LMFDB - Embedded newform 342.2.f.g.7.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [342,2,Mod(7,342)]

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([4, 2]))

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

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

chi := DirichletCharacter("342.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 342 = 2 \cdot 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	342.f (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:	$18$
Relative dimension:	$9$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} + 4 x^{16} - 6 x^{15} + x^{14} - 21 x^{13} - 12 x^{12} + 9 x^{10} + 135 x^{9} + 27 x^{8} + \cdots + 19683 $ x^18 + 4x^16 - 6x^15 + x^14 - 21x^13 - 12x^12 + 9x^10 + 135x^9 + 27x^8 - 324x^6 - 1701x^5 + 243x^4 - 4374x^3 + 8748x^2 + 19683
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{4}\cdot 3^{3} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			7.8
Root			$1.55117 - 0.770640i$ of defining polynomial
Character	$\chi$	$=$	342.7
Dual form			342.2.f.g.49.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +(1.44298 + 0.958029i) q^{3} +1.00000 q^{4} +(1.19924 - 2.07714i) q^{5} +(-1.44298 - 0.958029i) q^{6} +(0.959469 - 1.66185i) q^{7} -1.00000 q^{8} +(1.16436 + 2.76483i) q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +(1.44298 + 0.958029i) q^{3} +1.00000 q^{4} +(1.19924 - 2.07714i) q^{5} +(-1.44298 - 0.958029i) q^{6} +(0.959469 - 1.66185i) q^{7} -1.00000 q^{8} +(1.16436 + 2.76483i) q^{9} +(-1.19924 + 2.07714i) q^{10} +(2.87780 - 4.98450i) q^{11} +(1.44298 + 0.958029i) q^{12} -4.60353 q^{13} +(-0.959469 + 1.66185i) q^{14} +(3.72043 - 1.84836i) q^{15} +1.00000 q^{16} +(-2.41833 - 4.18868i) q^{17} +(-1.16436 - 2.76483i) q^{18} +(0.469393 + 4.33355i) q^{19} +(1.19924 - 2.07714i) q^{20} +(2.97659 - 1.47881i) q^{21} +(-2.87780 + 4.98450i) q^{22} -1.28511 q^{23} +(-1.44298 - 0.958029i) q^{24} +(-0.376334 - 0.651829i) q^{25} +4.60353 q^{26} +(-0.968634 + 5.10507i) q^{27} +(0.959469 - 1.66185i) q^{28} +(3.18764 + 5.52115i) q^{29} +(-3.72043 + 1.84836i) q^{30} +(2.04176 + 3.53644i) q^{31} -1.00000 q^{32} +(8.92790 - 4.43550i) q^{33} +(2.41833 + 4.18868i) q^{34} +(-2.30126 - 3.98590i) q^{35} +(1.16436 + 2.76483i) q^{36} +5.76979 q^{37} +(-0.469393 - 4.33355i) q^{38} +(-6.64279 - 4.41032i) q^{39} +(-1.19924 + 2.07714i) q^{40} +(-1.30274 + 2.25641i) q^{41} +(-2.97659 + 1.47881i) q^{42} -3.96969 q^{43} +(2.87780 - 4.98450i) q^{44} +(7.13927 + 0.897137i) q^{45} +1.28511 q^{46} +(1.92168 + 3.32844i) q^{47} +(1.44298 + 0.958029i) q^{48} +(1.65884 + 2.87319i) q^{49} +(0.376334 + 0.651829i) q^{50} +(0.523273 - 8.36100i) q^{51} -4.60353 q^{52} +(5.14637 - 8.91377i) q^{53} +(0.968634 - 5.10507i) q^{54} +(-6.90233 - 11.9552i) q^{55} +(-0.959469 + 1.66185i) q^{56} +(-3.47434 + 6.70291i) q^{57} +(-3.18764 - 5.52115i) q^{58} +(-3.92209 + 6.79326i) q^{59} +(3.72043 - 1.84836i) q^{60} +(0.474528 + 0.821907i) q^{61} +(-2.04176 - 3.53644i) q^{62} +(5.71189 + 0.717770i) q^{63} +1.00000 q^{64} +(-5.52072 + 9.56217i) q^{65} +(-8.92790 + 4.43550i) q^{66} -10.0357 q^{67} +(-2.41833 - 4.18868i) q^{68} +(-1.85438 - 1.23117i) q^{69} +(2.30126 + 3.98590i) q^{70} +(-2.68814 - 4.65600i) q^{71} +(-1.16436 - 2.76483i) q^{72} +(7.26581 + 12.5848i) q^{73} -5.76979 q^{74} +(0.0814302 - 1.30111i) q^{75} +(0.469393 + 4.33355i) q^{76} +(-5.52233 - 9.56495i) q^{77} +(6.64279 + 4.41032i) q^{78} -9.49078 q^{79} +(1.19924 - 2.07714i) q^{80} +(-6.28852 + 6.43852i) q^{81} +(1.30274 - 2.25641i) q^{82} +(-0.715228 + 1.23881i) q^{83} +(2.97659 - 1.47881i) q^{84} -11.6006 q^{85} +3.96969 q^{86} +(-0.689733 + 11.0207i) q^{87} +(-2.87780 + 4.98450i) q^{88} +(-6.59763 + 11.4274i) q^{89} +(-7.13927 - 0.897137i) q^{90} +(-4.41695 + 7.65038i) q^{91} -1.28511 q^{92} +(-0.441792 + 7.05906i) q^{93} +(-1.92168 - 3.32844i) q^{94} +(9.56430 + 4.22196i) q^{95} +(-1.44298 - 0.958029i) q^{96} +14.8163 q^{97} +(-1.65884 - 2.87319i) q^{98} +(17.1321 + 2.15286i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q - 18 q^{2} + 18 q^{4} + 5 q^{7} - 18 q^{8} + 4 q^{9}+O(q^{10}) $ 18 * q - 18 * q^2 + 18 * q^4 + 5 * q^7 - 18 * q^8 + 4 * q^9	$ 18 q - 18 q^{2} + 18 q^{4} + 5 q^{7} - 18 q^{8} + 4 q^{9} + q^{11} - 2 q^{13} - 5 q^{14} + 18 q^{16} - 5 q^{17} - 4 q^{18} + 9 q^{19} - 4 q^{21} - q^{22} + 4 q^{23} - 9 q^{25} + 2 q^{26} - 18 q^{27} + 5 q^{28} - 9 q^{29} + 4 q^{31} - 18 q^{32} + 16 q^{33} + 5 q^{34} + 6 q^{35} + 4 q^{36} + 20 q^{37} - 9 q^{38} + 4 q^{39} + q^{41} + 4 q^{42} - 14 q^{43} + q^{44} + 30 q^{45} - 4 q^{46} + 19 q^{47} + 6 q^{49} + 9 q^{50} + 16 q^{51} - 2 q^{52} - 10 q^{53} + 18 q^{54} + 6 q^{55} - 5 q^{56} - 36 q^{57} + 9 q^{58} - 5 q^{59} + 18 q^{61} - 4 q^{62} - 15 q^{63} + 18 q^{64} - 45 q^{65} - 16 q^{66} - 44 q^{67} - 5 q^{68} - 26 q^{69} - 6 q^{70} + 11 q^{71} - 4 q^{72} + 44 q^{73} - 20 q^{74} + 9 q^{76} - 2 q^{77} - 4 q^{78} - 4 q^{79} - 32 q^{81} - q^{82} - 7 q^{83} - 4 q^{84} + 14 q^{86} + 3 q^{87} - q^{88} + q^{89} - 30 q^{90} - 25 q^{91} + 4 q^{92} + 10 q^{93} - 19 q^{94} - 24 q^{95} - 6 q^{98} + 8 q^{99}+O(q^{100}) $ 18 * q - 18 * q^2 + 18 * q^4 + 5 * q^7 - 18 * q^8 + 4 * q^9 + q^11 - 2 * q^13 - 5 * q^14 + 18 * q^16 - 5 * q^17 - 4 * q^18 + 9 * q^19 - 4 * q^21 - q^22 + 4 * q^23 - 9 * q^25 + 2 * q^26 - 18 * q^27 + 5 * q^28 - 9 * q^29 + 4 * q^31 - 18 * q^32 + 16 * q^33 + 5 * q^34 + 6 * q^35 + 4 * q^36 + 20 * q^37 - 9 * q^38 + 4 * q^39 + q^41 + 4 * q^42 - 14 * q^43 + q^44 + 30 * q^45 - 4 * q^46 + 19 * q^47 + 6 * q^49 + 9 * q^50 + 16 * q^51 - 2 * q^52 - 10 * q^53 + 18 * q^54 + 6 * q^55 - 5 * q^56 - 36 * q^57 + 9 * q^58 - 5 * q^59 + 18 * q^61 - 4 * q^62 - 15 * q^63 + 18 * q^64 - 45 * q^65 - 16 * q^66 - 44 * q^67 - 5 * q^68 - 26 * q^69 - 6 * q^70 + 11 * q^71 - 4 * q^72 + 44 * q^73 - 20 * q^74 + 9 * q^76 - 2 * q^77 - 4 * q^78 - 4 * q^79 - 32 * q^81 - q^82 - 7 * q^83 - 4 * q^84 + 14 * q^86 + 3 * q^87 - q^88 + q^89 - 30 * q^90 - 25 * q^91 + 4 * q^92 + 10 * q^93 - 19 * q^94 - 24 * q^95 - 6 * q^98 + 8 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$191$	$325$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−1.00000			−0.707107
$2$	−1.00000			−0.707107
$3$	1.44298	+	0.958029i	0.833103	+	0.553118i
$3$	1.44298	+	0.958029i	0.833103	+	0.553118i
$4$	1.00000			0.500000
$5$	1.19924	−	2.07714i	0.536315	−	0.928924i	−0.462784	−	0.886471i	$-0.653149\pi$
$5$	1.19924	−	2.07714i	0.536315	−	0.928924i	0.999098	−	0.0424530i	$-0.0135173\pi$
$6$	−1.44298	−	0.958029i	−0.589093	−	0.391114i
$7$	0.959469	−	1.66185i	0.362645	−	0.628120i	−0.625750	−	0.780024i	$-0.715207\pi$
$7$	0.959469	−	1.66185i	0.362645	−	0.628120i	0.988395	+	0.151904i	$0.0485403\pi$
$8$	−1.00000			−0.353553
$9$	1.16436	+	2.76483i	0.388121	+	0.921608i
$10$	−1.19924	+	2.07714i	−0.379232	+	0.656849i
$11$	2.87780	−	4.98450i	0.867690	−	1.50288i	0.00333962	−	0.999994i	$-0.498937\pi$
$11$	2.87780	−	4.98450i	0.867690	−	1.50288i	0.864351	−	0.502889i	$-0.167730\pi$
$12$	1.44298	+	0.958029i	0.416551	+	0.276559i
$13$	−4.60353			−1.27679			−0.638395	−	0.769709i	$-0.720402\pi$
$13$	−4.60353			−1.27679			−0.638395	+	0.769709i	$0.720402\pi$
$14$	−0.959469	+	1.66185i	−0.256429	+	0.444148i
$15$	3.72043	−	1.84836i	0.960610	−	0.477244i
$16$	1.00000			0.250000
$17$	−2.41833	−	4.18868i	−0.586532	−	1.01590i	−0.994683	−	0.102989i	$-0.967159\pi$
$17$	−2.41833	−	4.18868i	−0.586532	−	1.01590i	0.408150	−	0.912915i	$-0.366174\pi$
$18$	−1.16436	−	2.76483i	−0.274443	−	0.651676i
$19$	0.469393	+	4.33355i	0.107686	+	0.994185i
$19$	0.469393	+	4.33355i	0.107686	+	0.994185i
$20$	1.19924	−	2.07714i	0.268157	−	0.464462i
$21$	2.97659	−	1.47881i	0.649545	−	0.322703i
$22$	−2.87780	+	4.98450i	−0.613550	+	1.06270i
$23$	−1.28511			−0.267964			−0.133982	−	0.990984i	$-0.542776\pi$
$23$	−1.28511			−0.267964			−0.133982	+	0.990984i	$0.542776\pi$
$24$	−1.44298	−	0.958029i	−0.294546	−	0.195557i
$25$	−0.376334	−	0.651829i	−0.0752668	−	0.130366i
$26$	4.60353			0.902827
$27$	−0.968634	+	5.10507i	−0.186414	+	0.982471i
$28$	0.959469	−	1.66185i	0.181323	−	0.314060i
$29$	3.18764	+	5.52115i	0.591929	+	1.02525i	0.993972	+	0.109631i	$0.0349668\pi$
$29$	3.18764	+	5.52115i	0.591929	+	1.02525i	−0.402043	+	0.915621i	$0.631700\pi$
$30$	−3.72043	+	1.84836i	−0.679254	+	0.337463i
$31$	2.04176	+	3.53644i	0.366712	+	0.635163i	0.989049	−	0.147586i	$-0.0471503\pi$
$31$	2.04176	+	3.53644i	0.366712	+	0.635163i	−0.622338	+	0.782749i	$0.713817\pi$
$32$	−1.00000			−0.176777
$33$	8.92790	−	4.43550i	1.55415	−	0.772122i
$34$	2.41833	+	4.18868i	0.414741	+	0.718352i
$35$	−2.30126	−	3.98590i	−0.388984	−	0.673740i
$36$	1.16436	+	2.76483i	0.194060	+	0.460804i
$37$	5.76979			0.948547			0.474274	−	0.880377i	$-0.342711\pi$
$37$	5.76979			0.948547			0.474274	+	0.880377i	$0.342711\pi$
$38$	−0.469393	−	4.33355i	−0.0761457	−	0.702995i
$39$	−6.64279	−	4.41032i	−1.06370	−	0.706216i
$40$	−1.19924	+	2.07714i	−0.189616	+	0.328424i
$41$	−1.30274	+	2.25641i	−0.203454	+	0.352393i	−0.949639	−	0.313346i	$-0.898550\pi$
$41$	−1.30274	+	2.25641i	−0.203454	+	0.352393i	0.746185	+	0.665739i	$0.231883\pi$
$42$	−2.97659	+	1.47881i	−0.459298	+	0.228185i
$43$	−3.96969			−0.605372			−0.302686	−	0.953090i	$-0.597883\pi$
$43$	−3.96969			−0.605372			−0.302686	+	0.953090i	$0.597883\pi$
$44$	2.87780	−	4.98450i	0.433845	−	0.751442i
$45$	7.13927	+	0.897137i	1.06426	+	0.133737i
$46$	1.28511			0.189479
$47$	1.92168	+	3.32844i	0.280305	+	0.485503i	0.971460	−	0.237204i	$-0.0762310\pi$
$47$	1.92168	+	3.32844i	0.280305	+	0.485503i	−0.691155	+	0.722707i	$0.742898\pi$
$48$	1.44298	+	0.958029i	0.208276	+	0.138280i
$49$	1.65884	+	2.87319i	0.236977	+	0.410456i
$50$	0.376334	+	0.651829i	0.0532216	+	0.0921826i
$51$	0.523273	−	8.36100i	0.0732729	−	1.17077i
$52$	−4.60353			−0.638395
$53$	5.14637	−	8.91377i	0.706908	−	1.22440i	−0.259091	−	0.965853i	$-0.583423\pi$
$53$	5.14637	−	8.91377i	0.706908	−	1.22440i	0.965999	−	0.258547i	$-0.0832438\pi$
$54$	0.968634	−	5.10507i	0.131814	−	0.694712i
$55$	−6.90233	−	11.9552i	−0.930710	−	1.61204i
$56$	−0.959469	+	1.66185i	−0.128214	+	0.222074i
$57$	−3.47434	+	6.70291i	−0.460188	+	0.887822i
$58$	−3.18764	−	5.52115i	−0.418557	−	0.724962i
$59$	−3.92209	+	6.79326i	−0.510613	+	0.884407i	0.489312	+	0.872109i	$0.337248\pi$
$59$	−3.92209	+	6.79326i	−0.510613	+	0.884407i	−0.999924	+	0.0122983i	$0.996085\pi$
$60$	3.72043	−	1.84836i	0.480305	−	0.238622i
$61$	0.474528	+	0.821907i	0.0607571	+	0.105234i	0.894804	−	0.446459i	$-0.147315\pi$
$61$	0.474528	+	0.821907i	0.0607571	+	0.105234i	−0.834047	+	0.551694i	$0.813982\pi$
$62$	−2.04176	−	3.53644i	−0.259304	−	0.449128i
$63$	5.71189	+	0.717770i	0.719631	+	0.0904305i
$64$	1.00000			0.125000
$65$	−5.52072	+	9.56217i	−0.684762	+	1.18604i
$66$	−8.92790	+	4.43550i	−1.09895	+	0.545972i
$67$	−10.0357			−1.22606			−0.613028	−	0.790061i	$-0.710049\pi$
$67$	−10.0357			−1.22606			−0.613028	+	0.790061i	$0.710049\pi$
$68$	−2.41833	−	4.18868i	−0.293266	−	0.507952i
$69$	−1.85438	−	1.23117i	−0.223241	−	0.148216i
$70$	2.30126	+	3.98590i	0.275053	+	0.476406i
$71$	−2.68814	−	4.65600i	−0.319024	−	0.552566i	0.661261	−	0.750156i	$-0.270022\pi$
$71$	−2.68814	−	4.65600i	−0.319024	−	0.552566i	−0.980285	+	0.197591i	$0.936688\pi$
$72$	−1.16436	−	2.76483i	−0.137221	−	0.325838i
$73$	7.26581	+	12.5848i	0.850399	+	1.47293i	0.880849	+	0.473398i	$0.156973\pi$
$73$	7.26581	+	12.5848i	0.850399	+	1.47293i	−0.0304502	+	0.999536i	$0.509694\pi$
$74$	−5.76979			−0.670724
$75$	0.0814302	−	1.30111i	0.00940275	−	0.150240i
$76$	0.469393	+	4.33355i	0.0538431	+	0.497092i
$77$	−5.52233	−	9.56495i	−0.629328	−	1.09003i
$78$	6.64279	+	4.41032i	0.752148	+	0.499370i
$79$	−9.49078			−1.06780			−0.533898	−	0.845549i	$-0.679273\pi$
$79$	−9.49078			−1.06780			−0.533898	+	0.845549i	$0.679273\pi$
$80$	1.19924	−	2.07714i	0.134079	−	0.232231i
$81$	−6.28852	+	6.43852i	−0.698724	+	0.715391i
$82$	1.30274	−	2.25641i	0.143864	−	0.249179i
$83$	−0.715228	+	1.23881i	−0.0785064	+	0.135977i	−0.902606	−	0.430468i	$-0.858348\pi$
$83$	−0.715228	+	1.23881i	−0.0785064	+	0.135977i	0.824099	+	0.566445i	$0.191682\pi$
$84$	2.97659	−	1.47881i	0.324773	−	0.161351i
$85$	−11.6006			−1.25826
$86$	3.96969			0.428063
$87$	−0.689733	+	11.0207i	−0.0739471	+	1.18155i
$88$	−2.87780	+	4.98450i	−0.306775	+	0.531350i
$89$	−6.59763	+	11.4274i	−0.699347	+	1.21130i	0.269346	+	0.963043i	$0.413192\pi$
$89$	−6.59763	+	11.4274i	−0.699347	+	1.21130i	−0.968693	+	0.248261i	$0.920141\pi$
$90$	−7.13927	−	0.897137i	−0.752545	−	0.0945665i
$91$	−4.41695	+	7.65038i	−0.463022	+	0.801978i
$92$	−1.28511			−0.133982
$93$	−0.441792	+	7.05906i	−0.0458117	+	0.731991i
$94$	−1.92168	−	3.32844i	−0.198206	−	0.343302i
$95$	9.56430	+	4.22196i	0.981276	+	0.433164i
$96$	−1.44298	−	0.958029i	−0.147273	−	0.0977784i
$97$	14.8163			1.50437			0.752184	−	0.658954i	$-0.229001\pi$
$97$	14.8163			1.50437			0.752184	+	0.658954i	$0.229001\pi$
$98$	−1.65884	−	2.87319i	−0.167568	−	0.290236i
$99$	17.1321	+	2.15286i	1.72184	+	0.216370i
$100$	−0.376334	−	0.651829i	−0.0376334	−	0.0651829i
$101$	−4.22793	−	7.32299i	−0.420695	−	0.728665i	0.575313	−	0.817933i	$-0.304880\pi$
$101$	−4.22793	−	7.32299i	−0.420695	−	0.728665i	−0.996008	+	0.0892688i	$0.971547\pi$
$102$	−0.523273	+	8.36100i	−0.0518118	+	0.827862i
$103$	−4.31756	−	7.47823i	−0.425422	−	0.736852i	0.571038	−	0.820924i	$-0.306541\pi$
$103$	−4.31756	−	7.47823i	−0.425422	−	0.736852i	−0.996460	+	0.0840716i	$0.973208\pi$
$104$	4.60353			0.451414
$105$	0.497941	−	7.95623i	0.0485941	−	0.776449i
$106$	−5.14637	+	8.91377i	−0.499859	+	0.865782i
$107$	−19.0406			−1.84073			−0.920364	−	0.391064i	$-0.872107\pi$
$107$	−19.0406			−1.84073			−0.920364	+	0.391064i	$0.872107\pi$
$108$	−0.968634	+	5.10507i	−0.0932068	+	0.491236i
$109$	−6.75552	−	11.7009i	−0.647061	−	1.12074i	−0.983821	−	0.179153i	$-0.942664\pi$
$109$	−6.75552	−	11.7009i	−0.647061	−	1.12074i	0.336760	−	0.941591i	$-0.390669\pi$
$110$	6.90233	+	11.9552i	0.658111	+	1.13988i
$111$	8.32567	+	5.52762i	0.790238	+	0.524659i
$112$	0.959469	−	1.66185i	0.0906613	−	0.157030i
$113$	2.66333	+	4.61303i	0.250545	+	0.433957i	0.963676	−	0.267074i	$-0.0860568\pi$
$113$	2.66333	+	4.61303i	0.250545	+	0.433957i	−0.713131	+	0.701031i	$0.752723\pi$
$114$	3.47434	−	6.70291i	0.325402	−	0.627785i
$115$	−1.54115	+	2.66935i	−0.143713	+	0.248918i
$116$	3.18764	+	5.52115i	0.295965	+	0.512626i
$117$	−5.36018	−	12.7280i	−0.495549	−	1.17670i
$118$	3.92209	−	6.79326i	0.361058	−	0.625370i
$119$	−9.28127			−0.850812
$120$	−3.72043	+	1.84836i	−0.339627	+	0.168731i
$121$	−11.0635	−	19.1626i	−1.00577	−	1.74205i
$122$	−0.474528	−	0.821907i	−0.0429618	−	0.0744120i
$123$	−4.04153	+	2.00789i	−0.364413	+	0.181045i
$124$	2.04176	+	3.53644i	0.183356	+	0.317582i
$125$	10.1871			0.911163
$126$	−5.71189	−	0.717770i	−0.508856	−	0.0639440i
$127$	8.11146	−	14.0495i	0.719776	−	1.24669i	−0.241313	−	0.970447i	$-0.577578\pi$
$127$	8.11146	−	14.0495i	0.719776	−	1.24669i	0.961089	−	0.276241i	$-0.0890886\pi$
$128$	−1.00000			−0.0883883
$129$	−5.72817	−	3.80308i	−0.504337	−	0.334842i
$130$	5.52072	−	9.56217i	0.484200	−	0.838658i
$131$	−5.23848	+	9.07332i	−0.457688	+	0.792739i	−0.998838	−	0.0481866i	$-0.984656\pi$
$131$	−5.23848	+	9.07332i	−0.457688	+	0.792739i	0.541150	+	0.840926i	$0.317989\pi$
$132$	8.92790	−	4.43550i	0.777074	−	0.386061i
$133$	7.65208	+	3.37785i	0.663519	+	0.292897i
$134$	10.0357			0.866952
$135$	9.44231	+	8.13417i	0.812665	+	0.700078i
$136$	2.41833	+	4.18868i	0.207370	+	0.359176i
$137$	−7.06335	−	12.2341i	−0.603463	−	1.04523i	−0.992292	−	0.123919i	$-0.960454\pi$
$137$	−7.06335	−	12.2341i	−0.603463	−	1.04523i	0.388829	−	0.921310i	$-0.372880\pi$
$138$	1.85438	+	1.23117i	0.157856	+	0.104804i
$139$	13.0525			1.10710			0.553549	−	0.832816i	$-0.313273\pi$
$139$	13.0525			1.10710			0.553549	+	0.832816i	$0.313273\pi$
$140$	−2.30126	−	3.98590i	−0.194492	−	0.336870i
$141$	−0.415808	+	6.64388i	−0.0350173	+	0.559516i
$142$	2.68814	+	4.65600i	0.225584	+	0.390723i
$143$	−13.2481	+	22.9463i	−1.10786	+	1.91887i
$144$	1.16436	+	2.76483i	0.0970302	+	0.230402i
$145$	15.2909			1.26984
$146$	−7.26581	−	12.5848i	−0.601323	−	1.04152i
$147$	−0.358935	+	5.73516i	−0.0296045	+	0.473028i
$148$	5.76979			0.474274
$149$	−2.99508	+	5.18763i	−0.245366	+	0.424987i	−0.962235	−	0.272222i	$-0.912242\pi$
$149$	−2.99508	+	5.18763i	−0.245366	+	0.424987i	0.716868	+	0.697209i	$0.245575\pi$
$150$	−0.0814302	+	1.30111i	−0.00664875	+	0.106235i
$151$	2.25398	−	3.90401i	0.183426	−	0.317704i	−0.759619	−	0.650369i	$-0.774614\pi$
$151$	2.25398	−	3.90401i	0.183426	−	0.317704i	0.943045	+	0.332665i	$0.107948\pi$
$152$	−0.469393	−	4.33355i	−0.0380728	−	0.351497i
$153$	8.76515	−	11.5634i	0.708620	−	0.934846i
$154$	5.52233	+	9.56495i	0.445002	+	0.770766i
$155$	9.79422			0.786691
$156$	−6.64279	−	4.41032i	−0.531849	−	0.353108i
$157$	1.28697	−	2.22909i	0.102711	−	0.177901i	−0.810090	−	0.586306i	$-0.800582\pi$
$157$	1.28697	−	2.22909i	0.102711	−	0.177901i	0.912801	+	0.408405i	$0.133915\pi$
$158$	9.49078			0.755046
$159$	15.9657	−	7.93199i	1.26617	−	0.629048i
$160$	−1.19924	+	2.07714i	−0.0948079	+	0.164212i
$161$	−1.23302	+	2.13566i	−0.0971758	+	0.168313i
$162$	6.28852	−	6.43852i	0.494073	−	0.505858i
$163$	−2.93134			−0.229600			−0.114800	−	0.993389i	$-0.536623\pi$
$163$	−2.93134			−0.229600			−0.114800	+	0.993389i	$0.536623\pi$
$164$	−1.30274	+	2.25641i	−0.101727	+	0.176196i
$165$	1.49351	−	23.8637i	0.116270	−	1.85779i
$166$	0.715228	−	1.23881i	0.0555124	−	0.0961503i
$167$	−13.0269			−1.00806			−0.504028	−	0.863688i	$-0.668149\pi$
$167$	−13.0269			−1.00806			−0.504028	+	0.863688i	$0.668149\pi$
$168$	−2.97659	+	1.47881i	−0.229649	+	0.114093i
$169$	8.19253			0.630195
$170$	11.6006			0.889726
$171$	−11.4350	+	6.34362i	−0.874454	+	0.485108i
$172$	−3.96969			−0.302686
$173$	22.6623			1.72298			0.861492	−	0.507770i	$-0.169530\pi$
$173$	22.6623			1.72298			0.861492	+	0.507770i	$0.169530\pi$
$174$	0.689733	−	11.0207i	0.0522885	−	0.835479i
$175$	−1.44432			−0.109181
$176$	2.87780	−	4.98450i	0.216923	−	0.375721i
$177$	−12.1676	+	6.04504i	−0.914575	+	0.454373i
$178$	6.59763	−	11.4274i	0.494513	−	0.856522i
$179$	14.4660			1.08124			0.540621	−	0.841266i	$-0.318189\pi$
$179$	14.4660			1.08124			0.540621	+	0.841266i	$0.318189\pi$
$180$	7.13927	+	0.897137i	0.532130	+	0.0668686i
$181$	6.69227	−	11.5914i	0.497433	−	0.861579i	−0.502563	−	0.864541i	$-0.667610\pi$
$181$	6.69227	−	11.5914i	0.497433	−	0.861579i	0.999996	+	0.00296203i	$0.000942845\pi$
$182$	4.41695	−	7.65038i	0.327406	−	0.567084i
$183$	−0.102677	+	1.64060i	−0.00759013	+	0.121277i
$184$	1.28511			0.0947395
$185$	6.91934	−	11.9846i	0.508720	−	0.881129i
$186$	0.441792	−	7.05906i	0.0323938	−	0.517596i
$187$	−27.8380			−2.03571
$188$	1.92168	+	3.32844i	0.140153	+	0.242751i
$189$	7.55448	+	6.50788i	0.549508	+	0.473379i
$190$	−9.56430	−	4.22196i	−0.693867	−	0.306293i
$191$	−0.456659	+	0.790956i	−0.0330427	+	0.0572316i	−0.882074	−	0.471111i	$-0.843853\pi$
$191$	−0.456659	+	0.790956i	−0.0330427	+	0.0572316i	0.849031	+	0.528343i	$0.177186\pi$
$192$	1.44298	+	0.958029i	0.104138	+	0.0691398i
$193$	−5.71936	+	9.90623i	−0.411689	+	0.713066i	−0.995075	−	0.0991293i	$-0.968394\pi$
$193$	−5.71936	+	9.90623i	−0.411689	+	0.713066i	0.583386	+	0.812195i	$0.301728\pi$
$194$	−14.8163			−1.06375
$195$	−17.1271	+	8.50898i	−1.22650	+	0.609341i
$196$	1.65884	+	2.87319i	0.118488	+	0.205228i
$197$	6.73643			0.479951			0.239975	−	0.970779i	$-0.422861\pi$
$197$	6.73643			0.479951			0.239975	+	0.970779i	$0.422861\pi$
$198$	−17.1321	−	2.15286i	−1.21752	−	0.152997i
$199$	1.28873	−	2.23215i	0.0913558	−	0.158233i	−0.816726	−	0.577026i	$-0.804213\pi$
$199$	1.28873	−	2.23215i	0.0913558	−	0.158233i	0.908082	+	0.418793i	$0.137547\pi$
$200$	0.376334	+	0.651829i	0.0266108	+	0.0460913i
$201$	−14.4813	−	9.61448i	−1.02143	−	0.678153i
$202$	4.22793	+	7.32299i	0.297476	+	0.515244i
$203$	12.2338			0.858641
$204$	0.523273	−	8.36100i	0.0366365	−	0.585387i
$205$	3.12459	+	5.41195i	0.218231	+	0.377987i
$206$	4.31756	+	7.47823i	0.300819	+	0.521033i
$207$	−1.49633	−	3.55310i	−0.104002	−	0.246958i
$208$	−4.60353			−0.319198
$209$	22.9514	+	10.1314i	1.58758	+	0.700805i
$210$	−0.497941	+	7.95623i	−0.0343612	+	0.549032i
$211$	−2.73974	+	4.74537i	−0.188612	+	0.326685i	−0.944788	−	0.327683i	$-0.893732\pi$
$211$	−2.73974	+	4.74537i	−0.188612	+	0.326685i	0.756176	+	0.654368i	$0.227065\pi$
$212$	5.14637	−	8.91377i	0.353454	−	0.612200i
$213$	0.581654	−	9.29382i	0.0398543	−	0.636802i
$214$	19.0406			1.30159
$215$	−4.76059	+	8.24559i	−0.324670	+	0.562345i
$216$	0.968634	−	5.10507i	0.0659072	−	0.347356i
$217$	7.83604			0.531945
$218$	6.75552	+	11.7009i	0.457542	+	0.792485i
$219$	−1.57216	+	25.1204i	−0.106237	+	1.69748i
$220$	−6.90233	−	11.9552i	−0.465355	−	0.806019i
$221$	11.1329	+	19.2827i	0.748879	+	1.29710i
$222$	−8.32567	−	5.52762i	−0.558782	−	0.370990i
$223$	−5.29073			−0.354293			−0.177147	−	0.984184i	$-0.556687\pi$
$223$	−5.29073			−0.354293			−0.177147	+	0.984184i	$0.556687\pi$
$224$	−0.959469	+	1.66185i	−0.0641072	+	0.111037i
$225$	1.36401	−	1.79946i	0.0909337	−	0.119964i
$226$	−2.66333	−	4.61303i	−0.177162	−	0.306854i
$227$	11.1702	−	19.3473i	0.741389	−	1.28412i	−0.210474	−	0.977600i	$-0.567501\pi$
$227$	11.1702	−	19.3473i	0.741389	−	1.28412i	0.951863	−	0.306524i	$-0.0991660\pi$
$228$	−3.47434	+	6.70291i	−0.230094	+	0.443911i
$229$	13.0283	+	22.5657i	0.860935	+	1.49118i	0.871028	+	0.491234i	$0.163454\pi$
$229$	13.0283	+	22.5657i	0.860935	+	1.49118i	−0.0100924	+	0.999949i	$0.503213\pi$
$230$	1.54115	−	2.66935i	0.101620	−	0.176012i
$231$	1.19491	−	19.0925i	0.0786192	−	1.25620i
$232$	−3.18764	−	5.52115i	−0.209279	−	0.362481i
$233$	−6.26856	−	10.8575i	−0.410667	−	0.711296i	0.584296	−	0.811541i	$-0.301371\pi$
$233$	−6.26856	−	10.8575i	−0.410667	−	0.711296i	−0.994963	+	0.100245i	$0.968037\pi$
$234$	5.36018	+	12.7280i	0.350406	+	0.832053i
$235$	9.21817			0.601327
$236$	−3.92209	+	6.79326i	−0.255306	+	0.442204i
$237$	−13.6950	−	9.09244i	−0.889584	−	0.590617i
$238$	9.28127			0.601615
$239$	4.88147	+	8.45495i	0.315756	+	0.546905i	0.979598	−	0.200967i	$-0.0644086\pi$
$239$	4.88147	+	8.45495i	0.315756	+	0.546905i	−0.663842	+	0.747873i	$0.731075\pi$
$240$	3.72043	−	1.84836i	0.240152	−	0.119311i
$241$	7.92117	+	13.7199i	0.510248	+	0.883775i	0.999930	+	0.0118736i	$0.00377959\pi$
$241$	7.92117	+	13.7199i	0.510248	+	0.883775i	−0.489682	+	0.871901i	$0.662887\pi$
$242$	11.0635	+	19.1626i	0.711189	+	1.23182i
$243$	−15.2425	+	3.26605i	−0.977805	+	0.209517i
$244$	0.474528	+	0.821907i	0.0303786	+	0.0526172i
$245$	7.95735			0.508377
$246$	4.04153	−	2.00789i	0.257679	−	0.128018i
$247$	−2.16087	−	19.9497i	−0.137493	−	1.26937i
$248$	−2.04176	−	3.53644i	−0.129652	−	0.224564i
$249$	−2.21887	+	1.10237i	−0.140615	+	0.0698596i
$250$	−10.1871			−0.644289
$251$	−8.25797	+	14.3032i	−0.521238	+	0.902811i	0.478457	+	0.878111i	$0.341196\pi$
$251$	−8.25797	+	14.3032i	−0.521238	+	0.902811i	−0.999695	+	0.0247000i	$0.992137\pi$
$252$	5.71189	+	0.717770i	0.359815	+	0.0452152i
$253$	−3.69829	+	6.40563i	−0.232510	+	0.402718i
$254$	−8.11146	+	14.0495i	−0.508958	+	0.881541i
$255$	−16.7394	−	11.1137i	−1.04826	−	0.695968i
$256$	1.00000			0.0625000
$257$	−14.1564			−0.883049			−0.441525	−	0.897249i	$-0.645562\pi$
$257$	−14.1564			−0.883049			−0.441525	+	0.897249i	$0.645562\pi$
$258$	5.72817	+	3.80308i	0.356620	+	0.236769i
$259$	5.53593	−	9.58852i	0.343986	−	0.595802i
$260$	−5.52072	+	9.56217i	−0.342381	+	0.593021i
$261$	−11.5534	+	15.2419i	−0.715140	+	0.943448i
$262$	5.23848	−	9.07332i	0.323635	−	0.560551i
$263$	−22.8420			−1.40850			−0.704249	−	0.709953i	$-0.748716\pi$
$263$	−22.8420			−1.40850			−0.704249	+	0.709953i	$0.748716\pi$
$264$	−8.92790	+	4.43550i	−0.549474	+	0.272986i
$265$	−12.3434	−	21.3794i	−0.758250	−	1.31333i
$266$	−7.65208	−	3.37785i	−0.469179	−	0.207109i
$267$	−20.4680	+	10.1688i	−1.25262	+	0.622320i
$268$	−10.0357			−0.613028
$269$	−9.39374	−	16.2704i	−0.572746	−	0.992026i	−0.996282	−	0.0861466i	$-0.972545\pi$
$269$	−9.39374	−	16.2704i	−0.572746	−	0.992026i	0.423536	−	0.905879i	$-0.360789\pi$
$270$	−9.44231	−	8.13417i	−0.574641	−	0.495030i
$271$	−11.9001	−	20.6116i	−0.722879	−	1.25206i	−0.959841	−	0.280544i	$-0.909485\pi$
$271$	−11.9001	−	20.6116i	−0.722879	−	1.25206i	0.236962	−	0.971519i	$-0.423848\pi$
$272$	−2.41833	−	4.18868i	−0.146633	−	0.253976i
$273$	−13.7028	+	6.80776i	−0.829333	+	0.412024i
$274$	7.06335	+	12.2341i	0.426713	+	0.739088i
$275$	−4.33206			−0.261233
$276$	−1.85438	−	1.23117i	−0.111621	−	0.0741078i
$277$	−9.74197	+	16.8736i	−0.585338	+	1.01384i	0.409495	+	0.912312i	$0.365705\pi$
$277$	−9.74197	+	16.8736i	−0.585338	+	1.01384i	−0.994833	+	0.101523i	$0.967628\pi$
$278$	−13.0525			−0.782837
$279$	−7.40028	+	9.76282i	−0.443043	+	0.584484i
$280$	2.30126	+	3.98590i	0.137527	+	0.238203i
$281$	5.38694	+	9.33045i	0.321358	+	0.556608i	0.980768	−	0.195175i	$-0.0625275\pi$
$281$	5.38694	+	9.33045i	0.321358	+	0.556608i	−0.659411	+	0.751783i	$0.729194\pi$
$282$	0.415808	−	6.64388i	0.0247610	−	0.395637i
$283$	10.1095	−	17.5102i	0.600950	−	1.04088i	−0.391728	−	0.920081i	$-0.628123\pi$
$283$	10.1095	−	17.5102i	0.600950	−	1.04088i	0.992678	−	0.120794i	$-0.0385441\pi$
$284$	−2.68814	−	4.65600i	−0.159512	−	0.276283i
$285$	9.75630	+	15.2551i	0.577913	+	0.903631i
$286$	13.2481	−	22.9463i	0.783375	−	1.35684i
$287$	2.49988	+	4.32992i	0.147563	+	0.255587i
$288$	−1.16436	−	2.76483i	−0.0686107	−	0.162919i
$289$	−3.19668	+	5.53682i	−0.188040	+	0.325695i
$290$	−15.2909			−0.897913
$291$	21.3796	+	14.1944i	1.25329	+	0.832093i
$292$	7.26581	+	12.5848i	0.425199	+	0.736467i
$293$	−14.4603	−	25.0459i	−0.844777	−	1.46320i	−0.885815	−	0.464039i	$-0.846400\pi$
$293$	−14.4603	−	25.0459i	−0.844777	−	1.46320i	0.0410377	−	0.999158i	$-0.486934\pi$
$294$	0.358935	−	5.73516i	0.0209335	−	0.334481i
$295$	9.40703	+	16.2934i	0.547698	+	0.948641i
$296$	−5.76979			−0.335362
$297$	22.6587	+	19.5195i	1.31479	+	1.13264i
$298$	2.99508	−	5.18763i	0.173500	−	0.300511i
$299$	5.91604			0.342134
$300$	0.0814302	−	1.30111i	0.00470138	−	0.0751198i
$301$	−3.80879	+	6.59702i	−0.219535	+	0.380246i
$302$	−2.25398	+	3.90401i	−0.129702	+	0.224650i
$303$	0.914829	−	14.6174i	0.0525556	−	0.839746i
$304$	0.469393	+	4.33355i	0.0269216	+	0.248546i
$305$	2.27629			0.130340
$306$	−8.76515	+	11.5634i	−0.501070	+	0.661036i
$307$	2.90114	+	5.02491i	0.165577	+	0.286787i	0.936860	−	0.349705i	$-0.113718\pi$
$307$	2.90114	+	5.02491i	0.165577	+	0.286787i	−0.771283	+	0.636492i	$0.780385\pi$
$308$	−5.52233	−	9.56495i	−0.314664	−	0.545014i
$309$	0.934223	−	14.9273i	0.0531461	−	0.849182i
$310$	−9.79422			−0.556275
$311$	−3.00615	−	5.20680i	−0.170463	−	0.295250i	0.768119	−	0.640307i	$-0.221193\pi$
$311$	−3.00615	−	5.20680i	−0.170463	−	0.295250i	−0.938582	+	0.345057i	$0.887860\pi$
$312$	6.64279	+	4.41032i	0.376074	+	0.249685i
$313$	0.962646	+	1.66735i	0.0544120	+	0.0942443i	0.891948	−	0.452137i	$-0.149338\pi$
$313$	0.962646	+	1.66735i	0.0544120	+	0.0942443i	−0.837536	+	0.546381i	$0.816005\pi$
$314$	−1.28697	+	2.22909i	−0.0726278	+	0.125795i
$315$	8.34081	−	11.0036i	0.469952	−	0.619983i
$316$	−9.49078			−0.533898
$317$	4.41910	+	7.65410i	0.248201	+	0.429897i	0.963027	−	0.269406i	$-0.0868272\pi$
$317$	4.41910	+	7.65410i	0.248201	+	0.429897i	−0.714826	+	0.699303i	$0.753494\pi$
$318$	−15.9657	+	7.93199i	−0.895314	+	0.444804i
$319$	36.6936			2.05444
$320$	1.19924	−	2.07714i	0.0670393	−	0.116116i
$321$	−27.4752	−	18.2415i	−1.53351	−	1.01814i
$322$	1.23302	−	2.13566i	0.0687137	−	0.119016i
$323$	17.0167	−	12.4461i	0.946835	−	0.692520i
$324$	−6.28852	+	6.43852i	−0.349362	+	0.357695i
$325$	1.73247	+	3.00072i	0.0960999	+	0.166450i
$326$	2.93134			0.162352
$327$	1.46174	−	23.3561i	0.0808346	−	1.29160i
$328$	1.30274	−	2.25641i	0.0719319	−	0.124590i
$329$	7.37516			0.406605
$330$	−1.49351	+	23.8637i	−0.0822150	+	1.31365i
$331$	−4.22053	+	7.31017i	−0.231981	+	0.401803i	−0.958391	−	0.285459i	$-0.907854\pi$
$331$	−4.22053	+	7.31017i	−0.231981	+	0.401803i	0.726410	+	0.687262i	$0.241187\pi$
$332$	−0.715228	+	1.23881i	−0.0392532	+	0.0679886i
$333$	6.71813	+	15.9525i	0.368151	+	0.874189i
$334$	13.0269			0.712803
$335$	−12.0352	+	20.8455i	−0.657552	+	1.13891i
$336$	2.97659	−	1.47881i	0.162386	−	0.0806757i
$337$	−1.44990	+	2.51130i	−0.0789811	+	0.136799i	−0.902811	−	0.430038i	$-0.858500\pi$
$337$	−1.44990	+	2.51130i	−0.0789811	+	0.136799i	0.823829	+	0.566838i	$0.191833\pi$
$338$	−8.19253			−0.445615
$339$	−0.576286	+	9.20804i	−0.0312995	+	0.500112i
$340$	−11.6006			−0.629132
$341$	23.5032			1.27277
$342$	11.4350	−	6.34362i	0.618332	−	0.343023i
$343$	19.7990			1.06904
$344$	3.96969			0.214031
$345$	−4.78115	+	2.37534i	−0.257409	+	0.127884i
$346$	−22.6623			−1.21833
$347$	−10.9942	+	19.0426i	−0.590202	+	1.02226i	0.404003	+	0.914758i	$0.367619\pi$
$347$	−10.9942	+	19.0426i	−0.590202	+	1.02226i	−0.994205	+	0.107502i	$0.965715\pi$
$348$	−0.689733	+	11.0207i	−0.0369736	+	0.590773i
$349$	7.68613	−	13.3128i	0.411429	−	0.712616i	−0.583617	−	0.812029i	$-0.698363\pi$
$349$	7.68613	−	13.3128i	0.411429	−	0.712616i	0.995046	+	0.0994129i	$0.0316965\pi$
$350$	1.44432			0.0772023
$351$	4.45914	−	23.5014i	0.238011	−	1.25441i
$352$	−2.87780	+	4.98450i	−0.153387	+	0.265675i
$353$	4.77068	−	8.26306i	0.253918	−	0.439798i	−0.710683	−	0.703512i	$-0.751614\pi$
$353$	4.77068	−	8.26306i	0.253918	−	0.439798i	0.964601	+	0.263714i	$0.0849475\pi$
$354$	12.1676	−	6.04504i	0.646702	−	0.321290i
$355$	−12.8949			−0.684389
$356$	−6.59763	+	11.4274i	−0.349674	+	0.605652i
$357$	−13.3927	−	8.89172i	−0.708814	−	0.470600i
$358$	−14.4660			−0.764554
$359$	−5.29564	−	9.17231i	−0.279493	−	0.484096i	0.691766	−	0.722122i	$-0.256833\pi$
$359$	−5.29564	−	9.17231i	−0.279493	−	0.484096i	−0.971259	+	0.238026i	$0.923500\pi$
$360$	−7.13927	−	0.897137i	−0.376272	−	0.0472833i
$361$	−18.5593	+	4.06828i	−0.976807	+	0.214120i
$362$	−6.69227	+	11.5914i	−0.351738	+	0.609228i
$363$	2.39389	−	38.2503i	0.125647	−	2.00762i
$364$	−4.41695	+	7.65038i	−0.231511	+	0.400989i
$365$	34.8537			1.82433
$366$	0.102677	−	1.64060i	0.00536703	−	0.0857558i
$367$	12.5207	+	21.6864i	0.653574	+	1.13202i	0.982249	+	0.187580i	$0.0600643\pi$
$367$	12.5207	+	21.6864i	0.653574	+	1.13202i	−0.328676	+	0.944443i	$0.606602\pi$
$368$	−1.28511			−0.0669909
$369$	−7.75545	−	0.974568i	−0.403733	−	0.0507340i
$370$	−6.91934	+	11.9846i	−0.359719	+	0.623052i
$371$	−9.87556	−	17.1050i	−0.512714	−	0.888046i
$372$	−0.441792	+	7.05906i	−0.0229058	+	0.365995i
$373$	−0.522500	−	0.904997i	−0.0270540	−	0.0468589i	0.852181	−	0.523246i	$-0.175279\pi$
$373$	−0.522500	−	0.904997i	−0.0270540	−	0.0468589i	−0.879235	+	0.476388i	$0.841946\pi$
$374$	27.8380			1.43947
$375$	14.6998	+	9.75954i	0.759092	+	0.503980i
$376$	−1.92168	−	3.32844i	−0.0991029	−	0.171651i
$377$	−14.6744	−	25.4168i	−0.755770	−	1.30903i
$378$	−7.55448	−	6.50788i	−0.388561	−	0.334729i
$379$	6.50829			0.334308			0.167154	−	0.985931i	$-0.446542\pi$
$379$	6.50829			0.334308			0.167154	+	0.985931i	$0.446542\pi$
$380$	9.56430	+	4.22196i	0.490638	+	0.216582i
$381$	25.1644	−	12.5020i	1.28921	−	0.640498i
$382$	0.456659	−	0.790956i	0.0233647	−	0.0404688i
$383$	−9.26906	+	16.0545i	−0.473627	+	0.820345i	−0.999544	−	0.0301902i	$-0.990389\pi$
$383$	−9.26906	+	16.0545i	−0.473627	+	0.820345i	0.525918	+	0.850536i	$0.323722\pi$
$384$	−1.44298	−	0.958029i	−0.0736366	−	0.0488892i
$385$	−26.4903			−1.35007
$386$	5.71936	−	9.90623i	0.291108	−	0.504214i
$387$	−4.62216	−	10.9755i	−0.234957	−	0.557916i
$388$	14.8163			0.752184
$389$	−2.88127	−	4.99051i	−0.146086	−	0.253029i	0.783691	−	0.621150i	$-0.213334\pi$
$389$	−2.88127	−	4.99051i	−0.146086	−	0.253029i	−0.929778	+	0.368122i	$0.880001\pi$
$390$	17.1271	−	8.50898i	0.867265	−	0.430869i
$391$	3.10782	+	5.38291i	0.157169	+	0.272225i
$392$	−1.65884	−	2.87319i	−0.0837840	−	0.145118i
$393$	−16.2515	+	8.07397i	−0.819780	+	0.407278i
$394$	−6.73643			−0.339376
$395$	−11.3817	+	19.7137i	−0.572675	+	0.991902i
$396$	17.1321	+	2.15286i	0.860920	+	0.108185i
$397$	−11.2508	−	19.4869i	−0.564660	−	0.978019i	−0.997081	−	0.0763476i	$-0.975674\pi$
$397$	−11.2508	−	19.4869i	−0.564660	−	0.978019i	0.432422	−	0.901672i	$-0.357659\pi$
$398$	−1.28873	+	2.23215i	−0.0645983	+	0.111888i
$399$	7.80569	+	12.2051i	0.390773	+	0.611017i
$400$	−0.376334	−	0.651829i	−0.0188167	−	0.0325915i
$401$	14.8292	−	25.6850i	0.740536	−	1.28265i	−0.211715	−	0.977331i	$-0.567905\pi$
$401$	14.8292	−	25.6850i	0.740536	−	1.28265i	0.952251	−	0.305315i	$-0.0987617\pi$
$402$	14.4813	+	9.61448i	0.722260	+	0.479527i
$403$	−9.39933	−	16.2801i	−0.468214	−	0.810970i
$404$	−4.22793	−	7.32299i	−0.210347	−	0.364332i
$405$	5.83227	+	20.7834i	0.289808	+	1.03274i
$406$	−12.2338			−0.607151
$407$	16.6043	−	28.7595i	0.823045	−	1.42556i
$408$	−0.523273	+	8.36100i	−0.0259059	+	0.413931i
$409$	10.7688			0.532485			0.266242	−	0.963906i	$-0.414218\pi$
$409$	10.7688			0.532485			0.266242	+	0.963906i	$0.414218\pi$
$410$	−3.12459	−	5.41195i	−0.154312	−	0.267277i
$411$	1.52835	−	24.4204i	0.0753880	−	1.20457i
$412$	−4.31756	−	7.47823i	−0.212711	−	0.368426i
$413$	7.52625	+	13.0358i	0.370343	+	0.641452i
$414$	1.49633	+	3.55310i	0.0735408	+	0.174625i
$415$	1.71545	+	2.97125i	0.0842083	+	0.145853i
$416$	4.60353			0.225707
$417$	18.8345	+	12.5047i	0.922327	+	0.612356i
$418$	−22.9514	−	10.1314i	−1.12259	−	0.495544i
$419$	7.02033	+	12.1596i	0.342966	+	0.594034i	0.984982	−	0.172657i	$-0.0552352\pi$
$419$	7.02033	+	12.1596i	0.342966	+	0.594034i	−0.642016	+	0.766691i	$0.721902\pi$
$420$	0.497941	−	7.95623i	0.0242970	−	0.388224i
$421$	31.2338			1.52224			0.761122	−	0.648608i	$-0.224649\pi$
$421$	31.2338			1.52224			0.761122	+	0.648608i	$0.224649\pi$
$422$	2.73974	−	4.74537i	0.133369	−	0.231001i
$423$	−6.96503	+	9.18861i	−0.338651	+	0.446766i
$424$	−5.14637	+	8.91377i	−0.249930	+	0.432891i
$425$	−1.82020	+	3.15268i	−0.0882928	+	0.152928i
$426$	−0.581654	+	9.29382i	−0.0281812	+	0.450287i
$427$	1.82118			0.0881332
$428$	−19.0406			−0.920364
$429$	−41.0999	+	20.4190i	−1.98432	+	0.985838i
$430$	4.76059	−	8.24559i	0.229576	−	0.397638i
$431$	−2.72081	+	4.71257i	−0.131057	+	0.226997i	−0.924084	−	0.382189i	$-0.875170\pi$
$431$	−2.72081	+	4.71257i	−0.131057	+	0.226997i	0.793028	+	0.609186i	$0.208504\pi$
$432$	−0.968634	+	5.10507i	−0.0466034	+	0.245618i
$433$	−12.0743	+	20.9134i	−0.580256	+	1.00503i	0.415193	+	0.909733i	$0.363714\pi$
$433$	−12.0743	+	20.9134i	−0.580256	+	1.00503i	−0.995449	+	0.0952989i	$0.969619\pi$
$434$	−7.83604			−0.376142
$435$	22.0644	+	14.6491i	1.05791	+	0.702372i
$436$	−6.75552	−	11.7009i	−0.323531	−	0.560372i
$437$	−0.603222	−	5.56909i	−0.0288560	−	0.266406i
$438$	1.57216	−	25.1204i	0.0751206	−	1.20030i
$439$	5.14760			0.245682			0.122841	−	0.992426i	$-0.460800\pi$
$439$	5.14760			0.245682			0.122841	+	0.992426i	$0.460800\pi$
$440$	6.90233	+	11.9552i	0.329056	+	0.569941i
$441$	−6.01239	+	7.93184i	−0.286304	+	0.377706i
$442$	−11.1329	−	19.2827i	−0.529537	−	0.917186i
$443$	−17.2826	−	29.9343i	−0.821119	−	1.42222i	−0.904849	−	0.425732i	$-0.860017\pi$
$443$	−17.2826	−	29.9343i	−0.821119	−	1.42222i	0.0837297	−	0.996489i	$-0.473317\pi$
$444$	8.32567	+	5.52762i	0.395119	+	0.262329i
$445$	15.8242	+	27.4084i	0.750140	+	1.29928i
$446$	5.29073			0.250523
$447$	−9.29172	+	4.61625i	−0.439483	+	0.218341i
$448$	0.959469	−	1.66185i	0.0453307	−	0.0785150i
$449$	−34.5463			−1.63034			−0.815170	−	0.579222i	$-0.803356\pi$
$449$	−34.5463			−1.63034			−0.815170	+	0.579222i	$0.803356\pi$
$450$	−1.36401	+	1.79946i	−0.0642998	+	0.0848275i
$451$	7.49807	+	12.9870i	0.353070	+	0.611535i
$452$	2.66333	+	4.61303i	0.125273	+	0.216979i
$453$	6.99259	−	3.47401i	0.328541	−	0.163223i
$454$	−11.1702	+	19.3473i	−0.524241	+	0.908013i
$455$	10.5939	+	18.3492i	0.496651	+	0.860225i
$456$	3.47434	−	6.70291i	0.162701	−	0.313892i
$457$	−9.42288	+	16.3209i	−0.440784	+	0.763460i	−0.997748	−	0.0670770i	$-0.978633\pi$
$457$	−9.42288	+	16.3209i	−0.440784	+	0.763460i	0.556964	+	0.830536i	$0.311966\pi$
$458$	−13.0283	−	22.5657i	−0.608773	−	1.05443i
$459$	23.7260	−	8.28847i	1.10743	−	0.386873i
$460$	−1.54115	+	2.66935i	−0.0718565	+	0.124459i
$461$	−11.8841			−0.553498			−0.276749	−	0.960942i	$-0.589257\pi$
$461$	−11.8841			−0.553498			−0.276749	+	0.960942i	$0.589257\pi$
$462$	−1.19491	+	19.0925i	−0.0555921	+	0.888266i
$463$	8.16080	+	14.1349i	0.379264	+	0.656905i	0.990955	−	0.134192i	$-0.0428437\pi$
$463$	8.16080	+	14.1349i	0.379264	+	0.656905i	−0.611691	+	0.791097i	$0.709510\pi$
$464$	3.18764	+	5.52115i	0.147982	+	0.256313i
$465$	14.1328	+	9.38315i	0.655395	+	0.435133i
$466$	6.26856	+	10.8575i	0.290385	+	0.502962i
$467$	23.0830			1.06815			0.534077	−	0.845436i	$-0.320659\pi$
$467$	23.0830			1.06815			0.534077	+	0.845436i	$0.320659\pi$
$468$	−5.36018	−	12.7280i	−0.247775	−	0.588351i
$469$	−9.62894	+	16.6778i	−0.444623	+	0.770110i
$470$	−9.21817			−0.425203
$471$	3.99260	−	1.98358i	0.183969	−	0.0913985i
$472$	3.92209	−	6.79326i	0.180529	−	0.312685i
$473$	−11.4240	+	19.7869i	−0.525275	+	0.909804i
$474$	13.6950	+	9.09244i	0.629031	+	0.417630i
$475$	2.64809	−	1.93683i	0.121503	−	0.0888677i
$476$	−9.28127			−0.425406
$477$	30.6373	+	3.84995i	1.40278	+	0.176277i
$478$	−4.88147	−	8.45495i	−0.223273	−	0.386721i
$479$	−1.74756	−	3.02686i	−0.0798480	−	0.138301i	0.823336	−	0.567554i	$-0.192110\pi$
$479$	−1.74756	−	3.02686i	−0.0798480	−	0.138301i	−0.903184	+	0.429253i	$0.858777\pi$
$480$	−3.72043	+	1.84836i	−0.169813	+	0.0843656i
$481$	−26.5614			−1.21110
$482$	−7.92117	−	13.7199i	−0.360800	−	0.624923i
$483$	−3.82524	+	1.90043i	−0.174055	+	0.0864727i
$484$	−11.0635	−	19.1626i	−0.502887	−	0.871025i
$485$	17.7682	−	30.7755i	0.806814	−	1.39744i
$486$	15.2425	−	3.26605i	0.691413	−	0.148151i
$487$	−35.7125			−1.61829			−0.809144	−	0.587610i	$-0.800069\pi$
$487$	−35.7125			−1.61829			−0.809144	+	0.587610i	$0.800069\pi$
$488$	−0.474528	−	0.821907i	−0.0214809	−	0.0372060i
$489$	−4.22985	−	2.80831i	−0.191281	−	0.126996i
$490$	−7.95735			−0.359477
$491$	14.5235	−	25.1555i	0.655438	−	1.13525i	−0.326345	−	0.945251i	$-0.605817\pi$
$491$	14.5235	−	25.1555i	0.655438	−	1.13525i	0.981784	−	0.190002i	$-0.0608494\pi$
$492$	−4.04153	+	2.00789i	−0.182206	+	0.0905226i
$493$	15.4175	−	26.7040i	0.694371	−	1.20269i
$494$	2.16087	+	19.9497i	0.0972221	+	0.897577i
$495$	25.0172	−	33.0039i	1.12444	−	1.48342i
$496$	2.04176	+	3.53644i	0.0916779	+	0.158791i
$497$	−10.3168			−0.462770
$498$	2.21887	−	1.10237i	0.0994301	−	0.0493982i
$499$	0.555395	−	0.961973i	0.0248629	−	0.0430638i	−0.853326	−	0.521377i	$-0.825418\pi$
$499$	0.555395	−	0.961973i	0.0248629	−	0.0430638i	0.878189	+	0.478314i	$0.158752\pi$
$500$	10.1871			0.455581
$501$	−18.7976	−	12.4802i	−0.839814	−	0.557573i
$502$	8.25797	−	14.3032i	0.368571	−	0.638384i
$503$	−7.26482	+	12.5830i	−0.323922	+	0.561050i	−0.981294	−	0.192517i	$-0.938335\pi$
$503$	−7.26482	+	12.5830i	−0.323922	+	0.561050i	0.657371	+	0.753567i	$0.271668\pi$
$504$	−5.71189	−	0.717770i	−0.254428	−	0.0319720i
$505$	−20.2811			−0.902499
$506$	3.69829	−	6.40563i	0.164409	−	0.284765i
$507$	11.8216	+	7.84868i	0.525017	+	0.348572i
$508$	8.11146	−	14.0495i	0.359888	−	0.623344i
$509$	10.9597			0.485782			0.242891	−	0.970054i	$-0.421904\pi$
$509$	10.9597			0.485782			0.242891	+	0.970054i	$0.421904\pi$
$510$	16.7394	+	11.1137i	0.741234	+	0.492124i
$511$	27.8853			1.23357
$512$	−1.00000			−0.0441942
$513$	−22.5778	−	1.80134i	−0.996832	−	0.0795310i
$514$	14.1564			0.624410
$515$	−20.7111			−0.912640
$516$	−5.72817	−	3.80308i	−0.252169	−	0.167421i
$517$	22.1208			0.972873
$518$	−5.53593	+	9.58852i	−0.243235	+	0.421295i
$519$	32.7012	+	21.7112i	1.43542	+	0.953014i
$520$	5.52072	−	9.56217i	0.242100	−	0.419329i
$521$	7.07139			0.309803			0.154902	−	0.987930i	$-0.450494\pi$
$521$	7.07139			0.309803			0.154902	+	0.987930i	$0.450494\pi$
$522$	11.5534	−	15.2419i	0.505680	−	0.667119i
$523$	7.47365	−	12.9447i	0.326800	−	0.566034i	−0.655075	−	0.755564i	$-0.727363\pi$
$523$	7.47365	−	12.9447i	0.326800	−	0.566034i	0.981875	+	0.189530i	$0.0606964\pi$
$524$	−5.23848	+	9.07332i	−0.228844	+	0.396370i
$525$	−2.08412	−	1.38370i	−0.0909586	−	0.0603897i
$526$	22.8420			0.995958
$527$	9.87533	−	17.1046i	0.430176	−	0.745087i
$528$	8.92790	−	4.43550i	0.388537	−	0.193030i
$529$	−21.3485			−0.928195
$530$	12.3434	+	21.3794i	0.536164	+	0.928663i
$531$	−23.3489	−	2.93408i	−1.01326	−	0.127328i
$532$	7.65208	+	3.37785i	0.331760	+	0.146448i
$533$	5.99721	−	10.3875i	0.259768	−	0.449932i
$534$	20.4680	−	10.1688i	0.885738	−	0.440047i
$535$	−22.8342	+	39.5500i	−0.987209	+	1.70990i
$536$	10.0357			0.433476
$537$	20.8742	+	13.8589i	0.900787	+	0.598055i
$538$	9.39374	+	16.2704i	0.404993	+	0.701468i
$539$	19.0952			0.822490
$540$	9.44231	+	8.13417i	0.406333	+	0.350039i
$541$	−2.28695	+	3.96112i	−0.0983238	+	0.170302i	−0.910991	−	0.412426i	$-0.864681\pi$
$541$	−2.28695	+	3.96112i	−0.0983238	+	0.170302i	0.812667	+	0.582728i	$0.198015\pi$
$542$	11.9001	+	20.6116i	0.511153	+	0.885342i
$543$	20.7616	−	10.3147i	0.890967	−	0.442645i
$544$	2.41833	+	4.18868i	0.103685	+	0.179588i
$545$	−32.4058			−1.38811
$546$	13.7028	−	6.80776i	0.586427	−	0.291345i
$547$	−13.0218	−	22.5544i	−0.556772	−	0.964357i	−0.997763	−	0.0668459i	$-0.978706\pi$
$547$	−13.0218	−	22.5544i	−0.556772	−	0.964357i	0.440991	−	0.897511i	$-0.354627\pi$
$548$	−7.06335	−	12.2341i	−0.301732	−	0.522614i
$549$	−1.71991	+	2.26899i	−0.0734039	+	0.0968380i
$550$	4.33206			0.184720
$551$	−22.4299	+	16.4054i	−0.955547	+	0.698892i
$552$	1.85438	+	1.23117i	0.0789278	+	0.0524021i
$553$	−9.10611	+	15.7722i	−0.387231	+	0.670704i
$554$	9.74197	−	16.8736i	0.413897	−	0.716890i
$555$	21.4661	−	10.6646i	0.911184	−	0.452689i
$556$	13.0525			0.553549
$557$	0.187568	−	0.324877i	0.00794750	−	0.0137655i	−0.862024	−	0.506867i	$-0.830804\pi$
$557$	0.187568	−	0.324877i	0.00794750	−	0.0137655i	0.869972	+	0.493101i	$0.164137\pi$
$558$	7.40028	−	9.76282i	0.313279	−	0.413293i
$559$	18.2746			0.772933
$560$	−2.30126	−	3.98590i	−0.0972460	−	0.168435i
$561$	−40.1695	−	26.6696i	−1.69596	−	1.12599i
$562$	−5.38694	−	9.33045i	−0.227234	−	0.393581i
$563$	3.12450	+	5.41180i	0.131682	+	0.228080i	0.924325	−	0.381606i	$-0.124629\pi$
$563$	3.12450	+	5.41180i	0.131682	+	0.228080i	−0.792643	+	0.609686i	$0.791296\pi$
$564$	−0.415808	+	6.64388i	−0.0175087	+	0.279758i
$565$	12.7759			0.537484
$566$	−10.1095	+	17.5102i	−0.424936	+	0.736010i
$567$	4.66621	+	16.6281i	0.195962	+	0.698316i
$568$	2.68814	+	4.65600i	0.112792	+	0.195361i
$569$	0.597276	−	1.03451i	0.0250391	−	0.0433690i	−0.853234	−	0.521528i	$-0.825362\pi$
$569$	0.597276	−	1.03451i	0.0250391	−	0.0433690i	0.878273	+	0.478159i	$0.158696\pi$
$570$	−9.75630	−	15.2551i	−0.408646	−	0.638964i
$571$	0.105048	+	0.181949i	0.00439614	+	0.00761434i	0.868215	−	0.496188i	$-0.165267\pi$
$571$	0.105048	+	0.181949i	0.00439614	+	0.00761434i	−0.863819	+	0.503802i	$0.831934\pi$
$572$	−13.2481	+	22.9463i	−0.553930	+	0.959434i
$573$	−1.41671	+	0.703839i	−0.0591838	+	0.0294033i
$574$	−2.49988	−	4.32992i	−0.104343	−	0.180727i
$575$	0.483630	+	0.837672i	0.0201688	+	0.0349333i
$576$	1.16436	+	2.76483i	0.0485151	+	0.115201i
$577$	−30.8533			−1.28444			−0.642220	−	0.766520i	$-0.721987\pi$
$577$	−30.8533			−1.28444			−0.642220	+	0.766520i	$0.721987\pi$
$578$	3.19668	−	5.53682i	0.132964	−	0.230301i
$579$	−17.7434	+	8.81514i	−0.737389	+	0.366345i
$580$	15.2909			0.634920
$581$	1.37248	+	2.37720i	0.0569400	+	0.0986229i
$582$	−21.3796	−	14.1944i	−0.886212	−	0.588378i
$583$	−29.6205	−	51.3042i	−1.22675	−	2.12480i
$584$	−7.26581	−	12.5848i	−0.300661	−	0.520761i
$585$	−32.8659	−	4.13000i	−1.35884	−	0.170754i
$586$	14.4603	+	25.0459i	0.597348	+	1.03464i
$587$	29.6277			1.22287			0.611433	−	0.791296i	$-0.290594\pi$
$587$	29.6277			1.22287			0.611433	+	0.791296i	$0.290594\pi$
$588$	−0.358935	+	5.73516i	−0.0148022	+	0.236514i
$589$	−14.3669	+	10.5081i	−0.591980	+	0.432977i
$590$	−9.40703	−	16.2934i	−0.387281	−	0.670791i
$591$	9.72051	+	6.45369i	0.399848	+	0.265469i
$592$	5.76979			0.237137
$593$	15.2032	−	26.3328i	0.624323	−	1.08136i	−0.364349	−	0.931263i	$-0.618708\pi$
$593$	15.2032	−	26.3328i	0.624323	−	1.08136i	0.988671	−	0.150096i	$-0.0479582\pi$
$594$	−22.6587	−	19.5195i	−0.929698	−	0.800897i
$595$	−11.1304	+	19.2785i	−0.456303	+	0.790340i
$596$	−2.99508	+	5.18763i	−0.122683	+	0.212493i
$597$	3.99807	−	1.98630i	0.163630	−	0.0812937i
$598$	−5.91604			−0.241925
$599$	19.4128			0.793185			0.396593	−	0.917995i	$-0.370193\pi$
$599$	19.4128			0.793185			0.396593	+	0.917995i	$0.370193\pi$
$600$	−0.0814302	+	1.30111i	−0.00332437	+	0.0531177i
$601$	−8.00680	+	13.8682i	−0.326604	+	0.565695i	−0.981836	−	0.189733i	$-0.939238\pi$
$601$	−8.00680	+	13.8682i	−0.326604	+	0.565695i	0.655232	+	0.755428i	$0.272571\pi$
$602$	3.80879	−	6.59702i	0.155235	−	0.268875i
$603$	−11.6852	−	27.7470i	−0.475858	−	1.12994i
$604$	2.25398	−	3.90401i	0.0917132	−	0.158852i
$605$	−53.0710			−2.15764
$606$	−0.914829	+	14.6174i	−0.0371624	+	0.593790i
$607$	−18.3201	−	31.7313i	−0.743590	−	1.28794i	−0.950851	−	0.309649i	$-0.899788\pi$
$607$	−18.3201	−	31.7313i	−0.743590	−	1.28794i	0.207261	−	0.978286i	$-0.433545\pi$
$608$	−0.469393	−	4.33355i	−0.0190364	−	0.175749i
$609$	17.6530	+	11.7203i	0.715336	+	0.474930i
$610$	−2.27629			−0.0921641
$611$	−8.84650	−	15.3226i	−0.357891	−	0.619886i
$612$	8.76515	−	11.5634i	0.354310	−	0.467423i
$613$	19.3100	+	33.4460i	0.779925	+	1.35087i	0.931984	+	0.362498i	$0.118076\pi$
$613$	19.3100	+	33.4460i	0.779925	+	1.35087i	−0.152060	+	0.988371i	$0.548591\pi$
$614$	−2.90114	−	5.02491i	−0.117080	−	0.202789i
$615$	−0.676091	+	10.8028i	−0.0272626	+	0.435609i
$616$	5.52233	+	9.56495i	0.222501	+	0.385383i
$617$	25.0947			1.01028			0.505138	−	0.863039i	$-0.331442\pi$
$617$	25.0947			1.01028			0.505138	+	0.863039i	$0.331442\pi$
$618$	−0.934223	+	14.9273i	−0.0375800	+	0.600462i
$619$	22.3637	−	38.7350i	0.898873	−	1.55689i	0.0699352	−	0.997552i	$-0.477721\pi$
$619$	22.3637	−	38.7350i	0.898873	−	1.55689i	0.828937	−	0.559341i	$-0.188946\pi$
$620$	9.79422			0.393346
$621$	1.24480	−	6.56057i	0.0499521	−	0.263267i
$622$	3.00615	+	5.20680i	0.120535	+	0.208774i
$623$	12.6604	+	21.9285i	0.507230	+	0.878548i
$624$	−6.64279	−	4.41032i	−0.265925	−	0.176554i
$625$	14.0984	−	24.4192i	0.563937	−	0.976767i
$626$	−0.962646	−	1.66735i	−0.0384751	−	0.0666408i
$627$	23.4122	+	36.6075i	0.934992	+	1.46196i
$628$	1.28697	−	2.22909i	0.0513556	−	0.0889506i
$629$	−13.9533	−	24.1678i	−0.556354	−	0.963633i
$630$	−8.34081	+	11.0036i	−0.332306	+	0.438394i
$631$	7.29450	−	12.6345i	0.290390	−	0.502970i	−0.683512	−	0.729939i	$-0.739548\pi$
$631$	7.29450	−	12.6345i	0.290390	−	0.502970i	0.973902	+	0.226969i	$0.0728817\pi$
$632$	9.49078			0.377523
$633$	−8.49959	+	4.22271i	−0.337828	+	0.167838i
$634$	−4.41910	−	7.65410i	−0.175505	−	0.303983i
$635$	−19.4551	−	33.6972i	−0.772052	−	1.33723i
$636$	15.9657	−	7.93199i	0.633083	−	0.314524i
$637$	−7.63652	−	13.2268i	−0.302570	−	0.524066i
$638$	−36.6936			−1.45271
$639$	9.74305	−	12.8535i	0.385429	−	0.508477i
$640$	−1.19924	+	2.07714i	−0.0474040	+	0.0821061i
$641$	19.0973			0.754298			0.377149	−	0.926153i	$-0.376905\pi$
$641$	19.0973			0.754298			0.377149	+	0.926153i	$0.376905\pi$
$642$	27.4752	+	18.2415i	1.08436	+	0.719933i
$643$	−7.03569	+	12.1862i	−0.277461	+	0.480576i	−0.970753	−	0.240081i	$-0.922826\pi$
$643$	−7.03569	+	12.1862i	−0.277461	+	0.480576i	0.693292	+	0.720656i	$0.256159\pi$
$644$	−1.23302	+	2.13566i	−0.0485879	+	0.0841567i
$645$	−14.7689	+	7.33741i	−0.581526	+	0.288910i
$646$	−17.0167	+	12.4461i	−0.669513	+	0.489686i
$647$	0.543543			0.0213689			0.0106844	−	0.999943i	$-0.496599\pi$
$647$	0.543543			0.0213689			0.0106844	+	0.999943i	$0.496599\pi$
$648$	6.28852	−	6.43852i	0.247036	−	0.252929i
$649$	22.5740	+	39.0993i	0.886108	+	1.53478i
$650$	−1.73247	−	3.00072i	−0.0679529	−	0.117698i
$651$	11.3072	+	7.50715i	0.443165	+	0.294228i
$652$	−2.93134			−0.114800
$653$	−1.76674	−	3.06009i	−0.0691380	−	0.119750i	0.829384	−	0.558679i	$-0.188692\pi$
$653$	−1.76674	−	3.06009i	−0.0691380	−	0.119750i	−0.898522	+	0.438928i	$0.855358\pi$
$654$	−1.46174	+	23.3561i	−0.0571587	+	0.913296i
$655$	12.5644	+	21.7621i	0.490930	+	0.850316i
$656$	−1.30274	+	2.25641i	−0.0508635	+	0.0880982i
$657$	−26.3346	+	34.7419i	−1.02741	+	1.35541i
$658$	−7.37516			−0.287513
$659$	−5.16712	−	8.94972i	−0.201283	−	0.348632i	0.747659	−	0.664082i	$-0.231178\pi$
$659$	−5.16712	−	8.94972i	−0.201283	−	0.348632i	−0.948942	+	0.315451i	$0.897844\pi$
$660$	1.49351	−	23.8637i	0.0581348	−	0.928893i
$661$	39.7393			1.54568			0.772839	−	0.634602i	$-0.218836\pi$
$661$	39.7393			1.54568			0.772839	+	0.634602i	$0.218836\pi$
$662$	4.22053	−	7.31017i	0.164035	−	0.284118i
$663$	−2.40891	+	38.4901i	−0.0935542	+	1.49483i
$664$	0.715228	−	1.23881i	0.0277562	−	0.0480752i
$665$	16.1929	−	11.8436i	0.627934	−	0.459274i
$666$	−6.71813	−	15.9525i	−0.260322	−	0.618145i
$667$	−4.09646	−	7.09528i	−0.158616	−	0.274730i
$668$	−13.0269			−0.504028
$669$	−7.63440	−	5.06867i	−0.295163	−	0.195966i
$670$	12.0352	−	20.8455i	0.464959	−	0.805333i
$671$	5.46240			0.210874
$672$	−2.97659	+	1.47881i	−0.114824	+	0.0570464i
$673$	−8.87488	+	15.3717i	−0.342101	+	0.592537i	−0.984823	−	0.173563i	$-0.944472\pi$
$673$	−8.87488	+	15.3717i	−0.342101	+	0.592537i	0.642721	+	0.766100i	$0.277805\pi$
$674$	1.44990	−	2.51130i	0.0558481	−	0.0967317i
$675$	3.69216	−	1.28983i	0.142111	−	0.0496455i
$676$	8.19253			0.315097
$677$	−9.27923	+	16.0721i	−0.356630	+	0.617701i	−0.987395	−	0.158273i	$-0.949408\pi$
$677$	−9.27923	+	16.0721i	−0.356630	+	0.617701i	0.630766	+	0.775973i	$0.282741\pi$
$678$	0.576286	−	9.20804i	0.0221321	−	0.353633i
$679$	14.2158	−	24.6225i	0.545552	−	0.944923i
$680$	11.6006			0.444863
$681$	34.6535	−	17.2163i	1.32793	−	0.659731i
$682$	−23.5032			−0.899983
$683$	12.5535			0.480347			0.240174	−	0.970730i	$-0.422796\pi$
$683$	12.5535			0.480347			0.240174	+	0.970730i	$0.422796\pi$
$684$	−11.4350	+	6.34362i	−0.437227	+	0.242554i
$685$	−33.8825			−1.29458
$686$	−19.7990			−0.755929
$687$	−2.81903	+	45.0433i	−0.107553	+	1.71851i
$688$	−3.96969			−0.151343
$689$	−23.6915	+	41.0348i	−0.902574	+	1.56330i
$690$	4.78115	−	2.37534i	0.182015	−	0.0904277i
$691$	−20.4471	+	35.4153i	−0.777843	+	1.34726i	0.155340	+	0.987861i	$0.450353\pi$
$691$	−20.4471	+	35.4153i	−0.777843	+	1.34726i	−0.933183	+	0.359402i	$0.882981\pi$
$692$	22.6623			0.861492
$693$	20.0154	−	26.4053i	0.760323	−	1.00306i
$694$	10.9942	−	19.0426i	0.417336	−	0.722847i
$695$	15.6530	−	27.1118i	0.593753	−	1.02841i
$696$	0.689733	−	11.0207i	0.0261443	−	0.417740i
$697$	12.6019			0.477329
$698$	−7.68613	+	13.3128i	−0.290924	+	0.503896i
$699$	1.35638	−	21.6725i	0.0513028	−	0.819730i
$700$	−1.44432			−0.0545903
$701$	−7.47020	−	12.9388i	−0.282146	−	0.488691i	0.689767	−	0.724031i	$-0.257713\pi$
$701$	−7.47020	−	12.9388i	−0.282146	−	0.488691i	−0.971913	+	0.235340i	$0.924379\pi$
$702$	−4.45914	+	23.5014i	−0.168299	+	0.887002i
$703$	2.70830	+	25.0037i	0.102145	+	0.943031i
$704$	2.87780	−	4.98450i	0.108461	−	0.187860i
$705$	13.3016	+	8.83127i	0.500967	+	0.332605i
$706$	−4.77068	+	8.26306i	−0.179547	+	0.310984i
$707$	−16.2263			−0.610252
$708$	−12.1676	+	6.04504i	−0.457287	+	0.227187i
$709$	−18.3174	−	31.7266i	−0.687923	−	1.19152i	−0.972508	−	0.232868i	$-0.925189\pi$
$709$	−18.3174	−	31.7266i	−0.687923	−	1.19152i	0.284585	−	0.958651i	$-0.408144\pi$
$710$	12.8949			0.483936
$711$	−11.0507	−	26.2404i	−0.414434	−	0.984090i
$712$	6.59763	−	11.4274i	0.247257	−	0.428261i
$713$	−2.62389	−	4.54471i	−0.0982654	−	0.170201i
$714$	13.3927	+	8.89172i	0.501207	+	0.332764i
$715$	31.7751	+	55.0361i	1.18832	+	2.05823i
$716$	14.4660			0.540621
$717$	−1.05624	+	16.8769i	−0.0394460	+	0.630279i
$718$	5.29564	+	9.17231i	0.197631	+	0.342308i
$719$	−12.8765	−	22.3028i	−0.480213	−	0.831753i	0.519529	−	0.854453i	$-0.326107\pi$
$719$	−12.8765	−	22.3028i	−0.480213	−	0.831753i	−0.999742	+	0.0226993i	$0.992774\pi$
$720$	7.13927	+	0.897137i	0.266065	+	0.0334343i
$721$	−16.5703			−0.617109
$722$	18.5593	−	4.06828i	0.690707	−	0.151406i
$723$	−1.71396	+	27.3862i	−0.0637430	+	1.01850i
$724$	6.69227	−	11.5914i	0.248716	−	0.430789i
$725$	2.39923	−	4.15559i	0.0891052	−	0.154335i
$726$	−2.39389	+	38.2503i	−0.0888458	+	1.41960i
$727$	−39.5876			−1.46822			−0.734112	−	0.679029i	$-0.762401\pi$
$727$	−39.5876			−1.46822			−0.734112	+	0.679029i	$0.762401\pi$
$728$	4.41695	−	7.65038i	0.163703	−	0.283542i
$729$	−25.1235	−	9.88989i	−0.930500	−	0.366292i
$730$	−34.8537			−1.28999
$731$	9.60003	+	16.6277i	0.355070	+	0.614999i
$732$	−0.102677	+	1.64060i	−0.00379506	+	0.0606385i
$733$	14.3395	+	24.8367i	0.529641	+	0.917364i	0.999402	+	0.0345711i	$0.0110065\pi$
$733$	14.3395	+	24.8367i	0.529641	+	0.917364i	−0.469762	+	0.882793i	$0.655660\pi$
$734$	−12.5207	−	21.6864i	−0.462146	−	0.800461i
$735$	11.4823	+	7.62337i	0.423530	+	0.281192i
$736$	1.28511			0.0473698
$737$	−28.8808	+	50.0230i	−1.06384	+	1.84262i
$738$	7.75545	+	0.974568i	0.285482	+	0.0358743i
$739$	−13.3123	−	23.0576i	−0.489702	−	0.848189i	0.510227	−	0.860039i	$-0.329561\pi$
$739$	−13.3123	−	23.0576i	−0.489702	−	0.848189i	−0.999930	+	0.0118502i	$0.996228\pi$
$740$	6.91934	−	11.9846i	0.254360	−	0.440564i
$741$	15.9943	−	30.8571i	0.587564	−	1.13356i
$742$	9.87556	+	17.1050i	0.362543	+	0.627943i
$743$	−21.2317	+	36.7744i	−0.778917	+	1.34912i	0.153650	+	0.988125i	$0.450897\pi$
$743$	−21.2317	+	36.7744i	−0.778917	+	1.34912i	−0.932567	+	0.360998i	$0.882436\pi$
$744$	0.441792	−	7.05906i	0.0161969	−	0.258798i
$745$	7.18361	+	12.4424i	0.263187	+	0.455853i
$746$	0.522500	+	0.904997i	0.0191301	+	0.0331343i
$747$	−4.25788	−	0.535055i	−0.155788	−	0.0195766i
$748$	−27.8380			−1.01786
$749$	−18.2689	+	31.6427i	−0.667531	+	1.15620i
$750$	−14.6998	−	9.75954i	−0.536759	−	0.356368i
$751$	−37.7494			−1.37749			−0.688747	−	0.725002i	$-0.741839\pi$
$751$	−37.7494			−1.37749			−0.688747	+	0.725002i	$0.741839\pi$
$752$	1.92168	+	3.32844i	0.0700763	+	0.121376i
$753$	−25.6189	+	12.7278i	−0.933606	+	0.463828i
$754$	14.6744	+	25.4168i	0.534410	+	0.925625i
$755$	−5.40611	−	9.36365i	−0.196748	−	0.340778i
$756$	7.55448	+	6.50788i	0.274754	+	0.236689i
$757$	16.6770	+	28.8854i	0.606135	+	1.04986i	0.991871	+	0.127247i	$0.0406142\pi$
$757$	16.6770	+	28.8854i	0.606135	+	1.04986i	−0.385736	+	0.922609i	$0.626053\pi$
$758$	−6.50829			−0.236392
$759$	−11.4733	+	5.70010i	−0.416455	+	0.206901i
$760$	−9.56430	−	4.22196i	−0.346933	−	0.153146i
$761$	−8.72979	−	15.1204i	−0.316455	−	0.548116i	0.663291	−	0.748362i	$-0.269159\pi$
$761$	−8.72979	−	15.1204i	−0.316455	−	0.548116i	−0.979746	+	0.200246i	$0.935826\pi$
$762$	−25.1644	+	12.5020i	−0.911611	+	0.452901i
$763$	−25.9268			−0.938615
$764$	−0.456659	+	0.790956i	−0.0165213	+	0.0286158i
$765$	−13.5073	−	32.0737i	−0.488358	−	1.15963i
$766$	9.26906	−	16.0545i	0.334905	−	0.580072i
$767$	18.0555	−	31.2730i	0.651946	−	1.12920i
$768$	1.44298	+	0.958029i	0.0520689	+	0.0345699i
$769$	35.0240			1.26300			0.631500	−	0.775376i	$-0.282440\pi$
$769$	35.0240			1.26300			0.631500	+	0.775376i	$0.282440\pi$
$770$	26.4903			0.954644
$771$	−20.4273	−	13.5622i	−0.735671	−	0.488430i
$772$	−5.71936	+	9.90623i	−0.205844	+	0.356533i
$773$	−17.9543	+	31.0977i	−0.645771	+	1.11851i	0.338352	+	0.941020i	$0.390131\pi$
$773$	−17.9543	+	31.0977i	−0.645771	+	1.11851i	−0.984123	+	0.177488i	$0.943203\pi$
$774$	4.62216	+	10.9755i	0.166140	+	0.394506i
$775$	1.53677	−	2.66176i	0.0552024	−	0.0956133i
$776$	−14.8163			−0.531874
$777$	17.1743	−	8.53242i	0.616124	−	0.306099i
$778$	2.88127	+	4.99051i	0.103299	+	0.178918i
$779$	−10.3898	−	4.58635i	−0.372253	−	0.164323i
$780$	−17.1271	+	8.50898i	−0.613249	+	0.304670i
$781$	−30.9438			−1.10726
$782$	−3.10782	−	5.38291i	−0.111136	−	0.192492i
$783$	−31.2735	+	10.9251i	−1.11762	+	0.390432i
$784$	1.65884	+	2.87319i	0.0592442	+	0.102614i
$785$	−3.08676	−	5.34642i	−0.110171	−	0.190822i
$786$	16.2515	−	8.07397i	0.579672	−	0.287989i
$787$	−4.90320	−	8.49259i	−0.174780	−	0.302728i	0.765305	−	0.643668i	$-0.222588\pi$
$787$	−4.90320	−	8.49259i	−0.174780	−	0.302728i	−0.940085	+	0.340940i	$0.889255\pi$
$788$	6.73643			0.239975
$789$	−32.9605	−	21.8833i	−1.17342	−	0.779065i
$790$	11.3817	−	19.7137i	0.404942	−	0.701380i
$791$	10.2215			0.363436
$792$	−17.1321	−	2.15286i	−0.608762	−	0.0764984i
$793$	−2.18451	−	3.78368i	−0.0775742	−	0.134362i
$794$	11.2508	+	19.4869i	0.399275	+	0.691564i
$795$	2.67084	−	42.6754i	0.0947249	−	1.51354i
$796$	1.28873	−	2.23215i	0.0456779	−	0.0791165i
$797$	−7.90385	−	13.6899i	−0.279969	−	0.484920i	0.691408	−	0.722465i	$-0.256991\pi$
$797$	−7.90385	−	13.6899i	−0.279969	−	0.484920i	−0.971377	+	0.237545i	$0.923657\pi$
$798$	−7.80569	−	12.2051i	−0.276319	−	0.432055i
$799$	9.29451	−	16.0986i	0.328816	−	0.569526i
$800$	0.376334	+	0.651829i	0.0133054	+	0.0230456i
$801$	−39.2769	−	4.93562i	−1.38778	−	0.174392i
$802$	−14.8292	+	25.6850i	−0.523638	+	0.906968i
$803$	83.6383			2.95153
$804$	−14.4813	−	9.61448i	−0.510715	−	0.339077i
$805$	2.95737	+	5.12232i	0.104234	+	0.180538i
$806$	9.39933	+	16.2801i	0.331077	+	0.573443i
$807$	2.03259	−	32.4773i	0.0715507	−	1.14326i
$808$	4.22793	+	7.32299i	0.148738	+	0.257622i
$809$	10.5955			0.372519			0.186260	−	0.982501i	$-0.440363\pi$
$809$	10.5955			0.372519			0.186260	+	0.982501i	$0.440363\pi$
$810$	−5.83227	−	20.7834i	−0.204925	−	0.730255i
$811$	3.26510	−	5.65532i	0.114653	−	0.198585i	−0.802988	−	0.595995i	$-0.796758\pi$
$811$	3.26510	−	5.65532i	0.114653	−	0.198585i	0.917641	+	0.397410i	$0.130091\pi$
$812$	12.2338			0.429320
$813$	2.57491	−	41.1426i	0.0903061	−	1.44293i
$814$	−16.6043	+	28.7595i	−0.581981	+	1.00802i
$815$	−3.51537	+	6.08879i	−0.123138	+	0.213281i
$816$	0.523273	−	8.36100i	0.0183182	−	0.292693i
$817$	−1.86335	−	17.2029i	−0.0651902	−	0.601852i
$818$	−10.7688			−0.376524
$819$	−26.2949	−	3.30428i	−0.918818	−	0.115461i
$820$	3.12459	+	5.41195i	0.109115	+	0.188993i
$821$	10.1086	+	17.5085i	0.352791	+	0.611052i	0.986737	−	0.162325i	$-0.0518993\pi$
$821$	10.1086	+	17.5085i	0.352791	+	0.611052i	−0.633946	+	0.773377i	$0.718566\pi$
$822$	−1.52835	+	24.4204i	−0.0533074	+	0.851759i
$823$	−45.9146			−1.60048			−0.800242	−	0.599678i	$-0.795295\pi$
$823$	−45.9146			−1.60048			−0.800242	+	0.599678i	$0.795295\pi$
$824$	4.31756	+	7.47823i	0.150409	+	0.260517i
$825$	−6.25106	−	4.15024i	−0.217634	−	0.144493i
$826$	−7.52625	−	13.0358i	−0.261872	−	0.453575i
$827$	−11.1316	+	19.2806i	−0.387085	+	0.670451i	−0.992056	−	0.125796i	$-0.959851\pi$
$827$	−11.1316	+	19.2806i	−0.387085	+	0.670451i	0.604971	+	0.796248i	$0.293185\pi$
$828$	−1.49633	−	3.55310i	−0.0520012	−	0.123479i
$829$	53.2926			1.85093			0.925465	−	0.378833i	$-0.123675\pi$
$829$	53.2926			1.85093			0.925465	+	0.378833i	$0.123675\pi$
$830$	−1.71545	−	2.97125i	−0.0595443	−	0.103134i
$831$	−30.2228	+	15.0151i	−1.04842	+	0.520868i
$832$	−4.60353			−0.159599
$833$	8.02325	−	13.8967i	0.277989	−	0.481491i
$834$	−18.8345	−	12.5047i	−0.652184	−	0.433001i
$835$	−15.6224	+	27.0588i	−0.540635	+	0.936407i
$836$	22.9514	+	10.1314i	0.793791	+	0.350402i
$837$	−20.0315	+	6.99783i	−0.692390	+	0.241881i
$838$	−7.02033	−	12.1596i	−0.242513	−	0.420046i
$839$	−16.2780			−0.561979			−0.280990	−	0.959711i	$-0.590663\pi$
$839$	−16.2780			−0.561979			−0.280990	+	0.959711i	$0.590663\pi$
$840$	−0.497941	+	7.95623i	−0.0171806	+	0.274516i
$841$	−5.82204	+	10.0841i	−0.200760	+	0.347726i
$842$	−31.2338			−1.07639
$843$	−1.16561	+	18.6245i	−0.0401458	+	0.641461i
$844$	−2.73974	+	4.74537i	−0.0943059	+	0.163343i
$845$	9.82478	−	17.0170i	0.337983	−	0.585403i
$846$	6.96503	−	9.18861i	0.239463	−	0.315911i
$847$	−42.4604			−1.45896
$848$	5.14637	−	8.91377i	0.176727	−	0.306100i
$849$	31.3631	−	15.5816i	1.07638	−	0.534760i
$850$	1.82020	−	3.15268i	0.0624324	−	0.108136i
$851$	−7.41481			−0.254176
$852$	0.581654	−	9.29382i	0.0199271	−	0.318401i
$853$	45.1710			1.54663			0.773313	−	0.634025i	$-0.218598\pi$
$853$	45.1710			1.54663			0.773313	+	0.634025i	$0.218598\pi$
$854$	−1.82118			−0.0623196
$855$	−0.536664	+	31.3595i	−0.0183535	+	1.07247i
$856$	19.0406			0.650795
$857$	43.9379			1.50089			0.750446	−	0.660932i	$-0.229839\pi$
$857$	43.9379			1.50089			0.750446	+	0.660932i	$0.229839\pi$
$858$	41.0999	−	20.4190i	1.40313	−	0.697093i
$859$	37.2164			1.26981			0.634904	−	0.772591i	$-0.281039\pi$
$859$	37.2164			1.26981			0.634904	+	0.772591i	$0.281039\pi$
$860$	−4.76059	+	8.24559i	−0.162335	+	0.281172i
$861$	−0.540918	+	8.64293i	−0.0184344	+	0.294550i
$862$	2.72081	−	4.71257i	0.0926710	−	0.160511i
$863$	−18.7725			−0.639024			−0.319512	−	0.947582i	$-0.603519\pi$
$863$	−18.7725			−0.639024			−0.319512	+	0.947582i	$0.603519\pi$
$864$	0.968634	−	5.10507i	0.0329536	−	0.173678i
$865$	27.1775	−	47.0728i	0.924062	−	1.60052i
$866$	12.0743	−	20.9134i	0.410303	−	0.710665i
$867$	−9.91716	+	4.92698i	−0.336805	+	0.167329i
$868$	7.83604			0.265972
$869$	−27.3126	+	47.3068i	−0.926517	+	1.60477i
$870$	−22.0644	−	14.6491i	−0.748054	−	0.496652i
$871$	46.1997			1.56542
$872$	6.75552	+	11.7009i	0.228771	+	0.396243i
$873$	17.2515	+	40.9645i	0.583876	+	1.38644i
$874$	0.603222	+	5.56909i	0.0204043	+	0.188377i
$875$	9.77421	−	16.9294i	0.330429	−	0.572319i
$876$	−1.57216	+	25.1204i	−0.0531183	+	0.848738i
$877$	9.85460	−	17.0687i	0.332766	−	0.576368i	−0.650287	−	0.759689i	$-0.725351\pi$
$877$	9.85460	−	17.0687i	0.332766	−	0.576368i	0.983053	+	0.183321i	$0.0586846\pi$
$878$	−5.14760			−0.173723
$879$	3.12887	−	49.9940i	0.105534	−	1.68625i
$880$	−6.90233	−	11.9552i	−0.232678	−	0.403009i
$881$	49.7502			1.67613			0.838063	−	0.545573i	$-0.183688\pi$
$881$	49.7502			1.67613			0.838063	+	0.545573i	$0.183688\pi$
$882$	6.01239	−	7.93184i	0.202448	−	0.267079i
$883$	6.19727	−	10.7340i	0.208555	−	0.361227i	−0.742705	−	0.669619i	$-0.766457\pi$
$883$	6.19727	−	10.7340i	0.208555	−	0.361227i	0.951259	+	0.308392i	$0.0997907\pi$
$884$	11.1329	+	19.2827i	0.374439	+	0.648548i
$885$	−2.03547	+	32.5233i	−0.0684216	+	1.09326i
$886$	17.2826	+	29.9343i	0.580619	+	1.00566i
$887$	17.6858			0.593833			0.296916	−	0.954904i	$-0.404042\pi$
$887$	17.6858			0.593833			0.296916	+	0.954904i	$0.404042\pi$
$888$	−8.32567	−	5.52762i	−0.279391	−	0.185495i
$889$	−15.5654	−	26.9600i	−0.522046	−	0.904211i
$890$	−15.8242	−	27.4084i	−0.530429	−	0.918730i
$891$	13.9957	+	49.8739i	0.468873	+	1.67084i
$892$	−5.29073			−0.177147
$893$	−13.5219	+	9.89003i	−0.452495	+	0.330957i
$894$	9.29172	−	4.61625i	0.310762	−	0.154391i
$895$	17.3482	−	30.0480i	0.579886	−	1.00439i
$896$	−0.959469	+	1.66185i	−0.0320536	+	0.0555185i
$897$	8.53671	+	5.66774i	0.285033	+	0.189240i
$898$	34.5463			1.15282
$899$	−13.0168	+	22.5458i	−0.434134	+	0.751943i
$900$	1.36401	−	1.79946i	0.0454668	−	0.0599821i
$901$	−49.7825			−1.65850
$902$	−7.49807	−	12.9870i	−0.249658	−	0.432421i
$903$	−11.8161	+	5.87042i	−0.393216	+	0.195355i
$904$	−2.66333	−	4.61303i	−0.0885811	−	0.153427i
$905$	−16.0512	−	27.8015i	−0.533561	−	0.924154i
$906$	−6.99259	+	3.47401i	−0.232313	+	0.115416i
$907$	41.0155			1.36190			0.680948	−	0.732332i	$-0.261568\pi$
$907$	41.0155			1.36190			0.680948	+	0.732332i	$0.261568\pi$
$908$	11.1702	−	19.3473i	0.370695	−	0.642062i
$909$	15.3239	−	20.2161i	0.508263	−	0.670526i
$910$	−10.5939	−	18.3492i	−0.351185	−	0.608271i
$911$	−8.26837	+	14.3212i	−0.273943	+	0.474484i	−0.969868	−	0.243631i	$-0.921661\pi$
$911$	−8.26837	+	14.3212i	−0.273943	+	0.474484i	0.695925	+	0.718115i	$0.254995\pi$
$912$	−3.47434	+	6.70291i	−0.115047	+	0.221955i
$913$	4.11657	+	7.13011i	0.136239	+	0.235972i
$914$	9.42288	−	16.3209i	0.311681	−	0.539847i
$915$	3.28463	+	2.18075i	0.108586	+	0.0720933i
$916$	13.0283	+	22.5657i	0.430468	+	0.745592i
$917$	10.0523	+	17.4111i	0.331957	+	0.574966i
$918$	−23.7260	+	8.28847i	−0.783074	+	0.273560i
$919$	−30.5299			−1.00709			−0.503544	−	0.863969i	$-0.667971\pi$
$919$	−30.5299			−1.00709			−0.503544	+	0.863969i	$0.667971\pi$
$920$	1.54115	−	2.66935i	0.0508102	−	0.0880058i
$921$	−0.627741	+	10.0302i	−0.0206848	+	0.330507i
$922$	11.8841			0.391382
$923$	12.3750	+	21.4341i	0.407327	+	0.705511i
$924$	1.19491	−	19.0925i	0.0393096	−	0.628099i
$925$	−2.17137	−	3.76092i	−0.0713941	−	0.123658i
$926$	−8.16080	−	14.1349i	−0.268180	−	0.464502i
$927$	15.6488	−	20.6447i	0.513974	−	0.678060i
$928$	−3.18764	−	5.52115i	−0.104639	−	0.181241i
$929$	−43.3700			−1.42292			−0.711462	−	0.702725i	$-0.751966\pi$
$929$	−43.3700			−1.42292			−0.711462	+	0.702725i	$0.751966\pi$
$930$	−14.1328	−	9.38315i	−0.463434	−	0.307686i
$931$	−11.6725	+	8.53732i	−0.382550	+	0.279799i
$932$	−6.26856	−	10.8575i	−0.205334	−	0.355648i
$933$	0.650463	−	10.3933i	0.0212952	−	0.340260i
$934$	−23.0830			−0.755298
$935$	−33.3843	+	57.8233i	−1.09178	+	1.89102i
$936$	5.36018	+	12.7280i	0.175203	+	0.416027i
$937$	4.93199	−	8.54246i	0.161121	−	0.279070i	−0.774150	−	0.633002i	$-0.781822\pi$
$937$	4.93199	−	8.54246i	0.161121	−	0.279070i	0.935271	+	0.353932i	$0.115156\pi$
$938$	9.62894	−	16.6778i	0.314396	−	0.544550i
$939$	−0.208295	+	3.32819i	−0.00679745	+	0.108611i
$940$	9.21817			0.300664
$941$	15.4217			0.502733			0.251366	−	0.967892i	$-0.419120\pi$
$941$	15.4217			0.502733			0.251366	+	0.967892i	$0.419120\pi$
$942$	−3.99260	+	1.98358i	−0.130086	+	0.0646285i
$943$	1.67416	−	2.89974i	0.0545183	−	0.0944285i
$944$	−3.92209	+	6.79326i	−0.127653	+	0.221102i
$945$	22.5774	−	7.88722i	0.734442	−	0.256571i
$946$	11.4240	−	19.7869i	0.371426	−	0.643328i
$947$	35.8307			1.16434			0.582171	−	0.813067i	$-0.302204\pi$
$947$	35.8307			1.16434			0.582171	+	0.813067i	$0.302204\pi$
$948$	−13.6950	−	9.09244i	−0.444792	−	0.295309i
$949$	−33.4484	−	57.9343i	−1.08578	−	1.88063i
$950$	−2.64809	+	1.93683i	−0.0859153	+	0.0628389i
$951$	−0.956194	+	15.2783i	−0.0310067	+	0.495433i
$952$	9.28127			0.300808
$953$	−7.62328	−	13.2039i	−0.246942	−	0.427716i	0.715734	−	0.698373i	$-0.246092\pi$
$953$	−7.62328	−	13.2039i	−0.246942	−	0.427716i	−0.962676	+	0.270657i	$0.912759\pi$
$954$	−30.6373	−	3.84995i	−0.991918	−	0.124647i
$955$	1.09528	+	1.89709i	0.0354425	+	0.0613883i
$956$	4.88147	+	8.45495i	0.157878	+	0.273453i
$957$	52.9479	+	35.1535i	1.71156	+	1.13635i
$958$	1.74756	+	3.02686i	0.0564610	+	0.0977934i
$959$	−27.1083			−0.875372
$960$	3.72043	−	1.84836i	0.120076	−	0.0596555i
$961$	7.16240	−	12.4056i	0.231045	−	0.400182i
$962$	26.5614			0.856375
$963$	−22.1702	−	52.6440i	−0.714425	−	1.69643i
$964$	7.92117	+	13.7199i	0.255124	+	0.441887i
$965$	13.7177	+	23.7598i	0.441589	+	0.764855i
$966$	3.82524	−	1.90043i	0.123075	−	0.0611454i
$967$	28.9919	−	50.2154i	0.932316	−	1.61482i	0.152964	−	0.988232i	$-0.451118\pi$
$967$	28.9919	−	50.2154i	0.932316	−	1.61482i	0.779352	−	0.626586i	$-0.215548\pi$
$968$	11.0635	+	19.1626i	0.355595	+	0.615908i
$969$	36.4784	−	1.65696i	1.17186	−	0.0532294i
$970$	−17.7682	+	30.7755i	−0.570504	+	0.988141i
$971$	−27.1784	−	47.0743i	−0.872196	−	1.51069i	−0.859720	−	0.510765i	$-0.829362\pi$
$971$	−27.1784	−	47.0743i	−0.872196	−	1.51069i	−0.0124758	−	0.999922i	$-0.503971\pi$
$972$	−15.2425	+	3.26605i	−0.488902	+	0.104759i
$973$	12.5235	−	21.6913i	0.401484	−	0.695391i
$974$	35.7125			1.14430
$975$	−0.374867	+	5.98972i	−0.0120053	+	0.191824i
$976$	0.474528	+	0.821907i	0.0151893	+	0.0263086i
$977$	−2.90031	−	5.02348i	−0.0927890	−	0.160715i	0.815895	−	0.578201i	$-0.196245\pi$
$977$	−2.90031	−	5.02348i	−0.0927890	−	0.160715i	−0.908684	+	0.417485i	$0.862912\pi$
$978$	4.22985	+	2.80831i	0.135256	+	0.0897997i
$979$	37.9733	+	65.7718i	1.21363	+	2.10207i
$980$	7.95735			0.254188
$981$	24.4851	−	32.3019i	0.781748	−	1.03132i
$982$	−14.5235	+	25.1555i	−0.463465	+	0.802745i
$983$	−54.7039			−1.74478			−0.872391	−	0.488809i	$-0.837432\pi$
$983$	−54.7039			−1.74478			−0.872391	+	0.488809i	$0.837432\pi$
$984$	4.04153	−	2.00789i	0.128839	−	0.0640092i
$985$	8.07857	−	13.9925i	0.257405	−	0.445838i
$986$	−15.4175	+	26.7040i	−0.490994	+	0.850427i
$987$	10.6422	+	7.06561i	0.338744	+	0.224901i
$988$	−2.16087	−	19.9497i	−0.0687464	−	0.634683i
$989$	5.10148			0.162218
$990$	−25.0172	+	33.0039i	−0.795099	+	1.04893i
$991$	−3.71585	−	6.43604i	−0.118038	−	0.204448i	0.800952	−	0.598728i	$-0.204327\pi$
$991$	−3.71585	−	6.43604i	−0.118038	−	0.204448i	−0.918990	+	0.394281i	$0.870994\pi$
$992$	−2.04176	−	3.53644i	−0.0648261	−	0.112282i
$993$	−13.0935	+	6.50501i	−0.415509	+	0.206430i
$994$	10.3168			0.327228
$995$	−3.09099	−	5.35375i	−0.0979909	−	0.169725i
$996$	−2.21887	+	1.10237i	−0.0703077	+	0.0349298i
$997$	−12.9838	−	22.4887i	−0.411202	−	0.712223i	0.583819	−	0.811883i	$-0.301558\pi$
$997$	−12.9838	−	22.4887i	−0.411202	−	0.712223i	−0.995021	+	0.0996608i	$0.968224\pi$
$998$	−0.555395	+	0.961973i	−0.0175807	+	0.0304507i
$999$	−5.58881	+	29.4552i	−0.176822	+	0.931921i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	342.2.f.g.7.8	✓	18
3.2	odd	2		1026.2.f.g.235.2		18
9.4	even	3		342.2.h.g.121.5	yes	18
9.5	odd	6		1026.2.h.g.577.8		18
19.11	even	3		342.2.h.g.277.5	yes	18
57.11	odd	6		1026.2.h.g.505.8		18
171.49	even	3	inner	342.2.f.g.49.8	yes	18
171.68	odd	6		1026.2.f.g.847.2		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
342.2.f.g.7.8	✓	18	1.1	even	1	trivial
342.2.f.g.49.8	yes	18	171.49	even	3	inner
342.2.h.g.121.5	yes	18	9.4	even	3
342.2.h.g.277.5	yes	18	19.11	even	3
1026.2.f.g.235.2		18	3.2	odd	2
1026.2.f.g.847.2		18	171.68	odd	6
1026.2.h.g.505.8		18	57.11	odd	6
1026.2.h.g.577.8		18	9.5	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.f (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +(1.44298 + 0.958029i) q^{3} +1.00000 q^{4} +(1.19924 - 2.07714i) q^{5} +(-1.44298 - 0.958029i) q^{6} +(0.959469 - 1.66185i) q^{7} -1.00000 q^{8} +(1.16436 + 2.76483i) q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +(1.44298 + 0.958029i) q^{3} +1.00000 q^{4} +(1.19924 - 2.07714i) q^{5} +(-1.44298 - 0.958029i) q^{6} +(0.959469 - 1.66185i) q^{7} -1.00000 q^{8} +(1.16436 + 2.76483i) q^{9} +(-1.19924 + 2.07714i) q^{10} +(2.87780 - 4.98450i) q^{11} +(1.44298 + 0.958029i) q^{12} -4.60353 q^{13} +(-0.959469 + 1.66185i) q^{14} +(3.72043 - 1.84836i) q^{15} +1.00000 q^{16} +(-2.41833 - 4.18868i) q^{17} +(-1.16436 - 2.76483i) q^{18} +(0.469393 + 4.33355i) q^{19} +(1.19924 - 2.07714i) q^{20} +(2.97659 - 1.47881i) q^{21} +(-2.87780 + 4.98450i) q^{22} -1.28511 q^{23} +(-1.44298 - 0.958029i) q^{24} +(-0.376334 - 0.651829i) q^{25} +4.60353 q^{26} +(-0.968634 + 5.10507i) q^{27} +(0.959469 - 1.66185i) q^{28} +(3.18764 + 5.52115i) q^{29} +(-3.72043 + 1.84836i) q^{30} +(2.04176 + 3.53644i) q^{31} -1.00000 q^{32} +(8.92790 - 4.43550i) q^{33} +(2.41833 + 4.18868i) q^{34} +(-2.30126 - 3.98590i) q^{35} +(1.16436 + 2.76483i) q^{36} +5.76979 q^{37} +(-0.469393 - 4.33355i) q^{38} +(-6.64279 - 4.41032i) q^{39} +(-1.19924 + 2.07714i) q^{40} +(-1.30274 + 2.25641i) q^{41} +(-2.97659 + 1.47881i) q^{42} -3.96969 q^{43} +(2.87780 - 4.98450i) q^{44} +(7.13927 + 0.897137i) q^{45} +1.28511 q^{46} +(1.92168 + 3.32844i) q^{47} +(1.44298 + 0.958029i) q^{48} +(1.65884 + 2.87319i) q^{49} +(0.376334 + 0.651829i) q^{50} +(0.523273 - 8.36100i) q^{51} -4.60353 q^{52} +(5.14637 - 8.91377i) q^{53} +(0.968634 - 5.10507i) q^{54} +(-6.90233 - 11.9552i) q^{55} +(-0.959469 + 1.66185i) q^{56} +(-3.47434 + 6.70291i) q^{57} +(-3.18764 - 5.52115i) q^{58} +(-3.92209 + 6.79326i) q^{59} +(3.72043 - 1.84836i) q^{60} +(0.474528 + 0.821907i) q^{61} +(-2.04176 - 3.53644i) q^{62} +(5.71189 + 0.717770i) q^{63} +1.00000 q^{64} +(-5.52072 + 9.56217i) q^{65} +(-8.92790 + 4.43550i) q^{66} -10.0357 q^{67} +(-2.41833 - 4.18868i) q^{68} +(-1.85438 - 1.23117i) q^{69} +(2.30126 + 3.98590i) q^{70} +(-2.68814 - 4.65600i) q^{71} +(-1.16436 - 2.76483i) q^{72} +(7.26581 + 12.5848i) q^{73} -5.76979 q^{74} +(0.0814302 - 1.30111i) q^{75} +(0.469393 + 4.33355i) q^{76} +(-5.52233 - 9.56495i) q^{77} +(6.64279 + 4.41032i) q^{78} -9.49078 q^{79} +(1.19924 - 2.07714i) q^{80} +(-6.28852 + 6.43852i) q^{81} +(1.30274 - 2.25641i) q^{82} +(-0.715228 + 1.23881i) q^{83} +(2.97659 - 1.47881i) q^{84} -11.6006 q^{85} +3.96969 q^{86} +(-0.689733 + 11.0207i) q^{87} +(-2.87780 + 4.98450i) q^{88} +(-6.59763 + 11.4274i) q^{89} +(-7.13927 - 0.897137i) q^{90} +(-4.41695 + 7.65038i) q^{91} -1.28511 q^{92} +(-0.441792 + 7.05906i) q^{93} +(-1.92168 - 3.32844i) q^{94} +(9.56430 + 4.22196i) q^{95} +(-1.44298 - 0.958029i) q^{96} +14.8163 q^{97} +(-1.65884 - 2.87319i) q^{98} +(17.1321 + 2.15286i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q - 18 q^{2} + 18 q^{4} + 5 q^{7} - 18 q^{8} + 4 q^{9}+O(q^{10}) \) 18 * q - 18 * q^2 + 18 * q^4 + 5 * q^7 - 18 * q^8 + 4 * q^9	\( 18 q - 18 q^{2} + 18 q^{4} + 5 q^{7} - 18 q^{8} + 4 q^{9} + q^{11} - 2 q^{13} - 5 q^{14} + 18 q^{16} - 5 q^{17} - 4 q^{18} + 9 q^{19} - 4 q^{21} - q^{22} + 4 q^{23} - 9 q^{25} + 2 q^{26} - 18 q^{27} + 5 q^{28} - 9 q^{29} + 4 q^{31} - 18 q^{32} + 16 q^{33} + 5 q^{34} + 6 q^{35} + 4 q^{36} + 20 q^{37} - 9 q^{38} + 4 q^{39} + q^{41} + 4 q^{42} - 14 q^{43} + q^{44} + 30 q^{45} - 4 q^{46} + 19 q^{47} + 6 q^{49} + 9 q^{50} + 16 q^{51} - 2 q^{52} - 10 q^{53} + 18 q^{54} + 6 q^{55} - 5 q^{56} - 36 q^{57} + 9 q^{58} - 5 q^{59} + 18 q^{61} - 4 q^{62} - 15 q^{63} + 18 q^{64} - 45 q^{65} - 16 q^{66} - 44 q^{67} - 5 q^{68} - 26 q^{69} - 6 q^{70} + 11 q^{71} - 4 q^{72} + 44 q^{73} - 20 q^{74} + 9 q^{76} - 2 q^{77} - 4 q^{78} - 4 q^{79} - 32 q^{81} - q^{82} - 7 q^{83} - 4 q^{84} + 14 q^{86} + 3 q^{87} - q^{88} + q^{89} - 30 q^{90} - 25 q^{91} + 4 q^{92} + 10 q^{93} - 19 q^{94} - 24 q^{95} - 6 q^{98} + 8 q^{99}+O(q^{100}) \) 18 * q - 18 * q^2 + 18 * q^4 + 5 * q^7 - 18 * q^8 + 4 * q^9 + q^11 - 2 * q^13 - 5 * q^14 + 18 * q^16 - 5 * q^17 - 4 * q^18 + 9 * q^19 - 4 * q^21 - q^22 + 4 * q^23 - 9 * q^25 + 2 * q^26 - 18 * q^27 + 5 * q^28 - 9 * q^29 + 4 * q^31 - 18 * q^32 + 16 * q^33 + 5 * q^34 + 6 * q^35 + 4 * q^36 + 20 * q^37 - 9 * q^38 + 4 * q^39 + q^41 + 4 * q^42 - 14 * q^43 + q^44 + 30 * q^45 - 4 * q^46 + 19 * q^47 + 6 * q^49 + 9 * q^50 + 16 * q^51 - 2 * q^52 - 10 * q^53 + 18 * q^54 + 6 * q^55 - 5 * q^56 - 36 * q^57 + 9 * q^58 - 5 * q^59 + 18 * q^61 - 4 * q^62 - 15 * q^63 + 18 * q^64 - 45 * q^65 - 16 * q^66 - 44 * q^67 - 5 * q^68 - 26 * q^69 - 6 * q^70 + 11 * q^71 - 4 * q^72 + 44 * q^73 - 20 * q^74 + 9 * q^76 - 2 * q^77 - 4 * q^78 - 4 * q^79 - 32 * q^81 - q^82 - 7 * q^83 - 4 * q^84 + 14 * q^86 + 3 * q^87 - q^88 + q^89 - 30 * q^90 - 25 * q^91 + 4 * q^92 + 10 * q^93 - 19 * q^94 - 24 * q^95 - 6 * q^98 + 8 * q^99

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