LMFDB - Embedded newform 343.2.e.d.295.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [343,2,Mod(50,343)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(343, base_ring=CyclotomicField(14))

chi = DirichletCharacter(H, H._module([12]))

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

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

chi := DirichletCharacter("343.50");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 343 = 7^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	343.e (of order $7$, degree $6$, not 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:	$2.73886878933$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$8$ over $\Q(\zeta_{7})$
Twist minimal:	no (minimal twist has level 49)
Sato-Tate group:	$\mathrm{SU}(2)[C_{7}]$

Embedding invariants

Embedding label			295.2
Character	$\chi$	$=$	343.295
Dual form			343.2.e.d.50.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.12619 + 1.41219i) q^{2} +(2.10003 + 1.01132i) q^{3} +(-0.280953 - 1.23093i) q^{4} +(3.18734 + 1.53494i) q^{5} +(-3.79321 + 1.82671i) q^{6} +(-1.20005 - 0.577915i) q^{8} +(1.51689 + 1.90212i) q^{9} +O(q^{10})$	\(q+(-1.12619 + 1.41219i) q^{2} +(2.10003 + 1.01132i) q^{3} +(-0.280953 - 1.23093i) q^{4} +(3.18734 + 1.53494i) q^{5} +(-3.79321 + 1.82671i) q^{6} +(-1.20005 - 0.577915i) q^{8} +(1.51689 + 1.90212i) q^{9} +(-5.75717 + 2.77251i) q^{10} +(-0.281296 + 0.352734i) q^{11} +(0.654861 - 2.86913i) q^{12} +(-0.882307 + 1.10638i) q^{13} +(5.14119 + 6.44685i) q^{15} +(4.44272 - 2.13950i) q^{16} +(1.29133 - 5.65770i) q^{17} -4.39447 q^{18} -1.35536 q^{19} +(0.993919 - 4.35465i) q^{20} +(-0.181337 - 0.794490i) q^{22} +(0.220045 + 0.964081i) q^{23} +(-1.93569 - 2.42728i) q^{24} +(4.68562 + 5.87558i) q^{25} +(-0.568777 - 2.49198i) q^{26} +(-0.294132 - 1.28868i) q^{27} +(0.913633 - 4.00289i) q^{29} -14.8941 q^{30} -2.23370 q^{31} +(-1.38917 + 6.08633i) q^{32} +(-0.947459 + 0.456272i) q^{33} +(6.53549 + 8.19524i) q^{34} +(1.91521 - 2.40160i) q^{36} +(-0.624857 + 2.73768i) q^{37} +(1.52639 - 1.91403i) q^{38} +(-2.97178 + 1.43113i) q^{39} +(-2.93791 - 3.68402i) q^{40} +(-7.49293 - 3.60841i) q^{41} +(-4.88385 + 2.35194i) q^{43} +(0.513224 + 0.247155i) q^{44} +(1.91520 + 8.39104i) q^{45} +(-1.60928 - 0.774989i) q^{46} +(-0.636883 + 0.798627i) q^{47} +11.4936 q^{48} -13.5743 q^{50} +(8.43360 - 10.5754i) q^{51} +(1.60976 + 0.775221i) q^{52} +(-2.34896 - 10.2915i) q^{53} +(2.15111 + 1.03592i) q^{54} +(-1.43801 + 0.692510i) q^{55} +(-2.84630 - 1.37071i) q^{57} +(4.62393 + 5.79823i) q^{58} +(-4.60865 + 2.21941i) q^{59} +(6.49121 - 8.13972i) q^{60} +(-0.800262 + 3.50618i) q^{61} +(2.51556 - 3.15442i) q^{62} +(-0.881710 - 1.10563i) q^{64} +(-4.51043 + 2.17211i) q^{65} +(0.422671 - 1.85184i) q^{66} +15.2117 q^{67} -7.32706 q^{68} +(-0.512895 + 2.24714i) q^{69} +(2.56178 + 11.2239i) q^{71} +(-0.721085 - 3.15928i) q^{72} +(0.806072 + 1.01078i) q^{73} +(-3.16242 - 3.96556i) q^{74} +(3.89785 + 17.0776i) q^{75} +(0.380792 + 1.66836i) q^{76} +(1.32574 - 5.80845i) q^{78} +7.98591 q^{79} +17.4444 q^{80} +(2.30970 - 10.1194i) q^{81} +(13.5342 - 6.51773i) q^{82} +(-5.09487 - 6.38876i) q^{83} +(12.8001 - 16.0509i) q^{85} +(2.17874 - 9.54568i) q^{86} +(5.96687 - 7.48222i) q^{87} +(0.541421 - 0.260734i) q^{88} +(-1.93054 - 2.42082i) q^{89} +(-14.0067 - 6.74525i) q^{90} +(1.12490 - 0.541722i) q^{92} +(-4.69084 - 2.25899i) q^{93} +(-0.410566 - 1.79881i) q^{94} +(-4.31999 - 2.08040i) q^{95} +(-9.07254 + 11.3766i) q^{96} +15.6655 q^{97} -1.09764 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 5 q^{2} + 7 q^{3} - 3 q^{4} + 7 q^{5} - 20 q^{8} + 9 q^{9}+O(q^{10}) $ 48 * q + 5 * q^2 + 7 * q^3 - 3 * q^4 + 7 * q^5 - 20 * q^8 + 9 * q^9	$ 48 q + 5 q^{2} + 7 q^{3} - 3 q^{4} + 7 q^{5} - 20 q^{8} + 9 q^{9} + 7 q^{10} + 6 q^{11} + 42 q^{12} - 14 q^{13} - 12 q^{15} - 15 q^{16} - 7 q^{17} - 4 q^{18} - 42 q^{19} + 14 q^{20} - 20 q^{22} + 12 q^{23} + 49 q^{24} - 13 q^{25} + 21 q^{26} + 7 q^{27} + 12 q^{29} - 22 q^{30} - 70 q^{31} + 15 q^{32} + 7 q^{33} + 70 q^{34} - 12 q^{36} - 9 q^{37} - 7 q^{38} - 28 q^{39} - 63 q^{40} - 42 q^{41} - 30 q^{43} + 37 q^{44} + 28 q^{45} + 9 q^{46} + 21 q^{47} - 84 q^{48} + 40 q^{50} - q^{51} + 77 q^{52} + 20 q^{53} + 7 q^{54} - 7 q^{55} - 12 q^{57} + 31 q^{58} - 7 q^{59} + 35 q^{60} + 7 q^{61} - 28 q^{62} - 32 q^{64} - 49 q^{65} - 119 q^{66} - 22 q^{67} - 154 q^{68} + 70 q^{69} + 19 q^{71} - 46 q^{72} + 28 q^{73} - 47 q^{74} + 7 q^{75} + 119 q^{76} + 28 q^{78} - 30 q^{79} - 140 q^{80} + 61 q^{81} + 112 q^{82} - 26 q^{85} + 24 q^{86} + 77 q^{87} + 28 q^{88} + 28 q^{89} - 182 q^{90} - 38 q^{92} + 34 q^{93} - 28 q^{94} - 67 q^{95} - 28 q^{96} - 16 q^{99}+O(q^{100}) $ 48 * q + 5 * q^2 + 7 * q^3 - 3 * q^4 + 7 * q^5 - 20 * q^8 + 9 * q^9 + 7 * q^10 + 6 * q^11 + 42 * q^12 - 14 * q^13 - 12 * q^15 - 15 * q^16 - 7 * q^17 - 4 * q^18 - 42 * q^19 + 14 * q^20 - 20 * q^22 + 12 * q^23 + 49 * q^24 - 13 * q^25 + 21 * q^26 + 7 * q^27 + 12 * q^29 - 22 * q^30 - 70 * q^31 + 15 * q^32 + 7 * q^33 + 70 * q^34 - 12 * q^36 - 9 * q^37 - 7 * q^38 - 28 * q^39 - 63 * q^40 - 42 * q^41 - 30 * q^43 + 37 * q^44 + 28 * q^45 + 9 * q^46 + 21 * q^47 - 84 * q^48 + 40 * q^50 - q^51 + 77 * q^52 + 20 * q^53 + 7 * q^54 - 7 * q^55 - 12 * q^57 + 31 * q^58 - 7 * q^59 + 35 * q^60 + 7 * q^61 - 28 * q^62 - 32 * q^64 - 49 * q^65 - 119 * q^66 - 22 * q^67 - 154 * q^68 + 70 * q^69 + 19 * q^71 - 46 * q^72 + 28 * q^73 - 47 * q^74 + 7 * q^75 + 119 * q^76 + 28 * q^78 - 30 * q^79 - 140 * q^80 + 61 * q^81 + 112 * q^82 - 26 * q^85 + 24 * q^86 + 77 * q^87 + 28 * q^88 + 28 * q^89 - 182 * q^90 - 38 * q^92 + 34 * q^93 - 28 * q^94 - 67 * q^95 - 28 * q^96 - 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/343\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{1}{7}\right)$

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 $

$2$	−1.12619	+	1.41219i	−0.796335	+	0.998572i	0.203475	+	0.979080i	$0.434776\pi$
$2$	−1.12619	+	1.41219i	−0.796335	+	0.998572i	−0.999810	+	0.0194919i	$0.993795\pi$
$3$	2.10003	+	1.01132i	1.21245	+	0.583887i	0.927201	−	0.374565i	$-0.122208\pi$
$3$	2.10003	+	1.01132i	1.21245	+	0.583887i	0.285253	+	0.958452i	$0.407922\pi$
$4$	−0.280953	−	1.23093i	−0.140476	−	0.615467i
$5$	3.18734	+	1.53494i	1.42542	+	0.686446i	0.978140	−	0.207948i	$-0.0666784\pi$
$5$	3.18734	+	1.53494i	1.42542	+	0.686446i	0.447280	+	0.894394i	$0.352393\pi$
$6$	−3.79321	+	1.82671i	−1.54857	+	0.745753i
$7$		0			0
$7$		0			0
$8$	−1.20005	−	0.577915i	−0.424283	−	0.204324i
$9$	1.51689	+	1.90212i	0.505631	+	0.634041i
$10$	−5.75717	+	2.77251i	−1.82058	+	0.876744i
$11$	−0.281296	+	0.352734i	−0.0848140	+	0.106353i	−0.822428	−	0.568869i	$-0.807381\pi$
$11$	−0.281296	+	0.352734i	−0.0848140	+	0.106353i	0.737614	+	0.675223i	$0.235952\pi$
$12$	0.654861	−	2.86913i	0.189042	−	0.828248i
$13$	−0.882307	+	1.10638i	−0.244708	+	0.306854i	−0.888983	−	0.457940i	$-0.848588\pi$
$13$	−0.882307	+	1.10638i	−0.244708	+	0.306854i	0.644275	+	0.764793i	$0.277159\pi$
$14$		0			0
$15$	5.14119	+	6.44685i	1.32745	+	1.66457i
$16$	4.44272	−	2.13950i	1.11068	−	0.534875i
$17$	1.29133	−	5.65770i	0.313194	−	1.37219i	−0.536047	−	0.844188i	$-0.680083\pi$
$17$	1.29133	−	5.65770i	0.313194	−	1.37219i	0.849241	−	0.528005i	$-0.177060\pi$
$18$	−4.39447			−1.03579
$19$	−1.35536			−0.310941			−0.155471	−	0.987841i	$-0.549689\pi$
$19$	−1.35536			−0.310941			−0.155471	+	0.987841i	$0.549689\pi$
$20$	0.993919	−	4.35465i	0.222247	−	0.973728i
$21$		0			0
$22$	−0.181337	−	0.794490i	−0.0386612	−	0.169386i
$23$	0.220045	+	0.964081i	0.0458826	+	0.201025i	0.992674	−	0.120823i	$-0.0385533\pi$
$23$	0.220045	+	0.964081i	0.0458826	+	0.201025i	−0.946791	+	0.321848i	$0.895696\pi$
$24$	−1.93569	−	2.42728i	−0.395121	−	0.495466i
$25$	4.68562	+	5.87558i	0.937124	+	1.17512i
$26$	−0.568777	−	2.49198i	−0.111546	−	0.488717i
$27$	−0.294132	−	1.28868i	−0.0566058	−	0.248006i
$28$		0			0
$29$	0.913633	−	4.00289i	0.169657	−	0.743318i	−0.816478	−	0.577376i	$-0.804077\pi$
$29$	0.913633	−	4.00289i	0.169657	−	0.743318i	0.986136	−	0.165942i	$-0.0530663\pi$
$30$	−14.8941			−2.71929
$31$	−2.23370			−0.401184			−0.200592	−	0.979675i	$-0.564287\pi$
$31$	−2.23370			−0.401184			−0.200592	+	0.979675i	$0.564287\pi$
$32$	−1.38917	+	6.08633i	−0.245572	+	1.07592i
$33$	−0.947459	+	0.456272i	−0.164931	+	0.0794268i
$34$	6.53549	+	8.19524i	1.12083	+	1.40547i
$35$		0			0
$36$	1.91521	−	2.40160i	0.319202	−	0.400267i
$37$	−0.624857	+	2.73768i	−0.102726	+	0.450071i	0.897238	+	0.441548i	$0.145570\pi$
$37$	−0.624857	+	2.73768i	−0.102726	+	0.450071i	−0.999964	+	0.00852370i	$0.997287\pi$
$38$	1.52639	−	1.91403i	0.247613	−	0.310497i
$39$	−2.97178	+	1.43113i	−0.475865	+	0.229164i
$40$	−2.93791	−	3.68402i	−0.464524	−	0.582494i
$41$	−7.49293	−	3.60841i	−1.17020	−	0.563538i	−0.255159	−	0.966899i	$-0.582128\pi$
$41$	−7.49293	−	3.60841i	−1.17020	−	0.563538i	−0.915041	+	0.403361i	$0.867842\pi$
$42$		0			0
$43$	−4.88385	+	2.35194i	−0.744781	+	0.358668i	−0.767478	−	0.641075i	$-0.778489\pi$
$43$	−4.88385	+	2.35194i	−0.744781	+	0.358668i	0.0226976	+	0.999742i	$0.492775\pi$
$44$	0.513224	+	0.247155i	0.0773714	+	0.0372601i
$45$	1.91520	+	8.39104i	0.285501	+	1.25086i
$46$	−1.60928	−	0.774989i	−0.237276	−	0.114266i
$47$	−0.636883	+	0.798627i	−0.0928990	+	0.116492i	−0.826108	−	0.563511i	$-0.809450\pi$
$47$	−0.636883	+	0.798627i	−0.0928990	+	0.116492i	0.733209	+	0.680003i	$0.238022\pi$
$48$	11.4936			1.65895
$49$		0			0
$50$	−13.5743			−1.91970
$51$	8.43360	−	10.5754i	1.18094	−	1.48085i
$52$	1.60976	+	0.775221i	0.223234	+	0.107504i
$53$	−2.34896	−	10.2915i	−0.322654	−	1.41364i	−0.832810	−	0.553558i	$-0.813270\pi$
$53$	−2.34896	−	10.2915i	−0.322654	−	1.41364i	0.510156	−	0.860082i	$-0.329588\pi$
$54$	2.15111	+	1.03592i	0.292729	+	0.140971i
$55$	−1.43801	+	0.692510i	−0.193901	+	0.0933780i
$56$		0			0
$57$	−2.84630	−	1.37071i	−0.377002	−	0.181554i
$58$	4.62393	+	5.79823i	0.607152	+	0.761345i
$59$	−4.60865	+	2.21941i	−0.599995	+	0.288942i	−0.709122	−	0.705085i	$-0.750909\pi$
$59$	−4.60865	+	2.21941i	−0.599995	+	0.288942i	0.109127	+	0.994028i	$0.465194\pi$
$60$	6.49121	−	8.13972i	0.838012	−	1.05083i
$61$	−0.800262	+	3.50618i	−0.102463	+	0.448920i	0.897506	+	0.441003i	$0.145377\pi$
$61$	−0.800262	+	3.50618i	−0.102463	+	0.448920i	−0.999969	+	0.00791690i	$0.997480\pi$
$62$	2.51556	−	3.15442i	0.319477	−	0.400611i
$63$		0			0
$64$	−0.881710	−	1.10563i	−0.110214	−	0.138204i
$65$	−4.51043	+	2.17211i	−0.559450	+	0.269417i
$66$	0.422671	−	1.85184i	0.0520272	−	0.227946i
$67$	15.2117			1.85840			0.929202	−	0.369571i	$-0.120495\pi$
$67$	15.2117			1.85840			0.929202	+	0.369571i	$0.120495\pi$
$68$	−7.32706			−0.888536
$69$	−0.512895	+	2.24714i	−0.0617452	+	0.270524i
$70$		0			0
$71$	2.56178	+	11.2239i	0.304027	+	1.33203i	0.863989	+	0.503511i	$0.167959\pi$
$71$	2.56178	+	11.2239i	0.304027	+	1.33203i	−0.559962	+	0.828519i	$0.689184\pi$
$72$	−0.721085	−	3.15928i	−0.0849807	−	0.372325i
$73$	0.806072	+	1.01078i	0.0943436	+	0.118303i	0.826762	−	0.562551i	$-0.190180\pi$
$73$	0.806072	+	1.01078i	0.0943436	+	0.118303i	−0.732419	+	0.680854i	$0.761609\pi$
$74$	−3.16242	−	3.96556i	−0.367624	−	0.460986i
$75$	3.89785	+	17.0776i	0.450085	+	1.97195i
$76$	0.380792	+	1.66836i	0.0436799	+	0.191374i
$77$		0			0
$78$	1.32574	−	5.80845i	0.150110	−	0.657677i
$79$	7.98591			0.898485			0.449242	−	0.893410i	$-0.351694\pi$
$79$	7.98591			0.898485			0.449242	+	0.893410i	$0.351694\pi$
$80$	17.4444			1.95035
$81$	2.30970	−	10.1194i	0.256633	−	1.12438i
$82$	13.5342	−	6.51773i	1.49460	−	0.719763i
$83$	−5.09487	−	6.38876i	−0.559234	−	0.701258i	0.419182	−	0.907902i	$-0.362317\pi$
$83$	−5.09487	−	6.38876i	−0.559234	−	0.701258i	−0.978416	+	0.206645i	$0.933746\pi$
$84$		0			0
$85$	12.8001	−	16.0509i	1.38837	−	1.74096i
$86$	2.17874	−	9.54568i	0.234939	−	1.02934i
$87$	5.96687	−	7.48222i	0.639715	−	0.802178i
$88$	0.541421	−	0.260734i	0.0577156	−	0.0277944i
$89$	−1.93054	−	2.42082i	−0.204637	−	0.256607i	0.668913	−	0.743340i	$-0.266760\pi$
$89$	−1.93054	−	2.42082i	−0.204637	−	0.256607i	−0.873550	+	0.486734i	$0.838188\pi$
$90$	−14.0067	−	6.74525i	−1.47643	−	0.711012i
$91$		0			0
$92$	1.12490	−	0.541722i	0.117279	−	0.0564785i
$93$	−4.69084	−	2.25899i	−0.486417	−	0.234246i
$94$	−0.410566	−	1.79881i	−0.0423466	−	0.185533i
$95$	−4.31999	−	2.08040i	−0.443222	−	0.213444i
$96$	−9.07254	+	11.3766i	−0.925962	+	1.16112i
$97$	15.6655			1.59059			0.795294	−	0.606224i	$-0.207316\pi$
$97$	15.6655			1.59059			0.795294	+	0.606224i	$0.207316\pi$
$98$		0			0
$99$	−1.09764			−0.110317
$100$	5.91602	−	7.41845i	0.591602	−	0.741845i
$101$	10.7345	+	5.16945i	1.06812	+	0.514379i	0.883500	−	0.468431i	$-0.155180\pi$
$101$	10.7345	+	5.16945i	1.06812	+	0.514379i	0.184619	+	0.982810i	$0.440895\pi$
$102$	5.43670	+	23.8198i	0.538314	+	2.35851i
$103$	−7.53691	−	3.62958i	−0.742633	−	0.357633i	0.0240056	−	0.999712i	$-0.492358\pi$
$103$	−7.53691	−	3.62958i	−0.742633	−	0.357633i	−0.766639	+	0.642078i	$0.778072\pi$
$104$	1.69821	−	0.817813i	0.166523	−	0.0801932i
$105$		0			0
$106$	17.1789	+	8.27292i	1.66856	+	0.803537i
$107$	6.47856	+	8.12385i	0.626306	+	0.785362i	0.989216	−	0.146462i	$-0.0467885\pi$
$107$	6.47856	+	8.12385i	0.626306	+	0.785362i	−0.362911	+	0.931824i	$0.618217\pi$
$108$	−1.50364	+	0.724114i	−0.144688	+	0.0696779i
$109$	−5.90779	+	7.40813i	−0.565863	+	0.709570i	−0.979630	−	0.200813i	$-0.935642\pi$
$109$	−5.90779	+	7.40813i	−0.565863	+	0.709570i	0.413766	+	0.910383i	$0.364213\pi$
$110$	0.641512	−	2.81065i	0.0611658	−	0.267985i
$111$	−4.08089	+	5.11728i	−0.387341	+	0.485710i
$112$		0			0
$113$	−8.96794	−	11.2454i	−0.843633	−	1.05788i	−0.997561	−	0.0698004i	$-0.977764\pi$
$113$	−8.96794	−	11.2454i	−0.843633	−	1.05788i	0.153928	−	0.988082i	$-0.450808\pi$
$114$	5.14117	−	2.47586i	0.481515	−	0.231885i
$115$	−0.778449	+	3.41061i	−0.0725907	+	0.318041i
$116$	−5.18398			−0.481320
$117$	−3.44283			−0.318290
$118$	2.05597	−	9.00778i	0.189267	−	0.829233i
$119$		0			0
$120$	−2.44397	−	10.7077i	−0.223103	−	0.977477i
$121$	2.40244	+	10.5258i	0.218403	+	0.956887i
$122$	−4.05016	−	5.07874i	−0.366684	−	0.459807i
$123$	−12.0861	−	15.1555i	−1.08977	−	1.36653i
$124$	0.627564	+	2.74954i	0.0563569	+	0.246916i
$125$	1.97995	+	8.67471i	0.177092	+	0.775889i
$126$		0			0
$127$	−0.596431	+	2.61314i	−0.0529247	+	0.231878i	−0.994472	−	0.105003i	$-0.966515\pi$
$127$	−0.596431	+	2.61314i	−0.0529247	+	0.231878i	0.941547	+	0.336881i	$0.109372\pi$
$128$	−9.93138			−0.877818
$129$	−12.6348			−1.11243
$130$	2.01215	−	8.81580i	0.176477	−	0.773197i
$131$	−3.29797	+	1.58822i	−0.288145	+	0.138763i	−0.572373	−	0.819993i	$-0.693977\pi$
$131$	−3.29797	+	1.58822i	−0.288145	+	0.138763i	0.284228	+	0.958757i	$0.408263\pi$
$132$	0.827832	+	1.03807i	0.0720535	+	0.0903523i
$133$		0			0
$134$	−17.1312	+	21.4819i	−1.47991	+	1.85575i
$135$	1.04054	−	4.55892i	0.0895558	−	0.392370i
$136$	−4.81934	+	6.04326i	−0.413255	+	0.518205i
$137$	1.43360	−	0.690387i	0.122481	−	0.0589838i	−0.371640	−	0.928377i	$-0.621204\pi$
$137$	1.43360	−	0.690387i	0.122481	−	0.0589838i	0.494121	+	0.869393i	$0.335490\pi$
$138$	−2.59578	−	3.25500i	−0.220967	−	0.277084i
$139$	−4.63173	−	2.23052i	−0.392858	−	0.189190i	0.227017	−	0.973891i	$-0.427103\pi$
$139$	−4.63173	−	2.23052i	−0.392858	−	0.189190i	−0.619875	+	0.784700i	$0.712817\pi$
$140$		0			0
$141$	−2.14514	+	1.03305i	−0.180654	+	0.0869983i
$142$	−18.7353	−	9.02246i	−1.57223	−	0.757148i
$143$	−0.142068	−	0.622440i	−0.0118803	−	0.0520510i
$144$	10.8087	+	5.20520i	0.900726	+	0.433767i
$145$	9.05625	−	11.3562i	0.752081	−	0.943079i
$146$	−2.33521			−0.193263
$147$		0			0
$148$	3.54545			0.291435
$149$	−1.97583	+	2.47761i	−0.161866	+	0.202974i	−0.856150	−	0.516728i	$-0.827150\pi$
$149$	−1.97583	+	2.47761i	−0.161866	+	0.202974i	0.694284	+	0.719702i	$0.255721\pi$
$150$	−28.5066	−	13.7280i	−2.32755	−	1.12089i
$151$	0.799574	+	3.50316i	0.0650684	+	0.285083i	0.996985	−	0.0775881i	$-0.0247219\pi$
$151$	0.799574	+	3.50316i	0.0650684	+	0.285083i	−0.931917	+	0.362671i	$0.881865\pi$
$152$	1.62650	+	0.783283i	0.131927	+	0.0635326i
$153$	12.7204	−	6.12585i	1.02839	−	0.495245i
$154$		0			0
$155$	−7.11955	−	3.42859i	−0.571856	−	0.275391i
$156$	2.59656	+	3.25598i	0.207891	+	0.260687i
$157$	6.12915	−	2.95164i	0.489159	−	0.235567i	−0.173011	−	0.984920i	$-0.555350\pi$
$157$	6.12915	−	2.95164i	0.489159	−	0.235567i	0.662171	+	0.749353i	$0.269635\pi$
$158$	−8.99362	+	11.2776i	−0.715494	+	0.897202i
$159$	5.47509	−	23.9879i	0.434203	−	1.90237i
$160$	−13.7699	+	17.2669i	−1.08861	+	1.36507i
$161$		0			0
$162$	11.6895	+	14.6581i	0.918412	+	1.15165i
$163$	−13.3750	+	6.44107i	−1.04761	+	0.504504i	−0.876828	−	0.480805i	$-0.840345\pi$
$163$	−13.3750	+	6.44107i	−1.04761	+	0.504504i	−0.170785	+	0.985308i	$0.554630\pi$
$164$	−2.33655	+	10.2371i	−0.182454	+	0.799383i
$165$	−3.72022			−0.289619
$166$	14.7599			1.14559
$167$	2.03740	−	8.92642i	0.157659	−	0.690747i	−0.832873	−	0.553464i	$-0.813306\pi$
$167$	2.03740	−	8.92642i	0.157659	−	0.690747i	0.990532	−	0.137283i	$-0.0438371\pi$
$168$		0			0
$169$	2.44717	+	10.7217i	0.188244	+	0.824749i
$170$	8.25159	+	36.1526i	0.632868	+	2.77278i
$171$	−2.05594	−	2.57806i	−0.157221	−	0.197149i
$172$	4.26721	+	5.35092i	0.325372	+	0.408004i
$173$	−2.92920	−	12.8337i	−0.222703	−	0.975725i	−0.955433	−	0.295207i	$-0.904612\pi$
$173$	−2.92920	−	12.8337i	−0.222703	−	0.975725i	0.732730	−	0.680519i	$-0.238246\pi$
$174$	3.84653	+	16.8528i	0.291605	+	1.27760i
$175$		0			0
$176$	−0.495045	+	2.16893i	−0.0373154	+	0.163490i
$177$	−11.9228			−0.896176
$178$	5.59282			0.419200
$179$	−4.90270	+	21.4801i	−0.366445	+	1.60550i	0.370021	+	0.929024i	$0.379351\pi$
$179$	−4.90270	+	21.4801i	−0.366445	+	1.60550i	−0.736465	+	0.676475i	$0.763506\pi$
$180$	9.79073	−	4.71497i	0.729758	−	0.351433i
$181$	2.98235	+	3.73974i	0.221676	+	0.277973i	0.880216	−	0.474572i	$-0.157397\pi$
$181$	2.98235	+	3.73974i	0.221676	+	0.277973i	−0.658540	+	0.752545i	$0.728826\pi$
$182$		0			0
$183$	−5.22645	+	6.55376i	−0.386350	+	0.484468i
$184$	0.293091	−	1.28412i	0.0216070	−	0.0946663i
$185$	−6.19380	+	7.76678i	−0.455377	+	0.571025i
$186$	8.47289	−	4.08033i	0.621263	−	0.299184i
$187$	1.63242	+	2.04699i	0.119374	+	0.149691i
$188$	1.16199	+	0.559585i	0.0847469	+	0.0408119i
$189$		0			0
$190$	7.80304	−	3.75775i	0.566092	−	0.272616i
$191$	4.05429	+	1.95244i	0.293358	+	0.141274i	0.574774	−	0.818312i	$-0.305090\pi$
$191$	4.05429	+	1.95244i	0.293358	+	0.141274i	−0.281416	+	0.959586i	$0.590804\pi$
$192$	−0.733472	−	3.21355i	−0.0529338	−	0.231918i
$193$	3.20300	+	1.54248i	0.230557	+	0.111030i	0.545596	−	0.838048i	$-0.316303\pi$
$193$	3.20300	+	1.54248i	0.230557	+	0.111030i	−0.315039	+	0.949079i	$0.602018\pi$
$194$	−17.6423	+	22.1227i	−1.26664	+	1.58832i
$195$	−11.6687			−0.835616
$196$		0			0
$197$	14.2934			1.01836			0.509182	−	0.860659i	$-0.329948\pi$
$197$	14.2934			1.01836			0.509182	+	0.860659i	$0.329948\pi$
$198$	1.23615	−	1.55008i	0.0878492	−	0.110159i
$199$	−4.75941	−	2.29201i	−0.337386	−	0.162476i	0.257518	−	0.966274i	$-0.417095\pi$
$199$	−4.75941	−	2.29201i	−0.337386	−	0.162476i	−0.594903	+	0.803797i	$0.702810\pi$
$200$	−2.22740	−	9.75890i	−0.157501	−	0.690058i
$201$	31.9450	+	15.3839i	2.25323	+	1.08510i
$202$	−19.3893	+	9.33739i	−1.36423	+	0.656976i
$203$		0			0
$204$	−15.3871	−	7.41001i	−1.07731	−	0.518805i
$205$	−18.3438	−	23.0024i	−1.28119	−	1.60656i
$206$	13.6136	−	6.55598i	0.948507	−	0.456777i
$207$	−1.50002	+	1.88096i	−0.104258	+	0.130736i
$208$	−1.55274	+	6.80302i	−0.107663	+	0.471705i
$209$	0.381258	−	0.478082i	0.0263722	−	0.0330696i
$210$		0			0
$211$	−6.42413	−	8.05560i	−0.442255	−	0.554571i	0.509881	−	0.860245i	$-0.329689\pi$
$211$	−6.42413	−	8.05560i	−0.442255	−	0.554571i	−0.952136	+	0.305675i	$0.901118\pi$
$212$	−12.0082	+	5.78282i	−0.824724	+	0.397166i
$213$	−5.97114	+	26.1613i	−0.409136	+	1.79254i
$214$	−18.7685			−1.28299
$215$	−19.1766			−1.30783
$216$	−0.391772	+	1.71646i	−0.0266567	+	0.116791i
$217$		0			0
$218$	−3.80844	−	16.6859i	−0.257940	−	1.13011i
$219$	0.670550	+	2.93787i	0.0453116	+	0.198523i
$220$	1.25645	+	1.57553i	0.0847097	+	0.106223i
$221$	5.12020	+	6.42053i	0.344422	+	0.431891i
$222$	−2.63074	−	11.5260i	−0.176564	−	0.773576i
$223$	−0.402994	−	1.76563i	−0.0269865	−	0.118236i	0.959641	−	0.281229i	$-0.0907421\pi$
$223$	−0.402994	−	1.76563i	−0.0269865	−	0.118236i	−0.986627	+	0.162994i	$0.947885\pi$
$224$		0			0
$225$	−4.06850	+	17.8252i	−0.271233	+	1.18835i
$226$	25.9803			1.72819
$227$	−16.9509			−1.12507			−0.562536	−	0.826772i	$-0.690174\pi$
$227$	−16.9509			−1.12507			−0.562536	+	0.826772i	$0.690174\pi$
$228$	−0.887573	+	3.88871i	−0.0587810	+	0.257536i
$229$	−19.0814	+	9.18912i	−1.26093	+	0.607234i	−0.940422	−	0.340010i	$-0.889569\pi$
$229$	−19.0814	+	9.18912i	−1.26093	+	0.607234i	−0.320513	+	0.947244i	$0.603855\pi$
$230$	−3.93976	−	4.94030i	−0.259780	−	0.325754i
$231$		0			0
$232$	−3.40974	+	4.27568i	−0.223860	+	0.280712i
$233$	2.35537	−	10.3196i	0.154305	−	0.676056i	−0.837299	−	0.546746i	$-0.815866\pi$
$233$	2.35537	−	10.3196i	0.154305	−	0.676056i	0.991604	−	0.129311i	$-0.0412764\pi$
$234$	3.87727	−	4.86194i	0.253465	−	0.317835i
$235$	−3.25581	+	1.56791i	−0.212385	+	0.102279i
$236$	4.02676	+	5.04940i	0.262120	+	0.328688i
$237$	16.7707	+	8.07632i	1.08937	+	0.524614i
$238$		0			0
$239$	23.5566	−	11.3443i	1.52375	−	0.733801i	0.530275	−	0.847826i	$-0.322089\pi$
$239$	23.5566	−	11.3443i	1.52375	−	0.733801i	0.993478	+	0.114025i	$0.0363744\pi$
$240$	36.6339	+	17.6420i	2.36471	+	1.13878i
$241$	−4.61134	−	20.2036i	−0.297043	−	1.30143i	−0.874507	−	0.485013i	$-0.838815\pi$
$241$	−4.61134	−	20.2036i	−0.297043	−	1.30143i	0.577465	−	0.816416i	$-0.304042\pi$
$242$	−17.5700	−	8.46127i	−1.12944	−	0.543911i
$243$	12.6120	−	15.8150i	0.809063	−	1.01453i
$244$	4.54071			0.290689
$245$		0			0
$246$	35.0138			2.23240
$247$	1.19584	−	1.49954i	0.0760897	−	0.0954135i
$248$	2.68056	+	1.29089i	0.170216	+	0.0819715i
$249$	−4.23829	−	18.5692i	−0.268591	−	1.17677i
$250$	−14.4802	−	6.97328i	−0.915806	−	0.441029i
$251$	−13.0986	+	6.30797i	−0.826778	+	0.398155i	−0.798906	−	0.601456i	$-0.794587\pi$
$251$	−13.0986	+	6.30797i	−0.826778	+	0.398155i	−0.0278723	+	0.999611i	$0.508873\pi$
$252$		0			0
$253$	−0.401962	−	0.193575i	−0.0252712	−	0.0121700i
$254$	−3.01856	−	3.78516i	−0.189401	−	0.237502i
$255$	43.1133	−	20.7623i	2.69986	−	1.30018i
$256$	12.9480	−	16.2363i	0.809251	−	1.01477i
$257$	2.14612	−	9.40276i	0.133871	−	0.586528i	−0.862839	−	0.505479i	$-0.831316\pi$
$257$	2.14612	−	9.40276i	0.133871	−	0.586528i	0.996710	−	0.0810489i	$-0.0258270\pi$
$258$	14.2292	−	17.8428i	0.885869	−	1.11085i
$259$		0			0
$260$	3.94094	+	4.94178i	0.244407	+	0.306476i
$261$	8.99987	−	4.33411i	0.557078	−	0.268275i
$262$	1.47126	−	6.44600i	0.0908946	−	0.398235i
$263$	2.30113			0.141894			0.0709469	−	0.997480i	$-0.477398\pi$
$263$	2.30113			0.141894			0.0709469	+	0.997480i	$0.477398\pi$
$264$	1.40069			0.0862063
$265$	8.30985	−	36.4078i	0.510470	−	2.23652i
$266$		0			0
$267$	−1.60597	−	7.03620i	−0.0982836	−	0.430609i
$268$	−4.27377	−	18.7246i	−0.261062	−	1.14379i
$269$	5.46421	+	6.85190i	0.333159	+	0.417768i	0.919990	−	0.391941i	$-0.128196\pi$
$269$	5.46421	+	6.85190i	0.333159	+	0.417768i	−0.586832	+	0.809709i	$0.699625\pi$
$270$	5.26624	+	6.60365i	0.320493	+	0.401885i
$271$	5.82714	+	25.5304i	0.353973	+	1.55086i	0.767913	+	0.640555i	$0.221295\pi$
$271$	5.82714	+	25.5304i	0.353973	+	1.55086i	−0.413939	+	0.910305i	$0.635847\pi$
$272$	−6.36762	−	27.8984i	−0.386094	−	1.69159i
$273$		0			0
$274$	−0.639546	+	2.80203i	−0.0386364	+	0.169277i
$275$	−3.39057			−0.204459
$276$	2.91018			0.175172
$277$	3.12397	−	13.6870i	0.187701	−	0.822372i	−0.790124	−	0.612947i	$-0.789984\pi$
$277$	3.12397	−	13.6870i	0.187701	−	0.822372i	0.977825	−	0.209424i	$-0.0671590\pi$
$278$	8.36612	−	4.02891i	0.501767	−	0.241638i
$279$	−3.38828	−	4.24877i	−0.202851	−	0.254367i
$280$		0			0
$281$	7.22040	−	9.05410i	0.430733	−	0.540122i	−0.518341	−	0.855174i	$-0.673450\pi$
$281$	7.22040	−	9.05410i	0.430733	−	0.540122i	0.949075	+	0.315051i	$0.102022\pi$
$282$	0.956971	−	4.19276i	0.0569868	−	0.249675i
$283$	−9.49862	+	11.9109i	−0.564635	+	0.708029i	−0.979407	−	0.201896i	$-0.935290\pi$
$283$	−9.49862	+	11.9109i	−0.564635	+	0.708029i	0.414772	+	0.909925i	$0.363861\pi$
$284$	13.0961	−	6.30676i	0.777112	−	0.374237i
$285$	−6.96816	−	8.73780i	−0.412758	−	0.517583i
$286$	1.03900	+	0.500356i	0.0614374	+	0.0295867i
$287$		0			0
$288$	−13.6842	+	6.58995i	−0.806347	+	0.388316i
$289$	−15.0256	−	7.23593i	−0.883856	−	0.425643i
$290$	5.83810	+	25.5784i	0.342825	+	1.50201i
$291$	32.8980	+	15.8428i	1.92851	+	0.928724i
$292$	1.01774	−	1.27620i	0.0595586	−	0.0746841i
$293$	−32.7724			−1.91458			−0.957292	−	0.289124i	$-0.906636\pi$
$293$	−32.7724			−1.91458			−0.957292	+	0.289124i	$0.906636\pi$
$294$		0			0
$295$	−18.0960			−1.05359
$296$	2.33201	−	2.92424i	0.135545	−	0.169968i
$297$	0.537299	+	0.258750i	0.0311772	+	0.0150142i
$298$	−1.27371	−	5.58051i	−0.0737843	−	0.323270i
$299$	−1.26079	−	0.607162i	−0.0729131	−	0.0351131i
$300$	19.9263	−	9.59598i	1.15044	−	0.554024i
$301$		0			0
$302$	−5.84761	−	2.81606i	−0.336492	−	0.162046i
$303$	17.3147	+	21.7120i	0.994706	+	1.24732i
$304$	−6.02149	+	2.89980i	−0.345356	+	0.166315i
$305$	−7.93248	+	9.94701i	−0.454212	+	0.569564i
$306$	−5.67472	+	24.8626i	−0.324402	+	1.42130i
$307$	−17.7303	+	22.2331i	−1.01192	+	1.26891i	−0.0490953	+	0.998794i	$0.515634\pi$
$307$	−17.7303	+	22.2331i	−1.01192	+	1.26891i	−0.962828	+	0.270117i	$0.912938\pi$
$308$		0			0
$309$	−12.1571	−	15.2445i	−0.691591	−	0.867228i
$310$	12.8598	−	6.19295i	0.730387	−	0.351736i
$311$	6.28999	−	27.5583i	0.356673	−	1.56269i	−0.404748	−	0.914428i	$-0.632641\pi$
$311$	6.28999	−	27.5583i	0.356673	−	1.56269i	0.761421	−	0.648258i	$-0.224502\pi$
$312$	4.39336			0.248725
$313$	12.4441			0.703379			0.351690	−	0.936117i	$-0.385607\pi$
$313$	12.4441			0.703379			0.351690	+	0.936117i	$0.385607\pi$
$314$	−2.73428	+	11.9797i	−0.154304	+	0.676051i
$315$		0			0
$316$	−2.24366	−	9.83012i	−0.126216	−	0.552988i
$317$	−5.47082	−	23.9692i	−0.307272	−	1.34625i	−0.858895	−	0.512152i	$-0.828848\pi$
$317$	−5.47082	−	23.9692i	−0.307272	−	1.34625i	0.551623	−	0.834094i	$-0.314009\pi$
$318$	27.7096	+	34.7468i	1.55388	+	1.94850i
$319$	1.15495	+	1.44827i	0.0646651	+	0.0810874i
$320$	−1.11323	−	4.87738i	−0.0622315	−	0.272654i
$321$	5.38934	+	23.6123i	0.300804	+	1.31791i
$322$		0			0
$323$	−1.75022	+	7.66822i	−0.0973850	+	0.426671i
$324$	−13.1053			−0.728071
$325$	−10.6348			−0.589911
$326$	5.96674	−	26.1420i	0.330467	−	1.44787i
$327$	−19.8985	+	9.58263i	−1.10039	+	0.529921i
$328$	6.90656	+	8.66055i	0.381351	+	0.478199i
$329$		0			0
$330$	4.18967	−	5.25367i	0.230633	−	0.289205i
$331$	−5.64233	+	24.7207i	−0.310131	+	1.35877i	0.544162	+	0.838980i	$0.316848\pi$
$331$	−5.64233	+	24.7207i	−0.310131	+	1.35877i	−0.854293	+	0.519792i	$0.826010\pi$
$332$	−6.43273	+	8.06638i	−0.353042	+	0.442700i
$333$	−6.15524	+	2.96421i	−0.337305	+	0.162437i
$334$	10.3113	+	12.9300i	0.564212	+	0.707499i
$335$	48.4848	+	23.3490i	2.64901	+	1.27569i
$336$		0			0
$337$	−24.8082	+	11.9470i	−1.35139	+	0.650794i	−0.962699	−	0.270575i	$-0.912786\pi$
$337$	−24.8082	+	11.9470i	−1.35139	+	0.650794i	−0.388689	+	0.921369i	$0.627072\pi$
$338$	−17.8971	−	8.61881i	−0.973476	−	0.468801i
$339$	−7.46020	−	32.6853i	−0.405182	−	1.77522i
$340$	−23.3538	−	11.2466i	−1.26654	−	0.609932i
$341$	0.628331	−	0.787903i	0.0340260	−	0.0426673i
$342$	5.95609			0.322069
$343$		0			0
$344$	7.22010			0.389282
$345$	−5.08399	+	6.37512i	−0.273713	+	0.343225i
$346$	21.4225	+	10.3165i	1.15168	+	0.554619i
$347$	4.57867	+	20.0604i	0.245796	+	1.07690i	0.935643	+	0.352947i	$0.114820\pi$
$347$	4.57867	+	20.0604i	0.245796	+	1.07690i	−0.689848	+	0.723954i	$0.742323\pi$
$348$	−10.8865	−	5.24267i	−0.583579	−	0.281037i
$349$	27.7821	−	13.3792i	1.48714	−	0.716170i	0.498561	−	0.866855i	$-0.333862\pi$
$349$	27.7821	−	13.3792i	1.48714	−	0.716170i	0.988582	+	0.150684i	$0.0481477\pi$
$350$		0			0
$351$	1.68528	+	0.811587i	0.0899535	+	0.0433193i
$352$	−1.75609	−	2.20207i	−0.0936000	−	0.117371i
$353$	−11.2898	+	5.43689i	−0.600897	+	0.289377i	−0.709496	−	0.704709i	$-0.751078\pi$
$353$	−11.2898	+	5.43689i	−0.600897	+	0.289377i	0.108600	+	0.994086i	$0.465363\pi$
$354$	13.4274	−	16.8374i	0.713656	−	0.894897i
$355$	−9.06274	+	39.7065i	−0.481000	+	2.10740i
$356$	−2.43748	+	3.05651i	−0.129186	+	0.161994i
$357$		0			0
$358$	−24.8127	−	31.1142i	−1.31139	−	1.64444i
$359$	14.5180	−	6.99151i	0.766232	−	0.368998i	−0.00958674	−	0.999954i	$-0.503052\pi$
$359$	14.5180	−	6.99151i	0.766232	−	0.368998i	0.775818	+	0.630956i	$0.217337\pi$
$360$	2.55097	−	11.1765i	0.134448	−	0.589054i
$361$	−17.1630			−0.903316
$362$	−8.63992			−0.454104
$363$	−5.59974	+	24.5341i	−0.293910	+	1.28770i
$364$		0			0
$365$	1.01773	+	4.45897i	0.0532705	+	0.233393i
$366$	−3.36922	−	14.7615i	−0.176112	−	0.771597i
$367$	−4.76050	−	5.96948i	−0.248496	−	0.311605i	0.641902	−	0.766787i	$-0.278146\pi$
$367$	−4.76050	−	5.96948i	−0.248496	−	0.311605i	−0.890398	+	0.455182i	$0.849574\pi$
$368$	3.04025	+	3.81236i	0.158484	+	0.198733i
$369$	−4.50234	−	19.7260i	−0.234382	−	1.02690i
$370$	−3.99282	−	17.4937i	−0.207577	−	0.909454i
$371$		0			0
$372$	−1.46276	+	6.40878i	−0.0758407	+	0.332280i
$373$	7.43498			0.384968			0.192484	−	0.981300i	$-0.438346\pi$
$373$	7.43498			0.384968			0.192484	+	0.981300i	$0.438346\pi$
$374$	−4.72915			−0.244539
$375$	−4.61497	+	20.2195i	−0.238316	+	1.04413i
$376$	1.22583	−	0.590330i	0.0632175	−	0.0304439i
$377$	3.62260	+	4.54260i	0.186573	+	0.233956i
$378$		0			0
$379$	−19.5138	+	24.4695i	−1.00236	+	1.25691i	−0.0360947	+	0.999348i	$0.511492\pi$
$379$	−19.5138	+	24.4695i	−1.00236	+	1.25691i	−0.966261	+	0.257566i	$0.917080\pi$
$380$	−1.34712	+	5.90211i	−0.0691058	+	0.302772i
$381$	−3.89525	+	4.88449i	−0.199560	+	0.250240i
$382$	−7.32312	+	3.52663i	−0.374683	+	0.180438i
$383$	−7.94788	−	9.96633i	−0.406118	−	0.509256i	0.536147	−	0.844125i	$-0.319879\pi$
$383$	−7.94788	−	9.96633i	−0.406118	−	0.509256i	−0.942265	+	0.334869i	$0.891308\pi$
$384$	−20.8562	−	10.0438i	−1.06431	−	0.512547i
$385$		0			0
$386$	−5.78546	+	2.78613i	−0.294472	+	0.141810i
$387$	−11.8820	−	5.72205i	−0.603994	−	0.290868i
$388$	−4.40126	−	19.2832i	−0.223440	−	0.978954i
$389$	5.51311	+	2.65497i	0.279526	+	0.134612i	0.568394	−	0.822756i	$-0.307565\pi$
$389$	5.51311	+	2.65497i	0.279526	+	0.134612i	−0.288869	+	0.957369i	$0.593279\pi$
$390$	13.1412	−	16.4785i	0.665430	−	0.834423i
$391$	5.73863			0.290215
$392$		0			0
$393$	−8.53204			−0.430384
$394$	−16.0971	+	20.1851i	−0.810959	+	1.01691i
$395$	25.4538	+	12.2579i	1.28072	+	0.616761i
$396$	0.308385	+	1.35112i	0.0154969	+	0.0678964i
$397$	−28.9500	−	13.9416i	−1.45296	−	0.699707i	−0.469852	−	0.882745i	$-0.655693\pi$
$397$	−28.9500	−	13.9416i	−1.45296	−	0.699707i	−0.983106	+	0.183038i	$0.941407\pi$
$398$	8.59675	−	4.13998i	0.430916	−	0.207518i
$399$		0			0
$400$	33.3877	+	16.0787i	1.66939	+	0.803934i
$401$	9.61969	+	12.0627i	0.480385	+	0.602383i	0.961680	−	0.274175i	$-0.0884049\pi$
$401$	9.61969	+	12.0627i	0.480385	+	0.602383i	−0.481295	+	0.876559i	$0.659833\pi$
$402$	−57.7012	+	27.7874i	−2.87787	+	1.38591i
$403$	1.97081	−	2.47131i	0.0981729	−	0.123105i
$404$	3.34737	−	14.6658i	0.166538	−	0.729650i
$405$	22.8945	−	28.7088i	1.13764	−	1.42655i
$406$		0			0
$407$	−0.789903	−	0.990507i	−0.0391540	−	0.0490976i
$408$	−16.2324	+	7.81713i	−0.803625	+	0.387006i
$409$	−1.58363	+	6.93832i	−0.0783053	+	0.343078i	−0.998871	−	0.0475105i	$-0.984871\pi$
$409$	−1.58363	+	6.93832i	−0.0783053	+	0.343078i	0.920565	+	0.390588i	$0.127728\pi$
$410$	53.1424			2.62452
$411$	3.70882			0.182943
$412$	−2.35026	+	10.2972i	−0.115789	+	0.507305i
$413$		0			0
$414$	−0.966982	−	4.23663i	−0.0475246	−	0.208219i
$415$	−6.43269	−	28.1834i	−0.315768	−	1.38347i
$416$	−5.50811	−	6.90696i	−0.270057	−	0.338641i
$417$	−7.47100	−	9.36834i	−0.365856	−	0.458769i
$418$	0.245777	+	1.07682i	0.0120214	+	0.0526690i
$419$	1.49334	+	6.54274i	0.0729543	+	0.319634i	0.998217	−	0.0596938i	$-0.0190124\pi$
$419$	1.49334	+	6.54274i	0.0729543	+	0.319634i	−0.925262	+	0.379328i	$0.876155\pi$
$420$		0			0
$421$	1.57074	−	6.88188i	0.0765534	−	0.335402i	−0.922119	−	0.386905i	$-0.873544\pi$
$421$	1.57074	−	6.88188i	0.0765534	−	0.335402i	0.998673	+	0.0515029i	$0.0164011\pi$
$422$	18.6108			0.905962
$423$	−2.48517			−0.120833
$424$	−3.12871	+	13.7078i	−0.151944	+	0.665709i
$425$	39.2930	−	18.9225i	1.90599	−	0.917876i
$426$	−30.2202	−	37.8949i	−1.46417	−	1.83602i
$427$		0			0
$428$	8.17976	−	10.2571i	0.395383	−	0.495795i
$429$	0.331140	−	1.45082i	0.0159876	−	0.0700462i
$430$	21.5964	−	27.0810i	1.04147	−	1.30596i
$431$	−14.5245	+	6.99461i	−0.699618	+	0.336918i	−0.749655	−	0.661829i	$-0.769781\pi$
$431$	−14.5245	+	6.99461i	−0.699618	+	0.336918i	0.0500365	+	0.998747i	$0.484066\pi$
$432$	−4.06387	−	5.09593i	−0.195523	−	0.245178i
$433$	−29.3462	−	14.1324i	−1.41029	−	0.679159i	−0.435069	−	0.900397i	$-0.643276\pi$
$433$	−29.3462	−	14.1324i	−1.41029	−	0.679159i	−0.975220	+	0.221237i	$0.928990\pi$
$434$		0			0
$435$	30.5032	−	14.6896i	1.46252	−	0.704310i
$436$	10.7787	+	5.19076i	0.516207	+	0.248592i
$437$	−0.298241	−	1.30668i	−0.0142668	−	0.0625069i
$438$	−4.90401	−	2.36165i	−0.234323	−	0.112844i
$439$	7.01015	−	8.79045i	0.334576	−	0.419545i	−0.585876	−	0.810401i	$-0.699249\pi$
$439$	7.01015	−	8.79045i	0.334576	−	0.419545i	0.920452	+	0.390855i	$0.127821\pi$
$440$	2.12590			0.101348
$441$		0			0
$442$	−14.8333			−0.705550
$443$	−3.79237	+	4.75548i	−0.180181	+	0.225940i	−0.863717	−	0.503977i	$-0.831870\pi$
$443$	−3.79237	+	4.75548i	−0.180181	+	0.225940i	0.683536	+	0.729916i	$0.260441\pi$
$444$	7.44557	+	3.58560i	0.353351	+	0.170165i
$445$	−2.43747	−	10.6792i	−0.115547	−	0.506245i
$446$	2.94727	+	1.41933i	0.139557	+	0.0672071i
$447$	−6.65497	+	3.20486i	−0.314769	+	0.151585i
$448$		0			0
$449$	−5.94996	−	2.86535i	−0.280796	−	0.135224i	0.288185	−	0.957575i	$-0.406948\pi$
$449$	−5.94996	−	2.86535i	−0.280796	−	0.135224i	−0.568981	+	0.822350i	$0.692662\pi$
$450$	−20.5908	−	25.8201i	−0.970660	−	1.21717i
$451$	3.38054	−	1.62798i	0.159184	−	0.0766588i
$452$	−11.3228	+	14.1984i	−0.532581	+	0.667836i
$453$	−1.86369	+	8.16537i	−0.0875640	+	0.383643i
$454$	19.0899	−	23.9380i	0.895934	−	1.12347i
$455$		0			0
$456$	2.62356	+	3.28984i	0.122859	+	0.154061i
$457$	23.6659	−	11.3969i	1.10705	−	0.533125i	0.211179	−	0.977447i	$-0.432270\pi$
$457$	23.6659	−	11.3969i	1.10705	−	0.533125i	0.895867	+	0.444322i	$0.146556\pi$
$458$	8.51241	−	37.2953i	0.397759	−	1.74270i
$459$	−7.67077			−0.358041
$460$	4.41694			0.205941
$461$	−3.21905	+	14.1036i	−0.149926	+	0.656870i	0.842978	+	0.537949i	$0.180801\pi$
$461$	−3.21905	+	14.1036i	−0.149926	+	0.656870i	−0.992904	+	0.118921i	$0.962057\pi$
$462$		0			0
$463$	7.78614	+	34.1133i	0.361853	+	1.58538i	0.748489	+	0.663147i	$0.230780\pi$
$463$	7.78614	+	34.1133i	0.361853	+	1.58538i	−0.386636	+	0.922232i	$0.626363\pi$
$464$	−4.50517	−	19.7384i	−0.209147	−	0.916334i
$465$	−11.4839	−	14.4003i	−0.532552	−	0.667799i
$466$	11.9206	+	14.9480i	0.552212	+	0.692452i
$467$	2.58735	+	11.3359i	0.119728	+	0.524563i	0.998849	+	0.0479643i	$0.0152734\pi$
$467$	2.58735	+	11.3359i	0.119728	+	0.524563i	−0.879121	+	0.476599i	$0.841869\pi$
$468$	0.967272	+	4.23789i	0.0447121	+	0.195897i
$469$		0			0
$470$	1.45245	−	6.36359i	0.0669965	−	0.293531i
$471$	15.8565			0.730628
$472$	6.81325			0.313605
$473$	0.544200	−	2.38430i	0.0250223	−	0.109630i
$474$	−30.2922	+	14.5880i	−1.39137	+	0.670048i
$475$	−6.35071	−	7.96353i	−0.291390	−	0.365392i
$476$		0			0
$477$	16.0125	−	20.0790i	0.733162	−	0.919356i
$478$	−10.5089	+	46.0423i	−0.480664	+	2.10593i
$479$	−3.17960	+	3.98710i	−0.145280	+	0.182175i	−0.849147	−	0.528156i	$-0.822883\pi$
$479$	−3.17960	+	3.98710i	−0.145280	+	0.182175i	0.703867	+	0.710331i	$0.251455\pi$
$480$	−46.3796	+	22.3353i	−2.11693	+	1.01946i
$481$	−2.47759	−	3.10680i	−0.112968	−	0.141658i
$482$	33.7246	+	16.2409i	1.53612	+	0.739754i
$483$		0			0
$484$	12.2815	−	5.91448i	0.558252	−	0.268840i
$485$	49.9311	+	24.0456i	2.26726	+	1.09185i
$486$	8.13033	+	35.6213i	0.368799	+	1.61581i
$487$	−17.8164	−	8.57993i	−0.807339	−	0.388794i	−0.0157712	−	0.999876i	$-0.505020\pi$
$487$	−17.8164	−	8.57993i	−0.807339	−	0.388794i	−0.791567	+	0.611082i	$0.790735\pi$
$488$	2.98663	−	3.74511i	0.135198	−	0.169533i
$489$	−34.6020			−1.56476
$490$		0			0
$491$	−9.54322			−0.430680			−0.215340	−	0.976539i	$-0.569086\pi$
$491$	−9.54322			−0.430680			−0.215340	+	0.976539i	$0.569086\pi$
$492$	−15.2598	+	19.1352i	−0.687966	+	0.862682i
$493$	−21.4673	−	10.3381i	−0.966840	−	0.465606i
$494$	0.770898	+	3.37753i	0.0346844	+	0.151962i
$495$	−3.49855	−	1.68481i	−0.157248	−	0.0757266i
$496$	−9.92370	+	4.77900i	−0.445587	+	0.214584i
$497$		0			0
$498$	30.9964	+	14.9271i	1.38898	+	0.668897i
$499$	−11.9422	−	14.9750i	−0.534606	−	0.670375i	0.439032	−	0.898471i	$-0.355321\pi$
$499$	−11.9422	−	14.9750i	−0.534606	−	0.670375i	−0.973639	+	0.228096i	$0.926750\pi$
$500$	10.1217	−	4.87436i	0.452657	−	0.217988i
$501$	13.3061	−	16.6853i	0.594472	−	0.745444i
$502$	5.84343	−	25.6018i	0.260805	−	1.14266i
$503$	−9.58470	+	12.0188i	−0.427361	+	0.535893i	−0.948163	−	0.317784i	$-0.897061\pi$
$503$	−9.58470	+	12.0188i	−0.427361	+	0.535893i	0.520802	+	0.853677i	$0.325633\pi$
$504$		0			0
$505$	26.2796	+	32.9535i	1.16943	+	1.46641i
$506$	0.726050	−	0.349647i	0.0322769	−	0.0155437i
$507$	−5.70400	+	24.9909i	−0.253324	+	1.10988i
$508$	3.38417			0.150148
$509$	26.5081			1.17495			0.587476	−	0.809242i	$-0.300122\pi$
$509$	26.5081			1.17495			0.587476	+	0.809242i	$0.300122\pi$
$510$	−19.2333	+	84.2666i	−0.851665	+	3.73139i
$511$		0			0
$512$	3.92703	+	17.2055i	0.173552	+	0.760381i
$513$	0.398655	+	1.74662i	0.0176011	+	0.0771153i
$514$	10.8616	+	13.6200i	0.479084	+	0.600752i
$515$	−18.4515	−	23.1374i	−0.813068	−	1.01956i
$516$	3.54979	+	15.5526i	0.156271	+	0.684666i
$517$	−0.102550	−	0.449301i	−0.00451015	−	0.0197603i
$518$		0			0
$519$	6.82755	−	29.9135i	0.299696	−	1.31306i
$520$	6.66805			0.292413
$521$	−4.95167			−0.216937			−0.108468	−	0.994100i	$-0.534595\pi$
$521$	−4.95167			−0.216937			−0.108468	+	0.994100i	$0.534595\pi$
$522$	−4.01493	+	17.5906i	−0.175729	+	0.769919i
$523$	−7.42162	+	3.57407i	−0.324525	+	0.156283i	−0.589052	−	0.808095i	$-0.700499\pi$
$523$	−7.42162	+	3.57407i	−0.324525	+	0.156283i	0.264527	+	0.964378i	$0.414784\pi$
$524$	2.88156	+	3.61337i	0.125882	+	0.157851i
$525$		0			0
$526$	−2.59150	+	3.24964i	−0.112995	+	0.141691i
$527$	−2.88445	+	12.6376i	−0.125649	+	0.550503i
$528$	−3.23310	+	4.05418i	−0.140703	+	0.176436i
$529$	19.8413	−	9.55504i	0.862663	−	0.415437i
$530$	42.0565	+	52.7372i	1.82682	+	2.29076i
$531$	−11.2124	−	5.39961i	−0.486577	−	0.234323i
$532$		0			0
$533$	10.6033	−	5.10629i	0.459281	−	0.221178i
$534$	11.7451	+	5.65614i	0.508260	+	0.244765i
$535$	8.17971	+	35.8376i	0.353640	+	1.54940i
$536$	−18.2548	−	8.79107i	−0.788489	−	0.379716i
$537$	−32.0191	+	40.1507i	−1.38173	+	1.73263i
$538$	−15.8299			−0.682477
$539$		0			0
$540$	−5.90408			−0.254071
$541$	−14.2092	+	17.8178i	−0.610902	+	0.766047i	−0.987033	−	0.160520i	$-0.948683\pi$
$541$	−14.2092	+	17.8178i	−0.610902	+	0.766047i	0.376130	+	0.926567i	$0.377254\pi$
$542$	−42.6163	−	20.5229i	−1.83053	−	0.881535i
$543$	2.48094	+	10.8697i	0.106467	+	0.466463i
$544$	32.6408	+	15.7190i	1.39946	+	0.673945i
$545$	−30.2011	+	14.5441i	−1.29367	+	0.623001i
$546$		0			0
$547$	−37.1562	−	17.8935i	−1.58868	−	0.765070i	−0.589594	−	0.807700i	$-0.700712\pi$
$547$	−37.1562	−	17.8935i	−1.58868	−	0.765070i	−0.999091	+	0.0426300i	$0.986426\pi$
$548$	−1.25260	−	1.57071i	−0.0535082	−	0.0670972i
$549$	−7.88309	+	3.79629i	−0.336442	+	0.162022i
$550$	3.81841	−	4.78814i	0.162818	−	0.204167i
$551$	−1.23830	+	5.42536i	−0.0527535	+	0.231128i
$552$	1.91415	−	2.40027i	0.0814718	−	0.102162i
$553$		0			0
$554$	15.8105	+	19.8258i	0.671725	+	0.842316i
$555$	−20.8619	+	10.0466i	−0.885538	+	0.426453i
$556$	−1.44433	+	6.32802i	−0.0612532	+	0.268368i
$557$	42.2159			1.78874			0.894372	−	0.447323i	$-0.147623\pi$
$557$	42.2159			1.78874			0.894372	+	0.447323i	$0.147623\pi$
$558$	9.81592			0.415541
$559$	1.70692	−	7.47852i	0.0721952	−	0.316308i
$560$		0			0
$561$	1.35797	+	5.94964i	0.0573334	+	0.251194i
$562$	4.65462	+	20.3932i	0.196343	+	0.860236i
$563$	−14.2653	−	17.8881i	−0.601212	−	0.753895i	0.384355	−	0.923185i	$-0.374424\pi$
$563$	−14.2653	−	17.8881i	−0.601212	−	0.753895i	−0.985566	+	0.169290i	$0.945853\pi$
$564$	1.87430	+	2.35029i	0.0789221	+	0.0989652i
$565$	−11.3228	−	49.6083i	−0.476352	−	2.08704i
$566$	−6.12327	−	26.8278i	−0.257380	−	1.12766i
$567$		0			0
$568$	3.41218	−	14.9497i	0.143172	−	0.627277i
$569$	−37.8435			−1.58648			−0.793240	−	0.608909i	$-0.791607\pi$
$569$	−37.8435			−1.58648			−0.793240	+	0.608909i	$0.791607\pi$
$570$	20.1869			0.845537
$571$	4.33431	−	18.9898i	0.181385	−	0.794700i	−0.799587	−	0.600550i	$-0.794948\pi$
$571$	4.33431	−	18.9898i	0.181385	−	0.794700i	0.980972	−	0.194150i	$-0.0621947\pi$
$572$	−0.726268	+	0.349752i	−0.0303668	+	0.0146239i
$573$	6.53959	+	8.20039i	0.273195	+	0.342576i
$574$		0			0
$575$	−4.63349	+	5.81021i	−0.193230	+	0.242303i
$576$	0.765583	−	3.35424i	0.0318993	−	0.139760i
$577$	21.8354	−	27.3808i	0.909021	−	1.13988i	−0.0806823	−	0.996740i	$-0.525710\pi$
$577$	21.8354	−	27.3808i	0.909021	−	1.13988i	0.989703	−	0.143136i	$-0.0457187\pi$
$578$	27.1401	−	13.0700i	1.12888	−	0.543640i
$579$	5.16645	+	6.47852i	0.214710	+	0.269238i
$580$	−16.5231	−	7.95710i	−0.686084	−	0.330401i
$581$		0			0
$582$	−59.4225	+	28.6164i	−2.46314	+	1.18619i
$583$	4.29090	+	2.06639i	0.177711	+	0.0855811i
$584$	−0.383183	−	1.67883i	−0.0158562	−	0.0694706i
$585$	−10.9735	−	5.28454i	−0.453696	−	0.218489i
$586$	36.9078	−	46.2810i	1.52465	−	1.91185i
$587$	37.5954			1.55173			0.775864	−	0.630900i	$-0.217314\pi$
$587$	37.5954			1.55173			0.775864	+	0.630900i	$0.217314\pi$
$588$		0			0
$589$	3.02747			0.124745
$590$	20.3795	−	25.5550i	0.839009	−	1.05208i
$591$	30.0167	+	14.4553i	1.23472	+	0.594610i
$592$	3.08120	+	13.4996i	0.126636	+	0.554831i
$593$	−7.84803	−	3.77941i	−0.322280	−	0.155202i	0.265748	−	0.964043i	$-0.414381\pi$
$593$	−7.84803	−	3.77941i	−0.322280	−	0.155202i	−0.588028	+	0.808841i	$0.700095\pi$
$594$	−0.970504	+	0.467370i	−0.0398203	+	0.0191764i
$595$		0			0
$596$	3.60489	+	1.73602i	0.147662	+	0.0711103i
$597$	−7.67695	−	9.62659i	−0.314197	−	0.393990i
$598$	2.27731	−	1.09669i	0.0931262	−	0.0448472i
$599$	−8.53595	+	10.7037i	−0.348770	+	0.437343i	−0.925013	−	0.379935i	$-0.875946\pi$
$599$	−8.53595	+	10.7037i	−0.348770	+	0.437343i	0.576244	+	0.817278i	$0.304518\pi$
$600$	5.19177	−	22.7466i	0.211953	−	0.928627i
$601$	2.24775	−	2.81859i	0.0916876	−	0.114973i	−0.733871	−	0.679288i	$-0.762289\pi$
$601$	2.24775	−	2.81859i	0.0916876	−	0.114973i	0.825559	+	0.564316i	$0.190860\pi$
$602$		0			0
$603$	23.0745	+	28.9345i	0.939666	+	1.17830i
$604$	4.08752	−	1.96844i	0.166319	−	0.0800949i
$605$	−8.49904	+	37.2367i	−0.345535	+	1.51389i
$606$	−50.1612			−2.03766
$607$	41.8239			1.69758			0.848789	−	0.528731i	$-0.177332\pi$
$607$	41.8239			1.69758			0.848789	+	0.528731i	$0.177332\pi$
$608$	1.88282	−	8.24918i	0.0763585	−	0.334548i
$609$		0			0
$610$	−5.11366	−	22.4044i	−0.207046	−	0.907127i
$611$	−0.321656	−	1.40927i	−0.0130128	−	0.0570128i
$612$	−11.1144	−	13.9370i	−0.449271	−	0.563368i
$613$	13.5051	+	16.9349i	0.545467	+	0.683994i	0.975797	−	0.218678i	$-0.0701744\pi$
$613$	13.5051	+	16.9349i	0.545467	+	0.683994i	−0.430330	+	0.902671i	$0.641603\pi$
$614$	−11.4298	−	50.0773i	−0.461270	−	2.02096i
$615$	−15.2597	−	66.8573i	−0.615332	−	2.69595i
$616$		0			0
$617$	0.123935	−	0.542996i	0.00498945	−	0.0218602i	−0.972372	−	0.233437i	$-0.925003\pi$
$617$	0.123935	−	0.542996i	0.00498945	−	0.0218602i	0.977361	+	0.211577i	$0.0678599\pi$
$618$	35.2193			1.41673
$619$	17.4530			0.701496			0.350748	−	0.936470i	$-0.385927\pi$
$619$	17.4530			0.701496			0.350748	+	0.936470i	$0.385927\pi$
$620$	−2.22012	+	9.72697i	−0.0891620	+	0.390644i
$621$	1.17767	−	0.567135i	0.0472581	−	0.0227583i
$622$	31.8339	+	39.9185i	1.27642	+	1.60058i
$623$		0			0
$624$	−10.1409	+	12.7162i	−0.405959	+	0.509057i
$625$	1.35699	−	5.94535i	0.0542795	−	0.237814i
$626$	−14.0143	+	17.5734i	−0.560125	+	0.702375i
$627$	1.28415	−	0.618413i	0.0512840	−	0.0246971i
$628$	−5.35528	−	6.71531i	−0.213699	−	0.267970i
$629$	14.6821	+	7.07051i	0.585412	+	0.281919i
$630$		0			0
$631$	28.2950	−	13.6262i	1.12641	−	0.542450i	0.224542	−	0.974464i	$-0.427912\pi$
$631$	28.2950	−	13.6262i	1.12641	−	0.542450i	0.901866	+	0.432015i	$0.142197\pi$
$632$	−9.58351	−	4.61517i	−0.381211	−	0.183582i
$633$	−5.34407	−	23.4139i	−0.212408	−	0.930618i
$634$	40.0104	+	19.2680i	1.58902	+	0.765229i
$635$	−5.91204	+	7.41346i	−0.234612	+	0.294194i
$636$	−31.0658			−1.23184
$637$		0			0
$638$	−3.34593			−0.132467
$639$	−17.4633	+	21.8982i	−0.690836	+	0.866281i
$640$	−31.6546	−	15.2441i	−1.25126	−	0.602575i
$641$	−4.25561	−	18.6450i	−0.168086	−	0.736435i	−0.986762	−	0.162178i	$-0.948148\pi$
$641$	−4.25561	−	18.6450i	−0.168086	−	0.736435i	0.818675	−	0.574257i	$-0.194709\pi$
$642$	−39.4145	−	18.9810i	−1.55557	−	0.749121i
$643$	25.9778	−	12.5103i	1.02447	−	0.493356i	0.155294	−	0.987868i	$-0.450367\pi$
$643$	25.9778	−	12.5103i	1.02447	−	0.493356i	0.869171	+	0.494512i	$0.164653\pi$
$644$		0			0
$645$	−40.2714	−	19.3937i	−1.58569	−	0.763626i
$646$	−8.85794	−	11.1075i	−0.348511	−	0.437019i
$647$	−28.6265	+	13.7858i	−1.12542	+	0.541975i	−0.901564	−	0.432647i	$-0.857580\pi$
$647$	−28.6265	+	13.7858i	−1.12542	+	0.541975i	−0.223859	+	0.974622i	$0.571866\pi$
$648$	−8.61994	+	10.8091i	−0.338623	+	0.424620i
$649$	0.513534	−	2.24994i	0.0201580	−	0.0883179i
$650$	11.9767	−	15.0184i	0.469766	−	0.589068i
$651$		0			0
$652$	11.6863	+	14.6541i	0.457670	+	0.573900i
$653$	−7.93079	+	3.81927i	−0.310356	+	0.149459i	−0.582578	−	0.812775i	$-0.697956\pi$
$653$	−7.93079	+	3.81927i	−0.310356	+	0.149459i	0.272222	+	0.962235i	$0.412242\pi$
$654$	8.87695	−	38.8924i	0.347116	−	1.52081i
$655$	−12.9496			−0.505981
$656$	−41.0092			−1.60114
$657$	−0.699907	+	3.06649i	−0.0273060	+	0.119635i
$658$		0			0
$659$	−2.14561	−	9.40054i	−0.0835812	−	0.366193i	0.915790	−	0.401658i	$-0.131566\pi$
$659$	−2.14561	−	9.40054i	−0.0835812	−	0.366193i	−0.999371	+	0.0354649i	$0.988709\pi$
$660$	1.04521	+	4.57935i	0.0406846	+	0.178251i
$661$	14.4671	+	18.1412i	0.562707	+	0.705612i	0.979056	−	0.203593i	$-0.0652619\pi$
$661$	14.4671	+	18.1412i	0.562707	+	0.705612i	−0.416349	+	0.909205i	$0.636691\pi$
$662$	−28.5561	−	35.8082i	−1.10986	−	1.39172i
$663$	4.25936	+	18.6615i	0.165420	+	0.724752i
$664$	2.42195	+	10.6112i	0.0939898	+	0.411796i
$665$		0			0
$666$	2.74591	−	12.0306i	0.106402	−	0.466178i
$667$	4.06015			0.157210
$668$	−11.5602			−0.447279
$669$	0.939323	−	4.11544i	0.0363163	−	0.159112i
$670$	−87.5763	+	42.1745i	−3.38337	+	1.62934i
$671$	−1.01164	−	1.26855i	−0.0390539	−	0.0489720i
$672$		0			0
$673$	22.0430	−	27.6411i	0.849696	−	1.06549i	−0.147381	−	0.989080i	$-0.547084\pi$
$673$	22.0430	−	27.6411i	0.849696	−	1.06549i	0.997077	−	0.0764054i	$-0.0243443\pi$
$674$	11.0672	−	48.4885i	0.426292	−	1.86771i
$675$	6.19354	−	7.76645i	0.238389	−	0.298931i
$676$	12.5102	−	6.02460i	0.481162	−	0.231715i
$677$	12.6901	+	15.9129i	0.487722	+	0.611584i	0.963411	−	0.268030i	$-0.0863726\pi$
$677$	12.6901	+	15.9129i	0.487722	+	0.611584i	−0.475689	+	0.879614i	$0.657801\pi$
$678$	54.5595	+	26.2745i	2.09535	+	1.00907i
$679$		0			0
$680$	−24.6369	+	11.8645i	−0.944781	+	0.454983i
$681$	−35.5975	−	17.1429i	−1.36410	−	0.656915i
$682$	0.405053	+	1.77465i	0.0155103	+	0.0679549i
$683$	22.1808	+	10.6817i	0.848726	+	0.408725i	0.807104	−	0.590409i	$-0.201033\pi$
$683$	22.1808	+	10.6817i	0.848726	+	0.408725i	0.0416212	+	0.999133i	$0.486748\pi$
$684$	−2.59580	+	3.25503i	−0.0992530	+	0.124459i
$685$	5.62908			0.215076
$686$		0			0
$687$	−49.3647			−1.88338
$688$	−16.6656	+	20.8980i	−0.635371	+	0.796730i
$689$	13.4587	+	6.48139i	0.512737	+	0.246921i
$690$	−3.27738	−	14.3592i	−0.124768	−	0.546644i
$691$	0.456415	+	0.219798i	0.0173629	+	0.00836151i	0.442545	−	0.896746i	$-0.354076\pi$
$691$	0.456415	+	0.219798i	0.0173629	+	0.00836151i	−0.425182	+	0.905108i	$0.639790\pi$
$692$	−14.9744	+	7.21130i	−0.569242	+	0.274133i
$693$		0			0
$694$	−33.4857	−	16.1259i	−1.27110	−	0.612129i
$695$	−11.3392	−	14.2188i	−0.430119	−	0.539352i
$696$	−11.4846	+	5.53071i	−0.435324	+	0.209641i
$697$	−30.0912	+	37.7331i	−1.13978	+	1.42924i
$698$	−12.3939	+	54.3012i	−0.469116	+	2.05533i
$699$	15.3827	−	19.2894i	0.581829	−	0.729590i
$700$		0			0
$701$	6.84039	+	8.57758i	0.258358	+	0.323971i	0.894046	−	0.447976i	$-0.147855\pi$
$701$	6.84039	+	8.57758i	0.258358	+	0.323971i	−0.635688	+	0.771946i	$0.719283\pi$
$702$	−3.04406	+	1.46594i	−0.114891	+	0.0553284i
$703$	0.846906	−	3.71054i	0.0319417	−	0.139946i
$704$	0.638015			0.0240461
$705$	−8.42296			−0.317227
$706$	5.03651	−	22.0664i	0.189551	−	0.830479i
$707$		0			0
$708$	3.34976	+	14.6762i	0.125892	+	0.551567i
$709$	8.51515	+	37.3073i	0.319793	+	1.40111i	0.837916	+	0.545799i	$0.183774\pi$
$709$	8.51515	+	37.3073i	0.319793	+	1.40111i	−0.518123	+	0.855306i	$0.673369\pi$
$710$	−45.8669	−	57.5153i	−1.72135	−	2.15851i
$711$	12.1138	+	15.1902i	0.454301	+	0.569676i
$712$	0.917722	+	4.02080i	0.0343931	+	0.150686i
$713$	−0.491515	−	2.15347i	−0.0184074	−	0.0806480i
$714$		0			0
$715$	0.502590	−	2.20199i	0.0187958	−	0.0823498i
$716$	27.8180			1.03961
$717$	60.9424			2.27594
$718$	−6.47664	+	28.3760i	−0.241706	+	1.05898i
$719$	21.7258	−	10.4626i	0.810237	−	0.390190i	0.0175709	−	0.999846i	$-0.494407\pi$
$719$	21.7258	−	10.4626i	0.810237	−	0.390190i	0.792666	+	0.609656i	$0.208692\pi$
$720$	26.4613	+	33.1815i	0.986156	+	1.23660i
$721$		0			0
$722$	19.3287	−	24.2375i	0.719341	−	0.902026i
$723$	10.7484	−	47.0918i	0.399737	−	1.75136i
$724$	3.76548	−	4.72176i	0.139943	−	0.175483i
$725$	27.8002	−	13.3879i	1.03248	−	0.497214i
$726$	−28.3405	−	35.5379i	−1.05181	−	1.31893i
$727$	2.53479	+	1.22069i	0.0940100	+	0.0452728i	0.480298	−	0.877105i	$-0.340529\pi$
$727$	2.53479	+	1.22069i	0.0940100	+	0.0452728i	−0.386288	+	0.922378i	$0.626243\pi$
$728$		0			0
$729$	14.4244	−	6.94643i	0.534237	−	0.257275i
$730$	−7.44309	−	3.58440i	−0.275481	−	0.132665i
$731$	6.99989	+	30.6685i	0.258900	+	1.13432i
$732$	9.53563	+	4.59212i	0.352447	+	0.169730i
$733$	−11.9290	+	14.9585i	−0.440607	+	0.552503i	−0.951703	−	0.307020i	$-0.900668\pi$
$733$	−11.9290	+	14.9585i	−0.440607	+	0.552503i	0.511096	+	0.859523i	$0.329240\pi$
$734$	13.7913			0.509046
$735$		0			0
$736$	−6.17340			−0.227555
$737$	−4.27899	+	5.36569i	−0.157619	+	0.197648i
$738$	32.9275	+	15.8570i	1.21208	+	0.583705i
$739$	3.14732	+	13.7893i	0.115776	+	0.507247i	0.999248	+	0.0387642i	$0.0123421\pi$
$739$	3.14732	+	13.7893i	0.115776	+	0.507247i	−0.883473	+	0.468483i	$0.844801\pi$
$740$	11.3006	+	5.44206i	0.415417	+	0.200054i
$741$	4.02783	−	1.93970i	0.147966	−	0.0712566i
$742$		0			0
$743$	44.3325	+	21.3494i	1.62640	+	0.783235i	0.999993	+	0.00374113i	$0.00119084\pi$
$743$	44.3325	+	21.3494i	1.62640	+	0.783235i	0.626410	+	0.779493i	$0.284523\pi$
$744$	4.32375	+	5.42181i	0.158516	+	0.198773i
$745$	−10.1006	+	4.86420i	−0.370058	+	0.178211i
$746$	−8.37318	+	10.4996i	−0.306564	+	0.384419i
$747$	4.42384	−	19.3821i	0.161860	−	0.709155i
$748$	2.06107	−	2.58451i	0.0753603	−	0.0944989i
$749$		0			0
$750$	−23.3566	−	29.2882i	−0.852861	−	1.06945i
$751$	31.7250	−	15.2779i	1.15766	−	0.557500i	0.246335	−	0.969185i	$-0.420774\pi$
$751$	31.7250	−	15.2779i	1.15766	−	0.557500i	0.911326	+	0.411685i	$0.135059\pi$
$752$	−1.12083	+	4.91069i	−0.0408725	+	0.179074i
$753$	−33.8869			−1.23491
$754$	−10.4948			−0.382197
$755$	−2.82863	+	12.3930i	−0.102944	+	0.451029i
$756$		0			0
$757$	−6.77214	−	29.6707i	−0.246137	−	1.07840i	−0.935318	−	0.353809i	$-0.884886\pi$
$757$	−6.77214	−	29.6707i	−0.246137	−	1.07840i	0.689180	−	0.724590i	$-0.257971\pi$
$758$	−12.5795	−	55.1145i	−0.456909	−	2.00185i
$759$	−0.648367	−	0.813027i	−0.0235342	−	0.0295110i
$760$	3.98192	+	4.99317i	0.144440	+	0.181121i
$761$	1.97566	+	8.65593i	0.0716176	+	0.313777i	0.998030	−	0.0627322i	$-0.0199814\pi$
$761$	1.97566	+	8.65593i	0.0716176	+	0.313777i	−0.926413	+	0.376509i	$0.877124\pi$
$762$	−2.51106	−	11.0017i	−0.0909662	−	0.398549i
$763$		0			0
$764$	1.26427	−	5.53911i	0.0457395	−	0.200398i
$765$	49.9471			1.80584
$766$	23.0252			0.831934
$767$	1.61074	−	7.05711i	0.0581604	−	0.254817i
$768$	43.6114	−	21.0021i	1.57369	−	0.757849i
$769$	−20.0771	−	25.1759i	−0.724000	−	0.907868i	0.274557	−	0.961571i	$-0.411469\pi$
$769$	−20.0771	−	25.1759i	−0.724000	−	0.907868i	−0.998557	+	0.0537033i	$0.982897\pi$
$770$		0			0
$771$	14.0161	−	17.5757i	0.504779	−	0.632972i
$772$	0.998803	−	4.37604i	0.0359477	−	0.157497i
$773$	20.1060	−	25.2121i	0.723161	−	0.906816i	−0.275351	−	0.961344i	$-0.588794\pi$
$773$	20.1060	−	25.2121i	0.723161	−	0.906816i	0.998512	+	0.0545281i	$0.0173654\pi$
$774$	21.4619	−	10.3355i	0.771434	−	0.371503i
$775$	−10.4663	−	13.1243i	−0.375959	−	0.471438i
$776$	−18.7994	−	9.05331i	−0.674859	−	0.324995i
$777$		0			0
$778$	−9.95813	+	4.79558i	−0.357016	+	0.171930i
$779$	10.1556	+	4.89069i	0.363863	+	0.175227i
$780$	3.27837	+	14.3635i	0.117384	+	0.514294i
$781$	−4.67967	−	2.25361i	−0.167452	−	0.0806405i
$782$	−6.46278	+	8.10406i	−0.231108	+	0.289801i
$783$	−5.42716			−0.193951
$784$		0			0
$785$	24.0663			0.858962
$786$	9.60867	−	12.0489i	0.342730	−	0.429770i
$787$	10.9850	+	5.29009i	0.391572	+	0.188571i	0.619302	−	0.785153i	$-0.287416\pi$
$787$	10.9850	+	5.29009i	0.391572	+	0.188571i	−0.227729	+	0.973724i	$0.573130\pi$
$788$	−4.01578	−	17.5943i	−0.143056	−	0.626770i
$789$	4.83244	+	2.32718i	0.172040	+	0.0828499i
$790$	−45.9762	+	22.1410i	−1.63576	+	0.787741i
$791$		0			0
$792$	1.31723	+	0.634342i	0.0468056	+	0.0225404i
$793$	−3.17308	−	3.97891i	−0.112679	−	0.141295i
$794$	52.2913	−	25.1822i	1.85575	−	0.893681i
$795$	54.2710	−	68.0537i	1.92479	−	2.41362i
$796$	−1.48415	+	6.50247i	−0.0526041	+	0.230474i
$797$	23.6735	−	29.6856i	0.838559	−	1.05152i	−0.159372	−	0.987219i	$-0.550947\pi$
$797$	23.6735	−	29.6856i	0.838559	−	1.05152i	0.997931	−	0.0643010i	$-0.0204818\pi$
$798$		0			0
$799$	3.69596	+	4.63459i	0.130754	+	0.163960i
$800$	−42.2699	+	20.3561i	−1.49447	+	0.719697i
$801$	1.67628	−	7.34425i	0.0592283	−	0.259496i
$802$	−27.8685			−0.984070
$803$	−0.583283			−0.0205836
$804$	9.96155	−	43.6444i	0.351317	−	1.53922i
$805$		0			0
$806$	1.27048	+	5.56633i	0.0447507	+	0.196065i
$807$	4.54553	+	19.9153i	0.160010	+	0.701051i
$808$	−9.89443	−	12.4072i	−0.348085	−	0.436484i
$809$	6.66773	+	8.36107i	0.234425	+	0.293959i	0.885104	−	0.465393i	$-0.154087\pi$
$809$	6.66773	+	8.36107i	0.234425	+	0.293959i	−0.650679	+	0.759353i	$0.725516\pi$
$810$	14.7589	+	64.6630i	0.518575	+	2.27203i
$811$	4.21109	+	18.4500i	0.147871	+	0.647866i	0.993475	+	0.114054i	$0.0363838\pi$
$811$	4.21109	+	18.4500i	0.147871	+	0.647866i	−0.845603	+	0.533812i	$0.820759\pi$
$812$		0			0
$813$	−13.5822	+	59.5077i	−0.476350	+	2.08703i
$814$	2.28837			0.0802072
$815$	−52.5174			−1.83960
$816$	14.8420	−	65.0272i	0.519575	−	2.27641i
$817$	6.61938	−	3.18773i	0.231583	−	0.111524i
$818$	−8.01479	−	10.0502i	−0.280231	−	0.351398i
$819$		0			0
$820$	−23.1607	+	29.0426i	−0.808807	+	1.01421i
$821$	−4.23411	+	18.5508i	−0.147771	+	0.647429i	0.845730	+	0.533611i	$0.179165\pi$
$821$	−4.23411	+	18.5508i	−0.147771	+	0.647429i	−0.993502	+	0.113818i	$0.963692\pi$
$822$	−4.17682	+	5.23757i	−0.145683	+	0.182681i
$823$	26.9019	−	12.9553i	0.937741	−	0.451592i	0.0983693	−	0.995150i	$-0.468637\pi$
$823$	26.9019	−	12.9553i	0.937741	−	0.451592i	0.839372	+	0.543558i	$0.182923\pi$
$824$	6.94709	+	8.71138i	0.242013	+	0.303475i
$825$	−7.12030	−	3.42896i	−0.247897	−	0.119381i
$826$		0			0
$827$	−25.5992	+	12.3279i	−0.890171	+	0.428684i	−0.822329	−	0.569012i	$-0.807326\pi$
$827$	−25.5992	+	12.3279i	−0.890171	+	0.428684i	−0.0678419	+	0.997696i	$0.521611\pi$
$828$	2.73677	+	1.31796i	0.0951093	+	0.0458022i
$829$	4.22752	+	18.5220i	0.146828	+	0.643294i	0.993755	+	0.111585i	$0.0355928\pi$
$829$	4.22752	+	18.5220i	0.146828	+	0.643294i	−0.846927	+	0.531709i	$0.821550\pi$
$830$	47.0449	+	22.6556i	1.63295	+	0.786388i
$831$	20.4024	−	25.5838i	0.707751	−	0.887492i
$832$	2.00118			0.0693785
$833$		0			0
$834$	21.6437			0.749458
$835$	20.1954	−	25.3242i	0.698890	−	0.876381i
$836$	−0.695603	−	0.334985i	−0.0240579	−	0.0115857i
$837$	0.657003	+	2.87852i	0.0227093	+	0.0994961i
$838$	−10.9214	−	5.25947i	−0.377274	−	0.181685i
$839$	2.88511	−	1.38940i	0.0996051	−	0.0479673i	−0.383418	−	0.923575i	$-0.625253\pi$
$839$	2.88511	−	1.38940i	0.0996051	−	0.0479673i	0.483023	+	0.875608i	$0.339539\pi$
$840$		0			0
$841$	10.9397	+	5.26828i	0.377231	+	0.181665i
$842$	7.94960	+	9.96849i	0.273961	+	0.343537i
$843$	24.3197	−	11.7117i	0.837615	−	0.403374i
$844$	−8.11104	+	10.1709i	−0.279193	+	0.350097i
$845$	−8.65728	+	37.9300i	−0.297820	+	1.30483i
$846$	2.79877	−	3.50954i	0.0962235	−	0.120660i
$847$		0			0
$848$	−32.4543	−	40.6965i	−1.11449	−	1.39752i
$849$	−31.9932	+	15.4071i	−1.09800	+	0.528770i
$850$	−17.5290	+	76.7996i	−0.601240	+	2.63420i
$851$	−2.77684			−0.0951888
$852$	33.8804			1.16072
$853$	−6.65688	+	29.1657i	−0.227927	+	0.998614i	0.723399	+	0.690430i	$0.242579\pi$
$853$	−6.65688	+	29.1657i	−0.227927	+	0.998614i	−0.951327	+	0.308184i	$0.900279\pi$
$854$		0			0
$855$	−2.59579	−	11.3729i	−0.0887740	−	0.388944i
$856$	−3.07971	−	13.4931i	−0.105262	−	0.461185i
$857$	21.5362	+	27.0056i	0.735664	+	0.922493i	0.999110	−	0.0421809i	$-0.0134306\pi$
$857$	21.5362	+	27.0056i	0.735664	+	0.922493i	−0.263446	+	0.964674i	$0.584859\pi$
$858$	1.67591	+	2.10153i	0.0572147	+	0.0717450i
$859$	−4.34074	−	19.0180i	−0.148104	−	0.648887i	−0.993411	−	0.114606i	$-0.963440\pi$
$859$	−4.34074	−	19.0180i	−0.148104	−	0.648887i	0.845307	−	0.534281i	$-0.179418\pi$
$860$	5.38771	+	23.6051i	0.183719	+	0.804927i
$861$		0			0
$862$	6.47951	−	28.3886i	0.220693	−	0.966919i
$863$	14.0747			0.479108			0.239554	−	0.970883i	$-0.422999\pi$
$863$	14.0747			0.479108			0.239554	+	0.970883i	$0.422999\pi$
$864$	8.25192			0.280736
$865$	10.3626	−	45.4014i	0.352338	−	1.54369i
$866$	53.0070	−	25.5268i	1.80125	−	0.867437i
$867$	−24.2363	−	30.3914i	−0.823108	−	1.03214i
$868$		0			0
$869$	−2.24641	+	2.81690i	−0.0762041	+	0.0955569i
$870$	−13.6078	+	59.6196i	−0.461347	+	2.02129i
$871$	−13.4214	+	16.8299i	−0.454766	+	0.570259i
$872$	11.3709	−	5.47595i	0.385068	−	0.185439i
$873$	23.7628	+	29.7976i	0.804250	+	1.00850i
$874$	2.18116	+	1.05039i	0.0737788	+	0.0355300i
$875$		0			0
$876$	3.42793	−	1.65081i	0.115819	−	0.0557756i
$877$	41.9762	+	20.2147i	1.41744	+	0.682601i	0.976615	−	0.214994i	$-0.0689731\pi$
$877$	41.9762	+	20.2147i	1.41744	+	0.682601i	0.440821	+	0.897595i	$0.354687\pi$
$878$	4.51908	+	19.7994i	0.152512	+	0.668197i
$879$	−68.8231	−	33.1434i	−2.32134	−	1.11790i
$880$	−4.90706	+	6.15326i	−0.165417	+	0.207426i
$881$	−21.2165			−0.714802			−0.357401	−	0.933951i	$-0.616337\pi$
$881$	−21.2165			−0.714802			−0.357401	+	0.933951i	$0.616337\pi$
$882$		0			0
$883$	17.0167			0.572656			0.286328	−	0.958132i	$-0.407565\pi$
$883$	17.0167			0.572656			0.286328	+	0.958132i	$0.407565\pi$
$884$	6.46471	−	8.10649i	0.217432	−	0.272651i
$885$	−38.0021	−	18.3009i	−1.27743	−	0.615177i
$886$	−2.44474	−	10.7111i	−0.0821327	−	0.359847i
$887$	−3.72673	−	1.79470i	−0.125131	−	0.0602601i	0.370271	−	0.928924i	$-0.379265\pi$
$887$	−3.72673	−	1.79470i	−0.125131	−	0.0602601i	−0.495402	+	0.868664i	$0.664979\pi$
$888$	7.85463	−	3.78259i	0.263584	−	0.126936i
$889$		0			0
$890$	17.8262	+	8.58465i	0.597536	+	0.287758i
$891$	2.91977	+	3.66127i	0.0978159	+	0.122657i
$892$	−2.06016	+	0.992119i	−0.0689791	+	0.0332186i
$893$	0.863207	−	1.08243i	0.0288861	−	0.0362220i
$894$	2.96885	−	13.0074i	0.0992932	−	0.435032i
$895$	−48.5972	+	60.9390i	−1.62443	+	2.03697i
$896$		0			0
$897$	−2.03365	−	2.55012i	−0.0679017	−	0.0851460i
$898$	10.7472	−	5.17558i	0.358639	−	0.172711i
$899$	−2.04078	+	8.94125i	−0.0680639	+	0.298207i
$900$	23.0848			0.769492
$901$	−61.2593			−2.04084
$902$	−1.50810	+	6.60740i	−0.0502141	+	0.220002i
$903$		0			0
$904$	4.26309	+	18.6778i	0.141788	+	0.621215i
$905$	3.76546	+	16.4975i	0.125168	+	0.548397i
$906$	−9.43223	−	11.8276i	−0.313365	−	0.392947i
$907$	−23.0270	−	28.8749i	−0.764599	−	0.958776i	0.235315	−	0.971919i	$-0.424388\pi$
$907$	−23.0270	−	28.8749i	−0.764599	−	0.958776i	−0.999914	+	0.0131428i	$0.995816\pi$
$908$	4.76241	+	20.8655i	0.158046	+	0.692445i
$909$	6.45011	+	28.2598i	0.213937	+	0.937317i
$910$		0			0
$911$	−0.995566	+	4.36186i	−0.0329846	+	0.144515i	−0.988739	−	0.149651i	$-0.952185\pi$
$911$	−0.995566	+	4.36186i	−0.0329846	+	0.144515i	0.955754	+	0.294166i	$0.0950420\pi$
$912$	−15.5779			−0.515837
$913$	3.68670			0.122012
$914$	−10.5576	+	46.2559i	−0.349215	+	1.53001i
$915$	−26.7181	+	12.8667i	−0.883272	+	0.425362i
$916$	16.6722	+	20.9062i	0.550864	+	0.690761i
$917$		0			0
$918$	8.63872	−	10.8326i	0.285120	−	0.357530i
$919$	−4.87747	+	21.3696i	−0.160893	+	0.704918i	0.828540	+	0.559930i	$0.189172\pi$
$919$	−4.87747	+	21.3696i	−0.160893	+	0.704918i	−0.989433	+	0.144989i	$0.953685\pi$
$920$	2.90522	−	3.64303i	0.0957823	−	0.120107i
$921$	−59.7191	+	28.7592i	−1.96781	+	0.947648i
$922$	−16.2917	−	20.4292i	−0.536540	−	0.672800i
$923$	−14.6781	−	7.06861i	−0.483136	−	0.232666i
$924$		0			0
$925$	−19.0133	+	9.15632i	−0.625153	+	0.301058i
$926$	−56.9433	−	27.4224i	−1.87127	−	0.901157i
$927$	−4.52876	−	19.8418i	−0.148744	−	0.651690i
$928$	23.0937	+	11.1214i	0.758089	+	0.365076i
$929$	−8.99711	+	11.2820i	−0.295186	+	0.370151i	−0.907203	−	0.420693i	$-0.861787\pi$
$929$	−8.99711	+	11.2820i	−0.295186	+	0.370151i	0.612017	+	0.790844i	$0.290358\pi$
$930$	33.2690			1.09093
$931$		0			0
$932$	−13.3644			−0.437767
$933$	41.0795	−	51.5120i	1.34488	−	1.68643i
$934$	−18.9223	−	9.11251i	−0.619157	−	0.298171i
$935$	2.06106	+	9.03010i	0.0674039	+	0.295316i
$936$	4.13157	+	1.98966i	0.135045	+	0.0650341i
$937$	20.6735	−	9.95585i	0.675375	−	0.325244i	−0.0645676	−	0.997913i	$-0.520567\pi$
$937$	20.6735	−	9.95585i	0.675375	−	0.325244i	0.739943	+	0.672670i	$0.234853\pi$
$938$		0			0
$939$	26.1329	+	12.5849i	0.852815	+	0.410694i
$940$	2.84472	+	3.56717i	0.0927847	+	0.116348i
$941$	53.2413	−	25.6396i	1.73562	−	0.835828i	0.751176	−	0.660102i	$-0.229487\pi$
$941$	53.2413	−	25.6396i	1.73562	−	0.835828i	0.984439	−	0.175727i	$-0.0562275\pi$
$942$	−17.8574	+	22.3924i	−0.581824	+	0.729584i
$943$	1.83001	−	8.01781i	0.0595934	−	0.261096i
$944$	−15.7265	+	19.7204i	−0.511854	+	0.641845i
$945$		0			0
$946$	2.75422	+	3.45368i	0.0895473	+	0.112289i
$947$	0.617024	−	0.297143i	0.0200506	−	0.00965586i	−0.423832	−	0.905741i	$-0.639315\pi$
$947$	0.617024	−	0.297143i	0.0200506	−	0.00965586i	0.443882	+	0.896085i	$0.353601\pi$
$948$	5.22966	−	22.9126i	0.169851	−	0.744168i
$949$	−1.82951			−0.0593884
$950$	18.3981			0.596914
$951$	12.7517	−	55.8689i	0.413503	−	1.81167i
$952$		0			0
$953$	0.779818	+	3.41660i	0.0252608	+	0.110675i	0.985987	−	0.166825i	$-0.0533514\pi$
$953$	0.779818	+	3.41660i	0.0252608	+	0.110675i	−0.960726	+	0.277500i	$0.910494\pi$
$954$	10.3224	+	45.2255i	0.334201	+	1.46423i
$955$	9.92550	+	12.4462i	0.321182	+	0.402749i
$956$	−20.5824	−	25.8095i	−0.665681	−	0.834738i
$957$	0.960777	+	4.20944i	0.0310575	+	0.136072i
$958$	−2.04972	−	8.98043i	−0.0662236	−	0.290145i
$959$		0			0
$960$	2.59479	−	11.3685i	0.0837463	−	0.366917i
$961$	−26.0106			−0.839051
$962$	7.17763			0.231416
$963$	−5.62529	+	24.6460i	−0.181272	+	0.794206i
$964$	−23.5737	+	11.3525i	−0.759259	+	0.365640i
$965$	7.84141	+	9.83281i	0.252424	+	0.316530i
$966$		0			0
$967$	19.8683	−	24.9140i	0.638920	−	0.801180i	−0.351947	−	0.936020i	$-0.614480\pi$
$967$	19.8683	−	24.9140i	0.638920	−	0.801180i	0.990867	+	0.134839i	$0.0430518\pi$
$968$	3.19994	−	14.0199i	0.102850	−	0.450616i
$969$	−11.4306	+	14.3335i	−0.367203	+	0.460458i
$970$	−90.1888	+	43.4326i	−2.89579	+	1.39454i
$971$	−21.2923	−	26.6997i	−0.683301	−	0.856833i	0.312352	−	0.949966i	$-0.398883\pi$
$971$	−21.2923	−	26.6997i	−0.683301	−	0.856833i	−0.995654	+	0.0931336i	$0.970312\pi$
$972$	−23.0106	−	11.0813i	−0.738065	−	0.355434i
$973$		0			0
$974$	32.1811	−	15.4976i	1.03115	−	0.496576i
$975$	−22.3333	−	10.7552i	−0.715239	−	0.344441i
$976$	3.94613	+	17.2891i	0.126313	+	0.553411i
$977$	−5.92022	−	2.85103i	−0.189404	−	0.0912124i	0.336778	−	0.941584i	$-0.390663\pi$
$977$	−5.92022	−	2.85103i	−0.189404	−	0.0912124i	−0.526182	+	0.850372i	$0.676377\pi$
$978$	38.9683	−	48.8647i	1.24607	−	1.56252i
$979$	1.39696			0.0446471
$980$		0			0
$981$	−23.0526			−0.736014
$982$	10.7475	−	13.4769i	0.342965	−	0.430065i
$983$	−44.2225	−	21.2964i	−1.41048	−	0.679251i	−0.435221	−	0.900324i	$-0.643330\pi$
$983$	−44.2225	−	21.2964i	−1.41048	−	0.679251i	−0.975257	+	0.221073i	$0.929044\pi$
$984$	5.74539	+	25.1722i	0.183156	+	0.802460i
$985$	45.5580	+	21.9396i	1.45160	+	0.699053i
$986$	38.7757	−	18.6734i	1.23487	−	0.594682i
$987$		0			0
$988$	−2.18181	−	1.05070i	−0.0694126	−	0.0334274i
$989$	−3.34213	−	4.19090i	−0.106274	−	0.133263i
$990$	6.31930	−	3.04321i	0.200841	−	0.0967197i
$991$	11.1568	−	13.9902i	0.354409	−	0.444414i	−0.572385	−	0.819985i	$-0.693982\pi$
$991$	11.1568	−	13.9902i	0.354409	−	0.444414i	0.926794	+	0.375570i	$0.122553\pi$
$992$	3.10298	−	13.5950i	0.0985197	−	0.431643i
$993$	−36.8496	+	46.2080i	−1.16939	+	1.46637i
$994$		0			0
$995$	−11.6517	−	14.6108i	−0.369385	−	0.463194i
$996$	−21.6666	+	10.4341i	−0.686534	+	0.330617i
$997$	8.51187	−	37.2929i	0.269574	−	1.18108i	−0.640937	−	0.767593i	$-0.721454\pi$
$997$	8.51187	−	37.2929i	0.269574	−	1.18108i	0.910511	−	0.413486i	$-0.135689\pi$
$998$	34.5968			1.09514
$999$	3.71177			0.117435

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	343.2.e.d.295.2		48
7.2	even	3		49.2.g.a.39.4	✓	48
7.3	odd	6		343.2.g.h.226.1		48
7.4	even	3		343.2.g.i.226.1		48
7.5	odd	6		343.2.g.g.165.4		48
7.6	odd	2		343.2.e.c.295.2		48
21.2	odd	6		441.2.bb.d.235.1		48
28.23	odd	6		784.2.bg.c.529.3		48
49.3	odd	42		343.2.g.g.79.4		48
49.5	odd	42		343.2.g.h.214.1		48
49.8	even	7	inner	343.2.e.d.50.2		48
49.20	odd	14		2401.2.a.i.1.6		24
49.29	even	7		2401.2.a.h.1.6		24
49.41	odd	14		343.2.e.c.50.2		48
49.44	even	21		343.2.g.i.214.1		48
49.46	even	21		49.2.g.a.44.4	yes	48
147.95	odd	42		441.2.bb.d.289.1		48
196.95	odd	42		784.2.bg.c.289.3		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
49.2.g.a.39.4	✓	48	7.2	even	3
49.2.g.a.44.4	yes	48	49.46	even	21
343.2.e.c.50.2		48	49.41	odd	14
343.2.e.c.295.2		48	7.6	odd	2
343.2.e.d.50.2		48	49.8	even	7	inner
343.2.e.d.295.2		48	1.1	even	1	trivial
343.2.g.g.79.4		48	49.3	odd	42
343.2.g.g.165.4		48	7.5	odd	6
343.2.g.h.214.1		48	49.5	odd	42
343.2.g.h.226.1		48	7.3	odd	6
343.2.g.i.214.1		48	49.44	even	21
343.2.g.i.226.1		48	7.4	even	3
441.2.bb.d.235.1		48	21.2	odd	6
441.2.bb.d.289.1		48	147.95	odd	42
784.2.bg.c.289.3		48	196.95	odd	42
784.2.bg.c.529.3		48	28.23	odd	6
2401.2.a.h.1.6		24	49.29	even	7
2401.2.a.i.1.6		24	49.20	odd	14

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:	\( N \)	\(=\)	\( 343 = 7^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	343.e (of order \(7\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.12619 + 1.41219i) q^{2} +(2.10003 + 1.01132i) q^{3} +(-0.280953 - 1.23093i) q^{4} +(3.18734 + 1.53494i) q^{5} +(-3.79321 + 1.82671i) q^{6} +(-1.20005 - 0.577915i) q^{8} +(1.51689 + 1.90212i) q^{9} +O(q^{10})\)	\(q+(-1.12619 + 1.41219i) q^{2} +(2.10003 + 1.01132i) q^{3} +(-0.280953 - 1.23093i) q^{4} +(3.18734 + 1.53494i) q^{5} +(-3.79321 + 1.82671i) q^{6} +(-1.20005 - 0.577915i) q^{8} +(1.51689 + 1.90212i) q^{9} +(-5.75717 + 2.77251i) q^{10} +(-0.281296 + 0.352734i) q^{11} +(0.654861 - 2.86913i) q^{12} +(-0.882307 + 1.10638i) q^{13} +(5.14119 + 6.44685i) q^{15} +(4.44272 - 2.13950i) q^{16} +(1.29133 - 5.65770i) q^{17} -4.39447 q^{18} -1.35536 q^{19} +(0.993919 - 4.35465i) q^{20} +(-0.181337 - 0.794490i) q^{22} +(0.220045 + 0.964081i) q^{23} +(-1.93569 - 2.42728i) q^{24} +(4.68562 + 5.87558i) q^{25} +(-0.568777 - 2.49198i) q^{26} +(-0.294132 - 1.28868i) q^{27} +(0.913633 - 4.00289i) q^{29} -14.8941 q^{30} -2.23370 q^{31} +(-1.38917 + 6.08633i) q^{32} +(-0.947459 + 0.456272i) q^{33} +(6.53549 + 8.19524i) q^{34} +(1.91521 - 2.40160i) q^{36} +(-0.624857 + 2.73768i) q^{37} +(1.52639 - 1.91403i) q^{38} +(-2.97178 + 1.43113i) q^{39} +(-2.93791 - 3.68402i) q^{40} +(-7.49293 - 3.60841i) q^{41} +(-4.88385 + 2.35194i) q^{43} +(0.513224 + 0.247155i) q^{44} +(1.91520 + 8.39104i) q^{45} +(-1.60928 - 0.774989i) q^{46} +(-0.636883 + 0.798627i) q^{47} +11.4936 q^{48} -13.5743 q^{50} +(8.43360 - 10.5754i) q^{51} +(1.60976 + 0.775221i) q^{52} +(-2.34896 - 10.2915i) q^{53} +(2.15111 + 1.03592i) q^{54} +(-1.43801 + 0.692510i) q^{55} +(-2.84630 - 1.37071i) q^{57} +(4.62393 + 5.79823i) q^{58} +(-4.60865 + 2.21941i) q^{59} +(6.49121 - 8.13972i) q^{60} +(-0.800262 + 3.50618i) q^{61} +(2.51556 - 3.15442i) q^{62} +(-0.881710 - 1.10563i) q^{64} +(-4.51043 + 2.17211i) q^{65} +(0.422671 - 1.85184i) q^{66} +15.2117 q^{67} -7.32706 q^{68} +(-0.512895 + 2.24714i) q^{69} +(2.56178 + 11.2239i) q^{71} +(-0.721085 - 3.15928i) q^{72} +(0.806072 + 1.01078i) q^{73} +(-3.16242 - 3.96556i) q^{74} +(3.89785 + 17.0776i) q^{75} +(0.380792 + 1.66836i) q^{76} +(1.32574 - 5.80845i) q^{78} +7.98591 q^{79} +17.4444 q^{80} +(2.30970 - 10.1194i) q^{81} +(13.5342 - 6.51773i) q^{82} +(-5.09487 - 6.38876i) q^{83} +(12.8001 - 16.0509i) q^{85} +(2.17874 - 9.54568i) q^{86} +(5.96687 - 7.48222i) q^{87} +(0.541421 - 0.260734i) q^{88} +(-1.93054 - 2.42082i) q^{89} +(-14.0067 - 6.74525i) q^{90} +(1.12490 - 0.541722i) q^{92} +(-4.69084 - 2.25899i) q^{93} +(-0.410566 - 1.79881i) q^{94} +(-4.31999 - 2.08040i) q^{95} +(-9.07254 + 11.3766i) q^{96} +15.6655 q^{97} -1.09764 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 5 q^{2} + 7 q^{3} - 3 q^{4} + 7 q^{5} - 20 q^{8} + 9 q^{9}+O(q^{10}) \) 48 * q + 5 * q^2 + 7 * q^3 - 3 * q^4 + 7 * q^5 - 20 * q^8 + 9 * q^9	\( 48 q + 5 q^{2} + 7 q^{3} - 3 q^{4} + 7 q^{5} - 20 q^{8} + 9 q^{9} + 7 q^{10} + 6 q^{11} + 42 q^{12} - 14 q^{13} - 12 q^{15} - 15 q^{16} - 7 q^{17} - 4 q^{18} - 42 q^{19} + 14 q^{20} - 20 q^{22} + 12 q^{23} + 49 q^{24} - 13 q^{25} + 21 q^{26} + 7 q^{27} + 12 q^{29} - 22 q^{30} - 70 q^{31} + 15 q^{32} + 7 q^{33} + 70 q^{34} - 12 q^{36} - 9 q^{37} - 7 q^{38} - 28 q^{39} - 63 q^{40} - 42 q^{41} - 30 q^{43} + 37 q^{44} + 28 q^{45} + 9 q^{46} + 21 q^{47} - 84 q^{48} + 40 q^{50} - q^{51} + 77 q^{52} + 20 q^{53} + 7 q^{54} - 7 q^{55} - 12 q^{57} + 31 q^{58} - 7 q^{59} + 35 q^{60} + 7 q^{61} - 28 q^{62} - 32 q^{64} - 49 q^{65} - 119 q^{66} - 22 q^{67} - 154 q^{68} + 70 q^{69} + 19 q^{71} - 46 q^{72} + 28 q^{73} - 47 q^{74} + 7 q^{75} + 119 q^{76} + 28 q^{78} - 30 q^{79} - 140 q^{80} + 61 q^{81} + 112 q^{82} - 26 q^{85} + 24 q^{86} + 77 q^{87} + 28 q^{88} + 28 q^{89} - 182 q^{90} - 38 q^{92} + 34 q^{93} - 28 q^{94} - 67 q^{95} - 28 q^{96} - 16 q^{99}+O(q^{100}) \) 48 * q + 5 * q^2 + 7 * q^3 - 3 * q^4 + 7 * q^5 - 20 * q^8 + 9 * q^9 + 7 * q^10 + 6 * q^11 + 42 * q^12 - 14 * q^13 - 12 * q^15 - 15 * q^16 - 7 * q^17 - 4 * q^18 - 42 * q^19 + 14 * q^20 - 20 * q^22 + 12 * q^23 + 49 * q^24 - 13 * q^25 + 21 * q^26 + 7 * q^27 + 12 * q^29 - 22 * q^30 - 70 * q^31 + 15 * q^32 + 7 * q^33 + 70 * q^34 - 12 * q^36 - 9 * q^37 - 7 * q^38 - 28 * q^39 - 63 * q^40 - 42 * q^41 - 30 * q^43 + 37 * q^44 + 28 * q^45 + 9 * q^46 + 21 * q^47 - 84 * q^48 + 40 * q^50 - q^51 + 77 * q^52 + 20 * q^53 + 7 * q^54 - 7 * q^55 - 12 * q^57 + 31 * q^58 - 7 * q^59 + 35 * q^60 + 7 * q^61 - 28 * q^62 - 32 * q^64 - 49 * q^65 - 119 * q^66 - 22 * q^67 - 154 * q^68 + 70 * q^69 + 19 * q^71 - 46 * q^72 + 28 * q^73 - 47 * q^74 + 7 * q^75 + 119 * q^76 + 28 * q^78 - 30 * q^79 - 140 * q^80 + 61 * q^81 + 112 * q^82 - 26 * q^85 + 24 * q^86 + 77 * q^87 + 28 * q^88 + 28 * q^89 - 182 * q^90 - 38 * q^92 + 34 * q^93 - 28 * q^94 - 67 * q^95 - 28 * q^96 - 16 * q^99

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