LMFDB - Embedded newform 425.2.k.c.86.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [425,2,Mod(86,425)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(425, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([8, 0]))

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

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

chi := DirichletCharacter("425.86");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 425 = 5^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	425.k (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:	$3.39364208590$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$20$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			86.13
Character	$\chi$	$=$	425.86
Dual form			425.2.k.c.341.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.545657 - 0.396443i) q^{2} +(0.335346 - 1.03209i) q^{3} +(-0.477459 + 1.46947i) q^{4} +(1.35235 + 1.78077i) q^{5} +(-0.226180 - 0.696112i) q^{6} -5.02070 q^{7} +(0.738877 + 2.27403i) q^{8} +(1.47430 + 1.07114i) q^{9} +(1.44389 + 0.435563i) q^{10} +(1.60579 - 1.16668i) q^{11} +(1.35651 + 0.985560i) q^{12} +(3.76928 + 2.73854i) q^{13} +(-2.73958 + 1.99042i) q^{14} +(2.29142 - 0.798567i) q^{15} +(-1.19531 - 0.868444i) q^{16} +(-0.309017 - 0.951057i) q^{17} +1.22911 q^{18} +(2.38975 + 7.35489i) q^{19} +(-3.26248 + 1.13699i) q^{20} +(-1.68367 + 5.18180i) q^{21} +(0.413692 - 1.27321i) q^{22} +(-2.61778 + 1.90193i) q^{23} +2.59478 q^{24} +(-1.34231 + 4.81645i) q^{25} +3.14241 q^{26} +(4.23375 - 3.07600i) q^{27} +(2.39718 - 7.37776i) q^{28} +(2.77198 - 8.53126i) q^{29} +(0.933743 - 1.34416i) q^{30} +(-0.141612 - 0.435836i) q^{31} -5.77863 q^{32} +(-0.665618 - 2.04856i) q^{33} +(-0.545657 - 0.396443i) q^{34} +(-6.78973 - 8.94073i) q^{35} +(-2.27793 + 1.65501i) q^{36} +(-1.45116 - 1.05433i) q^{37} +(4.21978 + 3.06585i) q^{38} +(4.09042 - 2.97187i) q^{39} +(-3.05031 + 4.39105i) q^{40} +(1.51824 + 1.10306i) q^{41} +(1.13558 + 3.49497i) q^{42} -9.16394 q^{43} +(0.947695 + 2.91670i) q^{44} +(0.0863057 + 4.07396i) q^{45} +(-0.674405 + 2.07560i) q^{46} +(4.12605 - 12.6987i) q^{47} +(-1.29715 + 0.942437i) q^{48} +18.2074 q^{49} +(1.17701 + 3.16028i) q^{50} -1.08520 q^{51} +(-5.82388 + 4.23129i) q^{52} +(-1.03188 + 3.17579i) q^{53} +(1.09072 - 3.35689i) q^{54} +(4.24918 + 1.28180i) q^{55} +(-3.70968 - 11.4172i) q^{56} +8.39228 q^{57} +(-1.86961 - 5.75408i) q^{58} +(-0.148926 - 0.108201i) q^{59} +(0.0794099 + 3.74845i) q^{60} +(3.55488 - 2.58277i) q^{61} +(-0.250056 - 0.181676i) q^{62} +(-7.40203 - 5.37789i) q^{63} +(-0.762532 + 0.554012i) q^{64} +(0.220653 + 10.4157i) q^{65} +(-1.17534 - 0.853933i) q^{66} +(-0.910785 - 2.80311i) q^{67} +1.54509 q^{68} +(1.08510 + 3.33958i) q^{69} +(-7.24936 - 2.18683i) q^{70} +(1.11849 - 3.44235i) q^{71} +(-1.34648 + 4.14405i) q^{72} +(-2.00618 + 1.45757i) q^{73} -1.20982 q^{74} +(4.52086 + 3.00056i) q^{75} -11.9488 q^{76} +(-8.06221 + 5.85754i) q^{77} +(1.05379 - 3.24324i) q^{78} +(-0.0254567 + 0.0783476i) q^{79} +(-0.0699735 - 3.30302i) q^{80} +(-0.0655323 - 0.201688i) q^{81} +1.26574 q^{82} +(0.672295 + 2.06911i) q^{83} +(-6.81061 - 4.94820i) q^{84} +(1.27572 - 1.83645i) q^{85} +(-5.00037 + 3.63298i) q^{86} +(-7.87544 - 5.72184i) q^{87} +(3.83954 + 2.78959i) q^{88} +(6.34536 - 4.61018i) q^{89} +(1.66219 + 2.18877i) q^{90} +(-18.9244 - 13.7494i) q^{91} +(-1.54494 - 4.75484i) q^{92} -0.497310 q^{93} +(-2.78290 - 8.56488i) q^{94} +(-9.86563 + 14.2020i) q^{95} +(-1.93784 + 5.96405i) q^{96} +(2.29941 - 7.07684i) q^{97} +(9.93502 - 7.21821i) q^{98} +3.61711 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q + 2 q^{2} + 2 q^{3} - 20 q^{4} - 17 q^{6} - 44 q^{7} + 15 q^{8} - 22 q^{9} - 2 q^{10} + 4 q^{11} + 14 q^{12} + 6 q^{13} - 10 q^{14} + 14 q^{15} - 32 q^{16} + 20 q^{17} - 62 q^{18} - 3 q^{19} + 16 q^{21}+ \cdots + 76 q^{99}+O(q^{100}) $ 80 * q + 2 * q^2 + 2 * q^3 - 20 * q^4 - 17 * q^6 - 44 * q^7 + 15 * q^8 - 22 * q^9 - 2 * q^10 + 4 * q^11 + 14 * q^12 + 6 * q^13 - 10 * q^14 + 14 * q^15 - 32 * q^16 + 20 * q^17 - 62 * q^18 - 3 * q^19 + 16 * q^21 + 17 * q^22 - 5 * q^23 + 30 * q^24 - 14 * q^25 + 18 * q^26 + 17 * q^27 + 32 * q^28 + 20 * q^29 - 114 * q^30 - 21 * q^31 - 88 * q^32 - 2 * q^34 - 2 * q^35 + 47 * q^36 + 6 * q^37 + 22 * q^38 - 46 * q^39 + 59 * q^40 - 26 * q^41 - 3 * q^42 - 102 * q^43 - 44 * q^44 + 74 * q^45 + 2 * q^46 + 2 * q^47 + 72 * q^48 + 108 * q^49 + 7 * q^50 + 18 * q^51 + 65 * q^52 - 18 * q^53 - 29 * q^54 - 49 * q^55 - 117 * q^56 + 2 * q^57 + 42 * q^58 + 21 * q^59 + 112 * q^60 + 4 * q^61 + 15 * q^62 + 41 * q^63 - 11 * q^64 + 8 * q^65 - 156 * q^66 + 21 * q^67 - 80 * q^68 - 67 * q^69 + 32 * q^70 - 4 * q^71 + 83 * q^72 - 2 * q^73 + 78 * q^74 - 68 * q^75 + 16 * q^76 + 2 * q^77 - 2 * q^78 - 53 * q^79 - 54 * q^80 - 21 * q^81 - 72 * q^82 - 42 * q^83 - 52 * q^84 + 42 * q^86 - 8 * q^87 + 68 * q^88 - 73 * q^89 + 97 * q^90 - 83 * q^91 + 117 * q^92 - 120 * q^93 + 80 * q^94 + 16 * q^95 + 88 * q^96 + 57 * q^97 + 17 * q^98 + 76 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/425\mathbb{Z}\right)^\times$.

$n$	$52$	$326$
$\chi(n)$	$e\left(\frac{4}{5}\right)$	$1$

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 $

$2$	0.545657	−	0.396443i	0.385838	−	0.280328i	−0.377910	−	0.925842i	$-0.623357\pi$
$2$	0.545657	−	0.396443i	0.385838	−	0.280328i	0.763748	+	0.645515i	$0.223357\pi$
$3$	0.335346	−	1.03209i	0.193612	−	0.595876i	−0.806378	−	0.591400i	$-0.798575\pi$
$3$	0.335346	−	1.03209i	0.193612	−	0.595876i	0.999990	−	0.00447574i	$-0.00142468\pi$
$4$	−0.477459	+	1.46947i	−0.238730	+	0.734734i
$5$	1.35235	+	1.78077i	0.604788	+	0.796386i
$5$	1.35235	+	1.78077i	0.604788	+	0.796386i
$6$	−0.226180	−	0.696112i	−0.0923378	−	0.284186i
$7$	−5.02070			−1.89765			−0.948823	−	0.315808i	$-0.897724\pi$
$7$	−5.02070			−1.89765			−0.948823	+	0.315808i	$0.897724\pi$
$8$	0.738877	+	2.27403i	0.261232	+	0.803991i
$9$	1.47430	+	1.07114i	0.491434	+	0.357048i
$10$	1.44389	+	0.435563i	0.456600	+	0.137737i
$11$	1.60579	−	1.16668i	0.484165	−	0.351767i	−0.318771	−	0.947832i	$-0.603270\pi$
$11$	1.60579	−	1.16668i	0.484165	−	0.351767i	0.802936	+	0.596065i	$0.203270\pi$
$12$	1.35651	+	0.985560i	0.391590	+	0.284507i
$13$	3.76928	+	2.73854i	1.04541	+	0.759535i	0.971334	−	0.237718i	$-0.0763994\pi$
$13$	3.76928	+	2.73854i	1.04541	+	0.759535i	0.0740755	+	0.997253i	$0.476399\pi$
$14$	−2.73958	+	1.99042i	−0.732184	+	0.531963i
$15$	2.29142	−	0.798567i	0.591642	−	0.206189i
$16$	−1.19531	−	0.868444i	−0.298828	−	0.217111i
$17$	−0.309017	−	0.951057i	−0.0749476	−	0.230665i
$17$	−0.309017	−	0.951057i	−0.0749476	−	0.230665i
$18$	1.22911			0.289705
$19$	2.38975	+	7.35489i	0.548246	+	1.68733i	0.713144	+	0.701017i	$0.247270\pi$
$19$	2.38975	+	7.35489i	0.548246	+	1.68733i	−0.164898	+	0.986311i	$0.552730\pi$
$20$	−3.26248	+	1.13699i	−0.729513	+	0.254238i
$21$	−1.68367	+	5.18180i	−0.367407	+	1.13076i
$22$	0.413692	−	1.27321i	0.0881994	−	0.271450i
$23$	−2.61778	+	1.90193i	−0.545845	+	0.396580i	−0.826251	−	0.563302i	$-0.809531\pi$
$23$	−2.61778	+	1.90193i	−0.545845	+	0.396580i	0.280406	+	0.959881i	$0.409531\pi$
$24$	2.59478			0.529657
$25$	−1.34231	+	4.81645i	−0.268462	+	0.963290i
$26$	3.14241			0.616278
$27$	4.23375	−	3.07600i	0.814786	−	0.591977i
$28$	2.39718	−	7.37776i	0.453024	−	1.39427i
$29$	2.77198	−	8.53126i	0.514743	−	1.58422i	−0.269006	−	0.963138i	$-0.586695\pi$
$29$	2.77198	−	8.53126i	0.514743	−	1.58422i	0.783749	−	0.621078i	$-0.213305\pi$
$30$	0.933743	−	1.34416i	0.170477	−	0.245409i
$31$	−0.141612	−	0.435836i	−0.0254342	−	0.0782784i	0.937534	−	0.347894i	$-0.113103\pi$
$31$	−0.141612	−	0.435836i	−0.0254342	−	0.0782784i	−0.962968	+	0.269616i	$0.913103\pi$
$32$	−5.77863			−1.02153
$33$	−0.665618	−	2.04856i	−0.115869	−	0.356609i
$34$	−0.545657	−	0.396443i	−0.0935795	−	0.0679895i
$35$	−6.78973	−	8.94073i	−1.14767	−	1.51126i
$36$	−2.27793	+	1.65501i	−0.379655	+	0.275836i
$37$	−1.45116	−	1.05433i	−0.238569	−	0.173330i	0.462077	−	0.886840i	$-0.347104\pi$
$37$	−1.45116	−	1.05433i	−0.238569	−	0.173330i	−0.700645	+	0.713510i	$0.747104\pi$
$38$	4.21978	+	3.06585i	0.684539	+	0.497347i
$39$	4.09042	−	2.97187i	0.654992	−	0.475880i
$40$	−3.05031	+	4.39105i	−0.482297	+	0.694286i
$41$	1.51824	+	1.10306i	0.237109	+	0.172269i	0.699994	−	0.714149i	$-0.253186\pi$
$41$	1.51824	+	1.10306i	0.237109	+	0.172269i	−0.462886	+	0.886418i	$0.653186\pi$
$42$	1.13558	+	3.49497i	0.175224	+	0.539285i
$43$	−9.16394			−1.39749			−0.698744	−	0.715372i	$-0.746257\pi$
$43$	−9.16394			−1.39749			−0.698744	+	0.715372i	$0.746257\pi$
$44$	0.947695	+	2.91670i	0.142870	+	0.439710i
$45$	0.0863057	+	4.07396i	0.0128657	+	0.607310i
$46$	−0.674405	+	2.07560i	−0.0994356	+	0.306031i
$47$	4.12605	−	12.6987i	0.601847	−	1.85229i	0.0846808	−	0.996408i	$-0.473013\pi$
$47$	4.12605	−	12.6987i	0.601847	−	1.85229i	0.517166	−	0.855885i	$-0.326987\pi$
$48$	−1.29715	+	0.942437i	−0.187228	+	0.136029i
$49$	18.2074			2.60106
$50$	1.17701	+	3.16028i	0.166454	+	0.446931i
$51$	−1.08520			−0.151959
$52$	−5.82388	+	4.23129i	−0.807626	+	0.586775i
$53$	−1.03188	+	3.17579i	−0.141739	+	0.436228i	−0.996577	−	0.0826668i	$-0.973656\pi$
$53$	−1.03188	+	3.17579i	−0.141739	+	0.436228i	0.854838	+	0.518895i	$0.173656\pi$
$54$	1.09072	−	3.35689i	0.148428	−	0.456814i
$55$	4.24918	+	1.28180i	0.572960	+	0.172838i
$56$	−3.70968	−	11.4172i	−0.495727	−	1.52569i
$57$	8.39228			1.11159
$58$	−1.86961	−	5.75408i	−0.245492	−	0.755548i
$59$	−0.148926	−	0.108201i	−0.0193885	−	0.0140865i	0.578049	−	0.816002i	$-0.303814\pi$
$59$	−0.148926	−	0.108201i	−0.0193885	−	0.0140865i	−0.597437	+	0.801916i	$0.703814\pi$
$60$	0.0794099	+	3.74845i	0.0102518	+	0.483923i
$61$	3.55488	−	2.58277i	0.455156	−	0.330690i	−0.336472	−	0.941693i	$-0.609234\pi$
$61$	3.55488	−	2.58277i	0.455156	−	0.330690i	0.791628	+	0.611003i	$0.209234\pi$
$62$	−0.250056	−	0.181676i	−0.0317571	−	0.0230729i
$63$	−7.40203	−	5.37789i	−0.932568	−	0.677551i
$64$	−0.762532	+	0.554012i	−0.0953164	+	0.0692515i
$65$	0.220653	+	10.4157i	0.0273687	+	1.29191i
$66$	−1.17534	−	0.853933i	−0.144674	−	0.105112i
$67$	−0.910785	−	2.80311i	−0.111270	−	0.342454i	0.879881	−	0.475195i	$-0.157622\pi$
$67$	−0.910785	−	2.80311i	−0.111270	−	0.342454i	−0.991151	+	0.132740i	$0.957622\pi$
$68$	1.54509			0.187370
$69$	1.08510	+	3.33958i	0.130630	+	0.402039i
$70$	−7.24936	−	2.18683i	−0.866464	−	0.261376i
$71$	1.11849	−	3.44235i	0.132740	−	0.408531i	−0.862492	−	0.506071i	$-0.831097\pi$
$71$	1.11849	−	3.44235i	0.132740	−	0.408531i	0.995232	+	0.0975398i	$0.0310973\pi$
$72$	−1.34648	+	4.14405i	−0.158685	+	0.488381i
$73$	−2.00618	+	1.45757i	−0.234805	+	0.170596i	−0.698966	−	0.715155i	$-0.746356\pi$
$73$	−2.00618	+	1.45757i	−0.234805	+	0.170596i	0.464161	+	0.885751i	$0.346356\pi$
$74$	−1.20982			−0.140638
$75$	4.52086	+	3.00056i	0.522024	+	0.346475i
$76$	−11.9488			−1.37062
$77$	−8.06221	+	5.85754i	−0.918774	+	0.667528i
$78$	1.05379	−	3.24324i	0.119319	−	0.367225i
$79$	−0.0254567	+	0.0783476i	−0.00286410	+	0.00881479i	−0.952478	−	0.304606i	$-0.901475\pi$
$79$	−0.0254567	+	0.0783476i	−0.00286410	+	0.00881479i	0.949614	+	0.313421i	$0.101475\pi$
$80$	−0.0699735	−	3.30302i	−0.00782327	−	0.369289i
$81$	−0.0655323	−	0.201688i	−0.00728137	−	0.0224097i
$82$	1.26574			0.139777
$83$	0.672295	+	2.06911i	0.0737940	+	0.227115i	0.981150	−	0.193249i	$-0.0619025\pi$
$83$	0.672295	+	2.06911i	0.0737940	+	0.227115i	−0.907356	+	0.420364i	$0.861903\pi$
$84$	−6.81061	−	4.94820i	−0.743099	−	0.539893i
$85$	1.27572	−	1.83645i	0.138371	−	0.199191i
$86$	−5.00037	+	3.63298i	−0.539204	+	0.391755i
$87$	−7.87544	−	5.72184i	−0.844336	−	0.613446i
$88$	3.83954	+	2.78959i	0.409297	+	0.297372i
$89$	6.34536	−	4.61018i	0.672607	−	0.488678i	−0.198290	−	0.980143i	$-0.563539\pi$
$89$	6.34536	−	4.61018i	0.672607	−	0.488678i	0.870897	+	0.491466i	$0.163539\pi$
$90$	1.66219	+	2.18877i	0.175210	+	0.230717i
$91$	−18.9244	−	13.7494i	−1.98382	−	1.44133i
$92$	−1.54494	−	4.75484i	−0.161071	−	0.495726i
$93$	−0.497310			−0.0515686
$94$	−2.78290	−	8.56488i	−0.287034	−	0.883400i
$95$	−9.86563	+	14.2020i	−1.01219	+	1.45709i
$96$	−1.93784	+	5.96405i	−0.197780	+	0.608704i
$97$	2.29941	−	7.07684i	0.233469	−	0.718545i	−0.763851	−	0.645392i	$-0.776694\pi$
$97$	2.29941	−	7.07684i	0.233469	−	0.718545i	0.997321	−	0.0731526i	$-0.0233060\pi$
$98$	9.93502	−	7.21821i	1.00359	−	0.729150i
$99$	3.61711			0.363533
$100$	−6.43672	−	4.27214i	−0.643672	−	0.427214i
$101$	−4.59151			−0.456872			−0.228436	−	0.973559i	$-0.573361\pi$
$101$	−4.59151			−0.456872			−0.228436	+	0.973559i	$0.573361\pi$
$102$	−0.592148	+	0.430221i	−0.0586314	+	0.0425982i
$103$	4.79899	−	14.7698i	0.472859	−	1.45531i	−0.375965	−	0.926634i	$-0.622689\pi$
$103$	4.79899	−	14.7698i	0.472859	−	1.45531i	0.848824	−	0.528676i	$-0.177311\pi$
$104$	−3.44249	+	10.5949i	−0.337564	+	1.03891i
$105$	−11.5045	+	4.00936i	−1.12273	+	0.391274i
$106$	0.695969	+	2.14197i	0.0675985	+	0.208047i
$107$	2.18797			0.211519			0.105760	−	0.994392i	$-0.466273\pi$
$107$	2.18797			0.211519			0.105760	+	0.994392i	$0.466273\pi$
$108$	2.49864	+	7.69003i	0.240432	+	0.739974i
$109$	−3.82838	−	2.78148i	−0.366692	−	0.266417i	0.389146	−	0.921176i	$-0.372770\pi$
$109$	−3.82838	−	2.78148i	−0.366692	−	0.266417i	−0.755838	+	0.654759i	$0.772770\pi$
$110$	2.82676	−	0.985135i	0.269521	−	0.0939289i
$111$	−1.57480	+	1.14416i	−0.149473	+	0.108599i
$112$	6.00130	+	4.36020i	0.567069	+	0.412000i
$113$	10.1469	+	7.37213i	0.954537	+	0.693512i	0.951876	−	0.306485i	$-0.0991529\pi$
$113$	10.1469	+	7.37213i	0.954537	+	0.693512i	0.00266134	+	0.999996i	$0.499153\pi$
$114$	4.57931	−	3.32707i	0.428892	−	0.311608i
$115$	−6.92706	−	2.08961i	−0.645952	−	0.194857i
$116$	11.2129	+	8.14666i	1.04109	+	0.756399i
$117$	2.62369	+	8.07488i	0.242560	+	0.746523i
$118$	−0.124158			−0.0114297
$119$	1.55148	+	4.77497i	0.142224	+	0.437721i
$120$	3.50904	+	4.62071i	0.320330	+	0.421811i
$121$	−2.18175	+	6.71473i	−0.198341	+	0.610430i
$122$	0.915824	−	2.81862i	0.0829148	−	0.255186i
$123$	1.64759	−	1.19704i	0.148558	−	0.107934i
$124$	0.708061			0.0635857
$125$	−10.3923	+	4.12317i	−0.929514	+	0.368787i
$126$	−6.17100			−0.549757
$127$	5.39396	−	3.91894i	0.478636	−	0.347749i	−0.322161	−	0.946685i	$-0.604409\pi$
$127$	5.39396	−	3.91894i	0.478636	−	0.347749i	0.800797	+	0.598935i	$0.204409\pi$
$128$	3.37494	−	10.3870i	0.298306	−	0.918091i
$129$	−3.07309	+	9.45799i	−0.270570	+	0.832729i
$130$	4.24963	+	5.59592i	0.372717	+	0.490795i
$131$	4.82600	+	14.8529i	0.421650	+	1.29770i	0.906166	+	0.422923i	$0.138996\pi$
$131$	4.82600	+	14.8529i	0.421650	+	1.29770i	−0.484516	+	0.874782i	$0.661004\pi$
$132$	3.32810			0.289674
$133$	−11.9982	−	36.9267i	−1.04038	−	3.20195i
$134$	−1.60825	−	1.16846i	−0.138932	−	0.100940i
$135$	11.2032	+	3.37953i	0.964215	+	0.290864i
$136$	1.93441	−	1.40543i	0.165874	−	0.120514i
$137$	−3.50650	−	2.54762i	−0.299580	−	0.217658i	0.427832	−	0.903858i	$-0.359277\pi$
$137$	−3.50650	−	2.54762i	−0.299580	−	0.217658i	−0.727413	+	0.686200i	$0.759277\pi$
$138$	1.91605	+	1.39209i	0.163105	+	0.118503i
$139$	−15.9076	+	11.5576i	−1.34927	+	0.980301i	−0.350220	+	0.936667i	$0.613893\pi$
$139$	−15.9076	+	11.5576i	−1.34927	+	0.980301i	−0.999048	+	0.0436332i	$0.986107\pi$
$140$	16.3799	−	5.70846i	1.38436	−	0.482453i
$141$	−11.7225	−	8.51690i	−0.987213	−	0.717252i
$142$	−0.754385	−	2.32176i	−0.0633066	−	0.194838i
$143$	9.24768			0.773330
$144$	−0.832022	−	2.56070i	−0.0693352	−	0.213392i
$145$	18.9409	−	6.60098i	1.57296	−	0.548181i
$146$	−0.516841	+	1.59067i	−0.0427740	+	0.131645i
$147$	6.10578	−	18.7917i	0.503596	−	1.54991i
$148$	2.24217	−	1.62903i	0.184305	−	0.133906i
$149$	12.5778			1.03041			0.515207	−	0.857066i	$-0.327715\pi$
$149$	12.5778			1.03041			0.515207	+	0.857066i	$0.327715\pi$
$150$	3.65639	−	0.154989i	0.298543	−	0.0126548i
$151$	9.33432			0.759616			0.379808	−	0.925065i	$-0.375990\pi$
$151$	9.33432			0.759616			0.379808	+	0.925065i	$0.375990\pi$
$152$	−14.9595	+	10.8687i	−1.21338	+	0.881570i
$153$	0.563134	−	1.73315i	0.0455267	−	0.140117i
$154$	−2.07702	+	6.39242i	−0.167371	+	0.515116i
$155$	0.584617	−	0.841580i	0.0469576	−	0.0675973i
$156$	2.41405	+	7.42970i	0.193279	+	0.594852i
$157$	−4.93120			−0.393553			−0.196776	−	0.980448i	$-0.563047\pi$
$157$	−4.93120			−0.393553			−0.196776	+	0.980448i	$0.563047\pi$
$158$	0.0171698	+	0.0528431i	0.00136595	+	0.00420397i
$159$	2.93166	+	2.12997i	0.232495	+	0.168918i
$160$	−7.81472	−	10.2904i	−0.617808	−	0.813530i
$161$	13.1431	−	9.54902i	1.03582	−	0.752568i
$162$	−0.115716	−	0.0840725i	−0.00909150	−	0.00660536i
$163$	9.88138	+	7.17924i	0.773969	+	0.562322i	0.903163	−	0.429298i	$-0.141239\pi$
$163$	9.88138	+	7.17924i	0.773969	+	0.562322i	−0.129194	+	0.991619i	$0.541239\pi$
$164$	−2.34581	+	1.70433i	−0.183177	+	0.133086i
$165$	2.74788	−	3.95568i	0.213922	−	0.307949i
$166$	1.18713	+	0.862500i	0.0921391	+	0.0669430i
$167$	1.03075	+	3.17231i	0.0797616	+	0.245481i	0.982984	−	0.183692i	$-0.0588050\pi$
$167$	1.03075	+	3.17231i	0.0797616	+	0.245481i	−0.903222	+	0.429173i	$0.858805\pi$
$168$	−13.0276			−1.00510
$169$	2.69063	+	8.28091i	0.206972	+	0.636993i
$170$	−0.0319428	−	1.50782i	−0.00244990	−	0.115645i
$171$	−4.35493	+	13.4031i	−0.333030	+	1.02496i
$172$	4.37541	−	13.4661i	0.333622	−	1.02678i
$173$	−1.78226	+	1.29489i	−0.135503	+	0.0984484i	−0.653472	−	0.756951i	$-0.726688\pi$
$173$	−1.78226	+	1.29489i	−0.135503	+	0.0984484i	0.517969	+	0.855399i	$0.326688\pi$
$174$	−6.56568			−0.497743
$175$	6.73934	−	24.1820i	0.509446	−	1.82798i
$176$	−2.93262			−0.221054
$177$	−0.161614	+	0.117420i	−0.0121477	+	0.00882580i
$178$	1.63472	−	5.03116i	0.122528	−	0.377101i
$179$	1.44940	−	4.46079i	0.108333	−	0.333415i	−0.882165	−	0.470940i	$-0.843915\pi$
$179$	1.44940	−	4.46079i	0.108333	−	0.333415i	0.990498	+	0.137525i	$0.0439147\pi$
$180$	−6.02776	−	1.81833i	−0.449283	−	0.135530i
$181$	−5.19396	−	15.9854i	−0.386064	−	1.18818i	−0.935705	−	0.352783i	$-0.885235\pi$
$181$	−5.19396	−	15.9854i	−0.386064	−	1.18818i	0.549641	−	0.835401i	$-0.314765\pi$
$182$	−15.7771			−1.16948
$183$	−1.47353	−	4.53507i	−0.108927	−	0.335242i
$184$	−6.25926	−	4.54762i	−0.461439	−	0.335255i
$185$	−0.0849507	−	4.01000i	−0.00624570	−	0.294821i
$186$	−0.271361	+	0.197155i	−0.0198971	+	0.0144561i
$187$	−1.60579	−	1.16668i	−0.117427	−	0.0853159i
$188$	16.6903	+	12.1262i	1.21726	+	0.884395i
$189$	−21.2564	+	15.4437i	−1.54618	+	1.12336i
$190$	0.247026	+	11.6606i	0.0179211	+	0.845947i
$191$	1.33843	+	0.972425i	0.0968452	+	0.0703622i	0.635154	−	0.772385i	$-0.280937\pi$
$191$	1.33843	+	0.972425i	0.0968452	+	0.0703622i	−0.538309	+	0.842748i	$0.680937\pi$
$192$	0.316077	+	0.972785i	0.0228109	+	0.0702047i
$193$	22.4153			1.61349			0.806746	−	0.590899i	$-0.201227\pi$
$193$	22.4153			1.61349			0.806746	+	0.590899i	$0.201227\pi$
$194$	−1.55088	−	4.77312i	−0.111347	−	0.342690i
$195$	10.8239	+	3.26512i	0.775116	+	0.233820i
$196$	−8.69330	+	26.7552i	−0.620950	+	1.91109i
$197$	−5.52474	+	17.0034i	−0.393621	+	1.21144i	0.536409	+	0.843958i	$0.319781\pi$
$197$	−5.52474	+	17.0034i	−0.393621	+	1.21144i	−0.930030	+	0.367483i	$0.880219\pi$
$198$	1.97370	−	1.43398i	0.140265	−	0.101908i
$199$	−18.4626			−1.30878			−0.654391	−	0.756157i	$-0.727075\pi$
$199$	−18.4626			−1.30878			−0.654391	+	0.756157i	$0.727075\pi$
$200$	−11.9446	+	0.506311i	−0.844608	+	0.0358016i
$201$	−3.19848			−0.225604
$202$	−2.50539	+	1.82027i	−0.176279	+	0.128074i
$203$	−13.9173	+	42.8329i	−0.976800	+	3.00628i
$204$	0.518139	−	1.59467i	0.0362770	−	0.111649i
$205$	0.0888775	+	4.19536i	0.00620747	+	0.293016i
$206$	−3.23678	−	9.96177i	−0.225517	−	0.694070i
$207$	−5.89664			−0.409845
$208$	−2.12719	−	6.54682i	−0.147494	−	0.453940i
$209$	12.4182	+	9.02237i	0.858987	+	0.624091i
$210$	−4.68804	+	6.74863i	−0.323506	+	0.465700i
$211$	6.06067	−	4.40333i	0.417234	−	0.303138i	−0.359290	−	0.933226i	$-0.616981\pi$
$211$	6.06067	−	4.40333i	0.417234	−	0.303138i	0.776524	+	0.630088i	$0.216981\pi$
$212$	−4.17404	−	3.03262i	−0.286674	−	0.208281i
$213$	−3.17772	−	2.30875i	−0.217734	−	0.158193i
$214$	1.19388	−	0.867407i	0.0816122	−	0.0592947i
$215$	−12.3928	−	16.3189i	−0.845184	−	1.11294i
$216$	10.1231	+	7.35489i	0.688793	+	0.500437i
$217$	0.710990	+	2.18820i	0.0482651	+	0.148545i
$218$	−3.19168			−0.216168
$219$	0.831581	+	2.55934i	0.0561930	+	0.172944i
$220$	−3.91238	+	5.63203i	−0.263773	+	0.379711i
$221$	1.43974	−	4.43105i	0.0968471	−	0.298065i
$222$	−0.405706	+	1.24864i	−0.0272292	+	0.0838030i
$223$	7.30097	−	5.30446i	0.488909	−	0.355213i	−0.315856	−	0.948807i	$-0.602292\pi$
$223$	7.30097	−	5.30446i	0.488909	−	0.355213i	0.804765	+	0.593594i	$0.202292\pi$
$224$	29.0128			1.93850
$225$	−7.13808	+	5.66310i	−0.475872	+	0.377540i
$226$	8.45935			0.562707
$227$	17.6300	−	12.8090i	1.17015	−	0.850161i	0.179120	−	0.983827i	$-0.442675\pi$
$227$	17.6300	−	12.8090i	1.17015	−	0.850161i	0.991026	+	0.133666i	$0.0426751\pi$
$228$	−4.00697	+	12.3322i	−0.265368	+	0.816720i
$229$	2.19320	−	6.74998i	0.144931	−	0.446051i	−0.852071	−	0.523426i	$-0.824654\pi$
$229$	2.19320	−	6.74998i	0.144931	−	0.446051i	0.997002	+	0.0773747i	$0.0246538\pi$
$230$	−4.60821	+	1.60598i	−0.303856	+	0.105895i
$231$	3.34187	+	10.2852i	0.219879	+	0.676717i
$232$	21.4485			1.40816
$233$	−0.457527	−	1.40812i	−0.0299736	−	0.0922493i	0.934951	−	0.354778i	$-0.115444\pi$
$233$	−0.457527	−	1.40812i	−0.0299736	−	0.0922493i	−0.964924	+	0.262529i	$0.915444\pi$
$234$	4.63287	+	3.36597i	0.302860	+	0.220041i
$235$	28.1933	−	9.82547i	1.83913	−	0.640943i
$236$	0.230104	−	0.167180i	0.0149785	−	0.0108825i
$237$	0.0723248	+	0.0525470i	0.00469800	+	0.00341330i
$238$	2.73958	+	1.99042i	0.177581	+	0.129020i
$239$	15.3863	−	11.1788i	0.995256	−	0.723096i	0.0341905	−	0.999415i	$-0.489115\pi$
$239$	15.3863	−	11.1788i	0.995256	−	0.723096i	0.961066	+	0.276319i	$0.0891147\pi$
$240$	−3.43247	−	1.03543i	−0.221565	−	0.0668370i
$241$	−7.88470	−	5.72857i	−0.507898	−	0.369010i	0.304127	−	0.952631i	$-0.401635\pi$
$241$	−7.88470	−	5.72857i	−0.507898	−	0.369010i	−0.812026	+	0.583622i	$0.801635\pi$
$242$	1.47152	+	4.52888i	0.0945931	+	0.291128i
$243$	15.4695			0.992368
$244$	2.09799	+	6.45695i	0.134310	+	0.413364i
$245$	24.6228	+	32.4233i	1.57309	+	2.07145i
$246$	0.424460	−	1.30635i	0.0270626	−	0.0832900i
$247$	−11.1340	+	34.2671i	−0.708442	+	2.18036i
$248$	0.886470	−	0.644058i	0.0562909	−	0.0408977i
$249$	2.36096			0.149620
$250$	−4.03602	+	6.36979i	−0.255261	+	0.402861i
$251$	−7.96862			−0.502975			−0.251488	−	0.967861i	$-0.580920\pi$
$251$	−7.96862			−0.502975			−0.251488	+	0.967861i	$0.580920\pi$
$252$	11.4368	−	8.30933i	0.720451	−	0.523438i
$253$	−1.98468	+	6.10822i	−0.124776	+	0.384020i
$254$	1.38962	−	4.27680i	0.0871922	−	0.268350i
$255$	−1.46757	−	1.93250i	−0.0919028	−	0.121018i
$256$	−2.85882	−	8.79854i	−0.178676	−	0.549909i
$257$	5.88602			0.367160			0.183580	−	0.983005i	$-0.441231\pi$
$257$	5.88602			0.367160			0.183580	+	0.983005i	$0.441231\pi$
$258$	2.07270	+	6.37913i	0.129041	+	0.397147i
$259$	7.28582	+	5.29346i	0.452719	+	0.328920i
$260$	−15.4109	−	4.64882i	−0.955742	−	0.288308i
$261$	13.2249	−	9.60848i	0.818603	−	0.594750i
$262$	8.52168	+	6.19137i	0.526471	+	0.382504i
$263$	−11.2513	−	8.17458i	−0.693788	−	0.504066i	0.184115	−	0.982905i	$-0.441058\pi$
$263$	−11.2513	−	8.17458i	−0.693788	−	0.504066i	−0.877903	+	0.478838i	$0.841058\pi$
$264$	4.16668	−	3.02727i	0.256441	−	0.186316i
$265$	−7.05081	+	2.45723i	−0.433128	+	0.150947i
$266$	−21.1863	−	15.3927i	−1.29901	−	0.943788i
$267$	−2.63022	−	8.09497i	−0.160967	−	0.495404i
$268$	4.55394			0.278176
$269$	−4.29828	−	13.2287i	−0.262071	−	0.806571i	−0.992354	−	0.123426i	$-0.960612\pi$
$269$	−4.29828	−	13.2287i	−0.262071	−	0.806571i	0.730283	−	0.683145i	$-0.239388\pi$
$270$	7.45289	−	2.59736i	0.453568	−	0.158070i
$271$	−8.20421	+	25.2499i	−0.498370	+	1.53383i	0.313268	+	0.949665i	$0.398576\pi$
$271$	−8.20421	+	25.2499i	−0.498370	+	1.53383i	−0.811638	+	0.584160i	$0.801424\pi$
$272$	−0.456568	+	1.40517i	−0.0276835	+	0.0852011i
$273$	−20.5368	+	14.9209i	−1.24294	+	0.903051i
$274$	−2.92333			−0.176605
$275$	3.46377	+	9.30027i	0.208873	+	0.560828i
$276$	−5.42550			−0.326577
$277$	4.99055	−	3.62584i	0.299853	−	0.217856i	−0.427677	−	0.903931i	$-0.640668\pi$
$277$	4.99055	−	3.62584i	0.299853	−	0.217856i	0.727530	+	0.686076i	$0.240668\pi$
$278$	−4.09820	+	12.6130i	−0.245794	+	0.756475i
$279$	0.258064	−	0.794241i	0.0154499	−	0.0475499i
$280$	15.3147	−	22.0462i	0.915229	−	1.31751i
$281$	−4.18364	−	12.8759i	−0.249575	−	0.768113i	−0.994850	−	0.101356i	$-0.967682\pi$
$281$	−4.18364	−	12.8759i	−0.249575	−	0.768113i	0.745275	−	0.666757i	$-0.232318\pi$
$282$	−9.77294			−0.581970
$283$	5.59306	+	17.2137i	0.332473	+	1.02325i	0.967953	+	0.251130i	$0.0808020\pi$
$283$	5.59306	+	17.2137i	0.332473	+	1.02325i	−0.635481	+	0.772117i	$0.719198\pi$
$284$	4.52439	+	3.28716i	0.268473	+	0.195057i
$285$	11.3493	+	14.9448i	0.672274	+	0.885251i
$286$	5.04607	−	3.66618i	0.298380	−	0.216786i
$287$	−7.62260	−	5.53815i	−0.449948	−	0.326906i
$288$	−8.51945	−	6.18975i	−0.502014	−	0.364734i
$289$	−0.809017	+	0.587785i	−0.0475892	+	0.0345756i
$290$	7.71835	−	11.1109i	0.453237	−	0.652453i
$291$	−6.53283	−	4.74638i	−0.382961	−	0.278238i
$292$	−1.18399	−	3.64395i	−0.0692878	−	0.213246i
$293$	−18.9895			−1.10938			−0.554691	−	0.832057i	$-0.687163\pi$
$293$	−18.9895			−1.10938			−0.554691	+	0.832057i	$0.687163\pi$
$294$	−4.11816	−	12.6744i	−0.240176	−	0.739186i
$295$	−0.00871810	−	0.411528i	−0.000507587	−	0.0239601i
$296$	1.32535	−	4.07899i	0.0770341	−	0.237087i
$297$	3.20983	−	9.87885i	0.186253	−	0.573229i
$298$	6.86317	−	4.98639i	0.397573	−	0.288854i
$299$	−15.0757			−0.871848
$300$	−6.56775	+	5.21062i	−0.379189	+	0.300835i
$301$	46.0094			2.65194
$302$	5.09334	−	3.70053i	0.293089	−	0.212941i
$303$	−1.53974	+	4.73884i	−0.0884559	+	0.272239i
$304$	3.53082	−	10.8667i	0.202506	−	0.623251i
$305$	9.40676	+	2.83763i	0.538630	+	0.162482i
$306$	−0.379817	−	1.16896i	−0.0217127	−	0.0668247i
$307$	−18.6035			−1.06176			−0.530878	−	0.847449i	$-0.678138\pi$
$307$	−18.6035			−1.06176			−0.530878	+	0.847449i	$0.678138\pi$
$308$	−4.75809	−	14.6439i	−0.271117	−	0.834414i
$309$	−13.6344	−	9.90596i	−0.775633	−	0.563531i
$310$	−0.0146383	−	0.690982i	−0.000831397	−	0.0392451i
$311$	2.71339	−	1.97139i	0.153862	−	0.111787i	−0.508191	−	0.861245i	$-0.669685\pi$
$311$	2.71339	−	1.97139i	0.153862	−	0.111787i	0.662053	+	0.749457i	$0.269685\pi$
$312$	9.78044	+	7.10590i	0.553708	+	0.402293i
$313$	−23.7303	−	17.2411i	−1.34132	−	0.974523i	−0.999395	−	0.0347939i	$-0.988923\pi$
$313$	−23.7303	−	17.2411i	−1.34132	−	0.974523i	−0.341921	−	0.939729i	$-0.611077\pi$
$314$	−2.69075	+	1.95494i	−0.151848	+	0.110324i
$315$	−0.433315	−	20.4541i	−0.0244145	−	1.15246i
$316$	−0.102975	−	0.0748155i	−0.00579278	−	0.00420870i
$317$	−3.16472	−	9.74000i	−0.177748	−	0.547053i	0.822000	−	0.569487i	$-0.192858\pi$
$317$	−3.16472	−	9.74000i	−0.177748	−	0.547053i	−0.999748	+	0.0224345i	$0.992858\pi$
$318$	2.44409			0.137058
$319$	−5.50201	−	16.9335i	−0.308054	−	0.948092i
$320$	−2.01778	−	0.608680i	−0.112797	−	0.0340262i
$321$	0.733727	−	2.25818i	0.0409526	−	0.126039i
$322$	3.38598	−	10.4210i	0.188693	−	0.580739i
$323$	6.25644	−	4.54557i	0.348118	−	0.252922i
$324$	0.327663			0.0182035
$325$	−18.2496	+	14.4786i	−1.01231	+	0.803127i
$326$	8.23801			0.456261
$327$	−4.15456	+	3.01846i	−0.229748	+	0.166921i
$328$	−1.38661	+	4.26754i	−0.0765626	+	0.235635i
$329$	−20.7157	+	63.7563i	−1.14209	+	3.51500i
$330$	−0.0688042	−	3.24782i	−0.00378755	−	0.178787i
$331$	2.90436	+	8.93869i	0.159638	+	0.491315i	0.998601	−	0.0528730i	$-0.0168379\pi$
$331$	2.90436	+	8.93869i	0.159638	+	0.491315i	−0.838963	+	0.544188i	$0.816838\pi$
$332$	−3.36149			−0.184486
$333$	−1.01011	−	3.10880i	−0.0553536	−	0.170361i
$334$	1.82008	+	1.32236i	0.0995902	+	0.0723565i
$335$	3.76000	−	5.41268i	0.205431	−	0.295726i
$336$	6.51262	−	4.73169i	0.355292	−	0.258135i
$337$	8.55016	+	6.21205i	0.465757	+	0.338392i	0.795785	−	0.605579i	$-0.207058\pi$
$337$	8.55016	+	6.21205i	0.465757	+	0.338392i	−0.330028	+	0.943971i	$0.607058\pi$
$338$	4.75107	+	3.45186i	0.258424	+	0.187756i
$339$	11.0114	−	8.00024i	0.598057	−	0.434514i
$340$	2.08950	+	2.75146i	0.113319	+	0.149219i
$341$	−0.735879	−	0.534648i	−0.0398501	−	0.0289528i
$342$	2.93727	+	9.03999i	0.158829	+	0.488826i
$343$	−56.2691			−3.03825
$344$	−6.77102	−	20.8391i	−0.365069	−	1.12357i
$345$	−4.47962	+	6.44859i	−0.241174	+	0.347180i
$346$	−0.459154	+	1.41313i	−0.0246842	+	0.0759703i
$347$	−3.16813	+	9.75051i	−0.170074	+	0.523435i	−0.999374	−	0.0353686i	$-0.988739\pi$
$347$	−3.16813	+	9.75051i	−0.170074	+	0.523435i	0.829300	+	0.558804i	$0.188739\pi$
$348$	12.1683	−	8.84077i	0.652288	−	0.473915i
$349$	2.00912			0.107546			0.0537729	−	0.998553i	$-0.482875\pi$
$349$	2.00912			0.107546			0.0537729	+	0.998553i	$0.482875\pi$
$350$	−5.90941	−	15.8668i	−0.315871	−	0.848118i
$351$	24.3820			1.30141
$352$	−9.27929	+	6.74180i	−0.494588	+	0.359339i
$353$	−10.1087	+	31.1114i	−0.538031	+	1.65589i	0.198975	+	0.980005i	$0.436239\pi$
$353$	−10.1087	+	31.1114i	−0.538031	+	1.65589i	−0.737006	+	0.675886i	$0.763761\pi$
$354$	−0.0416358	+	0.128142i	−0.00221292	+	0.00681066i
$355$	7.64262	−	2.66348i	0.405628	−	0.141363i
$356$	3.74486	+	11.5255i	0.198477	+	0.610849i
$357$	5.44847			0.288364
$358$	−0.977576	−	3.00867i	−0.0516665	−	0.159013i
$359$	17.9176	+	13.0179i	0.945655	+	0.687059i	0.949775	−	0.312933i	$-0.101311\pi$
$359$	17.9176	+	13.0179i	0.945655	+	0.687059i	−0.00412006	+	0.999992i	$0.501311\pi$
$360$	−9.20053	+	3.20642i	−0.484911	+	0.168993i
$361$	−33.0122	+	23.9848i	−1.73748	+	1.26236i
$362$	−9.17142	−	6.66343i	−0.482039	−	0.350222i
$363$	6.19855	+	4.50351i	0.325340	+	0.236373i
$364$	29.2399	−	21.2441i	1.53259	−	1.11349i
$365$	−5.30866	−	1.60140i	−0.277868	−	0.0838212i
$366$	−2.60194	−	1.89042i	−0.136006	−	0.0988139i
$367$	−10.0016	−	30.7817i	−0.522078	−	1.60679i	−0.770023	−	0.638016i	$-0.779755\pi$
$367$	−10.0016	−	30.7817i	−0.522078	−	1.60679i	0.247946	−	0.968774i	$-0.420245\pi$
$368$	4.78078			0.249216
$369$	1.05680	+	3.25250i	0.0550148	+	0.169318i
$370$	−1.63609	−	2.15441i	−0.0850564	−	0.112002i
$371$	5.18074	−	15.9447i	0.268970	−	0.827806i
$372$	0.237445	−	0.730781i	0.0123110	−	0.0378892i
$373$	0.246632	−	0.179189i	0.0127701	−	0.00927805i	−0.581382	−	0.813631i	$-0.697488\pi$
$373$	0.246632	−	0.179189i	0.0127701	−	0.00927805i	0.594152	+	0.804353i	$0.297488\pi$
$374$	−1.33874			−0.0692244
$375$	0.770463	+	12.1084i	0.0397865	+	0.625277i
$376$	31.9258			1.64645
$377$	33.8116	−	24.5655i	1.74138	−	1.26519i
$378$	−5.47617	+	16.8539i	−0.281664	+	0.866872i
$379$	7.92610	−	24.3940i	0.407136	−	1.25304i	−0.511962	−	0.859008i	$-0.671081\pi$
$379$	7.92610	−	24.3940i	0.407136	−	1.25304i	0.919098	−	0.394029i	$-0.128919\pi$
$380$	−16.1589	−	21.2781i	−0.828935	−	1.09154i
$381$	−2.23585	−	6.88123i	−0.114546	−	0.352536i
$382$	1.11583			0.0570910
$383$	0.0755631	+	0.232559i	0.00386109	+	0.0118832i	0.952969	−	0.303069i	$-0.0980114\pi$
$383$	0.0755631	+	0.232559i	0.00386109	+	0.0118832i	−0.949107	+	0.314953i	$0.898011\pi$
$384$	−9.58853	−	6.96648i	−0.489313	−	0.355507i
$385$	−21.3339	−	6.43554i	−1.08727	−	0.327986i
$386$	12.2311	−	8.88641i	0.622546	−	0.452306i
$387$	−13.5104	−	9.81589i	−0.686773	−	0.498970i
$388$	9.30133	+	6.75781i	0.472203	+	0.343076i
$389$	−25.8682	+	18.7943i	−1.31157	+	0.952910i	−0.311572	+	0.950223i	$0.600855\pi$
$389$	−25.8682	+	18.7943i	−1.31157	+	0.952910i	−0.999996	+	0.00268742i	$0.999145\pi$
$390$	7.20058	−	2.50943i	0.364615	−	0.127070i
$391$	2.61778	+	1.90193i	0.132387	+	0.0961847i
$392$	13.4530	+	41.4042i	0.679481	+	2.09123i
$393$	16.9479			0.854908
$394$	3.72627	+	11.4683i	0.187727	+	0.577763i
$395$	−0.173946	+	0.0606206i	−0.00875215	+	0.00305015i
$396$	−1.72702	+	5.31522i	−0.0867861	+	0.267100i
$397$	−6.95295	+	21.3990i	−0.348959	+	1.07398i	0.610472	+	0.792038i	$0.290980\pi$
$397$	−6.95295	+	21.3990i	−0.348959	+	1.07398i	−0.959430	+	0.281946i	$0.909020\pi$
$398$	−10.0743	+	7.31939i	−0.504978	+	0.366888i
$399$	−42.1351			−2.10940
$400$	5.78730	−	4.59144i	0.289365	−	0.229572i
$401$	−12.2225			−0.610362			−0.305181	−	0.952294i	$-0.598717\pi$
$401$	−12.2225			−0.610362			−0.305181	+	0.952294i	$0.598717\pi$
$402$	−1.74528	+	1.26802i	−0.0870464	+	0.0632429i
$403$	0.659781	−	2.03060i	0.0328660	−	0.101151i
$404$	2.19226	−	6.74708i	0.109069	−	0.335680i
$405$	0.270538	−	0.389450i	0.0134431	−	0.0193519i
$406$	9.38677	+	28.8895i	0.465858	+	1.43376i
$407$	−3.56032			−0.176479
$408$	−0.801830	−	2.46778i	−0.0396965	−	0.122173i
$409$	−21.9508	−	15.9482i	−1.08540	−	0.788587i	−0.106781	−	0.994283i	$-0.534054\pi$
$409$	−21.9508	−	15.9482i	−1.08540	−	0.788587i	−0.978616	+	0.205696i	$0.934054\pi$
$410$	1.71172	+	2.25399i	0.0845357	+	0.111317i
$411$	−3.80526	+	2.76468i	−0.187699	+	0.136372i
$412$	19.4124	+	14.1039i	0.956381	+	0.694851i
$413$	0.747711	+	0.543244i	0.0367924	+	0.0267313i
$414$	−3.21755	+	2.33769i	−0.158134	+	0.114891i
$415$	−2.77544	+	3.99537i	−0.136241	+	0.196125i
$416$	−21.7813	−	15.8250i	−1.06791	−	0.775885i
$417$	6.59387	+	20.2939i	0.322903	+	0.993794i
$418$	10.3530			0.506380
$419$	−2.72916	−	8.39949i	−0.133328	−	0.410342i	0.861998	−	0.506911i	$-0.169213\pi$
$419$	−2.72916	−	8.39949i	−0.133328	−	0.410342i	−0.995326	+	0.0965698i	$0.969213\pi$
$420$	−0.398693	−	18.8198i	−0.0194542	−	0.918314i
$421$	8.82554	−	27.1622i	0.430130	−	1.32381i	−0.467865	−	0.883800i	$-0.654977\pi$
$421$	8.82554	−	27.1622i	0.430130	−	1.32381i	0.897995	−	0.440005i	$-0.145023\pi$
$422$	1.56138	−	4.80542i	0.0760066	−	0.233924i
$423$	19.6852	−	14.3021i	0.957126	−	0.695392i
$424$	−7.98426			−0.387750
$425$	4.99551	−	0.211752i	0.242318	−	0.0102715i
$426$	−2.64924			−0.128356
$427$	−17.8480	+	12.9673i	−0.863724	+	0.627532i
$428$	−1.04467	+	3.21516i	−0.0504959	+	0.155410i
$429$	3.10117	−	9.54442i	0.149726	−	0.460809i
$430$	−13.2318	−	3.99147i	−0.638092	−	0.192486i
$431$	−3.61445	−	11.1241i	−0.174102	−	0.535830i	0.825489	−	0.564418i	$-0.190899\pi$
$431$	−3.61445	−	11.1241i	−0.174102	−	0.535830i	−0.999591	+	0.0285871i	$0.990899\pi$
$432$	−7.73199			−0.372006
$433$	−4.44408	−	13.6775i	−0.213569	−	0.657297i	−0.999252	−	0.0386681i	$-0.987688\pi$
$433$	−4.44408	−	13.6775i	−0.213569	−	0.657297i	0.785683	−	0.618629i	$-0.212312\pi$
$434$	1.25545	+	0.912141i	0.0602638	+	0.0437842i
$435$	−0.461028	−	21.7623i	−0.0221046	−	1.04342i
$436$	5.91519	−	4.29763i	0.283286	−	0.205819i
$437$	−20.2443	−	14.7084i	−0.968418	−	0.703597i
$438$	1.46839	+	1.06685i	0.0701625	+	0.0509760i
$439$	−23.7819	+	17.2786i	−1.13505	+	0.824662i	−0.986422	−	0.164231i	$-0.947486\pi$
$439$	−23.7819	+	17.2786i	−1.13505	+	0.824662i	−0.148628	+	0.988893i	$0.547486\pi$
$440$	0.224767	+	10.6099i	0.0107153	+	0.505805i
$441$	26.8433	+	19.5028i	1.27825	+	0.928703i
$442$	−0.971058	−	2.98861i	−0.0461885	−	0.142154i
$443$	4.53428			0.215430			0.107715	−	0.994182i	$-0.465647\pi$
$443$	4.53428			0.215430			0.107715	+	0.994182i	$0.465647\pi$
$444$	−0.929402	−	2.86040i	−0.0441074	−	0.135749i
$445$	16.7908	+	5.06510i	0.795961	+	0.240109i
$446$	1.88091	−	5.78884i	0.0890636	−	0.274110i
$447$	4.21791	−	12.9814i	0.199500	−	0.613999i
$448$	3.82844	−	2.78153i	0.180877	−	0.131415i
$449$	−7.31892			−0.345401			−0.172700	−	0.984974i	$-0.555249\pi$
$449$	−7.31892			−0.345401			−0.172700	+	0.984974i	$0.555249\pi$
$450$	−1.64985	+	5.91996i	−0.0777747	+	0.279070i
$451$	3.72489			0.175398
$452$	−15.6778	+	11.3906i	−0.737423	+	0.535769i
$453$	3.13022	−	9.63383i	0.147071	−	0.452637i
$454$	4.54193	−	13.9786i	0.213163	−	0.656049i
$455$	−1.10783	−	52.2941i	−0.0519361	−	2.45158i
$456$	6.20087	+	19.0843i	0.290382	+	0.893704i
$457$	−18.0440			−0.844064			−0.422032	−	0.906581i	$-0.638683\pi$
$457$	−18.0440			−0.844064			−0.422032	+	0.906581i	$0.638683\pi$
$458$	−1.47925	−	4.55265i	−0.0691207	−	0.212732i
$459$	−4.23375	−	3.07600i	−0.197615	−	0.143575i
$460$	6.37800	−	9.18139i	0.297376	−	0.428085i
$461$	0.264494	−	0.192166i	0.0123187	−	0.00895008i	−0.581609	−	0.813469i	$-0.697577\pi$
$461$	0.264494	−	0.192166i	0.0123187	−	0.00895008i	0.593928	+	0.804519i	$0.297577\pi$
$462$	5.90102	+	4.28734i	0.274540	+	0.199465i
$463$	−13.8180	−	10.0393i	−0.642175	−	0.466568i	0.218422	−	0.975854i	$-0.429909\pi$
$463$	−13.8180	−	10.0393i	−0.642175	−	0.466568i	−0.860597	+	0.509287i	$0.829909\pi$
$464$	−10.7223	+	7.79021i	−0.497770	+	0.361651i
$465$	−0.672536	−	0.885596i	−0.0311881	−	0.0410685i
$466$	−0.807895	−	0.586970i	−0.0374250	−	0.0271909i
$467$	5.86791	+	18.0596i	0.271534	+	0.835697i	0.990116	+	0.140254i	$0.0447918\pi$
$467$	5.86791	+	18.0596i	0.271534	+	0.835697i	−0.718581	+	0.695443i	$0.755208\pi$
$468$	−13.1185			−0.606402
$469$	4.57278	+	14.0736i	0.211151	+	0.649857i
$470$	11.4887	−	16.5384i	0.529933	−	0.762860i
$471$	−1.65366	+	5.08943i	−0.0761964	+	0.234509i
$472$	0.136014	−	0.418608i	0.00626056	−	0.0192680i
$473$	−14.7154	+	10.6914i	−0.676615	+	0.491589i
$474$	0.0602965			0.00276951
$475$	−38.6323	+	1.63756i	−1.77257	+	0.0751365i
$476$	−7.75744			−0.355561
$477$	−4.92302	+	3.57678i	−0.225410	+	0.163770i
$478$	3.96389	−	12.1996i	0.181304	−	0.557996i
$479$	7.97791	−	24.5535i	0.364520	−	1.12188i	−0.585761	−	0.810484i	$-0.699204\pi$
$479$	7.97791	−	24.5535i	0.364520	−	1.12188i	0.950281	−	0.311394i	$-0.100796\pi$
$480$	−13.2413	+	4.61462i	−0.604378	+	0.210628i
$481$	−2.58250	−	7.94811i	−0.117752	−	0.362403i
$482$	−6.57340			−0.299410
$483$	−5.44794	−	16.7670i	−0.247890	−	0.762927i
$484$	−8.82539	−	6.41202i	−0.401154	−	0.291456i
$485$	15.7119	−	5.47563i	0.713439	−	0.248636i
$486$	8.44104	−	6.13278i	0.382893	−	0.278188i
$487$	17.9277	+	13.0252i	0.812381	+	0.590229i	0.914520	−	0.404541i	$-0.132569\pi$
$487$	17.9277	+	13.0252i	0.812381	+	0.590229i	−0.102139	+	0.994770i	$0.532569\pi$
$488$	8.49992	+	6.17555i	0.384773	+	0.279554i
$489$	10.7233	−	7.79092i	0.484924	−	0.352318i
$490$	26.2896	+	7.93048i	1.18764	+	0.358263i
$491$	0.877649	+	0.637650i	0.0396078	+	0.0287767i	0.607413	−	0.794386i	$-0.292207\pi$
$491$	0.877649	+	0.637650i	0.0396078	+	0.0287767i	−0.567805	+	0.823163i	$0.692207\pi$
$492$	0.972362	+	2.99262i	0.0438375	+	0.134918i
$493$	−8.97030			−0.404002
$494$	7.50957	+	23.1121i	0.337872	+	1.03986i
$495$	4.89159	+	6.44125i	0.219860	+	0.289513i
$496$	−0.209229	+	0.643941i	−0.00939467	+	0.0289138i
$497$	−5.61558	+	17.2830i	−0.251893	+	0.775248i
$498$	1.28827	−	0.935986i	0.0577289	−	0.0419425i
$499$	−14.1270			−0.632410			−0.316205	−	0.948691i	$-0.602409\pi$
$499$	−14.1270			−0.632410			−0.316205	+	0.948691i	$0.602409\pi$
$500$	−1.09697	−	17.2398i	−0.0490581	−	0.770986i
$501$	3.61976			0.161719
$502$	−4.34814	+	3.15911i	−0.194067	+	0.140998i
$503$	−11.8200	+	36.3782i	−0.527028	+	1.62202i	0.233243	+	0.972419i	$0.425066\pi$
$503$	−11.8200	+	36.3782i	−0.527028	+	1.62202i	−0.760271	+	0.649606i	$0.774934\pi$
$504$	6.76029	−	20.8060i	0.301127	−	0.926775i
$505$	−6.20932	−	8.17644i	−0.276311	−	0.363847i
$506$	1.33861	+	4.11981i	0.0595083	+	0.183148i
$507$	9.44892			0.419641
$508$	3.18336	+	9.79738i	0.141239	+	0.434688i
$509$	−5.06274	−	3.67830i	−0.224402	−	0.163038i	0.469904	−	0.882718i	$-0.344289\pi$
$509$	−5.06274	−	3.67830i	−0.224402	−	0.163038i	−0.694306	+	0.719680i	$0.744289\pi$
$510$	−1.56692	−	0.472674i	−0.0693842	−	0.0209303i
$511$	10.0724	−	7.31804i	0.445577	−	0.323731i
$512$	12.6234	+	9.17142i	0.557880	+	0.405323i
$513$	32.7413	+	23.7879i	1.44556	+	1.05026i
$514$	3.21175	−	2.33347i	0.141664	−	0.102925i
$515$	32.7916	−	11.4280i	1.44497	−	0.503576i
$516$	−12.4309	−	9.03161i	−0.547242	−	0.397594i
$517$	−8.18968	−	25.2052i	−0.360182	−	1.10853i
$518$	6.07412			0.266882
$519$	0.738764	+	2.27368i	0.0324281	+	0.0998035i
$520$	−23.5226	+	8.19769i	−1.03153	+	0.359492i
$521$	−10.7767	+	33.1673i	−0.472136	+	1.45309i	0.377644	+	0.925951i	$0.376734\pi$
$521$	−10.7767	+	33.1673i	−0.472136	+	1.45309i	−0.849781	+	0.527136i	$0.823266\pi$
$522$	3.40707	−	10.4859i	0.149123	−	0.458955i
$523$	10.1249	−	7.35620i	0.442733	−	0.321664i	−0.343987	−	0.938974i	$-0.611778\pi$
$523$	10.1249	−	7.35620i	0.442733	−	0.321664i	0.786720	+	0.617310i	$0.211778\pi$
$524$	−24.1301			−1.05413
$525$	−22.6979	−	15.0649i	−0.990617	−	0.657486i
$526$	−9.38014			−0.408994
$527$	−0.370744	+	0.269361i	−0.0161499	+	0.0117336i
$528$	−0.983441	+	3.02672i	−0.0427988	+	0.131721i
$529$	−3.87195	+	11.9166i	−0.168345	+	0.518114i
$530$	−2.87318	+	4.13605i	−0.124803	+	0.179659i
$531$	−0.103663	−	0.319041i	−0.00449858	−	0.0138452i
$532$	59.9913			2.60095
$533$	2.70187	+	8.31550i	0.117031	+	0.360184i
$534$	−4.64440	−	3.37435i	−0.200983	−	0.146022i
$535$	2.95890	+	3.89628i	0.127924	+	0.168451i
$536$	5.70139	−	4.14231i	0.246263	−	0.178920i
$537$	−4.11788	−	2.99182i	−0.177700	−	0.129106i
$538$	−7.58984	−	5.51434i	−0.327221	−	0.237740i
$539$	29.2374	−	21.2422i	1.25934	−	0.914966i
$540$	−10.3152	+	14.8491i	−0.443894	+	0.639004i
$541$	−18.2258	−	13.2418i	−0.783589	−	0.569310i	0.122465	−	0.992473i	$-0.460920\pi$
$541$	−18.2258	−	13.2418i	−0.783589	−	0.569310i	−0.906054	+	0.423162i	$0.860920\pi$
$542$	5.53349	+	17.0303i	0.237684	+	0.731515i
$543$	−18.2401			−0.782757
$544$	1.78570	+	5.49581i	0.0765611	+	0.235631i
$545$	−0.224113	−	10.5790i	−0.00959995	−	0.453154i
$546$	−5.29078	+	16.2834i	−0.226425	+	0.696863i
$547$	−1.22375	+	3.76632i	−0.0523238	+	0.161036i	−0.973804	−	0.227389i	$-0.926981\pi$
$547$	−1.22375	+	3.76632i	−0.0523238	+	0.161036i	0.921480	+	0.388426i	$0.126981\pi$
$548$	5.41786	−	3.93630i	0.231439	−	0.168151i
$549$	8.00749			0.341751
$550$	5.57706	+	3.70157i	0.237807	+	0.157836i
$551$	69.3709			2.95530
$552$	−6.79256	+	4.93508i	−0.289111	+	0.210051i
$553$	0.127810	−	0.393360i	0.00543505	−	0.0167274i
$554$	1.28569	−	3.95694i	0.0546236	−	0.168114i
$555$	−4.16716	−	1.25706i	−0.176886	−	0.0533592i
$556$	−9.38824	−	28.8940i	−0.398150	−	1.22538i
$557$	4.59054			0.194507			0.0972537	−	0.995260i	$-0.468994\pi$
$557$	4.59054			0.194507			0.0972537	+	0.995260i	$0.468994\pi$
$558$	−0.174057	−	0.535691i	−0.00736840	−	0.0226776i
$559$	−34.5414	−	25.0958i	−1.46095	−	1.06144i
$560$	0.351316	+	16.5835i	0.0148458	+	0.700779i
$561$	−1.74261	+	1.26608i	−0.0735730	+	0.0534539i
$562$	−7.38741	−	5.36727i	−0.311619	−	0.226405i
$563$	−18.7588	−	13.6291i	−0.790591	−	0.574398i	0.117548	−	0.993067i	$-0.462497\pi$
$563$	−18.7588	−	13.6291i	−0.790591	−	0.574398i	−0.908139	+	0.418670i	$0.862497\pi$
$564$	18.1123	−	13.1594i	0.762666	−	0.554110i
$565$	0.593997	+	28.0390i	0.0249897	+	1.17961i
$566$	9.87614	+	7.17544i	0.415125	+	0.301606i
$567$	0.329018	+	1.01261i	0.0138175	+	0.0425258i
$568$	8.65442			0.363131
$569$	12.4137	+	38.2053i	0.520408	+	1.60165i	0.773221	+	0.634136i	$0.218644\pi$
$569$	12.4137	+	38.2053i	0.520408	+	1.60165i	−0.252813	+	0.967515i	$0.581356\pi$
$570$	12.1176	+	3.65537i	0.507549	+	0.153107i
$571$	3.54937	−	10.9239i	0.148537	−	0.457149i	−0.848912	−	0.528534i	$-0.822742\pi$
$571$	3.54937	−	10.9239i	0.148537	−	0.457149i	0.997449	+	0.0713850i	$0.0227419\pi$
$572$	−4.41539	+	13.5892i	−0.184617	+	0.568192i
$573$	1.45246	−	1.05528i	0.0606775	−	0.0440848i
$574$	−6.35489			−0.265248
$575$	−5.64668	−	15.1614i	−0.235483	−	0.632274i
$576$	−1.71763			−0.0715679
$577$	27.4500	−	19.9436i	1.14276	−	0.830262i	0.155256	−	0.987874i	$-0.450380\pi$
$577$	27.4500	−	19.9436i	1.14276	−	0.830262i	0.987501	+	0.157613i	$0.0503797\pi$
$578$	−0.208423	+	0.641459i	−0.00866924	+	0.0266812i
$579$	7.51688	−	23.1346i	0.312391	−	0.961441i
$580$	0.656404	+	30.9848i	0.0272557	+	1.28657i
$581$	−3.37539	−	10.3884i	−0.140035	−	0.430983i
$582$	−5.44636			−0.225759
$583$	2.04814	+	6.30353i	0.0848253	+	0.261065i
$584$	−4.79688	−	3.48514i	−0.198496	−	0.144216i
$585$	−10.8314	+	15.5922i	−0.447823	+	0.644660i
$586$	−10.3618	+	7.52828i	−0.428041	+	0.310990i
$587$	7.43000	+	5.39821i	0.306669	+	0.222808i	0.730466	−	0.682949i	$-0.239303\pi$
$587$	7.43000	+	5.39821i	0.306669	+	0.222808i	−0.423797	+	0.905757i	$0.639303\pi$
$588$	24.6985	+	17.9445i	1.01855	+	0.740019i
$589$	2.86711	−	2.08308i	0.118137	−	0.0858317i
$590$	−0.167905	−	0.221097i	−0.00691252	−	0.00910242i
$591$	15.6963	+	11.4040i	0.645659	+	0.469099i
$592$	0.818960	+	2.52050i	0.0336590	+	0.103592i
$593$	−12.1712			−0.499810			−0.249905	−	0.968270i	$-0.580399\pi$
$593$	−12.1712			−0.499810			−0.249905	+	0.968270i	$0.580399\pi$
$594$	−2.16494	−	6.66299i	−0.0888284	−	0.273386i
$595$	−6.40500	+	9.22026i	−0.262579	+	0.377994i
$596$	−6.00539	+	18.4827i	−0.245990	+	0.757080i
$597$	−6.19136	+	19.0551i	−0.253396	+	0.779871i
$598$	−8.22615	+	5.97665i	−0.336392	+	0.244403i
$599$	28.1034			1.14828			0.574138	−	0.818759i	$-0.305337\pi$
$599$	28.1034			1.14828			0.574138	+	0.818759i	$0.305337\pi$
$600$	−3.48300	+	12.4976i	−0.142193	+	0.510213i
$601$	14.7698			0.602471			0.301236	−	0.953550i	$-0.402601\pi$
$601$	14.7698			0.602471			0.301236	+	0.953550i	$0.402601\pi$
$602$	25.1054	−	18.2401i	1.02322	−	0.743411i
$603$	1.65976	−	5.10821i	0.0675906	−	0.208023i
$604$	−4.45676	+	13.7165i	−0.181343	+	0.558116i
$605$	−14.9079	+	5.19545i	−0.606092	+	0.211225i
$606$	1.03851	+	3.19620i	0.0421866	+	0.129837i
$607$	12.1969			0.495057			0.247528	−	0.968881i	$-0.420382\pi$
$607$	12.1969			0.495057			0.247528	+	0.968881i	$0.420382\pi$
$608$	−13.8095	−	42.5012i	−0.560048	−	1.72365i
$609$	39.5402	+	28.7277i	1.60225	+	1.16410i
$610$	6.25783	−	2.18087i	0.253372	−	0.0883010i
$611$	50.3281	−	36.5655i	2.03606	−	1.47928i
$612$	2.27793	+	1.65501i	0.0920799	+	0.0669000i
$613$	13.4094	+	9.74248i	0.541599	+	0.393495i	0.824679	−	0.565601i	$-0.191356\pi$
$613$	13.4094	+	9.74248i	0.541599	+	0.393495i	−0.283079	+	0.959097i	$0.591356\pi$
$614$	−10.1511	+	7.37522i	−0.409666	+	0.297639i
$615$	4.35978	+	1.31517i	0.175803	+	0.0530326i
$616$	−19.2772	−	14.0057i	−0.776700	−	0.564306i
$617$	−2.01203	−	6.19239i	−0.0810012	−	0.249296i	0.902352	−	0.431000i	$-0.141839\pi$
$617$	−2.01203	−	6.19239i	−0.0810012	−	0.249296i	−0.983353	+	0.181703i	$0.941839\pi$
$618$	−11.3669			−0.457242
$619$	−1.24019	−	3.81692i	−0.0498476	−	0.153415i	0.923034	−	0.384718i	$-0.125701\pi$
$619$	−1.24019	−	3.81692i	−0.0498476	−	0.153415i	−0.972882	+	0.231303i	$0.925701\pi$
$620$	0.957545	+	1.26090i	0.0384559	+	0.0506388i
$621$	−5.23270	+	16.1046i	−0.209981	+	0.646255i
$622$	0.699035	−	2.15141i	0.0280288	−	0.0862636i
$623$	−31.8582	+	23.1463i	−1.27637	+	0.927337i
$624$	−7.47023			−0.299049
$625$	−21.3964	−	12.9303i	−0.855856	−	0.517214i
$626$	−19.7837			−0.790716
$627$	13.4763	−	9.79109i	0.538191	−	0.391019i
$628$	2.35445	−	7.24624i	0.0939526	−	0.289156i
$629$	−0.554293	+	1.70594i	−0.0221011	+	0.0680202i
$630$	−8.34534	−	10.9892i	−0.332486	−	0.437819i
$631$	3.91785	+	12.0579i	0.155967	+	0.480017i	0.998258	−	0.0590067i	$-0.0187933\pi$
$631$	3.91785	+	12.0579i	0.155967	+	0.480017i	−0.842291	+	0.539024i	$0.818793\pi$
$632$	−0.196974			−0.00783521
$633$	−2.51221	−	7.73178i	−0.0998513	−	0.307311i
$634$	−5.58821	−	4.06007i	−0.221936	−	0.161246i
$635$	14.2732	+	4.30565i	0.566416	+	0.170864i
$636$	−4.52967	+	3.29100i	−0.179613	+	0.130497i
$637$	68.6288	+	49.8618i	2.71917	+	1.97560i
$638$	−9.71537	−	7.05863i	−0.384635	−	0.279454i
$639$	5.33623	−	3.87700i	0.211098	−	0.153372i
$640$	23.0610	−	8.03684i	0.911567	−	0.317684i
$641$	−13.3819	−	9.72252i	−0.528553	−	0.384017i	0.291263	−	0.956643i	$-0.405925\pi$
$641$	−13.3819	−	9.72252i	−0.528553	−	0.384017i	−0.819816	+	0.572627i	$0.805925\pi$
$642$	−0.494877	−	1.52307i	−0.0195312	−	0.0601109i
$643$	−39.9620			−1.57595			−0.787973	−	0.615710i	$-0.788869\pi$
$643$	−39.9620			−1.57595			−0.787973	+	0.615710i	$0.788869\pi$
$644$	7.75669	+	23.8726i	0.305656	+	0.940713i
$645$	−20.9984	+	7.31802i	−0.826812	+	0.288147i
$646$	1.61181	−	4.96065i	0.0634160	−	0.195174i
$647$	−4.71046	+	14.4973i	−0.185187	+	0.569948i	−0.999952	−	0.00984433i	$-0.996866\pi$
$647$	−4.71046	+	14.4973i	−0.185187	+	0.569948i	0.814764	+	0.579793i	$0.196866\pi$
$648$	0.410223	−	0.298045i	0.0161151	−	0.0117083i
$649$	−0.365379			−0.0143424
$650$	−4.21809	+	15.1353i	−0.165447	+	0.593654i
$651$	2.49684			0.0978590
$652$	−15.2676	+	11.0926i	−0.597926	+	0.434419i
$653$	0.723446	−	2.22654i	0.0283106	−	0.0871311i	−0.935903	−	0.352258i	$-0.885414\pi$
$653$	0.723446	−	2.22654i	0.0283106	−	0.0871311i	0.964213	+	0.265127i	$0.0854139\pi$
$654$	−1.07032	+	3.29409i	−0.0418527	+	0.128809i
$655$	−19.9232	+	28.6803i	−0.778465	+	1.12063i
$656$	−0.856815	−	2.63701i	−0.0334530	−	0.102958i
$657$	−4.51898			−0.176302
$658$	13.9721	+	43.0017i	0.544689	+	1.67638i
$659$	38.7921	+	28.1841i	1.51112	+	1.09790i	0.965676	+	0.259751i	$0.0836406\pi$
$659$	38.7921	+	28.1841i	1.51112	+	1.09790i	0.545448	+	0.838145i	$0.316359\pi$
$660$	4.50075	+	5.92659i	0.175191	+	0.230692i
$661$	12.2839	−	8.92480i	0.477790	−	0.347135i	−0.322680	−	0.946508i	$-0.604584\pi$
$661$	12.2839	−	8.92480i	0.477790	−	0.347135i	0.800469	+	0.599374i	$0.204584\pi$
$662$	5.12847	+	3.72605i	0.199324	+	0.144817i
$663$	−4.09042	−	2.97187i	−0.158859	−	0.115418i
$664$	−4.20848	+	3.05764i	−0.163321	+	0.118659i
$665$	49.5323	−	71.3038i	1.92078	−	2.76504i
$666$	−1.78364	−	1.29589i	−0.0691145	−	0.0502146i
$667$	8.96944	+	27.6051i	0.347298	+	1.06887i
$668$	−5.15375			−0.199405
$669$	−3.02632	−	9.31407i	−0.117004	−	0.360103i
$670$	−0.0941470	−	4.44410i	−0.00363721	−	0.171691i
$671$	2.69514	−	8.29480i	0.104045	−	0.320217i
$672$	9.72931	−	29.9437i	0.375316	−	1.15510i
$673$	−12.5911	+	9.14798i	−0.485352	+	0.352629i	−0.803394	−	0.595448i	$-0.796975\pi$
$673$	−12.5911	+	9.14798i	−0.485352	+	0.352629i	0.318042	+	0.948077i	$0.396975\pi$
$674$	7.12819			0.274567
$675$	9.13240	+	24.5206i	0.351506	+	0.943799i
$676$	−13.4532			−0.517431
$677$	−38.8042	+	28.1929i	−1.49137	+	1.08354i	−0.517702	+	0.855561i	$0.673212\pi$
$677$	−38.8042	+	28.1929i	−1.49137	+	1.08354i	−0.973666	+	0.227981i	$0.926788\pi$
$678$	2.83680	−	8.73079i	0.108947	−	0.335304i
$679$	−11.5446	+	35.5307i	−0.443042	+	1.36354i
$680$	5.11874	+	1.54411i	0.196295	+	0.0592140i
$681$	−7.30782	−	22.4912i	−0.280036	−	0.861863i
$682$	−0.613496			−0.0234920
$683$	4.43667	+	13.6547i	0.169765	+	0.522481i	0.999356	−	0.0358897i	$-0.0114265\pi$
$683$	4.43667	+	13.6547i	0.169765	+	0.522481i	−0.829591	+	0.558371i	$0.811427\pi$
$684$	−17.6161	−	12.7989i	−0.673570	−	0.489377i
$685$	−0.205270	−	9.68955i	−0.00784298	−	0.370219i
$686$	−30.7037	+	22.3075i	−1.17227	+	0.851705i
$687$	−6.23109	−	4.52715i	−0.237731	−	0.172722i
$688$	10.9538	+	7.95837i	0.417608	+	0.303410i
$689$	−12.5864	+	9.14459i	−0.479505	+	0.348381i
$690$	0.112165	+	5.29464i	0.00427006	+	0.201563i
$691$	−14.5934	−	10.6027i	−0.555160	−	0.403347i	0.274524	−	0.961580i	$-0.411480\pi$
$691$	−14.5934	−	10.6027i	−0.555160	−	0.403347i	−0.829684	+	0.558233i	$0.811480\pi$
$692$	−1.05184	−	3.23723i	−0.0399849	−	0.123061i
$693$	−18.1604			−0.689857
$694$	2.13681	+	6.57643i	0.0811122	+	0.249638i
$695$	−42.0941	−	12.6980i	−1.59672	−	0.481664i
$696$	7.19266	−	22.1367i	0.272637	−	0.839091i
$697$	0.579914	−	1.78479i	0.0219658	−	0.0676038i
$698$	1.09629	−	0.796503i	0.0414953	−	0.0301481i
$699$	−1.60674			−0.0607724
$700$	32.3169	+	21.4491i	1.22146	+	0.810701i
$701$	−44.8280			−1.69313			−0.846566	−	0.532284i	$-0.821334\pi$
$701$	−44.8280			−1.69313			−0.846566	+	0.532284i	$0.821334\pi$
$702$	13.3042	−	9.66606i	0.502134	−	0.364822i
$703$	4.28656	−	13.1927i	0.161671	−	0.497571i
$704$	−0.578116	+	1.77926i	−0.0217886	+	0.0670583i
$705$	−0.686235	−	32.3929i	−0.0258451	−	1.21999i
$706$	6.81801	+	20.9837i	0.256599	+	0.789731i
$707$	23.0526			0.866982
$708$	−0.0953802	−	0.293550i	−0.00358461	−	0.0110323i
$709$	21.5958	+	15.6903i	0.811048	+	0.589261i	0.914134	−	0.405411i	$-0.132872\pi$
$709$	21.5958	+	15.6903i	0.811048	+	0.589261i	−0.103086	+	0.994672i	$0.532872\pi$
$710$	3.11434	−	4.48321i	0.116879	−	0.168252i
$711$	−0.121452	+	0.0882403i	−0.00455482	+	0.00330927i
$712$	15.1721	+	11.0232i	0.568599	+	0.413112i
$713$	1.19964	+	0.871588i	0.0449268	+	0.0326412i
$714$	2.97300	−	2.16001i	0.111262	−	0.0808363i
$715$	12.5061	+	16.4680i	0.467701	+	0.615869i
$716$	5.86297	+	4.25969i	0.219109	+	0.159192i
$717$	−6.37777	−	19.6288i	−0.238182	−	0.733049i
$718$	14.9377			0.557471
$719$	−11.4162	−	35.1355i	−0.425754	−	1.31033i	−0.902271	−	0.431170i	$-0.858101\pi$
$719$	−11.4162	−	35.1355i	−0.425754	−	1.31033i	0.476517	−	0.879165i	$-0.341899\pi$
$720$	3.43484	−	4.94460i	0.128009	−	0.184274i
$721$	−24.0943	+	74.1546i	−0.897319	+	2.76166i
$722$	−8.50475	+	26.1749i	−0.316514	+	0.974130i
$723$	−8.55649	+	6.21665i	−0.318219	+	0.231200i
$724$	25.9699			0.965164
$725$	37.3696	+	24.8027i	1.38787	+	0.921149i
$726$	5.16767			0.191790
$727$	−30.7882	+	22.3689i	−1.14187	+	0.829618i	−0.987379	−	0.158376i	$-0.949374\pi$
$727$	−30.7882	+	22.3689i	−1.14187	+	0.829618i	−0.154493	+	0.987994i	$0.549374\pi$
$728$	17.2837	−	53.1938i	0.640577	−	1.97149i
$729$	5.38422	−	16.5709i	0.199416	−	0.613738i
$730$	−3.53158	+	1.23077i	−0.130709	+	0.0455527i
$731$	2.83181	+	8.71542i	0.104738	+	0.322352i
$732$	7.36769			0.272318
$733$	10.9548	+	33.7153i	0.404624	+	1.24530i	0.921209	+	0.389068i	$0.127203\pi$
$733$	10.9548	+	33.7153i	0.404624	+	1.24530i	−0.516586	+	0.856236i	$0.672797\pi$
$734$	−17.6606	−	12.8312i	−0.651865	−	0.473608i
$735$	41.7208	−	14.5398i	1.53890	−	0.536310i
$736$	15.1272	−	10.9906i	0.557596	−	0.405117i
$737$	−4.73286	−	3.43862i	−0.174337	−	0.126663i
$738$	1.86608	+	1.35579i	0.0686914	+	0.0499072i
$739$	−25.9199	+	18.8319i	−0.953480	+	0.692744i	−0.951627	−	0.307254i	$-0.900590\pi$
$739$	−25.9199	+	18.8319i	−0.953480	+	0.692744i	−0.00185273	+	0.999998i	$0.500590\pi$
$740$	5.93313	+	1.78978i	0.218106	+	0.0657936i
$741$	31.6329	+	22.9826i	1.16206	+	0.844287i
$742$	−3.49425	−	10.7542i	−0.128278	−	0.394799i
$743$	−21.3456			−0.783095			−0.391548	−	0.920158i	$-0.628060\pi$
$743$	−21.3456			−0.783095			−0.391548	+	0.920158i	$0.628060\pi$
$744$	−0.367451	−	1.13090i	−0.0134714	−	0.0414607i
$745$	17.0096	+	22.3982i	0.623182	+	0.820608i
$746$	0.0635385	−	0.195552i	0.00232631	−	0.00715965i
$747$	−1.22515	+	3.77062i	−0.0448259	+	0.137960i
$748$	2.48110	−	1.80262i	0.0907179	−	0.0659104i
$749$	−10.9852			−0.401389
$750$	5.22072	+	6.30161i	0.190634	+	0.230102i
$751$	19.5208			0.712325			0.356163	−	0.934424i	$-0.384085\pi$
$751$	19.5208			0.712325			0.356163	+	0.934424i	$0.384085\pi$
$752$	−15.9600	+	11.5956i	−0.582002	+	0.422849i
$753$	−2.67224	+	8.22432i	−0.0973819	+	0.299711i
$754$	8.71069	−	26.8087i	0.317225	−	0.976317i
$755$	12.6232	+	16.6223i	0.459407	+	0.604948i
$756$	−12.5449	−	38.6093i	−0.456255	−	1.40421i
$757$	6.64499			0.241516			0.120758	−	0.992682i	$-0.461467\pi$
$757$	6.64499			0.241516			0.120758	+	0.992682i	$0.461467\pi$
$758$	−5.34591	−	16.4530i	−0.194172	−	0.597601i
$759$	5.63866	+	4.09673i	0.204670	+	0.148702i
$760$	−39.5852	−	11.9412i	−1.43591	−	0.433153i
$761$	17.8007	−	12.9330i	0.645276	−	0.468820i	−0.216383	−	0.976309i	$-0.569426\pi$
$761$	17.8007	−	12.9330i	0.645276	−	0.468820i	0.861659	+	0.507488i	$0.169426\pi$
$762$	−3.94803	−	2.86841i	−0.143022	−	0.103911i
$763$	19.2211	+	13.9650i	0.695851	+	0.505566i
$764$	−2.06799	+	1.50248i	−0.0748173	+	0.0543580i
$765$	3.84790	−	1.34100i	0.139121	−	0.0484841i
$766$	0.133428	+	0.0969412i	0.00482096	+	0.00350263i
$767$	−0.265030	−	0.815678i	−0.00956967	−	0.0294524i
$768$	−10.0396			−0.362271
$769$	1.43915	+	4.42926i	0.0518972	+	0.159723i	0.973646	−	0.228064i	$-0.0732395\pi$
$769$	1.43915	+	4.42926i	0.0518972	+	0.159723i	−0.921749	+	0.387787i	$0.873240\pi$
$770$	−14.1923	+	4.94607i	−0.511455	+	0.178244i
$771$	1.97385	−	6.07489i	0.0710865	−	0.218782i

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:	\( N \)	\(=\)	\( 425 = 5^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	425.k (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.545657 - 0.396443i) q^{2} +(0.335346 - 1.03209i) q^{3} +(-0.477459 + 1.46947i) q^{4} +(1.35235 + 1.78077i) q^{5} +(-0.226180 - 0.696112i) q^{6} -5.02070 q^{7} +(0.738877 + 2.27403i) q^{8} +(1.47430 + 1.07114i) q^{9} +(1.44389 + 0.435563i) q^{10} +(1.60579 - 1.16668i) q^{11} +(1.35651 + 0.985560i) q^{12} +(3.76928 + 2.73854i) q^{13} +(-2.73958 + 1.99042i) q^{14} +(2.29142 - 0.798567i) q^{15} +(-1.19531 - 0.868444i) q^{16} +(-0.309017 - 0.951057i) q^{17} +1.22911 q^{18} +(2.38975 + 7.35489i) q^{19} +(-3.26248 + 1.13699i) q^{20} +(-1.68367 + 5.18180i) q^{21} +(0.413692 - 1.27321i) q^{22} +(-2.61778 + 1.90193i) q^{23} +2.59478 q^{24} +(-1.34231 + 4.81645i) q^{25} +3.14241 q^{26} +(4.23375 - 3.07600i) q^{27} +(2.39718 - 7.37776i) q^{28} +(2.77198 - 8.53126i) q^{29} +(0.933743 - 1.34416i) q^{30} +(-0.141612 - 0.435836i) q^{31} -5.77863 q^{32} +(-0.665618 - 2.04856i) q^{33} +(-0.545657 - 0.396443i) q^{34} +(-6.78973 - 8.94073i) q^{35} +(-2.27793 + 1.65501i) q^{36} +(-1.45116 - 1.05433i) q^{37} +(4.21978 + 3.06585i) q^{38} +(4.09042 - 2.97187i) q^{39} +(-3.05031 + 4.39105i) q^{40} +(1.51824 + 1.10306i) q^{41} +(1.13558 + 3.49497i) q^{42} -9.16394 q^{43} +(0.947695 + 2.91670i) q^{44} +(0.0863057 + 4.07396i) q^{45} +(-0.674405 + 2.07560i) q^{46} +(4.12605 - 12.6987i) q^{47} +(-1.29715 + 0.942437i) q^{48} +18.2074 q^{49} +(1.17701 + 3.16028i) q^{50} -1.08520 q^{51} +(-5.82388 + 4.23129i) q^{52} +(-1.03188 + 3.17579i) q^{53} +(1.09072 - 3.35689i) q^{54} +(4.24918 + 1.28180i) q^{55} +(-3.70968 - 11.4172i) q^{56} +8.39228 q^{57} +(-1.86961 - 5.75408i) q^{58} +(-0.148926 - 0.108201i) q^{59} +(0.0794099 + 3.74845i) q^{60} +(3.55488 - 2.58277i) q^{61} +(-0.250056 - 0.181676i) q^{62} +(-7.40203 - 5.37789i) q^{63} +(-0.762532 + 0.554012i) q^{64} +(0.220653 + 10.4157i) q^{65} +(-1.17534 - 0.853933i) q^{66} +(-0.910785 - 2.80311i) q^{67} +1.54509 q^{68} +(1.08510 + 3.33958i) q^{69} +(-7.24936 - 2.18683i) q^{70} +(1.11849 - 3.44235i) q^{71} +(-1.34648 + 4.14405i) q^{72} +(-2.00618 + 1.45757i) q^{73} -1.20982 q^{74} +(4.52086 + 3.00056i) q^{75} -11.9488 q^{76} +(-8.06221 + 5.85754i) q^{77} +(1.05379 - 3.24324i) q^{78} +(-0.0254567 + 0.0783476i) q^{79} +(-0.0699735 - 3.30302i) q^{80} +(-0.0655323 - 0.201688i) q^{81} +1.26574 q^{82} +(0.672295 + 2.06911i) q^{83} +(-6.81061 - 4.94820i) q^{84} +(1.27572 - 1.83645i) q^{85} +(-5.00037 + 3.63298i) q^{86} +(-7.87544 - 5.72184i) q^{87} +(3.83954 + 2.78959i) q^{88} +(6.34536 - 4.61018i) q^{89} +(1.66219 + 2.18877i) q^{90} +(-18.9244 - 13.7494i) q^{91} +(-1.54494 - 4.75484i) q^{92} -0.497310 q^{93} +(-2.78290 - 8.56488i) q^{94} +(-9.86563 + 14.2020i) q^{95} +(-1.93784 + 5.96405i) q^{96} +(2.29941 - 7.07684i) q^{97} +(9.93502 - 7.21821i) q^{98} +3.61711 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 2 q^{2} + 2 q^{3} - 20 q^{4} - 17 q^{6} - 44 q^{7} + 15 q^{8} - 22 q^{9} - 2 q^{10} + 4 q^{11} + 14 q^{12} + 6 q^{13} - 10 q^{14} + 14 q^{15} - 32 q^{16} + 20 q^{17} - 62 q^{18} - 3 q^{19} + 16 q^{21}+ \cdots + 76 q^{99}+O(q^{100}) \) 80 * q + 2 * q^2 + 2 * q^3 - 20 * q^4 - 17 * q^6 - 44 * q^7 + 15 * q^8 - 22 * q^9 - 2 * q^10 + 4 * q^11 + 14 * q^12 + 6 * q^13 - 10 * q^14 + 14 * q^15 - 32 * q^16 + 20 * q^17 - 62 * q^18 - 3 * q^19 + 16 * q^21 + 17 * q^22 - 5 * q^23 + 30 * q^24 - 14 * q^25 + 18 * q^26 + 17 * q^27 + 32 * q^28 + 20 * q^29 - 114 * q^30 - 21 * q^31 - 88 * q^32 - 2 * q^34 - 2 * q^35 + 47 * q^36 + 6 * q^37 + 22 * q^38 - 46 * q^39 + 59 * q^40 - 26 * q^41 - 3 * q^42 - 102 * q^43 - 44 * q^44 + 74 * q^45 + 2 * q^46 + 2 * q^47 + 72 * q^48 + 108 * q^49 + 7 * q^50 + 18 * q^51 + 65 * q^52 - 18 * q^53 - 29 * q^54 - 49 * q^55 - 117 * q^56 + 2 * q^57 + 42 * q^58 + 21 * q^59 + 112 * q^60 + 4 * q^61 + 15 * q^62 + 41 * q^63 - 11 * q^64 + 8 * q^65 - 156 * q^66 + 21 * q^67 - 80 * q^68 - 67 * q^69 + 32 * q^70 - 4 * q^71 + 83 * q^72 - 2 * q^73 + 78 * q^74 - 68 * q^75 + 16 * q^76 + 2 * q^77 - 2 * q^78 - 53 * q^79 - 54 * q^80 - 21 * q^81 - 72 * q^82 - 42 * q^83 - 52 * q^84 + 42 * q^86 - 8 * q^87 + 68 * q^88 - 73 * q^89 + 97 * q^90 - 83 * q^91 + 117 * q^92 - 120 * q^93 + 80 * q^94 + 16 * q^95 + 88 * q^96 + 57 * q^97 + 17 * q^98 + 76 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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