LMFDB - Embedded newform 322.2.i.d.29.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [322,2,Mod(29,322)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(322, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 18]))

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

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

chi := DirichletCharacter("322.29");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 322 = 2 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	322.i (of order $11$, degree $10$, 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:	$2.57118294509$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$4$ over $\Q(\zeta_{11})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			29.2
Character	$\chi$	$=$	322.29
Dual form			322.2.i.d.211.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.415415 - 0.909632i) q^{2} +(-2.34488 - 0.688518i) q^{3} +(-0.654861 - 0.755750i) q^{4} +(3.30897 - 2.12655i) q^{5} +(-1.60040 + 1.84696i) q^{6} +(0.142315 - 0.989821i) q^{7} +(-0.959493 + 0.281733i) q^{8} +(2.50063 + 1.60706i) q^{9} +O(q^{10})$	\(q+(0.415415 - 0.909632i) q^{2} +(-2.34488 - 0.688518i) q^{3} +(-0.654861 - 0.755750i) q^{4} +(3.30897 - 2.12655i) q^{5} +(-1.60040 + 1.84696i) q^{6} +(0.142315 - 0.989821i) q^{7} +(-0.959493 + 0.281733i) q^{8} +(2.50063 + 1.60706i) q^{9} +(-0.559779 - 3.89335i) q^{10} +(-0.709559 - 1.55372i) q^{11} +(1.01522 + 2.22302i) q^{12} +(0.236236 + 1.64306i) q^{13} +(-0.841254 - 0.540641i) q^{14} +(-9.22331 + 2.70821i) q^{15} +(-0.142315 + 0.989821i) q^{16} +(0.789136 - 0.910712i) q^{17} +(2.50063 - 1.60706i) q^{18} +(-4.52344 - 5.22033i) q^{19} +(-3.77405 - 1.10816i) q^{20} +(-1.01522 + 2.22302i) q^{21} -1.70807 q^{22} +(-4.22900 + 2.26177i) q^{23} +2.44387 q^{24} +(4.35002 - 9.52522i) q^{25} +(1.59271 + 0.467662i) q^{26} +(0.0439942 + 0.0507720i) q^{27} +(-0.841254 + 0.540641i) q^{28} +(-5.81739 + 6.71362i) q^{29} +(-1.36803 + 9.51485i) q^{30} +(3.71059 - 1.08953i) q^{31} +(0.841254 + 0.540641i) q^{32} +(0.594066 + 4.13182i) q^{33} +(-0.500594 - 1.09615i) q^{34} +(-1.63399 - 3.57793i) q^{35} +(-0.423032 - 2.94225i) q^{36} +(-4.57912 - 2.94282i) q^{37} +(-6.62768 + 1.94606i) q^{38} +(0.577330 - 4.01542i) q^{39} +(-2.57582 + 2.97265i) q^{40} +(9.12128 - 5.86189i) q^{41} +(1.60040 + 1.84696i) q^{42} +(7.57469 + 2.22413i) q^{43} +(-0.709559 + 1.55372i) q^{44} +11.6920 q^{45} +(0.300589 + 4.78640i) q^{46} +10.8331 q^{47} +(1.01522 - 2.22302i) q^{48} +(-0.959493 - 0.281733i) q^{49} +(-6.85738 - 7.91384i) q^{50} +(-2.47747 + 1.59217i) q^{51} +(1.08704 - 1.25451i) q^{52} +(-0.0724635 + 0.503995i) q^{53} +(0.0644597 - 0.0189271i) q^{54} +(-5.65197 - 3.63230i) q^{55} +(0.142315 + 0.989821i) q^{56} +(7.01263 + 15.3555i) q^{57} +(3.69030 + 8.08062i) q^{58} +(0.267207 + 1.85847i) q^{59} +(8.08671 + 5.19701i) q^{60} +(8.34071 - 2.44905i) q^{61} +(0.550365 - 3.82787i) q^{62} +(1.94658 - 2.24647i) q^{63} +(0.841254 - 0.540641i) q^{64} +(4.27573 + 4.93446i) q^{65} +(4.00522 + 1.17604i) q^{66} +(-0.817784 + 1.79070i) q^{67} -1.20504 q^{68} +(11.4737 - 2.39183i) q^{69} -3.93338 q^{70} +(3.12425 - 6.84115i) q^{71} +(-2.85210 - 0.837453i) q^{72} +(7.09559 + 8.18875i) q^{73} +(-4.57912 + 2.94282i) q^{74} +(-16.7586 + 19.3404i) q^{75} +(-0.983038 + 6.83718i) q^{76} +(-1.63888 + 0.481220i) q^{77} +(-3.41272 - 2.19322i) q^{78} +(0.490637 + 3.41246i) q^{79} +(1.63399 + 3.57793i) q^{80} +(-3.77268 - 8.26102i) q^{81} +(-1.54305 - 10.7321i) q^{82} +(-2.06514 - 1.32719i) q^{83} +(2.34488 - 0.688518i) q^{84} +(0.674559 - 4.69166i) q^{85} +(5.16978 - 5.96624i) q^{86} +(18.2635 - 11.7373i) q^{87} +(1.11855 + 1.29087i) q^{88} +(-8.28631 - 2.43308i) q^{89} +(4.85704 - 10.6354i) q^{90} +1.65995 q^{91} +(4.47873 + 1.71492i) q^{92} -9.45103 q^{93} +(4.50022 - 9.85411i) q^{94} +(-26.0692 - 7.65462i) q^{95} +(-1.60040 - 1.84696i) q^{96} +(0.500548 - 0.321683i) q^{97} +(-0.654861 + 0.755750i) q^{98} +(0.722570 - 5.02558i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 4 q^{2} - 4 q^{4} + 9 q^{5} + 4 q^{7} - 4 q^{8} - 8 q^{9}+O(q^{10}) $ 40 * q - 4 * q^2 - 4 * q^4 + 9 * q^5 + 4 * q^7 - 4 * q^8 - 8 * q^9	\( 40 q - 4 q^{2} - 4 q^{4} + 9 q^{5} + 4 q^{7} - 4 q^{8} - 8 q^{9} - 2 q^{10} + 6 q^{11} + 2 q^{13} + 4 q^{14} - 3 q^{15} - 4 q^{16} - 13 q^{17} - 8 q^{18} - 22 q^{19} - 2 q^{20} - 16 q^{22} - 9 q^{23} + 22 q^{24} - 15 q^{25} - 9 q^{26} + 21 q^{27} + 4 q^{28} - 10 q^{29} - 14 q^{30} - 2 q^{31} - 4 q^{32} + 8 q^{33} - 2 q^{34} + 13 q^{35} - 8 q^{36} - 45 q^{37} + 11 q^{38} - 22 q^{39} + 9 q^{40} + 21 q^{41} + 31 q^{43} + 6 q^{44} + 2 q^{45} - 9 q^{46} + 64 q^{47} - 4 q^{49} + 7 q^{50} + 65 q^{51} + 2 q^{52} + 69 q^{53} + 21 q^{54} - 74 q^{55} + 4 q^{56} - 68 q^{57} + 12 q^{58} + 48 q^{59} - 3 q^{60} + 6 q^{61} - 13 q^{62} + 8 q^{63} - 4 q^{64} - 64 q^{65} - 69 q^{66} + 31 q^{67} - 2 q^{68} - 62 q^{69} + 2 q^{70} - 57 q^{71} - 19 q^{72} + 70 q^{73} - 45 q^{74} - 11 q^{75} + 22 q^{76} - 6 q^{77} + 33 q^{78} + 34 q^{79} - 13 q^{80} + 30 q^{81} - 12 q^{82} - 56 q^{83} - 17 q^{85} + 42 q^{86} - 3 q^{87} + 6 q^{88} + 16 q^{89} + 46 q^{90} - 46 q^{91} + 24 q^{92} + 48 q^{93} + 9 q^{94} - 42 q^{95} - 36 q^{97} - 4 q^{98} + 112 q^{99}+O(q^{100}) \) 40 * q - 4 * q^2 - 4 * q^4 + 9 * q^5 + 4 * q^7 - 4 * q^8 - 8 * q^9 - 2 * q^10 + 6 * q^11 + 2 * q^13 + 4 * q^14 - 3 * q^15 - 4 * q^16 - 13 * q^17 - 8 * q^18 - 22 * q^19 - 2 * q^20 - 16 * q^22 - 9 * q^23 + 22 * q^24 - 15 * q^25 - 9 * q^26 + 21 * q^27 + 4 * q^28 - 10 * q^29 - 14 * q^30 - 2 * q^31 - 4 * q^32 + 8 * q^33 - 2 * q^34 + 13 * q^35 - 8 * q^36 - 45 * q^37 + 11 * q^38 - 22 * q^39 + 9 * q^40 + 21 * q^41 + 31 * q^43 + 6 * q^44 + 2 * q^45 - 9 * q^46 + 64 * q^47 - 4 * q^49 + 7 * q^50 + 65 * q^51 + 2 * q^52 + 69 * q^53 + 21 * q^54 - 74 * q^55 + 4 * q^56 - 68 * q^57 + 12 * q^58 + 48 * q^59 - 3 * q^60 + 6 * q^61 - 13 * q^62 + 8 * q^63 - 4 * q^64 - 64 * q^65 - 69 * q^66 + 31 * q^67 - 2 * q^68 - 62 * q^69 + 2 * q^70 - 57 * q^71 - 19 * q^72 + 70 * q^73 - 45 * q^74 - 11 * q^75 + 22 * q^76 - 6 * q^77 + 33 * q^78 + 34 * q^79 - 13 * q^80 + 30 * q^81 - 12 * q^82 - 56 * q^83 - 17 * q^85 + 42 * q^86 - 3 * q^87 + 6 * q^88 + 16 * q^89 + 46 * q^90 - 46 * q^91 + 24 * q^92 + 48 * q^93 + 9 * q^94 - 42 * q^95 - 36 * q^97 - 4 * q^98 + 112 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/322\mathbb{Z}\right)^\times$.

$n$	$185$	$281$
$\chi(n)$	$1$	$e\left(\frac{9}{11}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.415415	−	0.909632i	0.293743	−	0.643207i
$2$	0.415415	−	0.909632i	0.293743	−	0.643207i
$3$	−2.34488	−	0.688518i	−1.35382	−	0.397516i	−0.477237	−	0.878775i	$-0.658362\pi$
$3$	−2.34488	−	0.688518i	−1.35382	−	0.397516i	−0.876579	+	0.481258i	$0.840180\pi$
$4$	−0.654861	−	0.755750i	−0.327430	−	0.377875i
$5$	3.30897	−	2.12655i	1.47982	−	0.951021i	0.482650	−	0.875813i	$-0.339674\pi$
$5$	3.30897	−	2.12655i	1.47982	−	0.951021i	0.997168	−	0.0752081i	$-0.0239621\pi$
$6$	−1.60040	+	1.84696i	−0.653359	+	0.754016i
$7$	0.142315	−	0.989821i	0.0537900	−	0.374117i
$7$	0.142315	−	0.989821i	0.0537900	−	0.374117i
$8$	−0.959493	+	0.281733i	−0.339232	+	0.0996075i
$9$	2.50063	+	1.60706i	0.833545	+	0.535687i
$10$	−0.559779	−	3.89335i	−0.177018	−	1.23118i
$11$	−0.709559	−	1.55372i	−0.213940	−	0.468463i	0.771987	−	0.635638i	$-0.219263\pi$
$11$	−0.709559	−	1.55372i	−0.213940	−	0.468463i	−0.985927	+	0.167175i	$0.946536\pi$
$12$	1.01522	+	2.22302i	0.293069	+	0.641732i
$13$	0.236236	+	1.64306i	0.0655200	+	0.455702i	0.996000	+	0.0893579i	$0.0284815\pi$
$13$	0.236236	+	1.64306i	0.0655200	+	0.455702i	−0.930480	+	0.366344i	$0.880609\pi$
$14$	−0.841254	−	0.540641i	−0.224834	−	0.144492i
$15$	−9.22331	+	2.70821i	−2.38145	+	0.699256i
$16$	−0.142315	+	0.989821i	−0.0355787	+	0.247455i
$17$	0.789136	−	0.910712i	0.191394	−	0.220880i	−0.651940	−	0.758271i	$-0.726044\pi$
$17$	0.789136	−	0.910712i	0.191394	−	0.220880i	0.843333	+	0.537391i	$0.180590\pi$
$18$	2.50063	−	1.60706i	0.589405	−	0.378788i
$19$	−4.52344	−	5.22033i	−1.03775	−	1.19763i	−0.979939	−	0.199298i	$-0.936134\pi$
$19$	−4.52344	−	5.22033i	−1.03775	−	1.19763i	−0.0578098	−	0.998328i	$-0.518412\pi$
$20$	−3.77405	−	1.10816i	−0.843904	−	0.247793i
$21$	−1.01522	+	2.22302i	−0.221539	+	0.485104i
$22$	−1.70807			−0.364162
$23$	−4.22900	+	2.26177i	−0.881806	+	0.471611i
$23$	−4.22900	+	2.26177i	−0.881806	+	0.471611i
$24$	2.44387			0.498853
$25$	4.35002	−	9.52522i	0.870005	−	1.90504i
$26$	1.59271	+	0.467662i	0.312356	+	0.0917161i
$27$	0.0439942	+	0.0507720i	0.00846669	+	0.00977108i
$28$	−0.841254	+	0.540641i	−0.158982	+	0.102172i
$29$	−5.81739	+	6.71362i	−1.08026	+	1.24669i	−0.112815	+	0.993616i	$0.535987\pi$
$29$	−5.81739	+	6.71362i	−1.08026	+	1.24669i	−0.967447	+	0.253073i	$0.918559\pi$
$30$	−1.36803	+	9.51485i	−0.249767	+	1.73717i
$31$	3.71059	−	1.08953i	0.666441	−	0.195685i	0.0690233	−	0.997615i	$-0.478012\pi$
$31$	3.71059	−	1.08953i	0.666441	−	0.195685i	0.597418	+	0.801930i	$0.296194\pi$
$32$	0.841254	+	0.540641i	0.148714	+	0.0955727i
$33$	0.594066	+	4.13182i	0.103414	+	0.719258i
$34$	−0.500594	−	1.09615i	−0.0858511	−	0.187988i
$35$	−1.63399	−	3.57793i	−0.276194	−	0.604781i
$36$	−0.423032	−	2.94225i	−0.0705054	−	0.490376i
$37$	−4.57912	−	2.94282i	−0.752803	−	0.483797i	0.107104	−	0.994248i	$-0.465842\pi$
$37$	−4.57912	−	2.94282i	−0.752803	−	0.483797i	−0.859907	+	0.510451i	$0.829479\pi$
$38$	−6.62768	+	1.94606i	−1.07515	+	0.315693i
$39$	0.577330	−	4.01542i	0.0924468	−	0.642981i
$40$	−2.57582	+	2.97265i	−0.407273	+	0.470018i
$41$	9.12128	−	5.86189i	1.42450	−	0.915474i	0.424555	−	0.905402i	$-0.360430\pi$
$41$	9.12128	−	5.86189i	1.42450	−	0.915474i	0.999949	−	0.0100716i	$-0.00320596\pi$
$42$	1.60040	+	1.84696i	0.246946	+	0.284991i
$43$	7.57469	+	2.22413i	1.15513	+	0.339176i	0.802538	−	0.596601i	$-0.203483\pi$
$43$	7.57469	+	2.22413i	1.15513	+	0.339176i	0.352591	+	0.935778i	$0.385301\pi$
$44$	−0.709559	+	1.55372i	−0.106970	+	0.234232i
$45$	11.6920			1.74294
$46$	0.300589	+	4.78640i	0.0443195	+	0.705717i
$47$	10.8331			1.58017			0.790083	−	0.613000i	$-0.210037\pi$
$47$	10.8331			1.58017			0.790083	+	0.613000i	$0.210037\pi$
$48$	1.01522	−	2.22302i	0.146535	−	0.320866i
$49$	−0.959493	−	0.281733i	−0.137070	−	0.0402475i
$50$	−6.85738	−	7.91384i	−0.969780	−	1.11919i
$51$	−2.47747	+	1.59217i	−0.346915	+	0.222949i
$52$	1.08704	−	1.25451i	0.150745	−	0.173969i
$53$	−0.0724635	+	0.503995i	−0.00995363	+	0.0692290i	−0.994193	−	0.107613i	$-0.965679\pi$
$53$	−0.0724635	+	0.503995i	−0.00995363	+	0.0692290i	0.984239	+	0.176842i	$0.0565883\pi$
$54$	0.0644597	−	0.0189271i	0.00877186	−	0.00257565i
$55$	−5.65197	−	3.63230i	−0.762111	−	0.489779i
$56$	0.142315	+	0.989821i	0.0190176	+	0.132270i
$57$	7.01263	+	15.3555i	0.928845	+	2.03389i
$58$	3.69030	+	8.08062i	0.484560	+	1.06104i
$59$	0.267207	+	1.85847i	0.0347874	+	0.241952i	0.999795	−	0.0202721i	$-0.00645324\pi$
$59$	0.267207	+	1.85847i	0.0347874	+	0.241952i	−0.965007	+	0.262224i	$0.915544\pi$
$60$	8.08671	+	5.19701i	1.04399	+	0.670931i
$61$	8.34071	−	2.44905i	1.06792	−	0.313569i	0.299883	−	0.953976i	$-0.403052\pi$
$61$	8.34071	−	2.44905i	1.06792	−	0.313569i	0.768036	+	0.640407i	$0.221234\pi$
$62$	0.550365	−	3.82787i	0.0698964	−	0.486140i
$63$	1.94658	−	2.24647i	0.245246	−	0.283029i
$64$	0.841254	−	0.540641i	0.105157	−	0.0675801i
$65$	4.27573	+	4.93446i	0.530340	+	0.612045i
$66$	4.00522	+	1.17604i	0.493009	+	0.144760i
$67$	−0.817784	+	1.79070i	−0.0999082	+	0.218769i	−0.952985	−	0.303016i	$-0.902006\pi$
$67$	−0.817784	+	1.79070i	−0.0999082	+	0.218769i	0.853077	+	0.521785i	$0.174734\pi$
$68$	−1.20504			−0.146133
$69$	11.4737	−	2.39183i	1.38128	−	0.287943i
$70$	−3.93338			−0.470129
$71$	3.12425	−	6.84115i	0.370780	−	0.811895i	−0.628635	−	0.777700i	$-0.716386\pi$
$71$	3.12425	−	6.84115i	0.370780	−	0.811895i	0.999415	−	0.0341949i	$-0.0108867\pi$
$72$	−2.85210	−	0.837453i	−0.336124	−	0.0986948i
$73$	7.09559	+	8.18875i	0.830476	+	0.958421i	0.999631	−	0.0271687i	$-0.00864912\pi$
$73$	7.09559	+	8.18875i	0.830476	+	0.958421i	−0.169154	+	0.985590i	$0.554104\pi$
$74$	−4.57912	+	2.94282i	−0.532312	+	0.342096i
$75$	−16.7586	+	19.3404i	−1.93511	+	2.23324i
$76$	−0.983038	+	6.83718i	−0.112762	+	0.784278i
$77$	−1.63888	+	0.481220i	−0.186768	+	0.0548401i
$78$	−3.41272	−	2.19322i	−0.386415	−	0.248334i
$79$	0.490637	+	3.41246i	0.0552010	+	0.383932i	0.998629	+	0.0523530i	$0.0166721\pi$
$79$	0.490637	+	3.41246i	0.0552010	+	0.383932i	−0.943428	+	0.331579i	$0.892419\pi$
$80$	1.63399	+	3.57793i	0.182685	+	0.400025i
$81$	−3.77268	−	8.26102i	−0.419187	−	0.917891i
$82$	−1.54305	−	10.7321i	−0.170401	−	1.18517i
$83$	−2.06514	−	1.32719i	−0.226679	−	0.145678i	0.422372	−	0.906422i	$-0.361198\pi$
$83$	−2.06514	−	1.32719i	−0.226679	−	0.145678i	−0.649051	+	0.760745i	$0.724834\pi$
$84$	2.34488	−	0.688518i	0.255847	−	0.0751235i
$85$	0.674559	−	4.69166i	0.0731661	−	0.508882i
$86$	5.16978	−	5.96624i	0.557471	−	0.643356i
$87$	18.2635	−	11.7373i	1.95805	−	1.25837i
$88$	1.11855	+	1.29087i	0.119238	+	0.137608i
$89$	−8.28631	−	2.43308i	−0.878347	−	0.257906i	−0.188685	−	0.982038i	$-0.560423\pi$
$89$	−8.28631	−	2.43308i	−0.878347	−	0.257906i	−0.689662	+	0.724132i	$0.742241\pi$
$90$	4.85704	−	10.6354i	0.511977	−	1.12107i
$91$	1.65995			0.174010
$92$	4.47873	+	1.71492i	0.466940	+	0.178793i
$93$	−9.45103			−0.980026
$94$	4.50022	−	9.85411i	0.464162	−	1.01637i
$95$	−26.0692	−	7.65462i	−2.67465	−	0.785347i
$96$	−1.60040	−	1.84696i	−0.163340	−	0.188504i
$97$	0.500548	−	0.321683i	0.0508230	−	0.0326620i	−0.514983	−	0.857201i	$-0.672202\pi$
$97$	0.500548	−	0.321683i	0.0508230	−	0.0326620i	0.565806	+	0.824539i	$0.308565\pi$
$98$	−0.654861	+	0.755750i	−0.0661509	+	0.0763422i
$99$	0.722570	−	5.02558i	0.0726210	−	0.505090i
$100$	−10.0473	+	2.95017i	−1.00473	+	0.295017i
$101$	−9.26849	−	5.95650i	−0.922249	−	0.592694i	−0.00893985	−	0.999960i	$-0.502846\pi$
$101$	−9.26849	−	5.95650i	−0.922249	−	0.592694i	−0.913309	+	0.407266i	$0.866482\pi$
$102$	0.419114	+	2.91500i	0.0414984	+	0.288628i
$103$	−2.38468	−	5.22173i	−0.234970	−	0.514512i	0.755011	−	0.655712i	$-0.227631\pi$
$103$	−2.38468	−	5.22173i	−0.234970	−	0.514512i	−0.989981	+	0.141199i	$0.954904\pi$
$104$	−0.689569	−	1.50995i	−0.0676178	−	0.148062i
$105$	1.36803	+	9.51485i	0.133506	+	0.928554i
$106$	0.428347	+	0.275282i	0.0416048	+	0.0267378i
$107$	−5.53911	+	1.62643i	−0.535486	+	0.157233i	−0.538285	−	0.842763i	$-0.680927\pi$
$107$	−5.53911	+	1.62643i	−0.535486	+	0.157233i	0.00279831	+	0.999996i	$0.499109\pi$
$108$	0.00956086	−	0.0664972i	0.000919994	−	0.00639870i
$109$	7.77436	−	8.97209i	0.744649	−	0.859370i	−0.249389	−	0.968403i	$-0.580230\pi$
$109$	7.77436	−	8.97209i	0.744649	−	0.859370i	0.994038	+	0.109033i	$0.0347754\pi$
$110$	−5.65197	+	3.63230i	−0.538894	+	0.346326i
$111$	8.71129	+	10.0534i	0.826839	+	0.954224i
$112$	0.959493	+	0.281733i	0.0906636	+	0.0266212i
$113$	−6.77975	+	14.8456i	−0.637785	+	1.39655i	0.264065	+	0.964505i	$0.414937\pi$
$113$	−6.77975	+	14.8456i	−0.637785	+	1.39655i	−0.901850	+	0.432049i	$0.857791\pi$
$114$	16.8810			1.58105
$115$	−9.18387	+	16.4773i	−0.856401	+	1.53652i
$116$	8.88340			0.824803
$117$	−2.04975	+	4.48833i	−0.189499	+	0.414946i
$118$	1.80152	+	0.528975i	0.165844	+	0.0486961i
$119$	−0.789136	−	0.910712i	−0.0723400	−	0.0834848i
$120$	8.08671	−	5.19701i	0.738212	−	0.474420i
$121$	5.29291	−	6.10834i	0.481173	−	0.555303i
$122$	1.23712	−	8.60435i	0.112004	−	0.779002i
$123$	−25.4243	+	7.46525i	−2.29243	+	0.673119i
$124$	−3.25333	−	2.09079i	−0.292157	−	0.187758i
$125$	−3.06284	−	21.3025i	−0.273949	−	1.90535i
$126$	−1.23483	−	2.70389i	−0.110007	−	0.240882i
$127$	8.69083	+	19.0303i	0.771186	+	1.68866i	0.724024	+	0.689775i	$0.242290\pi$
$127$	8.69083	+	19.0303i	0.771186	+	1.68866i	0.0471621	+	0.998887i	$0.484982\pi$
$128$	−0.142315	−	0.989821i	−0.0125790	−	0.0874887i
$129$	−16.2304	−	10.4306i	−1.42900	−	0.918365i
$130$	6.26475	−	1.83950i	0.549455	−	0.161334i
$131$	0.275375	−	1.91528i	0.0240596	−	0.167338i	−0.974249	−	0.225475i	$-0.927607\pi$
$131$	0.275375	−	1.91528i	0.0240596	−	0.167338i	0.998309	+	0.0581363i	$0.0185158\pi$
$132$	2.73359	−	3.15473i	0.237929	−	0.274584i
$133$	−5.81095	+	3.73447i	−0.503873	+	0.323820i
$134$	1.28916	+	1.48777i	0.111366	+	0.128523i
$135$	0.253545	+	0.0744475i	0.0218217	+	0.00640742i
$136$	−0.500594	+	1.09615i	−0.0429255	+	0.0939938i
$137$	8.30571			0.709605			0.354803	−	0.934941i	$-0.384548\pi$
$137$	8.30571			0.709605			0.354803	+	0.934941i	$0.384548\pi$
$138$	2.59068	−	11.4305i	0.220533	−	0.973028i
$139$	19.0588			1.61655			0.808274	−	0.588806i	$-0.200402\pi$
$139$	19.0588			1.61655			0.808274	+	0.588806i	$0.200402\pi$
$140$	−1.63399	+	3.57793i	−0.138097	+	0.302390i
$141$	−25.4022	−	7.45877i	−2.13925	−	0.628142i
$142$	−4.92507	−	5.68383i	−0.413303	−	0.476977i
$143$	2.38522	−	1.53289i	0.199462	−	0.128187i
$144$	−1.94658	+	2.24647i	−0.162215	+	0.187206i
$145$	−4.97274	+	34.5862i	−0.412964	+	2.87222i
$146$	10.3964	−	3.05265i	0.860409	−	0.252639i
$147$	2.05592	+	1.32126i	0.169569	+	0.108975i
$148$	0.774650	+	5.38781i	0.0636758	+	0.442875i
$149$	−2.81446	−	6.16280i	−0.230569	−	0.504876i	0.758618	−	0.651536i	$-0.225875\pi$
$149$	−2.81446	−	6.16280i	−0.230569	−	0.504876i	−0.989187	+	0.146660i	$0.953148\pi$
$150$	10.6309	+	23.2784i	0.868010	+	1.90068i
$151$	1.92505	+	13.3890i	0.156659	+	1.08958i	0.904736	+	0.425973i	$0.140068\pi$
$151$	1.92505	+	13.3890i	0.156659	+	1.08958i	−0.748077	+	0.663612i	$0.769023\pi$
$152$	5.81095	+	3.73447i	0.471330	+	0.302905i
$153$	3.43691	−	1.00917i	0.277858	−	0.0815864i
$154$	−0.243084	+	1.69069i	−0.0195883	+	0.136239i
$155$	9.96130	−	11.4960i	0.800111	−	0.923377i
$156$	−3.41272	+	2.19322i	−0.273236	+	0.175598i
$157$	9.66219	+	11.1508i	0.771127	+	0.889928i	0.996435	−	0.0843596i	$-0.0268845\pi$
$157$	9.66219	+	11.1508i	0.771127	+	0.889928i	−0.225309	+	0.974287i	$0.572339\pi$
$158$	3.30790	+	0.971287i	0.263162	+	0.0772714i
$159$	0.516928	−	1.13191i	0.0409950	−	0.0897666i
$160$	3.93338			0.310961
$161$	1.63690	+	4.50783i	0.129006	+	0.355267i
$162$	−9.08171			−0.713527
$163$	−5.01451	+	10.9802i	−0.392767	+	0.860039i	0.605186	+	0.796084i	$0.293099\pi$
$163$	−5.01451	+	10.9802i	−0.392767	+	0.860039i	−0.997953	+	0.0639550i	$0.979629\pi$
$164$	−10.4033	−	3.05468i	−0.812360	−	0.238531i
$165$	10.7523	+	12.4088i	0.837063	+	0.966022i
$166$	−2.06514	+	1.32719i	−0.160286	+	0.103010i
$167$	2.25737	−	2.60514i	0.174680	−	0.201592i	−0.661658	−	0.749806i	$-0.730147\pi$
$167$	2.25737	−	2.60514i	0.174680	−	0.201592i	0.836338	+	0.548214i	$0.184692\pi$
$168$	0.347799	−	2.41900i	0.0268333	−	0.186630i
$169$	9.82958	−	2.88623i	0.756122	−	0.222017i
$170$	−3.98746	−	2.56259i	−0.305824	−	0.196541i
$171$	−2.92209	−	20.3236i	−0.223458	−	1.55418i
$172$	−3.27948	−	7.18106i	−0.250058	−	0.547551i
$173$	−0.275780	−	0.603874i	−0.0209672	−	0.0459117i	0.898859	−	0.438239i	$-0.144397\pi$
$173$	−0.275780	−	0.603874i	−0.0209672	−	0.0459117i	−0.919826	+	0.392327i	$0.871670\pi$
$174$	−3.08964	−	21.4889i	−0.234225	−	1.62907i
$175$	−8.80920	−	5.66133i	−0.665913	−	0.427956i
$176$	1.63888	−	0.481220i	0.123535	−	0.0362733i
$177$	0.653020	−	4.54185i	0.0490840	−	0.341387i
$178$	−5.65546	+	6.52675i	−0.423895	+	0.489201i
$179$	16.0692	−	10.3271i	1.20107	−	0.771880i	0.221928	−	0.975063i	$-0.428765\pi$
$179$	16.0692	−	10.3271i	1.20107	−	0.771880i	0.979141	+	0.203183i	$0.0651286\pi$
$180$	−7.65665	−	8.83624i	−0.570693	−	0.658615i
$181$	−13.2545	−	3.89188i	−0.985201	−	0.289281i	−0.250831	−	0.968031i	$-0.580704\pi$
$181$	−13.2545	−	3.89188i	−0.985201	−	0.289281i	−0.734370	+	0.678750i	$0.762522\pi$
$182$	0.689569	−	1.50995i	0.0511142	−	0.111925i
$183$	−21.2442			−1.57041
$184$	3.42048	−	3.36160i	0.252161	−	0.247820i
$185$	−21.4102			−1.57411
$186$	−3.92610	+	8.59696i	−0.287876	+	0.630360i
$187$	−1.97493	−	0.579891i	−0.144421	−	0.0424058i
$188$	−7.09415	−	8.18709i	−0.517394	−	0.597105i
$189$	0.0565163	−	0.0363208i	0.00411095	−	0.00264195i
$190$	−17.7924	+	20.5336i	−1.29080	+	1.48966i
$191$	−2.12967	+	14.8122i	−0.154098	+	1.07177i	0.755160	+	0.655540i	$0.227559\pi$
$191$	−2.12967	+	14.8122i	−0.154098	+	1.07177i	−0.909258	+	0.416233i	$0.863350\pi$
$192$	−2.34488	+	0.688518i	−0.169227	+	0.0496895i
$193$	6.73490	+	4.32826i	0.484789	+	0.311555i	0.760107	−	0.649798i	$-0.225147\pi$
$193$	6.73490	+	4.32826i	0.484789	+	0.311555i	−0.275318	+	0.961353i	$0.588783\pi$
$194$	−0.0846778	−	0.588947i	−0.00607951	−	0.0422839i
$195$	−6.62861	−	14.5146i	−0.474685	−	1.03941i
$196$	0.415415	+	0.909632i	0.0296725	+	0.0649737i
$197$	−2.07367	−	14.4227i	−0.147743	−	1.02758i	−0.919903	−	0.392147i	$-0.871733\pi$
$197$	−2.07367	−	14.4227i	−0.147743	−	1.02758i	0.772160	−	0.635429i	$-0.219177\pi$
$198$	−4.27126	−	2.74498i	−0.303546	−	0.195077i
$199$	1.33729	−	0.392664i	0.0947981	−	0.0278352i	−0.233990	−	0.972239i	$-0.575178\pi$
$199$	1.33729	−	0.392664i	0.0947981	−	0.0278352i	0.328788	+	0.944404i	$0.393360\pi$
$200$	−1.49025	+	10.3649i	−0.105377	+	0.732911i
$201$	3.15053	−	3.63591i	0.222221	−	0.256457i
$202$	−9.26849	+	5.95650i	−0.652129	+	0.419098i
$203$	5.81739	+	6.71362i	0.408301	+	0.471204i
$204$	2.82568	+	0.829695i	0.197837	+	0.0580903i
$205$	17.7165	−	38.7937i	1.23737	−	2.70947i
$206$	−5.74049			−0.399959
$207$	−14.2100	−	1.14039i	−0.987661	−	0.0792628i
$208$	−1.65995			−0.115097
$209$	−4.90127	+	10.7323i	−0.339028	+	0.742367i
$210$	9.22331	+	2.70821i	0.636469	+	0.186884i
$211$	−4.99541	−	5.76502i	−0.343899	−	0.396880i	0.557282	−	0.830323i	$-0.311844\pi$
$211$	−4.99541	−	5.76502i	−0.343899	−	0.396880i	−0.901181	+	0.433443i	$0.857299\pi$
$212$	0.428347	−	0.275282i	0.0294190	−	0.0189065i
$213$	−12.0362	+	13.8906i	−0.824710	+	0.951766i
$214$	−0.821578	+	5.71420i	−0.0561619	+	0.390615i
$215$	29.7942	−	8.74835i	2.03194	−	0.596633i
$216$	−0.0565163	−	0.0363208i	−0.00384545	−	0.00247132i
$217$	−0.550365	−	3.82787i	−0.0373612	−	0.259853i
$218$	−4.93171	−	10.7989i	−0.334018	−	0.731397i
$219$	−11.0002	−	24.0871i	−0.743324	−	1.62765i
$220$	0.956143	+	6.65012i	0.0644631	+	0.448351i
$221$	1.68277	+	1.08145i	0.113196	+	0.0727463i
$222$	12.7637	−	3.74775i	0.856641	−	0.251533i
$223$	−2.64677	+	18.4087i	−0.177241	+	1.23274i	0.685871	+	0.727723i	$0.259421\pi$
$223$	−2.64677	+	18.4087i	−0.177241	+	1.23274i	−0.863112	+	0.505013i	$0.831488\pi$
$224$	0.654861	−	0.755750i	0.0437547	−	0.0504956i
$225$	26.1854	−	16.8284i	1.74570	−	1.12189i
$226$	10.6876	+	12.3341i	0.710929	+	0.820455i
$227$	−23.5259	−	6.90783i	−1.56147	−	0.458489i	−0.616965	−	0.786990i	$-0.711638\pi$
$227$	−23.5259	−	6.90783i	−1.56147	−	0.458489i	−0.944503	+	0.328502i	$0.893456\pi$
$228$	7.01263	−	15.3555i	0.464423	−	1.01694i
$229$	−18.5146			−1.22348			−0.611739	−	0.791060i	$-0.709530\pi$
$229$	−18.5146			−1.22348			−0.611739	+	0.791060i	$0.709530\pi$
$230$	11.1732	+	15.1989i	0.736736	+	1.00218i
$231$	4.17431			0.274649
$232$	3.69030	−	8.08062i	0.242280	−	0.530519i
$233$	7.55570	+	2.21855i	0.494990	+	0.145342i	0.519694	−	0.854353i	$-0.326046\pi$
$233$	7.55570	+	2.21855i	0.494990	+	0.145342i	−0.0247035	+	0.999695i	$0.507864\pi$
$234$	3.23123	+	3.72904i	0.211232	+	0.243775i
$235$	35.8464	−	23.0371i	2.33836	−	1.50277i
$236$	1.22955	−	1.41898i	0.0800370	−	0.0923676i
$237$	1.19906	−	8.33961i	0.0778870	−	0.541716i
$238$	−1.15623	+	0.339500i	−0.0749474	+	0.0220065i
$239$	−4.93246	−	3.16990i	−0.319055	−	0.205044i	0.371304	−	0.928511i	$-0.378911\pi$
$239$	−4.93246	−	3.16990i	−0.319055	−	0.205044i	−0.690358	+	0.723467i	$0.742547\pi$
$240$	−1.36803	−	9.51485i	−0.0883058	−	0.614181i
$241$	−0.459695	−	1.00659i	−0.0296115	−	0.0648402i	0.894248	−	0.447571i	$-0.147711\pi$
$241$	−0.459695	−	1.00659i	−0.0296115	−	0.0648402i	−0.923860	+	0.382731i	$0.874984\pi$
$242$	−3.35759	−	7.35209i	−0.215834	−	0.472610i
$243$	3.12993	+	21.7691i	0.200785	+	1.39649i
$244$	−7.31288	−	4.69970i	−0.468159	−	0.300868i
$245$	−3.77405	+	1.10816i	−0.241116	+	0.0707979i
$246$	−3.77101	+	26.2279i	−0.240431	+	1.67223i
$247$	7.50869	−	8.66549i	0.477767	−	0.551372i
$248$	−3.25333	+	2.09079i	−0.206586	+	0.132765i
$249$	3.92872	+	4.53398i	0.248972	+	0.287329i
$250$	−20.6498	−	6.06333i	−1.30601	−	0.383478i
$251$	−4.06410	+	8.89915i	−0.256524	+	0.561709i	−0.993450	−	0.114264i	$-0.963549\pi$
$251$	−4.06410	+	8.89915i	−0.256524	+	0.561709i	0.736926	+	0.675973i	$0.236276\pi$
$252$	−2.97251			−0.187251
$253$	6.51487	+	4.96580i	0.409586	+	0.312197i
$254$	20.9208			1.31269
$255$	−4.81205	+	10.5369i	−0.301342	+	0.659847i
$256$	−0.959493	−	0.281733i	−0.0599683	−	0.0176083i
$257$	14.0308	+	16.1924i	0.875219	+	1.01006i	0.999841	+	0.0178522i	$0.00568285\pi$
$257$	14.0308	+	16.1924i	0.875219	+	1.01006i	−0.124622	+	0.992204i	$0.539772\pi$
$258$	−16.2304	+	10.4306i	−1.01046	+	0.649382i
$259$	−3.56455	+	4.11371i	−0.221490	+	0.255613i
$260$	0.929206	−	6.46277i	0.0576269	−	0.400804i
$261$	−25.3364	+	7.43943i	−1.56828	+	0.460489i
$262$	−1.62780	−	1.04612i	−0.100566	−	0.0646298i
$263$	−2.54516	−	17.7019i	−0.156941	−	1.09155i	−0.904229	−	0.427048i	$-0.859553\pi$
$263$	−2.54516	−	17.7019i	−0.156941	−	1.09155i	0.747288	−	0.664500i	$-0.231356\pi$
$264$	−1.73407	−	3.79709i	−0.106725	−	0.233694i
$265$	0.831989	+	1.82180i	0.0511087	+	0.111912i
$266$	0.983038	+	6.83718i	0.0602739	+	0.419214i
$267$	17.7552	+	11.4105i	1.08660	+	0.698314i
$268$	1.88885	−	0.554617i	0.115380	−	0.0338787i
$269$	−1.93818	+	13.4804i	−0.118173	+	0.821912i	0.841392	+	0.540425i	$0.181737\pi$
$269$	−1.93818	+	13.4804i	−0.118173	+	0.821912i	−0.959565	+	0.281487i	$0.909172\pi$
$270$	0.173046	−	0.199706i	0.0105313	−	0.0121537i
$271$	−8.91298	+	5.72803i	−0.541425	+	0.347953i	−0.782596	−	0.622530i	$-0.786105\pi$
$271$	−8.91298	+	5.72803i	−0.541425	+	0.347953i	0.241171	+	0.970483i	$0.422469\pi$
$272$	0.789136	+	0.910712i	0.0478484	+	0.0552200i
$273$	−3.89238	−	1.14291i	−0.235578	−	0.0691719i
$274$	3.45032	−	7.55514i	0.208441	−	0.456423i
$275$	−17.8861			−1.07857
$276$	−9.32133	−	7.10496i	−0.561078	−	0.427669i
$277$	5.83581			0.350640			0.175320	−	0.984512i	$-0.443904\pi$
$277$	5.83581			0.350640			0.175320	+	0.984512i	$0.443904\pi$
$278$	7.91732	−	17.3365i	0.474850	−	1.03978i
$279$	11.0298	+	3.23863i	0.660334	+	0.193892i
$280$	2.57582	+	2.97265i	0.153935	+	0.177650i
$281$	−12.1260	+	7.79291i	−0.723377	+	0.464886i	−0.849810	−	0.527089i	$-0.823283\pi$
$281$	−12.1260	+	7.79291i	−0.723377	+	0.464886i	0.126433	+	0.991975i	$0.459647\pi$
$282$	−17.3372	+	20.0082i	−1.03242	+	1.19147i
$283$	3.03154	−	21.0848i	0.180206	−	1.25336i	−0.676068	−	0.736839i	$-0.736317\pi$
$283$	3.03154	−	21.0848i	0.180206	−	1.25336i	0.856274	−	0.516522i	$-0.172774\pi$
$284$	−7.21615	+	2.11885i	−0.428199	+	0.125731i
$285$	55.8588	+	35.8983i	3.30879	+	2.12643i
$286$	−0.403508	−	2.80646i	−0.0238599	−	0.165949i
$287$	−4.50413	−	9.86267i	−0.265871	−	0.582175i
$288$	1.23483	+	2.70389i	0.0727628	+	0.159328i
$289$	2.21269	+	15.3896i	0.130158	+	0.905271i
$290$	29.3949	+	18.8910i	1.72613	+	1.10932i
$291$	−1.39521	+	0.409671i	−0.0817886	+	0.0240153i
$292$	1.54202	−	10.7250i	0.0902399	−	0.627632i
$293$	−20.0460	+	23.1343i	−1.17110	+	1.35152i	−0.247166	+	0.968973i	$0.579499\pi$
$293$	−20.0460	+	23.1343i	−1.17110	+	1.35152i	−0.923935	+	0.382549i	$0.875046\pi$
$294$	2.05592	−	1.32126i	0.119903	−	0.0770573i
$295$	4.83630	+	5.58139i	0.281580	+	0.324961i
$296$	5.22272	+	1.53353i	0.303565	+	0.0891346i
$297$	0.0476689	−	0.104380i	0.00276603	−	0.00605676i
$298$	−6.77505			−0.392468
$299$	−4.71525	−	6.41416i	−0.272690	−	0.370941i
$300$	25.5910			1.47750
$301$	3.27948	−	7.18106i	0.189026	−	0.413909i
$302$	12.9788	+	3.81092i	0.746846	+	0.219294i
$303$	17.6323	+	20.3488i	1.01295	+	1.16901i
$304$	5.81095	−	3.73447i	0.333281	−	0.214186i
$305$	22.3912	−	25.8408i	1.28211	−	1.47964i
$306$	0.509773	−	3.54555i	0.0291418	−	0.202685i
$307$	25.4194	−	7.46381i	1.45076	−	0.425982i	0.540968	−	0.841043i	$-0.318058\pi$
$307$	25.4194	−	7.46381i	1.45076	−	0.425982i	0.909794	+	0.415061i	$0.136240\pi$
$308$	1.43692	+	0.923454i	0.0818762	+	0.0526186i
$309$	1.99654	+	13.8862i	0.113579	+	0.789960i
$310$	−6.31901	−	13.8367i	−0.358896	−	0.785872i
$311$	−9.73908	−	21.3256i	−0.552253	−	1.20926i	−0.955722	−	0.294271i	$-0.904923\pi$
$311$	−9.73908	−	21.3256i	−0.552253	−	1.20926i	0.403469	−	0.914993i	$-0.367804\pi$
$312$	0.577330	+	4.01542i	0.0326849	+	0.227328i
$313$	−21.5378	−	13.8415i	−1.21739	−	0.782369i	−0.235510	−	0.971872i	$-0.575676\pi$
$313$	−21.5378	−	13.8415i	−1.21739	−	0.782369i	−0.981880	+	0.189503i	$0.939312\pi$
$314$	14.1569	−	4.15684i	0.798921	−	0.234584i
$315$	1.66395	−	11.5730i	0.0937529	−	0.652066i
$316$	2.25766	−	2.60548i	0.127004	−	0.146570i
$317$	−20.9352	+	13.4542i	−1.17584	+	0.755664i	−0.974616	−	0.223882i	$-0.928127\pi$
$317$	−20.9352	+	13.4542i	−1.17584	+	0.755664i	−0.201220	+	0.979546i	$0.564490\pi$
$318$	−0.814885	−	0.940428i	−0.0456965	−	0.0527366i
$319$	14.5589	+	4.27486i	0.815139	+	0.239346i
$320$	1.63399	−	3.57793i	0.0913427	−	0.200013i
$321$	14.1084			0.787453
$322$	4.78046	+	0.383646i	0.266405	+	0.0213798i
$323$	−8.32383			−0.463150
$324$	−3.77268	+	8.26102i	−0.209593	+	0.458945i
$325$	16.6781	+	4.89713i	0.925135	+	0.271644i
$326$	7.90488	+	9.12272i	0.437811	+	0.505261i
$327$	−24.4074	+	15.6857i	−1.34973	+	0.867419i
$328$	−7.10032	+	8.19421i	−0.392050	+	0.452449i
$329$	1.54171	−	10.7228i	0.0849971	−	0.591167i
$330$	15.7541	−	4.62581i	0.867233	−	0.254643i
$331$	−4.57721	−	2.94159i	−0.251586	−	0.161685i	0.408769	−	0.912638i	$-0.365958\pi$
$331$	−4.57721	−	2.94159i	−0.251586	−	0.161685i	−0.660356	+	0.750953i	$0.729594\pi$
$332$	0.349360	+	2.42985i	0.0191736	+	0.133356i
$333$	−6.72142	−	14.7178i	−0.368331	−	0.806533i
$334$	−1.43198	−	3.13559i	−0.0783542	−	0.171572i
$335$	1.10198	+	7.66443i	0.0602075	+	0.418752i
$336$	−2.05592	−	1.32126i	−0.112159	−	0.0720805i
$337$	−12.4140	+	3.64507i	−0.676232	+	0.198560i	−0.601776	−	0.798665i	$-0.705540\pi$
$337$	−12.4140	+	3.64507i	−0.676232	+	0.198560i	−0.0744556	+	0.997224i	$0.523722\pi$
$338$	1.45795	−	10.1403i	0.0793022	−	0.551559i
$339$	26.1191	−	30.1431i	1.41860	−	1.63715i
$340$	−3.98746	+	2.56259i	−0.216250	+	0.138976i
$341$	−4.32569	−	4.99212i	−0.234249	−	0.270338i
$342$	−19.7009	−	5.78470i	−1.06530	−	0.312800i
$343$	−0.415415	+	0.909632i	−0.0224303	+	0.0491155i
$344$	−7.89447			−0.425641
$345$	32.8800	−	32.3140i	1.77020	−	1.73973i
$346$	−0.663866			−0.0356897
$347$	−7.81487	+	17.1122i	−0.419524	+	0.918630i	0.575387	+	0.817881i	$0.304851\pi$
$347$	−7.81487	+	17.1122i	−0.419524	+	0.918630i	−0.994912	+	0.100749i	$0.967876\pi$
$348$	−20.8305	−	6.11638i	−1.11663	−	0.327873i
$349$	7.26652	+	8.38601i	0.388968	+	0.448893i	0.916136	−	0.400868i	$-0.131292\pi$
$349$	7.26652	+	8.38601i	0.388968	+	0.448893i	−0.527168	+	0.849761i	$0.676746\pi$
$350$	−8.80920	+	5.66133i	−0.470871	+	0.302611i
$351$	−0.0730283	+	0.0842791i	−0.00389796	+	0.00449849i
$352$	0.243084	−	1.69069i	0.0129564	−	0.0901139i
$353$	−6.62131	+	1.94419i	−0.352417	+	0.103479i	−0.453149	−	0.891435i	$-0.649700\pi$
$353$	−6.62131	+	1.94419i	−0.352417	+	0.103479i	0.100732	+	0.994914i	$0.467881\pi$
$354$	−3.86014	−	2.48076i	−0.205164	−	0.131851i
$355$	−4.20998	−	29.2811i	−0.223443	−	1.55408i
$356$	3.58758	+	7.85570i	0.190141	+	0.416351i
$357$	1.22339	+	2.67884i	0.0647485	+	0.141779i
$358$	−2.71843	−	18.9071i	−0.143673	−	0.999270i
$359$	21.8455	+	14.0392i	1.15296	+	0.740962i	0.970226	−	0.242200i	$-0.0778691\pi$
$359$	21.8455	+	14.0392i	1.15296	+	0.740962i	0.182733	+	0.983162i	$0.441505\pi$
$360$	−11.2184	+	3.29402i	−0.591263	+	0.173610i
$361$	−4.08634	+	28.4211i	−0.215070	+	1.49585i
$362$	−9.04631	+	10.4400i	−0.475463	+	0.548714i
$363$	−16.6169	+	10.6790i	−0.872162	+	0.560505i
$364$	−1.08704	−	1.25451i	−0.0569762	−	0.0657541i
$365$	40.8929	+	12.0072i	2.14043	+	0.628488i
$366$	−8.82515	+	19.3244i	−0.461298	+	1.01010i
$367$	−11.1062			−0.579738			−0.289869	−	0.957066i	$-0.593612\pi$
$367$	−11.1062			−0.579738			−0.289869	+	0.957066i	$0.593612\pi$
$368$	−1.63690	−	4.50783i	−0.0853292	−	0.234987i
$369$	32.2294			1.67780
$370$	−8.89414	+	19.4754i	−0.462384	+	1.01248i
$371$	0.488552	+	0.143452i	0.0253644	+	0.00744765i
$372$	6.18911	+	7.14261i	0.320890	+	0.370327i
$373$	−16.4336	+	10.5612i	−0.850897	+	0.546838i	−0.891854	−	0.452322i	$-0.850596\pi$
$373$	−16.4336	+	10.5612i	−0.850897	+	0.546838i	0.0409573	+	0.999161i	$0.486959\pi$
$374$	−1.34790	+	1.55556i	−0.0696983	+	0.0804362i
$375$	−7.48519	+	52.0606i	−0.386533	+	2.68840i
$376$	−10.3943	+	3.05203i	−0.536043	+	0.157396i
$377$	−12.4051	−	7.97230i	−0.638897	−	0.410594i
$378$	−0.00956086	−	0.0664972i	−0.000491757	−	0.00342025i
$379$	9.38513	+	20.5506i	0.482082	+	1.05561i	0.981886	+	0.189473i	$0.0606780\pi$
$379$	9.38513	+	20.5506i	0.482082	+	1.05561i	−0.499804	+	0.866138i	$0.666595\pi$
$380$	11.2867	+	24.7145i	0.578998	+	1.26783i
$381$	−7.27625	−	50.6074i	−0.372773	−	2.59270i
$382$	12.5890	+	8.09043i	0.644107	+	0.413942i
$383$	25.6957	−	7.54494i	1.31299	−	0.385528i	0.451031	−	0.892508i	$-0.351056\pi$
$383$	25.6957	−	7.54494i	1.31299	−	0.385528i	0.861958	+	0.506980i	$0.169238\pi$
$384$	−0.347799	+	2.41900i	−0.0177486	+	0.123444i
$385$	−4.39968	+	5.07751i	−0.224229	+	0.258774i
$386$	6.73490	−	4.32826i	0.342798	−	0.220303i
$387$	15.3672	+	17.7347i	0.781159	+	0.901506i
$388$	−0.570901	−	0.167632i	−0.0289831	−	0.00851021i
$389$	−2.57192	+	5.63171i	−0.130401	+	0.285539i	−0.963559	−	0.267497i	$-0.913804\pi$
$389$	−2.57192	+	5.63171i	−0.130401	+	0.285539i	0.833157	+	0.553036i	$0.186531\pi$
$390$	−15.9566			−0.807994
$391$	−1.27743	+	5.63624i	−0.0646026	+	0.285037i
$392$	1.00000			0.0505076
$393$	−1.96442	+	4.30149i	−0.0990920	+	0.216981i
$394$	−13.9808	−	4.10513i	−0.704342	−	0.206813i
$395$	8.88026	+	10.2484i	0.446815	+	0.515651i
$396$	−4.27126	+	2.74498i	−0.214639	+	0.137940i
$397$	6.91672	−	7.98232i	0.347140	−	0.400621i	−0.555150	−	0.831750i	$-0.687339\pi$
$397$	6.91672	−	7.98232i	0.347140	−	0.400621i	0.902290	+	0.431129i	$0.141885\pi$
$398$	0.198351	−	1.37956i	0.00994244	−	0.0691512i
$399$	16.1972	−	4.75593i	0.810875	−	0.238094i
$400$	8.80920	+	5.66133i	0.440460	+	0.283066i
$401$	−2.71132	−	18.8576i	−0.135397	−	0.941705i	−0.938356	−	0.345671i	$-0.887651\pi$
$401$	−2.71132	−	18.8576i	−0.135397	−	0.941705i	0.802959	−	0.596034i	$-0.203258\pi$
$402$	−1.99856	−	4.37624i	−0.0996791	−	0.218267i
$403$	2.66672	+	5.83931i	0.132839	+	0.290877i
$404$	1.56795	+	10.9053i	0.0780084	+	0.542561i
$405$	−30.0511	−	19.3127i	−1.49325	−	0.959656i
$406$	8.52356	−	2.50274i	0.423017	−	0.124209i
$407$	−1.32316	+	9.20276i	−0.0655865	+	0.456164i
$408$	1.92855	−	2.22566i	0.0954774	−	0.110187i
$409$	8.98815	−	5.77633i	0.444435	−	0.285621i	−0.299220	−	0.954184i	$-0.596727\pi$
$409$	8.98815	−	5.77633i	0.444435	−	0.285621i	0.743656	+	0.668563i	$0.233090\pi$
$410$	−27.9283	−	32.2310i	−1.37928	−	1.59177i
$411$	−19.4759	−	5.71864i	−0.960675	−	0.282080i
$412$	−2.38468	+	5.22173i	−0.117485	+	0.257256i
$413$	1.87758			0.0923895
$414$	−6.94037	+	12.4521i	−0.341101	+	0.611988i
$415$	−9.65583			−0.473986
$416$	−0.689569	+	1.50995i	−0.0338089	+	0.0740311i
$417$	−44.6906	−	13.1224i	−2.18851	−	0.642604i
$418$	7.72636	+	8.91670i	0.377909	+	0.436130i
$419$	−28.1253	+	18.0750i	−1.37401	+	0.883022i	−0.999031	−	0.0440113i	$-0.985986\pi$
$419$	−28.1253	+	18.0750i	−1.37401	+	0.883022i	−0.374978	+	0.927034i	$0.622350\pi$
$420$	6.29497	−	7.26479i	0.307163	−	0.354485i
$421$	2.86485	−	19.9255i	0.139624	−	0.971109i	−0.792733	−	0.609570i	$-0.791342\pi$
$421$	2.86485	−	19.9255i	0.139624	−	0.971109i	0.932357	−	0.361539i	$-0.117749\pi$
$422$	−7.31921	+	2.14911i	−0.356294	+	0.104617i
$423$	27.0896	+	17.4094i	1.31714	+	0.846474i
$424$	−0.0724635	−	0.503995i	−0.00351914	−	0.0244761i
$425$	−5.24197	−	11.4783i	−0.254273	−	0.556780i
$426$	7.63527	+	16.7189i	0.369930	+	0.810033i
$427$	−1.23712	−	8.60435i	−0.0598684	−	0.416394i
$428$	4.85652	+	3.12110i	0.234749	+	0.150864i
$429$	−6.64847	+	1.95217i	−0.320991	+	0.0942515i
$430$	4.41916	−	30.7359i	0.213111	−	1.48222i
$431$	−8.89181	+	10.2617i	−0.428303	+	0.494288i	−0.928349	−	0.371711i	$-0.878771\pi$
$431$	−8.89181	+	10.2617i	−0.428303	+	0.494288i	0.500045	+	0.865999i	$0.333317\pi$
$432$	−0.0565163	+	0.0363208i	−0.00271914	+	0.00174749i
$433$	−3.55449	−	4.10210i	−0.170818	−	0.197134i	0.663885	−	0.747834i	$-0.268906\pi$
$433$	−3.55449	−	4.10210i	−0.170818	−	0.197134i	−0.834703	+	0.550700i	$0.814361\pi$
$434$	−3.71059	−	1.08953i	−0.178114	−	0.0522989i
$435$	35.4737	−	77.6765i	1.70083	−	3.72430i
$436$	−11.8718			−0.568555
$437$	30.9368	+	11.8458i	1.47991	+	0.566660i
$438$	−26.4800			−1.26526
$439$	−2.00846	+	4.39792i	−0.0958586	+	0.209901i	−0.951487	−	0.307690i	$-0.900444\pi$
$439$	−2.00846	+	4.39792i	−0.0958586	+	0.209901i	0.855628	+	0.517591i	$0.173171\pi$
$440$	6.44636	+	1.89282i	0.307318	+	0.0902367i
$441$	−1.94658	−	2.24647i	−0.0926943	−	0.106975i
$442$	1.68277	−	1.08145i	0.0800413	−	0.0514394i
$443$	−7.67843	+	8.86138i	−0.364813	+	0.421017i	−0.908247	−	0.418435i	$-0.862579\pi$
$443$	−7.67843	+	8.86138i	−0.364813	+	0.421017i	0.543433	+	0.839452i	$0.317124\pi$
$444$	1.89315	−	13.1671i	0.0898447	−	0.624884i
$445$	−32.5932	+	9.57024i	−1.54507	+	0.453673i
$446$	15.6456	+	10.0548i	0.740841	+	0.476110i
$447$	2.35636	+	16.3888i	0.111452	+	0.775165i
$448$	−0.415415	−	0.909632i	−0.0196265	−	0.0429761i
$449$	0.598261	+	1.31001i	0.0282337	+	0.0618232i	0.923223	−	0.384264i	$-0.125545\pi$
$449$	0.598261	+	1.31001i	0.0282337	+	0.0618232i	−0.894990	+	0.446087i	$0.852817\pi$
$450$	−4.42979	−	30.8099i	−0.208822	−	1.45239i
$451$	−15.5798	−	10.0125i	−0.733624	−	0.471472i
$452$	15.6593	−	4.59799i	0.736553	−	0.216271i
$453$	4.70458	−	32.7211i	0.221041	−	1.53737i
$454$	−16.0566	+	18.5303i	−0.753573	+	0.869670i
$455$	5.49274	−	3.52997i	0.257503	−	0.165487i
$456$	−11.0547	−	12.7578i	−0.517684	−	0.597440i
$457$	18.9021	+	5.55015i	0.884202	+	0.259625i	0.692145	−	0.721759i	$-0.256666\pi$
$457$	18.9021	+	5.55015i	0.884202	+	0.259625i	0.192057	+	0.981384i	$0.438484\pi$
$458$	−7.69123	+	16.8414i	−0.359388	+	0.786949i
$459$	0.0809561			0.00377871
$460$	18.4669	−	3.84963i	0.861022	−	0.179490i
$461$	9.79082			0.456004			0.228002	−	0.973661i	$-0.426781\pi$
$461$	9.79082			0.456004			0.228002	+	0.973661i	$0.426781\pi$
$462$	1.73407	−	3.79709i	0.0806763	−	0.176656i
$463$	−30.0954	−	8.83681i	−1.39865	−	0.410681i	−0.506431	−	0.862280i	$-0.669036\pi$
$463$	−30.0954	−	8.83681i	−1.39865	−	0.410681i	−0.892221	+	0.451599i	$0.850854\pi$
$464$	−5.81739	−	6.71362i	−0.270065	−	0.311672i
$465$	−31.2732	+	20.0981i	−1.45026	+	0.932026i
$466$	5.15682	−	5.95129i	0.238885	−	0.275688i
$467$	5.06204	−	35.2073i	0.234243	−	1.62920i	−0.445172	−	0.895445i	$-0.646857\pi$
$467$	5.06204	−	35.2073i	0.234243	−	1.62920i	0.679415	−	0.733754i	$-0.262233\pi$
$468$	4.73435	−	1.39013i	0.218846	−	0.0642588i
$469$	1.65609	+	1.06430i	0.0764710	+	0.0491450i
$470$	−6.06413	−	42.1769i	−0.279717	−	1.94548i
$471$	−14.9792	−	32.7998i	−0.690203	−	1.51133i
$472$	−0.779974	−	1.70790i	−0.0359012	−	0.0786127i
$473$	−1.91902	−	13.3471i	−0.0882366	−	0.613699i
$474$	−7.08787	−	4.55510i	−0.325557	−	0.209223i
$475$	−69.4019	+	20.3782i	−3.18438	+	0.935018i
$476$	−0.171496	+	1.19278i	−0.00786049	+	0.0546709i
$477$	−0.991155	+	1.14385i	−0.0453819	+	0.0523735i
$478$	−4.93246	+	3.16990i	−0.225606	+	0.144988i
$479$	17.0755	+	19.7062i	0.780200	+	0.900399i	0.997124	−	0.0757895i	$-0.0241477\pi$
$479$	17.0755	+	19.7062i	0.780200	+	0.900399i	−0.216924	+	0.976189i	$0.569602\pi$
$480$	−9.22331	−	2.70821i	−0.420984	−	0.123612i
$481$	3.75347	−	8.21895i	0.171143	−	0.374752i
$482$	−1.10659			−0.0504039
$483$	−0.734601	−	11.6974i	−0.0334255	−	0.532248i
$484$	−8.08249			−0.367386
$485$	0.972227	−	2.12888i	0.0441466	−	0.0966675i
$486$	21.1021	+	6.19614i	0.957212	+	0.281063i
$487$	14.2136	+	16.4034i	0.644082	+	0.743310i	0.980091	−	0.198549i	$-0.0636228\pi$
$487$	14.2136	+	16.4034i	0.644082	+	0.743310i	−0.336009	+	0.941859i	$0.609077\pi$
$488$	−7.31288	+	4.69970i	−0.331038	+	0.212745i
$489$	19.3185	−	22.2948i	0.873613	−	1.00820i
$490$	−0.559779	+	3.89335i	−0.0252882	+	0.175884i
$491$	−12.4282	+	3.64924i	−0.560876	+	0.164688i	−0.549868	−	0.835251i	$-0.685322\pi$
$491$	−12.4282	+	3.64924i	−0.560876	+	0.164688i	−0.0110077	+	0.999939i	$0.503504\pi$
$492$	22.2912	+	14.3257i	1.00497	+	0.645853i
$493$	1.52346	+	10.5959i	0.0686134	+	0.477217i
$494$	−4.76319	−	10.4299i	−0.214306	−	0.469265i
$495$	−8.29618	−	18.1661i	−0.372886	−	0.816506i
$496$	0.550365	+	3.82787i	0.0247121	+	0.171877i
$497$	−6.32689	−	4.06605i	−0.283800	−	0.182387i
$498$	5.75630	−	1.69020i	0.257946	−	0.0757398i
$499$	5.03274	−	35.0035i	0.225296	−	1.56697i	−0.492246	−	0.870456i	$-0.663824\pi$
$499$	5.03274	−	35.0035i	0.225296	−	1.56697i	0.717542	−	0.696515i	$-0.245267\pi$
$500$	−14.0936	+	16.2649i	−0.630286	+	0.727389i
$501$	−7.08694	+	4.55450i	−0.316621	+	0.203480i
$502$	6.40666	+	7.39368i	0.285943	+	0.329996i
$503$	16.1655	+	4.74661i	0.720782	+	0.211641i	0.621495	−	0.783418i	$-0.286526\pi$
$503$	16.1655	+	4.74661i	0.720782	+	0.211641i	0.0992872	+	0.995059i	$0.468344\pi$
$504$	−1.23483	+	2.70389i	−0.0550035	+	0.120441i
$505$	−43.3360			−1.92843
$506$	7.22343	−	3.86326i	0.321121	−	0.171743i
$507$	−25.0364			−1.11191
$508$	8.69083	−	19.0303i	0.385593	−	0.844331i
$509$	−29.0532	−	8.53080i	−1.28776	−	0.378121i	−0.435004	−	0.900428i	$-0.643253\pi$
$509$	−29.0532	−	8.53080i	−1.28776	−	0.378121i	−0.852757	+	0.522307i	$0.825071\pi$
$510$	7.58572	+	8.75439i	0.335901	+	0.387651i
$511$	9.11521	−	5.85799i	0.403233	−	0.259142i
$512$	−0.654861	+	0.755750i	−0.0289410	+	0.0333997i
$513$	0.0660415	−	0.459329i	0.00291580	−	0.0202799i
$514$	20.5578	−	6.03631i	0.906765	−	0.266250i
$515$	−18.9951	−	12.2074i	−0.837025	−	0.537923i
$516$	2.74569	+	19.0967i	0.120872	+	0.840685i
$517$	−7.68670	−	16.8315i	−0.338061	−	0.740250i
$518$	2.26119	+	4.95132i	0.0993511	+	0.217548i
$519$	0.230892	+	1.60589i	0.0101350	+	0.0704908i
$520$	−5.49274	−	3.52997i	−0.240872	−	0.154799i
$521$	4.07496	−	1.19652i	0.178527	−	0.0524203i	−0.191247	−	0.981542i	$-0.561253\pi$
$521$	4.07496	−	1.19652i	0.178527	−	0.0524203i	0.369774	+	0.929122i	$0.379435\pi$
$522$	−3.75796	+	26.1372i	−0.164482	+	1.14400i
$523$	13.9416	−	16.0894i	0.609622	−	0.703541i	−0.364080	−	0.931368i	$-0.618616\pi$
$523$	13.9416	−	16.0894i	0.609622	−	0.703541i	0.973702	+	0.227827i	$0.0731619\pi$
$524$	−1.62780	+	1.04612i	−0.0711108	+	0.0457001i
$525$	16.7586	+	19.3404i	0.731404	+	0.844085i
$526$	−17.1596	−	5.03850i	−0.748192	−	0.219689i
$527$	1.93591	−	4.23906i	0.0843297	−	0.184656i
$528$	−4.17431			−0.181664
$529$	12.7688	−	19.1300i	0.555165	−	0.831740i
$530$	2.00279			0.0869957
$531$	−2.31848	+	5.07676i	−0.100613	+	0.220313i
$532$	6.62768	+	1.94606i	0.287347	+	0.0843726i
$533$	11.7862	+	13.6020i	0.510516	+	0.589167i
$534$	17.7552	−	11.4105i	0.768341	−	0.493783i
$535$	−14.8701	+	17.1610i	−0.642890	+	0.741935i
$536$	0.280160	−	1.94856i	0.0121011	−	0.0841649i
$537$	−44.7907	+	13.1517i	−1.93286	+	0.567539i
$538$	11.4570	+	7.36298i	0.493947	+	0.317441i
$539$	0.243084	+	1.69069i	0.0104704	+	0.0728230i
$540$	−0.109773	−	0.240369i	−0.00472387	−	0.0103438i
$541$	10.3558	+	22.6760i	0.445230	+	0.974917i	0.990609	+	0.136727i	$0.0436585\pi$
$541$	10.3558	+	22.6760i	0.445230	+	0.974917i	−0.545379	+	0.838190i	$0.683614\pi$
$542$	1.50781	+	10.4870i	0.0647659	+	0.450457i
$543$	28.4006	+	18.2520i	1.21879	+	0.783267i
$544$	1.15623	−	0.339500i	0.0495730	−	0.0145560i
$545$	6.64557	−	46.2210i	0.284665	−	1.97989i
$546$	−2.65658	+	3.06586i	−0.113691	+	0.131207i
$547$	21.7694	−	13.9904i	0.930794	−	0.598185i	0.0150236	−	0.999887i	$-0.495218\pi$
$547$	21.7694	−	13.9904i	0.930794	−	0.598185i	0.915770	+	0.401702i	$0.131581\pi$
$548$	−5.43909	−	6.27704i	−0.232346	−	0.268142i
$549$	24.7929	+	7.27984i	1.05813	+	0.310696i
$550$	−7.43016	+	16.2698i	−0.316823	+	0.693745i
$551$	61.3620			2.61411
$552$	−10.3351	+	5.52747i	−0.439892	+	0.235265i
$553$	3.44755			0.146605
$554$	2.42428	−	5.30844i	0.102998	−	0.225534i
$555$	50.2044	+	14.7413i	2.13106	+	0.625735i
$556$	−12.4809	−	14.4037i	−0.529307	−	0.610853i
$557$	−21.2628	+	13.6648i	−0.900933	+	0.578995i	−0.907067	−	0.420987i	$-0.861684\pi$
$557$	−21.2628	+	13.6648i	−0.900933	+	0.578995i	0.00613377	+	0.999981i	$0.498048\pi$
$558$	7.52788	−	8.68764i	0.318681	−	0.367777i
$559$	−1.86496	+	12.9710i	−0.0788792	+	0.548617i
$560$	3.77405	−	1.10816i	0.159483	−	0.0468284i
$561$	4.23170	+	2.71955i	0.178662	+	0.114819i
$562$	2.05136	+	14.2675i	0.0865312	+	0.601838i
$563$	7.59027	+	16.6204i	0.319892	+	0.700465i	0.999450	−	0.0331563i	$-0.0105559\pi$
$563$	7.59027	+	16.6204i	0.319892	+	0.700465i	−0.679559	+	0.733621i	$0.737829\pi$
$564$	10.9980	+	24.0822i	0.463098	+	1.01404i
$565$	9.13583	+	63.5411i	0.384347	+	2.67319i
$566$	−17.9201	−	11.5165i	−0.753236	−	0.484076i
$567$	−8.71384	+	2.55861i	−0.365947	+	0.107452i
$568$	−1.07032	+	7.44424i	−0.0449096	+	0.312353i
$569$	−19.7661	+	22.8113i	−0.828639	+	0.956301i	−0.999580	−	0.0289808i	$-0.990774\pi$
$569$	−19.7661	+	22.8113i	−0.828639	+	0.956301i	0.170941	+	0.985281i	$0.445319\pi$
$570$	55.8588	−	35.8983i	2.33967	−	1.50361i
$571$	−20.8738	−	24.0897i	−0.873542	−	1.00812i	−0.999870	−	0.0161330i	$-0.994864\pi$
$571$	−20.8738	−	24.0897i	−0.873542	−	1.00812i	0.126327	−	0.991989i	$-0.459681\pi$
$572$	−2.72047	−	0.798801i	−0.113748	−	0.0333996i
$573$	15.1923	−	33.2665i	0.634667	−	1.38973i
$574$	−10.8425			−0.452557
$575$	3.14762	+	50.1209i	0.131265	+	2.09019i
$576$	2.97251			0.123855
$577$	−15.3765	+	33.6699i	−0.640133	+	1.40170i	0.259797	+	0.965663i	$0.416344\pi$
$577$	−15.3765	+	33.6699i	−0.640133	+	1.40170i	−0.899931	+	0.436033i	$0.856383\pi$
$578$	14.9181	+	4.38034i	0.620510	+	0.182198i
$579$	−12.8124	−	14.7863i	−0.532467	−	0.614499i
$580$	29.3949	−	18.8910i	1.22056	−	0.784405i
$581$	−1.60758	+	1.85524i	−0.0666936	+	0.0769685i
$582$	−0.206942	+	1.43931i	−0.00857801	+	0.0596613i
$583$	0.834482	−	0.245026i	0.0345607	−	0.0101479i
$584$	−9.11521	−	5.85799i	−0.377190	−	0.242405i
$585$	2.76207	+	19.2106i	0.114198	+	0.794263i
$586$	12.7163	+	27.8448i	0.525306	+	1.15026i
$587$	4.94270	+	10.8230i	0.204007	+	0.446713i	0.983787	−	0.179341i	$-0.0573964\pi$
$587$	4.94270	+	10.8230i	0.204007	+	0.446713i	−0.779780	+	0.626053i	$0.784669\pi$
$588$	−0.347799	−	2.41900i	−0.0143430	−	0.0997578i
$589$	−22.4723	−	14.4421i	−0.925955	−	0.595075i
$590$	7.08608	−	2.08066i	0.291729	−	0.0856595i
$591$	−5.06779	+	35.2473i	−0.208461	+	1.44988i
$592$	3.56455	−	4.11371i	0.146502	−	0.169072i
$593$	−18.5520	+	11.9226i	−0.761839	+	0.489604i	−0.862961	−	0.505270i	$-0.831393\pi$
$593$	−18.5520	+	11.9226i	−0.761839	+	0.489604i	0.101123	+	0.994874i	$0.467757\pi$
$594$	−0.0751453	−	0.0867223i	−0.00308325	−	0.00355826i
$595$	−4.54790	−	1.33539i	−0.186446	−	0.0547454i
$596$	−2.81446	+	6.16280i	−0.115285	+	0.252438i
$597$	−3.40614			−0.139404
$598$	−7.79332	+	1.62460i	−0.318692	+	0.0664350i
$599$	4.76413			0.194657			0.0973285	−	0.995252i	$-0.468970\pi$
$599$	4.76413			0.194657			0.0973285	+	0.995252i	$0.468970\pi$
$600$	10.6309	−	23.2784i	0.434005	−	0.950338i
$601$	35.7906	+	10.5091i	1.45993	+	0.428673i	0.912811	−	0.408383i	$-0.133907\pi$
$601$	35.7906	+	10.5091i	1.45993	+	0.428673i	0.547117	+	0.837056i	$0.315725\pi$
$602$	−5.16978	−	5.96624i	−0.210704	−	0.243166i
$603$	−4.92274	+	3.16365i	−0.200469	+	0.128834i
$604$	8.85812	−	10.2228i	0.360432	−	0.415960i
$605$	4.52441	−	31.4679i	0.183943	−	1.27935i
$606$	25.8346	−	7.58573i	1.04946	−	0.308149i
$607$	−4.80110	−	3.08548i	−0.194871	−	0.125236i	0.439567	−	0.898210i	$-0.355132\pi$
$607$	−4.80110	−	3.08548i	−0.194871	−	0.125236i	−0.634438	+	0.772974i	$0.718768\pi$
$608$	−0.983038	−	6.83718i	−0.0398674	−	0.277284i
$609$	−9.01861	−	19.7480i	−0.365453	−	0.800230i
$610$	−14.2040	−	31.1024i	−0.575102	−	1.25930i
$611$	2.55916	+	17.7993i	0.103532	+	0.720084i
$612$	−3.01338	−	1.93658i	−0.121809	−	0.0782816i
$613$	11.5732	−	3.39821i	0.467438	−	0.137252i	−0.0395275	−	0.999218i	$-0.512585\pi$
$613$	11.5732	−	3.39821i	0.467438	−	0.137252i	0.506966	+	0.861966i	$0.330767\pi$
$614$	3.77028	−	26.2229i	0.152156	−	1.05827i
$615$	−68.2532	+	78.7683i	−2.75223	+	3.17625i
$616$	1.43692	−	0.923454i	0.0578952	−	0.0372070i
$617$	−6.17484	−	7.12614i	−0.248590	−	0.286888i	0.617717	−	0.786401i	$-0.288058\pi$
$617$	−6.17484	−	7.12614i	−0.248590	−	0.286888i	−0.866306	+	0.499513i	$0.833512\pi$
$618$	13.4607	+	3.95243i	0.541471	+	0.158990i
$619$	4.16651	−	9.12339i	0.167466	−	0.366700i	−0.807229	−	0.590239i	$-0.799034\pi$
$619$	4.16651	−	9.12339i	0.167466	−	0.366700i	0.974695	+	0.223539i	$0.0717609\pi$
$620$	−15.2113			−0.610902
$621$	−0.300886	−	0.115210i	−0.0120741	−	0.00462322i
$622$	−23.4442			−0.940028
$623$	−3.58758	+	7.85570i	−0.143733	+	0.314732i
$624$	3.89238	+	1.14291i	0.155820	+	0.0457529i
$625$	−21.1488	−	24.4070i	−0.845950	−	0.976279i
$626$	−21.5378	+	13.8415i	−0.860825	+	0.553219i
$627$	18.8822	−	21.7913i	0.754084	−	0.870260i
$628$	2.09979	−	14.6044i	0.0837909	−	0.582779i
$629$	−6.29361	+	1.84797i	−0.250943	+	0.0736835i
$630$	−9.83596	−	6.32119i	−0.391874	−	0.251842i
$631$	0.618521	+	4.30191i	0.0246229	+	0.171256i	0.998422	−	0.0561532i	$-0.0178835\pi$
$631$	0.618521	+	4.30191i	0.0246229	+	0.171256i	−0.973799	+	0.227409i	$0.926974\pi$
$632$	−1.43216	−	3.13600i	−0.0569684	−	0.124743i
$633$	7.74432	+	16.9577i	0.307809	+	0.674008i
$634$	3.54160	+	24.6324i	0.140655	+	0.978276i
$635$	69.2265	+	44.4892i	2.74717	+	1.76550i
$636$	−1.19396	+	0.350578i	−0.0473436	+	0.0139013i
$637$	0.236236	−	1.64306i	0.00936000	−	0.0651002i
$638$	9.93652	−	11.4674i	0.393391	−	0.453997i
$639$	18.8068	−	12.0864i	0.743984	−	0.478129i
$640$	−2.57582	−	2.97265i	−0.101818	−	0.117504i
$641$	−37.5036	−	11.0121i	−1.48130	−	0.434950i	−0.561549	−	0.827444i	$-0.689794\pi$
$641$	−37.5036	−	11.0121i	−1.48130	−	0.434950i	−0.919755	+	0.392494i	$0.871612\pi$
$642$	5.86083	−	12.8334i	0.231309	−	0.506495i
$643$	16.2243			0.639824			0.319912	−	0.947447i	$-0.396347\pi$
$643$	16.2243			0.639824			0.319912	+	0.947447i	$0.396347\pi$
$644$	2.33485	−	4.18909i	0.0920061	−	0.165073i
$645$	−75.8870			−2.98805
$646$	−3.45784	+	7.57162i	−0.136047	+	0.297901i
$647$	−37.1424	−	10.9060i	−1.46022	−	0.428758i	−0.547311	−	0.836929i	$-0.684349\pi$
$647$	−37.1424	−	10.9060i	−1.46022	−	0.428758i	−0.912906	+	0.408171i	$0.866167\pi$
$648$	5.94726	+	6.86350i	0.233630	+	0.269624i
$649$	2.69793	−	1.73386i	0.105903	−	0.0680598i
$650$	11.3829	−	13.1366i	0.446475	−	0.515260i
$651$	−1.34502	+	9.35483i	−0.0527156	+	0.366645i
$652$	11.5821	−	3.40082i	0.453591	−	0.133186i
$653$	−41.1224	−	26.4278i	−1.60924	−	1.03420i	−0.962422	−	0.271557i	$-0.912462\pi$
$653$	−41.1224	−	26.4278i	−1.60924	−	1.03420i	−0.646821	−	0.762641i	$-0.723902\pi$
$654$	4.12900	+	28.7178i	0.161456	+	1.12295i
$655$	−3.16172	−	6.92319i	−0.123539	−	0.270512i
$656$	4.50413	+	9.86267i	0.175857	+	0.385073i
$657$	4.58367	+	31.8801i	0.178826	+	1.24376i
$658$	−9.11336	−	5.85680i	−0.355276	−	0.228322i
$659$	−6.95402	+	2.04189i	−0.270890	+	0.0795405i	−0.414356	−	0.910115i	$-0.635993\pi$
$659$	−6.95402	+	2.04189i	−0.270890	+	0.0795405i	0.143466	+	0.989655i	$0.454175\pi$
$660$	2.33669	−	16.2520i	0.0909556	−	0.632610i
$661$	2.83275	−	3.26917i	0.110181	−	0.127156i	−0.697980	−	0.716117i	$-0.745918\pi$
$661$	2.83275	−	3.26917i	0.110181	−	0.127156i	0.808161	+	0.588961i	$0.200463\pi$
$662$	−4.57721	+	2.94159i	−0.177898	+	0.114328i
$663$	−3.20130	−	3.69449i	−0.124328	−	0.143482i
$664$	2.35540	+	0.691608i	0.0914073	+	0.0268396i
$665$	−11.2867	+	24.7145i	−0.437681	+	0.958388i
$666$	−16.1800			−0.626962
$667$	9.41704	−	41.5495i	0.364629	−	1.60880i
$668$	−3.44710			−0.133372
$669$	18.8810	−	41.3437i	0.729984	−	1.59844i
$670$	7.42959	+	2.18152i	0.287030	+	0.0842796i
$671$	−9.72337	−	11.2214i	−0.375366	−	0.433196i
$672$	−2.05592	+	1.32126i	−0.0793087	+	0.0509686i
$673$	18.1404	−	20.9351i	0.699259	−	0.806988i	−0.289393	−	0.957210i	$-0.593453\pi$
$673$	18.1404	−	20.9351i	0.699259	−	0.806988i	0.988652	+	0.150222i	$0.0479989\pi$
$674$	−1.84128	+	12.8064i	−0.0709233	+	0.493282i
$675$	0.674991	−	0.198195i	0.0259804	−	0.00762854i
$676$	−8.61827	−	5.53863i	−0.331472	−	0.213024i
$677$	−6.31071	−	43.8919i	−0.242540	−	1.68690i	−0.639281	−	0.768973i	$-0.720768\pi$
$677$	−6.31071	−	43.8919i	−0.242540	−	1.68690i	0.396741	−	0.917931i	$-0.370141\pi$
$678$	−16.5688	−	36.2807i	−0.636322	−	1.39335i
$679$	−0.247173	−	0.541234i	−0.00948564	−	0.0207706i
$680$	0.674559	+	4.69166i	0.0258681	+	0.179917i
$681$	50.4092	+	32.3960i	1.93168	+	1.24142i
$682$	−6.33795	+	1.86099i	−0.242693	+	0.0712610i
$683$	−6.23625	+	43.3741i	−0.238624	+	1.65966i	0.420249	+	0.907409i	$0.361943\pi$
$683$	−6.23625	+	43.3741i	−0.238624	+	1.65966i	−0.658873	+	0.752254i	$0.728966\pi$
$684$	−13.4460	+	15.5175i	−0.514120	+	0.593326i
$685$	27.4834	−	17.6625i	1.05009	−	0.674850i
$686$	0.654861	+	0.755750i	0.0250027	+	0.0288547i
$687$	43.4144	+	12.7476i	1.65636	+	0.486352i
$688$	−3.27948	+	7.18106i	−0.125029	+	0.273775i
$689$	−0.845210			−0.0321999
$690$	−15.7350	−	43.3324i	−0.599021	−	1.64964i
$691$	−6.70613			−0.255113			−0.127557	−	0.991831i	$-0.540713\pi$
$691$	−6.70613			−0.255113			−0.127557	+	0.991831i	$0.540713\pi$
$692$	−0.275780	+	0.603874i	−0.0104836	+	0.0229558i
$693$	−4.87160	−	1.43043i	−0.185057	−	0.0543375i
$694$	12.3194	+	14.2173i	0.467637	+	0.539682i
$695$	63.0652	−	40.5295i	2.39220	−	1.53737i
$696$	−14.2170	+	16.4072i	−0.538892	+	0.621915i
$697$	1.85944	−	12.9327i	0.0704313	−	0.489861i
$698$	10.6468	−	3.12618i	0.402987	−	0.118328i
$699$	−16.1897	−	10.4045i	−0.612350	−	0.393533i
$700$	1.49025	+	10.3649i	0.0563262	+	0.391758i
$701$	10.7092	+	23.4500i	0.404483	+	0.885693i	0.996796	+	0.0799856i	$0.0254874\pi$
$701$	10.7092	+	23.4500i	0.404483	+	0.885693i	−0.592314	+	0.805708i	$0.701785\pi$
$702$	0.0463259	+	0.101440i	0.00174846	+	0.00382859i
$703$	5.35088	+	37.2162i	0.201812	+	1.40364i
$704$	−1.43692	−	0.923454i	−0.0541560	−	0.0348040i
$705$	−99.9168	+	29.3382i	−3.76308	+	1.10494i
$706$	−0.982093	+	6.83061i	−0.0369616	+	0.257073i
$707$	−7.21491	+	8.32645i	−0.271345	+	0.313148i
$708$	−3.86014	+	2.48076i	−0.145073	+	0.0932328i
$709$	5.47351	+	6.31676i	0.205562	+	0.237231i	0.849164	−	0.528129i	$-0.177106\pi$
$709$	5.47351	+	6.31676i	0.205562	+	0.237231i	−0.643602	+	0.765360i	$0.722561\pi$
$710$	−28.3839	−	8.33426i	−1.06523	−	0.312779i
$711$	−4.25712	+	9.32180i	−0.159655	+	0.349595i
$712$	8.63613			0.323653
$713$	−13.2278	+	13.0001i	−0.495385	+	0.486857i
$714$	2.94497			0.110213
$715$	4.63287	−	10.1446i	0.173260	−	0.379386i
$716$	−18.3278	−	5.38152i	−0.684941	−	0.201117i
$717$	9.38349	+	10.8291i	0.350433	+	0.404421i
$718$	21.8455	−	14.0392i	0.815266	−	0.523939i
$719$	15.5178	−	17.9085i	0.578717	−	0.667875i	−0.388611	−	0.921402i	$-0.627045\pi$
$719$	15.5178	−	17.9085i	0.578717	−	0.667875i	0.967328	+	0.253527i	$0.0815905\pi$
$720$	−1.66395	+	11.5730i	−0.0620117	+	0.431301i
$721$	−5.50796	+	1.61728i	−0.205127	+	0.0602307i
$722$	24.1552	+	15.5236i	0.898964	+	0.577729i
$723$	0.384872	+	2.67684i	0.0143135	+	0.0995528i
$724$	5.73858	+	12.5657i	0.213273	+	0.467002i
$725$	38.6430	+	84.6164i	1.43516	+	3.14257i
$726$	2.81108	+	19.5515i	0.104329	+	0.725625i
$727$	12.4499	+	8.00108i	0.461742	+	0.296744i	0.750754	−	0.660582i	$-0.229690\pi$
$727$	12.4499	+	8.00108i	0.461742	+	0.296744i	−0.289012	+	0.957325i	$0.593327\pi$
$728$	−1.59271	+	0.467662i	−0.0590298	+	0.0173327i
$729$	3.77176	−	26.2332i	0.139695	−	0.971599i
$730$	27.9097	−	32.2095i	1.03298	−	1.19213i
$731$	8.00300	−	5.14321i	0.296002	−	0.190229i
$732$	13.9120	+	16.0553i	0.514201	+	0.593420i
$733$	45.8736	+	13.4697i	1.69438	+	0.497515i	0.979451	−	0.201682i	$-0.0646407\pi$
$733$	45.8736	+	13.4697i	1.69438	+	0.497515i	0.714929	+	0.699197i	$0.246459\pi$
$734$	−4.61368	+	10.1025i	−0.170294	+	0.372892i
$735$	9.61269			0.354569
$736$	−4.78046	−	0.383646i	−0.176210	−	0.0141414i
$737$	3.36250			0.123859
$738$	13.3886	−	29.3169i	0.492840	−	1.07917i
$739$	−21.9761	−	6.45278i	−0.808405	−	0.237369i	−0.148689	−	0.988884i	$-0.547505\pi$
$739$	−21.9761	−	6.45278i	−0.808405	−	0.237369i	−0.659716	+	0.751515i	$0.729324\pi$
$740$	14.0207	+	16.1808i	0.515412	+	0.594817i
$741$	−23.5733	+	15.1497i	−0.865988	+	0.556536i
$742$	0.333440	−	0.384811i	0.0122410	−	0.0141268i
$743$	2.63247	−	18.3092i	0.0965759	−	0.671700i	−0.882814	−	0.469722i	$-0.844354\pi$
$743$	2.63247	−	18.3092i	0.0965759	−	0.671700i	0.979390	−	0.201978i	$-0.0647369\pi$
$744$	9.06820	−	2.66266i	0.332456	−	0.0976179i
$745$	−22.4185	−	14.4075i	−0.821349	−	0.527849i
$746$	2.78006	+	19.3358i	0.101785	+	0.707933i
$747$	−3.03130	−	6.63762i	−0.110909	−	0.242858i
$748$	0.855050	+	1.87230i	0.0312637	+	0.0684580i
$749$	0.821578	+	5.71420i	0.0300198	+	0.208792i
$750$	44.2465	+	28.4355i	1.61566	+	1.03832i
$751$	10.8518	−	3.18637i	0.395988	−	0.116272i	−0.0776752	−	0.996979i	$-0.524750\pi$
$751$	10.8518	−	3.18637i	0.395988	−	0.116272i	0.473663	+	0.880706i	$0.342932\pi$
$752$	−1.54171	+	10.7228i	−0.0562203	+	0.391021i
$753$	15.6571	−	18.0692i	0.570575	−	0.658478i
$754$	−12.4051	+	7.97230i	−0.451768	+	0.290334i
$755$	34.8424	+	40.2103i	1.26804	+	1.46340i
$756$	−0.0644597	−	0.0189271i	−0.00234438	−	0.000688371i
$757$	−17.9104	+	39.2183i	−0.650964	+	1.42541i	0.239743	+	0.970836i	$0.422937\pi$
$757$	−17.9104	+	39.2183i	−0.650964	+	1.42541i	−0.890708	+	0.454577i	$0.849791\pi$
$758$	22.5922			0.820585
$759$	−11.8575	−	16.1298i	−0.430401	−	0.585475i
$760$	27.1698			0.985552
$761$	−9.88292	+	21.6406i	−0.358256	+	0.784470i	0.641593	+	0.767046i	$0.278274\pi$
$761$	−9.88292	+	21.6406i	−0.358256	+	0.784470i	−0.999848	+	0.0174248i	$0.994453\pi$
$762$	−49.0568	−	14.4044i	−1.77714	−	0.521815i
$763$	−7.77436	−	8.97209i	−0.281451	−	0.324811i
$764$	12.5890	−	8.09043i	0.455452	−	0.292701i
$765$	9.22660	−	10.6481i	0.333589	−	0.384982i
$766$	3.81126	−	26.5079i	0.137707	−	0.957770i
$767$	−2.99044	+	0.878072i	−0.107979	+	0.0317054i
$768$	2.05592	+	1.32126i	0.0741865	+	0.0476768i
$769$	−3.14179	−	21.8517i	−0.113296	−	0.787991i	−0.964676	−	0.263441i	$-0.915143\pi$
$769$	−3.14179	−	21.8517i	−0.113296	−	0.787991i	0.851380	−	0.524550i	$-0.175766\pi$
$770$	2.79097	+	6.11137i	0.100579	+	0.220238i
$771$	−21.7518	−	47.6298i	−0.783372	−	1.71534i
$772$	−1.13934	−	7.92431i	−0.0410059	−	0.285202i
$773$	25.8875	+	16.6369i	0.931109	+	0.598387i	0.915861	−	0.401496i	$-0.131510\pi$
$773$	25.8875	+	16.6369i	0.931109	+	0.598387i	0.0152484	+	0.999884i	$0.495146\pi$
$774$	22.5158	−	6.61124i	0.809315	−	0.237636i
$775$	5.76316	−	40.0836i	0.207019	−	1.43985i
$776$	−0.389644	+	0.449673i	−0.0139874	+	0.0161423i
$777$	11.1908	−	7.19188i	0.401467	−	0.258007i
$778$	4.05437	+	4.67900i	0.145356	+	0.167750i
$779$	−71.8606	−	21.1002i	−2.57467	−	0.755992i
$780$	−6.62861	+	14.5146i	−0.237342	+	0.519707i
$781$	−12.8461			−0.459668
$782$	4.59624	+	3.50337i	0.164361	+	0.125280i
$783$	−0.596796			−0.0213277
$784$	0.415415	−	0.909632i	0.0148363	−	0.0324869i
$785$	55.6846	+	16.3505i	1.98747	+	0.583573i
$786$	3.09672	+	3.57380i	0.110456	+	0.127473i
$787$	23.4874	−	15.0945i	0.837236	−	0.538059i	−0.0503334	−	0.998732i	$-0.516028\pi$
$787$	23.4874	−	15.0945i	0.837236	−	0.538059i	0.887570	+	0.460673i	$0.152392\pi$
$788$	−9.54199	+	11.0120i	−0.339919	+	0.392288i
$789$	−6.22003	+	43.2613i	−0.221439	+	1.54014i
$790$	13.0112	−	3.82044i	0.462919	−	0.135925i
$791$	13.7296	+	8.82348i	0.488169	+	0.313727i
$792$	0.722570	+	5.02558i	0.0256754	+	0.178576i
$793$	5.99431	+	13.1257i	0.212864	+	0.466107i
$794$	−4.38766	−	9.60765i	−0.155712	−	0.340963i
$795$	−0.696569	−	4.84474i	−0.0247048	−	0.171825i
$796$	−1.17250	−	0.753517i	−0.0415580	−	0.0267077i
$797$	−29.8123	+	8.75368i	−1.05601	+	0.310071i	−0.763241	−	0.646114i	$-0.776393\pi$
$797$	−29.8123	+	8.75368i	−1.05601	+	0.310071i	−0.292764	+	0.956185i	$0.594575\pi$
$798$	2.40242	−	16.7092i	0.0850447	−	0.591499i
$799$	8.54877	−	9.86581i	0.302434	−	0.349027i
$800$	8.80920	−	5.66133i	0.311452	−	0.200158i
$801$	−16.8109	−	19.4008i	−0.593985	−	0.685495i
$802$	−18.2798	−	5.36744i	−0.645483	−	0.189531i
$803$	7.68826	−	16.8349i	0.271313	−	0.594092i
$804$	−4.81100			−0.169671
$805$	15.0026	+	11.4354i	0.528771	+	0.403043i
$806$	6.41942			0.226115
$807$	13.8263	−	30.2753i	0.486708	−	1.06574i
$808$	10.5712	+	3.10398i	0.371893	+	0.109198i
$809$	14.9641	+	17.2695i	0.526109	+	0.607162i	0.955150	−	0.296123i	$-0.0956938\pi$
$809$	14.9641	+	17.2695i	0.526109	+	0.607162i	−0.429041	+	0.903285i	$0.641148\pi$
$810$	−30.0511	+	19.3127i	−1.05589	+	0.678579i
$811$	−36.2006	+	41.7777i	−1.27118	+	1.46701i	−0.453586	+	0.891213i	$0.649855\pi$
$811$	−36.2006	+	41.7777i	−1.27118	+	1.46701i	−0.817589	+	0.575802i	$0.804690\pi$
$812$	1.26424	−	8.79298i	0.0443661	−	0.308573i
$813$	24.8437	−	7.29477i	0.871307	−	0.255839i
$814$	7.82147	+	5.02655i	0.274142	+	0.176181i
$815$	6.75714	+	46.9969i	0.236692	+	1.64623i
$816$	−1.22339	−	2.67884i	−0.0428271	−	0.0937783i
$817$	−22.6530	−	49.6031i	−0.792527	−	1.73539i
$818$	−1.52053	−	10.5755i	−0.0531639	−	0.369763i
$819$	4.15093	+	2.66764i	0.145045	+	0.0932150i
$820$	−40.9201	+	12.0152i	−1.42899	+	0.419590i
$821$	−1.90291	+	13.2350i	−0.0664121	+	0.461906i	0.929294	+	0.369340i	$0.120416\pi$
$821$	−1.90291	+	13.2350i	−0.0664121	+	0.461906i	−0.995707	+	0.0925664i	$0.970493\pi$
$822$	−13.2924	+	15.3403i	−0.463627	+	0.535054i
$823$	−2.90510	+	1.86699i	−0.101265	+	0.0650793i	−0.590293	−	0.807189i	$-0.700988\pi$
$823$	−2.90510	+	1.86699i	−0.101265	+	0.0650793i	0.489028	+	0.872268i	$0.337352\pi$
$824$	3.75922	+	4.33837i	0.130959	+	0.151134i
$825$	41.9407	+	12.3149i	1.46019	+	0.428750i
$826$	0.779974	−	1.70790i	0.0271388	−	0.0594256i
$827$	38.4527			1.33713			0.668566	−	0.743653i	$-0.266908\pi$
$827$	38.4527			1.33713			0.668566	+	0.743653i	$0.266908\pi$
$828$	8.44370	+	11.4860i	0.293439	+	0.399165i
$829$	22.8506			0.793632			0.396816	−	0.917898i	$-0.370115\pi$
$829$	22.8506			0.793632			0.396816	+	0.917898i	$0.370115\pi$
$830$	−4.01118	+	8.78325i	−0.139230	+	0.304871i
$831$	−13.6843	−	4.01806i	−0.474702	−	0.139385i
$832$	1.08704	+	1.25451i	0.0376862	+	0.0434922i
$833$	−1.01375	+	0.651496i	−0.0351243	+	0.0225730i
$834$	−30.5017	+	35.2008i	−1.05619	+	1.21890i
$835$	1.92961	−	13.4207i	0.0667770	−	0.464444i
$836$	11.3206	−	3.32402i	0.391530	−	0.114964i
$837$	0.218562	+	0.140461i	0.00755460	+	0.00485505i
$838$	4.75795	+	33.0923i	0.164361	+	1.14315i
$839$	−2.55286	−	5.58998i	−0.0881345	−	0.192988i	0.860432	−	0.509565i	$-0.170194\pi$
$839$	−2.55286	−	5.58998i	−0.0881345	−	0.192988i	−0.948567	+	0.316577i	$0.897466\pi$
$840$	−3.99326	−	8.74401i	−0.137780	−	0.301697i
$841$	−7.10361	−	49.4067i	−0.244952	−	1.70368i
$842$	−16.9348	−	10.8833i	−0.583610	−	0.375064i
$843$	33.7996	−	9.92445i	1.16412	−	0.341816i
$844$	−1.08561	+	7.55057i	−0.0373681	+	0.259901i
$845$	26.3881	−	30.4535i	0.907779	−	1.04763i
$846$	27.0896	−	17.4094i	0.931358	−	0.598548i
$847$	−5.29291	−	6.10834i	−0.181866	−	0.209885i
$848$	−0.488552	−	0.143452i	−0.0167770	−	0.00492616i
$849$	−21.6259	+	47.3540i	−0.742197	+	1.62519i
$850$	−12.6186			−0.432816
$851$	26.0211	+	2.08827i	0.891991	+	0.0715849i
$852$	18.3798			0.629683
$853$	16.7383	−	36.6519i	0.573110	−	1.25494i	−0.372015	−	0.928227i	$-0.621333\pi$
$853$	16.7383	−	36.6519i	0.573110	−	1.25494i	0.945125	−	0.326709i	$-0.105940\pi$
$854$	−8.34071	−	2.44905i	−0.285413	−	0.0838049i
$855$	−52.8882	−	61.0362i	−1.80874	−	2.08740i
$856$	4.85652	−	3.12110i	0.165993	−	0.106677i
$857$	22.7439	−	26.2479i	0.776917	−	0.896610i	−0.219966	−	0.975508i	$-0.570595\pi$
$857$	22.7439	−	26.2479i	0.776917	−	0.896610i	0.996883	+	0.0788976i	$0.0251400\pi$
$858$	−0.986121	+	6.85862i	−0.0336656	+	0.234150i
$859$	−7.14699	+	2.09855i	−0.243852	+	0.0716015i	−0.401375	−	0.915914i	$-0.631467\pi$
$859$	−7.14699	+	2.09855i	−0.243852	+	0.0716015i	0.157523	+	0.987515i	$0.449649\pi$
$860$	−26.1226	−	16.7880i	−0.890773	−	0.572465i
$861$	3.77101	+	26.2279i	0.128516	+	0.893846i
$862$	5.64058	+	12.3511i	0.192119	+	0.420681i
$863$	−1.69697	−	3.71584i	−0.0577654	−	0.126489i	0.878548	−	0.477654i	$-0.158513\pi$
$863$	−1.69697	−	3.71584i	−0.0577654	−	0.126489i	−0.936313	+	0.351165i	$0.885785\pi$
$864$	0.00956086	+	0.0664972i	0.000325267	+	0.00226228i
$865$	−2.19672	−	1.41174i	−0.0746906	−	0.0480007i
$866$	−5.20799	+	1.52920i	−0.176975	+	0.0519645i
$867$	5.40754	−	37.6102i	0.183650	−	1.27731i
$868$	−2.53250	+	2.92266i	−0.0859587	+	0.0992016i
$869$	4.95386	−	3.18365i	0.168048	−	0.107998i
$870$	−55.9207	−	64.5360i	−1.89589	−	2.18797i
$871$	−3.13541	−	0.920638i	−0.106239	−	0.0311946i
$872$	−4.93171	+	10.7989i	−0.167009	+	0.365699i
$873$	1.76865			0.0598598
$874$	23.6269	−	23.2202i	0.799192	−	0.785435i
$875$	−21.5216			−0.727562
$876$	−11.0002	+	24.0871i	−0.371662	+	0.813827i
$877$	14.9806	+	4.39870i	0.505859	+	0.148534i	0.524697	−	0.851289i	$-0.324179\pi$
$877$	14.9806	+	4.39870i	0.505859	+	0.148534i	−0.0188383	+	0.999823i	$0.505997\pi$
$878$	3.16614	+	3.65392i	0.106852	+	0.123314i
$879$	62.9339	−	40.4451i	2.12271	−	1.36418i
$880$	4.39968	−	5.07751i	0.148313	−	0.171163i
$881$	3.33267	−	23.1793i	0.112281	−	0.780929i	−0.853411	−	0.521238i	$-0.825470\pi$
$881$	3.33267	−	23.1793i	0.112281	−	0.780929i	0.965692	−	0.259691i	$-0.0836206\pi$
$882$	−2.85210	+	0.837453i	−0.0960353	+	0.0281985i
$883$	−36.2939	−	23.3247i	−1.22139	−	0.784937i	−0.238859	−	0.971054i	$-0.576773\pi$
$883$	−36.2939	−	23.3247i	−1.22139	−	0.784937i	−0.982528	+	0.186117i	$0.940410\pi$
$884$	−0.284675	−	1.97995i	−0.00957464	−	0.0665931i
$885$	−7.49765	−	16.4176i	−0.252031	−	0.551870i
$886$	4.87086	+	10.6657i	0.163640	+	0.358321i
$887$	−0.412515	−	2.86910i	−0.0138509	−	0.0963350i	0.981723	−	0.190314i	$-0.0609505\pi$
$887$	−0.412515	−	2.86910i	−0.0138509	−	0.0963350i	−0.995574	+	0.0939787i	$0.970041\pi$
$888$	−11.1908	−	7.19188i	−0.375538	−	0.241344i
$889$	20.0734	−	5.89408i	0.673240	−	0.197681i
$890$	−4.83432	+	33.6235i	−0.162047	+	1.12706i
$891$	−10.1583	+	11.7234i	−0.340317	+	0.392747i
$892$	15.6456	−	10.0548i	0.523854	−	0.336660i
$893$	−49.0028	−	56.5522i	−1.63982	−	1.89245i
$894$	15.8867	+	4.66475i	0.531330	+	0.156012i
$895$	31.2116	−	68.3439i	1.04329	−	2.28448i
$896$	−1.00000			−0.0334077
$897$	6.64042	+	18.2870i	0.221717	+	0.610584i
$898$	1.44015			0.0480585
$899$	−14.2712	+	31.2497i	−0.475973	+	1.04223i
$900$	−29.8658	−	8.76940i	−0.995528	−	0.292313i
$901$	0.401810	+	0.463714i	0.0133862	+	0.0154485i
$902$	−15.5798	+	10.0125i	−0.518751	+	0.333381i
$903$	−12.6343	+	14.5807i	−0.420442	+	0.485216i
$904$	2.32264	−	16.1543i	0.0772498	−	0.537284i
$905$	−52.1352	+	15.3083i	−1.73303	+	0.508864i
$906$	−27.8098	−	17.8723i	−0.923919	−	0.593767i
$907$	−2.52342	−	17.5508i	−0.0837889	−	0.582764i	−0.987856	−	0.155374i	$-0.950342\pi$
$907$	−2.52342	−	17.5508i	−0.0837889	−	0.582764i	0.904067	−	0.427391i	$-0.140567\pi$
$908$	10.1856	+	22.3034i	0.338021	+	0.740163i
$909$	−13.6047	−	29.7900i	−0.451238	−	0.988074i
$910$	−0.929206	−	6.46277i	−0.0308029	−	0.214239i
$911$	19.6828	+	12.6493i	0.652119	+	0.419091i	0.824440	−	0.565949i	$-0.191490\pi$
$911$	19.6828	+	12.6493i	0.652119	+	0.419091i	−0.172321	+	0.985041i	$0.555127\pi$
$912$	−16.1972	+	4.75593i	−0.536343	+	0.157485i
$913$	−0.596732	+	4.15037i	−0.0197490	+	0.137357i
$914$	12.9008	−	14.8883i	0.426721	−	0.492462i
$915$	−70.2964	+	45.1768i	−2.32393	+	1.49350i
$916$	12.1245	+	13.9924i	0.400604	+	0.462321i
$917$	−1.85659	−	0.545144i	−0.0613100	−	0.0180022i
$918$	0.0336304	−	0.0736403i	0.00110997	−	0.00243049i
$919$	−20.9924			−0.692477			−0.346238	−	0.938147i	$-0.612541\pi$
$919$	−20.9924			−0.692477			−0.346238	+	0.938147i	$0.612541\pi$
$920$	4.16967	−	18.3972i	0.137470	−	0.606539i
$921$	−64.7444			−2.13340
$922$	4.06725	−	8.90604i	0.133948	−	0.293305i
$923$	11.9785	+	3.51719i	0.394276	+	0.115770i
$924$	−2.73359	−	3.15473i	−0.0899286	−	0.103783i
$925$	−47.9503	+	30.8158i	−1.57660	+	1.01322i
$926$	−20.5403	+	23.7048i	−0.674997	+	0.778988i
$927$	2.42841	−	16.8900i	0.0797595	−	0.554740i
$928$	−8.52356	+	2.50274i	−0.279800	+	0.0821565i
$929$	8.47725	+	5.44800i	0.278130	+	0.178743i	0.672268	−	0.740308i	$-0.265320\pi$
$929$	8.47725	+	5.44800i	0.278130	+	0.178743i	−0.394138	+	0.919051i	$0.628957\pi$
$930$	5.29049	+	36.7961i	0.173482	+	1.20659i
$931$	2.86947	+	6.28327i	0.0940432	+	0.205926i
$932$	−3.27126	−	7.16306i	−0.107154	−	0.234634i
$933$	8.15388	+	56.7115i	0.266946	+	1.85665i
$934$	−29.9228	−	19.2302i	−0.979105	−	0.629232i
$935$	−7.76815	+	2.28093i	−0.254046	+	0.0745945i
$936$	0.702213	−	4.88400i	0.0229526	−	0.159639i
$937$	15.0900	−	17.4148i	0.492970	−	0.568918i	−0.453687	−	0.891161i	$-0.649891\pi$
$937$	15.0900	−	17.4148i	0.492970	−	0.568918i	0.946657	+	0.322243i	$0.104437\pi$
$938$	1.65609	−	1.06430i	0.0540732	−	0.0347507i
$939$	40.9734	+	47.2859i	1.33712	+	1.54312i
$940$	−40.8846	−	12.0048i	−1.33351	−	0.391554i
$941$	17.2858	−	37.8506i	0.563501	−	1.23389i	−0.386685	−	0.922212i	$-0.626380\pi$
$941$	17.2858	−	37.8506i	0.563501	−	1.23389i	0.950186	−	0.311683i	$-0.100893\pi$
$942$	−36.0583			−1.17484
$943$	−25.3156	+	45.4201i	−0.824390	+	1.47908i
$944$	−1.87758			−0.0611099
$945$	0.109773	−	0.240369i	0.00357091	−	0.00781921i
$946$	−12.9381	−	3.79897i	−0.420654	−	0.123515i
$947$	0.796407	+	0.919103i	0.0258798	+	0.0298668i	0.768542	−	0.639799i	$-0.220983\pi$
$947$	0.796407	+	0.919103i	0.0258798	+	0.0298668i	−0.742662	+	0.669666i	$0.766437\pi$
$948$	−7.08787	+	4.55510i	−0.230203	+	0.147943i
$949$	−11.7783	+	13.5929i	−0.382341	+	0.441245i
$950$	−10.2939	+	71.5956i	−0.333978	+	2.32287i
$951$	58.3539	−	17.1342i	1.89225	−	0.555616i
$952$	1.01375	+	0.651496i	0.0328558	+	0.0211151i
$953$	−3.91533	−	27.2317i	−0.126830	−	0.882122i	−0.949537	−	0.313656i	$-0.898446\pi$
$953$	−3.91533	−	27.2317i	−0.126830	−	0.882122i	0.822707	−	0.568466i	$-0.192463\pi$
$954$	0.628745	+	1.37676i	0.0203564	+	0.0445743i
$955$	24.4518	+	53.5420i	0.791243	+	1.73258i
$956$	0.834425	+	5.80355i	0.0269872	+	0.187700i
$957$	−31.1954	−	20.0481i	−1.00840	−	0.648062i
$958$	25.0188	−	7.34619i	0.808321	−	0.237344i
$959$	1.18203	−	8.22117i	0.0381696	−	0.265476i
$960$	−6.29497	+	7.26479i	−0.203169	+	0.234470i
$961$	−13.4975	+	8.67431i	−0.435403	+	0.279816i
$962$	−5.91697	−	6.82855i	−0.190771	−	0.220161i
$963$	−16.4651	−	4.83458i	−0.530580	−	0.155792i
$964$	−0.459695	+	1.00659i	−0.0148058	+	0.0324201i
$965$	31.4899			1.01369
$966$	−10.9455	−	4.19104i	−0.352164	−	0.134844i
$967$	1.18779			0.0381967			0.0190984	−	0.999818i	$-0.493920\pi$
$967$	1.18779			0.0381967			0.0190984	+	0.999818i	$0.493920\pi$
$968$	−3.35759	+	7.35209i	−0.107917	+	0.236305i
$969$	19.5184	+	5.73111i	0.627020	+	0.184110i
$970$	−1.53262	−	1.76874i	−0.0492095	−	0.0567908i
$971$	−13.6525	+	8.77394i	−0.438130	+	0.281569i	−0.741054	−	0.671446i	$-0.765674\pi$
$971$	−13.6525	+	8.77394i	−0.438130	+	0.281569i	0.302924	+	0.953015i	$0.402037\pi$
$972$	14.4024	−	16.6212i	0.461956	−	0.533125i
$973$	2.71235	−	18.8648i	0.0869541	−	0.604779i
$974$	20.8256	−	6.11496i	0.667297	−	0.195936i
$975$	−35.7364	−	22.9664i	−1.14448	−	0.735512i
$976$	1.23712	+	8.60435i	0.0395992	+	0.275419i
$977$	9.54989	+	20.9113i	0.305528	+	0.669013i	0.998657	−	0.0518001i	$-0.0164959\pi$
$977$	9.54989	+	20.9113i	0.305528	+	0.669013i	−0.693129	+	0.720813i	$0.743769\pi$
$978$	−12.2548	−	26.8343i	−0.391866	−	0.858067i
$979$	2.09931	+	14.6010i	0.0670941	+	0.466650i
$980$	3.30897	+	2.12655i	0.105701	+	0.0679301i
$981$	33.8595	−	9.94205i	1.08105	−	0.317425i
$982$	−1.84339	+	12.8210i	−0.0588248	+	0.409135i
$983$	−31.1651	+	35.9664i	−0.994012	+	1.14715i	−0.00489938	+	0.999988i	$0.501560\pi$
$983$	−31.1651	+	35.9664i	−0.994012	+	1.14715i	−0.989112	+	0.147163i	$0.952986\pi$
$984$	22.2912	−	14.3257i	0.710619	−	0.456687i
$985$	−37.5323	−	43.3146i	−1.19588	−	1.38012i
$986$	10.2713	+	3.01592i	0.327104	+	0.0960463i
$987$	−10.9980	+	24.0822i	−0.350069	+	0.766544i
$988$	−11.4661			−0.364785
$989$	−37.0638	+	7.72636i	−1.17856	+	0.245684i
$990$	−19.9708			−0.634714
$991$	2.10377	−	4.60661i	0.0668284	−	0.146334i	−0.873270	−	0.487236i	$-0.838005\pi$
$991$	2.10377	−	4.60661i	0.0668284	−	0.146334i	0.940099	+	0.340902i	$0.110732\pi$
$992$	3.71059	+	1.08953i	0.117811	+	0.0345925i
$993$	8.70766	+	10.0492i	0.276329	+	0.318901i
$994$	−6.32689	+	4.06605i	−0.200677	+	0.128967i
$995$	3.59004	−	4.14313i	0.113812	−	0.131346i
$996$	0.853792	−	5.93825i	0.0270534	−	0.188161i
$997$	−33.6718	+	9.88694i	−1.06640	+	0.313122i	−0.767425	−	0.641139i	$-0.778462\pi$
$997$	−33.6718	+	9.88694i	−1.06640	+	0.313122i	−0.298973	+	0.954262i	$0.596644\pi$
$998$	−29.7496	−	19.1189i	−0.941708	−	0.605199i
$999$	−0.0520418	−	0.361958i	−0.00164653	−	0.0114519i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	322.2.i.d.29.2	✓	40
23.2	even	11		7406.2.a.bu.1.15		20
23.4	even	11	inner	322.2.i.d.211.2	yes	40
23.21	odd	22		7406.2.a.bv.1.15		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
322.2.i.d.29.2	✓	40	1.1	even	1	trivial
322.2.i.d.211.2	yes	40	23.4	even	11	inner
7406.2.a.bu.1.15		20	23.2	even	11
7406.2.a.bv.1.15		20	23.21	odd	22

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:	\( N \)	\(=\)	\( 322 = 2 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	322.i (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(0.415415 - 0.909632i) q^{2} +(-2.34488 - 0.688518i) q^{3} +(-0.654861 - 0.755750i) q^{4} +(3.30897 - 2.12655i) q^{5} +(-1.60040 + 1.84696i) q^{6} +(0.142315 - 0.989821i) q^{7} +(-0.959493 + 0.281733i) q^{8} +(2.50063 + 1.60706i) q^{9} +O(q^{10})\)	\(q+(0.415415 - 0.909632i) q^{2} +(-2.34488 - 0.688518i) q^{3} +(-0.654861 - 0.755750i) q^{4} +(3.30897 - 2.12655i) q^{5} +(-1.60040 + 1.84696i) q^{6} +(0.142315 - 0.989821i) q^{7} +(-0.959493 + 0.281733i) q^{8} +(2.50063 + 1.60706i) q^{9} +(-0.559779 - 3.89335i) q^{10} +(-0.709559 - 1.55372i) q^{11} +(1.01522 + 2.22302i) q^{12} +(0.236236 + 1.64306i) q^{13} +(-0.841254 - 0.540641i) q^{14} +(-9.22331 + 2.70821i) q^{15} +(-0.142315 + 0.989821i) q^{16} +(0.789136 - 0.910712i) q^{17} +(2.50063 - 1.60706i) q^{18} +(-4.52344 - 5.22033i) q^{19} +(-3.77405 - 1.10816i) q^{20} +(-1.01522 + 2.22302i) q^{21} -1.70807 q^{22} +(-4.22900 + 2.26177i) q^{23} +2.44387 q^{24} +(4.35002 - 9.52522i) q^{25} +(1.59271 + 0.467662i) q^{26} +(0.0439942 + 0.0507720i) q^{27} +(-0.841254 + 0.540641i) q^{28} +(-5.81739 + 6.71362i) q^{29} +(-1.36803 + 9.51485i) q^{30} +(3.71059 - 1.08953i) q^{31} +(0.841254 + 0.540641i) q^{32} +(0.594066 + 4.13182i) q^{33} +(-0.500594 - 1.09615i) q^{34} +(-1.63399 - 3.57793i) q^{35} +(-0.423032 - 2.94225i) q^{36} +(-4.57912 - 2.94282i) q^{37} +(-6.62768 + 1.94606i) q^{38} +(0.577330 - 4.01542i) q^{39} +(-2.57582 + 2.97265i) q^{40} +(9.12128 - 5.86189i) q^{41} +(1.60040 + 1.84696i) q^{42} +(7.57469 + 2.22413i) q^{43} +(-0.709559 + 1.55372i) q^{44} +11.6920 q^{45} +(0.300589 + 4.78640i) q^{46} +10.8331 q^{47} +(1.01522 - 2.22302i) q^{48} +(-0.959493 - 0.281733i) q^{49} +(-6.85738 - 7.91384i) q^{50} +(-2.47747 + 1.59217i) q^{51} +(1.08704 - 1.25451i) q^{52} +(-0.0724635 + 0.503995i) q^{53} +(0.0644597 - 0.0189271i) q^{54} +(-5.65197 - 3.63230i) q^{55} +(0.142315 + 0.989821i) q^{56} +(7.01263 + 15.3555i) q^{57} +(3.69030 + 8.08062i) q^{58} +(0.267207 + 1.85847i) q^{59} +(8.08671 + 5.19701i) q^{60} +(8.34071 - 2.44905i) q^{61} +(0.550365 - 3.82787i) q^{62} +(1.94658 - 2.24647i) q^{63} +(0.841254 - 0.540641i) q^{64} +(4.27573 + 4.93446i) q^{65} +(4.00522 + 1.17604i) q^{66} +(-0.817784 + 1.79070i) q^{67} -1.20504 q^{68} +(11.4737 - 2.39183i) q^{69} -3.93338 q^{70} +(3.12425 - 6.84115i) q^{71} +(-2.85210 - 0.837453i) q^{72} +(7.09559 + 8.18875i) q^{73} +(-4.57912 + 2.94282i) q^{74} +(-16.7586 + 19.3404i) q^{75} +(-0.983038 + 6.83718i) q^{76} +(-1.63888 + 0.481220i) q^{77} +(-3.41272 - 2.19322i) q^{78} +(0.490637 + 3.41246i) q^{79} +(1.63399 + 3.57793i) q^{80} +(-3.77268 - 8.26102i) q^{81} +(-1.54305 - 10.7321i) q^{82} +(-2.06514 - 1.32719i) q^{83} +(2.34488 - 0.688518i) q^{84} +(0.674559 - 4.69166i) q^{85} +(5.16978 - 5.96624i) q^{86} +(18.2635 - 11.7373i) q^{87} +(1.11855 + 1.29087i) q^{88} +(-8.28631 - 2.43308i) q^{89} +(4.85704 - 10.6354i) q^{90} +1.65995 q^{91} +(4.47873 + 1.71492i) q^{92} -9.45103 q^{93} +(4.50022 - 9.85411i) q^{94} +(-26.0692 - 7.65462i) q^{95} +(-1.60040 - 1.84696i) q^{96} +(0.500548 - 0.321683i) q^{97} +(-0.654861 + 0.755750i) q^{98} +(0.722570 - 5.02558i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 4 q^{2} - 4 q^{4} + 9 q^{5} + 4 q^{7} - 4 q^{8} - 8 q^{9}+O(q^{10}) \) 40 * q - 4 * q^2 - 4 * q^4 + 9 * q^5 + 4 * q^7 - 4 * q^8 - 8 * q^9	\( 40 q - 4 q^{2} - 4 q^{4} + 9 q^{5} + 4 q^{7} - 4 q^{8} - 8 q^{9} - 2 q^{10} + 6 q^{11} + 2 q^{13} + 4 q^{14} - 3 q^{15} - 4 q^{16} - 13 q^{17} - 8 q^{18} - 22 q^{19} - 2 q^{20} - 16 q^{22} - 9 q^{23} + 22 q^{24} - 15 q^{25} - 9 q^{26} + 21 q^{27} + 4 q^{28} - 10 q^{29} - 14 q^{30} - 2 q^{31} - 4 q^{32} + 8 q^{33} - 2 q^{34} + 13 q^{35} - 8 q^{36} - 45 q^{37} + 11 q^{38} - 22 q^{39} + 9 q^{40} + 21 q^{41} + 31 q^{43} + 6 q^{44} + 2 q^{45} - 9 q^{46} + 64 q^{47} - 4 q^{49} + 7 q^{50} + 65 q^{51} + 2 q^{52} + 69 q^{53} + 21 q^{54} - 74 q^{55} + 4 q^{56} - 68 q^{57} + 12 q^{58} + 48 q^{59} - 3 q^{60} + 6 q^{61} - 13 q^{62} + 8 q^{63} - 4 q^{64} - 64 q^{65} - 69 q^{66} + 31 q^{67} - 2 q^{68} - 62 q^{69} + 2 q^{70} - 57 q^{71} - 19 q^{72} + 70 q^{73} - 45 q^{74} - 11 q^{75} + 22 q^{76} - 6 q^{77} + 33 q^{78} + 34 q^{79} - 13 q^{80} + 30 q^{81} - 12 q^{82} - 56 q^{83} - 17 q^{85} + 42 q^{86} - 3 q^{87} + 6 q^{88} + 16 q^{89} + 46 q^{90} - 46 q^{91} + 24 q^{92} + 48 q^{93} + 9 q^{94} - 42 q^{95} - 36 q^{97} - 4 q^{98} + 112 q^{99}+O(q^{100}) \) 40 * q - 4 * q^2 - 4 * q^4 + 9 * q^5 + 4 * q^7 - 4 * q^8 - 8 * q^9 - 2 * q^10 + 6 * q^11 + 2 * q^13 + 4 * q^14 - 3 * q^15 - 4 * q^16 - 13 * q^17 - 8 * q^18 - 22 * q^19 - 2 * q^20 - 16 * q^22 - 9 * q^23 + 22 * q^24 - 15 * q^25 - 9 * q^26 + 21 * q^27 + 4 * q^28 - 10 * q^29 - 14 * q^30 - 2 * q^31 - 4 * q^32 + 8 * q^33 - 2 * q^34 + 13 * q^35 - 8 * q^36 - 45 * q^37 + 11 * q^38 - 22 * q^39 + 9 * q^40 + 21 * q^41 + 31 * q^43 + 6 * q^44 + 2 * q^45 - 9 * q^46 + 64 * q^47 - 4 * q^49 + 7 * q^50 + 65 * q^51 + 2 * q^52 + 69 * q^53 + 21 * q^54 - 74 * q^55 + 4 * q^56 - 68 * q^57 + 12 * q^58 + 48 * q^59 - 3 * q^60 + 6 * q^61 - 13 * q^62 + 8 * q^63 - 4 * q^64 - 64 * q^65 - 69 * q^66 + 31 * q^67 - 2 * q^68 - 62 * q^69 + 2 * q^70 - 57 * q^71 - 19 * q^72 + 70 * q^73 - 45 * q^74 - 11 * q^75 + 22 * q^76 - 6 * q^77 + 33 * q^78 + 34 * q^79 - 13 * q^80 + 30 * q^81 - 12 * q^82 - 56 * q^83 - 17 * q^85 + 42 * q^86 - 3 * q^87 + 6 * q^88 + 16 * q^89 + 46 * q^90 - 46 * q^91 + 24 * q^92 + 48 * q^93 + 9 * q^94 - 42 * q^95 - 36 * q^97 - 4 * q^98 + 112 * q^99

Introduction

L-functions

Modular forms

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Database

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