LMFDB - Embedded newform 425.2.k.c.86.10

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			86.10
Character	$\chi$	$=$	425.86
Dual form			425.2.k.c.341.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.0822620 + 0.0597668i) q^{2} +(-0.947924 + 2.91741i) q^{3} +(-0.614839 + 1.89228i) q^{4} +(1.94015 - 1.11167i) q^{5} +(-0.0963862 - 0.296646i) q^{6} -3.50410 q^{7} +(-0.125360 - 0.385819i) q^{8} +(-5.18567 - 3.76761i) q^{9} +(-0.0931599 + 0.207405i) q^{10} +(-2.78840 + 2.02589i) q^{11} +(-4.93773 - 3.58747i) q^{12} +(5.10738 + 3.71073i) q^{13} +(0.288254 - 0.209429i) q^{14} +(1.40408 + 6.71400i) q^{15} +(-3.18597 - 2.31474i) q^{16} +(-0.309017 - 0.951057i) q^{17} +0.651761 q^{18} +(-1.07692 - 3.31441i) q^{19} +(0.910707 + 4.35481i) q^{20} +(3.32162 - 10.2229i) q^{21} +(0.108298 - 0.333308i) q^{22} +(-1.72797 + 1.25544i) q^{23} +1.24442 q^{24} +(2.52838 - 4.31361i) q^{25} -0.641922 q^{26} +(8.46218 - 6.14813i) q^{27} +(2.15446 - 6.63073i) q^{28} +(-1.77238 + 5.45482i) q^{29} +(-0.516776 - 0.468389i) q^{30} +(-0.432855 - 1.33219i) q^{31} +1.21178 q^{32} +(-3.26716 - 10.0553i) q^{33} +(0.0822620 + 0.0597668i) q^{34} +(-6.79849 + 3.89540i) q^{35} +(10.3177 - 7.49626i) q^{36} +(6.09623 + 4.42917i) q^{37} +(0.286681 + 0.208286i) q^{38} +(-15.6671 + 11.3828i) q^{39} +(-0.672121 - 0.609189i) q^{40} +(-6.41466 - 4.66052i) q^{41} +(0.337747 + 1.03948i) q^{42} +1.10370 q^{43} +(-2.11914 - 6.52203i) q^{44} +(-14.2493 - 1.54499i) q^{45} +(0.0671123 - 0.206550i) q^{46} +(-1.23200 + 3.79171i) q^{47} +(9.77310 - 7.10057i) q^{48} +5.27870 q^{49} +(0.0498211 + 0.505960i) q^{50} +3.06755 q^{51} +(-10.1620 + 7.38310i) q^{52} +(-3.24860 + 9.99815i) q^{53} +(-0.328661 + 1.01151i) q^{54} +(-3.15780 + 7.03032i) q^{55} +(0.439275 + 1.35195i) q^{56} +10.6903 q^{57} +(-0.180218 - 0.554654i) q^{58} +(-4.30237 - 3.12586i) q^{59} +(-13.5680 - 1.47112i) q^{60} +(0.335913 - 0.244055i) q^{61} +(0.115228 + 0.0837183i) q^{62} +(18.1711 + 13.2021i) q^{63} +(6.27225 - 4.55706i) q^{64} +(14.0342 + 1.52167i) q^{65} +(0.869737 + 0.631901i) q^{66} +(1.55629 + 4.78976i) q^{67} +1.98966 q^{68} +(-2.02466 - 6.23126i) q^{69} +(0.326441 - 0.726767i) q^{70} +(-0.272326 + 0.838134i) q^{71} +(-0.803538 + 2.47304i) q^{72} +(-8.95860 + 6.50880i) q^{73} -0.766205 q^{74} +(10.1879 + 11.4653i) q^{75} +6.93393 q^{76} +(9.77083 - 7.09892i) q^{77} +(0.608493 - 1.87275i) q^{78} +(-4.72915 + 14.5548i) q^{79} +(-8.75449 - 0.949210i) q^{80} +(3.97287 + 12.2272i) q^{81} +0.806227 q^{82} +(2.14543 + 6.60294i) q^{83} +(17.3023 + 12.5709i) q^{84} +(-1.65680 - 1.50167i) q^{85} +(-0.0907928 + 0.0659649i) q^{86} +(-14.2339 - 10.3415i) q^{87} +(1.13118 + 0.821852i) q^{88} +(-4.72607 + 3.43369i) q^{89} +(1.26452 - 0.724542i) q^{90} +(-17.8968 - 13.0028i) q^{91} +(-1.31323 - 4.04170i) q^{92} +4.29686 q^{93} +(-0.125272 - 0.385547i) q^{94} +(-5.77392 - 5.23329i) q^{95} +(-1.14867 + 3.53525i) q^{96} +(-2.27449 + 7.00015i) q^{97} +(-0.434237 + 0.315491i) q^{98} +22.0925 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 $

$2$	−0.0822620	+	0.0597668i	−0.0581680	+	0.0422615i	−0.616489	−	0.787363i	$-0.711446\pi$
$2$	−0.0822620	+	0.0597668i	−0.0581680	+	0.0422615i	0.558321	+	0.829625i	$0.311446\pi$
$3$	−0.947924	+	2.91741i	−0.547284	+	1.68437i	0.168213	+	0.985751i	$0.446200\pi$
$3$	−0.947924	+	2.91741i	−0.547284	+	1.68437i	−0.715497	+	0.698616i	$0.753800\pi$
$4$	−0.614839	+	1.89228i	−0.307420	+	0.946140i
$5$	1.94015	−	1.11167i	0.867663	−	0.497153i
$5$	1.94015	−	1.11167i	0.867663	−	0.497153i
$6$	−0.0963862	−	0.296646i	−0.0393495	−	0.121105i
$7$	−3.50410			−1.32442			−0.662212	−	0.749316i	$-0.730382\pi$
$7$	−3.50410			−1.32442			−0.662212	+	0.749316i	$0.730382\pi$
$8$	−0.125360	−	0.385819i	−0.0443215	−	0.136408i
$9$	−5.18567	−	3.76761i	−1.72856	−	1.25587i
$10$	−0.0931599	+	0.207405i	−0.0294597	+	0.0655872i
$11$	−2.78840	+	2.02589i	−0.840735	+	0.610829i	−0.922576	−	0.385816i	$-0.873920\pi$
$11$	−2.78840	+	2.02589i	−0.840735	+	0.610829i	0.0818412	+	0.996645i	$0.473920\pi$
$12$	−4.93773	−	3.58747i	−1.42540	−	1.03561i
$13$	5.10738	+	3.71073i	1.41653	+	1.02917i	0.992332	+	0.123604i	$0.0394452\pi$
$13$	5.10738	+	3.71073i	1.41653	+	1.02917i	0.424202	+	0.905568i	$0.360555\pi$
$14$	0.288254	−	0.209429i	0.0770391	−	0.0559722i
$15$	1.40408	+	6.71400i	0.362531	+	1.73355i
$16$	−3.18597	−	2.31474i	−0.796492	−	0.578685i
$17$	−0.309017	−	0.951057i	−0.0749476	−	0.230665i
$17$	−0.309017	−	0.951057i	−0.0749476	−	0.230665i
$18$	0.651761			0.153622
$19$	−1.07692	−	3.31441i	−0.247062	−	0.760379i	−0.995290	−	0.0969375i	$-0.969095\pi$
$19$	−1.07692	−	3.31441i	−0.247062	−	0.760379i	0.748229	−	0.663441i	$-0.230905\pi$
$20$	0.910707	+	4.35481i	0.203640	+	0.973765i
$21$	3.32162	−	10.2229i	0.724836	−	2.23082i
$22$	0.108298	−	0.333308i	0.0230893	−	0.0710614i
$23$	−1.72797	+	1.25544i	−0.360307	+	0.261778i	−0.753180	−	0.657815i	$-0.771481\pi$
$23$	−1.72797	+	1.25544i	−0.360307	+	0.261778i	0.392873	+	0.919593i	$0.371481\pi$
$24$	1.24442			0.254017
$25$	2.52838	−	4.31361i	0.505677	−	0.862723i
$26$	−0.641922			−0.125891
$27$	8.46218	−	6.14813i	1.62855	−	1.18321i
$28$	2.15446	−	6.63073i	0.407154	−	1.25309i
$29$	−1.77238	+	5.45482i	−0.329123	+	1.01293i	0.640423	+	0.768023i	$0.278759\pi$
$29$	−1.77238	+	5.45482i	−0.329123	+	1.01293i	−0.969545	+	0.244912i	$0.921241\pi$
$30$	−0.516776	−	0.468389i	−0.0943500	−	0.0855158i
$31$	−0.432855	−	1.33219i	−0.0777431	−	0.239269i	0.904630	−	0.426197i	$-0.140147\pi$
$31$	−0.432855	−	1.33219i	−0.0777431	−	0.239269i	−0.982374	+	0.186928i	$0.940147\pi$
$32$	1.21178			0.214214
$33$	−3.26716	−	10.0553i	−0.568740	−	1.75040i
$34$	0.0822620	+	0.0597668i	0.0141078	+	0.0102499i
$35$	−6.79849	+	3.89540i	−1.14915	+	0.658442i
$36$	10.3177	−	7.49626i	1.71962	−	1.24938i
$37$	6.09623	+	4.42917i	1.00221	+	0.728151i	0.962562	−	0.271063i	$-0.0873751\pi$
$37$	6.09623	+	4.42917i	1.00221	+	0.728151i	0.0396518	+	0.999214i	$0.487375\pi$
$38$	0.286681	+	0.208286i	0.0465059	+	0.0337885i
$39$	−15.6671	+	11.3828i	−2.50875	+	1.82271i
$40$	−0.672121	−	0.609189i	−0.106272	−	0.0963212i
$41$	−6.41466	−	4.66052i	−1.00180	−	0.727851i	−0.0393279	−	0.999226i	$-0.512522\pi$
$41$	−6.41466	−	4.66052i	−1.00180	−	0.727851i	−0.962474	+	0.271375i	$0.912522\pi$
$42$	0.337747	+	1.03948i	0.0521154	+	0.160395i
$43$	1.10370			0.168313			0.0841566	−	0.996453i	$-0.473180\pi$
$43$	1.10370			0.168313			0.0841566	+	0.996453i	$0.473180\pi$
$44$	−2.11914	−	6.52203i	−0.319472	−	0.983233i
$45$	−14.2493	−	1.54499i	−2.12416	−	0.230313i
$46$	0.0671123	−	0.206550i	0.00989517	−	0.0304542i
$47$	−1.23200	+	3.79171i	−0.179706	+	0.553078i	−0.999817	−	0.0191260i	$-0.993912\pi$
$47$	−1.23200	+	3.79171i	−0.179706	+	0.553078i	0.820111	+	0.572204i	$0.193912\pi$
$48$	9.77310	−	7.10057i	1.41063	−	1.02488i
$49$	5.27870			0.754100
$50$	0.0498211	+	0.505960i	0.00704577	+	0.0715535i
$51$	3.06755			0.429542
$52$	−10.1620	+	7.38310i	−1.40921	+	1.02385i
$53$	−3.24860	+	9.99815i	−0.446229	+	1.37335i	0.434901	+	0.900478i	$0.356783\pi$
$53$	−3.24860	+	9.99815i	−0.446229	+	1.37335i	−0.881130	+	0.472873i	$0.843217\pi$
$54$	−0.328661	+	1.01151i	−0.0447251	+	0.137650i
$55$	−3.15780	+	7.03032i	−0.425798	+	0.947968i
$56$	0.439275	+	1.35195i	0.0587005	+	0.180662i
$57$	10.6903			1.41597
$58$	−0.180218	−	0.554654i	−0.0236638	−	0.0728296i
$59$	−4.30237	−	3.12586i	−0.560121	−	0.406952i	0.271382	−	0.962472i	$-0.412519\pi$
$59$	−4.30237	−	3.12586i	−0.560121	−	0.406952i	−0.831503	+	0.555520i	$0.812519\pi$
$60$	−13.5680	−	1.47112i	−1.75163	−	0.189921i
$61$	0.335913	−	0.244055i	0.0430092	−	0.0312480i	−0.566073	−	0.824355i	$-0.691538\pi$
$61$	0.335913	−	0.244055i	0.0430092	−	0.0312480i	0.609082	+	0.793107i	$0.291538\pi$
$62$	0.115228	+	0.0837183i	0.0146340	+	0.0106322i
$63$	18.1711	+	13.2021i	2.28934	+	1.66330i
$64$	6.27225	−	4.55706i	0.784031	−	0.569632i
$65$	14.0342	+	1.52167i	1.74073	+	0.188739i
$66$	0.869737	+	0.631901i	0.107057	+	0.0777816i
$67$	1.55629	+	4.78976i	0.190131	+	0.585163i	0.999999	−	0.00144935i	$-0.000461342\pi$
$67$	1.55629	+	4.78976i	0.190131	+	0.585163i	−0.809868	+	0.586612i	$0.800461\pi$
$68$	1.98966			0.241282
$69$	−2.02466	−	6.23126i	−0.243740	−	0.750155i
$70$	0.326441	−	0.726767i	0.0390172	−	0.0868653i
$71$	−0.272326	+	0.838134i	−0.0323192	+	0.0994682i	−0.965915	−	0.258860i	$-0.916653\pi$
$71$	−0.272326	+	0.838134i	−0.0323192	+	0.0994682i	0.933596	+	0.358328i	$0.116653\pi$
$72$	−0.803538	+	2.47304i	−0.0946979	+	0.291450i
$73$	−8.95860	+	6.50880i	−1.04852	+	0.761798i	−0.971931	−	0.235265i	$-0.924404\pi$
$73$	−8.95860	+	6.50880i	−1.04852	+	0.761798i	−0.0765933	+	0.997062i	$0.524404\pi$
$74$	−0.766205			−0.0890695
$75$	10.1879	+	11.4653i	1.17639	+	1.32390i
$76$	6.93393			0.795376
$77$	9.77083	−	7.09892i	1.11349	−	0.808998i
$78$	0.608493	−	1.87275i	0.0688983	−	0.212047i
$79$	−4.72915	+	14.5548i	−0.532070	+	1.63754i	0.217825	+	0.975988i	$0.430104\pi$
$79$	−4.72915	+	14.5548i	−0.532070	+	1.63754i	−0.749895	+	0.661556i	$0.769896\pi$
$80$	−8.75449	−	0.949210i	−0.978782	−	0.106125i
$81$	3.97287	+	12.2272i	0.441430	+	1.35858i
$82$	0.806227			0.0890329
$83$	2.14543	+	6.60294i	0.235491	+	0.724767i	0.997056	+	0.0766784i	$0.0244315\pi$
$83$	2.14543	+	6.60294i	0.235491	+	0.724767i	−0.761565	+	0.648089i	$0.775569\pi$
$84$	17.3023	+	12.5709i	1.88784	+	1.37159i
$85$	−1.65680	−	1.50167i	−0.179705	−	0.162879i
$86$	−0.0907928	+	0.0659649i	−0.00979044	+	0.00711317i
$87$	−14.2339	−	10.3415i	−1.52603	−	1.10873i
$88$	1.13118	+	0.821852i	0.120584	+	0.0876097i
$89$	−4.72607	+	3.43369i	−0.500962	+	0.363970i	−0.809384	−	0.587279i	$-0.800199\pi$
$89$	−4.72607	+	3.43369i	−0.500962	+	0.363970i	0.308422	+	0.951250i	$0.400199\pi$
$90$	1.26452	−	0.724542i	0.133292	−	0.0763735i
$91$	−17.8968	−	13.0028i	−1.87609	−	1.36306i
$92$	−1.31323	−	4.04170i	−0.136913	−	0.421376i
$93$	4.29686			0.445564
$94$	−0.125272	−	0.385547i	−0.0129208	−	0.0397661i
$95$	−5.77392	−	5.23329i	−0.592391	−	0.536924i
$96$	−1.14867	+	3.53525i	−0.117236	+	0.360815i
$97$	−2.27449	+	7.00015i	−0.230939	+	0.710757i	0.766695	+	0.642011i	$0.221900\pi$
$97$	−2.27449	+	7.00015i	−0.230939	+	0.710757i	−0.997634	+	0.0687461i	$0.978100\pi$
$98$	−0.434237	+	0.315491i	−0.0438645	+	0.0318694i
$99$	22.0925			2.22038
$100$	6.60802	+	7.43659i	0.660802	+	0.743659i
$101$	15.1685			1.50933			0.754663	−	0.656112i	$-0.227800\pi$
$101$	15.1685			1.50933			0.754663	+	0.656112i	$0.227800\pi$
$102$	−0.252342	+	0.183337i	−0.0249856	+	0.0181531i
$103$	2.73910	−	8.43009i	0.269892	−	0.830642i	−0.720634	−	0.693316i	$-0.756149\pi$
$103$	2.73910	−	8.43009i	0.269892	−	0.830642i	0.990526	−	0.137326i	$-0.0438509\pi$
$104$	0.791408	−	2.43570i	0.0776040	−	0.238840i
$105$	−4.92002	−	23.5265i	−0.480145	−	2.29595i
$106$	−0.330322	−	1.01663i	−0.0320837	−	0.0987434i
$107$	12.7136			1.22907			0.614536	−	0.788889i	$-0.289343\pi$
$107$	12.7136			1.22907			0.614536	+	0.788889i	$0.289343\pi$
$108$	6.43111	+	19.7929i	0.618834	+	1.90457i
$109$	3.05778	+	2.22161i	0.292882	+	0.212791i	0.724517	−	0.689257i	$-0.242063\pi$
$109$	3.05778	+	2.22161i	0.292882	+	0.212791i	−0.431635	+	0.902049i	$0.642063\pi$
$110$	−0.160413	−	0.767060i	−0.0152947	−	0.0731363i
$111$	−18.7005	+	13.5867i	−1.77497	+	1.28959i
$112$	11.1639	+	8.11108i	1.05489	+	0.766425i
$113$	−13.5495	−	9.84428i	−1.27463	−	0.926072i	−0.275251	−	0.961372i	$-0.588761\pi$
$113$	−13.5495	−	9.84428i	−1.27463	−	0.926072i	−0.999377	+	0.0353008i	$0.988761\pi$
$114$	−0.879408	+	0.638927i	−0.0823641	+	0.0598410i
$115$	−1.95689	+	4.35668i	−0.182481	+	0.406263i
$116$	−9.23232	−	6.70767i	−0.857200	−	0.622792i
$117$	−12.5046	−	38.4852i	−1.15605	−	3.55796i
$118$	0.540744			0.0497795
$119$	1.08283	+	3.33260i	0.0992625	+	0.305499i
$120$	2.41437	−	1.38339i	0.220401	−	0.126285i
$121$	0.271756	−	0.836378i	0.0247051	−	0.0760343i
$122$	−0.0130465	+	0.0401529i	−0.00118117	+	0.00363527i
$123$	19.6773	−	14.2964i	1.77424	−	1.28906i
$124$	2.78702			0.250281
$125$	0.110142	−	11.1798i	0.00985137	−	0.999951i
$126$	−2.28383			−0.203460
$127$	−3.46271	+	2.51581i	−0.307266	+	0.223242i	−0.730723	−	0.682675i	$-0.760817\pi$
$127$	−3.46271	+	2.51581i	−0.307266	+	0.223242i	0.423456	+	0.905916i	$0.360817\pi$
$128$	−0.992526	+	3.05468i	−0.0877278	+	0.269998i
$129$	−1.04623	+	3.21996i	−0.0921151	+	0.283501i
$130$	−1.24543	+	0.713605i	−0.109231	+	0.0625873i
$131$	1.07038	+	3.29430i	0.0935198	+	0.287824i	0.986865	−	0.161546i	$-0.0516482\pi$
$131$	1.07038	+	3.29430i	0.0935198	+	0.287824i	−0.893345	+	0.449371i	$0.851648\pi$
$132$	21.0362			1.83097
$133$	3.77363	+	11.6140i	0.327215	+	1.00706i
$134$	−0.414292	−	0.301001i	−0.0357894	−	0.0260025i
$135$	9.58323	−	21.3354i	0.824793	−	1.83626i
$136$	−0.328197	+	0.238449i	−0.0281427	+	0.0204469i
$137$	−2.62270	−	1.90550i	−0.224072	−	0.162798i	0.470086	−	0.882621i	$-0.344223\pi$
$137$	−2.62270	−	1.90550i	−0.224072	−	0.162798i	−0.694158	+	0.719823i	$0.744223\pi$
$138$	0.538975	+	0.391588i	0.0458806	+	0.0333342i
$139$	8.66193	−	6.29326i	0.734696	−	0.533788i	−0.156350	−	0.987702i	$-0.549973\pi$
$139$	8.66193	−	6.29326i	0.734696	−	0.533788i	0.891045	+	0.453914i	$0.149973\pi$
$140$	−3.19121	−	15.2597i	−0.269706	−	1.28968i
$141$	−9.89414	−	7.18851i	−0.833237	−	0.605382i
$142$	−0.0276905	−	0.0852227i	−0.00232374	−	0.00715173i
$143$	−21.7590			−1.81958
$144$	7.80033	+	24.0069i	0.650027	+	2.00058i
$145$	2.62527	+	12.5535i	0.218017	+	1.04251i
$146$	0.347942	−	1.07085i	0.0287958	−	0.0886245i
$147$	−5.00381	+	15.4001i	−0.412707	+	1.27018i
$148$	−12.1294	+	8.81254i	−0.997032	+	0.724386i
$149$	−4.24652			−0.347889			−0.173944	−	0.984755i	$-0.555651\pi$
$149$	−4.24652			−0.347889			−0.173944	+	0.984755i	$0.555651\pi$
$150$	−1.52332	−	0.334263i	−0.124378	−	0.0272924i
$151$	−5.87104			−0.477779			−0.238889	−	0.971047i	$-0.576783\pi$
$151$	−5.87104			−0.477779			−0.238889	+	0.971047i	$0.576783\pi$
$152$	−1.14376	+	0.830991i	−0.0927713	+	0.0674023i
$153$	−1.98075	+	6.09612i	−0.160134	+	0.492842i
$154$	−0.379488	+	1.16794i	−0.0305800	+	0.0941155i
$155$	−2.32076	−	2.10346i	−0.186408	−	0.168954i
$156$	−11.9068	−	36.6452i	−0.953303	−	2.93396i
$157$	25.0260			1.99729			0.998647	−	0.0520047i	$-0.0165611\pi$
$157$	25.0260			1.99729			0.998647	+	0.0520047i	$0.0165611\pi$
$158$	−0.480866	−	1.47995i	−0.0382556	−	0.117739i
$159$	−26.0893	−	18.9550i	−2.06901	−	1.50323i
$160$	2.35103	−	1.34709i	0.185865	−	0.106497i
$161$	6.05497	−	4.39920i	0.477199	−	0.346705i
$162$	−1.05760	−	0.768391i	−0.0830929	−	0.0603705i
$163$	13.0716	+	9.49706i	1.02384	+	0.743867i	0.967068	−	0.254520i	$-0.0819175\pi$
$163$	13.0716	+	9.49706i	1.02384	+	0.743867i	0.0567775	+	0.998387i	$0.481917\pi$
$164$	12.7630	−	9.27286i	0.996623	−	0.724089i
$165$	−17.5170	−	15.8768i	−1.36369	−	1.23601i
$166$	−0.571124	−	0.414946i	−0.0443278	−	0.0322060i
$167$	0.359577	+	1.10666i	0.0278249	+	0.0856362i	0.964005	−	0.265886i	$-0.0856643\pi$
$167$	0.359577	+	1.10666i	0.0278249	+	0.0856362i	−0.936180	+	0.351522i	$0.885664\pi$
$168$	−4.36058			−0.336426
$169$	8.29862	+	25.5405i	0.638355	+	1.96466i
$170$	0.226042	+	0.0245087i	0.0173366	+	0.00187973i
$171$	−6.90287	+	21.2448i	−0.527876	+	1.62463i
$172$	−0.678600	+	2.08852i	−0.0517428	+	0.159248i
$173$	−20.9877	+	15.2485i	−1.59567	+	1.15932i	−0.700434	+	0.713717i	$0.747010\pi$
$173$	−20.9877	+	15.2485i	−1.59567	+	1.15932i	−0.895231	+	0.445601i	$0.852990\pi$
$174$	1.78898			0.135623
$175$	−8.85971	+	15.1153i	−0.669731	+	1.14261i
$176$	13.5732			1.02312
$177$	13.1977	−	9.58871i	0.992002	−	0.720732i
$178$	0.183555	−	0.564924i	0.0137580	−	0.0423429i
$179$	1.13623	−	3.49696i	0.0849258	−	0.261375i	−0.899572	−	0.436773i	$-0.856121\pi$
$179$	1.13623	−	3.49696i	0.0849258	−	0.261375i	0.984498	+	0.175398i	$0.0561213\pi$
$180$	11.6846	−	26.0138i	0.870918	−	1.93895i
$181$	3.30862	+	10.1829i	0.245927	+	0.756887i	0.995483	+	0.0949449i	$0.0302675\pi$
$181$	3.30862	+	10.1829i	0.245927	+	0.756887i	−0.749555	+	0.661942i	$0.769732\pi$
$182$	2.24936			0.166733
$183$	0.393589	+	1.21134i	0.0290949	+	0.0895449i
$184$	0.700993	+	0.509301i	0.0516779	+	0.0375462i
$185$	16.7514	+	1.81628i	1.23159	+	0.133535i
$186$	−0.353468	+	0.256810i	−0.0259176	+	0.0188302i
$187$	2.78840	+	2.02589i	0.203908	+	0.148148i
$188$	−6.41750	−	4.66259i	−0.468044	−	0.340054i
$189$	−29.6523	+	21.5437i	−2.15689	+	1.56707i
$190$	0.787751	+	0.0854123i	0.0571495	+	0.00619646i
$191$	14.2279	+	10.3372i	1.02949	+	0.747971i	0.968207	−	0.250149i	$-0.0804795\pi$
$191$	14.2279	+	10.3372i	1.02949	+	0.747971i	0.0612869	+	0.998120i	$0.480480\pi$
$192$	7.34919	+	22.6185i	0.530382	+	1.63235i
$193$	5.18040			0.372893			0.186447	−	0.982465i	$-0.440303\pi$
$193$	5.18040			0.372893			0.186447	+	0.982465i	$0.440303\pi$
$194$	−0.231273	−	0.711785i	−0.0166044	−	0.0511032i
$195$	−17.7427	+	39.5011i	−1.27058	+	2.82873i
$196$	−3.24555	+	9.98878i	−0.231825	+	0.713485i
$197$	6.52675	−	20.0873i	0.465012	−	1.43116i	−0.393956	−	0.919129i	$-0.628894\pi$
$197$	6.52675	−	20.0873i	0.465012	−	1.43116i	0.858968	−	0.512029i	$-0.171106\pi$
$198$	−1.81737	+	1.32040i	−0.129155	+	0.0938365i
$199$	3.70626			0.262730			0.131365	−	0.991334i	$-0.458064\pi$
$199$	3.70626			0.262730			0.131365	+	0.991334i	$0.458064\pi$
$200$	−1.98123	−	0.434744i	−0.140094	−	0.0307410i
$201$	−15.4489			−1.08968
$202$	−1.24779	+	0.906576i	−0.0877945	+	0.0637864i
$203$	6.21059	−	19.1142i	0.435898	−	1.34156i
$204$	−1.88605	+	5.80465i	−0.132050	+	0.406407i
$205$	−17.6264	−	1.91115i	−1.23108	−	0.133480i
$206$	0.278516	+	0.857184i	0.0194051	+	0.0597228i
$207$	13.6907			0.951569
$208$	−7.68258	−	23.6445i	−0.532691	−	1.63945i
$209$	9.71752	+	7.06019i	0.672175	+	0.488364i
$210$	1.81083	+	1.64128i	0.124959	+	0.113259i
$211$	−20.5354	+	14.9198i	−1.41372	+	1.02712i	−0.420946	+	0.907086i	$0.638302\pi$
$211$	−20.5354	+	14.9198i	−1.41372	+	1.02712i	−0.992769	+	0.120038i	$0.961698\pi$
$212$	−16.9219	−	12.2945i	−1.16220	−	0.844390i
$213$	−2.18704	−	1.58897i	−0.149853	−	0.108875i
$214$	−1.04585	+	0.759852i	−0.0714926	+	0.0519424i
$215$	2.14135	−	1.22695i	0.146039	−	0.0836775i
$216$	−3.43289	−	2.49414i	−0.233578	−	0.169705i
$217$	1.51677	+	4.66813i	0.102965	+	0.316893i
$218$	−0.384317			−0.0260292
$219$	−10.4968	−	32.3057i	−0.709306	−	2.18302i
$220$	−11.3618	−	10.2980i	−0.766012	−	0.694288i
$221$	1.95085	−	6.00409i	0.131228	−	0.403879i
$222$	0.726304	−	2.23533i	0.0487463	−	0.150026i
$223$	10.5998	−	7.70120i	0.709814	−	0.515710i	−0.173300	−	0.984869i	$-0.555443\pi$
$223$	10.5998	−	7.70120i	0.709814	−	0.515710i	0.883114	+	0.469159i	$0.155443\pi$
$224$	−4.24619			−0.283710
$225$	−29.3634	+	12.8430i	−1.95756	+	0.856200i
$226$	1.70297			0.113280
$227$	1.61938	−	1.17655i	0.107482	−	0.0780902i	−0.532746	−	0.846275i	$-0.678840\pi$
$227$	1.61938	−	1.17655i	0.107482	−	0.0780902i	0.640228	+	0.768185i	$0.278840\pi$
$228$	−6.57284	+	20.2291i	−0.435297	+	1.33971i
$229$	7.05507	−	21.7133i	0.466212	−	1.43485i	−0.391240	−	0.920289i	$-0.627954\pi$
$229$	7.05507	−	21.7133i	0.466212	−	1.43485i	0.857452	−	0.514564i	$-0.172046\pi$
$230$	−0.0994076	−	0.475346i	−0.00655474	−	0.0313434i
$231$	11.4485	+	35.2348i	0.753254	+	2.31828i
$232$	2.32676			0.152759
$233$	−5.85541	−	18.0211i	−0.383601	−	1.18060i	−0.937490	−	0.348012i	$-0.886857\pi$
$233$	−5.85541	−	18.0211i	−0.383601	−	1.18060i	0.553889	−	0.832590i	$-0.313143\pi$
$234$	3.32879	+	2.41851i	0.217610	+	0.158103i
$235$	1.82486	+	8.72608i	0.119041	+	0.569227i
$236$	8.56026	−	6.21940i	0.557226	−	0.404848i
$237$	−37.9795	−	27.5937i	−2.46703	−	1.79240i
$238$	−0.288254	−	0.209429i	−0.0186847	−	0.0135753i
$239$	13.6489	−	9.91648i	0.882872	−	0.641444i	−0.0511377	−	0.998692i	$-0.516285\pi$
$239$	13.6489	−	9.91648i	0.882872	−	0.641444i	0.934010	+	0.357248i	$0.116285\pi$
$240$	11.0678	−	24.6406i	0.714425	−	1.59055i
$241$	13.4680	+	9.78509i	0.867552	+	0.630313i	0.929929	−	0.367739i	$-0.119868\pi$
$241$	13.4680	+	9.78509i	0.867552	+	0.630313i	−0.0623772	+	0.998053i	$0.519868\pi$
$242$	0.0276325	+	0.0850440i	0.00177628	+	0.00546684i
$243$	−8.05837			−0.516945
$244$	0.255288	+	0.785696i	0.0163431	+	0.0502990i
$245$	10.2415	−	5.86817i	0.654305	−	0.374904i
$246$	−0.764242	+	2.35209i	−0.0487263	+	0.149964i
$247$	6.79866	−	20.9241i	0.432589	−	1.33137i
$248$	−0.459722	+	0.334008i	−0.0291924	+	0.0212095i
$249$	−21.2972			−1.34965
$250$	0.659120	+	0.926255i	0.0416864	+	0.0585815i
$251$	5.98008			0.377460			0.188730	−	0.982029i	$-0.439563\pi$
$251$	5.98008			0.377460			0.188730	+	0.982029i	$0.439563\pi$
$252$	−36.1543	+	26.2676i	−2.27751	+	1.65471i
$253$	2.27488	−	7.00136i	0.143020	−	0.440172i
$254$	0.134488	−	0.413911i	0.00843851	−	0.0259711i
$255$	5.95151	−	3.41009i	0.372698	−	0.213548i
$256$	4.69065	+	14.4363i	0.293166	+	0.902271i
$257$	−1.41662			−0.0883662			−0.0441831	−	0.999023i	$-0.514069\pi$
$257$	−1.41662			−0.0883662			−0.0441831	+	0.999023i	$0.514069\pi$
$258$	−0.106382	−	0.327410i	−0.00662304	−	0.0203836i
$259$	−21.3618	−	15.5202i	−1.32736	−	0.964381i
$260$	−11.5082	+	25.6211i	−0.713708	+	1.58895i
$261$	29.7426	−	21.6093i	1.84102	−	1.33758i
$262$	−0.284942	−	0.207022i	−0.0176038	−	0.0127899i
$263$	−8.13930	−	5.91354i	−0.501890	−	0.364645i	0.307848	−	0.951435i	$-0.400391\pi$
$263$	−8.13930	−	5.91354i	−0.501890	−	0.364645i	−0.809739	+	0.586791i	$0.800391\pi$
$264$	−3.46995	+	2.52107i	−0.213561	+	0.155161i
$265$	4.81186	+	23.0093i	0.295590	+	1.41345i
$266$	−1.00456	−	0.729855i	−0.0615935	−	0.0447503i
$267$	−5.53753	−	17.0428i	−0.338891	−	1.04300i
$268$	−10.0204			−0.612096
$269$	2.45136	+	7.54452i	0.149462	+	0.459997i	0.997558	−	0.0698459i	$-0.0222508\pi$
$269$	2.45136	+	7.54452i	0.149462	+	0.459997i	−0.848096	+	0.529843i	$0.822251\pi$
$270$	0.486817	+	2.32786i	0.0296267	+	0.141669i
$271$	9.35822	−	28.8016i	0.568472	−	1.74958i	−0.0889328	−	0.996038i	$-0.528346\pi$
$271$	9.35822	−	28.8016i	0.568472	−	1.74958i	0.657404	−	0.753538i	$-0.271654\pi$
$272$	−1.21693	+	3.74533i	−0.0737873	+	0.227094i
$273$	54.8992	−	39.8866i	3.32265	−	2.41405i
$274$	0.329634			0.0199139
$275$	1.68877	+	17.1503i	0.101836	+	1.03420i
$276$	13.0361			0.784682
$277$	−0.696894	+	0.506323i	−0.0418723	+	0.0304220i	−0.608525	−	0.793535i	$-0.708238\pi$
$277$	−0.696894	+	0.506323i	−0.0418723	+	0.0304220i	0.566652	+	0.823957i	$0.308238\pi$
$278$	−0.336419	+	1.03539i	−0.0201771	+	0.0620987i
$279$	−2.77453	+	8.53913i	−0.166107	+	0.511224i
$280$	2.35518	+	2.13466i	0.140749	+	0.127570i
$281$	−6.23872	−	19.2008i	−0.372171	−	1.14542i	−0.945368	−	0.326006i	$-0.894297\pi$
$281$	−6.23872	−	19.2008i	−0.372171	−	1.14542i	0.573197	−	0.819418i	$-0.305703\pi$
$282$	1.24355			0.0740521
$283$	0.394815	+	1.21511i	0.0234693	+	0.0722311i	0.962105	−	0.272679i	$-0.0879096\pi$
$283$	0.394815	+	1.21511i	0.0234693	+	0.0722311i	−0.938636	+	0.344910i	$0.887910\pi$
$284$	−1.41855	−	1.03064i	−0.0841753	−	0.0611570i
$285$	20.7409	−	11.8841i	1.22858	−	0.703954i
$286$	1.78994	−	1.30046i	0.105841	−	0.0768981i
$287$	22.4776	+	16.3309i	1.32681	+	0.963984i
$288$	−6.28387	−	4.56550i	−0.370281	−	0.269025i
$289$	−0.809017	+	0.587785i	−0.0475892	+	0.0345756i
$290$	−0.966242	−	0.875770i	−0.0567397	−	0.0514270i
$291$	−18.2663	−	13.2712i	−1.07079	−	0.777972i
$292$	−6.80838	−	20.9540i	−0.398430	−	1.22624i
$293$	−12.6880			−0.741239			−0.370619	−	0.928785i	$-0.620855\pi$
$293$	−12.6880			−0.741239			−0.370619	+	0.928785i	$0.620855\pi$
$294$	−0.508794	−	1.56591i	−0.0296735	−	0.0913256i
$295$	−11.8222	−	1.28183i	−0.688314	−	0.0746308i
$296$	0.944633	−	2.90728i	0.0549057	−	0.168982i
$297$	−11.1405	+	34.2869i	−0.646437	+	1.98953i
$298$	0.349327	−	0.253801i	0.0202360	−	0.0147023i
$299$	−13.4840			−0.779801
$300$	−27.9595	+	12.2290i	−1.61424	+	0.706040i
$301$	−3.86749			−0.222918
$302$	0.482964	−	0.350894i	0.0277914	−	0.0201917i
$303$	−14.3786	+	44.2529i	−0.826030	+	2.54226i
$304$	−4.24098	+	13.0524i	−0.243237	+	0.748606i
$305$	0.380414	−	0.846928i	0.0217824	−	0.0484950i
$306$	−0.201405	−	0.619861i	−0.0115136	−	0.0354351i
$307$	6.50877			0.371475			0.185737	−	0.982599i	$-0.440533\pi$
$307$	6.50877			0.371475			0.185737	+	0.982599i	$0.440533\pi$
$308$	7.42566	+	22.8538i	0.423116	+	1.30222i
$309$	21.9976	+	15.9822i	1.25140	+	0.909194i
$310$	0.316628	+	0.0343305i	0.0179832	+	0.00194984i
$311$	22.1093	−	16.0633i	1.25370	−	0.910869i	0.255273	−	0.966869i	$-0.417835\pi$
$311$	22.1093	−	16.0633i	1.25370	−	0.910869i	0.998431	+	0.0560003i	$0.0178348\pi$
$312$	6.35575	+	4.61772i	0.359824	+	0.261427i
$313$	6.96580	+	5.06095i	0.393730	+	0.286062i	0.766982	−	0.641668i	$-0.221757\pi$
$313$	6.96580	+	5.06095i	0.393730	+	0.286062i	−0.373252	+	0.927730i	$0.621757\pi$
$314$	−2.05869	+	1.49573i	−0.116179	+	0.0844087i
$315$	49.9310	+	5.41379i	2.81329	+	0.305033i
$316$	−24.6341	−	17.8977i	−1.38578	−	1.00683i
$317$	7.06516	+	21.7443i	0.396819	+	1.22128i	0.927536	+	0.373734i	$0.121923\pi$
$317$	7.06516	+	21.7443i	0.396819	+	1.22128i	−0.530717	+	0.847549i	$0.678077\pi$
$318$	3.27903			0.183879
$319$	−6.10878	−	18.8009i	−0.342026	−	1.05265i
$320$	7.10319	−	15.8141i	0.397080	−	0.884032i
$321$	−12.0515	+	37.0908i	−0.672651	+	2.07021i
$322$	−0.235168	+	0.723773i	−0.0131054	+	0.0403343i
$323$	−2.81941	+	2.04842i	−0.156876	+	0.113977i
$324$	−25.5800			−1.42111
$325$	28.9201	−	12.6491i	1.60420	−	0.701647i
$326$	−1.64290			−0.0909920
$327$	−9.37987	+	6.81488i	−0.518708	+	0.376864i
$328$	−0.993976	+	3.05914i	−0.0548831	+	0.168913i
$329$	4.31706	−	13.2865i	0.238007	−	0.732511i
$330$	2.38989	+	0.259125i	0.131559	+	0.0142643i
$331$	−0.391859	−	1.20602i	−0.0215385	−	0.0662887i	0.939710	−	0.341974i	$-0.111095\pi$
$331$	−0.391859	−	1.20602i	−0.0215385	−	0.0662887i	−0.961248	+	0.275685i	$0.911095\pi$
$332$	−13.8137			−0.758126
$333$	−14.9256	−	45.9364i	−0.817919	−	2.51730i
$334$	−0.0957212	−	0.0695455i	−0.00523763	−	0.00380536i
$335$	8.34407	+	7.56279i	0.455885	+	0.413200i
$336$	−34.2459	+	24.8811i	−1.86827	+	1.35738i
$337$	−11.0832	−	8.05244i	−0.603742	−	0.438644i	0.243463	−	0.969910i	$-0.421717\pi$
$337$	−11.0832	−	8.05244i	−0.603742	−	0.438644i	−0.847205	+	0.531266i	$0.821717\pi$
$338$	−2.20914	−	1.60503i	−0.120161	−	0.0873022i
$339$	41.5637	−	30.1978i	2.25743	−	1.64012i
$340$	3.86025	−	2.21184i	0.209351	−	0.119954i
$341$	3.90585	+	2.83777i	0.211514	+	0.153674i
$342$	−0.701893	−	2.16021i	−0.0379540	−	0.116811i
$343$	6.03159			0.325675
$344$	−0.138361	−	0.425830i	−0.00745990	−	0.0229592i
$345$	−10.8552	−	9.83884i	−0.584427	−	0.529705i
$346$	0.815138	−	2.50874i	0.0438221	−	0.134870i
$347$	−2.72201	+	8.37747i	−0.146125	+	0.449726i	−0.997154	−	0.0753923i	$-0.975979\pi$
$347$	−2.72201	+	8.37747i	−0.146125	+	0.449726i	0.851029	+	0.525119i	$0.175979\pi$
$348$	28.3206	−	20.5761i	1.51814	−	1.10299i
$349$	4.45931			0.238701			0.119351	−	0.992852i	$-0.461919\pi$
$349$	4.45931			0.238701			0.119351	+	0.992852i	$0.461919\pi$
$350$	−0.174578	−	1.77293i	−0.00933159	−	0.0947673i
$351$	66.0336			3.52461
$352$	−3.37892	+	2.45493i	−0.180097	+	0.130848i
$353$	−5.74969	+	17.6957i	−0.306025	+	0.941848i	0.673268	+	0.739399i	$0.264890\pi$
$353$	−5.74969	+	17.6957i	−0.306025	+	0.941848i	−0.979293	+	0.202449i	$0.935110\pi$
$354$	−0.512584	+	1.57757i	−0.0272435	+	0.0838470i
$355$	0.403373	+	1.92885i	0.0214088	+	0.102372i
$356$	−3.59173	−	11.0542i	−0.190361	−	0.585872i
$357$	−10.7490			−0.568896
$358$	0.115533	+	0.355575i	0.00610613	+	0.0187927i
$359$	20.6888	+	15.0313i	1.09191	+	0.793321i	0.979721	−	0.200365i	$-0.0642129\pi$
$359$	20.6888	+	15.0313i	1.09191	+	0.793321i	0.112192	+	0.993687i	$0.464213\pi$
$360$	1.19021	+	5.69134i	0.0627296	+	0.299960i
$361$	5.54574	−	4.02922i	0.291881	−	0.212064i
$362$	−0.880771	−	0.639918i	−0.0462923	−	0.0336333i
$363$	2.18245	+	1.58564i	0.114549	+	0.0832248i
$364$	35.6085	−	25.8711i	1.86639	−	1.35601i
$365$	−10.1454	+	22.5871i	−0.531035	+	1.18226i
$366$	−0.104775	−	0.0761238i	−0.00547670	−	0.00397905i
$367$	0.490243	+	1.50881i	0.0255905	+	0.0787594i	0.963036	−	0.269372i	$-0.0868162\pi$
$367$	0.490243	+	1.50881i	0.0255905	+	0.0787594i	−0.937446	+	0.348132i	$0.886816\pi$
$368$	8.41128			0.438468
$369$	15.7053	+	48.3358i	0.817583	+	2.51626i
$370$	−1.48655	+	0.851766i	−0.0772823	+	0.0442812i
$371$	11.3834	−	35.0345i	0.590997	−	1.81890i
$372$	−2.64188	+	8.13087i	−0.136975	+	0.421566i
$373$	−19.2024	+	13.9513i	−0.994261	+	0.722373i	−0.960850	−	0.277069i	$-0.910637\pi$
$373$	−19.2024	+	13.9513i	−0.994261	+	0.722373i	−0.0334108	+	0.999442i	$0.510637\pi$
$374$	−0.350460			−0.0181219
$375$	32.5116	+	10.9189i	1.67889	+	0.563851i
$376$	1.61736			0.0834090
$377$	−29.2936	+	21.2830i	−1.50870	+	1.09613i
$378$	1.15166	−	3.54445i	0.0592350	−	0.182307i
$379$	1.43308	−	4.41057i	0.0736124	−	0.226556i	−0.907480	−	0.420095i	$-0.861997\pi$
$379$	1.43308	−	4.41057i	0.0736124	−	0.226556i	0.981093	+	0.193539i	$0.0619967\pi$
$380$	13.4529	−	7.70823i	0.690118	−	0.395424i
$381$	−4.05725	−	12.4869i	−0.207859	−	0.639726i
$382$	−1.78823			−0.0914940
$383$	−9.30640	−	28.6421i	−0.475535	−	1.46355i	−0.845235	−	0.534394i	$-0.820540\pi$
$383$	−9.30640	−	28.6421i	−0.475535	−	1.46355i	0.369701	−	0.929151i	$-0.379460\pi$
$384$	−7.97092	−	5.79121i	−0.406764	−	0.295532i
$385$	11.0653	−	24.6349i	0.563937	−	1.25551i
$386$	−0.426150	+	0.309616i	−0.0216905	+	0.0157590i
$387$	−5.72344	−	4.15832i	−0.290939	−	0.211379i
$388$	−11.8478	−	8.60793i	−0.601481	−	0.437001i
$389$	−6.95352	+	5.05203i	−0.352558	+	0.256148i	−0.749941	−	0.661504i	$-0.769918\pi$
$389$	−6.95352	+	5.05203i	−0.352558	+	0.256148i	0.397384	+	0.917653i	$0.369918\pi$
$390$	−0.901307	−	4.30986i	−0.0456395	−	0.218238i
$391$	1.72797	+	1.25544i	0.0873872	+	0.0634905i
$392$	−0.661740	−	2.03662i	−0.0334229	−	0.102865i
$393$	−10.6255			−0.535984
$394$	0.663649	+	2.04250i	0.0334341	+	0.102900i
$395$	7.00487	+	33.4958i	0.352453	+	1.68536i
$396$	−13.5833	+	41.8052i	−0.682587	+	2.10079i
$397$	−6.99873	+	21.5399i	−0.351256	+	1.08105i	0.606893	+	0.794784i	$0.292416\pi$
$397$	−6.99873	+	21.5399i	−0.351256	+	1.08105i	−0.958149	+	0.286271i	$0.907584\pi$
$398$	−0.304884	+	0.221511i	−0.0152825	+	0.0111034i
$399$	−37.4600			−1.87534
$400$	−18.0403	+	7.89048i	−0.902013	+	0.394524i
$401$	1.77578			0.0886782			0.0443391	−	0.999017i	$-0.485882\pi$
$401$	1.77578			0.0886782			0.0443391	+	0.999017i	$0.485882\pi$
$402$	1.27086	−	0.923334i	0.0633848	−	0.0460517i
$403$	2.73265	−	8.41022i	0.136123	−	0.418943i
$404$	−9.32621	+	28.7031i	−0.463996	+	1.42803i
$405$	21.3006	+	19.3062i	1.05844	+	0.959333i
$406$	0.631501	+	1.94356i	0.0313409	+	0.0964573i
$407$	−25.9717			−1.28737
$408$	−0.384548	−	1.18352i	−0.0190380	−	0.0585929i
$409$	−14.4324	−	10.4858i	−0.713637	−	0.518488i	0.170708	−	0.985322i	$-0.445395\pi$
$409$	−14.4324	−	10.4858i	−0.713637	−	0.518488i	−0.884345	+	0.466834i	$0.845395\pi$
$410$	1.56420	−	0.896258i	0.0772505	−	0.0442630i
$411$	8.04524	−	5.84521i	0.396843	−	0.288323i
$412$	14.2680	+	10.3663i	0.702933	+	0.510711i
$413$	15.0759	+	10.9533i	0.741838	+	0.538977i
$414$	−1.12622	+	0.818249i	−0.0553508	+	0.0402147i
$415$	11.5027	+	10.4257i	0.564647	+	0.511778i
$416$	6.18901	+	4.49658i	0.303441	+	0.220463i
$417$	10.1492	+	31.2359i	0.497007	+	1.52963i
$418$	−1.22135			−0.0597381
$419$	−0.732042	−	2.25299i	−0.0357626	−	0.110066i	0.931582	−	0.363532i	$-0.118429\pi$
$419$	−0.732042	−	2.25299i	−0.0357626	−	0.110066i	−0.967344	+	0.253466i	$0.918429\pi$
$420$	47.5437	+	5.15496i	2.31990	+	0.251536i
$421$	1.53448	−	4.72265i	0.0747860	−	0.230168i	−0.906675	−	0.421830i	$-0.861388\pi$
$421$	1.53448	−	4.72265i	0.0747860	−	0.230168i	0.981461	+	0.191662i	$0.0613879\pi$
$422$	0.797571	−	2.45467i	0.0388251	−	0.119492i
$423$	20.6744	−	15.0209i	1.00523	−	0.730339i
$424$	4.26472			0.207113
$425$	−4.88381	−	1.07166i	−0.236899	−	0.0519830i
$426$	0.274878			0.0133179
$427$	−1.17707	+	0.855193i	−0.0569625	+	0.0413857i
$428$	−7.81683	+	24.0577i	−0.377841	+	1.16287i
$429$	20.6258	−	63.4798i	0.995825	−	3.06484i
$430$	−0.102821	+	0.228913i	−0.00495846	+	0.0110392i
$431$	−3.94608	−	12.1448i	−0.190076	−	0.584993i	0.809923	−	0.586536i	$-0.199509\pi$
$431$	−3.94608	−	12.1448i	−0.190076	−	0.584993i	−0.999999	+	0.00154300i	$0.999509\pi$
$432$	−41.1915			−1.98183
$433$	10.5628	+	32.5090i	0.507617	+	1.56229i	0.796326	+	0.604868i	$0.206774\pi$
$433$	10.5628	+	32.5090i	0.507617	+	1.56229i	−0.288708	+	0.957417i	$0.593226\pi$
$434$	−0.403772	−	0.293357i	−0.0193817	−	0.0140816i
$435$	−39.1122	−	4.24076i	−1.87529	−	0.203329i
$436$	−6.08394	+	4.42024i	−0.291368	+	0.211691i
$437$	6.02194	+	4.37520i	0.288068	+	0.209294i
$438$	2.79430	+	2.03018i	0.133517	+	0.0970055i
$439$	−7.55033	+	5.48563i	−0.360357	+	0.261815i	−0.753201	−	0.657790i	$-0.771491\pi$
$439$	−7.55033	+	5.48563i	−0.360357	+	0.261815i	0.392844	+	0.919605i	$0.371491\pi$
$440$	3.10829	+	0.337018i	0.148182	+	0.0160667i
$441$	−27.3736	−	19.8881i	−1.30350	−	0.947051i
$442$	0.198365	+	0.610504i	0.00943525	+	0.0290387i
$443$	−28.4781			−1.35304			−0.676518	−	0.736426i	$-0.736512\pi$
$443$	−28.4781			−1.35304			−0.676518	+	0.736426i	$0.736512\pi$
$444$	−14.2120	−	43.7401i	−0.674473	−	2.07581i
$445$	−5.35217	+	11.9157i	−0.253717	+	0.564859i
$446$	−0.411683	+	1.26703i	−0.0194938	+	0.0599957i
$447$	4.02538	−	12.3888i	0.190394	−	0.585972i
$448$	−21.9786	+	15.9684i	−1.03839	+	0.754435i
$449$	−12.8444			−0.606164			−0.303082	−	0.952964i	$-0.598016\pi$
$449$	−12.8444			−0.606164			−0.303082	+	0.952964i	$0.598016\pi$
$450$	1.64790	−	2.81145i	0.0776829	−	0.132533i
$451$	27.3284			1.28684
$452$	26.9589	−	19.5868i	1.26804	−	0.921284i
$453$	5.56530	−	17.1282i	0.261481	−	0.804755i
$454$	−0.0628948	+	0.193570i	−0.00295180	+	0.00908470i
$455$	−49.1772	−	5.33207i	−2.30546	−	0.249971i
$456$	−1.34014	−	4.12454i	−0.0627579	−	0.193149i
$457$	23.4349			1.09624			0.548119	−	0.836401i	$-0.315344\pi$
$457$	23.4349			1.09624			0.548119	+	0.836401i	$0.315344\pi$
$458$	0.717369	+	2.20784i	0.0335205	+	0.103165i
$459$	−8.46218	−	6.14813i	−0.394981	−	0.286970i
$460$	−7.04089	−	6.38164i	−0.328283	−	0.297545i
$461$	−7.95922	+	5.78271i	−0.370698	+	0.269328i	−0.757500	−	0.652835i	$-0.773580\pi$
$461$	−7.95922	+	5.78271i	−0.370698	+	0.269328i	0.386802	+	0.922163i	$0.373580\pi$
$462$	−3.04764	−	2.21424i	−0.141789	−	0.103016i
$463$	26.8169	+	19.4836i	1.24629	+	0.905482i	0.998001	−	0.0632042i	$-0.0201319\pi$
$463$	26.8169	+	19.4836i	1.24629	+	0.905482i	0.248288	+	0.968686i	$0.420132\pi$
$464$	18.2732	−	13.2763i	0.848314	−	0.616336i
$465$	8.33657	−	4.77669i	0.386599	−	0.221514i
$466$	1.55874	+	1.13249i	0.0722073	+	0.0524617i
$467$	2.98822	+	9.19681i	0.138279	+	0.425577i	0.996086	−	0.0883944i	$-0.0281736\pi$
$467$	2.98822	+	9.19681i	0.138279	+	0.425577i	−0.857807	+	0.513972i	$0.828174\pi$
$468$	80.5131			3.72172
$469$	−5.45339	−	16.7838i	−0.251814	−	0.775004i
$470$	−0.671647	−	0.608759i	−0.0309807	−	0.0280800i
$471$	−23.7228	+	73.0111i	−1.09309	+	3.36418i
$472$	−0.666669	+	2.05180i	−0.0306859	+	0.0944416i
$473$	−3.07757	+	2.23598i	−0.141507	+	0.102811i
$474$	4.77345			0.219252
$475$	−17.0200	−	3.73470i	−0.780930	−	0.171360i
$476$	−6.97197			−0.319560
$477$	54.5152	−	39.6076i	2.49608	−	1.81351i
$478$	−0.530106	+	1.63150i	−0.0242465	+	0.0746230i
$479$	6.30236	−	19.3967i	0.287962	−	0.886257i	−0.697533	−	0.716553i	$-0.745719\pi$
$479$	6.30236	−	19.3967i	0.287962	−	0.886257i	0.985495	−	0.169704i	$-0.0542812\pi$
$480$	1.70143	+	8.13587i	0.0776592	+	0.371350i
$481$	14.7003	+	45.2429i	0.670277	+	2.06290i
$482$	−1.69273			−0.0771017
$483$	7.09460	+	21.8349i	0.322816	+	0.993524i
$484$	1.41557	+	1.02848i	0.0643443	+	0.0467489i
$485$	3.36900	+	16.1098i	0.152978	+	0.731510i
$486$	0.662897	−	0.481623i	0.0300696	−	0.0218469i
$487$	22.3551	+	16.2419i	1.01301	+	0.735992i	0.964837	−	0.262847i	$-0.0846615\pi$
$487$	22.3551	+	16.2419i	1.01301	+	0.735992i	0.0481687	+	0.998839i	$0.484662\pi$
$488$	−0.136271	−	0.0990068i	−0.00616871	−	0.00448183i
$489$	−40.0977	+	29.1327i	−1.81328	+	1.31742i
$490$	−0.491763	+	1.09483i	−0.0222156	+	0.0494593i
$491$	1.17111	+	0.850858i	0.0528513	+	0.0383987i	0.613897	−	0.789386i	$-0.289601\pi$
$491$	1.17111	+	0.850858i	0.0528513	+	0.0383987i	−0.561046	+	0.827785i	$0.689601\pi$
$492$	14.9544	+	46.0249i	0.674196	+	2.07496i
$493$	5.73554			0.258316
$494$	0.691297	+	2.12759i	0.0311029	+	0.0957250i
$495$	42.8628	−	24.5595i	1.92654	−	1.10387i
$496$	−1.70462	+	5.24627i	−0.0765395	+	0.235564i
$497$	0.954258	−	2.93690i	0.0428043	−	0.131738i
$498$	1.75195	−	1.27287i	0.0785067	−	0.0570385i
$499$	41.8534			1.87361			0.936807	−	0.349846i	$-0.113766\pi$
$499$	41.8534			1.87361			0.936807	+	0.349846i	$0.113766\pi$
$500$	21.0876	+	7.08219i	0.943066	+	0.316725i
$501$	−3.56944			−0.159471
$502$	−0.491933	+	0.357411i	−0.0219561	+	0.0159520i
$503$	−3.88515	+	11.9573i	−0.173230	+	0.533148i	−0.999548	−	0.0300560i	$-0.990431\pi$
$503$	−3.88515	+	11.9573i	−0.173230	+	0.533148i	0.826318	+	0.563204i	$0.190431\pi$
$504$	2.81568	−	8.66576i	0.125420	−	0.386004i
$505$	29.4293	−	16.8624i	1.30959	−	0.750367i
$506$	0.231313	+	0.711908i	0.0102831	+	0.0316482i
$507$	−82.3786			−3.65856
$508$	−2.63160	−	8.09924i	−0.116758	−	0.359346i
$509$	16.8778	+	12.2625i	0.748096	+	0.543524i	0.895236	−	0.445592i	$-0.147007\pi$
$509$	16.8778	+	12.2625i	0.748096	+	0.543524i	−0.147140	+	0.989116i	$0.547007\pi$
$510$	−0.285772	+	0.636224i	−0.0126542	+	0.0281725i
$511$	31.3918	−	22.8075i	1.38869	−	1.00894i
$512$	−6.44561	−	4.68301i	−0.284859	−	0.206962i
$513$	−29.4905	−	21.4261i	−1.30204	−	0.945986i
$514$	0.116534	−	0.0846668i	0.00514009	−	0.00373449i
$515$	−4.05719	−	19.4006i	−0.178781	−	0.854895i
$516$	−5.44980	−	3.95951i	−0.239914	−	0.174308i
$517$	−4.24629	−	13.0687i	−0.186751	−	0.574762i
$518$	2.68486			0.117966
$519$	−24.5912	−	75.6841i	−1.07944	−	3.32216i
$520$	−1.17224	−	5.60542i	−0.0514063	−	0.245814i
$521$	−5.06417	+	15.5859i	−0.221865	+	0.682831i	0.776729	+	0.629835i	$0.216877\pi$
$521$	−5.06417	+	15.5859i	−0.221865	+	0.682831i	−0.998595	+	0.0529968i	$0.983123\pi$
$522$	−1.15517	+	3.55524i	−0.0505603	+	0.155609i
$523$	−0.912008	+	0.662613i	−0.0398793	+	0.0289740i	−0.607546	−	0.794284i	$-0.707846\pi$
$523$	−0.912008	+	0.662613i	−0.0398793	+	0.0289740i	0.567667	+	0.823258i	$0.307846\pi$
$524$	−6.89185			−0.301072
$525$	−35.6993	−	40.1756i	−1.55804	−	1.75341i
$526$	1.02299			0.0446044
$527$	−1.13323	+	0.823340i	−0.0493643	+	0.0358652i
$528$	−12.8663	+	39.5985i	−0.559935	+	1.72330i
$529$	−5.69765	+	17.5356i	−0.247724	+	0.762416i
$530$	−1.77103	−	1.60520i	−0.0769284	−	0.0697255i
$531$	10.5337	+	32.4193i	0.457122	+	1.40688i
$532$	−24.2972			−1.05342
$533$	−15.4682	−	47.6062i	−0.670001	−	2.06205i
$534$	1.47412	+	1.07101i	0.0637914	+	0.0463471i
$535$	24.6663	−	14.1333i	1.06642	−	0.611037i
$536$	1.65289	−	1.20089i	0.0713938	−	0.0518706i
$537$	9.12499	+	6.62970i	0.393772	+	0.286092i
$538$	−0.652566	−	0.474117i	−0.0281341	−	0.0204406i
$539$	−14.7191	+	10.6941i	−0.633998	+	0.460627i
$540$	34.4805	+	31.2520i	1.48380	+	1.34487i
$541$	−37.4583	−	27.2150i	−1.61046	−	1.17007i	−0.862042	−	0.506836i	$-0.830815\pi$
$541$	−37.4583	−	27.2150i	−1.61046	−	1.17007i	−0.748416	−	0.663230i	$-0.769185\pi$
$542$	0.951557	+	2.92859i	0.0408729	+	0.125794i
$543$	−32.8439			−1.40947
$544$	−0.374460	−	1.15247i	−0.0160548	−	0.0494117i
$545$	8.40225	+	0.911018i	0.359913	+	0.0390237i
$546$	−2.13222	+	6.56230i	−0.0912506	+	0.280840i
$547$	1.39011	−	4.27832i	0.0594369	−	0.182928i	−0.916930	−	0.399049i	$-0.869340\pi$
$547$	1.39011	−	4.27832i	0.0594369	−	0.182928i	0.976367	+	0.216121i	$0.0693405\pi$
$548$	5.21828	−	3.79130i	0.222914	−	0.161956i
$549$	−2.66144			−0.113587
$550$	−1.16394	−	1.30989i	−0.0496306	−	0.0558538i
$551$	19.9882			0.851528
$552$	−2.15033	+	1.56230i	−0.0915240	+	0.0664961i
$553$	16.5714	−	51.0015i	0.704687	−	2.16880i
$554$	0.0270665	−	0.0833023i	0.00114995	−	0.00353917i
$555$	−21.1778	+	47.1489i	−0.898950	+	2.00136i
$556$	6.58292	+	20.2601i	0.279178	+	0.859222i
$557$	−7.05349			−0.298866			−0.149433	−	0.988772i	$-0.547745\pi$
$557$	−7.05349			−0.298866			−0.149433	+	0.988772i	$0.547745\pi$
$558$	−0.282118	−	0.868271i	−0.0119430	−	0.0367568i
$559$	5.63704	+	4.09555i	0.238421	+	0.173223i
$560$	30.6766	+	3.32612i	1.29632	+	0.140554i
$561$	−8.55355	+	6.21452i	−0.361131	+	0.262377i
$562$	1.66078	+	1.20663i	0.0700558	+	0.0508985i
$563$	25.0272	+	18.1833i	1.05477	+	0.766335i	0.973114	−	0.230326i	$-0.0739792\pi$
$563$	25.0272	+	18.1833i	1.05477	+	0.766335i	0.0816557	+	0.996661i	$0.473979\pi$
$564$	19.6860	−	14.3027i	0.828929	−	0.602252i
$565$	−37.2316	−	4.03686i	−1.56635	−	0.169832i
$566$	−0.105102	−	0.0763609i	−0.00441776	−	0.00320969i
$567$	−13.9213	−	42.8455i	−0.584641	−	1.79934i
$568$	0.357507			0.0150007
$569$	−8.02751	−	24.7061i	−0.336531	−	1.03573i	−0.965963	−	0.258680i	$-0.916713\pi$
$569$	−8.02751	−	24.7061i	−0.336531	−	1.03573i	0.629433	−	0.777055i	$-0.283287\pi$
$570$	−0.995910	+	2.21723i	−0.0417141	+	0.0928694i
$571$	−7.75790	+	23.8764i	−0.324658	+	0.999195i	0.646937	+	0.762544i	$0.276050\pi$
$571$	−7.75790	+	23.8764i	−0.324658	+	0.999195i	−0.971595	+	0.236651i	$0.923950\pi$
$572$	13.3783	−	41.1741i	0.559373	−	1.72157i
$573$	−43.6447	+	31.7097i	−1.82328	+	1.32469i
$574$	−2.82510			−0.117917
$575$	1.04653	+	10.6280i	0.0436432	+	0.443220i
$576$	−49.6950			−2.07063
$577$	15.0281	−	10.9186i	0.625630	−	0.454547i	−0.229254	−	0.973367i	$-0.573628\pi$
$577$	15.0281	−	10.9186i	0.625630	−	0.454547i	0.854884	+	0.518820i	$0.173628\pi$
$578$	0.0314213	−	0.0967047i	0.00130695	−	0.00402239i
$579$	−4.91062	+	15.1133i	−0.204079	+	0.628089i
$580$	−25.3688	−	2.75063i	−1.05338	−	0.114214i
$581$	−7.51779	−	23.1374i	−0.311890	−	0.959900i
$582$	2.29580			0.0951638
$583$	−11.1968	−	34.4602i	−0.463723	−	1.42719i
$584$	3.63427	+	2.64045i	0.150387	+	0.109263i
$585$	−67.0437	−	60.7662i	−2.77191	−	2.51237i
$586$	1.04374	−	0.758319i	0.0431164	−	0.0313259i
$587$	10.0507	+	7.30223i	0.414835	+	0.301395i	0.775556	−	0.631278i	$-0.217469\pi$
$587$	10.0507	+	7.30223i	0.414835	+	0.301395i	−0.360721	+	0.932674i	$0.617469\pi$
$588$	−26.0648	−	18.9372i	−1.07490	−	0.780957i
$589$	−3.94928	+	2.86932i	−0.162727	+	0.118228i
$590$	1.04913	−	0.601129i	0.0431919	−	0.0247481i
$591$	52.4159	+	38.0824i	2.15610	+	1.56650i
$592$	−9.17000	−	28.2224i	−0.376885	−	1.15993i
$593$	−11.3916			−0.467798			−0.233899	−	0.972261i	$-0.575149\pi$
$593$	−11.3916			−0.467798			−0.233899	+	0.972261i	$0.575149\pi$
$594$	−1.13278	−	3.48634i	−0.0464786	−	0.143046i
$595$	5.80559	+	5.26200i	0.238006	+	0.215721i
$596$	2.61093	−	8.03561i	0.106948	−	0.329151i
$597$	−3.51325	+	10.8127i	−0.143788	+	0.442534i
$598$	1.10922	−	0.805897i	0.0453594	−	0.0329556i
$599$	−9.85014			−0.402466			−0.201233	−	0.979543i	$-0.564495\pi$
$599$	−9.85014			−0.402466			−0.201233	+	0.979543i	$0.564495\pi$
$600$	3.14638	−	5.36797i	0.128451	−	0.219146i
$601$	−4.57552			−0.186640			−0.0933198	−	0.995636i	$-0.529748\pi$
$601$	−4.57552			−0.186640			−0.0933198	+	0.995636i	$0.529748\pi$
$602$	0.318147	−	0.231147i	0.0129667	−	0.00942086i
$603$	9.97555	−	30.7016i	0.406236	−	1.25027i
$604$	3.60975	−	11.1097i	0.146879	−	0.452046i
$605$	−0.402528	−	1.92480i	−0.0163651	−	0.0782544i
$606$	−1.46204	−	4.49969i	−0.0593912	−	0.182787i
$607$	−28.2904			−1.14827			−0.574136	−	0.818760i	$-0.694662\pi$
$607$	−28.2904			−1.14827			−0.574136	+	0.818760i	$0.694662\pi$
$608$	−1.30498	−	4.01633i	−0.0529241	−	0.162884i
$609$	49.8769	+	36.2377i	2.02111	+	1.46842i
$610$	0.0193246	+	0.0924061i	0.000782430	+	0.00374141i
$611$	−20.3623	+	14.7941i	−0.823772	+	0.598506i
$612$	−10.3177	−	7.49626i	−0.417069	−	0.303018i
$613$	−9.10967	−	6.61856i	−0.367936	−	0.267321i	0.388418	−	0.921483i	$-0.373022\pi$
$613$	−9.10967	−	6.61856i	−0.367936	−	0.267321i	−0.756355	+	0.654162i	$0.773022\pi$
$614$	−0.535424	+	0.389008i	−0.0216079	+	0.0156991i
$615$	22.2841	−	49.6117i	0.898580	−	2.00054i
$616$	−3.96377	−	2.87985i	−0.159705	−	0.116032i
$617$	12.0516	+	37.0910i	0.485179	+	1.49323i	0.831721	+	0.555194i	$0.187356\pi$
$617$	12.0516	+	37.0910i	0.485179	+	1.49323i	−0.346542	+	0.938035i	$0.612644\pi$
$618$	−2.76477			−0.111215
$619$	10.8378	+	33.3552i	0.435607	+	1.34066i	0.892463	+	0.451120i	$0.148975\pi$
$619$	10.8378	+	33.3552i	0.435607	+	1.34066i	−0.456857	+	0.889540i	$0.651025\pi$
$620$	5.40724	−	3.09824i	0.217160	−	0.124428i
$621$	−6.90375	+	21.2476i	−0.277038	+	0.852635i
$622$	−0.858699	+	2.64281i	−0.0344307	+	0.105967i
$623$	16.5606	−	12.0320i	0.663487	−	0.482051i
$624$	76.2633			3.05297
$625$	−12.2145	−	21.8130i	−0.488582	−	0.872518i
$626$	−0.875497			−0.0349919
$627$	−29.8089	+	21.6575i	−1.19045	+	0.864916i
$628$	−15.3870	+	47.3562i	−0.614007	+	1.88972i
$629$	2.32855	−	7.16654i	0.0928454	−	0.285749i
$630$	−4.43099	+	2.53887i	−0.176535	+	0.101151i
$631$	−10.0023	−	30.7838i	−0.398184	−	1.22548i	−0.926454	−	0.376407i	$-0.877159\pi$
$631$	−10.0023	−	30.7838i	−0.398184	−	1.22548i	0.528271	−	0.849076i	$-0.322841\pi$
$632$	6.20837			0.246956
$633$	−24.0613	−	74.0530i	−0.956350	−	2.94334i
$634$	−1.88078	−	1.36647i	−0.0746954	−	0.0542694i
$635$	−3.92145	+	8.73044i	−0.155618	+	0.346457i
$636$	51.9088	−	37.7140i	2.05832	−	1.49546i
$637$	26.9604	+	19.5878i	1.06821	+	0.776099i
$638$	1.62619	+	1.18150i	0.0643814	+	0.0467758i
$639$	4.56995	−	3.32027i	0.180785	−	0.131348i
$640$	1.47014	+	7.02991i	0.0581125	+	0.277882i
$641$	−18.2799	−	13.2811i	−0.722012	−	0.524573i	0.165014	−	0.986291i	$-0.447233\pi$
$641$	−18.2799	−	13.2811i	−0.722012	−	0.524573i	−0.887026	+	0.461719i	$0.847233\pi$
$642$	−1.22542	−	3.77144i	−0.0483633	−	0.148847i
$643$	−40.4702			−1.59599			−0.797995	−	0.602664i	$-0.794106\pi$
$643$	−40.4702			−1.59599			−0.797995	+	0.602664i	$0.794106\pi$
$644$	4.60168	+	14.1625i	0.181331	+	0.558081i
$645$	1.54968	+	7.41026i	0.0610188	+	0.291779i
$646$	0.109503	−	0.337014i	0.00430832	−	0.0132596i
$647$	−6.98023	+	21.4829i	−0.274421	+	0.844582i	0.714951	+	0.699175i	$0.246449\pi$
$647$	−6.98023	+	21.4829i	−0.274421	+	0.844582i	−0.989372	+	0.145407i	$0.953551\pi$
$648$	4.21946	−	3.06562i	0.165756	−	0.120429i
$649$	18.3294			0.719492
$650$	−1.62303	+	2.76900i	−0.0636603	+	0.108609i
$651$	−15.0566			−0.590116
$652$	−26.0080	+	18.8959i	−1.01855	+	0.740021i
$653$	1.38336	−	4.25754i	0.0541350	−	0.166610i	−0.920334	−	0.391134i	$-0.872083\pi$
$653$	1.38336	−	4.25754i	0.0541350	−	0.166610i	0.974469	+	0.224524i	$0.0720827\pi$
$654$	0.364303	−	1.12121i	0.0142454	−	0.0438428i
$655$	5.73888	+	5.20153i	0.224237	+	0.203241i
$656$	9.64899	+	29.6966i	0.376730	+	1.15946i
$657$	70.9789			2.76915
$658$	0.438964	+	1.35099i	0.0171126	+	0.0526672i
$659$	8.34203	+	6.06084i	0.324959	+	0.236097i	0.738289	−	0.674485i	$-0.235634\pi$
$659$	8.34203	+	6.06084i	0.324959	+	0.236097i	−0.413329	+	0.910582i	$0.635634\pi$
$660$	40.8135	−	23.3853i	1.58866	−	0.910272i
$661$	−8.70879	+	6.32731i	−0.338733	+	0.246104i	−0.744127	−	0.668038i	$-0.767134\pi$
$661$	−8.70879	+	6.32731i	−0.338733	+	0.246104i	0.405394	+	0.914142i	$0.367134\pi$
$662$	0.104315	+	0.0757892i	0.00405431	+	0.00294563i
$663$	15.6671	+	11.3828i	0.608461	+	0.442073i
$664$	2.27859	−	1.65549i	0.0884265	−	0.0642456i
$665$	20.2324	+	18.3380i	0.784578	+	0.711116i
$666$	3.97328	+	2.88676i	0.153962	+	0.111860i
$667$	−3.78560	−	11.6509i	−0.146579	−	0.451124i
$668$	−2.31520			−0.0895777
$669$	12.4197	+	38.2241i	0.480175	+	1.47783i
$670$	−1.13840	−	0.123432i	−0.0439804	−	0.00476859i
$671$	−0.442231	+	1.36105i	−0.0170721	+	0.0525426i
$672$	4.02506	−	12.3879i	0.155270	−	0.477872i
$673$	6.99014	−	5.07864i	0.269450	−	0.195767i	−0.444853	−	0.895604i	$-0.646744\pi$
$673$	6.99014	−	5.07864i	0.269450	−	0.195767i	0.714303	+	0.699837i	$0.246744\pi$
$674$	1.39300			0.0536563
$675$	−5.12503	−	52.0474i	−0.197262	−	2.00331i
$676$	−53.4321			−2.05508
$677$	−6.90715	+	5.01834i	−0.265464	+	0.192871i	−0.712552	−	0.701619i	$-0.752461\pi$
$677$	−6.90715	+	5.01834i	−0.265464	+	0.192871i	0.447089	+	0.894490i	$0.352461\pi$
$678$	−1.61428	+	4.96825i	−0.0619962	+	0.190805i
$679$	7.97002	−	24.5292i	0.305861	−	0.941345i
$680$	−0.371676	+	0.827475i	−0.0142531	+	0.0317322i
$681$	1.89742	+	5.83967i	0.0727094	+	0.223777i
$682$	−0.490907			−0.0187978
$683$	−1.15887	−	3.56664i	−0.0443430	−	0.136474i	0.926434	−	0.376458i	$-0.122858\pi$
$683$	−1.15887	−	3.56664i	−0.0443430	−	0.136474i	−0.970777	+	0.239984i	$0.922858\pi$
$684$	−35.9570	−	26.1243i	−1.37485	−	0.998888i
$685$	−7.20672	−	0.781392i	−0.275355	−	0.0298555i
$686$	−0.496171	+	0.360489i	−0.0189439	+	0.0137635i
$687$	56.6588	+	41.1650i	2.16167	+	1.57054i
$688$	−3.51636	−	2.55479i	−0.134060	−	0.0974004i
$689$	−53.6923	+	39.0097i	−2.04551	+	1.48615i
$690$	1.48101	+	0.160579i	0.0563811	+	0.00611315i
$691$	−24.3153	−	17.6661i	−0.924996	−	0.672049i	0.0197667	−	0.999805i	$-0.493708\pi$
$691$	−24.3153	−	17.6661i	−0.924996	−	0.672049i	−0.944762	+	0.327756i	$0.893708\pi$
$692$	−15.9503	−	49.0900i	−0.606339	−	1.86612i
$693$	−77.4142			−2.94072
$694$	−0.276777	−	0.851833i	−0.0105063	−	0.0323351i
$695$	9.80945	−	21.8391i	0.372094	−	0.828404i
$696$	−2.20559	+	6.78811i	−0.0836027	+	0.257303i
$697$	−2.45018	+	7.54088i	−0.0928073	+	0.285631i
$698$	−0.366832	+	0.266519i	−0.0138848	+	0.0100879i
$699$	58.1254			2.19851
$700$	−23.1551	−	26.0585i	−0.875182	−	0.984920i
$701$	−48.3478			−1.82607			−0.913036	−	0.407878i	$-0.866269\pi$
$701$	−48.3478			−1.82607			−0.913036	+	0.407878i	$0.866269\pi$
$702$	−5.43206	+	3.94662i	−0.205020	+	0.148956i
$703$	8.11496	−	24.9753i	0.306061	−	0.941960i
$704$	−8.25745	+	25.4138i	−0.311214	+	0.957819i
$705$	−27.1874	−	2.94781i	−1.02394	−	0.111021i
$706$	−0.584636	−	1.79933i	−0.0220031	−	0.0677185i
$707$	−53.1521			−1.99899
$708$	10.0300	+	30.8693i	0.376952	+	1.16014i
$709$	−20.6521	−	15.0046i	−0.775605	−	0.563510i	0.128052	−	0.991768i	$-0.459128\pi$
$709$	−20.6521	−	15.0046i	−0.775605	−	0.563510i	−0.903657	+	0.428257i	$0.859128\pi$
$710$	−0.148463	−	0.134562i	−0.00557172	−	0.00505003i
$711$	79.3606	−	57.6588i	2.97625	−	2.16238i
$712$	1.91724	+	1.39296i	0.0718518	+	0.0522034i
$713$	2.42045	+	1.75856i	0.0906466	+	0.0658586i
$714$	0.884232	−	0.642432i	0.0330916	−	0.0240424i
$715$	−42.2157	+	24.1888i	−1.57878	+	0.904609i
$716$	5.91862	+	4.30013i	0.221189	+	0.160703i
$717$	15.9924	+	49.2194i	0.597245	+	1.83813i
$718$	−2.60027			−0.0970414
$719$	10.0406	+	30.9019i	0.374452	+	1.15245i	0.943847	+	0.330382i	$0.107178\pi$
$719$	10.0406	+	30.9019i	0.374452	+	1.15245i	−0.569395	+	0.822064i	$0.692822\pi$
$720$	41.8216	+	37.9058i	1.55860	+	1.41266i
$721$	−9.59809	+	29.5399i	−0.357451	+	1.10012i
$722$	−0.215390	+	0.662902i	−0.00801599	+	0.0246707i
$723$	−41.3138	+	30.0162i	−1.53648	+	1.11632i
$724$	−21.3031			−0.791724
$725$	19.0487	+	21.4372i	0.707453	+	0.796159i
$726$	−0.274302			−0.0101803
$727$	8.08668	−	5.87531i	0.299918	−	0.217903i	−0.427640	−	0.903949i	$-0.640655\pi$
$727$	8.08668	−	5.87531i	0.299918	−	0.217903i	0.727558	+	0.686046i	$0.240655\pi$
$728$	−2.77317	+	8.53495i	−0.102781	+	0.316326i
$729$	−4.27989	+	13.1722i	−0.158515	+	0.487858i
$730$	−0.515375	−	2.46442i	−0.0190749	−	0.0912121i
$731$	−0.341063	−	1.04968i	−0.0126147	−	0.0388240i
$732$	−2.53419			−0.0936664
$733$	5.39987	+	16.6191i	0.199449	+	0.613841i	0.999896	+	0.0144369i	$0.00459556\pi$
$733$	5.39987	+	16.6191i	0.199449	+	0.613841i	−0.800447	+	0.599404i	$0.795404\pi$
$734$	−0.130505	−	0.0948176i	−0.00481704	−	0.00349978i
$735$	7.41170	+	35.4412i	0.273385	+	1.30727i
$736$	−2.09391	+	1.52132i	−0.0771827	+	0.0560765i
$737$	−14.0431	−	10.2029i	−0.517284	−	0.375829i
$738$	−4.18082	−	3.03755i	−0.153898	−	0.111814i
$739$	17.0472	−	12.3855i	0.627092	−	0.455609i	−0.228300	−	0.973591i	$-0.573317\pi$
$739$	17.0472	−	12.3855i	0.627092	−	0.455609i	0.855391	+	0.517982i	$0.173317\pi$
$740$	−13.7363	+	30.5816i	−0.504957	+	1.12420i
$741$	54.5996	+	39.6690i	2.00577	+	1.45728i
$742$	1.15748	+	3.56236i	0.0424924	+	0.130778i
$743$	−34.1552			−1.25303			−0.626517	−	0.779408i	$-0.715520\pi$
$743$	−34.1552			−1.25303			−0.626517	+	0.779408i	$0.715520\pi$
$744$	−0.538656	−	1.65781i	−0.0197481	−	0.0607783i
$745$	−8.23890	+	4.72073i	−0.301850	+	0.172954i
$746$	0.745797	−	2.29533i	0.0273056	−	0.0840380i
$747$	13.7518	−	42.3238i	0.503153	−	1.54855i
$748$	−5.54797	+	4.03084i	−0.202854	+	0.147382i
$749$	−44.5497			−1.62781
$750$	−3.32706	+	1.04490i	−0.121487	+	0.0381545i
$751$	14.7168			0.537025			0.268512	−	0.963276i	$-0.413468\pi$
$751$	14.7168			0.537025			0.268512	+	0.963276i	$0.413468\pi$
$752$	12.7020	−	9.22851i	0.463193	−	0.336529i
$753$	−5.66866	+	17.4463i	−0.206578	+	0.635780i
$754$	1.13773	−	3.50157i	0.0414337	−	0.127520i
$755$	−11.3907	+	6.52666i	−0.414551	+	0.237529i
$756$	−22.5352	−	69.3563i	−0.819599	−	2.52247i
$757$	−36.4500			−1.32480			−0.662400	−	0.749151i	$-0.730462\pi$
$757$	−36.4500			−1.32480			−0.662400	+	0.749151i	$0.730462\pi$
$758$	0.145718	+	0.448473i	0.00529270	+	0.0162893i
$759$	18.2694	+	13.2735i	0.663138	+	0.481798i
$760$	−1.29528	+	2.88373i	−0.0469849	+	0.104604i
$761$	25.1638	−	18.2826i	0.912187	−	0.662743i	−0.0293800	−	0.999568i	$-0.509353\pi$
$761$	25.1638	−	18.2826i	0.912187	−	0.662743i	0.941567	+	0.336826i	$0.109353\pi$
$762$	1.08006	+	0.784712i	0.0391265	+	0.0284271i
$763$	−10.7148	−	7.78472i	−0.387900	−	0.281826i
$764$	−28.3087	+	20.5675i	−1.02417	+	0.744105i
$765$	2.93391	+	14.0293i	0.106076	+	0.507232i
$766$	2.47741	+	1.79995i	0.0895126	+	0.0650347i
$767$	−10.3747	−	31.9299i	−0.374607	−	1.15292i
$768$	−46.5631			−1.68020
$769$	10.1720	+	31.3062i	0.366812	+	1.12893i	0.948839	+	0.315761i	$0.102260\pi$
$769$	10.1720	+	31.3062i	0.366812	+	1.12893i	−0.582027	+	0.813169i	$0.697740\pi$
$770$	0.562102	+	2.68785i	0.0202567	+	0.0968635i
$771$	1.34285	−	4.13286i	0.0483614	−	0.148841i

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+(-0.0822620 + 0.0597668i) q^{2} +(-0.947924 + 2.91741i) q^{3} +(-0.614839 + 1.89228i) q^{4} +(1.94015 - 1.11167i) q^{5} +(-0.0963862 - 0.296646i) q^{6} -3.50410 q^{7} +(-0.125360 - 0.385819i) q^{8} +(-5.18567 - 3.76761i) q^{9} +(-0.0931599 + 0.207405i) q^{10} +(-2.78840 + 2.02589i) q^{11} +(-4.93773 - 3.58747i) q^{12} +(5.10738 + 3.71073i) q^{13} +(0.288254 - 0.209429i) q^{14} +(1.40408 + 6.71400i) q^{15} +(-3.18597 - 2.31474i) q^{16} +(-0.309017 - 0.951057i) q^{17} +0.651761 q^{18} +(-1.07692 - 3.31441i) q^{19} +(0.910707 + 4.35481i) q^{20} +(3.32162 - 10.2229i) q^{21} +(0.108298 - 0.333308i) q^{22} +(-1.72797 + 1.25544i) q^{23} +1.24442 q^{24} +(2.52838 - 4.31361i) q^{25} -0.641922 q^{26} +(8.46218 - 6.14813i) q^{27} +(2.15446 - 6.63073i) q^{28} +(-1.77238 + 5.45482i) q^{29} +(-0.516776 - 0.468389i) q^{30} +(-0.432855 - 1.33219i) q^{31} +1.21178 q^{32} +(-3.26716 - 10.0553i) q^{33} +(0.0822620 + 0.0597668i) q^{34} +(-6.79849 + 3.89540i) q^{35} +(10.3177 - 7.49626i) q^{36} +(6.09623 + 4.42917i) q^{37} +(0.286681 + 0.208286i) q^{38} +(-15.6671 + 11.3828i) q^{39} +(-0.672121 - 0.609189i) q^{40} +(-6.41466 - 4.66052i) q^{41} +(0.337747 + 1.03948i) q^{42} +1.10370 q^{43} +(-2.11914 - 6.52203i) q^{44} +(-14.2493 - 1.54499i) q^{45} +(0.0671123 - 0.206550i) q^{46} +(-1.23200 + 3.79171i) q^{47} +(9.77310 - 7.10057i) q^{48} +5.27870 q^{49} +(0.0498211 + 0.505960i) q^{50} +3.06755 q^{51} +(-10.1620 + 7.38310i) q^{52} +(-3.24860 + 9.99815i) q^{53} +(-0.328661 + 1.01151i) q^{54} +(-3.15780 + 7.03032i) q^{55} +(0.439275 + 1.35195i) q^{56} +10.6903 q^{57} +(-0.180218 - 0.554654i) q^{58} +(-4.30237 - 3.12586i) q^{59} +(-13.5680 - 1.47112i) q^{60} +(0.335913 - 0.244055i) q^{61} +(0.115228 + 0.0837183i) q^{62} +(18.1711 + 13.2021i) q^{63} +(6.27225 - 4.55706i) q^{64} +(14.0342 + 1.52167i) q^{65} +(0.869737 + 0.631901i) q^{66} +(1.55629 + 4.78976i) q^{67} +1.98966 q^{68} +(-2.02466 - 6.23126i) q^{69} +(0.326441 - 0.726767i) q^{70} +(-0.272326 + 0.838134i) q^{71} +(-0.803538 + 2.47304i) q^{72} +(-8.95860 + 6.50880i) q^{73} -0.766205 q^{74} +(10.1879 + 11.4653i) q^{75} +6.93393 q^{76} +(9.77083 - 7.09892i) q^{77} +(0.608493 - 1.87275i) q^{78} +(-4.72915 + 14.5548i) q^{79} +(-8.75449 - 0.949210i) q^{80} +(3.97287 + 12.2272i) q^{81} +0.806227 q^{82} +(2.14543 + 6.60294i) q^{83} +(17.3023 + 12.5709i) q^{84} +(-1.65680 - 1.50167i) q^{85} +(-0.0907928 + 0.0659649i) q^{86} +(-14.2339 - 10.3415i) q^{87} +(1.13118 + 0.821852i) q^{88} +(-4.72607 + 3.43369i) q^{89} +(1.26452 - 0.724542i) q^{90} +(-17.8968 - 13.0028i) q^{91} +(-1.31323 - 4.04170i) q^{92} +4.29686 q^{93} +(-0.125272 - 0.385547i) q^{94} +(-5.77392 - 5.23329i) q^{95} +(-1.14867 + 3.53525i) q^{96} +(-2.27449 + 7.00015i) q^{97} +(-0.434237 + 0.315491i) q^{98} +22.0925 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

Related objects

Downloads

Learn more