LMFDB - Embedded newform 930.2.y.a.29.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [930,2,Mod(29,930)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(930, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([5, 5, 3]))

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

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

chi := DirichletCharacter("930.29");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.y (of order $10$, 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:	$7.42608738798$
Analytic rank:	$0$
Dimension:	$128$
Relative dimension:	$32$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			29.10
Character	$\chi$	$=$	930.29
Dual form			930.2.y.a.449.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.809017 - 0.587785i) q^{2} +(-1.02011 - 1.39978i) q^{3} +(0.309017 + 0.951057i) q^{4} +(-2.08406 + 0.810354i) q^{5} +(0.00251367 + 1.73205i) q^{6} +(-2.70101 + 0.877611i) q^{7} +(0.309017 - 0.951057i) q^{8} +(-0.918766 + 2.85585i) q^{9} +O(q^{10})$	\(q+(-0.809017 - 0.587785i) q^{2} +(-1.02011 - 1.39978i) q^{3} +(0.309017 + 0.951057i) q^{4} +(-2.08406 + 0.810354i) q^{5} +(0.00251367 + 1.73205i) q^{6} +(-2.70101 + 0.877611i) q^{7} +(0.309017 - 0.951057i) q^{8} +(-0.918766 + 2.85585i) q^{9} +(2.16236 + 0.569392i) q^{10} +(-0.682712 - 2.10117i) q^{11} +(1.01604 - 1.40273i) q^{12} +(-3.46448 + 2.51709i) q^{13} +(2.70101 + 0.877611i) q^{14} +(3.26029 + 2.09058i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(2.19758 + 0.714038i) q^{17} +(2.42192 - 1.77039i) q^{18} +(0.227369 + 0.165193i) q^{19} +(-1.41470 - 1.73165i) q^{20} +(3.98378 + 2.88556i) q^{21} +(-0.682712 + 2.10117i) q^{22} +(0.615571 + 0.200011i) q^{23} +(-1.64650 + 0.537623i) q^{24} +(3.68665 - 3.37766i) q^{25} +4.28233 q^{26} +(4.93480 - 1.62720i) q^{27} +(-1.66932 - 2.29762i) q^{28} +(-7.56787 - 5.49838i) q^{29} +(-1.40881 - 3.60767i) q^{30} +(4.69907 - 2.98642i) q^{31} +1.00000 q^{32} +(-2.24474 + 3.09906i) q^{33} +(-1.35818 - 1.86938i) q^{34} +(4.91790 - 4.01777i) q^{35} +(-2.99999 + 0.00870760i) q^{36} +7.71298 q^{37} +(-0.0868472 - 0.267288i) q^{38} +(7.05751 + 2.28180i) q^{39} +(0.126681 + 2.23248i) q^{40} +(-3.76009 + 5.17532i) q^{41} +(-1.52685 - 4.67607i) q^{42} +(8.50897 + 6.18213i) q^{43} +(1.78736 - 1.29860i) q^{44} +(-0.399482 - 6.69630i) q^{45} +(-0.380444 - 0.523636i) q^{46} +(3.01546 - 2.19086i) q^{47} +(1.64805 + 0.532842i) q^{48} +(0.862129 - 0.626374i) q^{49} +(-4.96790 + 0.565626i) q^{50} +(-1.24227 - 3.80453i) q^{51} +(-3.46448 - 2.51709i) q^{52} +(-0.420438 - 0.136608i) q^{53} +(-4.94878 - 1.58417i) q^{54} +(3.12551 + 3.82574i) q^{55} +2.84001i q^{56} +(-0.000706450 - 0.486781i) q^{57} +(2.89067 + 8.89657i) q^{58} +(2.61334 + 3.59696i) q^{59} +(-0.980780 + 3.74674i) q^{60} -12.4400i q^{61} +(-5.55700 - 0.345977i) q^{62} +(-0.0247297 - 8.51999i) q^{63} +(-0.809017 - 0.587785i) q^{64} +(5.18046 - 8.05323i) q^{65} +(3.63762 - 1.18777i) q^{66} -5.64028i q^{67} +2.31067i q^{68} +(-0.347976 - 1.06570i) q^{69} +(-6.34025 + 0.359776i) q^{70} +(-4.43959 - 1.44251i) q^{71} +(2.43216 + 1.75630i) q^{72} +(-2.66579 - 8.20445i) q^{73} +(-6.23993 - 4.53357i) q^{74} +(-8.48876 - 1.71493i) q^{75} +(-0.0868472 + 0.267288i) q^{76} +(3.68802 + 5.07613i) q^{77} +(-4.36843 - 5.99432i) q^{78} +(1.37862 + 0.447940i) q^{79} +(1.20973 - 1.88057i) q^{80} +(-7.31174 - 5.24771i) q^{81} +(6.08395 - 1.97679i) q^{82} +(2.60415 - 3.58431i) q^{83} +(-1.51328 + 4.68049i) q^{84} +(-5.15853 + 0.292719i) q^{85} +(-3.25014 - 10.0029i) q^{86} +(0.0235139 + 16.2023i) q^{87} -2.20930 q^{88} +(5.37218 + 16.5339i) q^{89} +(-3.61280 + 5.65223i) q^{90} +(7.14856 - 9.83914i) q^{91} +0.647249i q^{92} +(-8.97389 - 3.53119i) q^{93} -3.72731 q^{94} +(-0.607716 - 0.160024i) q^{95} +(-1.02011 - 1.39978i) q^{96} +(8.35086 - 2.71336i) q^{97} -1.06565 q^{98} +(6.62788 - 0.0192377i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 128 q - 32 q^{2} - 32 q^{4} + 2 q^{5} - 32 q^{8} - 4 q^{9}+O(q^{10}) $ 128 * q - 32 * q^2 - 32 * q^4 + 2 * q^5 - 32 * q^8 - 4 * q^9	$ 128 q - 32 q^{2} - 32 q^{4} + 2 q^{5} - 32 q^{8} - 4 q^{9} + 2 q^{10} + 25 q^{15} - 32 q^{16} + 6 q^{18} - 8 q^{19} - 3 q^{20} - 20 q^{23} - 10 q^{25} - 48 q^{31} + 128 q^{32} - 8 q^{33} + 10 q^{34} + 16 q^{35} - 4 q^{36} + 12 q^{38} + 4 q^{39} - 3 q^{40} + 37 q^{45} + 10 q^{46} + 6 q^{47} + 46 q^{49} - 5 q^{50} + 34 q^{51} - 20 q^{53} - 25 q^{60} - 8 q^{62} + 36 q^{63} - 32 q^{64} - 8 q^{66} + 8 q^{69} + 16 q^{70} + 6 q^{72} + 5 q^{75} + 12 q^{76} + 50 q^{77} + 4 q^{78} - 10 q^{79} + 2 q^{80} - 24 q^{81} - 40 q^{83} - 30 q^{85} - 4 q^{87} - 53 q^{90} + 20 q^{91} - 26 q^{93} - 4 q^{94} - 26 q^{95} - 124 q^{98}+O(q^{100}) $ 128 * q - 32 * q^2 - 32 * q^4 + 2 * q^5 - 32 * q^8 - 4 * q^9 + 2 * q^10 + 25 * q^15 - 32 * q^16 + 6 * q^18 - 8 * q^19 - 3 * q^20 - 20 * q^23 - 10 * q^25 - 48 * q^31 + 128 * q^32 - 8 * q^33 + 10 * q^34 + 16 * q^35 - 4 * q^36 + 12 * q^38 + 4 * q^39 - 3 * q^40 + 37 * q^45 + 10 * q^46 + 6 * q^47 + 46 * q^49 - 5 * q^50 + 34 * q^51 - 20 * q^53 - 25 * q^60 - 8 * q^62 + 36 * q^63 - 32 * q^64 - 8 * q^66 + 8 * q^69 + 16 * q^70 + 6 * q^72 + 5 * q^75 + 12 * q^76 + 50 * q^77 + 4 * q^78 - 10 * q^79 + 2 * q^80 - 24 * q^81 - 40 * q^83 - 30 * q^85 - 4 * q^87 - 53 * q^90 + 20 * q^91 - 26 * q^93 - 4 * q^94 - 26 * q^95 - 124 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/930\mathbb{Z}\right)^\times$.

$n$	$187$	$311$	$871$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{3}{10}\right)$

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 $

$2$	−0.809017	−	0.587785i	−0.572061	−	0.415627i
$2$	−0.809017	−	0.587785i	−0.572061	−	0.415627i
$3$	−1.02011	−	1.39978i	−0.588959	−	0.808163i
$3$	−1.02011	−	1.39978i	−0.588959	−	0.808163i
$4$	0.309017	+	0.951057i	0.154508	+	0.475528i
$5$	−2.08406	+	0.810354i	−0.932022	+	0.362401i
$5$	−2.08406	+	0.810354i	−0.932022	+	0.362401i
$6$	0.00251367	+	1.73205i	0.00102620	+	0.707106i
$7$	−2.70101	+	0.877611i	−1.02089	+	0.331706i	−0.771181	−	0.636616i	$-0.780334\pi$
$7$	−2.70101	+	0.877611i	−1.02089	+	0.331706i	−0.249705	+	0.968322i	$0.580334\pi$
$8$	0.309017	−	0.951057i	0.109254	−	0.336249i
$9$	−0.918766	+	2.85585i	−0.306255	+	0.951949i
$10$	2.16236	+	0.569392i	0.683798	+	0.180058i
$11$	−0.682712	−	2.10117i	−0.205845	−	0.633527i	−0.999678	−	0.0253902i	$-0.991917\pi$
$11$	−0.682712	−	2.10117i	−0.205845	−	0.633527i	0.793832	−	0.608137i	$-0.208083\pi$
$12$	1.01604	−	1.40273i	0.293305	−	0.404935i
$13$	−3.46448	+	2.51709i	−0.960873	+	0.698115i	−0.953353	−	0.301857i	$-0.902394\pi$
$13$	−3.46448	+	2.51709i	−0.960873	+	0.698115i	−0.00751956	+	0.999972i	$0.502394\pi$
$14$	2.70101	+	0.877611i	0.721875	+	0.234551i
$15$	3.26029	+	2.09058i	0.841802	+	0.539786i
$16$	−0.809017	+	0.587785i	−0.202254	+	0.146946i
$17$	2.19758	+	0.714038i	0.532992	+	0.173180i	0.563133	−	0.826366i	$-0.309596\pi$
$17$	2.19758	+	0.714038i	0.532992	+	0.173180i	−0.0301413	+	0.999546i	$0.509596\pi$
$18$	2.42192	−	1.77039i	0.570853	−	0.417286i
$19$	0.227369	+	0.165193i	0.0521620	+	0.0378979i	0.613561	−	0.789648i	$-0.289737\pi$
$19$	0.227369	+	0.165193i	0.0521620	+	0.0378979i	−0.561399	+	0.827545i	$0.689737\pi$
$20$	−1.41470	−	1.73165i	−0.316337	−	0.387209i
$21$	3.98378	+	2.88556i	0.869332	+	0.629681i
$22$	−0.682712	+	2.10117i	−0.145555	+	0.447971i
$23$	0.615571	+	0.200011i	0.128355	+	0.0417052i	0.372490	−	0.928036i	$-0.378504\pi$
$23$	0.615571	+	0.200011i	0.128355	+	0.0417052i	−0.244135	+	0.969741i	$0.578504\pi$
$24$	−1.64650	+	0.537623i	−0.336090	+	0.109742i
$25$	3.68665	−	3.37766i	0.737330	−	0.675532i
$26$	4.28233			0.839834
$27$	4.93480	−	1.62720i	0.949702	−	0.313155i
$28$	−1.66932	−	2.29762i	−0.315471	−	0.434209i
$29$	−7.56787	−	5.49838i	−1.40532	−	1.02102i	−0.993982	−	0.109540i	$-0.965062\pi$
$29$	−7.56787	−	5.49838i	−1.40532	−	1.02102i	−0.411336	−	0.911484i	$-0.634938\pi$
$30$	−1.40881	−	3.60767i	−0.257213	−	0.658667i
$31$	4.69907	−	2.98642i	0.843978	−	0.536378i
$31$	4.69907	−	2.98642i	0.843978	−	0.536378i
$32$	1.00000			0.176777
$33$	−2.24474	+	3.09906i	−0.390759	+	0.539478i
$34$	−1.35818	−	1.86938i	−0.232926	−	0.320595i
$35$	4.91790	−	4.01777i	0.831277	−	0.679127i
$36$	−2.99999	+	0.00870760i	−0.499998	+	0.00145127i
$37$	7.71298			1.26801			0.634003	−	0.773331i	$-0.281411\pi$
$37$	7.71298			1.26801			0.634003	+	0.773331i	$0.281411\pi$
$38$	−0.0868472	−	0.267288i	−0.0140885	−	0.0433599i
$39$	7.05751	+	2.28180i	1.13011	+	0.365381i
$40$	0.126681	+	2.23248i	0.0200301	+	0.352986i
$41$	−3.76009	+	5.17532i	−0.587227	+	0.808249i	−0.994464	−	0.105074i	$-0.966492\pi$
$41$	−3.76009	+	5.17532i	−0.587227	+	0.808249i	0.407237	+	0.913322i	$0.366492\pi$
$42$	−1.52685	−	4.67607i	−0.235599	−	0.721534i
$43$	8.50897	+	6.18213i	1.29761	+	0.942766i	0.999929	−	0.0119009i	$-0.00378827\pi$
$43$	8.50897	+	6.18213i	1.29761	+	0.942766i	0.297677	+	0.954667i	$0.403788\pi$
$44$	1.78736	−	1.29860i	0.269455	−	0.195771i
$45$	−0.399482	−	6.69630i	−0.0595512	−	0.998225i
$46$	−0.380444	−	0.523636i	−0.0560933	−	0.0772059i
$47$	3.01546	−	2.19086i	0.439849	−	0.319569i	−0.345726	−	0.938336i	$-0.612367\pi$
$47$	3.01546	−	2.19086i	0.439849	−	0.319569i	0.785575	+	0.618766i	$0.212367\pi$
$48$	1.64805	+	0.532842i	0.237876	+	0.0769091i
$49$	0.862129	−	0.626374i	0.123161	−	0.0894820i
$50$	−4.96790	+	0.565626i	−0.702568	+	0.0799916i
$51$	−1.24227	−	3.80453i	−0.173953	−	0.532740i
$52$	−3.46448	−	2.51709i	−0.480436	−	0.349058i
$53$	−0.420438	−	0.136608i	−0.0577515	−	0.0187646i	0.279999	−	0.960000i	$-0.409666\pi$
$53$	−0.420438	−	0.136608i	−0.0577515	−	0.0187646i	−0.337750	+	0.941236i	$0.609666\pi$
$54$	−4.94878	−	1.58417i	−0.673443	−	0.215578i
$55$	3.12551	+	3.82574i	0.421444	+	0.515863i
$56$			2.84001i			0.379512i
$57$	−0.000706450	−	0.486781i	−9.35717e−5	−	0.0644757i
$58$	2.89067	+	8.89657i	0.379564	+	1.16818i
$59$	2.61334	+	3.59696i	0.340228	+	0.468284i	0.944508	−	0.328488i	$-0.106539\pi$
$59$	2.61334	+	3.59696i	0.340228	+	0.468284i	−0.604280	+	0.796772i	$0.706539\pi$
$60$	−0.980780	+	3.74674i	−0.126618	+	0.483702i
$61$		−	12.4400i		−	1.59278i	−0.604787	−	0.796388i	$-0.706742\pi$
$61$		−	12.4400i		−	1.59278i	0.604787	−	0.796388i	$-0.293258\pi$
$62$	−5.55700	−	0.345977i	−0.705740	−	0.0439392i
$63$	−0.0247297	−	8.51999i	−0.00311565	−	1.07342i
$64$	−0.809017	−	0.587785i	−0.101127	−	0.0734732i
$65$	5.18046	−	8.05323i	0.642557	−	0.998880i
$66$	3.63762	−	1.18777i	0.447760	−	0.146205i
$67$		−	5.64028i		−	0.689070i	−0.938773	−	0.344535i	$-0.888037\pi$
$67$		−	5.64028i		−	0.689070i	0.938773	−	0.344535i	$-0.111963\pi$
$68$			2.31067i			0.280210i
$69$	−0.347976	−	1.06570i	−0.0418914	−	0.128295i
$70$	−6.34025	+	0.359776i	−0.757805	+	0.0430014i
$71$	−4.43959	−	1.44251i	−0.526882	−	0.171194i	0.0334842	−	0.999439i	$-0.489340\pi$
$71$	−4.43959	−	1.44251i	−0.526882	−	0.171194i	−0.560366	+	0.828245i	$0.689340\pi$
$72$	2.43216	+	1.75630i	0.286633	+	0.206982i
$73$	−2.66579	−	8.20445i	−0.312007	−	0.960258i	−0.976969	−	0.213381i	$-0.931552\pi$
$73$	−2.66579	−	8.20445i	−0.312007	−	0.960258i	0.664962	−	0.746877i	$-0.268448\pi$
$74$	−6.23993	−	4.53357i	−0.725377	−	0.527017i
$75$	−8.48876	−	1.71493i	−0.980197	−	0.198023i
$76$	−0.0868472	+	0.267288i	−0.00996205	+	0.0306600i
$77$	3.68802	+	5.07613i	0.420289	+	0.578478i
$78$	−4.36843	−	5.99432i	−0.494627	−	0.678723i
$79$	1.37862	+	0.447940i	0.155106	+	0.0503972i	0.385541	−	0.922691i	$-0.374015\pi$
$79$	1.37862	+	0.447940i	0.155106	+	0.0503972i	−0.230435	+	0.973088i	$0.574015\pi$
$80$	1.20973	−	1.88057i	0.135252	−	0.210254i
$81$	−7.31174	−	5.24771i	−0.812415	−	0.583079i
$82$	6.08395	−	1.97679i	0.671860	−	0.218300i
$83$	2.60415	−	3.58431i	0.285843	−	0.393429i	−0.641815	−	0.766859i	$-0.721818\pi$
$83$	2.60415	−	3.58431i	0.285843	−	0.393429i	0.927658	+	0.373430i	$0.121818\pi$
$84$	−1.51328	+	4.68049i	−0.165112	+	0.510683i
$85$	−5.15853	+	0.292719i	−0.559521	+	0.0317499i
$86$	−3.25014	−	10.0029i	−0.350471	−	1.07864i
$87$	0.0235139	+	16.2023i	0.00252095	+	1.73707i
$88$	−2.20930			−0.235512
$89$	5.37218	+	16.5339i	0.569450	+	1.75259i	0.654344	+	0.756197i	$0.272945\pi$
$89$	5.37218	+	16.5339i	0.569450	+	1.75259i	−0.0848946	+	0.996390i	$0.527055\pi$
$90$	−3.61280	+	5.65223i	−0.380822	+	0.595797i
$91$	7.14856	−	9.83914i	0.749372	−	1.03142i
$92$			0.647249i			0.0674804i
$93$	−8.97389	−	3.53119i	−0.930549	−	0.366168i
$94$	−3.72731			−0.384442
$95$	−0.607716	−	0.160024i	−0.0623504	−	0.0164181i
$96$	−1.02011	−	1.39978i	−0.104114	−	0.142864i
$97$	8.35086	−	2.71336i	0.847901	−	0.275500i	0.147335	−	0.989087i	$-0.452931\pi$
$97$	8.35086	−	2.71336i	0.847901	−	0.275500i	0.700567	+	0.713587i	$0.252931\pi$
$98$	−1.06565			−0.107647
$99$	6.62788	−	0.0192377i	0.666127	−	0.00193346i
$100$	4.35159	+	2.46246i	0.435159	+	0.246246i
$101$	3.99097	+	1.29674i	0.397116	+	0.129031i	0.500766	−	0.865583i	$-0.333052\pi$
$101$	3.99097	+	1.29674i	0.397116	+	0.129031i	−0.103649	+	0.994614i	$0.533052\pi$
$102$	−1.23122	+	3.80811i	−0.121909	+	0.377060i
$103$	−2.87681	+	3.95959i	−0.283460	+	0.390150i	−0.926876	−	0.375367i	$-0.877517\pi$
$103$	−2.87681	+	3.95959i	−0.283460	+	0.390150i	0.643416	+	0.765517i	$0.277517\pi$
$104$	1.32331	+	4.07274i	0.129761	+	0.399365i
$105$	−10.6408	−	2.78542i	−1.03843	−	0.271829i
$106$	0.259845	+	0.357646i	0.0252383	+	0.0347376i
$107$	4.95353	−	15.2454i	0.478875	−	1.47383i	−0.361784	−	0.932262i	$-0.617832\pi$
$107$	4.95353	−	15.2454i	0.478875	−	1.47383i	0.840659	−	0.541565i	$-0.182168\pi$
$108$	3.07250	+	4.19044i	0.295651	+	0.403225i
$109$	−1.89084	+	1.37377i	−0.181109	+	0.131584i	−0.674646	−	0.738141i	$-0.735704\pi$
$109$	−1.89084	+	1.37377i	−0.181109	+	0.131584i	0.493537	+	0.869725i	$0.335704\pi$
$110$	−0.279877	−	4.93222i	−0.0266852	−	0.470268i
$111$	−7.86806	−	10.7965i	−0.746803	−	1.02476i
$112$	1.66932	−	2.29762i	0.157735	−	0.217104i
$113$	3.89078	+	11.9746i	0.366014	+	1.12648i	0.949344	+	0.314240i	$0.101750\pi$
$113$	3.89078	+	11.9746i	0.366014	+	1.12648i	−0.583329	+	0.812236i	$0.698250\pi$
$114$	−0.285551	+	0.394229i	−0.0267443	+	0.0369229i
$115$	−1.44497	+	0.0819944i	−0.134744	+	0.00764601i
$116$	2.89067	−	8.89657i	0.268392	−	0.826025i
$117$	−4.00538	−	12.2066i	−0.370298	−	1.12850i
$118$		−	4.44609i		−	0.409295i
$119$	−6.56234			−0.601568
$120$	2.99575	−	2.45469i	0.273473	−	0.224081i
$121$	4.95036	−	3.59665i	0.450033	−	0.326968i
$122$	−7.31203	+	10.0641i	−0.662000	+	0.911165i
$123$	11.0800	−	0.0160801i	0.999049	−	0.00144989i
$124$	4.29235	+	3.54623i	0.385464	+	0.318461i
$125$	−4.94612	+	10.0268i	−0.442394	+	0.896821i
$126$	−4.98792	+	6.90735i	−0.444359	+	0.615356i
$127$	−6.86015	+	4.98419i	−0.608740	+	0.442275i	−0.848970	−	0.528440i	$-0.822777\pi$
$127$	−6.86015	+	4.98419i	−0.608740	+	0.442275i	0.240230	+	0.970716i	$0.422777\pi$
$128$	0.309017	+	0.951057i	0.0273135	+	0.0840623i
$129$	−0.0264380	−	18.2171i	−0.00232773	−	1.60393i
$130$	−8.92465	+	3.47020i	−0.782744	+	0.304357i
$131$	6.83740	−	2.22160i	0.597386	−	0.194102i	0.00531174	−	0.999986i	$-0.498309\pi$
$131$	6.83740	−	2.22160i	0.597386	−	0.194102i	0.592074	+	0.805883i	$0.298309\pi$
$132$	−3.64105	−	1.17721i	−0.316913	−	0.102463i
$133$	−0.759101	−	0.246647i	−0.0658224	−	0.0213870i
$134$	−3.31527	+	4.56308i	−0.286396	+	0.394190i
$135$	−8.96583	+	7.39012i	−0.771656	+	0.636041i
$136$	1.35818	−	1.86938i	0.116463	−	0.160298i
$137$	3.54766	+	4.88293i	0.303097	+	0.417177i	0.933213	−	0.359324i	$-0.116993\pi$
$137$	3.54766	+	4.88293i	0.303097	+	0.417177i	−0.630116	+	0.776501i	$0.716993\pi$
$138$	−0.344882	+	1.06670i	−0.0293583	+	0.0908036i
$139$	11.0537	+	15.2141i	0.937563	+	1.29045i	0.956835	+	0.290631i	$0.0938652\pi$
$139$	11.0537	+	15.2141i	0.937563	+	1.29045i	−0.0192718	+	0.999814i	$0.506135\pi$
$140$	5.34084	+	3.43564i	0.451384	+	0.290365i
$141$	−6.14280	−	1.98607i	−0.517317	−	0.167257i
$142$	2.74382	+	3.77654i	0.230256	+	0.316920i
$143$	7.65408	+	5.56101i	0.640066	+	0.465035i
$144$	−0.935328	−	2.85047i	−0.0779440	−	0.237539i
$145$	20.2276	+	5.32632i	1.67981	+	0.442327i
$146$	−2.66579	+	8.20445i	−0.220622	+	0.679005i
$147$	−1.75625	−	0.567823i	−0.144853	−	0.0468333i
$148$	2.38344	+	7.33548i	0.195918	+	0.602973i
$149$		−	23.7054i		−	1.94203i	−0.239027	−	0.971013i	$-0.576829\pi$
$149$		−	23.7054i		−	1.94203i	0.239027	−	0.971013i	$-0.423171\pi$
$150$	5.85954	+	6.37697i	0.478430	+	0.520678i
$151$	20.7062	−	6.72784i	1.68504	−	0.547504i	0.699164	−	0.714961i	$-0.253556\pi$
$151$	20.7062	−	6.72784i	1.68504	−	0.547504i	0.985879	+	0.167458i	$0.0535558\pi$
$152$	0.227369	−	0.165193i	0.0184420	−	0.0133989i
$153$	−4.05825	+	5.61993i	−0.328090	+	0.454344i
$154$		−	6.27444i		−	0.505609i
$155$	−7.37311	+	10.0318i	−0.592222	+	0.805775i
$156$	0.0107644	+	7.41720i	0.000861839	+	0.593851i
$157$	−9.65025	+	13.2824i	−0.770174	+	1.06005i	0.226125	+	0.974098i	$0.427394\pi$
$157$	−9.65025	+	13.2824i	−0.770174	+	1.06005i	−0.996299	+	0.0859552i	$0.972606\pi$
$158$	−0.852032	−	1.17272i	−0.0677840	−	0.0932967i
$159$	0.237669	+	0.727875i	0.0188484	+	0.0577242i
$160$	−2.08406	+	0.810354i	−0.164760	+	0.0640641i
$161$	−1.83819			−0.144870
$162$	2.83079	+	8.54322i	0.222408	+	0.671219i
$163$	−0.666709	−	0.216627i	−0.0522206	−	0.0169675i	0.282790	−	0.959182i	$-0.408740\pi$
$163$	−0.666709	−	0.216627i	−0.0522206	−	0.0169675i	−0.335011	+	0.942214i	$0.608740\pi$
$164$	−6.08395	−	1.97679i	−0.475077	−	0.154362i
$165$	2.16684	−	8.27768i	0.168688	−	0.644417i
$166$	−4.21361	+	1.36908i	−0.327039	+	0.106262i
$167$	1.98562	−	2.73297i	0.153652	−	0.211484i	−0.725251	−	0.688485i	$-0.758276\pi$
$167$	1.98562	−	2.73297i	0.153652	−	0.211484i	0.878903	+	0.477001i	$0.158276\pi$
$168$	3.97539	−	2.89711i	0.306708	−	0.223517i
$169$	1.64964	−	5.07706i	0.126895	−	0.390543i
$170$	4.34539	+	2.79529i	0.333276	+	0.214389i
$171$	−0.680665	+	0.497557i	−0.0520518	+	0.0380491i
$172$	−3.25014	+	10.0029i	−0.247821	+	0.762714i
$173$	−3.72618	+	2.70723i	−0.283296	+	0.205827i	−0.720354	−	0.693607i	$-0.756021\pi$
$173$	−3.72618	+	2.70723i	−0.283296	+	0.205827i	0.437057	+	0.899434i	$0.356021\pi$
$174$	9.50444	−	13.1217i	0.720530	−	0.994757i
$175$	−6.99341	+	12.3585i	−0.528652	+	0.934218i
$176$	1.78736	+	1.29860i	0.134728	+	0.0978853i
$177$	2.36906	−	7.32739i	0.178070	−	0.550760i
$178$	5.37218	−	16.5339i	0.402662	−	1.23927i
$179$	3.12349	+	9.61310i	0.233460	+	0.718517i	0.997322	+	0.0731368i	$0.0233010\pi$
$179$	3.12349	+	9.61310i	0.233460	+	0.718517i	−0.763862	+	0.645380i	$0.776699\pi$
$180$	6.24511	−	2.44920i	0.465483	−	0.182553i
$181$		−	16.5526i		−	1.23034i	−0.788393	−	0.615172i	$-0.789087\pi$
$181$		−	16.5526i		−	1.23034i	0.788393	−	0.615172i	$-0.210913\pi$
$182$	−11.5666	+	3.75822i	−0.857374	+	0.278578i
$183$	−17.4132	+	12.6901i	−1.28722	+	0.938079i
$184$	0.380444	−	0.523636i	0.0280467	−	0.0386029i
$185$	−16.0743	+	6.25024i	−1.18181	+	0.459527i
$186$	5.18444	+	8.13152i	0.380142	+	0.596232i
$187$		−	5.10498i		−	0.373313i
$188$	3.01546	+	2.19086i	0.219925	+	0.159785i
$189$	−11.9009	+	8.72591i	−0.865662	+	0.634717i
$190$	0.397593	+	0.486669i	0.0288444	+	0.0353067i
$191$			18.9480i			1.37103i	0.728059	+	0.685515i	$0.240423\pi$
$191$			18.9480i			1.37103i	−0.728059	+	0.685515i	$0.759577\pi$
$192$	0.00251367	+	1.73205i	0.000181409	+	0.125000i
$193$	13.1130	−	4.26067i	0.943894	−	0.306690i	0.203662	−	0.979041i	$-0.434716\pi$
$193$	13.1130	−	4.26067i	0.943894	−	0.306690i	0.740232	+	0.672352i	$0.234716\pi$
$194$	−8.35086	−	2.71336i	−0.599557	−	0.194808i
$195$	−16.5574	+	0.963652i	−1.18570	+	0.0690085i
$196$	0.862129	+	0.626374i	0.0615807	+	0.0447410i
$197$	−10.0418	+	3.26277i	−0.715447	+	0.232463i	−0.644048	−	0.764985i	$-0.722746\pi$
$197$	−10.0418	+	3.26277i	−0.715447	+	0.232463i	−0.0713989	+	0.997448i	$0.522746\pi$
$198$	−5.37337	−	3.88021i	−0.381869	−	0.275754i
$199$	15.5115	+	21.3497i	1.09958	+	1.51344i	0.835943	+	0.548816i	$0.184921\pi$
$199$	15.5115	+	21.3497i	1.09958	+	1.51344i	0.263635	+	0.964623i	$0.415079\pi$
$200$	−2.07311	−	4.54997i	−0.146591	−	0.321731i
$201$	−7.89515	+	5.75369i	−0.556881	+	0.405834i
$202$	−2.46656	−	3.39492i	−0.173546	−	0.238866i
$203$	25.2663	+	8.20953i	1.77335	+	0.576196i
$204$	3.23444	−	2.35713i	0.226456	−	0.165032i
$205$	3.64243	−	13.8327i	0.254398	−	0.966117i
$206$	4.65477	−	1.51243i	0.324313	−	0.105376i
$207$	−1.13677	+	1.57421i	−0.0790107	+	0.109415i
$208$	1.32331	−	4.07274i	0.0917552	−	0.282393i
$209$	0.191872	−	0.590520i	0.0132720	−	0.0408471i
$210$	6.97134	+	8.50795i	0.481068	+	0.587104i
$211$	14.7248			1.01370			0.506850	−	0.862034i	$-0.330810\pi$
$211$	14.7248			1.01370			0.506850	+	0.862034i	$0.330810\pi$
$212$		−	0.442074i		−	0.0303618i
$213$	2.50966	+	7.68596i	0.171959	+	0.526633i
$214$	−12.9685	+	9.42217i	−0.886508	+	0.644086i
$215$	−22.7430	−	5.98868i	−1.55106	−	0.408424i
$216$	−0.0226230	−	5.19610i	−0.00153930	−	0.353550i
$217$	−10.0713	+	12.1903i	−0.683685	+	0.827532i
$218$	2.33720			0.158295
$219$	−8.76503	+	12.1009i	−0.592286	+	0.817705i
$220$	−2.67266	+	4.15475i	−0.180191	+	0.280113i
$221$	−9.41077	+	3.05774i	−0.633037	+	0.205686i
$222$	0.0193879	+	13.3593i	0.00130123	+	0.896615i
$223$	−15.5056			−1.03833			−0.519165	−	0.854674i	$-0.673757\pi$
$223$	−15.5056			−1.03833			−0.519165	+	0.854674i	$0.673757\pi$
$224$	−2.70101	+	0.877611i	−0.180469	+	0.0586379i
$225$	6.25892	+	13.6318i	0.417261	+	0.908787i
$226$	3.89078	−	11.9746i	0.258811	−	0.796539i
$227$	1.62410	+	1.17998i	0.107795	+	0.0783179i	0.640377	−	0.768061i	$-0.278778\pi$
$227$	1.62410	+	1.17998i	0.107795	+	0.0783179i	−0.532582	+	0.846379i	$0.678778\pi$
$228$	0.462738	−	0.151095i	0.0306456	−	0.0100065i
$229$	−13.2180	+	18.1930i	−0.873470	+	1.20223i	0.104718	+	0.994502i	$0.466606\pi$
$229$	−13.2180	+	18.1930i	−0.873470	+	1.20223i	−0.978187	+	0.207726i	$0.933394\pi$
$230$	1.21720	+	0.782997i	0.0802598	+	0.0516293i
$231$	3.34328	−	10.3406i	0.219972	−	0.680362i
$232$	−7.56787	+	5.49838i	−0.496855	+	0.360986i
$233$	2.78712	−	2.02496i	0.182590	−	0.132659i	−0.492736	−	0.870179i	$-0.664003\pi$
$233$	2.78712	−	2.02496i	0.182590	−	0.132659i	0.675326	+	0.737520i	$0.264003\pi$
$234$	−3.93446	+	12.2297i	−0.257203	+	0.799479i
$235$	−4.50903	+	7.00947i	−0.294137	+	0.457248i
$236$	−2.61334	+	3.59696i	−0.170114	+	0.234142i
$237$	−0.779319	−	2.38671i	−0.0506222	−	0.155033i
$238$	5.30904	+	3.85724i	0.344134	+	0.250028i
$239$	1.57128	−	4.83591i	0.101638	−	0.312809i	−0.887289	−	0.461214i	$-0.847414\pi$
$239$	1.57128	−	4.83591i	0.101638	−	0.312809i	0.988927	+	0.148405i	$0.0474140\pi$
$240$	−3.86644	+	0.225030i	−0.249578	+	0.0145256i
$241$	5.92389	−	1.92479i	0.381591	−	0.123986i	−0.111939	−	0.993715i	$-0.535706\pi$
$241$	5.92389	−	1.92479i	0.381591	−	0.123986i	0.493530	+	0.869729i	$0.335706\pi$
$242$	−6.11898			−0.393343
$243$	0.113114	+	15.5880i	0.00725628	+	0.999974i
$244$	11.8311	−	3.84416i	0.757410	−	0.246097i
$245$	−1.28915	+	2.00403i	−0.0823607	+	0.128033i
$246$	−8.97335	−	6.49965i	−0.572120	−	0.414402i
$247$	−1.20352			−0.0765781
$248$	−1.38816	−	5.39194i	−0.0881486	−	0.342388i
$249$	−7.67375	+	0.0111367i	−0.486304	+	0.000705759i
$250$	9.89508	−	5.20456i	0.625820	−	0.329165i
$251$	18.1029	−	13.1525i	1.14264	−	0.830179i	0.155158	−	0.987890i	$-0.450411\pi$
$251$	18.1029	−	13.1525i	1.14264	−	0.830179i	0.987485	+	0.157711i	$0.0504114\pi$
$252$	8.09535	−	2.65634i	0.509959	−	0.167334i
$253$		−	1.42997i		−	0.0899014i
$254$	8.47961			0.532058
$255$	5.67199	+	6.92220i	0.355194	+	0.433485i
$256$	0.309017	−	0.951057i	0.0193136	−	0.0594410i
$257$	−4.41906	+	13.6005i	−0.275653	+	0.848373i	0.713393	+	0.700764i	$0.247158\pi$
$257$	−4.41906	+	13.6005i	−0.275653	+	0.848373i	−0.989046	+	0.147609i	$0.952842\pi$
$258$	−10.6864	+	14.7535i	−0.665304	+	0.918512i
$259$	−20.8328	+	6.76899i	−1.29449	+	0.420605i
$260$	9.25993	+	2.43832i	0.574276	+	0.151218i
$261$	22.6556	−	16.5610i	1.40235	−	1.02510i
$262$	−6.83740	−	2.22160i	−0.422416	−	0.137251i
$263$	13.3559	+	18.3829i	0.823563	+	1.13354i	0.989087	+	0.147332i	$0.0470684\pi$
$263$	13.3559	+	18.3829i	0.823563	+	1.13354i	−0.165524	+	0.986206i	$0.552932\pi$
$264$	2.25372	+	3.09254i	0.138707	+	0.190332i
$265$	0.986920	−	0.0560025i	0.0606260	−	0.00344021i
$266$	0.469150	+	0.645730i	0.0287654	+	0.0395922i
$267$	17.6636	−	24.3862i	1.08099	−	1.49241i
$268$	5.36423	−	1.74294i	0.327672	−	0.106467i
$269$	1.84977	+	1.34394i	0.112783	+	0.0819414i	0.642747	−	0.766079i	$-0.277795\pi$
$269$	1.84977	+	1.34394i	0.112783	+	0.0819414i	−0.529964	+	0.848020i	$0.677795\pi$
$270$	11.5973	−	0.708754i	0.705790	−	0.0431334i
$271$	−1.30005	−	0.422411i	−0.0789722	−	0.0256596i	0.269264	−	0.963066i	$-0.413219\pi$
$271$	−1.30005	−	0.422411i	−0.0789722	−	0.0256596i	−0.348237	+	0.937407i	$0.613219\pi$
$272$	−2.19758	+	0.714038i	−0.133248	+	0.0432949i
$273$	−21.0649	+	0.0305709i	−1.27491	+	0.00185023i
$274$		−	6.03564i		−	0.364626i
$275$	−9.61397	−	5.44032i	−0.579744	−	0.328064i
$276$	0.906006	−	0.660263i	0.0545352	−	0.0397432i
$277$	13.0683	+	9.49469i	0.785200	+	0.570481i	0.906535	−	0.422131i	$-0.138718\pi$
$277$	13.0683	+	9.49469i	0.785200	+	0.570481i	−0.121335	+	0.992612i	$0.538718\pi$
$278$		−	18.8057i		−	1.12789i
$279$	4.21143	+	16.1637i	0.252132	+	0.967693i
$280$	−2.30141	−	5.91876i	−0.137536	−	0.353714i
$281$	0.889359	−	1.22410i	0.0530547	−	0.0730236i	−0.781665	−	0.623698i	$-0.785629\pi$
$281$	0.889359	−	1.22410i	0.0530547	−	0.0730236i	0.834720	+	0.550675i	$0.185629\pi$
$282$	3.80225	+	5.21741i	0.226421	+	0.310692i
$283$	−23.7491	+	7.71655i	−1.41174	+	0.458701i	−0.912967	−	0.408033i	$-0.866215\pi$
$283$	−23.7491	+	7.71655i	−1.41174	+	0.458701i	−0.498770	+	0.866735i	$0.666215\pi$
$284$		−	4.66806i		−	0.276998i
$285$	0.395937	+	1.01391i	0.0234533	+	0.0600589i
$286$	−2.92360	−	8.99791i	−0.172876	−	0.532057i
$287$	5.61411	−	17.2785i	0.331391	−	1.01992i
$288$	−0.918766	+	2.85585i	−0.0541388	+	0.168282i
$289$	−9.43377	−	6.85404i	−0.554928	−	0.403179i
$290$	−13.2337	−	16.1986i	−0.777110	−	0.951212i
$291$	−12.3169	−	8.92145i	−0.722028	−	0.522985i
$292$	6.97912	−	5.07063i	0.408422	−	0.296736i
$293$	4.32883	−	13.3228i	0.252893	−	0.778324i	−0.741345	−	0.671124i	$-0.765812\pi$
$293$	4.32883	−	13.3228i	0.252893	−	0.778324i	0.994238	−	0.107199i	$-0.0341883\pi$
$294$	1.08708	+	1.49168i	0.0633996	+	0.0869963i
$295$	−8.36119	−	5.37856i	−0.486807	−	0.313152i
$296$	2.38344	−	7.33548i	0.138535	−	0.426366i
$297$	−6.78807	−	9.25795i	−0.393884	−	0.537200i
$298$	−13.9337	+	19.1781i	−0.807158	+	1.11096i
$299$	−2.63608	+	0.856513i	−0.152448	+	0.0495334i
$300$	−0.992179	−	8.60323i	−0.0572835	−	0.496708i
$301$	−28.4083	−	9.23042i	−1.63743	−	0.532033i
$302$	−20.7062	−	6.72784i	−1.19151	−	0.387144i
$303$	−2.25606	−	6.90930i	−0.129607	−	0.396929i
$304$	−0.281043			−0.0161189
$305$	10.0808	+	25.9257i	0.577224	+	1.48450i
$306$	6.58650	−	2.16124i	0.376525	−	0.123550i
$307$	−7.08027	−	9.74516i	−0.404093	−	0.556186i	0.557673	−	0.830061i	$-0.311694\pi$
$307$	−7.08027	−	9.74516i	−0.404093	−	0.556186i	−0.961765	+	0.273875i	$0.911694\pi$
$308$	−3.68802	+	5.07613i	−0.210145	+	0.289239i
$309$	8.47720	−	0.0123027i	0.482251	−	0.000699877i
$310$	11.8615	−	3.78210i	0.673689	−	0.214809i
$311$		−	1.13624i		−	0.0644303i	−0.999481	−	0.0322151i	$-0.989744\pi$
$311$		−	1.13624i		−	0.0644303i	0.999481	−	0.0322151i	$-0.0102562\pi$
$312$	4.35101	−	6.00697i	0.246328	−	0.340078i
$313$	14.4885	−	10.5265i	0.818937	−	0.594993i	−0.0974705	−	0.995238i	$-0.531075\pi$
$313$	14.4885	−	10.5265i	0.818937	−	0.594993i	0.916408	+	0.400246i	$0.131075\pi$
$314$	15.6144	−	5.07344i	0.881174	−	0.286311i
$315$	6.95575	+	17.7362i	0.391912	+	0.999320i
$316$			1.44956i			0.0815443i
$317$	−8.33623	−	25.6563i	−0.468209	−	1.44100i	−0.854901	−	0.518791i	$-0.826382\pi$
$317$	−8.33623	−	25.6563i	−0.468209	−	1.44100i	0.386692	−	0.922209i	$-0.373618\pi$
$318$	0.235556	−	0.728562i	0.0132093	−	0.0408557i
$319$	−6.38636	+	19.6552i	−0.357568	+	1.10048i
$320$	2.16236	+	0.569392i	0.120879	+	0.0318300i
$321$	−26.3933	+	8.61807i	−1.47313	+	0.481014i
$322$	1.48713	+	1.08046i	0.0828745	+	0.0602119i
$323$	0.381708	+	0.525375i	0.0212388	+	0.0292327i
$324$	2.73142	−	8.57551i	0.151745	−	0.476417i
$325$	−4.27044	+	20.9815i	−0.236882	+	1.16384i
$326$	0.412049	+	0.567136i	0.0228213	+	0.0314108i
$327$	3.85183	+	1.24536i	0.213007	+	0.0688685i
$328$	3.76009	+	5.17532i	0.207616	+	0.285759i
$329$	−6.22205	+	8.56392i	−0.343033	+	0.472144i
$330$	−6.61851	+	5.42315i	−0.364337	+	0.298535i
$331$	9.89461	−	13.6188i	0.543857	−	0.748555i	−0.445305	−	0.895379i	$-0.646905\pi$
$331$	9.89461	−	13.6188i	0.543857	−	0.748555i	0.989163	+	0.146823i	$0.0469049\pi$
$332$	4.21361	+	1.36908i	0.231252	+	0.0751382i
$333$	−7.08642	+	22.0271i	−0.388333	+	1.20708i
$334$	−3.21280	+	1.04390i	−0.175797	+	0.0571198i
$335$	4.57063	+	11.7547i	0.249720	+	0.642229i
$336$	−4.91903	+	0.00713885i	−0.268355	+	0.000389456i
$337$	−6.65129	−	20.4706i	−0.362319	−	1.11510i	−0.951643	−	0.307206i	$-0.900606\pi$
$337$	−6.65129	−	20.4706i	−0.362319	−	1.11510i	0.589325	−	0.807896i	$-0.299394\pi$
$338$	−4.31880	+	3.13780i	−0.234912	+	0.170674i
$339$	12.7928	−	17.6616i	0.694809	−	0.959247i
$340$	−1.87247	−	4.81560i	−0.101549	−	0.261162i
$341$	−9.48310	−	7.83469i	−0.513539	−	0.424272i
$342$	0.843126	−	0.00244721i	0.0455911	−	0.000132330i
$343$	9.90630	−	13.6349i	0.534890	−	0.736213i
$344$	8.50897	−	6.18213i	0.458773	−	0.333318i
$345$	1.58880	+	1.93899i	0.0855379	+	0.104392i
$346$	4.60582			0.247610
$347$		−	14.4000i		−	0.773031i	−0.922283	−	0.386516i	$-0.873679\pi$
$347$		−	14.4000i		−	0.773031i	0.922283	−	0.386516i	$-0.126321\pi$
$348$	−15.4020	+	5.02914i	−0.825635	+	0.269590i
$349$	1.58610	−	4.88151i	0.0849020	−	0.261301i	−0.899589	−	0.436738i	$-0.856134\pi$
$349$	1.58610	−	4.88151i	0.0849020	−	0.261301i	0.984491	+	0.175437i	$0.0561337\pi$
$350$	12.9220	−	5.88765i	0.690707	−	0.314708i
$351$	−13.0007	+	18.0587i	−0.693925	+	0.963903i
$352$	−0.682712	−	2.10117i	−0.0363887	−	0.111993i
$353$	2.96640	−	4.08290i	0.157886	−	0.217311i	−0.722744	−	0.691115i	$-0.757120\pi$
$353$	2.96640	−	4.08290i	0.157886	−	0.217311i	0.880630	+	0.473804i	$0.157120\pi$
$354$	−6.22354	+	4.53548i	−0.330777	+	0.241058i
$355$	10.4213	−	0.591356i	0.553107	−	0.0313859i
$356$	−14.0645	+	10.2185i	−0.745420	+	0.541579i
$357$	6.69428	+	9.18582i	0.354299	+	0.486165i
$358$	3.12349	−	9.61310i	0.165081	−	0.508068i
$359$	−7.78581	−	10.7163i	−0.410920	−	0.565582i	0.552523	−	0.833498i	$-0.313665\pi$
$359$	−7.78581	−	10.7163i	−0.410920	−	0.565582i	−0.963442	+	0.267916i	$0.913665\pi$
$360$	−6.49201	−	1.68934i	−0.342159	−	0.0890361i
$361$	−5.84692	−	17.9950i	−0.307732	−	0.947103i
$362$	−9.72937	+	13.3913i	−0.511364	+	0.703832i
$363$	−10.0844	−	3.26045i	−0.529294	−	0.171129i
$364$	11.5666	+	3.75822i	0.606255	+	0.196984i
$365$	12.2042	+	14.9384i	0.638796	+	0.781910i
$366$	21.5466	−	0.0312700i	1.12626	−	0.00163451i
$367$	30.4492			1.58944			0.794718	−	0.606979i	$-0.207619\pi$
$367$	30.4492			1.58944			0.794718	+	0.606979i	$0.207619\pi$
$368$	−0.615571	+	0.200011i	−0.0320888	+	0.0104263i
$369$	−11.3253	−	15.4931i	−0.589570	−	0.806541i
$370$	16.6782	+	4.39171i	0.867059	+	0.228314i
$371$	1.25549			0.0651820
$372$	0.585281	−	9.62587i	0.0303454	−	0.499078i
$373$			1.37935i			0.0714200i	0.999362	+	0.0357100i	$0.0113693\pi$
$373$			1.37935i			0.0714200i	−0.999362	+	0.0357100i	$0.988631\pi$
$374$	−3.00063	+	4.13001i	−0.155159	+	0.213558i
$375$	19.0808	−	3.30489i	0.985329	−	0.170664i
$376$	−1.15180	−	3.54488i	−0.0593996	−	0.182813i
$377$	40.0586			2.06312
$378$	14.7570	−	0.0642494i	0.759017	−	0.00330464i
$379$	−4.16004	−	12.8033i	−0.213687	−	0.657661i	−0.999244	−	0.0388719i	$-0.987624\pi$
$379$	−4.16004	−	12.8033i	−0.213687	−	0.657661i	0.785557	−	0.618789i	$-0.212376\pi$
$380$	−0.0356029	−	0.627423i	−0.00182639	−	0.0321861i
$381$	13.9749	+	4.51829i	0.715953	+	0.231479i
$382$	11.1374	−	15.3293i	0.569837	−	0.784313i
$383$	−8.97486	+	2.91611i	−0.458594	+	0.149006i	−0.529198	−	0.848498i	$-0.677507\pi$
$383$	−8.97486	+	2.91611i	−0.458594	+	0.149006i	0.0706045	+	0.997504i	$0.477507\pi$
$384$	1.01604	−	1.40273i	0.0518495	−	0.0715830i
$385$	−11.7995	−	7.59037i	−0.601360	−	0.386841i
$386$	−13.1130	−	4.26067i	−0.667434	−	0.216862i
$387$	−25.4730	+	18.6204i	−1.29486	+	0.946528i
$388$	5.16112	+	7.10367i	0.262016	+	0.360634i
$389$	−4.34119	+	13.3608i	−0.220107	+	0.677420i	0.778644	+	0.627466i	$0.215908\pi$
$389$	−4.34119	+	13.3608i	−0.220107	+	0.677420i	−0.998751	+	0.0499546i	$0.984092\pi$
$390$	13.9616	+	8.95257i	0.706974	+	0.453331i
$391$	1.20995	+	0.879081i	0.0611899	+	0.0444571i
$392$	−0.329304	−	1.01349i	−0.0166324	−	0.0511892i
$393$	−10.0846	−	7.30457i	−0.508702	−	0.368467i
$394$	10.0418	+	3.26277i	0.505897	+	0.164376i
$395$	−3.23612	+	0.183632i	−0.162827	+	0.00923955i
$396$	2.06642	+	6.29754i	0.103842	+	0.316463i
$397$		−	7.03491i		−	0.353072i	−0.984294	−	0.176536i	$-0.943511\pi$
$397$		−	7.03491i		−	0.353072i	0.984294	−	0.176536i	$-0.0564892\pi$
$398$		−	26.3897i		−	1.32279i
$399$	0.429112	+	1.31418i	0.0214825	+	0.0657913i
$400$	−0.997224	+	4.89955i	−0.0498612	+	0.244977i
$401$	25.5503	+	18.5634i	1.27592	+	0.927011i	0.999422	−	0.0340028i	$-0.0108255\pi$
$401$	25.5503	+	18.5634i	1.27592	+	0.927011i	0.276500	+	0.961014i	$0.410826\pi$
$402$	9.76924	−	0.0141778i	0.487246	−	0.000707125i
$403$	−8.76273	+	22.1744i	−0.436502	+	1.10458i
$404$			4.19635i			0.208776i
$405$	19.4906	+	5.01147i	0.968498	+	0.249022i
$406$	−15.6155	−	21.4928i	−0.774982	−	1.06667i
$407$	−5.26574	−	16.2063i	−0.261013	−	0.803316i
$408$	−4.00220	+	0.00580828i	−0.198139	+	0.000287553i
$409$			5.74750i			0.284195i	0.989853	+	0.142098i	$0.0453847\pi$
$409$			5.74750i			0.284195i	−0.989853	+	0.142098i	$0.954615\pi$
$410$	−11.0774	+	9.04992i	−0.547076	+	0.446944i
$411$	3.21604	−	9.94705i	0.158636	−	0.490652i
$412$	−4.65477	−	1.51243i	−0.229324	−	0.0745120i
$413$	−10.2154	−	7.42192i	−0.502667	−	0.365209i
$414$	1.84496	−	0.605391i	0.0906750	−	0.0297533i
$415$	−2.52266	+	9.58022i	−0.123833	+	0.470274i
$416$	−3.46448	+	2.51709i	−0.169860	+	0.123410i
$417$	10.0205	−	30.9928i	0.490704	−	1.51772i
$418$	−0.502327	+	0.364962i	−0.0245696	+	0.0178509i
$419$	8.72568	+	12.0099i	0.426278	+	0.586721i	0.967094	−	0.254420i	$-0.0818846\pi$
$419$	8.72568	+	12.0099i	0.426278	+	0.586721i	−0.540816	+	0.841141i	$0.681885\pi$
$420$	−0.639087	−	10.9807i	−0.0311842	−	0.535805i
$421$	−20.9089	+	15.1912i	−1.01904	+	0.740374i	−0.966085	−	0.258223i	$-0.916863\pi$
$421$	−20.9089	+	15.1912i	−1.01904	+	0.740374i	−0.0529526	+	0.998597i	$0.516863\pi$
$422$	−11.9126	−	8.65504i	−0.579899	−	0.421321i
$423$	3.48626	+	10.6246i	0.169508	+	0.516584i
$424$	−0.259845	+	0.357646i	−0.0126192	+	0.0173688i
$425$	10.5135	−	4.79028i	0.509980	−	0.232363i
$426$	2.48734	−	7.69321i	0.120512	−	0.372737i
$427$	10.9175	+	33.6005i	0.528333	+	1.62604i
$428$	16.0299			0.774837
$429$	−0.0237817	−	16.3868i	−0.00114819	−	0.791164i
$430$	14.8794	+	18.2129i	0.717548	+	0.878305i
$431$	−6.52145	−	8.97601i	−0.314127	−	0.432359i	0.622536	−	0.782592i	$-0.286103\pi$
$431$	−6.52145	−	8.97601i	−0.314127	−	0.432359i	−0.936663	+	0.350232i	$0.886103\pi$
$432$	−3.03589	+	4.21703i	−0.146064	+	0.202892i
$433$	9.96900			0.479080			0.239540	−	0.970887i	$-0.423003\pi$
$433$	9.96900			0.479080			0.239540	+	0.970887i	$0.423003\pi$
$434$	15.3132	−	3.94240i	0.735055	−	0.189241i
$435$	−13.1786	−	33.7476i	−0.631865	−	1.61807i
$436$	−1.89084	−	1.37377i	−0.0905547	−	0.0657918i
$437$	0.106921	+	0.147164i	0.00511473	+	0.00703982i
$438$	14.2038	−	4.63790i	0.678684	−	0.221607i
$439$	3.79627			0.181186			0.0905930	−	0.995888i	$-0.471124\pi$
$439$	3.79627			0.181186			0.0905930	+	0.995888i	$0.471124\pi$
$440$	4.60433	−	1.79032i	0.219503	−	0.0853500i
$441$	0.996733	+	3.03760i	0.0474635	+	0.144648i
$442$	9.41077	+	3.05774i	0.447625	+	0.145442i
$443$	10.9644	−	33.7449i	0.520933	−	1.60327i	−0.251287	−	0.967913i	$-0.580854\pi$
$443$	10.9644	−	33.7449i	0.520933	−	1.60327i	0.772220	−	0.635355i	$-0.219146\pi$
$444$	7.83669	−	10.8193i	0.371913	−	0.513459i
$445$	−24.5943	−	30.1043i	−1.16588	−	1.42708i
$446$	12.5443	+	9.11395i	0.593989	+	0.431558i
$447$	−33.1824	+	24.1821i	−1.56947	+	1.14377i
$448$	2.70101	+	0.877611i	0.127611	+	0.0414632i
$449$	−10.1989	+	7.40997i	−0.481318	+	0.349698i	−0.801836	−	0.597545i	$-0.796143\pi$
$449$	−10.1989	+	7.40997i	−0.481318	+	0.349698i	0.320518	+	0.947242i	$0.396143\pi$
$450$	2.94900	−	14.7073i	0.139017	−	0.693307i
$451$	13.4413	+	4.36734i	0.632925	+	0.205650i
$452$	−10.1862	+	7.40071i	−0.479119	+	0.348100i
$453$	−30.5400	−	22.1209i	−1.43489	−	1.03933i
$454$	−0.620351	−	1.90925i	−0.0291145	−	0.0896053i
$455$	−6.92486	+	26.2983i	−0.324643	+	1.23288i
$456$	−0.463174	−	0.149752i	−0.0216901	−	0.00701276i
$457$	6.00814	−	18.4912i	0.281049	−	0.864980i	−0.706506	−	0.707707i	$-0.749730\pi$
$457$	6.00814	−	18.4912i	0.281049	−	0.864980i	0.987555	−	0.157273i	$-0.0502703\pi$
$458$	21.3872	−	6.94911i	0.999356	−	0.324711i
$459$	12.0065	−	0.0522743i	0.560416	−	0.00243996i
$460$	−0.524501	−	1.34891i	−0.0244550	−	0.0628932i
$461$	−9.03404	−	27.8039i	−0.420757	−	1.29496i	−0.906999	−	0.421133i	$-0.861633\pi$
$461$	−9.03404	−	27.8039i	−0.420757	−	1.29496i	0.486242	−	0.873824i	$-0.338367\pi$
$462$	−8.78283	+	6.40060i	−0.408614	+	0.297783i
$463$	−8.21913	−	5.97155i	−0.381975	−	0.277521i	0.380184	−	0.924911i	$-0.375861\pi$
$463$	−8.21913	−	5.97155i	−0.381975	−	0.277521i	−0.762159	+	0.647390i	$0.775861\pi$
$464$	9.35440			0.434267
$465$	21.5637	+	0.0872084i	0.999992	+	0.00404419i
$466$	−3.44507			−0.159590
$467$	−5.79914	−	4.21332i	−0.268352	−	0.194969i	0.445469	−	0.895297i	$-0.353037\pi$
$467$	−5.79914	−	4.21332i	−0.268352	−	0.194969i	−0.713821	+	0.700328i	$0.753037\pi$
$468$	10.3715	−	7.58140i	0.479421	−	0.350451i
$469$	4.94997	+	15.2345i	0.228569	+	0.703462i
$470$	7.76795	−	3.02044i	0.358309	−	0.139323i
$471$	28.4368	−	0.0412694i	1.31030	−	0.00190159i
$472$	4.22848	−	1.37392i	0.194632	−	0.0632396i
$473$	7.18054	−	22.0994i	0.330161	−	1.01613i
$474$	−0.772388	+	2.38896i	−0.0354770	+	0.109728i
$475$	1.39620	−	0.158965i	0.0640619	−	0.00729383i
$476$	−2.02787	−	6.24115i	−0.0929474	−	0.286063i
$477$	0.776417	−	1.07519i	0.0355497	−	0.0492298i
$478$	−4.11367	+	2.98876i	−0.188155	+	0.136703i
$479$	31.8710	+	10.3555i	1.45623	+	0.473156i	0.926915	−	0.375272i	$-0.122451\pi$
$479$	31.8710	+	10.3555i	1.45623	+	0.473156i	0.529311	+	0.848428i	$0.322451\pi$
$480$	3.26029	+	2.09058i	0.148811	+	0.0954217i
$481$	−26.7214	+	19.4143i	−1.21839	+	0.885214i
$482$	−5.92389	−	1.92479i	−0.269826	−	0.0876717i
$483$	1.87515	+	2.57307i	0.0853224	+	0.117079i
$484$	4.95036	+	3.59665i	0.225016	+	0.163484i
$485$	−15.2050	+	12.4220i	−0.690421	+	0.564053i
$486$	9.07091	−	12.6775i	0.411465	−	0.575062i
$487$	5.92651	−	18.2399i	0.268556	−	0.826529i	−0.722297	−	0.691583i	$-0.756914\pi$
$487$	5.92651	−	18.2399i	0.268556	−	0.826529i	0.990853	−	0.134947i	$-0.0430863\pi$
$488$	−11.8311	−	3.84416i	−0.535569	−	0.174017i
$489$	0.376884	+	1.15423i	0.0170433	+	0.0521960i
$490$	2.22089	−	0.863555i	0.100329	−	0.0390114i
$491$	−6.61166			−0.298380			−0.149190	−	0.988809i	$-0.547667\pi$
$491$	−6.61166			−0.298380			−0.149190	+	0.988809i	$0.547667\pi$
$492$	3.43920	+	10.5327i	0.155051	+	0.474852i
$493$	−12.7050	−	17.4869i	−0.572203	−	0.787570i
$494$	0.973668	+	0.707411i	0.0438074	+	0.0318279i
$495$	−13.7973	+	5.41102i	−0.620144	+	0.243207i
$496$	−2.04625	+	5.17811i	−0.0918795	+	0.232504i
$497$	13.2573			0.594672
$498$	6.21474	+	4.50151i	0.278489	+	0.201717i
$499$	−3.23027	−	4.44609i	−0.144607	−	0.199034i	0.730569	−	0.682838i	$-0.239255\pi$
$499$	−3.23027	−	4.44609i	−0.144607	−	0.199034i	−0.875176	+	0.483804i	$0.839255\pi$
$500$	−11.0644	−	1.60560i	−0.494817	−	0.0718046i
$501$	−5.85111	+	0.00849154i	−0.261408	+	0.000379374i
$502$	−22.3764			−0.998707
$503$	−8.47935	−	26.0968i	−0.378076	−	1.16360i	−0.941380	−	0.337348i	$-0.890470\pi$
$503$	−8.47935	−	26.0968i	−0.378076	−	1.16360i	0.563304	−	0.826249i	$-0.309530\pi$
$504$	−8.11063	−	2.60930i	−0.361276	−	0.116228i
$505$	−9.36826	+	0.531599i	−0.416882	+	0.0236559i
$506$	−0.840515	+	1.15687i	−0.0373654	+	0.0514291i
$507$	−8.78957	+	2.87001i	−0.390358	+	0.127462i
$508$	−6.86015	−	4.98419i	−0.304370	−	0.221138i
$509$	16.9783	−	12.3354i	0.752549	−	0.546759i	−0.144067	−	0.989568i	$-0.546018\pi$
$509$	16.9783	−	12.3354i	0.752549	−	0.546759i	0.896616	+	0.442809i	$0.146018\pi$
$510$	−0.519971	−	8.93409i	−0.0230247	−	0.395608i
$511$	14.4006	+	19.8208i	0.637046	+	0.876819i
$512$	−0.809017	+	0.587785i	−0.0357538	+	0.0259767i
$513$	1.39082	+	0.445220i	0.0614063	+	0.0196569i
$514$	11.5692	−	8.40554i	0.510297	−	0.370753i
$515$	2.78679	−	10.5833i	0.122801	−	0.466355i
$516$	17.3173	−	5.65454i	0.762353	−	0.248927i
$517$	−6.66205	−	4.84027i	−0.292997	−	0.212875i
$518$	20.8328	+	6.76899i	0.915342	+	0.297413i
$519$	7.59063	+	2.45417i	0.333192	+	0.107726i
$520$	−6.05823	−	7.41549i	−0.265671	−	0.325191i
$521$			18.7980i			0.823556i	0.911284	+	0.411778i	$0.135092\pi$
$521$			18.7980i			0.823556i	−0.911284	+	0.411778i	$0.864908\pi$
$522$	−28.0631	+	0.0814544i	−1.22829	+	0.00356516i
$523$	7.18865	+	22.1244i	0.314338	+	0.967431i	0.976026	+	0.217653i	$0.0698400\pi$
$523$	7.18865	+	22.1244i	0.314338	+	0.967431i	−0.661689	+	0.749779i	$0.730160\pi$
$524$	4.22574	+	5.81624i	0.184602	+	0.254083i
$525$	24.4333	−	2.81780i	1.06635	−	0.122979i
$526$		−	22.7225i		−	0.990748i
$527$	12.4590	−	3.20760i	0.542723	−	0.139725i
$528$	−0.00555346	−	3.82662i	−0.000241683	−	0.166532i
$529$	−18.2685	−	13.2728i	−0.794281	−	0.577079i
$530$	−0.831353	−	0.534790i	−0.0361117	−	0.0232298i
$531$	−12.6734	+	4.15855i	−0.549980	+	0.180466i
$532$		−	0.798166i		−	0.0346049i
$533$		−	27.3942i		−	1.18658i
$534$	−28.6240	+	9.34644i	−1.23868	+	0.404460i
$535$	2.03069	+	35.7865i	0.0877945	+	1.54718i
$536$	−5.36423	−	1.74294i	−0.231699	−	0.0752837i
$537$	10.2699	−	14.1786i	0.443180	−	0.611851i
$538$	−0.706551	−	2.17454i	−0.0304616	−	0.0937511i
$539$	−1.90470	−	1.38385i	−0.0820414	−	0.0596066i
$540$	−9.79902	−	6.24334i	−0.421683	−	0.268670i
$541$	4.76208	−	14.6562i	0.204738	−	0.630119i	−0.794986	−	0.606628i	$-0.792522\pi$
$541$	4.76208	−	14.6562i	0.204738	−	0.630119i	0.999724	−	0.0234910i	$-0.00747809\pi$
$542$	0.803473	+	1.10589i	0.0345121	+	0.0475019i
$543$	−23.1700	+	16.8854i	−0.994319	+	0.724622i
$544$	2.19758	+	0.714038i	0.0942206	+	0.0306141i
$545$	2.82738	−	4.39528i	0.121112	−	0.188273i
$546$	17.0598	+	12.3569i	0.730094	+	0.528827i
$547$	−1.34310	+	0.436400i	−0.0574269	+	0.0186591i	−0.337590	−	0.941293i	$-0.609612\pi$
$547$	−1.34310	+	0.436400i	−0.0574269	+	0.0186591i	0.280163	+	0.959953i	$0.409612\pi$
$548$	−3.54766	+	4.88293i	−0.151548	+	0.208589i
$549$	35.5267	+	11.4294i	1.51624	+	0.487796i
$550$	4.58012	+	10.0523i	0.195297	+	0.428630i
$551$	−0.812404	−	2.50032i	−0.0346096	−	0.106517i
$552$	−1.12107	+	0.00162697i	−0.0477158	+	6.92485e-5i
$553$	−4.11677			−0.175063
$554$	−4.99166	−	15.3627i	−0.212075	−	0.652700i
$555$	25.1465	+	16.1246i	1.06741	+	0.684452i
$556$	−11.0537	+	15.2141i	−0.468782	+	0.645223i
$557$			13.2121i			0.559813i	0.960027	+	0.279906i	$0.0903035\pi$
$557$			13.2121i			0.559813i	−0.960027	+	0.279906i	$0.909697\pi$
$558$	6.09364	−	15.5521i	0.257964	−	0.658372i
$559$	−45.0401			−1.90499
$560$	−1.61708	+	6.14112i	−0.0683341	+	0.259510i
$561$	−7.14585	+	5.20762i	−0.301698	+	0.219866i
$562$	−1.43901	+	0.467564i	−0.0607011	+	0.0197230i
$563$	45.5900			1.92139			0.960695	−	0.277606i	$-0.0895408\pi$
$563$	45.5900			1.92139			0.960695	+	0.277606i	$0.0895408\pi$
$564$	−0.00936923	−	6.45588i	−0.000394516	−	0.271842i
$565$	−17.8123	−	21.8029i	−0.749370	−	0.917256i
$566$	23.7491	+	7.71655i	0.998249	+	0.324351i
$567$	24.3545	+	7.75725i	1.02279	+	0.325774i
$568$	−2.74382	+	3.77654i	−0.115128	+	0.158460i
$569$	−8.79089	−	27.0556i	−0.368533	−	1.13423i	−0.947739	−	0.319047i	$-0.896637\pi$
$569$	−8.79089	−	27.0556i	−0.368533	−	1.13423i	0.579206	−	0.815181i	$-0.303363\pi$
$570$	0.275642	−	1.05300i	0.0115454	−	0.0441052i
$571$	14.3410	+	19.7388i	0.600154	+	0.826041i	0.995722	−	0.0923953i	$-0.0294523\pi$
$571$	14.3410	+	19.7388i	0.600154	+	0.826041i	−0.395568	+	0.918437i	$0.629452\pi$
$572$	−2.92360	+	8.99791i	−0.122242	+	0.376221i
$573$	26.5230	−	19.3290i	1.10802	−	0.807480i
$574$	−14.6979	+	10.6787i	−0.613480	+	0.445720i
$575$	2.94496	−	1.34182i	0.122814	−	0.0559577i
$576$	2.42192	−	1.77039i	0.100913	−	0.0737664i
$577$	−27.0091	+	37.1749i	−1.12440	+	1.54761i	−0.326120	+	0.945328i	$0.605742\pi$
$577$	−27.0091	+	37.1749i	−1.12440	+	1.54761i	−0.798284	+	0.602281i	$0.794258\pi$
$578$	3.60338	+	11.0901i	0.149881	+	0.461286i
$579$	−19.3406	−	14.0090i	−0.803770	−	0.582193i
$580$	1.18503	+	20.8835i	0.0492056	+	0.867140i
$581$	−3.88821	+	11.9667i	−0.161310	+	0.496462i
$582$	4.72066	+	14.4573i	0.195678	+	0.599273i
$583$			0.976676i			0.0404498i
$584$	−8.62667			−0.356974
$585$	18.2392	+	22.1936i	0.754097	+	0.917594i
$586$	−11.3330	+	8.23391i	−0.468162	+	0.340140i
$587$	−17.5896	+	24.2100i	−0.726000	+	0.999253i	0.273304	+	0.961928i	$0.411884\pi$
$587$	−17.5896	+	24.2100i	−0.726000	+	0.999253i	−0.999303	+	0.0373249i	$0.988116\pi$
$588$	−0.00267870	−	1.84576i	−0.000110468	−	0.0761178i
$589$	1.56176	+	0.0972346i	0.0643512	+	0.00400648i
$590$	3.60291	+	9.26593i	0.148329	+	0.381472i
$591$	14.8108	+	10.7279i	0.609237	+	0.441287i
$592$	−6.23993	+	4.53357i	−0.256460	+	0.186329i
$593$	11.8443	+	36.4531i	0.486389	+	1.49695i	0.829960	+	0.557824i	$0.188363\pi$
$593$	11.8443	+	36.4531i	0.486389	+	1.49695i	−0.343571	+	0.939127i	$0.611637\pi$
$594$	0.0499810	+	11.4798i	0.00205074	+	0.471020i
$595$	13.6763	−	5.31782i	0.560675	−	0.218009i
$596$	22.5452	−	7.32539i	0.923488	−	0.300059i
$597$	14.0615	−	43.4916i	0.575500	−	1.77999i
$598$	2.63608	+	0.856513i	0.107797	+	0.0350254i
$599$	8.32085	−	11.4527i	0.339981	−	0.467943i	−0.604455	−	0.796639i	$-0.706609\pi$
$599$	8.32085	−	11.4527i	0.339981	−	0.467943i	0.944436	+	0.328696i	$0.106609\pi$
$600$	−4.25416	+	7.54335i	−0.173675	+	0.307956i
$601$	−18.7401	+	25.7936i	−0.764426	+	1.05214i	0.232407	+	0.972619i	$0.425340\pi$
$601$	−18.7401	+	25.7936i	−0.764426	+	1.05214i	−0.996833	+	0.0795235i	$0.974660\pi$
$602$	17.5573	+	24.1656i	0.715582	+	0.984914i
$603$	16.1078	+	5.18210i	0.655960	+	0.211031i
$604$	12.7971	+	17.6137i	0.520707	+	0.716692i
$605$	−7.40231	+	11.5072i	−0.300947	+	0.467834i
$606$	−2.23599	+	6.91582i	−0.0908310	+	0.280936i
$607$	−19.9948	−	27.5204i	−0.811563	−	1.11702i	−0.991080	−	0.133266i	$-0.957454\pi$
$607$	−19.9948	−	27.5204i	−0.811563	−	1.11702i	0.179517	−	0.983755i	$-0.442546\pi$
$608$	0.227369	+	0.165193i	0.00922102	+	0.00669947i
$609$	−14.2828	−	43.7419i	−0.578769	−	1.77251i
$610$	7.08322	−	26.8997i	0.286791	−	1.08914i
$611$	−4.93239	+	15.1803i	−0.199543	+	0.614131i
$612$	−6.59894	−	2.12297i	−0.266746	−	0.0858159i
$613$	−12.2107	−	37.5806i	−0.493185	−	1.51787i	−0.819766	−	0.572698i	$-0.805897\pi$
$613$	−12.2107	−	37.5806i	−0.493185	−	1.51787i	0.326581	−	0.945169i	$-0.394103\pi$
$614$			12.0457i			0.486124i
$615$	−23.0784	+	9.01223i	−0.930610	+	0.363408i
$616$	5.96735	−	1.93891i	0.240431	−	0.0781208i
$617$	15.2958	−	11.1131i	0.615787	−	0.447395i	−0.235661	−	0.971835i	$-0.575725\pi$
$617$	15.2958	−	11.1131i	0.615787	−	0.447395i	0.851447	+	0.524440i	$0.175725\pi$
$618$	−6.86543	−	4.97282i	−0.276168	−	0.200036i
$619$		−	23.7475i		−	0.954491i	−0.878770	−	0.477246i	$-0.841635\pi$
$619$		−	23.7475i		−	0.954491i	0.878770	−	0.477246i	$-0.158365\pi$
$620$	−11.8192	−	3.91224i	−0.474672	−	0.157119i
$621$	3.36317	−	0.0146427i	0.134960	−	0.000587591i
$622$	−0.667865	+	0.919238i	−0.0267790	+	0.0368581i
$623$	−29.0206	−	39.9434i	−1.16269	−	1.60030i
$624$	−7.05085	+	2.30228i	−0.282260	+	0.0921649i
$625$	2.18281	−	24.9045i	0.0873122	−	0.996181i
$626$	−17.9087			−0.715778
$627$	−1.02233	+	0.333815i	−0.0408278	+	0.0133313i
$628$	−15.6144	−	5.07344i	−0.623084	−	0.202452i
$629$	16.9499	+	5.50736i	0.675837	+	0.219593i
$630$	4.79774	−	18.4374i	0.191147	−	0.734562i
$631$	−33.2235	+	10.7950i	−1.32261	+	0.429740i	−0.883389	−	0.468641i	$-0.844744\pi$
$631$	−33.2235	+	10.7950i	−1.32261	+	0.429740i	−0.439216	+	0.898381i	$0.644744\pi$
$632$	0.852032	−	1.17272i	0.0338920	−	0.0466483i
$633$	−15.0209	−	20.6115i	−0.597027	−	0.819235i
$634$	−8.33623	+	25.6563i	−0.331074	+	1.01894i
$635$	10.2580	−	15.9465i	0.407078	−	0.632819i
$636$	−0.618806	+	0.450963i	−0.0245373	+	0.0178818i
$637$	−1.41019	+	4.34011i	−0.0558737	+	0.171962i
$638$	16.7197	−	12.1476i	0.661940	−	0.480928i
$639$	8.19853	−	11.3535i	0.324329	−	0.449136i
$640$	−1.41470	−	1.73165i	−0.0559211	−	0.0684495i
$641$	−21.0459	−	15.2907i	−0.831262	−	0.603948i	0.0886538	−	0.996063i	$-0.471744\pi$
$641$	−21.0459	−	15.2907i	−0.831262	−	0.603948i	−0.919916	+	0.392115i	$0.871744\pi$
$642$	26.4182	+	8.54143i	1.04264	+	0.337103i
$643$	10.5892	−	32.5902i	0.417597	−	1.28523i	−0.492311	−	0.870419i	$-0.663848\pi$
$643$	10.5892	−	32.5902i	0.417597	−	1.28523i	0.909908	−	0.414811i	$-0.136152\pi$
$644$	−0.568033	−	1.74823i	−0.0223836	−	0.0688898i
$645$	14.8174	+	37.9442i	0.583435	+	1.49405i
$646$		−	0.649400i		−	0.0255503i
$647$	−9.11222	+	2.96074i	−0.358238	+	0.116399i	−0.482606	−	0.875837i	$-0.660310\pi$
$647$	−9.11222	+	2.96074i	−0.358238	+	0.116399i	0.124368	+	0.992236i	$0.460310\pi$
$648$	−7.25032	+	5.33225i	−0.284820	+	0.209470i
$649$	5.77367	−	7.94677i	0.226636	−	0.311938i
$650$	15.7875	−	14.4643i	0.619235	−	0.567335i
$651$	27.3376	+	1.66220i	1.07144	+	0.0651469i
$652$		−	0.701019i		−	0.0274540i
$653$	−0.319776	−	0.232331i	−0.0125138	−	0.00909180i	0.581511	−	0.813539i	$-0.302462\pi$
$653$	−0.319776	−	0.232331i	−0.0125138	−	0.00909180i	−0.594025	+	0.804447i	$0.702462\pi$
$654$	−2.38420	−	3.27157i	−0.0932294	−	0.127928i
$655$	−12.4493	+	10.1707i	−0.486434	+	0.397401i
$656$		−	6.39704i		−	0.249763i
$657$	25.8799	−	0.0751176i	1.00967	−	0.00293062i
$658$	10.0675	−	3.27113i	0.392472	−	0.127522i
$659$	19.4597	+	6.32284i	0.758042	+	0.246303i	0.662438	−	0.749117i	$-0.269522\pi$
$659$	19.4597	+	6.32284i	0.758042	+	0.246303i	0.0956039	+	0.995419i	$0.469522\pi$
$660$	8.54214	−	0.497159i	0.332502	−	0.0193519i
$661$	29.9248	+	21.7416i	1.16394	+	0.845651i	0.990271	−	0.139153i	$-0.0444379\pi$
$661$	29.9248	+	21.7416i	1.16394	+	0.845651i	0.173668	+	0.984804i	$0.444438\pi$
$662$	−16.0098	+	5.20191i	−0.622239	+	0.202178i
$663$	13.8802	+	10.0538i	0.539060	+	0.390456i
$664$	−2.60415	−	3.58431i	−0.101061	−	0.139098i
$665$	1.78189	−	0.101113i	0.0690986	−	0.00392098i
$666$	18.6802	−	13.6550i	0.723844	−	0.529121i
$667$	−3.55882	−	4.89830i	−0.137798	−	0.189663i
$668$	3.21280	+	1.04390i	0.124307	+	0.0403898i
$669$	15.8173	+	21.7044i	0.611534	+	0.839140i
$670$	3.21153	−	12.1963i	0.124072	−	0.471185i
$671$	−26.1385	+	8.49292i	−1.00907	+	0.327865i
$672$	3.98378	+	2.88556i	0.153678	+	0.111313i
$673$	−3.74085	+	11.5131i	−0.144199	+	0.443799i	−0.996907	−	0.0785886i	$-0.974959\pi$
$673$	−3.74085	+	11.5131i	−0.144199	+	0.443799i	0.852708	+	0.522388i	$0.174959\pi$
$674$	−6.65129	+	20.4706i	−0.256198	+	0.788496i
$675$	12.6967	−	22.6670i	0.488698	−	0.872453i
$676$	5.33834			0.205321
$677$			25.9992i			0.999230i	0.866248	+	0.499615i	$0.166525\pi$
$677$			25.9992i			0.999230i	−0.866248	+	0.499615i	$0.833475\pi$
$678$	−20.7308	+	6.76913i	−0.796162	+	0.259967i
$679$	−20.1745	+	14.6576i	−0.774225	+	0.562508i
$680$	−1.31568	+	4.99651i	−0.0504540	+	0.191607i
$681$	−0.00504619	−	3.47709i	−0.000193371	−	0.133242i
$682$	3.06688	+	11.9124i	0.117437	+	0.456150i
$683$	−4.24452			−0.162412			−0.0812060	−	0.996697i	$-0.525877\pi$
$683$	−4.24452			−0.162412			−0.0812060	+	0.996697i	$0.525877\pi$
$684$	−0.683542	−	0.493597i	−0.0261359	−	0.0188732i
$685$	−11.3505	−	7.30149i	−0.433679	−	0.278975i
$686$	−16.0287	+	5.20805i	−0.611980	+	0.198844i
$687$	38.9500	−	0.0565269i	1.48603	−	0.00215664i
$688$	−10.5177			−0.400982
$689$	1.80045	−	0.585002i	0.0685917	−	0.0222868i
$690$	−0.145650	−	2.50255i	−0.00554482	−	0.0952705i
$691$	6.00638	−	18.4857i	0.228493	−	0.703230i	−0.769425	−	0.638737i	$-0.779457\pi$
$691$	6.00638	−	18.4857i	0.228493	−	0.703230i	0.997918	−	0.0644930i	$-0.0205430\pi$
$692$	−3.72618	−	2.70723i	−0.141648	−	0.102913i
$693$	−17.8851	+	5.86866i	−0.679398	+	0.222932i
$694$	−8.46409	+	11.6498i	−0.321293	+	0.442221i
$695$	−35.3655	−	22.7498i	−1.34149	−	0.862949i
$696$	15.4166	+	4.98442i	0.584363	+	0.188934i
$697$	−11.9585	+	8.68834i	−0.452959	+	0.329094i
$698$	−4.15246	+	3.01694i	−0.157173	+	0.114193i
$699$	−5.67765	−	1.83568i	−0.214749	−	0.0694316i
$700$	−13.9148	−	2.83213i	−0.525928	−	0.107044i
$701$	21.9351	−	30.1910i	0.828476	−	1.14030i	−0.159728	−	0.987161i	$-0.551062\pi$
$701$	21.9351	−	30.1910i	0.828476	−	1.14030i	0.988205	−	0.153139i	$-0.0489382\pi$
$702$	21.1324	−	6.96820i	0.797592	−	0.262998i
$703$	1.75369	+	1.27413i	0.0661417	+	0.0480548i
$704$	−0.682712	+	2.10117i	−0.0257307	+	0.0791909i
$705$	14.4114	−	0.838756i	0.542765	−	0.0315894i
$706$	−4.79974	+	1.55953i	−0.180641	+	0.0586937i
$707$	−11.9177			−0.448211
$708$	7.70084	−	0.0111760i	0.289415	−	0.000420020i
$709$	−32.5643	+	10.5808i	−1.22298	+	0.397370i	−0.848166	−	0.529730i	$-0.822293\pi$
$709$	−32.5643	+	10.5808i	−1.22298	+	0.397370i	−0.374813	+	0.927100i	$0.622293\pi$
$710$	−8.77862	−	5.64709i	−0.329456	−	0.211931i
$711$	−2.54587	+	3.52557i	−0.0954777	+	0.132219i
$712$	17.3847			0.651521
$713$	3.48993	−	0.898489i	0.130699	−	0.0336487i
$714$	−0.0164956	−	11.3663i	−0.000617331	−	0.425373i
$715$	−20.4580	−	5.38700i	−0.765085	−	0.201462i
$716$	−8.17739	+	5.94122i	−0.305603	+	0.222034i
$717$	−8.37209	+	2.73369i	−0.312661	+	0.102092i
$718$			13.2460i			0.494337i
$719$	−42.4478			−1.58303			−0.791517	−	0.611147i	$-0.790709\pi$
$719$	−42.4478			−1.58303			−0.791517	+	0.611147i	$0.790709\pi$
$720$	4.25917	+	5.18261i	0.158730	+	0.193144i
$721$	4.29531	−	13.2196i	0.159966	−	0.492324i
$722$	−5.84692	+	17.9950i	−0.217600	+	0.669703i
$723$	−8.73727	−	6.32865i	−0.324943	−	0.235365i
$724$	15.7424	−	5.11503i	0.585063	−	0.190099i
$725$	−46.4718	+	5.29109i	−1.72592	+	0.196506i
$726$	6.24201	+	8.56523i	0.231663	+	0.317885i
$727$	−3.38853	−	1.10100i	−0.125674	−	0.0408338i	0.245505	−	0.969395i	$-0.421046\pi$
$727$	−3.38853	−	1.10100i	−0.125674	−	0.0408338i	−0.371179	+	0.928562i	$0.621046\pi$
$728$	−7.14856	−	9.83914i	−0.264943	−	0.364663i
$729$	21.7044	−	16.0598i	0.803868	−	0.594807i
$730$	−1.09284	−	19.2588i	−0.0404477	−	0.712801i
$731$	14.2849	+	19.6615i	0.528346	+	0.727205i
$732$	−17.4500	−	12.6395i	−0.644970	−	0.467169i
$733$	20.4013	−	6.62878i	0.753539	−	0.244840i	0.0930356	−	0.995663i	$-0.470343\pi$
$733$	20.4013	−	6.62878i	0.753539	−	0.244840i	0.660503	+	0.750823i	$0.270343\pi$
$734$	−24.6339	−	17.8976i	−0.909255	−	0.660612i
$735$	4.12027	−	0.239803i	0.151979	−	0.00884527i
$736$	0.615571	+	0.200011i	0.0226902	+	0.00737250i
$737$	−11.8512	+	3.85069i	−0.436545	+	0.141842i
$738$	0.0557029	+	19.1910i	0.00205045	+	0.706432i
$739$		−	50.2810i		−	1.84962i	−0.380434	−	0.924808i	$-0.624226\pi$
$739$		−	50.2810i		−	1.84962i	0.380434	−	0.924808i	$-0.375774\pi$
$740$	−10.9116	−	13.3562i	−0.401118	−	0.490983i
$741$	1.22772	+	1.68466i	0.0451014	+	0.0618876i
$742$	−1.01572	−	0.737961i	−0.0372881	−	0.0270914i
$743$			21.4594i			0.787267i	0.919267	+	0.393634i	$0.128782\pi$
$743$			21.4594i			0.787267i	−0.919267	+	0.393634i	$0.871218\pi$
$744$	−6.13145	+	7.44348i	−0.224790	+	0.272891i
$745$	19.2098	+	49.4037i	0.703793	+	1.81001i
$746$	0.810761	−	1.11592i	0.0296841	−	0.0408566i
$747$	7.84363	+	10.7302i	0.286984	+	0.392598i
$748$	4.85512	−	1.57753i	0.177521	−	0.0576800i
$749$			45.5252i			1.66345i
$750$	−17.3793	−	8.54172i	−0.634601	−	0.311899i
$751$	12.3073	+	37.8779i	0.449099	+	1.38218i	0.877926	+	0.478797i	$0.158927\pi$
$751$	12.3073	+	37.8779i	0.449099	+	1.38218i	−0.428827	+	0.903387i	$0.641073\pi$
$752$	−1.15180	+	3.54488i	−0.0420019	+	0.129269i
$753$	−36.8775	−	11.9231i	−1.34389	−	0.434501i
$754$	−32.4081	−	23.5459i	−1.18023	−	0.857490i
$755$	−37.7010	+	30.8006i	−1.37208	+	1.12095i
$756$	−11.9764	−	8.62196i	−0.435578	−	0.313578i
$757$	36.2582	−	26.3431i	1.31783	−	0.957457i	0.317870	−	0.948134i	$-0.397032\pi$
$757$	36.2582	−	26.3431i	1.31783	−	0.957457i	0.999957	−	0.00932278i	$-0.00296758\pi$
$758$	−4.16004	+	12.8033i	−0.151100	+	0.465036i
$759$	−2.00164	+	1.45872i	−0.0726550	+	0.0529482i
$760$	−0.339986	+	0.528522i	−0.0123326	+	0.0191715i
$761$	−3.32639	+	10.2376i	−0.120582	+	0.371112i	−0.993070	−	0.117522i	$-0.962505\pi$
$761$	−3.32639	+	10.2376i	−0.120582	+	0.371112i	0.872489	+	0.488634i	$0.162505\pi$
$762$	−8.65011	−	11.8696i	−0.313360	−	0.429990i
$763$	3.90153	−	5.36999i	0.141245	−	0.194407i
$764$	−18.0206	+	5.85525i	−0.651963	+	0.211836i
$765$	3.90352	−	15.0009i	0.141132	−	0.542359i
$766$	8.97486	+	2.91611i	0.324275	+	0.105363i
$767$	−18.1077	−	5.88356i	−0.653833	−	0.212443i
$768$	−1.64650	+	0.537623i	−0.0594129	+	0.0193998i
$769$	−19.2632			−0.694648			−0.347324	−	0.937745i	$-0.612910\pi$
$769$	−19.2632			−0.694648			−0.347324	+	0.937745i	$0.612910\pi$
$770$	5.08452	+	13.0763i	0.183233	+	0.471238i
$771$	23.5455	−	7.68821i	0.847972	−	0.276884i
$772$	8.10428	+	11.1546i	0.291679	+	0.401462i
$773$	−12.5511	+	17.2750i	−0.451430	+	0.621340i	−0.972704	−	0.232049i	$-0.925457\pi$
$773$	−12.5511	+	17.2750i	−0.451430	+	0.621340i	0.521274	+	0.853389i	$0.325457\pi$
$774$	31.5529	−	0.0915837i	1.13414	−	0.00329191i
$775$	7.23671	−	26.8818i	0.259950	−	0.965622i
$776$		−	8.78061i		−	0.315206i
$777$	30.7268	+	22.2563i	1.10232	+	0.798439i
$778$	11.3654	−	8.25744i	0.407469	−	0.296043i
$779$	−1.70985	+	0.555565i	−0.0612619	+	0.0199052i
$780$	−6.03300	−	15.4492i	−0.216016	−	0.553170i
$781$			10.3132i			0.369034i
$782$	−0.462160	−	1.42238i	−0.0165268	−	0.0508643i
$783$	−46.2929	−	14.8190i	−1.65437	−	0.529586i
$784$	−0.329304	+	1.01349i	−0.0117609	+	0.0361962i
$785$	9.34827	−	35.5016i	0.333654	−	1.26711i
$786$	3.86511	+	11.8371i	0.137864	+	0.422216i
$787$	−14.9637	−	10.8718i	−0.533399	−	0.387537i	0.288229	−	0.957562i	$-0.406934\pi$
$787$	−14.9637	−	10.8718i	−0.533399	−	0.387537i	−0.821627	+	0.570025i	$0.806934\pi$
$788$	−6.20616	−	8.54205i	−0.221085	−	0.304298i
$789$	12.1075	−	37.4479i	0.431038	−	1.33318i
$790$	2.72601	+	1.75358i	0.0969871	+	0.0623896i
$791$	−21.0181	−	28.9289i	−0.747317	−	1.02859i
$792$	2.02983	−	6.30943i	0.0721269	−	0.224196i
$793$	31.3125	+	43.0980i	1.11194	+	1.53045i
$794$	−4.13502	+	5.69136i	−0.146746	+	0.201979i
$795$	−1.08515	−	1.32434i	−0.0384865	−	0.0469696i
$796$	−15.5115	+	21.3497i	−0.549789	+	0.756719i
$797$	44.6285	+	14.5007i	1.58082	+	0.513641i	0.962269	−	0.272101i	$-0.0877186\pi$
$797$	44.6285	+	14.5007i	1.58082	+	0.513641i	0.618554	+	0.785742i	$0.287719\pi$
$798$	0.425296	−	1.31542i	0.0150553	−	0.0465653i
$799$	8.19107	−	2.66144i	0.289779	−	0.0941549i
$800$	3.68665	−	3.37766i	0.130343	−	0.119418i
$801$	−52.1540	+	0.151379i	−1.84277	+	0.00534873i
$802$	−9.75935	−	30.0362i	−0.344615	−	1.06061i
$803$	−15.4190	+	11.2025i	−0.544124	+	0.395329i
$804$	−7.91182	−	5.73075i	−0.279028	−	0.202108i
$805$	3.83091	−	1.48959i	0.135022	−	0.0525011i
$806$	20.1230	−	12.7888i	0.708801	−	0.450468i
$807$	−0.00574737	−	3.96024i	−0.000202317	−	0.139407i
$808$	2.46656	−	3.39492i	0.0867731	−	0.119433i
$809$	14.5843	−	10.5961i	0.512757	−	0.372540i	−0.301111	−	0.953589i	$-0.597358\pi$
$809$	14.5843	−	10.5961i	0.512757	−	0.372540i	0.813869	+	0.581049i	$0.197358\pi$
$810$	−12.8226	−	15.5107i	−0.450540	−	0.544990i
$811$	14.1097			0.495458			0.247729	−	0.968829i	$-0.420316\pi$
$811$	14.1097			0.495458			0.247729	+	0.968829i	$0.420316\pi$
$812$			26.5666i			0.932305i
$813$	0.734904	+	2.25068i	0.0257742	+	0.0789349i
$814$	−5.26574	+	16.2063i	−0.184564	+	0.568030i
$815$	1.56501	−	0.0888060i	0.0548199	−	0.00311074i
$816$	3.24126	+	2.34774i	0.113467	+	0.0821872i
$817$	0.913430	+	2.81125i	0.0319569	+	0.0983531i
$818$	3.37829	−	4.64982i	0.118119	−	0.162577i
$819$	21.5313	+	29.4551i	0.752363	+	1.02924i
$820$	14.2812	−	0.810385i	0.498723	−	0.0282999i
$821$	6.88707	−	5.00375i	0.240360	−	0.174632i	−0.461083	−	0.887357i	$-0.652539\pi$
$821$	6.88707	−	5.00375i	0.240360	−	0.174632i	0.701444	+	0.712725i	$0.252539\pi$
$822$	−8.44856	+	6.15699i	−0.294677	+	0.214750i
$823$	−12.1792	+	37.4838i	−0.424541	+	1.30660i	0.478891	+	0.877874i	$0.341039\pi$
$823$	−12.1792	+	37.4838i	−0.424541	+	1.30660i	−0.903433	+	0.428730i	$0.858961\pi$
$824$	2.87681	+	3.95959i	0.100218	+	0.137939i
$825$	2.19202	+	19.0071i	0.0763165	+	0.661744i
$826$	3.90193	+	12.0089i	0.135766	+	0.417844i
$827$	−19.5392	+	26.8934i	−0.679445	+	0.935176i	−0.999927	−	0.0120784i	$-0.996155\pi$
$827$	−19.5392	+	26.8934i	−0.679445	+	0.935176i	0.320482	+	0.947255i	$0.396155\pi$
$828$	−1.84845	−	0.594670i	−0.0642379	−	0.0206662i
$829$	14.8295	+	4.81840i	0.515051	+	0.167350i	0.554998	−	0.831852i	$-0.312719\pi$
$829$	14.8295	+	4.81840i	0.515051	+	0.167350i	−0.0399473	+	0.999202i	$0.512719\pi$
$830$	7.67199	−	6.26777i	0.266299	−	0.217558i
$831$	−0.0406042	−	27.9784i	−0.00140854	−	0.970559i
$832$	4.28233			0.148463
$833$	2.34185	−	0.760915i	0.0811405	−	0.0263641i
$834$	−26.3238	+	19.1838i	−0.911520	+	0.664281i
$835$	−1.92349	+	7.30475i	−0.0665650	+	0.252791i
$836$	0.620910			0.0214746
$837$	18.3295	−	22.3837i	0.633559	−	0.773695i
$838$		−	14.8450i		−	0.512813i
$839$	24.6816	−	33.9714i	0.852105	−	1.17282i	−0.131290	−	0.991344i	$-0.541912\pi$
$839$	24.6816	−	33.9714i	0.852105	−	1.17282i	0.983395	−	0.181478i	$-0.0580881\pi$
$840$	−5.93728	+	9.25924i	−0.204855	+	0.319474i
$841$	18.0790	+	55.6414i	0.623414	+	1.91867i
$842$	25.8448			0.890672
$843$	−2.62071	+	0.00380336i	−0.0902620	+	0.000130995i
$844$	4.55023	+	14.0042i	0.156625	+	0.482043i
$845$	0.676267	+	11.9177i	0.0232643	+	0.409982i
$846$	3.42452	−	10.6446i	0.117738	−	0.365970i
$847$	−10.2145	+	14.0591i	−0.350975	+	0.483075i
$848$	0.420438	−	0.136608i	0.0144379	−	0.00469115i
$849$	35.0281	+	25.3718i	1.20216	+	0.870758i
$850$	−11.3213	−	2.30426i	−0.388316	−	0.0790355i
$851$	4.74788	+	1.54268i	0.162755	+	0.0528824i
$852$	−6.53425	+	4.76192i	−0.223860	+	0.163141i
$853$	18.3189	+	25.2138i	0.627227	+	0.863304i	0.997854	−	0.0654779i	$-0.0208572\pi$
$853$	18.3189	+	25.2138i	0.627227	+	0.863304i	−0.370627	+	0.928782i	$0.620857\pi$
$854$	10.9175	−	33.6005i	0.373588	−	1.14978i
$855$	1.01535	−	1.58852i	0.0347243	−	0.0543263i
$856$	−12.9685	−	9.42217i	−0.443254	−	0.322043i
$857$	16.2110	+	49.8922i	0.553756	+	1.70429i	0.699206	+	0.714921i	$0.253537\pi$
$857$	16.2110	+	49.8922i	0.553756	+	1.70429i	−0.145450	+	0.989366i	$0.546463\pi$
$858$	−9.61271	+	13.2712i	−0.328172	+	0.453072i
$859$	3.72949	+	1.21179i	0.127249	+	0.0413456i	0.371949	−	0.928253i	$-0.378690\pi$
$859$	3.72949	+	1.21179i	0.127249	+	0.0413456i	−0.244700	+	0.969599i	$0.578690\pi$
$860$	−1.33239	−	23.4804i	−0.0454342	−	0.800676i
$861$	−29.9130	+	9.76735i	−1.01943	+	0.332871i
$862$			11.0950i			0.377896i
$863$			15.0898i			0.513663i	0.966456	+	0.256831i	$0.0826785\pi$
$863$			15.0898i			0.513663i	−0.966456	+	0.256831i	$0.917322\pi$
$864$	4.93480	−	1.62720i	0.167885	−	0.0553585i
$865$	5.57179	−	8.66157i	0.189447	−	0.294502i
$866$	−8.06509	−	5.85963i	−0.274063	−	0.199118i
$867$	0.0293114	+	20.1970i	0.000995466	+	0.685928i
$868$	−14.7059	−	5.81138i	−0.499150	−	0.197251i
$869$		−	3.20252i		−	0.108638i
$870$	−9.17461	+	35.0485i	−0.311048	+	1.18826i
$871$	14.1971	+	19.5406i	0.481050	+	0.662109i
$872$	0.722235	+	2.22281i	0.0244580	+	0.0752739i
$873$	0.0764581	+	26.3417i	0.00258771	+	0.891532i
$874$		−	0.181905i		−	0.00615303i
$875$	4.55992	−	31.4231i	0.154153	−	1.06230i
$876$	−14.2172	−	4.59665i	−0.480355	−	0.155306i
$877$	17.3533	+	5.63844i	0.585980	+	0.190397i	0.586978	−	0.809603i	$-0.300318\pi$
$877$	17.3533	+	5.63844i	0.585980	+	0.190397i	−0.000997653		1.00000i	$0.500318\pi$
$878$	−3.07125	−	2.23139i	−0.103650	−	0.0753058i
$879$	−23.0648	+	7.53123i	−0.777956	+	0.254022i
$880$	−4.77730	−	1.25796i	−0.161043	−	0.0424058i
$881$	−22.7784	+	16.5495i	−0.767424	+	0.557566i	−0.901178	−	0.433448i	$-0.857297\pi$
$881$	−22.7784	+	16.5495i	−0.767424	+	0.557566i	0.133755	+	0.991014i	$0.457297\pi$
$882$	0.979083	−	3.04334i	0.0329674	−	0.102474i
$883$	12.9833	−	9.43294i	0.436924	−	0.317444i	−0.347488	−	0.937685i	$-0.612965\pi$
$883$	12.9833	−	9.43294i	0.436924	−	0.317444i	0.784411	+	0.620241i	$0.212965\pi$
$884$	−5.81617	−	8.00528i	−0.195619	−	0.269247i
$885$	1.00050	+	17.1905i	0.0336315	+	0.577853i
$886$	−28.7051	+	20.8555i	−0.964367	+	0.700654i
$887$	25.5309	+	18.5493i	0.857243	+	0.622824i	0.927134	−	0.374731i	$-0.122265\pi$
$887$	25.5309	+	18.5493i	0.857243	+	0.622824i	−0.0698902	+	0.997555i	$0.522265\pi$
$888$	−12.6994	+	4.14668i	−0.426164	+	0.139153i
$889$	14.1551	−	19.4829i	0.474748	−	0.653435i
$890$	2.20232	+	38.8110i	0.0738219	+	1.30095i
$891$	−6.03453	+	18.9459i	−0.202164	+	0.634711i
$892$	−4.79149	−	14.7467i	−0.160431	−	0.493755i
$893$	1.04754			0.0350544
$894$	41.0590	−	0.0595877i	1.37322	−	0.00199291i
$895$	−14.2996	−	17.5032i	−0.477982	−	0.585067i
$896$	−1.66932	−	2.29762i	−0.0557679	−	0.0767579i
$897$	3.88801	+	2.81619i	0.129817	+	0.0940299i
$898$	12.6066			0.420687
$899$	−51.9825	−	3.23641i	−1.73371	−	0.107940i
$900$	−11.0305	+	10.1650i	−0.367683	+	0.338835i
$901$	−0.826402	−	0.600417i	−0.0275315	−	0.0200028i
$902$	−8.30717	−	11.4338i	−0.276598	−	0.380705i
$903$	16.0589	+	49.1814i	0.534408	+	1.63665i
$904$	12.5908			0.418765
$905$	13.4135	+	34.4967i	0.445878	+	1.14671i
$906$	11.7050	+	35.8472i	0.388872	+	1.19094i
$907$	25.9715	+	8.43866i	0.862370	+	0.280201i	0.706618	−	0.707595i	$-0.250220\pi$
$907$	25.9715	+	8.43866i	0.862370	+	0.280201i	0.155752	+	0.987796i	$0.450220\pi$
$908$	−0.620351	+	1.90925i	−0.0205871	+	0.0633605i
$909$	−7.37007	+	10.2062i	−0.244450	+	0.338518i
$910$	21.0601	−	17.2054i	0.698135	−	0.570354i
$911$	48.3287	+	35.1129i	1.60120	+	1.16334i	0.885164	+	0.465278i	$0.154046\pi$
$911$	48.3287	+	35.1129i	1.60120	+	1.16334i	0.716037	+	0.698062i	$0.245954\pi$
$912$	0.286694	+	0.393399i	0.00949339	+	0.0130267i
$913$	−9.30913	−	3.02472i	−0.308087	−	0.100104i
$914$	−15.7295	+	11.4282i	−0.520286	+	0.378010i
$915$	26.0068	−	40.5579i	0.859758	−	1.34080i
$916$	−21.3872	−	6.94911i	−0.706652	−	0.229605i
$917$	−16.5182	+	12.0011i	−0.545478	+	0.396313i
$918$	−9.74419	−	7.01496i	−0.321606	−	0.231528i
$919$	−5.36573	−	16.5140i	−0.176999	−	0.544747i	0.822720	−	0.568447i	$-0.192455\pi$
$919$	−5.36573	−	16.5140i	−0.176999	−	0.544747i	−0.999719	+	0.0236998i	$0.992455\pi$
$920$	−0.368539	+	1.39958i	−0.0121504	+	0.0461429i
$921$	−6.41844	+	19.8519i	−0.211495	+	0.654143i
$922$	−9.03404	+	27.8039i	−0.297520	+	0.915673i
$923$	19.0118	−	6.17730i	0.625780	−	0.203328i
$924$	10.8676	−	0.0157719i	0.357519	−	0.000518857i
$925$	28.4351	−	26.0518i	0.934939	−	0.856579i
$926$	3.13943	+	9.66217i	0.103168	+	0.317519i
$927$	−8.66487	−	11.8537i	−0.284592	−	0.389325i
$928$	−7.56787	−	5.49838i	−0.248428	−	0.180493i
$929$	−55.3503			−1.81599			−0.907993	−	0.418986i	$-0.862386\pi$
$929$	−55.3503			−1.81599			−0.907993	+	0.418986i	$0.862386\pi$
$930$	−17.3941	−	12.7454i	−0.570376	−	0.417937i
$931$	0.299494			0.00981552
$932$	2.78712	+	2.02496i	0.0912950	+	0.0663297i
$933$	−1.59049	+	1.15909i	−0.0520702	+	0.0379468i
$934$	2.21507	+	6.81730i	0.0724794	+	0.223069i
$935$	4.13684	+	10.6391i	0.135289	+	0.347936i
$936$	−12.8469	+	0.0372888i	−0.419915	+	0.00121882i
$937$	9.78902	−	3.18064i	0.319793	−	0.103907i	−0.144722	−	0.989472i	$-0.546229\pi$
$937$	9.78902	−	3.18064i	0.319793	−	0.103907i	0.464515	+	0.885565i	$0.346229\pi$
$938$	4.94997	−	15.2345i	0.161622	−	0.497422i
$939$	−29.5146	−	9.54253i	−0.963172	−	0.311409i
$940$	−8.05978	−	2.12230i	−0.262881	−	0.0692218i
$941$	−3.88320	−	11.9513i	−0.126589	−	0.389600i	0.867599	−	0.497265i	$-0.165662\pi$
$941$	−3.88320	−	11.9513i	−0.126589	−	0.389600i	−0.994187	+	0.107666i	$0.965662\pi$
$942$	−23.0301	−	16.6813i	−0.750361	−	0.543507i
$943$	−3.34972	+	2.43371i	−0.109082	+	0.0792526i
$944$	−4.22848	−	1.37392i	−0.137625	−	0.0447172i
$945$	17.7311	−	27.8293i	0.576794	−	0.905287i
$946$	−18.7989	+	13.6582i	−0.611205	+	0.444066i
$947$	−13.4620	−	4.37407i	−0.437456	−	0.142138i	0.0820054	−	0.996632i	$-0.473868\pi$
$947$	−13.4620	−	4.37407i	−0.437456	−	0.142138i	−0.519462	+	0.854494i	$0.673868\pi$
$948$	2.02907	−	1.47871i	0.0659011	−	0.0480262i
$949$	29.8869	+	21.7141i	0.970169	+	0.704869i
$950$	−1.22298	−	0.692058i	−0.0396788	−	0.0224533i
$951$	−27.4093	+	37.8410i	−0.888807	+	1.22708i
$952$	−2.02787	+	6.24115i	−0.0657238	+	0.202277i
$953$	4.69230	+	1.52462i	0.151998	+	0.0493873i	0.384028	−	0.923321i	$-0.374537\pi$
$953$	4.69230	+	1.52462i	0.151998	+	0.0493873i	−0.232030	+	0.972709i	$0.574537\pi$
$954$	−1.26012	+	0.413485i	−0.0407978	+	0.0133871i
$955$	−15.3546	−	39.4889i	−0.496863	−	1.27783i
$956$	5.08478			0.164453
$957$	34.0277	−	11.1109i	1.09996	−	0.359164i
$958$	−19.6974	−	27.1111i	−0.636394	−	0.875921i
$959$	−13.8676	−	10.0754i	−0.447807	−	0.325351i
$960$	−1.40881	−	3.60767i	−0.0454692	−	0.116437i
$961$	13.1625	−	28.0668i	0.424598	−	0.905382i
$962$	33.0295			1.06491
$963$	38.9874	+	28.1535i	1.25635	+	0.907232i
$964$	3.66116	+	5.03916i	0.117918	+	0.162300i
$965$	−23.8757	+	19.5057i	−0.768585	+	0.627910i
$966$	−0.00462061	−	3.18384i	−0.000148666	−	0.102438i
$967$	−22.6637			−0.728817			−0.364408	−	0.931239i	$-0.618729\pi$
$967$	−22.6637			−0.728817			−0.364408	+	0.931239i	$0.618729\pi$
$968$	−1.89087	−	5.81950i	−0.0607749	−	0.187046i
$969$	0.346027	−	1.07025i	0.0111160	−	0.0343812i
$970$	19.6025	−	1.11234i	0.629399	−	0.0357151i
$971$	16.7807	−	23.0967i	0.538519	−	0.741208i	−0.449879	−	0.893089i	$-0.648533\pi$
$971$	16.7807	−	23.0967i	0.538519	−	0.741208i	0.988399	+	0.151881i	$0.0485330\pi$
$972$	−14.7902	+	4.92455i	−0.474395	+	0.157955i
$973$	−43.2083	−	31.3926i	−1.38519	−	1.00640i
$974$	−15.5158	+	11.2729i	−0.497158	+	0.361207i
$975$	33.7257	−	15.4256i	1.08009	−	0.494016i
$976$	7.31203	+	10.0641i	0.234052	+	0.322146i
$977$	−26.0237	+	18.9073i	−0.832572	+	0.604899i	−0.920286	−	0.391247i	$-0.872044\pi$
$977$	−26.0237	+	18.9073i	−0.832572	+	0.604899i	0.0877136	+	0.996146i	$0.472044\pi$
$978$	0.373532	−	1.15532i	0.0119442	−	0.0369429i
$979$	31.0728	−	22.5757i	0.993092	−	0.721524i
$980$	−2.30432	−	0.606773i	−0.0736087	−	0.0193827i
$981$	−2.18605	−	6.66212i	−0.0697953	−	0.212705i
$982$	5.34895	+	3.88624i	0.170692	+	0.124015i
$983$	38.5354	+	12.5209i	1.22909	+	0.399355i	0.850384	−	0.526162i	$-0.176369\pi$
$983$	38.5354	+	12.5209i	1.22909	+	0.399355i	0.378705	+	0.925517i	$0.376369\pi$
$984$	3.40861	−	10.5427i	0.108663	−	0.336088i
$985$	18.2837	−	14.9372i	0.582568	−	0.475939i
$986$			21.6150i			0.688361i
$987$	18.3348	−	0.0266087i	0.583602	−	0.000846964i
$988$	−0.371908	−	1.14462i	−0.0118320	−	0.0364151i
$989$	4.00138	+	5.50743i	0.127236	+	0.175126i
$990$	14.3428	+	3.73226i	0.455844	+	0.118619i
$991$		−	12.2502i		−	0.389141i	−0.980889	−	0.194571i	$-0.937669\pi$
$991$		−	12.2502i		−	0.389141i	0.980889	−	0.194571i	$-0.0623313\pi$
$992$	4.69907	−	2.98642i	0.149196	−	0.0948191i
$993$	−29.1568	+	0.0423144i	−0.925264	+	0.00134281i
$994$	−10.7254	−	7.79246i	−0.340189	−	0.247162i
$995$	−49.6277	−	31.9244i	−1.57330	−	1.01207i
$996$	−2.38191	−	7.29473i	−0.0754738	−	0.231142i
$997$			2.52746i			0.0800456i	0.999199	+	0.0400228i	$0.0127431\pi$
$997$			2.52746i			0.0800456i	−0.999199	+	0.0400228i	$0.987257\pi$
$998$			5.49567i			0.173962i
$999$	38.0620	−	12.5506i	1.20423	−	0.397082i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.y.a.29.10	✓	128
3.2	odd	2		930.2.y.b.29.22	yes	128
5.4	even	2		930.2.y.b.29.23	yes	128
15.14	odd	2	inner	930.2.y.a.29.11	yes	128
31.15	odd	10	inner	930.2.y.a.449.11	yes	128
93.77	even	10		930.2.y.b.449.23	yes	128
155.139	odd	10		930.2.y.b.449.22	yes	128
465.449	even	10	inner	930.2.y.a.449.10	yes	128

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.y.a.29.10	✓	128	1.1	even	1	trivial
930.2.y.a.29.11	yes	128	15.14	odd	2	inner
930.2.y.a.449.10	yes	128	465.449	even	10	inner
930.2.y.a.449.11	yes	128	31.15	odd	10	inner
930.2.y.b.29.22	yes	128	3.2	odd	2
930.2.y.b.29.23	yes	128	5.4	even	2
930.2.y.b.449.22	yes	128	155.139	odd	10
930.2.y.b.449.23	yes	128	93.77	even	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:	\( N \)	\(=\)	\( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	930.y (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.809017 - 0.587785i) q^{2} +(-1.02011 - 1.39978i) q^{3} +(0.309017 + 0.951057i) q^{4} +(-2.08406 + 0.810354i) q^{5} +(0.00251367 + 1.73205i) q^{6} +(-2.70101 + 0.877611i) q^{7} +(0.309017 - 0.951057i) q^{8} +(-0.918766 + 2.85585i) q^{9} +O(q^{10})\)	\(q+(-0.809017 - 0.587785i) q^{2} +(-1.02011 - 1.39978i) q^{3} +(0.309017 + 0.951057i) q^{4} +(-2.08406 + 0.810354i) q^{5} +(0.00251367 + 1.73205i) q^{6} +(-2.70101 + 0.877611i) q^{7} +(0.309017 - 0.951057i) q^{8} +(-0.918766 + 2.85585i) q^{9} +(2.16236 + 0.569392i) q^{10} +(-0.682712 - 2.10117i) q^{11} +(1.01604 - 1.40273i) q^{12} +(-3.46448 + 2.51709i) q^{13} +(2.70101 + 0.877611i) q^{14} +(3.26029 + 2.09058i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(2.19758 + 0.714038i) q^{17} +(2.42192 - 1.77039i) q^{18} +(0.227369 + 0.165193i) q^{19} +(-1.41470 - 1.73165i) q^{20} +(3.98378 + 2.88556i) q^{21} +(-0.682712 + 2.10117i) q^{22} +(0.615571 + 0.200011i) q^{23} +(-1.64650 + 0.537623i) q^{24} +(3.68665 - 3.37766i) q^{25} +4.28233 q^{26} +(4.93480 - 1.62720i) q^{27} +(-1.66932 - 2.29762i) q^{28} +(-7.56787 - 5.49838i) q^{29} +(-1.40881 - 3.60767i) q^{30} +(4.69907 - 2.98642i) q^{31} +1.00000 q^{32} +(-2.24474 + 3.09906i) q^{33} +(-1.35818 - 1.86938i) q^{34} +(4.91790 - 4.01777i) q^{35} +(-2.99999 + 0.00870760i) q^{36} +7.71298 q^{37} +(-0.0868472 - 0.267288i) q^{38} +(7.05751 + 2.28180i) q^{39} +(0.126681 + 2.23248i) q^{40} +(-3.76009 + 5.17532i) q^{41} +(-1.52685 - 4.67607i) q^{42} +(8.50897 + 6.18213i) q^{43} +(1.78736 - 1.29860i) q^{44} +(-0.399482 - 6.69630i) q^{45} +(-0.380444 - 0.523636i) q^{46} +(3.01546 - 2.19086i) q^{47} +(1.64805 + 0.532842i) q^{48} +(0.862129 - 0.626374i) q^{49} +(-4.96790 + 0.565626i) q^{50} +(-1.24227 - 3.80453i) q^{51} +(-3.46448 - 2.51709i) q^{52} +(-0.420438 - 0.136608i) q^{53} +(-4.94878 - 1.58417i) q^{54} +(3.12551 + 3.82574i) q^{55} +2.84001i q^{56} +(-0.000706450 - 0.486781i) q^{57} +(2.89067 + 8.89657i) q^{58} +(2.61334 + 3.59696i) q^{59} +(-0.980780 + 3.74674i) q^{60} -12.4400i q^{61} +(-5.55700 - 0.345977i) q^{62} +(-0.0247297 - 8.51999i) q^{63} +(-0.809017 - 0.587785i) q^{64} +(5.18046 - 8.05323i) q^{65} +(3.63762 - 1.18777i) q^{66} -5.64028i q^{67} +2.31067i q^{68} +(-0.347976 - 1.06570i) q^{69} +(-6.34025 + 0.359776i) q^{70} +(-4.43959 - 1.44251i) q^{71} +(2.43216 + 1.75630i) q^{72} +(-2.66579 - 8.20445i) q^{73} +(-6.23993 - 4.53357i) q^{74} +(-8.48876 - 1.71493i) q^{75} +(-0.0868472 + 0.267288i) q^{76} +(3.68802 + 5.07613i) q^{77} +(-4.36843 - 5.99432i) q^{78} +(1.37862 + 0.447940i) q^{79} +(1.20973 - 1.88057i) q^{80} +(-7.31174 - 5.24771i) q^{81} +(6.08395 - 1.97679i) q^{82} +(2.60415 - 3.58431i) q^{83} +(-1.51328 + 4.68049i) q^{84} +(-5.15853 + 0.292719i) q^{85} +(-3.25014 - 10.0029i) q^{86} +(0.0235139 + 16.2023i) q^{87} -2.20930 q^{88} +(5.37218 + 16.5339i) q^{89} +(-3.61280 + 5.65223i) q^{90} +(7.14856 - 9.83914i) q^{91} +0.647249i q^{92} +(-8.97389 - 3.53119i) q^{93} -3.72731 q^{94} +(-0.607716 - 0.160024i) q^{95} +(-1.02011 - 1.39978i) q^{96} +(8.35086 - 2.71336i) q^{97} -1.06565 q^{98} +(6.62788 - 0.0192377i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 128 q - 32 q^{2} - 32 q^{4} + 2 q^{5} - 32 q^{8} - 4 q^{9}+O(q^{10}) \) 128 * q - 32 * q^2 - 32 * q^4 + 2 * q^5 - 32 * q^8 - 4 * q^9	\( 128 q - 32 q^{2} - 32 q^{4} + 2 q^{5} - 32 q^{8} - 4 q^{9} + 2 q^{10} + 25 q^{15} - 32 q^{16} + 6 q^{18} - 8 q^{19} - 3 q^{20} - 20 q^{23} - 10 q^{25} - 48 q^{31} + 128 q^{32} - 8 q^{33} + 10 q^{34} + 16 q^{35} - 4 q^{36} + 12 q^{38} + 4 q^{39} - 3 q^{40} + 37 q^{45} + 10 q^{46} + 6 q^{47} + 46 q^{49} - 5 q^{50} + 34 q^{51} - 20 q^{53} - 25 q^{60} - 8 q^{62} + 36 q^{63} - 32 q^{64} - 8 q^{66} + 8 q^{69} + 16 q^{70} + 6 q^{72} + 5 q^{75} + 12 q^{76} + 50 q^{77} + 4 q^{78} - 10 q^{79} + 2 q^{80} - 24 q^{81} - 40 q^{83} - 30 q^{85} - 4 q^{87} - 53 q^{90} + 20 q^{91} - 26 q^{93} - 4 q^{94} - 26 q^{95} - 124 q^{98}+O(q^{100}) \) 128 * q - 32 * q^2 - 32 * q^4 + 2 * q^5 - 32 * q^8 - 4 * q^9 + 2 * q^10 + 25 * q^15 - 32 * q^16 + 6 * q^18 - 8 * q^19 - 3 * q^20 - 20 * q^23 - 10 * q^25 - 48 * q^31 + 128 * q^32 - 8 * q^33 + 10 * q^34 + 16 * q^35 - 4 * q^36 + 12 * q^38 + 4 * q^39 - 3 * q^40 + 37 * q^45 + 10 * q^46 + 6 * q^47 + 46 * q^49 - 5 * q^50 + 34 * q^51 - 20 * q^53 - 25 * q^60 - 8 * q^62 + 36 * q^63 - 32 * q^64 - 8 * q^66 + 8 * q^69 + 16 * q^70 + 6 * q^72 + 5 * q^75 + 12 * q^76 + 50 * q^77 + 4 * q^78 - 10 * q^79 + 2 * q^80 - 24 * q^81 - 40 * q^83 - 30 * q^85 - 4 * q^87 - 53 * q^90 + 20 * q^91 - 26 * q^93 - 4 * q^94 - 26 * q^95 - 124 * q^98

Introduction

L-functions

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