LMFDB - Embedded newform 187.2.g.c.103.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [187,2,Mod(69,187)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(187, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([8, 0]))

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

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

chi := DirichletCharacter("187.69");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 187 = 11 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	187.g (of order $5$, degree $4$, 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:	$1.49320251780$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{10})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + x^{2} - x + 1 $ x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			103.1
Root			$0.809017 - 0.587785i$ of defining polynomial
Character	$\chi$	$=$	187.103
Dual form			187.2.g.c.69.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.80902 + 1.31433i) q^{2} +(-0.809017 + 2.48990i) q^{3} +(0.927051 + 2.85317i) q^{4} +(1.61803 - 1.17557i) q^{5} +(-4.73607 + 3.44095i) q^{6} +(-0.500000 - 1.53884i) q^{7} +(-0.690983 + 2.12663i) q^{8} +(-3.11803 - 2.26538i) q^{9} +O(q^{10})$	\(q+(1.80902 + 1.31433i) q^{2} +(-0.809017 + 2.48990i) q^{3} +(0.927051 + 2.85317i) q^{4} +(1.61803 - 1.17557i) q^{5} +(-4.73607 + 3.44095i) q^{6} +(-0.500000 - 1.53884i) q^{7} +(-0.690983 + 2.12663i) q^{8} +(-3.11803 - 2.26538i) q^{9} +4.47214 q^{10} +(-1.23607 - 3.07768i) q^{11} -7.85410 q^{12} +(-0.500000 - 0.363271i) q^{13} +(1.11803 - 3.44095i) q^{14} +(1.61803 + 4.97980i) q^{15} +(0.809017 - 0.587785i) q^{16} +(0.809017 - 0.587785i) q^{17} +(-2.66312 - 8.19624i) q^{18} +(-1.61803 + 4.97980i) q^{19} +(4.85410 + 3.52671i) q^{20} +4.23607 q^{21} +(1.80902 - 7.19218i) q^{22} -3.85410 q^{23} +(-4.73607 - 3.44095i) q^{24} +(-0.309017 + 0.951057i) q^{25} +(-0.427051 - 1.31433i) q^{26} +(1.80902 - 1.31433i) q^{27} +(3.92705 - 2.85317i) q^{28} +(1.76393 + 5.42882i) q^{29} +(-3.61803 + 11.1352i) q^{30} +(-2.00000 - 1.45309i) q^{31} +6.70820 q^{32} +(8.66312 - 0.587785i) q^{33} +2.23607 q^{34} +(-2.61803 - 1.90211i) q^{35} +(3.57295 - 10.9964i) q^{36} +(-2.00000 - 6.15537i) q^{37} +(-9.47214 + 6.88191i) q^{38} +(1.30902 - 0.951057i) q^{39} +(1.38197 + 4.25325i) q^{40} +(3.38197 - 10.4086i) q^{41} +(7.66312 + 5.56758i) q^{42} +7.23607 q^{43} +(7.63525 - 6.37988i) q^{44} -7.70820 q^{45} +(-6.97214 - 5.06555i) q^{46} +(-2.76393 + 8.50651i) q^{47} +(0.809017 + 2.48990i) q^{48} +(3.54508 - 2.57565i) q^{49} +(-1.80902 + 1.31433i) q^{50} +(0.809017 + 2.48990i) q^{51} +(0.572949 - 1.76336i) q^{52} +(-9.16312 - 6.65740i) q^{53} +5.00000 q^{54} +(-5.61803 - 3.52671i) q^{55} +3.61803 q^{56} +(-11.0902 - 8.05748i) q^{57} +(-3.94427 + 12.1392i) q^{58} +(4.23607 + 13.0373i) q^{59} +(-12.7082 + 9.23305i) q^{60} +(-4.23607 + 3.07768i) q^{61} +(-1.70820 - 5.25731i) q^{62} +(-1.92705 + 5.93085i) q^{63} +(10.5172 + 7.64121i) q^{64} -1.23607 q^{65} +(16.4443 + 10.3229i) q^{66} -12.0000 q^{67} +(2.42705 + 1.76336i) q^{68} +(3.11803 - 9.59632i) q^{69} +(-2.23607 - 6.88191i) q^{70} +(-1.23607 + 0.898056i) q^{71} +(6.97214 - 5.06555i) q^{72} +(2.85410 + 8.78402i) q^{73} +(4.47214 - 13.7638i) q^{74} +(-2.11803 - 1.53884i) q^{75} -15.7082 q^{76} +(-4.11803 + 3.44095i) q^{77} +3.61803 q^{78} +(-8.54508 - 6.20837i) q^{79} +(0.618034 - 1.90211i) q^{80} +(-1.76393 - 5.42882i) q^{81} +(19.7984 - 14.3844i) q^{82} +(4.61803 - 3.35520i) q^{83} +(3.92705 + 12.0862i) q^{84} +(0.618034 - 1.90211i) q^{85} +(13.0902 + 9.51057i) q^{86} -14.9443 q^{87} +(7.39919 - 0.502029i) q^{88} +14.7984 q^{89} +(-13.9443 - 10.1311i) q^{90} +(-0.309017 + 0.951057i) q^{91} +(-3.57295 - 10.9964i) q^{92} +(5.23607 - 3.80423i) q^{93} +(-16.1803 + 11.7557i) q^{94} +(3.23607 + 9.95959i) q^{95} +(-5.42705 + 16.7027i) q^{96} +(-4.85410 - 3.52671i) q^{97} +9.79837 q^{98} +(-3.11803 + 12.3965i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 5 q^{2} - q^{3} - 3 q^{4} + 2 q^{5} - 10 q^{6} - 2 q^{7} - 5 q^{8} - 8 q^{9}+O(q^{10}) $ 4 * q + 5 * q^2 - q^3 - 3 * q^4 + 2 * q^5 - 10 * q^6 - 2 * q^7 - 5 * q^8 - 8 * q^9	\( 4 q + 5 q^{2} - q^{3} - 3 q^{4} + 2 q^{5} - 10 q^{6} - 2 q^{7} - 5 q^{8} - 8 q^{9} + 4 q^{11} - 18 q^{12} - 2 q^{13} + 2 q^{15} + q^{16} + q^{17} + 5 q^{18} - 2 q^{19} + 6 q^{20} + 8 q^{21} + 5 q^{22} - 2 q^{23} - 10 q^{24} + q^{25} + 5 q^{26} + 5 q^{27} + 9 q^{28} + 16 q^{29} - 10 q^{30} - 8 q^{31} + 19 q^{33} - 6 q^{35} + 21 q^{36} - 8 q^{37} - 20 q^{38} + 3 q^{39} + 10 q^{40} + 18 q^{41} + 15 q^{42} + 20 q^{43} - 3 q^{44} - 4 q^{45} - 10 q^{46} - 20 q^{47} + q^{48} + 3 q^{49} - 5 q^{50} + q^{51} + 9 q^{52} - 21 q^{53} + 20 q^{54} - 18 q^{55} + 10 q^{56} - 22 q^{57} + 20 q^{58} + 8 q^{59} - 24 q^{60} - 8 q^{61} + 20 q^{62} - q^{63} + 13 q^{64} + 4 q^{65} + 30 q^{66} - 48 q^{67} + 3 q^{68} + 8 q^{69} + 4 q^{71} + 10 q^{72} - 2 q^{73} - 4 q^{75} - 36 q^{76} - 12 q^{77} + 10 q^{78} - 23 q^{79} - 2 q^{80} - 16 q^{81} + 30 q^{82} + 14 q^{83} + 9 q^{84} - 2 q^{85} + 30 q^{86} - 24 q^{87} + 5 q^{88} + 10 q^{89} - 20 q^{90} + q^{91} - 21 q^{92} + 12 q^{93} - 20 q^{94} + 4 q^{95} - 15 q^{96} - 6 q^{97} - 10 q^{98} - 8 q^{99}+O(q^{100}) \) 4 * q + 5 * q^2 - q^3 - 3 * q^4 + 2 * q^5 - 10 * q^6 - 2 * q^7 - 5 * q^8 - 8 * q^9 + 4 * q^11 - 18 * q^12 - 2 * q^13 + 2 * q^15 + q^16 + q^17 + 5 * q^18 - 2 * q^19 + 6 * q^20 + 8 * q^21 + 5 * q^22 - 2 * q^23 - 10 * q^24 + q^25 + 5 * q^26 + 5 * q^27 + 9 * q^28 + 16 * q^29 - 10 * q^30 - 8 * q^31 + 19 * q^33 - 6 * q^35 + 21 * q^36 - 8 * q^37 - 20 * q^38 + 3 * q^39 + 10 * q^40 + 18 * q^41 + 15 * q^42 + 20 * q^43 - 3 * q^44 - 4 * q^45 - 10 * q^46 - 20 * q^47 + q^48 + 3 * q^49 - 5 * q^50 + q^51 + 9 * q^52 - 21 * q^53 + 20 * q^54 - 18 * q^55 + 10 * q^56 - 22 * q^57 + 20 * q^58 + 8 * q^59 - 24 * q^60 - 8 * q^61 + 20 * q^62 - q^63 + 13 * q^64 + 4 * q^65 + 30 * q^66 - 48 * q^67 + 3 * q^68 + 8 * q^69 + 4 * q^71 + 10 * q^72 - 2 * q^73 - 4 * q^75 - 36 * q^76 - 12 * q^77 + 10 * q^78 - 23 * q^79 - 2 * q^80 - 16 * q^81 + 30 * q^82 + 14 * q^83 + 9 * q^84 - 2 * q^85 + 30 * q^86 - 24 * q^87 + 5 * q^88 + 10 * q^89 - 20 * q^90 + q^91 - 21 * q^92 + 12 * q^93 - 20 * q^94 + 4 * q^95 - 15 * q^96 - 6 * q^97 - 10 * q^98 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/187\mathbb{Z}\right)^\times$.

$n$	$35$	$122$
$\chi(n)$	$e\left(\frac{1}{5}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	1.80902	+	1.31433i	1.27917	+	0.929370i	0.999528	−	0.0307347i	$-0.00978469\pi$
$2$	1.80902	+	1.31433i	1.27917	+	0.929370i	0.279641	+	0.960105i	$0.409785\pi$
$3$	−0.809017	+	2.48990i	−0.467086	+	1.43754i	0.389254	+	0.921131i	$0.372733\pi$
$3$	−0.809017	+	2.48990i	−0.467086	+	1.43754i	−0.856340	+	0.516413i	$0.827267\pi$
$4$	0.927051	+	2.85317i	0.463525	+	1.42658i
$5$	1.61803	−	1.17557i	0.723607	−	0.525731i	−0.163928	−	0.986472i	$-0.552416\pi$
$5$	1.61803	−	1.17557i	0.723607	−	0.525731i	0.887535	+	0.460741i	$0.152416\pi$
$6$	−4.73607	+	3.44095i	−1.93349	+	1.40476i
$7$	−0.500000	−	1.53884i	−0.188982	−	0.581628i	0.811012	−	0.585030i	$-0.198917\pi$
$7$	−0.500000	−	1.53884i	−0.188982	−	0.581628i	−0.999994	+	0.00340203i	$0.998917\pi$
$8$	−0.690983	+	2.12663i	−0.244299	+	0.751876i
$9$	−3.11803	−	2.26538i	−1.03934	−	0.755128i
$10$	4.47214			1.41421
$11$	−1.23607	−	3.07768i	−0.372689	−	0.927957i
$11$	−1.23607	−	3.07768i	−0.372689	−	0.927957i
$12$	−7.85410			−2.26728
$13$	−0.500000	−	0.363271i	−0.138675	−	0.100753i	0.516285	−	0.856417i	$-0.327315\pi$
$13$	−0.500000	−	0.363271i	−0.138675	−	0.100753i	−0.654960	+	0.755664i	$0.727315\pi$
$14$	1.11803	−	3.44095i	0.298807	−	0.919634i
$15$	1.61803	+	4.97980i	0.417775	+	1.28578i
$16$	0.809017	−	0.587785i	0.202254	−	0.146946i
$17$	0.809017	−	0.587785i	0.196215	−	0.142559i
$17$	0.809017	−	0.587785i	0.196215	−	0.142559i
$18$	−2.66312	−	8.19624i	−0.627703	−	1.93187i
$19$	−1.61803	+	4.97980i	−0.371202	+	1.14244i	0.574803	+	0.818292i	$0.305079\pi$
$19$	−1.61803	+	4.97980i	−0.371202	+	1.14244i	−0.946005	+	0.324152i	$0.894921\pi$
$20$	4.85410	+	3.52671i	1.08541	+	0.788597i
$21$	4.23607			0.924386
$22$	1.80902	−	7.19218i	0.385684	−	1.53338i
$23$	−3.85410			−0.803636			−0.401818	−	0.915720i	$-0.631622\pi$
$23$	−3.85410			−0.803636			−0.401818	+	0.915720i	$0.631622\pi$
$24$	−4.73607	−	3.44095i	−0.966746	−	0.702382i
$25$	−0.309017	+	0.951057i	−0.0618034	+	0.190211i
$26$	−0.427051	−	1.31433i	−0.0837516	−	0.257761i
$27$	1.80902	−	1.31433i	0.348145	−	0.252942i
$28$	3.92705	−	2.85317i	0.742143	−	0.539198i
$29$	1.76393	+	5.42882i	0.327554	+	1.00811i	0.970275	+	0.242007i	$0.0778056\pi$
$29$	1.76393	+	5.42882i	0.327554	+	1.00811i	−0.642721	+	0.766101i	$0.722194\pi$
$30$	−3.61803	+	11.1352i	−0.660560	+	2.03299i
$31$	−2.00000	−	1.45309i	−0.359211	−	0.260982i	0.393512	−	0.919319i	$-0.371260\pi$
$31$	−2.00000	−	1.45309i	−0.359211	−	0.260982i	−0.752723	+	0.658338i	$0.771260\pi$
$32$	6.70820			1.18585
$33$	8.66312	−	0.587785i	1.50806	−	0.102320i
$34$	2.23607			0.383482
$35$	−2.61803	−	1.90211i	−0.442529	−	0.321516i
$36$	3.57295	−	10.9964i	0.595492	−	1.83273i
$37$	−2.00000	−	6.15537i	−0.328798	−	1.01194i	−0.969697	−	0.244311i	$-0.921438\pi$
$37$	−2.00000	−	6.15537i	−0.328798	−	1.01194i	0.640899	−	0.767625i	$-0.278562\pi$
$38$	−9.47214	+	6.88191i	−1.53658	+	1.11639i
$39$	1.30902	−	0.951057i	0.209610	−	0.152291i
$40$	1.38197	+	4.25325i	0.218508	+	0.672499i
$41$	3.38197	−	10.4086i	0.528174	−	1.62555i	−0.229778	−	0.973243i	$-0.573800\pi$
$41$	3.38197	−	10.4086i	0.528174	−	1.62555i	0.757952	−	0.652310i	$-0.226200\pi$
$42$	7.66312	+	5.56758i	1.18244	+	0.859097i
$43$	7.23607			1.10349			0.551745	−	0.834013i	$-0.313962\pi$
$43$	7.23607			1.10349			0.551745	+	0.834013i	$0.313962\pi$
$44$	7.63525	−	6.37988i	1.15106	−	0.961803i
$45$	−7.70820			−1.14907
$46$	−6.97214	−	5.06555i	−1.02799	−	0.746875i
$47$	−2.76393	+	8.50651i	−0.403161	+	1.24080i	0.519260	+	0.854616i	$0.326208\pi$
$47$	−2.76393	+	8.50651i	−0.403161	+	1.24080i	−0.922421	+	0.386186i	$0.873792\pi$
$48$	0.809017	+	2.48990i	0.116772	+	0.359386i
$49$	3.54508	−	2.57565i	0.506441	−	0.367951i
$50$	−1.80902	+	1.31433i	−0.255834	+	0.185874i
$51$	0.809017	+	2.48990i	0.113285	+	0.348655i
$52$	0.572949	−	1.76336i	0.0794537	−	0.244533i
$53$	−9.16312	−	6.65740i	−1.25865	−	0.914464i	−0.259960	−	0.965619i	$-0.583710\pi$
$53$	−9.16312	−	6.65740i	−1.25865	−	0.914464i	−0.998691	+	0.0511556i	$0.983710\pi$
$54$	5.00000			0.680414
$55$	−5.61803	−	3.52671i	−0.757536	−	0.475542i
$56$	3.61803			0.483480
$57$	−11.0902	−	8.05748i	−1.46893	−	1.06724i
$58$	−3.94427	+	12.1392i	−0.517908	+	1.59396i
$59$	4.23607	+	13.0373i	0.551489	+	1.69731i	0.705039	+	0.709168i	$0.250929\pi$
$59$	4.23607	+	13.0373i	0.551489	+	1.69731i	−0.153550	+	0.988141i	$0.549071\pi$
$60$	−12.7082	+	9.23305i	−1.64062	+	1.19198i
$61$	−4.23607	+	3.07768i	−0.542373	+	0.394057i	−0.824966	−	0.565183i	$-0.808806\pi$
$61$	−4.23607	+	3.07768i	−0.542373	+	0.394057i	0.282593	+	0.959240i	$0.408806\pi$
$62$	−1.70820	−	5.25731i	−0.216942	−	0.667679i
$63$	−1.92705	+	5.93085i	−0.242786	+	0.747217i
$64$	10.5172	+	7.64121i	1.31465	+	0.955151i
$65$	−1.23607			−0.153315
$66$	16.4443	+	10.3229i	2.02415	+	1.27066i
$67$	−12.0000			−1.46603			−0.733017	−	0.680211i	$-0.761888\pi$
$67$	−12.0000			−1.46603			−0.733017	+	0.680211i	$0.761888\pi$
$68$	2.42705	+	1.76336i	0.294323	+	0.213838i
$69$	3.11803	−	9.59632i	0.375367	−	1.15526i
$70$	−2.23607	−	6.88191i	−0.267261	−	0.822546i
$71$	−1.23607	+	0.898056i	−0.146694	+	0.106580i	−0.658712	−	0.752395i	$-0.728898\pi$
$71$	−1.23607	+	0.898056i	−0.146694	+	0.106580i	0.512017	+	0.858975i	$0.328898\pi$
$72$	6.97214	−	5.06555i	0.821674	−	0.596981i
$73$	2.85410	+	8.78402i	0.334047	+	1.02809i	0.967189	+	0.254056i	$0.0817649\pi$
$73$	2.85410	+	8.78402i	0.334047	+	1.02809i	−0.633142	+	0.774036i	$0.718235\pi$
$74$	4.47214	−	13.7638i	0.519875	−	1.60001i
$75$	−2.11803	−	1.53884i	−0.244569	−	0.177690i
$76$	−15.7082			−1.80185
$77$	−4.11803	+	3.44095i	−0.469294	+	0.392133i
$78$	3.61803			0.409662
$79$	−8.54508	−	6.20837i	−0.961397	−	0.698496i	−0.00792236	−	0.999969i	$-0.502522\pi$
$79$	−8.54508	−	6.20837i	−0.961397	−	0.698496i	−0.953475	+	0.301473i	$0.902522\pi$
$80$	0.618034	−	1.90211i	0.0690983	−	0.212663i
$81$	−1.76393	−	5.42882i	−0.195992	−	0.603203i
$82$	19.7984	−	14.3844i	2.18636	−	1.58849i
$83$	4.61803	−	3.35520i	0.506895	−	0.368281i	−0.304749	−	0.952433i	$-0.598573\pi$
$83$	4.61803	−	3.35520i	0.506895	−	0.368281i	0.811644	+	0.584152i	$0.198573\pi$
$84$	3.92705	+	12.0862i	0.428476	+	1.31871i
$85$	0.618034	−	1.90211i	0.0670352	−	0.206313i
$86$	13.0902	+	9.51057i	1.41155	+	1.02555i
$87$	−14.9443			−1.60219
$88$	7.39919	−	0.502029i	0.788756	−	0.0535164i
$89$	14.7984			1.56862			0.784312	−	0.620366i	$-0.213016\pi$
$89$	14.7984			1.56862			0.784312	+	0.620366i	$0.213016\pi$
$90$	−13.9443	−	10.1311i	−1.46986	−	1.06791i
$91$	−0.309017	+	0.951057i	−0.0323938	+	0.0996978i
$92$	−3.57295	−	10.9964i	−0.372506	−	1.14645i
$93$	5.23607	−	3.80423i	0.542955	−	0.394480i
$94$	−16.1803	+	11.7557i	−1.66887	+	1.21251i
$95$	3.23607	+	9.95959i	0.332014	+	1.02183i
$96$	−5.42705	+	16.7027i	−0.553896	+	1.70472i
$97$	−4.85410	−	3.52671i	−0.492859	−	0.358083i	0.313423	−	0.949613i	$-0.398524\pi$
$97$	−4.85410	−	3.52671i	−0.492859	−	0.358083i	−0.806283	+	0.591530i	$0.798524\pi$
$98$	9.79837			0.989785
$99$	−3.11803	+	12.3965i	−0.313374	+	1.24589i
$100$	−3.00000			−0.300000
$101$	5.78115	+	4.20025i	0.575246	+	0.417941i	0.837007	−	0.547192i	$-0.184303\pi$
$101$	5.78115	+	4.20025i	0.575246	+	0.417941i	−0.261761	+	0.965133i	$0.584303\pi$
$102$	−1.80902	+	5.56758i	−0.179119	+	0.551273i
$103$	−2.52786	−	7.77997i	−0.249078	−	0.766583i	−0.994939	−	0.100481i	$-0.967962\pi$
$103$	−2.52786	−	7.77997i	−0.249078	−	0.766583i	0.745861	−	0.666102i	$-0.232038\pi$
$104$	1.11803	−	0.812299i	0.109632	−	0.0796525i
$105$	6.85410	−	4.97980i	0.668892	−	0.485978i
$106$	−7.82624	−	24.0867i	−0.760151	−	2.33951i
$107$	1.73607	−	5.34307i	0.167832	−	0.516534i	−0.831402	−	0.555672i	$-0.812461\pi$
$107$	1.73607	−	5.34307i	0.167832	−	0.516534i	0.999234	+	0.0391379i	$0.0124611\pi$
$108$	5.42705	+	3.94298i	0.522218	+	0.379414i
$109$	−0.472136			−0.0452224			−0.0226112	−	0.999744i	$-0.507198\pi$
$109$	−0.472136			−0.0452224			−0.0226112	+	0.999744i	$0.507198\pi$
$110$	−5.52786	−	13.7638i	−0.527061	−	1.31233i
$111$	16.9443			1.60828
$112$	−1.30902	−	0.951057i	−0.123690	−	0.0898664i
$113$	−1.23607	+	3.80423i	−0.116279	+	0.357871i	−0.992212	−	0.124563i	$-0.960247\pi$
$113$	−1.23607	+	3.80423i	−0.116279	+	0.357871i	0.875932	+	0.482434i	$0.160247\pi$
$114$	−9.47214	−	29.1522i	−0.887147	−	2.73036i
$115$	−6.23607	+	4.53077i	−0.581516	+	0.422496i
$116$	−13.8541	+	10.0656i	−1.28632	+	0.934567i
$117$	0.736068	+	2.26538i	0.0680495	+	0.209435i
$118$	−9.47214	+	29.1522i	−0.871981	+	2.68368i
$119$	−1.30902	−	0.951057i	−0.119997	−	0.0871832i
$120$	−11.7082			−1.06881
$121$	−7.94427	+	7.60845i	−0.722207	+	0.691677i
$122$	−11.7082			−1.06001
$123$	23.1803	+	16.8415i	2.09010	+	1.51855i
$124$	2.29180	−	7.05342i	0.205809	−	0.633416i
$125$	3.70820	+	11.4127i	0.331672	+	1.02078i
$126$	−11.2812	+	8.19624i	−1.00500	+	0.730179i
$127$	−1.23607	+	0.898056i	−0.109683	+	0.0796896i	−0.641275	−	0.767311i	$-0.721594\pi$
$127$	−1.23607	+	0.898056i	−0.109683	+	0.0796896i	0.531592	+	0.847001i	$0.321594\pi$
$128$	4.83688	+	14.8864i	0.427524	+	1.31578i
$129$	−5.85410	+	18.0171i	−0.515425	+	1.58631i
$130$	−2.23607	−	1.62460i	−0.196116	−	0.142487i
$131$	17.3820			1.51867			0.759335	−	0.650700i	$-0.225525\pi$
$131$	17.3820			1.51867			0.759335	+	0.650700i	$0.225525\pi$
$132$	9.70820	+	24.1724i	0.844991	+	2.10394i
$133$	8.47214			0.734627
$134$	−21.7082	−	15.7719i	−1.87530	−	1.36249i
$135$	1.38197	−	4.25325i	0.118941	−	0.366062i
$136$	0.690983	+	2.12663i	0.0592513	+	0.182357i
$137$	−4.38197	+	3.18368i	−0.374377	+	0.272001i	−0.759023	−	0.651063i	$-0.774323\pi$
$137$	−4.38197	+	3.18368i	−0.374377	+	0.272001i	0.384647	+	0.923064i	$0.374323\pi$
$138$	18.2533	−	13.2618i	1.55382	−	1.12892i
$139$	1.23607	+	3.80423i	0.104842	+	0.322670i	0.989693	−	0.143203i	$-0.0457402\pi$
$139$	1.23607	+	3.80423i	0.104842	+	0.322670i	−0.884851	+	0.465873i	$0.845740\pi$
$140$	3.00000	−	9.23305i	0.253546	−	0.780335i
$141$	−18.9443	−	13.7638i	−1.59540	−	1.15912i
$142$	−3.41641			−0.286699
$143$	−0.500000	+	1.98787i	−0.0418121	+	0.166234i
$144$	−3.85410			−0.321175
$145$	9.23607	+	6.71040i	0.767014	+	0.557268i
$146$	−6.38197	+	19.6417i	−0.528175	+	1.62556i
$147$	3.54508	+	10.9106i	0.292394	+	0.899895i
$148$	15.7082	−	11.4127i	1.29121	−	0.938116i
$149$	16.8713	−	12.2577i	1.38215	−	1.00419i	0.385477	−	0.922717i	$-0.374037\pi$
$149$	16.8713	−	12.2577i	1.38215	−	1.00419i	0.996675	−	0.0814753i	$-0.0259632\pi$
$150$	−1.80902	−	5.56758i	−0.147706	−	0.454591i
$151$	0.381966	−	1.17557i	0.0310840	−	0.0956666i	−0.934311	−	0.356459i	$-0.883984\pi$
$151$	0.381966	−	1.17557i	0.0310840	−	0.0956666i	0.965395	+	0.260793i	$0.0839839\pi$
$152$	−9.47214	−	6.88191i	−0.768292	−	0.558197i
$153$	−3.85410			−0.311586
$154$	−11.9721	+	0.812299i	−0.964742	+	0.0654569i
$155$	−4.94427			−0.397133
$156$	3.92705	+	2.85317i	0.314416	+	0.228436i
$157$	−3.42705	+	10.5474i	−0.273508	+	0.841772i	0.716102	+	0.697996i	$0.245925\pi$
$157$	−3.42705	+	10.5474i	−0.273508	+	0.841772i	−0.989610	+	0.143777i	$0.954075\pi$
$158$	−7.29837	−	22.4621i	−0.580627	−	1.78699i
$159$	23.9894	−	17.4293i	1.90248	−	1.38223i
$160$	10.8541	−	7.88597i	0.858092	−	0.623440i
$161$	1.92705	+	5.93085i	0.151873	+	0.467417i
$162$	3.94427	−	12.1392i	0.309891	−	0.953747i
$163$	3.30902	+	2.40414i	0.259182	+	0.188307i	0.709786	−	0.704417i	$-0.248791\pi$
$163$	3.30902	+	2.40414i	0.259182	+	0.188307i	−0.450604	+	0.892724i	$0.648791\pi$
$164$	32.8328			2.56381
$165$	13.3262	−	11.1352i	1.03745	−	0.866871i
$166$	12.7639			0.990673
$167$	1.88197	+	1.36733i	0.145631	+	0.105807i	0.658215	−	0.752830i	$-0.271312\pi$
$167$	1.88197	+	1.36733i	0.145631	+	0.105807i	−0.512584	+	0.858637i	$0.671312\pi$
$168$	−2.92705	+	9.00854i	−0.225827	+	0.695024i
$169$	−3.89919	−	12.0005i	−0.299937	−	0.923113i
$170$	3.61803	−	2.62866i	0.277491	−	0.201609i
$171$	16.3262	−	11.8617i	1.24850	−	0.907087i
$172$	6.70820	+	20.6457i	0.511496	+	1.57422i
$173$	−5.38197	+	16.5640i	−0.409183	+	1.25934i	0.508168	+	0.861258i	$0.330323\pi$
$173$	−5.38197	+	16.5640i	−0.409183	+	1.25934i	−0.917351	+	0.398079i	$0.869677\pi$
$174$	−27.0344	−	19.6417i	−2.04948	−	1.48903i
$175$	1.61803			0.122312
$176$	−2.80902	−	1.76336i	−0.211738	−	0.132918i
$177$	−35.8885			−2.69755
$178$	26.7705	+	19.4499i	2.00653	+	1.45783i
$179$	2.09017	−	6.43288i	0.156227	−	0.480816i	−0.842056	−	0.539389i	$-0.818655\pi$
$179$	2.09017	−	6.43288i	0.156227	−	0.480816i	0.998283	+	0.0585732i	$0.0186551\pi$
$180$	−7.14590	−	21.9928i	−0.532624	−	1.63925i
$181$	0.618034	−	0.449028i	0.0459381	−	0.0333760i	−0.564579	−	0.825379i	$-0.690962\pi$
$181$	0.618034	−	0.449028i	0.0459381	−	0.0333760i	0.610517	+	0.792003i	$0.290962\pi$
$182$	−1.80902	+	1.31433i	−0.134093	+	0.0974245i
$183$	−4.23607	−	13.0373i	−0.313139	−	0.963743i
$184$	2.66312	−	8.19624i	0.196328	−	0.604235i
$185$	−10.4721	−	7.60845i	−0.769927	−	0.559385i
$186$	14.4721			1.06115
$187$	−2.80902	−	1.76336i	−0.205416	−	0.128949i
$188$	−26.8328			−1.95698
$189$	−2.92705	−	2.12663i	−0.212912	−	0.154689i
$190$	−7.23607	+	22.2703i	−0.524960	+	1.61566i
$191$	−5.56231	−	17.1190i	−0.402474	−	1.23869i	−0.922986	−	0.384834i	$-0.874259\pi$
$191$	−5.56231	−	17.1190i	−0.402474	−	1.23869i	0.520511	−	0.853855i	$-0.325741\pi$
$192$	−27.5344	+	20.0049i	−1.98713	+	1.44373i
$193$	−14.0902	+	10.2371i	−1.01423	+	0.736883i	−0.965093	−	0.261909i	$-0.915648\pi$
$193$	−14.0902	+	10.2371i	−1.01423	+	0.736883i	−0.0491400	+	0.998792i	$0.515648\pi$
$194$	−4.14590	−	12.7598i	−0.297658	−	0.916098i
$195$	1.00000	−	3.07768i	0.0716115	−	0.220397i
$196$	10.6353	+	7.72696i	0.759661	+	0.551926i
$197$	10.2918			0.733260			0.366630	−	0.930367i	$-0.380511\pi$
$197$	10.2918			0.733260			0.366630	+	0.930367i	$0.380511\pi$
$198$	−21.9336	+	18.3273i	−1.55876	+	1.30247i
$199$	−15.1459			−1.07366			−0.536832	−	0.843689i	$-0.680379\pi$
$199$	−15.1459			−1.07366			−0.536832	+	0.843689i	$0.680379\pi$
$200$	−1.80902	−	1.31433i	−0.127917	−	0.0929370i
$201$	9.70820	−	29.8788i	0.684764	−	2.10749i
$202$	4.93769	+	15.1967i	0.347415	+	1.06923i
$203$	7.47214	−	5.42882i	0.524441	−	0.381029i
$204$	−6.35410	+	4.61653i	−0.444876	+	0.323221i
$205$	−6.76393	−	20.8172i	−0.472414	−	1.45394i
$206$	5.65248	−	17.3965i	0.393827	−	1.21207i
$207$	12.0172	+	8.73102i	0.835255	+	0.606848i
$208$	−0.618034			−0.0428529
$209$	17.3262	−	1.17557i	1.19848	−	0.0813159i
$210$	18.9443			1.30728
$211$	19.4164	+	14.1068i	1.33668	+	0.971155i	0.999559	+	0.0296942i	$0.00945335\pi$
$211$	19.4164	+	14.1068i	1.33668	+	0.971155i	0.337122	+	0.941461i	$0.390547\pi$
$212$	10.5000	−	32.3157i	0.721143	−	2.21945i
$213$	−1.23607	−	3.80423i	−0.0846940	−	0.260661i
$214$	10.1631	−	7.38394i	0.694737	−	0.504756i
$215$	11.7082	−	8.50651i	0.798493	−	0.580139i
$216$	1.54508	+	4.75528i	0.105130	+	0.323556i
$217$	−1.23607	+	3.80423i	−0.0839098	+	0.258248i
$218$	−0.854102	−	0.620541i	−0.0578471	−	0.0420284i
$219$	−24.1803			−1.63396
$220$	4.85410	−	19.2986i	0.327263	−	1.30111i
$221$	−0.618034			−0.0415735
$222$	30.6525	+	22.2703i	2.05726	+	1.49469i
$223$	−2.70820	+	8.33499i	−0.181355	+	0.558153i	−0.999867	−	0.0163372i	$-0.994799\pi$
$223$	−2.70820	+	8.33499i	−0.181355	+	0.558153i	0.818512	+	0.574490i	$0.194799\pi$
$224$	−3.35410	−	10.3229i	−0.224105	−	0.689725i
$225$	3.11803	−	2.26538i	0.207869	−	0.151026i
$226$	−7.23607	+	5.25731i	−0.481336	+	0.349711i
$227$	−2.02786	−	6.24112i	−0.134594	−	0.414238i	0.860933	−	0.508719i	$-0.169881\pi$
$227$	−2.02786	−	6.24112i	−0.134594	−	0.414238i	−0.995527	+	0.0944811i	$0.969881\pi$
$228$	12.7082	−	39.1118i	0.841621	−	2.59024i
$229$	−11.7812	−	8.55951i	−0.778521	−	0.565628i	0.126014	−	0.992028i	$-0.459782\pi$
$229$	−11.7812	−	8.55951i	−0.778521	−	0.565628i	−0.904535	+	0.426400i	$0.859782\pi$
$230$	−17.2361			−1.13651
$231$	−5.23607	−	13.0373i	−0.344508	−	0.857790i
$232$	−12.7639			−0.837993
$233$	23.3262	+	16.9475i	1.52815	+	1.11027i	0.957254	+	0.289247i	$0.0934049\pi$
$233$	23.3262	+	16.9475i	1.52815	+	1.11027i	0.570898	+	0.821021i	$0.306595\pi$
$234$	−1.64590	+	5.06555i	−0.107596	+	0.331146i
$235$	5.52786	+	17.0130i	0.360598	+	1.10981i
$236$	−33.2705	+	24.1724i	−2.16573	+	1.57349i
$237$	22.3713	−	16.2537i	1.45317	−	1.05579i
$238$	−1.11803	−	3.44095i	−0.0724714	−	0.223044i
$239$	0.0557281	−	0.171513i	0.00360475	−	0.0110943i	−0.949238	−	0.314559i	$-0.898143\pi$
$239$	0.0557281	−	0.171513i	0.00360475	−	0.0110943i	0.952843	+	0.303465i	$0.0981434\pi$
$240$	4.23607	+	3.07768i	0.273437	+	0.198664i
$241$	−3.70820			−0.238866			−0.119433	−	0.992842i	$-0.538108\pi$
$241$	−3.70820			−0.238866			−0.119433	+	0.992842i	$0.538108\pi$
$242$	−24.3713	+	3.32244i	−1.56665	+	0.213575i
$243$	21.6525			1.38901
$244$	−12.7082	−	9.23305i	−0.813559	−	0.591085i
$245$	2.70820	−	8.33499i	0.173021	−	0.532503i
$246$	19.7984	+	60.9331i	1.26230	+	3.88495i
$247$	2.61803	−	1.90211i	0.166582	−	0.121029i
$248$	4.47214	−	3.24920i	0.283981	−	0.206324i
$249$	4.61803	+	14.2128i	0.292656	+	0.900703i
$250$	−8.29180	+	25.5195i	−0.524419	+	1.61400i
$251$	7.47214	+	5.42882i	0.471637	+	0.342664i	0.798079	−	0.602553i	$-0.205850\pi$
$251$	7.47214	+	5.42882i	0.471637	+	0.342664i	−0.326442	+	0.945217i	$0.605850\pi$
$252$	−18.7082			−1.17851
$253$	4.76393	+	11.8617i	0.299506	+	0.745739i
$254$	−3.41641			−0.214364
$255$	4.23607	+	3.07768i	0.265273	+	0.192732i
$256$	−2.78115	+	8.55951i	−0.173822	+	0.534969i
$257$	1.79180	+	5.51458i	0.111769	+	0.343990i	0.991259	−	0.131927i	$-0.0421163\pi$
$257$	1.79180	+	5.51458i	0.111769	+	0.343990i	−0.879490	+	0.475917i	$0.842116\pi$
$258$	−34.2705	+	24.8990i	−2.13359	+	1.55014i
$259$	−8.47214	+	6.15537i	−0.526433	+	0.382476i
$260$	−1.14590	−	3.52671i	−0.0710656	−	0.218717i
$261$	6.79837	−	20.9232i	0.420809	−	1.29512i
$262$	31.4443	+	22.8456i	1.94263	+	1.41141i
$263$	−23.1246			−1.42592			−0.712962	−	0.701202i	$-0.752647\pi$
$263$	−23.1246			−1.42592			−0.712962	+	0.701202i	$0.752647\pi$
$264$	−4.73607	+	18.8294i	−0.291485	+	1.15887i
$265$	−22.6525			−1.39153
$266$	15.3262	+	11.1352i	0.939712	+	0.682741i
$267$	−11.9721	+	36.8464i	−0.732683	+	2.25497i
$268$	−11.1246	−	34.2380i	−0.679544	−	2.09142i
$269$	−16.4721	+	11.9677i	−1.00432	+	0.729684i	−0.963011	−	0.269462i	$-0.913154\pi$
$269$	−16.4721	+	11.9677i	−1.00432	+	0.729684i	−0.0413129	+	0.999146i	$0.513154\pi$
$270$	8.09017	−	5.87785i	0.492352	−	0.357715i
$271$	−4.43769	−	13.6578i	−0.269571	−	0.829653i	−0.990605	−	0.136754i	$-0.956333\pi$
$271$	−4.43769	−	13.6578i	−0.269571	−	0.829653i	0.721034	−	0.692899i	$-0.243667\pi$
$272$	0.309017	−	0.951057i	0.0187369	−	0.0576663i
$273$	−2.11803	−	1.53884i	−0.128189	−	0.0931349i
$274$	−12.1115			−0.731680
$275$	3.30902	−	0.224514i	0.199541	−	0.0135387i
$276$	30.2705			1.82207
$277$	1.14590	+	0.832544i	0.0688503	+	0.0500227i	0.621678	−	0.783273i	$-0.286451\pi$
$277$	1.14590	+	0.832544i	0.0688503	+	0.0500227i	−0.552828	+	0.833296i	$0.686451\pi$
$278$	−2.76393	+	8.50651i	−0.165770	+	0.510186i
$279$	2.94427	+	9.06154i	0.176269	+	0.542500i
$280$	5.85410	−	4.25325i	0.349850	−	0.254181i
$281$	−8.73607	+	6.34712i	−0.521150	+	0.378638i	−0.817037	−	0.576585i	$-0.804385\pi$
$281$	−8.73607	+	6.34712i	−0.521150	+	0.378638i	0.295887	+	0.955223i	$0.404385\pi$
$282$	−16.1803	−	49.7980i	−0.963525	−	2.96543i
$283$	2.44427	−	7.52270i	0.145297	−	0.447178i	−0.851752	−	0.523945i	$-0.824460\pi$
$283$	2.44427	−	7.52270i	0.145297	−	0.447178i	0.997049	+	0.0767671i	$0.0244598\pi$
$284$	−3.70820	−	2.69417i	−0.220041	−	0.159869i
$285$	−27.4164			−1.62401
$286$	−3.51722	+	2.93893i	−0.207978	+	0.173782i
$287$	−17.7082			−1.04528
$288$	−20.9164	−	15.1967i	−1.23251	−	0.895472i
$289$	0.309017	−	0.951057i	0.0181775	−	0.0559445i
$290$	7.88854	+	24.2784i	0.463231	+	1.42568i
$291$	12.7082	−	9.23305i	0.744968	−	0.541251i
$292$	−22.4164	+	16.2865i	−1.31182	+	0.953094i
$293$	4.57295	+	14.0741i	0.267155	+	0.822217i	0.991189	+	0.132454i	$0.0422855\pi$
$293$	4.57295	+	14.0741i	0.267155	+	0.822217i	−0.724035	+	0.689764i	$0.757714\pi$
$294$	−7.92705	+	24.3970i	−0.462315	+	1.42286i
$295$	22.1803	+	16.1150i	1.29139	+	0.938249i
$296$	14.4721			0.841176
$297$	−6.28115	−	3.94298i	−0.364469	−	0.228795i
$298$	46.6312			2.70127
$299$	1.92705	+	1.40008i	0.111444	+	0.0809690i
$300$	2.42705	−	7.46969i	0.140126	−	0.431263i
$301$	−3.61803	−	11.1352i	−0.208540	−	0.641820i
$302$	2.23607	−	1.62460i	0.128671	−	0.0934851i
$303$	−15.1353	+	10.9964i	−0.869498	+	0.631727i
$304$	1.61803	+	4.97980i	0.0928006	+	0.285611i
$305$	−3.23607	+	9.95959i	−0.185297	+	0.570285i
$306$	−6.97214	−	5.06555i	−0.398570	−	0.289578i
$307$	−12.2918			−0.701530			−0.350765	−	0.936464i	$-0.614078\pi$
$307$	−12.2918			−0.701530			−0.350765	+	0.936464i	$0.614078\pi$
$308$	−13.6353	−	8.55951i	−0.776941	−	0.487723i
$309$	21.4164			1.21834
$310$	−8.94427	−	6.49839i	−0.508001	−	0.369084i
$311$	5.91641	−	18.2088i	0.335489	−	1.03253i	−0.630992	−	0.775789i	$-0.717352\pi$
$311$	5.91641	−	18.2088i	0.335489	−	1.03253i	0.966481	−	0.256739i	$-0.0826480\pi$
$312$	1.11803	+	3.44095i	0.0632962	+	0.194806i
$313$	−8.23607	+	5.98385i	−0.465530	+	0.338227i	−0.795697	−	0.605695i	$-0.792895\pi$
$313$	−8.23607	+	5.98385i	−0.465530	+	0.338227i	0.330167	+	0.943923i	$0.392895\pi$
$314$	−20.0623	+	14.5761i	−1.13218	+	0.822578i
$315$	3.85410	+	11.8617i	0.217154	+	0.668331i
$316$	9.79180	−	30.1360i	0.550832	−	1.69529i
$317$	−5.76393	−	4.18774i	−0.323735	−	0.235207i	0.414033	−	0.910262i	$-0.364120\pi$
$317$	−5.76393	−	4.18774i	−0.323735	−	0.235207i	−0.737767	+	0.675055i	$0.764120\pi$
$318$	66.3050			3.71820
$319$	14.5279	−	12.1392i	0.813404	−	0.679666i
$320$	26.0000			1.45344
$321$	11.8992	+	8.64527i	0.664148	+	0.482532i
$322$	−4.30902	+	13.2618i	−0.240132	+	0.739051i
$323$	1.61803	+	4.97980i	0.0900298	+	0.277083i
$324$	13.8541	−	10.0656i	0.769672	−	0.559200i
$325$	0.500000	−	0.363271i	0.0277350	−	0.0201507i
$326$	2.82624	+	8.69827i	0.156531	+	0.481752i
$327$	0.381966	−	1.17557i	0.0211228	−	0.0650092i
$328$	19.7984	+	14.3844i	1.09318	+	0.794243i
$329$	14.4721			0.797875
$330$	38.7426	−	2.62866i	2.13271	−	0.144703i
$331$	5.23607			0.287800			0.143900	−	0.989592i	$-0.454036\pi$
$331$	5.23607			0.287800			0.143900	+	0.989592i	$0.454036\pi$
$332$	13.8541	+	10.0656i	0.760343	+	0.552421i
$333$	−7.70820	+	23.7234i	−0.422407	+	1.30003i
$334$	1.60739	+	4.94704i	0.0879525	+	0.270690i
$335$	−19.4164	+	14.1068i	−1.06083	+	0.770739i
$336$	3.42705	−	2.48990i	0.186961	−	0.135835i
$337$	−9.03444	−	27.8052i	−0.492137	−	1.51464i	−0.821371	−	0.570395i	$-0.806790\pi$
$337$	−9.03444	−	27.8052i	−0.492137	−	1.51464i	0.329233	−	0.944249i	$-0.393210\pi$
$338$	8.71885	−	26.8339i	0.474243	−	1.45957i
$339$	−8.47214	−	6.15537i	−0.460143	−	0.334314i
$340$	6.00000			0.325396
$341$	−2.00000	+	7.95148i	−0.108306	+	0.430597i
$342$	45.1246			2.44006
$343$	−14.8992	−	10.8249i	−0.804480	−	0.584489i
$344$	−5.00000	+	15.3884i	−0.269582	+	0.829688i
$345$	−6.23607	−	19.1926i	−0.335739	−	1.03330i
$346$	−31.5066	+	22.8909i	−1.69380	+	1.23062i
$347$	0.881966	−	0.640786i	0.0473464	−	0.0343992i	−0.563860	−	0.825870i	$-0.690684\pi$
$347$	0.881966	−	0.640786i	0.0473464	−	0.0343992i	0.611207	+	0.791471i	$0.290684\pi$
$348$	−13.8541	−	42.6385i	−0.742658	−	2.28567i
$349$	1.97214	−	6.06961i	0.105566	−	0.324899i	−0.884297	−	0.466925i	$-0.845362\pi$
$349$	1.97214	−	6.06961i	0.105566	−	0.324899i	0.989863	+	0.142026i	$0.0453618\pi$
$350$	2.92705	+	2.12663i	0.156457	+	0.113673i
$351$	−1.38197			−0.0737639
$352$	−8.29180	−	20.6457i	−0.441954	−	1.10042i
$353$	−13.9787			−0.744012			−0.372006	−	0.928230i	$-0.621330\pi$
$353$	−13.9787			−0.744012			−0.372006	+	0.928230i	$0.621330\pi$
$354$	−64.9230	−	47.1693i	−3.45062	−	2.50702i
$355$	−0.944272	+	2.90617i	−0.0501167	+	0.154243i
$356$	13.7188	+	42.2223i	0.727097	+	2.23778i
$357$	3.42705	−	2.48990i	0.181379	−	0.131779i
$358$	12.2361	−	8.89002i	0.646696	−	0.469852i
$359$	8.94427	+	27.5276i	0.472061	+	1.45285i	0.849881	+	0.526974i	$0.176674\pi$
$359$	8.94427	+	27.5276i	0.472061	+	1.45285i	−0.377821	+	0.925879i	$0.623326\pi$
$360$	5.32624	−	16.3925i	0.280717	−	0.863959i
$361$	−6.80902	−	4.94704i	−0.358369	−	0.260371i
$362$	1.70820			0.0897812
$363$	−12.5172	−	25.9358i	−0.656984	−	1.36128i
$364$	−3.00000			−0.157243
$365$	14.9443	+	10.8576i	0.782219	+	0.568315i
$366$	9.47214	−	29.1522i	0.495116	−	1.52381i
$367$	−7.91641	−	24.3642i	−0.413233	−	1.27180i	−0.913822	−	0.406115i	$-0.866883\pi$
$367$	−7.91641	−	24.3642i	−0.413233	−	1.27180i	0.500589	−	0.865685i	$-0.333117\pi$
$368$	−3.11803	+	2.26538i	−0.162539	+	0.118091i
$369$	−34.1246	+	24.7930i	−1.77646	+	1.29067i
$370$	−8.94427	−	27.5276i	−0.464991	−	1.43109i
$371$	−5.66312	+	17.4293i	−0.294014	+	0.904884i
$372$	15.7082	+	11.4127i	0.814432	+	0.591720i
$373$	25.2148			1.30557			0.652786	−	0.757542i	$-0.273600\pi$
$373$	25.2148			1.30557			0.652786	+	0.757542i	$0.273600\pi$
$374$	−2.76393	−	6.88191i	−0.142920	−	0.355855i
$375$	−31.4164			−1.62234
$376$	−16.1803	−	11.7557i	−0.834437	−	0.606254i
$377$	1.09017	−	3.35520i	0.0561466	−	0.172801i
$378$	−2.50000	−	7.69421i	−0.128586	−	0.395747i
$379$	16.8713	−	12.2577i	0.866622	−	0.629637i	−0.0630566	−	0.998010i	$-0.520085\pi$
$379$	16.8713	−	12.2577i	0.866622	−	0.629637i	0.929678	+	0.368372i	$0.120085\pi$
$380$	−25.4164	+	18.4661i	−1.30383	+	0.947291i
$381$	−1.23607	−	3.80423i	−0.0633257	−	0.194896i
$382$	12.4377	−	38.2793i	0.636368	−	1.95854i
$383$	15.9443	+	11.5842i	0.814714	+	0.591925i	0.915194	−	0.403015i	$-0.132038\pi$
$383$	15.9443	+	11.5842i	0.814714	+	0.591925i	−0.100479	+	0.994939i	$0.532038\pi$
$384$	−40.9787			−2.09119
$385$	−2.61803	+	10.4086i	−0.133427	+	0.530472i
$386$	−38.9443			−1.98221
$387$	−22.5623	−	16.3925i	−1.14691	−	0.833276i
$388$	5.56231	−	17.1190i	0.282383	−	0.869086i
$389$	−9.50000	−	29.2380i	−0.481669	−	1.48243i	−0.836748	−	0.547589i	$-0.815546\pi$
$389$	−9.50000	−	29.2380i	−0.481669	−	1.48243i	0.355079	−	0.934836i	$-0.384454\pi$
$390$	5.85410	−	4.25325i	0.296434	−	0.215372i
$391$	−3.11803	+	2.26538i	−0.157686	+	0.114565i
$392$	3.02786	+	9.31881i	0.152930	+	0.470671i
$393$	−14.0623	+	43.2793i	−0.709349	+	2.18315i
$394$	18.6180	+	13.5268i	0.937963	+	0.681470i
$395$	−21.1246			−1.06289
$396$	−38.2599	+	2.59590i	−1.92263	+	0.130449i
$397$	21.5967			1.08391			0.541955	−	0.840408i	$-0.317684\pi$
$397$	21.5967			1.08391			0.541955	+	0.840408i	$0.317684\pi$
$398$	−27.3992	−	19.9067i	−1.37340	−	0.997831i
$399$	−6.85410	+	21.0948i	−0.343134	+	1.05606i
$400$	0.309017	+	0.951057i	0.0154508	+	0.0475528i
$401$	−20.0344	+	14.5559i	−1.00047	+	0.726886i	−0.962189	−	0.272381i	$-0.912189\pi$
$401$	−20.0344	+	14.5559i	−1.00047	+	0.726886i	−0.0382829	+	0.999267i	$0.512189\pi$
$402$	56.8328	−	41.2915i	2.83456	−	2.05943i
$403$	0.472136	+	1.45309i	0.0235188	+	0.0723833i
$404$	−6.62461	+	20.3885i	−0.329587	+	1.01436i
$405$	−9.23607	−	6.71040i	−0.458944	−	0.333442i
$406$	20.6525			1.02497
$407$	−16.4721	+	13.7638i	−0.816493	+	0.682247i
$408$	−5.85410			−0.289821
$409$	−2.02786	−	1.47333i	−0.100271	−	0.0728515i	0.536520	−	0.843888i	$-0.319739\pi$
$409$	−2.02786	−	1.47333i	−0.100271	−	0.0728515i	−0.636791	+	0.771036i	$0.719739\pi$
$410$	15.1246	−	46.5488i	0.746951	−	2.29888i
$411$	−4.38197	−	13.4863i	−0.216146	−	0.665230i
$412$	19.8541	−	14.4248i	0.978141	−	0.710661i
$413$	17.9443	−	13.0373i	0.882980	−	0.641522i
$414$	10.2639	+	31.5891i	0.504445	+	1.55252i
$415$	3.52786	−	10.8576i	0.173176	−	0.532981i
$416$	−3.35410	−	2.43690i	−0.164448	−	0.119479i
$417$	−10.4721			−0.512823
$418$	32.8885	+	20.6457i	1.60863	+	1.00982i
$419$	12.0000			0.586238			0.293119	−	0.956076i	$-0.405307\pi$
$419$	12.0000			0.586238			0.293119	+	0.956076i	$0.405307\pi$
$420$	20.5623	+	14.9394i	1.00334	+	0.728968i
$421$	4.19098	−	12.8985i	0.204256	−	0.628635i	−0.795487	−	0.605971i	$-0.792785\pi$
$421$	4.19098	−	12.8985i	0.204256	−	0.628635i	0.999743	−	0.0226649i	$-0.00721507\pi$
$422$	16.5836	+	51.0390i	0.807277	+	2.48454i
$423$	27.8885	−	20.2622i	1.35599	−	0.985183i
$424$	20.4894	−	14.8864i	0.995051	−	0.722947i
$425$	0.309017	+	0.951057i	0.0149895	+	0.0461330i
$426$	2.76393	−	8.50651i	0.133913	−	0.412142i
$427$	6.85410	+	4.97980i	0.331693	+	0.240989i
$428$	16.8541			0.814674
$429$	−4.54508	−	2.85317i	−0.219439	−	0.137752i
$430$	32.3607			1.56057
$431$	20.0623	+	14.5761i	0.966367	+	0.702107i	0.954621	−	0.297824i	$-0.0962609\pi$
$431$	20.0623	+	14.5761i	0.966367	+	0.702107i	0.0117465	+	0.999931i	$0.496261\pi$
$432$	0.690983	−	2.12663i	0.0332449	−	0.102317i
$433$	−4.39261	−	13.5191i	−0.211095	−	0.649685i	−0.999408	−	0.0344095i	$-0.989045\pi$
$433$	−4.39261	−	13.5191i	−0.211095	−	0.649685i	0.788312	−	0.615275i	$-0.210955\pi$
$434$	−7.23607	+	5.25731i	−0.347342	+	0.252359i
$435$	−24.1803	+	17.5680i	−1.15936	+	0.842323i
$436$	−0.437694	−	1.34708i	−0.0209617	−	0.0645136i
$437$	6.23607	−	19.1926i	0.298312	−	0.918109i
$438$	−43.7426	−	31.7809i	−2.09010	−	1.51855i
$439$	−11.8541			−0.565765			−0.282883	−	0.959155i	$-0.591291\pi$
$439$	−11.8541			−0.565765			−0.282883	+	0.959155i	$0.591291\pi$
$440$	11.3820	−	9.51057i	0.542614	−	0.453398i
$441$	−16.8885			−0.804216
$442$	−1.11803	−	0.812299i	−0.0531795	−	0.0386371i
$443$	5.67376	−	17.4620i	0.269569	−	0.829647i	−0.721037	−	0.692897i	$-0.756334\pi$
$443$	5.67376	−	17.4620i	0.269569	−	0.829647i	0.990606	−	0.136750i	$-0.0436658\pi$
$444$	15.7082	+	48.3449i	0.745478	+	2.29435i
$445$	23.9443	−	17.3965i	1.13507	−	0.824675i
$446$	−15.8541	+	11.5187i	−0.750713	+	0.545425i
$447$	16.8713	+	51.9246i	0.797986	+	2.45595i
$448$	6.50000	−	20.0049i	0.307096	−	0.945145i
$449$	25.9443	+	18.8496i	1.22439	+	0.889568i	0.996457	−	0.0841093i	$-0.0268045\pi$
$449$	25.9443	+	18.8496i	1.22439	+	0.889568i	0.227929	+	0.973678i	$0.426804\pi$
$450$	8.61803			0.406258
$451$	−36.2148	+	2.45714i	−1.70529	+	0.115702i
$452$	−12.0000			−0.564433
$453$	2.61803	+	1.90211i	0.123006	+	0.0893691i
$454$	4.53444	−	13.9556i	0.212812	−	0.654968i
$455$	0.618034	+	1.90211i	0.0289739	+	0.0891724i
$456$	24.7984	−	18.0171i	1.16129	−	0.843727i
$457$	−0.690983	+	0.502029i	−0.0323228	+	0.0234839i	−0.603829	−	0.797114i	$-0.706359\pi$
$457$	−0.690983	+	0.502029i	−0.0323228	+	0.0234839i	0.571507	+	0.820598i	$0.306359\pi$
$458$	−10.0623	−	30.9686i	−0.470181	−	1.44707i
$459$	0.690983	−	2.12663i	0.0322523	−	0.0992624i
$460$	−18.7082	−	13.5923i	−0.872275	−	0.633745i
$461$	17.7984			0.828953			0.414476	−	0.910060i	$-0.363965\pi$
$461$	17.7984			0.828953			0.414476	+	0.910060i	$0.363965\pi$
$462$	7.66312	−	30.4666i	0.356521	−	1.41743i
$463$	9.12461			0.424057			0.212028	−	0.977264i	$-0.431993\pi$
$463$	9.12461			0.424057			0.212028	+	0.977264i	$0.431993\pi$
$464$	4.61803	+	3.35520i	0.214387	+	0.155761i
$465$	4.00000	−	12.3107i	0.185496	−	0.570897i
$466$	19.9230	+	61.3166i	0.922914	+	2.84044i
$467$	8.38197	−	6.08985i	0.387871	−	0.281805i	−0.376711	−	0.926331i	$-0.622945\pi$
$467$	8.38197	−	6.08985i	0.387871	−	0.281805i	0.764583	+	0.644526i	$0.222945\pi$
$468$	−5.78115	+	4.20025i	−0.267234	+	0.194157i
$469$	6.00000	+	18.4661i	0.277054	+	0.852685i
$470$	−12.3607	+	38.0423i	−0.570156	+	1.75476i
$471$	−23.4894	−	17.0660i	−1.08233	−	0.786361i
$472$	−30.6525			−1.41089
$473$	−8.94427	−	22.2703i	−0.411258	−	1.02399i
$474$	61.8328			2.84008
$475$	−4.23607	−	3.07768i	−0.194364	−	0.141214i
$476$	1.50000	−	4.61653i	0.0687524	−	0.211598i
$477$	13.4894	+	41.5160i	0.617635	+	1.90089i
$478$	0.326238	−	0.237026i	0.0149218	−	0.0108413i
$479$	−0.0729490	+	0.0530006i	−0.00333313	+	0.00242166i	−0.589451	−	0.807804i	$-0.700656\pi$
$479$	−0.0729490	+	0.0530006i	−0.00333313	+	0.00242166i	0.586117	+	0.810226i	$0.300656\pi$
$480$	10.8541	+	33.4055i	0.495420	+	1.52475i
$481$	−1.23607	+	3.80423i	−0.0563598	+	0.173458i
$482$	−6.70820	−	4.87380i	−0.305550	−	0.221995i
$483$	−16.3262			−0.742870
$484$	−29.0729	−	15.6129i	−1.32150	−	0.709679i
$485$	−12.0000			−0.544892
$486$	39.1697	+	28.4585i	1.77677	+	1.29090i
$487$	−7.20820	+	22.1846i	−0.326635	+	1.00528i	0.644062	+	0.764973i	$0.277248\pi$
$487$	−7.20820	+	22.1846i	−0.326635	+	1.00528i	−0.970697	+	0.240306i	$0.922752\pi$
$488$	−3.61803	−	11.1352i	−0.163781	−	0.504065i
$489$	−8.66312	+	6.29412i	−0.391760	+	0.284630i
$490$	15.8541	−	11.5187i	0.716215	−	0.520361i
$491$	−8.18034	−	25.1765i	−0.369174	−	1.13620i	−0.947326	−	0.320271i	$-0.896226\pi$
$491$	−8.18034	−	25.1765i	−0.369174	−	1.13620i	0.578152	−	0.815929i	$-0.303774\pi$
$492$	−26.5623	+	81.7504i	−1.19752	+	3.68559i
$493$	4.61803	+	3.35520i	0.207986	+	0.151111i
$494$	7.23607			0.325566
$495$	9.52786	+	23.7234i	0.428246	+	1.06629i
$496$	−2.47214			−0.111002
$497$	2.00000	+	1.45309i	0.0897123	+	0.0651798i
$498$	−10.3262	+	31.7809i	−0.462730	+	1.42414i
$499$	0.427051	+	1.31433i	0.0191174	+	0.0588374i	0.960160	−	0.279450i	$-0.0901523\pi$
$499$	0.427051	+	1.31433i	0.0191174	+	0.0588374i	−0.941043	+	0.338288i	$0.890152\pi$
$500$	−29.1246	+	21.1603i	−1.30249	+	0.946316i
$501$	−4.92705	+	3.57971i	−0.220124	+	0.159930i
$502$	6.38197	+	19.6417i	0.284841	+	0.876651i
$503$	6.62868	−	20.4010i	0.295558	−	0.909634i	−0.687475	−	0.726208i	$-0.741281\pi$
$503$	6.62868	−	20.4010i	0.295558	−	0.909634i	0.983033	−	0.183427i	$-0.0587190\pi$
$504$	−11.2812	−	8.19624i	−0.502502	−	0.365089i
$505$	14.2918			0.635977
$506$	−6.97214	+	27.7194i	−0.309949	+	1.23228i
$507$	33.0344			1.46711
$508$	−3.70820	−	2.69417i	−0.164525	−	0.119534i
$509$	6.97214	−	21.4580i	0.309034	−	0.951110i	−0.669106	−	0.743167i	$-0.733323\pi$
$509$	6.97214	−	21.4580i	0.309034	−	0.951110i	0.978141	−	0.207944i	$-0.0666771\pi$
$510$	3.61803	+	11.1352i	0.160209	+	0.493073i
$511$	12.0902	−	8.78402i	0.534838	−	0.388582i
$512$	9.04508	−	6.57164i	0.399740	−	0.290428i
$513$	3.61803	+	11.1352i	0.159740	+	0.491629i
$514$	−4.00658	+	12.3310i	−0.176723	+	0.543896i
$515$	−13.2361	−	9.61657i	−0.583251	−	0.423757i
$516$	−56.8328			−2.50193
$517$	29.5967	−	2.00811i	1.30166	−	0.0883168i
$518$	−23.4164			−1.02886
$519$	−36.8885	−	26.8011i	−1.61923	−	1.17644i
$520$	0.854102	−	2.62866i	0.0374548	−	0.115274i
$521$	12.9443	+	39.8384i	0.567099	+	1.74535i	0.661632	+	0.749829i	$0.269864\pi$
$521$	12.9443	+	39.8384i	0.567099	+	1.74535i	−0.0945328	+	0.995522i	$0.530136\pi$
$522$	39.7984	−	28.9152i	1.74193	−	1.26558i
$523$	15.3262	−	11.1352i	0.670170	−	0.486907i	−0.199912	−	0.979814i	$-0.564066\pi$
$523$	15.3262	−	11.1352i	0.670170	−	0.486907i	0.870082	+	0.492907i	$0.164066\pi$
$524$	16.1140	+	49.5937i	0.703942	+	2.16651i
$525$	−1.30902	+	4.02874i	−0.0571302	+	0.175829i
$526$	−41.8328	−	30.3933i	−1.82400	−	1.32521i
$527$	−2.47214			−0.107688
$528$	6.66312	−	5.56758i	0.289975	−	0.242298i
$529$	−8.14590			−0.354169
$530$	−40.9787	−	29.7728i	−1.78000	−	1.29325i
$531$	16.3262	−	50.2470i	0.708498	−	2.18053i
$532$	7.85410	+	24.1724i	0.340519	+	1.04801i
$533$	−5.47214	+	3.97574i	−0.237025	+	0.172208i
$534$	−70.0861	+	50.9205i	−3.03292	+	2.20355i
$535$	−3.47214	−	10.6861i	−0.150114	−	0.462002i
$536$	8.29180	−	25.5195i	0.358151	−	1.10228i
$537$	14.3262	+	10.4086i	0.618223	+	0.449165i
$538$	−45.5279			−1.96285
$539$	−12.3090	−	7.72696i	−0.530187	−	0.332824i
$540$	13.4164			0.577350
$541$	1.85410	+	1.34708i	0.0797141	+	0.0579157i	0.626929	−	0.779077i	$-0.284312\pi$
$541$	1.85410	+	1.34708i	0.0797141	+	0.0579157i	−0.547214	+	0.836992i	$0.684312\pi$
$542$	9.92299	−	30.5398i	0.426229	−	1.31180i
$543$	0.618034	+	1.90211i	0.0265224	+	0.0816275i
$544$	5.42705	−	3.94298i	0.232683	−	0.169054i
$545$	−0.763932	+	0.555029i	−0.0327233	+	0.0237748i
$546$	−1.80902	−	5.56758i	−0.0774188	−	0.238271i
$547$	3.75329	−	11.5514i	0.160479	−	0.493904i	−0.838196	−	0.545370i	$-0.816389\pi$
$547$	3.75329	−	11.5514i	0.160479	−	0.493904i	0.998675	+	0.0514658i	$0.0163893\pi$
$548$	−13.1459	−	9.55105i	−0.561565	−	0.408001i
$549$	20.1803			0.861276
$550$	6.28115	+	3.94298i	0.267829	+	0.168129i
$551$	−29.8885			−1.27329
$552$	18.2533	+	13.2618i	0.776912	+	0.564459i
$553$	−5.28115	+	16.2537i	−0.224577	+	0.691178i
$554$	0.978714	+	3.01217i	0.0415816	+	0.127975i
$555$	27.4164	−	19.9192i	1.16376	−	0.845522i
$556$	−9.70820	+	7.05342i	−0.411720	+	0.299132i
$557$	9.60739	+	29.5685i	0.407078	+	1.25286i	0.919147	+	0.393914i	$0.128879\pi$
$557$	9.60739	+	29.5685i	0.407078	+	1.25286i	−0.512069	+	0.858944i	$0.671121\pi$
$558$	−6.58359	+	20.2622i	−0.278706	+	0.857768i
$559$	−3.61803	−	2.62866i	−0.153027	−	0.111180i
$560$	−3.23607			−0.136749
$561$	6.66312	−	5.56758i	0.281317	−	0.235063i
$562$	−24.1459			−1.01853
$563$	−33.3607	−	24.2380i	−1.40599	−	1.02151i	−0.993891	−	0.110367i	$-0.964798\pi$
$563$	−33.3607	−	24.2380i	−1.40599	−	1.02151i	−0.412094	−	0.911141i	$-0.635202\pi$
$564$	21.7082	−	66.8110i	0.914080	−	2.81325i
$565$	2.47214	+	7.60845i	0.104004	+	0.320090i
$566$	14.3090	−	10.3961i	0.601453	−	0.436981i
$567$	−7.47214	+	5.42882i	−0.313800	+	0.227989i
$568$	−1.05573	−	3.24920i	−0.0442974	−	0.136333i
$569$	7.80902	−	24.0337i	0.327371	−	1.00754i	−0.642988	−	0.765876i	$-0.722305\pi$
$569$	7.80902	−	24.0337i	0.327371	−	1.00754i	0.970359	−	0.241668i	$-0.0776945\pi$
$570$	−49.5967	−	36.0341i	−2.07738	−	1.50930i
$571$	−1.09017			−0.0456222			−0.0228111	−	0.999740i	$-0.507262\pi$
$571$	−1.09017			−0.0456222			−0.0228111	+	0.999740i	$0.507262\pi$
$572$	−6.13525	+	0.416272i	−0.256528	+	0.0174052i
$573$	47.1246			1.96866
$574$	−32.0344	−	23.2744i	−1.33709	−	0.971454i
$575$	1.19098	−	3.66547i	0.0496674	−	0.152861i
$576$	−15.4828	−	47.6511i	−0.645116	−	1.98546i
$577$	28.1074	−	20.4212i	1.17013	−	0.850146i	0.179102	−	0.983831i	$-0.442681\pi$
$577$	28.1074	−	20.4212i	1.17013	−	0.850146i	0.991024	+	0.133684i	$0.0426808\pi$
$578$	1.80902	−	1.31433i	0.0752452	−	0.0546688i
$579$	−14.0902	−	43.3651i	−0.585567	−	1.80219i
$580$	−10.5836	+	32.5729i	−0.439460	+	1.35252i
$581$	−7.47214	−	5.42882i	−0.309996	−	0.225226i
$582$	35.1246			1.45596
$583$	−9.16312	+	36.4302i	−0.379498	+	1.50878i
$584$	−20.6525			−0.854606
$585$	3.85410	+	2.80017i	0.159348	+	0.115773i
$586$	−10.2254	+	31.4706i	−0.422408	+	1.30004i
$587$	−6.94427	−	21.3723i	−0.286621	−	0.882128i	−0.985908	−	0.167287i	$-0.946499\pi$
$587$	−6.94427	−	21.3723i	−0.286621	−	0.882128i	0.699287	−	0.714841i	$-0.253501\pi$
$588$	−27.8435	+	20.2295i	−1.14824	+	0.834249i
$589$	10.4721	−	7.60845i	0.431497	−	0.313501i
$590$	18.9443	+	58.3045i	0.779923	+	2.40036i
$591$	−8.32624	+	25.6255i	−0.342496	+	1.05409i
$592$	−5.23607	−	3.80423i	−0.215201	−	0.156353i
$593$	−44.0344			−1.80828			−0.904139	−	0.427239i	$-0.859486\pi$
$593$	−44.0344			−1.80828			−0.904139	+	0.427239i	$0.859486\pi$
$594$	−6.18034	−	15.3884i	−0.253582	−	0.631394i
$595$	−3.23607			−0.132666
$596$	50.6140	+	36.7732i	2.07323	+	1.50629i
$597$	12.2533	−	37.7117i	0.501494	−	1.54344i
$598$	1.64590	+	5.06555i	0.0673058	+	0.207146i
$599$	33.6525	−	24.4500i	1.37500	−	0.998998i	0.377675	−	0.925938i	$-0.376724\pi$
$599$	33.6525	−	24.4500i	1.37500	−	0.998998i	0.997328	−	0.0730600i	$-0.0232765\pi$
$600$	4.73607	−	3.44095i	0.193349	−	0.140476i
$601$	−14.4164	−	44.3691i	−0.588058	−	1.80986i	−0.586629	−	0.809856i	$-0.699545\pi$
$601$	−14.4164	−	44.3691i	−0.588058	−	1.80986i	−0.00142887	−	0.999999i	$-0.500455\pi$
$602$	8.09017	−	24.8990i	0.329731	−	1.01481i
$603$	37.4164	+	27.1846i	1.52371	+	1.10704i
$604$	3.70820			0.150885
$605$	−3.90983	+	21.6498i	−0.158957	+	0.880189i
$606$	−41.8328			−1.69934
$607$	−32.0066	−	23.2541i	−1.29911	−	0.943856i	−0.299160	−	0.954203i	$-0.596707\pi$
$607$	−32.0066	−	23.2541i	−1.29911	−	0.943856i	−0.999946	+	0.0103464i	$0.996707\pi$
$608$	−10.8541	+	33.4055i	−0.440192	+	1.35477i
$609$	7.47214	+	22.9969i	0.302786	+	0.931880i
$610$	−18.9443	+	13.7638i	−0.767031	+	0.557281i
$611$	4.47214	−	3.24920i	0.180923	−	0.131448i
$612$	−3.57295	−	10.9964i	−0.144428	−	0.444503i
$613$	0.392609	−	1.20833i	0.0158573	−	0.0488039i	−0.942815	−	0.333317i	$-0.891832\pi$
$613$	0.392609	−	1.20833i	0.0158573	−	0.0488039i	0.958672	+	0.284513i	$0.0918320\pi$
$614$	−22.2361	−	16.1554i	−0.897375	−	0.651981i
$615$	57.3050			2.31076
$616$	−4.47214	−	11.1352i	−0.180187	−	0.448649i
$617$	−16.0000			−0.644136			−0.322068	−	0.946717i	$-0.604378\pi$
$617$	−16.0000			−0.644136			−0.322068	+	0.946717i	$0.604378\pi$
$618$	38.7426	+	28.1482i	1.55846	+	1.13229i
$619$	−7.41641	+	22.8254i	−0.298091	+	0.917429i	0.684075	+	0.729412i	$0.260206\pi$
$619$	−7.41641	+	22.8254i	−0.298091	+	0.917429i	−0.982166	+	0.188017i	$0.939794\pi$
$620$	−4.58359	−	14.1068i	−0.184081	−	0.566545i
$621$	−6.97214	+	5.06555i	−0.279782	+	0.203274i
$622$	34.6353	−	25.1640i	1.38875	−	1.00898i
$623$	−7.39919	−	22.7724i	−0.296442	−	0.912355i
$624$	0.500000	−	1.53884i	0.0200160	−	0.0616030i
$625$	15.3713	+	11.1679i	0.614853	+	0.446717i
$626$	−22.7639			−0.909830
$627$	−11.0902	+	44.0916i	−0.442899	+	1.76085i
$628$	−33.2705			−1.32764
$629$	−5.23607	−	3.80423i	−0.208776	−	0.151684i
$630$	−8.61803	+	26.5236i	−0.343351	+	1.05672i
$631$	−4.88854	−	15.0454i	−0.194610	−	0.598948i	−0.999981	−	0.00617657i	$-0.998034\pi$
$631$	−4.88854	−	15.0454i	−0.194610	−	0.598948i	0.805371	−	0.592771i	$-0.201966\pi$
$632$	19.1074	−	13.8823i	0.760051	−	0.552210i
$633$	−50.8328	+	36.9322i	−2.02042	+	1.46792i
$634$	−4.92299	−	15.1514i	−0.195517	−	0.601739i
$635$	−0.944272	+	2.90617i	−0.0374723	+	0.115328i
$636$	71.9681	+	52.2879i	2.85372	+	2.07335i
$637$	−2.70820			−0.107303
$638$	42.2361	−	2.86568i	1.67214	−	0.113453i
$639$	5.88854			0.232947
$640$	25.3262	+	18.4006i	1.00111	+	0.727347i
$641$	−3.88854	+	11.9677i	−0.153588	+	0.472696i	−0.998015	−	0.0629748i	$-0.979941\pi$
$641$	−3.88854	+	11.9677i	−0.153588	+	0.472696i	0.844427	+	0.535671i	$0.179941\pi$
$642$	10.1631	+	31.2789i	0.401106	+	1.23448i
$643$	−28.2984	+	20.5600i	−1.11598	+	0.810806i	−0.983595	−	0.180392i	$-0.942263\pi$
$643$	−28.2984	+	20.5600i	−1.11598	+	0.810806i	−0.132384	+	0.991198i	$0.542263\pi$
$644$	−15.1353	+	10.9964i	−0.596413	+	0.433319i
$645$	11.7082	+	36.0341i	0.461010	+	1.41884i
$646$	−3.61803	+	11.1352i	−0.142350	+	0.438107i
$647$	23.3262	+	16.9475i	0.917049	+	0.666275i	0.942788	−	0.333394i	$-0.108194\pi$
$647$	23.3262	+	16.9475i	0.917049	+	0.666275i	−0.0257387	+	0.999669i	$0.508194\pi$
$648$	12.7639			0.501415
$649$	34.8885	−	29.1522i	1.36950	−	1.14433i
$650$	1.38197			0.0542052
$651$	−8.47214	−	6.15537i	−0.332049	−	0.241248i
$652$	−3.79180	+	11.6699i	−0.148498	+	0.457030i
$653$	−2.14590	−	6.60440i	−0.0839755	−	0.258450i	0.900249	−	0.435376i	$-0.143385\pi$
$653$	−2.14590	−	6.60440i	−0.0839755	−	0.258450i	−0.984224	+	0.176926i	$0.943385\pi$
$654$	2.23607	−	1.62460i	0.0874372	−	0.0635268i
$655$	28.1246	−	20.4337i	1.09892	−	0.798412i
$656$	−3.38197	−	10.4086i	−0.132044	−	0.406388i
$657$	11.0000	−	33.8545i	0.429151	−	1.32079i
$658$	26.1803	+	19.0211i	1.02062	+	0.741521i
$659$	−0.875388			−0.0341003			−0.0170501	−	0.999855i	$-0.505427\pi$
$659$	−0.875388			−0.0341003			−0.0170501	+	0.999855i	$0.505427\pi$
$660$	44.1246	+	27.6992i	1.71755	+	1.07819i
$661$	4.25735			0.165592			0.0827959	−	0.996567i	$-0.473615\pi$
$661$	4.25735			0.165592			0.0827959	+	0.996567i	$0.473615\pi$
$662$	9.47214	+	6.88191i	0.368145	+	0.267473i
$663$	0.500000	−	1.53884i	0.0194184	−	0.0597637i
$664$	3.94427	+	12.1392i	0.153067	+	0.471093i
$665$	13.7082	−	9.95959i	0.531581	−	0.386216i
$666$	−45.1246	+	32.7849i	−1.74854	+	1.27039i
$667$	−6.79837	−	20.9232i	−0.263234	−	0.810151i
$668$	−2.15654	+	6.63715i	−0.0834391	+	0.256799i
$669$	−18.5623	−	13.4863i	−0.717660	−	0.521411i
$670$	−53.6656			−2.07328
$671$	14.7082	+	9.23305i	0.567804	+	0.356438i
$672$	28.4164			1.09619
$673$	15.3262	+	11.1352i	0.590783	+	0.429229i	0.842595	−	0.538547i	$-0.181027\pi$
$673$	15.3262	+	11.1352i	0.590783	+	0.429229i	−0.251812	+	0.967776i	$0.581027\pi$
$674$	20.2016	−	62.1742i	0.778138	−	2.39486i
$675$	0.690983	+	2.12663i	0.0265959	+	0.0818539i
$676$	30.6246	−	22.2501i	1.17787	−	0.855772i
$677$	6.94427	−	5.04531i	0.266890	−	0.193907i	−0.446289	−	0.894889i	$-0.647255\pi$
$677$	6.94427	−	5.04531i	0.266890	−	0.193907i	0.713179	+	0.700982i	$0.247255\pi$
$678$	−7.23607	−	22.2703i	−0.277900	−	0.855287i
$679$	−3.00000	+	9.23305i	−0.115129	+	0.354332i
$680$	3.61803	+	2.62866i	0.138745	+	0.100804i
$681$	17.1803			0.658352
$682$	−14.0689	+	11.7557i	−0.538725	+	0.450149i
$683$	−11.1459			−0.426486			−0.213243	−	0.976999i	$-0.568403\pi$
$683$	−11.1459			−0.426486			−0.213243	+	0.976999i	$0.568403\pi$
$684$	48.9787	+	35.5851i	1.87275	+	1.36063i
$685$	−3.34752	+	10.3026i	−0.127902	+	0.393643i
$686$	−12.7254	−	39.1648i	−0.485859	−	1.49532i
$687$	30.8435	−	22.4091i	1.17675	−	0.854960i
$688$	5.85410	−	4.25325i	0.223186	−	0.162154i
$689$	2.16312	+	6.65740i	0.0824083	+	0.253627i
$690$	13.9443	−	42.9161i	0.530849	−	1.63379i
$691$	4.35410	+	3.16344i	0.165638	+	0.120343i	0.667516	−	0.744595i	$-0.267357\pi$
$691$	4.35410	+	3.16344i	0.165638	+	0.120343i	−0.501878	+	0.864938i	$0.667357\pi$
$692$	−52.2492			−1.98622
$693$	20.6353	−	1.40008i	0.783869	−	0.0531848i
$694$	2.43769			0.0925336
$695$	6.47214	+	4.70228i	0.245502	+	0.178368i
$696$	10.3262	−	31.7809i	0.391415	−	1.20465i
$697$	−3.38197	−	10.4086i	−0.128101	−	0.394255i
$698$	11.5451	−	8.38800i	0.436988	−	0.317490i
$699$	−61.0689	+	44.3691i	−2.30984	+	1.67820i
$700$	1.50000	+	4.61653i	0.0566947	+	0.174488i
$701$	−9.15654	+	28.1809i	−0.345838	+	1.06438i	0.615296	+	0.788296i	$0.289036\pi$
$701$	−9.15654	+	28.1809i	−0.345838	+	1.06438i	−0.961134	+	0.276083i	$0.910964\pi$
$702$	−2.50000	−	1.81636i	−0.0943564	−	0.0685540i
$703$	33.8885			1.27813
$704$	10.5172	−	41.8137i	0.396383	−	1.57591i
$705$	−46.8328			−1.76383
$706$	−25.2877	−	18.3726i	−0.951716	−	0.691462i
$707$	3.57295	−	10.9964i	0.134375	−	0.413562i
$708$	−33.2705	−	102.396i	−1.25038	−	3.84828i
$709$	−25.7984	+	18.7436i	−0.968878	+	0.703931i	−0.955196	−	0.295975i	$-0.904355\pi$
$709$	−25.7984	+	18.7436i	−0.968878	+	0.703931i	−0.0136826	+	0.999906i	$0.504355\pi$
$710$	−5.52786	+	4.01623i	−0.207457	+	0.150726i
$711$	12.5795	+	38.7158i	0.471769	+	1.45196i
$712$	−10.2254	+	31.4706i	−0.383214	+	1.17941i
$713$	7.70820	+	5.60034i	0.288675	+	0.209734i
$714$	9.47214			0.354486
$715$	1.52786	+	3.80423i	0.0571389	+	0.142270i
$716$	20.2918			0.758340
$717$	0.381966	+	0.277515i	0.0142648	+	0.0103640i
$718$	−20.0000	+	61.5537i	−0.746393	+	2.29716i
$719$	−14.3156	−	44.0589i	−0.533882	−	1.64312i	−0.746053	−	0.665886i	$-0.768054\pi$
$719$	−14.3156	−	44.0589i	−0.533882	−	1.64312i	0.212172	−	0.977232i	$-0.431946\pi$
$720$	−6.23607	+	4.53077i	−0.232405	+	0.168852i
$721$	−10.7082	+	7.77997i	−0.398794	+	0.289741i
$722$	−5.81559	−	17.8986i	−0.216434	−	0.666115i
$723$	3.00000	−	9.23305i	0.111571	−	0.343381i
$724$	1.85410	+	1.34708i	0.0689072	+	0.0500640i
$725$	−5.70820			−0.211997
$726$	11.4443	−	63.3700i	0.424737	−	2.35188i
$727$	45.4853			1.68696			0.843478	−	0.537164i	$-0.180504\pi$
$727$	45.4853			1.68696			0.843478	+	0.537164i	$0.180504\pi$
$728$	−1.80902	−	1.31433i	−0.0670466	−	0.0487122i
$729$	−12.2254	+	37.6260i	−0.452794	+	1.39356i
$730$	12.7639	+	39.2833i	0.472414	+	1.45394i
$731$	5.85410	−	4.25325i	0.216522	−	0.157312i
$732$	33.2705	−	24.1724i	1.22971	−	0.893439i
$733$	10.1459	+	31.2259i	0.374747	+	1.15335i	0.943649	+	0.330948i	$0.107368\pi$
$733$	10.1459	+	31.2259i	0.374747	+	1.15335i	−0.568902	+	0.822406i	$0.692632\pi$
$734$	17.7016	−	54.4800i	0.653379	−	2.01089i
$735$	18.5623	+	13.4863i	0.684681	+	0.497450i
$736$	−25.8541			−0.952995
$737$	14.8328	+	36.9322i	0.546374	+	1.36042i
$738$	−94.3181			−3.47190
$739$	25.4164	+	18.4661i	0.934958	+	0.679287i	0.947202	−	0.320639i	$-0.103897\pi$
$739$	25.4164	+	18.4661i	0.934958	+	0.679287i	−0.0122440	+	0.999925i	$0.503897\pi$
$740$	12.0000	−	36.9322i	0.441129	−	1.35765i
$741$	2.61803	+	8.05748i	0.0961759	+	0.295999i
$742$	−33.1525	+	24.0867i	−1.21707	+	0.884250i
$743$	7.82624	−	5.68609i	0.287117	−	0.208603i	−0.434899	−	0.900479i	$-0.643216\pi$
$743$	7.82624	−	5.68609i	0.287117	−	0.208603i	0.722016	+	0.691877i	$0.243216\pi$
$744$	4.47214	+	13.7638i	0.163956	+	0.504606i
$745$	12.8885	−	39.6669i	0.472200	−	1.45328i
$746$	45.6140	+	33.1405i	1.67005	+	1.21336i
$747$	−22.0000			−0.804938
$748$	2.42705	−	9.64932i	0.0887418	−	0.352814i
$749$	−9.09017			−0.332148
$750$	−56.8328	−	41.2915i	−2.07524	−	1.50775i
$751$	−16.1353	+	49.6592i	−0.588784	+	1.81209i	−0.00527130	+	0.999986i	$0.501678\pi$
$751$	−16.1353	+	49.6592i	−0.588784	+	1.81209i	−0.583513	+	0.812104i	$0.698322\pi$
$752$	2.76393	+	8.50651i	0.100790	+	0.310200i
$753$	−19.5623	+	14.2128i	−0.712890	+	0.517945i
$754$	6.38197	−	4.63677i	0.232417	−	0.168861i
$755$	−0.763932	−	2.35114i	−0.0278023	−	0.0855668i
$756$	3.35410	−	10.3229i	0.121988	−	0.375439i
$757$	−12.8541	−	9.33905i	−0.467190	−	0.339434i	0.329155	−	0.944276i	$-0.393236\pi$
$757$	−12.8541	−	9.33905i	−0.467190	−	0.339434i	−0.796345	+	0.604842i	$0.793236\pi$
$758$	46.6312			1.69372
$759$	−33.3885	+	2.26538i	−1.21193	+	0.0822282i
$760$	−23.4164			−0.849402
$761$	−15.4894	−	11.2537i	−0.561489	−	0.407945i	0.270515	−	0.962716i	$-0.412806\pi$
$761$	−15.4894	−	11.2537i	−0.561489	−	0.407945i	−0.832004	+	0.554770i	$0.812806\pi$
$762$	2.76393	−	8.50651i	0.100127	−	0.308158i
$763$	0.236068	+	0.726543i	0.00854623	+	0.0263026i
$764$	43.6869	−	31.7404i	1.58054	−	1.14833i
$765$	−6.23607	+	4.53077i	−0.225466	+	0.163810i
$766$	13.6180	+	41.9120i	0.492040	+	1.51434i
$767$	2.61803	−	8.05748i	0.0945317	−	0.290939i
$768$	−19.0623	−	13.8496i	−0.687852	−	0.499754i
$769$	−11.9098			−0.429479			−0.214740	−	0.976671i	$-0.568890\pi$
$769$	−11.9098			−0.429479			−0.214740	+	0.976671i	$0.568890\pi$
$770$	−18.4164	+	15.3884i	−0.663681	+	0.554560i
$771$	−15.1803			−0.546707
$772$	−42.2705	−	30.7113i	−1.52135	−	1.10532i
$773$	−10.8475	+	33.3852i	−0.390158	+	1.20078i	0.542510	+	0.840049i	$0.317474\pi$
$773$	−10.8475	+	33.3852i	−0.390158	+	1.20078i	−0.932668	+	0.360735i	$0.882526\pi$
$774$	−19.2705	−	59.3085i	−0.692664	−	2.13180i
$775$	2.00000	−	1.45309i	0.0718421	−	0.0521964i
$776$	10.8541	−	7.88597i	0.389640	−	0.283090i
$777$	−8.47214	−	26.0746i	−0.303936	−	0.935419i
$778$	21.2426	−	65.3781i	0.761586	−	2.34392i
$779$	46.3607	+	33.6830i	1.66104	+	1.20682i
$780$	9.70820			0.347609
$781$	4.29180	+	2.69417i	0.153573	+	0.0964049i
$782$	−8.61803			−0.308180
$783$	10.3262	+	7.50245i	0.369030	+	0.268116i
$784$	1.35410	−	4.16750i	0.0483608	−	0.148839i
$785$	6.85410	+	21.0948i	0.244633	+	0.752904i
$786$	−82.3222	+	59.8106i	−2.93633	+	2.13337i
$787$	−16.0623	+	11.6699i	−0.572559	+	0.415989i	−0.836034	−	0.548678i	$-0.815131\pi$
$787$	−16.0623	+	11.6699i	−0.572559	+	0.415989i	0.263475	+	0.964666i	$0.415131\pi$
$788$	9.54102	+	29.3642i	0.339885	+	1.04606i
$789$	18.7082	−	57.5779i	0.666030	−	2.04983i
$790$	−38.2148	−	27.7647i	−1.35962	−	0.987822i
$791$	6.47214			0.230123
$792$	−24.2082	−	15.1967i	−0.860201	−	0.539990i
$793$	3.23607			0.114916
$794$	39.0689	+	28.3852i	1.38650	+	1.00735i
$795$	18.3262	−	56.4024i	0.649965	−	2.00039i
$796$	−14.0410	−	43.2138i	−0.497671	−	1.53167i
$797$	0.263932	−	0.191758i	0.00934895	−	0.00679241i	−0.583101	−	0.812400i	$-0.698161\pi$
$797$	0.263932	−	0.191758i	0.00934895	−	0.00679241i	0.592450	+	0.805607i	$0.298161\pi$
$798$	−40.1246	+	29.1522i	−1.42040	+	1.03198i
$799$	2.76393	+	8.50651i	0.0977809	+	0.300939i
$800$	−2.07295	+	6.37988i	−0.0732898	+	0.225563i
$801$	−46.1418	−	33.5240i	−1.63034	−	1.18451i
$802$	−55.3738			−1.95532
$803$	23.5066	−	19.6417i	0.829529	−	0.693140i
$804$	94.2492			3.32391
$805$	10.0902	+	7.33094i	0.355632	+	0.258382i
$806$	−1.05573	+	3.24920i	−0.0371864	+	0.114448i
$807$	−16.4721	−	50.6960i	−0.579847	−	1.78458i
$808$	−12.9271	+	9.39205i	−0.454772	+	0.330411i
$809$	19.7984	−	14.3844i	0.696074	−	0.505727i	−0.182577	−	0.983191i	$-0.558444\pi$
$809$	19.7984	−	14.3844i	0.696074	−	0.505727i	0.878651	+	0.477464i	$0.158444\pi$
$810$	−7.88854	−	24.2784i	−0.277175	−	0.853057i
$811$	−2.71885	+	8.36775i	−0.0954716	+	0.293831i	−0.987376	−	0.158392i	$-0.949369\pi$
$811$	−2.71885	+	8.36775i	−0.0954716	+	0.293831i	0.891905	+	0.452223i	$0.149369\pi$
$812$	22.4164	+	16.2865i	0.786662	+	0.571543i
$813$	37.5967			1.31858
$814$	−47.8885	+	3.24920i	−1.67849	+	0.113884i
$815$	8.18034			0.286545
$816$	2.11803	+	1.53884i	0.0741460	+	0.0538702i
$817$	−11.7082	+	36.0341i	−0.409618	+	1.26068i
$818$	−1.73200	−	5.33056i	−0.0605581	−	0.186379i
$819$	3.11803	−	2.26538i	0.108953	−	0.0791589i
$820$	53.1246	−	38.5973i	1.85519	−	1.34788i
$821$	−10.6525	−	32.7849i	−0.371774	−	1.14420i	−0.945629	−	0.325246i	$-0.894553\pi$
$821$	−10.6525	−	32.7849i	−0.371774	−	1.14420i	0.573855	−	0.818957i	$-0.305447\pi$
$822$	9.79837	−	30.1563i	0.341758	−	1.05182i
$823$	−0.690983	−	0.502029i	−0.0240862	−	0.0174996i	0.575677	−	0.817677i	$-0.304739\pi$
$823$	−0.690983	−	0.502029i	−0.0240862	−	0.0174996i	−0.599763	+	0.800178i	$0.704739\pi$
$824$	18.2918			0.637225
$825$	−2.11803	+	8.42075i	−0.0737405	+	0.293173i
$826$	49.5967			1.72569
$827$	−10.4721	−	7.60845i	−0.364152	−	0.264572i	0.390630	−	0.920548i	$-0.372257\pi$
$827$	−10.4721	−	7.60845i	−0.364152	−	0.264572i	−0.754782	+	0.655976i	$0.772257\pi$
$828$	−13.7705	+	42.3813i	−0.478558	+	1.47285i
$829$	13.2639	+	40.8222i	0.460675	+	1.41781i	0.864341	+	0.502906i	$0.167736\pi$
$829$	13.2639	+	40.8222i	0.460675	+	1.41781i	−0.403665	+	0.914907i	$0.632264\pi$
$830$	20.6525	−	15.0049i	0.716858	−	0.520828i
$831$	−3.00000	+	2.17963i	−0.104069	+	0.0756104i
$832$	−2.48278	−	7.64121i	−0.0860749	−	0.264911i
$833$	1.35410	−	4.16750i	0.0469169	−	0.144395i
$834$	−18.9443	−	13.7638i	−0.655986	−	0.476602i
$835$	4.65248			0.161006
$836$	19.4164	+	48.3449i	0.671531	+	1.67204i
$837$	−5.52786			−0.191071
$838$	21.7082	+	15.7719i	0.749897	+	0.544832i
$839$	−6.78773	+	20.8905i	−0.234338	+	0.721220i	0.762870	+	0.646552i	$0.223790\pi$
$839$	−6.78773	+	20.8905i	−0.234338	+	0.721220i	−0.997208	+	0.0746678i	$0.976210\pi$
$840$	5.85410	+	18.0171i	0.201986	+	0.621648i
$841$	−2.89919	+	2.10638i	−0.0999720	+	0.0726339i
$842$	24.5344	−	17.8253i	0.845513	−	0.614301i
$843$	−8.73607	−	26.8869i	−0.300886	−	0.926032i
$844$	−22.2492	+	68.4761i	−0.765850	+	2.35704i
$845$	−20.4164	−	14.8334i	−0.702346	−	0.510284i
$846$	77.0820			2.65014
$847$	15.6803	+	8.42075i	0.538783	+	0.289340i
$848$	−11.3262			−0.388945
$849$	16.7533	+	12.1720i	0.574971	+	0.417741i
$850$	−0.690983	+	2.12663i	−0.0237005	+	0.0729427i
$851$	7.70820	+	23.7234i	0.264234	+	0.813228i
$852$	9.70820	−	7.05342i	0.332598	−	0.241646i
$853$	−16.5623	+	12.0332i	−0.567083	+	0.412010i	−0.834044	−	0.551698i	$-0.813980\pi$
$853$	−16.5623	+	12.0332i	−0.567083	+	0.412010i	0.266962	+	0.963707i	$0.413980\pi$
$854$	5.85410	+	18.0171i	0.200323	+	0.616532i
$855$	12.4721	−	38.3853i	0.426538	−	1.31275i
$856$	10.1631	+	7.38394i	0.347368	+	0.252378i
$857$	29.8197			1.01862			0.509310	−	0.860583i	$-0.329901\pi$
$857$	29.8197			1.01862			0.509310	+	0.860583i	$0.329901\pi$
$858$	−4.47214	−	11.1352i	−0.152676	−	0.380148i
$859$	18.1115			0.617955			0.308977	−	0.951069i	$-0.400013\pi$
$859$	18.1115			0.617955			0.308977	+	0.951069i	$0.400013\pi$
$860$	35.1246	+	25.5195i	1.19774	+	0.870209i
$861$	14.3262	−	44.0916i	0.488237	−	1.50264i
$862$	17.1353	+	52.7369i	0.583629	+	1.79623i
$863$	−39.2705	+	28.5317i	−1.33678	+	0.971230i	−0.337228	+	0.941423i	$0.609489\pi$
$863$	−39.2705	+	28.5317i	−1.33678	+	0.971230i	−0.999556	+	0.0298072i	$0.990511\pi$
$864$	12.1353	−	8.81678i	0.412850	−	0.299953i
$865$	10.7639	+	33.1280i	0.365985	+	1.12638i
$866$	9.82217	−	30.2295i	0.333771	−	1.02724i
$867$	2.11803	+	1.53884i	0.0719322	+	0.0522618i
$868$	−12.0000			−0.407307
$869$	−8.54508	+	33.9730i	−0.289872	+	1.15246i
$870$	−66.8328			−2.26584
$871$	6.00000	+	4.35926i	0.203302	+	0.147708i
$872$	0.326238	−	1.00406i	0.0110478	−	0.0340017i
$873$	7.14590	+	21.9928i	0.241852	+	0.744344i
$874$	36.5066	−	26.5236i	1.23485	−	0.897174i
$875$	15.7082	−	11.4127i	0.531034	−	0.385819i
$876$	−22.4164	−	68.9906i	−0.757380	−	2.33098i
$877$	−1.00000	+	3.07768i	−0.0337676	+	0.103926i	−0.966520	−	0.256592i	$-0.917400\pi$
$877$	−1.00000	+	3.07768i	−0.0337676	+	0.103926i	0.932752	+	0.360518i	$0.117400\pi$
$878$	−21.4443	−	15.5802i	−0.723709	−	0.525805i
$879$	−38.7426			−1.30676
$880$	−6.61803	+	0.449028i	−0.223094	+	0.0151367i
$881$	17.5967			0.592849			0.296425	−	0.955056i	$-0.404206\pi$
$881$	17.5967			0.592849			0.296425	+	0.955056i	$0.404206\pi$
$882$	−30.5517	−	22.1971i	−1.02873	−	0.747415i
$883$	3.32624	−	10.2371i	0.111937	−	0.344506i	−0.879359	−	0.476159i	$-0.842029\pi$
$883$	3.32624	−	10.2371i	0.111937	−	0.344506i	0.991296	+	0.131653i	$0.0420285\pi$
$884$	−0.572949	−	1.76336i	−0.0192704	−	0.0593081i
$885$	−58.0689	+	42.1895i	−1.95196	+	1.41818i
$886$	33.2148	−	24.1320i	1.11587	−	0.810729i
$887$	−11.8197	−	36.3772i	−0.396865	−	1.22143i	−0.927499	−	0.373825i	$-0.878046\pi$
$887$	−11.8197	−	36.3772i	−0.396865	−	1.22143i	0.530634	−	0.847601i	$-0.321954\pi$
$888$	−11.7082	+	36.0341i	−0.392902	+	1.20923i
$889$	2.00000	+	1.45309i	0.0670778	+	0.0487349i
$890$	66.1803			2.21837
$891$	−14.5279	+	12.1392i	−0.486702	+	0.406679i
$892$	−26.2918			−0.880314
$893$	−37.8885	−	27.5276i	−1.26789	−	0.921177i
$894$	−37.7254	+	116.107i	−1.26173	+	3.88320i
$895$	−4.18034	−	12.8658i	−0.139733	−	0.430055i
$896$	20.4894	−	14.8864i	0.684501	−	0.497319i
$897$	−5.04508	+	3.66547i	−0.168450	+	0.122386i
$898$	22.1591	+	68.1986i	0.739457	+	2.27582i
$899$	4.36068	−	13.4208i	0.145437	−	0.447608i
$900$	9.35410	+	6.79615i	0.311803	+	0.226538i
$901$	−11.3262			−0.377332
$902$	−68.7426	−	43.1531i	−2.28888	−	1.43684i
$903$	30.6525			1.02005
$904$	−7.23607	−	5.25731i	−0.240668	−	0.174856i
$905$	0.472136	−	1.45309i	0.0156943	−	0.0483022i
$906$	2.23607	+	6.88191i	0.0742884	+	0.228636i
$907$	−34.1803	+	24.8335i	−1.13494	+	0.824582i	−0.986406	−	0.164326i	$-0.947455\pi$
$907$	−34.1803	+	24.8335i	−1.13494	+	0.824582i	−0.148533	+	0.988907i	$0.547455\pi$
$908$	15.9271	−	11.5717i	0.528558	−	0.384020i
$909$	−8.51064	−	26.1931i	−0.282280	−	0.868769i
$910$	−1.38197	+	4.25325i	−0.0458117	+	0.140994i
$911$	−10.8262	−	7.86572i	−0.358689	−	0.260603i	0.393816	−	0.919189i	$-0.371155\pi$
$911$	−10.8262	−	7.86572i	−0.358689	−	0.260603i	−0.752505	+	0.658586i	$0.771155\pi$
$912$	−13.7082			−0.453924
$913$	−16.0344	−	10.0656i	−0.530663	−	0.333123i
$914$	−1.90983			−0.0631716
$915$	−22.1803	−	16.1150i	−0.733259	−	0.532744i
$916$	13.5000	−	41.5487i	0.446053	−	1.37281i
$917$	−8.69098	−	26.7481i	−0.287002	−	0.883300i
$918$	4.04508	−	2.93893i	0.133508	−	0.0969990i
$919$	34.5623	−	25.1110i	1.14011	−	0.828335i	0.152971	−	0.988231i	$-0.451116\pi$
$919$	34.5623	−	25.1110i	1.14011	−	0.828335i	0.987134	+	0.159896i	$0.0511158\pi$
$920$	−5.32624	−	16.3925i	−0.175601	−	0.540444i
$921$	9.94427	−	30.6053i	0.327675	−	1.00848i
$922$	32.1976	+	23.3929i	1.06037	+	0.770404i
$923$	0.944272			0.0310811
$924$	32.3435	−	27.0256i	1.06402	−	0.889077i
$925$	6.47214			0.212803
$926$	16.5066	+	11.9927i	0.542440	+	0.394106i
$927$	−9.74265	+	29.9848i	−0.319990	+	0.984829i
$928$	11.8328	+	36.4177i	0.388431	+	1.19547i
$929$	−35.1803	+	25.5600i	−1.15423	+	0.838597i	−0.989037	−	0.147665i	$-0.952824\pi$
$929$	−35.1803	+	25.5600i	−1.15423	+	0.838597i	−0.165192	+	0.986261i	$0.552824\pi$
$930$	23.4164	−	17.0130i	0.767854	−	0.557879i
$931$	7.09017	+	21.8213i	0.232371	+	0.715164i
$932$	−26.7295	+	82.2649i	−0.875554	+	2.69468i
$933$	40.5517	+	29.4625i	1.32760	+	0.964559i
$934$	23.1672			0.758053
$935$	−6.61803	+	0.449028i	−0.216433	+	0.0146848i
$936$	−5.32624			−0.174094
$937$	−0.444272	−	0.322782i	−0.0145137	−	0.0105448i	0.580505	−	0.814257i	$-0.302855\pi$
$937$	−0.444272	−	0.322782i	−0.0145137	−	0.0105448i	−0.595018	+	0.803712i	$0.702855\pi$
$938$	−13.4164	+	41.2915i	−0.438061	+	1.34821i
$939$	−8.23607	−	25.3480i	−0.268774	−	0.827201i
$940$	−43.4164	+	31.5439i	−1.41609	+	1.02885i
$941$	13.6180	−	9.89408i	0.443935	−	0.322538i	−0.343261	−	0.939240i	$-0.611532\pi$
$941$	13.6180	−	9.89408i	0.443935	−	0.322538i	0.787197	+	0.616702i	$0.211532\pi$
$942$	−20.0623	−	61.7454i	−0.653665	−	2.01177i
$943$	−13.0344	+	40.1159i	−0.424460	+	1.30635i
$944$	11.0902	+	8.05748i	0.360954	+	0.262249i
$945$	−7.23607			−0.235389
$946$	13.0902	−	52.0431i	0.425598	−	1.69207i
$947$	8.79837			0.285909			0.142954	−	0.989729i	$-0.454340\pi$
$947$	8.79837			0.285909			0.142954	+	0.989729i	$0.454340\pi$
$948$	67.1140	+	48.7612i	2.17976	+	1.58369i
$949$	1.76393	−	5.42882i	0.0572597	−	0.176227i
$950$	−3.61803	−	11.1352i	−0.117385	−	0.361272i
$951$	15.0902	−	10.9637i	0.489332	−	0.355521i
$952$	2.92705	−	2.12663i	0.0948663	−	0.0689244i
$953$	−7.38854	−	22.7396i	−0.239338	−	0.736608i	−0.996516	−	0.0833991i	$-0.973422\pi$
$953$	−7.38854	−	22.7396i	−0.239338	−	0.736608i	0.757178	−	0.653209i	$-0.226578\pi$
$954$	−30.1631	+	92.8325i	−0.976567	+	3.00556i
$955$	−29.1246	−	21.1603i	−0.942450	−	0.684730i
$956$	0.541020			0.0174978
$957$	18.4721	+	45.9937i	0.597119	+	1.48677i
$958$	−0.201626			−0.00651424
$959$	7.09017	+	5.15131i	0.228954	+	0.166344i
$960$	−21.0344	+	64.7374i	−0.678884	+	2.08939i
$961$	−7.69098	−	23.6704i	−0.248096	−	0.763562i
$962$	−7.23607	+	5.25731i	−0.233300	+	0.169503i
$963$	−17.5172	+	12.7270i	−0.564485	+	0.410122i
$964$	−3.43769	−	10.5801i	−0.110721	−	0.340763i
$965$	−10.7639	+	33.1280i	−0.346503	+	1.06643i
$966$	−29.5344	−	21.4580i	−0.950255	−	0.690401i
$967$	−28.9443			−0.930785			−0.465393	−	0.885104i	$-0.654087\pi$
$967$	−28.9443			−0.930785			−0.465393	+	0.885104i	$0.654087\pi$
$968$	−10.6910	−	22.1518i	−0.343621	−	0.711986i
$969$	−13.7082			−0.440371
$970$	−21.7082	−	15.7719i	−0.697008	−	0.506406i
$971$	−5.56231	+	17.1190i	−0.178503	+	0.549375i	−0.999776	−	0.0211597i	$-0.993264\pi$
$971$	−5.56231	+	17.1190i	−0.178503	+	0.549375i	0.821273	+	0.570535i	$0.193264\pi$
$972$	20.0729	+	61.7782i	0.643840	+	1.98154i
$973$	5.23607	−	3.80423i	0.167861	−	0.121958i
$974$	−42.1976	+	30.6583i	−1.35210	+	0.982356i
$975$	0.500000	+	1.53884i	0.0160128	+	0.0492824i
$976$	−1.61803	+	4.97980i	−0.0517920	+	0.159399i
$977$	8.50000	+	6.17561i	0.271939	+	0.197575i	0.715394	−	0.698721i	$-0.246247\pi$
$977$	8.50000	+	6.17561i	0.271939	+	0.197575i	−0.443455	+	0.896297i	$0.646247\pi$
$978$	−23.9443			−0.765653
$979$	−18.2918	−	45.5447i	−0.584608	−	1.45562i
$980$	26.2918			0.839861
$981$	1.47214	+	1.06957i	0.0470017	+	0.0341487i
$982$	18.2918	−	56.2964i	0.583715	−	1.79649i
$983$	−10.6976	−	32.9237i	−0.341199	−	1.05010i	−0.963587	−	0.267394i	$-0.913837\pi$
$983$	−10.6976	−	32.9237i	−0.341199	−	1.05010i	0.622388	−	0.782709i	$-0.286163\pi$
$984$	−51.8328	+	37.6587i	−1.65237	+	1.20052i
$985$	16.6525	−	12.0987i	0.530592	−	0.385498i
$986$	3.94427	+	12.1392i	0.125611	+	0.386592i
$987$	−11.7082	+	36.0341i	−0.372676	+	1.14698i
$988$	7.85410	+	5.70634i	0.249872	+	0.181543i
$989$	−27.8885			−0.886804
$990$	−13.9443	+	55.4388i	−0.443178	+	1.76196i
$991$	−41.4508			−1.31673			−0.658365	−	0.752699i	$-0.728752\pi$
$991$	−41.4508			−1.31673			−0.658365	+	0.752699i	$0.728752\pi$
$992$	−13.4164	−	9.74759i	−0.425971	−	0.309486i
$993$	−4.23607	+	13.0373i	−0.134428	+	0.413725i
$994$	1.70820	+	5.25731i	0.0541809	+	0.166752i
$995$	−24.5066	+	17.8051i	−0.776911	+	0.564459i
$996$	−36.2705	+	26.3521i	−1.14928	+	0.834997i
$997$	0.819660	+	2.52265i	0.0259589	+	0.0798933i	0.963197	−	0.268798i	$-0.0866263\pi$
$997$	0.819660	+	2.52265i	0.0259589	+	0.0798933i	−0.937238	+	0.348691i	$0.886626\pi$
$998$	−0.954915	+	2.93893i	−0.0302273	+	0.0930301i
$999$	−11.7082	−	8.50651i	−0.370431	−	0.269134i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	187.2.g.c.103.1	yes	4
11.3	even	5	inner	187.2.g.c.69.1	✓	4
11.5	even	5		2057.2.a.k.1.1		2
11.6	odd	10		2057.2.a.j.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
187.2.g.c.69.1	✓	4	11.3	even	5	inner
187.2.g.c.103.1	yes	4	1.1	even	1	trivial
2057.2.a.j.1.2		2	11.6	odd	10
2057.2.a.k.1.1		2	11.5	even	5

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:	\( N \)	\(=\)	\( 187 = 11 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	187.g (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.80902 + 1.31433i) q^{2} +(-0.809017 + 2.48990i) q^{3} +(0.927051 + 2.85317i) q^{4} +(1.61803 - 1.17557i) q^{5} +(-4.73607 + 3.44095i) q^{6} +(-0.500000 - 1.53884i) q^{7} +(-0.690983 + 2.12663i) q^{8} +(-3.11803 - 2.26538i) q^{9} +O(q^{10})\)	\(q+(1.80902 + 1.31433i) q^{2} +(-0.809017 + 2.48990i) q^{3} +(0.927051 + 2.85317i) q^{4} +(1.61803 - 1.17557i) q^{5} +(-4.73607 + 3.44095i) q^{6} +(-0.500000 - 1.53884i) q^{7} +(-0.690983 + 2.12663i) q^{8} +(-3.11803 - 2.26538i) q^{9} +4.47214 q^{10} +(-1.23607 - 3.07768i) q^{11} -7.85410 q^{12} +(-0.500000 - 0.363271i) q^{13} +(1.11803 - 3.44095i) q^{14} +(1.61803 + 4.97980i) q^{15} +(0.809017 - 0.587785i) q^{16} +(0.809017 - 0.587785i) q^{17} +(-2.66312 - 8.19624i) q^{18} +(-1.61803 + 4.97980i) q^{19} +(4.85410 + 3.52671i) q^{20} +4.23607 q^{21} +(1.80902 - 7.19218i) q^{22} -3.85410 q^{23} +(-4.73607 - 3.44095i) q^{24} +(-0.309017 + 0.951057i) q^{25} +(-0.427051 - 1.31433i) q^{26} +(1.80902 - 1.31433i) q^{27} +(3.92705 - 2.85317i) q^{28} +(1.76393 + 5.42882i) q^{29} +(-3.61803 + 11.1352i) q^{30} +(-2.00000 - 1.45309i) q^{31} +6.70820 q^{32} +(8.66312 - 0.587785i) q^{33} +2.23607 q^{34} +(-2.61803 - 1.90211i) q^{35} +(3.57295 - 10.9964i) q^{36} +(-2.00000 - 6.15537i) q^{37} +(-9.47214 + 6.88191i) q^{38} +(1.30902 - 0.951057i) q^{39} +(1.38197 + 4.25325i) q^{40} +(3.38197 - 10.4086i) q^{41} +(7.66312 + 5.56758i) q^{42} +7.23607 q^{43} +(7.63525 - 6.37988i) q^{44} -7.70820 q^{45} +(-6.97214 - 5.06555i) q^{46} +(-2.76393 + 8.50651i) q^{47} +(0.809017 + 2.48990i) q^{48} +(3.54508 - 2.57565i) q^{49} +(-1.80902 + 1.31433i) q^{50} +(0.809017 + 2.48990i) q^{51} +(0.572949 - 1.76336i) q^{52} +(-9.16312 - 6.65740i) q^{53} +5.00000 q^{54} +(-5.61803 - 3.52671i) q^{55} +3.61803 q^{56} +(-11.0902 - 8.05748i) q^{57} +(-3.94427 + 12.1392i) q^{58} +(4.23607 + 13.0373i) q^{59} +(-12.7082 + 9.23305i) q^{60} +(-4.23607 + 3.07768i) q^{61} +(-1.70820 - 5.25731i) q^{62} +(-1.92705 + 5.93085i) q^{63} +(10.5172 + 7.64121i) q^{64} -1.23607 q^{65} +(16.4443 + 10.3229i) q^{66} -12.0000 q^{67} +(2.42705 + 1.76336i) q^{68} +(3.11803 - 9.59632i) q^{69} +(-2.23607 - 6.88191i) q^{70} +(-1.23607 + 0.898056i) q^{71} +(6.97214 - 5.06555i) q^{72} +(2.85410 + 8.78402i) q^{73} +(4.47214 - 13.7638i) q^{74} +(-2.11803 - 1.53884i) q^{75} -15.7082 q^{76} +(-4.11803 + 3.44095i) q^{77} +3.61803 q^{78} +(-8.54508 - 6.20837i) q^{79} +(0.618034 - 1.90211i) q^{80} +(-1.76393 - 5.42882i) q^{81} +(19.7984 - 14.3844i) q^{82} +(4.61803 - 3.35520i) q^{83} +(3.92705 + 12.0862i) q^{84} +(0.618034 - 1.90211i) q^{85} +(13.0902 + 9.51057i) q^{86} -14.9443 q^{87} +(7.39919 - 0.502029i) q^{88} +14.7984 q^{89} +(-13.9443 - 10.1311i) q^{90} +(-0.309017 + 0.951057i) q^{91} +(-3.57295 - 10.9964i) q^{92} +(5.23607 - 3.80423i) q^{93} +(-16.1803 + 11.7557i) q^{94} +(3.23607 + 9.95959i) q^{95} +(-5.42705 + 16.7027i) q^{96} +(-4.85410 - 3.52671i) q^{97} +9.79837 q^{98} +(-3.11803 + 12.3965i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 5 q^{2} - q^{3} - 3 q^{4} + 2 q^{5} - 10 q^{6} - 2 q^{7} - 5 q^{8} - 8 q^{9}+O(q^{10}) \) 4 * q + 5 * q^2 - q^3 - 3 * q^4 + 2 * q^5 - 10 * q^6 - 2 * q^7 - 5 * q^8 - 8 * q^9	\( 4 q + 5 q^{2} - q^{3} - 3 q^{4} + 2 q^{5} - 10 q^{6} - 2 q^{7} - 5 q^{8} - 8 q^{9} + 4 q^{11} - 18 q^{12} - 2 q^{13} + 2 q^{15} + q^{16} + q^{17} + 5 q^{18} - 2 q^{19} + 6 q^{20} + 8 q^{21} + 5 q^{22} - 2 q^{23} - 10 q^{24} + q^{25} + 5 q^{26} + 5 q^{27} + 9 q^{28} + 16 q^{29} - 10 q^{30} - 8 q^{31} + 19 q^{33} - 6 q^{35} + 21 q^{36} - 8 q^{37} - 20 q^{38} + 3 q^{39} + 10 q^{40} + 18 q^{41} + 15 q^{42} + 20 q^{43} - 3 q^{44} - 4 q^{45} - 10 q^{46} - 20 q^{47} + q^{48} + 3 q^{49} - 5 q^{50} + q^{51} + 9 q^{52} - 21 q^{53} + 20 q^{54} - 18 q^{55} + 10 q^{56} - 22 q^{57} + 20 q^{58} + 8 q^{59} - 24 q^{60} - 8 q^{61} + 20 q^{62} - q^{63} + 13 q^{64} + 4 q^{65} + 30 q^{66} - 48 q^{67} + 3 q^{68} + 8 q^{69} + 4 q^{71} + 10 q^{72} - 2 q^{73} - 4 q^{75} - 36 q^{76} - 12 q^{77} + 10 q^{78} - 23 q^{79} - 2 q^{80} - 16 q^{81} + 30 q^{82} + 14 q^{83} + 9 q^{84} - 2 q^{85} + 30 q^{86} - 24 q^{87} + 5 q^{88} + 10 q^{89} - 20 q^{90} + q^{91} - 21 q^{92} + 12 q^{93} - 20 q^{94} + 4 q^{95} - 15 q^{96} - 6 q^{97} - 10 q^{98} - 8 q^{99}+O(q^{100}) \) 4 * q + 5 * q^2 - q^3 - 3 * q^4 + 2 * q^5 - 10 * q^6 - 2 * q^7 - 5 * q^8 - 8 * q^9 + 4 * q^11 - 18 * q^12 - 2 * q^13 + 2 * q^15 + q^16 + q^17 + 5 * q^18 - 2 * q^19 + 6 * q^20 + 8 * q^21 + 5 * q^22 - 2 * q^23 - 10 * q^24 + q^25 + 5 * q^26 + 5 * q^27 + 9 * q^28 + 16 * q^29 - 10 * q^30 - 8 * q^31 + 19 * q^33 - 6 * q^35 + 21 * q^36 - 8 * q^37 - 20 * q^38 + 3 * q^39 + 10 * q^40 + 18 * q^41 + 15 * q^42 + 20 * q^43 - 3 * q^44 - 4 * q^45 - 10 * q^46 - 20 * q^47 + q^48 + 3 * q^49 - 5 * q^50 + q^51 + 9 * q^52 - 21 * q^53 + 20 * q^54 - 18 * q^55 + 10 * q^56 - 22 * q^57 + 20 * q^58 + 8 * q^59 - 24 * q^60 - 8 * q^61 + 20 * q^62 - q^63 + 13 * q^64 + 4 * q^65 + 30 * q^66 - 48 * q^67 + 3 * q^68 + 8 * q^69 + 4 * q^71 + 10 * q^72 - 2 * q^73 - 4 * q^75 - 36 * q^76 - 12 * q^77 + 10 * q^78 - 23 * q^79 - 2 * q^80 - 16 * q^81 + 30 * q^82 + 14 * q^83 + 9 * q^84 - 2 * q^85 + 30 * q^86 - 24 * q^87 + 5 * q^88 + 10 * q^89 - 20 * q^90 + q^91 - 21 * q^92 + 12 * q^93 - 20 * q^94 + 4 * q^95 - 15 * q^96 - 6 * q^97 - 10 * q^98 - 8 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more