LMFDB - Embedded newform 385.2.i.c.221.8

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:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 3 x^{15} + 17 x^{14} - 28 x^{13} + 127 x^{12} - 178 x^{11} + 612 x^{10} - 527 x^{9} + 1556 x^{8} + \cdots + 81 $ x^16 - 3x^15 + 17x^14 - 28x^13 + 127x^12 - 178x^11 + 612x^10 - 527x^9 + 1556x^8 - 1065x^7 + 2812x^6 - 1224x^5 + 2359x^4 - 1154x^3 + 1351x^2 - 333*x + 81
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			221.8
Root			$-1.15525 - 2.00096i$ of defining polynomial
Character	$\chi$	$=$	385.221
Dual form			385.2.i.c.331.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.15525 + 2.00096i) q^{2} +(-1.21680 + 2.10756i) q^{3} +(-1.66923 + 2.89118i) q^{4} +(-0.500000 - 0.866025i) q^{5} -5.62286 q^{6} +(-2.34636 + 1.22254i) q^{7} -3.09251 q^{8} +(-1.46121 - 2.53090i) q^{9} +O(q^{10})$	\(q+(1.15525 + 2.00096i) q^{2} +(-1.21680 + 2.10756i) q^{3} +(-1.66923 + 2.89118i) q^{4} +(-0.500000 - 0.866025i) q^{5} -5.62286 q^{6} +(-2.34636 + 1.22254i) q^{7} -3.09251 q^{8} +(-1.46121 - 2.53090i) q^{9} +(1.15525 - 2.00096i) q^{10} +(0.500000 - 0.866025i) q^{11} +(-4.06224 - 7.03600i) q^{12} +3.20660 q^{13} +(-5.15690 - 3.28261i) q^{14} +2.43360 q^{15} +(-0.234179 - 0.405609i) q^{16} +(-3.27172 + 5.66679i) q^{17} +(3.37615 - 5.84766i) q^{18} +(-2.59226 - 4.48993i) q^{19} +3.33845 q^{20} +(0.278463 - 6.43269i) q^{21} +2.31051 q^{22} +(0.314321 + 0.544419i) q^{23} +(3.76297 - 6.51765i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(3.70444 + 6.41628i) q^{26} -0.188777 q^{27} +(0.382000 - 8.82445i) q^{28} +8.12920 q^{29} +(2.81143 + 4.86954i) q^{30} +(-1.58580 + 2.74669i) q^{31} +(-2.55143 + 4.41921i) q^{32} +(1.21680 + 2.10756i) q^{33} -15.1187 q^{34} +(2.23193 + 1.42073i) q^{35} +9.75639 q^{36} +(5.85379 + 10.1391i) q^{37} +(5.98945 - 10.3740i) q^{38} +(-3.90180 + 6.75812i) q^{39} +(1.54625 + 2.67819i) q^{40} -4.12565 q^{41} +(13.1932 - 6.87420i) q^{42} -4.61012 q^{43} +(1.66923 + 2.89118i) q^{44} +(-1.46121 + 2.53090i) q^{45} +(-0.726241 + 1.25789i) q^{46} +(-1.22159 - 2.11585i) q^{47} +1.13980 q^{48} +(4.01077 - 5.73705i) q^{49} -2.31051 q^{50} +(-7.96208 - 13.7907i) q^{51} +(-5.35254 + 9.27088i) q^{52} +(3.61808 - 6.26670i) q^{53} +(-0.218086 - 0.377736i) q^{54} -1.00000 q^{55} +(7.25612 - 3.78072i) q^{56} +12.6171 q^{57} +(9.39130 + 16.2662i) q^{58} +(-3.02502 + 5.23948i) q^{59} +(-4.06224 + 7.03600i) q^{60} +(0.174556 + 0.302340i) q^{61} -7.32802 q^{62} +(6.52266 + 4.15199i) q^{63} -12.7269 q^{64} +(-1.60330 - 2.77700i) q^{65} +(-2.81143 + 4.86954i) q^{66} +(-1.09141 + 1.89038i) q^{67} +(-10.9225 - 18.9183i) q^{68} -1.52986 q^{69} +(-0.264378 + 6.10731i) q^{70} -3.53524 q^{71} +(4.51881 + 7.82681i) q^{72} +(0.863854 - 1.49624i) q^{73} +(-13.5252 + 23.4264i) q^{74} +(-1.21680 - 2.10756i) q^{75} +17.3083 q^{76} +(-0.114424 + 2.64328i) q^{77} -18.0303 q^{78} +(7.27928 + 12.6081i) q^{79} +(-0.234179 + 0.405609i) q^{80} +(4.61335 - 7.99055i) q^{81} +(-4.76618 - 8.25526i) q^{82} +14.7347 q^{83} +(18.1333 + 11.5427i) q^{84} +6.54345 q^{85} +(-5.32586 - 9.22466i) q^{86} +(-9.89163 + 17.1328i) q^{87} +(-1.54625 + 2.67819i) q^{88} +(2.72994 + 4.72840i) q^{89} -6.75230 q^{90} +(-7.52383 + 3.92021i) q^{91} -2.09869 q^{92} +(-3.85922 - 6.68436i) q^{93} +(2.82249 - 4.88869i) q^{94} +(-2.59226 + 4.48993i) q^{95} +(-6.20918 - 10.7546i) q^{96} +19.4672 q^{97} +(16.1131 + 1.39765i) q^{98} -2.92243 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 3 q^{2} - q^{3} - 9 q^{4} - 8 q^{5} - 6 q^{6} - q^{7} + 18 q^{8} - 19 q^{9}+O(q^{10}) $ 16 * q - 3 * q^2 - q^3 - 9 * q^4 - 8 * q^5 - 6 * q^6 - q^7 + 18 * q^8 - 19 * q^9	\( 16 q - 3 q^{2} - q^{3} - 9 q^{4} - 8 q^{5} - 6 q^{6} - q^{7} + 18 q^{8} - 19 q^{9} - 3 q^{10} + 8 q^{11} - 9 q^{12} + 28 q^{13} - 9 q^{14} + 2 q^{15} - 7 q^{16} - 5 q^{17} - 27 q^{18} - q^{19} + 18 q^{20} - 18 q^{21} - 6 q^{22} + 2 q^{23} + 24 q^{24} - 8 q^{25} - 21 q^{26} - 10 q^{27} + 32 q^{28} + 52 q^{29} + 3 q^{30} - 2 q^{31} - 16 q^{32} + q^{33} - 52 q^{34} + 5 q^{35} + 108 q^{36} + q^{37} + 31 q^{38} - 19 q^{39} - 9 q^{40} - 6 q^{41} + 44 q^{42} + 8 q^{43} + 9 q^{44} - 19 q^{45} - 10 q^{46} - q^{47} - 42 q^{48} + 17 q^{49} + 6 q^{50} - 3 q^{51} - 37 q^{52} - 26 q^{53} + 5 q^{54} - 16 q^{55} + 40 q^{57} + q^{58} + 19 q^{59} - 9 q^{60} - 52 q^{62} - 21 q^{63} + 2 q^{64} - 14 q^{65} - 3 q^{66} + 13 q^{67} - 15 q^{68} - 28 q^{69} + 15 q^{70} - 18 q^{71} - 32 q^{72} - 11 q^{73} - 24 q^{74} - q^{75} - 36 q^{76} + 4 q^{77} - 66 q^{78} + 8 q^{79} - 7 q^{80} - 52 q^{81} - 41 q^{82} + 64 q^{83} + 138 q^{84} + 10 q^{85} - 28 q^{86} + 16 q^{87} + 9 q^{88} - 5 q^{89} + 54 q^{90} + 13 q^{91} + 60 q^{92} + 14 q^{93} + 5 q^{94} - q^{95} - q^{96} + 18 q^{97} + 22 q^{98} - 38 q^{99}+O(q^{100}) \) 16 * q - 3 * q^2 - q^3 - 9 * q^4 - 8 * q^5 - 6 * q^6 - q^7 + 18 * q^8 - 19 * q^9 - 3 * q^10 + 8 * q^11 - 9 * q^12 + 28 * q^13 - 9 * q^14 + 2 * q^15 - 7 * q^16 - 5 * q^17 - 27 * q^18 - q^19 + 18 * q^20 - 18 * q^21 - 6 * q^22 + 2 * q^23 + 24 * q^24 - 8 * q^25 - 21 * q^26 - 10 * q^27 + 32 * q^28 + 52 * q^29 + 3 * q^30 - 2 * q^31 - 16 * q^32 + q^33 - 52 * q^34 + 5 * q^35 + 108 * q^36 + q^37 + 31 * q^38 - 19 * q^39 - 9 * q^40 - 6 * q^41 + 44 * q^42 + 8 * q^43 + 9 * q^44 - 19 * q^45 - 10 * q^46 - q^47 - 42 * q^48 + 17 * q^49 + 6 * q^50 - 3 * q^51 - 37 * q^52 - 26 * q^53 + 5 * q^54 - 16 * q^55 + 40 * q^57 + q^58 + 19 * q^59 - 9 * q^60 - 52 * q^62 - 21 * q^63 + 2 * q^64 - 14 * q^65 - 3 * q^66 + 13 * q^67 - 15 * q^68 - 28 * q^69 + 15 * q^70 - 18 * q^71 - 32 * q^72 - 11 * q^73 - 24 * q^74 - q^75 - 36 * q^76 + 4 * q^77 - 66 * q^78 + 8 * q^79 - 7 * q^80 - 52 * q^81 - 41 * q^82 + 64 * q^83 + 138 * q^84 + 10 * q^85 - 28 * q^86 + 16 * q^87 + 9 * q^88 - 5 * q^89 + 54 * q^90 + 13 * q^91 + 60 * q^92 + 14 * q^93 + 5 * q^94 - q^95 - q^96 + 18 * q^97 + 22 * q^98 - 38 * 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 $

$2$	1.15525	+	2.00096i	0.816888	+	1.41489i	0.907964	+	0.419048i	$0.137636\pi$
$2$	1.15525	+	2.00096i	0.816888	+	1.41489i	−0.0910758	+	0.995844i	$0.529031\pi$
$3$	−1.21680	+	2.10756i	−0.702521	+	1.21680i	0.265058	+	0.964233i	$0.414609\pi$
$3$	−1.21680	+	2.10756i	−0.702521	+	1.21680i	−0.967579	+	0.252570i	$0.918724\pi$
$4$	−1.66923	+	2.89118i	−0.834613	+	1.44559i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$6$	−5.62286			−2.29552
$7$	−2.34636	+	1.22254i	−0.886839	+	0.462078i
$7$	−2.34636	+	1.22254i	−0.886839	+	0.462078i
$8$	−3.09251			−1.09337
$9$	−1.46121	−	2.53090i	−0.487071	−	0.843633i
$10$	1.15525	−	2.00096i	0.365324	−	0.632759i
$11$	0.500000	−	0.866025i	0.150756	−	0.261116i
$11$	0.500000	−	0.866025i	0.150756	−	0.261116i
$12$	−4.06224	−	7.03600i	−1.17267	−	2.03112i
$13$	3.20660			0.889351			0.444676	−	0.895692i	$-0.353319\pi$
$13$	3.20660			0.889351			0.444676	+	0.895692i	$0.353319\pi$
$14$	−5.15690	−	3.28261i	−1.37824	−	0.877316i
$15$	2.43360			0.628354
$16$	−0.234179	−	0.405609i	−0.0585446	−	0.101402i
$17$	−3.27172	+	5.66679i	−0.793509	+	1.37440i	0.130272	+	0.991478i	$0.458415\pi$
$17$	−3.27172	+	5.66679i	−0.793509	+	1.37440i	−0.923781	+	0.382920i	$0.874918\pi$
$18$	3.37615	−	5.84766i	0.795766	−	1.37831i
$19$	−2.59226	−	4.48993i	−0.594706	−	1.03006i	−0.993588	−	0.113059i	$-0.963935\pi$
$19$	−2.59226	−	4.48993i	−0.594706	−	1.03006i	0.398882	−	0.917002i	$-0.369398\pi$
$20$	3.33845			0.746501
$21$	0.278463	−	6.43269i	0.0607657	−	1.40373i
$22$	2.31051			0.492602
$23$	0.314321	+	0.544419i	0.0655404	+	0.113519i	0.896934	−	0.442165i	$-0.145790\pi$
$23$	0.314321	+	0.544419i	0.0655404	+	0.113519i	−0.831393	+	0.555685i	$0.812456\pi$
$24$	3.76297	−	6.51765i	0.768112	−	1.33041i
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	3.70444	+	6.41628i	0.726501	+	1.25834i
$27$	−0.188777			−0.0363302
$28$	0.382000	−	8.82445i	0.0721912	−	1.66766i
$29$	8.12920			1.50956			0.754778	−	0.655981i	$-0.227745\pi$
$29$	8.12920			1.50956			0.754778	+	0.655981i	$0.227745\pi$
$30$	2.81143	+	4.86954i	0.513295	+	0.889053i
$31$	−1.58580	+	2.74669i	−0.284819	+	0.493320i	−0.972565	−	0.232631i	$-0.925267\pi$
$31$	−1.58580	+	2.74669i	−0.284819	+	0.493320i	0.687747	+	0.725951i	$0.258600\pi$
$32$	−2.55143	+	4.41921i	−0.451034	+	0.781214i
$33$	1.21680	+	2.10756i	0.211818	+	0.366880i
$34$	−15.1187			−2.59283
$35$	2.23193	+	1.42073i	0.377265	+	0.240148i
$36$	9.75639			1.62606
$37$	5.85379	+	10.1391i	0.962357	+	1.66685i	0.716555	+	0.697530i	$0.245718\pi$
$37$	5.85379	+	10.1391i	0.962357	+	1.66685i	0.245801	+	0.969320i	$0.420949\pi$
$38$	5.98945	−	10.3740i	0.971617	−	1.68289i
$39$	−3.90180	+	6.75812i	−0.624788	+	1.08216i
$40$	1.54625	+	2.67819i	0.244484	+	0.423459i
$41$	−4.12565			−0.644318			−0.322159	−	0.946685i	$-0.604409\pi$
$41$	−4.12565			−0.644318			−0.322159	+	0.946685i	$0.604409\pi$
$42$	13.1932	−	6.87420i	2.03576	−	1.06071i
$43$	−4.61012			−0.703036			−0.351518	−	0.936181i	$-0.614334\pi$
$43$	−4.61012			−0.703036			−0.351518	+	0.936181i	$0.614334\pi$
$44$	1.66923	+	2.89118i	0.251645	+	0.435862i
$45$	−1.46121	+	2.53090i	−0.217825	+	0.377284i
$46$	−0.726241	+	1.25789i	−0.107078	+	0.185465i
$47$	−1.22159	−	2.11585i	−0.178187	−	0.308628i	0.763073	−	0.646313i	$-0.223690\pi$
$47$	−1.22159	−	2.11585i	−0.178187	−	0.308628i	−0.941259	+	0.337684i	$0.890356\pi$
$48$	1.13980			0.164515
$49$	4.01077	−	5.73705i	0.572968	−	0.819578i
$50$	−2.31051			−0.326755
$51$	−7.96208	−	13.7907i	−1.11491	−	1.93109i
$52$	−5.35254	+	9.27088i	−0.742264	+	1.28564i
$53$	3.61808	−	6.26670i	0.496981	−	0.860797i	−0.503012	−	0.864279i	$-0.667775\pi$
$53$	3.61808	−	6.26670i	0.496981	−	0.860797i	0.999994	+	0.00348202i	$0.00110836\pi$
$54$	−0.218086	−	0.377736i	−0.0296777	−	0.0514033i
$55$	−1.00000			−0.134840
$56$	7.25612	−	3.78072i	0.969640	−	0.505220i
$57$	12.6171			1.67117
$58$	9.39130	+	16.2662i	1.23314	+	2.13586i
$59$	−3.02502	+	5.23948i	−0.393823	+	0.682122i	−0.992950	−	0.118532i	$-0.962181\pi$
$59$	−3.02502	+	5.23948i	−0.393823	+	0.682122i	0.599127	+	0.800654i	$0.295515\pi$
$60$	−4.06224	+	7.03600i	−0.524432	+	0.908343i
$61$	0.174556	+	0.302340i	0.0223496	+	0.0387107i	0.876984	−	0.480520i	$-0.159552\pi$
$61$	0.174556	+	0.302340i	0.0223496	+	0.0387107i	−0.854634	+	0.519230i	$0.826219\pi$
$62$	−7.32802			−0.930660
$63$	6.52266	+	4.15199i	0.821778	+	0.523101i
$64$	−12.7269			−1.59087
$65$	−1.60330	−	2.77700i	−0.198865	−	0.344444i
$66$	−2.81143	+	4.86954i	−0.346063	+	0.599399i
$67$	−1.09141	+	1.89038i	−0.133337	+	0.230947i	−0.924961	−	0.380062i	$-0.875903\pi$
$67$	−1.09141	+	1.89038i	−0.133337	+	0.230947i	0.791624	+	0.611009i	$0.209236\pi$
$68$	−10.9225	−	18.9183i	−1.32455	−	2.29418i
$69$	−1.52986			−0.184174
$70$	−0.264378	+	6.10731i	−0.0315992	+	0.729963i
$71$	−3.53524			−0.419556			−0.209778	−	0.977749i	$-0.567274\pi$
$71$	−3.53524			−0.419556			−0.209778	+	0.977749i	$0.567274\pi$
$72$	4.51881	+	7.82681i	0.532547	+	0.922399i
$73$	0.863854	−	1.49624i	0.101107	−	0.175122i	−0.811034	−	0.584999i	$-0.801095\pi$
$73$	0.863854	−	1.49624i	0.101107	−	0.175122i	0.912141	+	0.409877i	$0.134428\pi$
$74$	−13.5252	+	23.4264i	−1.57228	+	2.72326i
$75$	−1.21680	−	2.10756i	−0.140504	−	0.243360i
$76$	17.3083			1.98540
$77$	−0.114424	+	2.64328i	−0.0130398	+	0.301229i
$78$	−18.0303			−2.04153
$79$	7.27928	+	12.6081i	0.818983	+	1.41852i	0.906433	+	0.422351i	$0.138795\pi$
$79$	7.27928	+	12.6081i	0.818983	+	1.41852i	−0.0874500	+	0.996169i	$0.527872\pi$
$80$	−0.234179	+	0.405609i	−0.0261820	+	0.0453485i
$81$	4.61335	−	7.99055i	0.512594	−	0.887839i
$82$	−4.76618	−	8.25526i	−0.526336	−	0.911641i
$83$	14.7347			1.61735			0.808673	−	0.588258i	$-0.200186\pi$
$83$	14.7347			1.61735			0.808673	+	0.588258i	$0.200186\pi$
$84$	18.1333	+	11.5427i	1.97850	+	1.25941i
$85$	6.54345			0.709736
$86$	−5.32586	−	9.22466i	−0.574302	−	0.994721i
$87$	−9.89163	+	17.1328i	−1.06049	+	1.83683i
$88$	−1.54625	+	2.67819i	−0.164831	+	0.285496i
$89$	2.72994	+	4.72840i	0.289373	+	0.501209i	0.973660	−	0.228004i	$-0.0732198\pi$
$89$	2.72994	+	4.72840i	0.289373	+	0.501209i	−0.684287	+	0.729213i	$0.739886\pi$
$90$	−6.75230			−0.711755
$91$	−7.52383	+	3.92021i	−0.788712	+	0.410950i
$92$	−2.09869			−0.218803
$93$	−3.85922	−	6.68436i	−0.400182	−	0.693136i
$94$	2.82249	−	4.88869i	0.291117	−	0.504230i
$95$	−2.59226	+	4.48993i	−0.265961	+	0.460657i
$96$	−6.20918	−	10.7546i	−0.633722	−	1.09764i
$97$	19.4672			1.97660			0.988300	−	0.152525i	$-0.0487406\pi$
$97$	19.4672			1.97660			0.988300	+	0.152525i	$0.0487406\pi$
$98$	16.1131	+	1.39765i	1.62766	+	0.141184i
$99$	−2.92243			−0.293715
$100$	−1.66923	−	2.89118i	−0.166923	−	0.289118i
$101$	−4.25773	+	7.37460i	−0.423659	+	0.733800i	−0.996294	−	0.0860109i	$-0.972588\pi$
$101$	−4.25773	+	7.37460i	−0.423659	+	0.733800i	0.572635	+	0.819811i	$0.305921\pi$
$102$	18.3965	−	31.8636i	1.82152	−	3.15497i
$103$	−2.30020	−	3.98406i	−0.226645	−	0.392561i	0.730166	−	0.683269i	$-0.239443\pi$
$103$	−2.30020	−	3.98406i	−0.226645	−	0.392561i	−0.956812	+	0.290708i	$0.906109\pi$
$104$	−9.91643			−0.972386
$105$	−5.71010	+	2.97519i	−0.557249	+	0.290349i
$106$	16.7192			1.62391
$107$	−3.64132	−	6.30695i	−0.352019	−	0.609715i	0.634584	−	0.772854i	$-0.281172\pi$
$107$	−3.64132	−	6.30695i	−0.352019	−	0.609715i	−0.986603	+	0.163139i	$0.947838\pi$
$108$	0.315112	−	0.545790i	0.0303217	−	0.0525187i
$109$	2.86576	−	4.96365i	0.274490	−	0.475431i	−0.695516	−	0.718511i	$-0.744824\pi$
$109$	2.86576	−	4.96365i	0.274490	−	0.475431i	0.970006	+	0.243079i	$0.0781575\pi$
$110$	−1.15525	−	2.00096i	−0.110149	−	0.190784i
$111$	−28.4916			−2.70430
$112$	1.04534	+	0.665410i	0.0987755	+	0.0628753i
$113$	3.55560			0.334483			0.167242	−	0.985916i	$-0.446514\pi$
$113$	3.55560			0.334483			0.167242	+	0.985916i	$0.446514\pi$
$114$	14.5759	+	25.2463i	1.36516	+	2.36453i
$115$	0.314321	−	0.544419i	0.0293106	−	0.0507674i
$116$	−13.5695	+	23.5030i	−1.25989	+	2.18220i
$117$	−4.68553	−	8.11558i	−0.433178	−	0.750286i
$118$	−13.9786			−1.28684
$119$	0.748729	−	17.2961i	0.0686359	−	1.58553i
$120$	−7.52593			−0.687021
$121$	−0.500000	−	0.866025i	−0.0454545	−	0.0787296i
$122$	−0.403313	+	0.698559i	−0.0365143	+	0.0632446i
$123$	5.02010	−	8.69507i	0.452647	−	0.784008i
$124$	−5.29413	−	9.16970i	−0.475427	−	0.823463i
$125$	1.00000			0.0894427
$126$	−0.772626	+	17.8482i	−0.0688310	+	1.59004i
$127$	12.2678			1.08859			0.544297	−	0.838893i	$-0.316796\pi$
$127$	12.2678			1.08859			0.544297	+	0.838893i	$0.316796\pi$
$128$	−9.59998	−	16.6277i	−0.848526	−	1.46969i
$129$	5.60960	−	9.71611i	0.493898	−	0.855456i
$130$	3.70444	−	6.41628i	0.324901	−	0.562745i
$131$	5.77853	+	10.0087i	0.504872	+	0.874464i	0.999984	+	0.00563498i	$0.00179368\pi$
$131$	5.77853	+	10.0087i	0.504872	+	0.874464i	−0.495112	+	0.868829i	$0.664873\pi$
$132$	−8.12447			−0.707144
$133$	11.5715	+	7.36582i	1.00338	+	0.638698i
$134$	−5.04343			−0.435686
$135$	0.0943886	+	0.163486i	0.00812368	+	0.0140706i
$136$	10.1178	−	17.5246i	0.867596	−	1.50272i
$137$	−6.75438	+	11.6989i	−0.577066	+	0.999508i	0.418748	+	0.908103i	$0.362469\pi$
$137$	−6.75438	+	11.6989i	−0.577066	+	0.999508i	−0.995814	+	0.0914050i	$0.970864\pi$
$138$	−1.76738	−	3.06120i	−0.150450	−	0.260586i
$139$	4.07266			0.345438			0.172719	−	0.984971i	$-0.444745\pi$
$139$	4.07266			0.345438			0.172719	+	0.984971i	$0.444745\pi$
$140$	−7.83320	+	4.08140i	−0.662026	+	0.344942i
$141$	5.94572			0.500720
$142$	−4.08410	−	7.07387i	−0.342730	−	0.593626i
$143$	1.60330	−	2.77700i	0.134075	−	0.232224i
$144$	−0.684370	+	1.18536i	−0.0570309	+	0.0987803i
$145$	−4.06460	−	7.04010i	−0.337547	−	0.584648i
$146$	3.99189			0.330371
$147$	7.21087	+	15.4338i	0.594742	+	1.27296i
$148$	−39.0852			−3.21278
$149$	−3.34832	−	5.79946i	−0.274305	−	0.475111i	0.695654	−	0.718377i	$-0.255115\pi$
$149$	−3.34832	−	5.79946i	−0.274305	−	0.475111i	−0.969960	+	0.243266i	$0.921781\pi$
$150$	2.81143	−	4.86954i	0.229552	−	0.397597i
$151$	11.0970	−	19.2206i	0.903065	−	1.56415i	0.0795710	−	0.996829i	$-0.474645\pi$
$151$	11.0970	−	19.2206i	0.903065	−	1.56415i	0.823494	−	0.567325i	$-0.192022\pi$
$152$	8.01659	+	13.8851i	0.650231	+	1.12623i
$153$	19.1228			1.54598
$154$	−5.42128	+	2.82470i	−0.436859	+	0.227621i
$155$	3.17161			0.254749
$156$	−13.0260	−	22.5616i	−1.04291	−	1.80638i
$157$	1.52312	−	2.63812i	0.121558	−	0.210545i	−0.798824	−	0.601564i	$-0.794544\pi$
$157$	1.52312	−	2.63812i	0.121558	−	0.210545i	0.920382	+	0.391020i	$0.127878\pi$
$158$	−16.8188	+	29.1311i	−1.33803	+	2.31754i
$159$	8.80497	+	15.2507i	0.698280	+	1.20946i
$160$	5.10287			0.403417
$161$	−1.40308	−	0.893131i	−0.110579	−	0.0703886i
$162$	21.3184			1.67493
$163$	6.87224	+	11.9031i	0.538276	+	0.932321i	0.998997	+	0.0447761i	$0.0142574\pi$
$163$	6.87224	+	11.9031i	0.538276	+	0.932321i	−0.460721	+	0.887545i	$0.652409\pi$
$164$	6.88664	−	11.9280i	0.537757	−	0.931422i
$165$	1.21680	−	2.10756i	0.0947279	−	0.164074i
$166$	17.0224	+	29.4836i	1.32119	+	2.28837i
$167$	−4.71638			−0.364965			−0.182482	−	0.983209i	$-0.558413\pi$
$167$	−4.71638			−0.364965			−0.182482	+	0.983209i	$0.558413\pi$
$168$	−0.861149	+	19.8931i	−0.0664391	+	1.53479i
$169$	−2.71770			−0.209054
$170$	7.55935	+	13.0932i	0.579775	+	1.00420i
$171$	−7.57571	+	13.1215i	−0.579329	+	1.00343i
$172$	7.69533	−	13.3287i	0.586763	−	1.01630i
$173$	−9.72784	−	16.8491i	−0.739594	−	1.28101i	−0.952678	−	0.303981i	$-0.901684\pi$
$173$	−9.72784	−	16.8491i	−0.739594	−	1.28101i	0.213084	−	0.977034i	$-0.431649\pi$
$174$	−45.7094			−3.46522
$175$	0.114424	−	2.64328i	0.00864966	−	0.199813i
$176$	−0.468357			−0.0353037
$177$	−7.36169	−	12.7508i	−0.553338	−	0.958410i
$178$	−6.30756	+	10.9250i	−0.472771	+	0.818864i
$179$	4.39684	−	7.61554i	0.328635	−	0.569212i	−0.653606	−	0.756835i	$-0.726745\pi$
$179$	4.39684	−	7.61554i	0.328635	−	0.569212i	0.982241	+	0.187622i	$0.0600781\pi$
$180$	−4.87819	−	8.44928i	−0.363599	−	0.629772i
$181$	22.0176			1.63656			0.818278	−	0.574823i	$-0.194929\pi$
$181$	22.0176			1.63656			0.818278	+	0.574823i	$0.194929\pi$
$182$	−16.5361	−	10.5260i	−1.22574	−	0.780242i
$183$	−0.849601			−0.0628043
$184$	−0.972038	−	1.68362i	−0.0716596	−	0.124118i
$185$	5.85379	−	10.1391i	0.430379	−	0.745438i
$186$	8.91675	−	15.4443i	0.653808	−	1.13243i
$187$	3.27172	+	5.66679i	0.239252	+	0.414397i
$188$	8.15642			0.594868
$189$	0.442939	−	0.230788i	0.0322191	−	0.0167874i
$190$	−11.9789			−0.869041
$191$	−5.67489	−	9.82919i	−0.410620	−	0.711215i	0.584337	−	0.811511i	$-0.301355\pi$
$191$	−5.67489	−	9.82919i	−0.410620	−	0.711215i	−0.994958	+	0.100296i	$0.968021\pi$
$192$	15.4862	−	26.8228i	1.11762	−	1.93577i
$193$	0.431639	−	0.747620i	0.0310700	−	0.0538149i	−0.850072	−	0.526666i	$-0.823442\pi$
$193$	0.431639	−	0.747620i	0.0310700	−	0.0538149i	0.881142	+	0.472851i	$0.156775\pi$
$194$	22.4896	+	38.9532i	1.61466	+	2.79667i
$195$	7.80360			0.558827
$196$	9.89197	+	21.1723i	0.706569	+	1.51231i
$197$	−22.3064			−1.58926			−0.794632	−	0.607092i	$-0.792336\pi$
$197$	−22.3064			−1.58926			−0.794632	+	0.607092i	$0.792336\pi$
$198$	−3.37615	−	5.84766i	−0.239932	−	0.415575i
$199$	9.19662	−	15.9290i	0.651931	−	1.12918i	−0.330723	−	0.943728i	$-0.607292\pi$
$199$	9.19662	−	15.9290i	0.651931	−	1.12918i	0.982654	−	0.185450i	$-0.0593742\pi$
$200$	1.54625	−	2.67819i	0.109337	−	0.189376i
$201$	−2.65606	−	4.60043i	−0.187344	−	0.324490i
$202$	−19.6750			−1.38433
$203$	−19.0740	+	9.93831i	−1.33873	+	0.697532i
$204$	53.1620			3.72209
$205$	2.06283	+	3.57292i	0.144074	+	0.249543i
$206$	5.31463	−	9.20521i	0.370288	−	0.641358i
$207$	0.918580	−	1.59103i	0.0638457	−	0.110584i
$208$	−0.750917	−	1.30063i	−0.0520668	−	0.0901823i
$209$	−5.18453			−0.358621
$210$	−12.5499	−	7.98858i	−0.866022	−	0.551265i
$211$	6.45964			0.444700			0.222350	−	0.974967i	$-0.428627\pi$
$211$	6.45964			0.444700			0.222350	+	0.974967i	$0.428627\pi$
$212$	12.0788	+	20.9211i	0.829574	+	1.43686i
$213$	4.30169	−	7.45074i	0.294747	−	0.510517i
$214$	8.41330	−	14.5723i	0.575121	−	0.996139i
$215$	2.30506	+	3.99248i	0.157204	+	0.272285i
$216$	0.583795			0.0397222
$217$	0.362908	−	8.38343i	0.0246358	−	0.569104i
$218$	13.2427			0.896912
$219$	2.10228	+	3.64125i	0.142059	+	0.246053i
$220$	1.66923	−	2.89118i	0.112539	−	0.194924i
$221$	−10.4911	+	18.1711i	−0.705709	+	1.22232i
$222$	−32.9150	−	57.0105i	−2.20911	−	3.82630i
$223$	12.2844			0.822627			0.411313	−	0.911494i	$-0.365070\pi$
$223$	12.2844			0.822627			0.411313	+	0.911494i	$0.365070\pi$
$224$	0.583892	−	13.4883i	0.0390129	−	0.901224i
$225$	2.92243			0.194829
$226$	4.10763	+	7.11462i	0.273235	+	0.473257i
$227$	4.65056	−	8.05501i	0.308669	−	0.534630i	−0.669403	−	0.742900i	$-0.733450\pi$
$227$	4.65056	−	8.05501i	0.308669	−	0.534630i	0.978071	+	0.208270i	$0.0667833\pi$
$228$	−21.0608	+	36.4783i	−1.39478	+	2.41584i
$229$	11.3897	+	19.7276i	0.752653	+	1.30363i	0.946532	+	0.322609i	$0.104560\pi$
$229$	11.3897	+	19.7276i	0.752653	+	1.30363i	−0.193879	+	0.981025i	$0.562107\pi$
$230$	1.45248			0.0957738
$231$	−5.43164	−	3.45750i	−0.357376	−	0.227487i
$232$	−25.1396			−1.65050
$233$	−8.63862	−	14.9625i	−0.565935	−	0.980228i	−0.996962	−	0.0778889i	$-0.975182\pi$
$233$	−8.63862	−	14.9625i	−0.565935	−	0.980228i	0.431027	−	0.902339i	$-0.358151\pi$
$234$	10.8260	−	18.7511i	0.707716	−	1.22580i
$235$	−1.22159	+	2.11585i	−0.0796875	+	0.138023i
$236$	−10.0989	−	17.4918i	−0.657380	−	1.13862i
$237$	−35.4298			−2.30141
$238$	35.4738	−	18.4833i	2.29943	−	1.19809i
$239$	−13.2416			−0.856527			−0.428264	−	0.903654i	$-0.640875\pi$
$239$	−13.2416			−0.856527			−0.428264	+	0.903654i	$0.640875\pi$
$240$	−0.569898	−	0.987092i	−0.0367868	−	0.0637165i
$241$	11.0938	−	19.2151i	0.714616	−	1.23775i	−0.248492	−	0.968634i	$-0.579935\pi$
$241$	11.0938	−	19.2151i	0.714616	−	1.23775i	0.963108	−	0.269117i	$-0.0867318\pi$
$242$	1.15525	−	2.00096i	0.0742626	−	0.128627i
$243$	10.9439	+	18.9554i	0.702051	+	1.21599i
$244$	−1.16549			−0.0746131
$245$	−6.97381	−	0.604909i	−0.445541	−	0.0386463i
$246$	23.1980			1.47905
$247$	−8.31236	−	14.3974i	−0.528903	−	0.916086i
$248$	4.90410	−	8.49416i	0.311411	−	0.539379i
$249$	−17.9292	+	31.0544i	−1.13622	+	1.96799i
$250$	1.15525	+	2.00096i	0.0730647	+	0.126552i
$251$	2.35495			0.148643			0.0743216	−	0.997234i	$-0.476321\pi$
$251$	2.35495			0.148643			0.0743216	+	0.997234i	$0.476321\pi$
$252$	−22.8920	+	11.9276i	−1.44206	+	0.751369i
$253$	0.628641			0.0395223
$254$	14.1725	+	24.5474i	0.889260	+	1.54024i
$255$	−7.96208	+	13.7907i	−0.498605	+	0.863609i
$256$	9.45391	−	16.3746i	0.590869	−	1.02342i
$257$	−6.36744	−	11.0287i	−0.397190	−	0.687953i	0.596188	−	0.802845i	$-0.296681\pi$
$257$	−6.36744	−	11.0287i	−0.397190	−	0.687953i	−0.993378	+	0.114892i	$0.963348\pi$
$258$	25.9221			1.61384
$259$	−26.1305	−	16.6333i	−1.62367	−	1.03354i
$260$	10.7051			0.663901
$261$	−11.8785	−	20.5742i	−0.735261	−	1.27351i
$262$	−13.3513	+	23.1252i	−0.824848	+	1.42868i
$263$	−4.97785	+	8.62189i	−0.306947	+	0.531649i	−0.977693	−	0.210039i	$-0.932641\pi$
$263$	−4.97785	+	8.62189i	−0.306947	+	0.531649i	0.670746	+	0.741688i	$0.265974\pi$
$264$	−3.76297	−	6.51765i	−0.231595	−	0.401134i
$265$	−7.23616			−0.444514
$266$	−1.37068	+	31.6635i	−0.0840415	+	1.94142i
$267$	−13.2872			−0.813163
$268$	−3.64362	−	6.31094i	−0.222570	−	0.385502i
$269$	−6.29812	+	10.9087i	−0.384003	+	0.665113i	−0.991630	−	0.129109i	$-0.958788\pi$
$269$	−6.29812	+	10.9087i	−0.384003	+	0.665113i	0.607627	+	0.794223i	$0.292122\pi$
$270$	−0.218086	+	0.377736i	−0.0132723	+	0.0229883i
$271$	−13.8318	−	23.9573i	−0.840219	−	1.45530i	−0.889709	−	0.456528i	$-0.849093\pi$
$271$	−13.8318	−	23.9573i	−0.840219	−	1.45530i	0.0494897	−	0.998775i	$-0.484240\pi$
$272$	3.06467			0.185823
$273$	0.892921	−	20.6271i	0.0540420	−	1.24841i
$274$	−31.2121			−1.88559
$275$	0.500000	+	0.866025i	0.0301511	+	0.0522233i
$276$	2.55369	−	4.42312i	0.153714	−	0.266240i
$277$	−13.1230	+	22.7297i	−0.788484	+	1.36569i	0.138411	+	0.990375i	$0.455800\pi$
$277$	−13.1230	+	22.7297i	−0.788484	+	1.36569i	−0.926895	+	0.375320i	$0.877533\pi$
$278$	4.70496	+	8.14923i	0.282185	+	0.488758i
$279$	9.26879			0.554908
$280$	−6.90226	−	4.39362i	−0.412489	−	0.262569i
$281$	5.89612			0.351733			0.175867	−	0.984414i	$-0.443727\pi$
$281$	5.89612			0.351733			0.175867	+	0.984414i	$0.443727\pi$
$282$	6.86882	+	11.8971i	0.409032	+	0.708464i
$283$	−9.43204	+	16.3368i	−0.560677	+	0.971120i	0.436761	+	0.899578i	$0.356126\pi$
$283$	−9.43204	+	16.3368i	−0.560677	+	0.971120i	−0.997438	+	0.0715428i	$0.977208\pi$
$284$	5.90112	−	10.2210i	0.350167	−	0.606507i
$285$	−6.30854	−	10.9267i	−0.373686	−	0.647243i
$286$	7.40888			0.438096
$287$	9.68025	−	5.04379i	0.571407	−	0.297725i
$288$	14.9128			0.878743
$289$	−12.9083	−	22.3579i	−0.759315	−	1.31517i
$290$	9.39130	−	16.2662i	0.551476	−	0.955184i
$291$	−23.6878	+	41.0284i	−1.38860	+	2.40513i
$292$	2.88394	+	4.99512i	0.168770	+	0.292318i
$293$	−20.2422			−1.18256			−0.591281	−	0.806466i	$-0.701377\pi$
$293$	−20.2422			−1.18256			−0.591281	+	0.806466i	$0.701377\pi$
$294$	−22.5520	+	32.2586i	−1.31526	+	1.88136i
$295$	6.05003			0.352246
$296$	−18.1029	−	31.3551i	−1.05221	−	1.82248i
$297$	−0.0943886	+	0.163486i	−0.00547698	+	0.00948642i
$298$	7.73633	−	13.3997i	0.448153	−	0.776224i
$299$	1.00790	+	1.74574i	0.0582884	+	0.100959i
$300$	8.12447			0.469067
$301$	10.8170	−	5.63607i	0.623480	−	0.324858i
$302$	51.2797			2.95081
$303$	−10.3616	−	17.9468i	−0.595259	−	1.03102i
$304$	−1.21411	+	2.10289i	−0.0696337	+	0.120609i
$305$	0.174556	−	0.302340i	0.00999505	−	0.0173119i
$306$	22.0917	+	38.2639i	1.26290	+	2.18740i
$307$	−21.6422			−1.23518			−0.617592	−	0.786498i	$-0.711892\pi$
$307$	−21.6422			−1.23518			−0.617592	+	0.786498i	$0.711892\pi$
$308$	−7.45120	−	4.74305i	−0.424571	−	0.270260i
$309$	11.1956			0.636893
$310$	3.66401	+	6.34625i	0.208102	+	0.360443i
$311$	−9.40509	+	16.2901i	−0.533314	+	0.923726i	0.465929	+	0.884822i	$0.345720\pi$
$311$	−9.40509	+	16.2901i	−0.533314	+	0.923726i	−0.999243	+	0.0389044i	$0.987613\pi$
$312$	12.0663	−	20.8995i	0.683122	−	1.18320i
$313$	15.7535	+	27.2859i	0.890441	+	1.54229i	0.839348	+	0.543595i	$0.182937\pi$
$313$	15.7535	+	27.2859i	0.890441	+	1.54229i	0.0510928	+	0.998694i	$0.483730\pi$
$314$	7.03835			0.397197
$315$	0.334397	−	7.72479i	0.0188411	−	0.435242i
$316$	−48.6030			−2.73413
$317$	−9.20861	−	15.9498i	−0.517207	−	0.895829i	−0.999800	−	0.0199844i	$-0.993638\pi$
$317$	−9.20861	−	15.9498i	−0.517207	−	0.895829i	0.482593	−	0.875845i	$-0.339695\pi$
$318$	−20.3440	+	35.2368i	−1.14083	+	1.97598i
$319$	4.06460	−	7.04010i	0.227574	−	0.394170i
$320$	6.36347	+	11.0218i	0.355729	+	0.616140i
$321$	17.7230			0.989204
$322$	0.166199	−	3.83931i	0.00926191	−	0.213956i
$323$	33.9247			1.88762
$324$	15.4014	+	26.6761i	0.855636	+	1.48200i
$325$	−1.60330	+	2.77700i	−0.0889351	+	0.154040i
$326$	−15.8784	+	27.5022i	−0.879422	+	1.52320i
$327$	6.97413	+	12.0796i	0.385670	+	0.668001i
$328$	12.7586			0.704476
$329$	5.45300	+	3.47109i	0.300633	+	0.191368i
$330$	5.62286			0.309528
$331$	8.43720	+	14.6137i	0.463750	+	0.803239i	0.999144	−	0.0413634i	$-0.0131701\pi$
$331$	8.43720	+	14.6137i	0.463750	+	0.803239i	−0.535394	+	0.844603i	$0.679837\pi$
$332$	−24.5956	+	42.6008i	−1.34986	+	2.33802i
$333$	17.1073	−	29.6307i	0.937473	−	1.62375i
$334$	−5.44862	−	9.43729i	−0.298135	−	0.516386i
$335$	2.18282			0.119260
$336$	−2.67437	+	1.39345i	−0.145899	+	0.0760189i
$337$	17.9700			0.978886			0.489443	−	0.872035i	$-0.337200\pi$
$337$	17.9700			0.978886			0.489443	+	0.872035i	$0.337200\pi$
$338$	−3.13964	−	5.43802i	−0.170774	−	0.295789i
$339$	−4.32647	+	7.49366i	−0.234981	+	0.407000i
$340$	−10.9225	+	18.9183i	−0.592355	+	1.02599i
$341$	1.58580	+	2.74669i	0.0858760	+	0.148742i
$342$	−35.0075			−1.89299
$343$	−2.39692	+	18.3645i	−0.129421	+	0.991590i
$344$	14.2568			0.768676
$345$	0.764932	+	1.32490i	0.0411826	+	0.0713303i
$346$	22.4763	−	38.9300i	1.20833	−	2.09289i
$347$	0.835880	−	1.44779i	0.0448724	−	0.0777213i	−0.842717	−	0.538357i	$-0.819045\pi$
$347$	0.835880	−	1.44779i	0.0448724	−	0.0777213i	0.887589	+	0.460636i	$0.152379\pi$
$348$	−33.0227	−	57.1971i	−1.77020	−	3.06608i
$349$	−10.7676			−0.576378			−0.288189	−	0.957574i	$-0.593053\pi$
$349$	−10.7676			−0.576378			−0.288189	+	0.957574i	$0.593053\pi$
$350$	5.42128	−	2.82470i	0.289779	−	0.150986i
$351$	−0.605334			−0.0323103
$352$	2.55143	+	4.41921i	0.135992	+	0.235545i
$353$	4.11841	−	7.13329i	0.219201	−	0.379667i	−0.735363	−	0.677673i	$-0.762988\pi$
$353$	4.11841	−	7.13329i	0.219201	−	0.379667i	0.954564	+	0.298006i	$0.0963217\pi$
$354$	17.0092	−	29.4609i	0.904031	−	1.56583i
$355$	1.76762	+	3.06161i	0.0938156	+	0.162493i
$356$	−18.2276			−0.966059
$357$	35.5416	+	22.6240i	1.88106	+	1.19739i
$358$	20.3179			1.07383
$359$	−9.22646	−	15.9807i	−0.486954	−	0.843429i	0.512934	−	0.858428i	$-0.328559\pi$
$359$	−9.22646	−	15.9807i	−0.486954	−	0.843429i	−0.999888	+	0.0149995i	$0.995225\pi$
$360$	4.51881	−	7.82681i	0.238162	−	0.412509i
$361$	−3.93966	+	6.82369i	−0.207351	+	0.359142i
$362$	25.4359	+	44.0563i	1.33688	+	2.31555i
$363$	2.43360			0.127731
$364$	1.22492	−	28.2965i	0.0642033	−	1.48314i
$365$	−1.72771			−0.0904324
$366$	−0.981505	−	1.70002i	−0.0513041	−	0.0888613i
$367$	6.68342	−	11.5760i	0.348872	−	0.604264i	−0.637178	−	0.770717i	$-0.719898\pi$
$367$	6.68342	−	11.5760i	0.348872	−	0.604264i	0.986049	+	0.166453i	$0.0532315\pi$
$368$	0.147214	−	0.254983i	0.00767408	−	0.0132919i
$369$	6.02846	+	10.4416i	0.313829	+	0.543568i
$370$	27.0505			1.40629
$371$	−0.827992	+	19.1272i	−0.0429872	+	0.993033i
$372$	25.7676			1.33599
$373$	−11.1321	−	19.2814i	−0.576399	−	0.998352i	−0.995888	−	0.0905916i	$-0.971124\pi$
$373$	−11.1321	−	19.2814i	−0.576399	−	0.998352i	0.419489	−	0.907760i	$-0.362209\pi$
$374$	−7.55935	+	13.0932i	−0.390885	+	0.677032i
$375$	−1.21680	+	2.10756i	−0.0628354	+	0.108834i
$376$	3.77776	+	6.54328i	0.194823	+	0.337444i
$377$	26.0671			1.34252
$378$	0.973505	+	0.619683i	0.0500717	+	0.0318731i
$379$	−11.6602			−0.598944			−0.299472	−	0.954105i	$-0.596810\pi$
$379$	−11.6602			−0.598944			−0.299472	+	0.954105i	$0.596810\pi$
$380$	−8.65415	−	14.9894i	−0.443948	−	0.768941i
$381$	−14.9275	+	25.8552i	−0.764760	+	1.32460i
$382$	13.1119	−	22.7104i	0.670862	−	1.16197i
$383$	−2.86195	−	4.95704i	−0.146239	−	0.253293i	0.783596	−	0.621271i	$-0.213383\pi$
$383$	−2.86195	−	4.95704i	−0.146239	−	0.253293i	−0.929834	+	0.367978i	$0.880050\pi$
$384$	46.7251			2.38443
$385$	2.34636	−	1.22254i	0.119581	−	0.0623066i
$386$	1.99461			0.101523
$387$	6.73637	+	11.6677i	0.342429	+	0.593104i
$388$	−32.4952	+	56.2834i	−1.64970	+	2.85736i
$389$	−2.69556	+	4.66884i	−0.136670	+	0.236720i	−0.926234	−	0.376948i	$-0.876973\pi$
$389$	−2.69556	+	4.66884i	−0.136670	+	0.236720i	0.789564	+	0.613668i	$0.210307\pi$
$390$	9.01514	+	15.6147i	0.456500	+	0.790680i
$391$	−4.11348			−0.208028
$392$	−12.4033	+	17.7418i	−0.626463	+	0.896098i
$393$	−28.1253			−1.41873
$394$	−25.7695	−	44.6342i	−1.29825	−	2.24864i
$395$	7.27928	−	12.6081i	0.366260	−	0.634381i
$396$	4.87819	−	8.44928i	0.245138	−	0.424592i
$397$	3.01244	+	5.21769i	0.151190	+	0.261868i	0.931665	−	0.363318i	$-0.118356\pi$
$397$	3.01244	+	5.21769i	0.151190	+	0.261868i	−0.780475	+	0.625187i	$0.785023\pi$
$398$	42.4977			2.13022
$399$	−29.6042	+	15.4249i	−1.48206	+	0.772213i
$400$	0.468357			0.0234179
$401$	−3.68021	−	6.37432i	−0.183781	−	0.318318i	0.759384	−	0.650643i	$-0.225500\pi$
$401$	−3.68021	−	6.37432i	−0.183781	−	0.318318i	−0.943165	+	0.332324i	$0.892167\pi$
$402$	6.13686	−	10.6293i	0.306079	−	0.530144i
$403$	−5.08504	+	8.80754i	−0.253304	+	0.438735i
$404$	−14.2142	−	24.6197i	−0.707183	−	1.22488i
$405$	−9.22670			−0.458478
$406$	−41.9215	−	26.6850i	−2.08053	−	1.32436i
$407$	11.7076			0.580323
$408$	24.6228	+	42.6479i	1.21901	+	2.11139i
$409$	−0.355733	+	0.616147i	−0.0175898	+	0.0304665i	−0.874686	−	0.484689i	$-0.838933\pi$
$409$	−0.355733	+	0.616147i	−0.0175898	+	0.0304665i	0.857096	+	0.515156i	$0.172266\pi$
$410$	−4.76618	+	8.25526i	−0.235385	+	0.407698i
$411$	−16.4375	−	28.4706i	−0.810802	−	1.40435i
$412$	15.3582			0.756645
$413$	0.692270	−	15.9919i	0.0340644	−	0.786910i
$414$	4.24477			0.208619
$415$	−7.36736	−	12.7606i	−0.361650	−	0.626396i
$416$	−8.18143	+	14.1707i	−0.401128	+	0.694773i
$417$	−4.95562	+	8.58339i	−0.242678	+	0.420330i
$418$	−5.98945	−	10.3740i	−0.292954	−	0.507410i
$419$	28.8401			1.40893			0.704465	−	0.709739i	$-0.251187\pi$
$419$	28.8401			1.40893			0.704465	+	0.709739i	$0.251187\pi$
$420$	0.929636	−	21.4752i	0.0453616	−	1.04788i
$421$	−25.9579			−1.26511			−0.632556	−	0.774515i	$-0.717994\pi$
$421$	−25.9579			−1.26511			−0.632556	+	0.774515i	$0.717994\pi$
$422$	7.46253	+	12.9255i	0.363270	+	0.629203i
$423$	−3.57000	+	6.18342i	−0.173579	+	0.300648i
$424$	−11.1889	+	19.3798i	−0.543382	+	0.941166i
$425$	−3.27172	−	5.66679i	−0.158702	−	0.274880i
$426$	19.8782			0.963101
$427$	−0.779195	−	0.495995i	−0.0377079	−	0.0240029i
$428$	24.3127			1.17520
$429$	3.90180	+	6.75812i	0.188381	+	0.326285i
$430$	−5.32586	+	9.22466i	−0.256836	+	0.444853i
$431$	8.80210	−	15.2457i	0.423982	−	0.734359i	−0.572343	−	0.820015i	$-0.693965\pi$
$431$	8.80210	−	15.2457i	0.423982	−	0.734359i	0.996325	+	0.0856559i	$0.0272986\pi$
$432$	0.0442076	+	0.0765698i	0.00212694	+	0.00368397i
$433$	21.5929			1.03769			0.518845	−	0.854869i	$-0.326362\pi$
$433$	21.5929			1.03769			0.518845	+	0.854869i	$0.326362\pi$
$434$	17.1942	−	8.95883i	0.825346	−	0.430037i
$435$	19.7833			0.948535
$436$	9.56721	+	16.5709i	0.458186	+	0.793602i
$437$	1.62960	−	2.82256i	0.0779545	−	0.135021i
$438$	−4.85734	+	8.41315i	−0.232092	+	0.401996i
$439$	13.5456	+	23.4616i	0.646495	+	1.11976i	0.983954	+	0.178422i	$0.0570991\pi$
$439$	13.5456	+	23.4616i	0.646495	+	1.11976i	−0.337459	+	0.941340i	$0.609568\pi$
$440$	3.09251			0.147429
$441$	−20.3805	−	1.76781i	−0.970499	−	0.0841812i
$442$	−48.4796			−2.30594
$443$	14.6550	+	25.3832i	0.696279	+	1.20599i	0.969747	+	0.244110i	$0.0784959\pi$
$443$	14.6550	+	25.3832i	0.696279	+	1.20599i	−0.273468	+	0.961881i	$0.588171\pi$
$444$	47.5589	−	82.3745i	2.25705	−	3.90932i
$445$	2.72994	−	4.72840i	0.129412	−	0.224148i
$446$	14.1916	+	24.5807i	0.671994	+	1.16393i
$447$	16.2970			0.770821
$448$	29.8619	−	15.5592i	1.41084	−	0.735105i
$449$	8.65218			0.408322			0.204161	−	0.978937i	$-0.434553\pi$
$449$	8.65218			0.408322			0.204161	+	0.978937i	$0.434553\pi$
$450$	3.37615	+	5.84766i	0.159153	+	0.275661i
$451$	−2.06283	+	3.57292i	−0.0971347	+	0.168242i
$452$	−5.93511	+	10.2799i	−0.279164	+	0.483526i
$453$	27.0058	+	46.7755i	1.26884	+	2.19770i
$454$	21.4903			1.00859
$455$	7.15692	+	4.55572i	0.335521	+	0.213576i
$456$	−39.0184			−1.82720
$457$	−8.67466	−	15.0250i	−0.405783	−	0.702838i	0.588629	−	0.808403i	$-0.299668\pi$
$457$	−8.67466	−	15.0250i	−0.405783	−	0.702838i	−0.994412	+	0.105566i	$0.966335\pi$
$458$	−26.3160	+	45.5807i	−1.22967	+	2.12985i
$459$	0.617627	−	1.06976i	0.0288284	−	0.0499322i
$460$	1.04934	+	1.81752i	0.0489259	+	0.0847422i
$461$	6.29921			0.293383			0.146692	−	0.989182i	$-0.453137\pi$
$461$	6.29921			0.293383			0.146692	+	0.989182i	$0.453137\pi$
$462$	0.643392	−	14.8628i	0.0299333	−	0.691479i
$463$	−30.2281			−1.40482			−0.702409	−	0.711774i	$-0.747892\pi$
$463$	−30.2281			−1.40482			−0.702409	+	0.711774i	$0.747892\pi$
$464$	−1.90369	−	3.29728i	−0.0883764	−	0.153072i
$465$	−3.85922	+	6.68436i	−0.178967	+	0.309980i
$466$	19.9596	−	34.5711i	0.924611	−	1.60147i
$467$	4.86043	+	8.41851i	0.224914	+	0.389562i	0.956294	−	0.292408i	$-0.0944566\pi$
$467$	4.86043	+	8.41851i	0.224914	+	0.389562i	−0.731380	+	0.681970i	$0.761123\pi$
$468$	31.2849			1.44614
$469$	0.249768	−	5.76980i	0.0115332	−	0.266425i
$470$	−5.64497			−0.260383
$471$	3.70666	+	6.42013i	0.170794	+	0.295824i
$472$	9.35487	−	16.2031i	0.430593	−	0.745809i
$473$	−2.30506	+	3.99248i	−0.105987	+	0.183574i
$474$	−40.9304	−	70.8935i	−1.87999	−	3.25625i
$475$	5.18453			0.237882
$476$	48.7565	+	31.0359i	2.23475	+	1.42253i
$477$	−21.1472			−0.968262
$478$	−15.2974	−	26.4959i	−0.699687	−	1.21189i
$479$	8.02319	−	13.8966i	0.366589	−	0.634951i	−0.622441	−	0.782667i	$-0.713859\pi$
$479$	8.02319	−	13.8966i	0.366589	−	0.634951i	0.989030	+	0.147716i	$0.0471922\pi$
$480$	−6.20918	+	10.7546i	−0.283409	+	0.490879i
$481$	18.7708	+	32.5119i	0.855873	+	1.48242i
$482$	51.2647			2.33505
$483$	3.58961	−	1.87033i	0.163333	−	0.0851028i
$484$	3.33845			0.151748
$485$	−9.73362	−	16.8591i	−0.441981	−	0.765534i
$486$	−25.2860	+	43.7966i	−1.14699	+	1.98665i
$487$	−10.5127	+	18.2085i	−0.476375	+	0.825105i	−0.999634	−	0.0270687i	$-0.991383\pi$
$487$	−10.5127	+	18.2085i	−0.476375	+	0.825105i	0.523259	+	0.852174i	$0.324716\pi$
$488$	−0.539816	−	0.934988i	−0.0244363	−	0.0423249i
$489$	−33.4486			−1.51260
$490$	−6.84613	−	14.6531i	−0.309277	−	0.661962i
$491$	−29.5538			−1.33375			−0.666873	−	0.745172i	$-0.732368\pi$
$491$	−29.5538			−1.33375			−0.666873	+	0.745172i	$0.732368\pi$
$492$	16.7594	+	29.0281i	0.755571	+	1.30869i
$493$	−26.5965	+	46.0665i	−1.19785	+	2.07473i
$494$	19.2058	−	33.2654i	0.864109	−	1.49668i
$495$	1.46121	+	2.53090i	0.0656767	+	0.113755i
$496$	1.48544			0.0666984
$497$	8.29493	−	4.32199i	0.372079	−	0.193868i
$498$	−82.8514			−3.71266
$499$	16.2949	+	28.2237i	0.729462	+	1.26346i	0.957111	+	0.289722i	$0.0935628\pi$
$499$	16.2949	+	28.2237i	0.729462	+	1.26346i	−0.227649	+	0.973743i	$0.573104\pi$
$500$	−1.66923	+	2.89118i	−0.0746501	+	0.129298i
$501$	5.73890	−	9.94007i	0.256395	−	0.444090i
$502$	2.72057	+	4.71216i	0.121425	+	0.210314i
$503$	−41.3000			−1.84148			−0.920739	−	0.390180i	$-0.872413\pi$
$503$	−41.3000			−1.84148			−0.920739	+	0.390180i	$0.872413\pi$
$504$	−20.1714	−	12.8400i	−0.898504	−	0.571941i
$505$	8.51545			0.378933
$506$	0.726241	+	1.25789i	0.0322853	+	0.0559198i
$507$	3.30691	−	5.72773i	0.146865	−	0.254378i
$508$	−20.4778	+	35.4686i	−0.908555	+	1.57366i
$509$	15.1791	+	26.2909i	0.672800	+	1.16532i	0.977107	+	0.212749i	$0.0682418\pi$
$509$	15.1791	+	26.2909i	0.672800	+	1.16532i	−0.304307	+	0.952574i	$0.598425\pi$
$510$	−36.7929			−1.62922
$511$	−0.197692	+	4.56681i	−0.00874537	+	0.202024i
$512$	5.28676			0.233644
$513$	0.489361	+	0.847597i	0.0216058	+	0.0374223i
$514$	14.7120	−	25.4820i	0.648919	−	1.12396i
$515$	−2.30020	+	3.98406i	−0.101359	+	0.175559i
$516$	18.7274	+	32.4368i	0.824427	+	1.42795i
$517$	−2.44317			−0.107451
$518$	3.09523	−	71.5018i	0.135996	−	3.14161i
$519$	47.3474			2.07832
$520$	4.95822	+	8.58788i	0.217432	+	0.376604i
$521$	11.9599	−	20.7152i	0.523973	−	0.907548i	−0.475637	−	0.879641i	$-0.657783\pi$
$521$	11.9599	−	20.7152i	0.523973	−	0.907548i	0.999611	−	0.0279068i	$-0.00888415\pi$
$522$	27.4454	−	47.5368i	1.20125	−	2.08063i
$523$	−5.88222	−	10.1883i	−0.257212	−	0.445504i	0.708282	−	0.705929i	$-0.249470\pi$
$523$	−5.88222	−	10.1883i	−0.257212	−	0.445504i	−0.965494	+	0.260426i	$0.916137\pi$
$524$	−38.5827			−1.68549
$525$	5.43164	+	3.45750i	0.237056	+	0.150898i
$526$	−23.0027			−1.00297
$527$	−10.3766	−	17.9728i	−0.452012	−	0.782909i
$528$	0.569898	−	0.987092i	0.0248016	−	0.0429577i
$529$	11.3024	−	19.5763i	0.491409	−	0.851145i
$530$	−8.35961	−	14.4793i	−0.363118	−	0.628939i
$531$	17.6808			0.767281
$532$	−40.6114	+	21.1601i	−1.76073	+	0.917409i
$533$	−13.2293			−0.573026
$534$	−15.3501	−	26.5871i	−0.664264	−	1.15054i
$535$	−3.64132	+	6.30695i	−0.157428	+	0.272673i
$536$	3.37519	−	5.84601i	0.145786	−	0.252509i
$537$	10.7002	+	18.5332i	0.461746	+	0.799767i
$538$	−29.1037			−1.25475
$539$	−2.96304	−	6.34196i	−0.127627	−	0.273167i
$540$	−0.630224			−0.0271205
$541$	−15.3134	−	26.5236i	−0.658376	−	1.14034i	−0.981036	−	0.193825i	$-0.937911\pi$
$541$	−15.3134	−	26.5236i	−0.658376	−	1.14034i	0.322661	−	0.946515i	$-0.395423\pi$
$542$	31.9584	−	55.3536i	1.37273	−	2.37764i
$543$	−26.7911	+	46.4035i	−1.14972	+	1.99136i
$544$	−16.6952	−	28.9169i	−0.715799	−	1.23980i
$545$	−5.73153			−0.245512
$546$	42.3055	−	22.0428i	1.81051	−	0.943345i
$547$	31.1658			1.33255			0.666276	−	0.745705i	$-0.267887\pi$
$547$	31.1658			1.33255			0.666276	+	0.745705i	$0.267887\pi$
$548$	−22.5492	−	39.0563i	−0.963253	−	1.66840i
$549$	0.510128	−	0.883567i	0.0217717	−	0.0377097i
$550$	−1.15525	+	2.00096i	−0.0492602	+	0.0853212i
$551$	−21.0730	−	36.4996i	−0.897742	−	1.55493i
$552$	4.73111			0.201370
$553$	−32.4937	−	20.6838i	−1.38177	−	0.879565i
$554$	−60.6416			−2.57641
$555$	14.2458	+	24.6744i	0.604701	+	1.04737i
$556$	−6.79819	+	11.7748i	−0.288307	+	0.499363i
$557$	−3.25005	+	5.62925i	−0.137709	+	0.238519i	−0.926629	−	0.375977i	$-0.877307\pi$
$557$	−3.25005	+	5.62925i	−0.137709	+	0.238519i	0.788920	+	0.614496i	$0.210641\pi$
$558$	10.7078	+	18.5465i	0.453298	+	0.785135i
$559$	−14.7828			−0.625246
$560$	0.0535914	−	1.23800i	0.00226465	−	0.0523149i
$561$	−15.9242			−0.672319
$562$	6.81152	+	11.7979i	0.287327	+	0.497665i
$563$	0.816053	−	1.41344i	0.0343925	−	0.0595696i	−0.848317	−	0.529489i	$-0.822384\pi$
$563$	0.816053	−	1.41344i	0.0343925	−	0.0595696i	0.882709	+	0.469919i	$0.155717\pi$
$564$	−9.92474	+	17.1902i	−0.417907	+	0.723836i
$565$	−1.77780	−	3.07924i	−0.0747927	−	0.129545i
$566$	−43.5856			−1.83204
$567$	−1.05576	+	24.3887i	−0.0443376	+	1.02423i
$568$	10.9328			0.458728
$569$	−13.3266	−	23.0824i	−0.558680	−	0.967663i	−0.997607	−	0.0691398i	$-0.977975\pi$
$569$	−13.3266	−	23.0824i	−0.558680	−	0.967663i	0.438927	−	0.898523i	$-0.355359\pi$
$570$	14.5759	−	25.2463i	0.610519	−	1.05745i
$571$	19.9139	−	34.4918i	0.833370	−	1.44344i	−0.0619810	−	0.998077i	$-0.519742\pi$
$571$	19.9139	−	34.4918i	0.833370	−	1.44344i	0.895351	−	0.445362i	$-0.146925\pi$
$572$	5.35254	+	9.27088i	0.223801	+	0.387635i
$573$	27.6209			1.15388
$574$	21.2756	+	13.5429i	0.888025	+	0.565271i
$575$	−0.628641			−0.0262162
$576$	18.5968	+	32.2106i	0.774866	+	1.34211i
$577$	13.3096	−	23.0529i	0.554085	−	0.959703i	−0.443889	−	0.896082i	$-0.646402\pi$
$577$	13.3096	−	23.0529i	0.554085	−	0.959703i	0.997974	−	0.0636217i	$-0.0202651\pi$
$578$	29.8249	−	51.6582i	1.24055	−	2.14870i
$579$	1.05044	+	1.81941i	0.0436547	+	0.0756122i
$580$	27.1390			1.12688
$581$	−34.5729	+	18.0138i	−1.43433	+	0.747340i
$582$	−109.462			−4.53733
$583$	−3.61808	−	6.26670i	−0.149846	−	0.259540i
$584$	−2.67147	+	4.62713i	−0.110546	+	0.191472i
$585$	−4.68553	+	8.11558i	−0.193723	+	0.335538i
$586$	−23.3849	−	40.5038i	−0.966020	−	1.67320i
$587$	19.0155			0.784853			0.392427	−	0.919783i	$-0.371636\pi$
$587$	19.0155			0.784853			0.392427	+	0.919783i	$0.371636\pi$
$588$	−56.6585	−	4.91457i	−2.33656	−	0.202673i
$589$	16.4433			0.677533
$590$	6.98932	+	12.1059i	0.287746	+	0.498391i
$591$	27.1424	−	47.0121i	1.11649	−	1.93382i
$592$	2.74166	−	4.74870i	0.112682	−	0.195170i
$593$	−19.6537	−	34.0412i	−0.807080	−	1.39790i	−0.914878	−	0.403731i	$-0.867713\pi$
$593$	−19.6537	−	34.0412i	−0.807080	−	1.39790i	0.107797	−	0.994173i	$-0.465620\pi$
$594$	−0.436172			−0.0178963
$595$	−15.3533	+	7.99965i	−0.629422	+	0.327954i
$596$	22.3564			0.915755
$597$	22.3809	+	38.7649i	0.915991	+	1.58654i
$598$	−2.32876	+	4.03354i	−0.0952303	+	0.164944i
$599$	−3.42145	+	5.92613i	−0.139797	+	0.242135i	−0.927420	−	0.374023i	$-0.877978\pi$
$599$	−3.42145	+	5.92613i	−0.139797	+	0.242135i	0.787623	+	0.616158i	$0.211312\pi$
$600$	3.76297	+	6.51765i	0.153622	+	0.266082i
$601$	0.192760			0.00786285			0.00393143	−	0.999992i	$-0.498749\pi$
$601$	0.192760			0.00786285			0.00393143	+	0.999992i	$0.498749\pi$
$602$	23.7739	+	15.1332i	0.968952	+	0.616785i
$603$	6.37914			0.259779
$604$	37.0470	+	64.1672i	1.50742	+	2.61093i
$605$	−0.500000	+	0.866025i	−0.0203279	+	0.0352089i
$606$	23.9406	−	41.4664i	0.972521	−	1.68446i
$607$	19.6257	+	33.9928i	0.796585	+	1.37973i	0.921828	+	0.387599i	$0.126695\pi$
$607$	19.6257	+	33.9928i	0.796585	+	1.37973i	−0.125243	+	0.992126i	$0.539971\pi$
$608$	26.4560			1.07293
$609$	2.26368	−	52.2926i	0.0917291	−	2.11900i
$610$	0.806627			0.0326594
$611$	−3.91714	−	6.78469i	−0.158471	−	0.274479i
$612$	−31.9202	+	55.2874i	−1.29030	+	2.23486i
$613$	15.3514	−	26.5894i	0.620037	−	1.07393i	−0.369442	−	0.929254i	$-0.620451\pi$
$613$	15.3514	−	26.5894i	0.620037	−	1.07393i	0.989478	−	0.144681i	$-0.0462156\pi$
$614$	−25.0022	−	43.3051i	−1.00901	−	1.74765i
$615$	−10.0402			−0.404860
$616$	0.353857	−	8.17434i	0.0142573	−	0.329354i
$617$	5.45361			0.219554			0.109777	−	0.993956i	$-0.464986\pi$
$617$	5.45361			0.219554			0.109777	+	0.993956i	$0.464986\pi$
$618$	12.9337	+	22.4018i	0.520270	+	0.901134i
$619$	−4.71027	+	8.15842i	−0.189322	+	0.327915i	−0.945024	−	0.327000i	$-0.893962\pi$
$619$	−4.71027	+	8.15842i	−0.189322	+	0.327915i	0.755703	+	0.654915i	$0.227296\pi$
$620$	−5.29413	+	9.16970i	−0.212617	+	0.368264i
$621$	−0.0593366	−	0.102774i	−0.00238110	−	0.00412418i
$622$	−43.4611			−1.74263
$623$	−12.1861	−	7.75703i	−0.488225	−	0.310779i
$624$	3.65487			0.146312
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	−36.3986	+	63.0442i	−1.45478	+	2.51975i
$627$	6.30854	−	10.9267i	0.251939	−	0.436371i
$628$	5.08485	+	8.80722i	0.202908	+	0.351446i
$629$	−76.6079			−3.05456
$630$	15.8433	−	8.25498i	0.631212	−	0.328886i
$631$	−8.00713			−0.318759			−0.159379	−	0.987217i	$-0.550949\pi$
$631$	−8.00713			−0.318759			−0.159379	+	0.987217i	$0.550949\pi$
$632$	−22.5112	−	38.9905i	−0.895447	−	1.55096i
$633$	−7.86011	+	13.6141i	−0.312411	+	0.541112i
$634$	21.2766	−	36.8521i	0.845001	−	1.46358i
$635$	−6.13392	−	10.6243i	−0.243417	−	0.421611i
$636$	−58.7900			−2.33117
$637$	12.8610	−	18.3964i	0.509570	−	0.728893i
$638$	18.7826			0.743610
$639$	5.16575	+	8.94733i	0.204354	+	0.353951i
$640$	−9.59998	+	16.6277i	−0.379473	+	0.657266i
$641$	10.0144	−	17.3454i	0.395544	−	0.685102i	−0.597627	−	0.801775i	$-0.703889\pi$
$641$	10.0144	−	17.3454i	0.395544	−	0.685102i	0.993170	+	0.116672i	$0.0372228\pi$
$642$	20.4746	+	35.4631i	0.808069	+	1.39962i
$643$	20.2186			0.797344			0.398672	−	0.917094i	$-0.369471\pi$
$643$	20.2186			0.797344			0.398672	+	0.917094i	$0.369471\pi$
$644$	4.92427	−	2.56574i	0.194043	−	0.101104i
$645$	−11.2192			−0.441756
$646$	39.1916	+	67.8819i	1.54197	+	2.67078i
$647$	−6.59157	+	11.4169i	−0.259141	+	0.448846i	−0.966012	−	0.258497i	$-0.916773\pi$
$647$	−6.59157	+	11.4169i	−0.259141	+	0.448846i	0.706871	+	0.707343i	$0.250106\pi$
$648$	−14.2668	+	24.7108i	−0.560453	+	0.970733i
$649$	3.02502	+	5.23948i	0.118742	+	0.205668i
$650$	−7.40888			−0.290600
$651$	17.2270	+	10.9658i	0.675180	+	0.429785i
$652$	−45.8853			−1.79701
$653$	13.2527	+	22.9543i	0.518618	+	0.898272i	0.999766	+	0.0216330i	$0.00688652\pi$
$653$	13.2527	+	22.9543i	0.518618	+	0.898272i	−0.481148	+	0.876639i	$0.659780\pi$
$654$	−16.1138	+	27.9099i	−0.630099	+	1.09136i
$655$	5.77853	−	10.0087i	0.225786	−	0.391072i
$656$	0.966139	+	1.67340i	0.0377214	+	0.0653354i
$657$	−5.04911			−0.196984
$658$	−0.645922	+	14.9212i	−0.0251806	+	0.581690i
$659$	50.0915			1.95129			0.975644	−	0.219360i	$-0.0703968\pi$
$659$	50.0915			1.95129			0.975644	+	0.219360i	$0.0703968\pi$
$660$	4.06224	+	7.03600i	0.158122	+	0.273876i
$661$	2.55591	−	4.42696i	0.0994133	−	0.172189i	−0.812029	−	0.583618i	$-0.801637\pi$
$661$	2.55591	−	4.42696i	0.0994133	−	0.172189i	0.911442	+	0.411429i	$0.134970\pi$
$662$	−19.4942	+	33.7650i	−0.757664	+	1.31231i
$663$	−25.5312	−	44.2214i	−0.991550	−	1.71742i
$664$	−45.5672			−1.76835
$665$	0.593235	−	13.7041i	0.0230047	−	0.531424i
$666$	79.0530			3.06324
$667$	2.55518	+	4.42570i	0.0989368	+	0.171364i
$668$	7.87271	−	13.6359i	0.304604	−	0.527590i
$669$	−14.9477	+	25.8902i	−0.577912	+	1.00097i
$670$	2.52171	+	4.36774i	0.0974223	+	0.168740i
$671$	0.349112			0.0134773
$672$	27.7169	+	17.6432i	1.06920	+	0.680600i
$673$	−27.1170			−1.04528			−0.522642	−	0.852552i	$-0.675054\pi$
$673$	−27.1170			−1.04528			−0.522642	+	0.852552i	$0.675054\pi$
$674$	20.7599	+	35.9572i	0.799641	+	1.38502i
$675$	0.0943886	−	0.163486i	0.00363302	−	0.00629258i
$676$	4.53646	−	7.85738i	0.174479	−	0.302207i
$677$	10.0105	+	17.3388i	0.384736	+	0.666382i	0.991733	−	0.128322i	$-0.0409591\pi$
$677$	10.0105	+	17.3388i	0.384736	+	0.666382i	−0.606996	+	0.794705i	$0.707626\pi$
$678$	−19.9927			−0.767814
$679$	−45.6771	+	23.7996i	−1.75293	+	0.913343i
$680$	−20.2356			−0.776001
$681$	11.3176	+	19.6027i	0.433692	+	0.751177i
$682$	−3.66401	+	6.34625i	−0.140302	+	0.243011i
$683$	−5.80852	+	10.0607i	−0.222257	+	0.384960i	−0.955493	−	0.295014i	$-0.904676\pi$
$683$	−5.80852	+	10.0607i	−0.222257	+	0.384960i	0.733236	+	0.679974i	$0.238009\pi$
$684$	−25.2911	−	43.8055i	−0.967031	−	1.67495i
$685$	13.5088			0.516143
$686$	−39.5157	+	16.4195i	−1.50872	+	0.626901i
$687$	−55.4361			−2.11502
$688$	1.07959	+	1.86991i	0.0411590	+	0.0712895i
$689$	11.6017	−	20.0948i	0.441991	−	0.765551i
$690$	−1.76738	+	3.06120i	−0.0672831	+	0.116538i
$691$	−11.4370	−	19.8095i	−0.435085	−	0.753590i	0.562217	−	0.826990i	$-0.309948\pi$
$691$	−11.4370	−	19.8095i	−0.435085	−	0.753590i	−0.997303	+	0.0733997i	$0.976615\pi$
$692$	64.9519			2.46910
$693$	6.85706	−	3.57280i	0.260478	−	0.135719i
$694$	3.86262			0.146623
$695$	−2.03633	−	3.52703i	−0.0772424	−	0.133788i
$696$	30.5899	−	52.9833i	1.15951	−	2.00833i
$697$	13.4980	−	23.3792i	0.511273	−	0.885551i
$698$	−12.4394	−	21.5456i	−0.470837	−	0.815513i
$699$	42.0460			1.59032
$700$	7.45120	+	4.74305i	0.281629	+	0.179270i
$701$	21.6055			0.816030			0.408015	−	0.912975i	$-0.366221\pi$
$701$	21.6055			0.816030			0.408015	+	0.912975i	$0.366221\pi$
$702$	−0.699314	−	1.21125i	−0.0263939	−	0.0457156i
$703$	30.3491	−	52.5662i	1.14464	−	1.98257i
$704$	−6.36347	+	11.0218i	−0.239832	+	0.415402i
$705$	−2.97286	−	5.14914i	−0.111964	−	0.193928i
$706$	19.0312			0.716250
$707$	0.974374	−	22.5087i	0.0366451	−	0.846526i
$708$	49.1533			1.84729
$709$	11.3262	+	19.6176i	0.425366	+	0.736755i	0.996455	−	0.0841332i	$-0.0268121\pi$
$709$	11.3262	+	19.6176i	0.425366	+	0.736755i	−0.571089	+	0.820888i	$0.693479\pi$
$710$	−4.08410	+	7.07387i	−0.153274	+	0.265478i
$711$	21.2732	−	36.8462i	0.797806	−	1.38184i
$712$	−8.44236	−	14.6226i	−0.316391	−	0.548005i
$713$	−1.99380			−0.0746685
$714$	−4.21000	+	97.2538i	−0.157555	+	3.63963i
$715$	−3.20660			−0.119920
$716$	14.6786	+	25.4241i	0.548566	+	0.950144i
$717$	16.1124	−	27.9075i	0.601728	−	1.04222i
$718$	21.3178	−	36.9235i	0.795574	−	1.37797i
$719$	−1.49735	−	2.59348i	−0.0558416	−	0.0967204i	0.836753	−	0.547580i	$-0.184451\pi$
$719$	−1.49735	−	2.59348i	−0.0558416	−	0.0967204i	−0.892595	+	0.450860i	$0.851118\pi$
$720$	1.36874			0.0510099
$721$	10.2678	+	6.53594i	0.382392	+	0.243411i
$722$	−18.2052			−0.677529
$723$	26.9980	+	46.7619i	1.00407	+	1.73909i
$724$	−36.7524	+	63.6570i	−1.36589	+	2.36579i
$725$	−4.06460	+	7.04010i	−0.150956	+	0.261463i
$726$	2.81143	+	4.86954i	0.104342	+	0.180726i
$727$	2.41320			0.0895005			0.0447502	−	0.998998i	$-0.485751\pi$
$727$	2.41320			0.0895005			0.0447502	+	0.998998i	$0.485751\pi$
$728$	23.2675	−	12.1233i	0.862350	−	0.449318i
$729$	−25.5861			−0.947635
$730$	−1.99594	−	3.45708i	−0.0738732	−	0.127952i
$731$	15.0830	−	26.1246i	0.557866	−	0.966252i
$732$	1.41818	−	2.45635i	0.0524173	−	0.0907894i
$733$	7.03998	+	12.1936i	0.260027	+	0.450381i	0.966249	−	0.257610i	$-0.0829350\pi$
$733$	7.03998	+	12.1936i	0.260027	+	0.450381i	−0.706221	+	0.707991i	$0.749602\pi$
$734$	30.8842			1.13996
$735$	9.76064	−	13.9617i	0.360026	−	0.514985i
$736$	−3.20787			−0.118244
$737$	1.09141	+	1.89038i	0.0402026	+	0.0696330i
$738$	−13.9288	+	24.1254i	−0.512727	+	0.888069i
$739$	14.5375	−	25.1797i	0.534770	−	0.926249i	−0.464405	−	0.885623i	$-0.653732\pi$
$739$	14.5375	−	25.1797i	0.534770	−	0.926249i	0.999174	−	0.0406255i	$-0.0129351\pi$
$740$	19.5426	+	33.8488i	0.718400	+	1.24430i
$741$	40.4580			1.48626
$742$	−39.2292	+	20.4400i	−1.44015	+	0.750375i
$743$	−22.4717			−0.824408			−0.412204	−	0.911092i	$-0.635241\pi$
$743$	−22.4717			−0.824408			−0.412204	+	0.911092i	$0.635241\pi$
$744$	11.9346	+	20.6714i	0.437545	+	0.757851i
$745$	−3.34832	+	5.79946i	−0.122673	+	0.212476i
$746$	25.7208	−	44.5498i	0.941707	−	1.63108i
$747$	−21.5306	−	37.2921i	−0.787763	−	1.36445i
$748$	−21.8450			−0.798732
$749$	16.2543	+	10.3467i	0.593921	+	0.378059i
$750$	−5.62286			−0.205318
$751$	15.1907	+	26.3110i	0.554315	+	0.960102i	0.997956	+	0.0638973i	$0.0203530\pi$
$751$	15.1907	+	26.3110i	0.554315	+	0.960102i	−0.443642	+	0.896204i	$0.646314\pi$
$752$	−0.572139	+	0.990974i	−0.0208638	+	0.0361371i
$753$	−2.86551	+	4.96321i	−0.104425	+	0.180869i
$754$	30.1142	+	52.1592i	1.09669	+	1.89953i
$755$	−22.1941			−0.807726
$756$	−0.0721129	+	1.66586i	−0.00262272	+	0.0605866i
$757$	27.7970			1.01030			0.505149	−	0.863032i	$-0.331437\pi$
$757$	27.7970			1.01030			0.505149	+	0.863032i	$0.331437\pi$
$758$	−13.4705	−	23.3316i	−0.489270	−	0.847441i
$759$	−0.764932	+	1.32490i	−0.0277653	+	0.0480909i
$760$	8.01659	−	13.8851i	0.290792	−	0.503667i
$761$	11.6817	+	20.2332i	0.423460	+	0.733455i	0.996275	−	0.0862301i	$-0.0274820\pi$
$761$	11.6817	+	20.2332i	0.423460	+	0.733455i	−0.572815	+	0.819685i	$0.694149\pi$
$762$	−68.9804			−2.49889
$763$	−0.655825	+	15.1500i	−0.0237425	+	0.548467i
$764$	37.8907			1.37084
$765$	−9.56138	−	16.5608i	−0.345692	−	0.598757i
$766$	6.61256	−	11.4533i	0.238922	−	0.413824i
$767$	−9.70002	+	16.8009i	−0.350247	+	0.606646i
$768$	23.0071	+	39.8494i	0.830196	+	1.43794i
$769$	−14.6465			−0.528165			−0.264082	−	0.964500i	$-0.585069\pi$
$769$	−14.6465			−0.528165			−0.264082	+	0.964500i	$0.585069\pi$
$770$	5.15690	+	3.28261i	0.185842	+	0.118297i
$771$	30.9916			1.11614
$772$	1.44100	+	2.49589i	0.0518629	+	0.0898292i
$773$	22.6241	−	39.1862i	0.813734	−	1.40943i	−0.0964993	−	0.995333i	$-0.530765\pi$
$773$	22.6241	−	39.1862i	0.813734	−	1.40943i	0.910233	−	0.414096i	$-0.135902\pi$
$774$	−15.5644	+	26.9584i	−0.559453	+	0.969000i
$775$	−1.58580	−	2.74669i	−0.0569637	−	0.0986640i
$776$	−60.2026			−2.16115
$777$	66.8514	−	34.8322i	2.39828	−	1.24960i
$778$	−12.4562			−0.446577
$779$	10.6948	+	18.5239i	0.383180	+	0.663687i
$780$	−13.0260	+	22.5616i	−0.466405	+	0.807836i
$781$	−1.76762	+	3.06161i	−0.0632504	+	0.109553i
$782$	−4.75212	−	8.23091i	−0.169935	−	0.294337i
$783$	−1.53461			−0.0548424
$784$	−3.26624	−	0.283314i	−0.116651	−	0.0101183i
$785$	−3.04623			−0.108725
$786$	−32.4919	−	56.2776i	−1.15895	−	2.00735i
$787$	10.1147	−	17.5191i	0.360549	−	0.624488i	−0.627503	−	0.778614i	$-0.715923\pi$
$787$	10.1147	−	17.5191i	0.360549	−	0.624488i	0.988051	+	0.154126i	$0.0492562\pi$
$788$	37.2344	−	64.4919i	1.32642	−	2.29743i
$789$	−12.1141	−	20.9823i	−0.431274	−	0.746989i
$790$	33.6377			1.19677
$791$	−8.34271	+	4.34688i	−0.296633	+	0.154557i
$792$	9.03763			0.321138
$793$	0.559732	+	0.969484i	0.0198767	+	0.0344274i
$794$	−6.96026	+	12.0555i	−0.247010	+	0.427835i
$795$	8.80497	−	15.2507i	0.312280	−	0.540885i
$796$	30.7025	+	53.1782i	1.08822	+	1.88485i
$797$	−47.5120			−1.68296			−0.841481	−	0.540287i	$-0.818316\pi$
$797$	−47.5120			−1.68296			−0.841481	+	0.540287i	$0.818316\pi$
$798$	−65.0650	−	41.4170i	−2.30328	−	1.46615i
$799$	15.9868			0.565571
$800$	−2.55143	−	4.41921i	−0.0902068	−	0.156243i
$801$	7.97806	−	13.8184i	0.281891	−	0.488250i
$802$	8.50317	−	14.7279i	0.300257	−	0.520061i
$803$	−0.863854	−	1.49624i	−0.0304848	−	0.0528011i
$804$	17.7343			0.625440
$805$	−0.0719318	+	1.66167i	−0.00253526	+	0.0585663i
$806$	−23.4981			−0.827684
$807$	−15.3271	−	26.5474i	−0.539541	−	0.934512i
$808$	13.1670	−	22.8060i	0.463215	−	0.802311i
$809$	−19.0776	+	33.0434i	−0.670733	+	1.16174i	0.306963	+	0.951721i	$0.400687\pi$
$809$	−19.0776	+	33.0434i	−0.670733	+	1.16174i	−0.977697	+	0.210023i	$0.932646\pi$
$810$	−10.6592	−	18.4622i	−0.374525	−	0.648697i
$811$	−15.3906			−0.540435			−0.270218	−	0.962799i	$-0.587096\pi$
$811$	−15.3906			−0.540435			−0.270218	+	0.962799i	$0.587096\pi$
$812$	3.10535	−	71.7357i	0.108977	−	2.51743i
$813$	67.3220			2.36109
$814$	13.5252	+	23.4264i	0.474059	+	0.821094i
$815$	6.87224	−	11.9031i	0.240724	−	0.416947i
$816$	−3.72910	+	6.45899i	−0.130545	+	0.226110i
$817$	11.9506	+	20.6991i	0.418100	+	0.724171i
$818$	−1.64385			−0.0574758
$819$	20.9156	+	13.3138i	0.730850	+	0.465221i
$820$	−13.7733			−0.480984
$821$	19.5041	+	33.7822i	0.680699	+	1.17901i	0.974768	+	0.223221i	$0.0716571\pi$
$821$	19.5041	+	33.7822i	0.680699	+	1.17901i	−0.294069	+	0.955784i	$0.595010\pi$
$822$	37.9790	−	65.7815i	1.32467	−	2.29439i
$823$	7.15843	−	12.3988i	0.249527	−	0.432194i	−0.713868	−	0.700281i	$-0.753058\pi$
$823$	7.15843	−	12.3988i	0.249527	−	0.432194i	0.963395	+	0.268087i	$0.0863915\pi$
$824$	7.11338	+	12.3207i	0.247806	+	0.429213i
$825$	−2.43360			−0.0847272
$826$	32.7989	−	17.0895i	1.14122	−	0.594620i
$827$	−26.6302			−0.926024			−0.463012	−	0.886352i	$-0.653231\pi$
$827$	−26.6302			−0.926024			−0.463012	+	0.886352i	$0.653231\pi$
$828$	3.06663	+	5.31157i	0.106573	+	0.184590i
$829$	3.58880	−	6.21598i	0.124644	−	0.215890i	−0.796950	−	0.604046i	$-0.793554\pi$
$829$	3.58880	−	6.21598i	0.124644	−	0.215890i	0.921594	+	0.388156i	$0.126888\pi$
$830$	17.0224	−	29.4836i	0.590855	−	1.02339i
$831$	−31.9362	−	55.3151i	−1.10785	−	1.91886i
$832$	−40.8102			−1.41484
$833$	19.3885	+	41.4982i	0.671772	+	1.43783i
$834$	−22.9000			−0.792963
$835$	2.35819	+	4.08451i	0.0816086	+	0.141350i
$836$	8.65415	−	14.9894i	0.299310	−	0.518420i
$837$	0.299364	−	0.518513i	0.0103475	−	0.0179224i
$838$	33.3176	+	57.7078i	1.15094	+	1.99348i
$839$	13.9891			0.482957			0.241478	−	0.970406i	$-0.422368\pi$
$839$	13.9891			0.482957			0.241478	+	0.970406i	$0.422368\pi$
$840$	17.6585	−	9.20078i	0.609277	−	0.317457i
$841$	37.0839			1.27876
$842$	−29.9880	−	51.9407i	−1.03345	−	1.79000i
$843$	−7.17442	+	12.4265i	−0.247100	+	0.427990i
$844$	−10.7826	+	18.6760i	−0.371153	+	0.642855i
$845$	1.35885	+	2.35360i	0.0467459	+	0.0809663i
$846$	−16.4970			−0.567180
$847$	2.23193	+	1.42073i	0.0766901	+	0.0488169i
$848$	−3.38911			−0.116382
$849$	−22.9539	−	39.7572i	−0.787774	−	1.36446i
$850$	7.55935	−	13.0932i	0.259283	−	0.449092i
$851$	−3.67993	+	6.37383i	−0.126146	+	0.218492i
$852$	14.3610	+	24.8739i	0.491999	+	0.852167i
$853$	7.70058			0.263663			0.131831	−	0.991272i	$-0.457914\pi$
$853$	7.70058			0.263663			0.131831	+	0.991272i	$0.457914\pi$
$854$	0.0922976	−	2.13214i	0.00315836	−	0.0729602i
$855$	15.1514			0.518167
$856$	11.2608	+	19.5043i	0.384886	+	0.666642i
$857$	4.60377	−	7.97396i	0.157262	−	0.272385i	−0.776619	−	0.629971i	$-0.783067\pi$
$857$	4.60377	−	7.97396i	0.157262	−	0.272385i	0.933880	+	0.357586i	$0.116400\pi$
$858$	−9.01514	+	15.6147i	−0.307772	+	0.533077i
$859$	3.38878	+	5.86953i	0.115624	+	0.200266i	0.918029	−	0.396514i	$-0.129780\pi$
$859$	3.38878	+	5.86953i	0.115624	+	0.200266i	−0.802405	+	0.596779i	$0.796447\pi$
$860$	−15.3907			−0.524817
$861$	−1.14884	+	26.5390i	−0.0391524	+	0.904447i
$862$	40.6747			1.38538
$863$	24.9992	+	43.2999i	0.850982	+	1.47394i	0.880323	+	0.474375i	$0.157326\pi$
$863$	24.9992	+	43.2999i	0.850982	+	1.47394i	−0.0293409	+	0.999569i	$0.509341\pi$
$864$	0.481653	−	0.834247i	0.0163862	−	0.0283817i
$865$	−9.72784	+	16.8491i	−0.330757	+	0.572887i
$866$	24.9453	+	43.2065i	0.847676	+	1.46822i
$867$	62.8276			2.13374
$868$	23.6323	+	15.0431i	0.802131	+	0.510595i
$869$	14.5586			0.493865
$870$	22.8547	+	39.5855i	0.774847	+	1.34207i
$871$	−3.49972	+	6.06169i	−0.118584	+	0.205393i
$872$	−8.86239	+	15.3501i	−0.300118	+	0.519820i
$873$	−28.4458	−	49.2696i	−0.962745	−	1.66752i
$874$	7.53043			0.254721
$875$	−2.34636	+	1.22254i	−0.0793213	+	0.0413295i
$876$	−14.0367			−0.474257
$877$	−14.2961	−	24.7616i	−0.482745	−	0.836139i	0.517058	−	0.855950i	$-0.327027\pi$
$877$	−14.2961	−	24.7616i	−0.482745	−	0.836139i	−0.999804	+	0.0198107i	$0.993694\pi$
$878$	−31.2972	+	54.2083i	−1.05623	+	1.82944i
$879$	24.6307	−	42.6617i	0.830774	−	1.43894i
$880$	0.234179	+	0.405609i	0.00789416	+	0.0136731i
$881$	−51.5099			−1.73541			−0.867707	−	0.497077i	$-0.834407\pi$
$881$	−51.5099			−1.73541			−0.867707	+	0.497077i	$0.834407\pi$
$882$	−20.0073	−	42.8228i	−0.673682	−	1.44192i
$883$	−37.3621			−1.25733			−0.628667	−	0.777675i	$-0.716399\pi$
$883$	−37.3621			−1.25733			−0.628667	+	0.777675i	$0.716399\pi$
$884$	−35.0241	−	60.6635i	−1.17799	−	2.04033i
$885$	−7.36169	+	12.7508i	−0.247460	+	0.428614i
$886$	−33.8605	+	58.6481i	−1.13757	+	1.97032i
$887$	−15.9642	−	27.6508i	−0.536025	−	0.928423i	−0.999113	−	0.0421106i	$-0.986592\pi$
$887$	−15.9642	−	27.6508i	−0.536025	−	0.928423i	0.463088	−	0.886313i	$-0.346742\pi$
$888$	88.1104			2.95679
$889$	−28.7847	+	14.9980i	−0.965408	+	0.503016i
$890$	12.6151			0.422860
$891$	−4.61335	−	7.99055i	−0.154553	−	0.267694i
$892$	−20.5055	+	35.5166i	−0.686575	+	1.18918i
$893$	−6.33335	+	10.9697i	−0.211937	+	0.367086i
$894$	18.8272	+	32.6096i	0.629674	+	1.09063i
$895$	−8.79367			−0.293940
$896$	42.8530	+	27.2780i	1.43162	+	0.911294i
$897$	−4.90566			−0.163795
$898$	9.99547	+	17.3127i	0.333553	+	0.577731i
$899$	−12.8913	+	22.3284i	−0.429949	+	0.744694i
$900$	−4.87819	+	8.44928i	−0.162606	+	0.281643i
$901$	23.6747	+	41.0058i	0.788719	+	1.36610i
$902$	−9.53235			−0.317393
$903$	−1.28375	+	29.6554i	−0.0427205	+	0.986872i
$904$	−10.9957			−0.365712
$905$	−11.0088	−	19.0678i	−0.365945	−	0.633835i
$906$	−62.3972	+	108.075i	−2.07301	+	3.59055i
$907$	−4.63221	+	8.02323i	−0.153810	+	0.266407i	−0.932625	−	0.360847i	$-0.882488\pi$
$907$	−4.63221	+	8.02323i	−0.153810	+	0.266407i	0.778815	+	0.627254i	$0.215821\pi$
$908$	15.5257	+	26.8913i	0.515238	+	0.892418i
$909$	24.8858			0.825410
$910$	−0.847756	+	19.5837i	−0.0281028	+	0.649194i
$911$	45.6615			1.51283			0.756416	−	0.654090i	$-0.226948\pi$
$911$	45.6615			1.51283			0.756416	+	0.654090i	$0.226948\pi$
$912$	−2.95465	−	5.11761i	−0.0978383	−	0.169461i
$913$	7.36736	−	12.7606i	0.243824	−	0.422316i
$914$	20.0429	−	34.7153i	0.662960	−	1.14828i
$915$	0.424800	+	0.735776i	0.0140435	+	0.0243240i
$916$	−76.0480			−2.51270
$917$	−25.7945	−	16.4195i	−0.851811	−	0.542219i
$918$	2.85407			0.0941982
$919$	16.7543	+	29.0192i	0.552672	+	0.957256i	0.998081	+	0.0619289i	$0.0197252\pi$
$919$	16.7543	+	29.0192i	0.552672	+	0.957256i	−0.445408	+	0.895328i	$0.646941\pi$
$920$	−0.972038	+	1.68362i	−0.0320471	+	0.0555073i
$921$	26.3343	−	45.6123i	0.867743	−	1.50298i
$922$	7.27719	+	12.6045i	0.239662	+	0.415106i
$923$	−11.3361			−0.373133
$924$	19.0629	−	9.93252i	0.627123	−	0.326756i
$925$	−11.7076			−0.384943
$926$	−34.9211	−	60.4852i	−1.14758	−	1.98767i
$927$	−6.72217	+	11.6431i	−0.220785	+	0.382411i
$928$	−20.7411	+	35.9247i	−0.680861	+	1.17929i
$929$	15.8224	+	27.4051i	0.519115	+	0.899134i	0.999753	+	0.0222147i	$0.00707175\pi$
$929$	15.8224	+	27.4051i	0.519115	+	0.899134i	−0.480638	+	0.876919i	$0.659595\pi$
$930$	−17.8335			−0.584784
$931$	−36.1559	−	3.13617i	−1.18496	−	0.102784i
$932$	57.6792			1.88935
$933$	−22.8883	−	39.6436i	−0.749328	−	1.29787i
$934$	−11.2301	+	19.4510i	−0.367459	+	0.636457i
$935$	3.27172	−	5.66679i	0.106997	−	0.185324i
$936$	14.4900	+	25.0975i	0.473622	+	0.820337i
$937$	53.2220			1.73869			0.869343	−	0.494208i	$-0.164542\pi$
$937$	53.2220			1.73869			0.869343	+	0.494208i	$0.164542\pi$
$938$	11.8337	−	6.16581i	0.386383	−	0.201321i
$939$	−76.6756			−2.50221
$940$	−4.07821	−	7.06366i	−0.133016	−	0.230391i
$941$	−13.0773	+	22.6505i	−0.426306	+	0.738384i	−0.996541	−	0.0830974i	$-0.973519\pi$
$941$	−13.0773	+	22.6505i	−0.426306	+	0.738384i	0.570235	+	0.821482i	$0.306852\pi$
$942$	−8.56428	+	14.8338i	−0.279039	+	0.483310i
$943$	−1.29678	−	2.24608i	−0.0422289	−	0.0731426i
$944$	2.83357			0.0922250
$945$	−0.421338	−	0.268202i	−0.0137061	−	0.00872461i
$946$	−10.6517			−0.346317
$947$	−17.0258	−	29.4896i	−0.553265	−	0.958283i	−0.998036	−	0.0626387i	$-0.980048\pi$
$947$	−17.0258	−	29.4896i	−0.553265	−	0.958283i	0.444771	−	0.895644i	$-0.353285\pi$
$948$	59.1403	−	102.434i	1.92079	−	3.32690i
$949$	2.77004	−	4.79784i	0.0899192	−	0.155745i
$950$	5.98945	+	10.3740i	0.194323	+	0.336578i
$951$	44.8202			1.45340
$952$	−2.31545	+	53.4884i	−0.0750441	+	1.73357i
$953$	7.32161			0.237170			0.118585	−	0.992944i	$-0.462164\pi$
$953$	7.32161			0.237170			0.118585	+	0.992944i	$0.462164\pi$
$954$	−24.4304	−	42.3146i	−0.790962	−	1.36999i
$955$	−5.67489	+	9.82919i	−0.183635	+	0.318065i
$956$	22.1032	−	38.2839i	0.714869	−	1.23819i
$957$	9.89163	+	17.1328i	0.319751	+	0.553825i
$958$	37.0753			1.19785
$959$	1.54573	−	35.7074i	0.0499142	−	1.15305i
$960$	−30.9723			−0.999627
$961$	10.4705	+	18.1354i	0.337757	+	0.585012i
$962$	−43.3700	+	75.1191i	−1.39831	+	2.42194i
$963$	−10.6415	+	18.4316i	−0.342917	+	0.593950i
$964$	37.0362	+	64.1486i	1.19286	+	2.06609i
$965$	−0.863277			−0.0277899
$966$	7.88935	+	5.02195i	0.253836	+	0.161579i
$967$	−13.2356			−0.425629			−0.212814	−	0.977093i	$-0.568263\pi$
$967$	−13.2356			−0.425629			−0.212814	+	0.977093i	$0.568263\pi$
$968$	1.54625	+	2.67819i	0.0496984	+	0.0860802i
$969$	−41.2796	+	71.4984i	−1.32609	+	2.29686i
$970$	22.4896	−	38.9532i	0.722098	−	1.25071i
$971$	−20.6247	−	35.7230i	−0.661878	−	1.14641i	−0.980122	−	0.198398i	$-0.936426\pi$
$971$	−20.6247	−	35.7230i	−0.661878	−	1.14641i	0.318243	−	0.948009i	$-0.396907\pi$
$972$	−73.0713			−2.34376
$973$	−9.55591	+	4.97900i	−0.306348	+	0.159620i
$974$	−48.5792			−1.55658
$975$	−3.90180	−	6.75812i	−0.124958	−	0.216433i
$976$	0.0817546	−	0.141603i	0.00261690	−	0.00453260i
$977$	−14.2275	+	24.6427i	−0.455177	+	0.788390i	−0.998698	−	0.0510052i	$-0.983757\pi$
$977$	−14.2275	+	24.6427i	−0.455177	+	0.788390i	0.543521	+	0.839396i	$0.317091\pi$
$978$	−38.6417	−	66.9294i	−1.23563	−	2.14017i
$979$	5.45988			0.174499
$980$	13.3898	−	19.1529i	0.427721	−	0.611815i
$981$	−16.7500			−0.534786
$982$	−34.1422	−	59.1360i	−1.08952	−	1.88711i
$983$	1.77637	−	3.07676i	0.0566573	−	0.0981334i	−0.836306	−	0.548264i	$-0.815289\pi$
$983$	1.77637	−	3.07676i	0.0566573	−	0.0981334i	0.892963	+	0.450130i	$0.148622\pi$
$984$	−15.5247	+	26.8895i	−0.494909	+	0.857207i
$985$	11.1532	+	19.3179i	0.355370	+	0.615519i
$986$	−122.903			−3.91403
$987$	−13.9508	+	7.26890i	−0.444058	+	0.231372i
$988$	55.5008			1.76572
$989$	−1.44906	−	2.50984i	−0.0460773	−	0.0798082i
$990$	−3.37615	+	5.84766i	−0.107301	+	0.185851i
$991$	−19.8295	+	34.3456i	−0.629903	+	1.09102i	0.357667	+	0.933849i	$0.383572\pi$
$991$	−19.8295	+	34.3456i	−0.629903	+	1.09102i	−0.987571	+	0.157176i	$0.949761\pi$
$992$	−8.09214	−	14.0160i	−0.256926	−	0.445008i
$993$	−41.0656			−1.30318
$994$	18.2309	+	11.6048i	0.578248	+	0.368083i
$995$	−18.3932			−0.583105
$996$	−59.8559	−	103.674i	−1.89661	−	3.28502i
$997$	−26.1729	+	45.3328i	−0.828904	+	1.43570i	0.0699942	+	0.997547i	$0.477702\pi$
$997$	−26.1729	+	45.3328i	−0.828904	+	1.43570i	−0.898898	+	0.438157i	$0.855631\pi$
$998$	−37.6496	+	65.2110i	−1.19178	+	2.06422i
$999$	−1.10506	−	1.91402i	−0.0349626	−	0.0605570i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	385.2.i.c.221.8	✓	16
7.2	even	3	inner	385.2.i.c.331.8	yes	16
7.3	odd	6		2695.2.a.s.1.1		8
7.4	even	3		2695.2.a.t.1.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
385.2.i.c.221.8	✓	16	1.1	even	1	trivial
385.2.i.c.331.8	yes	16	7.2	even	3	inner
2695.2.a.s.1.1		8	7.3	odd	6
2695.2.a.t.1.1		8	7.4	even	3

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)

\(f(q)\)	\(=\)	\(q+(1.15525 + 2.00096i) q^{2} +(-1.21680 + 2.10756i) q^{3} +(-1.66923 + 2.89118i) q^{4} +(-0.500000 - 0.866025i) q^{5} -5.62286 q^{6} +(-2.34636 + 1.22254i) q^{7} -3.09251 q^{8} +(-1.46121 - 2.53090i) q^{9} +O(q^{10})\)	\(q+(1.15525 + 2.00096i) q^{2} +(-1.21680 + 2.10756i) q^{3} +(-1.66923 + 2.89118i) q^{4} +(-0.500000 - 0.866025i) q^{5} -5.62286 q^{6} +(-2.34636 + 1.22254i) q^{7} -3.09251 q^{8} +(-1.46121 - 2.53090i) q^{9} +(1.15525 - 2.00096i) q^{10} +(0.500000 - 0.866025i) q^{11} +(-4.06224 - 7.03600i) q^{12} +3.20660 q^{13} +(-5.15690 - 3.28261i) q^{14} +2.43360 q^{15} +(-0.234179 - 0.405609i) q^{16} +(-3.27172 + 5.66679i) q^{17} +(3.37615 - 5.84766i) q^{18} +(-2.59226 - 4.48993i) q^{19} +3.33845 q^{20} +(0.278463 - 6.43269i) q^{21} +2.31051 q^{22} +(0.314321 + 0.544419i) q^{23} +(3.76297 - 6.51765i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(3.70444 + 6.41628i) q^{26} -0.188777 q^{27} +(0.382000 - 8.82445i) q^{28} +8.12920 q^{29} +(2.81143 + 4.86954i) q^{30} +(-1.58580 + 2.74669i) q^{31} +(-2.55143 + 4.41921i) q^{32} +(1.21680 + 2.10756i) q^{33} -15.1187 q^{34} +(2.23193 + 1.42073i) q^{35} +9.75639 q^{36} +(5.85379 + 10.1391i) q^{37} +(5.98945 - 10.3740i) q^{38} +(-3.90180 + 6.75812i) q^{39} +(1.54625 + 2.67819i) q^{40} -4.12565 q^{41} +(13.1932 - 6.87420i) q^{42} -4.61012 q^{43} +(1.66923 + 2.89118i) q^{44} +(-1.46121 + 2.53090i) q^{45} +(-0.726241 + 1.25789i) q^{46} +(-1.22159 - 2.11585i) q^{47} +1.13980 q^{48} +(4.01077 - 5.73705i) q^{49} -2.31051 q^{50} +(-7.96208 - 13.7907i) q^{51} +(-5.35254 + 9.27088i) q^{52} +(3.61808 - 6.26670i) q^{53} +(-0.218086 - 0.377736i) q^{54} -1.00000 q^{55} +(7.25612 - 3.78072i) q^{56} +12.6171 q^{57} +(9.39130 + 16.2662i) q^{58} +(-3.02502 + 5.23948i) q^{59} +(-4.06224 + 7.03600i) q^{60} +(0.174556 + 0.302340i) q^{61} -7.32802 q^{62} +(6.52266 + 4.15199i) q^{63} -12.7269 q^{64} +(-1.60330 - 2.77700i) q^{65} +(-2.81143 + 4.86954i) q^{66} +(-1.09141 + 1.89038i) q^{67} +(-10.9225 - 18.9183i) q^{68} -1.52986 q^{69} +(-0.264378 + 6.10731i) q^{70} -3.53524 q^{71} +(4.51881 + 7.82681i) q^{72} +(0.863854 - 1.49624i) q^{73} +(-13.5252 + 23.4264i) q^{74} +(-1.21680 - 2.10756i) q^{75} +17.3083 q^{76} +(-0.114424 + 2.64328i) q^{77} -18.0303 q^{78} +(7.27928 + 12.6081i) q^{79} +(-0.234179 + 0.405609i) q^{80} +(4.61335 - 7.99055i) q^{81} +(-4.76618 - 8.25526i) q^{82} +14.7347 q^{83} +(18.1333 + 11.5427i) q^{84} +6.54345 q^{85} +(-5.32586 - 9.22466i) q^{86} +(-9.89163 + 17.1328i) q^{87} +(-1.54625 + 2.67819i) q^{88} +(2.72994 + 4.72840i) q^{89} -6.75230 q^{90} +(-7.52383 + 3.92021i) q^{91} -2.09869 q^{92} +(-3.85922 - 6.68436i) q^{93} +(2.82249 - 4.88869i) q^{94} +(-2.59226 + 4.48993i) q^{95} +(-6.20918 - 10.7546i) q^{96} +19.4672 q^{97} +(16.1131 + 1.39765i) q^{98} -2.92243 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 3 q^{2} - q^{3} - 9 q^{4} - 8 q^{5} - 6 q^{6} - q^{7} + 18 q^{8} - 19 q^{9}+O(q^{10}) \) 16 * q - 3 * q^2 - q^3 - 9 * q^4 - 8 * q^5 - 6 * q^6 - q^7 + 18 * q^8 - 19 * q^9	\( 16 q - 3 q^{2} - q^{3} - 9 q^{4} - 8 q^{5} - 6 q^{6} - q^{7} + 18 q^{8} - 19 q^{9} - 3 q^{10} + 8 q^{11} - 9 q^{12} + 28 q^{13} - 9 q^{14} + 2 q^{15} - 7 q^{16} - 5 q^{17} - 27 q^{18} - q^{19} + 18 q^{20} - 18 q^{21} - 6 q^{22} + 2 q^{23} + 24 q^{24} - 8 q^{25} - 21 q^{26} - 10 q^{27} + 32 q^{28} + 52 q^{29} + 3 q^{30} - 2 q^{31} - 16 q^{32} + q^{33} - 52 q^{34} + 5 q^{35} + 108 q^{36} + q^{37} + 31 q^{38} - 19 q^{39} - 9 q^{40} - 6 q^{41} + 44 q^{42} + 8 q^{43} + 9 q^{44} - 19 q^{45} - 10 q^{46} - q^{47} - 42 q^{48} + 17 q^{49} + 6 q^{50} - 3 q^{51} - 37 q^{52} - 26 q^{53} + 5 q^{54} - 16 q^{55} + 40 q^{57} + q^{58} + 19 q^{59} - 9 q^{60} - 52 q^{62} - 21 q^{63} + 2 q^{64} - 14 q^{65} - 3 q^{66} + 13 q^{67} - 15 q^{68} - 28 q^{69} + 15 q^{70} - 18 q^{71} - 32 q^{72} - 11 q^{73} - 24 q^{74} - q^{75} - 36 q^{76} + 4 q^{77} - 66 q^{78} + 8 q^{79} - 7 q^{80} - 52 q^{81} - 41 q^{82} + 64 q^{83} + 138 q^{84} + 10 q^{85} - 28 q^{86} + 16 q^{87} + 9 q^{88} - 5 q^{89} + 54 q^{90} + 13 q^{91} + 60 q^{92} + 14 q^{93} + 5 q^{94} - q^{95} - q^{96} + 18 q^{97} + 22 q^{98} - 38 q^{99}+O(q^{100}) \) 16 * q - 3 * q^2 - q^3 - 9 * q^4 - 8 * q^5 - 6 * q^6 - q^7 + 18 * q^8 - 19 * q^9 - 3 * q^10 + 8 * q^11 - 9 * q^12 + 28 * q^13 - 9 * q^14 + 2 * q^15 - 7 * q^16 - 5 * q^17 - 27 * q^18 - q^19 + 18 * q^20 - 18 * q^21 - 6 * q^22 + 2 * q^23 + 24 * q^24 - 8 * q^25 - 21 * q^26 - 10 * q^27 + 32 * q^28 + 52 * q^29 + 3 * q^30 - 2 * q^31 - 16 * q^32 + q^33 - 52 * q^34 + 5 * q^35 + 108 * q^36 + q^37 + 31 * q^38 - 19 * q^39 - 9 * q^40 - 6 * q^41 + 44 * q^42 + 8 * q^43 + 9 * q^44 - 19 * q^45 - 10 * q^46 - q^47 - 42 * q^48 + 17 * q^49 + 6 * q^50 - 3 * q^51 - 37 * q^52 - 26 * q^53 + 5 * q^54 - 16 * q^55 + 40 * q^57 + q^58 + 19 * q^59 - 9 * q^60 - 52 * q^62 - 21 * q^63 + 2 * q^64 - 14 * q^65 - 3 * q^66 + 13 * q^67 - 15 * q^68 - 28 * q^69 + 15 * q^70 - 18 * q^71 - 32 * q^72 - 11 * q^73 - 24 * q^74 - q^75 - 36 * q^76 + 4 * q^77 - 66 * q^78 + 8 * q^79 - 7 * q^80 - 52 * q^81 - 41 * q^82 + 64 * q^83 + 138 * q^84 + 10 * q^85 - 28 * q^86 + 16 * q^87 + 9 * q^88 - 5 * q^89 + 54 * q^90 + 13 * q^91 + 60 * q^92 + 14 * q^93 + 5 * q^94 - q^95 - q^96 + 18 * q^97 + 22 * q^98 - 38 * q^99

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