LMFDB - Embedded newform 322.2.m.a.261.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [322,2,Mod(9,322)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(322, base_ring=CyclotomicField(66))

chi = DirichletCharacter(H, H._module([22, 30]))

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

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

chi := DirichletCharacter("322.9");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 322 = 2 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	322.m (of order $33$, degree $20$, 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:	$160$
Relative dimension:	$8$ over $\Q(\zeta_{33})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{33}]$

Embedding invariants

Embedding label			261.8
Character	$\chi$	$=$	322.261
Dual form			322.2.m.a.95.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.786053 + 0.618159i) q^{2} +(1.87711 - 2.63604i) q^{3} +(0.235759 + 0.971812i) q^{4} +(-2.62021 + 0.505003i) q^{5} +(3.10500 - 0.911711i) q^{6} +(2.59333 + 0.524038i) q^{7} +(-0.415415 + 0.909632i) q^{8} +(-2.44393 - 7.06129i) q^{9} +O(q^{10})$	\(q+(0.786053 + 0.618159i) q^{2} +(1.87711 - 2.63604i) q^{3} +(0.235759 + 0.971812i) q^{4} +(-2.62021 + 0.505003i) q^{5} +(3.10500 - 0.911711i) q^{6} +(2.59333 + 0.524038i) q^{7} +(-0.415415 + 0.909632i) q^{8} +(-2.44393 - 7.06129i) q^{9} +(-2.37179 - 1.22274i) q^{10} +(3.59938 - 2.83059i) q^{11} +(3.00428 + 1.20273i) q^{12} +(0.551529 - 0.354446i) q^{13} +(1.71456 + 2.01502i) q^{14} +(-3.58722 + 7.85491i) q^{15} +(-0.888835 + 0.458227i) q^{16} +(-0.156473 - 0.149197i) q^{17} +(2.44393 - 7.06129i) q^{18} +(-5.07244 + 4.83656i) q^{19} +(-1.10850 - 2.42729i) q^{20} +(6.24937 - 5.85245i) q^{21} +4.57906 q^{22} +(3.02270 + 3.72335i) q^{23} +(1.61804 + 2.80253i) q^{24} +(1.96861 - 0.788113i) q^{25} +(0.652635 + 0.0623191i) q^{26} +(-13.8864 - 4.07740i) q^{27} +(0.102135 + 2.64378i) q^{28} +(-5.60759 + 1.64654i) q^{29} +(-7.67533 + 3.95691i) q^{30} +(1.53278 - 0.146363i) q^{31} +(-0.981929 - 0.189251i) q^{32} +(-0.705080 - 14.8014i) q^{33} +(-0.0307689 - 0.214002i) q^{34} +(-7.05971 - 0.0634460i) q^{35} +(6.28606 - 4.03981i) q^{36} +(2.48684 + 7.18527i) q^{37} +(-6.97697 + 0.666220i) q^{38} +(0.100949 - 2.11919i) q^{39} +(0.629106 - 2.59321i) q^{40} +(-6.86671 - 7.92460i) q^{41} +(8.53008 - 0.737231i) q^{42} +(4.10528 + 8.98931i) q^{43} +(3.59938 + 2.83059i) q^{44} +(9.96958 + 17.2678i) q^{45} +(0.0743811 + 4.79525i) q^{46} +(-1.35197 + 2.34168i) q^{47} +(-0.460543 + 3.20315i) q^{48} +(6.45077 + 2.71801i) q^{49} +(2.03461 + 0.597416i) q^{50} +(-0.687007 + 0.132410i) q^{51} +(0.474483 + 0.452418i) q^{52} +(-0.0962662 + 2.02088i) q^{53} +(-8.39493 - 11.7890i) q^{54} +(-8.00167 + 9.23442i) q^{55} +(-1.55399 + 2.14129i) q^{56} +(3.22781 + 22.4499i) q^{57} +(-5.42569 - 2.17212i) q^{58} +(0.895234 + 0.461525i) q^{59} +(-8.47921 - 1.63423i) q^{60} +(3.19239 + 4.48309i) q^{61} +(1.29532 + 0.832453i) q^{62} +(-2.63756 - 19.5930i) q^{63} +(-0.654861 - 0.755750i) q^{64} +(-1.26612 + 1.20725i) q^{65} +(8.59542 - 12.0706i) q^{66} +(2.42745 - 0.971803i) q^{67} +(0.108101 - 0.187237i) q^{68} +(15.4888 - 0.978800i) q^{69} +(-5.51009 - 4.41390i) q^{70} +(1.49803 - 10.4190i) q^{71} +(7.43842 + 0.710283i) q^{72} +(-0.471812 - 1.94484i) q^{73} +(-2.48684 + 7.18527i) q^{74} +(1.61781 - 6.66871i) q^{75} +(-5.89610 - 3.78919i) q^{76} +(10.8177 - 5.45444i) q^{77} +(1.38935 - 1.60339i) q^{78} +(-0.374031 - 7.85187i) q^{79} +(2.09753 - 1.64951i) q^{80} +(-19.1937 + 15.0941i) q^{81} +(-0.498932 - 10.4739i) q^{82} +(0.982708 - 1.13411i) q^{83} +(7.16082 + 4.69344i) q^{84} +(0.485337 + 0.311907i) q^{85} +(-2.32985 + 9.60379i) q^{86} +(-6.18576 + 17.8726i) q^{87} +(1.07955 + 4.44998i) q^{88} +(-12.1239 - 1.15769i) q^{89} +(-2.83764 + 19.7362i) q^{90} +(1.61604 - 0.630175i) q^{91} +(-2.90576 + 3.81530i) q^{92} +(2.49139 - 4.31521i) q^{93} +(-2.51025 + 1.00495i) q^{94} +(10.8484 - 15.2344i) q^{95} +(-2.34207 + 2.23316i) q^{96} +(-7.72205 - 8.91172i) q^{97} +(3.39048 + 6.12410i) q^{98} +(-28.7842 - 18.4985i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 160 q - 8 q^{2} + 2 q^{3} + 8 q^{4} - 2 q^{5} + 4 q^{6} + 15 q^{7} + 16 q^{8} + 28 q^{9}+O(q^{10}) $ 160 * q - 8 * q^2 + 2 * q^3 + 8 * q^4 - 2 * q^5 + 4 * q^6 + 15 * q^7 + 16 * q^8 + 28 * q^9	\( 160 q - 8 q^{2} + 2 q^{3} + 8 q^{4} - 2 q^{5} + 4 q^{6} + 15 q^{7} + 16 q^{8} + 28 q^{9} + 2 q^{10} - 8 q^{11} - 9 q^{12} - 12 q^{13} + 7 q^{14} + 4 q^{15} + 8 q^{16} - 14 q^{17} - 28 q^{18} - 2 q^{19} - 18 q^{20} + 72 q^{21} - 16 q^{22} - 22 q^{23} - 2 q^{24} - 30 q^{25} - 6 q^{26} - 70 q^{27} + 14 q^{28} - 20 q^{30} + 4 q^{31} - 8 q^{32} + 40 q^{33} - 28 q^{34} - 79 q^{35} - 12 q^{36} - 14 q^{37} - 9 q^{38} + 16 q^{39} + 2 q^{40} + 12 q^{41} + 16 q^{42} + 106 q^{43} - 8 q^{44} + 40 q^{45} - 50 q^{47} + 18 q^{48} - 55 q^{49} + 28 q^{50} - 47 q^{51} - 16 q^{52} - 4 q^{53} - 24 q^{54} - 15 q^{56} + 8 q^{57} + 22 q^{58} - 42 q^{59} - 2 q^{60} - 80 q^{61} + 8 q^{62} + 5 q^{63} - 16 q^{64} + 71 q^{65} + 4 q^{66} + 12 q^{67} + 8 q^{68} - 72 q^{70} - 112 q^{71} + 16 q^{72} - 64 q^{73} + 14 q^{74} - 126 q^{75} + 4 q^{76} - 69 q^{77} + 54 q^{78} + 52 q^{79} - 2 q^{80} - 30 q^{81} - 49 q^{82} + 26 q^{83} - q^{84} - 22 q^{85} - 46 q^{86} + 4 q^{87} - 3 q^{88} - 72 q^{89} - 8 q^{90} + 44 q^{91} + 54 q^{93} + 6 q^{94} - 58 q^{95} - 2 q^{96} + 20 q^{97} - 19 q^{98} - 264 q^{99}+O(q^{100}) \) 160 * q - 8 * q^2 + 2 * q^3 + 8 * q^4 - 2 * q^5 + 4 * q^6 + 15 * q^7 + 16 * q^8 + 28 * q^9 + 2 * q^10 - 8 * q^11 - 9 * q^12 - 12 * q^13 + 7 * q^14 + 4 * q^15 + 8 * q^16 - 14 * q^17 - 28 * q^18 - 2 * q^19 - 18 * q^20 + 72 * q^21 - 16 * q^22 - 22 * q^23 - 2 * q^24 - 30 * q^25 - 6 * q^26 - 70 * q^27 + 14 * q^28 - 20 * q^30 + 4 * q^31 - 8 * q^32 + 40 * q^33 - 28 * q^34 - 79 * q^35 - 12 * q^36 - 14 * q^37 - 9 * q^38 + 16 * q^39 + 2 * q^40 + 12 * q^41 + 16 * q^42 + 106 * q^43 - 8 * q^44 + 40 * q^45 - 50 * q^47 + 18 * q^48 - 55 * q^49 + 28 * q^50 - 47 * q^51 - 16 * q^52 - 4 * q^53 - 24 * q^54 - 15 * q^56 + 8 * q^57 + 22 * q^58 - 42 * q^59 - 2 * q^60 - 80 * q^61 + 8 * q^62 + 5 * q^63 - 16 * q^64 + 71 * q^65 + 4 * q^66 + 12 * q^67 + 8 * q^68 - 72 * q^70 - 112 * q^71 + 16 * q^72 - 64 * q^73 + 14 * q^74 - 126 * q^75 + 4 * q^76 - 69 * q^77 + 54 * q^78 + 52 * q^79 - 2 * q^80 - 30 * q^81 - 49 * q^82 + 26 * q^83 - q^84 - 22 * q^85 - 46 * q^86 + 4 * q^87 - 3 * q^88 - 72 * q^89 - 8 * q^90 + 44 * q^91 + 54 * q^93 + 6 * q^94 - 58 * q^95 - 2 * q^96 + 20 * q^97 - 19 * q^98 - 264 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$185$	$281$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{3}{11}\right)$

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 $

$2$	0.786053	+	0.618159i	0.555823	+	0.437104i
$2$	0.786053	+	0.618159i	0.555823	+	0.437104i
$3$	1.87711	−	2.63604i	1.08375	−	1.52192i	0.251229	−	0.967928i	$-0.419165\pi$
$3$	1.87711	−	2.63604i	1.08375	−	1.52192i	0.832524	−	0.553989i	$-0.186895\pi$
$4$	0.235759	+	0.971812i	0.117879	+	0.485906i
$5$	−2.62021	+	0.505003i	−1.17179	+	0.225844i	−0.737766	−	0.675056i	$-0.764119\pi$
$5$	−2.62021	+	0.505003i	−1.17179	+	0.225844i	−0.434025	+	0.900901i	$0.642907\pi$
$6$	3.10500	−	0.911711i	1.26761	−	0.372204i
$7$	2.59333	+	0.524038i	0.980188	+	0.198068i
$7$	2.59333	+	0.524038i	0.980188	+	0.198068i
$8$	−0.415415	+	0.909632i	−0.146871	+	0.321603i
$9$	−2.44393	−	7.06129i	−0.814645	−	2.35376i
$10$	−2.37179	−	1.22274i	−0.750027	−	0.386666i
$11$	3.59938	−	2.83059i	1.08525	−	0.853454i	0.0953864	−	0.995440i	$-0.469591\pi$
$11$	3.59938	−	2.83059i	1.08525	−	0.853454i	0.989869	+	0.141986i	$0.0453489\pi$
$12$	3.00428	+	1.20273i	0.867261	+	0.347199i
$13$	0.551529	−	0.354446i	0.152967	−	0.0983056i	−0.461919	−	0.886922i	$-0.652839\pi$
$13$	0.551529	−	0.354446i	0.152967	−	0.0983056i	0.614885	+	0.788617i	$0.289202\pi$
$14$	1.71456	+	2.01502i	0.458235	+	0.538535i
$15$	−3.58722	+	7.85491i	−0.926216	+	2.02813i
$16$	−0.888835	+	0.458227i	−0.222209	+	0.114557i
$17$	−0.156473	−	0.149197i	−0.0379503	−	0.0361856i	0.670867	−	0.741578i	$-0.265922\pi$
$17$	−0.156473	−	0.149197i	−0.0379503	−	0.0361856i	−0.708817	+	0.705392i	$0.750771\pi$
$18$	2.44393	−	7.06129i	0.576041	−	1.66436i
$19$	−5.07244	+	4.83656i	−1.16370	+	1.10958i	−0.171465	+	0.985190i	$0.554850\pi$
$19$	−5.07244	+	4.83656i	−1.16370	+	1.10958i	−0.992233	+	0.124394i	$0.960301\pi$
$20$	−1.10850	−	2.42729i	−0.247869	−	0.542758i
$21$	6.24937	−	5.85245i	1.36372	−	1.27711i
$22$	4.57906			0.976259
$23$	3.02270	+	3.72335i	0.630276	+	0.776371i
$23$	3.02270	+	3.72335i	0.630276	+	0.776371i
$24$	1.61804	+	2.80253i	0.330282	+	0.572065i
$25$	1.96861	−	0.788113i	0.393722	−	0.157623i
$26$	0.652635	+	0.0623191i	0.127992	+	0.0122218i
$27$	−13.8864	−	4.07740i	−2.67243	−	0.784696i
$28$	0.102135	+	2.64378i	0.0193017	+	0.499627i
$29$	−5.60759	+	1.64654i	−1.04130	+	0.305754i	−0.757299	−	0.653068i	$-0.773481\pi$
$29$	−5.60759	+	1.64654i	−1.04130	+	0.305754i	−0.284005	+	0.958823i	$0.591663\pi$
$30$	−7.67533	+	3.95691i	−1.40132	+	0.722429i
$31$	1.53278	−	0.146363i	0.275296	−	0.0262875i	0.0435048	−	0.999053i	$-0.486148\pi$
$31$	1.53278	−	0.146363i	0.275296	−	0.0262875i	0.231791	+	0.972766i	$0.425542\pi$
$32$	−0.981929	−	0.189251i	−0.173582	−	0.0334552i
$33$	−0.705080	−	14.8014i	−0.122739	−	2.57660i
$34$	−0.0307689	−	0.214002i	−0.00527682	−	0.0367011i
$35$	−7.05971	−	0.0634460i	−1.19331	−	0.0107243i
$36$	6.28606	−	4.03981i	1.04768	−	0.673301i
$37$	2.48684	+	7.18527i	0.408835	+	1.18125i	0.942109	+	0.335308i	$0.108840\pi$
$37$	2.48684	+	7.18527i	0.408835	+	1.18125i	−0.533274	+	0.845943i	$0.679039\pi$
$38$	−6.97697	+	0.666220i	−1.13181	+	0.108075i
$39$	0.100949	−	2.11919i	0.0161648	−	0.339341i
$40$	0.629106	−	2.59321i	0.0994703	−	0.410022i
$41$	−6.86671	−	7.92460i	−1.07240	−	1.23762i	−0.970060	−	0.242866i	$-0.921913\pi$
$41$	−6.86671	−	7.92460i	−1.07240	−	1.23762i	−0.102340	−	0.994750i	$-0.532633\pi$
$42$	8.53008	−	0.737231i	1.31622	−	0.113757i
$43$	4.10528	+	8.98931i	0.626049	+	1.37086i	0.911037	+	0.412325i	$0.135283\pi$
$43$	4.10528	+	8.98931i	0.626049	+	1.37086i	−0.284987	+	0.958531i	$0.591989\pi$
$44$	3.59938	+	2.83059i	0.542627	+	0.426727i
$45$	9.96958	+	17.2678i	1.48618	+	2.57414i
$46$	0.0743811	+	4.79525i	0.0109669	+	0.707022i
$47$	−1.35197	+	2.34168i	−0.197205	+	0.341569i	−0.947621	−	0.319397i	$-0.896520\pi$
$47$	−1.35197	+	2.34168i	−0.197205	+	0.341569i	0.750416	+	0.660966i	$0.229853\pi$
$48$	−0.460543	+	3.20315i	−0.0664737	+	0.462335i
$49$	6.45077	+	2.71801i	0.921538	+	0.388288i
$50$	2.03461	+	0.597416i	0.287737	+	0.0844874i
$51$	−0.687007	+	0.132410i	−0.0962002	+	0.0185411i
$52$	0.474483	+	0.452418i	0.0657989	+	0.0627391i
$53$	−0.0962662	+	2.02088i	−0.0132232	+	0.277589i	0.982566	+	0.185915i	$0.0595248\pi$
$53$	−0.0962662	+	2.02088i	−0.0132232	+	0.277589i	−0.995789	+	0.0916740i	$0.970778\pi$
$54$	−8.39493	−	11.7890i	−1.14241	−	1.60428i
$55$	−8.00167	+	9.23442i	−1.07895	+	1.24517i
$56$	−1.55399	+	2.14129i	−0.207661	+	0.286141i
$57$	3.22781	+	22.4499i	0.427534	+	2.97357i
$58$	−5.42569	−	2.17212i	−0.712428	−	0.285213i
$59$	0.895234	+	0.461525i	0.116550	+	0.0600855i	0.515515	−	0.856880i	$-0.327600\pi$
$59$	0.895234	+	0.461525i	0.116550	+	0.0600855i	−0.398966	+	0.916966i	$0.630631\pi$
$60$	−8.47921	−	1.63423i	−1.09466	−	0.210979i
$61$	3.19239	+	4.48309i	0.408744	+	0.574001i	0.966714	−	0.255861i	$-0.0823588\pi$
$61$	3.19239	+	4.48309i	0.408744	+	0.574001i	−0.557970	+	0.829861i	$0.688419\pi$
$62$	1.29532	+	0.832453i	0.164506	+	0.105722i
$63$	−2.63756	−	19.5930i	−0.332301	−	2.46848i
$64$	−0.654861	−	0.755750i	−0.0818576	−	0.0944687i
$65$	−1.26612	+	1.20725i	−0.157043	+	0.149740i
$66$	8.59542	−	12.0706i	1.05802	−	1.48578i
$67$	2.42745	−	0.971803i	0.296560	−	0.118725i	−0.218611	−	0.975812i	$-0.570153\pi$
$67$	2.42745	−	0.971803i	0.296560	−	0.118725i	0.515171	+	0.857087i	$0.327728\pi$
$68$	0.108101	−	0.187237i	0.0131092	−	0.0227058i
$69$	15.4888	−	0.978800i	1.86464	−	0.117834i
$70$	−5.51009	−	4.41390i	−0.658581	−	0.527561i
$71$	1.49803	−	10.4190i	0.177783	−	1.23651i	−0.684094	−	0.729394i	$-0.739802\pi$
$71$	1.49803	−	10.4190i	0.177783	−	1.23651i	0.861878	−	0.507116i	$-0.169289\pi$
$72$	7.43842	+	0.710283i	0.876626	+	0.0837076i
$73$	−0.471812	−	1.94484i	−0.0552214	−	0.227626i	0.937513	−	0.347949i	$-0.113122\pi$
$73$	−0.471812	−	1.94484i	−0.0552214	−	0.227626i	−0.992735	+	0.120324i	$0.961607\pi$
$74$	−2.48684	+	7.18527i	−0.289090	+	0.835270i
$75$	1.61781	−	6.66871i	0.186809	−	0.770036i
$76$	−5.89610	−	3.78919i	−0.676329	−	0.434650i
$77$	10.8177	−	5.45444i	1.23280	−	0.621591i
$78$	1.38935	−	1.60339i	0.157312	−	0.181548i
$79$	−0.374031	−	7.85187i	−0.0420817	−	0.883404i	−0.916940	−	0.399025i	$-0.869349\pi$
$79$	−0.374031	−	7.85187i	−0.0420817	−	0.883404i	0.874858	−	0.484379i	$-0.160954\pi$
$80$	2.09753	−	1.64951i	0.234511	−	0.184421i
$81$	−19.1937	+	15.0941i	−2.13263	+	1.67712i
$82$	−0.498932	−	10.4739i	−0.0550979	−	1.15665i
$83$	0.982708	−	1.13411i	0.107866	−	0.124484i	−0.699249	−	0.714878i	$-0.746482\pi$
$83$	0.982708	−	1.13411i	0.107866	−	0.124484i	0.807115	+	0.590394i	$0.201028\pi$
$84$	7.16082	+	4.69344i	0.781310	+	0.512097i
$85$	0.485337	+	0.311907i	0.0526422	+	0.0338311i
$86$	−2.32985	+	9.60379i	−0.251235	+	1.03560i
$87$	−6.18576	+	17.8726i	−0.663183	+	1.91614i
$88$	1.07955	+	4.44998i	0.115081	+	0.474370i
$89$	−12.1239	−	1.15769i	−1.28513	−	0.122715i	−0.569964	−	0.821669i	$-0.693043\pi$
$89$	−12.1239	−	1.15769i	−1.28513	−	0.122715i	−0.715166	+	0.698954i	$0.753649\pi$
$90$	−2.83764	+	19.7362i	−0.299113	+	2.08038i
$91$	1.61604	−	0.630175i	0.169407	−	0.0660603i
$92$	−2.90576	+	3.81530i	−0.302947	+	0.397773i
$93$	2.49139	−	4.31521i	0.258345	−	0.447466i
$94$	−2.51025	+	1.00495i	−0.258913	+	0.103653i
$95$	10.8484	−	15.2344i	1.11302	−	1.56302i
$96$	−2.34207	+	2.23316i	−0.239036	+	0.227920i
$97$	−7.72205	−	8.91172i	−0.784055	−	0.904848i	0.213340	−	0.976978i	$-0.431566\pi$
$97$	−7.72205	−	8.91172i	−0.784055	−	0.904848i	−0.997395	+	0.0721302i	$0.977020\pi$
$98$	3.39048	+	6.12410i	0.342490	+	0.618628i
$99$	−28.7842	−	18.4985i	−2.89292	−	1.85917i
$100$	1.23001	+	1.72731i	0.123001	+	0.172731i
$101$	−7.77969	−	1.49941i	−0.774108	−	0.149197i	−0.213126	−	0.977025i	$-0.568364\pi$
$101$	−7.77969	−	1.49941i	−0.774108	−	0.149197i	−0.560983	+	0.827828i	$0.689577\pi$
$102$	−0.621874	−	0.320599i	−0.0615747	−	0.0317440i
$103$	−2.79104	−	1.11737i	−0.275010	−	0.110097i	0.230058	−	0.973177i	$-0.426108\pi$
$103$	−2.79104	−	1.11737i	−0.275010	−	0.110097i	−0.505068	+	0.863080i	$0.668533\pi$
$104$	0.0933021	+	0.648930i	0.00914902	+	0.0636329i
$105$	−13.4191	+	18.4906i	−1.30957	+	1.80449i
$106$	−1.32489	+	1.52901i	−0.128685	+	0.148510i
$107$	3.08403	+	4.33092i	0.298145	+	0.418685i	0.936289	−	0.351232i	$-0.114237\pi$
$107$	3.08403	+	4.33092i	0.298145	+	0.418685i	−0.638144	+	0.769917i	$0.720298\pi$
$108$	0.688634	−	14.4562i	0.0662638	−	1.39105i
$109$	5.90790	+	5.63317i	0.565874	+	0.539560i	0.918097	−	0.396357i	$-0.129726\pi$
$109$	5.90790	+	5.63317i	0.565874	+	0.539560i	−0.352223	+	0.935916i	$0.614574\pi$
$110$	−11.9981	+	2.31244i	−1.14397	+	0.220482i
$111$	23.6087	+	6.93215i	2.24084	+	0.657970i
$112$	−2.54518	+	0.722551i	−0.240497	+	0.0682746i
$113$	0.798908	−	5.55653i	0.0751550	−	0.522714i	−0.917116	−	0.398621i	$-0.869489\pi$
$113$	0.798908	−	5.55653i	0.0751550	−	0.522714i	0.992271	−	0.124093i	$-0.0396021\pi$
$114$	−11.3404	+	19.6421i	−1.06213	+	1.83965i
$115$	−9.80039	−	8.22946i	−0.913891	−	0.767401i
$116$	−2.92217	−	5.06134i	−0.271316	−	0.469934i
$117$	−3.85074	−	3.02826i	−0.356001	−	0.279963i
$118$	0.418406	+	0.916181i	0.0385174	+	0.0843413i
$119$	−0.327603	−	0.468916i	−0.0300313	−	0.0429854i
$120$	−5.65489	−	6.52610i	−0.516219	−	0.595748i
$121$	2.34999	−	9.68681i	0.213636	−	0.880619i
$122$	−0.261871	+	5.49735i	−0.0237087	+	0.497707i
$123$	−33.7792	+	3.22552i	−3.04576	+	0.290835i
$124$	0.503604	+	1.45507i	0.0452250	+	0.130669i
$125$	6.46396	−	4.15413i	0.578154	−	0.371557i
$126$	10.0383	−	17.0316i	0.894285	−	1.51729i
$127$	−1.10105	−	7.65800i	−0.0977028	−	0.679538i	−0.978531	−	0.206101i	$-0.933922\pi$
$127$	−1.10105	−	7.65800i	−0.0977028	−	0.679538i	0.880828	−	0.473437i	$-0.156987\pi$
$128$	−0.0475819	−	0.998867i	−0.00420569	−	0.0882882i
$129$	31.4022	+	6.05228i	2.76481	+	0.532874i
$130$	−1.74151	+	0.166294i	−0.152740	+	0.0145849i
$131$	15.0937	−	7.78133i	1.31874	−	0.679858i	0.352092	−	0.935965i	$-0.385470\pi$
$131$	15.0937	−	7.78133i	1.31874	−	0.679858i	0.966648	+	0.256108i	$0.0824402\pi$
$132$	14.2180	−	4.17478i	1.23752	−	0.363368i
$133$	−15.6891	+	9.88467i	−1.36042	+	0.857110i
$134$	2.50883	+	0.736659i	0.216730	+	0.0636376i
$135$	38.4442	+	3.67098i	3.30875	+	0.315947i
$136$	0.200716	−	0.0803544i	0.0172112	−	0.00689034i
$137$	−5.43732	−	9.41771i	−0.464541	−	0.804609i	0.534639	−	0.845080i	$-0.320448\pi$
$137$	−5.43732	−	9.41771i	−0.464541	−	0.804609i	−0.999181	+	0.0404710i	$0.987114\pi$
$138$	12.7801	+	8.80517i	1.08791	+	0.749546i
$139$	−1.31447			−0.111492			−0.0557461	−	0.998445i	$-0.517754\pi$
$139$	−1.31447			−0.111492			−0.0557461	+	0.998445i	$0.517754\pi$
$140$	−1.60273	−	6.87567i	−0.135456	−	0.581100i
$141$	3.63496	+	7.95945i	0.306119	+	0.670306i
$142$	7.61814	−	7.26388i	0.639300	−	0.609571i
$143$	0.981874	−	2.83694i	0.0821084	−	0.237237i
$144$	5.40792	+	5.15645i	0.450660	+	0.429704i
$145$	13.8615	−	7.14612i	1.15114	−	0.593453i
$146$	0.831349	−	1.82040i	0.0688029	−	0.150657i
$147$	19.2736	−	11.9024i	1.58966	−	0.981697i
$148$	−6.39643	+	4.11073i	−0.525783	+	0.337900i
$149$	−13.8940	−	5.56232i	−1.13824	−	0.455683i	−0.275485	−	0.961305i	$-0.588839\pi$
$149$	−13.8940	−	5.56232i	−1.13824	−	0.455683i	−0.862755	+	0.505623i	$0.831263\pi$
$150$	5.39401	−	4.24189i	0.440419	−	0.346349i
$151$	1.94279	+	1.00158i	0.158102	+	0.0815071i	0.535462	−	0.844560i	$-0.320138\pi$
$151$	1.94279	+	1.00158i	0.158102	+	0.0815071i	−0.377360	+	0.926067i	$0.623168\pi$
$152$	−2.29232	−	6.62324i	−0.185932	−	0.537215i
$153$	−0.671112	+	1.46953i	−0.0542562	+	0.118804i
$154$	11.8750	+	2.39960i	0.956917	+	0.193366i
$155$	−3.94229	+	1.15756i	−0.316652	+	0.0929774i
$156$	2.08325	−	0.401513i	0.166793	−	0.0321468i
$157$	−1.65553	−	6.82421i	−0.132126	−	0.544631i	−0.998941	−	0.0460016i	$-0.985352\pi$
$157$	−1.65553	−	6.82421i	−0.132126	−	0.544631i	0.866815	−	0.498629i	$-0.166163\pi$
$158$	4.55970	−	6.40320i	0.362750	−	0.509411i
$159$	5.14640	+	4.04718i	0.408136	+	0.320962i
$160$	2.66843			0.210958
$161$	5.88769	+	11.2399i	0.464015	+	0.885827i
$162$	−24.4178			−1.91844
$163$	−13.5228	−	10.6345i	−1.05919	−	0.832956i	−0.0727949	−	0.997347i	$-0.523192\pi$
$163$	−13.5228	−	10.6345i	−1.05919	−	0.832956i	−0.986395	+	0.164391i	$0.947434\pi$
$164$	6.08233	−	8.54144i	0.474950	−	0.666975i
$165$	9.32223	+	38.4268i	0.725735	+	2.99152i
$166$	1.47352	−	0.283997i	0.114367	−	0.0220425i
$167$	−1.56978	+	0.460928i	−0.121473	+	0.0356677i	−0.341904	−	0.939735i	$-0.611072\pi$
$167$	−1.56978	+	0.460928i	−0.121473	+	0.0356677i	0.220431	+	0.975403i	$0.429254\pi$
$168$	2.72749	+	8.11582i	0.210431	+	0.626149i
$169$	−5.22184	+	11.4342i	−0.401680	+	0.879557i
$170$	0.188693	+	0.545191i	0.0144721	+	0.0418143i
$171$	46.5491	+	23.9977i	3.55970	+	1.83515i
$172$	−7.76806	+	6.10887i	−0.592309	+	0.465797i
$173$	21.3251	+	8.53728i	1.62132	+	0.649077i	0.991787	−	0.127900i	$-0.0408235\pi$
$173$	21.3251	+	8.53728i	1.62132	+	0.649077i	0.629529	+	0.776977i	$0.283248\pi$
$174$	−15.9104	+	10.2250i	−1.20617	+	0.775156i
$175$	5.51827	−	1.01221i	0.417142	−	0.0765161i
$176$	−1.90221	+	4.16526i	−0.143384	+	0.313968i
$177$	2.89706	−	1.49354i	0.217756	−	0.112261i
$178$	−8.81439	−	8.40450i	−0.660666	−	0.629944i
$179$	2.31536	−	6.68980i	0.173058	−	0.500019i	−0.824800	−	0.565424i	$-0.808713\pi$
$179$	2.31536	−	6.68980i	0.173058	−	0.500019i	0.997859	+	0.0654045i	$0.0208338\pi$
$180$	−14.4307	+	13.7596i	−1.07560	+	1.02558i
$181$	5.57704	+	12.2120i	0.414538	+	0.907712i	0.995587	+	0.0938432i	$0.0299152\pi$
$181$	5.57704	+	12.2120i	0.414538	+	0.907712i	−0.581049	+	0.813869i	$0.697357\pi$
$182$	1.65984	+	0.503620i	0.123036	+	0.0373308i
$183$	17.8101			1.31656
$184$	−4.64255	+	1.20281i	−0.342253	+	0.0886722i
$185$	−10.1446	−	17.5710i	−0.745848	−	1.29185i
$186$	4.62585	−	1.85191i	0.339183	−	0.135789i
$187$	−0.985522	−	0.0941060i	−0.0720685	−	0.00688171i
$188$	−2.59441	−	0.761788i	−0.189217	−	0.0555591i
$189$	−33.8752	−	17.8510i	−2.46406	−	1.29847i
$190$	17.9447	−	5.26903i	1.30184	−	0.382256i
$191$	−12.3691	+	6.37673i	−0.894999	+	0.461404i	−0.843414	−	0.537265i	$-0.819458\pi$
$191$	−12.3691	+	6.37673i	−0.894999	+	0.461404i	−0.0515852	+	0.998669i	$0.516427\pi$
$192$	−3.22143	+	0.307610i	−0.232487	+	0.0221998i
$193$	5.03557	+	0.970527i	0.362469	+	0.0698601i	0.367234	−	0.930129i	$-0.380305\pi$
$193$	5.03557	+	0.970527i	0.362469	+	0.0698601i	−0.00476550	+	0.999989i	$0.501517\pi$
$194$	−0.561081	−	11.7785i	−0.0402833	−	0.845650i
$195$	0.805688	+	5.60368i	0.0576965	+	0.401288i
$196$	−1.12057	+	6.90973i	−0.0800408	+	0.493552i
$197$	−0.323955	+	0.208193i	−0.0230808	+	0.0148331i	−0.552130	−	0.833758i	$-0.686185\pi$
$197$	−0.323955	+	0.208193i	−0.0230808	+	0.0148331i	0.529050	+	0.848591i	$0.322549\pi$
$198$	−11.1909	−	32.3340i	−0.795304	−	2.29788i
$199$	12.1406	−	1.15928i	0.860621	−	0.0821794i	0.344594	−	0.938752i	$-0.388017\pi$
$199$	12.1406	−	1.15928i	0.860621	−	0.0821794i	0.516027	+	0.856572i	$0.327410\pi$
$200$	−0.100898	+	2.11810i	−0.00713455	+	0.149773i
$201$	1.99488	−	8.22302i	0.140708	−	0.580007i
$202$	−5.18838	−	5.98771i	−0.365053	−	0.421293i
$203$	−15.4052	+	1.33143i	−1.08123	+	0.0934480i
$204$	−0.290645	−	0.636425i	−0.0203492	−	0.0445586i
$205$	21.9941	+	17.2964i	1.53614	+	1.20803i
$206$	−1.50320	−	2.60362i	−0.104733	−	0.181403i
$207$	18.9043	−	30.4437i	1.31394	−	2.11599i
$208$	−0.327802	+	0.567769i	−0.0227290	+	0.0393677i
$209$	−4.56735	+	31.7666i	−0.315930	+	2.19734i
$210$	−21.9783	+	6.23941i	−1.51664	+	0.430561i
$211$	20.7269	+	6.08598i	1.42690	+	0.418976i	0.901833	−	0.432084i	$-0.142222\pi$
$211$	20.7269	+	6.08598i	1.42690	+	0.418976i	0.525068	+	0.851060i	$0.324040\pi$
$212$	−1.98661	+	0.382887i	−0.136441	+	0.0262968i
$213$	−24.6530	−	23.5065i	−1.68919	−	1.61064i
$214$	−0.252982	+	5.31075i	−0.0172935	+	0.363035i
$215$	−15.2963	−	21.4807i	−1.04320	−	1.46497i
$216$	9.47753	−	10.9377i	0.644865	−	0.744213i
$217$	4.05171	+	0.423668i	0.275048	+	0.0287605i
$218$	1.16173	+	8.07999i	0.0786821	+	0.547246i
$219$	−6.01231	−	2.40697i	−0.406274	−	0.162648i
$220$	−10.8606	−	5.59902i	−0.732220	−	0.377486i
$221$	−0.139182	−	0.0268251i	−0.00936238	−	0.00180445i
$222$	14.2725	+	20.0430i	0.957910	+	1.34520i
$223$	−11.9998	−	7.71180i	−0.803566	−	0.516421i	0.0732116	−	0.997316i	$-0.476675\pi$
$223$	−11.9998	−	7.71180i	−0.803566	−	0.516421i	−0.876778	+	0.480896i	$0.840312\pi$
$224$	−2.44729	−	1.00536i	−0.163517	−	0.0671734i
$225$	−10.3762	−	11.9748i	−0.691750	−	0.798322i
$226$	4.06280	−	3.87387i	0.270254	−	0.257686i
$227$	−14.2457	+	20.0052i	−0.945518	+	1.32779i	−0.000768274		1.00000i	$0.500245\pi$
$227$	−14.2457	+	20.0052i	−0.945518	+	1.32779i	−0.944749	+	0.327794i	$0.893695\pi$
$228$	−21.0561	+	8.42960i	−1.39448	+	0.558264i
$229$	−2.70506	+	4.68530i	−0.178755	+	0.309613i	−0.941454	−	0.337140i	$-0.890540\pi$
$229$	−2.70506	+	4.68530i	−0.178755	+	0.309613i	0.762699	+	0.646753i	$0.223874\pi$
$230$	−2.61651	−	12.5270i	−0.172528	−	0.826005i
$231$	5.92802	−	38.7546i	0.390035	−	2.54986i
$232$	0.831735	−	5.78484i	0.0546061	−	0.379794i
$233$	−3.58169	−	0.342010i	−0.234644	−	0.0224058i	−0.0229286	−	0.999737i	$-0.507299\pi$
$233$	−3.58169	−	0.342010i	−0.234644	−	0.0224058i	−0.211716	+	0.977331i	$0.567905\pi$
$234$	−1.15494	−	4.76075i	−0.0755011	−	0.311220i
$235$	2.35988	−	6.81843i	0.153942	−	0.444786i
$236$	−0.237456	+	0.978808i	−0.0154571	+	0.0637150i
$237$	−21.3999	−	13.7529i	−1.39007	−	0.893346i
$238$	0.0323514	−	0.571103i	0.00209703	−	0.0370191i
$239$	12.9433	−	14.9374i	0.837233	−	0.966219i	−0.162557	−	0.986699i	$-0.551974\pi$
$239$	12.9433	−	14.9374i	0.837233	−	0.966219i	0.999790	+	0.0204805i	$0.00651960\pi$
$240$	−0.410882	−	8.62548i	−0.0265223	−	0.556772i
$241$	6.46038	−	5.08050i	0.416149	−	0.327263i	−0.388034	−	0.921645i	$-0.626846\pi$
$241$	6.46038	−	5.08050i	0.416149	−	0.327263i	0.804183	+	0.594382i	$0.202603\pi$
$242$	7.83521	−	6.16167i	0.503666	−	0.396087i
$243$	1.69393	+	35.5600i	0.108666	+	2.28118i
$244$	−3.60408	+	4.15933i	−0.230728	+	0.266274i
$245$	−18.2749	−	3.86410i	−1.16754	−	0.246868i
$246$	−28.5461	−	18.3455i	−1.82003	−	1.16966i
$247$	−1.08330	+	4.46541i	−0.0689285	+	0.284127i
$248$	−0.503604	+	1.45507i	−0.0319789	+	0.0923969i
$249$	−1.14489	−	4.71930i	−0.0725544	−	0.299073i
$250$	7.64893	+	0.730384i	0.483761	+	0.0461935i
$251$	0.424961	−	2.95567i	0.0268233	−	0.186560i	−0.972005	−	0.234961i	$-0.924504\pi$
$251$	0.424961	−	2.95567i	0.0268233	−	0.186560i	0.998828	+	0.0484015i	$0.0154127\pi$
$252$	18.4189	−	7.18243i	1.16028	−	0.452451i
$253$	21.4191	+	4.84574i	1.34661	+	0.304649i
$254$	3.86838	−	6.70022i	0.242723	−	0.420409i
$255$	1.73323	−	0.693882i	0.108539	−	0.0434526i
$256$	0.580057	−	0.814576i	0.0362536	−	0.0509110i
$257$	−1.91792	+	1.82874i	−0.119637	+	0.114073i	−0.747536	−	0.664221i	$-0.768763\pi$
$257$	−1.91792	+	1.82874i	−0.119637	+	0.114073i	0.627900	+	0.778294i	$0.283915\pi$
$258$	20.9425	+	24.1690i	1.30383	+	1.50470i
$259$	2.68386	+	19.9370i	0.166767	+	1.23882i
$260$	−1.47171	−	0.945814i	−0.0912719	−	0.0586569i
$261$	25.3313	+	35.5728i	1.56797	+	2.20190i
$262$	16.6745	+	3.21375i	1.03016	+	0.198546i
$263$	−15.8287	−	8.16025i	−0.976038	−	0.503183i	−0.105039	−	0.994468i	$-0.533497\pi$
$263$	−15.8287	−	8.16025i	−0.976038	−	0.503183i	−0.870999	+	0.491286i	$0.836527\pi$
$264$	13.7568	+	5.50738i	0.846671	+	0.338956i
$265$	−0.768312	−	5.34373i	−0.0471970	−	0.328263i
$266$	−18.4428	−	1.92847i	−1.13080	−	0.118242i
$267$	−25.8097	+	29.7859i	−1.57953	+	1.82287i
$268$	1.51670	+	2.12991i	0.0926473	+	0.130105i
$269$	−0.00426917	+	0.0896209i	−0.000260296	+	0.00546428i	−0.998994	−	0.0448496i	$-0.985719\pi$
$269$	−0.00426917	+	0.0896209i	−0.000260296	+	0.00546428i	0.998733	+	0.0503139i	$0.0160222\pi$
$270$	27.9499	+	26.6502i	1.70098	+	1.62188i
$271$	−22.4199	+	4.32107i	−1.36191	+	0.262487i	−0.817304	−	0.576206i	$-0.804533\pi$
$271$	−22.4199	+	4.32107i	−1.36191	+	0.262487i	−0.544605	+	0.838693i	$0.683320\pi$
$272$	0.207445	+	0.0609114i	0.0125782	+	0.00369329i
$273$	1.37233	−	5.44286i	0.0830572	−	0.329417i
$274$	1.54762	−	10.7639i	0.0934953	−	0.650274i
$275$	4.85496	−	8.40904i	0.292765	−	0.507084i
$276$	4.60284	+	14.8215i	0.277058	+	0.892147i
$277$	10.7952	+	18.6978i	0.648621	+	1.12344i	0.983452	+	0.181167i	$0.0579873\pi$
$277$	10.7952	+	18.6978i	0.648621	+	1.12344i	−0.334831	+	0.942278i	$0.608679\pi$
$278$	−1.03325	−	0.812554i	−0.0619700	−	0.0487337i
$279$	−4.77953	−	10.4657i	−0.286143	−	0.626565i
$280$	2.99042	−	6.39538i	0.178712	−	0.382197i
$281$	16.8691	+	19.4680i	1.00633	+	1.16136i	0.986864	+	0.161552i	$0.0516501\pi$
$281$	16.8691	+	19.4680i	1.00633	+	1.16136i	0.0194626	+	0.999811i	$0.493804\pi$
$282$	−2.06293	+	8.50353i	−0.122846	+	0.506378i
$283$	0.299269	−	6.28243i	0.0177897	−	0.373452i	−0.972364	−	0.233469i	$-0.924992\pi$
$283$	0.299269	−	6.28243i	0.0177897	−	0.373452i	0.990154	−	0.139983i	$-0.0447047\pi$
$284$	10.4785	−	1.00057i	0.621784	−	0.0593732i
$285$	−19.7948	−	57.1934i	−1.17254	−	3.38784i
$286$	2.52548	−	1.62303i	0.149335	−	0.0959717i
$287$	−13.6549	−	24.1496i	−0.806022	−	1.42550i
$288$	1.06341	+	7.39620i	0.0626622	+	0.435825i
$289$	−0.806668	−	16.9341i	−0.0474511	−	0.996121i
$290$	15.3133	+	2.95141i	0.899231	+	0.173313i
$291$	−37.9868	+	3.62730i	−2.22682	+	0.212636i
$292$	1.77878	−	0.917025i	0.104095	−	0.0536648i
$293$	6.35377	−	1.86563i	0.371191	−	0.108992i	−0.0908162	−	0.995868i	$-0.528948\pi$
$293$	6.35377	−	1.86563i	0.371191	−	0.108992i	0.462007	+	0.886876i	$0.347129\pi$
$294$	22.5077	+	2.55820i	1.31267	+	0.149197i
$295$	−2.57877	−	0.757195i	−0.150142	−	0.0440856i
$296$	−7.56902	−	0.722754i	−0.439940	−	0.0420092i
$297$	−61.5238	+	24.6304i	−3.56997	+	1.42920i
$298$	−7.48302	−	12.9610i	−0.433480	−	0.750809i
$299$	2.98683	+	0.982149i	0.172733	+	0.0567992i
$300$	6.86214			0.396186
$301$	5.93562	+	25.4636i	0.342123	+	1.46770i
$302$	0.908001	+	1.98824i	0.0522496	+	0.114411i
$303$	−18.5559	+	17.6930i	−1.06601	+	1.01644i
$304$	2.29232	−	6.62324i	0.131474	−	0.379869i
$305$	−10.6287	−	10.1344i	−0.608598	−	0.580297i
$306$	−1.43593	+	0.740275i	−0.0820868	+	0.0423187i
$307$	2.70279	−	5.91829i	0.154257	−	0.337775i	−0.816688	−	0.577080i	$-0.804192\pi$
$307$	2.70279	−	5.91829i	0.154257	−	0.337775i	0.970945	+	0.239305i	$0.0769195\pi$
$308$	7.85107	+	9.22687i	0.447356	+	0.525750i
$309$	−8.18453	+	5.25987i	−0.465601	+	0.299224i
$310$	−3.81440	−	1.52706i	−0.216644	−	0.0867310i
$311$	−23.7745	+	18.6964i	−1.34813	+	1.06018i	−0.356060	+	0.934463i	$0.615880\pi$
$311$	−23.7745	+	18.6964i	−1.34813	+	1.06018i	−0.992066	+	0.125715i	$0.959878\pi$
$312$	1.88574	+	0.972169i	0.106759	+	0.0550382i
$313$	−5.04750	−	14.5838i	−0.285302	−	0.824325i	−0.993032	−	0.117843i	$-0.962402\pi$
$313$	−5.04750	−	14.5838i	−0.285302	−	0.824325i	0.707731	−	0.706482i	$-0.249719\pi$
$314$	2.91711	−	6.38757i	0.164622	−	0.360472i
$315$	16.8055	+	50.0057i	0.946880	+	2.81750i
$316$	7.54236	−	2.21464i	0.424291	−	0.124583i
$317$	14.1191	−	2.72124i	0.793009	−	0.152840i	0.223369	−	0.974734i	$-0.428295\pi$
$317$	14.1191	−	2.72124i	0.793009	−	0.152840i	0.569640	+	0.821894i	$0.307082\pi$
$318$	1.54355	+	6.36259i	0.0865579	+	0.356796i
$319$	−15.5232	+	21.7993i	−0.869133	+	1.22053i
$320$	2.09753	+	1.64951i	0.117255	+	0.0922106i
$321$	17.2055			0.960319
$322$	−2.32000	+	12.4747i	−0.129289	+	0.695187i
$323$	1.51530			0.0843137
$324$	−19.1937	−	15.0941i	−1.06632	−	0.838560i
$325$	0.806402	−	1.13243i	0.0447311	−	0.0628161i
$326$	−4.05587	−	16.7185i	−0.224634	−	0.925953i
$327$	25.9390	−	4.99934i	1.43443	−	0.276464i
$328$	10.0610	−	2.95418i	0.555526	−	0.163117i
$329$	−4.73324	+	5.36428i	−0.260952	+	0.295742i
$330$	−16.4261	+	35.9681i	−0.904226	+	1.97998i
$331$	−0.141958	−	0.410162i	−0.00780274	−	0.0225445i	0.941032	−	0.338317i	$-0.109858\pi$
$331$	−0.141958	−	0.410162i	−0.00780274	−	0.0225445i	−0.948835	+	0.315772i	$0.897736\pi$
$332$	1.33382	+	0.687631i	0.0732028	+	0.0377387i
$333$	44.6595	−	35.1206i	2.44733	−	1.92460i
$334$	−1.51885	−	0.608057i	−0.0831080	−	0.0332714i
$335$	−5.86964	+	3.77219i	−0.320693	+	0.206097i
$336$	−2.87291	+	8.06549i	−0.156730	+	0.440009i
$337$	9.77798	−	21.4108i	0.532641	−	1.16632i	−0.431788	−	0.901975i	$-0.642117\pi$
$337$	9.77798	−	21.4108i	0.532641	−	1.16632i	0.964428	−	0.264345i	$-0.0851557\pi$
$338$	−11.1728	+	5.75999i	−0.607722	+	0.313302i
$339$	−13.1476	−	12.5362i	−0.714078	−	0.680872i
$340$	−0.188693	+	0.545191i	−0.0102333	+	0.0295671i
$341$	5.10277	−	4.86548i	0.276331	−	0.263481i
$342$	21.7556	+	47.6382i	1.17641	+	2.57598i
$343$	15.3047	+	10.4292i	0.826374	+	0.563122i
$344$	−9.88236			−0.532821
$345$	−40.0896	+	10.3866i	−2.15835	+	0.559194i
$346$	11.4853	+	19.8930i	0.617451	+	1.06946i
$347$	3.34876	−	1.34064i	0.179771	−	0.0719694i	−0.280031	−	0.959991i	$-0.590345\pi$
$347$	3.34876	−	1.34064i	0.179771	−	0.0719694i	0.459802	+	0.888022i	$0.347920\pi$
$348$	−18.8271	−	1.79777i	−1.00924	−	0.0963707i
$349$	19.7663	+	5.80391i	1.05807	+	0.310676i	0.764072	−	0.645131i	$-0.223197\pi$
$349$	19.7663	+	5.80391i	1.05807	+	0.310676i	0.293994	+	0.955807i	$0.405015\pi$
$350$	4.96336	+	2.61551i	0.265303	+	0.139805i
$351$	−9.10394	+	2.67316i	−0.485933	+	0.142683i
$352$	−4.07003	+	2.09825i	−0.216933	+	0.111837i
$353$	31.8311	−	3.03950i	1.69420	−	0.161776i	0.797172	−	0.603753i	$-0.206329\pi$
$353$	31.8311	−	3.03950i	1.69420	−	0.161776i	0.897027	+	0.441977i	$0.145723\pi$
$354$	3.20048	+	0.616842i	0.170104	+	0.0327848i
$355$	1.33649	+	28.0565i	0.0709338	+	1.48908i
$356$	−1.73326	−	12.0551i	−0.0918625	−	0.638918i
$357$	−1.85103	−	0.0166353i	−0.0979667	−	0.000880433i
$358$	5.95536	−	3.82728i	0.314751	−	0.202278i
$359$	1.41555	+	4.08997i	0.0747099	+	0.215860i	0.976172	−	0.216998i	$-0.0696264\pi$
$359$	1.41555	+	4.08997i	0.0747099	+	0.215860i	−0.901462	+	0.432858i	$0.857505\pi$
$360$	−19.8489	+	1.89534i	−1.04613	+	0.0998931i
$361$	1.43326	−	30.0879i	0.0754349	−	1.58357i
$362$	−3.16512	+	13.0468i	−0.166355	+	0.685724i
$363$	−21.1236	−	24.3779i	−1.10870	−	1.27951i
$364$	0.993408	+	1.42192i	0.0520687	+	0.0745288i
$365$	2.21839	+	4.85761i	0.116116	+	0.254259i
$366$	13.9997	+	11.0095i	0.731775	+	0.575474i
$367$	−1.78688	−	3.09497i	−0.0932744	−	0.161556i	0.815613	−	0.578598i	$-0.196400\pi$
$367$	−1.78688	−	3.09497i	−0.0932744	−	0.161556i	−0.908887	+	0.417042i	$0.863067\pi$
$368$	−4.39282	−	1.92436i	−0.228991	−	0.100314i
$369$	−39.1761	+	67.8550i	−2.03943	+	3.53239i
$370$	2.88746	−	20.0827i	0.150112	−	1.04405i
$371$	−1.30867	+	5.19036i	−0.0679426	+	0.269470i
$372$	4.78094	+	1.40381i	0.247880	+	0.0727841i
$373$	−2.63936	+	0.508696i	−0.136661	+	0.0263393i	−0.257123	−	0.966379i	$-0.582775\pi$
$373$	−2.63936	+	0.508696i	−0.136661	+	0.0263393i	0.120462	+	0.992718i	$0.461562\pi$
$374$	−0.716500	−	0.683182i	−0.0370494	−	0.0353265i
$375$	1.18313	−	24.8370i	0.0610967	−	1.28258i
$376$	−1.56844	−	2.20256i	−0.0808861	−	0.113589i
$377$	−2.50914	+	2.89570i	−0.129227	+	0.149136i
$378$	−15.5930	−	34.9722i	−0.802015	−	1.79877i
$379$	−1.13716	−	7.90914i	−0.0584121	−	0.406265i	−0.997960	−	0.0638469i	$-0.979663\pi$
$379$	−1.13716	−	7.90914i	−0.0584121	−	0.406265i	0.939548	−	0.342418i	$-0.111246\pi$
$380$	17.3626	+	6.95092i	0.890680	+	0.356575i
$381$	−22.2536	−	11.4725i	−1.14009	−	0.587755i
$382$	−13.6646	−	2.63364i	−0.699143	−	0.134749i
$383$	5.12150	+	7.19214i	0.261696	+	0.367501i	0.924428	−	0.381355i	$-0.124543\pi$
$383$	5.12150	+	7.19214i	0.261696	+	0.367501i	−0.662732	+	0.748856i	$0.730603\pi$
$384$	−2.72237	−	1.74956i	−0.138925	−	0.0892819i
$385$	−25.5902	+	19.7548i	−1.30420	+	1.00680i
$386$	3.35829	+	3.87567i	0.170932	+	0.197267i
$387$	53.4430	−	50.9578i	2.71666	−	2.59033i
$388$	6.83997	−	9.60539i	0.347247	−	0.487640i
$389$	−1.69073	+	0.676867i	−0.0857236	+	0.0343185i	−0.414128	−	0.910219i	$-0.635913\pi$
$389$	−1.69073	+	0.676867i	−0.0857236	+	0.0343185i	0.328404	+	0.944537i	$0.393489\pi$
$390$	−2.83065	+	4.90284i	−0.143336	+	0.248265i
$391$	0.0825405	−	1.03358i	0.00417425	−	0.0522705i
$392$	−5.15214	+	4.73872i	−0.260222	+	0.239342i
$393$	7.82067	−	54.3939i	0.394500	−	2.74381i
$394$	−0.383342	−	0.0366047i	−0.0193125	−	0.00184412i
$395$	4.94526	+	20.3846i	0.248823	+	1.02566i
$396$	11.1909	−	32.3340i	0.562365	−	1.62485i
$397$	−2.89846	+	11.9476i	−0.145469	+	0.599633i	0.851672	+	0.524075i	$0.175589\pi$
$397$	−2.89846	+	11.9476i	−0.145469	+	0.599633i	−0.997141	+	0.0755580i	$0.975926\pi$
$398$	10.2597	+	6.59354i	0.514274	+	0.330504i
$399$	−3.39383	+	59.9117i	−0.169904	+	2.99934i
$400$	−1.38864	+	1.60257i	−0.0694318	+	0.0801286i
$401$	0.0385561	+	0.809393i	0.00192540	+	0.0404191i	0.999626	−	0.0273626i	$-0.00871087\pi$
$401$	0.0385561	+	0.809393i	0.00192540	+	0.0404191i	−0.997700	+	0.0677817i	$0.978408\pi$
$402$	6.65122	−	5.23058i	0.331733	−	0.260877i
$403$	0.793495	−	0.624011i	0.0395268	−	0.0310842i
$404$	−0.376985	−	7.91390i	−0.0187557	−	0.393731i
$405$	42.6689	−	49.2425i	2.12023	−	2.44688i
$406$	−12.9324	−	8.47630i	−0.641822	−	0.420672i
$407$	29.2896	+	18.8233i	1.45183	+	0.933036i
$408$	0.164949	−	0.679929i	0.00816619	−	0.0336615i
$409$	5.39918	−	15.5999i	0.266972	−	0.771366i	−0.729228	−	0.684271i	$-0.760120\pi$
$409$	5.39918	−	15.5999i	0.266972	−	0.771366i	0.996200	−	0.0870948i	$-0.0277583\pi$
$410$	6.59665	+	27.1918i	0.325785	+	1.34290i
$411$	−35.0319	−	3.34514i	−1.72800	−	0.165004i
$412$	0.427855	−	2.97580i	0.0210789	−	0.146607i
$413$	2.07979	+	1.66603i	0.102340	+	0.0819798i
$414$	33.6789	−	12.2445i	1.65523	−	0.601785i
$415$	−2.00217	+	3.46786i	−0.0982826	+	0.170231i
$416$	−0.608641	+	0.243663i	−0.0298411	+	0.0119466i
$417$	−2.46742	+	3.46500i	−0.120830	+	0.169682i
$418$	−23.2270	+	22.1469i	−1.13607	+	1.08324i
$419$	−12.0355	−	13.8897i	−0.587973	−	0.678557i	0.381326	−	0.924441i	$-0.375467\pi$
$419$	−12.0355	−	13.8897i	−0.587973	−	0.678557i	−0.969299	+	0.245883i	$0.920922\pi$
$420$	−21.1330	−	8.68155i	−1.03119	−	0.423616i
$421$	−24.8890	−	15.9952i	−1.21302	−	0.779558i	−0.231855	−	0.972750i	$-0.574480\pi$
$421$	−24.8890	−	15.9952i	−1.21302	−	0.779558i	−0.981161	+	0.193192i	$0.938116\pi$
$422$	12.5304	+	17.5964i	0.609969	+	0.856582i
$423$	19.8394	+	3.82373i	0.964625	+	0.185916i
$424$	−1.79826	−	0.927069i	−0.0873314	−	0.0450225i
$425$	−0.425619	−	0.170392i	−0.0206456	−	0.00826523i
$426$	−4.84775	−	33.7168i	−0.234874	−	1.63359i
$427$	5.92963	+	13.2991i	0.286955	+	0.643588i
$428$	−3.48175	+	4.01815i	−0.168297	+	0.194225i
$429$	−5.63519	−	7.91351i	−0.272069	−	0.382068i
$430$	1.25475	−	26.3405i	0.0605095	−	1.27025i
$431$	−7.92360	−	7.55514i	−0.381667	−	0.363918i	0.474824	−	0.880081i	$-0.342512\pi$
$431$	−7.92360	−	7.55514i	−0.381667	−	0.363918i	−0.856491	+	0.516162i	$0.827360\pi$
$432$	14.2111	−	2.73896i	0.683730	−	0.131778i
$433$	27.9414	+	8.20435i	1.34278	+	0.394276i	0.872661	−	0.488327i	$-0.162393\pi$
$433$	27.9414	+	8.20435i	1.34278	+	0.394276i	0.470119	+	0.882603i	$0.344211\pi$
$434$	2.92297	+	2.83763i	0.140307	+	0.136211i
$435$	7.18225	−	49.9536i	0.344363	−	2.39509i
$436$	−4.08154	+	7.06943i	−0.195470	+	0.338564i
$437$	−33.3407	−	4.26699i	−1.59490	−	0.204118i
$438$	−3.23811	−	5.60856i	−0.154723	−	0.267988i
$439$	17.0250	+	13.3886i	0.812559	+	0.639003i	0.935467	−	0.353415i	$-0.114980\pi$
$439$	17.0250	+	13.3886i	0.812559	+	0.639003i	−0.122908	+	0.992418i	$0.539222\pi$
$440$	−5.07591	−	11.1147i	−0.241985	−	0.529872i
$441$	3.42742	−	52.1934i	0.163210	−	2.48540i
$442$	−0.0928221	−	0.107122i	−0.00441510	−	0.00509529i
$443$	−6.32758	+	26.0826i	−0.300632	+	1.23922i	0.598349	+	0.801236i	$0.295824\pi$
$443$	−6.32758	+	26.0826i	−0.300632	+	1.23922i	−0.898981	+	0.437987i	$0.855692\pi$
$444$	−1.17077	+	24.5775i	−0.0555624	+	1.16640i
$445$	32.3517	−	3.08922i	1.53362	−	0.146443i
$446$	−4.66536	−	13.4797i	−0.220911	−	0.638281i
$447$	−40.7431	+	26.1840i	−1.92708	+	1.23846i
$448$	−1.30223	−	2.30308i	−0.0615246	−	0.108810i
$449$	5.95144	+	41.3932i	0.280866	+	1.95347i	0.300867	+	0.953666i	$0.402724\pi$
$449$	5.95144	+	41.3932i	0.280866	+	1.95347i	−0.0200012	+	0.999800i	$0.506367\pi$
$450$	−0.753934	−	15.8270i	−0.0355408	−	0.746093i
$451$	−47.1472	−	9.08688i	−2.22007	−	0.427884i
$452$	5.58825	−	0.533613i	0.262849	−	0.0250990i
$453$	6.28703	−	3.24119i	0.295390	−	0.152284i
$454$	−23.5643	+	6.91909i	−1.10593	+	0.324729i
$455$	−3.91612	+	2.46729i	−0.183591	+	0.115669i
$456$	−21.7621	−	6.38992i	−1.01910	−	0.299235i
$457$	−39.6558	−	3.78667i	−1.85502	−	0.177133i	−0.892991	−	0.450075i	$-0.851397\pi$
$457$	−39.6558	−	3.78667i	−1.85502	−	0.177133i	−0.962030	+	0.272942i	$0.912003\pi$
$458$	−5.02258	+	2.01074i	−0.234690	+	0.0939555i
$459$	1.56451	+	2.70981i	0.0730250	+	0.126483i
$460$	5.68695	−	11.4643i	0.265156	−	0.534526i
$461$	−36.1953			−1.68578			−0.842892	−	0.538082i	$-0.819149\pi$
$461$	−36.1953			−1.68578			−0.842892	+	0.538082i	$0.819149\pi$
$462$	28.6162	−	26.7987i	1.33135	−	1.24679i
$463$	7.34050	+	16.0735i	0.341142	+	0.746997i	0.999986	−	0.00528283i	$-0.00168159\pi$
$463$	7.34050	+	16.0735i	0.341142	+	0.746997i	−0.658844	+	0.752280i	$0.728954\pi$
$464$	4.22974	−	4.03305i	0.196361	−	0.187230i
$465$	−4.34875	+	12.5649i	−0.201668	+	0.582683i
$466$	−2.60398	−	2.48289i	−0.120627	−	0.115018i
$467$	−0.831534	+	0.428685i	−0.0384788	+	0.0198372i	−0.477359	−	0.878709i	$-0.658406\pi$
$467$	−0.831534	+	0.428685i	−0.0384788	+	0.0198372i	0.438880	+	0.898546i	$0.355375\pi$
$468$	2.03505	−	4.45614i	0.0940702	−	0.205985i
$469$	6.80444	−	1.24813i	0.314200	−	0.0576335i
$470$	6.06987	−	3.90087i	0.279982	−	0.179934i
$471$	−21.0965	−	8.44576i	−0.972075	−	0.389160i
$472$	−0.791712	+	0.622609i	−0.0364415	+	0.0286579i
$473$	40.2215	+	20.7356i	1.84939	+	0.953425i
$474$	−8.32000	−	24.0391i	−0.382150	−	1.10415i
$475$	−6.17390	+	13.5190i	−0.283278	+	0.620293i
$476$	0.378462	−	0.428919i	0.0173468	−	0.0196595i
$477$	14.5053	−	4.25913i	0.664150	−	0.195012i
$478$	19.4078	−	3.74055i	0.887692	−	0.171089i
$479$	2.55351	+	10.5257i	0.116673	+	0.480931i	0.999928	+	0.0120382i	$0.00383196\pi$
$479$	2.55351	+	10.5257i	0.116673	+	0.480931i	−0.883255	+	0.468893i	$0.844653\pi$
$480$	5.00894	−	7.03408i	0.228626	−	0.321060i
$481$	3.91836	+	3.08143i	0.178662	+	0.140501i
$482$	8.21875			0.374354
$483$	40.6806	+	5.57838i	1.85103	+	0.253825i
$484$	9.96778			0.453081
$485$	24.7338	+	19.4509i	1.12310	+	0.883219i
$486$	−20.6502	+	28.9992i	−0.936713	+	1.31543i
$487$	−9.11999	−	37.5931i	−0.413266	−	1.70351i	−0.674537	−	0.738241i	$-0.735657\pi$
$487$	−9.11999	−	37.5931i	−0.413266	−	1.70351i	0.261270	−	0.965266i	$-0.415859\pi$
$488$	−5.40413	+	1.04156i	−0.244634	+	0.0471492i
$489$	−53.4168	+	15.6846i	−2.41559	+	0.709281i
$490$	−11.9765	−	14.3342i	−0.541041	−	0.647553i
$491$	8.31744	−	18.2127i	0.375361	−	0.821926i	−0.623824	−	0.781565i	$-0.714422\pi$
$491$	8.31744	−	18.2127i	0.375361	−	0.821926i	0.999185	−	0.0403610i	$-0.0128508\pi$
$492$	−11.0983	−	32.0665i	−0.500351	−	1.44567i
$493$	1.12310	+	0.578997i	0.0505818	+	0.0260767i
$494$	−3.61186	+	2.84040i	−0.162505	+	0.127796i
$495$	84.7624	+	33.9338i	3.80979	+	1.52521i
$496$	−1.29532	+	0.832453i	−0.0581617	+	0.0373783i
$497$	9.34485	−	26.2350i	0.419174	−	1.17680i
$498$	2.01733	−	4.41734i	0.0903989	−	0.197946i
$499$	−16.6044	+	8.56016i	−0.743315	+	0.383206i	−0.787903	−	0.615800i	$-0.788833\pi$
$499$	−16.6044	+	8.56016i	−0.743315	+	0.383206i	0.0445874	+	0.999005i	$0.485803\pi$
$500$	5.56097	+	5.30237i	0.248694	+	0.237129i
$501$	−1.73163	+	5.00320i	−0.0773633	+	0.223527i
$502$	2.16111	−	2.06062i	0.0964552	−	0.0919698i
$503$	−2.19915	−	4.81546i	−0.0980550	−	0.214711i	0.854247	−	0.519867i	$-0.174019\pi$
$503$	−2.19915	−	4.81546i	−0.0980550	−	0.214711i	−0.952302	+	0.305156i	$0.901291\pi$
$504$	18.9181	+	5.74002i	0.842679	+	0.255681i
$505$	21.1416			0.940789
$506$	13.8411	+	17.0494i	0.615312	+	0.757939i
$507$	20.3391	+	35.2284i	0.903291	+	1.56455i
$508$	7.18255	−	2.87546i	0.318674	−	0.127578i
$509$	−7.89278	−	0.753669i	−0.349841	−	0.0334058i	−0.0813436	−	0.996686i	$-0.525921\pi$
$509$	−7.89278	−	0.753669i	−0.349841	−	0.0334058i	−0.268498	+	0.963280i	$0.586527\pi$
$510$	1.79134	+	0.525985i	0.0793220	+	0.0232910i
$511$	−0.204398	−	5.29086i	−0.00904203	−	0.234054i
$512$	0.959493	−	0.281733i	0.0424040	−	0.0124509i
$513$	90.1583	−	46.4799i	3.98059	−	2.05214i
$514$	−2.63804	+	0.251902i	−0.116359	+	0.0111109i
$515$	7.87738	+	1.51824i	0.347119	+	0.0669017i
$516$	1.52168	+	31.9439i	0.0669881	+	1.40625i
$517$	1.76207	+	12.2555i	0.0774958	+	0.538995i
$518$	−10.2146	+	17.3306i	−0.448803	+	0.761463i
$519$	62.5342	−	40.1883i	2.74495	−	1.76407i
$520$	−0.572183	−	1.65321i	−0.0250919	−	0.0724982i
$521$	17.1960	−	1.64202i	0.753372	−	0.0719383i	0.288698	−	0.957420i	$-0.406778\pi$
$521$	17.1960	−	1.64202i	0.753372	−	0.0719383i	0.464674	+	0.885482i	$0.346172\pi$
$522$	−2.07792	+	43.6209i	−0.0909480	+	1.90923i
$523$	−2.90920	+	11.9919i	−0.127210	+	0.524369i	0.872171	+	0.489201i	$0.162712\pi$
$523$	−2.90920	+	11.9919i	−0.127210	+	0.524369i	−0.999381	+	0.0351675i	$0.988804\pi$
$524$	11.1205	+	12.8337i	0.485799	+	0.560642i
$525$	7.69019	−	16.4464i	0.335627	−	0.717780i
$526$	−7.39785	−	16.1990i	−0.322562	−	0.706311i
$527$	−0.261676	−	0.205784i	−0.0113988	−	0.00896411i
$528$	7.40911	+	12.8330i	0.322440	+	0.558483i
$529$	−4.72660	+	22.5091i	−0.205504	+	0.978656i
$530$	2.69934	−	4.67539i	0.117252	−	0.203086i
$531$	1.07107	−	7.44944i	0.0464804	−	0.323278i
$532$	−13.3049	−	12.9164i	−0.576840	−	0.559998i
$533$	−6.59603	−	1.93677i	−0.285706	−	0.0838908i
$534$	−38.7002	+	7.45885i	−1.67472	+	0.322776i
$535$	−10.2679	−	9.79044i	−0.443921	−	0.423278i
$536$	−0.124415	+	2.61178i	−0.00537389	+	0.112812i
$537$	−13.2884	−	18.6609i	−0.573436	−	0.805278i
$538$	−0.0587557	+	0.0678077i	−0.00253314	+	0.00292340i
$539$	30.9124	−	8.47628i	1.33149	−	0.365099i
$540$	5.49607	+	38.2260i	0.236513	+	1.64498i
$541$	−22.5372	−	9.02252i	−0.968948	−	0.387908i	−0.167434	−	0.985883i	$-0.553548\pi$
$541$	−22.5372	−	9.02252i	−0.968948	−	0.387908i	−0.801515	+	0.597975i	$0.795972\pi$
$542$	−20.2943	−	10.4624i	−0.871715	−	0.449400i
$543$	42.6601	+	8.22206i	1.83072	+	0.352842i
$544$	0.125410	+	0.176114i	0.00537690	+	0.00755081i
$545$	−18.3247	−	11.7765i	−0.784943	−	0.504452i
$546$	4.44328	−	3.43006i	0.190155	−	0.146793i
$547$	−16.3833	−	18.9074i	−0.700501	−	0.808422i	0.288319	−	0.957534i	$-0.406904\pi$
$547$	−16.3833	−	18.9074i	−0.700501	−	0.808422i	−0.988820	+	0.149113i	$0.952358\pi$
$548$	7.87034	−	7.50436i	0.336204	−	0.320570i
$549$	23.8544	−	33.4988i	1.01808	−	1.42969i
$550$	9.01438	−	3.60881i	0.384375	−	0.153880i
$551$	20.4806	−	35.4735i	0.872503	−	1.51122i
$552$	−5.54394	+	14.4957i	−0.235966	+	0.616980i
$553$	3.14469	−	20.5585i	0.133726	−	0.874238i
$554$	−3.07264	+	21.3707i	−0.130544	+	0.907952i
$555$	−65.3605	−	6.24117i	−2.77440	−	0.264923i
$556$	−0.309899	−	1.27742i	−0.0131426	−	0.0541747i
$557$	−7.32777	+	21.1722i	−0.310488	+	0.897095i	0.676520	+	0.736424i	$0.263487\pi$
$557$	−7.32777	+	21.1722i	−0.310488	+	0.897095i	−0.987008	+	0.160671i	$0.948634\pi$
$558$	2.71251	−	11.1811i	0.114830	−	0.473334i
$559$	5.45040	+	3.50276i	0.230528	+	0.148151i
$560$	6.30399	−	3.17855i	0.266392	−	0.134318i
$561$	−2.09800	+	2.42123i	−0.0885778	+	0.102224i
$562$	1.22570	+	25.7307i	0.0517031	+	1.08538i
$563$	−11.3797	+	8.94912i	−0.479599	+	0.377161i	−0.828491	−	0.560002i	$-0.810800\pi$
$563$	−11.3797	+	8.94912i	−0.479599	+	0.377161i	0.348892	+	0.937163i	$0.386558\pi$
$564$	−6.87811	+	5.40900i	−0.289621	+	0.227760i
$565$	0.712761	+	14.9627i	0.0299861	+	0.629486i
$566$	4.11878	−	4.75333i	0.173125	−	0.199797i
$567$	−57.6855	+	29.0858i	−2.42257	+	1.22149i
$568$	8.85517	+	5.69087i	0.371555	+	0.238784i
$569$	5.07590	−	20.9231i	0.212793	−	0.877144i	−0.760825	−	0.648958i	$-0.775205\pi$
$569$	5.07590	−	20.9231i	0.212793	−	0.877144i	0.973617	−	0.228186i	$-0.0732796\pi$
$570$	19.7948	−	57.1934i	0.829114	−	2.39557i
$571$	5.00554	+	20.6331i	0.209475	+	0.863470i	0.975383	+	0.220519i	$0.0707750\pi$
$571$	5.00554	+	20.6331i	0.209475	+	0.863470i	−0.765907	+	0.642951i	$0.777710\pi$
$572$	2.98845	+	0.285363i	0.124954	+	0.0119316i
$573$	−6.40897	+	44.5753i	−0.267738	+	1.86216i
$574$	4.19482	−	27.4237i	0.175088	−	1.14464i
$575$	8.88493	+	4.94759i	0.370527	+	0.206329i
$576$	−3.73613	+	6.47116i	−0.155672	+	0.269632i
$577$	23.3437	−	9.34542i	0.971812	−	0.389055i	0.169217	−	0.985579i	$-0.445876\pi$
$577$	23.3437	−	9.34542i	0.971812	−	0.389055i	0.802595	+	0.596524i	$0.203452\pi$
$578$	9.83385	−	13.8097i	0.409034	−	0.574408i
$579$	12.0107	−	11.4522i	0.499147	−	0.475936i
$580$	10.2127	+	11.7860i	0.424058	+	0.489389i
$581$	3.14280	−	2.42614i	0.130385	−	0.100653i
$582$	−32.1019	−	20.6306i	−1.33067	−	0.855167i
$583$	5.37377	+	7.54640i	0.222559	+	0.312540i
$584$	1.96508	+	0.378739i	0.0813157	+	0.0156723i
$585$	11.6190	+	5.99002i	0.480388	+	0.247657i
$586$	6.14766	+	2.46115i	0.253957	+	0.101669i
$587$	−1.70060	−	11.8279i	−0.0701911	−	0.488190i	−0.994347	−	0.106175i	$-0.966139\pi$
$587$	−1.70060	−	11.8279i	−0.0701911	−	0.488190i	0.924156	−	0.382015i	$-0.124770\pi$
$588$	16.1109	+	15.9242i	0.664401	+	0.656703i
$589$	−7.06705	+	8.15581i	−0.291193	+	0.336054i
$590$	−1.55898	−	2.18929i	−0.0641823	−	0.0901315i
$591$	−0.0592952	+	1.24476i	−0.00243908	+	0.0512026i
$592$	−5.50287	−	5.24698i	−0.226167	−	0.215650i
$593$	42.7662	−	8.24252i	1.75620	−	0.338480i	0.793401	−	0.608700i	$-0.208309\pi$
$593$	42.7662	−	8.24252i	1.75620	−	0.338480i	0.962799	+	0.270220i	$0.0870964\pi$
$594$	−63.5864	−	18.6707i	−2.60898	−	0.766067i
$595$	1.09519	+	1.06322i	0.0448984	+	0.0435876i
$596$	2.12989	−	14.8137i	0.0872437	−	0.606793i
$597$	19.7333	−	34.1791i	0.807630	−	1.39886i
$598$	1.74068	+	2.61836i	0.0711818	+	0.107073i
$599$	−5.04320	−	8.73507i	−0.206059	−	0.356905i	0.744410	−	0.667722i	$-0.232731\pi$
$599$	−5.04320	−	8.73507i	−0.206059	−	0.356905i	−0.950470	+	0.310817i	$0.899397\pi$
$600$	5.39401	+	4.24189i	0.220209	+	0.173175i
$601$	−3.48584	−	7.63293i	−0.142190	−	0.311354i	0.825116	−	0.564963i	$-0.191110\pi$
$601$	−3.48584	−	7.63293i	−0.142190	−	0.311354i	−0.967307	+	0.253609i	$0.918382\pi$
$602$	−11.0748	+	23.6849i	−0.451377	+	0.965325i
$603$	−12.7947	−	14.7659i	−0.521040	−	0.601312i
$604$	−0.515314	+	2.12415i	−0.0209678	+	0.0864306i
$605$	−1.26560	+	26.5682i	−0.0514539	+	1.08015i
$606$	−25.5230	+	2.43715i	−1.03680	+	0.0990025i
$607$	15.1688	+	43.8275i	0.615684	+	1.77890i	0.627065	+	0.778967i	$0.284256\pi$
$607$	15.1688	+	43.8275i	0.615684	+	1.77890i	−0.0113815	+	0.999935i	$0.503623\pi$
$608$	5.89610	−	3.78919i	0.239119	−	0.153672i
$609$	−25.4077	+	43.1080i	−1.02957	+	1.74682i
$610$	−2.09003	−	14.5364i	−0.0846227	−	0.588563i
$611$	0.0843491	+	1.77070i	0.00341240	+	0.0716350i
$612$	−1.58633	−	0.305739i	−0.0641235	−	0.0123588i
$613$	−1.22722	+	0.117185i	−0.0495668	+	0.00473306i	−0.119810	−	0.992797i	$-0.538229\pi$
$613$	−1.22722	+	0.117185i	−0.0495668	+	0.00473306i	0.0702432	+	0.997530i	$0.477622\pi$
$614$	5.78299	−	2.98134i	0.233382	−	0.120317i
$615$	86.8794	−	25.5101i	3.50332	−	1.02867i
$616$	0.467683	+	12.1060i	0.0188435	+	0.487766i
$617$	−37.8414	−	11.1112i	−1.52344	−	0.447322i	−0.590403	−	0.807108i	$-0.701031\pi$
$617$	−37.8414	−	11.1112i	−1.52344	−	0.447322i	−0.933035	+	0.359787i	$0.882850\pi$
$618$	−9.68491	−	0.924797i	−0.389584	−	0.0372008i
$619$	−42.1999	+	16.8943i	−1.69616	+	0.679039i	−0.999272	−	0.0381446i	$-0.987855\pi$
$619$	−42.1999	+	16.8943i	−1.69616	+	0.679039i	−0.696885	+	0.717183i	$0.745431\pi$
$620$	−2.05436	−	3.55826i	−0.0825051	−	0.142903i
$621$	−26.7927	−	64.0284i	−1.07515	−	2.56937i
$622$	−30.2454			−1.21273
$623$	−30.8346	−	9.35567i	−1.23536	−	0.374827i
$624$	0.881340	+	1.92987i	0.0352818	+	0.0772565i
$625$	−22.5125	+	21.4656i	−0.900498	+	0.858623i
$626$	5.04750	−	14.5838i	0.201739	−	0.582886i
$627$	75.1646	+	71.6693i	3.00179	+	2.86220i
$628$	6.24154	−	3.21774i	0.249064	−	0.128402i
$629$	0.682895	−	1.49533i	0.0272288	−	0.0596228i
$630$	−17.7015	+	49.6956i	−0.705244	+	1.97992i
$631$	−40.3969	+	25.9615i	−1.60818	+	1.03351i	−0.645168	+	0.764041i	$0.723213\pi$
$631$	−40.3969	+	25.9615i	−1.60818	+	1.03351i	−0.963008	+	0.269471i	$0.913151\pi$
$632$	7.29769	+	2.92155i	0.290286	+	0.116213i
$633$	54.9497	−	43.2129i	2.18405	−	1.71756i
$634$	12.7805	+	6.58883i	0.507580	+	0.261676i
$635$	6.75230	+	19.5095i	0.267957	+	0.774211i
$636$	−2.71978	+	5.95549i	−0.107846	+	0.236151i
$637$	4.52117	−	0.787386i	0.179135	−	0.0311974i
$638$	−25.6775	+	7.53960i	−1.01658	+	0.298495i
$639$	−77.2327	+	14.8854i	−3.05528	+	0.588857i
$640$	0.629106	+	2.59321i	0.0248676	+	0.102506i
$641$	−19.8402	+	27.8617i	−0.783642	+	1.10047i	0.208824	+	0.977953i	$0.433036\pi$
$641$	−19.8402	+	27.8617i	−0.783642	+	1.10047i	−0.992466	+	0.122518i	$0.960903\pi$
$642$	13.5245	+	10.6358i	0.533768	+	0.419760i
$643$	−26.0529			−1.02743			−0.513713	−	0.857962i	$-0.671730\pi$
$643$	−26.0529			−1.02743			−0.513713	+	0.857962i	$0.671730\pi$
$644$	−9.53498	+	8.37163i	−0.375731	+	0.329888i
$645$	−85.3367			−3.36013
$646$	1.19111	+	0.936698i	0.0468635	+	0.0368539i
$647$	1.24927	−	1.75436i	0.0491139	−	0.0689709i	−0.789289	−	0.614022i	$-0.789550\pi$
$647$	1.24927	−	1.75436i	0.0491139	−	0.0689709i	0.838403	+	0.545051i	$0.183490\pi$
$648$	−5.75672	−	23.7295i	−0.226145	−	0.932183i
$649$	4.52868	−	0.872831i	0.177766	−	0.0342616i
$650$	1.33390	−	0.391668i	0.0523198	−	0.0153625i
$651$	8.72233	−	9.88519i	0.341855	−	0.387431i
$652$	7.14658	−	15.6488i	0.279882	−	0.612855i
$653$	−7.73410	−	22.3462i	−0.302659	−	0.874475i	−0.989094	−	0.147284i	$-0.952947\pi$
$653$	−7.73410	−	22.3462i	−0.302659	−	0.874475i	0.686436	−	0.727191i	$-0.259174\pi$
$654$	23.4798	+	12.1047i	0.918135	+	0.473331i
$655$	−35.6189	+	28.0110i	−1.39175	+	1.09448i
$656$	9.73464	+	3.89716i	0.380074	+	0.152159i
$657$	−12.5800	+	8.08465i	−0.490791	+	0.315412i
$658$	−7.03655	+	1.29071i	−0.274313	+	0.0503172i
$659$	3.85224	−	8.43523i	0.150062	−	0.328590i	−0.819641	−	0.572878i	$-0.805827\pi$
$659$	3.85224	−	8.43523i	0.150062	−	0.328590i	0.969703	+	0.244288i	$0.0785542\pi$
$660$	−35.1458	+	18.1189i	−1.36805	+	0.705277i
$661$	4.48556	+	4.27697i	0.174468	+	0.166355i	0.772282	−	0.635280i	$-0.219115\pi$
$661$	4.48556	+	4.27697i	0.174468	+	0.166355i	−0.597814	+	0.801635i	$0.703964\pi$
$662$	0.141958	−	0.410162i	0.00551737	−	0.0159414i
$663$	−0.331972	+	0.316535i	−0.0128927	+	0.0122932i
$664$	0.623387	+	1.36503i	0.0241921	+	0.0529733i
$665$	36.1168	−	33.8229i	1.40055	−	1.31160i
$666$	56.8149			2.20153
$667$	−23.0807	−	15.9020i	−0.893688	−	0.615729i
$668$	−0.818024	−	1.41686i	−0.0316503	−	0.0548199i
$669$	−42.8536	+	17.1560i	−1.65682	+	0.663289i
$670$	−6.94567	−	0.663231i	−0.268334	−	0.0256228i
$671$	24.1804	+	7.10001i	0.933475	+	0.274093i
$672$	−7.24402	+	4.56399i	−0.279444	+	0.176060i
$673$	22.9150	−	6.72845i	0.883308	−	0.259363i	0.191542	−	0.981484i	$-0.438651\pi$
$673$	22.9150	−	6.72845i	0.883308	−	0.259363i	0.691766	+	0.722122i	$0.256833\pi$
$674$	20.9213	−	10.7857i	0.805858	−	0.415449i
$675$	−30.5503	+	2.91720i	−1.17588	+	0.112283i
$676$	−12.3430	−	2.37892i	−0.474732	−	0.0914970i
$677$	1.40194	+	29.4303i	0.0538808	+	1.13110i	0.850281	+	0.526328i	$0.176432\pi$
$677$	1.40194	+	29.4303i	0.0538808	+	1.13110i	−0.796400	+	0.604770i	$0.793265\pi$
$678$	−2.58534	−	17.9814i	−0.0992892	−	0.690572i
$679$	−15.3558	−	27.1577i	−0.589300	−	1.04222i
$680$	−0.485337	+	0.311907i	−0.0186118	+	0.0119611i
$681$	25.9938	+	75.1042i	0.996085	+	2.87800i
$682$	7.01869	−	0.670204i	0.268760	−	0.0256634i
$683$	0.356209	−	7.47776i	0.0136300	−	0.286128i	−0.981754	−	0.190156i	$-0.939101\pi$
$683$	0.356209	−	7.47776i	0.0136300	−	0.286128i	0.995384	−	0.0959729i	$-0.0305962\pi$
$684$	−12.3469	+	50.8946i	−0.472095	+	1.94600i
$685$	19.0029	+	21.9305i	0.726062	+	0.837921i
$686$	5.58339	+	17.6586i	0.213175	+	0.674208i
$687$	7.27292	+	15.9255i	0.277479	+	0.607595i
$688$	−7.76806	−	6.10887i	−0.296154	−	0.232898i
$689$	0.663198	+	1.14869i	0.0252658	+	0.0437617i
$690$	−37.9331	−	16.6174i	−1.44409	−	0.632612i
$691$	16.7246	−	28.9678i	0.636233	−	1.10199i	−0.350020	−	0.936742i	$-0.613825\pi$
$691$	16.7246	−	28.9678i	0.636233	−	1.10199i	0.986253	−	0.165245i	$-0.0528416\pi$
$692$	−3.26904	+	22.7367i	−0.124270	+	0.864320i
$693$	−64.9532	−	63.0569i	−2.46737	−	2.39533i
$694$	3.46103	+	1.01625i	0.131379	+	0.0385763i
$695$	3.44419	−	0.663814i	0.130646	−	0.0251799i
$696$	−13.6878	−	13.0513i	−0.518835	−	0.494708i
$697$	−0.107871	+	2.26448i	−0.00408589	+	0.0857733i
$698$	11.9496	+	16.7809i	0.452300	+	0.635166i
$699$	−7.62479	+	8.79948i	−0.288396	+	0.332827i
$700$	2.28466	+	5.12408i	0.0863520	+	0.193672i
$701$	4.72036	+	32.8308i	0.178286	+	1.24000i	0.860728	+	0.509064i	$0.170008\pi$
$701$	4.72036	+	32.8308i	0.178286	+	1.24000i	−0.682443	+	0.730939i	$0.739082\pi$
$702$	−8.80862	−	3.52644i	−0.332460	−	0.133097i
$703$	−47.3664	−	24.4191i	−1.78646	−	0.920982i
$704$	−4.49631	−	0.866593i	−0.169461	−	0.0326609i
$705$	−13.5439	−	19.0197i	−0.510092	−	0.716324i
$706$	26.8998	+	17.2875i	1.01239	+	0.650622i
$707$	−19.3896	−	7.96534i	−0.729221	−	0.299567i
$708$	2.13444	+	2.46328i	0.0802172	+	0.0925756i
$709$	25.7771	−	24.5784i	0.968080	−	0.923063i	−0.0289879	−	0.999580i	$-0.509228\pi$
$709$	25.7771	−	24.5784i	0.968080	−	0.923063i	0.997068	+	0.0765170i	$0.0243799\pi$
$710$	−16.2928	+	22.8800i	−0.611458	+	0.858673i
$711$	−54.5302	+	21.8306i	−2.04504	+	0.818711i
$712$	6.08952	−	10.5474i	0.228215	−	0.395279i
$713$	5.17809	+	5.26466i	0.193921	+	0.197163i
$714$	−1.44472	−	1.15731i	−0.0540674	−	0.0433111i
$715$	−1.14005	+	7.92921i	−0.0426354	+	0.296536i
$716$	7.04710	+	0.672916i	0.263362	+	0.0251481i
$717$	−15.0794	−	62.1582i	−0.563151	−	2.32134i
$718$	−1.41555	+	4.08997i	−0.0528279	+	0.152636i
$719$	−5.58501	+	23.0217i	−0.208286	+	0.858565i	0.767714	+	0.640793i	$0.221394\pi$
$719$	−5.58501	+	23.0217i	−0.208286	+	0.858565i	−0.976000	+	0.217772i	$0.930121\pi$
$720$	−16.7739	−	10.7799i	−0.625126	−	0.401744i
$721$	−6.65257	−	4.36032i	−0.247755	−	0.162387i
$722$	19.7257	−	22.7647i	0.734115	−	0.847214i
$723$	−1.26552	−	26.5665i	−0.0470651	−	0.988017i
$724$	−10.5529	+	8.29892i	−0.392197	+	0.308427i
$725$	−9.74151	+	7.66081i	−0.361791	+	0.284515i
$726$	−1.53483	−	32.2201i	−0.0569629	−	1.19580i
$727$	12.1727	−	14.0481i	0.451461	−	0.521014i	−0.483701	−	0.875233i	$-0.660708\pi$
$727$	12.1727	−	14.0481i	0.451461	−	0.521014i	0.935162	+	0.354219i	$0.115253\pi$
$728$	−0.0981009	+	1.73179i	−0.00363586	+	0.0641843i
$729$	35.2925	+	22.6811i	1.30713	+	0.840042i
$730$	−1.25900	+	5.18966i	−0.0465976	+	0.192078i
$731$	0.698811	−	2.01908i	0.0258465	−	0.0746784i
$732$	4.19889	+	17.3080i	0.155195	+	0.639724i
$733$	9.18727	+	0.877278i	0.339339	+	0.0324030i	0.263335	−	0.964704i	$-0.415178\pi$
$733$	9.18727	+	0.877278i	0.339339	+	0.0324030i	0.0760046	+	0.997107i	$0.475784\pi$
$734$	0.508599	−	3.53738i	0.0187727	−	0.130567i
$735$	−44.4901	+	40.9201i	−1.64104	+	1.50936i
$736$	−2.26343	−	4.22811i	−0.0834310	−	0.155850i
$737$	5.98654	−	10.3690i	0.220517	−	0.381946i
$738$	−72.7397	+	29.1206i	−2.67758	+	1.07194i
$739$	16.4821	−	23.1459i	0.606305	−	0.851436i	−0.391325	−	0.920253i	$-0.627983\pi$
$739$	16.4821	−	23.1459i	0.606305	−	0.851436i	0.997629	+	0.0688169i	$0.0219224\pi$
$740$	14.6840	−	14.0012i	0.539795	−	0.514694i
$741$	9.73752	+	11.2377i	0.357717	+	0.412827i
$742$	−4.23715	+	3.27094i	−0.155551	+	0.120080i
$743$	38.7273	+	24.8885i	1.42077	+	0.913070i	0.999983	+	0.00590881i	$0.00188084\pi$
$743$	38.7273	+	24.8885i	1.42077	+	0.913070i	0.420783	+	0.907162i	$0.361756\pi$
$744$	2.89029	+	4.05885i	0.105963	+	0.148805i
$745$	39.2141	+	7.55790i	1.43669	+	0.276900i
$746$	−2.38913	−	1.23168i	−0.0874724	−	0.0450952i
$747$	−10.4099	−	4.16750i	−0.380879	−	0.152481i
$748$	−0.140892	−	0.979928i	−0.00515154	−	0.0358297i
$749$	5.72836	+	12.8477i	0.209310	+	0.469443i
$750$	16.2832	−	18.7918i	0.594579	−	0.686181i
$751$	7.58519	+	10.6519i	0.276788	+	0.388694i	0.929446	−	0.368959i	$-0.120286\pi$
$751$	7.58519	+	10.6519i	0.276788	+	0.388694i	−0.652658	+	0.757653i	$0.726346\pi$
$752$	0.128659	−	2.70088i	0.00469170	−	0.0984909i
$753$	−6.99355	−	6.66833i	−0.254859	−	0.243008i
$754$	−3.76232	+	0.725128i	−0.137016	+	0.0264076i
$755$	−5.59630	−	1.64322i	−0.203670	−	0.0598030i
$756$	9.36146	−	37.1289i	0.340473	−	1.35037i
$757$	2.47533	−	17.2163i	0.0899675	−	0.625738i	−0.894090	−	0.447887i	$-0.852177\pi$
$757$	2.47533	−	17.2163i	0.0899675	−	0.625738i	0.984058	−	0.177850i	$-0.0569143\pi$
$758$	3.99524	−	6.91995i	0.145114	−	0.251344i
$759$	52.9797	−	47.3655i	1.92304	−	1.71926i
$760$	9.35112	+	16.1966i	0.339201	+	0.587513i
$761$	28.2072	+	22.1824i	1.02251	+	0.804111i	0.980800	−	0.195019i	$-0.0624767\pi$
$761$	28.2072	+	22.1824i	1.02251	+	0.804111i	0.0417110	+	0.999130i	$0.486719\pi$
$762$	−10.4007	−	22.7743i	−0.376776	−	0.825025i
$763$	12.3692	+	17.7046i	0.447793	+	0.640951i
$764$	−9.11311	−	10.5171i	−0.329701	−	0.380495i
$765$	1.01633	−	4.18939i	0.0367456	−	0.151468i
$766$	−0.420115	+	8.81930i	−0.0151794	+	0.318654i
$767$	0.657333	−	0.0627677i	0.0237349	−	0.00226641i
$768$	−1.05842	−	3.05810i	−0.0381924	−	0.110350i
$769$	20.4223	−	13.1246i	0.736446	−	0.473285i	−0.117877	−	0.993028i	$-0.537609\pi$
$769$	20.4223	−	13.1246i	0.736446	−	0.473285i	0.854322	+	0.519743i	$0.173972\pi$
$770$	−32.3268	−	0.290523i	−1.16498	−	0.0104697i
$771$	1.22046	+	8.48846i	0.0439537	+	0.305704i
$772$	0.244012	+	5.12244i	0.00878218	+	0.184361i
$773$	−32.2909	−	6.22357i	−1.16142	−	0.223846i	−0.428104	−	0.903729i	$-0.640818\pi$
$773$	−32.2909	−	6.22357i	−1.16142	−	0.223846i	−0.733320	+	0.679883i	$0.762030\pi$
$774$	73.5091	−	7.01927i	2.64223	−	0.252302i
$775$	2.90210	−	1.49614i	0.104246	−	0.0537428i
$776$	11.3142	−	3.32216i	0.406157	−	0.119259i
$777$	57.5926	+	30.3493i	2.06612	+	1.08877i
$778$	−1.74742	−	0.513088i	−0.0626480	−	0.0183951i
$779$	73.1588	+	6.98582i	2.62119	+	0.250293i
$780$	−5.25578	+	2.10410i	−0.188187	+	0.0753387i
$781$	−24.1000	−	41.7423i	−0.862364	−	1.49366i
$782$	0.703799	−	0.761427i	0.0251678	−	0.0272286i
$783$	84.5826			3.02274
$784$	−6.97914	+	0.540046i	−0.249255	+	0.0192874i
$785$	7.78409	+	17.0448i	0.277826	+	0.608354i
$786$	39.7716	−	37.9221i	1.41860	−	1.35264i
$787$	1.12601	−	3.25339i	0.0401379	−	0.115971i	−0.923151	−	0.384437i	$-0.874396\pi$
$787$	1.12601	−	3.25339i	0.0401379	−	0.115971i	0.963289	+	0.268466i	$0.0865168\pi$
$788$	−0.278700	−	0.265740i	−0.00992827	−	0.00946658i
$789$	−51.2230	+	26.4073i	−1.82359	+	0.940124i
$790$	−8.71370	+	19.0804i	−0.310020	+	0.678848i
$791$	4.98367	−	13.9913i	0.177199	−	0.497473i
$792$	28.7842	−	18.4985i	1.02280	−	0.657316i
$793$	3.34971	+	1.34102i	0.118952	+	0.0476211i
$794$	−9.66386	+	7.59975i	−0.342958	+	0.269705i
$795$	−15.5285	−	8.00549i	−0.550738	−	0.283925i
$796$	3.98885	+	11.5250i	0.141381	+	0.408494i
$797$	3.08462	−	6.75438i	0.109263	−	0.239252i	−0.847100	−	0.531433i	$-0.821654\pi$
$797$	3.08462	−	6.75438i	0.109263	−	0.239252i	0.956363	+	0.292181i	$0.0943809\pi$
$798$	−39.7027	+	44.9958i	−1.40546	+	1.59284i
$799$	0.560919	−	0.164701i	0.0198439	−	0.00582669i
$800$	−2.08219	+	0.401309i	−0.0736164	+	0.0141884i
$801$	21.4552	+	88.4396i	0.758083	+	3.12486i
$802$	−0.470026	+	0.660059i	−0.0165972	+	0.0233075i
$803$	−7.20326	−	5.66471i	−0.254198	−	0.199903i
$804$	8.46154			0.298416
$805$	−21.1031	−	26.4775i	−0.743788	−	0.933210i
$806$	1.00947			0.0355570
$807$	0.228230	+	0.179482i	0.00803409	+	0.00631808i
$808$	4.59572	−	6.45378i	0.161677	−	0.227043i
$809$	5.56798	+	22.9515i	0.195760	+	0.806933i	0.981980	+	0.188986i	$0.0605202\pi$
$809$	5.56798	+	22.9515i	0.195760	+	0.806933i	−0.786220	+	0.617947i	$0.787965\pi$
$810$	63.9797	−	12.3311i	2.24802	−	0.433270i
$811$	31.0030	−	9.10330i	1.08866	−	0.319660i	0.312323	−	0.949976i	$-0.398893\pi$
$811$	31.0030	−	9.10330i	1.08866	−	0.319660i	0.776339	+	0.630316i	$0.217075\pi$
$812$	−4.92582	−	14.6571i	−0.172862	−	0.514362i
$813$	−30.6941	+	67.2108i	−1.07649	+	2.35718i
$814$	11.3874	+	32.9018i	0.399128	+	1.15321i
$815$	40.8031	+	21.0354i	1.42927	+	0.736839i
$816$	0.549963	−	0.432495i	0.0192525	−	0.0151404i
$817$	−64.3011	−	25.7423i	−2.24961	−	0.900609i
$818$	13.8873	−	8.92480i	0.485557	−	0.312048i
$819$	−8.39935	−	9.87123i	−0.293497	−	0.344929i
$820$	−11.6235	+	25.4519i	−0.405911	+	0.888820i
$821$	13.2699	−	6.84113i	0.463124	−	0.238757i	−0.210841	−	0.977520i	$-0.567620\pi$
$821$	13.2699	−	6.84113i	0.463124	−	0.238757i	0.673965	+	0.738763i	$0.264590\pi$
$822$	−25.4691	−	24.2848i	−0.888337	−	0.847028i
$823$	7.01859	−	20.2789i	0.244653	−	0.706877i	−0.754091	−	0.656770i	$-0.771922\pi$
$823$	7.01859	−	20.2789i	0.244653	−	0.706877i	0.998744	−	0.0501076i	$-0.0159564\pi$
$824$	2.17583	−	2.07465i	0.0757987	−	0.0722739i
$825$	−13.0532	−	28.5826i	−0.454455	−	0.995118i
$826$	0.604952	+	2.59522i	0.0210490	+	0.0902994i
$827$	6.77705			0.235661			0.117831	−	0.993034i	$-0.462406\pi$
$827$	6.77705			0.235661			0.117831	+	0.993034i	$0.462406\pi$
$828$	34.0424	+	11.1941i	1.18306	+	0.389021i
$829$	3.11155	+	5.38936i	0.108068	+	0.187180i	0.914988	−	0.403482i	$-0.132200\pi$
$829$	3.11155	+	5.38936i	0.108068	+	0.187180i	−0.806919	+	0.590662i	$0.798867\pi$
$830$	−3.71750	+	1.48826i	−0.129036	+	0.0516583i
$831$	69.5521	+	6.64142i	2.41273	+	0.230388i
$832$	−0.629047	−	0.184705i	−0.0218083	−	0.00640349i
$833$	−0.603853	−	1.38773i	−0.0209223	−	0.0480820i
$834$	−4.08144	+	1.19842i	−0.141329	+	0.0414979i
$835$	3.88037	−	2.00047i	0.134286	−	0.0692291i
$836$	−31.9480	+	3.05066i	−1.10494	+	0.105509i
$837$	−21.8815	−	4.21732i	−0.756336	−	0.145772i
$838$	−0.874495	−	18.3579i	−0.0302089	−	0.634164i
$839$	4.38618	+	30.5066i	0.151428	+	1.05320i	0.913829	+	0.406099i	$0.133111\pi$
$839$	4.38618	+	30.5066i	0.151428	+	1.05320i	−0.762401	+	0.647104i	$0.775980\pi$
$840$	−11.2451	−	19.8877i	−0.387993	−	0.686192i
$841$	4.33768	−	2.78765i	0.149575	−	0.0961260i
$842$	−9.67651	−	27.9584i	−0.333475	−	0.963512i
$843$	82.9836	−	7.92397i	2.85811	−	0.272916i
$844$	−1.02786	+	21.5775i	−0.0353805	+	0.742728i
$845$	7.90797	−	32.5971i	0.272043	−	1.12137i
$846$	13.2311	+	15.2696i	0.454896	+	0.524978i
$847$	11.1706	−	23.8896i	0.383826	−	0.820858i
$848$	−0.840454	−	1.84034i	−0.0288613	−	0.0631975i
$849$	−15.9990	−	12.5817i	−0.549083	−	0.431804i
$850$	−0.229230	−	0.397037i	−0.00786251	−	0.0136183i
$851$	−19.2362	+	30.9783i	−0.659410	+	1.06192i
$852$	17.0318	−	29.4999i	0.583499	−	1.01065i
$853$	2.71455	−	18.8801i	0.0929445	−	0.646443i	−0.889089	−	0.457735i	$-0.848661\pi$
$853$	2.71455	−	18.8801i	0.0929445	−	0.646443i	0.982033	−	0.188708i	$-0.0604300\pi$
$854$	−3.55994	+	14.1192i	−0.121819	+	0.483151i
$855$	−134.087	−	39.3715i	−4.58568	−	1.34648i
$856$	−5.22069	+	1.00621i	−0.178440	+	0.0343914i
$857$	−5.65869	−	5.39555i	−0.193297	−	0.184308i	0.587250	−	0.809406i	$-0.300211\pi$
$857$	−5.65869	−	5.39555i	−0.193297	−	0.184308i	−0.780547	+	0.625097i	$0.785059\pi$
$858$	0.462253	−	9.70388i	0.0157810	−	0.331285i
$859$	7.48767	+	10.5150i	0.255476	+	0.358766i	0.922317	−	0.386434i	$-0.126293\pi$
$859$	7.48767	+	10.5150i	0.255476	+	0.358766i	−0.666841	+	0.745200i	$0.732354\pi$
$860$	17.2689	−	19.9294i	0.588865	−	0.679586i
$861$	−89.2909	−	9.33673i	−3.04303	−	0.318195i
$862$	−1.55810	−	10.8368i	−0.0530689	−	0.369103i
$863$	24.1605	+	9.67241i	0.822433	+	0.329253i	0.744430	−	0.667701i	$-0.232721\pi$
$863$	24.1605	+	9.67241i	0.822433	+	0.329253i	0.0780031	+	0.996953i	$0.475146\pi$
$864$	12.8638	+	6.63173i	0.437634	+	0.225616i
$865$	−60.1875	−	11.6002i	−2.04644	−	0.394418i
$866$	16.8919	+	23.7213i	0.574009	+	0.806083i
$867$	−46.1530	−	29.6607i	−1.56744	−	1.00733i
$868$	0.543502	+	4.03738i	0.0184477	+	0.137038i
$869$	−23.5717	−	27.2032i	−0.799614	−	0.922804i
$870$	36.5249	−	34.8264i	1.23831	−	1.18073i
$871$	0.994355	−	1.39638i	0.0336924	−	0.0473144i
$872$	−7.57834	+	3.03391i	−0.256635	+	0.102741i
$873$	−44.0560	+	76.3072i	−1.49107	+	2.58261i
$874$	−23.5698	−	23.9639i	−0.797262	−	0.810591i
$875$	18.9401	−	7.38569i	0.640293	−	0.249682i
$876$	0.921661	−	6.41029i	0.0311400	−	0.216584i
$877$	−36.4897	−	3.48435i	−1.23217	−	0.117658i	−0.541421	−	0.840752i	$-0.682113\pi$
$877$	−36.4897	−	3.48435i	−1.23217	−	0.117658i	−0.690750	+	0.723094i	$0.742720\pi$
$878$	5.10626	+	21.0483i	0.172328	+	0.710346i
$879$	7.00886	−	20.2508i	0.236403	−	0.683042i
$880$	2.88071	−	11.8745i	0.0971088	−	0.400288i
$881$	−3.05265	−	1.96182i	−0.102846	−	0.0660953i	0.488207	−	0.872728i	$-0.337651\pi$
$881$	−3.05265	−	1.96182i	−0.102846	−	0.0660953i	−0.591053	+	0.806633i	$0.701288\pi$
$882$	34.9579	−	38.9081i	1.17709	−	1.31010i
$883$	25.6511	−	29.6029i	0.863227	−	0.996218i	−0.136757	−	0.990605i	$-0.543668\pi$
$883$	25.6511	−	29.6029i	0.863227	−	0.996218i	0.999984	−	0.00561296i	$-0.00178667\pi$
$884$	−0.00674442	−	0.141583i	−0.000226839	−	0.00476194i
$885$	−6.83664	+	5.37639i	−0.229811	+	0.180725i
$886$	−21.0970	+	16.5909i	−0.708768	+	0.557381i
$887$	−2.82680	−	59.3419i	−0.0949148	−	1.99251i	−0.119676	−	0.992813i	$-0.538186\pi$
$887$	−2.82680	−	59.3419i	−0.0949148	−	1.99251i	0.0247610	−	0.999693i	$-0.492118\pi$
$888$	−16.1131	+	18.5955i	−0.540721	+	0.624025i
$889$	1.15768	−	20.4368i	0.0388275	−	0.685427i
$890$	27.3398	+	17.5702i	0.916433	+	0.588956i
$891$	−26.3603	+	108.659i	−0.883105	+	3.64021i
$892$	4.66536	−	13.4797i	0.156208	−	0.451333i
$893$	−4.46790	−	18.4169i	−0.149513	−	0.616299i
$894$	−48.2121	−	4.60370i	−1.61245	−	0.153971i
$895$	−2.68836	+	18.6979i	−0.0898619	+	0.625003i
$896$	0.400049	−	2.61533i	0.0133647	−	0.0873721i
$897$	8.19560	−	6.02979i	0.273643	−	0.201329i
$898$	−20.9094	+	36.2162i	−0.697757	+	1.20855i
$899$	−8.35422	+	3.34453i	−0.278629	+	0.111546i
$900$	9.19098	−	12.9069i	0.306366	−	0.430231i
$901$	0.316572	−	0.301851i	0.0105465	−	0.0100561i
$902$	−31.4431	−	36.2872i	−1.04694	−	1.20823i
$903$	78.2649	+	32.1516i	2.60449	+	1.06994i
$904$	4.72252	+	3.03498i	0.157069	+	0.100942i
$905$	−20.7801	−	29.1816i	−0.690754	−	0.970028i
$906$	6.94551	+	1.33864i	0.230749	+	0.0444732i
$907$	52.6296	+	27.1324i	1.74754	+	0.900918i	0.957783	+	0.287494i	$0.0928221\pi$
$907$	52.6296	+	27.1324i	1.74754	+	0.900918i	0.789754	+	0.613424i	$0.210208\pi$
$908$	−22.7999	−	9.12768i	−0.756640	−	0.302913i
$909$	8.42528	+	58.5991i	0.279449	+	1.94361i
$910$	−4.60346	−	0.481362i	−0.152603	−	0.0159570i
$911$	22.6935	−	26.1897i	0.751870	−	0.867704i	−0.242879	−	0.970057i	$-0.578092\pi$
$911$	22.6935	−	26.1897i	0.751870	−	0.867704i	0.994748	+	0.102353i	$0.0326371\pi$
$912$	−13.1561	−	18.4752i	−0.435644	−	0.611776i
$913$	0.326959	−	6.86372i	0.0108208	−	0.227156i
$914$	−28.8308	−	27.4901i	−0.953639	−	0.909293i
$915$	−46.6661	+	8.99415i	−1.54273	+	0.297337i
$916$	−5.19097	−	1.52421i	−0.171514	−	0.0503612i
$917$	43.2206	−	12.2699i	1.42727	−	0.405189i
$918$	−0.445305	+	3.09717i	−0.0146973	+	0.102222i
$919$	8.10467	−	14.0377i	0.267348	−	0.463061i	−0.700828	−	0.713330i	$-0.747186\pi$
$919$	8.10467	−	14.0377i	0.267348	−	0.463061i	0.968176	+	0.250269i	$0.0805192\pi$
$920$	11.5570	−	5.49611i	0.381023	−	0.181201i
$921$	−10.5274	−	18.2340i	−0.346889	−	0.600830i
$922$	−28.4515	−	22.3745i	−0.936999	−	0.736864i
$923$	−2.86677	−	6.27736i	−0.0943610	−	0.206622i
$924$	39.0597	−	3.37582i	1.28497	−	0.111056i
$925$	10.5584	+	12.1851i	0.347159	+	0.400643i
$926$	−4.16593	+	17.1722i	−0.136901	+	0.564313i
$927$	−1.06891	+	22.4391i	−0.0351075	+	0.736998i
$928$	5.81787	−	0.555539i	0.190981	−	0.0182365i
$929$	11.2572	+	32.5257i	0.369338	+	1.06713i	0.964627	+	0.263620i	$0.0849165\pi$
$929$	11.2572	+	32.5257i	0.369338	+	1.06713i	−0.595289	+	0.803512i	$0.702962\pi$
$930$	−11.1854	+	7.18845i	−0.366785	+	0.235719i
$931$	−45.8670	+	17.4126i	−1.50323	+	0.570674i
$932$	−0.512046	−	3.56136i	−0.0167726	−	0.116656i
$933$	4.65716	+	97.7657i	0.152468	+	3.20071i
$934$	−0.918625	−	0.177051i	−0.0300583	−	0.00579327i
$935$	2.62980	−	0.251115i	0.0860035	−	0.00821234i
$936$	4.35426	−	2.24478i	0.142323	−	0.0733728i
$937$	22.8064	−	6.69656i	0.745052	−	0.218767i	0.112894	−	0.993607i	$-0.463988\pi$
$937$	22.8064	−	6.69656i	0.745052	−	0.218767i	0.632157	+	0.774840i	$0.282170\pi$
$938$	6.12020	+	3.22513i	0.199832	+	0.105304i
$939$	−47.9182	−	14.0700i	−1.56375	−	0.459159i
$940$	7.18260	+	0.685855i	0.234270	+	0.0223701i
$941$	16.6971	−	6.68450i	0.544309	−	0.217908i	−0.0831793	−	0.996535i	$-0.526507\pi$
$941$	16.6971	−	6.68450i	0.544309	−	0.217908i	0.627488	+	0.778626i	$0.284083\pi$
$942$	−11.3621	−	19.6798i	−0.370199	−	0.641203i
$943$	8.75006	−	49.5208i	0.284941	−	1.61262i
$944$	−1.00720			−0.0327815
$945$	97.7750	+	29.6663i	3.18062	+	0.965045i
$946$	18.7983	+	41.1626i	0.611186	+	1.33831i
$947$	1.87518	−	1.78798i	0.0609352	−	0.0581016i	−0.659000	−	0.752143i	$-0.729020\pi$
$947$	1.87518	−	1.78798i	0.0609352	−	0.0581016i	0.719935	+	0.694042i	$0.244172\pi$
$948$	8.32000	−	24.0391i	0.270221	−	0.780752i
$949$	−0.949558	−	0.905401i	−0.0308239	−	0.0293906i
$950$	−13.2099	+	6.81017i	−0.428585	+	0.220951i
$951$	19.3299	−	42.3266i	0.626816	−	1.37253i
$952$	0.562632	−	0.103203i	0.0182350	−	0.00334484i
$953$	−25.7912	+	16.5750i	−0.835461	+	0.536918i	−0.887009	−	0.461753i	$-0.847221\pi$
$953$	−25.7912	+	16.5750i	−0.835461	+	0.536918i	0.0515482	+	0.998671i	$0.483584\pi$
$954$	14.0347	+	5.61865i	0.454391	+	0.181911i
$955$	29.1894	−	22.9548i	0.944547	−	0.742800i
$956$	17.5678	+	9.05684i	0.568184	+	0.292919i
$957$	28.3249	+	81.8396i	0.915616	+	2.64550i
$958$	−4.49936	+	9.85223i	−0.145368	+	0.318311i
$959$	−9.16554	−	27.2726i	−0.295971	−	0.880680i
$960$	8.28547	−	2.43283i	0.267412	−	0.0785194i
$961$	−28.1118	+	5.41810i	−0.906832	+	0.174778i
$962$	1.17522	+	4.84433i	0.0378907	+	0.156188i
$963$	23.0447	−	32.3617i	0.742604	−	1.04284i
$964$	6.46038	+	5.08050i	0.208075	+	0.163632i
$965$	−13.6844			−0.440515
$966$	28.5288	+	29.5320i	0.917900	+	0.950177i
$967$	−61.0036			−1.96174			−0.980872	−	0.194655i	$-0.937641\pi$
$967$	−61.0036			−1.96174			−0.980872	+	0.194655i	$0.937641\pi$
$968$	7.83521	+	6.16167i	0.251833	+	0.198044i
$969$	2.84440	−	3.99439i	0.0913751	−	0.128318i
$970$	7.41835	+	30.5788i	0.238189	+	0.981827i
$971$	10.3675	−	1.99817i	0.332708	−	0.0641243i	−0.0201613	−	0.999797i	$-0.506418\pi$
$971$	10.3675	−	1.99817i	0.332708	−	0.0641243i	0.352870	+	0.935672i	$0.385206\pi$
$972$	−34.1583	+	10.0298i	−1.09563	+	0.321705i
$973$	−3.40887	−	0.688835i	−0.109283	−	0.0220830i
$974$	16.0697	−	35.1878i	0.514907	−	1.12749i
$975$	−1.47143	−	4.25141i	−0.0471234	−	0.136154i
$976$	−4.89178	−	2.52189i	−0.156582	−	0.0807237i
$977$	41.9382	−	32.9806i	1.34172	−	1.05514i	0.348698	−	0.937235i	$-0.386624\pi$
$977$	41.9382	−	32.9806i	1.34172	−	1.05514i	0.993025	−	0.117907i	$-0.0376184\pi$
$978$	−51.6840	−	20.6912i	−1.65267	−	0.661630i
$979$	−46.9155	+	30.1508i	−1.49943	+	0.963623i
$980$	−0.553308	−	18.6708i	−0.0176748	−	0.596417i
$981$	25.3389	−	55.4844i	0.809008	−	1.77148i
$982$	17.7963	−	9.17461i	0.567902	−	0.292774i
$983$	−20.6517	−	19.6914i	−0.658688	−	0.628058i	0.285143	−	0.958485i	$-0.407959\pi$
$983$	−20.6517	−	19.6914i	−0.658688	−	0.628058i	−0.943832	+	0.330427i	$0.892807\pi$
$984$	11.0983	−	32.0665i	0.353802	−	1.02224i
$985$	0.743690	−	0.709107i	0.0236959	−	0.0225940i
$986$	0.524902	+	1.14937i	0.0167163	+	0.0366036i
$987$	5.25560	+	22.5464i	0.167288	+	0.717659i
$988$	−4.59494			−0.146184
$989$	−21.0613	+	42.4573i	−0.669710	+	1.35006i
$990$	45.6513	+	79.0704i	1.45089	+	2.51302i
$991$	4.68698	−	1.87639i	0.148887	−	0.0596053i	−0.296022	−	0.955181i	$-0.595660\pi$
$991$	4.68698	−	1.87639i	0.148887	−	0.0596053i	0.444909	+	0.895576i	$0.353236\pi$
$992$	−1.53278	−	0.146363i	−0.0486658	−	0.00464702i
$993$	−1.34767	−	0.395713i	−0.0427672	−	0.0125576i
$994$	23.5629	−	14.8455i	0.747371	−	0.470870i
$995$	−31.2253	+	9.16858i	−0.989909	+	0.290664i
$996$	4.31635	−	2.22523i	0.136769	−	0.0705092i
$997$	38.2090	−	3.64851i	1.21009	−	0.115550i	0.529562	−	0.848271i	$-0.322356\pi$
$997$	38.2090	−	3.64851i	1.21009	−	0.115550i	0.680528	+	0.732722i	$0.261750\pi$
$998$	−18.3435	−	3.53542i	−0.580653	−	0.111912i
$999$	−5.23599	−	109.917i	−0.165659	−	3.47762i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	322.2.m.a.261.8	yes	160
7.4	even	3	inner	322.2.m.a.123.1	yes	160
23.3	even	11	inner	322.2.m.a.233.1	yes	160
161.95	even	33	inner	322.2.m.a.95.8	✓	160

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
322.2.m.a.95.8	✓	160	161.95	even	33	inner
322.2.m.a.123.1	yes	160	7.4	even	3	inner
322.2.m.a.233.1	yes	160	23.3	even	11	inner
322.2.m.a.261.8	yes	160	1.1	even	1	trivial

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.m (of order \(33\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(0.786053 + 0.618159i) q^{2} +(1.87711 - 2.63604i) q^{3} +(0.235759 + 0.971812i) q^{4} +(-2.62021 + 0.505003i) q^{5} +(3.10500 - 0.911711i) q^{6} +(2.59333 + 0.524038i) q^{7} +(-0.415415 + 0.909632i) q^{8} +(-2.44393 - 7.06129i) q^{9} +O(q^{10})\)	\(q+(0.786053 + 0.618159i) q^{2} +(1.87711 - 2.63604i) q^{3} +(0.235759 + 0.971812i) q^{4} +(-2.62021 + 0.505003i) q^{5} +(3.10500 - 0.911711i) q^{6} +(2.59333 + 0.524038i) q^{7} +(-0.415415 + 0.909632i) q^{8} +(-2.44393 - 7.06129i) q^{9} +(-2.37179 - 1.22274i) q^{10} +(3.59938 - 2.83059i) q^{11} +(3.00428 + 1.20273i) q^{12} +(0.551529 - 0.354446i) q^{13} +(1.71456 + 2.01502i) q^{14} +(-3.58722 + 7.85491i) q^{15} +(-0.888835 + 0.458227i) q^{16} +(-0.156473 - 0.149197i) q^{17} +(2.44393 - 7.06129i) q^{18} +(-5.07244 + 4.83656i) q^{19} +(-1.10850 - 2.42729i) q^{20} +(6.24937 - 5.85245i) q^{21} +4.57906 q^{22} +(3.02270 + 3.72335i) q^{23} +(1.61804 + 2.80253i) q^{24} +(1.96861 - 0.788113i) q^{25} +(0.652635 + 0.0623191i) q^{26} +(-13.8864 - 4.07740i) q^{27} +(0.102135 + 2.64378i) q^{28} +(-5.60759 + 1.64654i) q^{29} +(-7.67533 + 3.95691i) q^{30} +(1.53278 - 0.146363i) q^{31} +(-0.981929 - 0.189251i) q^{32} +(-0.705080 - 14.8014i) q^{33} +(-0.0307689 - 0.214002i) q^{34} +(-7.05971 - 0.0634460i) q^{35} +(6.28606 - 4.03981i) q^{36} +(2.48684 + 7.18527i) q^{37} +(-6.97697 + 0.666220i) q^{38} +(0.100949 - 2.11919i) q^{39} +(0.629106 - 2.59321i) q^{40} +(-6.86671 - 7.92460i) q^{41} +(8.53008 - 0.737231i) q^{42} +(4.10528 + 8.98931i) q^{43} +(3.59938 + 2.83059i) q^{44} +(9.96958 + 17.2678i) q^{45} +(0.0743811 + 4.79525i) q^{46} +(-1.35197 + 2.34168i) q^{47} +(-0.460543 + 3.20315i) q^{48} +(6.45077 + 2.71801i) q^{49} +(2.03461 + 0.597416i) q^{50} +(-0.687007 + 0.132410i) q^{51} +(0.474483 + 0.452418i) q^{52} +(-0.0962662 + 2.02088i) q^{53} +(-8.39493 - 11.7890i) q^{54} +(-8.00167 + 9.23442i) q^{55} +(-1.55399 + 2.14129i) q^{56} +(3.22781 + 22.4499i) q^{57} +(-5.42569 - 2.17212i) q^{58} +(0.895234 + 0.461525i) q^{59} +(-8.47921 - 1.63423i) q^{60} +(3.19239 + 4.48309i) q^{61} +(1.29532 + 0.832453i) q^{62} +(-2.63756 - 19.5930i) q^{63} +(-0.654861 - 0.755750i) q^{64} +(-1.26612 + 1.20725i) q^{65} +(8.59542 - 12.0706i) q^{66} +(2.42745 - 0.971803i) q^{67} +(0.108101 - 0.187237i) q^{68} +(15.4888 - 0.978800i) q^{69} +(-5.51009 - 4.41390i) q^{70} +(1.49803 - 10.4190i) q^{71} +(7.43842 + 0.710283i) q^{72} +(-0.471812 - 1.94484i) q^{73} +(-2.48684 + 7.18527i) q^{74} +(1.61781 - 6.66871i) q^{75} +(-5.89610 - 3.78919i) q^{76} +(10.8177 - 5.45444i) q^{77} +(1.38935 - 1.60339i) q^{78} +(-0.374031 - 7.85187i) q^{79} +(2.09753 - 1.64951i) q^{80} +(-19.1937 + 15.0941i) q^{81} +(-0.498932 - 10.4739i) q^{82} +(0.982708 - 1.13411i) q^{83} +(7.16082 + 4.69344i) q^{84} +(0.485337 + 0.311907i) q^{85} +(-2.32985 + 9.60379i) q^{86} +(-6.18576 + 17.8726i) q^{87} +(1.07955 + 4.44998i) q^{88} +(-12.1239 - 1.15769i) q^{89} +(-2.83764 + 19.7362i) q^{90} +(1.61604 - 0.630175i) q^{91} +(-2.90576 + 3.81530i) q^{92} +(2.49139 - 4.31521i) q^{93} +(-2.51025 + 1.00495i) q^{94} +(10.8484 - 15.2344i) q^{95} +(-2.34207 + 2.23316i) q^{96} +(-7.72205 - 8.91172i) q^{97} +(3.39048 + 6.12410i) q^{98} +(-28.7842 - 18.4985i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 160 q - 8 q^{2} + 2 q^{3} + 8 q^{4} - 2 q^{5} + 4 q^{6} + 15 q^{7} + 16 q^{8} + 28 q^{9}+O(q^{10}) \) 160 * q - 8 * q^2 + 2 * q^3 + 8 * q^4 - 2 * q^5 + 4 * q^6 + 15 * q^7 + 16 * q^8 + 28 * q^9	\( 160 q - 8 q^{2} + 2 q^{3} + 8 q^{4} - 2 q^{5} + 4 q^{6} + 15 q^{7} + 16 q^{8} + 28 q^{9} + 2 q^{10} - 8 q^{11} - 9 q^{12} - 12 q^{13} + 7 q^{14} + 4 q^{15} + 8 q^{16} - 14 q^{17} - 28 q^{18} - 2 q^{19} - 18 q^{20} + 72 q^{21} - 16 q^{22} - 22 q^{23} - 2 q^{24} - 30 q^{25} - 6 q^{26} - 70 q^{27} + 14 q^{28} - 20 q^{30} + 4 q^{31} - 8 q^{32} + 40 q^{33} - 28 q^{34} - 79 q^{35} - 12 q^{36} - 14 q^{37} - 9 q^{38} + 16 q^{39} + 2 q^{40} + 12 q^{41} + 16 q^{42} + 106 q^{43} - 8 q^{44} + 40 q^{45} - 50 q^{47} + 18 q^{48} - 55 q^{49} + 28 q^{50} - 47 q^{51} - 16 q^{52} - 4 q^{53} - 24 q^{54} - 15 q^{56} + 8 q^{57} + 22 q^{58} - 42 q^{59} - 2 q^{60} - 80 q^{61} + 8 q^{62} + 5 q^{63} - 16 q^{64} + 71 q^{65} + 4 q^{66} + 12 q^{67} + 8 q^{68} - 72 q^{70} - 112 q^{71} + 16 q^{72} - 64 q^{73} + 14 q^{74} - 126 q^{75} + 4 q^{76} - 69 q^{77} + 54 q^{78} + 52 q^{79} - 2 q^{80} - 30 q^{81} - 49 q^{82} + 26 q^{83} - q^{84} - 22 q^{85} - 46 q^{86} + 4 q^{87} - 3 q^{88} - 72 q^{89} - 8 q^{90} + 44 q^{91} + 54 q^{93} + 6 q^{94} - 58 q^{95} - 2 q^{96} + 20 q^{97} - 19 q^{98} - 264 q^{99}+O(q^{100}) \) 160 * q - 8 * q^2 + 2 * q^3 + 8 * q^4 - 2 * q^5 + 4 * q^6 + 15 * q^7 + 16 * q^8 + 28 * q^9 + 2 * q^10 - 8 * q^11 - 9 * q^12 - 12 * q^13 + 7 * q^14 + 4 * q^15 + 8 * q^16 - 14 * q^17 - 28 * q^18 - 2 * q^19 - 18 * q^20 + 72 * q^21 - 16 * q^22 - 22 * q^23 - 2 * q^24 - 30 * q^25 - 6 * q^26 - 70 * q^27 + 14 * q^28 - 20 * q^30 + 4 * q^31 - 8 * q^32 + 40 * q^33 - 28 * q^34 - 79 * q^35 - 12 * q^36 - 14 * q^37 - 9 * q^38 + 16 * q^39 + 2 * q^40 + 12 * q^41 + 16 * q^42 + 106 * q^43 - 8 * q^44 + 40 * q^45 - 50 * q^47 + 18 * q^48 - 55 * q^49 + 28 * q^50 - 47 * q^51 - 16 * q^52 - 4 * q^53 - 24 * q^54 - 15 * q^56 + 8 * q^57 + 22 * q^58 - 42 * q^59 - 2 * q^60 - 80 * q^61 + 8 * q^62 + 5 * q^63 - 16 * q^64 + 71 * q^65 + 4 * q^66 + 12 * q^67 + 8 * q^68 - 72 * q^70 - 112 * q^71 + 16 * q^72 - 64 * q^73 + 14 * q^74 - 126 * q^75 + 4 * q^76 - 69 * q^77 + 54 * q^78 + 52 * q^79 - 2 * q^80 - 30 * q^81 - 49 * q^82 + 26 * q^83 - q^84 - 22 * q^85 - 46 * q^86 + 4 * q^87 - 3 * q^88 - 72 * q^89 - 8 * q^90 + 44 * q^91 + 54 * q^93 + 6 * q^94 - 58 * q^95 - 2 * q^96 + 20 * q^97 - 19 * q^98 - 264 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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