LMFDB - Embedded newform 98.2.g.b.23.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [98,2,Mod(9,98)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(98, base_ring=CyclotomicField(42))

chi = DirichletCharacter(H, H._module([2]))

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

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

chi := DirichletCharacter("98.9");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 98 = 2 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	98.g (of order $21$, degree $12$, 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:	$0.782533939809$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$2$ over $\Q(\zeta_{21})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label			23.2
Character	$\chi$	$=$	98.23
Dual form			98.2.g.b.81.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.0747301 - 0.997204i) q^{2} +(1.95066 - 0.601698i) q^{3} +(-0.988831 - 0.149042i) q^{4} +(0.958118 + 0.889004i) q^{5} +(-0.454243 - 1.99017i) q^{6} +(-2.43754 + 1.02877i) q^{7} +(-0.222521 + 0.974928i) q^{8} +(0.964304 - 0.657452i) q^{9} +O(q^{10})$	\(q+(0.0747301 - 0.997204i) q^{2} +(1.95066 - 0.601698i) q^{3} +(-0.988831 - 0.149042i) q^{4} +(0.958118 + 0.889004i) q^{5} +(-0.454243 - 1.99017i) q^{6} +(-2.43754 + 1.02877i) q^{7} +(-0.222521 + 0.974928i) q^{8} +(0.964304 - 0.657452i) q^{9} +(0.958118 - 0.889004i) q^{10} +(-2.30365 - 1.57060i) q^{11} +(-2.01855 + 0.304247i) q^{12} +(-0.810304 + 0.390222i) q^{13} +(0.843740 + 2.50761i) q^{14} +(2.40387 + 1.15764i) q^{15} +(0.955573 + 0.294755i) q^{16} +(0.719733 - 1.83385i) q^{17} +(-0.583551 - 1.01074i) q^{18} +(0.387065 - 0.670417i) q^{19} +(-0.814918 - 1.02187i) q^{20} +(-4.13580 + 3.47345i) q^{21} +(-1.73836 + 2.17983i) q^{22} +(2.28676 + 5.82658i) q^{23} +(0.152550 + 2.03564i) q^{24} +(-0.245988 - 3.28248i) q^{25} +(0.328576 + 0.837199i) q^{26} +(-2.33284 + 2.92529i) q^{27} +(2.56365 - 0.653987i) q^{28} +(6.52548 + 8.18270i) q^{29} +(1.33405 - 2.31064i) q^{30} +(-4.21876 - 7.30711i) q^{31} +(0.365341 - 0.930874i) q^{32} +(-5.43865 - 1.67760i) q^{33} +(-1.77494 - 0.854764i) q^{34} +(-3.25004 - 1.18130i) q^{35} +(-1.05152 + 0.506386i) q^{36} +(3.65860 - 0.551445i) q^{37} +(-0.639617 - 0.436083i) q^{38} +(-1.34583 + 1.24875i) q^{39} +(-1.07992 + 0.736274i) q^{40} +(-1.26678 + 5.55015i) q^{41} +(3.15467 + 4.38381i) q^{42} +(-2.00714 - 8.79388i) q^{43} +(2.04383 + 1.89640i) q^{44} +(1.50839 + 0.227354i) q^{45} +(5.98118 - 1.84495i) q^{46} +(0.907661 - 12.1119i) q^{47} +2.04135 q^{48} +(4.88324 - 5.01537i) q^{49} -3.29168 q^{50} +(0.300528 - 4.01027i) q^{51} +(0.859413 - 0.265094i) q^{52} +(6.87650 + 1.03647i) q^{53} +(2.74278 + 2.54492i) q^{54} +(-0.810897 - 3.55277i) q^{55} +(-0.460577 - 2.60535i) q^{56} +(0.351643 - 1.54065i) q^{57} +(8.64747 - 5.89574i) q^{58} +(3.85448 - 3.57644i) q^{59} +(-2.20448 - 1.50299i) q^{60} +(-12.1696 + 1.83427i) q^{61} +(-7.60195 + 3.66091i) q^{62} +(-1.67417 + 2.59462i) q^{63} +(-0.900969 - 0.433884i) q^{64} +(-1.12328 - 0.346485i) q^{65} +(-2.07934 + 5.29807i) q^{66} +(0.734787 + 1.27269i) q^{67} +(-0.985015 + 1.70610i) q^{68} +(7.96653 + 9.98972i) q^{69} +(-1.42087 + 3.15267i) q^{70} +(-3.74129 + 4.69143i) q^{71} +(0.426390 + 1.08642i) q^{72} +(0.00237545 + 0.0316982i) q^{73} +(-0.276496 - 3.68958i) q^{74} +(-2.45490 - 6.25498i) q^{75} +(-0.482663 + 0.605240i) q^{76} +(7.23103 + 1.45847i) q^{77} +(1.14468 + 1.43538i) q^{78} +(-6.94343 + 12.0264i) q^{79} +(0.653513 + 1.13192i) q^{80} +(-4.06960 + 10.3692i) q^{81} +(5.43996 + 1.67801i) q^{82} +(-9.26679 - 4.46265i) q^{83} +(4.60730 - 2.81825i) q^{84} +(2.31989 - 1.11720i) q^{85} +(-8.91928 + 1.34437i) q^{86} +(17.6525 + 12.0353i) q^{87} +(2.04383 - 1.89640i) q^{88} +(2.43024 - 1.65691i) q^{89} +(0.339441 - 1.48719i) q^{90} +(1.57370 - 1.78480i) q^{91} +(-1.39282 - 6.10233i) q^{92} +(-12.6260 - 11.7153i) q^{93} +(-12.0102 - 1.81025i) q^{94} +(0.966857 - 0.298236i) q^{95} +(0.152550 - 2.03564i) q^{96} +9.86141 q^{97} +(-4.63642 - 5.24439i) q^{98} -3.25401 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 2 q^{2} - 7 q^{3} + 2 q^{4} - 7 q^{6} - 4 q^{8} + 19 q^{9}+O(q^{10}) $ 24 * q + 2 * q^2 - 7 * q^3 + 2 * q^4 - 7 * q^6 - 4 * q^8 + 19 * q^9	\( 24 q + 2 q^{2} - 7 q^{3} + 2 q^{4} - 7 q^{6} - 4 q^{8} + 19 q^{9} - 11 q^{11} - 14 q^{13} + 9 q^{15} + 2 q^{16} - 7 q^{17} - 9 q^{18} - 14 q^{19} - 7 q^{20} - 7 q^{21} + q^{22} - 29 q^{23} - 8 q^{25} - 7 q^{26} - 7 q^{27} + 14 q^{28} + 13 q^{29} - 8 q^{30} - 28 q^{31} + 2 q^{32} - 14 q^{33} - 7 q^{34} - 35 q^{35} - 17 q^{36} + 20 q^{37} + 35 q^{38} + 56 q^{39} + 14 q^{40} + 28 q^{41} - 21 q^{42} + 6 q^{43} + 3 q^{44} + 7 q^{45} + 34 q^{46} + 42 q^{47} + 14 q^{48} + 28 q^{49} + 16 q^{50} + 32 q^{51} - 7 q^{52} - 60 q^{53} + 21 q^{54} - 14 q^{55} + 7 q^{56} + 23 q^{57} + 18 q^{58} + 49 q^{59} + 6 q^{60} - 14 q^{61} - 28 q^{63} - 4 q^{64} - 28 q^{65} + 21 q^{66} + 24 q^{67} - 14 q^{68} + 7 q^{69} - 28 q^{70} + 6 q^{71} - 2 q^{72} - 35 q^{73} - 15 q^{74} - 56 q^{75} + 49 q^{77} + 6 q^{79} - 14 q^{80} - 45 q^{81} - 14 q^{82} - 77 q^{83} - 21 q^{84} - 33 q^{85} - 38 q^{86} + 63 q^{87} + 3 q^{88} - 21 q^{90} - 21 q^{91} - 5 q^{92} - 38 q^{93} - 35 q^{94} + 86 q^{95} + 98 q^{97} + 28 q^{98} - 106 q^{99}+O(q^{100}) \) 24 * q + 2 * q^2 - 7 * q^3 + 2 * q^4 - 7 * q^6 - 4 * q^8 + 19 * q^9 - 11 * q^11 - 14 * q^13 + 9 * q^15 + 2 * q^16 - 7 * q^17 - 9 * q^18 - 14 * q^19 - 7 * q^20 - 7 * q^21 + q^22 - 29 * q^23 - 8 * q^25 - 7 * q^26 - 7 * q^27 + 14 * q^28 + 13 * q^29 - 8 * q^30 - 28 * q^31 + 2 * q^32 - 14 * q^33 - 7 * q^34 - 35 * q^35 - 17 * q^36 + 20 * q^37 + 35 * q^38 + 56 * q^39 + 14 * q^40 + 28 * q^41 - 21 * q^42 + 6 * q^43 + 3 * q^44 + 7 * q^45 + 34 * q^46 + 42 * q^47 + 14 * q^48 + 28 * q^49 + 16 * q^50 + 32 * q^51 - 7 * q^52 - 60 * q^53 + 21 * q^54 - 14 * q^55 + 7 * q^56 + 23 * q^57 + 18 * q^58 + 49 * q^59 + 6 * q^60 - 14 * q^61 - 28 * q^63 - 4 * q^64 - 28 * q^65 + 21 * q^66 + 24 * q^67 - 14 * q^68 + 7 * q^69 - 28 * q^70 + 6 * q^71 - 2 * q^72 - 35 * q^73 - 15 * q^74 - 56 * q^75 + 49 * q^77 + 6 * q^79 - 14 * q^80 - 45 * q^81 - 14 * q^82 - 77 * q^83 - 21 * q^84 - 33 * q^85 - 38 * q^86 + 63 * q^87 + 3 * q^88 - 21 * q^90 - 21 * q^91 - 5 * q^92 - 38 * q^93 - 35 * q^94 + 86 * q^95 + 98 * q^97 + 28 * q^98 - 106 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/98\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{19}{21}\right)$

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 $

$2$	0.0747301	−	0.997204i	0.0528422	−	0.705130i
$2$	0.0747301	−	0.997204i	0.0528422	−	0.705130i
$3$	1.95066	−	0.601698i	1.12621	−	0.347390i	0.324966	−	0.945726i	$-0.394647\pi$
$3$	1.95066	−	0.601698i	1.12621	−	0.347390i	0.801246	+	0.598335i	$0.204171\pi$
$4$	−0.988831	−	0.149042i	−0.494415	−	0.0745211i
$5$	0.958118	+	0.889004i	0.428484	+	0.397575i	0.864717	−	0.502259i	$-0.167497\pi$
$5$	0.958118	+	0.889004i	0.428484	+	0.397575i	−0.436234	+	0.899833i	$0.643688\pi$
$6$	−0.454243	−	1.99017i	−0.185444	−	0.812482i
$7$	−2.43754	+	1.02877i	−0.921305	+	0.388840i
$7$	−2.43754	+	1.02877i	−0.921305	+	0.388840i
$8$	−0.222521	+	0.974928i	−0.0786730	+	0.344689i
$9$	0.964304	−	0.657452i	0.321435	−	0.219151i
$10$	0.958118	−	0.889004i	0.302984	−	0.281128i
$11$	−2.30365	−	1.57060i	−0.694575	−	0.473553i	0.163854	−	0.986485i	$-0.447607\pi$
$11$	−2.30365	−	1.57060i	−0.694575	−	0.473553i	−0.858430	+	0.512931i	$0.828560\pi$
$12$	−2.01855	+	0.304247i	−0.582705	+	0.0878286i
$13$	−0.810304	+	0.390222i	−0.224738	+	0.108228i	−0.542865	−	0.839820i	$-0.682660\pi$
$13$	−0.810304	+	0.390222i	−0.224738	+	0.108228i	0.318127	+	0.948048i	$0.396946\pi$
$14$	0.843740	+	2.50761i	0.225499	+	0.670187i
$15$	2.40387	+	1.15764i	0.620677	+	0.298902i
$16$	0.955573	+	0.294755i	0.238893	+	0.0736888i
$17$	0.719733	−	1.83385i	0.174561	−	0.444774i	−0.816639	−	0.577149i	$-0.804165\pi$
$17$	0.719733	−	1.83385i	0.174561	−	0.444774i	0.991200	+	0.132375i	$0.0422604\pi$
$18$	−0.583551	−	1.01074i	−0.137544	−	0.238234i
$19$	0.387065	−	0.670417i	0.0887989	−	0.153804i	−0.818205	−	0.574927i	$-0.805030\pi$
$19$	0.387065	−	0.670417i	0.0887989	−	0.153804i	0.907004	+	0.421123i	$0.138364\pi$
$20$	−0.814918	−	1.02187i	−0.182221	−	0.228498i
$21$	−4.13580	+	3.47345i	−0.902506	+	0.757969i
$22$	−1.73836	+	2.17983i	−0.370619	+	0.464742i
$23$	2.28676	+	5.82658i	0.476823	+	1.21493i	0.943759	+	0.330635i	$0.107263\pi$
$23$	2.28676	+	5.82658i	0.476823	+	1.21493i	−0.466936	+	0.884291i	$0.654642\pi$
$24$	0.152550	+	2.03564i	0.0311392	+	0.415523i
$25$	−0.245988	−	3.28248i	−0.0491975	−	0.656495i
$26$	0.328576	+	0.837199i	0.0644391	+	0.164188i
$27$	−2.33284	+	2.92529i	−0.448955	+	0.562972i
$28$	2.56365	−	0.653987i	0.484484	−	0.123592i
$29$	6.52548	+	8.18270i	1.21175	+	1.51949i	0.790399	+	0.612592i	$0.209873\pi$
$29$	6.52548	+	8.18270i	1.21175	+	1.51949i	0.421353	+	0.906897i	$0.361555\pi$
$30$	1.33405	−	2.31064i	0.243563	−	0.421863i
$31$	−4.21876	−	7.30711i	−0.757713	−	1.31240i	−0.944014	−	0.329904i	$-0.892984\pi$
$31$	−4.21876	−	7.30711i	−0.757713	−	1.31240i	0.186302	−	0.982493i	$-0.440350\pi$
$32$	0.365341	−	0.930874i	0.0645838	−	0.164557i
$33$	−5.43865	−	1.67760i	−0.946747	−	0.292033i
$34$	−1.77494	−	0.854764i	−0.304399	−	0.146591i
$35$	−3.25004	−	1.18130i	−0.549357	−	0.199676i
$36$	−1.05152	+	0.506386i	−0.175254	+	0.0843977i
$37$	3.65860	−	0.551445i	0.601470	−	0.0906570i	0.158753	−	0.987318i	$-0.449253\pi$
$37$	3.65860	−	0.551445i	0.601470	−	0.0906570i	0.442717	+	0.896661i	$0.354015\pi$
$38$	−0.639617	−	0.436083i	−0.103760	−	0.0707421i
$39$	−1.34583	+	1.24875i	−0.215505	+	0.199959i
$40$	−1.07992	+	0.736274i	−0.170750	+	0.116415i
$41$	−1.26678	+	5.55015i	−0.197838	+	0.866787i	0.774382	+	0.632719i	$0.218061\pi$
$41$	−1.26678	+	5.55015i	−0.197838	+	0.866787i	−0.972220	+	0.234068i	$0.924796\pi$
$42$	3.15467	+	4.38381i	0.486776	+	0.676436i
$43$	−2.00714	−	8.79388i	−0.306087	−	1.34105i	−0.860771	−	0.508993i	$-0.830018\pi$
$43$	−2.00714	−	8.79388i	−0.306087	−	1.34105i	0.554684	−	0.832061i	$-0.312839\pi$
$44$	2.04383	+	1.89640i	0.308119	+	0.285893i
$45$	1.50839	+	0.227354i	0.224858	+	0.0338919i
$46$	5.98118	−	1.84495i	0.881877	−	0.272023i
$47$	0.907661	−	12.1119i	0.132396	−	1.76670i	−0.396520	−	0.918026i	$-0.629782\pi$
$47$	0.907661	−	12.1119i	0.132396	−	1.76670i	0.528915	−	0.848675i	$-0.322599\pi$
$48$	2.04135			0.294643
$49$	4.88324	−	5.01537i	0.697606	−	0.716481i
$50$	−3.29168			−0.465514
$51$	0.300528	−	4.01027i	0.0420824	−	0.561551i
$52$	0.859413	−	0.265094i	0.119179	−	0.0367619i
$53$	6.87650	+	1.03647i	0.944560	+	0.142369i	0.603224	−	0.797572i	$-0.293883\pi$
$53$	6.87650	+	1.03647i	0.944560	+	0.142369i	0.341336	+	0.939941i	$0.389121\pi$
$54$	2.74278	+	2.54492i	0.373244	+	0.346320i
$55$	−0.810897	−	3.55277i	−0.109341	−	0.479055i
$56$	−0.460577	−	2.60535i	−0.0615471	−	0.348155i
$57$	0.351643	−	1.54065i	0.0465763	−	0.204064i
$58$	8.64747	−	5.89574i	1.13547	−	0.774149i
$59$	3.85448	−	3.57644i	0.501811	−	0.465613i	−0.388185	−	0.921582i	$-0.626898\pi$
$59$	3.85448	−	3.57644i	0.501811	−	0.465613i	0.889996	+	0.455969i	$0.150707\pi$
$60$	−2.20448	−	1.50299i	−0.284598	−	0.194035i
$61$	−12.1696	+	1.83427i	−1.55815	+	0.234854i	−0.870862	−	0.491527i	$-0.836439\pi$
$61$	−12.1696	+	1.83427i	−1.55815	+	0.234854i	−0.687292	+	0.726381i	$0.741201\pi$
$62$	−7.60195	+	3.66091i	−0.965449	+	0.464936i
$63$	−1.67417	+	2.59462i	−0.210925	+	0.326891i
$64$	−0.900969	−	0.433884i	−0.112621	−	0.0542355i
$65$	−1.12328	−	0.346485i	−0.139325	−	0.0429761i
$66$	−2.07934	+	5.29807i	−0.255949	+	0.652148i
$67$	0.734787	+	1.27269i	0.0897685	+	0.155484i	0.907413	−	0.420240i	$-0.138054\pi$
$67$	0.734787	+	1.27269i	0.0897685	+	0.155484i	−0.817645	+	0.575723i	$0.804721\pi$
$68$	−0.985015	+	1.70610i	−0.119451	+	0.206895i
$69$	7.96653	+	9.98972i	0.959058	+	1.20262i
$70$	−1.42087	+	3.15267i	−0.169827	+	0.376817i
$71$	−3.74129	+	4.69143i	−0.444010	+	0.556771i	−0.952595	−	0.304241i	$-0.901597\pi$
$71$	−3.74129	+	4.69143i	−0.444010	+	0.556771i	0.508585	+	0.861012i	$0.330169\pi$
$72$	0.426390	+	1.08642i	0.0502505	+	0.128036i
$73$	0.00237545	+	0.0316982i	0.000278025	+	0.00370999i	0.997341	−	0.0728750i	$-0.0232174\pi$
$73$	0.00237545	+	0.0316982i	0.000278025	+	0.00370999i	−0.997063	+	0.0765850i	$0.975598\pi$
$74$	−0.276496	−	3.68958i	−0.0321420	−	0.428905i
$75$	−2.45490	−	6.25498i	−0.283467	−	0.722262i
$76$	−0.482663	+	0.605240i	−0.0553652	+	0.0694258i
$77$	7.23103	+	1.45847i	0.824052	+	0.166208i
$78$	1.14468	+	1.43538i	0.129610	+	0.162525i
$79$	−6.94343	+	12.0264i	−0.781196	+	1.35307i	0.150049	+	0.988679i	$0.452057\pi$
$79$	−6.94343	+	12.0264i	−0.781196	+	1.35307i	−0.931245	+	0.364393i	$0.881276\pi$
$80$	0.653513	+	1.13192i	0.0730650	+	0.126552i
$81$	−4.06960	+	10.3692i	−0.452178	+	1.15213i
$82$	5.43996	+	1.67801i	0.600743	+	0.185305i
$83$	−9.26679	−	4.46265i	−1.01716	−	0.489840i	−0.150434	−	0.988620i	$-0.548067\pi$
$83$	−9.26679	−	4.46265i	−1.01716	−	0.489840i	−0.866728	+	0.498780i	$0.833781\pi$
$84$	4.60730	−	2.81825i	0.502697	−	0.307496i
$85$	2.31989	−	1.11720i	0.251627	−	0.121177i
$86$	−8.91928	+	1.34437i	−0.961791	+	0.144967i
$87$	17.6525	+	12.0353i	1.89255	+	1.29032i
$88$	2.04383	−	1.89640i	0.217873	−	0.202157i
$89$	2.43024	−	1.65691i	0.257605	−	0.175632i	−0.427631	−	0.903954i	$-0.640652\pi$
$89$	2.43024	−	1.65691i	0.257605	−	0.175632i	0.685236	+	0.728321i	$0.259699\pi$
$90$	0.339441	−	1.48719i	0.0357802	−	0.156763i
$91$	1.57370	−	1.78480i	0.164969	−	0.187098i
$92$	−1.39282	−	6.10233i	−0.145211	−	0.636212i
$93$	−12.6260	−	11.7153i	−1.30926	−	1.21481i
$94$	−12.0102	−	1.81025i	−1.23876	−	0.186713i
$95$	0.966857	−	0.298236i	0.0991975	−	0.0305984i
$96$	0.152550	−	2.03564i	0.0155696	−	0.207762i
$97$	9.86141			1.00127			0.500637	−	0.865657i	$-0.333099\pi$
$97$	9.86141			1.00127			0.500637	+	0.865657i	$0.333099\pi$
$98$	−4.63642	−	5.24439i	−0.468349	−	0.529763i
$99$	−3.25401			−0.327040
$100$	−0.245988	+	3.28248i	−0.0245988	+	0.328248i
$101$	−5.62063	+	1.73374i	−0.559274	+	0.172513i	−0.561489	−	0.827484i	$-0.689771\pi$
$101$	−5.62063	+	1.73374i	−0.559274	+	0.172513i	0.00221489	+	0.999998i	$0.499295\pi$
$102$	−3.97660	−	0.599376i	−0.393742	−	0.0593471i
$103$	13.3780	+	12.4130i	1.31817	+	1.22308i	0.956829	+	0.290651i	$0.0938719\pi$
$103$	13.3780	+	12.4130i	1.31817	+	1.22308i	0.361342	+	0.932433i	$0.382319\pi$
$104$	−0.200128	−	0.876820i	−0.0196242	−	0.0859793i
$105$	−7.05050	−	0.348765i	−0.688058	−	0.0340360i
$106$	1.54745	−	6.77981i	0.150301	−	0.658514i
$107$	−6.87906	+	4.69006i	−0.665024	+	0.453405i	−0.848201	−	0.529674i	$-0.822314\pi$
$107$	−6.87906	+	4.69006i	−0.665024	+	0.453405i	0.183177	+	0.983080i	$0.441362\pi$
$108$	2.74278	−	2.54492i	0.263924	−	0.244885i
$109$	−5.04810	−	3.44174i	−0.483521	−	0.329659i	0.296905	−	0.954907i	$-0.404045\pi$
$109$	−5.04810	−	3.44174i	−0.483521	−	0.329659i	−0.780426	+	0.625248i	$0.784998\pi$
$110$	−3.60343	+	0.543130i	−0.343574	+	0.0517854i
$111$	6.80486	−	3.27705i	0.645889	−	0.311044i
$112$	−2.63249	+	0.264590i	−0.248747	+	0.0250014i
$113$	11.4501	+	5.51408i	1.07714	+	0.518721i	0.886400	−	0.462920i	$-0.153198\pi$
$113$	11.4501	+	5.51408i	1.07714	+	0.518721i	0.190736	+	0.981641i	$0.438913\pi$
$114$	−1.51006	−	0.465793i	−0.141430	−	0.0436255i
$115$	−2.98886	+	7.61550i	−0.278713	+	0.710149i
$116$	−5.23303	−	9.06388i	−0.485875	−	0.841560i
$117$	−0.524827	+	0.909028i	−0.0485203	+	0.0840397i
$118$	−3.27839	−	4.11097i	−0.301800	−	0.378446i
$119$	0.132237	+	5.21053i	0.0121222	+	0.477649i
$120$	−1.66353	+	2.08600i	−0.151859	+	0.190425i
$121$	−1.17875	−	3.00340i	−0.107159	−	0.273037i
$122$	0.919706	+	12.2726i	0.0832663	+	1.11111i
$123$	0.868449	+	11.5886i	0.0783054	+	1.04491i
$124$	3.08258	+	7.85427i	0.276823	+	0.705335i
$125$	6.75704	−	8.47306i	0.604368	−	0.757853i
$126$	2.46225	+	1.86338i	0.219355	+	0.166003i
$127$	−1.38226	−	1.73330i	−0.122656	−	0.153805i	0.716712	−	0.697369i	$-0.245646\pi$
$127$	−1.38226	−	1.73330i	−0.122656	−	0.153805i	−0.839368	+	0.543564i	$0.817075\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$	−9.20651	−	15.9461i	−0.810588	−	1.40398i
$130$	−0.429458	+	1.09424i	−0.0376660	+	0.0959713i
$131$	3.85124	+	1.18795i	0.336484	+	0.103792i	0.458393	−	0.888750i	$-0.348425\pi$
$131$	3.85124	+	1.18795i	0.336484	+	0.103792i	−0.121909	+	0.992541i	$0.538902\pi$
$132$	5.12787	+	2.46945i	0.446324	+	0.214938i
$133$	−0.253781	+	2.03237i	−0.0220056	+	0.176229i
$134$	1.32404	−	0.637624i	0.114380	−	0.0550823i
$135$	−4.83573	+	0.728869i	−0.416193	+	0.0627310i
$136$	1.62772	+	1.10976i	0.139575	+	0.0951610i
$137$	−1.61689	+	1.50025i	−0.138140	+	0.128175i	−0.746217	−	0.665703i	$-0.768132\pi$
$137$	−1.61689	+	1.50025i	−0.138140	+	0.128175i	0.608077	+	0.793878i	$0.291941\pi$
$138$	10.5571	−	7.19772i	0.898682	−	0.612711i
$139$	2.32127	−	10.1701i	0.196887	−	0.862620i	−0.775888	−	0.630871i	$-0.782698\pi$
$139$	2.32127	−	10.1701i	0.196887	−	0.862620i	0.972776	−	0.231749i	$-0.0744450\pi$
$140$	3.03768	+	1.65250i	0.256731	+	0.139662i
$141$	−5.51716	−	24.1723i	−0.464629	−	2.03567i
$142$	4.39873	+	4.08142i	0.369133	+	0.342505i
$143$	2.47953	+	0.373730i	0.207349	+	0.0312528i
$144$	1.11525	−	0.344009i	0.0929375	−	0.0286674i
$145$	−1.02226	+	13.6412i	−0.0848945	+	1.13284i
$146$	0.0317871			0.00263072
$147$	6.50780	−	12.7215i	0.536754	−	1.04925i
$148$	−3.69992			−0.304132
$149$	0.246120	−	3.28424i	0.0201629	−	0.269056i	−0.978006	−	0.208575i	$-0.933118\pi$
$149$	0.246120	−	3.28424i	0.0201629	−	0.269056i	0.998169	−	0.0604809i	$-0.0192634\pi$
$150$	−6.42094	+	1.98060i	−0.524268	+	0.161715i
$151$	13.8574	+	2.08866i	1.12770	+	0.169973i	0.686285	−	0.727332i	$-0.259240\pi$
$151$	13.8574	+	2.08866i	1.12770	+	0.169973i	0.441411	+	0.897305i	$0.354478\pi$
$152$	0.567478	+	0.526543i	0.0460285	+	0.0427082i
$153$	−0.511626	−	2.24158i	−0.0413625	−	0.181221i
$154$	1.99477	−	7.10182i	0.160743	−	0.572281i
$155$	2.45398	−	10.7516i	0.197108	−	0.863588i
$156$	1.51691	−	1.03421i	0.121450	−	0.0828034i
$157$	−2.22740	+	2.06673i	−0.177766	+	0.164943i	−0.764037	−	0.645172i	$-0.776786\pi$
$157$	−2.22740	+	2.06673i	−0.177766	+	0.164943i	0.586271	+	0.810115i	$0.300595\pi$
$158$	11.4739	+	7.82274i	0.912811	+	0.622344i
$159$	14.0373	−	2.11579i	1.11323	−	0.167793i
$160$	1.17759	−	0.567098i	0.0930967	−	0.0448330i
$161$	−11.5683	−	11.8500i	−0.911712	−	0.933909i
$162$	10.0361	+	4.83311i	0.788507	+	0.379725i
$163$	8.08053	+	2.49251i	0.632916	+	0.195229i	0.594580	−	0.804036i	$-0.297318\pi$
$163$	8.08053	+	2.49251i	0.632916	+	0.195229i	0.0383356	+	0.999265i	$0.487794\pi$
$164$	2.07984	−	5.29935i	0.162408	−	0.413810i
$165$	−3.71947	−	6.44232i	−0.289561	−	0.501534i
$166$	−5.14268	+	8.90738i	−0.399149	+	0.691347i
$167$	6.48156	+	8.12762i	0.501558	+	0.628934i	0.966580	−	0.256365i	$-0.0825249\pi$
$167$	6.48156	+	8.12762i	0.501558	+	0.628934i	−0.465022	+	0.885299i	$0.653954\pi$
$168$	−2.46606	−	4.80502i	−0.190261	−	0.370716i
$169$	−7.60105	+	9.53141i	−0.584696	+	0.733186i
$170$	−0.940710	−	2.39689i	−0.0721492	−	0.183833i
$171$	−0.0675178	−	0.900963i	−0.00516322	−	0.0688983i
$172$	0.674067	+	8.99481i	0.0513972	+	0.685848i
$173$	0.215003	+	0.547818i	0.0163464	+	0.0416499i	0.938814	−	0.344425i	$-0.111926\pi$
$173$	0.215003	+	0.547818i	0.0163464	+	0.0416499i	−0.922468	+	0.386075i	$0.873831\pi$
$174$	13.3208	−	16.7037i	1.00985	−	1.26631i
$175$	3.97654	+	7.74812i	0.300598	+	0.585703i
$176$	−1.73836	−	2.17983i	−0.131034	−	0.164311i
$177$	5.36684	−	9.29564i	0.403396	−	0.698703i
$178$	−1.47067	−	2.54727i	−0.110231	−	0.190926i
$179$	−3.75370	+	9.56427i	−0.280565	+	0.714867i	0.719233	+	0.694769i	$0.244493\pi$
$179$	−3.75370	+	9.56427i	−0.280565	+	0.714867i	−0.999798	+	0.0200985i	$0.993602\pi$
$180$	−1.45766	−	0.449629i	−0.108648	−	0.0335134i
$181$	−7.89317	−	3.80115i	−0.586694	−	0.282537i	0.116895	−	0.993144i	$-0.462706\pi$
$181$	−7.89317	−	3.80115i	−0.586694	−	0.282537i	−0.703589	+	0.710607i	$0.748420\pi$
$182$	−1.66221	−	1.70268i	−0.123211	−	0.126211i
$183$	−22.6350	+	10.9004i	−1.67323	+	0.805784i
$184$	−6.18935	+	0.932894i	−0.456285	+	0.0687739i
$185$	3.99561	+	2.72416i	0.293763	+	0.200284i
$186$	−12.6260	+	11.7153i	−0.925786	+	0.859004i
$187$	−4.53825	+	3.09413i	−0.331870	+	0.226265i
$188$	−2.70271	+	11.8413i	−0.197115	+	0.863618i
$189$	2.67694	−	9.53049i	0.194718	−	0.693241i
$190$	−0.225149	−	0.986441i	−0.0163340	−	0.0715640i
$191$	1.39907	+	1.29815i	0.101233	+	0.0939309i	0.729166	−	0.684337i	$-0.239908\pi$
$191$	1.39907	+	1.29815i	0.101233	+	0.0939309i	−0.627933	+	0.778268i	$0.716099\pi$
$192$	−2.01855	−	0.304247i	−0.145676	−	0.0219571i
$193$	−5.90845	+	1.82252i	−0.425300	+	0.131188i	−0.500014	−	0.866017i	$-0.666672\pi$
$193$	−5.90845	+	1.82252i	−0.425300	+	0.131188i	0.0747142	+	0.997205i	$0.476196\pi$
$194$	0.736944	−	9.83383i	0.0529095	−	0.706028i
$195$	−2.39960			−0.171839
$196$	−5.57620	+	4.23154i	−0.398300	+	0.302253i
$197$	1.17887			0.0839912			0.0419956	−	0.999118i	$-0.486628\pi$
$197$	1.17887			0.0839912			0.0419956	+	0.999118i	$0.486628\pi$
$198$	−0.243172	+	3.24491i	−0.0172815	+	0.230606i
$199$	−24.2165	+	7.46981i	−1.71666	+	0.529521i	−0.987880	−	0.155222i	$-0.950391\pi$
$199$	−24.2165	+	7.46981i	−1.71666	+	0.529521i	−0.728785	+	0.684743i	$0.759914\pi$
$200$	3.25492	+	0.490600i	0.230157	+	0.0346906i
$201$	2.19909	+	2.04046i	0.155112	+	0.143923i
$202$	1.30886	+	5.73448i	0.0920909	+	0.403476i
$203$	−24.3243	−	13.2324i	−1.70723	−	0.928735i
$204$	−0.894872	+	3.92069i	−0.0626536	+	0.274503i
$205$	−6.14783	+	4.19152i	−0.429383	+	0.292748i
$206$	13.3780	−	12.4130i	0.932088	−	0.864851i
$207$	6.03583	+	4.11516i	0.419519	+	0.286023i
$208$	−0.889324	+	0.134044i	−0.0616635	+	0.00929428i
$209$	−1.94462	+	0.936478i	−0.134512	+	0.0647776i
$210$	−0.874674	+	7.00472i	−0.0603582	+	0.483372i
$211$	−2.62115	−	1.26228i	−0.180447	−	0.0868988i	0.341479	−	0.939889i	$-0.389072\pi$
$211$	−2.62115	−	1.26228i	−0.180447	−	0.0868988i	−0.521926	+	0.852991i	$0.674786\pi$
$212$	−6.64522	−	2.04978i	−0.456395	−	0.140779i
$213$	−4.47515	+	11.4025i	−0.306632	+	0.781286i
$214$	4.16287	+	7.21031i	0.284568	+	0.492887i
$215$	5.89471	−	10.2099i	0.402016	−	0.696312i
$216$	−2.33284	−	2.92529i	−0.158730	−	0.199041i
$217$	17.8008	+	13.4713i	1.20840	+	0.914489i
$218$	−3.80936	+	4.77679i	−0.258002	+	0.323525i
$219$	0.0237064	+	0.0604029i	0.00160193	+	0.00408165i
$220$	0.272327	+	3.63395i	0.0183603	+	0.245001i
$221$	0.132406	+	1.76683i	0.00890657	+	0.118850i
$222$	−2.75936	−	7.03073i	−0.185196	−	0.471872i
$223$	4.76555	−	5.97581i	0.319125	−	0.400170i	−0.596233	−	0.802811i	$-0.703337\pi$
$223$	4.76555	−	5.97581i	0.319125	−	0.400170i	0.915358	+	0.402642i	$0.131908\pi$
$224$	0.0671245	+	2.64490i	0.00448495	+	0.176720i
$225$	−2.39528	−	3.00358i	−0.159685	−	0.200239i
$226$	6.35433	−	11.0060i	0.422684	−	0.732110i
$227$	−1.33112	−	2.30558i	−0.0883498	−	0.153026i	0.818464	−	0.574558i	$-0.194826\pi$
$227$	−1.33112	−	2.30558i	−0.0883498	−	0.153026i	−0.906814	+	0.421532i	$0.861493\pi$
$228$	−0.577337	+	1.47103i	−0.0382351	+	0.0974215i
$229$	−6.98904	−	2.15583i	−0.461848	−	0.142461i	0.0550947	−	0.998481i	$-0.482454\pi$
$229$	−6.98904	−	2.15583i	−0.461848	−	0.142461i	−0.516943	+	0.856020i	$0.672930\pi$
$230$	7.37084	+	3.54961i	0.486019	+	0.234054i
$231$	14.9828	−	1.50592i	0.985797	−	0.0990821i
$232$	−9.42960	+	4.54106i	−0.619083	+	0.298135i
$233$	22.1214	−	3.33426i	1.44922	−	0.218434i	0.623193	−	0.782068i	$-0.285835\pi$
$233$	22.1214	−	3.33426i	1.44922	−	0.218434i	0.826025	+	0.563634i	$0.190597\pi$
$234$	0.867266	+	0.591292i	0.0566949	+	0.0386539i
$235$	11.6372	−	10.7977i	0.759125	−	0.704365i
$236$	−4.34447	+	2.96201i	−0.282801	+	0.192810i
$237$	−6.30800	+	27.6372i	−0.409749	+	1.79523i
$238$	5.20585	+	0.257516i	0.337445	+	0.0166923i
$239$	6.35223	+	27.8309i	0.410892	+	1.80023i	0.579978	+	0.814632i	$0.303061\pi$
$239$	6.35223	+	27.8309i	0.410892	+	1.80023i	−0.169087	+	0.985601i	$0.554082\pi$
$240$	1.95585	+	1.81477i	0.126250	+	0.117143i
$241$	−23.4344	−	3.53217i	−1.50954	−	0.227527i	−0.658483	−	0.752595i	$-0.728802\pi$
$241$	−23.4344	−	3.53217i	−1.50954	−	0.227527i	−0.851060	+	0.525068i	$0.824040\pi$
$242$	−3.08309	+	0.951009i	−0.198189	+	0.0611331i
$243$	−0.860456	+	11.4820i	−0.0551983	+	0.736570i
$244$	12.3070			0.787877
$245$	9.13741	−	0.464093i	0.583768	−	0.0296498i
$246$	11.6211			0.740937
$247$	−0.0520293	+	0.694282i	−0.00331054	+	0.0441761i
$248$	8.06267	−	2.48701i	0.511980	−	0.157925i
$249$	−20.7615	−	3.12929i	−1.31571	−	0.198311i
$250$	−7.94441	−	7.37134i	−0.502449	−	0.466204i
$251$	−4.43306	−	19.4225i	−0.279813	−	1.22594i	−0.898031	−	0.439933i	$-0.855002\pi$
$251$	−4.43306	−	19.4225i	−0.279813	−	1.22594i	0.618218	−	0.786006i	$-0.287855\pi$
$252$	2.04217	−	2.31612i	0.128645	−	0.145902i
$253$	3.88333	−	17.0140i	0.244143	−	1.06966i
$254$	−1.83175	+	1.24886i	−0.114934	+	0.0783607i
$255$	3.85309	−	3.57515i	0.241290	−	0.223884i
$256$	0.826239	+	0.563320i	0.0516399	+	0.0352075i
$257$	18.8787	−	2.84551i	1.17762	−	0.177498i	0.469073	−	0.883159i	$-0.344588\pi$
$257$	18.8787	−	2.84551i	1.17762	−	0.177498i	0.708550	+	0.705661i	$0.249350\pi$
$258$	−16.5896	+	7.98911i	−1.03282	+	0.497380i
$259$	−8.35068	+	5.10804i	−0.518886	+	0.317398i
$260$	1.05909	+	0.510030i	0.0656819	+	0.0316307i
$261$	11.6723	+	3.60042i	0.722496	+	0.222861i
$262$	1.47243	−	3.75169i	0.0909670	−	0.231780i
$263$	−4.17870	−	7.23772i	−0.257670	−	0.446297i	0.707947	−	0.706265i	$-0.249621\pi$
$263$	−4.17870	−	7.23772i	−0.257670	−	0.446297i	−0.965617	+	0.259968i	$0.916288\pi$
$264$	2.84575	−	4.92899i	0.175144	−	0.303358i
$265$	5.66708	+	7.10629i	0.348126	+	0.436536i
$266$	2.00773	+	0.404951i	0.123102	+	0.0248291i
$267$	3.74361	−	4.69433i	0.229105	−	0.287289i
$268$	−0.536896	−	1.36799i	−0.0327961	−	0.0835632i
$269$	−0.180738	−	2.41178i	−0.0110198	−	0.147049i	0.988980	−	0.148051i	$-0.0473000\pi$
$269$	−0.180738	−	2.41178i	−0.0110198	−	0.147049i	−0.999999	+	0.00100230i	$0.999681\pi$
$270$	0.365456	+	4.87668i	0.0222410	+	0.296785i
$271$	−3.86903	−	9.85814i	−0.235027	−	0.598839i	0.763891	−	0.645345i	$-0.223287\pi$
$271$	−3.86903	−	9.85814i	−0.235027	−	0.598839i	−0.998918	+	0.0465061i	$0.985191\pi$
$272$	1.22829	−	1.54023i	0.0744763	−	0.0933903i
$273$	1.99584	−	4.42843i	0.120794	−	0.268021i
$274$	1.37523	+	1.72448i	0.0830804	+	0.104180i
$275$	−4.58879	+	7.94801i	−0.276714	+	0.479283i
$276$	−6.38866	−	11.0655i	−0.384552	−	0.666064i
$277$	7.54038	−	19.2126i	0.453057	−	1.15437i	−0.503802	−	0.863819i	$-0.668066\pi$
$277$	7.54038	−	19.2126i	0.453057	−	1.15437i	0.956859	−	0.290552i	$-0.0938390\pi$
$278$	−9.96823	−	3.07479i	−0.597855	−	0.184414i
$279$	−8.87225	−	4.27265i	−0.531168	−	0.255797i
$280$	1.87488	−	2.90569i	0.112046	−	0.173648i
$281$	−9.57033	+	4.60883i	−0.570918	+	0.274940i	−0.696989	−	0.717082i	$-0.745477\pi$
$281$	−9.57033	+	4.60883i	−0.570918	+	0.274940i	0.126071	+	0.992021i	$0.459763\pi$
$282$	−24.5170	+	3.69534i	−1.45997	+	0.220054i
$283$	20.3972	+	13.9065i	1.21249	+	0.826658i	0.988981	−	0.148045i	$-0.0472979\pi$
$283$	20.3972	+	13.9065i	1.21249	+	0.826658i	0.223504	+	0.974703i	$0.428250\pi$
$284$	4.39873	−	4.08142i	0.261016	−	0.242188i
$285$	1.70656	−	1.16351i	0.101088	−	0.0689205i
$286$	0.557980	−	2.44467i	0.0329941	−	0.144556i
$287$	−2.62201	−	14.8320i	−0.154772	−	0.875503i
$288$	−0.259704	−	1.13784i	−0.0153032	−	0.0670478i
$289$	9.61689	+	8.92317i	0.565700	+	0.524892i
$290$	13.5266	+	2.03881i	0.794311	+	0.119723i
$291$	19.2362	−	5.93359i	1.12765	−	0.347833i
$292$	0.00237545	−	0.0316982i	0.000139013	−	0.00185500i
$293$	−10.9148			−0.637647			−0.318823	−	0.947814i	$-0.603288\pi$
$293$	−10.9148			−0.637647			−0.318823	+	0.947814i	$0.603288\pi$
$294$	−12.1996	−	7.44028i	−0.711495	−	0.433926i
$295$	6.87252			0.400133
$296$	−0.276496	+	3.68958i	−0.0160710	+	0.214452i
$297$	9.96849	−	3.07487i	0.578430	−	0.178422i
$298$	−3.25667	−	0.490864i	−0.188654	−	0.0284350i
$299$	−4.12663	−	3.82895i	−0.238649	−	0.221434i
$300$	1.49522	+	6.55100i	0.0863267	+	0.378222i
$301$	13.9394	+	19.3706i	0.803455	+	1.11650i
$302$	3.11838	−	13.6625i	0.179443	−	0.786190i
$303$	−9.92074	+	6.76384i	−0.569931	+	0.388573i
$304$	0.567478	−	0.526543i	0.0325471	−	0.0301993i
$305$	−13.2906	−	9.06136i	−0.761016	−	0.518852i
$306$	−2.27355	+	0.342682i	−0.129970	+	0.0195898i
$307$	−11.4673	+	5.52234i	−0.654471	+	0.315177i	−0.731489	−	0.681853i	$-0.761174\pi$
$307$	−11.4673	+	5.52234i	−0.654471	+	0.315177i	0.0770182	+	0.997030i	$0.475460\pi$
$308$	−6.93289	−	2.51991i	−0.395038	−	0.143585i
$309$	33.5647	+	16.1639i	1.90943	+	0.919532i
$310$	−10.5381	−	3.25058i	−0.598526	−	0.184621i
$311$	−1.43091	+	3.64589i	−0.0811394	+	0.206740i	−0.965686	−	0.259712i	$-0.916372\pi$
$311$	−1.43091	+	3.64589i	−0.0811394	+	0.206740i	0.884547	+	0.466451i	$0.154468\pi$
$312$	−0.917963	−	1.58996i	−0.0519694	−	0.0900136i
$313$	−8.01115	+	13.8757i	−0.452817	+	0.784302i	−0.998560	−	0.0536505i	$-0.982914\pi$
$313$	−8.01115	+	13.8757i	−0.452817	+	0.784302i	0.545743	+	0.837953i	$0.316248\pi$
$314$	1.89450	+	2.37562i	0.106913	+	0.134064i
$315$	−3.91068	+	0.997613i	−0.220342	+	0.0562091i
$316$	8.65831	−	10.8572i	0.487068	−	0.610764i
$317$	−12.7743	−	32.5483i	−0.717474	−	1.82809i	−0.534929	−	0.844897i	$-0.679662\pi$
$317$	−12.7743	−	32.5483i	−0.717474	−	1.82809i	−0.182545	−	0.983197i	$-0.558434\pi$
$318$	−1.06086	−	14.1562i	−0.0594900	−	0.793840i
$319$	−2.18067	−	29.0990i	−0.122094	−	1.62923i
$320$	−0.477510	−	1.21668i	−0.0266936	−	0.0680143i
$321$	−10.5967	+	13.2878i	−0.591449	+	0.741653i
$322$	−12.6813	+	10.6504i	−0.706704	+	0.593525i
$323$	−0.950860	−	1.19234i	−0.0529073	−	0.0663436i
$324$	5.56959	−	9.64681i	0.309422	−	0.535934i
$325$	1.48022	+	2.56381i	0.0821077	+	0.142215i
$326$	3.08940	−	7.87167i	0.171106	−	0.435971i
$327$	−11.9180	−	3.67622i	−0.659067	−	0.203295i
$328$	−5.12911	−	2.47005i	−0.283207	−	0.136386i
$329$	10.2479	+	30.4570i	0.564987	+	1.67915i
$330$	−6.70226	+	3.22764i	−0.368947	+	0.177676i
$331$	32.3808	−	4.88062i	1.77981	−	0.268263i	0.824926	−	0.565241i	$-0.191217\pi$
$331$	32.3808	−	4.88062i	1.77981	−	0.268263i	0.954885	+	0.296977i	$0.0959785\pi$
$332$	8.49816	+	5.79395i	0.466397	+	0.317984i
$333$	3.16545	−	2.93711i	0.173466	−	0.160953i
$334$	8.58926	−	5.85606i	0.469983	−	0.320429i
$335$	−0.427412	+	1.87261i	−0.0233520	+	0.102312i
$336$	−4.97588	+	2.10009i	−0.271456	+	0.114569i
$337$	−5.67596	−	24.8680i	−0.309189	−	1.35465i	−0.855820	−	0.517274i	$-0.826947\pi$
$337$	−5.67596	−	24.8680i	−0.309189	−	1.35465i	0.546631	−	0.837374i	$-0.315910\pi$
$338$	8.93673	+	8.29208i	0.486094	+	0.451030i
$339$	25.6531	+	3.86658i	1.39328	+	0.210004i
$340$	−2.46049	+	0.758960i	−0.133439	+	0.0411604i
$341$	−1.75801	+	23.4590i	−0.0952015	+	1.27038i
$342$	−0.903489			−0.0488551
$343$	−6.74344	+	17.2489i	−0.364112	+	0.931355i
$344$	9.02003			0.486327
$345$	−1.24802	+	16.6536i	−0.0671909	+	0.896600i
$346$	0.562354	−	0.173463i	0.0302323	−	0.00932544i
$347$	−2.44095	−	0.367914i	−0.131037	−	0.0197507i	0.0831962	−	0.996533i	$-0.473487\pi$
$347$	−2.44095	−	0.367914i	−0.131037	−	0.0197507i	−0.214233	+	0.976783i	$0.568725\pi$
$348$	−15.6616	−	14.5318i	−0.839548	−	0.778987i
$349$	−4.98979	−	21.8617i	−0.267097	−	1.17023i	−0.913373	−	0.407125i	$-0.866531\pi$
$349$	−4.98979	−	21.8617i	−0.267097	−	1.17023i	0.646275	−	0.763104i	$-0.276326\pi$
$350$	8.02362	−	3.38640i	0.428880	−	0.181011i
$351$	0.748797	−	3.28070i	0.0399678	−	0.175111i
$352$	−2.30365	+	1.57060i	−0.122785	+	0.0837132i
$353$	17.6865	−	16.4107i	0.941359	−	0.873453i	−0.0507656	−	0.998711i	$-0.516166\pi$
$353$	17.6865	−	16.4107i	0.941359	−	0.873453i	0.992124	+	0.125257i	$0.0399757\pi$
$354$	−8.86858	−	6.04649i	−0.471360	−	0.321368i
$355$	−7.75530	+	1.16892i	−0.411609	+	0.0620400i
$356$	−2.65005	+	1.27620i	−0.140452	+	0.0676382i
$357$	3.39312	+	10.0844i	0.179583	+	0.533723i
$358$	9.25701	+	4.45794i	0.489248	+	0.235610i
$359$	0.376522	+	0.116142i	0.0198721	+	0.00612972i	0.304675	−	0.952456i	$-0.401452\pi$
$359$	0.376522	+	0.116142i	0.0198721	+	0.00612972i	−0.284803	+	0.958586i	$0.591928\pi$
$360$	−0.557303	+	1.41999i	−0.0293725	+	0.0748398i
$361$	9.20036	+	15.9355i	0.484230	+	0.838710i
$362$	−4.38038	+	7.58703i	−0.230227	+	0.398766i
$363$	−4.10648	−	5.14936i	−0.215534	−	0.270271i
$364$	−1.82213	+	1.53032i	−0.0955058	+	0.0802106i
$365$	−0.0259038	+	0.0324824i	−0.00135587	+	0.00170021i
$366$	9.17844	+	23.3863i	0.479765	+	1.22242i
$367$	1.16772	+	15.5822i	0.0609546	+	0.813383i	0.940981	+	0.338459i	$0.109906\pi$
$367$	1.16772	+	15.5822i	0.0609546	+	0.813383i	−0.880027	+	0.474924i	$0.842475\pi$
$368$	0.467755	+	6.24176i	0.0243834	+	0.325374i
$369$	2.42739	+	6.18488i	0.126365	+	0.321972i
$370$	3.01513	−	3.78086i	0.156749	−	0.196557i
$371$	−17.8281	+	4.54794i	−0.925587	+	0.236117i
$372$	10.7389	+	13.4662i	0.556788	+	0.698191i
$373$	−2.63813	+	4.56937i	−0.136597	+	0.236593i	−0.926206	−	0.377017i	$-0.876950\pi$
$373$	−2.63813	+	4.56937i	−0.136597	+	0.236593i	0.789609	+	0.613610i	$0.210283\pi$
$374$	2.74633	+	4.75679i	0.142009	+	0.245968i
$375$	8.08244	−	20.5937i	0.417375	−	1.06346i
$376$	11.6062	+	3.58005i	0.598546	+	0.184627i
$377$	−8.48069	−	4.08408i	−0.436778	−	0.210341i
$378$	−9.30379	−	3.38167i	−0.478535	−	0.173934i
$379$	−32.2676	+	15.5393i	−1.65748	+	0.798199i	−0.658518	+	0.752565i	$0.728816\pi$
$379$	−32.2676	+	15.5393i	−1.65748	+	0.798199i	−0.998958	+	0.0456335i	$0.985469\pi$
$380$	−1.00051	+	0.150802i	−0.0513250	+	0.00773600i
$381$	−3.73923	−	2.54937i	−0.191567	−	0.130608i
$382$	1.39907	−	1.29815i	0.0715828	−	0.0664192i
$383$	−12.5326	+	8.54457i	−0.640385	+	0.436607i	−0.839493	−	0.543370i	$-0.817148\pi$
$383$	−12.5326	+	8.54457i	−0.640385	+	0.436607i	0.199108	+	0.979978i	$0.436196\pi$
$384$	−0.454243	+	1.99017i	−0.0231805	+	0.101560i
$385$	5.63160	+	7.82580i	0.287013	+	0.398840i
$386$	1.37588	+	6.02813i	0.0700305	+	0.306823i
$387$	−7.71705	−	7.16037i	−0.392280	−	0.363982i
$388$	−9.75126	−	1.46977i	−0.495045	−	0.0746161i
$389$	−23.0643	+	7.11438i	−1.16940	+	0.360714i	−0.817838	−	0.575449i	$-0.804827\pi$
$389$	−23.0643	+	7.11438i	−1.16940	+	0.360714i	−0.351567	+	0.936163i	$0.614351\pi$
$390$	−0.179323	+	2.39289i	−0.00908035	+	0.121169i
$391$	12.3309			0.623602
$392$	3.80300	+	5.87684i	0.192080	+	0.296825i
$393$	8.22722			0.415009
$394$	0.0880973	−	1.17558i	0.00443828	−	0.0592247i
$395$	−17.3441	+	5.34995i	−0.872677	+	0.269185i
$396$	3.21766	+	0.484985i	0.161694	+	0.0243714i
$397$	−28.0957	−	26.0690i	−1.41008	−	1.30837i	−0.891267	−	0.453479i	$-0.850183\pi$
$397$	−28.0957	−	26.0690i	−1.41008	−	1.30837i	−0.518815	−	0.854886i	$-0.673627\pi$
$398$	5.63922	+	24.7070i	0.282669	+	1.23845i
$399$	0.727835	+	4.11716i	0.0364373	+	0.206116i
$400$	0.732468	−	3.20915i	0.0366234	−	0.160458i
$401$	6.81287	−	4.64494i	0.340219	−	0.231957i	−0.381142	−	0.924516i	$-0.624469\pi$
$401$	6.81287	−	4.64494i	0.340219	−	0.231957i	0.721361	+	0.692559i	$0.243517\pi$
$402$	2.19909	−	2.04046i	0.109681	−	0.101769i
$403$	6.26987	+	4.27473i	0.312325	+	0.212939i
$404$	5.81625	−	0.876659i	0.289369	−	0.0436154i
$405$	−13.1174	+	6.31700i	−0.651808	+	0.313894i
$406$	−15.0132	+	23.2674i	−0.745092	+	1.15474i
$407$	−9.29421	−	4.47586i	−0.460697	−	0.221860i
$408$	3.84285	+	1.18536i	0.190250	+	0.0586842i
$409$	3.36816	−	8.58193i	0.166545	−	0.424349i	−0.823098	−	0.567899i	$-0.807756\pi$
$409$	3.36816	−	8.58193i	0.166545	−	0.424349i	0.989643	+	0.143550i	$0.0458517\pi$
$410$	3.72037	+	6.44387i	0.183736	+	0.318240i
$411$	−2.25129	+	3.89935i	−0.111048	+	0.192341i
$412$	−11.3785	−	14.2682i	−0.560579	−	0.702943i
$413$	−5.71612	+	12.6831i	−0.281272	+	0.624096i
$414$	4.55471	−	5.71143i	0.223852	−	0.280701i
$415$	−4.91137	−	12.5140i	−0.241090	−	0.614286i
$416$	0.0672099	+	0.896854i	0.00329524	+	0.0439719i
$417$	−1.59135	−	21.2352i	−0.0779290	−	1.03989i
$418$	0.788538	+	2.00916i	0.0385687	+	0.0982714i
$419$	−5.67594	+	7.11741i	−0.277288	+	0.347708i	−0.900901	−	0.434025i	$-0.857093\pi$
$419$	−5.67594	+	7.11741i	−0.277288	+	0.347708i	0.623613	+	0.781733i	$0.285664\pi$
$420$	6.91977	+	1.39569i	0.337650	+	0.0681028i
$421$	−5.52252	−	6.92502i	−0.269151	−	0.337505i	0.628827	−	0.777545i	$-0.283535\pi$
$421$	−5.52252	−	6.92502i	−0.269151	−	0.337505i	−0.897978	+	0.440041i	$0.854964\pi$
$422$	−1.45463	+	2.51949i	−0.0708101	+	0.122647i
$423$	−7.08772	−	12.2763i	−0.344617	−	0.596894i
$424$	−2.54064	+	6.47345i	−0.123385	+	0.314379i
$425$	−6.19662	−	1.91140i	−0.300580	−	0.0927167i
$426$	11.0362	+	5.31475i	0.534705	+	0.257500i
$427$	27.7768	−	16.9909i	1.34422	−	0.822246i
$428$	7.50124	−	3.61241i	0.362586	−	0.174612i
$429$	5.06159	−	0.762912i	0.244376	−	0.0368337i
$430$	−9.74087	−	6.64121i	−0.469747	−	0.320268i
$431$	−8.29095	+	7.69288i	−0.399361	+	0.370553i	−0.854133	−	0.520055i	$-0.825911\pi$
$431$	−8.29095	+	7.69288i	−0.399361	+	0.370553i	0.454772	+	0.890608i	$0.349721\pi$
$432$	−3.09144	+	2.10771i	−0.148737	+	0.101407i
$433$	4.98736	−	21.8511i	0.239677	−	1.05010i	−0.701629	−	0.712542i	$-0.747544\pi$
$433$	4.98736	−	21.8511i	0.239677	−	1.05010i	0.941307	−	0.337553i	$-0.109599\pi$
$434$	14.7638	−	16.7443i	0.708687	−	0.803753i
$435$	6.21378	+	27.2243i	0.297928	+	1.30531i
$436$	4.47876	+	4.15568i	0.214494	+	0.199021i
$437$	4.79136	+	0.722182i	0.229202	+	0.0345466i
$438$	0.0620056	−	0.0191262i	0.00296274	−	0.000913885i
$439$	0.909800	−	12.1404i	0.0434224	−	0.579431i	−0.932480	−	0.361222i	$-0.882360\pi$
$439$	0.909800	−	12.1404i	0.0434224	−	0.579431i	0.975902	−	0.218209i	$-0.0700214\pi$
$440$	3.64414			0.173727
$441$	1.41157	−	8.04684i	0.0672177	−	0.383183i
$442$	1.77179			0.0842752
$443$	1.15486	−	15.4105i	0.0548689	−	0.732175i	−0.900141	−	0.435599i	$-0.856536\pi$
$443$	1.15486	−	15.4105i	0.0548689	−	0.732175i	0.955010	−	0.296575i	$-0.0958445\pi$
$444$	−7.21728	+	2.22624i	−0.342517	+	0.105652i
$445$	3.80146	+	0.572978i	0.180206	+	0.0271617i
$446$	−5.60297	−	5.19879i	−0.265308	−	0.246170i
$447$	−1.49603	−	6.55452i	−0.0707596	−	0.310018i
$448$	2.64252	+	0.130717i	0.124847	+	0.00617579i
$449$	−7.02794	+	30.7914i	−0.331669	+	1.45314i	0.484229	+	0.874942i	$0.339100\pi$
$449$	−7.02794	+	30.7914i	−0.331669	+	1.45314i	−0.815898	+	0.578196i	$0.803757\pi$
$450$	−3.17418	+	2.16412i	−0.149632	+	0.102018i
$451$	11.6353	−	10.7960i	0.547884	−	0.508362i
$452$	−10.5004	−	7.15905i	−0.493897	−	0.336733i
$453$	28.2877	−	4.26368i	1.32907	−	0.200325i
$454$	−2.39860	+	1.15511i	−0.112572	+	0.0542118i
$455$	3.09449	−	0.311026i	0.145072	−	0.0145811i
$456$	1.42377	+	0.685653i	0.0666743	+	0.0321087i
$457$	−0.891393	−	0.274958i	−0.0416976	−	0.0128620i	0.273836	−	0.961776i	$-0.411707\pi$
$457$	−0.891393	−	0.274958i	−0.0416976	−	0.0128620i	−0.315534	+	0.948914i	$0.602184\pi$
$458$	−2.67209	+	6.80839i	−0.124859	+	0.318135i
$459$	3.68552	+	6.38350i	0.172025	+	0.297956i
$460$	4.09051	−	7.08497i	0.190721	−	0.330338i
$461$	12.5568	+	15.7457i	0.584827	+	0.733350i	0.982928	−	0.183992i	$-0.0589019\pi$
$461$	12.5568	+	15.7457i	0.584827	+	0.733350i	−0.398101	+	0.917342i	$0.630331\pi$
$462$	−0.382040	−	15.0535i	−0.0177741	−	0.700350i
$463$	−2.87011	+	3.59901i	−0.133385	+	0.167260i	−0.844038	−	0.536283i	$-0.819828\pi$
$463$	−2.87011	+	3.59901i	−0.133385	+	0.167260i	0.710653	+	0.703543i	$0.248400\pi$
$464$	3.82368	+	9.74258i	0.177510	+	0.452288i
$465$	−1.68233	−	22.4492i	−0.0780164	−	1.04106i
$466$	−1.67180	−	22.3087i	−0.0774448	−	1.03343i
$467$	−6.33240	−	16.1347i	−0.293028	−	0.746624i	−0.999253	−	0.0386366i	$-0.987699\pi$
$467$	−6.33240	−	16.1347i	−0.293028	−	0.746624i	0.706225	−	0.707987i	$-0.250397\pi$
$468$	0.654449	−	0.820653i	0.0302519	−	0.0379347i
$469$	−3.10039	−	2.34630i	−0.143163	−	0.108342i
$470$	−9.89787	−	12.4115i	−0.456555	−	0.572502i
$471$	−3.10135	+	5.37170i	−0.142903	+	0.247515i
$472$	2.62907	+	4.55368i	0.121013	+	0.209600i
$473$	−9.18790	+	23.4104i	−0.422460	+	1.07641i
$474$	27.0885	+	8.35569i	1.24421	+	0.383789i
$475$	−2.29584	−	1.10562i	−0.105340	−	0.0507293i
$476$	0.645829	−	5.17205i	0.0296015	−	0.237060i
$477$	7.31246	−	3.52150i	0.334815	−	0.161238i
$478$	28.2278	−	4.25466i	1.29111	−	0.194604i
$479$	−23.4773	−	16.0065i	−1.07270	−	0.731357i	−0.107856	−	0.994167i	$-0.534398\pi$
$479$	−23.4773	−	16.0065i	−1.07270	−	0.731357i	−0.964848	+	0.262810i	$0.915351\pi$
$480$	1.95585	−	1.81477i	0.0892721	−	0.0828324i
$481$	−2.74939	+	1.87450i	−0.125361	+	0.0854699i
$482$	−5.27355	+	23.1049i	−0.240204	+	1.05240i
$483$	−29.6959	−	16.1546i	−1.35121	−	0.735060i
$484$	0.717949	+	3.14554i	0.0326341	+	0.142979i
$485$	9.44840	+	8.76683i	0.429030	+	0.398081i
$486$	11.3856	+	1.71610i	0.516461	+	0.0778439i
$487$	6.54184	−	2.01789i	0.296439	−	0.0914394i	−0.142968	−	0.989727i	$-0.545665\pi$
$487$	6.54184	−	2.01789i	0.296439	−	0.0914394i	0.439407	+	0.898288i	$0.355188\pi$
$488$	0.919706	−	12.2726i	0.0416331	−	0.555556i
$489$	17.2621			0.780618
$490$	0.220044	−	9.14654i	0.00994059	−	0.413199i
$491$	2.07001			0.0934182			0.0467091	−	0.998909i	$-0.485127\pi$
$491$	2.07001			0.0934182			0.0467091	+	0.998909i	$0.485127\pi$
$492$	0.868449	−	11.5886i	0.0391527	−	0.522457i
$493$	19.7024	−	6.07740i	0.887354	−	0.273712i
$494$	0.688453	+	0.103768i	0.0309750	+	0.00466872i
$495$	−3.11773	−	2.89283i	−0.140131	−	0.130023i
$496$	−1.87753	−	8.22598i	−0.0843034	−	0.369358i
$497$	4.29314	−	15.2845i	0.192574	−	0.685604i
$498$	−4.67205	+	20.4696i	−0.209360	+	0.917264i
$499$	28.9169	−	19.7152i	1.29450	−	0.882575i	0.297115	−	0.954842i	$-0.403976\pi$
$499$	28.9169	−	19.7152i	1.29450	−	0.882575i	0.997385	+	0.0722666i	$0.0230232\pi$
$500$	−7.94441	+	7.37134i	−0.355285	+	0.329656i
$501$	17.5337	+	11.9543i	0.783347	+	0.534077i
$502$	−19.6995	+	2.96922i	−0.879232	+	0.132523i
$503$	26.7920	−	12.9023i	1.19460	−	0.575287i	0.272465	−	0.962166i	$-0.412161\pi$
$503$	26.7920	−	12.9023i	1.19460	−	0.575287i	0.922131	+	0.386879i	$0.126447\pi$
$504$	−2.15703	−	2.20955i	−0.0960818	−	0.0984211i
$505$	−6.92653	−	3.33564i	−0.308226	−	0.148434i
$506$	−16.6762	−	5.14392i	−0.741347	−	0.228675i
$507$	−9.09200	+	23.1660i	−0.403790	+	1.02884i
$508$	1.10849	+	1.91995i	0.0491811	+	0.0851841i
$509$	12.1114	−	20.9775i	0.536827	−	0.929811i	−0.462246	−	0.886752i	$-0.652956\pi$
$509$	12.1114	−	20.9775i	0.536827	−	0.929811i	0.999073	−	0.0430594i	$-0.0137105\pi$
$510$	−3.27721	−	4.10949i	−0.145117	−	0.181971i
$511$	−0.0384005	−	0.0748219i	−0.00169874	−	0.00330993i
$512$	0.623490	−	0.781831i	0.0275546	−	0.0345524i
$513$	1.05820	+	2.69625i	0.0467207	+	0.119042i
$514$	−1.42675	−	19.0386i	−0.0629310	−	0.839756i
$515$	1.78253	+	23.7862i	0.0785475	+	1.04814i
$516$	6.72703	+	17.1402i	0.296141	+	0.754555i
$517$	−21.1139	+	26.4759i	−0.928586	+	1.16441i
$518$	4.46971	+	8.70906i	0.196388	+	0.382654i
$519$	0.749018	+	0.939239i	0.0328782	+	0.0412280i
$520$	0.587750	−	1.01801i	0.0257745	−	0.0446428i
$521$	3.63482	+	6.29570i	0.159244	+	0.275820i	0.934596	−	0.355710i	$-0.115761\pi$
$521$	3.63482	+	6.29570i	0.159244	+	0.275820i	−0.775352	+	0.631529i	$0.782428\pi$
$522$	4.46263	−	11.3706i	0.195324	−	0.497677i
$523$	27.4232	+	8.45895i	1.19913	+	0.369884i	0.829082	−	0.559127i	$-0.188864\pi$
$523$	27.4232	+	8.45895i	1.19913	+	0.369884i	0.370052	+	0.929011i	$0.379340\pi$
$524$	−3.63117	−	1.74868i	−0.158628	−	0.0763913i
$525$	12.4189	+	12.7212i	0.542004	+	0.555201i
$526$	−7.52976	+	3.62614i	−0.328313	+	0.158107i
$527$	−16.4365	+	2.47741i	−0.715987	+	0.107918i
$528$	−4.70254	−	3.20614i	−0.204652	−	0.139529i
$529$	−11.8596	+	11.0041i	−0.515633	+	0.478437i
$530$	7.50992	−	5.12018i	0.326210	−	0.222406i
$531$	1.36556	−	5.98291i	0.0592603	−	0.259636i
$532$	0.553856	−	1.97185i	0.0240127	−	0.0854905i
$533$	−1.13931	−	4.99163i	−0.0493489	−	0.216211i
$534$	−4.40145	−	4.08395i	−0.190469	−	0.176730i
$535$	−10.7604	−	1.62187i	−0.465214	−	0.0701198i
$536$	−1.40428	+	0.433165i	−0.0606559	+	0.0187099i
$537$	−1.56738	+	20.9152i	−0.0676373	+	0.902558i
$538$	−2.41854			−0.104271
$539$	−19.1264	+	3.88401i	−0.823832	+	0.167296i
$540$	4.89035			0.210447
$541$	−1.28289	+	17.1190i	−0.0551559	+	0.736005i	0.899239	+	0.437458i	$0.144121\pi$
$541$	−1.28289	+	17.1190i	−0.0551559	+	0.736005i	−0.954395	+	0.298547i	$0.903498\pi$
$542$	−10.1197	+	3.12152i	−0.434679	+	0.134081i
$543$	−17.6840	−	2.66543i	−0.758893	−	0.114385i
$544$	−1.44413	−	1.33996i	−0.0619168	−	0.0574504i
$545$	−1.77696	−	7.78538i	−0.0761167	−	0.333489i
$546$	−4.26690	−	2.32119i	−0.182606	−	0.0993379i
$547$	2.85144	−	12.4930i	0.121919	−	0.534161i	−0.876672	−	0.481089i	$-0.840242\pi$
$547$	2.85144	−	12.4930i	0.121919	−	0.534161i	0.998591	−	0.0530721i	$-0.0169013\pi$
$548$	1.82243	−	1.24251i	0.0778502	−	0.0530774i
$549$	−10.5292	+	9.76970i	−0.449377	+	0.416961i
$550$	7.58287	+	5.16991i	0.323335	+	0.220446i
$551$	8.01161	−	1.20756i	0.341306	−	0.0514436i
$552$	−11.5120	+	5.54387i	−0.489982	+	0.235963i
$553$	4.55249	−	36.4580i	0.193591	−	1.55035i
$554$	−18.5954	−	8.95505i	−0.790041	−	0.380464i
$555$	9.43318	+	2.90975i	0.400416	+	0.123512i
$556$	−3.81112	+	9.71058i	−0.161628	+	0.411820i
$557$	8.24287	+	14.2771i	0.349262	+	0.604939i	0.986118	−	0.166043i	$-0.0530991\pi$
$557$	8.24287	+	14.2771i	0.349262	+	0.604939i	−0.636857	+	0.770982i	$0.719766\pi$
$558$	−4.92373	+	8.52814i	−0.208438	+	0.361025i
$559$	5.05796	+	6.34248i	0.213929	+	0.268258i
$560$	−2.75746	−	2.08678i	−0.116524	−	0.0881827i
$561$	−6.99084	+	8.76624i	−0.295154	+	0.370111i
$562$	3.88075	+	9.88798i	0.163699	+	0.417099i
$563$	1.76787	+	23.5906i	0.0745068	+	0.994224i	0.901716	+	0.432330i	$0.142308\pi$
$563$	1.76787	+	23.5906i	0.0745068	+	0.994224i	−0.827209	+	0.561895i	$0.810073\pi$
$564$	1.85285	+	24.7246i	0.0780191	+	1.04109i
$565$	6.06852	+	15.4623i	0.255305	+	0.650506i
$566$	15.3919	−	19.3009i	0.646972	−	0.811277i
$567$	−0.747712	−	29.4620i	−0.0314010	−	1.23729i
$568$	−3.74129	−	4.69143i	−0.156981	−	0.196848i
$569$	5.28419	−	9.15248i	0.221525	−	0.383692i	−0.733746	−	0.679423i	$-0.762230\pi$
$569$	5.28419	−	9.15248i	0.221525	−	0.383692i	0.955271	+	0.295731i	$0.0955633\pi$
$570$	−1.03273	−	1.78874i	−0.0432562	−	0.0749219i
$571$	4.15751	−	10.5932i	0.173986	−	0.443310i	−0.817106	−	0.576488i	$-0.804423\pi$
$571$	4.15751	−	10.5932i	0.173986	−	0.443310i	0.991092	+	0.133178i	$0.0425181\pi$
$572$	−2.39614	−	0.739111i	−0.100188	−	0.0309038i
$573$	3.51021	+	1.69043i	0.146641	+	0.0706186i
$574$	−14.9864	+	1.50628i	−0.625522	+	0.0628710i
$575$	18.5631	−	8.93952i	0.774135	−	0.372804i
$576$	−1.15407	+	0.173947i	−0.0480861	+	0.00724781i
$577$	−21.5931	−	14.7219i	−0.898932	−	0.612882i	0.0232108	−	0.999731i	$-0.492611\pi$
$577$	−21.5931	−	14.7219i	−0.898932	−	0.612882i	−0.922143	+	0.386849i	$0.873563\pi$
$578$	9.61689	−	8.92317i	0.400010	−	0.371155i
$579$	−10.4288	+	7.11020i	−0.433404	+	0.295490i
$580$	3.04396	−	13.3365i	0.126393	−	0.553766i
$581$	27.1793	+	1.34447i	1.12759	+	0.0557780i
$582$	−4.47947	−	19.6259i	−0.185680	−	0.813518i
$583$	−14.2131	−	13.1879i	−0.588648	−	0.546186i
$584$	−0.0314320	−	0.00473761i	−0.00130067	−	0.000196044i
$585$	−1.31098	+	0.404383i	−0.0542022	+	0.0167192i
$586$	−0.815661	+	10.8842i	−0.0336946	+	0.449624i
$587$	−14.8726			−0.613856			−0.306928	−	0.951733i	$-0.599301\pi$
$587$	−14.8726			−0.613856			−0.306928	+	0.951733i	$0.599301\pi$
$588$	−8.33115	+	11.6095i	−0.343571	+	0.478767i
$589$	−6.53175			−0.269136
$590$	0.513584	−	6.85330i	0.0211439	−	0.282146i
$591$	2.29958	−	0.709325i	0.0945919	−	0.0291777i
$592$	3.65860	+	0.551445i	0.150367	+	0.0226642i
$593$	23.9114	+	22.1865i	0.981924	+	0.911092i	0.996049	−	0.0888083i	$-0.0283059\pi$
$593$	23.9114	+	22.1865i	0.981924	+	0.911092i	−0.0141252	+	0.999900i	$0.504496\pi$
$594$	−2.32133	−	10.1704i	−0.0952452	−	0.417297i
$595$	−4.50549	+	5.10987i	−0.184707	+	0.209484i
$596$	−0.732862	+	3.21088i	−0.0300192	+	0.131523i
$597$	−42.7436	+	29.1421i	−1.74938	+	1.19271i
$598$	−4.12663	+	3.82895i	−0.168750	+	0.156578i
$599$	7.22033	+	4.92274i	0.295015	+	0.201138i	0.701777	−	0.712396i	$-0.252390\pi$
$599$	7.22033	+	4.92274i	0.295015	+	0.201138i	−0.406763	+	0.913534i	$0.633342\pi$
$600$	6.64442	−	1.00148i	0.271257	−	0.0408854i
$601$	34.6215	−	16.6728i	1.41224	−	0.680099i	0.436636	−	0.899638i	$-0.356170\pi$
$601$	34.6215	−	16.6728i	1.41224	−	0.680099i	0.975604	+	0.219539i	$0.0704554\pi$
$602$	20.3581	−	12.4529i	0.829734	−	0.507542i
$603$	1.54529	+	0.744172i	0.0629290	+	0.0303050i
$604$	−13.3913	−	4.13067i	−0.544884	−	0.168074i
$605$	1.54066	−	3.92553i	0.0626366	−	0.159595i
$606$	6.00355	+	10.3985i	0.243878	+	0.422409i
$607$	7.79218	−	13.4965i	0.316275	−	0.547804i	−0.663433	−	0.748236i	$-0.730901\pi$
$607$	7.79218	−	13.4965i	0.316275	−	0.547804i	0.979708	+	0.200432i	$0.0642344\pi$
$608$	−0.482663	−	0.605240i	−0.0195746	−	0.0245457i
$609$	−55.4103	−	11.1761i	−2.24534	−	0.452877i
$610$	−10.0292	+	12.5763i	−0.406071	+	0.509197i
$611$	3.99084	+	10.1685i	0.161452	+	0.411373i
$612$	0.171821	+	2.29280i	0.00694547	+	0.0926808i
$613$	1.74858	+	23.3332i	0.0706244	+	0.942418i	0.914162	+	0.405348i	$0.132850\pi$
$613$	1.74858	+	23.3332i	0.0706244	+	0.942418i	−0.843538	+	0.537070i	$0.819531\pi$
$614$	4.64995	+	11.8479i	0.187657	+	0.478141i
$615$	−9.47028	+	11.8754i	−0.381878	+	0.478860i
$616$	−3.03096	+	6.72519i	−0.122121	+	0.270966i
$617$	3.98193	+	4.99318i	0.160307	+	0.201018i	0.855497	−	0.517807i	$-0.173252\pi$
$617$	3.98193	+	4.99318i	0.160307	+	0.201018i	−0.695191	+	0.718825i	$0.744680\pi$
$618$	18.6270	−	32.2629i	0.749288	−	1.29780i
$619$	3.54447	+	6.13920i	0.142464	+	0.246755i	0.928424	−	0.371522i	$-0.121164\pi$
$619$	3.54447	+	6.13920i	0.142464	+	0.246755i	−0.785960	+	0.618278i	$0.787831\pi$
$620$	−4.02901	+	10.2657i	−0.161809	+	0.412282i
$621$	−22.3791	−	6.90303i	−0.898041	−	0.277009i
$622$	3.52877	+	1.69937i	0.141491	+	0.0681383i
$623$	−4.21923	+	6.53896i	−0.169040	+	0.261978i
$624$	−1.65411	+	0.796578i	−0.0662175	+	0.0318886i
$625$	−2.26795	+	0.341839i	−0.0907182	+	0.0136736i
$626$	13.2383	+	9.02569i	0.529107	+	0.360739i
$627$	−3.22980	+	2.99682i	−0.128986	+	0.119681i
$628$	2.51056	−	1.71167i	0.100182	−	0.0683030i
$629$	1.62195	−	7.10621i	0.0646712	−	0.283343i
$630$	0.702579	+	3.97429i	0.0279914	+	0.158340i
$631$	−1.78951	−	7.84035i	−0.0712392	−	0.312119i	0.926737	−	0.375711i	$-0.122602\pi$
$631$	−1.78951	−	7.84035i	−0.0712392	−	0.312119i	−0.997976	+	0.0635919i	$0.979744\pi$
$632$	−10.1798	−	9.44546i	−0.404930	−	0.375720i
$633$	−5.87247	−	0.885132i	−0.233410	−	0.0351808i
$634$	−33.4119	+	10.3062i	−1.32696	+	0.409312i
$635$	0.216541	−	2.88954i	0.00859316	−	0.114668i
$636$	−14.1959			−0.562903
$637$	−1.99981	+	5.96952i	−0.0792352	+	0.236521i
$638$	−29.1806			−1.15527
$639$	−0.523355	+	6.98369i	−0.0207036	+	0.276270i
$640$	−1.24896	+	0.385253i	−0.0493694	+	0.0152285i
$641$	−11.9061	−	1.79455i	−0.470261	−	0.0708805i	−0.0903633	−	0.995909i	$-0.528803\pi$
$641$	−11.9061	−	1.79455i	−0.470261	−	0.0708805i	−0.379898	+	0.925028i	$0.624041\pi$
$642$	12.4588	+	11.5600i	0.491708	+	0.456239i
$643$	7.58886	+	33.2490i	0.299276	+	1.31121i	0.871209	+	0.490912i	$0.163336\pi$
$643$	7.58886	+	33.2490i	0.299276	+	1.31121i	−0.571934	+	0.820300i	$0.693806\pi$
$644$	9.67297	+	13.4418i	0.381168	+	0.529681i
$645$	5.35526	−	23.4629i	0.210863	−	0.923851i
$646$	−1.26006	+	0.859098i	−0.0495766	+	0.0338007i
$647$	5.96156	−	5.53152i	0.234373	−	0.217466i	−0.554239	−	0.832358i	$-0.686991\pi$
$647$	5.96156	−	5.53152i	0.234373	−	0.217466i	0.788612	+	0.614891i	$0.210800\pi$
$648$	−9.20362	−	6.27492i	−0.361552	−	0.246502i
$649$	−14.4965	+	2.18500i	−0.569038	+	0.0857687i
$650$	2.66726	−	1.28449i	0.104619	−	0.0503817i
$651$	42.8289	+	15.5671i	1.67860	+	0.610122i
$652$	−7.61879	−	3.66901i	−0.298375	−	0.143690i
$653$	−29.1599	−	8.99463i	−1.14111	−	0.351987i	−0.334110	−	0.942534i	$-0.608436\pi$
$653$	−29.1599	−	8.99463i	−1.14111	−	0.351987i	−0.807003	+	0.590547i	$0.798912\pi$
$654$	−4.55657	+	11.6100i	−0.178176	+	0.453985i
$655$	2.63385	+	4.56196i	0.102913	+	0.178250i
$656$	−2.84644	+	4.93018i	−0.111135	+	0.192491i
$657$	0.0231307	+	0.0290049i	0.000902413	+	0.00113159i
$658$	31.1377	−	7.94323i	1.21387	−	0.309659i
$659$	28.4700	−	35.7003i	1.10903	−	1.39068i	0.197082	−	0.980387i	$-0.436854\pi$
$659$	28.4700	−	35.7003i	1.10903	−	1.39068i	0.911952	−	0.410297i	$-0.134575\pi$
$660$	2.71775	+	6.92472i	0.105788	+	0.269544i
$661$	1.59640	+	21.3025i	0.0620927	+	0.828570i	0.938120	+	0.346309i	$0.112565\pi$
$661$	1.59640	+	21.3025i	0.0620927	+	0.828570i	−0.876028	+	0.482261i	$0.839816\pi$
$662$	−2.44715	−	32.6550i	−0.0951114	−	1.26917i
$663$	1.32138	+	3.36681i	0.0513180	+	0.130756i
$664$	6.41282	−	8.04142i	0.248866	−	0.312068i
$665$	−2.04994	+	1.72164i	−0.0794933	+	0.0667624i
$666$	−2.69234	−	3.37609i	−0.104326	−	0.130821i
$667$	−32.7549	+	56.7332i	−1.26827	+	2.19672i
$668$	−5.19781	−	9.00287i	−0.201109	−	0.348331i
$669$	5.70032	−	14.5242i	0.220387	−	0.561537i
$670$	1.83544	+	0.566158i	0.0709092	+	0.0218726i
$671$	30.9153	+	14.8880i	1.19347	+	0.574746i
$672$	1.72237	+	5.11890i	0.0664418	+	0.197466i
$673$	30.9578	−	14.9085i	1.19333	−	0.574679i	0.271565	−	0.962420i	$-0.412459\pi$
$673$	30.9578	−	14.9085i	1.19333	−	0.574679i	0.921768	+	0.387741i	$0.126744\pi$
$674$	−25.2226	+	3.80170i	−0.971540	+	0.146436i
$675$	10.1760	+	6.93791i	0.391676	+	0.267040i
$676$	8.93673	−	8.29208i	0.343721	−	0.318926i
$677$	2.03381	−	1.38663i	0.0781658	−	0.0532925i	−0.523607	−	0.851960i	$-0.675414\pi$
$677$	2.03381	−	1.38663i	0.0781658	−	0.0532925i	0.601772	+	0.798668i	$0.294461\pi$
$678$	5.77282	−	25.2924i	0.221704	−	0.971348i
$679$	−24.0376	+	10.1452i	−0.922479	+	0.389336i
$680$	0.572965	+	2.51033i	0.0219722	+	0.0962666i
$681$	−3.98383	−	3.69645i	−0.152661	−	0.141648i
$682$	23.2620	+	3.50619i	0.890749	+	0.134259i
$683$	−20.7884	+	6.41236i	−0.795445	+	0.245362i	−0.665733	−	0.746190i	$-0.731881\pi$
$683$	−20.7884	+	6.41236i	−0.795445	+	0.245362i	−0.129711	+	0.991552i	$0.541405\pi$
$684$	−0.0675178	+	0.900963i	−0.00258161	+	0.0344492i
$685$	−2.88290			−0.110150
$686$	16.6968	+	8.01360i	0.637486	+	0.305961i
$687$	−14.9304			−0.569629
$688$	0.674067	−	8.99481i	0.0256986	−	0.342924i
$689$	−5.97650	+	1.84351i	−0.227687	+	0.0702320i
$690$	16.5138	+	2.48905i	0.628669	+	0.0947566i
$691$	13.3249	+	12.3637i	0.506901	+	0.470336i	0.891676	−	0.452675i	$-0.149530\pi$
$691$	13.3249	+	12.3637i	0.506901	+	0.470336i	−0.384774	+	0.923011i	$0.625721\pi$
$692$	−0.130953	−	0.573744i	−0.00497810	−	0.0218105i
$693$	7.93179	−	3.34764i	0.301304	−	0.127166i
$694$	−0.549297	+	2.40663i	−0.0208510	+	0.0913544i
$695$	11.2653	−	7.68058i	0.427319	−	0.291341i
$696$	−15.6616	+	14.5318i	−0.593650	+	0.550827i
$697$	9.26639	+	6.31772i	0.350989	+	0.239301i
$698$	−22.1734	+	3.34211i	−0.839277	+	0.126501i
$699$	41.1449	−	19.8144i	1.55624	−	0.749448i
$700$	−2.77732	−	8.25425i	−0.104973	−	0.311981i
$701$	−18.6892	−	9.00026i	−0.705882	−	0.339935i	0.0462657	−	0.998929i	$-0.485268\pi$
$701$	−18.6892	−	9.00026i	−0.705882	−	0.339935i	−0.752148	+	0.658994i	$0.770982\pi$
$702$	−3.21556	−	0.991870i	−0.121364	−	0.0374357i
$703$	1.04642	−	2.66623i	0.0394664	−	0.100559i
$704$	1.39406	+	2.41458i	0.0525404	+	0.0910027i
$705$	16.2032	−	28.0647i	0.610246	−	1.05698i
$706$	−15.0431	−	18.8634i	−0.566154	−	0.709935i
$707$	11.9169	−	10.0084i	0.448182	−	0.376405i
$708$	−6.69234	+	8.39193i	−0.251513	+	0.315388i
$709$	−7.99824	−	20.3792i	−0.300380	−	0.765356i	−0.998767	−	0.0496362i	$-0.984194\pi$
$709$	−7.99824	−	20.3792i	−0.300380	−	0.765356i	0.698387	−	0.715720i	$-0.253901\pi$
$710$	0.586101	+	7.82097i	0.0219960	+	0.293516i
$711$	1.21118	+	16.1620i	0.0454227	+	0.606124i
$712$	1.07459	+	2.73801i	0.0402719	+	0.102611i
$713$	32.9282	−	41.2906i	1.23317	−	1.54635i
$714$	10.3098	−	2.63002i	0.385833	−	0.0984261i
$715$	2.04344	+	2.56239i	0.0764203	+	0.0958281i
$716$	5.13725	−	8.89799i	0.191988	−	0.332533i
$717$	29.1368	+	50.4665i	1.08813	+	1.88470i
$718$	0.143954	−	0.366790i	0.00537233	−	0.0136885i
$719$	35.3017	+	10.8891i	1.31653	+	0.406096i	0.871929	−	0.489632i	$-0.162869\pi$
$719$	35.3017	+	10.8891i	1.31653	+	0.406096i	0.444602	+	0.895728i	$0.353345\pi$
$720$	1.37437	+	0.661860i	0.0512196	+	0.0246661i
$721$	−45.3795	−	16.4942i	−1.69002	−	0.614276i
$722$	16.5785	−	7.98377i	0.616987	−	0.297125i
$723$	−47.8378	+	7.21039i	−1.77911	+	0.268157i
$724$	7.23847	+	4.93511i	0.269016	+	0.183412i
$725$	25.2543	−	23.4326i	0.937922	−	0.870265i
$726$	−5.44184	+	3.71018i	−0.201966	+	0.137698i
$727$	1.96182	−	8.59528i	0.0727598	−	0.318781i	−0.925430	−	0.378918i	$-0.876296\pi$
$727$	1.96182	−	8.59528i	0.0727598	−	0.318781i	0.998190	+	0.0601362i	$0.0191535\pi$
$728$	1.38987	+	1.93140i	0.0515121	+	0.0715825i
$729$	−2.20587	−	9.66453i	−0.0816987	−	0.357946i
$730$	0.0304558	+	0.0282588i	0.00112722	+	0.00104591i
$731$	−17.5713	−	2.64844i	−0.649897	−	0.0979561i
$732$	24.0068	−	7.40512i	0.887317	−	0.273701i
$733$	2.41969	−	32.2885i	0.0893732	−	1.19260i	−0.754588	−	0.656198i	$-0.772163\pi$
$733$	2.41969	−	32.2885i	0.0893732	−	1.19260i	0.843962	−	0.536404i	$-0.180217\pi$
$734$	15.6259			0.576761
$735$	17.5447	−	6.40324i	0.647146	−	0.236187i
$736$	6.25926			0.230719
$737$	0.306194	−	4.08588i	0.0112788	−	0.150505i
$738$	6.34898	−	1.95840i	0.233709	−	0.0720898i
$739$	−10.7112	−	1.61446i	−0.394019	−	0.0593888i	−0.0509554	−	0.998701i	$-0.516227\pi$
$739$	−10.7112	−	1.61446i	−0.394019	−	0.0593888i	−0.343064	+	0.939312i	$0.611465\pi$
$740$	−3.54496	−	3.28925i	−0.130315	−	0.120915i
$741$	0.316257	+	1.38561i	0.0116180	+	0.0509017i
$742$	3.20293	+	18.1181i	0.117583	+	0.665135i
$743$	4.99972	−	21.9052i	0.183422	−	0.803624i	−0.796563	−	0.604555i	$-0.793351\pi$
$743$	4.99972	−	21.9052i	0.183422	−	0.803624i	0.979985	−	0.199069i	$-0.0637919\pi$
$744$	14.2311	−	9.70259i	0.521737	−	0.355714i
$745$	3.15552	−	2.92789i	0.115609	−	0.107270i
$746$	4.35945	+	2.97222i	0.159611	+	0.108821i
$747$	−11.8700	+	1.78911i	−0.434300	+	0.0654602i
$748$	4.94872	−	2.38318i	0.180943	−	0.0871376i
$749$	11.9430	−	18.5092i	0.436387	−	0.676313i
$750$	−19.9321	−	9.59881i	−0.727819	−	0.350499i
$751$	3.44913	+	1.06392i	0.125861	+	0.0388229i	0.357046	−	0.934087i	$-0.383784\pi$
$751$	3.44913	+	1.06392i	0.125861	+	0.0388229i	−0.231185	+	0.972910i	$0.574260\pi$
$752$	4.43738	−	11.3063i	0.161815	−	0.412297i
$753$	−20.3339	−	35.2193i	−0.741008	−	1.28346i
$754$	−4.70643	+	8.15177i	−0.171398	+	0.296870i
$755$	11.4202	+	14.3204i	0.415622	+	0.521174i
$756$	−4.06748	+	9.02506i	−0.147933	+	0.328238i
$757$	−6.57798	+	8.24853i	−0.239081	+	0.299798i	−0.886867	−	0.462024i	$-0.847123\pi$
$757$	−6.57798	+	8.24853i	−0.239081	+	0.299798i	0.647787	+	0.761822i	$0.275695\pi$
$758$	13.0845	+	33.3386i	0.475249	+	1.21091i
$759$	−2.66223	−	35.5250i	−0.0966328	−	1.28948i
$760$	0.0756126	+	1.00898i	0.00274276	+	0.0365996i
$761$	2.61759	+	6.66950i	0.0948874	+	0.241769i	0.970435	−	0.241363i	$-0.0775944\pi$
$761$	2.61759	+	6.66950i	0.0948874	+	0.241769i	−0.875548	+	0.483132i	$0.839499\pi$
$762$	−2.82167	+	3.53826i	−0.102218	+	0.128178i
$763$	15.8458	+	3.19603i	0.573655	+	0.115704i
$764$	−1.18997	−	1.49217i	−0.0430515	−	0.0539849i
$765$	1.50257	−	2.60254i	0.0543257	−	0.0940949i
$766$	7.58412	+	13.1361i	0.274025	+	0.474626i
$767$	−1.72770	+	4.40210i	−0.0623836	+	0.158951i
$768$	1.95066	+	0.601698i	0.0703883	+	0.0217119i
$769$	−34.9092	−	16.8114i	−1.25886	−	0.606233i	−0.318984	−	0.947760i	$-0.603342\pi$
$769$	−34.9092	−	16.8114i	−1.25886	−	0.606233i	−0.939872	+	0.341527i	$0.889056\pi$
$770$	8.22477	−	5.03103i	0.296400	−	0.181306i
$771$	35.1138	−	16.9099i	1.26459	−	0.608995i
$772$	6.11409	−	0.921551i	0.220051	−	0.0331673i
$773$	−41.2797	−	28.1440i	−1.48473	−	1.01227i	−0.989663	−	0.143413i	$-0.954192\pi$
$773$	−41.2797	−	28.1440i	−1.48473	−	1.01227i	−0.495064	−	0.868857i	$-0.664855\pi$
$774$	−7.71705	+	7.16037i	−0.277384	+	0.257374i
$775$	−22.9477	+	15.6455i	−0.824305	+	0.562001i
$776$	−2.19437	+	9.61416i	−0.0787733	+	0.345128i
$777$	−13.2158	+	14.9886i	−0.474115	+	0.537714i
$778$	5.37090	+	23.5314i	0.192556	+	0.843643i
$779$	3.23058	+	2.99754i	0.115748	+	0.107398i
$780$	2.37280	+	0.357642i	0.0849599	+	0.0128056i
$781$	15.9870	−	4.93133i	0.572059	−	0.176457i
$782$	0.921492	−	12.2965i	0.0329525	−	0.439720i
$783$	−39.1597			−1.39945
$784$	6.14460	−	3.35319i	0.219450	−	0.119757i
$785$	−3.97145			−0.141747
$786$	0.614821	−	8.20422i	0.0219299	−	0.292635i
$787$	19.6095	−	6.04872i	0.699002	−	0.215614i	0.0751685	−	0.997171i	$-0.476051\pi$
$787$	19.6095	−	6.04872i	0.699002	−	0.215614i	0.623833	+	0.781557i	$0.285574\pi$
$788$	−1.16571	−	0.175702i	−0.0415266	−	0.00625912i
$789$	−12.5061	−	11.6040i	−0.445230	−	0.413113i
$790$	4.03886	+	17.6954i	0.143696	+	0.629575i
$791$	−33.5829	−	1.66124i	−1.19407	−	0.0590668i
$792$	0.724085	−	3.17242i	0.0257292	−	0.112727i
$793$	9.14528	−	6.23515i	0.324759	−	0.221417i
$794$	−28.0957	+	26.0690i	−0.997079	+	0.925154i
$795$	15.3304	+	10.4521i	0.543712	+	0.370696i
$796$	25.0594	−	3.77709i	0.888206	−	0.133875i
$797$	−39.4794	+	19.0123i	−1.39843	+	0.673449i	−0.972842	−	0.231468i	$-0.925647\pi$
$797$	−39.4794	+	19.0123i	−1.39843	+	0.673449i	−0.425588	+	0.904917i	$0.639933\pi$
$798$	4.16004	−	0.418124i	0.147264	−	0.0148014i
$799$	−21.5581	−	10.3818i	−0.762671	−	0.367283i
$800$	−3.14544	−	0.970240i	−0.111208	−	0.0343032i
$801$	1.25415	−	3.19553i	0.0443134	−	0.112909i
$802$	−4.12282	−	7.14094i	−0.145582	−	0.252155i
$803$	0.0443129	−	0.0767522i	0.00156377	−	0.00270853i
$804$	−1.87041	−	2.34543i	−0.0659644	−	0.0827168i
$805$	−0.549147	−	21.6380i	−0.0193549	−	0.762638i
$806$	4.73132	−	5.93289i	0.166654	−	0.208977i
$807$	−1.80372	−	4.59580i	−0.0634940	−	0.161780i
$808$	−0.439559	−	5.86550i	−0.0154636	−	0.206348i
$809$	1.37442	+	18.3404i	0.0483221	+	0.644814i	0.967808	+	0.251690i	$0.0809864\pi$
$809$	1.37442	+	18.3404i	0.0483221	+	0.644814i	−0.919486	+	0.393123i	$0.871395\pi$
$810$	5.31907	+	13.5528i	0.186893	+	0.476196i
$811$	−29.3696	+	36.8283i	−1.03131	+	1.29322i	−0.0761551	+	0.997096i	$0.524264\pi$
$811$	−29.3696	+	36.8283i	−1.03131	+	1.29322i	−0.955151	+	0.296120i	$0.904307\pi$
$812$	22.0804	+	16.7100i	0.774871	+	0.586406i
$813$	−13.4788	−	16.9019i	−0.472721	−	0.592774i
$814$	−5.15790	+	8.93374i	−0.180784	+	0.313127i
$815$	5.52625	+	9.57175i	0.193576	+	0.335284i
$816$	1.46923	−	3.74353i	0.0514332	−	0.131050i
$817$	−6.67246	−	2.05818i	−0.233440	−	0.0720066i
$818$	−8.30623	−	4.00007i	−0.290420	−	0.139859i
$819$	0.344105	−	2.75573i	0.0120240	−	0.0962928i
$820$	6.70388	−	3.22842i	0.234110	−	0.112741i
$821$	−28.3588	+	4.27441i	−0.989730	+	0.149178i	−0.623900	−	0.781504i	$-0.714453\pi$
$821$	−28.3588	+	4.27441i	−0.989730	+	0.149178i	−0.365830	+	0.930682i	$0.619215\pi$
$822$	3.72021	+	2.53640i	0.129757	+	0.0884669i
$823$	−9.80982	+	9.10218i	−0.341949	+	0.317282i	−0.832388	−	0.554193i	$-0.813027\pi$
$823$	−9.80982	+	9.10218i	−0.341949	+	0.317282i	0.490439	+	0.871475i	$0.336836\pi$
$824$	−15.0786	+	10.2804i	−0.525288	+	0.358136i
$825$	−4.16885	+	18.2649i	−0.145141	+	0.635902i
$826$	12.2205	+	6.64795i	0.425205	+	0.231312i
$827$	5.62773	+	24.6567i	0.195695	+	0.857398i	0.973463	+	0.228846i	$0.0734951\pi$
$827$	5.62773	+	24.6567i	0.195695	+	0.857398i	−0.777767	+	0.628552i	$0.783648\pi$
$828$	−5.35508	−	4.96879i	−0.186102	−	0.172677i
$829$	8.45919	+	1.27502i	0.293800	+	0.0442832i	0.294288	−	0.955717i	$-0.404917\pi$
$829$	8.45919	+	1.27502i	0.293800	+	0.0442832i	−0.000488539		1.00000i	$0.500156\pi$
$830$	−12.8460	+	3.96247i	−0.445891	+	0.137539i
$831$	3.14853	−	42.0142i	0.109221	−	1.45745i
$832$	0.899369			0.0311800
$833$	−5.68280	−	12.5649i	−0.196897	−	0.435347i
$834$	−21.2947			−0.737375
$835$	−1.01538	+	13.5494i	−0.0351388	+	0.468895i
$836$	2.06247	−	0.636188i	0.0713321	−	0.0220030i
$837$	31.2171	+	4.70522i	1.07902	+	0.162636i
$838$	6.67334	+	6.19196i	0.230527	+	0.213898i
$839$	2.46700	+	10.8086i	0.0851702	+	0.373155i	0.999493	−	0.0318306i	$-0.0101337\pi$
$839$	2.46700	+	10.8086i	0.0851702	+	0.373155i	−0.914323	+	0.404986i	$0.867277\pi$
$840$	1.90890	−	6.79612i	0.0658634	−	0.234488i
$841$	−17.9215	+	78.5192i	−0.617983	+	2.70756i
$842$	−7.31835	+	4.98957i	−0.252207	+	0.171952i
$843$	−15.8953	+	14.7487i	−0.547463	+	0.507972i
$844$	2.40374	+	1.63884i	0.0827401	+	0.0564112i
$845$	−15.7562	+	2.37486i	−0.542029	+	0.0816977i
$846$	−12.7716	+	6.15049i	−0.439098	+	0.211458i
$847$	5.96308	+	6.10826i	0.204894	+	0.209882i
$848$	6.26549	+	3.01730i	0.215158	+	0.103615i
$849$	48.1554	+	14.8540i	1.65269	+	0.509787i
$850$	−2.36913	+	6.03645i	−0.0812606	+	0.207049i
$851$	11.5794	+	20.0561i	0.396936	+	0.687514i
$852$	6.12462	−	10.6082i	0.209826	−	0.363429i
$853$	28.5086	+	35.7487i	0.976118	+	1.22401i	0.974586	+	0.224014i	$0.0719161\pi$
$853$	28.5086	+	35.7487i	0.976118	+	1.22401i	0.00153161	+	0.999999i	$0.499512\pi$
$854$	−14.8676	−	28.9689i	−0.508759	−	0.991295i
$855$	0.736269	−	0.923252i	0.0251799	−	0.0315746i
$856$	−3.04174	−	7.75022i	−0.103964	−	0.264897i
$857$	−0.155888	−	2.08018i	−0.00532502	−	0.0710575i	0.993908	−	0.110211i	$-0.0351528\pi$
$857$	−0.155888	−	2.08018i	−0.00532502	−	0.0710575i	−0.999233	+	0.0391539i	$0.987534\pi$
$858$	−0.382526	−	5.10445i	−0.0130592	−	0.174263i
$859$	7.18902	+	18.3173i	0.245286	+	0.624979i	0.999499	−	0.0316512i	$-0.0100766\pi$
$859$	7.18902	+	18.3173i	0.245286	+	0.624979i	−0.754213	+	0.656630i	$0.771981\pi$
$860$	−7.35058	+	9.21734i	−0.250653	+	0.314309i
$861$	−14.0390	−	27.3544i	−0.478448	−	0.932236i
$862$	7.05178	+	8.84266i	0.240185	+	0.301182i
$863$	7.30885	−	12.6593i	0.248796	−	0.430928i	−0.714396	−	0.699742i	$-0.753298\pi$
$863$	7.30885	−	12.6593i	0.248796	−	0.430928i	0.963192	+	0.268814i	$0.0866317\pi$
$864$	1.87079	+	3.24031i	0.0636456	+	0.110237i
$865$	−0.281015	+	0.716013i	−0.00955478	+	0.0243452i
$866$	−21.4173	−	6.60635i	−0.727788	−	0.224493i
$867$	24.1283	+	11.6196i	0.819440	+	0.394622i
$868$	−15.5942	−	15.9739i	−0.529301	−	0.542188i
$869$	34.8838	−	16.7991i	1.18335	−	0.569872i
$870$	27.6126	−	4.16193i	0.936154	−	0.141102i
$871$	−1.09203	−	0.744534i	−0.0370021	−	0.0252276i
$872$	4.47876	−	4.15568i	0.151670	−	0.140729i
$873$	9.50940	−	6.48340i	0.321844	−	0.219430i
$874$	1.07822	−	4.72400i	0.0364714	−	0.159792i
$875$	−7.75371	+	27.6049i	−0.262123	+	0.933217i
$876$	−0.0144390	−	0.0632615i	−0.000487850	−	0.00213741i
$877$	−15.1681	−	14.0739i	−0.512189	−	0.475242i	0.381221	−	0.924484i	$-0.375504\pi$
$877$	−15.1681	−	14.0739i	−0.512189	−	0.475242i	−0.893410	+	0.449242i	$0.851694\pi$
$878$	−12.0385	−	1.81451i	−0.406280	−	0.0612368i
$879$	−21.2909	+	6.56739i	−0.718126	+	0.221512i
$880$	0.272327	−	3.63395i	0.00918013	−	0.122500i
$881$	9.01313			0.303660			0.151830	−	0.988407i	$-0.451483\pi$
$881$	9.01313			0.303660			0.151830	+	0.988407i	$0.451483\pi$
$882$	−7.91885	−	2.00897i	−0.266642	−	0.0676454i
$883$	−7.70553			−0.259312			−0.129656	−	0.991559i	$-0.541387\pi$
$883$	−7.70553			−0.259312			−0.129656	+	0.991559i	$0.541387\pi$
$884$	0.132406	−	1.76683i	0.00445328	−	0.0594249i
$885$	13.4059	−	4.13518i	0.450635	−	0.139003i
$886$	−15.2811	−	2.30326i	−0.513379	−	0.0773794i
$887$	7.17257	+	6.65517i	0.240831	+	0.223459i	0.791349	−	0.611365i	$-0.209379\pi$
$887$	7.17257	+	6.65517i	0.240831	+	0.223459i	−0.550518	+	0.834824i	$0.685570\pi$
$888$	1.68066	+	7.36346i	0.0563993	+	0.247102i
$889$	5.15249	+	2.80296i	0.172809	+	0.0940081i
$890$	0.855459	−	3.74801i	0.0286750	−	0.125634i
$891$	25.6607	−	17.4952i	0.859666	−	0.586111i
$892$	−5.60297	+	5.19879i	−0.187601	+	0.174068i
$893$	−7.76869	−	5.29660i	−0.259969	−	0.177244i
$894$	−6.64799	+	1.00202i	−0.222342	+	0.0335127i
$895$	−12.0992	+	5.82665i	−0.404430	+	0.194763i
$896$	0.327827	−	2.62536i	0.0109519	−	0.0877072i
$897$	−10.3535	−	4.98599i	−0.345694	−	0.166477i
$898$	30.1801	+	9.30934i	1.00712	+	0.310657i
$899$	32.2624	−	82.2033i	1.07601	−	2.74163i
$900$	1.92086	+	3.32703i	0.0640288	+	0.110901i
$901$	6.84997	−	11.8645i	0.228205	−	0.395263i
$902$	−9.89626	−	12.4095i	−0.329510	−	0.413192i
$903$	38.8463	+	29.3980i	1.29272	+	0.978304i
$904$	−7.92373	+	9.93604i	−0.263539	+	0.330468i
$905$	−4.18335	−	10.6590i	−0.139059	−	0.354317i
$906$	−2.13782	−	28.5272i	−0.0710243	−	0.947753i
$907$	−0.860141	−	11.4778i	−0.0285605	−	0.381114i	−0.993108	−	0.117204i	$-0.962607\pi$
$907$	−0.860141	−	11.4778i	−0.0285605	−	0.381114i	0.964547	−	0.263910i	$-0.0850121\pi$
$908$	0.972629	+	2.47822i	0.0322778	+	0.0822426i
$909$	−4.28015	+	5.36714i	−0.141964	+	0.178017i
$910$	−0.0789048	−	3.10908i	−0.00261567	−	0.103065i
$911$	18.6532	+	23.3904i	0.618009	+	0.774958i	0.988063	−	0.154052i	$-0.0492323\pi$
$911$	18.6532	+	23.3904i	0.618009	+	0.774958i	−0.370054	+	0.929010i	$0.620661\pi$
$912$	0.790135	−	1.36855i	0.0261640	−	0.0453173i
$913$	14.3384	+	24.8348i	0.474531	+	0.821911i
$914$	−0.340803	+	0.868353i	−0.0112728	+	0.0287226i
$915$	−31.3775	−	9.67869i	−1.03731	−	0.319968i
$916$	6.58966	+	3.17341i	0.217729	+	0.104853i
$917$	−10.6097	+	1.06638i	−0.350363	+	0.0352148i
$918$	6.64107	−	3.19817i	0.219188	−	0.105555i
$919$	26.9527	−	4.06247i	0.889089	−	0.134009i	0.311413	−	0.950275i	$-0.399198\pi$
$919$	26.9527	−	4.06247i	0.889089	−	0.134009i	0.577676	+	0.816266i	$0.303960\pi$
$920$	−6.75947	−	4.60853i	−0.222853	−	0.151939i
$921$	−19.0459	+	17.6720i	−0.627584	+	0.582313i
$922$	16.6400	−	11.3450i	0.548010	−	0.373627i
$923$	1.20088	−	5.26142i	0.0395276	−	0.173182i
$924$	−15.0399	−	0.743975i	−0.494777	−	0.0244750i
$925$	−2.71007	−	11.8736i	−0.0891067	−	0.390402i
$926$	3.37446	+	3.13104i	0.110892	+	0.102892i
$927$	21.0614	+	3.17449i	0.691746	+	0.104264i
$928$	10.0011	−	3.08493i	0.328302	−	0.101268i
$929$	−2.75547	+	36.7691i	−0.0904039	+	1.20636i	0.748896	+	0.662687i	$0.230584\pi$
$929$	−2.75547	+	36.7691i	−0.0904039	+	1.20636i	−0.839300	+	0.543669i	$0.817035\pi$
$930$	−22.5121			−0.738202
$931$	−1.47225	−	5.21508i	−0.0482511	−	0.170917i
$932$	−22.3712			−0.732794
$933$	−0.597483	+	7.97286i	−0.0195607	+	0.261020i
$934$	−16.5628	+	5.10894i	−0.541951	+	0.167170i
$935$	−7.09888	−	1.06998i	−0.232158	−	0.0349922i
$936$	−0.769452	−	0.713947i	−0.0251503	−	0.0233361i
$937$	9.07808	+	39.7737i	0.296568	+	1.29935i	0.875201	+	0.483760i	$0.160729\pi$
$937$	9.07808	+	39.7737i	0.296568	+	1.29935i	−0.578633	+	0.815588i	$0.696414\pi$
$938$	−2.57144	+	2.91638i	−0.0839603	+	0.0952231i
$939$	−7.27802	+	31.8871i	−0.237509	+	1.04060i
$940$	−13.1165	+	8.94268i	−0.427813	+	0.291678i
$941$	−33.6083	+	31.1839i	−1.09560	+	1.01657i	−0.0958226	+	0.995398i	$0.530548\pi$
$941$	−33.6083	+	31.1839i	−1.09560	+	1.01657i	−0.999776	+	0.0211684i	$0.993261\pi$
$942$	5.12492	+	3.49411i	0.166979	+	0.113844i
$943$	−35.2352	+	5.31085i	−1.14742	+	0.172945i
$944$	4.73741	−	2.28142i	0.154190	−	0.0742538i
$945$	11.0375	−	6.75153i	0.359049	−	0.219627i
$946$	22.6583	+	10.9117i	0.736686	+	0.354769i
$947$	24.1913	+	7.46202i	0.786111	+	0.242483i	0.661721	−	0.749750i	$-0.269826\pi$
$947$	24.1913	+	7.46202i	0.786111	+	0.242483i	0.124390	+	0.992233i	$0.460303\pi$
$948$	10.3566	−	26.3883i	0.336368	−	0.857052i
$949$	−0.0142941	−	0.0247582i	−0.000464008	−	0.000803685i
$950$	−1.27410	+	2.20680i	−0.0413371	+	0.0715980i
$951$	−44.5024	−	55.8043i	−1.44309	−	1.80958i
$952$	−5.10932	−	1.03053i	−0.165594	−	0.0333997i
$953$	−22.7416	+	28.5171i	−0.736673	+	0.923759i	−0.999152	−	0.0411790i	$-0.986889\pi$
$953$	−22.7416	+	28.5171i	−0.736673	+	0.923759i	0.262479	+	0.964938i	$0.415460\pi$
$954$	−2.96519	−	7.55518i	−0.0960015	−	0.244608i
$955$	0.186417	+	2.48756i	0.00603232	+	0.0804957i
$956$	−2.13329	−	28.4668i	−0.0689957	−	0.920683i
$957$	−21.7625	−	55.4500i	−0.703482	−	1.79244i
$958$	−17.7162	+	22.2154i	−0.572385	+	0.717749i
$959$	2.39781	−	5.32034i	0.0774294	−	0.171803i
$960$	−1.66353	−	2.08600i	−0.0536902	−	0.0673254i
$961$	−20.0960	+	34.8072i	−0.648257	+	1.12281i
$962$	1.66380	+	2.88178i	0.0536430	+	0.0929124i
$963$	−3.55002	+	9.04529i	−0.114398	+	0.291481i
$964$	22.6462	+	6.98544i	0.729386	+	0.224986i
$965$	−7.28122	−	3.50645i	−0.234391	−	0.112877i
$966$	−18.3286	+	28.4057i	−0.589714	+	0.913938i
$967$	17.3723	−	8.36604i	0.558654	−	0.269034i	−0.133178	−	0.991092i	$-0.542518\pi$
$967$	17.3723	−	8.36604i	0.558654	−	0.269034i	0.691832	+	0.722059i	$0.256804\pi$
$968$	3.19040	−	0.480875i	0.102543	−	0.0154559i
$969$	−2.57223	−	1.75372i	−0.0826319	−	0.0563375i
$970$	9.44840	−	8.76683i	0.303370	−	0.281486i
$971$	0.413401	−	0.281852i	0.0132667	−	0.00904506i	−0.556669	−	0.830735i	$-0.687921\pi$
$971$	0.413401	−	0.281852i	0.0132667	−	0.00904506i	0.569935	+	0.821690i	$0.306968\pi$
$972$	2.56215	−	11.2255i	0.0821809	−	0.360058i
$973$	4.80459	+	27.1782i	0.154028	+	0.871294i
$974$	−1.52338	−	6.67435i	−0.0488121	−	0.213860i
$975$	4.43004	+	4.11048i	0.141875	+	0.131641i
$976$	−12.1696	−	1.83427i	−0.389539	−	0.0587135i
$977$	55.2462	−	17.0412i	1.76748	−	0.545196i	0.771621	−	0.636082i	$-0.219446\pi$
$977$	55.2462	−	17.0412i	1.76748	−	0.545196i	0.995861	+	0.0908860i	$0.0289699\pi$
$978$	1.29000	−	17.2138i	0.0412496	−	0.550437i
$979$	−8.20076			−0.262097
$980$	−9.10452	−	0.902951i	−0.290833	−	0.0288437i
$981$	−7.13069			−0.227665
$982$	0.154692	−	2.06422i	0.00493642	−	0.0658720i
$983$	−9.11468	+	2.81150i	−0.290713	+	0.0896731i	−0.436682	−	0.899616i	$-0.643846\pi$
$983$	−9.11468	+	2.81150i	−0.290713	+	0.0896731i	0.145969	+	0.989289i	$0.453370\pi$
$984$	−11.4913	−	1.73204i	−0.366331	−	0.0552155i
$985$	1.12950	+	1.04802i	0.0359889	+	0.0333928i
$986$	−4.58804	−	20.1015i	−0.146113	−	0.640163i
$987$	38.3162	+	53.2451i	1.21962	+	1.69481i
$988$	0.154926	−	0.678773i	0.00492884	−	0.0215947i
$989$	46.6484	−	31.8043i	1.48333	−	1.01132i
$990$	−3.11773	+	2.89283i	−0.0990878	+	0.0919401i
$991$	−29.9345	−	20.4090i	−0.950900	−	0.648312i	−0.0147413	−	0.999891i	$-0.504692\pi$
$991$	−29.9345	−	20.4090i	−0.950900	−	0.648312i	−0.936158	+	0.351579i	$0.885645\pi$
$992$	−8.34329	+	1.25755i	−0.264900	+	0.0399272i
$993$	60.2272	−	29.0039i	1.91125	−	0.920411i
$994$	−14.9210	−	5.42335i	−0.473264	−	0.172018i
$995$	−29.8430	−	14.3716i	−0.946086	−	0.455611i
$996$	20.0632	+	6.18868i	0.635727	+	0.196096i
$997$	7.51602	−	19.1505i	0.238035	−	0.606502i	−0.761076	−	0.648662i	$-0.775329\pi$
$997$	7.51602	−	19.1505i	0.238035	−	0.606502i	0.999111	+	0.0421600i	$0.0134239\pi$
$998$	−17.4991	−	30.3094i	−0.553926	−	0.959427i
$999$	−6.92179	+	11.9889i	−0.218996	+	0.379311i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	98.2.g.b.23.2	✓	24
3.2	odd	2		882.2.z.b.415.1		24
4.3	odd	2		784.2.bg.b.513.1		24
7.2	even	3		686.2.e.c.491.2		24
7.3	odd	6		686.2.g.d.263.2		24
7.4	even	3		686.2.g.f.263.1		24
7.5	odd	6		686.2.e.d.491.3		24
7.6	odd	2		686.2.g.e.275.1		24
49.9	even	21		4802.2.a.o.1.9		12
49.12	odd	42		686.2.e.d.197.3		24
49.17	odd	42		686.2.g.e.459.1		24
49.20	odd	14		686.2.g.d.373.2		24
49.29	even	7		686.2.g.f.373.1		24
49.32	even	21	inner	98.2.g.b.81.2	yes	24
49.37	even	21		686.2.e.c.197.2		24
49.40	odd	42		4802.2.a.l.1.4		12
147.32	odd	42		882.2.z.b.865.1		24
196.179	odd	42		784.2.bg.b.81.1		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
98.2.g.b.23.2	✓	24	1.1	even	1	trivial
98.2.g.b.81.2	yes	24	49.32	even	21	inner
686.2.e.c.197.2		24	49.37	even	21
686.2.e.c.491.2		24	7.2	even	3
686.2.e.d.197.3		24	49.12	odd	42
686.2.e.d.491.3		24	7.5	odd	6
686.2.g.d.263.2		24	7.3	odd	6
686.2.g.d.373.2		24	49.20	odd	14
686.2.g.e.275.1		24	7.6	odd	2
686.2.g.e.459.1		24	49.17	odd	42
686.2.g.f.263.1		24	7.4	even	3
686.2.g.f.373.1		24	49.29	even	7
784.2.bg.b.81.1		24	196.179	odd	42
784.2.bg.b.513.1		24	4.3	odd	2
882.2.z.b.415.1		24	3.2	odd	2
882.2.z.b.865.1		24	147.32	odd	42
4802.2.a.l.1.4		12	49.40	odd	42
4802.2.a.o.1.9		12	49.9	even	21

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:	\( N \)	\(=\)	\( 98 = 2 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	98.g (of order \(21\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(0.0747301 - 0.997204i) q^{2} +(1.95066 - 0.601698i) q^{3} +(-0.988831 - 0.149042i) q^{4} +(0.958118 + 0.889004i) q^{5} +(-0.454243 - 1.99017i) q^{6} +(-2.43754 + 1.02877i) q^{7} +(-0.222521 + 0.974928i) q^{8} +(0.964304 - 0.657452i) q^{9} +O(q^{10})\)	\(q+(0.0747301 - 0.997204i) q^{2} +(1.95066 - 0.601698i) q^{3} +(-0.988831 - 0.149042i) q^{4} +(0.958118 + 0.889004i) q^{5} +(-0.454243 - 1.99017i) q^{6} +(-2.43754 + 1.02877i) q^{7} +(-0.222521 + 0.974928i) q^{8} +(0.964304 - 0.657452i) q^{9} +(0.958118 - 0.889004i) q^{10} +(-2.30365 - 1.57060i) q^{11} +(-2.01855 + 0.304247i) q^{12} +(-0.810304 + 0.390222i) q^{13} +(0.843740 + 2.50761i) q^{14} +(2.40387 + 1.15764i) q^{15} +(0.955573 + 0.294755i) q^{16} +(0.719733 - 1.83385i) q^{17} +(-0.583551 - 1.01074i) q^{18} +(0.387065 - 0.670417i) q^{19} +(-0.814918 - 1.02187i) q^{20} +(-4.13580 + 3.47345i) q^{21} +(-1.73836 + 2.17983i) q^{22} +(2.28676 + 5.82658i) q^{23} +(0.152550 + 2.03564i) q^{24} +(-0.245988 - 3.28248i) q^{25} +(0.328576 + 0.837199i) q^{26} +(-2.33284 + 2.92529i) q^{27} +(2.56365 - 0.653987i) q^{28} +(6.52548 + 8.18270i) q^{29} +(1.33405 - 2.31064i) q^{30} +(-4.21876 - 7.30711i) q^{31} +(0.365341 - 0.930874i) q^{32} +(-5.43865 - 1.67760i) q^{33} +(-1.77494 - 0.854764i) q^{34} +(-3.25004 - 1.18130i) q^{35} +(-1.05152 + 0.506386i) q^{36} +(3.65860 - 0.551445i) q^{37} +(-0.639617 - 0.436083i) q^{38} +(-1.34583 + 1.24875i) q^{39} +(-1.07992 + 0.736274i) q^{40} +(-1.26678 + 5.55015i) q^{41} +(3.15467 + 4.38381i) q^{42} +(-2.00714 - 8.79388i) q^{43} +(2.04383 + 1.89640i) q^{44} +(1.50839 + 0.227354i) q^{45} +(5.98118 - 1.84495i) q^{46} +(0.907661 - 12.1119i) q^{47} +2.04135 q^{48} +(4.88324 - 5.01537i) q^{49} -3.29168 q^{50} +(0.300528 - 4.01027i) q^{51} +(0.859413 - 0.265094i) q^{52} +(6.87650 + 1.03647i) q^{53} +(2.74278 + 2.54492i) q^{54} +(-0.810897 - 3.55277i) q^{55} +(-0.460577 - 2.60535i) q^{56} +(0.351643 - 1.54065i) q^{57} +(8.64747 - 5.89574i) q^{58} +(3.85448 - 3.57644i) q^{59} +(-2.20448 - 1.50299i) q^{60} +(-12.1696 + 1.83427i) q^{61} +(-7.60195 + 3.66091i) q^{62} +(-1.67417 + 2.59462i) q^{63} +(-0.900969 - 0.433884i) q^{64} +(-1.12328 - 0.346485i) q^{65} +(-2.07934 + 5.29807i) q^{66} +(0.734787 + 1.27269i) q^{67} +(-0.985015 + 1.70610i) q^{68} +(7.96653 + 9.98972i) q^{69} +(-1.42087 + 3.15267i) q^{70} +(-3.74129 + 4.69143i) q^{71} +(0.426390 + 1.08642i) q^{72} +(0.00237545 + 0.0316982i) q^{73} +(-0.276496 - 3.68958i) q^{74} +(-2.45490 - 6.25498i) q^{75} +(-0.482663 + 0.605240i) q^{76} +(7.23103 + 1.45847i) q^{77} +(1.14468 + 1.43538i) q^{78} +(-6.94343 + 12.0264i) q^{79} +(0.653513 + 1.13192i) q^{80} +(-4.06960 + 10.3692i) q^{81} +(5.43996 + 1.67801i) q^{82} +(-9.26679 - 4.46265i) q^{83} +(4.60730 - 2.81825i) q^{84} +(2.31989 - 1.11720i) q^{85} +(-8.91928 + 1.34437i) q^{86} +(17.6525 + 12.0353i) q^{87} +(2.04383 - 1.89640i) q^{88} +(2.43024 - 1.65691i) q^{89} +(0.339441 - 1.48719i) q^{90} +(1.57370 - 1.78480i) q^{91} +(-1.39282 - 6.10233i) q^{92} +(-12.6260 - 11.7153i) q^{93} +(-12.0102 - 1.81025i) q^{94} +(0.966857 - 0.298236i) q^{95} +(0.152550 - 2.03564i) q^{96} +9.86141 q^{97} +(-4.63642 - 5.24439i) q^{98} -3.25401 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 2 q^{2} - 7 q^{3} + 2 q^{4} - 7 q^{6} - 4 q^{8} + 19 q^{9}+O(q^{10}) \) 24 * q + 2 * q^2 - 7 * q^3 + 2 * q^4 - 7 * q^6 - 4 * q^8 + 19 * q^9	\( 24 q + 2 q^{2} - 7 q^{3} + 2 q^{4} - 7 q^{6} - 4 q^{8} + 19 q^{9} - 11 q^{11} - 14 q^{13} + 9 q^{15} + 2 q^{16} - 7 q^{17} - 9 q^{18} - 14 q^{19} - 7 q^{20} - 7 q^{21} + q^{22} - 29 q^{23} - 8 q^{25} - 7 q^{26} - 7 q^{27} + 14 q^{28} + 13 q^{29} - 8 q^{30} - 28 q^{31} + 2 q^{32} - 14 q^{33} - 7 q^{34} - 35 q^{35} - 17 q^{36} + 20 q^{37} + 35 q^{38} + 56 q^{39} + 14 q^{40} + 28 q^{41} - 21 q^{42} + 6 q^{43} + 3 q^{44} + 7 q^{45} + 34 q^{46} + 42 q^{47} + 14 q^{48} + 28 q^{49} + 16 q^{50} + 32 q^{51} - 7 q^{52} - 60 q^{53} + 21 q^{54} - 14 q^{55} + 7 q^{56} + 23 q^{57} + 18 q^{58} + 49 q^{59} + 6 q^{60} - 14 q^{61} - 28 q^{63} - 4 q^{64} - 28 q^{65} + 21 q^{66} + 24 q^{67} - 14 q^{68} + 7 q^{69} - 28 q^{70} + 6 q^{71} - 2 q^{72} - 35 q^{73} - 15 q^{74} - 56 q^{75} + 49 q^{77} + 6 q^{79} - 14 q^{80} - 45 q^{81} - 14 q^{82} - 77 q^{83} - 21 q^{84} - 33 q^{85} - 38 q^{86} + 63 q^{87} + 3 q^{88} - 21 q^{90} - 21 q^{91} - 5 q^{92} - 38 q^{93} - 35 q^{94} + 86 q^{95} + 98 q^{97} + 28 q^{98} - 106 q^{99}+O(q^{100}) \) 24 * q + 2 * q^2 - 7 * q^3 + 2 * q^4 - 7 * q^6 - 4 * q^8 + 19 * q^9 - 11 * q^11 - 14 * q^13 + 9 * q^15 + 2 * q^16 - 7 * q^17 - 9 * q^18 - 14 * q^19 - 7 * q^20 - 7 * q^21 + q^22 - 29 * q^23 - 8 * q^25 - 7 * q^26 - 7 * q^27 + 14 * q^28 + 13 * q^29 - 8 * q^30 - 28 * q^31 + 2 * q^32 - 14 * q^33 - 7 * q^34 - 35 * q^35 - 17 * q^36 + 20 * q^37 + 35 * q^38 + 56 * q^39 + 14 * q^40 + 28 * q^41 - 21 * q^42 + 6 * q^43 + 3 * q^44 + 7 * q^45 + 34 * q^46 + 42 * q^47 + 14 * q^48 + 28 * q^49 + 16 * q^50 + 32 * q^51 - 7 * q^52 - 60 * q^53 + 21 * q^54 - 14 * q^55 + 7 * q^56 + 23 * q^57 + 18 * q^58 + 49 * q^59 + 6 * q^60 - 14 * q^61 - 28 * q^63 - 4 * q^64 - 28 * q^65 + 21 * q^66 + 24 * q^67 - 14 * q^68 + 7 * q^69 - 28 * q^70 + 6 * q^71 - 2 * q^72 - 35 * q^73 - 15 * q^74 - 56 * q^75 + 49 * q^77 + 6 * q^79 - 14 * q^80 - 45 * q^81 - 14 * q^82 - 77 * q^83 - 21 * q^84 - 33 * q^85 - 38 * q^86 + 63 * q^87 + 3 * q^88 - 21 * q^90 - 21 * q^91 - 5 * q^92 - 38 * q^93 - 35 * q^94 + 86 * q^95 + 98 * q^97 + 28 * q^98 - 106 * q^99

Introduction

L-functions

Modular forms

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