LMFDB - Embedded newform 287.2.h.c.141.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [287,2,Mod(57,287)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(287, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 6]))

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

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

chi := DirichletCharacter("287.57");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 287 = 7 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	287.h (of order $5$, degree $4$, 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:	$2.29170653801$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$10$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			141.4
Character	$\chi$	$=$	287.141
Dual form			287.2.h.c.57.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.279797 - 0.861126i) q^{2} +2.59818 q^{3} +(0.954783 - 0.693690i) q^{4} +(-1.43627 + 1.04351i) q^{5} +(-0.726962 - 2.23736i) q^{6} +(0.309017 - 0.951057i) q^{7} +(-2.32953 - 1.69251i) q^{8} +3.75053 q^{9} +O(q^{10})$	\(q+(-0.279797 - 0.861126i) q^{2} +2.59818 q^{3} +(0.954783 - 0.693690i) q^{4} +(-1.43627 + 1.04351i) q^{5} +(-0.726962 - 2.23736i) q^{6} +(0.309017 - 0.951057i) q^{7} +(-2.32953 - 1.69251i) q^{8} +3.75053 q^{9} +(1.30046 + 0.944836i) q^{10} +(0.466493 + 0.338927i) q^{11} +(2.48069 - 1.80233i) q^{12} +(-1.21418 - 3.73686i) q^{13} -0.905441 q^{14} +(-3.73168 + 2.71122i) q^{15} +(-0.0762754 + 0.234751i) q^{16} +(4.18832 + 3.04299i) q^{17} +(-1.04939 - 3.22968i) q^{18} +(-0.0189501 + 0.0583223i) q^{19} +(-0.647451 + 1.99265i) q^{20} +(0.802881 - 2.47101i) q^{21} +(0.161336 - 0.496540i) q^{22} +(2.63719 + 8.11643i) q^{23} +(-6.05254 - 4.39743i) q^{24} +(-0.571133 + 1.75777i) q^{25} +(-2.87818 + 2.09112i) q^{26} +1.95001 q^{27} +(-0.364694 - 1.12241i) q^{28} +(-4.38882 + 3.18867i) q^{29} +(3.37881 + 2.45485i) q^{30} +(-1.55162 - 1.12732i) q^{31} -5.53543 q^{32} +(1.21203 + 0.880592i) q^{33} +(1.44852 - 4.45809i) q^{34} +(0.548605 + 1.68843i) q^{35} +(3.58094 - 2.60171i) q^{36} +(-2.61722 + 1.90152i) q^{37} +0.0555250 q^{38} +(-3.15466 - 9.70903i) q^{39} +5.11198 q^{40} +(6.36431 - 0.703919i) q^{41} -2.35250 q^{42} +(-1.94808 - 5.99557i) q^{43} +0.680509 q^{44} +(-5.38676 + 3.91371i) q^{45} +(6.25139 - 4.54190i) q^{46} +(-2.69233 - 8.28614i) q^{47} +(-0.198177 + 0.609926i) q^{48} +(-0.809017 - 0.587785i) q^{49} +1.67346 q^{50} +(10.8820 + 7.90624i) q^{51} +(-3.75150 - 2.72562i) q^{52} +(-8.25797 + 5.99976i) q^{53} +(-0.545606 - 1.67920i) q^{54} -1.02368 q^{55} +(-2.32953 + 1.69251i) q^{56} +(-0.0492356 + 0.151532i) q^{57} +(3.97382 + 2.88715i) q^{58} +(0.848609 + 2.61175i) q^{59} +(-1.68219 + 5.17726i) q^{60} +(-1.57426 + 4.84506i) q^{61} +(-0.536623 + 1.65156i) q^{62} +(1.15898 - 3.56697i) q^{63} +(1.70135 + 5.23621i) q^{64} +(5.64333 + 4.10012i) q^{65} +(0.419178 - 1.29010i) q^{66} +(-8.74883 + 6.35639i) q^{67} +6.10983 q^{68} +(6.85188 + 21.0879i) q^{69} +(1.30046 - 0.944836i) q^{70} +(-7.28093 - 5.28990i) q^{71} +(-8.73699 - 6.34779i) q^{72} +5.24158 q^{73} +(2.36974 + 1.72172i) q^{74} +(-1.48391 + 4.56699i) q^{75} +(0.0223644 + 0.0688306i) q^{76} +(0.466493 - 0.338927i) q^{77} +(-7.47803 + 5.43311i) q^{78} +12.5277 q^{79} +(-0.135413 - 0.416760i) q^{80} -6.18512 q^{81} +(-2.38688 - 5.28352i) q^{82} +3.41972 q^{83} +(-0.947541 - 2.91623i) q^{84} -9.19094 q^{85} +(-4.61788 + 3.35508i) q^{86} +(-11.4029 + 8.28472i) q^{87} +(-0.513075 - 1.57908i) q^{88} +(2.37950 - 7.32335i) q^{89} +(4.87740 + 3.54364i) q^{90} -3.92917 q^{91} +(8.14823 + 5.92003i) q^{92} +(-4.03138 - 2.92897i) q^{93} +(-6.38210 + 4.63687i) q^{94} +(-0.0336425 - 0.103541i) q^{95} -14.3820 q^{96} +(-1.29344 + 0.939736i) q^{97} +(-0.279797 + 0.861126i) q^{98} +(1.74959 + 1.27116i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 3 q^{2} - 3 q^{4} - 4 q^{5} - 19 q^{6} - 10 q^{7} + 16 q^{8} + 60 q^{9}+O(q^{10}) $ 40 * q - 3 * q^2 - 3 * q^4 - 4 * q^5 - 19 * q^6 - 10 * q^7 + 16 * q^8 + 60 * q^9	\( 40 q - 3 q^{2} - 3 q^{4} - 4 q^{5} - 19 q^{6} - 10 q^{7} + 16 q^{8} + 60 q^{9} + 5 q^{10} - 10 q^{11} - 12 q^{12} - 17 q^{13} + 2 q^{14} - 3 q^{15} - 23 q^{16} - 8 q^{17} - 2 q^{18} + 23 q^{19} - 13 q^{22} - q^{23} + 46 q^{24} - 34 q^{25} + 3 q^{26} - 18 q^{28} - 18 q^{29} - 19 q^{30} - 3 q^{31} - 26 q^{32} - 6 q^{33} - 44 q^{34} + q^{35} - 38 q^{36} - 5 q^{37} + 28 q^{38} + 17 q^{39} + 14 q^{40} - 11 q^{41} - 24 q^{42} + 13 q^{43} + 66 q^{44} + 43 q^{45} - 20 q^{46} - 27 q^{47} + 39 q^{48} - 10 q^{49} + 106 q^{50} - 18 q^{51} - 30 q^{52} - 30 q^{53} - 109 q^{54} + 118 q^{55} + 16 q^{56} - 40 q^{57} - 23 q^{58} - 37 q^{59} + 96 q^{60} - 41 q^{61} - 13 q^{62} - 30 q^{63} + 10 q^{64} + 6 q^{65} - 30 q^{66} - 6 q^{67} - 26 q^{68} - 31 q^{69} + 5 q^{70} - 31 q^{71} + 107 q^{72} - 46 q^{73} + 75 q^{74} - 61 q^{75} + 43 q^{76} - 10 q^{77} + 34 q^{78} + 76 q^{79} + 64 q^{80} + 16 q^{81} - 16 q^{82} - 52 q^{83} - 7 q^{84} + 86 q^{85} - 17 q^{86} - 20 q^{87} - 52 q^{88} - 16 q^{89} + 6 q^{90} + 18 q^{91} + 97 q^{92} + 32 q^{93} - 5 q^{94} - 102 q^{95} + 38 q^{96} - 18 q^{97} - 3 q^{98} - 71 q^{99}+O(q^{100}) \) 40 * q - 3 * q^2 - 3 * q^4 - 4 * q^5 - 19 * q^6 - 10 * q^7 + 16 * q^8 + 60 * q^9 + 5 * q^10 - 10 * q^11 - 12 * q^12 - 17 * q^13 + 2 * q^14 - 3 * q^15 - 23 * q^16 - 8 * q^17 - 2 * q^18 + 23 * q^19 - 13 * q^22 - q^23 + 46 * q^24 - 34 * q^25 + 3 * q^26 - 18 * q^28 - 18 * q^29 - 19 * q^30 - 3 * q^31 - 26 * q^32 - 6 * q^33 - 44 * q^34 + q^35 - 38 * q^36 - 5 * q^37 + 28 * q^38 + 17 * q^39 + 14 * q^40 - 11 * q^41 - 24 * q^42 + 13 * q^43 + 66 * q^44 + 43 * q^45 - 20 * q^46 - 27 * q^47 + 39 * q^48 - 10 * q^49 + 106 * q^50 - 18 * q^51 - 30 * q^52 - 30 * q^53 - 109 * q^54 + 118 * q^55 + 16 * q^56 - 40 * q^57 - 23 * q^58 - 37 * q^59 + 96 * q^60 - 41 * q^61 - 13 * q^62 - 30 * q^63 + 10 * q^64 + 6 * q^65 - 30 * q^66 - 6 * q^67 - 26 * q^68 - 31 * q^69 + 5 * q^70 - 31 * q^71 + 107 * q^72 - 46 * q^73 + 75 * q^74 - 61 * q^75 + 43 * q^76 - 10 * q^77 + 34 * q^78 + 76 * q^79 + 64 * q^80 + 16 * q^81 - 16 * q^82 - 52 * q^83 - 7 * q^84 + 86 * q^85 - 17 * q^86 - 20 * q^87 - 52 * q^88 - 16 * q^89 + 6 * q^90 + 18 * q^91 + 97 * q^92 + 32 * q^93 - 5 * q^94 - 102 * q^95 + 38 * q^96 - 18 * q^97 - 3 * q^98 - 71 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/287\mathbb{Z}\right)^\times$.

$n$	$206$	$211$
$\chi(n)$	$1$	$e\left(\frac{2}{5}\right)$

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 $

$2$	−0.279797	−	0.861126i	−0.197846	−	0.608908i	−0.999932	−	0.0116986i	$-0.996276\pi$
$2$	−0.279797	−	0.861126i	−0.197846	−	0.608908i	0.802085	−	0.597209i	$-0.203724\pi$
$3$	2.59818			1.50006			0.750029	−	0.661404i	$-0.230039\pi$
$3$	2.59818			1.50006			0.750029	+	0.661404i	$0.230039\pi$
$4$	0.954783	−	0.693690i	0.477391	−	0.346845i
$5$	−1.43627	+	1.04351i	−0.642318	+	0.466671i	−0.860646	−	0.509204i	$-0.829940\pi$
$5$	−1.43627	+	1.04351i	−0.642318	+	0.466671i	0.218328	+	0.975876i	$0.429940\pi$
$6$	−0.726962	−	2.23736i	−0.296781	−	0.913398i
$7$	0.309017	−	0.951057i	0.116797	−	0.359466i
$7$	0.309017	−	0.951057i	0.116797	−	0.359466i
$8$	−2.32953	−	1.69251i	−0.823615	−	0.598391i
$9$	3.75053			1.25018
$10$	1.30046	+	0.944836i	0.411240	+	0.298783i
$11$	0.466493	+	0.338927i	0.140653	+	0.102190i	0.655887	−	0.754859i	$-0.272295\pi$
$11$	0.466493	+	0.338927i	0.140653	+	0.102190i	−0.515234	+	0.857050i	$0.672295\pi$
$12$	2.48069	−	1.80233i	0.716115	−	0.520288i
$13$	−1.21418	−	3.73686i	−0.336753	−	1.03642i	−0.965852	−	0.259094i	$-0.916576\pi$
$13$	−1.21418	−	3.73686i	−0.336753	−	1.03642i	0.629099	−	0.777325i	$-0.283424\pi$
$14$	−0.905441			−0.241989
$15$	−3.73168	+	2.71122i	−0.963515	+	0.700035i
$16$	−0.0762754	+	0.234751i	−0.0190688	+	0.0586878i
$17$	4.18832	+	3.04299i	1.01582	+	0.738034i	0.965421	−	0.260695i	$-0.0839517\pi$
$17$	4.18832	+	3.04299i	1.01582	+	0.738034i	0.0503959	+	0.998729i	$0.483952\pi$
$18$	−1.04939	−	3.22968i	−0.247343	−	0.761242i
$19$	−0.0189501	+	0.0583223i	−0.00434744	+	0.0133800i	−0.953207	−	0.302319i	$-0.902239\pi$
$19$	−0.0189501	+	0.0583223i	−0.00434744	+	0.0133800i	0.948859	+	0.315699i	$0.102239\pi$
$20$	−0.647451	+	1.99265i	−0.144774	+	0.445570i
$21$	0.802881	−	2.47101i	0.175203	−	0.539220i
$22$	0.161336	−	0.496540i	0.0343968	−	0.105863i
$23$	2.63719	+	8.11643i	0.549892	+	1.69239i	0.709066	+	0.705142i	$0.249117\pi$
$23$	2.63719	+	8.11643i	0.549892	+	1.69239i	−0.159174	+	0.987251i	$0.550883\pi$
$24$	−6.05254	−	4.39743i	−1.23547	−	0.897622i
$25$	−0.571133	+	1.75777i	−0.114227	+	0.351554i
$26$	−2.87818	+	2.09112i	−0.564458	+	0.410103i
$27$	1.95001			0.375279
$28$	−0.364694	−	1.12241i	−0.0689208	−	0.212116i
$29$	−4.38882	+	3.18867i	−0.814984	+	0.592120i	−0.915271	−	0.402838i	$-0.868024\pi$
$29$	−4.38882	+	3.18867i	−0.814984	+	0.592120i	0.100288	+	0.994958i	$0.468024\pi$
$30$	3.37881	+	2.45485i	0.616884	+	0.448193i
$31$	−1.55162	−	1.12732i	−0.278679	−	0.202472i	0.439662	−	0.898163i	$-0.355098\pi$
$31$	−1.55162	−	1.12732i	−0.278679	−	0.202472i	−0.718341	+	0.695691i	$0.755098\pi$
$32$	−5.53543			−0.978536
$33$	1.21203	+	0.880592i	0.210988	+	0.153291i
$34$	1.44852	−	4.45809i	0.248419	−	0.764556i
$35$	0.548605	+	1.68843i	0.0927312	+	0.285397i
$36$	3.58094	−	2.60171i	0.596823	−	0.433618i
$37$	−2.61722	+	1.90152i	−0.430268	+	0.312608i	−0.781756	−	0.623584i	$-0.785676\pi$
$37$	−2.61722	+	1.90152i	−0.430268	+	0.312608i	0.351488	+	0.936192i	$0.385676\pi$
$38$	0.0555250			0.00900734
$39$	−3.15466	−	9.70903i	−0.505149	−	1.55469i
$40$	5.11198			0.808275
$41$	6.36431	−	0.703919i	0.993939	−	0.109934i
$41$	6.36431	−	0.703919i	0.993939	−	0.109934i
$42$	−2.35250			−0.362998
$43$	−1.94808	−	5.99557i	−0.297079	−	0.914317i	−0.982515	−	0.186183i	$-0.940388\pi$
$43$	−1.94808	−	5.99557i	−0.297079	−	0.914317i	0.685436	−	0.728133i	$-0.259612\pi$
$44$	0.680509			0.102591
$45$	−5.38676	+	3.91371i	−0.803011	+	0.583422i
$46$	6.25139	−	4.54190i	0.921717	−	0.669667i
$47$	−2.69233	−	8.28614i	−0.392717	−	1.20866i	−0.930726	−	0.365718i	$-0.880823\pi$
$47$	−2.69233	−	8.28614i	−0.392717	−	1.20866i	0.538009	−	0.842939i	$-0.319177\pi$
$48$	−0.198177	+	0.609926i	−0.0286044	+	0.0880352i
$49$	−0.809017	−	0.587785i	−0.115574	−	0.0839693i
$50$	1.67346			0.236663
$51$	10.8820	+	7.90624i	1.52379	+	1.10709i
$52$	−3.75150	−	2.72562i	−0.520240	−	0.377976i
$53$	−8.25797	+	5.99976i	−1.13432	+	0.824131i	−0.986318	−	0.164856i	$-0.947284\pi$
$53$	−8.25797	+	5.99976i	−1.13432	+	0.824131i	−0.148001	+	0.988987i	$0.547284\pi$
$54$	−0.545606	−	1.67920i	−0.0742476	−	0.228511i
$55$	−1.02368			−0.138033
$56$	−2.32953	+	1.69251i	−0.311297	+	0.226171i
$57$	−0.0492356	+	0.151532i	−0.00652142	+	0.0200709i
$58$	3.97382	+	2.88715i	0.521788	+	0.379101i
$59$	0.848609	+	2.61175i	0.110480	+	0.340021i	0.990977	−	0.134029i	$-0.0427916\pi$
$59$	0.848609	+	2.61175i	0.110480	+	0.340021i	−0.880498	+	0.474050i	$0.842792\pi$
$60$	−1.68219	+	5.17726i	−0.217170	+	0.668381i
$61$	−1.57426	+	4.84506i	−0.201563	+	0.620346i	0.798274	+	0.602294i	$0.205747\pi$
$61$	−1.57426	+	4.84506i	−0.201563	+	0.620346i	−0.999837	+	0.0180522i	$0.994253\pi$
$62$	−0.536623	+	1.65156i	−0.0681512	+	0.209748i
$63$	1.15898	−	3.56697i	0.146017	−	0.449395i
$64$	1.70135	+	5.23621i	0.212668	+	0.654526i
$65$	5.64333	+	4.10012i	0.699969	+	0.508558i
$66$	0.419178	−	1.29010i	0.0515973	−	0.158800i
$67$	−8.74883	+	6.35639i	−1.06884	+	0.776557i	−0.975703	−	0.219096i	$-0.929689\pi$
$67$	−8.74883	+	6.35639i	−1.06884	+	0.776557i	−0.0931359	+	0.995653i	$0.529689\pi$
$68$	6.10983			0.740926
$69$	6.85188	+	21.0879i	0.824870	+	2.53869i
$70$	1.30046	−	0.944836i	0.155434	−	0.112930i
$71$	−7.28093	−	5.28990i	−0.864087	−	0.627796i	0.0649065	−	0.997891i	$-0.479325\pi$
$71$	−7.28093	−	5.28990i	−0.864087	−	0.627796i	−0.928994	+	0.370095i	$0.879325\pi$
$72$	−8.73699	−	6.34779i	−1.02966	−	0.748094i
$73$	5.24158			0.613481			0.306740	−	0.951793i	$-0.400762\pi$
$73$	5.24158			0.613481			0.306740	+	0.951793i	$0.400762\pi$
$74$	2.36974	+	1.72172i	0.275477	+	0.200145i
$75$	−1.48391	+	4.56699i	−0.171347	+	0.527351i
$76$	0.0223644	+	0.0688306i	0.00256537	+	0.00789541i
$77$	0.466493	−	0.338927i	0.0531618	−	0.0386243i
$78$	−7.47803	+	5.43311i	−0.846721	+	0.615179i
$79$	12.5277			1.40948			0.704740	−	0.709466i	$-0.251064\pi$
$79$	12.5277			1.40948			0.704740	+	0.709466i	$0.251064\pi$
$80$	−0.135413	−	0.416760i	−0.0151397	−	0.0465951i
$81$	−6.18512			−0.687235
$82$	−2.38688	−	5.28352i	−0.263587	−	0.583467i
$83$	3.41972			0.375363			0.187682	−	0.982230i	$-0.439903\pi$
$83$	3.41972			0.375363			0.187682	+	0.982230i	$0.439903\pi$
$84$	−0.947541	−	2.91623i	−0.103385	−	0.318187i
$85$	−9.19094			−0.996897
$86$	−4.61788	+	3.35508i	−0.497959	+	0.361788i
$87$	−11.4029	+	8.28472i	−1.22252	+	0.888215i
$88$	−0.513075	−	1.57908i	−0.0546940	−	0.168331i
$89$	2.37950	−	7.32335i	0.252226	−	0.776273i	−0.742137	−	0.670248i	$-0.766188\pi$
$89$	2.37950	−	7.32335i	0.252226	−	0.776273i	0.994363	−	0.106025i	$-0.0338123\pi$
$90$	4.87740	+	3.54364i	0.514123	+	0.373532i
$91$	−3.92917			−0.411889
$92$	8.14823	+	5.92003i	0.849512	+	0.617206i
$93$	−4.03138	−	2.92897i	−0.418034	−	0.303720i
$94$	−6.38210	+	4.63687i	−0.658264	+	0.478256i
$95$	−0.0336425	−	0.103541i	−0.00345165	−	0.0106231i
$96$	−14.3820			−1.46786
$97$	−1.29344	+	0.939736i	−0.131328	+	0.0954157i	−0.651510	−	0.758640i	$-0.725864\pi$
$97$	−1.29344	+	0.939736i	−0.131328	+	0.0954157i	0.520182	+	0.854056i	$0.325864\pi$
$98$	−0.279797	+	0.861126i	−0.0282637	+	0.0869868i
$99$	1.74959	+	1.27116i	0.175841	+	0.127756i
$100$	0.674038	+	2.07448i	0.0674038	+	0.207448i
$101$	2.32146	−	7.14472i	0.230994	−	0.710926i	−0.766634	−	0.642085i	$-0.778070\pi$
$101$	2.32146	−	7.14472i	0.230994	−	0.710926i	0.997628	−	0.0688416i	$-0.0219303\pi$
$102$	3.76352	−	11.5829i	0.372644	−	1.14688i
$103$	1.88451	−	5.79993i	0.185686	−	0.571484i	−0.814273	−	0.580482i	$-0.802864\pi$
$103$	1.88451	−	5.79993i	0.185686	−	0.571484i	0.999960	+	0.00899810i	$0.00286422\pi$
$104$	−3.49619	+	10.7602i	−0.342829	+	1.05512i
$105$	1.42537	+	4.38685i	0.139102	+	0.428113i
$106$	7.47710	+	5.43243i	0.726241	+	0.527645i
$107$	1.64798	−	5.07197i	0.159316	−	0.490326i	−0.839256	−	0.543736i	$-0.817009\pi$
$107$	1.64798	−	5.07197i	0.159316	−	0.490326i	0.998573	+	0.0534106i	$0.0170092\pi$
$108$	1.86183	−	1.35270i	0.179155	−	0.130164i
$109$	17.6401			1.68962			0.844808	−	0.535070i	$-0.179715\pi$
$109$	17.6401			1.68962			0.844808	+	0.535070i	$0.179715\pi$
$110$	0.286423	+	0.881519i	0.0273093	+	0.0840495i
$111$	−6.80001	+	4.94049i	−0.645428	+	0.468931i
$112$	0.199691	+	0.145084i	0.0188691	+	0.0137092i
$113$	15.1953	+	11.0400i	1.42946	+	1.03856i	0.990118	+	0.140238i	$0.0447867\pi$
$113$	15.1953	+	11.0400i	1.42946	+	1.03856i	0.439337	+	0.898322i	$0.355213\pi$
$114$	0.144264			0.0135115
$115$	−12.2573	−	8.90543i	−1.14300	−	0.830436i
$116$	−1.97842	+	6.08896i	−0.183692	+	0.565346i
$117$	−4.55382	−	14.0152i	−0.421000	−	1.29571i
$118$	2.01161	−	1.46152i	0.185183	−	0.134544i
$119$	4.18832	−	3.04299i	0.383943	−	0.278951i
$120$	13.2818			1.21246
$121$	−3.29644	−	10.1454i	−0.299677	−	0.922310i
$122$	4.61268			0.417612
$123$	16.5356	−	1.82891i	1.49097	−	0.164907i
$124$	−2.26346			−0.203265
$125$	−3.75697	−	11.5628i	−0.336034	−	1.03421i
$126$	−3.39588			−0.302529
$127$	3.83681	−	2.78760i	0.340462	−	0.247360i	−0.404395	−	0.914584i	$-0.632518\pi$
$127$	3.83681	−	2.78760i	0.340462	−	0.247360i	0.744857	+	0.667225i	$0.232518\pi$
$128$	−4.92352	+	3.57714i	−0.435182	+	0.316178i
$129$	−5.06146	−	15.5776i	−0.445637	−	1.37153i
$130$	1.95173	−	6.00682i	0.171178	−	0.526833i
$131$	−1.81991	−	1.32224i	−0.159006	−	0.115525i	0.505437	−	0.862863i	$-0.331331\pi$
$131$	−1.81991	−	1.32224i	−0.159006	−	0.115525i	−0.664443	+	0.747339i	$0.731331\pi$
$132$	1.76808			0.153892
$133$	0.0496119	+	0.0360452i	0.00430190	+	0.00312551i
$134$	7.92155	+	5.75534i	0.684317	+	0.497186i
$135$	−2.80073	+	2.03485i	−0.241049	+	0.175132i
$136$	−4.60655	−	14.1775i	−0.395009	−	1.21571i
$137$	−11.7757			−1.00607			−0.503033	−	0.864267i	$-0.667782\pi$
$137$	−11.7757			−1.00607			−0.503033	+	0.864267i	$0.667782\pi$
$138$	16.2422	−	11.8007i	1.38263	−	1.00454i
$139$	1.36461	−	4.19984i	0.115745	−	0.356226i	−0.876357	−	0.481663i	$-0.840033\pi$
$139$	1.36461	−	4.19984i	0.115745	−	0.356226i	0.992102	+	0.125436i	$0.0400331\pi$
$140$	1.69505	+	1.23152i	0.143258	+	0.104083i
$141$	−6.99515	−	21.5289i	−0.589098	−	1.81306i
$142$	−2.51809	+	7.74989i	−0.211314	+	0.650357i
$143$	0.700116	−	2.15474i	0.0585467	−	0.180188i
$144$	−0.286073	+	0.880442i	−0.0238394	+	0.0733702i
$145$	2.97612	−	9.15955i	0.247153	−	0.760659i
$146$	−1.46658	−	4.51366i	−0.121375	−	0.373553i
$147$	−2.10197	−	1.52717i	−0.173368	−	0.125959i
$148$	−1.17981	+	3.63108i	−0.0969797	+	0.298473i
$149$	−7.84762	+	5.70163i	−0.642902	+	0.467095i	−0.860846	−	0.508866i	$-0.830065\pi$
$149$	−7.84762	+	5.70163i	−0.642902	+	0.467095i	0.217944	+	0.975961i	$0.430065\pi$
$150$	4.34795			0.355008
$151$	1.37597	+	4.23481i	0.111975	+	0.344624i	0.991304	−	0.131591i	$-0.0420085\pi$
$151$	1.37597	+	4.23481i	0.111975	+	0.344624i	−0.879329	+	0.476215i	$0.842009\pi$
$152$	0.142856	−	0.103791i	0.0115871	−	0.00841854i
$153$	15.7084	+	11.4128i	1.26995	+	0.922673i
$154$	−0.422382	−	0.306878i	−0.0340365	−	0.0247290i
$155$	3.40490			0.273488
$156$	−9.74707	−	7.08166i	−0.780390	−	0.566986i
$157$	4.60562	−	14.1746i	0.367568	−	1.13126i	−0.580789	−	0.814054i	$-0.697256\pi$
$157$	4.60562	−	14.1746i	0.367568	−	1.13126i	0.948357	−	0.317204i	$-0.102744\pi$
$158$	−3.50522	−	10.7880i	−0.278860	−	0.858244i
$159$	−21.4557	+	15.5885i	−1.70155	+	1.23624i
$160$	7.95036	−	5.77627i	0.628531	−	0.456655i
$161$	8.53412			0.672583
$162$	1.73058	+	5.32616i	0.135967	+	0.418463i
$163$	22.2939			1.74619			0.873097	−	0.487547i	$-0.162108\pi$
$163$	22.2939			1.74619			0.873097	+	0.487547i	$0.162108\pi$
$164$	5.58823	−	5.08695i	0.436368	−	0.397224i
$165$	−2.65971			−0.207058
$166$	−0.956827	−	2.94481i	−0.0742642	−	0.228562i
$167$	−7.58870			−0.587231			−0.293616	−	0.955924i	$-0.594859\pi$
$167$	−7.58870			−0.587231			−0.293616	+	0.955924i	$0.594859\pi$
$168$	−6.05254	+	4.39743i	−0.466964	+	0.339269i
$169$	−1.97268	+	1.43323i	−0.151744	+	0.110249i
$170$	2.57159	+	7.91455i	0.197232	+	0.607019i
$171$	−0.0710727	+	0.218739i	−0.00543507	+	0.0167274i
$172$	−6.01906	−	4.37311i	−0.458949	−	0.333446i
$173$	−6.19352			−0.470884			−0.235442	−	0.971888i	$-0.575654\pi$
$173$	−6.19352			−0.470884			−0.235442	+	0.971888i	$0.575654\pi$
$174$	10.3247	+	7.50133i	0.782713	+	0.568674i
$175$	1.49525	+	1.08636i	0.113030	+	0.0821211i
$176$	−0.115145	+	0.0836581i	−0.00867942	+	0.00630596i
$177$	2.20484	+	6.78579i	0.165726	+	0.510051i
$178$	−6.97210			−0.522581
$179$	11.1945	−	8.13331i	0.836719	−	0.607912i	−0.0847332	−	0.996404i	$-0.527004\pi$
$179$	11.1945	−	8.13331i	0.836719	−	0.607912i	0.921452	+	0.388492i	$0.127004\pi$
$180$	−2.42828	+	7.47349i	−0.180994	+	0.557041i
$181$	−19.0052	−	13.8081i	−1.41264	−	1.02635i	−0.992931	−	0.118690i	$-0.962131\pi$
$181$	−19.0052	−	13.8081i	−1.41264	−	1.02635i	−0.419714	−	0.907657i	$-0.637869\pi$
$182$	1.09937	+	3.38351i	0.0814906	+	0.250802i
$183$	−4.09019	+	12.5883i	−0.302356	+	0.930556i
$184$	7.59368	−	23.3710i	0.559814	−	1.72293i
$185$	1.77477	−	5.46219i	0.130484	−	0.401588i
$186$	−1.39424	+	4.29104i	−0.102231	+	0.314634i
$187$	0.922470	+	2.83907i	0.0674577	+	0.207613i
$188$	−8.31860	−	6.04382i	−0.606696	−	0.440791i
$189$	0.602586	−	1.85457i	0.0438317	−	0.134900i
$190$	−0.0797487	+	0.0579408i	−0.00578558	+	0.00420347i
$191$	0.522525			0.0378086			0.0189043	−	0.999821i	$-0.493982\pi$
$191$	0.522525			0.0378086			0.0189043	+	0.999821i	$0.493982\pi$
$192$	4.42040	+	13.6046i	0.319015	+	0.981827i
$193$	−5.41297	+	3.93276i	−0.389634	+	0.283086i	−0.765306	−	0.643667i	$-0.777412\pi$
$193$	−5.41297	+	3.93276i	−0.389634	+	0.283086i	0.375671	+	0.926753i	$0.377412\pi$
$194$	1.17113	+	0.850876i	0.0840822	+	0.0610893i
$195$	14.6624	+	10.6528i	1.05000	+	0.762866i
$196$	−1.18018			−0.0842983
$197$	−16.1193	−	11.7114i	−1.14845	−	0.834401i	−0.160180	−	0.987088i	$-0.551208\pi$
$197$	−16.1193	−	11.7114i	−1.14845	−	0.834401i	−0.988275	+	0.152686i	$0.951208\pi$
$198$	0.605094	−	1.86229i	0.0430021	−	0.132347i
$199$	5.66138	+	17.4239i	0.401325	+	1.23515i	0.923925	+	0.382573i	$0.124962\pi$
$199$	5.66138	+	17.4239i	0.401325	+	1.23515i	−0.522601	+	0.852578i	$0.675038\pi$
$200$	4.30551	−	3.12813i	0.304445	−	0.221192i
$201$	−22.7310	+	16.5150i	−1.60332	+	1.16488i
$202$	−6.80204			−0.478590
$203$	1.67638	+	5.15937i	0.117659	+	0.362117i
$204$	15.8744			1.11143
$205$	−8.40631	+	7.65224i	−0.587122	+	0.534455i
$206$	−5.52175			−0.384718
$207$	9.89085	+	30.4409i	0.687462	+	2.11579i
$208$	0.969845			0.0672467
$209$	−0.0286071	+	0.0207842i	−0.00197879	+	0.00143768i
$210$	3.37881	−	2.45485i	0.233160	−	0.169401i
$211$	4.14780	+	12.7656i	0.285546	+	0.878821i	0.986234	+	0.165353i	$0.0528765\pi$
$211$	4.14780	+	12.7656i	0.285546	+	0.878821i	−0.700688	+	0.713468i	$0.747124\pi$
$212$	−3.72259	+	11.4569i	−0.255668	+	0.786866i
$213$	−18.9172	−	13.7441i	−1.29618	−	0.941731i
$214$	−4.82870			−0.330083
$215$	9.05440	+	6.57841i	0.617505	+	0.448644i
$216$	−4.54261	−	3.30040i	−0.309086	−	0.224564i
$217$	−1.55162	+	1.12732i	−0.105331	+	0.0765272i
$218$	−4.93564	−	15.1904i	−0.334284	−	1.02882i
$219$	13.6186			0.920257
$220$	−0.977393	+	0.710118i	−0.0658958	+	0.0478761i
$221$	6.28587	−	19.3459i	0.422833	−	1.30135i
$222$	6.15701	+	4.47333i	0.413231	+	0.300230i
$223$	−4.73046	−	14.5589i	−0.316775	−	0.974934i	−0.975018	−	0.222128i	$-0.928700\pi$
$223$	−4.73046	−	14.5589i	−0.316775	−	0.974934i	0.658242	−	0.752806i	$-0.271300\pi$
$224$	−1.71054	+	5.26451i	−0.114290	+	0.351750i
$225$	−2.14205	+	6.59256i	−0.142803	+	0.439504i
$226$	5.25527	−	16.1740i	0.349575	−	1.07588i
$227$	4.28078	−	13.1749i	0.284125	−	0.874447i	−0.702534	−	0.711650i	$-0.747948\pi$
$227$	4.28078	−	13.1749i	0.284125	−	0.874447i	0.986660	−	0.162797i	$-0.0520517\pi$
$228$	0.0581067	+	0.178834i	0.00384821	+	0.0118436i
$229$	20.7308	+	15.0618i	1.36993	+	0.995310i	0.997743	+	0.0671515i	$0.0213911\pi$
$229$	20.7308	+	15.0618i	1.36993	+	0.995310i	0.372184	+	0.928159i	$0.378609\pi$
$230$	−4.23915	+	13.0468i	−0.279521	+	0.860278i
$231$	1.21203	−	0.880592i	0.0797458	−	0.0579387i
$232$	15.6207			1.02555
$233$	3.32802	+	10.2426i	0.218026	+	0.671015i	0.998925	+	0.0463578i	$0.0147614\pi$
$233$	3.32802	+	10.2426i	0.218026	+	0.671015i	−0.780899	+	0.624658i	$0.785239\pi$
$234$	−10.7947	+	7.84282i	−0.705672	+	0.512701i
$235$	12.5136	+	9.09164i	0.816295	+	0.593073i
$236$	2.62198	+	1.90498i	0.170677	+	0.124004i
$237$	32.5493			2.11430
$238$	−3.79228	−	2.75525i	−0.245817	−	0.178596i
$239$	−0.471584	+	1.45139i	−0.0305042	+	0.0938824i	−0.965149	−	0.261699i	$-0.915717\pi$
$239$	−0.471584	+	1.45139i	−0.0305042	+	0.0938824i	0.934645	+	0.355582i	$0.115717\pi$
$240$	−0.351828	−	1.08282i	−0.0227104	−	0.0698955i
$241$	20.1724	−	14.6561i	1.29942	−	0.944084i	0.299471	−	0.954105i	$-0.403190\pi$
$241$	20.1724	−	14.6561i	1.29942	−	0.944084i	0.999950	+	0.0100212i	$0.00318989\pi$
$242$	−7.81414	+	5.67730i	−0.502312	+	0.364951i
$243$	−21.9201			−1.40617
$244$	1.85790	+	5.71802i	0.118940	+	0.366059i
$245$	1.77532			0.113421
$246$	−6.20153	−	13.7275i	−0.395395	−	0.875235i
$247$	0.240951			0.0153313
$248$	1.70656	+	5.25224i	0.108366	+	0.333518i
$249$	8.88504			0.563067
$250$	−8.90581	+	6.47045i	−0.563253	+	0.409227i
$251$	−22.3062	+	16.2064i	−1.40796	+	1.02294i	−0.414340	+	0.910122i	$0.635987\pi$
$251$	−22.3062	+	16.2064i	−1.40796	+	1.02294i	−0.993616	+	0.112817i	$0.964013\pi$
$252$	−1.36780	−	4.20965i	−0.0861631	−	0.265183i
$253$	−1.52065	+	4.68007i	−0.0956023	+	0.294233i
$254$	−3.47400	−	2.52401i	−0.217978	−	0.158371i
$255$	−23.8797			−1.49540
$256$	13.3663	+	9.71120i	0.835395	+	0.606950i
$257$	−9.78467	−	7.10898i	−0.610351	−	0.443446i	0.239187	−	0.970974i	$-0.423119\pi$
$257$	−9.78467	−	7.10898i	−0.610351	−	0.443446i	−0.849538	+	0.527528i	$0.823119\pi$
$258$	−11.9981	+	8.71711i	−0.746967	+	0.542703i
$259$	0.999689	+	3.07673i	0.0621177	+	0.191179i
$260$	8.23237			0.510550
$261$	−16.4604	+	11.9592i	−1.01887	+	0.740255i
$262$	−0.629411	+	1.93713i	−0.0388851	+	0.119676i
$263$	−5.20880	−	3.78442i	−0.321188	−	0.233357i	0.415494	−	0.909596i	$-0.363609\pi$
$263$	−5.20880	−	3.78442i	−0.321188	−	0.233357i	−0.736682	+	0.676239i	$0.763609\pi$
$264$	−1.33306	−	4.10274i	−0.0820442	−	0.252506i
$265$	5.59984	−	17.2345i	0.343995	−	1.05871i
$266$	0.0171582	−	0.0528074i	0.00105203	−	0.00323783i
$267$	6.18236	−	19.0274i	0.378354	−	1.16446i
$268$	−3.94386	+	12.1379i	−0.240909	+	0.741443i
$269$	4.80212	+	14.7794i	0.292790	+	0.901115i	0.983955	+	0.178418i	$0.0570980\pi$
$269$	4.80212	+	14.7794i	0.292790	+	0.901115i	−0.691165	+	0.722697i	$0.742902\pi$
$270$	2.53590	+	1.84244i	0.154330	+	0.112127i
$271$	−4.11144	+	12.6537i	−0.249752	+	0.768658i	0.745066	+	0.666991i	$0.232418\pi$
$271$	−4.11144	+	12.6537i	−0.249752	+	0.768658i	−0.994818	+	0.101668i	$0.967582\pi$
$272$	−1.03381	+	0.751109i	−0.0626841	+	0.0455427i
$273$	−10.2087			−0.617857
$274$	3.29480	+	10.1404i	0.199046	+	0.612601i
$275$	−0.862184	+	0.626414i	−0.0519917	+	0.0377742i
$276$	21.1705	+	15.3813i	1.27432	+	0.925846i
$277$	−26.0314	−	18.9129i	−1.56408	−	1.13637i	−0.932564	−	0.361004i	$-0.882434\pi$
$277$	−26.0314	−	18.9129i	−1.56408	−	1.13637i	−0.631513	−	0.775365i	$-0.717566\pi$
$278$	−3.99841			−0.239809
$279$	−5.81938	−	4.22803i	−0.348397	−	0.253125i
$280$	1.57969	−	4.86178i	0.0944044	−	0.290547i
$281$	−1.69384	−	5.21309i	−0.101046	−	0.310987i	0.887736	−	0.460352i	$-0.152277\pi$
$281$	−1.69384	−	5.21309i	−0.101046	−	0.310987i	−0.988782	+	0.149365i	$0.952277\pi$
$282$	−16.5818	+	12.0474i	−0.987434	+	0.717413i
$283$	2.97167	−	2.15905i	0.176647	−	0.128342i	−0.495948	−	0.868352i	$-0.665179\pi$
$283$	2.97167	−	2.15905i	0.176647	−	0.128342i	0.672596	+	0.740010i	$0.265179\pi$
$284$	−10.6213			−0.630256
$285$	−0.0874092	−	0.269018i	−0.00517767	−	0.0159352i
$286$	−2.05139			−0.121301
$287$	1.29721	−	6.27035i	0.0765721	−	0.370127i
$288$	−20.7608			−1.22334
$289$	3.02894	+	9.32211i	0.178173	+	0.548359i
$290$	−8.72023			−0.512070
$291$	−3.36058	+	2.44160i	−0.197000	+	0.143129i
$292$	5.00457	−	3.63603i	0.292870	−	0.212783i
$293$	−6.47885	−	19.9398i	−0.378498	−	1.16490i	−0.941088	−	0.338162i	$-0.890195\pi$
$293$	−6.47885	−	19.9398i	−0.378498	−	1.16490i	0.562590	−	0.826736i	$-0.309805\pi$
$294$	−0.726962	+	2.23736i	−0.0423973	+	0.130485i
$295$	−3.94421	−	2.86564i	−0.229641	−	0.166844i
$296$	9.31524			0.541437
$297$	0.909665	+	0.660910i	0.0527841	+	0.0383499i
$298$	7.10556	+	5.16249i	0.411614	+	0.299055i
$299$	27.1279	−	19.7096i	1.56885	−	1.13984i
$300$	1.75127	+	5.38986i	0.101110	+	0.311183i
$301$	−6.30412			−0.363363
$302$	3.26171	−	2.36977i	0.187690	−	0.136365i
$303$	6.03157	−	18.5633i	0.346505	−	1.06643i
$304$	−0.0122458	−	0.00889710i	−0.000702346	−	0.000510284i
$305$	−2.79481	−	8.60155i	−0.160030	−	0.492523i
$306$	5.43272	−	16.7202i	0.310568	−	0.955830i
$307$	−6.27059	+	19.2989i	−0.357882	+	1.10145i	0.596438	+	0.802659i	$0.296582\pi$
$307$	−6.27059	+	19.2989i	−0.357882	+	1.10145i	−0.954320	+	0.298787i	$0.903418\pi$
$308$	0.210289	−	0.647203i	0.0119823	−	0.0368778i
$309$	4.89629	−	15.0692i	0.278540	−	0.857259i
$310$	−0.952680	−	2.93205i	−0.0541086	−	0.166529i
$311$	8.69176	+	6.31493i	0.492864	+	0.358087i	0.806285	−	0.591528i	$-0.201475\pi$
$311$	8.69176	+	6.31493i	0.492864	+	0.358087i	−0.313420	+	0.949614i	$0.601475\pi$
$312$	−9.08371	+	27.9568i	−0.514264	+	1.58274i
$313$	−3.53643	+	2.56937i	−0.199891	+	0.145229i	−0.683228	−	0.730205i	$-0.739425\pi$
$313$	−3.53643	+	2.56937i	−0.199891	+	0.145229i	0.483337	+	0.875434i	$0.339425\pi$
$314$	−13.4948			−0.761554
$315$	2.05756	+	6.33252i	0.115930	+	0.356797i
$316$	11.9613	−	8.69037i	0.672874	−	0.488871i
$317$	−27.6728	−	20.1055i	−1.55426	−	1.12924i	−0.940525	−	0.339725i	$-0.889666\pi$
$317$	−27.6728	−	20.1055i	−1.55426	−	1.12924i	−0.613736	−	0.789512i	$-0.710334\pi$
$318$	19.4268	+	14.1144i	1.08940	+	0.791498i
$319$	−3.12808			−0.175139
$320$	−7.90762	−	5.74522i	−0.442049	−	0.321168i
$321$	4.28175	−	13.1779i	0.238984	−	0.735517i
$322$	−2.38782	−	7.34895i	−0.133068	−	0.409541i
$323$	−0.256843	+	0.186608i	−0.0142911	+	0.0103831i
$324$	−5.90544	+	4.29055i	−0.328080	+	0.238364i
$325$	7.26199			0.402823
$326$	−6.23776	−	19.1979i	−0.345478	−	1.06327i
$327$	45.8321			2.53452
$328$	−16.0173	−	9.13183i	−0.884406	−	0.504221i
$329$	−8.71256			−0.480339
$330$	0.744177	+	2.29034i	0.0409656	+	0.126079i
$331$	21.2155			1.16611			0.583054	−	0.812433i	$-0.301858\pi$
$331$	21.2155			1.16611			0.583054	+	0.812433i	$0.301858\pi$
$332$	3.26509	−	2.37223i	0.179195	−	0.130193i
$333$	−9.81596	+	7.13171i	−0.537911	+	0.390816i
$334$	2.12329	+	6.53482i	0.116181	+	0.357570i
$335$	5.93269	−	18.2590i	0.324138	−	0.997593i
$336$	0.518834	+	0.376955i	0.0283047	+	0.0205646i
$337$	−16.9813			−0.925032			−0.462516	−	0.886611i	$-0.653053\pi$
$337$	−16.9813			−0.925032			−0.462516	+	0.886611i	$0.653053\pi$
$338$	1.78614	+	1.29771i	0.0971533	+	0.0705860i
$339$	39.4801	+	28.6840i	2.14427	+	1.55790i
$340$	−8.77535	+	6.37566i	−0.475910	+	0.345769i
$341$	−0.341740	−	1.05177i	−0.0185063	−	0.0569565i
$342$	0.208248			0.0112608
$343$	−0.809017	+	0.587785i	−0.0436828	+	0.0317374i
$344$	−5.60942	+	17.2640i	−0.302440	+	0.930814i
$345$	−31.8466	−	23.1379i	−1.71456	−	1.24570i
$346$	1.73293	+	5.33340i	0.0931627	+	0.286725i
$347$	−7.47017	+	22.9908i	−0.401020	+	1.23421i	0.523153	+	0.852239i	$0.324756\pi$
$347$	−7.47017	+	22.9908i	−0.401020	+	1.23421i	−0.924173	+	0.381974i	$0.875244\pi$
$348$	−5.14030	+	15.8202i	−0.275549	+	0.848052i
$349$	6.47966	−	19.9423i	0.346848	−	1.06749i	−0.613739	−	0.789509i	$-0.710335\pi$
$349$	6.47966	−	19.9423i	0.346848	−	1.06749i	0.960587	−	0.277980i	$-0.0896647\pi$
$350$	0.517128	−	1.59156i	0.0276416	−	0.0850722i
$351$	−2.36766	−	7.28691i	−0.126376	−	0.388947i
$352$	−2.58224	−	1.87611i	−0.137634	−	0.0999968i
$353$	−6.64214	+	20.4424i	−0.353525	+	1.08804i	0.603334	+	0.797488i	$0.293839\pi$
$353$	−6.64214	+	20.4424i	−0.353525	+	1.08804i	−0.956860	+	0.290551i	$0.906161\pi$
$354$	5.22651	−	3.79729i	0.277786	−	0.201823i
$355$	15.9774			0.847993
$356$	−2.80823	−	8.64284i	−0.148836	−	0.458070i
$357$	10.8820	−	7.90624i	0.575937	−	0.418443i
$358$	−10.1360	−	7.36423i	−0.535704	−	0.389212i
$359$	−0.307741	−	0.223587i	−0.0162419	−	0.0118005i	0.579635	−	0.814876i	$-0.303195\pi$
$359$	−0.307741	−	0.223587i	−0.0162419	−	0.0118005i	−0.595877	+	0.803076i	$0.703195\pi$
$360$	19.1726			1.01049
$361$	15.3683	+	11.1657i	0.808857	+	0.587669i
$362$	−6.57290	+	20.2293i	−0.345464	+	1.06323i
$363$	−8.56475	−	26.3596i	−0.449533	−	1.38352i
$364$	−3.75150	+	2.72562i	−0.196632	+	0.142862i
$365$	−7.52831	+	5.46964i	−0.394050	+	0.286294i
$366$	11.9846			0.626443
$367$	7.76985	+	23.9132i	0.405583	+	1.24826i	0.920407	+	0.390961i	$0.127857\pi$
$367$	7.76985	+	23.9132i	0.405583	+	1.24826i	−0.514824	+	0.857296i	$0.672143\pi$
$368$	−2.10650			−0.109809
$369$	23.8695	−	2.64007i	1.24260	−	0.137437i
$370$	−5.20021			−0.270346
$371$	3.15426	+	9.70782i	0.163761	+	0.504005i
$372$	−5.88088			−0.304910
$373$	−10.4213	+	7.57151i	−0.539594	+	0.392038i	−0.823934	−	0.566686i	$-0.808225\pi$
$373$	−10.4213	+	7.57151i	−0.539594	+	0.392038i	0.284340	+	0.958723i	$0.408225\pi$
$374$	2.18669	−	1.58872i	0.113071	−	0.0821510i
$375$	−9.76128	−	30.0421i	−0.504070	−	1.55137i
$376$	−7.75246	+	23.8596i	−0.399803	+	1.23047i
$377$	17.2444	+	12.5288i	0.888133	+	0.645266i
$378$	−1.76562			−0.0908136
$379$	−5.08338	−	3.69329i	−0.261115	−	0.189711i	0.449523	−	0.893269i	$-0.351594\pi$
$379$	−5.08338	−	3.69329i	−0.261115	−	0.189711i	−0.710639	+	0.703557i	$0.751594\pi$
$380$	−0.103947	−	0.0755216i	−0.00533235	−	0.00387418i
$381$	9.96871	−	7.24269i	0.510712	−	0.371054i
$382$	−0.146201	−	0.449960i	−0.00748029	−	0.0230220i
$383$	26.2052			1.33902			0.669511	−	0.742802i	$-0.266504\pi$
$383$	26.2052			1.33902			0.669511	+	0.742802i	$0.266504\pi$
$384$	−12.7922	+	9.29406i	−0.652798	+	0.474285i
$385$	−0.316335	+	0.973579i	−0.0161219	+	0.0496182i
$386$	4.90113	+	3.56088i	0.249461	+	0.181244i
$387$	−7.30633	−	22.4866i	−0.371402	−	1.14306i
$388$	−0.583064	+	1.79449i	−0.0296006	+	0.0911013i
$389$	1.45733	−	4.48520i	0.0738895	−	0.227409i	−0.907290	−	0.420505i	$-0.861853\pi$
$389$	1.45733	−	4.48520i	0.0738895	−	0.227409i	0.981180	+	0.193096i	$0.0618530\pi$
$390$	5.07095	−	15.6068i	0.256778	−	0.790281i
$391$	−13.6529	+	42.0192i	−0.690454	+	2.12500i
$392$	0.889803	+	2.73853i	0.0449418	+	0.138317i
$393$	−4.72844	−	3.43541i	−0.238518	−	0.173294i
$394$	−5.57484	+	17.1576i	−0.280856	+	0.864386i
$395$	−17.9932	+	13.0728i	−0.905335	+	0.657764i
$396$	2.55227			0.128256
$397$	1.68095	+	5.17344i	0.0843646	+	0.259647i	0.984336	−	0.176301i	$-0.0564131\pi$
$397$	1.68095	+	5.17344i	0.0843646	+	0.259647i	−0.899972	+	0.435948i	$0.856413\pi$
$398$	13.4202	−	9.75032i	0.672692	−	0.488740i
$399$	0.128901	+	0.0936517i	0.00645310	+	0.00468845i
$400$	−0.369075	−	0.268149i	−0.0184538	−	0.0134074i
$401$	−15.2142			−0.759762			−0.379881	−	0.925035i	$-0.624035\pi$
$401$	−15.2142			−0.759762			−0.379881	+	0.925035i	$0.624035\pi$
$402$	20.5816	+	14.9534i	1.02652	+	0.745808i
$403$	−2.32868	+	7.16694i	−0.116000	+	0.357011i
$404$	−2.73973	−	8.43203i	−0.136307	−	0.419509i
$405$	8.88348	−	6.45423i	0.441424	−	0.320713i
$406$	3.97382	−	2.88715i	0.197217	−	0.143287i
$407$	−1.86539			−0.0924640
$408$	−11.9686	−	36.8357i	−0.592536	−	1.82364i
$409$	−27.8492			−1.37706			−0.688528	−	0.725210i	$-0.741743\pi$
$409$	−27.8492			−1.37706			−0.688528	+	0.725210i	$0.741743\pi$
$410$	8.94160	+	5.09782i	0.441594	+	0.251763i
$411$	−30.5953			−1.50916
$412$	−2.22405	−	6.84493i	−0.109571	−	0.337226i
$413$	2.74616			0.135130
$414$	23.4460	−	17.0345i	1.15231	−	0.837202i
$415$	−4.91163	+	3.56851i	−0.241103	+	0.175171i
$416$	6.72101	+	20.6851i	0.329525	+	1.01417i
$417$	3.54550	−	10.9119i	0.173624	−	0.534360i
$418$	0.0259020	+	0.0188189i	0.00126691	+	0.000920463i
$419$	11.4474			0.559243			0.279622	−	0.960110i	$-0.409791\pi$
$419$	11.4474			0.559243			0.279622	+	0.960110i	$0.409791\pi$
$420$	4.40404	+	3.19972i	0.214895	+	0.156130i
$421$	−6.06924	−	4.40956i	−0.295796	−	0.214909i	0.429982	−	0.902838i	$-0.358520\pi$
$421$	−6.06924	−	4.40956i	−0.295796	−	0.214909i	−0.725778	+	0.687929i	$0.758520\pi$
$422$	9.83226	−	7.14356i	0.478627	−	0.347743i
$423$	−10.0977	−	31.0774i	−0.490965	−	1.51103i
$424$	29.3919			1.42739
$425$	−7.74097	+	5.62414i	−0.375492	+	0.272811i
$426$	−6.54246	+	20.1356i	−0.316983	+	0.975573i
$427$	4.12145	+	2.99441i	0.199451	+	0.144910i
$428$	−1.94491	−	5.98581i	−0.0940107	−	0.289335i
$429$	1.81903	−	5.59839i	0.0878235	−	0.270293i
$430$	3.13144	−	9.63759i	0.151012	−	0.464766i
$431$	7.80590	−	24.0241i	0.375997	−	1.15720i	−0.566807	−	0.823851i	$-0.691821\pi$
$431$	7.80590	−	24.0241i	0.375997	−	1.15720i	0.942804	−	0.333349i	$-0.108179\pi$
$432$	−0.148738	+	0.457767i	−0.00715614	+	0.0220243i
$433$	−11.8407	−	36.4420i	−0.569028	−	1.75129i	−0.655668	−	0.755049i	$-0.727613\pi$
$433$	−11.8407	−	36.4420i	−0.569028	−	1.75129i	0.0866399	−	0.996240i	$-0.472387\pi$
$434$	1.40490	+	1.02072i	0.0674372	+	0.0489960i
$435$	7.73248	−	23.7981i	0.370744	−	1.14103i
$436$	16.8425	−	12.2368i	0.806608	−	0.586035i
$437$	−0.523344			−0.0250349
$438$	−3.81043	−	11.7273i	−0.182069	−	0.560352i
$439$	16.8806	−	12.2645i	0.805669	−	0.585353i	−0.106903	−	0.994269i	$-0.534093\pi$
$439$	16.8806	−	12.2645i	0.805669	−	0.585353i	0.912572	+	0.408917i	$0.134093\pi$
$440$	2.38470	+	1.73259i	0.113686	+	0.0825978i
$441$	−3.03424	−	2.20451i	−0.144488	−	0.104976i
$442$	−18.4180			−0.876056
$443$	−0.965819	−	0.701709i	−0.0458875	−	0.0333392i	0.564605	−	0.825361i	$-0.309028\pi$
$443$	−0.965819	−	0.701709i	−0.0458875	−	0.0333392i	−0.610493	+	0.792022i	$0.709028\pi$
$444$	−3.06536	+	9.43419i	−0.145475	+	0.447727i
$445$	4.22438	+	13.0013i	0.200255	+	0.616321i
$446$	−11.2134	+	8.14705i	−0.530972	+	0.385774i
$447$	−20.3895	+	14.8138i	−0.964390	+	0.700671i
$448$	5.50567			0.260119
$449$	6.06597	+	18.6691i	0.286271	+	0.881051i	0.986015	+	0.166657i	$0.0532974\pi$
$449$	6.06597	+	18.6691i	0.286271	+	0.881051i	−0.699744	+	0.714394i	$0.746703\pi$
$450$	6.27636			0.295871
$451$	3.20748	+	1.82866i	0.151035	+	0.0861084i
$452$	22.1666			1.04263
$453$	3.57502	+	11.0028i	0.167969	+	0.516956i
$454$	−12.5430			−0.588671
$455$	5.64333	−	4.10012i	0.264564	−	0.192217i
$456$	0.371164	−	0.269667i	0.0173814	−	0.0126283i
$457$	−2.67967	−	8.24718i	−0.125350	−	0.385787i	0.868615	−	0.495488i	$-0.165011\pi$
$457$	−2.67967	−	8.24718i	−0.125350	−	0.385787i	−0.993965	+	0.109701i	$0.965011\pi$
$458$	7.16969	−	22.0660i	0.335017	−	1.03108i
$459$	8.16726	+	5.93386i	0.381215	+	0.276969i
$460$	−17.8806			−0.833689
$461$	28.6001	+	20.7792i	1.33204	+	0.967782i	0.999697	+	0.0246232i	$0.00783859\pi$
$461$	28.6001	+	20.7792i	1.33204	+	0.967782i	0.332341	+	0.943159i	$0.392161\pi$
$462$	−1.09742	−	0.797325i	−0.0510567	−	0.0370949i
$463$	−2.18270	+	1.58582i	−0.101438	+	0.0736994i	−0.637348	−	0.770576i	$-0.719969\pi$
$463$	−2.18270	+	1.58582i	−0.101438	+	0.0736994i	0.535910	+	0.844275i	$0.319969\pi$
$464$	−0.413785	−	1.27350i	−0.0192095	−	0.0591207i
$465$	8.84653			0.410248
$466$	7.88900	−	5.73169i	0.365451	−	0.265516i
$467$	−0.366416	+	1.12771i	−0.0169557	+	0.0521843i	−0.959176	−	0.282809i	$-0.908734\pi$
$467$	−0.366416	+	1.12771i	−0.0169557	+	0.0521843i	0.942221	+	0.334993i	$0.108734\pi$
$468$	−14.0701	−	10.2225i	−0.650391	−	0.472537i
$469$	3.34175	+	10.2849i	0.154308	+	0.474911i
$470$	4.32779	−	13.3196i	0.199626	−	0.614386i
$471$	11.9662	−	36.8282i	0.551374	−	1.69695i
$472$	2.44354	−	7.52044i	0.112473	−	0.346156i
$473$	1.12330	−	3.45715i	0.0516492	−	0.158960i
$474$	−9.10718	−	28.0290i	−0.418307	−	1.28742i
$475$	−0.0916940	−	0.0666196i	−0.00420721	−	0.00305672i
$476$	1.88804	−	5.81079i	0.0865382	−	0.266337i
$477$	−30.9717	+	22.5023i	−1.41810	+	1.03031i
$478$	1.38177			0.0632009
$479$	−0.799874	−	2.46176i	−0.0365472	−	0.112481i	0.931119	−	0.364717i	$-0.118834\pi$
$479$	−0.799874	−	2.46176i	−0.0365472	−	0.112481i	−0.967666	+	0.252236i	$0.918834\pi$
$480$	20.6565	−	15.0078i	0.942834	−	0.685009i
$481$	10.2835	+	7.47140i	0.468887	+	0.340667i
$482$	−18.2650	−	13.2703i	−0.831946	−	0.604444i
$483$	22.1732			1.00891
$484$	−10.1852	−	7.39995i	−0.462962	−	0.336361i
$485$	0.877096	−	2.69942i	0.0398269	−	0.122575i
$486$	6.13316	+	18.8759i	0.278206	+	0.856230i
$487$	−14.2229	+	10.3335i	−0.644502	+	0.468258i	−0.861394	−	0.507938i	$-0.830408\pi$
$487$	−14.2229	+	10.3335i	−0.644502	+	0.468258i	0.216892	+	0.976196i	$0.430408\pi$
$488$	11.8676	−	8.62230i	0.537220	−	0.390313i
$489$	57.9235			2.61939
$490$	−0.496730	−	1.52878i	−0.0224400	−	0.0690631i
$491$	−12.8550			−0.580138			−0.290069	−	0.957006i	$-0.593678\pi$
$491$	−12.8550			−0.580138			−0.290069	+	0.957006i	$0.593678\pi$
$492$	14.5192	−	13.2168i	0.654577	−	0.595860i
$493$	−28.0849			−1.26488
$494$	−0.0674173	−	0.207489i	−0.00303325	−	0.00933538i
$495$	−3.83935			−0.172566
$496$	0.382989	−	0.278258i	0.0171967	−	0.0124941i
$497$	−7.28093	+	5.28990i	−0.326594	+	0.237285i
$498$	−2.48601	−	7.65114i	−0.111401	−	0.342856i
$499$	−10.5528	+	32.4781i	−0.472407	+	1.45392i	0.377016	+	0.926207i	$0.376950\pi$
$499$	−10.5528	+	32.4781i	−0.472407	+	1.45392i	−0.849423	+	0.527713i	$0.823050\pi$
$500$	−11.6081	−	8.43376i	−0.519129	−	0.377169i
$501$	−19.7168			−0.880881
$502$	20.1970	+	14.6740i	0.901435	+	0.654931i
$503$	22.4985	+	16.3461i	1.00316	+	0.728838i	0.962763	−	0.270346i	$-0.0871380\pi$
$503$	22.4985	+	16.3461i	1.00316	+	0.728838i	0.0403960	+	0.999184i	$0.487138\pi$
$504$	−8.73699	+	6.34779i	−0.389176	+	0.282753i
$505$	4.12134	+	12.6842i	0.183397	+	0.564439i
$506$	4.45560			0.198076
$507$	−5.12536	+	3.72379i	−0.227625	+	0.165379i
$508$	1.72958	−	5.32311i	0.0767378	−	0.236175i
$509$	25.8666	+	18.7932i	1.14652	+	0.832992i	0.988014	−	0.154367i	$-0.0493338\pi$
$509$	25.8666	+	18.7932i	1.14652	+	0.832992i	0.158501	+	0.987359i	$0.449334\pi$
$510$	6.68146	+	20.5634i	0.295860	+	0.910564i
$511$	1.61974	−	4.98504i	0.0716530	−	0.220525i
$512$	0.861481	−	2.65137i	0.0380724	−	0.117175i
$513$	−0.0369528	+	0.113729i	−0.00163151	+	0.00502126i
$514$	−3.38401	+	10.4149i	−0.149262	+	0.459381i
$515$	3.34562	+	10.2967i	0.147425	+	0.453729i
$516$	−15.6386	−	11.3621i	−0.688451	−	0.500189i
$517$	1.55244	−	4.77793i	0.0682763	−	0.210133i
$518$	2.36974	−	1.72172i	0.104120	−	0.0756479i
$519$	−16.0919			−0.706354
$520$	−6.20686	−	19.1028i	−0.272189	−	0.837711i
$521$	30.6971	−	22.3027i	1.34486	−	0.977101i	0.345614	−	0.938377i	$-0.387671\pi$
$521$	30.6971	−	22.3027i	1.34486	−	0.977101i	0.999250	−	0.0387242i	$-0.0123294\pi$
$522$	14.9039	+	10.8283i	0.652327	+	0.473943i
$523$	13.1828	+	9.57787i	0.576444	+	0.418811i	0.837440	−	0.546529i	$-0.184051\pi$
$523$	13.1828	+	9.57787i	0.576444	+	0.418811i	−0.260997	+	0.965340i	$0.584051\pi$
$524$	−2.65484			−0.115977
$525$	3.88492	+	2.82256i	0.169552	+	0.123186i
$526$	−1.80145	+	5.54430i	−0.0785471	+	0.241743i
$527$	−3.06826	−	9.44312i	−0.133655	−	0.411349i
$528$	−0.299168	+	0.217359i	−0.0130196	+	0.00945932i
$529$	−40.3143	+	29.2900i	−1.75279	+	1.27348i
$530$	−16.4079			−0.712714
$531$	3.18273	+	9.79545i	0.138119	+	0.425086i
$532$	0.0723727			0.00313776
$533$	−10.3579	−	22.9279i	−0.448649	−	0.993116i
$534$	−18.1148			−0.783902
$535$	2.92570	+	9.00438i	0.126489	+	0.389293i
$536$	31.1389			1.34500
$537$	29.0854	−	21.1318i	1.25513	−	0.911904i
$538$	11.3833	−	8.27045i	0.490769	−	0.356564i
$539$	−0.178184	−	0.548395i	−0.00767495	−	0.0236211i
$540$	−1.26253	+	3.88568i	−0.0543308	+	0.167213i
$541$	16.9385	+	12.3065i	0.728242	+	0.529099i	0.889007	−	0.457894i	$-0.151396\pi$
$541$	16.9385	+	12.3065i	0.728242	+	0.529099i	−0.160764	+	0.986993i	$0.551396\pi$
$542$	12.0468			0.517455
$543$	−49.3789	−	35.8759i	−2.11905	−	1.53958i
$544$	−23.1842	−	16.8443i	−0.994013	−	0.722193i
$545$	−25.3359	+	18.4076i	−1.08527	+	0.788495i
$546$	2.85635	+	8.79096i	0.122241	+	0.376218i
$547$	29.3451			1.25471			0.627353	−	0.778735i	$-0.284138\pi$
$547$	29.3451			1.25471			0.627353	+	0.778735i	$0.284138\pi$
$548$	−11.2432	+	8.16868i	−0.480287	+	0.348949i
$549$	−5.90429	+	18.1715i	−0.251989	+	0.775542i
$550$	0.780657	+	0.567181i	0.0332873	+	0.0241847i
$551$	−0.102802	−	0.316391i	−0.00437950	−	0.0134787i
$552$	19.7297	−	60.7219i	0.839754	−	2.58450i
$553$	3.87128	−	11.9146i	0.164624	−	0.506660i
$554$	−9.00292	+	27.7081i	−0.382497	+	1.17721i
$555$	4.61117	−	14.1917i	0.195733	−	0.602406i
$556$	−1.61048	−	4.95655i	−0.0682997	−	0.210205i
$557$	−4.56659	−	3.31782i	−0.193492	−	0.140581i	0.486821	−	0.873502i	$-0.338156\pi$
$557$	−4.56659	−	3.31782i	−0.193492	−	0.140581i	−0.680314	+	0.732921i	$0.738156\pi$
$558$	−2.01262	+	6.19421i	−0.0852010	+	0.262222i
$559$	−20.0393	+	14.5594i	−0.847572	+	0.615797i
$560$	−0.438207			−0.0185176
$561$	2.39674	+	7.37641i	0.101190	+	0.311432i
$562$	−4.01520	+	2.91721i	−0.169371	+	0.123055i
$563$	−18.2463	−	13.2567i	−0.768992	−	0.558705i	0.132663	−	0.991161i	$-0.457647\pi$
$563$	−18.2463	−	13.2567i	−0.768992	−	0.558705i	−0.901655	+	0.432456i	$0.857647\pi$
$564$	−21.6132	−	15.7029i	−0.910080	−	0.661212i
$565$	−33.3449			−1.40283
$566$	−2.69067	−	1.95489i	−0.113097	−	0.0821701i
$567$	−1.91131	+	5.88240i	−0.0802673	+	0.247037i
$568$	8.00798	+	24.6460i	0.336007	+	1.03412i
$569$	32.2537	−	23.4337i	1.35215	−	0.982391i	0.353244	−	0.935531i	$-0.385078\pi$
$569$	32.2537	−	23.4337i	1.35215	−	0.982391i	0.998901	−	0.0468604i	$-0.0149216\pi$
$570$	−0.207201	+	0.150541i	−0.00867871	+	0.00630545i
$571$	7.18457			0.300665			0.150332	−	0.988636i	$-0.451966\pi$
$571$	7.18457			0.300665			0.150332	+	0.988636i	$0.451966\pi$
$572$	−0.826261	−	2.54297i	−0.0345477	−	0.106327i
$573$	1.35761			0.0567151
$574$	−5.76251	+	0.637357i	−0.240523	+	0.0266028i
$575$	−15.7730			−0.657779
$576$	6.38095	+	19.6385i	0.265873	+	0.818273i
$577$	−26.2604			−1.09323			−0.546617	−	0.837383i	$-0.684084\pi$
$577$	−26.2604			−1.09323			−0.546617	+	0.837383i	$0.684084\pi$
$578$	7.18002	−	5.21659i	0.298650	−	0.216982i
$579$	−14.0639	+	10.2180i	−0.584474	+	0.424646i
$580$	−3.51234	−	10.8099i	−0.145842	−	0.448856i
$581$	1.05675	−	3.25235i	0.0438415	−	0.134930i
$582$	3.04280	+	2.21073i	0.126128	+	0.0916376i
$583$	−5.88576			−0.243763
$584$	−12.2104	−	8.87140i	−0.505272	−	0.367101i
$585$	21.1655	+	15.3776i	0.875085	+	0.635787i
$586$	−15.3580	+	11.1582i	−0.634431	+	0.460941i
$587$	−7.32635	−	22.5482i	−0.302391	−	0.930663i	−0.980638	−	0.195829i	$-0.937260\pi$
$587$	−7.32635	−	22.5482i	−0.302391	−	0.930663i	0.678247	−	0.734834i	$-0.262740\pi$
$588$	−3.06631			−0.126452
$589$	0.0951508	−	0.0691311i	0.00392062	−	0.00284850i
$590$	−1.36410	+	4.19826i	−0.0561590	+	0.172840i
$591$	−41.8809	−	30.4283i	−1.72275	−	1.25165i
$592$	−0.246756	−	0.759435i	−0.0101416	−	0.0312126i
$593$	−4.64843	+	14.3064i	−0.190888	+	0.587493i	−1.00000		0.000161533i	$-0.999949\pi$
$593$	−4.64843	+	14.3064i	−0.190888	+	0.587493i	0.809112	+	0.587655i	$0.199949\pi$
$594$	0.314606	−	0.968257i	0.0129084	−	0.0397281i
$595$	−2.84016	+	8.74110i	−0.116435	+	0.358350i
$596$	−3.53760	+	10.8876i	−0.144906	+	0.445975i
$597$	14.7093	+	45.2705i	0.602011	+	1.85280i
$598$	−24.5628	−	17.8459i	−1.00445	−	0.729773i
$599$	−13.7890	+	42.4381i	−0.563403	+	1.73398i	0.109247	+	0.994015i	$0.465156\pi$
$599$	−13.7890	+	42.4381i	−0.563403	+	1.73398i	−0.672650	+	0.739961i	$0.734844\pi$
$600$	11.1865	−	8.12745i	0.456686	−	0.331802i
$601$	2.22099			0.0905960			0.0452980	−	0.998974i	$-0.485576\pi$
$601$	2.22099			0.0905960			0.0452980	+	0.998974i	$0.485576\pi$
$602$	1.76387	+	5.42864i	0.0718901	+	0.221255i
$603$	−32.8127	+	23.8398i	−1.33624	+	0.970833i
$604$	4.25140	+	3.08882i	0.172987	+	0.125682i
$605$	15.3214	+	11.1316i	0.622903	+	0.452566i
$606$	−17.6729			−0.717913
$607$	36.3471	+	26.4077i	1.47528	+	1.07185i	0.979040	+	0.203670i	$0.0652871\pi$
$607$	36.3471	+	26.4077i	1.47528	+	1.07185i	0.496242	+	0.868184i	$0.334713\pi$
$608$	0.104897	−	0.322839i	0.00425413	−	0.0130929i
$609$	4.35554	+	13.4050i	0.176495	+	0.543196i
$610$	−6.62504	+	4.81337i	−0.268240	+	0.194888i
$611$	−27.6952	+	20.1217i	−1.12043	+	0.814038i
$612$	22.9151			0.926288
$613$	11.7198	+	36.0698i	0.473358	+	1.45685i	0.848160	+	0.529741i	$0.177711\pi$
$613$	11.7198	+	36.0698i	0.473358	+	1.45685i	−0.374802	+	0.927105i	$0.622289\pi$
$614$	18.3733			0.741485
$615$	−21.8411	+	19.8819i	−0.880718	+	0.801714i
$616$	−1.66035			−0.0668973
$617$	3.04575	+	9.37387i	0.122617	+	0.377378i	0.993459	−	0.114185i	$-0.0364258\pi$
$617$	3.04575	+	9.37387i	0.122617	+	0.377378i	−0.870842	+	0.491563i	$0.836426\pi$
$618$	−14.3465			−0.577100
$619$	1.16207	−	0.844290i	0.0467073	−	0.0339349i	−0.564187	−	0.825647i	$-0.690810\pi$
$619$	1.16207	−	0.844290i	0.0467073	−	0.0339349i	0.610894	+	0.791712i	$0.290810\pi$
$620$	3.25094	−	2.36194i	0.130561	−	0.0948580i
$621$	5.14254	+	15.8271i	0.206363	+	0.635120i
$622$	3.00603	−	9.25159i	0.120531	−	0.370955i
$623$	−6.22961	−	4.52608i	−0.249584	−	0.181333i
$624$	2.51983			0.100874
$625$	9.98564	+	7.25499i	0.399426	+	0.290200i
$626$	3.20203	+	2.32641i	0.127979	+	0.0929821i
$627$	−0.0743262	+	0.0540012i	−0.00296830	+	0.00215660i
$628$	−5.43544	−	16.7286i	−0.216898	−	0.667542i
$629$	−16.7481			−0.667790
$630$	4.87740	−	3.54364i	0.194320	−	0.141182i
$631$	−6.37789	+	19.6291i	−0.253900	+	0.781423i	0.740145	+	0.672448i	$0.234757\pi$
$631$	−6.37789	+	19.6291i	−0.253900	+	0.781423i	−0.994044	+	0.108975i	$0.965243\pi$
$632$	−29.1838	−	21.2033i	−1.16087	−	0.843420i
$633$	10.7767	+	33.1673i	0.428336	+	1.31828i
$634$	−9.57058	+	29.4552i	−0.380096	+	1.16982i
$635$	−2.60179	+	8.00748i	−0.103249	+	0.317767i
$636$	−9.67194	+	29.7672i	−0.383517	+	1.18035i
$637$	−1.21418	+	3.73686i	−0.0481076	+	0.148060i
$638$	0.875226	+	2.69367i	0.0346505	+	0.106643i
$639$	−27.3073	−	19.8399i	−1.08026	−	0.784856i
$640$	3.33870	−	10.2755i	0.131974	−	0.406174i
$641$	30.2387	−	21.9697i	1.19436	−	0.867750i	0.200638	−	0.979665i	$-0.435698\pi$
$641$	30.2387	−	21.9697i	1.19436	−	0.867750i	0.993718	+	0.111915i	$0.0356984\pi$
$642$	−12.5458			−0.495144
$643$	4.11409	+	12.6619i	0.162244	+	0.499335i	0.998823	−	0.0485113i	$-0.0154477\pi$
$643$	4.11409	+	12.6619i	0.162244	+	0.499335i	−0.836579	+	0.547847i	$0.815448\pi$
$644$	8.14823	−	5.92003i	0.321085	−	0.233282i
$645$	23.5249	+	17.0919i	0.926294	+	0.672992i
$646$	0.232556	+	0.168962i	0.00914981	+	0.00664773i
$647$	−14.1018			−0.554398			−0.277199	−	0.960813i	$-0.589406\pi$
$647$	−14.1018			−0.554398			−0.277199	+	0.960813i	$0.589406\pi$
$648$	14.4084	+	10.4683i	0.566017	+	0.411236i
$649$	−0.489322	+	1.50598i	−0.0192076	+	0.0591149i
$650$	−2.03188	−	6.25349i	−0.0796970	−	0.245282i
$651$	−4.03138	+	2.92897i	−0.158002	+	0.114795i
$652$	21.2858	−	15.4651i	0.833618	−	0.605659i
$653$	−22.0805			−0.864077			−0.432038	−	0.901855i	$-0.642205\pi$
$653$	−22.0805			−0.864077			−0.432038	+	0.901855i	$0.642205\pi$
$654$	−12.8237	−	39.4672i	−0.501446	−	1.54329i
$655$	3.99364			0.156044
$656$	−0.320194	+	1.54772i	−0.0125015	+	0.0604284i
$657$	19.6587			0.766959
$658$	2.43775	+	7.50261i	0.0950332	+	0.292482i
$659$	27.2461			1.06136			0.530679	−	0.847573i	$-0.321937\pi$
$659$	27.2461			1.06136			0.530679	+	0.847573i	$0.321937\pi$
$660$	−2.53944	+	1.84501i	−0.0988476	+	0.0718170i
$661$	−36.1676	+	26.2773i	−1.40676	+	1.02207i	−0.412974	+	0.910743i	$0.635510\pi$
$661$	−36.1676	+	26.2773i	−1.40676	+	1.02207i	−0.993784	+	0.111326i	$0.964490\pi$
$662$	−5.93602	−	18.2692i	−0.230710	−	0.710052i
$663$	16.3318	−	50.2641i	0.634275	−	1.95210i
$664$	−7.96636	−	5.78790i	−0.309155	−	0.224614i
$665$	−0.108869			−0.00422177
$666$	8.88778	+	6.45735i	0.344394	+	0.250217i
$667$	−37.4547	−	27.2125i	−1.45025	−	1.05367i
$668$	−7.24556	+	5.26421i	−0.280339	+	0.203678i
$669$	−12.2906	−	37.8265i	−0.475182	−	1.46246i
$670$	−17.3832			−0.671572
$671$	−2.37650	+	1.72663i	−0.0917437	+	0.0666557i
$672$	−4.44430	+	13.6781i	−0.171442	+	0.527645i
$673$	−16.8803	−	12.2643i	−0.650689	−	0.472753i	0.212817	−	0.977092i	$-0.431736\pi$
$673$	−16.8803	−	12.2643i	−0.650689	−	0.472753i	−0.863506	+	0.504339i	$0.831736\pi$
$674$	4.75132	+	14.6231i	0.183014	+	0.563259i
$675$	−1.11372	+	3.42766i	−0.0428669	+	0.131931i
$676$	−0.889257	+	2.73685i	−0.0342022	+	0.105263i
$677$	−3.89871	+	11.9990i	−0.149840	+	0.461159i	−0.997602	−	0.0692180i	$-0.977950\pi$
$677$	−3.89871	+	11.9990i	−0.149840	+	0.461159i	0.847762	+	0.530377i	$0.177950\pi$
$678$	13.6541	−	42.0231i	0.524383	−	1.61389i
$679$	0.494048	+	1.52052i	0.0189598	+	0.0583524i
$680$	21.4106	+	15.5557i	0.821059	+	0.596534i
$681$	11.1222	−	34.2307i	0.426204	−	1.31172i
$682$	−0.810088	+	0.588563i	−0.0310199	+	0.0225372i
$683$	−1.59842			−0.0611617			−0.0305809	−	0.999532i	$-0.509736\pi$
$683$	−1.59842			−0.0611617			−0.0305809	+	0.999532i	$0.509736\pi$
$684$	0.0838784	+	0.258151i	0.00320717	+	0.00987065i
$685$	16.9130	−	12.2880i	0.646214	−	0.469502i
$686$	0.732517	+	0.532205i	0.0279676	+	0.0203197i
$687$	53.8622	+	39.1332i	2.05497	+	1.49302i
$688$	1.55606			0.0593242
$689$	32.4469	+	23.5741i	1.23613	+	0.898101i
$690$	−11.0141	+	33.8978i	−0.419298	+	1.29047i
$691$	−2.07242	−	6.37826i	−0.0788387	−	0.242640i	0.903867	−	0.427813i	$-0.140716\pi$
$691$	−2.07242	−	6.37826i	−0.0788387	−	0.242640i	−0.982706	+	0.185172i	$0.940716\pi$
$692$	−5.91346	+	4.29638i	−0.224796	+	0.163324i
$693$	1.74959	−	1.27116i	0.0664616	−	0.0482872i
$694$	21.8881			0.830862
$695$	2.42263	+	7.45608i	0.0918955	+	0.282825i
$696$	40.5855			1.53839
$697$	28.7978	+	16.4183i	1.09080	+	0.621889i
$698$	−18.9858			−0.718625
$699$	8.64680	+	26.6121i	0.327052	+	1.00656i
$700$	2.18123			0.0824428
$701$	35.6564	−	25.9059i	1.34672	−	0.978451i	0.347554	−	0.937660i	$-0.387012\pi$
$701$	35.6564	−	25.9059i	1.34672	−	0.978451i	0.999168	−	0.0407909i	$-0.0129878\pi$
$702$	−5.61248	+	4.07771i	−0.211830	+	0.153903i
$703$	−0.0613046	−	0.188676i	−0.00231215	−	0.00711606i
$704$	−0.981025	+	3.01929i	−0.0369738	+	0.113794i
$705$	32.5125	+	23.6217i	1.22449	+	0.889644i
$706$	19.4619			0.732459
$707$	−6.07766	−	4.41568i	−0.228574	−	0.166069i
$708$	6.81238	+	4.94948i	0.256025	+	0.186013i
$709$	−19.8839	+	14.4465i	−0.746755	+	0.542550i	−0.894819	−	0.446428i	$-0.852696\pi$
$709$	−19.8839	+	14.4465i	−0.746755	+	0.542550i	0.148064	+	0.988978i	$0.452696\pi$
$710$	−4.47043	−	13.7586i	−0.167772	−	0.516350i
$711$	46.9856			1.76210
$712$	−17.9379	+	13.0327i	−0.672252	+	0.488420i
$713$	5.05787	−	15.5665i	0.189419	−	0.582971i
$714$	−9.85302	−	7.15864i	−0.368740	−	0.267905i
$715$	1.24293	+	3.82535i	0.0464831	+	0.143060i
$716$	5.04635	−	15.5311i	0.188591	−	0.580424i
$717$	−1.22526	+	3.77096i	−0.0457581	+	0.140829i
$718$	−0.106432	+	0.327563i	−0.00397199	+	0.0122245i
$719$	14.0619	−	43.2781i	0.524421	−	1.61400i	−0.241037	−	0.970516i	$-0.577488\pi$
$719$	14.0619	−	43.2781i	0.524421	−	1.61400i	0.765458	−	0.643486i	$-0.222512\pi$
$720$	−0.507872	−	1.56307i	−0.0189273	−	0.0582522i
$721$	−4.93371	−	3.58455i	−0.183741	−	0.133496i
$722$	5.31509	−	16.3582i	0.197807	−	0.608787i
$723$	52.4116	−	38.0792i	1.94921	−	1.41618i
$724$	−27.7244			−1.03037
$725$	−3.09833	−	9.53568i	−0.115069	−	0.354146i
$726$	−20.3025	+	14.7506i	−0.753497	+	0.547448i
$727$	−33.0858	−	24.0383i	−1.22709	−	0.891530i	−0.230418	−	0.973092i	$-0.574009\pi$
$727$	−33.0858	−	24.0383i	−1.22709	−	0.891530i	−0.996668	+	0.0815615i	$0.974009\pi$
$728$	9.15313	+	6.65014i	0.339238	+	0.246471i
$729$	−38.3969			−1.42211
$730$	6.81644	+	4.95243i	0.252288	+	0.183298i
$731$	10.0853	−	31.0394i	0.373019	−	1.14803i
$732$	4.82715	+	14.8564i	0.178417	+	0.549110i
$733$	3.71670	−	2.70034i	0.137279	−	0.0997392i	−0.517026	−	0.855970i	$-0.672961\pi$
$733$	3.71670	−	2.70034i	0.137279	−	0.0997392i	0.654306	+	0.756230i	$0.272961\pi$
$734$	18.4183	−	13.3816i	0.679830	−	0.493925i
$735$	4.61261			0.170139
$736$	−14.5980	−	44.9280i	−0.538089	−	1.65607i
$737$	−6.23562			−0.229692
$738$	−8.95205	−	19.8160i	−0.329530	−	0.729437i
$739$	15.4638			0.568845			0.284423	−	0.958699i	$-0.408198\pi$
$739$	15.4638			0.568845			0.284423	+	0.958699i	$0.408198\pi$
$740$	−2.09454	−	6.44634i	−0.0769970	−	0.236972i
$741$	0.626034			0.0229979
$742$	7.47710	−	5.43243i	0.274493	−	0.199431i
$743$	−24.1822	+	17.5694i	−0.887158	+	0.644558i	−0.935135	−	0.354291i	$-0.884722\pi$
$743$	−24.1822	+	17.5694i	−0.887158	+	0.644558i	0.0479777	+	0.998848i	$0.484722\pi$
$744$	4.43394	+	13.6463i	0.162556	+	0.500296i
$745$	5.32157	−	16.3781i	0.194967	−	0.600048i
$746$	9.43586	+	6.85556i	0.345471	+	0.251000i
$747$	12.8258			0.469270
$748$	2.85019	+	2.07079i	0.104213	+	0.0757154i
$749$	−4.31447	−	3.13465i	−0.157647	−	0.114538i
$750$	−23.1389	+	16.8114i	−0.844913	+	0.613865i
$751$	8.54059	+	26.2852i	0.311650	+	0.959161i	0.977111	+	0.212729i	$0.0682350\pi$
$751$	8.54059	+	26.2852i	0.311650	+	0.959161i	−0.665461	+	0.746433i	$0.731765\pi$
$752$	2.15054			0.0784221
$753$	−57.9555	+	42.1071i	−2.11202	+	1.53447i
$754$	5.96394	−	18.3551i	0.217194	−	0.668454i
$755$	−6.39532	−	4.64648i	−0.232750	−	0.169103i
$756$	−0.711157	−	2.18872i	−0.0258645	−	0.0796029i
$757$	13.8516	−	42.6310i	0.503446	−	1.54945i	−0.299921	−	0.953964i	$-0.596960\pi$
$757$	13.8516	−	42.6310i	0.503446	−	1.54945i	0.803367	−	0.595484i	$-0.203040\pi$
$758$	−1.75807	+	5.41080i	−0.0638561	+	0.196529i
$759$	−3.95091	+	12.1597i	−0.143409	+	0.441368i
$760$	−0.0968723	+	0.298142i	−0.00351393	+	0.0108148i
$761$	−5.53069	−	17.0217i	−0.200488	−	0.617037i	−0.999869	−	0.0162127i	$-0.994839\pi$
$761$	−5.53069	−	17.0217i	−0.200488	−	0.617037i	0.799381	−	0.600824i	$-0.205161\pi$
$762$	−9.02608	−	6.55783i	−0.326980	−	0.237565i
$763$	5.45109	−	16.7767i	0.197343	−	0.607359i
$764$	0.498898	−	0.362471i	0.0180495	−	0.0131137i
$765$	−34.4709			−1.24630
$766$	−7.33213	−	22.5660i	−0.264921	−	0.815342i
$767$	8.72938	−	6.34227i	0.315200	−	0.229006i
$768$	34.7281	+	25.2314i	1.25314	+	0.910461i
$769$	7.88236	+	5.72687i	0.284245	+	0.206516i	0.720767	−	0.693177i	$-0.243790\pi$
$769$	7.88236	+	5.72687i	0.284245	+	0.206516i	−0.436522	+	0.899694i	$0.643790\pi$
$770$	0.926883			0.0334026
$771$	−25.4223	−	18.4704i	−0.915562	−	0.665195i
$772$	−2.44010	+	7.50985i	−0.0878211	+	0.270285i
$773$	−1.74661	−	5.37550i	−0.0628210	−	0.193343i	0.914720	−	0.404088i	$-0.132411\pi$
$773$	−1.74661	−	5.37550i	−0.0628210	−	0.193343i	−0.977541	+	0.210745i	$0.932411\pi$
$774$	−17.3195	+	12.5833i	−0.622536	+	0.452299i
$775$	2.86774	−	2.08353i	0.103012	−	0.0748427i
$776$	4.60361			0.165260
$777$	2.59737	+	7.99389i	0.0931802	+	0.286779i
$778$	−4.27008			−0.153090
$779$	−0.0795500	+	0.384521i	−0.00285017	+	0.0137769i
$780$	21.3892			0.765855
$781$	−1.60361	−	4.93541i	−0.0573817	−	0.176603i
$782$	40.0038			1.43053
$783$	−8.55824	+	6.21793i	−0.305847	+	0.222211i
$784$	0.199691	−	0.145084i	0.00713184	−	0.00518158i
$785$	8.17646	+	25.1646i	0.291830	+	0.898161i
$786$	−1.63532	+	5.03300i	−0.0583300	+	0.179521i
$787$	−32.1342	−	23.3469i	−1.14546	−	0.832226i	−0.157590	−	0.987505i	$-0.550373\pi$
$787$	−32.1342	−	23.3469i	−1.14546	−	0.832226i	−0.987871	+	0.155278i	$0.950373\pi$
$788$	−23.5145			−0.837670
$789$	−13.5334	−	9.83259i	−0.481802	−	0.350049i
$790$	16.2918	+	11.8367i	0.579635	+	0.421129i
$791$	15.1953	−	11.0400i	0.540283	−	0.392539i
$792$	−1.92430	−	5.92240i	−0.0683772	−	0.210443i
$793$	20.0167			0.710815
$794$	3.98466	−	2.89502i	0.141410	−	0.102740i
$795$	14.5494	−	44.7784i	0.516013	−	1.58813i
$796$	17.4922	+	12.7088i	0.619995	+	0.450453i
$797$	15.1366	+	46.5857i	0.536166	+	1.65015i	0.741116	+	0.671377i	$0.234297\pi$
$797$	15.1366	+	46.5857i	0.536166	+	1.65015i	−0.204949	+	0.978773i	$0.565703\pi$
$798$	0.0445800	−	0.137203i	0.00157811	−	0.00485693i
$799$	13.9383	−	42.8977i	0.493102	−	1.51761i
$800$	3.16147	−	9.73001i	0.111775	−	0.344008i
$801$	8.92438	−	27.4664i	0.315328	−	0.970478i
$802$	4.25689	+	13.1014i	0.150316	+	0.462625i
$803$	2.44516	+	1.77651i	0.0862878	+	0.0626918i
$804$	−10.2468	+	31.5365i	−0.361378	+	1.11221i
$805$	−12.2573	+	8.90543i	−0.432012	+	0.313875i
$806$	6.82319			0.240337
$807$	12.4768	+	38.3995i	0.439202	+	1.35173i
$808$	−17.5004	+	12.7148i	−0.615662	+	0.447305i
$809$	−21.5628	−	15.6663i	−0.758106	−	0.550796i	0.140223	−	0.990120i	$-0.455218\pi$
$809$	−21.5628	−	15.6663i	−0.758106	−	0.550796i	−0.898329	+	0.439324i	$0.855218\pi$
$810$	−8.04347	−	5.84392i	−0.282619	−	0.205335i
$811$	−30.4730			−1.07005			−0.535026	−	0.844836i	$-0.679698\pi$
$811$	−30.4730			−1.07005			−0.535026	+	0.844836i	$0.679698\pi$
$812$	5.17958	+	3.76319i	0.181768	+	0.132062i
$813$	−10.6823	+	32.8766i	−0.374643	+	1.15303i
$814$	0.521930	+	1.60634i	0.0182937	+	0.0563021i
$815$	−32.0200	+	23.2639i	−1.12161	+	0.814899i
$816$	−2.68603	+	1.95151i	−0.0940298	+	0.0683167i
$817$	0.386592			0.0135251
$818$	7.79212	+	23.9817i	0.272445	+	0.838500i
$819$	−14.7365			−0.514934
$820$	−2.71792	+	13.1376i	−0.0949138	+	0.458785i
$821$	−16.5347			−0.577066			−0.288533	−	0.957470i	$-0.593167\pi$
$821$	−16.5347			−0.577066			−0.288533	+	0.957470i	$0.593167\pi$
$822$	8.56048	+	26.3464i	0.298581	+	0.918938i
$823$	51.1357			1.78248			0.891239	−	0.453534i	$-0.149837\pi$
$823$	51.1357			1.78248			0.891239	+	0.453534i	$0.149837\pi$
$824$	−14.2064	+	10.3216i	−0.494905	+	0.359569i
$825$	−2.24011	+	1.62753i	−0.0779906	+	0.0566635i
$826$	−0.768366	−	2.36479i	−0.0267349	−	0.0822814i
$827$	0.326672	−	1.00539i	0.0113595	−	0.0349609i	−0.945216	−	0.326445i	$-0.894149\pi$
$827$	0.326672	−	1.00539i	0.0113595	−	0.0349609i	0.956576	+	0.291484i	$0.0941491\pi$
$828$	30.5602	+	22.2033i	1.06204	+	0.771617i
$829$	9.76510			0.339156			0.169578	−	0.985517i	$-0.445760\pi$
$829$	9.76510			0.339156			0.169578	+	0.985517i	$0.445760\pi$
$830$	4.44719	+	3.23108i	0.154364	+	0.112152i
$831$	−67.6343	−	49.1392i	−2.34621	−	1.70462i
$832$	17.5012	−	12.7154i	0.606746	−	0.440827i
$833$	−1.59980	−	4.92367i	−0.0554297	−	0.170595i
$834$	−10.3886			−0.359727
$835$	10.8994	−	7.91888i	0.377189	−	0.274044i
$836$	−0.0128957	+	0.0396889i	−0.000446007	+	0.00137267i
$837$	−3.02567	−	2.19827i	−0.104582	−	0.0759835i
$838$	−3.20295	−	9.85767i	−0.110644	−	0.340528i
$839$	7.80818	−	24.0311i	0.269568	−	0.829646i	−0.721037	−	0.692896i	$-0.756334\pi$
$839$	7.80818	−	24.0311i	0.269568	−	0.829646i	0.990606	−	0.136750i	$-0.0436656\pi$
$840$	4.10431	−	12.6318i	0.141612	−	0.435837i
$841$	0.132673	−	0.408327i	0.00457495	−	0.0140802i
$842$	−2.09903	+	6.46016i	−0.0723374	+	0.222632i
$843$	−4.40089	−	13.5445i	−0.151575	−	0.466499i
$844$	12.8156	+	9.31110i	0.441132	+	0.320501i
$845$	1.33770	−	4.11701i	0.0460182	−	0.141629i
$846$	−23.9363	+	17.3907i	−0.822946	+	0.597905i
$847$	−10.6675			−0.366540
$848$	−0.778574	−	2.39620i	−0.0267363	−	0.0822860i
$849$	7.72093	−	5.60958i	0.264982	−	0.192520i
$850$	7.00899	+	5.09233i	0.240406	+	0.174665i
$851$	−22.3357	−	16.2278i	−0.765657	−	0.556282i
$852$	−27.5959			−0.945421
$853$	5.96084	+	4.33080i	0.204095	+	0.148284i	0.685138	−	0.728413i	$-0.259742\pi$
$853$	5.96084	+	4.33080i	0.204095	+	0.148284i	−0.481043	+	0.876697i	$0.659742\pi$
$854$	1.42540	−	4.38692i	0.0487760	−	0.150117i
$855$	−0.126177	−	0.388333i	−0.00431517	−	0.0132807i
$856$	−12.4234	+	9.02610i	−0.424622	+	0.308506i
$857$	39.4752	−	28.6804i	1.34845	−	0.979705i	0.349361	−	0.936988i	$-0.386399\pi$
$857$	39.4752	−	28.6804i	1.34845	−	0.979705i	0.999087	−	0.0427166i	$-0.0136012\pi$
$858$	−5.32988			−0.181959
$859$	11.4944	+	35.3763i	0.392185	+	1.20702i	0.931132	+	0.364682i	$0.118822\pi$
$859$	11.4944	+	35.3763i	0.392185	+	1.20702i	−0.538947	+	0.842340i	$0.681178\pi$
$860$	13.2084			0.450401
$861$	3.37039	−	16.2915i	0.114863	−	0.555212i
$862$	−22.8718			−0.779018
$863$	7.92680	+	24.3962i	0.269831	+	0.830455i	0.990541	+	0.137218i	$0.0438161\pi$
$863$	7.92680	+	24.3962i	0.269831	+	0.830455i	−0.720710	+	0.693237i	$0.756184\pi$
$864$	−10.7941			−0.367224
$865$	8.89554	−	6.46299i	0.302458	−	0.219748i
$866$	−28.0681	+	20.3927i	−0.953794	+	0.692972i
$867$	7.86972	+	24.2205i	0.267270	+	0.822571i
$868$	−0.699449	+	2.15268i	−0.0237408	+	0.0730668i
$869$	5.84410	+	4.24599i	0.198247	+	0.144035i
$870$	−22.6567			−0.768135
$871$	34.3756	+	24.9753i	1.16477	+	0.846257i
$872$	−41.0932	−	29.8560i	−1.39159	−	1.01105i
$873$	−4.85107	+	3.52451i	−0.164184	+	0.119286i
$874$	0.146430	+	0.450665i	0.00495306	+	0.0152440i
$875$	−12.1578			−0.411009
$876$	13.0028	−	9.44706i	0.439323	−	0.319187i
$877$	1.03048	−	3.17148i	0.0347968	−	0.107093i	−0.932150	−	0.362074i	$-0.882069\pi$
$877$	1.03048	−	3.17148i	0.0347968	−	0.107093i	0.966946	+	0.254980i	$0.0820689\pi$
$878$	−15.2844	−	11.1048i	−0.515824	−	0.374768i
$879$	−16.8332	−	51.8073i	−0.567770	−	1.74742i
$880$	0.0780817	−	0.240311i	0.00263213	−	0.00810087i
$881$	−11.4803	+	35.3328i	−0.386782	+	1.19039i	0.548397	+	0.836218i	$0.315238\pi$
$881$	−11.4803	+	35.3328i	−0.386782	+	1.19039i	−0.935179	+	0.354175i	$0.884762\pi$
$882$	−1.04939	+	3.22968i	−0.0353347	+	0.108749i
$883$	10.6667	−	32.8289i	0.358964	−	1.10478i	−0.594710	−	0.803940i	$-0.702733\pi$
$883$	10.6667	−	32.8289i	0.358964	−	1.10478i	0.953675	−	0.300839i	$-0.0972667\pi$
$884$	−7.41843	−	22.8316i	−0.249509	−	0.767909i
$885$	−10.2478	−	7.44544i	−0.344475	−	0.250276i
$886$	−0.334026	+	1.02803i	−0.0112218	+	0.0345373i
$887$	40.4800	−	29.4104i	1.35919	−	0.987506i	0.360689	−	0.932686i	$-0.382541\pi$
$887$	40.4800	−	29.4104i	1.35919	−	0.987506i	0.998496	−	0.0548201i	$-0.0174585\pi$
$888$	24.2027			0.812188
$889$	−1.46553	−	4.51044i	−0.0491523	−	0.151275i
$890$	10.0138	−	7.27545i	0.335663	−	0.243874i
$891$	−2.88531	−	2.09630i	−0.0966616	−	0.0702288i
$892$	−14.6159	−	10.6191i	−0.489377	−	0.355553i
$893$	0.534286			0.0178792
$894$	18.4615	+	13.4131i	0.617445	+	0.448600i
$895$	−7.59116	+	23.3632i	−0.253745	+	0.780946i
$896$	1.88062	+	5.78794i	0.0628270	+	0.193362i
$897$	70.4832	−	51.2091i	2.35337	−	1.70982i
$898$	14.3792	−	10.4471i	0.479841	−	0.348625i
$899$	10.4044			0.347006
$900$	2.52800	+	7.78038i	0.0842666	+	0.259346i
$901$	−52.8443			−1.76050
$902$	0.677266	−	3.27370i	0.0225505	−	0.109002i
$903$	−16.3792			−0.545067
$904$	−16.7127	−	51.4363i	−0.555855	−	1.71075i
$905$	41.7054			1.38633
$906$	8.47450	−	6.15709i	0.281547	−	0.204556i
$907$	24.3206	−	17.6699i	0.807551	−	0.586720i	−0.105569	−	0.994412i	$-0.533666\pi$
$907$	24.3206	−	17.6699i	0.807551	−	0.586720i	0.913120	+	0.407692i	$0.133666\pi$
$908$	−5.05207	−	15.5487i	−0.167659	−	0.516001i
$909$	8.70671	−	26.7965i	0.288783	−	0.888783i
$910$	−5.10971	−	3.71242i	−0.169385	−	0.123066i
$911$	−6.01087			−0.199149			−0.0995745	−	0.995030i	$-0.531748\pi$
$911$	−6.01087			−0.199149			−0.0995745	+	0.995030i	$0.531748\pi$
$912$	−0.0318168	−	0.0231163i	−0.00105356	−	0.000765456i
$913$	1.59528	+	1.15904i	0.0527959	+	0.0383585i
$914$	−6.35209	+	4.61507i	−0.210109	+	0.152653i
$915$	−7.26142	−	22.3484i	−0.240055	−	0.738814i
$916$	30.2416			0.999210
$917$	−1.81991	+	1.32224i	−0.0600986	+	0.0436642i
$918$	2.82463	−	8.69332i	0.0932267	−	0.286922i
$919$	22.9371	+	16.6648i	0.756627	+	0.549721i	0.897874	−	0.440253i	$-0.145111\pi$
$919$	22.9371	+	16.6648i	0.756627	+	0.549721i	−0.141247	+	0.989974i	$0.545111\pi$
$920$	13.4812	+	41.4910i	0.444464	+	1.36792i
$921$	−16.2921	+	50.1420i	−0.536843	+	1.65223i
$922$	9.89127	−	30.4422i	0.325752	−	1.00256i
$923$	−10.9273	+	33.6307i	−0.359676	+	1.10697i
$924$	0.546368	−	1.68155i	0.0179742	−	0.0553189i
$925$	−1.84765	−	5.68649i	−0.0607504	−	0.186971i
$926$	1.97630	+	1.43587i	0.0649453	+	0.0471856i
$927$	7.06791	−	21.7528i	0.232141	−	0.714456i
$928$	24.2940	−	17.6506i	0.797491	−	0.579411i
$929$	−17.1532			−0.562777			−0.281389	−	0.959594i	$-0.590795\pi$
$929$	−17.1532			−0.562777			−0.281389	+	0.959594i	$0.590795\pi$
$930$	−2.47523	−	7.61798i	−0.0811660	−	0.249803i
$931$	0.0496119	−	0.0360452i	0.00162596	−	0.00118133i
$932$	10.2827	+	7.47084i	0.336822	+	0.244716i
$933$	22.5827	+	16.4073i	0.739325	+	0.537151i
$934$	1.07362			0.0351300
$935$	−4.28751	−	3.11506i	−0.140216	−	0.101873i
$936$	−13.1125	+	40.3563i	−0.428597	+	1.31909i
$937$	−9.70746	−	29.8765i	−0.317129	−	0.976022i	−0.974869	−	0.222778i	$-0.928488\pi$
$937$	−9.70746	−	29.8765i	−0.317129	−	0.976022i	0.657740	−	0.753245i	$-0.271512\pi$
$938$	7.92155	−	5.75534i	0.258648	−	0.187919i
$939$	−9.18828	+	6.67567i	−0.299848	+	0.217852i
$940$	18.2545			0.595396
$941$	9.78415	+	30.1125i	0.318954	+	0.981640i	0.974096	+	0.226134i	$0.0726088\pi$
$941$	9.78415	+	30.1125i	0.318954	+	0.981640i	−0.655142	+	0.755506i	$0.727391\pi$
$942$	−35.0618			−1.14238
$943$	22.4972	+	49.7991i	0.732610	+	1.62168i
$944$	−0.677840			−0.0220618
$945$	1.06978	+	3.29246i	0.0348001	+	0.107104i
$946$	−3.29134			−0.107011
$947$	−21.7835	+	15.8267i	−0.707870	+	0.514298i	−0.882486	−	0.470339i	$-0.844132\pi$
$947$	−21.7835	+	15.8267i	−0.707870	+	0.514298i	0.174616	+	0.984637i	$0.444132\pi$
$948$	31.0775	−	22.5791i	1.00935	−	0.733336i
$949$	−6.36422	−	19.5871i	−0.206591	−	0.635823i
$950$	−0.0317122	+	0.0976000i	−0.00102888	+	0.00316656i
$951$	−71.8989	−	52.2376i	−2.33148	−	1.69392i
$952$	−14.9071			−0.483143
$953$	−23.5773	−	17.1299i	−0.763745	−	0.554893i	0.136312	−	0.990666i	$-0.456475\pi$
$953$	−23.5773	−	17.1299i	−0.763745	−	0.554893i	−0.900057	+	0.435773i	$0.856475\pi$
$954$	28.0431	+	20.3745i	0.907929	+	0.659649i
$955$	−0.750486	+	0.545260i	−0.0242851	+	0.0176442i
$956$	0.556552	+	1.71289i	0.0180002	+	0.0553989i
$957$	−8.12730			−0.262718
$958$	−1.89608	+	1.37758i	−0.0612596	+	0.0445077i
$959$	−3.63889	+	11.1994i	−0.117506	+	0.361646i
$960$	−20.5454	−	14.9271i	−0.663100	−	0.481770i
$961$	−8.44285	−	25.9844i	−0.272350	−	0.838207i
$962$	3.55653	−	10.9459i	0.114667	−	0.352909i
$963$	6.18080	−	19.0226i	0.199174	−	0.612993i
$964$	9.09347	−	27.9868i	0.292881	−	0.901395i
$965$	3.67061	−	11.2970i	0.118161	−	0.363662i
$966$	−6.20398	−	19.0939i	−0.199610	−	0.614336i
$967$	−12.9251	−	9.39067i	−0.415645	−	0.301983i	0.360238	−	0.932860i	$-0.382695\pi$
$967$	−12.9251	−	9.39067i	−0.415645	−	0.301983i	−0.775883	+	0.630877i	$0.782695\pi$
$968$	−9.49198	+	29.2133i	−0.305084	+	0.938952i
$969$	−0.667325	+	0.484840i	−0.0214376	+	0.0155753i
$970$	−2.56995			−0.0825162
$971$	4.69197	+	14.4404i	0.150573	+	0.463415i	0.997685	−	0.0679983i	$-0.0216612\pi$
$971$	4.69197	+	14.4404i	0.150573	+	0.463415i	−0.847113	+	0.531413i	$0.821661\pi$
$972$	−20.9289	+	15.2057i	−0.671295	+	0.487724i
$973$	−3.57260	−	2.59565i	−0.114532	−	0.0832126i
$974$	12.8780	+	9.35642i	0.412638	+	0.299799i
$975$	18.8679			0.604258
$976$	−1.01731	−	0.739117i	−0.0325632	−	0.0236586i
$977$	−6.54203	+	20.1343i	−0.209298	+	0.644153i	0.790211	+	0.612834i	$0.209971\pi$
$977$	−6.54203	+	20.1343i	−0.209298	+	0.644153i	−0.999509	+	0.0313189i	$0.990029\pi$
$978$	−16.2068	−	49.8795i	−0.518237	−	1.59497i
$979$	3.59210	−	2.60981i	0.114804	−	0.0834100i
$980$	1.69505	−	1.23152i	0.0541463	−	0.0393396i
$981$	66.1597			2.11232
$982$	3.59679	+	11.0698i	0.114778	+	0.353250i
$983$	−2.71318			−0.0865369			−0.0432685	−	0.999063i	$-0.513777\pi$
$983$	−2.71318			−0.0865369			−0.0432685	+	0.999063i	$0.513777\pi$
$984$	−41.6157	−	23.7261i	−1.32666	−	0.756362i
$985$	35.3726			1.12706
$986$	7.85806	+	24.1846i	0.250252	+	0.770195i
$987$	−22.6368			−0.720537
$988$	0.230056	−	0.167145i	0.00731905	−	0.00531760i
$989$	43.5252	−	31.6229i	1.38402	−	1.00555i
$990$	1.07424	+	3.30616i	0.0341415	+	0.105077i
$991$	−15.6582	+	48.1911i	−0.497400	+	1.53084i	0.315783	+	0.948831i	$0.397733\pi$
$991$	−15.6582	+	48.1911i	−0.497400	+	1.53084i	−0.813183	+	0.582008i	$0.802267\pi$
$992$	8.58887	+	6.24018i	0.272697	+	0.198126i
$993$	55.1216			1.74923
$994$	6.59245	+	4.78970i	0.209100	+	0.151920i
$995$	−26.3133	−	19.1177i	−0.834187	−	0.606073i
$996$	8.48328	−	6.16347i	0.268803	−	0.195297i
$997$	8.15750	+	25.1062i	0.258350	+	0.795121i	0.993151	+	0.116838i	$0.0372758\pi$
$997$	8.15750	+	25.1062i	0.258350	+	0.795121i	−0.734801	+	0.678283i	$0.762724\pi$
$998$	30.9204			0.978767
$999$	−5.10360	+	3.70798i	−0.161471	+	0.117315i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	287.2.h.c.141.4	yes	40
41.16	even	5	inner	287.2.h.c.57.4	✓	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
287.2.h.c.57.4	✓	40	41.16	even	5	inner
287.2.h.c.141.4	yes	40	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 287 = 7 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	287.h (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.279797 - 0.861126i) q^{2} +2.59818 q^{3} +(0.954783 - 0.693690i) q^{4} +(-1.43627 + 1.04351i) q^{5} +(-0.726962 - 2.23736i) q^{6} +(0.309017 - 0.951057i) q^{7} +(-2.32953 - 1.69251i) q^{8} +3.75053 q^{9} +O(q^{10})\)	\(q+(-0.279797 - 0.861126i) q^{2} +2.59818 q^{3} +(0.954783 - 0.693690i) q^{4} +(-1.43627 + 1.04351i) q^{5} +(-0.726962 - 2.23736i) q^{6} +(0.309017 - 0.951057i) q^{7} +(-2.32953 - 1.69251i) q^{8} +3.75053 q^{9} +(1.30046 + 0.944836i) q^{10} +(0.466493 + 0.338927i) q^{11} +(2.48069 - 1.80233i) q^{12} +(-1.21418 - 3.73686i) q^{13} -0.905441 q^{14} +(-3.73168 + 2.71122i) q^{15} +(-0.0762754 + 0.234751i) q^{16} +(4.18832 + 3.04299i) q^{17} +(-1.04939 - 3.22968i) q^{18} +(-0.0189501 + 0.0583223i) q^{19} +(-0.647451 + 1.99265i) q^{20} +(0.802881 - 2.47101i) q^{21} +(0.161336 - 0.496540i) q^{22} +(2.63719 + 8.11643i) q^{23} +(-6.05254 - 4.39743i) q^{24} +(-0.571133 + 1.75777i) q^{25} +(-2.87818 + 2.09112i) q^{26} +1.95001 q^{27} +(-0.364694 - 1.12241i) q^{28} +(-4.38882 + 3.18867i) q^{29} +(3.37881 + 2.45485i) q^{30} +(-1.55162 - 1.12732i) q^{31} -5.53543 q^{32} +(1.21203 + 0.880592i) q^{33} +(1.44852 - 4.45809i) q^{34} +(0.548605 + 1.68843i) q^{35} +(3.58094 - 2.60171i) q^{36} +(-2.61722 + 1.90152i) q^{37} +0.0555250 q^{38} +(-3.15466 - 9.70903i) q^{39} +5.11198 q^{40} +(6.36431 - 0.703919i) q^{41} -2.35250 q^{42} +(-1.94808 - 5.99557i) q^{43} +0.680509 q^{44} +(-5.38676 + 3.91371i) q^{45} +(6.25139 - 4.54190i) q^{46} +(-2.69233 - 8.28614i) q^{47} +(-0.198177 + 0.609926i) q^{48} +(-0.809017 - 0.587785i) q^{49} +1.67346 q^{50} +(10.8820 + 7.90624i) q^{51} +(-3.75150 - 2.72562i) q^{52} +(-8.25797 + 5.99976i) q^{53} +(-0.545606 - 1.67920i) q^{54} -1.02368 q^{55} +(-2.32953 + 1.69251i) q^{56} +(-0.0492356 + 0.151532i) q^{57} +(3.97382 + 2.88715i) q^{58} +(0.848609 + 2.61175i) q^{59} +(-1.68219 + 5.17726i) q^{60} +(-1.57426 + 4.84506i) q^{61} +(-0.536623 + 1.65156i) q^{62} +(1.15898 - 3.56697i) q^{63} +(1.70135 + 5.23621i) q^{64} +(5.64333 + 4.10012i) q^{65} +(0.419178 - 1.29010i) q^{66} +(-8.74883 + 6.35639i) q^{67} +6.10983 q^{68} +(6.85188 + 21.0879i) q^{69} +(1.30046 - 0.944836i) q^{70} +(-7.28093 - 5.28990i) q^{71} +(-8.73699 - 6.34779i) q^{72} +5.24158 q^{73} +(2.36974 + 1.72172i) q^{74} +(-1.48391 + 4.56699i) q^{75} +(0.0223644 + 0.0688306i) q^{76} +(0.466493 - 0.338927i) q^{77} +(-7.47803 + 5.43311i) q^{78} +12.5277 q^{79} +(-0.135413 - 0.416760i) q^{80} -6.18512 q^{81} +(-2.38688 - 5.28352i) q^{82} +3.41972 q^{83} +(-0.947541 - 2.91623i) q^{84} -9.19094 q^{85} +(-4.61788 + 3.35508i) q^{86} +(-11.4029 + 8.28472i) q^{87} +(-0.513075 - 1.57908i) q^{88} +(2.37950 - 7.32335i) q^{89} +(4.87740 + 3.54364i) q^{90} -3.92917 q^{91} +(8.14823 + 5.92003i) q^{92} +(-4.03138 - 2.92897i) q^{93} +(-6.38210 + 4.63687i) q^{94} +(-0.0336425 - 0.103541i) q^{95} -14.3820 q^{96} +(-1.29344 + 0.939736i) q^{97} +(-0.279797 + 0.861126i) q^{98} +(1.74959 + 1.27116i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 3 q^{2} - 3 q^{4} - 4 q^{5} - 19 q^{6} - 10 q^{7} + 16 q^{8} + 60 q^{9}+O(q^{10}) \) 40 * q - 3 * q^2 - 3 * q^4 - 4 * q^5 - 19 * q^6 - 10 * q^7 + 16 * q^8 + 60 * q^9	\( 40 q - 3 q^{2} - 3 q^{4} - 4 q^{5} - 19 q^{6} - 10 q^{7} + 16 q^{8} + 60 q^{9} + 5 q^{10} - 10 q^{11} - 12 q^{12} - 17 q^{13} + 2 q^{14} - 3 q^{15} - 23 q^{16} - 8 q^{17} - 2 q^{18} + 23 q^{19} - 13 q^{22} - q^{23} + 46 q^{24} - 34 q^{25} + 3 q^{26} - 18 q^{28} - 18 q^{29} - 19 q^{30} - 3 q^{31} - 26 q^{32} - 6 q^{33} - 44 q^{34} + q^{35} - 38 q^{36} - 5 q^{37} + 28 q^{38} + 17 q^{39} + 14 q^{40} - 11 q^{41} - 24 q^{42} + 13 q^{43} + 66 q^{44} + 43 q^{45} - 20 q^{46} - 27 q^{47} + 39 q^{48} - 10 q^{49} + 106 q^{50} - 18 q^{51} - 30 q^{52} - 30 q^{53} - 109 q^{54} + 118 q^{55} + 16 q^{56} - 40 q^{57} - 23 q^{58} - 37 q^{59} + 96 q^{60} - 41 q^{61} - 13 q^{62} - 30 q^{63} + 10 q^{64} + 6 q^{65} - 30 q^{66} - 6 q^{67} - 26 q^{68} - 31 q^{69} + 5 q^{70} - 31 q^{71} + 107 q^{72} - 46 q^{73} + 75 q^{74} - 61 q^{75} + 43 q^{76} - 10 q^{77} + 34 q^{78} + 76 q^{79} + 64 q^{80} + 16 q^{81} - 16 q^{82} - 52 q^{83} - 7 q^{84} + 86 q^{85} - 17 q^{86} - 20 q^{87} - 52 q^{88} - 16 q^{89} + 6 q^{90} + 18 q^{91} + 97 q^{92} + 32 q^{93} - 5 q^{94} - 102 q^{95} + 38 q^{96} - 18 q^{97} - 3 q^{98} - 71 q^{99}+O(q^{100}) \) 40 * q - 3 * q^2 - 3 * q^4 - 4 * q^5 - 19 * q^6 - 10 * q^7 + 16 * q^8 + 60 * q^9 + 5 * q^10 - 10 * q^11 - 12 * q^12 - 17 * q^13 + 2 * q^14 - 3 * q^15 - 23 * q^16 - 8 * q^17 - 2 * q^18 + 23 * q^19 - 13 * q^22 - q^23 + 46 * q^24 - 34 * q^25 + 3 * q^26 - 18 * q^28 - 18 * q^29 - 19 * q^30 - 3 * q^31 - 26 * q^32 - 6 * q^33 - 44 * q^34 + q^35 - 38 * q^36 - 5 * q^37 + 28 * q^38 + 17 * q^39 + 14 * q^40 - 11 * q^41 - 24 * q^42 + 13 * q^43 + 66 * q^44 + 43 * q^45 - 20 * q^46 - 27 * q^47 + 39 * q^48 - 10 * q^49 + 106 * q^50 - 18 * q^51 - 30 * q^52 - 30 * q^53 - 109 * q^54 + 118 * q^55 + 16 * q^56 - 40 * q^57 - 23 * q^58 - 37 * q^59 + 96 * q^60 - 41 * q^61 - 13 * q^62 - 30 * q^63 + 10 * q^64 + 6 * q^65 - 30 * q^66 - 6 * q^67 - 26 * q^68 - 31 * q^69 + 5 * q^70 - 31 * q^71 + 107 * q^72 - 46 * q^73 + 75 * q^74 - 61 * q^75 + 43 * q^76 - 10 * q^77 + 34 * q^78 + 76 * q^79 + 64 * q^80 + 16 * q^81 - 16 * q^82 - 52 * q^83 - 7 * q^84 + 86 * q^85 - 17 * q^86 - 20 * q^87 - 52 * q^88 - 16 * q^89 + 6 * q^90 + 18 * q^91 + 97 * q^92 + 32 * q^93 - 5 * q^94 - 102 * q^95 + 38 * q^96 - 18 * q^97 - 3 * q^98 - 71 * q^99

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