LMFDB - Embedded newform 414.2.p.a.5.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [414,2,Mod(5,414)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(414, base_ring=CyclotomicField(66))

chi = DirichletCharacter(H, H._module([55, 3]))

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

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

chi := DirichletCharacter("414.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 414 = 2 \cdot 3^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	414.p (of order $66$, degree $20$, 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:	$3.30580664368$
Analytic rank:	$0$
Dimension:	$480$
Relative dimension:	$24$ over $\Q(\zeta_{66})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{66}]$

Embedding invariants

Embedding label			5.9
Character	$\chi$	$=$	414.5
Dual form			414.2.p.a.83.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.971812 + 0.235759i) q^{2} +(0.893014 + 1.48409i) q^{3} +(0.888835 - 0.458227i) q^{4} +(1.85702 + 1.46038i) q^{5} +(-1.21773 - 1.23172i) q^{6} +(1.69311 + 1.20566i) q^{7} +(-0.755750 + 0.654861i) q^{8} +(-1.40505 + 2.65063i) q^{9} +O(q^{10})$	\(q+(-0.971812 + 0.235759i) q^{2} +(0.893014 + 1.48409i) q^{3} +(0.888835 - 0.458227i) q^{4} +(1.85702 + 1.46038i) q^{5} +(-1.21773 - 1.23172i) q^{6} +(1.69311 + 1.20566i) q^{7} +(-0.755750 + 0.654861i) q^{8} +(-1.40505 + 2.65063i) q^{9} +(-2.14898 - 0.981404i) q^{10} +(2.05541 + 1.95983i) q^{11} +(1.47379 + 0.909910i) q^{12} +(-2.64080 - 3.70848i) q^{13} +(-1.92963 - 0.772509i) q^{14} +(-0.508989 + 4.06013i) q^{15} +(0.580057 - 0.814576i) q^{16} +(-0.575493 + 0.369847i) q^{17} +(0.740538 - 2.90716i) q^{18} +(2.15872 - 3.35903i) q^{19} +(2.31977 + 0.447100i) q^{20} +(-0.277337 + 3.58941i) q^{21} +(-2.45952 - 1.42000i) q^{22} +(3.65075 - 3.10999i) q^{23} +(-1.64677 - 0.536802i) q^{24} +(0.137034 + 0.564864i) q^{25} +(3.44066 + 2.98135i) q^{26} +(-5.18850 + 0.281820i) q^{27} +(2.05737 + 0.295805i) q^{28} +(-2.49178 + 4.83337i) q^{29} +(-0.462571 - 4.06568i) q^{30} +(-7.68194 + 1.48057i) q^{31} +(-0.371662 + 0.928368i) q^{32} +(-1.07306 + 4.80057i) q^{33} +(0.472076 - 0.495099i) q^{34} +(1.38343 + 4.71153i) q^{35} +(-0.0342732 + 2.99980i) q^{36} +(4.54735 - 0.653810i) q^{37} +(-1.30595 + 3.77328i) q^{38} +(3.14546 - 7.23091i) q^{39} +(-2.35979 + 0.112411i) q^{40} +(0.519976 - 0.661203i) q^{41} +(-0.576716 - 3.55361i) q^{42} +(0.429362 - 2.22774i) q^{43} +(2.72497 + 0.800122i) q^{44} +(-6.48014 + 2.87037i) q^{45} +(-2.81464 + 3.88302i) q^{46} +(-4.49568 + 2.59558i) q^{47} +(1.72690 + 0.133430i) q^{48} +(-0.876459 - 2.53236i) q^{49} +(-0.266343 - 0.516634i) q^{50} +(-1.06281 - 0.523806i) q^{51} +(-4.04656 - 2.08615i) q^{52} +(4.90057 + 10.7307i) q^{53} +(4.97581 - 1.49711i) q^{54} +(0.954850 + 6.64113i) q^{55} +(-2.06911 + 0.197576i) q^{56} +(6.91288 + 0.204074i) q^{57} +(1.28203 - 5.28458i) q^{58} +(-5.70916 + 4.06548i) q^{59} +(1.40805 + 3.84202i) q^{60} +(1.65893 + 0.574162i) q^{61} +(7.11634 - 3.24992i) q^{62} +(-5.57467 + 2.79380i) q^{63} +(0.142315 - 0.989821i) q^{64} +(0.511767 - 10.7433i) q^{65} +(-0.0889688 - 4.91823i) q^{66} +(-3.11217 - 3.26395i) q^{67} +(-0.342045 + 0.592439i) q^{68} +(7.87567 + 2.64079i) q^{69} +(-2.45522 - 4.25256i) q^{70} +(3.76333 - 12.8167i) q^{71} +(-0.673924 - 2.92332i) q^{72} +(10.9883 + 7.06173i) q^{73} +(-4.26503 + 1.70746i) q^{74} +(-0.715935 + 0.707802i) q^{75} +(0.379548 - 3.97481i) q^{76} +(1.11715 + 5.79634i) q^{77} +(-1.35204 + 7.76865i) q^{78} +(-0.910656 - 9.53682i) q^{79} +(2.26677 - 0.665584i) q^{80} +(-5.05165 - 7.44854i) q^{81} +(-0.349434 + 0.765154i) q^{82} +(13.4956 - 10.6130i) q^{83} +(1.39825 + 3.31748i) q^{84} +(-1.60882 - 0.153624i) q^{85} +(0.107951 + 2.26617i) q^{86} +(-9.39835 + 0.618244i) q^{87} +(-2.83679 - 0.135133i) q^{88} +(1.17088 - 1.35127i) q^{89} +(5.62076 - 4.31721i) q^{90} -9.46279i q^{91} +(1.81984 - 4.43714i) q^{92} +(-9.05738 - 10.0785i) q^{93} +(3.75702 - 3.58232i) q^{94} +(8.91426 - 3.08525i) q^{95} +(-1.70968 + 0.277464i) q^{96} +(1.76732 + 4.41456i) q^{97} +(1.44878 + 2.25435i) q^{98} +(-8.08273 + 2.69446i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 480 q - 4 q^{3} - 24 q^{4} + 8 q^{6}+O(q^{10}) $ 480 * q - 4 * q^3 - 24 * q^4 + 8 * q^6	$ 480 q - 4 q^{3} - 24 q^{4} + 8 q^{6} + 4 q^{12} - 44 q^{15} + 24 q^{16} + 28 q^{18} + 66 q^{21} + 6 q^{23} + 4 q^{24} + 12 q^{25} + 86 q^{27} - 48 q^{29} + 44 q^{30} - 12 q^{31} - 44 q^{33} + 24 q^{39} - 60 q^{41} + 12 q^{46} + 48 q^{47} + 8 q^{48} - 78 q^{49} + 24 q^{50} - 30 q^{54} - 24 q^{55} - 66 q^{56} - 66 q^{57} - 72 q^{59} - 22 q^{60} - 110 q^{63} + 48 q^{64} - 462 q^{65} - 88 q^{66} - 70 q^{69} + 12 q^{70} - 52 q^{72} - 264 q^{74} - 76 q^{75} - 12 q^{77} - 58 q^{78} - 96 q^{81} - 198 q^{83} - 22 q^{84} + 178 q^{87} + 6 q^{92} - 20 q^{93} - 12 q^{94} + 12 q^{95} - 4 q^{96} - 66 q^{97} - 132 q^{99}+O(q^{100}) $ 480 * q - 4 * q^3 - 24 * q^4 + 8 * q^6 + 4 * q^12 - 44 * q^15 + 24 * q^16 + 28 * q^18 + 66 * q^21 + 6 * q^23 + 4 * q^24 + 12 * q^25 + 86 * q^27 - 48 * q^29 + 44 * q^30 - 12 * q^31 - 44 * q^33 + 24 * q^39 - 60 * q^41 + 12 * q^46 + 48 * q^47 + 8 * q^48 - 78 * q^49 + 24 * q^50 - 30 * q^54 - 24 * q^55 - 66 * q^56 - 66 * q^57 - 72 * q^59 - 22 * q^60 - 110 * q^63 + 48 * q^64 - 462 * q^65 - 88 * q^66 - 70 * q^69 + 12 * q^70 - 52 * q^72 - 264 * q^74 - 76 * q^75 - 12 * q^77 - 58 * q^78 - 96 * q^81 - 198 * q^83 - 22 * q^84 + 178 * q^87 + 6 * q^92 - 20 * q^93 - 12 * q^94 + 12 * q^95 - 4 * q^96 - 66 * q^97 - 132 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/414\mathbb{Z}\right)^\times$.

$n$	$47$	$235$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{22}\right)$

Coefficient data

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

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

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

$2$	−0.971812	+	0.235759i	−0.687175	+	0.166707i
$2$	−0.971812	+	0.235759i	−0.687175	+	0.166707i
$3$	0.893014	+	1.48409i	0.515582	+	0.856840i
$3$	0.893014	+	1.48409i	0.515582	+	0.856840i
$4$	0.888835	−	0.458227i	0.444418	−	0.229113i
$5$	1.85702	+	1.46038i	0.830486	+	0.653102i	0.940110	−	0.340871i	$-0.110722\pi$
$5$	1.85702	+	1.46038i	0.830486	+	0.653102i	−0.109623	+	0.993973i	$0.534965\pi$
$6$	−1.21773	−	1.23172i	−0.497136	−	0.502848i
$7$	1.69311	+	1.20566i	0.639937	+	0.455697i	0.853402	−	0.521254i	$-0.174535\pi$
$7$	1.69311	+	1.20566i	0.639937	+	0.455697i	−0.213465	+	0.976951i	$0.568475\pi$
$8$	−0.755750	+	0.654861i	−0.267198	+	0.231528i
$9$	−1.40505	+	2.65063i	−0.468351	+	0.883542i
$10$	−2.14898	−	0.981404i	−0.679566	−	0.310347i
$11$	2.05541	+	1.95983i	0.619729	+	0.590911i	0.933495	−	0.358590i	$-0.116742\pi$
$11$	2.05541	+	1.95983i	0.619729	+	0.590911i	−0.313766	+	0.949500i	$0.601591\pi$
$12$	1.47379	+	0.909910i	0.425447	+	0.262668i
$13$	−2.64080	−	3.70848i	−0.732425	−	1.02855i	−0.997922	−	0.0644356i	$-0.979475\pi$
$13$	−2.64080	−	3.70848i	−0.732425	−	1.02855i	0.265497	−	0.964112i	$-0.414464\pi$
$14$	−1.92963	−	0.772509i	−0.515716	−	0.206462i
$15$	−0.508989	+	4.06013i	−0.131420	+	1.04832i
$16$	0.580057	−	0.814576i	0.145014	−	0.203644i
$17$	−0.575493	+	0.369847i	−0.139578	+	0.0897010i	−0.608566	−	0.793503i	$-0.708255\pi$
$17$	−0.575493	+	0.369847i	−0.139578	+	0.0897010i	0.468988	+	0.883204i	$0.344619\pi$
$18$	0.740538	−	2.90716i	0.174546	−	0.685225i
$19$	2.15872	−	3.35903i	0.495244	−	0.770615i	−0.500205	−	0.865907i	$-0.666742\pi$
$19$	2.15872	−	3.35903i	0.495244	−	0.770615i	0.995449	+	0.0952920i	$0.0303785\pi$
$20$	2.31977	+	0.447100i	0.518717	+	0.0999745i
$21$	−0.277337	+	3.58941i	−0.0605199	+	0.783273i
$22$	−2.45952	−	1.42000i	−0.524371	−	0.302746i
$23$	3.65075	−	3.10999i	0.761234	−	0.648477i
$23$	3.65075	−	3.10999i	0.761234	−	0.648477i
$24$	−1.64677	−	0.536802i	−0.336145	−	0.109574i
$25$	0.137034	+	0.564864i	0.0274069	+	0.112973i
$26$	3.44066	+	2.98135i	0.674770	+	0.584691i
$27$	−5.18850	+	0.281820i	−0.998528	+	0.0542362i
$28$	2.05737	+	0.295805i	0.388806	+	0.0559018i
$29$	−2.49178	+	4.83337i	−0.462711	+	0.897534i	0.535871	+	0.844300i	$0.319983\pi$
$29$	−2.49178	+	4.83337i	−0.462711	+	0.897534i	−0.998582	+	0.0532344i	$0.983047\pi$
$30$	−0.462571	−	4.06568i	−0.0844536	−	0.742289i
$31$	−7.68194	+	1.48057i	−1.37972	+	0.265919i	−0.824535	−	0.565811i	$-0.808563\pi$
$31$	−7.68194	+	1.48057i	−1.37972	+	0.265919i	−0.555181	+	0.831729i	$0.687351\pi$
$32$	−0.371662	+	0.928368i	−0.0657013	+	0.164114i
$33$	−1.07306	+	4.80057i	−0.186795	+	0.835672i
$34$	0.472076	−	0.495099i	0.0809604	−	0.0849088i
$35$	1.38343	+	4.71153i	0.233842	+	0.796394i
$36$	−0.0342732	+	2.99980i	−0.00571220	+	0.499967i
$37$	4.54735	−	0.653810i	0.747580	−	0.107486i	0.242013	−	0.970273i	$-0.422192\pi$
$37$	4.54735	−	0.653810i	0.747580	−	0.107486i	0.505567	+	0.862787i	$0.331283\pi$
$38$	−1.30595	+	3.77328i	−0.211852	+	0.612107i
$39$	3.14546	−	7.23091i	0.503676	−	1.15787i
$40$	−2.35979	+	0.112411i	−0.373116	+	0.0177737i
$41$	0.519976	−	0.661203i	0.0812066	−	0.103263i	−0.743752	−	0.668455i	$-0.766956\pi$
$41$	0.519976	−	0.661203i	0.0812066	−	0.103263i	0.824959	+	0.565193i	$0.191198\pi$
$42$	−0.576716	−	3.55361i	−0.0889892	−	0.548334i
$43$	0.429362	−	2.22774i	0.0654772	−	0.339728i	−0.934386	−	0.356262i	$-0.884051\pi$
$43$	0.429362	−	2.22774i	0.0654772	−	0.339728i	0.999863	+	0.0165341i	$0.00526322\pi$
$44$	2.72497	+	0.800122i	0.410804	+	0.120623i
$45$	−6.48014	+	2.87037i	−0.966002	+	0.427889i
$46$	−2.81464	+	3.88302i	−0.414995	+	0.572520i
$47$	−4.49568	+	2.59558i	−0.655763	+	0.378605i	−0.790661	−	0.612255i	$-0.790263\pi$
$47$	−4.49568	+	2.59558i	−0.655763	+	0.378605i	0.134898	+	0.990860i	$0.456929\pi$
$48$	1.72690	+	0.133430i	0.249257	+	0.0192589i
$49$	−0.876459	−	2.53236i	−0.125208	−	0.361766i
$50$	−0.266343	−	0.516634i	−0.0376666	−	0.0730631i
$51$	−1.06281	−	0.523806i	−0.148823	−	0.0733475i
$52$	−4.04656	−	2.08615i	−0.561157	−	0.289296i
$53$	4.90057	+	10.7307i	0.673145	+	1.47398i	0.869747	+	0.493498i	$0.164282\pi$
$53$	4.90057	+	10.7307i	0.673145	+	1.47398i	−0.196602	+	0.980483i	$0.562991\pi$
$54$	4.97581	−	1.49711i	0.677122	−	0.203731i
$55$	0.954850	+	6.64113i	0.128752	+	0.895489i
$56$	−2.06911	+	0.197576i	−0.276496	+	0.0264022i
$57$	6.91288	+	0.204074i	0.915633	+	0.0270302i
$58$	1.28203	−	5.28458i	0.168338	−	0.693900i
$59$	−5.70916	+	4.06548i	−0.743270	+	0.529280i	−0.887805	−	0.460220i	$-0.847771\pi$
$59$	−5.70916	+	4.06548i	−0.743270	+	0.529280i	0.144535	+	0.989500i	$0.453831\pi$
$60$	1.40805	+	3.84202i	0.181779	+	0.496003i
$61$	1.65893	+	0.574162i	0.212405	+	0.0735139i	0.431198	−	0.902257i	$-0.358091\pi$
$61$	1.65893	+	0.574162i	0.212405	+	0.0735139i	−0.218794	+	0.975771i	$0.570212\pi$
$62$	7.11634	−	3.24992i	0.903776	−	0.412741i
$63$	−5.57467	+	2.79380i	−0.702343	+	0.351985i
$64$	0.142315	−	0.989821i	0.0177894	−	0.123728i
$65$	0.511767	−	10.7433i	0.0634768	−	1.33254i
$66$	−0.0889688	−	4.91823i	−0.0109513	−	0.605392i
$67$	−3.11217	−	3.26395i	−0.380212	−	0.398754i	0.505624	−	0.862754i	$-0.331262\pi$
$67$	−3.11217	−	3.26395i	−0.380212	−	0.398754i	−0.885835	+	0.464000i	$0.846414\pi$
$68$	−0.342045	+	0.592439i	−0.0414790	+	0.0718438i
$69$	7.87567	+	2.64079i	0.948120	+	0.317914i
$70$	−2.45522	−	4.25256i	−0.293455	−	0.508279i
$71$	3.76333	−	12.8167i	0.446625	−	1.52106i	−0.361681	−	0.932302i	$-0.617797\pi$
$71$	3.76333	−	12.8167i	0.446625	−	1.52106i	0.808306	−	0.588763i	$-0.200385\pi$
$72$	−0.673924	−	2.92332i	−0.0794227	−	0.344517i
$73$	10.9883	+	7.06173i	1.28608	+	0.826513i	0.991625	−	0.129153i	$-0.0412257\pi$
$73$	10.9883	+	7.06173i	1.28608	+	0.826513i	0.294454	+	0.955666i	$0.404862\pi$
$74$	−4.26503	+	1.70746i	−0.495799	+	0.198488i
$75$	−0.715935	+	0.707802i	−0.0826691	+	0.0817300i
$76$	0.379548	−	3.97481i	0.0435372	−	0.455942i
$77$	1.11715	+	5.79634i	0.127311	+	0.660554i
$78$	−1.35204	+	7.76865i	−0.153088	+	0.879626i
$79$	−0.910656	−	9.53682i	−0.102457	−	1.07298i	−0.889766	−	0.456417i	$-0.849132\pi$
$79$	−0.910656	−	9.53682i	−0.102457	−	1.07298i	0.787309	−	0.616559i	$-0.211474\pi$
$80$	2.26677	−	0.665584i	0.253433	−	0.0744145i
$81$	−5.05165	−	7.44854i	−0.561295	−	0.827616i
$82$	−0.349434	+	0.765154i	−0.0385885	+	0.0844971i
$83$	13.4956	−	10.6130i	1.48133	−	1.16493i	0.533652	−	0.845704i	$-0.320819\pi$
$83$	13.4956	−	10.6130i	1.48133	−	1.16493i	0.947678	−	0.319227i	$-0.103423\pi$
$84$	1.39825	+	3.31748i	0.152562	+	0.361966i
$85$	−1.60882	−	0.153624i	−0.174501	−	0.0166628i
$86$	0.107951	+	2.26617i	0.0116407	+	0.244368i
$87$	−9.39835	+	0.618244i	−1.00761	+	0.0662827i
$88$	−2.83679	−	0.135133i	−0.302403	−	0.0144052i
$89$	1.17088	−	1.35127i	0.124113	−	0.143234i	−0.690292	−	0.723531i	$-0.742518\pi$
$89$	1.17088	−	1.35127i	0.124113	−	0.143234i	0.814405	+	0.580297i	$0.197063\pi$
$90$	5.62076	−	4.31721i	0.592480	−	0.455074i
$91$		−	9.46279i		−	0.991970i
$92$	1.81984	−	4.43714i	0.189731	−	0.462604i
$93$	−9.05738	−	10.0785i	−0.939206	−	1.04509i
$94$	3.75702	−	3.58232i	0.387508	−	0.369488i
$95$	8.91426	−	3.08525i	0.914583	−	0.316540i
$96$	−1.70968	+	0.277464i	−0.174494	+	0.0283186i
$97$	1.76732	+	4.41456i	0.179445	+	0.448231i	0.990633	−	0.136555i	$-0.0436029\pi$
$97$	1.76732	+	4.41456i	0.179445	+	0.448231i	−0.811188	+	0.584786i	$0.801179\pi$
$98$	1.44878	+	2.25435i	0.146349	+	0.227723i
$99$	−8.08273	+	2.69446i	−0.812345	+	0.270803i
$100$	0.380637	+	0.439278i	0.0380637	+	0.0439278i
$101$	−5.00601	−	6.36566i	−0.498117	−	0.633407i	0.470371	−	0.882469i	$-0.344120\pi$
$101$	−5.00601	−	6.36566i	−0.498117	−	0.633407i	−0.968488	+	0.249062i	$0.919878\pi$
$102$	1.15634	+	0.258474i	0.114495	+	0.0255927i
$103$	−1.27487	−	0.309280i	−0.125617	−	0.0304743i	0.172458	−	0.985017i	$-0.444829\pi$
$103$	−1.27487	−	0.309280i	−0.125617	−	0.0304743i	−0.298074	+	0.954543i	$0.596344\pi$
$104$	4.42432	+	1.07333i	0.433840	+	0.105248i
$105$	−5.75692	+	6.26060i	−0.561818	+	0.610972i
$106$	−7.29230	−	9.27291i	−0.708291	−	0.900665i
$107$	−1.26928	−	1.46483i	−0.122706	−	0.141610i	0.691073	−	0.722785i	$-0.257138\pi$
$107$	−1.26928	−	1.46483i	−0.122706	−	0.141610i	−0.813778	+	0.581175i	$0.802593\pi$
$108$	−4.48259	+	2.62800i	−0.431337	+	0.252880i
$109$	−4.89788	−	7.62125i	−0.469132	−	0.729983i	0.523385	−	0.852097i	$-0.324669\pi$
$109$	−4.89788	−	7.62125i	−0.469132	−	0.729983i	−0.992516	+	0.122114i	$0.961033\pi$
$110$	−2.49364	−	6.22881i	−0.237759	−	0.593894i
$111$	5.03116	+	6.16482i	0.477537	+	0.585139i
$112$	1.96420	−	0.679818i	0.185600	−	0.0642368i
$113$	−10.8334	+	10.3296i	−1.01912	+	0.971726i	−0.999606	−	0.0280841i	$-0.991059\pi$
$113$	−10.8334	+	10.3296i	−1.01912	+	0.971726i	−0.0195108	+	0.999810i	$0.506211\pi$
$114$	−6.76612	+	1.43145i	−0.633706	+	0.134068i
$115$	11.3213	−	0.443835i	1.05572	−	0.0413878i
$116$			5.43787i			0.504893i
$117$	13.5403	−	1.78916i	1.25180	−	0.165408i
$118$	4.58976	−	5.29686i	0.422522	−	0.487616i
$119$	−1.42029	−	0.0676565i	−0.130197	−	0.00620206i
$120$	−2.27415	−	3.40176i	−0.207601	−	0.310537i
$121$	−0.139623	−	2.93104i	−0.0126930	−	0.266458i
$122$	−1.74753	−	0.166869i	−0.158214	−	0.0151076i
$123$	1.44563	+	0.181228i	0.130348	+	0.0163408i
$124$	−6.14954	+	4.83605i	−0.552245	+	0.434290i
$125$	4.33658	−	9.49579i	0.387876	−	0.849329i
$126$	4.75887	−	4.02932i	0.423954	−	0.358961i
$127$	−0.512487	+	0.150480i	−0.0454758	+	0.0133529i	−0.304391	−	0.952547i	$-0.598453\pi$
$127$	−0.512487	+	0.150480i	−0.0454758	+	0.0133529i	0.258916	+	0.965900i	$0.416635\pi$
$128$	0.0950560	+	0.995472i	0.00840185	+	0.0879881i
$129$	3.68960	−	1.35219i	0.324851	−	0.119054i
$130$	2.03549	+	10.5611i	0.178524	+	0.926272i
$131$	1.63112	−	17.0819i	0.142512	−	1.49245i	−0.587614	−	0.809141i	$-0.699933\pi$
$131$	1.63112	−	17.0819i	0.142512	−	1.49245i	0.730126	−	0.683312i	$-0.239461\pi$
$132$	1.24598	+	4.75862i	0.108448	+	0.414184i
$133$	7.70481	−	3.08454i	0.668092	−	0.267464i
$134$	3.79394	+	2.43822i	0.327747	+	0.210630i
$135$	−10.0467	−	7.05384i	−0.864686	−	0.607098i
$136$	0.192730	−	0.656379i	0.0165265	−	0.0562841i
$137$	−0.293897	−	0.509045i	−0.0251093	−	0.0434907i	0.853198	−	0.521588i	$-0.174660\pi$
$137$	−0.293897	−	0.509045i	−0.0251093	−	0.0434907i	−0.878307	+	0.478097i	$0.841327\pi$
$138$	−8.27626	−	0.709588i	−0.704522	−	0.0604041i
$139$	2.82700	−	4.89650i	0.239783	−	0.415316i	−0.720869	−	0.693071i	$-0.756257\pi$
$139$	2.82700	−	4.89650i	0.239783	−	0.415316i	0.960652	+	0.277755i	$0.0895904\pi$
$140$	3.38859	+	3.55385i	0.286388	+	0.300355i
$141$	−7.86679	−	4.35411i	−0.662503	−	0.366682i
$142$	−0.635590	+	13.3427i	−0.0533375	+	1.11969i
$143$	1.84007	−	12.7980i	0.153874	−	1.07022i
$144$	1.34413	+	2.68204i	0.112011	+	0.223503i
$145$	−11.6858	+	5.33675i	−0.970457	+	0.443193i
$146$	−12.3434	−	4.27209i	−1.02155	−	0.353561i
$147$	2.97557	−	3.56218i	0.245421	−	0.293804i
$148$	3.74225	−	2.66485i	0.307611	−	0.219049i
$149$	−2.11028	+	8.69868i	−0.172881	+	0.712624i	0.817694	+	0.575653i	$0.195252\pi$
$149$	−2.11028	+	8.69868i	−0.172881	+	0.712624i	−0.990575	+	0.136971i	$0.956263\pi$
$150$	0.528884	−	0.856639i	0.0431832	−	0.0699443i
$151$	20.5626	−	1.96349i	1.67336	−	0.159787i	0.785176	−	0.619273i	$-0.212572\pi$
$151$	20.5626	−	1.96349i	1.67336	−	0.159787i	0.888185	+	0.459486i	$0.151966\pi$
$152$	0.568247	+	3.95225i	0.0460910	+	0.320570i
$153$	−0.171728	−	2.04507i	−0.0138834	−	0.165334i
$154$	−2.45220	−	5.36957i	−0.197604	−	0.432692i
$155$	−16.4277	−	8.46909i	−1.31951	−	0.680254i
$156$	−0.517601	−	7.86842i	−0.0414413	−	0.629978i
$157$	10.2590	+	19.8997i	0.818758	+	1.58817i	0.808701	+	0.588219i	$0.200171\pi$
$157$	10.2590	+	19.8997i	0.818758	+	1.58817i	0.0100565	+	0.999949i	$0.496799\pi$
$158$	3.13338	+	9.05330i	0.249278	+	0.720242i
$159$	−11.5491	+	16.8556i	−0.915906	+	1.33674i
$160$	−2.04596	+	1.18123i	−0.161747	+	0.0933847i
$161$	9.93073	−	0.863992i	0.782651	−	0.0680921i
$162$	6.66531	+	6.04761i	0.523677	+	0.475145i
$163$	17.5159	+	5.14314i	1.37195	+	0.402842i	0.882961	−	0.469446i	$-0.155547\pi$
$163$	17.5159	+	5.14314i	1.37195	+	0.402842i	0.488992	+	0.872288i	$0.337365\pi$
$164$	0.159192	−	0.825968i	0.0124308	−	0.0644972i
$165$	−9.00334	+	7.34770i	−0.700909	+	0.572018i
$166$	−10.6130	+	13.4956i	−0.823731	+	1.04746i
$167$	−16.4618	+	0.784173i	−1.27385	+	0.0606811i	−0.673580	−	0.739114i	$-0.735244\pi$
$167$	−16.4618	+	0.784173i	−1.27385	+	0.0606811i	−0.600273	+	0.799795i	$0.704941\pi$
$168$	−2.14096	−	2.89431i	−0.165179	−	0.223301i
$169$	−2.52714	+	7.30168i	−0.194395	+	0.561668i
$170$	1.59969	−	0.230001i	0.122691	−	0.0176402i
$171$	5.87043	+	10.4416i	0.448923	+	0.798487i
$172$	−0.639179	−	2.17684i	−0.0487369	−	0.165983i
$173$	−1.97744	+	2.07388i	−0.150342	+	0.157674i	−0.794598	−	0.607136i	$-0.792318\pi$
$173$	−1.97744	+	2.07388i	−0.150342	+	0.157674i	0.644256	+	0.764810i	$0.277167\pi$
$174$	8.98767	−	2.81656i	0.681354	−	0.213523i
$175$	−0.449019	+	1.12160i	−0.0339427	+	0.0847847i
$176$	2.78868	−	0.537475i	0.210205	−	0.0405137i
$177$	−11.1319	−	4.84239i	−0.836725	−	0.363977i
$178$	−0.819302	+	1.58922i	−0.0614093	+	0.119117i
$179$	−22.6578	−	3.25769i	−1.69352	−	0.243491i	−0.773061	−	0.634331i	$-0.781276\pi$
$179$	−22.6578	−	3.25769i	−1.69352	−	0.243491i	−0.920459	+	0.390840i	$0.872185\pi$
$180$	−4.44450	+	5.52066i	−0.331273	+	0.411485i
$181$	2.51228	+	2.17690i	0.186736	+	0.161808i	0.743212	−	0.669056i	$-0.233301\pi$
$181$	2.51228	+	2.17690i	0.186736	+	0.161808i	−0.556476	+	0.830864i	$0.687847\pi$
$182$	2.23094	+	9.19605i	0.165368	+	0.681656i
$183$	0.629340	+	2.97474i	0.0465222	+	0.219899i
$184$	−0.722446	+	4.74110i	−0.0532594	+	0.349519i
$185$	9.39935	+	5.42672i	0.691054	+	0.398980i
$186$	11.1782	+	7.65907i	0.819623	+	0.561590i
$187$	−1.90771	−	0.367681i	−0.139506	−	0.0268875i
$188$	−2.80656	+	4.36709i	−0.204689	+	0.318503i
$189$	−9.12451	−	5.77842i	−0.663710	−	0.420319i
$190$	−7.93560	+	5.09990i	−0.575709	+	0.369986i
$191$	−0.0380910	+	0.0534913i	−0.00275617	+	0.00387050i	−0.815952	−	0.578120i	$-0.803787\pi$
$191$	−0.0380910	+	0.0534913i	−0.00275617	+	0.00387050i	0.813196	+	0.581991i	$0.197726\pi$
$192$	1.59607	−	0.672716i	0.115187	−	0.0485491i
$193$	20.7699	+	8.31503i	1.49505	+	0.598529i	0.967921	−	0.251254i	$-0.0808431\pi$
$193$	20.7699	+	8.31503i	1.49505	+	0.598529i	0.527132	+	0.849783i	$0.323267\pi$
$194$	−2.75828	−	3.87346i	−0.198033	−	0.278098i
$195$	16.4011	−	8.83441i	1.17450	−	0.632645i
$196$	−1.93942	−	1.84924i	−0.138530	−	0.132088i
$197$	1.47415	+	0.673221i	0.105029	+	0.0479650i	0.467237	−	0.884132i	$-0.345250\pi$
$197$	1.47415	+	0.673221i	0.105029	+	0.0479650i	−0.362208	+	0.932097i	$0.617977\pi$
$198$	7.21965	−	4.52408i	0.513078	−	0.321513i
$199$	−18.1018	+	15.6853i	−1.28320	+	1.11190i	−0.295538	+	0.955331i	$0.595499\pi$
$199$	−18.1018	+	15.6853i	−1.28320	+	1.11190i	−0.987666	+	0.156572i	$0.949956\pi$
$200$	−0.473471	−	0.337157i	−0.0334794	−	0.0238406i
$201$	2.06479	−	7.53349i	0.145639	−	0.531371i
$202$	6.36566	+	5.00601i	0.447887	+	0.352222i
$203$	−10.0463	+	5.17921i	−0.705110	+	0.363509i
$204$	−1.18468	+	0.0214305i	−0.0829445	+	0.00150043i
$205$	1.93122	−	0.468508i	0.134882	−	0.0327220i
$206$	1.31185			0.0914009
$207$	3.11391	+	14.0465i	0.216432	+	0.976298i
$208$	−4.55265			−0.315670
$209$	11.0202	−	2.67347i	0.762282	−	0.184928i
$210$	4.11865	−	7.44137i	0.284214	−	0.513503i
$211$	8.02848	−	4.13897i	0.552704	−	0.284939i	−0.159164	−	0.987252i	$-0.550880\pi$
$211$	8.02848	−	4.13897i	0.552704	−	0.284939i	0.711868	+	0.702314i	$0.247850\pi$
$212$	9.27291	+	7.29230i	0.636866	+	0.500837i
$213$	22.3819	−	5.86038i	1.53358	−	0.401547i
$214$	1.57884	+	1.12429i	0.107928	+	0.0768549i
$215$	4.05069	−	3.50994i	0.276255	−	0.239376i
$216$	3.73666	−	3.61073i	0.254247	−	0.245679i
$217$	−14.7915	−	6.75503i	−1.00411	−	0.458562i
$218$	6.55659	+	6.25170i	0.444068	+	0.423418i
$219$	−0.667579	+	22.6138i	−0.0451108	+	1.52810i
$220$	3.89184	+	5.46533i	0.262388	+	0.368473i
$221$	2.89133	+	1.15751i	0.194492	+	0.0778628i
$222$	−6.34275	−	4.80490i	−0.425698	−	0.322484i
$223$	−7.05745	+	9.91080i	−0.472602	+	0.663676i	−0.980221	−	0.197905i	$-0.936586\pi$
$223$	−7.05745	+	9.91080i	−0.472602	+	0.663676i	0.507619	+	0.861581i	$0.330526\pi$
$224$	−1.74856	+	1.12373i	−0.116831	+	0.0750826i
$225$	−1.68978	−	0.430436i	−0.112652	−	0.0286957i
$226$	8.09269	−	12.5925i	0.538318	−	0.837639i
$227$	−15.4229	−	2.97252i	−1.02365	−	0.197293i	−0.350318	−	0.936631i	$-0.613926\pi$
$227$	−15.4229	−	2.97252i	−1.02365	−	0.197293i	−0.673335	+	0.739338i	$0.735139\pi$
$228$	6.23792	−	2.98627i	0.413116	−	0.197771i
$229$	−24.9441	−	14.4015i	−1.64835	−	0.951676i	−0.977727	−	0.209880i	$-0.932693\pi$
$229$	−24.9441	−	14.4015i	−1.64835	−	0.951676i	−0.670625	−	0.741797i	$-0.733974\pi$
$230$	−10.8975	+	3.10042i	−0.718562	+	0.204436i
$231$	−7.60466	+	6.83417i	−0.500350	+	0.449655i
$232$	−1.28203	−	5.28458i	−0.0841691	−	0.346950i
$233$	8.60125	+	7.45302i	0.563486	+	0.488264i	0.889396	−	0.457137i	$-0.151125\pi$
$233$	8.60125	+	7.45302i	0.563486	+	0.488264i	−0.325910	+	0.945401i	$0.605671\pi$
$234$	−12.7368	+	4.93096i	−0.832629	+	0.322347i
$235$	−12.1391	−	1.74534i	−0.791870	−	0.113854i
$236$	−3.21160	+	6.22963i	−0.209057	+	0.405514i
$237$	13.3403	−	9.86801i	0.866544	−	0.640996i
$238$	1.39620	−	0.269096i	0.0905022	−	0.0174429i
$239$	−2.94698	+	7.36120i	−0.190624	+	0.476156i	−0.992634	−	0.121155i	$-0.961340\pi$
$239$	−2.94698	+	7.36120i	−0.190624	+	0.476156i	0.802009	+	0.597311i	$0.203764\pi$
$240$	3.01204	+	2.76972i	0.194427	+	0.178785i
$241$	−3.15212	+	3.30585i	−0.203046	+	0.212948i	−0.817382	−	0.576096i	$-0.804575\pi$
$241$	−3.15212	+	3.30585i	−0.203046	+	0.212948i	0.614336	+	0.789044i	$0.289424\pi$
$242$	0.826707	+	2.81550i	0.0531427	+	0.180987i
$243$	6.54312	−	14.1488i	0.419742	−	0.907644i
$244$	1.73761	−	0.249831i	0.111239	−	0.0159938i
$245$	2.07061	−	5.98262i	0.132286	−	0.382216i
$246$	−1.44761	+	0.164701i	−0.0922961	+	0.0105009i
$247$	−18.1576	+	0.864955i	−1.15534	+	0.0550358i
$248$	4.83605	−	6.14954i	0.307090	−	0.390496i
$249$	27.8024	+	10.5511i	1.76191	+	0.668647i
$250$	−1.97562	+	10.2505i	−0.124949	+	0.648299i
$251$	7.79042	+	2.28747i	0.491727	+	0.144384i	0.518190	−	0.855266i	$-0.326606\pi$
$251$	7.79042	+	2.28747i	0.491727	+	0.144384i	−0.0264628	+	0.999650i	$0.508424\pi$
$252$	−3.67478	+	5.03769i	−0.231489	+	0.317345i
$253$	13.5988	+	0.762554i	0.854951	+	0.0479413i
$254$	0.462564	−	0.267061i	0.0290238	−	0.0167569i
$255$	−1.20871	−	2.52483i	−0.0756922	−	0.158111i
$256$	−0.327068	−	0.945001i	−0.0204417	−	0.0590626i
$257$	6.79093	+	13.1726i	0.423607	+	0.821683i	0.999990	+	0.00450302i	$0.00143336\pi$
$257$	6.79093	+	13.1726i	0.423607	+	0.821683i	−0.576383	+	0.817180i	$0.695536\pi$
$258$	−3.26681	+	2.18393i	−0.203382	+	0.135966i
$259$	8.48746	+	4.37559i	0.527385	+	0.271886i
$260$	−4.46799	−	9.78354i	−0.277093	−	0.606749i
$261$	−9.31039	−	13.3959i	−0.576298	−	0.829186i
$262$	2.44207	+	16.9849i	0.150871	+	1.04933i
$263$	11.2842	−	1.07751i	0.695812	−	0.0664420i	0.258844	−	0.965919i	$-0.416658\pi$
$263$	11.2842	−	1.07751i	0.695812	−	0.0664420i	0.436968	+	0.899477i	$0.356052\pi$
$264$	−2.33274	−	4.33073i	−0.143570	−	0.266538i
$265$	−6.57049	+	27.0839i	−0.403622	+	1.66375i
$266$	−6.76042	+	4.81407i	−0.414508	+	0.295170i
$267$	3.05102	+	0.530993i	0.186719	+	0.0324962i
$268$	−4.26183	−	1.47503i	−0.260333	−	0.0901020i
$269$	−7.03537	+	3.21294i	−0.428954	+	0.195897i	−0.618180	−	0.786037i	$-0.712130\pi$
$269$	−7.03537	+	3.21294i	−0.428954	+	0.195897i	0.189226	+	0.981934i	$0.439402\pi$
$270$	11.4265	+	4.48640i	0.695397	+	0.273033i
$271$	−2.64665	+	18.4078i	−0.160772	+	1.11820i	0.736410	+	0.676536i	$0.236520\pi$
$271$	−2.64665	+	18.4078i	−0.160772	+	1.11820i	−0.897182	+	0.441661i	$0.854389\pi$
$272$	−0.0325503	+	0.683315i	−0.00197365	+	0.0414321i
$273$	14.0436	−	8.45040i	0.849960	−	0.511441i
$274$	0.405625	+	0.425407i	0.0245047	+	0.0256998i
$275$	−0.825374	+	1.42959i	−0.0497719	+	0.0862075i
$276$	8.21026	−	1.26162i	0.494199	−	0.0759404i
$277$	−0.00423712	−	0.00733891i	−0.000254584	−	0.000440952i	0.865898	−	0.500220i	$-0.166748\pi$
$277$	−0.00423712	−	0.00733891i	−0.000254584	−	0.000440952i	−0.866153	+	0.499780i	$0.833414\pi$
$278$	−1.59291	+	5.42497i	−0.0955367	+	0.325368i
$279$	6.86908	−	22.4422i	0.411241	−	1.34358i
$280$	−4.13092	−	2.65478i	−0.246870	−	0.158654i
$281$	−1.12584	+	0.450719i	−0.0671621	+	0.0268877i	−0.405000	−	0.914317i	$-0.632729\pi$
$281$	−1.12584	+	0.450719i	−0.0671621	+	0.0268877i	0.337838	+	0.941204i	$0.390304\pi$
$282$	8.67156	+	2.37671i	0.516384	+	0.141531i
$283$	3.13489	−	32.8300i	0.186350	−	1.95154i	−0.103888	−	0.994589i	$-0.533128\pi$
$283$	3.13489	−	32.8300i	0.186350	−	1.95154i	0.290238	−	0.956955i	$-0.406266\pi$
$284$	−2.52798	−	13.1164i	−0.150008	−	0.778316i
$285$	12.5394	+	10.4744i	0.742767	+	0.620450i
$286$	1.22903	+	12.8710i	0.0726742	+	0.761079i
$287$	1.67757	−	0.492578i	0.0990235	−	0.0290759i
$288$	−1.93855	−	2.28954i	−0.114230	−	0.134913i
$289$	−6.86765	+	15.0381i	−0.403979	+	0.884591i
$290$	10.0983	−	7.94135i	0.592990	−	0.466332i
$291$	−4.97337	+	6.56514i	−0.291544	+	0.384855i
$292$	13.0026	+	1.24160i	0.760921	+	0.0726592i
$293$	−0.0396712	−	0.832802i	−0.00231762	−	0.0486528i	0.997412	−	0.0718942i	$-0.0229044\pi$
$293$	−0.0396712	−	0.832802i	−0.00231762	−	0.0486528i	−0.999730	+	0.0232414i	$0.992601\pi$
$294$	−2.05187	+	4.16328i	−0.119668	+	0.242808i
$295$	−16.5392	−	0.787859i	−0.962949	−	0.0458709i
$296$	−3.00850	+	3.47200i	−0.174866	+	0.201806i
$297$	−11.2168	−	9.58932i	−0.650866	−	0.556429i
$298$		−	8.95100i		−	0.518517i
$299$	−21.1742	−	5.32590i	−1.22454	−	0.308005i
$300$	−0.312015	+	0.957181i	−0.0180142	+	0.0552628i
$301$	3.41286	−	3.25416i	0.196714	−	0.187567i
$302$	−19.5201	+	6.75596i	−1.12325	+	0.388762i
$303$	4.97679	−	13.1140i	0.285909	−	0.753380i
$304$	−1.48401	−	3.70687i	−0.0851136	−	0.212604i
$305$	2.24218	+	3.48890i	0.128387	+	0.199774i
$306$	0.649031	+	1.94694i	0.0371027	+	0.111299i
$307$	−3.11013	−	3.58929i	−0.177505	−	0.204851i	0.660024	−	0.751244i	$-0.270546\pi$
$307$	−3.11013	−	3.58929i	−0.177505	−	0.204851i	−0.837529	+	0.546393i	$0.816001\pi$
$308$	3.64900	+	4.64008i	0.207921	+	0.264393i
$309$	−0.679477	−	2.16822i	−0.0386541	−	0.123346i
$310$	17.9613	+	4.35737i	1.02013	+	0.247482i
$311$	−14.3944	−	3.49204i	−0.816231	−	0.198015i	−0.194153	−	0.980971i	$-0.562196\pi$
$311$	−14.3944	−	3.49204i	−0.816231	−	0.198015i	−0.622077	+	0.782956i	$0.713711\pi$
$312$	2.35806	+	7.52459i	0.133499	+	0.425996i
$313$	−15.4023	−	19.5857i	−0.870592	−	1.10705i	−0.993410	−	0.114618i	$-0.963435\pi$
$313$	−15.4023	−	19.5857i	−0.870592	−	1.10705i	0.122818	−	0.992429i	$-0.460807\pi$
$314$	−14.6614	−	16.9201i	−0.827388	−	0.954857i
$315$	−14.4323	−	2.95299i	−0.813168	−	0.166382i
$316$	−5.17945	−	8.05938i	−0.291367	−	0.453375i
$317$	−10.5781	−	26.4228i	−0.594124	−	1.48405i	−0.854974	−	0.518672i	$-0.826427\pi$
$317$	−10.5781	−	26.4228i	−0.594124	−	1.48405i	0.260849	−	0.965380i	$-0.415998\pi$
$318$	7.24972	−	19.1033i	0.406544	−	1.07126i
$319$	−14.5942	+	5.05110i	−0.817118	+	0.282807i
$320$	1.70980	−	1.63029i	0.0955806	−	0.0911359i
$321$	1.04045	−	3.19183i	0.0580723	−	0.178151i
$322$	−9.44710	+	3.18090i	−0.526466	+	0.177264i
$323$			2.73149i			0.151984i
$324$	−7.90321	−	4.30573i	−0.439067	−	0.239207i
$325$	1.73291	−	1.99988i	0.0961243	−	0.110933i
$326$	−18.2347	−	0.868627i	−1.00993	−	0.0481088i
$327$	6.93675	−	14.0748i	0.383603	−	0.778337i
$328$	0.0400244	+	0.840216i	0.00220998	+	0.0463932i
$329$	−10.7411	−	1.02565i	−0.592176	−	0.0565459i
$330$	7.01727	−	9.26320i	0.386288	−	0.509922i
$331$	2.43662	−	1.91618i	0.133929	−	0.105323i	−0.548947	−	0.835857i	$-0.684971\pi$
$331$	2.43662	−	1.91618i	0.133929	−	0.105323i	0.682876	+	0.730534i	$0.260729\pi$
$332$	7.13216	−	15.6173i	0.391428	−	0.857109i
$333$	−4.65626	+	12.9720i	−0.255162	+	0.710860i
$334$	15.8129	−	4.64309i	0.865244	−	0.254058i
$335$	−1.01277	−	10.6062i	−0.0553333	−	0.579477i
$336$	2.76297	+	2.30797i	0.150733	+	0.125910i
$337$	3.31942	+	17.2228i	0.180820	+	0.938185i	0.953043	+	0.302834i	$0.0979326\pi$
$337$	3.31942	+	17.2228i	0.180820	+	0.938185i	−0.772223	+	0.635351i	$0.780855\pi$
$338$	0.734464	−	7.69165i	0.0399495	−	0.418371i
$339$	−25.0044	−	6.85323i	−1.35805	−	0.372216i
$340$	−1.50037	+	0.600658i	−0.0813691	+	0.0325753i
$341$	−18.6912	−	12.0121i	−1.01218	−	0.650492i
$342$	−8.16665	−	8.76324i	−0.441602	−	0.473862i
$343$	5.66834	−	19.3046i	0.306061	−	1.04235i
$344$	1.13437	+	1.96479i	0.0611612	+	0.105934i
$345$	10.7688	+	16.4055i	0.579771	+	0.883241i
$346$	1.43276	−	2.48162i	0.0770258	−	0.133413i
$347$	−2.77418	−	2.90947i	−0.148926	−	0.156189i	0.645045	−	0.764144i	$-0.276838\pi$
$347$	−2.77418	−	2.90947i	−0.148926	−	0.156189i	−0.793971	+	0.607955i	$0.791990\pi$
$348$	−8.07029	+	4.85609i	−0.432613	+	0.260314i
$349$	1.32661	−	27.8490i	0.0710118	−	1.49072i	−0.629456	−	0.777036i	$-0.716722\pi$
$349$	1.32661	−	27.8490i	0.0710118	−	1.49072i	0.700468	−	0.713684i	$-0.252975\pi$
$350$	0.171936	−	1.19584i	0.00919036	−	0.0639203i
$351$	14.7469	+	18.4972i	0.787132	+	0.987310i
$352$	−2.58336	+	1.17978i	−0.137694	+	0.0628825i
$353$	26.3013	+	9.10298i	1.39988	+	0.484503i	0.919684	−	0.392660i	$-0.128445\pi$
$353$	26.3013	+	9.10298i	1.39988	+	0.484503i	0.480194	+	0.877162i	$0.340566\pi$
$354$	11.9597	+	2.08145i	0.635653	+	0.110628i
$355$	25.7059	−	18.3051i	1.36433	−	0.971532i
$356$	0.421533	−	1.73758i	0.0223412	−	0.0920918i
$357$	−1.16793	−	2.16825i	−0.0618132	−	0.114756i
$358$	22.7871	−	2.17590i	1.20434	−	0.115000i
$359$	−3.78122	−	26.2990i	−0.199565	−	1.38801i	−0.805548	−	0.592530i	$-0.798129\pi$
$359$	−3.78122	−	26.2990i	−0.199565	−	1.38801i	0.605983	−	0.795478i	$-0.292780\pi$
$360$	3.01767	−	6.41287i	0.159045	−	0.337988i
$361$	1.26985	+	2.78059i	0.0668345	+	0.146347i
$362$	−2.95469	−	1.52325i	−0.155295	−	0.0800601i
$363$	4.22525	−	2.82467i	0.221768	−	0.148257i
$364$	−4.33610	−	8.41086i	−0.227273	−	0.440849i
$365$	10.0927	+	29.1608i	0.528274	+	1.52635i
$366$	−1.31292	−	2.74252i	−0.0686275	−	0.143354i
$367$	13.9729	−	8.06724i	0.729378	−	0.421107i	−0.0888164	−	0.996048i	$-0.528308\pi$
$367$	13.9729	−	8.06724i	0.729378	−	0.421107i	0.818195	+	0.574941i	$0.194975\pi$
$368$	−0.415676	−	4.77778i	−0.0216686	−	0.249059i
$369$	1.02201	+	2.30729i	0.0532037	+	0.120113i
$370$	−10.4138	−	3.05777i	−0.541387	−	0.158966i
$371$	−4.64042	+	24.0768i	−0.240919	+	1.25001i
$372$	−12.6688	−	4.80782i	−0.656845	−	0.249274i
$373$	−16.5850	+	21.0895i	−0.858737	+	1.09197i	0.136121	+	0.990692i	$0.456536\pi$
$373$	−16.5850	+	21.0895i	−0.858737	+	1.09197i	−0.994858	+	0.101281i	$0.967706\pi$
$374$	1.94062	−	0.0924431i	0.100347	−	0.00478012i
$375$	17.9652	−	2.04399i	0.927721	−	0.105551i
$376$	1.69786	−	4.90566i	0.0875607	−	0.252990i
$377$	24.5047	−	3.52325i	1.26206	−	0.181457i
$378$	10.2296	+	3.46436i	0.526155	+	0.178187i
$379$	6.74000	+	22.9543i	0.346211	+	1.17909i	0.930117	+	0.367264i	$0.119706\pi$
$379$	6.74000	+	22.9543i	0.346211	+	1.17909i	−0.583906	+	0.811821i	$0.698476\pi$
$380$	6.50956	−	6.82703i	0.333933	−	0.350219i
$381$	−0.680983	−	0.626197i	−0.0348878	−	0.0320810i
$382$	0.0244062	−	0.0609638i	0.00124873	−	0.00311918i
$383$	−21.5900	+	4.16114i	−1.10320	+	0.212624i	−0.708169	−	0.706043i	$-0.750478\pi$
$383$	−21.5900	+	4.16114i	−1.10320	+	0.212624i	−0.395031	+	0.918668i	$0.629266\pi$
$384$	−1.39248	+	1.03004i	−0.0710599	+	0.0525641i
$385$	−6.39028	+	12.3954i	−0.325679	+	0.631729i
$386$	−22.1448	−	3.18394i	−1.12714	−	0.162058i
$387$	5.30164	+	4.26818i	0.269498	+	0.216964i
$388$	3.59373	+	3.11399i	0.182444	+	0.158089i
$389$	0.152125	+	0.627066i	0.00771302	+	0.0317935i	0.975538	−	0.219831i	$-0.0705505\pi$
$389$	0.152125	+	0.627066i	0.00771302	+	0.0317935i	−0.967825	+	0.251624i	$0.919035\pi$
$390$	−13.8559	+	12.4521i	−0.701623	+	0.630535i
$391$	−0.950763	+	3.13999i	−0.0480822	+	0.158796i
$392$	2.32073	+	1.33987i	0.117214	+	0.0676738i
$393$	26.8077	−	12.8336i	1.35227	−	0.647372i
$394$	−1.59131	−	0.306700i	−0.0801692	−	0.0154513i
$395$	12.2363	−	19.0400i	0.615674	−	0.958007i
$396$	−5.94955	+	6.09865i	−0.298976	+	0.306469i
$397$	−25.3444	+	16.2879i	−1.27200	+	0.817464i	−0.989879	−	0.141915i	$-0.954674\pi$
$397$	−25.3444	+	16.2879i	−1.27200	+	0.817464i	−0.282120	+	0.959379i	$0.591038\pi$
$398$	13.8936	−	19.5108i	0.696424	−	0.977991i
$399$	11.4582	+	8.68011i	0.573630	+	0.434549i
$400$	0.539612	+	0.216028i	0.0269806	+	0.0108014i
$401$	4.04278	+	5.67728i	0.201887	+	0.283510i	0.903090	−	0.429451i	$-0.141293\pi$
$401$	4.04278	+	5.67728i	0.201887	+	0.283510i	−0.701204	+	0.712961i	$0.747354\pi$
$402$	−0.230496	+	7.80792i	−0.0114961	+	0.389424i
$403$	25.7771	+	24.5784i	1.28405	+	1.22434i
$404$	−7.36644	−	3.36414i	−0.366494	−	0.167372i
$405$	1.49667	−	21.2095i	0.0743699	−	1.05391i
$406$	8.54203	−	7.40171i	0.423934	−	0.367341i
$407$	10.6280	+	7.56818i	0.526811	+	0.375141i
$408$	1.14624	−	0.300126i	0.0567472	−	0.0148585i
$409$	−2.26082	−	1.77793i	−0.111790	−	0.0879128i	0.560699	−	0.828020i	$-0.310532\pi$
$409$	−2.26082	−	1.77793i	−0.111790	−	0.0879128i	−0.672489	+	0.740107i	$0.734775\pi$
$410$	−1.76632	+	0.910603i	−0.0872325	+	0.0449715i
$411$	0.493015	−	0.890755i	0.0243186	−	0.0439377i
$412$	−1.27487	+	0.309280i	−0.0628084	+	0.0152372i
$413$	−14.5679			−0.716837
$414$	−6.33772	−	12.9164i	−0.311482	−	0.634806i
$415$	40.5606			1.99104
$416$	4.42432	−	1.07333i	0.216920	−	0.0526242i
$417$	9.79141	−	0.177123i	0.479487	−	0.00867373i
$418$	−10.0792	+	5.19621i	−0.492992	+	0.254155i
$419$	12.9022	+	10.1464i	0.630312	+	0.495683i	0.881455	−	0.472267i	$-0.156564\pi$
$419$	12.9022	+	10.1464i	0.630312	+	0.495683i	−0.251144	+	0.967950i	$0.580807\pi$
$420$	−2.24818	+	8.20262i	−0.109700	+	0.400247i
$421$	−22.5145	−	16.0325i	−1.09729	−	0.781376i	−0.119892	−	0.992787i	$-0.538255\pi$
$421$	−22.5145	−	16.0325i	−1.09729	−	0.781376i	−0.977397	+	0.211411i	$0.932194\pi$
$422$	−6.82637	+	5.91509i	−0.332303	+	0.287942i
$423$	−0.563252	−	15.5633i	−0.0273863	−	0.756714i
$424$	−10.7307	−	4.90057i	−0.521131	−	0.237993i
$425$	−0.287775	−	0.274393i	−0.0139592	−	0.0133100i
$426$	−20.3693	+	10.9719i	−0.986897	+	0.531591i
$427$	2.11652	+	2.97223i	0.102425	+	0.143836i
$428$	−1.79940	−	0.720372i	−0.0869773	−	0.0348205i
$429$	20.6365	−	8.69792i	0.996341	−	0.419939i
$430$	−3.10901	+	4.36599i	−0.149930	+	0.210547i
$431$	−17.8508	+	11.4720i	−0.859843	+	0.552587i	−0.894630	−	0.446807i	$-0.852561\pi$
$431$	−17.8508	+	11.4720i	−0.859843	+	0.552587i	0.0347876	+	0.999395i	$0.488925\pi$
$432$	−2.78006	+	4.38990i	−0.133756	+	0.211209i
$433$	3.29567	−	5.12816i	0.158380	−	0.246443i	−0.752990	−	0.658031i	$-0.771389\pi$
$433$	3.29567	−	5.12816i	0.158380	−	0.246443i	0.911370	+	0.411588i	$0.135026\pi$
$434$	15.9671	+	3.07740i	0.766444	+	0.147720i
$435$	−18.3558	−	12.5771i	−0.880095	−	0.603024i
$436$	−7.84566	−	4.52970i	−0.375739	−	0.216933i
$437$	−2.56560	−	18.9766i	−0.122729	−	0.907773i
$438$	−4.68265	−	22.1337i	−0.223746	−	1.05759i
$439$	2.38370	+	9.82573i	0.113768	+	0.468956i	0.999984	+	0.00568457i	$0.00180946\pi$
$439$	2.38370	+	9.82573i	0.113768	+	0.468956i	−0.886216	+	0.463272i	$0.846675\pi$
$440$	−5.07064	−	4.39373i	−0.241733	−	0.209463i
$441$	7.94382	+	1.23494i	0.378277	+	0.0588065i
$442$	−3.08272	−	0.443229i	−0.146630	−	0.0210822i
$443$	−13.3526	+	25.9004i	−0.634401	+	1.23057i	0.324247	+	0.945973i	$0.394889\pi$
$443$	−13.3526	+	25.9004i	−0.634401	+	1.23057i	−0.958648	+	0.284594i	$0.908141\pi$
$444$	7.29676	+	3.17410i	0.346289	+	0.150636i
$445$	4.14772	−	0.799408i	0.196621	−	0.0378956i
$446$	4.52195	−	11.2953i	0.214121	−	0.534847i
$447$	−14.7941	+	4.63620i	−0.699739	+	0.219285i
$448$	1.43434	−	1.50430i	0.0677664	−	0.0710714i
$449$	8.92154	+	30.3840i	0.421034	+	1.43391i	0.848171	+	0.529722i	$0.177704\pi$
$449$	8.92154	+	30.3840i	0.421034	+	1.43391i	−0.427137	+	0.904187i	$0.640478\pi$
$450$	1.74363	+	0.0199212i	0.0821955	+	0.000939095i
$451$	2.36461	−	0.339979i	0.111345	−	0.0160090i
$452$	−4.89578	+	14.1454i	−0.230278	+	0.665345i
$453$	21.2767	+	28.7634i	0.999666	+	1.35142i
$454$	15.6889	−	0.747356i	0.736318	−	0.0350752i
$455$	13.8193	−	17.5726i	0.647857	−	0.823817i
$456$	−5.35804	+	4.37274i	−0.250913	+	0.204772i
$457$	−0.0885208	+	0.459290i	−0.00414083	+	0.0214847i	−0.983940	−	0.178498i	$-0.942876\pi$
$457$	−0.0885208	+	0.459290i	−0.00414083	+	0.0214847i	0.979800	+	0.199982i	$0.0640884\pi$
$458$	27.6362	+	8.11473i	1.29136	+	0.379176i
$459$	2.88172	−	2.08114i	0.134507	−	0.0971392i
$460$	9.85939	−	5.58221i	0.459696	−	0.260272i
$461$	−18.5042	+	10.6834i	−0.861826	+	0.497575i	−0.864623	−	0.502421i	$-0.832443\pi$
$461$	−18.5042	+	10.6834i	−0.861826	+	0.497575i	0.00279761	+	0.999996i	$0.499109\pi$
$462$	5.77908	−	8.43439i	0.268867	−	0.392403i
$463$	−7.83622	−	22.6413i	−0.364180	−	1.05223i	−0.967093	−	0.254423i	$-0.918115\pi$
$463$	−7.83622	−	22.6413i	−0.364180	−	1.05223i	0.602913	−	0.797807i	$-0.294007\pi$
$464$	2.49178	+	4.83337i	0.115678	+	0.224384i
$465$	−2.10130	−	31.9433i	−0.0974453	−	1.48133i
$466$	−10.1159	−	5.21511i	−0.468610	−	0.241585i
$467$	7.09374	+	15.5331i	0.328259	+	0.718787i	0.999753	−	0.0222230i	$-0.00707438\pi$
$467$	7.09374	+	15.5331i	0.328259	+	0.718787i	−0.671494	+	0.741010i	$0.734347\pi$
$468$	11.2152	−	7.79477i	0.518424	−	0.360313i
$469$	−1.33404	−	9.27845i	−0.0616002	−	0.428439i
$470$	12.2084	−	1.16576i	0.563133	−	0.0537727i
$471$	−20.3715	+	32.9960i	−0.938671	+	1.52038i
$472$	1.65238	−	6.81119i	0.0760568	−	0.313510i
$473$	5.24851	−	3.73745i	0.241327	−	0.171848i
$474$	−10.6378	+	12.7349i	−0.488609	+	0.584935i
$475$	2.19321	+	0.759079i	0.100632	+	0.0348289i
$476$	−1.29340	+	0.590677i	−0.0592830	+	0.0270736i
$477$	−35.3288	−	2.08769i	−1.61759	−	0.0955887i
$478$	1.12844	−	7.84847i	0.0516136	−	0.358981i
$479$	−1.39175	+	29.2163i	−0.0635905	+	1.33493i	0.711325	+	0.702863i	$0.248095\pi$
$479$	−1.39175	+	29.2163i	−0.0635905	+	1.33493i	−0.774916	+	0.632065i	$0.782208\pi$
$480$	−3.58012	−	1.98153i	−0.163410	−	0.0904440i
$481$	−14.4333	−	15.1372i	−0.658101	−	0.690196i
$482$	2.28388	−	3.95580i	0.104028	−	0.180182i
$483$	10.1505	+	13.9665i	0.461865	+	0.635500i
$484$	−1.46718	−	2.54124i	−0.0666901	−	0.115511i
$485$	−3.16498	+	10.7789i	−0.143714	+	0.489445i
$486$	−3.02299	+	15.2925i	−0.137125	+	0.693683i
$487$	−29.6892	−	19.0801i	−1.34534	−	0.864600i	−0.348005	−	0.937493i	$-0.613141\pi$
$487$	−29.6892	−	19.0801i	−1.34534	−	0.864600i	−0.997340	+	0.0728925i	$0.976777\pi$
$488$	−1.62973	+	0.652447i	−0.0737746	+	0.0295349i
$489$	8.00907	+	30.5881i	0.362183	+	1.38324i
$490$	−0.601782	+	6.30214i	−0.0271857	+	0.284702i
$491$	0.479339	+	2.48705i	0.0216323	+	0.112239i	0.991140	−	0.132822i	$-0.0424040\pi$
$491$	0.479339	+	2.48705i	0.0216323	+	0.112239i	−0.969508	+	0.245061i	$0.921192\pi$
$492$	1.36797	−	0.501345i	0.0616729	−	0.0226024i
$493$	−0.353608	−	3.70315i	−0.0159257	−	0.166781i
$494$	17.4419	−	5.12140i	0.784748	−	0.230423i
$495$	−18.9448	−	6.80018i	−0.851504	−	0.305646i
$496$	−3.24992	+	7.11634i	−0.145926	+	0.319533i
$497$	21.8244	−	17.1629i	0.978956	−	0.769860i
$498$	−29.5062	−	3.69898i	−1.32221	−	0.165755i
$499$	42.0221	+	4.01262i	1.88117	+	0.179630i	0.971711	−	0.236172i	$-0.0758929\pi$
$499$	42.0221	+	4.01262i	1.88117	+	0.179630i	0.909455	+	0.415802i	$0.136499\pi$
$500$	−0.496715	−	10.4273i	−0.0222138	−	0.466324i
$501$	−15.8644	−	23.7306i	−0.708769	−	1.06020i
$502$	−8.11011	−	0.386332i	−0.361972	−	0.0172428i
$503$	−2.74264	+	3.16517i	−0.122288	+	0.141128i	−0.813592	−	0.581436i	$-0.802491\pi$
$503$	−2.74264	+	3.16517i	−0.122288	+	0.141128i	0.691304	+	0.722564i	$0.257037\pi$
$504$	2.38351	−	5.76205i	0.106170	−	0.256662i
$505$		−	19.1319i		−	0.851357i
$506$	−13.3953	+	2.46499i	−0.595493	+	0.109582i
$507$	−13.0931	+	2.77000i	−0.581486	+	0.123020i
$508$	−0.386563	+	0.368587i	−0.0171509	+	0.0163534i
$509$	0.723911	−	0.250548i	0.0320868	−	0.0111053i	−0.310977	−	0.950417i	$-0.600656\pi$
$509$	0.723911	−	0.250548i	0.0320868	−	0.0111053i	0.343064	+	0.939312i	$0.388535\pi$
$510$	1.76989	+	2.16869i	0.0783719	+	0.0960313i
$511$	10.0903	+	25.2044i	0.446370	+	1.11498i
$512$	0.540641	+	0.841254i	0.0238932	+	0.0371785i
$513$	−10.2539	+	18.0367i	−0.452720	+	0.796341i
$514$	−9.70506	−	11.2002i	−0.428072	−	0.494021i
$515$	−1.91580	−	2.43614i	−0.0844202	−	0.107349i
$516$	2.65984	−	2.89255i	0.117093	−	0.127337i
$517$	−14.3274	−	3.47578i	−0.630117	−	0.152865i
$518$	−9.27979	−	2.25125i	−0.407731	−	0.0989144i
$519$	−4.84370	−	1.08270i	−0.212615	−	0.0475252i
$520$	6.64860	+	8.45438i	0.291560	+	0.370749i
$521$	16.5763	+	19.1301i	0.726221	+	0.838103i	0.992040	−	0.125919i	$-0.0401881\pi$
$521$	16.5763	+	19.1301i	0.726221	+	0.838103i	−0.265820	+	0.964023i	$0.585643\pi$
$522$	12.2061	+	10.8233i	0.534249	+	0.473723i
$523$	15.6781	+	24.3957i	0.685558	+	1.06675i	0.993332	+	0.115289i	$0.0367794\pi$
$523$	15.6781	+	24.3957i	0.685558	+	1.06675i	−0.307774	+	0.951459i	$0.599584\pi$
$524$	−6.37758	−	15.9304i	−0.278606	−	0.695924i
$525$	−2.06553	+	0.335215i	−0.0901471	+	0.0146300i
$526$	−10.7121	+	3.70748i	−0.467068	+	0.161654i
$527$	3.87332	−	3.69320i	0.168724	−	0.160878i
$528$	3.28799	+	3.65869i	0.143092	+	0.159224i
$529$	3.65597	−	22.7076i	0.158955	−	0.987286i
$530$		−	27.8695i		−	1.21058i
$531$	−2.75439	−	20.8451i	−0.119530	−	0.904599i
$532$	5.43489	−	6.27220i	0.235632	−	0.271934i
$533$	−3.82521	−	0.182217i	−0.165688	−	0.00789270i
$534$	−3.09020	+	0.203280i	−0.133726	+	0.00879679i
$535$	−0.217879	−	4.57384i	−0.00941973	−	0.197745i
$536$	4.48945	+	0.428690i	0.193915	+	0.0185166i
$537$	−15.3990	−	36.5353i	−0.664515	−	1.57662i
$538$	6.07957	−	4.78103i	0.262109	−	0.206125i
$539$	3.16151	−	6.92275i	0.136176	−	0.298184i
$540$	−12.1622	−	1.66602i	−0.523376	−	0.0716941i
$541$	−38.8086	+	11.3952i	−1.66851	+	0.489920i	−0.973425	−	0.229005i	$-0.926453\pi$
$541$	−38.8086	+	11.3952i	−1.66851	+	0.489920i	−0.695088	+	0.718925i	$0.744635\pi$
$542$	−1.76777	−	18.5129i	−0.0759322	−	0.795198i
$543$	−0.987222	+	5.67246i	−0.0423658	+	0.243429i
$544$	−0.129465	−	0.671727i	−0.00555076	−	0.0288001i
$545$	2.03444	−	21.3056i	0.0871458	−	0.912632i
$546$	−11.6555	+	11.5231i	−0.498810	+	0.493143i
$547$	4.50044	−	1.80170i	0.192425	−	0.0770353i	−0.273449	−	0.961887i	$-0.588164\pi$
$547$	4.50044	−	1.80170i	0.192425	−	0.0770353i	0.465874	+	0.884851i	$0.345740\pi$
$548$	−0.494484	−	0.317786i	−0.0211233	−	0.0135751i
$549$	−3.85278	+	3.59048i	−0.164433	+	0.153238i
$550$	0.465069	−	1.58388i	0.0198306	−	0.0675369i
$551$	10.8564	+	18.8038i	0.462498	+	0.801071i
$552$	−7.68139	+	3.16170i	−0.326941	+	0.134571i
$553$	9.95633	−	17.2449i	0.423386	−	0.733326i
$554$	0.00584789	+	0.00613309i	0.000248453	+	0.000260570i
$555$	0.340005	+	18.7956i	0.0144324	+	0.797830i
$556$	0.269028	−	5.64759i	0.0114093	−	0.239511i
$557$	−6.50425	+	45.2381i	−0.275594	+	1.91680i	0.109625	+	0.993973i	$0.465035\pi$
$557$	−6.50425	+	45.2381i	−0.275594	+	1.91680i	−0.385219	+	0.922825i	$0.625874\pi$
$558$	−1.38450	+	23.4291i	−0.0586105	+	0.991832i
$559$	−9.39540	+	4.29074i	−0.397383	+	0.181479i
$560$	4.64037	+	1.60605i	0.196091	+	0.0678679i
$561$	−1.15794	−	3.15956i	−0.0488882	−	0.133397i
$562$	0.987846	−	0.703442i	0.0416698	−	0.0296729i
$563$	6.17133	−	25.4386i	0.260090	−	1.07211i	−0.680550	−	0.732702i	$-0.738259\pi$
$563$	6.17133	−	25.4386i	0.260090	−	1.07211i	0.940640	−	0.339405i	$-0.110226\pi$
$564$	−8.98745	−	0.265317i	−0.378440	−	0.0111719i
$565$	−35.2029	+	3.36147i	−1.48100	+	0.141418i
$566$	4.69345	+	32.6437i	0.197281	+	1.37212i
$567$	0.427397	−	18.7018i	0.0179490	−	0.785402i
$568$	5.54903	+	12.1507i	0.232832	+	0.509831i
$569$	−2.64500	−	1.36359i	−0.110884	−	0.0571648i	0.401892	−	0.915687i	$-0.368353\pi$
$569$	−2.64500	−	1.36359i	−0.110884	−	0.0571648i	−0.512776	+	0.858522i	$0.671383\pi$
$570$	−14.6553	−	7.22287i	−0.613844	−	0.302533i
$571$	−10.8541	−	21.0540i	−0.454229	−	0.881081i	−0.999094	−	0.0425573i	$-0.986449\pi$
$571$	−10.8541	−	21.0540i	−0.454229	−	0.881081i	0.544865	−	0.838524i	$-0.316581\pi$
$572$	−4.22884	−	12.2184i	−0.176817	−	0.510879i
$573$	−0.113402	−	0.00876203i	−0.00473743	−	0.000366039i
$574$	−1.51415	+	0.874194i	−0.0631993	+	0.0364881i
$575$	2.25700	+	1.63600i	0.0941233	+	0.0682260i
$576$	2.42369	+	1.76798i	0.100987	+	0.0736656i
$577$	−9.75263	−	2.86363i	−0.406007	−	0.119214i	0.0723511	−	0.997379i	$-0.476950\pi$
$577$	−9.75263	−	2.86363i	−0.406007	−	0.119214i	−0.478358	+	0.878165i	$0.658768\pi$
$578$	3.12871	−	16.2333i	0.130137	−	0.675215i
$579$	6.20758	+	38.2499i	0.257978	+	1.58961i
$580$	−7.94135	+	10.0983i	−0.329747	+	0.419307i
$581$	35.6452	−	1.69799i	1.47881	−	0.0704446i
$582$	3.28539	−	7.55259i	0.136184	−	0.313065i
$583$	−10.9578	+	31.6603i	−0.453824	+	1.31124i
$584$	−12.9288	+	1.85888i	−0.534999	+	0.0769212i
$585$	27.7574	+	16.4514i	1.14763	+	0.680182i
$586$	0.234893	+	0.799973i	0.00970336	+	0.0330466i
$587$	4.58088	−	4.80429i	0.189073	−	0.198294i	−0.622374	−	0.782720i	$-0.713832\pi$
$587$	4.58088	−	4.80429i	0.189073	−	0.198294i	0.811447	+	0.584426i	$0.198680\pi$
$588$	1.01250	−	4.52968i	0.0417550	−	0.186801i
$589$	−11.6099	+	29.0000i	−0.478376	+	1.19492i
$590$	16.2587	−	3.13361i	0.669361	−	0.129009i
$591$	0.317313	+	2.78897i	0.0130525	+	0.114723i
$592$	2.10514	−	4.08341i	0.0865209	−	0.167827i
$593$	−12.8709	−	1.85055i	−0.528544	−	0.0759932i	−0.127123	−	0.991887i	$-0.540574\pi$
$593$	−12.8709	−	1.85055i	−0.528544	−	0.0759932i	−0.401421	+	0.915894i	$0.631483\pi$
$594$	13.1614	+	6.67455i	0.540019	+	0.273860i
$595$	−2.53870	−	2.19980i	−0.104077	−	0.0901828i
$596$	2.11028	+	8.69868i	0.0864403	+	0.356312i
$597$	−39.4436	−	12.8576i	−1.61432	−	0.526225i
$598$	21.8330	+	0.183760i	0.892817	+	0.00751449i
$599$	5.30136	+	3.06074i	0.216608	+	0.125058i	0.604378	−	0.796697i	$-0.293422\pi$
$599$	5.30136	+	3.06074i	0.216608	+	0.125058i	−0.387771	+	0.921756i	$0.626755\pi$
$600$	0.0775558	−	1.00376i	0.00316620	−	0.0409783i
$601$	19.0814	+	3.67764i	0.778347	+	0.150014i	0.562926	−	0.826507i	$-0.309675\pi$
$601$	19.0814	+	3.67764i	0.778347	+	0.150014i	0.215421	+	0.976521i	$0.430888\pi$
$602$	−2.54946	+	3.96704i	−0.103908	+	0.161685i
$603$	13.0243	−	3.66318i	0.530389	−	0.149176i
$604$	17.3770	−	11.1676i	0.707062	−	0.454401i
$605$	4.02115	−	5.64692i	0.163483	−	0.229580i
$606$	−1.74476	+	13.9177i	−0.0708758	+	0.565367i
$607$	−6.38994	−	2.55815i	−0.259360	−	0.103832i	0.238339	−	0.971182i	$-0.423397\pi$
$607$	−6.38994	−	2.55815i	−0.259360	−	0.103832i	−0.497698	+	0.867350i	$0.665821\pi$
$608$	2.31610	+	3.25251i	0.0939304	+	0.131907i
$609$	−16.6579	−	10.2845i	−0.675011	−	0.416748i
$610$	−3.00152	−	2.86194i	−0.121528	−	0.115877i
$611$	21.4979	+	9.81774i	0.869710	+	0.397183i
$612$	−1.08974	−	1.73904i	−0.0440503	−	0.0702966i
$613$	35.3500	−	30.6309i	1.42777	−	1.23717i	0.498956	−	0.866627i	$-0.333717\pi$
$613$	35.3500	−	30.6309i	1.42777	−	1.23717i	0.928815	−	0.370543i	$-0.120829\pi$
$614$	3.86867	+	2.75487i	0.156127	+	0.111177i
$615$	2.41991	+	2.44772i	0.0975802	+	0.0987014i
$616$	−4.64008	−	3.64900i	−0.186954	−	0.147022i
$617$	−32.5686	+	16.7903i	−1.31116	+	0.675952i	−0.965007	−	0.262225i	$-0.915544\pi$
$617$	−32.5686	+	16.7903i	−1.31116	+	0.675952i	−0.346157	+	0.938177i	$0.612513\pi$
$618$	1.17150	+	1.94691i	0.0471246	+	0.0783160i
$619$	−14.8846	+	3.61095i	−0.598261	+	0.145137i	−0.523443	−	0.852061i	$-0.675353\pi$
$619$	−14.8846	+	3.61095i	−0.598261	+	0.145137i	−0.0748179	+	0.997197i	$0.523838\pi$
$620$	−18.4823			−0.742268
$621$	−18.0655	+	17.1650i	−0.724943	+	0.688809i
$622$	14.8119			0.593903
$623$	3.61161	−	0.876167i	0.144696	−	0.0351029i
$624$	−4.06558	−	6.75655i	−0.162753	−	0.270478i
$625$	24.5038	−	12.6326i	0.980151	−	0.505303i
$626$	19.5857	+	15.4023i	0.782801	+	0.615601i
$627$	13.8088	+	13.9675i	0.551472	+	0.557808i
$628$	18.2371	+	12.9866i	0.727741	+	0.518222i
$629$	−2.37516	+	2.05809i	−0.0947038	+	0.0820613i
$630$	14.7217	−	0.532793i	0.586526	−	0.0212270i
$631$	16.2477	+	7.42007i	0.646810	+	0.295388i	0.711678	−	0.702505i	$-0.247935\pi$
$631$	16.2477	+	7.42007i	0.646810	+	0.295388i	−0.0648680	+	0.997894i	$0.520663\pi$
$632$	6.93352	+	6.61110i	0.275800	+	0.262975i
$633$	13.3122	+	8.21884i	0.529111	+	0.326670i
$634$	16.5093	+	23.1841i	0.655669	+	0.920758i
$635$	−1.17146	−	0.468981i	−0.0464879	−	0.0186109i
$636$	−2.54160	+	20.2740i	−0.100781	+	0.803915i
$637$	−7.07667	+	9.93779i	−0.280388	+	0.393749i
$638$	12.9920	−	8.34943i	0.514357	−	0.330557i
$639$	28.6847	+	27.9833i	1.13475	+	1.10700i
$640$	−1.27725	+	1.98743i	−0.0504876	+	0.0785602i
$641$	23.5849	+	4.54561i	0.931546	+	0.179541i	0.632378	−	0.774660i	$-0.282079\pi$
$641$	23.5849	+	4.54561i	0.931546	+	0.179541i	0.299168	+	0.954201i	$0.403291\pi$
$642$	−0.258619	+	3.34716i	−0.0102069	+	0.132102i
$643$	−10.5902	−	6.11427i	−0.417638	−	0.241123i	0.276428	−	0.961035i	$-0.410849\pi$
$643$	−10.5902	−	6.11427i	−0.417638	−	0.241123i	−0.694066	+	0.719911i	$0.744182\pi$
$644$	8.43088	−	5.31847i	0.332223	−	0.209577i
$645$	8.82639	+	2.87717i	0.347539	+	0.113288i
$646$	−0.643974	−	2.65450i	−0.0253368	−	0.104440i
$647$	30.2927	+	26.2488i	1.19093	+	1.03195i	0.998719	+	0.0505910i	$0.0161105\pi$
$647$	30.2927	+	26.2488i	1.19093	+	1.03195i	0.192209	+	0.981354i	$0.438435\pi$
$648$	8.69554	+	2.32111i	0.341593	+	0.0911817i
$649$	−19.7023	−	2.83276i	−0.773383	−	0.111196i
$650$	−1.21257	+	2.35205i	−0.0475608	+	0.0922551i
$651$	−3.18389	−	27.9842i	−0.124787	−	1.09679i
$652$	17.9255	−	3.45486i	0.702017	−	0.135303i
$653$	11.7401	−	29.3255i	0.459428	−	1.14759i	−0.500097	−	0.865969i	$-0.666702\pi$
$653$	11.7401	−	29.3255i	0.459428	−	1.14759i	0.959525	−	0.281625i	$-0.0908735\pi$
$654$	−3.42296	+	15.3134i	−0.133848	+	0.598803i
$655$	27.9751	−	29.3395i	1.09308	−	1.14639i
$656$	−0.236985	−	0.807095i	−0.00925269	−	0.0315118i
$657$	−34.1571	+	19.2037i	−1.33260	+	0.749207i
$658$	10.6801	−	1.53557i	0.416355	−	0.0598628i
$659$	6.94442	−	20.0646i	0.270516	−	0.781606i	−0.725149	−	0.688592i	$-0.758229\pi$
$659$	6.94442	−	20.0646i	0.270516	−	0.781606i	0.995665	−	0.0930131i	$-0.0296499\pi$
$660$	−4.63558	+	10.6565i	−0.180440	+	0.414802i
$661$	−18.0886	+	0.861667i	−0.703566	+	0.0335150i	−0.396316	−	0.918114i	$-0.629712\pi$
$661$	−18.0886	+	0.861667i	−0.703566	+	0.0335150i	−0.307250	+	0.951629i	$0.599409\pi$
$662$	−1.91618	+	2.43662i	−0.0744743	+	0.0947018i
$663$	0.864141	+	5.32467i	0.0335605	+	0.206793i
$664$	−3.24921	+	16.8585i	−0.126094	+	0.654237i
$665$	18.8126	+	5.52388i	0.729522	+	0.214207i
$666$	1.46675	−	13.7041i	0.0568354	−	0.531022i
$667$	5.93486	+	25.3948i	0.229799	+	0.983291i
$668$	−14.2725	+	8.24024i	−0.552220	+	0.318824i
$669$	−21.0109	−	1.62342i	−0.812329	−	0.0627649i
$670$	3.48472	+	10.0684i	0.134626	+	0.388977i
$671$	2.28453	+	4.43136i	0.0881931	+	0.171071i
$672$	−3.22921	−	1.59152i	−0.124570	−	0.0613942i
$673$	8.82607	+	4.55016i	0.340220	+	0.175396i	0.619866	−	0.784708i	$-0.287187\pi$
$673$	8.82607	+	4.55016i	0.340220	+	0.175396i	−0.279646	+	0.960103i	$0.590217\pi$
$674$	−7.28628	−	15.9547i	−0.280657	−	0.614553i
$675$	−0.870193	−	2.89218i	−0.0334938	−	0.111320i
$676$	1.09962	+	7.64799i	0.0422929	+	0.294153i
$677$	−25.4511	+	2.43029i	−0.978167	+	0.0934036i	−0.571876	−	0.820340i	$-0.693784\pi$
$677$	−25.4511	+	2.43029i	−0.978167	+	0.0934036i	−0.406291	+	0.913744i	$0.633178\pi$
$678$	25.9153	+	0.765040i	0.995269	+	0.0293812i
$679$	−2.33019	+	9.60516i	−0.0894243	+	0.368612i
$680$	1.31647	−	0.937453i	0.0504842	−	0.0359497i
$681$	−9.36136	−	25.5435i	−0.358728	−	0.978827i
$682$	20.9963	+	7.26688i	0.803989	+	0.278263i
$683$	−34.7847	+	15.8857i	−1.33100	+	0.607848i	−0.948696	−	0.316189i	$-0.897597\pi$
$683$	−34.7847	+	15.8857i	−1.33100	+	0.607848i	−0.382304	+	0.924036i	$0.624869\pi$
$684$	10.0025	+	6.59086i	0.382453	+	0.252008i
$685$	0.197625	−	1.37451i	0.00755086	−	0.0525174i
$686$	−0.957327	+	20.0968i	−0.0365509	+	0.767299i
$687$	−0.902309	−	49.8800i	−0.0344253	−	1.90304i
$688$	−1.56561	−	1.64197i	−0.0596884	−	0.0625994i
$689$	26.8534	−	46.5114i	1.02303	−	1.77194i
$690$	−14.3329	−	13.4042i	−0.545646	−	0.510289i
$691$	−3.73556	−	6.47018i	−0.142107	−	0.246137i	0.786183	−	0.617994i	$-0.212055\pi$
$691$	−3.73556	−	6.47018i	−0.142107	−	0.246137i	−0.928290	+	0.371857i	$0.878721\pi$
$692$	−0.807312	+	2.74945i	−0.0306894	+	0.104518i
$693$	−16.9336	−	5.18301i	−0.643254	−	0.196886i
$694$	3.38191	+	2.17342i	0.128376	+	0.0825020i
$695$	12.4006	−	4.96444i	0.470380	−	0.188312i
$696$	6.69794	−	6.62185i	0.253885	−	0.251001i
$697$	−0.0546986	+	0.572829i	−0.00207186	+	0.0216975i
$698$	5.27643	+	27.3767i	0.199716	+	1.03622i
$699$	−3.37993	+	19.4207i	−0.127841	+	0.734558i
$700$	0.114841	+	1.20267i	0.00434057	+	0.0454565i
$701$	−28.0108	+	8.22473i	−1.05796	+	0.310644i	−0.764027	−	0.645184i	$-0.776781\pi$
$701$	−28.0108	+	8.22473i	−1.05796	+	0.310644i	−0.293928	+	0.955828i	$0.594963\pi$
$702$	−18.6921	−	14.4991i	−0.705488	−	0.547234i
$703$	7.62028	−	16.6861i	0.287404	−	0.629328i
$704$	2.23240	−	1.75558i	0.0841366	−	0.0661657i
$705$	−8.25016	−	19.5742i	−0.310719	−	0.737207i
$706$	−27.7060	−	2.64561i	−1.04273	−	0.0995687i
$707$	−0.800919	−	16.8134i	−0.0301216	−	0.632331i
$708$	−12.1133	+	0.796842i	−0.455247	+	0.0299471i
$709$	−43.7626	−	2.08467i	−1.64354	−	0.0782915i	−0.794721	−	0.606975i	$-0.792383\pi$
$709$	−43.7626	−	2.08467i	−1.64354	−	0.0782915i	−0.848819	+	0.528683i	$0.822686\pi$
$710$	−20.6657	+	23.8495i	−0.775569	+	0.895054i
$711$	26.5581	+	10.9859i	0.996006	+	0.412005i
$712$			1.78799i			0.0670076i
$713$	−23.4403	+	29.2959i	−0.877846	+	1.09714i
$714$	1.64619	+	1.83178i	0.0616070	+	0.0685527i
$715$	22.1069	−	21.0789i	0.826752	−	0.788307i
$716$	−21.6318	+	7.48683i	−0.808417	+	0.279796i
$717$	−13.5564	+	2.20006i	−0.506272	+	0.0821629i
$718$	9.87486	+	24.6662i	0.368527	+	0.920535i
$719$	−21.3327	−	33.1944i	−0.795577	−	1.23794i	−0.967510	−	0.252833i	$-0.918638\pi$
$719$	−21.3327	−	33.1944i	−0.795577	−	1.23794i	0.171933	−	0.985109i	$-0.444999\pi$
$720$	−1.42072	+	6.94354i	−0.0529470	+	0.258771i
$721$	−1.78561	−	2.06071i	−0.0664998	−	0.0767448i
$722$	−1.88961	−	2.40283i	−0.0703240	−	0.0894242i
$723$	−7.72106	−	1.72586i	−0.287149	−	0.0641856i
$724$	3.23052	+	0.783716i	0.120061	+	0.0291266i
$725$	−3.07165	−	0.745175i	−0.114078	−	0.0276751i
$726$	−3.44020	+	3.74119i	−0.127678	+	0.138849i
$727$	−8.58007	−	10.9104i	−0.318217	−	0.404646i	0.600460	−	0.799655i	$-0.294984\pi$
$727$	−8.58007	−	10.9104i	−0.318217	−	0.404646i	−0.918677	+	0.395009i	$0.870742\pi$
$728$	6.19681	+	7.15150i	0.229669	+	0.265052i
$729$	26.8412	−	2.92445i	0.994117	−	0.108313i
$730$	−16.6831	−	25.9594i	−0.617469	−	0.960801i
$731$	0.576829	+	1.44085i	0.0213348	+	0.0532917i
$732$	1.92249	+	2.35567i	0.0710571	+	0.0870683i
$733$	−38.2306	+	13.2317i	−1.41208	+	0.488725i	−0.923434	−	0.383757i	$-0.874630\pi$
$733$	−38.2306	+	13.2317i	−1.41208	+	0.488725i	−0.488645	+	0.872483i	$0.662509\pi$
$734$	−11.6771	+	11.1341i	−0.431009	+	0.410966i
$735$	10.7278	−	2.26960i	0.395702	−	0.0837153i
$736$	1.53036	+	4.54511i	0.0564100	+	0.167535i
$737$		−	12.8081i		−	0.471791i
$738$	−1.53716	−	2.00130i	−0.0565838	−	0.0736689i
$739$	19.3359	−	22.3148i	0.711283	−	0.820864i	−0.278947	−	0.960306i	$-0.589986\pi$
$739$	19.3359	−	22.3148i	0.711283	−	0.820864i	0.990230	+	0.139442i	$0.0445310\pi$
$740$	10.8411	+	0.516427i	0.398528	+	0.0189842i
$741$	−17.4987	−	26.1752i	−0.642831	−	0.961569i
$742$	−1.16670	−	24.4921i	−0.0428311	−	0.899134i
$743$	2.75011	+	0.262604i	0.100892	+	0.00963400i	0.145380	−	0.989376i	$-0.453560\pi$
$743$	2.75011	+	0.262604i	0.100892	+	0.00963400i	−0.0444880	+	0.999010i	$0.514166\pi$
$744$	13.4451	+	1.68552i	0.492923	+	0.0617941i
$745$	−16.6222	+	13.0719i	−0.608991	+	0.478916i
$746$	11.1454	−	24.4051i	0.408063	−	0.893533i
$747$	9.16920	+	50.6836i	0.335484	+	1.85442i
$748$	−1.86412	+	0.547355i	−0.0681590	+	0.0200133i
$749$	−0.382950	−	4.01043i	−0.0139927	−	0.146538i
$750$	−16.9769	+	6.22184i	−0.619910	+	0.227189i
$751$	3.00402	+	15.5863i	0.109618	+	0.568753i	0.994657	+	0.103236i	$0.0329196\pi$
$751$	3.00402	+	15.5863i	0.109618	+	0.568753i	−0.885039	+	0.465517i	$0.845868\pi$
$752$	−0.493452	+	5.16766i	−0.0179943	+	0.188445i
$753$	3.56213	+	13.6044i	0.129811	+	0.495773i
$754$	−22.9833	+	9.20114i	−0.837004	+	0.335086i
$755$	41.0527	+	26.3830i	1.49406	+	0.960174i
$756$	−10.7580	−	0.954977i	−0.391265	−	0.0347322i
$757$	3.65567	−	12.4501i	0.132868	−	0.452505i	−0.866002	−	0.500040i	$-0.833318\pi$
$757$	3.65567	−	12.4501i	0.132868	−	0.452505i	0.998870	+	0.0475353i	$0.0151367\pi$
$758$	−11.9617	−	20.7183i	−0.434469	−	0.752522i
$759$	11.0122	+	20.8629i	0.399719	+	0.757274i
$760$	−4.71653	+	8.16928i	−0.171087	+	0.296331i
$761$	−15.7162	−	16.4827i	−0.569712	−	0.597497i	0.374341	−	0.927291i	$-0.377869\pi$
$761$	−15.7162	−	16.4827i	−0.569712	−	0.597497i	−0.944053	+	0.329794i	$0.893021\pi$
$762$	0.809419	+	0.447997i	0.0293222	+	0.0162292i
$763$	0.895975	−	18.8088i	0.0324365	−	0.680925i
$764$	−0.00934549	+	0.0649993i	−0.000338108	+	0.00235159i
$765$	2.66768	−	4.04854i	0.0964501	−	0.146375i
$766$	20.0004	−	9.13389i	0.722645	−	0.330021i
$767$	30.1535	+	10.4362i	1.08878	+	0.376830i
$768$	1.11039	−	1.32930i	0.0400678	−	0.0479669i
$769$	14.8954	−	10.6070i	0.537141	−	0.382497i	−0.279052	−	0.960276i	$-0.590020\pi$
$769$	14.8954	−	10.6070i	0.537141	−	0.382497i	0.816193	+	0.577780i	$0.196081\pi$
$770$	3.28782	−	13.5526i	0.118485	−	0.488401i
$771$	−13.4849	+	21.8417i	−0.485647	+	0.786608i
$772$	22.2712	−	2.12664i	0.801559	−	0.0765396i
$773$	−5.64937	−	39.2922i	−0.203194	−	1.41324i	−0.794729	−	0.606964i	$-0.792387\pi$
$773$	−5.64937	−	39.2922i	−0.203194	−	1.41324i	0.591535	−	0.806279i	$-0.298522\pi$
$774$	−6.15846	−	2.89796i	−0.221361	−	0.104165i
$775$	−1.88901	−	4.13636i	−0.0678553	−	0.148582i
$776$	−4.22658	−	2.17895i	−0.151725	−	0.0782199i
$777$	1.08564	+	16.5036i	0.0389472	+	0.592064i
$778$	−0.295673	−	0.573525i	−0.0106004	−	0.0205619i
$779$	−1.09852	−	3.17397i	−0.0393586	−	0.113719i
$780$	10.5297	−	15.3677i	0.377023	−	0.550253i
$781$	32.8537	−	18.9681i	1.17560	−	0.678733i
$782$	0.183681	−	3.27563i	0.00656842	−	0.117136i
$783$	11.5664	−	25.7802i	0.413351	−	0.921309i
$784$	−2.57120	−	0.754972i	−0.0918285	−	0.0269633i
$785$	−10.0099	+	51.9363i	−0.357268	+	1.85368i
$786$	−23.0264	+	18.7920i	−0.821325	+	0.670290i
$787$	21.0135	−	26.7208i	0.749049	−	0.952493i	−0.250830	−	0.968031i	$-0.580704\pi$
$787$	21.0135	−	26.7208i	0.749049	−	0.952493i	0.999879	+	0.0155380i	$0.00494609\pi$
$788$	1.61876	−	0.0771112i	0.0576661	−	0.00274697i
$789$	11.6760	+	15.7845i	0.415678	+	0.561943i
$790$	−7.40250	+	21.3881i	−0.263369	+	0.760955i
$791$	−30.7961	+	4.42781i	−1.09498	+	0.157435i
$792$	4.34403	−	7.32940i	0.154358	−	0.260439i
$793$	−2.25163	−	7.66836i	−0.0799579	−	0.272312i
$794$	20.7900	−	21.8039i	0.737809	−	0.773791i
$795$	−46.0626	+	14.4351i	−1.63367	+	0.511961i
$796$	−8.90212	+	22.2364i	−0.315527	+	0.788149i
$797$	47.6815	−	9.18985i	1.68896	−	0.325521i	0.747916	−	0.663794i	$-0.231055\pi$
$797$	47.6815	−	9.18985i	1.68896	−	0.325521i	0.941048	+	0.338272i	$0.109843\pi$
$798$	−13.1817	−	5.73404i	−0.466626	−	0.202983i
$799$	1.62727	−	3.15645i	0.0575685	−	0.111667i
$800$	−0.575332	−	0.0827202i	−0.0203411	−	0.00292460i
$801$	1.93656	+	5.00217i	0.0684250	+	0.176743i
$802$	−5.26729	−	4.56413i	−0.185994	−	0.161165i
$803$	8.74560	+	36.0499i	0.308626	+	1.27217i
$804$	−1.61679	−	7.64217i	−0.0570197	−	0.269519i
$805$	19.7034	+	12.8982i	0.694452	+	0.454601i
$806$	−30.8451	−	17.8084i	−1.08647	−	0.627275i
$807$	−11.0510	−	7.57192i	−0.389013	−	0.266544i
$808$	7.95192	+	1.53261i	0.279747	+	0.0539169i
$809$	−0.193158	+	0.300560i	−0.00679108	+	0.0105671i	−0.844632	−	0.535347i	$-0.820181\pi$
$809$	−0.193158	+	0.300560i	−0.00679108	+	0.0105671i	0.837841	+	0.545914i	$0.183817\pi$
$810$	3.54584	+	20.9644i	0.124588	+	0.736616i
$811$	−12.5712	+	8.07901i	−0.441434	+	0.283693i	−0.742418	−	0.669937i	$-0.766321\pi$
$811$	−12.5712	+	8.07901i	−0.441434	+	0.283693i	0.300984	+	0.953629i	$0.402685\pi$
$812$	−6.55623	+	9.20693i	−0.230078	+	0.323100i
$813$	−29.6824	+	12.5106i	−1.04101	+	0.438766i
$814$	−12.1127	−	4.84919i	−0.424550	−	0.169964i
$815$	25.0166	+	35.1308i	0.876292	+	1.23058i
$816$	−1.04317	+	0.561902i	−0.0365182	+	0.0196705i
$817$	−6.55619	−	6.25132i	−0.229372	−	0.218706i
$818$	2.61625	+	1.19480i	0.0914751	+	0.0417753i
$819$	25.0823	+	13.2957i	0.876447	+	0.464590i
$820$	1.50185	−	1.30136i	0.0524469	−	0.0454455i
$821$	8.17318	+	5.82010i	0.285246	+	0.203123i	0.713720	−	0.700432i	$-0.247009\pi$
$821$	8.17318	+	5.82010i	0.285246	+	0.203123i	−0.428474	+	0.903554i	$0.640948\pi$
$822$	−0.269114	+	0.981878i	−0.00938644	+	0.0342469i
$823$	3.92948	+	3.09018i	0.136973	+	0.107717i	0.684295	−	0.729205i	$-0.260110\pi$
$823$	3.92948	+	3.09018i	0.136973	+	0.107717i	−0.547322	+	0.836922i	$0.684353\pi$
$824$	1.16602	−	0.601125i	0.0406202	−	0.0209412i
$825$	−2.85871	+	0.0517129i	−0.0995276	+	0.00180041i
$826$	14.1572	−	3.43450i	0.492592	−	0.119502i
$827$	−34.6520			−1.20497			−0.602485	−	0.798130i	$-0.705823\pi$
$827$	−34.6520			−1.20497			−0.602485	+	0.798130i	$0.705823\pi$
$828$	9.20423	+	11.0581i	0.319869	+	0.384297i
$829$	3.11000			0.108015			0.0540073	−	0.998541i	$-0.482801\pi$
$829$	3.11000			0.108015			0.0540073	+	0.998541i	$0.482801\pi$
$830$	−39.4173	+	9.56253i	−1.36819	+	0.331920i
$831$	0.00710780	−	0.0128420i	0.000246567	−	0.000445485i
$832$	−4.04656	+	2.08615i	−0.140289	+	0.0723241i
$833$	1.44098	+	1.13320i	0.0499271	+	0.0392631i
$834$	−9.47364	+	2.48054i	−0.328045	+	0.0858941i
$835$	−31.7152	−	22.5843i	−1.09755	−	0.781561i
$836$	8.57007	−	7.42601i	0.296402	−	0.256834i
$837$	39.4405	−	9.84688i	1.36326	−	0.340358i
$838$	−14.9306	−	6.81856i	−0.515768	−	0.235543i
$839$	−5.66451	−	5.40110i	−0.195560	−	0.186467i	0.585972	−	0.810332i	$-0.300713\pi$
$839$	−5.66451	−	5.40110i	−0.195560	−	0.186467i	−0.781532	+	0.623865i	$0.785561\pi$
$840$	0.250969	−	8.50143i	0.00865926	−	0.293327i
$841$	−0.330873	−	0.464646i	−0.0114094	−	0.0160223i
$842$	25.6597	+	10.2726i	0.884290	+	0.354016i
$843$	−1.67430	−	1.26835i	−0.0576660	−	0.0436844i
$844$	5.23941	−	7.35773i	0.180348	−	0.253263i
$845$	−15.3562	+	9.86881i	−0.528268	+	0.339498i
$846$	4.21657	+	14.9918i	0.144969	+	0.515429i
$847$	3.29745	−	5.13093i	0.113302	−	0.176301i
$848$	11.5836	+	2.23256i	0.397783	+	0.0766664i
$849$	51.5223	−	24.6652i	1.76824	−	0.846508i
$850$	0.344354	+	0.198813i	0.0118112	+	0.00681923i
$851$	14.5679	−	16.5291i	0.499381	−	0.566610i
$852$	17.2084	−	15.4649i	0.589551	−	0.529818i
$853$	−8.53958	−	35.2006i	−0.292390	−	1.20525i	−0.908601	−	0.417666i	$-0.862848\pi$
$853$	−8.53958	−	35.2006i	−0.292390	−	1.20525i	0.616211	−	0.787581i	$-0.288667\pi$
$854$	−2.75759	−	2.38946i	−0.0943626	−	0.0817657i
$855$	−4.34714	+	27.9633i	−0.148669	+	0.956325i
$856$	1.91851	+	0.275841i	0.0655734	+	0.00942803i
$857$	−12.3123	+	23.8825i	−0.420580	+	0.815812i	0.579420	+	0.815029i	$0.303279\pi$
$857$	−12.3123	+	23.8825i	−0.420580	+	0.815812i	−1.00000		0.000782276i	$0.999751\pi$
$858$	−18.0042	+	13.3180i	−0.614654	+	0.454669i
$859$	−28.6034	+	5.51285i	−0.975934	+	0.188096i	−0.652196	−	0.758051i	$-0.726152\pi$
$859$	−28.6034	+	5.51285i	−0.975934	+	0.188096i	−0.323739	+	0.946147i	$0.604940\pi$
$860$	1.99205	−	4.97589i	0.0679282	−	0.169677i
$861$	2.22912	+	2.04978i	0.0759682	+	0.0698564i
$862$	14.6430	−	15.3571i	0.498742	−	0.523065i
$863$	0.607160	+	2.06780i	0.0206680	+	0.0703886i	0.969181	−	0.246349i	$-0.0792308\pi$
$863$	0.607160	+	2.06780i	0.0206680	+	0.0703886i	−0.948513	+	0.316737i	$0.897413\pi$
$864$	1.66674	−	4.92158i	0.0567036	−	0.167436i
$865$	−6.70080	+	0.963430i	−0.227834	+	0.0327576i
$866$	−1.99376	+	5.76058i	−0.0677506	+	0.195753i
$867$	−28.4508	+	3.23697i	−0.966238	+	0.109933i
$868$	−16.2425	+	0.773726i	−0.551307	+	0.0262620i
$869$	16.8188	−	21.3868i	0.570537	−	0.725497i
$870$	20.8036	+	7.89499i	0.705307	+	0.267665i
$871$	−3.88568	+	20.1608i	−0.131661	+	0.683124i
$872$	8.69242	+	2.55233i	0.294363	+	0.0864327i
$873$	−14.1846	−	1.51818i	−0.480074	−	0.0513825i
$874$	6.96717	+	17.8368i	0.235668	+	0.603339i
$875$	18.7910	−	10.8490i	0.635253	−	0.366763i
$876$	9.76888	+	20.4059i	0.330060	+	0.689450i
$877$	−0.904614	−	2.61371i	−0.0305466	−	0.0882587i	0.928697	−	0.370841i	$-0.120930\pi$
$877$	−0.904614	−	2.61371i	−0.0305466	−	0.0882587i	−0.959243	+	0.282582i	$0.908809\pi$
$878$	−4.63301	−	8.98678i	−0.156356	−	0.303289i
$879$	1.20053	−	0.802579i	0.0404928	−	0.0270703i
$880$	5.96357	+	3.07443i	0.201032	+	0.103639i
$881$	−12.7661	−	27.9539i	−0.430101	−	0.941790i	−0.993310	−	0.115475i	$-0.963161\pi$
$881$	−12.7661	−	27.9539i	−0.430101	−	0.941790i	0.563209	−	0.826314i	$-0.309566\pi$
$882$	−8.01105	+	0.672701i	−0.269746	+	0.0226510i
$883$	1.97211	+	13.7163i	0.0663668	+	0.461592i	0.995722	+	0.0924036i	$0.0294550\pi$
$883$	1.97211	+	13.7163i	0.0663668	+	0.461592i	−0.929355	+	0.369188i	$0.879636\pi$
$884$	3.10032	−	0.296045i	0.104275	−	0.00995706i
$885$	−13.6005	−	25.2492i	−0.457175	−	0.848744i
$886$	6.86995	−	28.3183i	0.230801	−	0.951373i
$887$	16.6181	−	11.8337i	0.557982	−	0.397337i	−0.265983	−	0.963978i	$-0.585697\pi$
$887$	16.6181	−	11.8337i	0.557982	−	0.397337i	0.823965	+	0.566640i	$0.191757\pi$
$888$	−7.83940	−	1.36435i	−0.263073	−	0.0457846i
$889$	−1.04913	−	0.363106i	−0.0351866	−	0.0121782i
$890$	−3.84234	+	1.75474i	−0.128795	+	0.0588189i
$891$	4.21466	−	25.2102i	0.141196	−	0.844573i
$892$	−1.73152	+	12.0430i	−0.0579756	+	0.403229i
$893$	−0.986266	+	20.7043i	−0.0330041	+	0.692842i
$894$	13.2841	−	7.99336i	0.444287	−	0.267338i
$895$	−37.3185	−	39.1385i	−1.24742	−	1.30826i
$896$	−1.03926	+	1.80005i	−0.0347193	+	0.0601355i
$897$	−11.0047	−	36.1806i	−0.367438	−	1.20803i
$898$	−15.8334	−	27.4242i	−0.528366	−	0.915157i
$899$	11.9855	−	40.8189i	0.399739	−	1.36139i
$900$	−1.69918	+	0.391717i	−0.0566392	+	0.0130572i
$901$	−6.78897	−	4.36301i	−0.226174	−	0.145353i
$902$	−2.21780	+	0.887873i	−0.0738447	+	0.0295629i
$903$	7.87720	+	2.15899i	0.262137	+	0.0718468i
$904$	1.42287	−	14.9009i	0.0473238	−	0.495597i
$905$	1.48626	+	7.71145i	0.0494049	+	0.256337i
$906$	−27.4581	−	22.9364i	−0.912236	−	0.762011i
$907$	0.187588	+	1.96451i	0.00622876	+	0.0652305i	0.998052	−	0.0623897i	$-0.0198722\pi$
$907$	0.187588	+	1.96451i	0.00622876	+	0.0652305i	−0.991823	+	0.127620i	$0.959266\pi$
$908$	−15.0705	+	4.42509i	−0.500132	+	0.146852i
$909$	23.9067	−	4.32498i	0.792936	−	0.143451i
$910$	−9.28682	+	20.3353i	−0.307855	+	0.674108i
$911$	43.9052	−	34.5274i	1.45464	−	1.14395i	0.492870	−	0.870103i	$-0.335948\pi$
$911$	43.9052	−	34.5274i	1.45464	−	1.14395i	0.961775	−	0.273843i	$-0.0882947\pi$
$912$	4.17610	−	5.51269i	0.138284	−	0.182543i
$913$	48.5386	+	4.63488i	1.60639	+	0.153392i
$914$	−0.0222561	−	0.467212i	−0.000736165	−	0.0154540i
$915$	−3.17555	+	6.44324i	−0.104981	+	0.213007i
$916$	−28.7703	−	1.37050i	−0.950598	−	0.0452826i
$917$	23.3567	−	26.9550i	0.771305	−	0.890134i
$918$	−2.30984	+	2.70186i	−0.0762361	+	0.0891748i
$919$			18.0067i			0.593987i	0.954880	+	0.296993i	$0.0959839\pi$
$919$			18.0067i			0.593987i	−0.954880	+	0.296993i	$0.904016\pi$
$920$	−8.26541	+	7.74930i	−0.272503	+	0.255487i
$921$	2.54943	−	7.82100i	0.0840067	−	0.257711i
$922$	15.4639	−	14.7448i	0.509275	−	0.485593i
$923$	−57.4687	+	19.8901i	−1.89161	+	0.654691i
$924$	−3.62770	+	9.55911i	−0.119342	+	0.314472i
$925$	0.992457	+	2.47904i	0.0326318	+	0.0815103i
$926$	12.9532	+	20.1556i	0.425669	+	0.662354i
$927$	2.61105	−	2.94465i	0.0857581	−	0.0967151i
$928$	−3.56105	−	4.10967i	−0.116897	−	0.134906i
$929$	−12.4250	−	15.7997i	−0.407651	−	0.518371i	0.538268	−	0.842774i	$-0.319079\pi$
$929$	−12.4250	−	15.7997i	−0.407651	−	0.518371i	−0.945919	+	0.324403i	$0.894837\pi$
$930$	9.57298	+	30.5474i	0.313910	+	1.00169i
$931$	−10.3983	−	2.52260i	−0.340791	−	0.0826750i
$932$	11.0603	+	2.68319i	0.362291	+	0.0878909i
$933$	−7.67188	−	24.4810i	−0.251166	−	0.801473i
$934$	−10.5558	−	13.4229i	−0.345398	−	0.439209i
$935$	−3.00571	−	3.46877i	−0.0982972	−	0.113441i
$936$	−9.06140	+	10.2191i	−0.296181	+	0.334023i
$937$	18.2410	+	28.3835i	0.595907	+	0.927249i	0.999922	+	0.0124969i	$0.00397799\pi$
$937$	18.2410	+	28.3835i	0.595907	+	0.927249i	−0.404015	+	0.914752i	$0.632386\pi$
$938$	3.48391	+	8.70239i	0.113754	+	0.284143i
$939$	15.3124	−	40.3488i	0.499702	−	1.31673i
$940$	−11.5895	+	4.01115i	−0.378006	+	0.130829i
$941$	−32.4366	+	30.9282i	−1.05740	+	1.00823i	−0.0574511	+	0.998348i	$0.518297\pi$
$941$	−32.4366	+	30.9282i	−1.05740	+	1.00823i	−0.999951	+	0.00988271i	$0.996854\pi$
$942$	12.0182	−	36.8687i	0.391574	−	1.20125i
$943$	−0.158030	−	4.03101i	−0.00514616	−	0.131268i
$944$			7.00876i			0.228116i
$945$	−8.50574	−	24.0559i	−0.276692	−	0.782539i
$946$	−4.21943	+	4.86948i	−0.137185	+	0.158320i
$947$	−59.4356	−	2.83126i	−1.93140	−	0.0920037i	−0.953538	−	0.301273i	$-0.902589\pi$
$947$	−59.4356	−	2.83126i	−1.93140	−	0.0920037i	−0.977858	+	0.209269i	$0.932892\pi$
$948$	7.33553	−	14.8839i	0.238247	−	0.483407i
$949$	−2.82949	−	59.3984i	−0.0918492	−	1.92815i
$950$	−2.31035	−	0.220612i	−0.0749577	−	0.00715759i
$951$	29.7674	−	39.2947i	0.965275	−	1.27422i
$952$	1.11769	−	0.878958i	0.0362244	−	0.0284872i
$953$	−14.9866	+	32.8160i	−0.485462	+	1.06301i	0.495463	+	0.868629i	$0.334998\pi$
$953$	−14.9866	+	32.8160i	−0.485462	+	1.06301i	−0.980925	+	0.194385i	$0.937729\pi$
$954$	34.8251	−	6.30023i	1.12750	−	0.203978i
$955$	−0.148854	+	0.0437073i	−0.00481679	+	0.00141434i
$956$	0.753717	+	7.89328i	0.0243769	+	0.255287i
$957$	−20.5291	−	17.1484i	−0.663612	−	0.554329i
$958$	−5.53550	−	28.7209i	−0.178844	−	0.927929i
$959$	0.116134	−	1.21621i	0.00375017	−	0.0392735i
$960$	3.94637	+	1.08163i	0.127369	+	0.0349093i
$961$	28.0406	−	11.2258i	0.904537	−	0.362122i
$962$	17.5951	+	11.3077i	0.567290	+	0.364575i
$963$	5.66611	−	1.30623i	0.182588	−	0.0420926i
$964$	−1.28689	+	4.38274i	−0.0414479	+	0.141158i
$965$	26.4272	+	45.7732i	0.850721	+	1.47349i
$966$	−13.1571	−	11.1798i	−0.423324	−	0.359703i
$967$	−29.2504	+	50.6632i	−0.940630	+	1.62922i	−0.176358	+	0.984326i	$0.556431\pi$
$967$	−29.2504	+	50.6632i	−0.940630	+	1.62922i	−0.764273	+	0.644893i	$0.776902\pi$
$968$	2.02494	+	2.12370i	0.0650842	+	0.0682583i
$969$	−4.05379	+	2.43926i	−0.130226	+	0.0783604i
$970$	0.534534	−	11.2212i	0.0171629	−	0.360293i
$971$	7.01378	−	48.7819i	0.225083	−	1.56549i	−0.493313	−	0.869852i	$-0.664214\pi$
$971$	7.01378	−	48.7819i	0.225083	−	1.56549i	0.718396	−	0.695635i	$-0.244877\pi$
$972$	−0.667578	−	15.5742i	−0.0214126	−	0.499541i
$973$	10.6900	−	4.88194i	0.342704	−	0.156508i
$974$	33.3506	+	11.5427i	1.06862	+	0.369853i
$975$	4.51551	+	0.785870i	0.144612	+	0.0251680i
$976$	1.42997	−	1.01828i	0.0457723	−	0.0325943i
$977$	−1.27319	+	5.24818i	−0.0407331	+	0.167904i	−0.988545	−	0.150926i	$-0.951775\pi$
$977$	−1.27319	+	5.24818i	−0.0407331	+	0.167904i	0.947812	+	0.318830i	$0.103290\pi$
$978$	−14.9947	−	27.8377i	−0.479479	−	0.890151i
$979$	5.05490	−	0.482684i	0.161555	−	0.0154266i
$980$	−0.900968	−	6.26637i	−0.0287804	−	0.200172i
$981$	27.0829	−	2.27419i	0.864689	−	0.0726094i
$982$	−1.05217	−	2.30393i	−0.0335761	−	0.0735215i
$983$	12.0511	+	6.21279i	0.384371	+	0.198157i	0.639572	−	0.768731i	$-0.279111\pi$
$983$	12.0511	+	6.21279i	0.384371	+	0.198157i	−0.255201	+	0.966888i	$0.582142\pi$
$984$	−1.21121	+	0.809724i	−0.0386121	+	0.0258131i
$985$	1.75437	+	3.40301i	0.0558989	+	0.108429i
$986$	1.21669	+	3.51539i	0.0387473	+	0.111953i
$987$	−8.06979	−	16.8567i	−0.256864	−	0.536554i
$988$	−15.7428	+	9.08912i	−0.500846	+	0.289163i
$989$	−5.36076	−	9.46825i	−0.170462	−	0.301073i
$990$	20.0139	+	2.14210i	0.636085	+	0.0680804i
$991$	13.1034	+	3.84749i	0.416242	+	0.122220i	0.483146	−	0.875540i	$-0.339494\pi$
$991$	13.1034	+	3.84749i	0.416242	+	0.122220i	−0.0669042	+	0.997759i	$0.521312\pi$
$992$	1.48057	−	7.68194i	0.0470082	−	0.243902i
$993$	5.01971	+	1.90499i	0.159296	+	0.0604530i
$994$	−17.1629	+	21.8244i	−0.544373	+	0.692227i
$995$	−56.5221	+	2.69248i	−1.79187	+	0.0853573i
$996$	29.5466	−	3.36165i	0.936219	−	0.106518i
$997$	−18.6615	+	53.9188i	−0.591015	+	1.70763i	0.109499	+	0.993987i	$0.465075\pi$
$997$	−18.6615	+	53.9188i	−0.591015	+	1.70763i	−0.700514	+	0.713639i	$0.747046\pi$
$998$	−41.7836	+	6.00757i	−1.32264	+	0.190166i
$999$	−23.4097	+	4.67383i	−0.740650	+	0.147873i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	414.2.p.a.5.9	✓	480
9.2	odd	6	inner	414.2.p.a.281.2	yes	480
23.14	odd	22	inner	414.2.p.a.221.2	yes	480
207.83	even	66	inner	414.2.p.a.83.9	yes	480

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
414.2.p.a.5.9	✓	480	1.1	even	1	trivial
414.2.p.a.83.9	yes	480	207.83	even	66	inner
414.2.p.a.221.2	yes	480	23.14	odd	22	inner
414.2.p.a.281.2	yes	480	9.2	odd	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 414 = 2 \cdot 3^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	414.p (of order \(66\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.971812 + 0.235759i) q^{2} +(0.893014 + 1.48409i) q^{3} +(0.888835 - 0.458227i) q^{4} +(1.85702 + 1.46038i) q^{5} +(-1.21773 - 1.23172i) q^{6} +(1.69311 + 1.20566i) q^{7} +(-0.755750 + 0.654861i) q^{8} +(-1.40505 + 2.65063i) q^{9} +O(q^{10})\)	\(q+(-0.971812 + 0.235759i) q^{2} +(0.893014 + 1.48409i) q^{3} +(0.888835 - 0.458227i) q^{4} +(1.85702 + 1.46038i) q^{5} +(-1.21773 - 1.23172i) q^{6} +(1.69311 + 1.20566i) q^{7} +(-0.755750 + 0.654861i) q^{8} +(-1.40505 + 2.65063i) q^{9} +(-2.14898 - 0.981404i) q^{10} +(2.05541 + 1.95983i) q^{11} +(1.47379 + 0.909910i) q^{12} +(-2.64080 - 3.70848i) q^{13} +(-1.92963 - 0.772509i) q^{14} +(-0.508989 + 4.06013i) q^{15} +(0.580057 - 0.814576i) q^{16} +(-0.575493 + 0.369847i) q^{17} +(0.740538 - 2.90716i) q^{18} +(2.15872 - 3.35903i) q^{19} +(2.31977 + 0.447100i) q^{20} +(-0.277337 + 3.58941i) q^{21} +(-2.45952 - 1.42000i) q^{22} +(3.65075 - 3.10999i) q^{23} +(-1.64677 - 0.536802i) q^{24} +(0.137034 + 0.564864i) q^{25} +(3.44066 + 2.98135i) q^{26} +(-5.18850 + 0.281820i) q^{27} +(2.05737 + 0.295805i) q^{28} +(-2.49178 + 4.83337i) q^{29} +(-0.462571 - 4.06568i) q^{30} +(-7.68194 + 1.48057i) q^{31} +(-0.371662 + 0.928368i) q^{32} +(-1.07306 + 4.80057i) q^{33} +(0.472076 - 0.495099i) q^{34} +(1.38343 + 4.71153i) q^{35} +(-0.0342732 + 2.99980i) q^{36} +(4.54735 - 0.653810i) q^{37} +(-1.30595 + 3.77328i) q^{38} +(3.14546 - 7.23091i) q^{39} +(-2.35979 + 0.112411i) q^{40} +(0.519976 - 0.661203i) q^{41} +(-0.576716 - 3.55361i) q^{42} +(0.429362 - 2.22774i) q^{43} +(2.72497 + 0.800122i) q^{44} +(-6.48014 + 2.87037i) q^{45} +(-2.81464 + 3.88302i) q^{46} +(-4.49568 + 2.59558i) q^{47} +(1.72690 + 0.133430i) q^{48} +(-0.876459 - 2.53236i) q^{49} +(-0.266343 - 0.516634i) q^{50} +(-1.06281 - 0.523806i) q^{51} +(-4.04656 - 2.08615i) q^{52} +(4.90057 + 10.7307i) q^{53} +(4.97581 - 1.49711i) q^{54} +(0.954850 + 6.64113i) q^{55} +(-2.06911 + 0.197576i) q^{56} +(6.91288 + 0.204074i) q^{57} +(1.28203 - 5.28458i) q^{58} +(-5.70916 + 4.06548i) q^{59} +(1.40805 + 3.84202i) q^{60} +(1.65893 + 0.574162i) q^{61} +(7.11634 - 3.24992i) q^{62} +(-5.57467 + 2.79380i) q^{63} +(0.142315 - 0.989821i) q^{64} +(0.511767 - 10.7433i) q^{65} +(-0.0889688 - 4.91823i) q^{66} +(-3.11217 - 3.26395i) q^{67} +(-0.342045 + 0.592439i) q^{68} +(7.87567 + 2.64079i) q^{69} +(-2.45522 - 4.25256i) q^{70} +(3.76333 - 12.8167i) q^{71} +(-0.673924 - 2.92332i) q^{72} +(10.9883 + 7.06173i) q^{73} +(-4.26503 + 1.70746i) q^{74} +(-0.715935 + 0.707802i) q^{75} +(0.379548 - 3.97481i) q^{76} +(1.11715 + 5.79634i) q^{77} +(-1.35204 + 7.76865i) q^{78} +(-0.910656 - 9.53682i) q^{79} +(2.26677 - 0.665584i) q^{80} +(-5.05165 - 7.44854i) q^{81} +(-0.349434 + 0.765154i) q^{82} +(13.4956 - 10.6130i) q^{83} +(1.39825 + 3.31748i) q^{84} +(-1.60882 - 0.153624i) q^{85} +(0.107951 + 2.26617i) q^{86} +(-9.39835 + 0.618244i) q^{87} +(-2.83679 - 0.135133i) q^{88} +(1.17088 - 1.35127i) q^{89} +(5.62076 - 4.31721i) q^{90} -9.46279i q^{91} +(1.81984 - 4.43714i) q^{92} +(-9.05738 - 10.0785i) q^{93} +(3.75702 - 3.58232i) q^{94} +(8.91426 - 3.08525i) q^{95} +(-1.70968 + 0.277464i) q^{96} +(1.76732 + 4.41456i) q^{97} +(1.44878 + 2.25435i) q^{98} +(-8.08273 + 2.69446i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 480 q - 4 q^{3} - 24 q^{4} + 8 q^{6}+O(q^{10}) \) 480 * q - 4 * q^3 - 24 * q^4 + 8 * q^6	\( 480 q - 4 q^{3} - 24 q^{4} + 8 q^{6} + 4 q^{12} - 44 q^{15} + 24 q^{16} + 28 q^{18} + 66 q^{21} + 6 q^{23} + 4 q^{24} + 12 q^{25} + 86 q^{27} - 48 q^{29} + 44 q^{30} - 12 q^{31} - 44 q^{33} + 24 q^{39} - 60 q^{41} + 12 q^{46} + 48 q^{47} + 8 q^{48} - 78 q^{49} + 24 q^{50} - 30 q^{54} - 24 q^{55} - 66 q^{56} - 66 q^{57} - 72 q^{59} - 22 q^{60} - 110 q^{63} + 48 q^{64} - 462 q^{65} - 88 q^{66} - 70 q^{69} + 12 q^{70} - 52 q^{72} - 264 q^{74} - 76 q^{75} - 12 q^{77} - 58 q^{78} - 96 q^{81} - 198 q^{83} - 22 q^{84} + 178 q^{87} + 6 q^{92} - 20 q^{93} - 12 q^{94} + 12 q^{95} - 4 q^{96} - 66 q^{97} - 132 q^{99}+O(q^{100}) \) 480 * q - 4 * q^3 - 24 * q^4 + 8 * q^6 + 4 * q^12 - 44 * q^15 + 24 * q^16 + 28 * q^18 + 66 * q^21 + 6 * q^23 + 4 * q^24 + 12 * q^25 + 86 * q^27 - 48 * q^29 + 44 * q^30 - 12 * q^31 - 44 * q^33 + 24 * q^39 - 60 * q^41 + 12 * q^46 + 48 * q^47 + 8 * q^48 - 78 * q^49 + 24 * q^50 - 30 * q^54 - 24 * q^55 - 66 * q^56 - 66 * q^57 - 72 * q^59 - 22 * q^60 - 110 * q^63 + 48 * q^64 - 462 * q^65 - 88 * q^66 - 70 * q^69 + 12 * q^70 - 52 * q^72 - 264 * q^74 - 76 * q^75 - 12 * q^77 - 58 * q^78 - 96 * q^81 - 198 * q^83 - 22 * q^84 + 178 * q^87 + 6 * q^92 - 20 * q^93 - 12 * q^94 + 12 * q^95 - 4 * q^96 - 66 * q^97 - 132 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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