LMFDB - Embedded newform 425.2.r.a.69.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [425,2,Mod(69,425)]

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([9, 0]))

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

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

chi := DirichletCharacter("425.69");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 425 = 5^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	425.r (of order $10$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.39364208590$
Analytic rank:	$0$
Dimension:	$160$
Relative dimension:	$40$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			69.15
Character	$\chi$	$=$	425.69
Dual form			425.2.r.a.154.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.03358 + 0.335830i) q^{2} +(0.604115 + 0.831493i) q^{3} +(-0.662529 + 0.481355i) q^{4} +(-2.14816 + 0.620799i) q^{5} +(-0.903642 - 0.656534i) q^{6} -1.04210i q^{7} +(1.80070 - 2.47845i) q^{8} +(0.600625 - 1.84853i) q^{9} +(2.01182 - 1.36306i) q^{10} +(-1.09155 - 3.35946i) q^{11} +(-0.800488 - 0.260094i) q^{12} +(-1.99532 - 0.648320i) q^{13} +(0.349969 + 1.07709i) q^{14} +(-1.81393 - 1.41115i) q^{15} +(-0.522699 + 1.60870i) q^{16} +(0.587785 - 0.809017i) q^{17} +2.11232i q^{18} +(6.96860 + 5.06298i) q^{19} +(1.12440 - 1.44533i) q^{20} +(0.866500 - 0.629549i) q^{21} +(2.25641 + 3.10569i) q^{22} +(1.51064 - 0.490838i) q^{23} +3.14864 q^{24} +(4.22922 - 2.66716i) q^{25} +2.28005 q^{26} +(4.83233 - 1.57012i) q^{27} +(0.501621 + 0.690422i) q^{28} +(2.25432 - 1.63786i) q^{29} +(2.34875 + 0.849364i) q^{30} +(-6.55683 - 4.76382i) q^{31} +4.28880i q^{32} +(2.13394 - 2.93712i) q^{33} +(-0.335830 + 1.03358i) q^{34} +(0.646935 + 2.23860i) q^{35} +(0.491870 + 1.51382i) q^{36} +(-4.65636 - 1.51294i) q^{37} +(-8.90291 - 2.89273i) q^{38} +(-0.666332 - 2.05076i) q^{39} +(-2.32958 + 6.44198i) q^{40} +(1.76652 - 5.43680i) q^{41} +(-0.684175 + 0.941686i) q^{42} +3.23038i q^{43} +(2.34028 + 1.70031i) q^{44} +(-0.142674 + 4.34382i) q^{45} +(-1.39653 + 1.01464i) q^{46} +(-5.43867 - 7.48569i) q^{47} +(-1.65340 + 0.537221i) q^{48} +5.91403 q^{49} +(-3.47552 + 4.17702i) q^{50} +1.02778 q^{51} +(1.63403 - 0.530929i) q^{52} +(-5.10553 - 7.02716i) q^{53} +(-4.46730 + 3.24569i) q^{54} +(4.43038 + 6.53903i) q^{55} +(-2.58279 - 1.87651i) q^{56} +8.85297i q^{57} +(-1.77998 + 2.44993i) q^{58} +(3.75671 - 11.5620i) q^{59} +(1.88104 + 0.0617833i) q^{60} +(-3.15527 - 9.71092i) q^{61} +(8.37684 + 2.72180i) q^{62} +(-1.92636 - 0.625912i) q^{63} +(-2.48571 - 7.65022i) q^{64} +(4.68876 + 0.154003i) q^{65} +(-1.21922 + 3.75239i) q^{66} +(-7.99532 + 11.0046i) q^{67} +0.818931i q^{68} +(1.32073 + 0.959568i) q^{69} +(-1.42045 - 2.09652i) q^{70} +(12.4889 - 9.07368i) q^{71} +(-3.49995 - 4.81727i) q^{72} +(3.39865 - 1.10429i) q^{73} +5.32081 q^{74} +(4.77266 + 1.90530i) q^{75} -7.05399 q^{76} +(-3.50089 + 1.13751i) q^{77} +(1.37741 + 1.89585i) q^{78} +(4.97488 - 3.61446i) q^{79} +(0.124163 - 3.78025i) q^{80} +(-0.492545 - 0.357855i) q^{81} +6.21262i q^{82} +(-10.0424 + 13.8221i) q^{83} +(-0.271044 + 0.834189i) q^{84} +(-0.760422 + 2.10280i) q^{85} +(-1.08486 - 3.33885i) q^{86} +(2.72374 + 0.884996i) q^{87} +(-10.2918 - 3.34401i) q^{88} +(3.15686 + 9.71583i) q^{89} +(-1.31132 - 4.53760i) q^{90} +(-0.675615 + 2.07933i) q^{91} +(-0.764578 + 1.05235i) q^{92} -8.32985i q^{93} +(8.13522 + 5.91058i) q^{94} +(-18.1128 - 6.55002i) q^{95} +(-3.56611 + 2.59093i) q^{96} +(4.86853 + 6.70096i) q^{97} +(-6.11262 + 1.98611i) q^{98} -6.86568 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 160 q + 40 q^{4} - 8 q^{5} + 4 q^{6} - 30 q^{8} + 36 q^{9} - 6 q^{10} + 8 q^{11} - 40 q^{12} - 20 q^{14} - 40 q^{15} - 64 q^{16} + 6 q^{19} + 2 q^{20} - 50 q^{22} + 20 q^{23} + 20 q^{24} + 32 q^{25} + 20 q^{26}+ \cdots + 44 q^{99}+O(q^{100}) $ 160 * q + 40 * q^4 - 8 * q^5 + 4 * q^6 - 30 * q^8 + 36 * q^9 - 6 * q^10 + 8 * q^11 - 40 * q^12 - 20 * q^14 - 40 * q^15 - 64 * q^16 + 6 * q^19 + 2 * q^20 - 50 * q^22 + 20 * q^23 + 20 * q^24 + 32 * q^25 + 20 * q^26 + 30 * q^27 + 60 * q^28 + 16 * q^30 + 12 * q^31 - 40 * q^33 - 4 * q^34 - 54 * q^36 - 40 * q^38 - 12 * q^39 - 52 * q^40 - 2 * q^41 + 30 * q^42 - 20 * q^44 + 42 * q^45 + 48 * q^46 + 40 * q^47 - 100 * q^48 - 184 * q^49 + 46 * q^50 - 32 * q^51 - 10 * q^52 - 20 * q^53 - 40 * q^54 + 18 * q^55 + 24 * q^56 - 120 * q^58 + 6 * q^59 - 40 * q^60 + 12 * q^61 - 10 * q^62 + 90 * q^63 + 58 * q^64 - 20 * q^65 + 48 * q^66 - 90 * q^67 - 74 * q^69 - 120 * q^70 - 16 * q^71 - 10 * q^72 + 52 * q^74 + 76 * q^75 + 96 * q^76 + 80 * q^77 + 40 * q^78 - 60 * q^79 - 24 * q^80 - 118 * q^81 - 76 * q^84 + 2 * q^85 + 44 * q^86 + 40 * q^87 + 140 * q^88 + 50 * q^89 + 224 * q^90 + 28 * q^91 - 170 * q^92 + 96 * q^94 - 44 * q^95 - 116 * q^96 + 110 * q^97 + 70 * q^98 + 44 * q^99

Character values

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

$n$	$52$	$326$
$\chi(n)$	$e\left(\frac{9}{10}\right)$	$1$

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 $

$2$	−1.03358	+	0.335830i	−0.730851	+	0.237468i	−0.650722	−	0.759316i	$-0.725533\pi$
$2$	−1.03358	+	0.335830i	−0.730851	+	0.237468i	−0.0801298	+	0.996784i	$0.525533\pi$
$3$	0.604115	+	0.831493i	0.348786	+	0.480063i	0.946982	−	0.321287i	$-0.104115\pi$
$3$	0.604115	+	0.831493i	0.348786	+	0.480063i	−0.598196	+	0.801350i	$0.704115\pi$
$4$	−0.662529	+	0.481355i	−0.331264	+	0.240678i
$5$	−2.14816	+	0.620799i	−0.960688	+	0.277630i
$5$	−2.14816	+	0.620799i	−0.960688	+	0.277630i
$6$	−0.903642	−	0.656534i	−0.368910	−	0.268029i
$7$		−	1.04210i		−	0.393877i	−0.980416	−	0.196939i	$-0.936900\pi$
$7$		−	1.04210i		−	0.393877i	0.980416	−	0.196939i	$-0.0631000\pi$
$8$	1.80070	−	2.47845i	0.636643	−	0.876264i
$9$	0.600625	−	1.84853i	0.200208	−	0.616178i
$10$	2.01182	−	1.36306i	0.636192	−	0.431039i
$11$	−1.09155	−	3.35946i	−0.329116	−	1.01291i	−0.969548	−	0.244900i	$-0.921245\pi$
$11$	−1.09155	−	3.35946i	−0.329116	−	1.01291i	0.640433	−	0.768014i	$-0.278755\pi$
$12$	−0.800488	−	0.260094i	−0.231081	−	0.0750827i
$13$	−1.99532	−	0.648320i	−0.553403	−	0.179812i	0.0189477	−	0.999820i	$-0.493968\pi$
$13$	−1.99532	−	0.648320i	−0.553403	−	0.179812i	−0.572351	+	0.820009i	$0.693968\pi$
$14$	0.349969	+	1.07709i	0.0935332	+	0.287866i
$15$	−1.81393	−	1.41115i	−0.468354	−	0.364357i
$16$	−0.522699	+	1.60870i	−0.130675	+	0.402176i
$17$	0.587785	−	0.809017i	0.142559	−	0.196215i
$17$	0.587785	−	0.809017i	0.142559	−	0.196215i
$18$			2.11232i			0.497878i
$19$	6.96860	+	5.06298i	1.59871	+	1.16153i	0.889933	+	0.456091i	$0.150751\pi$
$19$	6.96860	+	5.06298i	1.59871	+	1.16153i	0.708773	+	0.705437i	$0.249249\pi$
$20$	1.12440	−	1.44533i	0.251423	−	0.323185i
$21$	0.866500	−	0.629549i	0.189086	−	0.137379i
$22$	2.25641	+	3.10569i	0.481069	+	0.662135i
$23$	1.51064	−	0.490838i	0.314991	−	0.102347i	−0.147255	−	0.989099i	$-0.547044\pi$
$23$	1.51064	−	0.490838i	0.314991	−	0.102347i	0.462246	+	0.886752i	$0.347044\pi$
$24$	3.14864			0.642714
$25$	4.22922	−	2.66716i	0.845844	−	0.533431i
$26$	2.28005			0.447155
$27$	4.83233	−	1.57012i	0.929982	−	0.302169i
$28$	0.501621	+	0.690422i	0.0947974	+	0.130477i
$29$	2.25432	−	1.63786i	0.418617	−	0.304143i	−0.358464	−	0.933543i	$-0.616700\pi$
$29$	2.25432	−	1.63786i	0.418617	−	0.304143i	0.777081	+	0.629401i	$0.216700\pi$
$30$	2.34875	+	0.849364i	0.428821	+	0.155072i
$31$	−6.55683	−	4.76382i	−1.17764	−	0.855607i	−0.185738	−	0.982599i	$-0.559467\pi$
$31$	−6.55683	−	4.76382i	−1.17764	−	0.855607i	−0.991904	+	0.126993i	$0.959467\pi$
$32$			4.28880i			0.758159i
$33$	2.13394	−	2.93712i	0.371471	−	0.511287i
$34$	−0.335830	+	1.03358i	−0.0575944	+	0.177257i
$35$	0.646935	+	2.23860i	0.109352	+	0.378393i
$36$	0.491870	+	1.51382i	0.0819784	+	0.252304i
$37$	−4.65636	−	1.51294i	−0.765501	−	0.248726i	−0.0998631	−	0.995001i	$-0.531840\pi$
$37$	−4.65636	−	1.51294i	−0.765501	−	0.248726i	−0.665638	+	0.746275i	$0.731840\pi$
$38$	−8.90291	−	2.89273i	−1.44424	−	0.469263i
$39$	−0.666332	−	2.05076i	−0.106698	−	0.328384i
$40$	−2.32958	+	6.44198i	−0.368338	+	1.01857i
$41$	1.76652	−	5.43680i	0.275885	−	0.849085i	−0.713099	−	0.701063i	$-0.752709\pi$
$41$	1.76652	−	5.43680i	0.275885	−	0.849085i	0.988984	−	0.148022i	$-0.0472908\pi$
$42$	−0.684175	+	0.941686i	−0.105571	+	0.145305i
$43$			3.23038i			0.492628i	0.969190	+	0.246314i	$0.0792194\pi$
$43$			3.23038i			0.492628i	−0.969190	+	0.246314i	$0.920781\pi$
$44$	2.34028	+	1.70031i	0.352810	+	0.256332i
$45$	−0.142674	+	4.34382i	−0.0212685	+	0.647539i
$46$	−1.39653	+	1.01464i	−0.205908	+	0.149601i
$47$	−5.43867	−	7.48569i	−0.793312	−	1.09190i	−0.993688	−	0.112181i	$-0.964216\pi$
$47$	−5.43867	−	7.48569i	−0.793312	−	1.09190i	0.200376	−	0.979719i	$-0.435784\pi$
$48$	−1.65340	+	0.537221i	−0.238647	+	0.0775412i
$49$	5.91403			0.844861
$50$	−3.47552	+	4.17702i	−0.491513	+	0.590720i
$51$	1.02778			0.143918
$52$	1.63403	−	0.530929i	0.226599	−	0.0736266i
$53$	−5.10553	−	7.02716i	−0.701298	−	0.965254i	−0.999941	−	0.0108891i	$-0.996534\pi$
$53$	−5.10553	−	7.02716i	−0.701298	−	0.965254i	0.298643	−	0.954365i	$-0.403466\pi$
$54$	−4.46730	+	3.24569i	−0.607923	+	0.441682i
$55$	4.43038	+	6.53903i	0.597393	+	0.881722i
$56$	−2.58279	−	1.87651i	−0.345140	−	0.250759i
$57$			8.85297i			1.17260i
$58$	−1.77998	+	2.44993i	−0.233722	+	0.321691i
$59$	3.75671	−	11.5620i	0.489082	−	1.50524i	−0.336899	−	0.941541i	$-0.609378\pi$
$59$	3.75671	−	11.5620i	0.489082	−	1.50524i	0.825981	−	0.563698i	$-0.190622\pi$
$60$	1.88104	+	0.0617833i	0.242842	+	0.00797619i
$61$	−3.15527	−	9.71092i	−0.403991	−	1.24336i	−0.921735	−	0.387820i	$-0.873228\pi$
$61$	−3.15527	−	9.71092i	−0.403991	−	1.24336i	0.517744	−	0.855535i	$-0.326772\pi$
$62$	8.37684	+	2.72180i	1.06386	+	0.345669i
$63$	−1.92636	−	0.625912i	−0.242698	−	0.0788575i
$64$	−2.48571	−	7.65022i	−0.310713	−	0.956278i
$65$	4.68876	+	0.154003i	0.581569	+	0.0191017i
$66$	−1.21922	+	3.75239i	−0.150076	+	0.461887i
$67$	−7.99532	+	11.0046i	−0.976783	+	1.34443i	−0.0382390	+	0.999269i	$0.512175\pi$
$67$	−7.99532	+	11.0046i	−0.976783	+	1.34443i	−0.938544	+	0.345158i	$0.887825\pi$
$68$			0.818931i			0.0993099i
$69$	1.32073	+	0.959568i	0.158997	+	0.115518i
$70$	−1.42045	−	2.09652i	−0.169776	−	0.250582i
$71$	12.4889	−	9.07368i	1.48215	−	1.07685i	0.505300	−	0.862944i	$-0.331382\pi$
$71$	12.4889	−	9.07368i	1.48215	−	1.07685i	0.976855	−	0.213904i	$-0.0686180\pi$
$72$	−3.49995	−	4.81727i	−0.412473	−	0.567720i
$73$	3.39865	−	1.10429i	0.397781	−	0.129247i	−0.103294	−	0.994651i	$-0.532938\pi$
$73$	3.39865	−	1.10429i	0.397781	−	0.129247i	0.501075	+	0.865404i	$0.332938\pi$
$74$	5.32081			0.618532
$75$	4.77266	+	1.90530i	0.551099	+	0.220005i
$76$	−7.05399			−0.809148
$77$	−3.50089	+	1.13751i	−0.398964	+	0.129631i
$78$	1.37741	+	1.89585i	0.155961	+	0.214662i
$79$	4.97488	−	3.61446i	0.559718	−	0.406659i	−0.271638	−	0.962400i	$-0.587565\pi$
$79$	4.97488	−	3.61446i	0.559718	−	0.406659i	0.831356	+	0.555741i	$0.187565\pi$
$80$	0.124163	−	3.78025i	0.0138819	−	0.422645i
$81$	−0.492545	−	0.357855i	−0.0547272	−	0.0397616i
$82$			6.21262i			0.686069i
$83$	−10.0424	+	13.8221i	−1.10229	+	1.51717i	−0.269980	+	0.962866i	$0.587017\pi$
$83$	−10.0424	+	13.8221i	−1.10229	+	1.51717i	−0.832311	+	0.554308i	$0.812983\pi$
$84$	−0.271044	+	0.834189i	−0.0295734	+	0.0910175i
$85$	−0.760422	+	2.10280i	−0.0824794	+	0.228080i
$86$	−1.08486	−	3.33885i	−0.116983	−	0.360038i
$87$	2.72374	+	0.884996i	0.292015	+	0.0948815i
$88$	−10.2918	−	3.34401i	−1.09711	−	0.356472i
$89$	3.15686	+	9.71583i	0.334627	+	1.02988i	0.966906	+	0.255135i	$0.0821198\pi$
$89$	3.15686	+	9.71583i	0.334627	+	1.02988i	−0.632279	+	0.774741i	$0.717880\pi$
$90$	−1.31132	−	4.53760i	−0.138226	−	0.478305i
$91$	−0.675615	+	2.07933i	−0.0708237	+	0.217973i
$92$	−0.764578	+	1.05235i	−0.0797128	+	0.109715i
$93$		−	8.32985i		−	0.863766i
$94$	8.13522	+	5.91058i	0.839084	+	0.609630i
$95$	−18.1128	−	6.55002i	−1.85833	−	0.672018i
$96$	−3.56611	+	2.59093i	−0.363964	+	0.264435i
$97$	4.86853	+	6.70096i	0.494325	+	0.680380i	0.981178	−	0.193104i	$-0.0618554\pi$
$97$	4.86853	+	6.70096i	0.494325	+	0.680380i	−0.486854	+	0.873484i	$0.661855\pi$
$98$	−6.11262	+	1.98611i	−0.617468	+	0.200627i
$99$	−6.86568			−0.690027
$100$	−1.51813	+	3.80282i	−0.151813	+	0.380282i
$101$	2.69963			0.268623			0.134312	−	0.990939i	$-0.457118\pi$
$101$	2.69963			0.268623			0.134312	+	0.990939i	$0.457118\pi$
$102$	−1.06230	+	0.345161i	−0.105183	+	0.0341760i
$103$	2.47211	+	3.40257i	0.243584	+	0.335265i	0.913251	−	0.407396i	$-0.133563\pi$
$103$	2.47211	+	3.40257i	0.243584	+	0.335265i	−0.669667	+	0.742661i	$0.733563\pi$
$104$	−5.19980	+	3.77788i	−0.509882	+	0.370451i
$105$	−1.47056	+	1.89030i	−0.143512	+	0.184474i
$106$	7.63690	+	5.54854i	0.741762	+	0.538921i
$107$		−	16.8290i		−	1.62692i	−0.581619	−	0.813461i	$-0.697580\pi$
$107$		−	16.8290i		−	1.62692i	0.581619	−	0.813461i	$-0.302420\pi$
$108$	−2.44577	+	3.36632i	−0.235344	+	0.323924i
$109$	−5.36122	+	16.5001i	−0.513511	+	1.58043i	0.272463	+	0.962166i	$0.412162\pi$
$109$	−5.36122	+	16.5001i	−0.513511	+	1.58043i	−0.785974	+	0.618259i	$0.787838\pi$
$110$	−6.77516	−	5.27075i	−0.645986	−	0.502546i
$111$	−1.55498	−	4.78573i	−0.147592	−	0.454241i
$112$	1.67643	+	0.544706i	0.158408	+	0.0514698i
$113$	−11.6915	−	3.79879i	−1.09984	−	0.357360i	−0.297800	−	0.954628i	$-0.596253\pi$
$113$	−11.6915	−	3.79879i	−1.09984	−	0.357360i	−0.802042	+	0.597268i	$0.796253\pi$
$114$	−2.97310	−	9.15025i	−0.278456	−	0.856999i
$115$	−2.94040	+	1.99221i	−0.274194	+	0.185774i
$116$	−0.705159	+	2.17026i	−0.0654724	+	0.201503i
$117$	−2.39688	+	3.29902i	−0.221592	+	0.304995i
$118$			13.2118i			1.21625i
$119$	−0.843077	−	0.612532i	−0.0772848	−	0.0561507i
$120$	−6.76380	+	1.95467i	−0.617448	+	0.178436i
$121$	−1.19527	+	0.868412i	−0.108661	+	0.0789466i
$122$	6.52244	+	8.97737i	0.590514	+	0.812773i
$123$	5.58785	−	1.81560i	0.503839	−	0.163707i
$124$	6.63718			0.596036
$125$	−7.42929	+	8.35498i	−0.664496	+	0.747292i
$126$	2.20125			0.196103
$127$	11.8259	−	3.84246i	1.04938	−	0.340964i	0.266954	−	0.963709i	$-0.413983\pi$
$127$	11.8259	−	3.84246i	1.04938	−	0.340964i	0.782424	+	0.622746i	$0.213983\pi$
$128$	0.0965706	+	0.132918i	0.00853572	+	0.0117484i
$129$	−2.68604	+	1.95152i	−0.236492	+	0.171822i
$130$	−4.89792	+	1.41545i	−0.429576	+	0.124143i
$131$	0.835062	+	0.606708i	0.0729597	+	0.0530083i	0.623667	−	0.781690i	$-0.285642\pi$
$131$	0.835062	+	0.606708i	0.0729597	+	0.0530083i	−0.550708	+	0.834698i	$0.685642\pi$
$132$			2.97311i			0.258776i
$133$	5.27614	−	7.26198i	0.457499	−	0.629694i
$134$	4.56812	−	14.0592i	0.394625	−	1.21453i
$135$	−9.40591	+	6.37277i	−0.809531	+	0.548481i
$136$	−0.946683	−	2.91359i	−0.0811774	−	0.249838i
$137$	−15.3076	−	4.97373i	−1.30781	−	0.424934i	−0.429520	−	0.903057i	$-0.641317\pi$
$137$	−15.3076	−	4.97373i	−1.30781	−	0.424934i	−0.878293	+	0.478123i	$0.841317\pi$
$138$	−1.68733	−	0.548248i	−0.143635	−	0.0466700i
$139$	0.194094	+	0.597359i	0.0164628	+	0.0506674i	0.958950	−	0.283574i	$-0.0915200\pi$
$139$	0.194094	+	0.597359i	0.0164628	+	0.0506674i	−0.942488	+	0.334241i	$0.891520\pi$
$140$	−1.50618	−	1.17173i	−0.127295	−	0.0990296i
$141$	2.93872	−	9.04444i	0.247484	−	0.761679i
$142$	−9.86101	+	13.5725i	−0.827517	+	1.13898i
$143$			7.41087i			0.619728i
$144$	2.65980	+	1.93246i	0.221650	+	0.161038i
$145$	−3.82587	+	4.91787i	−0.317721	+	0.408407i
$146$	−3.14192	+	2.28274i	−0.260027	+	0.188921i
$147$	3.57275	+	4.91747i	0.294676	+	0.405586i
$148$	3.81324	−	1.23900i	0.313446	−	0.101845i
$149$	2.43409			0.199409			0.0997043	−	0.995017i	$-0.468210\pi$
$149$	2.43409			0.199409			0.0997043	+	0.995017i	$0.468210\pi$
$150$	−5.57278	−	0.366473i	−0.455015	−	0.0299224i
$151$	−10.0394			−0.816997			−0.408498	−	0.912759i	$-0.633947\pi$
$151$	−10.0394			−0.816997			−0.408498	+	0.912759i	$0.633947\pi$
$152$	25.0967	−	8.15440i	2.03561	−	0.661409i
$153$	−1.14246	−	1.57246i	−0.0923622	−	0.127126i
$154$	3.23644	−	2.35141i	0.260800	−	0.189482i
$155$	17.0425	+	6.16299i	1.36889	+	0.495023i
$156$	1.42861	+	1.03794i	0.114380	+	0.0831020i
$157$			1.66854i			0.133164i	0.997781	+	0.0665820i	$0.0212094\pi$
$157$			1.66854i			0.133164i	−0.997781	+	0.0665820i	$0.978791\pi$
$158$	−3.92809	+	5.40655i	−0.312502	+	0.430122i
$159$	2.75871	−	8.49042i	0.218780	−	0.673334i
$160$	−2.66248	−	9.21304i	−0.210488	−	0.728355i
$161$	−0.511503	−	1.57424i	−0.0403121	−	0.124068i
$162$	0.629263	+	0.204460i	0.0494395	+	0.0160639i
$163$	5.74780	+	1.86757i	0.450202	+	0.146280i	0.525338	−	0.850894i	$-0.323939\pi$
$163$	5.74780	+	1.86757i	0.450202	+	0.146280i	−0.0751355	+	0.997173i	$0.523939\pi$
$164$	1.44666	+	4.45236i	0.112965	+	0.347671i
$165$	−2.76070	+	7.63416i	−0.214920	+	0.594318i
$166$	5.73769	−	17.6588i	0.445331	−	1.37059i
$167$	2.71069	−	3.73094i	0.209759	−	0.288709i	−0.691154	−	0.722707i	$-0.742898\pi$
$167$	2.71069	−	3.73094i	0.209759	−	0.288709i	0.900914	+	0.433998i	$0.142898\pi$
$168$		−	3.28120i		−	0.253150i
$169$	−6.95623	−	5.05399i	−0.535094	−	0.388769i
$170$	0.0797739	−	2.42878i	0.00611838	−	0.186279i
$171$	13.5446	−	9.84073i	1.03578	−	0.752540i
$172$	−1.55496	−	2.14022i	−0.118565	−	0.163190i
$173$	2.01008	−	0.653116i	0.152824	−	0.0496555i	−0.231606	−	0.972810i	$-0.574398\pi$
$173$	2.01008	−	0.653116i	0.152824	−	0.0496555i	0.384430	+	0.923154i	$0.374398\pi$
$174$	−3.11241			−0.235951
$175$	−2.77944	−	4.40727i	−0.210106	−	0.333158i
$176$	5.97492			0.450377
$177$	11.8832	−	3.86108i	0.893194	−	0.290216i
$178$	−6.52574	−	8.98191i	−0.489125	−	0.673223i
$179$	−7.83976	+	5.69592i	−0.585971	+	0.425733i	−0.840872	−	0.541234i	$-0.817957\pi$
$179$	−7.83976	+	5.69592i	−0.585971	+	0.425733i	0.254901	+	0.966967i	$0.417957\pi$
$180$	−1.99640	−	2.94658i	−0.148803	−	0.219625i
$181$	13.2926	+	9.65763i	0.988031	+	0.717846i	0.959489	−	0.281746i	$-0.0909136\pi$
$181$	13.2926	+	9.65763i	0.988031	+	0.717846i	0.0285418	+	0.999593i	$0.490914\pi$
$182$		−	2.37604i		−	0.176124i
$183$	6.16842	−	8.49010i	0.455983	−	0.627606i
$184$	1.50370	−	4.62790i	0.110854	−	0.341174i
$185$	10.9419	+	0.359388i	0.804462	+	0.0264227i
$186$	2.79742	+	8.60957i	0.205117	+	0.631284i
$187$	−3.35946	−	1.09155i	−0.245668	−	0.0798223i
$188$	7.20655	+	2.34155i	0.525592	+	0.170775i
$189$	−1.63622	−	5.03577i	−0.119018	−	0.366299i
$190$	20.9207	+	0.687145i	1.51775	+	0.0498507i
$191$	−5.26911	+	16.2167i	−0.381260	+	1.17340i	0.557898	+	0.829910i	$0.311608\pi$
$191$	−5.26911	+	16.2167i	−0.381260	+	1.17340i	−0.939158	+	0.343487i	$0.888392\pi$
$192$	4.85945	−	6.68847i	0.350701	−	0.482698i
$193$			8.40325i			0.604879i	0.953169	+	0.302440i	$0.0978010\pi$
$193$			8.40325i			0.604879i	−0.953169	+	0.302440i	$0.902199\pi$
$194$	−7.28241	−	5.29098i	−0.522846	−	0.379870i
$195$	2.70450	+	3.99171i	0.193673	+	0.285852i
$196$	−3.91821	+	2.84675i	−0.279872	+	0.203339i
$197$	10.3891	+	14.2994i	0.740196	+	1.01879i	0.998607	+	0.0527576i	$0.0168011\pi$
$197$	10.3891	+	14.2994i	0.740196	+	1.01879i	−0.258411	+	0.966035i	$0.583199\pi$
$198$	7.09623	−	2.30570i	0.504307	−	0.163859i
$199$	−7.82140			−0.554445			−0.277222	−	0.960806i	$-0.589414\pi$
$199$	−7.82140			−0.554445			−0.277222	+	0.960806i	$0.589414\pi$
$200$	1.00514	−	15.2846i	0.0710740	−	1.08079i
$201$	−13.9804			−0.986098
$202$	−2.79028	+	0.906618i	−0.196324	+	0.0637894i
$203$	−1.70681	−	2.34923i	−0.119795	−	0.164884i
$204$	−0.680935	+	0.494729i	−0.0476750	+	0.0346379i
$205$	−0.419624	+	12.7758i	−0.0293078	+	0.892300i
$206$	−3.69781	−	2.68661i	−0.257638	−	0.187185i
$207$		−	3.08729i		−	0.214581i
$208$	2.08591	−	2.87101i	0.144632	−	0.199068i
$209$	9.40227	−	28.9372i	0.650369	−	2.00163i
$210$	0.885123	−	2.44763i	0.0610793	−	0.168903i
$211$	−3.34033	−	10.2805i	−0.229958	−	0.707738i	−0.997750	−	0.0670393i	$-0.978645\pi$
$211$	−3.34033	−	10.2805i	−0.229958	−	0.707738i	0.767792	−	0.640699i	$-0.221355\pi$
$212$	6.76512	+	2.19812i	0.464630	+	0.150968i
$213$	15.0894	+	4.90285i	1.03391	+	0.335938i
$214$	5.65170	+	17.3941i	0.386342	+	1.18904i
$215$	−2.00541	−	6.93938i	−0.136768	−	0.473262i
$216$	4.81010	−	14.8040i	0.327286	−	1.00728i
$217$	−4.96438	+	6.83288i	−0.337004	+	0.463846i
$218$		−	18.8547i		−	1.27700i
$219$	2.97138	+	2.15883i	0.200787	+	0.145881i
$220$	−6.08285	−	2.19971i	−0.410106	−	0.148304i
$221$	−1.69732	+	1.23318i	−0.114174	+	0.0829525i
$222$	3.21438	+	4.42422i	0.215735	+	0.296934i
$223$	12.6279	−	4.10306i	0.845628	−	0.274761i	0.146015	−	0.989282i	$-0.453355\pi$
$223$	12.6279	−	4.10306i	0.845628	−	0.274761i	0.699614	+	0.714521i	$0.253355\pi$
$224$	4.46936			0.298622
$225$	−2.39015	−	9.41981i	−0.159343	−	0.627988i
$226$	13.3598			0.888682
$227$	11.7532	−	3.81884i	0.780085	−	0.253465i	0.108209	−	0.994128i	$-0.465488\pi$
$227$	11.7532	−	3.81884i	0.780085	−	0.253465i	0.671877	+	0.740663i	$0.265488\pi$
$228$	−4.26142	−	5.86535i	−0.282220	−	0.388442i
$229$	0.363414	−	0.264036i	0.0240151	−	0.0174480i	−0.575713	−	0.817652i	$-0.695275\pi$
$229$	0.363414	−	0.264036i	0.0240151	−	0.0174480i	0.599728	+	0.800204i	$0.295275\pi$
$230$	2.37010	−	3.04658i	0.156279	−	0.200886i
$231$	−3.06077	−	2.22378i	−0.201384	−	0.146314i
$232$		−	8.53650i		−	0.560449i
$233$	0.611163	−	0.841193i	0.0400386	−	0.0551084i	−0.788528	−	0.614998i	$-0.789157\pi$
$233$	0.611163	−	0.841193i	0.0400386	−	0.0551084i	0.828567	+	0.559890i	$0.189157\pi$
$234$	1.36946	−	4.21475i	0.0895241	−	0.275527i
$235$	16.3303	+	12.7042i	1.06527	+	0.828728i
$236$	3.07648	+	9.46844i	0.200262	+	0.616343i
$237$	6.01081	+	1.95303i	0.390444	+	0.126863i
$238$	1.07709	+	0.349969i	0.0698177	+	0.0226851i
$239$	−6.04327	−	18.5993i	−0.390907	−	1.20309i	−0.932104	−	0.362192i	$-0.882029\pi$
$239$	−6.04327	−	18.5993i	−0.390907	−	1.20309i	0.541197	−	0.840896i	$-0.317971\pi$
$240$	3.21826	−	2.18047i	0.207738	−	0.140748i
$241$	−7.47347	+	23.0010i	−0.481409	+	1.48162i	0.355707	+	0.934598i	$0.384240\pi$
$241$	−7.47347	+	23.0010i	−0.481409	+	1.48162i	−0.837116	+	0.547026i	$0.815760\pi$
$242$	0.943765	−	1.29898i	0.0606675	−	0.0835016i
$243$		−	15.8688i		−	1.01798i
$244$	6.76486	+	4.91496i	0.433076	+	0.314648i
$245$	−12.7043	+	3.67142i	−0.811648	+	0.234558i
$246$	−5.16575	+	3.75314i	−0.329356	+	0.239291i
$247$	−10.6222	−	14.6202i	−0.675873	−	0.930259i
$248$	−23.6137	+	7.67257i	−1.49947	+	0.487208i
$249$	−17.5597			−1.11280
$250$	4.87290	−	11.1305i	0.308190	−	0.703956i
$251$	14.7139			0.928736			0.464368	−	0.885642i	$-0.346282\pi$
$251$	14.7139			0.928736			0.464368	+	0.885642i	$0.346282\pi$
$252$	1.57755	−	0.512579i	0.0993766	−	0.0322894i
$253$	−3.29790	−	4.53917i	−0.207337	−	0.285375i
$254$	−10.9326	+	7.94299i	−0.685971	+	0.498387i
$255$	−2.20785	+	0.638046i	−0.138261	+	0.0399560i
$256$	12.8709	+	9.35124i	0.804430	+	0.584453i
$257$			16.5455i			1.03208i	0.856564	+	0.516041i	$0.172595\pi$
$257$			16.5455i			1.03208i	−0.856564	+	0.516041i	$0.827405\pi$
$258$	2.12085	−	2.91911i	0.132039	−	0.181736i
$259$	−1.57664	+	4.85240i	−0.0979676	+	0.301513i
$260$	−3.18057	+	2.15493i	−0.197250	+	0.133643i
$261$	−1.67364	−	5.15092i	−0.103596	−	0.318834i
$262$	−1.06685	−	0.346642i	−0.0659105	−	0.0214156i
$263$	−13.5004	−	4.38655i	−0.832471	−	0.270486i	−0.138385	−	0.990379i	$-0.544191\pi$
$263$	−13.5004	−	4.38655i	−0.832471	−	0.270486i	−0.694086	+	0.719892i	$0.744191\pi$
$264$	−3.43691	−	10.5777i	−0.211527	−	0.651014i
$265$	15.3300	+	11.9260i	0.941712	+	0.732607i
$266$	−3.01452	+	9.27773i	−0.184832	+	0.568854i
$267$	−6.17154	+	8.49439i	−0.377692	+	0.519848i
$268$		−	11.1395i		−	0.680451i
$269$	16.9255	+	12.2971i	1.03196	+	0.749766i	0.968701	−	0.248231i	$-0.0798491\pi$
$269$	16.9255	+	12.2971i	1.03196	+	0.749766i	0.0632635	+	0.997997i	$0.479849\pi$
$270$	7.58158	−	9.74556i	0.461400	−	0.593096i
$271$	5.24419	−	3.81013i	0.318562	−	0.231449i	−0.417000	−	0.908907i	$-0.636918\pi$
$271$	5.24419	−	3.81013i	0.318562	−	0.231449i	0.735562	+	0.677458i	$0.236918\pi$
$272$	0.994233	+	1.36844i	0.0602843	+	0.0829742i
$273$	−2.13710	+	0.694385i	−0.129343	+	0.0420261i
$274$	17.4919			1.05672
$275$	−13.5766	−	11.2965i	−0.818700	−	0.681206i
$276$	−1.33692			−0.0804729
$277$	2.44558	−	0.794617i	0.146941	−	0.0477439i	−0.234623	−	0.972086i	$-0.575386\pi$
$277$	2.44558	−	0.794617i	0.146941	−	0.0477439i	0.381564	+	0.924342i	$0.375386\pi$
$278$	−0.401223	−	0.552236i	−0.0240637	−	0.0331209i
$279$	−12.7443	+	9.25925i	−0.762980	+	0.554337i
$280$	6.71320	+	2.42765i	0.401190	+	0.145080i
$281$	5.65840	+	4.11107i	0.337552	+	0.245246i	0.743628	−	0.668593i	$-0.233103\pi$
$281$	5.65840	+	4.11107i	0.337552	+	0.245246i	−0.406076	+	0.913839i	$0.633103\pi$
$282$			10.3351i			0.615444i
$283$	−0.949366	+	1.30669i	−0.0564340	+	0.0776747i	−0.836301	−	0.548270i	$-0.815287\pi$
$283$	−0.949366	+	1.30669i	−0.0564340	+	0.0776747i	0.779867	+	0.625945i	$0.215287\pi$
$284$	−3.90656	+	12.0232i	−0.231812	+	0.713443i
$285$	−5.49591	−	19.0176i	−0.325550	−	1.12651i
$286$	−2.48880	−	7.65973i	−0.147166	−	0.452929i
$287$	−5.66569	−	1.84090i	−0.334435	−	0.108665i
$288$	7.92799	+	2.57596i	0.467161	+	0.151790i
$289$	−0.309017	−	0.951057i	−0.0181775	−	0.0559445i
$290$	2.30277	−	6.36785i	0.135223	−	0.373933i
$291$	−2.63065	+	8.09631i	−0.154211	+	0.474614i
$292$	−1.72015	+	2.36758i	−0.100664	+	0.138552i
$293$			6.85091i			0.400235i	0.979772	+	0.200117i	$0.0641323\pi$
$293$			6.85091i			0.400235i	−0.979772	+	0.200117i	$0.935868\pi$
$294$	−5.34416	−	3.88276i	−0.311678	−	0.226447i
$295$	−0.892376	+	27.1691i	−0.0519561	+	1.58185i
$296$	−12.1344	+	8.81619i	−0.705301	+	0.512431i
$297$	−10.5495	−	14.5201i	−0.612143	−	0.842543i
$298$	−2.51583	+	0.817443i	−0.145738	+	0.0473532i
$299$	−3.33244			−0.192720
$300$	−4.07915	+	1.03503i	−0.235510	+	0.0597575i
$301$	3.36638			0.194035
$302$	10.3765	−	3.37154i	0.597103	−	0.194011i
$303$	1.63089	+	2.24472i	0.0936920	+	0.128956i
$304$	−11.7873	+	8.56399i	−0.676049	+	0.491178i
$305$	12.8066	+	18.9019i	0.733302	+	1.08232i
$306$	1.70890	+	1.24159i	0.0976913	+	0.0709769i
$307$		−	7.58160i		−	0.432705i	−0.976315	−	0.216352i	$-0.930584\pi$
$307$		−	7.58160i		−	0.432705i	0.976315	−	0.216352i	$-0.0694160\pi$
$308$	1.77190	−	2.43881i	0.100963	−	0.138964i
$309$	−1.33577	+	4.11108i	−0.0759894	+	0.233871i
$310$	−19.6845	−	0.646542i	−1.11801	−	0.0367211i
$311$	−6.86008	−	21.1132i	−0.389000	−	1.19722i	−0.933537	−	0.358481i	$-0.883295\pi$
$311$	−6.86008	−	21.1132i	−0.389000	−	1.19722i	0.544538	−	0.838736i	$-0.316705\pi$
$312$	−6.28256	−	2.04133i	−0.355680	−	0.115567i
$313$	27.9365	+	9.07710i	1.57906	+	0.513068i	0.961815	−	0.273701i	$-0.0882479\pi$
$313$	27.9365	+	9.07710i	1.57906	+	0.513068i	0.617247	+	0.786769i	$0.288248\pi$
$314$	−0.560347	−	1.72457i	−0.0316222	−	0.0973231i
$315$	4.52670	+	0.148680i	0.255051	+	0.00837719i
$316$	−1.55616	+	4.78937i	−0.0875409	+	0.269423i
$317$	0.0861148	−	0.118527i	0.00483669	−	0.00665713i	−0.806592	−	0.591109i	$-0.798690\pi$
$317$	0.0861148	−	0.118527i	0.00483669	−	0.00665713i	0.811428	+	0.584452i	$0.198690\pi$
$318$			9.70199i			0.544061i
$319$	−7.96302	−	5.78548i	−0.445844	−	0.323924i
$320$	10.0890	+	14.8908i	0.563990	+	0.832421i
$321$	13.9932	−	10.1667i	0.781025	−	0.567448i
$322$	1.05736	+	1.45533i	0.0589243	+	0.0811023i
$323$	8.19208	−	2.66177i	0.455819	−	0.148105i
$324$	0.498580			0.0276989
$325$	−10.1678	+	2.57995i	−0.564009	+	0.143110i
$326$	−6.56800			−0.363768
$327$	−16.9585	+	5.51016i	−0.937809	+	0.304713i
$328$	−10.2938	−	14.1683i	−0.568383	−	0.782312i
$329$	−7.80084	+	5.66764i	−0.430074	+	0.312467i
$330$	0.289617	−	8.81764i	0.0159429	−	0.485395i
$331$	−8.02902	−	5.83342i	−0.441315	−	0.320634i	0.344842	−	0.938661i	$-0.387932\pi$
$331$	−8.02902	−	5.83342i	−0.441315	−	0.320634i	−0.786157	+	0.618027i	$0.787932\pi$
$332$		−	13.9915i		−	0.767883i
$333$	−5.59345	+	7.69873i	−0.306519	+	0.421888i
$334$	−1.54875	+	4.76656i	−0.0847438	+	0.260815i
$335$	10.3436	−	28.6032i	0.565132	−	1.56276i
$336$	0.559839	+	1.72301i	0.0305417	+	0.0939977i
$337$	−27.3797	−	8.89621i	−1.49147	−	0.484608i	−0.553952	−	0.832549i	$-0.686881\pi$
$337$	−27.3797	−	8.89621i	−1.49147	−	0.484608i	−0.937516	+	0.347941i	$0.886881\pi$
$338$	8.88710	+	2.88759i	0.483395	+	0.157064i
$339$	−3.90433	−	12.0163i	−0.212054	−	0.652636i
$340$	−0.508391	−	1.75920i	−0.0275714	−	0.0954059i
$341$	−8.84670	+	27.2273i	−0.479076	+	1.47444i
$342$	−10.6946	+	14.7199i	−0.578299	+	0.795960i
$343$		−	13.4577i		−	0.726648i
$344$	8.00632	+	5.81693i	0.431672	+	0.313628i
$345$	−3.43285	−	1.24140i	−0.184818	−	0.0668348i
$346$	−1.85825	+	1.35010i	−0.0999000	+	0.0725816i
$347$	−8.44150	−	11.6187i	−0.453163	−	0.623726i	0.519910	−	0.854221i	$-0.325965\pi$
$347$	−8.44150	−	11.6187i	−0.453163	−	0.623726i	−0.973073	+	0.230495i	$0.925965\pi$
$348$	−2.23055	+	0.724750i	−0.119570	+	0.0388507i
$349$	22.0697			1.18136			0.590682	−	0.806904i	$-0.298859\pi$
$349$	22.0697			1.18136			0.590682	+	0.806904i	$0.298859\pi$
$350$	4.35287	+	3.62185i	0.232671	+	0.193596i
$351$	−10.6600			−0.568988
$352$	14.4080	−	4.68145i	0.767950	−	0.249522i
$353$	12.6258	+	17.3780i	0.672006	+	0.924937i	0.999804	−	0.0198112i	$-0.00630652\pi$
$353$	12.6258	+	17.3780i	0.672006	+	0.924937i	−0.327798	+	0.944748i	$0.606307\pi$
$354$	−10.9855	+	7.98146i	−0.583875	+	0.424210i
$355$	−21.1952	+	27.2448i	−1.12492	+	1.44601i
$356$	−6.76828	−	4.91744i	−0.358718	−	0.260624i
$357$		−	1.07105i		−	0.0566861i
$358$	6.19015	−	8.52001i	0.327160	−	0.450297i
$359$	−1.36041	+	4.18693i	−0.0717999	+	0.220978i	−0.980517	−	0.196436i	$-0.937063\pi$
$359$	−1.36041	+	4.18693i	−0.0717999	+	0.220978i	0.908717	+	0.417413i	$0.137063\pi$
$360$	10.5090	+	8.17552i	0.553874	+	0.430888i
$361$	17.0562	+	52.4937i	0.897697	+	2.76283i
$362$	−16.9823	−	5.51788i	−0.892569	−	0.290013i
$363$	−1.44416	−	0.469235i	−0.0757987	−	0.0246285i
$364$	−0.553282	−	1.70283i	−0.0289998	−	0.0892523i
$365$	−6.61531	+	4.48206i	−0.346261	+	0.234602i
$366$	−3.52432	+	10.8467i	−0.184219	+	0.566968i
$367$	10.4481	−	14.3806i	0.545387	−	0.750661i	−0.443990	−	0.896032i	$-0.646437\pi$
$367$	10.4481	−	14.3806i	0.545387	−	0.750661i	0.989377	+	0.145370i	$0.0464374\pi$
$368$			2.68674i			0.140056i
$369$	−8.98909	−	6.53096i	−0.467953	−	0.339988i
$370$	−11.4300	+	3.30315i	−0.594216	+	0.171723i
$371$	−7.32301	+	5.32048i	−0.380192	+	0.276225i
$372$	4.00962	+	5.51877i	0.207889	+	0.286135i
$373$	−3.38213	+	1.09892i	−0.175120	+	0.0569000i	−0.395265	−	0.918567i	$-0.629347\pi$
$373$	−3.38213	+	1.09892i	−0.175120	+	0.0569000i	0.220144	+	0.975467i	$0.429347\pi$
$374$	3.83884			0.198502
$375$	−11.4353	−	1.13003i	−0.590514	−	0.0583546i
$376$	−28.3463			−1.46185
$377$	−5.55995	+	1.80654i	−0.286352	+	0.0930414i
$378$	3.38233	+	4.65538i	0.173968	+	0.239447i
$379$	−2.47837	+	1.80064i	−0.127305	+	0.0924927i	−0.649616	−	0.760263i	$-0.725070\pi$
$379$	−2.47837	+	1.80064i	−0.127305	+	0.0924927i	0.522311	+	0.852755i	$0.325070\pi$
$380$	15.1531	−	4.37911i	0.777339	−	0.224644i
$381$	10.3392	+	7.51186i	0.529692	+	0.384844i
$382$		−	18.5307i		−	0.948115i
$383$	−0.902672	+	1.24242i	−0.0461244	+	0.0634848i	−0.831456	−	0.555590i	$-0.812492\pi$
$383$	−0.902672	+	1.24242i	−0.0461244	+	0.0634848i	0.785332	+	0.619075i	$0.212492\pi$
$384$	−0.0521807	+	0.160596i	−0.00266283	+	0.00819536i
$385$	6.81433	−	4.61690i	0.347290	−	0.235299i
$386$	−2.82207	−	8.68543i	−0.143639	−	0.442077i
$387$	5.97146	+	1.94025i	0.303547	+	0.0986282i
$388$	−6.45109	−	2.09609i	−0.327504	−	0.106413i
$389$	3.12693	+	9.62371i	0.158542	+	0.487941i	0.998503	−	0.0547058i	$-0.0174221\pi$
$389$	3.12693	+	9.62371i	0.158542	+	0.487941i	−0.839961	+	0.542647i	$0.817422\pi$
$390$	−4.13585	−	3.21749i	−0.209427	−	0.162924i
$391$	0.490838	−	1.51064i	0.0248228	−	0.0763966i
$392$	10.6494	−	14.6576i	0.537874	−	0.740321i
$393$			1.06087i			0.0535138i
$394$	−15.5402	−	11.2906i	−0.782904	−	0.568813i
$395$	−8.44301	+	10.8529i	−0.424814	+	0.546067i
$396$	4.54871	−	3.30483i	0.228581	−	0.166074i
$397$	−4.50258	−	6.19727i	−0.225978	−	0.311032i	0.680940	−	0.732339i	$-0.261571\pi$
$397$	−4.50258	−	6.19727i	−0.225978	−	0.311032i	−0.906918	+	0.421307i	$0.861571\pi$
$398$	8.08405	−	2.62667i	0.405217	−	0.131663i
$399$	9.22569			0.461862
$400$	2.08005	+	8.19768i	0.104003	+	0.409884i
$401$	3.48349			0.173957			0.0869787	−	0.996210i	$-0.472279\pi$
$401$	3.48349			0.173957			0.0869787	+	0.996210i	$0.472279\pi$
$402$	14.4498	−	4.69503i	0.720691	−	0.234167i
$403$	9.99452	+	13.7563i	0.497862	+	0.685249i
$404$	−1.78858	+	1.29948i	−0.0889853	+	0.0646516i
$405$	1.28022	+	0.462959i	0.0636148	+	0.0230046i
$406$	2.55307	+	1.85491i	0.126707	+	0.0920579i
$407$			17.2943i			0.857247i
$408$	1.85073	−	2.54730i	0.0916245	−	0.126110i
$409$	2.45726	−	7.56267i	0.121504	−	0.373950i	−0.871744	−	0.489961i	$-0.837011\pi$
$409$	2.45726	−	7.56267i	0.121504	−	0.373950i	0.993248	+	0.116011i	$0.0370109\pi$
$410$	−3.85679	−	13.3457i	−0.190473	−	0.659098i
$411$	−5.11191	−	15.7328i	−0.252152	−	0.776043i
$412$	−3.27569	−	1.06434i	−0.161382	−	0.0524360i
$413$	−12.0487	−	3.91487i	−0.592879	−	0.192638i
$414$	1.03681	+	3.19096i	0.0509562	+	0.156827i
$415$	12.9919	−	35.9265i	0.637746	−	1.76356i
$416$	2.78051	−	8.55754i	0.136326	−	0.419568i
$417$	−0.379445	+	0.522262i	−0.0185815	+	0.0255753i
$418$			33.0665i			1.61733i
$419$	20.1446	+	14.6359i	0.984127	+	0.715010i	0.958627	−	0.284664i	$-0.0918821\pi$
$419$	20.1446	+	14.6359i	0.984127	+	0.715010i	0.0255002	+	0.999675i	$0.491882\pi$
$420$	0.0643844	−	1.96024i	0.00314164	−	0.0956499i
$421$	−6.42627	+	4.66896i	−0.313197	+	0.227551i	−0.733267	−	0.679941i	$-0.762006\pi$
$421$	−6.42627	+	4.66896i	−0.313197	+	0.227551i	0.420070	+	0.907492i	$0.362006\pi$
$422$	6.90500	+	9.50392i	0.336130	+	0.462644i
$423$	−17.1041	+	5.55747i	−0.831632	+	0.270214i
$424$	−26.6099			−1.29229
$425$	0.328098	−	4.98922i	0.0159151	−	0.242013i
$426$	−17.2426			−0.835409
$427$	−10.1198	+	3.28811i	−0.489729	+	0.159123i
$428$	8.10074	+	11.1497i	0.391564	+	0.538942i
$429$	−6.16209	+	4.47702i	−0.297509	+	0.216153i
$430$	4.40321	+	6.49893i	0.212342	+	0.313406i
$431$	−17.2156	−	12.5079i	−0.829245	−	0.602482i	0.0901004	−	0.995933i	$-0.471281\pi$
$431$	−17.2156	−	12.5079i	−0.829245	−	0.602482i	−0.919346	+	0.393451i	$0.871281\pi$
$432$			8.59448i			0.413502i
$433$	11.0282	−	15.1790i	0.529980	−	0.729455i	−0.457147	−	0.889391i	$-0.651129\pi$
$433$	11.0282	−	15.1790i	0.529980	−	0.729455i	0.987127	+	0.159936i	$0.0511287\pi$
$434$	2.83639	−	8.72951i	0.136151	−	0.419030i
$435$	−6.40044	−	0.210224i	−0.306878	−	0.0100795i
$436$	−4.39046	−	13.5125i	−0.210265	−	0.647130i
$437$	13.0122	+	4.22791i	0.622457	+	0.202249i
$438$	−3.79616	−	1.23345i	−0.181388	−	0.0589364i
$439$	−7.14062	−	21.9766i	−0.340803	−	1.04889i	−0.963792	−	0.266654i	$-0.914082\pi$
$439$	−7.14062	−	21.9766i	−0.340803	−	1.04889i	0.622989	−	0.782231i	$-0.285918\pi$
$440$	24.1844	+	0.794342i	1.15295	+	0.0378688i
$441$	3.55211	−	10.9323i	0.169148	−	0.520585i
$442$	1.34018	−	1.84460i	0.0637459	−	0.0877387i
$443$			22.2591i			1.05756i	0.848758	+	0.528781i	$0.177351\pi$
$443$			22.2591i			1.05756i	−0.848758	+	0.528781i	$0.822649\pi$
$444$	3.33385	+	2.42219i	0.158218	+	0.114952i
$445$	−12.8130	−	18.9114i	−0.607396	−	0.896487i
$446$	−11.6740	+	8.48168i	−0.552782	+	0.401619i
$447$	1.47047	+	2.02393i	0.0695510	+	0.0957287i
$448$	−7.97230	+	2.59036i	−0.376656	+	0.122383i
$449$	1.21042			0.0571231			0.0285616	−	0.999592i	$-0.490907\pi$
$449$	1.21042			0.0571231			0.0285616	+	0.999592i	$0.490907\pi$
$450$	5.63387	+	8.93344i	0.265583	+	0.421127i
$451$	−20.1929			−0.950848
$452$	9.57451	−	3.11095i	0.450347	−	0.146327i
$453$	−6.06497	−	8.34772i	−0.284957	−	0.392210i
$454$	−10.8654	+	7.89415i	−0.509937	+	0.370491i
$455$	0.160487	−	4.88616i	0.00752374	−	0.229067i
$456$	21.9416	+	15.9415i	1.02751	+	0.746530i
$457$		−	19.0465i		−	0.890958i	−0.895292	−	0.445479i	$-0.853033\pi$
$457$		−	19.0465i		−	0.890958i	0.895292	−	0.445479i	$-0.146967\pi$
$458$	−0.286946	+	0.394948i	−0.0134081	+	0.0184547i
$459$	1.57012	−	4.83233i	0.0732869	−	0.225554i
$460$	0.989141	−	2.73527i	0.0461189	−	0.127533i
$461$	7.16446	+	22.0500i	0.333682	+	1.02697i	0.967367	+	0.253378i	$0.0815415\pi$
$461$	7.16446	+	22.0500i	0.333682	+	1.02697i	−0.633685	+	0.773591i	$0.718458\pi$
$462$	3.91037	+	1.27056i	0.181927	+	0.0591116i
$463$	30.0910	+	9.77716i	1.39845	+	0.454383i	0.908688	−	0.417475i	$-0.137085\pi$
$463$	30.0910	+	9.77716i	1.39845	+	0.454383i	0.489759	+	0.871858i	$0.337085\pi$
$464$	1.45650	+	4.48264i	0.0676162	+	0.208101i
$465$	5.17116	+	17.8939i	0.239807	+	0.829809i
$466$	−0.349187	+	1.07469i	−0.0161758	+	0.0497839i
$467$	−0.770988	+	1.06117i	−0.0356771	+	0.0491053i	−0.826483	−	0.562962i	$-0.809662\pi$
$467$	−0.770988	+	1.06117i	−0.0356771	+	0.0491053i	0.790806	+	0.612067i	$0.209662\pi$
$468$		−	3.33945i		−	0.154366i
$469$	11.4679	+	8.33193i	0.529539	+	0.384733i
$470$	−21.1451	−	7.64657i	−0.975349	−	0.352710i
$471$	−1.38738	+	1.00799i	−0.0639271	+	0.0464458i
$472$	−21.8910	−	30.1304i	−1.00762	−	1.38686i
$473$	10.8523	−	3.52613i	0.498990	−	0.162132i
$474$	−6.86853			−0.315482
$475$	42.9755	+	2.82613i	1.97185	+	0.129672i
$476$	0.853408			0.0391159
$477$	−16.0564	+	5.21706i	−0.735174	+	0.238873i
$478$	12.4924	+	17.1943i	0.571390	+	0.786450i
$479$	−24.8447	+	18.0507i	−1.13518	+	0.824760i	−0.986441	−	0.164116i	$-0.947523\pi$
$479$	−24.8447	+	18.0507i	−1.13518	+	0.824760i	−0.148743	+	0.988876i	$0.547523\pi$
$480$	6.05214	−	7.77957i	0.276241	−	0.355087i
$481$	8.31007	+	6.03762i	0.378907	+	0.275292i
$482$		−	26.2832i		−	1.19717i
$483$	0.999967	−	1.37634i	0.0455001	−	0.0626255i
$484$	0.373884	−	1.15070i	0.0169947	−	0.0523044i
$485$	−14.6184	−	11.3724i	−0.663786	−	0.516394i
$486$	5.32921	+	16.4016i	0.241738	+	0.743993i
$487$	−23.9496	−	7.78169i	−1.08526	−	0.352622i	−0.288847	−	0.957375i	$-0.593272\pi$
$487$	−23.9496	−	7.78169i	−1.08526	−	0.352622i	−0.796413	+	0.604753i	$0.793272\pi$
$488$	−29.7497	−	9.66626i	−1.34671	−	0.437571i
$489$	1.91946	+	5.90749i	0.0868009	+	0.267146i
$490$	11.8979	−	8.06119i	0.537494	−	0.364168i
$491$	4.32256	−	13.3035i	0.195074	−	0.600377i	−0.804901	−	0.593409i	$-0.797782\pi$
$491$	4.32256	−	13.3035i	0.195074	−	0.600377i	0.999976	−	0.00696856i	$-0.00221818\pi$
$492$	−2.82816	+	3.89263i	−0.127503	+	0.175493i
$493$		−	2.78649i		−	0.125497i
$494$	15.8888	+	11.5439i	0.714869	+	0.519383i
$495$	14.7486	−	4.26221i	0.662901	−	0.191572i
$496$	11.0908	−	8.05795i	0.497992	−	0.361813i
$497$	−9.45569	−	13.0146i	−0.424146	−	0.583787i
$498$	18.1494	−	5.89709i	0.813294	−	0.264255i
$499$	17.7477			0.794496			0.397248	−	0.917711i	$-0.369965\pi$
$499$	17.7477			0.794496			0.397248	+	0.917711i	$0.369965\pi$
$500$	0.900403	−	9.11154i	0.0402672	−	0.407481i
$501$	4.73982			0.211760
$502$	−15.2080	+	4.94139i	−0.678768	+	0.220545i
$503$	−0.420746	−	0.579107i	−0.0187601	−	0.0258211i	0.799534	−	0.600621i	$-0.205080\pi$
$503$	−0.420746	−	0.579107i	−0.0187601	−	0.0258211i	−0.818294	+	0.574800i	$0.805080\pi$
$504$	−5.02008	+	3.64730i	−0.223612	+	0.162464i
$505$	−5.79925	+	1.67593i	−0.258063	+	0.0745777i
$506$	4.93303	+	3.58406i	0.219300	+	0.159331i
$507$		−	8.83725i		−	0.392476i
$508$	−5.98540	+	8.23820i	−0.265559	+	0.365511i
$509$	−10.2436	+	31.5267i	−0.454041	+	1.39740i	0.418215	+	0.908348i	$0.362656\pi$
$509$	−10.2436	+	31.5267i	−0.454041	+	1.39740i	−0.872257	+	0.489048i	$0.837344\pi$
$510$	2.06771	−	1.40093i	0.0915597	−	0.0620344i
$511$	−1.15078	−	3.54173i	−0.0509074	−	0.156677i
$512$	−16.7560	−	5.44436i	−0.740519	−	0.240609i
$513$	41.6240	+	13.5245i	1.83775	+	0.597120i
$514$	−5.55649	−	17.1011i	−0.245086	−	0.754298i
$515$	−7.42280	−	5.77459i	−0.327088	−	0.254459i
$516$	0.840203	−	2.58588i	0.0369879	−	0.113837i
$517$	−19.2112	+	26.4420i	−0.844909	+	1.16292i
$518$		−	5.54482i		−	0.243626i
$519$	1.75738	+	1.27681i	0.0771406	+	0.0560459i
$520$	8.82472	−	11.3435i	0.386990	−	0.497446i
$521$	18.0912	−	13.1440i	0.792589	−	0.575849i	−0.116142	−	0.993233i	$-0.537053\pi$
$521$	18.0912	−	13.1440i	0.792589	−	0.575849i	0.908731	+	0.417383i	$0.137053\pi$
$522$	3.45967	+	4.76183i	0.151426	+	0.208420i
$523$	27.8023	−	9.03351i	1.21571	−	0.395008i	0.370192	−	0.928955i	$-0.379292\pi$
$523$	27.8023	−	9.03351i	1.21571	−	0.395008i	0.845518	+	0.533947i	$0.179292\pi$
$524$	−0.845295			−0.0369269
$525$	1.98551	−	4.97359i	0.0866549	−	0.217065i
$526$	15.4269			0.672644
$527$	−7.70802	+	2.50449i	−0.335766	+	0.109097i
$528$	3.60954	+	4.96811i	0.157085	+	0.216209i
$529$	−16.5663	+	12.0361i	−0.720272	+	0.523309i
$530$	−19.8498	−	7.17818i	−0.862222	−	0.311800i
$531$	−19.1163	−	13.8888i	−0.829577	−	0.602723i
$532$			7.35097i			0.318705i
$533$	−7.04957	+	9.70290i	−0.305351	+	0.420279i
$534$	3.52610	−	10.8522i	0.152589	−	0.469622i
$535$	10.4474	+	36.1515i	0.451682	+	1.56297i
$536$	12.8772	+	39.6319i	0.556210	+	1.71184i
$537$	−9.47223	−	3.07772i	−0.408757	−	0.132813i
$538$	−21.6236	−	7.02592i	−0.932258	−	0.302909i
$539$	−6.45547	−	19.8679i	−0.278057	−	0.855771i
$540$	3.16411	−	8.74973i	0.136162	−	0.376528i
$541$	−0.580880	+	1.78776i	−0.0249740	+	0.0768620i	−0.962767	−	0.270334i	$-0.912866\pi$
$541$	−0.580880	+	1.78776i	−0.0249740	+	0.0768620i	0.937793	+	0.347196i	$0.112866\pi$
$542$	−4.14073	+	5.69923i	−0.177860	+	0.244803i
$543$			16.8870i			0.724692i
$544$	3.46971	+	2.52089i	0.148763	+	0.108082i
$545$	1.27351	−	38.7732i	0.0545514	−	1.66086i
$546$	1.97566	−	1.43540i	0.0845506	−	0.0614296i
$547$	26.5449	+	36.5360i	1.13498	+	1.56217i	0.778247	+	0.627958i	$0.216109\pi$
$547$	26.5449	+	36.5360i	1.13498	+	1.56217i	0.356732	+	0.934207i	$0.383891\pi$
$548$	12.5358	−	4.07314i	0.535504	−	0.173996i
$549$	−19.8461			−0.847011
$550$	17.8262	+	7.11643i	0.760113	+	0.303445i
$551$	24.0019			1.02252
$552$	4.75648	−	1.54547i	0.202449	−	0.0657797i
$553$	−3.76664	−	5.18433i	−0.160174	−	0.220460i
$554$	−2.26085	+	1.64260i	−0.0960542	+	0.0697874i
$555$	6.31132	+	9.31520i	0.267900	+	0.395408i
$556$	−0.416135	−	0.302340i	−0.0176481	−	0.0128221i
$557$			18.7543i			0.794647i	0.917679	+	0.397323i	$0.130061\pi$
$557$			18.7543i			0.794647i	−0.917679	+	0.397323i	$0.869939\pi$
$558$	10.0627	−	13.8501i	0.425987	−	0.586321i
$559$	2.09432	−	6.44565i	0.0885802	−	0.272622i
$560$	−3.93940	−	0.129390i	−0.166470	−	0.00546775i
$561$	−1.12188	−	3.45279i	−0.0473658	−	0.145777i
$562$	−7.22902	−	2.34885i	−0.304938	−	0.0990804i
$563$	−0.00112965		0.000367047i	−4.76092e−5		1.54692e-5i	0.308993	−	0.951064i	$-0.400008\pi$
$563$	−0.00112965		0.000367047i	−4.76092e−5		1.54692e-5i	−0.309041	+	0.951049i	$0.600008\pi$
$564$	2.40660	+	7.40677i	0.101336	+	0.311881i
$565$	27.4735	+	0.902373i	1.15582	+	0.0379631i
$566$	0.542419	−	1.66939i	0.0227996	−	0.0701699i
$567$	−0.372921	+	0.513281i	−0.0156612	+	0.0215558i
$568$		−	47.2919i		−	1.98433i
$569$	34.1247	+	24.7930i	1.43058	+	1.03938i	0.989908	+	0.141710i	$0.0452601\pi$
$569$	34.1247	+	24.7930i	1.43058	+	1.03938i	0.440673	+	0.897668i	$0.354740\pi$
$570$	12.0672	+	17.8105i	0.505438	+	0.746001i
$571$	9.02403	−	6.55634i	0.377644	−	0.274374i	−0.382730	−	0.923860i	$-0.625016\pi$
$571$	9.02403	−	6.55634i	0.377644	−	0.274374i	0.760374	+	0.649486i	$0.225016\pi$
$572$	−3.56726	−	4.90992i	−0.149155	−	0.205294i
$573$	−16.6672	+	5.41550i	−0.696282	+	0.226236i
$574$	6.47418			0.270227
$575$	5.07970	−	6.10499i	0.211838	−	0.254595i
$576$	−15.6347			−0.651445
$577$	−23.8404	+	7.74622i	−0.992490	+	0.322479i	−0.759861	−	0.650086i	$-0.774733\pi$
$577$	−23.8404	+	7.74622i	−0.992490	+	0.322479i	−0.232629	+	0.972566i	$0.574733\pi$
$578$	0.638787	+	0.879215i	0.0265701	+	0.0365705i
$579$	−6.98725	+	5.07653i	−0.290380	+	0.210973i
$580$	0.167505	−	5.09983i	0.00695527	−	0.211759i
$581$	14.4040	+	10.4651i	0.597580	+	0.434167i
$582$		−	9.25163i		−	0.383493i
$583$	−18.0345	+	24.8223i	−0.746911	+	1.02804i
$584$	3.38302	−	10.4119i	0.139990	−	0.430845i
$585$	3.10087	−	8.57483i	0.128205	−	0.354525i
$586$	−2.30075	−	7.08097i	−0.0950429	−	0.292512i
$587$	−26.1388	−	8.49301i	−1.07886	−	0.350544i	−0.284930	−	0.958548i	$-0.591970\pi$
$587$	−26.1388	−	8.49301i	−1.07886	−	0.350544i	−0.793934	+	0.608004i	$0.791970\pi$
$588$	−4.73410	−	1.53820i	−0.195231	−	0.0634345i
$589$	−21.5728	−	66.3942i	−0.888891	−	2.73573i
$590$	−8.20188	−	28.3812i	−0.337666	−	1.16843i
$591$	−5.61364	+	17.2770i	−0.230914	+	0.710681i
$592$	4.86776	−	6.69989i	0.200064	−	0.275364i
$593$			24.8287i			1.01959i	0.860295	+	0.509796i	$0.170279\pi$
$593$			24.8287i			1.01959i	−0.860295	+	0.509796i	$0.829721\pi$
$594$	15.7800	+	11.4649i	0.647463	+	0.470409i
$595$	2.19133	+	0.792437i	0.0898357	+	0.0324867i
$596$	−1.61266	+	1.17166i	−0.0660570	+	0.0479932i
$597$	−4.72503	−	6.50345i	−0.193383	−	0.266168i
$598$	3.44435	−	1.11914i	0.140850	−	0.0457649i
$599$	8.93541			0.365091			0.182545	−	0.983197i	$-0.441566\pi$
$599$	8.93541			0.365091			0.182545	+	0.983197i	$0.441566\pi$
$600$	13.3163	−	8.39792i	0.543635	−	0.342843i
$601$	6.99378			0.285282			0.142641	−	0.989774i	$-0.454441\pi$
$601$	6.99378			0.285282			0.142641	+	0.989774i	$0.454441\pi$
$602$	−3.47942	+	1.13053i	−0.141811	+	0.0460771i
$603$	15.5402	+	21.3893i	0.632846	+	0.871038i
$604$	6.65141	−	4.83253i	0.270642	−	0.196633i
$605$	2.02852	−	2.60751i	0.0824711	−	0.106010i
$606$	−2.43950	−	1.77240i	−0.0990979	−	0.0719988i
$607$		−	16.0758i		−	0.652497i	−0.945284	−	0.326248i	$-0.894215\pi$
$607$		−	16.0758i		−	0.652497i	0.945284	−	0.326248i	$-0.105785\pi$
$608$	−21.7141	+	29.8869i	−0.880623	+	1.21207i
$609$	0.922255	−	2.83841i	0.0373717	−	0.115018i
$610$	−19.5844	−	15.2357i	−0.792950	−	0.616877i
$611$	5.99878	+	18.4624i	0.242685	+	0.746907i
$612$	1.51382	+	0.491870i	0.0611926	+	0.0198827i
$613$	7.82748	+	2.54330i	0.316149	+	0.102723i	0.462793	−	0.886466i	$-0.346847\pi$
$613$	7.82748	+	2.54330i	0.316149	+	0.102723i	−0.146644	+	0.989189i	$0.546847\pi$
$614$	2.54613	+	7.83619i	0.102754	+	0.316243i
$615$	−10.8765	+	7.36914i	−0.438582	+	0.297152i
$616$	−3.48479	+	10.7251i	−0.140406	+	0.432126i
$617$	6.36283	−	8.75768i	0.256158	−	0.352571i	−0.661498	−	0.749947i	$-0.730079\pi$
$617$	6.36283	−	8.75768i	0.256158	−	0.352571i	0.917656	+	0.397376i	$0.130079\pi$
$618$		−	4.69773i		−	0.188970i
$619$	−11.9884	−	8.71009i	−0.481855	−	0.350088i	0.320189	−	0.947354i	$-0.396254\pi$
$619$	−11.9884	−	8.71009i	−0.481855	−	0.350088i	−0.802043	+	0.597266i	$0.796254\pi$
$620$	−14.2577	+	4.12035i	−0.572605	+	0.165477i
$621$	6.52926	−	4.74378i	0.262010	−	0.190361i
$622$	14.1809	+	19.5183i	0.568602	+	0.782613i
$623$	10.1249	−	3.28977i	0.405645	−	0.131802i
$624$	3.64735			0.146011
$625$	10.7726	−	22.5600i	0.430903	−	0.902398i
$626$	−31.9229			−1.27590
$627$	29.7412	−	9.66349i	1.18775	−	0.385922i
$628$	−0.803161	−	1.10546i	−0.0320496	−	0.0441125i
$629$	−3.96094	+	2.87779i	−0.157933	+	0.114745i
$630$	−4.72864	+	1.36653i	−0.188393	+	0.0544439i
$631$	−3.71561	−	2.69955i	−0.147916	−	0.107467i	0.511366	−	0.859363i	$-0.329140\pi$
$631$	−3.71561	−	2.69955i	−0.147916	−	0.107467i	−0.659282	+	0.751896i	$0.729140\pi$
$632$		−	18.8385i		−	0.749357i
$633$	6.53021	−	8.98807i	0.259553	−	0.357244i
$634$	−0.0492016	+	0.151427i	−0.00195404	+	0.00601393i
$635$	−23.0186	+	15.5957i	−0.913463	+	0.618898i
$636$	2.25919	+	6.95307i	0.0895827	+	0.275707i
$637$	−11.8004	−	3.83418i	−0.467548	−	0.151916i
$638$	10.1734	+	3.30553i	0.402767	+	0.130867i
$639$	−9.27189	−	28.5360i	−0.366790	−	1.12886i
$640$	−0.289965	−	0.225579i	−0.0114619	−	0.00891679i
$641$	12.5392	−	38.5918i	0.495270	−	1.52428i	−0.321267	−	0.946989i	$-0.604109\pi$
$641$	12.5392	−	38.5918i	0.495270	−	1.52428i	0.816536	−	0.577294i	$-0.195891\pi$
$642$	−11.0488	+	15.2074i	−0.436063	+	0.600189i
$643$		−	37.3344i		−	1.47232i	−0.676805	−	0.736162i	$-0.736636\pi$
$643$		−	37.3344i		−	1.47232i	0.676805	−	0.736162i	$-0.263364\pi$
$644$	1.09666	+	0.796768i	0.0432143	+	0.0313970i
$645$	4.55855	−	5.85968i	0.179493	−	0.230724i
$646$	−7.57326	+	5.50230i	−0.297966	+	0.216485i
$647$	0.226750	+	0.312094i	0.00891444	+	0.0122697i	0.813451	−	0.581634i	$-0.197586\pi$
$647$	0.226750	+	0.312094i	0.00891444	+	0.0122697i	−0.804537	+	0.593903i	$0.797586\pi$
$648$	−1.77385	+	0.576358i	−0.0696833	+	0.0226415i
$649$	−42.9425			−1.68564
$650$	9.64283	−	6.08125i	0.378223	−	0.238526i
$651$	−8.68055			−0.340218
$652$	−4.70705	+	1.52941i	−0.184342	+	0.0598964i
$653$	4.19359	+	5.77198i	0.164108	+	0.225875i	0.883149	−	0.469092i	$-0.155419\pi$
$653$	4.19359	+	5.77198i	0.164108	+	0.225875i	−0.719041	+	0.694967i	$0.755419\pi$
$654$	15.6775	−	11.3904i	0.613040	−	0.445399i
$655$	−2.17049	−	0.784903i	−0.0848082	−	0.0306687i
$656$	7.82284	+	5.68362i	0.305430	+	0.221908i
$657$		−	6.94577i		−	0.270980i
$658$	6.15943	−	8.47772i	0.240119	−	0.330496i
$659$	−6.36085	+	19.5767i	−0.247784	+	0.762599i	0.747383	+	0.664394i	$0.231310\pi$
$659$	−6.36085	+	19.5767i	−0.247784	+	0.762599i	−0.995166	+	0.0982054i	$0.968690\pi$
$660$	−1.84570	−	6.38673i	−0.0718439	−	0.248603i
$661$	−13.3533	−	41.0972i	−0.519383	−	1.59850i	−0.775164	−	0.631761i	$-0.782333\pi$
$661$	−13.3533	−	41.0972i	−0.519383	−	1.59850i	0.255781	−	0.966735i	$-0.417667\pi$
$662$	10.2577	+	3.33292i	0.398676	+	0.129538i
$663$	−2.05076	−	0.666332i	−0.0796448	−	0.0258782i
$664$	16.1741	+	49.7789i	0.627679	+	1.93180i
$665$	−6.82578	+	18.8753i	−0.264693	+	0.731955i
$666$	3.19581	−	9.83570i	0.123835	−	0.381126i
$667$	2.60155	−	3.58073i	0.100732	−	0.138646i
$668$			3.77666i			0.146123i
$669$	11.0404	+	8.02131i	0.426846	+	0.310122i
$670$	−1.08512	+	33.0374i	−0.0419218	+	1.27635i
$671$	−29.1793	+	21.2000i	−1.12645	+	0.818416i
$672$	2.70001	+	3.71624i	0.104155	+	0.143357i
$673$	−21.9828	+	7.14265i	−0.847376	+	0.275329i	−0.700346	−	0.713803i	$-0.746971\pi$
$673$	−21.9828	+	7.14265i	−0.847376	+	0.275329i	−0.147029	+	0.989132i	$0.546971\pi$
$674$	31.2867			1.20512
$675$	16.2492	−	19.5289i	0.625433	−	0.751669i
$676$	7.04147			0.270826
$677$	2.61130	−	0.848461i	0.100360	−	0.0326090i	−0.258406	−	0.966036i	$-0.583197\pi$
$677$	2.61130	−	0.848461i	0.100360	−	0.0326090i	0.358767	+	0.933427i	$0.383197\pi$
$678$	8.07088	+	11.1086i	0.309960	+	0.426624i
$679$	6.98308	−	5.07350i	0.267986	−	0.194703i
$680$	3.84238	+	5.67117i	0.147349	+	0.217479i
$681$	10.2756	+	7.46567i	0.393762	+	0.286085i
$682$		−	31.1126i		−	1.19136i
$683$	−8.09092	+	11.1362i	−0.309590	+	0.426115i	−0.935253	−	0.353979i	$-0.884828\pi$
$683$	−8.09092	+	11.1362i	−0.309590	+	0.426115i	0.625663	+	0.780093i	$0.284828\pi$
$684$	−4.23680	+	13.0395i	−0.161998	+	0.498579i
$685$	35.9708	+	1.18147i	1.37437	+	0.0451416i
$686$	4.51951	+	13.9096i	0.172556	+	0.531072i
$687$	0.439088	+	0.142668i	0.0167523	+	0.00544314i
$688$	−5.19672	−	1.68852i	−0.198123	−	0.0643741i
$689$	5.63133	+	17.3315i	0.214537	+	0.660276i
$690$	3.96502	+	0.130232i	0.150946	+	0.00495785i
$691$	3.16315	−	9.73518i	0.120332	−	0.370344i	−0.872690	−	0.488275i	$-0.837626\pi$
$691$	3.16315	−	9.73518i	0.120332	−	0.370344i	0.993022	+	0.117931i	$0.0376263\pi$
$692$	−1.01736	+	1.40027i	−0.0386742	+	0.0532304i
$693$			7.15473i			0.271786i
$694$	12.6269	+	9.17397i	0.479310	+	0.348239i
$695$	−0.787785	−	1.16273i	−0.0298824	−	0.0441050i
$696$	7.09804	−	5.15703i	0.269051	−	0.195477i
$697$	−3.36013	−	4.62482i	−0.127274	−	0.175177i
$698$	−22.8108	+	7.41168i	−0.863402	+	0.280536i
$699$	1.06866			0.0404204
$700$	3.96293	+	1.58204i	0.149785	+	0.0597956i
$701$	35.5084			1.34113			0.670567	−	0.741849i	$-0.266051\pi$
$701$	35.5084			1.34113			0.670567	+	0.741849i	$0.266051\pi$
$702$	11.0180	−	3.57995i	0.415846	−	0.135116i
$703$	−24.7883	−	34.1182i	−0.934908	−	1.28679i
$704$	−22.9873	+	16.7012i	−0.866366	+	0.629452i
$705$	−0.698068	+	21.2533i	−0.0262908	+	0.800445i
$706$	−18.8859	−	13.7214i	−0.710779	−	0.516411i
$707$		−	2.81329i		−	0.105805i
$708$	−6.01440	+	8.27811i	−0.226035	+	0.311110i
$709$	−2.60965	+	8.03166i	−0.0980073	+	0.301635i	−0.988026	−	0.154289i	$-0.950691\pi$
$709$	−2.60965	+	8.03166i	−0.0980073	+	0.301635i	0.890018	+	0.455925i	$0.150691\pi$
$710$	12.7573	−	35.2777i	0.478772	−	1.32395i
$711$	−3.69342	−	11.3672i	−0.138514	−	0.426302i
$712$	29.7647	+	9.67115i	1.11548	+	0.362442i
$713$	−12.2433	−	3.97809i	−0.458515	−	0.148981i
$714$	0.359692	+	1.10702i	0.0134611	+	0.0414291i
$715$	−4.60066	−	15.9198i	−0.172055	−	0.595366i
$716$	2.45231	−	7.54742i	0.0916469	−	0.282060i
$717$	11.8143	−	16.2611i	0.441215	−	0.607280i
$718$		−	4.78439i		−	0.178552i
$719$	−14.9355	−	10.8513i	−0.557001	−	0.404685i	0.273359	−	0.961912i	$-0.411865\pi$
$719$	−14.9355	−	10.8513i	−0.557001	−	0.404685i	−0.830360	+	0.557227i	$0.811865\pi$
$720$	−6.91335	−	2.50003i	−0.257645	−	0.0931707i
$721$	3.54582	−	2.57619i	0.132053	−	0.0959422i
$722$	−35.2580	−	48.5284i	−1.31217	−	1.80604i
$723$	−23.6400	+	7.68110i	−0.879181	+	0.285663i
$724$	−13.4555			−0.500069
$725$	5.16558	−	12.9395i	0.191845	−	0.480560i
$726$	1.65024			0.0612460
$727$	37.6329	−	12.2277i	1.39573	−	0.453500i	0.487921	−	0.872888i	$-0.337755\pi$
$727$	37.6329	−	12.2277i	1.39573	−	0.453500i	0.907807	+	0.419388i	$0.137755\pi$
$728$	3.93693	+	5.41872i	0.145912	+	0.200831i
$729$	11.7171	−	8.51300i	0.433968	−	0.315296i
$730$	5.33224	−	6.85419i	0.197355	−	0.253685i
$731$	2.61343	+	1.89877i	0.0966612	+	0.0702285i
$732$			8.59414i			0.317648i
$733$	27.5428	−	37.9095i	1.01732	−	1.40022i	0.103251	−	0.994655i	$-0.467075\pi$
$733$	27.5428	−	37.9095i	1.01732	−	1.40022i	0.914067	−	0.405563i	$-0.132925\pi$
$734$	−5.96952	+	18.3723i	−0.220339	+	0.678134i
$735$	−10.7276	−	8.34558i	−0.395694	−	0.307831i
$736$	2.10511	+	6.47885i	0.0775952	+	0.238814i
$737$	45.6968	+	14.8478i	1.68326	+	0.546926i
$738$	11.4842	+	3.73145i	0.422741	+	0.137357i
$739$	−7.26619	−	22.3630i	−0.267291	−	0.822637i	−0.991157	−	0.132696i	$-0.957637\pi$
$739$	−7.26619	−	22.3630i	−0.267291	−	0.822637i	0.723866	−	0.689941i	$-0.242363\pi$
$740$	−7.42229	+	5.02882i	−0.272849	+	0.184863i
$741$	5.73955	−	17.6645i	0.210848	−	0.648923i
$742$	5.78213	−	7.95842i	0.212269	−	0.292163i
$743$			37.2594i			1.36692i	0.729990	+	0.683458i	$0.239525\pi$
$743$			37.2594i			1.36692i	−0.729990	+	0.683458i	$0.760475\pi$
$744$	−20.6451	−	14.9995i	−0.756886	−	0.549910i
$745$	−5.22883	+	1.51108i	−0.191570	+	0.0553618i
$746$	3.12665	−	2.27165i	0.114475	−	0.0831709i
$747$	19.5190	+	26.8655i	0.714161	+	0.982959i
$748$	2.75116	−	0.893907i	0.100592	−	0.0326845i
$749$	−17.5375			−0.640808
$750$	12.1987	−	2.67233i	0.445435	−	0.0975796i
$751$	20.6116			0.752127			0.376063	−	0.926594i	$-0.377278\pi$
$751$	20.6116			0.752127			0.376063	+	0.926594i	$0.377278\pi$
$752$	14.8850	−	4.83644i	0.542802	−	0.176367i
$753$	8.88892	+	12.2345i	0.323930	+	0.445852i
$754$	5.13996	−	3.73440i	0.187186	−	0.135999i
$755$	21.5663	−	6.23246i	0.784879	−	0.226823i
$756$	3.50804	+	2.54874i	0.127586	+	0.0926968i
$757$			8.67222i			0.315197i	0.987503	+	0.157599i	$0.0503752\pi$
$757$			8.67222i			0.315197i	−0.987503	+	0.157599i	$0.949625\pi$
$758$	1.95688	−	2.69342i	0.0710771	−	0.0978293i
$759$	1.78198	−	5.48436i	0.0646817	−	0.199070i
$760$	−48.8495	+	33.0970i	−1.77196	+	1.20055i
$761$	−2.07924	−	6.39925i	−0.0753725	−	0.231973i	0.906271	−	0.422697i	$-0.138916\pi$
$761$	−2.07924	−	6.39925i	−0.0753725	−	0.231973i	−0.981644	+	0.190724i	$0.938916\pi$
$762$	−13.2091	−	4.29189i	−0.478514	−	0.155479i
$763$	17.1948	+	5.58693i	0.622493	+	0.202260i
$764$	−4.31504	−	13.2803i	−0.156113	−	0.480465i
$765$	3.43036	+	2.66866i	0.124025	+	0.0964856i
$766$	0.515741	−	1.58729i	0.0186345	−	0.0573510i
$767$	−14.9917	+	20.6343i	−0.541319	+	0.745061i
$768$			16.3513i			0.590026i
$769$	20.5982	+	14.9655i	0.742790	+	0.539668i	0.893584	−	0.448897i	$-0.148183\pi$
$769$	20.5982	+	14.9655i	0.742790	+	0.539668i	−0.150794	+	0.988565i	$0.548183\pi$
$770$	−5.49265	+	7.06040i	−0.197941	+	0.254439i
$771$	−13.7575	+	9.99540i	−0.495464	+	0.359976i

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.r (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.03358 + 0.335830i) q^{2} +(0.604115 + 0.831493i) q^{3} +(-0.662529 + 0.481355i) q^{4} +(-2.14816 + 0.620799i) q^{5} +(-0.903642 - 0.656534i) q^{6} -1.04210i q^{7} +(1.80070 - 2.47845i) q^{8} +(0.600625 - 1.84853i) q^{9} +(2.01182 - 1.36306i) q^{10} +(-1.09155 - 3.35946i) q^{11} +(-0.800488 - 0.260094i) q^{12} +(-1.99532 - 0.648320i) q^{13} +(0.349969 + 1.07709i) q^{14} +(-1.81393 - 1.41115i) q^{15} +(-0.522699 + 1.60870i) q^{16} +(0.587785 - 0.809017i) q^{17} +2.11232i q^{18} +(6.96860 + 5.06298i) q^{19} +(1.12440 - 1.44533i) q^{20} +(0.866500 - 0.629549i) q^{21} +(2.25641 + 3.10569i) q^{22} +(1.51064 - 0.490838i) q^{23} +3.14864 q^{24} +(4.22922 - 2.66716i) q^{25} +2.28005 q^{26} +(4.83233 - 1.57012i) q^{27} +(0.501621 + 0.690422i) q^{28} +(2.25432 - 1.63786i) q^{29} +(2.34875 + 0.849364i) q^{30} +(-6.55683 - 4.76382i) q^{31} +4.28880i q^{32} +(2.13394 - 2.93712i) q^{33} +(-0.335830 + 1.03358i) q^{34} +(0.646935 + 2.23860i) q^{35} +(0.491870 + 1.51382i) q^{36} +(-4.65636 - 1.51294i) q^{37} +(-8.90291 - 2.89273i) q^{38} +(-0.666332 - 2.05076i) q^{39} +(-2.32958 + 6.44198i) q^{40} +(1.76652 - 5.43680i) q^{41} +(-0.684175 + 0.941686i) q^{42} +3.23038i q^{43} +(2.34028 + 1.70031i) q^{44} +(-0.142674 + 4.34382i) q^{45} +(-1.39653 + 1.01464i) q^{46} +(-5.43867 - 7.48569i) q^{47} +(-1.65340 + 0.537221i) q^{48} +5.91403 q^{49} +(-3.47552 + 4.17702i) q^{50} +1.02778 q^{51} +(1.63403 - 0.530929i) q^{52} +(-5.10553 - 7.02716i) q^{53} +(-4.46730 + 3.24569i) q^{54} +(4.43038 + 6.53903i) q^{55} +(-2.58279 - 1.87651i) q^{56} +8.85297i q^{57} +(-1.77998 + 2.44993i) q^{58} +(3.75671 - 11.5620i) q^{59} +(1.88104 + 0.0617833i) q^{60} +(-3.15527 - 9.71092i) q^{61} +(8.37684 + 2.72180i) q^{62} +(-1.92636 - 0.625912i) q^{63} +(-2.48571 - 7.65022i) q^{64} +(4.68876 + 0.154003i) q^{65} +(-1.21922 + 3.75239i) q^{66} +(-7.99532 + 11.0046i) q^{67} +0.818931i q^{68} +(1.32073 + 0.959568i) q^{69} +(-1.42045 - 2.09652i) q^{70} +(12.4889 - 9.07368i) q^{71} +(-3.49995 - 4.81727i) q^{72} +(3.39865 - 1.10429i) q^{73} +5.32081 q^{74} +(4.77266 + 1.90530i) q^{75} -7.05399 q^{76} +(-3.50089 + 1.13751i) q^{77} +(1.37741 + 1.89585i) q^{78} +(4.97488 - 3.61446i) q^{79} +(0.124163 - 3.78025i) q^{80} +(-0.492545 - 0.357855i) q^{81} +6.21262i q^{82} +(-10.0424 + 13.8221i) q^{83} +(-0.271044 + 0.834189i) q^{84} +(-0.760422 + 2.10280i) q^{85} +(-1.08486 - 3.33885i) q^{86} +(2.72374 + 0.884996i) q^{87} +(-10.2918 - 3.34401i) q^{88} +(3.15686 + 9.71583i) q^{89} +(-1.31132 - 4.53760i) q^{90} +(-0.675615 + 2.07933i) q^{91} +(-0.764578 + 1.05235i) q^{92} -8.32985i q^{93} +(8.13522 + 5.91058i) q^{94} +(-18.1128 - 6.55002i) q^{95} +(-3.56611 + 2.59093i) q^{96} +(4.86853 + 6.70096i) q^{97} +(-6.11262 + 1.98611i) q^{98} -6.86568 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 160 q + 40 q^{4} - 8 q^{5} + 4 q^{6} - 30 q^{8} + 36 q^{9} - 6 q^{10} + 8 q^{11} - 40 q^{12} - 20 q^{14} - 40 q^{15} - 64 q^{16} + 6 q^{19} + 2 q^{20} - 50 q^{22} + 20 q^{23} + 20 q^{24} + 32 q^{25} + 20 q^{26}+ \cdots + 44 q^{99}+O(q^{100}) \) 160 * q + 40 * q^4 - 8 * q^5 + 4 * q^6 - 30 * q^8 + 36 * q^9 - 6 * q^10 + 8 * q^11 - 40 * q^12 - 20 * q^14 - 40 * q^15 - 64 * q^16 + 6 * q^19 + 2 * q^20 - 50 * q^22 + 20 * q^23 + 20 * q^24 + 32 * q^25 + 20 * q^26 + 30 * q^27 + 60 * q^28 + 16 * q^30 + 12 * q^31 - 40 * q^33 - 4 * q^34 - 54 * q^36 - 40 * q^38 - 12 * q^39 - 52 * q^40 - 2 * q^41 + 30 * q^42 - 20 * q^44 + 42 * q^45 + 48 * q^46 + 40 * q^47 - 100 * q^48 - 184 * q^49 + 46 * q^50 - 32 * q^51 - 10 * q^52 - 20 * q^53 - 40 * q^54 + 18 * q^55 + 24 * q^56 - 120 * q^58 + 6 * q^59 - 40 * q^60 + 12 * q^61 - 10 * q^62 + 90 * q^63 + 58 * q^64 - 20 * q^65 + 48 * q^66 - 90 * q^67 - 74 * q^69 - 120 * q^70 - 16 * q^71 - 10 * q^72 + 52 * q^74 + 76 * q^75 + 96 * q^76 + 80 * q^77 + 40 * q^78 - 60 * q^79 - 24 * q^80 - 118 * q^81 - 76 * q^84 + 2 * q^85 + 44 * q^86 + 40 * q^87 + 140 * q^88 + 50 * q^89 + 224 * q^90 + 28 * q^91 - 170 * q^92 + 96 * q^94 - 44 * q^95 - 116 * q^96 + 110 * q^97 + 70 * q^98 + 44 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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