LMFDB - Embedded newform 425.2.k.c.86.20

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			86.20
Character	$\chi$	$=$	425.86
Dual form			425.2.k.c.341.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.11757 - 1.53851i) q^{2} +(-0.828858 + 2.55096i) q^{3} +(1.49908 - 4.61370i) q^{4} +(0.550931 + 2.16714i) q^{5} +(2.16951 + 6.67705i) q^{6} +2.04850 q^{7} +(-2.30611 - 7.09748i) q^{8} +(-3.39335 - 2.46541i) q^{9} +(4.50079 + 3.74146i) q^{10} +(-2.69467 + 1.95779i) q^{11} +(10.5268 + 7.64820i) q^{12} +(4.00858 + 2.91241i) q^{13} +(4.33786 - 3.15164i) q^{14} +(-5.98492 - 0.390842i) q^{15} +(-7.95360 - 5.77863i) q^{16} +(-0.309017 - 0.951057i) q^{17} -10.9787 q^{18} +(-1.34103 - 4.12725i) q^{19} +(10.8244 + 0.706882i) q^{20} +(-1.69792 + 5.22565i) q^{21} +(-2.69409 + 8.29155i) q^{22} +(5.23929 - 3.80657i) q^{23} +20.0168 q^{24} +(-4.39295 + 2.38788i) q^{25} +12.9692 q^{26} +(2.59184 - 1.88308i) q^{27} +(3.07087 - 9.45117i) q^{28} +(0.228870 - 0.704388i) q^{29} +(-13.2748 + 8.38021i) q^{30} +(-1.37016 - 4.21693i) q^{31} -10.8073 q^{32} +(-2.76076 - 8.49674i) q^{33} +(-2.11757 - 1.53851i) q^{34} +(1.12858 + 4.43938i) q^{35} +(-16.4616 + 11.9600i) q^{36} +(-7.46083 - 5.42061i) q^{37} +(-9.18954 - 6.67659i) q^{38} +(-10.7520 + 7.81177i) q^{39} +(14.1107 - 8.90788i) q^{40} +(6.04225 + 4.38995i) q^{41} +(4.44424 + 13.6780i) q^{42} -8.85083 q^{43} +(4.99314 + 15.3673i) q^{44} +(3.47338 - 8.71212i) q^{45} +(5.23816 - 16.1214i) q^{46} +(2.60199 - 8.00809i) q^{47} +(21.3335 - 15.4997i) q^{48} -2.80363 q^{49} +(-5.62862 + 11.8151i) q^{50} +2.68224 q^{51} +(19.4462 - 14.1285i) q^{52} +(0.591818 - 1.82143i) q^{53} +(2.59128 - 7.97513i) q^{54} +(-5.72739 - 4.76111i) q^{55} +(-4.72408 - 14.5392i) q^{56} +11.6400 q^{57} +(-0.599059 - 1.84371i) q^{58} +(1.93010 + 1.40230i) q^{59} +(-10.7751 + 27.0267i) q^{60} +(-8.73136 + 6.34370i) q^{61} +(-9.38920 - 6.82165i) q^{62} +(-6.95129 - 5.05040i) q^{63} +(-6.97816 + 5.06993i) q^{64} +(-4.10312 + 10.2917i) q^{65} +(-18.9184 - 13.7450i) q^{66} +(1.62854 + 5.01214i) q^{67} -4.85113 q^{68} +(5.36778 + 16.5203i) q^{69} +(9.21989 + 7.66439i) q^{70} +(3.62525 - 11.1574i) q^{71} +(-9.67277 + 29.7697i) q^{72} +(-9.48784 + 6.89332i) q^{73} -24.1385 q^{74} +(-2.45027 - 13.1855i) q^{75} -21.0522 q^{76} +(-5.52005 + 4.01055i) q^{77} +(-10.7496 + 33.0840i) q^{78} +(0.165581 - 0.509605i) q^{79} +(8.14118 - 20.4202i) q^{80} +(-1.23303 - 3.79487i) q^{81} +19.5489 q^{82} +(0.531093 + 1.63454i) q^{83} +(21.5643 + 15.6674i) q^{84} +(1.89082 - 1.19365i) q^{85} +(-18.7423 + 13.6171i) q^{86} +(1.60717 + 1.16768i) q^{87} +(20.1096 + 14.6105i) q^{88} +(-8.34088 + 6.06000i) q^{89} +(-6.04852 - 23.7924i) q^{90} +(8.21160 + 5.96607i) q^{91} +(-9.70823 - 29.8789i) q^{92} +11.8929 q^{93} +(-6.81061 - 20.9609i) q^{94} +(8.20550 - 5.18002i) q^{95} +(8.95775 - 27.5691i) q^{96} +(0.122530 - 0.377109i) q^{97} +(-5.93690 + 4.31341i) q^{98} +13.9707 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 $

$2$	2.11757	−	1.53851i	1.49735	−	1.08789i	0.525930	−	0.850528i	$-0.323717\pi$
$2$	2.11757	−	1.53851i	1.49735	−	1.08789i	0.971421	−	0.237362i	$-0.0762826\pi$
$3$	−0.828858	+	2.55096i	−0.478541	+	1.47280i	0.362581	+	0.931952i	$0.381896\pi$
$3$	−0.828858	+	2.55096i	−0.478541	+	1.47280i	−0.841122	+	0.540846i	$0.818104\pi$
$4$	1.49908	−	4.61370i	0.749541	−	2.30685i
$5$	0.550931	+	2.16714i	0.246384	+	0.969172i
$5$	0.550931	+	2.16714i	0.246384	+	0.969172i
$6$	2.16951	+	6.67705i	0.885697	+	2.72590i
$7$	2.04850			0.774261			0.387131	−	0.922025i	$-0.373466\pi$
$7$	2.04850			0.774261			0.387131	+	0.922025i	$0.373466\pi$
$8$	−2.30611	−	7.09748i	−0.815333	−	2.50934i
$9$	−3.39335	−	2.46541i	−1.13112	−	0.821804i
$10$	4.50079	+	3.74146i	1.42328	+	1.18315i
$11$	−2.69467	+	1.95779i	−0.812475	+	0.590297i	−0.914547	−	0.404480i	$-0.867453\pi$
$11$	−2.69467	+	1.95779i	−0.812475	+	0.590297i	0.102072	+	0.994777i	$0.467453\pi$
$12$	10.5268	+	7.64820i	3.03884	+	2.20784i
$13$	4.00858	+	2.91241i	1.11178	+	0.807756i	0.982943	−	0.183909i	$-0.0588753\pi$
$13$	4.00858	+	2.91241i	1.11178	+	0.807756i	0.128838	+	0.991666i	$0.458875\pi$
$14$	4.33786	−	3.15164i	1.15934	−	0.842311i
$15$	−5.98492	−	0.390842i	−1.54530	−	0.100915i
$16$	−7.95360	−	5.77863i	−1.98840	−	1.44466i
$17$	−0.309017	−	0.951057i	−0.0749476	−	0.230665i
$17$	−0.309017	−	0.951057i	−0.0749476	−	0.230665i
$18$	−10.9787			−2.58771
$19$	−1.34103	−	4.12725i	−0.307652	−	0.946857i	−0.978674	−	0.205419i	$-0.934144\pi$
$19$	−1.34103	−	4.12725i	−0.307652	−	0.946857i	0.671022	−	0.741438i	$-0.265856\pi$
$20$	10.8244	+	0.706882i	2.42041	+	0.158064i
$21$	−1.69792	+	5.22565i	−0.370516	+	1.14033i
$22$	−2.69409	+	8.29155i	−0.574382	+	1.76776i
$23$	5.23929	−	3.80657i	1.09247	−	0.793725i	0.112654	−	0.993634i	$-0.464065\pi$
$23$	5.23929	−	3.80657i	1.09247	−	0.793725i	0.979814	+	0.199910i	$0.0640649\pi$
$24$	20.0168			4.08592
$25$	−4.39295	+	2.38788i	−0.878590	+	0.477577i
$26$	12.9692			2.54348
$27$	2.59184	−	1.88308i	0.498800	−	0.362399i
$28$	3.07087	−	9.45117i	0.580340	−	1.78610i
$29$	0.228870	−	0.704388i	0.0425000	−	0.130802i	−0.927555	−	0.373686i	$-0.878094\pi$
$29$	0.228870	−	0.704388i	0.0425000	−	0.130802i	0.970055	+	0.242885i	$0.0780937\pi$
$30$	−13.2748	+	8.38021i	−2.42364	+	1.53001i
$31$	−1.37016	−	4.21693i	−0.246088	−	0.757382i	−0.995456	−	0.0952276i	$-0.969642\pi$
$31$	−1.37016	−	4.21693i	−0.246088	−	0.757382i	0.749367	−	0.662155i	$-0.230358\pi$
$32$	−10.8073			−1.91049
$33$	−2.76076	−	8.49674i	−0.480586	−	1.47909i
$34$	−2.11757	−	1.53851i	−0.363161	−	0.263852i
$35$	1.12858	+	4.43938i	0.190766	+	0.750393i
$36$	−16.4616	+	11.9600i	−2.74359	+	1.99334i
$37$	−7.46083	−	5.42061i	−1.22655	−	0.891143i	−0.229926	−	0.973208i	$-0.573848\pi$
$37$	−7.46083	−	5.42061i	−1.22655	−	0.891143i	−0.996627	+	0.0820657i	$0.973848\pi$
$38$	−9.18954	−	6.67659i	−1.49074	−	1.08309i
$39$	−10.7520	+	7.81177i	−1.72170	+	1.25088i
$40$	14.1107	−	8.90788i	2.23110	−	1.40846i
$41$	6.04225	+	4.38995i	0.943642	+	0.685596i	0.949294	−	0.314388i	$-0.101799\pi$
$41$	6.04225	+	4.38995i	0.943642	+	0.685596i	−0.00565294	+	0.999984i	$0.501799\pi$
$42$	4.44424	+	13.6780i	0.685761	+	2.11056i
$43$	−8.85083			−1.34974			−0.674870	−	0.737937i	$-0.735800\pi$
$43$	−8.85083			−1.34974			−0.674870	+	0.737937i	$0.735800\pi$
$44$	4.99314	+	15.3673i	0.752744	+	2.31671i
$45$	3.47338	−	8.71212i	0.517781	−	1.29873i
$46$	5.23816	−	16.1214i	0.772324	−	2.37697i
$47$	2.60199	−	8.00809i	0.379539	−	1.16810i	−0.560826	−	0.827934i	$-0.689516\pi$
$47$	2.60199	−	8.00809i	0.379539	−	1.16810i	0.940365	−	0.340167i	$-0.110484\pi$
$48$	21.3335	−	15.4997i	3.07922	−	2.23718i
$49$	−2.80363			−0.400519
$50$	−5.62862	+	11.8151i	−0.796007	+	1.67091i
$51$	2.68224			0.375589
$52$	19.4462	−	14.1285i	2.69670	−	1.95926i
$53$	0.591818	−	1.82143i	0.0812925	−	0.250192i	−0.902147	−	0.431428i	$-0.858010\pi$
$53$	0.591818	−	1.82143i	0.0812925	−	0.250192i	0.983440	+	0.181236i	$0.0580098\pi$
$54$	2.59128	−	7.97513i	0.352628	−	1.08528i
$55$	−5.72739	−	4.76111i	−0.772280	−	0.641988i
$56$	−4.72408	−	14.5392i	−0.631281	−	1.94288i
$57$	11.6400			1.54175
$58$	−0.599059	−	1.84371i	−0.0786602	−	0.242091i
$59$	1.93010	+	1.40230i	0.251278	+	0.182564i	0.706293	−	0.707920i	$-0.250366\pi$
$59$	1.93010	+	1.40230i	0.251278	+	0.182564i	−0.455015	+	0.890484i	$0.650366\pi$
$60$	−10.7751	+	27.0267i	−1.39106	+	3.48913i
$61$	−8.73136	+	6.34370i	−1.11794	+	0.812228i	−0.983895	−	0.178748i	$-0.942795\pi$
$61$	−8.73136	+	6.34370i	−1.11794	+	0.812228i	−0.134041	+	0.990976i	$0.542795\pi$
$62$	−9.38920	−	6.82165i	−1.19243	−	0.866351i
$63$	−6.95129	−	5.05040i	−0.875780	−	0.636291i
$64$	−6.97816	+	5.06993i	−0.872270	+	0.633741i
$65$	−4.10312	+	10.2917i	−0.508930	+	1.27653i
$66$	−18.9184	−	13.7450i	−2.32870	−	1.69190i
$67$	1.62854	+	5.01214i	0.198958	+	0.612331i	0.999908	+	0.0135985i	$0.00432868\pi$
$67$	1.62854	+	5.01214i	0.198958	+	0.612331i	−0.800949	+	0.598732i	$0.795671\pi$
$68$	−4.85113			−0.588286
$69$	5.36778	+	16.5203i	0.646205	+	1.98882i
$70$	9.21989	+	7.66439i	1.10199	+	0.916070i
$71$	3.62525	−	11.1574i	0.430238	−	1.32414i	−0.467650	−	0.883914i	$-0.654899\pi$
$71$	3.62525	−	11.1574i	0.430238	−	1.32414i	0.897888	−	0.440224i	$-0.145101\pi$
$72$	−9.67277	+	29.7697i	−1.13995	+	3.50840i
$73$	−9.48784	+	6.89332i	−1.11047	+	0.806802i	−0.982737	−	0.185007i	$-0.940769\pi$
$73$	−9.48784	+	6.89332i	−1.11047	+	0.806802i	−0.127730	+	0.991809i	$0.540769\pi$
$74$	−24.1385			−2.80604
$75$	−2.45027	−	13.1855i	−0.282933	−	1.52253i
$76$	−21.0522			−2.41485
$77$	−5.52005	+	4.01055i	−0.629068	+	0.457044i
$78$	−10.7496	+	33.0840i	−1.21716	+	3.74603i
$79$	0.165581	−	0.509605i	0.0186293	−	0.0573351i	−0.941310	−	0.337544i	$-0.890404\pi$
$79$	0.165581	−	0.509605i	0.0186293	−	0.0573351i	0.959939	+	0.280209i	$0.0904038\pi$
$80$	8.14118	−	20.4202i	0.910212	−	2.28304i
$81$	−1.23303	−	3.79487i	−0.137003	−	0.421652i
$82$	19.5489			2.15882
$83$	0.531093	+	1.63454i	0.0582950	+	0.179414i	0.975964	−	0.217932i	$-0.0699313\pi$
$83$	0.531093	+	1.63454i	0.0582950	+	0.179414i	−0.917669	+	0.397346i	$0.869931\pi$
$84$	21.5643	+	15.6674i	2.35285	+	1.70945i
$85$	1.89082	−	1.19365i	0.205088	−	0.129469i
$86$	−18.7423	+	13.6171i	−2.02103	+	1.46837i
$87$	1.60717	+	1.16768i	0.172306	+	0.125188i
$88$	20.1096	+	14.6105i	2.14369	+	1.55748i
$89$	−8.34088	+	6.06000i	−0.884131	+	0.642359i	−0.934341	−	0.356380i	$-0.884011\pi$
$89$	−8.34088	+	6.06000i	−0.884131	+	0.642359i	0.0502099	+	0.998739i	$0.484011\pi$
$90$	−6.04852	−	23.7924i	−0.637570	−	2.50794i
$91$	8.21160	+	5.96607i	0.860809	+	0.625415i
$92$	−9.70823	−	29.8789i	−1.01215	−	3.11509i
$93$	11.8929			1.23324
$94$	−6.81061	−	20.9609i	−0.702461	−	2.16195i
$95$	8.20550	−	5.18002i	0.841867	−	0.531459i
$96$	8.95775	−	27.5691i	0.914247	−	2.81376i
$97$	0.122530	−	0.377109i	0.0124411	−	0.0382896i	−0.944643	−	0.328099i	$-0.893592\pi$
$97$	0.122530	−	0.377109i	0.0124411	−	0.0382896i	0.957084	+	0.289810i	$0.0935920\pi$
$98$	−5.93690	+	4.31341i	−0.599718	+	0.435721i
$99$	13.9707			1.40411
$100$	4.43159	+	23.8474i	0.443159	+	2.38474i
$101$	12.7894			1.27260			0.636298	−	0.771443i	$-0.280465\pi$
$101$	12.7894			1.27260			0.636298	+	0.771443i	$0.280465\pi$
$102$	5.67984	−	4.12665i	0.562388	−	0.408599i
$103$	4.46164	−	13.7315i	0.439619	−	1.35301i	−0.448660	−	0.893702i	$-0.648099\pi$
$103$	4.46164	−	13.7315i	0.439619	−	1.35301i	0.888279	−	0.459305i	$-0.151901\pi$
$104$	11.4265	−	35.1672i	1.12046	−	3.44843i
$105$	−12.2601	−	0.800642i	−1.19647	−	0.0781346i
$106$	−1.54906	−	4.76753i	−0.150458	−	0.463063i
$107$	−7.12071			−0.688385			−0.344192	−	0.938899i	$-0.611847\pi$
$107$	−7.12071			−0.688385			−0.344192	+	0.938899i	$0.611847\pi$
$108$	−4.80259	−	14.7809i	−0.462130	−	1.42229i
$109$	16.2337	+	11.7945i	1.55491	+	1.12971i	0.940036	+	0.341077i	$0.110792\pi$
$109$	16.2337	+	11.7945i	1.55491	+	1.12971i	0.614870	+	0.788628i	$0.289208\pi$
$110$	−19.4532	−	1.27038i	−1.85479	−	0.121126i
$111$	20.0117	−	14.5394i	1.89943	−	1.38002i
$112$	−16.2930	−	11.8375i	−1.53954	−	1.11854i
$113$	11.6476	+	8.46249i	1.09572	+	0.796084i	0.980355	−	0.197239i	$-0.0631976\pi$
$113$	11.6476	+	8.46249i	1.09572	+	0.796084i	0.115361	+	0.993324i	$0.463198\pi$
$114$	24.6485	−	17.9082i	2.30855	−	1.67726i
$115$	11.1358	+	9.25710i	1.03842	+	0.863229i
$116$	−2.90674	−	2.11187i	−0.269884	−	0.196082i
$117$	−6.42224	−	19.7656i	−0.593736	−	1.82733i
$118$	6.24459			0.574862
$119$	−0.633022	−	1.94824i	−0.0580291	−	0.178595i
$120$	11.0279	+	43.3792i	1.00670	+	3.95996i
$121$	0.0291166	−	0.0896117i	0.00264697	−	0.00814652i
$122$	−8.72946	+	26.8665i	−0.790329	+	2.43238i
$123$	−16.2068	+	11.7749i	−1.46132	+	1.06171i
$124$	−21.5096			−1.93162
$125$	−7.59508	−	8.20456i	−0.679325	−	0.733838i
$126$	−22.4900			−2.00356
$127$	10.4077	−	7.56165i	0.923536	−	0.670988i	−0.0208657	−	0.999782i	$-0.506642\pi$
$127$	10.4077	−	7.56165i	0.923536	−	0.670988i	0.944402	+	0.328794i	$0.106642\pi$
$128$	−0.297338	+	0.915113i	−0.0262812	+	0.0808853i
$129$	7.33608	−	22.5781i	0.645906	−	1.98789i
$130$	7.14516	+	28.1061i	0.626672	+	2.46507i
$131$	5.05428	+	15.5555i	0.441595	+	1.35909i	0.886175	+	0.463350i	$0.153353\pi$
$131$	5.05428	+	15.5555i	0.441595	+	1.35909i	−0.444580	+	0.895739i	$0.646647\pi$
$132$	−43.3400			−3.77226
$133$	−2.74710	−	8.45469i	−0.238203	−	0.733115i
$134$	11.1598	+	8.10806i	0.964059	+	0.700430i
$135$	5.50882	+	4.57942i	0.474124	+	0.394134i
$136$	−6.03748	+	4.38648i	−0.517709	+	0.376138i
$137$	−8.06885	−	5.86236i	−0.689368	−	0.500855i	0.187084	−	0.982344i	$-0.440096\pi$
$137$	−8.06885	−	5.86236i	−0.689368	−	0.500855i	−0.876452	+	0.481489i	$0.840096\pi$
$138$	36.7834	+	26.7247i	3.13121	+	2.27496i
$139$	−0.719651	+	0.522857i	−0.0610400	+	0.0443482i	−0.617887	−	0.786267i	$-0.712011\pi$
$139$	−0.719651	+	0.522857i	−0.0610400	+	0.0443482i	0.556847	+	0.830615i	$0.312011\pi$
$140$	22.1738	+	1.44805i	1.87403	+	0.122383i
$141$	18.2717	+	13.2751i	1.53875	+	1.11797i
$142$	−9.48898	−	29.2041i	−0.796297	−	2.45075i
$143$	−16.5037			−1.38011
$144$	12.7426	+	39.2178i	1.06189	+	3.26815i
$145$	1.65260	+	0.107922i	0.137241	+	0.00896243i
$146$	−9.48578	+	29.1942i	−0.785049	+	2.41613i
$147$	2.32381	−	7.15196i	0.191665	−	0.589884i
$148$	−36.1934	+	26.2961i	−2.97508	+	2.16152i
$149$	12.4990			1.02396			0.511980	−	0.858997i	$-0.328912\pi$
$149$	12.4990			1.02396			0.511980	+	0.858997i	$0.328912\pi$
$150$	−25.4746	−	24.1514i	−2.07999	−	1.97196i
$151$	−5.39750			−0.439243			−0.219621	−	0.975585i	$-0.570482\pi$
$151$	−5.39750			−0.439243			−0.219621	+	0.975585i	$0.570482\pi$
$152$	−26.2005	+	19.0358i	−2.12515	+	1.54401i
$153$	−1.29614	+	3.98912i	−0.104787	+	0.322501i
$154$	−5.51885	+	16.9853i	−0.444722	+	1.36871i
$155$	8.38379	−	5.29256i	0.673402	−	0.425109i
$156$	19.9231	+	61.3169i	1.59512	+	4.90928i
$157$	5.78787			0.461922			0.230961	−	0.972963i	$-0.425813\pi$
$157$	5.78787			0.461922			0.230961	+	0.972963i	$0.425813\pi$
$158$	−0.433402	−	1.33387i	−0.0344796	−	0.106117i
$159$	4.15586	+	3.01941i	0.329581	+	0.239455i
$160$	−5.95410	−	23.4210i	−0.470713	−	1.85159i
$161$	10.7327	−	7.79777i	0.845856	−	0.614550i
$162$	−8.44946	−	6.13889i	−0.663852	−	0.482317i
$163$	−0.0270147	−	0.0196273i	−0.00211595	−	0.00153733i	0.586727	−	0.809785i	$-0.300416\pi$
$163$	−0.0270147	−	0.0196273i	−0.00211595	−	0.00153733i	−0.588843	+	0.808248i	$0.700416\pi$
$164$	29.3118	−	21.2962i	2.28886	−	1.66296i
$165$	16.8926	−	10.6641i	1.31509	−	0.830196i
$166$	3.63937	+	2.64416i	0.282470	+	0.205227i
$167$	1.43054	+	4.40276i	0.110699	+	0.340696i	0.991026	−	0.133672i	$-0.0426768\pi$
$167$	1.43054	+	4.40276i	0.110699	+	0.340696i	−0.880327	+	0.474367i	$0.842677\pi$
$168$	41.0046			3.16357
$169$	3.56941	+	10.9855i	0.274570	+	0.845040i
$170$	2.16752	−	5.43668i	0.166241	−	0.416974i
$171$	−5.62481	+	17.3114i	−0.430140	+	1.32384i
$172$	−13.2681	+	40.8351i	−1.01168	+	3.11364i
$173$	4.25106	−	3.08858i	0.323202	−	0.234820i	−0.414339	−	0.910123i	$-0.635987\pi$
$173$	4.25106	−	3.08858i	0.323202	−	0.234820i	0.737541	+	0.675303i	$0.235987\pi$
$174$	5.19977			0.394194
$175$	−8.99897	+	4.89159i	−0.680258	+	0.369769i
$176$	32.7457			2.46830
$177$	−5.17700	+	3.76131i	−0.389127	+	0.282718i
$178$	−8.33907	+	25.6650i	−0.625040	+	1.92367i
$179$	−1.32024	+	4.06328i	−0.0986794	+	0.303704i	−0.988195	−	0.153201i	$-0.951042\pi$
$179$	−1.32024	+	4.06328i	−0.0986794	+	0.303704i	0.889516	+	0.456905i	$0.151042\pi$
$180$	−34.9882	−	29.0853i	−2.60787	−	2.16789i
$181$	−2.05009	−	6.30952i	−0.152382	−	0.468983i	0.845504	−	0.533968i	$-0.179300\pi$
$181$	−2.05009	−	6.30952i	−0.152382	−	0.468983i	−0.997886	+	0.0649855i	$0.979300\pi$
$182$	26.5675			1.96932
$183$	−8.94549	−	27.5314i	−0.661270	−	2.03518i
$184$	−39.0994	−	28.4074i	−2.88245	−	2.09422i
$185$	7.63679	−	19.1550i	0.561468	−	1.40830i
$186$	25.1841	−	18.2973i	1.84659	−	1.34162i
$187$	2.69467	+	1.95779i	0.197054	+	0.143168i
$188$	−33.0463	−	24.0096i	−2.41015	−	1.75108i
$189$	5.30939	−	3.85750i	0.386202	−	0.280592i
$190$	9.40627	−	23.5933i	0.682402	−	1.71164i
$191$	4.60596	+	3.34643i	0.333276	+	0.242139i	0.741819	−	0.670600i	$-0.233963\pi$
$191$	4.60596	+	3.34643i	0.333276	+	0.242139i	−0.408544	+	0.912739i	$0.633963\pi$
$192$	−7.14929	−	22.0033i	−0.515956	−	1.58795i
$193$	−16.2922			−1.17274			−0.586371	−	0.810043i	$-0.699444\pi$
$193$	−16.2922			−1.17274			−0.586371	+	0.810043i	$0.699444\pi$
$194$	−0.320718	−	0.987070i	−0.0230262	−	0.0708675i
$195$	−22.8528	−	18.9972i	−1.63652	−	1.36042i
$196$	−4.20288	+	12.9351i	−0.300205	+	0.923937i
$197$	−5.02136	+	15.4541i	−0.357757	+	1.10106i	0.596637	+	0.802511i	$0.296503\pi$
$197$	−5.02136	+	15.4541i	−0.357757	+	1.10106i	−0.954394	+	0.298551i	$0.903497\pi$
$198$	29.5841	−	21.4941i	2.10245	−	1.52752i
$199$	−9.47856			−0.671917			−0.335959	−	0.941877i	$-0.609060\pi$
$199$	−9.47856			−0.671917			−0.335959	+	0.941877i	$0.609060\pi$
$200$	27.0786	+	25.6721i	1.91475	+	1.81529i
$201$	−14.1356			−0.997050
$202$	27.0826	−	19.6766i	1.90552	−	1.38444i
$203$	0.468840	−	1.44294i	0.0329061	−	0.101275i
$204$	4.02089	−	12.3750i	0.281519	−	0.866426i
$205$	−6.18476	+	15.5129i	−0.431962	+	1.08347i
$206$	−11.6782	−	35.9418i	−0.813659	−	2.50418i
$207$	−27.1635			−1.88799
$208$	−15.0530	−	46.3282i	−1.04373	−	3.21229i
$209$	11.6939	+	8.49615i	0.808887	+	0.587691i
$210$	−27.1935	+	17.1669i	−1.87653	+	1.18463i
$211$	−13.2398	+	9.61925i	−0.911463	+	0.662217i	−0.941384	−	0.337336i	$-0.890474\pi$
$211$	−13.2398	+	9.61925i	−0.911463	+	0.662217i	0.0299215	+	0.999552i	$0.490474\pi$
$212$	−7.51634	−	5.46094i	−0.516224	−	0.375059i
$213$	25.4572	+	18.4958i	1.74430	+	1.26731i
$214$	−15.0786	+	10.9553i	−1.03075	+	0.748887i
$215$	−4.87620	−	19.1809i	−0.332554	−	1.30813i
$216$	−19.3422	−	14.0529i	−1.31607	−	0.956182i
$217$	−2.80678	−	8.63839i	−0.190537	−	0.586412i
$218$	52.5219			3.55723
$219$	−9.72052	−	29.9167i	−0.656852	−	2.02158i
$220$	−30.5521	+	19.2871i	−2.05982	+	1.30034i
$221$	1.53114	−	4.71237i	0.102996	−	0.316988i
$222$	20.0074	−	61.5764i	1.34281	−	4.13274i
$223$	−3.18770	+	2.31600i	−0.213464	+	0.155091i	−0.689380	−	0.724400i	$-0.742117\pi$
$223$	−3.18770	+	2.31600i	−0.213464	+	0.155091i	0.475915	+	0.879491i	$0.342117\pi$
$224$	−22.1389			−1.47922
$225$	20.7939	+	2.72751i	1.38626	+	0.181834i
$226$	37.6843			2.50672
$227$	−3.81837	+	2.77421i	−0.253434	+	0.184131i	−0.707247	−	0.706966i	$-0.750063\pi$
$227$	−3.81837	+	2.77421i	−0.253434	+	0.184131i	0.453813	+	0.891097i	$0.350063\pi$
$228$	17.4493	−	53.7034i	1.15561	−	3.55659i
$229$	−4.06853	+	12.5217i	−0.268856	+	0.827455i	0.721924	+	0.691973i	$0.243258\pi$
$229$	−4.06853	+	12.5217i	−0.268856	+	0.827455i	−0.990780	+	0.135482i	$0.956742\pi$
$230$	37.8231	+	2.47002i	2.49398	+	0.162868i
$231$	−5.65542	−	17.4056i	−0.372099	−	1.14520i
$232$	−5.52718			−0.362877
$233$	6.96586	+	21.4387i	0.456349	+	1.40450i	0.869544	+	0.493855i	$0.164413\pi$
$233$	6.96586	+	21.4387i	0.456349	+	1.40450i	−0.413195	+	0.910643i	$0.635587\pi$
$234$	−44.0091	−	31.9745i	−2.87697	−	2.09024i
$235$	18.7881	+	1.22695i	1.22560	+	0.0800374i
$236$	9.36319	−	6.80275i	0.609491	−	0.442821i
$237$	1.16274	+	0.844781i	0.0755281	+	0.0548744i
$238$	−4.33786	−	3.15164i	−0.281182	−	0.204290i
$239$	−4.79517	+	3.48389i	−0.310174	+	0.225354i	−0.731971	−	0.681336i	$-0.761399\pi$
$239$	−4.79517	+	3.48389i	−0.310174	+	0.225354i	0.421797	+	0.906690i	$0.361399\pi$
$240$	45.3431	+	37.6933i	2.92689	+	2.43309i
$241$	−4.16720	−	3.02765i	−0.268433	−	0.195028i	0.445424	−	0.895320i	$-0.353053\pi$
$241$	−4.16720	−	3.02765i	−0.268433	−	0.195028i	−0.713856	+	0.700292i	$0.753053\pi$
$242$	−0.0762118	−	0.234556i	−0.00489908	−	0.0150778i
$243$	20.3136			1.30312
$244$	16.1789	+	49.7936i	1.03575	+	3.18771i
$245$	−1.54461	−	6.07585i	−0.0986815	−	0.388172i
$246$	−16.2033	+	49.8685i	−1.03308	+	3.17950i
$247$	6.64463	−	20.4501i	0.422787	−	1.30121i
$248$	−26.7698	+	19.4494i	−1.69988	+	1.23504i
$249$	−4.60984			−0.292137
$250$	−28.7059	−	5.68866i	−1.81552	−	0.359783i
$251$	−11.0271			−0.696026			−0.348013	−	0.937490i	$-0.613143\pi$
$251$	−11.0271			−0.696026			−0.348013	+	0.937490i	$0.613143\pi$
$252$	−33.7216	+	24.5002i	−2.12426	+	1.54337i
$253$	−6.66570	+	20.5149i	−0.419069	+	1.28976i
$254$	10.4055	−	32.0247i	0.652897	−	2.00941i
$255$	1.47773	+	5.81278i	0.0925390	+	0.364010i
$256$	−4.55257	−	14.0114i	−0.284535	−	0.875710i
$257$	5.06662			0.316047			0.158024	−	0.987435i	$-0.449488\pi$
$257$	5.06662			0.316047			0.158024	+	0.987435i	$0.449488\pi$
$258$	−19.2019	−	59.0975i	−1.19546	−	3.67925i
$259$	−15.2835	−	11.1041i	−0.949672	−	0.689977i
$260$	41.3318	+	34.3586i	2.56329	+	2.13083i
$261$	−2.51324	+	1.82598i	−0.155566	+	0.113025i
$262$	34.6351	+	25.1638i	2.13976	+	1.55463i
$263$	−16.3196	−	11.8569i	−1.00631	−	0.731128i	−0.0428794	−	0.999080i	$-0.513653\pi$
$263$	−16.3196	−	11.8569i	−1.00631	−	0.731128i	−0.963432	+	0.267952i	$0.913653\pi$
$264$	−53.9388	+	39.1889i	−3.31971	+	2.41191i
$265$	4.27333	+	0.279068i	0.262509	+	0.0171430i
$266$	−18.8248	−	13.6770i	−1.15422	−	0.838592i
$267$	−8.54543	−	26.3001i	−0.522972	−	1.60954i
$268$	25.5658			1.56168
$269$	−0.523248	−	1.61039i	−0.0319030	−	0.0981873i	0.933837	−	0.357699i	$-0.116439\pi$
$269$	−0.523248	−	1.61039i	−0.0319030	−	0.0981873i	−0.965740	+	0.259511i	$0.916439\pi$
$270$	18.7108	+	1.22190i	1.13870	+	0.0743625i
$271$	−3.33620	+	10.2678i	−0.202660	+	0.623723i	0.797142	+	0.603792i	$0.206344\pi$
$271$	−3.33620	+	10.2678i	−0.202660	+	0.623723i	−0.999801	+	0.0199303i	$0.993656\pi$
$272$	−3.03801	+	9.35002i	−0.184206	+	0.566928i
$273$	−22.0255	+	16.0024i	−1.33304	+	0.968512i
$274$	−26.1057			−1.57710
$275$	7.16258	−	15.0351i	0.431920	−	0.906648i
$276$	84.2666			5.07225
$277$	1.52161	−	1.10551i	0.0914247	−	0.0664239i	−0.541134	−	0.840936i	$-0.682005\pi$
$277$	1.52161	−	1.10551i	0.0914247	−	0.0664239i	0.632559	+	0.774513i	$0.282005\pi$
$278$	−0.719495	+	2.21438i	−0.0431524	+	0.132810i
$279$	−5.74702	+	17.6875i	−0.344065	+	1.05892i
$280$	28.9058	−	18.2478i	1.72745	−	1.09052i
$281$	9.62876	+	29.6343i	0.574404	+	1.76783i	0.638200	+	0.769871i	$0.279679\pi$
$281$	9.62876	+	29.6343i	0.574404	+	1.76783i	−0.0637960	+	0.997963i	$0.520321\pi$
$282$	59.1155			3.52028
$283$	−0.772036	−	2.37608i	−0.0458928	−	0.141243i	0.925484	−	0.378786i	$-0.123658\pi$
$283$	−0.772036	−	2.37608i	−0.0458928	−	0.141243i	−0.971377	+	0.237542i	$0.923658\pi$
$284$	−46.0422	−	33.4516i	−2.73210	−	1.98499i
$285$	6.41283	+	25.2254i	0.379863	+	1.49422i
$286$	−34.9479	+	25.3911i	−2.06651	+	1.50141i
$287$	12.3776	+	8.99284i	0.730625	+	0.530830i
$288$	36.6731	+	26.6446i	2.16098	+	1.57005i
$289$	−0.809017	+	0.587785i	−0.0475892	+	0.0345756i
$290$	3.66553	−	2.31400i	0.215248	−	0.135883i
$291$	0.860430	+	0.625139i	0.0504393	+	0.0366463i
$292$	17.5806	+	54.1077i	1.02883	+	3.16641i
$293$	18.5121			1.08149			0.540744	−	0.841187i	$-0.318143\pi$
$293$	18.5121			1.08149			0.540744	+	0.841187i	$0.318143\pi$
$294$	−6.08250	−	18.7200i	−0.354739	−	1.09177i
$295$	−1.97563	+	4.95537i	−0.115025	+	0.288513i
$296$	−21.2672	+	65.4536i	−1.23613	+	3.80441i
$297$	−3.29747	+	10.1486i	−0.191339	+	0.588881i
$298$	26.4676	−	19.2299i	1.53323	−	1.11396i
$299$	32.0884			1.85572
$300$	−64.5069	−	8.46126i	−3.72431	−	0.488511i
$301$	−18.1310			−1.04505
$302$	−11.4296	+	8.30410i	−0.657700	+	0.477847i
$303$	−10.6006	+	32.6254i	−0.608990	+	1.87428i
$304$	−13.1839	+	40.5758i	−0.756148	+	2.32718i
$305$	−18.5580	−	15.4271i	−1.06263	−	0.883353i
$306$	3.39261	+	10.4414i	0.193943	+	0.596894i
$307$	−1.77631			−0.101380			−0.0506898	−	0.998714i	$-0.516142\pi$
$307$	−1.77631			−0.101380			−0.0506898	+	0.998714i	$0.516142\pi$
$308$	10.2285	+	31.4800i	0.582821	+	1.79374i
$309$	31.3305	+	22.7630i	1.78233	+	1.29494i
$310$	9.61064	−	24.1059i	0.545848	−	1.36912i
$311$	8.84550	−	6.42663i	0.501583	−	0.364421i	−0.308039	−	0.951374i	$-0.599673\pi$
$311$	8.84550	−	6.42663i	0.501583	−	0.364421i	0.809621	+	0.586953i	$0.199673\pi$
$312$	80.2392	+	58.2972i	4.54265	+	3.30043i
$313$	9.60132	+	6.97577i	0.542699	+	0.394294i	0.825086	−	0.565007i	$-0.191126\pi$
$313$	9.60132	+	6.97577i	0.542699	+	0.394294i	−0.282388	+	0.959300i	$0.591126\pi$
$314$	12.2562	−	8.90469i	0.691660	−	0.502521i
$315$	7.11523	−	17.8468i	0.400898	−	1.00555i
$316$	−2.10295	−	1.52788i	−0.118300	−	0.0859500i
$317$	−10.7400	−	33.0543i	−0.603218	−	1.85651i	−0.508604	−	0.861001i	$-0.669838\pi$
$317$	−10.7400	−	33.0543i	−0.603218	−	1.85651i	−0.0946142	−	0.995514i	$-0.530162\pi$
$318$	13.4457			0.753999
$319$	0.762319	+	2.34618i	0.0426817	+	0.131361i
$320$	−14.8317	−	12.3294i	−0.829118	−	0.689236i
$321$	5.90205	−	18.1647i	0.329421	−	1.01385i
$322$	10.7304	−	33.0247i	0.597981	−	1.84040i
$323$	−3.51085	+	2.55078i	−0.195349	+	0.141929i
$324$	−19.3568			−1.07538
$325$	−24.5640	−	3.22202i	−1.36257	−	0.178726i
$326$	−0.0874023			−0.00484077
$327$	−43.5426	+	31.6356i	−2.40791	+	1.74945i
$328$	17.2235	−	53.0085i	0.951009	−	2.92690i
$329$	5.33018	−	16.4046i	0.293862	−	0.904415i
$330$	19.3646	−	48.5713i	1.06599	−	2.67376i
$331$	−8.29891	−	25.5414i	−0.456149	−	1.40388i	−0.869781	−	0.493439i	$-0.835740\pi$
$331$	−8.29891	−	25.5414i	−0.456149	−	1.40388i	0.413631	−	0.910445i	$-0.364260\pi$
$332$	8.33740			0.457574
$333$	11.9532	+	36.7880i	0.655029	+	2.01597i
$334$	9.80296	+	7.12227i	0.536394	+	0.389713i
$335$	−9.96478	+	6.29062i	−0.544434	+	0.343693i
$336$	43.7017	−	31.7511i	2.38412	−	1.73217i
$337$	−23.2447	−	16.8883i	−1.26622	−	0.919962i	−0.267174	−	0.963648i	$-0.586090\pi$
$337$	−23.2447	−	16.8883i	−1.26622	−	0.919962i	−0.999045	+	0.0436860i	$0.986090\pi$
$338$	24.4598	+	17.7711i	1.33044	+	0.966620i
$339$	−31.2417	+	22.6984i	−1.69682	+	1.23281i
$340$	−2.67264	−	10.5131i	−0.144944	−	0.570150i
$341$	11.9480	+	8.68074i	0.647021	+	0.470089i
$342$	14.7228	+	45.3120i	0.796115	+	2.45019i
$343$	−20.0828			−1.08437
$344$	20.4110	+	62.8186i	1.10049	+	3.38695i
$345$	−32.8445	+	20.7343i	−1.76829	+	1.11630i
$346$	4.25014	−	13.0806i	0.228489	−	0.703216i
$347$	3.25543	−	10.0192i	0.174761	−	0.537858i	−0.824862	−	0.565334i	$-0.808747\pi$
$347$	3.25543	−	10.0192i	0.174761	−	0.537858i	0.999622	+	0.0274765i	$0.00874713\pi$
$348$	7.79657	−	5.66454i	0.417940	−	0.303651i
$349$	24.9005			1.33289			0.666446	−	0.745553i	$-0.267815\pi$
$349$	24.9005			1.33289			0.666446	+	0.745553i	$0.267815\pi$
$350$	−11.5302	+	24.2033i	−0.616317	+	1.29372i
$351$	15.8739			0.847287
$352$	29.1223	−	21.1586i	1.55222	−	1.12776i
$353$	−3.19014	+	9.81825i	−0.169794	+	0.522573i	−0.999358	−	0.0358399i	$-0.988589\pi$
$353$	−3.19014	+	9.81825i	−0.169794	+	0.522573i	0.829563	+	0.558413i	$0.188589\pi$
$354$	−5.17588	+	15.9297i	−0.275095	+	0.846655i
$355$	26.1768	+	1.70946i	1.38932	+	0.0907289i
$356$	15.4554	+	47.5667i	0.819133	+	2.52103i
$357$	5.49458			0.290804
$358$	3.45568	+	10.6355i	0.182639	+	0.562104i
$359$	10.3711	+	7.53502i	0.547364	+	0.397683i	0.826812	−	0.562478i	$-0.190152\pi$
$359$	10.3711	+	7.53502i	0.547364	+	0.397683i	−0.279449	+	0.960161i	$0.590152\pi$
$360$	−69.8441	−	4.56113i	−3.68111	−	0.240393i
$361$	0.135449	−	0.0984098i	0.00712892	−	0.00517946i
$362$	−14.0485	−	10.2068i	−0.738371	−	0.536458i
$363$	0.204463	+	0.148551i	0.0107315	+	0.00779689i
$364$	39.8355	−	28.9422i	2.08795	−	1.51698i
$365$	−20.1659	−	16.7637i	−1.05553	−	0.877451i
$366$	−61.3000	−	44.5371i	−3.20420	−	2.32799i
$367$	0.380324	+	1.17052i	0.0198528	+	0.0611005i	0.960492	−	0.278307i	$-0.0897733\pi$
$367$	0.380324	+	1.17052i	0.0198528	+	0.0611005i	−0.940639	+	0.339408i	$0.889773\pi$
$368$	−63.6680			−3.31892
$369$	−9.68043	−	29.7933i	−0.503943	−	1.55098i
$370$	−13.2987	−	52.3114i	−0.691364	−	2.71954i
$371$	1.21234	−	3.73120i	0.0629416	−	0.193714i
$372$	17.8284	−	54.8702i	0.924360	−	2.84489i
$373$	7.92486	−	5.75774i	0.410333	−	0.298125i	−0.363403	−	0.931632i	$-0.618385\pi$
$373$	7.92486	−	5.75774i	0.410333	−	0.298125i	0.773737	+	0.633507i	$0.218385\pi$
$374$	8.71825			0.450810
$375$	27.2247	−	12.5744i	1.40588	−	0.649337i
$376$	−62.8378			−3.24061
$377$	2.96891	−	2.15704i	0.152907	−	0.111093i
$378$	5.30824	−	16.3371i	0.273027	−	0.840289i
$379$	−8.39916	+	25.8500i	−0.431436	+	1.32782i	0.465259	+	0.885175i	$0.345961\pi$
$379$	−8.39916	+	25.8500i	−0.431436	+	1.32782i	−0.896695	+	0.442649i	$0.854039\pi$
$380$	−11.5983	−	45.6230i	−0.594981	−	2.34041i
$381$	10.6630	+	32.8172i	0.546280	+	1.68128i
$382$	14.9020			0.762451
$383$	2.44510	+	7.52523i	0.124939	+	0.384521i	0.993890	−	0.110376i	$-0.0352056\pi$
$383$	2.44510	+	7.52523i	0.124939	+	0.384521i	−0.868951	+	0.494898i	$0.835206\pi$
$384$	−2.08797	−	1.51700i	−0.106551	−	0.0774139i
$385$	−11.7326	−	9.75315i	−0.597947	−	0.497067i
$386$	−34.5001	+	25.0658i	−1.75601	+	1.27581i
$387$	30.0340	+	21.8209i	1.52671	+	1.10922i
$388$	−1.55618	−	1.13063i	−0.0790033	−	0.0573992i
$389$	−27.1744	+	19.7434i	−1.37780	+	1.00103i	−0.380716	+	0.924692i	$0.624323\pi$
$389$	−27.1744	+	19.7434i	−1.37780	+	1.00103i	−0.997082	+	0.0763372i	$0.975677\pi$
$390$	−77.6199	−	5.06893i	−3.93043	−	0.256675i
$391$	−5.23929	−	3.80657i	−0.264962	−	0.192506i
$392$	6.46549	+	19.8987i	0.326557	+	1.00504i
$393$	−43.8707			−2.21299
$394$	13.1432	+	40.4507i	0.662146	+	2.03788i
$395$	1.19561	+	0.0780785i	0.0601575	+	0.00392856i
$396$	20.9433	−	64.4567i	1.05244	−	3.23907i
$397$	5.23648	−	16.1162i	0.262811	−	0.808850i	−0.729378	−	0.684110i	$-0.760191\pi$
$397$	5.23648	−	16.1162i	0.262811	−	0.808850i	0.992190	−	0.124739i	$-0.0398094\pi$
$398$	−20.0716	+	14.5828i	−1.00610	+	0.730972i
$399$	23.8445			1.19372
$400$	48.7385	+	6.39295i	2.43692	+	0.319647i
$401$	−22.9745			−1.14729			−0.573646	−	0.819103i	$-0.694471\pi$
$401$	−22.9745			−1.14729			−0.573646	+	0.819103i	$0.694471\pi$
$402$	−29.9332	+	21.7478i	−1.49293	+	1.08468i
$403$	6.78899	−	20.8944i	0.338184	−	1.04082i
$404$	19.1724	−	59.0066i	0.953863	−	2.93569i
$405$	7.54468	−	4.76285i	0.374898	−	0.236668i
$406$	−1.22717	−	3.77685i	−0.0609036	−	0.187442i
$407$	30.7169			1.52258
$408$	−6.18554	−	19.0371i	−0.306230	−	0.942479i
$409$	27.3635	+	19.8808i	1.35304	+	0.983041i	0.998854	+	0.0478663i	$0.0152421\pi$
$409$	27.3635	+	19.8808i	1.35304	+	0.983041i	0.354186	+	0.935175i	$0.384758\pi$
$410$	10.7701	+	42.3651i	0.531897	+	2.09226i
$411$	21.6426	−	15.7243i	1.06755	−	0.775620i
$412$	−56.6647	−	41.1693i	−2.79167	−	2.02827i
$413$	3.95383	+	2.87262i	0.194555	+	0.141353i
$414$	−57.5208	+	41.7913i	−2.82699	+	2.05393i
$415$	−3.24966	+	2.05147i	−0.159520	+	0.100703i
$416$	−43.3222	−	31.4754i	−2.12404	−	1.54321i
$417$	−0.737300	−	2.26918i	−0.0361057	−	0.111122i
$418$	37.8342			1.85053
$419$	3.50008	+	10.7722i	0.170990	+	0.526254i	0.999428	−	0.0338276i	$-0.0107697\pi$
$419$	3.50008	+	10.7722i	0.170990	+	0.526254i	−0.828437	+	0.560082i	$0.810770\pi$
$420$	−22.0729	+	55.3643i	−1.07704	+	2.70150i
$421$	−2.99693	+	9.22360i	−0.146061	+	0.449531i	−0.997146	−	0.0754980i	$-0.975945\pi$
$421$	−2.99693	+	9.22360i	−0.146061	+	0.449531i	0.851085	+	0.525029i	$0.175945\pi$
$422$	−13.2369	+	40.7390i	−0.644362	+	1.98314i
$423$	−28.5727	+	20.7593i	−1.38925	+	1.00935i
$424$	−14.2924			−0.694098
$425$	3.62851	+	3.44005i	0.176009	+	0.166867i
$426$	82.3635			3.99052
$427$	−17.8862	+	12.9951i	−0.865575	+	0.628877i
$428$	−10.6745	+	32.8528i	−0.515973	+	1.58800i
$429$	13.6792	−	42.1003i	0.660440	−	2.03262i
$430$	−39.8358	−	33.1150i	−1.92105	−	1.59695i
$431$	−4.89786	−	15.0741i	−0.235922	−	0.726092i	−0.996998	−	0.0774294i	$-0.975329\pi$
$431$	−4.89786	−	15.0741i	−0.235922	−	0.726092i	0.761076	−	0.648662i	$-0.224671\pi$
$432$	−31.4961			−1.51536
$433$	−8.64120	−	26.5949i	−0.415270	−	1.27807i	−0.912010	−	0.410169i	$-0.865470\pi$
$433$	−8.64120	−	26.5949i	−0.415270	−	1.27807i	0.496740	−	0.867899i	$-0.334530\pi$
$434$	−19.2338	−	13.9742i	−0.923252	−	0.670782i
$435$	−1.64507	+	4.12626i	−0.0788751	+	0.197839i
$436$	78.7517	−	57.2165i	3.77152	−	2.74017i
$437$	−22.7367	−	16.5192i	−1.08764	−	0.790220i
$438$	−66.6110	−	48.3957i	−3.18280	−	2.31244i
$439$	−18.2491	+	13.2588i	−0.870983	+	0.632806i	−0.930850	−	0.365400i	$-0.880932\pi$
$439$	−18.2491	+	13.2588i	−0.870983	+	0.632806i	0.0598677	+	0.998206i	$0.480932\pi$
$440$	−20.5839	+	51.6297i	−0.981299	+	2.46135i
$441$	9.51371	+	6.91211i	0.453034	+	0.329148i
$442$	−4.00771	−	12.3345i	−0.190628	−	0.586691i
$443$	−15.7511			−0.748355			−0.374178	−	0.927357i	$-0.622075\pi$
$443$	−15.7511			−0.748355			−0.374178	+	0.927357i	$0.622075\pi$
$444$	−37.0811	−	114.124i	−1.75979	−	5.41607i
$445$	−17.7281	−	14.7372i	−0.840392	−	0.698609i
$446$	−3.18701	+	9.80861i	−0.150909	+	0.464451i
$447$	−10.3599	+	31.8846i	−0.490007	+	1.50809i
$448$	−14.2948	+	10.3858i	−0.675365	+	0.490681i
$449$	13.4657			0.635485			0.317742	−	0.948177i	$-0.397075\pi$
$449$	13.4657			0.635485			0.317742	+	0.948177i	$0.397075\pi$
$450$	48.2290	−	26.2159i	2.27354	−	1.23583i
$451$	−24.8765			−1.17139
$452$	56.5041	−	41.0526i	2.65773	−	1.93095i
$453$	4.47376	−	13.7688i	0.210196	−	0.646916i
$454$	−3.81754	+	11.7492i	−0.179166	+	0.551417i
$455$	−8.40527	+	21.0825i	−0.394045	+	0.988365i
$456$	−26.8431	−	82.6146i	−1.25704	−	3.86878i
$457$	24.4168			1.14217			0.571085	−	0.820891i	$-0.306523\pi$
$457$	24.4168			1.14217			0.571085	+	0.820891i	$0.306523\pi$
$458$	10.6493	+	32.7750i	0.497607	+	1.53148i
$459$	−2.59184	−	1.88308i	−0.120977	−	0.0878948i
$460$	59.4030	−	37.5003i	2.76968	−	1.74846i
$461$	13.7531	−	9.99222i	0.640546	−	0.465384i	−0.219492	−	0.975614i	$-0.570440\pi$
$461$	13.7531	−	9.99222i	0.640546	−	0.465384i	0.860038	+	0.510230i	$0.170440\pi$
$462$	−38.7544	−	28.1567i	−1.80302	−	1.30997i
$463$	3.07402	+	2.23340i	0.142862	+	0.103795i	0.656920	−	0.753960i	$-0.271859\pi$
$463$	3.07402	+	2.23340i	0.142862	+	0.103795i	−0.514059	+	0.857755i	$0.671859\pi$
$464$	−5.89074	+	4.27987i	−0.273471	+	0.198688i
$465$	6.55216	+	25.7735i	0.303849	+	1.19522i
$466$	47.7344	+	34.6811i	2.21125	+	1.60657i
$467$	4.19435	+	12.9089i	0.194091	+	0.597352i	0.999986	+	0.00529281i	$0.00168476\pi$
$467$	4.19435	+	12.9089i	0.194091	+	0.597352i	−0.805895	+	0.592059i	$0.798315\pi$
$468$	−100.820			−4.66041
$469$	3.33608	+	10.2674i	0.154046	+	0.474104i
$470$	41.6730	−	26.3075i	1.92223	−	1.21348i
$471$	−4.79732	+	14.7646i	−0.221049	+	0.680319i
$472$	5.50178	−	16.9327i	0.253240	−	0.779393i
$473$	23.8501	−	17.3281i	1.09663	−	0.796747i
$474$	3.76189			0.172789
$475$	15.7465	+	14.9286i	0.722497	+	0.684971i
$476$	−9.93755			−0.455487
$477$	−6.49882	+	4.72167i	−0.297560	+	0.216190i
$478$	−4.79413	+	14.7548i	−0.219278	+	0.674869i
$479$	−0.933231	+	2.87219i	−0.0426404	+	0.131234i	−0.970110	−	0.242664i	$-0.921979\pi$
$479$	−0.933231	+	2.87219i	−0.0426404	+	0.131234i	0.927470	+	0.373897i	$0.121979\pi$
$480$	64.6811	+	4.22397i	2.95228	+	0.192797i
$481$	−14.1203	−	43.4579i	−0.643832	−	1.98151i
$482$	−13.4824			−0.614107
$483$	10.9959	+	33.8420i	0.500332	+	1.53986i
$484$	−0.369793	−	0.268671i	−0.0168088	−	0.0122123i
$485$	0.884752	+	0.0577783i	0.0401745	+	0.00262358i
$486$	43.0156	−	31.2527i	1.95123	−	1.41765i
$487$	20.1087	+	14.6099i	0.911214	+	0.662036i	0.941322	−	0.337511i	$-0.109585\pi$
$487$	20.1087	+	14.6099i	0.911214	+	0.662036i	−0.0301076	+	0.999547i	$0.509585\pi$
$488$	65.1598	+	47.3414i	2.94965	+	2.14304i
$489$	0.0724598	−	0.0526451i	0.00327674	−	0.00238069i
$490$	−12.6186	−	10.4897i	−0.570049	−	0.473875i
$491$	−21.1140	−	15.3402i	−0.952861	−	0.692294i	−0.00137893	−	0.999999i	$-0.500439\pi$
$491$	−21.1140	−	15.3402i	−0.952861	−	0.692294i	−0.951482	+	0.307705i	$0.900439\pi$
$492$	30.0306	+	92.4247i	1.35388	+	4.16683i
$493$	−0.740638			−0.0333566
$494$	−17.3921	−	53.5273i	−0.782507	−	2.40831i
$495$	7.69691	+	30.2765i	0.345951	+	1.36083i
$496$	−13.4703	+	41.4574i	−0.604836	+	1.86149i
$497$	7.42634	−	22.8559i	0.333117	−	1.02523i
$498$	−9.76167	+	7.09227i	−0.437431	+	0.317812i
$499$	6.11520			0.273754			0.136877	−	0.990588i	$-0.456293\pi$
$499$	6.11520			0.273754			0.136877	+	0.990588i	$0.456293\pi$
$500$	−49.2390	+	22.7421i	−2.20203	+	1.01706i
$501$	−12.4170			−0.554750
$502$	−23.3507	+	16.9653i	−1.04219	+	0.757199i
$503$	9.60330	−	29.5559i	0.428190	−	1.31783i	−0.471716	−	0.881750i	$-0.656365\pi$
$503$	9.60330	−	29.5559i	0.428190	−	1.31783i	0.899906	−	0.436083i	$-0.143635\pi$
$504$	−19.8147	+	60.9834i	−0.882617	+	2.71642i
$505$	7.04610	+	27.7164i	0.313547	+	1.23337i
$506$	17.4472	+	53.6971i	0.775625	+	2.38713i
$507$	−30.9822			−1.37597
$508$	−19.2852	−	59.3536i	−0.855640	−	2.63339i
$509$	−15.8902	−	11.5449i	−0.704319	−	0.511718i	0.177017	−	0.984208i	$-0.443355\pi$
$509$	−15.8902	−	11.5449i	−0.704319	−	0.511718i	−0.881336	+	0.472490i	$0.843355\pi$
$510$	12.0722	+	10.0355i	0.534566	+	0.444379i
$511$	−19.4359	+	14.1210i	−0.859792	+	0.624676i
$512$	−32.7539	−	23.7971i	−1.44753	−	1.05169i
$513$	−11.2477	−	8.17192i	−0.496597	−	0.360799i
$514$	10.7290	−	7.79504i	0.473234	−	0.343824i
$515$	32.2161	+	2.10386i	1.41961	+	0.0927070i
$516$	−93.1713	−	67.6929i	−4.10164	−	2.98001i
$517$	8.66670	+	26.6734i	0.381161	+	1.17309i
$518$	−49.4478			−2.17261
$519$	4.35531	+	13.4043i	0.191177	+	0.588382i
$520$	82.5072	+	5.38809i	3.61818	+	0.236284i
$521$	−9.23398	+	28.4193i	−0.404548	+	1.24507i	0.516724	+	0.856152i	$0.327151\pi$
$521$	−9.23398	+	28.4193i	−0.404548	+	1.24507i	−0.921272	+	0.388919i	$0.872849\pi$
$522$	−2.51270	+	7.73328i	−0.109978	+	0.338477i
$523$	−5.62560	+	4.08723i	−0.245990	+	0.178722i	−0.703948	−	0.710252i	$-0.748581\pi$
$523$	−5.62560	+	4.08723i	−0.245990	+	0.178722i	0.457958	+	0.888974i	$0.348581\pi$
$524$	79.3451			3.46621
$525$	−5.01939	−	27.0105i	−0.219064	−	1.17883i
$526$	−52.8000			−2.30219
$527$	−3.58713	+	2.60620i	−0.156258	+	0.113528i
$528$	−27.1415	+	83.5331i	−1.18118	+	3.63531i
$529$	5.85283	−	18.0132i	0.254471	−	0.783181i
$530$	9.47845	−	5.98361i	0.411718	−	0.259911i
$531$	−3.09226	−	9.51700i	−0.134193	−	0.413003i
$532$	−43.1255			−1.86973
$533$	11.4355	+	35.1950i	0.495329	+	1.52446i
$534$	−58.5586	−	42.5453i	−2.53408	−	1.84111i
$535$	−3.92302	−	15.4315i	−0.169607	−	0.667164i
$536$	31.8180	−	23.1171i	1.37433	−	0.998508i
$537$	−9.27098	−	6.73576i	−0.400072	−	0.290670i
$538$	−3.58562	−	2.60510i	−0.154587	−	0.112314i
$539$	7.55488	−	5.48894i	0.325412	−	0.236425i
$540$	29.3862	−	18.5511i	1.26458	−	0.798313i
$541$	1.90220	+	1.38203i	0.0817820	+	0.0594181i	0.627925	−	0.778274i	$-0.283904\pi$
$541$	1.90220	+	1.38203i	0.0817820	+	0.0594181i	−0.546143	+	0.837692i	$0.683904\pi$
$542$	8.73239	+	26.8755i	0.375088	+	1.15440i
$543$	17.7946			0.763638
$544$	3.33965	+	10.2784i	0.143186	+	0.440683i
$545$	−16.6166	+	41.6785i	−0.711775	+	1.78531i
$546$	−22.0207	+	67.7727i	−0.942399	+	2.90040i
$547$	−12.0919	+	37.2152i	−0.517014	+	1.59121i	0.262574	+	0.964912i	$0.415429\pi$
$547$	−12.0919	+	37.2152i	−0.517014	+	1.59121i	−0.779588	+	0.626293i	$0.784571\pi$
$548$	−39.1430	+	28.4391i	−1.67211	+	1.21486i
$549$	45.2684			1.93201
$550$	−7.96427	−	42.8575i	−0.339598	−	1.82745i
$551$	−3.21411			−0.136926
$552$	104.874	−	76.1955i	4.46374	−	3.24310i
$553$	0.339193	−	1.04393i	0.0144239	−	0.0443924i
$554$	1.52128	−	4.68202i	0.0646330	−	0.198920i
$555$	42.5339	+	35.3579i	1.80546	+	1.50086i
$556$	1.33349	+	4.10406i	0.0565525	+	0.174051i
$557$	−1.54294			−0.0653764			−0.0326882	−	0.999466i	$-0.510407\pi$
$557$	−1.54294			−0.0653764			−0.0326882	+	0.999466i	$0.510407\pi$
$558$	15.0426	+	46.2965i	0.636806	+	1.95989i
$559$	−35.4793	−	25.7772i	−1.50061	−	1.09026i
$560$	16.6772	−	41.8308i	0.704742	−	1.76767i
$561$	−7.22776	+	5.25127i	−0.305156	+	0.221709i
$562$	65.9822	+	47.9389i	2.78329	+	2.02218i
$563$	−8.32576	−	6.04902i	−0.350889	−	0.254936i	0.398353	−	0.917232i	$-0.369582\pi$
$563$	−8.32576	−	6.04902i	−0.350889	−	0.254936i	−0.749242	+	0.662297i	$0.769582\pi$
$564$	88.6382	−	64.3994i	3.73234	−	2.71170i
$565$	−11.9223	+	29.9042i	−0.501576	+	1.25808i
$566$	−5.29046	−	3.84375i	−0.222375	−	0.161565i
$567$	−2.52586	−	7.77380i	−0.106076	−	0.326469i
$568$	−87.5495			−3.67350
$569$	8.19048	+	25.2077i	0.343363	+	1.05676i	0.962454	+	0.271443i	$0.0875010\pi$
$569$	8.19048	+	25.2077i	0.343363	+	1.05676i	−0.619092	+	0.785319i	$0.712499\pi$
$570$	52.3892	+	43.5505i	2.19434	+	1.82413i
$571$	8.61564	−	26.5162i	0.360553	−	1.10967i	−0.592166	−	0.805816i	$-0.701727\pi$
$571$	8.61564	−	26.5162i	0.360553	−	1.10967i	0.952719	−	0.303852i	$-0.0982730\pi$
$572$	−24.7404	+	76.1432i	−1.03445	+	3.18371i
$573$	−12.3543	+	8.97592i	−0.516108	+	0.374974i
$574$	40.0460			1.67149
$575$	−13.9263	+	29.2329i	−0.580767	+	1.21910i
$576$	36.1788			1.50745
$577$	−10.9872	+	7.98266i	−0.457403	+	0.332323i	−0.792512	−	0.609857i	$-0.791227\pi$
$577$	−10.9872	+	7.98266i	−0.457403	+	0.332323i	0.335109	+	0.942179i	$0.391227\pi$
$578$	−0.808842	+	2.48936i	−0.0336434	+	0.103544i
$579$	13.5040	−	41.5609i	0.561205	−	1.72721i
$580$	2.97530	−	7.46280i	0.123542	−	0.309876i
$581$	1.08795	+	3.34835i	0.0451356	+	0.138913i
$582$	2.78381			0.115393
$583$	1.97123	+	6.06681i	0.0816399	+	0.251262i
$584$	70.8052	+	51.4430i	2.92994	+	2.12873i
$585$	39.2966	−	24.8074i	1.62471	−	1.02566i
$586$	39.2007	−	28.4810i	1.61937	−	1.17654i
$587$	15.6832	+	11.3945i	0.647316	+	0.470303i	0.862356	−	0.506303i	$-0.168988\pi$
$587$	15.6832	+	11.3945i	0.647316	+	0.470303i	−0.215040	+	0.976605i	$0.568988\pi$
$588$	−29.5134	−	21.4427i	−1.21711	−	0.884284i
$589$	−15.5669	+	11.3100i	−0.641423	+	0.466021i
$590$	3.44034	+	13.5329i	0.141637	+	0.557140i
$591$	−35.2609	−	25.6186i	−1.45044	−	1.05381i
$592$	28.0168	+	86.2267i	1.15148	+	3.54390i
$593$	−8.43082			−0.346212			−0.173106	−	0.984903i	$-0.555380\pi$
$593$	−8.43082			−0.346212			−0.173106	+	0.984903i	$0.555380\pi$
$594$	8.63103	+	26.5636i	0.354135	+	1.08992i
$595$	3.87335	−	2.44519i	0.158792	−	0.100243i
$596$	18.7371	−	57.6668i	0.767500	−	2.36212i
$597$	7.85638	−	24.1794i	0.321540	−	0.989598i
$598$	67.9496	−	49.3683i	2.77867	−	2.01882i
$599$	−1.54935			−0.0633046			−0.0316523	−	0.999499i	$-0.510077\pi$
$599$	−1.54935			−0.0633046			−0.0316523	+	0.999499i	$0.510077\pi$
$600$	−87.9330	+	47.7979i	−3.58985	+	1.95134i
$601$	2.63492			0.107481			0.0537403	−	0.998555i	$-0.482886\pi$
$601$	2.63492			0.107481			0.0537403	+	0.998555i	$0.482886\pi$
$602$	−38.3937	+	27.8946i	−1.56481	+	1.13690i
$603$	6.83078	−	21.0230i	0.278171	−	0.856122i
$604$	−8.09129	+	24.9024i	−0.329230	+	1.01327i
$605$	0.210242	+	0.0137297i	0.00854755	+	0.000558194i
$606$	27.7468	+	85.3958i	1.12714	+	3.46897i
$607$	21.6457			0.878571			0.439285	−	0.898348i	$-0.355232\pi$
$607$	21.6457			0.878571			0.439285	+	0.898348i	$0.355232\pi$
$608$	14.4929	+	44.6047i	0.587766	+	1.80896i
$609$	3.29229	+	2.39199i	0.133410	+	0.0969282i
$610$	−63.0327	−	4.11632i	−2.55212	−	0.166665i
$611$	33.7531	−	24.5231i	1.36550	−	0.992097i
$612$	16.4616	+	11.9600i	0.665419	+	0.483456i
$613$	−26.8522	−	19.5092i	−1.08455	−	0.787971i	−0.106079	−	0.994358i	$-0.533830\pi$
$613$	−26.8522	−	19.5092i	−1.08455	−	0.787971i	−0.978471	+	0.206387i	$0.933830\pi$
$614$	−3.76148	+	2.73287i	−0.151801	+	0.110290i
$615$	−34.4466	−	28.6351i	−1.38902	−	1.15468i
$616$	41.1946	+	29.9297i	1.65978	+	1.20590i
$617$	−7.52429	−	23.1574i	−0.302916	−	0.932281i	−0.980446	−	0.196786i	$-0.936950\pi$
$617$	−7.52429	−	23.1574i	−0.302916	−	0.932281i	0.677530	−	0.735495i	$-0.263050\pi$
$618$	101.366			4.07753
$619$	−8.61329	−	26.5090i	−0.346197	−	1.06549i	−0.960940	−	0.276758i	$-0.910740\pi$
$619$	−8.61329	−	26.5090i	−0.346197	−	1.06549i	0.614742	−	0.788728i	$-0.289260\pi$
$620$	−11.8503	−	46.6142i	−0.475920	−	1.87207i
$621$	6.41133	−	19.7320i	0.257278	−	0.791820i
$622$	8.84359	−	27.2178i	0.354595	−	1.09133i
$623$	−17.0863	+	12.4139i	−0.684549	+	0.497354i
$624$	130.658			5.23052
$625$	13.5960	−	20.9797i	0.543841	−	0.839189i
$626$	31.0638			1.24156
$627$	−31.3660	+	22.7887i	−1.25264	+	0.910093i
$628$	8.67649	−	26.7035i	0.346230	−	1.06559i
$629$	−2.84978	+	8.77073i	−0.113628	+	0.349712i
$630$	−12.3904	−	48.7388i	−0.493646	−	1.94180i
$631$	−4.24565	−	13.0668i	−0.169016	−	0.520179i	0.830293	−	0.557327i	$-0.188173\pi$
$631$	−4.24565	−	13.0668i	−0.169016	−	0.520179i	−0.999310	+	0.0371474i	$0.988173\pi$
$632$	−3.99876			−0.159062
$633$	−13.5645	−	41.7471i	−0.539139	−	1.65930i
$634$	−73.5970	−	53.4714i	−2.92291	−	2.12362i
$635$	22.1211	+	18.3890i	0.877847	+	0.729745i
$636$	20.1606	−	14.6475i	0.799420	−	0.580813i
$637$	−11.2386	−	8.16532i	−0.445290	−	0.323522i
$638$	5.22388	+	3.79537i	0.206815	+	0.150260i
$639$	−39.8093	+	28.9231i	−1.57483	+	1.14418i
$640$	−2.14699	−	0.140208i	−0.0848671	−	0.00554220i
$641$	−26.2985	−	19.1070i	−1.03873	−	0.754682i	−0.0686928	−	0.997638i	$-0.521883\pi$
$641$	−26.2985	−	19.1070i	−1.03873	−	0.754682i	−0.970037	+	0.242956i	$0.921883\pi$
$642$	−15.4484	−	47.5454i	−0.609701	−	1.87647i
$643$	8.59928			0.339122			0.169561	−	0.985520i	$-0.445765\pi$
$643$	8.59928			0.339122			0.169561	+	0.985520i	$0.445765\pi$
$644$	−19.8874	−	61.2070i	−0.783671	−	2.41189i
$645$	52.9715	+	3.45928i	2.08575	+	0.136209i
$646$	−3.51009	+	10.8029i	−0.138103	+	0.425036i
$647$	−4.87838	+	15.0141i	−0.191789	+	0.590265i	0.808210	+	0.588894i	$0.200437\pi$
$647$	−4.87838	+	15.0141i	−0.191789	+	0.590265i	−0.999999	+	0.00137132i	$0.999563\pi$
$648$	−24.0905	+	17.5028i	−0.946364	+	0.687574i
$649$	−7.94642			−0.311924
$650$	−56.9732	+	30.9690i	−2.23467	+	1.21471i
$651$	24.3626			0.954846
$652$	−0.131052	+	0.0952145i	−0.00513238	+	0.00372889i
$653$	−0.172818	+	0.531879i	−0.00676289	+	0.0208140i	−0.954381	−	0.298591i	$-0.903483\pi$
$653$	−0.172818	+	0.531879i	−0.00676289	+	0.0208140i	0.947618	+	0.319406i	$0.103483\pi$
$654$	−43.5332	+	133.981i	−1.70228	+	5.23909i
$655$	−30.9263	+	19.5233i	−1.20839	+	0.762839i
$656$	−22.6898	−	69.8319i	−0.885886	−	2.72648i
$657$	49.1904			1.91910
$658$	−13.9516	−	42.9385i	−0.543889	−	1.67392i
$659$	−10.3106	−	7.49112i	−0.401645	−	0.291812i	0.368565	−	0.929602i	$-0.379849\pi$
$659$	−10.3106	−	7.49112i	−0.401645	−	0.291812i	−0.770211	+	0.637789i	$0.779849\pi$
$660$	−23.8774	−	93.9236i	−0.929425	−	3.65597i
$661$	−18.5999	+	13.5137i	−0.723454	+	0.525620i	−0.887486	−	0.460835i	$-0.847550\pi$
$661$	−18.5999	+	13.5137i	−0.723454	+	0.525620i	0.164032	+	0.986455i	$0.447550\pi$
$662$	−56.8692	−	41.3179i	−2.21029	−	1.60587i
$663$	10.7520	+	7.81177i	0.417572	+	0.303384i
$664$	10.3763	−	7.53884i	0.402680	−	0.292564i
$665$	16.8090	−	10.6113i	0.651825	−	0.411488i
$666$	81.9104	+	59.5114i	3.17396	+	2.30602i
$667$	−1.48219	−	4.56171i	−0.0573905	−	0.176630i
$668$	22.4575			0.868906
$669$	−3.26588	−	10.0513i	−0.126266	−	0.388607i
$670$	−11.4230	+	28.6518i	−0.441309	+	1.10691i
$671$	11.1085	−	34.1884i	0.428838	−	1.31983i
$672$	18.3500	−	56.4754i	0.707866	−	2.17859i
$673$	13.0969	−	9.51545i	0.504848	−	0.366794i	−0.306017	−	0.952026i	$-0.598997\pi$
$673$	13.0969	−	9.51545i	0.504848	−	0.366794i	0.810866	+	0.585232i	$0.198997\pi$
$674$	−75.2051			−2.89679
$675$	−6.88924	+	14.4613i	−0.265167	+	0.556616i
$676$	56.0347			2.15518
$677$	36.1960	−	26.2979i	1.39112	−	1.01071i	0.395384	−	0.918516i	$-0.370612\pi$
$677$	36.1960	−	26.2979i	1.39112	−	1.01071i	0.995741	−	0.0921954i	$-0.0293885\pi$
$678$	−31.2349	+	96.1313i	−1.19957	+	3.69190i
$679$	0.251003	−	0.772509i	0.00963263	−	0.0296462i
$680$	−12.8323	−	10.6674i	−0.492098	−	0.409075i
$681$	−3.91201	−	12.0399i	−0.149909	−	0.461371i
$682$	38.6562			1.48022
$683$	−14.1611	−	43.5833i	−0.541858	−	1.66767i	−0.728345	−	0.685210i	$-0.759710\pi$
$683$	−14.1611	−	43.5833i	−0.541858	−	1.66767i	0.186487	−	0.982457i	$-0.440290\pi$
$684$	71.4375	+	51.9024i	2.73148	+	1.98454i
$685$	8.25915	−	20.7160i	0.315566	−	0.791519i
$686$	−42.5268	+	30.8975i	−1.62368	+	1.17967i
$687$	−28.5700	−	20.7573i	−1.09002	−	0.791942i
$688$	70.3960	+	51.1457i	2.68382	+	1.94991i
$689$	7.67709	−	5.57773i	0.292474	−	0.212495i
$690$	−37.6509	+	94.4380i	−1.43334	+	3.59519i
$691$	−11.5559	−	8.39586i	−0.439607	−	0.319393i	0.345872	−	0.938282i	$-0.387583\pi$
$691$	−11.5559	−	8.39586i	−0.439607	−	0.319393i	−0.785479	+	0.618888i	$0.787583\pi$
$692$	−7.87707	−	24.2431i	−0.299441	−	0.921585i
$693$	28.6191			1.08715
$694$	−8.52098	−	26.2249i	−0.323452	−	0.995483i
$695$	−1.52958	−	1.27152i	−0.0580203	−	0.0482316i
$696$	4.58125	−	14.0996i	0.173652	−	0.534445i
$697$	2.30794	−	7.10310i	0.0874193	−	0.269049i
$698$	52.7286	−	38.3096i	1.99581	−	1.45004i
$699$	−60.4631			−2.28692
$700$	9.07813	+	48.8514i	0.343121	+	1.84641i
$701$	16.7217			0.631568			0.315784	−	0.948831i	$-0.397732\pi$
$701$	16.7217			0.631568			0.315784	+	0.948831i	$0.397732\pi$
$702$	33.6142	−	24.4221i	1.26869	−	0.921754i
$703$	−12.3671	+	38.0619i	−0.466433	+	1.43553i
$704$	8.87798	−	27.3236i	0.334601	−	1.02980i
$705$	−18.7026	+	46.9109i	−0.704380	+	1.76676i
$706$	8.35009	+	25.6989i	0.314260	+	0.967192i
$707$	26.1992			0.985322
$708$	9.59281	+	29.5236i	0.360520	+	1.10957i
$709$	11.2230	+	8.15400i	0.421489	+	0.306230i	0.778237	−	0.627971i	$-0.216114\pi$
$709$	11.2230	+	8.15400i	0.421489	+	0.306230i	−0.356748	+	0.934201i	$0.616114\pi$
$710$	58.0614	−	36.6533i	2.17901	−	1.37558i
$711$	−1.81826	+	1.32104i	−0.0681901	+	0.0495430i
$712$	62.2457	+	45.2242i	2.33276	+	1.69485i
$713$	−23.2307	−	16.8781i	−0.869997	−	0.632090i
$714$	11.6352	−	8.45345i	0.435436	−	0.316362i
$715$	−9.09241	−	35.7658i	−0.340037	−	1.33756i
$716$	16.7676	+	12.1824i	0.626635	+	0.455277i
$717$	−4.91276	−	15.1199i	−0.183471	−	0.564664i
$718$	33.5542			1.25223
$719$	14.7897	+	45.5179i	0.551562	+	1.69753i	0.704854	+	0.709352i	$0.251012\pi$
$719$	14.7897	+	45.5179i	0.551562	+	1.69753i	−0.153292	+	0.988181i	$0.548988\pi$
$720$	−77.9700	+	49.2213i	−2.90577	+	1.83437i
$721$	9.13969	−	28.1291i	0.340380	−	1.04758i
$722$	0.135420	−	0.416780i	0.00503981	−	0.0155109i
$723$	11.1774	−	8.12088i	0.415693	−	0.302019i
$724$	−32.1835			−1.19609
$725$	0.676585	+	3.64086i	0.0251277	+	0.135218i
$726$	0.661511			0.0245510
$727$	22.8487	−	16.6006i	0.847411	−	0.615680i	−0.0770197	−	0.997030i	$-0.524540\pi$
$727$	22.8487	−	16.6006i	0.847411	−	0.615680i	0.924431	+	0.381349i	$0.124540\pi$
$728$	23.4072	−	72.0401i	0.867530	−	2.66998i
$729$	−13.1380	+	40.4347i	−0.486594	+	1.49758i
$730$	−68.4939	−	4.47296i	−2.53507	−	0.165552i
$731$	2.73506	+	8.41764i	0.101160	+	0.311338i
$732$	−140.431			−5.19050
$733$	−2.58990	−	7.97088i	−0.0956600	−	0.294411i	0.891765	−	0.452499i	$-0.149467\pi$
$733$	−2.58990	−	7.97088i	−0.0956600	−	0.294411i	−0.987425	+	0.158087i	$0.949467\pi$
$734$	2.60622	+	1.89353i	0.0961972	+	0.0698914i
$735$	16.7795	+	1.09578i	0.618922	+	0.0404184i
$736$	−56.6229	+	41.1389i	−2.08715	+	1.51640i
$737$	−14.2011	−	10.3177i	−0.523106	−	0.380059i
$738$	−66.3362	−	48.1961i	−2.44187	−	1.77412i
$739$	4.33153	−	3.14704i	0.159338	−	0.115766i	−0.505259	−	0.862968i	$-0.668603\pi$
$739$	4.33153	−	3.14704i	0.159338	−	0.115766i	0.664597	+	0.747202i	$0.268603\pi$
$740$	−76.9272	−	63.9487i	−2.82790	−	2.35080i
$741$	46.6599	+	33.9004i	1.71409	+	1.24536i
$742$	−3.17326	−	9.76630i	−0.116494	−	0.358532i
$743$	40.4165			1.48274			0.741368	−	0.671098i	$-0.234177\pi$
$743$	40.4165			1.48274			0.741368	+	0.671098i	$0.234177\pi$
$744$	−27.4263	−	84.4095i	−1.00550	−	3.09460i
$745$	6.88611	+	27.0871i	0.252287	+	0.992394i
$746$	7.92314	−	24.3849i	0.290087	−	0.892795i
$747$	2.22762	−	6.85591i	0.0815044	−	0.250845i
$748$	13.0722	−	9.49751i	0.477967	−	0.347263i
$749$	−14.5868			−0.532990
$750$	38.3047	−	68.5126i	1.39869	−	2.50173i
$751$	−36.5021			−1.33198			−0.665991	−	0.745960i	$-0.731991\pi$
$751$	−36.5021			−1.33198			−0.665991	+	0.745960i	$0.731991\pi$
$752$	−66.9710	+	48.6573i	−2.44218	+	1.77435i
$753$	9.13991	−	28.1298i	0.333077	−	1.02511i
$754$	2.96826	−	9.13538i	0.108098	−	0.332691i
$755$	−2.97365	−	11.6971i	−0.108222	−	0.425702i
$756$	−9.83813	−	30.2786i	−0.357809	−	1.10122i
$757$	20.4414			0.742954			0.371477	−	0.928442i	$-0.378851\pi$
$757$	20.4414			0.742954			0.371477	+	0.928442i	$0.378851\pi$
$758$	21.9845	+	67.6614i	0.798514	+	2.45757i
$759$	−46.8079	−	34.0079i	−1.69902	−	1.23441i
$760$	−55.6879	−	46.2927i	−2.02001	−	1.67921i
$761$	40.9998	−	29.7881i	1.48624	−	1.07982i	0.510761	−	0.859723i	$-0.329364\pi$
$761$	40.9998	−	29.7881i	1.48624	−	1.07982i	0.975479	−	0.220094i	$-0.0706364\pi$
$762$	73.0692	+	53.0879i	2.64702	+	1.92317i
$763$	33.2548	+	24.1610i	1.20390	+	0.874687i
$764$	22.3441	−	16.2339i	0.808382	−	0.587324i
$765$	−9.35905	−	0.611188i	−0.338377	−	0.0220975i
$766$	16.7553	+	12.1734i	0.605394	+	0.439844i
$767$	3.65291	+	11.2425i	0.131899	+	0.405943i
$768$	39.5159			1.42591
$769$	−13.3319	−	41.0314i	−0.480760	−	1.47963i	−0.838028	−	0.545627i	$-0.816292\pi$
$769$	−13.3319	−	41.0314i	−0.480760	−	1.47963i	0.357268	−	0.934002i	$-0.383708\pi$
$770$	−39.8499	−	2.60238i	−1.43609	−	0.0937832i
$771$	−4.19951	+	12.9248i	−0.151242	+	0.465474i
$772$	−24.4234	+	75.1675i	−0.879018	+

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+(2.11757 - 1.53851i) q^{2} +(-0.828858 + 2.55096i) q^{3} +(1.49908 - 4.61370i) q^{4} +(0.550931 + 2.16714i) q^{5} +(2.16951 + 6.67705i) q^{6} +2.04850 q^{7} +(-2.30611 - 7.09748i) q^{8} +(-3.39335 - 2.46541i) q^{9} +(4.50079 + 3.74146i) q^{10} +(-2.69467 + 1.95779i) q^{11} +(10.5268 + 7.64820i) q^{12} +(4.00858 + 2.91241i) q^{13} +(4.33786 - 3.15164i) q^{14} +(-5.98492 - 0.390842i) q^{15} +(-7.95360 - 5.77863i) q^{16} +(-0.309017 - 0.951057i) q^{17} -10.9787 q^{18} +(-1.34103 - 4.12725i) q^{19} +(10.8244 + 0.706882i) q^{20} +(-1.69792 + 5.22565i) q^{21} +(-2.69409 + 8.29155i) q^{22} +(5.23929 - 3.80657i) q^{23} +20.0168 q^{24} +(-4.39295 + 2.38788i) q^{25} +12.9692 q^{26} +(2.59184 - 1.88308i) q^{27} +(3.07087 - 9.45117i) q^{28} +(0.228870 - 0.704388i) q^{29} +(-13.2748 + 8.38021i) q^{30} +(-1.37016 - 4.21693i) q^{31} -10.8073 q^{32} +(-2.76076 - 8.49674i) q^{33} +(-2.11757 - 1.53851i) q^{34} +(1.12858 + 4.43938i) q^{35} +(-16.4616 + 11.9600i) q^{36} +(-7.46083 - 5.42061i) q^{37} +(-9.18954 - 6.67659i) q^{38} +(-10.7520 + 7.81177i) q^{39} +(14.1107 - 8.90788i) q^{40} +(6.04225 + 4.38995i) q^{41} +(4.44424 + 13.6780i) q^{42} -8.85083 q^{43} +(4.99314 + 15.3673i) q^{44} +(3.47338 - 8.71212i) q^{45} +(5.23816 - 16.1214i) q^{46} +(2.60199 - 8.00809i) q^{47} +(21.3335 - 15.4997i) q^{48} -2.80363 q^{49} +(-5.62862 + 11.8151i) q^{50} +2.68224 q^{51} +(19.4462 - 14.1285i) q^{52} +(0.591818 - 1.82143i) q^{53} +(2.59128 - 7.97513i) q^{54} +(-5.72739 - 4.76111i) q^{55} +(-4.72408 - 14.5392i) q^{56} +11.6400 q^{57} +(-0.599059 - 1.84371i) q^{58} +(1.93010 + 1.40230i) q^{59} +(-10.7751 + 27.0267i) q^{60} +(-8.73136 + 6.34370i) q^{61} +(-9.38920 - 6.82165i) q^{62} +(-6.95129 - 5.05040i) q^{63} +(-6.97816 + 5.06993i) q^{64} +(-4.10312 + 10.2917i) q^{65} +(-18.9184 - 13.7450i) q^{66} +(1.62854 + 5.01214i) q^{67} -4.85113 q^{68} +(5.36778 + 16.5203i) q^{69} +(9.21989 + 7.66439i) q^{70} +(3.62525 - 11.1574i) q^{71} +(-9.67277 + 29.7697i) q^{72} +(-9.48784 + 6.89332i) q^{73} -24.1385 q^{74} +(-2.45027 - 13.1855i) q^{75} -21.0522 q^{76} +(-5.52005 + 4.01055i) q^{77} +(-10.7496 + 33.0840i) q^{78} +(0.165581 - 0.509605i) q^{79} +(8.14118 - 20.4202i) q^{80} +(-1.23303 - 3.79487i) q^{81} +19.5489 q^{82} +(0.531093 + 1.63454i) q^{83} +(21.5643 + 15.6674i) q^{84} +(1.89082 - 1.19365i) q^{85} +(-18.7423 + 13.6171i) q^{86} +(1.60717 + 1.16768i) q^{87} +(20.1096 + 14.6105i) q^{88} +(-8.34088 + 6.06000i) q^{89} +(-6.04852 - 23.7924i) q^{90} +(8.21160 + 5.96607i) q^{91} +(-9.70823 - 29.8789i) q^{92} +11.8929 q^{93} +(-6.81061 - 20.9609i) q^{94} +(8.20550 - 5.18002i) q^{95} +(8.95775 - 27.5691i) q^{96} +(0.122530 - 0.377109i) q^{97} +(-5.93690 + 4.31341i) q^{98} +13.9707 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

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Database

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