LMFDB - Embedded newform 342.2.h.f.277.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [342,2,Mod(121,342)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(342, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 2]))

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

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

chi := DirichletCharacter("342.121");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 342 = 2 \cdot 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	342.h (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$2.73088374913$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{3})$
Coefficient field:	10.0.50911458676875.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 4x^{9} + 12x^{8} - 28x^{7} + 58x^{6} - 111x^{5} + 174x^{4} - 252x^{3} + 324x^{2} - 324x + 243 $ x^10 - 4x^9 + 12x^8 - 28x^7 + 58x^6 - 111x^5 + 174x^4 - 252x^3 + 324x^2 - 324*x + 243
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			277.3
Root			$0.776413 + 1.54828i$ of defining polynomial
Character	$\chi$	$=$	342.277
Dual form			342.2.h.f.121.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{2} +(-0.776413 + 1.54828i) q^{3} +(-0.500000 + 0.866025i) q^{4} +3.45812 q^{5} +(1.72906 - 0.101749i) q^{6} +(-2.30306 + 3.98902i) q^{7} +1.00000 q^{8} +(-1.79437 - 2.40422i) q^{9} +O(q^{10})$	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.776413 + 1.54828i) q^{3} +(-0.500000 + 0.866025i) q^{4} +3.45812 q^{5} +(1.72906 - 0.101749i) q^{6} +(-2.30306 + 3.98902i) q^{7} +1.00000 q^{8} +(-1.79437 - 2.40422i) q^{9} +(-1.72906 - 2.99482i) q^{10} +(-0.118132 + 0.204611i) q^{11} +(-0.952647 - 1.44654i) q^{12} +(-0.105455 + 0.182653i) q^{13} +4.60612 q^{14} +(-2.68493 + 5.35415i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-2.92119 + 5.05965i) q^{17} +(-1.18493 + 2.75607i) q^{18} +(-0.908515 - 4.26317i) q^{19} +(-1.72906 + 2.99482i) q^{20} +(-4.38801 - 6.66292i) q^{21} +0.236264 q^{22} +(-3.32649 + 5.76164i) q^{23} +(-0.776413 + 1.54828i) q^{24} +6.95859 q^{25} +0.210910 q^{26} +(5.11558 - 0.911525i) q^{27} +(-2.30306 - 3.98902i) q^{28} +4.90529 q^{29} +(5.97929 - 0.351859i) q^{30} +(4.91797 + 8.51818i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(-0.225077 - 0.341765i) q^{33} +5.84239 q^{34} +(-7.96426 + 13.7945i) q^{35} +(2.97929 - 0.351859i) q^{36} -1.63014 q^{37} +(-3.23775 + 2.91838i) q^{38} +(-0.200923 - 0.305088i) q^{39} +3.45812 q^{40} +7.48645 q^{41} +(-3.57625 + 7.13158i) q^{42} +(-2.58495 - 4.47726i) q^{43} +(-0.118132 - 0.204611i) q^{44} +(-6.20513 - 8.31406i) q^{45} +6.65297 q^{46} +0.105651 q^{47} +(1.72906 - 0.101749i) q^{48} +(-7.10818 - 12.3117i) q^{49} +(-3.47929 - 6.02631i) q^{50} +(-5.56573 - 8.45122i) q^{51} +(-0.105455 - 0.182653i) q^{52} +(0.347192 + 0.601354i) q^{53} +(-3.34719 - 3.97446i) q^{54} +(-0.408515 + 0.707569i) q^{55} +(-2.30306 + 3.98902i) q^{56} +(7.30598 + 1.90334i) q^{57} +(-2.45265 - 4.24811i) q^{58} +4.43276 q^{59} +(-3.29437 - 5.00229i) q^{60} -4.36043 q^{61} +(4.91797 - 8.51818i) q^{62} +(13.7230 - 1.62071i) q^{63} +1.00000 q^{64} +(-0.364676 + 0.631637i) q^{65} +(-0.183439 + 0.365805i) q^{66} +(2.75969 - 4.77992i) q^{67} +(-2.92119 - 5.05965i) q^{68} +(-6.33793 - 9.62376i) q^{69} +15.9285 q^{70} +(-1.04188 + 1.80459i) q^{71} +(-1.79437 - 2.40422i) q^{72} +(3.29586 - 5.70859i) q^{73} +(0.815072 + 1.41175i) q^{74} +(-5.40274 + 10.7739i) q^{75} +(4.14627 + 1.34479i) q^{76} +(-0.544131 - 0.942463i) q^{77} +(-0.163753 + 0.326548i) q^{78} +(-6.07625 - 10.5244i) q^{79} +(-1.72906 - 2.99482i) q^{80} +(-2.56050 + 8.62808i) q^{81} +(-3.74323 - 6.48346i) q^{82} +(5.48799 - 9.50548i) q^{83} +(7.96426 - 0.468667i) q^{84} +(-10.1018 + 17.4969i) q^{85} +(-2.58495 + 4.47726i) q^{86} +(-3.80853 + 7.59479i) q^{87} +(-0.118132 + 0.204611i) q^{88} +(-1.63061 - 2.82430i) q^{89} +(-4.09762 + 9.53083i) q^{90} +(-0.485738 - 0.841323i) q^{91} +(-3.32649 - 5.76164i) q^{92} +(-17.0069 + 1.00079i) q^{93} +(-0.0528257 - 0.0914968i) q^{94} +(-3.14175 - 14.7425i) q^{95} +(-0.952647 - 1.44654i) q^{96} +(-2.61813 - 4.53474i) q^{97} +(-7.10818 + 12.3117i) q^{98} +(0.703901 - 0.0831318i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 5 q^{2} - 4 q^{3} - 5 q^{4} + 4 q^{5} + 2 q^{6} - 5 q^{7} + 10 q^{8} - 8 q^{9}+O(q^{10}) $ 10 * q - 5 * q^2 - 4 * q^3 - 5 * q^4 + 4 * q^5 + 2 * q^6 - 5 * q^7 + 10 * q^8 - 8 * q^9	\( 10 q - 5 q^{2} - 4 q^{3} - 5 q^{4} + 4 q^{5} + 2 q^{6} - 5 q^{7} + 10 q^{8} - 8 q^{9} - 2 q^{10} + q^{11} + 2 q^{12} - 7 q^{13} + 10 q^{14} - 11 q^{15} - 5 q^{16} - 9 q^{17} + 4 q^{18} + 3 q^{19} - 2 q^{20} + 15 q^{21} - 2 q^{22} + 10 q^{23} - 4 q^{24} + 18 q^{25} + 14 q^{26} - 4 q^{27} - 5 q^{28} + 26 q^{29} + 34 q^{30} + 18 q^{31} - 5 q^{32} + 13 q^{33} + 18 q^{34} + 12 q^{35} + 4 q^{36} - 48 q^{37} - 9 q^{38} - 20 q^{39} + 4 q^{40} - 10 q^{41} - 3 q^{42} + 15 q^{43} + q^{44} - 10 q^{45} - 20 q^{46} - 14 q^{47} + 2 q^{48} - 26 q^{49} - 9 q^{50} + 30 q^{51} - 7 q^{52} - 14 q^{53} - 16 q^{54} + 8 q^{55} - 5 q^{56} - 17 q^{57} - 13 q^{58} + 30 q^{59} - 23 q^{60} - 28 q^{61} + 18 q^{62} + 48 q^{63} + 10 q^{64} - q^{65} - 5 q^{66} - 2 q^{67} - 9 q^{68} - 44 q^{69} - 24 q^{70} - 41 q^{71} - 8 q^{72} + 4 q^{73} + 24 q^{74} + 22 q^{75} + 6 q^{76} - 6 q^{77} + 19 q^{78} - 28 q^{79} - 2 q^{80} - 8 q^{81} + 5 q^{82} + 21 q^{83} - 12 q^{84} + 18 q^{85} + 15 q^{86} - q^{87} + q^{88} - 27 q^{89} + 8 q^{90} - q^{91} + 10 q^{92} - 49 q^{93} + 7 q^{94} + 17 q^{95} + 2 q^{96} - 24 q^{97} - 26 q^{98} - 13 q^{99}+O(q^{100}) \) 10 * q - 5 * q^2 - 4 * q^3 - 5 * q^4 + 4 * q^5 + 2 * q^6 - 5 * q^7 + 10 * q^8 - 8 * q^9 - 2 * q^10 + q^11 + 2 * q^12 - 7 * q^13 + 10 * q^14 - 11 * q^15 - 5 * q^16 - 9 * q^17 + 4 * q^18 + 3 * q^19 - 2 * q^20 + 15 * q^21 - 2 * q^22 + 10 * q^23 - 4 * q^24 + 18 * q^25 + 14 * q^26 - 4 * q^27 - 5 * q^28 + 26 * q^29 + 34 * q^30 + 18 * q^31 - 5 * q^32 + 13 * q^33 + 18 * q^34 + 12 * q^35 + 4 * q^36 - 48 * q^37 - 9 * q^38 - 20 * q^39 + 4 * q^40 - 10 * q^41 - 3 * q^42 + 15 * q^43 + q^44 - 10 * q^45 - 20 * q^46 - 14 * q^47 + 2 * q^48 - 26 * q^49 - 9 * q^50 + 30 * q^51 - 7 * q^52 - 14 * q^53 - 16 * q^54 + 8 * q^55 - 5 * q^56 - 17 * q^57 - 13 * q^58 + 30 * q^59 - 23 * q^60 - 28 * q^61 + 18 * q^62 + 48 * q^63 + 10 * q^64 - q^65 - 5 * q^66 - 2 * q^67 - 9 * q^68 - 44 * q^69 - 24 * q^70 - 41 * q^71 - 8 * q^72 + 4 * q^73 + 24 * q^74 + 22 * q^75 + 6 * q^76 - 6 * q^77 + 19 * q^78 - 28 * q^79 - 2 * q^80 - 8 * q^81 + 5 * q^82 + 21 * q^83 - 12 * q^84 + 18 * q^85 + 15 * q^86 - q^87 + q^88 - 27 * q^89 + 8 * q^90 - q^91 + 10 * q^92 - 49 * q^93 + 7 * q^94 + 17 * q^95 + 2 * q^96 - 24 * q^97 - 26 * q^98 - 13 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/342\mathbb{Z}\right)^\times$.

$n$	$191$	$325$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$

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
$3$	−0.776413	+	1.54828i	−0.448262	+	0.893902i
$3$	−0.776413	+	1.54828i	−0.448262	+	0.893902i
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	3.45812			1.54652			0.773259	−	0.634090i	$-0.218625\pi$
$5$	3.45812			1.54652			0.773259	+	0.634090i	$0.218625\pi$
$6$	1.72906	−	0.101749i	0.705886	−	0.0415387i
$7$	−2.30306	+	3.98902i	−0.870475	+	1.50771i	−0.00896894	+	0.999960i	$0.502855\pi$
$7$	−2.30306	+	3.98902i	−0.870475	+	1.50771i	−0.861506	+	0.507747i	$0.830478\pi$
$8$	1.00000			0.353553
$9$	−1.79437	−	2.40422i	−0.598122	−	0.801405i
$10$	−1.72906	−	2.99482i	−0.546777	−	0.947045i
$11$	−0.118132	+	0.204611i	−0.0356182	+	0.0616926i	−0.883285	−	0.468836i	$-0.844673\pi$
$11$	−0.118132	+	0.204611i	−0.0356182	+	0.0616926i	0.847667	+	0.530529i	$0.178007\pi$
$12$	−0.952647	−	1.44654i	−0.275005	−	0.417579i
$13$	−0.105455	+	0.182653i	−0.0292479	+	0.0506589i	−0.880279	−	0.474457i	$-0.842645\pi$
$13$	−0.105455	+	0.182653i	−0.0292479	+	0.0506589i	0.851031	+	0.525116i	$0.175978\pi$
$14$	4.60612			1.23104
$15$	−2.68493	+	5.35415i	−0.693245	+	1.38244i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−2.92119	+	5.05965i	−0.708493	+	1.22715i	0.256923	+	0.966432i	$0.417291\pi$
$17$	−2.92119	+	5.05965i	−0.708493	+	1.22715i	−0.965416	+	0.260714i	$0.916042\pi$
$18$	−1.18493	+	2.75607i	−0.279290	+	0.649613i
$19$	−0.908515	−	4.26317i	−0.208428	−	0.978038i
$19$	−0.908515	−	4.26317i	−0.208428	−	0.978038i
$20$	−1.72906	+	2.99482i	−0.386629	+	0.669662i
$21$	−4.38801	−	6.66292i	−0.957541	−	1.45397i
$22$	0.236264			0.0503718
$23$	−3.32649	+	5.76164i	−0.693620	+	1.20139i	0.277023	+	0.960863i	$0.410652\pi$
$23$	−3.32649	+	5.76164i	−0.693620	+	1.20139i	−0.970644	+	0.240522i	$0.922681\pi$
$24$	−0.776413	+	1.54828i	−0.158485	+	0.316042i
$25$	6.95859			1.39172
$26$	0.210910			0.0413628
$27$	5.11558	−	0.911525i	0.984493	−	0.175423i
$28$	−2.30306	−	3.98902i	−0.435238	−	0.753853i
$29$	4.90529			0.910890			0.455445	−	0.890264i	$-0.349480\pi$
$29$	4.90529			0.910890			0.455445	+	0.890264i	$0.349480\pi$
$30$	5.97929	−	0.351859i	1.09166	−	0.0642404i
$31$	4.91797	+	8.51818i	0.883294	+	1.52991i	0.847657	+	0.530545i	$0.178013\pi$
$31$	4.91797	+	8.51818i	0.883294	+	1.52991i	0.0356367	+	0.999365i	$0.488654\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$	−0.225077	−	0.341765i	−0.0391808	−	0.0594936i
$34$	5.84239			1.00196
$35$	−7.96426	+	13.7945i	−1.34621	+	2.33170i
$36$	2.97929	−	0.351859i	0.496549	−	0.0586432i
$37$	−1.63014			−0.267994			−0.133997	−	0.990982i	$-0.542781\pi$
$37$	−1.63014			−0.267994			−0.133997	+	0.990982i	$0.542781\pi$
$38$	−3.23775	+	2.91838i	−0.525233	+	0.473424i
$39$	−0.200923	−	0.305088i	−0.0321734	−	0.0488533i
$40$	3.45812			0.546777
$41$	7.48645			1.16919			0.584594	−	0.811326i	$-0.301254\pi$
$41$	7.48645			1.16919			0.584594	+	0.811326i	$0.301254\pi$
$42$	−3.57625	+	7.13158i	−0.551828	+	1.10043i
$43$	−2.58495	−	4.47726i	−0.394201	−	0.682775i	0.598798	−	0.800900i	$-0.295645\pi$
$43$	−2.58495	−	4.47726i	−0.394201	−	0.682775i	−0.992999	+	0.118125i	$0.962312\pi$
$44$	−0.118132	−	0.204611i	−0.0178091	−	0.0308463i
$45$	−6.20513	−	8.31406i	−0.925006	−	1.23939i
$46$	6.65297			0.980927
$47$	0.105651			0.0154108			0.00770542	−	0.999970i	$-0.497547\pi$
$47$	0.105651			0.0154108			0.00770542	+	0.999970i	$0.497547\pi$
$48$	1.72906	−	0.101749i	0.249568	−	0.0146862i
$49$	−7.10818	−	12.3117i	−1.01545	−	1.75882i
$50$	−3.47929	−	6.02631i	−0.492047	−	0.852250i
$51$	−5.56573	−	8.45122i	−0.779358	−	1.18341i
$52$	−0.105455	−	0.182653i	−0.0146240	−	0.0253294i
$53$	0.347192	+	0.601354i	0.0476905	+	0.0826023i	0.888885	−	0.458130i	$-0.151481\pi$
$53$	0.347192	+	0.601354i	0.0476905	+	0.0826023i	−0.841195	+	0.540732i	$0.818147\pi$
$54$	−3.34719	−	3.97446i	−0.455495	−	0.540855i
$55$	−0.408515	+	0.707569i	−0.0550842	+	0.0954086i
$56$	−2.30306	+	3.98902i	−0.307759	+	0.533055i
$57$	7.30598	+	1.90334i	0.967700	+	0.252103i
$58$	−2.45265	−	4.24811i	−0.322048	−	0.557804i
$59$	4.43276			0.577097			0.288548	−	0.957465i	$-0.406827\pi$
$59$	4.43276			0.577097			0.288548	+	0.957465i	$0.406827\pi$
$60$	−3.29437	−	5.00229i	−0.425301	−	0.645793i
$61$	−4.36043			−0.558296			−0.279148	−	0.960248i	$-0.590052\pi$
$61$	−4.36043			−0.558296			−0.279148	+	0.960248i	$0.590052\pi$
$62$	4.91797	−	8.51818i	0.624583	−	1.08181i
$63$	13.7230	−	1.62071i	1.72893	−	0.204190i
$64$	1.00000			0.125000
$65$	−0.364676	+	0.631637i	−0.0452324	+	0.0783449i
$66$	−0.183439	+	0.365805i	−0.0225798	+	0.0450274i
$67$	2.75969	−	4.77992i	0.337150	−	0.583961i	−0.646746	−	0.762706i	$-0.723870\pi$
$67$	2.75969	−	4.77992i	0.337150	−	0.583961i	0.983895	+	0.178745i	$0.0572038\pi$
$68$	−2.92119	−	5.05965i	−0.354247	−	0.613573i
$69$	−6.33793	−	9.62376i	−0.762997	−	1.15856i
$70$	15.9285			1.90382
$71$	−1.04188	+	1.80459i	−0.123648	+	0.214165i	−0.921204	−	0.389080i	$-0.872793\pi$
$71$	−1.04188	+	1.80459i	−0.123648	+	0.214165i	0.797555	+	0.603246i	$0.206126\pi$
$72$	−1.79437	−	2.40422i	−0.211468	−	0.283339i
$73$	3.29586	−	5.70859i	0.385751	−	0.668140i	−0.606122	−	0.795371i	$-0.707276\pi$
$73$	3.29586	−	5.70859i	0.385751	−	0.668140i	0.991873	+	0.127232i	$0.0406091\pi$
$74$	0.815072	+	1.41175i	0.0947502	+	0.164112i
$75$	−5.40274	+	10.7739i	−0.623854	+	1.24406i
$76$	4.14627	+	1.34479i	0.475610	+	0.154258i
$77$	−0.544131	−	0.942463i	−0.0620095	−	0.107404i
$78$	−0.163753	+	0.326548i	−0.0185414	+	0.0369743i
$79$	−6.07625	−	10.5244i	−0.683632	−	1.18408i	−0.973865	−	0.227129i	$-0.927066\pi$
$79$	−6.07625	−	10.5244i	−0.683632	−	1.18408i	0.290233	−	0.956956i	$-0.406267\pi$
$80$	−1.72906	−	2.99482i	−0.193315	−	0.334831i
$81$	−2.56050	+	8.62808i	−0.284500	+	0.958676i
$82$	−3.74323	−	6.48346i	−0.413370	−	0.715978i
$83$	5.48799	−	9.50548i	0.602385	−	1.04336i	−0.390074	−	0.920784i	$-0.627551\pi$
$83$	5.48799	−	9.50548i	0.602385	−	1.04336i	0.992459	−	0.122578i	$-0.0391161\pi$
$84$	7.96426	−	0.468667i	0.868972	−	0.0511357i
$85$	−10.1018	+	17.4969i	−1.09570	+	1.89780i
$86$	−2.58495	+	4.47726i	−0.278742	+	0.482795i
$87$	−3.80853	+	7.59479i	−0.408318	+	0.814247i
$88$	−0.118132	+	0.204611i	−0.0125929	+	0.0218116i
$89$	−1.63061	−	2.82430i	−0.172845	−	0.299376i	0.766569	−	0.642162i	$-0.221963\pi$
$89$	−1.63061	−	2.82430i	−0.172845	−	0.299376i	−0.939413	+	0.342787i	$0.888629\pi$
$90$	−4.09762	+	9.53083i	−0.431927	+	1.00464i
$91$	−0.485738	−	0.841323i	−0.0509192	−	0.0881946i
$92$	−3.32649	−	5.76164i	−0.346810	−	0.600693i
$93$	−17.0069	+	1.00079i	−1.76354	+	0.103778i
$94$	−0.0528257	−	0.0914968i	−0.00544856	−	0.00943717i
$95$	−3.14175	−	14.7425i	−0.322337	−	1.51255i
$96$	−0.952647	−	1.44654i	−0.0972291	−	0.147636i
$97$	−2.61813	−	4.53474i	−0.265831	−	0.460433i	0.701950	−	0.712226i	$-0.252313\pi$
$97$	−2.61813	−	4.53474i	−0.265831	−	0.460433i	−0.967781	+	0.251793i	$0.918980\pi$
$98$	−7.10818	+	12.3117i	−0.718034	+	1.24367i
$99$	0.703901	−	0.0831318i	0.0707448	−	0.00835506i
$100$	−3.47929	+	6.02631i	−0.347929	+	0.602631i
$101$	13.2312			1.31655			0.658274	−	0.752778i	$-0.271287\pi$
$101$	13.2312			1.31655			0.658274	+	0.752778i	$0.271287\pi$
$102$	−4.53610	+	9.04567i	−0.449141	+	0.895655i
$103$	7.40068	+	12.8184i	0.729211	+	1.26303i	0.957217	+	0.289371i	$0.0934461\pi$
$103$	7.40068	+	12.8184i	0.729211	+	1.26303i	−0.228006	+	0.973660i	$0.573221\pi$
$104$	−0.105455	+	0.182653i	−0.0103407	+	0.0179106i
$105$	−15.1742	−	23.0412i	−1.48086	−	2.24859i
$106$	0.347192	−	0.601354i	0.0337223	−	0.0584087i
$107$	15.6260			1.51062			0.755310	−	0.655368i	$-0.227486\pi$
$107$	15.6260			1.51062			0.755310	+	0.655368i	$0.227486\pi$
$108$	−1.76838	+	4.88598i	−0.170163	+	0.470154i
$109$	1.49519	−	2.58975i	0.143214	−	0.248053i	−0.785491	−	0.618872i	$-0.787590\pi$
$109$	1.49519	−	2.58975i	0.143214	−	0.248053i	0.928705	+	0.370819i	$0.120923\pi$
$110$	0.817031			0.0779008
$111$	1.26566	−	2.52393i	0.120132	−	0.239560i
$112$	4.60612			0.435238
$113$	6.53806	+	11.3243i	0.615049	+	1.06530i	0.990376	+	0.138404i	$0.0441972\pi$
$113$	6.53806	+	11.3243i	0.615049	+	1.06530i	−0.375327	+	0.926893i	$0.622469\pi$
$114$	−2.00465	−	7.27883i	−0.187753	−	0.681725i
$115$	−11.5034	+	19.9244i	−1.07270	+	1.85796i
$116$	−2.45265	+	4.24811i	−0.227723	+	0.394427i
$117$	0.628362	−	0.0742105i	0.0580921	−	0.00686077i
$118$	−2.21638	−	3.83889i	−0.204035	−	0.353398i
$119$	−13.4554	−	23.3054i	−1.23345	−	2.13640i
$120$	−2.68493	+	5.35415i	−0.245099	+	0.488765i
$121$	5.47209	+	9.47794i	0.497463	+	0.861631i
$122$	2.18022	+	3.77625i	0.197388	+	0.341885i
$123$	−5.81258	+	11.5912i	−0.524103	+	1.04514i
$124$	−9.83594			−0.883294
$125$	6.77303			0.605799
$126$	−8.26507	−	11.0741i	−0.736311	−	0.986560i
$127$	−0.917971	−	1.58997i	−0.0814567	−	0.141087i	0.822419	−	0.568882i	$-0.192624\pi$
$127$	−0.917971	−	1.58997i	−0.0814567	−	0.141087i	−0.903876	+	0.427795i	$0.859291\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$	8.93905	−	0.526030i	0.787040	−	0.0463143i
$130$	0.729351			0.0639683
$131$	−0.157615			−0.0137708			−0.00688542	−	0.999976i	$-0.502192\pi$
$131$	−0.157615			−0.0137708			−0.00688542	+	0.999976i	$0.502192\pi$
$132$	0.408515	−	0.0240396i	0.0355567	−	0.00209238i
$133$	19.0982	+	6.19425i	1.65603	+	0.537110i
$134$	−5.51938			−0.476802
$135$	17.6903	−	3.15216i	1.52254	−	0.271295i
$136$	−2.92119	+	5.05965i	−0.250490	+	0.433862i
$137$	3.91624			0.334587			0.167293	−	0.985907i	$-0.446497\pi$
$137$	3.91624			0.334587			0.167293	+	0.985907i	$0.446497\pi$
$138$	−5.16545	+	10.3007i	−0.439713	+	0.876853i
$139$	9.11109	−	15.7809i	0.772793	−	1.33852i	−0.163234	−	0.986587i	$-0.552193\pi$
$139$	9.11109	−	15.7809i	0.772793	−	1.33852i	0.936027	−	0.351929i	$-0.114474\pi$
$140$	−7.96426	−	13.7945i	−0.673103	−	1.16585i
$141$	−0.0820291	+	0.163578i	−0.00690810	+	0.0137758i
$142$	2.08376			0.174865
$143$	−0.0249152	−	0.0431545i	−0.00208352	−	0.00360876i
$144$	−1.18493	+	2.75607i	−0.0987440	+	0.229673i
$145$	16.9631			1.40871
$146$	−6.59171			−0.545534
$147$	24.5809	−	1.44650i	2.02740	−	0.119305i
$148$	0.815072	−	1.41175i	0.0669985	−	0.116045i
$149$	−9.63856			−0.789622			−0.394811	−	0.918762i	$-0.629190\pi$
$149$	−9.63856			−0.789622			−0.394811	+	0.918762i	$0.629190\pi$
$150$	12.0318	−	0.708027i	0.982394	−	0.0578102i
$151$	10.3282	−	17.8889i	0.840495	−	1.45578i	−0.0489823	−	0.998800i	$-0.515598\pi$
$151$	10.3282	−	17.8889i	0.840495	−	1.45578i	0.889477	−	0.456980i	$-0.151069\pi$
$152$	−0.908515	−	4.26317i	−0.0736903	−	0.345789i
$153$	17.4062	−	2.05570i	1.40721	−	0.166193i
$154$	−0.544131	+	0.942463i	−0.0438474	+	0.0759459i
$155$	17.0069	+	29.4569i	1.36603	+	2.36603i
$156$	0.364676	−	0.0214598i	0.0291974	−	0.00171816i
$157$	−3.76957			−0.300844			−0.150422	−	0.988622i	$-0.548063\pi$
$157$	−3.76957			−0.300844			−0.150422	+	0.988622i	$0.548063\pi$
$158$	−6.07625	+	10.5244i	−0.483401	+	0.837274i
$159$	−1.20063	+	0.0706526i	−0.0952162	+	0.00560312i
$160$	−1.72906	+	2.99482i	−0.136694	+	0.236761i
$161$	−15.3222	−	26.5388i	−1.20756	−	2.09155i
$162$	8.75239	−	2.09658i	0.687653	−	0.164723i
$163$	−13.8249			−1.08285			−0.541425	−	0.840749i	$-0.682115\pi$
$163$	−13.8249			−1.08285			−0.541425	+	0.840749i	$0.682115\pi$
$164$	−3.74323	+	6.48346i	−0.292297	+	0.506273i
$165$	−0.778342	−	1.18186i	−0.0605938	−	0.0920080i
$166$	−10.9760			−0.851901
$167$	5.71986	−	9.90709i	0.442616	−	0.766634i	−0.555266	−	0.831673i	$-0.687384\pi$
$167$	5.71986	−	9.90709i	0.442616	−	0.766634i	0.997883	+	0.0650385i	$0.0207170\pi$
$168$	−4.38801	−	6.66292i	−0.338542	−	0.514055i
$169$	6.47776	+	11.2198i	0.498289	+	0.863062i
$170$	20.2037			1.54955
$171$	−8.61936	+	9.83395i	−0.659139	+	0.752021i
$172$	5.16989			0.394201
$173$	−2.00696	−	3.47616i	−0.152586	−	0.264288i	0.779591	−	0.626289i	$-0.215427\pi$
$173$	−2.00696	−	3.47616i	−0.152586	−	0.264288i	−0.932178	+	0.362001i	$0.882094\pi$
$174$	8.48155	−	0.499107i	0.642984	−	0.0378372i
$175$	−16.0261	+	27.7579i	−1.21146	+	2.09830i
$176$	0.236264			0.0178091
$177$	−3.44166	+	6.86318i	−0.258691	+	0.515868i
$178$	−1.63061	+	2.82430i	−0.122220	+	0.211691i
$179$	−12.4460			−0.930256			−0.465128	−	0.885243i	$-0.653992\pi$
$179$	−12.4460			−0.930256			−0.465128	+	0.885243i	$0.653992\pi$
$180$	10.3028	−	1.21677i	0.767922	−	0.0906928i
$181$	1.59762	+	2.76716i	0.118750	+	0.205682i	0.919273	−	0.393621i	$-0.128778\pi$
$181$	1.59762	+	2.76716i	0.118750	+	0.205682i	−0.800522	+	0.599303i	$0.795445\pi$
$182$	−0.485738	+	0.841323i	−0.0360053	+	0.0623630i
$183$	3.38550	−	6.75119i	0.250263	−	0.499062i
$184$	−3.32649	+	5.76164i	−0.245232	+	0.424754i
$185$	−5.63723			−0.414457
$186$	9.37018	+	14.2280i	0.687055	+	1.04325i
$187$	−0.690174	−	1.19542i	−0.0504705	−	0.0874175i
$188$	−0.0528257	+	0.0914968i	−0.00385271	+	0.00667309i
$189$	−8.14539	+	22.5054i	−0.592490	+	1.63703i
$190$	−11.1965	+	10.0921i	−0.812282	+	0.732159i
$191$	−11.9347	+	20.6714i	−0.863562	+	1.49573i	0.00490638	+	0.999988i	$0.498438\pi$
$191$	−11.9347	+	20.6714i	−0.863562	+	1.49573i	−0.868468	+	0.495745i	$0.834895\pi$
$192$	−0.776413	+	1.54828i	−0.0560328	+	0.111738i
$193$	−20.1962			−1.45375			−0.726877	−	0.686768i	$-0.759029\pi$
$193$	−20.1962			−1.45375			−0.726877	+	0.686768i	$0.759029\pi$
$194$	−2.61813	+	4.53474i	−0.187971	+	0.325575i
$195$	−0.694814	−	1.05503i	−0.0497567	−	0.0755524i
$196$	14.2164			1.01545
$197$	24.2462			1.72747			0.863735	−	0.503946i	$-0.168119\pi$
$197$	24.2462			1.72747			0.863735	+	0.503946i	$0.168119\pi$
$198$	−0.423945	−	0.568031i	−0.0301285	−	0.0403682i
$199$	−2.65875	−	4.60509i	−0.188474	−	0.326446i	0.756268	−	0.654262i	$-0.227021\pi$
$199$	−2.65875	−	4.60509i	−0.188474	−	0.326446i	−0.944742	+	0.327816i	$0.893687\pi$
$200$	6.95859			0.492047
$201$	5.25802	+	7.98398i	0.370872	+	0.563146i
$202$	−6.61558	−	11.4585i	−0.465470	−	0.806218i
$203$	−11.2972	+	19.5673i	−0.792907	+	1.37336i
$204$	10.1018	−	0.594455i	0.707270	−	0.0416202i
$205$	25.8890			1.80817
$206$	7.40068	−	12.8184i	0.515630	−	0.893097i
$207$	19.8212	−	2.34091i	1.37767	−	0.162704i
$208$	0.210910			0.0146240
$209$	0.979616	+	0.317725i	0.0677615	+	0.0219775i
$210$	−12.3671	+	24.6619i	−0.853411	+	1.70183i
$211$	4.38041			0.301560			0.150780	−	0.988567i	$-0.451822\pi$
$211$	4.38041			0.301560			0.150780	+	0.988567i	$0.451822\pi$
$212$	−0.694384			−0.0476905
$213$	−1.98509	−	3.01423i	−0.136016	−	0.206532i
$214$	−7.81299	−	13.5325i	−0.534085	−	0.925062i
$215$	−8.93905	−	15.4829i	−0.609638	−	1.05592i
$216$	5.11558	−	0.911525i	0.348071	−	0.0620214i
$217$	−45.3055			−3.07554
$218$	−2.99039			−0.202535
$219$	6.27957	+	9.53514i	0.424334	+	0.644325i
$220$	−0.408515	−	0.707569i	−0.0275421	−	0.0477043i
$221$	−0.616108	−	1.06713i	−0.0414439	−	0.0717830i
$222$	−2.81862	+	0.165865i	−0.189173	+	0.0111321i
$223$	−0.970797	−	1.68147i	−0.0650093	−	0.112599i	0.831689	−	0.555242i	$-0.187374\pi$
$223$	−0.970797	−	1.68147i	−0.0650093	−	0.112599i	−0.896698	+	0.442643i	$0.854041\pi$
$224$	−2.30306	−	3.98902i	−0.153880	−	0.266527i
$225$	−12.4863	−	16.7299i	−0.832417	−	1.11533i
$226$	6.53806	−	11.3243i	0.434905	−	0.753278i
$227$	3.38355	−	5.86049i	0.224574	−	0.388974i	−0.731617	−	0.681716i	$-0.761234\pi$
$227$	3.38355	−	5.86049i	0.224574	−	0.388974i	0.956192	+	0.292741i	$0.0945675\pi$
$228$	−5.30133	+	5.37549i	−0.351089	+	0.356001i
$229$	−1.00193	−	1.73539i	−0.0662093	−	0.114678i	0.831020	−	0.556242i	$-0.187757\pi$
$229$	−1.00193	−	1.73539i	−0.0662093	−	0.114678i	−0.897230	+	0.441564i	$0.854424\pi$
$230$	23.0068			1.51702
$231$	1.88167	−	0.110729i	0.123805	−	0.00728546i
$232$	4.90529			0.322048
$233$	−0.969369	+	1.67900i	−0.0635055	+	0.109995i	−0.896030	−	0.443993i	$-0.853561\pi$
$233$	−0.969369	+	1.67900i	−0.0635055	+	0.109995i	0.832525	+	0.553988i	$0.186895\pi$
$234$	−0.378449	−	0.507073i	−0.0247400	−	0.0331484i
$235$	0.365355			0.0238331
$236$	−2.21638	+	3.83889i	−0.144274	+	0.249890i
$237$	21.0124	−	1.23650i	1.36490	−	0.0803194i
$238$	−13.4554	+	23.3054i	−0.872182	+	1.51066i
$239$	13.2916	+	23.0217i	0.859760	+	1.48915i	0.872158	+	0.489225i	$0.162720\pi$
$239$	13.2916	+	23.0217i	0.859760	+	1.48915i	−0.0123976	+	0.999923i	$0.503946\pi$
$240$	5.97929	−	0.351859i	0.385962	−	0.0227124i
$241$	−20.2751			−1.30603			−0.653017	−	0.757344i	$-0.726497\pi$
$241$	−20.2751			−1.30603			−0.653017	+	0.757344i	$0.726497\pi$
$242$	5.47209	−	9.47794i	0.351759	−	0.609265i
$243$	−11.3707	−	10.6633i	−0.729432	−	0.684053i
$244$	2.18022	−	3.77625i	0.139574	−	0.241749i
$245$	−24.5809	−	42.5754i	−1.57042	−	2.72004i
$246$	12.9445	−	0.761737i	0.825313	−	0.0485666i
$247$	0.874489	+	0.283629i	0.0556424	+	0.0180469i
$248$	4.91797	+	8.51818i	0.312291	+	0.540905i
$249$	10.4562	+	15.8771i	0.662637	+	1.00617i
$250$	−3.38652	−	5.86562i	−0.214182	−	0.370974i
$251$	6.06875	+	10.5114i	0.383056	+	0.663473i	0.991497	−	0.130126i	$-0.0415381\pi$
$251$	6.06875	+	10.5114i	0.383056	+	0.663473i	−0.608441	+	0.793599i	$0.708205\pi$
$252$	−5.45792	+	12.6948i	−0.343817	+	0.799698i
$253$	−0.785931	−	1.36127i	−0.0494110	−	0.0855824i
$254$	−0.917971	+	1.58997i	−0.0575986	+	0.0997637i
$255$	−19.2470	−	29.2253i	−1.20529	−	1.83016i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	3.88848	−	6.73504i	0.242556	−	0.420120i	−0.718885	−	0.695129i	$-0.755347\pi$
$257$	3.88848	−	6.73504i	0.242556	−	0.420120i	0.961442	+	0.275009i	$0.0886807\pi$
$258$	−4.92508	−	7.47843i	−0.306622	−	0.465587i
$259$	3.75432	−	6.50267i	0.233282	−	0.404056i
$260$	−0.364676	−	0.631637i	−0.0226162	−	0.0391724i
$261$	−8.80189	−	11.7934i	−0.544823	−	0.729992i
$262$	0.0788073	+	0.136498i	0.00486873	+	0.00843289i
$263$	0.492326	+	0.852733i	0.0303581	+	0.0525818i	0.880805	−	0.473479i	$-0.157002\pi$
$263$	0.492326	+	0.852733i	0.0303581	+	0.0525818i	−0.850447	+	0.526060i	$0.823669\pi$
$264$	−0.225077	−	0.341765i	−0.0138525	−	0.0210342i
$265$	1.20063	+	2.07955i	0.0737542	+	0.127746i
$266$	−4.18473	−	19.6367i	−0.256582	−	1.20400i
$267$	5.63885	−	0.331826i	0.345092	−	0.0203074i
$268$	2.75969	+	4.77992i	0.168575	+	0.291980i
$269$	6.42610	−	11.1303i	0.391806	−	0.678628i	−0.600882	−	0.799338i	$-0.705184\pi$
$269$	6.42610	−	11.1303i	0.391806	−	0.678628i	0.992688	+	0.120710i	$0.0385170\pi$
$270$	−11.5750	−	13.7441i	−0.704431	−	0.836442i
$271$	−6.36856	+	11.0307i	−0.386863	+	0.670066i	−0.992026	−	0.126036i	$-0.959775\pi$
$271$	−6.36856	+	11.0307i	−0.386863	+	0.670066i	0.605163	+	0.796102i	$0.293108\pi$
$272$	5.84239			0.354247
$273$	1.67974	−	0.0988464i	0.101662	−	0.00598246i
$274$	−1.95812	−	3.39156i	−0.118294	−	0.204892i
$275$	−0.822034	+	1.42380i	−0.0495705	+	0.0858586i
$276$	11.5034	−	0.676931i	0.692422	−	0.0407465i
$277$	−3.14052	+	5.43955i	−0.188696	+	0.326831i	−0.944816	−	0.327602i	$-0.893759\pi$
$277$	−3.14052	+	5.43955i	−0.188696	+	0.326831i	0.756120	+	0.654433i	$0.227093\pi$
$278$	−18.2222			−1.09289
$279$	11.6549	−	27.1086i	0.697760	−	1.62295i
$280$	−7.96426	+	13.7945i	−0.475955	+	0.824379i
$281$	−27.9948			−1.67003			−0.835015	−	0.550228i	$-0.814541\pi$
$281$	−27.9948			−1.67003			−0.835015	+	0.550228i	$0.814541\pi$
$282$	0.182678	−	0.0107499i	0.0108783	−	0.000640147i
$283$	−29.3872			−1.74689			−0.873443	−	0.486926i	$-0.838118\pi$
$283$	−29.3872			−1.74689			−0.873443	+	0.486926i	$0.838118\pi$
$284$	−1.04188	−	1.80459i	−0.0618242	−	0.107083i
$285$	25.2649	+	6.58197i	1.49657	+	0.389882i
$286$	−0.0249152	+	0.0431545i	−0.00147327	+	0.00255178i
$287$	−17.2418	+	29.8636i	−1.01775	+	1.76279i
$288$	2.97929	−	0.351859i	0.175557	−	0.0207335i
$289$	−8.56673	−	14.8380i	−0.503926	−	0.872825i
$290$	−8.48155	−	14.6905i	−0.498053	−	0.862654i
$291$	9.05381	−	0.532783i	0.530744	−	0.0312323i
$292$	3.29586	+	5.70859i	0.192875	+	0.334070i
$293$	−1.88964	−	3.27295i	−0.110394	−	0.191208i	0.805535	−	0.592548i	$-0.201878\pi$
$293$	−1.88964	−	3.27295i	−0.110394	−	0.191208i	−0.915929	+	0.401340i	$0.868545\pi$
$294$	−13.5432	−	20.5645i	−0.789853	−	1.19934i
$295$	15.3290			0.892491
$296$	−1.63014			−0.0947502
$297$	−0.417806	+	1.15438i	−0.0242436	+	0.0669841i
$298$	4.81928	+	8.34724i	0.279173	+	0.483543i
$299$	−0.701589	−	1.21519i	−0.0405739	−	0.0702761i
$300$	−6.62908	−	10.0658i	−0.382730	−	0.581152i
$301$	23.8131			1.37257
$302$	−20.6563			−1.18864
$303$	−10.2728	+	20.4856i	−0.590159	+	1.17687i
$304$	−3.23775	+	2.91838i	−0.185698	+	0.167381i
$305$	−15.0789			−0.863415
$306$	−10.4834	−	14.0464i	−0.599295	−	0.802976i
$307$	−3.38336	+	5.86015i	−0.193098	+	0.334456i	−0.946275	−	0.323362i	$-0.895187\pi$
$307$	−3.38336	+	5.86015i	−0.193098	+	0.334456i	0.753177	+	0.657818i	$0.228520\pi$
$308$	1.08826			0.0620095
$309$	−25.5924	+	1.50602i	−1.45590	+	0.0856745i
$310$	17.0069	−	29.4569i	0.965929	−	1.67304i
$311$	0.516369	+	0.894377i	0.0292806	+	0.0507155i	0.880294	−	0.474428i	$-0.157345\pi$
$311$	0.516369	+	0.894377i	0.0292806	+	0.0507155i	−0.851014	+	0.525143i	$0.824012\pi$
$312$	−0.200923	−	0.305088i	−0.0113750	−	0.0172722i
$313$	26.7665			1.51293			0.756466	−	0.654033i	$-0.226924\pi$
$313$	26.7665			1.51293			0.756466	+	0.654033i	$0.226924\pi$
$314$	1.88478	+	3.26454i	0.106365	+	0.184229i
$315$	47.4557	−	5.60459i	2.67383	−	0.315783i
$316$	12.1525			0.683632
$317$	21.9949			1.23536			0.617678	−	0.786431i	$-0.288074\pi$
$317$	21.9949			1.23536			0.617678	+	0.786431i	$0.288074\pi$
$318$	0.661502	+	1.00445i	0.0370952	+	0.0563268i
$319$	−0.579473	+	1.00368i	−0.0324443	+	0.0561951i
$320$	3.45812			0.193315
$321$	−12.1322	+	24.1934i	−0.677154	+	1.35035i
$322$	−15.3222	+	26.5388i	−0.853873	+	1.47895i
$323$	24.2241	+	7.85676i	1.34787	+	0.437162i
$324$	−6.19189	−	6.53150i	−0.343994	−	0.362861i
$325$	−0.733817	+	1.27101i	−0.0407049	+	0.0705029i
$326$	6.91245	+	11.9727i	0.382845	+	0.663108i
$327$	2.84878	+	4.32570i	0.157538	+	0.239212i
$328$	7.48645			0.413370
$329$	−0.243322	+	0.421445i	−0.0134148	+	0.0232350i
$330$	−0.634353	+	1.26500i	−0.0349200	+	0.0696357i
$331$	12.5849	−	21.7977i	0.691729	−	1.19811i	−0.279541	−	0.960134i	$-0.590182\pi$
$331$	12.5849	−	21.7977i	0.691729	−	1.19811i	0.971271	−	0.237977i	$-0.0764842\pi$
$332$	5.48799	+	9.50548i	0.301193	+	0.521681i
$333$	2.92507	+	3.91922i	0.160293	+	0.214772i
$334$	−11.4397			−0.625954
$335$	9.54334	−	16.5295i	0.521408	−	0.903106i
$336$	−3.57625	+	7.13158i	−0.195101	+	0.389060i
$337$	−6.07315			−0.330825			−0.165413	−	0.986224i	$-0.552896\pi$
$337$	−6.07315			−0.330825			−0.165413	+	0.986224i	$0.552896\pi$
$338$	6.47776	−	11.2198i	0.352344	−	0.610277i
$339$	−22.6094	+	1.33048i	−1.22797	+	0.0722617i
$340$	−10.1018	−	17.4969i	−0.547849	−	0.948902i
$341$	−2.32388			−0.125845
$342$	12.8261	+	2.54761i	0.693558	+	0.137759i
$343$	33.2394			1.79476
$344$	−2.58495	−	4.47726i	−0.139371	−	0.241398i
$345$	−21.9173	−	33.2801i	−1.17999	−	1.79174i
$346$	−2.00696	+	3.47616i	−0.107895	+	0.186880i
$347$	−11.0238			−0.591787			−0.295893	−	0.955221i	$-0.595617\pi$
$347$	−11.0238			−0.591787			−0.295893	+	0.955221i	$0.595617\pi$
$348$	−4.67301	−	7.09568i	−0.250500	−	0.380368i
$349$	−12.2557	+	21.2275i	−0.656033	+	1.13628i	0.325601	+	0.945507i	$0.394433\pi$
$349$	−12.2557	+	21.2275i	−0.656033	+	1.13628i	−0.981634	+	0.190775i	$0.938900\pi$
$350$	32.0521			1.71326
$351$	−0.372970	+	1.03050i	−0.0199076	+	0.0550041i
$352$	−0.118132	−	0.204611i	−0.00629647	−	0.0109058i
$353$	6.47378	−	11.2129i	0.344564	−	0.596803i	−0.640710	−	0.767783i	$-0.721360\pi$
$353$	6.47378	−	11.2129i	0.344564	−	0.596803i	0.985275	+	0.170980i	$0.0546933\pi$
$354$	7.66451	−	0.451028i	0.407364	−	0.0239719i
$355$	−3.60295	+	6.24049i	−0.191225	+	0.331211i
$356$	3.26123			0.172845
$357$	46.5303	−	2.73813i	2.46264	−	0.144917i
$358$	6.22299	+	10.7785i	0.328895	+	0.569663i
$359$	2.92928	−	5.07367i	0.154602	−	0.267778i	−0.778312	−	0.627877i	$-0.783924\pi$
$359$	2.92928	−	5.07367i	0.154602	−	0.267778i	0.932914	+	0.360099i	$0.117257\pi$
$360$	−6.20513	−	8.31406i	−0.327039	−	0.438190i
$361$	−17.3492	+	7.74631i	−0.913116	+	0.407700i
$362$	1.59762	−	2.76716i	0.0839692	−	0.145439i
$363$	−18.9231	+	1.11356i	−0.993207	+	0.0584465i
$364$	0.971476			0.0509192
$365$	11.3975	−	19.7410i	0.596570	−	1.03329i
$366$	−7.53945	+	0.443669i	−0.394093	+	0.0231909i
$367$	−17.9299			−0.935934			−0.467967	−	0.883746i	$-0.655013\pi$
$367$	−17.9299			−0.935934			−0.467967	+	0.883746i	$0.655013\pi$
$368$	6.65297			0.346810
$369$	−13.4334	−	17.9990i	−0.699317	−	0.936993i
$370$	2.81862	+	4.88199i	0.146533	+	0.253802i
$371$	−3.19842			−0.166053
$372$	7.63675	−	15.2288i	0.395947	−	0.789578i
$373$	1.76548	+	3.05791i	0.0914133	+	0.158333i	0.908106	−	0.418740i	$-0.137528\pi$
$373$	1.76548	+	3.05791i	0.0914133	+	0.158333i	−0.816693	+	0.577073i	$0.804195\pi$
$374$	−0.690174	+	1.19542i	−0.0356881	+	0.0618135i
$375$	−5.25867	+	10.4866i	−0.271557	+	0.541525i
$376$	0.105651			0.00544856
$377$	−0.517287	+	0.895968i	−0.0266417	+	0.0461447i
$378$	23.5630	−	4.19859i	1.21195	−	0.215952i
$379$	6.46356			0.332011			0.166005	−	0.986125i	$-0.446913\pi$
$379$	6.46356			0.332011			0.166005	+	0.986125i	$0.446913\pi$
$380$	14.3383	+	4.65043i	0.735539	+	0.238562i
$381$	3.17445	−	0.186805i	0.162632	−	0.00957029i
$382$	23.8693			1.22126
$383$	−7.18436			−0.367104			−0.183552	−	0.983010i	$-0.558760\pi$
$383$	−7.18436			−0.367104			−0.183552	+	0.983010i	$0.558760\pi$
$384$	1.72906	−	0.101749i	0.0882357	−	0.00519234i
$385$	−1.88167	−	3.25915i	−0.0958988	−	0.166102i
$386$	10.0981	+	17.4904i	0.513979	+	0.890238i
$387$	−6.12595	+	14.2486i	−0.311400	+	0.724297i
$388$	5.23626			0.265831
$389$	6.32744			0.320814			0.160407	−	0.987051i	$-0.448719\pi$
$389$	6.32744			0.320814			0.160407	+	0.987051i	$0.448719\pi$
$390$	−0.566278	+	1.12924i	−0.0286746	+	0.0571814i
$391$	−19.4346	−	33.6617i	−0.982851	−	1.70235i
$392$	−7.10818	−	12.3117i	−0.359017	−	0.621836i
$393$	0.122374	−	0.244032i	0.00617295	−	0.0123098i
$394$	−12.1231	−	20.9978i	−0.610753	−	1.05786i
$395$	−21.0124	−	36.3945i	−1.05725	−	1.83121i
$396$	−0.279956	+	0.651162i	−0.0140683	+	0.0327221i
$397$	−5.10403	+	8.84045i	−0.256164	+	0.443689i	−0.965211	−	0.261472i	$-0.915792\pi$
$397$	−5.10403	+	8.84045i	−0.256164	+	0.443689i	0.709047	+	0.705161i	$0.249125\pi$
$398$	−2.65875	+	4.60509i	−0.133271	+	0.230832i
$399$	−24.4186	+	24.7602i	−1.22246	+	1.23956i
$400$	−3.47929	−	6.02631i	−0.173965	−	0.301316i
$401$	7.23319			0.361208			0.180604	−	0.983556i	$-0.442195\pi$
$401$	7.23319			0.361208			0.180604	+	0.983556i	$0.442195\pi$
$402$	4.28532	−	8.54557i	0.213732	−	0.426214i
$403$	−2.07450			−0.103338
$404$	−6.61558	+	11.4585i	−0.329137	+	0.570082i
$405$	−8.85451	+	29.8369i	−0.439984	+	1.48261i
$406$	22.5944			1.12134
$407$	0.192573	−	0.333545i	0.00954546	−	0.0165332i
$408$	−5.56573	−	8.45122i	−0.275545	−	0.418398i
$409$	10.1596	−	17.5970i	0.502362	−	0.870117i	−0.497634	−	0.867387i	$-0.665798\pi$
$409$	10.1596	−	17.5970i	0.502362	−	0.870117i	0.999996	−	0.00272956i	$-0.000868847\pi$
$410$	−12.9445	−	22.4206i	−0.639284	−	1.10727i
$411$	−3.04062	+	6.06345i	−0.149983	+	0.299088i
$412$	−14.8014			−0.729211
$413$	−10.2089	+	17.6824i	−0.502348	+	0.870093i
$414$	−11.9379	−	15.9952i	−0.586714	−	0.786120i
$415$	18.9781	−	32.8711i	0.931599	−	1.61358i
$416$	−0.105455	−	0.182653i	−0.00517035	−	0.00895531i
$417$	17.3593	+	26.3590i	0.850089	+	1.29081i
$418$	−0.214650	−	1.00724i	−0.0104989	−	0.0492655i
$419$	13.6876	+	23.7076i	0.668683	+	1.15819i	0.978273	+	0.207323i	$0.0664750\pi$
$419$	13.6876	+	23.7076i	0.668683	+	1.15819i	−0.309589	+	0.950870i	$0.600192\pi$
$420$	27.5414	−	1.62071i	1.34388	−	0.0790823i
$421$	0.938050	+	1.62475i	0.0457177	+	0.0791854i	0.887979	−	0.459884i	$-0.152109\pi$
$421$	0.938050	+	1.62475i	0.0457177	+	0.0791854i	−0.842261	+	0.539070i	$0.818776\pi$
$422$	−2.19020	−	3.79354i	−0.106617	−	0.184667i
$423$	−0.189577	−	0.254009i	−0.00921756	−	0.0123503i
$424$	0.347192	+	0.601354i	0.0168611	+	0.0292043i
$425$	−20.3274	+	35.2081i	−0.986023	+	1.70784i
$426$	−1.61786	+	3.22625i	−0.0783855	+	0.156313i
$427$	10.0423	−	17.3938i	0.485983	−	0.841747i
$428$	−7.81299	+	13.5325i	−0.377655	+	0.654117i
$429$	0.0861599	−	0.00507019i	0.00415984	−	0.000244791i
$430$	−8.93905	+	15.4829i	−0.431079	+	0.746651i
$431$	−13.6359	−	23.6181i	−0.656820	−	1.13765i	−0.981434	−	0.191800i	$-0.938568\pi$
$431$	−13.6359	−	23.6181i	−0.656820	−	1.13765i	0.324614	−	0.945847i	$-0.394766\pi$
$432$	−3.34719	−	3.97446i	−0.161042	−	0.191221i
$433$	7.68349	+	13.3082i	0.369245	+	0.639551i	0.989448	−	0.144891i	$-0.0462830\pi$
$433$	7.68349	+	13.3082i	0.369245	+	0.639551i	−0.620203	+	0.784441i	$0.712950\pi$
$434$	22.6528	+	39.2357i	1.08737	+	1.88338i
$435$	−13.1704	+	26.2637i	−0.631470	+	1.25925i
$436$	1.49519	+	2.58975i	0.0716068	+	0.124027i
$437$	27.5850	+	8.94683i	1.31957	+	0.427985i
$438$	5.11789	−	10.2058i	0.244542	−	0.487654i
$439$	−10.2936	−	17.8290i	−0.491285	−	0.850930i	0.508665	−	0.860965i	$-0.330139\pi$
$439$	−10.2936	−	17.8290i	−0.491285	−	0.850930i	−0.999950	+	0.0100344i	$0.996806\pi$
$440$	−0.408515	+	0.707569i	−0.0194752	+	0.0337320i
$441$	−16.8454	+	39.1813i	−0.802160	+	1.86578i
$442$	−0.616108	+	1.06713i	−0.0293053	+	0.0507582i
$443$	22.2957			1.05930			0.529651	−	0.848216i	$-0.322323\pi$
$443$	22.2957			1.05930			0.529651	+	0.848216i	$0.322323\pi$
$444$	1.55295	+	2.35806i	0.0736998	+	0.111909i
$445$	−5.63885	−	9.76678i	−0.267307	−	0.462990i
$446$	−0.970797	+	1.68147i	−0.0459686	+	0.0796199i
$447$	7.48350	−	14.9232i	0.353958	−	0.705845i
$448$	−2.30306	+	3.98902i	−0.108809	+	0.188463i
$449$	−9.69377			−0.457477			−0.228739	−	0.973488i	$-0.573460\pi$
$449$	−9.69377			−0.457477			−0.228739	+	0.973488i	$0.573460\pi$
$450$	−8.24543	+	19.1784i	−0.388693	+	0.904078i
$451$	−0.884391	+	1.53181i	−0.0416444	+	0.0721302i
$452$	−13.0761			−0.615049
$453$	19.6782	+	29.8801i	0.924562	+	1.40389i
$454$	−6.76711			−0.317596
$455$	−1.67974	−	2.90940i	−0.0787474	−	0.136395i
$456$	7.30598	+	1.90334i	0.342134	+	0.0891320i
$457$	−8.31027	+	14.3938i	−0.388738	+	0.673314i	−0.992280	−	0.124017i	$-0.960422\pi$
$457$	−8.31027	+	14.3938i	−0.388738	+	0.673314i	0.603542	+	0.797331i	$0.293755\pi$
$458$	−1.00193	+	1.73539i	−0.0468171	+	0.0810895i
$459$	−10.3316	+	28.5458i	−0.482237	+	1.33240i
$460$	−11.5034	−	19.9244i	−0.536348	−	0.928982i
$461$	5.58519	+	9.67383i	0.260128	+	0.450555i	0.966276	−	0.257509i	$-0.0829018\pi$
$461$	5.58519	+	9.67383i	0.260128	+	0.450555i	−0.706148	+	0.708065i	$0.749569\pi$
$462$	−1.03673	−	1.57421i	−0.0482330	−	0.0732389i
$463$	−9.16587	−	15.8758i	−0.425974	−	0.737809i	0.570537	−	0.821272i	$-0.306735\pi$
$463$	−9.16587	−	15.8758i	−0.425974	−	0.737809i	−0.996511	+	0.0834633i	$0.973402\pi$
$464$	−2.45265	−	4.24811i	−0.113861	−	0.197214i
$465$	−58.8120	+	3.46087i	−2.72734	+	0.160494i
$466$	1.93874			0.0898103
$467$	−35.7260			−1.65320			−0.826602	−	0.562787i	$-0.809729\pi$
$467$	−35.7260			−1.65320			−0.826602	+	0.562787i	$0.809729\pi$
$468$	−0.249913	+	0.581283i	−0.0115522	+	0.0268698i
$469$	12.7115	+	22.0169i	0.586961	+	1.01665i
$470$	−0.182678	−	0.316407i	−0.00842629	−	0.0145948i
$471$	2.92674	−	5.83636i	0.134857	−	0.268925i
$472$	4.43276			0.204035
$473$	1.22146			0.0561629
$474$	−11.5770	−	17.5790i	−0.531751	−	0.807431i
$475$	−6.32198	−	29.6656i	−0.290073	−	1.36115i
$476$	26.9107			1.23345
$477$	0.822795	−	1.91377i	0.0376732	−	0.0876257i
$478$	13.2916	−	23.0217i	0.607942	−	1.05299i
$479$	−21.3812			−0.976933			−0.488467	−	0.872583i	$-0.662444\pi$
$479$	−21.3812			−0.976933			−0.488467	+	0.872583i	$0.662444\pi$
$480$	−3.29437	−	5.00229i	−0.150367	−	0.228322i
$481$	0.171907	−	0.297751i	0.00783827	−	0.0135763i
$482$	10.1375	+	17.5587i	0.461752	+	0.799779i
$483$	52.9860	−	3.11803i	2.41095	−	0.141875i
$484$	−10.9442			−0.497463
$485$	−9.05381	−	15.6817i	−0.411112	−	0.712068i
$486$	−3.54936	+	15.1790i	−0.161002	+	0.688533i
$487$	25.1494			1.13963			0.569815	−	0.821773i	$-0.307015\pi$
$487$	25.1494			1.13963			0.569815	+	0.821773i	$0.307015\pi$
$488$	−4.36043			−0.197388
$489$	10.7338	−	21.4049i	0.485401	−	0.967962i
$490$	−24.5809	+	42.5754i	−1.11045	+	1.92336i
$491$	−35.4237			−1.59865			−0.799325	−	0.600899i	$-0.794810\pi$
$491$	−35.4237			−1.59865			−0.799325	+	0.600899i	$0.794810\pi$
$492$	−7.13195	−	10.8294i	−0.321533	−	0.488228i
$493$	−14.3293	+	24.8191i	−0.645360	+	1.11780i
$494$	−0.191615	−	0.899144i	−0.00862116	−	0.0404544i
$495$	2.43418	−	0.287480i	0.109408	−	0.0129213i
$496$	4.91797	−	8.51818i	0.220823	−	0.382477i
$497$	−4.79903	−	8.31216i	−0.215266	−	0.372851i
$498$	8.52189	−	16.9939i	0.381875	−	0.761516i
$499$	34.8335			1.55936			0.779681	−	0.626177i	$-0.215381\pi$
$499$	34.8335			1.55936			0.779681	+	0.626177i	$0.215381\pi$
$500$	−3.38652	+	5.86562i	−0.151450	+	0.262318i
$501$	10.8980	+	16.5480i	0.486888	+	0.739309i
$502$	6.06875	−	10.5114i	0.270862	−	0.469146i
$503$	3.14810	+	5.45266i	0.140367	+	0.243122i	0.927635	−	0.373489i	$-0.121839\pi$
$503$	3.14810	+	5.45266i	0.140367	+	0.243122i	−0.787268	+	0.616611i	$0.788505\pi$
$504$	13.7230	−	1.62071i	0.611271	−	0.0721920i
$505$	45.7549			2.03607
$506$	−0.785931	+	1.36127i	−0.0349389	+	0.0605159i
$507$	−22.4009	+	1.31821i	−0.994857	+	0.0585436i
$508$	1.83594			0.0814567
$509$	2.83853	−	4.91647i	0.125816	−	0.217919i	−0.796236	−	0.604986i	$-0.793179\pi$
$509$	2.83853	−	4.91647i	0.125816	−	0.217919i	0.922051	+	0.387067i	$0.126512\pi$
$510$	−15.6864	+	31.2810i	−0.694605	+	1.38515i
$511$	15.1811	+	26.2945i	0.671573	+	1.16320i
$512$	1.00000			0.0441942
$513$	−8.53356	−	20.9804i	−0.376766	−	0.926308i
$514$	−7.77695			−0.343027
$515$	25.5924	+	44.3274i	1.12774	+	1.95330i
$516$	−4.01397	+	8.00446i	−0.176705	+	0.352377i
$517$	−0.0124808	+	0.0216174i	−0.000548907	+	0.000950734i
$518$	−7.50864			−0.329911
$519$	6.94031	−	0.408412i	0.304646	−	0.0179273i
$520$	−0.364676	+	0.631637i	−0.0159921	+	0.0276991i
$521$	16.8983			0.740328			0.370164	−	0.928966i	$-0.379301\pi$
$521$	16.8983			0.740328			0.370164	+	0.928966i	$0.379301\pi$
$522$	−5.81242	+	13.5194i	−0.254403	+	0.591726i
$523$	0.0707790	+	0.122593i	0.00309495	+	0.00536061i	0.867569	−	0.497317i	$-0.165682\pi$
$523$	0.0707790	+	0.122593i	0.00309495	+	0.00536061i	−0.864474	+	0.502678i	$0.832348\pi$
$524$	0.0788073	−	0.136498i	0.00344271	−	0.00596295i
$525$	−30.5343	−	46.3645i	−1.33263	−	2.02351i
$526$	0.492326	−	0.852733i	0.0214664	−	0.0371809i
$527$	−57.4654			−2.50323
$528$	−0.183439	+	0.365805i	−0.00798315	+	0.0159196i
$529$	−10.6310	−	18.4135i	−0.462218	−	0.800586i
$530$	1.20063	−	2.07955i	0.0521521	−	0.0903300i
$531$	−7.95400	−	10.6573i	−0.345174	−	0.462488i
$532$	−14.9135	+	13.4424i	−0.646582	+	0.582803i
$533$	−0.789483	+	1.36742i	−0.0341963	+	0.0592298i
$534$	−3.10680	−	4.71748i	−0.134444	−	0.204145i
$535$	54.0365			2.33620
$536$	2.75969	−	4.77992i	0.119200	−	0.206461i
$537$	9.66322	−	19.2699i	0.416999	−	0.831558i
$538$	−12.8522			−0.554098
$539$	3.35882			0.144675
$540$	−6.11528	+	16.8963i	−0.263160	+	0.727101i
$541$	19.7179	+	34.1524i	0.847738	+	1.46832i	0.883222	+	0.468955i	$0.155369\pi$
$541$	19.7179	+	34.1524i	0.847738	+	1.46832i	−0.0354844	+	0.999370i	$0.511297\pi$
$542$	12.7371			0.547106
$543$	−5.52477	+	0.325112i	−0.237091	+	0.0139519i
$544$	−2.92119	−	5.05965i	−0.125245	−	0.216931i
$545$	5.17056	−	8.95567i	0.221482	−	0.383619i
$546$	−0.925474	−	1.40527i	−0.0396066	−	0.0601402i
$547$	−45.7057			−1.95424			−0.977118	−	0.212699i	$-0.931775\pi$
$547$	−45.7057			−1.95424			−0.977118	+	0.212699i	$0.931775\pi$
$548$	−1.95812	+	3.39156i	−0.0836467	+	0.144880i
$549$	7.82422	+	10.4834i	0.333929	+	0.447422i
$550$	1.64407			0.0701033
$551$	−4.45653	−	20.9121i	−0.189855	−	0.890885i
$552$	−6.33793	−	9.62376i	−0.269760	−	0.409614i
$553$	55.9759			2.38034
$554$	6.28105			0.266856
$555$	4.37682	−	8.72803i	0.185786	−	0.370484i
$556$	9.11109	+	15.7809i	0.386396	+	0.669258i
$557$	11.8787	+	20.5745i	0.503317	+	0.871771i	0.999993	+	0.00383475i	$0.00122064\pi$
$557$	11.8787	+	20.5745i	0.503317	+	0.871771i	−0.496675	+	0.867936i	$0.665446\pi$
$558$	−29.3042	+	3.46087i	−1.24054	+	0.146510i
$559$	1.09038			0.0461182
$560$	15.9285			0.673103
$561$	2.38670	−	0.140449i	0.100767	−	0.00592975i
$562$	13.9974	+	24.2442i	0.590445	+	1.02268i
$563$	12.6646	+	21.9358i	0.533751	+	0.924484i	0.999223	+	0.0394213i	$0.0125514\pi$
$563$	12.6646	+	21.9358i	0.533751	+	0.924484i	−0.465471	+	0.885063i	$0.654115\pi$
$564$	−0.100648	−	0.152828i	−0.00423807	−	0.00643524i
$565$	22.6094	+	39.1606i	0.951185	+	1.64750i
$566$	14.6936	+	25.4500i	0.617618	+	1.06975i
$567$	−28.5206	−	30.0849i	−1.19775	−	1.26345i
$568$	−1.04188	+	1.80459i	−0.0437163	+	0.0757189i
$569$	6.60868	−	11.4466i	0.277050	−	0.479865i	−0.693600	−	0.720360i	$-0.743977\pi$
$569$	6.60868	−	11.4466i	0.277050	−	0.479865i	0.970650	+	0.240495i	$0.0773099\pi$
$570$	−6.93232	−	25.1711i	−0.290363	−	1.05430i
$571$	−8.76834	−	15.1872i	−0.366944	−	0.635565i	0.622142	−	0.782904i	$-0.286262\pi$
$571$	−8.76834	−	15.1872i	−0.366944	−	0.635565i	−0.989086	+	0.147339i	$0.952929\pi$
$572$	0.0498305			0.00208352
$573$	−22.7390	−	34.5278i	−0.949937	−	1.44242i
$574$	34.4835			1.43931
$575$	−23.1477	+	40.0929i	−0.965324	+	1.67199i
$576$	−1.79437	−	2.40422i	−0.0747653	−	0.100176i
$577$	−16.6775			−0.694295			−0.347147	−	0.937811i	$-0.612850\pi$
$577$	−16.6775			−0.694295			−0.347147	+	0.937811i	$0.612850\pi$
$578$	−8.56673	+	14.8380i	−0.356329	+	0.617180i
$579$	15.6806	−	31.2694i	0.651663	−	1.29951i
$580$	−8.48155	+	14.6905i	−0.352177	+	0.609988i
$581$	25.2783	+	43.7834i	1.04872	+	1.81644i
$582$	−4.98831	−	7.57444i	−0.206772	−	0.313971i
$583$	−0.164058			−0.00679460
$584$	3.29586	−	5.70859i	0.136383	−	0.236223i
$585$	2.17295	−	0.256629i	0.0898405	−	0.0106103i
$586$	−1.88964	+	3.27295i	−0.0780602	+	0.135204i
$587$	−7.35779	−	12.7441i	−0.303689	−	0.526004i	0.673280	−	0.739388i	$-0.264885\pi$
$587$	−7.35779	−	12.7441i	−0.303689	−	0.526004i	−0.976968	+	0.213384i	$0.931552\pi$
$588$	−11.0378	+	22.0109i	−0.455189	+	0.907716i
$589$	31.8464	−	28.7050i	1.31221	−	1.18277i
$590$	−7.66451	−	13.2753i	−0.315543	−	0.546537i
$591$	−18.8251	+	37.5400i	−0.774360	+	1.54419i
$592$	0.815072	+	1.41175i	0.0334992	+	0.0580224i
$593$	−5.00567	−	8.67007i	−0.205558	−	0.356037i	0.744752	−	0.667341i	$-0.232568\pi$
$593$	−5.00567	−	8.67007i	−0.205558	−	0.356037i	−0.950310	+	0.311304i	$0.899234\pi$
$594$	1.20863	−	0.215361i	0.0495906	−	0.00883637i
$595$	−46.5303	−	80.5928i	−1.90755	−	3.30398i
$596$	4.81928	−	8.34724i	0.197405	−	0.341916i
$597$	9.19428	−	0.541049i	0.376297	−	0.0221437i
$598$	−0.701589	+	1.21519i	−0.0286901	+	0.0496927i
$599$	8.94790	−	15.4982i	0.365601	−	0.633240i	−0.623271	−	0.782006i	$-0.714197\pi$
$599$	8.94790	−	15.4982i	0.365601	−	0.633240i	0.988872	+	0.148766i	$0.0475300\pi$
$600$	−5.40274	+	10.7739i	−0.220566	+	0.439841i
$601$	−0.571006	+	0.989011i	−0.0232918	+	0.0403426i	−0.877436	−	0.479693i	$-0.840748\pi$
$601$	−0.571006	+	0.989011i	−0.0232918	+	0.0403426i	0.854145	+	0.520036i	$0.174081\pi$
$602$	−11.9066	−	20.6228i	−0.485276	−	0.840522i
$603$	−16.4439	+	1.94204i	−0.669646	+	0.0790862i
$604$	10.3282	+	17.8889i	0.420247	+	0.727890i
$605$	18.9231	+	32.7758i	0.769335	+	1.33253i
$606$	22.8775	−	1.34625i	0.929333	−	0.0546878i
$607$	10.2307	+	17.7202i	0.415253	+	0.719240i	0.995455	−	0.0952332i	$-0.0303597\pi$
$607$	10.2307	+	17.7202i	0.415253	+	0.719240i	−0.580202	+	0.814473i	$0.697026\pi$
$608$	4.14627	+	1.34479i	0.168153	+	0.0545383i
$609$	−21.5245	−	32.6836i	−0.872215	−	1.32440i
$610$	7.53945	+	13.0587i	0.305263	+	0.528732i
$611$	−0.0111415	+	0.0192976i	−0.000450735	+	0.000780696i
$612$	−6.92281	+	16.1020i	−0.279838	+	0.650887i
$613$	17.9823	−	31.1462i	0.726297	−	1.25798i	−0.232141	−	0.972682i	$-0.574573\pi$
$613$	17.9823	−	31.1462i	0.726297	−	1.25798i	0.958438	−	0.285301i	$-0.0920937\pi$
$614$	6.76671			0.273082
$615$	−20.1006	+	40.0836i	−0.810534	+	1.61633i
$616$	−0.544131	−	0.942463i	−0.0219237	−	0.0379729i
$617$	8.59778	−	14.8918i	0.346134	−	0.599521i	−0.639425	−	0.768853i	$-0.720828\pi$
$617$	8.59778	−	14.8918i	0.346134	−	0.599521i	0.985559	+	0.169332i	$0.0541611\pi$
$618$	14.1005	+	21.4107i	0.567204	+	0.861265i
$619$	4.74683	−	8.22176i	0.190791	−	0.330460i	−0.754721	−	0.656045i	$-0.772228\pi$
$619$	4.74683	−	8.22176i	0.190791	−	0.330460i	0.945513	+	0.325585i	$0.105561\pi$
$620$	−34.0139			−1.36603
$621$	−11.7650	+	32.5063i	−0.472114	+	1.30443i
$622$	0.516369	−	0.894377i	0.0207045	−	0.0358612i
$623$	15.0216			0.601828
$624$	−0.163753	+	0.326548i	−0.00655537	+	0.0130724i
$625$	−11.3710			−0.454839
$626$	−13.3832	−	23.1805i	−0.534902	−	0.926478i
$627$	−1.25252	+	1.27004i	−0.0500207	+	0.0507204i
$628$	1.88478	−	3.26454i	0.0752111	−	0.130269i
$629$	4.76196	−	8.24796i	0.189872	−	0.328868i
$630$	−28.5816	−	38.2956i	−1.13872	−	1.52573i
$631$	11.8995	+	20.6106i	0.473712	+	0.820494i	0.999547	−	0.0300930i	$-0.00958035\pi$
$631$	11.8995	+	20.6106i	0.473712	+	0.820494i	−0.525835	+	0.850587i	$0.676247\pi$
$632$	−6.07625	−	10.5244i	−0.241700	−	0.418637i
$633$	−3.40101	+	6.78212i	−0.135178	+	0.269565i
$634$	−10.9974	−	19.0481i	−0.436764	−	0.756498i
$635$	−3.17445	−	5.49831i	−0.125974	−	0.218194i
$636$	0.539128	−	1.07510i	0.0213778	−	0.0426306i
$637$	2.99837			0.118800
$638$	1.15895			0.0458831
$639$	6.20814	−	0.733191i	0.245590	−	0.0290046i
$640$	−1.72906	−	2.99482i	−0.0683471	−	0.118381i
$641$	−1.72498	−	2.98774i	−0.0681324	−	0.118009i	0.829947	−	0.557843i	$-0.188371\pi$
$641$	−1.72498	−	2.98774i	−0.0681324	−	0.118009i	−0.898079	+	0.439834i	$0.855037\pi$
$642$	27.0182	−	1.58992i	1.06632	−	0.0627492i
$643$	−0.999139			−0.0394022			−0.0197011	−	0.999806i	$-0.506271\pi$
$643$	−0.999139			−0.0394022			−0.0197011	+	0.999806i	$0.506271\pi$
$644$	30.6444			1.20756
$645$	30.9123	−	1.81907i	1.21717	−	0.0716260i
$646$	−5.30790	−	24.9071i	−0.208836	−	0.979956i
$647$	4.56798			0.179586			0.0897930	−	0.995960i	$-0.471379\pi$
$647$	4.56798			0.179586			0.0897930	+	0.995960i	$0.471379\pi$
$648$	−2.56050	+	8.62808i	−0.100586	+	0.338943i
$649$	−0.523652	+	0.906993i	−0.0205552	+	0.0356026i
$650$	1.46763			0.0575654
$651$	35.1758	−	70.1458i	1.37865	−	2.74923i
$652$	6.91245	−	11.9727i	0.270713	−	0.468888i
$653$	−14.9389	−	25.8750i	−0.584606	−	1.01257i	−0.994924	−	0.100625i	$-0.967916\pi$
$653$	−14.9389	−	25.8750i	−0.584606	−	1.01257i	0.410318	−	0.911942i	$-0.365418\pi$
$654$	2.32177	−	4.62997i	0.0907886	−	0.181046i
$655$	−0.545050			−0.0212969
$656$	−3.74323	−	6.48346i	−0.146148	−	0.253137i
$657$	−19.6386	+	2.31935i	−0.766177	+	0.0904866i
$658$	0.486643			0.0189713
$659$	2.90338			0.113100			0.0565498	−	0.998400i	$-0.481990\pi$
$659$	2.90338			0.113100			0.0565498	+	0.998400i	$0.481990\pi$
$660$	1.41269	−	0.0831318i	0.0549891	−	0.00323590i
$661$	−11.1112	+	19.2452i	−0.432176	+	0.748551i	−0.997060	−	0.0766190i	$-0.975588\pi$
$661$	−11.1112	+	19.2452i	−0.432176	+	0.748551i	0.564884	+	0.825170i	$0.308921\pi$
$662$	−25.1698			−0.978253
$663$	2.13058	−	0.125376i	0.0827447	−	0.00486922i
$664$	5.48799	−	9.50548i	0.212975	−	0.368884i
$665$	66.0439	+	21.4205i	2.56107	+	0.830650i
$666$	1.93160	−	4.49280i	0.0748481	−	0.174092i
$667$	−16.3174	+	28.2626i	−0.631812	+	1.09433i
$668$	5.71986	+	9.90709i	0.221308	+	0.383317i
$669$	3.35713	−	0.197555i	0.129794	−	0.00763790i
$670$	−19.0867			−0.737383
$671$	0.515108	−	0.892193i	0.0198855	−	0.0344427i
$672$	7.96426	−	0.468667i	0.307228	−	0.0180792i
$673$	18.9081	−	32.7497i	0.728852	−	1.26241i	−0.228517	−	0.973540i	$-0.573388\pi$
$673$	18.9081	−	32.7497i	0.728852	−	1.26241i	0.957369	−	0.288869i	$-0.0932790\pi$
$674$	3.03657	+	5.25950i	0.116964	+	0.202588i
$675$	35.5972	−	6.34293i	1.37014	−	0.244139i
$676$	−12.9555			−0.498289
$677$	−10.9106	+	18.8977i	−0.419327	+	0.726296i	−0.995872	−	0.0907695i	$-0.971067\pi$
$677$	−10.9106	+	18.8977i	−0.419327	+	0.726296i	0.576545	+	0.817066i	$0.304401\pi$
$678$	12.4569	+	18.9151i	0.478405	+	0.726429i
$679$	24.1189			0.925597
$680$	−10.1018	+	17.4969i	−0.387388	+	0.670975i
$681$	6.44666	+	9.78886i	0.247037	+	0.375110i
$682$	1.16194	+	2.01254i	0.0444931	+	0.0770642i
$683$	0.314869			0.0120481			0.00602407	−	0.999982i	$-0.498082\pi$
$683$	0.314869			0.0120481			0.00602407	+	0.999982i	$0.498082\pi$
$684$	−4.20677	−	12.3816i	−0.160850	−	0.473421i
$685$	13.5428			0.517445
$686$	−16.6197	−	28.7861i	−0.634543	−	1.09906i
$687$	3.46479	−	0.203890i	0.132190	−	0.00777889i
$688$	−2.58495	+	4.47726i	−0.0985501	+	0.170694i
$689$	−0.146452			−0.00557939
$690$	−17.8628	+	35.6210i	−0.680023	+	1.35607i
$691$	−3.87776	+	6.71648i	−0.147517	+	0.255507i	−0.930309	−	0.366776i	$-0.880461\pi$
$691$	−3.87776	+	6.71648i	−0.147517	+	0.255507i	0.782792	+	0.622283i	$0.213795\pi$
$692$	4.01392			0.152586
$693$	−1.28951	+	2.99933i	−0.0489846	+	0.113935i
$694$	5.51188	+	9.54686i	0.209228	+	0.362394i
$695$	31.5072	−	54.5721i	1.19514	−	2.07004i
$696$	−3.80853	+	7.59479i	−0.144362	+	0.287880i
$697$	−21.8694	+	37.8789i	−0.828362	+	1.43476i
$698$	24.5114			0.927771
$699$	−1.84693	−	2.80445i	−0.0698574	−	0.106074i
$700$	−16.0261	−	27.7579i	−0.605728	−	1.04915i
$701$	1.77996	−	3.08298i	0.0672280	−	0.116442i	−0.830452	−	0.557090i	$-0.811918\pi$
$701$	1.77996	−	3.08298i	0.0672280	−	0.116442i	0.897680	+	0.440648i	$0.145251\pi$
$702$	1.07893	−	0.192250i	0.0407214	−	0.00725599i
$703$	1.48101	+	6.94958i	0.0558574	+	0.262108i
$704$	−0.118132	+	0.204611i	−0.00445228	+	0.00771157i
$705$	−0.283666	+	0.565674i	−0.0106835	+	0.0213045i
$706$	−12.9476			−0.487288
$707$	−30.4721	+	52.7793i	−1.14602	+	1.98497i
$708$	−4.22286	−	6.41215i	−0.158705	−	0.240983i
$709$	0.177465			0.00666483			0.00333241	−	0.999994i	$-0.498939\pi$
$709$	0.177465			0.00666483			0.00333241	+	0.999994i	$0.498939\pi$
$710$	7.20590			0.270432
$711$	−14.3998	+	33.4932i	−0.540036	+	1.25609i
$712$	−1.63061	−	2.82430i	−0.0611098	−	0.105845i
$713$	−65.4383			−2.45068
$714$	−25.6364	−	38.9273i	−0.959419	−	1.45682i
$715$	−0.0861599	−	0.149233i	−0.00322220	−	0.00558101i
$716$	6.22299	−	10.7785i	0.232564	−	0.402813i
$717$	−45.9638	+	2.70480i	−1.71655	+	0.101013i
$718$	−5.85857			−0.218640
$719$	−11.0494	+	19.1382i	−0.412074	+	0.713733i	−0.995116	−	0.0987084i	$-0.968529\pi$
$719$	−11.0494	+	19.1382i	−0.412074	+	0.713733i	0.583042	+	0.812442i	$0.301862\pi$
$720$	−4.09762	+	9.53083i	−0.152709	+	0.355193i
$721$	−68.1769			−2.53904
$722$	15.3831	+	11.1517i	0.572500	+	0.415023i
$723$	15.7418	−	31.3916i	0.585445	−	1.16747i
$724$	−3.19525			−0.118750
$725$	34.1339			1.26770
$726$	10.4259	+	15.8311i	0.386943	+	0.587549i
$727$	−17.8326	−	30.8870i	−0.661374	−	1.14553i	−0.980255	−	0.197739i	$-0.936640\pi$
$727$	−17.8326	−	30.8870i	−0.661374	−	1.14553i	0.318880	−	0.947795i	$-0.396693\pi$
$728$	−0.485738	−	0.841323i	−0.0180027	−	0.0311815i
$729$	25.3382	−	9.32595i	0.938454	−	0.345406i
$730$	−22.7949			−0.843678
$731$	30.2045			1.11715
$732$	4.15395	+	6.30752i	0.153535	+	0.233133i
$733$	−13.5416	−	23.4548i	−0.500171	−	0.866322i	−1.00000		0.000197820i	$-0.999937\pi$
$733$	−13.5416	−	23.4548i	−0.500171	−	0.866322i	0.499829	−	0.866124i	$-0.333396\pi$
$734$	8.96496	+	15.5278i	0.330903	+	0.573140i
$735$	85.0037	−	5.00215i	3.13541	−	0.184507i
$736$	−3.32649	−	5.76164i	−0.122616	−	0.212377i
$737$	0.652017	+	1.12933i	0.0240173	+	0.0415993i
$738$	−8.87091	+	20.6332i	−0.326543	+	0.759519i
$739$	11.1698	−	19.3466i	0.410887	−	0.711677i	−0.584100	−	0.811682i	$-0.698552\pi$
$739$	11.1698	−	19.3466i	0.410887	−	0.711677i	0.994987	+	0.100005i	$0.0318857\pi$
$740$	2.81862	−	4.88199i	0.103614	−	0.179465i
$741$	−1.11810	+	1.13374i	−0.0410745	+	0.0416491i
$742$	1.59921	+	2.76991i	0.0587088	+	0.101687i
$743$	46.7329			1.71446			0.857231	−	0.514932i	$-0.172183\pi$
$743$	46.7329			1.71446			0.857231	+	0.514932i	$0.172183\pi$
$744$	−17.0069	+	1.00079i	−0.623504	+	0.0366909i
$745$	−33.3313			−1.22116
$746$	1.76548	−	3.05791i	0.0646390	−	0.111958i
$747$	−32.7007	+	3.86200i	−1.19645	+	0.141303i
$748$	1.38035			0.0504705
$749$	−35.9876	+	62.3323i	−1.31496	+	2.27757i
$750$	11.7110	−	0.689147i	0.427624	−	0.0251641i
$751$	10.4745	−	18.1423i	0.382219	−	0.662024i	−0.609160	−	0.793048i	$-0.708493\pi$
$751$	10.4745	−	18.1423i	0.382219	−	0.662024i	0.991379	+	0.131024i	$0.0418265\pi$
$752$	−0.0528257	−	0.0914968i	−0.00192636	−	0.00333655i
$753$	−20.9865	+	1.23498i	−0.764790	+	0.0450050i
$754$	1.03457			0.0376770
$755$	35.7161	−	61.8620i	1.29984	−	2.25139i
$756$	−15.4176	−	18.3068i	−0.560732	−	0.665813i
$757$	−2.07507	+	3.59412i	−0.0754196	+	0.130631i	−0.901269	−	0.433261i	$-0.857363\pi$
$757$	−2.07507	+	3.59412i	−0.0754196	+	0.130631i	0.825849	+	0.563891i	$0.190696\pi$
$758$	−3.23178	−	5.59761i	−0.117384	−	0.203314i
$759$	2.71784	−	0.159935i	0.0986514	−	0.00580527i
$760$	−3.14175	−	14.7425i	−0.113963	−	0.534768i
$761$	−15.3632	−	26.6098i	−0.556915	−	0.964605i	−0.997752	−	0.0670181i	$-0.978651\pi$
$761$	−15.3632	−	26.6098i	−0.556915	−	0.964605i	0.440837	−	0.897587i	$-0.354682\pi$
$762$	−1.74900	−	2.65575i	−0.0633597	−	0.0962078i
$763$	6.88704	+	11.9287i	0.249328	+	0.431848i
$764$	−11.9347	−	20.6714i	−0.431781	−	0.747866i
$765$	60.1927	−	7.10884i	2.17627	−	0.257021i
$766$	3.59218	+	6.22184i	0.129791	+	0.224804i
$767$	−0.467457	+	0.809659i	−0.0168789	+	0.0292351i
$768$	−0.952647	−	1.44654i	−0.0343757	−	0.0521973i
$769$	−19.1502	+	33.1691i	−0.690573	+	1.19611i	0.281077	+	0.959685i	$0.409308\pi$
$769$	−19.1502	+	33.1691i	−0.690573	+	1.19611i	−0.971650	+	0.236422i	$0.924025\pi$
$770$	−1.88167	+	3.25915i	−0.0678107	+	0.117452i
$771$	7.40869	+	11.2496i	0.266817	+	0.405146i
$772$	10.0981	−	17.4904i	0.363438	−	0.629494i
$773$	−1.23238	−	2.13454i	−0.0443255	−	0.0767740i	0.843011	−	0.537896i	$-0.180781\pi$
$773$	−1.23238	−	2.13454i	−0.0443255	−	0.0767740i	−0.887337	+	0.461122i	$0.847447\pi$
$774$	15.4026	−	1.81907i	0.553636	−	0.0653853i
$775$	34.2221	+	59.2745i	1.22930	+	2.12920i
$776$	−2.61813	−	4.53474i	−0.0939855	−	0.162788i
$777$	7.15308	+	10.8615i	0.256615	+	0.389654i
$778$	−3.16372	−	5.47973i	−0.113425	−	0.196458i
$779$	−6.80156	−	31.9160i	−0.243691	−	1.14351i
$780$	1.26109	−	0.0742105i	0.0451543	−	0.00265716i
$781$	−0.246159	−	0.426361i	−0.00880828	−	0.0152564i
$782$	−19.4346	+	33.6617i	−0.694980	+	1.20374i
$783$	25.0934	−	4.47130i	0.896765	−	0.159791i
$784$	−7.10818	+	12.3117i	−0.253863	+	0.439704i
$785$	−13.0356			−0.465261
$786$	−0.272525	+	0.0160371i	−0.00972064	+	0.000572024i
$787$	−24.9675	−	43.2450i	−0.889995	−	1.54152i	−0.839880	−	0.542773i	$-0.817374\pi$
$787$	−24.9675	−	43.2450i	−0.889995	−	1.54152i	−0.0501152	−	0.998743i	$-0.515959\pi$
$788$	−12.1231	+	20.9978i	−0.431868	+	0.748017i
$789$	−1.70252	+	0.100187i	−0.0606113	+	0.00356675i
$790$	−21.0124	+	36.3945i	−0.747588	+	1.29486i
$791$	−60.2302			−2.14154
$792$	0.703901	−	0.0831318i	0.0250120	−	0.00295396i
$793$	0.459829	−	0.796447i	0.0163290	−	0.0282827i
$794$	10.2081			0.362271
$795$	−4.15192	+	0.244325i	−0.147254	+	0.00866532i
$796$	5.31750			0.188474
$797$	−16.5105	−	28.5970i	−0.584832	−	1.01296i	−0.994896	−	0.100902i	$-0.967827\pi$
$797$	−16.5105	−	28.5970i	−0.584832	−	1.01296i	0.410064	−	0.912057i	$-0.365506\pi$
$798$	33.6522	+	8.76701i	1.19128	+	0.310349i
$799$	−0.308628	+	0.534560i	−0.0109185	+	0.0189114i
$800$	−3.47929	+	6.02631i	−0.123012	+	0.213062i
$801$	−3.86432	+	8.98818i	−0.136539	+	0.317582i
$802$	−3.61660	−	6.26413i	−0.127706	−	0.221194i
$803$	0.778694	+	1.34874i	0.0274795	+	0.0475959i
$804$	−9.54334	+	0.561590i	−0.336568	+	0.0198057i
$805$	−52.9860	−	91.7744i	−1.86751	−	3.23462i
$806$	1.03725	+	1.79657i	0.0365355	+	0.0632814i
$807$	12.2436	+	18.5912i	0.430995	+	0.654440i
$808$	13.2312			0.465470
$809$	−27.7891			−0.977013			−0.488506	−	0.872560i	$-0.662458\pi$
$809$	−27.7891			−0.977013			−0.488506	+	0.872560i	$0.662458\pi$
$810$	30.2668	−	7.25024i	1.06347	−	0.254747i
$811$	11.1967	+	19.3932i	0.393168	+	0.680987i	0.992865	−	0.119240i	$-0.0380457\pi$
$811$	11.1967	+	19.3932i	0.393168	+	0.680987i	−0.599697	+	0.800227i	$0.704712\pi$
$812$	−11.2972	−	19.5673i	−0.396454	−	0.686678i
$813$	−12.1340	−	18.4247i	−0.425557	−	0.646183i
$814$	−0.385145			−0.0134993
$815$	−47.8082			−1.67465
$816$	−4.53610	+	9.04567i	−0.158795	+	0.316662i
$817$	−16.7388	+	15.0877i	−0.585618	+	0.527852i
$818$	−20.3193			−0.710447
$819$	−1.15113	+	2.67746i	−0.0402237	+	0.0935580i
$820$	−12.9445	+	22.4206i	−0.452042	+	0.782960i
$821$	33.4757			1.16831			0.584155	−	0.811642i	$-0.301426\pi$
$821$	33.4757			1.16831			0.584155	+	0.811642i	$0.301426\pi$
$822$	6.77141	−	0.398472i	0.236180	−	0.0138983i
$823$	−12.1450	+	21.0358i	−0.423349	+	0.733263i	−0.996265	−	0.0863519i	$-0.972479\pi$
$823$	−12.1450	+	21.0358i	−0.423349	+	0.733263i	0.572915	+	0.819615i	$0.305812\pi$
$824$	7.40068	+	12.8184i	0.257815	+	0.446549i
$825$	−1.56622	−	2.37820i	−0.0545286	−	0.0827983i
$826$	20.4178			0.710428
$827$	−21.0036	−	36.3794i	−0.730368	−	1.26504i	−0.956726	−	0.290991i	$-0.906015\pi$
$827$	−21.0036	−	36.3794i	−0.730368	−	1.26504i	0.226358	−	0.974044i	$-0.427318\pi$
$828$	−7.88330	+	18.3361i	−0.273963	+	0.637223i
$829$	18.0577			0.627169			0.313584	−	0.949560i	$-0.398470\pi$
$829$	18.0577			0.627169			0.313584	+	0.949560i	$0.398470\pi$
$830$	−37.9562			−1.31748
$831$	−5.98362	−	9.08576i	−0.207569	−	0.315181i
$832$	−0.105455	+	0.182653i	−0.00365599	+	0.00633236i
$833$	83.0574			2.87777
$834$	14.1479	−	28.2131i	0.489903	−	0.976940i
$835$	19.7800	−	34.2599i	0.684514	−	1.18561i
$836$	−0.764966	+	0.689510i	−0.0264569	+	0.0238472i
$837$	32.9228	+	39.0925i	1.13798	+	1.35124i
$838$	13.6876	−	23.7076i	0.472830	−	0.818966i
$839$	−17.8630	−	30.9396i	−0.616700	−	1.06816i	−0.990084	−	0.140478i	$-0.955136\pi$
$839$	−17.8630	−	30.9396i	−0.616700	−	1.06816i	0.373384	−	0.927677i	$-0.378197\pi$
$840$	−15.1742	−	23.0412i	−0.523561	−	0.794996i
$841$	−4.93810			−0.170279
$842$	0.938050	−	1.62475i	0.0323273	−	0.0559926i
$843$	21.7355	−	43.3439i	0.748611	−	1.49284i
$844$	−2.19020	+	3.79354i	−0.0753899	+	0.130579i
$845$	22.4009	+	38.7994i	0.770613	+	1.33474i
$846$	−0.125189	+	0.291183i	−0.00430410	+	0.0100111i
$847$	−50.4102			−1.73212
$848$	0.347192	−	0.601354i	0.0119226	−	0.0206506i
$849$	22.8166	−	45.4997i	0.783063	−	1.56155i
$850$	40.6548			1.39445
$851$	5.42265	−	9.39231i	0.185886	−	0.321964i
$852$	3.60295	−	0.212020i	0.123435	−	0.00726369i
$853$	−23.6771	−	41.0100i	−0.810690	−	1.40416i	−0.912382	−	0.409340i	$-0.865759\pi$
$853$	−23.6771	−	41.0100i	−0.810690	−	1.40416i	0.101692	−	0.994816i	$-0.467574\pi$
$854$	−20.0847			−0.687284
$855$	−29.8068	+	34.0070i	−1.01937	+	1.16301i
$856$	15.6260			0.534085
$857$	−15.4053	−	26.6827i	−0.526234	−	0.911464i	−0.999533	−	0.0305618i	$-0.990270\pi$
$857$	−15.4053	−	26.6827i	−0.526234	−	0.911464i	0.473299	−	0.880902i	$-0.343063\pi$
$858$	−0.0474709	−	0.0720816i	−0.00162063	−	0.00246082i
$859$	7.53387	−	13.0490i	0.257052	−	0.445228i	−0.708399	−	0.705813i	$-0.750582\pi$
$859$	7.53387	−	13.0490i	0.257052	−	0.445228i	0.965451	+	0.260585i	$0.0839154\pi$
$860$	17.8781			0.609638
$861$	−32.8506	−	49.8816i	−1.11955	−	1.69996i
$862$	−13.6359	+	23.6181i	−0.464442	+	0.804437i
$863$	38.1514			1.29869			0.649344	−	0.760495i	$-0.275043\pi$
$863$	38.1514			1.29869			0.649344	+	0.760495i	$0.275043\pi$
$864$	−1.76838	+	4.88598i	−0.0601617	+	0.166224i
$865$	−6.94031	−	12.0210i	−0.235978	−	0.408725i
$866$	7.68349	−	13.3082i	0.261096	−	0.452231i
$867$	29.6248	−	1.74331i	1.00611	−	0.0592058i
$868$	22.6528	−	39.2357i	0.768885	−	1.33175i
$869$	2.87120			0.0973990
$870$	29.3302	−	1.72597i	0.994387	−	0.0585159i
$871$	0.582046	+	1.00813i	0.0197219	+	0.0341593i
$872$	1.49519	−	2.58975i	0.0506336	−	0.0877000i
$873$	−6.20460	+	14.4315i	−0.209994	+	0.488433i
$874$	−6.04433	−	28.3627i	−0.204452	−	0.959384i
$875$	−15.5987	+	27.0178i	−0.527333	+	0.913367i
$876$	−11.3975	+	0.670698i	−0.385085	+	0.0226608i
$877$	42.5324			1.43622			0.718109	−	0.695931i	$-0.245008\pi$
$877$	42.5324			1.43622			0.718109	+	0.695931i	$0.245008\pi$
$878$	−10.2936	+	17.8290i	−0.347391	+	0.601698i
$879$	6.53459	−	0.384536i	0.220406	−	0.0129701i
$880$	0.817031			0.0275421
$881$	6.43788			0.216898			0.108449	−	0.994102i	$-0.465412\pi$
$881$	6.43788			0.216898			0.108449	+	0.994102i	$0.465412\pi$
$882$	42.3547	−	5.00215i	1.42616	−	0.168431i
$883$	−9.84079	−	17.0447i	−0.331169	−	0.573601i	0.651572	−	0.758586i	$-0.274110\pi$
$883$	−9.84079	−	17.0447i	−0.331169	−	0.573601i	−0.982741	+	0.184985i	$0.940776\pi$
$884$	1.23222			0.0414439
$885$	−11.9017	+	23.7337i	−0.400070	+	0.797799i
$886$	−11.1479	−	19.3086i	−0.374519	−	0.648687i
$887$	10.6893	−	18.5144i	0.358911	−	0.621651i	−0.628868	−	0.777512i	$-0.716482\pi$
$887$	10.6893	−	18.5144i	0.358911	−	0.621651i	0.987779	+	0.155860i	$0.0498149\pi$
$888$	1.26566	−	2.52393i	0.0424729	−	0.0846974i
$889$	8.45657			0.283624
$890$	−5.63885	+	9.76678i	−0.189015	+	0.327383i
$891$	−1.46292	−	1.54316i	−0.0490098	−	0.0516979i
$892$	1.94159			0.0650093
$893$	−0.0959859	−	0.450410i	−0.00321205	−	0.0150724i
$894$	−16.6656	+	0.980711i	−0.557383	+	0.0327999i
$895$	−43.0397			−1.43866
$896$	4.60612			0.153880
$897$	2.42618	−	0.142771i	0.0810077	−	0.00476700i
$898$	4.84689	+	8.39505i	0.161743	+	0.280147i
$899$	24.1241	+	41.7842i	0.804583	+	1.39358i
$900$	20.7317	−	2.44844i	0.691056	−	0.0816148i
$901$	−4.05686			−0.135154
$902$	1.76878			0.0588940
$903$	−18.4888	+	36.8695i	−0.615270	+	1.22694i
$904$	6.53806	+	11.3243i	0.217453	+	0.376639i
$905$	5.52477	+	9.56918i	0.183650	+	0.318090i
$906$	16.0379	−	31.9819i	0.532822	−	1.06253i
$907$	16.5561	+	28.6759i	0.549735	+	0.952169i	0.998292	+	0.0584150i	$0.0186047\pi$
$907$	16.5561	+	28.6759i	0.549735	+	0.952169i	−0.448557	+	0.893754i	$0.648062\pi$
$908$	3.38355	+	5.86049i	0.112287	+	0.194487i
$909$	−23.7415	−	31.8105i	−0.787457	−	1.05509i
$910$	−1.67974	+	2.90940i	−0.0556828	+	0.0964455i
$911$	26.2010	−	45.3814i	0.868077	−	1.50355i	0.00411816	−	0.999992i	$-0.498689\pi$
$911$	26.2010	−	45.3814i	0.868077	−	1.50355i	0.863959	−	0.503562i	$-0.167978\pi$
$912$	−2.00465	−	7.27883i	−0.0663806	−	0.241026i
$913$	1.29662	+	2.24581i	0.0429118	+	0.0743253i
$914$	16.6205			0.549758
$915$	11.7075	−	23.3464i	0.387036	−	0.771809i
$916$	2.00386			0.0662093
$917$	0.362996	−	0.628727i	0.0119872	−	0.0207624i
$918$	29.8872	−	5.32548i	0.986424	−	0.175767i
$919$	49.8934			1.64583			0.822916	−	0.568163i	$-0.192346\pi$
$919$	49.8934			1.64583			0.822916	+	0.568163i	$0.192346\pi$
$920$	−11.5034	+	19.9244i	−0.379255	+	0.656890i
$921$	−6.44629	−	9.78829i	−0.212412	−	0.322535i
$922$	5.58519	−	9.67383i	0.183938	−	0.318591i
$923$	−0.219743	−	0.380606i	−0.00723292	−	0.0125278i
$924$	−0.844941	+	1.68494i	−0.0277965	+	0.0554304i
$925$	−11.3435			−0.372972
$926$	−9.16587	+	15.8758i	−0.301209	+	0.521710i
$927$	17.5386	−	40.7937i	0.576042	−	1.33984i
$928$	−2.45265	+	4.24811i	−0.0805121	+	0.139451i
$929$	−20.7388	−	35.9206i	−0.680418	−	1.17852i	−0.974853	−	0.222847i	$-0.928465\pi$
$929$	−20.7388	−	35.9206i	−0.680418	−	1.17852i	0.294436	−	0.955671i	$-0.404868\pi$
$930$	32.4032	+	49.2022i	1.06254	+	1.61341i
$931$	−46.0290	+	41.4887i	−1.50854	+	1.35974i
$932$	−0.969369	−	1.67900i	−0.0317527	−	0.0549974i
$933$	−1.78566	+	0.105080i	−0.0584600	+	0.00344015i
$934$	17.8630	+	30.9396i	0.584496	+	1.01238i
$935$	−2.38670	−	4.13389i	−0.0780536	−	0.135193i
$936$	0.628362	−	0.0742105i	0.0205387	−	0.00242565i
$937$	19.1266	+	33.1283i	0.624839	+	1.08225i	0.988572	+	0.150750i	$0.0481688\pi$
$937$	19.1266	+	33.1283i	0.624839	+	1.08225i	−0.363733	+	0.931503i	$0.618498\pi$
$938$	12.7115	−	22.0169i	0.415044	−	0.718877i
$939$	−20.7819	+	41.4421i	−0.678190	+	1.35241i
$940$	−0.182678	+	0.316407i	−0.00595829	+	0.0103201i
$941$	−8.79725	+	15.2373i	−0.286782	+	0.496721i	−0.973040	−	0.230637i	$-0.925919\pi$
$941$	−8.79725	+	15.2373i	−0.286782	+	0.496721i	0.686258	+	0.727359i	$0.259252\pi$
$942$	−6.51781	+	0.383549i	−0.212362	+	0.0124967i
$943$	−24.9036	+	43.1343i	−0.810972	+	1.40465i
$944$	−2.21638	−	3.83889i	−0.0721371	−	0.124945i
$945$	−28.1677	+	77.8264i	−0.916297	+	2.53169i
$946$	−0.610731	−	1.05782i	−0.0198566	−	0.0343926i
$947$	−2.49504	−	4.32153i	−0.0810778	−	0.140431i	0.822635	−	0.568569i	$-0.192503\pi$
$947$	−2.49504	−	4.32153i	−0.0810778	−	0.140431i	−0.903713	+	0.428138i	$0.859170\pi$
$948$	−9.43536	+	18.8155i	−0.306446	+	0.611100i
$949$	0.695128	+	1.20400i	0.0225648	+	0.0390834i
$950$	−22.5302	+	20.3078i	−0.730976	+	0.658873i
$951$	−17.0771	+	34.0543i	−0.553763	+	1.10429i
$952$	−13.4554	−	23.3054i	−0.436091	−	0.755332i
$953$	−18.6055	+	32.2256i	−0.602691	+	1.04389i	0.389721	+	0.920933i	$0.372571\pi$
$953$	−18.6055	+	32.2256i	−0.602691	+	1.04389i	−0.992412	+	0.122958i	$0.960762\pi$
$954$	−2.06877	+	0.244325i	−0.0669790	+	0.00791032i
$955$	−41.2715	+	71.4843i	−1.33551	+	2.31318i
$956$	−26.5831			−0.859760
$957$	−1.10407	−	1.67646i	−0.0356894	−	0.0541922i
$958$	10.6906	+	18.5167i	0.345398	+	0.598247i
$959$	−9.01933	+	15.6219i	−0.291249	+	0.504459i
$960$	−2.68493	+	5.35415i	−0.0866557	+	0.172804i
$961$	−32.8729	+	56.9375i	−1.06042	+	1.83669i
$962$	−0.343813			−0.0110850
$963$	−28.0387	−	37.5682i	−0.903535	−	1.21062i
$964$	10.1375	−	17.5587i	0.326508	−	0.565529i
$965$	−69.8408			−2.24826
$966$	−29.1933	−	44.3282i	−0.939279	−	1.42624i
$967$	3.37983			0.108688			0.0543439	−	0.998522i	$-0.482693\pi$
$967$	3.37983			0.108688			0.0543439	+	0.998522i	$0.482693\pi$
$968$	5.47209	+	9.47794i	0.175880	+	0.304632i
$969$	−30.9724	+	31.4057i	−0.994977	+	1.00890i
$970$	−9.05381	+	15.6817i	−0.290700	+	0.503508i
$971$	−3.09803	+	5.36595i	−0.0994205	+	0.172201i	−0.911445	−	0.411422i	$-0.865032\pi$
$971$	−3.09803	+	5.36595i	−0.0994205	+	0.172201i	0.812024	+	0.583623i	$0.198366\pi$
$972$	14.9201	−	4.51566i	0.478562	−	0.144840i
$973$	41.9668	+	72.6886i	1.34539	+	2.33029i
$974$	−12.5747	−	21.7800i	−0.402920	−	0.697878i
$975$	−1.39814	−	2.12299i	−0.0447762	−	0.0679899i
$976$	2.18022	+	3.77625i	0.0697870	+	0.120875i
$977$	4.49613	+	7.78753i	0.143844	+	0.249145i	0.928941	−	0.370228i	$-0.120720\pi$
$977$	4.49613	+	7.78753i	0.143844	+	0.249145i	−0.785097	+	0.619373i	$0.787387\pi$
$978$	−23.9041	+	1.40667i	−0.764368	+	0.0449802i
$979$	0.770512			0.0246257
$980$	49.1618			1.57042
$981$	−8.90924	+	1.05220i	−0.284450	+	0.0335940i
$982$	17.7119	+	30.6779i	0.565208	+	0.978970i
$983$	11.2619	+	19.5061i	0.359198	+	0.622148i	0.987827	−	0.155557i	$-0.0497171\pi$
$983$	11.2619	+	19.5061i	0.359198	+	0.622148i	−0.628629	+	0.777705i	$0.716384\pi$
$984$	−5.81258	+	11.5912i	−0.185298	+	0.369513i
$985$	83.8463			2.67156
$986$	28.6586			0.912676
$987$	−0.463599	−	0.703946i	−0.0147565	−	0.0224069i
$988$	−0.682874	+	0.615515i	−0.0217251	+	0.0195821i
$989$	34.3951			1.09370
$990$	−1.46605	−	1.96432i	−0.0465942	−	0.0624301i
$991$	11.2999	−	19.5719i	0.358952	−	0.621723i	−0.628834	−	0.777539i	$-0.716468\pi$
$991$	11.2999	−	19.5719i	0.358952	−	0.621723i	0.987786	+	0.155817i	$0.0498009\pi$
$992$	−9.83594			−0.312291
$993$	23.9780	+	36.4090i	0.760917	+	1.15541i
$994$	−4.79903	+	8.31216i	−0.152216	+	0.263646i
$995$	−9.19428	−	15.9250i	−0.291478	−	0.504855i
$996$	−18.9781	+	1.11679i	−0.601345	+	0.0353869i
$997$	−8.43417			−0.267113			−0.133557	−	0.991041i	$-0.542640\pi$
$997$	−8.43417			−0.267113			−0.133557	+	0.991041i	$0.542640\pi$
$998$	−17.4167	−	30.1667i	−0.551317	−	0.954910i
$999$	−8.33912	+	1.48592i	−0.263838	+	0.0470123i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	342.2.h.f.277.3	yes	10
3.2	odd	2		1026.2.h.f.505.1		10
9.4	even	3		342.2.f.f.49.2	yes	10
9.5	odd	6		1026.2.f.f.847.5		10
19.7	even	3		342.2.f.f.7.2	✓	10
57.26	odd	6		1026.2.f.f.235.5		10
171.121	even	3	inner	342.2.h.f.121.3	yes	10
171.140	odd	6		1026.2.h.f.577.1		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
342.2.f.f.7.2	✓	10	19.7	even	3
342.2.f.f.49.2	yes	10	9.4	even	3
342.2.h.f.121.3	yes	10	171.121	even	3	inner
342.2.h.f.277.3	yes	10	1.1	even	1	trivial
1026.2.f.f.235.5		10	57.26	odd	6
1026.2.f.f.847.5		10	9.5	odd	6
1026.2.h.f.505.1		10	3.2	odd	2
1026.2.h.f.577.1		10	171.140	odd	6

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:	\( N \)	\(=\)	\( 342 = 2 \cdot 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	342.h (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.776413 + 1.54828i) q^{3} +(-0.500000 + 0.866025i) q^{4} +3.45812 q^{5} +(1.72906 - 0.101749i) q^{6} +(-2.30306 + 3.98902i) q^{7} +1.00000 q^{8} +(-1.79437 - 2.40422i) q^{9} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.776413 + 1.54828i) q^{3} +(-0.500000 + 0.866025i) q^{4} +3.45812 q^{5} +(1.72906 - 0.101749i) q^{6} +(-2.30306 + 3.98902i) q^{7} +1.00000 q^{8} +(-1.79437 - 2.40422i) q^{9} +(-1.72906 - 2.99482i) q^{10} +(-0.118132 + 0.204611i) q^{11} +(-0.952647 - 1.44654i) q^{12} +(-0.105455 + 0.182653i) q^{13} +4.60612 q^{14} +(-2.68493 + 5.35415i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-2.92119 + 5.05965i) q^{17} +(-1.18493 + 2.75607i) q^{18} +(-0.908515 - 4.26317i) q^{19} +(-1.72906 + 2.99482i) q^{20} +(-4.38801 - 6.66292i) q^{21} +0.236264 q^{22} +(-3.32649 + 5.76164i) q^{23} +(-0.776413 + 1.54828i) q^{24} +6.95859 q^{25} +0.210910 q^{26} +(5.11558 - 0.911525i) q^{27} +(-2.30306 - 3.98902i) q^{28} +4.90529 q^{29} +(5.97929 - 0.351859i) q^{30} +(4.91797 + 8.51818i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(-0.225077 - 0.341765i) q^{33} +5.84239 q^{34} +(-7.96426 + 13.7945i) q^{35} +(2.97929 - 0.351859i) q^{36} -1.63014 q^{37} +(-3.23775 + 2.91838i) q^{38} +(-0.200923 - 0.305088i) q^{39} +3.45812 q^{40} +7.48645 q^{41} +(-3.57625 + 7.13158i) q^{42} +(-2.58495 - 4.47726i) q^{43} +(-0.118132 - 0.204611i) q^{44} +(-6.20513 - 8.31406i) q^{45} +6.65297 q^{46} +0.105651 q^{47} +(1.72906 - 0.101749i) q^{48} +(-7.10818 - 12.3117i) q^{49} +(-3.47929 - 6.02631i) q^{50} +(-5.56573 - 8.45122i) q^{51} +(-0.105455 - 0.182653i) q^{52} +(0.347192 + 0.601354i) q^{53} +(-3.34719 - 3.97446i) q^{54} +(-0.408515 + 0.707569i) q^{55} +(-2.30306 + 3.98902i) q^{56} +(7.30598 + 1.90334i) q^{57} +(-2.45265 - 4.24811i) q^{58} +4.43276 q^{59} +(-3.29437 - 5.00229i) q^{60} -4.36043 q^{61} +(4.91797 - 8.51818i) q^{62} +(13.7230 - 1.62071i) q^{63} +1.00000 q^{64} +(-0.364676 + 0.631637i) q^{65} +(-0.183439 + 0.365805i) q^{66} +(2.75969 - 4.77992i) q^{67} +(-2.92119 - 5.05965i) q^{68} +(-6.33793 - 9.62376i) q^{69} +15.9285 q^{70} +(-1.04188 + 1.80459i) q^{71} +(-1.79437 - 2.40422i) q^{72} +(3.29586 - 5.70859i) q^{73} +(0.815072 + 1.41175i) q^{74} +(-5.40274 + 10.7739i) q^{75} +(4.14627 + 1.34479i) q^{76} +(-0.544131 - 0.942463i) q^{77} +(-0.163753 + 0.326548i) q^{78} +(-6.07625 - 10.5244i) q^{79} +(-1.72906 - 2.99482i) q^{80} +(-2.56050 + 8.62808i) q^{81} +(-3.74323 - 6.48346i) q^{82} +(5.48799 - 9.50548i) q^{83} +(7.96426 - 0.468667i) q^{84} +(-10.1018 + 17.4969i) q^{85} +(-2.58495 + 4.47726i) q^{86} +(-3.80853 + 7.59479i) q^{87} +(-0.118132 + 0.204611i) q^{88} +(-1.63061 - 2.82430i) q^{89} +(-4.09762 + 9.53083i) q^{90} +(-0.485738 - 0.841323i) q^{91} +(-3.32649 - 5.76164i) q^{92} +(-17.0069 + 1.00079i) q^{93} +(-0.0528257 - 0.0914968i) q^{94} +(-3.14175 - 14.7425i) q^{95} +(-0.952647 - 1.44654i) q^{96} +(-2.61813 - 4.53474i) q^{97} +(-7.10818 + 12.3117i) q^{98} +(0.703901 - 0.0831318i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 5 q^{2} - 4 q^{3} - 5 q^{4} + 4 q^{5} + 2 q^{6} - 5 q^{7} + 10 q^{8} - 8 q^{9}+O(q^{10}) \) 10 * q - 5 * q^2 - 4 * q^3 - 5 * q^4 + 4 * q^5 + 2 * q^6 - 5 * q^7 + 10 * q^8 - 8 * q^9	\( 10 q - 5 q^{2} - 4 q^{3} - 5 q^{4} + 4 q^{5} + 2 q^{6} - 5 q^{7} + 10 q^{8} - 8 q^{9} - 2 q^{10} + q^{11} + 2 q^{12} - 7 q^{13} + 10 q^{14} - 11 q^{15} - 5 q^{16} - 9 q^{17} + 4 q^{18} + 3 q^{19} - 2 q^{20} + 15 q^{21} - 2 q^{22} + 10 q^{23} - 4 q^{24} + 18 q^{25} + 14 q^{26} - 4 q^{27} - 5 q^{28} + 26 q^{29} + 34 q^{30} + 18 q^{31} - 5 q^{32} + 13 q^{33} + 18 q^{34} + 12 q^{35} + 4 q^{36} - 48 q^{37} - 9 q^{38} - 20 q^{39} + 4 q^{40} - 10 q^{41} - 3 q^{42} + 15 q^{43} + q^{44} - 10 q^{45} - 20 q^{46} - 14 q^{47} + 2 q^{48} - 26 q^{49} - 9 q^{50} + 30 q^{51} - 7 q^{52} - 14 q^{53} - 16 q^{54} + 8 q^{55} - 5 q^{56} - 17 q^{57} - 13 q^{58} + 30 q^{59} - 23 q^{60} - 28 q^{61} + 18 q^{62} + 48 q^{63} + 10 q^{64} - q^{65} - 5 q^{66} - 2 q^{67} - 9 q^{68} - 44 q^{69} - 24 q^{70} - 41 q^{71} - 8 q^{72} + 4 q^{73} + 24 q^{74} + 22 q^{75} + 6 q^{76} - 6 q^{77} + 19 q^{78} - 28 q^{79} - 2 q^{80} - 8 q^{81} + 5 q^{82} + 21 q^{83} - 12 q^{84} + 18 q^{85} + 15 q^{86} - q^{87} + q^{88} - 27 q^{89} + 8 q^{90} - q^{91} + 10 q^{92} - 49 q^{93} + 7 q^{94} + 17 q^{95} + 2 q^{96} - 24 q^{97} - 26 q^{98} - 13 q^{99}+O(q^{100}) \) 10 * q - 5 * q^2 - 4 * q^3 - 5 * q^4 + 4 * q^5 + 2 * q^6 - 5 * q^7 + 10 * q^8 - 8 * q^9 - 2 * q^10 + q^11 + 2 * q^12 - 7 * q^13 + 10 * q^14 - 11 * q^15 - 5 * q^16 - 9 * q^17 + 4 * q^18 + 3 * q^19 - 2 * q^20 + 15 * q^21 - 2 * q^22 + 10 * q^23 - 4 * q^24 + 18 * q^25 + 14 * q^26 - 4 * q^27 - 5 * q^28 + 26 * q^29 + 34 * q^30 + 18 * q^31 - 5 * q^32 + 13 * q^33 + 18 * q^34 + 12 * q^35 + 4 * q^36 - 48 * q^37 - 9 * q^38 - 20 * q^39 + 4 * q^40 - 10 * q^41 - 3 * q^42 + 15 * q^43 + q^44 - 10 * q^45 - 20 * q^46 - 14 * q^47 + 2 * q^48 - 26 * q^49 - 9 * q^50 + 30 * q^51 - 7 * q^52 - 14 * q^53 - 16 * q^54 + 8 * q^55 - 5 * q^56 - 17 * q^57 - 13 * q^58 + 30 * q^59 - 23 * q^60 - 28 * q^61 + 18 * q^62 + 48 * q^63 + 10 * q^64 - q^65 - 5 * q^66 - 2 * q^67 - 9 * q^68 - 44 * q^69 - 24 * q^70 - 41 * q^71 - 8 * q^72 + 4 * q^73 + 24 * q^74 + 22 * q^75 + 6 * q^76 - 6 * q^77 + 19 * q^78 - 28 * q^79 - 2 * q^80 - 8 * q^81 + 5 * q^82 + 21 * q^83 - 12 * q^84 + 18 * q^85 + 15 * q^86 - q^87 + q^88 - 27 * q^89 + 8 * q^90 - q^91 + 10 * q^92 - 49 * q^93 + 7 * q^94 + 17 * q^95 + 2 * q^96 - 24 * q^97 - 26 * q^98 - 13 * q^99

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