LMFDB - Embedded newform 547.2.c.a.40.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [547,2,Mod(40,547)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(547, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("547.40");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 547 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	547.c (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:	$4.36781699056$
Analytic rank:	$0$
Dimension:	$90$
Relative dimension:	$45$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			40.14
Character	$\chi$	$=$	547.40
Dual form			547.2.c.a.506.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.701193 - 1.21450i) q^{2} +2.83551 q^{3} +(0.0166570 - 0.0288508i) q^{4} +(1.44371 - 2.50058i) q^{5} +(-1.98824 - 3.44374i) q^{6} +(0.560388 + 0.970620i) q^{7} -2.85149 q^{8} +5.04014 q^{9} +O(q^{10})$	\(q+(-0.701193 - 1.21450i) q^{2} +2.83551 q^{3} +(0.0166570 - 0.0288508i) q^{4} +(1.44371 - 2.50058i) q^{5} +(-1.98824 - 3.44374i) q^{6} +(0.560388 + 0.970620i) q^{7} -2.85149 q^{8} +5.04014 q^{9} -4.04928 q^{10} +(2.15796 + 3.73769i) q^{11} +(0.0472313 - 0.0818070i) q^{12} +(-1.79797 - 3.11417i) q^{13} +(0.785880 - 1.36118i) q^{14} +(4.09367 - 7.09044i) q^{15} +(1.96613 + 3.40544i) q^{16} +(-0.449791 - 0.779061i) q^{17} +(-3.53411 - 6.12126i) q^{18} +(-0.496525 + 0.860007i) q^{19} +(-0.0480959 - 0.0833046i) q^{20} +(1.58899 + 2.75221i) q^{21} +(3.02629 - 5.24169i) q^{22} +(-2.73269 + 4.73316i) q^{23} -8.08544 q^{24} +(-1.66861 - 2.89011i) q^{25} +(-2.52144 + 4.36727i) q^{26} +5.78486 q^{27} +0.0373376 q^{28} -3.24643 q^{29} -11.4818 q^{30} -0.0997291 q^{31} +(-0.0942166 + 0.163188i) q^{32} +(6.11892 + 10.5983i) q^{33} +(-0.630781 + 1.09254i) q^{34} +3.23615 q^{35} +(0.0839539 - 0.145412i) q^{36} +(2.69914 + 4.67506i) q^{37} +1.39264 q^{38} +(-5.09816 - 8.83028i) q^{39} +(-4.11673 + 7.13039i) q^{40} +(-3.87298 - 6.70820i) q^{41} +(2.22837 - 3.85966i) q^{42} +(4.01711 + 6.95783i) q^{43} +0.143781 q^{44} +(7.27651 - 12.6033i) q^{45} +7.66458 q^{46} +(-4.64325 + 8.04235i) q^{47} +(5.57499 + 9.65617i) q^{48} +(2.87193 - 4.97433i) q^{49} +(-2.34003 + 4.05305i) q^{50} +(-1.27539 - 2.20904i) q^{51} -0.119795 q^{52} +(-4.11876 - 7.13391i) q^{53} +(-4.05630 - 7.02572i) q^{54} +12.4619 q^{55} +(-1.59794 - 2.76771i) q^{56} +(-1.40790 + 2.43856i) q^{57} +(2.27637 + 3.94279i) q^{58} +(0.803803 + 1.39223i) q^{59} +(-0.136377 - 0.236211i) q^{60} +(-2.05389 - 3.55744i) q^{61} +(0.0699294 + 0.121121i) q^{62} +(2.82444 + 4.89207i) q^{63} +8.12878 q^{64} -10.3830 q^{65} +(8.58109 - 14.8629i) q^{66} +(4.51816 + 7.82569i) q^{67} -0.0299688 q^{68} +(-7.74859 + 13.4210i) q^{69} +(-2.26917 - 3.93032i) q^{70} +(-5.48629 - 9.50254i) q^{71} -14.3719 q^{72} +(0.167772 + 0.290590i) q^{73} +(3.78524 - 6.55623i) q^{74} +(-4.73136 - 8.19496i) q^{75} +(0.0165413 + 0.0286503i) q^{76} +(-2.41859 + 4.18912i) q^{77} +(-7.14959 + 12.3835i) q^{78} -10.5169 q^{79} +11.3541 q^{80} +1.28261 q^{81} +(-5.43141 + 9.40748i) q^{82} +(-1.46932 - 2.54494i) q^{83} +0.105871 q^{84} -2.59748 q^{85} +(5.63353 - 9.75756i) q^{86} -9.20530 q^{87} +(-6.15340 - 10.6580i) q^{88} +1.31265 q^{89} -20.4090 q^{90} +(2.01512 - 3.49029i) q^{91} +(0.0910372 + 0.157681i) q^{92} -0.282783 q^{93} +13.0233 q^{94} +(1.43368 + 2.48320i) q^{95} +(-0.267153 + 0.462722i) q^{96} +(3.45640 - 5.98665i) q^{97} -8.05511 q^{98} +(10.8764 + 18.8385i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 90 q - q^{2} - 4 q^{3} - 47 q^{4} + q^{5} - 3 q^{6} + 2 q^{7} - 30 q^{8} + 82 q^{9}+O(q^{10}) $ 90 * q - q^2 - 4 * q^3 - 47 * q^4 + q^5 - 3 * q^6 + 2 * q^7 - 30 * q^8 + 82 * q^9	\( 90 q - q^{2} - 4 q^{3} - 47 q^{4} + q^{5} - 3 q^{6} + 2 q^{7} - 30 q^{8} + 82 q^{9} - 10 q^{10} + q^{11} + 4 q^{12} - 3 q^{13} + 2 q^{14} - 7 q^{15} - 39 q^{16} - 4 q^{17} - 11 q^{18} - 2 q^{19} + 25 q^{20} - 27 q^{21} - 7 q^{22} + q^{23} + 32 q^{24} - 40 q^{25} - 10 q^{26} - 34 q^{27} - 28 q^{28} + 26 q^{29} - 40 q^{30} - 24 q^{31} + 19 q^{32} + q^{33} - 6 q^{34} - 8 q^{35} - 36 q^{36} - 10 q^{37} + 24 q^{38} + 22 q^{39} + 20 q^{40} + 3 q^{41} + 38 q^{42} - 12 q^{43} - 30 q^{44} - 2 q^{45} - 40 q^{46} + 32 q^{47} + 14 q^{48} - 43 q^{49} + 14 q^{50} + 13 q^{51} + 46 q^{52} + 9 q^{53} - 8 q^{54} + 4 q^{55} - 8 q^{56} - 8 q^{57} + 4 q^{58} + 22 q^{59} - 2 q^{60} - 12 q^{61} + 11 q^{62} + 8 q^{63} + 22 q^{64} + 18 q^{65} + 12 q^{66} - 22 q^{67} + 6 q^{68} - q^{69} - 6 q^{70} - 4 q^{71} - 140 q^{72} + 17 q^{73} + 17 q^{74} + 39 q^{75} + 84 q^{76} - 4 q^{77} + 33 q^{78} - 72 q^{79} - 40 q^{80} + 18 q^{81} - 9 q^{82} + 24 q^{83} + 114 q^{84} + 40 q^{85} - 72 q^{86} - 78 q^{87} - 22 q^{88} + 14 q^{89} + 96 q^{90} - 8 q^{92} - 76 q^{93} + 108 q^{94} - 11 q^{95} - 34 q^{96} - 74 q^{98} - 62 q^{99}+O(q^{100}) \) 90 * q - q^2 - 4 * q^3 - 47 * q^4 + q^5 - 3 * q^6 + 2 * q^7 - 30 * q^8 + 82 * q^9 - 10 * q^10 + q^11 + 4 * q^12 - 3 * q^13 + 2 * q^14 - 7 * q^15 - 39 * q^16 - 4 * q^17 - 11 * q^18 - 2 * q^19 + 25 * q^20 - 27 * q^21 - 7 * q^22 + q^23 + 32 * q^24 - 40 * q^25 - 10 * q^26 - 34 * q^27 - 28 * q^28 + 26 * q^29 - 40 * q^30 - 24 * q^31 + 19 * q^32 + q^33 - 6 * q^34 - 8 * q^35 - 36 * q^36 - 10 * q^37 + 24 * q^38 + 22 * q^39 + 20 * q^40 + 3 * q^41 + 38 * q^42 - 12 * q^43 - 30 * q^44 - 2 * q^45 - 40 * q^46 + 32 * q^47 + 14 * q^48 - 43 * q^49 + 14 * q^50 + 13 * q^51 + 46 * q^52 + 9 * q^53 - 8 * q^54 + 4 * q^55 - 8 * q^56 - 8 * q^57 + 4 * q^58 + 22 * q^59 - 2 * q^60 - 12 * q^61 + 11 * q^62 + 8 * q^63 + 22 * q^64 + 18 * q^65 + 12 * q^66 - 22 * q^67 + 6 * q^68 - q^69 - 6 * q^70 - 4 * q^71 - 140 * q^72 + 17 * q^73 + 17 * q^74 + 39 * q^75 + 84 * q^76 - 4 * q^77 + 33 * q^78 - 72 * q^79 - 40 * q^80 + 18 * q^81 - 9 * q^82 + 24 * q^83 + 114 * q^84 + 40 * q^85 - 72 * q^86 - 78 * q^87 - 22 * q^88 + 14 * q^89 + 96 * q^90 - 8 * q^92 - 76 * q^93 + 108 * q^94 - 11 * q^95 - 34 * q^96 - 74 * q^98 - 62 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/547\mathbb{Z}\right)^\times$.

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

Coefficient data

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

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

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

$2$	−0.701193	−	1.21450i	−0.495818	−	0.858782i	0.504170	−	0.863604i	$-0.331798\pi$
$2$	−0.701193	−	1.21450i	−0.495818	−	0.858782i	−0.999988	+	0.00482195i	$0.998465\pi$
$3$	2.83551			1.63709			0.818543	−	0.574446i	$-0.194782\pi$
$3$	2.83551			1.63709			0.818543	+	0.574446i	$0.194782\pi$
$4$	0.0166570	−	0.0288508i	0.00832852	−	0.0144254i
$5$	1.44371	−	2.50058i	0.645648	−	1.11829i	−0.338504	−	0.940965i	$-0.609921\pi$
$5$	1.44371	−	2.50058i	0.645648	−	1.11829i	0.984152	−	0.177329i	$-0.0567458\pi$
$6$	−1.98824	−	3.44374i	−0.811697	−	1.40590i
$7$	0.560388	+	0.970620i	0.211807	+	0.366860i	0.952280	−	0.305226i	$-0.0987319\pi$
$7$	0.560388	+	0.970620i	0.211807	+	0.366860i	−0.740473	+	0.672086i	$0.765399\pi$
$8$	−2.85149			−1.00815
$9$	5.04014			1.68005
$10$	−4.04928			−1.28050
$11$	2.15796	+	3.73769i	0.650649	+	1.12696i	0.982966	+	0.183789i	$0.0588364\pi$
$11$	2.15796	+	3.73769i	0.650649	+	1.12696i	−0.332317	+	0.943168i	$0.607830\pi$
$12$	0.0472313	−	0.0818070i	0.0136345	−	0.0236156i
$13$	−1.79797	−	3.11417i	−0.498667	−	0.863716i	0.501332	−	0.865255i	$-0.332843\pi$
$13$	−1.79797	−	3.11417i	−0.498667	−	0.863716i	−0.999999	+	0.00153911i	$0.999510\pi$
$14$	0.785880	−	1.36118i	0.210035	−	0.363792i
$15$	4.09367	−	7.09044i	1.05698	−	1.83074i
$16$	1.96613	+	3.40544i	0.491533	+	0.851360i
$17$	−0.449791	−	0.779061i	−0.109090	−	0.188950i	0.806312	−	0.591491i	$-0.201460\pi$
$17$	−0.449791	−	0.779061i	−0.109090	−	0.188950i	−0.915402	+	0.402541i	$0.868127\pi$
$18$	−3.53411	−	6.12126i	−0.832998	−	1.44280i
$19$	−0.496525	+	0.860007i	−0.113911	+	0.197299i	−0.917344	−	0.398096i	$-0.869671\pi$
$19$	−0.496525	+	0.860007i	−0.113911	+	0.197299i	0.803433	+	0.595395i	$0.203004\pi$
$20$	−0.0480959	−	0.0833046i	−0.0107546	−	0.0186275i
$21$	1.58899	+	2.75221i	0.346746	+	0.600581i
$22$	3.02629	−	5.24169i	0.645207	−	1.11753i
$23$	−2.73269	+	4.73316i	−0.569806	+	0.986933i	0.426779	+	0.904356i	$0.359648\pi$
$23$	−2.73269	+	4.73316i	−0.569806	+	0.986933i	−0.996585	+	0.0825770i	$0.973685\pi$
$24$	−8.08544			−1.65043
$25$	−1.66861	−	2.89011i	−0.333722	−	0.578023i
$26$	−2.52144	+	4.36727i	−0.494496	+	0.856492i
$27$	5.78486			1.11330
$28$	0.0373376			0.00705615
$29$	−3.24643			−0.602847			−0.301423	−	0.953490i	$-0.597462\pi$
$29$	−3.24643			−0.602847			−0.301423	+	0.953490i	$0.597462\pi$
$30$	−11.4818			−2.09628
$31$	−0.0997291			−0.0179119			−0.00895594	−	0.999960i	$-0.502851\pi$
$31$	−0.0997291			−0.0179119			−0.00895594	+	0.999960i	$0.502851\pi$
$32$	−0.0942166	+	0.163188i	−0.0166553	+	0.0288478i
$33$	6.11892	+	10.5983i	1.06517	+	1.84492i
$34$	−0.630781	+	1.09254i	−0.108178	+	0.187370i
$35$	3.23615			0.547010
$36$	0.0839539	−	0.145412i	0.0139923	−	0.0242354i
$37$	2.69914	+	4.67506i	0.443737	+	0.768575i	0.997963	−	0.0637914i	$-0.0203192\pi$
$37$	2.69914	+	4.67506i	0.443737	+	0.768575i	−0.554227	+	0.832366i	$0.686986\pi$
$38$	1.39264			0.225916
$39$	−5.09816	−	8.83028i	−0.816360	−	1.41398i
$40$	−4.11673	+	7.13039i	−0.650912	+	1.12741i
$41$	−3.87298	−	6.70820i	−0.604858	−	1.04764i	−0.992074	−	0.125656i	$-0.959897\pi$
$41$	−3.87298	−	6.70820i	−0.604858	−	1.04764i	0.387216	−	0.921989i	$-0.373437\pi$
$42$	2.22837	−	3.85966i	0.343846	−	0.595558i
$43$	4.01711	+	6.95783i	0.612603	+	1.06106i	0.990800	+	0.135334i	$0.0432108\pi$
$43$	4.01711	+	6.95783i	0.612603	+	1.06106i	−0.378197	+	0.925725i	$0.623456\pi$
$44$	0.143781			0.0216758
$45$	7.27651	−	12.6033i	1.08472	−	1.87879i
$46$	7.66458			1.13008
$47$	−4.64325	+	8.04235i	−0.677288	+	1.17310i	0.298506	+	0.954408i	$0.403512\pi$
$47$	−4.64325	+	8.04235i	−0.677288	+	1.17310i	−0.975794	+	0.218690i	$0.929822\pi$
$48$	5.57499	+	9.65617i	0.804681	+	1.39375i
$49$	2.87193	−	4.97433i	0.410276	−	0.710619i
$50$	−2.34003	+	4.05305i	−0.330931	+	0.573188i
$51$	−1.27539	−	2.20904i	−0.178590	−	0.309327i
$52$	−0.119795			−0.0166126
$53$	−4.11876	−	7.13391i	−0.565756	−	0.979918i	−0.996979	−	0.0776726i	$-0.975251\pi$
$53$	−4.11876	−	7.13391i	−0.565756	−	0.979918i	0.431223	−	0.902245i	$-0.358082\pi$
$54$	−4.05630	−	7.02572i	−0.551992	−	0.956079i
$55$	12.4619			1.68036
$56$	−1.59794	−	2.76771i	−0.213534	−	0.369851i
$57$	−1.40790	+	2.43856i	−0.186482	+	0.322995i
$58$	2.27637	+	3.94279i	0.298902	+	0.517714i
$59$	0.803803	+	1.39223i	0.104646	+	0.181253i	0.913594	−	0.406628i	$-0.133296\pi$
$59$	0.803803	+	1.39223i	0.104646	+	0.181253i	−0.808947	+	0.587881i	$0.799962\pi$
$60$	−0.136377	−	0.236211i	−0.0176062	−	0.0304948i
$61$	−2.05389	−	3.55744i	−0.262974	−	0.455484i	0.704057	−	0.710143i	$-0.251370\pi$
$61$	−2.05389	−	3.55744i	−0.262974	−	0.455484i	−0.967031	+	0.254660i	$0.918037\pi$
$62$	0.0699294	+	0.121121i	0.00888104	+	0.0153824i
$63$	2.82444	+	4.89207i	0.355845	+	0.616342i
$64$	8.12878			1.01610
$65$	−10.3830			−1.28785
$66$	8.58109	−	14.8629i	1.05626	−	1.82949i
$67$	4.51816	+	7.82569i	0.551981	+	0.956060i	0.998132	+	0.0611016i	$0.0194614\pi$
$67$	4.51816	+	7.82569i	0.551981	+	0.956060i	−0.446150	+	0.894958i	$0.647205\pi$
$68$	−0.0299688			−0.00363425
$69$	−7.74859	+	13.4210i	−0.932821	+	1.61569i
$70$	−2.26917	−	3.93032i	−0.271218	−	0.469763i
$71$	−5.48629	−	9.50254i	−0.651103	−	1.12774i	−0.982856	−	0.184377i	$-0.940973\pi$
$71$	−5.48629	−	9.50254i	−0.651103	−	1.12774i	0.331753	−	0.943366i	$-0.392360\pi$
$72$	−14.3719			−1.69375
$73$	0.167772	+	0.290590i	0.0196362	+	0.0340110i	0.875677	−	0.482898i	$-0.160416\pi$
$73$	0.167772	+	0.290590i	0.0196362	+	0.0340110i	−0.856040	+	0.516909i	$0.827083\pi$
$74$	3.78524	−	6.55623i	0.440026	−	0.762147i
$75$	−4.73136	−	8.19496i	−0.546331	−	0.946272i
$76$	0.0165413	+	0.0286503i	0.00189742	+	0.00328642i
$77$	−2.41859	+	4.18912i	−0.275624	+	0.477394i
$78$	−7.14959	+	12.3835i	−0.809532	+	1.40215i
$79$	−10.5169			−1.18324			−0.591620	−	0.806217i	$-0.701511\pi$
$79$	−10.5169			−1.18324			−0.591620	+	0.806217i	$0.701511\pi$
$80$	11.3541			1.26943
$81$	1.28261			0.142512
$82$	−5.43141	+	9.40748i	−0.599799	+	1.03888i
$83$	−1.46932	−	2.54494i	−0.161279	−	0.279344i	0.774048	−	0.633126i	$-0.218229\pi$
$83$	−1.46932	−	2.54494i	−0.161279	−	0.279344i	−0.935328	+	0.353783i	$0.884895\pi$
$84$	0.105871			0.0115515
$85$	−2.59748			−0.281736
$86$	5.63353	−	9.75756i	0.607479	−	1.05219i
$87$	−9.20530			−0.986911
$88$	−6.15340	−	10.6580i	−0.655955	−	1.13615i
$89$	1.31265			0.139140			0.0695702	−	0.997577i	$-0.477837\pi$
$89$	1.31265			0.139140			0.0695702	+	0.997577i	$0.477837\pi$
$90$	−20.4090			−2.15129
$91$	2.01512	−	3.49029i	0.211242	−	0.365882i
$92$	0.0910372	+	0.157681i	0.00949128	+	0.0164394i
$93$	−0.282783			−0.0293233
$94$	13.0233			1.34325
$95$	1.43368	+	2.48320i	0.147092	+	0.254771i
$96$	−0.267153	+	0.462722i	−0.0272661	+	0.0472263i
$97$	3.45640	−	5.98665i	0.350944	−	0.607853i	−0.635471	−	0.772125i	$-0.719194\pi$
$97$	3.45640	−	5.98665i	0.350944	−	0.607853i	0.986415	+	0.164272i	$0.0525275\pi$
$98$	−8.05511			−0.813689
$99$	10.8764	+	18.8385i	1.09312	+	1.89334i
$100$	−0.111176			−0.0111176
$101$	−9.22588			−0.918009			−0.459005	−	0.888434i	$-0.651794\pi$
$101$	−9.22588			−0.918009			−0.459005	+	0.888434i	$0.651794\pi$
$102$	−1.78859	+	3.09793i	−0.177097	+	0.306740i
$103$	13.7198			1.35186			0.675928	−	0.736967i	$-0.263743\pi$
$103$	13.7198			1.35186			0.675928	+	0.736967i	$0.263743\pi$
$104$	5.12689	+	8.88003i	0.502733	+	0.870759i
$105$	9.17616			0.895502
$106$	−5.77610	+	10.0045i	−0.561024	+	0.971722i
$107$	3.90314			0.377331			0.188665	−	0.982041i	$-0.439584\pi$
$107$	3.90314			0.377331			0.188665	+	0.982041i	$0.439584\pi$
$108$	0.0963586	−	0.166898i	0.00927211	−	0.0160598i
$109$	6.54554	−	11.3372i	0.626949	−	1.08591i	−0.361212	−	0.932484i	$-0.617637\pi$
$109$	6.54554	−	11.3372i	0.626949	−	1.08591i	0.988161	−	0.153423i	$-0.0490298\pi$
$110$	−8.73818	−	15.1350i	−0.833153	−	1.44306i
$111$	7.65346	+	13.2562i	0.726435	+	1.25822i
$112$	−2.20359	+	3.81673i	−0.208220	+	0.360647i
$113$	6.50971	−	11.2752i	0.612382	−	1.06068i	−0.378456	−	0.925619i	$-0.623545\pi$
$113$	6.50971	−	11.2752i	0.612382	−	1.06068i	0.990838	−	0.135058i	$-0.0431219\pi$
$114$	3.94885			0.369844
$115$	7.89045	+	13.6667i	0.735788	+	1.27442i
$116$	−0.0540759	+	0.0936622i	−0.00502082	+	0.00869632i
$117$	−9.06201	−	15.6959i	−0.837783	−	1.45108i
$118$	1.12724	−	1.95244i	0.103771	−	0.179737i
$119$	0.504115	−	0.873153i	0.0462122	−	0.0800418i
$120$	−11.6731	+	20.2183i	−1.06560	+	1.84567i
$121$	−3.81357	+	6.60530i	−0.346688	+	0.600482i
$122$	−2.88034	+	4.98890i	−0.260774	+	0.451674i
$123$	−10.9819	−	19.0212i	−0.990204	−	1.71508i
$124$	−0.00166119	+	0.00287727i	−0.000149179	+	0.000258386i
$125$	4.80116			0.429429
$126$	3.96095	−	6.86056i	0.352869	−	0.611187i
$127$	−8.88522	+	15.3896i	−0.788435	+	1.36561i	0.138490	+	0.990364i	$0.455775\pi$
$127$	−8.88522	+	15.3896i	−0.788435	+	1.36561i	−0.926925	+	0.375246i	$0.877558\pi$
$128$	−5.51141	−	9.54604i	−0.487144	−	0.843759i
$129$	11.3906	+	19.7290i	1.00288	+	1.73704i
$130$	7.28048	+	12.6102i	0.638540	+	1.10598i
$131$	19.6169			1.71394			0.856970	−	0.515366i	$-0.172344\pi$
$131$	19.6169			1.71394			0.856970	+	0.515366i	$0.172344\pi$
$132$	0.407693			0.0354851
$133$	−1.11299			−0.0965082
$134$	6.33621	−	10.9746i	0.547365	−	0.948064i
$135$	8.35166	−	14.4655i	0.718797	−	1.24499i
$136$	1.28258	+	2.22149i	0.109980	+	0.190491i
$137$	9.62043	+	16.6631i	0.821929	+	1.42362i	0.904244	+	0.427016i	$0.140435\pi$
$137$	9.62043	+	16.6631i	0.821929	+	1.42362i	−0.0823150	+	0.996606i	$0.526231\pi$
$138$	21.7330			1.85004
$139$	11.1917	+	19.3845i	0.949265	+	1.64417i	0.746979	+	0.664848i	$0.231504\pi$
$139$	11.1917	+	19.3845i	0.949265	+	1.64417i	0.202286	+	0.979327i	$0.435163\pi$
$140$	0.0539048	−	0.0933658i	0.00455578	−	0.00789085i
$141$	−13.1660	+	22.8042i	−1.10878	+	1.92046i
$142$	−7.69390	+	13.3262i	−0.645658	+	1.11831i
$143$	7.75988	−	13.4405i	0.648914	−	1.12395i
$144$	9.90958	+	17.1639i	0.825798	+	1.43032i
$145$	−4.68691	+	8.11796i	−0.389227	+	0.674160i
$146$	0.235281	−	0.407519i	0.0194720	−	0.0337265i
$147$	8.14340	−	14.1048i	0.671656	−	1.16334i
$148$	0.179839			0.0147827
$149$	−17.2618			−1.41414			−0.707071	−	0.707143i	$-0.749984\pi$
$149$	−17.2618			−1.41414			−0.707071	+	0.707143i	$0.749984\pi$
$150$	−6.63520	+	11.4925i	−0.541761	+	0.938358i
$151$	2.59305			0.211020			0.105510	−	0.994418i	$-0.466353\pi$
$151$	2.59305			0.211020			0.105510	+	0.994418i	$0.466353\pi$
$152$	1.41584	−	2.45230i	0.114840	−	0.198908i
$153$	−2.26701	−	3.92658i	−0.183277	−	0.317445i
$154$	6.78359			0.546637
$155$	−0.143980	+	0.249381i	−0.0115648	+	0.0200308i
$156$	−0.339681			−0.0271963
$157$	0.840611	+	1.45598i	0.0670881	+	0.116200i	0.897618	−	0.440774i	$-0.145296\pi$
$157$	0.840611	+	1.45598i	0.0670881	+	0.116200i	−0.830530	+	0.556973i	$0.811962\pi$
$158$	7.37435	+	12.7727i	0.586672	+	1.01615i
$159$	−11.6788	−	20.2283i	−0.926191	−	1.60421i
$160$	0.272043	+	0.471193i	0.0215069	+	0.0372511i
$161$	−6.12547			−0.482755
$162$	−0.899359	−	1.55773i	−0.0706603	−	0.122387i
$163$	−4.52985	−	7.84593i	−0.354805	−	0.614540i	0.632279	−	0.774740i	$-0.282119\pi$
$163$	−4.52985	−	7.84593i	−0.354805	−	0.614540i	−0.987085	+	0.160200i	$0.948786\pi$
$164$	−0.258050			−0.0201503
$165$	35.3358			2.75089
$166$	−2.06056	+	3.56899i	−0.159930	+	0.277008i
$167$	−21.2548			−1.64475			−0.822375	−	0.568946i	$-0.807351\pi$
$167$	−21.2548			−1.64475			−0.822375	+	0.568946i	$0.807351\pi$
$168$	−4.53098	−	7.84790i	−0.349573	−	0.605478i
$169$	0.0346248	−	0.0599718i	0.00266344	−	0.00461322i
$170$	1.82133	+	3.15464i	0.139690	+	0.241950i
$171$	−2.50256	+	4.33456i	−0.191375	+	0.331472i
$172$	0.267652			0.0204083
$173$	22.9625			1.74581			0.872905	−	0.487890i	$-0.162233\pi$
$173$	22.9625			1.74581			0.872905	+	0.487890i	$0.162233\pi$
$174$	6.45469	+	11.1798i	0.489329	+	0.847542i
$175$	1.87014	−	3.23917i	0.141369	−	0.244858i
$176$	−8.48566	+	14.6976i	−0.639631	+	1.10787i
$177$	2.27920	+	3.94768i	0.171315	+	0.296726i
$178$	−0.920419	−	1.59421i	−0.0689883	−	0.119491i
$179$	−18.1223			−1.35453			−0.677264	−	0.735740i	$-0.736834\pi$
$179$	−18.1223			−1.35453			−0.677264	+	0.735740i	$0.736834\pi$
$180$	−0.242410	−	0.419867i	−0.0180682	−	0.0312950i
$181$	11.4671	−	19.8616i	0.852341	−	1.47630i	−0.0267487	−	0.999642i	$-0.508515\pi$
$181$	11.4671	−	19.8616i	0.852341	−	1.47630i	0.879090	−	0.476656i	$-0.158151\pi$
$182$	−5.65195			−0.418950
$183$	−5.82383	−	10.0872i	−0.430510	−	0.745665i
$184$	7.79225	−	13.4966i	0.574452	−	0.994981i
$185$	15.5872			1.14599
$186$	0.198286	+	0.343441i	0.0145390	+	0.0251823i
$187$	1.94126	−	3.36236i	0.141959	−	0.245880i
$188$	0.154686	+	0.267924i	0.0112816	+	0.0195403i
$189$	3.24176	+	5.61490i	0.235804	+	0.408424i
$190$	2.01057	−	3.48241i	0.145862	−	0.252641i
$191$	−11.5572	+	20.0176i	−0.836249	+	1.44843i	0.0567607	+	0.998388i	$0.481923\pi$
$191$	−11.5572	+	20.0176i	−0.836249	+	1.44843i	−0.893010	+	0.450038i	$0.851411\pi$
$192$	23.0493			1.66344
$193$	−6.83366	+	11.8362i	−0.491898	+	0.851992i	−0.999956	−	0.00933064i	$-0.997030\pi$
$193$	−6.83366	+	11.8362i	−0.491898	+	0.851992i	0.508059	+	0.861322i	$0.330363\pi$
$194$	−9.69440			−0.696017
$195$	−29.4411			−2.10832
$196$	−0.0956757	−	0.165715i	−0.00683398	−	0.0118368i
$197$	4.44659			0.316807			0.158403	−	0.987374i	$-0.449365\pi$
$197$	4.44659			0.316807			0.158403	+	0.987374i	$0.449365\pi$
$198$	15.2529	−	26.4189i	1.08398	−	1.87751i
$199$	6.68655	−	11.5814i	0.473997	−	0.820986i	−0.525560	−	0.850756i	$-0.676144\pi$
$199$	6.68655	−	11.5814i	0.473997	−	0.820986i	0.999557	+	0.0297701i	$0.00947753\pi$
$200$	4.75802	+	8.24113i	0.336443	+	0.582736i
$201$	12.8113	+	22.1898i	0.903640	+	1.56515i
$202$	6.46912	+	11.2048i	0.455166	+	0.788370i
$203$	−1.81926	−	3.15105i	−0.127687	−	0.221160i
$204$	−0.0849769			−0.00594957
$205$	−22.3659			−1.56210
$206$	−9.62026	−	16.6628i	−0.670275	−	1.16095i
$207$	−13.7732	+	23.8558i	−0.957301	+	1.65809i
$208$	7.07008	−	12.2457i	0.490222	−	0.849089i
$209$	−4.28592			−0.296464
$210$	−6.43426	−	11.1445i	−0.444006	−	0.769041i
$211$	−3.06405	+	5.30709i	−0.210938	+	0.365355i	−0.952008	−	0.306072i	$-0.900985\pi$
$211$	−3.06405	+	5.30709i	−0.210938	+	0.365355i	0.741070	+	0.671427i	$0.234318\pi$
$212$	−0.274426			−0.0188476
$213$	−15.5565	−	26.9446i	−1.06591	−	1.84621i
$214$	−2.73685	−	4.74037i	−0.187087	−	0.324045i
$215$	23.1982			1.58210
$216$	−16.4955			−1.12237
$217$	−0.0558870	−	0.0967991i	−0.00379386	−	0.00657115i
$218$	−18.3587			−1.24341
$219$	0.475720	+	0.823972i	0.0321462	+	0.0556789i
$220$	0.207578	−	0.359536i	0.0139949	−	0.0242399i
$221$	−1.61742	+	2.80145i	−0.108799	+	0.188446i
$222$	10.7331	−	18.5903i	0.720359	−	1.24770i
$223$	−4.56788	+	7.91180i	−0.305888	+	0.529813i	−0.977459	−	0.211127i	$-0.932287\pi$
$223$	−4.56788	+	7.91180i	−0.305888	+	0.529813i	0.671571	+	0.740940i	$0.265620\pi$
$224$	−0.211191			−0.0141108
$225$	−8.41002	−	14.5666i	−0.560668	−	0.971106i
$226$	−18.2583			−1.21452
$227$	−4.55518	+	7.88981i	−0.302338	+	0.523665i	−0.976665	−	0.214768i	$-0.931100\pi$
$227$	−4.55518	+	7.88981i	−0.302338	+	0.523665i	0.674327	+	0.738433i	$0.264434\pi$
$228$	0.0469031	+	0.0812385i	0.00310623	+	0.00538015i
$229$	−4.94937	+	8.57255i	−0.327063	+	0.566490i	−0.981928	−	0.189256i	$-0.939392\pi$
$229$	−4.94937	+	8.57255i	−0.327063	+	0.566490i	0.654864	+	0.755746i	$0.272726\pi$
$230$	11.0654	−	19.1659i	0.729634	−	1.26376i
$231$	−6.85794	+	11.8783i	−0.451219	+	0.781535i
$232$	9.25716			0.607762
$233$	2.54506	−	4.40817i	0.166732	−	0.288789i	−0.770537	−	0.637395i	$-0.780012\pi$
$233$	2.54506	−	4.40817i	0.166732	−	0.288789i	0.937269	+	0.348607i	$0.113345\pi$
$234$	−12.7084	+	22.0117i	−0.830777	+	1.43895i
$235$	13.4070	+	23.2217i	0.874579	+	1.51482i
$236$	0.0535559			0.00348619
$237$	−29.8207			−1.93706
$238$	−1.41393			−0.0916513
$239$	−5.16390	−	8.94414i	−0.334025	−	0.578549i	0.649272	−	0.760556i	$-0.275074\pi$
$239$	−5.16390	−	8.94414i	−0.334025	−	0.578549i	−0.983297	+	0.182008i	$0.941740\pi$
$240$	32.1947			2.07816
$241$	−6.06808	+	10.5102i	−0.390879	+	0.677023i	−0.992566	−	0.121709i	$-0.961162\pi$
$241$	−6.06808	+	10.5102i	−0.390879	+	0.677023i	0.601686	+	0.798732i	$0.294496\pi$
$242$	10.6962			0.687577
$243$	−13.7177			−0.879991
$244$	−0.136847			−0.00876072
$245$	−8.29248	−	14.3630i	−0.529787	−	0.917618i
$246$	−15.4009	+	26.6751i	−0.981922	+	1.70074i
$247$	3.57095			0.227214
$248$	0.284377			0.0180579
$249$	−4.16629	−	7.21622i	−0.264028	−	0.457310i
$250$	−3.36654	−	5.83102i	−0.212919	−	0.368786i
$251$	−2.99253	−	5.18321i	−0.188887	−	0.327161i	0.755993	−	0.654580i	$-0.227155\pi$
$251$	−2.99253	−	5.18321i	−0.188887	−	0.327161i	−0.944879	+	0.327419i	$0.893821\pi$
$252$	0.188187			0.0118547
$253$	−23.5882			−1.48298
$254$	24.9210			1.56368
$255$	−7.36518			−0.461225
$256$	0.399657	−	0.692227i	0.0249786	−	0.0432642i
$257$	8.40337			0.524188			0.262094	−	0.965042i	$-0.415587\pi$
$257$	8.40337			0.524188			0.262094	+	0.965042i	$0.415587\pi$
$258$	15.9740	−	27.6677i	0.994495	−	1.72252i
$259$	−3.02514	+	5.23969i	−0.187973	+	0.325578i
$260$	−0.172950	+	0.299558i	−0.0107259	+	0.0185778i
$261$	−16.3625			−1.01281
$262$	−13.7553	−	23.8248i	−0.849803	−	1.47190i
$263$	3.90768			0.240958			0.120479	−	0.992716i	$-0.461557\pi$
$263$	3.90768			0.240958			0.120479	+	0.992716i	$0.461557\pi$
$264$	−17.4481	−	30.2209i	−1.07385	−	1.85997i
$265$	−23.7852			−1.46112
$266$	0.780419	+	1.35172i	0.0478505	+	0.0828796i
$267$	3.72203			0.227785
$268$	0.301037			0.0183888
$269$	13.2248	−	22.9060i	0.806330	−	1.39660i	−0.109060	−	0.994035i	$-0.534784\pi$
$269$	13.2248	−	22.9060i	0.806330	−	1.39660i	0.915390	−	0.402569i	$-0.131883\pi$
$270$	−23.4245			−1.42557
$271$	−6.37191	−	11.0365i	−0.387066	−	0.670418i	0.604987	−	0.796235i	$-0.293178\pi$
$271$	−6.37191	−	11.0365i	−0.387066	−	0.670418i	−0.992053	+	0.125817i	$0.959845\pi$
$272$	1.76870	−	3.06347i	0.107243	−	0.185750i
$273$	5.71390	−	9.89676i	0.345821	−	0.598979i
$274$	13.4916	−	23.3681i	0.815055	−	1.41172i
$275$	7.20157	−	12.4735i	0.434271	−	0.752180i
$276$	0.258137	+	0.447107i	0.0155380	+	0.0269127i
$277$	21.7237			1.30525			0.652626	−	0.757680i	$-0.273667\pi$
$277$	21.7237			1.30525			0.652626	+	0.757680i	$0.273667\pi$
$278$	15.6950	−	27.1846i	0.941325	−	1.63042i
$279$	−0.502649			−0.0300928
$280$	−9.22786			−0.551470
$281$	−6.55832	−	11.3593i	−0.391236	−	0.677641i	0.601377	−	0.798966i	$-0.294619\pi$
$281$	−6.55832	−	11.3593i	−0.391236	−	0.677641i	−0.992613	+	0.121324i	$0.961286\pi$
$282$	36.9277			2.19901
$283$	−5.20741	−	9.01951i	−0.309549	−	0.536154i	0.668715	−	0.743519i	$-0.266845\pi$
$283$	−5.20741	−	9.01951i	−0.309549	−	0.536154i	−0.978264	+	0.207365i	$0.933511\pi$
$284$	−0.365542			−0.0216909
$285$	4.06522	+	7.04116i	0.240803	+	0.417083i
$286$	−21.7647			−1.28697
$287$	4.34074	−	7.51839i	0.256226	−	0.443796i
$288$	−0.474865	+	0.822490i	−0.0279817	+	0.0484657i
$289$	8.09538	−	14.0216i	0.476199	−	0.824800i
$290$	13.1457			0.771942
$291$	9.80066	−	16.9752i	0.574525	−	0.995106i
$292$	0.0111783			0.000654163
$293$	−0.107334			−0.00627053			−0.00313526	−	0.999995i	$-0.500998\pi$
$293$	−0.107334			−0.00627053			−0.00313526	+	0.999995i	$0.500998\pi$
$294$	−22.8404			−1.33208
$295$	4.64184			0.270258
$296$	−7.69659	−	13.3309i	−0.447355	−	0.774842i
$297$	12.4835	+	21.6220i	0.724365	+	1.25464i
$298$	12.1038	+	20.9645i	0.701157	+	1.21444i
$299$	19.6532			1.13657
$300$	−0.315242			−0.0182005
$301$	−4.50227	+	7.79817i	−0.259507	+	0.449479i
$302$	−1.81823	−	3.14927i	−0.104627	−	0.181220i
$303$	−26.1601			−1.50286
$304$	−3.90494			−0.223963
$305$	−11.8609			−0.679153
$306$	−3.17923	+	5.50658i	−0.181744	+	0.314790i
$307$	−22.8005			−1.30129			−0.650647	−	0.759380i	$-0.725502\pi$
$307$	−22.8005			−1.30129			−0.650647	+	0.759380i	$0.725502\pi$
$308$	0.0805730	+	0.139557i	0.00459107	+	0.00795197i
$309$	38.9028			2.21310
$310$	0.403831			0.0229361
$311$	−1.49093			−0.0845427			−0.0422713	−	0.999106i	$-0.513459\pi$
$311$	−1.49093			−0.0845427			−0.0422713	+	0.999106i	$0.513459\pi$
$312$	14.5374	+	25.1795i	0.823016	+	1.42551i
$313$	15.7449	−	27.2710i	0.889956	−	1.54145i	0.0500294	−	0.998748i	$-0.484069\pi$
$313$	15.7449	−	27.2710i	0.889956	−	1.54145i	0.839926	−	0.542701i	$-0.182598\pi$
$314$	1.17886	−	2.04185i	0.0665270	−	0.115228i
$315$	16.3107			0.919003
$316$	−0.175180	+	0.303420i	−0.00985463	+	0.0170687i
$317$	−13.0251	+	22.5601i	−0.731562	+	1.26710i	0.224653	+	0.974439i	$0.427875\pi$
$317$	−13.0251	+	22.5601i	−0.731562	+	1.26710i	−0.956215	+	0.292664i	$0.905458\pi$
$318$	−16.3782	+	28.3679i	−0.918444	+	1.59079i
$319$	−7.00566	−	12.1342i	−0.392242	−	0.679382i
$320$	11.7356	−	20.3267i	0.656041	−	1.13630i
$321$	11.0674			0.617722
$322$	4.29514	+	7.43940i	0.239359	+	0.414582i
$323$	0.893331			0.0497063
$324$	0.0213645	−	0.0370044i	0.00118692	−	0.00205580i
$325$	−6.00021	+	10.3927i	−0.332832	+	0.576481i
$326$	−6.35259	+	11.0030i	−0.351838	+	0.609401i
$327$	18.5600	−	32.1468i	1.02637	−	1.77772i
$328$	11.0438	+	19.1284i	0.609790	+	1.05619i
$329$	−10.4081			−0.573817
$330$	−24.7772	−	42.9154i	−1.36394	−	2.36242i
$331$	−5.76227			−0.316723			−0.158361	−	0.987381i	$-0.550621\pi$
$331$	−5.76227			−0.316723			−0.158361	+	0.987381i	$0.550621\pi$
$332$	−0.0978983			−0.00537287
$333$	13.6041	+	23.5630i	0.745499	+	1.29124i
$334$	14.9037	+	25.8140i	0.815497	+	1.41248i
$335$	26.0917			1.42554
$336$	−6.24832	+	10.8224i	−0.340874	+	0.590410i
$337$	−5.92448	−	10.2615i	−0.322727	−	0.558979i	0.658323	−	0.752736i	$-0.271266\pi$
$337$	−5.92448	−	10.2615i	−0.322727	−	0.558979i	−0.981050	+	0.193756i	$0.937933\pi$
$338$	−0.0971145			−0.00528233
$339$	18.4584	−	31.9709i	1.00252	−	1.73642i
$340$	−0.0432663	+	0.0749394i	−0.00234644	+	0.00406416i
$341$	−0.215211	−	0.372757i	−0.0116543	−	0.0201859i
$342$	7.01910			0.379550
$343$	14.2830			0.771210
$344$	−11.4547	−	19.8402i	−0.617598	−	1.06971i
$345$	22.3735	+	38.7520i	1.20455	+	2.08634i
$346$	−16.1012	−	27.8881i	−0.865605	−	1.49927i
$347$	−16.7284	−	28.9745i	−0.898030	−	1.55543i	−0.830009	−	0.557750i	$-0.811665\pi$
$347$	−16.7284	−	28.9745i	−0.898030	−	1.55543i	−0.0680208	−	0.997684i	$-0.521668\pi$
$348$	−0.153333	+	0.265581i	−0.00821951	+	0.0142366i
$349$	−9.60616	+	16.6384i	−0.514206	+	0.890631i	0.485658	+	0.874149i	$0.338580\pi$
$349$	−9.60616	+	16.6384i	−0.514206	+	0.890631i	−0.999864	+	0.0164823i	$0.994753\pi$
$350$	−5.24530			−0.280373
$351$	−10.4010	−	18.0150i	−0.555163	−	0.961571i
$352$	−0.813262			−0.0433470
$353$	−12.8955			−0.686356			−0.343178	−	0.939270i	$-0.611503\pi$
$353$	−12.8955			−0.686356			−0.343178	+	0.939270i	$0.611503\pi$
$354$	3.19631	−	5.53618i	0.169882	−	0.294244i
$355$	−31.6825			−1.68153
$356$	0.0218648	−	0.0378710i	0.00115883	−	0.00200716i
$357$	1.42943	−	2.47584i	0.0756532	−	0.131035i
$358$	12.7073	+	22.0096i	0.671599	+	1.16324i
$359$	−13.5734	−	23.5098i	−0.716378	−	1.24080i	−0.962426	−	0.271545i	$-0.912465\pi$
$359$	−13.5734	−	23.5098i	−0.716378	−	1.24080i	0.246048	−	0.969258i	$-0.420868\pi$
$360$	−20.7489	+	35.9382i	−1.09356	+	1.89411i
$361$	9.00693	+	15.6005i	0.474049	+	0.821076i
$362$	−32.1625			−1.69043
$363$	−10.8134	+	18.7294i	−0.567558	+	0.983040i
$364$	−0.0671318	−	0.116276i	−0.00351866	−	0.00609450i
$365$	0.968859			0.0507124
$366$	−8.16726	+	14.1461i	−0.426909	+	0.739429i
$367$	−2.68445	−	4.64961i	−0.140127	−	0.242707i	0.787417	−	0.616420i	$-0.211418\pi$
$367$	−2.68445	−	4.64961i	−0.140127	−	0.242707i	−0.927544	+	0.373713i	$0.878084\pi$
$368$	−21.4913			−1.12031
$369$	−19.5204	−	33.8103i	−1.01619	−	1.76009i
$370$	−10.9296	−	18.9306i	−0.568203	−	0.984156i
$371$	4.61621	−	7.99551i	0.239662	−	0.415106i
$372$	−0.00471033	+	0.00815854i	−0.000244219	+	0.000423001i
$373$	−2.12914	−	3.68778i	−0.110243	−	0.190946i	0.805625	−	0.592425i	$-0.201829\pi$
$373$	−2.12914	−	3.68778i	−0.110243	−	0.190946i	−0.915868	+	0.401479i	$0.868496\pi$
$374$	−5.44480			−0.281544
$375$	13.6138			0.703012
$376$	13.2402	−	22.9327i	0.682811	−	1.18266i
$377$	5.83697	+	10.1099i	0.300619	+	0.520688i
$378$	4.54620	−	7.87425i	0.233831	−	0.405008i
$379$	14.3163	+	24.7966i	0.735379	+	1.27371i	0.954557	+	0.298029i	$0.0963293\pi$
$379$	14.3163	+	24.7966i	0.735379	+	1.27371i	−0.219177	+	0.975685i	$0.570337\pi$
$380$	0.0955234			0.00490025
$381$	−25.1942	+	43.6376i	−1.29074	+	2.23562i
$382$	32.4153			1.65851
$383$	19.6147			1.00227			0.501133	−	0.865370i	$-0.332917\pi$
$383$	19.6147			1.00227			0.501133	+	0.865370i	$0.332917\pi$
$384$	−15.6277	−	27.0679i	−0.797497	−	1.38131i
$385$	6.98349	+	12.0958i	0.355911	+	0.616457i
$386$	19.1669			0.975567
$387$	20.2468	+	35.0685i	1.02920	+	1.78263i
$388$	−0.115147	−	0.199440i	−0.00584569	−	0.0101250i
$389$	−17.9625	−	31.1120i	−0.910737	−	1.57744i	−0.813025	−	0.582228i	$-0.802181\pi$
$389$	−17.9625	−	31.1120i	−0.910737	−	1.57744i	−0.0977116	−	0.995215i	$-0.531152\pi$
$390$	20.6439	+	35.7563i	1.04534	+	1.81059i
$391$	4.91657			0.248641
$392$	−8.18928	+	14.1843i	−0.413621	+	0.716413i
$393$	55.6241			2.80587
$394$	−3.11792	−	5.40040i	−0.157079	−	0.272068i
$395$	−15.1833	+	26.2983i	−0.763956	+	1.32321i
$396$	0.724676			0.0364163
$397$	−18.5896	+	32.1981i	−0.932984	+	1.61597i	−0.154793	+	0.987947i	$0.549471\pi$
$397$	−18.5896	+	32.1981i	−0.932984	+	1.61597i	−0.778191	+	0.628028i	$0.783862\pi$
$398$	−18.7542			−0.940065
$399$	−3.15589			−0.157992
$400$	6.56140	−	11.3647i	0.328070	−	0.568234i
$401$	−11.4760	+	19.8771i	−0.573085	+	0.992613i	0.423161	+	0.906054i	$0.360920\pi$
$401$	−11.4760	+	19.8771i	−0.573085	+	0.992613i	−0.996247	+	0.0865586i	$0.972413\pi$
$402$	17.9664	−	31.1187i	0.896083	−	1.55206i
$403$	0.179310	+	0.310574i	0.00893205	+	0.0154708i
$404$	−0.153676	+	0.266174i	−0.00764566	+	0.0132427i
$405$	1.85172	−	3.20728i	0.0920128	−	0.159371i
$406$	−2.55130	+	4.41899i	−0.126619	+	0.219311i
$407$	−11.6493	+	20.1772i	−0.577434	+	1.00014i
$408$	3.63676	+	6.29906i	0.180047	+	0.311850i
$409$	0.156297			0.00772841			0.00386421	−	0.999993i	$-0.498770\pi$
$409$	0.156297			0.00772841			0.00386421	+	0.999993i	$0.498770\pi$
$410$	15.6828	+	27.1634i	0.774518	+	1.34150i
$411$	27.2789	+	47.2484i	1.34557	+	2.33059i
$412$	0.228532	−	0.395829i	0.0112590	−	0.0195011i
$413$	−0.900883	+	1.56038i	−0.0443296	+	0.0767811i
$414$	38.6306			1.89859
$415$	−8.48512			−0.416518
$416$	0.677594			0.0332218
$417$	31.7341	+	54.9651i	1.55403	+	2.69165i
$418$	3.00526	+	5.20526i	0.146992	+	0.254598i
$419$	−1.07930	−	1.86941i	−0.0527274	−	0.0913265i	0.838457	−	0.544968i	$-0.183458\pi$
$419$	−1.07930	−	1.86941i	−0.0527274	−	0.0913265i	−0.891184	+	0.453641i	$0.850125\pi$
$420$	0.152848	−	0.264740i	0.00745821	−	0.0129180i
$421$	11.4538	−	19.8386i	0.558224	−	0.966872i	−0.439421	−	0.898281i	$-0.644816\pi$
$421$	11.4538	−	19.8386i	0.558224	−	0.966872i	0.997645	−	0.0685911i	$-0.0218504\pi$
$422$	8.59396			0.418347
$423$	−23.4027	+	40.5346i	−1.13788	+	1.97086i
$424$	11.7446	+	20.3423i	0.570369	+	0.987908i
$425$	−1.50105	+	2.59990i	−0.0728116	+	0.126113i
$426$	−21.8162	+	37.7867i	−1.05700	+	1.83077i
$427$	2.30195	−	3.98709i	0.111399	−	0.192949i
$428$	0.0650147	−	0.112609i	0.00314261	−	0.00544315i
$429$	22.0033	−	38.1107i	1.06233	−	1.84000i
$430$	−16.2664	−	28.1742i	−0.784435	−	1.35868i
$431$	14.8440	−	25.7105i	0.715009	−	1.23843i	−0.247948	−	0.968773i	$-0.579756\pi$
$431$	14.8440	−	25.7105i	0.715009	−	1.23843i	0.962956	−	0.269658i	$-0.0869106\pi$
$432$	11.3738	+	19.7000i	0.547221	+	0.947815i
$433$	1.34419			0.0645975			0.0322988	−	0.999478i	$-0.489717\pi$
$433$	1.34419			0.0645975			0.0322988	+	0.999478i	$0.489717\pi$
$434$	−0.0783751	+	0.135750i	−0.00376213	+	0.00651619i
$435$	−13.2898	+	23.0186i	−0.637197	+	1.10366i
$436$	−0.218059	−	0.377689i	−0.0104431	−	0.0180880i
$437$	−2.71370	−	4.70027i	−0.129814	−	0.224845i
$438$	0.667143	−	1.15553i	0.0318773	−	0.0552132i
$439$	18.7570	−	32.4881i	0.895222	−	1.55057i	0.0616931	−	0.998095i	$-0.480350\pi$
$439$	18.7570	−	32.4881i	0.895222	−	1.55057i	0.833529	−	0.552475i	$-0.186317\pi$
$440$	−35.5349			−1.69406
$441$	14.4749	−	25.0713i	0.689283	−	1.19387i
$442$	4.53649			0.215779
$443$	1.80932	+	3.13383i	0.0859632	+	0.148893i	0.905801	−	0.423703i	$-0.139270\pi$
$443$	1.80932	+	3.13383i	0.0859632	+	0.148893i	−0.819838	+	0.572595i	$0.805937\pi$
$444$	0.509936			0.0242005
$445$	1.89508	−	3.28238i	0.0898356	−	0.155600i
$446$	12.8119			0.606659
$447$	−48.9461			−2.31507
$448$	4.55527	+	7.88996i	0.215216	+	0.372766i
$449$	−0.822602			−0.0388210			−0.0194105	−	0.999812i	$-0.506179\pi$
$449$	−0.822602			−0.0388210			−0.0194105	+	0.999812i	$0.506179\pi$
$450$	−11.7941	+	20.4280i	−0.555979	+	0.962984i
$451$	16.7155	−	28.9520i	0.787100	−	1.36330i
$452$	−0.216865	−	0.375621i	−0.0102005	−	0.0176677i
$453$	7.35264			0.345457
$454$	12.7762			0.599619
$455$	−5.81850	−	10.0779i	−0.272776	−	0.472461i
$456$	4.01463	−	6.95354i	0.188002	−	0.325629i
$457$	−0.455436			−0.0213044			−0.0106522	−	0.999943i	$-0.503391\pi$
$457$	−0.455436			−0.0213044			−0.0106522	+	0.999943i	$0.503391\pi$
$458$	13.8818			0.648656
$459$	−2.60198	−	4.50676i	−0.121450	−	0.210357i
$460$	0.525726			0.0245121
$461$	−16.4554	+	28.5016i	−0.766405	+	1.32745i	0.173096	+	0.984905i	$0.444623\pi$
$461$	−16.4554	+	28.5016i	−0.766405	+	1.32745i	−0.939501	+	0.342547i	$0.888710\pi$
$462$	19.2350			0.894891
$463$	22.0561			1.02503			0.512517	−	0.858677i	$-0.328713\pi$
$463$	22.0561			1.02503			0.512517	+	0.858677i	$0.328713\pi$
$464$	−6.38290	−	11.0555i	−0.296319	−	0.513239i
$465$	−0.408258	+	0.707123i	−0.0189325	+	0.0327920i
$466$	−7.13830			−0.330676
$467$	−16.3270			−0.755525			−0.377762	−	0.925903i	$-0.623306\pi$
$467$	−16.3270			−0.755525			−0.377762	+	0.925903i	$0.623306\pi$
$468$	−0.603785			−0.0279100
$469$	−5.06385	+	8.77084i	−0.233827	+	0.405000i
$470$	18.8018	−	32.5657i	0.867264	−	1.50215i
$471$	2.38356	+	4.12845i	0.109829	+	0.190229i
$472$	−2.29204	−	3.96993i	−0.105500	−	0.182731i
$473$	−17.3375	+	30.0294i	−0.797179	+	1.38075i
$474$	20.9101	+	36.2173i	0.960432	+	1.66352i
$475$	3.31402			0.152058
$476$	−0.0167941	−	0.0290883i	−0.000769758	−	0.00133326i
$477$	−20.7592	−	35.9559i	−0.950497	−	1.64631i
$478$	−7.24179	+	12.5431i	−0.331232	+	0.573710i
$479$	3.39425			0.155087			0.0775437	−	0.996989i	$-0.475292\pi$
$479$	3.39425			0.155087			0.0775437	+	0.996989i	$0.475292\pi$
$480$	0.771383	+	1.33607i	0.0352086	+	0.0609831i
$481$	9.70595	−	16.8112i	0.442553	−	0.766525i
$482$	17.0196			0.775221
$483$	−17.3689			−0.790311
$484$	0.127046	+	0.220049i	0.00577480	+	0.0100022i
$485$	−9.98008	−	17.2860i	−0.453172	−	0.784917i
$486$	9.61875	+	16.6602i	0.436316	+	0.755721i
$487$	−13.1651	−	22.8026i	−0.596567	−	1.03328i	−0.993324	−	0.115361i	$-0.963198\pi$
$487$	−13.1651	−	22.8026i	−0.596567	−	1.03328i	0.396757	−	0.917924i	$-0.370136\pi$
$488$	5.85665	+	10.1440i	0.265118	+	0.459198i
$489$	−12.8445	−	22.2472i	−0.580846	−	1.00606i
$490$	−11.6293	+	20.1425i	−0.525356	+	0.909944i
$491$	−4.87921	−	8.45104i	−0.220196	−	0.381390i	0.734672	−	0.678423i	$-0.237336\pi$
$491$	−4.87921	−	8.45104i	−0.220196	−	0.381390i	−0.954867	+	0.297033i	$0.904003\pi$
$492$	−0.731703			−0.0329877
$493$	1.46022	+	2.52917i	0.0657648	+	0.113908i
$494$	−2.50392	−	4.33692i	−0.112657	−	0.195127i
$495$	62.8097			2.82308
$496$	−0.196081	−	0.339621i	−0.00880428	−	0.0152495i
$497$	6.14890	−	10.6502i	0.275816	−	0.477727i
$498$	−5.84274	+	10.1199i	−0.261820	+	0.453485i
$499$	−5.88454	−	10.1923i	−0.263428	−	0.456271i	0.703722	−	0.710475i	$-0.251520\pi$
$499$	−5.88454	−	10.1923i	−0.263428	−	0.456271i	−0.967151	+	0.254204i	$0.918187\pi$
$500$	0.0799732	−	0.138518i	0.00357651	−	0.00619469i
$501$	−60.2684			−2.69259
$502$	−4.19668	+	7.26885i	−0.187307	+	0.324425i
$503$	2.93523			0.130876			0.0654378	−	0.997857i	$-0.479156\pi$
$503$	2.93523			0.130876			0.0654378	+	0.997857i	$0.479156\pi$
$504$	−8.05385	−	13.9497i	−0.358747	−	0.621368i
$505$	−13.3195	+	23.0701i	−0.592711	+	1.02660i
$506$	16.5399	+	28.6479i	0.735286	+	1.27355i
$507$	0.0981790	−	0.170051i	0.00436028	−	0.00755223i
$508$	0.296003	+	0.512692i	0.0131330	+	0.0227470i
$509$	17.0299			0.754839			0.377419	−	0.926042i	$-0.376812\pi$
$509$	17.0299			0.754839			0.377419	+	0.926042i	$0.376812\pi$
$510$	5.16441	+	8.94502i	0.228684	+	0.396092i
$511$	−0.188035	+	0.325686i	−0.00831818	+	0.0144075i
$512$	−23.1666			−1.02383
$513$	−2.87233	+	4.97502i	−0.126816	+	0.219652i
$514$	−5.89238	−	10.2059i	−0.259902	−	0.450163i
$515$	19.8075	−	34.3076i	0.872823	−	1.51177i
$516$	0.758932			0.0334101
$517$	−40.0798			−1.76271
$518$	8.48482			0.372801
$519$	65.1106			2.85804
$520$	29.6070			1.29835
$521$	−9.06041	+	15.6931i	−0.396944	+	0.687527i	−0.993347	−	0.115158i	$-0.963263\pi$
$521$	−9.06041	+	15.6931i	−0.396944	+	0.687527i	0.596403	+	0.802685i	$0.296596\pi$
$522$	11.4732	+	19.8722i	0.502170	+	0.869784i
$523$	−6.12038			−0.267626			−0.133813	−	0.991007i	$-0.542722\pi$
$523$	−6.12038			−0.267626			−0.133813	+	0.991007i	$0.542722\pi$
$524$	0.326760	−	0.565965i	0.0142746	−	0.0247243i
$525$	5.30280	−	9.18471i	0.231433	−	0.400854i
$526$	−2.74004	−	4.74588i	−0.119471	−	0.206930i
$527$	0.0448573	+	0.0776951i	0.00195401	+	0.00338445i
$528$	−24.0612	+	41.6752i	−1.04713	+	1.81368i
$529$	−3.43523	−	5.95000i	−0.149358	−	0.258696i
$530$	16.6780	+	28.8872i	0.724448	+	1.25478i
$531$	4.05128	+	7.01703i	0.175811	+	0.304513i
$532$	−0.0185391	+	0.0321106i	−0.000803771	+	0.00139217i
$533$	−13.9270	+	24.1223i	−0.603245	+	1.04485i
$534$	−2.60986	−	4.52041i	−0.112940	−	0.195617i
$535$	5.63501	−	9.76012i	0.243623	−	0.421967i
$536$	−12.8835	−	22.3149i	−0.556482	−	0.963856i
$537$	−51.3862			−2.21748
$538$	−37.0925			−1.59917
$539$	24.7900			1.06778
$540$	−0.278228	−	0.481905i	−0.0119730	−	0.0207379i
$541$	4.26465	+	7.38659i	0.183352	+	0.317574i	0.943020	−	0.332737i	$-0.107972\pi$
$541$	4.26465	+	7.38659i	0.183352	+	0.317574i	−0.759668	+	0.650311i	$0.774639\pi$
$542$	−8.93588	+	15.4774i	−0.383829	+	0.664811i
$543$	32.5151	−	56.3177i	1.39536	−	2.41683i
$544$	0.169511			0.00726773
$545$	−18.8997	−	32.7353i	−0.809576	−	1.40223i
$546$	−16.0262			−0.685857
$547$	8.31973	+	21.8582i	0.355726	+	0.934590i
$547$	8.31973	+	21.8582i	0.355726	+	0.934590i
$548$	0.640992			0.0273818
$549$	−10.3519	−	17.9300i	−0.441808	−	0.765234i
$550$	−20.1988			−0.861278
$551$	1.61193	−	2.79195i	0.0686707	−	0.118941i
$552$	22.0950	−	38.2697i	0.940428	−	1.62887i
$553$	−5.89352	−	10.2079i	−0.250618	−	0.434083i
$554$	−15.2325	−	26.3835i	−0.647168	−	1.12093i
$555$	44.1976			1.87608
$556$	0.745680			0.0316239
$557$	38.2614			1.62119			0.810593	−	0.585610i	$-0.199145\pi$
$557$	38.2614			1.62119			0.810593	+	0.585610i	$0.199145\pi$
$558$	0.352454	+	0.610468i	0.0149206	+	0.0258432i
$559$	14.4453	−	25.0199i	0.610969	−	1.05823i
$560$	6.36270	+	11.0205i	0.268873	+	0.465702i
$561$	5.50448	−	9.53403i	0.232399	−	0.402527i
$562$	−9.19729	+	15.9302i	−0.387964	+	0.671974i
$563$	−19.5103	−	33.7928i	−0.822260	−	1.42420i	−0.903995	−	0.427543i	$-0.859379\pi$
$563$	−19.5103	−	33.7928i	−0.822260	−	1.42420i	0.0817349	−	0.996654i	$-0.473954\pi$
$564$	0.438614	+	0.759701i	0.0184690	+	0.0319892i
$565$	−18.7963	−	32.5561i	−0.790766	−	1.36965i
$566$	−7.30280	+	12.6488i	−0.306960	+	0.531670i
$567$	0.718760	+	1.24493i	0.0301851	+	0.0522821i
$568$	15.6441	+	27.0964i	0.656412	+	1.13694i
$569$	−6.36154	+	11.0185i	−0.266690	+	0.461920i	−0.968005	−	0.250931i	$-0.919263\pi$
$569$	−6.36154	+	11.0185i	−0.266690	+	0.461920i	0.701315	+	0.712851i	$0.252597\pi$
$570$	5.70100	−	9.87443i	0.238789	−	0.413594i
$571$	−5.08306			−0.212719			−0.106360	−	0.994328i	$-0.533919\pi$
$571$	−5.08306			−0.212719			−0.106360	+	0.994328i	$0.533919\pi$
$572$	−0.258513	−	0.447758i	−0.0108090	−	0.0187217i
$573$	−32.7706	+	56.7603i	−1.36901	+	2.37120i
$574$	−12.1748			−0.508166
$575$	18.2392			0.760626
$576$	40.9702			1.70709
$577$	−42.9850			−1.78949			−0.894744	−	0.446579i	$-0.852642\pi$
$577$	−42.9850			−1.78949			−0.894744	+	0.446579i	$0.852642\pi$
$578$	−22.7057			−0.944432
$579$	−19.3769	+	33.5619i	−0.805278	+	1.39478i
$580$	0.156140	+	0.270442i	0.00648336	+	0.0112295i
$581$	1.64678	−	2.85231i	0.0683200	−	0.118334i
$582$	−27.4886			−1.13944
$583$	17.7762	−	30.7894i	0.736217	−	1.27517i
$584$	−0.478401	−	0.828614i	−0.0197964	−	0.0342883i
$585$	−52.3317			−2.16365
$586$	0.0752619	+	0.130357i	0.00310904	+	0.00538502i
$587$	−18.5867	+	32.1932i	−0.767156	+	1.32875i	0.171942	+	0.985107i	$0.444996\pi$
$587$	−18.5867	+	32.1932i	−0.767156	+	1.32875i	−0.939099	+	0.343647i	$0.888338\pi$
$588$	−0.271290	−	0.469888i	−0.0111878	−	0.0193779i
$589$	0.0495180	−	0.0857677i	0.00204035	−	0.00353400i
$590$	−3.25483	−	5.63752i	−0.133999	−	0.232093i
$591$	12.6084			0.518640
$592$	−10.6137	+	18.3835i	−0.436222	+	0.755559i
$593$	19.7818			0.812342			0.406171	−	0.913797i	$-0.366864\pi$
$593$	19.7818			0.812342			0.406171	+	0.913797i	$0.366864\pi$
$594$	17.5067	−	30.3224i	0.718307	−	1.24414i
$595$	−1.45559	−	2.52116i	−0.0596735	−	0.103358i
$596$	−0.287530	+	0.498017i	−0.0117777	+	0.0203996i
$597$	18.9598	−	32.8393i	0.775973	−	1.34402i
$598$	−13.7807	−	23.8688i	−0.563534	−	0.976069i
$599$	−39.6901			−1.62169			−0.810846	−	0.585260i	$-0.800993\pi$
$599$	−39.6901			−1.62169			−0.810846	+	0.585260i	$0.800993\pi$
$600$	13.4914	+	23.3679i	0.550786	+	0.953989i
$601$	−22.2331	−	38.5088i	−0.906905	−	1.57081i	−0.818339	−	0.574736i	$-0.805105\pi$
$601$	−22.2331	−	38.5088i	−0.906905	−	1.57081i	−0.0885662	−	0.996070i	$-0.528228\pi$
$602$	12.6279			0.514673
$603$	22.7722	+	39.4426i	0.927355	+	1.60623i
$604$	0.0431926	−	0.0748118i	0.00175748	−	0.00304405i
$605$	11.0114	+	19.0723i	0.447677	+	0.775399i
$606$	18.3433	+	31.7715i	0.745145	+	1.29063i
$607$	−9.75985	−	16.9046i	−0.396140	−	0.686135i	0.597106	−	0.802163i	$-0.296317\pi$
$607$	−9.75985	−	16.9046i	−0.396140	−	0.686135i	−0.993246	+	0.116027i	$0.962984\pi$
$608$	−0.0935618	−	0.162054i	−0.00379443	−	0.00657215i
$609$	−5.15854	−	8.93485i	−0.209034	−	0.362058i
$610$	8.31678	+	14.4051i	0.336736	+	0.583245i
$611$	33.3937			1.35096
$612$	−0.151047			−0.00610571
$613$	−9.81724	+	17.0040i	−0.396515	+	0.686783i	−0.993293	−	0.115623i	$-0.963114\pi$
$613$	−9.81724	+	17.0040i	−0.396515	+	0.686783i	0.596779	+	0.802406i	$0.296447\pi$
$614$	15.9876	+	27.6913i	0.645206	+	1.11753i
$615$	−63.4188			−2.55729
$616$	6.89658	−	11.9452i	0.277871	−	0.481287i
$617$	17.7834	+	30.8017i	0.715931	+	1.24003i	0.962599	+	0.270929i	$0.0873309\pi$
$617$	17.7834	+	30.8017i	0.715931	+	1.24003i	−0.246668	+	0.969100i	$0.579336\pi$
$618$	−27.2784	−	47.2475i	−1.09730	−	1.90057i
$619$	−4.05760			−0.163089			−0.0815444	−	0.996670i	$-0.525985\pi$
$619$	−4.05760			−0.163089			−0.0815444	+	0.996670i	$0.525985\pi$
$620$	0.00479657	+	0.00830789i	0.000192635	+	0.000333653i
$621$	−15.8082	+	27.3807i	−0.634363	+	1.09875i
$622$	1.04543	+	1.81073i	0.0419178	+	0.0726038i
$623$	0.735592	+	1.27408i	0.0294709	+	0.0510450i
$624$	20.0473	−	34.7230i	0.802535	−	1.39003i
$625$	15.2745	−	26.4563i	0.610981	−	1.05825i
$626$	−44.1609			−1.76502
$627$	−12.1528			−0.485336
$628$	0.0560084			0.00223498
$629$	2.42810	−	4.20560i	0.0968148	−	0.167688i
$630$	−11.4369	−	19.8094i	−0.455658	−	0.789223i
$631$	−3.36553			−0.133979			−0.0669897	−	0.997754i	$-0.521339\pi$
$631$	−3.36553			−0.133979			−0.0669897	+	0.997754i	$0.521339\pi$
$632$	29.9887			1.19289
$633$	−8.68816	+	15.0483i	−0.345323	+	0.598117i
$634$	36.5324			1.45089
$635$	25.6554	+	44.4364i	1.01810	+	1.76341i
$636$	−0.778138			−0.0308552
$637$	−20.6546			−0.818363
$638$	−9.82464	+	17.0168i	−0.388961	+	0.673700i
$639$	−27.6517	−	47.8941i	−1.09388	−	1.89466i
$640$	−31.8276			−1.25809
$641$	−14.4139			−0.569314			−0.284657	−	0.958629i	$-0.591880\pi$
$641$	−14.4139			−0.569314			−0.284657	+	0.958629i	$0.591880\pi$
$642$	−7.76039	−	13.4414i	−0.306278	−	0.530489i
$643$	14.8700	−	25.7555i	0.586414	−	1.01570i	−0.408283	−	0.912855i	$-0.633872\pi$
$643$	14.8700	−	25.7555i	0.586414	−	1.01570i	0.994697	−	0.102844i	$-0.0327943\pi$
$644$	−0.102032	+	0.176725i	−0.00402064	+	0.00696394i
$645$	65.7788			2.59004
$646$	−0.626397	−	1.08495i	−0.0246453	−	0.0426869i
$647$	31.5833			1.24167			0.620833	−	0.783943i	$-0.286794\pi$
$647$	31.5833			1.24167			0.620833	+	0.783943i	$0.286794\pi$
$648$	−3.65736			−0.143675
$649$	−3.46915	+	6.00874i	−0.136176	+	0.235864i
$650$	16.8292			0.660096
$651$	−0.158468	−	0.274475i	−0.00621087	−	0.0107575i
$652$	−0.301815			−0.0118200
$653$	−0.861164	+	1.49158i	−0.0337000	+	0.0583700i	−0.882383	−	0.470531i	$-0.844062\pi$
$653$	−0.861164	+	1.49158i	−0.0337000	+	0.0583700i	0.848684	+	0.528901i	$0.177396\pi$
$654$	−52.0565			−2.03557
$655$	28.3212	−	49.0538i	1.10660	−	1.91669i
$656$	15.2296	−	26.3784i	0.594615	−	1.02990i
$657$	0.845596	+	1.46461i	0.0329898	+	0.0571401i
$658$	7.29808	+	12.6406i	0.284509	+	0.492784i
$659$	−19.7633	+	34.2310i	−0.769867	+	1.33345i	0.167767	+	0.985827i	$0.446344\pi$
$659$	−19.7633	+	34.2310i	−0.769867	+	1.33345i	−0.937635	+	0.347622i	$0.886989\pi$
$660$	0.588591	−	1.01947i	0.0229109	−	0.0396828i
$661$	−40.1929			−1.56332			−0.781661	−	0.623704i	$-0.785627\pi$
$661$	−40.1929			−1.56332			−0.781661	+	0.623704i	$0.785627\pi$
$662$	4.04046	+	6.99828i	0.157037	+	0.271996i
$663$	−4.58622	+	7.94356i	−0.178114	+	0.308502i
$664$	4.18976	+	7.25688i	0.162594	+	0.281622i
$665$	−1.60683	+	2.78312i	−0.0623103	+	0.107925i
$666$	19.0782	−	33.0443i	0.739264	−	1.28044i
$667$	8.87150	−	15.3659i	0.343506	−	0.594969i
$668$	−0.354043	+	0.613220i	−0.0136983	+	0.0237262i
$669$	−12.9523	+	22.4340i	−0.500764	+	0.867349i
$670$	−18.2953	−	31.6884i	−0.706810	−	1.22423i
$671$	8.86441	−	15.3536i	0.342207	−	0.592720i
$672$	−0.598836			−0.0231006
$673$	6.78592	−	11.7536i	0.261578	−	0.453067i	−0.705083	−	0.709124i	$-0.749090\pi$
$673$	6.78592	−	11.7536i	0.261578	−	0.453067i	0.966661	+	0.256058i	$0.0824238\pi$
$674$	−8.30841	+	14.3906i	−0.320028	+	0.554304i
$675$	−9.65266	−	16.7189i	−0.371531	−	0.643510i
$676$	−0.00115349	−	0.00199791i	−4.43651e−5	−	7.68426e-5i
$677$	5.30602	+	9.19030i	0.203927	+	0.353212i	0.949790	−	0.312887i	$-0.101296\pi$
$677$	5.30602	+	9.19030i	0.203927	+	0.353212i	−0.745863	+	0.666099i	$0.767963\pi$
$678$	−51.7715			−1.98827
$679$	7.74769			0.297329
$680$	7.40668			0.284033
$681$	−12.9163	+	22.3717i	−0.494953	+	0.857284i
$682$	−0.301809	+	0.522749i	−0.0115569	+	0.0200171i
$683$	−4.73552	−	8.20217i	−0.181200	−	0.313847i	0.761090	−	0.648647i	$-0.224665\pi$
$683$	−4.73552	−	8.20217i	−0.181200	−	0.313847i	−0.942289	+	0.334800i	$0.891331\pi$
$684$	0.0833704	+	0.144402i	0.00318775	+	0.00552134i
$685$	55.5565			2.12271
$686$	−10.0151	−	17.3467i	−0.382380	−	0.662302i
$687$	−14.0340	+	24.3076i	−0.535430	+	0.927393i
$688$	−15.7963	+	27.3600i	−0.602229	+	1.04309i
$689$	−14.8108	+	25.6531i	−0.564247	+	0.977304i
$690$	31.3762	−	54.3452i	1.19447	−	2.06889i
$691$	19.7044	+	34.1291i	0.749592	+	1.29833i	0.948018	+	0.318215i	$0.103084\pi$
$691$	19.7044	+	34.1291i	0.749592	+	1.29833i	−0.198427	+	0.980116i	$0.563583\pi$
$692$	0.382488	−	0.662489i	0.0145400	−	0.0251840i
$693$	−12.1900	+	21.1137i	−0.463061	+	0.802045i
$694$	−23.4597	+	40.6335i	−0.890519	+	1.54242i
$695$	64.6302			2.45156
$696$	26.2488			0.994959
$697$	−3.48407	+	6.03458i	−0.131968	+	0.228576i
$698$	26.9431			1.01981
$699$	7.21655	−	12.4994i	0.272955	−	0.472772i
$700$	−0.0623018	−	0.107910i	−0.00235479	−	0.00407861i
$701$	41.4185			1.56436			0.782178	−	0.623055i	$-0.214109\pi$
$701$	41.4185			1.56436			0.782178	+	0.623055i	$0.214109\pi$
$702$	−14.5862	+	25.2640i	−0.550520	+	0.953529i
$703$	−5.36077			−0.202185
$704$	17.5416	+	30.3829i	0.661123	+	1.14510i
$705$	38.0159	+	65.8454i	1.43176	+	2.47988i
$706$	9.04221	+	15.6616i	0.340308	+	0.589431i
$707$	−5.17007	−	8.95483i	−0.194441	−	0.336781i
$708$	0.151859			0.00570720
$709$	−6.92262	−	11.9903i	−0.259985	−	0.450306i	0.706253	−	0.707960i	$-0.250384\pi$
$709$	−6.92262	−	11.9903i	−0.259985	−	0.450306i	−0.966237	+	0.257653i	$0.917051\pi$
$710$	22.2155	+	38.4785i	0.833734	+	1.44407i
$711$	−53.0065			−1.98790
$712$	−3.74300			−0.140275
$713$	0.272529	−	0.472034i	0.0102063	−	0.0176778i
$714$	−4.00921			−0.150041
$715$	−22.4061	−	38.8084i	−0.837939	−	1.45135i
$716$	−0.301865	+	0.522845i	−0.0112812	+	0.0195396i
$717$	−14.6423	−	25.3613i	−0.546828	−	0.947133i
$718$	−19.0352	+	32.9699i	−0.710386	+	1.23042i
$719$	39.5937			1.47660			0.738298	−	0.674475i	$-0.235630\pi$
$719$	39.5937			1.47660			0.738298	+	0.674475i	$0.235630\pi$
$720$	57.2263			2.13270
$721$	7.68843	+	13.3168i	0.286332	+	0.495942i
$722$	12.6312	−	21.8779i	0.470084	−	0.814209i
$723$	−17.2061	+	29.8019i	−0.639903	+	1.10834i
$724$	−0.382015	−	0.661670i	−0.0141975	−	0.0245908i
$725$	5.41702	+	9.38255i	0.201183	+	0.348459i
$726$	30.3292			1.12562
$727$	24.4293	+	42.3128i	0.906032	+	1.56929i	0.819526	+	0.573042i	$0.194237\pi$
$727$	24.4293	+	42.3128i	0.906032	+	1.56929i	0.0865057	+	0.996251i	$0.472430\pi$
$728$	−5.74609	+	9.95252i	−0.212964	+	0.368865i
$729$	−42.7446			−1.58313
$730$	−0.679357	−	1.17668i	−0.0251441	−	0.0435509i
$731$	3.61372	−	6.25914i	0.133658	−	0.231503i
$732$	−0.388031			−0.0143420
$733$	10.1410	+	17.5647i	0.374566	+	0.648768i	0.990262	−	0.139216i	$-0.0444583\pi$
$733$	10.1410	+	17.5647i	0.374566	+	0.648768i	−0.615696	+	0.787984i	$0.711125\pi$
$734$	−3.76464	+	6.52054i	−0.138955	+	0.240678i
$735$	−23.5135	−	40.7265i	−0.867307	−	1.50222i
$736$	−0.514930	−	0.891885i	−0.0189806	−	0.0328753i
$737$	−19.5000	+	33.7750i	−0.718292	+	1.24412i
$738$	−27.3751	+	47.4151i	−1.00769	+	1.74537i
$739$	−13.0509			−0.480084			−0.240042	−	0.970762i	$-0.577161\pi$
$739$	−13.0509			−0.480084			−0.240042	+	0.970762i	$0.577161\pi$
$740$	0.259636	−	0.449702i	0.00954440	−	0.0165314i
$741$	10.1255			0.371968
$742$	−12.9474			−0.475315
$743$	12.7752	+	22.1272i	0.468676	+	0.811770i	0.999359	−	0.0358002i	$-0.0113980\pi$
$743$	12.7752	+	22.1272i	0.468676	+	0.811770i	−0.530683	+	0.847570i	$0.678065\pi$
$744$	0.806354			0.0295624
$745$	−24.9211	+	43.1645i	−0.913037	+	1.58143i
$746$	−2.98588	+	5.17169i	−0.109321	+	0.189349i
$747$	−7.40560	−	12.8269i	−0.270957	−	0.469311i
$748$	−0.0646713	−	0.112014i	−0.00236462	−	0.00409564i
$749$	2.18727	+	3.78847i	0.0799212	+	0.138428i
$750$	−9.54588	−	16.5339i	−0.348566	−	0.603734i
$751$	2.05521			0.0749958			0.0374979	−	0.999297i	$-0.488061\pi$
$751$	2.05521			0.0749958			0.0374979	+	0.999297i	$0.488061\pi$
$752$	−36.5170			−1.33164
$753$	−8.48535	−	14.6971i	−0.309223	−	0.535591i
$754$	8.18569	−	14.1780i	0.298105	−	0.516333i
$755$	3.74362	−	6.48415i	0.136244	−	0.235982i
$756$	0.215993			0.00785558
$757$	5.71429	+	9.89744i	0.207689	+	0.359729i	0.950986	−	0.309233i	$-0.100072\pi$
$757$	5.71429	+	9.89744i	0.207689	+	0.359729i	−0.743297	+	0.668962i	$0.766739\pi$
$758$	20.0770	−	34.7744i	0.729229	−	1.26306i
$759$	−66.8846			−2.42776
$760$	−4.08812	−	7.08084i	−0.148292	−	0.256849i
$761$	7.80444	+	13.5177i	0.282911	+	0.490016i	0.972100	−	0.234565i	$-0.0753666\pi$
$761$	7.80444	+	13.5177i	0.282911	+	0.490016i	−0.689190	+	0.724581i	$0.742033\pi$
$762$	70.6639			2.55988
$763$	14.6722			0.531168
$764$	0.385017	+	0.666869i	0.0139294	+	0.0241265i
$765$	−13.0916			−0.473330
$766$	−13.7537	−	23.8221i	−0.496942	−	0.860728i
$767$	2.89042	−	5.00636i	0.104367	−	0.180769i
$768$	1.13323	−	1.96282i	0.0408921	−	0.0708272i
$769$	15.8445	−	27.4435i	0.571368	−	0.989639i	−0.425058	−	0.905166i	$-0.639746\pi$
$769$	15.8445	−	27.4435i	0.571368	−	0.989639i	0.996426	−	0.0844725i	$-0.0269205\pi$
$770$	9.79354	−	16.9629i	0.352935	−	0.611301i
$771$	23.8279			0.858140
$772$	0.227657	+	0.394314i	0.00819356	+	0.0141917i
$773$	−46.8017			−1.68334			−0.841670	−	0.539992i	$-0.818427\pi$
$773$	−46.8017			−1.68334			−0.841670	+	0.539992i	$0.818427\pi$
$774$	28.3938	−	49.1795i	1.02059	−	1.76772i
$775$	0.166409	+	0.288229i	0.00597758	+	0.0103535i
$776$	−9.85588	+	17.0709i	−0.353806	+	0.612809i
$777$	−8.57782	+	14.8572i	−0.307728	+	0.533000i
$778$	−25.1904	+	43.6311i	−0.903120	+	1.56425i
$779$	7.69213			0.275599
$780$	−0.490402	+	0.849401i	−0.0175592	+	0.0304134i
$781$	23.6784	−	41.0122i	0.847279	−	1.46753i
$782$	−3.44746	−	5.97118i	−0.123281	−	0.213529i
$783$	−18.7801			−0.671147
$784$	22.5864			0.806656
$785$	4.85440			0.173261
$786$	−39.0032	−	67.5556i	−1.39120	−	2.40963i
$787$	−8.50943			−0.303328			−0.151664	−	0.988432i	$-0.548463\pi$
$787$	−8.50943			−0.303328			−0.151664	+	0.988432i	$0.548463\pi$
$788$	0.0740671	−	0.128288i	0.00263853	−	0.00457007i
$789$	11.0803			0.394468
$790$	42.5857			1.51513
$791$	14.5919			0.518827
$792$	−31.0140	−	53.7178i	−1.10203	−	1.90878i
$793$	−7.38565	+	12.7923i	−0.262272	+	0.454269i
$794$	52.1395			1.85036
$795$	−67.4434			−2.39197
$796$	−0.222756	−	0.385825i	−0.00789538	−	0.0136752i
$797$	10.0716	+	17.4445i	0.356754	+	0.617916i	0.987416	−	0.158141i	$-0.0505502\pi$
$797$	10.0716	+	17.4445i	0.356754	+	0.617916i	−0.630663	+	0.776057i	$0.717217\pi$
$798$	2.21289	+	3.83284i	0.0783354	+	0.135681i
$799$	8.35398			0.295543
$800$	0.628842			0.0222329
$801$	6.61593			0.233762
$802$	32.1876			1.13658
$803$	−0.724091	+	1.25416i	−0.0255526	+	0.0442584i
$804$	0.853594			0.0301039
$805$	−8.84342	+	15.3173i	−0.311690	+	0.539862i
$806$	0.251461	−	0.435544i	0.00885735	−	0.0153414i
$807$	37.4991	−	64.9503i	1.32003	−	2.28636i
$808$	26.3075			0.925495
$809$	17.0333	+	29.5025i	0.598859	+	1.03725i	0.992990	+	0.118200i	$0.0377124\pi$
$809$	17.0333	+	29.5025i	0.598859	+	1.03725i	−0.394131	+	0.919054i	$0.628954\pi$
$810$	−5.19366			−0.182487
$811$	−2.96545	−	5.13632i	−0.104131	−	0.180360i	0.809252	−	0.587462i	$-0.199873\pi$
$811$	−2.96545	−	5.13632i	−0.104131	−	0.180360i	−0.913383	+	0.407102i	$0.866539\pi$
$812$	−0.121214			−0.00425377
$813$	−18.0677	−	31.2941i	−0.633660	−	1.09753i
$814$	32.6736			1.14521
$815$	−26.1592			−0.916316
$816$	5.01517	−	8.68652i	0.175566	−	0.304089i
$817$	−7.97838			−0.279128
$818$	−0.109595	−	0.189824i	−0.00383189	−	0.00663702i
$819$	10.1565	−	17.5915i	0.354896	−	0.614698i
$820$	−0.372549	+	0.645274i	−0.0130100	+	0.0225340i
$821$	−3.32386	+	5.75710i	−0.116004	+	0.200924i	−0.918180	−	0.396162i	$-0.870342\pi$
$821$	−3.32386	+	5.75710i	−0.116004	+	0.200924i	0.802177	+	0.597086i	$0.203675\pi$
$822$	38.2555	−	66.2605i	1.33431	−	2.31110i
$823$	−9.80346	−	16.9801i	−0.341727	−	0.591889i	0.643027	−	0.765844i	$-0.277678\pi$
$823$	−9.80346	−	16.9801i	−0.341727	−	0.591889i	−0.984754	+	0.173955i	$0.944345\pi$
$824$	−39.1220			−1.36288
$825$	20.4202	−	35.3688i	0.710939	−	1.23138i
$826$	2.52677			0.0879176
$827$	3.18383			0.110713			0.0553563	−	0.998467i	$-0.482371\pi$
$827$	3.18383			0.110713			0.0553563	+	0.998467i	$0.482371\pi$
$828$	0.458840	+	0.794735i	0.0159458	+	0.0276190i
$829$	46.3439			1.60959			0.804795	−	0.593553i	$-0.202275\pi$
$829$	46.3439			1.60959			0.804795	+	0.593553i	$0.202275\pi$
$830$	5.94971	+	10.3052i	0.206517	+	0.357698i
$831$	61.5980			2.13681
$832$	−14.6153	−	25.3144i	−0.506694	−	0.877619i
$833$	−5.16708			−0.179029
$834$	44.5035	−	77.0823i	1.54103	−	2.66914i
$835$	−30.6859	+	53.1495i	−1.06193	+	1.83931i
$836$	−0.0713908	+	0.123653i	−0.00246910	+	0.00427661i
$837$	−0.576919			−0.0199412
$838$	−1.51360	+	2.62163i	−0.0522864	+	0.0905627i
$839$	−15.0336			−0.519017			−0.259509	−	0.965741i	$-0.583561\pi$
$839$	−15.0336			−0.519017			−0.259509	+	0.965741i	$0.583561\pi$
$840$	−26.1657			−0.902804
$841$	−18.4607			−0.636576
$842$	−32.1253			−1.10711
$843$	−18.5962	−	32.2096i	−0.640487	−	1.10936i
$844$	0.102076	+	0.176801i	0.00351360	+	0.00608574i
$845$	−0.0999763	−	0.173164i	−0.00343929	−	0.00595703i
$846$	65.6391			2.25672
$847$	−8.54831			−0.293724
$848$	16.1961	−	28.0524i	0.556175	−	0.963323i
$849$	−14.7657	−	25.5749i	−0.506757	−	0.877730i
$850$	4.21010			0.144405
$851$	−29.5037			−1.01138
$852$	−1.03650			−0.0355099
$853$	−2.66995	+	4.62449i	−0.0914174	+	0.158340i	−0.908108	−	0.418737i	$-0.862473\pi$
$853$	−2.66995	+	4.62449i	−0.0914174	+	0.158340i	0.816690	+	0.577076i	$0.195806\pi$
$854$	−6.45644			−0.220935
$855$	7.22595	+	12.5157i	0.247122	+	0.428028i
$856$	−11.1298			−0.380407
$857$	32.5860			1.11312			0.556558	−	0.830808i	$-0.312122\pi$
$857$	32.5860			1.11312			0.556558	+	0.830808i	$0.312122\pi$
$858$	−61.7141			−2.10688
$859$	−22.0426	−	38.1789i	−0.752084	−	1.30265i	−0.946811	−	0.321791i	$-0.895715\pi$
$859$	−22.0426	−	38.1789i	−0.752084	−	1.30265i	0.194726	−	0.980858i	$-0.437618\pi$
$860$	0.386413	−	0.669287i	0.0131766	−	0.0228225i
$861$	12.3082	−	21.3185i	0.419464	−	0.726532i
$862$	−41.6339			−1.41806
$863$	0.742070	−	1.28530i	0.0252604	−	0.0437522i	−0.853119	−	0.521717i	$-0.825292\pi$
$863$	0.742070	−	1.28530i	0.0252604	−	0.0437522i	0.878379	+	0.477964i	$0.158625\pi$
$864$	−0.545029	+	0.944019i	−0.0185423	+	0.0321162i
$865$	33.1513	−	57.4197i	1.12718	−	1.95233i
$866$	−0.942535	−	1.63252i	−0.0320286	−	0.0554752i
$867$	22.9546	−	39.7585i	0.779578	−	1.35027i
$868$	−0.00372365			−0.000126389
$869$	−22.6950	−	39.3088i	−0.769874	−	1.33346i
$870$	37.2748			1.26374
$871$	16.2470	−	28.1407i	0.550509	−	0.953510i
$872$	−18.6645	+	32.3279i	−0.632061	+	1.09476i
$873$	17.4207	−	30.1736i	0.589602	−	1.02122i
$874$	−3.80566	+	6.59159i	−0.128728	+	0.222964i
$875$	2.69051	+	4.66011i	0.0909559	+	0.157540i
$876$	0.0316964			0.00107092
$877$	−10.5873	−	18.3377i	−0.357508	−	0.619221i	0.630036	−	0.776566i	$-0.283040\pi$
$877$	−10.5873	−	18.3377i	−0.357508	−	0.619221i	−0.987544	+	0.157344i	$0.949707\pi$
$878$	−52.6091			−1.77547
$879$	−0.304347			−0.0102654
$880$	24.5017	+	42.4382i	0.825952	+	1.43059i
$881$	7.14649	+	12.3781i	0.240771	+	0.417028i	0.960934	−	0.276777i	$-0.0892662\pi$
$881$	7.14649	+	12.3781i	0.240771	+	0.417028i	−0.720163	+	0.693805i	$0.755933\pi$
$882$	−40.5989			−1.36704
$883$	−13.5333	+	23.4403i	−0.455431	+	0.788830i	−0.998713	−	0.0507204i	$-0.983848\pi$
$883$	−13.5333	+	23.4403i	−0.455431	+	0.788830i	0.543282	+	0.839551i	$0.317182\pi$
$884$	0.0538829	+	0.0933279i	0.00181228	+	0.00313896i
$885$	13.1620			0.442436
$886$	2.53736	−	4.39484i	0.0852443	−	0.147647i
$887$	−2.30329	+	3.98942i	−0.0773371	+	0.133952i	−0.902100	−	0.431527i	$-0.857975\pi$
$887$	−2.30329	+	3.98942i	−0.0773371	+	0.133952i	0.824763	+	0.565478i	$0.191308\pi$
$888$	−21.8238	−	37.7999i	−0.732358	−	1.26848i
$889$	−19.9167			−0.667984
$890$	−5.31528			−0.178169
$891$	2.76782	+	4.79401i	0.0927256	+	0.160605i
$892$	0.152175	+	0.263574i	0.00509518	+	0.00882512i
$893$	−4.61099	−	7.98646i	−0.154301	−	0.267257i
$894$	34.3206	+	59.4451i	1.14785	+	1.98814i
$895$	−26.1634	+	45.3164i	−0.874547	+	1.51476i
$896$	6.17705	−	10.6990i	0.206361	−	0.357428i
$897$	55.7269			1.86067
$898$	0.576803	+	0.999052i	0.0192482	+	0.0333388i
$899$	0.323763			0.0107981
$900$	−0.560344			−0.0186781
$901$	−3.70517	+	6.41754i	−0.123437	+	0.213799i
$902$	−46.8831			−1.56104
$903$	−12.7663	+	22.1118i	−0.424835	+	0.735835i
$904$	−18.5624	+	32.1510i	−0.617376	+	1.06933i
$905$	−33.1103	−	57.3487i	−1.10062	−	1.90634i
$906$	−5.15562	−	8.92980i	−0.171284	−	0.296673i
$907$	15.6257	−	27.0644i	0.518841	−	0.898659i	−0.480919	−	0.876765i	$-0.659697\pi$
$907$	15.6257	−	27.0644i	0.518841	−	0.898659i	0.999760	−	0.0218944i	$-0.00696975\pi$
$908$	0.151752	+	0.262842i	0.00503606	+	0.00872271i
$909$	−46.4998			−1.54230
$910$	−8.15978	+	14.1332i	−0.270494	+	0.468510i
$911$	7.36427	+	12.7553i	0.243989	+	0.422602i	0.961847	−	0.273588i	$-0.0882105\pi$
$911$	7.36427	+	12.7553i	0.243989	+	0.422602i	−0.717858	+	0.696190i	$0.754877\pi$
$912$	−11.0725			−0.366647
$913$	6.34148	−	10.9838i	0.209872	−	0.363510i
$914$	0.319348	+	0.553128i	0.0105631	+	0.0182958i
$915$	−33.6317			−1.11183
$916$	0.164884	+	0.285587i	0.00544791	+	0.00943605i
$917$	10.9931	+	19.0406i	0.363024	+	0.628776i
$918$	−3.64898	+	6.32021i	−0.120434	+	0.208598i
$919$	−6.64501	+	11.5095i	−0.219199	+	0.379663i	−0.954563	−	0.298009i	$-0.903678\pi$
$919$	−6.64501	+	11.5095i	−0.219199	+	0.379663i	0.735365	+	0.677672i	$0.237011\pi$
$920$	−22.4995	−	38.9703i	−0.741788	−	1.28481i
$921$	−64.6512			−2.13033
$922$	46.1537			1.51999
$923$	−19.7284	+	34.1705i	−0.649367	+	1.12474i
$924$	0.228466	+	0.395715i	0.00751598	+	0.0130181i
$925$	9.00763	−	15.6017i	0.296169	−	0.512980i
$926$	−15.4656	−	26.7872i	−0.508231	−	0.880282i
$927$	69.1500			2.27118
$928$	0.305867	−	0.529778i	0.0100406	−	0.0173908i
$929$	36.5116			1.19791			0.598953	−	0.800784i	$-0.295584\pi$
$929$	36.5116			1.19791			0.598953	+	0.800784i	$0.295584\pi$
$930$	1.14507			0.0375483
$931$	2.85197	+	4.93976i	0.0934696	+	0.161894i
$932$	−0.0847862	−	0.146854i	−0.00277727	−	0.00481037i
$933$	−4.22754			−0.138404
$934$	11.4484	+	19.8292i	0.374603	+	0.648831i
$935$	−5.60524	−	9.70857i	−0.183311	−	0.317504i
$936$	25.8402	+	44.7566i	0.844615	+	1.46292i
$937$	11.4870	+	19.8960i	0.375263	+	0.649975i	0.990366	−	0.138472i	$-0.0442190\pi$
$937$	11.4870	+	19.8960i	0.375263	+	0.649975i	−0.615103	+	0.788447i	$0.710886\pi$
$938$	14.2029			0.463742
$939$	44.6450	−	77.3273i	1.45693	−	2.52348i
$940$	0.893286			0.0291358
$941$	13.5664	+	23.4977i	0.442252	+	0.766004i	0.997856	−	0.0654435i	$-0.0208462\pi$
$941$	13.5664	+	23.4977i	0.442252	+	0.766004i	−0.555604	+	0.831447i	$0.687513\pi$
$942$	3.34268	−	5.78969i	0.108910	−	0.188638i
$943$	42.3347			1.37861
$944$	−3.16077	+	5.47461i	−0.102874	+	0.178183i
$945$	18.7207			0.608984
$946$	48.6277			1.58102
$947$	1.43576	−	2.48681i	0.0466560	−	0.0808106i	−0.841754	−	0.539861i	$-0.818477\pi$
$947$	1.43576	−	2.48681i	0.0466560	−	0.0808106i	0.888410	+	0.459050i	$0.151810\pi$
$948$	−0.496725	+	0.860353i	−0.0161329	+	0.0279430i
$949$	0.603298	−	1.04494i	0.0195839	−	0.0339203i
$950$	−2.32377	−	4.02489i	−0.0753931	−	0.130585i
$951$	−36.9328	+	63.9696i	−1.19763	+	2.07435i
$952$	−1.43748	+	2.48979i	−0.0465890	+	0.0806945i
$953$	−8.36514	+	14.4888i	−0.270973	+	0.469340i	−0.969111	−	0.246624i	$-0.920679\pi$
$953$	−8.36514	+	14.4888i	−0.270973	+	0.469340i	0.698138	+	0.715963i	$0.254012\pi$
$954$	−29.1124	+	50.4241i	−0.942547	+	1.63254i
$955$	33.3705	+	57.7994i	1.07984	+	1.87034i
$956$	−0.344061			−0.0111277
$957$	−19.8646	−	34.4066i	−0.642133	−	1.11221i
$958$	−2.38003	−	4.12232i	−0.0768951	−	0.133186i
$959$	−10.7823	+	18.6756i	−0.348180	+	0.603066i
$960$	33.2765	−	57.6366i	1.07399	−	1.86021i
$961$	−30.9901			−0.999679
$962$	−27.2230			−0.877704
$963$	19.6724			0.633933
$964$	0.202153	+	0.350138i	0.00651090	+	0.0112772i
$965$	19.7317	+	34.1763i	0.635185	+	1.10017i
$966$	12.1789	+	21.0945i	0.391851	+	0.678705i
$967$	2.96653	−	5.13819i	0.0953973	−	0.165233i	−0.814377	−	0.580336i	$-0.802921\pi$
$967$	2.96653	−	5.13819i	0.0953973	−	0.165233i	0.909774	+	0.415103i	$0.136255\pi$
$968$	10.8744	−	18.8349i	0.349515	−	0.605378i
$969$	2.53305			0.0813734
$970$	−13.9959	+	24.2416i	−0.449382	+	0.778352i
$971$	7.09185	+	12.2834i	0.227588	+	0.394194i	0.957093	−	0.289781i	$-0.0935826\pi$
$971$	7.09185	+	12.2834i	0.227588	+	0.394194i	−0.729505	+	0.683976i	$0.760249\pi$
$972$	−0.228496	+	0.395767i	−0.00732902	+	0.0126942i
$973$	−12.5433	+	21.7257i	−0.402121	+	0.696494i
$974$	−18.4625	+	31.9780i	−0.591578	+	1.02464i
$975$	−17.0137	+	29.4685i	−0.544874	+	0.943749i
$976$	8.07643	−	13.9888i	0.258520	−	0.447770i
$977$	14.6981	+	25.4579i	0.470234	+	0.814470i	0.999421	−	0.0340360i	$-0.0108361\pi$
$977$	14.6981	+	25.4579i	0.470234	+	0.814470i	−0.529186	+	0.848506i	$0.677503\pi$
$978$	−18.0129	+	31.1992i	−0.575988	+	0.997641i
$979$	2.83264	+	4.90627i	0.0905315	+	0.156805i
$980$	−0.552513			−0.0176494
$981$	32.9904	−	57.1411i	1.05330	−	1.82438i
$982$	−6.84254	+	11.8516i	−0.218354	+	0.378200i
$983$	0.248884	+	0.431080i	0.00793817	+	0.0137493i	0.869967	−	0.493110i	$-0.164140\pi$
$983$	0.248884	+	0.431080i	0.00793817	+	0.0137493i	−0.862029	+	0.506859i	$0.830807\pi$
$984$	31.3148	+	54.2388i	0.998278	+	1.72907i
$985$	6.41960	−	11.1191i	0.204546	−	0.354283i
$986$	2.04779	−	3.54687i	0.0652148	−	0.112955i
$987$	−29.5123			−0.939387
$988$	0.0594814	−	0.103025i	0.00189236	−	0.00327766i
$989$	−43.9101			−1.39626
$990$	−44.0417	−	76.2824i	−1.39974	−	2.42442i
$991$	5.82589			0.185065			0.0925327	−	0.995710i	$-0.470504\pi$
$991$	5.82589			0.185065			0.0925327	+	0.995710i	$0.470504\pi$
$992$	0.00939614	−	0.0162746i	0.000298328	−	0.000516719i
$993$	−16.3390			−0.518502
$994$	−17.2463			−0.547018
$995$	−19.3069	−	33.4405i	−0.612070	−	1.06014i
$996$	−0.277592			−0.00879584
$997$	−2.17457	+	3.76646i	−0.0688692	+	0.119285i	−0.898404	−	0.439170i	$-0.855272\pi$
$997$	−2.17457	+	3.76646i	−0.0688692	+	0.119285i	0.829535	+	0.558455i	$0.188606\pi$
$998$	−8.25240	+	14.2936i	−0.261225	+	0.452455i
$999$	15.6142	+	27.0445i	0.494010	+	0.855651i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	547.2.c.a.40.14	✓	90
547.506	even	3	inner	547.2.c.a.506.14	yes	90

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
547.2.c.a.40.14	✓	90	1.1	even	1	trivial
547.2.c.a.506.14	yes	90	547.506	even	3	inner

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:	\( N \)	\(=\)	\( 547 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	547.c (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.701193 - 1.21450i) q^{2} +2.83551 q^{3} +(0.0166570 - 0.0288508i) q^{4} +(1.44371 - 2.50058i) q^{5} +(-1.98824 - 3.44374i) q^{6} +(0.560388 + 0.970620i) q^{7} -2.85149 q^{8} +5.04014 q^{9} +O(q^{10})\)	\(q+(-0.701193 - 1.21450i) q^{2} +2.83551 q^{3} +(0.0166570 - 0.0288508i) q^{4} +(1.44371 - 2.50058i) q^{5} +(-1.98824 - 3.44374i) q^{6} +(0.560388 + 0.970620i) q^{7} -2.85149 q^{8} +5.04014 q^{9} -4.04928 q^{10} +(2.15796 + 3.73769i) q^{11} +(0.0472313 - 0.0818070i) q^{12} +(-1.79797 - 3.11417i) q^{13} +(0.785880 - 1.36118i) q^{14} +(4.09367 - 7.09044i) q^{15} +(1.96613 + 3.40544i) q^{16} +(-0.449791 - 0.779061i) q^{17} +(-3.53411 - 6.12126i) q^{18} +(-0.496525 + 0.860007i) q^{19} +(-0.0480959 - 0.0833046i) q^{20} +(1.58899 + 2.75221i) q^{21} +(3.02629 - 5.24169i) q^{22} +(-2.73269 + 4.73316i) q^{23} -8.08544 q^{24} +(-1.66861 - 2.89011i) q^{25} +(-2.52144 + 4.36727i) q^{26} +5.78486 q^{27} +0.0373376 q^{28} -3.24643 q^{29} -11.4818 q^{30} -0.0997291 q^{31} +(-0.0942166 + 0.163188i) q^{32} +(6.11892 + 10.5983i) q^{33} +(-0.630781 + 1.09254i) q^{34} +3.23615 q^{35} +(0.0839539 - 0.145412i) q^{36} +(2.69914 + 4.67506i) q^{37} +1.39264 q^{38} +(-5.09816 - 8.83028i) q^{39} +(-4.11673 + 7.13039i) q^{40} +(-3.87298 - 6.70820i) q^{41} +(2.22837 - 3.85966i) q^{42} +(4.01711 + 6.95783i) q^{43} +0.143781 q^{44} +(7.27651 - 12.6033i) q^{45} +7.66458 q^{46} +(-4.64325 + 8.04235i) q^{47} +(5.57499 + 9.65617i) q^{48} +(2.87193 - 4.97433i) q^{49} +(-2.34003 + 4.05305i) q^{50} +(-1.27539 - 2.20904i) q^{51} -0.119795 q^{52} +(-4.11876 - 7.13391i) q^{53} +(-4.05630 - 7.02572i) q^{54} +12.4619 q^{55} +(-1.59794 - 2.76771i) q^{56} +(-1.40790 + 2.43856i) q^{57} +(2.27637 + 3.94279i) q^{58} +(0.803803 + 1.39223i) q^{59} +(-0.136377 - 0.236211i) q^{60} +(-2.05389 - 3.55744i) q^{61} +(0.0699294 + 0.121121i) q^{62} +(2.82444 + 4.89207i) q^{63} +8.12878 q^{64} -10.3830 q^{65} +(8.58109 - 14.8629i) q^{66} +(4.51816 + 7.82569i) q^{67} -0.0299688 q^{68} +(-7.74859 + 13.4210i) q^{69} +(-2.26917 - 3.93032i) q^{70} +(-5.48629 - 9.50254i) q^{71} -14.3719 q^{72} +(0.167772 + 0.290590i) q^{73} +(3.78524 - 6.55623i) q^{74} +(-4.73136 - 8.19496i) q^{75} +(0.0165413 + 0.0286503i) q^{76} +(-2.41859 + 4.18912i) q^{77} +(-7.14959 + 12.3835i) q^{78} -10.5169 q^{79} +11.3541 q^{80} +1.28261 q^{81} +(-5.43141 + 9.40748i) q^{82} +(-1.46932 - 2.54494i) q^{83} +0.105871 q^{84} -2.59748 q^{85} +(5.63353 - 9.75756i) q^{86} -9.20530 q^{87} +(-6.15340 - 10.6580i) q^{88} +1.31265 q^{89} -20.4090 q^{90} +(2.01512 - 3.49029i) q^{91} +(0.0910372 + 0.157681i) q^{92} -0.282783 q^{93} +13.0233 q^{94} +(1.43368 + 2.48320i) q^{95} +(-0.267153 + 0.462722i) q^{96} +(3.45640 - 5.98665i) q^{97} -8.05511 q^{98} +(10.8764 + 18.8385i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 90 q - q^{2} - 4 q^{3} - 47 q^{4} + q^{5} - 3 q^{6} + 2 q^{7} - 30 q^{8} + 82 q^{9}+O(q^{10}) \) 90 * q - q^2 - 4 * q^3 - 47 * q^4 + q^5 - 3 * q^6 + 2 * q^7 - 30 * q^8 + 82 * q^9	\( 90 q - q^{2} - 4 q^{3} - 47 q^{4} + q^{5} - 3 q^{6} + 2 q^{7} - 30 q^{8} + 82 q^{9} - 10 q^{10} + q^{11} + 4 q^{12} - 3 q^{13} + 2 q^{14} - 7 q^{15} - 39 q^{16} - 4 q^{17} - 11 q^{18} - 2 q^{19} + 25 q^{20} - 27 q^{21} - 7 q^{22} + q^{23} + 32 q^{24} - 40 q^{25} - 10 q^{26} - 34 q^{27} - 28 q^{28} + 26 q^{29} - 40 q^{30} - 24 q^{31} + 19 q^{32} + q^{33} - 6 q^{34} - 8 q^{35} - 36 q^{36} - 10 q^{37} + 24 q^{38} + 22 q^{39} + 20 q^{40} + 3 q^{41} + 38 q^{42} - 12 q^{43} - 30 q^{44} - 2 q^{45} - 40 q^{46} + 32 q^{47} + 14 q^{48} - 43 q^{49} + 14 q^{50} + 13 q^{51} + 46 q^{52} + 9 q^{53} - 8 q^{54} + 4 q^{55} - 8 q^{56} - 8 q^{57} + 4 q^{58} + 22 q^{59} - 2 q^{60} - 12 q^{61} + 11 q^{62} + 8 q^{63} + 22 q^{64} + 18 q^{65} + 12 q^{66} - 22 q^{67} + 6 q^{68} - q^{69} - 6 q^{70} - 4 q^{71} - 140 q^{72} + 17 q^{73} + 17 q^{74} + 39 q^{75} + 84 q^{76} - 4 q^{77} + 33 q^{78} - 72 q^{79} - 40 q^{80} + 18 q^{81} - 9 q^{82} + 24 q^{83} + 114 q^{84} + 40 q^{85} - 72 q^{86} - 78 q^{87} - 22 q^{88} + 14 q^{89} + 96 q^{90} - 8 q^{92} - 76 q^{93} + 108 q^{94} - 11 q^{95} - 34 q^{96} - 74 q^{98} - 62 q^{99}+O(q^{100}) \) 90 * q - q^2 - 4 * q^3 - 47 * q^4 + q^5 - 3 * q^6 + 2 * q^7 - 30 * q^8 + 82 * q^9 - 10 * q^10 + q^11 + 4 * q^12 - 3 * q^13 + 2 * q^14 - 7 * q^15 - 39 * q^16 - 4 * q^17 - 11 * q^18 - 2 * q^19 + 25 * q^20 - 27 * q^21 - 7 * q^22 + q^23 + 32 * q^24 - 40 * q^25 - 10 * q^26 - 34 * q^27 - 28 * q^28 + 26 * q^29 - 40 * q^30 - 24 * q^31 + 19 * q^32 + q^33 - 6 * q^34 - 8 * q^35 - 36 * q^36 - 10 * q^37 + 24 * q^38 + 22 * q^39 + 20 * q^40 + 3 * q^41 + 38 * q^42 - 12 * q^43 - 30 * q^44 - 2 * q^45 - 40 * q^46 + 32 * q^47 + 14 * q^48 - 43 * q^49 + 14 * q^50 + 13 * q^51 + 46 * q^52 + 9 * q^53 - 8 * q^54 + 4 * q^55 - 8 * q^56 - 8 * q^57 + 4 * q^58 + 22 * q^59 - 2 * q^60 - 12 * q^61 + 11 * q^62 + 8 * q^63 + 22 * q^64 + 18 * q^65 + 12 * q^66 - 22 * q^67 + 6 * q^68 - q^69 - 6 * q^70 - 4 * q^71 - 140 * q^72 + 17 * q^73 + 17 * q^74 + 39 * q^75 + 84 * q^76 - 4 * q^77 + 33 * q^78 - 72 * q^79 - 40 * q^80 + 18 * q^81 - 9 * q^82 + 24 * q^83 + 114 * q^84 + 40 * q^85 - 72 * q^86 - 78 * q^87 - 22 * q^88 + 14 * q^89 + 96 * q^90 - 8 * q^92 - 76 * q^93 + 108 * q^94 - 11 * q^95 - 34 * q^96 - 74 * q^98 - 62 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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