LMFDB - Embedded newform 342.2.h.g.277.5

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:	$18$
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:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{4}\cdot 3^{3} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			277.5
Root			$1.55117 - 0.770640i$ of defining polynomial
Character	$\chi$	$=$	342.277
Dual form			342.2.h.g.121.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 0.866025i) q^{2} +(0.108189 - 1.72867i) q^{3} +(-0.500000 + 0.866025i) q^{4} -2.39847 q^{5} +(1.55117 - 0.770640i) q^{6} +(0.959469 - 1.66185i) q^{7} -1.00000 q^{8} +(-2.97659 - 0.374045i) q^{9} +O(q^{10})$	\(q+(0.500000 + 0.866025i) q^{2} +(0.108189 - 1.72867i) q^{3} +(-0.500000 + 0.866025i) q^{4} -2.39847 q^{5} +(1.55117 - 0.770640i) q^{6} +(0.959469 - 1.66185i) q^{7} -1.00000 q^{8} +(-2.97659 - 0.374045i) q^{9} +(-1.19924 - 2.07714i) q^{10} +(2.87780 - 4.98450i) q^{11} +(1.44298 + 0.958029i) q^{12} +(2.30177 - 3.98678i) q^{13} +1.91894 q^{14} +(-0.259488 + 4.14616i) q^{15} +(-0.500000 - 0.866025i) 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} +(-2.76898 - 1.83840i) q^{21} +5.75561 q^{22} +(0.642555 - 1.11294i) q^{23} +(-0.108189 + 1.72867i) q^{24} +0.752668 q^{25} +4.60353 q^{26} +(-0.968634 + 5.10507i) q^{27} +(0.959469 + 1.66185i) q^{28} -6.37527 q^{29} +(-3.72043 + 1.84836i) q^{30} +(2.04176 + 3.53644i) q^{31} +(0.500000 - 0.866025i) q^{32} +(-8.30521 - 5.51404i) q^{33} -4.83667 q^{34} +(-2.30126 + 3.98590i) q^{35} +(1.81223 - 2.39078i) q^{36} +5.76979 q^{37} +(3.98766 - 1.76027i) q^{38} +(-6.64279 - 4.41032i) q^{39} +2.39847 q^{40} +2.60548 q^{41} +(0.207608 - 3.31721i) q^{42} +(1.98484 + 3.43785i) q^{43} +(2.87780 + 4.98450i) q^{44} +(7.13927 + 0.897137i) q^{45} +1.28511 q^{46} -3.84335 q^{47} +(-1.55117 + 0.770640i) q^{48} +(1.65884 + 2.87319i) q^{49} +(0.376334 + 0.651829i) q^{50} +(6.97920 + 4.63367i) q^{51} +(2.30177 + 3.98678i) q^{52} +(5.14637 + 8.91377i) q^{53} +(-4.90544 + 1.71367i) q^{54} +(-6.90233 + 11.9552i) q^{55} +(-0.959469 + 1.66185i) q^{56} +(-7.44049 - 1.28027i) q^{57} +(-3.18764 - 5.52115i) q^{58} +7.84418 q^{59} +(-3.46094 - 2.29780i) q^{60} -0.949057 q^{61} +(-2.04176 + 3.53644i) q^{62} +(-3.47755 + 4.58776i) q^{63} +1.00000 q^{64} +(-5.52072 + 9.56217i) q^{65} +(0.622692 - 9.94954i) q^{66} +(5.01785 - 8.69117i) q^{67} +(-2.41833 - 4.18868i) q^{68} +(-1.85438 - 1.23117i) q^{69} -4.60252 q^{70} +(-2.68814 + 4.65600i) q^{71} +(2.97659 + 0.374045i) q^{72} +(7.26581 - 12.5848i) q^{73} +(2.88489 + 4.99678i) q^{74} +(0.0814302 - 1.30111i) q^{75} +(3.51827 + 2.57328i) q^{76} +(-5.52233 - 9.56495i) q^{77} +(0.498051 - 7.95799i) q^{78} +(4.74539 + 8.21926i) q^{79} +(1.19924 + 2.07714i) q^{80} +(8.72018 + 2.22676i) q^{81} +(1.30274 + 2.25641i) q^{82} +(-0.715228 + 1.23881i) q^{83} +(2.97659 - 1.47881i) q^{84} +(5.80031 - 10.0464i) q^{85} +(-1.98484 + 3.43785i) q^{86} +(-0.689733 + 11.0207i) q^{87} +(-2.87780 + 4.98450i) q^{88} +(-6.59763 - 11.4274i) q^{89} +(2.79269 + 6.63136i) q^{90} +(-4.41695 - 7.65038i) q^{91} +(0.642555 + 1.11294i) q^{92} +(6.33423 - 3.14693i) q^{93} +(-1.92168 - 3.32844i) q^{94} +(-1.12583 + 10.3939i) q^{95} +(-1.44298 - 0.958029i) q^{96} +(-7.40815 - 12.8313i) q^{97} +(-1.65884 + 2.87319i) q^{98} +(-10.4305 + 13.7604i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q + 9 q^{2} - 9 q^{4} + 5 q^{7} - 18 q^{8} + 4 q^{9}+O(q^{10}) $ 18 * q + 9 * q^2 - 9 * q^4 + 5 * q^7 - 18 * q^8 + 4 * q^9	$ 18 q + 9 q^{2} - 9 q^{4} + 5 q^{7} - 18 q^{8} + 4 q^{9} + q^{11} + q^{13} + 10 q^{14} - 3 q^{15} - 9 q^{16} - 5 q^{17} - 4 q^{18} + 9 q^{19} - 19 q^{21} + 2 q^{22} - 2 q^{23} + 18 q^{25} + 2 q^{26} - 18 q^{27} + 5 q^{28} + 18 q^{29} + 4 q^{31} + 9 q^{32} - 23 q^{33} - 10 q^{34} + 6 q^{35} - 8 q^{36} + 20 q^{37} + 3 q^{38} + 4 q^{39} - 2 q^{41} - 23 q^{42} + 7 q^{43} + q^{44} + 30 q^{45} - 4 q^{46} - 38 q^{47} + 6 q^{49} + 9 q^{50} + 4 q^{51} + q^{52} - 10 q^{53} - 18 q^{54} + 6 q^{55} - 5 q^{56} - 33 q^{57} + 9 q^{58} + 10 q^{59} + 3 q^{60} - 36 q^{61} - 4 q^{62} + 12 q^{63} + 18 q^{64} - 45 q^{65} - 7 q^{66} + 22 q^{67} - 5 q^{68} - 26 q^{69} + 12 q^{70} + 11 q^{71} - 4 q^{72} + 44 q^{73} + 10 q^{74} - 6 q^{76} - 2 q^{77} + 23 q^{78} + 2 q^{79} + 4 q^{81} - q^{82} - 7 q^{83} - 4 q^{84} - 7 q^{86} + 3 q^{87} - q^{88} + q^{89} + 60 q^{90} - 25 q^{91} - 2 q^{92} + 25 q^{93} - 19 q^{94} + 21 q^{95} - 6 q^{98} - 19 q^{99}+O(q^{100}) $ 18 * q + 9 * q^2 - 9 * q^4 + 5 * q^7 - 18 * q^8 + 4 * q^9 + q^11 + q^13 + 10 * q^14 - 3 * q^15 - 9 * q^16 - 5 * q^17 - 4 * q^18 + 9 * q^19 - 19 * q^21 + 2 * q^22 - 2 * q^23 + 18 * q^25 + 2 * q^26 - 18 * q^27 + 5 * q^28 + 18 * q^29 + 4 * q^31 + 9 * q^32 - 23 * q^33 - 10 * q^34 + 6 * q^35 - 8 * q^36 + 20 * q^37 + 3 * q^38 + 4 * q^39 - 2 * q^41 - 23 * q^42 + 7 * q^43 + q^44 + 30 * q^45 - 4 * q^46 - 38 * q^47 + 6 * q^49 + 9 * q^50 + 4 * q^51 + q^52 - 10 * q^53 - 18 * q^54 + 6 * q^55 - 5 * q^56 - 33 * q^57 + 9 * q^58 + 10 * q^59 + 3 * q^60 - 36 * q^61 - 4 * q^62 + 12 * q^63 + 18 * q^64 - 45 * q^65 - 7 * q^66 + 22 * q^67 - 5 * q^68 - 26 * q^69 + 12 * q^70 + 11 * q^71 - 4 * q^72 + 44 * q^73 + 10 * q^74 - 6 * q^76 - 2 * q^77 + 23 * q^78 + 2 * q^79 + 4 * q^81 - q^82 - 7 * q^83 - 4 * q^84 - 7 * q^86 + 3 * q^87 - q^88 + q^89 + 60 * q^90 - 25 * q^91 - 2 * q^92 + 25 * q^93 - 19 * q^94 + 21 * q^95 - 6 * q^98 - 19 * 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
$3$	0.108189	−	1.72867i	0.0624628	−	0.998047i
$3$	0.108189	−	1.72867i	0.0624628	−	0.998047i
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	−2.39847			−1.07263			−0.536315	−	0.844018i	$-0.680184\pi$
$5$	−2.39847			−1.07263			−0.536315	+	0.844018i	$0.680184\pi$
$6$	1.55117	−	0.770640i	0.633261	−	0.314612i
$7$	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
$9$	−2.97659	−	0.374045i	−0.992197	−	0.124682i
$10$	−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
$13$	2.30177	−	3.98678i	0.638395	−	1.10573i	−0.347390	−	0.937721i	$-0.612932\pi$
$13$	2.30177	−	3.98678i	0.638395	−	1.10573i	0.985785	−	0.168012i	$-0.0537348\pi$
$14$	1.91894			0.512858
$15$	−0.259488	+	4.14616i	−0.0669995	+	1.07053i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−2.41833	+	4.18868i	−0.586532	+	1.01590i	0.408150	+	0.912915i	$0.366174\pi$
$17$	−2.41833	+	4.18868i	−0.586532	+	1.01590i	−0.994683	+	0.102989i	$0.967159\pi$
$18$	−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
$21$	−2.76898	−	1.83840i	−0.604242	−	0.401171i
$22$	5.75561			1.22710
$23$	0.642555	−	1.11294i	0.133982	−	0.232063i	−0.791226	−	0.611524i	$-0.790557\pi$
$23$	0.642555	−	1.11294i	0.133982	−	0.232063i	0.925208	+	0.379460i	$0.123890\pi$
$24$	−0.108189	+	1.72867i	−0.0220839	+	0.352863i
$25$	0.752668			0.150534
$26$	4.60353			0.902827
$27$	−0.968634	+	5.10507i	−0.186414	+	0.982471i
$28$	0.959469	+	1.66185i	0.181323	+	0.314060i
$29$	−6.37527			−1.18386			−0.591929	−	0.805990i	$-0.701633\pi$
$29$	−6.37527			−1.18386			−0.591929	+	0.805990i	$0.701633\pi$
$30$	−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	$0.713817\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$	−8.30521	−	5.51404i	−1.44575	−	0.959870i
$34$	−4.83667			−0.829482
$35$	−2.30126	+	3.98590i	−0.388984	+	0.673740i
$36$	1.81223	−	2.39078i	0.302038	−	0.398463i
$37$	5.76979			0.948547			0.474274	−	0.880377i	$-0.342711\pi$
$37$	5.76979			0.948547			0.474274	+	0.880377i	$0.342711\pi$
$38$	3.98766	−	1.76027i	0.646884	−	0.285553i
$39$	−6.64279	−	4.41032i	−1.06370	−	0.706216i
$40$	2.39847			0.379232
$41$	2.60548			0.406908			0.203454	−	0.979085i	$-0.434783\pi$
$41$	2.60548			0.406908			0.203454	+	0.979085i	$0.434783\pi$
$42$	0.207608	−	3.31721i	0.0320346	−	0.511856i
$43$	1.98484	+	3.43785i	0.302686	+	0.524267i	0.976743	−	0.214411i	$-0.0687833\pi$
$43$	1.98484	+	3.43785i	0.302686	+	0.524267i	−0.674057	+	0.738679i	$0.735450\pi$
$44$	2.87780	+	4.98450i	0.433845	+	0.751442i
$45$	7.13927	+	0.897137i	1.06426	+	0.133737i
$46$	1.28511			0.189479
$47$	−3.84335			−0.560611			−0.280305	−	0.959911i	$-0.590436\pi$
$47$	−3.84335			−0.560611			−0.280305	+	0.959911i	$0.590436\pi$
$48$	−1.55117	+	0.770640i	−0.223891	+	0.111232i
$49$	1.65884	+	2.87319i	0.236977	+	0.410456i
$50$	0.376334	+	0.651829i	0.0532216	+	0.0921826i
$51$	6.97920	+	4.63367i	0.977283	+	0.648843i
$52$	2.30177	+	3.98678i	0.319198	+	0.552867i
$53$	5.14637	+	8.91377i	0.706908	+	1.22440i	0.965999	+	0.258547i	$0.0832438\pi$
$53$	5.14637	+	8.91377i	0.706908	+	1.22440i	−0.259091	+	0.965853i	$0.583423\pi$
$54$	−4.90544	+	1.71367i	−0.667546	+	0.233201i
$55$	−6.90233	+	11.9552i	−0.930710	+	1.61204i
$56$	−0.959469	+	1.66185i	−0.128214	+	0.222074i
$57$	−7.44049	−	1.28027i	−0.985517	−	0.169576i
$58$	−3.18764	−	5.52115i	−0.418557	−	0.724962i
$59$	7.84418			1.02123			0.510613	−	0.859811i	$-0.329419\pi$
$59$	7.84418			1.02123			0.510613	+	0.859811i	$0.329419\pi$
$60$	−3.46094	−	2.29780i	−0.446805	−	0.296645i
$61$	−0.949057			−0.121514			−0.0607571	−	0.998153i	$-0.519352\pi$
$61$	−0.949057			−0.121514			−0.0607571	+	0.998153i	$0.519352\pi$
$62$	−2.04176	+	3.53644i	−0.259304	+	0.449128i
$63$	−3.47755	+	4.58776i	−0.438131	+	0.578003i
$64$	1.00000			0.125000
$65$	−5.52072	+	9.56217i	−0.684762	+	1.18604i
$66$	0.622692	−	9.94954i	0.0766481	−	1.22470i
$67$	5.01785	−	8.69117i	0.613028	−	1.06180i	−0.377699	−	0.925928i	$-0.623285\pi$
$67$	5.01785	−	8.69117i	0.613028	−	1.06180i	0.990727	−	0.135867i	$-0.0433820\pi$
$68$	−2.41833	−	4.18868i	−0.293266	−	0.507952i
$69$	−1.85438	−	1.23117i	−0.223241	−	0.148216i
$70$	−4.60252			−0.550106
$71$	−2.68814	+	4.65600i	−0.319024	+	0.552566i	−0.980285	−	0.197591i	$-0.936688\pi$
$71$	−2.68814	+	4.65600i	−0.319024	+	0.552566i	0.661261	+	0.750156i	$0.270022\pi$
$72$	2.97659	+	0.374045i	0.350795	+	0.0440816i
$73$	7.26581	−	12.5848i	0.850399	−	1.47293i	−0.0304502	−	0.999536i	$-0.509694\pi$
$73$	7.26581	−	12.5848i	0.850399	−	1.47293i	0.880849	−	0.473398i	$-0.156973\pi$
$74$	2.88489	+	4.99678i	0.335362	+	0.580864i
$75$	0.0814302	−	1.30111i	0.00940275	−	0.150240i
$76$	3.51827	+	2.57328i	0.403573	+	0.295176i
$77$	−5.52233	−	9.56495i	−0.629328	−	1.09003i
$78$	0.498051	−	7.95799i	0.0563932	−	0.901064i
$79$	4.74539	+	8.21926i	0.533898	+	0.924739i	0.999216	+	0.0395950i	$0.0126068\pi$
$79$	4.74539	+	8.21926i	0.533898	+	0.924739i	−0.465318	+	0.885144i	$0.654060\pi$
$80$	1.19924	+	2.07714i	0.134079	+	0.232231i
$81$	8.72018	+	2.22676i	0.968909	+	0.247418i
$82$	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
$85$	5.80031	−	10.0464i	0.629132	−	1.08969i
$86$	−1.98484	+	3.43785i	−0.214031	+	0.370713i
$87$	−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	−0.968693	−	0.248261i	$-0.920141\pi$
$89$	−6.59763	−	11.4274i	−0.699347	−	1.21130i	0.269346	−	0.963043i	$-0.413192\pi$
$90$	2.79269	+	6.63136i	0.294375	+	0.699006i
$91$	−4.41695	−	7.65038i	−0.463022	−	0.801978i
$92$	0.642555	+	1.11294i	0.0669909	+	0.116032i
$93$	6.33423	−	3.14693i	0.656829	−	0.326321i
$94$	−1.92168	−	3.32844i	−0.198206	−	0.343302i
$95$	−1.12583	+	10.3939i	−0.115507	+	1.06639i
$96$	−1.44298	−	0.958029i	−0.147273	−	0.0977784i
$97$	−7.40815	−	12.8313i	−0.752184	−	1.30282i	−0.946762	−	0.321933i	$-0.895667\pi$
$97$	−7.40815	−	12.8313i	−0.752184	−	1.30282i	0.194579	−	0.980887i	$-0.437666\pi$
$98$	−1.65884	+	2.87319i	−0.167568	+	0.290236i
$99$	−10.4305	+	13.7604i	−1.04830	+	1.38297i
$100$	−0.376334	+	0.651829i	−0.0376334	+	0.0651829i
$101$	8.45586			0.841389			0.420695	−	0.907202i	$-0.361786\pi$
$101$	8.45586			0.841389			0.420695	+	0.907202i	$0.361786\pi$
$102$	−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	$0.973208\pi$
$104$	−2.30177	+	3.98678i	−0.225707	+	0.390936i
$105$	6.64133	+	4.40934i	0.648127	+	0.430308i
$106$	−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	$0.872107\pi$
$108$	−3.93680	−	3.39140i	−0.378819	−	0.326337i
$109$	−6.75552	+	11.7009i	−0.647061	+	1.12074i	0.336760	+	0.941591i	$0.390669\pi$
$109$	−6.75552	+	11.7009i	−0.647061	+	1.12074i	−0.983821	+	0.179153i	$0.942664\pi$
$110$	−13.8047			−1.31622
$111$	0.624226	−	9.97405i	0.0592490	−	0.946695i
$112$	−1.91894			−0.181323
$113$	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	$0.752723\pi$
$114$	−2.61150	−	7.08379i	−0.244590	−	0.663458i
$115$	−1.54115	+	2.66935i	−0.143713	+	0.248918i
$116$	3.18764	−	5.52115i	0.295965	−	0.512626i
$117$	−8.34265	+	11.0060i	−0.771279	+	1.01751i
$118$	3.92209	+	6.79326i	0.361058	+	0.625370i
$119$	4.64063	+	8.03781i	0.425406	+	0.736825i
$120$	0.259488	−	4.14616i	0.0236879	−	0.378491i
$121$	−11.0635	−	19.1626i	−1.00577	−	1.74205i
$122$	−0.474528	−	0.821907i	−0.0429618	−	0.0744120i
$123$	0.281884	−	4.50402i	0.0254166	−	0.406113i
$124$	−4.08353			−0.366712
$125$	10.1871			0.911163
$126$	−5.71189	−	0.717770i	−0.508856	−	0.0639440i
$127$	8.11146	+	14.0495i	0.719776	+	1.24669i	0.961089	+	0.276241i	$0.0890886\pi$
$127$	8.11146	+	14.0495i	0.719776	+	1.24669i	−0.241313	+	0.970447i	$0.577578\pi$
$128$	0.500000	+	0.866025i	0.0441942	+	0.0765466i
$129$	6.15764	−	3.05920i	0.542150	−	0.269348i
$130$	−11.0414			−0.968399
$131$	10.4770			0.915377			0.457688	−	0.889113i	$-0.348678\pi$
$131$	10.4770			0.915377			0.457688	+	0.889113i	$0.348678\pi$
$132$	8.92790	−	4.43550i	0.777074	−	0.386061i
$133$	−6.75134	−	4.93797i	−0.585416	−	0.428176i
$134$	10.0357			0.866952
$135$	2.32324	−	12.2444i	0.199953	−	1.05383i
$136$	2.41833	−	4.18868i	0.207370	−	0.359176i
$137$	14.1267			1.20693			0.603463	−	0.797391i	$-0.293787\pi$
$137$	14.1267			1.20693			0.603463	+	0.797391i	$0.293787\pi$
$138$	0.139034	−	2.22153i	0.0118354	−	0.189109i
$139$	−6.52625	+	11.3038i	−0.553549	+	0.958776i	0.444465	+	0.895796i	$0.353394\pi$
$139$	−6.52625	+	11.3038i	−0.553549	+	0.958776i	−0.998015	+	0.0629797i	$0.979940\pi$
$140$	−2.30126	−	3.98590i	−0.194492	−	0.336870i
$141$	−0.415808	+	6.64388i	−0.0350173	+	0.559516i
$142$	−5.37629			−0.451168
$143$	−13.2481	−	22.9463i	−1.10786	−	1.91887i
$144$	1.16436	+	2.76483i	0.0970302	+	0.230402i
$145$	15.2909			1.26984
$146$	14.5316			1.20265
$147$	5.14626	−	2.55673i	0.424457	−	0.210876i
$148$	−2.88489	+	4.99678i	−0.237137	+	0.410733i
$149$	5.99015			0.490733			0.245366	−	0.969430i	$-0.421092\pi$
$149$	5.99015			0.490733			0.245366	+	0.969430i	$0.421092\pi$
$150$	1.16751	−	0.580036i	0.0953269	−	0.0473597i
$151$	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
$155$	−4.89711	−	8.48205i	−0.393346	−	0.681294i
$156$	7.14084	−	3.54767i	0.571725	−	0.284041i
$157$	−2.57394			−0.205423			−0.102711	−	0.994711i	$-0.532752\pi$
$157$	−2.57394			−0.205423			−0.102711	+	0.994711i	$0.532752\pi$
$158$	−4.74539	+	8.21926i	−0.377523	+	0.653889i
$159$	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
$162$	2.43166	+	8.66528i	0.191049	+	0.680808i
$163$	−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
$165$	19.9198	+	13.2253i	1.55075	+	1.02959i
$166$	−1.43046			−0.111025
$167$	6.51347	−	11.2817i	0.504028	−	0.873001i	−0.495962	−	0.868344i	$-0.665184\pi$
$167$	6.51347	−	11.2817i	0.504028	−	0.873001i	0.999989	−	0.00465689i	$-0.00148234\pi$
$168$	2.76898	+	1.83840i	0.213632	+	0.141835i
$169$	−4.09626	−	7.09494i	−0.315097	−	0.545765i
$170$	11.6006			0.889726
$171$	−3.01814	+	12.7236i	−0.230803	+	0.973001i
$172$	−3.96969			−0.302686
$173$	−11.3312	−	19.6262i	−0.861492	−	1.49215i	−0.870488	−	0.492189i	$-0.836197\pi$
$173$	−11.3312	−	19.6262i	−0.861492	−	1.49215i	0.00899577	−	0.999960i	$-0.497137\pi$
$174$	−9.88910	+	4.91304i	−0.749691	+	0.372457i
$175$	0.722161	−	1.25082i	0.0545903	−	0.0945531i
$176$	−5.75561			−0.433845
$177$	0.848653	−	13.5600i	0.0637886	−	1.01923i
$178$	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	$0.318189\pi$
$180$	−4.34658	+	5.73422i	−0.323975	+	0.427403i
$181$	6.69227	+	11.5914i	0.497433	+	0.861579i	0.999996	−	0.00296203i	$-0.000942845\pi$
$181$	6.69227	+	11.5914i	0.497433	+	0.861579i	−0.502563	+	0.864541i	$0.667610\pi$
$182$	4.41695	−	7.65038i	0.327406	−	0.567084i
$183$	−0.102677	+	1.64060i	−0.00759013	+	0.121277i
$184$	−0.642555	+	1.11294i	−0.0473698	+	0.0820468i
$185$	−13.8387			−1.01744
$186$	5.89243	+	3.91214i	0.432054	+	0.286852i
$187$	13.9190	+	24.1084i	1.01786	+	1.76298i
$188$	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	$0.177186\pi$
$192$	0.108189	−	1.72867i	0.00780785	−	0.124756i
$193$	11.4387			0.823378			0.411689	−	0.911324i	$-0.364939\pi$
$193$	11.4387			0.823378			0.411689	+	0.911324i	$0.364939\pi$
$194$	7.40815	−	12.8313i	0.531874	−	0.921233i
$195$	15.9326	+	10.5780i	1.14095	+	0.757508i
$196$	−3.31768			−0.236977
$197$	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	0.908082	−	0.418793i	$-0.137547\pi$
$199$	1.28873	+	2.23215i	0.0913558	+	0.158233i	−0.816726	+	0.577026i	$0.804213\pi$
$200$	−0.752668			−0.0532216
$201$	−14.4813	−	9.61448i	−1.02143	−	0.678153i
$202$	4.22793	+	7.32299i	0.297476	+	0.515244i
$203$	−6.11688	+	10.5947i	−0.429320	+	0.743605i
$204$	−7.50247	+	3.72733i	−0.525278	+	0.260965i
$205$	−6.24918			−0.436461
$206$	4.31756	−	7.47823i	0.300819	−	0.521033i
$207$	−2.32891	+	3.07241i	−0.161870	+	0.213548i
$208$	−4.60353			−0.319198
$209$	−20.2498	−	14.8108i	−1.40071	−	1.02448i
$210$	−0.497941	+	7.95623i	−0.0343612	+	0.549032i
$211$	5.47949			0.377223			0.188612	−	0.982052i	$-0.439601\pi$
$211$	5.47949			0.377223			0.188612	+	0.982052i	$0.439601\pi$
$212$	−10.2927			−0.706908
$213$	7.75785	+	5.15064i	0.531559	+	0.352916i
$214$	−9.52031	−	16.4897i	−0.650795	−	1.12721i
$215$	−4.76059	−	8.24559i	−0.324670	−	0.562345i
$216$	0.968634	−	5.10507i	0.0659072	−	0.347356i
$217$	7.83604			0.531945
$218$	−13.5110			−0.915083
$219$	−20.9688	−	13.9217i	−1.41694	−	0.940742i
$220$	−6.90233	−	11.9552i	−0.465355	−	0.806019i
$221$	11.1329	+	19.2827i	0.748879	+	1.29710i
$222$	8.94990	−	4.44643i	0.600678	−	0.298425i
$223$	2.64536	+	4.58191i	0.177147	+	0.306827i	0.940902	−	0.338679i	$-0.109980\pi$
$223$	2.64536	+	4.58191i	0.177147	+	0.306827i	−0.763755	+	0.645506i	$0.776647\pi$
$224$	−0.959469	−	1.66185i	−0.0641072	−	0.111037i
$225$	−2.24038	−	0.281532i	−0.149359	−	0.0187688i
$226$	−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	$-0.0991660\pi$
$228$	4.82899	−	5.80352i	0.319808	−	0.384348i
$229$	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	$0.503213\pi$
$230$	−3.08230			−0.203241
$231$	−17.1321	+	8.51145i	−1.12721	+	0.560012i
$232$	6.37527			0.418557
$233$	−6.26856	+	10.8575i	−0.410667	+	0.711296i	−0.994963	−	0.100245i	$-0.968037\pi$
$233$	−6.26856	+	10.8575i	−0.410667	+	0.711296i	0.584296	+	0.811541i	$0.301371\pi$
$234$	−13.7028	−	1.72193i	−0.895782	−	0.112566i
$235$	9.21817			0.601327
$236$	−3.92209	+	6.79326i	−0.255306	+	0.442204i
$237$	14.7218	−	7.31398i	0.956282	−	0.475094i
$238$	−4.64063	+	8.03781i	−0.300808	+	0.521014i
$239$	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
$241$	−15.8423			−1.02050			−0.510248	−	0.860028i	$-0.670446\pi$
$241$	−15.8423			−1.02050			−0.510248	+	0.860028i	$0.670446\pi$
$242$	11.0635	−	19.1626i	0.711189	−	1.23182i
$243$	4.79275	−	14.8334i	0.307455	−	0.951563i
$244$	0.474528	−	0.821907i	0.0303786	−	0.0526172i
$245$	−3.97868	−	6.89127i	−0.254188	−	0.440267i
$246$	4.04153	−	2.00789i	0.257679	−	0.128018i
$247$	−16.1965	−	11.8462i	−1.03056	−	0.753755i
$248$	−2.04176	−	3.53644i	−0.129652	−	0.224564i
$249$	2.06411	+	1.37042i	0.130808	+	0.0868466i
$250$	5.09355	+	8.82229i	0.322145	+	0.557971i
$251$	−8.25797	−	14.3032i	−0.521238	−	0.902811i	−0.999695	−	0.0247000i	$-0.992137\pi$
$251$	−8.25797	−	14.3032i	−0.521238	−	0.902811i	0.478457	−	0.878111i	$-0.341196\pi$
$252$	−2.23434	−	5.30553i	−0.140750	−	0.334217i
$253$	−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
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	7.07818	−	12.2598i	0.441525	−	0.764743i	−0.556278	−	0.830996i	$-0.687771\pi$
$257$	7.07818	−	12.2598i	0.441525	−	0.764743i	0.997803	+	0.0662532i	$0.0211045\pi$
$258$	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
$261$	18.9766	+	2.38464i	1.17462	+	0.147605i
$262$	5.23848	+	9.07332i	0.323635	+	0.560551i
$263$	11.4210	+	19.7817i	0.704249	+	1.21979i	0.966962	+	0.254921i	$0.0820494\pi$
$263$	11.4210	+	19.7817i	0.704249	+	1.21979i	−0.262713	+	0.964874i	$0.584617\pi$
$264$	8.30521	+	5.51404i	0.511150	+	0.339365i
$265$	−12.3434	−	21.3794i	−0.758250	−	1.31333i
$266$	0.900737	−	8.31582i	0.0552277	−	0.509875i
$267$	−20.4680	+	10.1688i	−1.25262	+	0.622320i
$268$	5.01785	+	8.69117i	0.306514	+	0.530898i
$269$	−9.39374	+	16.2704i	−0.572746	+	0.992026i	0.423536	+	0.905879i	$0.360789\pi$
$269$	−9.39374	+	16.2704i	−0.572746	+	0.992026i	−0.996282	+	0.0861466i	$0.972545\pi$
$270$	11.7656	−	4.11020i	0.716029	−	0.250139i
$271$	−11.9001	+	20.6116i	−0.722879	+	1.25206i	0.236962	+	0.971519i	$0.423848\pi$
$271$	−11.9001	+	20.6116i	−0.722879	+	1.25206i	−0.959841	+	0.280544i	$0.909485\pi$
$272$	4.83667			0.293266
$273$	−13.7028	+	6.80776i	−0.829333	+	0.412024i
$274$	7.06335	+	12.2341i	0.426713	+	0.739088i
$275$	2.16603	−	3.75167i	0.130616	−	0.226234i
$276$	1.99342	−	0.990357i	0.119990	−	0.0596125i
$277$	−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
$279$	−4.75471	−	11.2902i	−0.284657	−	0.675929i
$280$	2.30126	−	3.98590i	0.137527	−	0.238203i
$281$	−10.7739			−0.642716			−0.321358	−	0.946958i	$-0.604139\pi$
$281$	−10.7739			−0.642716			−0.321358	+	0.946958i	$0.604139\pi$
$282$	−5.96167	+	2.96184i	−0.355013	+	0.176375i
$283$	−20.2191			−1.20190			−0.600950	−	0.799287i	$-0.705211\pi$
$283$	−20.2191			−1.20190			−0.600950	+	0.799287i	$0.705211\pi$
$284$	−2.68814	−	4.65600i	−0.159512	−	0.276283i
$285$	17.8458	+	3.07069i	1.05709	+	0.181892i
$286$	13.2481	−	22.9463i	0.783375	−	1.35684i
$287$	2.49988	−	4.32992i	0.147563	−	0.255587i
$288$	−1.81223	+	2.39078i	−0.106787	+	0.140878i
$289$	−3.19668	−	5.53682i	−0.188040	−	0.325695i
$290$	7.64545	+	13.2423i	0.448957	+	0.777615i
$291$	−22.9825	+	11.4180i	−1.34726	+	0.669337i
$292$	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	$-0.486934\pi$
$294$	4.78733	+	3.17843i	0.279203	+	0.185370i
$295$	−18.8141			−1.09540
$296$	−5.76979			−0.335362
$297$	22.6587	+	19.5195i	1.31479	+	1.13264i
$298$	2.99508	+	5.18763i	0.173500	+	0.300511i
$299$	−2.95802	−	5.12344i	−0.171067	−	0.296296i
$300$	1.08608	+	0.721077i	0.0627050	+	0.0416314i
$301$	7.61759			0.439070
$302$	4.50796			0.259404
$303$	0.914829	−	14.6174i	0.0525556	−	0.839746i
$304$	−3.98766	+	1.76027i	−0.228708	+	0.100958i
$305$	2.27629			0.130340
$306$	14.3968	+	1.80913i	0.823009	+	0.103421i
$307$	2.90114	−	5.02491i	0.165577	−	0.286787i	−0.771283	−	0.636492i	$-0.780385\pi$
$307$	2.90114	−	5.02491i	0.165577	−	0.286787i	0.936860	+	0.349705i	$0.113718\pi$
$308$	11.0447			0.629328
$309$	−13.3945	+	6.65457i	−0.761986	+	0.378565i
$310$	4.89711	−	8.48205i	0.278137	−	0.481748i
$311$	−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
$313$	−1.92529			−0.108824			−0.0544120	−	0.998519i	$-0.517328\pi$
$313$	−1.92529			−0.108824			−0.0544120	+	0.998519i	$0.517328\pi$
$314$	−1.28697	−	2.22909i	−0.0726278	−	0.125795i
$315$	8.34081	−	11.0036i	0.469952	−	0.619983i
$316$	−9.49078			−0.533898
$317$	−8.83820			−0.496403			−0.248201	−	0.968708i	$-0.579839\pi$
$317$	−8.83820			−0.496403			−0.248201	+	0.968708i	$0.579839\pi$
$318$	14.8522	+	9.86073i	0.832869	+	0.552963i
$319$	−18.3468	+	31.7775i	−1.02722	+	1.77920i
$320$	−2.39847			−0.134079
$321$	−2.05998	+	32.9149i	−0.114977	+	1.83713i
$322$	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
$326$	−1.46567	−	2.53861i	−0.0811759	−	0.140601i
$327$	19.4961	+	12.9440i	1.07814	+	0.715803i
$328$	−2.60548			−0.143864
$329$	−3.68758	+	6.38707i	−0.203303	+	0.352131i
$330$	−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
$333$	−17.1743	−	2.15816i	−0.941146	−	0.118267i
$334$	13.0269			0.712803
$335$	−12.0352	+	20.8455i	−0.657552	+	1.13891i
$336$	−0.207608	+	3.31721i	−0.0113259	+	0.180969i
$337$	2.89980			0.157962			0.0789811	−	0.996876i	$-0.474833\pi$
$337$	2.89980			0.157962			0.0789811	+	0.996876i	$0.474833\pi$
$338$	4.09626	−	7.09494i	0.222807	−	0.385914i
$339$	8.26254	−	4.10494i	0.448759	−	0.222950i
$340$	5.80031	+	10.0464i	0.314566	+	0.544844i
$341$	23.5032			1.27277
$342$	−12.5281	+	3.74803i	−0.677440	+	0.202671i
$343$	19.7990			1.06904
$344$	−1.98484	−	3.43785i	−0.107016	−	0.185357i
$345$	4.44768	+	2.95293i	0.239455	+	0.158980i
$346$	11.3312	−	19.6262i	0.609167	−	1.05511i
$347$	21.9885			1.18040			0.590202	−	0.807256i	$-0.299048\pi$
$347$	21.9885			1.18040			0.590202	+	0.807256i	$0.299048\pi$
$348$	−9.19937	−	6.10769i	−0.493138	−	0.327407i
$349$	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
$351$	18.1232	+	15.6124i	0.967346	+	0.833329i
$352$	−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
$355$	6.44744	−	11.1673i	0.342194	−	0.592698i
$356$	13.1953			0.699347
$357$	14.3968	−	7.15252i	0.761958	−	0.378551i
$358$	7.23302	+	12.5280i	0.382277	+	0.662123i
$359$	−5.29564	+	9.17231i	−0.279493	+	0.484096i	−0.971259	−	0.238026i	$-0.923500\pi$
$359$	−5.29564	+	9.17231i	−0.279493	+	0.484096i	0.691766	+	0.722122i	$0.256833\pi$
$360$	−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
$363$	−34.3227	+	17.0520i	−1.80147	+	0.894996i
$364$	8.83390			0.463022
$365$	−17.4268	+	30.1842i	−0.912163	+	1.57991i
$366$	−1.47214	+	0.731381i	−0.0769502	+	0.0382299i
$367$	−25.0413			−1.30715			−0.653574	−	0.756863i	$-0.726731\pi$
$367$	−25.0413			−1.30715			−0.653574	+	0.756863i	$0.726731\pi$
$368$	−1.28511			−0.0669909
$369$	−7.75545	−	0.974568i	−0.403733	−	0.0507340i
$370$	−6.91934	−	11.9846i	−0.359719	−	0.623052i
$371$	19.7511			1.02543
$372$	−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	$0.841946\pi$
$374$	−13.9190	+	24.1084i	−0.719733	+	1.24661i
$375$	1.10213	−	17.6101i	0.0569138	−	0.909383i
$376$	3.84335			0.198206
$377$	−14.6744	+	25.4168i	−0.755770	+	1.30903i
$378$	−1.85875	+	9.79632i	−0.0956037	+	0.503868i
$379$	6.50829			0.334308			0.167154	−	0.985931i	$-0.446542\pi$
$379$	6.50829			0.334308			0.167154	+	0.985931i	$0.446542\pi$
$380$	−8.43847	−	6.17195i	−0.432884	−	0.316614i
$381$	25.1644	−	12.5020i	1.28921	−	0.640498i
$382$	−0.913317			−0.0467294
$383$	18.5381			0.947253			0.473627	−	0.880726i	$-0.342945\pi$
$383$	18.5381			0.947253			0.473627	+	0.880726i	$0.342945\pi$
$384$	1.55117	−	0.770640i	0.0791576	−	0.0393266i
$385$	13.2451	+	22.9413i	0.675035	+	1.16920i
$386$	5.71936	+	9.90623i	0.291108	+	0.504214i
$387$	−4.62216	−	10.9755i	−0.234957	−	0.557916i
$388$	14.8163			0.752184
$389$	5.76254			0.292173			0.146086	−	0.989272i	$-0.453332\pi$
$389$	5.76254			0.292173			0.146086	+	0.989272i	$0.453332\pi$
$390$	−1.19456	+	19.0870i	−0.0604889	+	0.966508i
$391$	3.10782	+	5.38291i	0.157169	+	0.272225i
$392$	−1.65884	−	2.87319i	−0.0837840	−	0.145118i
$393$	1.13349	−	18.1112i	0.0571770	−	0.913589i
$394$	3.36821	+	5.83392i	0.169688	+	0.293909i
$395$	−11.3817	−	19.7137i	−0.572675	−	0.991902i
$396$	−6.70161	−	15.9132i	−0.336769	−	0.799671i
$397$	−11.2508	+	19.4869i	−0.564660	+	0.978019i	0.432422	+	0.901672i	$0.357659\pi$
$397$	−11.2508	+	19.4869i	−0.564660	+	0.978019i	−0.997081	+	0.0763476i	$0.975674\pi$
$398$	−1.28873	+	2.23215i	−0.0645983	+	0.111888i
$399$	−9.26653	+	11.1366i	−0.463907	+	0.557527i
$400$	−0.376334	−	0.651829i	−0.0188167	−	0.0325915i
$401$	−29.6584			−1.48107			−0.740536	−	0.672017i	$-0.765428\pi$
$401$	−29.6584			−1.48107			−0.740536	+	0.672017i	$0.765428\pi$
$402$	1.08575	−	17.3484i	0.0541523	−	0.865259i
$403$	18.7987			0.936428
$404$	−4.22793	+	7.32299i	−0.210347	+	0.364332i
$405$	−20.9151	−	5.34082i	−1.03928	−	0.265387i
$406$	−12.2338			−0.607151
$407$	16.6043	−	28.7595i	0.823045	−	1.42556i
$408$	−6.97920	−	4.63367i	−0.345522	−	0.229401i
$409$	−5.38442	+	9.32609i	−0.266242	+	0.461145i	−0.967888	−	0.251380i	$-0.919116\pi$
$409$	−5.38442	+	9.32609i	−0.266242	+	0.461145i	0.701646	+	0.712526i	$0.252449\pi$
$410$	−3.12459	−	5.41195i	−0.154312	−	0.267277i
$411$	1.52835	−	24.4204i	0.0753880	−	1.20457i
$412$	8.63512			0.425422
$413$	7.52625	−	13.0358i	0.370343	−	0.641452i
$414$	−3.82524	−	0.480689i	−0.188000	−	0.0236246i
$415$	1.71545	−	2.97125i	0.0842083	−	0.145853i
$416$	−2.30177	−	3.98678i	−0.112853	−	0.195468i
$417$	18.8345	+	12.5047i	0.922327	+	0.612356i
$418$	2.70164	−	24.9422i	0.132142	−	1.21996i
$419$	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	$0.721902\pi$
$420$	−7.13927	+	3.54689i	−0.348361	+	0.173070i
$421$	−15.6169	−	27.0493i	−0.761122	−	1.31830i	−0.942272	−	0.334847i	$-0.891315\pi$
$421$	−15.6169	−	27.0493i	−0.761122	−	1.31830i	0.181150	−	0.983455i	$-0.442018\pi$
$422$	2.73974	+	4.74537i	0.133369	+	0.231001i
$423$	11.4401	+	1.43759i	0.556236	+	0.0698979i
$424$	−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
$427$	−0.910591	+	1.57719i	−0.0440666	+	0.0763256i
$428$	9.52031	−	16.4897i	0.460182	−	0.797058i
$429$	−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	0.793028	−	0.609186i	$-0.208504\pi$
$431$	−2.72081	−	4.71257i	−0.131057	−	0.226997i	−0.924084	+	0.382189i	$0.875170\pi$
$432$	4.90544	−	1.71367i	0.236013	−	0.0824492i
$433$	−12.0743	−	20.9134i	−0.580256	−	1.00503i	−0.995449	−	0.0952989i	$-0.969619\pi$
$433$	−12.0743	−	20.9134i	−0.580256	−	1.00503i	0.415193	−	0.909733i	$-0.363714\pi$
$434$	3.91802	+	6.78621i	0.188071	+	0.325748i
$435$	1.65430	−	26.4329i	0.0793179	−	1.26736i
$436$	−6.75552	−	11.7009i	−0.323531	−	0.560372i
$437$	−4.52136	−	3.30695i	−0.216286	−	0.158193i
$438$	1.57216	−	25.1204i	0.0751206	−	1.20030i
$439$	−2.57380	−	4.45795i	−0.122841	−	0.212767i	0.798046	−	0.602596i	$-0.205867\pi$
$439$	−2.57380	−	4.45795i	−0.122841	−	0.212767i	−0.920887	+	0.389830i	$0.872534\pi$
$440$	6.90233	−	11.9552i	0.329056	−	0.569941i
$441$	−3.86298	−	9.17280i	−0.183951	−	0.436800i
$442$	−11.1329	+	19.2827i	−0.529537	+	0.917186i
$443$	34.5651			1.64224			0.821119	−	0.570756i	$-0.193350\pi$
$443$	34.5651			1.64224			0.821119	+	0.570756i	$0.193350\pi$
$444$	8.32567	+	5.52762i	0.395119	+	0.262329i
$445$	15.8242	+	27.4084i	0.750140	+	1.29928i
$446$	−2.64536	+	4.58191i	−0.125262	+	0.216960i
$447$	0.648068	−	10.3550i	0.0306525	−	0.489774i
$448$	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	$0.803356\pi$
$450$	−0.876378	−	2.08099i	−0.0413129	−	0.0980990i
$451$	7.49807	−	12.9870i	0.353070	−	0.611535i
$452$	−5.32667			−0.250545
$453$	−6.50488	−	4.31875i	−0.305626	−	0.202913i
$454$	22.3403			1.04848
$455$	10.5939	+	18.3492i	0.496651	+	0.860225i
$456$	7.44049	+	1.28027i	0.348433	+	0.0599540i
$457$	−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
$459$	−19.0410	−	16.4031i	−0.888759	−	0.765629i
$460$	−1.54115	−	2.66935i	−0.0718565	−	0.124459i
$461$	5.94206	+	10.2919i	0.276749	+	0.479344i	0.970575	−	0.240799i	$-0.0774096\pi$
$461$	5.94206	+	10.2919i	0.276749	+	0.479344i	−0.693826	+	0.720143i	$0.744076\pi$
$462$	−15.9372	−	10.5811i	−0.741465	−	0.492277i
$463$	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
$465$	−15.1925	+	7.54782i	−0.704534	+	0.350022i
$466$	−12.5371			−0.580771
$467$	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
$470$	4.60909	+	7.98317i	0.212601	+	0.368236i
$471$	−0.278471	+	4.44948i	−0.0128313	+	0.205021i
$472$	−7.84418			−0.361058
$473$	22.8480			1.05055
$474$	13.6950	+	9.09244i	0.629031	+	0.417630i
$475$	0.353297	−	3.26172i	0.0162104	−	0.149658i
$476$	−9.28127			−0.425406
$477$	−11.9845	−	28.4576i	−0.548731	−	1.30298i
$478$	−4.88147	+	8.45495i	−0.223273	+	0.386721i
$479$	3.49512			0.159696			0.0798480	−	0.996807i	$-0.474557\pi$
$479$	3.49512			0.159696			0.0798480	+	0.996807i	$0.474557\pi$
$480$	3.46094	+	2.29780i	0.157970	+	0.104880i
$481$	13.2807	−	23.0029i	0.605548	−	1.04884i
$482$	−7.92117	−	13.7199i	−0.360800	−	0.624923i
$483$	−3.82524	+	1.90043i	−0.174055	+	0.0864727i
$484$	22.1270			1.00577
$485$	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	$0.800069\pi$
$488$	0.949057			0.0429618
$489$	−0.317138	+	5.06731i	−0.0143415	+	0.229152i
$490$	3.97868	−	6.89127i	0.179738	−	0.311316i
$491$	−29.0471			−1.31088			−0.655438	−	0.755249i	$-0.727516\pi$
$491$	−29.0471			−1.31088			−0.655438	+	0.755249i	$0.727516\pi$
$492$	3.75965	+	2.49613i	0.169498	+	0.112534i
$493$	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
$497$	5.15838	+	8.93458i	0.231385	+	0.400771i
$498$	−0.154759	+	2.47278i	−0.00693493	+	0.110808i
$499$	−1.11079			−0.0497258			−0.0248629	−	0.999691i	$-0.507915\pi$
$499$	−1.11079			−0.0497258			−0.0248629	+	0.999691i	$0.507915\pi$
$500$	−5.09355	+	8.82229i	−0.227791	+	0.394545i
$501$	−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	0.657371	−	0.753567i	$-0.271668\pi$
$503$	−7.26482	−	12.5830i	−0.323922	−	0.561050i	−0.981294	+	0.192517i	$0.938335\pi$
$504$	3.47755	−	4.58776i	0.154903	−	0.204355i
$505$	−20.2811			−0.902499
$506$	3.69829	−	6.40563i	0.164409	−	0.284765i
$507$	−12.7080	+	6.31349i	−0.564381	+	0.280392i
$508$	−16.2229			−0.719776
$509$	−5.47987	+	9.49141i	−0.242891	+	0.420699i	−0.961537	−	0.274677i	$-0.911429\pi$
$509$	−5.47987	+	9.49141i	−0.242891	+	0.420699i	0.718646	+	0.695376i	$0.244762\pi$
$510$	1.25506	−	20.0536i	0.0555748	−	0.887989i
$511$	−13.9426	−	24.1494i	−0.616786	−	1.06830i
$512$	−1.00000			−0.0441942
$513$	21.6684	+	6.59391i	0.956684	+	0.291128i
$514$	14.1564			0.624410
$515$	10.3555	+	17.9363i	0.456320	+	0.790369i
$516$	−0.429476	+	6.86228i	−0.0189066	+	0.302095i
$517$	−11.0604	+	19.1572i	−0.486436	+	0.842533i
$518$	11.0719			0.486470
$519$	−35.1530	+	17.4645i	−1.54305	+	0.766606i
$520$	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	$0.450494\pi$
$522$	7.42313	+	17.6265i	0.324901	+	0.771491i
$523$	7.47365	+	12.9447i	0.326800	+	0.566034i	0.981875	−	0.189530i	$-0.0606964\pi$
$523$	7.47365	+	12.9447i	0.326800	+	0.566034i	−0.655075	+	0.755564i	$0.727363\pi$
$524$	−5.23848	+	9.07332i	−0.228844	+	0.396370i
$525$	−2.08412	−	1.38370i	−0.0909586	−	0.0603897i
$526$	−11.4210	+	19.7817i	−0.497979	+	0.862525i
$527$	−19.7507			−0.860353
$528$	−0.622692	+	9.94954i	−0.0270992	+	0.432998i
$529$	10.6742	+	18.4883i	0.464098	+	0.803841i
$530$	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
$534$	−19.0404	−	12.6414i	−0.823960	−	0.547048i
$535$	45.6684			1.97442
$536$	−5.01785	+	8.69117i	−0.216738	+	0.375401i
$537$	1.56506	−	25.0070i	0.0675375	−	1.07913i
$538$	−18.7875			−0.809986
$539$	19.0952			0.822490
$540$	9.44231	+	8.13417i	0.406333	+	0.350039i
$541$	−2.28695	−	3.96112i	−0.0983238	−	0.170302i	0.812667	−	0.582728i	$-0.198015\pi$
$541$	−2.28695	−	3.96112i	−0.0983238	−	0.170302i	−0.910991	+	0.412426i	$0.864681\pi$
$542$	−23.8002			−1.02231
$543$	20.7616	−	10.3147i	0.890967	−	0.442645i
$544$	2.41833	+	4.18868i	0.103685	+	0.179588i
$545$	16.2029	−	28.0643i	0.694057	−	1.20214i
$546$	−12.7471	−	8.46313i	−0.545526	−	0.362188i
$547$	26.0436			1.11354			0.556772	−	0.830665i	$-0.312040\pi$
$547$	26.0436			1.11354			0.556772	+	0.830665i	$0.312040\pi$
$548$	−7.06335	+	12.2341i	−0.301732	+	0.522614i
$549$	2.82495	+	0.354990i	0.120566	+	0.0151506i
$550$	4.33206			0.184720
$551$	−2.99251	+	27.6276i	−0.127485	+	1.17697i
$552$	1.85438	+	1.23117i	0.0789278	+	0.0524021i
$553$	18.2122			0.774462
$554$	−19.4839			−0.827793
$555$	−1.49719	+	23.9225i	−0.0635522	+	1.01545i
$556$	−6.52625	−	11.3038i	−0.276775	−	0.479388i
$557$	0.187568	+	0.324877i	0.00794750	+	0.0137655i	0.869972	−	0.493101i	$-0.164137\pi$
$557$	0.187568	+	0.324877i	0.00794750	+	0.0137655i	−0.862024	+	0.506867i	$0.830804\pi$
$558$	7.40028	−	9.76282i	0.313279	−	0.413293i
$559$	18.2746			0.772933
$560$	4.60252			0.194492
$561$	43.1813	−	21.4531i	1.82312	−	0.905748i
$562$	−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	$0.791296\pi$
$564$	−5.54587	−	3.68204i	−0.233523	−	0.155042i
$565$	−6.38793	−	11.0642i	−0.268742	−	0.465475i
$566$	−10.1095	−	17.5102i	−0.424936	−	0.736010i
$567$	12.0673	−	12.3551i	0.506778	−	0.518866i
$568$	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	$0.158696\pi$
$570$	6.26361	+	16.9903i	0.262354	+	0.711644i
$571$	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	$0.831934\pi$
$572$	26.4961			1.10786
$573$	1.31790	+	0.874984i	0.0550559	+	0.0365530i
$574$	4.99976			0.208686
$575$	0.483630	−	0.837672i	0.0201688	−	0.0349333i
$576$	−2.97659	−	0.374045i	−0.124025	−	0.0155852i
$577$	−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
$579$	1.23754	−	19.7738i	0.0514305	−	0.821770i
$580$	−7.64545	+	13.2423i	−0.317460	+	0.549857i
$581$	1.37248	+	2.37720i	0.0569400	+	0.0986229i
$582$	−21.3796	−	14.1944i	−0.886212	−	0.588378i
$583$	59.2409			2.45351
$584$	−7.26581	+	12.5848i	−0.300661	+	0.520761i
$585$	20.0096	−	26.3977i	0.827296	−	1.09141i
$586$	14.4603	−	25.0459i	0.597348	−	1.03464i
$587$	−14.8138	−	25.6583i	−0.611433	−	1.05903i	−0.990999	−	0.133868i	$-0.957260\pi$
$587$	−14.8138	−	25.6583i	−0.611433	−	1.05903i	0.379567	−	0.925164i	$-0.376073\pi$
$588$	−0.358935	+	5.73516i	−0.0148022	+	0.236514i
$589$	16.2837	−	7.18811i	0.670959	−	0.296181i
$590$	−9.40703	−	16.2934i	−0.387281	−	0.670791i
$591$	0.728806	−	11.6451i	0.0299791	−	0.479013i
$592$	−2.88489	−	4.99678i	−0.118568	−	0.205367i
$593$	15.2032	+	26.3328i	0.624323	+	1.08136i	0.988671	+	0.150096i	$0.0479582\pi$
$593$	15.2032	+	26.3328i	0.624323	+	1.08136i	−0.364349	+	0.931263i	$0.618708\pi$
$594$	−5.57508	+	29.3828i	−0.228748	+	1.20559i
$595$	−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
$598$	2.95802	−	5.12344i	0.120963	−	0.209513i
$599$	−9.70640	+	16.8120i	−0.396593	+	0.686919i	−0.993303	−	0.115538i	$-0.963141\pi$
$599$	−9.70640	+	16.8120i	−0.396593	+	0.686919i	0.596710	+	0.802457i	$0.296474\pi$
$600$	−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
$603$	−18.1870	+	23.9931i	−0.740631	+	0.977077i
$604$	2.25398	+	3.90401i	0.0917132	+	0.158852i
$605$	26.5355	+	45.9608i	1.07882	+	1.86857i
$606$	13.1164	−	6.51642i	0.532819	−	0.264712i
$607$	−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	$-0.433545\pi$
$608$	−3.51827	−	2.57328i	−0.142685	−	0.104360i
$609$	17.6530	+	11.7203i	0.715336	+	0.474930i
$610$	1.13814	+	1.97132i	0.0460821	+	0.0798165i
$611$	−8.84650	+	15.3226i	−0.357891	+	0.619886i
$612$	5.63164	+	13.3725i	0.227645	+	0.540553i
$613$	19.3100	−	33.4460i	0.779925	−	1.35087i	−0.152060	−	0.988371i	$-0.548591\pi$
$613$	19.3100	−	33.4460i	0.779925	−	1.35087i	0.931984	−	0.362498i	$-0.118076\pi$
$614$	5.80227			0.234161
$615$	−0.676091	+	10.8028i	−0.0272626	+	0.435609i
$616$	5.52233	+	9.56495i	0.222501	+	0.385383i
$617$	−12.5474	+	21.7327i	−0.505138	+	0.874925i	0.494844	+	0.868982i	$0.335225\pi$
$617$	−12.5474	+	21.7327i	−0.505138	+	0.874925i	−0.999982	+	0.00594317i	$0.998108\pi$
$618$	−12.4603	−	8.27269i	−0.501226	−	0.332776i
$619$	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
$621$	5.05922	+	4.35832i	0.203020	+	0.174893i
$622$	3.00615	−	5.20680i	0.120535	−	0.208774i
$623$	−25.3209			−1.01446
$624$	−0.498051	+	7.95799i	−0.0199380	+	0.318574i
$625$	−28.1968			−1.12787
$626$	−0.962646	−	1.66735i	−0.0384751	−	0.0666408i
$627$	−27.7938	+	33.4028i	−1.10998	+	1.33398i
$628$	1.28697	−	2.22909i	0.0513556	−	0.0889506i
$629$	−13.9533	+	24.1678i	−0.556354	+	0.963633i
$630$	13.6998	+	1.72155i	0.545814	+	0.0685882i
$631$	7.29450	+	12.6345i	0.290390	+	0.502970i	0.973902	−	0.226969i	$-0.0728817\pi$
$631$	7.29450	+	12.6345i	0.290390	+	0.502970i	−0.683512	+	0.729939i	$0.739548\pi$
$632$	−4.74539	−	8.21926i	−0.188761	−	0.326945i
$633$	0.592819	−	9.47222i	0.0235624	−	0.376487i
$634$	−4.41910	−	7.65410i	−0.175505	−	0.303983i
$635$	−19.4551	−	33.6972i	−0.772052	−	1.33723i
$636$	−1.11356	+	17.7927i	−0.0441555	+	0.705528i
$637$	15.2730			0.605140
$638$	−36.6936			−1.45271
$639$	9.74305	−	12.8535i	0.385429	−	0.508477i
$640$	−1.19924	−	2.07714i	−0.0474040	−	0.0821061i
$641$	−9.54864	−	16.5387i	−0.377149	−	0.653241i	0.613497	−	0.789697i	$-0.289762\pi$
$641$	−9.54864	−	16.5387i	−0.377149	−	0.653241i	−0.990646	+	0.136456i	$0.956429\pi$
$642$	−29.5352	+	14.6735i	−1.16566	+	0.579116i
$643$	14.0714			0.554921			0.277461	−	0.960737i	$-0.410507\pi$
$643$	14.0714			0.554921			0.277461	+	0.960737i	$0.410507\pi$
$644$	2.46605			0.0971758
$645$	−14.7689	+	7.33741i	−0.581526	+	0.288910i
$646$	−2.27030	+	20.9600i	−0.0893238	+	0.824658i
$647$	0.543543			0.0213689			0.0106844	−	0.999943i	$-0.496599\pi$
$647$	0.543543			0.0213689			0.0106844	+	0.999943i	$0.496599\pi$
$648$	−8.72018	−	2.22676i	−0.342561	−	0.0874753i
$649$	22.5740	−	39.0993i	0.886108	−	1.53478i
$650$	3.46493			0.135906
$651$	0.847771	−	13.5459i	0.0332268	−	0.530906i
$652$	1.46567	−	2.53861i	0.0574001	−	0.0994198i
$653$	−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
$655$	−25.1287			−0.981860
$656$	−1.30274	−	2.25641i	−0.0508635	−	0.0880982i
$657$	−26.3346	+	34.7419i	−1.02741	+	1.35541i
$658$	−7.37516			−0.287513
$659$	10.3342			0.402565			0.201283	−	0.979533i	$-0.435489\pi$
$659$	10.3342			0.402565			0.201283	+	0.979533i	$0.435489\pi$
$660$	−21.4133	+	10.6384i	−0.833512	+	0.414100i
$661$	−19.8696	+	34.4152i	−0.772839	+	1.33860i	0.163162	+	0.986599i	$0.447831\pi$
$661$	−19.8696	+	34.4152i	−0.772839	+	1.33860i	−0.936001	+	0.351998i	$0.885503\pi$
$662$	−8.44105			−0.328071
$663$	34.5379	−	17.1589i	1.34134	−	0.666396i
$664$	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
$668$	6.51347	+	11.2817i	0.252014	+	0.436501i
$669$	8.20679	−	4.07725i	0.317293	−	0.157635i
$670$	−24.0703			−0.929918
$671$	−2.73120	+	4.73058i	−0.105437	+	0.182622i
$672$	−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
$675$	−0.729059	+	3.84242i	−0.0280615	+	0.147895i
$676$	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	$0.282741\pi$
$678$	7.68625	+	5.10310i	0.295189	+	0.195983i
$679$	−28.4316			−1.09110
$680$	−5.80031	+	10.0464i	−0.222432	+	0.385263i
$681$	−32.2365	−	21.4027i	−1.23531	−	0.820151i
$682$	11.7516	+	20.3543i	0.449992	+	0.779408i
$683$	12.5535			0.480347			0.240174	−	0.970730i	$-0.422796\pi$
$683$	12.5535			0.480347			0.240174	+	0.970730i	$0.422796\pi$
$684$	−9.50992	−	8.97560i	−0.363621	−	0.343191i
$685$	−33.8825			−1.29458
$686$	9.89949	+	17.1464i	0.377964	+	0.654653i
$687$	40.4181	−	20.0803i	1.54205	−	0.766110i
$688$	1.98484	−	3.43785i	0.0756715	−	0.131067i
$689$	47.3830			1.80515
$690$	−0.333470	+	5.32827i	−0.0126950	+	0.202844i
$691$	−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
$693$	12.8600	+	30.5365i	0.488510	+	1.15999i
$694$	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
$697$	−6.30093	+	10.9135i	−0.238665	+	0.413379i
$698$	15.3723			0.581848
$699$	18.0908	+	12.0109i	0.684256	+	0.454295i
$700$	0.722161	+	1.25082i	0.0272951	+	0.0472766i
$701$	−7.47020	+	12.9388i	−0.282146	+	0.488691i	−0.971913	−	0.235340i	$-0.924379\pi$
$701$	−7.47020	+	12.9388i	−0.282146	+	0.488691i	0.689767	+	0.724031i	$0.257713\pi$
$702$	−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
$705$	0.997303	−	15.9352i	0.0375606	−	0.600153i
$706$	9.54136			0.359094
$707$	8.11314	−	14.0524i	0.305126	−	0.528493i
$708$	11.3190	+	7.51495i	0.425393	+	0.282429i
$709$	36.6347			1.37585			0.687923	−	0.725783i	$-0.258522\pi$
$709$	36.6347			1.37585			0.687923	+	0.725783i	$0.258522\pi$
$710$	12.8949			0.483936
$711$	−11.0507	−	26.2404i	−0.414434	−	0.984090i
$712$	6.59763	+	11.4274i	0.247257	+	0.428261i
$713$	5.24778			0.196531
$714$	13.3927	+	8.89172i	0.501207	+	0.332764i
$715$	31.7751	+	55.0361i	1.18832	+	2.05823i
$716$	−7.23302	+	12.5280i	−0.270311	+	0.468192i
$717$	15.1439	−	7.52371i	0.565561	−	0.280978i
$718$	−10.5913			−0.395263
$719$	−12.8765	+	22.3028i	−0.480213	+	0.831753i	−0.999742	−	0.0226993i	$-0.992774\pi$
$719$	−12.8765	+	22.3028i	−0.480213	+	0.831753i	0.519529	+	0.854453i	$0.326107\pi$
$720$	−2.79269	−	6.63136i	−0.104077	−	0.247136i
$721$	−16.5703			−0.617109
$722$	−5.75644	−	18.1070i	−0.214232	−	0.673873i
$723$	−1.71396	+	27.3862i	−0.0637430	+	1.01850i
$724$	−13.3845			−0.497433
$725$	−4.79846			−0.178210
$726$	−31.9288	−	21.1983i	−1.18499	−	0.786743i
$727$	19.7938	+	34.2839i	0.734112	+	1.27152i	0.955112	+	0.296245i	$0.0957346\pi$
$727$	19.7938	+	34.2839i	0.734112	+	1.27152i	−0.221000	+	0.975274i	$0.570932\pi$
$728$	4.41695	+	7.65038i	0.163703	+	0.283542i
$729$	−25.1235	−	9.88989i	−0.930500	−	0.366292i
$730$	−34.8537			−1.28999
$731$	−19.2001			−0.710140
$732$	−1.36947	−	0.909224i	−0.0506170	−	0.0336059i
$733$	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
$735$	−12.3432	+	6.13226i	−0.455285	+	0.226192i
$736$	−0.642555	−	1.11294i	−0.0236849	−	0.0410234i
$737$	−28.8808	−	50.0230i	−1.06384	−	1.84262i
$738$	−3.03373	−	7.20370i	−0.111673	−	0.265172i
$739$	−13.3123	+	23.0576i	−0.489702	+	0.848189i	−0.999930	−	0.0118502i	$-0.996228\pi$
$739$	−13.3123	+	23.0576i	−0.489702	+	0.848189i	0.510227	+	0.860039i	$0.329561\pi$
$740$	6.91934	−	11.9846i	0.254360	−	0.440564i
$741$	−22.2304	+	26.7167i	−0.816655	+	0.981463i
$742$	9.87556	+	17.1050i	0.362543	+	0.627943i
$743$	42.4635			1.55783			0.778917	−	0.627127i	$-0.215769\pi$
$743$	42.4635			1.55783			0.778917	+	0.627127i	$0.215769\pi$
$744$	−6.33423	+	3.14693i	−0.232224	+	0.115372i
$745$	−14.3672			−0.526374
$746$	0.522500	−	0.904997i	0.0191301	−	0.0331343i
$747$	2.59231	−	3.41990i	0.0948477	−	0.125128i
$748$	−27.8380			−1.01786
$749$	−18.2689	+	31.6427i	−0.667531	+	1.15620i
$750$	15.8019	−	7.85059i	0.577003	−	0.286663i
$751$	18.8747	−	32.6919i	0.688747	−	1.19295i	−0.283496	−	0.958973i	$-0.591494\pi$
$751$	18.8747	−	32.6919i	0.688747	−	1.19295i	0.972243	−	0.233972i	$-0.0751724\pi$
$752$	1.92168	+	3.32844i	0.0700763	+	0.121376i
$753$	−25.6189	+	12.7278i	−0.933606	+	0.463828i
$754$	−29.3488			−1.06882
$755$	−5.40611	+	9.36365i	−0.196748	+	0.340778i
$756$	−9.41323	+	3.28843i	−0.342356	+	0.119599i
$757$	16.6770	−	28.8854i	0.606135	−	1.04986i	−0.385736	−	0.922609i	$-0.626053\pi$
$757$	16.6770	−	28.8854i	0.606135	−	1.04986i	0.991871	−	0.127247i	$-0.0406142\pi$
$758$	3.25414	+	5.63634i	0.118196	+	0.204721i
$759$	−11.4733	+	5.70010i	−0.416455	+	0.206901i
$760$	1.12583	−	10.3939i	0.0408380	−	0.377026i
$761$	−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	$0.935826\pi$
$762$	23.4093	+	15.5420i	0.848029	+	0.563028i
$763$	12.9634	+	22.4533i	0.469307	+	0.812864i
$764$	−0.456659	−	0.790956i	−0.0165213	−	0.0286158i
$765$	−21.0230	+	27.7345i	−0.760087	+	1.00274i
$766$	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
$769$	−17.5120	+	30.3317i	−0.631500	+	1.09379i	0.355745	+	0.934583i	$0.384227\pi$
$769$	−17.5120	+	30.3317i	−0.631500	+	1.09379i	−0.987245	+	0.159207i	$0.949106\pi$
$770$	−13.2451	+	22.9413i	−0.477322	+	0.826746i
$771$	−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	−0.984123	−	0.177488i	$-0.943203\pi$
$773$	−17.9543	−	31.0977i	−0.645771	−	1.11851i	0.338352	−	0.941020i	$-0.390131\pi$
$774$	7.19398	−	9.49065i	0.258582	−	0.341134i
$775$	1.53677	+	2.66176i	0.0552024	+	0.0956133i
$776$	7.40815	+	12.8313i	0.265937	+	0.460616i
$777$	−15.9764	−	10.6072i	−0.573152	−	0.380530i
$778$	2.88127	+	4.99051i	0.103299	+	0.178918i
$779$	1.22300	−	11.2910i	0.0438184	−	0.404542i
$780$	−17.1271	+	8.50898i	−0.613249	+	0.304670i
$781$	15.4719	+	26.7981i	0.553628	+	0.958912i
$782$	−3.10782	+	5.38291i	−0.111136	+	0.192492i
$783$	6.17530	−	32.5462i	0.220687	−	1.16311i
$784$	1.65884	−	2.87319i	0.0592442	−	0.102614i
$785$	6.17351			0.220342
$786$	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	$0.889255\pi$
$788$	−3.36821	+	5.83392i	−0.119988	+	0.207825i
$789$	35.4317	−	17.6030i	1.26140	−	0.626682i
$790$	11.3817	−	19.7137i	0.404942	−	0.701380i
$791$	10.2215			0.363436
$792$	10.4305	−	13.7604i	0.370631	−	0.488954i
$793$	−2.18451	+	3.78368i	−0.0775742	+	0.134362i
$794$	−22.5015			−0.798549
$795$	−38.2934	+	19.0247i	−1.35813	+	0.674735i
$796$	−2.57746			−0.0913558
$797$	−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	$0.923657\pi$
$798$	−14.2778	−	2.45675i	−0.505430	−	0.0869681i
$799$	9.29451	−	16.0986i	0.328816	−	0.569526i
$800$	0.376334	−	0.651829i	0.0133054	−	0.0230456i
$801$	15.3641	+	36.4826i	0.542862	+	1.28905i
$802$	−14.8292	−	25.6850i	−0.523638	−	0.906968i
$803$	−41.8191	−	72.4329i	−1.47577	−	2.55610i
$804$	15.5670	−	7.73391i	0.549007	−	0.272754i
$805$	2.95737	+	5.12232i	0.104234	+	0.180538i
$806$	9.39933	+	16.2801i	0.331077	+	0.573443i
$807$	27.1099	+	17.9989i	0.954313	+	0.633593i
$808$	−8.45586			−0.297476
$809$	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	0.917641	−	0.397410i	$-0.130091\pi$
$811$	3.26510	+	5.65532i	0.114653	+	0.198585i	−0.802988	+	0.595995i	$0.796758\pi$
$812$	−6.11688	−	10.5947i	−0.214660	−	0.371802i
$813$	34.3431	+	22.8012i	1.20446	+	0.799675i
$814$	33.2086			1.16396
$815$	7.03073			0.246276
$816$	0.523273	−	8.36100i	0.0183182	−	0.292693i
$817$	15.8298	−	6.98772i	0.553814	−	0.244469i
$818$	−10.7688			−0.376524
$819$	10.2859	+	24.4242i	0.359417	+	0.853450i
$820$	3.12459	−	5.41195i	0.109115	−	0.188993i
$821$	−20.2171			−0.705582			−0.352791	−	0.935702i	$-0.614767\pi$
$821$	−20.2171			−0.705582			−0.352791	+	0.935702i	$0.614767\pi$
$822$	21.9129	−	10.8866i	0.764299	−	0.379714i
$823$	22.9573	−	39.7632i	0.800242	−	1.38606i	−0.119215	−	0.992868i	$-0.538038\pi$
$823$	22.9573	−	39.7632i	0.800242	−	1.38606i	0.919457	−	0.393191i	$-0.128629\pi$
$824$	4.31756	+	7.47823i	0.150409	+	0.260517i
$825$	−6.25106	−	4.15024i	−0.217634	−	0.144493i
$826$	15.0525			0.523744
$827$	−11.1316	−	19.2806i	−0.387085	−	0.670451i	0.604971	−	0.796248i	$-0.293185\pi$
$827$	−11.1316	−	19.2806i	−0.387085	−	0.670451i	−0.992056	+	0.125796i	$0.959851\pi$
$828$	−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	$0.123675\pi$
$830$	3.43091			0.119089
$831$	28.1149	+	18.6662i	0.975294	+	0.647522i
$832$	2.30177	−	3.98678i	0.0797994	−	0.138217i
$833$	−16.0465			−0.555978
$834$	−1.41213	+	22.5635i	−0.0488982	+	0.781308i
$835$	−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
$839$	8.13901	+	14.0972i	0.280990	+	0.486688i	0.971629	−	0.236511i	$-0.0760040\pi$
$839$	8.13901	+	14.0972i	0.280990	+	0.486688i	−0.690639	+	0.723200i	$0.742671\pi$
$840$	−6.64133	−	4.40934i	−0.229148	−	0.152137i
$841$	11.6441			0.401520
$842$	15.6169	−	27.0493i	0.538195	−	0.932181i
$843$	−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
$846$	4.47506	+	10.6262i	0.153856	+	0.365336i
$847$	−42.4604			−1.45896
$848$	5.14637	−	8.91377i	0.176727	−	0.306100i
$849$	−2.18748	+	34.9521i	−0.0750740	+	1.19955i
$850$	−3.64040			−0.124865
$851$	3.70740	−	6.42141i	0.127088	−	0.220123i
$852$	−8.33951	+	4.14318i	−0.285707	+	0.141943i
$853$	−22.5855	−	39.1192i	−0.773313	−	1.33942i	−0.935738	−	0.352696i	$-0.885265\pi$
$853$	−22.5855	−	39.1192i	−0.773313	−	1.33942i	0.162425	−	0.986721i	$-0.448068\pi$
$854$	−1.82118			−0.0623196
$855$	7.23891	−	30.5173i	0.247566	−	1.04367i
$856$	19.0406			0.650795
$857$	−21.9690	−	38.0514i	−0.750446	−	1.29981i	−0.947607	−	0.319439i	$-0.896506\pi$
$857$	−21.9690	−	38.0514i	−0.750446	−	1.29981i	0.197161	−	0.980371i	$-0.436828\pi$
$858$	−38.2333	−	25.3841i	−1.30526	−	0.866597i
$859$	−18.6082	+	32.2304i	−0.634904	+	1.09969i	0.351631	+	0.936139i	$0.385627\pi$
$859$	−18.6082	+	32.2304i	−0.634904	+	1.09969i	−0.986535	+	0.163548i	$0.947706\pi$
$860$	9.52119			0.324670
$861$	−7.21454	−	4.78991i	−0.245871	−	0.163240i
$862$	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	$0.603519\pi$
$864$	3.93680	+	3.39140i	0.133933	+	0.115378i
$865$	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
$868$	−3.91802	+	6.78621i	−0.132986	+	0.230339i
$869$	54.6252			1.85303
$870$	23.7187	−	11.7838i	0.804140	−	0.399508i
$871$	−23.0998	−	40.0101i	−0.782708	−	1.35569i
$872$	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
$876$	22.5409	−	11.1986i	0.761588	−	0.378367i
$877$	−19.7092			−0.665533			−0.332766	−	0.943009i	$-0.607982\pi$
$877$	−19.7092			−0.665533			−0.332766	+	0.943009i	$0.607982\pi$
$878$	2.57380	−	4.45795i	0.0868616	−	0.150449i
$879$	−44.8605	+	22.2873i	−1.51311	+	0.751732i
$880$	13.8047			0.465355
$881$	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	0.951259	−	0.308392i	$-0.0997907\pi$
$883$	6.19727	+	10.7340i	0.208555	+	0.361227i	−0.742705	+	0.669619i	$0.766457\pi$
$884$	−22.2658			−0.748879
$885$	−2.03547	+	32.5233i	−0.0684216	+	1.09326i
$886$	17.2826	+	29.9343i	0.580619	+	1.00566i
$887$	−8.84292	+	15.3164i	−0.296916	+	0.514274i	−0.975429	−	0.220315i	$-0.929292\pi$
$887$	−8.84292	+	15.3164i	−0.296916	+	0.514274i	0.678513	+	0.734589i	$0.262625\pi$
$888$	−0.624226	+	9.97405i	−0.0209477	+	0.334707i
$889$	31.1308			1.04409
$890$	−15.8242	+	27.4084i	−0.530429	+	0.918730i
$891$	36.1942	−	37.0576i	1.21255	−	1.24148i
$892$	−5.29073			−0.177147
$893$	−1.80404	+	16.6554i	−0.0603700	+	0.557351i
$894$	9.29172	−	4.61625i	0.310762	−	0.154391i
$895$	−34.6964			−1.15977
$896$	1.91894			0.0641072
$897$	−9.17676	+	4.55914i	−0.306403	+	0.152225i
$898$	−17.2731	−	29.9180i	−0.576412	−	0.998375i
$899$	−13.0168	−	22.5458i	−0.434134	−	0.751943i
$900$	1.36401	−	1.79946i	0.0454668	−	0.0599821i
$901$	−49.7825			−1.65850
$902$	14.9961			0.499317
$903$	0.824138	−	13.1683i	0.0274256	−	0.438213i
$904$	−2.66333	−	4.61303i	−0.0885811	−	0.153427i
$905$	−16.0512	−	27.8015i	−0.533561	−	0.924154i
$906$	0.487711	−	7.79277i	0.0162031	−	0.258897i
$907$	−20.5077	−	35.5204i	−0.680948	−	1.17944i	−0.974692	−	0.223552i	$-0.928235\pi$
$907$	−20.5077	−	35.5204i	−0.680948	−	1.17944i	0.293744	−	0.955884i	$-0.405099\pi$
$908$	11.1702	+	19.3473i	0.370695	+	0.642062i
$909$	−25.1696	−	3.16287i	−0.834824	−	0.104906i
$910$	−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	$0.254995\pi$
$912$	2.61150	+	7.08379i	0.0864755	+	0.234568i
$913$	4.11657	+	7.13011i	0.136239	+	0.235972i
$914$	−18.8458			−0.623362
$915$	0.246269	−	3.93494i	0.00814139	−	0.130085i
$916$	−26.0566			−0.860935
$917$	10.0523	−	17.4111i	0.331957	−	0.574966i
$918$	4.68496	−	24.6915i	0.154627	−	0.814942i
$919$	−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
$921$	−8.37254	−	5.55874i	−0.275885	−	0.183167i
$922$	−5.94206	+	10.2919i	−0.195691	+	0.338947i
$923$	12.3750	+	21.4341i	0.407327	+	0.705511i
$924$	1.19491	−	19.0925i	0.0393096	−	0.628099i
$925$	4.34273			0.142788
$926$	−8.16080	+	14.1349i	−0.268180	+	0.464502i
$927$	10.0544	+	23.8746i	0.330230	+	0.784145i
$928$	−3.18764	+	5.52115i	−0.104639	+	0.181241i
$929$	21.6850	+	37.5595i	0.711462	+	1.23229i	0.964308	+	0.264781i	$0.0852998\pi$
$929$	21.6850	+	37.5595i	0.711462	+	1.23229i	−0.252847	+	0.967506i	$0.581367\pi$
$930$	−14.1328	−	9.38315i	−0.463434	−	0.307686i
$931$	13.2298	−	5.84000i	0.433588	−	0.191398i
$932$	−6.26856	−	10.8575i	−0.205334	−	0.355648i
$933$	−9.32606	+	4.63331i	−0.305322	+	0.151688i
$934$	11.5415	+	19.9905i	0.377649	+	0.654108i
$935$	−33.3843	−	57.8233i	−1.09178	−	1.89102i
$936$	8.34265	−	11.0060i	0.272688	−	0.359744i
$937$	4.93199	+	8.54246i	0.161121	+	0.279070i	0.935271	−	0.353932i	$-0.115156\pi$
$937$	4.93199	+	8.54246i	0.161121	+	0.279070i	−0.774150	+	0.633002i	$0.781822\pi$
$938$	9.62894	−	16.6778i	0.314396	−	0.544550i
$939$	−0.208295	+	3.32819i	−0.00679745	+	0.108611i
$940$	−4.60909	+	7.98317i	−0.150332	+	0.260382i
$941$	−7.71085	+	13.3556i	−0.251366	+	0.435379i	−0.963902	−	0.266256i	$-0.914213\pi$
$941$	−7.71085	+	13.3556i	−0.251366	+	0.435379i	0.712536	+	0.701636i	$0.247547\pi$
$942$	−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
$945$	−18.1192	−	15.6090i	−0.589418	−	0.507760i
$946$	11.4240	+	19.7869i	0.371426	+	0.643328i
$947$	−17.9153	−	31.0303i	−0.582171	−	1.00835i	−0.995222	−	0.0976411i	$-0.968870\pi$
$947$	−17.9153	−	31.0303i	−0.582171	−	1.00835i	0.413051	−	0.910708i	$-0.364463\pi$
$948$	−1.02680	+	16.4064i	−0.0333488	+	0.532856i
$949$	−33.4484	−	57.9343i	−1.08578	−	1.88063i
$950$	3.00138	−	1.32490i	0.0973778	−	0.0429854i
$951$	−0.956194	+	15.2783i	−0.0310067	+	0.495433i
$952$	−4.64063	−	8.03781i	−0.150404	−	0.260507i
$953$	−7.62328	+	13.2039i	−0.246942	+	0.427716i	−0.962676	−	0.270657i	$-0.912759\pi$
$953$	−7.62328	+	13.2039i	−0.246942	+	0.427716i	0.715734	+	0.698373i	$0.246092\pi$
$954$	18.6528	−	24.6077i	0.603906	−	0.796703i
$955$	1.09528	−	1.89709i	0.0354425	−	0.0613883i
$956$	−9.76294			−0.315756
$957$	52.9479	+	35.1535i	1.71156	+	1.13635i
$958$	1.74756	+	3.02686i	0.0564610	+	0.0977934i
$959$	13.5541	−	23.4765i	0.437686	−	0.758094i
$960$	−0.259488	+	4.14616i	−0.00837493	+	0.133817i
$961$	7.16240	−	12.4056i	0.231045	−	0.400182i
$962$	26.5614			0.856375
$963$	56.6762	+	7.12205i	1.82636	+	0.229505i
$964$	7.92117	−	13.7199i	0.255124	−	0.441887i
$965$	−27.4355			−0.883179
$966$	−3.55845	−	2.36254i	−0.114491	−	0.0760135i
$967$	−57.9837			−1.86463			−0.932316	−	0.361646i	$-0.882215\pi$
$967$	−57.9837			−1.86463			−0.932316	+	0.361646i	$0.882215\pi$
$968$	11.0635	+	19.1626i	0.355595	+	0.615908i
$969$	23.3562	−	28.0697i	0.750310	−	0.901729i
$970$	−17.7682	+	30.7755i	−0.570504	+	0.988141i
$971$	−27.1784	+	47.0743i	−0.872196	+	1.51069i	−0.0124758	+	0.999922i	$0.503971\pi$
$971$	−27.1784	+	47.0743i	−0.872196	+	1.51069i	−0.859720	+	0.510765i	$0.829362\pi$
$972$	10.4497	+	11.5673i	0.335175	+	0.371023i
$973$	12.5235	+	21.6913i	0.401484	+	0.695391i
$974$	−17.8563	−	30.9279i	−0.572151	−	0.990995i
$975$	−4.99981	−	3.31950i	−0.160122	−	0.106309i
$976$	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	$0.862912\pi$
$978$	−4.54699	+	2.25901i	−0.145397	+	0.0722351i
$979$	−75.9467			−2.42727
$980$	7.95735			0.254188
$981$	24.4851	−	32.3019i	0.781748	−	1.03132i
$982$	−14.5235	−	25.1555i	−0.463465	−	0.802745i
$983$	27.3519	+	47.3749i	0.872391	+	1.51103i	0.859516	+	0.511108i	$0.170765\pi$
$983$	27.3519	+	47.3749i	0.872391	+	1.51103i	0.0128746	+	0.999917i	$0.495902\pi$
$984$	−0.281884	+	4.50402i	−0.00898613	+	0.143583i
$985$	−16.1571			−0.514809
$986$	30.8351			0.981989
$987$	10.6422	+	7.06561i	0.338744	+	0.224901i
$988$	18.3573	−	8.10346i	0.584025	−	0.257805i
$989$	5.10148			0.162218
$990$	41.0908	+	5.16357i	1.30595	+	0.164109i
$991$	−3.71585	+	6.43604i	−0.118038	+	0.204448i	−0.918990	−	0.394281i	$-0.870994\pi$
$991$	−3.71585	+	6.43604i	−0.118038	+	0.204448i	0.800952	+	0.598728i	$0.204327\pi$
$992$	4.08353			0.129652
$993$	12.1802	+	8.08677i	0.386528	+	0.256626i
$994$	−5.15838	+	8.93458i	−0.163614	+	0.283388i
$995$	−3.09099	−	5.35375i	−0.0979909	−	0.169725i
$996$	−2.21887	+	1.10237i	−0.0703077	+	0.0349298i
$997$	25.9677			0.822404			0.411202	−	0.911544i	$-0.365109\pi$
$997$	25.9677			0.822404			0.411202	+	0.911544i	$0.365109\pi$
$998$	−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.h.g.277.5	yes	18
3.2	odd	2		1026.2.h.g.505.8		18
9.4	even	3		342.2.f.g.49.8	yes	18
9.5	odd	6		1026.2.f.g.847.2		18
19.7	even	3		342.2.f.g.7.8	✓	18
57.26	odd	6		1026.2.f.g.235.2		18
171.121	even	3	inner	342.2.h.g.121.5	yes	18
171.140	odd	6		1026.2.h.g.577.8		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
342.2.f.g.7.8	✓	18	19.7	even	3
342.2.f.g.49.8	yes	18	9.4	even	3
342.2.h.g.121.5	yes	18	171.121	even	3	inner
342.2.h.g.277.5	yes	18	1.1	even	1	trivial
1026.2.f.g.235.2		18	57.26	odd	6
1026.2.f.g.847.2		18	9.5	odd	6
1026.2.h.g.505.8		18	3.2	odd	2
1026.2.h.g.577.8		18	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)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +(0.108189 - 1.72867i) q^{3} +(-0.500000 + 0.866025i) q^{4} -2.39847 q^{5} +(1.55117 - 0.770640i) q^{6} +(0.959469 - 1.66185i) q^{7} -1.00000 q^{8} +(-2.97659 - 0.374045i) q^{9} +O(q^{10})\)	\(q+(0.500000 + 0.866025i) q^{2} +(0.108189 - 1.72867i) q^{3} +(-0.500000 + 0.866025i) q^{4} -2.39847 q^{5} +(1.55117 - 0.770640i) q^{6} +(0.959469 - 1.66185i) q^{7} -1.00000 q^{8} +(-2.97659 - 0.374045i) q^{9} +(-1.19924 - 2.07714i) q^{10} +(2.87780 - 4.98450i) q^{11} +(1.44298 + 0.958029i) q^{12} +(2.30177 - 3.98678i) q^{13} +1.91894 q^{14} +(-0.259488 + 4.14616i) q^{15} +(-0.500000 - 0.866025i) 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} +(-2.76898 - 1.83840i) q^{21} +5.75561 q^{22} +(0.642555 - 1.11294i) q^{23} +(-0.108189 + 1.72867i) q^{24} +0.752668 q^{25} +4.60353 q^{26} +(-0.968634 + 5.10507i) q^{27} +(0.959469 + 1.66185i) q^{28} -6.37527 q^{29} +(-3.72043 + 1.84836i) q^{30} +(2.04176 + 3.53644i) q^{31} +(0.500000 - 0.866025i) q^{32} +(-8.30521 - 5.51404i) q^{33} -4.83667 q^{34} +(-2.30126 + 3.98590i) q^{35} +(1.81223 - 2.39078i) q^{36} +5.76979 q^{37} +(3.98766 - 1.76027i) q^{38} +(-6.64279 - 4.41032i) q^{39} +2.39847 q^{40} +2.60548 q^{41} +(0.207608 - 3.31721i) q^{42} +(1.98484 + 3.43785i) q^{43} +(2.87780 + 4.98450i) q^{44} +(7.13927 + 0.897137i) q^{45} +1.28511 q^{46} -3.84335 q^{47} +(-1.55117 + 0.770640i) q^{48} +(1.65884 + 2.87319i) q^{49} +(0.376334 + 0.651829i) q^{50} +(6.97920 + 4.63367i) q^{51} +(2.30177 + 3.98678i) q^{52} +(5.14637 + 8.91377i) q^{53} +(-4.90544 + 1.71367i) q^{54} +(-6.90233 + 11.9552i) q^{55} +(-0.959469 + 1.66185i) q^{56} +(-7.44049 - 1.28027i) q^{57} +(-3.18764 - 5.52115i) q^{58} +7.84418 q^{59} +(-3.46094 - 2.29780i) q^{60} -0.949057 q^{61} +(-2.04176 + 3.53644i) q^{62} +(-3.47755 + 4.58776i) q^{63} +1.00000 q^{64} +(-5.52072 + 9.56217i) q^{65} +(0.622692 - 9.94954i) q^{66} +(5.01785 - 8.69117i) q^{67} +(-2.41833 - 4.18868i) q^{68} +(-1.85438 - 1.23117i) q^{69} -4.60252 q^{70} +(-2.68814 + 4.65600i) q^{71} +(2.97659 + 0.374045i) q^{72} +(7.26581 - 12.5848i) q^{73} +(2.88489 + 4.99678i) q^{74} +(0.0814302 - 1.30111i) q^{75} +(3.51827 + 2.57328i) q^{76} +(-5.52233 - 9.56495i) q^{77} +(0.498051 - 7.95799i) q^{78} +(4.74539 + 8.21926i) q^{79} +(1.19924 + 2.07714i) q^{80} +(8.72018 + 2.22676i) q^{81} +(1.30274 + 2.25641i) q^{82} +(-0.715228 + 1.23881i) q^{83} +(2.97659 - 1.47881i) q^{84} +(5.80031 - 10.0464i) q^{85} +(-1.98484 + 3.43785i) q^{86} +(-0.689733 + 11.0207i) q^{87} +(-2.87780 + 4.98450i) q^{88} +(-6.59763 - 11.4274i) q^{89} +(2.79269 + 6.63136i) q^{90} +(-4.41695 - 7.65038i) q^{91} +(0.642555 + 1.11294i) q^{92} +(6.33423 - 3.14693i) q^{93} +(-1.92168 - 3.32844i) q^{94} +(-1.12583 + 10.3939i) q^{95} +(-1.44298 - 0.958029i) q^{96} +(-7.40815 - 12.8313i) q^{97} +(-1.65884 + 2.87319i) q^{98} +(-10.4305 + 13.7604i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 9 q^{2} - 9 q^{4} + 5 q^{7} - 18 q^{8} + 4 q^{9}+O(q^{10}) \) 18 * q + 9 * q^2 - 9 * q^4 + 5 * q^7 - 18 * q^8 + 4 * q^9	\( 18 q + 9 q^{2} - 9 q^{4} + 5 q^{7} - 18 q^{8} + 4 q^{9} + q^{11} + q^{13} + 10 q^{14} - 3 q^{15} - 9 q^{16} - 5 q^{17} - 4 q^{18} + 9 q^{19} - 19 q^{21} + 2 q^{22} - 2 q^{23} + 18 q^{25} + 2 q^{26} - 18 q^{27} + 5 q^{28} + 18 q^{29} + 4 q^{31} + 9 q^{32} - 23 q^{33} - 10 q^{34} + 6 q^{35} - 8 q^{36} + 20 q^{37} + 3 q^{38} + 4 q^{39} - 2 q^{41} - 23 q^{42} + 7 q^{43} + q^{44} + 30 q^{45} - 4 q^{46} - 38 q^{47} + 6 q^{49} + 9 q^{50} + 4 q^{51} + q^{52} - 10 q^{53} - 18 q^{54} + 6 q^{55} - 5 q^{56} - 33 q^{57} + 9 q^{58} + 10 q^{59} + 3 q^{60} - 36 q^{61} - 4 q^{62} + 12 q^{63} + 18 q^{64} - 45 q^{65} - 7 q^{66} + 22 q^{67} - 5 q^{68} - 26 q^{69} + 12 q^{70} + 11 q^{71} - 4 q^{72} + 44 q^{73} + 10 q^{74} - 6 q^{76} - 2 q^{77} + 23 q^{78} + 2 q^{79} + 4 q^{81} - q^{82} - 7 q^{83} - 4 q^{84} - 7 q^{86} + 3 q^{87} - q^{88} + q^{89} + 60 q^{90} - 25 q^{91} - 2 q^{92} + 25 q^{93} - 19 q^{94} + 21 q^{95} - 6 q^{98} - 19 q^{99}+O(q^{100}) \) 18 * q + 9 * q^2 - 9 * q^4 + 5 * q^7 - 18 * q^8 + 4 * q^9 + q^11 + q^13 + 10 * q^14 - 3 * q^15 - 9 * q^16 - 5 * q^17 - 4 * q^18 + 9 * q^19 - 19 * q^21 + 2 * q^22 - 2 * q^23 + 18 * q^25 + 2 * q^26 - 18 * q^27 + 5 * q^28 + 18 * q^29 + 4 * q^31 + 9 * q^32 - 23 * q^33 - 10 * q^34 + 6 * q^35 - 8 * q^36 + 20 * q^37 + 3 * q^38 + 4 * q^39 - 2 * q^41 - 23 * q^42 + 7 * q^43 + q^44 + 30 * q^45 - 4 * q^46 - 38 * q^47 + 6 * q^49 + 9 * q^50 + 4 * q^51 + q^52 - 10 * q^53 - 18 * q^54 + 6 * q^55 - 5 * q^56 - 33 * q^57 + 9 * q^58 + 10 * q^59 + 3 * q^60 - 36 * q^61 - 4 * q^62 + 12 * q^63 + 18 * q^64 - 45 * q^65 - 7 * q^66 + 22 * q^67 - 5 * q^68 - 26 * q^69 + 12 * q^70 + 11 * q^71 - 4 * q^72 + 44 * q^73 + 10 * q^74 - 6 * q^76 - 2 * q^77 + 23 * q^78 + 2 * q^79 + 4 * q^81 - q^82 - 7 * q^83 - 4 * q^84 - 7 * q^86 + 3 * q^87 - q^88 + q^89 + 60 * q^90 - 25 * q^91 - 2 * q^92 + 25 * q^93 - 19 * q^94 + 21 * q^95 - 6 * q^98 - 19 * q^99

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