LMFDB - Embedded newform 315.2.i.e.106.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [315,2,Mod(106,315)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(315, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 0, 0]))

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

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

chi := DirichletCharacter("315.106");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 315 = 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	315.i (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:	$2.51528766367$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - x^{11} + 2 x^{10} - x^{9} - 4 x^{8} + 20 x^{7} - 38 x^{6} + 60 x^{5} - 36 x^{4} - 27 x^{3} + \cdots + 729 $ x^12 - x^11 + 2x^10 - x^9 - 4x^8 + 20x^7 - 38x^6 + 60x^5 - 36x^4 - 27x^3 + 162x^2 - 243*x + 729
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			106.3
Root			$-0.764584 - 1.55416i$ of defining polynomial
Character	$\chi$	$=$	315.106
Dual form			315.2.i.e.211.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.368623 - 0.638475i) q^{2} +(-0.764584 + 1.55416i) q^{3} +(0.728233 + 1.26134i) q^{4} +(0.500000 + 0.866025i) q^{5} +(0.710448 + 1.06107i) q^{6} +(-0.500000 + 0.866025i) q^{7} +2.54827 q^{8} +(-1.83082 - 2.37657i) q^{9} +O(q^{10})$	\(q+(0.368623 - 0.638475i) q^{2} +(-0.764584 + 1.55416i) q^{3} +(0.728233 + 1.26134i) q^{4} +(0.500000 + 0.866025i) q^{5} +(0.710448 + 1.06107i) q^{6} +(-0.500000 + 0.866025i) q^{7} +2.54827 q^{8} +(-1.83082 - 2.37657i) q^{9} +0.737247 q^{10} +(-3.17448 + 5.49836i) q^{11} +(-2.51711 + 0.167393i) q^{12} +(-2.94625 - 5.10305i) q^{13} +(0.368623 + 0.638475i) q^{14} +(-1.72823 + 0.114931i) q^{15} +(-0.517115 + 0.895669i) q^{16} +5.01986 q^{17} +(-2.19226 + 0.292875i) q^{18} -0.158143 q^{19} +(-0.728233 + 1.26134i) q^{20} +(-0.963650 - 1.43923i) q^{21} +(2.34037 + 4.05365i) q^{22} +(3.10641 + 5.38046i) q^{23} +(-1.94837 + 3.96042i) q^{24} +(-0.500000 + 0.866025i) q^{25} -4.34422 q^{26} +(5.09339 - 1.02830i) q^{27} -1.45647 q^{28} +(-0.235416 + 0.407753i) q^{29} +(-0.563687 + 1.14580i) q^{30} +(-0.660163 - 1.14344i) q^{31} +(2.92951 + 5.07406i) q^{32} +(-6.11817 - 9.13760i) q^{33} +(1.85044 - 3.20506i) q^{34} -1.00000 q^{35} +(1.66439 - 4.03998i) q^{36} +9.21792 q^{37} +(-0.0582951 + 0.100970i) q^{38} +(10.1836 - 0.677229i) q^{39} +(1.27413 + 2.20687i) q^{40} +(-1.06624 - 1.84678i) q^{41} +(-1.27413 + 0.0847324i) q^{42} +(1.32442 - 2.29396i) q^{43} -9.24705 q^{44} +(1.14276 - 2.77382i) q^{45} +4.58038 q^{46} +(4.47541 - 7.75164i) q^{47} +(-0.996635 - 1.48849i) q^{48} +(-0.500000 - 0.866025i) q^{49} +(0.368623 + 0.638475i) q^{50} +(-3.83811 + 7.80167i) q^{51} +(4.29111 - 7.43242i) q^{52} -3.52147 q^{53} +(1.22100 - 3.63106i) q^{54} -6.34896 q^{55} +(-1.27413 + 2.20687i) q^{56} +(0.120913 - 0.245779i) q^{57} +(0.173560 + 0.300615i) q^{58} +(3.09358 + 5.35823i) q^{59} +(-1.40352 - 2.09619i) q^{60} +(0.284541 - 0.492840i) q^{61} -0.973406 q^{62} +(2.97358 - 0.397255i) q^{63} +2.25109 q^{64} +(2.94625 - 5.10305i) q^{65} +(-8.08943 + 0.537962i) q^{66} +(-5.27833 - 9.14234i) q^{67} +(3.65563 + 6.33174i) q^{68} +(-10.7372 + 0.714044i) q^{69} +(-0.368623 + 0.638475i) q^{70} +4.75075 q^{71} +(-4.66543 - 6.05614i) q^{72} +1.95043 q^{73} +(3.39794 - 5.88541i) q^{74} +(-0.963650 - 1.43923i) q^{75} +(-0.115165 - 0.199471i) q^{76} +(-3.17448 - 5.49836i) q^{77} +(3.32152 - 6.75161i) q^{78} +(3.45725 - 5.98813i) q^{79} -1.03423 q^{80} +(-2.29617 + 8.70216i) q^{81} -1.57216 q^{82} +(2.17010 - 3.75871i) q^{83} +(1.11359 - 2.26358i) q^{84} +(2.50993 + 4.34733i) q^{85} +(-0.976424 - 1.69122i) q^{86} +(-0.453718 - 0.677636i) q^{87} +(-8.08943 + 14.0113i) q^{88} +3.25273 q^{89} +(-1.34977 - 1.75212i) q^{90} +5.89249 q^{91} +(-4.52438 + 7.83646i) q^{92} +(2.28183 - 0.151746i) q^{93} +(-3.29948 - 5.71487i) q^{94} +(-0.0790713 - 0.136956i) q^{95} +(-10.1258 + 0.673382i) q^{96} +(-2.35084 + 4.07177i) q^{97} -0.737247 q^{98} +(18.8791 - 2.52215i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 3 q^{2} + q^{3} - 11 q^{4} + 6 q^{5} - 6 q^{6} - 6 q^{7} + 6 q^{8} - 3 q^{9}+O(q^{10}) $ 12 * q + 3 * q^2 + q^3 - 11 * q^4 + 6 * q^5 - 6 * q^6 - 6 * q^7 + 6 * q^8 - 3 * q^9	\( 12 q + 3 q^{2} + q^{3} - 11 q^{4} + 6 q^{5} - 6 q^{6} - 6 q^{7} + 6 q^{8} - 3 q^{9} + 6 q^{10} + 7 q^{11} - 37 q^{12} - 10 q^{13} + 3 q^{14} - q^{15} - 13 q^{16} + 14 q^{17} + 24 q^{18} + 30 q^{19} + 11 q^{20} - 2 q^{21} + 7 q^{22} + 14 q^{23} + 6 q^{24} - 6 q^{25} - 26 q^{26} - 2 q^{27} + 22 q^{28} - 13 q^{29} - 9 q^{30} - 10 q^{31} - 18 q^{32} - 14 q^{33} - 15 q^{34} - 12 q^{35} - 4 q^{36} + 42 q^{37} - 4 q^{38} - 11 q^{39} + 3 q^{40} - 4 q^{41} - 3 q^{42} - 13 q^{43} - 78 q^{44} - 30 q^{46} + 8 q^{47} + 42 q^{48} - 6 q^{49} + 3 q^{50} - 19 q^{51} - 31 q^{52} + 20 q^{53} + 84 q^{54} + 14 q^{55} - 3 q^{56} - 22 q^{57} - 3 q^{58} + 21 q^{59} - 17 q^{60} - 2 q^{61} + 50 q^{62} + 3 q^{63} + 62 q^{64} + 10 q^{65} + 19 q^{66} - 6 q^{67} - 33 q^{68} - 19 q^{69} - 3 q^{70} - 58 q^{71} + 51 q^{72} + 16 q^{73} - 5 q^{74} - 2 q^{75} - 31 q^{76} + 7 q^{77} - 5 q^{78} + 22 q^{79} - 26 q^{80} + 21 q^{81} + 36 q^{82} + 5 q^{83} + 20 q^{84} + 7 q^{85} + 23 q^{86} - 19 q^{87} + 19 q^{88} + 2 q^{89} + 9 q^{90} + 20 q^{91} + 9 q^{92} + 31 q^{93} - 31 q^{94} + 15 q^{95} - 66 q^{96} - 32 q^{97} - 6 q^{98} + 38 q^{99}+O(q^{100}) \) 12 * q + 3 * q^2 + q^3 - 11 * q^4 + 6 * q^5 - 6 * q^6 - 6 * q^7 + 6 * q^8 - 3 * q^9 + 6 * q^10 + 7 * q^11 - 37 * q^12 - 10 * q^13 + 3 * q^14 - q^15 - 13 * q^16 + 14 * q^17 + 24 * q^18 + 30 * q^19 + 11 * q^20 - 2 * q^21 + 7 * q^22 + 14 * q^23 + 6 * q^24 - 6 * q^25 - 26 * q^26 - 2 * q^27 + 22 * q^28 - 13 * q^29 - 9 * q^30 - 10 * q^31 - 18 * q^32 - 14 * q^33 - 15 * q^34 - 12 * q^35 - 4 * q^36 + 42 * q^37 - 4 * q^38 - 11 * q^39 + 3 * q^40 - 4 * q^41 - 3 * q^42 - 13 * q^43 - 78 * q^44 - 30 * q^46 + 8 * q^47 + 42 * q^48 - 6 * q^49 + 3 * q^50 - 19 * q^51 - 31 * q^52 + 20 * q^53 + 84 * q^54 + 14 * q^55 - 3 * q^56 - 22 * q^57 - 3 * q^58 + 21 * q^59 - 17 * q^60 - 2 * q^61 + 50 * q^62 + 3 * q^63 + 62 * q^64 + 10 * q^65 + 19 * q^66 - 6 * q^67 - 33 * q^68 - 19 * q^69 - 3 * q^70 - 58 * q^71 + 51 * q^72 + 16 * q^73 - 5 * q^74 - 2 * q^75 - 31 * q^76 + 7 * q^77 - 5 * q^78 + 22 * q^79 - 26 * q^80 + 21 * q^81 + 36 * q^82 + 5 * q^83 + 20 * q^84 + 7 * q^85 + 23 * q^86 - 19 * q^87 + 19 * q^88 + 2 * q^89 + 9 * q^90 + 20 * q^91 + 9 * q^92 + 31 * q^93 - 31 * q^94 + 15 * q^95 - 66 * q^96 - 32 * q^97 - 6 * q^98 + 38 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/315\mathbb{Z}\right)^\times$.

$n$	$127$	$136$	$281$
$\chi(n)$	$1$	$1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	0.368623	−	0.638475i	0.260656	−	0.451470i	−0.705760	−	0.708451i	$-0.749394\pi$
$2$	0.368623	−	0.638475i	0.260656	−	0.451470i	0.966416	+	0.256981i	$0.0827278\pi$
$3$	−0.764584	+	1.55416i	−0.441433	+	0.897294i
$3$	−0.764584	+	1.55416i	−0.441433	+	0.897294i
$4$	0.728233	+	1.26134i	0.364117	+	0.630669i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$6$	0.710448	+	1.06107i	0.290039	+	0.433179i
$7$	−0.500000	+	0.866025i	−0.188982	+	0.327327i
$7$	−0.500000	+	0.866025i	−0.188982	+	0.327327i
$8$	2.54827			0.900949
$9$	−1.83082	−	2.37657i	−0.610274	−	0.792190i
$10$	0.737247			0.233138
$11$	−3.17448	+	5.49836i	−0.957141	+	1.65782i	−0.227751	+	0.973719i	$0.573137\pi$
$11$	−3.17448	+	5.49836i	−0.957141	+	1.65782i	−0.729390	+	0.684098i	$0.760196\pi$
$12$	−2.51711	+	0.167393i	−0.726628	+	0.0483222i
$13$	−2.94625	−	5.10305i	−0.817141	−	1.41533i	−0.907780	−	0.419446i	$-0.862224\pi$
$13$	−2.94625	−	5.10305i	−0.817141	−	1.41533i	0.0906387	−	0.995884i	$-0.471109\pi$
$14$	0.368623	+	0.638475i	0.0985188	+	0.170640i
$15$	−1.72823	+	0.114931i	−0.446228	+	0.0296750i
$16$	−0.517115	+	0.895669i	−0.129279	+	0.223917i
$17$	5.01986			1.21750			0.608748	−	0.793364i	$-0.291672\pi$
$17$	5.01986			1.21750			0.608748	+	0.793364i	$0.291672\pi$
$18$	−2.19226	+	0.292875i	−0.516722	+	0.0690312i
$19$	−0.158143			−0.0362804			−0.0181402	−	0.999835i	$-0.505775\pi$
$19$	−0.158143			−0.0362804			−0.0181402	+	0.999835i	$0.505775\pi$
$20$	−0.728233	+	1.26134i	−0.162838	+	0.282044i
$21$	−0.963650	−	1.43923i	−0.210286	−	0.314065i
$22$	2.34037	+	4.05365i	0.498970	+	0.864241i
$23$	3.10641	+	5.38046i	0.647731	+	1.12190i	0.983664	+	0.180017i	$0.0576152\pi$
$23$	3.10641	+	5.38046i	0.647731	+	1.12190i	−0.335933	+	0.941886i	$0.609051\pi$
$24$	−1.94837	+	3.96042i	−0.397708	+	0.808417i
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	−4.34422			−0.851972
$27$	5.09339	−	1.02830i	0.980223	−	0.197897i
$28$	−1.45647			−0.275246
$29$	−0.235416	+	0.407753i	−0.0437157	+	0.0757178i	−0.887055	−	0.461663i	$-0.847253\pi$
$29$	−0.235416	+	0.407753i	−0.0437157	+	0.0757178i	0.843340	+	0.537381i	$0.180586\pi$
$30$	−0.563687	+	1.14580i	−0.102915	+	0.209193i
$31$	−0.660163	−	1.14344i	−0.118569	−	0.205367i	0.800632	−	0.599156i	$-0.204497\pi$
$31$	−0.660163	−	1.14344i	−0.118569	−	0.205367i	−0.919201	+	0.393789i	$0.871164\pi$
$32$	2.92951	+	5.07406i	0.517869	+	0.896976i
$33$	−6.11817	−	9.13760i	−1.06504	−	1.59065i
$34$	1.85044	−	3.20506i	0.317348	−	0.549663i
$35$	−1.00000			−0.169031
$36$	1.66439	−	4.03998i	0.277398	−	0.673331i
$37$	9.21792			1.51542			0.757708	−	0.652593i	$-0.226319\pi$
$37$	9.21792			1.51542			0.757708	+	0.652593i	$0.226319\pi$
$38$	−0.0582951	+	0.100970i	−0.00945671	+	0.0163795i
$39$	10.1836	−	0.677229i	1.63068	−	0.108443i
$40$	1.27413	+	2.20687i	0.201458	+	0.348936i
$41$	−1.06624	−	1.84678i	−0.166519	−	0.288419i	0.770675	−	0.637229i	$-0.219919\pi$
$41$	−1.06624	−	1.84678i	−0.166519	−	0.288419i	−0.937194	+	0.348810i	$0.886586\pi$
$42$	−1.27413	+	0.0847324i	−0.196603	+	0.0130745i
$43$	1.32442	−	2.29396i	0.201972	−	0.349826i	−0.747192	−	0.664609i	$-0.768598\pi$
$43$	1.32442	−	2.29396i	0.201972	−	0.349826i	0.949164	+	0.314783i	$0.101932\pi$
$44$	−9.24705			−1.39404
$45$	1.14276	−	2.77382i	0.170352	−	0.413497i
$46$	4.58038			0.675340
$47$	4.47541	−	7.75164i	0.652806	−	1.13069i	−0.329633	−	0.944109i	$-0.606925\pi$
$47$	4.47541	−	7.75164i	0.652806	−	1.13069i	0.982439	−	0.186584i	$-0.0597417\pi$
$48$	−0.996635	−	1.48849i	−0.143852	−	0.214845i
$49$	−0.500000	−	0.866025i	−0.0714286	−	0.123718i
$50$	0.368623	+	0.638475i	0.0521312	+	0.0902939i
$51$	−3.83811	+	7.80167i	−0.537442	+	1.09245i
$52$	4.29111	−	7.43242i	0.595070	−	1.03069i
$53$	−3.52147			−0.483710			−0.241855	−	0.970312i	$-0.577756\pi$
$53$	−3.52147			−0.483710			−0.241855	+	0.970312i	$0.577756\pi$
$54$	1.22100	−	3.63106i	0.166156	−	0.494124i
$55$	−6.34896			−0.856093
$56$	−1.27413	+	2.20687i	−0.170263	+	0.294905i
$57$	0.120913	−	0.245779i	0.0160154	−	0.0325542i
$58$	0.173560	+	0.300615i	0.0227895	+	0.0394726i
$59$	3.09358	+	5.35823i	0.402749	+	0.697582i	0.994057	−	0.108864i	$-0.0347213\pi$
$59$	3.09358	+	5.35823i	0.402749	+	0.697582i	−0.591307	+	0.806446i	$0.701388\pi$
$60$	−1.40352	−	2.09619i	−0.181194	−	0.270617i
$61$	0.284541	−	0.492840i	0.0364318	−	0.0631017i	−0.847235	−	0.531219i	$-0.821734\pi$
$61$	0.284541	−	0.492840i	0.0364318	−	0.0631017i	0.883666	+	0.468117i	$0.155068\pi$
$62$	−0.973406			−0.123623
$63$	2.97358	−	0.397255i	0.374636	−	0.0500494i
$64$	2.25109			0.281386
$65$	2.94625	−	5.10305i	0.365437	−	0.632955i
$66$	−8.08943	+	0.537962i	−0.995740	+	0.0662186i
$67$	−5.27833	−	9.14234i	−0.644851	−	1.11691i	−0.984336	−	0.176303i	$-0.943586\pi$
$67$	−5.27833	−	9.14234i	−0.644851	−	1.11691i	0.339485	−	0.940612i	$-0.389747\pi$
$68$	3.65563	+	6.33174i	0.443311	+	0.767837i
$69$	−10.7372	+	0.714044i	−1.29261	+	0.0859608i
$70$	−0.368623	+	0.638475i	−0.0440589	+	0.0763123i
$71$	4.75075			0.563810			0.281905	−	0.959442i	$-0.409034\pi$
$71$	4.75075			0.563810			0.281905	+	0.959442i	$0.409034\pi$
$72$	−4.66543	−	6.05614i	−0.549826	−	0.713723i
$73$	1.95043			0.228281			0.114140	−	0.993465i	$-0.463589\pi$
$73$	1.95043			0.228281			0.114140	+	0.993465i	$0.463589\pi$
$74$	3.39794	−	5.88541i	0.395003	−	0.684165i
$75$	−0.963650	−	1.43923i	−0.111273	−	0.166188i
$76$	−0.115165	−	0.199471i	−0.0132103	−	0.0228809i
$77$	−3.17448	−	5.49836i	−0.361765	−	0.626596i
$78$	3.32152	−	6.75161i	0.376088	−	0.764469i
$79$	3.45725	−	5.98813i	0.388971	−	0.673717i	−0.603341	−	0.797483i	$-0.706164\pi$
$79$	3.45725	−	5.98813i	0.388971	−	0.673717i	0.992311	+	0.123767i	$0.0394974\pi$
$80$	−1.03423			−0.115630
$81$	−2.29617	+	8.70216i	−0.255130	+	0.966907i
$82$	−1.57216			−0.173616
$83$	2.17010	−	3.75871i	0.238199	−	0.412573i	−0.721999	−	0.691894i	$-0.756776\pi$
$83$	2.17010	−	3.75871i	0.238199	−	0.412573i	0.960198	+	0.279322i	$0.0901097\pi$
$84$	1.11359	−	2.26358i	0.121503	−	0.246977i
$85$	2.50993	+	4.34733i	0.272240	+	0.471534i
$86$	−0.976424	−	1.69122i	−0.105291	−	0.182369i
$87$	−0.453718	−	0.677636i	−0.0486436	−	0.0726502i
$88$	−8.08943	+	14.0113i	−0.862336	+	1.49361i
$89$	3.25273			0.344789			0.172394	−	0.985028i	$-0.444850\pi$
$89$	3.25273			0.344789			0.172394	+	0.985028i	$0.444850\pi$
$90$	−1.34977	−	1.75212i	−0.142278	−	0.184690i
$91$	5.89249			0.617701
$92$	−4.52438	+	7.83646i	−0.471699	+	0.817007i
$93$	2.28183	−	0.151746i	0.236615	−	0.0157353i
$94$	−3.29948	−	5.71487i	−0.340316	−	0.589444i
$95$	−0.0790713	−	0.136956i	−0.00811255	−	0.0140513i
$96$	−10.1258	+	0.673382i	−1.03346	+	0.0687268i
$97$	−2.35084	+	4.07177i	−0.238691	+	0.413426i	−0.960339	−	0.278835i	$-0.910052\pi$
$97$	−2.35084	+	4.07177i	−0.238691	+	0.413426i	0.721648	+	0.692261i	$0.243385\pi$
$98$	−0.737247			−0.0744732
$99$	18.8791	−	2.52215i	1.89743	−	0.253486i
$100$	−1.45647			−0.145647
$101$	−3.70182	+	6.41173i	−0.368344	+	0.637991i	−0.989307	−	0.145849i	$-0.953409\pi$
$101$	−3.70182	+	6.41173i	−0.368344	+	0.637991i	0.620962	+	0.783840i	$0.286742\pi$
$102$	3.56635	+	5.32641i	0.353121	+	0.527393i
$103$	−2.28454	−	3.95694i	−0.225103	−	0.389889i	0.731248	−	0.682112i	$-0.238938\pi$
$103$	−2.28454	−	3.95694i	−0.225103	−	0.389889i	−0.956350	+	0.292223i	$0.905605\pi$
$104$	−7.50783	−	13.0039i	−0.736203	−	1.27514i
$105$	0.764584	−	1.55416i	0.0746157	−	0.151670i
$106$	−1.29809	+	2.24837i	−0.126082	+	0.218381i
$107$	−10.9237			−1.05603			−0.528015	−	0.849235i	$-0.677063\pi$
$107$	−10.9237			−1.05603			−0.528015	+	0.849235i	$0.677063\pi$
$108$	5.00621	+	5.67563i	0.481723	+	0.546138i
$109$	8.86010			0.848643			0.424322	−	0.905512i	$-0.360513\pi$
$109$	8.86010			0.848643			0.424322	+	0.905512i	$0.360513\pi$
$110$	−2.34037	+	4.05365i	−0.223146	+	0.386500i
$111$	−7.04787	+	14.3261i	−0.668954	+	1.35978i
$112$	−0.517115	−	0.895669i	−0.0488628	−	0.0846328i
$113$	0.670817	+	1.16189i	0.0631052	+	0.109301i	0.895852	−	0.444353i	$-0.146566\pi$
$113$	0.670817	+	1.16189i	0.0631052	+	0.109301i	−0.832747	+	0.553654i	$0.813233\pi$
$114$	−0.112352	−	0.167800i	−0.0105227	−	0.0157159i
$115$	−3.10641	+	5.38046i	−0.289674	+	0.501730i
$116$	−0.685752			−0.0636705
$117$	−6.73369	+	16.3447i	−0.622530	+	1.51107i
$118$	4.56146			0.419916
$119$	−2.50993	+	4.34733i	−0.230085	+	0.398519i
$120$	−4.40400	+	0.292875i	−0.402029	+	0.0267357i
$121$	−14.6546	−	25.3826i	−1.33224	−	2.30751i
$122$	−0.209777	−	0.363345i	−0.0189923	−	0.0328957i
$123$	3.68542	−	0.245088i	0.332303	−	0.0220988i
$124$	0.961506	−	1.66538i	0.0863458	−	0.149555i
$125$	−1.00000			−0.0894427
$126$	0.842495	−	2.04499i	0.0750554	−	0.182183i
$127$	20.6070			1.82857			0.914287	−	0.405067i	$-0.132752\pi$
$127$	20.6070			1.82857			0.914287	+	0.405067i	$0.132752\pi$
$128$	−5.02922	+	8.71086i	−0.444524	+	0.769939i
$129$	2.55255	+	3.81229i	0.224740	+	0.335653i
$130$	−2.17211	−	3.76221i	−0.190507	−	0.329967i
$131$	−5.52136	−	9.56328i	−0.482404	−	0.835548i	0.517392	−	0.855748i	$-0.326903\pi$
$131$	−5.52136	−	9.56328i	−0.482404	−	0.835548i	−0.999796	+	0.0202007i	$0.993569\pi$
$132$	7.07014	−	14.3714i	0.615377	−	1.25087i
$133$	0.0790713	−	0.136956i	0.00685635	−	0.0118756i
$134$	−7.78287			−0.672338
$135$	3.43723	+	3.89685i	0.295830	+	0.335387i
$136$	12.7920			1.09690
$137$	7.14983	−	12.3839i	0.610852	−	1.05803i	−0.380246	−	0.924886i	$-0.624161\pi$
$137$	7.14983	−	12.3839i	0.610852	−	1.05803i	0.991097	−	0.133140i	$-0.0425061\pi$
$138$	−3.50208	+	7.11864i	−0.298117	+	0.605979i
$139$	9.69800	+	16.7974i	0.822574	+	1.42474i	0.903759	+	0.428041i	$0.140796\pi$
$139$	9.69800	+	16.7974i	0.822574	+	1.42474i	−0.0811854	+	0.996699i	$0.525871\pi$
$140$	−0.728233	−	1.26134i	−0.0615470	−	0.106602i
$141$	8.62546	+	12.8823i	0.726395	+	1.08488i
$142$	1.75124	−	3.03323i	0.146961	−	0.254543i
$143$	37.4112			3.12848
$144$	3.07537	−	0.410853i	0.256281	−	0.0342377i
$145$	−0.470833			−0.0391005
$146$	0.718975	−	1.24530i	0.0595028	−	0.103062i
$147$	1.72823	−	0.114931i	0.142542	−	0.00947933i
$148$	6.71280	+	11.6269i	0.551789	+	0.955726i
$149$	7.79033	+	13.4932i	0.638209	+	1.10541i	0.985826	+	0.167773i	$0.0536576\pi$
$149$	7.79033	+	13.4932i	0.638209	+	1.10541i	−0.347617	+	0.937637i	$0.613009\pi$
$150$	−1.27413	+	0.0847324i	−0.104033	+	0.00691837i
$151$	−2.45849	+	4.25822i	−0.200069	+	0.346529i	−0.948550	−	0.316626i	$-0.897450\pi$
$151$	−2.45849	+	4.25822i	−0.200069	+	0.346529i	0.748482	+	0.663156i	$0.230783\pi$
$152$	−0.402990			−0.0326868
$153$	−9.19049	−	11.9301i	−0.743007	−	0.964488i
$154$	−4.68075			−0.377186
$155$	0.660163	−	1.14344i	0.0530256	−	0.0918430i
$156$	8.27025	+	12.3518i	0.662150	+	0.988933i
$157$	−10.4238	−	18.0545i	−0.831908	−	1.44091i	−0.896523	−	0.442997i	$-0.853915\pi$
$157$	−10.4238	−	18.0545i	−0.831908	−	1.44091i	0.0646152	−	0.997910i	$-0.479418\pi$
$158$	−2.54884	−	4.41473i	−0.202775	−	0.351217i
$159$	2.69246	−	5.47292i	0.213526	−	0.434031i
$160$	−2.92951	+	5.07406i	−0.231598	+	0.401140i
$161$	−6.21282			−0.489639
$162$	4.70969	+	4.67387i	0.370028	+	0.367214i
$163$	−24.9758			−1.95626			−0.978128	−	0.208006i	$-0.933303\pi$
$163$	−24.9758			−1.95626			−0.978128	+	0.208006i	$0.933303\pi$
$164$	1.55294	−	2.68978i	0.121264	−	0.210036i
$165$	4.85431	−	9.86729i	0.377907	−	0.768168i
$166$	−1.59990	−	2.77110i	−0.124176	−	0.215079i
$167$	0.210696	+	0.364936i	0.0163041	+	0.0282396i	0.874062	−	0.485814i	$-0.161477\pi$
$167$	0.210696	+	0.364936i	0.0163041	+	0.0282396i	−0.857758	+	0.514053i	$0.828143\pi$
$168$	−2.45564	−	3.66754i	−0.189457	−	0.282957i
$169$	−10.8607	+	18.8113i	−0.835440	+	1.44702i
$170$	3.70088			0.283845
$171$	0.289531	+	0.375837i	0.0221410	+	0.0287410i
$172$	3.85795			0.294166
$173$	1.43298	−	2.48200i	0.108948	−	0.188703i	−0.806397	−	0.591375i	$-0.798585\pi$
$173$	1.43298	−	2.48200i	0.108948	−	0.188703i	0.915344	+	0.402672i	$0.131919\pi$
$174$	−0.599904	+	0.0398948i	−0.0454786	+	0.00302441i
$175$	−0.500000	−	0.866025i	−0.0377964	−	0.0654654i
$176$	−3.28314	−	5.68657i	−0.247476	−	0.428641i
$177$	−10.6928	+	0.711095i	−0.803723	+	0.0534491i
$178$	1.19903	−	2.07679i	0.0898713	−	0.155662i
$179$	−2.75693			−0.206063			−0.103031	−	0.994678i	$-0.532854\pi$
$179$	−2.75693			−0.206063			−0.103031	+	0.994678i	$0.532854\pi$
$180$	4.33092	−	0.578588i	0.322808	−	0.0431254i
$181$	−15.8921			−1.18125			−0.590626	−	0.806945i	$-0.701119\pi$
$181$	−15.8921			−1.18125			−0.590626	+	0.806945i	$0.701119\pi$
$182$	2.17211	−	3.76221i	0.161008	−	0.278873i
$183$	0.548396	+	0.819040i	0.0405386	+	0.0605451i
$184$	7.91597	+	13.7109i	0.583573	+	1.01078i
$185$	4.60896	+	7.98295i	0.338858	+	0.586918i
$186$	0.744251	−	1.51283i	0.0545711	−	0.110926i
$187$	−15.9355	+	27.6010i	−1.16532	+	2.01839i
$188$	13.0366			0.950790
$189$	−1.65616	+	4.92515i	−0.120468	+	0.358252i
$190$	−0.116590			−0.00845834
$191$	1.57006	−	2.71942i	0.113605	−	0.196770i	−0.803616	−	0.595148i	$-0.797093\pi$
$191$	1.57006	−	2.71942i	0.113605	−	0.196770i	0.917221	+	0.398378i	$0.130427\pi$
$192$	−1.72114	+	3.49855i	−0.124213	+	0.252486i
$193$	−0.651093	−	1.12773i	−0.0468667	−	0.0811755i	0.841640	−	0.540038i	$-0.181590\pi$
$193$	−0.651093	−	1.12773i	−0.0468667	−	0.0811755i	−0.888507	+	0.458863i	$0.848257\pi$
$194$	1.73315	+	3.00190i	0.124433	+	0.215524i
$195$	5.67830	+	8.48064i	0.406631	+	0.607311i
$196$	0.728233	−	1.26134i	0.0520167	−	0.0900955i
$197$	−8.39417			−0.598060			−0.299030	−	0.954244i	$-0.596663\pi$
$197$	−8.39417			−0.598060			−0.299030	+	0.954244i	$0.596663\pi$
$198$	5.34897	−	12.9836i	0.380134	−	0.922703i
$199$	−12.3178			−0.873186			−0.436593	−	0.899659i	$-0.643815\pi$
$199$	−12.3178			−0.873186			−0.436593	+	0.899659i	$0.643815\pi$
$200$	−1.27413	+	2.20687i	−0.0900949	+	0.156049i
$201$	18.2444	−	1.21329i	1.28686	−	0.0855786i
$202$	2.72915	+	4.72703i	0.192022	+	0.332593i
$203$	−0.235416	−	0.407753i	−0.0165230	−	0.0286186i
$204$	−12.6356	+	0.840290i	−0.884667	+	0.0588321i
$205$	1.06624	−	1.84678i	0.0744694	−	0.128985i
$206$	−3.36854			−0.234697
$207$	7.09975	−	17.2333i	0.493467	−	1.19779i
$208$	6.09419			0.422556
$209$	0.502020	−	0.869525i	0.0347255	−	0.0601463i
$210$	−0.710448	−	1.06107i	−0.0490256	−	0.0732206i
$211$	11.7357	+	20.3269i	0.807920	+	1.39936i	0.914302	+	0.405034i	$0.132740\pi$
$211$	11.7357	+	20.3269i	0.807920	+	1.39936i	−0.106382	+	0.994325i	$0.533927\pi$
$212$	−2.56445	−	4.44176i	−0.176127	−	0.305061i
$213$	−3.63235	+	7.38342i	−0.248884	+	0.505904i
$214$	−4.02671	+	6.97447i	−0.275261	+	0.476765i
$215$	2.64884			0.180649
$216$	12.9793	−	2.62040i	0.883131	−	0.178296i
$217$	1.32033			0.0896296
$218$	3.26604	−	5.65695i	0.221204	−	0.383137i
$219$	−1.49127	+	3.03128i	−0.100771	+	0.204835i
$220$	−4.62352	−	8.00818i	−0.311718	−	0.539911i
$221$	−14.7897	−	25.6166i	−0.994866	−	1.72316i
$222$	6.54885	+	9.78083i	0.439530	+	0.656446i
$223$	−11.4284	+	19.7946i	−0.765303	+	1.32554i	0.174783	+	0.984607i	$0.444078\pi$
$223$	−11.4284	+	19.7946i	−0.765303	+	1.32554i	−0.940086	+	0.340937i	$0.889256\pi$
$224$	−5.85902			−0.391472
$225$	2.97358	−	0.397255i	0.198239	−	0.0264836i
$226$	0.989116			0.0657950
$227$	−4.02594	+	6.97313i	−0.267211	+	0.462823i	−0.968141	−	0.250408i	$-0.919435\pi$
$227$	−4.02594	+	6.97313i	−0.267211	+	0.462823i	0.700930	+	0.713230i	$0.252769\pi$
$228$	0.398063	−	0.0264720i	0.0263624	−	0.00175315i
$229$	−13.1344	−	22.7495i	−0.867947	−	1.50333i	−0.864091	−	0.503335i	$-0.832106\pi$
$229$	−13.1344	−	22.7495i	−0.867947	−	1.50333i	−0.00385544	−	0.999993i	$-0.501227\pi$
$230$	2.29019	+	3.96673i	0.151011	+	0.261558i
$231$	10.9725	−	0.729691i	0.721936	−	0.0480101i
$232$	−0.599904	+	1.03906i	−0.0393856	+	0.0682179i
$233$	11.3153			0.741290			0.370645	−	0.928775i	$-0.379137\pi$
$233$	11.3153			0.741290			0.370645	+	0.928775i	$0.379137\pi$
$234$	7.95350	+	10.3243i	0.519937	+	0.674923i
$235$	8.95082			0.583887
$236$	−4.50569	+	7.80409i	−0.293296	+	0.508003i
$237$	6.66315	+	9.95153i	0.432818	+	0.646422i
$238$	1.85044	+	3.20506i	0.119946	+	0.207753i
$239$	−9.68147	−	16.7688i	−0.626242	−	1.08468i	−0.988299	−	0.152528i	$-0.951259\pi$
$239$	−9.68147	−	16.7688i	−0.626242	−	1.08468i	0.362057	−	0.932156i	$-0.382075\pi$
$240$	0.790755	−	1.60736i	0.0510430	−	0.103755i
$241$	5.38815	−	9.33255i	0.347081	−	0.601162i	−0.638648	−	0.769499i	$-0.720506\pi$
$241$	5.38815	−	9.33255i	0.347081	−	0.601162i	0.985730	+	0.168336i	$0.0538395\pi$
$242$	−21.6082			−1.38903
$243$	−11.7689	−	10.2221i	−0.754977	−	0.655751i
$244$	0.828850			0.0530617
$245$	0.500000	−	0.866025i	0.0319438	−	0.0553283i
$246$	1.20205	−	2.44339i	0.0766400	−	0.155785i
$247$	0.465927	+	0.807009i	0.0296462	+	0.0513488i
$248$	−1.68227	−	2.91378i	−0.106824	−	0.185025i
$249$	4.18242	+	6.24653i	0.265050	+	0.395858i
$250$	−0.368623	+	0.638475i	−0.0233138	+	0.0403807i
$251$	−26.0826			−1.64632			−0.823160	−	0.567809i	$-0.807791\pi$
$251$	−26.0826			−1.64632			−0.823160	+	0.567809i	$0.807791\pi$
$252$	2.66653	+	3.46140i	0.167976	+	0.218047i
$253$	−39.4449			−2.47988
$254$	7.59622	−	13.1570i	0.476629	−	0.825546i
$255$	−8.67550	+	0.576937i	−0.543281	+	0.0361292i
$256$	5.95886	+	10.3211i	0.372429	+	0.645066i
$257$	4.00425	+	6.93557i	0.249778	+	0.432629i	0.963464	−	0.267837i	$-0.0863089\pi$
$257$	4.00425	+	6.93557i	0.249778	+	0.432629i	−0.713686	+	0.700466i	$0.752976\pi$
$258$	3.37498	−	0.224443i	0.210117	−	0.0139732i
$259$	−4.60896	+	7.98295i	−0.286387	+	0.496037i
$260$	8.58222			0.532247
$261$	1.40006	−	0.187040i	0.0866615	−	0.0115775i
$262$	−8.14122			−0.502966
$263$	−10.7968	+	18.7005i	−0.665757	+	1.15312i	0.313323	+	0.949647i	$0.398558\pi$
$263$	−10.7968	+	18.7005i	−0.665757	+	1.15312i	−0.979080	+	0.203478i	$0.934776\pi$
$264$	−15.5907	−	23.2851i	−0.959544	−	1.43310i
$265$	−1.76073	−	3.04968i	−0.108161	−	0.187340i
$266$	−0.0582951	−	0.100970i	−0.00357430	−	0.00619087i
$267$	−2.48699	+	5.05526i	−0.152201	+	0.309377i
$268$	7.68772	−	13.3155i	0.469602	−	0.813375i
$269$	−2.64506			−0.161272			−0.0806362	−	0.996744i	$-0.525695\pi$
$269$	−2.64506			−0.161272			−0.0806362	+	0.996744i	$0.525695\pi$
$270$	3.75508	−	0.758115i	0.228527	−	0.0461374i
$271$	19.8774			1.20747			0.603734	−	0.797186i	$-0.293679\pi$
$271$	19.8774			1.20747			0.603734	+	0.797186i	$0.293679\pi$
$272$	−2.59585	+	4.49614i	−0.157396	+	0.272618i
$273$	−4.50530	+	9.15787i	−0.272673	+	0.554259i
$274$	−5.27119	−	9.12997i	−0.318444	−	0.551562i
$275$	−3.17448	−	5.49836i	−0.191428	−	0.331563i
$276$	−8.71984	−	13.0232i	−0.524872	−	0.783907i
$277$	4.44972	−	7.70713i	0.267358	−	0.463077i	−0.700821	−	0.713337i	$-0.747183\pi$
$277$	4.44972	−	7.70713i	0.267358	−	0.463077i	0.968179	+	0.250260i	$0.0805162\pi$
$278$	14.2996			0.857636
$279$	−1.50881	+	3.66235i	−0.0903303	+	0.219259i
$280$	−2.54827			−0.152288
$281$	13.5680	−	23.5004i	0.809398	−	1.40192i	−0.103883	−	0.994590i	$-0.533127\pi$
$281$	13.5680	−	23.5004i	0.809398	−	1.40192i	0.913281	−	0.407329i	$-0.133540\pi$
$282$	11.4046	−	0.758425i	0.679132	−	0.0451635i
$283$	−4.63018	−	8.01971i	−0.275236	−	0.476722i	0.694959	−	0.719050i	$-0.255423\pi$
$283$	−4.63018	−	8.01971i	−0.275236	−	0.476722i	−0.970195	+	0.242327i	$0.922089\pi$
$284$	3.45966	+	5.99230i	0.205293	+	0.355578i
$285$	0.273307	−	0.0181755i	0.0161893	−	0.00107662i
$286$	13.7906	−	23.8861i	0.815457	−	1.41241i
$287$	2.13248			0.125876
$288$	6.69545	−	16.2519i	0.394533	−	0.957652i
$289$	8.19904			0.482296
$290$	−0.173560	+	0.300615i	−0.0101918	+	0.0176527i
$291$	−4.53077	−	6.76679i	−0.265598	−	0.396676i
$292$	1.42037	+	2.46015i	0.0831209	+	0.143970i
$293$	0.0998078	+	0.172872i	0.00583083	+	0.0100993i	0.868926	−	0.494942i	$-0.164811\pi$
$293$	0.0998078	+	0.172872i	0.00583083	+	0.0100993i	−0.863095	+	0.505041i	$0.831477\pi$
$294$	0.563687	−	1.14580i	0.0328749	−	0.0668244i
$295$	−3.09358	+	5.35823i	−0.180115	+	0.311968i
$296$	23.4898			1.36531
$297$	−10.5149	+	31.2696i	−0.610134	+	1.81445i
$298$	11.4868			0.665412
$299$	18.3045	−	31.7043i	1.05858	−	1.83351i
$300$	1.11359	−	2.26358i	0.0642932	−	0.130688i
$301$	1.32442	+	2.29396i	0.0763383	+	0.132222i
$302$	1.81251	+	3.13936i	0.104298	+	0.180650i
$303$	−7.13451	−	10.6555i	−0.409867	−	0.612143i
$304$	0.0817779	−	0.141643i	0.00469028	−	0.00812381i
$305$	0.569082			0.0325856
$306$	−11.0049	+	1.47019i	−0.629106	+	0.0840452i
$307$	3.59108			0.204954			0.102477	−	0.994735i	$-0.467323\pi$
$307$	3.59108			0.204954			0.102477	+	0.994735i	$0.467323\pi$
$308$	4.62352	−	8.00818i	0.263450	−	0.456308i
$309$	7.89644	−	0.525128i	0.449213	−	0.0298735i
$310$	−0.486703	−	0.842995i	−0.0276429	−	0.0478789i
$311$	1.98655	+	3.44080i	0.112647	+	0.195110i	0.916837	−	0.399263i	$-0.130734\pi$
$311$	1.98655	+	3.44080i	0.112647	+	0.195110i	−0.804190	+	0.594372i	$0.797401\pi$
$312$	25.9506	−	1.72576i	1.46916	−	0.0977020i
$313$	−9.53097	+	16.5081i	−0.538722	+	0.933094i	0.460251	+	0.887789i	$0.347759\pi$
$313$	−9.53097	+	16.5081i	−0.538722	+	0.933094i	−0.998973	+	0.0453051i	$0.985574\pi$
$314$	−15.3698			−0.867368
$315$	1.83082	+	2.37657i	0.103155	+	0.133905i
$316$	10.0707			0.566523
$317$	4.22804	−	7.32319i	0.237471	−	0.411311i	−0.722517	−	0.691353i	$-0.757015\pi$
$317$	4.22804	−	7.32319i	0.237471	−	0.411311i	0.959988	+	0.280042i	$0.0903483\pi$
$318$	−2.50182	−	3.73651i	−0.140295	−	0.209533i
$319$	−1.49465	−	2.58881i	−0.0836842	−	0.144945i
$320$	1.12554	+	1.94950i	0.0629198	+	0.108980i
$321$	8.35205	−	16.9771i	0.466166	−	0.947569i
$322$	−2.29019	+	3.96673i	−0.127627	+	0.221057i
$323$	−0.793855			−0.0441712
$324$	−12.6485	+	3.44096i	−0.702695	+	0.191164i
$325$	5.89249			0.326857
$326$	−9.20666	+	15.9464i	−0.509910	+	0.883190i
$327$	−6.77429	+	13.7700i	−0.374619	+	0.761483i
$328$	−2.71707	−	4.70610i	−0.150025	−	0.259851i
$329$	4.47541	+	7.75164i	0.246737	+	0.427362i
$330$	−4.51060	−	6.73667i	−0.248301	−	0.370841i
$331$	6.25479	−	10.8336i	0.343794	−	0.595469i	−0.641340	−	0.767257i	$-0.721621\pi$
$331$	6.25479	−	10.8336i	0.343794	−	0.595469i	0.985134	+	0.171788i	$0.0549543\pi$
$332$	6.32134			0.346929
$333$	−16.8764	−	21.9070i	−0.924820	−	1.20050i
$334$	0.310669			0.0169991
$335$	5.27833	−	9.14234i	0.288386	−	0.499500i
$336$	1.78739	−	0.118865i	0.0975101	−	0.00648461i
$337$	−7.62337	−	13.2041i	−0.415271	−	0.719271i	0.580186	−	0.814484i	$-0.302980\pi$
$337$	−7.62337	−	13.2041i	−0.415271	−	0.719271i	−0.995457	+	0.0952134i	$0.969647\pi$
$338$	8.00703	+	13.8686i	0.435525	+	0.754352i
$339$	−2.31866	+	0.154195i	−0.125932	+	0.00837473i
$340$	−3.65563	+	6.33174i	−0.198255	+	0.343387i
$341$	8.38269			0.453948
$342$	0.346690	−	0.0463160i	0.0187469	−	0.00250448i
$343$	1.00000			0.0539949
$344$	3.37498	−	5.84563i	0.181967	−	0.315175i
$345$	−5.98698	−	8.94166i	−0.322328	−	0.481403i
$346$	−1.05646	−	1.82984i	−0.0567957	−	0.0983730i
$347$	−11.7438	−	20.3408i	−0.630438	−	1.09195i	−0.987462	−	0.157855i	$-0.949542\pi$
$347$	−11.7438	−	20.3408i	−0.630438	−	1.09195i	0.357024	−	0.934095i	$-0.383791\pi$
$348$	0.524315	−	1.06577i	0.0281062	−	0.0571312i
$349$	4.90822	−	8.50129i	0.262731	−	0.455064i	−0.704236	−	0.709966i	$-0.748710\pi$
$349$	4.90822	−	8.50129i	0.262731	−	0.455064i	0.966967	+	0.254903i	$0.0820435\pi$
$350$	−0.737247			−0.0394075
$351$	−20.2539	−	22.9621i	−1.08107	−	1.22563i
$352$	−37.1987			−1.98270
$353$	−5.31351	+	9.20327i	−0.282810	+	0.489841i	−0.972076	−	0.234668i	$-0.924600\pi$
$353$	−5.31351	+	9.20327i	−0.282810	+	0.489841i	0.689266	+	0.724508i	$0.257933\pi$
$354$	−3.48762	+	7.08924i	−0.185365	+	0.376789i
$355$	2.37538	+	4.11427i	0.126072	+	0.218363i
$356$	2.36875	+	4.10279i	0.125543	+	0.217447i
$357$	−4.83739	−	7.22473i	−0.256022	−	0.382373i
$358$	−1.01627	+	1.76023i	−0.0537115	+	0.0930310i
$359$	6.63407			0.350133			0.175067	−	0.984557i	$-0.443986\pi$
$359$	6.63407			0.350133			0.175067	+	0.984557i	$0.443986\pi$
$360$	2.91206	−	7.06845i	0.153479	−	0.372540i
$361$	−18.9750			−0.998684
$362$	−5.85821	+	10.1467i	−0.307901	+	0.533300i
$363$	50.6532	−	3.36854i	2.65861	−	0.176802i
$364$	4.29111	+	7.43242i	0.224915	+	0.389565i
$365$	0.975216	+	1.68912i	0.0510451	+	0.0884128i
$366$	0.725088	−	0.0482197i	0.0379009	−	0.00252048i
$367$	16.2821	−	28.2014i	0.849919	−	1.47210i	−0.0313613	−	0.999508i	$-0.509984\pi$
$367$	16.2821	−	28.2014i	0.849919	−	1.47210i	0.881280	−	0.472594i	$-0.156682\pi$
$368$	−6.42548			−0.334951
$369$	−2.43691	+	5.91512i	−0.126860	+	0.307929i
$370$	6.79588			0.353301
$371$	1.76073	−	3.04968i	0.0914127	−	0.158331i
$372$	1.85311	+	2.76765i	0.0960792	+	0.143496i
$373$	13.0637	+	22.6270i	0.676413	+	1.17158i	0.976054	+	0.217530i	$0.0697998\pi$
$373$	13.0637	+	22.6270i	0.676413	+	1.17158i	−0.299641	+	0.954052i	$0.596867\pi$
$374$	11.7484	+	20.3488i	0.607493	+	1.05221i
$375$	0.764584	−	1.55416i	0.0394829	−	0.0802565i
$376$	11.4046	−	19.7533i	0.588145	−	1.01870i
$377$	2.77438			0.142888
$378$	2.53409	+	2.87294i	0.130339	+	0.147768i
$379$	1.74316			0.0895402			0.0447701	−	0.998997i	$-0.485744\pi$
$379$	1.74316			0.0895402			0.0447701	+	0.998997i	$0.485744\pi$
$380$	0.115165	−	0.199471i	0.00590783	−	0.0102327i
$381$	−15.7558	+	32.0265i	−0.807192	+	1.64077i
$382$	−1.15752	−	2.00488i	−0.0592239	−	0.102579i
$383$	−16.6075	−	28.7651i	−0.848605	−	1.46983i	−0.882453	−	0.470401i	$-0.844109\pi$
$383$	−16.6075	−	28.7651i	−0.848605	−	1.46983i	0.0338474	−	0.999427i	$-0.489224\pi$
$384$	−9.69281	−	14.4764i	−0.494634	−	0.738745i
$385$	3.17448	−	5.49836i	0.161786	−	0.280222i
$386$	−0.960032			−0.0488643
$387$	−7.87654	+	1.05226i	−0.400387	+	0.0534896i
$388$	−6.84784			−0.347646
$389$	−10.0431	+	17.3952i	−0.509206	+	0.881970i	0.490738	+	0.871307i	$0.336727\pi$
$389$	−10.0431	+	17.3952i	−0.509206	+	0.881970i	−0.999943	+	0.0106625i	$0.996606\pi$
$390$	7.50783	−	0.499285i	0.380174	−	0.0252823i
$391$	15.5937	+	27.0092i	0.788610	+	1.36591i
$392$	−1.27413	−	2.20687i	−0.0643535	−	0.111464i
$393$	19.0844	−	1.26915i	0.962681	−	0.0640201i
$394$	−3.09429	+	5.35946i	−0.155888	+	0.270006i
$395$	6.91449			0.347906
$396$	16.9297	+	21.9763i	0.850750	+	1.10435i
$397$	24.8513			1.24725			0.623625	−	0.781724i	$-0.285659\pi$
$397$	24.8513			1.24725			0.623625	+	0.781724i	$0.285659\pi$
$398$	−4.54063	+	7.86461i	−0.227601	+	0.394217i
$399$	0.152394	+	0.227603i	0.00762925	+	0.0113944i
$400$	−0.517115	−	0.895669i	−0.0258557	−	0.0447835i
$401$	4.74340	+	8.21582i	0.236874	+	0.410278i	0.959816	−	0.280631i	$-0.0905437\pi$
$401$	4.74340	+	8.21582i	0.236874	+	0.410278i	−0.722941	+	0.690909i	$0.757210\pi$
$402$	5.95066	−	12.0958i	0.296792	−	0.603285i
$403$	−3.89000	+	6.73768i	−0.193775	+	0.335628i
$404$	−10.7831			−0.536481
$405$	−8.68438	+	2.36254i	−0.431530	+	0.117395i
$406$	−0.347120			−0.0172273
$407$	−29.2621	+	50.6834i	−1.45047	+	2.51228i
$408$	−9.78053	+	19.8808i	−0.484208	+	0.984244i
$409$	−5.42015	−	9.38797i	−0.268009	−	0.464205i	0.700338	−	0.713811i	$-0.253032\pi$
$409$	−5.42015	−	9.38797i	−0.268009	−	0.464205i	−0.968348	+	0.249605i	$0.919699\pi$
$410$	−0.786082	−	1.36153i	−0.0388218	−	0.0672414i
$411$	13.7799	+	20.5805i	0.679711	+	1.01516i
$412$	3.32736	−	5.76315i	0.163927	−	0.283930i
$413$	−6.18715			−0.304450
$414$	−8.38587	−	10.8856i	−0.412143	−	0.534998i
$415$	4.34019			0.213052
$416$	17.2621	−	29.8989i	0.846345	−	1.46591i
$417$	−33.5208	+	2.22920i	−1.64152	+	0.109164i
$418$	−0.370113	−	0.641055i	−0.0181028	−	0.0313550i
$419$	11.2291	+	19.4494i	0.548578	+	0.950166i	0.998372	+	0.0570332i	$0.0181641\pi$
$419$	11.2291	+	19.4494i	0.548578	+	0.950166i	−0.449794	+	0.893132i	$0.648503\pi$
$420$	2.51711	−	0.167393i	0.122823	−	0.00816794i
$421$	0.542817	−	0.940187i	0.0264553	−	0.0458219i	−0.852495	−	0.522736i	$-0.824911\pi$
$421$	0.542817	−	0.940187i	0.0264553	−	0.0458219i	0.878950	+	0.476914i	$0.158245\pi$
$422$	17.3042			0.842358
$423$	−26.6160	+	3.55576i	−1.29411	+	0.172887i
$424$	−8.97364			−0.435799
$425$	−2.50993	+	4.34733i	−0.121750	+	0.210876i
$426$	3.37516	+	5.04086i	0.163527	+	0.244231i
$427$	0.284541	+	0.492840i	0.0137699	+	0.0238502i
$428$	−7.95497	−	13.7784i	−0.384518	−	0.666005i
$429$	−28.6040	+	58.1429i	−1.38101	+	2.80717i
$430$	0.976424	−	1.69122i	0.0470874	−	0.0815577i
$431$	36.5576			1.76092			0.880458	−	0.474124i	$-0.157235\pi$
$431$	36.5576			1.76092			0.880458	+	0.474124i	$0.157235\pi$
$432$	−1.71285	+	5.09374i	−0.0824093	+	0.245073i
$433$	9.17731			0.441034			0.220517	−	0.975383i	$-0.429226\pi$
$433$	9.17731			0.441034			0.220517	+	0.975383i	$0.429226\pi$
$434$	0.486703	−	0.842995i	0.0233625	−	0.0404650i
$435$	0.359991	−	0.731749i	0.0172602	−	0.0350847i
$436$	6.45222	+	11.1756i	0.309005	+	0.535213i
$437$	−0.491256	−	0.850880i	−0.0234999	−	0.0407031i
$438$	1.38568	+	2.06954i	0.0662104	+	0.0988864i
$439$	17.7088	−	30.6726i	0.845196	−	1.46392i	−0.0402550	−	0.999189i	$-0.512817\pi$
$439$	17.7088	−	30.6726i	0.845196	−	1.46392i	0.885451	−	0.464733i	$-0.153850\pi$
$440$	−16.1789			−0.771297
$441$	−1.14276	+	2.77382i	−0.0544171	+	0.132087i
$442$	−21.8074			−1.03727
$443$	−8.79206	+	15.2283i	−0.417723	+	0.723518i	−0.995710	−	0.0925281i	$-0.970505\pi$
$443$	−8.79206	+	15.2283i	−0.417723	+	0.723518i	0.577987	+	0.816046i	$0.303839\pi$
$444$	−23.2026	+	1.54302i	−1.10115	+	0.0732283i
$445$	1.62637	+	2.81695i	0.0770971	+	0.133536i
$446$	8.42556	+	14.5935i	0.398962	+	0.691022i
$447$	−26.9270	+	1.79070i	−1.27360	+	0.0846971i
$448$	−1.12554	+	1.94950i	−0.0531769	+	0.0921051i
$449$	−22.5794			−1.06559			−0.532794	−	0.846245i	$-0.678858\pi$
$449$	−22.5794			−1.06559			−0.532794	+	0.846245i	$0.678858\pi$
$450$	0.842495	−	2.04499i	0.0397156	−	0.0964019i
$451$	13.5390			0.637528
$452$	−0.977023	+	1.69225i	−0.0459553	+	0.0795969i
$453$	−4.73824	−	7.07665i	−0.222622	−	0.332490i
$454$	2.96811	+	5.14092i	0.139300	+	0.241275i
$455$	2.94625	+	5.10305i	0.138122	+	0.239234i
$456$	0.308120	−	0.626311i	0.0144290	−	0.0293297i
$457$	9.50324	−	16.4601i	0.444543	−	0.769970i	−0.553478	−	0.832864i	$-0.686700\pi$
$457$	9.50324	−	16.4601i	0.444543	−	0.769970i	0.998020	+	0.0628937i	$0.0200329\pi$
$458$	−19.3666			−0.904943
$459$	25.5681	−	5.16195i	1.19342	−	0.240939i
$460$	−9.04876			−0.421901
$461$	−20.5902	+	35.6632i	−0.958979	+	1.66100i	−0.233993	+	0.972238i	$0.575179\pi$
$461$	−20.5902	+	35.6632i	−0.958979	+	1.66100i	−0.724987	+	0.688763i	$0.758154\pi$
$462$	3.57882	−	7.27463i	0.166502	−	0.338446i
$463$	−3.70885	−	6.42391i	−0.172365	−	0.298545i	0.766881	−	0.641789i	$-0.221807\pi$
$463$	−3.70885	−	6.42391i	−0.172365	−	0.298545i	−0.939246	+	0.343244i	$0.888474\pi$
$464$	−0.243475	−	0.421710i	−0.0113030	−	0.0195774i
$465$	1.27233	+	1.90025i	0.0590030	+	0.0881220i
$466$	4.17109	−	7.22454i	0.193222	−	0.334670i
$467$	7.90222			0.365671			0.182835	−	0.983144i	$-0.441472\pi$
$467$	7.90222			0.365671			0.182835	+	0.983144i	$0.441472\pi$
$468$	−25.5199	+	3.40933i	−1.17966	+	0.157596i
$469$	10.5567			0.487462
$470$	3.29948	−	5.71487i	0.152194	−	0.263607i
$471$	36.0294	−	2.39603i	1.66015	−	0.110403i
$472$	7.88327	+	13.6542i	0.362857	+	0.628486i
$473$	8.40868	+	14.5643i	0.386632	+	0.669666i
$474$	8.81000	−	0.585881i	0.404656	−	0.0269104i
$475$	0.0790713	−	0.136956i	0.00362804	−	0.00628395i
$476$	−7.31127			−0.335111
$477$	6.44718	+	8.36901i	0.295196	+	0.383191i
$478$	−14.2753			−0.652936
$479$	−15.1137	+	26.1778i	−0.690564	+	1.19609i	0.281089	+	0.959682i	$0.409304\pi$
$479$	−15.1137	+	26.1778i	−0.690564	+	1.19609i	−0.971653	+	0.236411i	$0.924029\pi$
$480$	−5.64605	−	8.43247i	−0.257706	−	0.384888i
$481$	−27.1583	−	47.0395i	−1.23831	−	2.14482i
$482$	−3.97240	−	6.88039i	−0.180938	−	0.313393i
$483$	4.75022	−	9.65571i	0.216142	−	0.439350i
$484$	21.3440	−	36.9689i	0.970181	−	1.68040i
$485$	−4.70168			−0.213492
$486$	−10.8649	+	3.74604i	−0.492841	+	0.169924i
$487$	3.53871			0.160354			0.0801772	−	0.996781i	$-0.474451\pi$
$487$	3.53871			0.160354			0.0801772	+	0.996781i	$0.474451\pi$
$488$	0.725088	−	1.25589i	0.0328232	−	0.0568514i
$489$	19.0961	−	38.8164i	0.863555	−	1.75534i
$490$	−0.368623	−	0.638475i	−0.0166527	−	0.0288433i
$491$	−11.3339	−	19.6309i	−0.511491	−	0.885929i	−0.999911	−	0.0133200i	$-0.995760\pi$
$491$	−11.3339	−	19.6309i	−0.511491	−	0.885929i	0.488420	−	0.872609i	$-0.337573\pi$
$492$	2.99299	+	4.47008i	0.134934	+	0.201527i
$493$	−1.18176	+	2.04686i	−0.0532237	+	0.0921861i
$494$	0.687006			0.0309099
$495$	11.6238	+	15.0887i	0.522452	+	0.678188i
$496$	1.36552			0.0613137
$497$	−2.37538	+	4.11427i	−0.106550	+	0.184550i
$498$	5.52999	−	0.367755i	0.247805	−	0.0164795i
$499$	7.21714	+	12.5005i	0.323084	+	0.559597i	0.981123	−	0.193387i	$-0.0619471\pi$
$499$	7.21714	+	12.5005i	0.323084	+	0.559597i	−0.658039	+	0.752984i	$0.728614\pi$
$500$	−0.728233	−	1.26134i	−0.0325676	−	0.0564087i
$501$	−0.728263	+	0.0484309i	−0.0325364	+	0.00216373i
$502$	−9.61467	+	16.6531i	−0.429124	+	0.743264i
$503$	5.40703			0.241087			0.120544	−	0.992708i	$-0.461536\pi$
$503$	5.40703			0.241087			0.120544	+	0.992708i	$0.461536\pi$
$504$	7.57749	−	1.01231i	0.337528	−	0.0450920i
$505$	−7.40363			−0.329457
$506$	−14.5403	+	25.1846i	−0.646396	+	1.11959i
$507$	−20.9319	−	31.2621i	−0.929617	−	1.38840i
$508$	15.0067	+	25.9924i	0.665815	+	1.15322i
$509$	12.7325	+	22.0533i	0.564357	+	0.977496i	0.997109	+	0.0759826i	$0.0242093\pi$
$509$	12.7325	+	22.0533i	0.564357	+	0.977496i	−0.432752	+	0.901513i	$0.642457\pi$
$510$	−2.82963	+	5.75176i	−0.125298	+	0.254692i
$511$	−0.975216	+	1.68912i	−0.0431410	+	0.0747224i
$512$	−11.3306			−0.500745
$513$	−0.805482	+	0.162619i	−0.0355629	+	0.00717980i
$514$	5.90424			0.260425
$515$	2.28454	−	3.95694i	0.100669	−	0.174364i
$516$	−2.94972	+	5.99586i	−0.129854	+	0.263953i
$517$	28.4142	+	49.2148i	1.24966	+	2.16447i
$518$	3.39794	+	5.88541i	0.149297	+	0.258590i
$519$	2.76178	+	4.12478i	0.121229	+	0.181058i
$520$	7.50783	−	13.0039i	0.329240	−	0.570260i
$521$	16.1907			0.709327			0.354664	−	0.934994i	$-0.384595\pi$
$521$	16.1907			0.709327			0.354664	+	0.934994i	$0.384595\pi$
$522$	0.396674	−	0.962850i	0.0173620	−	0.0421428i
$523$	13.0798			0.571938			0.285969	−	0.958239i	$-0.407685\pi$
$523$	13.0798			0.571938			0.285969	+	0.958239i	$0.407685\pi$
$524$	8.04168	−	13.9286i	0.351302	−	0.608474i
$525$	1.72823	−	0.114931i	0.0754263	−	0.00501599i
$526$	7.95988	+	13.7869i	0.347067	+	0.601138i
$527$	−3.31393	−	5.73989i	−0.144357	−	0.250034i
$528$	11.3481	−	0.754668i	0.493861	−	0.0328427i
$529$	−7.79954	+	13.5092i	−0.339111	+	0.587357i
$530$	−2.59619			−0.112771
$531$	7.07042	−	17.1621i	0.306830	−	0.744771i
$532$	0.230330			0.00998605
$533$	−6.28281	+	10.8821i	−0.272139	+	0.471358i
$534$	2.31090	+	3.45137i	0.100002	+	0.149355i
$535$	−5.46183	−	9.46016i	−0.236135	−	0.408998i
$536$	−13.4506	−	23.2972i	−0.580978	−	1.00628i
$537$	2.10790	−	4.28471i	0.0909627	−	0.184899i
$538$	−0.975033	+	1.68881i	−0.0420366	+	0.0728096i
$539$	6.34896			0.273469
$540$	−2.41214	+	7.17333i	−0.103802	+	0.308691i
$541$	14.6121			0.628223			0.314111	−	0.949386i	$-0.398293\pi$
$541$	14.6121			0.628223			0.314111	+	0.949386i	$0.398293\pi$
$542$	7.32729	−	12.6912i	0.314734	−	0.545135i
$543$	12.1509	−	24.6989i	0.521443	−	1.05993i
$544$	14.7057	+	25.4711i	0.630504	+	1.09206i
$545$	4.43005	+	7.67307i	0.189762	+	0.328678i
$546$	4.18631	+	6.25233i	0.179157	+	0.267575i
$547$	−9.38767	+	16.2599i	−0.401388	+	0.695224i	−0.993894	−	0.110342i	$-0.964805\pi$
$547$	−9.38767	+	16.2599i	−0.401388	+	0.695224i	0.592506	+	0.805566i	$0.298139\pi$
$548$	20.8270			0.889685
$549$	−1.69221	+	0.226071i	−0.0722219	+	0.00964846i
$550$	−4.68075			−0.199588
$551$	0.0372294	−	0.0644831i	0.00158602	−	0.00274707i
$552$	−27.3613	+	1.81958i	−1.16457	+	0.0774463i
$553$	3.45725	+	5.98813i	0.147017	+	0.254641i
$554$	−3.28054	−	5.68206i	−0.139377	−	0.241408i
$555$	−15.9307	+	1.05942i	−0.676221	+	0.0449700i
$556$	−14.1248	+	24.4649i	−0.599026	+	1.03754i
$557$	1.91160			0.0809972			0.0404986	−	0.999180i	$-0.487105\pi$
$557$	1.91160			0.0809972			0.0404986	+	0.999180i	$0.487105\pi$
$558$	1.78214	+	2.31337i	0.0754438	+	0.0979327i
$559$	−15.6083			−0.660159
$560$	0.517115	−	0.895669i	0.0218521	−	0.0378489i
$561$	−30.7124	−	45.8695i	−1.29668	−	1.93661i
$562$	−10.0030	−	17.3256i	−0.421949	−	0.730838i
$563$	−6.91510	−	11.9773i	−0.291437	−	0.504784i	0.682713	−	0.730687i	$-0.260800\pi$
$563$	−6.91510	−	11.9773i	−0.291437	−	0.504784i	−0.974150	+	0.225903i	$0.927467\pi$
$564$	−9.96756	+	20.2609i	−0.419710	+	0.853139i
$565$	−0.670817	+	1.16189i	−0.0282215	+	0.0488811i
$566$	−6.82718			−0.286968
$567$	−6.38821	−	6.33962i	−0.268279	−	0.266239i
$568$	12.1062			0.507965
$569$	7.52636	−	13.0360i	0.315522	−	0.546499i	−0.664027	−	0.747709i	$-0.731154\pi$
$569$	7.52636	−	13.0360i	0.315522	−	0.546499i	0.979548	+	0.201209i	$0.0644872\pi$
$570$	0.0891430	−	0.181200i	0.00373379	−	0.00758962i
$571$	−0.503864	−	0.872718i	−0.0210861	−	0.0365221i	0.855290	−	0.518150i	$-0.173379\pi$
$571$	−0.503864	−	0.872718i	−0.0210861	−	0.0365221i	−0.876376	+	0.481628i	$0.840046\pi$
$572$	27.2441	+	47.1881i	1.13913	+	1.97303i
$573$	3.02597	+	4.51934i	0.126412	+	0.188798i
$574$	0.786082	−	1.36153i	0.0328104	−	0.0568293i
$575$	−6.21282			−0.259092
$576$	−4.12134	−	5.34987i	−0.171723	−	0.222911i
$577$	29.0147			1.20790			0.603948	−	0.797024i	$-0.293593\pi$
$577$	29.0147			1.20790			0.603948	+	0.797024i	$0.293593\pi$
$578$	3.02236	−	5.23488i	0.125713	−	0.217742i
$579$	2.25048	−	0.149661i	0.0935268	−	0.00621971i
$580$	−0.342876	−	0.593879i	−0.0142372	−	0.0246595i
$581$	2.17010	+	3.75871i	0.0900307	+	0.155938i
$582$	−5.99057	+	0.398384i	−0.248317	+	0.0165136i
$583$	11.1788	−	19.3623i	0.462979	−	0.801904i
$584$	4.97023			0.205669
$585$	−17.5218	+	2.34082i	−0.724437	+	0.0967809i
$586$	0.147166			0.00607937
$587$	21.3201	−	36.9276i	0.879976	−	1.52416i	0.0286106	−	0.999591i	$-0.490892\pi$
$587$	21.3201	−	36.9276i	0.879976	−	1.52416i	0.851366	−	0.524573i	$-0.175775\pi$
$588$	1.40352	+	2.09619i	0.0578804	+	0.0864454i
$589$	0.104400	+	0.180826i	0.00430172	+	0.00745080i
$590$	2.28073	+	3.95034i	0.0938962	+	0.162633i
$591$	6.41805	−	13.0459i	0.264003	−	0.536636i
$592$	−4.76672	+	8.25621i	−0.195911	+	0.339328i
$593$	−8.17244			−0.335602			−0.167801	−	0.985821i	$-0.553667\pi$
$593$	−8.17244			−0.335602			−0.167801	+	0.985821i	$0.553667\pi$
$594$	16.0888	+	18.2402i	0.660132	+	0.748404i
$595$	−5.01986			−0.205794
$596$	−11.3464	+	19.6525i	−0.464765	+	0.804996i
$597$	9.41800	−	19.1438i	0.385453	−	0.783505i
$598$	−13.4949	−	23.3739i	−0.551848	−	0.955829i
$599$	14.1708	+	24.5445i	0.579002	+	1.00286i	0.995594	+	0.0937672i	$0.0298909\pi$
$599$	14.1708	+	24.5445i	0.579002	+	1.00286i	−0.416592	+	0.909093i	$0.636776\pi$
$600$	−2.45564	−	3.66754i	−0.100251	−	0.149727i
$601$	9.18174	−	15.9032i	0.374531	−	0.648707i	−0.615726	−	0.787961i	$-0.711137\pi$
$601$	9.18174	−	15.9032i	0.374531	−	0.648707i	0.990257	+	0.139254i	$0.0444703\pi$
$602$	1.95285			0.0795922
$603$	−12.0637	+	29.2823i	−0.491273	+	1.19247i
$604$	−7.16141			−0.291394
$605$	14.6546	−	25.3826i	0.595795	−	1.03195i
$606$	−9.43322	+	0.627327i	−0.383199	+	0.0254834i
$607$	13.0252	+	22.5603i	0.528677	+	0.915695i	0.999441	+	0.0334361i	$0.0106450\pi$
$607$	13.0252	+	22.5603i	0.528677	+	0.915695i	−0.470764	+	0.882259i	$0.656022\pi$
$608$	−0.463281	−	0.802426i	−0.0187885	−	0.0325427i
$609$	0.813709	−	0.0541132i	0.0329731	−	0.00219278i
$610$	0.209777	−	0.363345i	0.00849363	−	0.0147114i
$611$	−52.7426			−2.13374
$612$	8.35501	−	20.2802i	0.337731	−	0.819777i
$613$	40.5775			1.63891			0.819455	−	0.573143i	$-0.194276\pi$
$613$	40.5775			1.63891			0.819455	+	0.573143i	$0.194276\pi$
$614$	1.32376	−	2.29281i	0.0534224	−	0.0925303i
$615$	2.05496	+	3.06913i	0.0828641	+	0.123759i
$616$	−8.08943	−	14.0113i	−0.325932	−	0.564531i
$617$	−18.1264	−	31.3958i	−0.729741	−	1.26395i	−0.956993	−	0.290112i	$-0.906307\pi$
$617$	−18.1264	−	31.3958i	−0.729741	−	1.26395i	0.227252	−	0.973836i	$-0.427026\pi$
$618$	2.57553	−	5.23525i	0.103603	−	0.210593i
$619$	4.34919	−	7.53302i	0.174809	−	0.302778i	−0.765286	−	0.643690i	$-0.777403\pi$
$619$	4.34919	−	7.53302i	0.174809	−	0.302778i	0.940095	+	0.340912i	$0.110736\pi$
$620$	1.92301			0.0772300
$621$	21.3549	+	24.2104i	0.856942	+	0.971530i
$622$	2.92915			0.117448
$623$	−1.62637	+	2.81695i	−0.0651590	+	0.112859i
$624$	−4.65952	+	9.47134i	−0.186530	+	0.379157i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	7.02668	+	12.1706i	0.280842	+	0.486433i
$627$	0.967544	+	1.44504i	0.0386400	+	0.0577095i
$628$	15.1819	−	26.2958i	0.605823	−	1.04932i
$629$	46.2727			1.84501
$630$	2.19226	−	0.292875i	0.0873419	−	0.0116684i
$631$	−19.1829			−0.763660			−0.381830	−	0.924233i	$-0.624706\pi$
$631$	−19.1829			−0.763660			−0.381830	+	0.924233i	$0.624706\pi$
$632$	8.81000	−	15.2594i	0.350443	−	0.606985i
$633$	−40.5641	+	2.69759i	−1.61228	+	0.107220i
$634$	−3.11711	−	5.39900i	−0.123796	−	0.214422i
$635$	10.3035	+	17.8462i	0.408882	+	0.708204i
$636$	8.86393	−	0.589468i	0.351478	−	0.0233739i
$637$	−2.94625	+	5.10305i	−0.116734	+	0.202190i
$638$	−2.20385			−0.0872512
$639$	−8.69779	−	11.2905i	−0.344079	−	0.446645i
$640$	−10.0584			−0.397595
$641$	17.9543	−	31.0977i	0.709151	−	1.22828i	−0.256022	−	0.966671i	$-0.582412\pi$
$641$	17.9543	−	31.0977i	0.709151	−	1.22828i	0.965173	−	0.261614i	$-0.0842547\pi$
$642$	−7.76068	−	11.5907i	−0.306290	−	0.457449i
$643$	−17.7505	−	30.7448i	−0.700011	−	1.21245i	−0.968462	−	0.249161i	$-0.919845\pi$
$643$	−17.7505	−	30.7448i	−0.700011	−	1.21245i	0.268451	−	0.963293i	$-0.413488\pi$
$644$	−4.52438	−	7.83646i	−0.178286	−	0.308800i
$645$	−2.02526	+	4.11672i	−0.0797445	+	0.162096i
$646$	−0.292633	+	0.506856i	−0.0115135	+	0.0199420i
$647$	−23.5546			−0.926025			−0.463012	−	0.886352i	$-0.653231\pi$
$647$	−23.5546			−0.926025			−0.463012	+	0.886352i	$0.653231\pi$
$648$	−5.85126	+	22.1755i	−0.229859	+	0.871134i
$649$	−39.2820			−1.54195
$650$	2.17211	−	3.76221i	0.0851972	−	0.147566i
$651$	−1.00950	+	2.05200i	−0.0395654	+	0.0804241i
$652$	−18.1882	−	31.5029i	−0.712305	−	1.23375i
$653$	−1.20702	−	2.09063i	−0.0472345	−	0.0818126i	0.841442	−	0.540348i	$-0.181707\pi$
$653$	−1.20702	−	2.09063i	−0.0472345	−	0.0818126i	−0.888676	+	0.458536i	$0.848374\pi$
$654$	6.29464	+	9.40116i	0.246140	+	0.367614i
$655$	5.52136	−	9.56328i	0.215737	−	0.373668i
$656$	2.20547			0.0861093
$657$	−3.57090	−	4.63534i	−0.139314	−	0.180842i
$658$	6.59897			0.257255
$659$	1.83024	−	3.17008i	0.0712962	−	0.123489i	−0.828173	−	0.560472i	$-0.810620\pi$
$659$	1.83024	−	3.17008i	0.0712962	−	0.123489i	0.899470	+	0.436983i	$0.143953\pi$
$660$	15.9811	−	1.06277i	0.622062	−	0.0413683i
$661$	0.0528998	+	0.0916251i	0.00205756	+	0.00356380i	0.867052	−	0.498217i	$-0.166012\pi$
$661$	0.0528998	+	0.0916251i	0.00205756	+	0.00356380i	−0.864995	+	0.501781i	$0.832678\pi$
$662$	−4.61133	−	7.98705i	−0.179224	−	0.310426i
$663$	51.1203	−	3.39960i	1.98535	−	0.132029i
$664$	5.52999	−	9.57822i	0.214605	−	0.371707i
$665$	0.158143			0.00613251
$666$	−20.2081	+	2.69970i	−0.783049	+	0.104611i
$667$	−2.92520			−0.113264
$668$	−0.306871	+	0.531517i	−0.0118732	+	0.0205650i
$669$	−22.0260	−	32.8962i	−0.851573	−	1.27184i
$670$	−3.89144	−	6.74016i	−0.150339	−	0.260395i
$671$	1.80654	+	3.12902i	0.0697407	+	0.120794i
$672$	4.47971	−	9.10585i	0.172809	−	0.351266i
$673$	16.0478	−	27.7957i	0.618599	−	1.07144i	−0.371143	−	0.928576i	$-0.621034\pi$
$673$	16.0478	−	27.7957i	0.618599	−	1.07144i	0.989742	−	0.142868i	$-0.0456326\pi$
$674$	−11.2406			−0.432972
$675$	−1.65616	+	4.92515i	−0.0637454	+	0.189569i
$676$	−31.6366			−1.21679
$677$	−10.8921	+	18.8657i	−0.418617	+	0.725066i	−0.995801	−	0.0915483i	$-0.970818\pi$
$677$	−10.8921	+	18.8657i	−0.418617	+	0.725066i	0.577183	+	0.816614i	$0.304152\pi$
$678$	−0.756262	+	1.53724i	−0.0290441	+	0.0590375i
$679$	−2.35084	−	4.07177i	−0.0902169	−	0.156260i
$680$	6.39598	+	11.0782i	0.245275	+	0.424828i
$681$	−7.75919	−	11.5885i	−0.297333	−	0.444072i
$682$	3.09006	−	5.35214i	0.118324	−	0.204944i
$683$	−22.2621			−0.851837			−0.425919	−	0.904762i	$-0.640049\pi$
$683$	−22.2621			−0.851837			−0.425919	+	0.904762i	$0.640049\pi$
$684$	−0.263211	+	0.638894i	−0.0100641	+	0.0244287i
$685$	14.2997			0.546362
$686$	0.368623	−	0.638475i	0.0140741	−	0.0243771i
$687$	45.3987	−	3.01910i	1.73207	−	0.115186i
$688$	1.36975	+	2.37248i	0.0522214	+	0.0904501i
$689$	10.3751	+	17.9702i	0.395260	+	0.684610i
$690$	−7.91597	+	0.526427i	−0.301356	+	0.0200407i
$691$	−18.9433	+	32.8108i	−0.720639	+	1.24818i	0.240105	+	0.970747i	$0.422818\pi$
$691$	−18.9433	+	32.8108i	−0.720639	+	1.24818i	−0.960744	+	0.277436i	$0.910515\pi$
$692$	4.17418			0.158678
$693$	−7.25532	+	17.6109i	−0.275607	+	0.668983i
$694$	−17.3161			−0.657310
$695$	−9.69800	+	16.7974i	−0.367866	+	0.637163i
$696$	−1.15620	−	1.72680i	−0.0438255	−	0.0654541i
$697$	−5.35238	−	9.27059i	−0.202736	−	0.351149i
$698$	−3.61857	−	6.26755i	−0.136965	−	0.237230i
$699$	−8.65150	+	17.5858i	−0.327230	+	0.665156i
$700$	0.728233	−	1.26134i	0.0275246	−	0.0476741i
$701$	20.7367			0.783214			0.391607	−	0.920133i	$-0.371919\pi$
$701$	20.7367			0.783214			0.391607	+	0.920133i	$0.371919\pi$
$702$	−22.1268	+	4.46718i	−0.835122	+	0.168603i
$703$	−1.45775			−0.0549799
$704$	−7.14603	+	12.3773i	−0.269326	+	0.466486i
$705$	−6.84366	+	13.9110i	−0.257747	+	0.523919i
$706$	3.91737	+	6.78508i	0.147432	+	0.255360i
$707$	−3.70182	−	6.41173i	−0.139221	−	0.241138i
$708$	−8.68382	−	12.9694i	−0.326358	−	0.487421i
$709$	10.3074	−	17.8530i	0.387103	−	0.670482i	−0.604955	−	0.796259i	$-0.706809\pi$
$709$	10.3074	−	17.8530i	0.387103	−	0.670482i	0.992059	+	0.125777i	$0.0401424\pi$
$710$	3.50248			0.131446
$711$	−20.5608	+	2.74681i	−0.771091	+	0.103014i
$712$	8.28884			0.310637
$713$	4.10147	−	7.10396i	0.153601	−	0.266045i
$714$	−6.39598	+	0.425345i	−0.239364	+	0.0159181i
$715$	18.7056	+	32.3990i	0.699549	+	1.21165i
$716$	−2.00769	−	3.47742i	−0.0750308	−	0.129957i
$717$	33.4637	−	2.22540i	1.24972	−	0.0831090i
$718$	2.44548	−	4.23569i	0.0912643	−	0.158074i
$719$	−44.7699			−1.66964			−0.834818	−	0.550526i	$-0.814427\pi$
$719$	−44.7699			−1.66964			−0.834818	+	0.550526i	$0.814427\pi$
$720$	1.89349	+	2.45792i	0.0705663	+	0.0916013i
$721$	4.56908			0.170162
$722$	−6.99463	+	12.1150i	−0.260313	+	0.450875i
$723$	10.3846	+	15.5096i	0.386207	+	0.576807i
$724$	−11.5732	−	20.0453i	−0.430114	−	0.744979i
$725$	−0.235416	−	0.407753i	−0.00874314	−	0.0151436i
$726$	16.5212	−	33.5825i	0.613161	−	1.24636i
$727$	−10.6274	+	18.4073i	−0.394150	+	0.682688i	−0.992992	−	0.118179i	$-0.962294\pi$
$727$	−10.6274	+	18.4073i	−0.394150	+	0.682688i	0.598842	+	0.800867i	$0.295628\pi$
$728$	15.0157			0.556517
$729$	24.8852	−	10.4751i	0.921673	−	0.387967i
$730$	1.43795			0.0532209
$731$	6.64841	−	11.5154i	0.245900	−	0.425912i
$732$	−0.633725	+	1.28816i	−0.0234231	+	0.0476119i
$733$	5.21248	+	9.02827i	0.192527	+	0.333467i	0.946087	−	0.323912i	$-0.104998\pi$
$733$	5.21248	+	9.02827i	0.192527	+	0.333467i	−0.753560	+	0.657379i	$0.771665\pi$
$734$	−12.0039	−	20.7914i	−0.443073	−	0.767425i
$735$	0.963650	+	1.43923i	0.0355448	+	0.0530867i
$736$	−18.2005	+	31.5242i	−0.670880	+	1.16200i
$737$	67.0238			2.46885
$738$	2.87835	+	3.73636i	0.105954	+	0.137537i
$739$	1.45276			0.0534406			0.0267203	−	0.999643i	$-0.491494\pi$
$739$	1.45276			0.0534406			0.0267203	+	0.999643i	$0.491494\pi$
$740$	−6.71280	+	11.6269i	−0.246767	+	0.427414i
$741$	−1.61046	+	0.107099i	−0.0591618	+	0.00393437i
$742$	−1.29809	−	2.24837i	−0.0476546	−	0.0825401i
$743$	−6.13638	−	10.6285i	−0.225122	−	0.389923i	0.731234	−	0.682127i	$-0.238945\pi$
$743$	−6.13638	−	10.6285i	−0.225122	−	0.389923i	−0.956356	+	0.292204i	$0.905611\pi$
$744$	5.81472	−	0.386690i	0.213178	−	0.0141767i
$745$	−7.79033	+	13.4932i	−0.285416	+	0.494354i
$746$	19.2624			0.705245
$747$	−12.9059	+	1.72416i	−0.472203	+	0.0630837i
$748$	−46.4189			−1.69724
$749$	5.46183	−	9.46016i	0.199571	−	0.345667i
$750$	−0.710448	−	1.06107i	−0.0259419	−	0.0387447i
$751$	14.1349	+	24.4824i	0.515790	+	0.893374i	0.999832	+	0.0183294i	$0.00583475\pi$
$751$	14.1349	+	24.4824i	0.515790	+	0.893374i	−0.484042	+	0.875045i	$0.660832\pi$
$752$	4.62860	+	8.01698i	0.168788	+	0.292349i
$753$	19.9424	−	40.5366i	0.726740	−	1.47723i
$754$	1.02270	−	1.77137i	0.0372445	−	0.0645094i
$755$	−4.91697			−0.178947
$756$	−7.41835	+	1.49769i	−0.269803	+	0.0544705i
$757$	−16.7780			−0.609807			−0.304903	−	0.952383i	$-0.598624\pi$
$757$	−16.7780			−0.609807			−0.304903	+	0.952383i	$0.598624\pi$
$758$	0.642570	−	1.11296i	0.0233392	−	0.0404247i
$759$	30.1589	−	61.3037i	1.09470	−	2.22518i
$760$	−0.201495	−	0.349000i	−0.00730899	−	0.0126595i
$761$	−7.94668	−	13.7641i	−0.288067	−	0.498947i	0.685281	−	0.728279i	$-0.259679\pi$
$761$	−7.94668	−	13.7641i	−0.288067	−	0.498947i	−0.973348	+	0.229332i	$0.926346\pi$
$762$	14.6402	+	21.8654i	0.530358	+	0.792100i
$763$	−4.43005	+	7.67307i	−0.160379	+	0.277784i
$764$	4.57347			0.165463
$765$	5.73649	−	13.9242i	0.207403	−	0.503431i
$766$	−24.4877			−0.884777
$767$	18.2289	−	31.5733i	0.658206	−	1.14005i
$768$	−20.5966	+	1.36971i	−0.743216	+	0.0494253i
$769$	−12.0519	−	20.8745i	−0.434604	−	0.752756i	0.562660	−	0.826689i	$-0.309778\pi$
$769$	−12.0519	−	20.8745i	−0.434604	−	0.752756i	−0.997263	+	0.0739332i	$0.976445\pi$
$770$	−2.34037	−	4.05365i	−0.0843412	−	0.146083i
$771$	−13.8406	+	0.920424i	−0.498456	+	0.0331482i
$772$	0.948295	−	1.64249i	0.0341299	−	0.0591147i
$773$	23.9145			0.860145			0.430072	−	0.902794i	$-0.358488\pi$
$773$	23.9145			0.860145			0.430072	+	0.902794i	$0.358488\pi$
$774$	−2.23163	+	5.41686i	−0.0802144	+	0.194705i
$775$	1.32033			0.0474275
$776$	−5.99057	+	10.3760i	−0.215049	+	0.372476i
$777$	−8.88285	−	13.2667i	−0.318670	−	0.475940i
$778$	7.40425	+	12.8245i	0.265455	+	0.459782i
$779$	0.168618	+	0.292055i	0.00604137	+	0.0104640i
$780$	−6.56182	+	13.3381i	−0.234951	+	0.477582i
$781$	−15.0812	+	26.1213i	−0.539646	+	0.934695i
$782$	22.9929			0.822224
$783$	−0.779772	+	2.31892i	−0.0278668	+	0.0828716i
$784$	1.03423			0.0369368
$785$	10.4238	−	18.0545i	0.372041	−	0.644393i
$786$	6.22464	−	12.6527i	0.222026	−	0.451309i
$787$	−7.80093	−	13.5116i	−0.278073	−	0.481637i	0.692833	−	0.721098i	$-0.256362\pi$
$787$	−7.80093	−	13.5116i	−0.278073	−	0.481637i	−0.970906	+	0.239462i	$0.923029\pi$
$788$	−6.11292	−	10.5879i	−0.217764	−	0.377178i
$789$	−20.8086	−	31.0780i	−0.740805	−	1.10641i
$790$	2.54884	−	4.41473i	0.0906838	−	0.157069i
$791$	−1.34163			−0.0477030
$792$	48.1091	−	6.42712i	1.70948	−	0.228378i
$793$	−3.35331			−0.119080
$794$	9.16076	−	15.8669i	0.325103	−	0.563095i
$795$	6.08591	−	0.404725i	0.215845	−	0.0143541i
$796$	−8.97024	−	15.5369i	−0.317942	−	0.550691i
$797$	6.06687	+	10.5081i	0.214899	+	0.372217i	0.953241	−	0.302210i	$-0.0977243\pi$
$797$	6.06687	+	10.5081i	0.214899	+	0.372217i	−0.738342	+	0.674426i	$0.764391\pi$
$798$	0.201495	−	0.0133998i	0.00713285	−	0.000474348i
$799$	22.4660	−	38.9122i	0.794789	−	1.37661i
$800$	−5.85902			−0.207148
$801$	−5.95518	−	7.73034i	−0.210416	−	0.273138i
$802$	6.99412			0.246971
$803$	−6.19160	+	10.7242i	−0.218497	+	0.378448i
$804$	14.8165	+	22.1288i	0.522539	+	0.780422i
$805$	−3.10641	−	5.38046i	−0.109486	−	0.189636i
$806$	2.86789	+	4.96734i	0.101017	+	0.174967i
$807$	2.02237	−	4.11085i	0.0711909	−	0.144709i
$808$	−9.43322	+	16.3388i	−0.331860	+	0.574798i
$809$	−51.6794			−1.81695			−0.908475	−	0.417938i	$-0.862753\pi$
$809$	−51.6794			−1.81695			−0.908475	+	0.417938i	$0.862753\pi$
$810$	−1.69284	+	6.41564i	−0.0594805	+	0.225423i
$811$	−29.7724			−1.04545			−0.522725	−	0.852501i	$-0.675085\pi$
$811$	−29.7724			−1.04545			−0.522725	+	0.852501i	$0.675085\pi$
$812$	0.342876	−	0.593879i	0.0120326	−	0.0208411i
$813$	−15.1980	+	30.8927i	−0.533016	+	1.08345i
$814$	21.5734	+	37.3662i	0.756147	+	1.30968i
$815$	−12.4879	−	21.6297i	−0.437432	−	0.757654i
$816$	−5.00297	−	7.47203i	−0.175139	−	0.261573i
$817$	−0.209447	+	0.362773i	−0.00732763	+	0.0126918i
$818$	−7.99198			−0.279433
$819$	−10.7881	−	14.0039i	−0.376967	−	0.489336i
$820$	3.10589			0.108462
$821$	−1.65717	+	2.87030i	−0.0578355	+	0.100174i	−0.893494	−	0.449076i	$-0.851753\pi$
$821$	−1.65717	+	2.87030i	−0.0578355	+	0.100174i	0.835658	+	0.549250i	$0.185087\pi$
$822$	18.2197	−	1.21165i	0.635485	−	0.0422610i
$823$	3.41264	+	5.91086i	0.118957	+	0.206040i	0.919355	−	0.393430i	$-0.128712\pi$
$823$	3.41264	+	5.91086i	0.118957	+	0.206040i	−0.800398	+	0.599470i	$0.795378\pi$
$824$	−5.82163	−	10.0834i	−0.202806	−	0.351270i
$825$	10.9725	−	0.729691i	0.382013	−	0.0254046i
$826$	−2.28073	+	3.95034i	−0.0793567	+	0.137450i
$827$	14.3225			0.498044			0.249022	−	0.968498i	$-0.419891\pi$
$827$	14.3225			0.498044			0.249022	+	0.968498i	$0.419891\pi$
$828$	26.9072	−	3.59466i	0.935091	−	0.124923i
$829$	2.71380			0.0942543			0.0471272	−	0.998889i	$-0.484993\pi$
$829$	2.71380			0.0942543			0.0471272	+	0.998889i	$0.484993\pi$
$830$	1.59990	−	2.77110i	0.0555332	−	0.0961863i
$831$	8.57594	+	12.8083i	0.297496	+	0.444316i
$832$	−6.63225	−	11.4874i	−0.229932	−	0.398254i
$833$	−2.50993	−	4.34733i	−0.0869640	−	0.150626i
$834$	−10.9333	+	22.2239i	−0.378588	+	0.769552i
$835$	−0.210696	+	0.364936i	−0.00729142	+	0.0126291i
$836$	1.46235			0.0505765
$837$	−4.53827	−	5.14511i	−0.156865	−	0.177841i
$838$	16.5573			0.571961
$839$	0.569505	−	0.986411i	0.0196615	−	0.0340547i	−0.856027	−	0.516931i	$-0.827074\pi$
$839$	0.569505	−	0.986411i	0.0196615	−	0.0340547i	0.875689	+	0.482876i	$0.160408\pi$
$840$	1.94837	−	3.96042i	0.0672250	−	0.136647i
$841$	14.3892	+	24.9228i	0.496178	+	0.859405i
$842$	−0.400191	−	0.693150i	−0.0137915	−	0.0238875i
$843$	26.1496	+	39.0549i	0.900639	+	1.34512i
$844$	−17.0927	+	29.6054i	−0.588355	+	1.01906i
$845$	−21.7214			−0.747240
$846$	−7.54103	+	18.3044i	−0.259266	+	0.629318i
$847$	29.3093			1.00708
$848$	1.82100	−	3.15407i	0.0625335	−	0.108311i
$849$	16.0041	−	1.06430i	0.549258	−	0.0365267i
$850$	1.85044	+	3.20506i	0.0634696	+	0.109933i
$851$	28.6346	+	49.5966i	0.981582	+	1.70015i
$852$	−11.9582	+	0.795242i	−0.409681	+	0.0272445i
$853$	5.63751	−	9.76446i	0.193025	−	0.334329i	−0.753226	−	0.657761i	$-0.771504\pi$
$853$	5.63751	−	9.76446i	0.193025	−	0.334329i	0.946251	+	0.323433i	$0.104837\pi$
$854$	0.419554			0.0143568
$855$	−0.180719	+	0.438660i	−0.00618045	+	0.0150019i
$856$	−27.8364			−0.951429
$857$	−14.4836	+	25.0864i	−0.494751	+	0.856934i	−0.999982	−	0.00605040i	$-0.998074\pi$
$857$	−14.4836	+	25.0864i	−0.494751	+	0.856934i	0.505231	+	0.862984i	$0.331407\pi$
$858$	26.5787	+	39.6958i	0.907381	+	1.35519i
$859$	2.18766	+	3.78913i	0.0746419	+	0.129284i	0.900930	−	0.433963i	$-0.142885\pi$
$859$	2.18766	+	3.78913i	0.0746419	+	0.129284i	−0.826289	+	0.563247i	$0.809552\pi$
$860$	1.92897	+	3.34108i	0.0657774	+	0.113930i
$861$	−1.63046	+	3.31421i	−0.0555659	+	0.112948i
$862$	13.4760	−	23.3411i	0.458994	−	0.795000i
$863$	−39.0757			−1.33015			−0.665077	−	0.746775i	$-0.731601\pi$
$863$	−39.0757			−1.33015			−0.665077	+	0.746775i	$0.731601\pi$
$864$	20.1388	+	22.8317i	0.685136	+	0.776751i
$865$	2.86596			0.0974456
$866$	3.38297	−	5.85948i	0.114958	−	0.199113i
$867$	−6.26885	+	12.7426i	−0.212901	+	0.432762i
$868$	0.961506	+	1.66538i	0.0326356	+	0.0565266i
$869$	21.9499	+	38.0184i	0.744600	+	1.28968i
$870$	−0.334502	−	0.499585i	−0.0113407	−	0.0169375i
$871$	−31.1025	+	53.8712i	−1.05387	+	1.82535i
$872$	22.5779			0.764585
$873$	13.9808	−	1.86776i	0.473179	−	0.0632142i
$874$	−0.724353			−0.0245016
$875$	0.500000	−	0.866025i	0.0169031	−	0.0292770i
$876$	−4.90946	+	0.326489i	−0.165875	+	0.0110310i
$877$	13.9468	+	24.1566i	0.470951	+	0.815711i	0.999448	−	0.0332244i	$-0.0105776\pi$
$877$	13.9468	+	24.1566i	0.470951	+	0.815711i	−0.528497	+	0.848935i	$0.677244\pi$
$878$	−13.0558	−	22.6133i	−0.440611	−	0.763161i
$879$	−0.344982	+	0.0229420i	−0.0116360	+	0.000773814i
$880$	3.28314	−	5.68657i	0.110675	−	0.191694i
$881$	−32.9933			−1.11157			−0.555786	−	0.831325i	$-0.687583\pi$
$881$	−32.9933			−1.11157			−0.555786	+	0.831325i	$0.687583\pi$
$882$	1.34977	+	1.75212i	0.0454491	+	0.0589969i
$883$	23.4730			0.789929			0.394964	−	0.918696i	$-0.370757\pi$
$883$	23.4730			0.789929			0.394964	+	0.918696i	$0.370757\pi$
$884$	21.5408	−	37.3097i	0.724495	−	1.25486i
$885$	−5.96225	−	8.90473i	−0.200419	−	0.299329i
$886$	6.48192	+	11.2270i	0.217764	+	0.377179i
$887$	−20.1703	−	34.9361i	−0.677254	−	1.17304i	−0.975805	−	0.218644i	$-0.929837\pi$
$887$	−20.1703	−	34.9361i	−0.677254	−	1.17304i	0.298551	−	0.954394i	$-0.403497\pi$
$888$	−17.9599	+	36.5068i	−0.602694	+	1.22509i
$889$	−10.3035	+	17.8462i	−0.345568	+	0.598541i
$890$	2.39807			0.0803834
$891$	−40.5585	−	40.2500i	−1.35876	−	1.34843i
$892$	−33.2902			−1.11464
$893$	−0.707754	+	1.22587i	−0.0236841	+	0.0410220i
$894$	−8.78262	+	17.8523i	−0.293735	+	0.597071i
$895$	−1.37846	−	2.38757i	−0.0460770	−	0.0798077i
$896$	−5.02922	−	8.71086i	−0.168014	−	0.291009i
$897$	35.2782	+	52.6887i	1.17791	+	1.75922i
$898$	−8.32330	+	14.4164i	−0.277752	+	0.481081i
$899$	0.621653			0.0207333
$900$	2.66653	+	3.46140i	0.0888845	+	0.115380i
$901$	−17.6773			−0.588915
$902$	4.99080	−	8.64432i	0.166175	−	0.287824i
$903$	−4.57781	+	0.304433i	−0.152340	+	0.0101309i
$904$	1.70942	+	2.96081i	0.0568546	+	0.0984750i
$905$	−7.94606	−	13.7630i	−0.264136	−	0.457497i
$906$	−6.26489	+	0.416627i	−0.208137	+	0.0138415i
$907$	14.9570	−	25.9064i	0.496641	−	0.860207i	−0.503352	−	0.864081i	$-0.667900\pi$
$907$	14.9570	−	25.9064i	0.496641	−	0.860207i	0.999992	+	0.00387483i	$0.00123340\pi$
$908$	−11.7273			−0.389184
$909$	22.0153	−	2.94113i	0.730201	−	0.0975510i
$910$	4.34422			0.144010
$911$	2.15470	−	3.73206i	0.0713885	−	0.123649i	−0.828122	−	0.560549i	$-0.810590\pi$
$911$	2.15470	−	3.73206i	0.0713885	−	0.123649i	0.899510	+	0.436900i	$0.143924\pi$
$912$	0.157611	+	0.235394i	0.00521901	+	0.00779468i
$913$	13.7778	+	23.8639i	0.455980	+	0.789780i
$914$	−7.00623	−	12.1351i	−0.231746	−	0.401395i
$915$	−0.435111	+	0.884445i	−0.0143843	+	0.0292388i
$916$	19.1298	−	33.1339i	0.632068	−	1.09477i
$917$	11.0427			0.364663
$918$	6.12923	−	18.2274i	0.202295	−	0.601594i
$919$	−26.4376			−0.872097			−0.436049	−	0.899923i	$-0.643622\pi$
$919$	−26.4376			−0.872097			−0.436049	+	0.899923i	$0.643622\pi$
$920$	−7.91597	+	13.7109i	−0.260982	+	0.452033i
$921$	−2.74568	+	5.58111i	−0.0904732	+	0.183904i
$922$	15.1800	+	26.2926i	0.499928	+	0.865900i
$923$	−13.9969	−	24.2433i	−0.460713	−	0.797978i
$924$	8.91091	+	13.3086i	0.293148	+	0.437821i
$925$	−4.60896	+	7.98295i	−0.151542	+	0.262478i
$926$	−5.46867			−0.179712
$927$	−5.22136	+	12.6738i	−0.171492	+	0.416263i
$928$	−2.75862			−0.0905561
$929$	17.9146	−	31.0290i	0.587759	−	1.01803i	−0.406766	−	0.913532i	$-0.633344\pi$
$929$	17.9146	−	31.0290i	0.587759	−	1.01803i	0.994525	−	0.104496i	$-0.0333229\pi$
$930$	1.68227	−	0.111874i	0.0551639	−	0.00366851i
$931$	0.0790713	+	0.136956i	0.00259146	+	0.00448854i
$932$	8.24019	+	14.2724i	0.269916	+	0.467509i
$933$	−6.86643	+	0.456631i	−0.224797	+	0.0149494i
$934$	2.91294	−	5.04536i	0.0953144	−	0.165089i
$935$	−31.8709			−1.04229
$936$	−17.1593	+	41.6508i	−0.560868	+	1.36140i
$937$	−12.1293			−0.396247			−0.198124	−	0.980177i	$-0.563485\pi$
$937$	−12.1293			−0.396247			−0.198124	+	0.980177i	$0.563485\pi$
$938$	3.89144	−	6.74016i	0.127060	−	0.220074i
$939$	−18.3690	−	27.4345i	−0.599450	−	0.895290i
$940$	6.51829	+	11.2900i	0.212603	+	0.368240i
$941$	19.7462	+	34.2014i	0.643707	+	1.11493i	0.984599	+	0.174830i	$0.0559376\pi$
$941$	19.7462	+	34.2014i	0.643707	+	1.11493i	−0.340892	+	0.940102i	$0.610729\pi$
$942$	11.7515	−	23.8871i	0.382884	−	0.778284i
$943$	6.62435	−	11.4737i	0.215719	−	0.373636i
$944$	−6.39894			−0.208268
$945$	−5.09339	+	1.02830i	−0.165688	+	0.0334508i
$946$	12.3986			0.403112
$947$	7.83694	−	13.5740i	0.254666	−	0.441095i	−0.710138	−	0.704062i	$-0.751368\pi$
$947$	7.83694	−	13.5740i	0.254666	−	0.441095i	0.964805	+	0.262967i	$0.0847010\pi$
$948$	−7.69992	+	15.6515i	−0.250082	+	0.508338i
$949$	−5.74645	−	9.95314i	−0.186538	−	0.323093i
$950$	−0.0582951	−	0.100970i	−0.00189134	−	0.00327590i
$951$	8.14871	+	12.1702i	0.264240	+	0.394647i
$952$	−6.39598	+	11.0782i	−0.207295	+	0.359046i
$953$	−3.02804			−0.0980878			−0.0490439	−	0.998797i	$-0.515617\pi$
$953$	−3.02804			−0.0980878			−0.0490439	+	0.998797i	$0.515617\pi$
$954$	7.71998	−	1.03135i	0.249944	−	0.0333911i
$955$	3.14012			0.101612
$956$	14.1007	−	24.4232i	0.456051	−	0.789903i
$957$	5.16620	−	0.343562i	0.167000	−	0.0111058i
$958$	11.1426	+	19.2995i	0.360000	+	0.623538i
$959$	7.14983	+	12.3839i	0.230880	+	0.399896i
$960$	−3.89040	+	0.258719i	−0.125562	+	0.00835013i
$961$	14.6284	−	25.3371i	0.471883	−	0.817325i
$962$	−40.0447			−1.29109
$963$	19.9993	+	25.9608i	0.644468	+	0.836576i
$964$	15.6953			0.505512
$965$	0.651093	−	1.12773i	0.0209594	−	0.0363028i
$966$	−4.41388	−	6.59221i	−0.142014	−	0.212101i
$967$	10.5616	+	18.2933i	0.339639	+	0.588272i	0.984365	−	0.176142i	$-0.0563618\pi$
$967$	10.5616	+	18.2933i	0.339639	+	0.588272i	−0.644726	+	0.764414i	$0.723029\pi$
$968$	−37.3439	−	64.6816i	−1.20028	−	2.07895i
$969$	0.606968	−	1.23378i	0.0194986	−	0.0396346i
$970$	−1.73315	+	3.00190i	−0.0556480	+	0.0963852i
$971$	−43.5237			−1.39674			−0.698370	−	0.715736i	$-0.746091\pi$
$971$	−43.5237			−1.39674			−0.698370	+	0.715736i	$0.746091\pi$
$972$	4.32305	−	22.2887i	0.138662	−	0.714910i
$973$	−19.3960			−0.621807
$974$	1.30445	−	2.25938i	0.0417974	−	0.0723952i
$975$	−4.50530	+	9.15787i	−0.144285	+	0.293287i
$976$	0.294281	+	0.509710i	0.00941970	+	0.0163154i
$977$	17.2453	+	29.8698i	0.551727	+	0.955619i	0.998150	+	0.0607973i	$0.0193643\pi$
$977$	17.2453	+	29.8698i	0.551727	+	0.955619i	−0.446423	+	0.894822i	$0.647302\pi$
$978$	−17.7440	−	26.5010i	−0.567391	−	0.847408i
$979$	−10.3257	+	17.8847i	−0.330012	+	0.571597i
$980$	1.45647			0.0465251
$981$	−16.2213	−	21.0566i	−0.517905	−	0.672287i
$982$	−16.7117			−0.533293
$983$	−15.1246	+	26.1965i	−0.482399	+	0.835540i	−0.999796	−	0.0202057i	$-0.993568\pi$
$983$	−15.1246	+	26.1965i	−0.482399	+	0.835540i	0.517397	+	0.855746i	$0.326901\pi$
$984$	9.39145	−	0.624549i	0.299389	−	0.0199099i
$985$	−4.19709	−	7.26956i	−0.133730	−	0.231628i
$986$	0.871247	+	1.50904i	0.0277462	+	0.0480578i
$987$	−15.4691	+	1.02873i	−0.492387	+	0.0327447i
$988$	−0.678607	+	1.17538i	−0.0215894	+	0.0373939i
$989$	16.4568			0.523294
$990$	13.9186	−	1.85945i	0.442362	−	0.0590972i
$991$	2.93522			0.0932404			0.0466202	−	0.998913i	$-0.485155\pi$
$991$	2.93522			0.0932404			0.0466202	+	0.998913i	$0.485155\pi$
$992$	3.86791	−	6.69942i	0.122806	−	0.212707i
$993$	12.0549	+	18.0041i	0.382549	+	0.571344i
$994$	1.75124	+	3.03323i	0.0555459	+	0.0962083i
$995$	−6.15890	−	10.6675i	−0.195250	−	0.338184i
$996$	−4.83320	+	9.82438i	−0.153146	+	0.311297i
$997$	−29.2297	+	50.6274i	−0.925715	+	1.60338i	−0.135307	+	0.990804i	$0.543202\pi$
$997$	−29.2297	+	50.6274i	−0.925715	+	1.60338i	−0.790408	+	0.612581i	$0.790131\pi$
$998$	10.6416			0.336855
$999$	46.9504	−	9.47883i	1.48545	−	0.299897i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	315.2.i.e.106.3	✓	12
3.2	odd	2		945.2.i.e.316.4		12
9.2	odd	6		2835.2.a.v.1.3		6
9.4	even	3	inner	315.2.i.e.211.3	yes	12
9.5	odd	6		945.2.i.e.631.4		12
9.7	even	3		2835.2.a.u.1.4		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
315.2.i.e.106.3	✓	12	1.1	even	1	trivial
315.2.i.e.211.3	yes	12	9.4	even	3	inner
945.2.i.e.316.4		12	3.2	odd	2
945.2.i.e.631.4		12	9.5	odd	6
2835.2.a.u.1.4		6	9.7	even	3
2835.2.a.v.1.3		6	9.2	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:	\( N \)	\(=\)	\( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	315.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.368623 - 0.638475i) q^{2} +(-0.764584 + 1.55416i) q^{3} +(0.728233 + 1.26134i) q^{4} +(0.500000 + 0.866025i) q^{5} +(0.710448 + 1.06107i) q^{6} +(-0.500000 + 0.866025i) q^{7} +2.54827 q^{8} +(-1.83082 - 2.37657i) q^{9} +O(q^{10})\)	\(q+(0.368623 - 0.638475i) q^{2} +(-0.764584 + 1.55416i) q^{3} +(0.728233 + 1.26134i) q^{4} +(0.500000 + 0.866025i) q^{5} +(0.710448 + 1.06107i) q^{6} +(-0.500000 + 0.866025i) q^{7} +2.54827 q^{8} +(-1.83082 - 2.37657i) q^{9} +0.737247 q^{10} +(-3.17448 + 5.49836i) q^{11} +(-2.51711 + 0.167393i) q^{12} +(-2.94625 - 5.10305i) q^{13} +(0.368623 + 0.638475i) q^{14} +(-1.72823 + 0.114931i) q^{15} +(-0.517115 + 0.895669i) q^{16} +5.01986 q^{17} +(-2.19226 + 0.292875i) q^{18} -0.158143 q^{19} +(-0.728233 + 1.26134i) q^{20} +(-0.963650 - 1.43923i) q^{21} +(2.34037 + 4.05365i) q^{22} +(3.10641 + 5.38046i) q^{23} +(-1.94837 + 3.96042i) q^{24} +(-0.500000 + 0.866025i) q^{25} -4.34422 q^{26} +(5.09339 - 1.02830i) q^{27} -1.45647 q^{28} +(-0.235416 + 0.407753i) q^{29} +(-0.563687 + 1.14580i) q^{30} +(-0.660163 - 1.14344i) q^{31} +(2.92951 + 5.07406i) q^{32} +(-6.11817 - 9.13760i) q^{33} +(1.85044 - 3.20506i) q^{34} -1.00000 q^{35} +(1.66439 - 4.03998i) q^{36} +9.21792 q^{37} +(-0.0582951 + 0.100970i) q^{38} +(10.1836 - 0.677229i) q^{39} +(1.27413 + 2.20687i) q^{40} +(-1.06624 - 1.84678i) q^{41} +(-1.27413 + 0.0847324i) q^{42} +(1.32442 - 2.29396i) q^{43} -9.24705 q^{44} +(1.14276 - 2.77382i) q^{45} +4.58038 q^{46} +(4.47541 - 7.75164i) q^{47} +(-0.996635 - 1.48849i) q^{48} +(-0.500000 - 0.866025i) q^{49} +(0.368623 + 0.638475i) q^{50} +(-3.83811 + 7.80167i) q^{51} +(4.29111 - 7.43242i) q^{52} -3.52147 q^{53} +(1.22100 - 3.63106i) q^{54} -6.34896 q^{55} +(-1.27413 + 2.20687i) q^{56} +(0.120913 - 0.245779i) q^{57} +(0.173560 + 0.300615i) q^{58} +(3.09358 + 5.35823i) q^{59} +(-1.40352 - 2.09619i) q^{60} +(0.284541 - 0.492840i) q^{61} -0.973406 q^{62} +(2.97358 - 0.397255i) q^{63} +2.25109 q^{64} +(2.94625 - 5.10305i) q^{65} +(-8.08943 + 0.537962i) q^{66} +(-5.27833 - 9.14234i) q^{67} +(3.65563 + 6.33174i) q^{68} +(-10.7372 + 0.714044i) q^{69} +(-0.368623 + 0.638475i) q^{70} +4.75075 q^{71} +(-4.66543 - 6.05614i) q^{72} +1.95043 q^{73} +(3.39794 - 5.88541i) q^{74} +(-0.963650 - 1.43923i) q^{75} +(-0.115165 - 0.199471i) q^{76} +(-3.17448 - 5.49836i) q^{77} +(3.32152 - 6.75161i) q^{78} +(3.45725 - 5.98813i) q^{79} -1.03423 q^{80} +(-2.29617 + 8.70216i) q^{81} -1.57216 q^{82} +(2.17010 - 3.75871i) q^{83} +(1.11359 - 2.26358i) q^{84} +(2.50993 + 4.34733i) q^{85} +(-0.976424 - 1.69122i) q^{86} +(-0.453718 - 0.677636i) q^{87} +(-8.08943 + 14.0113i) q^{88} +3.25273 q^{89} +(-1.34977 - 1.75212i) q^{90} +5.89249 q^{91} +(-4.52438 + 7.83646i) q^{92} +(2.28183 - 0.151746i) q^{93} +(-3.29948 - 5.71487i) q^{94} +(-0.0790713 - 0.136956i) q^{95} +(-10.1258 + 0.673382i) q^{96} +(-2.35084 + 4.07177i) q^{97} -0.737247 q^{98} +(18.8791 - 2.52215i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 3 q^{2} + q^{3} - 11 q^{4} + 6 q^{5} - 6 q^{6} - 6 q^{7} + 6 q^{8} - 3 q^{9}+O(q^{10}) \) 12 * q + 3 * q^2 + q^3 - 11 * q^4 + 6 * q^5 - 6 * q^6 - 6 * q^7 + 6 * q^8 - 3 * q^9	\( 12 q + 3 q^{2} + q^{3} - 11 q^{4} + 6 q^{5} - 6 q^{6} - 6 q^{7} + 6 q^{8} - 3 q^{9} + 6 q^{10} + 7 q^{11} - 37 q^{12} - 10 q^{13} + 3 q^{14} - q^{15} - 13 q^{16} + 14 q^{17} + 24 q^{18} + 30 q^{19} + 11 q^{20} - 2 q^{21} + 7 q^{22} + 14 q^{23} + 6 q^{24} - 6 q^{25} - 26 q^{26} - 2 q^{27} + 22 q^{28} - 13 q^{29} - 9 q^{30} - 10 q^{31} - 18 q^{32} - 14 q^{33} - 15 q^{34} - 12 q^{35} - 4 q^{36} + 42 q^{37} - 4 q^{38} - 11 q^{39} + 3 q^{40} - 4 q^{41} - 3 q^{42} - 13 q^{43} - 78 q^{44} - 30 q^{46} + 8 q^{47} + 42 q^{48} - 6 q^{49} + 3 q^{50} - 19 q^{51} - 31 q^{52} + 20 q^{53} + 84 q^{54} + 14 q^{55} - 3 q^{56} - 22 q^{57} - 3 q^{58} + 21 q^{59} - 17 q^{60} - 2 q^{61} + 50 q^{62} + 3 q^{63} + 62 q^{64} + 10 q^{65} + 19 q^{66} - 6 q^{67} - 33 q^{68} - 19 q^{69} - 3 q^{70} - 58 q^{71} + 51 q^{72} + 16 q^{73} - 5 q^{74} - 2 q^{75} - 31 q^{76} + 7 q^{77} - 5 q^{78} + 22 q^{79} - 26 q^{80} + 21 q^{81} + 36 q^{82} + 5 q^{83} + 20 q^{84} + 7 q^{85} + 23 q^{86} - 19 q^{87} + 19 q^{88} + 2 q^{89} + 9 q^{90} + 20 q^{91} + 9 q^{92} + 31 q^{93} - 31 q^{94} + 15 q^{95} - 66 q^{96} - 32 q^{97} - 6 q^{98} + 38 q^{99}+O(q^{100}) \) 12 * q + 3 * q^2 + q^3 - 11 * q^4 + 6 * q^5 - 6 * q^6 - 6 * q^7 + 6 * q^8 - 3 * q^9 + 6 * q^10 + 7 * q^11 - 37 * q^12 - 10 * q^13 + 3 * q^14 - q^15 - 13 * q^16 + 14 * q^17 + 24 * q^18 + 30 * q^19 + 11 * q^20 - 2 * q^21 + 7 * q^22 + 14 * q^23 + 6 * q^24 - 6 * q^25 - 26 * q^26 - 2 * q^27 + 22 * q^28 - 13 * q^29 - 9 * q^30 - 10 * q^31 - 18 * q^32 - 14 * q^33 - 15 * q^34 - 12 * q^35 - 4 * q^36 + 42 * q^37 - 4 * q^38 - 11 * q^39 + 3 * q^40 - 4 * q^41 - 3 * q^42 - 13 * q^43 - 78 * q^44 - 30 * q^46 + 8 * q^47 + 42 * q^48 - 6 * q^49 + 3 * q^50 - 19 * q^51 - 31 * q^52 + 20 * q^53 + 84 * q^54 + 14 * q^55 - 3 * q^56 - 22 * q^57 - 3 * q^58 + 21 * q^59 - 17 * q^60 - 2 * q^61 + 50 * q^62 + 3 * q^63 + 62 * q^64 + 10 * q^65 + 19 * q^66 - 6 * q^67 - 33 * q^68 - 19 * q^69 - 3 * q^70 - 58 * q^71 + 51 * q^72 + 16 * q^73 - 5 * q^74 - 2 * q^75 - 31 * q^76 + 7 * q^77 - 5 * q^78 + 22 * q^79 - 26 * q^80 + 21 * q^81 + 36 * q^82 + 5 * q^83 + 20 * q^84 + 7 * q^85 + 23 * q^86 - 19 * q^87 + 19 * q^88 + 2 * q^89 + 9 * q^90 + 20 * q^91 + 9 * q^92 + 31 * q^93 - 31 * q^94 + 15 * q^95 - 66 * q^96 - 32 * q^97 - 6 * q^98 + 38 * q^99

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