LMFDB - Embedded newform 1232.2.be.c.1167.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1232,2,Mod(815,1232)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1232, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 0, 1, 0]))

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

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

chi := DirichletCharacter("1232.815");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1232 = 2^{4} \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1232.be (of order $6$, degree $2$, 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:	$9.83756952902$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$14$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			1167.11
Character	$\chi$	$=$	1232.1167
Dual form			1232.2.be.c.815.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.949508 + 1.64460i) q^{3} +(-0.525125 - 0.303181i) q^{5} +(0.0911016 - 2.64418i) q^{7} +(-0.303130 + 0.525037i) q^{9} +O(q^{10})$	\(q+(0.949508 + 1.64460i) q^{3} +(-0.525125 - 0.303181i) q^{5} +(0.0911016 - 2.64418i) q^{7} +(-0.303130 + 0.525037i) q^{9} +(-0.866025 + 0.500000i) q^{11} -1.17064i q^{13} -1.15149i q^{15} +(2.99044 - 1.72653i) q^{17} +(0.200869 - 0.347916i) q^{19} +(4.43511 - 2.36085i) q^{21} +(3.26086 + 1.88266i) q^{23} +(-2.31616 - 4.01171i) q^{25} +4.54575 q^{27} +6.42611 q^{29} +(-0.414132 - 0.717297i) q^{31} +(-1.64460 - 0.949508i) q^{33} +(-0.849506 + 1.36091i) q^{35} +(4.61983 - 8.00178i) q^{37} +(1.92523 - 1.11153i) q^{39} +0.664031i q^{41} +11.4163i q^{43} +(0.318363 - 0.183807i) q^{45} +(5.49685 - 9.52083i) q^{47} +(-6.98340 - 0.481778i) q^{49} +(5.67889 + 3.27871i) q^{51} +(-3.21007 - 5.56000i) q^{53} +0.606363 q^{55} +0.762908 q^{57} +(4.08696 + 7.07882i) q^{59} +(-1.52274 - 0.879154i) q^{61} +(1.36068 + 0.849364i) q^{63} +(-0.354916 + 0.614733i) q^{65} +(-5.94644 + 3.43318i) q^{67} +7.15039i q^{69} -8.80543i q^{71} +(-0.805258 + 0.464916i) q^{73} +(4.39843 - 7.61830i) q^{75} +(1.24319 + 2.33548i) q^{77} +(12.3771 + 7.14592i) q^{79} +(5.22562 + 9.05103i) q^{81} +4.65635 q^{83} -2.09381 q^{85} +(6.10164 + 10.5683i) q^{87} +(-14.3386 - 8.27842i) q^{89} +(-3.09539 - 0.106647i) q^{91} +(0.786442 - 1.36216i) q^{93} +(-0.210963 + 0.121800i) q^{95} +1.66695i q^{97} -0.606261i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q + 2 q^{3} - 2 q^{7} - 16 q^{9}+O(q^{10}) $ 28 * q + 2 * q^3 - 2 * q^7 - 16 * q^9	$ 28 q + 2 q^{3} - 2 q^{7} - 16 q^{9} + 18 q^{17} + 14 q^{19} - 2 q^{21} - 12 q^{23} + 14 q^{25} - 16 q^{27} + 16 q^{29} + 10 q^{31} + 6 q^{35} - 4 q^{37} + 42 q^{39} - 42 q^{45} + 6 q^{47} - 4 q^{49} - 24 q^{51} - 2 q^{53} - 48 q^{57} - 12 q^{59} - 12 q^{61} - 26 q^{63} + 6 q^{65} - 48 q^{67} + 6 q^{73} - 14 q^{75} + 2 q^{77} + 48 q^{79} - 22 q^{81} - 84 q^{83} + 16 q^{85} + 18 q^{87} + 6 q^{89} - 18 q^{91} + 28 q^{93} - 36 q^{95}+O(q^{100}) $ 28 * q + 2 * q^3 - 2 * q^7 - 16 * q^9 + 18 * q^17 + 14 * q^19 - 2 * q^21 - 12 * q^23 + 14 * q^25 - 16 * q^27 + 16 * q^29 + 10 * q^31 + 6 * q^35 - 4 * q^37 + 42 * q^39 - 42 * q^45 + 6 * q^47 - 4 * q^49 - 24 * q^51 - 2 * q^53 - 48 * q^57 - 12 * q^59 - 12 * q^61 - 26 * q^63 + 6 * q^65 - 48 * q^67 + 6 * q^73 - 14 * q^75 + 2 * q^77 + 48 * q^79 - 22 * q^81 - 84 * q^83 + 16 * q^85 + 18 * q^87 + 6 * q^89 - 18 * q^91 + 28 * q^93 - 36 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1232\mathbb{Z}\right)^\times$.

$n$	$309$	$353$	$463$	$673$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$-1$	$1$

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
$3$	0.949508	+	1.64460i	0.548199	+	0.949508i	0.998398	+	0.0565798i	$0.0180195\pi$
$3$	0.949508	+	1.64460i	0.548199	+	0.949508i	−0.450199	+	0.892928i	$0.648647\pi$
$4$		0			0
$5$	−0.525125	−	0.303181i	−0.234843	−	0.135587i	0.377961	−	0.925821i	$-0.376625\pi$
$5$	−0.525125	−	0.303181i	−0.234843	−	0.135587i	−0.612804	+	0.790235i	$0.709959\pi$
$6$		0			0
$7$	0.0911016	−	2.64418i	0.0344332	−	0.999407i
$7$	0.0911016	−	2.64418i	0.0344332	−	0.999407i
$8$		0			0
$9$	−0.303130	+	0.525037i	−0.101043	+	0.175012i
$10$		0			0
$11$	−0.866025	+	0.500000i	−0.261116	+	0.150756i
$11$	−0.866025	+	0.500000i	−0.261116	+	0.150756i
$12$		0			0
$13$		−	1.17064i		−	0.324677i	−0.986735	−	0.162339i	$-0.948096\pi$
$13$		−	1.17064i		−	0.324677i	0.986735	−	0.162339i	$-0.0519037\pi$
$14$		0			0
$15$		−	1.15149i		−	0.297314i
$16$		0			0
$17$	2.99044	−	1.72653i	0.725288	−	0.418746i	−0.0914076	−	0.995814i	$-0.529137\pi$
$17$	2.99044	−	1.72653i	0.725288	−	0.418746i	0.816696	+	0.577068i	$0.195803\pi$
$18$		0			0
$19$	0.200869	−	0.347916i	0.0460826	−	0.0798174i	−0.842064	−	0.539378i	$-0.818660\pi$
$19$	0.200869	−	0.347916i	0.0460826	−	0.0798174i	0.888147	+	0.459560i	$0.151993\pi$
$20$		0			0
$21$	4.43511	−	2.36085i	0.967821	−	0.515179i
$22$		0			0
$23$	3.26086	+	1.88266i	0.679936	+	0.392561i	0.799831	−	0.600225i	$-0.204922\pi$
$23$	3.26086	+	1.88266i	0.679936	+	0.392561i	−0.119895	+	0.992787i	$0.538256\pi$
$24$		0			0
$25$	−2.31616	−	4.01171i	−0.463232	−	0.802342i
$26$		0			0
$27$	4.54575			0.874830
$28$		0			0
$29$	6.42611			1.19330			0.596649	−	0.802502i	$-0.296498\pi$
$29$	6.42611			1.19330			0.596649	+	0.802502i	$0.296498\pi$
$30$		0			0
$31$	−0.414132	−	0.717297i	−0.0743802	−	0.128830i	0.826436	−	0.563030i	$-0.190365\pi$
$31$	−0.414132	−	0.717297i	−0.0743802	−	0.128830i	−0.900817	+	0.434200i	$0.857031\pi$
$32$		0			0
$33$	−1.64460	−	0.949508i	−0.286287	−	0.165288i
$34$		0			0
$35$	−0.849506	+	1.36091i	−0.143593	+	0.230035i
$36$		0			0
$37$	4.61983	−	8.00178i	0.759495	−	1.31548i	−0.183613	−	0.982999i	$-0.558779\pi$
$37$	4.61983	−	8.00178i	0.759495	−	1.31548i	0.943108	−	0.332486i	$-0.107887\pi$
$38$		0			0
$39$	1.92523	−	1.11153i	0.308284	−	0.177988i
$40$		0			0
$41$			0.664031i			0.103704i	0.998655	+	0.0518521i	$0.0165124\pi$
$41$			0.664031i			0.103704i	−0.998655	+	0.0518521i	$0.983488\pi$
$42$		0			0
$43$			11.4163i			1.74096i	0.492200	+	0.870482i	$0.336193\pi$
$43$			11.4163i			1.74096i	−0.492200	+	0.870482i	$0.663807\pi$
$44$		0			0
$45$	0.318363	−	0.183807i	0.0474587	−	0.0274003i
$46$		0			0
$47$	5.49685	−	9.52083i	0.801799	−	1.38876i	−0.116633	−	0.993175i	$-0.537210\pi$
$47$	5.49685	−	9.52083i	0.801799	−	1.38876i	0.918431	−	0.395581i	$-0.129457\pi$
$48$		0			0
$49$	−6.98340	−	0.481778i	−0.997629	−	0.0688255i
$50$		0			0
$51$	5.67889	+	3.27871i	0.795204	+	0.459111i
$52$		0			0
$53$	−3.21007	−	5.56000i	−0.440936	−	0.763724i	0.556823	−	0.830631i	$-0.312020\pi$
$53$	−3.21007	−	5.56000i	−0.440936	−	0.763724i	−0.997759	+	0.0669071i	$0.978687\pi$
$54$		0			0
$55$	0.606363			0.0817619
$56$		0			0
$57$	0.762908			0.101050
$58$		0			0
$59$	4.08696	+	7.07882i	0.532077	+	0.921584i	0.999299	+	0.0374442i	$0.0119216\pi$
$59$	4.08696	+	7.07882i	0.532077	+	0.921584i	−0.467222	+	0.884140i	$0.654745\pi$
$60$		0			0
$61$	−1.52274	−	0.879154i	−0.194967	−	0.112564i	0.399339	−	0.916803i	$-0.369240\pi$
$61$	−1.52274	−	0.879154i	−0.194967	−	0.112564i	−0.594306	+	0.804239i	$0.702573\pi$
$62$		0			0
$63$	1.36068	+	0.849364i	0.171429	+	0.107010i
$64$		0			0
$65$	−0.354916	+	0.614733i	−0.0440219	+	0.0762482i
$66$		0			0
$67$	−5.94644	+	3.43318i	−0.726474	+	0.419430i	−0.817131	−	0.576452i	$-0.804437\pi$
$67$	−5.94644	+	3.43318i	−0.726474	+	0.419430i	0.0906570	+	0.995882i	$0.471103\pi$
$68$		0			0
$69$			7.15039i			0.860806i
$70$		0			0
$71$		−	8.80543i		−	1.04501i	−0.852635	−	0.522506i	$-0.824997\pi$
$71$		−	8.80543i		−	1.04501i	0.852635	−	0.522506i	$-0.175003\pi$
$72$		0			0
$73$	−0.805258	+	0.464916i	−0.0942483	+	0.0544143i	−0.546383	−	0.837535i	$-0.683996\pi$
$73$	−0.805258	+	0.464916i	−0.0942483	+	0.0544143i	0.452135	+	0.891949i	$0.350662\pi$
$74$		0			0
$75$	4.39843	−	7.61830i	0.507887	−	0.879686i
$76$		0			0
$77$	1.24319	+	2.33548i	0.141675	+	0.266153i
$78$		0			0
$79$	12.3771	+	7.14592i	1.39253	+	0.803979i	0.993595	−	0.112999i	$-0.0360458\pi$
$79$	12.3771	+	7.14592i	1.39253	+	0.803979i	0.398937	+	0.916978i	$0.369379\pi$
$80$		0			0
$81$	5.22562	+	9.05103i	0.580624	+	1.00567i
$82$		0			0
$83$	4.65635			0.511101			0.255550	−	0.966796i	$-0.417743\pi$
$83$	4.65635			0.511101			0.255550	+	0.966796i	$0.417743\pi$
$84$		0			0
$85$	−2.09381			−0.227105
$86$		0			0
$87$	6.10164	+	10.5683i	0.654164	+	1.13305i
$88$		0			0
$89$	−14.3386	−	8.27842i	−1.51989	−	0.877511i	−0.999725	−	0.0234474i	$-0.992536\pi$
$89$	−14.3386	−	8.27842i	−1.51989	−	0.877511i	−0.520169	−	0.854064i	$-0.674131\pi$
$90$		0			0
$91$	−3.09539	−	0.106647i	−0.324485	−	0.0111797i
$92$		0			0
$93$	0.786442	−	1.36216i	0.0815503	−	0.141249i
$94$		0			0
$95$	−0.210963	+	0.121800i	−0.0216444	+	0.0124964i
$96$		0			0
$97$			1.66695i			0.169253i	0.996413	+	0.0846264i	$0.0269697\pi$
$97$			1.66695i			0.169253i	−0.996413	+	0.0846264i	$0.973030\pi$
$98$		0			0
$99$		−	0.606261i		−	0.0609315i
$100$		0			0
$101$	−4.45535	+	2.57230i	−0.443324	+	0.255953i	−0.705007	−	0.709201i	$-0.749056\pi$
$101$	−4.45535	+	2.57230i	−0.443324	+	0.255953i	0.261683	+	0.965154i	$0.415723\pi$
$102$		0			0
$103$	−7.57482	+	13.1200i	−0.746369	+	1.29275i	0.203184	+	0.979141i	$0.434871\pi$
$103$	−7.57482	+	13.1200i	−0.746369	+	1.29275i	−0.949553	+	0.313608i	$0.898462\pi$
$104$		0			0
$105$	−3.04475	−	0.104903i	−0.297138	−	0.0102375i
$106$		0			0
$107$	7.16761	+	4.13822i	0.692919	+	0.400057i	0.804705	−	0.593675i	$-0.202324\pi$
$107$	7.16761	+	4.13822i	0.692919	+	0.400057i	−0.111785	+	0.993732i	$0.535657\pi$
$108$		0			0
$109$	5.14123	+	8.90487i	0.492440	+	0.852932i	0.999962	−	0.00870728i	$-0.00277165\pi$
$109$	5.14123	+	8.90487i	0.492440	+	0.852932i	−0.507522	+	0.861639i	$0.669438\pi$
$110$		0			0
$111$	17.5463			1.66542
$112$		0			0
$113$	3.90124			0.366998			0.183499	−	0.983020i	$-0.441258\pi$
$113$	3.90124			0.366998			0.183499	+	0.983020i	$0.441258\pi$
$114$		0			0
$115$	−1.14157	−	1.97726i	−0.106452	−	0.184381i
$116$		0			0
$117$	0.614630	+	0.354857i	0.0568225	+	0.0328065i
$118$		0			0
$119$	−4.29283	−	8.06456i	−0.393523	−	0.739277i
$120$		0			0
$121$	0.500000	−	0.866025i	0.0454545	−	0.0787296i
$122$		0			0
$123$	−1.09206	+	0.630502i	−0.0984679	+	0.0568505i
$124$		0			0
$125$			5.84068i			0.522406i
$126$		0			0
$127$		−	5.46029i		−	0.484522i	−0.970211	−	0.242261i	$-0.922111\pi$
$127$		−	5.46029i		−	0.484522i	0.970211	−	0.242261i	$-0.0778891\pi$
$128$		0			0
$129$	−18.7751	+	10.8398i	−1.65306	+	0.954394i
$130$		0			0
$131$	−3.39129	+	5.87389i	−0.296299	+	0.513204i	−0.975286	−	0.220946i	$-0.929086\pi$
$131$	−3.39129	+	5.87389i	−0.296299	+	0.513204i	0.678988	+	0.734150i	$0.262419\pi$
$132$		0			0
$133$	−0.901654	−	0.562831i	−0.0781833	−	0.0488036i
$134$		0			0
$135$	−2.38709	−	1.37819i	−0.205448	−	0.118615i
$136$		0			0
$137$	−4.19626	−	7.26813i	−0.358511	−	0.620958i	0.629202	−	0.777242i	$-0.283382\pi$
$137$	−4.19626	−	7.26813i	−0.358511	−	0.620958i	−0.987712	+	0.156284i	$0.950049\pi$
$138$		0			0
$139$	−10.2406			−0.868596			−0.434298	−	0.900769i	$-0.643003\pi$
$139$	−10.2406			−0.868596			−0.434298	+	0.900769i	$0.643003\pi$
$140$		0			0
$141$	20.8772			1.75818
$142$		0			0
$143$	0.585320	+	1.01380i	0.0489469	+	0.0847786i
$144$		0			0
$145$	−3.37451	−	1.94828i	−0.280238	−	0.161795i
$146$		0			0
$147$	−5.83846	−	11.9423i	−0.481548	−	0.984986i
$148$		0			0
$149$	7.68123	−	13.3043i	0.629271	−	1.08993i	−0.358427	−	0.933558i	$-0.616687\pi$
$149$	7.68123	−	13.3043i	0.629271	−	1.08993i	0.987698	−	0.156372i	$-0.0499798\pi$
$150$		0			0
$151$	−15.5953	+	9.00395i	−1.26913	+	0.732731i	−0.974823	−	0.222981i	$-0.928421\pi$
$151$	−15.5953	+	9.00395i	−1.26913	+	0.732731i	−0.294305	+	0.955712i	$0.595088\pi$
$152$		0			0
$153$			2.09346i			0.169246i
$154$		0			0
$155$			0.502228i			0.0403399i
$156$		0			0
$157$	10.9552	−	6.32499i	0.874321	−	0.504789i	0.00553928	−	0.999985i	$-0.498237\pi$
$157$	10.9552	−	6.32499i	0.874321	−	0.504789i	0.868782	+	0.495195i	$0.164903\pi$
$158$		0			0
$159$	6.09596	−	10.5585i	0.483441	−	0.837345i
$160$		0			0
$161$	5.27516	−	8.45079i	0.415741	−	0.666016i
$162$		0			0
$163$	−4.80293	−	2.77297i	−0.376194	−	0.217196i	0.299967	−	0.953950i	$-0.403024\pi$
$163$	−4.80293	−	2.77297i	−0.376194	−	0.217196i	−0.676161	+	0.736754i	$0.736358\pi$
$164$		0			0
$165$	0.575746	+	0.997221i	0.0448218	+	0.0776336i
$166$		0			0
$167$	−13.2417			−1.02468			−0.512338	−	0.858784i	$-0.671220\pi$
$167$	−13.2417			−1.02468			−0.512338	+	0.858784i	$0.671220\pi$
$168$		0			0
$169$	11.6296			0.894585
$170$		0			0
$171$	0.121779	+	0.210928i	0.00931269	+	0.0161301i
$172$		0			0
$173$	−14.9559	−	8.63478i	−1.13707	−	0.656490i	−0.191370	−	0.981518i	$-0.561293\pi$
$173$	−14.9559	−	8.63478i	−1.13707	−	0.656490i	−0.945704	+	0.325028i	$0.894626\pi$
$174$		0			0
$175$	−10.8187	+	5.75888i	−0.817817	+	0.435331i
$176$		0			0
$177$	−7.76120	+	13.4428i	−0.583368	+	1.01042i
$178$		0			0
$179$	3.31662	−	1.91485i	0.247896	−	0.143123i	−0.370905	−	0.928671i	$-0.620952\pi$
$179$	3.31662	−	1.91485i	0.247896	−	0.143123i	0.618800	+	0.785548i	$0.287619\pi$
$180$		0			0
$181$			11.2199i			0.833966i	0.908914	+	0.416983i	$0.136913\pi$
$181$			11.2199i			0.833966i	−0.908914	+	0.416983i	$0.863087\pi$
$182$		0			0
$183$		−	3.33906i		−	0.246830i
$184$		0			0
$185$	−4.85198	+	2.80129i	−0.356725	+	0.205955i
$186$		0			0
$187$	−1.72653	+	2.99044i	−0.126257	+	0.218683i
$188$		0			0
$189$	0.414125	−	12.0198i	0.0301232	−	0.874311i
$190$		0			0
$191$	0.281351	+	0.162438i	0.0203579	+	0.0117536i	0.510144	−	0.860089i	$-0.329592\pi$
$191$	0.281351	+	0.162438i	0.0203579	+	0.0117536i	−0.489787	+	0.871842i	$0.662925\pi$
$192$		0			0
$193$	−3.90326	−	6.76065i	−0.280963	−	0.486642i	0.690659	−	0.723180i	$-0.257321\pi$
$193$	−3.90326	−	6.76065i	−0.280963	−	0.486642i	−0.971622	+	0.236538i	$0.923987\pi$
$194$		0			0
$195$	−1.34798			−0.0965311
$196$		0			0
$197$	19.9816			1.42363			0.711815	−	0.702367i	$-0.247873\pi$
$197$	19.9816			1.42363			0.711815	+	0.702367i	$0.247873\pi$
$198$		0			0
$199$	−8.36261	−	14.4845i	−0.592810	−	1.02678i	−0.993852	−	0.110717i	$-0.964685\pi$
$199$	−8.36261	−	14.4845i	−0.592810	−	1.02678i	0.401042	−	0.916060i	$-0.368648\pi$
$200$		0			0
$201$	−11.2924	−	6.51966i	−0.796504	−	0.459862i
$202$		0			0
$203$	0.585429	−	16.9918i	0.0410890	−	1.19259i
$204$		0			0
$205$	0.201322	−	0.348699i	0.0140609	−	0.0243542i
$206$		0			0
$207$	−1.97693	+	1.14138i	−0.137406	+	0.0793315i
$208$		0			0
$209$			0.401739i			0.0277889i
$210$		0			0
$211$		−	4.73174i		−	0.325746i	−0.986647	−	0.162873i	$-0.947924\pi$
$211$		−	4.73174i		−	0.325746i	0.986647	−	0.162873i	$-0.0520762\pi$
$212$		0			0
$213$	14.4814	−	8.36083i	0.992248	−	0.572874i
$214$		0			0
$215$	3.46120	−	5.99497i	0.236052	−	0.408854i
$216$		0			0
$217$	−1.93439	+	1.02969i	−0.131315	+	0.0699001i
$218$		0			0
$219$	−1.52920	−	0.882882i	−0.103334	−	0.0596596i
$220$		0			0
$221$	−2.02115	−	3.50073i	−0.135957	−	0.235485i
$222$		0			0
$223$	−0.0385537			−0.00258174			−0.00129087	−	0.999999i	$-0.500411\pi$
$223$	−0.0385537			−0.00258174			−0.00129087	+	0.999999i	$0.500411\pi$
$224$		0			0
$225$	2.80840			0.187226
$226$		0			0
$227$	−4.80396	−	8.32070i	−0.318850	−	0.552264i	0.661398	−	0.750035i	$-0.269963\pi$
$227$	−4.80396	−	8.32070i	−0.318850	−	0.552264i	−0.980248	+	0.197770i	$0.936630\pi$
$228$		0			0
$229$	2.69927	+	1.55842i	0.178373	+	0.102984i	0.586528	−	0.809929i	$-0.300494\pi$
$229$	2.69927	+	1.55842i	0.178373	+	0.102984i	−0.408155	+	0.912913i	$0.633828\pi$
$230$		0			0
$231$	−2.66050	+	4.26211i	−0.175048	+	0.280426i
$232$		0			0
$233$	−6.32874	+	10.9617i	−0.414609	+	0.718125i	−0.995387	−	0.0959375i	$-0.969415\pi$
$233$	−6.32874	+	10.9617i	−0.414609	+	0.718125i	0.580778	+	0.814062i	$0.302748\pi$
$234$		0			0
$235$	−5.77307	+	3.33309i	−0.376594	+	0.217427i
$236$		0			0
$237$			27.1404i			1.76296i
$238$		0			0
$239$			9.81890i			0.635132i	0.948236	+	0.317566i	$0.102865\pi$
$239$			9.81890i			0.635132i	−0.948236	+	0.317566i	$0.897135\pi$
$240$		0			0
$241$	1.34724	−	0.777828i	0.0867832	−	0.0501043i	−0.455980	−	0.889990i	$-0.650711\pi$
$241$	1.34724	−	0.777828i	0.0867832	−	0.0501043i	0.542764	+	0.839886i	$0.317378\pi$
$242$		0			0
$243$	−3.10490	+	5.37785i	−0.199180	+	0.344989i
$244$		0			0
$245$	3.52109	+	2.37023i	0.224954	+	0.151428i
$246$		0			0
$247$	−0.407285	−	0.235146i	−0.0259149	−	0.0149620i
$248$		0			0
$249$	4.42124	+	7.65781i	0.280185	+	0.485294i
$250$		0			0
$251$	−6.50237			−0.410426			−0.205213	−	0.978717i	$-0.565789\pi$
$251$	−6.50237			−0.410426			−0.205213	+	0.978717i	$0.565789\pi$
$252$		0			0
$253$	−3.76532			−0.236723
$254$		0			0
$255$	−1.98809	−	3.44347i	−0.124499	−	0.215638i
$256$		0			0
$257$	13.7631	+	7.94613i	0.858518	+	0.495666i	0.863516	−	0.504322i	$-0.168257\pi$
$257$	13.7631	+	7.94613i	0.858518	+	0.495666i	−0.00499746	+	0.999988i	$0.501591\pi$
$258$		0			0
$259$	−20.7373	−	12.9446i	−1.28855	−	0.804341i
$260$		0			0
$261$	−1.94795	+	3.37395i	−0.120575	+	0.208842i
$262$		0			0
$263$	−14.5619	+	8.40731i	−0.897925	+	0.518417i	−0.876526	−	0.481354i	$-0.840145\pi$
$263$	−14.5619	+	8.40731i	−0.897925	+	0.518417i	−0.0213984	+	0.999771i	$0.506812\pi$
$264$		0			0
$265$			3.89293i			0.239141i
$266$		0			0
$267$		−	31.4417i		−	1.92420i
$268$		0			0
$269$	−15.6069	+	9.01063i	−0.951568	+	0.549388i	−0.893568	−	0.448928i	$-0.851806\pi$
$269$	−15.6069	+	9.01063i	−0.951568	+	0.549388i	−0.0580004	+	0.998317i	$0.518472\pi$
$270$		0			0
$271$	−0.460171	+	0.797039i	−0.0279534	+	0.0484167i	−0.879664	−	0.475596i	$-0.842232\pi$
$271$	−0.460171	+	0.797039i	−0.0279534	+	0.0484167i	0.851710	+	0.524013i	$0.175566\pi$
$272$		0			0
$273$	−2.76370	−	5.19192i	−0.167267	−	0.314229i
$274$		0			0
$275$	4.01171	+	2.31616i	0.241915	+	0.139670i
$276$		0			0
$277$	0.225158	+	0.389985i	0.0135284	+	0.0234319i	0.872710	−	0.488238i	$-0.162360\pi$
$277$	0.225158	+	0.389985i	0.0135284	+	0.0234319i	−0.859182	+	0.511670i	$0.829027\pi$
$278$		0			0
$279$	0.502143			0.0300625
$280$		0			0
$281$	−9.73362			−0.580659			−0.290330	−	0.956927i	$-0.593765\pi$
$281$	−9.73362			−0.580659			−0.290330	+	0.956927i	$0.593765\pi$
$282$		0			0
$283$	14.3376	+	24.8335i	0.852284	+	1.47620i	0.879142	+	0.476560i	$0.158116\pi$
$283$	14.3376	+	24.8335i	0.852284	+	1.47620i	−0.0268583	+	0.999639i	$0.508550\pi$
$284$		0			0
$285$	−0.400623	−	0.231300i	−0.0237308	−	0.0137010i
$286$		0			0
$287$	1.75582	+	0.0604942i	0.103643	+	0.00357086i
$288$		0			0
$289$	−2.53817	+	4.39625i	−0.149304	+	0.258603i
$290$		0			0
$291$	−2.74146	+	1.58278i	−0.160707	+	0.0927842i
$292$		0			0
$293$		−	0.844522i		−	0.0493375i	−0.999696	−	0.0246687i	$-0.992147\pi$
$293$		−	0.844522i		−	0.0493375i	0.999696	−	0.0246687i	$-0.00785310\pi$
$294$		0			0
$295$		−	4.95636i		−	0.288570i
$296$		0			0
$297$	−3.93673	+	2.27287i	−0.228432	+	0.131886i
$298$		0			0
$299$	2.20391	−	3.81729i	0.127456	−	0.220760i
$300$		0			0
$301$	30.1867	+	1.04004i	1.73993	+	0.0599469i
$302$		0			0
$303$	−8.46078	−	4.88484i	−0.486059	−	0.280626i
$304$		0			0
$305$	0.533086	+	0.923333i	0.0305244	+	0.0528699i
$306$		0			0
$307$	−2.61490			−0.149240			−0.0746200	−	0.997212i	$-0.523774\pi$
$307$	−2.61490			−0.149240			−0.0746200	+	0.997212i	$0.523774\pi$
$308$		0			0
$309$	−28.7694			−1.63663
$310$		0			0
$311$	−3.20950	−	5.55902i	−0.181994	−	0.315223i	0.760565	−	0.649261i	$-0.224922\pi$
$311$	−3.20950	−	5.55902i	−0.181994	−	0.315223i	−0.942560	+	0.334038i	$0.891589\pi$
$312$		0			0
$313$	−15.4456	−	8.91752i	−0.873037	−	0.504048i	−0.00468043	−	0.999989i	$-0.501490\pi$
$313$	−15.4456	−	8.91752i	−0.873037	−	0.504048i	−0.868356	+	0.495941i	$0.834823\pi$
$314$		0			0
$315$	−0.457016	−	0.858555i	−0.0257499	−	0.0483741i
$316$		0			0
$317$	4.01195	−	6.94889i	0.225333	−	0.390289i	−0.731086	−	0.682285i	$-0.760986\pi$
$317$	4.01195	−	6.94889i	0.225333	−	0.390289i	0.956419	+	0.291996i	$0.0943196\pi$
$318$		0			0
$319$	−5.56517	+	3.21305i	−0.311590	+	0.179896i
$320$		0			0
$321$			15.7171i			0.877243i
$322$		0			0
$323$		−	1.38723i		−	0.0771875i
$324$		0			0
$325$	−4.69627	+	2.71139i	−0.260502	+	0.150401i
$326$		0			0
$327$	−9.76327	+	16.9105i	−0.539910	+	0.935152i
$328$		0			0
$329$	−24.6740	−	15.4020i	−1.36032	−	0.849142i
$330$		0			0
$331$	−3.50928	−	2.02608i	−0.192887	−	0.111364i	0.400446	−	0.916320i	$-0.368855\pi$
$331$	−3.50928	−	2.02608i	−0.192887	−	0.111364i	−0.593334	+	0.804957i	$0.702188\pi$
$332$		0			0
$333$	2.80082	+	4.85116i	0.153484	+	0.265842i
$334$		0			0
$335$	4.16350			0.227477
$336$		0			0
$337$	34.5398			1.88150			0.940750	−	0.339100i	$-0.110122\pi$
$337$	34.5398			1.88150			0.940750	+	0.339100i	$0.110122\pi$
$338$		0			0
$339$	3.70426	+	6.41597i	0.201188	+	0.348468i
$340$		0			0
$341$	0.717297	+	0.414132i	0.0388438	+	0.0224265i
$342$		0			0
$343$	−1.91011	+	18.4215i	−0.103136	+	0.994667i
$344$		0			0
$345$	2.16787	−	3.75485i	0.116714	−	0.202154i
$346$		0			0
$347$	18.1895	−	10.5017i	0.976462	−	0.563761i	0.0752619	−	0.997164i	$-0.476021\pi$
$347$	18.1895	−	10.5017i	0.976462	−	0.563761i	0.901200	+	0.433403i	$0.142687\pi$
$348$		0			0
$349$			24.6790i			1.32104i	0.750809	+	0.660519i	$0.229664\pi$
$349$			24.6790i			1.32104i	−0.750809	+	0.660519i	$0.770336\pi$
$350$		0			0
$351$		−	5.32144i		−	0.284037i
$352$		0			0
$353$	−31.8678	+	18.3989i	−1.69615	+	0.979273i	−0.746803	+	0.665046i	$0.768412\pi$
$353$	−31.8678	+	18.3989i	−1.69615	+	0.979273i	−0.949348	+	0.314227i	$0.898255\pi$
$354$		0			0
$355$	−2.66964	+	4.62396i	−0.141690	+	0.245414i
$356$		0			0
$357$	9.18687	−	14.7173i	0.486221	−	0.778924i
$358$		0			0
$359$	−16.0717	−	9.27902i	−0.848234	−	0.489728i	0.0118208	−	0.999930i	$-0.496237\pi$
$359$	−16.0717	−	9.27902i	−0.848234	−	0.489728i	−0.860055	+	0.510202i	$0.829571\pi$
$360$		0			0
$361$	9.41930	+	16.3147i	0.495753	+	0.858669i
$362$		0			0
$363$	1.89902			0.0996725
$364$		0			0
$365$	0.563815			0.0295114
$366$		0			0
$367$	−10.5659	−	18.3007i	−0.551535	−	0.955287i	−0.998164	−	0.0605680i	$-0.980709\pi$
$367$	−10.5659	−	18.3007i	−0.551535	−	0.955287i	0.446629	−	0.894719i	$-0.352625\pi$
$368$		0			0
$369$	−0.348641	−	0.201288i	−0.0181495	−	0.0104786i
$370$		0			0
$371$	−14.9941	+	7.98147i	−0.778454	+	0.414377i
$372$		0			0
$373$	−13.5099	+	23.3998i	−0.699514	+	1.21159i	0.269122	+	0.963106i	$0.413267\pi$
$373$	−13.5099	+	23.3998i	−0.699514	+	1.21159i	−0.968635	+	0.248487i	$0.920067\pi$
$374$		0			0
$375$	−9.60556	+	5.54577i	−0.496029	+	0.286382i
$376$		0			0
$377$		−	7.52266i		−	0.387437i
$378$		0			0
$379$			5.55687i			0.285437i	0.989763	+	0.142719i	$0.0455844\pi$
$379$			5.55687i			0.285437i	−0.989763	+	0.142719i	$0.954416\pi$
$380$		0			0
$381$	8.97997	−	5.18459i	0.460058	−	0.265615i
$382$		0			0
$383$	−4.93813	+	8.55309i	−0.252327	+	0.437043i	−0.964166	−	0.265300i	$-0.914529\pi$
$383$	−4.93813	+	8.55309i	−0.252327	+	0.437043i	0.711839	+	0.702342i	$0.247862\pi$
$384$		0			0
$385$	0.0552406	−	1.60333i	0.00281532	−	0.0817134i
$386$		0			0
$387$	−5.99397	−	3.46062i	−0.304690	−	0.175913i
$388$		0			0
$389$	−11.4937	−	19.9077i	−0.582754	−	1.00936i	−0.995151	−	0.0983556i	$-0.968642\pi$
$389$	−11.4937	−	19.9077i	−0.582754	−	1.00936i	0.412397	−	0.911004i	$-0.364692\pi$
$390$		0			0
$391$	13.0019			0.657533
$392$		0			0
$393$	−12.8802			−0.649722
$394$		0			0
$395$	−4.33302	−	7.50501i	−0.218018	−	0.377618i
$396$		0			0
$397$	−12.1933	−	7.03980i	−0.611964	−	0.353317i	0.161770	−	0.986829i	$-0.448280\pi$
$397$	−12.1933	−	7.03980i	−0.611964	−	0.353317i	−0.773734	+	0.633511i	$0.781613\pi$
$398$		0			0
$399$	0.0695022	−	2.01727i	0.00347946	−	0.100990i
$400$		0			0
$401$	−0.947027	+	1.64030i	−0.0472923	+	0.0819126i	−0.888703	−	0.458484i	$-0.848393\pi$
$401$	−0.947027	+	1.64030i	−0.0472923	+	0.0819126i	0.841410	+	0.540397i	$0.181726\pi$
$402$		0			0
$403$	−0.839697	+	0.484799i	−0.0418283	+	0.0241496i
$404$		0			0
$405$		−	6.33723i		−	0.314900i
$406$		0			0
$407$			9.23966i			0.457993i
$408$		0			0
$409$	−21.0032	+	12.1262i	−1.03854	+	0.599603i	−0.919420	−	0.393277i	$-0.871341\pi$
$409$	−21.0032	+	12.1262i	−1.03854	+	0.599603i	−0.119122	+	0.992880i	$0.538008\pi$
$410$		0			0
$411$	7.96876	−	13.8023i	0.393070	−	0.680817i
$412$		0			0
$413$	19.0900	−	10.1618i	0.939359	−	0.500028i
$414$		0			0
$415$	−2.44517	−	1.41172i	−0.120029	−	0.0692985i
$416$		0			0
$417$	−9.72352	−	16.8416i	−0.476163	−	0.824738i
$418$		0			0
$419$	16.6020			0.811063			0.405531	−	0.914081i	$-0.367087\pi$
$419$	16.6020			0.811063			0.405531	+	0.914081i	$0.367087\pi$
$420$		0			0
$421$	25.8425			1.25949			0.629743	−	0.776804i	$-0.283160\pi$
$421$	25.8425			1.25949			0.629743	+	0.776804i	$0.283160\pi$
$422$		0			0
$423$	3.33253	+	5.77211i	0.162033	+	0.280649i
$424$		0			0
$425$	−13.8527	−	7.99786i	−0.671954	−	0.387953i
$426$		0			0
$427$	−2.46337	+	3.94631i	−0.119211	+	0.190975i
$428$		0			0
$429$	−1.11153	+	1.92523i	−0.0536653	+	0.0929510i
$430$		0			0
$431$	16.2580	−	9.38656i	0.783120	−	0.452134i	−0.0544150	−	0.998518i	$-0.517329\pi$
$431$	16.2580	−	9.38656i	0.783120	−	0.452134i	0.837535	+	0.546384i	$0.183996\pi$
$432$		0			0
$433$			33.2857i			1.59961i	0.600261	+	0.799804i	$0.295063\pi$
$433$			33.2857i			1.59961i	−0.600261	+	0.799804i	$0.704937\pi$
$434$		0			0
$435$		−	7.39961i		−	0.354784i
$436$		0			0
$437$	1.31001	−	0.756337i	0.0626664	−	0.0361805i
$438$		0			0
$439$	−10.5517	+	18.2760i	−0.503603	+	0.872266i	0.496388	+	0.868101i	$0.334659\pi$
$439$	−10.5517	+	18.2760i	−0.503603	+	0.872266i	−0.999991	+	0.00416543i	$0.998674\pi$
$440$		0			0
$441$	2.36983	−	3.52050i	0.112849	−	0.167643i
$442$		0			0
$443$	9.79011	+	5.65232i	0.465142	+	0.268550i	0.714204	−	0.699938i	$-0.246789\pi$
$443$	9.79011	+	5.65232i	0.465142	+	0.268550i	−0.249062	+	0.968488i	$0.580122\pi$
$444$		0			0
$445$	5.01973	+	8.69442i	0.237958	+	0.412155i
$446$		0			0
$447$	29.1736			1.37986
$448$		0			0
$449$	39.4950			1.86388			0.931941	−	0.362609i	$-0.118114\pi$
$449$	39.4950			1.86388			0.931941	+	0.362609i	$0.118114\pi$
$450$		0			0
$451$	−0.332015	−	0.575067i	−0.0156340	−	0.0270789i
$452$		0			0
$453$	−29.6157	−	17.0986i	−1.39147	−	0.803364i
$454$		0			0
$455$	1.59313	+	0.994466i	0.0746872	+	0.0466213i
$456$		0			0
$457$	−7.95867	+	13.7848i	−0.372291	+	0.644826i	−0.989918	−	0.141645i	$-0.954761\pi$
$457$	−7.95867	+	13.7848i	−0.372291	+	0.644826i	0.617627	+	0.786471i	$0.288094\pi$
$458$		0			0
$459$	13.5938	−	7.84838i	0.634504	−	0.366331i
$460$		0			0
$461$			22.8625i			1.06481i	0.846489	+	0.532406i	$0.178712\pi$
$461$			22.8625i			1.06481i	−0.846489	+	0.532406i	$0.821288\pi$
$462$		0			0
$463$			7.34413i			0.341311i	0.985331	+	0.170655i	$0.0545885\pi$
$463$			7.34413i			0.341311i	−0.985331	+	0.170655i	$0.945412\pi$
$464$		0			0
$465$	−0.825962	+	0.476869i	−0.0383031	+	0.0221143i
$466$		0			0
$467$	−14.5154	+	25.1414i	−0.671693	+	1.16341i	0.305731	+	0.952118i	$0.401099\pi$
$467$	−14.5154	+	25.1414i	−0.671693	+	1.16341i	−0.977424	+	0.211288i	$0.932234\pi$
$468$		0			0
$469$	8.53623	+	16.0362i	0.394166	+	0.740485i
$470$		0			0
$471$	20.8041	+	12.0113i	0.958603	+	0.553450i
$472$		0			0
$473$	−5.70813	−	9.88678i	−0.262460	−	0.454595i
$474$		0			0
$475$	−1.86098			−0.0853878
$476$		0			0
$477$	3.89227			0.178215
$478$		0			0
$479$	−0.149734	−	0.259347i	−0.00684153	−	0.0118499i	0.862584	−	0.505913i	$-0.168844\pi$
$479$	−0.149734	−	0.259347i	−0.00684153	−	0.0118499i	−0.869426	+	0.494063i	$0.835511\pi$
$480$		0			0
$481$	−9.36720	−	5.40816i	−0.427108	−	0.246591i
$482$		0			0
$483$	18.9069	+	0.651412i	0.860296	+	0.0296403i
$484$		0			0
$485$	0.505387	−	0.875357i	0.0229485	−	0.0397479i
$486$		0			0
$487$	−9.13797	+	5.27581i	−0.414081	+	0.239070i	−0.692542	−	0.721378i	$-0.743509\pi$
$487$	−9.13797	+	5.27581i	−0.414081	+	0.239070i	0.278461	+	0.960448i	$0.410176\pi$
$488$		0			0
$489$		−	10.5318i		−	0.476266i
$490$		0			0
$491$		−	21.1743i		−	0.955583i	−0.878473	−	0.477792i	$-0.841437\pi$
$491$		−	21.1743i		−	0.955583i	0.878473	−	0.477792i	$-0.158563\pi$
$492$		0			0
$493$	19.2169	−	11.0949i	0.865485	−	0.499688i
$494$		0			0
$495$	−0.183807	+	0.318363i	−0.00826151	+	0.0143093i
$496$		0			0
$497$	−23.2832	−	0.802189i	−1.04439	−	0.0359831i
$498$		0			0
$499$	−21.5264	−	12.4283i	−0.963655	−	0.556367i	−0.0663593	−	0.997796i	$-0.521138\pi$
$499$	−21.5264	−	12.4283i	−0.963655	−	0.556367i	−0.897296	+	0.441429i	$0.854472\pi$
$500$		0			0
$501$	−12.5731	−	21.7773i	−0.561726	−	0.972937i
$502$		0			0
$503$	20.6831			0.922216			0.461108	−	0.887344i	$-0.347452\pi$
$503$	20.6831			0.922216			0.461108	+	0.887344i	$0.347452\pi$
$504$		0			0
$505$	3.11949			0.138816
$506$		0			0
$507$	11.0424	+	19.1260i	0.490410	+	0.849415i
$508$		0			0
$509$	24.2299	+	13.9891i	1.07397	+	0.620058i	0.929264	−	0.369416i	$-0.120442\pi$
$509$	24.2299	+	13.9891i	1.07397	+	0.620058i	0.144708	+	0.989474i	$0.453776\pi$
$510$		0			0
$511$	1.15596	+	2.17160i	0.0511367	+	0.0960660i
$512$		0			0
$513$	0.913102	−	1.58154i	0.0403144	−	0.0698266i
$514$		0			0
$515$	7.95546	−	4.59308i	0.350559	−	0.202395i
$516$		0			0
$517$			10.9937i			0.483503i
$518$		0			0
$519$		−	32.7952i		−	1.43955i
$520$		0			0
$521$	30.0522	−	17.3506i	1.31661	−	0.760146i	0.333429	−	0.942775i	$-0.391794\pi$
$521$	30.0522	−	17.3506i	1.31661	−	0.760146i	0.983182	+	0.182629i	$0.0584608\pi$
$522$		0			0
$523$	−16.1189	+	27.9188i	−0.704830	+	1.22080i	0.261922	+	0.965089i	$0.415644\pi$
$523$	−16.1189	+	27.9188i	−0.704830	+	1.22080i	−0.966753	+	0.255713i	$0.917690\pi$
$524$		0			0
$525$	−19.7435	−	12.3243i	−0.861676	−	0.537876i
$526$		0			0
$527$	−2.47687	−	1.43002i	−0.107894	−	0.0622928i
$528$		0			0
$529$	−4.41120	−	7.64042i	−0.191791	−	0.332192i
$530$		0			0
$531$	−4.95553			−0.215052
$532$		0			0
$533$	0.777341			0.0336704
$534$		0			0
$535$	−2.50926	−	4.34617i	−0.108485	−	0.187901i
$536$		0			0
$537$	6.29832	+	3.63633i	0.271792	+	0.156919i
$538$		0			0
$539$	6.28869	−	3.07447i	0.270873	−	0.132427i
$540$		0			0
$541$	−2.45618	+	4.25422i	−0.105599	+	0.182903i	−0.913983	−	0.405753i	$-0.867009\pi$
$541$	−2.45618	+	4.25422i	−0.105599	+	0.182903i	0.808384	+	0.588656i	$0.200343\pi$
$542$		0			0
$543$	−18.4522	+	10.6534i	−0.791858	+	0.457179i
$544$		0			0
$545$		−	6.23490i		−	0.267074i
$546$		0			0
$547$			19.6228i			0.839010i	0.907753	+	0.419505i	$0.137796\pi$
$547$			19.6228i			0.839010i	−0.907753	+	0.419505i	$0.862204\pi$
$548$		0			0
$549$	0.923178	−	0.532997i	0.0394003	−	0.0227477i
$550$		0			0
$551$	1.29081	−	2.23575i	0.0549903	−	0.0952460i
$552$		0			0
$553$	20.0227	−	32.0763i	0.851451	−	1.36402i
$554$		0			0
$555$	−9.21398	−	5.31970i	−0.391112	−	0.225808i
$556$		0			0
$557$	8.90676	+	15.4270i	0.377391	+	0.653661i	0.990682	−	0.136196i	$-0.0434878\pi$
$557$	8.90676	+	15.4270i	0.377391	+	0.653661i	−0.613290	+	0.789857i	$0.710154\pi$
$558$		0			0
$559$	13.3643			0.565252
$560$		0			0
$561$	−6.55742			−0.276855
$562$		0			0
$563$	16.6988	+	28.9232i	0.703771	+	1.21897i	0.967133	+	0.254270i	$0.0818353\pi$
$563$	16.6988	+	28.9232i	0.703771	+	1.21897i	−0.263362	+	0.964697i	$0.584831\pi$
$564$		0			0
$565$	−2.04864	−	1.18278i	−0.0861870	−	0.0497601i
$566$		0			0
$567$	24.4086	−	12.9929i	1.02507	−	0.545651i
$568$		0			0
$569$	−13.2500	+	22.9497i	−0.555470	+	0.962102i	0.442397	+	0.896819i	$0.354128\pi$
$569$	−13.2500	+	22.9497i	−0.555470	+	0.962102i	−0.997867	+	0.0652829i	$0.979205\pi$
$570$		0			0
$571$	40.0660	−	23.1321i	1.67671	−	0.968048i	0.712973	−	0.701192i	$-0.247348\pi$
$571$	40.0660	−	23.1321i	1.67671	−	0.968048i	0.963736	−	0.266857i	$-0.0859850\pi$
$572$		0			0
$573$			0.616945i			0.0257733i
$574$		0			0
$575$		−	17.4422i		−	0.727388i
$576$		0			0
$577$	20.7471	−	11.9783i	0.863712	−	0.498664i	−0.00154164	−	0.999999i	$-0.500491\pi$
$577$	20.7471	−	11.9783i	0.863712	−	0.498664i	0.865254	+	0.501335i	$0.167157\pi$
$578$		0			0
$579$	7.41236	−	12.8386i	0.308047	−	0.533553i
$580$		0			0
$581$	0.424201	−	12.3122i	0.0175988	−	0.510798i
$582$		0			0
$583$	5.56000	+	3.21007i	0.230272	+	0.132947i
$584$		0			0
$585$	−0.215172	−	0.372688i	−0.00889626	−	0.0154088i
$586$		0			0
$587$	45.3872			1.87333			0.936665	−	0.350228i	$-0.113896\pi$
$587$	45.3872			1.87333			0.936665	+	0.350228i	$0.113896\pi$
$588$		0			0
$589$	−0.332745			−0.0137105
$590$		0			0
$591$	18.9727	+	32.8616i	0.780432	+	1.35175i
$592$		0			0
$593$	14.5852	+	8.42079i	0.598944	+	0.345801i	0.768626	−	0.639698i	$-0.220941\pi$
$593$	14.5852	+	8.42079i	0.598944	+	0.345801i	−0.169682	+	0.985499i	$0.554274\pi$
$594$		0			0
$595$	−0.190749	+	5.53641i	−0.00781996	+	0.226971i
$596$		0			0
$597$	15.8807	−	27.5062i	0.649955	−	1.12576i
$598$		0			0
$599$	33.6784	−	19.4442i	1.37606	−	0.794469i	0.384378	−	0.923176i	$-0.374416\pi$
$599$	33.6784	−	19.4442i	1.37606	−	0.794469i	0.991683	+	0.128707i	$0.0410828\pi$
$600$		0			0
$601$		−	35.9080i		−	1.46472i	−0.680918	−	0.732359i	$-0.738419\pi$
$601$		−	35.9080i		−	1.46472i	0.680918	−	0.732359i	$-0.261581\pi$
$602$		0			0
$603$		−	4.16281i		−	0.169523i
$604$		0			0
$605$	−0.525125	+	0.303181i	−0.0213494	+	0.0123261i
$606$		0			0
$607$	−20.9342	+	36.2591i	−0.849693	+	1.47171i	0.0317899	+	0.999495i	$0.489879\pi$
$607$	−20.9342	+	36.2591i	−0.849693	+	1.47171i	−0.881483	+	0.472216i	$0.843454\pi$
$608$		0			0
$609$	28.5005	−	15.1711i	1.15490	−	0.614762i
$610$		0			0
$611$	−11.1455	−	6.43484i	−0.450897	−	0.260326i
$612$		0			0
$613$	−22.7052	−	39.3266i	−0.917056	−	1.58839i	−0.803863	−	0.594814i	$-0.797226\pi$
$613$	−22.7052	−	39.3266i	−0.917056	−	1.58839i	−0.113192	−	0.993573i	$-0.536108\pi$
$614$		0			0
$615$	0.764626			0.0308327
$616$		0			0
$617$	−2.04798			−0.0824487			−0.0412244	−	0.999150i	$-0.513126\pi$
$617$	−2.04798			−0.0824487			−0.0412244	+	0.999150i	$0.513126\pi$
$618$		0			0
$619$	−10.8676	−	18.8233i	−0.436807	−	0.756572i	0.560634	−	0.828064i	$-0.310557\pi$
$619$	−10.8676	−	18.8233i	−0.436807	−	0.756572i	−0.997441	+	0.0714914i	$0.977224\pi$
$620$		0			0
$621$	14.8230	+	8.55809i	0.594828	+	0.343424i
$622$		0			0
$623$	−23.1959	+	37.1598i	−0.929325	+	1.48878i
$624$		0			0
$625$	−9.81003	+	16.9915i	−0.392401	+	0.679659i
$626$		0			0
$627$	−0.660698	+	0.381454i	−0.0263857	+	0.0152338i
$628$		0			0
$629$		−	31.9051i		−	1.27214i
$630$		0			0
$631$		−	5.18026i		−	0.206223i	−0.994670	−	0.103112i	$-0.967120\pi$
$631$		−	5.18026i		−	0.206223i	0.994670	−	0.103112i	$-0.0328799\pi$
$632$		0			0
$633$	7.78180	−	4.49283i	0.309299	−	0.178574i
$634$		0			0
$635$	−1.65546	+	2.86734i	−0.0656948	+	0.113787i
$636$		0			0
$637$	−0.563989	+	8.17505i	−0.0223461	+	0.323907i
$638$		0			0
$639$	4.62318	+	2.66919i	0.182890	+	0.105592i
$640$		0			0
$641$	10.3817	+	17.9816i	0.410051	+	0.710229i	0.994895	−	0.100917i	$-0.0321775\pi$
$641$	10.3817	+	17.9816i	0.410051	+	0.710229i	−0.584844	+	0.811146i	$0.698844\pi$
$642$		0			0
$643$	−23.2831			−0.918197			−0.459099	−	0.888385i	$-0.651828\pi$
$643$	−23.2831			−0.918197			−0.459099	+	0.888385i	$0.651828\pi$
$644$		0			0
$645$	13.1457			0.517613
$646$		0			0
$647$	−16.6035	−	28.7581i	−0.652751	−	1.13060i	−0.982453	−	0.186513i	$-0.940281\pi$
$647$	−16.6035	−	28.7581i	−0.652751	−	1.13060i	0.329702	−	0.944085i	$-0.393052\pi$
$648$		0			0
$649$	−7.07882	−	4.08696i	−0.277868	−	0.160427i
$650$		0			0
$651$	−3.53015	−	2.20359i	−0.138357	−	0.0863656i
$652$		0			0
$653$	21.0065	−	36.3843i	0.822048	−	1.42383i	−0.0821062	−	0.996624i	$-0.526165\pi$
$653$	21.0065	−	36.3843i	0.822048	−	1.42383i	0.904154	−	0.427206i	$-0.140502\pi$
$654$		0			0
$655$	3.56171	−	2.05635i	0.139167	−	0.0803484i
$656$		0			0
$657$		−	0.563720i		−	0.0219928i
$658$		0			0
$659$		−	40.2619i		−	1.56838i	−0.620520	−	0.784190i	$-0.713079\pi$
$659$		−	40.2619i		−	1.56838i	0.620520	−	0.784190i	$-0.286921\pi$
$660$		0			0
$661$	−25.2375	+	14.5709i	−0.981626	+	0.566742i	−0.902761	−	0.430143i	$-0.858463\pi$
$661$	−25.2375	+	14.5709i	−0.981626	+	0.566742i	−0.0788656	+	0.996885i	$0.525130\pi$
$662$		0			0
$663$	3.83819	−	6.64794i	0.149063	−	0.258185i
$664$		0			0
$665$	0.302842	+	0.568921i	0.0117437	+	0.0220618i
$666$		0			0
$667$	20.9546	+	12.0982i	0.811366	+	0.468443i
$668$		0			0
$669$	−0.0366070	−	0.0634052i	−0.00141531	−	0.00245139i
$670$		0			0
$671$	1.75831			0.0678788
$672$		0			0
$673$	38.6255			1.48890			0.744452	−	0.667676i	$-0.232711\pi$
$673$	38.6255			1.48890			0.744452	+	0.667676i	$0.232711\pi$
$674$		0			0
$675$	−10.5287	−	18.2362i	−0.405250	−	0.701913i
$676$		0			0
$677$	−1.22643	−	0.708079i	−0.0471355	−	0.0272137i	0.476247	−	0.879312i	$-0.341997\pi$
$677$	−1.22643	−	0.708079i	−0.0471355	−	0.0272137i	−0.523383	+	0.852098i	$0.675330\pi$
$678$		0			0
$679$	4.40771	+	0.151862i	0.169153	+	0.00582791i
$680$		0			0
$681$	9.12280	−	15.8011i	0.349586	−	0.605501i
$682$		0			0
$683$	−8.23844	+	4.75647i	−0.315235	+	0.182001i	−0.649267	−	0.760561i	$-0.724924\pi$
$683$	−8.23844	+	4.75647i	−0.315235	+	0.182001i	0.334032	+	0.942562i	$0.391591\pi$
$684$		0			0
$685$			5.08891i			0.194437i
$686$		0			0
$687$			5.91894i			0.225822i
$688$		0			0
$689$	−6.50876	+	3.75783i	−0.247964	+	0.143162i
$690$		0			0
$691$	−4.31202	+	7.46864i	−0.164037	+	0.284121i	−0.936313	−	0.351167i	$-0.885785\pi$
$691$	−4.31202	+	7.46864i	−0.164037	+	0.284121i	0.772276	+	0.635287i	$0.219118\pi$
$692$		0			0
$693$	−1.60306	−	0.0552313i	−0.0608954	−	0.00209806i
$694$		0			0
$695$	5.37759	+	3.10476i	0.203984	+	0.117770i
$696$		0			0
$697$	1.14647	+	1.98574i	0.0434257	+	0.0752154i
$698$		0			0
$699$	−24.0367			−0.909153
$700$		0			0
$701$	−34.8238			−1.31528			−0.657639	−	0.753333i	$-0.728445\pi$
$701$	−34.8238			−1.31528			−0.657639	+	0.753333i	$0.728445\pi$
$702$		0			0
$703$	−1.85596	−	3.21462i	−0.0699990	−	0.121242i
$704$		0			0
$705$	−10.9632	−	6.32958i	−0.412896	−	0.238386i
$706$		0			0
$707$	6.39574	+	12.0151i	0.240536	+	0.451874i
$708$		0			0
$709$	3.00807	−	5.21013i	0.112971	−	0.195671i	−0.803996	−	0.594635i	$-0.797297\pi$
$709$	3.00807	−	5.21013i	0.112971	−	0.195671i	0.916967	+	0.398964i	$0.130630\pi$
$710$		0			0
$711$	−7.50375	+	4.33229i	−0.281413	+	0.162474i
$712$		0			0
$713$		−	3.11867i		−	0.116795i
$714$		0			0
$715$		−	0.709832i		−	0.0265462i
$716$		0			0
$717$	−16.1481	+	9.32312i	−0.603063	+	0.348178i
$718$		0			0
$719$	13.0374	−	22.5814i	0.486212	−	0.842143i	−0.513663	−	0.857992i	$-0.671712\pi$
$719$	13.0374	−	22.5814i	0.486212	−	0.842143i	0.999874	+	0.0158490i	$0.00504509\pi$
$720$		0			0
$721$	34.0015	+	21.2244i	1.26628	+	0.790440i
$722$		0			0
$723$	2.55842	+	1.47711i	0.0951488	+	0.0549342i
$724$		0			0
$725$	−14.8839	−	25.7797i	−0.552774	−	0.957433i
$726$		0			0
$727$	7.71377			0.286088			0.143044	−	0.989716i	$-0.454311\pi$
$727$	7.71377			0.286088			0.143044	+	0.989716i	$0.454311\pi$
$728$		0			0
$729$	19.5612			0.724488
$730$		0			0
$731$	19.7106	+	34.1397i	0.729021	+	1.26270i
$732$		0			0
$733$	24.7621	+	14.2964i	0.914610	+	0.528050i	0.881912	−	0.471415i	$-0.156257\pi$
$733$	24.7621	+	14.2964i	0.914610	+	0.528050i	0.0326984	+	0.999465i	$0.489590\pi$
$734$		0			0
$735$	−0.554764	+	8.04133i	−0.0204628	+	0.296609i
$736$		0			0
$737$	3.43318	−	5.94644i	0.126463	−	0.219040i
$738$		0			0
$739$	7.46330	−	4.30894i	0.274542	−	0.158507i	−0.356408	−	0.934330i	$-0.615999\pi$
$739$	7.46330	−	4.30894i	0.274542	−	0.158507i	0.630950	+	0.775824i	$0.282665\pi$
$740$		0			0
$741$		−	0.893091i		−	0.0328085i
$742$		0			0
$743$			37.4501i			1.37391i	0.726700	+	0.686955i	$0.241053\pi$
$743$			37.4501i			1.37391i	−0.726700	+	0.686955i	$0.758947\pi$
$744$		0			0
$745$	−8.06722	+	4.65761i	−0.295560	+	0.170642i
$746$		0			0
$747$	−1.41148	+	2.44476i	−0.0516434	+	0.0894489i
$748$		0			0
$749$	11.5952	−	18.5755i	0.423679	−	0.678733i
$750$		0			0
$751$	5.23677	+	3.02345i	0.191093	+	0.110327i	0.592494	−	0.805575i	$-0.298143\pi$
$751$	5.23677	+	3.02345i	0.191093	+	0.110327i	−0.401401	+	0.915902i	$0.631477\pi$
$752$		0			0
$753$	−6.17405	−	10.6938i	−0.224995	−	0.389702i
$754$		0			0
$755$	10.9193			0.397395
$756$		0			0
$757$	−8.99118			−0.326790			−0.163395	−	0.986561i	$-0.552245\pi$
$757$	−8.99118			−0.326790			−0.163395	+	0.986561i	$0.552245\pi$
$758$		0			0
$759$	−3.57520	−	6.19242i	−0.129771	−	0.224771i
$760$		0			0
$761$	35.7062	+	20.6150i	1.29435	+	0.747293i	0.979422	−	0.201823i	$-0.0646865\pi$
$761$	35.7062	+	20.6150i	1.29435	+	0.747293i	0.314927	+	0.949116i	$0.398020\pi$
$762$		0			0
$763$	24.0145	−	12.7831i	0.869382	−	0.462779i
$764$		0			0
$765$	0.634697	−	1.09933i	0.0229475	−	0.0397463i
$766$		0			0
$767$	8.28676	−	4.78436i	0.299217	−	0.172753i
$768$		0			0
$769$		−	39.1340i		−	1.41121i	−0.708606	−	0.705605i	$-0.750675\pi$
$769$		−	39.1340i		−	1.41121i	0.708606	−	0.705605i	$-0.249325\pi$
$770$		0			0
$771$			30.1796i			1.08689i
$772$		0			0
$773$	−14.9975	+	8.65879i	−0.539421	+	0.311435i	−0.744844	−	0.667238i	$-0.767476\pi$
$773$	−14.9975	+	8.65879i	−0.539421	+	0.311435i	0.205423	+	0.978673i	$0.434143\pi$
$774$		0			0
$775$	−1.91839	+	3.32275i	−0.0689107	+	0.119357i
$776$		0			0
$777$	1.59849	−	46.3955i	0.0573456	−	1.66443i
$778$		0			0
$779$	0.231027	+	0.133383i	0.00827740	+	0.00477896i
$780$		0			0
$781$	4.40272	+	7.62573i	0.157542	+	0.272870i
$782$		0			0
$783$	29.2115			1.04393
$784$		0			0
$785$	−7.67048			−0.273771
$786$		0			0
$787$	17.6971	+	30.6522i	0.630832	+	1.09263i	0.987382	+	0.158357i	$0.0506198\pi$
$787$	17.6971	+	30.6522i	0.630832	+	1.09263i	−0.356549	+	0.934276i	$0.616047\pi$
$788$		0			0
$789$	−27.6533	−	15.9656i	−0.984482	−	0.568391i
$790$		0			0
$791$	0.355409	−	10.3156i	0.0126369	−	0.366780i
$792$		0			0
$793$	−1.02917	+	1.78258i	−0.0365470	+	0.0633013i
$794$		0			0
$795$	−6.40229	+	3.69636i	−0.227066	+	0.131097i
$796$		0			0
$797$			41.5036i			1.47013i	0.677995	+	0.735067i	$0.262849\pi$
$797$			41.5036i			1.47013i	−0.677995	+	0.735067i	$0.737151\pi$
$798$		0			0
$799$		−	37.9620i		−	1.34300i
$800$		0			0
$801$	8.69296	−	5.01888i	0.307151	−	0.177333i
$802$		0			0
$803$	0.464916	−	0.805258i	0.0164065	−	0.0284169i
$804$		0			0
$805$	−5.33224	+	2.83840i	−0.187937	+	0.100040i
$806$		0			0
$807$	−29.6377	−	17.1113i	−1.04330	−	0.602348i
$808$		0			0
$809$	−7.37690	−	12.7772i	−0.259358	−	0.449221i	0.706712	−	0.707501i	$-0.250178\pi$
$809$	−7.37690	−	12.7772i	−0.259358	−	0.449221i	−0.966070	+	0.258280i	$0.916844\pi$
$810$		0			0
$811$	−30.4216			−1.06825			−0.534124	−	0.845406i	$-0.679358\pi$
$811$	−30.4216			−1.06825			−0.534124	+	0.845406i	$0.679358\pi$
$812$		0			0
$813$	−1.74774			−0.0612960
$814$		0			0
$815$	1.68143	+	2.91232i	0.0588978	+	0.102014i
$816$		0			0
$817$	3.97190	+	2.29318i	0.138959	+	0.0802282i
$818$		0			0
$819$	0.994299	−	1.59287i	0.0347436	−	0.0556592i
$820$		0			0
$821$	−10.0238	+	17.3617i	−0.349832	+	0.605926i	−0.986219	−	0.165443i	$-0.947095\pi$
$821$	−10.0238	+	17.3617i	−0.349832	+	0.605926i	0.636388	+	0.771369i	$0.280428\pi$
$822$		0			0
$823$	0.947521	−	0.547052i	0.0330285	−	0.0190690i	−0.483395	−	0.875402i	$-0.660596\pi$
$823$	0.947521	−	0.547052i	0.0330285	−	0.0190690i	0.516423	+	0.856333i	$0.327263\pi$
$824$		0			0
$825$			8.79686i			0.306267i
$826$		0			0
$827$			13.5808i			0.472252i	0.971722	+	0.236126i	$0.0758778\pi$
$827$			13.5808i			0.472252i	−0.971722	+	0.236126i	$0.924122\pi$
$828$		0			0
$829$	−10.8216	+	6.24784i	−0.375849	+	0.216997i	−0.676011	−	0.736892i	$-0.736293\pi$
$829$	−10.8216	+	6.24784i	−0.375849	+	0.216997i	0.300162	+	0.953888i	$0.402959\pi$
$830$		0			0
$831$	−0.427578	+	0.740588i	−0.0148325	+	0.0256907i
$832$		0			0
$833$	−21.7153	+	10.6163i	−0.752389	+	0.367834i
$834$		0			0
$835$	6.95357	+	4.01464i	0.240638	+	0.138932i
$836$		0			0
$837$	−1.88254	−	3.26065i	−0.0650700	−	0.112705i
$838$		0			0
$839$	38.5168			1.32975			0.664874	−	0.746956i	$-0.268485\pi$
$839$	38.5168			1.32975			0.664874	+	0.746956i	$0.268485\pi$
$840$		0			0
$841$	12.2949			0.423960
$842$		0			0
$843$	−9.24215	−	16.0079i	−0.318317	−	0.551341i
$844$		0			0
$845$	−6.10700	−	3.52588i	−0.210087	−	0.121294i
$846$		0			0
$847$	−2.24438	−	1.40099i	−0.0771178	−	0.0481385i
$848$		0			0
$849$	−27.2274	+	47.1592i	−0.934442	+	1.61850i
$850$		0			0
$851$	30.1292	−	17.3951i	1.03282	−	0.596297i
$852$		0			0
$853$			53.1118i			1.81851i	0.416236	+	0.909257i	$0.363349\pi$
$853$			53.1118i			1.81851i	−0.416236	+	0.909257i	$0.636651\pi$
$854$		0			0
$855$		−	0.147685i		−	0.00505071i
$856$		0			0
$857$	−31.6039	+	18.2465i	−1.07957	+	0.623289i	−0.930780	−	0.365580i	$-0.880871\pi$
$857$	−31.6039	+	18.2465i	−1.07957	+	0.623289i	−0.148789	+	0.988869i	$0.547537\pi$
$858$		0			0
$859$	−28.2333	+	48.9015i	−0.963307	+	1.66850i	−0.249212	+	0.968449i	$0.580172\pi$
$859$	−28.2333	+	48.9015i	−0.963307	+	1.66850i	−0.714095	+	0.700049i	$0.753162\pi$
$860$		0			0
$861$	1.56767	+	2.94505i	0.0534262	+	0.100367i
$862$		0			0
$863$	14.4522	+	8.34401i	0.491960	+	0.284033i	0.725387	−	0.688341i	$-0.241661\pi$
$863$	14.4522	+	8.34401i	0.491960	+	0.284033i	−0.233427	+	0.972374i	$0.574994\pi$
$864$		0			0
$865$	5.23581	+	9.06868i	0.178023	+	0.308344i
$866$		0			0
$867$	−9.64007			−0.327394
$868$		0			0
$869$	−14.2918			−0.484818
$870$		0			0
$871$	4.01902	+	6.96115i	0.136179	+	0.235869i
$872$		0			0
$873$	−0.875210	−	0.505302i	−0.0296214	−	0.0171019i
$874$		0			0
$875$	15.4438	+	0.532095i	0.522097	+	0.0179881i
$876$		0			0
$877$	−24.7614	+	42.8880i	−0.836134	+	1.44823i	0.0569701	+	0.998376i	$0.481856\pi$
$877$	−24.7614	+	42.8880i	−0.836134	+	1.44823i	−0.893104	+	0.449850i	$0.851477\pi$
$878$		0			0
$879$	1.38890	−	0.801880i	0.0468463	−	0.0270467i
$880$		0			0
$881$			45.2632i			1.52495i	0.647015	+	0.762477i	$0.276017\pi$
$881$			45.2632i			1.52495i	−0.647015	+	0.762477i	$0.723983\pi$
$882$		0			0
$883$			46.5668i			1.56710i	0.621330	+	0.783549i	$0.286592\pi$
$883$			46.5668i			1.56710i	−0.621330	+	0.783549i	$0.713408\pi$
$884$		0			0
$885$	8.15121	−	4.70610i	0.274000	−	0.158194i
$886$		0			0
$887$	16.6852	−	28.8997i	0.560235	−	0.970356i	−0.437240	−	0.899345i	$-0.644044\pi$
$887$	16.6852	−	28.8997i	0.560235	−	0.970356i	0.997476	−	0.0710112i	$-0.0226226\pi$
$888$		0			0
$889$	−14.4380	−	0.497441i	−0.484235	−	0.0166836i
$890$		0			0
$891$	−9.05103	−	5.22562i	−0.303221	−	0.175065i
$892$		0			0
$893$	−2.20830	−	3.82489i	−0.0738979	−	0.127995i
$894$		0			0
$895$	−2.32219			−0.0776222
$896$		0			0
$897$	8.37054			0.279484
$898$		0			0
$899$	−2.66125	−	4.60943i	−0.0887578	−	0.153733i
$900$		0			0
$901$	−19.1990	−	11.0846i	−0.639612	−	0.369280i
$902$		0			0
$903$	26.9521	+	50.6324i	0.896908	+	1.68494i
$904$		0			0
$905$	3.40165	−	5.89184i	0.113075	−	0.195851i
$906$		0			0
$907$	−41.8831	+	24.1812i	−1.39070	+	0.802924i	−0.993393	−	0.114760i	$-0.963390\pi$
$907$	−41.8831	+	24.1812i	−1.39070	+	0.802924i	−0.397312	+	0.917684i	$0.630057\pi$
$908$		0			0
$909$		−	3.11897i		−	0.103450i
$910$		0			0
$911$		−	47.9172i		−	1.58757i	−0.608200	−	0.793784i	$-0.708108\pi$
$911$		−	47.9172i		−	1.58757i	0.608200	−	0.793784i	$-0.291892\pi$
$912$		0			0
$913$	−4.03252	+	2.32817i	−0.133457	+	0.0770513i
$914$		0			0
$915$	−1.01234	+	1.75342i	−0.0334669	+	0.0579664i
$916$		0			0
$917$	15.2227	+	9.50232i	0.502697	+	0.313794i
$918$		0			0
$919$	−13.6860	−	7.90162i	−0.451460	−	0.260650i	0.256987	−	0.966415i	$-0.417270\pi$
$919$	−13.6860	−	7.90162i	−0.451460	−	0.260650i	−0.708447	+	0.705764i	$0.750604\pi$
$920$		0			0
$921$	−2.48287	−	4.30045i	−0.0818132	−	0.141705i
$922$		0			0
$923$	−10.3080			−0.339292
$924$		0			0
$925$	−42.8011			−1.40729
$926$		0			0
$927$	−4.59231	−	7.95412i	−0.150831	−	0.261248i
$928$		0			0
$929$	5.35869	+	3.09384i	0.175813	+	0.101506i	0.585324	−	0.810799i	$-0.300967\pi$
$929$	5.35869	+	3.09384i	0.175813	+	0.101506i	−0.409511	+	0.912305i	$0.634301\pi$
$930$		0			0
$931$	−1.57037	+	2.33286i	−0.0514668	+	0.0764565i
$932$		0			0
$933$	6.09490	−	10.5567i	0.199538	−	0.345610i
$934$		0			0
$935$	1.81329	−	1.04690i	0.0593010	−	0.0342374i
$936$		0			0
$937$		−	53.4517i		−	1.74619i	−0.487550	−	0.873095i	$-0.662109\pi$
$937$		−	53.4517i		−	1.74619i	0.487550	−	0.873095i	$-0.337891\pi$
$938$		0			0
$939$		−	33.8690i		−	1.10527i
$940$		0			0
$941$	27.9190	−	16.1191i	0.910134	−	0.525466i	0.0296600	−	0.999560i	$-0.490558\pi$
$941$	27.9190	−	16.1191i	0.910134	−	0.525466i	0.880474	+	0.474094i	$0.157224\pi$
$942$		0			0
$943$	−1.25014	+	2.16531i	−0.0407102	+	0.0705122i
$944$		0			0
$945$	−3.86164	+	6.18634i	−0.125619	+	0.201242i
$946$		0			0
$947$	−6.08836	−	3.51511i	−0.197845	−	0.114226i	0.397805	−	0.917470i	$-0.369772\pi$
$947$	−6.08836	−	3.51511i	−0.197845	−	0.114226i	−0.595650	+	0.803244i	$0.703105\pi$
$948$		0			0
$949$	0.544249	+	0.942667i	0.0176671	+	0.0306003i
$950$		0			0
$951$	15.2375			0.494110
$952$		0			0
$953$	20.2427			0.655726			0.327863	−	0.944725i	$-0.393672\pi$
$953$	20.2427			0.655726			0.327863	+	0.944725i	$0.393672\pi$
$954$		0			0
$955$	−0.0984964	−	0.170601i	−0.00318727	−	0.00552051i
$956$		0			0
$957$	−10.5683	−	6.10164i	−0.341626	−	0.197238i
$958$		0			0
$959$	−19.6006	+	10.4335i	−0.632935	+	0.336916i
$960$		0			0
$961$	15.1570	−	26.2527i	0.488935	−	0.846861i
$962$		0			0
$963$	−4.34544	+	2.50884i	−0.140030	+	0.0808463i
$964$		0			0
$965$			4.73359i			0.152379i
$966$		0			0
$967$		−	9.39799i		−	0.302219i	−0.988517	−	0.151110i	$-0.951715\pi$
$967$		−	9.39799i		−	0.302219i	0.988517	−	0.151110i	$-0.0482846\pi$
$968$		0			0
$969$	2.28143	−	1.31719i	0.0732902	−	0.0423141i
$970$		0			0
$971$	−9.52517	+	16.4981i	−0.305677	+	0.529449i	−0.977412	−	0.211343i	$-0.932216\pi$
$971$	−9.52517	+	16.4981i	−0.305677	+	0.529449i	0.671735	+	0.740792i	$0.265550\pi$
$972$		0			0
$973$	−0.932934	+	27.0780i	−0.0299085	+	0.868081i
$974$		0			0
$975$	−8.91829	−	5.14898i	−0.285614	−	0.164899i
$976$		0			0
$977$	14.1813	+	24.5628i	0.453701	+	0.785833i	0.998612	−	0.0526606i	$-0.0167702\pi$
$977$	14.1813	+	24.5628i	0.453701	+	0.785833i	−0.544912	+	0.838493i	$0.683437\pi$
$978$		0			0
$979$	16.5568			0.529159
$980$		0			0
$981$	−6.23385			−0.199031
$982$		0			0
$983$	−17.0222	−	29.4834i	−0.542925	−	0.940374i	−0.998734	−	0.0502967i	$-0.983983\pi$
$983$	−17.0222	−	29.4834i	−0.542925	−	0.940374i	0.455809	−	0.890078i	$-0.349350\pi$
$984$		0			0
$985$	−10.4928	−	6.05805i	−0.334330	−	0.193025i
$986$		0			0
$987$	1.90195	−	55.2032i	0.0605397	−	1.75714i
$988$		0			0
$989$	−21.4929	+	37.2268i	−0.683435	+	1.18374i
$990$		0			0
$991$	−20.6674	+	11.9323i	−0.656522	+	0.379043i	−0.790950	−	0.611880i	$-0.790413\pi$
$991$	−20.6674	+	11.9323i	−0.656522	+	0.379043i	0.134429	+	0.990923i	$0.457080\pi$
$992$		0			0
$993$		−	7.69513i		−	0.244198i
$994$		0			0
$995$			10.1416i			0.321509i
$996$		0			0
$997$	−34.7131	+	20.0416i	−1.09938	+	0.634725i	−0.936057	−	0.351848i	$-0.885553\pi$
$997$	−34.7131	+	20.0416i	−1.09938	+	0.634725i	−0.163319	+	0.986573i	$0.552220\pi$
$998$		0			0
$999$	21.0006	−	36.3741i	0.664429	−	1.15082i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1232.2.be.c.1167.11	yes	28
4.3	odd	2		1232.2.be.b.1167.4	yes	28
7.3	odd	6		1232.2.be.b.815.4	✓	28
28.3	even	6	inner	1232.2.be.c.815.11	yes	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1232.2.be.b.815.4	✓	28	7.3	odd	6
1232.2.be.b.1167.4	yes	28	4.3	odd	2
1232.2.be.c.815.11	yes	28	28.3	even	6	inner
1232.2.be.c.1167.11	yes	28	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 1232 = 2^{4} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1232.be (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.949508 + 1.64460i) q^{3} +(-0.525125 - 0.303181i) q^{5} +(0.0911016 - 2.64418i) q^{7} +(-0.303130 + 0.525037i) q^{9} +O(q^{10})\)	\(q+(0.949508 + 1.64460i) q^{3} +(-0.525125 - 0.303181i) q^{5} +(0.0911016 - 2.64418i) q^{7} +(-0.303130 + 0.525037i) q^{9} +(-0.866025 + 0.500000i) q^{11} -1.17064i q^{13} -1.15149i q^{15} +(2.99044 - 1.72653i) q^{17} +(0.200869 - 0.347916i) q^{19} +(4.43511 - 2.36085i) q^{21} +(3.26086 + 1.88266i) q^{23} +(-2.31616 - 4.01171i) q^{25} +4.54575 q^{27} +6.42611 q^{29} +(-0.414132 - 0.717297i) q^{31} +(-1.64460 - 0.949508i) q^{33} +(-0.849506 + 1.36091i) q^{35} +(4.61983 - 8.00178i) q^{37} +(1.92523 - 1.11153i) q^{39} +0.664031i q^{41} +11.4163i q^{43} +(0.318363 - 0.183807i) q^{45} +(5.49685 - 9.52083i) q^{47} +(-6.98340 - 0.481778i) q^{49} +(5.67889 + 3.27871i) q^{51} +(-3.21007 - 5.56000i) q^{53} +0.606363 q^{55} +0.762908 q^{57} +(4.08696 + 7.07882i) q^{59} +(-1.52274 - 0.879154i) q^{61} +(1.36068 + 0.849364i) q^{63} +(-0.354916 + 0.614733i) q^{65} +(-5.94644 + 3.43318i) q^{67} +7.15039i q^{69} -8.80543i q^{71} +(-0.805258 + 0.464916i) q^{73} +(4.39843 - 7.61830i) q^{75} +(1.24319 + 2.33548i) q^{77} +(12.3771 + 7.14592i) q^{79} +(5.22562 + 9.05103i) q^{81} +4.65635 q^{83} -2.09381 q^{85} +(6.10164 + 10.5683i) q^{87} +(-14.3386 - 8.27842i) q^{89} +(-3.09539 - 0.106647i) q^{91} +(0.786442 - 1.36216i) q^{93} +(-0.210963 + 0.121800i) q^{95} +1.66695i q^{97} -0.606261i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 2 q^{3} - 2 q^{7} - 16 q^{9}+O(q^{10}) \) 28 * q + 2 * q^3 - 2 * q^7 - 16 * q^9	\( 28 q + 2 q^{3} - 2 q^{7} - 16 q^{9} + 18 q^{17} + 14 q^{19} - 2 q^{21} - 12 q^{23} + 14 q^{25} - 16 q^{27} + 16 q^{29} + 10 q^{31} + 6 q^{35} - 4 q^{37} + 42 q^{39} - 42 q^{45} + 6 q^{47} - 4 q^{49} - 24 q^{51} - 2 q^{53} - 48 q^{57} - 12 q^{59} - 12 q^{61} - 26 q^{63} + 6 q^{65} - 48 q^{67} + 6 q^{73} - 14 q^{75} + 2 q^{77} + 48 q^{79} - 22 q^{81} - 84 q^{83} + 16 q^{85} + 18 q^{87} + 6 q^{89} - 18 q^{91} + 28 q^{93} - 36 q^{95}+O(q^{100}) \) 28 * q + 2 * q^3 - 2 * q^7 - 16 * q^9 + 18 * q^17 + 14 * q^19 - 2 * q^21 - 12 * q^23 + 14 * q^25 - 16 * q^27 + 16 * q^29 + 10 * q^31 + 6 * q^35 - 4 * q^37 + 42 * q^39 - 42 * q^45 + 6 * q^47 - 4 * q^49 - 24 * q^51 - 2 * q^53 - 48 * q^57 - 12 * q^59 - 12 * q^61 - 26 * q^63 + 6 * q^65 - 48 * q^67 + 6 * q^73 - 14 * q^75 + 2 * q^77 + 48 * q^79 - 22 * q^81 - 84 * q^83 + 16 * q^85 + 18 * q^87 + 6 * q^89 - 18 * q^91 + 28 * q^93 - 36 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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