LMFDB - Embedded newform 98.2.g.b.9.1

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			9.1
Character	$\chi$	$=$	98.9
Dual form			98.2.g.b.11.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.733052 - 0.680173i) q^{2} +(-2.81578 - 0.424410i) q^{3} +(0.0747301 + 0.997204i) q^{4} +(0.904721 + 2.30519i) q^{5} +(1.77544 + 2.22633i) q^{6} +(-1.30835 + 2.29961i) q^{7} +(0.623490 - 0.781831i) q^{8} +(4.88176 + 1.50582i) q^{9} +O(q^{10})$	\(q+(-0.733052 - 0.680173i) q^{2} +(-2.81578 - 0.424410i) q^{3} +(0.0747301 + 0.997204i) q^{4} +(0.904721 + 2.30519i) q^{5} +(1.77544 + 2.22633i) q^{6} +(-1.30835 + 2.29961i) q^{7} +(0.623490 - 0.781831i) q^{8} +(4.88176 + 1.50582i) q^{9} +(0.904721 - 2.30519i) q^{10} +(-1.71483 + 0.528954i) q^{11} +(0.212800 - 2.83962i) q^{12} +(-1.16866 + 5.12022i) q^{13} +(2.52322 - 0.795831i) q^{14} +(-1.56915 - 6.87488i) q^{15} +(-0.988831 + 0.149042i) q^{16} +(-5.15304 - 3.51328i) q^{17} +(-2.55436 - 4.42428i) q^{18} +(-0.588654 + 1.01958i) q^{19} +(-2.23114 + 1.07446i) q^{20} +(4.66000 - 5.91992i) q^{21} +(1.61684 + 0.778628i) q^{22} +(2.87850 - 1.96253i) q^{23} +(-2.08743 + 1.93685i) q^{24} +(-0.830133 + 0.770251i) q^{25} +(4.33932 - 2.95850i) q^{26} +(-5.41010 - 2.60537i) q^{27} +(-2.39096 - 1.13284i) q^{28} +(0.395404 - 0.190416i) q^{29} +(-3.52584 + 6.10694i) q^{30} +(5.26130 + 9.11284i) q^{31} +(0.826239 + 0.563320i) q^{32} +(5.05306 - 0.761627i) q^{33} +(1.38781 + 6.08037i) q^{34} +(-6.48474 - 0.935490i) q^{35} +(-1.13680 + 4.98064i) q^{36} +(-0.0500288 + 0.667588i) q^{37} +(1.12500 - 0.347018i) q^{38} +(5.46374 - 13.9214i) q^{39} +(2.36636 + 0.729924i) q^{40} +(3.47528 - 4.35787i) q^{41} +(-7.44259 + 1.17000i) q^{42} +(0.256903 + 0.322146i) q^{43} +(-0.655624 - 1.67050i) q^{44} +(0.945419 + 12.6157i) q^{45} +(-3.44495 - 0.519243i) q^{46} +(-4.51100 - 4.18560i) q^{47} +2.84758 q^{48} +(-3.57644 - 6.01740i) q^{49} +1.13243 q^{50} +(13.0187 + 12.0796i) q^{51} +(-5.19323 - 0.782754i) q^{52} +(0.935038 + 12.4772i) q^{53} +(2.19378 + 5.58967i) q^{54} +(-2.77078 - 3.47445i) q^{55} +(0.982167 + 2.45669i) q^{56} +(2.09024 - 2.62107i) q^{57} +(-0.419367 - 0.129358i) q^{58} +(2.14920 - 5.47607i) q^{59} +(6.73839 - 2.07852i) q^{60} +(-0.314914 + 4.20223i) q^{61} +(2.34150 - 10.2588i) q^{62} +(-9.84986 + 9.25601i) q^{63} +(-0.222521 - 0.974928i) q^{64} +(-12.8604 + 1.93839i) q^{65} +(-4.22220 - 2.87864i) q^{66} +(-0.229167 - 0.396929i) q^{67} +(3.11837 - 5.40118i) q^{68} +(-8.93814 + 4.30438i) q^{69} +(4.11736 + 5.09651i) q^{70} +(9.78160 + 4.71057i) q^{71} +(4.22102 - 2.87785i) q^{72} +(7.71074 - 7.15453i) q^{73} +(0.490749 - 0.455349i) q^{74} +(2.66437 - 1.81654i) q^{75} +(-1.06072 - 0.510815i) q^{76} +(1.02720 - 4.63550i) q^{77} +(-13.4742 + 6.48881i) q^{78} +(-1.29924 + 2.25035i) q^{79} +(-1.23819 - 2.14460i) q^{80} +(1.46482 + 0.998697i) q^{81} +(-5.51166 + 0.830750i) q^{82} +(1.80201 + 7.89513i) q^{83} +(6.25161 + 4.20457i) q^{84} +(3.43673 - 15.0573i) q^{85} +(0.0307918 - 0.410888i) q^{86} +(-1.19418 + 0.368357i) q^{87} +(-0.655624 + 1.67050i) q^{88} +(-4.69684 - 1.44878i) q^{89} +(7.88784 - 9.89104i) q^{90} +(-10.2455 - 9.38649i) q^{91} +(2.17215 + 2.72379i) q^{92} +(-10.9471 - 27.8927i) q^{93} +(0.459869 + 6.13652i) q^{94} +(-2.88289 - 0.434526i) q^{95} +(-2.08743 - 1.93685i) q^{96} +12.3065 q^{97} +(-1.47115 + 6.84366i) q^{98} -9.16788 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 $\left(\mathbb{Z}/98\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{1}{21}\right)$

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 $

$2$	−0.733052	−	0.680173i	−0.518346	−	0.480955i
$2$	−0.733052	−	0.680173i	−0.518346	−	0.480955i
$3$	−2.81578	−	0.424410i	−1.62569	−	0.245033i	−0.727973	−	0.685606i	$-0.759537\pi$
$3$	−2.81578	−	0.424410i	−1.62569	−	0.245033i	−0.897717	+	0.440573i	$0.854775\pi$
$4$	0.0747301	+	0.997204i	0.0373650	+	0.498602i
$5$	0.904721	+	2.30519i	0.404604	+	1.03091i	0.977434	+	0.211240i	$0.0677501\pi$
$5$	0.904721	+	2.30519i	0.404604	+	1.03091i	−0.572831	+	0.819674i	$0.694155\pi$
$6$	1.77544	+	2.22633i	0.724820	+	0.908895i
$7$	−1.30835	+	2.29961i	−0.494510	+	0.869172i
$7$	−1.30835	+	2.29961i	−0.494510	+	0.869172i
$8$	0.623490	−	0.781831i	0.220437	−	0.276419i
$9$	4.88176	+	1.50582i	1.62725	+	0.501941i
$10$	0.904721	−	2.30519i	0.286098	−	0.728966i
$11$	−1.71483	+	0.528954i	−0.517040	+	0.159486i	−0.542283	−	0.840196i	$-0.682440\pi$
$11$	−1.71483	+	0.528954i	−0.517040	+	0.159486i	0.0252436	+	0.999681i	$0.491964\pi$
$12$	0.212800	−	2.83962i	0.0614301	−	0.819728i
$13$	−1.16866	+	5.12022i	−0.324127	+	1.42009i	0.506008	+	0.862529i	$0.331121\pi$
$13$	−1.16866	+	5.12022i	−0.324127	+	1.42009i	−0.830134	+	0.557563i	$0.811736\pi$
$14$	2.52322	−	0.795831i	0.674360	−	0.212695i
$15$	−1.56915	−	6.87488i	−0.405152	−	1.77509i
$16$	−0.988831	+	0.149042i	−0.247208	+	0.0372606i
$17$	−5.15304	−	3.51328i	−1.24980	−	0.852096i	−0.256370	−	0.966579i	$-0.582527\pi$
$17$	−5.15304	−	3.51328i	−1.24980	−	0.852096i	−0.993425	+	0.114483i	$0.963479\pi$
$18$	−2.55436	−	4.42428i	−0.602069	−	1.04281i
$19$	−0.588654	+	1.01958i	−0.135046	+	0.233907i	−0.925615	−	0.378466i	$-0.876452\pi$
$19$	−0.588654	+	1.01958i	−0.135046	+	0.233907i	0.790569	+	0.612373i	$0.209785\pi$
$20$	−2.23114	+	1.07446i	−0.498897	+	0.240256i
$21$	4.66000	−	5.91992i	1.01690	−	1.29183i
$22$	1.61684	+	0.778628i	0.344711	+	0.166004i
$23$	2.87850	−	1.96253i	0.600209	−	0.409216i	−0.224743	−	0.974418i	$-0.572154\pi$
$23$	2.87850	−	1.96253i	0.600209	−	0.409216i	0.824952	+	0.565202i	$0.191202\pi$
$24$	−2.08743	+	1.93685i	−0.426094	+	0.395357i
$25$	−0.830133	+	0.770251i	−0.166027	+	0.154050i
$26$	4.33932	−	2.95850i	0.851010	−	0.580209i
$27$	−5.41010	−	2.60537i	−1.04117	−	0.501403i
$28$	−2.39096	−	1.13284i	−0.451848	−	0.214087i
$29$	0.395404	−	0.190416i	0.0734246	−	0.0353594i	−0.396811	−	0.917900i	$-0.629883\pi$
$29$	0.395404	−	0.190416i	0.0734246	−	0.0353594i	0.470236	+	0.882541i	$0.344169\pi$
$30$	−3.52584	+	6.10694i	−0.643727	+	1.11497i
$31$	5.26130	+	9.11284i	0.944958	+	1.63672i	0.755835	+	0.654762i	$0.227231\pi$
$31$	5.26130	+	9.11284i	0.944958	+	1.63672i	0.189123	+	0.981953i	$0.439436\pi$
$32$	0.826239	+	0.563320i	0.146060	+	0.0995819i
$33$	5.05306	−	0.761627i	0.879625	−	0.132582i
$34$	1.38781	+	6.08037i	0.238007	+	1.04278i
$35$	−6.48474	−	0.935490i	−1.09612	−	0.158127i
$36$	−1.13680	+	4.98064i	−0.189466	+	0.830106i
$37$	−0.0500288	+	0.667588i	−0.00822469	+	0.109751i	−0.999805	−	0.0197414i	$-0.993716\pi$
$37$	−0.0500288	+	0.667588i	−0.00822469	+	0.109751i	0.991580	+	0.129492i	$0.0413347\pi$
$38$	1.12500	−	0.347018i	0.182500	−	0.0562937i
$39$	5.46374	−	13.9214i	0.874899	−	2.22921i
$40$	2.36636	+	0.729924i	0.374154	+	0.115411i
$41$	3.47528	−	4.35787i	0.542748	−	0.680584i	−0.432516	−	0.901626i	$-0.642374\pi$
$41$	3.47528	−	4.35787i	0.542748	−	0.680584i	0.975264	+	0.221042i	$0.0709457\pi$
$42$	−7.44259	+	1.17000i	−1.14842	+	0.180535i
$43$	0.256903	+	0.322146i	0.0391773	+	0.0491268i	0.801034	−	0.598619i	$-0.204283\pi$
$43$	0.256903	+	0.322146i	0.0391773	+	0.0491268i	−0.761857	+	0.647745i	$0.775712\pi$
$44$	−0.655624	−	1.67050i	−0.0988391	−	0.251838i
$45$	0.945419	+	12.6157i	0.140935	+	1.88064i
$46$	−3.44495	−	0.519243i	−0.507930	−	0.0765582i
$47$	−4.51100	−	4.18560i	−0.657997	−	0.610532i	0.278823	−	0.960342i	$-0.410056\pi$
$47$	−4.51100	−	4.18560i	−0.657997	−	0.610532i	−0.936821	+	0.349810i	$0.886246\pi$
$48$	2.84758			0.411013
$49$	−3.57644	−	6.01740i	−0.510920	−	0.859628i
$50$	1.13243			0.160150
$51$	13.0187	+	12.0796i	1.82299	+	1.69149i
$52$	−5.19323	−	0.782754i	−0.720172	−	0.108548i
$53$	0.935038	+	12.4772i	0.128437	+	1.71388i	0.574191	+	0.818721i	$0.305317\pi$
$53$	0.935038	+	12.4772i	0.128437	+	1.71388i	−0.445754	+	0.895156i	$0.647064\pi$
$54$	2.19378	+	5.58967i	0.298536	+	0.760658i
$55$	−2.77078	−	3.47445i	−0.373612	−	0.468495i
$56$	0.982167	+	2.45669i	0.131248	+	0.328290i
$57$	2.09024	−	2.62107i	0.276859	−	0.347170i
$58$	−0.419367	−	0.129358i	−0.0550656	−	0.0169855i
$59$	2.14920	−	5.47607i	0.279802	−	0.712923i	−0.720018	−	0.693955i	$-0.755867\pi$
$59$	2.14920	−	5.47607i	0.279802	−	0.712923i	0.999820	−	0.0189681i	$-0.00603811\pi$
$60$	6.73839	−	2.07852i	0.869923	−	0.268336i
$61$	−0.314914	+	4.20223i	−0.0403206	+	0.538041i	0.940071	+	0.340980i	$0.110759\pi$
$61$	−0.314914	+	4.20223i	−0.0403206	+	0.538041i	−0.980391	+	0.197061i	$0.936860\pi$
$62$	2.34150	−	10.2588i	0.297371	−	1.30287i
$63$	−9.84986	+	9.25601i	−1.24097	+	1.16615i
$64$	−0.222521	−	0.974928i	−0.0278151	−	0.121866i
$65$	−12.8604	+	1.93839i	−1.59514	+	0.240428i
$66$	−4.22220	−	2.87864i	−0.519716	−	0.354337i
$67$	−0.229167	−	0.396929i	−0.0279972	−	0.0484926i	0.851687	−	0.524050i	$-0.175580\pi$
$67$	−0.229167	−	0.396929i	−0.0279972	−	0.0484926i	−0.879685	+	0.475558i	$0.842246\pi$
$68$	3.11837	−	5.40118i	0.378158	−	0.654989i
$69$	−8.93814	+	4.30438i	−1.07603	+	0.518186i
$70$	4.11736	+	5.09651i	0.492118	+	0.609149i
$71$	9.78160	+	4.71057i	1.16086	+	0.559042i	0.912279	−	0.409569i	$-0.134321\pi$
$71$	9.78160	+	4.71057i	1.16086	+	0.559042i	0.248583	+	0.968611i	$0.420035\pi$
$72$	4.22102	−	2.87785i	0.497453	−	0.339157i
$73$	7.71074	−	7.15453i	0.902474	−	0.837374i	−0.0848003	−	0.996398i	$-0.527025\pi$
$73$	7.71074	−	7.15453i	0.902474	−	0.837374i	0.987275	+	0.159024i	$0.0508348\pi$
$74$	0.490749	−	0.455349i	0.0570484	−	0.0529332i
$75$	2.66437	−	1.81654i	0.307655	−	0.209756i
$76$	−1.06072	−	0.510815i	−0.121673	−	0.0585945i
$77$	1.02720	−	4.63550i	0.117061	−	0.528264i
$78$	−13.4742	+	6.48881i	−1.52565	+	0.734713i
$79$	−1.29924	+	2.25035i	−0.146176	+	0.253184i	−0.929811	−	0.368037i	$-0.880030\pi$
$79$	−1.29924	+	2.25035i	−0.146176	+	0.253184i	0.783635	+	0.621221i	$0.213363\pi$
$80$	−1.23819	−	2.14460i	−0.138434	−	0.239774i
$81$	1.46482	+	0.998697i	0.162758	+	0.110966i
$82$	−5.51166	+	0.830750i	−0.608662	+	0.0917410i
$83$	1.80201	+	7.89513i	0.197796	+	0.866603i	0.972245	+	0.233966i	$0.0751703\pi$
$83$	1.80201	+	7.89513i	0.197796	+	0.866603i	−0.774448	+	0.632637i	$0.781973\pi$
$84$	6.25161	+	4.20457i	0.682106	+	0.458757i
$85$	3.43673	−	15.0573i	0.372765	−	1.63319i
$86$	0.0307918	−	0.410888i	0.00332036	−	0.0443072i
$87$	−1.19418	+	0.368357i	−0.128030	+	0.0394920i
$88$	−0.655624	+	1.67050i	−0.0698898	+	0.178076i
$89$	−4.69684	−	1.44878i	−0.497864	−	0.153571i	0.0356461	−	0.999364i	$-0.488651\pi$
$89$	−4.69684	−	1.44878i	−0.497864	−	0.153571i	−0.533510	+	0.845794i	$0.679127\pi$
$90$	7.88784	−	9.89104i	0.831451	−	1.04261i
$91$	−10.2455	−	9.38649i	−1.07402	−	0.983972i
$92$	2.17215	+	2.72379i	0.226463	+	0.283975i
$93$	−10.9471	−	27.8927i	−1.13516	−	2.89234i
$94$	0.459869	+	6.13652i	0.0474318	+	0.632934i
$95$	−2.88289	−	0.434526i	−0.295779	−	0.0445814i
$96$	−2.08743	−	1.93685i	−0.213047	−	0.197679i
$97$	12.3065			1.24954			0.624769	−	0.780810i	$-0.285193\pi$
$97$	12.3065			1.24954			0.624769	+	0.780810i	$0.285193\pi$
$98$	−1.47115	+	6.84366i	−0.148609	+	0.691314i
$99$	−9.16788			−0.921406
$100$	−0.830133	−	0.770251i	−0.0830133	−	0.0770251i
$101$	0.600770	+	0.0905516i	0.0597789	+	0.00901022i	0.178864	−	0.983874i	$-0.442758\pi$
$101$	0.600770	+	0.0905516i	0.0597789	+	0.00901022i	−0.119085	+	0.992884i	$0.537996\pi$
$102$	−1.32718	−	17.7100i	−0.131410	−	1.75355i
$103$	−0.310964	−	0.792323i	−0.0306402	−	0.0780699i	0.914735	−	0.404055i	$-0.132399\pi$
$103$	−0.310964	−	0.792323i	−0.0306402	−	0.0780699i	−0.945375	+	0.325985i	$0.894304\pi$
$104$	3.27450	+	4.10609i	0.321091	+	0.402636i
$105$	17.8626	+	5.38632i	1.74321	+	0.525651i
$106$	7.80123	−	9.78243i	0.757722	−	0.950154i
$107$	2.76219	+	0.852023i	0.267031	+	0.0823681i	0.425379	−	0.905015i	$-0.360141\pi$
$107$	2.76219	+	0.852023i	0.267031	+	0.0823681i	−0.158348	+	0.987383i	$0.550617\pi$
$108$	2.19378	−	5.58967i	0.211097	−	0.537867i
$109$	−7.66160	+	2.36329i	−0.733848	+	0.226362i	−0.639083	−	0.769137i	$-0.720686\pi$
$109$	−7.66160	+	2.36329i	−0.733848	+	0.226362i	−0.0947650	+	0.995500i	$0.530210\pi$
$110$	−0.332100	+	4.43156i	−0.0316645	+	0.422533i
$111$	0.424201	−	1.85855i	0.0402634	−	0.176405i
$112$	0.950998	−	2.46893i	0.0898608	−	0.233292i
$113$	3.30882	+	14.4969i	0.311268	+	1.36375i	0.852433	+	0.522837i	$0.175126\pi$
$113$	3.30882	+	14.4969i	0.311268	+	1.36375i	−0.541165	+	0.840916i	$0.682017\pi$
$114$	−3.31504	+	0.499661i	−0.310482	+	0.0467976i
$115$	7.12825	+	4.85996i	0.664713	+	0.453194i
$116$	0.219432	+	0.380068i	0.0203738	+	0.0352884i
$117$	−13.4152	+	23.2359i	−1.24024	+	2.14816i
$118$	−5.30014	+	2.55242i	−0.487918	+	0.234969i
$119$	14.8212	−	7.25339i	1.35865	−	0.664917i
$120$	−6.35335	−	3.05961i	−0.579978	−	0.279303i
$121$	−6.42779	+	4.38239i	−0.584344	+	0.398399i
$122$	3.08909	−	2.86626i	0.279673	−	0.259499i
$123$	−11.6351	+	10.7958i	−1.04911	+	0.973428i
$124$	−8.69419	+	5.92760i	−0.780761	+	0.532314i
$125$	8.62907	+	4.15554i	0.771807	+	0.371683i
$126$	13.5161	−	0.0855299i	1.20411	−	0.00761961i
$127$	3.08711	−	1.48667i	0.273937	−	0.131921i	−0.291872	−	0.956457i	$-0.594278\pi$
$127$	3.08711	−	1.48667i	0.273937	−	0.131921i	0.565809	+	0.824536i	$0.308564\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$	−0.586659	−	1.01612i	−0.0516524	−	0.0894646i
$130$	10.7458	+	7.32635i	0.942467	+	0.642563i
$131$	−8.18564	+	1.23379i	−0.715183	+	0.107796i	−0.496547	−	0.868010i	$-0.665399\pi$
$131$	−8.18564	+	1.23379i	−0.715183	+	0.107796i	−0.218636	+	0.975806i	$0.570161\pi$
$132$	1.13711	+	4.98202i	0.0989730	+	0.433629i
$133$	−1.57447	−	2.68764i	−0.136524	−	0.233048i
$134$	−0.101989	+	0.446843i	−0.00881051	+	0.0386014i
$135$	1.11124	−	14.8285i	0.0956403	−	1.27623i
$136$	−5.95966	+	1.83831i	−0.511037	+	0.157634i
$137$	−1.43763	+	3.66302i	−0.122825	+	0.312953i	−0.979040	−	0.203666i	$-0.934714\pi$
$137$	−1.43763	+	3.66302i	−0.122825	+	0.312953i	0.856216	+	0.516619i	$0.172810\pi$
$138$	9.47984	+	2.92414i	0.806978	+	0.248920i
$139$	−5.89054	+	7.38650i	−0.499629	+	0.626515i	−0.966146	−	0.257998i	$-0.916937\pi$
$139$	−5.89054	+	7.38650i	−0.499629	+	0.626515i	0.466517	+	0.884512i	$0.345509\pi$
$140$	0.448269	−	6.53652i	0.0378856	−	0.552437i
$141$	10.9256	+	13.7002i	0.920099	+	1.15377i
$142$	−3.96642	−	10.1063i	−0.332854	−	0.848099i
$143$	−0.704316	−	9.39845i	−0.0588979	−	0.785938i
$144$	−5.05166	−	0.761416i	−0.420972	−	0.0634513i
$145$	0.796677	+	0.739208i	0.0661604	+	0.0613879i
$146$	−10.5187			−0.870533
$147$	7.51661	+	18.4615i	0.619960	+	1.52268i
$148$	−0.669460			−0.0550293
$149$	−3.35579	−	3.11372i	−0.274917	−	0.255085i	0.530649	−	0.847592i	$-0.321948\pi$
$149$	−3.35579	−	3.11372i	−0.274917	−	0.255085i	−0.805566	+	0.592506i	$0.798139\pi$
$150$	−3.18868	−	0.480617i	−0.260355	−	0.0392422i
$151$	1.32007	+	17.6151i	0.107426	+	1.43350i	0.747028	+	0.664793i	$0.231480\pi$
$151$	1.32007	+	17.6151i	0.107426	+	1.43350i	−0.639602	+	0.768707i	$0.720901\pi$
$152$	0.430119	+	1.09593i	0.0348872	+	0.0888913i
$153$	−19.8655	−	24.9105i	−1.60603	−	2.01390i
$154$	−3.90593	+	2.69938i	−0.314749	+	0.217522i
$155$	−16.2468	+	20.3729i	−1.30498	+	1.63639i
$156$	14.2908	+	4.40812i	1.14418	+	0.352932i
$157$	6.56480	−	16.7268i	0.523928	−	1.33495i	−0.386885	−	0.922128i	$-0.626449\pi$
$157$	6.56480	−	16.7268i	0.523928	−	1.33495i	0.910813	−	0.412819i	$-0.135456\pi$
$158$	2.48304	−	0.765916i	0.197540	−	0.0609330i
$159$	2.66260	−	35.5299i	0.211158	−	2.81770i
$160$	−0.551045	+	2.41429i	−0.0435640	+	0.190866i
$161$	0.746969	+	9.18712i	0.0588694	+	0.724046i
$162$	−0.394502	−	1.72843i	−0.0309950	−	0.135798i
$163$	24.2610	−	3.65675i	1.90027	−	0.286419i	0.908846	−	0.417131i	$-0.136964\pi$
$163$	24.2610	−	3.65675i	1.90027	−	0.286419i	0.991420	+	0.130712i	$0.0417263\pi$
$164$	4.60539	+	3.13990i	0.359621	+	0.245185i
$165$	6.32731	+	10.9592i	0.492581	+	0.853174i
$166$	4.04908	−	7.01322i	0.314270	−	0.544331i
$167$	−2.53907	+	1.22275i	−0.196479	+	0.0946195i	−0.529536	−	0.848287i	$-0.677634\pi$
$167$	−2.53907	+	1.22275i	−0.196479	+	0.0946195i	0.333057	+	0.942907i	$0.391920\pi$
$168$	−1.72292	−	7.33434i	−0.132926	−	0.565857i
$169$	−13.1383	−	6.32705i	−1.01063	−	0.486696i
$170$	−12.7609	+	8.70020i	−0.978713	+	0.667275i
$171$	−4.40897	+	4.09093i	−0.337162	+	0.312841i
$172$	−0.302047	+	0.280258i	−0.0230308	+	0.0213695i
$173$	4.62379	−	3.15245i	0.351540	−	0.239676i	−0.374655	−	0.927164i	$-0.622239\pi$
$173$	4.62379	−	3.15245i	0.351540	−	0.239676i	0.726196	+	0.687488i	$0.241287\pi$
$174$	1.12594	+	0.542226i	0.0853576	+	0.0411061i
$175$	−0.685174	−	2.91674i	−0.0517943	−	0.220485i
$176$	1.61684	−	0.778628i	0.121874	−	0.0586913i
$177$	−8.37576	+	14.5072i	−0.629561	+	1.09043i
$178$	2.45760	+	4.25669i	0.184205	+	0.319053i
$179$	−6.04342	−	4.12034i	−0.451707	−	0.307968i	0.316012	−	0.948755i	$-0.397656\pi$
$179$	−6.04342	−	4.12034i	−0.451707	−	0.307968i	−0.767719	+	0.640787i	$0.778608\pi$
$180$	−12.5098	+	1.88555i	−0.932426	+	0.140541i
$181$	−4.26428	−	18.6830i	−0.316961	−	1.38870i	−0.842852	−	0.538145i	$-0.819125\pi$
$181$	−4.26428	−	18.6830i	−0.316961	−	1.38870i	0.525891	−	0.850552i	$-0.323732\pi$
$182$	1.12605	+	13.8495i	0.0834683	+	1.02659i
$183$	2.67020	−	11.6989i	0.197387	−	0.864808i
$184$	0.260349	−	3.47412i	0.0191932	−	0.256116i
$185$	−1.58418	+	0.488655i	−0.116471	+	0.0359267i
$186$	−10.9471	+	27.8927i	−0.802678	+	2.04519i
$187$	10.6949	+	3.29895i	0.782091	+	0.241243i
$188$	3.83679	−	4.81118i	0.279826	−	0.350891i
$189$	13.0696	−	9.03241i	0.950677	−	0.657011i
$190$	1.81776	+	2.27940i	0.131874	+	0.165365i
$191$	−0.556242	−	1.41728i	−0.0402483	−	0.102551i	0.909336	−	0.416062i	$-0.136590\pi$
$191$	−0.556242	−	1.41728i	−0.0402483	−	0.102551i	−0.949585	+	0.313511i	$0.898495\pi$
$192$	0.212800	+	2.83962i	0.0153575	+	0.204932i
$193$	12.2766	+	1.85040i	0.883687	+	0.133194i	0.575179	−	0.818027i	$-0.304932\pi$
$193$	12.2766	+	1.85040i	0.883687	+	0.133194i	0.308508	+	0.951222i	$0.400170\pi$
$194$	−9.02132	−	8.37056i	−0.647693	−	0.600971i
$195$	37.0347			2.65211
$196$	5.73330	−	4.01612i	0.409522	−	0.286866i
$197$	−11.7009			−0.833655			−0.416827	−	0.908986i	$-0.636858\pi$
$197$	−11.7009			−0.833655			−0.416827	+	0.908986i	$0.636858\pi$
$198$	6.72053	+	6.23574i	0.477607	+	0.443155i
$199$	19.4969	+	2.93868i	1.38210	+	0.208318i	0.797653	−	0.603116i	$-0.206075\pi$
$199$	19.4969	+	2.93868i	1.38210	+	0.208318i	0.584444	+	0.811434i	$0.301313\pi$
$200$	0.0846269	+	1.12927i	0.00598403	+	0.0798513i
$201$	0.476823	+	1.21493i	0.0336325	+	0.0856942i
$202$	−0.378805	−	0.475007i	−0.0266526	−	0.0334213i
$203$	−0.0794425	+	1.15841i	−0.00557577	+	0.0813042i
$204$	−11.0730	+	13.8850i	−0.775262	+	0.972147i
$205$	13.1899	+	4.06854i	0.921222	+	0.284159i
$206$	−0.310964	+	0.792323i	−0.0216659	+	0.0552038i
$207$	17.0074	−	5.24608i	1.18209	−	0.364628i
$208$	0.392474	−	5.23721i	0.0272132	−	0.363135i
$209$	0.470129	−	2.05977i	0.0325195	−	0.142477i
$210$	−9.43055	−	16.0981i	−0.650770	−	1.11087i
$211$	−0.470841	−	2.06289i	−0.0324141	−	0.142015i	0.956132	−	0.292938i	$-0.0946328\pi$
$211$	−0.470841	−	2.06289i	−0.0324141	−	0.142015i	−0.988546	+	0.150922i	$0.951776\pi$
$212$	−12.3724	+	1.86485i	−0.849743	+	0.128078i
$213$	−25.5436	−	17.4153i	−1.75022	−	1.19328i
$214$	−1.44531	−	2.50334i	−0.0987990	−	0.171125i
$215$	−0.510183	+	0.883663i	−0.0347942	+	0.0602653i
$216$	−5.41010	+	2.60537i	−0.368111	+	0.177273i
$217$	−27.8396	+	0.176169i	−1.88988	+	0.0119591i
$218$	7.22380	+	3.47880i	0.489257	+	0.235614i
$219$	−24.7482	+	16.8730i	−1.67233	+	1.14017i
$220$	3.25767	−	3.02268i	0.219632	−	0.203789i
$221$	24.0109	−	22.2788i	1.61515	−	1.49864i
$222$	−1.57509	+	1.07388i	−0.105713	+	0.0720742i
$223$	−9.59858	−	4.62243i	−0.642768	−	0.309541i	0.0839567	−	0.996469i	$-0.473244\pi$
$223$	−9.59858	−	4.62243i	−0.642768	−	0.309541i	−0.726725	+	0.686929i	$0.758959\pi$
$224$	−2.37643	+	1.16301i	−0.158782	+	0.0777068i
$225$	−5.21237	+	2.51014i	−0.347491	+	0.167343i
$226$	7.43486	−	12.8775i	0.494559	−	0.856602i
$227$	3.13620	+	5.43206i	0.208157	+	0.360539i	0.951134	−	0.308778i	$-0.0999202\pi$
$227$	3.13620	+	5.43206i	0.208157	+	0.360539i	−0.742977	+	0.669317i	$0.766587\pi$
$228$	2.76995	+	1.88852i	0.183444	+	0.125070i
$229$	−21.2911	+	3.20911i	−1.40695	+	0.212064i	−0.808218	−	0.588883i	$-0.799568\pi$
$229$	−21.2911	+	3.20911i	−1.40695	+	0.212064i	−0.598735	+	0.800947i	$0.704330\pi$
$230$	−1.91977	−	8.41104i	−0.126586	−	0.554608i
$231$	−4.85973	+	12.6166i	−0.319747	+	0.830109i
$232$	0.0976566	−	0.427862i	0.00641147	−	0.0280905i
$233$	−0.413108	+	5.51254i	−0.0270636	+	0.361139i	0.967187	+	0.254064i	$0.0817674\pi$
$233$	−0.413108	+	5.51254i	−0.0270636	+	0.361139i	−0.994251	+	0.107075i	$0.965852\pi$
$234$	25.6385	−	7.90842i	1.67604	−	0.516989i
$235$	5.56741	−	14.1855i	0.363178	−	0.925362i
$236$	5.62136	+	1.73396i	0.365920	+	0.112871i
$237$	4.61344	−	5.78508i	0.299675	−	0.375781i
$238$	−15.7982	−	4.76384i	−1.02405	−	0.308794i
$239$	−17.7605	−	22.2709i	−1.14883	−	1.44059i	−0.878450	−	0.477833i	$-0.841422\pi$
$239$	−17.7605	−	22.2709i	−1.14883	−	1.44059i	−0.270380	−	0.962754i	$-0.587149\pi$
$240$	2.57627	+	6.56422i	0.166297	+	0.423719i
$241$	−0.541597	−	7.22711i	−0.0348874	−	0.465539i	−0.987100	−	0.160104i	$-0.948817\pi$
$241$	−0.541597	−	7.22711i	−0.0348874	−	0.465539i	0.952213	−	0.305435i	$-0.0988020\pi$
$242$	7.69268	+	1.15949i	0.494504	+	0.0745346i
$243$	9.50465	+	8.81903i	0.609724	+	0.565741i
$244$	−4.21402			−0.269775
$245$	10.6356	−	13.6885i	0.679482	−	0.874523i
$246$	15.8722			1.01197
$247$	−4.53253	−	4.20557i	−0.288398	−	0.267594i
$248$	10.4051	+	1.56831i	0.660723	+	0.0995880i
$249$	−1.72329	−	22.9957i	−0.109209	−	1.45729i
$250$	−3.49907	−	8.91548i	−0.221301	−	0.563865i
$251$	−4.30073	−	5.39295i	−0.271460	−	0.340400i	0.627351	−	0.778737i	$-0.284139\pi$
$251$	−4.30073	−	5.39295i	−0.271460	−	0.340400i	−0.898811	+	0.438337i	$0.855568\pi$
$252$	−9.96621	−	9.13061i	−0.627812	−	0.575174i
$253$	−3.89805	+	4.88799i	−0.245068	+	0.307306i
$254$	−3.27421	−	1.00996i	−0.205442	−	0.0633705i
$255$	−16.0675	+	40.9394i	−1.00619	+	2.56372i
$256$	0.955573	−	0.294755i	0.0597233	−	0.0184222i
$257$	0.529616	−	7.06723i	0.0330365	−	0.440842i	−0.956020	−	0.293303i	$-0.905246\pi$
$257$	0.529616	−	7.06723i	0.0330365	−	0.440842i	0.989056	−	0.147539i	$-0.0471353\pi$
$258$	−0.261088	+	1.14390i	−0.0162546	+	0.0712161i
$259$	−1.46974	−	0.988486i	−0.0913252	−	0.0614216i
$260$	−2.89403	−	12.6796i	−0.179480	−	0.786354i
$261$	2.21700	−	0.334159i	0.137229	−	0.0206839i
$262$	6.83969	+	4.66322i	0.422557	+	0.288095i
$263$	−1.74334	−	3.01955i	−0.107499	−	0.186194i	0.807257	−	0.590199i	$-0.200951\pi$
$263$	−1.74334	−	3.01955i	−0.107499	−	0.186194i	−0.914756	+	0.404006i	$0.867618\pi$
$264$	2.55507	−	4.42551i	0.157254	−	0.272371i
$265$	−27.9164	+	13.4438i	−1.71489	+	0.825849i
$266$	−0.673892	+	3.04109i	−0.0413190	+	0.186461i
$267$	12.6104	+	6.07283i	0.771742	+	0.371651i
$268$	0.378694	−	0.258189i	0.0231324	−	0.0157714i
$269$	−5.22527	+	4.84834i	−0.318591	+	0.295609i	−0.823215	−	0.567730i	$-0.807822\pi$
$269$	−5.22527	+	4.84834i	−0.318591	+	0.295609i	0.504624	+	0.863339i	$0.331631\pi$
$270$	−10.9005	+	10.1142i	−0.663384	+	0.615530i
$271$	13.0380	−	8.88917i	0.792003	−	0.539978i	−0.0984025	−	0.995147i	$-0.531373\pi$
$271$	13.0380	−	8.88917i	0.792003	−	0.539978i	0.890405	+	0.455168i	$0.150421\pi$
$272$	5.61911	+	2.70602i	0.340709	+	0.164077i
$273$	24.8653	+	30.7786i	1.50492	+	1.86280i
$274$	3.54534	−	1.70735i	0.214182	−	0.103145i
$275$	1.01611	−	1.75995i	0.0612736	−	0.106129i
$276$	−4.96029	−	8.59148i	−0.298574	−	0.517146i
$277$	−2.14721	−	1.46395i	−0.129014	−	0.0879599i	0.497094	−	0.867697i	$-0.334400\pi$
$277$	−2.14721	−	1.46395i	−0.129014	−	0.0879599i	−0.626107	+	0.779737i	$0.715353\pi$
$278$	9.34216	−	1.40810i	0.560306	−	0.0844525i
$279$	11.9621	+	52.4093i	0.716151	+	3.13766i
$280$	−4.77457	+	4.48671i	−0.285335	+	0.268132i
$281$	−5.36157	+	23.4906i	−0.319845	+	1.40133i	0.517981	+	0.855392i	$0.326684\pi$
$281$	−5.36157	+	23.4906i	−0.319845	+	1.40133i	−0.837825	+	0.545938i	$0.816173\pi$
$282$	1.30951	−	17.4742i	0.0779804	−	1.04058i
$283$	−7.47153	+	2.30466i	−0.444137	+	0.136998i	−0.508754	−	0.860912i	$-0.669894\pi$
$283$	−7.47153	+	2.30466i	−0.444137	+	0.136998i	0.0646170	+	0.997910i	$0.479417\pi$
$284$	−3.96642	+	10.1063i	−0.235364	+	0.599697i
$285$	7.93317	+	2.44706i	0.469920	+	0.144951i
$286$	−5.87627	+	7.36861i	−0.347471	+	0.435715i
$287$	5.47452	+	13.6934i	0.323151	+	0.808297i
$288$	3.18524	+	3.99416i	0.187692	+	0.235358i
$289$	7.99986	+	20.3833i	0.470580	+	1.19902i
$290$	−0.0812162	−	1.08376i	−0.00476918	−	0.0636403i
$291$	−34.6524	−	5.22301i	−2.03136	−	0.306178i
$292$	7.71074	+	7.15453i	0.451237	+	0.418687i
$293$	26.0121			1.51964			0.759822	−	0.650131i	$-0.225286\pi$
$293$	26.0121			1.51964			0.759822	+	0.650131i	$0.225286\pi$
$294$	7.04696	−	18.6458i	0.410987	−	1.08745i
$295$	14.5678			0.848171
$296$	0.490749	+	0.455349i	0.0285242	+	0.0264666i
$297$	10.6555	+	1.60606i	0.618295	+	0.0931930i
$298$	0.342102	+	4.56503i	0.0198174	+	0.264445i
$299$	6.68460	+	17.0321i	0.386580	+	0.984990i
$300$	2.01057	+	2.52117i	0.116080	+	0.145560i
$301$	−1.07693	+	0.169297i	−0.0620732	+	0.00975813i
$302$	11.0137	−	13.8107i	0.633765	−	0.794716i
$303$	−1.65320	−	0.509946i	−0.0949741	−	0.0292956i
$304$	0.430119	−	1.09593i	0.0246690	−	0.0628556i
$305$	−9.97187	+	3.07591i	−0.570988	+	0.176126i
$306$	−2.38103	+	31.7727i	−0.136115	+	1.81632i
$307$	2.14025	−	9.37707i	0.122151	−	0.535178i	−0.876411	−	0.481564i	$-0.840069\pi$
$307$	2.14025	−	9.37707i	0.122151	−	0.535178i	0.998562	−	0.0536136i	$-0.0170739\pi$
$308$	4.69930	+	0.677921i	0.267767	+	0.0386282i
$309$	0.539335	+	2.36298i	0.0306817	+	0.134425i
$310$	25.7669	−	3.88373i	1.46346	−	0.220581i
$311$	−5.46179	−	3.72378i	−0.309710	−	0.211156i	0.398483	−	0.917176i	$-0.369537\pi$
$311$	−5.46179	−	3.72378i	−0.309710	−	0.211156i	−0.708193	+	0.706019i	$0.750489\pi$
$312$	−7.47760	−	12.9516i	−0.423335	−	0.733239i
$313$	−5.13834	+	8.89987i	−0.290436	+	0.503050i	−0.973913	−	0.226922i	$-0.927134\pi$
$313$	−5.13834	+	8.89987i	−0.290436	+	0.503050i	0.683477	+	0.729972i	$0.260467\pi$
$314$	−16.1895	+	7.79645i	−0.913626	+	0.439979i
$315$	−30.2483	−	14.3317i	−1.70430	−	0.807500i
$316$	−2.34115	−	1.12744i	−0.131700	−	0.0634234i
$317$	−9.76438	+	6.65724i	−0.548422	+	0.373908i	−0.805603	−	0.592455i	$-0.798159\pi$
$317$	−9.76438	+	6.65724i	−0.548422	+	0.373908i	0.257181	+	0.966363i	$0.417206\pi$
$318$	−26.1183	+	24.2342i	−1.46464	+	1.35899i
$319$	−0.577327	+	0.535681i	−0.0323241	+	0.0299924i
$320$	2.04608	−	1.39499i	0.114379	−	0.0779824i
$321$	−7.41610	−	3.57141i	−0.413926	−	0.199336i
$322$	5.70126	−	7.24270i	0.317719	−	0.403620i
$323$	6.61542	−	3.18582i	0.368092	−	0.177264i
$324$	−0.886438	+	1.53536i	−0.0492466	+	0.0852976i
$325$	−2.97371	−	5.15062i	−0.164952	−	0.285705i
$326$	−20.2718	−	13.8211i	−1.12275	−	0.765478i
$327$	22.5764	−	3.40284i	1.24848	−	0.188177i
$328$	−1.24031	−	5.43417i	−0.0684849	−	0.300052i
$329$	15.5272	−	4.89733i	0.856044	−	0.269999i
$330$	2.81592	−	12.3373i	0.155011	−	0.679148i
$331$	2.18069	−	29.0992i	0.119861	−	1.59944i	−0.535774	−	0.844361i	$-0.679980\pi$
$331$	2.18069	−	29.0992i	0.119861	−	1.59944i	0.655636	−	0.755077i	$-0.272401\pi$
$332$	−7.73838	+	2.38698i	−0.424699	+	0.131002i
$333$	−1.24950	+	3.18367i	−0.0684721	+	0.174464i
$334$	2.69296	+	0.830667i	0.147352	+	0.0454521i
$335$	0.707666	−	0.887385i	0.0386639	−	0.0484830i
$336$	−3.72563	+	6.54834i	−0.203250	+	0.357241i
$337$	−5.89679	−	7.39434i	−0.321219	−	0.402796i	0.594837	−	0.803846i	$-0.297217\pi$
$337$	−5.89679	−	7.39434i	−0.321219	−	0.402796i	−0.916056	+	0.401051i	$0.868645\pi$
$338$	5.32754	+	13.5743i	0.289780	+	0.738347i
$339$	−3.16428	−	42.2243i	−0.171860	−	2.29331i
$340$	15.2720	+	2.30189i	0.828241	+	0.124837i
$341$	−13.8425	−	12.8440i	−0.749613	−	0.695540i
$342$	6.01454			0.325229
$343$	18.5169	−	0.351562i	0.999820	−	0.0189825i
$344$	0.412040			0.0222157
$345$	−18.0089	−	16.7099i	−0.969569	−	0.899629i
$346$	−5.53369	−	0.834069i	−0.297493	−	0.0448398i
$347$	−1.87874	−	25.0701i	−0.100856	−	1.34583i	−0.786363	−	0.617765i	$-0.788038\pi$
$347$	−1.87874	−	25.0701i	−0.100856	−	1.34583i	0.685506	−	0.728067i	$-0.259581\pi$
$348$	−0.456568	−	1.16332i	−0.0244746	−	0.0623603i
$349$	11.0132	+	13.8102i	0.589525	+	0.739241i	0.983705	−	0.179792i	$-0.0575425\pi$
$349$	11.0132	+	13.8102i	0.589525	+	0.739241i	−0.394179	+	0.919034i	$0.628971\pi$
$350$	−1.48162	+	2.60416i	−0.0791960	+	0.139198i
$351$	19.6626	−	24.6561i	1.04951	−	1.31605i
$352$	−1.71483	−	0.528954i	−0.0914006	−	0.0281933i
$353$	−1.81639	+	4.62808i	−0.0966766	+	0.246328i	−0.971028	−	0.238965i	$-0.923192\pi$
$353$	−1.81639	+	4.62808i	−0.0966766	+	0.246328i	0.874352	+	0.485293i	$0.161287\pi$
$354$	16.0073	−	4.93760i	0.850778	−	0.262430i
$355$	−2.00915	+	26.8102i	−0.106635	+	1.42294i
$356$	1.09374	−	4.79197i	0.0579679	−	0.253974i
$357$	−44.8115	+	14.1337i	−2.37168	+	0.748033i
$358$	1.62760	+	7.13099i	0.0860214	+	0.376885i
$359$	−1.37633	+	0.207448i	−0.0726397	+	0.0109487i	−0.185262	−	0.982689i	$-0.559313\pi$
$359$	−1.37633	+	0.207448i	−0.0726397	+	0.0109487i	0.112622	+	0.993638i	$0.464075\pi$
$360$	10.4528	+	7.12663i	0.550913	+	0.375606i
$361$	8.80697	+	15.2541i	0.463525	+	0.802849i
$362$	−9.58174	+	16.5961i	−0.503605	+	0.872270i
$363$	19.9591	−	9.61182i	1.04758	−	0.504490i
$364$	8.59460	−	10.9183i	0.450479	−	0.572275i
$365$	23.4686	+	11.3019i	1.22840	+	0.591568i
$366$	−9.91467	+	6.75971i	−0.518248	+	0.353335i
$367$	−26.0962	+	24.2138i	−1.36221	+	1.26395i	−0.429625	+	0.903008i	$0.641354\pi$
$367$	−26.0962	+	24.2138i	−1.36221	+	1.26395i	−0.932588	+	0.360942i	$0.882455\pi$
$368$	−2.55385	+	2.36963i	−0.133129	+	0.123525i
$369$	23.5277	−	16.0409i	1.22480	−	0.835055i
$370$	1.49366	+	0.719308i	0.0776516	+	0.0373950i
$371$	−29.9161	−	14.1743i	−1.55317	−	0.735895i
$372$	26.9966	−	13.0009i	1.39971	−	0.674064i
$373$	12.4586	−	21.5790i	0.645083	−	1.11732i	−0.339199	−	0.940715i	$-0.610156\pi$
$373$	12.4586	−	21.5790i	0.645083	−	1.11732i	0.984282	−	0.176602i	$-0.0565106\pi$
$374$	−5.59609	−	9.69270i	−0.289367	−	0.501198i
$375$	−22.5339	−	15.3633i	−1.16364	−	0.793359i
$376$	−6.08500	+	0.917166i	−0.313810	+	0.0472992i
$377$	0.512882	+	2.24708i	0.0264148	+	0.115731i
$378$	−15.7243	−	2.26839i	−0.808772	−	0.116674i
$379$	2.34124	−	10.2577i	0.120262	−	0.526900i	−0.878527	−	0.477693i	$-0.841473\pi$
$379$	2.34124	−	10.2577i	0.120262	−	0.526900i	0.998789	−	0.0492077i	$-0.0156696\pi$
$380$	0.217872	−	2.90730i	0.0111766	−	0.149142i
$381$	−9.32357	+	2.87594i	−0.477661	+	0.147339i
$382$	−0.556242	+	1.41728i	−0.0284598	+	0.0725145i
$383$	−20.6811	−	6.37927i	−1.05675	−	0.325966i	−0.282782	−	0.959184i	$-0.591257\pi$
$383$	−20.6811	−	6.37927i	−1.05675	−	0.325966i	−0.773973	+	0.633219i	$0.781733\pi$
$384$	1.77544	−	2.22633i	0.0906025	−	0.113612i
$385$	11.6150	−	1.82593i	0.591957	−	0.0930579i
$386$	−7.74078	−	9.70663i	−0.393995	−	0.494054i
$387$	0.769042	+	1.95949i	0.0390926	+	0.0996064i
$388$	0.919668	+	12.2721i	0.0466891	+	0.623022i
$389$	20.1418	+	3.03589i	1.02123	+	0.153926i	0.638248	−	0.769831i	$-0.279659\pi$
$389$	20.1418	+	3.03589i	1.02123	+	0.153926i	0.382981	+	0.923756i	$0.374897\pi$
$390$	−27.1483	−	25.1900i	−1.37471	−	1.27554i
$391$	−21.7280			−1.09883
$392$	−6.93446	−	0.955614i	−0.350243	−	0.0482658i
$393$	23.5726			1.18908
$394$	8.57737	+	7.95864i	0.432122	+	0.400950i
$395$	−6.36295	−	0.959060i	−0.320155	−	0.0482555i
$396$	−0.685116	−	9.14224i	−0.0344284	−	0.459415i
$397$	5.97402	+	15.2216i	0.299827	+	0.763948i	0.998808	+	0.0488073i	$0.0155420\pi$
$397$	5.97402	+	15.2216i	0.299827	+	0.763948i	−0.698981	+	0.715140i	$0.746363\pi$
$398$	−12.2934	−	15.4155i	−0.616213	−	0.772707i
$399$	3.29270	+	8.23602i	0.164841	+	0.412317i
$400$	0.706061	−	0.885373i	0.0353031	−	0.0442686i
$401$	29.2054	+	9.00868i	1.45845	+	0.449872i	0.919709	−	0.392600i	$-0.128424\pi$
$401$	29.2054	+	9.00868i	1.45845	+	0.449872i	0.538740	+	0.842472i	$0.318901\pi$
$402$	0.476823	−	1.21493i	0.0237818	−	0.0605950i
$403$	−52.8084	+	16.2892i	−2.63057	+	0.811424i
$404$	−0.0454027	+	0.605857i	−0.00225887	+	0.0301425i
$405$	−0.976936	+	4.28023i	−0.0485443	+	0.212687i
$406$	0.846152	−	0.795138i	0.0419938	−	0.0394620i
$407$	−0.267333	−	1.17126i	−0.0132512	−	0.0580573i
$408$	17.5613	−	2.64694i	0.869413	−	0.131043i
$409$	20.8288	+	14.2008i	1.02992	+	0.702186i	0.955485	−	0.295040i	$-0.0953330\pi$
$409$	20.8288	+	14.2008i	1.02992	+	0.702186i	0.0744327	+	0.997226i	$0.476285\pi$
$410$	−6.90156	−	11.9539i	−0.340844	−	0.590359i
$411$	5.60266	−	9.70409i	0.276359	−	0.478668i
$412$	0.766869	−	0.369305i	0.0377809	−	0.0181943i
$413$	9.78093	+	12.1069i	0.481288	+	0.595743i
$414$	−16.0355	−	7.72230i	−0.788103	−	0.379530i
$415$	−16.5695	+	11.2969i	−0.813363	+	0.554542i
$416$	−3.84991	+	3.57219i	−0.188757	+	0.175141i
$417$	19.7213	−	18.2987i	0.965758	−	0.896092i
$418$	−1.74563	+	1.19015i	−0.0853815	+	0.0582122i
$419$	30.6278	+	14.7495i	1.49626	+	0.720563i	0.989901	−	0.141758i	$-0.0452756\pi$
$419$	30.6278	+	14.7495i	1.49626	+	0.720563i	0.506362	+	0.862321i	$0.330990\pi$
$420$	−4.03639	+	18.2151i	−0.196956	+	0.888807i
$421$	−0.351537	+	0.169291i	−0.0171329	+	0.00825076i	−0.442431	−	0.896803i	$-0.645884\pi$
$421$	−0.351537	+	0.169291i	−0.0171329	+	0.00825076i	0.425298	+	0.905054i	$0.360169\pi$
$422$	−1.05797	+	1.83246i	−0.0515012	+	0.0892027i
$423$	−15.7188	−	27.2258i	−0.764277	−	1.32377i
$424$	10.3381	+	7.04837i	0.502061	+	0.342299i
$425$	6.98382	−	1.05264i	0.338765	−	0.0510606i
$426$	6.87935	+	30.1404i	0.333305	+	1.46031i
$427$	−9.25149	−	6.22217i	−0.447711	−	0.301112i
$428$	−0.643221	+	2.81814i	−0.0310913	+	0.136220i
$429$	−2.00560	+	26.7629i	−0.0968312	+	1.29212i
$430$	0.975034	−	0.300758i	0.0470203	−	0.0145038i
$431$	3.96274	−	10.0969i	0.190878	−	0.486350i	−0.803111	−	0.595830i	$-0.796823\pi$
$431$	3.96274	−	10.0969i	0.190878	−	0.486350i	0.993989	+	0.109480i	$0.0349185\pi$
$432$	5.73798	+	1.76993i	0.276069	+	0.0851560i
$433$	−5.61800	+	7.04475i	−0.269984	+	0.338549i	−0.898279	−	0.439426i	$-0.855182\pi$
$433$	−5.61800	+	7.04475i	−0.269984	+	0.338549i	0.628295	+	0.777975i	$0.283753\pi$
$434$	20.5277	+	18.8066i	0.985362	+	0.902747i
$435$	−1.92954	−	2.41956i	−0.0925142	−	0.116009i
$436$	−2.92924	−	7.46357i	−0.140285	−	0.357440i
$437$	0.306511	+	4.09011i	0.0146624	+	0.195656i
$438$	29.6183	+	4.46424i	1.41522	+	0.213309i
$439$	14.0916	+	13.0751i	0.672557	+	0.624042i	0.940661	−	0.339348i	$-0.110206\pi$
$439$	14.0916	+	13.0751i	0.672557	+	0.624042i	−0.268104	+	0.963390i	$0.586397\pi$
$440$	−4.44399			−0.211859
$441$	−8.39817	−	34.7610i	−0.399913	−	1.65528i
$442$	−32.7547			−1.55798
$443$	5.06735	+	4.70181i	0.240757	+	0.223390i	0.791318	−	0.611405i	$-0.209395\pi$
$443$	5.06735	+	4.70181i	0.240757	+	0.223390i	−0.550561	+	0.834795i	$0.685586\pi$
$444$	1.88505	+	0.284126i	0.0894605	+	0.0134840i
$445$	−0.909607	−	12.1379i	−0.0431195	−	0.575390i
$446$	3.89220	+	9.91717i	0.184301	+	0.469592i
$447$	8.12765	+	10.1918i	0.384425	+	0.482054i
$448$	2.53309	+	0.763835i	0.119677	+	0.0360878i
$449$	13.8689	−	17.3911i	0.654515	−	0.820736i	−0.338219	−	0.941068i	$-0.609824\pi$
$449$	13.8689	−	17.3911i	0.654515	−	0.820736i	0.992734	+	0.120331i	$0.0383957\pi$
$450$	5.52827	+	1.70524i	0.260605	+	0.0803860i
$451$	−3.65440	+	9.31125i	−0.172079	+	0.438450i
$452$	−14.2091	+	4.38292i	−0.668339	+	0.206155i
$453$	3.75901	−	50.1605i	0.176614	−	2.35675i
$454$	1.39574	−	6.11514i	0.0655054	−	0.286998i
$455$	12.3683	−	32.1100i	0.579837	−	1.50534i
$456$	−0.745997	−	3.26843i	−0.0349345	−	0.153058i
$457$	−15.2921	+	2.30491i	−0.715332	+	0.107819i	−0.496617	−	0.867970i	$-0.665425\pi$
$457$	−15.2921	+	2.30491i	−0.715332	+	0.107819i	−0.218715	+	0.975789i	$0.570187\pi$
$458$	17.7902	+	12.1292i	0.831282	+	0.566759i
$459$	18.7251	+	32.4328i	0.874011	+	1.51383i
$460$	−4.31368	+	7.47150i	−0.201126	+	0.348361i
$461$	−4.23196	+	2.03801i	−0.197102	+	0.0949194i	−0.529831	−	0.848103i	$-0.677745\pi$
$461$	−4.23196	+	2.03801i	−0.197102	+	0.0949194i	0.332729	+	0.943022i	$0.392031\pi$
$462$	12.1439	−	5.94314i	0.564984	−	0.276500i
$463$	−23.3663	−	11.2526i	−1.08592	−	0.522953i	−0.196717	−	0.980460i	$-0.563028\pi$
$463$	−23.3663	−	11.2526i	−1.08592	−	0.522953i	−0.889206	+	0.457507i	$0.848742\pi$
$464$	−0.362607	+	0.247221i	−0.0168336	+	0.0114770i
$465$	54.3940	−	50.4702i	2.52246	−	2.34050i
$466$	4.05231	−	3.75999i	0.187720	−	0.174178i
$467$	20.7889	−	14.1736i	0.961996	−	0.655878i	0.0229744	−	0.999736i	$-0.492686\pi$
$467$	20.7889	−	14.1736i	0.961996	−	0.655878i	0.939022	+	0.343858i	$0.111734\pi$
$468$	−24.1734	−	11.6413i	−1.11742	−	0.538119i
$469$	1.21262	−	0.00767340i	0.0559934	−	0.000354325i
$470$	−13.7298	+	6.61193i	−0.633309	+	0.304986i
$471$	−25.5841	+	44.3129i	−1.17885	+	2.04183i
$472$	−2.94136	−	5.09458i	−0.135387	−	0.234497i
$473$	−0.610944	−	0.416535i	−0.0280912	−	0.0191523i
$474$	−7.31675	+	1.10282i	−0.336069	+	0.0506543i
$475$	−0.296670	−	1.29980i	−0.0136122	−	0.0596388i
$476$	8.34070	+	14.2377i	0.382295	+	0.652583i
$477$	−14.2238	+	62.3187i	−0.651265	+	2.85338i
$478$	−2.12873	+	28.4059i	−0.0973659	+	1.29926i
$479$	−24.5120	+	7.56094i	−1.11998	+	0.345468i	−0.798828	−	0.601560i	$-0.794546\pi$
$479$	−24.5120	+	7.56094i	−1.11998	+	0.345468i	−0.321152	+	0.947028i	$0.604070\pi$
$480$	2.57627	−	6.56422i	0.117590	−	0.299615i
$481$	−3.35973	−	1.03634i	−0.153190	−	0.0472530i
$482$	−4.51867	+	5.66623i	−0.205820	+	0.258090i
$483$	1.79581	−	26.1859i	0.0817120	−	1.19150i
$484$	−4.85049	−	6.08232i	−0.220477	−	0.276469i
$485$	11.1340	+	28.3689i	0.505568	+	1.28817i
$486$	−0.968940	−	12.9296i	−0.0439520	−	0.586499i
$487$	24.1912	+	3.64623i	1.09621	+	0.165226i	0.672154	−	0.740411i	$-0.265369\pi$
$487$	24.1912	+	3.64623i	1.09621	+	0.165226i	0.424052	+	0.905638i	$0.360607\pi$
$488$	3.08909	+	2.86626i	0.139837	+	0.129749i
$489$	−69.8655			−3.15943
$490$	−17.1069	+	2.80031i	−0.772813	+	0.126505i
$491$	−34.4755			−1.55586			−0.777929	−	0.628353i	$-0.783730\pi$
$491$	−34.4755			−1.55586			−0.777929	+	0.628353i	$0.783730\pi$
$492$	−11.6351	−	10.7958i	−0.524553	−	0.486714i
$493$	−2.70652	−	0.407942i	−0.121895	−	0.0183728i
$494$	0.462063	+	6.16580i	0.0207892	+	0.277413i
$495$	−8.29438	−	21.1337i	−0.372804	−	0.949890i
$496$	−6.56074	−	8.22690i	−0.294586	−	0.369399i
$497$	−23.6302	+	16.3308i	−1.05996	+	0.732537i
$498$	−14.3778	+	18.0292i	−0.644284	+	0.807907i
$499$	24.0038	+	7.40420i	1.07456	+	0.331458i	0.781031	−	0.624493i	$-0.214694\pi$
$499$	24.0038	+	7.40420i	1.07456	+	0.331458i	0.293528	+	0.955950i	$0.405170\pi$
$500$	−3.49907	+	8.91548i	−0.156483	+	0.398713i
$501$	7.66841	−	2.36539i	0.342599	−	0.105678i
$502$	−0.515476	+	6.87855i	−0.0230068	+	0.307005i
$503$	0.648335	−	2.84054i	0.0289078	−	0.126653i	−0.958415	−	0.285378i	$-0.907881\pi$
$503$	0.648335	−	2.84054i	0.0289078	−	0.126653i	0.987323	+	0.158724i	$0.0507381\pi$
$504$	1.09535	+	13.4720i	0.0487909	+	0.600088i
$505$	0.334791	+	1.46682i	0.0148980	+	0.0652724i
$506$	6.18215	−	0.931809i	0.274830	−	0.0414240i
$507$	34.3091	+	23.3916i	1.52372	+	1.03886i
$508$	1.71322	+	2.96738i	0.0760117	+	0.131656i
$509$	4.44435	−	7.69785i	0.196993	−	0.341201i	−0.750559	−	0.660803i	$-0.770216\pi$
$509$	4.44435	−	7.69785i	0.196993	−	0.341201i	0.947552	+	0.319602i	$0.103549\pi$
$510$	39.6242	−	19.0820i	1.75459	−	0.844965i
$511$	6.36428	+	27.0924i	0.281539	+	1.19850i
$512$	−0.900969	−	0.433884i	−0.0398176	−	0.0191751i
$513$	5.84105	−	3.98236i	0.257889	−	0.175826i
$514$	−5.19518	+	4.82042i	−0.229149	+	0.212620i
$515$	1.54512	−	1.43366i	0.0680862	−	0.0631748i
$516$	0.969441	−	0.660953i	0.0426772	−	0.0290969i
$517$	9.94958	+	4.79146i	0.437582	+	0.210728i
$518$	0.405054	+	1.72429i	0.0177970	+	0.0757609i
$519$	−14.3575	+	6.91420i	−0.630224	+	0.303500i
$520$	−6.50283	+	11.2632i	−0.285168	+	0.493925i
$521$	7.59074	+	13.1476i	0.332557	+	0.576005i	0.983012	−	0.183539i	$-0.0587554\pi$
$521$	7.59074	+	13.1476i	0.332557	+	0.576005i	−0.650456	+	0.759544i	$0.725422\pi$
$522$	−1.85246	−	1.26299i	−0.0810800	−	0.0552794i
$523$	−4.80512	+	0.724255i	−0.210113	+	0.0316695i	−0.253255	−	0.967399i	$-0.581501\pi$
$523$	−4.80512	+	0.724255i	−0.210113	+	0.0316695i	0.0431421	+	0.999069i	$0.486263\pi$
$524$	−1.84205	−	8.07055i	−0.0804703	−	0.352564i
$525$	0.691403	+	8.50369i	0.0301753	+	0.371132i
$526$	−0.775860	+	3.39926i	−0.0338291	+	0.148215i
$527$	4.90430	−	65.4433i	0.213634	−	2.85075i
$528$	−4.88311	+	1.50624i	−0.212510	+	0.0655507i
$529$	−3.96859	+	10.1118i	−0.172547	+	0.439644i
$530$	29.6083	+	9.13296i	1.28610	+	0.396710i
$531$	18.7378	−	23.4965i	0.813153	−	1.01966i
$532$	2.56247	−	1.77092i	0.111097	−	0.0767789i
$533$	18.2518	+	22.8870i	0.790574	+	0.991348i
$534$	−5.11348	−	13.0289i	−0.221282	−	0.563817i
$535$	0.534936	+	7.13822i	0.0231273	+	0.308612i
$536$	−0.453215	−	0.0683112i	−0.0195759	−	0.00295060i
$537$	15.2682	+	14.1668i	0.658872	+	0.611344i
$538$	7.12811			0.307315
$539$	9.31590	+	8.42702i	0.401264	+	0.362978i
$540$	14.8700			0.639905
$541$	−13.9663	−	12.9589i	−0.600460	−	0.557145i	0.320280	−	0.947323i	$-0.396223\pi$
$541$	−13.9663	−	12.9589i	−0.600460	−	0.557145i	−0.920740	+	0.390178i	$0.872414\pi$
$542$	−15.6037	−	2.35188i	−0.670237	−	0.101022i
$543$	4.07799	+	54.4170i	0.175003	+	2.33526i
$544$	−2.27854	−	5.80562i	−0.0976915	−	0.248914i
$545$	−12.3795	−	15.5233i	−0.530278	−	0.664947i
$546$	2.70716	−	39.4750i	0.115856	−	1.68937i
$547$	5.17270	−	6.48636i	0.221169	−	0.277337i	−0.658852	−	0.752273i	$-0.728957\pi$
$547$	5.17270	−	6.48636i	0.221169	−	0.277337i	0.880020	+	0.474936i	$0.157529\pi$
$548$	−3.76021	−	1.15987i	−0.160628	−	0.0495472i
$549$	−7.86515	+	20.0401i	−0.335676	+	0.855290i
$550$	−1.94193	+	0.599006i	−0.0828041	+	0.0255417i
$551$	−0.0386115	+	0.515234i	−0.00164490	+	0.0219497i
$552$	−2.20754	+	9.67185i	−0.0939590	+	0.411661i
$553$	−3.47508	−	5.93200i	−0.147775	−	0.252254i
$554$	0.578283	+	2.53362i	0.0245689	+	0.107643i
$555$	4.66809	−	0.703602i	0.198150	−	0.0298662i
$556$	−7.80604	−	5.32207i	−0.331050	−	0.225706i
$557$	−8.34150	−	14.4479i	−0.353441	−	0.612177i	0.633409	−	0.773817i	$-0.281655\pi$
$557$	−8.34150	−	14.4479i	−0.353441	−	0.612177i	−0.986850	+	0.161640i	$0.948322\pi$
$558$	26.8785	−	46.5550i	1.13786	−	1.97083i
$559$	−1.94969	+	0.938920i	−0.0824630	+	0.0397121i
$560$	6.55174	−	0.0414593i	0.276862	−	0.00175197i
$561$	−28.7144	−	13.8281i	−1.21232	−	0.583825i
$562$	19.9080	−	13.5730i	0.839767	−	0.572543i
$563$	−9.15841	+	8.49776i	−0.385981	+	0.358138i	−0.849168	−	0.528122i	$-0.822896\pi$
$563$	−9.15841	+	8.49776i	−0.385981	+	0.358138i	0.463187	+	0.886260i	$0.346706\pi$
$564$	−12.8454	+	11.9188i	−0.540891	+	0.501874i
$565$	−30.4246	+	20.7431i	−1.27997	+	0.872670i
$566$	7.04459	+	3.39250i	0.296106	+	0.142597i
$567$	−4.21311	+	2.06187i	−0.176934	+	0.0865905i
$568$	9.78160	−	4.71057i	0.410427	−	0.197651i
$569$	13.3782	−	23.1718i	0.560845	−	0.971412i	−0.436578	−	0.899666i	$-0.643810\pi$
$569$	13.3782	−	23.1718i	0.560845	−	0.971412i	0.997423	−	0.0717456i	$-0.0228570\pi$
$570$	−4.15100	−	7.18974i	−0.173866	−	0.301145i
$571$	29.1100	+	19.8469i	1.21822	+	0.830566i	0.989726	−	0.142979i	$-0.0456683\pi$
$571$	29.1100	+	19.8469i	1.21822	+	0.830566i	0.228492	+	0.973546i	$0.426621\pi$
$572$	9.31954	−	1.40469i	0.389669	−	0.0587332i
$573$	0.964746	+	4.22683i	0.0403028	+	0.176578i
$574$	5.30079	−	13.7616i	0.221250	−	0.574398i
$575$	−0.877900	+	3.84633i	−0.0366109	+	0.160403i
$576$	0.381775	−	5.09444i	0.0159073	−	0.212268i
$577$	34.6483	−	10.6876i	1.44243	−	0.444930i	0.527849	−	0.849338i	$-0.322999\pi$
$577$	34.6483	−	10.6876i	1.44243	−	0.444930i	0.914579	+	0.404408i	$0.132522\pi$
$578$	7.99986	−	20.3833i	0.332750	−	0.847834i
$579$	−33.7828	−	10.4206i	−1.40396	−	0.433065i
$580$	−0.677605	+	0.849690i	−0.0281360	+	0.0352815i
$581$	−20.5134	−	6.18566i	−0.851039	−	0.256625i
$582$	21.8495	+	27.3984i	0.905690	+	1.13570i
$583$	−8.20330	−	20.9017i	−0.339746	−	0.865659i
$584$	−0.786063	−	10.4893i	−0.0325275	−	0.434049i
$585$	−65.7002	−	9.90271i	−2.71637	−	0.409427i
$586$	−19.0682	−	17.6927i	−0.787701	−	0.730880i
$587$	−15.5856			−0.643287			−0.321644	−	0.946861i	$-0.604235\pi$
$587$	−15.5856			−0.643287			−0.321644	+	0.946861i	$0.604235\pi$
$588$	−17.8482	+	8.87522i	−0.736047	+	0.366008i
$589$	−12.3883			−0.510453
$590$	−10.6790	−	9.90863i	−0.439646	−	0.407932i
$591$	32.9471	+	4.96598i	1.35526	+	0.204273i
$592$	−0.0500288	−	0.667588i	−0.00205617	−	0.0274377i
$593$	6.09642	+	15.5334i	0.250350	+	0.637881i	0.999705	−	0.0242874i	$-0.00773168\pi$
$593$	6.09642	+	15.5334i	0.250350	+	0.637881i	−0.749355	+	0.662168i	$0.769636\pi$
$594$	−6.71864	−	8.42491i	−0.275669	−	0.345678i
$595$	30.1295	+	27.6034i	1.23519	+	1.13163i
$596$	2.85423	−	3.57909i	0.116914	−	0.146605i
$597$	−53.6517	−	16.5493i	−2.19582	−	0.677320i
$598$	6.68460	−	17.0321i	0.273353	−	0.696493i
$599$	30.8653	−	9.52068i	1.26112	−	0.389004i	0.409089	−	0.912494i	$-0.365847\pi$
$599$	30.8653	−	9.52068i	1.26112	−	0.389004i	0.852032	+	0.523490i	$0.175370\pi$
$600$	0.240982	−	3.21568i	0.00983805	−	0.131280i
$601$	4.90794	−	21.5031i	0.200199	−	0.877130i	−0.770616	−	0.637300i	$-0.780051\pi$
$601$	4.90794	−	21.5031i	0.200199	−	0.877130i	0.970815	−	0.239830i	$-0.0770916\pi$
$602$	0.904597	+	0.608395i	0.0368686	+	0.0247963i
$603$	−0.521034	−	2.28280i	−0.0212181	−	0.0929627i
$604$	−17.4672	+	2.63276i	−0.710732	+	0.107126i
$605$	−15.9176	−	10.8524i	−0.647143	−	0.441215i
$606$	0.865033	+	1.49828i	0.0351396	+	0.0608635i
$607$	−8.83998	+	15.3113i	−0.358804	+	0.621466i	−0.987761	−	0.155974i	$-0.950149\pi$
$607$	−8.83998	+	15.3113i	−0.358804	+	0.621466i	0.628958	+	0.777440i	$0.283482\pi$
$608$	−1.06072	+	0.510815i	−0.0430178	+	0.0207163i
$609$	0.715332	−	3.22810i	0.0289867	−	0.130809i
$610$	9.40205	+	4.52779i	0.380678	+	0.183325i
$611$	26.7030	−	18.2058i	1.08029	−	0.736527i
$612$	23.3563	−	21.6715i	0.944124	−	0.876019i
$613$	13.0262	−	12.0866i	0.526124	−	0.488171i	−0.371806	−	0.928310i	$-0.621261\pi$
$613$	13.0262	−	12.0866i	0.526124	−	0.488171i	0.897930	+	0.440139i	$0.145071\pi$
$614$	−7.94694	+	5.41813i	−0.320713	+	0.218658i
$615$	−35.4130	−	17.0540i	−1.42799	−	0.687685i
$616$	−2.98372	−	3.69329i	−0.120218	−	0.148807i
$617$	6.59825	−	3.17755i	0.265635	−	0.127923i	−0.296326	−	0.955087i	$-0.595761\pi$
$617$	6.59825	−	3.17755i	0.265635	−	0.127923i	0.561961	+	0.827164i	$0.310047\pi$
$618$	1.21187	−	2.09903i	0.0487488	−	0.0844353i
$619$	−21.5337	−	37.2975i	−0.865513	−	1.49911i	−0.866537	−	0.499112i	$-0.833660\pi$
$619$	−21.5337	−	37.2975i	−0.865513	−	1.49911i	0.00102470	−	0.999999i	$-0.499674\pi$
$620$	−21.5301	−	14.6789i	−0.864668	−	0.589521i
$621$	−20.6861	+	3.11793i	−0.830105	+	0.125118i
$622$	1.47096	+	6.44469i	0.0589800	+	0.258408i
$623$	9.47675	−	8.90539i	0.379678	−	0.356787i
$624$	−3.32784	+	14.5802i	−0.133220	+	0.583676i
$625$	−2.19555	+	29.2976i	−0.0878221	+	1.17190i
$626$	9.82012	−	3.02911i	0.392491	−	0.121067i
$627$	−2.19797	+	5.60033i	−0.0877784	+	0.223656i
$628$	17.1707	+	5.29645i	0.685184	+	0.211351i
$629$	2.60323	−	3.26434i	0.103797	−	0.130158i
$630$	12.4255	+	31.0799i	0.495044	+	1.23825i
$631$	1.68138	+	2.10839i	0.0669348	+	0.0839336i	0.814172	−	0.580624i	$-0.197191\pi$
$631$	1.68138	+	2.10839i	0.0669348	+	0.0839336i	−0.747237	+	0.664558i	$0.768620\pi$
$632$	0.949332	+	2.41886i	0.0377624	+	0.0962170i
$633$	0.450272	+	6.00847i	0.0178967	+	0.238815i
$634$	11.6859	+	1.76136i	0.464105	+	0.0699526i
$635$	6.22005	+	5.77136i	0.246835	+	0.229029i
$636$	35.6295			1.41280
$637$	34.9900	−	11.2799i	1.38635	−	0.446925i
$638$	0.787567			0.0311801
$639$	40.6581	+	37.7252i	1.60841	+	1.49239i
$640$	−2.44872	−	0.369085i	−0.0967940	−	0.0145893i
$641$	3.67089	+	48.9846i	0.144991	+	1.93478i	0.314520	+	0.949251i	$0.398157\pi$
$641$	3.67089	+	48.9846i	0.144991	+	1.93478i	−0.169528	+	0.985525i	$0.554224\pi$
$642$	3.00721	+	7.66226i	0.118685	+	0.302405i
$643$	8.24142	+	10.3344i	0.325010	+	0.407549i	0.917314	−	0.398165i	$-0.130353\pi$
$643$	8.24142	+	10.3344i	0.325010	+	0.407549i	−0.592304	+	0.805715i	$0.701782\pi$
$644$	−9.10561	+	1.43143i	−0.358811	+	0.0564064i
$645$	1.81160	−	2.27167i	0.0713315	−	0.0894469i
$646$	−7.01636	−	2.16426i	−0.276055	−	0.0851516i
$647$	0.879121	−	2.23996i	0.0345618	−	0.0880621i	−0.912551	−	0.408963i	$-0.865890\pi$
$647$	0.879121	−	2.23996i	0.0345618	−	0.0880621i	0.947113	+	0.320901i	$0.103986\pi$
$648$	1.69411	−	0.522565i	0.0665510	−	0.0205283i
$649$	−0.788915	+	10.5273i	−0.0309676	+	0.413234i
$650$	−1.32343	+	5.79831i	−0.0519090	+	0.227428i
$651$	78.4650	+	11.3194i	3.07529	+	0.443641i
$652$	5.45955	+	23.9199i	0.213813	+	0.936775i
$653$	−7.43812	+	1.12112i	−0.291076	+	0.0438726i	−0.292957	−	0.956126i	$-0.594639\pi$
$653$	−7.43812	+	1.12112i	−0.291076	+	0.0438726i	0.00188111	+	0.999998i	$0.499401\pi$
$654$	−18.8642	−	12.8614i	−0.737647	−	0.502919i
$655$	−10.2498	−	17.7532i	−0.400494	−	0.693676i
$656$	−2.78696	+	4.82716i	−0.108813	+	0.188469i
$657$	48.4154	−	23.3156i	1.88887	−	0.909630i
$658$	−14.7133	−	6.97120i	−0.573584	−	0.271766i
$659$	−25.6181	−	12.3370i	−0.997938	−	0.480582i	−0.137700	−	0.990474i	$-0.543971\pi$
$659$	−25.6181	−	12.3370i	−0.997938	−	0.480582i	−0.860238	+	0.509892i	$0.829685\pi$
$660$	−10.4557	+	7.12860i	−0.406989	+	0.277480i
$661$	8.95656	−	8.31047i	0.348370	−	0.323240i	−0.486507	−	0.873677i	$-0.661729\pi$
$661$	8.95656	−	8.31047i	0.348370	−	0.323240i	0.834877	+	0.550437i	$0.185539\pi$
$662$	−21.3911	+	19.8480i	−0.831387	+	0.771415i
$663$	−77.0647	+	52.5418i	−2.99294	+	2.04055i
$664$	7.29619	+	3.51366i	0.283147	+	0.136357i
$665$	4.77108	−	6.06103i	0.185014	−	0.235036i
$666$	3.08139	−	1.48392i	0.119402	−	0.0575007i
$667$	0.764473	−	1.32411i	0.0296005	−	0.0512696i
$668$	−1.40908	−	2.44060i	−0.0545189	−	0.0944295i
$669$	25.0656	+	17.0895i	0.969094	+	0.660717i
$670$	−1.12233	+	0.169164i	−0.0433594	+	0.00653538i
$671$	−1.68277	−	7.37268i	−0.0649625	−	0.284619i
$672$	7.18508	−	2.26620i	0.277171	−	0.0874204i
$673$	10.4091	−	45.6053i	0.401242	−	1.75795i	−0.221141	−	0.975242i	$-0.570978\pi$
$673$	10.4091	−	45.6053i	0.401242	−	1.75795i	0.622383	−	0.782713i	$-0.286165\pi$
$674$	−0.706776	+	9.43128i	−0.0272240	+	0.363279i
$675$	6.49789	−	2.00433i	0.250104	−	0.0771468i
$676$	5.32754	−	13.5743i	0.204905	−	0.522090i
$677$	−42.1399	−	12.9984i	−1.61957	−	0.499570i	−0.653297	−	0.757102i	$-0.726615\pi$
$677$	−42.1399	−	12.9984i	−1.61957	−	0.499570i	−0.966270	+	0.257531i	$0.917091\pi$
$678$	−26.4003	+	33.1049i	−1.01390	+	1.27138i
$679$	−16.1012	+	28.3002i	−0.617909	+	1.08606i
$680$	−9.62950	−	12.0750i	−0.369274	−	0.463055i
$681$	−6.52542	−	16.6265i	−0.250055	−	0.637129i
$682$	1.41116	+	18.8306i	0.0540360	+	0.721060i
$683$	−14.1110	−	2.12690i	−0.539944	−	0.0813835i	−0.126592	−	0.991955i	$-0.540404\pi$
$683$	−14.1110	−	2.12690i	−0.539944	−	0.0813835i	−0.413352	+	0.910571i	$0.635642\pi$
$684$	−4.40897	−	4.09093i	−0.168581	−	0.156420i
$685$	−9.74461			−0.372323
$686$	−13.8130	−	12.3370i	−0.527382	−	0.471029i
$687$	61.3129			2.33923
$688$	−0.302047	−	0.280258i	−0.0115154	−	0.0106848i
$689$	−64.9788	−	9.79397i	−2.47549	−	0.373121i
$690$	1.83590	+	24.4984i	0.0698915	+	0.932638i
$691$	−15.1275	−	38.5442i	−0.575477	−	1.46629i	−0.861344	−	0.508021i	$-0.830377\pi$
$691$	−15.1275	−	38.5442i	−0.575477	−	1.46629i	0.285868	−	0.958269i	$-0.407718\pi$
$692$	3.48917	+	4.37528i	0.132638	+	0.166323i
$693$	11.9948	−	21.0826i	0.455645	−	0.800861i
$694$	−15.6748	+	19.6555i	−0.595006	+	0.746114i
$695$	−22.3566	−	6.89610i	−0.848034	−	0.261584i
$696$	−0.456568	+	1.16332i	−0.0173062	+	0.0440954i
$697$	−33.2187	+	10.2466i	−1.25825	+	0.388118i
$698$	1.32002	−	17.6145i	0.0499636	−	0.666718i
$699$	3.50280	−	15.3468i	0.132488	−	0.580468i
$700$	2.85738	−	0.901227i	0.107999	−	0.0340632i
$701$	−5.98588	−	26.2259i	−0.226084	−	0.990537i	−0.952800	−	0.303599i	$-0.901812\pi$
$701$	−5.98588	−	26.2259i	−0.226084	−	0.990537i	0.726716	−	0.686938i	$-0.241046\pi$
$702$	−31.1841	+	4.70025i	−1.17697	+	0.177399i
$703$	−0.651209	−	0.443987i	−0.0245608	−	0.0167453i
$704$	0.897277	+	1.55413i	0.0338174	+	0.0585735i
$705$	−21.6971	+	37.5804i	−0.817159	+	1.41536i
$706$	4.47940	−	2.15717i	0.168585	−	0.0811861i
$707$	−0.994252	+	1.26307i	−0.0373927	+	0.0475025i
$708$	−15.0926	−	7.26821i	−0.567214	−	0.273156i
$709$	31.9644	−	21.7930i	1.20045	−	0.818452i	0.213102	−	0.977030i	$-0.431643\pi$
$709$	31.9644	−	21.7930i	1.20045	−	0.818452i	0.987346	+	0.158578i	$0.0506908\pi$
$710$	19.7084	−	18.2867i	0.739643	−	0.686288i
$711$	−9.73121	+	9.02924i	−0.364949	+	0.338623i
$712$	−4.06113	+	2.76883i	−0.152197	+	0.103766i
$713$	33.0289	+	15.9059i	1.23694	+	0.595680i
$714$	42.4625	+	20.1189i	1.58912	+	0.752929i
$715$	21.0280	−	10.1266i	0.786404	−	0.378712i
$716$	3.65719	−	6.33444i	0.136676	−	0.236729i
$717$	40.5575	+	70.2477i	1.51465	+	2.62345i
$718$	1.15002	+	0.784070i	0.0429183	+	0.0292612i
$719$	45.1551	−	6.80603i	1.68400	−	0.253822i	0.763851	−	0.645392i	$-0.223306\pi$
$719$	45.1551	−	6.80603i	1.68400	−	0.253822i	0.920148	+	0.391570i	$0.128068\pi$
$720$	−2.81514	−	12.3339i	−0.104914	−	0.459658i
$721$	2.22889	+	0.321540i	0.0830081	+	0.0119748i
$722$	3.91947	−	17.1723i	0.145868	−	0.639088i
$723$	−1.54224	+	20.5798i	−0.0573566	+	0.765371i
$724$	18.3121	−	5.64854i	0.680564	−	0.209926i
$725$	−0.181569	+	0.462631i	−0.00674331	+	0.0171817i
$726$	−21.1688	−	6.52971i	−0.785647	−	0.242340i
$727$	8.48127	−	10.6352i	0.314553	−	0.394437i	−0.599272	−	0.800546i	$-0.704543\pi$
$727$	8.48127	−	10.6352i	0.314553	−	0.394437i	0.913825	+	0.406109i	$0.133115\pi$
$728$	−13.7266	+	2.15788i	−0.508742	+	0.0799762i
$729$	−26.3362	−	33.0246i	−0.975415	−	1.22313i
$730$	−9.51648	−	24.2476i	−0.352221	−	0.897444i
$731$	−0.192040	−	2.56260i	−0.00710287	−	0.0947813i
$732$	11.8657	+	1.78847i	0.438570	+	0.0661038i
$733$	19.4621	+	18.0582i	0.718848	+	0.666994i	0.952227	−	0.305392i	$-0.0987876\pi$
$733$	19.4621	+	18.0582i	0.718848	+	0.666994i	−0.233378	+	0.972386i	$0.574978\pi$
$734$	35.5995			1.31400
$735$	−35.7569	+	34.0298i	−1.31891	+	1.25521i
$736$	3.48386			0.128417
$737$	0.602940	+	0.559446i	0.0222096	+	0.0206075i
$738$	−28.1576	−	4.24407i	−1.03649	−	0.156226i
$739$	−2.67410	−	35.6834i	−0.0983685	−	1.31264i	−0.799958	−	0.600056i	$-0.795145\pi$
$739$	−2.67410	−	35.6834i	−0.0983685	−	1.31264i	0.701590	−	0.712581i	$-0.252474\pi$
$740$	−0.605675	−	1.54323i	−0.0222651	−	0.0567304i
$741$	10.9777	+	13.7656i	0.403276	+	0.505692i
$742$	12.2891	+	30.7387i	0.451146	+	1.12845i
$743$	−20.1479	+	25.2647i	−0.739156	+	0.926872i	−0.999250	−	0.0387111i	$-0.987675\pi$
$743$	−20.1479	+	25.2647i	−0.739156	+	0.926872i	0.260095	+	0.965583i	$0.416246\pi$
$744$	−28.6328	−	8.83204i	−1.04973	−	0.323798i
$745$	4.14166	−	10.5528i	0.151739	−	0.386624i
$746$	−23.8102	+	7.34449i	−0.871755	+	0.268901i
$747$	−3.09168	+	41.2556i	−0.113119	+	1.50946i
$748$	−2.49049	+	10.9116i	−0.0910614	+	0.398966i
$749$	−5.57323	+	5.23722i	−0.203641	+	0.191364i
$750$	6.06878	+	26.5891i	0.221600	+	0.970895i
$751$	−9.85801	+	1.48586i	−0.359724	+	0.0542196i	−0.326418	−	0.945226i	$-0.605842\pi$
$751$	−9.85801	+	1.48586i	−0.359724	+	0.0542196i	−0.0333059	+	0.999445i	$0.510604\pi$
$752$	5.08445	+	3.46652i	0.185411	+	0.126411i
$753$	9.82108	+	17.0106i	0.357900	+	0.619901i
$754$	1.15244	−	1.99608i	0.0419692	−	0.0726928i
$755$	−39.4120	+	18.9798i	−1.43435	+	0.690746i
$756$	9.98385	+	12.3581i	0.363109	+	0.449460i
$757$	26.4927	+	12.7582i	0.962894	+	0.463705i	0.848189	−	0.529694i	$-0.177693\pi$
$757$	26.4927	+	12.7582i	0.962894	+	0.463705i	0.114705	+	0.993400i	$0.463408\pi$
$758$	−8.69323	+	5.92694i	−0.315752	+	0.215276i
$759$	13.0505	−	12.1091i	0.473705	−	0.439534i
$760$	−2.13718	+	1.98301i	−0.0775237	+	0.0719315i
$761$	19.0931	−	13.0174i	0.692123	−	0.471881i	−0.165467	−	0.986215i	$-0.552913\pi$
$761$	19.0931	−	13.0174i	0.692123	−	0.471881i	0.857590	+	0.514334i	$0.171961\pi$
$762$	8.79080	+	4.23343i	0.318457	+	0.153361i
$763$	4.58940	−	20.7107i	0.166148	−	0.749779i
$764$	1.37175	−	0.660601i	0.0496282	−	0.0238997i
$765$	39.4509	−	68.3309i	1.42635	−	2.47051i
$766$	10.8213	+	18.7431i	0.390990	+	0.677214i
$767$	25.5270	+	17.4040i	0.921725	+	0.628422i
$768$	−2.81578	+	0.424410i	−0.101606	+	0.0153146i
$769$	−8.63392	−	37.8277i	−0.311347	−	1.36410i	−0.852302	−	0.523049i	$-0.824794\pi$
$769$	−8.63392	−	37.8277i	−0.311347	−	1.36410i	0.540955	−	0.841051i	$-0.318063\pi$
$770$	−9.75638	−	6.56174i	−0.351595	−	0.236469i
$771$	−4.49068	+	19.6750i	−0.161728	+	0.708577i
$772$	−0.927792	+	12.3805i	−0.0333920	+	0.445585i
$773$	0.152750	−	0.0471170i	0.00549403	−	0.00169468i	−0.292007	−	0.956416i	$-0.594323\pi$
$773$	0.152750	−	0.0471170i	0.00549403	−	0.00169468i	0.297501	+	0.954722i	$0.403847\pi$
$774$	0.769042	−	1.95949i	0.0276427	−	0.0704323i
$775$	−11.3868	−	3.51235i	−0.409024	−	0.126167i
$776$	7.67299	−	9.62163i	0.275444	−	0.345396i
$777$	3.71893	+	3.40713i	0.133416	+	0.122230i
$778$	−12.7001	−	15.9254i	−0.455319	−	0.570952i
$779$	2.39745	+	6.10860i	0.0858975	+	0.218863i
$780$	2.76760	+	36.9311i	0.0990961	+	1.32235i
$781$	−19.2654	−	2.90380i	−0.689371	−	0.103906i
$782$	15.9277	+	14.7788i	0.569574	+	0.528487i
$783$	−2.63528			−0.0941772
$784$	4.43334	+	5.41715i	0.158334	+	0.193470i
$785$	44.4979			1.58820
$786$	−17.2799	−	16.0334i	−0.616354	−	0.571893i
$787$	12.8045	+	1.92997i	0.456431	+	0.0687959i	0.373234	−	0.927737i	$-0.378249\pi$
$787$	12.8045	+	1.92997i	0.456431	+	0.0687959i	0.0831971	+	0.996533i	$0.473487\pi$
$788$	−0.874410	−	11.6682i	−0.0311496	−	0.415662i
$789$	3.62733	+	9.24228i	0.129136	+	0.329034i
$790$	4.01204	+	5.03094i	0.142742	+	0.178993i
$791$	−37.6664	−	11.3580i	−1.33926	−	0.403844i
$792$	−5.71608	+	7.16774i	−0.203112	+	0.254694i
$793$	−21.1483	−	6.52339i	−0.750999	−	0.231652i
$794$	5.97402	−	15.2216i	0.212010	−	0.540193i
$795$	84.3121	−	26.0068i	2.99024	−	0.922368i
$796$	−1.47346	+	19.6620i	−0.0522254	+	0.696900i
$797$	−0.334644	+	1.46617i	−0.0118537	+	0.0519345i	−0.980509	−	0.196475i	$-0.937051\pi$
$797$	−0.334644	+	1.46617i	−0.0118537	+	0.0519345i	0.968655	+	0.248409i	$0.0799078\pi$
$798$	3.18820	−	8.27703i	0.112861	−	0.293004i
$799$	8.54018	+	37.4170i	0.302130	+	1.32372i
$800$	−1.11979	+	0.168781i	−0.0395904	+	0.00596729i
$801$	−20.7472	−	14.1452i	−0.733066	−	0.499796i
$802$	−15.2816	−	26.4686i	−0.539613	−	0.934637i
$803$	−9.43818	+	16.3474i	−0.333066	+	0.576887i
$804$	−1.17590	+	0.566281i	−0.0414706	+	0.0199712i
$805$	−20.5023	+	10.0337i	−0.722610	+	0.353641i
$806$	49.7908	+	23.9780i	1.75381	+	0.844588i
$807$	16.7709	−	11.4342i	0.590363	−	0.402503i
$808$	0.445370	−	0.413243i	0.0156681	−	0.0145378i
$809$	−24.2191	+	22.4720i	−0.851497	+	0.790074i	−0.979446	−	0.201707i	$-0.935351\pi$
$809$	−24.2191	+	22.4720i	−0.851497	+	0.790074i	0.127949	+	0.991781i	$0.459161\pi$
$810$	3.62744	−	2.47315i	0.127455	−	0.0868976i
$811$	−36.8198	−	17.7315i	−1.29292	−	0.622636i	−0.344240	−	0.938882i	$-0.611863\pi$
$811$	−36.8198	−	17.7315i	−1.29292	−	0.622636i	−0.948677	+	0.316246i	$0.897578\pi$
$812$	−1.16110	+	0.00734744i	−0.0407468	+	0.000257845i
$813$	−40.4848	+	19.4964i	−1.41986	+	0.683770i
$814$	−0.600691	+	1.04043i	−0.0210542	+	0.0364670i
$815$	30.3790	+	52.6179i	1.06413	+	1.84312i
$816$	−14.6737	−	10.0044i	−0.513682	−	0.350223i
$817$	−0.479680	+	0.0723001i	−0.0167819	+	0.00252946i
$818$	−5.60957	−	24.5771i	−0.196134	−	0.859319i
$819$	−35.8817	−	61.2505i	−1.25381	−	2.14026i
$820$	−3.07148	+	13.4570i	−0.107261	+	0.469940i
$821$	−3.86412	+	51.5631i	−0.134859	+	1.79957i	0.362461	+	0.931999i	$0.381937\pi$
$821$	−3.86412	+	51.5631i	−0.134859	+	1.79957i	−0.497320	+	0.867567i	$0.665682\pi$
$822$	−10.7075	+	3.30283i	−0.373467	+	0.115199i
$823$	5.40577	−	13.7737i	0.188433	−	0.480120i	−0.805170	−	0.593044i	$-0.797926\pi$
$823$	5.40577	−	13.7737i	0.188433	−	0.480120i	0.993604	+	0.112923i	$0.0360214\pi$
$824$	−0.813346	−	0.250884i	−0.0283342	−	0.00873996i
$825$	−3.60807	+	4.52438i	−0.125617	+	0.157519i
$826$	1.06488	−	15.5277i	0.0370519	−	0.540279i
$827$	13.1190	+	16.4507i	0.456193	+	0.572049i	0.955730	−	0.294244i	$-0.0950679\pi$
$827$	13.1190	+	16.4507i	0.456193	+	0.572049i	−0.499537	+	0.866293i	$0.666496\pi$
$828$	6.50237	+	16.5678i	0.225973	+	0.575770i
$829$	2.76652	+	36.9167i	0.0960853	+	1.28217i	0.811866	+	0.583844i	$0.198452\pi$
$829$	2.76652	+	36.9167i	0.0960853	+	1.28217i	−0.715781	+	0.698325i	$0.753929\pi$
$830$	19.8301	+	2.98891i	0.688313	+	0.103746i
$831$	5.42476	+	5.03344i	0.188183	+	0.174608i
$832$	5.25189			0.182077
$833$	−2.71129	+	43.5729i	−0.0939406	+	1.50971i
$834$	−26.9031			−0.931577
$835$	−5.11584	−	4.74680i	−0.177041	−	0.164270i
$836$	2.08914	+	0.314888i	0.0722546	+	0.0108906i
$837$	−4.72187	−	63.0090i	−0.163212	−	2.17791i
$838$	−12.4195	−	31.6443i	−0.429024	−	1.09314i
$839$	11.4571	+	14.3667i	0.395541	+	0.495993i	0.939227	−	0.343295i	$-0.111543\pi$
$839$	11.4571	+	14.3667i	0.395541	+	0.495993i	−0.543686	+	0.839289i	$0.682972\pi$
$840$	15.3483	−	10.6072i	0.529567	−	0.365983i
$841$	−17.9611	+	22.5225i	−0.619349	+	0.776639i
$842$	0.372843	+	0.115007i	0.0128490	+	0.00396339i
$843$	25.0666	−	63.8687i	0.863341	−	2.19976i
$844$	2.02194	−	0.623685i	0.0695979	−	0.0214681i
$845$	2.69861	−	36.0104i	0.0928349	−	1.23880i
$846$	−6.99555	+	30.6495i	−0.240512	+	1.05375i
$847$	−1.66801	−	20.5151i	−0.0573134	−	0.704908i
$848$	−2.78423	−	12.1985i	−0.0956107	−	0.418898i
$849$	22.0163	−	3.31842i	0.755597	−	0.113888i
$850$	−5.83548	−	3.97856i	−0.200155	−	0.136464i
$851$	1.16615	+	2.01984i	0.0399752	+	0.0692391i
$852$	15.4578	−	26.7736i	0.529574	−	0.917249i
$853$	7.87269	−	3.79129i	0.269556	−	0.129811i	−0.294224	−	0.955737i	$-0.595061\pi$
$853$	7.87269	−	3.79129i	0.269556	−	0.129811i	0.563779	+	0.825925i	$0.309347\pi$
$854$	2.54967	+	10.8538i	0.0872480	+	0.371409i
$855$	−13.4193	−	6.46238i	−0.458929	−	0.221009i
$856$	2.38833	−	1.62834i	0.0816316	−	0.0556555i
$857$	−0.639420	+	0.593295i	−0.0218422	+	0.0202666i	−0.691018	−	0.722837i	$-0.742838\pi$
$857$	−0.639420	+	0.593295i	−0.0218422	+	0.0202666i	0.669176	+	0.743104i	$0.266647\pi$
$858$	19.6736	−	18.2544i	0.671645	−	0.623195i
$859$	22.4760	−	15.3239i	0.766871	−	0.522844i	−0.115551	−	0.993301i	$-0.536864\pi$
$859$	22.4760	−	15.3239i	0.766871	−	0.522844i	0.882423	+	0.470458i	$0.155911\pi$
$860$	−0.919318	−	0.442720i	−0.0313485	−	0.0150966i
$861$	−9.60340	−	40.8811i	−0.327283	−	1.39322i
$862$	−9.77253	+	4.70620i	−0.332854	+	0.160294i
$863$	−11.4921	+	19.9049i	−0.391196	+	0.677572i	−0.992608	−	0.121368i	$-0.961272\pi$
$863$	−11.4921	+	19.9049i	−0.391196	+	0.677572i	0.601411	+	0.798940i	$0.294605\pi$
$864$	−3.00238	−	5.20027i	−0.102143	−	0.176917i
$865$	11.4502	+	7.80664i	0.389320	+	0.265434i
$866$	8.90994	−	1.34296i	0.302772	−	0.0456355i
$867$	−13.8749	−	60.7900i	−0.471217	−	2.06454i
$868$	−2.25614	−	27.7486i	−0.0765782	−	0.941850i
$869$	1.03764	−	4.54620i	0.0351996	−	0.154219i
$870$	−0.231270	+	3.08608i	−0.00784078	+	0.104628i
$871$	2.30018	−	0.709512i	0.0779387	−	0.0240409i
$872$	−2.92924	+	7.46357i	−0.0991964	+	0.252748i
$873$	60.0775	+	18.5314i	2.03331	+	0.627194i
$874$	2.55729	−	3.20674i	0.0865017	−	0.108470i
$875$	−20.8460	+	14.4066i	−0.704723	+	0.487033i
$876$	−18.6753	−	23.4181i	−0.630979	−	0.791223i
$877$	−10.1717	−	25.9170i	−0.343472	−	0.875154i	−0.993352	−	0.115116i	$-0.963276\pi$
$877$	−10.1717	−	25.9170i	−0.343472	−	0.875154i	0.649880	−	0.760037i	$-0.274819\pi$
$878$	−1.43656	−	19.1695i	−0.0484814	−	0.646939i
$879$	−73.2443	−	11.0398i	−2.47047	−	0.372363i
$880$	3.25767	+	3.02268i	0.109816	+	0.101895i
$881$	−26.5809			−0.895532			−0.447766	−	0.894151i	$-0.647780\pi$
$881$	−26.5809			−0.895532			−0.447766	+	0.894151i	$0.647780\pi$
$882$	−17.4872	+	31.1938i	−0.588823	+	1.05035i
$883$	−9.25756			−0.311542			−0.155771	−	0.987793i	$-0.549786\pi$
$883$	−9.25756			−0.311542			−0.155771	+	0.987793i	$0.549786\pi$
$884$	24.0109	+	22.2788i	0.807574	+	0.749319i
$885$	−41.0197	−	6.18273i	−1.37886	−	0.207830i
$886$	−0.516585	−	6.89335i	−0.0173550	−	0.231587i
$887$	4.82711	+	12.2993i	0.162078	+	0.412969i	0.988723	−	0.149755i	$-0.0478485\pi$
$887$	4.82711	+	12.2993i	0.162078	+	0.412969i	−0.826645	+	0.562724i	$0.809753\pi$
$888$	−1.18859	−	1.49044i	−0.0398863	−	0.0500159i
$889$	−0.620247	+	9.04425i	−0.0208024	+	0.303334i
$890$	−7.58905	+	9.51637i	−0.254386	+	0.318989i
$891$	−3.04018	−	0.937770i	−0.101850	−	0.0314165i
$892$	3.89220	−	9.91717i	0.130321	−	0.332052i
$893$	6.92297	−	2.13545i	0.231668	−	0.0714602i
$894$	0.974163	−	12.9993i	0.0325809	−	0.434761i
$895$	4.03055	−	17.6590i	0.134727	−	0.590276i
$896$	−1.33735	−	2.28287i	−0.0446777	−	0.0762654i
$897$	−11.5937	−	50.7955i	−0.387104	−	1.69601i
$898$	−21.9956	+	3.31530i	−0.734002	+	0.110633i
$899$	3.81557	+	2.60141i	0.127256	+	0.0867620i
$900$	−2.89265	−	5.01021i	−0.0964215	−	0.167007i
$901$	39.0177	−	67.5806i	1.29987	−	2.25144i
$902$	9.01212	−	4.34001i	0.300071	−	0.144507i
$903$	3.10424	−	0.0196436i	0.103303	−	0.000653698i
$904$	13.3971	+	6.45173i	0.445582	+	0.214581i
$905$	39.2100	−	26.7329i	1.30338	−	0.888632i
$906$	−36.8734	+	34.2135i	−1.22504	+	1.13667i
$907$	−9.82647	+	9.11763i	−0.326282	+	0.302746i	−0.826256	−	0.563295i	$-0.809534\pi$
$907$	−9.82647	+	9.11763i	−0.326282	+	0.302746i	0.499974	+	0.866041i	$0.333343\pi$
$908$	−5.18250	+	3.53337i	−0.171987	+	0.117259i
$909$	2.79646	+	1.34670i	0.0927527	+	0.0446674i
$910$	−30.9070	+	15.1257i	−1.02456	+	0.501412i
$911$	17.5986	−	8.47505i	0.583068	−	0.280791i	−0.119007	−	0.992893i	$-0.537971\pi$
$911$	17.5986	−	8.47505i	0.583068	−	0.280791i	0.702076	+	0.712102i	$0.252257\pi$
$912$	−1.67624	+	2.90333i	−0.0555059	+	0.0961390i
$913$	−7.26630	−	12.5856i	−0.240479	−	0.416522i
$914$	12.7776	+	8.71163i	0.422646	+	0.288155i
$915$	29.3840	−	4.42893i	0.971405	−	0.146416i
$916$	−4.79122	−	20.9917i	−0.158306	−	0.693586i
$917$	7.87245	−	20.4380i	0.259971	−	0.674923i
$918$	8.33344	−	36.5112i	0.275044	−	1.20505i
$919$	−1.66286	+	22.1893i	−0.0548527	+	0.731958i	0.900191	+	0.435494i	$0.143426\pi$
$919$	−1.66286	+	22.1893i	−0.0548527	+	0.731958i	−0.955044	+	0.296464i	$0.904193\pi$
$920$	8.24406	−	2.54296i	0.271799	−	0.0838388i
$921$	−10.0062	+	25.4954i	−0.329716	+	0.840101i
$922$	4.48845	+	1.38450i	0.147819	+	0.0455961i
$923$	−35.5505	+	44.5789i	−1.17016	+	1.46733i
$924$	−12.9445	−	3.90330i	−0.425841	−	0.128409i
$925$	−0.472680	−	0.592722i	−0.0155416	−	0.0194886i
$926$	9.47498	+	24.1419i	0.311367	+	0.793351i
$927$	−0.324952	−	4.33618i	−0.0106728	−	0.142419i
$928$	0.433963	+	0.0654094i	0.0142455	+	0.00214717i
$929$	−40.6712	−	37.7374i	−1.33438	−	1.23812i	−0.948966	−	0.315378i	$-0.897869\pi$
$929$	−40.6712	−	37.7374i	−1.33438	−	1.23812i	−0.385412	−	0.922744i	$-0.625941\pi$
$930$	−74.2021			−2.43318
$931$	8.24050	−	0.104296i	0.270071	−	0.00341815i
$932$	−5.52800			−0.181076
$933$	13.7988	+	12.8034i	0.451751	+	0.419164i
$934$	−24.8799	−	3.75004i	−0.814094	−	0.122705i
$935$	2.07122	+	27.6385i	0.0677361	+	0.903876i
$936$	9.80227	+	24.9758i	0.320397	+	0.816358i
$937$	27.7001	+	34.7348i	0.904921	+	1.13474i	0.990377	+	0.138394i	$0.0441939\pi$
$937$	27.7001	+	34.7348i	0.904921	+	1.13474i	−0.0854558	+	0.996342i	$0.527235\pi$
$938$	−0.894129	−	0.819163i	−0.0291943	−	0.0267466i
$939$	18.2456	−	22.8793i	0.595423	−	0.746637i
$940$	14.5619	+	4.49176i	0.474957	+	0.146505i
$941$	−12.7143	+	32.3955i	−0.414474	+	1.05606i	0.559385	+	0.828908i	$0.311037\pi$
$941$	−12.7143	+	32.3955i	−0.414474	+	1.05606i	−0.973859	+	0.227154i	$0.927058\pi$
$942$	48.8949	−	15.0821i	1.59308	−	0.491400i
$943$	1.45117	−	19.3645i	0.0472565	−	0.630594i
$944$	−1.30903	+	5.73522i	−0.0426052	+	0.186666i
$945$	32.6458	+	21.9562i	1.06197	+	0.714236i
$946$	0.164538	+	0.720889i	0.00534960	+	0.0234381i
$947$	−20.1195	+	3.03253i	−0.653797	+	0.0985440i	−0.467561	−	0.883961i	$-0.654867\pi$
$947$	−20.1195	+	3.03253i	−0.653797	+	0.0985440i	−0.186236	+	0.982505i	$0.559629\pi$
$948$	6.11366	+	4.16823i	0.198563	+	0.135378i
$949$	27.6215	+	47.8418i	0.896632	+	1.55301i
$950$	−0.666612	+	1.15461i	−0.0216277	+	0.0374604i
$951$	30.3197	−	14.6012i	0.983185	−	0.473477i
$952$	3.56992	−	16.1101i	0.115702	−	0.522130i
$953$	−39.4892	−	19.0170i	−1.27918	−	0.616020i	−0.334001	−	0.942573i	$-0.608399\pi$
$953$	−39.4892	−	19.0170i	−1.27918	−	0.616020i	−0.945179	+	0.326552i	$0.894113\pi$
$954$	52.8143	−	36.0082i	1.70993	−	1.16581i
$955$	2.76387	−	2.56449i	0.0894366	−	0.0829850i
$956$	20.8814	−	19.3751i	0.675353	−	0.626636i
$957$	1.85297	−	1.26334i	0.0598981	−	0.0408379i
$958$	23.1113	+	11.1298i	0.746692	+	0.359588i
$959$	−6.54260	−	8.09850i	−0.211272	−	0.261514i
$960$	−6.35335	+	3.05961i	−0.205053	+	0.0987485i
$961$	−39.8626	+	69.0441i	−1.28589	+	2.22723i
$962$	1.75797	+	3.04489i	0.0566791	+	0.0981711i
$963$	12.2013	+	8.31873i	0.393183	+	0.268067i
$964$	7.16643	−	1.08017i	0.230815	−	0.0347898i
$965$	6.84136	+	29.9740i	0.220231	+	0.964896i
$966$	−19.1273	+	17.9742i	−0.615412	+	0.578309i
$967$	−3.60112	+	15.7775i	−0.115804	+	0.507371i	0.883442	+	0.468541i	$0.155220\pi$
$967$	−3.60112	+	15.7775i	−0.115804	+	0.507371i	−0.999246	+	0.0388299i	$0.987637\pi$
$968$	−0.581368	+	7.75782i	−0.0186859	+	0.249346i
$969$	−19.9796	+	6.16291i	−0.641839	+	0.197981i
$970$	11.1340	−	28.3689i	0.357490	−	0.910871i
$971$	7.74973	+	2.39048i	0.248701	+	0.0767140i	0.416599	−	0.909090i	$-0.363222\pi$
$971$	7.74973	+	2.39048i	0.248701	+	0.0767140i	−0.167898	+	0.985804i	$0.553698\pi$
$972$	−8.08409	+	10.1371i	−0.259297	+	0.325148i
$973$	−9.27920	−	23.2101i	−0.297478	−	0.744081i
$974$	−15.2533	−	19.1270i	−0.488748	−	0.612870i
$975$	6.18733	+	15.7651i	0.198153	+	0.504886i
$976$	−0.314914	−	4.20223i	−0.0100801	−	0.134510i
$977$	8.03054	+	1.21041i	0.256920	+	0.0387244i	0.276239	−	0.961089i	$-0.410912\pi$
$977$	8.03054	+	1.21041i	0.256920	+	0.0387244i	−0.0193194	+	0.999813i	$0.506150\pi$
$978$	51.2150	+	47.5206i	1.63768	+	1.51954i
$979$	8.82060			0.281908
$980$	14.4450	+	9.58290i	0.461428	+	0.306115i
$981$	−40.9608			−1.30778
$982$	25.2723	+	23.4493i	0.806472	+	0.748297i
$983$	57.4457	+	8.65854i	1.83223	+	0.276165i	0.972213	−	0.234097i	$-0.0752133\pi$
$983$	57.4457	+	8.65854i	1.83223	+	0.276165i	0.860019	+	0.510262i	$0.170451\pi$
$984$	1.18613	+	15.8278i	0.0378125	+	0.504572i
$985$	−10.5861	−	26.9728i	−0.337300	−	0.859426i
$986$	1.70655	+	2.13994i	0.0543475	+	0.0681496i
$987$	−45.7997	+	7.19988i	−1.45782	+	0.229175i
$988$	3.85510	−	4.83414i	0.122647	−	0.153794i
$989$	1.37172	+	0.423118i	0.0436180	+	0.0134544i
$990$	−8.29438	+	21.1337i	−0.263613	+	0.671674i
$991$	−1.81209	+	0.558956i	−0.0575629	+	0.0177558i	−0.323403	−	0.946261i	$-0.604827\pi$
$991$	−1.81209	+	0.558956i	−0.0575629	+	0.0177558i	0.265840	+	0.964017i	$0.414351\pi$
$992$	−0.786355	+	10.4932i	−0.0249668	+	0.333159i
$993$	−18.4903	+	81.0114i	−0.586773	+	2.57082i
$994$	28.4300	+	4.10131i	0.901744	+	0.130086i
$995$	10.8650	+	47.6028i	0.344444	+	1.50911i
$996$	22.8026	−	3.43694i	0.722529	−	0.108904i
$997$	−11.0245	−	7.51637i	−0.349149	−	0.238046i	0.376028	−	0.926608i	$-0.377290\pi$
$997$	−11.0245	−	7.51637i	−0.349149	−	0.238046i	−0.725177	+	0.688562i	$0.758242\pi$
$998$	−12.5599	−	21.7544i	−0.397577	−	0.688624i
$999$	2.00997	−	3.48138i	0.0635928	−	0.110146i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	98.2.g.b.9.1	✓	24
3.2	odd	2		882.2.z.b.793.1		24
4.3	odd	2		784.2.bg.b.401.2		24
7.2	even	3		686.2.e.c.99.4		24
7.3	odd	6		686.2.g.d.67.1		24
7.4	even	3		686.2.g.f.67.2		24
7.5	odd	6		686.2.e.d.99.1		24
7.6	odd	2		686.2.g.e.177.2		24
49.2	even	21		686.2.e.c.589.4		24
49.11	even	21	inner	98.2.g.b.11.1	yes	24
49.13	odd	14		686.2.g.d.471.1		24
49.16	even	21		4802.2.a.o.1.11		12
49.33	odd	42		4802.2.a.l.1.2		12
49.36	even	7		686.2.g.f.471.2		24
49.38	odd	42		686.2.g.e.655.2		24
49.47	odd	42		686.2.e.d.589.1		24
147.11	odd	42		882.2.z.b.109.1		24
196.11	odd	42		784.2.bg.b.305.2		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
98.2.g.b.9.1	✓	24	1.1	even	1	trivial
98.2.g.b.11.1	yes	24	49.11	even	21	inner
686.2.e.c.99.4		24	7.2	even	3
686.2.e.c.589.4		24	49.2	even	21
686.2.e.d.99.1		24	7.5	odd	6
686.2.e.d.589.1		24	49.47	odd	42
686.2.g.d.67.1		24	7.3	odd	6
686.2.g.d.471.1		24	49.13	odd	14
686.2.g.e.177.2		24	7.6	odd	2
686.2.g.e.655.2		24	49.38	odd	42
686.2.g.f.67.2		24	7.4	even	3
686.2.g.f.471.2		24	49.36	even	7
784.2.bg.b.305.2		24	196.11	odd	42
784.2.bg.b.401.2		24	4.3	odd	2
882.2.z.b.109.1		24	147.11	odd	42
882.2.z.b.793.1		24	3.2	odd	2
4802.2.a.l.1.2		12	49.33	odd	42
4802.2.a.o.1.11		12	49.16	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)

\(f(q)\)	\(=\)	\(q+(-0.733052 - 0.680173i) q^{2} +(-2.81578 - 0.424410i) q^{3} +(0.0747301 + 0.997204i) q^{4} +(0.904721 + 2.30519i) q^{5} +(1.77544 + 2.22633i) q^{6} +(-1.30835 + 2.29961i) q^{7} +(0.623490 - 0.781831i) q^{8} +(4.88176 + 1.50582i) q^{9} +O(q^{10})\)	\(q+(-0.733052 - 0.680173i) q^{2} +(-2.81578 - 0.424410i) q^{3} +(0.0747301 + 0.997204i) q^{4} +(0.904721 + 2.30519i) q^{5} +(1.77544 + 2.22633i) q^{6} +(-1.30835 + 2.29961i) q^{7} +(0.623490 - 0.781831i) q^{8} +(4.88176 + 1.50582i) q^{9} +(0.904721 - 2.30519i) q^{10} +(-1.71483 + 0.528954i) q^{11} +(0.212800 - 2.83962i) q^{12} +(-1.16866 + 5.12022i) q^{13} +(2.52322 - 0.795831i) q^{14} +(-1.56915 - 6.87488i) q^{15} +(-0.988831 + 0.149042i) q^{16} +(-5.15304 - 3.51328i) q^{17} +(-2.55436 - 4.42428i) q^{18} +(-0.588654 + 1.01958i) q^{19} +(-2.23114 + 1.07446i) q^{20} +(4.66000 - 5.91992i) q^{21} +(1.61684 + 0.778628i) q^{22} +(2.87850 - 1.96253i) q^{23} +(-2.08743 + 1.93685i) q^{24} +(-0.830133 + 0.770251i) q^{25} +(4.33932 - 2.95850i) q^{26} +(-5.41010 - 2.60537i) q^{27} +(-2.39096 - 1.13284i) q^{28} +(0.395404 - 0.190416i) q^{29} +(-3.52584 + 6.10694i) q^{30} +(5.26130 + 9.11284i) q^{31} +(0.826239 + 0.563320i) q^{32} +(5.05306 - 0.761627i) q^{33} +(1.38781 + 6.08037i) q^{34} +(-6.48474 - 0.935490i) q^{35} +(-1.13680 + 4.98064i) q^{36} +(-0.0500288 + 0.667588i) q^{37} +(1.12500 - 0.347018i) q^{38} +(5.46374 - 13.9214i) q^{39} +(2.36636 + 0.729924i) q^{40} +(3.47528 - 4.35787i) q^{41} +(-7.44259 + 1.17000i) q^{42} +(0.256903 + 0.322146i) q^{43} +(-0.655624 - 1.67050i) q^{44} +(0.945419 + 12.6157i) q^{45} +(-3.44495 - 0.519243i) q^{46} +(-4.51100 - 4.18560i) q^{47} +2.84758 q^{48} +(-3.57644 - 6.01740i) q^{49} +1.13243 q^{50} +(13.0187 + 12.0796i) q^{51} +(-5.19323 - 0.782754i) q^{52} +(0.935038 + 12.4772i) q^{53} +(2.19378 + 5.58967i) q^{54} +(-2.77078 - 3.47445i) q^{55} +(0.982167 + 2.45669i) q^{56} +(2.09024 - 2.62107i) q^{57} +(-0.419367 - 0.129358i) q^{58} +(2.14920 - 5.47607i) q^{59} +(6.73839 - 2.07852i) q^{60} +(-0.314914 + 4.20223i) q^{61} +(2.34150 - 10.2588i) q^{62} +(-9.84986 + 9.25601i) q^{63} +(-0.222521 - 0.974928i) q^{64} +(-12.8604 + 1.93839i) q^{65} +(-4.22220 - 2.87864i) q^{66} +(-0.229167 - 0.396929i) q^{67} +(3.11837 - 5.40118i) q^{68} +(-8.93814 + 4.30438i) q^{69} +(4.11736 + 5.09651i) q^{70} +(9.78160 + 4.71057i) q^{71} +(4.22102 - 2.87785i) q^{72} +(7.71074 - 7.15453i) q^{73} +(0.490749 - 0.455349i) q^{74} +(2.66437 - 1.81654i) q^{75} +(-1.06072 - 0.510815i) q^{76} +(1.02720 - 4.63550i) q^{77} +(-13.4742 + 6.48881i) q^{78} +(-1.29924 + 2.25035i) q^{79} +(-1.23819 - 2.14460i) q^{80} +(1.46482 + 0.998697i) q^{81} +(-5.51166 + 0.830750i) q^{82} +(1.80201 + 7.89513i) q^{83} +(6.25161 + 4.20457i) q^{84} +(3.43673 - 15.0573i) q^{85} +(0.0307918 - 0.410888i) q^{86} +(-1.19418 + 0.368357i) q^{87} +(-0.655624 + 1.67050i) q^{88} +(-4.69684 - 1.44878i) q^{89} +(7.88784 - 9.89104i) q^{90} +(-10.2455 - 9.38649i) q^{91} +(2.17215 + 2.72379i) q^{92} +(-10.9471 - 27.8927i) q^{93} +(0.459869 + 6.13652i) q^{94} +(-2.88289 - 0.434526i) q^{95} +(-2.08743 - 1.93685i) q^{96} +12.3065 q^{97} +(-1.47115 + 6.84366i) q^{98} -9.16788 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

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