LMFDB - Embedded newform 403.2.l.c.129.27

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [403,2,Mod(25,403)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(403, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 2]))

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

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

chi := DirichletCharacter("403.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 403 = 13 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	403.l (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.21797120146$
Analytic rank:	$0$
Dimension:	$68$
Relative dimension:	$34$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			129.27
Character	$\chi$	$=$	403.129
Dual form			403.2.l.c.25.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.94813i q^{2} +(1.62865 - 2.82091i) q^{3} -1.79519 q^{4} +(2.42854 - 1.40212i) q^{5} +(5.49549 + 3.17282i) q^{6} +(0.340725 + 0.196718i) q^{7} +0.398987i q^{8} +(-3.80502 - 6.59049i) q^{9} +O(q^{10})$	\(q+1.94813i q^{2} +(1.62865 - 2.82091i) q^{3} -1.79519 q^{4} +(2.42854 - 1.40212i) q^{5} +(5.49549 + 3.17282i) q^{6} +(0.340725 + 0.196718i) q^{7} +0.398987i q^{8} +(-3.80502 - 6.59049i) q^{9} +(2.73150 + 4.73109i) q^{10} +(-2.51340 + 1.45111i) q^{11} +(-2.92375 + 5.06408i) q^{12} +(2.70929 + 2.37902i) q^{13} +(-0.383230 + 0.663775i) q^{14} -9.13424i q^{15} -4.36767 q^{16} +(1.09124 - 1.89008i) q^{17} +(12.8391 - 7.41266i) q^{18} +(-2.20920 - 1.27548i) q^{19} +(-4.35969 + 2.51707i) q^{20} +(1.10984 - 0.640769i) q^{21} +(-2.82695 - 4.89642i) q^{22} -2.50341 q^{23} +(1.12551 + 0.649812i) q^{24} +(1.43186 - 2.48005i) q^{25} +(-4.63464 + 5.27803i) q^{26} -15.0163 q^{27} +(-0.611667 - 0.353146i) q^{28} +9.69534 q^{29} +17.7946 q^{30} +(3.52734 + 4.30789i) q^{31} -7.71079i q^{32} +9.45343i q^{33} +(3.68211 + 2.12587i) q^{34} +1.10328 q^{35} +(6.83075 + 11.8312i) q^{36} +(-4.17266 - 2.40908i) q^{37} +(2.48480 - 4.30380i) q^{38} +(11.1235 - 3.76805i) q^{39} +(0.559426 + 0.968955i) q^{40} +(-5.06674 + 2.92529i) q^{41} +(1.24830 + 2.16212i) q^{42} +(-1.56578 + 2.71200i) q^{43} +(4.51204 - 2.60503i) q^{44} +(-18.4813 - 10.6702i) q^{45} -4.87696i q^{46} +11.6699i q^{47} +(-7.11341 + 12.3208i) q^{48} +(-3.42260 - 5.92812i) q^{49} +(4.83145 + 2.78944i) q^{50} +(-3.55449 - 6.15656i) q^{51} +(-4.86370 - 4.27081i) q^{52} +(0.927144 + 1.60586i) q^{53} -29.2537i q^{54} +(-4.06925 + 7.04815i) q^{55} +(-0.0784878 + 0.135945i) q^{56} +(-7.19604 + 4.15464i) q^{57} +18.8878i q^{58} +(1.79523 + 1.03648i) q^{59} +16.3977i q^{60} +2.32768 q^{61} +(-8.39231 + 6.87169i) q^{62} -2.99406i q^{63} +6.28625 q^{64} +(9.91527 + 1.97881i) q^{65} -18.4165 q^{66} +(-1.36143 + 0.786020i) q^{67} +(-1.95898 + 3.39305i) q^{68} +(-4.07719 + 7.06189i) q^{69} +2.14933i q^{70} +(4.18951 - 2.41881i) q^{71} +(2.62952 - 1.51816i) q^{72} +(-11.5768 + 6.68385i) q^{73} +(4.69320 - 8.12886i) q^{74} +(-4.66400 - 8.07828i) q^{75} +(3.96594 + 2.28974i) q^{76} -1.14184 q^{77} +(7.34064 + 21.6700i) q^{78} +(-6.66312 + 11.5409i) q^{79} +(-10.6070 + 6.12397i) q^{80} +(-13.0413 + 22.5882i) q^{81} +(-5.69882 - 9.87065i) q^{82} +(4.78636 - 2.76341i) q^{83} +(-1.99239 + 1.15031i) q^{84} -6.12016i q^{85} +(-5.28332 - 3.05033i) q^{86} +(15.7904 - 27.3497i) q^{87} +(-0.578975 - 1.00281i) q^{88} -14.3078i q^{89} +(20.7868 - 36.0038i) q^{90} +(0.455126 + 1.34356i) q^{91} +4.49411 q^{92} +(17.8970 - 2.93424i) q^{93} -22.7344 q^{94} -7.15350 q^{95} +(-21.7514 - 12.5582i) q^{96} -0.850308i q^{97} +(11.5487 - 6.66766i) q^{98} +(19.1271 + 11.0430i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 68 q - 6 q^{3} - 76 q^{4} - 40 q^{9}+O(q^{10}) $ 68 * q - 6 * q^3 - 76 * q^4 - 40 * q^9	$ 68 q - 6 q^{3} - 76 q^{4} - 40 q^{9} + 8 q^{10} - 10 q^{12} - 3 q^{13} + 10 q^{14} + 84 q^{16} + 6 q^{17} + 4 q^{22} - 44 q^{23} + 30 q^{25} - 3 q^{26} - 12 q^{27} + 48 q^{29} - 4 q^{30} - 48 q^{35} + 40 q^{36} + 60 q^{38} - 14 q^{39} + 20 q^{40} - 10 q^{42} - 12 q^{43} + 32 q^{48} + 58 q^{49} + 20 q^{51} - 27 q^{52} + 8 q^{53} - 36 q^{55} - 50 q^{56} - 12 q^{61} - 74 q^{62} - 15 q^{65} + 164 q^{66} + 4 q^{68} - 34 q^{69} - 4 q^{74} + 20 q^{75} - 200 q^{77} - 58 q^{78} - 80 q^{79} - 82 q^{81} - 66 q^{82} + 52 q^{87} + 16 q^{88} - 14 q^{90} - 70 q^{91} + 108 q^{92} - 4 q^{94} + 76 q^{95}+O(q^{100}) $ 68 * q - 6 * q^3 - 76 * q^4 - 40 * q^9 + 8 * q^10 - 10 * q^12 - 3 * q^13 + 10 * q^14 + 84 * q^16 + 6 * q^17 + 4 * q^22 - 44 * q^23 + 30 * q^25 - 3 * q^26 - 12 * q^27 + 48 * q^29 - 4 * q^30 - 48 * q^35 + 40 * q^36 + 60 * q^38 - 14 * q^39 + 20 * q^40 - 10 * q^42 - 12 * q^43 + 32 * q^48 + 58 * q^49 + 20 * q^51 - 27 * q^52 + 8 * q^53 - 36 * q^55 - 50 * q^56 - 12 * q^61 - 74 * q^62 - 15 * q^65 + 164 * q^66 + 4 * q^68 - 34 * q^69 - 4 * q^74 + 20 * q^75 - 200 * q^77 - 58 * q^78 - 80 * q^79 - 82 * q^81 - 66 * q^82 + 52 * q^87 + 16 * q^88 - 14 * q^90 - 70 * q^91 + 108 * q^92 - 4 * q^94 + 76 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/403\mathbb{Z}\right)^\times$.

$n$	$249$	$313$
$\chi(n)$	$-1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$			1.94813i			1.37753i	0.724983	+	0.688766i	$0.241847\pi$
$2$			1.94813i			1.37753i	−0.724983	+	0.688766i	$0.758153\pi$
$3$	1.62865	−	2.82091i	0.940303	−	1.62865i	0.175411	−	0.984495i	$-0.443875\pi$
$3$	1.62865	−	2.82091i	0.940303	−	1.62865i	0.764893	−	0.644158i	$-0.222792\pi$
$4$	−1.79519			−0.897597
$5$	2.42854	−	1.40212i	1.08607	−	0.627045i	0.153546	−	0.988142i	$-0.450931\pi$
$5$	2.42854	−	1.40212i	1.08607	−	0.627045i	0.932528	+	0.361096i	$0.117597\pi$
$6$	5.49549	+	3.17282i	2.24352	+	1.29530i
$7$	0.340725	+	0.196718i	0.128782	+	0.0743522i	0.563007	−	0.826452i	$-0.309644\pi$
$7$	0.340725	+	0.196718i	0.128782	+	0.0743522i	−0.434225	+	0.900804i	$0.642978\pi$
$8$			0.398987i			0.141063i
$9$	−3.80502	−	6.59049i	−1.26834	−	2.19683i
$10$	2.73150	+	4.73109i	0.863775	+	1.49610i
$11$	−2.51340	+	1.45111i	−0.757818	+	0.437526i	−0.828512	−	0.559972i	$-0.810812\pi$
$11$	−2.51340	+	1.45111i	−0.757818	+	0.437526i	0.0706938	+	0.997498i	$0.477479\pi$
$12$	−2.92375	+	5.06408i	−0.844014	+	1.46187i
$13$	2.70929	+	2.37902i	0.751421	+	0.659823i
$13$	2.70929	+	2.37902i	0.751421	+	0.659823i
$14$	−0.383230	+	0.663775i	−0.102423	+	0.177401i
$15$		−	9.13424i		−	2.35845i
$16$	−4.36767			−1.09192
$17$	1.09124	−	1.89008i	0.264664	−	0.458411i	−0.702812	−	0.711376i	$-0.748072\pi$
$17$	1.09124	−	1.89008i	0.264664	−	0.458411i	0.967475	+	0.252965i	$0.0814058\pi$
$18$	12.8391	−	7.41266i	3.02621	−	1.74718i
$19$	−2.20920	−	1.27548i	−0.506825	−	0.292616i	0.224702	−	0.974427i	$-0.427859\pi$
$19$	−2.20920	−	1.27548i	−0.506825	−	0.292616i	−0.731528	+	0.681812i	$0.761192\pi$
$20$	−4.35969	+	2.51707i	−0.974857	+	0.562834i
$21$	1.10984	−	0.640769i	0.242188	−	0.139827i
$22$	−2.82695	−	4.89642i	−0.602707	−	1.04392i
$23$	−2.50341			−0.521997			−0.260999	−	0.965339i	$-0.584052\pi$
$23$	−2.50341			−0.521997			−0.260999	+	0.965339i	$0.584052\pi$
$24$	1.12551	+	0.649812i	0.229743	+	0.132642i
$25$	1.43186	−	2.48005i	0.286371	−	0.496010i
$26$	−4.63464	+	5.27803i	−0.908928	+	1.03511i
$27$	−15.0163			−2.88989
$28$	−0.611667	−	0.353146i	−0.115594	−	0.0667384i
$29$	9.69534			1.80038			0.900190	−	0.435497i	$-0.143427\pi$
$29$	9.69534			1.80038			0.900190	+	0.435497i	$0.143427\pi$
$30$	17.7946			3.24884
$31$	3.52734	+	4.30789i	0.633528	+	0.773720i
$31$	3.52734	+	4.30789i	0.633528	+	0.773720i
$32$		−	7.71079i		−	1.36309i
$33$			9.45343i			1.64563i
$34$	3.68211	+	2.12587i	0.631476	+	0.364583i
$35$	1.10328			0.186489
$36$	6.83075	+	11.8312i	1.13846	+	1.97187i
$37$	−4.17266	−	2.40908i	−0.685980	−	0.396051i	0.116124	−	0.993235i	$-0.462953\pi$
$37$	−4.17266	−	2.40908i	−0.685980	−	0.396051i	−0.802104	+	0.597184i	$0.796286\pi$
$38$	2.48480	−	4.30380i	0.403088	−	0.698169i
$39$	11.1235	−	3.76805i	1.78119	−	0.603371i
$40$	0.559426	+	0.968955i	0.0884531	+	0.153205i
$41$	−5.06674	+	2.92529i	−0.791292	+	0.456853i	−0.840417	−	0.541940i	$-0.817690\pi$
$41$	−5.06674	+	2.92529i	−0.791292	+	0.456853i	0.0491250	+	0.998793i	$0.484357\pi$
$42$	1.24830	+	2.16212i	0.192617	+	0.333622i
$43$	−1.56578	+	2.71200i	−0.238779	+	0.413577i	−0.960364	−	0.278749i	$-0.910080\pi$
$43$	−1.56578	+	2.71200i	−0.238779	+	0.413577i	0.721586	+	0.692325i	$0.243414\pi$
$44$	4.51204	−	2.60503i	0.680215	−	0.392722i
$45$	−18.4813	−	10.6702i	−2.75502	−	1.59061i
$46$		−	4.87696i		−	0.719068i
$47$			11.6699i			1.70223i	0.524980	+	0.851114i	$0.324073\pi$
$47$			11.6699i			1.70223i	−0.524980	+	0.851114i	$0.675927\pi$
$48$	−7.11341	+	12.3208i	−1.02673	+	1.77835i
$49$	−3.42260	−	5.92812i	−0.488943	−	0.846875i
$50$	4.83145	+	2.78944i	0.683270	+	0.394486i
$51$	−3.55449	−	6.15656i	−0.497728	−	0.862090i
$52$	−4.86370	−	4.27081i	−0.674474	−	0.592255i
$53$	0.927144	+	1.60586i	0.127353	+	0.220582i	0.922650	−	0.385638i	$-0.126019\pi$
$53$	0.927144	+	1.60586i	0.127353	+	0.220582i	−0.795297	+	0.606220i	$0.792685\pi$
$54$		−	29.2537i		−	3.98092i
$55$	−4.06925	+	7.04815i	−0.548698	+	0.950372i
$56$	−0.0784878	+	0.135945i	−0.0104884	+	0.0181664i
$57$	−7.19604	+	4.15464i	−0.953139	+	0.550295i
$58$			18.8878i			2.48008i
$59$	1.79523	+	1.03648i	0.233719	+	0.134938i	0.612287	−	0.790636i	$-0.290250\pi$
$59$	1.79523	+	1.03648i	0.233719	+	0.134938i	−0.378568	+	0.925574i	$0.623583\pi$
$60$			16.3977i			2.11694i
$61$	2.32768			0.298029			0.149014	−	0.988835i	$-0.452390\pi$
$61$	2.32768			0.298029			0.149014	+	0.988835i	$0.452390\pi$
$62$	−8.39231	+	6.87169i	−1.06582	+	0.872706i
$63$		−	2.99406i		−	0.377216i
$64$	6.28625			0.785782
$65$	9.91527	+	1.97881i	1.22984	+	0.245441i
$66$	−18.4165			−2.26691
$67$	−1.36143	+	0.786020i	−0.166325	+	0.0960276i	−0.580852	−	0.814009i	$-0.697280\pi$
$67$	−1.36143	+	0.786020i	−0.166325	+	0.0960276i	0.414527	+	0.910037i	$0.363947\pi$
$68$	−1.95898	+	3.39305i	−0.237561	+	0.411468i
$69$	−4.07719	+	7.06189i	−0.490836	+	0.850152i
$70$			2.14933i			0.256895i
$71$	4.18951	−	2.41881i	0.497203	−	0.287060i	−0.230355	−	0.973107i	$-0.573989\pi$
$71$	4.18951	−	2.41881i	0.497203	−	0.287060i	0.727558	+	0.686046i	$0.240655\pi$
$72$	2.62952	−	1.51816i	0.309892	−	0.178916i
$73$	−11.5768	+	6.68385i	−1.35496	+	0.782286i	−0.988939	−	0.148322i	$-0.952613\pi$
$73$	−11.5768	+	6.68385i	−1.35496	+	0.782286i	−0.366019	+	0.930607i	$0.619280\pi$
$74$	4.69320	−	8.12886i	0.545573	−	0.944961i
$75$	−4.66400	−	8.07828i	−0.538552	−	0.932799i
$76$	3.96594	+	2.28974i	0.454925	+	0.262651i
$77$	−1.14184			−0.130124
$78$	7.34064	+	21.6700i	0.831164	+	2.45364i
$79$	−6.66312	+	11.5409i	−0.749660	+	1.29845i	0.198326	+	0.980136i	$0.436450\pi$
$79$	−6.66312	+	11.5409i	−0.749660	+	1.29845i	−0.947986	+	0.318313i	$0.896884\pi$
$80$	−10.6070	+	6.12397i	−1.18590	+	0.684681i
$81$	−13.0413	+	22.5882i	−1.44904	+	2.50980i
$82$	−5.69882	−	9.87065i	−0.629330	−	1.09003i
$83$	4.78636	−	2.76341i	0.525372	−	0.303323i	−0.213758	−	0.976887i	$-0.568570\pi$
$83$	4.78636	−	2.76341i	0.525372	−	0.303323i	0.739130	+	0.673563i	$0.235237\pi$
$84$	−1.99239	+	1.15031i	−0.217387	+	0.125509i
$85$		−	6.12016i		−	0.663824i
$86$	−5.28332	−	3.05033i	−0.569715	−	0.328925i
$87$	15.7904	−	27.3497i	1.69290	−	2.93219i
$88$	−0.578975	−	1.00281i	−0.0617189	−	0.106900i
$89$		−	14.3078i		−	1.51662i	−0.651895	−	0.758309i	$-0.726026\pi$
$89$		−	14.3078i		−	1.51662i	0.651895	−	0.758309i	$-0.273974\pi$
$90$	20.7868	−	36.0038i	2.19112	−	3.79514i
$91$	0.455126	+	1.34356i	0.0477101	+	0.140843i
$92$	4.49411			0.468543
$93$	17.8970	−	2.93424i	1.85583	−	0.304267i
$94$	−22.7344			−2.34488
$95$	−7.15350			−0.733933
$96$	−21.7514	−	12.5582i	−2.22000	−	1.28172i
$97$		−	0.850308i		−	0.0863357i	−0.999068	−	0.0431679i	$-0.986255\pi$
$97$		−	0.850308i		−	0.0863357i	0.999068	−	0.0431679i	$-0.0137450\pi$
$98$	11.5487	−	6.66766i	1.16660	−	0.673536i
$99$	19.1271	+	11.0430i	1.92234	+	1.10987i
$100$	−2.57046	+	4.45217i	−0.257046	+	0.445217i
$101$	17.8181			1.77297			0.886485	−	0.462756i	$-0.153140\pi$
$101$	17.8181			1.77297			0.886485	+	0.462756i	$0.153140\pi$
$102$	11.9937	−	6.92459i	1.18756	−	0.685637i
$103$	3.89946	+	6.75407i	0.384225	+	0.665498i	0.991661	−	0.128871i	$-0.0411352\pi$
$103$	3.89946	+	6.75407i	0.384225	+	0.665498i	−0.607436	+	0.794369i	$0.707802\pi$
$104$	−0.949201	+	1.08097i	−0.0930768	+	0.105998i
$105$	1.79687	−	3.11226i	0.175356	−	0.303726i
$106$	−3.12842	+	1.80619i	−0.303859	+	0.175433i
$107$	7.18086	−	12.4376i	0.694200	−	1.20239i	−0.276250	−	0.961086i	$-0.589092\pi$
$107$	7.18086	−	12.4376i	0.694200	−	1.20239i	0.970450	−	0.241303i	$-0.0775749\pi$
$108$	26.9572			2.59396
$109$		−	17.8815i		−	1.71274i	−0.516365	−	0.856369i	$-0.672715\pi$
$109$		−	17.8815i		−	1.71274i	0.516365	−	0.856369i	$-0.327285\pi$
$110$	−13.7307	−	7.92741i	−1.30917	−	0.755849i
$111$	−13.5916	+	7.84713i	−1.29006	+	0.744816i
$112$	−1.48817	−	0.859196i	−0.140619	−	0.0811864i
$113$	−2.42637	−	4.20260i	−0.228254	−	0.395348i	0.729037	−	0.684475i	$-0.239968\pi$
$113$	−2.42637	−	4.20260i	−0.228254	−	0.395348i	−0.957291	+	0.289127i	$0.906635\pi$
$114$	−8.09376	−	14.0188i	−0.758050	−	1.31298i
$115$	−6.07962	+	3.51007i	−0.566927	+	0.327316i
$116$	−17.4050			−1.61602
$117$	5.37004	−	26.9078i	0.496461	−	2.48763i
$118$	−2.01919	+	3.49733i	−0.185881	+	0.321956i
$119$	0.743622	−	0.429330i	0.0681677	−	0.0393567i
$120$	3.64445			0.332691
$121$	−1.28855	+	2.23184i	−0.117141	+	0.202895i
$122$			4.53461i			0.410544i
$123$			19.0571i			1.71832i
$124$	−6.33225	−	7.73350i	−0.568653	−	0.694488i
$125$			5.99064i			0.535819i
$126$	5.83280			0.519627
$127$	−6.57342	+	11.3855i	−0.583296	+	1.01030i	0.411789	+	0.911279i	$0.364904\pi$
$127$	−6.57342	+	11.3855i	−0.583296	+	1.01030i	−0.995085	+	0.0990198i	$0.968429\pi$
$128$		−	3.17516i		−	0.280647i
$129$	5.10021	+	8.83382i	0.449049	+	0.777775i
$130$	−3.85497	+	19.3162i	−0.338104	+	1.69414i
$131$	−0.169324	+	0.293278i	−0.0147939	+	0.0256238i	−0.873328	−	0.487133i	$-0.838043\pi$
$131$	−0.169324	+	0.293278i	−0.0147939	+	0.0256238i	0.858534	+	0.512757i	$0.171376\pi$
$132$		−	16.9707i		−	1.47711i
$133$	−0.501820	−	0.869177i	−0.0435133	−	0.0753672i
$134$	−1.53127	−	2.65223i	−0.132281	−	0.229118i
$135$	−36.4677	+	21.0546i	−3.13864	+	1.81209i
$136$	0.754117	+	0.435389i	0.0646650	+	0.0373343i
$137$	−6.77131	+	3.90942i	−0.578512	+	0.334004i	−0.760542	−	0.649289i	$-0.775067\pi$
$137$	−6.77131	+	3.90942i	−0.578512	+	0.334004i	0.182030	+	0.983293i	$0.441733\pi$
$138$	−13.7575	−	7.94287i	−1.17111	−	0.676142i
$139$	−9.90169			−0.839851			−0.419925	−	0.907559i	$-0.637944\pi$
$139$	−9.90169			−0.839851			−0.419925	+	0.907559i	$0.637944\pi$
$140$	−1.98061			−0.167392
$141$	32.9197	+	19.0062i	2.77234	+	1.60061i
$142$	4.71215	+	8.16169i	0.395435	+	0.684914i
$143$	−10.2617	−	2.04796i	−0.858130	−	0.171259i
$144$	16.6191	+	28.7851i	1.38492	+	2.39876i
$145$	23.5455	−	13.5940i	1.95535	−	1.12892i
$146$	−13.0210	−	22.5530i	−1.07762	−	1.86650i
$147$	−22.2969			−1.83902
$148$	7.49073	+	4.32477i	0.615734	+	0.355494i
$149$	−17.6455	−	10.1876i	−1.44558	−	0.834605i	−0.447364	−	0.894352i	$-0.647637\pi$
$149$	−17.6455	−	10.1876i	−1.44558	−	0.834605i	−0.998214	+	0.0597473i	$0.980971\pi$
$150$	15.7375	−	9.08605i	1.28496	−	0.741873i
$151$			8.06419i			0.656254i	0.944634	+	0.328127i	$0.106417\pi$
$151$			8.06419i			0.656254i	−0.944634	+	0.328127i	$0.893583\pi$
$152$	0.508901	−	0.881443i	0.0412774	−	0.0714945i
$153$	−16.6087			−1.34273
$154$		−	2.22444i		−	0.179250i
$155$	14.6064	+	5.51613i	1.17322	+	0.443066i
$156$	−19.9689	+	6.76438i	−1.59879	+	0.541584i
$157$	15.4316			1.23157			0.615786	−	0.787913i	$-0.288839\pi$
$157$	15.4316			1.23157			0.615786	+	0.787913i	$0.288839\pi$
$158$	−22.4831	−	12.9806i	−1.78866	−	1.03268i
$159$	6.03999			0.479002
$160$	−10.8114	−	18.7259i	−0.854718	−	1.48041i
$161$	−0.852974	−	0.492465i	−0.0672237	−	0.0388116i
$162$	−44.0047	−	25.4061i	−3.45734	−	1.99609i
$163$		−	7.78982i		−	0.610146i	−0.952329	−	0.305073i	$-0.901319\pi$
$163$		−	7.78982i		−	0.610146i	0.952329	−	0.305073i	$-0.0986808\pi$
$164$	9.09579	−	5.25146i	0.710262	−	0.410070i
$165$	13.2548	+	22.9580i	1.03188	+	1.78728i
$166$	5.38347	+	9.32444i	0.417838	+	0.723717i
$167$	−12.7372	−	7.35385i	−0.985637	−	0.569058i	−0.0816698	−	0.996659i	$-0.526025\pi$
$167$	−12.7372	−	7.35385i	−0.985637	−	0.569058i	−0.903967	+	0.427602i	$0.859359\pi$
$168$	0.255659	+	0.442814i	0.0197245	+	0.0341638i
$169$	1.68048	+	12.8909i	0.129268	+	0.991610i
$170$	11.9228			0.914440
$171$			19.4130i			1.48455i
$172$	2.81087	−	4.86857i	0.214327	−	0.371225i
$173$	−10.6538	−	18.4529i	−0.809995	−	1.40295i	−0.912867	−	0.408257i	$-0.866137\pi$
$173$	−10.6538	−	18.4529i	−0.809995	−	1.40295i	0.102872	−	0.994695i	$-0.467197\pi$
$174$	53.2806	+	30.7616i	4.03920	+	2.33203i
$175$	0.975738	−	0.563343i	0.0737589	−	0.0425847i
$176$	10.9777	−	6.33797i	0.827474	−	0.477742i
$177$	5.84761	−	3.37612i	0.439534	−	0.253765i
$178$	27.8733			2.08919
$179$	−7.16060	+	12.4025i	−0.535208	+	0.927008i	0.463945	+	0.885864i	$0.346433\pi$
$179$	−7.16060	+	12.4025i	−0.535208	+	0.927008i	−0.999153	+	0.0411437i	$0.986900\pi$
$180$	33.1775	+	19.1550i	2.47290	+	1.42773i
$181$	−2.97375	−	5.15069i	−0.221037	−	0.382848i	0.734086	−	0.679057i	$-0.237611\pi$
$181$	−2.97375	−	5.15069i	−0.221037	−	0.382848i	−0.955123	+	0.296209i	$0.904278\pi$
$182$	−2.61742	+	0.886642i	−0.194016	+	0.0657223i
$183$	3.79098	−	6.56617i	0.280237	−	0.485385i
$184$		−	0.998829i		−	0.0736346i
$185$	−13.5113			−0.993368
$186$	5.71627	+	34.8656i	0.419137	+	2.55647i
$187$			6.33402i			0.463189i
$188$		−	20.9497i		−	1.52792i
$189$	−5.11643	−	2.95397i	−0.372166	−	0.214870i
$190$		−	13.9359i		−	1.01102i
$191$	−5.05536	−	8.75614i	−0.365793	−	0.633572i	0.623110	−	0.782134i	$-0.285869\pi$
$191$	−5.05536	−	8.75614i	−0.365793	−	0.633572i	−0.988903	+	0.148562i	$0.952535\pi$
$192$	10.2381	−	17.7330i	0.738873	−	1.27977i
$193$	5.87357	+	3.39111i	0.422789	+	0.244097i	0.696270	−	0.717780i	$-0.254842\pi$
$193$	5.87357	+	3.39111i	0.422789	+	0.244097i	−0.273481	+	0.961877i	$0.588175\pi$
$194$	1.65651			0.118930
$195$	21.7306	−	24.7473i	1.55616	−	1.77219i
$196$	6.14424	+	10.6421i	0.438874	+	0.760153i
$197$	4.26406	−	2.46186i	0.303802	−	0.175400i	−0.340348	−	0.940300i	$-0.610545\pi$
$197$	4.26406	−	2.46186i	0.303802	−	0.175400i	0.644149	+	0.764900i	$0.277211\pi$
$198$	−21.5132	+	37.2619i	−1.52888	+	2.64809i
$199$	0.635290	+	1.10035i	0.0450345	+	0.0780020i	0.887664	−	0.460492i	$-0.152327\pi$
$199$	0.635290	+	1.10035i	0.0450345	+	0.0780020i	−0.842630	+	0.538494i	$0.818994\pi$
$200$	0.989508	+	0.571293i	0.0699688	+	0.0403965i
$201$			5.12062i			0.361180i
$202$			34.7120i			2.44233i
$203$	3.30344	+	1.90724i	0.231856	+	0.133862i
$204$	6.38100	+	11.0522i	0.446759	+	0.773810i
$205$	−8.20318	+	14.2083i	−0.572935	+	0.992352i
$206$	−13.1578	+	7.59664i	−0.916745	+	0.529283i
$207$	9.52553	+	16.4987i	0.662070	+	1.14674i
$208$	−11.8333	−	10.3908i	−0.820489	−	0.720471i
$209$	7.40347			0.512109
$210$	6.06308	+	3.50052i	0.418392	+	0.241559i
$211$	−1.78190	+	3.08634i	−0.122671	+	0.212472i	−0.920820	−	0.389988i	$-0.872479\pi$
$211$	−1.78190	+	3.08634i	−0.122671	+	0.212472i	0.798149	+	0.602460i	$0.205813\pi$
$212$	−1.66440	−	2.88283i	−0.114312	−	0.197994i
$213$		−	15.7576i		−	1.07970i
$214$	24.2300	+	13.9892i	1.65633	+	0.956283i
$215$			8.78159i			0.598900i
$216$		−	5.99132i		−	0.407658i
$217$	0.354413	+	2.16169i	0.0240592	+	0.146745i
$218$	34.8354			2.35935
$219$			43.5427i			2.94234i
$220$	7.30510	−	12.6528i	0.492509	−	0.853051i
$221$	7.45301	−	2.52468i	0.501344	−	0.169829i
$222$	−15.2872	−	26.4782i	−1.02601	−	1.77710i
$223$	−13.9231	−	8.03851i	−0.932360	−	0.538298i	−0.0448029	−	0.998996i	$-0.514266\pi$
$223$	−13.9231	−	8.03851i	−0.932360	−	0.538298i	−0.887557	+	0.460697i	$0.847599\pi$
$224$	1.51685	−	2.62726i	0.101349	−	0.175541i
$225$	−21.7930			−1.45287
$226$	8.18720	−	4.72688i	0.544604	−	0.314427i
$227$	21.1769	−	12.2265i	1.40556	−	0.811501i	0.410605	−	0.911813i	$-0.365318\pi$
$227$	21.1769	−	12.2265i	1.40556	−	0.811501i	0.994956	+	0.100312i	$0.0319842\pi$
$228$	12.9183	−	7.45838i	0.855535	−	0.493943i
$229$	−14.8865	−	8.59472i	−0.983727	−	0.567955i	−0.0803338	−	0.996768i	$-0.525599\pi$
$229$	−14.8865	−	8.59472i	−0.983727	−	0.567955i	−0.903393	+	0.428813i	$0.858932\pi$
$230$	−6.83806	−	11.8439i	−0.450888	−	0.780961i
$231$	−1.85965	+	3.22102i	−0.122356	+	0.211927i
$232$			3.86832i			0.253968i
$233$	25.1124			1.64517			0.822585	−	0.568643i	$-0.192531\pi$
$233$	25.1124			1.64517			0.822585	+	0.568643i	$0.192531\pi$
$234$	52.4197	+	10.4615i	3.42679	+	0.683891i
$235$	16.3625	+	28.3407i	1.06737	+	1.84875i
$236$	−3.22279	−	1.86068i	−0.209786	−	0.121120i
$237$	21.7038	+	37.5921i	1.40982	+	2.44187i
$238$	0.836390	+	1.44867i	0.0542151	+	0.0939033i
$239$	17.2799	−	9.97654i	1.11774	−	0.645329i	0.176918	−	0.984226i	$-0.443387\pi$
$239$	17.2799	−	9.97654i	1.11774	−	0.645329i	0.940824	+	0.338897i	$0.110054\pi$
$240$			39.8953i			2.57523i
$241$	−1.10454	−	0.637709i	−0.0711499	−	0.0410784i	0.464003	−	0.885834i	$-0.346413\pi$
$241$	−1.10454	−	0.637709i	−0.0711499	−	0.0410784i	−0.535153	+	0.844755i	$0.679746\pi$
$242$	−4.34791	−	2.51026i	−0.279494	−	0.161366i
$243$	19.9551	+	34.5632i	1.28012	+	2.21723i
$244$	−4.17863			−0.267510
$245$	−16.6238	−	9.59777i	−1.06206	−	0.613179i
$246$	−37.1256			−2.36704
$247$	−2.95096	−	8.71139i	−0.187765	−	0.554293i
$248$	−1.71879	+	1.40736i	−0.109143	+	0.0893676i
$249$		−	18.0025i		−	1.14086i
$250$	−11.6705			−0.738109
$251$	−3.60922	+	6.25136i	−0.227812	+	0.394582i	−0.957159	−	0.289561i	$-0.906491\pi$
$251$	−3.60922	+	6.25136i	−0.227812	+	0.394582i	0.729347	+	0.684144i	$0.239824\pi$
$252$			5.37492i			0.338588i
$253$	6.29207	−	3.63273i	0.395579	−	0.228388i
$254$	−22.1804	−	12.8058i	−1.39172	−	0.803510i
$255$	−17.2644	−	9.96761i	−1.08114	−	0.624196i
$256$	18.7581			1.17238
$257$	−2.29540	−	3.97575i	−0.143183	−	0.248001i	0.785510	−	0.618848i	$-0.212400\pi$
$257$	−2.29540	−	3.97575i	−0.143183	−	0.248001i	−0.928694	+	0.370848i	$0.879067\pi$
$258$	−17.2094	+	9.93585i	−1.07141	+	0.618579i
$259$	−0.947818	−	1.64167i	−0.0588946	−	0.102008i
$260$	−17.7998	−	3.55235i	−1.10390	−	0.220307i
$261$	−36.8910	−	63.8971i	−2.28350	−	3.95513i
$262$	−0.571342	−	0.329865i	−0.0352977	−	0.0203791i
$263$	19.5592			1.20607			0.603037	−	0.797713i	$-0.293957\pi$
$263$	19.5592			1.20607			0.603037	+	0.797713i	$0.293957\pi$
$264$	−3.77180			−0.232138
$265$	4.50321	+	2.59993i	0.276630	+	0.159712i
$266$	1.69327	−	0.977608i	0.103821	−	0.0599410i
$267$	−40.3609	−	23.3024i	−2.47005	−	1.42608i
$268$	2.44403	−	1.41106i	0.149293	−	0.0861941i
$269$	3.20526	+	5.55168i	0.195428	+	0.338492i	0.947041	−	0.321113i	$-0.104057\pi$
$269$	3.20526	+	5.55168i	0.195428	+	0.338492i	−0.751612	+	0.659605i	$0.770724\pi$
$270$	−41.0171	−	71.0436i	−2.49622	−	4.32358i
$271$		−	6.68566i		−	0.406125i	−0.979166	−	0.203063i	$-0.934911\pi$
$271$		−	6.68566i		−	0.406125i	0.979166	−	0.203063i	$-0.0650895\pi$
$272$	−4.76615	+	8.25522i	−0.288991	+	0.500546i
$273$	4.53130	+	0.904320i	0.274246	+	0.0547319i
$274$	−7.61604	−	13.1914i	−0.460102	−	0.796919i
$275$			8.31113i			0.501180i
$276$	7.31934	−	12.6775i	0.440573	−	0.763094i
$277$	−13.7416			−0.825655			−0.412827	−	0.910809i	$-0.635459\pi$
$277$	−13.7416			−0.825655			−0.412827	+	0.910809i	$0.635459\pi$
$278$		−	19.2897i		−	1.15692i
$279$	14.9695	−	39.6385i	0.896201	−	2.37309i
$280$			0.440196i			0.0263067i
$281$		−	7.63249i		−	0.455316i	−0.973741	−	0.227658i	$-0.926893\pi$
$281$		−	7.63249i		−	0.455316i	0.973741	−	0.227658i	$-0.0731068\pi$
$282$	−37.0265	+	64.1317i	−2.20489	+	3.81899i
$283$	3.47343			0.206474			0.103237	−	0.994657i	$-0.467080\pi$
$283$	3.47343			0.206474			0.103237	+	0.994657i	$0.467080\pi$
$284$	−7.52098	+	4.34224i	−0.446288	+	0.257665i
$285$	−11.6506	+	20.1794i	−0.690120	+	1.19532i
$286$	3.98968	−	19.9912i	0.235915	−	1.18210i
$287$	−2.30182			−0.135872
$288$	−50.8179	+	29.3397i	−2.99447	+	1.72886i
$289$	6.11841	+	10.5974i	0.359906	+	0.623376i
$290$	26.4828	+	45.8696i	1.55512	+	2.69355i
$291$	−2.39864	−	1.38486i	−0.140611	−	0.0811818i
$292$	20.7825	−	11.9988i	1.21621	−	0.702177i
$293$	17.5373	+	10.1252i	1.02454	+	0.591519i	0.915416	−	0.402509i	$-0.131862\pi$
$293$	17.5373	+	10.1252i	1.02454	+	0.591519i	0.109125	+	0.994028i	$0.465195\pi$
$294$		−	43.4372i		−	2.53331i
$295$	5.81304			0.338448
$296$	0.961194	−	1.66484i	0.0558683	−	0.0967667i
$297$	37.7420	−	21.7904i	2.19001	−	1.26440i
$298$	19.8468	−	34.3757i	1.14970	−	1.99133i
$299$	−6.78246	−	5.95567i	−0.392240	−	0.344426i
$300$	8.37278	+	14.5021i	0.483403	+	0.837278i
$301$	−1.06700	+	0.616031i	−0.0615007	+	0.0355074i
$302$	−15.7101			−0.904012
$303$	29.0196	−	50.2634i	1.66713	−	2.88755i
$304$	9.64905	+	5.57088i	0.553411	+	0.319512i
$305$	5.65285	−	3.26367i	0.323681	−	0.186877i
$306$		−	32.3559i		−	1.84966i
$307$	9.80736	+	5.66228i	0.559736	+	0.323164i	0.753039	−	0.657975i	$-0.228587\pi$
$307$	9.80736	+	5.66228i	0.559736	+	0.323164i	−0.193304	+	0.981139i	$0.561920\pi$
$308$	2.04982			0.116799
$309$	25.4035			1.44515
$310$	−10.7461	+	28.4551i	−0.610338	+	1.61614i
$311$	−26.9897			−1.53044			−0.765222	−	0.643766i	$-0.777371\pi$
$311$	−26.9897			−1.53044			−0.765222	+	0.643766i	$0.777371\pi$
$312$	1.50340	+	4.43814i	0.0851135	+	0.251260i
$313$	11.9234	−	20.6520i	0.673951	−	1.16732i	−0.302823	−	0.953047i	$-0.597929\pi$
$313$	11.9234	−	20.6520i	0.673951	−	1.16732i	0.976774	−	0.214271i	$-0.0687375\pi$
$314$			30.0626i			1.69653i
$315$	−4.19802	−	7.27118i	−0.236531	−	0.409684i
$316$	11.9616	−	20.7181i	0.672893	−	1.16548i
$317$	10.1857	+	5.88069i	0.572083	+	0.330293i	0.757981	−	0.652277i	$-0.226186\pi$
$317$	10.1857	+	5.88069i	0.572083	+	0.330293i	−0.185898	+	0.982569i	$0.559519\pi$
$318$			11.7667i			0.659841i
$319$	−24.3683	+	14.0690i	−1.36436	+	0.787714i
$320$	15.2664	−	8.81405i	0.853417	−	0.492721i
$321$	−23.3903	−	40.5131i	−1.30552	−	2.26122i
$322$	0.959383	−	1.66170i	0.0534643	−	0.0926029i
$323$	−4.82152	+	2.78370i	−0.268276	+	0.154889i
$324$	23.4117	−	40.5502i	1.30065	−	2.25279i
$325$	9.77941	−	3.31274i	0.542464	−	0.183758i
$326$	15.1755			0.840496
$327$	−50.4421	−	29.1228i	−2.78946	−	1.61049i
$328$	−1.16715	−	2.02157i	−0.0644452	−	0.111622i
$329$	−2.29567	+	3.97622i	−0.126565	+	0.219216i
$330$	−44.7250	+	25.8220i	−2.46203	+	1.42145i
$331$	−5.07397	+	2.92946i	−0.278891	+	0.161018i	−0.632921	−	0.774216i	$-0.718144\pi$
$331$	−5.07397	+	2.92946i	−0.278891	+	0.161018i	0.354030	+	0.935234i	$0.384811\pi$
$332$	−8.59245	+	4.96085i	−0.471572	+	0.272262i
$333$			36.6665i			2.00931i
$334$	14.3262	−	24.8137i	0.783896	−	1.35775i
$335$	−2.20418	+	3.81776i	−0.120427	+	0.208586i
$336$	−4.84743	+	2.79867i	−0.264449	+	0.152680i
$337$	8.18593			0.445916			0.222958	−	0.974828i	$-0.428429\pi$
$337$	8.18593			0.445916			0.222958	+	0.974828i	$0.428429\pi$
$338$	−25.1131	+	3.27379i	−1.36598	+	0.178071i
$339$	−15.8069			−0.858512
$340$			10.9869i			0.595847i
$341$	−15.1168	−	5.70888i	−0.818622	−	0.309153i
$342$	−37.8189			−2.04501
$343$		−	5.44719i		−	0.294121i
$344$	−1.08206	−	0.624725i	−0.0583405	−	0.0336829i
$345$			22.8667i			1.23110i
$346$	35.9487	−	20.7550i	1.93261	−	1.11579i
$347$	11.2534	−	19.4915i	0.604114	−	1.04636i	−0.388076	−	0.921627i	$-0.626860\pi$
$347$	11.2534	−	19.4915i	0.604114	−	1.04636i	0.992191	−	0.124730i	$-0.0398064\pi$
$348$	−28.3468	+	49.0980i	−1.51955	+	2.63193i
$349$			5.79633i			0.310270i	0.987893	+	0.155135i	$0.0495813\pi$
$349$			5.79633i			0.310270i	−0.987893	+	0.155135i	$0.950419\pi$
$350$	1.09746	+	1.90086i	0.0586618	+	0.101605i
$351$	−40.6835	−	35.7242i	−2.17153	−	1.90682i
$352$	11.1892	+	19.3803i	0.596387	+	1.03297i
$353$	15.1377	+	8.73976i	0.805699	+	0.465171i	0.845460	−	0.534039i	$-0.179326\pi$
$353$	15.1377	+	8.73976i	0.805699	+	0.465171i	−0.0397609	+	0.999209i	$0.512660\pi$
$354$	6.57711	+	11.3919i	0.349569	+	0.605472i
$355$	6.78291	−	11.7483i	0.360000	−	0.623538i
$356$			25.6852i			1.36131i
$357$		−	2.79692i		−	0.148029i
$358$	−24.1617	−	13.9497i	−1.27698	−	0.737267i
$359$	7.80566	−	4.50660i	0.411967	−	0.237849i	−0.279667	−	0.960097i	$-0.590224\pi$
$359$	7.80566	−	4.50660i	0.411967	−	0.237849i	0.691635	+	0.722248i	$0.256891\pi$
$360$	4.25726	−	7.37379i	0.224377	−	0.388633i
$361$	−6.24629	−	10.8189i	−0.328752	−	0.569415i
$362$	10.0342	−	5.79324i	0.527385	−	0.304486i
$363$	4.19721	+	7.26979i	0.220297	+	0.381565i
$364$	−0.817039	−	2.41195i	−0.0428245	−	0.126420i
$365$	−18.7431	+	32.4639i	−0.981057	+	1.69924i
$366$	12.7917	+	7.38531i	0.668634	+	0.386036i
$367$	−10.0816	−	17.4618i	−0.526253	−	0.911497i	−0.999532	−	0.0305842i	$-0.990263\pi$
$367$	−10.0816	−	17.4618i	−0.526253	−	0.911497i	0.473279	−	0.880912i	$-0.343070\pi$
$368$	10.9341			0.569977
$369$	38.5581	+	22.2616i	2.00726	+	1.15889i
$370$		−	26.3216i		−	1.36840i
$371$			0.729542i			0.0378759i
$372$	−32.1285	+	5.26753i	−1.66579	+	0.273109i
$373$	−7.83378			−0.405618			−0.202809	−	0.979218i	$-0.565007\pi$
$373$	−7.83378			−0.405618			−0.202809	+	0.979218i	$0.565007\pi$
$374$	−12.3395			−0.638059
$375$	16.8991	+	9.75668i	0.872664	+	0.503833i
$376$	−4.65614			−0.240122
$377$	26.2675	+	23.0655i	1.35284	+	1.18793i
$378$	5.75471	−	9.96746i	0.295990	−	0.512671i
$379$	−21.6672	−	12.5096i	−1.11297	−	0.642573i	−0.173372	−	0.984856i	$-0.555466\pi$
$379$	−21.6672	−	12.5096i	−1.11297	−	0.642573i	−0.939597	+	0.342283i	$0.888800\pi$
$380$	12.8419			0.658776
$381$	21.4116	+	37.0860i	1.09695	+	1.89997i
$382$	17.0581	−	9.84847i	0.872766	−	0.503892i
$383$	17.5110	−	10.1100i	0.894770	−	0.516595i	0.0192700	−	0.999814i	$-0.493866\pi$
$383$	17.5110	−	10.1100i	0.894770	−	0.516595i	0.875500	+	0.483219i	$0.160532\pi$
$384$	−8.95685	−	5.17124i	−0.457077	−	0.263894i
$385$	−2.77299	+	1.60099i	−0.141325	+	0.0815938i
$386$	−6.60630	+	11.4424i	−0.336252	+	0.582405i
$387$	23.8312			1.21141
$388$			1.52647i			0.0774947i
$389$	−8.14692	+	14.1109i	−0.413065	+	0.715450i	−0.995223	−	0.0976259i	$-0.968875\pi$
$389$	−8.14692	+	14.1109i	−0.413065	+	0.715450i	0.582158	+	0.813076i	$0.302208\pi$
$390$	48.2108	+	42.3339i	2.44125	+	2.14366i
$391$	−2.73181	+	4.73164i	−0.138154	+	0.239289i
$392$	2.36525	−	1.36558i	0.119463	−	0.0689720i
$393$	0.551540	+	0.955296i	0.0278215	+	0.0481883i
$394$	4.79601	+	8.30693i	0.241619	+	0.418497i
$395$			37.3699i			1.88028i
$396$	−34.3368	−	19.8244i	−1.72549	−	0.996212i
$397$	10.3254	+	5.96139i	0.518218	+	0.299194i	0.736205	−	0.676758i	$-0.236616\pi$
$397$	10.3254	+	5.96139i	0.518218	+	0.299194i	−0.217987	+	0.975952i	$0.569949\pi$
$398$	−2.14363	+	1.23762i	−0.107450	+	0.0620365i
$399$	−3.26916			−0.163663
$400$	−6.25387	+	10.8320i	−0.312694	+	0.541601i
$401$		−	12.7872i		−	0.638561i	−0.947660	−	0.319280i	$-0.896559\pi$
$401$		−	12.7872i		−	0.638561i	0.947660	−	0.319280i	$-0.103441\pi$
$402$	−9.97561			−0.497538
$403$	−0.692005	+	20.0629i	−0.0344712	+	0.999406i
$404$	−31.9870			−1.59141
$405$			73.1417i			3.63444i
$406$	−3.71555	+	6.43552i	−0.184400	+	0.319390i
$407$	13.9834			0.693131
$408$	2.45639	−	1.41820i	0.121609	−	0.0702112i
$409$	−16.9737	−	9.79976i	−0.839295	−	0.484567i	0.0177298	−	0.999843i	$-0.494356\pi$
$409$	−16.9737	−	9.79976i	−0.839295	−	0.484567i	−0.857024	+	0.515276i	$0.827689\pi$
$410$	−27.6796	−	15.9808i	−1.36700	−	0.789237i
$411$			25.4683i			1.25626i
$412$	−7.00029	−	12.1249i	−0.344880	−	0.597349i
$413$	0.407786	+	0.706306i	0.0200658	+	0.0347551i
$414$	−32.1415	+	18.5569i	−1.57967	+	0.912023i
$415$	7.74923	−	13.4221i	0.380395	−	0.658863i
$416$	18.3442	−	20.8907i	0.899396	−	1.02425i
$417$	−16.1264	+	27.9318i	−0.789714	+	1.36783i
$418$			14.4229i			0.705446i
$419$	27.0879			1.32333			0.661664	−	0.749800i	$-0.269850\pi$
$419$	27.0879			1.32333			0.661664	+	0.749800i	$0.269850\pi$
$420$	−3.22572	+	5.58711i	−0.157399	+	0.272623i
$421$	30.1768	−	17.4226i	1.47073	−	0.849125i	0.471267	−	0.881990i	$-0.343797\pi$
$421$	30.1768	−	17.4226i	1.47073	−	0.849125i	0.999460	+	0.0328657i	$0.0104634\pi$
$422$	−6.01257	−	3.47136i	−0.292687	−	0.168983i
$423$	76.9103	−	44.4042i	3.73951	−	2.15901i
$424$	−0.640718	+	0.369919i	−0.0311160	+	0.0179648i
$425$	−3.12499	−	5.41264i	−0.151584	−	0.262551i
$426$	30.6978			1.48732
$427$	0.793098	+	0.457895i	0.0383807	+	0.0221591i
$428$	−12.8910	+	22.3279i	−0.623112	+	1.07926i
$429$	−22.4899	+	25.6121i	−1.08582	+	1.23656i
$430$	−17.1077			−0.825004
$431$	−5.44350	−	3.14281i	−0.262204	−	0.151384i	0.363135	−	0.931736i	$-0.381706\pi$
$431$	−5.44350	−	3.14281i	−0.262204	−	0.151384i	−0.625340	+	0.780353i	$0.715040\pi$
$432$	65.5863			3.15552
$433$	−0.433677			−0.0208412			−0.0104206	−	0.999946i	$-0.503317\pi$
$433$	−0.433677			−0.0208412			−0.0104206	+	0.999946i	$0.503317\pi$
$434$	−4.21125	+	0.690442i	−0.202146	+	0.0331423i
$435$		−	88.5596i		−	4.24611i
$436$			32.1008i			1.53735i
$437$	5.53053	+	3.19306i	0.264561	+	0.152745i
$438$	−84.8266			−4.05317
$439$	10.2222	+	17.7053i	0.487877	+	0.845029i	0.999903	−	0.0139418i	$-0.00443795\pi$
$439$	10.2222	+	17.7053i	0.487877	+	0.845029i	−0.512025	+	0.858970i	$0.671105\pi$
$440$	−2.81212	−	1.62358i	−0.134063	−	0.0774011i
$441$	−26.0462	+	45.1133i	−1.24029	+	2.14825i
$442$	4.91840	+	14.5194i	0.233944	+	0.690618i
$443$	−9.05329	−	15.6808i	−0.430135	−	0.745015i	0.566750	−	0.823890i	$-0.308201\pi$
$443$	−9.05329	−	15.6808i	−0.430135	−	0.745015i	−0.996885	+	0.0788746i	$0.974867\pi$
$444$	24.3996	−	14.0871i	1.15795	−	0.668545i
$445$	−20.0611	−	34.7469i	−0.950988	−	1.64716i
$446$	15.6600	−	27.1240i	0.741524	−	1.28436i
$447$	−57.4769	+	33.1843i	−2.71856	+	1.56956i
$448$	2.14188	+	1.23662i	0.101194	+	0.0584246i
$449$		−	28.1251i		−	1.32731i	−0.748040	−	0.663654i	$-0.769005\pi$
$449$		−	28.1251i		−	1.32731i	0.748040	−	0.663654i	$-0.230995\pi$
$450$		−	42.4555i		−	2.00137i
$451$	8.48983	−	14.7048i	0.399770	−	0.692423i
$452$	4.35581	+	7.54449i	0.204880	+	0.354863i
$453$	22.7483	+	13.1338i	1.06881	+	0.617078i
$454$	23.8187	+	41.2553i	1.11787	+	1.93621i
$455$	2.98911	+	2.62474i	0.140132	+	0.123050i
$456$	−1.65765	−	2.87113i	−0.0776265	−	0.134453i
$457$			29.7195i			1.39022i	0.718904	+	0.695109i	$0.244644\pi$
$457$			29.7195i			1.39022i	−0.718904	+	0.695109i	$0.755356\pi$
$458$	16.7436	−	29.0008i	0.782377	−	1.35512i
$459$	−16.3864	+	28.3820i	−0.764849	+	1.32476i
$460$	10.9141	−	6.30126i	0.508872	−	0.293798i
$461$			34.5949i			1.61124i	0.592429	+	0.805622i	$0.298169\pi$
$461$			34.5949i			1.61124i	−0.592429	+	0.805622i	$0.701831\pi$
$462$	−6.27494	−	3.62284i	−0.291937	−	0.168550i
$463$		−	40.5868i		−	1.88623i	−0.332471	−	0.943113i	$-0.607882\pi$
$463$		−	40.5868i		−	1.88623i	0.332471	−	0.943113i	$-0.392118\pi$
$464$	−42.3460			−1.96586
$465$	39.3493	−	32.2195i	1.82478	−	1.49414i
$466$			48.9221i			2.26627i
$467$	−26.3998			−1.22164			−0.610818	−	0.791771i	$-0.709159\pi$
$467$	−26.3998			−1.22164			−0.610818	+	0.791771i	$0.709159\pi$
$468$	−9.64027	+	48.3047i	−0.445622	+	2.23289i
$469$	−0.618496			−0.0285595
$470$	−55.2113	+	31.8763i	−2.54671	+	1.47034i
$471$	25.1326	−	43.5310i	1.15805	−	2.00580i
$472$	−0.413541	+	0.716274i	−0.0190348	+	0.0329692i
$473$		−	9.08846i		−	0.417888i
$474$	−73.2342	+	42.2818i	−3.36376	+	1.94207i
$475$	−6.32652	+	3.65262i	−0.290280	+	0.167594i
$476$	−1.33495	+	0.770732i	−0.0611872	+	0.0353264i
$477$	7.05561	−	12.2207i	0.323054	−	0.559546i
$478$	19.4356	+	33.6634i	0.888962	+	1.53973i
$479$	30.8873	+	17.8328i	1.41128	+	0.814801i	0.995509	−	0.0946695i	$-0.0301794\pi$
$479$	30.8873	+	17.8328i	1.41128	+	0.814801i	0.415768	+	0.909471i	$0.363513\pi$
$480$	−70.4322			−3.21477
$481$	−5.57366	−	16.4538i	−0.254137	−	0.750227i
$482$	1.24234	−	2.15179i	0.0565869	−	0.0980114i
$483$	−2.77840	+	1.60411i	−0.126421	+	0.0729894i
$484$	2.31320	−	4.00659i	0.105146	−	0.182118i
$485$	−1.19223	−	2.06500i	−0.0541364	−	0.0937670i
$486$	−67.3335	+	38.8750i	−3.05431	+	1.76341i
$487$	−3.75934	+	2.17046i	−0.170352	+	0.0983529i	−0.582752	−	0.812650i	$-0.698024\pi$
$487$	−3.75934	+	2.17046i	−0.170352	+	0.0983529i	0.412400	+	0.911003i	$0.364691\pi$
$488$			0.928714i			0.0420409i
$489$	−21.9744	−	12.6869i	−0.993715	−	0.573722i
$490$	18.6977	−	32.3853i	0.844675	−	1.46302i
$491$	−4.11707	−	7.13097i	−0.185801	−	0.321816i	0.758045	−	0.652202i	$-0.226155\pi$
$491$	−4.11707	−	7.13097i	−0.185801	−	0.321816i	−0.943846	+	0.330386i	$0.892821\pi$
$492$		−	34.2112i		−	1.54236i
$493$	10.5799	−	18.3249i	0.476495	−	0.825314i
$494$	16.9709	−	5.74883i	0.763556	−	0.258652i
$495$	61.9344			2.78374
$496$	−15.4062	−	18.8154i	−0.691760	−	0.844837i
$497$	1.90329			0.0853743
$498$	35.0712			1.57158
$499$	−25.9484	−	14.9813i	−1.16161	−	0.670656i	−0.209921	−	0.977718i	$-0.567321\pi$
$499$	−25.9484	−	14.9813i	−1.16161	−	0.670656i	−0.951689	+	0.307063i	$0.900654\pi$
$500$		−	10.7544i		−	0.480950i
$501$	−41.4891	+	23.9537i	−1.85360	+	1.07017i
$502$	−12.1784	−	7.03122i	−0.543550	−	0.313819i
$503$	−13.2921	+	23.0225i	−0.592664	+	1.02652i	0.401208	+	0.915987i	$0.368590\pi$
$503$	−13.2921	+	23.0225i	−0.592664	+	1.02652i	−0.993872	+	0.110537i	$0.964743\pi$
$504$	1.19459			0.0532113
$505$	43.2720	−	24.9831i	1.92558	−	1.11173i
$506$	7.07701	+	12.2577i	0.314611	+	0.544923i
$507$	39.1011	+	16.2544i	1.73654	+	0.721881i
$508$	11.8006	−	20.4392i	0.523565	−	0.906841i
$509$	−7.60262	+	4.38937i	−0.336980	+	0.194556i	−0.658936	−	0.752199i	$-0.728993\pi$
$509$	−7.60262	+	4.38937i	−0.336980	+	0.194556i	0.321956	+	0.946755i	$0.395660\pi$
$510$	19.4182	−	33.6332i	0.859851	−	1.48930i
$511$	−5.25932			−0.232659
$512$			30.1929i			1.33435i
$513$	33.1741	+	19.1531i	1.46467	+	0.845628i
$514$	7.74526	−	4.47173i	0.341629	−	0.197240i
$515$	18.9400	+	10.9350i	0.834594	+	0.481853i
$516$	−9.15587	−	15.8584i	−0.403065	−	0.698128i
$517$	−16.9343	−	29.3311i	−0.744770	−	1.28998i
$518$	3.19818	−	1.84647i	0.140520	−	0.0811292i
$519$	−69.4055			−3.04656
$520$	−0.789521	+	3.95607i	−0.0346228	+	0.173485i
$521$	3.01336	−	5.21930i	0.132018	−	0.228662i	−0.792436	−	0.609954i	$-0.791188\pi$
$521$	3.01336	−	5.21930i	0.132018	−	0.228662i	0.924454	+	0.381293i	$0.124521\pi$
$522$	124.480	−	71.8683i	5.44832	−	3.14559i
$523$	−4.72338			−0.206539			−0.103269	−	0.994653i	$-0.532930\pi$
$523$	−4.72338			−0.206539			−0.103269	+	0.994653i	$0.532930\pi$
$524$	0.303970	−	0.526491i	0.0132790	−	0.0229999i
$525$		−	3.66996i		−	0.160170i
$526$			38.1038i			1.66141i
$527$	11.9914	−	1.96601i	0.522353	−	0.0856408i
$528$		−	41.2894i		−	1.79689i
$529$	−16.7329			−0.727519
$530$	−5.06499	+	8.77281i	−0.220009	+	0.381067i
$531$		−	15.7753i		−	0.684588i
$532$	0.900864	+	1.56034i	0.0390574	+	0.0676494i
$533$	−20.6866	−	4.12847i	−0.896036	−	0.178824i
$534$	45.3959	−	78.6281i	1.96447	−	3.40257i
$535$		−	40.2736i		−	1.74118i
$536$	−0.313612	−	0.543192i	−0.0135460	−	0.0234623i
$537$	23.3243	+	40.3988i	1.00652	+	1.74334i
$538$	−10.8154	+	6.24426i	−0.466284	+	0.269209i
$539$	17.2047	+	9.93316i	0.741060	+	0.427851i
$540$	65.4666	−	37.7971i	2.81723	−	1.62653i
$541$	29.0723	+	16.7849i	1.24992	+	0.721640i	0.971093	−	0.238702i	$-0.0767218\pi$
$541$	29.0723	+	16.7849i	1.24992	+	0.721640i	0.278825	+	0.960342i	$0.410055\pi$
$542$	13.0245			0.559451
$543$	−19.3728			−0.831368
$544$	−14.5740	−	8.41429i	−0.624854	−	0.360760i
$545$	−25.0719	−	43.4259i	−1.07396	−	1.86016i
$546$	−1.76173	+	8.82753i	−0.0753950	+	0.377784i
$547$	3.59702	+	6.23022i	0.153797	+	0.266385i	0.932620	−	0.360859i	$-0.117516\pi$
$547$	3.59702	+	6.23022i	0.153797	+	0.266385i	−0.778823	+	0.627244i	$0.784183\pi$
$548$	12.1558	−	7.01816i	0.519271	−	0.299801i
$549$	−8.85687	−	15.3405i	−0.378002	−	0.654718i
$550$	−16.1911			−0.690392
$551$	−21.4190	−	12.3662i	−0.912478	−	0.526820i
$552$	−2.81761	−	1.62675i	−0.119925	−	0.0692389i
$553$	−4.54058	+	2.62151i	−0.193085	+	0.111478i
$554$		−	26.7704i		−	1.13737i
$555$	−22.0052	+	38.1140i	−0.934067	+	1.61785i
$556$	17.7755			0.753847
$557$		−	22.0790i		−	0.935519i	−0.883856	−	0.467760i	$-0.845061\pi$
$557$		−	22.0790i		−	0.935519i	0.883856	−	0.467760i	$-0.154939\pi$
$558$	77.2208	+	29.1625i	3.26902	+	1.23455i
$559$	−10.6941	+	3.62258i	−0.452311	+	0.153219i
$560$	−4.81877			−0.203630
$561$	17.8677	+	10.3159i	0.754375	+	0.435538i
$562$	14.8691			0.627213
$563$	−8.70440	−	15.0765i	−0.366847	−	0.635397i	0.622224	−	0.782839i	$-0.286229\pi$
$563$	−8.70440	−	15.0765i	−0.366847	−	0.635397i	−0.989071	+	0.147442i	$0.952896\pi$
$564$	−59.0973	−	34.1198i	−2.48844	−	1.43670i
$565$	−11.7851	−	6.80411i	−0.495802	−	0.286251i
$566$			6.76667i			0.284425i
$567$	−8.88700	+	5.13091i	−0.373219	+	0.215478i
$568$	0.965076	+	1.67156i	0.0404937	+	0.0701371i
$569$	3.33911	+	5.78351i	0.139983	+	0.242457i	0.927490	−	0.373848i	$-0.121962\pi$
$569$	3.33911	+	5.78351i	0.139983	+	0.242457i	−0.787507	+	0.616306i	$0.788629\pi$
$570$	−39.3119	−	22.6968i	−1.64660	−	0.950663i
$571$	−3.28689	−	5.69306i	−0.137552	−	0.238247i	0.789017	−	0.614371i	$-0.210590\pi$
$571$	−3.28689	−	5.69306i	−0.137552	−	0.238247i	−0.926569	+	0.376124i	$0.877257\pi$
$572$	18.4218	+	3.67648i	0.770255	+	0.153721i
$573$	−32.9337			−1.37582
$574$		−	4.48423i		−	0.187168i
$575$	−3.58452	+	6.20858i	−0.149485	+	0.258916i
$576$	−23.9193	−	41.4295i	−0.996639	−	1.72623i
$577$	−3.95027	−	2.28069i	−0.164452	−	0.0949463i	0.415515	−	0.909586i	$-0.363601\pi$
$577$	−3.95027	−	2.28069i	−0.164452	−	0.0949463i	−0.579967	+	0.814640i	$0.696935\pi$
$578$	−20.6451	+	11.9194i	−0.858721	+	0.495783i
$579$	19.1320	−	11.0459i	0.795099	−	0.459051i
$580$	−42.2687	+	24.4039i	−1.75511	+	1.01332i
$581$	2.17444			0.0902111
$582$	2.69788	−	4.67286i	0.111831	−	0.193696i
$583$	−4.66057	−	2.69078i	−0.193021	−	0.111441i
$584$	−2.66677	−	4.61898i	−0.110352	−	0.191135i
$585$	−24.6865	−	72.8759i	−1.02066	−	3.01305i
$586$	−19.7251	+	34.1649i	−0.814837	+	1.41134i
$587$			39.3937i			1.62595i	0.582298	+	0.812976i	$0.302154\pi$
$587$			39.3937i			1.62595i	−0.582298	+	0.812976i	$0.697846\pi$
$588$	40.0273			1.65070
$589$	−2.29796	−	14.0160i	−0.0946856	−	0.577521i
$590$			11.3245i			0.466224i
$591$		−	16.0380i		−	0.659717i
$592$	18.2248	+	10.5221i	0.749033	+	0.432455i
$593$		−	3.85560i		−	0.158330i	−0.996862	−	0.0791652i	$-0.974775\pi$
$593$		−	3.85560i		−	0.158330i	0.996862	−	0.0791652i	$-0.0252255\pi$
$594$	42.4503	+	73.5262i	1.74176	+	3.01681i
$595$	1.20394	−	2.08529i	0.0493568	−	0.0854885i
$596$	31.6771	+	18.2888i	1.29755	+	0.749139i
$597$	4.13867			0.169384
$598$	11.6024	−	13.2131i	0.474458	−	0.540323i
$599$	−6.83397	−	11.8368i	−0.279228	−	0.483638i	0.691965	−	0.721931i	$-0.256745\pi$
$599$	−6.83397	−	11.8368i	−0.279228	−	0.483638i	−0.971193	+	0.238293i	$0.923412\pi$
$600$	3.22313	−	1.86088i	0.131584	−	0.0759699i
$601$	−9.64453	+	16.7048i	−0.393409	+	0.681404i	−0.992897	−	0.118980i	$-0.962038\pi$
$601$	−9.64453	+	16.7048i	−0.393409	+	0.681404i	0.599488	+	0.800384i	$0.295371\pi$
$602$	−1.20011	−	2.07864i	−0.0489127	−	0.0847192i
$603$	10.3605	+	5.98165i	0.421913	+	0.243592i
$604$		−	14.4768i		−	0.589052i
$605$			7.22680i			0.293811i
$606$	97.9193	+	56.5338i	3.97770	+	2.29653i
$607$	−3.13298	−	5.42648i	−0.127164	−	0.220254i	0.795413	−	0.606068i	$-0.207254\pi$
$607$	−3.13298	−	5.42648i	−0.127164	−	0.220254i	−0.922577	+	0.385814i	$0.873921\pi$
$608$	−9.83498	+	17.0347i	−0.398861	+	0.690847i
$609$	10.7603	−	6.21248i	0.436030	−	0.251742i
$610$	6.35805	+	11.0125i	0.257430	+	0.445882i
$611$	−27.7630	+	31.6171i	−1.12317	+	1.27909i
$612$	29.8159			1.20523
$613$	25.0505	+	14.4629i	1.01178	+	0.584151i	0.911712	−	0.410829i	$-0.134761\pi$
$613$	25.0505	+	14.4629i	1.01178	+	0.584151i	0.100068	+	0.994981i	$0.468094\pi$
$614$	−11.0308	+	19.1060i	−0.445168	+	0.771054i
$615$	26.7203	+	46.2808i	1.07746	+	1.86622i
$616$		−	0.455578i		−	0.0183558i
$617$	35.6906	+	20.6060i	1.43685	+	0.829566i	0.997630	−	0.0688134i	$-0.0219213\pi$
$617$	35.6906	+	20.6060i	1.43685	+	0.829566i	0.439221	+	0.898379i	$0.355255\pi$
$618$			49.4892i			1.99075i
$619$			48.9910i			1.96911i	0.175064	+	0.984557i	$0.443987\pi$
$619$			48.9910i			1.96911i	−0.175064	+	0.984557i	$0.556013\pi$
$620$	−26.2214	−	9.90252i	−1.05308	−	0.397695i
$621$	37.5920			1.50852
$622$		−	52.5793i		−	2.10824i
$623$	2.81459	−	4.87501i	0.112764	−	0.195313i
$624$	−48.5838	+	16.4576i	−1.94491	+	0.658831i
$625$	15.5589	+	26.9487i	0.622354	+	1.07795i
$626$	40.2326	+	23.2283i	1.60802	+	0.928390i
$627$	12.0577	−	20.8845i	0.481537	−	0.834047i
$628$	−27.7026			−1.10546
$629$	−9.10671	+	5.25776i	−0.363108	+	0.209641i
$630$	14.1652	−	8.17826i	0.564354	−	0.325830i
$631$	−31.2758	+	18.0571i	−1.24507	+	0.718842i	−0.970122	−	0.242617i	$-0.921994\pi$
$631$	−31.2758	+	18.0571i	−1.24507	+	0.718842i	−0.274948	+	0.961459i	$0.588661\pi$
$632$	−4.60466	−	2.65850i	−0.183164	−	0.105750i
$633$	5.80418	+	10.0531i	0.230696	+	0.399577i
$634$	−11.4563	+	19.8429i	−0.454989	+	0.788064i
$635$			36.8668i			1.46301i
$636$	−10.8429			−0.429951
$637$	4.83033	−	24.2035i	0.191385	−	0.958976i
$638$	−27.4082	−	47.4724i	−1.08510	−	1.87945i
$639$	−31.8823	−	18.4073i	−1.26125	−	0.728181i
$640$	−4.45195	−	7.71100i	−0.175979	−	0.304804i
$641$	12.0437	+	20.8603i	0.475698	+	0.823933i	0.999612	−	0.0278376i	$-0.00886214\pi$
$641$	12.0437	+	20.8603i	0.475698	+	0.823933i	−0.523914	+	0.851771i	$0.675529\pi$
$642$	78.9246	−	45.5672i	3.11491	−	1.79839i
$643$		−	1.44128i		−	0.0568384i	−0.999596	−	0.0284192i	$-0.990953\pi$
$643$		−	1.44128i		−	0.0568384i	0.999596	−	0.0284192i	$-0.00904733\pi$
$644$	1.53125	+	0.884070i	0.0603398	+	0.0348372i
$645$	24.7721	+	14.3022i	0.975400	+	0.563147i
$646$	−5.42301	−	9.39292i	−0.213365	−	0.369560i
$647$	−38.2012			−1.50184			−0.750922	−	0.660391i	$-0.770391\pi$
$647$	−38.2012			−1.50184			−0.750922	+	0.660391i	$0.770391\pi$
$648$	−9.01242	−	5.20332i	−0.354041	−	0.204406i
$649$	−6.01617			−0.236155
$650$	6.45364	+	19.0515i	0.253133	+	0.747262i
$651$	6.67516	+	2.52088i	0.261620	+	0.0988011i
$652$			13.9842i			0.547665i
$653$	−3.67676			−0.143883			−0.0719413	−	0.997409i	$-0.522919\pi$
$653$	−3.67676			−0.143883			−0.0719413	+	0.997409i	$0.522919\pi$
$654$	56.7348	−	98.2676i	2.21851	−	3.84257i
$655$			0.949648i			0.0371058i
$656$	22.1298	−	12.7767i	0.864025	−	0.498845i
$657$	88.0997	+	50.8644i	3.43710	+	1.98441i
$658$	−7.74618	−	4.47226i	−0.301977	−	0.174347i
$659$	−26.5259			−1.03330			−0.516652	−	0.856196i	$-0.672822\pi$
$659$	−26.5259			−1.03330			−0.516652	+	0.856196i	$0.672822\pi$
$660$	−23.7949	−	41.2140i	−0.926217	−	1.60425i
$661$	−13.5103	+	7.80019i	−0.525491	+	0.303392i	−0.739178	−	0.673510i	$-0.764786\pi$
$661$	−13.5103	+	7.80019i	−0.525491	+	0.303392i	0.213687	+	0.976902i	$0.431453\pi$
$662$	−5.70695	−	9.88473i	−0.221807	−	0.384181i
$663$	5.01646	−	25.1361i	0.194823	−	0.976205i
$664$	1.10256	+	1.90970i	0.0427878	+	0.0741107i
$665$	−2.43737	−	1.40722i	−0.0945173	−	0.0545696i
$666$	−71.4309			−2.76789
$667$	−24.2714			−0.939793
$668$	22.8658	+	13.2016i	0.884705	+	0.510785i
$669$	−45.3518	+	26.1839i	−1.75340	+	1.01233i
$670$	−7.43747	−	4.29402i	−0.287334	−	0.165893i
$671$	−5.85038	+	3.37772i	−0.225851	+	0.130395i
$672$	−4.94084	−	8.55778i	−0.190597	−	0.330123i
$673$	6.45759	+	11.1849i	0.248922	+	0.431145i	0.963227	−	0.268689i	$-0.0865905\pi$
$673$	6.45759	+	11.1849i	0.248922	+	0.431145i	−0.714305	+	0.699834i	$0.753257\pi$
$674$			15.9472i			0.614264i
$675$	−21.5012	+	37.2412i	−0.827582	+	1.43341i
$676$	−3.01679	−	23.1417i	−0.116030	−	0.890066i
$677$	5.27552	+	9.13747i	0.202755	+	0.351181i	0.949415	−	0.314024i	$-0.101677\pi$
$677$	5.27552	+	9.13747i	0.202755	+	0.351181i	−0.746660	+	0.665206i	$0.768344\pi$
$678$		−	30.7938i		−	1.18263i
$679$	0.167271	−	0.289721i	0.00641925	−	0.0111185i
$680$	2.44187			0.0936413
$681$		−	79.6509i		−	3.05223i
$682$	11.1216	−	29.4495i	0.425869	−	1.12768i
$683$			6.79560i			0.260027i	0.991512	+	0.130013i	$0.0415020\pi$
$683$			6.79560i			0.260027i	−0.991512	+	0.130013i	$0.958498\pi$
$684$		−	34.8500i		−	1.33252i
$685$	−10.9629	+	18.9883i	−0.418871	+	0.725506i
$686$	10.6118			0.405161
$687$	−48.4899	+	27.9956i	−1.85000	+	1.06810i
$688$	6.83879	−	11.8451i	0.260726	−	0.451591i
$689$	−1.30848	+	6.55644i	−0.0498492	+	0.249780i
$690$	−44.5473			−1.69589
$691$	12.8471	−	7.41725i	0.488725	−	0.282166i	−0.235320	−	0.971918i	$-0.575614\pi$
$691$	12.8471	−	7.41725i	0.488725	−	0.282166i	0.724045	+	0.689752i	$0.242281\pi$
$692$	19.1257	+	33.1266i	0.727049	+	1.25929i
$693$	4.34471	+	7.52526i	0.165042	+	0.285861i
$694$	37.9718	+	21.9231i	1.44139	+	0.832188i
$695$	−24.0466	+	13.8833i	−0.912140	+	0.526624i
$696$	10.9122	+	6.30015i	0.413625	+	0.238807i
$697$			12.7687i			0.483649i
$698$	−11.2920			−0.427408
$699$	40.8994	−	70.8399i	1.54696	−	2.67941i
$700$	−1.75164	+	1.01131i	−0.0662057	+	0.0382239i
$701$	−23.0742	+	39.9657i	−0.871500	+	1.50948i	−0.0110560	+	0.999939i	$0.503519\pi$
$701$	−23.0742	+	39.9657i	−0.871500	+	1.50948i	−0.860444	+	0.509544i	$0.829814\pi$
$702$	69.5952	−	79.2567i	2.62670	−	2.99135i
$703$	6.14549	+	10.6443i	0.231782	+	0.401457i
$704$	−15.7999	+	9.12205i	−0.595480	+	0.343800i
$705$	106.596			4.01462
$706$	−17.0262	+	29.4902i	−0.640788	+	1.10988i
$707$	6.07108	+	3.50514i	0.228326	+	0.131824i
$708$	−10.4976	+	6.06079i	−0.394524	+	0.227779i
$709$		−	11.5896i		−	0.435258i	−0.976032	−	0.217629i	$-0.930168\pi$
$709$		−	11.5896i		−	0.435258i	0.976032	−	0.217629i	$-0.0698323\pi$
$710$	22.8873	+	13.2140i	0.858944	+	0.495911i
$711$	101.413			3.80330
$712$	5.70861			0.213939
$713$	−8.83037	−	10.7844i	−0.330700	−	0.403879i
$714$	5.44876			0.203915
$715$	−27.7925	+	9.41462i	−1.03938	+	0.352087i
$716$	12.8547	−	22.2649i	0.480401	−	0.832079i
$717$		−	64.9933i		−	2.42722i
$718$	8.77943	+	15.2064i	0.327645	+	0.567498i
$719$	−5.78032	+	10.0118i	−0.215570	+	0.373377i	−0.953449	−	0.301556i	$-0.902494\pi$
$719$	−5.78032	+	10.0118i	−0.215570	+	0.373377i	0.737879	+	0.674933i	$0.235827\pi$
$720$	80.7200	+	46.6037i	3.00826	+	1.73682i
$721$			3.06837i			0.114272i
$722$	21.0766	−	12.1686i	0.784388	−	0.452867i
$723$	−3.59784	+	2.07721i	−0.133805	+	0.0772524i
$724$	5.33846	+	9.24649i	0.198402	+	0.343643i
$725$	13.8823	−	24.0449i	0.515577	−	0.893006i
$726$	−14.1625	+	8.17670i	−0.525618	+	0.303466i
$727$	6.81251	−	11.7996i	0.252662	−	0.437624i	−0.711596	−	0.702589i	$-0.752027\pi$
$727$	6.81251	−	11.7996i	0.252662	−	0.437624i	0.964258	+	0.264965i	$0.0853606\pi$
$728$	−0.536062	+	0.181589i	−0.0198678	+	0.00673015i
$729$	51.7517			1.91673
$730$	−63.2438	−	36.5138i	−2.34076	−	1.35144i
$731$	3.41726	+	5.91887i	0.126392	+	0.218917i
$732$	−6.80555	+	11.7876i	−0.251540	+	0.435680i
$733$	−31.7908	+	18.3544i	−1.17422	+	0.677936i	−0.954670	−	0.297665i	$-0.903792\pi$
$733$	−31.7908	+	18.3544i	−1.17422	+	0.677936i	−0.219549	+	0.975601i	$0.570459\pi$
$734$	34.0177	−	19.6401i	1.25562	−	0.724931i
$735$	−54.1489	+	31.2629i	−1.99731	+	1.15315i
$736$			19.3033i			0.711528i
$737$	2.28121	−	3.95116i	0.0840293	−	0.145543i
$738$	−43.3683	+	75.1161i	−1.59641	+	2.76506i
$739$	9.12783	−	5.26995i	0.335773	−	0.193858i	−0.322629	−	0.946526i	$-0.604566\pi$
$739$	9.12783	−	5.26995i	0.335773	−	0.193858i	0.658401	+	0.752667i	$0.271233\pi$
$740$	24.2553			0.891644
$741$	−29.3801	−	5.86346i	−1.07931	−	0.215399i
$742$	−1.42124			−0.0521754
$743$			15.6120i			0.572747i	0.958118	+	0.286374i	$0.0924498\pi$
$743$			15.6120i			0.572747i	−0.958118	+	0.286374i	$0.907550\pi$
$744$	1.17072	+	7.14067i	0.0429209	+	0.261790i
$745$	−57.1370			−2.09334
$746$		−	15.2612i		−	0.558752i
$747$	−36.4244	−	21.0297i	−1.33270	−	0.769435i
$748$		−	11.3708i		−	0.415757i
$749$	4.89339	−	2.82520i	0.178801	−	0.103231i
$750$	−19.0072	+	32.9215i	−0.694046	+	1.20212i
$751$	4.70463	−	8.14866i	0.171674	−	0.297349i	−0.767331	−	0.641251i	$-0.778416\pi$
$751$	4.70463	−	8.14866i	0.171674	−	0.297349i	0.939005	+	0.343903i	$0.111749\pi$
$752$		−	50.9702i		−	1.85869i
$753$	11.7563	+	20.3626i	0.428425	+	0.742054i
$754$	−44.9344	+	51.1724i	−1.63642	+	1.86359i
$755$	11.3069	+	19.5842i	0.411501	+	0.712741i
$756$	9.18499	+	5.30296i	0.334055	+	0.192867i
$757$	−11.7570	−	20.3638i	−0.427317	−	0.740135i	0.569317	−	0.822118i	$-0.307208\pi$
$757$	−11.7570	−	20.3638i	−0.427317	−	0.740135i	−0.996634	+	0.0819835i	$0.973875\pi$
$758$	24.3702	−	42.2104i	0.885165	−	1.53315i
$759$		−	23.6658i		−	0.859014i
$760$		−	2.85415i		−	0.103531i
$761$	−25.1743	−	14.5344i	−0.912567	−	0.526871i	−0.0313111	−	0.999510i	$-0.509968\pi$
$761$	−25.1743	−	14.5344i	−0.912567	−	0.526871i	−0.881256	+	0.472639i	$0.843302\pi$
$762$	−72.2483	+	41.7125i	−2.61728	+	1.51109i
$763$	3.51761	−	6.09267i	0.127346	−	0.220569i
$764$	9.07535	+	15.7190i	0.328335	+	0.568692i
$765$	−40.3348	+	23.2873i	−1.45831	+	0.841955i
$766$	19.6955	+	34.1136i	0.711627	+	1.23257i
$767$	2.39799	+	7.07901i	0.0865865	+	0.255608i
$768$	30.5505	−	52.9150i	1.10240	−	1.90940i
$769$	−17.0600	−	9.84957i	−0.615198	−	0.355184i	0.159799	−	0.987150i	$-0.448915\pi$
$769$	−17.0600	−	9.84957i	−0.615198	−	0.355184i	−0.774997	+	0.631965i	$0.782249\pi$
$770$	−3.11892	−	5.40213i	−0.112398	−	0.194679i
$771$	−14.9536			−0.538542
$772$	−10.5442	−	6.08769i	−0.379494	−	0.219101i
$773$			6.51384i			0.234287i	0.993115	+	0.117143i	$0.0373737\pi$
$773$			6.51384i			0.234287i	−0.993115	+	0.117143i	$0.962626\pi$
$774$			46.4263i			1.66876i
$775$	15.7344	−	2.57968i	0.565197	−	0.0926650i
$776$	0.339262			0.0121788
$777$	−6.17467			−0.221515
$778$	−27.4898	−	15.8712i	−0.985556	−	0.569011i
$779$	14.9246			0.534729
$780$	−39.0106	+	44.4262i	−1.39680	+	1.59071i
$781$	−7.01993	+	12.1589i	−0.251193	+	0.435079i
$782$	−9.21782	−	5.32191i	−0.329629	−	0.190311i
$783$	−145.588			−5.20291
$784$	14.9488	+	25.8921i	0.533885	+	0.924717i
$785$	37.4761	−	21.6368i	1.33758	−	0.772251i
$786$	−1.86104	+	1.07447i	−0.0663810	+	0.0383251i
$787$	4.03015	+	2.32681i	0.143659	+	0.0829418i	0.570107	−	0.821571i	$-0.306902\pi$
$787$	4.03015	+	2.32681i	0.143659	+	0.0829418i	−0.426448	+	0.904512i	$0.640235\pi$
$788$	−7.65482	+	4.41951i	−0.272692	+	0.157439i
$789$	31.8552	−	55.1748i	1.13408	−	1.96428i
$790$	−72.8012			−2.59015
$791$		−	1.90924i		−	0.0678848i
$792$	−4.40602	+	7.63146i	−0.156561	+	0.271172i
$793$	6.30635	+	5.53760i	0.223945	+	0.196646i
$794$	−11.6135	+	20.1152i	−0.412149	+	0.713863i
$795$	14.6683	−	8.46876i	0.520232	−	0.300356i
$796$	−1.14047	−	1.97535i	−0.0404228	−	0.0700144i
$797$	13.1898	+	22.8454i	0.467208	+	0.809227i	0.999298	−	0.0374602i	$-0.0119268\pi$
$797$	13.1898	+	22.8454i	0.467208	+	0.809227i	−0.532091	+	0.846687i	$0.678593\pi$
$798$		−	6.36873i		−	0.225451i
$799$	22.0570	+	12.7346i	0.780320	+	0.450518i
$800$	−19.1231	−	11.0407i	−0.676105	−	0.390349i
$801$	−94.2951	+	54.4413i	−3.33175	+	1.92359i
$802$	24.9110			0.879639
$803$	19.3980	−	33.5984i	0.684541	−	1.18566i
$804$		−	9.19250i		−	0.324195i
$805$	−2.76197			−0.0973466
$806$	−39.0851	−	1.34811i	−1.37671	−	0.0474853i
$807$	20.8810			0.735048
$808$			7.10921i			0.250101i
$809$	12.1653	−	21.0709i	0.427708	−	0.740812i	−0.568961	−	0.822365i	$-0.692654\pi$
$809$	12.1653	−	21.0709i	0.427708	−	0.740812i	0.996669	+	0.0815524i	$0.0259878\pi$
$810$	−142.489			−5.00656
$811$	20.1475	−	11.6322i	0.707476	−	0.408461i	−0.102650	−	0.994718i	$-0.532732\pi$
$811$	20.1475	−	11.6322i	0.707476	−	0.408461i	0.810126	+	0.586256i	$0.199399\pi$
$812$	−5.93032	−	3.42387i	−0.208114	−	0.120154i
$813$	−18.8597	−	10.8886i	−0.661437	−	0.381881i
$814$			27.2414i			0.954811i
$815$	−10.9222	−	18.9178i	−0.382589	−	0.662663i
$816$	15.5248	+	26.8898i	0.543478	+	0.941331i
$817$	6.91823	−	3.99424i	0.242038	−	0.139741i
$818$	19.0912	−	33.0669i	0.667507	−	1.15616i
$819$	7.12294	−	8.11176i	0.248896	−	0.283448i
$820$	14.7263	−	25.5067i	0.514265	−	0.890732i
$821$			15.3731i			0.536525i	0.963346	+	0.268262i	$0.0864494\pi$
$821$			15.3731i			0.536525i	−0.963346	+	0.268262i	$0.913551\pi$
$822$	−49.6155			−1.73054
$823$	−3.32392	+	5.75721i	−0.115865	+	0.200684i	−0.918125	−	0.396291i	$-0.870297\pi$
$823$	−3.32392	+	5.75721i	−0.115865	+	0.200684i	0.802260	+	0.596974i	$0.203631\pi$
$824$	−2.69479	+	1.55584i	−0.0938774	+	0.0542001i
$825$	23.4450	+	13.5359i	0.816248	+	0.471261i
$826$	−1.37597	+	0.794419i	−0.0478762	+	0.0276414i
$827$	5.75736	−	3.32401i	0.200203	−	0.115587i	−0.396547	−	0.918014i	$-0.629792\pi$
$827$	5.75736	−	3.32401i	0.200203	−	0.115587i	0.596750	+	0.802427i	$0.296458\pi$
$828$	−17.1002	−	29.6184i	−0.594272	−	1.02931i
$829$	−2.47043			−0.0858017			−0.0429008	−	0.999079i	$-0.513660\pi$
$829$	−2.47043			−0.0858017			−0.0429008	+	0.999079i	$0.513660\pi$
$830$	26.1479	+	15.0965i	0.907606	+	0.524007i
$831$	−22.3803	+	38.7639i	−0.776366	+	1.34470i
$832$	17.0313	+	14.9552i	0.590453	+	0.518477i
$833$	−14.9395			−0.517622
$834$	−54.4146	−	31.4163i	−1.88422	−	1.08786i
$835$	−41.2438			−1.42730
$836$	−13.2907			−0.459667
$837$	−52.9676	−	64.6886i	−1.83083	−	2.23597i
$838$			52.7706i			1.82293i
$839$		−	40.1371i		−	1.38569i	−0.721089	−	0.692843i	$-0.756358\pi$
$839$		−	40.1371i		−	1.38569i	0.721089	−	0.692843i	$-0.243642\pi$
$840$	1.24175	+	0.716926i	0.0428446	+	0.0247363i
$841$	64.9997			2.24137
$842$	33.9414	+	58.7882i	1.16970	+	2.02598i
$843$	−21.5306	−	12.4307i	−0.741552	−	0.428135i
$844$	3.19885	−	5.54057i	0.110109	−	0.190714i
$845$	22.1557	+	28.9498i	0.762179	+	0.995905i
$846$	86.5050	+	149.831i	2.97410	+	5.15130i
$847$	−0.878084	+	0.506962i	−0.0301713	+	0.0174194i
$848$	−4.04946	−	7.01386i	−0.139059	−	0.240857i
$849$	5.65701	−	9.79823i	0.194148	−	0.336274i
$850$	10.5445	−	6.08787i	0.361673	−	0.208812i
$851$	10.4459	+	6.03093i	0.358080	+	0.206737i
$852$			28.2880i			0.969131i
$853$		−	36.3668i		−	1.24518i	−0.782549	−	0.622588i	$-0.786081\pi$
$853$		−	36.3668i		−	1.24518i	0.782549	−	0.622588i	$-0.213919\pi$
$854$	−0.892037	+	1.54505i	−0.0305249	+	0.0528707i
$855$	27.2192	+	47.1451i	0.930877	+	1.61233i
$856$	4.96245	+	2.86507i	0.169613	+	0.0979261i
$857$	5.70845	+	9.88733i	0.194997	+	0.337745i	0.946900	−	0.321530i	$-0.104197\pi$
$857$	5.70845	+	9.88733i	0.194997	+	0.337745i	−0.751903	+	0.659274i	$0.770864\pi$
$858$	−49.8955	−	43.8132i	−1.70340	−	1.49576i
$859$	14.3563	+	24.8658i	0.489829	+	0.848409i	0.999931	−	0.0117047i	$-0.00372582\pi$
$859$	14.3563	+	24.8658i	0.489829	+	0.848409i	−0.510102	+	0.860114i	$0.670392\pi$
$860$		−	15.7647i		−	0.537571i
$861$	−3.74887	+	6.49323i	−0.127761	+	0.221289i
$862$	6.12258	−	10.6046i	0.208536	−	0.361195i
$863$	−28.1044	+	16.2261i	−0.956683	+	0.552341i	−0.895151	−	0.445764i	$-0.852932\pi$
$863$	−28.1044	+	16.2261i	−0.956683	+	0.552341i	−0.0615327	+	0.998105i	$0.519599\pi$
$864$			115.788i			3.93918i
$865$	−51.7463	−	29.8758i	−1.75943	−	1.01581i
$866$		−	0.844858i		−	0.0287094i
$867$	39.8591			1.35368
$868$	−0.636241	−	3.88066i	−0.0215954	−	0.131718i
$869$		−	38.6757i		−	1.31198i
$870$	172.525			5.84915
$871$	−5.55846	−	1.10931i	−0.188341	−	0.0375876i
$872$	7.13449			0.241604
$873$	−5.60395	+	3.23544i	−0.189665	+	0.109503i
$874$	−6.22047	+	10.7742i	−0.210411	+	0.364442i
$875$	−1.17846	+	2.04116i	−0.0398394	+	0.0690038i
$876$		−	78.1676i		−	2.64104i
$877$	8.37150	−	4.83329i	0.282685	−	0.163208i	−0.351953	−	0.936018i	$-0.614482\pi$
$877$	8.37150	−	4.83329i	0.282685	−	0.163208i	0.634638	+	0.772809i	$0.281149\pi$
$878$	−34.4922	+	19.9141i	−1.16405	+	0.672067i
$879$	57.1244	−	32.9808i	1.92676	−	1.11242i
$880$	17.7731	−	30.7840i	0.599132	−	1.03773i
$881$	8.79186	+	15.2279i	0.296205	+	0.513043i	0.975265	−	0.221041i	$-0.0709454\pi$
$881$	8.79186	+	15.2279i	0.296205	+	0.513043i	−0.679059	+	0.734083i	$0.737612\pi$
$882$	−87.8864	−	50.7412i	−2.95929	−	1.70855i
$883$	17.7866			0.598566			0.299283	−	0.954164i	$-0.403252\pi$
$883$	17.7866			0.598566			0.299283	+	0.954164i	$0.403252\pi$
$884$	−13.3796	+	4.53230i	−0.450005	+	0.152438i
$885$	9.46742	−	16.3981i	0.318244	−	0.551215i
$886$	30.5481	−	17.6370i	1.02628	−	0.592525i
$887$	0.448148	−	0.776215i	0.0150473	−	0.0260627i	−0.858404	−	0.512975i	$-0.828543\pi$
$887$	0.448148	−	0.776215i	0.0150473	−	0.0260627i	0.873451	+	0.486912i	$0.161877\pi$
$888$	−3.13090	−	5.42288i	−0.105066	−	0.181980i
$889$	−4.47945	+	2.58621i	−0.150236	+	0.0867388i
$890$	67.6913	−	39.0816i	2.26902	−	1.31002i
$891$		−	75.6976i		−	2.53596i
$892$	24.9947	+	14.4307i	0.836884	+	0.483175i
$893$	14.8847	−	25.7811i	0.498099	−	0.862733i
$894$	−64.6472	−	111.972i	−2.16212	−	3.74491i
$895$			40.1599i			1.34240i
$896$	0.624610	−	1.08186i	0.0208668	−	0.0361423i
$897$	−27.8467	+	9.43298i	−0.929774	+	0.314958i
$898$	54.7913			1.82841
$899$	34.1987	+	41.7665i	1.14059	+	1.39299i
$900$	39.1226			1.30409
$901$	4.04693			0.134823
$902$	28.6468	+	16.5393i	0.953835	+	0.550697i
$903$			4.01320i			0.133551i
$904$	1.67679	−	0.968092i	0.0557690	−	0.0321983i
$905$	−14.4437	−	8.33909i	−0.480126	−	0.277201i
$906$	−25.5862	+	44.3166i	−0.850045	+	1.47232i
$907$	34.9557			1.16069			0.580343	−	0.814372i	$-0.302919\pi$
$907$	34.9557			1.16069			0.580343	+	0.814372i	$0.302919\pi$
$908$	−38.0167	+	21.9489i	−1.26163	+	0.728401i
$909$	−67.7984	−	117.430i	−2.24873	−	3.89492i
$910$	−5.11332	+	5.82316i	−0.169505	+	0.193036i
$911$	−5.58653	+	9.67615i	−0.185090	+	0.320585i	−0.943607	−	0.331068i	$-0.892591\pi$
$911$	−5.58653	+	9.67615i	−0.185090	+	0.320585i	0.758517	+	0.651653i	$0.225924\pi$
$912$	31.4299	−	18.1461i	1.04075	−	0.600876i
$913$	−8.02002	+	13.8911i	−0.265424	+	0.459728i
$914$	−57.8973			−1.91507
$915$		−	21.2616i		−	0.702886i
$916$	26.7241	+	15.4292i	0.882991	+	0.509795i
$917$	−0.115386	+	0.0666180i	−0.00381038	+	0.00219992i
$918$	−55.2917	−	31.9227i	−1.82490	−	1.05361i
$919$	18.6007	+	32.2174i	0.613581	+	1.06275i	0.990632	+	0.136560i	$0.0436048\pi$
$919$	18.6007	+	32.2174i	0.613581	+	1.06275i	−0.377051	+	0.926192i	$0.623062\pi$
$920$	−1.40047	−	2.42569i	−0.0461723	−	0.0799727i
$921$	31.9456	−	18.4438i	1.05264	−	0.607743i
$922$	−67.3952			−2.21954
$923$	17.1050	+	3.41368i	0.563018	+	0.112363i
$924$	3.33844	−	5.78235i	0.109827	−	0.190225i
$925$	−11.9493	+	6.89893i	−0.392890	+	0.226835i
$926$	79.0681			2.59834
$927$	29.6751	−	51.3987i	0.974657	−	1.68816i
$928$		−	74.7588i		−	2.45408i
$929$		−	17.3158i		−	0.568112i	−0.958808	−	0.284056i	$-0.908320\pi$
$929$		−	17.3158i		−	0.568112i	0.958808	−	0.284056i	$-0.0916802\pi$
$930$	62.7677	+	76.6574i	2.05823	+	2.51369i
$931$			17.4619i			0.572290i
$932$	−45.0817			−1.47670
$933$	−43.9568	+	76.1355i	−1.43908	+	2.49256i
$934$		−	51.4301i		−	1.68284i
$935$	8.88103	+	15.3824i	0.290441	+	0.503058i
$936$	10.7359	+	2.14258i	0.350913	+	0.0700324i
$937$	18.0840	−	31.3223i	0.590777	−	1.02326i	−0.403351	−	0.915045i	$-0.632155\pi$
$937$	18.0840	−	31.3223i	0.590777	−	1.02326i	0.994128	−	0.108211i	$-0.0345121\pi$
$938$		−	1.20491i		−	0.0393416i
$939$	−38.8382	−	67.2697i	−1.26744	−	2.19527i
$940$	−29.3739	−	50.8771i	−0.958072	−	1.65943i
$941$	−37.5797	+	21.6967i	−1.22506	+	0.707291i	−0.965993	−	0.258567i	$-0.916750\pi$
$941$	−37.5797	+	21.6967i	−1.22506	+	0.707291i	−0.259071	+	0.965858i	$0.583416\pi$
$942$	84.8039	+	48.9616i	2.76306	+	1.59525i
$943$	12.6841	−	7.32319i	0.413052	−	0.238476i
$944$	−7.84096	−	4.52698i	−0.255202	−	0.147341i
$945$	−16.5673			−0.538933
$946$	17.7055			0.575654
$947$	3.59401	+	2.07500i	0.116790	+	0.0674286i	0.557257	−	0.830340i	$-0.311854\pi$
$947$	3.59401	+	2.07500i	0.116790	+	0.0674286i	−0.440467	+	0.897769i	$0.645187\pi$
$948$	−38.9626	−	67.4852i	−1.26545	−	2.19182i
$949$	−47.2658	−	9.43294i	−1.53431	−	0.306206i
$950$	−7.11576	−	12.3249i	−0.230866	−	0.399871i
$951$	33.1778	−	19.1552i	1.07586	−	0.621150i
$952$	0.171297	+	0.296696i	0.00555178	+	0.00961597i
$953$	52.6968			1.70702			0.853508	−	0.521080i	$-0.174471\pi$
$953$	52.6968			1.70702			0.853508	+	0.521080i	$0.174471\pi$
$954$	23.8074	+	13.7452i	0.770793	+	0.445018i
$955$	−24.5542	−	14.1764i	−0.794556	−	0.458737i
$956$	−31.0207	+	17.9098i	−1.00328	+	0.579245i
$957$			91.6542i			2.96276i
$958$	−34.7405	+	60.1724i	−1.12242	+	1.94408i
$959$	−3.07620			−0.0993358
$960$		−	57.4202i		−	1.85323i
$961$	−6.11581	+	30.3907i	−0.197284	+	0.980346i
$962$	32.0540	−	10.8582i	1.03346	−	0.350082i
$963$	−109.293			−3.52193
$964$	1.98287	+	1.14481i	0.0638640	+	0.0368719i
$965$	19.0189			0.612240
$966$	−3.12500	−	5.41267i	−0.100545	−	0.174150i
$967$	29.1183	+	16.8115i	0.936381	+	0.540620i	0.888824	−	0.458249i	$-0.151523\pi$
$967$	29.1183	+	16.8115i	0.936381	+	0.540620i	0.0475571	+	0.998869i	$0.484856\pi$
$968$	−0.890476	−	0.514117i	−0.0286210	−	0.0165243i
$969$			18.1348i			0.582572i
$970$	4.02289	−	2.32261i	0.129167	−	0.0745747i
$971$	−15.2891	−	26.4814i	−0.490649	−	0.849830i	0.509293	−	0.860593i	$-0.329907\pi$
$971$	−15.2891	−	26.4814i	−0.490649	−	0.849830i	−0.999942	+	0.0107636i	$0.996574\pi$
$972$	−35.8232	−	62.0477i	−1.14903	−	1.99018i
$973$	−3.37375	−	1.94784i	−0.108158	−	0.0624448i
$974$	−4.22833	−	7.32367i	−0.135484	−	0.234666i
$975$	6.58231	−	32.9821i	0.210803	−	1.05627i
$976$	−10.1665			−0.325422
$977$			31.8740i			1.01974i	0.860252	+	0.509869i	$0.170306\pi$
$977$			31.8740i			1.01974i	−0.860252	+	0.509869i	$0.829694\pi$
$978$	24.7157	−	42.8088i	0.790321	−	1.36888i
$979$	20.7621	+	35.9611i	0.663561	+	1.14932i
$980$	29.8430	+	17.2299i	0.953300	+	0.550388i
$981$	−117.848	+	68.0395i	−3.76259	+	2.17233i
$982$	13.8920	−	8.02057i	0.443313	−	0.255947i
$983$	8.68267	−	5.01294i	0.276934	−	0.159888i	−0.355100	−	0.934828i	$-0.615553\pi$
$983$	8.68267	−	5.01294i	0.276934	−	0.159888i	0.632035	+	0.774940i	$0.282220\pi$
$984$	−7.60354			−0.242392
$985$	6.90361	−	11.9574i	0.219967	−	0.380995i
$986$	35.6993	+	20.6110i	1.13690	+	0.656388i
$987$	7.47771	+	12.9518i	0.238018	+	0.412259i
$988$	5.29754	+	15.6386i	0.168537	+	0.497531i
$989$	3.91978	−	6.78926i	0.124642	−	0.215886i
$990$			120.656i			3.83470i
$991$	−22.5458			−0.716191			−0.358095	−	0.933685i	$-0.616574\pi$
$991$	−22.5458			−0.716191			−0.358095	+	0.933685i	$0.616574\pi$
$992$	33.2172	−	27.1985i	1.05465	−	0.863554i
$993$			19.0843i			0.605621i
$994$			3.70785i			0.117606i
$995$	3.08565	+	1.78150i	0.0978216	+	0.0564773i
$996$			32.3180i			1.02404i
$997$	−0.420908	−	0.729034i	−0.0133303	−	0.0230887i	0.859283	−	0.511500i	$-0.170910\pi$
$997$	−0.420908	−	0.729034i	−0.0133303	−	0.0230887i	−0.872614	+	0.488411i	$0.837577\pi$
$998$	29.1855	−	50.5508i	0.923851	−	1.60016i
$999$	62.6580	+	36.1756i	1.98241	+	1.14454i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	403.2.l.c.129.27	yes	68
13.12	even	2	inner	403.2.l.c.129.8	yes	68
31.25	even	3	inner	403.2.l.c.25.27	yes	68
403.25	even	6	inner	403.2.l.c.25.8	✓	68

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
403.2.l.c.25.8	✓	68	403.25	even	6	inner
403.2.l.c.25.27	yes	68	31.25	even	3	inner
403.2.l.c.129.8	yes	68	13.12	even	2	inner
403.2.l.c.129.27	yes	68	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:	\( N \)	\(=\)	\( 403 = 13 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	403.l (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+1.94813i q^{2} +(1.62865 - 2.82091i) q^{3} -1.79519 q^{4} +(2.42854 - 1.40212i) q^{5} +(5.49549 + 3.17282i) q^{6} +(0.340725 + 0.196718i) q^{7} +0.398987i q^{8} +(-3.80502 - 6.59049i) q^{9} +O(q^{10})\)	\(q+1.94813i q^{2} +(1.62865 - 2.82091i) q^{3} -1.79519 q^{4} +(2.42854 - 1.40212i) q^{5} +(5.49549 + 3.17282i) q^{6} +(0.340725 + 0.196718i) q^{7} +0.398987i q^{8} +(-3.80502 - 6.59049i) q^{9} +(2.73150 + 4.73109i) q^{10} +(-2.51340 + 1.45111i) q^{11} +(-2.92375 + 5.06408i) q^{12} +(2.70929 + 2.37902i) q^{13} +(-0.383230 + 0.663775i) q^{14} -9.13424i q^{15} -4.36767 q^{16} +(1.09124 - 1.89008i) q^{17} +(12.8391 - 7.41266i) q^{18} +(-2.20920 - 1.27548i) q^{19} +(-4.35969 + 2.51707i) q^{20} +(1.10984 - 0.640769i) q^{21} +(-2.82695 - 4.89642i) q^{22} -2.50341 q^{23} +(1.12551 + 0.649812i) q^{24} +(1.43186 - 2.48005i) q^{25} +(-4.63464 + 5.27803i) q^{26} -15.0163 q^{27} +(-0.611667 - 0.353146i) q^{28} +9.69534 q^{29} +17.7946 q^{30} +(3.52734 + 4.30789i) q^{31} -7.71079i q^{32} +9.45343i q^{33} +(3.68211 + 2.12587i) q^{34} +1.10328 q^{35} +(6.83075 + 11.8312i) q^{36} +(-4.17266 - 2.40908i) q^{37} +(2.48480 - 4.30380i) q^{38} +(11.1235 - 3.76805i) q^{39} +(0.559426 + 0.968955i) q^{40} +(-5.06674 + 2.92529i) q^{41} +(1.24830 + 2.16212i) q^{42} +(-1.56578 + 2.71200i) q^{43} +(4.51204 - 2.60503i) q^{44} +(-18.4813 - 10.6702i) q^{45} -4.87696i q^{46} +11.6699i q^{47} +(-7.11341 + 12.3208i) q^{48} +(-3.42260 - 5.92812i) q^{49} +(4.83145 + 2.78944i) q^{50} +(-3.55449 - 6.15656i) q^{51} +(-4.86370 - 4.27081i) q^{52} +(0.927144 + 1.60586i) q^{53} -29.2537i q^{54} +(-4.06925 + 7.04815i) q^{55} +(-0.0784878 + 0.135945i) q^{56} +(-7.19604 + 4.15464i) q^{57} +18.8878i q^{58} +(1.79523 + 1.03648i) q^{59} +16.3977i q^{60} +2.32768 q^{61} +(-8.39231 + 6.87169i) q^{62} -2.99406i q^{63} +6.28625 q^{64} +(9.91527 + 1.97881i) q^{65} -18.4165 q^{66} +(-1.36143 + 0.786020i) q^{67} +(-1.95898 + 3.39305i) q^{68} +(-4.07719 + 7.06189i) q^{69} +2.14933i q^{70} +(4.18951 - 2.41881i) q^{71} +(2.62952 - 1.51816i) q^{72} +(-11.5768 + 6.68385i) q^{73} +(4.69320 - 8.12886i) q^{74} +(-4.66400 - 8.07828i) q^{75} +(3.96594 + 2.28974i) q^{76} -1.14184 q^{77} +(7.34064 + 21.6700i) q^{78} +(-6.66312 + 11.5409i) q^{79} +(-10.6070 + 6.12397i) q^{80} +(-13.0413 + 22.5882i) q^{81} +(-5.69882 - 9.87065i) q^{82} +(4.78636 - 2.76341i) q^{83} +(-1.99239 + 1.15031i) q^{84} -6.12016i q^{85} +(-5.28332 - 3.05033i) q^{86} +(15.7904 - 27.3497i) q^{87} +(-0.578975 - 1.00281i) q^{88} -14.3078i q^{89} +(20.7868 - 36.0038i) q^{90} +(0.455126 + 1.34356i) q^{91} +4.49411 q^{92} +(17.8970 - 2.93424i) q^{93} -22.7344 q^{94} -7.15350 q^{95} +(-21.7514 - 12.5582i) q^{96} -0.850308i q^{97} +(11.5487 - 6.66766i) q^{98} +(19.1271 + 11.0430i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 68 q - 6 q^{3} - 76 q^{4} - 40 q^{9}+O(q^{10}) \) 68 * q - 6 * q^3 - 76 * q^4 - 40 * q^9	\( 68 q - 6 q^{3} - 76 q^{4} - 40 q^{9} + 8 q^{10} - 10 q^{12} - 3 q^{13} + 10 q^{14} + 84 q^{16} + 6 q^{17} + 4 q^{22} - 44 q^{23} + 30 q^{25} - 3 q^{26} - 12 q^{27} + 48 q^{29} - 4 q^{30} - 48 q^{35} + 40 q^{36} + 60 q^{38} - 14 q^{39} + 20 q^{40} - 10 q^{42} - 12 q^{43} + 32 q^{48} + 58 q^{49} + 20 q^{51} - 27 q^{52} + 8 q^{53} - 36 q^{55} - 50 q^{56} - 12 q^{61} - 74 q^{62} - 15 q^{65} + 164 q^{66} + 4 q^{68} - 34 q^{69} - 4 q^{74} + 20 q^{75} - 200 q^{77} - 58 q^{78} - 80 q^{79} - 82 q^{81} - 66 q^{82} + 52 q^{87} + 16 q^{88} - 14 q^{90} - 70 q^{91} + 108 q^{92} - 4 q^{94} + 76 q^{95}+O(q^{100}) \) 68 * q - 6 * q^3 - 76 * q^4 - 40 * q^9 + 8 * q^10 - 10 * q^12 - 3 * q^13 + 10 * q^14 + 84 * q^16 + 6 * q^17 + 4 * q^22 - 44 * q^23 + 30 * q^25 - 3 * q^26 - 12 * q^27 + 48 * q^29 - 4 * q^30 - 48 * q^35 + 40 * q^36 + 60 * q^38 - 14 * q^39 + 20 * q^40 - 10 * q^42 - 12 * q^43 + 32 * q^48 + 58 * q^49 + 20 * q^51 - 27 * q^52 + 8 * q^53 - 36 * q^55 - 50 * q^56 - 12 * q^61 - 74 * q^62 - 15 * q^65 + 164 * q^66 + 4 * q^68 - 34 * q^69 - 4 * q^74 + 20 * q^75 - 200 * q^77 - 58 * q^78 - 80 * q^79 - 82 * q^81 - 66 * q^82 + 52 * q^87 + 16 * q^88 - 14 * q^90 - 70 * q^91 + 108 * q^92 - 4 * q^94 + 76 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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