LMFDB - Embedded newform 93.2.e.b.25.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [93,2,Mod(25,93)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(93, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2]))

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

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

chi := DirichletCharacter("93.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 93 = 3 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	93.e (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:	$0.742608738798$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.591408.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} + 4x^{4} + x^{3} + 10x^{2} - 3x + 1 $ x^6 - x^5 + 4x^4 + x^3 + 10x^2 - 3*x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			25.1
Root			$-0.740597 - 1.28275i$ of defining polynomial
Character	$\chi$	$=$	93.25
Dual form			93.2.e.b.67.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.67513 q^{2} +(-0.500000 - 0.866025i) q^{3} +0.806063 q^{4} +(-1.64363 + 2.84685i) q^{5} +(0.837565 + 1.45071i) q^{6} +(1.07816 + 1.86743i) q^{7} +2.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q-1.67513 q^{2} +(-0.500000 - 0.866025i) q^{3} +0.806063 q^{4} +(-1.64363 + 2.84685i) q^{5} +(0.837565 + 1.45071i) q^{6} +(1.07816 + 1.86743i) q^{7} +2.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(2.75329 - 4.76884i) q^{10} +(-2.31876 + 4.01621i) q^{11} +(-0.403032 - 0.698071i) q^{12} +(-1.09697 + 1.90000i) q^{13} +(-1.80606 - 3.12819i) q^{14} +3.28726 q^{15} -4.96239 q^{16} +(-3.15633 - 5.46692i) q^{17} +(0.837565 - 1.45071i) q^{18} +(0.903032 + 1.56410i) q^{19} +(-1.32487 + 2.29474i) q^{20} +(1.07816 - 1.86743i) q^{21} +(3.88423 - 6.72768i) q^{22} +7.35026 q^{23} +(-1.00000 - 1.73205i) q^{24} +(-2.90303 - 5.02820i) q^{25} +(1.83757 - 3.18276i) q^{26} +1.00000 q^{27} +(0.869067 + 1.50527i) q^{28} -0.0630040 q^{29} -5.50659 q^{30} +(-5.44358 + 1.16936i) q^{31} +4.31265 q^{32} +4.63752 q^{33} +(5.28726 + 9.15780i) q^{34} -7.08840 q^{35} +(-0.403032 + 0.698071i) q^{36} +(1.96604 + 3.40527i) q^{37} +(-1.51270 - 2.62007i) q^{38} +2.19394 q^{39} +(-3.28726 + 5.69370i) q^{40} +(-2.12482 + 3.68030i) q^{41} +(-1.80606 + 3.12819i) q^{42} +(2.19029 + 3.79369i) q^{43} +(-1.86907 + 3.23732i) q^{44} +(-1.64363 - 2.84685i) q^{45} -12.3127 q^{46} +6.37565 q^{47} +(2.48119 + 4.29755i) q^{48} +(1.17513 - 2.03539i) q^{49} +(4.86296 + 8.42289i) q^{50} +(-3.15633 + 5.46692i) q^{51} +(-0.884226 + 1.53152i) q^{52} +(5.99389 - 10.3817i) q^{53} -1.67513 q^{54} +(-7.62236 - 13.2023i) q^{55} +(2.15633 + 3.73486i) q^{56} +(0.903032 - 1.56410i) q^{57} +0.105540 q^{58} +(4.48119 + 7.76166i) q^{59} +2.64974 q^{60} +3.19394 q^{61} +(9.11871 - 1.95883i) q^{62} -2.15633 q^{63} +2.70052 q^{64} +(-3.60602 - 6.24581i) q^{65} -7.76845 q^{66} +(-3.79090 + 6.56604i) q^{67} +(-2.54420 - 4.40668i) q^{68} +(-3.67513 - 6.36551i) q^{69} +11.8740 q^{70} +(-4.86907 + 8.43347i) q^{71} +(-1.00000 + 1.73205i) q^{72} +(4.94358 - 8.56254i) q^{73} +(-3.29337 - 5.70428i) q^{74} +(-2.90303 + 5.02820i) q^{75} +(0.727901 + 1.26076i) q^{76} -10.0000 q^{77} -3.67513 q^{78} +(-1.07816 - 1.86743i) q^{79} +(8.15633 - 14.1272i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(3.55936 - 6.16499i) q^{82} +(3.64363 - 6.31095i) q^{83} +(0.869067 - 1.50527i) q^{84} +20.7513 q^{85} +(-3.66902 - 6.35493i) q^{86} +(0.0315020 + 0.0545631i) q^{87} +(-4.63752 + 8.03242i) q^{88} -3.86177 q^{89} +(2.75329 + 4.76884i) q^{90} -4.73084 q^{91} +5.92478 q^{92} +(3.73449 + 4.12960i) q^{93} -10.6801 q^{94} -5.93700 q^{95} +(-2.15633 - 3.73486i) q^{96} -5.38787 q^{97} +(-1.96850 + 3.40954i) q^{98} +(-2.31876 - 4.01621i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 3 q^{3} + 4 q^{4} - 4 q^{5} - 4 q^{7} + 12 q^{8} - 3 q^{9}+O(q^{10}) $ 6 * q - 3 * q^3 + 4 * q^4 - 4 * q^5 - 4 * q^7 + 12 * q^8 - 3 * q^9	\( 6 q - 3 q^{3} + 4 q^{4} - 4 q^{5} - 4 q^{7} + 12 q^{8} - 3 q^{9} - 4 q^{10} + 2 q^{11} - 2 q^{12} - 7 q^{13} - 10 q^{14} + 8 q^{15} - 8 q^{16} + 2 q^{17} + 5 q^{19} - 18 q^{20} - 4 q^{21} + 12 q^{22} + 24 q^{23} - 6 q^{24} - 17 q^{25} + 6 q^{26} + 6 q^{27} - 4 q^{28} + 8 q^{29} + 8 q^{30} - 16 q^{32} - 4 q^{33} + 20 q^{34} - 4 q^{35} - 2 q^{36} + 3 q^{37} + 6 q^{38} + 14 q^{39} - 8 q^{40} + 4 q^{41} - 10 q^{42} + q^{43} - 2 q^{44} - 4 q^{45} - 32 q^{46} - 12 q^{47} + 4 q^{48} - 3 q^{49} - 6 q^{50} + 2 q^{51} + 6 q^{52} + 10 q^{53} - 16 q^{55} - 8 q^{56} + 5 q^{57} + 40 q^{58} + 16 q^{59} + 36 q^{60} + 20 q^{61} + 12 q^{62} + 8 q^{63} - 24 q^{64} + 6 q^{65} - 24 q^{66} - 24 q^{67} + 4 q^{68} - 12 q^{69} + 88 q^{70} - 20 q^{71} - 6 q^{72} - 3 q^{73} - 34 q^{74} - 17 q^{75} + 14 q^{76} - 60 q^{77} - 12 q^{78} + 4 q^{79} + 28 q^{80} - 3 q^{81} + 16 q^{83} - 4 q^{84} + 24 q^{85} + 14 q^{86} - 4 q^{87} + 4 q^{88} + 12 q^{89} - 4 q^{90} + 16 q^{91} - 8 q^{92} - 9 q^{93} - 80 q^{94} - 44 q^{95} + 8 q^{96} - 34 q^{97} - 16 q^{98} + 2 q^{99}+O(q^{100}) \) 6 * q - 3 * q^3 + 4 * q^4 - 4 * q^5 - 4 * q^7 + 12 * q^8 - 3 * q^9 - 4 * q^10 + 2 * q^11 - 2 * q^12 - 7 * q^13 - 10 * q^14 + 8 * q^15 - 8 * q^16 + 2 * q^17 + 5 * q^19 - 18 * q^20 - 4 * q^21 + 12 * q^22 + 24 * q^23 - 6 * q^24 - 17 * q^25 + 6 * q^26 + 6 * q^27 - 4 * q^28 + 8 * q^29 + 8 * q^30 - 16 * q^32 - 4 * q^33 + 20 * q^34 - 4 * q^35 - 2 * q^36 + 3 * q^37 + 6 * q^38 + 14 * q^39 - 8 * q^40 + 4 * q^41 - 10 * q^42 + q^43 - 2 * q^44 - 4 * q^45 - 32 * q^46 - 12 * q^47 + 4 * q^48 - 3 * q^49 - 6 * q^50 + 2 * q^51 + 6 * q^52 + 10 * q^53 - 16 * q^55 - 8 * q^56 + 5 * q^57 + 40 * q^58 + 16 * q^59 + 36 * q^60 + 20 * q^61 + 12 * q^62 + 8 * q^63 - 24 * q^64 + 6 * q^65 - 24 * q^66 - 24 * q^67 + 4 * q^68 - 12 * q^69 + 88 * q^70 - 20 * q^71 - 6 * q^72 - 3 * q^73 - 34 * q^74 - 17 * q^75 + 14 * q^76 - 60 * q^77 - 12 * q^78 + 4 * q^79 + 28 * q^80 - 3 * q^81 + 16 * q^83 - 4 * q^84 + 24 * q^85 + 14 * q^86 - 4 * q^87 + 4 * q^88 + 12 * q^89 - 4 * q^90 + 16 * q^91 - 8 * q^92 - 9 * q^93 - 80 * q^94 - 44 * q^95 + 8 * q^96 - 34 * q^97 - 16 * q^98 + 2 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/93\mathbb{Z}\right)^\times$.

$n$	$32$	$34$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	−1.67513			−1.18450			−0.592248	−	0.805756i	$-0.701760\pi$
$2$	−1.67513			−1.18450			−0.592248	+	0.805756i	$0.701760\pi$
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$4$	0.806063			0.403032
$5$	−1.64363	+	2.84685i	−0.735053	+	1.27315i	0.219647	+	0.975579i	$0.429509\pi$
$5$	−1.64363	+	2.84685i	−0.735053	+	1.27315i	−0.954700	+	0.297570i	$0.903824\pi$
$6$	0.837565	+	1.45071i	0.341935	+	0.592248i
$7$	1.07816	+	1.86743i	0.407507	+	0.705823i	0.994610	−	0.103689i	$-0.0330648\pi$
$7$	1.07816	+	1.86743i	0.407507	+	0.705823i	−0.587103	+	0.809513i	$0.699731\pi$
$8$	2.00000			0.707107
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	2.75329	−	4.76884i	0.870668	−	1.50804i
$11$	−2.31876	+	4.01621i	−0.699132	+	1.21093i	0.269635	+	0.962963i	$0.413097\pi$
$11$	−2.31876	+	4.01621i	−0.699132	+	1.21093i	−0.968768	+	0.247970i	$0.920236\pi$
$12$	−0.403032	−	0.698071i	−0.116345	−	0.201516i
$13$	−1.09697	+	1.90000i	−0.304244	+	0.526967i	−0.977093	−	0.212814i	$-0.931737\pi$
$13$	−1.09697	+	1.90000i	−0.304244	+	0.526967i	0.672849	+	0.739780i	$0.265071\pi$
$14$	−1.80606	−	3.12819i	−0.482691	−	0.836045i
$15$	3.28726			0.848766
$16$	−4.96239			−1.24060
$17$	−3.15633	−	5.46692i	−0.765521	−	1.32592i	−0.939971	−	0.341256i	$-0.889148\pi$
$17$	−3.15633	−	5.46692i	−0.765521	−	1.32592i	0.174449	−	0.984666i	$-0.444186\pi$
$18$	0.837565	−	1.45071i	0.197416	−	0.341935i
$19$	0.903032	+	1.56410i	0.207170	+	0.358828i	0.950822	−	0.309738i	$-0.100241\pi$
$19$	0.903032	+	1.56410i	0.207170	+	0.358828i	−0.743652	+	0.668567i	$0.766908\pi$
$20$	−1.32487	+	2.29474i	−0.296250	+	0.513120i
$21$	1.07816	−	1.86743i	0.235274	−	0.407507i
$22$	3.88423	−	6.72768i	0.828120	−	1.43435i
$23$	7.35026			1.53264			0.766318	−	0.642462i	$-0.222087\pi$
$23$	7.35026			1.53264			0.766318	+	0.642462i	$0.222087\pi$
$24$	−1.00000	−	1.73205i	−0.204124	−	0.353553i
$25$	−2.90303	−	5.02820i	−0.580606	−	1.00564i
$26$	1.83757	−	3.18276i	0.360376	−	0.624190i
$27$	1.00000			0.192450
$28$	0.869067	+	1.50527i	0.164238	+	0.284469i
$29$	−0.0630040			−0.0116995			−0.00584977	−	0.999983i	$-0.501862\pi$
$29$	−0.0630040			−0.0116995			−0.00584977	+	0.999983i	$0.501862\pi$
$30$	−5.50659			−1.00536
$31$	−5.44358	+	1.16936i	−0.977696	+	0.210023i
$31$	−5.44358	+	1.16936i	−0.977696	+	0.210023i
$32$	4.31265			0.762376
$33$	4.63752			0.807289
$34$	5.28726	+	9.15780i	0.906757	+	1.57055i
$35$	−7.08840			−1.19816
$36$	−0.403032	+	0.698071i	−0.0671720	+	0.116345i
$37$	1.96604	+	3.40527i	0.323214	+	0.559824i	0.981149	−	0.193251i	$-0.0619032\pi$
$37$	1.96604	+	3.40527i	0.323214	+	0.559824i	−0.657935	+	0.753075i	$0.728570\pi$
$38$	−1.51270	−	2.62007i	−0.245392	−	0.425031i
$39$	2.19394			0.351311
$40$	−3.28726	+	5.69370i	−0.519761	+	0.900253i
$41$	−2.12482	+	3.68030i	−0.331842	+	0.574767i	−0.982873	−	0.184284i	$-0.941003\pi$
$41$	−2.12482	+	3.68030i	−0.331842	+	0.574767i	0.651031	+	0.759051i	$0.274337\pi$
$42$	−1.80606	+	3.12819i	−0.278682	+	0.482691i
$43$	2.19029	+	3.79369i	0.334016	+	0.578533i	0.983295	−	0.182017i	$-0.0582627\pi$
$43$	2.19029	+	3.79369i	0.334016	+	0.578533i	−0.649279	+	0.760550i	$0.724929\pi$
$44$	−1.86907	+	3.23732i	−0.281773	+	0.488044i
$45$	−1.64363	−	2.84685i	−0.245018	−	0.424383i
$46$	−12.3127			−1.81540
$47$	6.37565			0.929985			0.464992	−	0.885315i	$-0.346057\pi$
$47$	6.37565			0.929985			0.464992	+	0.885315i	$0.346057\pi$
$48$	2.48119	+	4.29755i	0.358130	+	0.620299i
$49$	1.17513	−	2.03539i	0.167876	−	0.290769i
$50$	4.86296	+	8.42289i	0.687726	+	1.19118i
$51$	−3.15633	+	5.46692i	−0.441974	+	0.765521i
$52$	−0.884226	+	1.53152i	−0.122620	+	0.212384i
$53$	5.99389	−	10.3817i	0.823324	−	1.42604i	−0.0798691	−	0.996805i	$-0.525450\pi$
$53$	5.99389	−	10.3817i	0.823324	−	1.42604i	0.903193	−	0.429234i	$-0.141216\pi$
$54$	−1.67513			−0.227956
$55$	−7.62236	−	13.2023i	−1.02780	−	1.78020i
$56$	2.15633	+	3.73486i	0.288151	+	0.499092i
$57$	0.903032	−	1.56410i	0.119609	−	0.207170i
$58$	0.105540			0.0138581
$59$	4.48119	+	7.76166i	0.583402	+	1.01048i	0.995073	+	0.0991489i	$0.0316120\pi$
$59$	4.48119	+	7.76166i	0.583402	+	1.01048i	−0.411671	+	0.911333i	$0.635055\pi$
$60$	2.64974			0.342080
$61$	3.19394			0.408942			0.204471	−	0.978873i	$-0.434453\pi$
$61$	3.19394			0.408942			0.204471	+	0.978873i	$0.434453\pi$
$62$	9.11871	−	1.95883i	1.15808	−	0.248772i
$63$	−2.15633			−0.271671
$64$	2.70052			0.337565
$65$	−3.60602	−	6.24581i	−0.447271	−	0.774697i
$66$	−7.76845			−0.956230
$67$	−3.79090	+	6.56604i	−0.463133	+	0.802169i	−0.999115	−	0.0420597i	$-0.986608\pi$
$67$	−3.79090	+	6.56604i	−0.463133	+	0.802169i	0.535982	+	0.844229i	$0.319941\pi$
$68$	−2.54420	−	4.40668i	−0.308529	−	0.534389i
$69$	−3.67513	−	6.36551i	−0.442434	−	0.766318i
$70$	11.8740			1.41921
$71$	−4.86907	+	8.43347i	−0.577852	+	1.00087i	0.417873	+	0.908505i	$0.362776\pi$
$71$	−4.86907	+	8.43347i	−0.577852	+	1.00087i	−0.995725	+	0.0923637i	$0.970558\pi$
$72$	−1.00000	+	1.73205i	−0.117851	+	0.204124i
$73$	4.94358	−	8.56254i	0.578603	−	1.00217i	−0.417037	−	0.908889i	$-0.636932\pi$
$73$	4.94358	−	8.56254i	0.578603	−	1.00217i	0.995640	−	0.0932798i	$-0.0297351\pi$
$74$	−3.29337	−	5.70428i	−0.382846	−	0.663109i
$75$	−2.90303	+	5.02820i	−0.335213	+	0.580606i
$76$	0.727901	+	1.26076i	0.0834960	+	0.144619i
$77$	−10.0000			−1.13961
$78$	−3.67513			−0.416127
$79$	−1.07816	−	1.86743i	−0.121303	−	0.210103i	0.798979	−	0.601359i	$-0.205374\pi$
$79$	−1.07816	−	1.86743i	−0.121303	−	0.210103i	−0.920282	+	0.391256i	$0.872041\pi$
$80$	8.15633	−	14.1272i	0.911905	−	1.57947i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	3.55936	−	6.16499i	0.393065	−	0.680809i
$83$	3.64363	−	6.31095i	0.399940	−	0.692717i	−0.593778	−	0.804629i	$-0.702364\pi$
$83$	3.64363	−	6.31095i	0.399940	−	0.692717i	0.993718	+	0.111912i	$0.0356975\pi$
$84$	0.869067	−	1.50527i	0.0948230	−	0.164238i
$85$	20.7513			2.25080
$86$	−3.66902	−	6.35493i	−0.395641	−	0.685270i
$87$	0.0315020	+	0.0545631i	0.00337737	+	0.00584977i
$88$	−4.63752	+	8.03242i	−0.494361	+	0.856259i
$89$	−3.86177			−0.409347			−0.204674	−	0.978830i	$-0.565613\pi$
$89$	−3.86177			−0.409347			−0.204674	+	0.978830i	$0.565613\pi$
$90$	2.75329	+	4.76884i	0.290223	+	0.502680i
$91$	−4.73084			−0.495927
$92$	5.92478			0.617701
$93$	3.73449	+	4.12960i	0.387248	+	0.428220i
$94$	−10.6801			−1.10156
$95$	−5.93700			−0.609123
$96$	−2.15633	−	3.73486i	−0.220079	−	0.381188i
$97$	−5.38787			−0.547056			−0.273528	−	0.961864i	$-0.588191\pi$
$97$	−5.38787			−0.547056			−0.273528	+	0.961864i	$0.588191\pi$
$98$	−1.96850	+	3.40954i	−0.198848	+	0.344415i
$99$	−2.31876	−	4.01621i	−0.233044	−	0.403644i
$100$	−2.34003	−	4.05305i	−0.234003	−	0.405305i
$101$	2.06300			0.205277			0.102638	−	0.994719i	$-0.467272\pi$
$101$	2.06300			0.205277			0.102638	+	0.994719i	$0.467272\pi$
$102$	5.28726	−	9.15780i	0.523517	−	0.906757i
$103$	8.54055	−	14.7927i	0.841526	−	1.45756i	−0.0470792	−	0.998891i	$-0.514991\pi$
$103$	8.54055	−	14.7927i	0.841526	−	1.45756i	0.888605	−	0.458674i	$-0.151675\pi$
$104$	−2.19394	+	3.80001i	−0.215133	+	0.372622i
$105$	3.54420	+	6.13873i	0.345878	+	0.599079i
$106$	−10.0406	+	17.3907i	−0.975225	+	1.68914i
$107$	1.25576	+	2.17503i	0.121398	+	0.210268i	0.920319	−	0.391168i	$-0.127929\pi$
$107$	1.25576	+	2.17503i	0.121398	+	0.210268i	−0.798921	+	0.601436i	$0.794595\pi$
$108$	0.806063			0.0775635
$109$	14.1490			1.35523			0.677616	−	0.735416i	$-0.263013\pi$
$109$	14.1490			1.35523			0.677616	+	0.735416i	$0.263013\pi$
$110$	12.7685	+	22.1156i	1.21742	+	2.10864i
$111$	1.96604	−	3.40527i	0.186608	−	0.323214i
$112$	−5.35026	−	9.26693i	−0.505552	−	0.875642i
$113$	−9.67513	+	16.7578i	−0.910160	+	1.57644i	−0.0963224	+	0.995350i	$0.530708\pi$
$113$	−9.67513	+	16.7578i	−0.910160	+	1.57644i	−0.813837	+	0.581093i	$0.802625\pi$
$114$	−1.51270	+	2.62007i	−0.141677	+	0.245392i
$115$	−12.0811	+	20.9251i	−1.12657	+	1.95127i
$116$	−0.0507852			−0.00471529
$117$	−1.09697	−	1.90000i	−0.101415	−	0.175656i
$118$	−7.50659	−	13.0018i	−0.691037	−	1.19691i
$119$	6.80606	−	11.7884i	0.623911	−	1.08065i
$120$	6.57452			0.600168
$121$	−5.25329	−	9.09897i	−0.477572	−	0.827179i
$122$	−5.35026			−0.484390
$123$	4.24965			0.383178
$124$	−4.38787	+	0.942579i	−0.394043	+	0.0846461i
$125$	2.64974			0.237000
$126$	3.61213			0.321794
$127$	9.68172	+	16.7692i	0.859114	+	1.48803i	0.872776	+	0.488122i	$0.162318\pi$
$127$	9.68172	+	16.7692i	0.859114	+	1.48803i	−0.0136621	+	0.999907i	$0.504349\pi$
$128$	−13.1490			−1.16222
$129$	2.19029	−	3.79369i	0.192844	−	0.334016i
$130$	6.04055	+	10.4625i	0.529791	+	0.917626i
$131$	−0.200046	−	0.346490i	−0.0174781	−	0.0302730i	0.857154	−	0.515060i	$-0.172230\pi$
$131$	−0.200046	−	0.346490i	−0.0174781	−	0.0302730i	−0.874632	+	0.484787i	$0.838897\pi$
$132$	3.73813			0.325363
$133$	−1.94723	+	3.37270i	−0.168846	+	0.292450i
$134$	6.35026	−	10.9990i	0.548579	−	0.950167i
$135$	−1.64363	+	2.84685i	−0.141461	+	0.245018i
$136$	−6.31265	−	10.9338i	−0.541305	−	0.937568i
$137$	−1.60602	+	2.78170i	−0.137211	+	0.237657i	−0.926440	−	0.376442i	$-0.877147\pi$
$137$	−1.60602	+	2.78170i	−0.137211	+	0.237657i	0.789229	+	0.614099i	$0.210481\pi$
$138$	6.15633	+	10.6631i	0.524061	+	0.907701i
$139$	9.50659			0.806338			0.403169	−	0.915126i	$-0.367909\pi$
$139$	9.50659			0.806338			0.403169	+	0.915126i	$0.367909\pi$
$140$	−5.71370			−0.482896
$141$	−3.18783	−	5.52148i	−0.268463	−	0.464992i
$142$	8.15633	−	14.1272i	0.684464	−	1.18553i
$143$	−5.08721	−	8.81131i	−0.425414	−	0.736839i
$144$	2.48119	−	4.29755i	0.206766	−	0.358130i
$145$	0.103555	−	0.179363i	0.00859979	−	0.0148953i
$146$	−8.28115	+	14.3434i	−0.685353	+	1.18707i
$147$	−2.35026			−0.193846
$148$	1.58475	+	2.74487i	0.130266	+	0.225627i
$149$	−2.19394	−	3.80001i	−0.179734	−	0.311309i	0.762055	−	0.647512i	$-0.224190\pi$
$149$	−2.19394	−	3.80001i	−0.179734	−	0.311309i	−0.941789	+	0.336203i	$0.890857\pi$
$150$	4.86296	−	8.42289i	0.397059	−	0.687726i
$151$	−0.350262			−0.0285039			−0.0142519	−	0.999898i	$-0.504537\pi$
$151$	−0.350262			−0.0285039			−0.0142519	+	0.999898i	$0.504537\pi$
$152$	1.80606	+	3.12819i	0.146491	+	0.253730i
$153$	6.31265			0.510348
$154$	16.7513			1.34986
$155$	5.61824	−	17.4191i	0.451268	−	1.39913i
$156$	1.76845			0.141589
$157$	−23.1319			−1.84613			−0.923063	−	0.384649i	$-0.874322\pi$
$157$	−23.1319			−1.84613			−0.923063	+	0.384649i	$0.874322\pi$
$158$	1.80606	+	3.12819i	0.143683	+	0.248866i
$159$	−11.9878			−0.950693
$160$	−7.08840	+	12.2775i	−0.560387	+	0.970619i
$161$	7.92478	+	13.7261i	0.624560	+	1.08177i
$162$	0.837565	+	1.45071i	0.0658054	+	0.113978i
$163$	−10.8192			−0.847428			−0.423714	−	0.905796i	$-0.639274\pi$
$163$	−10.8192			−0.847428			−0.423714	+	0.905796i	$0.639274\pi$
$164$	−1.71274	+	2.96656i	−0.133743	+	0.231649i
$165$	−7.62236	+	13.2023i	−0.593400	+	1.02780i
$166$	−6.10356	+	10.5717i	−0.473728	+	0.820521i
$167$	6.18783	+	10.7176i	0.478828	+	0.829355i	0.999705	−	0.0242767i	$-0.00772826\pi$
$167$	6.18783	+	10.7176i	0.478828	+	0.829355i	−0.520877	+	0.853632i	$0.674395\pi$
$168$	2.15633	−	3.73486i	0.166364	−	0.288151i
$169$	4.09332	+	7.08984i	0.314871	+	0.545372i
$170$	−34.7612			−2.66606
$171$	−1.80606			−0.138113
$172$	1.76551	+	3.05796i	0.134619	+	0.233167i
$173$	−9.28726	+	16.0860i	−0.706097	+	1.22300i	0.260197	+	0.965556i	$0.416212\pi$
$173$	−9.28726	+	16.0860i	−0.706097	+	1.22300i	−0.966294	+	0.257441i	$0.917121\pi$
$174$	−0.0527700	−	0.0914003i	−0.00400048	−	0.00692904i
$175$	6.25988	−	10.8424i	0.473202	−	0.819611i
$176$	11.5066	−	19.9300i	0.867342	−	1.50228i
$177$	4.48119	−	7.76166i	0.336827	−	0.583402i
$178$	6.46898			0.484870
$179$	4.18783	+	7.25353i	0.313013	+	0.542154i	0.979013	−	0.203797i	$-0.0653284\pi$
$179$	4.18783	+	7.25353i	0.313013	+	0.542154i	−0.666000	+	0.745952i	$0.731995\pi$
$180$	−1.32487	−	2.29474i	−0.0987499	−	0.171040i
$181$	0.955802	−	1.65550i	0.0710442	−	0.123052i	−0.828315	−	0.560263i	$-0.810700\pi$
$181$	0.955802	−	1.65550i	0.0710442	−	0.123052i	0.899359	+	0.437211i	$0.144034\pi$
$182$	7.92478			0.587424
$183$	−1.59697	−	2.76603i	−0.118051	−	0.204471i
$184$	14.7005			1.08374
$185$	−12.9257			−0.950319
$186$	−6.25576	−	6.91762i	−0.458694	−	0.507225i
$187$	29.2750			2.14080
$188$	5.13918			0.374813
$189$	1.07816	+	1.86743i	0.0784248	+	0.135836i
$190$	9.94525			0.721504
$191$	7.11260	−	12.3194i	0.514650	−	0.891400i	−0.485206	−	0.874400i	$-0.661255\pi$
$191$	7.11260	−	12.3194i	0.514650	−	0.891400i	0.999855	−	0.0169998i	$-0.00541146\pi$
$192$	−1.35026	−	2.33872i	−0.0974467	−	0.168783i
$193$	−7.38423	−	12.7899i	−0.531528	−	0.920634i	−0.999323	−	0.0367966i	$-0.988285\pi$
$193$	−7.38423	−	12.7899i	−0.531528	−	0.920634i	0.467795	−	0.883837i	$-0.345049\pi$
$194$	9.02539			0.647985
$195$	−3.60602	+	6.24581i	−0.258232	+	0.447271i
$196$	0.947230	−	1.64065i	0.0676593	−	0.117189i
$197$	4.89938	−	8.48598i	0.349067	−	0.604601i	−0.637017	−	0.770850i	$-0.719832\pi$
$197$	4.89938	−	8.48598i	0.349067	−	0.604601i	0.986084	+	0.166248i	$0.0531653\pi$
$198$	3.88423	+	6.72768i	0.276040	+	0.478115i
$199$	−2.11577	+	3.66463i	−0.149983	+	0.259779i	−0.931221	−	0.364455i	$-0.881255\pi$
$199$	−2.11577	+	3.66463i	−0.149983	+	0.259779i	0.781238	+	0.624234i	$0.214589\pi$
$200$	−5.80606	−	10.0564i	−0.410551	−	0.711095i
$201$	7.58181			0.534780
$202$	−3.45580			−0.243149
$203$	−0.0679286	−	0.117656i	−0.00476765	−	0.00825781i
$204$	−2.54420	+	4.40668i	−0.178130	+	0.308529i
$205$	−6.98484	−	12.0981i	−0.487842	−	0.844968i
$206$	−14.3065	+	24.7797i	−0.996784	+	1.72648i
$207$	−3.67513	+	6.36551i	−0.255439	+	0.442434i
$208$	5.44358	−	9.42856i	0.377445	−	0.653753i
$209$	−8.37565			−0.579356
$210$	−5.93700	−	10.2832i	−0.409692	−	0.709607i
$211$	0.190289	+	0.329591i	0.0131001	+	0.0226900i	0.872501	−	0.488612i	$-0.162497\pi$
$211$	0.190289	+	0.329591i	0.0131001	+	0.0226900i	−0.859401	+	0.511302i	$0.829163\pi$
$212$	4.83146	−	8.36833i	0.331826	−	0.574739i
$213$	9.73813			0.667246
$214$	−2.10356	−	3.64346i	−0.143796	−	0.249062i
$215$	−14.4001			−0.982078
$216$	2.00000			0.136083
$217$	−8.05277	−	8.90476i	−0.546658	−	0.604495i
$218$	−23.7015			−1.60527
$219$	−9.88717			−0.668113
$220$	−6.14411	−	10.6419i	−0.414236	−	0.717477i
$221$	13.8496			0.931622
$222$	−3.29337	+	5.70428i	−0.221036	+	0.382846i
$223$	−1.26845	−	2.19702i	−0.0849418	−	0.147124i	0.820425	−	0.571755i	$-0.193737\pi$
$223$	−1.26845	−	2.19702i	−0.0849418	−	0.147124i	−0.905366	+	0.424631i	$0.860404\pi$
$224$	4.64974	+	8.05358i	0.310674	+	0.538103i
$225$	5.80606			0.387071
$226$	16.2071	−	28.0715i	1.07808	−	1.86729i
$227$	1.93700	−	3.35498i	0.128563	−	0.222678i	−0.794557	−	0.607189i	$-0.792297\pi$
$227$	1.93700	−	3.35498i	0.128563	−	0.222678i	0.923120	+	0.384512i	$0.125630\pi$
$228$	0.727901	−	1.26076i	0.0482064	−	0.0834960i
$229$	−7.35685	−	12.7424i	−0.486154	−	0.842044i	0.513719	−	0.857958i	$-0.328267\pi$
$229$	−7.35685	−	12.7424i	−0.486154	−	0.842044i	−0.999873	+	0.0159146i	$0.994934\pi$
$230$	20.2374	−	35.0523i	1.33442	−	2.31128i
$231$	5.00000	+	8.66025i	0.328976	+	0.569803i
$232$	−0.126008			−0.00827283
$233$	23.7889			1.55846			0.779232	−	0.626736i	$-0.215609\pi$
$233$	23.7889			1.55846			0.779232	+	0.626736i	$0.215609\pi$
$234$	1.83757	+	3.18276i	0.120125	+	0.208063i
$235$	−10.4792	+	18.1505i	−0.683588	+	1.18401i
$236$	3.61213	+	6.25639i	0.235129	+	0.407256i
$237$	−1.07816	+	1.86743i	−0.0700342	+	0.121303i
$238$	−11.4010	+	19.7472i	−0.739020	+	1.28002i
$239$	10.4690	−	18.1328i	0.677182	−	1.17291i	−0.298644	−	0.954364i	$-0.596534\pi$
$239$	10.4690	−	18.1328i	0.677182	−	1.17291i	0.975826	−	0.218549i	$-0.0701322\pi$
$240$	−16.3127			−1.05298
$241$	−0.865420	−	1.49895i	−0.0557466	−	0.0965560i	0.836805	−	0.547500i	$-0.184421\pi$
$241$	−0.865420	−	1.49895i	−0.0557466	−	0.0965560i	−0.892552	+	0.450944i	$0.851087\pi$
$242$	8.79995	+	15.2420i	0.565682	+	0.979791i
$243$	−0.500000	+	0.866025i	−0.0320750	+	0.0555556i
$244$	2.57452			0.164816
$245$	3.86296	+	6.69084i	0.246795	+	0.427462i
$246$	−7.11871			−0.453873
$247$	−3.96239			−0.252121
$248$	−10.8872	+	2.33872i	−0.691336	+	0.148509i
$249$	−7.28726			−0.461811
$250$	−4.43866			−0.280725
$251$	5.79995	+	10.0458i	0.366090	+	0.634086i	0.988950	−	0.148247i	$-0.0473629\pi$
$251$	5.79995	+	10.0458i	0.366090	+	0.634086i	−0.622861	+	0.782333i	$0.714030\pi$
$252$	−1.73813			−0.109492
$253$	−17.0435	+	29.5202i	−1.07152	+	1.85592i
$254$	−16.2181	−	28.0907i	−1.01762	−	1.76256i
$255$	−10.3757	−	17.9712i	−0.649749	−	1.12540i
$256$	16.6253			1.03908
$257$	2.03150	−	3.51866i	0.126722	−	0.219488i	−0.795683	−	0.605713i	$-0.792888\pi$
$257$	2.03150	−	3.51866i	0.126722	−	0.219488i	0.922405	+	0.386225i	$0.126221\pi$
$258$	−3.66902	+	6.35493i	−0.228423	+	0.395641i
$259$	−4.23941	+	7.34288i	−0.263424	+	0.456264i
$260$	−2.90668	−	5.03452i	−0.180265	−	0.312227i
$261$	0.0315020	−	0.0545631i	0.00194992	−	0.00337737i
$262$	0.335103	+	0.580416i	0.0207027	+	0.0358582i
$263$	19.0738			1.17614			0.588071	−	0.808810i	$-0.299888\pi$
$263$	19.0738			1.17614			0.588071	+	0.808810i	$0.299888\pi$
$264$	9.27504			0.570839
$265$	19.7035	+	34.1274i	1.21037	+	2.09643i
$266$	3.26187	−	5.64972i	0.199998	−	0.346406i
$267$	1.93089	+	3.34439i	0.118168	+	0.204674i
$268$	−3.05571	+	5.29264i	−0.186657	+	0.323300i
$269$	−10.4060	+	18.0237i	−0.634463	+	1.09892i	0.352165	+	0.935938i	$0.385445\pi$
$269$	−10.4060	+	18.0237i	−0.634463	+	1.09892i	−0.986629	+	0.162985i	$0.947888\pi$
$270$	2.75329	−	4.76884i	0.167560	−	0.290223i
$271$	−11.8119			−0.717524			−0.358762	−	0.933429i	$-0.616801\pi$
$271$	−11.8119			−0.717524			−0.358762	+	0.933429i	$0.616801\pi$
$272$	15.6629	+	27.1290i	0.949704	+	1.64493i
$273$	2.36542	+	4.09703i	0.143162	+	0.247963i
$274$	2.69029	−	4.65972i	0.162526	−	0.281504i
$275$	26.9257			1.62368
$276$	−2.96239	−	5.13101i	−0.178315	−	0.308850i
$277$	22.7137			1.36473			0.682367	−	0.731010i	$-0.260951\pi$
$277$	22.7137			1.36473			0.682367	+	0.731010i	$0.260951\pi$
$278$	−15.9248			−0.955105
$279$	1.70910	−	5.29896i	0.102321	−	0.317241i
$280$	−14.1768			−0.847225
$281$	10.0484			0.599438			0.299719	−	0.954027i	$-0.403107\pi$
$281$	10.0484			0.599438			0.299719	+	0.954027i	$0.403107\pi$
$282$	5.34003	+	9.24920i	0.317994	+	0.550782i
$283$	−0.0679286			−0.00403793			−0.00201897	−	0.999998i	$-0.500643\pi$
$283$	−0.0679286			−0.00403793			−0.00201897	+	0.999998i	$0.500643\pi$
$284$	−3.92478	+	6.79791i	−0.232893	+	0.403382i
$285$	2.96850	+	5.14159i	0.175839	+	0.304561i
$286$	8.52175	+	14.7601i	0.503901	+	0.872783i
$287$	−9.16362			−0.540911
$288$	−2.15633	+	3.73486i	−0.127063	+	0.220079i
$289$	−11.4248	+	19.7883i	−0.672046	+	1.16402i
$290$	−0.173469	+	0.300456i	−0.0101864	+	0.0176434i
$291$	2.69394	+	4.66604i	0.157921	+	0.273528i
$292$	3.98484	−	6.90195i	0.233195	−	0.403906i
$293$	−13.9248	−	24.1184i	−0.813494	−	1.40901i	−0.910404	−	0.413720i	$-0.864229\pi$
$293$	−13.9248	−	24.1184i	−0.813494	−	1.40901i	0.0969100	−	0.995293i	$-0.469104\pi$
$294$	3.93700			0.229610
$295$	−29.4617			−1.71533
$296$	3.93207	+	6.81055i	0.228547	+	0.395855i
$297$	−2.31876	+	4.01621i	−0.134548	+	0.233044i
$298$	3.67513	+	6.36551i	0.212895	+	0.368744i
$299$	−8.06300	+	13.9655i	−0.466296	+	0.807648i
$300$	−2.34003	+	4.05305i	−0.135102	+	0.234003i
$301$	−4.72298	+	8.18043i	−0.272228	+	0.471512i
$302$	0.586734			0.0337628
$303$	−1.03150	−	1.78661i	−0.0592582	−	0.102638i
$304$	−4.48119	−	7.76166i	−0.257014	−	0.445162i
$305$	−5.24965	+	9.09265i	−0.300594	+	0.520644i
$306$	−10.5745			−0.604505
$307$	−12.7721	−	22.1219i	−0.728942	−	1.26256i	−0.957331	−	0.288995i	$-0.906679\pi$
$307$	−12.7721	−	22.1219i	−0.728942	−	1.26256i	0.228388	−	0.973570i	$-0.426654\pi$
$308$	−8.06063			−0.459297
$309$	−17.0811			−0.971710
$310$	−9.41128	+	29.1792i	−0.534525	+	1.65727i
$311$	7.33804			0.416102			0.208051	−	0.978118i	$-0.433288\pi$
$311$	7.33804			0.416102			0.208051	+	0.978118i	$0.433288\pi$
$312$	4.38787			0.248414
$313$	−3.76187	−	6.51574i	−0.212633	−	0.368291i	0.739905	−	0.672712i	$-0.234871\pi$
$313$	−3.76187	−	6.51574i	−0.212633	−	0.368291i	−0.952538	+	0.304420i	$0.901537\pi$
$314$	38.7489			2.18673
$315$	3.54420	−	6.13873i	0.199693	−	0.345878i
$316$	−0.869067	−	1.50527i	−0.0488889	−	0.0846780i
$317$	−5.43747	−	9.41798i	−0.305399	−	0.528966i	0.671951	−	0.740595i	$-0.265456\pi$
$317$	−5.43747	−	9.41798i	−0.305399	−	0.528966i	−0.977350	+	0.211629i	$0.932123\pi$
$318$	20.0811			1.12609
$319$	0.146091	−	0.253037i	0.00817953	−	0.0141674i
$320$	−4.43866	+	7.68798i	−0.248129	+	0.429771i
$321$	1.25576	−	2.17503i	0.0700895	−	0.121398i
$322$	−13.2750	−	22.9930i	−0.739789	−	1.28135i
$323$	5.70052	−	9.87360i	0.317186	−	0.549382i
$324$	−0.403032	−	0.698071i	−0.0223907	−	0.0387817i
$325$	12.7381			0.706585
$326$	18.1236			1.00378
$327$	−7.07452	−	12.2534i	−0.391222	−	0.677616i
$328$	−4.24965	+	7.36060i	−0.234647	+	0.406421i
$329$	6.87399	+	11.9061i	0.378975	+	0.656405i
$330$	12.7685	−	22.1156i	0.702880	−	1.21742i
$331$	5.15268	−	8.92470i	0.283217	−	0.490546i	−0.688958	−	0.724801i	$-0.741932\pi$
$331$	5.15268	−	8.92470i	0.283217	−	0.490546i	0.972175	+	0.234255i	$0.0752651\pi$
$332$	2.93700	−	5.08703i	0.161189	−	0.279187i
$333$	−3.93207			−0.215476
$334$	−10.3654	−	17.9534i	−0.567171	−	0.982368i
$335$	−12.4617	−	21.5843i	−0.680854	−	1.17927i
$336$	−5.35026	+	9.26693i	−0.291881	+	0.505552i
$337$	−7.04349			−0.383683			−0.191842	−	0.981426i	$-0.561446\pi$
$337$	−7.04349			−0.383683			−0.191842	+	0.981426i	$0.561446\pi$
$338$	−6.85685	−	11.8764i	−0.372963	−	0.645992i
$339$	19.3503			1.05096
$340$	16.7269			0.907142
$341$	7.92596	−	24.5740i	0.429215	−	1.33076i
$342$	3.02539			0.163594
$343$	20.1622			1.08866
$344$	4.38058	+	7.58739i	0.236185	+	0.409084i
$345$	24.1622			1.30085
$346$	15.5574	−	26.9462i	0.836370	−	1.44863i
$347$	−4.12482	−	7.14440i	−0.221432	−	0.383532i	0.733811	−	0.679354i	$-0.237740\pi$
$347$	−4.12482	−	7.14440i	−0.221432	−	0.383532i	−0.955243	+	0.295822i	$0.904406\pi$
$348$	0.0253926	+	0.0439813i	0.00136119	+	0.00235764i
$349$	−16.0738			−0.860411			−0.430206	−	0.902731i	$-0.641559\pi$
$349$	−16.0738			−0.860411			−0.430206	+	0.902731i	$0.641559\pi$
$350$	−10.4861	+	18.1625i	−0.560507	+	0.970826i
$351$	−1.09697	+	1.90000i	−0.0585518	+	0.101415i
$352$	−10.0000	+	17.3205i	−0.533002	+	0.923186i
$353$	−14.9878	−	25.9596i	−0.797719	−	1.38169i	−0.921098	−	0.389330i	$-0.872706\pi$
$353$	−14.9878	−	25.9596i	−0.797719	−	1.38169i	0.123379	−	0.992360i	$-0.460627\pi$
$354$	−7.50659	+	13.0018i	−0.398971	+	0.691037i
$355$	−16.0059	−	27.7230i	−0.849504	−	1.47138i
$356$	−3.11283			−0.164980
$357$	−13.6121			−0.720430
$358$	−7.01516	−	12.1506i	−0.370763	−	0.642180i
$359$	3.21814	−	5.57399i	0.169847	−	0.294184i	−0.768519	−	0.639827i	$-0.779006\pi$
$359$	3.21814	−	5.57399i	0.169847	−	0.294184i	0.938366	+	0.345643i	$0.112339\pi$
$360$	−3.28726	−	5.69370i	−0.173254	−	0.300084i
$361$	7.86907	−	13.6296i	0.414161	−	0.717349i
$362$	−1.60109	+	2.77317i	−0.0841516	+	0.145755i
$363$	−5.25329	+	9.09897i	−0.275726	+	0.477572i
$364$	−3.81336			−0.199874
$365$	16.2508	+	28.1473i	0.850607	+	1.47330i
$366$	2.67513	+	4.63346i	0.139831	+	0.242195i
$367$	−1.47461	+	2.55409i	−0.0769739	+	0.133323i	−0.901943	−	0.431855i	$-0.857859\pi$
$367$	−1.47461	+	2.55409i	−0.0769739	+	0.133323i	0.824969	+	0.565178i	$0.191192\pi$
$368$	−36.4749			−1.90138
$369$	−2.12482	−	3.68030i	−0.110614	−	0.191589i
$370$	21.6523			1.12565
$371$	25.8496			1.34204
$372$	3.01023	+	3.32872i	0.156073	+	0.172586i
$373$	26.5125			1.37276			0.686382	−	0.727241i	$-0.259198\pi$
$373$	26.5125			1.37276			0.686382	+	0.727241i	$0.259198\pi$
$374$	−49.0395			−2.53577
$375$	−1.32487	−	2.29474i	−0.0684159	−	0.118500i
$376$	12.7513			0.657599
$377$	0.0691134	−	0.119708i	0.00355952	−	0.00616527i
$378$	−1.80606	−	3.12819i	−0.0928939	−	0.160897i
$379$	16.3496	+	28.3183i	0.839820	+	1.45461i	0.890045	+	0.455873i	$0.150673\pi$
$379$	16.3496	+	28.3183i	0.839820	+	1.45461i	−0.0502245	+	0.998738i	$0.515994\pi$
$380$	−4.78560			−0.245496
$381$	9.68172	−	16.7692i	0.496009	−	0.859114i
$382$	−11.9145	+	20.6366i	−0.609601	+	1.05586i
$383$	4.87518	−	8.44405i	0.249110	−	0.431471i	−0.714169	−	0.699973i	$-0.753195\pi$
$383$	4.87518	−	8.44405i	0.249110	−	0.431471i	0.963279	+	0.268502i	$0.0865286\pi$
$384$	6.57452	+	11.3874i	0.335504	+	0.581111i
$385$	16.4363	−	28.4685i	0.837671	−	1.45089i
$386$	12.3695	+	21.4247i	0.629593	+	1.09049i
$387$	−4.38058			−0.222677
$388$	−4.34297			−0.220481
$389$	−7.67021	−	13.2852i	−0.388895	−	0.673586i	0.603406	−	0.797434i	$-0.293810\pi$
$389$	−7.67021	−	13.2852i	−0.388895	−	0.673586i	−0.992301	+	0.123848i	$0.960476\pi$
$390$	6.04055	−	10.4625i	0.305875	−	0.529791i
$391$	−23.1998	−	40.1833i	−1.17327	−	2.03215i
$392$	2.35026	−	4.07077i	0.118706	−	0.205605i
$393$	−0.200046	+	0.346490i	−0.0100910	+	0.0174781i
$394$	−8.20711	+	14.2151i	−0.413468	+	0.716148i
$395$	7.08840			0.356656
$396$	−1.86907	−	3.23732i	−0.0939242	−	0.162681i
$397$	2.18370	+	3.78228i	0.109597	+	0.189827i	0.915607	−	0.402074i	$-0.131711\pi$
$397$	2.18370	+	3.78228i	0.109597	+	0.189827i	−0.806010	+	0.591902i	$0.798377\pi$
$398$	3.54420	−	6.13873i	0.177655	−	0.307707i
$399$	3.89446			0.194967
$400$	14.4060	+	24.9519i	0.720299	+	1.24759i
$401$	−26.6253			−1.32960			−0.664802	−	0.747020i	$-0.731484\pi$
$401$	−26.6253			−1.32960			−0.664802	+	0.747020i	$0.731484\pi$
$402$	−12.7005			−0.633445
$403$	3.74965	−	11.6256i	0.186783	−	0.579112i
$404$	1.66291			0.0827330
$405$	3.28726			0.163345
$406$	0.113789	+	0.197089i	0.00564726	+	0.00978135i
$407$	−18.2351			−0.903878
$408$	−6.31265	+	10.9338i	−0.312523	+	0.541305i
$409$	13.1629	+	22.7988i	0.650864	+	1.12733i	0.982914	+	0.184068i	$0.0589266\pi$
$409$	13.1629	+	22.7988i	0.650864	+	1.12733i	−0.332049	+	0.943262i	$0.607740\pi$
$410$	11.7005	+	20.2659i	0.577848	+	1.00086i
$411$	3.21203			0.158438
$412$	6.88423	−	11.9238i	0.339161	−	0.587445i
$413$	−9.66291	+	16.7367i	−0.475481	+	0.823557i
$414$	6.15633	−	10.6631i	0.302567	−	0.524061i
$415$	11.9775	+	20.7457i	0.587955	+	1.01837i
$416$	−4.73084	+	8.19406i	−0.231949	+	0.401747i
$417$	−4.75329	−	8.23295i	−0.232770	−	0.403169i
$418$	14.0303			0.686245
$419$	−23.4617			−1.14618			−0.573089	−	0.819493i	$-0.694255\pi$
$419$	−23.4617			−1.14618			−0.573089	+	0.819493i	$0.694255\pi$
$420$	2.85685	+	4.94821i	0.139400	+	0.241448i
$421$	−10.3625	+	17.9483i	−0.505036	+	0.874749i	0.494947	+	0.868923i	$0.335188\pi$
$421$	−10.3625	+	17.9483i	−0.505036	+	0.874749i	−0.999983	+	0.00582533i	$0.998146\pi$
$422$	−0.318760	−	0.552108i	−0.0155170	−	0.0268762i
$423$	−3.18783	+	5.52148i	−0.154997	+	0.268463i
$424$	11.9878	−	20.7634i	0.582178	−	1.00836i
$425$	−18.3258	+	31.7413i	−0.888933	+	1.53968i
$426$	−16.3127			−0.790350
$427$	3.44358	+	5.96446i	0.166647	+	0.288640i
$428$	1.01222	+	1.75321i	0.0489274	+	0.0847448i
$429$	−5.08721	+	8.81131i	−0.245613	+	0.425414i
$430$	24.1220			1.16327
$431$	−1.57452	−	2.72714i	−0.0758417	−	0.131362i	0.825610	−	0.564241i	$-0.190831\pi$
$431$	−1.57452	−	2.72714i	−0.0758417	−	0.131362i	−0.901452	+	0.432879i	$0.857498\pi$
$432$	−4.96239			−0.238753
$433$	24.3357			1.16950			0.584749	−	0.811214i	$-0.301193\pi$
$433$	24.3357			1.16950			0.584749	+	0.811214i	$0.301193\pi$
$434$	13.4894	+	14.9166i	0.647514	+	0.716022i
$435$	−0.207110			−0.00993018
$436$	11.4050			0.546201
$437$	6.63752	+	11.4965i	0.317516	+	0.549953i
$438$	16.5623			0.791377
$439$	9.16291	−	15.8706i	0.437322	−	0.757464i	−0.560160	−	0.828384i	$-0.689260\pi$
$439$	9.16291	−	15.8706i	0.437322	−	0.757464i	0.997482	+	0.0709206i	$0.0225937\pi$
$440$	−15.2447	−	26.4046i	−0.726764	−	1.25879i
$441$	1.17513	+	2.03539i	0.0559586	+	0.0969232i
$442$	−23.1998			−1.10350
$443$	−11.4060	+	19.7557i	−0.541914	+	0.938623i	0.456880	+	0.889528i	$0.348967\pi$
$443$	−11.4060	+	19.7557i	−0.541914	+	0.938623i	−0.998794	+	0.0490944i	$0.984366\pi$
$444$	1.58475	−	2.74487i	0.0752089	−	0.130266i
$445$	6.34732	−	10.9939i	0.300892	−	0.521160i
$446$	2.12482	+	3.68030i	0.100613	+	0.174267i
$447$	−2.19394	+	3.80001i	−0.103770	+	0.179734i
$448$	2.91160	+	5.04304i	0.137560	+	0.238261i
$449$	−3.79877			−0.179275			−0.0896375	−	0.995974i	$-0.528571\pi$
$449$	−3.79877			−0.179275			−0.0896375	+	0.995974i	$0.528571\pi$
$450$	−9.72592			−0.458484
$451$	−9.85391	−	17.0675i	−0.464002	−	0.803676i
$452$	−7.79877	+	13.5079i	−0.366823	+	0.635357i
$453$	0.175131	+	0.303336i	0.00822837	+	0.0142519i
$454$	−3.24472	+	5.62002i	−0.152282	+	0.263761i
$455$	7.77575	−	13.4680i	0.364533	−	0.631389i
$456$	1.80606	−	3.12819i	0.0845767	−	0.146491i
$457$	−5.22170			−0.244261			−0.122130	−	0.992514i	$-0.538973\pi$
$457$	−5.22170			−0.244261			−0.122130	+	0.992514i	$0.538973\pi$
$458$	12.3237	+	21.3452i	0.575848	+	0.997398i
$459$	−3.15633	−	5.46692i	−0.147325	−	0.255174i
$460$	−9.73813	+	16.8669i	−0.454043	+	0.786425i
$461$	9.27267			0.431871			0.215936	−	0.976408i	$-0.430720\pi$
$461$	9.27267			0.431871			0.215936	+	0.976408i	$0.430720\pi$
$462$	−8.37565	−	14.5071i	−0.389671	−	0.674929i
$463$	6.29551			0.292577			0.146289	−	0.989242i	$-0.453267\pi$
$463$	6.29551			0.292577			0.146289	+	0.989242i	$0.453267\pi$
$464$	0.312650			0.0145144
$465$	−17.8945	+	3.84399i	−0.829836	+	0.178261i
$466$	−39.8496			−1.84599
$467$	−12.8627			−0.595216			−0.297608	−	0.954688i	$-0.596189\pi$
$467$	−12.8627			−0.595216			−0.297608	+	0.954688i	$0.596189\pi$
$468$	−0.884226	−	1.53152i	−0.0408734	−	0.0707947i
$469$	−16.3488			−0.754920
$470$	17.5540	−	30.4045i	0.809708	−	1.40246i
$471$	11.5659	+	20.0328i	0.532931	+	0.923063i
$472$	8.96239	+	15.5233i	0.412527	+	0.714518i
$473$	−20.3150			−0.934086
$474$	1.80606	−	3.12819i	0.0829552	−	0.143683i
$475$	5.24306	−	9.08125i	0.240568	−	0.416676i
$476$	5.48612	−	9.50224i	0.251456	−	0.435534i
$477$	5.99389	+	10.3817i	0.274441	+	0.475346i
$478$	−17.5369	+	30.3748i	−0.802119	+	1.38931i
$479$	−0.400092	−	0.692980i	−0.0182807	−	0.0316630i	0.856740	−	0.515748i	$-0.172486\pi$
$479$	−0.400092	−	0.692980i	−0.0182807	−	0.0316630i	−0.875021	+	0.484085i	$0.839153\pi$
$480$	14.1768			0.647079
$481$	−8.62672			−0.393344
$482$	1.44969	+	2.51094i	0.0660317	+	0.114370i
$483$	7.92478	−	13.7261i	0.360590	−	0.624560i
$484$	−4.23449	−	7.33435i	−0.192477	−	0.333379i
$485$	8.85566	−	15.3385i	0.402115	−	0.696484i
$486$	0.837565	−	1.45071i	0.0379927	−	0.0658054i
$487$	1.67878	−	2.90773i	0.0760727	−	0.131762i	−0.825480	−	0.564432i	$-0.809095\pi$
$487$	1.67878	−	2.90773i	0.0760727	−	0.131762i	0.901552	+	0.432670i	$0.142429\pi$
$488$	6.38787			0.289165
$489$	5.40962	+	9.36973i	0.244631	+	0.423714i
$490$	−6.47096	−	11.2080i	−0.292328	−	0.506327i
$491$	−4.67513	+	8.09756i	−0.210986	+	0.365438i	−0.952023	−	0.306026i	$-0.901001\pi$
$491$	−4.67513	+	8.09756i	−0.210986	+	0.365438i	0.741038	+	0.671464i	$0.234334\pi$
$492$	3.42548			0.154433
$493$	0.198861	+	0.344438i	0.00895625	+	0.0155127i
$494$	6.63752			0.298636
$495$	15.2447			0.685199
$496$	27.0132	−	5.80282i	1.21293	−	0.260554i
$497$	−20.9986			−0.941915
$498$	12.2071			0.547014
$499$	−7.71568	−	13.3640i	−0.345401	−	0.598253i	0.640025	−	0.768354i	$-0.278924\pi$
$499$	−7.71568	−	13.3640i	−0.345401	−	0.598253i	−0.985427	+	0.170101i	$0.945591\pi$
$500$	2.13586			0.0955184
$501$	6.18783	−	10.7176i	0.276452	−	0.478828i
$502$	−9.71568	−	16.8281i	−0.433632	−	0.751073i
$503$	−2.50659	−	4.34154i	−0.111763	−	0.193580i	0.804718	−	0.593657i	$-0.202316\pi$
$503$	−2.50659	−	4.34154i	−0.111763	−	0.193580i	−0.916481	+	0.400078i	$0.868983\pi$
$504$	−4.31265			−0.192101
$505$	−3.39081	+	5.87306i	−0.150889	+	0.261348i
$506$	28.5501	−	49.4502i	1.26921	−	2.19833i
$507$	4.09332	−	7.08984i	0.181791	−	0.314871i
$508$	7.80408	+	13.5171i	0.346250	+	0.599723i
$509$	3.96968	−	6.87569i	0.175953	−	0.304760i	−0.764538	−	0.644579i	$-0.777033\pi$
$509$	3.96968	−	6.87569i	0.175953	−	0.304760i	0.940491	+	0.339819i	$0.110366\pi$
$510$	17.3806	+	30.1040i	0.769625	+	1.33303i
$511$	21.3199			0.943139
$512$	−1.55149			−0.0685669
$513$	0.903032	+	1.56410i	0.0398698	+	0.0690566i
$514$	−3.40303	+	5.89422i	−0.150101	+	0.259983i
$515$	28.0750	+	48.6273i	1.23713	+	2.14278i
$516$	1.76551	−	3.05796i	0.0777223	−	0.134619i
$517$	−14.7836	+	25.6060i	−0.650182	+	1.12615i
$518$	7.10157	−	12.3003i	0.312025	−	0.540443i
$519$	18.5745			0.815331
$520$	−7.21203	−	12.4916i	−0.316269	−	0.547793i
$521$	9.88106	+	17.1145i	0.432897	+	0.749799i	0.997121	−	0.0758220i	$-0.0241581\pi$
$521$	9.88106	+	17.1145i	0.432897	+	0.749799i	−0.564224	+	0.825621i	$0.690825\pi$
$522$	−0.0527700	+	0.0914003i	−0.00230968	+	0.00400048i
$523$	−16.0205			−0.700526			−0.350263	−	0.936651i	$-0.613908\pi$
$523$	−16.0205			−0.700526			−0.350263	+	0.936651i	$0.613908\pi$
$524$	−0.161250	−	0.279293i	−0.00704423	−	0.0122010i
$525$	−12.5198			−0.546407
$526$	−31.9511			−1.39314
$527$	23.5745	+	26.0687i	1.02692	+	1.13557i
$528$	−23.0132			−1.00152
$529$	31.0263			1.34897
$530$	−33.0059	−	57.1679i	−1.43368	−	2.48321i
$531$	−8.96239			−0.388935
$532$	−1.56959	+	2.71861i	−0.0680504	+	0.117867i
$533$	−4.66173	−	8.07435i	−0.201922	−	0.349739i
$534$	−3.23449	−	5.60230i	−0.139970	−	0.242435i
$535$	−8.25599			−0.356937
$536$	−7.58181	+	13.1321i	−0.327484	+	0.567219i
$537$	4.18783	−	7.25353i	0.180718	−	0.313013i
$538$	17.4314	−	30.1920i	0.751519	−	1.30167i
$539$	5.44969	+	9.43914i	0.234735	+	0.406573i
$540$	−1.32487	+	2.29474i	−0.0570133	+	0.0987499i
$541$	15.1507	+	26.2418i	0.651379	+	1.12822i	0.982788	+	0.184735i	$0.0591426\pi$
$541$	15.1507	+	26.2418i	0.651379	+	1.12822i	−0.331409	+	0.943487i	$0.607524\pi$
$542$	19.7866			0.849905
$543$	−1.91160			−0.0820348
$544$	−13.6121	−	23.5769i	−0.583615	−	1.01085i
$545$	−23.2558	+	40.2802i	−0.996167	+	1.72541i
$546$	−3.96239	−	6.86306i	−0.169575	−	0.293712i
$547$	−3.26845	+	5.66112i	−0.139749	+	0.242052i	−0.927402	−	0.374067i	$-0.877963\pi$
$547$	−3.26845	+	5.66112i	−0.139749	+	0.242052i	0.787653	+	0.616120i	$0.211296\pi$
$548$	−1.29455	+	2.24223i	−0.0553005	+	0.0957833i
$549$	−1.59697	+	2.76603i	−0.0681569	+	0.118051i
$550$	−45.1041			−1.92325
$551$	−0.0568946	−	0.0985444i	−0.00242379	−	0.00419813i
$552$	−7.35026	−	12.7310i	−0.312848	−	0.541868i
$553$	2.32487	−	4.02679i	0.0988635	−	0.171237i
$554$	−38.0484			−1.61652
$555$	6.46287	+	11.1940i	0.274333	+	0.475159i
$556$	7.66291			0.324980
$557$	13.0640			0.553538			0.276769	−	0.960937i	$-0.410736\pi$
$557$	13.0640			0.553538			0.276769	+	0.960937i	$0.410736\pi$
$558$	−2.86296	+	8.87645i	−0.121199	+	0.375770i
$559$	−9.61071			−0.406490
$560$	35.1754			1.48643
$561$	−14.6375	−	25.3529i	−0.617997	−	1.07040i
$562$	−16.8324			−0.710032
$563$	8.60602	−	14.9061i	0.362700	−	0.628216i	−0.625704	−	0.780061i	$-0.715188\pi$
$563$	8.60602	−	14.9061i	0.362700	−	0.628216i	0.988404	+	0.151845i	$0.0485215\pi$
$564$	−2.56959	−	4.45066i	−0.108199	−	0.187407i
$565$	−31.8046	−	55.0873i	−1.33803	−	2.31754i
$566$	0.113789			0.00478292
$567$	1.07816	−	1.86743i	0.0452786	−	0.0784248i
$568$	−9.73813	+	16.8669i	−0.408603	+	0.707721i
$569$	0.906679	−	1.57041i	0.0380100	−	0.0658352i	−0.846395	−	0.532556i	$-0.821231\pi$
$569$	0.906679	−	1.57041i	0.0380100	−	0.0658352i	0.884405	+	0.466721i	$0.154565\pi$
$570$	−4.97262	−	8.61284i	−0.208280	−	0.360752i
$571$	−10.1121	+	17.5147i	−0.423179	+	0.732968i	−0.996248	−	0.0865389i	$-0.972419\pi$
$571$	−10.1121	+	17.5147i	−0.423179	+	0.732968i	0.573069	+	0.819507i	$0.305753\pi$
$572$	−4.10062	−	7.10247i	−0.171455	−	0.296969i
$573$	−14.2252			−0.594267
$574$	15.3503			0.640708
$575$	−21.3380	−	36.9586i	−0.889858	−	1.54128i
$576$	−1.35026	+	2.33872i	−0.0562609	+	0.0974467i
$577$	15.1666	+	26.2693i	0.631392	+	1.09360i	0.987267	+	0.159070i	$0.0508495\pi$
$577$	15.1666	+	26.2693i	0.631392	+	1.09360i	−0.355875	+	0.934533i	$0.615817\pi$
$578$	19.1380	−	33.1480i	0.796036	−	1.37877i
$579$	−7.38423	+	12.7899i	−0.306878	+	0.531528i
$580$	0.0834721	−	0.144578i	0.00346599	−	0.00600327i
$581$	15.7137			0.651914
$582$	−4.51270	−	7.81622i	−0.187057	−	0.323993i
$583$	27.7968	+	48.1454i	1.15123	+	1.99398i
$584$	9.88717	−	17.1251i	0.409134	−	0.708641i
$585$	7.21203			0.298181
$586$	23.3258	+	40.4015i	0.963581	+	1.66897i
$587$	−42.3127			−1.74643			−0.873215	−	0.487335i	$-0.837969\pi$
$587$	−42.3127			−1.74643			−0.873215	+	0.487335i	$0.837969\pi$
$588$	−1.89446			−0.0781262
$589$	−6.74472	−	7.45832i	−0.277911	−	0.307315i
$590$	49.3522			2.03180
$591$	−9.79877			−0.403068
$592$	−9.75623	−	16.8983i	−0.400979	−	0.694516i
$593$	25.8641			1.06211			0.531057	−	0.847336i	$-0.321795\pi$
$593$	25.8641			1.06211			0.531057	+	0.847336i	$0.321795\pi$
$594$	3.88423	−	6.72768i	0.159372	−	0.276040i
$595$	22.3733	+	38.7517i	0.917215	+	1.58866i
$596$	−1.76845	−	3.06305i	−0.0724386	−	0.125467i
$597$	4.23155			0.173186
$598$	13.5066	−	23.3941i	0.552325	−	0.956656i
$599$	0.174653	−	0.302508i	0.00713614	−	0.0123602i	−0.862435	−	0.506167i	$-0.831062\pi$
$599$	0.174653	−	0.302508i	0.00713614	−	0.0123602i	0.869571	+	0.493807i	$0.164395\pi$
$600$	−5.80606	+	10.0564i	−0.237032	+	0.410551i
$601$	0.226623	+	0.392523i	0.00924416	+	0.0160114i	0.870610	−	0.491973i	$-0.163724\pi$
$601$	0.226623	+	0.392523i	0.00924416	+	0.0160114i	−0.861366	+	0.507984i	$0.830391\pi$
$602$	7.91160	−	13.7033i	0.322453	−	0.558505i
$603$	−3.79090	−	6.56604i	−0.154378	−	0.267390i
$604$	−0.282333			−0.0114880
$605$	34.5379			1.40416
$606$	1.72790	+	2.99281i	0.0701912	+	0.121575i
$607$	17.3618	−	30.0715i	0.704693	−	1.22056i	−0.262110	−	0.965038i	$-0.584418\pi$
$607$	17.3618	−	30.0715i	0.704693	−	1.22056i	0.966802	−	0.255525i	$-0.0822484\pi$
$608$	3.89446	+	6.74540i	0.157941	+	0.273562i
$609$	−0.0679286	+	0.117656i	−0.00275260	+	0.00476765i
$610$	8.79384	−	15.2314i	0.356052	−	0.616701i
$611$	−6.99389	+	12.1138i	−0.282943	+	0.490071i
$612$	5.08840			0.205686
$613$	3.06428	+	5.30749i	0.123765	+	0.214368i	0.921250	−	0.388972i	$-0.127170\pi$
$613$	3.06428	+	5.30749i	0.123765	+	0.214368i	−0.797484	+	0.603340i	$0.793836\pi$
$614$	21.3949	+	37.0571i	0.863429	+	1.49550i
$615$	−6.98484	+	12.0981i	−0.281656	+	0.487842i
$616$	−20.0000			−0.805823
$617$	−17.3442	−	30.0410i	−0.698249	−	1.20940i	−0.969073	−	0.246774i	$-0.920629\pi$
$617$	−17.3442	−	30.0410i	−0.698249	−	1.20940i	0.270824	−	0.962629i	$-0.412704\pi$
$618$	28.6131			1.15099
$619$	−40.0395			−1.60932			−0.804662	−	0.593733i	$-0.797654\pi$
$619$	−40.0395			−1.60932			−0.804662	+	0.593733i	$0.797654\pi$
$620$	4.52865	−	14.0409i	0.181875	−	0.563895i
$621$	7.35026			0.294956
$622$	−12.2922			−0.492872
$623$	−4.16362	−	7.21160i	−0.166812	−	0.288927i
$624$	−10.8872			−0.435835
$625$	10.1600	−	17.5976i	0.406399	−	0.703904i
$626$	6.30162	+	10.9147i	0.251863	+	0.436240i
$627$	4.18783	+	7.25353i	0.167246	+	0.289678i
$628$	−18.6458			−0.744047
$629$	12.4109	−	21.4963i	0.494855	−	0.857114i
$630$	−5.93700	+	10.2832i	−0.236536	+	0.409692i
$631$	0.0830871	−	0.143911i	0.00330765	−	0.00572901i	−0.864367	−	0.502862i	$-0.832280\pi$
$631$	0.0830871	−	0.143911i	0.00330765	−	0.00572901i	0.867674	+	0.497133i	$0.165614\pi$
$632$	−2.15633	−	3.73486i	−0.0857740	−	0.148565i
$633$	0.190289	−	0.329591i	0.00756333	−	0.0131001i
$634$	9.10848	+	15.7763i	0.361744	+	0.626559i
$635$	−63.6526			−2.52598
$636$	−9.66291			−0.383159
$637$	2.57816	+	4.46551i	0.102151	+	0.176930i
$638$	−0.244722	+	0.423871i	−0.00968863	+	0.0167812i
$639$	−4.86907	−	8.43347i	−0.192617	−	0.333623i
$640$	21.6121	−	37.4333i	0.854294	−	1.47968i
$641$	7.08721	−	12.2754i	0.279928	−	0.484850i	−0.691439	−	0.722435i	$-0.743023\pi$
$641$	7.08721	−	12.2754i	0.279928	−	0.484850i	0.971367	+	0.237586i	$0.0763561\pi$
$642$	−2.10356	+	3.64346i	−0.0830207	+	0.143796i
$643$	6.10886			0.240910			0.120455	−	0.992719i	$-0.461565\pi$
$643$	6.10886			0.240910			0.120455	+	0.992719i	$0.461565\pi$
$644$	6.38787	+	11.0641i	0.251717	+	0.435987i
$645$	7.20005	+	12.4708i	0.283502	+	0.491039i
$646$	−9.54912	+	16.5396i	−0.375705	+	0.650741i
$647$	16.8994			0.664383			0.332192	−	0.943212i	$-0.392212\pi$
$647$	16.8994			0.664383			0.332192	+	0.943212i	$0.392212\pi$
$648$	−1.00000	−	1.73205i	−0.0392837	−	0.0680414i
$649$	−41.5633			−1.63150
$650$	−21.3380			−0.836947
$651$	−3.68536	+	11.4263i	−0.144441	+	0.447831i
$652$	−8.72099			−0.341540
$653$	36.3512			1.42253			0.711267	−	0.702922i	$-0.248122\pi$
$653$	36.3512			1.42253			0.711267	+	0.702922i	$0.248122\pi$
$654$	11.8507	+	20.5261i	0.463401	+	0.802633i
$655$	1.31521			0.0513893
$656$	10.5442	−	18.2631i	0.411682	−	0.713054i
$657$	4.94358	+	8.56254i	0.192868	+	0.334056i
$658$	−11.5148	−	19.9443i	−0.448895	−	0.777509i
$659$	−33.9126			−1.32105			−0.660523	−	0.750806i	$-0.729665\pi$
$659$	−33.9126			−1.32105			−0.660523	+	0.750806i	$0.729665\pi$
$660$	−6.14411	+	10.6419i	−0.239159	+	0.414236i
$661$	5.83804	−	10.1118i	0.227074	−	0.393303i	−0.729866	−	0.683590i	$-0.760418\pi$
$661$	5.83804	−	10.1118i	0.227074	−	0.393303i	0.956940	+	0.290287i	$0.0937509\pi$
$662$	−8.63141	+	14.9500i	−0.335469	+	0.581050i
$663$	−6.92478	−	11.9941i	−0.268936	−	0.465811i
$664$	7.28726	−	12.6219i	0.282800	−	0.489825i
$665$	−6.40105	−	11.0869i	−0.248222	−	0.429933i
$666$	6.58673			0.255231
$667$	−0.463096			−0.0179311
$668$	4.98778	+	8.63909i	0.192983	+	0.334256i
$669$	−1.26845	+	2.19702i	−0.0490412	+	0.0849418i
$670$	20.8749	+	36.1565i	0.806470	+	1.39685i
$671$	−7.40597	+	12.8275i	−0.285904	+	0.495201i
$672$	4.64974	−	8.05358i	0.179368	−	0.310674i
$673$	24.2731	−	42.0422i	0.935657	−	1.62061i	0.162200	−	0.986758i	$-0.448141\pi$
$673$	24.2731	−	42.0422i	0.935657	−	1.62061i	0.773457	−	0.633848i	$-0.218526\pi$
$674$	11.7988			0.454472
$675$	−2.90303	−	5.02820i	−0.111738	−	0.193535i
$676$	3.29948	+	5.71486i	0.126903	+	0.219802i
$677$	−12.2934	+	21.2927i	−0.472472	+	0.818346i	−0.999504	−	0.0314995i	$-0.989972\pi$
$677$	−12.2934	+	21.2927i	−0.472472	+	0.818346i	0.527031	+	0.849846i	$0.323305\pi$
$678$	−32.4142			−1.24486
$679$	−5.80900	−	10.0615i	−0.222929	−	0.386124i
$680$	41.5026			1.59155
$681$	−3.87399			−0.148452
$682$	−13.2770	+	41.1647i	−0.508404	+	1.57628i
$683$	8.39772			0.321330			0.160665	−	0.987009i	$-0.448636\pi$
$683$	8.39772			0.321330			0.160665	+	0.987009i	$0.448636\pi$
$684$	−1.45580			−0.0556640
$685$	−5.27939	−	9.14418i	−0.201715	−	0.349381i
$686$	−33.7743			−1.28951
$687$	−7.35685	+	12.7424i	−0.280681	+	0.486154i
$688$	−10.8691	−	18.8258i	−0.414379	−	0.717726i
$689$	13.1502	+	22.7768i	0.500983	+	0.867729i
$690$	−40.4749			−1.54085
$691$	−4.81630	+	8.34207i	−0.183221	+	0.317347i	−0.942975	−	0.332862i	$-0.891986\pi$
$691$	−4.81630	+	8.34207i	−0.183221	+	0.317347i	0.759755	+	0.650210i	$0.225319\pi$
$692$	−7.48612	+	12.9663i	−0.284580	+	0.492906i
$693$	5.00000	−	8.66025i	0.189934	−	0.328976i
$694$	6.90962	+	11.9678i	0.262286	+	0.454292i
$695$	−15.6253	+	27.0638i	−0.592701	+	1.02659i
$696$	0.0630040	+	0.109126i	0.00238816	+	0.00413642i
$697$	26.8265			1.01613
$698$	26.9257			1.01915
$699$	−11.8945	−	20.6018i	−0.449890	−	0.779232i
$700$	5.04586	−	8.73969i	0.190716	−	0.330329i
$701$	−15.8994	−	27.5385i	−0.600511	−	1.04012i	−0.992744	−	0.120250i	$-0.961630\pi$
$701$	−15.8994	−	27.5385i	−0.600511	−	1.04012i	0.392232	−	0.919866i	$-0.371703\pi$
$702$	1.83757	−	3.18276i	0.0693544	−	0.120125i
$703$	−3.55079	+	6.15014i	−0.133920	+	0.231957i
$704$	−6.26187	+	10.8459i	−0.236003	+	0.408769i
$705$	20.9584			0.789340
$706$	25.1065	+	43.4857i	0.944895	+	1.63661i
$707$	2.22425	+	3.85252i	0.0836517	+	0.144889i
$708$	3.61213	−	6.25639i	0.135752	−	0.235129i
$709$	−26.9756			−1.01309			−0.506544	−	0.862214i	$-0.669077\pi$
$709$	−26.9756			−1.01309			−0.506544	+	0.862214i	$0.669077\pi$
$710$	26.8119	+	46.4396i	1.00623	+	1.74285i
$711$	2.15633			0.0808685
$712$	−7.72355			−0.289452
$713$	−40.0118	+	8.59511i	−1.49845	+	0.321889i
$714$	22.8021			0.853347
$715$	33.4460			1.25081
$716$	3.37565	+	5.84680i	0.126154	+	0.218505i
$717$	−20.9380			−0.781942
$718$	−5.39081	+	9.33716i	−0.201183	+	0.348460i
$719$	22.2931	+	38.6128i	0.831394	+	1.44002i	0.896933	+	0.442166i	$0.145790\pi$
$719$	22.2931	+	38.6128i	0.831394	+	1.44002i	−0.0655394	+	0.997850i	$0.520877\pi$
$720$	8.15633	+	14.1272i	0.303968	+	0.526489i
$721$	36.8324			1.37171
$722$	−13.1817	+	22.8314i	−0.490573	+	0.849697i
$723$	−0.865420	+	1.49895i	−0.0321853	+	0.0557466i
$724$	0.770437	−	1.33444i	0.0286331	−	0.0495939i
$725$	0.182903	+	0.316797i	0.00679283	+	0.0117655i
$726$	8.79995	−	15.2420i	0.326597	−	0.565682i
$727$	7.85320	+	13.6021i	0.291259	+	0.504476i	0.974108	−	0.226084i	$-0.0725925\pi$
$727$	7.85320	+	13.6021i	0.291259	+	0.504476i	−0.682849	+	0.730560i	$0.739259\pi$
$728$	−9.46168			−0.350673
$729$	1.00000			0.0370370
$730$	−27.2223	−	47.1504i	−1.00754	−	1.74511i
$731$	13.8265	−	23.9483i	0.511393	−	0.885758i
$732$	−1.28726	−	2.22960i	−0.0475784	−	0.0824082i
$733$	1.05936	−	1.83486i	0.0391282	−	0.0677721i	−0.845798	−	0.533503i	$-0.820875\pi$
$733$	1.05936	−	1.83486i	0.0391282	−	0.0677721i	0.884926	+	0.465731i	$0.154209\pi$
$734$	2.47016	−	4.27844i	0.0911753	−	0.157920i
$735$	3.86296	−	6.69084i	0.142487	−	0.246795i
$736$	31.6991			1.16844
$737$	−17.5804	−	30.4501i	−0.647582	−	1.12165i
$738$	3.55936	+	6.16499i	0.131022	+	0.226936i
$739$	11.3720	−	19.6969i	0.418326	−	0.724562i	−0.577445	−	0.816429i	$-0.695950\pi$
$739$	11.3720	−	19.6969i	0.418326	−	0.724562i	0.995771	+	0.0918675i	$0.0292836\pi$
$740$	−10.4190			−0.383009
$741$	1.98119	+	3.43153i	0.0727810	+	0.126060i
$742$	−43.3014			−1.58964
$743$	8.93795			0.327902			0.163951	−	0.986469i	$-0.447576\pi$
$743$	8.93795			0.327902			0.163951	+	0.986469i	$0.447576\pi$
$744$	7.46898	+	8.25920i	0.273826	+	0.302797i
$745$	14.4241			0.528457
$746$	−44.4119			−1.62603
$747$	3.64363	+	6.31095i	0.133313	+	0.230906i
$748$	23.5975			0.862811
$749$	−2.70782	+	4.69008i	−0.0989415	+	0.171372i
$750$	2.21933	+	3.84399i	0.0810384	+	0.140363i
$751$	13.8156	+	23.9293i	0.504138	+	0.873193i	0.999989	+	0.00478481i	$0.00152306\pi$
$751$	13.8156	+	23.9293i	0.504138	+	0.873193i	−0.495851	+	0.868408i	$0.665144\pi$
$752$	−31.6385			−1.15374
$753$	5.79995	−	10.0458i	0.211362	−	0.366090i
$754$	−0.115774	+	0.200526i	−0.00421624	+	0.00730274i
$755$	0.575700	−	0.997142i	0.0209519	−	0.0362897i
$756$	0.869067	+	1.50527i	0.0316077	+	0.0547461i
$757$	1.50365	−	2.60439i	0.0546510	−	0.0946583i	−0.837406	−	0.546582i	$-0.815929\pi$
$757$	1.50365	−	2.60439i	0.0546510	−	0.0946583i	0.892057	+	0.451924i	$0.149262\pi$
$758$	−27.3876	−	47.4368i	−0.994764	−	1.72298i
$759$	34.0870			1.23728
$760$	−11.8740			−0.430715
$761$	4.87518	+	8.44405i	0.176725	+	0.306097i	0.940757	−	0.339082i	$-0.110116\pi$
$761$	4.87518	+	8.44405i	0.176725	+	0.306097i	−0.764032	+	0.645178i	$0.776783\pi$
$762$	−16.2181	+	28.0907i	−0.587521	+	1.01762i
$763$	15.2550	+	26.4224i	0.552266	+	0.956554i
$764$	5.73321	−	9.93021i	0.207420	−	0.359262i
$765$	−10.3757	+	17.9712i	−0.375133	+	0.649749i
$766$	−8.16656	+	14.1449i	−0.295070	+	0.511076i
$767$	−19.6629			−0.709987
$768$	−8.31265	−	14.3979i	−0.299957	−	0.519541i
$769$	−9.77139	−	16.9245i	−0.352365	−	0.610315i	0.634298	−	0.773089i	$-0.281289\pi$
$769$	−9.77139	−	16.9245i	−0.352365	−	0.610315i	−0.986663	+	0.162774i	$0.947956\pi$
$770$	−27.5329	+	47.6884i	−0.992218	+	1.71857i
$771$	−4.06300			−0.146326
$772$	−5.95215	−	10.3094i	−0.214223	−	0.371045i
$773$	−2.32724			−0.0837050			−0.0418525	−	0.999124i	$-0.513326\pi$
$773$	−2.32724			−0.0837050			−0.0418525	+	0.999124i	$0.513326\pi$
$774$	7.33804			0.263761
$775$	21.6827	+	23.9767i	0.778865	+	0.861269i
$776$	−10.7757			−0.386827
$777$	8.47882			0.304176
$778$	12.8486	+	22.2544i	0.460645	+	0.797860i
$779$	−7.67513			−0.274990
$780$	−2.90668	+	5.03452i	−0.104076	+	0.180265i
$781$	−22.5804	−	39.1104i	−0.807990	−	1.39948i
$782$	38.8627	+	67.3122i	1.38973	+	2.40708i
$783$	−0.0630040			−0.00225158
$784$	−5.83146	+	10.1004i	−0.208266	+	0.360728i
$785$	38.0202	−	65.8530i	1.35700	−	2.35039i
$786$	0.335103	−	0.580416i	0.0119527	−	0.0207027i
$787$	17.1751	+	29.7482i	0.612227	+	1.06041i	0.990864	+	0.134863i	$0.0430596\pi$
$787$	17.1751	+	29.7482i	0.612227	+	1.06041i	−0.378637	+	0.925545i	$0.623607\pi$
$788$	3.94921	−	6.84024i	0.140685	−	0.243673i
$789$	−9.53690	−	16.5184i	−0.339523	−	0.588071i
$790$	−11.8740			−0.422458
$791$	−41.7255			−1.48359
$792$	−4.63752	−	8.03242i	−0.164787	−	0.285420i
$793$	−3.50365	+	6.06849i	−0.124418	+	0.215499i
$794$	−3.65799	−	6.33582i	−0.129817	−	0.224850i
$795$	19.7035	−	34.1274i	0.698810	−	1.21037i
$796$	−1.70545	+	2.95392i	−0.0604480	+	0.104699i
$797$	18.9624	−	32.8438i	0.671682	−	1.16339i	−0.305745	−	0.952114i	$-0.598905\pi$
$797$	18.9624	−	32.8438i	0.671682	−	1.16339i	0.977427	−	0.211274i	$-0.0677613\pi$
$798$	−6.52373			−0.230938
$799$	−20.1236	−	34.8552i	−0.711923	−	1.23309i
$800$	−12.5198	−	21.6849i	−0.442640	−	0.766676i
$801$	1.93089	−	3.34439i	0.0682245	−	0.118168i
$802$	44.6009			1.57491
$803$	22.9260	+	39.7089i	0.809040	+	1.40130i
$804$	6.11142			0.215533
$805$	−52.1016			−1.83634
$806$	−6.28115	+	19.4744i	−0.221244	+	0.685956i
$807$	20.8119			0.732615
$808$	4.12601			0.145152
$809$	−1.60602	−	2.78170i	−0.0564646	−	0.0977995i	0.836411	−	0.548102i	$-0.184649\pi$
$809$	−1.60602	−	2.78170i	−0.0564646	−	0.0977995i	−0.892876	+	0.450303i	$0.851316\pi$
$810$	−5.50659			−0.193482
$811$	12.4218	−	21.5153i	0.436190	−	0.755503i	−0.561202	−	0.827679i	$-0.689661\pi$
$811$	12.4218	−	21.5153i	0.436190	−	0.755503i	0.997392	+	0.0721760i	$0.0229943\pi$
$812$	−0.0547547	−	0.0948380i	−0.00192151	−	0.00332816i
$813$	5.90597	+	10.2294i	0.207131	+	0.358762i
$814$	30.5461			1.07064
$815$	17.7828	−	30.8007i	0.622905	−	1.07890i
$816$	15.6629	−	27.1290i	0.548312	−	0.949704i
$817$	−3.95580	+	6.85165i	−0.138396	+	0.239709i
$818$	−22.0496	−	38.1910i	−0.770946	−	1.33532i
$819$	2.36542	−	4.09703i	0.0826545	−	0.143162i
$820$	−5.63023	−	9.75184i	−0.196616	−	0.340549i
$821$	51.0757			1.78255			0.891277	−	0.453458i	$-0.149810\pi$
$821$	51.0757			1.78255			0.891277	+	0.453458i	$0.149810\pi$
$822$	−5.38058			−0.187669
$823$	−0.365420	−	0.632927i	−0.0127378	−	0.0220624i	0.859586	−	0.510991i	$-0.170721\pi$
$823$	−0.365420	−	0.632927i	−0.0127378	−	0.0220624i	−0.872324	+	0.488928i	$0.837388\pi$
$824$	17.0811	−	29.5853i	0.595048	−	1.03065i
$825$	−13.4629	−	23.3184i	−0.468717	−	0.811841i
$826$	16.1866	−	28.0361i	0.563205	−	0.975500i
$827$	23.3573	−	40.4561i	0.812214	−	1.40680i	−0.0990975	−	0.995078i	$-0.531596\pi$
$827$	23.3573	−	40.4561i	0.812214	−	1.40680i	0.911311	−	0.411718i	$-0.135071\pi$
$828$	−2.96239	+	5.13101i	−0.102950	+	0.178315i
$829$	−43.8773			−1.52392			−0.761961	−	0.647623i	$-0.775763\pi$
$829$	−43.8773			−1.52392			−0.761961	+	0.647623i	$0.775763\pi$
$830$	−20.0640	−	34.7518i	−0.696430	−	1.20625i
$831$	−11.3568	−	19.6706i	−0.393965	−	0.682367i
$832$	−2.96239	+	5.13101i	−0.102702	+	0.177886i
$833$	−14.8364			−0.514050
$834$	7.96239	+	13.7913i	0.275715	+	0.477552i
$835$	−40.6820			−1.40786
$836$	−6.75131			−0.233499
$837$	−5.44358	+	1.16936i	−0.188158	+	0.0404190i
$838$	39.3014			1.35764
$839$	22.2012			0.766472			0.383236	−	0.923651i	$-0.374810\pi$
$839$	22.2012			0.766472			0.383236	+	0.923651i	$0.374810\pi$
$840$	7.08840	+	12.2775i	0.244573	+	0.423613i
$841$	−28.9960			−0.999863
$842$	17.3585	−	30.0658i	0.598214	−	1.03614i
$843$	−5.02421	−	8.70218i	−0.173043	−	0.299719i
$844$	0.153385	+	0.265671i	0.00527974	+	0.00914478i
$845$	−26.9116			−0.925787
$846$	5.34003	−	9.24920i	0.183594	−	0.317994i
$847$	11.3278	−	19.6203i	0.389228	−	0.674163i
$848$	−29.7440	+	51.5181i	−1.02141	+	1.76914i
$849$	0.0339643	+	0.0588279i	0.00116565	+	0.00201897i
$850$	30.6982	−	53.1708i	1.05294	−	1.82374i
$851$	14.4509	+	25.0297i	0.495370	+	0.858005i
$852$	7.84955			0.268921
$853$	0.238842			0.00817780			0.00408890	−	0.999992i	$-0.498698\pi$
$853$	0.238842			0.00817780			0.00408890	+	0.999992i	$0.498698\pi$
$854$	−5.76845	−	9.99125i	−0.197392	−	0.341894i
$855$	2.96850	−	5.14159i	0.101520	−	0.175839i
$856$	2.51151	+	4.35007i	0.0858417	+	0.148682i
$857$	−15.3307	+	26.5536i	−0.523688	+	0.907055i	0.475931	+	0.879482i	$0.342111\pi$
$857$	−15.3307	+	26.5536i	−0.523688	+	0.907055i	−0.999620	+	0.0275725i	$0.991222\pi$
$858$	8.52175	−	14.7601i	0.290928	−	0.503901i
$859$	7.79020	−	13.4930i	0.265798	−	0.460376i	−0.701974	−	0.712202i	$-0.747698\pi$
$859$	7.79020	−	13.4930i	0.265798	−	0.460376i	0.967772	+	0.251826i	$0.0810312\pi$
$860$	−11.6074			−0.395809
$861$	4.58181	+	7.93593i	0.156148	+	0.270456i
$862$	2.63752	+	4.56832i	0.0898343	+	0.155598i
$863$	−3.08229	+	5.33868i	−0.104922	+	0.181731i	−0.913706	−	0.406375i	$-0.866793\pi$
$863$	−3.08229	+	5.33868i	−0.104922	+	0.181731i	0.808784	+	0.588106i	$0.200126\pi$
$864$	4.31265			0.146719
$865$	−30.5296	−	52.8788i	−1.03804	−	1.79793i
$866$	−40.7654			−1.38527
$867$	22.8496			0.776012
$868$	−6.49104	−	7.17780i	−0.220320	−	0.243631i
$869$	10.0000			0.339227
$870$	0.346937			0.0117623
$871$	−8.31700	−	14.4055i	−0.281811	−	0.488111i
$872$	28.2981			0.958293
$873$	2.69394	−	4.66604i	0.0911759	−	0.157921i
$874$	−11.1187	−	19.2582i	−0.376096	−	0.651418i
$875$	2.85685	+	4.94821i	0.0965791	+	0.167280i
$876$	−7.96968			−0.269271
$877$	−6.39938	+	11.0841i	−0.216092	+	0.374282i	−0.953610	−	0.301045i	$-0.902664\pi$
$877$	−6.39938	+	11.0841i	−0.216092	+	0.374282i	0.737518	+	0.675328i	$0.235998\pi$
$878$	−15.3491	+	26.5854i	−0.518006	+	0.897213i
$879$	−13.9248	+	24.1184i	−0.469671	+	0.813494i
$880$	37.8251	+	65.5150i	1.27508	+	2.20851i
$881$	3.06063	−	5.30117i	0.103115	−	0.178601i	−0.809851	−	0.586635i	$-0.800452\pi$
$881$	3.06063	−	5.30117i	0.103115	−	0.178601i	0.912967	+	0.408034i	$0.133786\pi$
$882$	−1.96850	−	3.40954i	−0.0662828	−	0.114805i
$883$	−19.8061			−0.666527			−0.333264	−	0.942834i	$-0.608150\pi$
$883$	−19.8061			−0.666527			−0.333264	+	0.942834i	$0.608150\pi$
$884$	11.1636			0.375473
$885$	14.7308	+	25.5146i	0.495172	+	0.857663i
$886$	19.1065	−	33.0934i	0.641895	−	1.11180i
$887$	0.406201	+	0.703561i	0.0136389	+	0.0236233i	0.872764	−	0.488142i	$-0.162325\pi$
$887$	0.406201	+	0.703561i	0.0136389	+	0.0236233i	−0.859125	+	0.511765i	$0.828992\pi$
$888$	3.93207	−	6.81055i	0.131952	−	0.228547i
$889$	−20.8769	+	36.1599i	−0.700190	+	1.21276i
$890$	−10.6326	+	18.4162i	−0.356405	+	0.617312i
$891$	4.63752			0.155363
$892$	−1.02245	−	1.77094i	−0.0342343	−	0.0592955i
$893$	5.75742	+	9.97214i	0.192665	+	0.333705i
$894$	3.67513	−	6.36551i	0.122915	−	0.212895i
$895$	−27.5329			−0.920325
$896$	−14.1768	−	24.5549i	−0.473613	−	0.820323i
$897$	16.1260			0.538432
$898$	6.36344			0.212351
$899$	0.342968	−	0.0736744i	0.0114386	−	0.00245718i
$900$	4.68006			0.156002
$901$	−75.6747			−2.52109
$902$	16.5066	+	28.5902i	0.549609	+	0.951951i
$903$	9.44595			0.314342
$904$	−19.3503	+	33.5156i	−0.643580	+	1.11471i
$905$	3.14197	+	5.44205i	0.104443	+	0.180900i
$906$	−0.293367	−	0.508127i	−0.00974647	−	0.0168814i
$907$	35.7802			1.18806			0.594031	−	0.804442i	$-0.297536\pi$
$907$	35.7802			1.18806			0.594031	+	0.804442i	$0.297536\pi$
$908$	1.56134	−	2.70432i	0.0518149	−	0.0897461i
$909$	−1.03150	+	1.78661i	−0.0342128	+	0.0592582i
$910$	−13.0254	+	22.5606i	−0.431788	+	0.747878i
$911$	19.0933	+	33.0706i	0.632590	+	1.09568i	0.987020	+	0.160596i	$0.0513415\pi$
$911$	19.0933	+	33.0706i	0.632590	+	1.09568i	−0.354430	+	0.935082i	$0.615325\pi$
$912$	−4.48119	+	7.76166i	−0.148387	+	0.257014i
$913$	16.8974	+	29.2672i	0.559222	+	0.968601i
$914$	8.74703			0.289326
$915$	10.4993			0.347096
$916$	−5.93009	−	10.2712i	−0.195936	−	0.339370i
$917$	0.431364	−	0.747145i	0.0142449	−	0.0246729i
$918$	5.28726	+	9.15780i	0.174506	+	0.302252i
$919$	−16.2938	+	28.2218i	−0.537484	+	0.930950i	0.461554	+	0.887112i	$0.347292\pi$
$919$	−16.2938	+	28.2218i	−0.537484	+	0.930950i	−0.999039	+	0.0438382i	$0.986041\pi$
$920$	−24.1622	+	41.8502i	−0.796604	+	1.37976i
$921$	−12.7721	+	22.1219i	−0.420855	+	0.728942i
$922$	−15.5329			−0.511550
$923$	−10.6824	−	18.5025i	−0.351616	−	0.609017i
$924$	4.03032	+	6.98071i	0.132588	+	0.229649i
$925$	11.4149	−	19.7712i	0.375321	−	0.650074i
$926$	−10.5458			−0.346556
$927$	8.54055	+	14.7927i	0.280509	+	0.485855i
$928$	−0.271714			−0.00891946
$929$	45.8397			1.50395			0.751976	−	0.659191i	$-0.229101\pi$
$929$	45.8397			1.50395			0.751976	+	0.659191i	$0.229101\pi$
$930$	29.9756	−	6.43919i	0.982937	−	0.211149i
$931$	4.24472			0.139115
$932$	19.1754			0.628110
$933$	−3.66902	−	6.35493i	−0.120118	−	0.208051i
$934$	21.5468			0.705031
$935$	−48.1173	+	83.3416i	−1.57360	+	2.72556i
$936$	−2.19394	−	3.80001i	−0.0717111	−	0.124207i
$937$	13.9841	+	24.2212i	0.456842	+	0.791273i	0.998792	−	0.0491374i	$-0.0156472\pi$
$937$	13.9841	+	24.2212i	0.456842	+	0.791273i	−0.541950	+	0.840411i	$0.682314\pi$
$938$	27.3865			0.894200
$939$	−3.76187	+	6.51574i	−0.122764	+	0.212633i
$940$	−8.44691	+	14.6305i	−0.275508	+	0.477193i
$941$	9.03032	−	15.6410i	0.294380	−	0.509881i	−0.680461	−	0.732785i	$-0.738220\pi$
$941$	9.03032	−	15.6410i	0.294380	−	0.509881i	0.974840	+	0.222904i	$0.0715536\pi$
$942$	−19.3745	−	33.5576i	−0.631254	−	1.09336i
$943$	−15.6180	+	27.0512i	−0.508592	+	0.880908i
$944$	−22.2374	−	38.5164i	−0.723767	−	1.25360i
$945$	−7.08840			−0.230586
$946$	34.0303			1.10642
$947$	−21.8437	−	37.8344i	−0.709824	−	1.22945i	−0.964922	−	0.262536i	$-0.915441\pi$
$947$	−21.8437	−	37.8344i	−0.709824	−	1.22945i	0.255098	−	0.966915i	$-0.417892\pi$
$948$	−0.869067	+	1.50527i	−0.0282260	+	0.0488889i
$949$	10.8459	+	18.7857i	0.352073	+	0.609808i
$950$	−8.78281	+	15.2123i	−0.284952	+	0.493551i
$951$	−5.43747	+	9.41798i	−0.176322	+	0.305399i
$952$	13.6121	−	23.5769i	0.441172	−	0.764132i
$953$	−20.5867			−0.666870			−0.333435	−	0.942773i	$-0.608208\pi$
$953$	−20.5867			−0.666870			−0.333435	+	0.942773i	$0.608208\pi$
$954$	−10.0406	−	17.3907i	−0.325075	−	0.563046i
$955$	23.3810	+	40.4970i	0.756590	+	1.31045i
$956$	8.43866	−	14.6162i	0.272926	−	0.472721i
$957$	−0.292182			−0.00944491
$958$	0.670206	+	1.16083i	0.0216534	+	0.0375048i
$959$	−6.92619			−0.223658
$960$	8.87732			0.286514
$961$	28.2652	−	12.7310i	0.911780	−	0.410678i
$962$	14.4509			0.465915
$963$	−2.51151			−0.0809323
$964$	−0.697584	−	1.20825i	−0.0224677	−	0.0389151i
$965$	48.5477			1.56281
$966$	−13.2750	+	22.9930i	−0.427117	+	0.739789i
$967$	−9.23449	−	15.9946i	−0.296961	−	0.514352i	0.678478	−	0.734621i	$-0.262640\pi$
$967$	−9.23449	−	15.9946i	−0.296961	−	0.514352i	−0.975439	+	0.220269i	$0.929307\pi$
$968$	−10.5066	−	18.1979i	−0.337694	−	0.584904i
$969$	−11.4010			−0.366254
$970$	−14.8344	+	25.6939i	−0.476304	+	0.824982i
$971$	−6.54183	+	11.3308i	−0.209937	+	0.363622i	−0.951695	−	0.307046i	$-0.900659\pi$
$971$	−6.54183	+	11.3308i	−0.209937	+	0.363622i	0.741757	+	0.670668i	$0.233993\pi$
$972$	−0.403032	+	0.698071i	−0.0129272	+	0.0223907i
$973$	10.2496	+	17.7529i	0.328589	+	0.569132i
$974$	−2.81217	+	4.87083i	−0.0901078	+	0.156071i
$975$	−6.36907	−	11.0315i	−0.203973	−	0.353292i
$976$	−15.8496			−0.507332
$977$	−50.2784			−1.60855			−0.804274	−	0.594259i	$-0.797445\pi$
$977$	−50.2784			−1.60855			−0.804274	+	0.594259i	$0.797445\pi$
$978$	−9.06182	−	15.6955i	−0.289765	−	0.501888i
$979$	8.95452	−	15.5097i	0.286188	−	0.495692i
$980$	3.11379	+	5.39324i	0.0994663	+	0.172281i
$981$	−7.07452	+	12.2534i	−0.225872	+	0.391222i
$982$	7.83146	−	13.5645i	0.249912	−	0.432860i
$983$	1.06793	−	1.84971i	0.0340616	−	0.0589965i	−0.848492	−	0.529208i	$-0.822489\pi$
$983$	1.06793	−	1.84971i	0.0340616	−	0.0589965i	0.882554	+	0.470212i	$0.155822\pi$
$984$	8.49929			0.270948
$985$	16.1055	+	27.8956i	0.513165	+	0.888828i
$986$	−0.333118	−	0.576978i	−0.0106087	−	0.0183747i
$987$	6.87399	−	11.9061i	0.218802	−	0.378975i
$988$	−3.19394			−0.101613
$989$	16.0992	+	27.8846i	0.511925	+	0.886680i
$990$	−25.5369			−0.811616
$991$	−19.5560			−0.621215			−0.310608	−	0.950538i	$-0.600533\pi$
$991$	−19.5560			−0.621215			−0.310608	+	0.950538i	$0.600533\pi$
$992$	−23.4763	+	5.04304i	−0.745372	+	0.160117i
$993$	−10.3054			−0.327031
$994$	35.1754			1.11570
$995$	−6.95509	−	12.0466i	−0.220491	−	0.381902i
$996$	−5.87399			−0.186125
$997$	20.0840	−	34.7866i	0.636068	−	1.10170i	−0.350220	−	0.936668i	$-0.613893\pi$
$997$	20.0840	−	34.7866i	0.636068	−	1.10170i	0.986288	−	0.165035i	$-0.0527736\pi$
$998$	12.9248	+	22.3864i	0.409127	+	0.708628i
$999$	1.96604	+	3.40527i	0.0622026	+	0.107738i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	93.2.e.b.25.1	✓	6
3.2	odd	2		279.2.h.d.118.3		6
4.3	odd	2		1488.2.q.m.769.2		6
31.5	even	3	inner	93.2.e.b.67.1	yes	6
31.6	odd	6		2883.2.a.g.1.1		3
31.25	even	3		2883.2.a.h.1.1		3
93.5	odd	6		279.2.h.d.253.3		6
93.56	odd	6		8649.2.a.o.1.3		3
93.68	even	6		8649.2.a.n.1.3		3
124.67	odd	6		1488.2.q.m.625.2		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
93.2.e.b.25.1	✓	6	1.1	even	1	trivial
93.2.e.b.67.1	yes	6	31.5	even	3	inner
279.2.h.d.118.3		6	3.2	odd	2
279.2.h.d.253.3		6	93.5	odd	6
1488.2.q.m.625.2		6	124.67	odd	6
1488.2.q.m.769.2		6	4.3	odd	2
2883.2.a.g.1.1		3	31.6	odd	6
2883.2.a.h.1.1		3	31.25	even	3
8649.2.a.n.1.3		3	93.68	even	6
8649.2.a.o.1.3		3	93.56	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:	\( N \)	\(=\)	\( 93 = 3 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	93.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.67513 q^{2} +(-0.500000 - 0.866025i) q^{3} +0.806063 q^{4} +(-1.64363 + 2.84685i) q^{5} +(0.837565 + 1.45071i) q^{6} +(1.07816 + 1.86743i) q^{7} +2.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q-1.67513 q^{2} +(-0.500000 - 0.866025i) q^{3} +0.806063 q^{4} +(-1.64363 + 2.84685i) q^{5} +(0.837565 + 1.45071i) q^{6} +(1.07816 + 1.86743i) q^{7} +2.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(2.75329 - 4.76884i) q^{10} +(-2.31876 + 4.01621i) q^{11} +(-0.403032 - 0.698071i) q^{12} +(-1.09697 + 1.90000i) q^{13} +(-1.80606 - 3.12819i) q^{14} +3.28726 q^{15} -4.96239 q^{16} +(-3.15633 - 5.46692i) q^{17} +(0.837565 - 1.45071i) q^{18} +(0.903032 + 1.56410i) q^{19} +(-1.32487 + 2.29474i) q^{20} +(1.07816 - 1.86743i) q^{21} +(3.88423 - 6.72768i) q^{22} +7.35026 q^{23} +(-1.00000 - 1.73205i) q^{24} +(-2.90303 - 5.02820i) q^{25} +(1.83757 - 3.18276i) q^{26} +1.00000 q^{27} +(0.869067 + 1.50527i) q^{28} -0.0630040 q^{29} -5.50659 q^{30} +(-5.44358 + 1.16936i) q^{31} +4.31265 q^{32} +4.63752 q^{33} +(5.28726 + 9.15780i) q^{34} -7.08840 q^{35} +(-0.403032 + 0.698071i) q^{36} +(1.96604 + 3.40527i) q^{37} +(-1.51270 - 2.62007i) q^{38} +2.19394 q^{39} +(-3.28726 + 5.69370i) q^{40} +(-2.12482 + 3.68030i) q^{41} +(-1.80606 + 3.12819i) q^{42} +(2.19029 + 3.79369i) q^{43} +(-1.86907 + 3.23732i) q^{44} +(-1.64363 - 2.84685i) q^{45} -12.3127 q^{46} +6.37565 q^{47} +(2.48119 + 4.29755i) q^{48} +(1.17513 - 2.03539i) q^{49} +(4.86296 + 8.42289i) q^{50} +(-3.15633 + 5.46692i) q^{51} +(-0.884226 + 1.53152i) q^{52} +(5.99389 - 10.3817i) q^{53} -1.67513 q^{54} +(-7.62236 - 13.2023i) q^{55} +(2.15633 + 3.73486i) q^{56} +(0.903032 - 1.56410i) q^{57} +0.105540 q^{58} +(4.48119 + 7.76166i) q^{59} +2.64974 q^{60} +3.19394 q^{61} +(9.11871 - 1.95883i) q^{62} -2.15633 q^{63} +2.70052 q^{64} +(-3.60602 - 6.24581i) q^{65} -7.76845 q^{66} +(-3.79090 + 6.56604i) q^{67} +(-2.54420 - 4.40668i) q^{68} +(-3.67513 - 6.36551i) q^{69} +11.8740 q^{70} +(-4.86907 + 8.43347i) q^{71} +(-1.00000 + 1.73205i) q^{72} +(4.94358 - 8.56254i) q^{73} +(-3.29337 - 5.70428i) q^{74} +(-2.90303 + 5.02820i) q^{75} +(0.727901 + 1.26076i) q^{76} -10.0000 q^{77} -3.67513 q^{78} +(-1.07816 - 1.86743i) q^{79} +(8.15633 - 14.1272i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(3.55936 - 6.16499i) q^{82} +(3.64363 - 6.31095i) q^{83} +(0.869067 - 1.50527i) q^{84} +20.7513 q^{85} +(-3.66902 - 6.35493i) q^{86} +(0.0315020 + 0.0545631i) q^{87} +(-4.63752 + 8.03242i) q^{88} -3.86177 q^{89} +(2.75329 + 4.76884i) q^{90} -4.73084 q^{91} +5.92478 q^{92} +(3.73449 + 4.12960i) q^{93} -10.6801 q^{94} -5.93700 q^{95} +(-2.15633 - 3.73486i) q^{96} -5.38787 q^{97} +(-1.96850 + 3.40954i) q^{98} +(-2.31876 - 4.01621i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 3 q^{3} + 4 q^{4} - 4 q^{5} - 4 q^{7} + 12 q^{8} - 3 q^{9}+O(q^{10}) \) 6 * q - 3 * q^3 + 4 * q^4 - 4 * q^5 - 4 * q^7 + 12 * q^8 - 3 * q^9	\( 6 q - 3 q^{3} + 4 q^{4} - 4 q^{5} - 4 q^{7} + 12 q^{8} - 3 q^{9} - 4 q^{10} + 2 q^{11} - 2 q^{12} - 7 q^{13} - 10 q^{14} + 8 q^{15} - 8 q^{16} + 2 q^{17} + 5 q^{19} - 18 q^{20} - 4 q^{21} + 12 q^{22} + 24 q^{23} - 6 q^{24} - 17 q^{25} + 6 q^{26} + 6 q^{27} - 4 q^{28} + 8 q^{29} + 8 q^{30} - 16 q^{32} - 4 q^{33} + 20 q^{34} - 4 q^{35} - 2 q^{36} + 3 q^{37} + 6 q^{38} + 14 q^{39} - 8 q^{40} + 4 q^{41} - 10 q^{42} + q^{43} - 2 q^{44} - 4 q^{45} - 32 q^{46} - 12 q^{47} + 4 q^{48} - 3 q^{49} - 6 q^{50} + 2 q^{51} + 6 q^{52} + 10 q^{53} - 16 q^{55} - 8 q^{56} + 5 q^{57} + 40 q^{58} + 16 q^{59} + 36 q^{60} + 20 q^{61} + 12 q^{62} + 8 q^{63} - 24 q^{64} + 6 q^{65} - 24 q^{66} - 24 q^{67} + 4 q^{68} - 12 q^{69} + 88 q^{70} - 20 q^{71} - 6 q^{72} - 3 q^{73} - 34 q^{74} - 17 q^{75} + 14 q^{76} - 60 q^{77} - 12 q^{78} + 4 q^{79} + 28 q^{80} - 3 q^{81} + 16 q^{83} - 4 q^{84} + 24 q^{85} + 14 q^{86} - 4 q^{87} + 4 q^{88} + 12 q^{89} - 4 q^{90} + 16 q^{91} - 8 q^{92} - 9 q^{93} - 80 q^{94} - 44 q^{95} + 8 q^{96} - 34 q^{97} - 16 q^{98} + 2 q^{99}+O(q^{100}) \) 6 * q - 3 * q^3 + 4 * q^4 - 4 * q^5 - 4 * q^7 + 12 * q^8 - 3 * q^9 - 4 * q^10 + 2 * q^11 - 2 * q^12 - 7 * q^13 - 10 * q^14 + 8 * q^15 - 8 * q^16 + 2 * q^17 + 5 * q^19 - 18 * q^20 - 4 * q^21 + 12 * q^22 + 24 * q^23 - 6 * q^24 - 17 * q^25 + 6 * q^26 + 6 * q^27 - 4 * q^28 + 8 * q^29 + 8 * q^30 - 16 * q^32 - 4 * q^33 + 20 * q^34 - 4 * q^35 - 2 * q^36 + 3 * q^37 + 6 * q^38 + 14 * q^39 - 8 * q^40 + 4 * q^41 - 10 * q^42 + q^43 - 2 * q^44 - 4 * q^45 - 32 * q^46 - 12 * q^47 + 4 * q^48 - 3 * q^49 - 6 * q^50 + 2 * q^51 + 6 * q^52 + 10 * q^53 - 16 * q^55 - 8 * q^56 + 5 * q^57 + 40 * q^58 + 16 * q^59 + 36 * q^60 + 20 * q^61 + 12 * q^62 + 8 * q^63 - 24 * q^64 + 6 * q^65 - 24 * q^66 - 24 * q^67 + 4 * q^68 - 12 * q^69 + 88 * q^70 - 20 * q^71 - 6 * q^72 - 3 * q^73 - 34 * q^74 - 17 * q^75 + 14 * q^76 - 60 * q^77 - 12 * q^78 + 4 * q^79 + 28 * q^80 - 3 * q^81 + 16 * q^83 - 4 * q^84 + 24 * q^85 + 14 * q^86 - 4 * q^87 + 4 * q^88 + 12 * q^89 - 4 * q^90 + 16 * q^91 - 8 * q^92 - 9 * q^93 - 80 * q^94 - 44 * q^95 + 8 * q^96 - 34 * q^97 - 16 * q^98 + 2 * q^99

Introduction

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