LMFDB - Embedded newform 385.2.i.a.221.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [385,2,Mod(221,385)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(385, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("385.221");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 385 = 5 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	385.i (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$3.07424047782$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	8.0.310217769.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 4x^{6} - 2x^{5} + 15x^{4} - 4x^{3} + 5x^{2} + x + 1 $ x^8 + 4x^6 - 2x^5 + 15x^4 - 4x^3 + 5*x^2 + x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			221.1
Root			$-0.198169 + 0.343239i$ of defining polynomial
Character	$\chi$	$=$	385.221
Dual form			385.2.i.a.331.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.563379 - 0.975800i) q^{2} +(-0.761548 + 1.31904i) q^{3} +(0.365209 - 0.632561i) q^{4} +(-0.500000 - 0.866025i) q^{5} +1.71616 q^{6} +(-0.779537 + 2.52830i) q^{7} -3.07652 q^{8} +(0.340090 + 0.589053i) q^{9} +O(q^{10})$	\(q+(-0.563379 - 0.975800i) q^{2} +(-0.761548 + 1.31904i) q^{3} +(0.365209 - 0.632561i) q^{4} +(-0.500000 - 0.866025i) q^{5} +1.71616 q^{6} +(-0.779537 + 2.52830i) q^{7} -3.07652 q^{8} +(0.340090 + 0.589053i) q^{9} +(-0.563379 + 0.975800i) q^{10} +(-0.500000 + 0.866025i) q^{11} +(0.556249 + 0.963451i) q^{12} -6.04619 q^{13} +(2.90629 - 0.663720i) q^{14} +1.52310 q^{15} +(1.00283 + 1.73695i) q^{16} +(0.556249 - 0.963451i) q^{17} +(0.383199 - 0.663720i) q^{18} +(2.07051 + 3.58623i) q^{19} -0.730419 q^{20} +(-2.74128 - 2.95366i) q^{21} +1.12676 q^{22} +(0.914328 + 1.58366i) q^{23} +(2.34292 - 4.05805i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(3.40629 + 5.89987i) q^{26} -5.60527 q^{27} +(1.31461 + 1.41646i) q^{28} +1.03193 q^{29} +(-0.858079 - 1.48624i) q^{30} +(-5.16784 + 8.95097i) q^{31} +(-1.94658 + 3.37157i) q^{32} +(-0.761548 - 1.31904i) q^{33} -1.25351 q^{34} +(2.57934 - 0.589053i) q^{35} +0.496816 q^{36} +(3.70813 + 6.42266i) q^{37} +(2.33296 - 4.04081i) q^{38} +(4.60446 - 7.97516i) q^{39} +(1.53826 + 2.66434i) q^{40} -4.44818 q^{41} +(-1.33781 + 4.33897i) q^{42} -5.56473 q^{43} +(0.365209 + 0.632561i) q^{44} +(0.340090 - 0.589053i) q^{45} +(1.03023 - 1.78440i) q^{46} +(2.25442 + 3.90477i) q^{47} -3.05480 q^{48} +(-5.78464 - 3.94181i) q^{49} +1.12676 q^{50} +(0.847220 + 1.46743i) q^{51} +(-2.20813 + 3.82458i) q^{52} +(5.29981 - 9.17953i) q^{53} +(3.15789 + 5.46962i) q^{54} +1.00000 q^{55} +(2.39826 - 7.77837i) q^{56} -6.30716 q^{57} +(-0.581368 - 1.00696i) q^{58} +(3.72207 - 6.44681i) q^{59} +(0.556249 - 0.963451i) q^{60} +(-3.22839 - 5.59174i) q^{61} +11.6458 q^{62} +(-1.75442 + 0.400662i) q^{63} +8.39794 q^{64} +(3.02310 + 5.23616i) q^{65} +(-0.858079 + 1.48624i) q^{66} +(6.83434 - 11.8374i) q^{67} +(-0.406294 - 0.703722i) q^{68} -2.78522 q^{69} +(-2.02795 - 2.18506i) q^{70} +1.84857 q^{71} +(-1.04629 - 1.81223i) q^{72} +(-5.23122 + 9.06074i) q^{73} +(4.17816 - 7.23678i) q^{74} +(-0.761548 - 1.31904i) q^{75} +3.02468 q^{76} +(-1.79981 - 1.93925i) q^{77} -10.3762 q^{78} +(-0.750114 - 1.29924i) q^{79} +(1.00283 - 1.73695i) q^{80} +(3.24841 - 5.62641i) q^{81} +(2.50601 + 4.34054i) q^{82} +10.7503 q^{83} +(-2.86951 + 0.655320i) q^{84} -1.11250 q^{85} +(3.13505 + 5.43006i) q^{86} +(-0.785865 + 1.36116i) q^{87} +(1.53826 - 2.66434i) q^{88} +(-7.02763 - 12.1722i) q^{89} -0.766397 q^{90} +(4.71323 - 15.2866i) q^{91} +1.33568 q^{92} +(-7.87112 - 13.6332i) q^{93} +(2.54018 - 4.39972i) q^{94} +(2.07051 - 3.58623i) q^{95} +(-2.96482 - 5.13522i) q^{96} -5.85152 q^{97} +(-0.587480 + 7.86539i) q^{98} -0.680180 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 3 q^{2} + 3 q^{3} - 3 q^{4} - 4 q^{5} + 14 q^{6} + q^{7} - 18 q^{8} + q^{9}+O(q^{10}) $ 8 * q + 3 * q^2 + 3 * q^3 - 3 * q^4 - 4 * q^5 + 14 * q^6 + q^7 - 18 * q^8 + q^9	\( 8 q + 3 q^{2} + 3 q^{3} - 3 q^{4} - 4 q^{5} + 14 q^{6} + q^{7} - 18 q^{8} + q^{9} + 3 q^{10} - 4 q^{11} + 3 q^{12} - 12 q^{13} + q^{14} - 6 q^{15} - 5 q^{16} + 3 q^{17} - q^{18} + 3 q^{19} + 6 q^{20} - 18 q^{21} - 6 q^{22} + 6 q^{23} + 4 q^{24} - 4 q^{25} + 5 q^{26} + 6 q^{27} - 20 q^{28} - 16 q^{29} - 7 q^{30} - 10 q^{31} - 4 q^{32} + 3 q^{33} + 20 q^{34} + q^{35} - 16 q^{36} + 9 q^{37} + 23 q^{38} + 13 q^{39} + 9 q^{40} + 30 q^{41} - 16 q^{42} - 4 q^{43} - 3 q^{44} + q^{45} - 16 q^{46} + 15 q^{47} - 2 q^{48} - 19 q^{49} - 6 q^{50} - q^{51} + 3 q^{52} + 30 q^{53} + 13 q^{54} + 8 q^{55} - 24 q^{56} - 12 q^{57} + q^{58} - 17 q^{59} + 3 q^{60} + 32 q^{62} - 11 q^{63} + 10 q^{64} + 6 q^{65} - 7 q^{66} + 25 q^{67} + 19 q^{68} + 12 q^{69} + q^{70} - 26 q^{71} - 26 q^{72} - 3 q^{73} + 16 q^{74} + 3 q^{75} + 80 q^{76} - 2 q^{77} - 10 q^{78} + 4 q^{79} - 5 q^{80} + 16 q^{81} + 27 q^{82} + 36 q^{83} - 24 q^{84} - 6 q^{85} + 10 q^{86} - 20 q^{87} + 9 q^{88} - 25 q^{89} + 2 q^{90} - 3 q^{91} - 52 q^{92} - 10 q^{93} - 23 q^{94} + 3 q^{95} + 7 q^{96} - 46 q^{97} - 60 q^{98} - 2 q^{99}+O(q^{100}) \) 8 * q + 3 * q^2 + 3 * q^3 - 3 * q^4 - 4 * q^5 + 14 * q^6 + q^7 - 18 * q^8 + q^9 + 3 * q^10 - 4 * q^11 + 3 * q^12 - 12 * q^13 + q^14 - 6 * q^15 - 5 * q^16 + 3 * q^17 - q^18 + 3 * q^19 + 6 * q^20 - 18 * q^21 - 6 * q^22 + 6 * q^23 + 4 * q^24 - 4 * q^25 + 5 * q^26 + 6 * q^27 - 20 * q^28 - 16 * q^29 - 7 * q^30 - 10 * q^31 - 4 * q^32 + 3 * q^33 + 20 * q^34 + q^35 - 16 * q^36 + 9 * q^37 + 23 * q^38 + 13 * q^39 + 9 * q^40 + 30 * q^41 - 16 * q^42 - 4 * q^43 - 3 * q^44 + q^45 - 16 * q^46 + 15 * q^47 - 2 * q^48 - 19 * q^49 - 6 * q^50 - q^51 + 3 * q^52 + 30 * q^53 + 13 * q^54 + 8 * q^55 - 24 * q^56 - 12 * q^57 + q^58 - 17 * q^59 + 3 * q^60 + 32 * q^62 - 11 * q^63 + 10 * q^64 + 6 * q^65 - 7 * q^66 + 25 * q^67 + 19 * q^68 + 12 * q^69 + q^70 - 26 * q^71 - 26 * q^72 - 3 * q^73 + 16 * q^74 + 3 * q^75 + 80 * q^76 - 2 * q^77 - 10 * q^78 + 4 * q^79 - 5 * q^80 + 16 * q^81 + 27 * q^82 + 36 * q^83 - 24 * q^84 - 6 * q^85 + 10 * q^86 - 20 * q^87 + 9 * q^88 - 25 * q^89 + 2 * q^90 - 3 * q^91 - 52 * q^92 - 10 * q^93 - 23 * q^94 + 3 * q^95 + 7 * q^96 - 46 * q^97 - 60 * q^98 - 2 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/385\mathbb{Z}\right)^\times$.

$n$	$211$	$232$	$276$
$\chi(n)$	$1$	$1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	−0.563379	−	0.975800i	−0.398369	−	0.689995i	0.595156	−	0.803610i	$-0.297090\pi$
$2$	−0.563379	−	0.975800i	−0.398369	−	0.689995i	−0.993525	+	0.113615i	$0.963757\pi$
$3$	−0.761548	+	1.31904i	−0.439680	+	0.761548i	−0.997665	−	0.0683034i	$-0.978241\pi$
$3$	−0.761548	+	1.31904i	−0.439680	+	0.761548i	0.557985	+	0.829851i	$0.311575\pi$
$4$	0.365209	−	0.632561i	0.182605	−	0.316281i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$6$	1.71616			0.700619
$7$	−0.779537	+	2.52830i	−0.294637	+	0.955609i
$7$	−0.779537	+	2.52830i	−0.294637	+	0.955609i
$8$	−3.07652			−1.08771
$9$	0.340090	+	0.589053i	0.113363	+	0.196351i
$10$	−0.563379	+	0.975800i	−0.178156	+	0.308575i
$11$	−0.500000	+	0.866025i	−0.150756	+	0.261116i
$11$	−0.500000	+	0.866025i	−0.150756	+	0.261116i
$12$	0.556249	+	0.963451i	0.160575	+	0.278124i
$13$	−6.04619			−1.67691			−0.838456	−	0.544970i	$-0.816541\pi$
$13$	−6.04619			−1.67691			−0.838456	+	0.544970i	$0.816541\pi$
$14$	2.90629	−	0.663720i	0.776740	−	0.177387i
$15$	1.52310			0.393262
$16$	1.00283	+	1.73695i	0.250706	+	0.434236i
$17$	0.556249	−	0.963451i	0.134910	−	0.233671i	−0.790653	−	0.612265i	$-0.790259\pi$
$17$	0.556249	−	0.963451i	0.134910	−	0.233671i	0.925563	+	0.378593i	$0.123592\pi$
$18$	0.383199	−	0.663720i	0.0903208	−	0.156440i
$19$	2.07051	+	3.58623i	0.475007	+	0.822737i	0.999590	−	0.0286226i	$-0.00911211\pi$
$19$	2.07051	+	3.58623i	0.475007	+	0.822737i	−0.524583	+	0.851359i	$0.675779\pi$
$20$	−0.730419			−0.163327
$21$	−2.74128	−	2.95366i	−0.598196	−	0.644543i
$22$	1.12676			0.240225
$23$	0.914328	+	1.58366i	0.190651	+	0.330216i	0.945466	−	0.325721i	$-0.105607\pi$
$23$	0.914328	+	1.58366i	0.190651	+	0.330216i	−0.754815	+	0.655937i	$0.772274\pi$
$24$	2.34292	−	4.05805i	0.478246	−	0.828346i
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	3.40629	+	5.89987i	0.668029	+	1.15706i
$27$	−5.60527			−1.07873
$28$	1.31461	+	1.41646i	0.248438	+	0.267687i
$29$	1.03193			0.191625			0.0958124	−	0.995399i	$-0.469455\pi$
$29$	1.03193			0.191625			0.0958124	+	0.995399i	$0.469455\pi$
$30$	−0.858079	−	1.48624i	−0.156663	−	0.271349i
$31$	−5.16784	+	8.95097i	−0.928172	+	1.60764i	−0.141793	+	0.989896i	$0.545287\pi$
$31$	−5.16784	+	8.95097i	−0.928172	+	1.60764i	−0.786379	+	0.617744i	$0.788047\pi$
$32$	−1.94658	+	3.37157i	−0.344109	+	0.596015i
$33$	−0.761548	−	1.31904i	−0.132568	−	0.229615i
$34$	−1.25351			−0.214976
$35$	2.57934	−	0.589053i	0.435989	−	0.0995681i
$36$	0.496816			0.0828027
$37$	3.70813	+	6.42266i	0.609612	+	1.05588i	0.991304	+	0.131590i	$0.0420081\pi$
$37$	3.70813	+	6.42266i	0.609612	+	1.05588i	−0.381692	+	0.924289i	$0.624659\pi$
$38$	2.33296	−	4.04081i	0.378456	−	0.655505i
$39$	4.60446	−	7.97516i	0.737304	−	1.27705i
$40$	1.53826	+	2.66434i	0.243220	+	0.421270i
$41$	−4.44818			−0.694689			−0.347345	−	0.937738i	$-0.612917\pi$
$41$	−4.44818			−0.694689			−0.347345	+	0.937738i	$0.612917\pi$
$42$	−1.33781	+	4.33897i	−0.206429	+	0.669518i
$43$	−5.56473			−0.848613			−0.424306	−	0.905519i	$-0.639482\pi$
$43$	−5.56473			−0.848613			−0.424306	+	0.905519i	$0.639482\pi$
$44$	0.365209	+	0.632561i	0.0550574	+	0.0953622i
$45$	0.340090	−	0.589053i	0.0506976	−	0.0878108i
$46$	1.03023	−	1.78440i	0.151898	−	0.263096i
$47$	2.25442	+	3.90477i	0.328841	+	0.569569i	0.982282	−	0.187408i	$-0.0600088\pi$
$47$	2.25442	+	3.90477i	0.328841	+	0.569569i	−0.653441	+	0.756977i	$0.726675\pi$
$48$	−3.05480			−0.440922
$49$	−5.78464	−	3.94181i	−0.826378	−	0.563116i
$50$	1.12676			0.159348
$51$	0.847220	+	1.46743i	0.118635	+	0.205481i
$52$	−2.20813	+	3.82458i	−0.306212	+	0.530374i
$53$	5.29981	−	9.17953i	0.727984	−	1.26091i	−0.229749	−	0.973250i	$-0.573791\pi$
$53$	5.29981	−	9.17953i	0.727984	−	1.26091i	0.957734	−	0.287656i	$-0.0928761\pi$
$54$	3.15789	+	5.46962i	0.429734	+	0.744321i
$55$	1.00000			0.134840
$56$	2.39826	−	7.77837i	0.320481	−	1.03943i
$57$	−6.30716			−0.835404
$58$	−0.581368	−	1.00696i	−0.0763374	−	0.132220i
$59$	3.72207	−	6.44681i	0.484572	−	0.839303i	−0.515271	−	0.857027i	$-0.672309\pi$
$59$	3.72207	−	6.44681i	0.484572	−	0.839303i	0.999843	+	0.0177242i	$0.00564209\pi$
$60$	0.556249	−	0.963451i	0.0718114	−	0.124381i
$61$	−3.22839	−	5.59174i	−0.413354	−	0.715949i	0.581900	−	0.813260i	$-0.302309\pi$
$61$	−3.22839	−	5.59174i	−0.413354	−	0.715949i	−0.995254	+	0.0973106i	$0.968976\pi$
$62$	11.6458			1.47902
$63$	−1.75442	+	0.400662i	−0.221036	+	0.0504787i
$64$	8.39794			1.04974
$65$	3.02310	+	5.23616i	0.374969	+	0.649465i
$66$	−0.858079	+	1.48624i	−0.105622	+	0.182943i
$67$	6.83434	−	11.8374i	0.834947	−	1.44617i	−0.0591264	−	0.998251i	$-0.518832\pi$
$67$	6.83434	−	11.8374i	0.834947	−	1.44617i	0.894073	−	0.447920i	$-0.147835\pi$
$68$	−0.406294	−	0.703722i	−0.0492704	−	0.0853389i
$69$	−2.78522			−0.335301
$70$	−2.02795	−	2.18506i	−0.242386	−	0.261165i
$71$	1.84857			0.219385			0.109692	−	0.993966i	$-0.465013\pi$
$71$	1.84857			0.219385			0.109692	+	0.993966i	$0.465013\pi$
$72$	−1.04629	−	1.81223i	−0.123307	−	0.213574i
$73$	−5.23122	+	9.06074i	−0.612268	+	1.06048i	0.378589	+	0.925565i	$0.376409\pi$
$73$	−5.23122	+	9.06074i	−0.612268	+	1.06048i	−0.990857	+	0.134915i	$0.956924\pi$
$74$	4.17816	−	7.23678i	0.485701	−	0.841258i
$75$	−0.761548	−	1.31904i	−0.0879360	−	0.152310i
$76$	3.02468			0.346954
$77$	−1.79981	−	1.93925i	−0.205107	−	0.220998i
$78$	−10.3762			−1.17488
$79$	−0.750114	−	1.29924i	−0.0843944	−	0.146175i	0.820739	−	0.571304i	$-0.193562\pi$
$79$	−0.750114	−	1.29924i	−0.0843944	−	0.146175i	−0.905133	+	0.425129i	$0.860229\pi$
$80$	1.00283	−	1.73695i	0.112119	−	0.194196i
$81$	3.24841	−	5.62641i	0.360934	−	0.625156i
$82$	2.50601	+	4.34054i	0.276742	+	0.479332i
$83$	10.7503			1.18000			0.590001	−	0.807403i	$-0.299127\pi$
$83$	10.7503			1.18000			0.590001	+	0.807403i	$0.299127\pi$
$84$	−2.86951	+	0.655320i	−0.313090	+	0.0715013i
$85$	−1.11250			−0.120667
$86$	3.13505	+	5.43006i	0.338061	+	0.585539i
$87$	−0.785865	+	1.36116i	−0.0842536	+	0.145931i
$88$	1.53826	−	2.66434i	0.163979	−	0.284020i
$89$	−7.02763	−	12.1722i	−0.744927	−	1.29025i	−0.950229	−	0.311553i	$-0.899151\pi$
$89$	−7.02763	−	12.1722i	−0.744927	−	1.29025i	0.205302	−	0.978699i	$-0.434182\pi$
$90$	−0.766397			−0.0807854
$91$	4.71323	−	15.2866i	0.494081	−	1.60247i
$92$	1.33568			0.139255
$93$	−7.87112	−	13.6332i	−0.816197	−	1.41369i
$94$	2.54018	−	4.39972i	0.262000	−	0.453797i
$95$	2.07051	−	3.58623i	0.212430	−	0.367939i
$96$	−2.96482	−	5.13522i	−0.302596	−	0.524112i
$97$	−5.85152			−0.594132			−0.297066	−	0.954857i	$-0.596008\pi$
$97$	−5.85152			−0.594132			−0.297066	+	0.954857i	$0.596008\pi$
$98$	−0.587480	+	7.86539i	−0.0593444	+	0.794524i
$99$	−0.680180			−0.0683606
$100$	0.365209	+	0.632561i	0.0365209	+	0.0632561i
$101$	−7.82088	+	13.5462i	−0.778207	+	1.34789i	0.154768	+	0.987951i	$0.450537\pi$
$101$	−7.82088	+	13.5462i	−0.778207	+	1.34789i	−0.932975	+	0.359942i	$0.882796\pi$
$102$	0.954611	−	1.65343i	0.0945206	−	0.163714i
$103$	10.0481	+	17.4038i	0.990070	+	1.71485i	0.616777	+	0.787138i	$0.288438\pi$
$103$	10.0481	+	17.4038i	0.990070	+	1.71485i	0.373293	+	0.927713i	$0.378228\pi$
$104$	18.6012			1.82400
$105$	−1.18731	+	3.85085i	−0.115870	+	0.375804i
$106$	−11.9432			−1.16003
$107$	−6.86681	−	11.8937i	−0.663840	−	1.14980i	−0.979598	−	0.200965i	$-0.935592\pi$
$107$	−6.86681	−	11.8937i	−0.663840	−	1.14980i	0.315759	−	0.948840i	$-0.397741\pi$
$108$	−2.04709	+	3.54567i	−0.196982	+	0.341182i
$109$	−0.216733	+	0.375393i	−0.0207593	+	0.0359561i	−0.876218	−	0.481914i	$-0.839942\pi$
$109$	−0.216733	+	0.375393i	−0.0207593	+	0.0359561i	0.855459	+	0.517870i	$0.173275\pi$
$110$	−0.563379	−	0.975800i	−0.0537160	−	0.0930389i
$111$	−11.2957			−1.07214
$112$	−5.17327	+	1.18144i	−0.488828	+	0.111635i
$113$	−9.58940			−0.902095			−0.451048	−	0.892500i	$-0.648950\pi$
$113$	−9.58940			−0.902095			−0.451048	+	0.892500i	$0.648950\pi$
$114$	3.55332	+	6.15453i	0.332799	+	0.576425i
$115$	0.914328	−	1.58366i	0.0852615	−	0.147677i
$116$	0.376871	−	0.652760i	0.0349916	−	0.0606072i
$117$	−2.05625	−	3.56153i	−0.190100	−	0.329263i
$118$	−8.38773			−0.772153
$119$	2.00228	+	2.15741i	0.183549	+	0.197770i
$120$	−4.68583			−0.427756
$121$	−0.500000	−	0.866025i	−0.0454545	−	0.0787296i
$122$	−3.63762	+	6.30054i	−0.329334	+	0.570424i
$123$	3.38750	−	5.86733i	0.305441	−	0.529039i
$124$	3.77469	+	6.53795i	0.338977	+	0.587125i
$125$	1.00000			0.0894427
$126$	1.37937	+	1.48624i	0.122884	+	0.132405i
$127$	1.48032			0.131357			0.0656784	−	0.997841i	$-0.479079\pi$
$127$	1.48032			0.131357			0.0656784	+	0.997841i	$0.479079\pi$
$128$	−0.838066	−	1.45157i	−0.0740753	−	0.128302i
$129$	4.23780	−	7.34009i	0.373118	−	0.646259i
$130$	3.40629	−	5.89987i	0.298752	−	0.517453i
$131$	−5.31031	−	9.19772i	−0.463964	−	0.803609i	0.535190	−	0.844732i	$-0.320240\pi$
$131$	−5.31031	−	9.19772i	−0.463964	−	0.803609i	−0.999154	+	0.0411227i	$0.986907\pi$
$132$	−1.11250			−0.0968305
$133$	−10.6811	+	2.43928i	−0.926170	+	0.211512i
$134$	−15.4013			−1.33047
$135$	2.80263	+	4.85430i	0.241212	+	0.417792i
$136$	−1.71131	+	2.96407i	−0.146744	+	0.254167i
$137$	1.34696	−	2.33301i	0.115079	−	0.199322i	−0.802732	−	0.596339i	$-0.796621\pi$
$137$	1.34696	−	2.33301i	0.115079	−	0.199322i	0.917811	+	0.397017i	$0.129955\pi$
$138$	1.56913	+	2.71782i	0.133573	+	0.231356i
$139$	−2.61336			−0.221662			−0.110831	−	0.993839i	$-0.535351\pi$
$139$	−2.61336			−0.221662			−0.110831	+	0.993839i	$0.535351\pi$
$140$	0.569388	−	1.84672i	0.0481221	−	0.156076i
$141$	−6.86739			−0.578338
$142$	−1.04144	−	1.80383i	−0.0873960	−	0.151374i
$143$	3.02310	−	5.23616i	0.252804	−	0.437869i
$144$	−0.682102	+	1.18144i	−0.0568418	+	0.0984529i
$145$	−0.515966	−	0.893679i	−0.0428486	−	0.0742160i
$146$	11.7886			0.975634
$147$	9.60469	−	4.62829i	0.792182	−	0.381735i
$148$	5.41697			0.445272
$149$	7.94333	+	13.7583i	0.650743	+	1.12712i	0.982943	+	0.183911i	$0.0588758\pi$
$149$	7.94333	+	13.7583i	0.650743	+	1.12712i	−0.332200	+	0.943209i	$0.607791\pi$
$150$	−0.858079	+	1.48624i	−0.0700619	+	0.121351i
$151$	−1.68674	+	2.92151i	−0.137265	+	0.237749i	−0.926460	−	0.376393i	$-0.877164\pi$
$151$	−1.68674	+	2.92151i	−0.137265	+	0.237749i	0.789196	+	0.614142i	$0.210498\pi$
$152$	−6.36996	−	11.0331i	−0.516672	−	0.894902i
$153$	0.756698			0.0611754
$154$	−0.878349	+	2.84878i	−0.0707794	+	0.229562i
$155$	10.3357			0.830182
$156$	−3.36319	−	5.82521i	−0.269270	−	0.466390i
$157$	2.99717	−	5.19126i	0.239201	−	0.414307i	−0.721285	−	0.692639i	$-0.756448\pi$
$157$	2.99717	−	5.19126i	0.239201	−	0.414307i	0.960485	+	0.278331i	$0.0897813\pi$
$158$	−0.845196	+	1.46392i	−0.0672402	+	0.116463i
$159$	8.07211	+	13.9813i	0.640160	+	1.10879i
$160$	3.89315			0.307781
$161$	−4.71673	+	1.07718i	−0.371731	+	0.0848933i
$162$	−7.32033			−0.575140
$163$	7.93595	+	13.7455i	0.621591	+	1.07663i	0.989189	+	0.146643i	$0.0468468\pi$
$163$	7.93595	+	13.7455i	0.621591	+	1.07663i	−0.367598	+	0.929985i	$0.619820\pi$
$164$	−1.62452	+	2.81375i	−0.126853	+	0.219717i
$165$	−0.761548	+	1.31904i	−0.0592864	+	0.102687i
$166$	−6.05651	−	10.4902i	−0.470076	−	0.814195i
$167$	12.3961			0.959242			0.479621	−	0.877476i	$-0.340774\pi$
$167$	12.3961			0.959242			0.479621	+	0.877476i	$0.340774\pi$
$168$	8.43359	+	9.08700i	0.650666	+	0.701078i
$169$	23.5564			1.81203
$170$	0.626757	+	1.08558i	0.0480701	+	0.0832598i
$171$	−1.40832	+	2.43928i	−0.107697	+	0.186536i
$172$	−2.03229	+	3.52003i	−0.154961	+	0.268400i
$173$	4.45143	+	7.71010i	0.338436	+	0.586188i	0.984139	−	0.177401i	$-0.0567689\pi$
$173$	4.45143	+	7.71010i	0.338436	+	0.586188i	−0.645703	+	0.763589i	$0.723436\pi$
$174$	1.77096			0.134256
$175$	−1.79981	−	1.93925i	−0.136053	−	0.146594i
$176$	−2.00565			−0.151182
$177$	5.66906	+	9.81911i	0.426113	+	0.738049i
$178$	−7.91843	+	13.7151i	−0.593511	+	1.02799i
$179$	−6.89533	+	11.9431i	−0.515381	+	0.892667i	0.484459	+	0.874814i	$0.339016\pi$
$179$	−6.89533	+	11.9431i	−0.515381	+	0.892667i	−0.999841	+	0.0178529i	$0.994317\pi$
$180$	−0.248408	−	0.430255i	−0.0185152	−	0.0320693i
$181$	8.23693			0.612246			0.306123	−	0.951992i	$-0.400968\pi$
$181$	8.23693			0.612246			0.306123	+	0.951992i	$0.400968\pi$
$182$	−17.5720	+	4.01298i	−1.30252	+	0.297462i
$183$	9.83431			0.726973
$184$	−2.81295	−	4.87217i	−0.207373	−	0.359181i
$185$	3.70813	−	6.42266i	0.272627	−	0.472203i
$186$	−8.86884	+	15.3613i	−0.650295	+	1.12634i
$187$	0.556249	+	0.963451i	0.0406769	+	0.0704545i
$188$	3.29334			0.240191
$189$	4.36951	−	14.1718i	0.317835	−	1.03085i
$190$	−4.66592			−0.338501
$191$	12.2923	+	21.2908i	0.889437	+	1.54055i	0.840543	+	0.541745i	$0.182236\pi$
$191$	12.2923	+	21.2908i	0.889437	+	1.54055i	0.0488938	+	0.998804i	$0.484430\pi$
$192$	−6.39543	+	11.0772i	−0.461551	+	0.799429i
$193$	−6.66807	+	11.5494i	−0.479978	+	0.831347i	−0.999736	−	0.0229669i	$-0.992689\pi$
$193$	−6.66807	+	11.5494i	−0.479978	+	0.831347i	0.519758	+	0.854314i	$0.326022\pi$
$194$	3.29662	+	5.70992i	0.236684	+	0.409948i
$195$	−9.20893			−0.659465
$196$	−4.60604	+	2.21955i	−0.329003	+	0.158539i
$197$	11.7257			0.835418			0.417709	−	0.908581i	$-0.362833\pi$
$197$	11.7257			0.835418			0.417709	+	0.908581i	$0.362833\pi$
$198$	0.383199	+	0.663720i	0.0272327	+	0.0471685i
$199$	3.70600	−	6.41898i	0.262711	−	0.455029i	−0.704250	−	0.709952i	$-0.748717\pi$
$199$	3.70600	−	6.41898i	0.262711	−	0.455029i	0.966961	+	0.254923i	$0.0820500\pi$
$200$	1.53826	−	2.66434i	0.108771	−	0.188398i
$201$	10.4093	+	18.0295i	0.734219	+	1.27170i
$202$	17.6245			1.24005
$203$	−0.804429	+	2.60904i	−0.0564598	+	0.183118i
$204$	1.23765			0.0866528
$205$	2.22409	+	3.85224i	0.155337	+	0.269052i
$206$	11.3218	−	19.6099i	0.788826	−	1.36629i
$207$	−0.621907	+	1.07718i	−0.0432256	+	0.0748689i
$208$	−6.06328	−	10.5019i	−0.420413	−	0.728176i
$209$	−4.14102			−0.286440
$210$	4.42656	−	1.01091i	0.305462	−	0.0697593i
$211$	−15.2495			−1.04982			−0.524908	−	0.851159i	$-0.675900\pi$
$211$	−15.2495			−1.04982			−0.524908	+	0.851159i	$0.675900\pi$
$212$	−3.87108	−	6.70490i	−0.265867	−	0.460495i
$213$	−1.40777	+	2.43833i	−0.0964590	+	0.167072i
$214$	−7.73723	+	13.4013i	−0.528906	+	0.916092i
$215$	2.78236	+	4.81919i	0.189756	+	0.328666i
$216$	17.2447			1.17335
$217$	−18.6022	−	20.0435i	−1.26280	−	1.36064i
$218$	0.488411			0.0330794
$219$	−7.96765	−	13.8004i	−0.538404	−	0.932543i
$220$	0.365209	−	0.632561i	0.0246224	−	0.0426473i
$221$	−3.36319	+	5.82521i	−0.226232	+	0.391846i
$222$	6.36373	+	11.0223i	0.427106	+	0.739769i
$223$	−13.8852			−0.929821			−0.464910	−	0.885358i	$-0.653913\pi$
$223$	−13.8852			−0.929821			−0.464910	+	0.885358i	$0.653913\pi$
$224$	−7.00693	−	7.54980i	−0.468170	−	0.504443i
$225$	−0.680180			−0.0453453
$226$	5.40246	+	9.35734i	0.359366	+	0.622441i
$227$	5.77832	−	10.0083i	0.383520	−	0.664277i	−0.608042	−	0.793905i	$-0.708045\pi$
$227$	5.77832	−	10.0083i	0.383520	−	0.664277i	0.991563	+	0.129628i	$0.0413783\pi$
$228$	−2.30343	+	3.98967i	−0.152549	+	0.264222i
$229$	4.89315	+	8.47519i	0.323349	+	0.560056i	0.981177	−	0.193112i	$-0.0618580\pi$
$229$	4.89315	+	8.47519i	0.323349	+	0.560056i	−0.657828	+	0.753168i	$0.728525\pi$
$230$	−2.06045			−0.135862
$231$	3.92859	−	0.897184i	0.258482	−	0.0590304i
$232$	−3.17476			−0.208433
$233$	1.82785	+	3.16594i	0.119747	+	0.207407i	0.919667	−	0.392699i	$-0.128458\pi$
$233$	1.82785	+	3.16594i	0.119747	+	0.207407i	−0.799921	+	0.600106i	$0.795125\pi$
$234$	−2.31689	+	4.01298i	−0.151460	+	0.262336i
$235$	2.25442	−	3.90477i	0.147062	−	0.254719i
$236$	−2.71867	−	4.70887i	−0.176970	−	0.306521i
$237$	2.28499			0.148426
$238$	0.977161	−	3.16926i	0.0633399	−	0.205433i
$239$	−6.41169			−0.414738			−0.207369	−	0.978263i	$-0.566490\pi$
$239$	−6.41169			−0.414738			−0.207369	+	0.978263i	$0.566490\pi$
$240$	1.52740	+	2.64553i	0.0985932	+	0.170768i
$241$	−1.72489	+	2.98760i	−0.111110	+	0.192448i	−0.916218	−	0.400680i	$-0.868774\pi$
$241$	−1.72489	+	2.98760i	−0.111110	+	0.192448i	0.805108	+	0.593128i	$0.202107\pi$
$242$	−0.563379	+	0.975800i	−0.0362153	+	0.0627268i
$243$	−3.46026	−	5.99335i	−0.221976	−	0.384474i
$244$	−4.71616			−0.301921
$245$	−0.521390	+	6.98056i	−0.0333104	+	0.445971i
$246$	−7.63379			−0.486712
$247$	−12.5187	−	21.6830i	−0.796545	−	1.37966i
$248$	15.8990	−	27.5378i	1.00959	−	1.74865i
$249$	−8.18689	+	14.1801i	−0.518823	+	0.898628i
$250$	−0.563379	−	0.975800i	−0.0356312	−	0.0617150i
$251$	7.12655			0.449824			0.224912	−	0.974379i	$-0.427791\pi$
$251$	7.12655			0.449824			0.224912	+	0.974379i	$0.427791\pi$
$252$	−0.387287	+	1.25610i	−0.0243968	+	0.0791270i
$253$	−1.82866			−0.114967
$254$	−0.833978	−	1.44449i	−0.0523285	−	0.0906355i
$255$	0.847220	−	1.46743i	0.0530550	−	0.0918939i
$256$	7.45365	−	12.9101i	0.465853	−	0.806881i
$257$	−3.42348	−	5.92964i	−0.213551	−	0.369881i	0.739272	−	0.673406i	$-0.235170\pi$
$257$	−3.42348	−	5.92964i	−0.213551	−	0.369881i	−0.952823	+	0.303525i	$0.901836\pi$
$258$	−9.54995			−0.594554
$259$	−19.1291	+	4.36856i	−1.18862	+	0.271449i
$260$	4.41625			0.273884
$261$	0.350949	+	0.607862i	0.0217232	+	0.0376257i
$262$	−5.98343	+	10.3636i	−0.369657	+	0.640265i
$263$	12.8482	−	22.2538i	0.792257	−	1.37223i	−0.132309	−	0.991208i	$-0.542239\pi$
$263$	12.8482	−	22.2538i	0.792257	−	1.37223i	0.924566	−	0.381021i	$-0.124427\pi$
$264$	2.34292	+	4.05805i	0.144196	+	0.249756i
$265$	−10.5996			−0.651129
$266$	8.39776	+	9.04839i	0.514899	+	0.554792i
$267$	21.4075			1.31012
$268$	−4.99193	−	8.64627i	−0.304930	−	0.528155i
$269$	−6.13639	+	10.6285i	−0.374143	+	0.648034i	−0.990198	−	0.139669i	$-0.955396\pi$
$269$	−6.13639	+	10.6285i	−0.374143	+	0.648034i	0.616056	+	0.787703i	$0.288730\pi$
$270$	3.15789	−	5.46962i	0.192183	−	0.332870i
$271$	3.52538	+	6.10613i	0.214151	+	0.370921i	0.953010	−	0.302940i	$-0.0979681\pi$
$271$	3.52538	+	6.10613i	0.214151	+	0.370921i	−0.738858	+	0.673861i	$0.764635\pi$
$272$	2.23128			0.135291
$273$	16.5743	+	17.8584i	1.00312	+	1.08084i
$274$	−3.03540			−0.183375
$275$	−0.500000	−	0.866025i	−0.0301511	−	0.0522233i
$276$	−1.01719	+	1.76182i	−0.0612275	+	0.106049i
$277$	−6.45744	+	11.1846i	−0.387990	+	0.672018i	−0.992179	−	0.124823i	$-0.960164\pi$
$277$	−6.45744	+	11.1846i	−0.387990	+	0.672018i	0.604189	+	0.796841i	$0.293497\pi$
$278$	1.47231	+	2.55012i	0.0883034	+	0.152946i
$279$	−7.03012			−0.420883
$280$	−7.93540	+	1.81223i	−0.474231	+	0.108302i
$281$	−23.8875			−1.42501			−0.712504	−	0.701668i	$-0.752439\pi$
$281$	−23.8875			−1.42501			−0.712504	+	0.701668i	$0.752439\pi$
$282$	3.86894	+	6.70120i	0.230392	+	0.399051i
$283$	−12.1049	+	20.9664i	−0.719564	+	1.24632i	0.241609	+	0.970374i	$0.422325\pi$
$283$	−12.1049	+	20.9664i	−0.719564	+	1.24632i	−0.961173	+	0.275947i	$0.911008\pi$
$284$	0.675114	−	1.16933i	0.0400606	−	0.0693871i
$285$	3.15358	+	5.46216i	0.186802	+	0.323551i
$286$	−6.81259			−0.402837
$287$	3.46752	−	11.2464i	0.204681	−	0.663851i
$288$	−2.64805			−0.156038
$289$	7.88117	+	13.6506i	0.463599	+	0.802976i
$290$	−0.581368	+	1.00696i	−0.0341391	+	0.0591307i
$291$	4.45622	−	7.71839i	0.261228	−	0.452460i
$292$	3.82098	+	6.61813i	0.223606	+	0.387297i
$293$	9.22074			0.538682			0.269341	−	0.963045i	$-0.413194\pi$
$293$	9.22074			0.538682			0.269341	+	0.963045i	$0.413194\pi$
$294$	−9.92737	−	6.76478i	−0.578976	−	0.394530i
$295$	−7.44413			−0.433414
$296$	−11.4081	−	19.7594i	−0.663083	−	1.14849i
$297$	2.80263	−	4.85430i	0.162625	−	0.281675i
$298$	8.95021	−	15.5022i	0.518471	−	0.898019i
$299$	−5.52820	−	9.57513i	−0.319704	−	0.553744i
$300$	−1.11250			−0.0642301
$301$	4.33791	−	14.0693i	0.250033	−	0.810942i
$302$	3.80108			0.218728
$303$	−11.9119	−	20.6321i	−0.684323	−	1.18528i
$304$	−4.15272	+	7.19272i	−0.238175	+	0.412531i
$305$	−3.22839	+	5.59174i	−0.184857	+	0.320182i
$306$	−0.426308	−	0.738386i	−0.0243704	−	0.0422107i
$307$	33.4594			1.90963			0.954813	−	0.297206i	$-0.0960549\pi$
$307$	33.4594			1.90963			0.954813	+	0.297206i	$0.0960549\pi$
$308$	−1.88400	+	0.430255i	−0.107351	+	0.0245161i
$309$	−30.6085			−1.74126
$310$	−5.82290	−	10.0856i	−0.330719	−	0.572821i
$311$	−12.1552	+	21.0535i	−0.689259	+	1.19383i	0.282819	+	0.959173i	$0.408730\pi$
$311$	−12.1552	+	21.0535i	−0.689259	+	1.19383i	−0.972078	+	0.234658i	$0.924603\pi$
$312$	−14.1657	+	24.5357i	−0.801976	+	1.38906i
$313$	1.58306	+	2.74194i	0.0894800	+	0.154984i	0.907291	−	0.420502i	$-0.138146\pi$
$313$	1.58306	+	2.74194i	0.0894800	+	0.154984i	−0.817811	+	0.575486i	$0.804813\pi$
$314$	−6.75417			−0.381160
$315$	1.22419	+	1.31904i	0.0689754	+	0.0743195i
$316$	−1.09579			−0.0616432
$317$	−7.20543	−	12.4802i	−0.404697	−	0.700956i	0.589589	−	0.807703i	$-0.299290\pi$
$317$	−7.20543	−	12.4802i	−0.404697	−	0.700956i	−0.994286	+	0.106748i	$0.965956\pi$
$318$	9.09531	−	15.7535i	0.510040	−	0.883415i
$319$	−0.515966	+	0.893679i	−0.0288885	+	0.0500364i
$320$	−4.19897	−	7.27283i	−0.234730	−	0.406564i
$321$	20.9176			1.16751
$322$	3.70841	+	3.99573i	0.206662	+	0.222673i
$323$	4.60687			0.256333
$324$	−2.37270	−	4.10963i	−0.131817	−	0.228313i
$325$	3.02310	−	5.23616i	0.167691	−	0.290450i
$326$	8.94188	−	15.4878i	0.495245	−	0.857790i
$327$	−0.330105	−	0.571759i	−0.0182549	−	0.0316184i
$328$	13.6849			0.755623
$329$	−11.6298	+	2.65594i	−0.641174	+	0.146427i
$330$	1.71616			0.0944714
$331$	13.4337	+	23.2678i	0.738383	+	1.27892i	0.953223	+	0.302267i	$0.0977434\pi$
$331$	13.4337	+	23.2678i	0.738383	+	1.27892i	−0.214841	+	0.976649i	$0.568923\pi$
$332$	3.92612	−	6.80024i	0.215474	−	0.373212i
$333$	−2.52219	+	4.36856i	−0.138215	+	0.239396i
$334$	−6.98372	−	12.0962i	−0.382132	−	0.661872i
$335$	−13.6687			−0.746799
$336$	2.38133	−	7.72346i	0.129912	−	0.421349i
$337$	−15.3425			−0.835758			−0.417879	−	0.908503i	$-0.637226\pi$
$337$	−15.3425			−0.835758			−0.417879	+	0.908503i	$0.637226\pi$
$338$	−13.2712	−	22.9864i	−0.721857	−	1.25029i
$339$	7.30279	−	12.6488i	0.396633	−	0.686988i
$340$	−0.406294	+	0.703722i	−0.0220344	+	0.0381647i
$341$	−5.16784	−	8.95097i	−0.279854	−	0.484722i
$342$	3.17366			0.171612
$343$	14.4755	−	11.5525i	0.781601	−	0.623779i
$344$	17.1200			0.923048
$345$	1.39261	+	2.41207i	0.0749755	+	0.129861i
$346$	5.01568	−	8.68741i	0.269644	−	0.467038i
$347$	−15.2446	+	26.4044i	−0.818372	+	1.41746i	0.0885096	+	0.996075i	$0.471790\pi$
$347$	−15.2446	+	26.4044i	−0.818372	+	1.41746i	−0.906881	+	0.421386i	$0.861544\pi$
$348$	0.574010	+	0.994215i	0.0307702	+	0.0532955i
$349$	13.8714			0.742521			0.371260	−	0.928529i	$-0.378926\pi$
$349$	13.8714			0.742521			0.371260	+	0.928529i	$0.378926\pi$
$350$	−0.878349	+	2.84878i	−0.0469497	+	0.152274i
$351$	33.8905			1.80894
$352$	−1.94658	−	3.37157i	−0.103753	−	0.179705i
$353$	−9.53951	+	16.5229i	−0.507737	+	0.879426i	0.492223	+	0.870469i	$0.336184\pi$
$353$	−9.53951	+	16.5229i	−0.507737	+	0.879426i	−0.999960	+	0.00895665i	$0.997149\pi$
$354$	6.38766	−	11.0637i	0.339500	−	0.588032i
$355$	−0.924284	−	1.60091i	−0.0490559	−	0.0849673i
$356$	−10.2662			−0.544108
$357$	−4.37054	+	0.998115i	−0.231314	+	0.0528258i
$358$	15.5387			0.821247
$359$	9.83568	+	17.0359i	0.519108	+	0.899121i	0.999753	+	0.0222059i	$0.00706893\pi$
$359$	9.83568	+	17.0359i	0.519108	+	0.899121i	−0.480646	+	0.876915i	$0.659598\pi$
$360$	−1.04629	+	1.81223i	−0.0551445	+	0.0955130i
$361$	0.925990	−	1.60386i	0.0487363	−	0.0844137i
$362$	−4.64051	−	8.03760i	−0.243900	−	0.422447i
$363$	1.52310			0.0799418
$364$	−7.94840	−	8.56422i	−0.416609	−	0.448887i
$365$	10.4624			0.547629
$366$	−5.54044	−	9.59632i	−0.289603	−	0.501608i
$367$	12.0566	−	20.8827i	0.629351	−	1.09007i	−0.358331	−	0.933595i	$-0.616654\pi$
$367$	12.0566	−	20.8827i	0.629351	−	1.09007i	0.987682	−	0.156473i	$-0.0500125\pi$
$368$	−1.83382	+	3.17628i	−0.0955947	+	0.165575i
$369$	−1.51278	−	2.62021i	−0.0787523	−	0.136403i
$370$	−8.35631			−0.434424
$371$	19.0773	+	20.5553i	0.990442	+	1.06718i
$372$	−11.4984			−0.596165
$373$	−13.5632	−	23.4921i	−0.702275	−	1.21638i	−0.967666	−	0.252235i	$-0.918835\pi$
$373$	−13.5632	−	23.4921i	−0.702275	−	1.21638i	0.265392	−	0.964141i	$-0.414499\pi$
$374$	0.626757	−	1.08558i	0.0324088	−	0.0561338i
$375$	−0.761548	+	1.31904i	−0.0393262	+	0.0681149i
$376$	−6.93576	−	12.0131i	−0.357684	−	0.619528i
$377$	−6.23925			−0.321338
$378$	−16.2906	+	3.72032i	−0.837896	+	0.191353i
$379$	4.42145			0.227114			0.113557	−	0.993531i	$-0.463775\pi$
$379$	4.42145			0.227114			0.113557	+	0.993531i	$0.463775\pi$
$380$	−1.51234	−	2.61945i	−0.0775813	−	0.134375i
$381$	−1.12733	+	1.95260i	−0.0577549	+	0.100034i
$382$	13.8504	−	23.9896i	0.708647	−	1.22741i
$383$	9.53929	+	16.5225i	0.487435	+	0.844262i	0.999896	−	0.0144487i	$-0.00459931\pi$
$383$	9.53929	+	16.5225i	0.487435	+	0.844262i	−0.512461	+	0.858711i	$0.671266\pi$
$384$	2.55291			0.130278
$385$	−0.779537	+	2.52830i	−0.0397289	+	0.128854i
$386$	15.0266			0.764833
$387$	−1.89251	−	3.27792i	−0.0962015	−	0.166626i
$388$	−2.13703	+	3.70145i	−0.108491	+	0.187912i
$389$	3.92486	−	6.79805i	0.198998	−	0.344675i	−0.749206	−	0.662337i	$-0.769565\pi$
$389$	3.92486	−	6.79805i	0.198998	−	0.344675i	0.948204	+	0.317662i	$0.102898\pi$
$390$	5.18811	+	8.98607i	0.262710	+	0.455028i
$391$	2.03437			0.102883
$392$	17.7966	+	12.1271i	0.898862	+	0.612509i
$393$	16.1762			0.815982
$394$	−6.60598	−	11.4419i	−0.332805	−	0.576434i
$395$	−0.750114	+	1.29924i	−0.0377423	+	0.0653716i
$396$	−0.248408	+	0.430255i	−0.0124830	+	0.0216211i
$397$	1.22974	+	2.12998i	0.0617190	+	0.106900i	0.895234	−	0.445597i	$-0.147008\pi$
$397$	1.22974	+	2.12998i	0.0617190	+	0.106900i	−0.833515	+	0.552497i	$0.813675\pi$
$398$	−8.35152			−0.418624
$399$	4.91667	−	15.9464i	0.246141	−	0.798320i
$400$	−2.00565			−0.100283
$401$	0.755867	+	1.30920i	0.0377462	+	0.0653783i	0.884281	−	0.466955i	$-0.154649\pi$
$401$	0.755867	+	1.30920i	0.0377462	+	0.0653783i	−0.846535	+	0.532333i	$0.821315\pi$
$402$	11.7288	−	20.3149i	0.584980	−	1.01321i
$403$	31.2458	−	54.1192i	1.55646	−	2.69587i
$404$	5.71251	+	9.89437i	0.284208	+	0.492263i
$405$	−6.49682			−0.322829
$406$	2.99910	−	0.684913i	0.148843	−	0.0339917i
$407$	−7.41625			−0.367610
$408$	−2.60649	−	4.51457i	−0.129040	−	0.223504i
$409$	9.51327	−	16.4775i	0.470401	−	0.814758i	−0.529026	−	0.848605i	$-0.677443\pi$
$409$	9.51327	−	16.4775i	0.470401	−	0.814758i	0.999427	+	0.0338475i	$0.0107760\pi$
$410$	2.50601	−	4.34054i	0.123763	−	0.214364i
$411$	2.05155	+	3.55340i	0.101196	+	0.175276i
$412$	14.6787			0.723165
$413$	13.3980	+	14.4360i	0.659273	+	0.710351i
$414$	1.40148			0.0688788
$415$	−5.37517	−	9.31006i	−0.263856	−	0.457013i
$416$	11.7694	−	20.3852i	0.577041	−	0.999465i
$417$	1.99020	−	3.44713i	0.0974605	−	0.168806i
$418$	2.33296	+	4.04081i	0.114109	+	0.197642i
$419$	−16.1270			−0.787856			−0.393928	−	0.919141i	$-0.628884\pi$
$419$	−16.1270			−0.787856			−0.393928	+	0.919141i	$0.628884\pi$
$420$	2.00228	+	2.15741i	0.0977013	+	0.105271i
$421$	17.9500			0.874829			0.437415	−	0.899260i	$-0.355894\pi$
$421$	17.9500			0.874829			0.437415	+	0.899260i	$0.355894\pi$
$422$	8.59122	+	14.8804i	0.418214	+	0.724368i
$423$	−1.53341	+	2.65594i	−0.0745569	+	0.129136i
$424$	−16.3050	+	28.2410i	−0.791839	+	1.37150i
$425$	0.556249	+	0.963451i	0.0269820	+	0.0467342i
$426$	3.17244			0.153705
$427$	16.6543	−	3.80339i	0.805957	−	0.184059i
$428$	−10.0313			−0.484881
$429$	4.60446	+	7.97516i	0.222306	+	0.385045i
$430$	3.13505	−	5.43006i	0.151185	−	0.261861i
$431$	−6.42283	+	11.1247i	−0.309377	+	0.535857i	−0.978226	−	0.207541i	$-0.933454\pi$
$431$	−6.42283	+	11.1247i	−0.309377	+	0.535857i	0.668849	+	0.743398i	$0.266787\pi$
$432$	−5.62111	−	9.73604i	−0.270446	−	0.468425i
$433$	−20.4163			−0.981142			−0.490571	−	0.871401i	$-0.663212\pi$
$433$	−20.4163			−0.981142			−0.490571	+	0.871401i	$0.663212\pi$
$434$	−9.07834	+	29.4441i	−0.435774	+	1.41336i
$435$	1.57173			0.0753587
$436$	0.158306	+	0.274194i	0.00758148	+	0.0131315i
$437$	−3.78625	+	6.55797i	−0.181121	+	0.313710i
$438$	−8.97760	+	15.5497i	−0.428967	+	0.742992i
$439$	1.12271	+	1.94459i	0.0535840	+	0.0928102i	0.891573	−	0.452877i	$-0.149602\pi$
$439$	1.12271	+	1.94459i	0.0535840	+	0.0928102i	−0.837989	+	0.545687i	$0.816269\pi$
$440$	−3.07652			−0.146667
$441$	0.354639	−	4.74803i	0.0168876	−	0.226097i
$442$	7.57899			0.360496
$443$	−5.95021	−	10.3061i	−0.282703	−	0.489656i	0.689347	−	0.724432i	$-0.257898\pi$
$443$	−5.95021	−	10.3061i	−0.282703	−	0.489656i	−0.972050	+	0.234776i	$0.924564\pi$
$444$	−4.12528	+	7.14519i	−0.195777	+	0.339096i
$445$	−7.02763	+	12.1722i	−0.333141	+	0.577018i
$446$	7.82261	+	13.5492i	0.370411	+	0.641572i
$447$	−24.1969			−1.14447
$448$	−6.54651	+	21.2326i	−0.309293	+	1.00314i
$449$	6.92804			0.326955			0.163477	−	0.986547i	$-0.447729\pi$
$449$	6.92804			0.326955			0.163477	+	0.986547i	$0.447729\pi$
$450$	0.383199	+	0.663720i	0.0180642	+	0.0312880i
$451$	2.22409	−	3.85224i	0.104728	−	0.181395i
$452$	−3.50214	+	6.06588i	−0.164727	+	0.285315i
$453$	−2.56906	−	4.44974i	−0.120705	−	0.209067i
$454$	−13.0215			−0.611130
$455$	−15.5952	+	3.56153i	−0.731115	+	0.166967i
$456$	19.4041			0.908681
$457$	19.7881	+	34.2740i	0.925649	+	1.60327i	0.790515	+	0.612443i	$0.209813\pi$
$457$	19.7881	+	34.2740i	0.925649	+	1.60327i	0.135134	+	0.990827i	$0.456853\pi$
$458$	5.51340	−	9.54948i	0.257624	−	0.446218i
$459$	−3.11792	+	5.40040i	−0.145532	+	0.252069i
$460$	−0.667842	−	1.15674i	−0.0311383	−	0.0539331i
$461$	−6.03649			−0.281147			−0.140574	−	0.990070i	$-0.544895\pi$
$461$	−6.03649			−0.281147			−0.140574	+	0.990070i	$0.544895\pi$
$462$	−3.08875	−	3.32806i	−0.143702	−	0.154835i
$463$	26.1311			1.21441			0.607207	−	0.794544i	$-0.292290\pi$
$463$	26.1311			1.21441			0.607207	+	0.794544i	$0.292290\pi$
$464$	1.03485	+	1.79241i	0.0480416	+	0.0832105i
$465$	−7.87112	+	13.6332i	−0.365014	+	0.632223i
$466$	2.05955	−	3.56724i	0.0954067	−	0.165249i
$467$	−9.25351	−	16.0276i	−0.428202	−	0.741667i	0.568512	−	0.822675i	$-0.307519\pi$
$467$	−9.25351	−	16.0276i	−0.428202	−	0.741667i	−0.996713	+	0.0810082i	$0.974186\pi$
$468$	−3.00384			−0.138853
$469$	24.6010	+	26.5070i	1.13597	+	1.22398i
$470$	−5.08036			−0.234340
$471$	4.56498	+	7.90678i	0.210343	+	0.364325i
$472$	−11.4510	+	19.8337i	−0.527075	+	0.912921i
$473$	2.78236	−	4.81919i	0.127933	−	0.221587i
$474$	−1.28731	−	2.22969i	−0.0591283	−	0.102413i
$475$	−4.14102			−0.190003
$476$	2.09595	−	0.478658i	0.0960675	−	0.0219392i
$477$	7.20964			0.330107
$478$	3.61221	+	6.25653i	0.165219	+	0.286167i
$479$	9.05242	−	15.6792i	0.413616	−	0.716403i	−0.581667	−	0.813427i	$-0.697599\pi$
$479$	9.05242	−	15.6792i	0.413616	−	0.716403i	0.995282	+	0.0970243i	$0.0309325\pi$
$480$	−2.96482	+	5.13522i	−0.135325	+	0.234390i
$481$	−22.4200	−	38.8326i	−1.02227	−	1.77062i
$482$	3.88707			0.177051
$483$	2.17118	−	7.04188i	0.0987922	−	0.320417i
$484$	−0.730419			−0.0332008
$485$	2.92576	+	5.06757i	0.132852	+	0.230106i
$486$	−3.89888	+	6.75305i	−0.176857	+	0.306325i
$487$	−18.5652	+	32.1559i	−0.841269	+	1.45712i	0.0475525	+	0.998869i	$0.484858\pi$
$487$	−18.5652	+	32.1559i	−0.841269	+	1.45712i	−0.888822	+	0.458253i	$0.848475\pi$
$488$	9.93222	+	17.2031i	0.449610	+	0.778748i
$489$	−24.1744			−1.09320
$490$	7.10537	−	3.42392i	0.320988	−	0.154677i
$491$	−20.8918			−0.942834			−0.471417	−	0.881910i	$-0.656257\pi$
$491$	−20.8918			−0.942834			−0.471417	+	0.881910i	$0.656257\pi$
$492$	−2.47429	−	4.28560i	−0.111550	−	0.193210i
$493$	0.574010	−	0.994215i	0.0258521	−	0.0447772i
$494$	−14.1055	+	24.4315i	−0.634637	+	1.09922i
$495$	0.340090	+	0.589053i	0.0152859	+	0.0264760i
$496$	−20.7298			−0.930795
$497$	−1.44103	+	4.67374i	−0.0646389	+	0.209646i
$498$	18.4493			0.826732
$499$	−12.6860	−	21.9727i	−0.567901	−	0.983634i	−0.996773	−	0.0802688i	$-0.974422\pi$
$499$	−12.6860	−	21.9727i	−0.567901	−	0.983634i	0.428872	−	0.903365i	$-0.358911\pi$
$500$	0.365209	−	0.632561i	0.0163327	−	0.0282890i
$501$	−9.44025	+	16.3510i	−0.421759	+	0.730508i
$502$	−4.01495	−	6.95409i	−0.179196	−	0.310376i
$503$	7.92170			0.353211			0.176606	−	0.984282i	$-0.443488\pi$
$503$	7.92170			0.353211			0.176606	+	0.984282i	$0.443488\pi$
$504$	5.39750	−	1.23264i	0.240424	−	0.0549063i
$505$	15.6418			0.696049
$506$	1.03023	+	1.78440i	0.0457991	+	0.0793264i
$507$	−17.9393	+	31.0719i	−0.796714	+	1.37995i
$508$	0.540625	−	0.936390i	0.0239864	−	0.0415456i
$509$	−19.1871	−	33.2330i	−0.850454	−	1.47303i	−0.880800	−	0.473489i	$-0.842994\pi$
$509$	−19.1871	−	33.2330i	−0.850454	−	1.47303i	0.0303460	−	0.999539i	$-0.490339\pi$
$510$	−1.90922			−0.0845418
$511$	−18.8304	−	20.2893i	−0.833007	−	0.897546i
$512$	−20.1492			−0.890476
$513$	−11.6057	−	20.1017i	−0.512406	−	0.887514i
$514$	−3.85743	+	6.68127i	−0.170144	+	0.294698i
$515$	10.0481	−	17.4038i	0.442773	−	0.766905i
$516$	−3.09537	−	5.36134i	−0.136266	−	0.236020i
$517$	−4.50884			−0.198298
$518$	15.0397	+	16.2050i	0.660809	+	0.712006i
$519$	−13.5599			−0.595213
$520$	−9.30061	−	16.1091i	−0.407859	−	0.706432i
$521$	−5.11782	+	8.86432i	−0.224216	+	0.388353i	−0.956084	−	0.293093i	$-0.905315\pi$
$521$	−5.11782	+	8.86432i	−0.224216	+	0.388353i	0.731868	+	0.681446i	$0.238649\pi$
$522$	0.395435	−	0.684913i	0.0173077	−	0.0299778i
$523$	2.07414	+	3.59251i	0.0906957	+	0.157089i	0.907804	−	0.419395i	$-0.137758\pi$
$523$	2.07414	+	3.59251i	0.0906957	+	0.157089i	−0.817108	+	0.576484i	$0.804424\pi$
$524$	−7.75750			−0.338888
$525$	3.92859	−	0.897184i	0.171458	−	0.0391563i
$526$	−28.9537			−1.26244
$527$	5.74921	+	9.95792i	0.250440	+	0.433774i
$528$	1.52740	−	2.64553i	0.0664715	−	0.115132i
$529$	9.82801	−	17.0226i	0.427305	−	0.740113i
$530$	5.97159	+	10.3431i	0.259390	+	0.449276i
$531$	5.06335			0.219731
$532$	−2.35785	+	7.64730i	−0.102226	+	0.331552i
$533$	26.8946			1.16493
$534$	−12.0605	−	20.8894i	−0.521910	−	0.903974i
$535$	−6.86681	+	11.8937i	−0.296878	+	0.514208i
$536$	−21.0260	+	36.4180i	−0.908183	+	1.57302i
$537$	−10.5023	−	18.1904i	−0.453206	−	0.784975i
$538$	13.8285			0.596187
$539$	6.30603	−	3.03874i	0.271620	−	0.130888i
$540$	4.09419			0.176186
$541$	−11.5956	−	20.0841i	−0.498532	−	0.863483i	0.501466	−	0.865177i	$-0.332794\pi$
$541$	−11.5956	−	20.0841i	−0.498532	−	0.863483i	−0.999999	+	0.00169388i	$0.999461\pi$
$542$	3.97224	−	6.88013i	0.170622	−	0.295527i
$543$	−6.27282	+	10.8648i	−0.269192	+	0.466255i
$544$	2.16556	+	3.75086i	0.0928477	+	0.160817i
$545$	0.433466			0.0185677
$546$	8.08865	−	26.2342i	0.346162	−	1.12272i
$547$	27.8077			1.18897			0.594486	−	0.804106i	$-0.297356\pi$
$547$	27.8077			1.18897			0.594486	+	0.804106i	$0.297356\pi$
$548$	−0.983847	−	1.70407i	−0.0420279	−	0.0727944i
$549$	2.19589	−	3.80339i	0.0937183	−	0.162325i
$550$	−0.563379	+	0.975800i	−0.0240225	+	0.0416083i
$551$	2.13662	+	3.70074i	0.0910232	+	0.157657i
$552$	8.56877			0.364711
$553$	3.86960	−	0.883714i	0.164552	−	0.0375793i
$554$	14.5519			0.618252
$555$	5.64783	+	9.78233i	0.239737	+	0.415237i
$556$	−0.954424	+	1.65311i	−0.0404766	+	0.0701075i
$557$	5.47195	−	9.47770i	0.231854	−	0.401583i	−0.726500	−	0.687167i	$-0.758854\pi$
$557$	5.47195	−	9.47770i	0.231854	−	0.401583i	0.958354	+	0.285584i	$0.0921875\pi$
$558$	3.96062	+	6.86000i	0.167666	+	0.290407i
$559$	33.6454			1.42305
$560$	3.60979	+	3.88946i	0.152541	+	0.164360i
$561$	−1.69444			−0.0715393
$562$	13.4577	+	23.3094i	0.567679	+	0.983249i
$563$	1.21047	−	2.09659i	0.0510151	−	0.0883607i	−0.839390	−	0.543529i	$-0.817088\pi$
$563$	1.21047	−	2.09659i	0.0510151	−	0.0883607i	0.890405	+	0.455169i	$0.150421\pi$
$564$	−2.50803	+	4.34404i	−0.105607	+	0.182917i
$565$	4.79470	+	8.30467i	0.201715	+	0.349380i
$566$	27.2786			1.14661
$567$	11.6930	+	12.5990i	0.491060	+	0.529106i
$568$	−5.68715			−0.238628
$569$	15.1717	+	26.2782i	0.636031	+	1.10164i	0.986296	+	0.164987i	$0.0527582\pi$
$569$	15.1717	+	26.2782i	0.636031	+	1.10164i	−0.350265	+	0.936651i	$0.613909\pi$
$570$	3.55332	−	6.15453i	0.148832	−	0.257785i
$571$	−9.40241	+	16.2855i	−0.393479	+	0.681525i	−0.992906	−	0.118904i	$-0.962062\pi$
$571$	−9.40241	+	16.2855i	−0.393479	+	0.681525i	0.599427	+	0.800429i	$0.295395\pi$
$572$	−2.20813	−	3.82458i	−0.0923263	−	0.159914i
$573$	−37.4446			−1.56427
$574$	−12.9277	+	2.95235i	−0.539593	+	0.123229i
$575$	−1.82866			−0.0762602
$576$	2.85606	+	4.94683i	0.119002	+	0.206118i
$577$	8.12933	−	14.0804i	0.338428	−	0.586175i	−0.645709	−	0.763584i	$-0.723438\pi$
$577$	8.12933	−	14.0804i	0.338428	−	0.586175i	0.984137	+	0.177409i	$0.0567714\pi$
$578$	8.88017	−	15.3809i	0.369366	−	0.639761i
$579$	−10.1561	−	17.5909i	−0.422073	−	0.731053i
$580$	−0.753742			−0.0312974
$581$	−8.38028	+	27.1801i	−0.347673	+	1.12762i
$582$	−10.0421			−0.416260
$583$	5.29981	+	9.17953i	0.219496	+	0.380177i
$584$	16.0939	−	27.8755i	0.665972	−	1.15350i
$585$	−2.05625	+	3.56153i	−0.0850154	+	0.147251i
$586$	−5.19477	−	8.99760i	−0.214594	−	0.371688i
$587$	−41.5442			−1.71471			−0.857357	−	0.514722i	$-0.827895\pi$
$587$	−41.5442			−1.71471			−0.857357	+	0.514722i	$0.827895\pi$
$588$	0.580045	−	7.76585i	0.0239206	−	0.320258i
$589$	−42.8002			−1.76355
$590$	4.19387	+	7.26399i	0.172659	+	0.299054i
$591$	−8.92965	+	15.4666i	−0.367317	+	0.636211i
$592$	−7.43721	+	12.8816i	−0.305667	+	0.529431i
$593$	11.0988	+	19.2237i	0.455774	+	0.789423i	0.998732	−	0.0503364i	$-0.0160293\pi$
$593$	11.0988	+	19.2237i	0.455774	+	0.789423i	−0.542959	+	0.839759i	$0.682696\pi$
$594$	−6.31577			−0.259139
$595$	0.867233	−	2.81273i	0.0355531	−	0.115311i
$596$	11.6039			0.475315
$597$	5.64459	+	9.77672i	0.231018	+	0.400134i
$598$	−6.22894	+	10.7888i	−0.254720	+	0.441189i
$599$	−7.10404	+	12.3046i	−0.290263	+	0.502751i	−0.973872	−	0.227098i	$-0.927076\pi$
$599$	−7.10404	+	12.3046i	−0.290263	+	0.502751i	0.683609	+	0.729849i	$0.260410\pi$
$600$	2.34292	+	4.05805i	0.0956491	+	0.165669i
$601$	−13.6487			−0.556742			−0.278371	−	0.960474i	$-0.589795\pi$
$601$	−13.6487			−0.556742			−0.278371	+	0.960474i	$0.589795\pi$
$602$	−16.1727	+	3.69342i	−0.659151	+	0.150532i
$603$	9.29716			0.378609
$604$	1.23202	+	2.13393i	0.0501303	+	0.0868282i
$605$	−0.500000	+	0.866025i	−0.0203279	+	0.0352089i
$606$	−13.4219	+	23.2474i	−0.545226	+	0.944359i
$607$	16.2511	+	28.1477i	0.659610	+	1.14248i	0.980717	+	0.195435i	$0.0626119\pi$
$607$	16.2511	+	28.1477i	0.659610	+	1.14248i	−0.321106	+	0.947043i	$0.604055\pi$
$608$	−16.1216			−0.653818
$609$	−2.82881	−	3.04798i	−0.114629	−	0.123510i
$610$	7.27523			0.294566
$611$	−13.6306	−	23.6090i	−0.551437	−	0.955116i
$612$	0.276353	−	0.478658i	0.0111709	−	0.0193486i
$613$	22.5551	−	39.0665i	0.910991	−	1.57788i	0.0983242	−	0.995154i	$-0.468652\pi$
$613$	22.5551	−	39.0665i	0.910991	−	1.57788i	0.812667	−	0.582728i	$-0.198015\pi$
$614$	−18.8503	−	32.6497i	−0.760736	−	1.31763i
$615$	−6.77501			−0.273195
$616$	5.53714	+	5.96614i	0.223098	+	0.240383i
$617$	−45.0684			−1.81439			−0.907194	−	0.420713i	$-0.861780\pi$
$617$	−45.0684			−1.81439			−0.907194	+	0.420713i	$0.861780\pi$
$618$	17.2442	+	29.8678i	0.693662	+	1.20146i
$619$	−1.19643	+	2.07229i	−0.0480888	+	0.0832922i	−0.889068	−	0.457775i	$-0.848646\pi$
$619$	−1.19643	+	2.07229i	−0.0480888	+	0.0832922i	0.840979	+	0.541068i	$0.181980\pi$
$620$	3.77469	−	6.53795i	0.151595	−	0.262570i
$621$	−5.12505	−	8.87685i	−0.205661	−	0.356216i
$622$	27.3919			1.09832
$623$	36.2533	−	8.27929i	1.45246	−	0.331703i
$624$	18.4699			0.739388
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	1.78373	−	3.08951i	0.0712921	−	0.123481i
$627$	3.15358	−	5.46216i	0.125942	−	0.218138i
$628$	−2.18919	−	3.79179i	−0.0873583	−	0.151309i
$629$	8.25056			0.328971
$630$	0.597435	−	1.93769i	0.0238024	−	0.0771992i
$631$	−0.0891740			−0.00354996			−0.00177498	−	0.999998i	$-0.500565\pi$
$631$	−0.0891740			−0.00354996			−0.00177498	+	0.999998i	$0.500565\pi$
$632$	2.30774	+	3.99712i	0.0917969	+	0.158997i
$633$	11.6132	−	20.1146i	0.461583	−	0.799485i
$634$	−8.11876	+	14.0621i	−0.322437	+	0.558478i
$635$	−0.740158	−	1.28199i	−0.0293723	−	0.0508743i
$636$	11.7920			0.467585
$637$	34.9751	+	23.8330i	1.38576	+	0.944296i
$638$	1.16274			0.0460332
$639$	0.628679	+	1.08890i	0.0248702	+	0.0430764i
$640$	−0.838066	+	1.45157i	−0.0331275	+	0.0573785i
$641$	8.94950	−	15.5010i	0.353484	−	0.612253i	−0.633373	−	0.773847i	$-0.718330\pi$
$641$	8.94950	−	15.5010i	0.353484	−	0.612253i	0.986857	+	0.161594i	$0.0516635\pi$
$642$	−11.7845	−	20.4114i	−0.465099	−	0.805575i
$643$	−28.2214			−1.11294			−0.556472	−	0.830867i	$-0.687845\pi$
$643$	−28.2214			−1.11294			−0.556472	+	0.830867i	$0.687845\pi$
$644$	−1.04122	+	3.37702i	−0.0410296	+	0.133073i
$645$	−8.47561			−0.333727
$646$	−2.59541	−	4.49538i	−0.102115	−	0.176869i
$647$	−1.84083	+	3.18841i	−0.0723705	+	0.125349i	−0.899940	−	0.436014i	$-0.856390\pi$
$647$	−1.84083	+	3.18841i	−0.0723705	+	0.125349i	0.827569	+	0.561364i	$0.189723\pi$
$648$	−9.99379	+	17.3097i	−0.392593	+	0.679991i
$649$	3.72207	+	6.44681i	0.146104	+	0.253059i
$650$	−6.81259			−0.267212
$651$	40.6046	−	9.27301i	1.59142	−	0.363438i
$652$	11.5931			0.454022
$653$	12.9833	+	22.4877i	0.508074	+	0.880010i	0.999956	+	0.00934838i	$0.00297573\pi$
$653$	12.9833	+	22.4877i	0.508074	+	0.880010i	−0.491882	+	0.870662i	$0.663691\pi$
$654$	−0.371948	+	0.644234i	−0.0145443	+	0.0251915i
$655$	−5.31031	+	9.19772i	−0.207491	+	0.359385i
$656$	−4.46075	−	7.72625i	−0.174163	−	0.301659i
$657$	−7.11634			−0.277635
$658$	9.14367	+	9.85210i	0.356457	+	0.384075i
$659$	−26.6814			−1.03936			−0.519679	−	0.854361i	$-0.673949\pi$
$659$	−26.6814			−1.03936			−0.519679	+	0.854361i	$0.673949\pi$
$660$	0.556249	+	0.963451i	0.0216519	+	0.0375023i
$661$	9.79187	−	16.9600i	0.380860	−	0.659669i	−0.610326	−	0.792151i	$-0.708961\pi$
$661$	9.79187	−	16.9600i	0.380860	−	0.659669i	0.991185	+	0.132482i	$0.0422947\pi$
$662$	15.1365	−	26.2172i	0.588297	−	1.01896i
$663$	−5.12245	−	8.87235i	−0.198940	−	0.344573i
$664$	−33.0736			−1.28350
$665$	7.45303	+	8.03047i	0.289016	+	0.311408i
$666$	5.68379			0.220243
$667$	0.943524	+	1.63423i	0.0365334	+	0.0632777i
$668$	4.52718	−	7.84131i	0.175162	−	0.303389i
$669$	10.5742	−	18.3151i	0.408823	−	0.708103i
$670$	7.70064	+	13.3379i	0.297502	+	0.515288i
$671$	6.45679			0.249262
$672$	15.2946	−	3.49288i	0.590002	−	0.134741i
$673$	5.33581			0.205680			0.102840	−	0.994698i	$-0.467207\pi$
$673$	5.33581			0.205680			0.102840	+	0.994698i	$0.467207\pi$
$674$	8.64363	+	14.9712i	0.332940	+	0.576669i
$675$	2.80263	−	4.85430i	0.107873	−	0.186842i
$676$	8.60303	−	14.9009i	0.330886	−	0.573111i
$677$	−11.5512	−	20.0073i	−0.443949	−	0.768941i	0.554030	−	0.832497i	$-0.313089\pi$
$677$	−11.5512	−	20.0073i	−0.443949	−	0.768941i	−0.997978	+	0.0635555i	$0.979756\pi$
$678$	−16.4569			−0.632025
$679$	4.56148	−	14.7944i	0.175054	−	0.567758i
$680$	3.42262			0.131251
$681$	8.80093	+	15.2437i	0.337252	+	0.584138i
$682$	−5.82290	+	10.0856i	−0.222970	+	0.386196i
$683$	−8.10756	+	14.0427i	−0.310227	+	0.537329i	−0.978411	−	0.206667i	$-0.933738\pi$
$683$	−8.10756	+	14.0427i	−0.310227	+	0.537329i	0.668184	+	0.743996i	$0.267072\pi$
$684$	1.02866	+	1.78169i	0.0393319	+	0.0681248i
$685$	−2.69393			−0.102930
$686$	−19.4281	−	7.61669i	−0.741770	−	0.290807i
$687$	−14.9055			−0.568680
$688$	−5.58045	−	9.66563i	−0.212753	−	0.368499i
$689$	−32.0436	+	55.5012i	−1.22077	+	2.11443i
$690$	1.56913	−	2.71782i	0.0597358	−	0.103465i
$691$	7.99624	+	13.8499i	0.304191	+	0.526875i	0.977081	−	0.212868i	$-0.0682804\pi$
$691$	7.99624	+	13.8499i	0.304191	+	0.526875i	−0.672890	+	0.739743i	$0.734947\pi$
$692$	6.50281			0.247200
$693$	0.530226	−	1.71970i	0.0201416	−	0.0653261i
$694$	34.3539			1.30406
$695$	1.30668	+	2.26324i	0.0495652	+	0.0858495i
$696$	2.41773	−	4.18763i	0.0916438	−	0.158732i
$697$	−2.47429	+	4.28560i	−0.0937206	+	0.162329i
$698$	−7.81487	−	13.5357i	−0.295797	−	0.512336i
$699$	−5.56799			−0.210601
$700$	−1.88400	+	0.430255i	−0.0712085	+	0.0162621i
$701$	49.8879			1.88424			0.942119	−	0.335278i	$-0.108830\pi$
$701$	49.8879			1.88424			0.942119	+	0.335278i	$0.108830\pi$
$702$	−19.0932	−	33.0704i	−0.720626	−	1.24816i
$703$	−15.3554	+	26.5963i	−0.579140	+	1.00310i
$704$	−4.19897	+	7.27283i	−0.158255	+	0.274105i
$705$	3.43369	+	5.94733i	0.129320	+	0.223989i
$706$	21.4974			0.809066
$707$	−28.1521	−	30.3333i	−1.05877	−	1.14080i
$708$	8.28158			0.311241
$709$	10.4984	+	18.1837i	0.394274	+	0.682903i	0.993008	−	0.118045i	$-0.0376627\pi$
$709$	10.4984	+	18.1837i	0.394274	+	0.682903i	−0.598734	+	0.800948i	$0.704329\pi$
$710$	−1.04144	+	1.80383i	−0.0390847	+	0.0676966i
$711$	0.510212	−	0.883714i	0.0191345	−	0.0331418i
$712$	21.6206	+	37.4480i	0.810267	+	1.40342i
$713$	−18.9004			−0.707826
$714$	3.43623	+	3.70246i	0.128598	+	0.138561i
$715$	−6.04619			−0.226115
$716$	5.03648	+	8.72344i	0.188222	+	0.326010i
$717$	4.88281	−	8.45727i	0.182352	−	0.315843i
$718$	11.0824	−	19.1953i	0.413592	−	0.716363i
$719$	−10.5297	−	18.2380i	−0.392692	−	0.680162i	0.600112	−	0.799916i	$-0.295123\pi$
$719$	−10.5297	−	18.2380i	−0.392692	−	0.680162i	−0.992804	+	0.119754i	$0.961789\pi$
$720$	1.36420			0.0508409
$721$	−51.8351	+	11.8377i	−1.93044	+	0.440861i
$722$	−2.08673			−0.0776601
$723$	−2.62718	−	4.55040i	−0.0977058	−	0.169231i
$724$	3.00820	−	5.21036i	0.111799	−	0.193642i
$725$	−0.515966	+	0.893679i	−0.0191625	+	0.0331904i
$726$	−0.858079	−	1.48624i	−0.0318463	−	0.0551594i
$727$	12.9133			0.478928			0.239464	−	0.970905i	$-0.423028\pi$
$727$	12.9133			0.478928			0.239464	+	0.970905i	$0.423028\pi$
$728$	−14.5003	+	47.0295i	−0.537418	+	1.74303i
$729$	30.0311			1.11226
$730$	−5.89431	−	10.2093i	−0.218158	−	0.377861i
$731$	−3.09537	+	5.36134i	−0.114486	+	0.198296i
$732$	3.59158	−	6.22080i	0.132749	−	0.229927i
$733$	−16.2459	−	28.1387i	−0.600055	−	1.03933i	−0.992812	−	0.119683i	$-0.961812\pi$
$733$	−16.2459	−	28.1387i	−0.600055	−	1.03933i	0.392758	−	0.919642i	$-0.371521\pi$
$734$	−27.1698			−1.00286
$735$	−8.81056	−	6.00376i	−0.324983	−	0.221452i
$736$	−7.11924			−0.262419
$737$	6.83434	+	11.8374i	0.251746	+	0.436037i
$738$	−1.70454	+	2.95235i	−0.0627449	+	0.108677i
$739$	7.80919	−	13.5259i	0.287266	−	0.497559i	−0.685890	−	0.727705i	$-0.740587\pi$
$739$	7.80919	−	13.5259i	0.287266	−	0.497559i	0.973156	+	0.230146i	$0.0739204\pi$
$740$	−2.70848	−	4.69123i	−0.0995658	−	0.172453i
$741$	38.1343			1.40090
$742$	9.31016	−	30.1960i	0.341787	−	1.10853i
$743$	−31.6042			−1.15945			−0.579723	−	0.814813i	$-0.696839\pi$
$743$	−31.6042			−1.15945			−0.579723	+	0.814813i	$0.696839\pi$
$744$	24.2156	+	41.9427i	0.887788	+	1.53769i
$745$	7.94333	−	13.7583i	0.291021	−	0.504063i
$746$	−15.2824	+	26.4699i	−0.559529	+	0.969132i
$747$	3.65608	+	6.33251i	0.133769	+	0.231695i
$748$	0.812589			0.0297112
$749$	35.4238	−	8.08983i	1.29436	−	0.295596i
$750$	1.71616			0.0626653
$751$	4.30982	+	7.46483i	0.157268	+	0.272396i	0.933882	−	0.357580i	$-0.116398\pi$
$751$	4.30982	+	7.46483i	0.157268	+	0.272396i	−0.776615	+	0.629976i	$0.783065\pi$
$752$	−4.52158	+	7.83160i	−0.164885	+	0.285589i
$753$	−5.42721	+	9.40021i	−0.197779	+	0.342563i
$754$	3.51506	+	6.08827i	0.128011	+	0.221722i
$755$	3.37347			0.122773
$756$	−7.36875	−	7.93966i	−0.267999	−	0.288763i
$757$	−14.8782			−0.540759			−0.270379	−	0.962754i	$-0.587149\pi$
$757$	−14.8782			−0.540759			−0.270379	+	0.962754i	$0.587149\pi$
$758$	−2.49095	−	4.31445i	−0.0904753	−	0.156708i
$759$	1.39261	−	2.41207i	0.0505485	−	0.0875526i
$760$	−6.36996	+	11.0331i	−0.231063	+	0.400212i
$761$	−19.2797	−	33.3933i	−0.698887	−	1.21051i	−0.968853	−	0.247638i	$-0.920346\pi$
$761$	−19.2797	−	33.3933i	−0.698887	−	1.21051i	0.269966	−	0.962870i	$-0.412988\pi$
$762$	2.54046			0.0920311
$763$	−0.780156	−	0.840600i	−0.0282435	−	0.0304318i
$764$	17.9570			0.649661
$765$	−0.378349	−	0.655320i	−0.0136792	−	0.0236931i
$766$	10.7485	−	18.6169i	0.388358	−	0.672655i
$767$	−22.5043	+	38.9786i	−0.812584	+	1.40744i
$768$	11.3526	+	19.6633i	0.409652	+	0.709538i
$769$	29.5603			1.06597			0.532986	−	0.846124i	$-0.321070\pi$
$769$	29.5603			1.06597			0.532986	+	0.846124i	$0.321070\pi$
$770$	2.90629	−	0.663720i	0.104736	−	0.0239188i
$771$	10.4286			0.375576
$772$	4.87048	+	8.43592i	0.175292	+	0.303615i
$773$	−13.0149	+	22.5425i	−0.468113	+	0.810796i	−0.999336	−	0.0364361i	$-0.988399\pi$
$773$	−13.0149	+	22.5425i	−0.468113	+	0.810796i	0.531223	+	0.847232i	$0.321733\pi$
$774$	−2.13240	+	3.69342i	−0.0766474	+	0.132757i
$775$	−5.16784	−	8.95097i	−0.185634	−	0.321528i
$776$	18.0023			0.646246
$777$	8.80539	−	28.5589i	0.315891	−	1.02454i
$778$	−8.84472			−0.317099
$779$	−9.21000	−	15.9522i	−0.329982	−	0.571546i
$780$	−3.36319	+	5.82521i	−0.120421	+	0.208576i
$781$	−0.924284	+	1.60091i	−0.0330735	+	0.0572849i
$782$	−1.14612	−	1.98514i	−0.0409853	−	0.0709886i
$783$	−5.78425			−0.206712
$784$	1.04573	−	14.0006i	0.0373474	−	0.500020i
$785$	−5.99435			−0.213947
$786$	−9.11333	−	15.7848i	−0.325062	−	0.563024i
$787$	19.0538	−	33.0021i	0.679194	−	1.17640i	−0.296029	−	0.955179i	$-0.595663\pi$
$787$	19.0538	−	33.0021i	0.679194	−	1.17640i	0.975224	−	0.221220i	$-0.0710040\pi$
$788$	4.28232	−	7.41719i	0.152551	−	0.264227i
$789$	19.5691	+	33.8947i	0.696679	+	1.20668i
$790$	1.69039			0.0601415
$791$	7.47530	−	24.2449i	0.265791	−	0.862050i
$792$	2.09259			0.0743568
$793$	19.5195	+	33.8088i	0.693157	+	1.20058i
$794$	1.38562	−	2.39997i	0.0491738	−	0.0851716i
$795$	8.07211	−	13.9813i	0.286288	−	0.495866i
$796$	−2.70693	−	4.68854i	−0.0959446	−	0.166181i
$797$	13.8428			0.490338			0.245169	−	0.969480i	$-0.421156\pi$
$797$	13.8428			0.490338			0.245169	+	0.969480i	$0.421156\pi$
$798$	−18.3305	+	4.18619i	−0.648892	+	0.148189i
$799$	5.01607			0.177456
$800$	−1.94658	−	3.37157i	−0.0688219	−	0.119203i
$801$	4.78005	−	8.27929i	0.168895	−	0.292534i
$802$	0.851679	−	1.47515i	0.0300738	−	0.0520894i
$803$	−5.23122	−	9.06074i	−0.184606	−	0.319747i
$804$	15.2064			0.536287
$805$	3.29123	+	3.54622i	0.116001	+	0.124988i
$806$	−70.4128			−2.48018
$807$	−9.34632	−	16.1883i	−0.329006	−	0.569855i
$808$	24.0611	−	41.6750i	0.846466	−	1.46612i
$809$	6.35266	−	11.0031i	0.223347	−	0.386849i	−0.732475	−	0.680794i	$-0.761635\pi$
$809$	6.35266	−	11.0031i	0.223347	−	0.386849i	0.955822	+	0.293945i	$0.0949682\pi$
$810$	3.66017	+	6.33959i	0.128605	+	0.222751i
$811$	38.5099			1.35227			0.676133	−	0.736780i	$-0.263654\pi$
$811$	38.5099			1.35227			0.676133	+	0.736780i	$0.263654\pi$
$812$	1.35659	+	1.46169i	0.0476070	+	0.0512954i
$813$	−10.7390			−0.376632
$814$	4.17816	+	7.23678i	0.146444	+	0.253649i
$815$	7.93595	−	13.7455i	0.277984	−	0.481482i
$816$	−1.69923	+	2.94315i	−0.0594849	+	0.103031i
$817$	−11.5218	−	19.9564i	−0.403097	−	0.698185i
$818$	−21.4383			−0.749572
$819$	10.6075	−	2.42248i	0.370658	−	0.0846483i
$820$	3.24903			0.113461
$821$	23.0156	+	39.8643i	0.803251	+	1.39127i	0.917465	+	0.397816i	$0.130232\pi$
$821$	23.0156	+	39.8643i	0.803251	+	1.39127i	−0.114214	+	0.993456i	$0.536435\pi$
$822$	2.31160	−	4.00381i	0.0806264	−	0.139649i
$823$	−18.2589	+	31.6254i	−0.636467	+	1.10239i	0.349736	+	0.936848i	$0.386271\pi$
$823$	−18.2589	+	31.6254i	−0.636467	+	1.10239i	−0.986202	+	0.165544i	$0.947062\pi$
$824$	−30.9132	−	53.5432i	−1.07691	−	1.86527i
$825$	1.52310			0.0530274
$826$	6.53855	−	21.2067i	0.227505	−	0.737877i
$827$	−5.94594			−0.206761			−0.103380	−	0.994642i	$-0.532966\pi$
$827$	−5.94594			−0.206761			−0.103380	+	0.994642i	$0.532966\pi$
$828$	0.454253	+	0.786789i	0.0157864	+	0.0273428i
$829$	9.85937	−	17.0769i	0.342430	−	0.593106i	−0.642453	−	0.766325i	$-0.722083\pi$
$829$	9.85937	−	17.0769i	0.342430	−	0.593106i	0.984883	+	0.173219i	$0.0554167\pi$
$830$	−6.05651	+	10.4902i	−0.210224	+	0.364119i
$831$	−9.83529	−	17.0352i	−0.341183	−	0.590946i
$832$	−50.7756			−1.76033
$833$	−7.01544	+	3.38059i	−0.243071	+	0.117131i
$834$	−4.48494			−0.155301
$835$	−6.19807	−	10.7354i	−0.214493	−	0.371513i
$836$	−1.51234	+	2.61945i	−0.0523053	+	0.0905954i
$837$	28.9671	−	50.1725i	1.00125	−	1.73422i
$838$	9.08561	+	15.7367i	0.313857	+	0.543617i
$839$	−29.1358			−1.00588			−0.502940	−	0.864321i	$-0.667748\pi$
$839$	−29.1358			−1.00588			−0.502940	+	0.864321i	$0.667748\pi$
$840$	3.65278	−	11.8472i	0.126033	−	0.408767i
$841$	−27.9351			−0.963280
$842$	−10.1126	−	17.5156i	−0.348505	−	0.603628i
$843$	18.1915	−	31.5086i	0.626548	−	1.08521i
$844$	−5.56925	+	9.64622i	−0.191701	+	0.332037i
$845$	−11.7782	−	20.4005i	−0.405183	−	0.701797i
$846$	3.45556			0.118805
$847$	2.57934	−	0.589053i	0.0886273	−	0.0202401i
$848$	21.2591			0.730042
$849$	−18.4370	−	31.9338i	−0.632755	−	1.09596i
$850$	0.626757	−	1.08558i	0.0214976	−	0.0372349i
$851$	−6.78088	+	11.7448i	−0.232446	+	0.402608i
$852$	1.02826	+	1.78100i	0.0352277	+	0.0610162i
$853$	−16.0906			−0.550931			−0.275465	−	0.961311i	$-0.588832\pi$
$853$	−16.0906			−0.550931			−0.275465	+	0.961311i	$0.588832\pi$
$854$	−13.0940	−	14.1085i	−0.448068	−	0.482783i
$855$	2.81664			0.0963269
$856$	21.1259	+	36.5911i	0.722068	+	1.25066i
$857$	21.4686	−	37.1848i	0.733355	−	1.27021i	−0.222087	−	0.975027i	$-0.571287\pi$
$857$	21.4686	−	37.1848i	0.733355	−	1.27021i	0.955441	−	0.295181i	$-0.0953799\pi$
$858$	5.18811	−	8.98607i	0.177119	−	0.306779i
$859$	15.6346	+	27.0799i	0.533445	+	0.923954i	0.999237	+	0.0390598i	$0.0124363\pi$
$859$	15.6346	+	27.0799i	0.533445	+	0.923954i	−0.465792	+	0.884894i	$0.654230\pi$
$860$	4.06458			0.138601
$861$	12.1937	+	13.1384i	0.415560	+	0.447757i
$862$	14.4739			0.492985
$863$	−22.3738	−	38.7525i	−0.761612	−	1.31915i	−0.942019	−	0.335559i	$-0.891075\pi$
$863$	−22.3738	−	38.7525i	−0.761612	−	1.31915i	0.180407	−	0.983592i	$-0.442259\pi$
$864$	10.9111	−	18.8985i	0.371203	−	0.642942i
$865$	4.45143	−	7.71010i	0.151353	−	0.262151i
$866$	11.5021	+	19.9222i	0.390856	+	0.676983i
$867$	−24.0076			−0.815340
$868$	−19.4724	+	4.44698i	−0.660938	+	0.150940i
$869$	1.50023			0.0508917
$870$	−0.885479	−	1.53369i	−0.0300205	−	0.0519971i
$871$	−41.3217	+	71.5713i	−1.40013	+	2.42510i
$872$	0.666783	−	1.15490i	0.0225801	−	0.0391099i
$873$	−1.99004	−	3.44686i	−0.0673528	−	0.116658i
$874$	8.53236			0.288611
$875$	−0.779537	+	2.52830i	−0.0263532	+	0.0854723i
$876$	−11.6394			−0.393260
$877$	−6.85730	−	11.8772i	−0.231555	−	0.401064i	0.726711	−	0.686943i	$-0.241048\pi$
$877$	−6.85730	−	11.8772i	−0.231555	−	0.401064i	−0.958266	+	0.285879i	$0.907715\pi$
$878$	1.26502	−	2.19108i	0.0426924	−	0.0739454i
$879$	−7.02204	+	12.1625i	−0.236847	+	0.410232i
$880$	1.00283	+	1.73695i	0.0338053	+	0.0585524i
$881$	−2.21143			−0.0745049			−0.0372525	−	0.999306i	$-0.511861\pi$
$881$	−2.21143			−0.0745049			−0.0372525	+	0.999306i	$0.511861\pi$
$882$	−4.83293	+	2.32888i	−0.162733	+	0.0784176i
$883$	20.6454			0.694772			0.347386	−	0.937722i	$-0.387069\pi$
$883$	20.6454			0.694772			0.347386	+	0.937722i	$0.387069\pi$
$884$	2.45653	+	4.25484i	0.0826221	+	0.143106i
$885$	5.66906	−	9.81911i	0.190563	−	0.330066i
$886$	−6.70444	+	11.6124i	−0.225240	+	0.390127i
$887$	0.512656	+	0.887946i	0.0172133	+	0.0298143i	0.874504	−	0.485019i	$-0.161187\pi$
$887$	0.512656	+	0.887946i	0.0172133	+	0.0298143i	−0.857290	+	0.514833i	$0.827854\pi$
$888$	34.7513			1.16618
$889$	−1.15396	+	3.74269i	−0.0387026	+	0.125526i
$890$	15.8369			0.530853
$891$	3.24841	+	5.62641i	0.108826	+	0.188492i
$892$	−5.07100	+	8.78322i	−0.169790	+	0.294084i
$893$	−9.33558	+	16.1697i	−0.312403	+	0.541098i
$894$	13.6320	+	23.6113i	0.455923	+	0.789682i
$895$	13.7907			0.460971
$896$	4.32332	−	0.987331i	0.144432	−	0.0329844i
$897$	16.8400			0.562270
$898$	−3.90311	−	6.76039i	−0.130248	−	0.225597i
$899$	−5.33286	+	9.23678i	−0.177861	+	0.308064i
$900$	−0.248408	+	0.430255i	−0.00828027	+	0.0143418i
$901$	−5.89602	−	10.2122i	−0.196425	−	0.340218i
$902$	−5.01202			−0.166882
$903$	15.2545	+	16.4363i	0.507637	+	0.546967i
$904$	29.5020			0.981221
$905$	−4.11847	−	7.13339i	−0.136902	−	0.237122i
$906$	−2.89471	+	5.01378i	−0.0961701	+	0.166572i
$907$	3.90055	−	6.75595i	0.129516	−	0.224328i	−0.793973	−	0.607953i	$-0.791991\pi$
$907$	3.90055	−	6.75595i	0.129516	−	0.224328i	0.923489	+	0.383625i	$0.125324\pi$
$908$	−4.22059	−	7.31027i	−0.140065	−	0.242600i
$909$	−10.6392			−0.352880
$910$	12.2613	+	13.2113i	0.406460	+	0.437951i
$911$	−50.5091			−1.67344			−0.836720	−	0.547631i	$-0.815530\pi$
$911$	−50.5091			−1.67344			−0.836720	+	0.547631i	$0.815530\pi$
$912$	−6.32499	−	10.9552i	−0.209441	−	0.362763i
$913$	−5.37517	+	9.31006i	−0.177892	+	0.308118i
$914$	22.2964	−	38.6185i	0.737499	−	1.27739i
$915$	−4.91715	−	8.51676i	−0.162556	−	0.281555i
$916$	7.14810			0.236180
$917$	27.3942	−	6.25611i	0.904637	−	0.206595i
$918$	7.02628			0.231902
$919$	15.3284	+	26.5495i	0.505636	+	0.875787i	0.999979	+	0.00652019i	$0.00207545\pi$
$919$	15.3284	+	26.5495i	0.505636	+	0.875787i	−0.494343	+	0.869267i	$0.664591\pi$
$920$	−2.81295	+	4.87217i	−0.0927401	+	0.160631i
$921$	−25.4809	+	44.1342i	−0.839624	+	1.45427i
$922$	3.40083	+	5.89041i	0.112000	+	0.193990i
$923$	−11.1768			−0.367889
$924$	0.867233	−	2.81273i	0.0285299	−	0.0925321i
$925$	−7.41625			−0.243845
$926$	−14.7217	−	25.4987i	−0.483784	−	0.837939i
$927$	−6.83452	+	11.8377i	−0.224475	+	0.388802i
$928$	−2.00873	+	3.47923i	−0.0659399	+	0.114211i
$929$	24.4568	+	42.3604i	0.802401	+	1.38980i	0.918032	+	0.396507i	$0.129778\pi$
$929$	24.4568	+	42.3604i	0.802401	+	1.38980i	−0.115631	+	0.993292i	$0.536889\pi$
$930$	17.7377			0.581641
$931$	2.15908	−	28.9066i	0.0707611	−	0.947375i
$932$	2.67020			0.0874652
$933$	−18.5136	−	32.0664i	−0.606107	−	1.04981i
$934$	−10.4265	+	18.0592i	−0.341164	+	0.590914i
$935$	0.556249	−	0.963451i	0.0181913	−	0.0315082i
$936$	6.32609	+	10.9571i	0.206775	+	0.358144i
$937$	−11.0411			−0.360697			−0.180348	−	0.983603i	$-0.557723\pi$
$937$	−11.0411			−0.360697			−0.180348	+	0.983603i	$0.557723\pi$
$938$	12.0059	−	38.9391i	0.392005	−	1.27141i
$939$	−4.82231			−0.157370
$940$	−1.64667	−	2.85211i	−0.0537084	−	0.0930257i
$941$	15.3460	−	26.5800i	0.500265	−	0.866484i	−0.499735	−	0.866178i	$-0.666569\pi$
$941$	15.3460	−	26.5800i	0.500265	−	0.866484i	1.00000		0.000305872i	$-9.73621e-5\pi$
$942$	5.14363	−	8.90902i	0.167588	−	0.290272i
$943$	−4.06710	−	7.04442i	−0.132443	−	0.229398i
$944$	14.9303			0.485941
$945$	−14.4579	+	3.30180i	−0.470316	+	0.107408i
$946$	−6.27009			−0.203858
$947$	13.6574	+	23.6553i	0.443806	+	0.768694i	0.997968	−	0.0637144i	$-0.0202947\pi$
$947$	13.6574	+	23.6553i	0.443806	+	0.768694i	−0.554162	+	0.832409i	$0.686961\pi$
$948$	0.834500	−	1.44540i	0.0271033	−	0.0469443i
$949$	31.6290	−	54.7830i	1.02672	−	1.77833i
$950$	2.33296	+	4.04081i	0.0756912	+	0.131101i
$951$	21.9491			0.711748
$952$	−6.16005	−	6.63732i	−0.199648	−	0.215117i
$953$	−45.3590			−1.46932			−0.734661	−	0.678434i	$-0.762659\pi$
$953$	−45.3590			−1.46932			−0.734661	+	0.678434i	$0.762659\pi$
$954$	−4.06176	−	7.03517i	−0.131504	−	0.227772i
$955$	12.2923	−	21.2908i	0.397768	−	0.688955i
$956$	−2.34161	+	4.05578i	−0.0757330	+	0.131173i
$957$	−0.785865	−	1.36116i	−0.0254034	−	0.0440000i
$958$	−20.3998			−0.659086
$959$	4.84855	+	5.22420i	0.156568	+	0.168698i
$960$	12.7909			0.412824
$961$	−37.9132	−	65.6676i	−1.22301	−	2.11831i
$962$	−25.2619	+	43.7549i	−0.814477	+	1.41072i
$963$	4.67067	−	8.08983i	0.150510	−	0.260691i
$964$	1.25989	+	2.18220i	0.0405784	+	0.0702839i
$965$	13.3361			0.429306
$966$	−8.09466	+	1.84860i	−0.260442	+	0.0594779i
$967$	6.54296			0.210407			0.105204	−	0.994451i	$-0.466451\pi$
$967$	6.54296			0.210407			0.105204	+	0.994451i	$0.466451\pi$
$968$	1.53826	+	2.66434i	0.0494415	+	0.0856352i
$969$	−3.50835	+	6.07664i	−0.112704	+	0.195210i
$970$	3.29662	−	5.70992i	0.105848	−	0.183334i
$971$	0.664471	+	1.15090i	0.0213239	+	0.0369340i	0.876490	−	0.481419i	$-0.159879\pi$
$971$	0.664471	+	1.15090i	0.0213239	+	0.0369340i	−0.855167	+	0.518353i	$0.826545\pi$
$972$	−5.05488			−0.162135
$973$	2.03721	−	6.60737i	0.0653100	−	0.211823i
$974$	41.8369			1.34054
$975$	4.60446	+	7.97516i	0.147461	+	0.255410i
$976$	6.47504	−	11.2151i	0.207261	−	0.358986i
$977$	4.66466	−	8.07942i	0.149236	−	0.258484i	−0.781710	−	0.623643i	$-0.785652\pi$
$977$	4.66466	−	8.07942i	0.149236	−	0.258484i	0.930945	+	0.365159i	$0.118985\pi$
$978$	13.6193	+	23.5894i	0.435499	+	0.754306i
$979$	14.0553			0.449208
$980$	4.22521	+	2.87917i	0.134969	+	0.0919718i
$981$	−0.294835			−0.00941336
$982$	11.7700	+	20.3862i	0.375596	+	0.650551i
$983$	14.1096	−	24.4385i	0.450025	−	0.779466i	−0.548362	−	0.836241i	$-0.684748\pi$
$983$	14.1096	−	24.4385i	0.450025	−	0.779466i	0.998387	+	0.0567749i	$0.0180817\pi$
$984$	−10.4217	+	18.0509i	−0.332232	+	0.575443i
$985$	−5.86283	−	10.1547i	−0.186805	−	0.323556i
$986$	−1.29354			−0.0411947
$987$	5.35338	−	17.3628i	0.170400	−	0.552665i
$988$	−18.2878			−0.581811
$989$	−5.08798	−	8.81265i	−0.161789	−	0.280226i
$990$	0.383199	−	0.663720i	0.0121789	−	0.0210944i
$991$	−4.31231	+	7.46914i	−0.136985	+	0.237265i	−0.926354	−	0.376654i	$-0.877075\pi$
$991$	−4.31231	+	7.46914i	−0.136985	+	0.237265i	0.789369	+	0.613919i	$0.210408\pi$
$992$	−20.1192	−	34.8475i	−0.638785	−	1.10641i
$993$	−40.9216			−1.29861
$994$	5.37248	−	1.22693i	0.170405	−	0.0389159i
$995$	−7.41200			−0.234976
$996$	5.97986	+	10.3574i	0.189479	+	0.328187i
$997$	−24.8826	+	43.0979i	−0.788039	+	1.36492i	0.139127	+	0.990275i	$0.455570\pi$
$997$	−24.8826	+	43.0979i	−0.788039	+	1.36492i	−0.927166	+	0.374650i	$0.877763\pi$
$998$	−14.2940	+	24.7579i	−0.452468	+	0.783698i
$999$	−20.7850	−	36.0007i	−0.657609	−	1.13901i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	385.2.i.a.221.1	✓	8
7.2	even	3	inner	385.2.i.a.331.1	yes	8
7.3	odd	6		2695.2.a.k.1.4		4
7.4	even	3		2695.2.a.j.1.4		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
385.2.i.a.221.1	✓	8	1.1	even	1	trivial
385.2.i.a.331.1	yes	8	7.2	even	3	inner
2695.2.a.j.1.4		4	7.4	even	3
2695.2.a.k.1.4		4	7.3	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:	\( N \)	\(=\)	\( 385 = 5 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	385.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.563379 - 0.975800i) q^{2} +(-0.761548 + 1.31904i) q^{3} +(0.365209 - 0.632561i) q^{4} +(-0.500000 - 0.866025i) q^{5} +1.71616 q^{6} +(-0.779537 + 2.52830i) q^{7} -3.07652 q^{8} +(0.340090 + 0.589053i) q^{9} +O(q^{10})\)	\(q+(-0.563379 - 0.975800i) q^{2} +(-0.761548 + 1.31904i) q^{3} +(0.365209 - 0.632561i) q^{4} +(-0.500000 - 0.866025i) q^{5} +1.71616 q^{6} +(-0.779537 + 2.52830i) q^{7} -3.07652 q^{8} +(0.340090 + 0.589053i) q^{9} +(-0.563379 + 0.975800i) q^{10} +(-0.500000 + 0.866025i) q^{11} +(0.556249 + 0.963451i) q^{12} -6.04619 q^{13} +(2.90629 - 0.663720i) q^{14} +1.52310 q^{15} +(1.00283 + 1.73695i) q^{16} +(0.556249 - 0.963451i) q^{17} +(0.383199 - 0.663720i) q^{18} +(2.07051 + 3.58623i) q^{19} -0.730419 q^{20} +(-2.74128 - 2.95366i) q^{21} +1.12676 q^{22} +(0.914328 + 1.58366i) q^{23} +(2.34292 - 4.05805i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(3.40629 + 5.89987i) q^{26} -5.60527 q^{27} +(1.31461 + 1.41646i) q^{28} +1.03193 q^{29} +(-0.858079 - 1.48624i) q^{30} +(-5.16784 + 8.95097i) q^{31} +(-1.94658 + 3.37157i) q^{32} +(-0.761548 - 1.31904i) q^{33} -1.25351 q^{34} +(2.57934 - 0.589053i) q^{35} +0.496816 q^{36} +(3.70813 + 6.42266i) q^{37} +(2.33296 - 4.04081i) q^{38} +(4.60446 - 7.97516i) q^{39} +(1.53826 + 2.66434i) q^{40} -4.44818 q^{41} +(-1.33781 + 4.33897i) q^{42} -5.56473 q^{43} +(0.365209 + 0.632561i) q^{44} +(0.340090 - 0.589053i) q^{45} +(1.03023 - 1.78440i) q^{46} +(2.25442 + 3.90477i) q^{47} -3.05480 q^{48} +(-5.78464 - 3.94181i) q^{49} +1.12676 q^{50} +(0.847220 + 1.46743i) q^{51} +(-2.20813 + 3.82458i) q^{52} +(5.29981 - 9.17953i) q^{53} +(3.15789 + 5.46962i) q^{54} +1.00000 q^{55} +(2.39826 - 7.77837i) q^{56} -6.30716 q^{57} +(-0.581368 - 1.00696i) q^{58} +(3.72207 - 6.44681i) q^{59} +(0.556249 - 0.963451i) q^{60} +(-3.22839 - 5.59174i) q^{61} +11.6458 q^{62} +(-1.75442 + 0.400662i) q^{63} +8.39794 q^{64} +(3.02310 + 5.23616i) q^{65} +(-0.858079 + 1.48624i) q^{66} +(6.83434 - 11.8374i) q^{67} +(-0.406294 - 0.703722i) q^{68} -2.78522 q^{69} +(-2.02795 - 2.18506i) q^{70} +1.84857 q^{71} +(-1.04629 - 1.81223i) q^{72} +(-5.23122 + 9.06074i) q^{73} +(4.17816 - 7.23678i) q^{74} +(-0.761548 - 1.31904i) q^{75} +3.02468 q^{76} +(-1.79981 - 1.93925i) q^{77} -10.3762 q^{78} +(-0.750114 - 1.29924i) q^{79} +(1.00283 - 1.73695i) q^{80} +(3.24841 - 5.62641i) q^{81} +(2.50601 + 4.34054i) q^{82} +10.7503 q^{83} +(-2.86951 + 0.655320i) q^{84} -1.11250 q^{85} +(3.13505 + 5.43006i) q^{86} +(-0.785865 + 1.36116i) q^{87} +(1.53826 - 2.66434i) q^{88} +(-7.02763 - 12.1722i) q^{89} -0.766397 q^{90} +(4.71323 - 15.2866i) q^{91} +1.33568 q^{92} +(-7.87112 - 13.6332i) q^{93} +(2.54018 - 4.39972i) q^{94} +(2.07051 - 3.58623i) q^{95} +(-2.96482 - 5.13522i) q^{96} -5.85152 q^{97} +(-0.587480 + 7.86539i) q^{98} -0.680180 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 3 q^{2} + 3 q^{3} - 3 q^{4} - 4 q^{5} + 14 q^{6} + q^{7} - 18 q^{8} + q^{9}+O(q^{10}) \) 8 * q + 3 * q^2 + 3 * q^3 - 3 * q^4 - 4 * q^5 + 14 * q^6 + q^7 - 18 * q^8 + q^9	\( 8 q + 3 q^{2} + 3 q^{3} - 3 q^{4} - 4 q^{5} + 14 q^{6} + q^{7} - 18 q^{8} + q^{9} + 3 q^{10} - 4 q^{11} + 3 q^{12} - 12 q^{13} + q^{14} - 6 q^{15} - 5 q^{16} + 3 q^{17} - q^{18} + 3 q^{19} + 6 q^{20} - 18 q^{21} - 6 q^{22} + 6 q^{23} + 4 q^{24} - 4 q^{25} + 5 q^{26} + 6 q^{27} - 20 q^{28} - 16 q^{29} - 7 q^{30} - 10 q^{31} - 4 q^{32} + 3 q^{33} + 20 q^{34} + q^{35} - 16 q^{36} + 9 q^{37} + 23 q^{38} + 13 q^{39} + 9 q^{40} + 30 q^{41} - 16 q^{42} - 4 q^{43} - 3 q^{44} + q^{45} - 16 q^{46} + 15 q^{47} - 2 q^{48} - 19 q^{49} - 6 q^{50} - q^{51} + 3 q^{52} + 30 q^{53} + 13 q^{54} + 8 q^{55} - 24 q^{56} - 12 q^{57} + q^{58} - 17 q^{59} + 3 q^{60} + 32 q^{62} - 11 q^{63} + 10 q^{64} + 6 q^{65} - 7 q^{66} + 25 q^{67} + 19 q^{68} + 12 q^{69} + q^{70} - 26 q^{71} - 26 q^{72} - 3 q^{73} + 16 q^{74} + 3 q^{75} + 80 q^{76} - 2 q^{77} - 10 q^{78} + 4 q^{79} - 5 q^{80} + 16 q^{81} + 27 q^{82} + 36 q^{83} - 24 q^{84} - 6 q^{85} + 10 q^{86} - 20 q^{87} + 9 q^{88} - 25 q^{89} + 2 q^{90} - 3 q^{91} - 52 q^{92} - 10 q^{93} - 23 q^{94} + 3 q^{95} + 7 q^{96} - 46 q^{97} - 60 q^{98} - 2 q^{99}+O(q^{100}) \) 8 * q + 3 * q^2 + 3 * q^3 - 3 * q^4 - 4 * q^5 + 14 * q^6 + q^7 - 18 * q^8 + q^9 + 3 * q^10 - 4 * q^11 + 3 * q^12 - 12 * q^13 + q^14 - 6 * q^15 - 5 * q^16 + 3 * q^17 - q^18 + 3 * q^19 + 6 * q^20 - 18 * q^21 - 6 * q^22 + 6 * q^23 + 4 * q^24 - 4 * q^25 + 5 * q^26 + 6 * q^27 - 20 * q^28 - 16 * q^29 - 7 * q^30 - 10 * q^31 - 4 * q^32 + 3 * q^33 + 20 * q^34 + q^35 - 16 * q^36 + 9 * q^37 + 23 * q^38 + 13 * q^39 + 9 * q^40 + 30 * q^41 - 16 * q^42 - 4 * q^43 - 3 * q^44 + q^45 - 16 * q^46 + 15 * q^47 - 2 * q^48 - 19 * q^49 - 6 * q^50 - q^51 + 3 * q^52 + 30 * q^53 + 13 * q^54 + 8 * q^55 - 24 * q^56 - 12 * q^57 + q^58 - 17 * q^59 + 3 * q^60 + 32 * q^62 - 11 * q^63 + 10 * q^64 + 6 * q^65 - 7 * q^66 + 25 * q^67 + 19 * q^68 + 12 * q^69 + q^70 - 26 * q^71 - 26 * q^72 - 3 * q^73 + 16 * q^74 + 3 * q^75 + 80 * q^76 - 2 * q^77 - 10 * q^78 + 4 * q^79 - 5 * q^80 + 16 * q^81 + 27 * q^82 + 36 * q^83 - 24 * q^84 - 6 * q^85 + 10 * q^86 - 20 * q^87 + 9 * q^88 - 25 * q^89 + 2 * q^90 - 3 * q^91 - 52 * q^92 - 10 * q^93 - 23 * q^94 + 3 * q^95 + 7 * q^96 - 46 * q^97 - 60 * q^98 - 2 * q^99

Introduction

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