LMFDB - Embedded newform 483.2.j.a.229.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [483,2,Mod(229,483)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(483, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 5, 3]))

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

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

chi := DirichletCharacter("483.229");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 483 = 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	483.j (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:	$3.85677441763$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$32$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			229.11
Character	$\chi$	$=$	483.229
Dual form			483.2.j.a.367.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.585633 + 1.01435i) q^{2} +(0.866025 - 0.500000i) q^{3} +(0.314069 + 0.543983i) q^{4} +(-1.31255 + 2.27340i) q^{5} +1.17127i q^{6} +(1.98677 + 1.74721i) q^{7} -3.07825 q^{8} +(0.500000 - 0.866025i) q^{9} +(-1.53734 - 2.66275i) q^{10} +(-3.83128 + 2.21199i) q^{11} +(0.543983 + 0.314069i) q^{12} -1.06902i q^{13} +(-2.93579 + 0.992054i) q^{14} +2.62510i q^{15} +(1.17458 - 2.03444i) q^{16} +(-0.631390 - 1.09360i) q^{17} +(0.585633 + 1.01435i) q^{18} +(-0.917929 + 1.58990i) q^{19} -1.64892 q^{20} +(2.59420 + 0.519738i) q^{21} -5.18166i q^{22} +(2.70696 - 3.95884i) q^{23} +(-2.66584 + 1.53912i) q^{24} +(-0.945565 - 1.63777i) q^{25} +(1.08436 + 0.626053i) q^{26} -1.00000i q^{27} +(-0.326467 + 1.62951i) q^{28} +4.39831 q^{29} +(-2.66275 - 1.53734i) q^{30} +(-6.19592 + 3.57722i) q^{31} +(-1.70250 - 2.94881i) q^{32} +(-2.21199 + 3.83128i) q^{33} +1.47905 q^{34} +(-6.57984 + 2.22344i) q^{35} +0.628138 q^{36} +(3.11767 + 1.79999i) q^{37} +(-1.07514 - 1.86219i) q^{38} +(-0.534510 - 0.925799i) q^{39} +(4.04035 - 6.99809i) q^{40} +5.29644i q^{41} +(-2.04644 + 2.32704i) q^{42} +1.08271i q^{43} +(-2.40657 - 1.38944i) q^{44} +(1.31255 + 2.27340i) q^{45} +(2.43035 + 5.06421i) q^{46} +(9.04435 + 5.22176i) q^{47} -2.34917i q^{48} +(0.894541 + 6.94261i) q^{49} +2.21502 q^{50} +(-1.09360 - 0.631390i) q^{51} +(0.581529 - 0.335746i) q^{52} +(-9.49829 + 5.48384i) q^{53} +(1.01435 + 0.585633i) q^{54} -11.6134i q^{55} +(-6.11578 - 5.37833i) q^{56} +1.83586i q^{57} +(-2.57579 + 4.46141i) q^{58} +(-4.60325 + 2.65769i) q^{59} +(-1.42801 + 0.824461i) q^{60} +(4.33014 - 7.50003i) q^{61} -8.37974i q^{62} +(2.50651 - 0.846993i) q^{63} +8.68649 q^{64} +(2.43031 + 1.40314i) q^{65} +(-2.59083 - 4.48745i) q^{66} +(3.49427 - 2.01742i) q^{67} +(0.396600 - 0.686931i) q^{68} +(0.364873 - 4.78193i) q^{69} +(1.59803 - 7.97634i) q^{70} +12.3268 q^{71} +(-1.53912 + 2.66584i) q^{72} +(-6.54424 + 3.77832i) q^{73} +(-3.65161 + 2.10826i) q^{74} +(-1.63777 - 0.945565i) q^{75} -1.15317 q^{76} +(-11.4767 - 2.29931i) q^{77} +1.25211 q^{78} +(-3.14200 - 1.81403i) q^{79} +(3.08340 + 5.34060i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-5.37242 - 3.10177i) q^{82} +7.03615 q^{83} +(0.532029 + 1.57443i) q^{84} +3.31492 q^{85} +(-1.09824 - 0.634071i) q^{86} +(3.80905 - 2.19916i) q^{87} +(11.7936 - 6.80906i) q^{88} +(6.35170 - 11.0015i) q^{89} -3.07468 q^{90} +(1.86780 - 2.12390i) q^{91} +(3.00371 + 0.229191i) q^{92} +(-3.57722 + 6.19592i) q^{93} +(-10.5933 + 6.11606i) q^{94} +(-2.40965 - 4.17364i) q^{95} +(-2.94881 - 1.70250i) q^{96} +3.50817 q^{97} +(-7.56607 - 3.15844i) q^{98} +4.42398i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q + 4 q^{2} - 36 q^{4} - 24 q^{8} + 32 q^{9} - 44 q^{16} - 4 q^{18} - 16 q^{23} - 12 q^{25} + 84 q^{26} + 24 q^{29} - 12 q^{31} + 8 q^{32} + 32 q^{35} - 72 q^{36} - 8 q^{46} - 12 q^{47} + 8 q^{49} - 96 q^{50}+ \cdots + 112 q^{98}+O(q^{100}) $ 64 * q + 4 * q^2 - 36 * q^4 - 24 * q^8 + 32 * q^9 - 44 * q^16 - 4 * q^18 - 16 * q^23 - 12 * q^25 + 84 * q^26 + 24 * q^29 - 12 * q^31 + 8 * q^32 + 32 * q^35 - 72 * q^36 - 8 * q^46 - 12 * q^47 + 8 * q^49 - 96 * q^50 - 108 * q^52 - 24 * q^58 + 36 * q^59 + 168 * q^64 - 40 * q^70 - 16 * q^71 - 12 * q^72 + 48 * q^73 - 48 * q^75 - 32 * q^78 - 32 * q^81 - 24 * q^82 + 88 * q^85 + 36 * q^87 + 152 * q^92 + 24 * q^93 - 108 * q^94 - 44 * q^95 + 60 * q^96 + 112 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/483\mathbb{Z}\right)^\times$.

$n$	$323$	$346$	$442$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$-1$

Coefficient data

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

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

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

$2$	−0.585633	+	1.01435i	−0.414105	+	0.717251i	−0.995334	−	0.0964893i	$-0.969239\pi$
$2$	−0.585633	+	1.01435i	−0.414105	+	0.717251i	0.581229	+	0.813740i	$0.302572\pi$
$3$	0.866025	−	0.500000i	0.500000	−	0.288675i
$3$	0.866025	−	0.500000i	0.500000	−	0.288675i
$4$	0.314069	+	0.543983i	0.157034	+	0.271992i
$5$	−1.31255	+	2.27340i	−0.586989	+	1.01670i	0.407635	+	0.913145i	$0.366354\pi$
$5$	−1.31255	+	2.27340i	−0.586989	+	1.01670i	−0.994624	+	0.103550i	$0.966980\pi$
$6$			1.17127i			0.478167i
$7$	1.98677	+	1.74721i	0.750930	+	0.660382i
$7$	1.98677	+	1.74721i	0.750930	+	0.660382i
$8$	−3.07825			−1.08832
$9$	0.500000	−	0.866025i	0.166667	−	0.288675i
$10$	−1.53734	−	2.66275i	−0.486150	−	0.842037i
$11$	−3.83128	+	2.21199i	−1.15518	+	0.666941i	−0.950143	−	0.311815i	$-0.899063\pi$
$11$	−3.83128	+	2.21199i	−1.15518	+	0.666941i	−0.205032	+	0.978755i	$0.565730\pi$
$12$	0.543983	+	0.314069i	0.157034	+	0.0906639i
$13$		−	1.06902i		−	0.296493i	−0.988950	−	0.148246i	$-0.952637\pi$
$13$		−	1.06902i		−	0.296493i	0.988950	−	0.148246i	$-0.0473629\pi$
$14$	−2.93579	+	0.992054i	−0.784623	+	0.265138i
$15$			2.62510i			0.677797i
$16$	1.17458	−	2.03444i	0.293646	−	0.508610i
$17$	−0.631390	−	1.09360i	−0.153134	−	0.265237i	0.779244	−	0.626721i	$-0.215603\pi$
$17$	−0.631390	−	1.09360i	−0.153134	−	0.265237i	−0.932378	+	0.361484i	$0.882270\pi$
$18$	0.585633	+	1.01435i	0.138035	+	0.239084i
$19$	−0.917929	+	1.58990i	−0.210587	+	0.364748i	−0.951898	−	0.306414i	$-0.900871\pi$
$19$	−0.917929	+	1.58990i	−0.210587	+	0.364748i	0.741311	+	0.671162i	$0.234204\pi$
$20$	−1.64892			−0.368710
$21$	2.59420	+	0.519738i	0.566101	+	0.113416i
$22$		−	5.18166i		−	1.10473i
$23$	2.70696	−	3.95884i	0.564439	−	0.825475i
$23$	2.70696	−	3.95884i	0.564439	−	0.825475i
$24$	−2.66584	+	1.53912i	−0.544162	+	0.314172i
$25$	−0.945565	−	1.63777i	−0.189113	−	0.327553i
$26$	1.08436	+	0.626053i	0.212660	+	0.122779i
$27$		−	1.00000i		−	0.192450i
$28$	−0.326467	+	1.62951i	−0.0616965	+	0.307949i
$29$	4.39831			0.816746			0.408373	−	0.912815i	$-0.366096\pi$
$29$	4.39831			0.816746			0.408373	+	0.912815i	$0.366096\pi$
$30$	−2.66275	−	1.53734i	−0.486150	−	0.280679i
$31$	−6.19592	+	3.57722i	−1.11282	+	0.642487i	−0.939558	−	0.342389i	$-0.888764\pi$
$31$	−6.19592	+	3.57722i	−1.11282	+	0.642487i	−0.173262	+	0.984876i	$0.555431\pi$
$32$	−1.70250	−	2.94881i	−0.300962	−	0.521281i
$33$	−2.21199	+	3.83128i	−0.385058	+	0.666941i
$34$	1.47905			0.253655
$35$	−6.57984	+	2.22344i	−1.11220	+	0.375830i
$36$	0.628138			0.104690
$37$	3.11767	+	1.79999i	0.512541	+	0.295916i	0.733878	−	0.679282i	$-0.237709\pi$
$37$	3.11767	+	1.79999i	0.512541	+	0.295916i	−0.221336	+	0.975198i	$0.571042\pi$
$38$	−1.07514	−	1.86219i	−0.174410	−	0.302088i
$39$	−0.534510	−	0.925799i	−0.0855901	−	0.148246i
$40$	4.04035	−	6.99809i	0.638835	−	1.10649i
$41$			5.29644i			0.827166i	0.910466	+	0.413583i	$0.135723\pi$
$41$			5.29644i			0.827166i	−0.910466	+	0.413583i	$0.864277\pi$
$42$	−2.04644	+	2.32704i	−0.315773	+	0.359070i
$43$			1.08271i			0.165112i	0.996586	+	0.0825560i	$0.0263083\pi$
$43$			1.08271i			0.165112i	−0.996586	+	0.0825560i	$0.973692\pi$
$44$	−2.40657	−	1.38944i	−0.362805	−	0.209465i
$45$	1.31255	+	2.27340i	0.195663	+	0.338898i
$46$	2.43035	+	5.06421i	0.358335	+	0.746677i
$47$	9.04435	+	5.22176i	1.31925	+	0.761672i	0.983609	−	0.180317i	$-0.0577122\pi$
$47$	9.04435	+	5.22176i	1.31925	+	0.761672i	0.335646	+	0.941988i	$0.391046\pi$
$48$		−	2.34917i		−	0.339073i
$49$	0.894541	+	6.94261i	0.127792	+	0.991801i
$50$	2.21502			0.313251
$51$	−1.09360	−	0.631390i	−0.153134	−	0.0884122i
$52$	0.581529	−	0.335746i	0.0806436	−	0.0465596i
$53$	−9.49829	+	5.48384i	−1.30469	+	0.753263i	−0.981205	−	0.192970i	$-0.938188\pi$
$53$	−9.49829	+	5.48384i	−1.30469	+	0.753263i	−0.323486	+	0.946233i	$0.604855\pi$
$54$	1.01435	+	0.585633i	0.138035	+	0.0796945i
$55$		−	11.6134i		−	1.56595i
$56$	−6.11578	−	5.37833i	−0.817255	−	0.718710i
$57$			1.83586i			0.243165i
$58$	−2.57579	+	4.46141i	−0.338218	+	0.585811i
$59$	−4.60325	+	2.65769i	−0.599292	+	0.346001i	−0.768763	−	0.639534i	$-0.779127\pi$
$59$	−4.60325	+	2.65769i	−0.599292	+	0.346001i	0.169471	+	0.985535i	$0.445794\pi$
$60$	−1.42801	+	0.824461i	−0.184355	+	0.106437i
$61$	4.33014	−	7.50003i	0.554418	−	0.960280i	−0.443531	−	0.896259i	$-0.646274\pi$
$61$	4.33014	−	7.50003i	0.554418	−	0.960280i	0.997949	−	0.0640207i	$-0.0203924\pi$
$62$		−	8.37974i		−	1.06423i
$63$	2.50651	−	0.846993i	0.315791	−	0.106711i
$64$	8.68649			1.08581
$65$	2.43031	+	1.40314i	0.301443	+	0.174038i
$66$	−2.59083	−	4.48745i	−0.318909	−	0.552367i
$67$	3.49427	−	2.01742i	0.426893	−	0.246467i	−0.271129	−	0.962543i	$-0.587397\pi$
$67$	3.49427	−	2.01742i	0.426893	−	0.246467i	0.698022	+	0.716076i	$0.254064\pi$
$68$	0.396600	−	0.686931i	0.0480948	−	0.0833026i
$69$	0.364873	−	4.78193i	0.0439256	−	0.575677i
$70$	1.59803	−	7.97634i	0.191001	−	0.953356i
$71$	12.3268			1.46293			0.731464	−	0.681880i	$-0.238838\pi$
$71$	12.3268			1.46293			0.731464	+	0.681880i	$0.238838\pi$
$72$	−1.53912	+	2.66584i	−0.181387	+	0.314172i
$73$	−6.54424	+	3.77832i	−0.765945	+	0.442219i	−0.831426	−	0.555635i	$-0.812475\pi$
$73$	−6.54424	+	3.77832i	−0.765945	+	0.442219i	0.0654811	+	0.997854i	$0.479142\pi$
$74$	−3.65161	+	2.10826i	−0.424492	+	0.245080i
$75$	−1.63777	−	0.945565i	−0.189113	−	0.109184i
$76$	−1.15317			−0.132278
$77$	−11.4767	−	2.29931i	−1.30789	−	0.262031i
$78$	1.25211			0.141773
$79$	−3.14200	−	1.81403i	−0.353502	−	0.204095i	0.312724	−	0.949844i	$-0.398758\pi$
$79$	−3.14200	−	1.81403i	−0.353502	−	0.204095i	−0.666227	+	0.745749i	$0.732092\pi$
$80$	3.08340	+	5.34060i	0.344734	+	0.597097i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	−5.37242	−	3.10177i	−0.593285	−	0.342533i
$83$	7.03615			0.772318			0.386159	−	0.922432i	$-0.373802\pi$
$83$	7.03615			0.772318			0.386159	+	0.922432i	$0.373802\pi$
$84$	0.532029	+	1.57443i	0.0580491	+	0.171785i
$85$	3.31492			0.359553
$86$	−1.09824	−	0.634071i	−0.118427	−	0.0683737i
$87$	3.80905	−	2.19916i	0.408373	−	0.235774i
$88$	11.7936	−	6.80906i	1.25721	−	0.725848i
$89$	6.35170	−	11.0015i	0.673278	−	1.16615i	−0.303690	−	0.952771i	$-0.598219\pi$
$89$	6.35170	−	11.0015i	0.673278	−	1.16615i	0.976969	−	0.213382i	$-0.0684478\pi$
$90$	−3.07468			−0.324100
$91$	1.86780	−	2.12390i	0.195799	−	0.222645i
$92$	3.00371	+	0.229191i	0.313159	+	0.0238948i
$93$	−3.57722	+	6.19592i	−0.370940	+	0.642487i
$94$	−10.5933	+	6.11606i	−1.09262	+	0.630824i
$95$	−2.40965	−	4.17364i	−0.247225	−	0.428206i
$96$	−2.94881	−	1.70250i	−0.300962	−	0.173760i
$97$	3.50817			0.356201			0.178100	−	0.984012i	$-0.443005\pi$
$97$	3.50817			0.356201			0.178100	+	0.984012i	$0.443005\pi$
$98$	−7.56607	−	3.15844i	−0.764289	−	0.319051i
$99$			4.42398i			0.444627i
$100$	0.593945	−	1.02874i	0.0593945	−	0.102874i
$101$	−4.01799	+	2.31979i	−0.399805	+	0.230828i	−0.686400	−	0.727224i	$-0.740810\pi$
$101$	−4.01799	+	2.31979i	−0.399805	+	0.230828i	0.286595	+	0.958052i	$0.407477\pi$
$102$	1.28089	−	0.739525i	0.126827	−	0.0732238i
$103$	−4.28222	+	7.41703i	−0.421940	+	0.730822i	−0.996129	−	0.0879011i	$-0.971984\pi$
$103$	−4.28222	+	7.41703i	−0.421940	+	0.730822i	0.574189	+	0.818723i	$0.305317\pi$
$104$			3.29071i			0.322680i
$105$	−4.58658	+	5.21547i	−0.447605	+	0.508978i
$106$		−	12.8461i		−	1.24772i
$107$	13.7376	+	7.93144i	1.32807	+	0.766761i	0.985001	−	0.172550i	$-0.0552006\pi$
$107$	13.7376	+	7.93144i	1.32807	+	0.766761i	0.343068	+	0.939311i	$0.388534\pi$
$108$	0.543983	−	0.314069i	0.0523448	−	0.0302213i
$109$	12.8951	−	7.44500i	1.23513	−	0.713101i	0.267033	−	0.963687i	$-0.413957\pi$
$109$	12.8951	−	7.44500i	1.23513	−	0.713101i	0.968094	+	0.250586i	$0.0806233\pi$
$110$	11.7800	+	6.80118i	1.12318	+	0.648467i
$111$	3.59997			0.341694
$112$	5.88822	−	1.98973i	0.556384	−	0.188012i
$113$			10.0045i			0.941141i	0.882362	+	0.470571i	$0.155952\pi$
$113$			10.0045i			0.941141i	−0.882362	+	0.470571i	$0.844048\pi$
$114$	−1.86219	−	1.07514i	−0.174410	−	0.100696i
$115$	5.44701	+	11.3502i	0.507937	+	1.05841i
$116$	1.38137	+	2.39261i	0.128257	+	0.222148i
$117$	−0.925799	−	0.534510i	−0.0855901	−	0.0494155i
$118$		−	6.22571i		−	0.573123i
$119$	0.656314	−	3.27590i	0.0601642	−	0.300301i
$120$		−	8.08069i		−	0.737663i
$121$	4.28582	−	7.42325i	0.389620	−	0.674841i
$122$	5.07174	+	8.78452i	0.459174	+	0.795313i
$123$	2.64822	+	4.58686i	0.238782	+	0.413583i
$124$	−3.89189	−	2.24698i	−0.349502	−	0.201785i
$125$	−8.16108			−0.729949
$126$	−0.608751	+	3.03850i	−0.0542319	+	0.270691i
$127$	15.8378			1.40538			0.702691	−	0.711496i	$-0.251982\pi$
$127$	15.8378			1.40538			0.702691	+	0.711496i	$0.251982\pi$
$128$	−1.68210	+	2.91347i	−0.148678	+	0.257517i
$129$	0.541356	+	0.937656i	0.0476637	+	0.0825560i
$130$	−2.84654	+	1.64345i	−0.249658	+	0.144140i
$131$	7.08700	+	4.09168i	0.619194	+	0.357492i	0.776555	−	0.630049i	$-0.216965\pi$
$131$	7.08700	+	4.09168i	0.619194	+	0.357492i	−0.157361	+	0.987541i	$0.550299\pi$
$132$	−2.77887			−0.241870
$133$	−4.60160	+	1.55496i	−0.399009	+	0.134832i
$134$			4.72586i			0.408252i
$135$	2.27340	+	1.31255i	0.195663	+	0.112966i
$136$	1.94357	+	3.36637i	0.166660	+	0.288664i
$137$	18.0495	−	10.4209i	1.54208	−	0.890318i	0.543369	−	0.839494i	$-0.317149\pi$
$137$	18.0495	−	10.4209i	1.54208	−	0.890318i	0.998708	−	0.0508242i	$-0.0161848\pi$
$138$	4.63685	+	3.17056i	0.394715	+	0.269896i
$139$		−	13.9439i		−	1.18271i	−0.806412	−	0.591355i	$-0.798593\pi$
$139$		−	13.9439i		−	1.18271i	0.806412	−	0.591355i	$-0.201407\pi$
$140$	−3.27604	−	2.88101i	−0.276876	−	0.243490i
$141$	10.4435			0.879503
$142$	−7.21900	+	12.5037i	−0.605805	+	1.04929i
$143$	2.36466	+	4.09572i	0.197743	+	0.342501i
$144$	−1.17458	−	2.03444i	−0.0978820	−	0.169537i
$145$	−5.77299	+	9.99912i	−0.479421	+	0.830382i
$146$		−	8.85082i		−	0.732499i
$147$	4.24600	+	5.56520i	0.350204	+	0.459010i
$148$			2.26128i			0.185876i
$149$	8.52284	+	4.92066i	0.698218	+	0.403116i	0.806683	−	0.590984i	$-0.201260\pi$
$149$	8.52284	+	4.92066i	0.698218	+	0.403116i	−0.108465	+	0.994100i	$0.534594\pi$
$150$	1.91826	−	1.10751i	0.156625	−	0.0904276i
$151$	1.75246	+	3.03535i	0.142613	+	0.247013i	0.928480	−	0.371383i	$-0.121116\pi$
$151$	1.75246	+	3.03535i	0.142613	+	0.247013i	−0.785867	+	0.618396i	$0.787783\pi$
$152$	2.82561	−	4.89410i	0.229187	−	0.396964i
$153$	−1.26278			−0.102090
$154$	9.05343	−	10.2948i	0.729546	−	0.829577i
$155$		−	18.7811i		−	1.50853i
$156$	0.335746	−	0.581529i	0.0268812	−	0.0465596i
$157$	−11.0316	−	19.1074i	−0.880420	−	1.52493i	−0.850874	−	0.525370i	$-0.823927\pi$
$157$	−11.0316	−	19.1074i	−0.880420	−	1.52493i	−0.0295463	−	0.999563i	$-0.509406\pi$
$158$	3.68011	−	2.12471i	0.292774	−	0.169033i
$159$	−5.48384	+	9.49829i	−0.434897	+	0.753263i
$160$	8.93844			0.706646
$161$	12.2950	−	3.13571i	0.968983	−	0.247128i
$162$	1.17127			0.0920233
$163$	−4.63786	+	8.03301i	−0.363265	+	0.629194i	−0.988496	−	0.151246i	$-0.951671\pi$
$163$	−4.63786	+	8.03301i	−0.363265	+	0.629194i	0.625231	+	0.780440i	$0.285005\pi$
$164$	−2.88118	+	1.66345i	−0.224982	+	0.129894i
$165$	−5.80669	−	10.0575i	−0.452050	−	0.782974i
$166$	−4.12060	+	7.13709i	−0.319821	+	0.553946i
$167$		−	0.776446i		−	0.0600832i	−0.999549	−	0.0300416i	$-0.990436\pi$
$167$		−	0.776446i		−	0.0600832i	0.999549	−	0.0300416i	$-0.00956398\pi$
$168$	−7.98559	−	1.59988i	−0.616101	−	0.123434i
$169$	11.8572			0.912092
$170$	−1.94132	+	3.36247i	−0.148893	+	0.257890i
$171$	0.917929	+	1.58990i	0.0701958	+	0.121583i
$172$	−0.588977	+	0.340046i	−0.0449091	+	0.0259283i
$173$	−14.2142	−	8.20657i	−1.08069	−	0.623934i	−0.149604	−	0.988746i	$-0.547800\pi$
$173$	−14.2142	−	8.20657i	−1.08069	−	0.623934i	−0.931081	+	0.364812i	$0.881133\pi$
$174$			5.15159i			0.390541i
$175$	0.982893	−	4.90597i	0.0742997	−	0.370857i
$176$			10.3927i			0.783378i
$177$	−2.65769	+	4.60325i	−0.199764	+	0.346001i
$178$	7.43952	+	12.8856i	0.557616	+	0.965819i
$179$	−5.92963	−	10.2704i	−0.443202	−	0.767648i	0.554723	−	0.832035i	$-0.312824\pi$
$179$	−5.92963	−	10.2704i	−0.443202	−	0.767648i	−0.997925	+	0.0643872i	$0.979491\pi$
$180$	−0.824461	+	1.42801i	−0.0614517	+	0.106437i
$181$	−16.7131			−1.24227			−0.621136	−	0.783702i	$-0.713329\pi$
$181$	−16.7131			−1.24227			−0.621136	+	0.783702i	$0.713329\pi$
$182$	1.06053	+	3.13842i	0.0786114	+	0.232635i
$183$		−	8.66028i		−	0.640187i
$184$	−8.33268	+	12.1863i	−0.614293	+	0.898384i
$185$	−8.18417	+	4.72514i	−0.601712	+	0.347399i
$186$	−4.18987	−	7.25706i	−0.307216	−	0.532114i
$187$	4.83806	+	2.79326i	0.353794	+	0.204263i
$188$			6.55997i			0.478435i
$189$	1.74721	−	1.98677i	0.127091	−	0.144517i
$190$	5.64468			0.409508
$191$	−10.6475	−	6.14735i	−0.770427	−	0.444806i	0.0625996	−	0.998039i	$-0.480061\pi$
$191$	−10.6475	−	6.14735i	−0.770427	−	0.444806i	−0.833027	+	0.553232i	$0.813394\pi$
$192$	7.52272	−	4.34324i	0.542905	−	0.313447i
$193$	11.6142	+	20.1163i	0.836006	+	1.44800i	0.893209	+	0.449642i	$0.148449\pi$
$193$	11.6142	+	20.1163i	0.836006	+	1.44800i	−0.0572028	+	0.998363i	$0.518218\pi$
$194$	−2.05450	+	3.55850i	−0.147504	+	0.255485i
$195$	2.80628			0.200962
$196$	−3.49571	+	2.66707i	−0.249694	+	0.190505i
$197$	−10.6853			−0.761293			−0.380646	−	0.924721i	$-0.624299\pi$
$197$	−10.6853			−0.761293			−0.380646	+	0.924721i	$0.624299\pi$
$198$	−4.48745	−	2.59083i	−0.318909	−	0.184122i
$199$	1.36584	+	2.36571i	0.0968222	+	0.167701i	0.910368	−	0.413800i	$-0.135799\pi$
$199$	1.36584	+	2.36571i	0.0968222	+	0.167701i	−0.813545	+	0.581501i	$0.802466\pi$
$200$	2.91068	+	5.04145i	0.205816	+	0.356484i
$201$	2.01742	−	3.49427i	0.142298	−	0.246467i
$202$		−	5.43418i		−	0.382347i
$203$	8.73845	+	7.68476i	0.613319	+	0.539364i
$204$		−	0.793199i		−	0.0555351i
$205$	−12.0409	−	6.95184i	−0.840976	−	0.485537i
$206$	−5.01562	−	8.68731i	−0.349455	−	0.605273i
$207$	−2.07498	−	4.32371i	−0.144221	−	0.300519i
$208$	−2.17486	−	1.25565i	−0.150799	−	0.0870639i
$209$		−	8.12181i		−	0.561797i
$210$	−2.60424	−	7.70673i	−0.179709	−	0.531815i
$211$	−20.0123			−1.37771			−0.688853	−	0.724901i	$-0.741886\pi$
$211$	−20.0123			−1.37771			−0.688853	+	0.724901i	$0.741886\pi$
$212$	−5.96624	−	3.44461i	−0.409763	−	0.236577i
$213$	10.6754	−	6.16342i	0.731464	−	0.422311i
$214$	−16.0904	+	9.28981i	−1.09992	+	0.635039i
$215$	−2.46144	−	1.42111i	−0.167869	−	0.0969190i
$216$			3.07825i			0.209448i
$217$	−18.5600	−	3.71843i	−1.25994	−	0.252423i
$218$			17.4401i			1.18119i
$219$	−3.77832	+	6.54424i	−0.255315	+	0.442219i
$220$	6.31749	−	3.64740i	0.425925	−	0.245908i
$221$	−1.16908	+	0.674968i	−0.0786408	+	0.0454033i
$222$	−2.10826	+	3.65161i	−0.141497	+	0.245080i
$223$			1.20048i			0.0803898i	0.999192	+	0.0401949i	$0.0127979\pi$
$223$			1.20048i			0.0803898i	−0.999192	+	0.0401949i	$0.987202\pi$
$224$	1.76971	−	8.83324i	0.118243	−	0.590195i
$225$	−1.89113			−0.126075
$226$	−10.1480	−	5.85894i	−0.675034	−	0.389731i
$227$	−3.07964	−	5.33409i	−0.204403	−	0.354036i	0.745540	−	0.666461i	$-0.232192\pi$
$227$	−3.07964	−	5.33409i	−0.204403	−	0.354036i	−0.949942	+	0.312425i	$0.898859\pi$
$228$	−0.998676	+	0.576586i	−0.0661389	+	0.0381853i
$229$	−7.44292	+	12.8915i	−0.491842	+	0.851895i	−0.999956	−	0.00939460i	$-0.997010\pi$
$229$	−7.44292	+	12.8915i	−0.491842	+	0.851895i	0.508114	+	0.861290i	$0.330343\pi$
$230$	−14.7029	−	1.12187i	−0.969482	−	0.0739739i
$231$	−11.0888	+	3.74709i	−0.729587	+	0.246540i
$232$	−13.5391			−0.888884
$233$	9.78731	−	16.9521i	0.641188	−	1.11057i	−0.343980	−	0.938977i	$-0.611775\pi$
$233$	9.78731	−	16.9521i	0.641188	−	1.11057i	0.985168	−	0.171593i	$-0.0548914\pi$
$234$	1.08436	−	0.626053i	0.0708866	−	0.0409264i
$235$	−23.7423	+	13.7076i	−1.54878	+	0.894186i
$236$	−2.89147	−	1.66939i	−0.188219	−	0.108668i
$237$	−3.62807			−0.235668
$238$	2.93854	+	2.58420i	0.190477	+	0.167509i
$239$	16.3375			1.05678			0.528392	−	0.849000i	$-0.322795\pi$
$239$	16.3375			1.05678			0.528392	+	0.849000i	$0.322795\pi$
$240$	5.34060	+	3.08340i	0.344734	+	0.199032i
$241$	−13.5181	−	23.4140i	−0.870776	−	1.50823i	−0.861196	−	0.508274i	$-0.830284\pi$
$241$	−13.5181	−	23.4140i	−0.870776	−	1.50823i	−0.00958007	−	0.999954i	$-0.503049\pi$
$242$	5.01983	+	8.69460i	0.322687	+	0.558910i
$243$	−0.866025	−	0.500000i	−0.0555556	−	0.0320750i
$244$	5.43985			0.348251
$245$	−16.9575	−	7.07886i	−1.08337	−	0.452252i
$246$	−6.20354			−0.395523
$247$	1.69964	+	0.981285i	0.108145	+	0.0624377i
$248$	19.0726	−	11.0116i	1.21111	−	0.699234i
$249$	6.09349	−	3.51808i	0.386159	−	0.222949i
$250$	4.77940	−	8.27816i	0.302275	−	0.523557i
$251$	−18.7998			−1.18663			−0.593317	−	0.804969i	$-0.702182\pi$
$251$	−18.7998			−1.18663			−0.593317	+	0.804969i	$0.702182\pi$
$252$	1.24797	+	1.09749i	0.0786146	+	0.0691351i
$253$	−1.61419	+	21.1552i	−0.101483	+	1.33002i
$254$	−9.27516	+	16.0650i	−0.581975	+	1.00801i
$255$	2.87080	−	1.65746i	0.179777	−	0.103794i
$256$	6.71631	+	11.6330i	0.419769	+	0.727062i
$257$	17.9778	+	10.3795i	1.12143	+	0.647456i	0.941765	−	0.336272i	$-0.109166\pi$
$257$	17.9778	+	10.3795i	1.12143	+	0.647456i	0.179662	+	0.983728i	$0.442500\pi$
$258$	−1.26814			−0.0789511
$259$	3.04915	+	9.02337i	0.189465	+	0.560685i
$260$			1.76273i			0.109320i
$261$	2.19916	−	3.80905i	0.136124	−	0.235774i
$262$	−8.30076	+	4.79244i	−0.512823	+	0.296078i
$263$	−4.46298	+	2.57670i	−0.275199	+	0.158886i	−0.631248	−	0.775581i	$-0.717457\pi$
$263$	−4.46298	+	2.57670i	−0.275199	+	0.158886i	0.356049	+	0.934467i	$0.384124\pi$
$264$	6.80906	−	11.7936i	0.419068	−	0.725848i
$265$		−	28.7912i		−	1.76863i
$266$	1.11758	−	5.57825i	0.0685233	−	0.342024i
$267$		−	12.7034i		−	0.777435i
$268$	2.19488	+	1.26722i	0.134074	+	0.0774075i
$269$	−8.06123	+	4.65415i	−0.491502	+	0.283769i	−0.725197	−	0.688541i	$-0.758251\pi$
$269$	−8.06123	+	4.65415i	−0.491502	+	0.283769i	0.233695	+	0.972310i	$0.424918\pi$
$270$	−2.66275	+	1.53734i	−0.162050	+	0.0935597i
$271$	−21.3007	−	12.2980i	−1.29393	−	0.747049i	−0.314578	−	0.949232i	$-0.601863\pi$
$271$	−21.3007	−	12.2980i	−1.29393	−	0.747049i	−0.979348	+	0.202183i	$0.935196\pi$
$272$	−2.96648			−0.179869
$273$	0.555611	−	2.77325i	0.0336271	−	0.167845i
$274$			24.4113i			1.47474i
$275$	7.24546	+	4.18317i	0.436918	+	0.252254i
$276$	2.71589	−	1.30337i	0.163477	−	0.0784537i
$277$	−1.03536	−	1.79330i	−0.0622088	−	0.107749i	0.833244	−	0.552906i	$-0.186481\pi$
$277$	−1.03536	−	1.79330i	−0.0622088	−	0.107749i	−0.895452	+	0.445157i	$0.853148\pi$
$278$	14.1440	+	8.16602i	0.848299	+	0.489766i
$279$			7.15443i			0.428325i
$280$	20.2544	−	6.84429i	1.21043	−	0.409025i
$281$		−	25.5993i		−	1.52712i	−0.645734	−	0.763562i	$-0.723449\pi$
$281$		−	25.5993i		−	1.52712i	0.645734	−	0.763562i	$-0.276551\pi$
$282$	−6.11606	+	10.5933i	−0.364206	+	0.630824i
$283$	5.56134	+	9.63251i	0.330587	+	0.572594i	0.982627	−	0.185591i	$-0.0594199\pi$
$283$	5.56134	+	9.63251i	0.330587	+	0.572594i	−0.652040	+	0.758185i	$0.726087\pi$
$284$	3.87148	+	6.70560i	0.229730	+	0.397904i
$285$	−4.17364	−	2.40965i	−0.247225	−	0.142735i
$286$	−5.53930			−0.327546
$287$	−9.25398	+	10.5228i	−0.546245	+	0.621143i
$288$	−3.40499			−0.200641
$289$	7.70269	−	13.3415i	0.453100	−	0.784792i
$290$	−6.76171	−	11.7116i	−0.397061	−	0.687730i
$291$	3.03817	−	1.75409i	0.178100	−	0.102826i
$292$	−4.11068	−	2.37330i	−0.240560	−	0.138887i
$293$	4.47517			0.261443			0.130721	−	0.991419i	$-0.458271\pi$
$293$	4.47517			0.261443			0.130721	+	0.991419i	$0.458271\pi$
$294$	−8.13163	+	1.04774i	−0.474247	+	0.0611057i
$295$		−	13.9534i		−	0.812396i
$296$	−9.59694	−	5.54080i	−0.557811	−	0.322052i
$297$	2.21199	+	3.83128i	0.128353	+	0.222314i
$298$	−9.98250	+	5.76340i	−0.578271	+	0.333865i
$299$	−4.23208	−	2.89379i	−0.244747	−	0.167352i
$300$		−	1.18789i		−	0.0685829i
$301$	−1.89172	+	2.15110i	−0.109037	+	0.123988i
$302$	−4.10519			−0.236227
$303$	−2.31979	+	4.01799i	−0.133268	+	0.230828i
$304$	2.15637	+	3.73494i	0.123676	+	0.214213i
$305$	11.3670	+	19.6883i	0.650875	+	1.12735i
$306$	0.739525	−	1.28089i	0.0422758	−	0.0732238i
$307$			20.6237i			1.17706i	0.808477	+	0.588528i	$0.200293\pi$
$307$			20.6237i			1.17706i	−0.808477	+	0.588528i	$0.799707\pi$
$308$	−2.35369	−	6.96527i	−0.134114	−	0.396883i
$309$			8.56445i			0.487214i
$310$	19.0505	+	10.9988i	1.08200	+	0.624690i
$311$	8.70064	−	5.02332i	0.493368	−	0.284846i	−0.232602	−	0.972572i	$-0.574724\pi$
$311$	8.70064	−	5.02332i	0.493368	−	0.284846i	0.725971	+	0.687726i	$0.241391\pi$
$312$	1.64535	+	2.84984i	0.0931498	+	0.161340i
$313$	13.7128	−	23.7513i	0.775094	−	1.34250i	−0.159647	−	0.987174i	$-0.551036\pi$
$313$	13.7128	−	23.7513i	0.775094	−	1.34250i	0.934741	−	0.355329i	$-0.115631\pi$
$314$	25.8419			1.45835
$315$	−1.36436	+	6.81002i	−0.0768731	+	0.383701i
$316$		−	2.27893i		−	0.128200i
$317$	0.0323349	−	0.0560058i	0.00181611	−	0.00314560i	−0.865116	−	0.501572i	$-0.832755\pi$
$317$	0.0323349	−	0.0560058i	0.00181611	−	0.00314560i	0.866932	+	0.498426i	$0.166089\pi$
$318$	−6.42303	−	11.1250i	−0.360186	−	0.623860i
$319$	−16.8512	+	9.72903i	−0.943484	+	0.544721i
$320$	−11.4014	+	19.7479i	−0.637359	+	1.10394i
$321$	15.8629			0.885379
$322$	−4.01967	+	14.3078i	−0.224008	+	0.797340i
$323$	2.31828			0.128993
$324$	0.314069	−	0.543983i	0.0174483	−	0.0302213i
$325$	−1.75081	+	1.01083i	−0.0971173	+	0.0560707i
$326$	−5.43216	−	9.40878i	−0.300860	−	0.521104i
$327$	7.44500	−	12.8951i	0.411709	−	0.713101i
$328$		−	16.3038i		−	0.900225i
$329$	8.84559	+	26.1768i	0.487673	+	1.44317i
$330$	13.6024			0.748785
$331$	−8.77689	+	15.2020i	−0.482421	+	0.835578i	−0.999796	−	0.0201804i	$-0.993576\pi$
$331$	−8.77689	+	15.2020i	−0.482421	+	0.835578i	0.517375	+	0.855759i	$0.326909\pi$
$332$	2.20984	+	3.82755i	0.121281	+	0.210064i
$333$	3.11767	−	1.79999i	0.170847	−	0.0986386i
$334$	0.787584	+	0.454712i	0.0430947	+	0.0248807i
$335$			10.5918i			0.578693i
$336$	4.10448	−	4.66726i	0.223918	−	0.254620i
$337$		−	5.11775i		−	0.278782i	−0.990237	−	0.139391i	$-0.955486\pi$
$337$		−	5.11775i		−	0.278782i	0.990237	−	0.139391i	$-0.0445144\pi$
$338$	−6.94396	+	12.0273i	−0.377702	+	0.654198i
$339$	5.00223	+	8.66412i	0.271684	+	0.470571i
$340$	1.04111	+	1.80326i	0.0564622	+	0.0977955i
$341$	15.8255	−	27.4106i	0.857001	−	1.48437i
$342$	−2.15028			−0.116274
$343$	−10.3529	+	15.3563i	−0.559005	+	0.829164i
$344$		−	3.33285i		−	0.179695i
$345$	10.3923	+	7.10602i	0.559504	+	0.382575i
$346$	16.6486	−	9.61207i	0.895034	−	0.516748i
$347$	2.10902	+	3.65293i	0.113218	+	0.196100i	0.917066	−	0.398735i	$-0.130551\pi$
$347$	2.10902	+	3.65293i	0.113218	+	0.196100i	−0.803848	+	0.594835i	$0.797217\pi$
$348$	2.39261	+	1.38137i	0.128257	+	0.0740493i
$349$		−	10.2932i		−	0.550983i	−0.961303	−	0.275492i	$-0.911159\pi$
$349$		−	10.2932i		−	0.550983i	0.961303	−	0.275492i	$-0.0888406\pi$
$350$	4.40074	+	3.87009i	0.235229	+	0.206865i
$351$	−1.06902			−0.0570601
$352$	13.0455	+	7.53182i	0.695327	+	0.401447i
$353$	−0.880590	+	0.508409i	−0.0468691	+	0.0270599i	−0.523251	−	0.852178i	$-0.675281\pi$
$353$	−0.880590	+	0.508409i	−0.0468691	+	0.0270599i	0.476382	+	0.879238i	$0.341948\pi$
$354$	−3.11285	−	5.39162i	−0.165446	−	0.286561i
$355$	−16.1796	+	28.0239i	−0.858723	+	1.48735i
$356$	7.97948			0.422912
$357$	−1.06957	−	3.16517i	−0.0566074	−	0.167519i
$358$	13.8903			0.734128
$359$	−3.34357	−	1.93041i	−0.176467	−	0.101883i	0.409165	−	0.912461i	$-0.365820\pi$
$359$	−3.34357	−	1.93041i	−0.176467	−	0.101883i	−0.585632	+	0.810577i	$0.699153\pi$
$360$	−4.04035	−	6.99809i	−0.212945	−	0.368832i
$361$	7.81481	+	13.5357i	0.411306	+	0.712403i
$362$	9.78772	−	16.9528i	0.514431	−	0.891021i
$363$		−	8.57164i		−	0.449894i
$364$	1.74198	+	0.349000i	0.0913048	+	0.0182926i
$365$		−	19.8369i		−	1.03831i
$366$	8.78452	+	5.07174i	0.459174	+	0.265104i
$367$	13.8594	+	24.0052i	0.723455	+	1.25306i	0.959607	+	0.281345i	$0.0907805\pi$
$367$	13.8594	+	24.0052i	0.723455	+	1.25306i	−0.236151	+	0.971716i	$0.575886\pi$
$368$	−4.87447	−	10.1571i	−0.254099	−	0.529476i
$369$	4.58686	+	2.64822i	0.238782	+	0.137861i
$370$		−	11.0688i		−	0.575438i
$371$	−28.4524	−	5.70032i	−1.47717	−	0.295946i
$372$	−4.49397			−0.233001
$373$	0.158538	+	0.0915320i	0.00820879	+	0.00473935i	0.504099	−	0.863646i	$-0.331825\pi$
$373$	0.158538	+	0.0915320i	0.00820879	+	0.00473935i	−0.495890	+	0.868385i	$0.665158\pi$
$374$	−5.66666	+	3.27165i	−0.293016	+	0.169173i
$375$	−7.06770	+	4.08054i	−0.364975	+	0.210718i
$376$	−27.8407	−	16.0739i	−1.43578	−	0.828946i
$377$		−	4.70188i		−	0.242159i
$378$	0.992054	+	2.93579i	0.0510258	+	0.151001i
$379$			33.5082i			1.72120i	0.509283	+	0.860599i	$0.329911\pi$
$379$			33.5082i			1.72120i	−0.509283	+	0.860599i	$0.670089\pi$
$380$	1.51359	−	2.62162i	0.0776457	−	0.134486i
$381$	13.7160	−	7.91892i	0.702691	−	0.405699i
$382$	12.4711	−	7.20017i	0.638075	−	0.368393i
$383$	−9.84454	+	17.0512i	−0.503033	+	0.871278i	0.496961	+	0.867773i	$0.334449\pi$
$383$	−9.84454	+	17.0512i	−0.503033	+	0.871278i	−0.999994	+	0.00350527i	$0.998884\pi$
$384$			3.36419i			0.171678i
$385$	20.2910	−	23.0732i	1.03412	−	1.17592i
$386$	−27.2065			−1.38478
$387$	0.937656	+	0.541356i	0.0476637	+	0.0275187i
$388$	1.10181	+	1.90839i	0.0559358	+	0.0968837i
$389$	−0.516198	+	0.298027i	−0.0261723	+	0.0151106i	−0.513029	−	0.858371i	$-0.671477\pi$
$389$	−0.516198	+	0.298027i	−0.0261723	+	0.0151106i	0.486857	+	0.873482i	$0.338143\pi$
$390$	−1.64345	+	2.84654i	−0.0832193	+	0.144140i
$391$	−6.03852	−	0.460754i	−0.305381	−	0.0233014i
$392$	−2.75362	−	21.3711i	−0.139079	−	1.07940i
$393$	8.18336			0.412796
$394$	6.25763	−	10.8385i	0.315255	−	0.546038i
$395$	8.24805	−	4.76201i	0.415004	−	0.239603i
$396$	−2.40657	+	1.38944i	−0.120935	+	0.0698218i
$397$	−8.28054	−	4.78077i	−0.415589	−	0.239940i	0.277600	−	0.960697i	$-0.410461\pi$
$397$	−8.28054	−	4.78077i	−0.415589	−	0.239940i	−0.693188	+	0.720757i	$0.743794\pi$
$398$	−3.19953			−0.160378
$399$	−3.20762	+	3.64743i	−0.160582	+	0.182600i
$400$	−4.44258			−0.222129
$401$	−13.5938	−	7.84838i	−0.678842	−	0.391929i	0.120577	−	0.992704i	$-0.461526\pi$
$401$	−13.5938	−	7.84838i	−0.678842	−	0.391929i	−0.799418	+	0.600775i	$0.794859\pi$
$402$	2.36293	+	4.09271i	0.117852	+	0.204126i
$403$	3.82412	+	6.62356i	0.190493	+	0.329943i
$404$	−2.52385	−	1.45715i	−0.125566	−	0.0724958i
$405$	2.62510			0.130442
$406$	−12.9125	+	4.36336i	−0.640837	+	0.216550i
$407$	−15.9262			−0.789433
$408$	3.36637	+	1.94357i	0.166660	+	0.0962212i
$409$	−21.3620	+	12.3333i	−1.05628	+	0.609844i	−0.924401	−	0.381421i	$-0.875435\pi$
$409$	−21.3620	+	12.3333i	−1.05628	+	0.609844i	−0.131880	+	0.991266i	$0.542101\pi$
$410$	14.1031	−	8.14245i	0.696504	−	0.402127i
$411$	10.4209	−	18.0495i	0.514025	−	0.890318i
$412$	−5.37965			−0.265036
$413$	−13.7891	−	2.76260i	−0.678519	−	0.135939i
$414$	5.60091	+	0.427363i	0.275270	+	0.0210038i
$415$	−9.23529	+	15.9960i	−0.453343	+	0.785213i
$416$	−3.15234	+	1.82000i	−0.154556	+	0.0892331i
$417$	−6.97197	−	12.0758i	−0.341419	−	0.591355i
$418$	8.23832	+	4.75639i	0.402949	+	0.232643i
$419$	27.5752			1.34714			0.673569	−	0.739124i	$-0.264760\pi$
$419$	27.5752			1.34714			0.673569	+	0.739124i	$0.264760\pi$
$420$	−4.27763	−	0.857008i	−0.208727	−	0.0418177i
$421$		−	17.6198i		−	0.858735i	−0.903130	−	0.429367i	$-0.858737\pi$
$421$		−	17.6198i		−	0.858735i	0.903130	−	0.429367i	$-0.141263\pi$
$422$	11.7199	−	20.2994i	0.570515	−	0.988161i
$423$	9.04435	−	5.22176i	0.439751	−	0.253891i
$424$	29.2381	−	16.8806i	1.41993	−	0.819795i
$425$	−1.19404	+	2.06814i	−0.0579195	+	0.100319i
$426$			14.4380i			0.699524i
$427$	21.7071	−	7.33520i	1.05048	−	0.354975i
$428$			9.96407i			0.481631i
$429$	4.09572	+	2.36466i	0.197743	+	0.114167i
$430$	2.88300	−	1.66450i	0.139030	−	0.0802692i
$431$	12.0768	−	6.97254i	0.581719	−	0.335856i	−0.180097	−	0.983649i	$-0.557641\pi$
$431$	12.0768	−	6.97254i	0.581719	−	0.335856i	0.761816	+	0.647793i	$0.224308\pi$
$432$	−2.03444	−	1.17458i	−0.0978820	−	0.0565122i
$433$	13.0347			0.626409			0.313204	−	0.949686i	$-0.398597\pi$
$433$	13.0347			0.626409			0.313204	+	0.949686i	$0.398597\pi$
$434$	14.6411	−	16.6486i	0.702797	−	0.799160i
$435$			11.5460i			0.553588i
$436$	8.09991	+	4.67648i	0.387915	+	0.223963i
$437$	3.80936	+	7.93772i	0.182226	+	0.379713i
$438$	−4.42541	−	7.66504i	−0.211454	−	0.366250i
$439$	26.1051	+	15.0718i	1.24593	+	0.719338i	0.970295	−	0.241924i	$-0.0777785\pi$
$439$	26.1051	+	15.0718i	1.24593	+	0.719338i	0.275635	+	0.961262i	$0.411112\pi$
$440$			35.7489i			1.70426i
$441$	6.45974	+	2.69661i	0.307607	+	0.128410i
$442$		−	1.58113i		−	0.0752069i
$443$	4.33873	−	7.51490i	0.206139	−	0.357044i	−0.744356	−	0.667783i	$-0.767243\pi$
$443$	4.33873	−	7.51490i	0.206139	−	0.357044i	0.950495	+	0.310739i	$0.100577\pi$
$444$	1.13064	+	1.95832i	0.0536577	+	0.0929379i
$445$	16.6738	+	28.8799i	0.790415	+	1.36904i
$446$	−1.21770	−	0.703038i	−0.0576597	−	0.0332898i
$447$	9.84132			0.465479
$448$	17.2581	+	15.1771i	0.815368	+	0.717050i
$449$	13.2107			0.623453			0.311727	−	0.950172i	$-0.399093\pi$
$449$	13.2107			0.623453			0.311727	+	0.950172i	$0.399093\pi$
$450$	1.10751	−	1.91826i	0.0522084	−	0.0904276i
$451$	−11.7157	−	20.2922i	−0.551670	−	0.955521i
$452$	−5.44226	+	3.14209i	−0.255983	+	0.147792i
$453$	3.03535	+	1.75246i	0.142613	+	0.0823377i
$454$	7.21414			0.338577
$455$	2.37690	+	7.03398i	0.111431	+	0.329758i
$456$		−	5.65122i		−	0.264643i
$457$	−13.2929	−	7.67468i	−0.621817	−	0.359006i	0.155759	−	0.987795i	$-0.450218\pi$
$457$	−13.2929	−	7.67468i	−0.621817	−	0.359006i	−0.777576	+	0.628789i	$0.783551\pi$
$458$	−8.71763	−	15.0994i	−0.407348	−	0.705548i
$459$	−1.09360	+	0.631390i	−0.0510448	+	0.0294707i
$460$	−4.46356	+	6.52781i	−0.208114	+	0.304361i
$461$		−	9.68259i		−	0.450963i	−0.974247	−	0.225482i	$-0.927604\pi$
$461$		−	9.68259i		−	0.450963i	0.974247	−	0.225482i	$-0.0723955\pi$
$462$	2.69311	−	13.4423i	0.125295	−	0.625390i
$463$	−20.1178			−0.934952			−0.467476	−	0.884006i	$-0.654837\pi$
$463$	−20.1178			−0.934952			−0.467476	+	0.884006i	$0.654837\pi$
$464$	5.16618	−	8.94809i	0.239834	−	0.415405i
$465$	−9.39054	−	16.2649i	−0.435476	−	0.754266i
$466$	11.4635	+	19.8554i	0.531038	+	0.919785i
$467$	−12.2019	+	21.1343i	−0.564637	+	0.977979i	0.432447	+	0.901659i	$0.357650\pi$
$467$	−12.2019	+	21.1343i	−0.564637	+	0.977979i	−0.997083	+	0.0763197i	$0.975683\pi$
$468$		−	0.671492i		−	0.0310397i
$469$	10.4672	+	2.09706i	0.483329	+	0.0968331i
$470$		−	32.1105i		−	1.48115i
$471$	−19.1074	−	11.0316i	−0.880420	−	0.508311i
$472$	14.1699	−	8.18101i	0.652224	−	0.376562i
$473$	−2.39495	−	4.14817i	−0.110120	−	0.190733i
$474$	2.12471	−	3.68011i	0.0975913	−	0.169033i
$475$	3.47185			0.159299
$476$	1.98816	−	0.671835i	0.0911273	−	0.0307935i
$477$			10.9677i			0.502176i
$478$	−9.56776	+	16.5719i	−0.437619	+	0.757979i
$479$	−14.7292	−	25.5117i	−0.672993	−	1.16566i	−0.977051	−	0.213004i	$-0.931675\pi$
$479$	−14.7292	−	25.5117i	−0.672993	−	1.16566i	0.304059	−	0.952653i	$-0.401658\pi$
$480$	7.74092	−	4.46922i	0.353323	−	0.203991i
$481$	1.92422	−	3.33285i	0.0877369	−	0.151965i
$482$	31.6665			1.44237
$483$	9.07994	−	8.86311i	0.413152	−	0.403285i
$484$	5.38417			0.244735
$485$	−4.60464	+	7.97548i	−0.209086	+	0.362148i
$486$	1.01435	−	0.585633i	0.0460116	−	0.0265648i
$487$	−3.19397	−	5.53212i	−0.144733	−	0.250684i	0.784540	−	0.620078i	$-0.212899\pi$
$487$	−3.19397	−	5.53212i	−0.144733	−	0.250684i	−0.929273	+	0.369393i	$0.879566\pi$
$488$	−13.3292	+	23.0869i	−0.603387	+	1.04510i
$489$			9.27572i			0.419462i
$490$	17.1112	−	13.0551i	0.773007	−	0.589769i
$491$	13.1737			0.594520			0.297260	−	0.954797i	$-0.403927\pi$
$491$	13.1737			0.594520			0.297260	+	0.954797i	$0.403927\pi$
$492$	−1.66345	+	2.88118i	−0.0749941	+	0.129894i
$493$	−2.77705	−	4.80999i	−0.125072	−	0.216631i
$494$	−1.99072	+	1.14934i	−0.0895669	+	0.0517115i
$495$	−10.0575	−	5.80669i	−0.452050	−	0.260991i
$496$			16.8070i			0.754655i
$497$	24.4907	+	21.5375i	1.09856	+	0.966091i
$498$			8.24120i			0.369297i
$499$	17.9870	−	31.1544i	0.805210	−	1.39466i	−0.110940	−	0.993827i	$-0.535386\pi$
$499$	17.9870	−	31.1544i	0.805210	−	1.39466i	0.916149	−	0.400837i	$-0.131281\pi$
$500$	−2.56314	−	4.43949i	−0.114627	−	0.198540i
$501$	−0.388223	−	0.672422i	−0.0173445	−	0.0300416i
$502$	11.0098	−	19.0695i	0.491391	−	0.851113i
$503$	−2.88055			−0.128437			−0.0642187	−	0.997936i	$-0.520456\pi$
$503$	−2.88055			−0.128437			−0.0642187	+	0.997936i	$0.520456\pi$
$504$	−7.71566	+	2.60725i	−0.343683	+	0.116136i
$505$		−	12.1793i		−	0.541974i
$506$	−20.5133	−	14.0265i	−0.911929	−	0.623555i
$507$	10.2686	−	5.92860i	0.456046	−	0.263298i
$508$	4.97417	+	8.61552i	0.220693	+	0.382252i
$509$	−23.4595	−	13.5444i	−1.03983	−	0.600344i	−0.120042	−	0.992769i	$-0.538303\pi$
$509$	−23.4595	−	13.5444i	−1.03983	−	0.600344i	−0.919784	+	0.392425i	$0.871636\pi$
$510$			3.88265i			0.171926i
$511$	−19.6034	−	3.92747i	−0.867204	−	0.173741i
$512$	−22.4615			−0.992669
$513$	1.58990	+	0.917929i	0.0701958	+	0.0405276i
$514$	−21.0568	+	12.1572i	−0.928776	+	0.536229i
$515$	−11.2412	−	19.4704i	−0.495349	−	0.857969i
$516$	−0.340046	+	0.588977i	−0.0149697	+	0.0259283i
$517$	−46.2020			−2.03196
$518$	−10.9385	−	2.19149i	−0.480610	−	0.0962884i
$519$	−16.4131			−0.720457
$520$	−7.48110	−	4.31921i	−0.328068	−	0.189410i
$521$	3.74848	+	6.49256i	0.164224	+	0.284444i	0.936379	−	0.350989i	$-0.114155\pi$
$521$	3.74848	+	6.49256i	0.164224	+	0.284444i	−0.772155	+	0.635434i	$0.780821\pi$
$522$	2.57579	+	4.46141i	0.112739	+	0.195270i
$523$	11.4128	−	19.7676i	0.499048	−	0.864376i	−0.500952	−	0.865475i	$-0.667017\pi$
$523$	11.4128	−	19.7676i	0.499048	−	0.864376i	0.999999	+	0.00109950i	$0.000349981\pi$
$524$			5.14028i			0.224554i
$525$	−1.60178	−	4.74014i	−0.0699072	−	0.206877i
$526$		−	6.03600i		−	0.263182i
$527$	7.82408	+	4.51723i	0.340822	+	0.196774i
$528$	5.19634	+	9.00032i	0.226142	+	0.391689i
$529$	−8.34479	−	21.4328i	−0.362817	−	0.931860i
$530$	29.2042	+	16.8611i	1.26855	+	0.732398i
$531$			5.31537i			0.230667i
$532$	−2.29109	−	2.01483i	−0.0993314	−	0.0873539i
$533$	5.66201			0.245249
$534$	12.8856	+	7.43952i	0.557616	+	0.321940i
$535$	−36.0627	+	20.8208i	−1.55912	+	0.900161i
$536$	−10.7562	+	6.21010i	−0.464598	+	0.268236i
$537$	−10.2704	−	5.92963i	−0.443202	−	0.255883i
$538$		−	10.9025i		−	0.470040i
$539$	−18.7842	−	24.6204i	−0.809094	−	1.06047i
$540$			1.64892i			0.0709583i
$541$	10.6982	−	18.5298i	0.459951	−	0.796659i	−0.539007	−	0.842302i	$-0.681200\pi$
$541$	10.6982	−	18.5298i	0.459951	−	0.796659i	0.998958	+	0.0456426i	$0.0145336\pi$
$542$	24.9488	−	14.4042i	1.07164	−	0.618713i
$543$	−14.4739	+	8.35654i	−0.621136	+	0.358613i
$544$	−2.14988	+	3.72370i	−0.0921753	+	0.159652i
$545$			39.0877i			1.67433i
$546$	2.48765	+	2.18769i	0.106462	+	0.0936244i
$547$	−5.94927			−0.254372			−0.127186	−	0.991879i	$-0.540595\pi$
$547$	−5.94927			−0.254372			−0.127186	+	0.991879i	$0.540595\pi$
$548$	11.3376	+	6.54577i	0.484318	+	0.279621i
$549$	−4.33014	−	7.50003i	−0.184806	−	0.320093i
$550$	−8.48635	+	4.89960i	−0.361859	+	0.208920i
$551$	−4.03734	+	6.99287i	−0.171996	+	0.297906i
$552$	−1.12317	+	14.7200i	−0.0478053	+	0.626523i
$553$	−3.07295	−	9.09379i	−0.130675	−	0.386707i
$554$	2.42536			0.103044
$555$	−4.72514	+	8.18417i	−0.200571	+	0.347399i
$556$	7.58527	−	4.37936i	0.321687	−	0.185726i
$557$	−10.1747	+	5.87438i	−0.431117	+	0.248905i	−0.699822	−	0.714317i	$-0.746737\pi$
$557$	−10.1747	+	5.87438i	−0.431117	+	0.248905i	0.268706	+	0.963222i	$0.413404\pi$
$558$	−7.25706	−	4.18987i	−0.307216	−	0.177371i
$559$	1.15744			0.0489545
$560$	−3.20512	+	15.9979i	−0.135441	+	0.676034i
$561$	5.58651			0.235863
$562$	25.9665	+	14.9918i	1.09533	+	0.632390i
$563$	11.3472	+	19.6540i	0.478229	+	0.828317i	0.999688	−	0.0249589i	$-0.00794549\pi$
$563$	11.3472	+	19.6540i	0.478229	+	0.828317i	−0.521459	+	0.853276i	$0.674612\pi$
$564$	3.27998	+	5.68110i	0.138112	+	0.239217i
$565$	−22.7442	−	13.1313i	−0.956854	−	0.552440i
$566$	−13.0276			−0.547591
$567$	0.519738	−	2.59420i	0.0218269	−	0.108946i
$568$	−37.9451			−1.59214
$569$	−36.2218	−	20.9127i	−1.51850	−	0.876704i	−0.999763	−	0.0217683i	$-0.993070\pi$
$569$	−36.2218	−	20.9127i	−1.51850	−	0.876704i	−0.518733	−	0.854936i	$-0.673596\pi$
$570$	4.88844	−	2.82234i	0.204754	−	0.118215i
$571$	10.4469	−	6.03155i	0.437191	−	0.252412i	−0.265214	−	0.964189i	$-0.585443\pi$
$571$	10.4469	−	6.03155i	0.437191	−	0.252412i	0.702405	+	0.711777i	$0.252109\pi$
$572$	−1.48534	+	2.57268i	−0.0621050	+	0.107569i
$573$	−12.2947			−0.513618
$574$	−5.25436	−	15.5493i	−0.219313	−	0.649013i
$575$	−9.04326	−	0.690023i	−0.377130	−	0.0287760i
$576$	4.34324	−	7.52272i	0.180968	−	0.313447i
$577$	−9.76872	+	5.63997i	−0.406677	+	0.234795i	−0.689361	−	0.724418i	$-0.742109\pi$
$577$	−9.76872	+	5.63997i	−0.406677	+	0.234795i	0.282684	+	0.959213i	$0.408775\pi$
$578$	9.02190	+	15.6264i	0.375261	+	0.649972i
$579$	20.1163	+	11.6142i	0.836006	+	0.482668i
$580$	−7.25247			−0.301143
$581$	13.9792	+	12.2936i	0.579957	+	0.510025i
$582$			4.10900i			0.170324i
$583$	24.2604	−	42.0203i	1.00476	−	1.74030i
$584$	20.1448	−	11.6306i	0.833597	−	0.481277i
$585$	2.43031	−	1.40314i	0.100481	−	0.0580127i
$586$	−2.62081	+	4.53937i	−0.108265	+	0.187520i
$587$			23.4925i			0.969641i	0.874614	+	0.484820i	$0.161115\pi$
$587$			23.4925i			0.969641i	−0.874614	+	0.484820i	$0.838885\pi$
$588$	−1.69384	+	4.05761i	−0.0698529	+	0.167333i
$589$		−	13.1345i		−	0.541198i
$590$	14.1535	+	8.17154i	0.582691	+	0.336417i
$591$	−9.25370	+	5.34263i	−0.380646	+	0.219766i
$592$	7.32392	−	4.22847i	0.301011	−	0.173789i
$593$	16.9633	+	9.79376i	0.696599	+	0.402181i	0.806079	−	0.591808i	$-0.201585\pi$
$593$	16.9633	+	9.79376i	0.696599	+	0.402181i	−0.109481	+	0.993989i	$0.534919\pi$
$594$	−5.18166			−0.212606
$595$	6.58599	+	5.79184i	0.269999	+	0.237442i
$596$			6.18171i			0.253213i
$597$	2.36571	+	1.36584i	0.0968222	+	0.0559003i
$598$	5.41375	−	2.59809i	0.221385	−	0.106244i
$599$	−19.3629	−	33.5375i	−0.791147	−	1.37031i	−0.925257	−	0.379341i	$-0.876151\pi$
$599$	−19.3629	−	33.5375i	−0.791147	−	1.37031i	0.134110	−	0.990966i	$-0.457182\pi$
$600$	5.04145	+	2.91068i	0.205816	+	0.118828i
$601$		−	17.9352i		−	0.731593i	−0.930695	−	0.365797i	$-0.880797\pi$
$601$		−	17.9352i		−	0.731593i	0.930695	−	0.365797i	$-0.119203\pi$
$602$	−1.07411	−	3.17861i	−0.0437774	−	0.129551i
$603$		−	4.03483i		−	0.164311i
$604$	−1.10079	+	1.90662i	−0.0447903	+	0.0775791i
$605$	11.2507	+	19.4868i	0.457405	+	0.792249i
$606$	−2.71709	−	4.70614i	−0.110374	−	0.191174i
$607$	−4.31043	−	2.48863i	−0.174955	−	0.101010i	0.409965	−	0.912101i	$-0.365541\pi$
$607$	−4.31043	−	2.48863i	−0.174955	−	0.101010i	−0.584920	+	0.811091i	$0.698874\pi$
$608$	6.25109			0.253515
$609$	11.4101	+	2.28597i	0.462360	+	0.0926322i
$610$	−26.6276			−1.07812
$611$	5.58217	−	9.66860i	0.225830	−	0.391150i
$612$	−0.396600	−	0.686931i	−0.0160316	−	0.0277675i
$613$	20.0317	−	11.5653i	0.809074	−	0.467119i	−0.0375602	−	0.999294i	$-0.511959\pi$
$613$	20.0317	−	11.5653i	0.809074	−	0.467119i	0.846634	+	0.532175i	$0.178625\pi$
$614$	−20.9196	−	12.0779i	−0.844245	−	0.487425i
$615$	−13.9037			−0.560650
$616$	35.3281	+	7.07785i	1.42341	+	0.285175i
$617$			37.3929i			1.50538i	0.658375	+	0.752690i	$0.271244\pi$
$617$			37.3929i			1.50538i	−0.658375	+	0.752690i	$0.728756\pi$
$618$	−8.68731	−	5.01562i	−0.349455	−	0.201758i
$619$	21.9986	+	38.1028i	0.884200	+	1.53148i	0.846628	+	0.532186i	$0.178629\pi$
$619$	21.9986	+	38.1028i	0.884200	+	1.53148i	0.0375728	+	0.999294i	$0.488037\pi$
$620$	10.2166	−	5.89855i	0.410308	−	0.236891i
$621$	−3.95884	−	2.70696i	−0.158863	−	0.108626i
$622$			11.7673i			0.471825i
$623$	31.8412	−	10.7597i	1.27569	−	0.431078i
$624$	−2.51131			−0.100533
$625$	15.4396	−	26.7422i	0.617586	−	1.06969i
$626$	16.0613	+	27.8191i	0.641941	+	1.11187i
$627$	−4.06090	−	7.03369i	−0.162177	−	0.280899i
$628$	6.92939	−	12.0021i	0.276513	−	0.478934i
$629$		−	4.54597i		−	0.181260i
$630$	−6.10870	−	5.37211i	−0.243377	−	0.214030i
$631$			10.1960i			0.405898i	0.979189	+	0.202949i	$0.0650525\pi$
$631$			10.1960i			0.405898i	−0.979189	+	0.202949i	$0.934947\pi$
$632$	9.67184	+	5.58404i	0.384725	+	0.222121i
$633$	−17.3312	+	10.0062i	−0.688853	+	0.397710i
$634$	0.0378728	+	0.0655976i	0.00150412	+	0.00260521i
$635$	−20.7879	+	36.0058i	−0.824944	+	1.42884i
$636$	−6.88921			−0.273175
$637$	7.42179	−	0.956282i	0.294062	−	0.0378893i
$638$		−	22.7905i		−	0.902286i
$639$	6.16342	−	10.6754i	0.243821	−	0.422311i
$640$	−4.41566	−	7.64815i	−0.174544	−	0.302320i
$641$	37.4979	−	21.6494i	1.48108	−	0.855102i	0.481309	−	0.876551i	$-0.340161\pi$
$641$	37.4979	−	21.6494i	1.48108	−	0.855102i	0.999770	+	0.0214491i	$0.00682800\pi$
$642$	−9.28981	+	16.0904i	−0.366640	+	0.635039i
$643$	−5.89071			−0.232307			−0.116154	−	0.993231i	$-0.537056\pi$
$643$	−5.89071			−0.232307			−0.116154	+	0.993231i	$0.537056\pi$
$644$	5.56725	+	5.70345i	0.219380	+	0.224748i
$645$	−2.84222			−0.111912
$646$	−1.35766	+	2.35154i	−0.0534165	+	0.0925201i
$647$	14.3694	−	8.29618i	0.564919	−	0.326156i	−0.190198	−	0.981746i	$-0.560913\pi$
$647$	14.3694	−	8.29618i	0.564919	−	0.326156i	0.755118	+	0.655589i	$0.227580\pi$
$648$	1.53912	+	2.66584i	0.0604625	+	0.104724i
$649$	11.7576	−	20.3647i	0.461525	−	0.799384i
$650$		−	2.36790i		−	0.0928766i
$651$	−17.9327	+	6.05976i	−0.702837	+	0.237501i
$652$	−5.82643			−0.228181
$653$	−9.87863	+	17.1103i	−0.386581	+	0.669578i	−0.991987	−	0.126339i	$-0.959677\pi$
$653$	−9.87863	+	17.1103i	−0.386581	+	0.669578i	0.605406	+	0.795917i	$0.293011\pi$
$654$	8.72006	+	15.1036i	0.340982	+	0.590597i
$655$	−18.6041	+	10.7411i	−0.726921	+	0.419688i
$656$	10.7753	+	6.22112i	0.420704	+	0.242894i
$657$			7.55663i			0.294812i
$658$	−31.7326	−	6.35750i	−1.23706	−	0.247841i
$659$		−	13.6631i		−	0.532238i	−0.963940	−	0.266119i	$-0.914259\pi$
$659$		−	13.6631i		−	0.532238i	0.963940	−	0.266119i	$-0.0857414\pi$
$660$	3.64740	−	6.31749i	0.141975	−	0.245908i
$661$	−20.5219	−	35.5450i	−0.798209	−	1.38254i	−0.920781	−	0.390079i	$-0.872448\pi$
$661$	−20.5219	−	35.5450i	−0.798209	−	1.38254i	0.122572	−	0.992460i	$-0.460886\pi$
$662$	−10.2801	−	17.8056i	−0.399546	−	0.692034i
$663$	−0.674968	+	1.16908i	−0.0262136	+	0.0454033i
$664$	−21.6590			−0.840533
$665$	2.50478	−	12.5022i	0.0971310	−	0.484816i
$666$			4.21652i			0.163387i
$667$	11.9060	−	17.4122i	0.461003	−	0.674203i
$668$	0.422374	−	0.243858i	0.0163421	−	0.00943513i
$669$	0.600238	+	1.03964i	0.0232065	+	0.0401949i
$670$	−10.7438	−	6.20292i	−0.415068	−	0.239640i
$671$			38.3130i			1.47906i
$672$	−2.88401	−	8.53466i	−0.111253	−	0.329232i
$673$	−6.56598			−0.253100			−0.126550	−	0.991960i	$-0.540390\pi$
$673$	−6.56598			−0.253100			−0.126550	+	0.991960i	$0.540390\pi$
$674$	5.19117	+	2.99712i	0.199956	+	0.115445i
$675$	−1.63777	+	0.945565i	−0.0630377	+	0.0363948i
$676$	3.72398	+	6.45012i	0.143230	+	0.248081i
$677$	23.3248	−	40.3997i	0.896444	−	1.55269i	0.0644363	−	0.997922i	$-0.479475\pi$
$677$	23.3248	−	40.3997i	0.896444	−	1.55269i	0.832007	−	0.554764i	$-0.187192\pi$
$678$	−11.7179			−0.450023
$679$	6.96994	+	6.12950i	0.267482	+	0.235229i
$680$	−10.2041			−0.391311
$681$	−5.33409	−	3.07964i	−0.204403	−	0.118012i
$682$	18.5359	+	32.1051i	0.709777	+	1.22937i
$683$	−13.9394	−	24.1438i	−0.533377	−	0.923836i	−0.999240	−	0.0389794i	$-0.987589\pi$
$683$	−13.9394	−	24.1438i	−0.533377	−	0.923836i	0.465863	−	0.884857i	$-0.345744\pi$
$684$	−0.576586	+	0.998676i	−0.0220463	+	0.0381853i
$685$			54.7118i			2.09043i
$686$	−9.51363	−	19.4946i	−0.363232	−	0.744308i
$687$			14.8858i			0.567930i
$688$	2.20271	+	1.27174i	0.0839775	+	0.0484845i
$689$	5.86234	+	10.1539i	0.223337	+	0.386831i
$690$	−13.2940	+	6.37990i	−0.506096	+	0.242878i
$691$	30.2632	+	17.4725i	1.15127	+	0.664685i	0.949196	−	0.314686i	$-0.101899\pi$
$691$	30.2632	+	17.4725i	1.15127	+	0.664685i	0.202072	+	0.979371i	$0.435232\pi$
$692$		−	10.3097i		−	0.391917i
$693$	−7.72961	+	8.78946i	−0.293624	+	0.333884i
$694$	−4.94044			−0.187537
$695$	31.7001	+	18.3021i	1.20246	+	0.694238i
$696$	−11.7252	+	6.76954i	−0.444442	+	0.256599i
$697$	5.79219	−	3.34412i	0.219395	−	0.126668i
$698$	10.4409	+	6.02804i	0.395193	+	0.228165i
$699$		−	19.5746i		−	0.740380i
$700$	2.97746	−	1.00614i	0.112538	−	0.0380284i
$701$			50.6216i			1.91195i	0.293446	+	0.955976i	$0.405198\pi$
$701$			50.6216i			1.91195i	−0.293446	+	0.955976i	$0.594802\pi$
$702$	0.626053	−	1.08436i	0.0236289	−	0.0409264i
$703$	−5.72359	+	3.30452i	−0.215869	+	0.124632i
$704$	−33.2804	+	19.2144i	−1.25430	+	0.724171i
$705$	−13.7076	+	23.7423i	−0.516259	+	0.894186i
$706$		−	1.19096i		−	0.0448225i
$707$	−12.0360	−	2.41137i	−0.452660	−	0.0906887i
$708$	−3.33879			−0.125479
$709$	−15.8772	−	9.16673i	−0.596282	−	0.344264i	0.171295	−	0.985220i	$-0.445205\pi$
$709$	−15.8772	−	9.16673i	−0.596282	−	0.344264i	−0.767578	+	0.640956i	$0.778538\pi$
$710$	−18.9506	−	32.8234i	−0.711203	−	1.23184i
$711$	−3.14200	+	1.81403i	−0.117834	+	0.0680316i
$712$	−19.5521	+	33.8652i	−0.732745	+	1.26915i
$713$	−2.61046	+	34.2120i	−0.0977625	+	1.28125i
$714$	3.83695	+	0.768718i	0.143594	+	0.0287686i
$715$	−12.4149			−0.464293
$716$	3.72463	−	6.45124i	0.139196	−	0.241094i
$717$	14.1487	−	8.16874i	0.528392	−	0.305067i
$718$	3.91621	−	2.26102i	0.146152	−	0.0843807i
$719$	7.94476	+	4.58691i	0.296290	+	0.171063i	0.640775	−	0.767729i	$-0.278613\pi$
$719$	7.94476	+	4.58691i	0.296290	+	0.171063i	−0.344485	+	0.938792i	$0.611947\pi$
$720$	6.16679			0.229823
$721$	−21.4669	+	7.25403i	−0.799469	+	0.270154i
$722$	−18.3064			−0.681295
$723$	−23.4140	−	13.5181i	−0.870776	−	0.502743i
$724$	−5.24906	−	9.09163i	−0.195080	−	0.337888i
$725$	−4.15889	−	7.20341i	−0.154457	−	0.267528i
$726$	8.69460	+	5.01983i	0.322687	+	0.186303i
$727$	43.0133			1.59528			0.797638	−	0.603137i	$-0.206083\pi$
$727$	43.0133			1.59528			0.797638	+	0.603137i	$0.206083\pi$
$728$	−5.74955	+	6.53789i	−0.213092	+	0.242310i
$729$	−1.00000			−0.0370370
$730$	20.1215	+	11.6171i	0.744729	+	0.429969i
$731$	1.18405	−	0.683613i	0.0437938	−	0.0252843i
$732$	4.71105	−	2.71993i	0.174125	−	0.100531i
$733$	14.1989	−	24.5931i	0.524447	−	0.908368i	−0.475148	−	0.879906i	$-0.657606\pi$
$733$	14.1989	−	24.5931i	0.524447	−	0.908368i	0.999595	−	0.0284625i	$-0.00906111\pi$
$734$	−32.4661			−1.19835
$735$	−18.2250	+	2.34826i	−0.672240	+	0.0866167i
$736$	−16.2825	−	1.24239i	−0.600179	−	0.0457952i
$737$	−8.92502	+	15.4586i	−0.328757	+	0.569424i
$738$	−5.37242	+	3.10177i	−0.197762	+	0.114178i
$739$	6.93883	+	12.0184i	0.255249	+	0.442104i	0.964963	−	0.262386i	$-0.0845093\pi$
$739$	6.93883	+	12.0184i	0.255249	+	0.442104i	−0.709714	+	0.704490i	$0.751176\pi$
$740$	−5.14079	−	2.96804i	−0.188979	−	0.109107i
$741$	1.96257			0.0720968
$742$	22.4447	−	25.5222i	0.823972	−	0.936950i
$743$			33.8390i			1.24143i	0.784035	+	0.620717i	$0.213158\pi$
$743$			33.8390i			1.24143i	−0.784035	+	0.620717i	$0.786842\pi$
$744$	11.0116	−	19.0726i	0.403703	−	0.699234i
$745$	−22.3733	+	12.9172i	−0.819693	+	0.473250i
$746$	−0.185690	+	0.107208i	−0.00679860	+	0.00392517i
$747$	3.51808	−	6.09349i	0.128720	−	0.222949i
$748$			3.50910i			0.128305i
$749$	13.4357	+	39.7605i	0.490932	+	1.45282i
$750$		−	9.55879i		−	0.349038i
$751$	−35.3689	−	20.4203i	−1.29063	−	0.745146i	−0.311864	−	0.950127i	$-0.600953\pi$
$751$	−35.3689	−	20.4203i	−1.29063	−	0.745146i	−0.978766	+	0.204981i	$0.934287\pi$
$752$	21.2467	−	12.2668i	0.774787	−	0.447324i
$753$	−16.2811	+	9.39990i	−0.593317	+	0.342552i
$754$	4.76933	+	2.75358i	0.173689	+	0.100279i
$755$	−9.20074			−0.334849
$756$	1.62951	+	0.326467i	0.0592649	+	0.0118735i
$757$			1.96542i			0.0714345i	0.999362	+	0.0357173i	$0.0113716\pi$
$757$			1.96542i			0.0714345i	−0.999362	+	0.0357173i	$0.988628\pi$
$758$	−33.9889	−	19.6235i	−1.23453	−	0.712757i
$759$	9.17966	+	19.1280i	0.333201	+	0.694303i
$760$	7.41750	+	12.8475i	0.269061	+	0.466027i
$761$	−37.1235	−	21.4333i	−1.34573	−	0.776956i	−0.358086	−	0.933689i	$-0.616570\pi$
$761$	−37.1235	−	21.4333i	−1.34573	−	0.776956i	−0.987641	+	0.156733i	$0.949904\pi$
$762$			18.5503i			0.672007i
$763$	38.6276	+	7.73890i	1.39841	+	0.280167i
$764$		−	7.72276i		−	0.279400i
$765$	1.65746	−	2.87080i	0.0599255	−	0.103794i
$766$	−11.5306	−	19.9715i	−0.416616	−	0.721601i
$767$	2.84112	+	4.92096i	0.102587	+	0.177686i
$768$	11.6330	+	6.71631i	0.419769	+	0.242354i
$769$	33.7742			1.21793			0.608965	−	0.793197i	$-0.291585\pi$
$769$	33.7742			1.21793			0.608965	+	0.793197i	$0.291585\pi$
$770$	11.5211	+	34.0945i	0.415192	+	1.22868i
$771$	20.7590			0.747618
$772$	−7.29530	+	12.6358i	−0.262563	+	0.454773i
$773$	18.4633	+	31.9794i	0.664079	+	1.15022i	0.979534	+	0.201279i	$0.0645096\pi$
$773$	18.4633	+	31.9794i	0.664079	+	1.15022i	−0.315455	+	0.948941i	\(0.60215

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:	\( N \)	\(=\)	\( 483 = 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	483.j (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.585633 + 1.01435i) q^{2} +(0.866025 - 0.500000i) q^{3} +(0.314069 + 0.543983i) q^{4} +(-1.31255 + 2.27340i) q^{5} +1.17127i q^{6} +(1.98677 + 1.74721i) q^{7} -3.07825 q^{8} +(0.500000 - 0.866025i) q^{9} +(-1.53734 - 2.66275i) q^{10} +(-3.83128 + 2.21199i) q^{11} +(0.543983 + 0.314069i) q^{12} -1.06902i q^{13} +(-2.93579 + 0.992054i) q^{14} +2.62510i q^{15} +(1.17458 - 2.03444i) q^{16} +(-0.631390 - 1.09360i) q^{17} +(0.585633 + 1.01435i) q^{18} +(-0.917929 + 1.58990i) q^{19} -1.64892 q^{20} +(2.59420 + 0.519738i) q^{21} -5.18166i q^{22} +(2.70696 - 3.95884i) q^{23} +(-2.66584 + 1.53912i) q^{24} +(-0.945565 - 1.63777i) q^{25} +(1.08436 + 0.626053i) q^{26} -1.00000i q^{27} +(-0.326467 + 1.62951i) q^{28} +4.39831 q^{29} +(-2.66275 - 1.53734i) q^{30} +(-6.19592 + 3.57722i) q^{31} +(-1.70250 - 2.94881i) q^{32} +(-2.21199 + 3.83128i) q^{33} +1.47905 q^{34} +(-6.57984 + 2.22344i) q^{35} +0.628138 q^{36} +(3.11767 + 1.79999i) q^{37} +(-1.07514 - 1.86219i) q^{38} +(-0.534510 - 0.925799i) q^{39} +(4.04035 - 6.99809i) q^{40} +5.29644i q^{41} +(-2.04644 + 2.32704i) q^{42} +1.08271i q^{43} +(-2.40657 - 1.38944i) q^{44} +(1.31255 + 2.27340i) q^{45} +(2.43035 + 5.06421i) q^{46} +(9.04435 + 5.22176i) q^{47} -2.34917i q^{48} +(0.894541 + 6.94261i) q^{49} +2.21502 q^{50} +(-1.09360 - 0.631390i) q^{51} +(0.581529 - 0.335746i) q^{52} +(-9.49829 + 5.48384i) q^{53} +(1.01435 + 0.585633i) q^{54} -11.6134i q^{55} +(-6.11578 - 5.37833i) q^{56} +1.83586i q^{57} +(-2.57579 + 4.46141i) q^{58} +(-4.60325 + 2.65769i) q^{59} +(-1.42801 + 0.824461i) q^{60} +(4.33014 - 7.50003i) q^{61} -8.37974i q^{62} +(2.50651 - 0.846993i) q^{63} +8.68649 q^{64} +(2.43031 + 1.40314i) q^{65} +(-2.59083 - 4.48745i) q^{66} +(3.49427 - 2.01742i) q^{67} +(0.396600 - 0.686931i) q^{68} +(0.364873 - 4.78193i) q^{69} +(1.59803 - 7.97634i) q^{70} +12.3268 q^{71} +(-1.53912 + 2.66584i) q^{72} +(-6.54424 + 3.77832i) q^{73} +(-3.65161 + 2.10826i) q^{74} +(-1.63777 - 0.945565i) q^{75} -1.15317 q^{76} +(-11.4767 - 2.29931i) q^{77} +1.25211 q^{78} +(-3.14200 - 1.81403i) q^{79} +(3.08340 + 5.34060i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-5.37242 - 3.10177i) q^{82} +7.03615 q^{83} +(0.532029 + 1.57443i) q^{84} +3.31492 q^{85} +(-1.09824 - 0.634071i) q^{86} +(3.80905 - 2.19916i) q^{87} +(11.7936 - 6.80906i) q^{88} +(6.35170 - 11.0015i) q^{89} -3.07468 q^{90} +(1.86780 - 2.12390i) q^{91} +(3.00371 + 0.229191i) q^{92} +(-3.57722 + 6.19592i) q^{93} +(-10.5933 + 6.11606i) q^{94} +(-2.40965 - 4.17364i) q^{95} +(-2.94881 - 1.70250i) q^{96} +3.50817 q^{97} +(-7.56607 - 3.15844i) q^{98} +4.42398i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 4 q^{2} - 36 q^{4} - 24 q^{8} + 32 q^{9} - 44 q^{16} - 4 q^{18} - 16 q^{23} - 12 q^{25} + 84 q^{26} + 24 q^{29} - 12 q^{31} + 8 q^{32} + 32 q^{35} - 72 q^{36} - 8 q^{46} - 12 q^{47} + 8 q^{49} - 96 q^{50}+ \cdots + 112 q^{98}+O(q^{100}) \) 64 * q + 4 * q^2 - 36 * q^4 - 24 * q^8 + 32 * q^9 - 44 * q^16 - 4 * q^18 - 16 * q^23 - 12 * q^25 + 84 * q^26 + 24 * q^29 - 12 * q^31 + 8 * q^32 + 32 * q^35 - 72 * q^36 - 8 * q^46 - 12 * q^47 + 8 * q^49 - 96 * q^50 - 108 * q^52 - 24 * q^58 + 36 * q^59 + 168 * q^64 - 40 * q^70 - 16 * q^71 - 12 * q^72 + 48 * q^73 - 48 * q^75 - 32 * q^78 - 32 * q^81 - 24 * q^82 + 88 * q^85 + 36 * q^87 + 152 * q^92 + 24 * q^93 - 108 * q^94 - 44 * q^95 + 60 * q^96 + 112 * q^98

Introduction

L-functions

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