LMFDB - Embedded newform 722.2.c.n.429.1

Newspace parameters

Level:	$ N $	$=$	$ 722 = 2 \cdot 19^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	722.c (of order $3$, degree $2$, not minimal)

Newform invariants

Self dual:	no
Analytic conductor:	$5.76519902594$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	8.0.324000000.2
Defining polynomial:	$ x^{8} + 5x^{6} + 20x^{4} + 25x^{2} + 25 $ x^8 + 5x^6 + 20x^4 + 25*x^2 + 25
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			429.1
Root			$-0.587785 + 1.01807i$ of defining polynomial
Character	$\chi$	$=$	722.429
Dual form			722.2.c.n.653.1

$q$-expansion

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{2} +(-1.26007 + 2.18251i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.22982 - 2.13012i) q^{5} +(1.26007 + 2.18251i) q^{6} -2.79360 q^{7} -1.00000 q^{8} +(-1.67557 - 2.90217i) q^{9} +O(q^{10})$	\(q+(0.500000 - 0.866025i) q^{2} +(-1.26007 + 2.18251i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.22982 - 2.13012i) q^{5} +(1.26007 + 2.18251i) q^{6} -2.79360 q^{7} -1.00000 q^{8} +(-1.67557 - 2.90217i) q^{9} +(-1.22982 - 2.13012i) q^{10} -1.67853 q^{11} +2.52015 q^{12} +(3.17229 + 5.49456i) q^{13} +(-1.39680 + 2.41933i) q^{14} +(3.09934 + 5.36821i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-2.48459 + 4.30343i) q^{17} -3.35114 q^{18} -2.45965 q^{20} +(3.52015 - 6.09707i) q^{21} +(-0.839266 + 1.45365i) q^{22} +(1.24945 + 2.16411i) q^{23} +(1.26007 - 2.18251i) q^{24} +(-0.524938 - 0.909219i) q^{25} +6.34458 q^{26} +0.884927 q^{27} +(1.39680 + 2.41933i) q^{28} +(2.96589 + 5.13708i) q^{29} +6.19868 q^{30} -7.28408 q^{31} +(0.500000 + 0.866025i) q^{32} +(2.11507 - 3.66341i) q^{33} +(2.48459 + 4.30343i) q^{34} +(-3.43564 + 5.95071i) q^{35} +(-1.67557 + 2.90217i) q^{36} -0.550972 q^{37} -15.9893 q^{39} +(-1.22982 + 2.13012i) q^{40} +(-1.30371 + 2.25809i) q^{41} +(-3.52015 - 6.09707i) q^{42} +(-1.43564 + 2.48661i) q^{43} +(0.839266 + 1.45365i) q^{44} -8.24263 q^{45} +2.49890 q^{46} +(-0.372797 - 0.645703i) q^{47} +(-1.26007 - 2.18251i) q^{48} +0.804226 q^{49} -1.04988 q^{50} +(-6.26153 - 10.8453i) q^{51} +(3.17229 - 5.49456i) q^{52} +(-0.735136 - 1.27329i) q^{53} +(0.442463 - 0.766369i) q^{54} +(-2.06430 + 3.57547i) q^{55} +2.79360 q^{56} +5.93179 q^{58} +(-2.48131 + 4.29775i) q^{59} +(3.09934 - 5.36821i) q^{60} +(-4.66843 - 8.08596i) q^{61} +(-3.64204 + 6.30820i) q^{62} +(4.68088 + 8.10752i) q^{63} +1.00000 q^{64} +15.6054 q^{65} +(-2.11507 - 3.66341i) q^{66} +(5.78022 + 10.0116i) q^{67} +4.96917 q^{68} -6.29761 q^{69} +(3.43564 + 5.95071i) q^{70} +(-3.49849 + 6.05956i) q^{71} +(1.67557 + 2.90217i) q^{72} +(3.09310 - 5.35740i) q^{73} +(-0.275486 + 0.477156i) q^{74} +2.64584 q^{75} +4.68915 q^{77} +(-7.99463 + 13.8471i) q^{78} +(-2.95579 + 5.11958i) q^{79} +(1.22982 + 2.13012i) q^{80} +(3.91164 - 6.77516i) q^{81} +(1.30371 + 2.25809i) q^{82} +15.1773 q^{83} -7.04029 q^{84} +(6.11121 + 10.5849i) q^{85} +(1.43564 + 2.48661i) q^{86} -14.9490 q^{87} +1.67853 q^{88} +(3.45251 + 5.97992i) q^{89} +(-4.12132 + 7.13833i) q^{90} +(-8.86212 - 15.3496i) q^{91} +(1.24945 - 2.16411i) q^{92} +(9.17848 - 15.8976i) q^{93} -0.745593 q^{94} -2.52015 q^{96} +(7.19369 - 12.4598i) q^{97} +(0.402113 - 0.696480i) q^{98} +(2.81250 + 4.87139i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{2} + 2 q^{3} - 4 q^{4} + 2 q^{5} - 2 q^{6} - 4 q^{7} - 8 q^{8} - 4 q^{9}+O(q^{10}) $ 8 * q + 4 * q^2 + 2 * q^3 - 4 * q^4 + 2 * q^5 - 2 * q^6 - 4 * q^7 - 8 * q^8 - 4 * q^9	\( 8 q + 4 q^{2} + 2 q^{3} - 4 q^{4} + 2 q^{5} - 2 q^{6} - 4 q^{7} - 8 q^{8} - 4 q^{9} - 2 q^{10} + 4 q^{11} - 4 q^{12} + 18 q^{13} - 2 q^{14} + 4 q^{15} - 4 q^{16} - 6 q^{17} - 8 q^{18} - 4 q^{20} + 4 q^{21} + 2 q^{22} + 10 q^{23} - 2 q^{24} - 6 q^{25} + 36 q^{26} + 8 q^{27} + 2 q^{28} - 2 q^{29} + 8 q^{30} - 52 q^{31} + 4 q^{32} + 16 q^{33} + 6 q^{34} - 6 q^{35} - 4 q^{36} - 8 q^{37} - 12 q^{39} - 2 q^{40} - 12 q^{41} - 4 q^{42} + 10 q^{43} - 2 q^{44} - 44 q^{45} + 20 q^{46} + 12 q^{47} + 2 q^{48} - 24 q^{49} - 12 q^{50} - 2 q^{51} + 18 q^{52} + 8 q^{53} + 4 q^{54} + 26 q^{55} + 4 q^{56} - 4 q^{58} - 8 q^{59} + 4 q^{60} - 26 q^{62} + 22 q^{63} + 8 q^{64} + 8 q^{65} - 16 q^{66} + 10 q^{67} + 12 q^{68} + 40 q^{69} + 6 q^{70} + 4 q^{72} + 14 q^{73} - 4 q^{74} - 16 q^{75} + 8 q^{77} - 6 q^{78} + 22 q^{79} + 2 q^{80} + 4 q^{81} + 12 q^{82} - 24 q^{83} - 8 q^{84} + 18 q^{85} - 10 q^{86} - 52 q^{87} - 4 q^{88} - 16 q^{89} - 22 q^{90} - 4 q^{91} + 10 q^{92} - 8 q^{93} + 24 q^{94} + 4 q^{96} + 28 q^{97} - 12 q^{98} - 22 q^{99}+O(q^{100}) \) 8 * q + 4 * q^2 + 2 * q^3 - 4 * q^4 + 2 * q^5 - 2 * q^6 - 4 * q^7 - 8 * q^8 - 4 * q^9 - 2 * q^10 + 4 * q^11 - 4 * q^12 + 18 * q^13 - 2 * q^14 + 4 * q^15 - 4 * q^16 - 6 * q^17 - 8 * q^18 - 4 * q^20 + 4 * q^21 + 2 * q^22 + 10 * q^23 - 2 * q^24 - 6 * q^25 + 36 * q^26 + 8 * q^27 + 2 * q^28 - 2 * q^29 + 8 * q^30 - 52 * q^31 + 4 * q^32 + 16 * q^33 + 6 * q^34 - 6 * q^35 - 4 * q^36 - 8 * q^37 - 12 * q^39 - 2 * q^40 - 12 * q^41 - 4 * q^42 + 10 * q^43 - 2 * q^44 - 44 * q^45 + 20 * q^46 + 12 * q^47 + 2 * q^48 - 24 * q^49 - 12 * q^50 - 2 * q^51 + 18 * q^52 + 8 * q^53 + 4 * q^54 + 26 * q^55 + 4 * q^56 - 4 * q^58 - 8 * q^59 + 4 * q^60 - 26 * q^62 + 22 * q^63 + 8 * q^64 + 8 * q^65 - 16 * q^66 + 10 * q^67 + 12 * q^68 + 40 * q^69 + 6 * q^70 + 4 * q^72 + 14 * q^73 - 4 * q^74 - 16 * q^75 + 8 * q^77 - 6 * q^78 + 22 * q^79 + 2 * q^80 + 4 * q^81 + 12 * q^82 - 24 * q^83 - 8 * q^84 + 18 * q^85 - 10 * q^86 - 52 * q^87 - 4 * q^88 - 16 * q^89 - 22 * q^90 - 4 * q^91 + 10 * q^92 - 8 * q^93 + 24 * q^94 + 4 * q^96 + 28 * q^97 - 12 * q^98 - 22 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/722\mathbb{Z}\right)^\times$.

$n$	$363$
$\chi(n)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$3$	−1.26007	+	2.18251i	−0.727504	+	1.26007i	0.230431	+	0.973089i	$0.425986\pi$
$3$	−1.26007	+	2.18251i	−0.727504	+	1.26007i	−0.957935	+	0.286985i	$0.907347\pi$
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	1.22982	−	2.13012i	0.549994	−	0.952618i	−0.448280	−	0.893893i	$-0.647963\pi$
$5$	1.22982	−	2.13012i	0.549994	−	0.952618i	0.998274	−	0.0587249i	$-0.0187035\pi$
$6$	1.26007	+	2.18251i	0.514423	+	0.891007i
$7$	−2.79360			−1.05588			−0.527942	−	0.849281i	$-0.677036\pi$
$7$	−2.79360			−1.05588			−0.527942	+	0.849281i	$0.677036\pi$
$8$	−1.00000			−0.353553
$9$	−1.67557	−	2.90217i	−0.558524	−	0.967391i
$10$	−1.22982	−	2.13012i	−0.388905	−	0.673603i
$11$	−1.67853			−0.506096			−0.253048	−	0.967454i	$-0.581433\pi$
$11$	−1.67853			−0.506096			−0.253048	+	0.967454i	$0.581433\pi$
$12$	2.52015			0.727504
$13$	3.17229	+	5.49456i	0.879834	+	1.52392i	0.851522	+	0.524319i	$0.175680\pi$
$13$	3.17229	+	5.49456i	0.879834	+	1.52392i	0.0283125	+	0.999599i	$0.490987\pi$
$14$	−1.39680	+	2.41933i	−0.373311	+	0.646594i
$15$	3.09934	+	5.36821i	0.800246	+	1.38607i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−2.48459	+	4.30343i	−0.602601	+	1.04374i	0.389825	+	0.920889i	$0.372536\pi$
$17$	−2.48459	+	4.30343i	−0.602601	+	1.04374i	−0.992426	+	0.122846i	$0.960798\pi$
$18$	−3.35114			−0.789872
$19$		0			0
$19$		0			0
$20$	−2.45965			−0.549994
$21$	3.52015	−	6.09707i	0.768159	−	1.33049i
$22$	−0.839266	+	1.45365i	−0.178932	+	0.309919i
$23$	1.24945	+	2.16411i	0.260529	+	0.451249i	0.966383	−	0.257109i	$-0.0827698\pi$
$23$	1.24945	+	2.16411i	0.260529	+	0.451249i	−0.705854	+	0.708358i	$0.749436\pi$
$24$	1.26007	−	2.18251i	0.257211	−	0.445503i
$25$	−0.524938	−	0.909219i	−0.104988	−	0.181844i
$26$	6.34458			1.24427
$27$	0.884927			0.170304
$28$	1.39680	+	2.41933i	0.263971	+	0.457211i
$29$	2.96589	+	5.13708i	0.550752	+	0.953931i	0.998220	+	0.0596313i	$0.0189925\pi$
$29$	2.96589	+	5.13708i	0.550752	+	0.953931i	−0.447468	+	0.894300i	$0.647674\pi$
$30$	6.19868			1.13172
$31$	−7.28408			−1.30826			−0.654130	−	0.756382i	$-0.726965\pi$
$31$	−7.28408			−1.30826			−0.654130	+	0.756382i	$0.726965\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$	2.11507	−	3.66341i	0.368187	−	0.637719i
$34$	2.48459	+	4.30343i	0.426103	+	0.738032i
$35$	−3.43564	+	5.95071i	−0.580730	+	1.00585i
$36$	−1.67557	+	2.90217i	−0.279262	+	0.483696i
$37$	−0.550972			−0.0905792			−0.0452896	−	0.998974i	$-0.514421\pi$
$37$	−0.550972			−0.0905792			−0.0452896	+	0.998974i	$0.514421\pi$
$38$		0			0
$39$	−15.9893			−2.56033
$40$	−1.22982	+	2.13012i	−0.194452	+	0.336801i
$41$	−1.30371	+	2.25809i	−0.203605	+	0.352654i	−0.949687	−	0.313200i	$-0.898599\pi$
$41$	−1.30371	+	2.25809i	−0.203605	+	0.352654i	0.746083	+	0.665853i	$0.231932\pi$
$42$	−3.52015	−	6.09707i	−0.543170	−	0.940799i
$43$	−1.43564	+	2.48661i	−0.218934	+	0.379204i	−0.954482	−	0.298268i	$-0.903591\pi$
$43$	−1.43564	+	2.48661i	−0.218934	+	0.379204i	0.735549	+	0.677472i	$0.236924\pi$
$44$	0.839266	+	1.45365i	0.126524	+	0.219146i
$45$	−8.24263			−1.22874
$46$	2.49890			0.368443
$47$	−0.372797	−	0.645703i	−0.0543780	−	0.0941854i	0.837555	−	0.546353i	$-0.183984\pi$
$47$	−0.372797	−	0.645703i	−0.0543780	−	0.0941854i	−0.891933	+	0.452167i	$0.850651\pi$
$48$	−1.26007	−	2.18251i	−0.181876	−	0.315018i
$49$	0.804226			0.114889
$50$	−1.04988			−0.148475
$51$	−6.26153	−	10.8453i	−0.876789	−	1.51864i
$52$	3.17229	−	5.49456i	0.439917	−	0.761959i
$53$	−0.735136	−	1.27329i	−0.100979	−	0.174900i	0.811109	−	0.584894i	$-0.198864\pi$
$53$	−0.735136	−	1.27329i	−0.100979	−	0.174900i	−0.912088	+	0.409994i	$0.865531\pi$
$54$	0.442463	−	0.766369i	0.0602117	−	0.104290i
$55$	−2.06430	+	3.57547i	−0.278350	+	0.482117i
$56$	2.79360			0.373311
$57$		0			0
$58$	5.93179			0.778882
$59$	−2.48131	+	4.29775i	−0.323038	+	0.559519i	−0.981113	−	0.193433i	$-0.938038\pi$
$59$	−2.48131	+	4.29775i	−0.323038	+	0.559519i	0.658075	+	0.752952i	$0.271371\pi$
$60$	3.09934	−	5.36821i	0.400123	−	0.693033i
$61$	−4.66843	−	8.08596i	−0.597731	−	1.03530i	−0.993155	−	0.116802i	$-0.962736\pi$
$61$	−4.66843	−	8.08596i	−0.597731	−	1.03530i	0.395424	−	0.918499i	$-0.370598\pi$
$62$	−3.64204	+	6.30820i	−0.462539	+	0.801142i
$63$	4.68088	+	8.10752i	0.589736	+	1.02145i
$64$	1.00000			0.125000
$65$	15.6054			1.93562
$66$	−2.11507	−	3.66341i	−0.260347	−	0.450935i
$67$	5.78022	+	10.0116i	0.706166	+	1.22312i	0.966269	+	0.257535i	$0.0829103\pi$
$67$	5.78022	+	10.0116i	0.706166	+	1.22312i	−0.260103	+	0.965581i	$0.583756\pi$
$68$	4.96917			0.602601
$69$	−6.29761			−0.758143
$70$	3.43564	+	5.95071i	0.410638	+	0.711246i
$71$	−3.49849	+	6.05956i	−0.415195	+	0.719138i	−0.995449	−	0.0952973i	$-0.969620\pi$
$71$	−3.49849	+	6.05956i	−0.415195	+	0.719138i	0.580254	+	0.814435i	$0.302953\pi$
$72$	1.67557	+	2.90217i	0.197468	+	0.342024i
$73$	3.09310	−	5.35740i	0.362020	−	0.627036i	−0.626274	−	0.779603i	$-0.715421\pi$
$73$	3.09310	−	5.35740i	0.362020	−	0.627036i	0.988293	+	0.152567i	$0.0487540\pi$
$74$	−0.275486	+	0.477156i	−0.0320246	+	0.0554682i
$75$	2.64584			0.305515
$76$		0			0
$77$	4.68915			0.534379
$78$	−7.99463	+	13.8471i	−0.905214	+	1.56788i
$79$	−2.95579	+	5.11958i	−0.332552	+	0.575998i	−0.983012	−	0.183543i	$-0.941243\pi$
$79$	−2.95579	+	5.11958i	−0.332552	+	0.575998i	0.650459	+	0.759541i	$0.274577\pi$
$80$	1.22982	+	2.13012i	0.137499	+	0.238155i
$81$	3.91164	−	6.77516i	0.434626	−	0.752795i
$82$	1.30371	+	2.25809i	0.143970	+	0.249364i
$83$	15.1773			1.66593			0.832964	−	0.553328i	$-0.186642\pi$
$83$	15.1773			1.66593			0.832964	+	0.553328i	$0.186642\pi$
$84$	−7.04029			−0.768159
$85$	6.11121	+	10.5849i	0.662854	+	1.14810i
$86$	1.43564	+	2.48661i	0.154809	+	0.268138i
$87$	−14.9490			−1.60270
$88$	1.67853			0.178932
$89$	3.45251	+	5.97992i	0.365965	+	0.633870i	0.988931	−	0.148379i	$-0.0474056\pi$
$89$	3.45251	+	5.97992i	0.365965	+	0.633870i	−0.622965	+	0.782249i	$0.714072\pi$
$90$	−4.12132	+	7.13833i	−0.434425	+	0.752446i
$91$	−8.86212	−	15.3496i	−0.929002	−	1.60908i
$92$	1.24945	−	2.16411i	0.130264	−	0.225625i
$93$	9.17848	−	15.8976i	0.951764	−	1.64850i
$94$	−0.745593			−0.0769021
$95$		0			0
$96$	−2.52015			−0.257211
$97$	7.19369	−	12.4598i	0.730408	−	1.26510i	−0.226300	−	0.974058i	$-0.572663\pi$
$97$	7.19369	−	12.4598i	0.730408	−	1.26510i	0.956709	−	0.291047i	$-0.0940036\pi$
$98$	0.402113	−	0.696480i	0.0406196	−	0.0703551i
$99$	2.81250	+	4.87139i	0.282667	+	0.489593i
$100$	−0.524938	+	0.909219i	−0.0524938	+	0.0909219i
$101$	−5.64146	−	9.77130i	−0.561347	−	0.972281i	−0.997379	−	0.0723500i	$-0.976950\pi$
$101$	−5.64146	−	9.77130i	−0.561347	−	0.972281i	0.436033	−	0.899931i	$-0.356383\pi$
$102$	−12.5231			−1.23997
$103$	−14.8280			−1.46104			−0.730522	−	0.682889i	$-0.760723\pi$
$103$	−14.8280			−1.46104			−0.730522	+	0.682889i	$0.760723\pi$
$104$	−3.17229	−	5.49456i	−0.311068	−	0.538786i
$105$	−8.65833	−	14.9967i	−0.844966	−	1.46352i
$106$	−1.47027			−0.142805
$107$	2.82849			0.273440			0.136720	−	0.990610i	$-0.456344\pi$
$107$	2.82849			0.273440			0.136720	+	0.990610i	$0.456344\pi$
$108$	−0.442463	−	0.766369i	−0.0425761	−	0.0737439i
$109$	0.862695	−	1.49423i	0.0826312	−	0.143121i	−0.821748	−	0.569851i	$-0.807001\pi$
$109$	0.862695	−	1.49423i	0.0826312	−	0.143121i	0.904379	+	0.426729i	$0.140334\pi$
$110$	2.06430	+	3.57547i	0.196823	+	0.340908i
$111$	0.694265	−	1.20250i	0.0658967	−	0.114137i
$112$	1.39680	−	2.41933i	0.131985	−	0.228605i
$113$	0.427785			0.0402426			0.0201213	−	0.999798i	$-0.493595\pi$
$113$	0.427785			0.0402426			0.0201213	+	0.999798i	$0.493595\pi$
$114$		0			0
$115$	6.14643			0.573157
$116$	2.96589	−	5.13708i	0.275376	−	0.476966i
$117$	10.6308	−	18.4131i	0.982816	−	1.70229i
$118$	2.48131	+	4.29775i	0.228423	+	0.395640i
$119$	6.94095	−	12.0221i	0.636276	−	1.10206i
$120$	−3.09934	−	5.36821i	−0.282930	−	0.490049i
$121$	−8.18253			−0.743867
$122$	−9.33686			−0.845320
$123$	−3.28553	−	5.69071i	−0.296246	−	0.513114i
$124$	3.64204	+	6.30820i	0.327065	+	0.566493i
$125$	9.71592			0.869018
$126$	9.36176			0.834012
$127$	−0.568158	−	0.984079i	−0.0504159	−	0.0873229i	0.839716	−	0.543026i	$-0.182721\pi$
$127$	−0.568158	−	0.984079i	−0.0504159	−	0.0873229i	−0.890132	+	0.455703i	$0.849388\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$	−3.61803	−	6.26662i	−0.318550	−	0.551745i
$130$	7.80272	−	13.5147i	0.684344	−	1.18532i
$131$	8.92075	−	15.4512i	0.779410	−	1.34998i	−0.152873	−	0.988246i	$-0.548852\pi$
$131$	8.92075	−	15.4512i	0.779410	−	1.34998i	0.932282	−	0.361731i	$-0.117814\pi$
$132$	−4.23015			−0.368187
$133$		0			0
$134$	11.5604			0.998670
$135$	1.08831	−	1.88500i	0.0936664	−	0.162235i
$136$	2.48459	−	4.30343i	0.213052	−	0.369016i
$137$	7.95782	+	13.7833i	0.679882	+	1.17759i	0.975016	+	0.222135i	$0.0713025\pi$
$137$	7.95782	+	13.7833i	0.679882	+	1.17759i	−0.295134	+	0.955456i	$0.595364\pi$
$138$	−3.14880	+	5.45389i	−0.268044	+	0.464266i
$139$	−5.06008	−	8.76432i	−0.429191	−	0.743380i	0.567611	−	0.823297i	$-0.307868\pi$
$139$	−5.06008	−	8.76432i	−0.429191	−	0.743380i	−0.996802	+	0.0799168i	$0.974535\pi$
$140$	6.87129			0.580730
$141$	1.87901			0.158241
$142$	3.49849	+	6.05956i	0.293587	+	0.508507i
$143$	−5.32479	−	9.22280i	−0.445281	−	0.771249i
$144$	3.35114			0.279262
$145$	14.5901			1.21164
$146$	−3.09310	−	5.35740i	−0.255986	−	0.443382i
$147$	−1.01338	+	1.75523i	−0.0835825	+	0.144769i
$148$	0.275486	+	0.477156i	0.0226448	+	0.0392220i
$149$	−4.69925	+	8.13935i	−0.384978	+	0.666801i	−0.991766	−	0.128062i	$-0.959124\pi$
$149$	−4.69925	+	8.13935i	−0.384978	+	0.666801i	0.606788	+	0.794864i	$0.292458\pi$
$150$	1.32292	−	2.29137i	0.108016	−	0.187089i
$151$	10.2632			0.835210			0.417605	−	0.908629i	$-0.362870\pi$
$151$	10.2632			0.835210			0.417605	+	0.908629i	$0.362870\pi$
$152$		0			0
$153$	16.6524			1.34627
$154$	2.34458	−	4.06093i	0.188931	−	0.327239i
$155$	−8.95814	+	15.5160i	−0.719535	+	1.24627i
$156$	7.99463	+	13.8471i	0.640083	+	1.10866i
$157$	−1.48694	+	2.57545i	−0.118671	+	0.205543i	−0.919241	−	0.393695i	$-0.871197\pi$
$157$	−1.48694	+	2.57545i	−0.118671	+	0.205543i	0.800571	+	0.599239i	$0.204530\pi$
$158$	2.95579	+	5.11958i	0.235150	+	0.407292i
$159$	3.70530			0.293849
$160$	2.45965			0.194452
$161$	−3.49047	−	6.04568i	−0.275088	−	0.476466i
$162$	−3.91164	−	6.77516i	−0.307327	−	0.532307i
$163$	5.59191			0.437992			0.218996	−	0.975726i	$-0.429722\pi$
$163$	5.59191			0.437992			0.218996	+	0.975726i	$0.429722\pi$
$164$	2.60741			0.203605
$165$	−5.20234	−	9.01071i	−0.405001	−	0.701483i
$166$	7.58866	−	13.1439i	0.588994	−	1.02017i
$167$	−3.54180	−	6.13458i	−0.274073	−	0.474708i	0.695828	−	0.718209i	$-0.255038\pi$
$167$	−3.54180	−	6.13458i	−0.274073	−	0.474708i	−0.969901	+	0.243500i	$0.921704\pi$
$168$	−3.52015	+	6.09707i	−0.271585	+	0.470399i
$169$	−13.6268	+	23.6024i	−1.04822	+	1.81557i
$170$	12.2224			0.937418
$171$		0			0
$172$	2.87129			0.218934
$173$	−11.5104	+	19.9366i	−0.875120	+	1.51575i	−0.0184843	+	0.999829i	$0.505884\pi$
$173$	−11.5104	+	19.9366i	−0.875120	+	1.51575i	−0.856635	+	0.515922i	$0.827449\pi$
$174$	−7.47449	+	12.9462i	−0.566639	+	0.981448i
$175$	1.46647	+	2.54000i	0.110855	+	0.192006i
$176$	0.839266	−	1.45365i	0.0632620	−	0.109573i
$177$	−6.25325	−	10.8310i	−0.470023	−	0.814104i
$178$	6.90502			0.517553
$179$	−8.21471			−0.613996			−0.306998	−	0.951710i	$-0.599325\pi$
$179$	−8.21471			−0.613996			−0.306998	+	0.951710i	$0.599325\pi$
$180$	4.12132	+	7.13833i	0.307185	+	0.532060i
$181$	−6.49994	−	11.2582i	−0.483137	−	0.836818i	0.516676	−	0.856181i	$-0.327169\pi$
$181$	−6.49994	−	11.2582i	−0.483137	−	0.836818i	−0.999813	+	0.0193635i	$0.993836\pi$
$182$	−17.7242			−1.31381
$183$	23.5303			1.73941
$184$	−1.24945	−	2.16411i	−0.0921108	−	0.159541i
$185$	−0.677599	+	1.17364i	−0.0498181	+	0.0862874i
$186$	−9.17848	−	15.8976i	−0.672998	−	1.16567i
$187$	4.17046	−	7.22345i	0.304974	−	0.528231i
$188$	−0.372797	+	0.645703i	−0.0271890	+	0.0470927i
$189$	−2.47214			−0.179821
$190$		0			0
$191$	6.57479			0.475735			0.237868	−	0.971298i	$-0.423552\pi$
$191$	6.57479			0.475735			0.237868	+	0.971298i	$0.423552\pi$
$192$	−1.26007	+	2.18251i	−0.0909380	+	0.157509i
$193$	13.4413	−	23.2810i	0.967527	−	1.67581i	0.264859	−	0.964287i	$-0.414675\pi$
$193$	13.4413	−	23.2810i	0.967527	−	1.67581i	0.702667	−	0.711518i	$-0.251992\pi$
$194$	−7.19369	−	12.4598i	−0.516477	−	0.894564i
$195$	−19.6640	+	34.0590i	−1.40817	+	2.43902i
$196$	−0.402113	−	0.696480i	−0.0287224	−	0.0497486i
$197$	−9.84940			−0.701741			−0.350870	−	0.936424i	$-0.614114\pi$
$197$	−9.84940			−0.701741			−0.350870	+	0.936424i	$0.614114\pi$
$198$	5.62500			0.399751
$199$	10.2331	+	17.7242i	0.725402	+	1.25643i	0.958808	+	0.284053i	$0.0916793\pi$
$199$	10.2331	+	17.7242i	0.725402	+	1.25643i	−0.233407	+	0.972379i	$0.574987\pi$
$200$	0.524938	+	0.909219i	0.0371187	+	0.0642915i
$201$	−29.1340			−2.05495
$202$	−11.2829			−0.793864
$203$	−8.28553	−	14.3510i	−0.581530	−	1.00724i
$204$	−6.26153	+	10.8453i	−0.438394	+	0.759322i
$205$	3.20666	+	5.55410i	0.223963	+	0.387915i
$206$	−7.41399	+	12.8414i	−0.516557	+	0.894703i
$207$	4.18709	−	7.25225i	0.291023	−	0.504066i
$208$	−6.34458			−0.439917
$209$		0			0
$210$	−17.3167			−1.19496
$211$	4.05815	−	7.02892i	0.279374	−	0.483891i	−0.691855	−	0.722036i	$-0.743206\pi$
$211$	4.05815	−	7.02892i	0.279374	−	0.483891i	0.971229	+	0.238146i	$0.0765396\pi$
$212$	−0.735136	+	1.27329i	−0.0504893	+	0.0874501i
$213$	−8.81671	−	15.2710i	−0.604111	−	1.04635i
$214$	1.41424	−	2.44954i	0.0966757	−	0.167447i
$215$	3.53118	+	6.11619i	0.240825	+	0.417120i
$216$	−0.884927			−0.0602117
$217$	20.3488			1.38137
$218$	−0.862695	−	1.49423i	−0.0584291	−	0.101202i
$219$	7.79506	+	13.5014i	0.526741	+	0.912342i
$220$	4.12860			0.278350
$221$	−31.5273			−2.12076
$222$	−0.694265	−	1.20250i	−0.0465960	−	0.0807067i
$223$	5.37701	−	9.31326i	0.360071	−	0.623662i	−0.627901	−	0.778293i	$-0.716086\pi$
$223$	5.37701	−	9.31326i	0.360071	−	0.623662i	0.987972	+	0.154631i	$0.0494190\pi$
$224$	−1.39680	−	2.41933i	−0.0933278	−	0.161648i
$225$	−1.75914	+	3.04692i	−0.117276	+	0.203128i
$226$	0.213892	−	0.370473i	0.0142279	−	0.0246435i
$227$	−27.0936			−1.79827			−0.899133	−	0.437676i	$-0.855802\pi$
$227$	−27.0936			−1.79827			−0.899133	+	0.437676i	$0.855802\pi$
$228$		0			0
$229$	9.46557			0.625503			0.312751	−	0.949835i	$-0.398749\pi$
$229$	9.46557			0.625503			0.312751	+	0.949835i	$0.398749\pi$
$230$	3.07321	−	5.32296i	0.202642	−	0.350986i
$231$	−5.90868	+	10.2341i	−0.388762	+	0.673356i
$232$	−2.96589	−	5.13708i	−0.194720	−	0.337266i
$233$	−11.4311	+	19.7992i	−0.748873	+	1.29709i	0.199490	+	0.979900i	$0.436071\pi$
$233$	−11.4311	+	19.7992i	−0.748873	+	1.29709i	−0.948363	+	0.317186i	$0.897262\pi$
$234$	−10.6308	−	18.4131i	−0.694956	−	1.20370i
$235$	−1.83390			−0.119630
$236$	4.96261			0.323038
$237$	−7.44903	−	12.9021i	−0.483866	−	0.838081i
$238$	−6.94095	−	12.0221i	−0.449915	−	0.779276i
$239$	8.66611			0.560564			0.280282	−	0.959918i	$-0.409572\pi$
$239$	8.66611			0.560564			0.280282	+	0.959918i	$0.409572\pi$
$240$	−6.19868			−0.400123
$241$	2.82913	+	4.90020i	0.182240	+	0.315649i	0.942643	−	0.333802i	$-0.108332\pi$
$241$	2.82913	+	4.90020i	0.182240	+	0.315649i	−0.760403	+	0.649452i	$0.774998\pi$
$242$	−4.09127	+	7.08628i	−0.262997	+	0.455523i
$243$	11.1853	+	19.3735i	0.717537	+	1.24281i
$244$	−4.66843	+	8.08596i	−0.298866	+	0.517650i
$245$	0.989057	−	1.71310i	0.0631885	−	0.109446i
$246$	−6.57106			−0.418956
$247$		0			0
$248$	7.28408			0.462539
$249$	−19.1245	+	33.1247i	−1.21197	+	2.09919i
$250$	4.85796	−	8.41423i	0.307244	−	0.532163i
$251$	6.77762	+	11.7392i	0.427799	+	0.740970i	0.996677	−	0.0814518i	$-0.0259557\pi$
$251$	6.77762	+	11.7392i	0.427799	+	0.740970i	−0.568878	+	0.822422i	$0.692622\pi$
$252$	4.68088	−	8.10752i	0.294868	−	0.510726i
$253$	−2.09724	−	3.63253i	−0.131853	−	0.228375i
$254$	−1.13632			−0.0712988
$255$	−30.8023			−1.92892
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	5.01963	+	8.69425i	0.313116	+	0.542332i	0.979035	−	0.203691i	$-0.0652939\pi$
$257$	5.01963	+	8.69425i	0.313116	+	0.542332i	−0.665919	+	0.746024i	$0.731961\pi$
$258$	−7.23607			−0.450498
$259$	1.53920			0.0956411
$260$	−7.80272	−	13.5147i	−0.483904	−	0.838146i
$261$	9.93912	−	17.2151i	0.615216	−	1.06559i
$262$	−8.92075	−	15.4512i	−0.551126	−	0.954578i
$263$	9.41309	−	16.3040i	0.580436	−	1.00534i	−0.414992	−	0.909825i	$-0.636215\pi$
$263$	9.41309	−	16.3040i	0.580436	−	1.00534i	0.995428	−	0.0955194i	$-0.0304512\pi$
$264$	−2.11507	+	3.66341i	−0.130174	+	0.225468i
$265$	−3.61635			−0.222151
$266$		0			0
$267$	−17.4017			−1.06496
$268$	5.78022	−	10.0116i	0.353083	−	0.611558i
$269$	−8.19134	+	14.1878i	−0.499435	+	0.865046i	−1.00000		0.000652557i	$-0.999792\pi$
$269$	−8.19134	+	14.1878i	−0.499435	+	0.865046i	0.500565	+	0.865699i	$0.333126\pi$
$270$	−1.08831	−	1.88500i	−0.0662321	−	0.114717i
$271$	1.38342	−	2.39615i	0.0840367	−	0.145556i	−0.820944	−	0.571009i	$-0.806552\pi$
$271$	1.38342	−	2.39615i	0.0840367	−	0.145556i	0.904980	+	0.425453i	$0.139885\pi$
$272$	−2.48459	−	4.30343i	−0.150650	−	0.260934i
$273$	44.6677			2.70341
$274$	15.9156			0.961499
$275$	0.881125	+	1.52615i	0.0531338	+	0.0920305i
$276$	3.14880	+	5.45389i	0.189536	+	0.328285i
$277$	24.5321			1.47399			0.736996	−	0.675897i	$-0.236244\pi$
$277$	24.5321			1.47399			0.736996	+	0.675897i	$0.236244\pi$
$278$	−10.1202			−0.606967
$279$	12.2050	+	21.1397i	0.730694	+	1.26560i
$280$	3.43564	−	5.95071i	0.205319	−	0.355623i
$281$	5.08518	+	8.80779i	0.303356	+	0.525429i	0.976894	−	0.213724i	$-0.0685594\pi$
$281$	5.08518	+	8.80779i	0.303356	+	0.525429i	−0.673538	+	0.739153i	$0.735226\pi$
$282$	0.939503	−	1.62727i	0.0559466	−	0.0969023i
$283$	−13.8339	+	23.9610i	−0.822340	+	1.42433i	0.0815955	+	0.996666i	$0.473998\pi$
$283$	−13.8339	+	23.9610i	−0.822340	+	1.42433i	−0.903935	+	0.427669i	$0.859335\pi$
$284$	6.99698			0.415195
$285$		0			0
$286$	−10.6496			−0.629722
$287$	3.64204	−	6.30820i	0.214983	−	0.372361i
$288$	1.67557	−	2.90217i	0.0987339	−	0.171012i
$289$	−3.84635	−	6.66207i	−0.226256	−	0.391887i
$290$	7.29506	−	12.6354i	0.428380	−	0.741977i
$291$	18.1292	+	31.4006i	1.06275	+	1.84074i
$292$	−6.18619			−0.362020
$293$	−23.8386			−1.39267			−0.696333	−	0.717719i	$-0.745186\pi$
$293$	−23.8386			−1.39267			−0.696333	+	0.717719i	$0.745186\pi$
$294$	1.01338	+	1.75523i	0.0591018	+	0.102367i
$295$	6.10314	+	10.5710i	0.355339	+	0.615465i
$296$	0.550972			0.0320246
$297$	−1.48538			−0.0861904
$298$	4.69925	+	8.13935i	0.272221	+	0.471500i
$299$	−7.92724	+	13.7304i	−0.458444	+	0.794049i
$300$	−1.32292	−	2.29137i	−0.0763789	−	0.132292i
$301$	4.01062	−	6.94660i	0.231168	−	0.400395i
$302$	5.13162	−	8.88822i	0.295291	−	0.511460i
$303$	28.4346			1.63353
$304$		0			0
$305$	−22.9654			−1.31500
$306$	8.32620	−	14.4214i	0.475977	−	0.824417i
$307$	12.9942	−	22.5066i	0.741619	−	1.28452i	−0.210138	−	0.977672i	$-0.567391\pi$
$307$	12.9942	−	22.5066i	0.741619	−	1.28452i	0.951758	−	0.306851i	$-0.0992752\pi$
$308$	−2.34458	−	4.06093i	−0.133595	−	0.231393i
$309$	18.6843	−	32.3622i	1.06291	−	1.84102i
$310$	8.95814	+	15.5160i	0.508788	+	0.881247i
$311$	−23.1043			−1.31013			−0.655063	−	0.755574i	$-0.727358\pi$
$311$	−23.1043			−1.31013			−0.655063	+	0.755574i	$0.727358\pi$
$312$	15.9893			0.905214
$313$	−6.13235	−	10.6215i	−0.346621	−	0.600365i	0.639026	−	0.769185i	$-0.279338\pi$
$313$	−6.13235	−	10.6215i	−0.346621	−	0.600365i	−0.985647	+	0.168820i	$0.946004\pi$
$314$	1.48694	+	2.57545i	0.0839127	+	0.145341i
$315$	23.0267			1.29741
$316$	5.91158			0.332552
$317$	−0.136152	−	0.235823i	−0.00764708	−	0.0132451i	0.862177	−	0.506608i	$-0.169101\pi$
$317$	−0.136152	−	0.235823i	−0.00764708	−	0.0132451i	−0.869824	+	0.493363i	$0.835767\pi$
$318$	1.85265	−	3.20888i	0.103891	−	0.179945i
$319$	−4.97834	−	8.62275i	−0.278734	−	0.482781i
$320$	1.22982	−	2.13012i	0.0687493	−	0.119077i
$321$	−3.56410	+	6.17320i	−0.198929	+	0.344555i
$322$	−6.98095			−0.389033
$323$		0			0
$324$	−7.82328			−0.434626
$325$	3.33051	−	5.76861i	0.184743	−	0.319985i
$326$	2.79595	−	4.84273i	0.154854	−	0.268214i
$327$	2.17412	+	3.76568i	0.120229	+	0.208243i
$328$	1.30371	−	2.25809i	0.0719851	−	0.124682i
$329$	1.04145	+	1.80384i	0.0574168	+	0.0994488i
$330$	−10.4047			−0.572759
$331$	19.9930			1.09891			0.549457	−	0.835522i	$-0.314835\pi$
$331$	19.9930			1.09891			0.549457	+	0.835522i	$0.314835\pi$
$332$	−7.58866	−	13.1439i	−0.416482	−	0.721368i
$333$	0.923192	+	1.59902i	0.0505906	+	0.0876256i
$334$	−7.08361			−0.387598
$335$	28.4346			1.55355
$336$	3.52015	+	6.09707i	0.192040	+	0.332623i
$337$	−8.64121	+	14.9670i	−0.470717	+	0.815305i	−0.999439	−	0.0334897i	$-0.989338\pi$
$337$	−8.64121	+	14.9670i	−0.470717	+	0.815305i	0.528722	+	0.848795i	$0.322671\pi$
$338$	13.6268	+	23.6024i	0.741202	+	1.28380i
$339$	−0.539040	+	0.933645i	−0.0292767	+	0.0507086i
$340$	6.11121	−	10.5849i	0.331427	−	0.574049i
$341$	12.2266			0.662105
$342$		0			0
$343$	17.3085			0.934573
$344$	1.43564	−	2.48661i	0.0774047	−	0.134069i
$345$	−7.74495	+	13.4146i	−0.416974	+	0.722220i
$346$	11.5104	+	19.9366i	0.618803	+	1.07180i
$347$	9.27279	−	16.0609i	0.497789	−	0.862197i	−0.502207	−	0.864747i	$-0.667479\pi$
$347$	9.27279	−	16.0609i	0.497789	−	0.862197i	0.999997	+	0.00255065i	$0.000811898\pi$
$348$	7.47449	+	12.9462i	0.400674	+	0.693989i
$349$	−20.1210			−1.07705			−0.538527	−	0.842609i	$-0.681019\pi$
$349$	−20.1210			−1.07705			−0.538527	+	0.842609i	$0.681019\pi$
$350$	2.93294			0.156772
$351$	2.80724	+	4.86229i	0.149840	+	0.259530i
$352$	−0.839266	−	1.45365i	−0.0447330	−	0.0774799i
$353$	24.0557			1.28035			0.640177	−	0.768227i	$-0.278861\pi$
$353$	24.0557			1.28035			0.640177	+	0.768227i	$0.278861\pi$
$354$	−12.5065			−0.664713
$355$	8.60506	+	14.9044i	0.456709	+	0.791044i
$356$	3.45251	−	5.97992i	0.182983	−	0.316935i
$357$	17.4922	+	30.2974i	0.925787	+	1.60351i
$358$	−4.10736	+	7.11415i	−0.217081	+	0.375994i
$359$	5.42673	−	9.39937i	0.286412	−	0.496080i	−0.686539	−	0.727093i	$-0.740871\pi$
$359$	5.42673	−	9.39937i	0.286412	−	0.496080i	0.972951	+	0.231013i	$0.0742041\pi$
$360$	8.24263			0.434425
$361$		0			0
$362$	−12.9999			−0.683259
$363$	10.3106	−	17.8585i	0.541166	−	0.937327i
$364$	−8.86212	+	15.3496i	−0.464501	+	0.804540i
$365$	−7.60793	−	13.1773i	−0.398217	−	0.689733i
$366$	11.7651	−	20.3778i	0.614973	−	1.06516i
$367$	16.3060	+	28.2429i	0.851168	+	1.47427i	0.880155	+	0.474687i	$0.157439\pi$
$367$	16.3060	+	28.2429i	0.851168	+	1.47427i	−0.0289868	+	0.999580i	$0.509228\pi$
$368$	−2.49890			−0.130264
$369$	8.73781			0.454872
$370$	0.677599	+	1.17364i	0.0352267	+	0.0610144i
$371$	2.05368	+	3.55707i	0.106622	+	0.184674i
$372$	−18.3570			−0.951764
$373$	5.30198			0.274526			0.137263	−	0.990535i	$-0.456169\pi$
$373$	5.30198			0.274526			0.137263	+	0.990535i	$0.456169\pi$
$374$	−4.17046	−	7.22345i	−0.215649	−	0.373515i
$375$	−12.2428	+	21.2051i	−0.632214	+	1.09503i
$376$	0.372797	+	0.645703i	0.0192255	+	0.0332996i
$377$	−18.8173	+	32.5926i	−0.969142	+	1.67860i
$378$	−1.23607	+	2.14093i	−0.0635765	+	0.110118i
$379$	−24.6656			−1.26699			−0.633494	−	0.773748i	$-0.718380\pi$
$379$	−24.6656			−1.26699			−0.633494	+	0.773748i	$0.718380\pi$
$380$		0			0
$381$	2.86368			0.146711
$382$	3.28740	−	5.69394i	0.168198	−	0.291327i
$383$	1.82208	−	3.15593i	0.0931039	−	0.161261i	−0.815712	−	0.578459i	$-0.803654\pi$
$383$	1.82208	−	3.15593i	0.0931039	−	0.161261i	0.908816	+	0.417198i	$0.136988\pi$
$384$	1.26007	+	2.18251i	0.0643029	+	0.111376i
$385$	5.76684	−	9.98845i	0.293905	−	0.509059i
$386$	−13.4413	−	23.2810i	−0.684145	−	1.18497i
$387$	9.62209			0.489118
$388$	−14.3874			−0.730408
$389$	−1.39677	−	2.41927i	−0.0708189	−	0.122662i	0.828442	−	0.560076i	$-0.189228\pi$
$389$	−1.39677	−	2.41927i	−0.0708189	−	0.122662i	−0.899260	+	0.437414i	$0.855895\pi$
$390$	19.6640	+	34.0590i	0.995725	+	1.72465i
$391$	−12.4175			−0.627979
$392$	−0.804226			−0.0406196
$393$	22.4816	+	38.9393i	1.13405	+	1.96423i
$394$	−4.92470	+	8.52983i	−0.248103	+	0.429727i
$395$	7.27021	+	12.5924i	0.365804	+	0.633591i
$396$	2.81250	−	4.87139i	0.141333	−	0.244797i
$397$	19.7551	−	34.2168i	0.991478	−	1.71729i	0.382919	−	0.923782i	$-0.374919\pi$
$397$	19.7551	−	34.2168i	0.991478	−	1.71729i	0.608559	−	0.793509i	$-0.291748\pi$
$398$	20.4661			1.02587
$399$		0			0
$400$	1.04988			0.0524938
$401$	−9.31073	+	16.1267i	−0.464956	+	0.805327i	−0.999200	−	0.0400033i	$-0.987263\pi$
$401$	−9.31073	+	16.1267i	−0.464956	+	0.805327i	0.534244	+	0.845331i	$0.320596\pi$
$402$	−14.5670	+	25.2308i	−0.726536	+	1.25840i
$403$	−23.1072	−	40.0228i	−1.15105	−	1.99368i
$404$	−5.64146	+	9.77130i	−0.280673	+	0.486140i
$405$	−9.62126	−	16.6645i	−0.478084	−	0.828066i
$406$	−16.5711			−0.822408
$407$	0.924824			0.0458418
$408$	6.26153	+	10.8453i	0.309992	+	0.536921i
$409$	−8.57164	−	14.8465i	−0.423840	−	0.734113i	0.572471	−	0.819925i	$-0.305985\pi$
$409$	−8.57164	−	14.8465i	−0.423840	−	0.734113i	−0.996311	+	0.0858120i	$0.972652\pi$
$410$	6.41332			0.316731
$411$	−40.1098			−1.97847
$412$	7.41399	+	12.8414i	0.365261	+	0.632651i
$413$	6.93179	−	12.0062i	0.341091	−	0.590787i
$414$	−4.18709	−	7.25225i	−0.205784	−	0.356429i
$415$	18.6654	−	32.3295i	0.916251	−	1.58699i
$416$	−3.17229	+	5.49456i	−0.155534	+	0.269393i
$417$	25.5043			1.24895
$418$		0			0
$419$	−18.5042			−0.903989			−0.451995	−	0.892021i	$-0.649287\pi$
$419$	−18.5042			−0.903989			−0.451995	+	0.892021i	$0.649287\pi$
$420$	−8.65833	+	14.9967i	−0.422483	+	0.731762i
$421$	−8.09980	+	14.0293i	−0.394760	+	0.683745i	−0.993071	−	0.117520i	$-0.962506\pi$
$421$	−8.09980	+	14.0293i	−0.394760	+	0.683745i	0.598310	+	0.801264i	$0.295839\pi$
$422$	−4.05815	−	7.02892i	−0.197548	−	0.342162i
$423$	−1.24929	+	2.16384i	−0.0607428	+	0.105210i
$424$	0.735136	+	1.27329i	0.0357013	+	0.0618365i
$425$	5.21702			0.253062
$426$	−17.6334			−0.854342
$427$	13.0417	+	22.5890i	0.631134	+	1.09316i
$428$	−1.41424	−	2.44954i	−0.0683600	−	0.118403i
$429$	26.8385			1.29577
$430$	7.06236			0.340577
$431$	6.34983	+	10.9982i	0.305861	+	0.529766i	0.977453	−	0.211155i	$-0.0677225\pi$
$431$	6.34983	+	10.9982i	0.305861	+	0.529766i	−0.671592	+	0.740921i	$0.734389\pi$
$432$	−0.442463	+	0.766369i	−0.0212880	+	0.0368720i
$433$	7.11751	+	12.3279i	0.342046	+	0.592441i	0.984813	−	0.173621i	$-0.0555468\pi$
$433$	7.11751	+	12.3279i	0.342046	+	0.592441i	−0.642767	+	0.766062i	$0.722213\pi$
$434$	10.1744	−	17.6226i	0.488388	−	0.845912i
$435$	−18.3846	+	31.8431i	−0.881475	+	1.52676i
$436$	−1.72539			−0.0826312
$437$		0			0
$438$	15.5901			0.744924
$439$	14.0950	−	24.4133i	0.672718	−	1.16518i	−0.304412	−	0.952540i	$-0.598460\pi$
$439$	14.0950	−	24.4133i	0.672718	−	1.16518i	0.977130	−	0.212642i	$-0.0682067\pi$
$440$	2.06430	−	3.57547i	0.0984116	−	0.170454i
$441$	−1.34754	−	2.33400i	−0.0641685	−	0.111143i
$442$	−15.7637	+	27.3035i	−0.749801	+	1.29869i
$443$	16.4972	+	28.5740i	0.783805	+	1.35759i	0.929711	+	0.368291i	$0.120057\pi$
$443$	16.4972	+	28.5740i	0.783805	+	1.35759i	−0.145906	+	0.989298i	$0.546610\pi$
$444$	−1.38853			−0.0658967
$445$	16.9839			0.805115
$446$	−5.37701	−	9.31326i	−0.254609	−	0.440995i
$447$	−11.8428	−	20.5124i	−0.560146	−	0.970201i
$448$	−2.79360			−0.131985
$449$	17.1975			0.811601			0.405801	−	0.913962i	$-0.366993\pi$
$449$	17.1975			0.811601			0.405801	+	0.913962i	$0.366993\pi$
$450$	1.75914	+	3.04692i	0.0829267	+	0.143633i
$451$	2.18831	−	3.79027i	0.103044	−	0.178477i
$452$	−0.213892	−	0.370473i	−0.0100607	−	0.0174256i
$453$	−12.9324	+	22.3996i	−0.607618	+	1.05243i
$454$	−13.5468	+	23.4637i	−0.635783	+	1.10121i
$455$	−43.5954			−2.04378
$456$		0			0
$457$	−31.1517			−1.45722			−0.728608	−	0.684931i	$-0.759832\pi$
$457$	−31.1517			−1.45722			−0.728608	+	0.684931i	$0.759832\pi$
$458$	4.73279	−	8.19743i	0.221149	−	0.383041i
$459$	−2.19868	+	3.80822i	−0.102626	+	0.177753i
$460$	−3.07321	−	5.32296i	−0.143289	−	0.248184i
$461$	−7.77050	+	13.4589i	−0.361908	+	0.626843i	−0.988275	−	0.152685i	$-0.951208\pi$
$461$	−7.77050	+	13.4589i	−0.361908	+	0.626843i	0.626367	+	0.779528i	$0.284541\pi$
$462$	5.90868	+	10.2341i	0.274897	+	0.476135i
$463$	20.6648			0.960374			0.480187	−	0.877166i	$-0.340569\pi$
$463$	20.6648			0.960374			0.480187	+	0.877166i	$0.340569\pi$
$464$	−5.93179			−0.275376
$465$	−22.5758	−	39.1025i	−1.04693	−	1.81333i
$466$	11.4311	+	19.7992i	0.529533	+	0.917178i
$467$	−28.4830			−1.31803			−0.659017	−	0.752128i	$-0.729028\pi$
$467$	−28.4830			−1.31803			−0.659017	+	0.752128i	$0.729028\pi$
$468$	−21.2616			−0.982816
$469$	−16.1477	−	27.9686i	−0.745629	−	1.29147i
$470$	−0.916949	+	1.58820i	−0.0422957	+	0.0732583i
$471$	−3.74730	−	6.49052i	−0.172667	−	0.299067i
$472$	2.48131	−	4.29775i	0.114211	−	0.197820i
$473$	2.40977	−	4.17385i	0.110802	−	0.191914i
$474$	−14.8981			−0.684290
$475$		0			0
$476$	−13.8819			−0.636276
$477$	−2.46354	+	4.26698i	−0.112798	+	0.195372i
$478$	4.33306	−	7.50508i	0.198189	−	0.343274i
$479$	5.23632	+	9.06958i	0.239254	+	0.414400i	0.960500	−	0.278279i	$-0.0897639\pi$
$479$	5.23632	+	9.06958i	0.239254	+	0.414400i	−0.721247	+	0.692678i	$0.756431\pi$
$480$	−3.09934	+	5.36821i	−0.141465	+	0.245024i
$481$	−1.74784	−	3.02735i	−0.0796947	−	0.138035i
$482$	5.65826			0.257727
$483$	17.5930			0.800510
$484$	4.09127	+	7.08628i	0.185967	+	0.322104i
$485$	−17.6940	−	30.6468i	−0.803441	−	1.39160i
$486$	22.3706			1.01475
$487$	−2.29894			−0.104175			−0.0520875	−	0.998643i	$-0.516587\pi$
$487$	−2.29894			−0.104175			−0.0520875	+	0.998643i	$0.516587\pi$
$488$	4.66843	+	8.08596i	0.211330	+	0.366034i
$489$	−7.04622	+	12.2044i	−0.318641	+	0.551902i
$490$	−0.989057	−	1.71310i	−0.0446810	−	0.0773898i
$491$	−6.08059	+	10.5319i	−0.274413	+	0.475297i	−0.969987	−	0.243157i	$-0.921817\pi$
$491$	−6.08059	+	10.5319i	−0.274413	+	0.475297i	0.695574	+	0.718455i	$0.255150\pi$
$492$	−3.28553	+	5.69071i	−0.148123	+	0.256557i
$493$	−29.4761			−1.32754
$494$		0			0
$495$	13.8355			0.621860
$496$	3.64204	−	6.30820i	0.163532	−	0.283246i
$497$	9.77340	−	16.9280i	0.438397	−	0.759326i
$498$	19.1245	+	33.1247i	0.856991	+	1.48435i
$499$	−7.56742	+	13.1072i	−0.338764	+	0.586757i	−0.984201	−	0.177057i	$-0.943342\pi$
$499$	−7.56742	+	13.1072i	−0.338764	+	0.586757i	0.645436	+	0.763814i	$0.276676\pi$
$500$	−4.85796	−	8.41423i	−0.217255	−	0.376296i
$501$	17.8517			0.797556
$502$	13.5552			0.605000
$503$	0.286841	+	0.496824i	0.0127896	+	0.0221523i	0.872349	−	0.488883i	$-0.162595\pi$
$503$	0.286841	+	0.496824i	0.0127896	+	0.0221523i	−0.859560	+	0.511035i	$0.829262\pi$
$504$	−4.68088	−	8.10752i	−0.208503	−	0.361138i
$505$	−27.7520			−1.23495
$506$	−4.19449			−0.186468
$507$	−34.3416	−	59.4814i	−1.52516	−	2.64166i
$508$	−0.568158	+	0.984079i	−0.0252079	+	0.0436614i
$509$	−13.1081	−	22.7039i	−0.581008	−	1.00633i	−0.995360	−	0.0962184i	$-0.969325\pi$
$509$	−13.1081	−	22.7039i	−0.581008	−	1.00633i	0.414353	−	0.910116i	$-0.364008\pi$
$510$	−15.4012	+	26.6756i	−0.681975	+	1.18121i
$511$	−8.64089	+	14.9665i	−0.382250	+	0.662077i
$512$	−1.00000			−0.0441942
$513$		0			0
$514$	10.0393			0.442813
$515$	−18.2358	+	31.5854i	−0.803566	+	1.39182i
$516$	−3.61803	+	6.26662i	−0.159275	+	0.275873i
$517$	0.625751	+	1.08383i	0.0275205	+	0.0476669i
$518$	0.769599	−	1.33298i	0.0338142	−	0.0585680i
$519$	−29.0079	−	50.2432i	−1.27331	−	2.20543i
$520$	−15.6054			−0.684344
$521$	12.9637			0.567948			0.283974	−	0.958832i	$-0.408347\pi$
$521$	12.9637			0.567948			0.283974	+	0.958832i	$0.408347\pi$
$522$	−9.93912	−	17.2151i	−0.435024	−	0.753483i
$523$	8.88963	+	15.3973i	0.388716	+	0.673276i	0.992277	−	0.124041i	$-0.0395853\pi$
$523$	8.88963	+	15.3973i	0.388716	+	0.673276i	−0.603561	+	0.797317i	$0.706252\pi$
$524$	−17.8415			−0.779410
$525$	−7.39144			−0.322589
$526$	−9.41309	−	16.3040i	−0.410430	−	0.710886i
$527$	18.0979	−	31.3465i	0.788358	−	1.36548i
$528$	2.11507	+	3.66341i	0.0920467	+	0.159430i
$529$	8.37774	−	14.5107i	0.364250	−	0.630899i
$530$	−1.80818	+	3.13185i	−0.0785421	+	0.136039i
$531$	16.6304			0.721698
$532$		0			0
$533$	−16.5429			−0.716554
$534$	−8.70083	+	15.0703i	−0.376522	+	0.652155i
$535$	3.47854	−	6.02501i	0.150391	−	0.260484i
$536$	−5.78022	−	10.0116i	−0.249668	−	0.432437i
$537$	10.3511	−	17.9287i	0.446685	−	0.773681i
$538$	8.19134	+	14.1878i	0.353154	+	0.611680i
$539$	−1.34992			−0.0581451
$540$	−2.17661			−0.0936664
$541$	2.67209	+	4.62820i	0.114882	+	0.198982i	0.917733	−	0.397199i	$-0.130018\pi$
$541$	2.67209	+	4.62820i	0.114882	+	0.198982i	−0.802851	+	0.596180i	$0.796684\pi$
$542$	−1.38342	−	2.39615i	−0.0594229	−	0.102923i
$543$	32.7616			1.40594
$544$	−4.96917			−0.213052
$545$	−2.12193	−	3.67529i	−0.0908934	−	0.157432i
$546$	22.3338	−	38.6833i	0.955800	−	1.65549i
$547$	2.55056	+	4.41770i	0.109054	+	0.188887i	0.915387	−	0.402574i	$-0.131885\pi$
$547$	2.55056	+	4.41770i	0.109054	+	0.188887i	−0.806333	+	0.591461i	$0.798551\pi$
$548$	7.95782	−	13.7833i	0.339941	−	0.588795i
$549$	−15.6446	+	27.0972i	−0.667694	+	1.15648i
$550$	1.76225			0.0751426
$551$		0			0
$552$	6.29761			0.268044
$553$	8.25731	−	14.3021i	0.351137	−	0.608186i
$554$	12.2661	−	21.2454i	0.521135	−	0.902632i
$555$	−1.70765	−	2.95774i	−0.0724857	−	0.125549i
$556$	−5.06008	+	8.76432i	−0.214595	+	0.371690i
$557$	5.36176	+	9.28685i	0.227185	+	0.393496i	0.956973	−	0.290178i	$-0.0937144\pi$
$557$	5.36176	+	9.28685i	0.227185	+	0.393496i	−0.729788	+	0.683674i	$0.760381\pi$
$558$	24.4100			1.03336
$559$	−18.2171			−0.770502
$560$	−3.43564	−	5.95071i	−0.145182	−	0.251463i
$561$	10.5102	+	18.2041i	0.443740	+	0.768580i
$562$	10.1704			0.429011
$563$	−9.76285			−0.411455			−0.205728	−	0.978609i	$-0.565956\pi$
$563$	−9.76285			−0.411455			−0.205728	+	0.978609i	$0.565956\pi$
$564$	−0.939503	−	1.62727i	−0.0395602	−	0.0685203i
$565$	0.526100	−	0.911233i	0.0221332	−	0.0383358i
$566$	13.8339	+	23.9610i	0.581482	+	1.00716i
$567$	−10.9276	+	18.9271i	−0.458915	+	0.794864i
$568$	3.49849	−	6.05956i	0.146793	−	0.254254i
$569$	8.84194			0.370674			0.185337	−	0.982675i	$-0.440662\pi$
$569$	8.84194			0.370674			0.185337	+	0.982675i	$0.440662\pi$
$570$		0			0
$571$	22.8411			0.955871			0.477935	−	0.878395i	$-0.341385\pi$
$571$	22.8411			0.955871			0.477935	+	0.878395i	$0.341385\pi$
$572$	−5.32479	+	9.22280i	−0.222640	+	0.385625i
$573$	−8.28472	+	14.3496i	−0.346099	+	0.599461i
$574$	−3.64204	−	6.30820i	−0.152016	−	0.263299i
$575$	1.31177	−	2.27205i	0.0547046	−	0.0947511i
$576$	−1.67557	−	2.90217i	−0.0698154	−	0.120924i
$577$	−14.0176			−0.583560			−0.291780	−	0.956486i	$-0.594247\pi$
$577$	−14.0176			−0.583560			−0.291780	+	0.956486i	$0.594247\pi$
$578$	−7.69270			−0.319974
$579$	33.8741	+	58.6716i	1.40776	+	2.43831i
$580$	−7.29506	−	12.6354i	−0.302911	−	0.524657i
$581$	−42.3994			−1.75903
$582$	36.2583			1.50296
$583$	1.23395	+	2.13726i	0.0511049	+	0.0885163i
$584$	−3.09310	+	5.35740i	−0.127993	+	0.221691i
$585$	−26.1480	−	45.2897i	−1.08109	−	1.87250i
$586$	−11.9193	+	20.6448i	−0.492382	+	0.852830i
$587$	−10.5178	+	18.2174i	−0.434116	+	0.751911i	−0.997223	−	0.0744731i	$-0.976273\pi$
$587$	−10.5178	+	18.2174i	−0.434116	+	0.751911i	0.563107	+	0.826384i	$0.309606\pi$
$588$	2.02677			0.0835825
$589$		0			0
$590$	12.2063			0.502525
$591$	12.4110	−	21.4964i	0.510519	−	0.884245i
$592$	0.275486	−	0.477156i	0.0113224	−	0.0196110i
$593$	17.4596	+	30.2410i	0.716981	+	1.24185i	0.962190	+	0.272377i	$0.0878099\pi$
$593$	17.4596	+	30.2410i	0.716981	+	1.24185i	−0.245210	+	0.969470i	$0.578857\pi$
$594$	−0.742689	+	1.28637i	−0.0304729	+	0.0527806i
$595$	−17.0723	−	29.5701i	−0.699897	−	1.21226i
$596$	9.39851			0.384978
$597$	−51.5776			−2.11093
$598$	7.92724	+	13.7304i	0.324169	+	0.561477i
$599$	10.7553	+	18.6288i	0.439450	+	0.761150i	0.997647	−	0.0685583i	$-0.0218399\pi$
$599$	10.7553	+	18.6288i	0.439450	+	0.761150i	−0.558197	+	0.829709i	$0.688507\pi$
$600$	−2.64584			−0.108016
$601$	14.3417			0.585012			0.292506	−	0.956264i	$-0.405511\pi$
$601$	14.3417			0.585012			0.292506	+	0.956264i	$0.405511\pi$
$602$	−4.01062	−	6.94660i	−0.163461	−	0.283122i
$603$	19.3703	−	33.5504i	0.788821	−	1.36628i
$604$	−5.13162	−	8.88822i	−0.208803	−	0.361657i
$605$	−10.0631	+	17.4298i	−0.409122	+	0.708621i
$606$	14.2173	−	24.6251i	0.577539	−	1.00033i
$607$	10.3488			0.420046			0.210023	−	0.977696i	$-0.432646\pi$
$607$	10.3488			0.420046			0.210023	+	0.977696i	$0.432646\pi$
$608$		0			0
$609$	41.7615			1.69226
$610$	−11.4827	+	19.8886i	−0.464921	+	0.805267i
$611$	2.36524	−	4.09671i	0.0956873	−	0.165735i
$612$	−8.32620	−	14.4214i	−0.336567	−	0.582951i
$613$	−9.78370	+	16.9459i	−0.395160	+	0.684437i	−0.993122	−	0.117088i	$-0.962644\pi$
$613$	−9.78370	+	16.9459i	−0.395160	+	0.684437i	0.597962	+	0.801525i	$0.295978\pi$
$614$	−12.9942	−	22.5066i	−0.524404	−	0.908294i
$615$	−16.1625			−0.651735
$616$	−4.68915			−0.188931
$617$	2.96261	+	5.13139i	0.119270	+	0.206582i	0.919479	−	0.393140i	$-0.128611\pi$
$617$	2.96261	+	5.13139i	0.119270	+	0.206582i	−0.800208	+	0.599722i	$0.795278\pi$
$618$	−18.6843	−	32.3622i	−0.751594	−	1.30180i
$619$	8.03958			0.323138			0.161569	−	0.986861i	$-0.448345\pi$
$619$	8.03958			0.323138			0.161569	+	0.986861i	$0.448345\pi$
$620$	17.9163			0.719535
$621$	1.10567	+	1.91508i	0.0443692	+	0.0768496i
$622$	−11.5522	+	20.0089i	−0.463200	+	0.802286i
$623$	−9.64494	−	16.7055i	−0.386417	−	0.669293i
$624$	7.99463	−	13.8471i	0.320041	−	0.554328i
$625$	14.5736	−	25.2422i	0.582943	−	1.00969i
$626$	−12.2647			−0.490196
$627$		0			0
$628$	2.97387			0.118671
$629$	1.36894	−	2.37107i	0.0545831	−	0.0945408i
$630$	11.5133	−	19.9417i	0.458702	−	0.794495i
$631$	6.45032	+	11.1723i	0.256783	+	0.444762i	0.965378	−	0.260854i	$-0.0840040\pi$
$631$	6.45032	+	11.1723i	0.256783	+	0.444762i	−0.708595	+	0.705615i	$0.750671\pi$
$632$	2.95579	−	5.11958i	0.117575	−	0.203646i
$633$	10.2271	+	17.7139i	0.406492	+	0.704065i
$634$	−0.272305			−0.0108146
$635$	−2.79494			−0.110914
$636$	−1.85265	−	3.20888i	−0.0734623	−	0.127241i
$637$	2.55124	+	4.41887i	0.101084	+	0.175082i
$638$	−9.95669			−0.394189
$639$	23.4479			0.927584
$640$	−1.22982	−	2.13012i	−0.0486131	−	0.0842003i
$641$	−14.4319	+	24.9969i	−0.570028	+	0.987317i	0.426535	+	0.904471i	$0.359734\pi$
$641$	−14.4319	+	24.9969i	−0.570028	+	0.987317i	−0.996562	+	0.0828458i	$0.973599\pi$
$642$	3.56410	+	6.17320i	0.140664	+	0.243637i
$643$	−13.1697	+	22.8106i	−0.519363	+	0.899563i	0.480384	+	0.877058i	$0.340497\pi$
$643$	−13.1697	+	22.8106i	−0.519363	+	0.899563i	−0.999747	+	0.0225047i	$0.992836\pi$
$644$	−3.49047	+	6.04568i	−0.137544	+	0.238233i
$645$	−17.7982			−0.700803
$646$		0			0
$647$	−3.04601			−0.119751			−0.0598756	−	0.998206i	$-0.519070\pi$
$647$	−3.04601			−0.119751			−0.0598756	+	0.998206i	$0.519070\pi$
$648$	−3.91164	+	6.77516i	−0.153664	+	0.266153i
$649$	4.16495	−	7.21390i	0.163489	−	0.283170i
$650$	−3.33051	−	5.76861i	−0.130633	−	0.226264i
$651$	−25.6410	+	44.4116i	−1.00495	+	1.74063i
$652$	−2.79595	−	4.84273i	−0.109498	−	0.189656i
$653$	−15.1973			−0.594717			−0.297359	−	0.954766i	$-0.596106\pi$
$653$	−15.1973			−0.594717			−0.297359	+	0.954766i	$0.596106\pi$
$654$	4.34824			0.170030
$655$	−21.9419	−	38.0045i	−0.857342	−	1.48496i
$656$	−1.30371	−	2.25809i	−0.0509012	−	0.0881634i
$657$	−20.7308			−0.808786
$658$	2.08289			0.0811996
$659$	8.93704	+	15.4794i	0.348138	+	0.602992i	0.985919	−	0.167226i	$-0.0534808\pi$
$659$	8.93704	+	15.4794i	0.348138	+	0.602992i	−0.637781	+	0.770218i	$0.720148\pi$
$660$	−5.20234	+	9.01071i	−0.202501	+	0.350742i
$661$	18.9263	+	32.7812i	0.736146	+	1.27504i	0.954219	+	0.299110i	$0.0966898\pi$
$661$	18.9263	+	32.7812i	0.736146	+	1.27504i	−0.218072	+	0.975933i	$0.569977\pi$
$662$	9.99650	−	17.3144i	0.388525	−	0.672945i
$663$	39.7267	−	68.8087i	1.54286	−	2.67231i
$664$	−15.1773			−0.588994
$665$		0			0
$666$	1.84638			0.0715460
$667$	−7.41148	+	12.8371i	−0.286974	+	0.497053i
$668$	−3.54180	+	6.13458i	−0.137036	+	0.237354i
$669$	13.5509	+	23.4708i	0.523906	+	0.907433i
$670$	14.2173	−	24.6251i	0.549263	−	0.951351i
$671$	7.83611	+	13.5725i	0.302510	+	0.523962i
$672$	7.04029			0.271585
$673$	8.28461			0.319348			0.159674	−	0.987170i	$-0.448956\pi$
$673$	8.28461			0.319348			0.159674	+	0.987170i	$0.448956\pi$
$674$	8.64121	+	14.9670i	0.332847	+	0.576508i
$675$	−0.464532	−	0.804593i	−0.0178798	−	0.0309688i
$676$	27.2537			1.04822
$677$	18.3233			0.704223			0.352111	−	0.935958i	$-0.385464\pi$
$677$	18.3233			0.704223			0.352111	+	0.935958i	$0.385464\pi$
$678$	0.539040	+	0.933645i	0.0207017	+	0.0358564i
$679$	−20.0963	+	34.8079i	−0.771226	+	1.33580i
$680$	−6.11121	−	10.5849i	−0.234354	−	0.405914i
$681$	34.1399	−	59.1321i	1.30825	−	2.26595i
$682$	6.11328	−	10.5885i	0.234090	−	0.405455i
$683$	49.2217			1.88342			0.941709	−	0.336429i	$-0.109219\pi$
$683$	49.2217			1.88342			0.941709	+	0.336429i	$0.109219\pi$
$684$		0			0
$685$	39.1469			1.49573
$686$	8.65427	−	14.9896i	0.330422	−	0.572307i
$687$	−11.9273	+	20.6587i	−0.455055	+	0.788179i
$688$	−1.43564	−	2.48661i	−0.0547334	−	0.0948011i
$689$	4.66412	−	8.07850i	0.177689	−	0.307766i
$690$	7.74495	+	13.4146i	0.294845	+	0.510687i
$691$	16.6779			0.634458			0.317229	−	0.948349i	$-0.397248\pi$
$691$	16.6779			0.634458			0.317229	+	0.948349i	$0.397248\pi$
$692$	23.0208			0.875120
$693$	−7.85701	−	13.6087i	−0.298463	−	0.516953i
$694$	−9.27279	−	16.0609i	−0.351990	−	0.609665i
$695$	−24.8921			−0.944210
$696$	14.9490			0.566639
$697$	−6.47834	−	11.2208i	−0.245385	−	0.425019i
$698$	−10.0605	+	17.4253i	−0.380796	+	0.659558i
$699$	−28.8079	−	49.8968i	−1.08962	−	1.88727i
$700$	1.46647	−	2.54000i	0.0554273	−	0.0960029i
$701$	15.4533	−	26.7659i	0.583663	−	1.01093i	−0.411378	−	0.911465i	$-0.634952\pi$
$701$	15.4533	−	26.7659i	0.583663	−	1.01093i	0.995041	−	0.0994688i	$-0.0317143\pi$
$702$	5.61449			0.211905
$703$		0			0
$704$	−1.67853			−0.0632620
$705$	2.31085	−	4.00250i	0.0870315	−	0.150743i
$706$	12.0278	−	20.8328i	0.452674	−	0.784054i
$707$	15.7600	+	27.2972i	0.592716	+	1.02661i
$708$	−6.25325	+	10.8310i	−0.235012	+	0.407052i
$709$	−20.0528	−	34.7325i	−0.753098	−	1.30440i	−0.946314	−	0.323248i	$-0.895225\pi$
$709$	−20.0528	−	34.7325i	−0.753098	−	1.30440i	0.193216	−	0.981156i	$-0.438108\pi$
$710$	17.2101			0.645884
$711$	19.8105			0.742953
$712$	−3.45251	−	5.97992i	−0.129388	−	0.224107i
$713$	−9.10111	−	15.7636i	−0.340839	−	0.590351i
$714$	34.9845			1.30926
$715$	−26.1942			−0.979608
$716$	4.10736	+	7.11415i	0.153499	+	0.265868i
$717$	−10.9199	+	18.9139i	−0.407813	+	0.706352i
$718$	−5.42673	−	9.39937i	−0.202524	−	0.350781i
$719$	22.8264	−	39.5365i	0.851282	−	1.47446i	−0.0287690	−	0.999586i	$-0.509159\pi$
$719$	22.8264	−	39.5365i	0.851282	−	1.47446i	0.880051	−	0.474878i	$-0.157508\pi$
$720$	4.12132	−	7.13833i	0.153592	−	0.266030i
$721$	41.4235			1.54269
$722$		0			0
$723$	−14.2596			−0.530322
$724$	−6.49994	+	11.2582i	−0.241569	+	0.418409i
$725$	3.11382	−	5.39329i	0.115644	−	0.200302i
$726$	−10.3106	−	17.8585i	−0.382662	−	0.662790i
$727$	7.59053	−	13.1472i	0.281517	−	0.487602i	−0.690242	−	0.723579i	$-0.742496\pi$
$727$	7.59053	−	13.1472i	0.281517	−	0.487602i	0.971759	+	0.235977i	$0.0758291\pi$
$728$	8.86212	+	15.3496i	0.328452	+	0.568896i
$729$	−32.9073			−1.21879
$730$	−15.2159			−0.563164
$731$	−7.13397	−	12.3564i	−0.263859	−	0.457018i
$732$	−11.7651	−	20.3778i	−0.434852	−	0.753185i
$733$	−26.9986			−0.997217			−0.498608	−	0.866827i	$-0.666155\pi$
$733$	−26.9986			−0.997217			−0.498608	+	0.866827i	$0.666155\pi$
$734$	32.6121			1.20373
$735$	2.49257	+	4.31726i	0.0919398	+	0.159244i
$736$	−1.24945	+	2.16411i	−0.0460554	+	0.0797703i
$737$	−9.70228	−	16.8048i	−0.357388	−	0.619014i
$738$	4.36890	−	7.56716i	0.160822	−	0.278551i
$739$	2.60391	−	4.51010i	0.0957864	−	0.165907i	−0.814150	−	0.580654i	$-0.802797\pi$
$739$	2.60391	−	4.51010i	0.0957864	−	0.165907i	0.909937	+	0.414748i	$0.136130\pi$
$740$	1.35520			0.0498181
$741$		0			0
$742$	4.10736			0.150786
$743$	11.0539	−	19.1460i	0.405529	−	0.702398i	−0.588853	−	0.808240i	$-0.700420\pi$
$743$	11.0539	−	19.1460i	0.405529	−	0.702398i	0.994383	+	0.105842i	$0.0337538\pi$
$744$	−9.17848	+	15.8976i	−0.336499	+	0.582834i
$745$	11.5585	+	20.0199i	0.423471	+	0.733474i
$746$	2.65099	−	4.59165i	0.0970596	−	0.168112i
$747$	−25.4307	−	44.0472i	−0.930460	−	1.61160i
$748$	−8.34092			−0.304974
$749$	−7.90167			−0.288721
$750$	12.2428	+	21.2051i	0.447043	+	0.774301i
$751$	−6.24798	−	10.8218i	−0.227992	−	0.394894i	0.729221	−	0.684279i	$-0.239883\pi$
$751$	−6.24798	−	10.8218i	−0.227992	−	0.394894i	−0.957213	+	0.289384i	$0.906549\pi$
$752$	0.745593			0.0271890
$753$	−34.1612			−1.24490
$754$	18.8173	+	32.5926i	0.685287	+	1.18695i
$755$	12.6220	−	21.8619i	0.459361	−	0.795636i
$756$	1.23607	+	2.14093i	0.0449554	+	0.0778650i
$757$	15.4994	−	26.8458i	0.563336	−	0.975727i	−0.433866	−	0.900977i	$-0.642851\pi$
$757$	15.4994	−	26.8458i	0.563336	−	0.975727i	0.997202	−	0.0747495i	$-0.0238157\pi$
$758$	−12.3328	+	21.3610i	−0.447948	+	0.775868i
$759$	10.5707			0.383693
$760$		0			0
$761$	1.96398			0.0711941			0.0355971	−	0.999366i	$-0.488667\pi$
$761$	1.96398			0.0711941			0.0355971	+	0.999366i	$0.488667\pi$
$762$	1.43184	−	2.48002i	0.0518702	−	0.0898418i
$763$	−2.41003	+	4.17429i	−0.0872489	+	0.151120i
$764$	−3.28740	−	5.69394i	−0.118934	−	0.205999i
$765$	20.4795	−	35.4716i	0.740439	−	1.28248i
$766$	−1.82208	−	3.15593i	−0.0658344	−	0.114029i
$767$	−31.4857			−1.13688
$768$	2.52015			0.0909380
$769$	11.1661	+	19.3402i	0.402659	+	0.697426i	0.994046	−	0.108962i	$-0.0347527\pi$
$769$	11.1661	+	19.3402i	0.402659	+	0.697426i	−0.591387	+	0.806388i	$0.701419\pi$
$770$	−5.76684	−	9.98845i	−0.207822	−	0.359959i
$771$	−25.3004			−0.911172
$772$	−26.8826			−0.967527
$773$	13.6776	+	23.6904i	0.491951	+	0.852084i	0.999957	−	0.00926978i	$-0.00295070\pi$
$773$	13.6776	+	23.6904i	0.491951	+	0.852084i	−0.508006	+	0.861353i	$0.669617\pi$
$774$	4.81105	−	8.33298i	0.172929	−	0.299523i
$775$	3.82369	+	6.62282i	0.137351	+	0.237899i
$776$	−7.19369	+	12.4598i	−0.258238	+	0.447282i
$777$	−1.93950	+	3.35932i	−0.0695793	+	0.120515i
$778$	−2.79353			−0.100153

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:	\( N \)	\(=\)	\( 722 = 2 \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	722.c (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(-1.26007 + 2.18251i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.22982 - 2.13012i) q^{5} +(1.26007 + 2.18251i) q^{6} -2.79360 q^{7} -1.00000 q^{8} +(-1.67557 - 2.90217i) q^{9} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{2} +(-1.26007 + 2.18251i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.22982 - 2.13012i) q^{5} +(1.26007 + 2.18251i) q^{6} -2.79360 q^{7} -1.00000 q^{8} +(-1.67557 - 2.90217i) q^{9} +(-1.22982 - 2.13012i) q^{10} -1.67853 q^{11} +2.52015 q^{12} +(3.17229 + 5.49456i) q^{13} +(-1.39680 + 2.41933i) q^{14} +(3.09934 + 5.36821i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-2.48459 + 4.30343i) q^{17} -3.35114 q^{18} -2.45965 q^{20} +(3.52015 - 6.09707i) q^{21} +(-0.839266 + 1.45365i) q^{22} +(1.24945 + 2.16411i) q^{23} +(1.26007 - 2.18251i) q^{24} +(-0.524938 - 0.909219i) q^{25} +6.34458 q^{26} +0.884927 q^{27} +(1.39680 + 2.41933i) q^{28} +(2.96589 + 5.13708i) q^{29} +6.19868 q^{30} -7.28408 q^{31} +(0.500000 + 0.866025i) q^{32} +(2.11507 - 3.66341i) q^{33} +(2.48459 + 4.30343i) q^{34} +(-3.43564 + 5.95071i) q^{35} +(-1.67557 + 2.90217i) q^{36} -0.550972 q^{37} -15.9893 q^{39} +(-1.22982 + 2.13012i) q^{40} +(-1.30371 + 2.25809i) q^{41} +(-3.52015 - 6.09707i) q^{42} +(-1.43564 + 2.48661i) q^{43} +(0.839266 + 1.45365i) q^{44} -8.24263 q^{45} +2.49890 q^{46} +(-0.372797 - 0.645703i) q^{47} +(-1.26007 - 2.18251i) q^{48} +0.804226 q^{49} -1.04988 q^{50} +(-6.26153 - 10.8453i) q^{51} +(3.17229 - 5.49456i) q^{52} +(-0.735136 - 1.27329i) q^{53} +(0.442463 - 0.766369i) q^{54} +(-2.06430 + 3.57547i) q^{55} +2.79360 q^{56} +5.93179 q^{58} +(-2.48131 + 4.29775i) q^{59} +(3.09934 - 5.36821i) q^{60} +(-4.66843 - 8.08596i) q^{61} +(-3.64204 + 6.30820i) q^{62} +(4.68088 + 8.10752i) q^{63} +1.00000 q^{64} +15.6054 q^{65} +(-2.11507 - 3.66341i) q^{66} +(5.78022 + 10.0116i) q^{67} +4.96917 q^{68} -6.29761 q^{69} +(3.43564 + 5.95071i) q^{70} +(-3.49849 + 6.05956i) q^{71} +(1.67557 + 2.90217i) q^{72} +(3.09310 - 5.35740i) q^{73} +(-0.275486 + 0.477156i) q^{74} +2.64584 q^{75} +4.68915 q^{77} +(-7.99463 + 13.8471i) q^{78} +(-2.95579 + 5.11958i) q^{79} +(1.22982 + 2.13012i) q^{80} +(3.91164 - 6.77516i) q^{81} +(1.30371 + 2.25809i) q^{82} +15.1773 q^{83} -7.04029 q^{84} +(6.11121 + 10.5849i) q^{85} +(1.43564 + 2.48661i) q^{86} -14.9490 q^{87} +1.67853 q^{88} +(3.45251 + 5.97992i) q^{89} +(-4.12132 + 7.13833i) q^{90} +(-8.86212 - 15.3496i) q^{91} +(1.24945 - 2.16411i) q^{92} +(9.17848 - 15.8976i) q^{93} -0.745593 q^{94} -2.52015 q^{96} +(7.19369 - 12.4598i) q^{97} +(0.402113 - 0.696480i) q^{98} +(2.81250 + 4.87139i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{2} + 2 q^{3} - 4 q^{4} + 2 q^{5} - 2 q^{6} - 4 q^{7} - 8 q^{8} - 4 q^{9}+O(q^{10}) \) 8 * q + 4 * q^2 + 2 * q^3 - 4 * q^4 + 2 * q^5 - 2 * q^6 - 4 * q^7 - 8 * q^8 - 4 * q^9	\( 8 q + 4 q^{2} + 2 q^{3} - 4 q^{4} + 2 q^{5} - 2 q^{6} - 4 q^{7} - 8 q^{8} - 4 q^{9} - 2 q^{10} + 4 q^{11} - 4 q^{12} + 18 q^{13} - 2 q^{14} + 4 q^{15} - 4 q^{16} - 6 q^{17} - 8 q^{18} - 4 q^{20} + 4 q^{21} + 2 q^{22} + 10 q^{23} - 2 q^{24} - 6 q^{25} + 36 q^{26} + 8 q^{27} + 2 q^{28} - 2 q^{29} + 8 q^{30} - 52 q^{31} + 4 q^{32} + 16 q^{33} + 6 q^{34} - 6 q^{35} - 4 q^{36} - 8 q^{37} - 12 q^{39} - 2 q^{40} - 12 q^{41} - 4 q^{42} + 10 q^{43} - 2 q^{44} - 44 q^{45} + 20 q^{46} + 12 q^{47} + 2 q^{48} - 24 q^{49} - 12 q^{50} - 2 q^{51} + 18 q^{52} + 8 q^{53} + 4 q^{54} + 26 q^{55} + 4 q^{56} - 4 q^{58} - 8 q^{59} + 4 q^{60} - 26 q^{62} + 22 q^{63} + 8 q^{64} + 8 q^{65} - 16 q^{66} + 10 q^{67} + 12 q^{68} + 40 q^{69} + 6 q^{70} + 4 q^{72} + 14 q^{73} - 4 q^{74} - 16 q^{75} + 8 q^{77} - 6 q^{78} + 22 q^{79} + 2 q^{80} + 4 q^{81} + 12 q^{82} - 24 q^{83} - 8 q^{84} + 18 q^{85} - 10 q^{86} - 52 q^{87} - 4 q^{88} - 16 q^{89} - 22 q^{90} - 4 q^{91} + 10 q^{92} - 8 q^{93} + 24 q^{94} + 4 q^{96} + 28 q^{97} - 12 q^{98} - 22 q^{99}+O(q^{100}) \) 8 * q + 4 * q^2 + 2 * q^3 - 4 * q^4 + 2 * q^5 - 2 * q^6 - 4 * q^7 - 8 * q^8 - 4 * q^9 - 2 * q^10 + 4 * q^11 - 4 * q^12 + 18 * q^13 - 2 * q^14 + 4 * q^15 - 4 * q^16 - 6 * q^17 - 8 * q^18 - 4 * q^20 + 4 * q^21 + 2 * q^22 + 10 * q^23 - 2 * q^24 - 6 * q^25 + 36 * q^26 + 8 * q^27 + 2 * q^28 - 2 * q^29 + 8 * q^30 - 52 * q^31 + 4 * q^32 + 16 * q^33 + 6 * q^34 - 6 * q^35 - 4 * q^36 - 8 * q^37 - 12 * q^39 - 2 * q^40 - 12 * q^41 - 4 * q^42 + 10 * q^43 - 2 * q^44 - 44 * q^45 + 20 * q^46 + 12 * q^47 + 2 * q^48 - 24 * q^49 - 12 * q^50 - 2 * q^51 + 18 * q^52 + 8 * q^53 + 4 * q^54 + 26 * q^55 + 4 * q^56 - 4 * q^58 - 8 * q^59 + 4 * q^60 - 26 * q^62 + 22 * q^63 + 8 * q^64 + 8 * q^65 - 16 * q^66 + 10 * q^67 + 12 * q^68 + 40 * q^69 + 6 * q^70 + 4 * q^72 + 14 * q^73 - 4 * q^74 - 16 * q^75 + 8 * q^77 - 6 * q^78 + 22 * q^79 + 2 * q^80 + 4 * q^81 + 12 * q^82 - 24 * q^83 - 8 * q^84 + 18 * q^85 - 10 * q^86 - 52 * q^87 - 4 * q^88 - 16 * q^89 - 22 * q^90 - 4 * q^91 + 10 * q^92 - 8 * q^93 + 24 * q^94 + 4 * q^96 + 28 * q^97 - 12 * q^98 - 22 * q^99

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