LMFDB - Embedded newform 403.2.l.c.25.8

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			25.8
Character	$\chi$	$=$	403.25
Dual form			403.2.l.c.129.27

$q$-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 $\left(\mathbb{Z}/403\mathbb{Z}\right)^\times$.

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

Coefficient data

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

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

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

$2$		−	1.94813i		−	1.37753i	−0.724983	−	0.688766i	$-0.758153\pi$
$2$		−	1.94813i		−	1.37753i	0.724983	−	0.688766i	$-0.241847\pi$
$3$	1.62865	+	2.82091i	0.940303	+	1.62865i	0.764893	+	0.644158i	$0.222792\pi$
$3$	1.62865	+	2.82091i	0.940303	+	1.62865i	0.175411	+	0.984495i	$0.443875\pi$
$4$	−1.79519			−0.897597
$5$	2.42854	+	1.40212i	1.08607	+	0.627045i	0.932528	−	0.361096i	$-0.117597\pi$
$5$	2.42854	+	1.40212i	1.08607	+	0.627045i	0.153546	+	0.988142i	$0.450931\pi$
$6$	5.49549	−	3.17282i	2.24352	−	1.29530i
$7$	0.340725	−	0.196718i	0.128782	−	0.0743522i	−0.434225	−	0.900804i	$-0.642978\pi$
$7$	0.340725	−	0.196718i	0.128782	−	0.0743522i	0.563007	+	0.826452i	$0.309644\pi$
$8$		−	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	0.0706938	−	0.997498i	$-0.477479\pi$
$11$	−2.51340	−	1.45111i	−0.757818	−	0.437526i	−0.828512	+	0.559972i	$0.810812\pi$
$12$	−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	0.967475	−	0.252965i	$-0.0814058\pi$
$17$	1.09124	+	1.89008i	0.264664	+	0.458411i	−0.702812	+	0.711376i	$0.748072\pi$
$18$	12.8391	+	7.41266i	3.02621	+	1.74718i
$19$	−2.20920	+	1.27548i	−0.506825	+	0.292616i	−0.731528	−	0.681812i	$-0.761192\pi$
$19$	−2.20920	+	1.27548i	−0.506825	+	0.292616i	0.224702	+	0.974427i	$0.427859\pi$
$20$	−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	−0.802104	−	0.597184i	$-0.796286\pi$
$37$	−4.17266	+	2.40908i	−0.685980	+	0.396051i	0.116124	+	0.993235i	$0.462953\pi$
$38$	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	0.0491250	−	0.998793i	$-0.484357\pi$
$41$	−5.06674	−	2.92529i	−0.791292	−	0.456853i	−0.840417	+	0.541940i	$0.817690\pi$
$42$	1.24830	−	2.16212i	0.192617	−	0.333622i
$43$	−1.56578	−	2.71200i	−0.238779	−	0.413577i	0.721586	−	0.692325i	$-0.243414\pi$
$43$	−1.56578	−	2.71200i	−0.238779	−	0.413577i	−0.960364	+	0.278749i	$0.910080\pi$
$44$	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	$-0.675927\pi$
$47$		−	11.6699i		−	1.70223i	0.524980	−	0.851114i	$-0.324073\pi$
$48$	−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	−0.795297	−	0.606220i	$-0.792685\pi$
$53$	0.927144	−	1.60586i	0.127353	−	0.220582i	0.922650	+	0.385638i	$0.126019\pi$
$54$			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	−0.378568	−	0.925574i	$-0.623583\pi$
$59$	1.79523	−	1.03648i	0.233719	−	0.134938i	0.612287	+	0.790636i	$0.290250\pi$
$60$		−	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	0.414527	−	0.910037i	$-0.363947\pi$
$67$	−1.36143	−	0.786020i	−0.166325	−	0.0960276i	−0.580852	+	0.814009i	$0.697280\pi$
$68$	−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	0.727558	−	0.686046i	$-0.240655\pi$
$71$	4.18951	+	2.41881i	0.497203	+	0.287060i	−0.230355	+	0.973107i	$0.573989\pi$
$72$	2.62952	+	1.51816i	0.309892	+	0.178916i
$73$	−11.5768	−	6.68385i	−1.35496	−	0.782286i	−0.366019	−	0.930607i	$-0.619280\pi$
$73$	−11.5768	−	6.68385i	−1.35496	−	0.782286i	−0.988939	+	0.148322i	$0.952613\pi$
$74$	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	−0.947986	−	0.318313i	$-0.896884\pi$
$79$	−6.66312	−	11.5409i	−0.749660	−	1.29845i	0.198326	−	0.980136i	$-0.436450\pi$
$80$	−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	0.739130	−	0.673563i	$-0.235237\pi$
$83$	4.78636	+	2.76341i	0.525372	+	0.303323i	−0.213758	+	0.976887i	$0.568570\pi$
$84$	−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	$0.273974\pi$
$89$			14.3078i			1.51662i	−0.651895	+	0.758309i	$0.726026\pi$
$90$	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	$0.0137450\pi$
$97$			0.850308i			0.0863357i	−0.999068	+	0.0431679i	$0.986255\pi$
$98$	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	−0.607436	−	0.794369i	$-0.707802\pi$
$103$	3.89946	−	6.75407i	0.384225	−	0.665498i	0.991661	+	0.128871i	$0.0411352\pi$
$104$	−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	0.970450	+	0.241303i	$0.0775749\pi$
$107$	7.18086	+	12.4376i	0.694200	+	1.20239i	−0.276250	+	0.961086i	$0.589092\pi$
$108$	26.9572			2.59396
$109$			17.8815i			1.71274i	0.516365	+	0.856369i	$0.327285\pi$
$109$			17.8815i			1.71274i	−0.516365	+	0.856369i	$0.672715\pi$
$110$	−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	−0.957291	−	0.289127i	$-0.906635\pi$
$113$	−2.42637	+	4.20260i	−0.228254	+	0.395348i	0.729037	+	0.684475i	$0.239968\pi$
$114$	−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	−0.995085	−	0.0990198i	$-0.968429\pi$
$127$	−6.57342	−	11.3855i	−0.583296	−	1.01030i	0.411789	−	0.911279i	$-0.364904\pi$
$128$			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	0.858534	−	0.512757i	$-0.171376\pi$
$131$	−0.169324	−	0.293278i	−0.0147939	−	0.0256238i	−0.873328	+	0.487133i	$0.838043\pi$
$132$			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	0.182030	−	0.983293i	$-0.441733\pi$
$137$	−6.77131	−	3.90942i	−0.578512	−	0.334004i	−0.760542	+	0.649289i	$0.775067\pi$
$138$	−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	−0.998214	−	0.0597473i	$-0.980971\pi$
$149$	−17.6455	+	10.1876i	−1.44558	+	0.834605i	−0.447364	+	0.894352i	$0.647637\pi$
$150$	15.7375	+	9.08605i	1.28496	+	0.741873i
$151$		−	8.06419i		−	0.656254i	−0.944634	−	0.328127i	$-0.893583\pi$
$151$		−	8.06419i		−	0.656254i	0.944634	−	0.328127i	$-0.106417\pi$
$152$	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	$0.0986808\pi$
$163$			7.78982i			0.610146i	−0.952329	+	0.305073i	$0.901319\pi$
$164$	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	−0.903967	−	0.427602i	$-0.859359\pi$
$167$	−12.7372	+	7.35385i	−0.985637	+	0.569058i	−0.0816698	+	0.996659i	$0.526025\pi$
$168$	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	0.102872	+	0.994695i	$0.467197\pi$
$173$	−10.6538	+	18.4529i	−0.809995	+	1.40295i	−0.912867	+	0.408257i	$0.866137\pi$
$174$	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	−0.999153	−	0.0411437i	$-0.986900\pi$
$179$	−7.16060	−	12.4025i	−0.535208	−	0.927008i	0.463945	−	0.885864i	$-0.346433\pi$
$180$	33.1775	−	19.1550i	2.47290	−	1.42773i
$181$	−2.97375	+	5.15069i	−0.221037	+	0.382848i	−0.955123	−	0.296209i	$-0.904278\pi$
$181$	−2.97375	+	5.15069i	−0.221037	+	0.382848i	0.734086	+	0.679057i	$0.237611\pi$
$182$	−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	−0.988903	−	0.148562i	$-0.952535\pi$
$191$	−5.05536	+	8.75614i	−0.365793	+	0.633572i	0.623110	+	0.782134i	$0.285869\pi$
$192$	10.2381	+	17.7330i	0.738873	+	1.27977i
$193$	5.87357	−	3.39111i	0.422789	−	0.244097i	−0.273481	−	0.961877i	$-0.588175\pi$
$193$	5.87357	−	3.39111i	0.422789	−	0.244097i	0.696270	+	0.717780i	$0.254842\pi$
$194$	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	0.644149	−	0.764900i	$-0.277211\pi$
$197$	4.26406	+	2.46186i	0.303802	+	0.175400i	−0.340348	+	0.940300i	$0.610545\pi$
$198$	−21.5132	−	37.2619i	−1.52888	−	2.64809i
$199$	0.635290	−	1.10035i	0.0450345	−	0.0780020i	−0.842630	−	0.538494i	$-0.818994\pi$
$199$	0.635290	−	1.10035i	0.0450345	−	0.0780020i	0.887664	+	0.460492i	$0.152327\pi$
$200$	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	0.798149	−	0.602460i	$-0.205813\pi$
$211$	−1.78190	−	3.08634i	−0.122671	−	0.212472i	−0.920820	+	0.389988i	$0.872479\pi$
$212$	−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	−0.887557	−	0.460697i	$-0.847599\pi$
$223$	−13.9231	+	8.03851i	−0.932360	+	0.538298i	−0.0448029	+	0.998996i	$0.514266\pi$
$224$	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	0.994956	−	0.100312i	$-0.0319842\pi$
$227$	21.1769	+	12.2265i	1.40556	+	0.811501i	0.410605	+	0.911813i	$0.365318\pi$
$228$	12.9183	+	7.45838i	0.855535	+	0.493943i
$229$	−14.8865	+	8.59472i	−0.983727	+	0.567955i	−0.903393	−	0.428813i	$-0.858932\pi$
$229$	−14.8865	+	8.59472i	−0.983727	+	0.567955i	−0.0803338	+	0.996768i	$0.525599\pi$
$230$	−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	0.940824	−	0.338897i	$-0.110054\pi$
$239$	17.2799	+	9.97654i	1.11774	+	0.645329i	0.176918	+	0.984226i	$0.443387\pi$
$240$		−	39.8953i		−	2.57523i
$241$	−1.10454	+	0.637709i	−0.0711499	+	0.0410784i	−0.535153	−	0.844755i	$-0.679746\pi$
$241$	−1.10454	+	0.637709i	−0.0711499	+	0.0410784i	0.464003	+	0.885834i	$0.346413\pi$
$242$	−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	0.729347	−	0.684144i	$-0.239824\pi$
$251$	−3.60922	−	6.25136i	−0.227812	−	0.394582i	−0.957159	+	0.289561i	$0.906491\pi$
$252$		−	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	−0.928694	−	0.370848i	$-0.879067\pi$
$257$	−2.29540	+	3.97575i	−0.143183	+	0.248001i	0.785510	+	0.618848i	$0.212400\pi$
$258$	−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	−0.751612	−	0.659605i	$-0.770724\pi$
$269$	3.20526	−	5.55168i	0.195428	−	0.338492i	0.947041	+	0.321113i	$0.104057\pi$
$270$	−41.0171	+	71.0436i	−2.49622	+	4.32358i
$271$			6.68566i			0.406125i	0.979166	+	0.203063i	$0.0650895\pi$
$271$			6.68566i			0.406125i	−0.979166	+	0.203063i	$0.934911\pi$
$272$	−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	$0.0731068\pi$
$281$			7.63249i			0.455316i	−0.973741	+	0.227658i	$0.926893\pi$
$282$	−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	0.109125	−	0.994028i	$-0.465195\pi$
$293$	17.5373	−	10.1252i	1.02454	−	0.591519i	0.915416	+	0.402509i	$0.131862\pi$
$294$			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	−0.193304	−	0.981139i	$-0.561920\pi$
$307$	9.80736	−	5.66228i	0.559736	−	0.323164i	0.753039	+	0.657975i	$0.228587\pi$
$308$	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	0.976774	+	0.214271i	$0.0687375\pi$
$313$	11.9234	+	20.6520i	0.673951	+	1.16732i	−0.302823	+	0.953047i	$0.597929\pi$
$314$		−	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	−0.185898	−	0.982569i	$-0.559519\pi$
$317$	10.1857	−	5.88069i	0.572083	−	0.330293i	0.757981	+	0.652277i	$0.226186\pi$
$318$		−	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	0.354030	−	0.935234i	$-0.384811\pi$
$331$	−5.07397	−	2.92946i	−0.278891	−	0.161018i	−0.632921	+	0.774216i	$0.718144\pi$
$332$	−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	0.992191	+	0.124730i	$0.0398064\pi$
$347$	11.2534	+	19.4915i	0.604114	+	1.04636i	−0.388076	+	0.921627i	$0.626860\pi$
$348$	−28.3468	−	49.0980i	−1.51955	−	2.63193i
$349$		−	5.79633i		−	0.310270i	−0.987893	−	0.155135i	$-0.950419\pi$
$349$		−	5.79633i		−	0.310270i	0.987893	−	0.155135i	$-0.0495813\pi$
$350$	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	−0.0397609	−	0.999209i	$-0.512660\pi$
$353$	15.1377	−	8.73976i	0.805699	−	0.465171i	0.845460	+	0.534039i	$0.179326\pi$
$354$	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	0.691635	−	0.722248i	$-0.256891\pi$
$359$	7.80566	+	4.50660i	0.411967	+	0.237849i	−0.279667	+	0.960097i	$0.590224\pi$
$360$	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	0.473279	+	0.880912i	$0.343070\pi$
$367$	−10.0816	+	17.4618i	−0.526253	+	0.911497i	−0.999532	+	0.0305842i	$0.990263\pi$
$368$	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	−0.939597	−	0.342283i	$-0.888800\pi$
$379$	−21.6672	+	12.5096i	−1.11297	+	0.642573i	−0.173372	+	0.984856i	$0.555466\pi$
$380$	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	0.875500	−	0.483219i	$-0.160532\pi$
$383$	17.5110	+	10.1100i	0.894770	+	0.516595i	0.0192700	+	0.999814i	$0.493866\pi$
$384$	−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	0.582158	−	0.813076i	$-0.302208\pi$
$389$	−8.14692	−	14.1109i	−0.413065	−	0.715450i	−0.995223	+	0.0976259i	$0.968875\pi$
$390$	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	−0.217987	−	0.975952i	$-0.569949\pi$
$397$	10.3254	−	5.96139i	0.518218	−	0.299194i	0.736205	+	0.676758i	$0.236616\pi$
$398$	−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	$0.103441\pi$
$401$			12.7872i			0.638561i	−0.947660	+	0.319280i	$0.896559\pi$
$402$	−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	−0.857024	−	0.515276i	$-0.827689\pi$
$409$	−16.9737	+	9.79976i	−0.839295	+	0.484567i	0.0177298	+	0.999843i	$0.494356\pi$
$410$	−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	0.999460	−	0.0328657i	$-0.0104634\pi$
$421$	30.1768	+	17.4226i	1.47073	+	0.849125i	0.471267	+	0.881990i	$0.343797\pi$
$422$	−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	−0.625340	−	0.780353i	$-0.715040\pi$
$431$	−5.44350	+	3.14281i	−0.262204	+	0.151384i	0.363135	+	0.931736i	$0.381706\pi$
$432$	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	−0.512025	−	0.858970i	$-0.671105\pi$
$439$	10.2222	−	17.7053i	0.487877	−	0.845029i	0.999903	+	0.0139418i	$0.00443795\pi$
$440$	−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	−0.996885	−	0.0788746i	$-0.974867\pi$
$443$	−9.05329	+	15.6808i	−0.430135	+	0.745015i	0.566750	+	0.823890i	$0.308201\pi$
$444$	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	$0.230995\pi$
$449$			28.1251i			1.32731i	−0.748040	+	0.663654i	$0.769005\pi$
$450$			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	$-0.755356\pi$
$457$		−	29.7195i		−	1.39022i	0.718904	−	0.695109i	$-0.244644\pi$
$458$	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	$-0.701831\pi$
$461$		−	34.5949i		−	1.61124i	0.592429	−	0.805622i	$-0.298169\pi$
$462$	−6.27494	+	3.62284i	−0.291937	+	0.168550i
$463$			40.5868i			1.88623i	0.332471	+	0.943113i	$0.392118\pi$
$463$			40.5868i			1.88623i	−0.332471	+	0.943113i	$0.607882\pi$
$464$	−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	0.415768	−	0.909471i	$-0.363513\pi$
$479$	30.8873	−	17.8328i	1.41128	−	0.814801i	0.995509	+	0.0946695i	$0.0301794\pi$
$480$	−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	0.412400	−	0.911003i	$-0.364691\pi$
$487$	−3.75934	−	2.17046i	−0.170352	−	0.0983529i	−0.582752	+	0.812650i	$0.698024\pi$
$488$		−	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	−0.943846	−	0.330386i	$-0.892821\pi$
$491$	−4.11707	+	7.13097i	−0.185801	+	0.321816i	0.758045	+	0.652202i	$0.226155\pi$
$492$			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	−0.951689	−	0.307063i	$-0.900654\pi$
$499$	−25.9484	+	14.9813i	−1.16161	+	0.670656i	−0.209921	+	0.977718i	$0.567321\pi$
$500$			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	−0.993872	−	0.110537i	$-0.964743\pi$
$503$	−13.2921	−	23.0225i	−0.592664	−	1.02652i	0.401208	−	0.915987i	$-0.368590\pi$
$504$	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	0.321956	−	0.946755i	$-0.395660\pi$
$509$	−7.60262	−	4.38937i	−0.336980	−	0.194556i	−0.658936	+	0.752199i	$0.728993\pi$
$510$	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	0.924454	−	0.381293i	$-0.124521\pi$
$521$	3.01336	+	5.21930i	0.132018	+	0.228662i	−0.792436	+	0.609954i	$0.791188\pi$
$522$	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	0.278825	−	0.960342i	$-0.410055\pi$
$541$	29.0723	−	16.7849i	1.24992	−	0.721640i	0.971093	+	0.238702i	$0.0767218\pi$
$542$	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	−0.778823	−	0.627244i	$-0.784183\pi$
$547$	3.59702	−	6.23022i	0.153797	−	0.266385i	0.932620	+	0.360859i	$0.117516\pi$
$548$	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	$0.154939\pi$
$557$			22.0790i			0.935519i	−0.883856	+	0.467760i	$0.845061\pi$
$558$	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	−0.989071	−	0.147442i	$-0.952896\pi$
$563$	−8.70440	+	15.0765i	−0.366847	+	0.635397i	0.622224	+	0.782839i	$0.286229\pi$
$564$	−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	−0.787507	−	0.616306i	$-0.788629\pi$
$569$	3.33911	−	5.78351i	0.139983	−	0.242457i	0.927490	+	0.373848i	$0.121962\pi$
$570$	−39.3119	+	22.6968i	−1.64660	+	0.950663i
$571$	−3.28689	+	5.69306i	−0.137552	+	0.238247i	−0.926569	−	0.376124i	$-0.877257\pi$
$571$	−3.28689	+	5.69306i	−0.137552	+	0.238247i	0.789017	+	0.614371i	$0.210590\pi$
$572$	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	−0.579967	−	0.814640i	$-0.696935\pi$
$577$	−3.95027	+	2.28069i	−0.164452	+	0.0949463i	0.415515	+	0.909586i	$0.363601\pi$
$578$	−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	$-0.697846\pi$
$587$		−	39.3937i		−	1.62595i	0.582298	−	0.812976i	$-0.302154\pi$
$588$	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	$0.0252255\pi$
$593$			3.85560i			0.158330i	−0.996862	+	0.0791652i	$0.974775\pi$
$594$	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	−0.971193	−	0.238293i	$-0.923412\pi$
$599$	−6.83397	+	11.8368i	−0.279228	+	0.483638i	0.691965	+	0.721931i	$0.256745\pi$
$600$	3.22313	+	1.86088i	0.131584	+	0.0759699i
$601$	−9.64453	−	16.7048i	−0.393409	−	0.681404i	0.599488	−	0.800384i	$-0.295371\pi$
$601$	−9.64453	−	16.7048i	−0.393409	−	0.681404i	−0.992897	+	0.118980i	$0.962038\pi$
$602$	−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	−0.922577	−	0.385814i	$-0.873921\pi$
$607$	−3.13298	+	5.42648i	−0.127164	+	0.220254i	0.795413	+	0.606068i	$0.207254\pi$
$608$	−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	0.100068	−	0.994981i	$-0.468094\pi$
$613$	25.0505	−	14.4629i	1.01178	−	0.584151i	0.911712	+	0.410829i	$0.134761\pi$
$614$	−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	0.439221	−	0.898379i	$-0.355255\pi$
$617$	35.6906	−	20.6060i	1.43685	−	0.829566i	0.997630	+	0.0688134i	$0.0219213\pi$
$618$		−	49.4892i		−	1.99075i
$619$		−	48.9910i		−	1.96911i	−0.175064	−	0.984557i	$-0.556013\pi$
$619$		−	48.9910i		−	1.96911i	0.175064	−	0.984557i	$-0.443987\pi$
$620$	−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	−0.274948	−	0.961459i	$-0.588661\pi$
$631$	−31.2758	−	18.0571i	−1.24507	−	0.718842i	−0.970122	+	0.242617i	$0.921994\pi$
$632$	−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	−0.523914	−	0.851771i	$-0.675529\pi$
$641$	12.0437	−	20.8603i	0.475698	−	0.823933i	0.999612	+	0.0278376i	$0.00886214\pi$
$642$	78.9246	+	45.5672i	3.11491	+	1.79839i
$643$			1.44128i			0.0568384i	0.999596	+	0.0284192i	$0.00904733\pi$
$643$			1.44128i			0.0568384i	−0.999596	+	0.0284192i	$0.990953\pi$
$644$	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	0.213687	−	0.976902i	$-0.431453\pi$
$661$	−13.5103	−	7.80019i	−0.525491	−	0.303392i	−0.739178	+	0.673510i	$0.764786\pi$
$662$	−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	−0.714305	−	0.699834i	$-0.753257\pi$
$673$	6.45759	−	11.1849i	0.248922	−	0.431145i	0.963227	+	0.268689i	$0.0865905\pi$
$674$		−	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	−0.746660	−	0.665206i	$-0.768344\pi$
$677$	5.27552	−	9.13747i	0.202755	−	0.351181i	0.949415	+	0.314024i	$0.101677\pi$
$678$			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	$-0.958498\pi$
$683$		−	6.79560i		−	0.260027i	0.991512	−	0.130013i	$-0.0415020\pi$
$684$			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	0.724045	−	0.689752i	$-0.242281\pi$
$691$	12.8471	+	7.41725i	0.488725	+	0.282166i	−0.235320	+	0.971918i	$0.575614\pi$
$692$	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	−0.860444	−	0.509544i	$-0.829814\pi$
$701$	−23.0742	−	39.9657i	−0.871500	−	1.50948i	−0.0110560	−	0.999939i	$-0.503519\pi$
$702$	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	$0.0698323\pi$
$709$			11.5896i			0.435258i	−0.976032	+	0.217629i	$0.930168\pi$
$710$	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	0.737879	−	0.674933i	$-0.235827\pi$
$719$	−5.78032	−	10.0118i	−0.215570	−	0.373377i	−0.953449	+	0.301556i	$0.902494\pi$
$720$	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	0.964258	−	0.264965i	$-0.0853606\pi$
$727$	6.81251	+	11.7996i	0.252662	+	0.437624i	−0.711596	+	0.702589i	$0.752027\pi$
$728$	−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	−0.219549	−	0.975601i	$-0.570459\pi$
$733$	−31.7908	−	18.3544i	−1.17422	−	0.677936i	−0.954670	+	0.297665i	$0.903792\pi$
$734$	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	0.658401	−	0.752667i	$-0.271233\pi$
$739$	9.12783	+	5.26995i	0.335773	+	0.193858i	−0.322629	+	0.946526i	$0.604566\pi$
$740$	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	$-0.907550\pi$
$743$		−	15.6120i		−	0.572747i	0.958118	−	0.286374i	$-0.0924498\pi$
$744$	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	0.939005	−	0.343903i	$-0.111749\pi$
$751$	4.70463	+	8.14866i	0.171674	+	0.297349i	−0.767331	+	0.641251i	$0.778416\pi$
$752$			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	−0.996634	−	0.0819835i	$-0.973875\pi$
$757$	−11.7570	+	20.3638i	−0.427317	+	0.740135i	0.569317	+	0.822118i	$0.307208\pi$
$758$	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	−0.881256	−	0.472639i	$-0.843302\pi$
$761$	−25.1743	+	14.5344i	−0.912567	+	0.526871i	−0.0313111	+	0.999510i	$0.509968\pi$
$762$	−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	−0.774997	−	0.631965i	$-0.782249\pi$
$769$	−17.0600	+	9.84957i	−0.615198	+	0.355184i	0.159799	+	0.987150i	$0.448915\pi$
$770$	−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	$-0.962626\pi$
$773$		−	6.51384i		−	0.234287i	0.993115	−	0.117143i	$-0.0373737\pi$
$774$		−	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	−0.426448	−	0.904512i	$-0.640235\pi$
$787$	4.03015	−	2.32681i	0.143659	−	0.0829418i	0.570107	+	0.821571i	$0.306902\pi$
$788$	−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	−0.532091	−	0.846687i	$-0.678593\pi$
$797$	13.1898	−	22.8454i	0.467208	−	0.809227i	0.999298	+	0.0374602i	$0.0119268\pi$
$798$			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	0.996669	−	0.0815524i	$-0.0259878\pi$
$809$	12.1653	+	21.0709i	0.427708	+	0.740812i	−0.568961	+	0.822365i	$0.692654\pi$
$810$	−142.489			−5.00656
$811$	20.1475	+	11.6322i	0.707476	+	0.408461i	0.810126	−	0.586256i	$-0.199399\pi$
$811$	20.1475	+	11.6322i	0.707476	+	0.408461i	−0.102650	+	0.994718i	$0.532732\pi$
$812$	−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	$-0.913551\pi$
$821$		−	15.3731i		−	0.536525i	0.963346	−	0.268262i	$-0.0864494\pi$
$822$	−49.6155			−1.73054
$823$	−3.32392	−	5.75721i	−0.115865	−	0.200684i	0.802260	−	0.596974i	$-0.203631\pi$
$823$	−3.32392	−	5.75721i	−0.115865	−	0.200684i	−0.918125	+	0.396291i	$0.870297\pi$
$824$	−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	0.596750	−	0.802427i	$-0.296458\pi$
$827$	5.75736	+	3.32401i	0.200203	+	0.115587i	−0.396547	+	0.918014i	$0.629792\pi$
$828$	−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	$0.243642\pi$
$839$			40.1371i			1.38569i	−0.721089	+	0.692843i	$0.756358\pi$
$840$	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	$0.213919\pi$
$853$			36.3668i			1.24518i	−0.782549	+	0.622588i	$0.786081\pi$
$854$	−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	−0.751903	−	0.659274i	$-0.770864\pi$
$857$	5.70845	−	9.88733i	0.194997	−	0.337745i	0.946900	+	0.321530i	$0.104197\pi$
$858$	−49.8955	+	43.8132i	−1.70340	+	1.49576i
$859$	14.3563	−	24.8658i	0.489829	−	0.848409i	−0.510102	−	0.860114i	$-0.670392\pi$
$859$	14.3563	−	24.8658i	0.489829	−	0.848409i	0.999931	+	0.0117047i	$0.00372582\pi$
$860$			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	−0.0615327	−	0.998105i	$-0.519599\pi$
$863$	−28.1044	−	16.2261i	−0.956683	−	0.552341i	−0.895151	+	0.445764i	$0.852932\pi$
$864$		−	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	0.634638	−	0.772809i	$-0.281149\pi$
$877$	8.37150	+	4.83329i	0.282685	+	0.163208i	−0.351953	+	0.936018i	$0.614482\pi$
$878$	−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	−0.679059	−	0.734083i	$-0.737612\pi$
$881$	8.79186	−	15.2279i	0.296205	−	0.513043i	0.975265	+	0.221041i	$0.0709454\pi$
$882$	−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	0.873451	−	0.486912i	$-0.161877\pi$
$887$	0.448148	+	0.776215i	0.0150473	+	0.0260627i	−0.858404	+	0.512975i	$0.828543\pi$
$888$	−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	0.758517	−	0.651653i	$-0.225924\pi$
$911$	−5.58653	−	9.67615i	−0.185090	−	0.320585i	−0.943607	+	0.331068i	$0.892591\pi$
$912$	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	−0.377051	−	0.926192i	$-0.623062\pi$
$919$	18.6007	−	32.2174i	0.613581	−	1.06275i	0.990632	−	0.136560i	$-0.0436048\pi$
$920$	−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	$0.0916802\pi$
$929$			17.3158i			0.568112i	−0.958808	+	0.284056i	$0.908320\pi$
$930$	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	0.994128	+	0.108211i	$0.0345121\pi$
$937$	18.0840	+	31.3223i	0.590777	+	1.02326i	−0.403351	+	0.915045i	$0.632155\pi$
$938$			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	−0.259071	−	0.965858i	$-0.583416\pi$
$941$	−37.5797	−	21.6967i	−1.22506	−	0.707291i	−0.965993	+	0.258567i	$0.916750\pi$
$942$	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	−0.440467	−	0.897769i	$-0.645187\pi$
$947$	3.59401	−	2.07500i	0.116790	−	0.0674286i	0.557257	+	0.830340i	$0.311854\pi$
$948$	−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	0.0475571	−	0.998869i	$-0.484856\pi$
$967$	29.1183	−	16.8115i	0.936381	−	0.540620i	0.888824	+	0.458249i	$0.151523\pi$
$968$	−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	−0.999942	−	0.0107636i	$-0.996574\pi$
$971$	−15.2891	+	26.4814i	−0.490649	+	0.849830i	0.509293	+	0.860593i	$0.329907\pi$
$972$	−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	$-0.829694\pi$
$977$		−	31.8740i		−	1.01974i	0.860252	−	0.509869i	$-0.170306\pi$
$978$	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	0.632035	−	0.774940i	$-0.282220\pi$
$983$	8.68267	+	5.01294i	0.276934	+	0.159888i	−0.355100	+	0.934828i	$0.615553\pi$
$984$	−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	−0.872614	−	0.488411i	$-0.837577\pi$
$997$	−0.420908	+	0.729034i	−0.0133303	+	0.0230887i	0.859283	+	0.511500i	$0.170910\pi$
$998$	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.25.8	✓	68
13.12	even	2	inner	403.2.l.c.25.27	yes	68
31.5	even	3	inner	403.2.l.c.129.8	yes	68
403.129	even	6	inner	403.2.l.c.129.27	yes	68

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
403.2.l.c.25.8	✓	68	1.1	even	1	trivial
403.2.l.c.25.27	yes	68	13.12	even	2	inner
403.2.l.c.129.8	yes	68	31.5	even	3	inner
403.2.l.c.129.27	yes	68	403.129	even	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 403 = 13 \cdot 31 \)
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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