LMFDB - Embedded newform 217.2.f.b.32.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [217,2,Mod(32,217)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(217, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([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("217.32");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 217 = 7 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	217.f (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:	$1.73275372386$
Analytic rank:	$0$
Dimension:	$26$
Relative dimension:	$13$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			32.11
Character	$\chi$	$=$	217.32
Dual form			217.2.f.b.156.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.735285 + 1.27355i) q^{2} +(0.779727 - 1.35053i) q^{3} +(-0.0812879 + 0.140795i) q^{4} +(-2.18553 - 3.78544i) q^{5} +2.29329 q^{6} +(-2.64504 + 0.0614602i) q^{7} +2.70206 q^{8} +(0.284053 + 0.491993i) q^{9} +O(q^{10})$	\(q+(0.735285 + 1.27355i) q^{2} +(0.779727 - 1.35053i) q^{3} +(-0.0812879 + 0.140795i) q^{4} +(-2.18553 - 3.78544i) q^{5} +2.29329 q^{6} +(-2.64504 + 0.0614602i) q^{7} +2.70206 q^{8} +(0.284053 + 0.491993i) q^{9} +(3.21397 - 5.56676i) q^{10} +(-0.167212 + 0.289620i) q^{11} +(0.126765 + 0.219563i) q^{12} +5.80839 q^{13} +(-2.02313 - 3.32340i) q^{14} -6.81646 q^{15} +(2.14936 + 3.72280i) q^{16} +(-1.43430 + 2.48429i) q^{17} +(-0.417719 + 0.723511i) q^{18} +(-0.210592 - 0.364756i) q^{19} +0.710628 q^{20} +(-1.97940 + 3.62011i) q^{21} -0.491795 q^{22} +(-1.00433 - 1.73954i) q^{23} +(2.10687 - 3.64920i) q^{24} +(-7.05306 + 12.2163i) q^{25} +(4.27082 + 7.39728i) q^{26} +5.56429 q^{27} +(0.206356 - 0.377404i) q^{28} +4.99544 q^{29} +(-5.01204 - 8.68110i) q^{30} +(-0.500000 + 0.866025i) q^{31} +(-0.458724 + 0.794533i) q^{32} +(0.260760 + 0.451650i) q^{33} -4.21849 q^{34} +(6.01346 + 9.87832i) q^{35} -0.0923602 q^{36} +(2.21280 + 3.83268i) q^{37} +(0.309690 - 0.536399i) q^{38} +(4.52896 - 7.84438i) q^{39} +(-5.90543 - 10.2285i) q^{40} -10.1180 q^{41} +(-6.06583 + 0.140946i) q^{42} -4.91910 q^{43} +(-0.0271847 - 0.0470853i) q^{44} +(1.24161 - 2.15053i) q^{45} +(1.47693 - 2.55812i) q^{46} +(0.601200 + 1.04131i) q^{47} +6.70365 q^{48} +(6.99245 - 0.325129i) q^{49} -20.7440 q^{50} +(2.23673 + 3.87413i) q^{51} +(-0.472152 + 0.817791i) q^{52} +(2.55380 - 4.42331i) q^{53} +(4.09134 + 7.08641i) q^{54} +1.46179 q^{55} +(-7.14705 + 0.166069i) q^{56} -0.656816 q^{57} +(3.67307 + 6.36194i) q^{58} +(3.97232 - 6.88026i) q^{59} +(0.554096 - 0.959722i) q^{60} +(0.512571 + 0.887799i) q^{61} -1.47057 q^{62} +(-0.781568 - 1.28388i) q^{63} +7.24827 q^{64} +(-12.6944 - 21.9873i) q^{65} +(-0.383466 + 0.664182i) q^{66} +(-3.58101 + 6.20248i) q^{67} +(-0.233183 - 0.403885i) q^{68} -3.13240 q^{69} +(-8.15894 + 14.9218i) q^{70} +1.51205 q^{71} +(0.767527 + 1.32940i) q^{72} +(-5.18324 + 8.97764i) q^{73} +(-3.25408 + 5.63622i) q^{74} +(10.9989 + 19.0507i) q^{75} +0.0684743 q^{76} +(0.424483 - 0.776334i) q^{77} +13.3203 q^{78} +(-3.87171 - 6.70600i) q^{79} +(9.39497 - 16.2726i) q^{80} +(3.48647 - 6.03874i) q^{81} +(-7.43960 - 12.8858i) q^{82} -12.5211 q^{83} +(-0.348792 - 0.572961i) q^{84} +12.5388 q^{85} +(-3.61694 - 6.26472i) q^{86} +(3.89507 - 6.74647i) q^{87} +(-0.451818 + 0.782572i) q^{88} +(-1.21772 - 2.10916i) q^{89} +3.65175 q^{90} +(-15.3634 + 0.356985i) q^{91} +0.326558 q^{92} +(0.779727 + 1.35053i) q^{93} +(-0.884107 + 1.53132i) q^{94} +(-0.920508 + 1.59437i) q^{95} +(0.715359 + 1.23904i) q^{96} +4.26302 q^{97} +(5.55551 + 8.66617i) q^{98} -0.189988 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 26 q - 5 q^{2} - 17 q^{4} - q^{5} - 4 q^{6} - q^{7} + 24 q^{8} - 25 q^{9}+O(q^{10}) $ 26 * q - 5 * q^2 - 17 * q^4 - q^5 - 4 * q^6 - q^7 + 24 * q^8 - 25 * q^9	\( 26 q - 5 q^{2} - 17 q^{4} - q^{5} - 4 q^{6} - q^{7} + 24 q^{8} - 25 q^{9} + 7 q^{10} - 15 q^{11} + 5 q^{12} + 8 q^{13} - 12 q^{14} + 8 q^{15} - 29 q^{16} + 4 q^{17} - 16 q^{18} - 2 q^{19} + 52 q^{20} - 10 q^{21} - 20 q^{22} - 14 q^{23} + 28 q^{24} - 24 q^{25} + 7 q^{26} + 24 q^{27} - 14 q^{28} + 44 q^{29} - 6 q^{30} - 13 q^{31} - 19 q^{32} + 5 q^{33} + 40 q^{34} - 20 q^{35} + 22 q^{36} - 12 q^{37} + 11 q^{38} - 11 q^{39} + 6 q^{40} + 8 q^{41} - 82 q^{42} - 6 q^{43} - 52 q^{44} + 12 q^{45} + 3 q^{46} + 14 q^{47} + 96 q^{48} - 5 q^{49} + 30 q^{50} - 16 q^{51} - 4 q^{52} - 19 q^{53} + 25 q^{54} + 36 q^{55} - 29 q^{56} + 26 q^{57} - 24 q^{58} - 19 q^{59} - 6 q^{60} + 11 q^{61} + 10 q^{62} - 63 q^{63} + 20 q^{64} - 68 q^{65} + 52 q^{66} + 25 q^{67} + 26 q^{68} + 104 q^{69} - 78 q^{70} + 56 q^{71} - 52 q^{72} + 29 q^{73} - 54 q^{74} + 71 q^{75} + 74 q^{76} - 42 q^{77} - 142 q^{78} - 30 q^{79} - 3 q^{80} - 25 q^{81} - 5 q^{82} - 20 q^{83} - 64 q^{84} - 2 q^{85} - 10 q^{86} - 50 q^{87} - 18 q^{88} + 11 q^{89} + 162 q^{90} - 50 q^{91} + 70 q^{92} + 36 q^{94} + 20 q^{95} + 12 q^{96} - 6 q^{97} + 10 q^{98} + 84 q^{99}+O(q^{100}) \) 26 * q - 5 * q^2 - 17 * q^4 - q^5 - 4 * q^6 - q^7 + 24 * q^8 - 25 * q^9 + 7 * q^10 - 15 * q^11 + 5 * q^12 + 8 * q^13 - 12 * q^14 + 8 * q^15 - 29 * q^16 + 4 * q^17 - 16 * q^18 - 2 * q^19 + 52 * q^20 - 10 * q^21 - 20 * q^22 - 14 * q^23 + 28 * q^24 - 24 * q^25 + 7 * q^26 + 24 * q^27 - 14 * q^28 + 44 * q^29 - 6 * q^30 - 13 * q^31 - 19 * q^32 + 5 * q^33 + 40 * q^34 - 20 * q^35 + 22 * q^36 - 12 * q^37 + 11 * q^38 - 11 * q^39 + 6 * q^40 + 8 * q^41 - 82 * q^42 - 6 * q^43 - 52 * q^44 + 12 * q^45 + 3 * q^46 + 14 * q^47 + 96 * q^48 - 5 * q^49 + 30 * q^50 - 16 * q^51 - 4 * q^52 - 19 * q^53 + 25 * q^54 + 36 * q^55 - 29 * q^56 + 26 * q^57 - 24 * q^58 - 19 * q^59 - 6 * q^60 + 11 * q^61 + 10 * q^62 - 63 * q^63 + 20 * q^64 - 68 * q^65 + 52 * q^66 + 25 * q^67 + 26 * q^68 + 104 * q^69 - 78 * q^70 + 56 * q^71 - 52 * q^72 + 29 * q^73 - 54 * q^74 + 71 * q^75 + 74 * q^76 - 42 * q^77 - 142 * q^78 - 30 * q^79 - 3 * q^80 - 25 * q^81 - 5 * q^82 - 20 * q^83 - 64 * q^84 - 2 * q^85 - 10 * q^86 - 50 * q^87 - 18 * q^88 + 11 * q^89 + 162 * q^90 - 50 * q^91 + 70 * q^92 + 36 * q^94 + 20 * q^95 + 12 * q^96 - 6 * q^97 + 10 * q^98 + 84 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/217\mathbb{Z}\right)^\times$.

$n$	$94$	$127$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

Coefficient data

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

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

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

$2$	0.735285	+	1.27355i	0.519925	+	0.900536i	0.999732	+	0.0231623i	$0.00737344\pi$
$2$	0.735285	+	1.27355i	0.519925	+	0.900536i	−0.479807	+	0.877374i	$0.659293\pi$
$3$	0.779727	−	1.35053i	0.450175	−	0.779727i	−0.548221	−	0.836333i	$-0.684695\pi$
$3$	0.779727	−	1.35053i	0.450175	−	0.779727i	0.998397	+	0.0566067i	$0.0180281\pi$
$4$	−0.0812879	+	0.140795i	−0.0406440	+	0.0703974i
$5$	−2.18553	−	3.78544i	−0.977397	−	1.69290i	−0.671785	−	0.740746i	$-0.734472\pi$
$5$	−2.18553	−	3.78544i	−0.977397	−	1.69290i	−0.305612	−	0.952156i	$-0.598861\pi$
$6$	2.29329			0.936230
$7$	−2.64504	+	0.0614602i	−0.999730	+	0.0232298i
$7$	−2.64504	+	0.0614602i	−0.999730	+	0.0232298i
$8$	2.70206			0.955323
$9$	0.284053	+	0.491993i	0.0946842	+	0.163998i
$10$	3.21397	−	5.56676i	1.01635	−	1.76036i
$11$	−0.167212	+	0.289620i	−0.0504164	+	0.0873238i	−0.890132	−	0.455702i	$-0.849388\pi$
$11$	−0.167212	+	0.289620i	−0.0504164	+	0.0873238i	0.839716	+	0.543026i	$0.182722\pi$
$12$	0.126765	+	0.219563i	0.0365938	+	0.0633824i
$13$	5.80839			1.61096			0.805479	−	0.592625i	$-0.201908\pi$
$13$	5.80839			1.61096			0.805479	+	0.592625i	$0.201908\pi$
$14$	−2.02313	−	3.32340i	−0.540704	−	0.888216i
$15$	−6.81646			−1.76000
$16$	2.14936	+	3.72280i	0.537340	+	0.930700i
$17$	−1.43430	+	2.48429i	−0.347870	+	0.602529i	−0.985871	−	0.167507i	$-0.946428\pi$
$17$	−1.43430	+	2.48429i	−0.347870	+	0.602529i	0.638001	+	0.770036i	$0.279762\pi$
$18$	−0.417719	+	0.723511i	−0.0984573	+	0.170533i
$19$	−0.210592	−	0.364756i	−0.0483131	−	0.0836807i	0.840858	−	0.541256i	$-0.182051\pi$
$19$	−0.210592	−	0.364756i	−0.0483131	−	0.0836807i	−0.889171	+	0.457576i	$0.848718\pi$
$20$	0.710628			0.158901
$21$	−1.97940	+	3.62011i	−0.431941	+	0.789974i
$22$	−0.491795			−0.104851
$23$	−1.00433	−	1.73954i	−0.209416	−	0.362720i	0.742114	−	0.670273i	$-0.233823\pi$
$23$	−1.00433	−	1.73954i	−0.209416	−	0.362720i	−0.951531	+	0.307553i	$0.900490\pi$
$24$	2.10687	−	3.64920i	0.430063	−	0.744891i
$25$	−7.05306	+	12.2163i	−1.41061	+	2.44325i
$26$	4.27082	+	7.39728i	0.837577	+	1.45073i
$27$	5.56429			1.07085
$28$	0.206356	−	0.377404i	0.0389977	−	0.0713226i
$29$	4.99544			0.927629			0.463814	−	0.885932i	$-0.346480\pi$
$29$	4.99544			0.927629			0.463814	+	0.885932i	$0.346480\pi$
$30$	−5.01204	−	8.68110i	−0.915069	−	1.58495i
$31$	−0.500000	+	0.866025i	−0.0898027	+	0.155543i
$31$	−0.500000	+	0.866025i	−0.0898027	+	0.155543i
$32$	−0.458724	+	0.794533i	−0.0810917	+	0.140455i
$33$	0.260760	+	0.451650i	0.0453925	+	0.0786221i
$34$	−4.21849			−0.723465
$35$	6.01346	+	9.87832i	1.01646	+	1.66974i
$36$	−0.0923602			−0.0153934
$37$	2.21280	+	3.83268i	0.363782	+	0.630089i	0.988580	−	0.150698i	$-0.0481520\pi$
$37$	2.21280	+	3.83268i	0.363782	+	0.630089i	−0.624798	+	0.780786i	$0.714819\pi$
$38$	0.309690	−	0.536399i	0.0502384	−	0.0870154i
$39$	4.52896	−	7.84438i	0.725214	−	1.25611i
$40$	−5.90543	−	10.2285i	−0.933730	−	1.61727i
$41$	−10.1180			−1.58016			−0.790081	−	0.613002i	$-0.789962\pi$
$41$	−10.1180			−1.58016			−0.790081	+	0.613002i	$0.789962\pi$
$42$	−6.06583	+	0.140946i	−0.935977	+	0.0217484i
$43$	−4.91910			−0.750155			−0.375078	−	0.926993i	$-0.622384\pi$
$43$	−4.91910			−0.750155			−0.375078	+	0.926993i	$0.622384\pi$
$44$	−0.0271847	−	0.0470853i	−0.00409825	−	0.00709837i
$45$	1.24161	−	2.15053i	0.185088	−	0.320582i
$46$	1.47693	−	2.55812i	0.217762	−	0.377174i
$47$	0.601200	+	1.04131i	0.0876940	+	0.151891i	0.906536	−	0.422128i	$-0.138717\pi$
$47$	0.601200	+	1.04131i	0.0876940	+	0.151891i	−0.818842	+	0.574019i	$0.805384\pi$
$48$	6.70365			0.967589
$49$	6.99245	−	0.325129i	0.998921	−	0.0464470i
$50$	−20.7440			−2.93365
$51$	2.23673	+	3.87413i	0.313205	+	0.542487i
$52$	−0.472152	+	0.817791i	−0.0654757	+	0.113407i
$53$	2.55380	−	4.42331i	0.350792	−	0.607589i	−0.635597	−	0.772021i	$-0.719246\pi$
$53$	2.55380	−	4.42331i	0.350792	−	0.607589i	0.986388	+	0.164432i	$0.0525792\pi$
$54$	4.09134	+	7.08641i	0.556761	+	0.964338i
$55$	1.46179			0.197108
$56$	−7.14705	+	0.166069i	−0.955065	+	0.0221919i
$57$	−0.656816			−0.0869974
$58$	3.67307	+	6.36194i	0.482297	+	0.835364i
$59$	3.97232	−	6.88026i	0.517152	−	0.895734i	−0.482649	−	0.875814i	$-0.660325\pi$
$59$	3.97232	−	6.88026i	0.517152	−	0.895734i	0.999802	−	0.0199204i	$-0.00634127\pi$
$60$	0.554096	−	0.959722i	0.0715334	−	0.123900i
$61$	0.512571	+	0.887799i	0.0656280	+	0.113671i	0.896972	−	0.442087i	$-0.145762\pi$
$61$	0.512571	+	0.887799i	0.0656280	+	0.113671i	−0.831344	+	0.555758i	$0.812428\pi$
$62$	−1.47057			−0.186763
$63$	−0.781568	−	1.28388i	−0.0984683	−	0.161754i
$64$	7.24827			0.906034
$65$	−12.6944	−	21.9873i	−1.57455	−	2.72719i
$66$	−0.383466	+	0.664182i	−0.0472014	+	0.0817552i
$67$	−3.58101	+	6.20248i	−0.437490	+	0.757754i	−0.997495	−	0.0707347i	$-0.977466\pi$
$67$	−3.58101	+	6.20248i	−0.437490	+	0.757754i	0.560006	+	0.828489i	$0.310799\pi$
$68$	−0.233183	−	0.403885i	−0.0282776	−	0.0489783i
$69$	−3.13240			−0.377096
$70$	−8.15894	+	14.9218i	−0.975180	+	1.78350i
$71$	1.51205			0.179447			0.0897237	−	0.995967i	$-0.471402\pi$
$71$	1.51205			0.179447			0.0897237	+	0.995967i	$0.471402\pi$
$72$	0.767527	+	1.32940i	0.0904540	+	0.156671i
$73$	−5.18324	+	8.97764i	−0.606653	+	1.05075i	0.385135	+	0.922860i	$0.374155\pi$
$73$	−5.18324	+	8.97764i	−0.606653	+	1.05075i	−0.991788	+	0.127893i	$0.959178\pi$
$74$	−3.25408	+	5.63622i	−0.378279	+	0.655198i
$75$	10.9989	+	19.0507i	1.27005	+	2.19978i
$76$	0.0684743			0.00785454
$77$	0.424483	−	0.776334i	0.0483743	−	0.0884714i
$78$	13.3203			1.50823
$79$	−3.87171	−	6.70600i	−0.435601	−	0.754484i	0.561743	−	0.827312i	$-0.310131\pi$
$79$	−3.87171	−	6.70600i	−0.435601	−	0.754484i	−0.997345	+	0.0728280i	$0.976798\pi$
$80$	9.39497	−	16.2726i	1.05039	−	1.81933i
$81$	3.48647	−	6.03874i	0.387386	−	0.670972i
$82$	−7.43960	−	12.8858i	−0.821566	−	1.42299i
$83$	−12.5211			−1.37437			−0.687184	−	0.726483i	$-0.741153\pi$
$83$	−12.5211			−1.37437			−0.687184	+	0.726483i	$0.741153\pi$
$84$	−0.348792	−	0.572961i	−0.0380563	−	0.0625152i
$85$	12.5388			1.36003
$86$	−3.61694	−	6.26472i	−0.390024	−	0.675542i
$87$	3.89507	−	6.74647i	0.417596	−	0.723297i
$88$	−0.451818	+	0.782572i	−0.0481640	+	0.0834224i
$89$	−1.21772	−	2.10916i	−0.129078	−	0.223570i	0.794241	−	0.607602i	$-0.207869\pi$
$89$	−1.21772	−	2.10916i	−0.129078	−	0.223570i	−0.923320	+	0.384032i	$0.874535\pi$
$90$	3.65175			0.384928
$91$	−15.3634	+	0.356985i	−1.61052	+	0.0374222i
$92$	0.326558			0.0340461
$93$	0.779727	+	1.35053i	0.0808539	+	0.140043i
$94$	−0.884107	+	1.53132i	−0.0911886	+	0.157943i
$95$	−0.920508	+	1.59437i	−0.0944422	+	0.163579i
$96$	0.715359	+	1.23904i	0.0730110	+	0.126459i
$97$	4.26302			0.432844			0.216422	−	0.976300i	$-0.430561\pi$
$97$	4.26302			0.432844			0.216422	+	0.976300i	$0.430561\pi$
$98$	5.55551	+	8.66617i	0.561191	+	0.875416i
$99$	−0.189988			−0.0190946
$100$	−1.14666	−	1.98607i	−0.114666	−	0.198607i
$101$	−0.605089	+	1.04805i	−0.0602086	+	0.104284i	−0.894559	−	0.446951i	$-0.852510\pi$
$101$	−0.605089	+	1.04805i	−0.0602086	+	0.104284i	0.834350	+	0.551235i	$0.185843\pi$
$102$	−3.28927	+	5.69718i	−0.325686	+	0.564105i
$103$	8.28237	+	14.3455i	0.816086	+	1.41350i	0.908546	+	0.417786i	$0.137194\pi$
$103$	8.28237	+	14.3455i	0.816086	+	1.41350i	−0.0924597	+	0.995716i	$0.529473\pi$
$104$	15.6946			1.53898
$105$	18.0298	−	0.418940i	1.75953	−	0.0408844i
$106$	7.51109			0.729541
$107$	−7.98618	−	13.8325i	−0.772053	−	1.33724i	−0.936436	−	0.350838i	$-0.885897\pi$
$107$	−7.98618	−	13.8325i	−0.772053	−	1.33724i	0.164383	−	0.986397i	$-0.447437\pi$
$108$	−0.452310	+	0.783424i	−0.0435235	+	0.0753850i
$109$	−2.61397	+	4.52753i	−0.250373	+	0.433659i	−0.963628	−	0.267245i	$-0.913887\pi$
$109$	−2.61397	+	4.52753i	−0.250373	+	0.433659i	0.713256	+	0.700904i	$0.247220\pi$
$110$	1.07483	+	1.86166i	0.102481	+	0.177503i
$111$	6.90151			0.655063
$112$	−5.91394	−	9.71485i	−0.558815	−	0.917967i
$113$	9.16180			0.861870			0.430935	−	0.902383i	$-0.358184\pi$
$113$	9.16180			0.861870			0.430935	+	0.902383i	$0.358184\pi$
$114$	−0.482947	−	0.836489i	−0.0452321	−	0.0783444i
$115$	−4.38996	+	7.60364i	−0.409366	+	0.709043i
$116$	−0.406069	+	0.703331i	−0.0377025	+	0.0653027i
$117$	1.64989	+	2.85769i	0.152532	+	0.264194i
$118$	11.6832			1.07552
$119$	3.64110	−	6.65919i	0.333780	−	0.610447i
$120$	−18.4185			−1.68137
$121$	5.44408	+	9.42942i	0.494916	+	0.857220i
$122$	−0.753772	+	1.30557i	−0.0682433	+	0.118201i
$123$	−7.88926	+	13.6646i	−0.711350	+	1.23210i
$124$	−0.0812879	−	0.140795i	−0.00729987	−	0.0126437i
$125$	39.8033			3.56012
$126$	1.06042	−	1.93939i	0.0944693	−	0.172774i
$127$	−3.84670			−0.341339			−0.170670	−	0.985328i	$-0.554593\pi$
$127$	−3.84670			−0.341339			−0.170670	+	0.985328i	$0.554593\pi$
$128$	6.24699	+	10.8201i	0.552161	+	0.956371i
$129$	−3.83555	+	6.64337i	−0.337701	+	0.584916i
$130$	18.6680	−	32.3339i	1.63729	−	2.83587i
$131$	−1.48968	−	2.58020i	−0.130154	−	0.225433i	0.793582	−	0.608464i	$-0.208214\pi$
$131$	−1.48968	−	2.58020i	−0.130154	−	0.225433i	−0.923736	+	0.383030i	$0.874881\pi$
$132$	−0.0847866			−0.00737972
$133$	0.579441	+	0.951850i	0.0502439	+	0.0825358i
$134$	−10.5322			−0.909847
$135$	−12.1609	−	21.0633i	−1.04664	−	1.81284i
$136$	−3.87558	+	6.71270i	−0.332328	+	0.575609i
$137$	−6.32269	+	10.9512i	−0.540184	+	0.935626i	0.458709	+	0.888586i	$0.348312\pi$
$137$	−6.32269	+	10.9512i	−0.540184	+	0.935626i	−0.998893	+	0.0470395i	$0.985021\pi$
$138$	−2.30321	−	3.98927i	−0.196062	−	0.339589i
$139$	−9.18944			−0.779438			−0.389719	−	0.920934i	$-0.627428\pi$
$139$	−9.18944			−0.779438			−0.389719	+	0.920934i	$0.627428\pi$
$140$	−1.87964	+	0.0436753i	−0.158858	+	0.00369124i
$141$	1.87509			0.157911
$142$	1.11179	+	1.92567i	0.0932992	+	0.161599i
$143$	−0.971235	+	1.68223i	−0.0812188	+	0.140675i
$144$	−1.22106	+	2.11494i	−0.101755	+	0.176245i
$145$	−10.9177	−	18.9099i	−0.906662	−	1.57039i
$146$	−15.2446			−1.26166
$147$	5.01310	−	9.69699i	0.413474	−	0.799794i
$148$	−0.719495			−0.0591421
$149$	−4.11832	−	7.13314i	−0.337386	−	0.584370i	0.646554	−	0.762868i	$-0.276209\pi$
$149$	−4.11832	−	7.13314i	−0.337386	−	0.584370i	−0.983940	+	0.178498i	$0.942876\pi$
$150$	−16.1747	+	28.0154i	−1.32066	+	2.28744i
$151$	3.24736	−	5.62459i	0.264266	−	0.457723i	−0.703105	−	0.711086i	$-0.748203\pi$
$151$	3.24736	−	5.62459i	0.264266	−	0.457723i	0.967371	+	0.253363i	$0.0815368\pi$
$152$	−0.569032	−	0.985592i	−0.0461546	−	0.0799421i
$153$	−1.62967			−0.131751
$154$	1.30082	−	0.0302258i	0.104823	−	0.00243567i
$155$	4.37105			0.351092
$156$	0.736299	+	1.27531i	0.0589511	+	0.102106i
$157$	−8.51960	+	14.7564i	−0.679938	+	1.17769i	0.295061	+	0.955478i	$0.404660\pi$
$157$	−8.51960	+	14.7564i	−0.679938	+	1.17769i	−0.974999	+	0.222209i	$0.928673\pi$
$158$	5.69362	−	9.86164i	0.452960	−	0.784550i
$159$	−3.98253	−	6.89795i	−0.315835	−	0.547043i
$160$	4.01022			0.317035
$161$	2.76339	+	4.53943i	0.217786	+	0.357757i
$162$	10.2542			0.805646
$163$	−1.77418	−	3.07296i	−0.138964	−	0.240693i	0.788141	−	0.615495i	$-0.211044\pi$
$163$	−1.77418	−	3.07296i	−0.138964	−	0.240693i	−0.927105	+	0.374802i	$0.877711\pi$
$164$	0.822470	−	1.42456i	0.0642241	−	0.111239i
$165$	1.13980	−	1.97418i	0.0887330	−	0.153690i
$166$	−9.20657	−	15.9462i	−0.714568	−	1.23767i
$167$	−24.6131			−1.90462			−0.952310	−	0.305133i	$-0.901299\pi$
$167$	−24.6131			−1.90462			−0.952310	+	0.305133i	$0.901299\pi$
$168$	−5.34847	+	9.78177i	−0.412643	+	0.754680i
$169$	20.7374			1.59518
$170$	9.21963	+	15.9689i	0.707113	+	1.22476i
$171$	0.119638	−	0.207220i	0.00914897	−	0.0158465i
$172$	0.399863	−	0.692583i	0.0304893	−	0.0528090i
$173$	−7.71711	−	13.3664i	−0.586721	−	1.01623i	−0.994658	−	0.103221i	$-0.967085\pi$
$173$	−7.71711	−	13.3664i	−0.586721	−	1.01623i	0.407937	−	0.913010i	$-0.366248\pi$
$174$	11.4560			0.868474
$175$	17.9048	−	32.7459i	1.35347	−	2.47536i
$176$	−1.43760			−0.108363
$177$	−6.19465	−	10.7295i	−0.465619	−	0.806475i
$178$	1.79075	−	3.10167i	0.134222	−	0.232480i
$179$	−9.83583	+	17.0362i	−0.735165	+	1.27334i	0.219486	+	0.975616i	$0.429562\pi$
$179$	−9.83583	+	17.0362i	−0.735165	+	1.27334i	−0.954651	+	0.297727i	$0.903772\pi$
$180$	0.201856	+	0.349624i	0.0150454	+	0.0260595i
$181$	12.4376			0.924477			0.462239	−	0.886756i	$-0.347046\pi$
$181$	12.4376			0.924477			0.462239	+	0.886756i	$0.347046\pi$
$182$	−11.7511	−	19.3036i	−0.871051	−	1.43088i
$183$	1.59866			0.118176
$184$	−2.71375	−	4.70035i	−0.200060	−	0.346515i
$185$	9.67226	−	16.7529i	0.711119	−	1.23169i
$186$	−1.14664	+	1.98604i	−0.0840759	+	0.145624i
$187$	−0.479667	−	0.830808i	−0.0350767	−	0.0607547i
$188$	−0.195481			−0.0142569
$189$	−14.7178	+	0.341982i	−1.07056	+	0.0248756i
$190$	−2.70734			−0.196411
$191$	2.36144	+	4.09014i	0.170868	+	0.295952i	0.938724	−	0.344671i	$-0.112010\pi$
$191$	2.36144	+	4.09014i	0.170868	+	0.295952i	−0.767856	+	0.640623i	$0.778676\pi$
$192$	5.65167	−	9.78898i	0.407874	−	0.706459i
$193$	1.05134	−	1.82097i	0.0756771	−	0.131077i	−0.825703	−	0.564104i	$-0.809222\pi$
$193$	1.05134	−	1.82097i	0.0756771	−	0.131077i	0.901381	+	0.433028i	$0.142555\pi$
$194$	3.13453	+	5.42917i	0.225046	+	0.389792i
$195$	−39.5926			−2.83529
$196$	−0.522625	+	1.01093i	−0.0373304	+	0.0722092i
$197$	−4.31625			−0.307520			−0.153760	−	0.988108i	$-0.549138\pi$
$197$	−4.31625			−0.307520			−0.153760	+	0.988108i	$0.549138\pi$
$198$	−0.139696	−	0.241960i	−0.00992774	−	0.0171953i
$199$	3.12742	−	5.41686i	0.221697	−	0.383991i	−0.733626	−	0.679553i	$-0.762174\pi$
$199$	3.12742	−	5.41686i	0.221697	−	0.383991i	0.955323	+	0.295562i	$0.0955070\pi$
$200$	−19.0578	+	33.0091i	−1.34759	+	2.33409i
$201$	5.58441	+	9.67249i	0.393894	+	0.682244i
$202$	−1.77965			−0.125216
$203$	−13.2131	+	0.307020i	−0.927379	+	0.0215486i
$204$	−0.727277			−0.0509196
$205$	22.1131	+	38.3010i	1.54445	+	2.67506i
$206$	−12.1798	+	21.0960i	−0.848607	+	1.46983i
$207$	0.570563	−	0.988244i	0.0396568	−	0.0686877i
$208$	12.4843	+	21.6235i	0.865632	+	1.49932i
$209$	0.140854			0.00974309
$210$	13.7906	+	22.6538i	0.951640	+	1.56326i
$211$	1.12522			0.0774631			0.0387316	−	0.999250i	$-0.487668\pi$
$211$	1.12522			0.0774631			0.0387316	+	0.999250i	$0.487668\pi$
$212$	0.415186	+	0.719124i	0.0285151	+	0.0493896i
$213$	1.17899	−	2.04206i	0.0807828	−	0.139920i
$214$	11.7442	−	20.3416i	0.802819	−	1.39052i
$215$	10.7508	+	18.6210i	0.733200	+	1.26994i
$216$	15.0351			1.02301
$217$	1.26929	−	2.32140i	0.0861652	−	0.157587i
$218$	−7.68805			−0.520700
$219$	8.08303	+	14.0002i	0.546200	+	0.946047i
$220$	−0.118826	+	0.205812i	−0.00801124	+	0.0138759i
$221$	−8.33100	+	14.4297i	−0.560404	+	0.970648i
$222$	5.07458	+	8.78943i	0.340583	+	0.589908i
$223$	−26.0719			−1.74590			−0.872952	−	0.487806i	$-0.837797\pi$
$223$	−26.0719			−1.74590			−0.872952	+	0.487806i	$0.837797\pi$
$224$	1.16451	−	2.12976i	0.0778071	−	0.142301i
$225$	−8.01376			−0.534250
$226$	6.73654	+	11.6680i	0.448108	+	0.776145i
$227$	−7.75837	+	13.4379i	−0.514941	+	0.891904i	0.484908	+	0.874565i	$0.338853\pi$
$227$	−7.75837	+	13.4379i	−0.514941	+	0.891904i	−0.999850	+	0.0173394i	$0.994480\pi$
$228$	0.0533912	−	0.0924763i	0.00353592	−	0.00612439i
$229$	−8.86817	−	15.3601i	−0.586025	−	1.01503i	−0.994747	−	0.102367i	$-0.967359\pi$
$229$	−8.86817	−	15.3601i	−0.586025	−	1.01503i	0.408721	−	0.912659i	$-0.365975\pi$
$230$	−12.9115			−0.851359
$231$	−0.717478	−	1.17860i	−0.0472066	−	0.0775464i
$232$	13.4980			0.886185
$233$	0.0776941	+	0.134570i	0.00508991	+	0.00881599i	0.868559	−	0.495586i	$-0.165046\pi$
$233$	0.0776941	+	0.134570i	0.00508991	+	0.00881599i	−0.863469	+	0.504402i	$0.831713\pi$
$234$	−2.42628	+	4.20243i	−0.158611	+	0.274722i
$235$	2.62788	−	4.55162i	0.171424	−	0.296915i
$236$	0.645804	+	1.11856i	0.0420382	+	0.0728124i
$237$	−12.0755			−0.784388
$238$	11.1581	−	0.259269i	0.723270	−	0.0168059i
$239$	18.2663			1.18155			0.590773	−	0.806838i	$-0.298823\pi$
$239$	18.2663			1.18155			0.590773	+	0.806838i	$0.298823\pi$
$240$	−14.6510	−	25.3763i	−0.945719	−	1.63803i
$241$	9.29014	−	16.0910i	0.598431	−	1.03651i	−0.394622	−	0.918843i	$-0.629125\pi$
$241$	9.29014	−	16.0910i	0.598431	−	1.03651i	0.993053	−	0.117669i	$-0.0375421\pi$
$242$	−8.00590	+	13.8666i	−0.514639	+	0.891380i
$243$	2.90945	+	5.03932i	0.186641	+	0.323272i
$244$	−0.166663			−0.0106695
$245$	−16.5129	−	25.7589i	−1.05497	−	1.64568i
$246$	−23.2034			−1.47940
$247$	−1.22320	−	2.11864i	−0.0778303	−	0.134806i
$248$	−1.35103	+	2.34005i	−0.0857905	+	0.148594i
$249$	−9.76303	+	16.9101i	−0.618707	+	1.07163i
$250$	29.2668	+	50.6916i	1.85099	+	3.20602i
$251$	17.8295			1.12539			0.562693	−	0.826666i	$-0.309765\pi$
$251$	17.8295			1.12539			0.562693	+	0.826666i	$0.309765\pi$
$252$	0.244296	−	0.00567647i	0.0153892	−	0.000357584i
$253$	0.671743			0.0422321
$254$	−2.82842	−	4.89897i	−0.177471	−	0.307389i
$255$	9.77687	−	16.9340i	0.612252	−	1.06045i
$256$	−1.93837	+	3.35735i	−0.121148	+	0.209835i
$257$	−4.62854	−	8.01687i	−0.288720	−	0.500079i	0.684784	−	0.728746i	$-0.259896\pi$
$257$	−4.62854	−	8.01687i	−0.288720	−	0.500079i	−0.973505	+	0.228667i	$0.926563\pi$
$258$	−11.2809			−0.702318
$259$	−6.08849	−	10.0016i	−0.378320	−	0.621468i
$260$	4.12760			0.255983
$261$	1.41897	+	2.45772i	0.0878318	+	0.152129i
$262$	2.19068	−	3.79437i	0.135341	−	0.234417i
$263$	9.43890	−	16.3486i	0.582027	−	1.00810i	−0.413212	−	0.910635i	$-0.635593\pi$
$263$	9.43890	−	16.3486i	0.582027	−	1.00810i	0.995239	−	0.0974657i	$-0.0310736\pi$
$264$	0.704589	+	1.22038i	0.0433645	+	0.0751095i
$265$	−22.3256			−1.37145
$266$	−0.786175	+	1.43783i	−0.0482035	+	0.0881589i
$267$	−3.79797			−0.232432
$268$	−0.582185	−	1.00837i	−0.0355626	−	0.0615963i
$269$	9.23616	−	15.9975i	0.563138	−	0.975384i	−0.434082	−	0.900873i	$-0.642927\pi$
$269$	9.23616	−	15.9975i	0.563138	−	0.975384i	0.997220	−	0.0745109i	$-0.0237396\pi$
$270$	17.8835	−	30.9751i	1.08835	−	1.88508i
$271$	−15.2888	−	26.4811i	−0.928731	−	1.60861i	−0.785448	−	0.618928i	$-0.787567\pi$
$271$	−15.2888	−	26.4811i	−0.928731	−	1.60861i	−0.143284	−	0.989682i	$-0.545766\pi$
$272$	−12.3314			−0.747698
$273$	−11.4971	+	21.0270i	−0.695839	+	1.27261i
$274$	−18.5959			−1.12342
$275$	−2.35872	−	4.08542i	−0.142236	−	0.246360i
$276$	0.254626	−	0.441026i	0.0153267	−	0.0265466i
$277$	13.6373	−	23.6205i	0.819387	−	1.41922i	−0.0867470	−	0.996230i	$-0.527647\pi$
$277$	13.6373	−	23.6205i	0.819387	−	1.41922i	0.906134	−	0.422990i	$-0.139020\pi$
$278$	−6.75686	−	11.7032i	−0.405249	−	0.701912i
$279$	−0.568105			−0.0340116
$280$	16.2487	+	26.6918i	0.971047	+	1.59514i
$281$	15.9872			0.953716			0.476858	−	0.878980i	$-0.341776\pi$
$281$	15.9872			0.953716			0.476858	+	0.878980i	$0.341776\pi$
$282$	1.37872	+	2.38802i	0.0821018	+	0.142204i
$283$	5.86885	−	10.1651i	0.348867	−	0.604255i	−0.637182	−	0.770714i	$-0.719900\pi$
$283$	5.86885	−	10.1651i	0.348867	−	0.604255i	0.986048	+	0.166459i	$0.0532333\pi$
$284$	−0.122911	+	0.212889i	−0.00729345	+	0.0126326i
$285$	1.43549	+	2.48634i	0.0850311	+	0.147278i
$286$	−2.85654			−0.168911
$287$	26.7624	−	0.621853i	1.57974	−	0.0367068i
$288$	−0.521207			−0.0307124
$289$	4.38554	+	7.59598i	0.257973	+	0.446822i
$290$	16.0552	−	27.8084i	0.942793	−	1.63296i
$291$	3.32399	−	5.75732i	0.194856	−	0.337500i
$292$	−0.842670	−	1.45955i	−0.0493136	−	0.0854136i
$293$	4.91819			0.287324			0.143662	−	0.989627i	$-0.454112\pi$
$293$	4.91819			0.287324			0.143662	+	0.989627i	$0.454112\pi$
$294$	16.0357	−	0.745613i	0.935219	−	0.0434850i
$295$	−34.7265			−2.02185
$296$	5.97912	+	10.3561i	0.347529	+	0.601938i
$297$	−0.930419	+	1.61153i	−0.0539884	+	0.0935106i
$298$	6.05628	−	10.4898i	0.350831	−	0.607657i
$299$	−5.83352	−	10.1039i	−0.337361	−	0.584326i
$300$	−3.57632			−0.206479
$301$	13.0112	−	0.302328i	0.749953	−	0.0174259i
$302$	9.55094			0.549595
$303$	0.943609	+	1.63438i	0.0542089	+	0.0938926i
$304$	0.905276	−	1.56798i	0.0519211	−	0.0899300i
$305$	2.24048	−	3.88062i	0.128289	−	0.222204i
$306$	−1.19827	−	2.07547i	−0.0685007	−	0.118647i
$307$	17.5101			0.999355			0.499677	−	0.866212i	$-0.333452\pi$
$307$	17.5101			0.999355			0.499677	+	0.866212i	$0.333452\pi$
$308$	0.0747984	+	0.122872i	0.00426204	+	0.00700126i
$309$	25.8319			1.46953
$310$	3.21397	+	5.56676i	0.182541	+	0.316171i
$311$	−5.63256	+	9.75588i	−0.319393	+	0.553205i	−0.980362	−	0.197209i	$-0.936812\pi$
$311$	−5.63256	+	9.75588i	−0.319393	+	0.553205i	0.660968	+	0.750414i	$0.270146\pi$
$312$	12.2375	−	21.1960i	0.692813	−	1.19999i
$313$	12.3663	+	21.4190i	0.698983	+	1.21067i	0.968819	+	0.247768i	$0.0796971\pi$
$313$	12.3663	+	21.4190i	0.698983	+	1.21067i	−0.269836	+	0.962906i	$0.586970\pi$
$314$	−25.0573			−1.41407
$315$	−3.15193	+	5.76454i	−0.177591	+	0.324795i
$316$	1.25889			0.0708183
$317$	13.6039	+	23.5626i	0.764071	+	1.32341i	0.940736	+	0.339139i	$0.110136\pi$
$317$	13.6039	+	23.5626i	0.764071	+	1.32341i	−0.176666	+	0.984271i	$0.556531\pi$
$318$	5.85659	−	10.1439i	0.328422	−	0.568843i
$319$	−0.835299	+	1.44678i	−0.0467678	+	0.0810041i
$320$	−15.8413	−	27.4379i	−0.885555	−	1.53383i
$321$	−24.9081			−1.39024
$322$	−3.74932	+	6.85710i	−0.208941	+	0.382131i
$323$	1.20821			0.0672267
$324$	0.566816	+	0.981754i	0.0314898	+	0.0545419i
$325$	−40.9669	+	70.9568i	−2.27244	+	3.93597i
$326$	2.60905	−	4.51901i	0.144502	−	0.250285i
$327$	4.07636	+	7.06047i	0.225423	+	0.390445i
$328$	−27.3394			−1.50957
$329$	−1.65420	−	2.71735i	−0.0911987	−	0.149812i
$330$	3.35230			0.184538
$331$	−13.1409	−	22.7607i	−0.722289	−	1.25104i	−0.960080	−	0.279725i	$-0.909757\pi$
$331$	−13.1409	−	22.7607i	−0.722289	−	1.25104i	0.237791	−	0.971316i	$-0.423577\pi$
$332$	1.01781	−	1.76290i	0.0558598	−	0.0967519i
$333$	−1.25710	+	2.17736i	−0.0688888	+	0.119319i
$334$	−18.0976	−	31.3460i	−0.990259	−	1.71518i
$335$	31.3055			1.71040
$336$	−17.7314	+	0.412008i	−0.967328	+	0.0224769i
$337$	−12.5855			−0.685576			−0.342788	−	0.939413i	$-0.611371\pi$
$337$	−12.5855			−0.685576			−0.342788	+	0.939413i	$0.611371\pi$
$338$	15.2479	+	26.4101i	0.829376	+	1.43652i
$339$	7.14370	−	12.3733i	0.387993	−	0.672023i
$340$	−1.01926	+	1.76540i	−0.0552770	+	0.0957425i
$341$	−0.167212	−	0.289620i	−0.00905506	−	0.0156838i
$342$	0.351873			0.0190271
$343$	−18.4753	+	1.28973i	−0.997572	+	0.0696391i
$344$	−13.2917			−0.716640
$345$	6.84594	+	11.8575i	0.368573	+	0.638387i
$346$	11.3486	−	19.6563i	0.610102	−	1.05673i
$347$	−5.08086	+	8.80030i	−0.272755	+	0.472425i	−0.969566	−	0.244829i	$-0.921268\pi$
$347$	−5.08086	+	8.80030i	−0.272755	+	0.472425i	0.696811	+	0.717254i	$0.254601\pi$
$348$	0.633245	+	1.09681i	0.0339455	+	0.0587953i
$349$	2.58840			0.138554			0.0692769	−	0.997597i	$-0.477931\pi$
$349$	2.58840			0.138554			0.0692769	+	0.997597i	$0.477931\pi$
$350$	54.8687	−	1.27493i	2.93286	−	0.0681480i
$351$	32.3196			1.72509
$352$	−0.153409	−	0.265712i	−0.00817671	−	0.0141625i
$353$	1.38218	−	2.39400i	0.0735659	−	0.127420i	−0.826896	−	0.562355i	$-0.809895\pi$
$353$	1.38218	−	2.39400i	0.0735659	−	0.127420i	0.900462	+	0.434935i	$0.143229\pi$
$354$	9.10967	−	15.7784i	0.484173	−	0.838613i
$355$	−3.30463	−	5.72378i	−0.175391	−	0.303787i
$356$	0.395945			0.0209850
$357$	−6.15434	−	10.1098i	−0.325722	−	0.535065i
$358$	−28.9286			−1.52892
$359$	−11.0813	−	19.1933i	−0.584848	−	1.01299i	−0.994894	−	0.100921i	$-0.967821\pi$
$359$	−11.0813	−	19.1933i	−0.584848	−	1.01299i	0.410047	−	0.912065i	$-0.365512\pi$
$360$	3.35490	−	5.81086i	0.176819	−	0.306259i
$361$	9.41130	−	16.3009i	0.495332	−	0.857940i
$362$	9.14516	+	15.8399i	0.480659	+	0.832526i
$363$	16.9796			0.891197
$364$	1.19860	−	2.19211i	0.0628236	−	0.114898i
$365$	45.3125			2.37176
$366$	1.17547	+	2.03598i	0.0614429	+	0.106422i
$367$	−3.44732	+	5.97093i	−0.179948	+	0.311680i	−0.941863	−	0.335998i	$-0.890926\pi$
$367$	−3.44732	+	5.97093i	−0.179948	+	0.311680i	0.761914	+	0.647678i	$0.224260\pi$
$368$	4.31732	−	7.47781i	0.225056	−	0.389808i
$369$	−2.87404	−	4.97798i	−0.149616	−	0.259143i
$370$	28.4475			1.47891
$371$	−6.48304	+	11.8568i	−0.336583	+	0.615574i
$372$	−0.253529			−0.0131449
$373$	5.05605	+	8.75734i	0.261792	+	0.453438i	0.966718	−	0.255843i	$-0.0823531\pi$
$373$	5.05605	+	8.75734i	0.261792	+	0.453438i	−0.704926	+	0.709281i	$0.749020\pi$
$374$	0.705384	−	1.22176i	0.0364745	−	0.0631758i
$375$	31.0357	−	53.7554i	1.60268	−	2.77592i
$376$	1.62448	+	2.81368i	0.0837761	+	0.145104i
$377$	29.0154			1.49437
$378$	−11.2573	−	18.4924i	−0.579012	−	0.951145i
$379$	−0.654720			−0.0336307			−0.0168154	−	0.999859i	$-0.505353\pi$
$379$	−0.654720			−0.0336307			−0.0168154	+	0.999859i	$0.505353\pi$
$380$	−0.149652	−	0.259206i	−0.00767701	−	0.0132970i
$381$	−2.99938	+	5.19507i	−0.153663	+	0.266152i
$382$	−3.47266	+	6.01483i	−0.177677	+	0.307745i
$383$	8.67942	+	15.0332i	0.443498	+	0.768161i	0.997946	−	0.0640575i	$-0.0204041\pi$
$383$	8.67942	+	15.0332i	0.443498	+	0.768161i	−0.554449	+	0.832218i	$0.687071\pi$
$384$	19.4838			0.994278
$385$	−3.86649	+	0.0898418i	−0.197054	+	0.00457876i
$386$	3.09214			0.157386
$387$	−1.39728	−	2.42016i	−0.0710278	−	0.123024i
$388$	−0.346532	+	0.600211i	−0.0175925	+	0.0304711i
$389$	−8.96657	+	15.5306i	−0.454623	+	0.787431i	−0.998666	−	0.0516265i	$-0.983559\pi$
$389$	−8.96657	+	15.5306i	−0.454623	+	0.787431i	0.544043	+	0.839057i	$0.316893\pi$
$390$	−29.1119	−	50.4232i	−1.47414	−	2.55328i
$391$	5.76204			0.291399
$392$	18.8940	−	0.878518i	0.954292	−	0.0443719i
$393$	−4.64618			−0.234369
$394$	−3.17367	−	5.49696i	−0.159887	−	0.276933i
$395$	−16.9235	+	29.3123i	−0.851511	+	1.47486i
$396$	0.0154438	−	0.0267494i	0.000776079	−	0.00134421i
$397$	−1.17147	−	2.02904i	−0.0587942	−	0.101835i	0.835130	−	0.550052i	$-0.185392\pi$
$397$	−1.17147	−	2.02904i	−0.0587942	−	0.101835i	−0.893924	+	0.448218i	$0.852059\pi$
$398$	9.19819			0.461064
$399$	1.73730	−	0.0403680i	0.0869740	−	0.00202093i
$400$	−60.6383			−3.03191
$401$	1.33982	+	2.32063i	0.0669073	+	0.115887i	0.897538	−	0.440936i	$-0.145353\pi$
$401$	1.33982	+	2.32063i	0.0669073	+	0.115887i	−0.830631	+	0.556823i	$0.812020\pi$
$402$	−8.21227	+	14.2241i	−0.409591	+	0.709432i
$403$	−2.90420	+	5.03021i	−0.144668	+	0.250573i
$404$	−0.0983729	−	0.170387i	−0.00489424	−	0.00847706i
$405$	−30.4791			−1.51452
$406$	−10.1064	−	16.6018i	−0.501573	−	0.823935i
$407$	−1.48003			−0.0733623
$408$	6.04378	+	10.4681i	0.299212	+	0.518250i
$409$	12.8530	−	22.2620i	0.635539	−	1.10079i	−0.350861	−	0.936427i	$-0.614111\pi$
$409$	12.8530	−	22.2620i	0.635539	−	1.10079i	0.986401	−	0.164359i	$-0.0525555\pi$
$410$	−32.5189	+	56.3244i	−1.60599	+	2.78166i
$411$	9.85994	+	17.0779i	0.486355	+	0.842392i
$412$	−2.69303			−0.132676
$413$	−10.0841	+	18.4427i	−0.496205	+	0.907506i
$414$	1.67810			0.0824743
$415$	27.3652	+	47.3979i	1.34330	+	2.32667i
$416$	−2.66445	+	4.61496i	−0.130635	+	0.226267i
$417$	−7.16525	+	12.4106i	−0.350884	+	0.607749i
$418$	0.103568	+	0.179385i	0.00506568	+	0.00877401i
$419$	−10.5209			−0.513979			−0.256989	−	0.966414i	$-0.582731\pi$
$419$	−10.5209			−0.513979			−0.256989	+	0.966414i	$0.582731\pi$
$420$	−1.40662	+	2.57255i	−0.0686360	+	0.125528i
$421$	8.38713			0.408764			0.204382	−	0.978891i	$-0.434482\pi$
$421$	8.38713			0.408764			0.204382	+	0.978891i	$0.434482\pi$
$422$	0.827355	+	1.43302i	0.0402750	+	0.0697584i
$423$	−0.341545	+	0.591573i	−0.0166065	+	0.0287633i
$424$	6.90053	−	11.9521i	0.335119	−	0.580443i
$425$	−20.2325	−	35.0437i	−0.981419	−	1.69987i
$426$	3.46756			0.168004
$427$	−1.41033	−	2.31676i	−0.0682508	−	0.112116i
$428$	2.59672			0.125517
$429$	1.51460	+	2.62336i	0.0731254	+	0.126657i
$430$	−15.8098	+	27.3834i	−0.762418	+	1.32055i
$431$	4.34340	−	7.52299i	0.209214	−	0.362370i	−0.742253	−	0.670120i	$-0.766243\pi$
$431$	4.34340	−	7.52299i	0.209214	−	0.362370i	0.951467	+	0.307750i	$0.0995760\pi$
$432$	11.9597	+	20.7148i	0.575410	+	0.996639i
$433$	−31.1680			−1.49784			−0.748918	−	0.662663i	$-0.769426\pi$
$433$	−31.1680			−1.49784			−0.748918	+	0.662663i	$0.769426\pi$
$434$	3.88971	−	0.0903815i	0.186712	−	0.00433845i
$435$	−34.0512			−1.63263
$436$	−0.424968	−	0.736067i	−0.0203523	−	0.0352512i
$437$	−0.423006	+	0.732667i	−0.0202351	+	0.0350482i
$438$	−11.8867	+	20.5883i	−0.567967	+	0.983747i
$439$	2.69464	+	4.66725i	0.128608	+	0.222756i	0.923138	−	0.384470i	$-0.125616\pi$
$439$	2.69464	+	4.66725i	0.128608	+	0.222756i	−0.794529	+	0.607226i	$0.792282\pi$
$440$	3.94984			0.188301
$441$	2.14618	+	3.34788i	0.102199	+	0.159423i
$442$	−24.5026			−1.16547
$443$	6.84289	+	11.8522i	0.325115	+	0.563116i	0.981536	−	0.191279i	$-0.0612635\pi$
$443$	6.84289	+	11.8522i	0.325115	+	0.563116i	−0.656420	+	0.754395i	$0.727930\pi$
$444$	−0.561010	+	0.971697i	−0.0266243	+	0.0461147i
$445$	−5.32273	+	9.21925i	−0.252322	+	0.437034i
$446$	−19.1703	−	33.2039i	−0.907739	−	1.57225i
$447$	−12.8447			−0.607532
$448$	−19.1719	+	0.445480i	−0.905789	+	0.0210469i
$449$	−19.7774			−0.933352			−0.466676	−	0.884428i	$-0.654549\pi$
$449$	−19.7774			−0.933352			−0.466676	+	0.884428i	$0.654549\pi$
$450$	−5.89240	−	10.2059i	−0.277770	−	0.481112i
$451$	1.69185	−	2.93037i	0.0796662	−	0.137986i
$452$	−0.744744	+	1.28993i	−0.0350298	+	0.0606734i
$453$	−5.06411	−	8.77129i	−0.237933	−	0.412111i
$454$	−22.8185			−1.07092
$455$	34.9285	+	57.3771i	1.63747	+	2.68988i
$456$	−1.77476			−0.0831106
$457$	0.803725	+	1.39209i	0.0375967	+	0.0651193i	0.884211	−	0.467087i	$-0.154696\pi$
$457$	0.803725	+	1.39209i	0.0375967	+	0.0651193i	−0.846615	+	0.532206i	$0.821363\pi$
$458$	13.0413	−	22.5881i	0.609379	−	1.05547i
$459$	−7.98089	+	13.8233i	−0.372516	+	0.645217i
$460$	−0.713702	−	1.23617i	−0.0332765	−	0.0576366i
$461$	0.957604			0.0446001			0.0223000	−	0.999751i	$-0.492901\pi$
$461$	0.957604			0.0446001			0.0223000	+	0.999751i	$0.492901\pi$
$462$	0.973461	−	1.78035i	0.0452895	−	0.0828296i
$463$	−14.3693			−0.667798			−0.333899	−	0.942609i	$-0.608365\pi$
$463$	−14.3693			−0.667798			−0.333899	+	0.942609i	$0.608365\pi$
$464$	10.7370	+	18.5970i	0.498452	+	0.863345i
$465$	3.40823	−	5.90322i	0.158053	−	0.273755i
$466$	−0.114255	+	0.197895i	−0.00529275	+	0.00916730i
$467$	6.40579	+	11.0952i	0.296425	+	0.513423i	0.975315	−	0.220817i	$-0.0708723\pi$
$467$	6.40579	+	11.0952i	0.296425	+	0.513423i	−0.678891	+	0.734239i	$0.737539\pi$
$468$	−0.536464			−0.0247981
$469$	9.09069	−	16.6259i	0.419769	−	0.767712i
$470$	7.72896			0.356510
$471$	13.2859	+	23.0119i	0.612183	+	1.06033i
$472$	10.7335	−	18.5909i	0.494047	−	0.855715i
$473$	0.822534	−	1.42467i	0.0378202	−	0.0655064i
$474$	−8.87893	−	15.3788i	−0.407823	−	0.706370i
$475$	5.94127			0.272604
$476$	0.641601	+	1.05396i	0.0294078	+	0.0483082i
$477$	2.90166			0.132858
$478$	13.4309	+	23.2630i	0.614316	+	1.06403i
$479$	6.09569	−	10.5580i	0.278519	−	0.482410i	−0.692498	−	0.721420i	$-0.743490\pi$
$479$	6.09569	−	10.5580i	0.278519	−	0.482410i	0.971017	+	0.239011i	$0.0768230\pi$
$480$	3.12687	−	5.41590i	0.142722	−	0.247201i
$481$	12.8528	+	22.2617i	0.586037	+	1.01505i
$482$	27.3236			1.24456
$483$	8.28531	−	0.192518i	0.376995	−	0.00875986i
$484$	−1.77015			−0.0804615
$485$	−9.31695	−	16.1374i	−0.423061	−	0.732763i
$486$	−4.27855	+	7.41067i	−0.194079	+	0.336155i
$487$	−19.7654	+	34.2347i	−0.895656	+	1.55132i	−0.0626663	+	0.998035i	$0.519960\pi$
$487$	−19.7654	+	34.2347i	−0.895656	+	1.55132i	−0.832990	+	0.553288i	$0.813373\pi$
$488$	1.38500	+	2.39889i	0.0626959	+	0.108593i
$489$	−5.53349			−0.250233
$490$	20.6636	−	39.9702i	0.933486	−	1.80567i
$491$	−5.77830			−0.260771			−0.130386	−	0.991463i	$-0.541622\pi$
$491$	−5.77830			−0.260771			−0.130386	+	0.991463i	$0.541622\pi$
$492$	−1.28260	−	2.22153i	−0.0578242	−	0.100154i
$493$	−7.16498	+	12.4101i	−0.322694	+	0.558923i
$494$	1.79880	−	3.11561i	0.0809319	−	0.140178i
$495$	0.415225	+	0.719191i	0.0186630	+	0.0323252i
$496$	−4.29872			−0.193018
$497$	−3.99943	+	0.0929309i	−0.179399	+	0.00416852i
$498$	−28.7144			−1.28672
$499$	−2.78586	−	4.82525i	−0.124712	−	0.216008i	0.796908	−	0.604100i	$-0.206467\pi$
$499$	−2.78586	−	4.82525i	−0.124712	−	0.216008i	−0.921620	+	0.388093i	$0.873134\pi$
$500$	−3.23553	+	5.60410i	−0.144697	+	0.250623i
$501$	−19.1915	+	33.2407i	−0.857413	+	1.48508i
$502$	13.1097	+	22.7067i	0.585116	+	1.01345i
$503$	8.93145			0.398234			0.199117	−	0.979976i	$-0.436193\pi$
$503$	8.93145			0.398234			0.199117	+	0.979976i	$0.436193\pi$
$504$	−2.11184	−	3.46913i	−0.0940690	−	0.154527i
$505$	5.28976			0.235391
$506$	0.493923	+	0.855499i	0.0219575	+	0.0380316i
$507$	16.1695	−	28.0064i	0.718113	−	1.24381i
$508$	0.312690	−	0.541596i	0.0138734	−	0.0240294i
$509$	−15.2294	−	26.3780i	−0.675030	−	1.16919i	−0.976460	−	0.215698i	$-0.930797\pi$
$509$	−15.2294	−	26.3780i	−0.675030	−	1.16919i	0.301430	−	0.953488i	$-0.402536\pi$
$510$	28.7552			1.27330
$511$	13.1581	−	24.0648i	0.582080	−	1.06456i
$512$	19.2870			0.852371
$513$	−1.17179	−	2.02961i	−0.0517360	−	0.0896094i
$514$	6.80659	−	11.7894i	0.300226	−	0.520007i
$515$	36.2027	−	62.7049i	1.59528	−	2.76311i
$516$	−0.623568	−	1.08005i	−0.0274510	−	0.0475466i
$517$	−0.402112			−0.0176849
$518$	8.26075	−	15.1080i	0.362956	−	0.663808i
$519$	−24.0690			−1.05651
$520$	−34.3010	−	59.4111i	−1.50420	−	2.60535i
$521$	−20.2765	+	35.1200i	−0.888331	+	1.53863i	−0.0464827	+	0.998919i	$0.514801\pi$
$521$	−20.2765	+	35.1200i	−0.888331	+	1.53863i	−0.841848	+	0.539715i	$0.818532\pi$
$522$	−2.08669	+	3.61425i	−0.0913319	+	0.158191i
$523$	15.7868	+	27.3435i	0.690308	+	1.19565i	0.971737	+	0.236067i	$0.0758585\pi$
$523$	15.7868	+	27.3435i	0.690308	+	1.19565i	−0.281428	+	0.959582i	$0.590808\pi$
$524$	0.484372			0.0211599
$525$	−30.2634	−	49.7138i	−1.32080	−	2.16969i
$526$	27.7611			1.21044
$527$	−1.43430	−	2.48429i	−0.0624793	−	0.108217i
$528$	−1.12093	+	1.94152i	−0.0487824	+	0.0844936i
$529$	9.48266	−	16.4244i	0.412290	−	0.714106i
$530$	−16.4157	−	28.4328i	−0.713052	−	1.23504i
$531$	4.51339			0.195865
$532$	−0.181117	+	0.00420844i	−0.00785242	+	0.000182459i
$533$	−58.7692			−2.54558
$534$	−2.79259	−	4.83690i	−0.120847	−	0.209313i
$535$	−34.9080	+	60.4625i	−1.50921	+	2.61402i
$536$	−9.67610	+	16.7595i	−0.417944	+	0.723900i
$537$	15.3385	+	26.5671i	0.661906	+	1.14645i
$538$	27.1648			1.17116
$539$	−1.07506	+	2.07952i	−0.0463061	+	0.0895713i
$540$	3.95414			0.170159
$541$	−0.841369	−	1.45729i	−0.0361733	−	0.0626540i	0.847372	−	0.531000i	$-0.178183\pi$
$541$	−0.841369	−	1.45729i	−0.0361733	−	0.0626540i	−0.883545	+	0.468346i	$0.844850\pi$
$542$	22.4833	−	38.9422i	0.965741	−	1.67271i
$543$	9.69791	−	16.7973i	0.416177	−	0.720840i
$544$	−1.31590	−	2.27921i	−0.0564188	−	0.0977202i
$545$	22.8516			0.978855
$546$	−35.2327	+	0.818668i	−1.50782	+	0.0350357i
$547$	−0.227486			−0.00972661			−0.00486331	−	0.999988i	$-0.501548\pi$
$547$	−0.227486			−0.00972661			−0.00486331	+	0.999988i	$0.501548\pi$
$548$	−1.02792	−	1.78040i	−0.0439104	−	0.0760551i
$549$	−0.291194	+	0.504363i	−0.0124279	+	0.0215257i
$550$	3.46866	−	6.00789i	0.147904	−	0.256178i
$551$	−1.05200	−	1.82211i	−0.0448166	−	0.0776247i
$552$	−8.46393			−0.360249
$553$	10.6530	+	17.4997i	0.453010	+	0.744161i
$554$	40.1093			1.70408
$555$	−15.0834	−	26.1253i	−0.640257	−	1.10896i
$556$	0.746990	−	1.29383i	0.0316795	−	0.0548704i
$557$	3.94106	−	6.82611i	0.166988	−	0.289232i	−0.770372	−	0.637595i	$-0.779929\pi$
$557$	3.94106	−	6.82611i	0.166988	−	0.289232i	0.937359	+	0.348364i	$0.113263\pi$
$558$	−0.417719	−	0.723511i	−0.0176835	−	0.0306287i
$559$	−28.5720			−1.20847
$560$	−23.8499	+	43.6190i	−1.00784	+	1.84324i
$561$	−1.49604			−0.0631627
$562$	11.7551	+	20.3605i	0.495861	+	0.858856i
$563$	−10.2712	+	17.7903i	−0.432880	+	0.749770i	−0.997120	−	0.0758405i	$-0.975836\pi$
$563$	−10.2712	+	17.7903i	−0.432880	+	0.749770i	0.564240	+	0.825611i	$0.309169\pi$
$564$	−0.152422	+	0.264002i	−0.00641812	+	0.0111165i
$565$	−20.0234	−	34.6815i	−0.842389	−	1.45906i
$566$	17.2611			0.725538
$567$	−8.85070	+	16.1870i	−0.371695	+	0.679789i
$568$	4.08565			0.171430
$569$	−13.0463	−	22.5969i	−0.546930	−	0.947311i	−0.998483	−	0.0550666i	$-0.982463\pi$
$569$	−13.0463	−	22.5969i	−0.546930	−	0.947311i	0.451552	−	0.892245i	$-0.350870\pi$
$570$	−2.11099	+	3.65634i	−0.0884196	+	0.153147i
$571$	6.33524	−	10.9730i	0.265122	−	0.459204i	−0.702474	−	0.711710i	$-0.747921\pi$
$571$	6.33524	−	10.9730i	0.265122	−	0.459204i	0.967595	+	0.252505i	$0.0812546\pi$
$572$	−0.157899	−	0.273490i	−0.00660210	−	0.0114352i
$573$	7.36511			0.307682
$574$	20.4700	+	33.6261i	0.854400	+	1.40353i
$575$	28.3343			1.18162
$576$	2.05889	+	3.56610i	0.0857871	+	0.148588i
$577$	−0.446874	+	0.774009i	−0.0186036	+	0.0322224i	−0.875177	−	0.483802i	$-0.839255\pi$
$577$	−0.446874	+	0.774009i	−0.0186036	+	0.0322224i	0.856574	+	0.516025i	$0.172589\pi$
$578$	−6.44924	+	11.1704i	−0.268253	+	0.464628i
$579$	−1.63952	−	2.83972i	−0.0681359	−	0.118015i
$580$	3.54990			0.147401
$581$	33.1187	−	0.769548i	1.37400	−	0.0319262i
$582$	9.77632			0.405242
$583$	0.854055	+	1.47927i	0.0353713	+	0.0612649i
$584$	−14.0054	+	24.2581i	−0.579549	+	1.00381i
$585$	7.21175	−	12.4911i	0.298169	−	0.516444i
$586$	3.61627	+	6.26356i	0.149387	+	0.258745i
$587$	−24.3556			−1.00526			−0.502631	−	0.864501i	$-0.667635\pi$
$587$	−24.3556			−1.00526			−0.502631	+	0.864501i	$0.667635\pi$
$588$	0.957782	+	1.49407i	0.0394983	+	0.0616143i
$589$	0.421184			0.0173546
$590$	−25.5339	−	44.2259i	−1.05121	−	1.82075i
$591$	−3.36549	+	5.82921i	−0.138438	+	0.239781i
$592$	−9.51220	+	16.4756i	−0.390949	+	0.677144i
$593$	6.65602	+	11.5286i	0.273330	+	0.473421i	0.969712	−	0.244250i	$-0.0785416\pi$
$593$	6.65602	+	11.5286i	0.273330	+	0.473421i	−0.696382	+	0.717671i	$0.745208\pi$
$594$	−2.73649			−0.112280
$595$	−33.1657	+	0.770640i	−1.35966	+	0.0315931i
$596$	1.33908			0.0548508
$597$	−4.87707	−	8.44734i	−0.199605	−	0.345726i
$598$	8.57859	−	14.8586i	0.350805	−	0.607612i
$599$	−4.46138	+	7.72734i	−0.182287	+	0.315731i	−0.942659	−	0.333757i	$-0.891683\pi$
$599$	−4.46138	+	7.72734i	−0.182287	+	0.315731i	0.760372	+	0.649488i	$0.225017\pi$
$600$	29.7197	+	51.4761i	1.21330	+	2.10150i
$601$	23.3119			0.950911			0.475455	−	0.879740i	$-0.342283\pi$
$601$	23.3119			0.950911			0.475455	+	0.879740i	$0.342283\pi$
$602$	9.95196	+	16.3481i	0.405612	+	0.666300i
$603$	−4.06878			−0.165693
$604$	0.527942	+	0.914423i	0.0214817	+	0.0372073i
$605$	23.7964	−	41.2165i	0.967460	−	1.67569i
$606$	−1.38764	+	2.40347i	−0.0563691	+	0.0976342i
$607$	7.38619	+	12.7933i	0.299796	+	0.519262i	0.976089	−	0.217370i	$-0.0697480\pi$
$607$	7.38619	+	12.7933i	0.299796	+	0.519262i	−0.676293	+	0.736633i	$0.736415\pi$
$608$	0.386414			0.0156712
$609$	−9.88798	+	18.0840i	−0.400681	+	0.732803i
$610$	6.58955			0.266803
$611$	3.49200	+	6.04833i	0.141271	+	0.244689i
$612$	0.132473	−	0.229449i	0.00535489	−	0.00927494i
$613$	5.50274	−	9.53102i	0.222254	−	0.384954i	−0.733238	−	0.679972i	$-0.761992\pi$
$613$	5.50274	−	9.53102i	0.222254	−	0.384954i	0.955492	+	0.295017i	$0.0953254\pi$
$614$	12.8749	+	22.3000i	0.519590	+	0.899956i
$615$	68.9688			2.78109
$616$	1.14698	−	2.09770i	0.0462131	−	0.0845188i
$617$	25.9673			1.04540			0.522701	−	0.852516i	$-0.324924\pi$
$617$	25.9673			1.04540			0.522701	+	0.852516i	$0.324924\pi$
$618$	18.9938	+	32.8983i	0.764044	+	1.32336i
$619$	10.9902	−	19.0356i	0.441734	−	0.765106i	−0.556084	−	0.831126i	$-0.687697\pi$
$619$	10.9902	−	19.0356i	0.441734	−	0.765106i	0.997818	+	0.0660201i	$0.0210301\pi$
$620$	−0.355314	+	0.615422i	−0.0142698	+	0.0247159i
$621$	−5.58836	−	9.67933i	−0.224253	−	0.388418i
$622$	−16.5661			−0.664242
$623$	3.35055	+	5.50396i	0.134237	+	0.220512i
$624$	38.9374			1.55875
$625$	−51.7260	−	89.5920i	−2.06904	−	3.58368i
$626$	−18.1855	+	31.4982i	−0.726838	+	1.25892i
$627$	0.109828	−	0.190227i	0.00438610	−	0.00759695i
$628$	−1.38508	−	2.39903i	−0.0552707	−	0.0957317i
$629$	−12.6953			−0.506195
$630$	−9.65901	+	0.224437i	−0.384824	+	0.00894178i
$631$	42.6583			1.69820			0.849100	−	0.528232i	$-0.177145\pi$
$631$	42.6583			1.69820			0.849100	+	0.528232i	$0.177145\pi$
$632$	−10.4616	−	18.1200i	−0.416140	−	0.720775i
$633$	0.877362	−	1.51964i	0.0348720	−	0.0604001i
$634$	−20.0055	+	34.6505i	−0.794519	+	1.37615i
$635$	8.40707	+	14.5615i	0.333624	+	0.577854i
$636$	1.29493			0.0513472
$637$	40.6149	−	1.88848i	1.60922	−	0.0748241i
$638$	−2.45673			−0.0972629
$639$	0.429502	+	0.743919i	0.0169908	+	0.0294290i
$640$	27.3059	−	47.2953i	1.07936	−	1.86951i
$641$	1.97660	−	3.42357i	0.0780709	−	0.135223i	−0.824347	−	0.566085i	$-0.808457\pi$
$641$	1.97660	−	3.42357i	0.0780709	−	0.135223i	0.902418	+	0.430863i	$0.141791\pi$
$642$	−18.3146	−	31.7218i	−0.722819	−	1.25196i
$643$	7.43895			0.293364			0.146682	−	0.989184i	$-0.453141\pi$
$643$	7.43895			0.293364			0.146682	+	0.989184i	$0.453141\pi$
$644$	−0.863759	+	0.0200703i	−0.0340369	+	0.000790882i
$645$	33.5308			1.32027
$646$	0.888380	+	1.53872i	0.0349528	+	0.0605401i
$647$	−5.66262	+	9.80795i	−0.222621	+	0.385590i	−0.955603	−	0.294657i	$-0.904794\pi$
$647$	−5.66262	+	9.80795i	−0.222621	+	0.385590i	0.732982	+	0.680248i	$0.238128\pi$
$648$	9.42065	−	16.3171i	0.370078	−	0.640994i
$649$	1.32844	+	2.30093i	0.0521460	+	0.0903195i
$650$	−120.489			−4.72598
$651$	−2.14541	−	3.52427i	−0.0840852	−	0.138127i
$652$	0.576876			0.0225922
$653$	−20.1651	−	34.9270i	−0.789122	−	1.36680i	−0.926506	−	0.376281i	$-0.877203\pi$
$653$	−20.1651	−	34.9270i	−0.789122	−	1.36680i	0.137384	−	0.990518i	$-0.456131\pi$
$654$	−5.99458	+	10.3829i	−0.234407	+	0.406004i
$655$	−6.51148	+	11.2782i	−0.254425	+	0.440676i
$656$	−21.7472	−	37.6672i	−0.849085	−	1.47066i
$657$	−5.88926			−0.229762
$658$	2.24438	−	4.10473i	0.0874950	−	0.160019i
$659$	−1.42326			−0.0554424			−0.0277212	−	0.999616i	$-0.508825\pi$
$659$	−1.42326			−0.0554424			−0.0277212	+	0.999616i	$0.508825\pi$
$660$	0.185303	+	0.320955i	0.00721292	+	0.0124931i
$661$	18.0701	−	31.2983i	0.702845	−	1.21736i	−0.264619	−	0.964353i	$-0.585246\pi$
$661$	18.0701	−	31.2983i	0.702845	−	1.21736i	0.967464	−	0.253009i	$-0.0814204\pi$
$662$	19.3246	−	33.4712i	0.751072	−	1.30090i
$663$	12.9918	+	22.5025i	0.504560	+	0.873924i
$664$	−33.8327			−1.31296
$665$	2.33679	−	4.27374i	0.0906168	−	0.165728i
$666$	−3.69731			−0.143268
$667$	−5.01704	−	8.68978i	−0.194261	−	0.336469i
$668$	2.00075	−	3.46540i	0.0774113	−	0.134080i
$669$	−20.3290	+	35.2108i	−0.785963	+	1.36133i
$670$	23.0185	+	39.8692i	0.889282	+	1.54028i
$671$	−0.342833			−0.0132349
$672$	−1.96830	−	3.23334i	−0.0759289	−	0.124729i
$673$	−27.3356			−1.05371			−0.526855	−	0.849955i	$-0.676629\pi$
$673$	−27.3356			−1.05371			−0.526855	+	0.849955i	$0.676629\pi$
$674$	−9.25393	−	16.0283i	−0.356448	−	0.617386i
$675$	−39.2453	+	67.9748i	−1.51055	+	2.61635i
$676$	−1.68570	+	2.91972i	−0.0648346	+	0.112297i
$677$	19.2362	+	33.3182i	0.739309	+	1.28052i	0.952807	+	0.303577i	$0.0981810\pi$
$677$	19.2362	+	33.3182i	0.739309	+	1.28052i	−0.213498	+	0.976944i	$0.568486\pi$
$678$	21.0106			0.806908
$679$	−11.2758	+	0.262006i	−0.432727	+	0.0100549i
$680$	33.8807			1.29927
$681$	12.0988	+	20.9558i	0.463628	+	0.803027i
$682$	0.245898	−	0.425907i	0.00941590	−	0.0163088i
$683$	11.9324	−	20.6675i	0.456580	−	0.790820i	−0.542197	−	0.840251i	$-0.682407\pi$
$683$	11.9324	−	20.6675i	0.456580	−	0.790820i	0.998778	+	0.0494308i	$0.0157407\pi$
$684$	0.0194503	+	0.0336889i	0.000743701	+	0.00128813i
$685$	55.2736			2.11190
$686$	−15.2272	−	22.5809i	−0.581375	−	0.862143i
$687$	−27.6590			−1.05526
$688$	−10.5729	−	18.3128i	−0.403088	−	0.698170i
$689$	14.8335	−	25.6923i	0.565110	−	0.978800i
$690$	−10.0674	+	17.4373i	−0.383261	+	0.663827i
$691$	7.57730	+	13.1243i	0.288254	+	0.499271i	0.973393	−	0.229142i	$-0.0735919\pi$
$691$	7.57730	+	13.1243i	0.288254	+	0.499271i	−0.685139	+	0.728412i	$0.740259\pi$
$692$	2.50923			0.0953867
$693$	0.502527	−	0.0116767i	0.0190894	−	0.000443562i
$694$	−14.9435			−0.567248
$695$	20.0838	+	34.7861i	0.761821	+	1.31951i
$696$	10.5247	−	18.2294i	0.398939	−	0.690982i
$697$	14.5123	−	25.1360i	0.549691	−	0.952093i
$698$	1.90321	+	3.29646i	0.0720376	+	0.124773i
$699$	0.242321			0.00916541
$700$	3.15501	+	5.18275i	0.119248	+	0.195890i
$701$	−24.5410			−0.926900			−0.463450	−	0.886123i	$-0.653389\pi$
$701$	−24.5410			−0.926900			−0.463450	+	0.886123i	$0.653389\pi$
$702$	23.7641	+	41.1606i	0.896918	+	1.55351i
$703$	0.931995	−	1.61426i	0.0351508	−	0.0608830i
$704$	−1.21200	+	2.09925i	−0.0456790	+	0.0791183i
$705$	−4.09805	−	7.09804i	−0.154342	−	0.267327i
$706$	4.06518			0.152995
$707$	1.53607	−	2.80931i	0.0577699	−	0.105655i
$708$	2.01420			0.0756983
$709$	8.35144	+	14.4651i	0.313645	+	0.543249i	0.979148	−	0.203146i	$-0.0651165\pi$
$709$	8.35144	+	14.4651i	0.313645	+	0.543249i	−0.665504	+	0.746395i	$0.731783\pi$
$710$	4.85969	−	8.41722i	0.182381	−	0.315893i
$711$	2.19954	−	3.80971i	0.0824891	−	0.142875i
$712$	−3.29036	−	5.69907i	−0.123312	−	0.213582i
$713$	2.00865			0.0752246
$714$	8.35009	−	15.2714i	0.312494	−	0.571519i
$715$	8.49064			0.317532
$716$	−1.59907	−	2.76967i	−0.0597600	−	0.103507i
$717$	14.2427	−	24.6691i	0.531903	−	0.921284i
$718$	16.2958	−	28.2252i	0.608154	−	1.05335i
$719$	0.0753295	+	0.130475i	0.00280932	+	0.00486588i	0.867427	−	0.497565i	$-0.165772\pi$
$719$	0.0753295	+	0.130475i	0.00280932	+	0.00486588i	−0.864617	+	0.502431i	$0.832439\pi$
$720$	10.6747			0.397821
$721$	−22.7888	−	37.4353i	−0.848701	−	1.39416i
$722$	27.6800			1.03014
$723$	−14.4875	−	25.0932i	−0.538798	−	0.933225i
$724$	−1.01102	+	1.75115i	−0.0375744	+	0.0650808i
$725$	−35.2331	+	61.0255i	−1.30852	+	2.26643i
$726$	12.4848	+	21.6244i	0.463355	+	0.802555i
$727$	−8.32486			−0.308752			−0.154376	−	0.988012i	$-0.549337\pi$
$727$	−8.32486			−0.308752			−0.154376	+	0.988012i	$0.549337\pi$
$728$	−41.5129	+	0.964594i	−1.53857	+	0.0357502i
$729$	29.9931			1.11086
$730$	33.3176	+	57.7078i	1.23314	+	2.13586i
$731$	7.05548	−	12.2205i	0.260956	−	0.451990i
$732$	−0.129952	+	0.225083i	−0.00480316	+	0.00831932i
$733$	−10.9472	−	18.9610i	−0.404343	−	0.700342i	0.589902	−	0.807475i	$-0.299166\pi$
$733$	−10.9472	−	18.9610i	−0.404343	−	0.700342i	−0.994245	+	0.107133i	$0.965833\pi$
$734$	−10.1390			−0.374239
$735$	−47.6637	+	2.21623i	−1.75810	+	0.0817467i
$736$	1.84283			0.0679278
$737$	−1.19758	−	2.07426i	−0.0441133	−	0.0764065i
$738$	4.22647	−	7.32047i	0.155579	−	0.269470i
$739$	0.824428	−	1.42795i	0.0303271	−	0.0525280i	−0.850464	−	0.526034i	$-0.823678\pi$
$739$	0.824428	−	1.42795i	0.0303271	−	0.0525280i	0.880791	+	0.473506i	$0.157012\pi$
$740$	1.57248	+	2.72361i	0.0578054	+	0.100122i
$741$	−3.81505			−0.140149
$742$	−19.8671	+	0.461633i	−0.729344	+	0.0169471i
$743$	5.14880			0.188891			0.0944455	−	0.995530i	$-0.469892\pi$
$743$	5.14880			0.188891			0.0944455	+	0.995530i	$0.469892\pi$
$744$	2.10687	+	3.64920i	0.0772416	+	0.133786i
$745$	−18.0014	+	31.1794i	−0.659521	+	1.14232i
$746$	−7.43528	+	12.8783i	−0.272225	+	0.471507i
$747$	−3.55665	−	6.16029i	−0.130131	−	0.225393i
$748$	0.155965			0.00570263
$749$	21.9739	+	36.0966i	0.802908	+	1.31894i
$750$	91.2804			3.33309
$751$	−17.4494	−	30.2232i	−0.636737	−	1.10286i	−0.986144	−	0.165890i	$-0.946950\pi$
$751$	−17.4494	−	30.2232i	−0.636737	−	1.10286i	0.349407	−	0.936971i	$-0.386383\pi$
$752$	−2.58439	+	4.47630i	−0.0942430	+	0.163234i
$753$	13.9021	−	24.0792i	0.506621	−	0.877493i
$754$	21.3346	+	36.9526i	0.776961	+	1.34574i
$755$	−28.3888			−1.03317
$756$	1.14823	−	2.09998i	0.0417606	−	0.0763757i
$757$	−24.3537			−0.885150			−0.442575	−	0.896732i	$-0.645935\pi$
$757$	−24.3537			−0.885150			−0.442575	+	0.896732i	$0.645935\pi$
$758$	−0.481406	−	0.833820i	−0.0174855	−	0.0302857i
$759$	0.523776	−	0.907207i	0.0190119	−	0.0329295i
$760$	−2.48727	+	4.30808i	−0.0902227	+	0.156270i
$761$	16.4565	+	28.5035i	0.596548	+	1.03325i	0.993326	+	0.115337i	$0.0367948\pi$
$761$	16.4565	+	28.5035i	0.596548	+	1.03325i	−0.396778	+	0.917914i	$0.629872\pi$
$762$	−8.82158			−0.319572
$763$	6.63578	−	12.1361i	0.240232	−	0.439358i
$764$	−0.767827			−0.0277790
$765$	3.56169	+	6.16903i	0.128773	+	0.223042i
$766$	−12.7637	+	22.1074i	−0.461171	+	0.798772i
$767$	23.0728	−	39.9633i	0.833111	−	1.44299i
$768$	3.02280	+	5.23564i	0.109076	+	0.188925i
$769$	−29.1096			−1.04972			−0.524859	−	0.851189i	$-0.675882\pi$
$769$	−29.1096			−1.04972			−0.524859	+	0.851189i	$0.675882\pi$
$770$	−2.95739	−	4.85811i	−0.106577	−	0.175074i
$771$	−14.4360			−0.519899
$772$	0.170923	+	0.296046i	0.00615164	+	0.0106549i
$773$	7.55689	−	13.0889i	0.271803	−	0.470776i	−0.697521	−	0.716564i	$-0.745714\pi$
$773$	7.55689	−	13.0889i	0.271803	−	0.470776i	0.969323	+	0.245789i	$0.0790469\pi$
$774$	2.05480	−	3.55902i	0.0738583	−	0.127926i
$775$	−7.05306	−	12.2163i	−0.253353	−	0.438821i
$776$	11.5189			0.413506
$777$	−18.2548	+	0.424168i	−0.654886	+	0.0152169i
$778$	−26.3719			−0.945480
$779$	2.13076	+	3.69059i	0.0763425	+	0.132229i
$780$	3.21840	−	5.57444i	0.115237	−	0.199597i
$781$	−0.252834	+	0.437921i	−0.00904710	+	0.0156700i
$782$	4.23674	+	7.33825i	0.151505	+	0.262415i
$783$	27.7961			0.993350
$784$	16.2397	+	25.3327i	0.579988	+	0.904738i
$785$	74.4792			2.65828
$786$	−3.41626	−	5.91714i	−0.121854	−	0.211058i
$787$	21.6335	−	37.4703i	0.771151	−	1.33567i	−0.165782	−	0.986162i	$-0.553015\pi$
$787$	21.6335	−	37.4703i	0.771151	−	1.33567i	0.936933	−	0.349510i	$-0.113652\pi$
$788$	0.350859	−	0.607705i	0.0124988	−	0.0216486i
$789$	−14.7195	−	25.4950i	−0.524029	−	0.907644i
$790$	−49.7742			−1.77089
$791$	−24.2333	+	0.563086i	−0.861637	+	0.0200210i
$792$	−0.513360			−0.0182415
$793$	2.97721	+	5.15668i	0.105724	+	0.183119i
$794$	1.72272	−	2.98385i	0.0611372	−	0.105893i
$795$	−17.4079	+	30.1513i	−0.617394	+	1.06936i
$796$	0.508444	+	0.880650i	0.0180213	+	0.0312138i
$797$	−9.61790			−0.340683			−0.170342	−	0.985385i	$-0.554487\pi$
$797$	−9.61790			−0.340683			−0.170342	+	0.985385i	$0.554487\pi$
$798$	1.32882	+	2.18286i	0.0470399	+	0.0772725i
$799$	−3.44922			−0.122024
$800$	−6.47082	−	11.2078i	−0.228778	−	0.396255i
$801$	0.691795	−	1.19822i	0.0244434	−	0.0423372i
$802$	−1.97029	+	3.41265i	−0.0695735	+	0.120505i
$803$	−1.73341	−	3.00235i	−0.0611706	−	0.105951i
$804$	−1.81578			−0.0640377
$805$	11.1443	−	20.3817i	0.392785	−	0.718361i
$806$	−8.54164			−0.300867
$807$	−14.4034	−	24.9473i	−0.507022	−	0.878188i
$808$	−1.63499	+	2.83188i	−0.0575187	+	0.0996253i
$809$	−9.01870	+	15.6208i	−0.317080	+	0.549199i	−0.979878	−	0.199600i	$-0.936036\pi$
$809$	−9.01870	+	15.6208i	−0.317080	+	0.549199i	0.662797	+	0.748799i	$0.269369\pi$
$810$	−22.4108	−	38.8167i	−0.787436	−	1.36388i
$811$	−28.6423			−1.00577			−0.502884	−	0.864354i	$-0.667728\pi$
$811$	−28.6423			−1.00577			−0.502884	+	0.864354i	$0.667728\pi$
$812$	1.03084	−	1.88529i	0.0361754	−	0.0661609i
$813$	−47.6845			−1.67237
$814$	−1.08824	−	1.88489i	−0.0381429	−	0.0660655i
$815$	−7.75502	+	13.4321i	−0.271646	+	0.470506i
$816$	−9.61508	+	16.6538i	−0.336595	+	0.583000i
$817$	1.03592	+	1.79427i	0.0362423	+	0.0627735i
$818$	37.8024			1.32173
$819$	−4.53965	−	7.45730i	−0.158628	−	0.260579i
$820$	−7.19012			−0.251090
$821$	7.32123	+	12.6807i	0.255513	+	0.442561i	0.965035	−	0.262122i	$-0.0844224\pi$
$821$	7.32123	+	12.6807i	0.255513	+	0.442561i	−0.709522	+	0.704683i	$0.751089\pi$
$822$	−14.4997	+	25.1143i	−0.505736	+	0.875961i
$823$	10.8211	−	18.7427i	0.377200	−	0.653329i	−0.613454	−	0.789731i	$-0.710220\pi$
$823$	10.8211	−	18.7427i	0.377200	−	0.653329i	0.990654	+	0.136401i	$0.0435536\pi$
$824$	22.3795	+	38.7624i	0.779625	+	1.35035i
$825$	−7.35662			−0.256125
$826$	−30.9024	+	0.718049i	−1.07523	+	0.0249841i
$827$	5.94455			0.206712			0.103356	−	0.994644i	$-0.467042\pi$
$827$	5.94455			0.206712			0.103356	+	0.994644i	$0.467042\pi$
$828$	0.0927597	+	0.160665i	0.00322362	+	0.00558348i
$829$	−5.03676	+	8.72392i	−0.174934	+	0.302994i	−0.940138	−	0.340793i	$-0.889304\pi$
$829$	−5.03676	+	8.72392i	−0.174934	+	0.302994i	0.765205	+	0.643787i	$0.222638\pi$
$830$	−40.2424	+	69.7019i	−1.39683	+	2.41939i
$831$	−21.2668	−	36.8351i	−0.737736	−	1.27780i
$832$	42.1008			1.45958
$833$	−9.22158	+	17.8376i	−0.319509	+	0.618036i
$834$	−21.0740			−0.729733
$835$	53.7926	+	93.1716i	1.86157	+	3.22433i
$836$	−0.0114498	+	0.0198316i	−0.000395998	+	0.000685889i
$837$	−2.78215	+	4.81882i	−0.0961651	+	0.166563i
$838$	−7.73585	−	13.3989i	−0.267230	−	0.462857i
$839$	14.2644			0.492461			0.246231	−	0.969211i	$-0.420808\pi$
$839$	14.2644			0.492461			0.246231	+	0.969211i	$0.420808\pi$
$840$	48.7176	−	1.13200i	1.68092	−	0.0390578i
$841$	−4.04563			−0.139504
$842$	6.16693	+	10.6814i	0.212526	+	0.368107i
$843$	12.4656	−	21.5911i	0.429339	−	0.743638i
$844$	−0.0914666	+	0.158425i	−0.00314841	+	0.00545320i
$845$	−45.3222	−	78.5003i	−1.55913	−	2.70049i
$846$	−1.00453			−0.0345365
$847$	−14.9793	−	24.6066i	−0.514696	−	0.845492i
$848$	21.9562			0.753978
$849$	−9.15219	−	15.8521i	−0.314102	−	0.544041i
$850$	29.7533	−	51.5342i	1.02053	−	1.76761i
$851$	4.44474	−	7.69852i	0.152364	−	0.263902i
$852$	0.191675	+	0.331990i	0.00656667	+	0.0113738i
$853$	3.41266			0.116847			0.0584236	−	0.998292i	$-0.481393\pi$
$853$	3.41266			0.116847			0.0584236	+	0.998292i	$0.481393\pi$
$854$	1.91351	−	3.49961i	0.0654791	−	0.119754i
$855$	−1.04589			−0.0357687
$856$	−21.5791	−	37.3762i	−0.737560	−	1.27749i
$857$	0.490016	−	0.848732i	0.0167386	−	0.0289921i	−0.857535	−	0.514426i	$-0.828005\pi$
$857$	0.490016	−	0.848732i	0.0167386	−	0.0289921i	0.874273	+	0.485434i	$0.161338\pi$
$858$	−2.22732	+	3.85783i	−0.0760394	+	0.131704i
$859$	22.2817	+	38.5931i	0.760242	+	1.31678i	0.942726	+	0.333569i	$0.108253\pi$
$859$	22.2817	+	38.5931i	0.760242	+	1.31678i	−0.182483	+	0.983209i	$0.558414\pi$
$860$	−3.49565			−0.119201
$861$	20.0276	−	36.6282i	0.682537	−	1.24829i
$862$	12.7746			0.435103
$863$	−22.4229	−	38.8377i	−0.763286	−	1.32205i	−0.941148	−	0.337994i	$-0.890251\pi$
$863$	−22.4229	−	38.8377i	−0.763286	−	1.32205i	0.177862	−	0.984055i	$-0.443082\pi$
$864$	−2.55248	+	4.42102i	−0.0868370	+	0.150406i
$865$	−33.7319	+	58.4254i	−1.14692	+	1.98652i
$866$	−22.9173	−	39.6940i	−0.778762	−	1.34886i
$867$	13.6781			0.464532
$868$	0.223663	+	0.367412i	0.00759161	+	0.0124708i
$869$	2.58959			0.0878459
$870$	−25.0373	−	43.3659i	−0.848844	−	1.47024i
$871$	−20.7999	+	36.0265i	−0.704777	+	1.22071i
$872$	−7.06310	+	12.2337i	−0.239187	+	0.414284i
$873$	1.21092	+	2.09738i	0.0409835	+	0.0709855i
$874$	−1.24412			−0.0420829
$875$	−105.281	+	2.44632i	−3.55916	+	0.0827007i
$876$	−2.62821			−0.0887990
$877$	−8.72741	−	15.1163i	−0.294704	−	0.510442i	0.680212	−	0.733015i	$-0.261888\pi$
$877$	−8.72741	−	15.1163i	−0.294704	−	0.510442i	−0.974916	+	0.222574i	$0.928554\pi$
$878$	−3.96265	+	6.86352i	−0.133733	+	0.231633i
$879$	3.83484	−	6.64214i	0.129346	−	0.224034i
$880$	3.14191	+	5.44195i	0.105914	+	0.183448i
$881$	−6.27922			−0.211552			−0.105776	−	0.994390i	$-0.533733\pi$
$881$	−6.27922			−0.211552			−0.105776	+	0.994390i	$0.533733\pi$
$882$	−2.68564	+	5.19492i	−0.0904303	+	0.174922i
$883$	8.89048			0.299189			0.149594	−	0.988747i	$-0.452203\pi$
$883$	8.89048			0.299189			0.149594	+	0.988747i	$0.452203\pi$
$884$	−1.35442	−	2.34592i	−0.0455541	−	0.0789020i
$885$	−27.0772	+	46.8990i	−0.910189	+	1.57649i
$886$	−10.0629	+	17.4295i	−0.338071	+	0.585557i
$887$	10.8687	+	18.8251i	0.364935	+	0.632086i	0.988766	−	0.149473i	$-0.0477578\pi$
$887$	10.8687	+	18.8251i	0.364935	+	0.632086i	−0.623831	+	0.781560i	$0.714424\pi$
$888$	18.6483			0.625796
$889$	10.1747	−	0.236419i	0.341247	−	0.00792923i
$890$	−15.6549			−0.524754
$891$	1.16596	+	2.01951i	0.0390612	+	0.0676560i
$892$	2.11933	−	3.67079i	0.0709605	−	0.122907i
$893$	0.253216	−	0.438582i	0.00847354	−	0.0146766i
$894$	−9.44449	−	16.3583i	−0.315871	−	0.547104i
$895$	85.9859			2.87419
$896$	−17.1885	−	28.2356i	−0.574229	−	0.943287i
$897$	−18.1942			−0.607486
$898$	−14.5420	−	25.1875i	−0.485273	−	0.840518i
$899$	−2.49772	+	4.32617i	−0.0833035	+	0.144286i
$900$	0.651422	−	1.12830i	0.0217141	−	0.0376099i
$901$	7.32586	+	12.6888i	0.244060	+	0.422724i
$902$	4.97597			0.165682
$903$	9.73687	−	17.8077i	0.324023	−	0.592603i
$904$	24.7557			0.823364
$905$	−27.1827	−	47.0817i	−0.903582	−	1.56505i
$906$	7.44712	−	12.8988i	0.247414	−	0.428534i
$907$	−3.58575	+	6.21071i	−0.119063	+	0.206223i	−0.919397	−	0.393332i	$-0.871322\pi$
$907$	−3.58575	+	6.21071i	−0.119063	+	0.206223i	0.800334	+	0.599555i	$0.204656\pi$
$908$	−1.26132	−	2.18468i	−0.0418585	−	0.0725011i
$909$	−0.687509			−0.0228032
$910$	−47.3903	+	86.6718i	−1.57097	+	2.87314i
$911$	34.7540			1.15145			0.575726	−	0.817643i	$-0.304720\pi$
$911$	34.7540			1.15145			0.575726	+	0.817643i	$0.304720\pi$
$912$	−1.41173	−	2.44520i	−0.0467472	−	0.0809686i
$913$	2.09368	−	3.62636i	0.0692907	−	0.120015i
$914$	−1.18193	+	2.04717i	−0.0390949	+	0.0677143i
$915$	−3.49392	−	6.05164i	−0.115505	−	0.200061i
$916$	2.88350			0.0952736
$917$	4.09884	+	6.73318i	0.135356	+	0.222349i
$918$	−23.4729			−0.774722
$919$	−25.5465	−	44.2478i	−0.842700	−	1.45960i	−0.887603	−	0.460609i	$-0.847631\pi$
$919$	−25.5465	−	44.2478i	−0.842700	−	1.45960i	0.0449029	−	0.998991i	$-0.485702\pi$
$920$	−11.8619	+	20.5455i	−0.391077	+	0.677365i
$921$	13.6531	−	23.6479i	0.449885	−	0.779224i
$922$	0.704112	+	1.21956i	0.0231887	+	0.0401640i
$923$	8.78258			0.289082
$924$	0.224264	−	0.00521100i	0.00737773	−	0.000171429i
$925$	−62.4280			−2.05262
$926$	−10.5655	−	18.3000i	−0.347205	−	0.601377i
$927$	−4.70526	+	8.14974i	−0.154541	+	0.267673i
$928$	−2.29153	+	3.96904i	−0.0752230	+	0.130290i
$929$	14.1814	+	24.5628i	0.465275	+	0.805880i	0.999214	−	0.0396429i	$-0.0126220\pi$
$929$	14.1814	+	24.5628i	0.465275	+	0.805880i	−0.533939	+	0.845523i	$0.679289\pi$
$930$	10.0241			0.328702
$931$	−1.59114	−	2.48207i	−0.0521477	−	0.0813464i
$932$	−0.0252624			−0.000827497
$933$	8.78371	+	15.2138i	0.287566	+	0.498079i
$934$	−9.42017	+	16.3162i	−0.308237	+	0.533883i
$935$	−2.09665	+	3.63151i	−0.0685678	+	0.118763i
$936$	4.45810	+	7.72165i	0.145717	+	0.252390i
$937$	43.8732			1.43328			0.716638	−	0.697446i	$-0.245680\pi$
$937$	43.8732			1.43328			0.716638	+	0.697446i	$0.245680\pi$
$938$	27.8582	−	0.647313i	0.909601	−	0.0211355i
$939$	38.5693			1.25866
$940$	0.427229	+	0.739983i	0.0139347	+	0.0241356i
$941$	−7.96137	+	13.7895i	−0.259533	+	0.449525i	−0.966117	−	0.258105i	$-0.916902\pi$
$941$	−7.96137	+	13.7895i	−0.259533	+	0.449525i	0.706584	+	0.707629i	$0.250235\pi$
$942$	−19.5379	+	33.8406i	−0.636578	+	1.10259i
$943$	10.1617	+	17.6007i	0.330912	+	0.573156i
$944$	34.1518			1.11155
$945$	33.4606	+	54.9659i	1.08847	+	1.78804i
$946$	2.41919			0.0786546
$947$	−5.84972	−	10.1320i	−0.190090	−	0.329246i	0.755190	−	0.655506i	$-0.227545\pi$
$947$	−5.84972	−	10.1320i	−0.190090	−	0.329246i	−0.945280	+	0.326260i	$0.894211\pi$
$948$	0.981593	−	1.70017i	0.0318806	−	0.0552189i
$949$	−30.1063	+	52.1457i	−0.977292	+	1.69272i
$950$	4.36852	+	7.56650i	0.141734	+	0.245490i
$951$	42.4293			1.37586
$952$	9.83849	−	17.9935i	0.318867	−	0.583174i
$953$	−53.1045			−1.72022			−0.860112	−	0.510105i	$-0.829606\pi$
$953$	−53.1045			−1.72022			−0.860112	+	0.510105i	$0.829606\pi$
$954$	2.13354	+	3.69541i	0.0690760	+	0.119643i
$955$	10.3220	−	17.8782i	0.334012	−	0.578525i
$956$	−1.48483	+	2.57180i	−0.0480227	+	0.0831778i
$957$	1.30261	+	2.25619i	0.0421074	+	0.0729321i
$958$	17.9283			0.579237
$959$	16.0507	−	29.3550i	0.518304	−	0.947922i
$960$	−49.4075			−1.59462
$961$	−0.500000	−	0.866025i	−0.0161290	−	0.0279363i
$962$	−18.9009	+	32.7374i	−0.609391	+	1.05550i
$963$	4.53699	−	7.85830i	0.146202	−	0.253230i
$964$	1.51035	+	2.61601i	0.0486452	+	0.0842559i
$965$	−9.19093			−0.295866
$966$	6.33725	+	10.4102i	0.203898	+	0.334943i
$967$	25.5960			0.823112			0.411556	−	0.911385i	$-0.364985\pi$
$967$	25.5960			0.823112			0.411556	+	0.911385i	$0.364985\pi$
$968$	14.7102	+	25.4789i	0.472805	+	0.818922i
$969$	0.942075	−	1.63172i	0.0302638	−	0.0524184i
$970$	13.7012	−	23.7312i	0.439920	−	0.761963i
$971$	27.0282	+	46.8141i	0.867375	+	1.50234i	0.864670	+	0.502341i	$0.167528\pi$
$971$	27.0282	+	46.8141i	0.867375	+	1.50234i	0.00270530	+	0.999996i	$0.499139\pi$
$972$	−0.946013			−0.0303434
$973$	24.3064	−	0.564784i	0.779228	−	0.0181062i
$974$	−58.1328			−1.86270
$975$	63.8860	+	110.654i	2.04599	+	3.54376i
$976$	−2.20340	+	3.81640i	−0.0705291	+	0.122160i
$977$	8.67123	−	15.0190i	0.277417	−	0.480501i	−0.693325	−	0.720625i	$-0.743855\pi$
$977$	8.67123	−	15.0190i	0.277417	−	0.480501i	0.970742	+	0.240124i	$0.0771883\pi$
$978$	−4.06869	−	7.04718i	−0.130102	−	0.225344i
$979$	0.814474			0.0260307
$980$	4.96903	−	0.231046i	0.158730	−	0.00738048i
$981$	−2.97002			−0.0948254
$982$	−4.24870	−	7.35896i	−0.135581	−	0.234834i
$983$	23.3635	−	40.4668i	0.745181	−	1.29069i	−0.204930	−	0.978777i	$-0.565697\pi$
$983$	23.3635	−	40.4668i	0.745181	−	1.29069i	0.950110	−	0.311914i	$-0.100970\pi$
$984$	−21.3173	+	36.9226i	−0.679569	+	1.17705i
$985$	9.43328	+	16.3389i	0.300569	+	0.520601i
$986$	−21.0732			−0.671107
$987$	−4.95967	+	0.115243i	−0.157868	+	0.00366823i
$988$	0.397725			0.0126533
$989$	4.94038	+	8.55698i	0.157095	+	0.272096i
$990$	−0.610617	+	1.05762i	−0.0194067	+	0.0336134i
$991$	28.5041	−	49.3706i	0.905464	−	1.56831i	0.0851704	−	0.996366i	$-0.472857\pi$
$991$	28.5041	−	49.3706i	0.905464	−	1.56831i	0.820293	−	0.571943i	$-0.193810\pi$
$992$	−0.458724	−	0.794533i	−0.0145645	−	0.0252265i
$993$	−40.9852			−1.30063
$994$	−3.05907	−	5.02515i	−0.0970279	−	0.159388i
$995$	−27.3403			−0.866745
$996$	−1.58723	−	2.74917i	−0.0502934	−	0.0871107i
$997$	−15.3077	+	26.5138i	−0.484801	+	0.839699i	−0.999848	−	0.0174626i	$-0.994441\pi$
$997$	−15.3077	+	26.5138i	−0.484801	+	0.839699i	0.515047	+	0.857162i	$0.327775\pi$
$998$	4.09680	−	7.09587i	0.129682	−	0.224616i
$999$	12.3127	+	21.3262i	0.389555	+	0.674730i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	217.2.f.b.32.11	✓	26
7.2	even	3	inner	217.2.f.b.156.11	yes	26
7.3	odd	6		1519.2.a.j.1.3		13
7.4	even	3		1519.2.a.k.1.3		13

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
217.2.f.b.32.11	✓	26	1.1	even	1	trivial
217.2.f.b.156.11	yes	26	7.2	even	3	inner
1519.2.a.j.1.3		13	7.3	odd	6
1519.2.a.k.1.3		13	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:	\( N \)	\(=\)	\( 217 = 7 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	217.f (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.735285 + 1.27355i) q^{2} +(0.779727 - 1.35053i) q^{3} +(-0.0812879 + 0.140795i) q^{4} +(-2.18553 - 3.78544i) q^{5} +2.29329 q^{6} +(-2.64504 + 0.0614602i) q^{7} +2.70206 q^{8} +(0.284053 + 0.491993i) q^{9} +O(q^{10})\)	\(q+(0.735285 + 1.27355i) q^{2} +(0.779727 - 1.35053i) q^{3} +(-0.0812879 + 0.140795i) q^{4} +(-2.18553 - 3.78544i) q^{5} +2.29329 q^{6} +(-2.64504 + 0.0614602i) q^{7} +2.70206 q^{8} +(0.284053 + 0.491993i) q^{9} +(3.21397 - 5.56676i) q^{10} +(-0.167212 + 0.289620i) q^{11} +(0.126765 + 0.219563i) q^{12} +5.80839 q^{13} +(-2.02313 - 3.32340i) q^{14} -6.81646 q^{15} +(2.14936 + 3.72280i) q^{16} +(-1.43430 + 2.48429i) q^{17} +(-0.417719 + 0.723511i) q^{18} +(-0.210592 - 0.364756i) q^{19} +0.710628 q^{20} +(-1.97940 + 3.62011i) q^{21} -0.491795 q^{22} +(-1.00433 - 1.73954i) q^{23} +(2.10687 - 3.64920i) q^{24} +(-7.05306 + 12.2163i) q^{25} +(4.27082 + 7.39728i) q^{26} +5.56429 q^{27} +(0.206356 - 0.377404i) q^{28} +4.99544 q^{29} +(-5.01204 - 8.68110i) q^{30} +(-0.500000 + 0.866025i) q^{31} +(-0.458724 + 0.794533i) q^{32} +(0.260760 + 0.451650i) q^{33} -4.21849 q^{34} +(6.01346 + 9.87832i) q^{35} -0.0923602 q^{36} +(2.21280 + 3.83268i) q^{37} +(0.309690 - 0.536399i) q^{38} +(4.52896 - 7.84438i) q^{39} +(-5.90543 - 10.2285i) q^{40} -10.1180 q^{41} +(-6.06583 + 0.140946i) q^{42} -4.91910 q^{43} +(-0.0271847 - 0.0470853i) q^{44} +(1.24161 - 2.15053i) q^{45} +(1.47693 - 2.55812i) q^{46} +(0.601200 + 1.04131i) q^{47} +6.70365 q^{48} +(6.99245 - 0.325129i) q^{49} -20.7440 q^{50} +(2.23673 + 3.87413i) q^{51} +(-0.472152 + 0.817791i) q^{52} +(2.55380 - 4.42331i) q^{53} +(4.09134 + 7.08641i) q^{54} +1.46179 q^{55} +(-7.14705 + 0.166069i) q^{56} -0.656816 q^{57} +(3.67307 + 6.36194i) q^{58} +(3.97232 - 6.88026i) q^{59} +(0.554096 - 0.959722i) q^{60} +(0.512571 + 0.887799i) q^{61} -1.47057 q^{62} +(-0.781568 - 1.28388i) q^{63} +7.24827 q^{64} +(-12.6944 - 21.9873i) q^{65} +(-0.383466 + 0.664182i) q^{66} +(-3.58101 + 6.20248i) q^{67} +(-0.233183 - 0.403885i) q^{68} -3.13240 q^{69} +(-8.15894 + 14.9218i) q^{70} +1.51205 q^{71} +(0.767527 + 1.32940i) q^{72} +(-5.18324 + 8.97764i) q^{73} +(-3.25408 + 5.63622i) q^{74} +(10.9989 + 19.0507i) q^{75} +0.0684743 q^{76} +(0.424483 - 0.776334i) q^{77} +13.3203 q^{78} +(-3.87171 - 6.70600i) q^{79} +(9.39497 - 16.2726i) q^{80} +(3.48647 - 6.03874i) q^{81} +(-7.43960 - 12.8858i) q^{82} -12.5211 q^{83} +(-0.348792 - 0.572961i) q^{84} +12.5388 q^{85} +(-3.61694 - 6.26472i) q^{86} +(3.89507 - 6.74647i) q^{87} +(-0.451818 + 0.782572i) q^{88} +(-1.21772 - 2.10916i) q^{89} +3.65175 q^{90} +(-15.3634 + 0.356985i) q^{91} +0.326558 q^{92} +(0.779727 + 1.35053i) q^{93} +(-0.884107 + 1.53132i) q^{94} +(-0.920508 + 1.59437i) q^{95} +(0.715359 + 1.23904i) q^{96} +4.26302 q^{97} +(5.55551 + 8.66617i) q^{98} -0.189988 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 26 q - 5 q^{2} - 17 q^{4} - q^{5} - 4 q^{6} - q^{7} + 24 q^{8} - 25 q^{9}+O(q^{10}) \) 26 * q - 5 * q^2 - 17 * q^4 - q^5 - 4 * q^6 - q^7 + 24 * q^8 - 25 * q^9	\( 26 q - 5 q^{2} - 17 q^{4} - q^{5} - 4 q^{6} - q^{7} + 24 q^{8} - 25 q^{9} + 7 q^{10} - 15 q^{11} + 5 q^{12} + 8 q^{13} - 12 q^{14} + 8 q^{15} - 29 q^{16} + 4 q^{17} - 16 q^{18} - 2 q^{19} + 52 q^{20} - 10 q^{21} - 20 q^{22} - 14 q^{23} + 28 q^{24} - 24 q^{25} + 7 q^{26} + 24 q^{27} - 14 q^{28} + 44 q^{29} - 6 q^{30} - 13 q^{31} - 19 q^{32} + 5 q^{33} + 40 q^{34} - 20 q^{35} + 22 q^{36} - 12 q^{37} + 11 q^{38} - 11 q^{39} + 6 q^{40} + 8 q^{41} - 82 q^{42} - 6 q^{43} - 52 q^{44} + 12 q^{45} + 3 q^{46} + 14 q^{47} + 96 q^{48} - 5 q^{49} + 30 q^{50} - 16 q^{51} - 4 q^{52} - 19 q^{53} + 25 q^{54} + 36 q^{55} - 29 q^{56} + 26 q^{57} - 24 q^{58} - 19 q^{59} - 6 q^{60} + 11 q^{61} + 10 q^{62} - 63 q^{63} + 20 q^{64} - 68 q^{65} + 52 q^{66} + 25 q^{67} + 26 q^{68} + 104 q^{69} - 78 q^{70} + 56 q^{71} - 52 q^{72} + 29 q^{73} - 54 q^{74} + 71 q^{75} + 74 q^{76} - 42 q^{77} - 142 q^{78} - 30 q^{79} - 3 q^{80} - 25 q^{81} - 5 q^{82} - 20 q^{83} - 64 q^{84} - 2 q^{85} - 10 q^{86} - 50 q^{87} - 18 q^{88} + 11 q^{89} + 162 q^{90} - 50 q^{91} + 70 q^{92} + 36 q^{94} + 20 q^{95} + 12 q^{96} - 6 q^{97} + 10 q^{98} + 84 q^{99}+O(q^{100}) \) 26 * q - 5 * q^2 - 17 * q^4 - q^5 - 4 * q^6 - q^7 + 24 * q^8 - 25 * q^9 + 7 * q^10 - 15 * q^11 + 5 * q^12 + 8 * q^13 - 12 * q^14 + 8 * q^15 - 29 * q^16 + 4 * q^17 - 16 * q^18 - 2 * q^19 + 52 * q^20 - 10 * q^21 - 20 * q^22 - 14 * q^23 + 28 * q^24 - 24 * q^25 + 7 * q^26 + 24 * q^27 - 14 * q^28 + 44 * q^29 - 6 * q^30 - 13 * q^31 - 19 * q^32 + 5 * q^33 + 40 * q^34 - 20 * q^35 + 22 * q^36 - 12 * q^37 + 11 * q^38 - 11 * q^39 + 6 * q^40 + 8 * q^41 - 82 * q^42 - 6 * q^43 - 52 * q^44 + 12 * q^45 + 3 * q^46 + 14 * q^47 + 96 * q^48 - 5 * q^49 + 30 * q^50 - 16 * q^51 - 4 * q^52 - 19 * q^53 + 25 * q^54 + 36 * q^55 - 29 * q^56 + 26 * q^57 - 24 * q^58 - 19 * q^59 - 6 * q^60 + 11 * q^61 + 10 * q^62 - 63 * q^63 + 20 * q^64 - 68 * q^65 + 52 * q^66 + 25 * q^67 + 26 * q^68 + 104 * q^69 - 78 * q^70 + 56 * q^71 - 52 * q^72 + 29 * q^73 - 54 * q^74 + 71 * q^75 + 74 * q^76 - 42 * q^77 - 142 * q^78 - 30 * q^79 - 3 * q^80 - 25 * q^81 - 5 * q^82 - 20 * q^83 - 64 * q^84 - 2 * q^85 - 10 * q^86 - 50 * q^87 - 18 * q^88 + 11 * q^89 + 162 * q^90 - 50 * q^91 + 70 * q^92 + 36 * q^94 + 20 * q^95 + 12 * q^96 - 6 * q^97 + 10 * q^98 + 84 * q^99

Introduction

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