
$437$	17.7672	+	4.05524i	0.849919	+	0.193988i
$438$		0			0
$439$	−9.24934	−	4.45425i	−0.441447	−	0.212590i	0.199939	−	0.979808i	$-0.435926\pi$
$439$	−9.24934	−	4.45425i	−0.441447	−	0.212590i	−0.641385	+	0.767219i	$0.721640\pi$
$440$		0			0
$441$	8.64875	+	37.8927i	0.411845	+	1.80441i
$442$		0			0
$443$	6.65783	+	5.30944i	0.316323	+	0.252259i	0.768760	−	0.639537i	$-0.220874\pi$
$443$	6.65783	+	5.30944i	0.316323	+	0.252259i	−0.452437	+	0.891796i	$0.649445\pi$
$444$		0			0
$445$	18.1401	−	37.6683i	0.859923	−	1.78565i
$446$		0			0
$447$			27.9152i			1.32034i
$448$		0			0
$449$	15.2580	−	3.48254i	0.720069	−	0.164351i	0.153243	−	0.988189i	$-0.451028\pi$
$449$	15.2580	−	3.48254i	0.720069	−	0.164351i	0.566826	+	0.823838i	$0.308171\pi$
$450$		0			0
$451$	0.462236	+	0.579625i	0.0217658	+	0.0272935i
$452$		0			0
$453$	36.6997	−	29.2670i	1.72430	−	1.37508i
$454$		0			0
$455$	−12.7712	+	16.0146i	−0.598724	+	0.750777i
$456$		0			0
$457$	−7.81040	+	3.76129i	−0.365355	+	0.175946i	−0.607549	−	0.794282i	$-0.707847\pi$
$457$	−7.81040	+	3.76129i	−0.365355	+	0.175946i	0.242194	+	0.970228i	$0.422133\pi$
$458$		0			0
$459$	−2.99433	+	13.1190i	−0.139763	+	0.612343i
$460$		0			0
$461$	−9.23188	−	19.1702i	−0.429971	−	0.892845i	−0.997579	−	0.0695453i	$-0.977845\pi$
$461$	−9.23188	−	19.1702i	−0.429971	−	0.892845i	0.567607	−	0.823299i	$-0.307869\pi$
$462$		0			0
$463$	−13.7875			−0.640757			−0.320379	−	0.947290i	$-0.603810\pi$
$463$	−13.7875			−0.640757			−0.320379	+	0.947290i	$0.603810\pi$
$464$		0			0
$465$	73.3478			3.40142
$466$		0			0
$467$	−10.5053	−	21.8145i	−0.486128	−	1.00945i	−0.989385	−	0.145318i	$-0.953580\pi$
$467$	−10.5053	−	21.8145i	−0.486128	−	1.00945i	0.503257	−	0.864137i	$-0.332135\pi$
$468$		0			0
$469$	−3.17671	+	13.9181i	−0.146687	+	0.642677i
$470$		0			0
$471$	−44.6615	+	21.5079i	−2.05790	+	0.991030i
$472$		0			0
$473$	−1.41006	+	1.76816i	−0.0648345	+	0.0812999i
$474$		0			0
$475$	−70.9761	+	56.6015i	−3.25661	+	2.59706i
$476$		0			0
$477$	−1.86913	−	2.34382i	−0.0855816	−	0.107316i
$478$		0			0
$479$	−4.71733	+	1.07670i	−0.215540	+	0.0491956i	−0.328927	−	0.944355i	$-0.606687\pi$
$479$	−4.71733	+	1.07670i	−0.215540	+	0.0491956i	0.113387	+	0.993551i	$0.463830\pi$
$480$		0			0
$481$			0.300897i			0.0137197i
$482$		0			0
$483$	−10.1132	+	21.0003i	−0.460166	+	0.955545i
$484$		0			0
$485$	19.8399	+	15.8218i	0.900884	+	0.718431i
$486$		0			0
$487$	−2.72853	−	11.9545i	−0.123642	−	0.541710i	−0.998369	−	0.0570938i	$-0.981817\pi$
$487$	−2.72853	−	11.9545i	−0.123642	−	0.541710i	0.874727	−	0.484616i	$-0.161041\pi$
$488$		0			0
$489$	−22.4099	−	10.7921i	−1.01341	−	0.488034i
$490$		0			0
$491$	29.2181	+	6.66883i	1.31859	+	0.300960i	0.823221	−	0.567721i	$-0.192175\pi$
$491$	29.2181	+	6.66883i	1.31859	+	0.300960i	0.495372	+	0.868681i	$0.335032\pi$
$492$		0			0
$493$	2.95193	+	15.8334i	0.132948	+	0.713101i
$494$		0			0
$495$	6.20926	+	1.41722i	0.279085	+	0.0636994i
$496$		0			0
$497$	22.0800	+	10.6332i	0.990425	+	0.476964i
$498$		0			0
$499$	4.40767	+	19.3113i	0.197315	+	0.864492i	0.972527	+	0.232791i	$0.0747858\pi$
$499$	4.40767	+	19.3113i	0.197315	+	0.864492i	−0.775212	+	0.631701i	$0.782357\pi$
$500$		0			0
$501$	−4.93531	−	3.93578i	−0.220494	−	0.175838i
$502$		0			0
$503$	15.0797	−	31.3134i	0.672371	−	1.39619i	−0.233380	−	0.972386i	$-0.574979\pi$
$503$	15.0797	−	31.3134i	0.672371	−	1.39619i	0.905752	−	0.423808i	$-0.139307\pi$
$504$		0			0
$505$			55.9214i			2.48847i
$506$		0			0
$507$	30.3364	−	6.92408i	1.34729	−	0.307509i
$508$		0			0
$509$	17.9656	+	22.5282i	0.796312	+	0.998544i	0.999810	+	0.0194689i	$0.00619752\pi$
$509$	17.9656	+	22.5282i	0.796312	+	0.998544i	−0.203498	+	0.979075i	$0.565231\pi$
$510$		0			0
$511$	37.0970	−	29.5839i	1.64108	−	1.30871i
$512$		0			0
$513$	−23.7704	+	29.8072i	−1.04949	+	1.31602i
$514$		0			0
$515$	−6.82922	+	3.28878i	−0.300931	+	0.144921i
$516$		0			0
$517$	−0.249821	+	1.09454i	−0.0109871	+	0.0481376i
$518$		0			0
$519$	−15.5865	−	32.3657i	−0.684172	−	1.42070i
$520$		0			0
$521$	−29.3404			−1.28542			−0.642712	−	0.766108i	$-0.722191\pi$
$521$	−29.3404			−1.28542			−0.642712	+	0.766108i	$0.722191\pi$
$522$		0			0
$523$	0.574665			0.0251283			0.0125642	−	0.999921i	$-0.496001\pi$
$523$	0.574665			0.0251283			0.0125642	+	0.999921i	$0.496001\pi$
$524$		0			0
$525$	−50.3781	−	104.611i	−2.19868	−	4.56561i
$526$		0			0
$527$	−4.45848	+	19.5339i	−0.194215	+	0.850910i
$528$		0			0
$529$	16.5550	−	7.97247i	0.719783	−	0.346629i
$530$		0			0
$531$	7.67137	−	9.61960i	0.332909	−	0.417455i
$532$		0			0
$533$	2.19913	−	1.75375i	0.0952550	−	0.0759634i
$534$		0			0
$535$	27.4957	+	34.4786i	1.18874	+	1.49064i
$536$		0			0
$537$	21.5163	−	4.91095i	0.928496	−	0.211923i
$538$		0			0
$539$			2.91444i			0.125534i
$540$		0			0
$541$	14.6370	−	30.3941i	0.629294	−	1.30674i	−0.305716	−	0.952123i	$-0.598896\pi$
$541$	14.6370	−	30.3941i	0.629294	−	1.30674i	0.935010	−	0.354620i	$-0.115390\pi$
$542$		0			0
$543$	−44.7448	−	35.6828i	−1.92018	−	1.53129i
$544$		0			0
$545$	−13.2696	−	58.1380i	−0.568408	−	2.49036i
$546$		0			0
$547$	35.6448	+	17.1656i	1.52406	+	0.733949i	0.993514	−	0.113707i	$-0.0362726\pi$
$547$	35.6448	+	17.1656i	1.52406	+	0.733949i	0.530546	+	0.847656i	$0.321987\pi$
$548$		0			0
$549$	−50.9489	−	11.6288i	−2.17445	−	0.496303i
$550$		0			0
$551$	−11.9286	+	44.0457i	−0.508175	+	1.87641i
$552$		0			0
$553$	−23.3990	−	5.34067i	−0.995026	−	0.227108i
$554$		0			0
$555$	−2.25391	−	1.08543i	−0.0956731	−	0.0460738i
$556$		0			0
$557$	2.27888	+	9.98443i	0.0965593	+	0.423054i	0.999984	−	0.00569332i	$-0.00181225\pi$
$557$	2.27888	+	9.98443i	0.0965593	+	0.423054i	−0.903425	+	0.428747i	$0.858955\pi$
$558$		0			0
$559$	6.70849	+	5.34984i	0.283739	+	0.226274i
$560$		0			0
$561$	−1.24409	+	2.58339i	−0.0525256	+	0.109071i
$562$		0			0
$563$		−	35.0173i		−	1.47581i	−0.674907	−	0.737903i	$-0.735816\pi$
$563$		−	35.0173i		−	1.47581i	0.674907	−	0.737903i	$-0.264184\pi$
$564$		0			0
$565$	16.7077	−	3.81343i	0.702900	−	0.160432i
$566$		0			0
$567$	3.57140	+	4.47839i	0.149985	+	0.188075i
$568$		0			0
$569$	21.7619	−	17.3546i	0.912307	−	0.727541i	−0.0502166	−	0.998738i	$-0.515991\pi$
$569$	21.7619	−	17.3546i	0.912307	−	0.727541i	0.962524	+	0.271198i	$0.0874197\pi$
$570$		0			0
$571$	−7.40142	+	9.28108i	−0.309740	+	0.388401i	−0.912198	−	0.409749i	$-0.865616\pi$
$571$	−7.40142	+	9.28108i	−0.309740	+	0.388401i	0.602459	+	0.798150i	$0.294188\pi$
$572$		0			0
$573$	2.06507	−	0.994486i	0.0862696	−	0.0415452i
$574$		0			0
$575$	5.12704	−	22.4630i	0.213812	−	0.936773i
$576$		0			0
$577$	−0.699259	−	1.45203i	−0.0291106	−	0.0604487i	0.885906	−	0.463864i	$-0.153537\pi$
$577$	−0.699259	−	1.45203i	−0.0291106	−	0.0604487i	−0.915017	+	0.403415i	$0.867823\pi$
$578$		0			0
$579$	−55.1288			−2.29108
$580$		0			0
$581$	−21.5151			−0.892596
$582$		0			0
$583$	−0.0975340	−	0.202531i	−0.00403945	−	0.00838799i
$584$		0			0
$585$	5.37703	−	23.5583i	0.222313	−	0.974016i
$586$		0			0
$587$	−23.4422	+	11.2892i	−0.967563	+	0.465954i	−0.849810	−	0.527089i	$-0.823283\pi$
$587$	−23.4422	+	11.2892i	−0.967563	+	0.465954i	−0.117753	+	0.993043i	$0.537569\pi$
$588$		0			0
$589$	−35.3936	+	44.3822i	−1.45837	+	1.82874i
$590$		0			0
$591$	48.5852	−	38.7454i	1.99853	−	1.59377i
$592$		0			0
$593$	1.77984	+	2.23185i	0.0730892	+	0.0916509i	0.817032	−	0.576592i	$-0.195618\pi$
$593$	1.77984	+	2.23185i	0.0730892	+	0.0916509i	−0.743943	+	0.668243i	$0.767047\pi$
$594$		0			0
$595$	45.3538	−	10.3517i	1.85932	−	0.424379i
$596$		0			0
$597$			6.17686i			0.252802i
$598$		0			0
$599$	−11.9731	+	24.8624i	−0.489208	+	1.01585i	0.499544	+	0.866288i	$0.333501\pi$
$599$	−11.9731	+	24.8624i	−0.489208	+	1.01585i	−0.988752	+	0.149562i	$0.952214\pi$
$600$		0			0
$601$	13.9087	+	11.0918i	0.567349	+	0.452445i	0.864676	−	0.502330i	$-0.167524\pi$
$601$	13.9087	+	11.0918i	0.567349	+	0.452445i	−0.297327	+	0.954776i	$0.596095\pi$
$602$		0			0
$603$	−3.74753	−	16.4190i	−0.152611	−	0.668634i
$604$		0			0
$605$	−38.8556	−	18.7119i	−1.57971	−	0.760746i
$606$		0			0
$607$	−24.7550	−	5.65016i	−1.00477	−	0.229333i	−0.311685	−	0.950186i	$-0.600893\pi$
$607$	−24.7550	−	5.65016i	−1.00477	−	0.229333i	−0.693088	+	0.720853i	$0.743750\pi$
$608$		0			0
$609$	−51.5270	−	27.4097i	−2.08798	−	1.11070i
$610$		0			0
$611$	4.15273	+	0.947834i	0.168002	+	0.0383453i
$612$		0			0
$613$	1.62008	+	0.780188i	0.0654343	+	0.0315115i	0.466315	−	0.884619i	$-0.345581\pi$
$613$	1.62008	+	0.780188i	0.0654343	+	0.0315115i	−0.400880	+	0.916130i	$0.631296\pi$
$614$		0			0
$615$	5.20377	+	22.7992i	0.209836	+	0.919353i
$616$		0			0
$617$	33.5723	+	26.7730i	1.35157	+	1.07784i	0.989320	+	0.145761i	$0.0465630\pi$
$617$	33.5723	+	26.7730i	1.35157	+	1.07784i	0.362251	+	0.932081i	$0.382008\pi$
$618$		0			0
$619$	−18.2923	+	37.9843i	−0.735229	+	1.52672i	0.110953	+	0.993826i	$0.464610\pi$
$619$	−18.2923	+	37.9843i	−0.735229	+	1.52672i	−0.846182	+	0.532894i	$0.821104\pi$
$620$		0			0
$621$		−	9.67620i		−	0.388293i
$622$		0			0
$623$	−40.3475	+	9.20905i	−1.61649	+	0.368953i
$624$		0			0
$625$	22.5758	+	28.3092i	0.903033	+	1.13237i
$626$		0			0
$627$	−6.35144	+	5.06510i	−0.253652	+	0.202281i
$628$		0			0
$629$	0.426074	−	0.534280i	0.0169887	−	0.0213031i
$630$		0			0
$631$	11.1827	−	5.38533i	0.445178	−	0.214386i	−0.197845	−	0.980233i	$-0.563394\pi$
$631$	11.1827	−	5.38533i	0.445178	−	0.214386i	0.643023	+	0.765847i	$0.277680\pi$
$632$		0			0
$633$	−5.66503	+	24.8201i	−0.225165	+	0.986511i
$634$		0			0
$635$	2.83430	+	5.88548i	0.112476	+	0.233558i
$636$		0			0
$637$	11.0576			0.438116
$638$		0			0
$639$	−28.9107			−1.14369
$640$		0			0
$641$	−7.84481	−	16.2899i	−0.309851	−	0.643413i	0.686650	−	0.726988i	$-0.259080\pi$
$641$	−7.84481	−	16.2899i	−0.309851	−	0.643413i	−0.996501	+	0.0835749i	$0.973366\pi$
$642$		0			0
$643$	−3.70011	+	16.2113i	−0.145918	+	0.639309i	0.848076	+	0.529875i	$0.177761\pi$
$643$	−3.70011	+	16.2113i	−0.145918	+	0.639309i	−0.993994	+	0.109434i	$0.965096\pi$
$644$		0			0
$645$	−64.2733	+	30.9524i	−2.53076	+	1.21875i
$646$		0			0
$647$	7.28179	−	9.13107i	0.286277	−	0.358980i	−0.617811	−	0.786327i	$-0.711980\pi$
$647$	7.28179	−	9.13107i	0.286277	−	0.358980i	0.904088	+	0.427347i	$0.140552\pi$
$648$		0			0
$649$	0.721322	−	0.575235i	0.0283144	−	0.0225800i
$650$		0			0
$651$	−45.2683	−	56.7647i	−1.77421	−	2.22478i
$652$		0			0
$653$	−19.7738	+	4.51325i	−0.773810	+	0.176617i	−0.591153	−	0.806560i	$-0.701327\pi$
$653$	−19.7738	+	4.51325i	−0.773810	+	0.176617i	−0.182657	+	0.983177i	$0.558470\pi$
$654$		0			0
$655$		−	41.8564i		−	1.63546i
$656$		0			0
$657$	−24.2866	+	50.4317i	−0.947512	+	1.96753i
$658$		0			0
$659$	−25.9989	−	20.7334i	−1.01277	−	0.807659i	−0.0313479	−	0.999509i	$-0.509980\pi$
$659$	−25.9989	−	20.7334i	−1.01277	−	0.807659i	−0.981424	+	0.191850i	$0.938551\pi$
$660$		0			0
$661$	−3.06435	−	13.4258i	−0.119190	−	0.522204i	−0.998909	−	0.0467096i	$-0.985126\pi$
$661$	−3.06435	−	13.4258i	−0.119190	−	0.522204i	0.879719	−	0.475494i	$-0.157731\pi$
$662$		0			0
$663$	9.80152	+	4.72016i	0.380660	+	0.183316i
$664$		0			0
$665$	128.497	+	29.3286i	4.98290	+	1.13731i
$666$		0			0
$667$	−4.60295	−	10.6277i	−0.178227	−	0.411505i
$668$		0			0
$669$	57.3924	+	13.0994i	2.21892	+	0.506454i
$670$		0			0
$671$	−3.53057	−	1.70023i	−0.136296	−	0.0656367i
$672$		0			0
$673$	8.01804	+	35.1293i	0.309073	+	1.35414i	0.856009	+	0.516962i	$0.172937\pi$
$673$	8.01804	+	35.1293i	0.309073	+	1.35414i	−0.546936	+	0.837175i	$0.684206\pi$
$674$		0			0
$675$	37.6852	+	30.0530i	1.45051	+	1.15674i
$676$		0			0
$677$	−1.67144	+	3.47077i	−0.0642385	+	0.133393i	−0.930616	−	0.365997i	$-0.880728\pi$
$677$	−1.67144	+	3.47077i	−0.0642385	+	0.133393i	0.866378	+	0.499390i	$0.166442\pi$
$678$		0			0
$679$		−	25.1191i		−	0.963984i
$680$		0			0
$681$	−54.9171	+	12.5345i	−2.10443	+	0.480322i
$682$		0			0
$683$	19.6677	+	24.6625i	0.752562	+	0.943683i	0.999680	−	0.0253021i	$-0.00805475\pi$
$683$	19.6677	+	24.6625i	0.752562	+	0.943683i	−0.247117	+	0.968986i	$0.579483\pi$
$684$		0			0
$685$	−18.9176	+	15.0863i	−0.722804	+	0.576417i
$686$		0			0
$687$	−17.4461	+	21.8768i	−0.665612	+	0.834651i
$688$		0			0
$689$	−0.768417	+	0.370050i	−0.0292743	+	0.0140978i
$690$		0			0
$691$	3.73670	−	16.3716i	0.142151	−	0.622804i	−0.852782	−	0.522266i	$-0.825087\pi$
$691$	3.73670	−	16.3716i	0.142151	−	0.622804i	0.994933	−	0.100537i	$-0.0320562\pi$
$692$		0			0
$693$	−2.73539	−	5.68009i	−0.103909	−	0.215769i
$694$		0			0
$695$	36.2128			1.37363
$696$		0			0
$697$	−6.38817			−0.241969
$698$		0			0
$699$	3.57978	+	7.43349i	0.135400	+	0.281160i
$700$		0			0
$701$	9.69740	−	42.4871i	0.366266	−	1.60471i	−0.370679	−	0.928761i	$-0.620875\pi$
$701$	9.69740	−	42.4871i	0.366266	−	1.60471i	0.736944	−	0.675953i	$-0.236268\pi$
$702$		0			0
$703$	1.74440	−	0.840057i	0.0657911	−	0.0316833i
$704$		0			0
$705$	−22.0800	+	27.6875i	−0.831582	+	1.04277i
$706$		0			0
$707$	43.2782	−	34.5132i	1.62764	−	1.29800i
$708$		0			0
$709$	31.3087	+	39.2598i	1.17582	+	1.47443i	0.848241	+	0.529611i	$0.177662\pi$
$709$	31.3087	+	39.2598i	1.17582	+	1.47443i	0.327581	+	0.944823i	$0.393766\pi$
$710$		0			0
$711$	27.6036	−	6.30034i	1.03521	−	0.236281i
$712$		0			0
$713$		−	14.4076i		−	0.539570i
$714$		0			0
$715$	0.786172	−	1.63250i	0.0294011	−	0.0610521i
$716$		0			0
$717$	42.9760	+	34.2722i	1.60497	+	1.27992i
$718$		0			0
$719$	9.51002	+	41.6661i	0.354664	+	1.55388i	0.766268	+	0.642521i	$0.222112\pi$
$719$	9.51002	+	41.6661i	0.354664	+	1.55388i	−0.411604	+	0.911363i	$0.635031\pi$
$720$		0			0
$721$	6.76004	+	3.25546i	0.251757	+	0.121240i
$722$		0			0
$723$	−17.3696	−	3.96450i	−0.645983	−	0.147441i
$724$		0			0
$725$	55.6870	+	15.0813i	2.06816	+	0.560105i
$726$		0			0
$727$	−10.5722	−	2.41303i	−0.392101	−	0.0894945i	0.0219248	−	0.999760i	$-0.493021\pi$
$727$	−10.5722	−	2.41303i	−0.392101	−	0.0894945i	−0.414026	+	0.910265i	$0.635878\pi$
$728$		0			0
$729$	−39.6771	−	19.1075i	−1.46952	−	0.707685i
$730$		0			0
$731$	−4.33631	−	18.9986i	−0.160384	−	0.702689i
$732$		0			0
$733$	9.93437	+	7.92239i	0.366934	+	0.292620i	0.789547	−	0.613690i	$-0.210316\pi$
$733$	9.93437	+	7.92239i	0.366934	+	0.292620i	−0.422613	+	0.906310i	$0.638887\pi$
$734$		0			0
$735$	−39.8879	+	82.8281i	−1.47129	+	3.05516i
$736$		0			0
$737$		−	1.26284i		−	0.0465172i
$738$		0			0
$739$	−6.42228	+	1.46584i	−0.236247	+	0.0539219i	−0.339005	−	0.940784i	$-0.610090\pi$
$739$	−6.42228	+	1.46584i	−0.236247	+	0.0539219i	0.102758	+	0.994706i	$0.467233\pi$
$740$		0			0
$741$	19.2173	+	24.0977i	0.705966	+	0.885253i
$742$		0			0
$743$	−16.2740	+	12.9781i	−0.597034	+	0.476119i	−0.874770	−	0.484539i	$-0.838987\pi$
$743$	−16.2740	+	12.9781i	−0.597034	+	0.476119i	0.277736	+	0.960657i	$0.410416\pi$
$744$		0			0
$745$	−24.9788	+	31.3225i	−0.915153	+	1.14757i
$746$		0			0
$747$	22.8676	−	11.0125i	0.836683	−	0.402925i
$748$		0			0
$749$	9.71371	−	42.5585i	0.354931	−	1.55505i
$750$		0			0
$751$	0.0310632	+	0.0645034i	0.00113351	+	0.00235376i	0.901535	−	0.432706i	$-0.142441\pi$
$751$	0.0310632	+	0.0645034i	0.00113351	+	0.00235376i	−0.900401	+	0.435060i	$0.856727\pi$
$752$		0			0
$753$	−52.2628			−1.90456
$754$		0			0
$755$	67.3677			2.45176
$756$		0			0
$757$	−2.88553	−	5.99186i	−0.104876	−	0.217778i	0.841927	−	0.539592i	$-0.181422\pi$
$757$	−2.88553	−	5.99186i	−0.104876	−	0.217778i	−0.946803	+	0.321814i	$0.895707\pi$
$758$		0			0
$759$	0.458803	−	2.01015i	0.0166535	−	0.0729638i
$760$		0			0
$761$	−14.2490	+	6.86198i	−0.516527	+	0.248747i	−0.673940	−	0.738786i	$-0.735399\pi$
$761$	−14.2490	+	6.86198i	−0.516527	+	0.248747i	0.157412	+	0.987533i	$0.449685\pi$
$762$		0			0
$763$	−36.8040	+	46.1508i	−1.33239	+	1.67077i
$764$		0			0
$765$	−42.9065	+	34.2168i	−1.55129	+	1.23711i
$766$		0			0
$767$	−2.18248	−	2.73674i	−0.0788047	−	0.0988180i
$768$		0			0
$769$	35.0399	−	7.99763i	1.26357	−	0.288402i	0.462311	−	0.886718i	$-0.347020\pi$
$769$	35.0399	−	7.99763i	1.26357	−	0.288402i	0.801260	+	0.598316i	$0.204163\pi$
$770$		0			0
$771$		−	1.21927i		−	0.0439111i
$772$		0			0
$773$	8.20735	−	17.0427i	0.295198	−	0.612984i	−0.699636	−	0.714499i	$-0.746655\pi$
$773$	8.20735	−	17.0427i	0.295198	−	0.612984i	0.994834	+	0.101515i	$0.0323689\pi$
$774$		0			0
$775$	56.1124	+	44.7482i	2.01562	+	1.60740i
$776$		0			0
$777$	0.551030	+	2.41422i	0.0197681	+	0.0866097i
$778$		0			0
$779$	−16.3067	−	7.85288i	−0.584247	−	0.281359i
$780$		0			0
$781$	−2.11351	−	0.482394i	−0.0756272	−	0.0172614i
$782$		0			0
$783$	24.2094	+	0.970806i	0.865173	+	0.0346938i
$784$		0			0
$785$	−69.3584	−	15.8306i	−2.47551	−	0.565018i
$786$		0			0
$787$	−5.51936	−	2.65798i	−0.196744	−	0.0947469i	0.332918	−	0.942956i	$-0.391967\pi$
$787$	−5.51936	−	2.65798i	−0.196744	−	0.0947469i	−0.529662	+	0.848209i	$0.677681\pi$
$788$		0			0
$789$	−3.50770	−	15.3682i	−0.124877	−	0.547124i
$790$		0			0
$791$	−13.2628	−	10.5768i	−0.471572	−	0.376066i
$792$		0			0
$793$	−6.45078	+	13.3952i	−0.229074	+	0.475677i
$794$		0			0
$795$		−	7.09081i		−	0.251485i
$796$		0			0
$797$	−43.7973	+	9.99645i	−1.55138	+	0.354093i	−0.910487	−	0.413537i	$-0.864293\pi$
$797$	−43.7973	+	9.99645i	−1.55138	+	0.354093i	−0.640893	+	0.767630i	$0.721436\pi$
$798$		0			0
$799$	−6.03155	−	7.56332i	−0.213381	−	0.267571i
$800$		0			0
$801$	38.1703	−	30.4398i	1.34868	−	1.07554i
$802$		0			0
$803$	−2.61695	+	3.28155i	−0.0923503	+	0.115804i
$804$		0			0
$805$	−30.1389	+	14.5141i	−1.06226	+	0.511556i
$806$		0			0
$807$	−2.33660	+	10.2373i	−0.0822520	+	0.360370i
$808$		0			0
$809$	20.9328	+	43.4673i	0.735957	+	1.52823i	0.845339	+	0.534230i	$0.179398\pi$
$809$	20.9328	+	43.4673i	0.735957	+	1.52823i	−0.109383	+	0.994000i	$0.534887\pi$
$810$		0			0
$811$	−22.7846			−0.800076			−0.400038	−	0.916498i	$-0.631003\pi$
$811$	−22.7846			−0.800076			−0.400038	+	0.916498i	$0.631003\pi$
$812$		0			0
$813$	9.97742			0.349923
$814$		0			0
$815$	−15.4884	−	32.1620i	−0.542535	−	1.12659i
$816$		0			0
$817$	12.2857	−	53.8272i	0.429822	−	1.88317i
$818$		0			0
$819$	−21.5506	+	10.3782i	−0.753039	+	0.362644i
$820$		0			0
$821$	5.74122	−	7.19926i	0.200370	−	0.251256i	−0.671487	−	0.741016i	$-0.734344\pi$
$821$	5.74122	−	7.19926i	0.200370	−	0.251256i	0.871857	+	0.489760i	$0.162916\pi$
$822$		0			0
$823$	−16.8041	+	13.4008i	−0.585753	+	0.467122i	−0.870967	−	0.491342i	$-0.836507\pi$
$823$	−16.8041	+	13.4008i	−0.585753	+	0.467122i	0.285214	+	0.958464i	$0.407935\pi$
$824$		0			0
$825$	6.40381	+	8.03012i	0.222952	+	0.279573i
$826$		0			0
$827$	32.0586	−	7.31716i	1.11479	−	0.254443i	0.374827	−	0.927095i	$-0.377702\pi$
$827$	32.0586	−	7.31716i	1.11479	−	0.254443i	0.739959	+	0.672652i	$0.234845\pi$
$828$		0			0
$829$		−	2.56419i		−	0.0890579i	−0.999008	−	0.0445290i	$-0.985821\pi$
$829$		−	2.56419i		−	0.0890579i	0.999008	−	0.0445290i	$-0.0141787\pi$
$830$		0			0
$831$	24.5229	−	50.9223i	0.850690	−	1.76648i
$832$		0			0
$833$	−19.6341	−	15.6576i	−0.680280	−	0.542505i
$834$		0			0
$835$	−2.01593	−	8.83235i	−0.0697640	−	0.305656i
$836$		0			0
$837$	27.1559	+	13.0776i	0.938646	+	0.452028i
$838$		0			0
$839$	−4.17819	−	0.953645i	−0.144247	−	0.0329235i	0.149788	−	0.988718i	$-0.452141\pi$
$839$	−4.17819	−	0.953645i	−0.144247	−	0.0329235i	−0.294035	+	0.955795i	$0.594998\pi$
$840$		0			0
$841$	27.0517	−	10.4501i	0.932818	−	0.360348i
$842$		0			0
$843$	31.9764	+	7.29840i	1.10132	+	0.251370i
$844$		0			0
$845$	40.2350	+	19.3761i	1.38412	+	0.666559i
$846$		0			0
$847$	9.49933	+	41.6193i	0.326401	+	1.43005i
$848$		0			0
$849$	−34.5063	−	27.5178i	−1.18425	−	0.944410i
$850$		0			0
$851$	−0.213209	+	0.442733i	−0.00730871	+	0.0151767i
$852$		0			0
$853$		−	36.8402i		−	1.26138i	−0.776033	−	0.630692i	$-0.782771\pi$
$853$		−	36.8402i		−	1.26138i	0.776033	−	0.630692i	$-0.217229\pi$
$854$		0			0
$855$	−151.587	+	34.5987i	−5.18416	+	1.18325i
$856$		0			0
$857$	−19.6464	−	24.6358i	−0.671109	−	0.841544i	0.323392	−	0.946265i	$-0.395177\pi$
$857$	−19.6464	−	24.6358i	−0.671109	−	0.841544i	−0.994502	+	0.104721i	$0.966605\pi$
$858$		0			0
$859$	−2.83907	+	2.26408i	−0.0968677	+	0.0772494i	−0.670726	−	0.741705i	$-0.734017\pi$
$859$	−2.83907	+	2.26408i	−0.0968677	+	0.0772494i	0.573858	+	0.818955i	$0.305446\pi$
$860$		0			0
$861$	14.4329	−	18.0983i	0.491873	−	0.616789i
$862$		0			0
$863$	−2.80299	+	1.34985i	−0.0954150	+	0.0459494i	−0.480983	−	0.876730i	$-0.659720\pi$
$863$	−2.80299	+	1.34985i	−0.0954150	+	0.0459494i	0.385568	+	0.922680i	$0.374006\pi$
$864$		0			0
$865$	11.4723	−	50.2632i	0.390068	−	1.70900i
$866$		0			0
$867$	9.65295	+	20.0446i	0.327831	+	0.680749i
$868$		0			0
$869$	2.12307			0.0720204
$870$		0			0
$871$	−4.79128			−0.162346
$872$		0			0
$873$	12.8572	+	26.6982i	0.435150	+	0.903599i
$874$		0			0
$875$	19.7745	−	86.6379i	0.668502	−	2.92890i
$876$		0			0
$877$	3.75498	−	1.80830i	0.126797	−	0.0610620i	−0.369410	−	0.929267i	$-0.620440\pi$
$877$	3.75498	−	1.80830i	0.126797	−	0.0610620i	0.496207	+	0.868205i	$0.334726\pi$
$878$		0			0
$879$	−25.5727	+	32.0672i	−0.862547	+	1.08160i
$880$		0			0
$881$	−1.34671	+	1.07397i	−0.0453719	+	0.0361829i	−0.645913	−	0.763411i	$-0.723523\pi$
$881$	−1.34671	+	1.07397i	−0.0453719	+	0.0361829i	0.600541	+	0.799594i	$0.294952\pi$
$882$		0			0
$883$	27.1802	+	34.0829i	0.914688	+	1.14698i	0.988727	+	0.149727i	$0.0478393\pi$
$883$	27.1802	+	34.0829i	0.914688	+	1.14698i	−0.0740399	+	0.997255i	$0.523589\pi$
$884$		0			0
$885$	28.3728	−	6.47590i	0.953740	−	0.217685i
$886$		0			0
$887$		−	20.8160i		−	0.698934i	−0.936949	−	0.349467i	$-0.886363\pi$
$887$		−	20.8160i		−	0.698934i	0.936949	−	0.349467i	$-0.113637\pi$
$888$		0			0
$889$	2.80558	−	5.82585i	0.0940962	−	0.195393i
$890$		0			0
$891$	−0.396153	−	0.315921i	−0.0132716	−	0.0105838i
$892$		0			0
$893$	−6.09888	−	26.7209i	−0.204091	−	0.894181i
$894$		0			0
$895$	28.5369	+	13.7427i	0.953884	+	0.459366i
$896$		0			0
$897$	−7.62663	−	1.74073i	−0.254646	−	0.0581212i
$898$		0			0
$899$	36.0472	+	1.44551i	1.20224	+	0.0482103i
$900$		0			0
$901$	1.88841	+	0.431018i	0.0629122	+	0.0143593i
$902$		0			0
$903$	63.6221	+	30.6388i	2.11721	+	1.01960i
$904$		0			0
$905$	−18.2769	−	80.0763i	−0.607545	−	2.66183i
$906$		0			0
$907$	7.29710	+	5.81924i	0.242296	+	0.193225i	0.737107	−	0.675776i	$-0.236191\pi$
$907$	7.29710	+	5.81924i	0.242296	+	0.193225i	−0.494811	+	0.869001i	$0.664763\pi$
$908$		0			0
$909$	−28.3333	+	58.8347i	−0.939757	+	1.95142i
$910$		0			0
$911$			31.8278i			1.05450i	0.849710	+	0.527251i	$0.176777\pi$
$911$			31.8278i			1.05450i	−0.849710	+	0.527251i	$0.823223\pi$
$912$		0			0
$913$	1.85548	−	0.423501i	0.0614074	−	0.0140158i
$914$		0			0
$915$	−77.0686	−	96.6409i	−2.54781	−	3.19485i
$916$		0			0
$917$	−32.3931	+	25.8327i	−1.06972	+	0.853070i
$918$		0			0
$919$	−19.0786	+	23.9238i	−0.629346	+	0.789175i	−0.989626	−	0.143670i	$-0.954110\pi$
$919$	−19.0786	+	23.9238i	−0.629346	+	0.789175i	0.360280	+	0.932844i	$0.382681\pi$
$920$		0			0
$921$	45.6624	−	21.9899i	1.50463	−	0.724591i
$922$		0			0
$923$	−1.83023	+	8.01877i	−0.0602428	+	0.263941i
$924$		0			0
$925$	−1.06208	−	2.20544i	−0.0349211	−	0.0725144i
$926$		0			0
$927$	−8.85131			−0.290715
$928$		0			0
$929$	13.2904			0.436044			0.218022	−	0.975944i	$-0.430040\pi$
$929$	13.2904			0.436044			0.218022	+	0.975944i	$0.430040\pi$
$930$		0			0
$931$	−30.8709	−	64.1042i	−1.01175	−	2.10093i
$932$		0			0
$933$	−13.9056	+	60.9243i	−0.455248	+	1.99457i
$934$		0			0
$935$	−3.70759	+	1.78548i	−0.121251	+	0.0583915i
$936$		0			0
$937$	−34.5906	+	43.3752i	−1.13003	+	1.41701i	−0.234433	+	0.972132i	$0.575323\pi$
$937$	−34.5906	+	43.3752i	−1.13003	+	1.41701i	−0.895593	+	0.444875i	$0.853248\pi$
$938$		0			0
$939$	17.2773	−	13.7782i	0.563823	−	0.449634i
$940$		0			0
$941$	24.7463	+	31.0309i	0.806707	+	1.01158i	0.999539	+	0.0303470i	$0.00966124\pi$
$941$	24.7463	+	31.0309i	0.806707	+	1.01158i	−0.192832	+	0.981232i	$0.561767\pi$
$942$		0			0
$943$	4.47842	−	1.02217i	0.145838	−	0.0332865i
$944$		0			0
$945$		−	69.9809i		−	2.27648i
$946$		0			0
$947$	−20.3311	+	42.2181i	−0.660674	+	1.37190i	0.253800	+	0.967257i	$0.418320\pi$
$947$	−20.3311	+	42.2181i	−0.660674	+	1.37190i	−0.914473	+	0.404646i	$0.867395\pi$
$948$		0			0
$949$	12.4504	+	9.92888i	0.404158	+	0.322305i
$950$		0			0
$951$	−20.4822	−	89.7382i	−0.664180	−	2.90996i
$952$		0			0
$953$	16.7715	+	8.07673i	0.543283	+	0.261631i	0.685335	−	0.728228i	$-0.259656\pi$
$953$	16.7715	+	8.07673i	0.543283	+	0.261631i	−0.142052	+	0.989859i	$0.545370\pi$
$954$		0			0
$955$	3.20701	+	0.731979i	0.103776	+	0.0236863i
$956$		0			0
$957$	4.98326	+	1.34958i	0.161086	+	0.0436257i
$958$		0			0
$959$	23.3509	+	5.32968i	0.754039	+	0.172104i
$960$		0			0
$961$	12.5045	+	6.02185i	0.403371	+	0.194253i
$962$		0			0
$963$	11.4592	+	50.2059i	0.369267	+	1.61786i
$964$		0			0
$965$	−61.8578	−	49.3299i	−1.99127	−	1.58799i
$966$		0			0
$967$	10.4391	−	21.6771i	0.335700	−	0.697089i	−0.662970	−	0.748646i	$-0.730704\pi$
$967$	10.4391	−	21.6771i	0.335700	−	0.697089i	0.998670	+	0.0515574i	$0.0164185\pi$
$968$		0			0
$969$		−	70.0005i		−	2.24874i
$970$		0			0
$971$	−7.73249	+	1.76489i	−0.248147	+	0.0566380i	−0.344785	−	0.938682i	$-0.612048\pi$
$971$	−7.73249	+	1.76489i	−0.248147	+	0.0566380i	0.0966379	+	0.995320i	$0.469191\pi$
$972$		0			0
$973$	−22.3496	−	28.0255i	−0.716494	−	0.898455i
$974$		0			0
$975$	30.4668	−	24.2964i	0.975718	−	0.778109i
$976$		0			0
$977$	−16.4895	+	20.6772i	−0.527547	+	0.661523i	−0.972192	−	0.234183i	$-0.924758\pi$
$977$	−16.4895	+	20.6772i	−0.527547	+	0.661523i	0.444645	+	0.895707i	$0.353330\pi$
$978$		0			0
$979$	3.29833	−	1.58839i	0.105415	−	0.0507653i
$980$		0			0
$981$	15.4955	−	67.8901i	0.494732	−	2.16756i
$982$		0			0
$983$	−1.09637	−	2.27663i	−0.0349686	−	0.0726131i	0.882753	−	0.469838i	$-0.155688\pi$
$983$	−1.09637	−	2.27663i	−0.0349686	−	0.0726131i	−0.917721	+	0.397225i	$0.869973\pi$
$984$		0			0
$985$	89.1852			2.84168
$986$		0			0
$987$	35.0549			1.11581
$988$		0			0
$989$	6.07994	+	12.6251i	0.193331	+	0.401456i
$990$		0			0
$991$	−2.95857	+	12.9624i	−0.0939822	+	0.411763i	−0.999932	−	0.0116213i	$-0.996301\pi$
$991$	−2.95857	+	12.9624i	−0.0939822	+	0.411763i	0.905950	+	0.423384i	$0.139158\pi$
$992$		0			0
$993$	56.9328	−	27.4174i	1.80671	−	0.870065i
$994$		0			0
$995$	−5.52713	+	6.93080i	−0.175222	+	0.219721i
$996$		0			0
$997$	−13.1125	+	10.4569i	−0.415277	+	0.331172i	−0.808738	−	0.588169i	$-0.799849\pi$
$997$	−13.1125	+	10.4569i	−0.415277	+	0.331172i	0.393461	+	0.919341i	$0.371278\pi$
$998$		0			0
$999$	−0.640949	−	0.803725i	−0.0202787	−	0.0254287i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	464.2.y.e.33.7		48
4.3	odd	2		232.2.q.a.33.2	✓	48
29.22	even	14	inner	464.2.y.e.225.7		48
116.15	even	28		6728.2.a.bf.1.3		24
116.43	even	28		6728.2.a.be.1.22		24
116.51	odd	14		232.2.q.a.225.2	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
232.2.q.a.33.2	✓	48	4.3	odd	2
232.2.q.a.225.2	yes	48	116.51	odd	14
464.2.y.e.33.7		48	1.1	even	1	trivial
464.2.y.e.225.7		48	29.22	even	14	inner
6728.2.a.be.1.22		24	116.43	even	28
6728.2.a.bf.1.3		24	116.15	even	28

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:	\( N \)	\(=\)	\( 464 = 2^{4} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	464.y (of order \(14\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.19841 + 2.48852i) q^{3} +(-0.882074 + 3.86462i) q^{5} +(3.53526 - 1.70249i) q^{7} +(-2.88609 + 3.61904i) q^{9} +O(q^{10})\)	\(q+(1.19841 + 2.48852i) q^{3} +(-0.882074 + 3.86462i) q^{5} +(3.53526 - 1.70249i) q^{7} +(-2.88609 + 3.61904i) q^{9} +(-0.271373 + 0.216412i) q^{11} +(0.821082 + 1.02960i) q^{13} +(-10.6743 + 2.43633i) q^{15} -2.99085i q^{17} +(3.67661 - 7.63456i) q^{19} +(8.47339 + 6.75730i) q^{21} +(0.478566 + 2.09674i) q^{23} +(-9.65238 - 4.64834i) q^{25} +(-4.38638 - 1.00116i) q^{27} +(-5.29395 + 0.986986i) q^{29} +(-6.53121 - 1.49071i) q^{31} +(-0.863762 - 0.415966i) q^{33} +(3.46112 + 15.1642i) q^{35} +(0.178638 + 0.142459i) q^{37} +(-1.57820 + 3.27717i) q^{39} -2.13590i q^{41} +(6.35224 - 1.44986i) q^{43} +(-11.4405 - 14.3459i) q^{45} +(2.52882 - 2.01667i) q^{47} +(5.23518 - 6.56471i) q^{49} +(7.44280 - 3.58426i) q^{51} +(-0.144112 + 0.631397i) q^{53} +(-0.596981 - 1.23964i) q^{55} +23.4049 q^{57} -2.65805 q^{59} +(4.89841 + 10.1717i) q^{61} +(-4.04169 + 17.7078i) q^{63} +(-4.70328 + 2.26498i) q^{65} +(-2.26842 + 2.84451i) q^{67} +(-4.64426 + 3.70367i) q^{69} +(3.89410 + 4.88305i) q^{71} +(11.7893 - 2.69082i) q^{73} -29.5908i q^{75} +(-0.590933 + 1.22708i) q^{77} +(-4.78218 - 3.81366i) q^{79} +(0.324838 + 1.42321i) q^{81} +(-4.94016 - 2.37906i) q^{83} +(11.5585 + 2.63815i) q^{85} +(-8.80045 - 11.9913i) q^{87} +(-10.2826 - 2.34694i) q^{89} +(4.65564 + 2.24204i) q^{91} +(-4.11741 - 18.0395i) q^{93} +(26.2616 + 20.9430i) q^{95} +(2.77758 - 5.76770i) q^{97} -1.60669i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 2 q^{5} + 4 q^{7} + 6 q^{9}+O(q^{10}) \) 48 * q - 2 * q^5 + 4 * q^7 + 6 * q^9	\( 48 q - 2 q^{5} + 4 q^{7} + 6 q^{9} + 10 q^{13} - 14 q^{15} + 14 q^{21} - 4 q^{23} - 48 q^{25} - 4 q^{29} + 10 q^{33} - 8 q^{35} - 38 q^{45} + 14 q^{47} - 18 q^{49} + 56 q^{51} - 48 q^{53} + 28 q^{55} - 12 q^{57} + 128 q^{59} - 28 q^{61} - 42 q^{63} - 28 q^{65} + 4 q^{67} + 28 q^{69} + 14 q^{71} - 28 q^{73} + 14 q^{77} - 32 q^{81} - 80 q^{83} + 112 q^{87} + 42 q^{89} + 28 q^{91} + 6 q^{93} + 70 q^{97}+O(q^{100}) \) 48 * q - 2 * q^5 + 4 * q^7 + 6 * q^9 + 10 * q^13 - 14 * q^15 + 14 * q^21 - 4 * q^23 - 48 * q^25 - 4 * q^29 + 10 * q^33 - 8 * q^35 - 38 * q^45 + 14 * q^47 - 18 * q^49 + 56 * q^51 - 48 * q^53 + 28 * q^55 - 12 * q^57 + 128 * q^59 - 28 * q^61 - 42 * q^63 - 28 * q^65 + 4 * q^67 + 28 * q^69 + 14 * q^71 - 28 * q^73 + 14 * q^77 - 32 * q^81 - 80 * q^83 + 112 * q^87 + 42 * q^89 + 28 * q^91 + 6 * q^93 + 70 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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