LMFDB - Embedded newform 483.2.j.a.229.12

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			229.12
Character	$\chi$	$=$	483.229
Dual form			483.2.j.a.367.12

$q$-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} +(2.07498 - 4.32371i) 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} +(3.17056 + 4.63685i) 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	$-0.633646\pi$
$5$	1.31255	−	2.27340i	0.586989	−	1.01670i	0.994624	−	0.103550i	$-0.0330203\pi$
$6$			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	0.205032	−	0.978755i	$-0.434270\pi$
$11$	3.83128	−	2.21199i	1.15518	−	0.666941i	0.950143	+	0.311815i	$0.100937\pi$
$12$	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	0.932378	−	0.361484i	$-0.117730\pi$
$17$	0.631390	+	1.09360i	0.153134	+	0.265237i	−0.779244	+	0.626721i	$0.784397\pi$
$18$	0.585633	+	1.01435i	0.138035	+	0.239084i
$19$	0.917929	−	1.58990i	0.210587	−	0.364748i	−0.741311	−	0.671162i	$-0.765796\pi$
$19$	0.917929	−	1.58990i	0.210587	−	0.364748i	0.951898	+	0.306414i	$0.0991290\pi$
$20$	1.64892			0.368710
$21$	−2.59420	−	0.519738i	−0.566101	−	0.113416i
$22$			5.18166i			1.10473i
$23$	2.07498	−	4.32371i	0.432662	−	0.901556i
$23$	2.07498	−	4.32371i	0.432662	−	0.901556i
$24$	−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	0.221336	−	0.975198i	$-0.428958\pi$
$37$	−3.11767	−	1.79999i	−0.512541	−	0.295916i	−0.733878	+	0.679282i	$0.762291\pi$
$38$	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	$-0.973692\pi$
$43$		−	1.08271i		−	0.165112i	0.996586	−	0.0825560i	$-0.0263083\pi$
$44$	2.40657	+	1.38944i	0.362805	+	0.209465i
$45$	−1.31255	−	2.27340i	−0.195663	−	0.338898i
$46$	3.17056	+	4.63685i	0.467474	+	0.683666i
$47$	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	0.323486	−	0.946233i	$-0.395145\pi$
$53$	9.49829	−	5.48384i	1.30469	−	0.753263i	0.981205	+	0.192970i	$0.0618119\pi$
$54$	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	$0.353726\pi$
$61$	−4.33014	+	7.50003i	−0.554418	+	0.960280i	−0.997949	+	0.0640207i	$0.979608\pi$
$62$		−	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	−0.698022	−	0.716076i	$-0.745936\pi$
$67$	−3.49427	+	2.01742i	−0.426893	+	0.246467i	0.271129	+	0.962543i	$0.412603\pi$
$68$	−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	0.666227	−	0.745749i	$-0.267908\pi$
$79$	3.14200	+	1.81403i	0.353502	+	0.204095i	−0.312724	+	0.949844i	$0.601242\pi$
$80$	−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	$-0.626198\pi$
$83$	−7.03615			−0.772318			−0.386159	+	0.922432i	$0.626198\pi$
$84$	−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	$0.401781\pi$
$89$	−6.35170	+	11.0015i	−0.673278	+	1.16615i	−0.976969	+	0.213382i	$0.931552\pi$
$90$	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	$-0.556995\pi$
$97$	−3.50817			−0.356201			−0.178100	+	0.984012i	$0.556995\pi$
$98$	−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	−0.574189	−	0.818723i	$-0.694683\pi$
$103$	4.28222	−	7.41703i	0.421940	−	0.730822i	0.996129	+	0.0879011i	$0.0280159\pi$
$104$			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	−0.343068	−	0.939311i	$-0.611466\pi$
$107$	−13.7376	−	7.93144i	−1.32807	−	0.766761i	−0.985001	+	0.172550i	$0.944799\pi$
$108$	0.543983	−	0.314069i	0.0523448	−	0.0302213i
$109$	−12.8951	+	7.44500i	−1.23513	+	0.713101i	−0.968094	−	0.250586i	$-0.919377\pi$
$109$	−12.8951	+	7.44500i	−1.23513	+	0.713101i	−0.267033	+	0.963687i	$0.586043\pi$
$110$	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	$-0.844048\pi$
$113$		−	10.0045i		−	0.941141i	0.882362	−	0.470571i	$-0.155952\pi$
$114$	1.86219	+	1.07514i	0.174410	+	0.100696i
$115$	−7.10602	−	10.3923i	−0.662640	−	0.969090i
$116$	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	$0.682851\pi$
$137$	−18.0495	+	10.4209i	−1.54208	+	0.890318i	−0.998708	+	0.0508242i	$0.983815\pi$
$138$	5.06421	+	2.43035i	0.431094	+	0.206885i
$139$		−	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	0.108465	−	0.994100i	$-0.465406\pi$
$149$	−8.52284	−	4.92066i	−0.698218	−	0.403116i	−0.806683	+	0.590984i	$0.798740\pi$
$150$	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	$0.176073\pi$
$157$	11.0316	+	19.1074i	0.880420	+	1.52493i	0.0295463	+	0.999563i	$0.490594\pi$
$158$	−3.68011	+	2.12471i	−0.292774	+	0.169033i
$159$	5.48384	−	9.49829i	0.434897	−	0.753263i
$160$	−8.93844			−0.706646
$161$	−11.6769	+	4.96482i	−0.920270	+	0.391283i
$162$	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	$-0.286671\pi$
$181$	16.7131			1.24227			0.621136	+	0.783702i	$0.286671\pi$
$182$	−1.06053	−	3.13842i	−0.0786114	−	0.232635i
$183$			8.66028i			0.640187i
$184$	−6.38729	+	13.3094i	−0.470877	+	0.981185i
$185$	−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	0.833027	−	0.553232i	$-0.186606\pi$
$191$	10.6475	+	6.14735i	0.770427	+	0.444806i	−0.0625996	+	0.998039i	$0.519939\pi$
$192$	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	0.813545	−	0.581501i	$-0.197534\pi$
$199$	−1.36584	−	2.36571i	−0.0968222	−	0.167701i	−0.910368	+	0.413800i	$0.864201\pi$
$200$	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
$207$	−2.70696	−	3.95884i	−0.188146	−	0.275158i
$208$	−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	0.949942	−	0.312425i	$-0.101141\pi$
$227$	3.07964	+	5.33409i	0.204403	+	0.354036i	−0.745540	+	0.666461i	$0.767808\pi$
$228$	0.998676	−	0.576586i	0.0661389	−	0.0381853i
$229$	7.44292	−	12.8915i	0.491842	−	0.851895i	−0.508114	−	0.861290i	$-0.669657\pi$
$229$	7.44292	−	12.8915i	0.491842	−	0.851895i	0.999956	+	0.00939460i	$0.00299044\pi$
$230$	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	$0.169716\pi$
$241$	13.5181	+	23.4140i	0.870776	+	1.50823i	0.00958007	+	0.999954i	$0.496951\pi$
$242$	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	$-0.297818\pi$
$251$	18.7998			1.18663			0.593317	+	0.804969i	$0.297818\pi$
$252$	−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	−0.356049	−	0.934467i	$-0.615876\pi$
$263$	4.46298	−	2.57670i	0.275199	−	0.158886i	0.631248	+	0.775581i	$0.282543\pi$
$264$	−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
$276$	2.48670	−	1.70034i	0.149681	−	0.102348i
$277$	−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	$0.276551\pi$
$281$			25.5993i			1.52712i	−0.645734	+	0.763562i	$0.723449\pi$
$282$	−6.11606	+	10.5933i	−0.364206	+	0.630824i
$283$	−5.56134	−	9.63251i	−0.330587	−	0.572594i	0.652040	−	0.758185i	$-0.273913\pi$
$283$	−5.56134	−	9.63251i	−0.330587	−	0.572594i	−0.982627	+	0.185591i	$0.940580\pi$
$284$	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	$-0.541729\pi$
$293$	−4.47517			−0.261443			−0.130721	+	0.991419i	$0.541729\pi$
$294$	−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
$299$	−4.62214	−	2.21819i	−0.267305	−	0.128281i
$300$		−	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	$0.448964\pi$
$313$	−13.7128	+	23.7513i	−0.775094	+	1.34250i	−0.934741	+	0.355329i	$0.884369\pi$
$314$	−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
$322$	1.80234	−	14.7520i	0.100440	−	0.822097i
$323$	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	$0.0445144\pi$
$337$			5.11775i			0.278782i	−0.990237	+	0.139391i	$0.955486\pi$
$338$	−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
$345$	−11.3502	−	5.44701i	−0.611072	−	0.293257i
$346$	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	0.585632	−	0.810577i	$-0.300847\pi$
$359$	3.34357	+	1.93041i	0.176467	+	0.101883i	−0.409165	+	0.912461i	$0.634180\pi$
$360$	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	$-0.909219\pi$
$367$	−13.8594	−	24.0052i	−0.723455	−	1.25306i	0.236151	−	0.971716i	$-0.424114\pi$
$368$	−6.35909	−	9.29997i	−0.331491	−	0.484795i
$369$	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	0.495890	−	0.868385i	$-0.334842\pi$
$373$	−0.158538	−	0.0915320i	−0.00820879	−	0.00473935i	−0.504099	+	0.863646i	$0.668175\pi$
$374$	−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	$-0.670089\pi$
$379$		−	33.5082i		−	1.72120i	0.509283	−	0.860599i	$-0.329911\pi$
$380$	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	$-0.665551\pi$
$383$	9.84454	−	17.0512i	0.503033	−	0.871278i	0.999994	−	0.00350527i	$-0.00111576\pi$
$384$			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	−0.486857	−	0.873482i	$-0.661857\pi$
$389$	0.516198	−	0.298027i	0.0261723	−	0.0151106i	0.513029	+	0.858371i	$0.328523\pi$
$390$	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	0.799418	−	0.600775i	$-0.205141\pi$
$401$	13.5938	+	7.84838i	0.678842	+	0.391929i	−0.120577	+	0.992704i	$0.538474\pi$
$402$	−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	$-0.735240\pi$
$419$	−27.5752			−1.34714			−0.673569	+	0.739124i	$0.735240\pi$
$420$	−4.27763	−	0.857008i	−0.208727	−	0.0418177i
$421$			17.6198i			0.858735i	0.903130	+	0.429367i	$0.141263\pi$
$421$			17.6198i			0.858735i	−0.903130	+	0.429367i	$0.858737\pi$
$422$	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	−0.761816	−	0.647793i	$-0.775692\pi$
$431$	−12.0768	+	6.97254i	−0.581719	+	0.335856i	0.180097	+	0.983649i	$0.442359\pi$
$432$	−2.03444	−	1.17458i	−0.0978820	−	0.0565122i
$433$	−13.0347			−0.626409			−0.313204	−	0.949686i	$-0.601403\pi$
$433$	−13.0347			−0.626409			−0.313204	+	0.949686i	$0.601403\pi$
$434$	−14.6411	+	16.6486i	−0.702797	+	0.799160i
$435$		−	11.5460i		−	0.553588i
$436$	−8.09991	−	4.67648i	−0.387915	−	0.223963i
$437$	−4.96958	−	7.26786i	−0.237727	−	0.347669i
$438$	−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	0.777576	−	0.628789i	$-0.216449\pi$
$457$	13.2929	+	7.67468i	0.621817	+	0.359006i	−0.155759	+	0.987795i	$0.549782\pi$
$458$	8.71763	+	15.0994i	0.407348	+	0.705548i
$459$	1.09360	−	0.631390i	0.0510448	−	0.0294707i
$460$	3.42147	−	7.12946i	0.159527	−	0.332413i
$461$		−	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	$-0.642350\pi$
$467$	12.2019	−	21.1343i	0.564637	−	0.977979i	0.997083	−	0.0763197i	$-0.0243170\pi$
$468$		−	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	$0.0683248\pi$
$479$	14.7292	+	25.5117i	0.672993	+	1.16566i	−0.304059	+	0.952653i	$0.598342\pi$
$480$	−7.74092	+	4.46922i	−0.353323	+	0.203991i
$481$	−1.92422	+	3.33285i	−0.0877369	+	0.151965i
$482$	−31.6665			−1.44237
$483$	−7.63010	+	10.1381i	−0.347182	+	0.461301i
$484$	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	$-0.479544\pi$
$503$	2.88055			0.128437			0.0642187	+	0.997936i	$0.479544\pi$
$504$	7.71566	−	2.60725i	0.343683	−	0.116136i
$505$			12.1793i			0.541974i
$506$	22.4040	+	10.7518i	0.995979	+	0.477977i
$507$	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	0.772155	−	0.635434i	$-0.219179\pi$
$521$	−3.74848	−	6.49256i	−0.164224	−	0.284444i	−0.936379	+	0.350989i	$0.885845\pi$
$522$	2.57579	+	4.46141i	0.112739	+	0.195270i
$523$	−11.4128	+	19.7676i	−0.499048	+	0.864376i	−0.999999	−	0.00109950i	$-0.999650\pi$
$523$	−11.4128	+	19.7676i	−0.499048	+	0.864376i	0.500952	+	0.865475i	$0.332983\pi$
$524$			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
$529$	−14.3889	−	17.9432i	−0.625606	−	0.780139i
$530$	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	−0.268706	−	0.963222i	$-0.586596\pi$
$557$	10.1747	−	5.87438i	0.431117	−	0.248905i	0.699822	+	0.714317i	$0.253263\pi$
$558$	−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	0.521459	−	0.853276i	$-0.325388\pi$
$563$	−11.3472	−	19.6540i	−0.478229	−	0.828317i	−0.999688	+	0.0249589i	$0.992055\pi$
$564$	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	$0.00692960\pi$
$569$	36.2218	+	20.9127i	1.51850	+	0.876704i	0.518733	+	0.854936i	$0.326404\pi$
$570$	4.88844	−	2.82234i	0.204754	−	0.118215i
$571$	−10.4469	+	6.03155i	−0.437191	+	0.252412i	−0.702405	−	0.711777i	$-0.747891\pi$
$571$	−10.4469	+	6.03155i	−0.437191	+	0.252412i	0.265214	+	0.964189i	$0.414557\pi$
$572$	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
$598$	4.95689	−	3.38940i	0.202702	−	0.138603i
$599$	−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	−0.846634	−	0.532175i	$-0.821375\pi$
$613$	−20.0317	+	11.5653i	−0.809074	+	0.467119i	0.0375602	+	0.999294i	$0.488041\pi$
$614$	−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	$-0.728756\pi$
$617$		−	37.3929i		−	1.50538i	0.658375	−	0.752690i	$-0.271244\pi$
$618$	8.68731	+	5.01562i	0.349455	+	0.201758i
$619$	−21.9986	−	38.1028i	−0.884200	−	1.53148i	−0.846628	−	0.532186i	$-0.821371\pi$
$619$	−21.9986	−	38.1028i	−0.884200	−	1.53148i	−0.0375728	−	0.999294i	$-0.511963\pi$
$620$	−10.2166	+	5.89855i	−0.410308	+	0.236891i
$621$	−4.32371	−	2.07498i	−0.173505	−	0.0832659i
$622$			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	$-0.934947\pi$
$631$		−	10.1960i		−	0.405898i	0.979189	−	0.202949i	$-0.0650525\pi$
$632$	−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	−0.999770	−	0.0214491i	$-0.993172\pi$
$641$	−37.4979	+	21.6494i	−1.48108	+	0.855102i	−0.481309	+	0.876551i	$0.659839\pi$
$642$	9.28981	−	16.0904i	0.366640	−	0.635039i
$643$	5.89071			0.232307			0.116154	−	0.993231i	$-0.462944\pi$
$643$	5.89071			0.232307			0.116154	+	0.993231i	$0.462944\pi$
$644$	−6.36814	−	4.79275i	−0.250940	−	0.188861i
$645$	−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	$0.0857414\pi$
$659$			13.6631i			0.532238i	−0.963940	+	0.266119i	$0.914259\pi$
$660$	3.64740	−	6.31749i	0.141975	−	0.245908i
$661$	20.5219	+	35.5450i	0.798209	+	1.38254i	0.920781	+	0.390079i	$0.127552\pi$
$661$	20.5219	+	35.5450i	0.798209	+	1.38254i	−0.122572	+	0.992460i	$0.539114\pi$
$662$	−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
$667$	9.12639	−	19.0170i	0.353375	−	0.736342i
$668$	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	$0.520525\pi$
$677$	−23.3248	+	40.3997i	−0.896444	+	1.55269i	−0.832007	+	0.554764i	$0.812808\pi$
$678$	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
$690$	12.1722	−	8.32303i	0.463387	−	0.316852i
$691$	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	$-0.594802\pi$
$701$		−	50.6216i		−	1.91195i	0.293446	−	0.955976i	$-0.405198\pi$
$702$	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	0.767578	−	0.640956i	$-0.221462\pi$
$709$	15.8772	+	9.16673i	0.596282	+	0.344264i	−0.171295	+	0.985220i	$0.554795\pi$
$710$	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	$-0.793917\pi$
$727$	−43.0133			−1.59528			−0.797638	+	0.603137i	$0.793917\pi$
$728$	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	$0.342394\pi$
$733$	−14.1989	+	24.5931i	−0.524447	+	0.908368i	−0.999595	+	0.0284625i	$0.990939\pi$
$734$	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	$-0.786842\pi$
$743$		−	33.8390i		−	1.24143i	0.784035	−	0.620717i	$-0.213158\pi$
$744$	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	0.978766	−	0.204981i	$-0.0657133\pi$
$751$	35.3689	+	20.4203i	1.29063	+	0.745146i	0.311864	+	0.950127i	$0.399047\pi$
$752$	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	$-0.988628\pi$
$757$		−	1.96542i		−	0.0714345i	0.999362	−	0.0357173i	$-0.0113716\pi$
$758$	33.9889	+	19.6235i	1.23453	+	0.712757i
$759$	−11.9755	−	17.5138i	−0.434684	−	0.635712i
$760$	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	$-0.708415\pi$
$769$	−33.7742			−1.21793			−0.608965	+	0.793197i	$0.708415\pi$
$770$	−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

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} +(2.07498 - 4.32371i) 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} +(3.17056 + 4.63685i) 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

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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