LMFDB - Embedded newform 209.2.f.c.191.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [209,2,Mod(20,209)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(209, base_ring=CyclotomicField(10))

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

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

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

chi := DirichletCharacter("209.20");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 209 = 11 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	209.f (of order $5$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.66887340224$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$10$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			191.5
Character	$\chi$	$=$	209.191
Dual form			209.2.f.c.58.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.207740 - 0.150932i) q^{2} +(0.859341 - 2.64478i) q^{3} +(-0.597658 - 1.83940i) q^{4} +(1.97532 - 1.43516i) q^{5} +(-0.577702 + 0.419725i) q^{6} +(0.905304 + 2.78624i) q^{7} +(-0.312167 + 0.960751i) q^{8} +(-3.82934 - 2.78218i) q^{9} -0.626965 q^{10} +(0.914084 + 3.18817i) q^{11} -5.37841 q^{12} +(1.20556 + 0.875893i) q^{13} +(0.232465 - 0.715454i) q^{14} +(-2.09819 - 6.45758i) q^{15} +(-2.91952 + 2.12116i) q^{16} +(-3.39760 + 2.46850i) q^{17} +(0.375588 + 1.15594i) q^{18} +(0.309017 - 0.951057i) q^{19} +(-3.82040 - 2.77568i) q^{20} +8.14695 q^{21} +(0.291306 - 0.800277i) q^{22} +3.73331 q^{23} +(2.27272 + 1.65123i) q^{24} +(0.297141 - 0.914506i) q^{25} +(-0.118244 - 0.363917i) q^{26} +(-3.89960 + 2.83323i) q^{27} +(4.58396 - 3.33044i) q^{28} +(-1.48321 - 4.56487i) q^{29} +(-0.538777 + 1.65818i) q^{30} +(-1.44407 - 1.04918i) q^{31} +2.94704 q^{32} +(9.21752 + 0.322177i) q^{33} +1.07839 q^{34} +(5.78695 + 4.20447i) q^{35} +(-2.82891 + 8.70649i) q^{36} +(2.61394 + 8.04488i) q^{37} +(-0.207740 + 0.150932i) q^{38} +(3.35253 - 2.43576i) q^{39} +(0.762197 + 2.34580i) q^{40} +(0.684304 - 2.10607i) q^{41} +(-1.69245 - 1.22964i) q^{42} -11.0941 q^{43} +(5.31803 - 3.58681i) q^{44} -11.5570 q^{45} +(-0.775559 - 0.563477i) q^{46} +(2.33295 - 7.18007i) q^{47} +(3.10113 + 9.54429i) q^{48} +(-1.28043 + 0.930289i) q^{49} +(-0.199757 + 0.145132i) q^{50} +(3.60894 + 11.1072i) q^{51} +(0.890606 - 2.74100i) q^{52} +(-11.2574 - 8.17895i) q^{53} +1.23773 q^{54} +(6.38114 + 4.98582i) q^{55} -2.95949 q^{56} +(-2.24978 - 1.63456i) q^{57} +(-0.380862 + 1.17217i) q^{58} +(3.01721 + 9.28603i) q^{59} +(-10.6241 + 7.71885i) q^{60} +(-9.96898 + 7.24289i) q^{61} +(0.141637 + 0.435913i) q^{62} +(4.28510 - 13.1882i) q^{63} +(5.22683 + 3.79751i) q^{64} +3.63842 q^{65} +(-1.86622 - 1.45815i) q^{66} +6.65052 q^{67} +(6.57117 + 4.77424i) q^{68} +(3.20819 - 9.87378i) q^{69} +(-0.567594 - 1.74687i) q^{70} +(8.53131 - 6.19836i) q^{71} +(3.86837 - 2.81054i) q^{72} +(1.58137 + 4.86697i) q^{73} +(0.671210 - 2.06577i) q^{74} +(-2.16332 - 1.57174i) q^{75} -1.93406 q^{76} +(-8.05549 + 5.43312i) q^{77} -1.06409 q^{78} +(-1.05579 - 0.767079i) q^{79} +(-2.72281 + 8.37994i) q^{80} +(-0.245862 - 0.756686i) q^{81} +(-0.460032 + 0.334233i) q^{82} +(7.41615 - 5.38815i) q^{83} +(-4.86909 - 14.9855i) q^{84} +(-3.16867 + 9.75217i) q^{85} +(2.30470 + 1.67446i) q^{86} -13.3476 q^{87} +(-3.34839 - 0.117035i) q^{88} -2.45131 q^{89} +(2.40086 + 1.74433i) q^{90} +(-1.34905 + 4.15194i) q^{91} +(-2.23124 - 6.86706i) q^{92} +(-4.01579 + 2.91764i) q^{93} +(-1.56835 + 1.13947i) q^{94} +(-0.754506 - 2.32213i) q^{95} +(2.53251 - 7.79427i) q^{96} +(-3.53874 - 2.57105i) q^{97} +0.406408 q^{98} +(5.36973 - 14.7517i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 3 q^{2} + 3 q^{3} - 13 q^{4} - 9 q^{5} + 10 q^{6} + 4 q^{7} - q^{8} - 21 q^{9} - 22 q^{10} + 8 q^{11} + 20 q^{12} + 13 q^{13} - 20 q^{14} - 9 q^{15} - 41 q^{16} + 21 q^{17} + 27 q^{18} - 10 q^{19}+ \cdots + 110 q^{99}+O(q^{100}) $ 40 * q + 3 * q^2 + 3 * q^3 - 13 * q^4 - 9 * q^5 + 10 * q^6 + 4 * q^7 - q^8 - 21 * q^9 - 22 * q^10 + 8 * q^11 + 20 * q^12 + 13 * q^13 - 20 * q^14 - 9 * q^15 - 41 * q^16 + 21 * q^17 + 27 * q^18 - 10 * q^19 - 26 * q^20 - 22 * q^21 + q^22 + 16 * q^23 + 12 * q^24 - 53 * q^25 - 14 * q^26 - 24 * q^27 + 29 * q^28 + 11 * q^29 + 10 * q^30 - 13 * q^31 - 4 * q^32 + 34 * q^33 - 38 * q^34 + 25 * q^35 - 61 * q^36 - 7 * q^37 + 3 * q^38 - 16 * q^39 + 77 * q^40 + 17 * q^41 - 12 * q^42 - 24 * q^43 + 29 * q^44 + 130 * q^45 + 32 * q^46 - 5 * q^47 - 6 * q^48 - 42 * q^49 - 5 * q^50 + 40 * q^51 - 19 * q^52 - 30 * q^53 + 52 * q^54 + 72 * q^55 + 74 * q^56 - 7 * q^57 - 67 * q^58 - 23 * q^59 - 94 * q^60 + 36 * q^61 + 35 * q^62 - 7 * q^63 - 111 * q^64 - 26 * q^65 - 9 * q^66 + 52 * q^67 + 70 * q^68 - 95 * q^69 - 38 * q^70 - 34 * q^71 + 112 * q^72 + 31 * q^73 + 80 * q^74 - 84 * q^75 + 42 * q^76 - 25 * q^77 - 90 * q^78 + 32 * q^79 - 58 * q^80 - 28 * q^81 - 50 * q^82 - 83 * q^83 + 135 * q^84 - 23 * q^85 - 45 * q^86 - 42 * q^87 + 101 * q^88 + 96 * q^89 - 4 * q^90 + 33 * q^91 - 48 * q^92 - 91 * q^93 + 67 * q^94 - 9 * q^95 - 18 * q^96 - 10 * q^97 - 90 * q^98 + 110 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/209\mathbb{Z}\right)^\times$.

$n$	$78$	$134$
$\chi(n)$	$1$	$e\left(\frac{1}{5}\right)$

Coefficient data

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

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

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

$2$	−0.207740	−	0.150932i	−0.146895	−	0.106725i	0.511911	−	0.859039i	$-0.328938\pi$
$2$	−0.207740	−	0.150932i	−0.146895	−	0.106725i	−0.658805	+	0.752314i	$0.728938\pi$
$3$	0.859341	−	2.64478i	0.496141	−	1.52696i	−0.319031	−	0.947744i	$-0.603357\pi$
$3$	0.859341	−	2.64478i	0.496141	−	1.52696i	0.815172	−	0.579220i	$-0.196643\pi$
$4$	−0.597658	−	1.83940i	−0.298829	−	0.919702i
$5$	1.97532	−	1.43516i	0.883391	−	0.641821i	−0.0507555	−	0.998711i	$-0.516163\pi$
$5$	1.97532	−	1.43516i	0.883391	−	0.641821i	0.934146	+	0.356890i	$0.116163\pi$
$6$	−0.577702	+	0.419725i	−0.235846	+	0.171352i
$7$	0.905304	+	2.78624i	0.342173	+	1.05310i	0.963080	+	0.269215i	$0.0867643\pi$
$7$	0.905304	+	2.78624i	0.342173	+	1.05310i	−0.620907	+	0.783884i	$0.713236\pi$
$8$	−0.312167	+	0.960751i	−0.110368	+	0.339677i
$9$	−3.82934	−	2.78218i	−1.27645	−	0.927392i
$10$	−0.626965			−0.198264
$11$	0.914084	+	3.18817i	0.275607	+	0.961270i
$11$	0.914084	+	3.18817i	0.275607	+	0.961270i
$12$	−5.37841			−1.55261
$13$	1.20556	+	0.875893i	0.334363	+	0.242929i	0.742280	−	0.670090i	$-0.233745\pi$
$13$	1.20556	+	0.875893i	0.334363	+	0.242929i	−0.407917	+	0.913019i	$0.633745\pi$
$14$	0.232465	−	0.715454i	0.0621289	−	0.191213i
$15$	−2.09819	−	6.45758i	−0.541751	−	1.66734i
$16$	−2.91952	+	2.12116i	−0.729881	+	0.530289i
$17$	−3.39760	+	2.46850i	−0.824039	+	0.598699i	−0.917867	−	0.396889i	$-0.870090\pi$
$17$	−3.39760	+	2.46850i	−0.824039	+	0.598699i	0.0938277	+	0.995588i	$0.470090\pi$
$18$	0.375588	+	1.15594i	0.0885269	+	0.272458i
$19$	0.309017	−	0.951057i	0.0708934	−	0.218187i
$19$	0.309017	−	0.951057i	0.0708934	−	0.218187i
$20$	−3.82040	−	2.77568i	−0.854267	−	0.620661i
$21$	8.14695			1.77781
$22$	0.291306	−	0.800277i	0.0621066	−	0.170620i
$23$	3.73331			0.778449			0.389225	−	0.921143i	$-0.372743\pi$
$23$	3.73331			0.778449			0.389225	+	0.921143i	$0.372743\pi$
$24$	2.27272	+	1.65123i	0.463916	+	0.337055i
$25$	0.297141	−	0.914506i	0.0594282	−	0.182901i
$26$	−0.118244	−	0.363917i	−0.0231895	−	0.0713700i
$27$	−3.89960	+	2.83323i	−0.750478	+	0.545254i
$28$	4.58396	−	3.33044i	0.866286	−	0.629394i
$29$	−1.48321	−	4.56487i	−0.275426	−	0.847674i	−0.989106	−	0.147203i	$-0.952973\pi$
$29$	−1.48321	−	4.56487i	−0.275426	−	0.847674i	0.713680	−	0.700472i	$-0.247027\pi$
$30$	−0.538777	+	1.65818i	−0.0983667	+	0.302742i
$31$	−1.44407	−	1.04918i	−0.259363	−	0.188438i	0.450503	−	0.892775i	$-0.351245\pi$
$31$	−1.44407	−	1.04918i	−0.259363	−	0.188438i	−0.709866	+	0.704337i	$0.751245\pi$
$32$	2.94704			0.520968
$33$	9.21752	+	0.322177i	1.60456	+	0.0560838i
$34$	1.07839			0.184943
$35$	5.78695	+	4.20447i	0.978174	+	0.710685i
$36$	−2.82891	+	8.70649i	−0.471485	+	1.45108i
$37$	2.61394	+	8.04488i	0.429729	+	1.32257i	0.898393	+	0.439193i	$0.144736\pi$
$37$	2.61394	+	8.04488i	0.429729	+	1.32257i	−0.468664	+	0.883377i	$0.655264\pi$
$38$	−0.207740	+	0.150932i	−0.0336999	+	0.0244844i
$39$	3.35253	−	2.43576i	0.536835	−	0.390034i
$40$	0.762197	+	2.34580i	0.120514	+	0.370904i
$41$	0.684304	−	2.10607i	0.106870	−	0.328913i	−0.883294	−	0.468819i	$-0.844680\pi$
$41$	0.684304	−	2.10607i	0.106870	−	0.328913i	0.990165	+	0.139905i	$0.0446798\pi$
$42$	−1.69245	−	1.22964i	−0.261151	−	0.189737i
$43$	−11.0941			−1.69184			−0.845920	−	0.533310i	$-0.820948\pi$
$43$	−11.0941			−1.69184			−0.845920	+	0.533310i	$0.820948\pi$
$44$	5.31803	−	3.58681i	0.801723	−	0.540732i
$45$	−11.5570			−1.72282
$46$	−0.775559	−	0.563477i	−0.114350	−	0.0830801i
$47$	2.33295	−	7.18007i	0.340295	−	1.04732i	−0.623759	−	0.781617i	$-0.714395\pi$
$47$	2.33295	−	7.18007i	0.340295	−	1.04732i	0.964055	−	0.265705i	$-0.0856046\pi$
$48$	3.10113	+	9.54429i	0.447609	+	1.37760i
$49$	−1.28043	+	0.930289i	−0.182919	+	0.132898i
$50$	−0.199757	+	0.145132i	−0.0282498	+	0.0205247i
$51$	3.60894	+	11.1072i	0.505353	+	1.55532i
$52$	0.890606	−	2.74100i	0.123505	−	0.380109i
$53$	−11.2574	−	8.17895i	−1.54632	−	1.12347i	−0.946213	−	0.323544i	$-0.895126\pi$
$53$	−11.2574	−	8.17895i	−1.54632	−	1.12347i	−0.600104	−	0.799922i	$-0.704874\pi$
$54$	1.23773			0.168434
$55$	6.38114	+	4.98582i	0.860432	+	0.672287i
$56$	−2.95949			−0.395478
$57$	−2.24978	−	1.63456i	−0.297991	−	0.216503i
$58$	−0.380862	+	1.17217i	−0.0500096	+	0.153914i
$59$	3.01721	+	9.28603i	0.392808	+	1.20894i	0.930656	+	0.365896i	$0.119237\pi$
$59$	3.01721	+	9.28603i	0.392808	+	1.20894i	−0.537848	+	0.843042i	$0.680763\pi$
$60$	−10.6241	+	7.71885i	−1.37156	+	0.996500i
$61$	−9.96898	+	7.24289i	−1.27640	+	0.927357i	−0.999438	−	0.0335250i	$-0.989327\pi$
$61$	−9.96898	+	7.24289i	−1.27640	+	0.927357i	−0.276959	+	0.960882i	$0.589327\pi$
$62$	0.141637	+	0.435913i	0.0179879	+	0.0553610i
$63$	4.28510	−	13.1882i	0.539871	−	1.66155i
$64$	5.22683	+	3.79751i	0.653353	+	0.474689i
$65$	3.63842			0.451290
$66$	−1.86622	−	1.45815i	−0.229716	−	0.179486i
$67$	6.65052			0.812491			0.406245	−	0.913764i	$-0.366838\pi$
$67$	6.65052			0.812491			0.406245	+	0.913764i	$0.366838\pi$
$68$	6.57117	+	4.77424i	0.796872	+	0.578961i
$69$	3.20819	−	9.87378i	0.386220	−	1.18866i
$70$	−0.567594	−	1.74687i	−0.0678405	−	0.208791i
$71$	8.53131	−	6.19836i	1.01248	−	0.735610i	0.0477525	−	0.998859i	$-0.484794\pi$
$71$	8.53131	−	6.19836i	1.01248	−	0.735610i	0.964728	+	0.263249i	$0.0847941\pi$
$72$	3.86837	−	2.81054i	0.455892	−	0.331225i
$73$	1.58137	+	4.86697i	0.185086	+	0.569636i	0.999950	−	0.0100166i	$-0.00318844\pi$
$73$	1.58137	+	4.86697i	0.185086	+	0.569636i	−0.814864	+	0.579652i	$0.803188\pi$
$74$	0.671210	−	2.06577i	0.0780266	−	0.240141i
$75$	−2.16332	−	1.57174i	−0.249799	−	0.181489i
$76$	−1.93406			−0.221852
$77$	−8.05549	+	5.43312i	−0.918008	+	0.619162i
$78$	−1.06409			−0.120485
$79$	−1.05579	−	0.767079i	−0.118786	−	0.0863031i	0.526806	−	0.849985i	$-0.323389\pi$
$79$	−1.05579	−	0.767079i	−0.118786	−	0.0863031i	−0.645592	+	0.763682i	$0.723389\pi$
$80$	−2.72281	+	8.37994i	−0.304419	+	0.936905i
$81$	−0.245862	−	0.756686i	−0.0273180	−	0.0840762i
$82$	−0.460032	+	0.334233i	−0.0508020	+	0.0369098i
$83$	7.41615	−	5.38815i	0.814028	−	0.591426i	−0.100968	−	0.994890i	$-0.532194\pi$
$83$	7.41615	−	5.38815i	0.814028	−	0.591426i	0.914996	+	0.403464i	$0.132194\pi$
$84$	−4.86909	−	14.9855i	−0.531262	−	1.63506i
$85$	−3.16867	+	9.75217i	−0.343691	+	1.05777i
$86$	2.30470	+	1.67446i	0.248522	+	0.180562i
$87$	−13.3476			−1.43102
$88$	−3.34839	−	0.117035i	−0.356939	−	0.0124760i
$89$	−2.45131			−0.259838			−0.129919	−	0.991525i	$-0.541472\pi$
$89$	−2.45131			−0.259838			−0.129919	+	0.991525i	$0.541472\pi$
$90$	2.40086	+	1.74433i	0.253073	+	0.183868i
$91$	−1.34905	+	4.15194i	−0.141419	+	0.435241i
$92$	−2.23124	−	6.86706i	−0.232623	−	0.715941i
$93$	−4.01579	+	2.91764i	−0.416418	+	0.302545i
$94$	−1.56835	+	1.13947i	−0.161763	+	0.117528i
$95$	−0.754506	−	2.32213i	−0.0774107	−	0.238246i
$96$	2.53251	−	7.79427i	0.258473	−	0.795499i
$97$	−3.53874	−	2.57105i	−0.359305	−	0.261050i	0.393457	−	0.919343i	$-0.371279\pi$
$97$	−3.53874	−	2.57105i	−0.359305	−	0.261050i	−0.752762	+	0.658293i	$0.771279\pi$
$98$	0.406408			0.0410534
$99$	5.36973	−	14.7517i	0.539678	−	1.48261i
$100$	−1.85973			−0.185973
$101$	−3.89991	−	2.83345i	−0.388056	−	0.281939i	0.376602	−	0.926375i	$-0.377092\pi$
$101$	−3.89991	−	2.83345i	−0.388056	−	0.281939i	−0.764658	+	0.644436i	$0.777092\pi$
$102$	0.926708	−	2.85212i	0.0917578	−	0.282401i
$103$	3.39521	+	10.4494i	0.334540	+	1.02961i	0.966948	+	0.254973i	$0.0820666\pi$
$103$	3.39521	+	10.4494i	0.334540	+	1.02961i	−0.632408	+	0.774635i	$0.717933\pi$
$104$	−1.21785	+	0.884822i	−0.119420	+	0.0867639i
$105$	16.0929	−	11.6921i	1.57050	−	1.14104i
$106$	1.10414	+	3.39820i	0.107244	+	0.330062i
$107$	4.77588	−	14.6987i	0.461702	−	1.42097i	−0.401381	−	0.915911i	$-0.631470\pi$
$107$	4.77588	−	14.6987i	0.461702	−	1.42097i	0.863083	−	0.505061i	$-0.168530\pi$
$108$	7.54207	+	5.47964i	0.725736	+	0.527278i
$109$	−10.5781			−1.01320			−0.506599	−	0.862182i	$-0.669098\pi$
$109$	−10.5781			−1.01320			−0.506599	+	0.862182i	$0.669098\pi$
$110$	−0.573099	−	1.99887i	−0.0546428	−	0.190585i
$111$	23.5232			2.23272
$112$	−8.55311	−	6.21420i	−0.808193	−	0.587186i
$113$	2.78405	−	8.56843i	0.261901	−	0.806050i	−0.730490	−	0.682924i	$-0.760708\pi$
$113$	2.78405	−	8.56843i	0.261901	−	0.806050i	0.992391	−	0.123126i	$-0.0392919\pi$
$114$	0.220663	+	0.679129i	0.0206669	+	0.0636063i
$115$	7.37449	−	5.35788i	0.687675	−	0.499625i
$116$	−7.51017	+	5.45646i	−0.697302	+	0.506620i
$117$	−2.17962	−	6.70818i	−0.201506	−	0.620172i
$118$	0.774763	−	2.38448i	0.0713228	−	0.219509i
$119$	−9.95369	−	7.23178i	−0.912453	−	0.662936i
$120$	6.85911			0.626148
$121$	−9.32890	+	5.82852i	−0.848082	+	0.529865i
$122$	3.16414			0.286468
$123$	−4.98205	−	3.61967i	−0.449216	−	0.326374i
$124$	−1.06680	+	3.28328i	−0.0958016	+	0.294847i
$125$	3.04702	+	9.37776i	0.272534	+	0.838773i
$126$	−2.88071	+	2.09296i	−0.256634	+	0.186455i
$127$	16.1968	−	11.7677i	1.43723	−	1.04421i	0.448621	−	0.893722i	$-0.351915\pi$
$127$	16.1968	−	11.7677i	1.43723	−	1.04421i	0.988612	−	0.150489i	$-0.0480849\pi$
$128$	−2.33403	−	7.18340i	−0.206301	−	0.634929i
$129$	−9.53364	+	29.3415i	−0.839391	+	2.58338i
$130$	−0.755847	−	0.549155i	−0.0662921	−	0.0481641i
$131$	−8.41811			−0.735493			−0.367747	−	0.929926i	$-0.619871\pi$
$131$	−8.41811			−0.735493			−0.367747	+	0.929926i	$0.619871\pi$
$132$	−4.91632	−	17.1473i	−0.427911	−	1.49248i
$133$	2.92963			0.254031
$134$	−1.38158	−	1.00378i	−0.119350	−	0.0867132i
$135$	−3.63685	+	11.1931i	−0.313010	+	0.963346i
$136$	−1.31100	−	4.03483i	−0.112417	−	0.345984i
$137$	−10.9277	+	7.93943i	−0.933615	+	0.678311i	−0.946875	−	0.321601i	$-0.895779\pi$
$137$	−10.9277	+	7.93943i	−0.933615	+	0.678311i	0.0132600	+	0.999912i	$0.495779\pi$
$138$	−2.15674	+	1.56696i	−0.183594	+	0.133389i
$139$	3.83679	+	11.8084i	0.325432	+	1.00158i	0.971245	+	0.238082i	$0.0765187\pi$
$139$	3.83679	+	11.8084i	0.325432	+	1.00158i	−0.645813	+	0.763496i	$0.723481\pi$
$140$	4.27509	−	13.1574i	0.361311	−	1.11200i
$141$	−16.9849	−	12.3403i	−1.43039	−	1.03924i
$142$	−2.70783			−0.227236
$143$	−1.69051	+	4.64419i	−0.141368	+	0.388366i
$144$	17.0813			1.42344
$145$	−9.48112	−	6.88844i	−0.787364	−	0.572053i
$146$	0.406067	−	1.24975i	0.0336063	−	0.103430i
$147$	1.36008	+	4.18590i	0.112178	+	0.345247i
$148$	13.2355	−	9.61618i	1.08795	−	0.790445i
$149$	−2.41470	+	1.75438i	−0.197820	+	0.143724i	−0.682286	−	0.731086i	$-0.739014\pi$
$149$	−2.41470	+	1.75438i	−0.197820	+	0.143724i	0.484466	+	0.874810i	$0.339014\pi$
$150$	0.212182	+	0.653029i	0.0173246	+	0.0533196i
$151$	−5.99443	+	18.4489i	−0.487820	+	1.50135i	0.340036	+	0.940413i	$0.389561\pi$
$151$	−5.99443	+	18.4489i	−0.487820	+	1.50135i	−0.827855	+	0.560942i	$0.810439\pi$
$152$	0.817264	+	0.593777i	0.0662888	+	0.0481617i
$153$	19.8784			1.60707
$154$	2.49348	+	0.0871538i	0.200931	+	0.00702305i
$155$	−4.35824			−0.350062
$156$	−6.48401	−	4.71091i	−0.519137	−	0.377175i
$157$	−5.55172	+	17.0864i	−0.443075	+	1.36365i	0.441505	+	0.897259i	$0.354445\pi$
$157$	−5.55172	+	17.0864i	−0.443075	+	1.36365i	−0.884581	+	0.466387i	$0.845555\pi$
$158$	0.103554	+	0.318706i	0.00823831	+	0.0253549i
$159$	−31.3054	+	22.7447i	−2.48268	+	1.80377i
$160$	5.82135	−	4.22946i	0.460218	−	0.334368i
$161$	3.37978	+	10.4019i	0.266364	+	0.819784i
$162$	−0.0631328	+	0.194303i	−0.00496018	+	0.0152659i
$163$	2.48450	+	1.80509i	0.194601	+	0.141386i	0.680819	−	0.732452i	$-0.261624\pi$
$163$	2.48450	+	1.80509i	0.194601	+	0.141386i	−0.486218	+	0.873837i	$0.661624\pi$
$164$	−4.28290			−0.334438
$165$	18.6700	−	12.5922i	1.45345	−	0.980300i
$166$	−2.35388			−0.182696
$167$	4.39380	+	3.19228i	0.340003	+	0.247026i	0.744663	−	0.667441i	$-0.232610\pi$
$167$	4.39380	+	3.19228i	0.340003	+	0.247026i	−0.404660	+	0.914467i	$0.632610\pi$
$168$	−2.54321	+	7.82719i	−0.196213	+	0.603881i
$169$	−3.33103	−	10.2518i	−0.256233	−	0.788603i
$170$	2.13018	−	1.54766i	0.163377	−	0.118700i
$171$	−3.82934	+	2.78218i	−0.292837	+	0.212758i
$172$	6.63050	+	20.4066i	0.505571	+	1.55599i
$173$	4.72993	−	14.5572i	0.359610	−	1.10677i	−0.593678	−	0.804703i	$-0.702325\pi$
$173$	4.72993	−	14.5572i	0.359610	−	1.10677i	0.953288	−	0.302063i	$-0.0976754\pi$
$174$	2.77284	+	2.01459i	0.210209	+	0.152726i
$175$	2.81703			0.212948
$176$	−9.43131	−	7.36903i	−0.710911	−	0.555461i
$177$	27.1523			2.04089
$178$	0.509235	+	0.369981i	0.0381688	+	0.0277312i
$179$	−4.33269	+	13.3346i	−0.323840	+	0.996678i	0.648121	+	0.761537i	$0.275555\pi$
$179$	−4.33269	+	13.3346i	−0.323840	+	0.996678i	−0.971961	+	0.235141i	$0.924445\pi$
$180$	6.90716	+	21.2580i	0.514829	+	1.58448i
$181$	−2.49788	+	1.81482i	−0.185666	+	0.134894i	−0.676736	−	0.736226i	$-0.736606\pi$
$181$	−2.49788	+	1.81482i	−0.185666	+	0.134894i	0.491070	+	0.871120i	$0.336606\pi$
$182$	0.906913	−	0.658911i	0.0672248	−	0.0488417i
$183$	10.5891	+	32.5899i	0.782768	+	2.40911i
$184$	−1.16542	+	3.58678i	−0.0859156	+	0.264421i
$185$	16.7090	+	12.1398i	1.22847	+	0.892537i
$186$	1.27461			0.0934588
$187$	−10.9757	−	8.57572i	−0.802623	−	0.627119i
$188$	−14.6014			−1.06491
$189$	−11.4244	−	8.30029i	−0.831000	−	0.603757i
$190$	−0.193743	+	0.596279i	−0.0140556	+	0.0432587i
$191$	−0.0250575	−	0.0771192i	−0.00181310	−	0.00558015i	0.950146	−	0.311806i	$-0.100934\pi$
$191$	−0.0250575	−	0.0771192i	−0.00181310	−	0.00558015i	−0.951959	+	0.306226i	$0.900934\pi$
$192$	14.5352	−	10.5604i	1.04899	−	0.762134i
$193$	20.8960	−	15.1818i	1.50413	−	1.09281i	0.535427	−	0.844581i	$-0.320151\pi$
$193$	20.8960	−	15.1818i	1.50413	−	1.09281i	0.968701	−	0.248232i	$-0.0798494\pi$
$194$	0.347086	+	1.06822i	0.0249193	+	0.0766937i
$195$	3.12664	−	9.62282i	0.223904	−	0.689104i
$196$	2.47644	+	1.79924i	0.176889	+	0.128517i
$197$	−12.5922			−0.897155			−0.448578	−	0.893744i	$-0.648069\pi$
$197$	−12.5922			−0.897155			−0.448578	+	0.893744i	$0.648069\pi$
$198$	−3.34202	+	2.25407i	−0.237507	+	0.160190i
$199$	−12.4747			−0.884309			−0.442154	−	0.896939i	$-0.645786\pi$
$199$	−12.4747			−0.884309			−0.442154	+	0.896939i	$0.645786\pi$
$200$	0.785855	+	0.570957i	0.0555683	+	0.0403727i
$201$	5.71507	−	17.5892i	0.403110	−	1.24064i
$202$	0.382510	+	1.17725i	0.0269133	+	0.0828307i
$203$	11.3760	−	8.26518i	0.798442	−	0.580102i
$204$	18.2737	−	13.2766i	1.27941	−	0.929548i
$205$	−1.67082	−	5.14225i	−0.116695	−	0.359151i
$206$	0.871826	−	2.68321i	0.0607430	−	0.186948i
$207$	−14.2961	−	10.3867i	−0.993648	−	0.721928i
$208$	−5.37758			−0.372868
$209$	3.31460	+	0.115854i	0.229276	+	0.00801379i
$210$	−5.10785			−0.352475
$211$	−2.24718	−	1.63267i	−0.154702	−	0.112398i	0.507742	−	0.861509i	$-0.330481\pi$
$211$	−2.24718	−	1.63267i	−0.154702	−	0.112398i	−0.662443	+	0.749112i	$0.730481\pi$
$212$	−8.31634	+	25.5951i	−0.571168	+	1.75788i
$213$	−9.06199	−	27.8899i	−0.620917	−	1.91099i
$214$	−3.21064	+	2.33267i	−0.219475	+	0.159458i
$215$	−21.9145	+	15.9218i	−1.49456	+	1.08586i
$216$	−1.50470	−	4.63098i	−0.102382	−	0.315099i
$217$	1.61594	−	4.97335i	0.109697	−	0.337613i
$218$	2.19750	+	1.59658i	0.148833	+	0.108134i
$219$	14.2310			0.961641
$220$	5.35719	−	14.7173i	0.361182	−	0.992240i
$221$	−6.25817			−0.420970
$222$	−4.88672	−	3.55041i	−0.327975	−	0.238288i
$223$	−0.617872	+	1.90162i	−0.0413758	+	0.127342i	−0.969611	−	0.244653i	$-0.921326\pi$
$223$	−0.617872	+	1.90162i	−0.0413758	+	0.127342i	0.928235	+	0.371995i	$0.121326\pi$
$224$	2.66797	+	8.21116i	0.178261	+	0.548631i
$225$	−3.68217	+	2.67525i	−0.245478	+	0.178350i
$226$	−1.87161	+	1.35981i	−0.124498	+	0.0904529i
$227$	4.21377	+	12.9687i	0.279678	+	0.860760i	0.987944	+	0.154814i	$0.0494779\pi$
$227$	4.21377	+	12.9687i	0.279678	+	0.860760i	−0.708266	+	0.705946i	$0.750522\pi$
$228$	−1.66202	+	5.11517i	−0.110070	+	0.338760i
$229$	−6.71129	−	4.87604i	−0.443494	−	0.322217i	0.343528	−	0.939143i	$-0.388378\pi$
$229$	−6.71129	−	4.87604i	−0.443494	−	0.322217i	−0.787022	+	0.616925i	$0.788378\pi$
$230$	−2.34066			−0.154338
$231$	7.44700	+	25.9739i	0.489977	+	1.70896i
$232$	4.84871			0.318333
$233$	23.3530	+	16.9669i	1.52990	+	1.11154i	0.956293	+	0.292411i	$0.0944575\pi$
$233$	23.3530	+	16.9669i	1.52990	+	1.11154i	0.573610	+	0.819128i	$0.305542\pi$
$234$	−0.559686	+	1.72254i	−0.0365878	+	0.112606i
$235$	−5.69620	−	17.5311i	−0.371579	−	1.14360i
$236$	15.2775	−	11.0997i	0.994480	−	0.722532i
$237$	−2.93604	+	2.13316i	−0.190716	+	0.138564i
$238$	0.976275	+	3.00467i	0.0632825	+	0.194764i
$239$	1.56151	−	4.80583i	0.101006	−	0.310863i	−0.887767	−	0.460294i	$-0.847744\pi$
$239$	1.56151	−	4.80583i	0.101006	−	0.310863i	0.988772	+	0.149431i	$0.0477440\pi$
$240$	19.8233	+	14.4024i	1.27959	+	0.929674i
$241$	6.28489			0.404846			0.202423	−	0.979298i	$-0.435118\pi$
$241$	6.28489			0.404846			0.202423	+	0.979298i	$0.435118\pi$
$242$	2.81770	+	0.197213i	0.181129	+	0.0126773i
$243$	−16.6731			−1.06958
$244$	19.2806	+	14.0082i	1.23432	+	0.896783i
$245$	−1.19416	+	3.67524i	−0.0762920	+	0.234803i
$246$	0.488647	+	1.50390i	0.0311550	+	0.0958853i
$247$	1.20556	−	0.875893i	0.0767082	−	0.0557318i
$248$	1.45879	−	1.05987i	0.0926332	−	0.0673020i
$249$	−7.87746	−	24.2443i	−0.499214	−	1.53642i
$250$	0.782417	−	2.40803i	0.0494844	−	0.152297i
$251$	12.0647	+	8.76549i	0.761515	+	0.553273i	0.899375	−	0.437179i	$-0.144022\pi$
$251$	12.0647	+	8.76549i	0.761515	+	0.553273i	−0.137860	+	0.990452i	$0.544022\pi$
$252$	−26.8194			−1.68946
$253$	3.41256	+	11.9024i	0.214546	+	0.748300i
$254$	−5.14085			−0.322565
$255$	23.0694	+	16.7609i	1.44466	+	1.04961i
$256$	3.39361	−	10.4444i	0.212100	−	0.652778i
$257$	−0.646336	−	1.98922i	−0.0403173	−	0.124084i	0.928872	−	0.370401i	$-0.120780\pi$
$257$	−0.646336	−	1.98922i	−0.0403173	−	0.124084i	−0.969189	+	0.246317i	$0.920780\pi$
$258$	6.40910	−	4.65649i	0.399013	−	0.289900i
$259$	−20.0485	+	14.5661i	−1.24576	+	0.905095i
$260$	−2.17453	−	6.69252i	−0.134859	−	0.415053i
$261$	−7.02053	+	21.6070i	−0.434560	+	1.33744i
$262$	1.74878	+	1.27056i	0.108040	+	0.0784957i
$263$	0.765101			0.0471781			0.0235891	−	0.999722i	$-0.492491\pi$
$263$	0.765101			0.0471781			0.0235891	+	0.999722i	$0.492491\pi$
$264$	−3.18694	+	8.75517i	−0.196142	+	0.538844i
$265$	−33.9750			−2.08707
$266$	−0.608601	−	0.442175i	−0.0373157	−	0.0271115i
$267$	−2.10651	+	6.48316i	−0.128916	+	0.396763i
$268$	−3.97474	−	12.2330i	−0.242796	−	0.747249i
$269$	−4.95055	+	3.59679i	−0.301841	+	0.219300i	−0.728387	−	0.685165i	$-0.759730\pi$
$269$	−4.95055	+	3.59679i	−0.301841	+	0.219300i	0.426547	+	0.904465i	$0.359730\pi$
$270$	2.44491	−	1.77633i	0.148793	−	0.108104i
$271$	−8.79259	−	27.0608i	−0.534112	−	1.64383i	−0.745561	−	0.666437i	$-0.767818\pi$
$271$	−8.79259	−	27.0608i	−0.534112	−	1.64383i	0.211449	−	0.977389i	$-0.432182\pi$
$272$	4.68329	−	14.4137i	0.283966	−	0.873958i
$273$	9.82167	+	7.13586i	0.594434	+	0.431882i
$274$	3.46844			0.209536
$275$	3.18721	+	0.111402i	0.192196	+	0.00671777i
$276$	−20.0793			−1.20863
$277$	−17.1958	−	12.4935i	−1.03320	−	0.750661i	−0.0642501	−	0.997934i	$-0.520466\pi$
$277$	−17.1958	−	12.4935i	−1.03320	−	0.750661i	−0.968946	+	0.247273i	$0.920466\pi$
$278$	0.985216	−	3.03218i	0.0590893	−	0.181858i
$279$	2.61083	+	8.03531i	0.156306	+	0.481062i
$280$	−5.84594	+	4.24733i	−0.349362	+	0.253826i
$281$	6.78589	−	4.93024i	0.404812	−	0.294113i	−0.366686	−	0.930345i	$-0.619508\pi$
$281$	6.78589	−	4.93024i	0.404812	−	0.294113i	0.771498	+	0.636231i	$0.219508\pi$
$282$	1.66591	+	5.12714i	0.0992034	+	0.305317i
$283$	5.95652	−	18.3323i	0.354078	−	1.08974i	−0.602464	−	0.798146i	$-0.705814\pi$
$283$	5.95652	−	18.3323i	0.354078	−	1.08974i	0.956542	−	0.291595i	$-0.0941859\pi$
$284$	−16.5001	−	11.9880i	−0.979101	−	0.711358i
$285$	−6.78990			−0.402199
$286$	1.05215	−	0.709632i	0.0622146	−	0.0419614i
$287$	6.48752			0.382946
$288$	−11.2852	−	8.19919i	−0.664988	−	0.483142i
$289$	0.196898	−	0.605990i	0.0115822	−	0.0356465i
$290$	0.929924	+	2.86201i	0.0546070	+	0.168063i
$291$	−9.84083	+	7.14978i	−0.576880	+	0.419128i
$292$	8.00720	−	5.81757i	0.468586	−	0.340447i
$293$	−0.299650	−	0.922227i	−0.0175057	−	0.0538771i	0.941922	−	0.335832i	$-0.109017\pi$
$293$	−0.299650	−	0.922227i	−0.0175057	−	0.0538771i	−0.959428	+	0.281954i	$0.909017\pi$
$294$	0.349243	−	1.07486i	0.0203683	−	0.0626871i
$295$	19.2869	+	14.0127i	1.12292	+	0.815852i
$296$	−8.54511			−0.496674
$297$	−12.5974	−	9.84279i	−0.730974	−	0.571137i
$298$	0.766422			0.0443977
$299$	4.50074	+	3.26998i	0.260285	+	0.189108i
$300$	−1.59815	+	4.91859i	−0.0922690	+	0.283975i
$301$	−10.0436	−	30.9109i	−0.578901	−	1.78168i
$302$	4.02982	−	2.92784i	0.231890	−	0.168478i
$303$	−10.8452	+	7.87951i	−0.623041	+	0.452666i
$304$	1.11516	+	3.43210i	0.0639587	+	0.196845i
$305$	−9.29728	+	28.6141i	−0.532360	+	1.63844i
$306$	−4.12954	−	3.00028i	−0.236070	−	0.171515i
$307$	−7.68745			−0.438746			−0.219373	−	0.975641i	$-0.570401\pi$
$307$	−7.68745			−0.438746			−0.219373	+	0.975641i	$0.570401\pi$
$308$	14.8081	+	11.5701i	0.843772	+	0.659270i
$309$	30.5540			1.73815
$310$	0.905381	+	0.657798i	0.0514222	+	0.0373604i
$311$	6.78354	−	20.8776i	0.384659	−	1.18386i	−0.552068	−	0.833799i	$-0.686161\pi$
$311$	6.78354	−	20.8776i	0.384659	−	1.18386i	0.936727	−	0.350060i	$-0.113839\pi$
$312$	1.29361	+	3.98131i	0.0732361	+	0.225398i
$313$	23.5402	−	17.1029i	1.33057	−	0.966716i	0.330835	−	0.943689i	$-0.392670\pi$
$313$	23.5402	−	17.1029i	1.33057	−	0.966716i	0.999735	−	0.0230269i	$-0.00733035\pi$
$314$	3.73221	−	2.71161i	0.210621	−	0.153025i
$315$	−10.4626	−	32.2007i	−0.589502	−	1.81430i
$316$	−0.779964	+	2.40048i	−0.0438764	+	0.135038i
$317$	−1.24895	−	0.907412i	−0.0701478	−	0.0509654i	0.552159	−	0.833739i	$-0.313804\pi$
$317$	−1.24895	−	0.907412i	−0.0701478	−	0.0509654i	−0.622307	+	0.782774i	$0.713804\pi$
$318$	9.93631			0.557201
$319$	13.1978	−	8.90142i	0.738935	−	0.498384i
$320$	15.7747			0.881832
$321$	−34.7706	−	25.2623i	−1.94070	−	1.41000i
$322$	0.867864	−	2.67101i	0.0483642	−	0.148850i
$323$	1.29777	+	3.99412i	0.0722097	+	0.222239i
$324$	−1.24491	+	0.904479i	−0.0691616	+	0.0502489i
$325$	1.15923	−	0.842231i	0.0643026	−	0.0467186i
$326$	−0.243684	−	0.749981i	−0.0134964	−	0.0415376i
$327$	−9.09019	+	27.9767i	−0.502689	+	1.54712i
$328$	1.80979	+	1.31489i	0.0999292	+	0.0726028i
$329$	22.1174			1.21937
$330$	−5.77907	−	0.201994i	−0.318127	−	0.0111194i
$331$	−16.3308			−0.897621			−0.448810	−	0.893627i	$-0.648152\pi$
$331$	−16.3308			−0.897621			−0.448810	+	0.893627i	$0.648152\pi$
$332$	−14.3433	−	10.4210i	−0.787191	−	0.571927i
$333$	12.3726	−	38.0790i	0.678015	−	2.08672i
$334$	−0.430952	−	1.32633i	−0.0235806	−	0.0725737i
$335$	13.1369	−	9.54453i	0.717747	−	0.521474i
$336$	−23.7852	+	17.2810i	−1.29759	+	0.942754i
$337$	1.88832	+	5.81166i	0.102863	+	0.316581i	0.989223	−	0.146416i	$-0.0467739\pi$
$337$	1.88832	+	5.81166i	0.102863	+	0.316581i	−0.886360	+	0.462997i	$0.846774\pi$
$338$	−0.855345	+	2.63248i	−0.0465246	+	0.143188i
$339$	−20.2691	−	14.7264i	−1.10087	−	0.799828i
$340$	19.8320			1.07554
$341$	2.02496	−	5.56298i	0.109658	−	0.301252i
$342$	1.21543			0.0657228
$343$	12.8396	+	9.32853i	0.693275	+	0.503693i
$344$	3.46322	−	10.6587i	0.186724	−	0.574679i
$345$	−7.83321	−	24.1081i	−0.421726	−	1.29794i
$346$	−3.17975	+	2.31023i	−0.170945	+	0.124199i
$347$	14.1378	−	10.2717i	0.758956	−	0.551414i	−0.139634	−	0.990203i	$-0.544593\pi$
$347$	14.1378	−	10.2717i	0.758956	−	0.551414i	0.898590	+	0.438789i	$0.144593\pi$
$348$	7.97733	+	24.5517i	0.427630	+	1.31611i
$349$	−5.82513	+	17.9279i	−0.311812	+	0.959658i	0.665235	+	0.746634i	$0.268331\pi$
$349$	−5.82513	+	17.9279i	−0.311812	+	0.959658i	−0.977047	+	0.213024i	$0.931669\pi$
$350$	−0.585212	−	0.425181i	−0.0312809	−	0.0227269i
$351$	−7.18282			−0.383391
$352$	2.69384	+	9.39568i	0.143582	+	0.500791i
$353$	−22.3648			−1.19036			−0.595180	−	0.803592i	$-0.702919\pi$
$353$	−22.3648			−1.19036			−0.595180	+	0.803592i	$0.702919\pi$
$354$	−5.64063	−	4.09816i	−0.299796	−	0.217815i
$355$	7.95648	−	24.4875i	0.422286	−	1.29966i
$356$	1.46504	+	4.50894i	0.0776472	+	0.238973i
$357$	−27.6801	+	20.1108i	−1.46498	+	1.06437i
$358$	2.91270	−	2.11620i	0.153941	−	0.111845i
$359$	1.19129	+	3.66641i	0.0628739	+	0.193506i	0.977559	−	0.210661i	$-0.0675616\pi$
$359$	1.19129	+	3.66641i	0.0628739	+	0.193506i	−0.914685	+	0.404167i	$0.867562\pi$
$360$	3.60772	−	11.1034i	0.190144	−	0.585202i
$361$	−0.809017	−	0.587785i	−0.0425798	−	0.0309361i
$362$	0.792825			0.0416700
$363$	7.39844	+	29.6816i	0.388317	+	1.55788i
$364$	8.44336			0.442552
$365$	10.1086	+	7.34431i	0.529107	+	0.384419i
$366$	2.71908	−	8.36846i	0.142128	−	0.437426i
$367$	3.29841	+	10.1515i	0.172175	+	0.529902i	0.999493	−	0.0318326i	$-0.0101343\pi$
$367$	3.29841	+	10.1515i	0.172175	+	0.529902i	−0.827318	+	0.561734i	$0.810134\pi$
$368$	−10.8995	+	7.91894i	−0.568175	+	0.412803i
$369$	−8.47990	+	6.16101i	−0.441446	+	0.320729i
$370$	−1.63885	−	5.04386i	−0.0851997	−	0.262218i
$371$	12.5972	−	38.7701i	0.654013	−	2.01285i
$372$	7.76679	+	5.64291i	0.402690	+	0.292571i
$373$	23.2599			1.20435			0.602177	−	0.798363i	$-0.294300\pi$
$373$	23.2599			1.20435			0.602177	+	0.798363i	$0.294300\pi$
$374$	0.985743	+	3.43811i	0.0509716	+	0.177780i
$375$	27.4205			1.41599
$376$	6.16999	+	4.48276i	0.318193	+	0.231181i
$377$	2.21023	−	6.80237i	0.113832	−	0.350340i
$378$	1.12052	+	3.44861i	0.0576334	+	0.177377i
$379$	26.4045	−	19.1840i	1.35631	−	0.985416i	0.357639	−	0.933860i	$-0.383582\pi$
$379$	26.4045	−	19.1840i	1.35631	−	0.985416i	0.998670	−	0.0515566i	$-0.0164182\pi$
$380$	−3.82040	+	2.77568i	−0.195982	+	0.142389i
$381$	−17.2043	−	52.9494i	−0.881403	−	2.71268i
$382$	−0.00643430	+	0.0198028i	−0.000329208	+	0.00101320i
$383$	−4.08957	−	2.97125i	−0.208967	−	0.151824i	0.478379	−	0.878154i	$-0.341225\pi$
$383$	−4.08957	−	2.97125i	−0.208967	−	0.151824i	−0.687346	+	0.726330i	$0.741225\pi$
$384$	−21.0042			−1.07187
$385$	−8.11481	+	22.2930i	−0.413569	+	1.13616i
$386$	−6.63237			−0.337579
$387$	42.4832	+	30.8659i	2.15954	+	1.56900i
$388$	−2.61423	+	8.04578i	−0.132718	+	0.408463i
$389$	8.28652	+	25.5033i	0.420143	+	1.29307i	0.907569	+	0.419904i	$0.137936\pi$
$389$	8.28652	+	25.5033i	0.420143	+	1.29307i	−0.487425	+	0.873165i	$0.662064\pi$
$390$	−2.10192	+	1.52714i	−0.106435	+	0.0773295i
$391$	−12.6843	+	9.21568i	−0.641472	+	0.466057i
$392$	−0.494068	−	1.52058i	−0.0249542	−	0.0768011i
$393$	−7.23402	+	22.2640i	−0.364908	+	1.12307i
$394$	2.61590	+	1.90056i	0.131787	+	0.0957491i
$395$	−3.18641			−0.160326
$396$	−30.3437	−	1.06059i	−1.52483	−	0.0532967i
$397$	11.6677			0.585583			0.292791	−	0.956176i	$-0.405416\pi$
$397$	11.6677			0.585583			0.292791	+	0.956176i	$0.405416\pi$
$398$	2.59150	+	1.88283i	0.129900	+	0.0943780i
$399$	2.51755	−	7.74821i	0.126035	−	0.387896i
$400$	1.07230	+	3.30020i	0.0536150	+	0.165010i
$401$	5.42203	−	3.93934i	0.270763	−	0.196721i	−0.444115	−	0.895970i	$-0.646482\pi$
$401$	5.42203	−	3.93934i	0.270763	−	0.196721i	0.714879	+	0.699249i	$0.246482\pi$
$402$	−3.84202	+	2.79139i	−0.191623	+	0.139222i
$403$	−0.821950	−	2.52970i	−0.0409442	−	0.126013i
$404$	−2.88105	+	8.86696i	−0.143338	+	0.441148i
$405$	−1.57162	−	1.14185i	−0.0780944	−	0.0567389i
$406$	−3.61075			−0.179198
$407$	−23.2591	+	15.6874i	−1.15291	+	0.777595i
$408$	−11.7978			−0.584080
$409$	15.8138	+	11.4894i	0.781943	+	0.568115i	0.905562	−	0.424215i	$-0.139450\pi$
$409$	15.8138	+	11.4894i	0.781943	+	0.568115i	−0.123618	+	0.992330i	$0.539450\pi$
$410$	−0.429035	+	1.32043i	−0.0211885	+	0.0652116i
$411$	11.6074	+	35.7240i	0.572552	+	1.76213i
$412$	17.1915	−	12.4903i	0.846962	−	0.615354i
$413$	−23.1416	+	16.8134i	−1.13872	+	0.827331i
$414$	1.40219	+	4.31549i	0.0689137	+	0.212095i
$415$	6.91645	−	21.2866i	0.339515	−	1.04492i
$416$	3.55285	+	2.58129i	0.174193	+	0.126558i
$417$	34.5278			1.69083
$418$	−0.671090	−	0.524347i	−0.0328241	−	0.0256467i
$419$	15.0965			0.737511			0.368755	−	0.929526i	$-0.379784\pi$
$419$	15.0965			0.737511			0.368755	+	0.929526i	$0.379784\pi$
$420$	−31.1246	−	22.6133i	−1.51872	−	1.10342i
$421$	−4.94165	+	15.2088i	−0.240841	+	0.741234i	0.755451	+	0.655205i	$0.227418\pi$
$421$	−4.94165	+	15.2088i	−0.240841	+	0.741234i	−0.996293	+	0.0860288i	$0.972582\pi$
$422$	0.220407	+	0.678342i	0.0107292	+	0.0330212i
$423$	−28.9099	+	21.0043i	−1.40565	+	1.02126i
$424$	11.3721	−	8.26232i	0.552279	−	0.401254i
$425$	1.24789	+	3.84062i	0.0605317	+	0.186297i
$426$	−2.32695	+	7.16161i	−0.112741	+	0.346981i
$427$	−29.2054	−	21.2189i	−1.41335	−	1.02686i
$428$	−29.8911			−1.44484
$429$	10.8301	+	8.46197i	0.522883	+	0.408548i
$430$	6.95564			0.335431
$431$	3.13205	+	2.27557i	0.150866	+	0.109610i	0.660657	−	0.750687i	$-0.270278\pi$
$431$	3.13205	+	2.27557i	0.150866	+	0.109610i	−0.509792	+	0.860298i	$0.670278\pi$
$432$	5.37525	−	16.5433i	0.258617	−	0.795941i
$433$	−9.49064	−	29.2092i	−0.456091	−	1.40370i	−0.869850	−	0.493317i	$-0.835784\pi$
$433$	−9.49064	−	29.2092i	−0.456091	−	1.40370i	0.413759	−	0.910386i	$-0.364216\pi$
$434$	−1.08633	+	0.789268i	−0.0521457	+	0.0378861i
$435$	−26.3659	+	19.1559i	−1.26415	+	0.918457i
$436$	6.32209	+	19.4574i	0.302773	+	0.931840i
$437$	1.15366	−	3.55059i	0.0551869	−	0.169848i
$438$	−2.95635	−	2.14792i	−0.141260	−	0.102631i
$439$	−9.99876			−0.477215			−0.238607	−	0.971116i	$-0.576691\pi$
$439$	−9.99876			−0.477215			−0.238607	+	0.971116i	$0.576691\pi$
$440$	−6.78211	+	4.57428i	−0.323324	+	0.218070i
$441$	7.49144			0.356735
$442$	1.30007	+	0.944559i	0.0618382	+	0.0449281i
$443$	4.48297	−	13.7972i	0.212993	−	0.655524i	−0.786297	−	0.617848i	$-0.788005\pi$
$443$	4.48297	−	13.7972i	0.212993	−	0.655524i	0.999290	−	0.0376756i	$-0.0119953\pi$
$444$	−14.0588	−	43.2686i	−0.667203	−	2.05344i
$445$	−4.84212	+	3.51800i	−0.229538	+	0.166769i
$446$	0.415372	−	0.301785i	0.0196684	−	0.0142900i
$447$	2.56490	+	7.89395i	0.121316	+	0.373371i
$448$	−5.84891	+	18.0011i	−0.276335	+	0.850471i
$449$	−10.2227	−	7.42725i	−0.482441	−	0.350514i	0.319829	−	0.947475i	$-0.396375\pi$
$449$	−10.2227	−	7.42725i	−0.482441	−	0.350514i	−0.802270	+	0.596961i	$0.796375\pi$
$450$	1.16872			0.0550938
$451$	7.34004	+	0.256554i	0.345629	+	0.0120806i
$452$	−17.4247			−0.819589
$453$	43.6421	+	31.7079i	2.05049	+	1.48977i
$454$	1.08202	−	3.33011i	0.0507816	−	0.156290i
$455$	3.29388	+	10.1375i	0.154419	+	0.475254i
$456$	2.27272	−	1.65123i	0.106430	−	0.0773257i
$457$	−3.77828	+	2.74508i	−0.176741	+	0.128410i	−0.672638	−	0.739971i	$-0.734839\pi$
$457$	−3.77828	+	2.74508i	−0.176741	+	0.128410i	0.495898	+	0.868381i	$0.334839\pi$
$458$	0.658254	+	2.02590i	0.0307582	+	0.0946640i
$459$	6.25546	−	19.2523i	0.291980	−	0.898622i
$460$	−14.2627	−	10.3625i	−0.665003	−	0.483153i
$461$	−1.86934			−0.0870639			−0.0435320	−	0.999052i	$-0.513861\pi$
$461$	−1.86934			−0.0870639			−0.0435320	+	0.999052i	$0.513861\pi$
$462$	2.37325	−	6.51982i	0.110414	−	0.303329i
$463$	21.3757			0.993414			0.496707	−	0.867918i	$-0.334542\pi$
$463$	21.3757			0.993414			0.496707	+	0.867918i	$0.334542\pi$
$464$	14.0131	+	10.1811i	0.650541	+	0.472645i
$465$	−3.74521	+	11.5266i	−0.173680	+	0.534532i
$466$	−2.29050	−	7.04942i	−0.106105	−	0.326558i
$467$	1.06413	−	0.773139i	0.0492423	−	0.0357766i	−0.562892	−	0.826531i	$-0.690311\pi$
$467$	1.06413	−	0.773139i	0.0492423	−	0.0357766i	0.612134	+	0.790754i	$0.290311\pi$
$468$	−11.0364	+	8.01841i	−0.510157	+	0.370651i
$469$	6.02074	+	18.5299i	0.278012	+	0.855633i
$470$	−1.46268	+	4.50165i	−0.0674682	+	0.207646i
$471$	40.4190	+	29.3661i	1.86241	+	1.35312i
$472$	−9.86343			−0.454001
$473$	−10.1410	−	35.3700i	−0.466283	−	1.62632i
$474$	0.931896			0.0428034
$475$	−0.777925	−	0.565196i	−0.0356936	−	0.0259330i
$476$	−7.35326	+	22.6310i	−0.337036	+	1.03729i
$477$	20.3530	+	62.6399i	0.931898	+	2.86809i
$478$	−1.04974	+	0.762683i	−0.0480141	+	0.0348843i
$479$	−30.0647	+	21.8433i	−1.37369	+	0.998045i	−0.376252	+	0.926517i	$0.622787\pi$
$479$	−30.0647	+	21.8433i	−1.37369	+	0.998045i	−0.997439	+	0.0715273i	$0.977213\pi$
$480$	−6.18346	−	19.0307i	−0.282235	−	0.868631i
$481$	−3.89518	+	11.9881i	−0.177605	+	0.546612i
$482$	−1.30563	−	0.948593i	−0.0594696	−	0.0432072i
$483$	30.4151			1.38393
$484$	16.2965	+	13.6761i	0.740750	+	0.621643i
$485$	−10.6800			−0.484954
$486$	3.46367	+	2.51650i	0.157115	+	0.114151i
$487$	2.07361	−	6.38190i	0.0939641	−	0.289192i	−0.893018	−	0.450020i	$-0.851417\pi$
$487$	2.07361	−	6.38190i	0.0939641	−	0.289192i	0.986982	+	0.160829i	$0.0514167\pi$
$488$	−3.84663	−	11.8387i	−0.174129	−	0.535913i
$489$	6.90910	−	5.01976i	0.312440	−	0.227001i
$490$	0.802787	−	0.583259i	0.0362662	−	0.0263490i
$491$	−8.59752	−	26.4604i	−0.388000	−	1.19414i	−0.934280	−	0.356540i	$-0.883956\pi$
$491$	−8.59752	−	26.4604i	−0.388000	−	1.19414i	0.546280	−	0.837603i	$-0.316044\pi$
$492$	−3.68047	+	11.3273i	−0.165928	+	0.510675i
$493$	16.3077	+	11.8483i	0.734464	+	0.533619i
$494$	−0.382645			−0.0172160
$495$	−10.5641	−	36.8458i	−0.474821	−	1.65610i
$496$	6.44146			0.289230
$497$	24.9935	+	18.1589i	1.12111	+	0.814537i
$498$	−2.02278	+	6.22548i	−0.0906431	+	0.278971i
$499$	8.09422	+	24.9114i	0.362347	+	1.11519i	0.951626	+	0.307260i	$0.0994120\pi$
$499$	8.09422	+	24.9114i	0.362347	+	1.11519i	−0.589279	+	0.807930i	$0.700588\pi$
$500$	15.4284	−	11.2094i	0.689980	−	0.501300i
$501$	12.2187	−	8.87738i	0.545889	−	0.396612i
$502$	−1.18332	−	3.64189i	−0.0528143	−	0.162546i
$503$	−2.85213	+	8.77797i	−0.127170	+	0.391390i	−0.994290	−	0.106709i	$-0.965969\pi$
$503$	−2.85213	+	8.77797i	−0.127170	+	0.391390i	0.867120	+	0.498099i	$0.165969\pi$
$504$	11.3329	+	8.23382i	0.504807	+	0.366763i
$505$	−11.7700			−0.523760
$506$	1.08754	−	2.98768i	0.0483468	−	0.132819i
$507$	−29.9763			−1.33130
$508$	−31.3256	−	22.7594i	−1.38985	−	1.00979i
$509$	8.38656	−	25.8112i	0.371728	−	1.14406i	−0.573932	−	0.818903i	$-0.694583\pi$
$509$	8.38656	−	25.8112i	0.371728	−	1.14406i	0.945660	−	0.325157i	$-0.105417\pi$
$510$	−2.26268	−	6.96382i	−0.100193	−	0.308363i
$511$	−12.1289	+	8.81217i	−0.536551	+	0.389827i
$512$	−14.5025	+	10.5367i	−0.640927	+	0.465660i
$513$	1.48951	+	4.58425i	0.0657637	+	0.202400i
$514$	−0.165967	+	0.510794i	−0.00732049	+	0.0225301i
$515$	21.7031	+	15.7682i	0.956354	+	0.694832i
$516$	59.6688			2.62677
$517$	25.0238	+	0.874649i	1.10055	+	0.0384670i
$518$	6.36339			0.279591
$519$	−34.4360	−	25.0193i	−1.51157	−	1.09822i
$520$	−1.13579	+	3.49562i	−0.0498079	+	0.153293i
$521$	−11.6759	−	35.9348i	−0.511532	−	1.57433i	−0.789505	−	0.613744i	$-0.789663\pi$
$521$	−11.6759	−	35.9348i	−0.511532	−	1.57433i	0.277973	−	0.960589i	$-0.410337\pi$
$522$	4.71964	−	3.42902i	0.206573	−	0.150084i
$523$	−15.5493	+	11.2973i	−0.679925	+	0.493995i	−0.873333	−	0.487124i	$-0.838046\pi$
$523$	−15.5493	+	11.2973i	−0.679925	+	0.493995i	0.193408	+	0.981118i	$0.438046\pi$
$524$	5.03115	+	15.4843i	0.219787	+	0.676435i
$525$	2.42079	−	7.45043i	0.105652	−	0.325164i
$526$	−0.158942	−	0.115478i	−0.00693021	−	0.00503509i
$527$	7.49627			0.326542
$528$	−27.5942	+	18.6112i	−1.20088	+	0.809949i
$529$	−9.06239			−0.394017
$530$	7.05797	+	5.12792i	0.306579	+	0.222743i
$531$	14.2814	−	43.9538i	0.619762	−	1.90743i
$532$	−1.75092	−	5.38876i	−0.0759118	−	0.233633i
$533$	2.66967	−	1.93963i	0.115636	−	0.0840146i
$534$	1.41612	−	1.02887i	0.0612817	−	0.0445238i
$535$	−11.6609	−	35.8887i	−0.504147	−	1.55160i
$536$	−2.07607	+	6.38950i	−0.0896727	+	0.275984i
$537$	31.5439	+	22.9180i	1.36122	+	0.988985i
$538$	1.57130			0.0677436
$539$	−4.13635	−	3.23188i	−0.178165	−	0.139207i
$540$	22.7622			0.979527
$541$	−9.41517	−	6.84052i	−0.404790	−	0.294097i	0.366699	−	0.930339i	$-0.380488\pi$
$541$	−9.41517	−	6.84052i	−0.404790	−	0.294097i	−0.771489	+	0.636243i	$0.780488\pi$
$542$	−2.25777	+	6.94870i	−0.0969796	+	0.298472i
$543$	2.65326	+	8.16589i	0.113862	+	0.350432i
$544$	−10.0129	+	7.27477i	−0.429298	+	0.311903i
$545$	−20.8952	+	15.1812i	−0.895050	+	0.650292i
$546$	−0.963326	−	2.96481i	−0.0412265	−	0.126882i
$547$	12.4580	−	38.3418i	0.532666	−	1.63938i	−0.215972	−	0.976400i	$-0.569292\pi$
$547$	12.4580	−	38.3418i	0.532666	−	1.63938i	0.748638	−	0.662979i	$-0.230708\pi$
$548$	21.1348	+	15.3554i	0.902836	+	0.655948i
$549$	58.3256			2.48928
$550$	−0.645299	−	0.504196i	−0.0275156	−	0.0214990i
$551$	−4.79978			−0.204478
$552$	8.48476	+	6.16454i	0.361135	+	0.262380i
$553$	1.18145	−	3.63613i	0.0502404	−	0.154624i
$554$	1.68659	+	5.19080i	0.0716565	+	0.220536i
$555$	46.4659	−	33.7594i	1.97237	−	1.43301i
$556$	19.4274	−	14.1148i	0.823904	−	0.598602i
$557$	−1.37432	−	4.22971i	−0.0582316	−	0.179219i	0.917710	−	0.397252i	$-0.130036\pi$
$557$	−1.37432	−	4.22971i	−0.0582316	−	0.179219i	−0.975941	+	0.218033i	$0.930036\pi$
$558$	0.670412	−	2.06332i	0.0283808	−	0.0873472i
$559$	−13.3747	−	9.71728i	−0.565689	−	0.410997i
$560$	−25.8135			−1.09082
$561$	−32.1127	+	21.6588i	−1.35580	+	0.914437i
$562$	−2.15384			−0.0908541
$563$	−11.2156	−	8.14864i	−0.472683	−	0.343424i	0.325803	−	0.945438i	$-0.394365\pi$
$563$	−11.2156	−	8.14864i	−0.472683	−	0.343424i	−0.798486	+	0.602013i	$0.794365\pi$
$564$	−12.5475	+	38.6174i	−0.528347	+	1.62608i
$565$	−6.79763	−	20.9209i	−0.285978	−	0.880151i
$566$	−4.00434	+	2.90932i	−0.168315	+	0.122288i
$567$	1.88573	−	1.37006i	0.0791931	−	0.0575372i
$568$	3.29189	+	10.1314i	0.138125	+	0.425104i
$569$	−8.86382	+	27.2800i	−0.371591	+	1.14364i	0.574159	+	0.818744i	$0.305329\pi$
$569$	−8.86382	+	27.2800i	−0.371591	+	1.14364i	−0.945750	+	0.324895i	$0.894671\pi$
$570$	1.41054	+	1.02481i	0.0590808	+	0.0429247i
$571$	8.27342			0.346232			0.173116	−	0.984901i	$-0.444616\pi$
$571$	8.27342			0.346232			0.173116	+	0.984901i	$0.444616\pi$
$572$	9.55288	+	0.333898i	0.399426	+	0.0139610i
$573$	−0.225496			−0.00942024
$574$	−1.34772	−	0.979176i	−0.0562528	−	0.0408700i
$575$	1.10932	−	3.41413i	0.0462618	−	0.142379i
$576$	−9.44994	−	29.0839i	−0.393747	−	1.21183i
$577$	7.33297	−	5.32772i	0.305276	−	0.221796i	−0.424591	−	0.905385i	$-0.639582\pi$
$577$	7.33297	−	5.32772i	0.305276	−	0.221796i	0.729867	+	0.683590i	$0.239582\pi$
$578$	−0.132367	+	0.0961703i	−0.00550574	+	0.00400016i
$579$	−22.1958	−	68.3117i	−0.922427	−	2.83894i
$580$	−7.00414	+	21.5565i	−0.290831	+	0.895086i
$581$	21.7265	+	15.7852i	0.901368	+	0.654882i
$582$	3.12347			0.129472
$583$	15.7857	−	43.3667i	0.653779	−	1.79606i
$584$	−5.16960			−0.213919
$585$	−13.9327	−	10.1227i	−0.576048	−	0.418523i
$586$	−0.0769444	+	0.236811i	−0.00317854	+	0.00978255i
$587$	3.74665	+	11.5310i	0.154641	+	0.475935i	0.998124	−	0.0612197i	$-0.0194990\pi$
$587$	3.74665	+	11.5310i	0.154641	+	0.475935i	−0.843484	+	0.537155i	$0.819499\pi$
$588$	6.88669	−	5.00348i	0.284003	−	0.206340i
$589$	−1.44407	+	1.04918i	−0.0595018	+	0.0432306i
$590$	−1.89169	−	5.82202i	−0.0778795	−	0.239689i
$591$	−10.8210	+	33.3035i	−0.445115	+	1.36992i
$592$	−24.6959	−	17.9426i	−1.01500	−	0.737437i
$593$	−24.9107			−1.02296			−0.511481	−	0.859295i	$-0.670903\pi$
$593$	−24.9107			−1.02296			−0.511481	+	0.859295i	$0.670903\pi$
$594$	1.13139	+	3.94609i	0.0464214	+	0.161910i
$595$	−30.0405			−1.23154
$596$	4.67018	+	3.39308i	0.191298	+	0.138986i
$597$	−10.7200	+	32.9928i	−0.438741	+	1.35031i
$598$	−0.441441	−	1.35861i	−0.0180518	−	0.0555579i
$599$	−33.5709	+	24.3907i	−1.37167	+	0.996577i	−0.374066	+	0.927402i	$0.622037\pi$
$599$	−33.5709	+	24.3907i	−1.37167	+	0.996577i	−0.997605	+	0.0691745i	$0.977963\pi$
$600$	2.18537	−	1.58777i	0.0892174	−	0.0648203i
$601$	−5.02921	−	15.4783i	−0.205146	−	0.631374i	−0.999707	−	0.0241903i	$-0.992299\pi$
$601$	−5.02921	−	15.4783i	−0.205146	−	0.631374i	0.794562	−	0.607184i	$-0.207701\pi$
$602$	−2.57900	+	7.93734i	−0.105112	+	0.323502i
$603$	−25.4671	−	18.5029i	−1.03710	−	0.753498i
$604$	37.5177			1.52657
$605$	−10.0628	+	24.9016i	−0.409109	+	1.01239i
$606$	3.44226			0.139832
$607$	−35.5984	−	25.8638i	−1.44489	−	1.04978i	−0.986991	−	0.160776i	$-0.948600\pi$
$607$	−35.5984	−	25.8638i	−1.44489	−	1.04978i	−0.457904	−	0.889002i	$-0.651400\pi$
$608$	0.910686	−	2.80280i	0.0369332	−	0.113669i
$609$	−12.0837	−	37.1897i	−0.489655	−	1.50700i
$610$	6.25020	−	4.54104i	0.253063	−	0.183861i
$611$	9.10149	−	6.61262i	0.368207	−	0.267518i
$612$	−11.8805	−	36.5643i	−0.480240	−	1.47803i
$613$	0.839362	−	2.58329i	0.0339015	−	0.104338i	−0.932674	−	0.360721i	$-0.882531\pi$
$613$	0.839362	−	2.58329i	0.0339015	−	0.104338i	0.966575	+	0.256383i	$0.0825307\pi$
$614$	1.59699	+	1.16028i	0.0644494	+	0.0468252i
$615$	−15.0359			−0.606307
$616$	−2.70522	−	9.43536i	−0.108996	−	0.380162i
$617$	35.6598			1.43561			0.717806	−	0.696244i	$-0.245147\pi$
$617$	35.6598			1.43561			0.717806	+	0.696244i	$0.245147\pi$
$618$	−6.34729	−	4.61158i	−0.255325	−	0.185505i
$619$	−3.37077	+	10.3741i	−0.135483	+	0.416972i	−0.995665	−	0.0930145i	$-0.970350\pi$
$619$	−3.37077	+	10.3741i	−0.135483	+	0.416972i	0.860182	+	0.509987i	$0.170350\pi$
$620$	2.60474	+	8.01655i	0.104609	+	0.321953i
$621$	−14.5584	+	10.5773i	−0.584209	+	0.424453i
$622$	−4.56031	+	3.31326i	−0.182852	+	0.132850i
$623$	−2.21918	−	6.82992i	−0.0889094	−	0.273635i
$624$	−4.62117	+	14.2225i	−0.184995	+	0.569356i
$625$	23.3670	+	16.9771i	0.934681	+	0.679085i
$626$	−7.47163			−0.298626
$627$	3.15478	−	8.66683i	0.125990	−	0.346120i
$628$	34.7469			1.38655
$629$	−28.7399	−	20.8808i	−1.14593	−	0.832570i
$630$	−2.68661	+	8.26852i	−0.107037	+	0.329426i
$631$	4.67032	+	14.3738i	0.185922	+	0.572210i	0.999963	−	0.00859751i	$-0.00273671\pi$
$631$	4.67032	+	14.3738i	0.185922	+	0.572210i	−0.814041	+	0.580808i	$0.802737\pi$
$632$	1.06656	−	0.774898i	0.0424253	−	0.0308238i
$633$	−6.24914	+	4.54026i	−0.248381	+	0.180459i
$634$	0.122499	+	0.377012i	0.00486505	+	0.0149731i
$635$	15.1055	−	46.4898i	0.599442	−	1.84489i
$636$	60.5467	+	43.9897i	2.40083	+	1.74431i
$637$	−2.35848			−0.0934463
$638$	−4.08523	−	0.142789i	−0.161736	−	0.00565309i
$639$	−49.9142			−1.97458
$640$	−14.9197	−	10.8398i	−0.589755	−	0.428482i
$641$	−2.63564	+	8.11167i	−0.104102	+	0.320392i	−0.989519	−	0.144406i	$-0.953873\pi$
$641$	−2.63564	+	8.11167i	−0.104102	+	0.320392i	0.885417	+	0.464798i	$0.153873\pi$
$642$	3.41036	+	10.4960i	0.134596	+	0.414244i
$643$	−15.0026	+	10.9001i	−0.591647	+	0.429856i	−0.842904	−	0.538064i	$-0.819156\pi$
$643$	−15.0026	+	10.9001i	−0.591647	+	0.429856i	0.251258	+	0.967920i	$0.419156\pi$
$644$	17.1133	−	12.4336i	0.674360	−	0.489951i
$645$	23.2777	+	71.6412i	0.916557	+	2.82087i
$646$	0.333242	−	1.02561i	0.0131112	−	0.0403523i
$647$	−0.224800	−	0.163327i	−0.00883782	−	0.00642105i	0.583358	−	0.812215i	$-0.301739\pi$
$647$	−0.224800	−	0.163327i	−0.00883782	−	0.00642105i	−0.592195	+	0.805794i	$0.701739\pi$
$648$	0.803737			0.0315738
$649$	−26.8475	+	18.1076i	−1.05386	+	0.710786i
$650$	−0.367939			−0.0144318
$651$	−11.7648	−	8.54760i	−0.461097	−	0.335007i
$652$	1.83541	−	5.64882i	0.0718803	−	0.221225i
$653$	−4.17075	−	12.8362i	−0.163214	−	0.502321i	0.835686	−	0.549207i	$-0.185070\pi$
$653$	−4.17075	−	12.8362i	−0.163214	−	0.502321i	−0.998900	+	0.0468861i	$0.985070\pi$
$654$	6.11099	−	4.43989i	0.238959	−	0.173614i
$655$	−16.6285	+	12.0813i	−0.649728	+	0.472055i
$656$	2.46947	+	7.60024i	0.0964166	+	0.296740i
$657$	7.48515	−	23.0369i	0.292024	−	0.898756i
$658$	−4.59468	−	3.33823i	−0.179119	−	0.130138i
$659$	−34.6157			−1.34843			−0.674217	−	0.738533i	$-0.735519\pi$
$659$	−34.6157			−1.34843			−0.674217	+	0.738533i	$0.735519\pi$
$660$	−34.3204	−	26.8158i	−1.33592	−	1.04380i
$661$	−28.9833			−1.12732			−0.563660	−	0.826007i	$-0.690607\pi$
$661$	−28.9833			−1.12732			−0.563660	+	0.826007i	$0.690607\pi$
$662$	3.39256	+	2.46484i	0.131856	+	0.0957988i
$663$	−5.37790	+	16.5515i	−0.208860	+	0.642806i
$664$	2.86159	+	8.80707i	0.111051	+	0.341781i
$665$	5.78695	−	4.20447i	0.224408	−	0.163042i
$666$	−8.31764	+	6.04312i	−0.322302	+	0.234166i
$667$	−5.53730	−	17.0421i	−0.214405	−	0.659871i
$668$	3.24591	−	9.98987i	0.125588	−	0.386520i
$669$	4.49839	+	3.26827i	0.173918	+	0.126359i
$670$	−4.16965			−0.161087
$671$	−32.2041	−	25.1622i	−1.24322	−	0.971377i
$672$	24.0094			0.926182
$673$	−1.23426	−	0.896740i	−0.0475771	−	0.0345668i	0.563743	−	0.825951i	$-0.309361\pi$
$673$	−1.23426	−	0.896740i	−0.0475771	−	0.0345668i	−0.611320	+	0.791384i	$0.709361\pi$
$674$	0.484886	−	1.49232i	0.0186771	−	0.0574822i
$675$	1.43227	+	4.40807i	0.0551281	+	0.169667i
$676$	−16.8665	+	12.2542i	−0.648710	+	0.471315i
$677$	16.7637	−	12.1795i	0.644281	−	0.468097i	−0.217037	−	0.976163i	$-0.569639\pi$
$677$	16.7637	−	12.1795i	0.644281	−	0.468097i	0.861318	+	0.508066i	$0.169639\pi$
$678$	1.98803	+	6.11853i	0.0763499	+	0.234981i
$679$	3.95991	−	12.1874i	0.151967	−	0.467708i
$680$	−8.38025	−	6.08861i	−0.321368	−	0.233487i
$681$	37.9203			1.45311
$682$	−1.26030	+	0.850024i	−0.0482593	+	0.0325491i
$683$	8.44932			0.323304			0.161652	−	0.986848i	$-0.448318\pi$
$683$	8.44932			0.323304			0.161652	+	0.986848i	$0.448318\pi$
$684$	7.40618	+	5.38091i	0.283182	+	0.205744i
$685$	−10.1914	+	31.3659i	−0.389393	+	1.19843i
$686$	−1.25933	−	3.87583i	−0.0480815	−	0.147980i
$687$	−18.6633	+	13.5597i	−0.712050	+	0.517335i
$688$	32.3896	−	23.5324i	1.23484	−	0.897165i
$689$	−6.40758	−	19.7205i	−0.244109	−	0.751291i
$690$	−2.01142	+	6.19052i	−0.0765735	+	0.235669i
$691$	14.6517	+	10.6451i	0.557378	+	0.404959i	0.830499	−	0.557021i	$-0.188056\pi$
$691$	14.6517	+	10.6451i	0.557378	+	0.404959i	−0.273120	+	0.961980i	$0.588056\pi$
$692$	−29.6035			−1.12536
$693$	45.9631	+	1.60653i	1.74599	+	0.0610271i
$694$	−4.48732			−0.170336
$695$	24.5258	+	17.8191i	0.930318	+	0.675916i
$696$	4.16669	−	12.8238i	0.157938	−	0.486084i
$697$	2.87385	+	8.84480i	0.108855	+	0.335021i
$698$	3.91601	−	2.84515i	0.148223	−	0.107690i
$699$	64.9419	−	47.1830i	2.45633	−	1.78463i
$700$	−1.68362	−	5.18166i	−0.0636350	−	0.195848i
$701$	−4.89093	+	15.0527i	−0.184728	+	0.568534i	−0.999944	−	0.0106236i	$-0.996618\pi$
$701$	−4.89093	+	15.0527i	−0.184728	+	0.568534i	0.815216	+	0.579157i	$0.196618\pi$
$702$	1.49216	+	1.08412i	0.0563180	+	0.0409174i
$703$	8.45889			0.319033
$704$	−7.32937	+	20.1353i	−0.276236	+	0.758877i
$705$	−51.2608			−1.93060
$706$	4.64608	+	3.37557i	0.174858	+	0.127041i
$707$	4.36407	−	13.4312i	0.164128	−	0.505133i
$708$	−16.2278	−	49.9440i	−0.609878	−	1.87701i
$709$	11.4458	−	8.31588i	0.429857	−	0.312309i	−0.351735	−	0.936100i	$-0.614408\pi$
$709$	11.4458	−	8.31588i	0.429857	−	0.312309i	0.781592	+	0.623790i	$0.214408\pi$
$710$	−5.34884	+	3.88616i	−0.200738	+	0.145845i
$711$	1.90884	+	5.87481i	0.0715871	+	0.220323i
$712$	0.765217	−	2.35509i	0.0286777	−	0.0882609i
$713$	−5.39116	−	3.91691i	−0.201901	−	0.146689i
$714$	8.78563			0.328794
$715$	3.32582	+	11.5999i	0.124379	+	0.433812i
$716$	27.1173			1.01342
$717$	−11.3685	−	8.25969i	−0.424564	−	0.308464i
$718$	0.305901	−	0.941466i	0.0114161	−	0.0351352i
$719$	−4.47734	−	13.7798i	−0.166977	−	0.513901i	0.832200	−	0.554476i	$-0.187081\pi$
$719$	−4.47734	−	13.7798i	−0.166977	−	0.513901i	−0.999177	+	0.0405745i	$0.987081\pi$
$720$	33.7410	−	24.5143i	1.25745	−	0.913593i
$721$	−26.0408	+	18.9197i	−0.969810	+	0.704608i
$722$	0.0793497	+	0.244213i	0.00295309	+	0.00908868i
$723$	5.40086	−	16.6222i	0.200860	−	0.618184i
$724$	4.83106	+	3.50997i	0.179545	+	0.130447i
$725$	−4.61532			−0.171409
$726$	2.94295	−	7.28272i	0.109223	−	0.270287i
$727$	−5.90862			−0.219139			−0.109569	−	0.993979i	$-0.534947\pi$
$727$	−5.90862			−0.219139			−0.109569	+	0.993979i	$0.534947\pi$
$728$	−3.56785	−	2.59220i	−0.132233	−	0.0960732i
$729$	−13.5903	+	41.8265i	−0.503343	+	1.54913i
$730$	−0.991466	−	3.05142i	−0.0366958	−	0.112938i
$731$	37.6934	−	27.3859i	1.39414	−	1.01290i
$732$	53.6172	−	38.9552i	1.98175	−	1.43983i
$733$	10.9899	+	33.8235i	0.405922	+	1.24930i	0.920123	+	0.391630i	$0.128089\pi$
$733$	10.9899	+	33.8235i	0.405922	+	1.24930i	−0.514201	+	0.857670i	$0.671911\pi$
$734$	0.846969	−	2.60670i	0.0312622	−	0.0962152i
$735$	8.69401	+	6.31657i	0.320684	+	0.232990i
$736$	11.0022			0.405547
$737$	6.07914	+	21.2030i	0.223928	+	0.781023i
$738$	2.69151			0.0990759
$739$	36.5396	+	26.5476i	1.34413	+	0.976568i	0.999281	+	0.0379099i	$0.0120700\pi$
$739$	36.5396	+	26.5476i	1.34413	+	0.976568i	0.344849	+	0.938658i	$0.387930\pi$
$740$	12.3437	−	37.9901i	0.453765	−	1.39654i
$741$	−1.28055	−	3.94114i	−0.0470423	−	0.144781i
$742$	−8.46860	+	6.15280i	−0.310892	+	0.225876i
$743$	21.5287	−	15.6415i	0.789813	−	0.573832i	−0.118095	−	0.993002i	$-0.537679\pi$
$743$	21.5287	−	15.6415i	0.789813	−	0.573832i	0.907908	+	0.419170i	$0.137679\pi$
$744$	−1.54953	−	4.76897i	−0.0568086	−	0.174839i
$745$	−2.25200	+	6.93093i	−0.0825068	+	0.253930i
$746$	−4.83202	−	3.51067i	−0.176913	−	0.128535i
$747$	−43.3897			−1.58755
$748$	−9.21449	+	25.3141i	−0.336915	+	0.925575i
$749$	45.2776			1.65441
$750$	−5.69635	−	4.13864i	−0.208001	−	0.151122i
$751$	0.758825	−	2.33542i	0.0276899	−	0.0852208i	−0.936257	−	0.351317i	$-0.885734\pi$
$751$	0.758825	−	2.33542i	0.0276899	−	0.0852208i	0.963946	+	0.266096i	$0.0857339\pi$
$752$	8.41897	+	25.9109i	0.307008	+	0.944874i
$753$	33.5504	−	24.3758i	1.22265	−	0.888304i
$754$	−1.48585	+	1.07953i	−0.0541115	+	0.0393143i
$755$	14.6362	+	45.0456i	0.532665	+	1.63938i
$756$	−8.43971	+	25.9748i	−0.306949	+	0.944693i
$757$	−30.1773	−	21.9251i	−1.09681	−	0.796881i	−0.116275	−	0.993217i	$-0.537096\pi$
$757$	−30.1773	−	21.9251i	−1.09681	−	0.796881i	−0.980537	+	0.196336i	$0.937096\pi$
$758$	−8.38077			−0.304403
$759$	34.4119	+	1.20279i	1.24907	+	0.0436584i
$760$	2.46652			0.0894701
$761$	−19.3904	−	14.0880i	−0.702903	−	0.510689i	0.177973	−	0.984035i	$-0.443046\pi$
$761$	−19.3904	−	14.0880i	−0.702903	−	0.510689i	−0.880876	+	0.473346i	$0.843046\pi$
$762$	−4.41774	+	13.5964i	−0.160038	+	0.492546i
$763$	−9.57640	−	29.4731i	−0.346689	−	1.06700i
$764$	−0.126877	+	0.0921819i	−0.00459026	+	0.00333502i
$765$	39.2662	−	28.5285i	1.41967	−	1.03145i
$766$	0.401112	+	1.23450i	0.0144928	+	0.0446042i
$767$	−4.49613	+	13.8377i	−0.162346	+	0.499649i
$768$	−24.7070	−	17.9507i	−0.891536	−	0.647739i
$769$	−10.6655			−0.384609			−0.192305	−	0.981335i	$-0.561596\pi$
$769$	−10.6655			−0.384609			−0.192305	+	0.981335i	$0.561596\pi$
$770$	5.05051	−	3.40638i	0.182008	−	0.122757i
$771$	−5.81647			−0.209475
$772$	−40.4142	−	29.3626i	−1.45454	−	1.05678i
$773$	8.74044	−	26.9003i	0.314372	−	0.967536i	−0.661641	−	0.749821i	$-0.730140\pi$
$773$	8.74044	−	26.9003i	0.314372	−	0.967536i	0.976012	−	0.217715i	$-0.0698605\pi$
$774$	−4.16682	−	12.8242i	−0.149773	−	0.460955i
$775$	−1.38857	+	1.00886i	−0.0498790	+	0.0362392i
$776$	3.57481	−	2.59725i	0.128328	−	0.0932360i
$777$	21.2956	+	65.5412i	0.763977	+	2.35128i
$778$	2.12782	−	6.54876i	0.0762861	−	0.234785i
$779$	−1.79153	−	1.30162i	−0.0641883	−	0.0466355i
$780$	−19.5689			−0.700679
$781$	27.5598	+	21.5335i	0.986167	+	0.770528i
$782$	4.02598			0.143969
$783$	18.7172	+	13.5989i	0.668899	+	0.485984i
$784$	1.76496	−	5.43200i	0.0630344	−	0.194000i
$785$	13.5553	+	41.7188i	0.483808	+	1.48901i
$786$	4.86316	−	3.53329i	0.173463	−	0.126028i
$787$	−22.8307	+	16.5875i	−0.813826	+	0.591279i	−0.914937	−	0.403596i	$-0.867760\pi$
$787$	−22.8307	+	16.5875i	−0.813826	+	0.591279i	0.101111	+	0.994875i	$0.467760\pi$
$788$	7.52582	+	23.1621i	0.268096	+	0.825115i
$789$	0.657482	−	2.02352i	0.0234070	−	0.0720393i
$790$	0.661946	+	0.480932i	0.0235510	+	0.0171108i
$791$	26.3941			0.938466
$792$	12.4965	+	9.76397i	0.444044	+	0.346948i
$793$	−18.3622			−0.652062
$794$	−2.42384	−	1.76102i	−0.0860189	−	0.0624964i
$795$	−29.1961	+	89.8563i	−1.03548	+	3.18688i
$796$	7.45561	+	22.9460i	0.264257	+	0.813300i
$797$	1.34432	−	0.976709i	0.0476184	−	0.0345968i	−0.563721	−	0.825965i	$-0.690631\pi$
$797$	1.34432	−	0.976709i	0.0476184	−	0.0345968i	0.611340	+	0.791368i	$0.290631\pi$
$798$	−1.69245	+	1.22964i	−0.0599121	+	0.0435287i
$799$	9.79759	+	30.1539i	0.346614	+	1.06677i
$800$	0.875686	−	2.69509i	0.0309602	−	0.0952857i
$801$	9.38688	+	6.81997i	0.331669	+	0.240972i
$802$	−1.72095			−0.0607687
$803$	−14.0712	+	9.49051i	−0.496563	+	0.334913i
$804$	−35.7692			−1.26148
$805$	21.6045	+	15.6966i	0.761458	+	0.553232i
$806$	−0.211061	+	0.649580i	−0.00743432	+	0.0228805i
$807$	5.25850	+	16.1840i	0.185108	+	0.569703i
$808$	3.93967	−	2.86234i	0.138597	−	0.100697i
$809$	1.97456	−	1.43460i	0.0694218	−	0.0504379i	−0.552533	−	0.833491i	$-0.686339\pi$
$809$	1.97456	−	1.43460i	0.0694218	−	0.0504379i	0.621955	+	0.783053i	$0.286339\pi$
$810$	0.154147	+	0.474416i	0.00541617	+	0.0166693i
$811$	−13.5218	+	41.6159i	−0.474816	+	1.46133i	0.371391	+	0.928477i	$0.378881\pi$
$811$	−13.5218	+	41.6159i	−0.474816	+	1.46133i	−0.846206	+	0.532855i	$0.821119\pi$
$812$	−22.0020	−	15.9854i	−0.772119	−	0.560977i
$813$	−79.1257			−2.77506
$814$	7.19959	+	0.251645i	0.252345	+	0.00882014i
$815$	7.49827			0.262653
$816$	−34.0965	−	24.7725i	−1.19362	−	0.867212i
$817$	−3.42828	+	10.5512i	−0.119940	+	0.369138i
$818$	−1.55105	−	4.77363i	−0.0542311	−	0.166906i
$819$	16.7174	−	12.1459i	0.584153	−	0.424412i
$820$	−8.46010	+	6.14662i	−0.295440	+	0.214649i
$821$	−5.14573	−	15.8369i	−0.179587	−	0.552713i	0.820226	−	0.572040i	$-0.193848\pi$
$821$	−5.14573	−	15.8369i	−0.179587	−	0.552713i	−0.999813	+	0.0193270i	$0.993848\pi$
$822$	2.98057	−	9.17325i	0.103959	−	0.319954i
$823$	1.53497	+	1.11522i	0.0535058	+	0.0388742i	0.614217	−	0.789137i	$-0.289472\pi$
$823$	1.53497	+	1.11522i	0.0535058	+	0.0388742i	−0.560711	+	0.828012i	$0.689472\pi$
$824$	−11.0991			−0.386657
$825$	3.03354	−	8.33375i	0.105614	−	0.290144i
$826$	7.34512			0.255569
$827$	−15.4965	−	11.2589i	−0.538866	−	0.391509i	0.284798	−	0.958588i	$-0.408074\pi$
$827$	−15.4965	−	11.2589i	−0.538866	−	0.391509i	−0.823664	+	0.567079i	$0.808074\pi$
$828$	−10.5612	+	32.5040i	−0.367027	+	1.12959i
$829$	−11.1626	−	34.3549i	−0.387693	−	1.19320i	−0.934508	−	0.355942i	$-0.884160\pi$
$829$	−11.1626	−	34.3549i	−0.387693	−	1.19320i	0.546815	−	0.837253i	$-0.315840\pi$
$830$	−4.64967	+	3.37818i	−0.161392	+	0.117258i
$831$	−47.8196	+	34.7429i	−1.65884	+	1.20522i
$832$	2.97506	+	9.15628i	0.103142	+	0.317437i
$833$	2.05398	−	6.32150i	0.0711662	−	0.219027i
$834$	−7.17282	−	5.21136i	−0.248374	−	0.180455i
$835$	13.2606			0.458902
$836$	−1.76790	−	6.16613i	−0.0611440	−	0.213260i
$837$	8.60385			0.297393
$838$	−3.13615	−	2.27854i	−0.108336	−	0.0787110i
$839$	−0.219173	+	0.674544i	−0.00756668	+	0.0232878i	−0.954769	−	0.297350i	$-0.903897\pi$
$839$	−0.219173	+	0.674544i	−0.00756668	+	0.0232878i	0.947202	+	0.320638i	$0.103897\pi$
$840$	6.20958	+	19.1111i	0.214251	+	0.659396i
$841$	4.82342	−	3.50442i	0.166325	−	0.120842i
$842$	3.32208	−	2.41364i	0.114487	−	0.0831794i
$843$	−7.20800	−	22.1839i	−0.248257	−	0.764056i
$844$	−1.66009	+	5.10924i	−0.0571428	+	0.175867i
$845$	−21.2928	−	15.4702i	−0.732496	−	0.532189i
$846$	9.17596			0.315476
$847$	−24.6851	−	20.7160i	−0.848191	−	0.711809i
$848$	50.2150			1.72439
$849$	−43.3662	−	31.5074i	−1.48832	−	1.08133i
$850$	0.320435	−	0.986198i	0.0109908	−	0.0338263i
$851$	9.75865	+	30.0340i	0.334522	+	1.02955i
$852$	−45.8849	+	33.3373i	−1.57199	+	1.14212i
$853$	−9.70836	+	7.05354i	−0.332408	+	0.241509i	−0.741452	−	0.671006i	$-0.765862\pi$
$853$	−9.70836	+	7.05354i	−0.332408	+	0.241509i	0.409044	+	0.912515i	$0.365862\pi$
$854$	2.86451	+	8.81606i	0.0980216	+	0.301679i
$855$	−3.57132	+	10.9914i	−0.122137	+	0.375898i
$856$	12.6309	+	9.17687i	0.431714	+	0.313659i
$857$	−24.5032			−0.837013			−0.418506	−	0.908214i	$-0.637446\pi$
$857$	−24.5032			−0.837013			−0.418506	+	0.908214i	$0.637446\pi$
$858$	−0.972669	−	3.39251i	−0.0332064	−	0.115818i
$859$	−1.96982			−0.0672093			−0.0336046	−	0.999435i	$-0.510699\pi$
$859$	−1.96982			−0.0672093			−0.0336046	+	0.999435i	$0.510699\pi$
$860$	42.3840	+	30.7938i	1.44528	+	1.05006i
$861$	5.57499	−	17.1581i	0.189995	−	0.584745i
$862$	−0.307197	−	0.945455i	−0.0104632	−	0.0322023i
$863$	−28.7235	+	20.8688i	−0.977759	+	0.710384i	−0.957207	−	0.289405i	$-0.906542\pi$
$863$	−28.7235	+	20.8688i	−0.977759	+	0.710384i	−0.0205524	+	0.999789i	$0.506542\pi$
$864$	−11.4923	+	8.34963i	−0.390975	+	0.284060i
$865$	−11.5488	−	35.5434i	−0.392669	−	1.20851i
$866$	−2.43702	+	7.50037i	−0.0828132	+	0.254873i
$867$	−1.43351	−	1.04150i	−0.0486844	−	0.0353713i
$868$	−10.1138			−0.343284
$869$	1.48050	−	4.06723i	0.0502224	−	0.137971i
$870$	8.36851			0.283719
$871$	8.01763	+	5.82515i	0.271667	+	0.197378i
$872$	3.30213	−	10.1629i	0.111824	−	0.344160i
$873$	6.39793	+	19.6908i	0.216537	+	0.666433i
$874$	−0.775559	+	0.563477i	−0.0262337	+	0.0190599i
$875$	−23.3702	+	16.9795i	−0.790057	+	0.574010i
$876$	−8.50527	−	26.1765i	−0.287367	−	0.884423i
$877$	−4.66665	+	14.3625i	−0.157582	+	0.484987i	−0.998413	−	0.0563101i	$-0.982066\pi$
$877$	−4.66665	+	14.3625i	−0.157582	+	0.484987i	0.840832	+	0.541297i	$0.182066\pi$
$878$	2.07714	+	1.50913i	0.0701002	+	0.0509308i
$879$	−2.69659			−0.0909537
$880$	−29.2056	−	1.02081i	−0.984519	−	0.0344116i
$881$	26.3321			0.887151			0.443575	−	0.896237i	$-0.353710\pi$
$881$	26.3321			0.887151			0.443575	+	0.896237i	$0.353710\pi$
$882$	−1.55627	−	1.13070i	−0.0524025	−	0.0380726i
$883$	1.27562	−	3.92597i	0.0429282	−	0.132119i	−0.927295	−	0.374330i	$-0.877873\pi$
$883$	1.27562	−	3.92597i	0.0429282	−	0.132119i	0.970224	+	0.242211i	$0.0778726\pi$
$884$	3.74025	+	11.5113i	0.125798	+	0.387167i
$885$	53.6345	−	38.9678i	1.80291	−	1.30989i
$886$	−3.01373	+	2.18961i	−0.101248	+	0.0735612i
$887$	−4.68582	−	14.4215i	−0.157335	−	0.484226i	0.841055	−	0.540949i	$-0.181935\pi$
$887$	−4.68582	−	14.4215i	−0.157335	−	0.484226i	−0.998390	+	0.0567231i	$0.981935\pi$
$888$	−7.34316	+	22.5999i	−0.246420	+	0.758404i
$889$	47.4505	+	34.4748i	1.59144	+	1.15625i
$890$	1.53688			0.0515164
$891$	2.18771	−	1.47553i	0.0732909	−	0.0494320i
$892$	3.86712			0.129481
$893$	−6.10773	−	4.43753i	−0.204388	−	0.148496i
$894$	0.658618	−	2.02702i	0.0220275	−	0.0677936i
$895$	10.5788	+	32.5583i	0.353611	+	1.08830i
$896$	17.9017	−	13.0063i	0.598052	−	0.434510i
$897$	12.5161	−	9.09344i	0.417899	−	0.303621i
$898$	1.00266	+	3.08588i	0.0334593	+	0.102977i
$899$	−2.64749	+	8.14814i	−0.0882988	+	0.271756i
$900$	7.12155	+	5.17411i	0.237385	+	0.172470i
$901$	58.4378			1.94684
$902$	−1.48610	−	1.16114i	−0.0494817	−	0.0386619i
$903$	−90.3834			−3.00777
$904$	7.36304	+	5.34956i	0.244891	+	0.177924i
$905$	−2.32958	+	7.16969i	−0.0774377	+	0.238329i
$906$	−4.28049	−	13.1740i	−0.142210	−	0.437677i
$907$	−7.02158	+	5.10147i	−0.233148	+	0.169392i	−0.698225	−	0.715878i	$-0.746026\pi$
$907$	−7.02158	+	5.10147i	−0.233148	+	0.169392i	0.465077	+	0.885270i	$0.346026\pi$
$908$	21.3362	−	15.5017i	0.708067	−	0.514441i
$909$	7.05092	+	21.7005i	0.233864	+	0.719760i
$910$	0.845805	−	2.60312i	0.0280382	−	0.0862926i
$911$	37.2081	+	27.0332i	1.23276	+	0.895652i	0.997094	−	0.0761829i	$-0.0242733\pi$
$911$	37.2081	+	27.0332i	1.23276	+	0.895652i	0.235665	+	0.971834i	$0.424273\pi$
$912$	10.0355			0.332307
$913$	23.9573	+	18.7187i	0.792872	+	0.619500i
$914$	1.19922			0.0396668
$915$	67.6884	+	49.1785i	2.23771	+	1.62579i
$916$	−4.95794	+	15.2590i	−0.163815	+	0.504171i
$917$	−7.62095	−	23.4549i	−0.251666	−	0.774548i
$918$	−4.20531	+	3.05533i	−0.138796	+	0.100841i
$919$	39.9885	−	29.0533i	1.31910	−	0.958381i	0.319155	−	0.947703i	$-0.396601\pi$
$919$	39.9885	−	29.0533i	1.31910	−	0.958381i	0.999943	−	0.0106778i	$-0.00339893\pi$
$920$	2.84552	+	8.75760i	0.0938139	+	0.288730i
$921$	−6.60614	+	20.3316i	−0.217680	+	0.669949i
$922$	0.388338	+	0.282144i	0.0127892	+	0.00929191i
$923$	15.7141			0.517237
$924$	43.3257	−	29.2216i	1.42531	−	0.961319i
$925$	8.13380			0.267438
$926$	−4.44060	−	3.22628i	−0.145927	−	0.106022i
$927$	16.0706	−	49.4603i	0.527829	−	1.62449i
$928$	−4.37109	−	13.4528i	−0.143488	−	0.441611i
$929$	40.7732	−	29.6235i	1.33773	−	0.971914i	0.338201	−	0.941074i	$-0.390182\pi$
$929$	40.7732	−	29.6235i	1.33773	−	0.971914i	0.999524	−	0.0308407i	$-0.00981845\pi$
$930$	2.51776	−	1.82926i	0.0825606	−	0.0599838i
$931$	0.489082	+	1.50524i	0.0160290	+	0.0493322i
$932$	17.2519	−	53.0959i	0.565105	−	1.73921i
$933$	−49.3872	−	35.8819i	−1.61686	−	1.17472i
$934$	−0.337755			−0.0110517
$935$	−33.9880	−	1.18797i	−1.11153	−	0.0388508i
$936$	7.12530			0.232898
$937$	47.6362	+	34.6097i	1.55621	+	1.13065i	0.939035	+	0.343823i	$0.111722\pi$
$937$	47.6362	+	34.6097i	1.55621	+	1.13065i	0.617172	+	0.786828i	$0.288278\pi$
$938$	1.54601	−	4.75814i	0.0504791	−	0.155359i
$939$	−25.0045	−	76.9558i	−0.815990	−	2.51136i
$940$	−28.8424	+	20.9552i	−0.940735	+	0.683484i
$941$	4.75380	−	3.45383i	0.154969	−	0.112592i	−0.507598	−	0.861594i	$-0.669467\pi$
$941$	4.75380	−	3.45383i	0.154969	−	0.112592i	0.662568	+	0.749002i	$0.269467\pi$
$942$	−3.96437	−	12.2011i	−0.129166	−	0.397532i
$943$	2.55472	−	7.86262i	0.0831932	−	0.256042i
$944$	−28.5059	−	20.7108i	−0.927789	−	0.674078i
$945$	−34.4790			−1.12160
$946$	−3.23179	+	8.87838i	−0.105074	+	0.288661i
$947$	40.9791			1.33164			0.665821	−	0.746111i	$-0.268081\pi$
$947$	40.9791			1.33164			0.665821	+	0.746111i	$0.268081\pi$
$948$	5.67849	+	4.12566i	0.184429	+	0.133995i
$949$	−2.35650	+	7.25256i	−0.0764952	+	0.235428i
$950$	0.0763002	+	0.234828i	0.00247551	+	0.00761882i
$951$	−3.47318	+	2.52341i	−0.112625	+	0.0818272i
$952$	10.0552	−	7.30550i	0.325889	−	0.236773i
$953$	−1.85914	−	5.72184i	−0.0602234	−	0.185348i	0.916419	−	0.400221i	$-0.131067\pi$
$953$	−1.85914	−	5.72184i	−0.0602234	−	0.185348i	−0.976642	+	0.214872i	$0.931067\pi$
$954$	5.22626	−	16.0848i	0.169206	−	0.520763i
$955$	−0.160175	−	0.116374i	−0.00518313	−	0.00376577i
$956$	−9.77311			−0.316085
$957$	−12.2009	−	42.5546i	−0.394398	−	1.37560i
$958$	9.54250			0.308304
$959$	−32.0140	−	23.2596i	−1.03379	−	0.751090i
$960$	13.5558	−	41.7205i	0.437512	−	1.34652i
$961$	−8.59496	−	26.4526i	−0.277257	−	0.853309i
$962$	2.61858	−	1.90251i	0.0844265	−	0.0613395i
$963$	−59.1827	+	42.9988i	−1.90714	+	1.38562i
$964$	−3.75622	−	11.5605i	−0.120980	−	0.372337i
$965$	19.4881	−	59.9781i	0.627343	−	1.93076i
$966$	−6.31844	−	4.59062i	−0.203293	−	0.147701i
$967$	15.5956			0.501522			0.250761	−	0.968049i	$-0.419319\pi$
$967$	15.5956			0.501522			0.250761	+	0.968049i	$0.419319\pi$
$968$	−2.68758	−	10.7822i	−0.0863821	−	0.346554i
$969$	11.6788			0.375177
$970$	2.21867	+	1.61196i	0.0712371	+	0.0517568i
$971$	−2.24197	+	6.90009i	−0.0719484	+	0.221434i	−0.980564	−	0.196199i	$-0.937140\pi$
$971$	−2.24197	+	6.90009i	−0.0719484	+	0.221434i	0.908616	+	0.417633i	$0.137140\pi$
$972$	9.96479	+	30.6685i	0.319621	+	0.983692i
$973$	−29.4276	+	21.3804i	−0.943407	+	0.685425i
$974$	−1.39401	+	1.01280i	−0.0446668	+	0.0324524i
$975$	−1.23134	−	3.78968i	−0.0394344	−	0.121367i
$976$	13.7414	−	42.2915i	0.439850	−	1.35372i
$977$	22.5919	+	16.4140i	0.722779	+	0.525130i	0.887271	−	0.461249i	$-0.152598\pi$
$977$	22.5919	+	16.4140i	0.722779	+	0.525130i	−0.164492	+	0.986378i	$0.552598\pi$
$978$	−2.19294			−0.0701225
$979$	−2.24070	−	7.81519i	−0.0716131	−	0.249774i
$980$	7.47395			0.238747
$981$	40.5071	+	29.4301i	1.29329	+	0.939632i
$982$	−2.20768	+	6.79454i	−0.0704499	+	0.216823i
$983$	2.96043	+	9.11126i	0.0944230	+	0.290604i	0.987103	−	0.160087i	$-0.0511775\pi$
$983$	2.96043	+	9.11126i	0.0944230	+	0.290604i	−0.892680	+	0.450691i	$0.851178\pi$
$984$	5.03283	−	3.65656i	0.160441	−	0.116567i
$985$	−24.8736	+	18.0717i	−0.792539	+	0.575813i
$986$	−1.59949	−	4.92273i	−0.0509382	−	0.156772i
$987$	19.0064	−	58.4957i	0.604980	−	1.86194i
$988$	−2.33164	−	1.69403i	−0.0741793	−	0.0538944i
$989$	−41.4179			−1.31701
$990$	−3.36663	+	9.24883i	−0.106999	+	0.293947i
$991$	−4.40388			−0.139894			−0.0699470	−	0.997551i	$-0.522283\pi$
$991$	−4.40388			−0.139894			−0.0699470	+	0.997551i	$0.522283\pi$
$992$	−4.25573	−	3.09197i	−0.135120	−	0.0981701i
$993$	−14.0337	+	43.1913i	−0.445346	+	1.37063i
$994$	−2.45141	−	7.54466i	−0.0777540	−	0.239302i
$995$	−24.6416	+	17.9031i	−0.781190	+	0.567568i
$996$	−39.8871	+	28.9796i	−1.26387	+	0.918255i
$997$	11.6540	+	35.8673i	0.369086	+	1.13593i	0.947383	+	0.320104i	$0.103718\pi$
$997$	11.6540	+	35.8673i	0.369086	+	1.13593i	−0.578296	+	0.815827i	$0.696282\pi$
$998$	2.07844	−	6.39679i	0.0657920	−	0.202487i
$999$	−32.9863	−	23.9659i	−1.04364	−	0.758248i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	209.2.f.c.191.5	yes	40
11.3	even	5	inner	209.2.f.c.58.5	✓	40
11.5	even	5		2299.2.a.x.1.11		20
11.6	odd	10		2299.2.a.y.1.10		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
209.2.f.c.58.5	✓	40	11.3	even	5	inner
209.2.f.c.191.5	yes	40	1.1	even	1	trivial
2299.2.a.x.1.11		20	11.5	even	5
2299.2.a.y.1.10		20	11.6	odd	10

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:	\( N \)	\(=\)	\( 209 = 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	209.f (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.207740 - 0.150932i) q^{2} +(0.859341 - 2.64478i) q^{3} +(-0.597658 - 1.83940i) q^{4} +(1.97532 - 1.43516i) q^{5} +(-0.577702 + 0.419725i) q^{6} +(0.905304 + 2.78624i) q^{7} +(-0.312167 + 0.960751i) q^{8} +(-3.82934 - 2.78218i) q^{9} -0.626965 q^{10} +(0.914084 + 3.18817i) q^{11} -5.37841 q^{12} +(1.20556 + 0.875893i) q^{13} +(0.232465 - 0.715454i) q^{14} +(-2.09819 - 6.45758i) q^{15} +(-2.91952 + 2.12116i) q^{16} +(-3.39760 + 2.46850i) q^{17} +(0.375588 + 1.15594i) q^{18} +(0.309017 - 0.951057i) q^{19} +(-3.82040 - 2.77568i) q^{20} +8.14695 q^{21} +(0.291306 - 0.800277i) q^{22} +3.73331 q^{23} +(2.27272 + 1.65123i) q^{24} +(0.297141 - 0.914506i) q^{25} +(-0.118244 - 0.363917i) q^{26} +(-3.89960 + 2.83323i) q^{27} +(4.58396 - 3.33044i) q^{28} +(-1.48321 - 4.56487i) q^{29} +(-0.538777 + 1.65818i) q^{30} +(-1.44407 - 1.04918i) q^{31} +2.94704 q^{32} +(9.21752 + 0.322177i) q^{33} +1.07839 q^{34} +(5.78695 + 4.20447i) q^{35} +(-2.82891 + 8.70649i) q^{36} +(2.61394 + 8.04488i) q^{37} +(-0.207740 + 0.150932i) q^{38} +(3.35253 - 2.43576i) q^{39} +(0.762197 + 2.34580i) q^{40} +(0.684304 - 2.10607i) q^{41} +(-1.69245 - 1.22964i) q^{42} -11.0941 q^{43} +(5.31803 - 3.58681i) q^{44} -11.5570 q^{45} +(-0.775559 - 0.563477i) q^{46} +(2.33295 - 7.18007i) q^{47} +(3.10113 + 9.54429i) q^{48} +(-1.28043 + 0.930289i) q^{49} +(-0.199757 + 0.145132i) q^{50} +(3.60894 + 11.1072i) q^{51} +(0.890606 - 2.74100i) q^{52} +(-11.2574 - 8.17895i) q^{53} +1.23773 q^{54} +(6.38114 + 4.98582i) q^{55} -2.95949 q^{56} +(-2.24978 - 1.63456i) q^{57} +(-0.380862 + 1.17217i) q^{58} +(3.01721 + 9.28603i) q^{59} +(-10.6241 + 7.71885i) q^{60} +(-9.96898 + 7.24289i) q^{61} +(0.141637 + 0.435913i) q^{62} +(4.28510 - 13.1882i) q^{63} +(5.22683 + 3.79751i) q^{64} +3.63842 q^{65} +(-1.86622 - 1.45815i) q^{66} +6.65052 q^{67} +(6.57117 + 4.77424i) q^{68} +(3.20819 - 9.87378i) q^{69} +(-0.567594 - 1.74687i) q^{70} +(8.53131 - 6.19836i) q^{71} +(3.86837 - 2.81054i) q^{72} +(1.58137 + 4.86697i) q^{73} +(0.671210 - 2.06577i) q^{74} +(-2.16332 - 1.57174i) q^{75} -1.93406 q^{76} +(-8.05549 + 5.43312i) q^{77} -1.06409 q^{78} +(-1.05579 - 0.767079i) q^{79} +(-2.72281 + 8.37994i) q^{80} +(-0.245862 - 0.756686i) q^{81} +(-0.460032 + 0.334233i) q^{82} +(7.41615 - 5.38815i) q^{83} +(-4.86909 - 14.9855i) q^{84} +(-3.16867 + 9.75217i) q^{85} +(2.30470 + 1.67446i) q^{86} -13.3476 q^{87} +(-3.34839 - 0.117035i) q^{88} -2.45131 q^{89} +(2.40086 + 1.74433i) q^{90} +(-1.34905 + 4.15194i) q^{91} +(-2.23124 - 6.86706i) q^{92} +(-4.01579 + 2.91764i) q^{93} +(-1.56835 + 1.13947i) q^{94} +(-0.754506 - 2.32213i) q^{95} +(2.53251 - 7.79427i) q^{96} +(-3.53874 - 2.57105i) q^{97} +0.406408 q^{98} +(5.36973 - 14.7517i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 3 q^{2} + 3 q^{3} - 13 q^{4} - 9 q^{5} + 10 q^{6} + 4 q^{7} - q^{8} - 21 q^{9} - 22 q^{10} + 8 q^{11} + 20 q^{12} + 13 q^{13} - 20 q^{14} - 9 q^{15} - 41 q^{16} + 21 q^{17} + 27 q^{18} - 10 q^{19}+ \cdots + 110 q^{99}+O(q^{100}) \) 40 * q + 3 * q^2 + 3 * q^3 - 13 * q^4 - 9 * q^5 + 10 * q^6 + 4 * q^7 - q^8 - 21 * q^9 - 22 * q^10 + 8 * q^11 + 20 * q^12 + 13 * q^13 - 20 * q^14 - 9 * q^15 - 41 * q^16 + 21 * q^17 + 27 * q^18 - 10 * q^19 - 26 * q^20 - 22 * q^21 + q^22 + 16 * q^23 + 12 * q^24 - 53 * q^25 - 14 * q^26 - 24 * q^27 + 29 * q^28 + 11 * q^29 + 10 * q^30 - 13 * q^31 - 4 * q^32 + 34 * q^33 - 38 * q^34 + 25 * q^35 - 61 * q^36 - 7 * q^37 + 3 * q^38 - 16 * q^39 + 77 * q^40 + 17 * q^41 - 12 * q^42 - 24 * q^43 + 29 * q^44 + 130 * q^45 + 32 * q^46 - 5 * q^47 - 6 * q^48 - 42 * q^49 - 5 * q^50 + 40 * q^51 - 19 * q^52 - 30 * q^53 + 52 * q^54 + 72 * q^55 + 74 * q^56 - 7 * q^57 - 67 * q^58 - 23 * q^59 - 94 * q^60 + 36 * q^61 + 35 * q^62 - 7 * q^63 - 111 * q^64 - 26 * q^65 - 9 * q^66 + 52 * q^67 + 70 * q^68 - 95 * q^69 - 38 * q^70 - 34 * q^71 + 112 * q^72 + 31 * q^73 + 80 * q^74 - 84 * q^75 + 42 * q^76 - 25 * q^77 - 90 * q^78 + 32 * q^79 - 58 * q^80 - 28 * q^81 - 50 * q^82 - 83 * q^83 + 135 * q^84 - 23 * q^85 - 45 * q^86 - 42 * q^87 + 101 * q^88 + 96 * q^89 - 4 * q^90 + 33 * q^91 - 48 * q^92 - 91 * q^93 + 67 * q^94 - 9 * q^95 - 18 * q^96 - 10 * q^97 - 90 * q^98 + 110 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more