LMFDB - Embedded newform 378.2.v.a.205.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [378,2,Mod(67,378)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(378, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([8, 12]))

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

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

chi := DirichletCharacter("378.67");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 378 = 2 \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	378.v (of order $9$, degree $6$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.01834519640$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$12$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			205.12
Character	$\chi$	$=$	378.205
Dual form			378.2.v.a.319.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.939693 - 0.342020i) q^{2} +(1.69499 - 0.356379i) q^{3} +(0.766044 - 0.642788i) q^{4} +(-0.642072 + 0.538762i) q^{5} +(1.47088 - 0.914608i) q^{6} +(1.56979 - 2.12973i) q^{7} +(0.500000 - 0.866025i) q^{8} +(2.74599 - 1.20812i) q^{9} +O(q^{10})$	\(q+(0.939693 - 0.342020i) q^{2} +(1.69499 - 0.356379i) q^{3} +(0.766044 - 0.642788i) q^{4} +(-0.642072 + 0.538762i) q^{5} +(1.47088 - 0.914608i) q^{6} +(1.56979 - 2.12973i) q^{7} +(0.500000 - 0.866025i) q^{8} +(2.74599 - 1.20812i) q^{9} +(-0.419082 + 0.725872i) q^{10} +(-2.11563 - 1.77522i) q^{11} +(1.06936 - 1.36252i) q^{12} +(-4.68288 + 3.92941i) q^{13} +(0.746710 - 2.53819i) q^{14} +(-0.896302 + 1.14202i) q^{15} +(0.173648 - 0.984808i) q^{16} +(0.609659 - 1.05596i) q^{17} +(2.16718 - 2.07444i) q^{18} +(3.80645 + 6.59297i) q^{19} +(-0.145546 + 0.825431i) q^{20} +(1.90179 - 4.16932i) q^{21} +(-2.59520 - 0.944576i) q^{22} +(-1.52208 - 0.553993i) q^{23} +(0.538862 - 1.64609i) q^{24} +(-0.746250 + 4.23219i) q^{25} +(-3.05653 + 5.29407i) q^{26} +(4.22388 - 3.02636i) q^{27} +(-0.166435 - 2.64051i) q^{28} +(-0.112406 - 0.0943199i) q^{29} +(-0.451655 + 1.37970i) q^{30} +(6.35524 - 5.33268i) q^{31} +(-0.173648 - 0.984808i) q^{32} +(-4.21862 - 2.25502i) q^{33} +(0.211732 - 1.20079i) q^{34} +(0.139500 + 2.21318i) q^{35} +(1.32699 - 2.69056i) q^{36} -0.0134567 q^{37} +(5.83182 + 4.89348i) q^{38} +(-6.53709 + 8.32919i) q^{39} +(0.145546 + 0.825431i) q^{40} +(-8.78401 + 7.37066i) q^{41} +(0.361108 - 4.56833i) q^{42} +(-5.97791 + 2.17578i) q^{43} -2.76176 q^{44} +(-1.11223 + 2.25513i) q^{45} -1.61977 q^{46} +(-8.41542 - 7.06138i) q^{47} +(-0.0566326 - 1.73112i) q^{48} +(-2.07151 - 6.68647i) q^{49} +(0.746250 + 4.23219i) q^{50} +(0.657045 - 2.00711i) q^{51} +(-1.06152 + 6.02020i) q^{52} +(-0.294028 - 0.509272i) q^{53} +(2.93407 - 4.28850i) q^{54} +2.31481 q^{55} +(-1.05951 - 2.42434i) q^{56} +(8.80150 + 9.81848i) q^{57} +(-0.137887 - 0.0501866i) q^{58} +(2.08406 + 11.8193i) q^{59} +(0.0474675 + 1.45097i) q^{60} +(3.77860 + 3.17062i) q^{61} +(4.14809 - 7.18470i) q^{62} +(1.73766 - 7.74471i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(0.889732 - 5.04592i) q^{65} +(-4.73547 - 0.676173i) q^{66} +(1.68197 + 0.612185i) q^{67} +(-0.211732 - 1.20079i) q^{68} +(-2.77735 - 0.396574i) q^{69} +(0.888041 + 2.03200i) q^{70} +(-5.50522 - 9.53532i) q^{71} +(0.326733 - 2.98215i) q^{72} +5.06718 q^{73} +(-0.0126451 + 0.00460246i) q^{74} +(0.243378 + 7.43947i) q^{75} +(7.15379 + 2.60377i) q^{76} +(-7.10184 + 1.71899i) q^{77} +(-3.29410 + 10.0627i) q^{78} +(-0.117699 + 0.0428391i) q^{79} +(0.419082 + 0.725872i) q^{80} +(6.08090 - 6.63496i) q^{81} +(-5.73336 + 9.93047i) q^{82} +(8.76959 + 7.35856i) q^{83} +(-1.22313 - 4.41633i) q^{84} +(0.177467 + 1.00646i) q^{85} +(-4.87324 + 4.08913i) q^{86} +(-0.224141 - 0.119812i) q^{87} +(-2.59520 + 0.944576i) q^{88} +(-2.46443 - 4.26851i) q^{89} +(-0.273856 + 2.49954i) q^{90} +(1.01743 + 16.1416i) q^{91} +(-1.52208 + 0.553993i) q^{92} +(8.87162 - 11.3037i) q^{93} +(-10.3230 - 3.75728i) q^{94} +(-5.99606 - 2.18239i) q^{95} +(-0.645297 - 1.60736i) q^{96} +(8.45999 - 3.07919i) q^{97} +(-4.23349 - 5.57473i) q^{98} +(-7.95417 - 2.31881i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q + 3 q^{6} - 6 q^{7} + 36 q^{8}+O(q^{10}) $ 72 * q + 3 * q^6 - 6 * q^7 + 36 * q^8	$ 72 q + 3 q^{6} - 6 q^{7} + 36 q^{8} + 6 q^{10} + 12 q^{11} + 12 q^{13} - 3 q^{14} - 6 q^{15} - 12 q^{17} + 18 q^{19} + 6 q^{22} + 12 q^{23} - 6 q^{25} - 18 q^{26} + 6 q^{27} + 3 q^{29} + 15 q^{30} - 9 q^{31} - 18 q^{33} - 9 q^{34} - 18 q^{35} - 3 q^{36} - 48 q^{39} - 6 q^{41} + 36 q^{42} - 24 q^{43} - 45 q^{45} - 27 q^{47} + 6 q^{48} + 48 q^{49} + 6 q^{50} + 15 q^{51} - 6 q^{52} - 15 q^{53} - 63 q^{54} - 72 q^{55} - 3 q^{56} + 57 q^{57} - 3 q^{58} - 30 q^{59} + 21 q^{60} + 9 q^{61} - 24 q^{62} - 21 q^{63} - 36 q^{64} + 45 q^{65} + 6 q^{67} + 9 q^{68} - 39 q^{69} + 15 q^{70} + 12 q^{71} - 60 q^{73} - 18 q^{74} + 42 q^{75} + 3 q^{77} + 6 q^{78} - 27 q^{79} - 6 q^{80} + 12 q^{81} + 33 q^{82} + 18 q^{83} - 21 q^{84} + 51 q^{85} - 12 q^{86} - 117 q^{87} + 6 q^{88} - 36 q^{89} - 69 q^{90} - 3 q^{91} + 12 q^{92} - 30 q^{93} - 27 q^{94} + 3 q^{95} + 48 q^{97} - 12 q^{98} + 90 q^{99}+O(q^{100}) $ 72 * q + 3 * q^6 - 6 * q^7 + 36 * q^8 + 6 * q^10 + 12 * q^11 + 12 * q^13 - 3 * q^14 - 6 * q^15 - 12 * q^17 + 18 * q^19 + 6 * q^22 + 12 * q^23 - 6 * q^25 - 18 * q^26 + 6 * q^27 + 3 * q^29 + 15 * q^30 - 9 * q^31 - 18 * q^33 - 9 * q^34 - 18 * q^35 - 3 * q^36 - 48 * q^39 - 6 * q^41 + 36 * q^42 - 24 * q^43 - 45 * q^45 - 27 * q^47 + 6 * q^48 + 48 * q^49 + 6 * q^50 + 15 * q^51 - 6 * q^52 - 15 * q^53 - 63 * q^54 - 72 * q^55 - 3 * q^56 + 57 * q^57 - 3 * q^58 - 30 * q^59 + 21 * q^60 + 9 * q^61 - 24 * q^62 - 21 * q^63 - 36 * q^64 + 45 * q^65 + 6 * q^67 + 9 * q^68 - 39 * q^69 + 15 * q^70 + 12 * q^71 - 60 * q^73 - 18 * q^74 + 42 * q^75 + 3 * q^77 + 6 * q^78 - 27 * q^79 - 6 * q^80 + 12 * q^81 + 33 * q^82 + 18 * q^83 - 21 * q^84 + 51 * q^85 - 12 * q^86 - 117 * q^87 + 6 * q^88 - 36 * q^89 - 69 * q^90 - 3 * q^91 + 12 * q^92 - 30 * q^93 - 27 * q^94 + 3 * q^95 + 48 * q^97 - 12 * q^98 + 90 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/378\mathbb{Z}\right)^\times$.

$n$	$29$	$325$
$\chi(n)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	0.939693	−	0.342020i	0.664463	−	0.241845i
$2$	0.939693	−	0.342020i	0.664463	−	0.241845i
$3$	1.69499	−	0.356379i	0.978603	−	0.205755i
$3$	1.69499	−	0.356379i	0.978603	−	0.205755i
$4$	0.766044	−	0.642788i	0.383022	−	0.321394i
$5$	−0.642072	+	0.538762i	−0.287143	+	0.240942i	−0.774969	−	0.631999i	$-0.782235\pi$
$5$	−0.642072	+	0.538762i	−0.287143	+	0.240942i	0.487826	+	0.872941i	$0.337790\pi$
$6$	1.47088	−	0.914608i	0.600485	−	0.373387i
$7$	1.56979	−	2.12973i	0.593325	−	0.804963i
$7$	1.56979	−	2.12973i	0.593325	−	0.804963i
$8$	0.500000	−	0.866025i	0.176777	−	0.306186i
$9$	2.74599	−	1.20812i	0.915329	−	0.402706i
$10$	−0.419082	+	0.725872i	−0.132526	+	0.229541i
$11$	−2.11563	−	1.77522i	−0.637886	−	0.535250i	0.265482	−	0.964116i	$-0.414469\pi$
$11$	−2.11563	−	1.77522i	−0.637886	−	0.535250i	−0.903368	+	0.428866i	$0.858913\pi$
$12$	1.06936	−	1.36252i	0.308698	−	0.393326i
$13$	−4.68288	+	3.92941i	−1.29880	+	1.08982i	−0.308447	+	0.951242i	$0.599809\pi$
$13$	−4.68288	+	3.92941i	−1.29880	+	1.08982i	−0.990351	+	0.138579i	$0.955746\pi$
$14$	0.746710	−	2.53819i	0.199567	−	0.678361i
$15$	−0.896302	+	1.14202i	−0.231424	+	0.294868i
$16$	0.173648	−	0.984808i	0.0434120	−	0.246202i
$17$	0.609659	−	1.05596i	0.147864	−	0.256108i	−0.782574	−	0.622558i	$-0.786094\pi$
$17$	0.609659	−	1.05596i	0.147864	−	0.256108i	0.930438	+	0.366450i	$0.119427\pi$
$18$	2.16718	−	2.07444i	0.510810	−	0.488951i
$19$	3.80645	+	6.59297i	0.873260	+	1.51253i	0.858605	+	0.512638i	$0.171332\pi$
$19$	3.80645	+	6.59297i	0.873260	+	1.51253i	0.0146556	+	0.999893i	$0.495335\pi$
$20$	−0.145546	+	0.825431i	−0.0325450	+	0.184572i
$21$	1.90179	−	4.16932i	0.415005	−	0.909819i
$22$	−2.59520	−	0.944576i	−0.553299	−	0.201384i
$23$	−1.52208	−	0.553993i	−0.317376	−	0.115515i	0.178420	−	0.983954i	$-0.442901\pi$
$23$	−1.52208	−	0.553993i	−0.317376	−	0.115515i	−0.495796	+	0.868439i	$0.665124\pi$
$24$	0.538862	−	1.64609i	0.109995	−	0.336008i
$25$	−0.746250	+	4.23219i	−0.149250	+	0.846438i
$26$	−3.05653	+	5.29407i	−0.599436	+	1.03825i
$27$	4.22388	−	3.02636i	0.812886	−	0.582423i
$28$	−0.166435	−	2.64051i	−0.0314533	−	0.499010i
$29$	−0.112406	−	0.0943199i	−0.0208733	−	0.0175148i	0.632291	−	0.774731i	$-0.282115\pi$
$29$	−0.112406	−	0.0943199i	−0.0208733	−	0.0175148i	−0.653165	+	0.757216i	$0.726559\pi$
$30$	−0.451655	+	1.37970i	−0.0824606	+	0.251897i
$31$	6.35524	−	5.33268i	1.14143	−	0.957777i	0.141950	−	0.989874i	$-0.454663\pi$
$31$	6.35524	−	5.33268i	1.14143	−	0.957777i	0.999485	+	0.0320966i	$0.0102184\pi$
$32$	−0.173648	−	0.984808i	−0.0306970	−	0.174091i
$33$	−4.21862	−	2.25502i	−0.734368	−	0.392549i
$34$	0.211732	−	1.20079i	0.0363118	−	0.205934i
$35$	0.139500	+	2.21318i	0.0235798	+	0.374096i
$36$	1.32699	−	2.69056i	0.221164	−	0.448427i
$37$	−0.0134567			−0.00221226			−0.00110613	−	0.999999i	$-0.500352\pi$
$37$	−0.0134567			−0.00221226			−0.00110613	+	0.999999i	$0.500352\pi$
$38$	5.83182	+	4.89348i	0.946047	+	0.793828i
$39$	−6.53709	+	8.32919i	−1.04677	+	1.33374i
$40$	0.145546	+	0.825431i	0.0230128	+	0.130512i
$41$	−8.78401	+	7.37066i	−1.37183	+	1.15110i	−0.399707	+	0.916643i	$0.630888\pi$
$41$	−8.78401	+	7.37066i	−1.37183	+	1.15110i	−0.972125	+	0.234461i	$0.924667\pi$
$42$	0.361108	−	4.56833i	0.0557203	−	0.704908i
$43$	−5.97791	+	2.17578i	−0.911623	+	0.331803i	−0.754901	−	0.655839i	$-0.772315\pi$
$43$	−5.97791	+	2.17578i	−0.911623	+	0.331803i	−0.156722	+	0.987643i	$0.550093\pi$
$44$	−2.76176			−0.416350
$45$	−1.11223	+	2.25513i	−0.165802	+	0.336175i
$46$	−1.61977			−0.238821
$47$	−8.41542	−	7.06138i	−1.22752	−	1.03001i	−0.998396	−	0.0566096i	$-0.981971\pi$
$47$	−8.41542	−	7.06138i	−1.22752	−	1.03001i	−0.229119	−	0.973398i	$-0.573585\pi$
$48$	−0.0566326	−	1.73112i	−0.00817421	−	0.249866i
$49$	−2.07151	−	6.68647i	−0.295930	−	0.955210i
$50$	0.746250	+	4.23219i	0.105536	+	0.598522i
$51$	0.657045	−	2.00711i	0.0920046	−	0.281052i
$52$	−1.06152	+	6.02020i	−0.147207	+	0.834851i
$53$	−0.294028	−	0.509272i	−0.0403879	−	0.0699539i	0.845125	−	0.534569i	$-0.179526\pi$
$53$	−0.294028	−	0.509272i	−0.0403879	−	0.0699539i	−0.885513	+	0.464615i	$0.846193\pi$
$54$	2.93407	−	4.28850i	0.399276	−	0.583591i
$55$	2.31481			0.312128
$56$	−1.05951	−	2.42434i	−0.141582	−	0.323967i
$57$	8.80150	+	9.81848i	1.16579	+	1.30049i
$58$	−0.137887	−	0.0501866i	−0.0181054	−	0.00658982i
$59$	2.08406	+	11.8193i	0.271321	+	1.53874i	0.750411	+	0.660972i	$0.229856\pi$
$59$	2.08406	+	11.8193i	0.271321	+	1.53874i	−0.479090	+	0.877766i	$0.659033\pi$
$60$	0.0474675	+	1.45097i	0.00612802	+	0.187319i
$61$	3.77860	+	3.17062i	0.483800	+	0.405956i	0.851798	−	0.523870i	$-0.175512\pi$
$61$	3.77860	+	3.17062i	0.483800	+	0.405956i	−0.367998	+	0.929826i	$0.619957\pi$
$62$	4.14809	−	7.18470i	0.526808	−	0.912458i
$63$	1.73766	−	7.74471i	0.218925	−	0.975742i
$64$	−0.500000	−	0.866025i	−0.0625000	−	0.108253i
$65$	0.889732	−	5.04592i	0.110358	−	0.625869i
$66$	−4.73547	−	0.676173i	−0.582896	−	0.0832311i
$67$	1.68197	+	0.612185i	0.205485	+	0.0747904i	0.442712	−	0.896664i	$-0.354016\pi$
$67$	1.68197	+	0.612185i	0.205485	+	0.0747904i	−0.237227	+	0.971454i	$0.576239\pi$
$68$	−0.211732	−	1.20079i	−0.0256763	−	0.145618i
$69$	−2.77735	−	0.396574i	−0.334353	−	0.0477420i
$70$	0.888041	+	2.03200i	0.106141	+	0.242871i
$71$	−5.50522	−	9.53532i	−0.653349	−	1.13163i	−0.982305	−	0.187288i	$-0.940030\pi$
$71$	−5.50522	−	9.53532i	−0.653349	−	1.13163i	0.328956	−	0.944345i	$-0.393303\pi$
$72$	0.326733	−	2.98215i	0.0385059	−	0.351450i
$73$	5.06718			0.593068			0.296534	−	0.955022i	$-0.404169\pi$
$73$	5.06718			0.593068			0.296534	+	0.955022i	$0.404169\pi$
$74$	−0.0126451	+	0.00460246i	−0.00146997	+	0.000535025i
$75$	0.243378	+	7.43947i	0.0281028	+	0.859036i
$76$	7.15379	+	2.60377i	0.820596	+	0.298673i
$77$	−7.10184	+	1.71899i	−0.809330	+	0.195897i
$78$	−3.29410	+	10.0627i	−0.372984	+	1.13938i
$79$	−0.117699	+	0.0428391i	−0.0132422	+	0.00481977i	−0.348633	−	0.937259i	$-0.613354\pi$
$79$	−0.117699	+	0.0428391i	−0.0132422	+	0.00481977i	0.335391	+	0.942079i	$0.391132\pi$
$80$	0.419082	+	0.725872i	0.0468548	+	0.0811550i
$81$	6.08090	−	6.63496i	0.675656	−	0.737217i
$82$	−5.73336	+	9.93047i	−0.633143	+	1.09664i
$83$	8.76959	+	7.35856i	0.962587	+	0.807707i	0.981372	−	0.192117i	$-0.0615353\pi$
$83$	8.76959	+	7.35856i	0.962587	+	0.807707i	−0.0187848	+	0.999824i	$0.505980\pi$
$84$	−1.22313	−	4.41633i	−0.133454	−	0.481861i
$85$	0.177467	+	1.00646i	0.0192490	+	0.109166i
$86$	−4.87324	+	4.08913i	−0.525495	+	0.440942i
$87$	−0.224141	−	0.119812i	−0.0240304	−	0.0128452i
$88$	−2.59520	+	0.944576i	−0.276649	+	0.100692i
$89$	−2.46443	−	4.26851i	−0.261229	−	0.452461i	0.705340	−	0.708869i	$-0.250794\pi$
$89$	−2.46443	−	4.26851i	−0.261229	−	0.452461i	−0.966569	+	0.256408i	$0.917461\pi$
$90$	−0.273856	+	2.49954i	−0.0288670	+	0.263474i
$91$	1.01743	+	16.1416i	0.106656	+	1.69210i
$92$	−1.52208	+	0.553993i	−0.158688	+	0.0577577i
$93$	8.87162	−	11.3037i	0.919944	−	1.17214i
$94$	−10.3230	−	3.75728i	−1.06474	−	0.387534i
$95$	−5.99606	−	2.18239i	−0.615182	−	0.223908i
$96$	−0.645297	−	1.60736i	−0.0658603	−	0.164050i
$97$	8.45999	−	3.07919i	0.858982	−	0.312644i	0.125285	−	0.992121i	$-0.460015\pi$
$97$	8.45999	−	3.07919i	0.858982	−	0.312644i	0.733697	+	0.679477i	$0.237793\pi$
$98$	−4.23349	−	5.57473i	−0.427647	−	0.563132i
$99$	−7.95417	−	2.31881i	−0.799424	−	0.233049i
$100$	2.14874	+	3.72173i	0.214874	+	0.372173i
$101$	2.75407	−	1.00240i	0.274040	−	0.0997423i	−0.201345	−	0.979520i	$-0.564531\pi$
$101$	2.75407	−	1.00240i	0.274040	−	0.0997423i	0.475385	+	0.879778i	$0.342309\pi$
$102$	−0.0690532	−	2.11079i	−0.00683728	−	0.209000i
$103$	−9.80379	+	8.22635i	−0.965996	+	0.810567i	−0.981918	−	0.189306i	$-0.939376\pi$
$103$	−9.80379	+	8.22635i	−0.965996	+	0.810567i	0.0159221	+	0.999873i	$0.494932\pi$
$104$	1.06152	+	6.02020i	0.104091	+	0.590329i
$105$	1.02518	+	3.70161i	0.100048	+	0.361240i
$106$	−0.450477	−	0.377995i	−0.0437542	−	0.0367142i
$107$	2.84573	−	4.92894i	0.275107	−	0.476499i	−0.695055	−	0.718956i	$-0.744620\pi$
$107$	2.84573	−	4.92894i	0.275107	−	0.476499i	0.970162	+	0.242457i	$0.0779535\pi$
$108$	1.29037	−	5.03338i	0.124166	−	0.484338i
$109$	−3.25389	−	5.63591i	−0.311666	−	0.539822i	0.667057	−	0.745007i	$-0.267554\pi$
$109$	−3.25389	−	5.63591i	−0.311666	−	0.539822i	−0.978723	+	0.205185i	$0.934220\pi$
$110$	2.17521	−	0.791710i	0.207398	−	0.0754866i
$111$	−0.0228089	+	0.00479568i	−0.00216493	+	0.000455185i
$112$	−1.82478	−	1.91577i	−0.172426	−	0.181023i
$113$	−16.9345	−	6.16366i	−1.59307	−	0.579829i	−0.615074	−	0.788470i	$-0.710874\pi$
$113$	−16.9345	−	6.16366i	−1.59307	−	0.579829i	−0.977992	+	0.208641i	$0.933096\pi$
$114$	11.6288	+	6.21607i	1.08914	+	0.582188i
$115$	1.27576	−	0.464337i	0.118965	−	0.0432997i
$116$	−0.146736			−0.0136241
$117$	−8.11196	+	16.4476i	−0.749951	+	1.52058i
$118$	6.00080	+	10.3937i	0.552418	+	0.956816i
$119$	−1.29187	−	2.95605i	−0.118426	−	0.270980i
$120$	0.540865	+	1.34723i	0.0493740	+	0.122985i
$121$	−0.585665	−	3.32147i	−0.0532422	−	0.301952i
$122$	4.63513	+	1.68705i	0.419645	+	0.152738i
$123$	−12.2621	+	15.6236i	−1.10563	+	1.40874i
$124$	1.44062	−	8.17014i	0.129371	−	0.733700i
$125$	−3.89641	−	6.74878i	−0.348506	−	0.603629i
$126$	−1.01598	−	7.87196i	−0.0905106	−	0.701290i
$127$	−1.08649	+	1.88185i	−0.0964102	+	0.166987i	−0.910196	−	0.414177i	$-0.864069\pi$
$127$	−1.08649	+	1.88185i	−0.0964102	+	0.166987i	0.813786	+	0.581165i	$0.197403\pi$
$128$	−0.766044	−	0.642788i	−0.0677094	−	0.0568149i
$129$	−9.35710	+	5.81833i	−0.823847	+	0.512275i
$130$	−0.889732	−	5.04592i	−0.0780346	−	0.442556i
$131$	16.2480	+	5.91380i	1.41960	+	0.516691i	0.933931	−	0.357454i	$-0.116355\pi$
$131$	16.2480	+	5.91380i	1.41960	+	0.516691i	0.485666	+	0.874145i	$0.338577\pi$
$132$	−4.68115	+	0.984231i	−0.407442	+	0.0856663i
$133$	20.0166	+	2.24286i	1.73566	+	0.194481i
$134$	1.78991			0.154625
$135$	−1.08154	+	4.21880i	−0.0930844	+	0.363097i
$136$	−0.609659	−	1.05596i	−0.0522778	−	0.0905479i
$137$	−0.415010	+	2.35364i	−0.0354567	+	0.201085i	−0.997390	−	0.0721983i	$-0.976999\pi$
$137$	−0.415010	+	2.35364i	−0.0354567	+	0.201085i	0.961934	+	0.273283i	$0.0881097\pi$
$138$	−2.74549	+	0.577250i	−0.233712	+	0.0491388i
$139$	−2.26072	−	12.8212i	−0.191752	−	1.08748i	−0.916969	−	0.398958i	$-0.869372\pi$
$139$	−2.26072	−	12.8212i	−0.191752	−	1.08748i	0.725218	−	0.688520i	$-0.241739\pi$
$140$	1.52947	+	1.60573i	0.129264	+	0.135709i
$141$	−16.7806	−	8.96989i	−1.41318	−	0.755401i
$142$	−8.43448	−	7.07737i	−0.707806	−	0.593920i
$143$	16.8828			1.41181
$144$	−0.712928	−	2.91406i	−0.0594107	−	0.242838i
$145$	0.122989			0.0102137
$146$	4.76159	−	1.73308i	0.394072	−	0.143430i
$147$	−5.89411	−	10.5953i	−0.486138	−	0.873882i
$148$	−0.0103084	+	0.00864979i	−0.000847346	+	0.000711008i
$149$	−2.28566	−	12.9626i	−0.187248	−	1.06194i	−0.923032	−	0.384722i	$-0.874297\pi$
$149$	−2.28566	−	12.9626i	−0.187248	−	1.06194i	0.735784	−	0.677216i	$-0.236814\pi$
$150$	2.77315	+	6.90758i	0.226427	+	0.564001i
$151$	15.9362	+	13.3720i	1.29687	+	1.08820i	0.990677	+	0.136232i	$0.0434992\pi$
$151$	15.9362	+	13.3720i	1.29687	+	1.08820i	0.306192	+	0.951970i	$0.400945\pi$
$152$	7.61291			0.617488
$153$	0.398392	−	3.63620i	0.0322081	−	0.293969i
$154$	−6.08562	+	4.04429i	−0.490393	+	0.325899i
$155$	−1.20747	+	6.84792i	−0.0969866	+	0.550038i
$156$	0.346199	+	10.5825i	0.0277181	+	0.847277i
$157$	−1.16583	−	6.61176i	−0.0930436	−	0.527676i	−0.995329	−	0.0965378i	$-0.969223\pi$
$157$	−1.16583	−	6.61176i	−0.0930436	−	0.527676i	0.902286	−	0.431139i	$-0.141888\pi$
$158$	−0.0959494	+	0.0805111i	−0.00763332	+	0.00640512i
$159$	−0.679869	−	0.758426i	−0.0539171	−	0.0601471i
$160$	0.642072	+	0.538762i	0.0507602	+	0.0425929i
$161$	−3.56921	+	2.37197i	−0.281293	+	0.186938i
$162$	3.44489	−	8.31461i	0.270656	−	0.653257i
$163$	2.24789	−	3.89345i	0.176068	−	0.304959i	−0.764462	−	0.644668i	$-0.776995\pi$
$163$	2.24789	−	3.89345i	0.176068	−	0.304959i	0.940530	+	0.339710i	$0.110329\pi$
$164$	−1.99117	+	11.2925i	−0.155485	+	0.881797i
$165$	3.92358	−	0.824948i	0.305450	−	0.0642221i
$166$	10.7575	+	3.91541i	0.834943	+	0.303894i
$167$	−11.2469	−	4.09353i	−0.870311	−	0.316767i	−0.132018	−	0.991247i	$-0.542146\pi$
$167$	−11.2469	−	4.09353i	−0.870311	−	0.316767i	−0.738293	+	0.674480i	$0.764368\pi$
$168$	−2.65984	−	3.73166i	−0.205211	−	0.287904i
$169$	4.23174	−	23.9994i	0.325519	−	1.84611i
$170$	0.510995	+	0.885069i	0.0391915	+	0.0678817i
$171$	18.4176	+	13.5056i	1.40843	+	1.03280i
$172$	−3.18078	+	5.50927i	−0.242532	+	0.420078i
$173$	1.66556	−	9.44586i	0.126630	−	0.718156i	−0.853696	−	0.520772i	$-0.825644\pi$
$173$	1.66556	−	9.44586i	0.126630	−	0.718156i	0.980326	−	0.197384i	$-0.0632446\pi$
$174$	−0.251602	−	0.0359260i	−0.0190739	−	0.00272354i
$175$	7.84197	+	8.23297i	0.592798	+	0.622354i
$176$	−2.11563	+	1.77522i	−0.159471	+	0.133812i
$177$	7.74459	+	19.2908i	0.582119	+	1.44999i
$178$	−3.77572	−	3.16820i	−0.283002	−	0.237467i
$179$	8.11042	−	14.0477i	0.606201	−	1.04997i	−0.385659	−	0.922641i	$-0.626026\pi$
$179$	8.11042	−	14.0477i	0.606201	−	1.04997i	0.991860	−	0.127330i	$-0.0406408\pi$
$180$	0.597551	+	2.44246i	0.0445388	+	0.182050i
$181$	3.30818	−	5.72994i	0.245895	−	0.425903i	−0.716488	−	0.697600i	$-0.754251\pi$
$181$	3.30818	−	5.72994i	0.245895	−	0.425903i	0.962383	+	0.271697i	$0.0875847\pi$
$182$	6.47683	+	14.8202i	0.480095	+	1.09855i
$183$	7.53463	+	4.02756i	0.556976	+	0.297726i
$184$	−1.24081	+	1.04117i	−0.0914739	+	0.0767557i
$185$	0.00864015	−	0.00724995i	0.000635237	−	0.000533027i
$186$	4.47050	−	13.6563i	0.327793	−	1.00133i
$187$	−3.16438	+	1.15174i	−0.231402	+	0.0842235i
$188$	−10.9856			−0.801204
$189$	0.185269	−	13.7465i	0.0134763	−	0.999909i
$190$	−6.38087			−0.462917
$191$	10.7672	−	3.91894i	0.779088	−	0.283565i	0.0782956	−	0.996930i	$-0.475052\pi$
$191$	10.7672	−	3.91894i	0.779088	−	0.283565i	0.700792	+	0.713365i	$0.252830\pi$
$192$	−1.15613	−	1.28972i	−0.0834364	−	0.0930772i
$193$	2.20925	−	1.85378i	0.159025	−	0.133438i	−0.559803	−	0.828626i	$-0.689123\pi$
$193$	2.20925	−	1.85378i	0.159025	−	0.133438i	0.718828	+	0.695188i	$0.244679\pi$
$194$	6.89665	−	5.78698i	0.495151	−	0.415481i
$195$	−0.290172	−	8.86987i	−0.0207796	−	0.635184i
$196$	−5.88485	−	3.79059i	−0.420346	−	0.270756i
$197$	3.85488	−	6.67686i	0.274649	−	0.475706i	−0.695397	−	0.718625i	$-0.744772\pi$
$197$	3.85488	−	6.67686i	0.274649	−	0.475706i	0.970047	+	0.242919i	$0.0781050\pi$
$198$	−8.26755	+	0.541515i	−0.587549	+	0.0384838i
$199$	−4.69027	+	8.12378i	−0.332484	+	0.575880i	−0.982998	−	0.183615i	$-0.941220\pi$
$199$	−4.69027	+	8.12378i	−0.332484	+	0.575880i	0.650514	+	0.759494i	$0.274553\pi$
$200$	3.29206	+	2.76237i	0.232784	+	0.195329i
$201$	3.06909	+	0.438232i	0.216477	+	0.0309105i
$202$	2.24513	−	1.88389i	0.157967	−	0.132550i
$203$	−0.377330	+	0.0913322i	−0.0264834	+	0.00641027i
$204$	−0.786822	−	1.95988i	−0.0550886	−	0.137219i
$205$	1.66893	−	9.46499i	0.116563	−	0.661063i
$206$	−6.39897	+	11.0833i	−0.445837	+	0.772213i
$207$	−4.84891	+	0.317598i	−0.337022	+	0.0220746i
$208$	3.05653	+	5.29407i	0.211933	+	0.367078i
$209$	3.65095	−	20.7056i	0.252541	−	1.43223i
$210$	2.22938	+	3.12774i	0.153842	+	0.215835i
$211$	−18.1064	−	6.59019i	−1.24650	−	0.453687i	−0.367279	−	0.930111i	$-0.619711\pi$
$211$	−18.1064	−	6.59019i	−1.24650	−	0.453687i	−0.879216	+	0.476424i	$0.841933\pi$
$212$	−0.552592	−	0.201127i	−0.0379522	−	0.0138135i
$213$	−12.7295	−	14.2003i	−0.872209	−	0.972991i
$214$	0.988310	−	5.60499i	0.0675595	−	0.383149i
$215$	2.66602	−	4.61768i	0.181821	−	0.314923i
$216$	−0.508967	−	5.17117i	−0.0346308	−	0.351853i
$217$	−1.38077	−	21.9061i	−0.0937331	−	1.48709i
$218$	−4.98525	−	4.18312i	−0.337644	−	0.283317i
$219$	8.58882	−	1.80584i	0.580379	−	0.122027i
$220$	1.77324	−	1.48793i	0.119552	−	0.100316i
$221$	1.29433	+	7.34054i	0.0870664	+	0.493778i
$222$	−0.0197932	+	0.0123076i	−0.00132843	+	0.000826031i
$223$	−1.95751	+	11.1016i	−0.131085	+	0.743418i	0.846422	+	0.532513i	$0.178752\pi$
$223$	−1.95751	+	11.1016i	−0.131085	+	0.743418i	−0.977507	+	0.210905i	$0.932359\pi$
$224$	−2.36997	−	1.17612i	−0.158350	−	0.0785827i
$225$	3.06379	+	12.5231i	0.204253	+	0.834874i
$226$	−18.0213			−1.19876
$227$	14.9091	+	12.5102i	0.989549	+	0.830330i	0.985502	−	0.169661i	$-0.0542674\pi$
$227$	14.9091	+	12.5102i	0.989549	+	0.830330i	0.00404679	+	0.999992i	$0.498712\pi$
$228$	13.0535	+	1.86390i	0.864492	+	0.123440i
$229$	−0.436099	−	2.47324i	−0.0288182	−	0.163436i	0.967002	−	0.254767i	$-0.0819989\pi$
$229$	−0.436099	−	2.47324i	−0.0288182	−	0.163436i	−0.995821	+	0.0913312i	$0.970888\pi$
$230$	1.04001	−	0.872668i	0.0685759	−	0.0575420i
$231$	−11.4249	+	5.44462i	−0.751706	+	0.358230i
$232$	−0.137887	+	0.0501866i	−0.00905269	+	0.00329491i
$233$	24.3439			1.59482			0.797411	−	0.603437i	$-0.206202\pi$
$233$	24.3439			1.59482			0.797411	+	0.603437i	$0.206202\pi$
$234$	−1.99734	+	18.2301i	−0.130570	+	1.19174i
$235$	9.20771			0.600645
$236$	9.19376	+	7.71448i	0.598463	+	0.502170i
$237$	−0.184232	+	0.114557i	−0.0119672	+	0.00744130i
$238$	−2.22499	−	2.33593i	−0.144225	−	0.151416i
$239$	3.34201	+	18.9535i	0.216177	+	1.22600i	0.878853	+	0.477092i	$0.158309\pi$
$239$	3.34201	+	18.9535i	0.216177	+	1.22600i	−0.662677	+	0.748906i	$0.730580\pi$
$240$	0.969026	+	1.08099i	0.0625504	+	0.0697779i
$241$	2.26167	−	12.8266i	0.145687	−	0.826232i	−0.821126	−	0.570747i	$-0.806654\pi$
$241$	2.26167	−	12.8266i	0.145687	−	0.826232i	0.966813	−	0.255485i	$-0.0822351\pi$
$242$	−1.68635	−	2.92085i	−0.108403	−	0.187759i
$243$	7.94252	−	13.4133i	0.509513	−	0.860463i
$244$	4.93261			0.315778
$245$	4.93247	+	3.17714i	0.315124	+	0.202980i
$246$	−6.17898	+	18.8753i	−0.393957	+	1.20345i
$247$	−43.7316	−	15.9170i	−2.78258	−	1.01278i
$248$	−1.44062	−	8.17014i	−0.0914792	−	0.518804i
$249$	17.4868	+	9.34739i	1.10818	+	0.592367i
$250$	−5.96965	−	5.00913i	−0.377554	−	0.316805i
$251$	−15.3520	+	26.5905i	−0.969011	+	1.67838i	−0.270582	+	0.962697i	$0.587216\pi$
$251$	−15.3520	+	26.5905i	−0.969011	+	1.67838i	−0.698429	+	0.715679i	$0.746117\pi$
$252$	−3.64708	−	7.04974i	−0.229744	−	0.444092i
$253$	2.23670	+	3.87408i	0.140620	+	0.243561i
$254$	−0.377333	+	2.13996i	−0.0236760	+	0.134273i
$255$	0.659487	+	1.64270i	0.0412987	+	0.102870i
$256$	−0.939693	−	0.342020i	−0.0587308	−	0.0213763i
$257$	0.180081	+	1.02129i	0.0112332	+	0.0637065i	0.989909	−	0.141704i	$-0.0452581\pi$
$257$	0.180081	+	1.02129i	0.0112332	+	0.0637065i	−0.978676	+	0.205411i	$0.934147\pi$
$258$	−6.80281	+	8.66776i	−0.423524	+	0.539631i
$259$	−0.0211242	+	0.0286591i	−0.00131259	+	0.00178079i
$260$	−2.56188	−	4.43731i	−0.158881	−	0.275190i
$261$	−0.422616	−	0.123202i	−0.0261592	−	0.00762599i
$262$	17.2908			1.06823
$263$	−1.90606	+	0.693750i	−0.117533	+	0.0427785i	−0.400117	−	0.916464i	$-0.631031\pi$
$263$	−1.90606	+	0.693750i	−0.117533	+	0.0427785i	0.282584	+	0.959242i	$0.408808\pi$
$264$	−4.06222	+	2.52592i	−0.250012	+	0.155460i
$265$	0.463164	+	0.168578i	0.0284519	+	0.0103556i
$266$	19.5765	−	4.73847i	1.20032	−	0.290535i
$267$	−5.69839	−	6.35682i	−0.348736	−	0.389031i
$268$	1.68197	−	0.612185i	0.102742	−	0.0373952i
$269$	−5.74892	−	9.95742i	−0.350518	−	0.607114i	0.635823	−	0.771835i	$-0.280661\pi$
$269$	−5.74892	−	9.95742i	−0.350518	−	0.607114i	−0.986340	+	0.164721i	$0.947328\pi$
$270$	0.426598	+	4.33429i	0.0259619	+	0.263776i
$271$	9.52489	−	16.4976i	0.578596	−	1.00216i	−0.417045	−	0.908886i	$-0.636934\pi$
$271$	9.52489	−	16.4976i	0.578596	−	1.00216i	0.995641	−	0.0932717i	$-0.0297325\pi$
$272$	−0.934052	−	0.783763i	−0.0566352	−	0.0475226i
$273$	7.47707	+	26.9973i	0.452533	+	1.63395i
$274$	0.415010	+	2.35364i	0.0250717	+	0.142189i
$275$	9.09187	−	7.62898i	0.548260	−	0.460045i
$276$	−2.38248	+	1.48145i	−0.143409	+	0.0891728i
$277$	−3.37549	+	1.22858i	−0.202813	+	0.0738180i	−0.441429	−	0.897296i	$-0.645528\pi$
$277$	−3.37549	+	1.22858i	−0.202813	+	0.0738180i	0.238616	+	0.971114i	$0.423306\pi$
$278$	−6.50948	−	11.2748i	−0.390413	−	0.676215i
$279$	11.0089	−	22.3213i	0.659086	−	1.33634i
$280$	1.98642	+	0.985781i	0.118712	+	0.0589117i
$281$	2.88678	−	1.05070i	0.172211	−	0.0626797i	−0.254476	−	0.967079i	$-0.581903\pi$
$281$	2.88678	−	1.05070i	0.172211	−	0.0626797i	0.426687	+	0.904399i	$0.359681\pi$
$282$	−18.8365	−	2.68964i	−1.12170	−	0.160166i
$283$	−13.3970	−	4.87612i	−0.796371	−	0.289855i	−0.0883894	−	0.996086i	$-0.528172\pi$
$283$	−13.3970	−	4.87612i	−0.796371	−	0.289855i	−0.707982	+	0.706231i	$0.750394\pi$
$284$	−10.3464	−	3.76579i	−0.613947	−	0.223459i
$285$	−10.9410	−	1.56226i	−0.648090	−	0.0925401i
$286$	15.8646	−	5.77426i	0.938096	−	0.341439i
$287$	1.90846	+	30.2780i	0.112653	+	1.78725i
$288$	−1.66660	−	2.49448i	−0.0982053	−	0.146989i
$289$	7.75663	+	13.4349i	0.456272	+	0.790287i
$290$	0.115572	−	0.0420646i	0.00678660	−	0.00247012i
$291$	13.2423	−	8.23416i	0.776275	−	0.482695i
$292$	3.88168	−	3.25712i	0.227158	−	0.190609i
$293$	3.63643	+	20.6232i	0.212443	+	1.20482i	0.885290	+	0.465040i	$0.153960\pi$
$293$	3.63643	+	20.6232i	0.212443	+	1.20482i	−0.672847	+	0.739782i	$0.734929\pi$
$294$	−9.16244	−	7.94038i	−0.534364	−	0.463092i
$295$	−7.70588	−	6.46600i	−0.448654	−	0.376465i
$296$	−0.00672834	+	0.0116538i	−0.000391077	+	0.000677365i
$297$	−14.3086	−	1.09567i	−0.830270	−	0.0635771i
$298$	−6.58129	−	11.3991i	−0.381244	−	0.660334i
$299$	9.30459	−	3.38660i	0.538099	−	0.195852i
$300$	4.96844	+	5.54253i	0.286853	+	0.319998i
$301$	−4.75024	+	16.1469i	−0.273799	+	0.930690i
$302$	19.5486	+	7.11512i	1.12490	+	0.409429i
$303$	4.31088	−	2.68055i	0.247654	−	0.153993i
$304$	7.15379	−	2.60377i	0.410298	−	0.149336i
$305$	−4.13434			−0.236732
$306$	−0.869286	−	3.55316i	−0.0496938	−	0.203121i
$307$	2.70989	+	4.69367i	0.154662	+	0.267882i	0.932936	−	0.360043i	$-0.117238\pi$
$307$	2.70989	+	4.69367i	0.154662	+	0.267882i	−0.778274	+	0.627925i	$0.783905\pi$
$308$	−4.33538	+	5.88180i	−0.247031	+	0.335146i
$309$	−13.6856	+	17.4375i	−0.778548	+	0.991982i
$310$	1.20747	+	6.84792i	0.0685799	+	0.388936i
$311$	13.2980	+	4.84007i	0.754060	+	0.274455i	0.690313	−	0.723511i	$-0.257473\pi$
$311$	13.2980	+	4.84007i	0.754060	+	0.274455i	0.0637467	+	0.997966i	$0.479695\pi$
$312$	3.94474	+	9.82588i	0.223327	+	0.556281i
$313$	−1.43889	+	8.16034i	−0.0813308	+	0.461250i	0.916757	+	0.399444i	$0.130797\pi$
$313$	−1.43889	+	8.16034i	−0.0813308	+	0.461250i	−0.998088	+	0.0618054i	$0.980314\pi$
$314$	−3.35688	−	5.81429i	−0.189440	−	0.328119i
$315$	3.05685	+	5.90884i	0.172234	+	0.332926i
$316$	−0.0626265	+	0.108472i	−0.00352302	+	0.00610204i
$317$	−1.28185	−	1.07560i	−0.0719960	−	0.0604118i	0.606079	−	0.795404i	$-0.292741\pi$
$317$	−1.28185	−	1.07560i	−0.0719960	−	0.0604118i	−0.678076	+	0.734992i	$0.737186\pi$
$318$	−0.898265	−	0.480158i	−0.0503722	−	0.0269259i
$319$	0.0703706	+	0.399092i	0.00394000	+	0.0223448i
$320$	0.787617	+	0.286669i	0.0440291	+	0.0160253i
$321$	3.06691	−	9.36867i	0.171178	−	0.522908i
$322$	−2.54269	+	3.44967i	−0.141699	+	0.192242i
$323$	9.28255			0.516495
$324$	0.393374	−	8.99140i	0.0218541	−	0.499522i
$325$	−13.1354	−	22.7512i	−0.728621	−	1.26201i
$326$	0.780683	−	4.42747i	0.0432380	−	0.245215i
$327$	−7.52384	−	8.39319i	−0.416069	−	0.464145i
$328$	1.99117	+	11.2925i	0.109944	+	0.623525i
$329$	−28.2493	+	6.83770i	−1.55743	+	0.376975i
$330$	3.40481	−	2.11714i	0.187428	−	0.116545i
$331$	17.5685	+	14.7417i	0.965650	+	0.810276i	0.981863	−	0.189592i	$-0.0607166\pi$
$331$	17.5685	+	14.7417i	0.965650	+	0.810276i	−0.0162132	+	0.999869i	$0.505161\pi$
$332$	11.4479			0.628284
$333$	−0.0369519	+	0.0162573i	−0.00202495	+	0.000890892i
$334$	−11.9687			−0.654898
$335$	−1.40976	+	0.513112i	−0.0770237	+	0.0280343i
$336$	−3.77573	−	2.59689i	−0.205983	−	0.141672i
$337$	17.8537	−	14.9810i	0.972553	−	0.816069i	−0.0103962	−	0.999946i	$-0.503309\pi$
$337$	17.8537	−	14.9810i	0.972553	−	0.816069i	0.982949	+	0.183877i	$0.0588648\pi$
$338$	−4.23174	−	23.9994i	−0.230176	−	1.30539i
$339$	−30.9005	−	4.41225i	−1.67828	−	0.239640i
$340$	0.782890	+	0.656922i	0.0424581	+	0.0356266i
$341$	−22.9120			−1.24075
$342$	21.9260	+	6.39191i	1.18562	+	0.345635i
$343$	−17.4922	−	6.08459i	−0.944491	−	0.328537i
$344$	−1.10467	+	6.26491i	−0.0595600	+	0.337781i
$345$	1.99691	−	1.24170i	0.107510	−	0.0668509i
$346$	−1.66556	−	9.44586i	−0.0895411	−	0.507813i
$347$	16.4314	−	13.7876i	0.882083	−	0.740156i	−0.0845231	−	0.996422i	$-0.526937\pi$
$347$	16.4314	−	13.7876i	0.882083	−	0.740156i	0.966606	+	0.256266i	$0.0824922\pi$
$348$	−0.248716	+	0.0522935i	−0.0133326	+	0.00280323i
$349$	−8.45401	−	7.09375i	−0.452533	−	0.379720i	0.387842	−	0.921726i	$-0.373221\pi$
$349$	−8.45401	−	7.09375i	−0.452533	−	0.379720i	−0.840375	+	0.542006i	$0.817665\pi$
$350$	10.1849	+	5.05435i	0.544405	+	0.270166i
$351$	−7.88812	+	30.7694i	−0.421037	+	1.64235i
$352$	−1.38088	+	2.39175i	−0.0736010	+	0.127481i
$353$	−5.20935	+	29.5437i	−0.277266	+	1.57245i	0.454407	+	0.890794i	$0.349851\pi$
$353$	−5.20935	+	29.5437i	−0.277266	+	1.57245i	−0.731672	+	0.681657i	$0.761260\pi$
$354$	13.8754	+	15.4786i	0.737469	+	0.822681i
$355$	8.67201	+	3.15635i	0.460262	+	0.167522i
$356$	−4.63160	−	1.68577i	−0.245475	−	0.0893454i
$357$	−3.24319	−	4.55008i	−0.171648	−	0.240816i
$358$	2.81672	−	15.9744i	0.148868	−	0.844274i
$359$	−3.41257	−	5.91075i	−0.180109	−	0.311957i	0.761809	−	0.647802i	$-0.224312\pi$
$359$	−3.41257	−	5.91075i	−0.180109	−	0.311957i	−0.941917	+	0.335845i	$0.890978\pi$
$360$	1.39689	+	2.09079i	0.0736223	+	0.110194i
$361$	−19.4782	+	33.7372i	−1.02517	+	1.77564i
$362$	1.14892	−	6.51585i	0.0603859	−	0.342465i
$363$	−2.17640	−	5.42114i	−0.114231	−	0.284536i
$364$	11.1550	+	11.7112i	0.584683	+	0.613834i
$365$	−3.25349	+	2.73000i	−0.170296	+	0.142895i
$366$	8.45774	+	1.20767i	0.442093	+	0.0631260i
$367$	−10.9675	−	9.20282i	−0.572498	−	0.480383i	0.309976	−	0.950745i	$-0.399679\pi$
$367$	−10.9675	−	9.20282i	−0.572498	−	0.480383i	−0.882474	+	0.470361i	$0.844124\pi$
$368$	−0.809883	+	1.40276i	−0.0422181	+	0.0731238i
$369$	−15.2162	+	30.8519i	−0.792122	+	1.60608i
$370$	0.00563946	−	0.00976783i	0.000293181	−	0.000507805i
$371$	−1.54618	−	0.173249i	−0.0802734	−	0.00899466i
$372$	−0.469834	−	14.3617i	−0.0243598	−	0.744620i
$373$	−17.6669	+	14.8243i	−0.914757	+	0.767573i	−0.973018	−	0.230729i	$-0.925889\pi$
$373$	−17.6669	+	14.8243i	−0.914757	+	0.767573i	0.0582606	+	0.998301i	$0.481445\pi$
$374$	−2.57962	+	2.16456i	−0.133389	+	0.111927i
$375$	−9.00950	−	10.0505i	−0.465249	−	0.519007i
$376$	−10.3230	+	3.75728i	−0.532370	+	0.193767i
$377$	0.897006			0.0461982
$378$	−4.52748	−	12.9808i	−0.232868	−	0.667662i
$379$	−8.80739			−0.452405			−0.226203	−	0.974080i	$-0.572631\pi$
$379$	−8.80739			−0.452405			−0.226203	+	0.974080i	$0.572631\pi$
$380$	−5.99606	+	2.18239i	−0.307591	+	0.111954i
$381$	−1.17093	+	3.57692i	−0.0599888	+	0.183251i
$382$	8.77751	−	7.36520i	0.449096	−	0.376837i
$383$	−9.34081	+	7.83787i	−0.477293	+	0.400497i	−0.849447	−	0.527675i	$-0.823064\pi$
$383$	−9.34081	+	7.83787i	−0.477293	+	0.400497i	0.372153	+	0.928171i	$0.378620\pi$
$384$	−1.52751	−	0.816517i	−0.0779506	−	0.0416677i
$385$	3.63376	−	4.92992i	0.185194	−	0.251252i
$386$	1.44198	−	2.49759i	0.0733950	−	0.127124i
$387$	−13.7867	+	13.1967i	−0.700816	+	0.670825i
$388$	4.50147	−	7.79677i	0.228527	−	0.395821i
$389$	−4.08756	−	3.42987i	−0.207247	−	0.173901i	0.533256	−	0.845954i	$-0.320968\pi$
$389$	−4.08756	−	3.42987i	−0.207247	−	0.173901i	−0.740503	+	0.672053i	$0.765413\pi$
$390$	−3.30635	−	8.23571i	−0.167423	−	0.417031i
$391$	−1.51295	+	1.26951i	−0.0765129	+	0.0642020i
$392$	−6.82641	−	1.54925i	−0.344786	−	0.0782490i
$393$	29.6478	+	4.23338i	1.49553	+	0.213546i
$394$	1.33879	−	7.59264i	0.0674471	−	0.382512i
$395$	0.0524913	−	0.0909177i	0.00264113	−	0.00457456i
$396$	−7.58375	+	3.33653i	−0.381098	+	0.167667i
$397$	−11.1587	−	19.3275i	−0.560041	−	0.970020i	−0.997492	−	0.0707777i	$-0.977452\pi$
$397$	−11.1587	−	19.3275i	−0.560041	−	0.970020i	0.437451	−	0.899242i	$-0.355881\pi$
$398$	−1.62891	+	9.23802i	−0.0816500	+	0.463060i
$399$	34.7272	−	3.33186i	1.73854	−	0.166801i
$400$	4.03831	+	1.46982i	0.201915	+	0.0734912i
$401$	−6.39133	−	2.32625i	−0.319168	−	0.116168i	0.177468	−	0.984127i	$-0.443209\pi$
$401$	−6.39133	−	2.32625i	−0.319168	−	0.116168i	−0.496636	+	0.867959i	$0.665432\pi$
$402$	3.03388	−	0.637886i	0.151316	−	0.0318149i
$403$	−8.80658	+	49.9446i	−0.438687	+	2.48792i
$404$	1.46541	−	2.53816i	0.0729067	−	0.126278i
$405$	−0.329712	+	7.53627i	−0.0163835	+	0.374481i
$406$	−0.323337	+	0.214879i	−0.0160469	+	0.0106643i
$407$	0.0284693	+	0.0238886i	0.00141117	+	0.00118411i
$408$	−1.40969	−	1.57257i	−0.0697900	−	0.0778540i
$409$	−10.9495	+	9.18769i	−0.541416	+	0.454302i	−0.872022	−	0.489467i	$-0.837191\pi$
$409$	−10.9495	+	9.18769i	−0.541416	+	0.454302i	0.330606	+	0.943769i	$0.392747\pi$
$410$	−1.66893	−	9.46499i	−0.0824227	−	0.467442i
$411$	0.135349	+	4.13730i	0.00667628	+	0.204078i
$412$	−2.22234	+	12.6035i	−0.109487	+	0.620930i
$413$	28.4434	+	14.1153i	1.39961	+	0.694569i
$414$	−4.44786	+	1.95687i	−0.218600	+	0.0961748i
$415$	−9.59521			−0.471011
$416$	4.68288	+	3.92941i	0.229597	+	0.192655i
$417$	−8.40109	−	20.9261i	−0.411403	−	1.02476i
$418$	−3.65095	−	20.7056i	−0.178574	−	1.01274i
$419$	−13.1051	+	10.9965i	−0.640228	+	0.537215i	−0.904088	−	0.427346i	$-0.859449\pi$
$419$	−13.1051	+	10.9965i	−0.640228	+	0.537215i	0.263860	+	0.964561i	$0.415004\pi$
$420$	3.16469	+	2.17662i	0.154421	+	0.106208i
$421$	9.27864	−	3.37715i	0.452213	−	0.164592i	−0.105865	−	0.994381i	$-0.533761\pi$
$421$	9.27864	−	3.37715i	0.452213	−	0.164592i	0.558078	+	0.829788i	$0.311539\pi$
$422$	−19.2684			−0.937972
$423$	−31.6396	−	9.22364i	−1.53837	−	0.448469i
$424$	−0.588057			−0.0285586
$425$	4.01407	+	3.36820i	0.194711	+	0.163382i
$426$	−16.8186	−	8.99021i	−0.814864	−	0.435577i
$427$	12.6842	−	3.07019i	0.613830	−	0.148577i
$428$	−0.988310	−	5.60499i	−0.0477718	−	0.270927i
$429$	28.6162	−	6.01667i	1.38160	−	0.290488i
$430$	0.925898	−	5.25103i	0.0446508	−	0.253227i
$431$	−0.771736	−	1.33669i	−0.0371732	−	0.0643859i	0.846840	−	0.531847i	$-0.178502\pi$
$431$	−0.771736	−	1.33669i	−0.0371732	−	0.0643859i	−0.884013	+	0.467461i	$0.845169\pi$
$432$	−2.24692	−	4.68523i	−0.108105	−	0.225418i
$433$	−6.19072			−0.297507			−0.148753	−	0.988874i	$-0.547526\pi$
$433$	−6.19072			−0.297507			−0.148753	+	0.988874i	$0.547526\pi$
$434$	−8.78985	−	20.1128i	−0.421926	−	0.965445i
$435$	0.208465	−	0.0438306i	0.00999513	−	0.00210152i
$436$	−6.11532	−	2.22579i	−0.292871	−	0.106596i
$437$	−2.14128	−	12.1438i	−0.102431	−	0.580916i
$438$	7.45322	−	4.63448i	0.356129	−	0.221444i
$439$	7.10898	+	5.96514i	0.339293	+	0.284701i	0.796474	−	0.604673i	$-0.206696\pi$
$439$	7.10898	+	5.96514i	0.339293	+	0.284701i	−0.457181	+	0.889374i	$0.651141\pi$
$440$	1.15740	−	2.00468i	0.0551770	−	0.0955694i
$441$	−13.7664	−	15.8583i	−0.655542	−	0.755159i
$442$	3.72689	+	6.45516i	0.177270	+	0.307041i
$443$	−0.476695	+	2.70347i	−0.0226485	+	0.128446i	−0.994036	−	0.109056i	$-0.965217\pi$
$443$	−0.476695	+	2.70347i	−0.0226485	+	0.128446i	0.971387	+	0.237501i	$0.0763284\pi$
$444$	−0.0143901	+	0.0183350i	−0.000682922	+	0.000870141i
$445$	3.88205	+	1.41295i	0.184027	+	0.0669803i
$446$	1.95751	+	11.1016i	0.0926909	+	0.525676i
$447$	−8.49377	−	21.1570i	−0.401742	−	1.00069i
$448$	−2.62930	−	0.294613i	−0.124223	−	0.0139192i
$449$	12.6188	+	21.8565i	0.595520	+	1.03147i	0.993473	+	0.114065i	$0.0363871\pi$
$449$	12.6188	+	21.8565i	0.595520	+	1.03147i	−0.397954	+	0.917406i	$0.630280\pi$
$450$	7.16218	+	10.7200i	0.337628	+	0.505345i
$451$	31.6683			1.49120
$452$	−16.9345	+	6.16366i	−0.796533	+	0.289914i
$453$	31.7772	+	16.9862i	1.49302	+	0.798080i
$454$	18.2887	+	6.65653i	0.858330	+	0.312407i
$455$	−9.34976	−	9.81593i	−0.438323	−	0.460178i
$456$	12.9038	−	2.71308i	0.604276	−	0.127052i
$457$	9.97543	−	3.63076i	0.466631	−	0.169840i	−0.0979948	−	0.995187i	$-0.531243\pi$
$457$	9.97543	−	3.63076i	0.466631	−	0.169840i	0.564625	+	0.825347i	$0.309021\pi$
$458$	−1.25570	−	2.17493i	−0.0586749	−	0.101628i
$459$	−0.620593	−	6.30530i	−0.0289668	−	0.294306i
$460$	0.678816	−	1.17574i	0.0316499	−	0.0548193i
$461$	6.68783	+	5.61175i	0.311483	+	0.261365i	0.785105	−	0.619363i	$-0.212609\pi$
$461$	6.68783	+	5.61175i	0.311483	+	0.261365i	−0.473621	+	0.880728i	$0.657054\pi$
$462$	−8.87376	+	9.02383i	−0.412845	+	0.419826i
$463$	3.97993	+	22.5713i	0.184963	+	1.04898i	0.926003	+	0.377516i	$0.123222\pi$
$463$	3.97993	+	22.5713i	0.184963	+	1.04898i	−0.741040	+	0.671461i	$0.765667\pi$
$464$	−0.112406	+	0.0943199i	−0.00521832	+	0.00437869i
$465$	0.393798	+	12.0375i	0.0182620	+	0.558225i
$466$	22.8758	−	8.32610i	1.05970	−	0.385699i
$467$	−12.7301	−	22.0493i	−0.589081	−	1.02032i	−0.994353	−	0.106122i	$-0.966157\pi$
$467$	−12.7301	−	22.0493i	−0.589081	−	1.02032i	0.405272	−	0.914196i	$-0.367177\pi$
$468$	4.35818	+	17.8138i	0.201457	+	0.823445i
$469$	3.94413	−	2.62113i	0.182123	−	0.121033i
$470$	8.65241	−	3.14922i	0.399106	−	0.145263i
$471$	−4.33237	−	10.7914i	−0.199625	−	0.497242i
$472$	11.2778	+	4.10479i	0.519103	+	0.188938i
$473$	16.5095	+	6.00897i	0.759109	+	0.276293i
$474$	−0.133941	+	0.170660i	−0.00615211	+	0.00783867i
$475$	−30.7433	+	11.1896i	−1.41060	+	0.513416i
$476$	−2.88974	−	1.43406i	−0.132451	−	0.0657302i
$477$	−1.42266	−	1.04323i	−0.0651391	−	0.0477664i
$478$	9.62293	+	16.6674i	0.440143	+	0.762349i
$479$	6.42132	−	2.33717i	0.293397	−	0.106788i	−0.191128	−	0.981565i	$-0.561215\pi$
$479$	6.42132	−	2.33717i	0.293397	−	0.106788i	0.484525	+	0.874777i	$0.338992\pi$
$480$	1.28031	+	0.684376i	0.0584378	+	0.0312373i
$481$	0.0630161	−	0.0528767i	0.00287328	−	0.00241097i
$482$	−2.26167	−	12.8266i	−0.103016	−	0.584234i
$483$	−5.20445	+	5.29246i	−0.236811	+	0.240815i
$484$	−2.58364	−	2.16793i	−0.117438	−	0.0985425i
$485$	−3.77297	+	6.53498i	−0.171322	+	0.296738i
$486$	2.87591	−	15.3209i	0.130454	−	0.694969i
$487$	−7.26911	−	12.5905i	−0.329395	−	0.570529i	0.652997	−	0.757361i	$-0.273511\pi$
$487$	−7.26911	−	12.5905i	−0.329395	−	0.570529i	−0.982392	+	0.186832i	$0.940178\pi$
$488$	4.63513	−	1.68705i	0.209823	−	0.0763692i
$489$	2.42260	−	7.40047i	0.109554	−	0.334661i
$490$	5.72165	+	1.29853i	0.258478	+	0.0586615i
$491$	15.1904	+	5.52885i	0.685532	+	0.249513i	0.661221	−	0.750191i	$-0.270038\pi$
$491$	15.1904	+	5.52885i	0.685532	+	0.249513i	0.0243113	+	0.999704i	$0.492261\pi$
$492$	0.649390	+	19.8503i	0.0292768	+	0.894921i
$493$	−0.168128	+	0.0611934i	−0.00757208	+	0.00275601i
$494$	−46.5382			−2.09385
$495$	6.35643	−	2.79656i	0.285700	−	0.125696i
$496$	−4.14809	−	7.18470i	−0.186255	−	0.322602i
$497$	−28.9497	−	3.24382i	−1.29857	−	0.145505i
$498$	19.6292	+	2.80284i	0.879606	+	0.125598i
$499$	6.11508	+	34.6803i	0.273748	+	1.55250i	0.742910	+	0.669392i	$0.233445\pi$
$499$	6.11508	+	34.6803i	0.273748	+	1.55250i	−0.469161	+	0.883113i	$0.655444\pi$
$500$	−7.32286	−	2.66530i	−0.327488	−	0.119196i
$501$	−20.5222	−	2.93035i	−0.916866	−	0.130918i
$502$	−5.33170	+	30.2376i	−0.237965	+	1.34957i
$503$	−21.3342	−	36.9519i	−0.951244	−	1.64760i	−0.742738	−	0.669582i	$-0.766473\pi$
$503$	−21.3342	−	36.9519i	−0.951244	−	1.64760i	−0.208506	−	0.978021i	$-0.566860\pi$
$504$	−5.83828	−	5.37721i	−0.260058	−	0.239520i
$505$	−1.22825	+	2.12740i	−0.0546565	+	0.0946679i
$506$	3.42682	+	2.87544i	0.152341	+	0.127829i
$507$	−1.38012	−	42.1869i	−0.0612931	−	1.87358i
$508$	0.377333	+	2.13996i	0.0167415	+	0.0949455i
$509$	−8.04687	−	2.92882i	−0.356671	−	0.129818i	0.157469	−	0.987524i	$-0.449667\pi$
$509$	−8.04687	−	2.92882i	−0.356671	−	0.129818i	−0.514140	+	0.857706i	$0.671889\pi$
$510$	1.18155	+	1.31808i	0.0523200	+	0.0583654i
$511$	7.95441	−	10.7917i	0.351882	−	0.477398i
$512$	−1.00000			−0.0441942
$513$	36.0307	+	16.3282i	1.59079	+	0.720907i
$514$	0.518524	+	0.898110i	0.0228711	+	0.0396139i
$515$	1.86269	−	10.5638i	0.0820798	−	0.465497i
$516$	−3.42800	+	10.4717i	−0.150909	+	0.460992i
$517$	5.26838	+	29.8785i	0.231703	+	1.31405i
$518$	−0.0100482	+	0.0341556i	−0.000441494	+	0.00150071i
$519$	−0.543196	−	16.6042i	−0.0238437	−	0.728844i
$520$	−3.92503	−	3.29349i	−0.172124	−	0.144429i
$521$	−13.2721			−0.581462			−0.290731	−	0.956805i	$-0.593898\pi$
$521$	−13.2721			−0.581462			−0.290731	+	0.956805i	$0.593898\pi$
$522$	−0.439266	+	0.0287714i	−0.0192262	+	0.00125929i
$523$	−21.9661			−0.960510			−0.480255	−	0.877129i	$-0.659456\pi$
$523$	−21.9661			−0.960510			−0.480255	+	0.877129i	$0.659456\pi$
$524$	16.2480	−	5.91380i	0.709798	−	0.258345i
$525$	16.2261	+	11.1601i	0.708166	+	0.487066i
$526$	−1.55384	+	1.30382i	−0.0677505	+	0.0568494i
$527$	−1.75657	−	9.96200i	−0.0765173	−	0.433951i
$528$	−2.95332	+	3.76295i	−0.128527	+	0.163761i
$529$	−15.6092	−	13.0977i	−0.678661	−	0.569464i
$530$	0.492888			0.0214097
$531$	20.0019	+	29.9378i	0.868007	+	1.29919i
$532$	16.7753	−	11.1483i	0.727301	−	0.483339i
$533$	12.1722	−	69.0319i	0.527236	−	2.99010i
$534$	−7.52889	−	4.02449i	−0.325807	−	0.174157i
$535$	0.828367	+	4.69790i	0.0358134	+	0.203108i
$536$	1.37115	−	1.15053i	0.0592247	−	0.0496954i
$537$	8.74080	−	26.7010i	0.377193	−	1.15224i
$538$	−8.80785	−	7.39067i	−0.379733	−	0.318634i
$539$	−7.48742	+	17.8235i	−0.322506	+	0.767711i
$540$	1.88329	+	3.92699i	0.0810437	+	0.168991i
$541$	−7.24109	+	12.5419i	−0.311319	+	0.539220i	−0.978648	−	0.205543i	$-0.934104\pi$
$541$	−7.24109	+	12.5419i	−0.311319	+	0.539220i	0.667329	+	0.744763i	$0.267437\pi$
$542$	3.30796	−	18.7604i	0.142089	−	0.805827i
$543$	3.56531	−	10.8912i	0.153002	−	0.467385i
$544$	−1.14578	−	0.417031i	−0.0491251	−	0.0178801i
$545$	5.12565	+	1.86558i	0.219559	+	0.0799128i
$546$	16.2598	+	22.8119i	0.695854	+	0.976258i
$547$	−4.12442	+	23.3907i	−0.176347	+	1.00012i	0.760230	+	0.649654i	$0.225086\pi$
$547$	−4.12442	+	23.3907i	−0.176347	+	1.00012i	−0.936577	+	0.350461i	$0.886025\pi$
$548$	1.19497	+	2.06976i	0.0510468	+	0.0884156i
$549$	14.2065	+	4.14149i	0.606317	+	0.176755i
$550$	5.93429	−	10.2785i	0.253039	−	0.438277i
$551$	0.193980	−	1.10011i	0.00826382	−	0.0468665i
$552$	−1.73212	+	2.20697i	−0.0737238	+	0.0939347i
$553$	−0.0935277	+	0.317916i	−0.00397720	+	0.0135192i
$554$	−2.75172	+	2.30897i	−0.116909	+	0.0980986i
$555$	0.0120612	−	0.0153678i	0.000511971	−	0.000652325i
$556$	−9.97310	−	8.36843i	−0.422954	−	0.354900i
$557$	−13.1357	+	22.7517i	−0.556577	+	0.964020i	0.441202	+	0.897408i	$0.354552\pi$
$557$	−13.1357	+	22.7517i	−0.556577	+	0.964020i	−0.997779	+	0.0666123i	$0.978781\pi$
$558$	2.71064	−	24.7405i	0.114750	−	1.04735i
$559$	19.4443	−	33.6786i	0.822407	−	1.42445i
$560$	2.20378	+	0.246935i	0.0931269	+	0.0104349i
$561$	−4.95313	+	3.07990i	−0.209121	+	0.130034i
$562$	2.35333	−	1.97468i	0.0992691	−	0.0832967i
$563$	27.4381	−	23.0233i	1.15638	−	0.970316i	0.156528	−	0.987673i	$-0.449970\pi$
$563$	27.4381	−	23.0233i	1.15638	−	0.970316i	0.999849	+	0.0173574i	$0.00552532\pi$
$564$	−18.6204	+	3.91502i	−0.784061	+	0.164852i
$565$	14.1939	−	5.16617i	0.597143	−	0.217342i
$566$	−14.2568			−0.599259
$567$	−4.58493	−	23.3662i	−0.192549	−	0.981287i
$568$	−11.0104			−0.461988
$569$	−23.6604	+	8.61168i	−0.991896	+	0.361021i	−0.786454	−	0.617649i	$-0.788085\pi$
$569$	−23.6604	+	8.61168i	−0.991896	+	0.361021i	−0.205442	+	0.978669i	$0.565863\pi$
$570$	−10.8155	+	2.27401i	−0.453012	+	0.0952477i
$571$	35.3759	−	29.6839i	1.48044	−	1.24223i	0.574721	−	0.818349i	$-0.305110\pi$
$571$	35.3759	−	29.6839i	1.48044	−	1.24223i	0.905716	−	0.423885i	$-0.139334\pi$
$572$	12.9330	−	10.8521i	0.540755	−	0.453747i
$573$	16.8537	−	10.4798i	0.704073	−	0.437799i
$574$	12.1491	+	27.7993i	0.507092	+	1.16032i
$575$	3.48046	−	6.02833i	0.145145	−	0.251399i
$576$	−2.41925	−	1.77404i	−0.100802	−	0.0739182i
$577$	10.8168	−	18.7352i	0.450307	−	0.779955i	−0.548097	−	0.836414i	$-0.684648\pi$
$577$	10.8168	−	18.7352i	0.450307	−	0.779955i	0.998405	+	0.0564591i	$0.0179811\pi$
$578$	11.8838	+	9.97173i	0.494303	+	0.414769i
$579$	3.08400	−	3.92946i	0.128167	−	0.163303i
$580$	0.0942149	−	0.0790557i	0.00391206	−	0.00328261i
$581$	29.4382	−	7.12547i	1.22130	−	0.295614i
$582$	9.62740	−	12.2667i	0.399069	−	0.508471i
$583$	−0.282017	+	1.59940i	−0.0116799	+	0.0662402i
$584$	2.53359	−	4.38831i	0.104841	−	0.181589i
$585$	−3.65287	−	14.9309i	−0.151028	−	0.617318i
$586$	10.4707	+	18.1358i	0.432540	+	0.749181i
$587$	−3.19095	+	18.0968i	−0.131705	+	0.746935i	0.845393	+	0.534144i	$0.179366\pi$
$587$	−3.19095	+	18.0968i	−0.131705	+	0.746935i	−0.977098	+	0.212790i	$0.931745\pi$
$588$	−11.3256	−	4.32778i	−0.467062	−	0.178475i
$589$	59.3491	+	21.6013i	2.44544	+	0.890066i
$590$	−9.45267	−	3.44049i	−0.389160	−	0.141643i
$591$	4.15450	−	12.6910i	0.170893	−	0.522038i
$592$	−0.00233673	+	0.0132522i	−9.60389e−5	+	0.000544664i
$593$	−8.36042	+	14.4807i	−0.343321	+	0.594650i	−0.985047	−	0.172284i	$-0.944885\pi$
$593$	−8.36042	+	14.4807i	−0.343321	+	0.594650i	0.641726	+	0.766934i	$0.278219\pi$
$594$	−13.8204	+	3.86424i	−0.567059	+	0.158552i
$595$	2.42208	+	1.20198i	0.0992957	+	0.0492764i
$596$	−10.0831	−	8.46075i	−0.413021	−	0.346566i
$597$	−5.05482	+	15.4412i	−0.206880	+	0.631968i
$598$	7.58518	−	6.36472i	0.310181	−	0.260273i
$599$	5.38758	+	30.5545i	0.220130	+	1.24842i	0.871779	+	0.489900i	$0.162967\pi$
$599$	5.38758	+	30.5545i	0.220130	+	1.24842i	−0.651648	+	0.758521i	$0.725922\pi$
$600$	6.56446	+	3.50897i	0.267993	+	0.143253i
$601$	−6.31452	+	35.8114i	−0.257574	+	1.46078i	0.531802	+	0.846868i	$0.321515\pi$
$601$	−6.31452	+	35.8114i	−0.257574	+	1.46078i	−0.789377	+	0.613909i	$0.789596\pi$
$602$	1.05879	+	16.7978i	0.0431529	+	0.684626i
$603$	5.35825	−	0.350959i	0.218205	−	0.0142922i
$604$	20.8032			0.846471
$605$	2.16552	+	1.81709i	0.0880409	+	0.0738751i
$606$	3.13410	−	3.99330i	0.127314	−	0.162217i
$607$	−3.43780	−	19.4967i	−0.139536	−	0.791347i	−0.971593	−	0.236657i	$-0.923948\pi$
$607$	−3.43780	−	19.4967i	−0.139536	−	0.791347i	0.832057	−	0.554690i	$-0.187163\pi$
$608$	5.83182	−	4.89348i	0.236512	−	0.198457i
$609$	−0.607023	+	0.289280i	−0.0245978	+	0.0117222i
$610$	−3.88501	+	1.41403i	−0.157299	+	0.0572523i
$611$	67.1555			2.71682
$612$	−2.03212	−	3.04157i	−0.0821434	−	0.122948i
$613$	9.73673			0.393263			0.196632	−	0.980477i	$-0.437000\pi$
$613$	9.73673			0.393263			0.196632	+	0.980477i	$0.437000\pi$
$614$	4.15180	+	3.48377i	0.167553	+	0.140594i
$615$	−0.544296	−	16.6378i	−0.0219481	−	0.670902i
$616$	−2.06223	+	7.00987i	−0.0830896	+	0.282436i
$617$	−2.89439	−	16.4149i	−0.116524	−	0.660839i	−0.985984	−	0.166837i	$-0.946645\pi$
$617$	−2.89439	−	16.4149i	−0.116524	−	0.660839i	0.869461	−	0.494002i	$-0.164467\pi$
$618$	−6.89633	+	21.0666i	−0.277411	+	0.847424i
$619$	4.82520	−	27.3651i	0.193941	−	1.09990i	−0.719977	−	0.693998i	$-0.755848\pi$
$619$	4.82520	−	27.3651i	0.193941	−	1.09990i	0.913919	−	0.405898i	$-0.133041\pi$
$620$	3.47678	+	6.02196i	0.139631	+	0.241848i
$621$	−8.10567	+	2.26637i	−0.325269	+	0.0909464i
$622$	14.1514			0.567420
$623$	−12.9594	−	1.45211i	−0.519208	−	0.0581774i
$624$	7.06750	+	7.88412i	0.282926	+	0.315617i
$625$	−14.0538	−	5.11516i	−0.562152	−	0.204606i
$626$	1.43889	+	8.16034i	0.0575095	+	0.326153i
$627$	−1.19070	−	36.3969i	−0.0475520	−	1.45355i
$628$	−5.14304	−	4.31552i	−0.205230	−	0.172208i
$629$	−0.00820399	+	0.0142097i	−0.000327114	+	0.000566579i
$630$	4.89345	+	4.50699i	0.194960	+	0.179563i
$631$	5.62446	+	9.74185i	0.223906	+	0.387817i	0.955991	−	0.293397i	$-0.0947858\pi$
$631$	5.62446	+	9.74185i	0.223906	+	0.387817i	−0.732085	+	0.681214i	$0.761452\pi$
$632$	−0.0217500	+	0.123350i	−0.000865167	+	0.00490661i
$633$	−33.0388	−	4.71757i	−1.31317	−	0.187507i
$634$	−1.57243	−	0.572316i	−0.0624490	−	0.0227296i
$635$	−0.316268	−	1.79364i	−0.0125507	−	0.0711785i
$636$	−1.00832	−	0.143976i	−0.0399824	−	0.00570904i
$637$	35.9745	+	23.1721i	1.42536	+	0.918113i
$638$	0.202624	+	0.350955i	0.00802197	+	0.0138945i
$639$	−26.6370	−	19.5329i	−1.05375	−	0.772710i
$640$	0.838165			0.0331314
$641$	−5.10157	+	1.85682i	−0.201500	+	0.0733400i	−0.440799	−	0.897606i	$-0.645305\pi$
$641$	−5.10157	+	1.85682i	−0.201500	+	0.0733400i	0.239299	+	0.970946i	$0.423083\pi$
$642$	−0.322322	−	9.85261i	−0.0127210	−	0.388852i
$643$	−6.44930	−	2.34735i	−0.254336	−	0.0925706i	0.211706	−	0.977333i	$-0.432098\pi$
$643$	−6.44930	−	2.34735i	−0.254336	−	0.0925706i	−0.466042	+	0.884763i	$0.654320\pi$
$644$	−1.20950	+	4.11128i	−0.0476608	+	0.162007i
$645$	2.87323	−	8.77703i	0.113133	−	0.345595i
$646$	8.72275	−	3.17482i	0.343192	−	0.124912i
$647$	−4.25208	−	7.36483i	−0.167167	−	0.289541i	0.770256	−	0.637735i	$-0.220128\pi$
$647$	−4.25208	−	7.36483i	−0.167167	−	0.289541i	−0.937423	+	0.348194i	$0.886795\pi$
$648$	−2.70559	−	8.58369i	−0.106286	−	0.337199i
$649$	16.5727	−	28.7048i	0.650537	−	1.12676i
$650$	−20.1246	−	16.8865i	−0.789352	−	0.662345i
$651$	−10.1473	−	36.6386i	−0.397704	−	1.43598i
$652$	−0.780683	−	4.42747i	−0.0305739	−	0.173393i
$653$	−20.7161	+	17.3829i	−0.810683	+	0.680244i	−0.950771	−	0.309895i	$-0.899706\pi$
$653$	−20.7161	+	17.3829i	−0.810683	+	0.680244i	0.140088	+	0.990139i	$0.455262\pi$
$654$	−9.94074	−	5.31372i	−0.388714	−	0.207783i
$655$	−13.6185	+	4.95674i	−0.532120	+	0.193676i
$656$	5.73336	+	9.93047i	0.223850	+	0.387720i
$657$	13.9144	−	6.12175i	0.542853	−	0.238832i
$658$	−24.2070	+	16.0872i	−0.943688	+	0.627143i
$659$	−18.9483	+	6.89660i	−0.738120	+	0.268654i	−0.683598	−	0.729859i	$-0.739586\pi$
$659$	−18.9483	+	6.89660i	−0.738120	+	0.268654i	−0.0545219	+	0.998513i	$0.517363\pi$
$660$	2.47537	−	3.15397i	0.0963535	−	0.122768i
$661$	−10.5264	−	3.83130i	−0.409429	−	0.149020i	0.129091	−	0.991633i	$-0.458794\pi$
$661$	−10.5264	−	3.83130i	−0.409429	−	0.149020i	−0.538520	+	0.842613i	$0.681016\pi$
$662$	21.5509	+	7.84389i	0.837600	+	0.304861i
$663$	4.80990	+	11.9809i	0.186801	+	0.465298i
$664$	10.7575	−	3.91541i	0.417472	−	0.151947i
$665$	−14.0605	+	9.34410i	−0.545241	+	0.362349i
$666$	−0.0291631	+	0.0279151i	−0.00113005	+	0.00108169i
$667$	0.118839	+	0.205835i	0.00460146	+	0.00796996i
$668$	−11.2469	+	4.09353i	−0.435155	+	0.158384i
$669$	0.638412	+	19.5147i	0.0246824	+	0.754483i
$670$	−1.14925	+	0.964336i	−0.0443994	+	0.0372555i
$671$	−2.36555	−	13.4157i	−0.0913210	−	0.517907i
$672$	−4.43622	−	1.14890i	−0.171131	−	0.0443199i
$673$	−23.6144	−	19.8148i	−0.910268	−	0.763806i	0.0619020	−	0.998082i	$-0.480283\pi$
$673$	−23.6144	−	19.8148i	−0.910268	−	0.763806i	−0.972170	+	0.234277i	$0.924728\pi$
$674$	11.6532	−	20.1839i	0.448864	−	0.777454i
$675$	9.65607	+	20.1347i	0.371662	+	0.774984i
$676$	−12.1848	−	21.1047i	−0.468647	−	0.811720i
$677$	−44.3034	+	16.1251i	−1.70272	+	0.619739i	−0.996130	−	0.0878874i	$-0.971988\pi$
$677$	−44.3034	+	16.1251i	−1.70272	+	0.619739i	−0.706587	+	0.707626i	$0.749766\pi$
$678$	−30.5460	+	6.42243i	−1.17311	+	0.246652i
$679$	6.72259	−	22.8512i	0.257989	−	0.876948i
$680$	0.960356	+	0.349541i	0.0368280	+	0.0134043i
$681$	29.7291	+	15.8914i	1.13922	+	0.608959i
$682$	−21.5302	+	7.83637i	−0.824436	+	0.300070i
$683$	15.6234			0.597814			0.298907	−	0.954282i	$-0.403378\pi$
$683$	15.6234			0.597814			0.298907	+	0.954282i	$0.403378\pi$
$684$	22.7899	−	1.49271i	0.871393	−	0.0570752i
$685$	−1.00159	−	1.73480i	−0.0382686	−	0.0662832i
$686$	−18.5184	+	0.265043i	−0.707034	+	0.0101194i
$687$	−1.62059	−	4.03670i	−0.0618295	−	0.154010i
$688$	1.10467	+	6.26491i	0.0421153	+	0.238848i
$689$	3.37804	+	1.22950i	0.128693	+	0.0468404i
$690$	1.45180	−	1.84980i	0.0552691	−	0.0704207i
$691$	−2.95153	+	16.7389i	−0.112281	+	0.636779i	0.875779	+	0.482712i	$0.160348\pi$
$691$	−2.95153	+	16.7389i	−0.112281	+	0.636779i	−0.988060	+	0.154067i	$0.950763\pi$
$692$	−4.79579	−	8.30655i	−0.182309	−	0.315768i
$693$	−17.4248	+	13.3002i	−0.661914	+	0.505232i
$694$	10.7248	−	18.5759i	0.407109	−	0.705133i
$695$	8.35910	+	7.01412i	0.317079	+	0.266061i
$696$	−0.215831	+	0.134206i	−0.00818105	+	0.00508705i
$697$	2.42788	+	13.7692i	0.0919623	+	0.521544i
$698$	−10.3704	−	3.77451i	−0.392524	−	0.142867i
$699$	41.2627	−	8.67565i	1.56070	−	0.328143i
$700$	11.2994	+	1.26609i	0.427075	+	0.0478539i
$701$	48.7133			1.83988			0.919938	−	0.392064i	$-0.128239\pi$
$701$	48.7133			1.83988			0.919938	+	0.392064i	$0.128239\pi$
$702$	3.11135	+	31.6117i	0.117430	+	1.19311i
$703$	−0.0512222	−	0.0887195i	−0.00193188	−	0.00334612i
$704$	−0.479574	+	2.71980i	−0.0180746	+	0.102506i
$705$	15.6070	−	3.28143i	0.587793	−	0.123586i
$706$	5.20935	+	29.5437i	0.196056	+	1.11189i
$707$	2.18847	−	7.43897i	0.0823059	−	0.279771i
$708$	18.3326	+	9.79951i	0.688982	+	0.368288i
$709$	1.15956	+	0.972986i	0.0435482	+	0.0365413i	0.664302	−	0.747464i	$-0.268729\pi$
$709$	1.15956	+	0.972986i	0.0435482	+	0.0365413i	−0.620754	+	0.784006i	$0.713173\pi$
$710$	9.22856			0.346342
$711$	−0.271446	+	0.259830i	−0.0101800	+	0.00974439i
$712$	−4.92885			−0.184716
$713$	−12.6275	+	4.59602i	−0.472902	+	0.172122i
$714$	−4.60382	−	3.16644i	−0.172294	−	0.118501i
$715$	−10.8400	+	9.09581i	−0.405392	+	0.340164i
$716$	−2.81672	−	15.9744i	−0.105266	−	0.596992i
$717$	12.4193	+	30.9349i	0.463807	+	1.15529i
$718$	−5.22836	−	4.38712i	−0.195121	−	0.163726i
$719$	25.1197			0.936806			0.468403	−	0.883515i	$-0.344829\pi$
$719$	25.1197			0.936806			0.468403	+	0.883515i	$0.344829\pi$
$720$	2.02773	+	1.48694i	0.0755692	+	0.0554148i
$721$	2.13003	+	33.7931i	0.0793263	+	1.25852i
$722$	−6.76470	+	38.3645i	−0.251756	+	1.42778i
$723$	−0.737608	−	22.5469i	−0.0274319	−	0.838529i
$724$	−1.14892	−	6.51585i	−0.0426993	−	0.242160i
$725$	0.483063	−	0.405338i	0.0179405	−	0.0150539i
$726$	−3.89928	−	4.34983i	−0.144716	−	0.161437i
$727$	−33.5994	−	28.1932i	−1.24613	−	1.04563i	−0.997019	−	0.0771552i	$-0.975416\pi$
$727$	−33.5994	−	28.1932i	−1.24613	−	1.04563i	−0.249114	−	0.968474i	$-0.580139\pi$
$728$	14.4878	+	7.18969i	0.536953	+	0.266468i
$729$	8.68228	−	25.5660i	0.321566	−	0.946887i
$730$	−2.12357	+	3.67812i	−0.0785967	+	0.136133i
$731$	−1.34695	+	7.63892i	−0.0498187	+	0.282536i
$732$	8.36072	−	1.75788i	0.309021	−	0.0649730i
$733$	14.4962	+	5.27620i	0.535431	+	0.194881i	0.595562	−	0.803310i	$-0.296930\pi$
$733$	14.4962	+	5.27620i	0.535431	+	0.194881i	−0.0601308	+	0.998191i	$0.519152\pi$
$734$	−13.4536	−	4.89672i	−0.496582	−	0.180741i
$735$	9.49276	+	3.62739i	0.350146	+	0.133798i
$736$	−0.281269	+	1.59516i	−0.0103677	+	0.0587983i
$737$	−2.47165	−	4.28102i	−0.0910443	−	0.157693i
$738$	−3.74656	+	34.1955i	−0.137913	+	1.25875i
$739$	−3.73935	+	6.47675i	−0.137554	+	0.238251i	−0.926570	−	0.376122i	$-0.877258\pi$
$739$	−3.73935	+	6.47675i	−0.137554	+	0.238251i	0.789016	+	0.614373i	$0.210591\pi$
$740$	0.00195856	−	0.0111076i	7.19982e−5	−	0.000408322i
$741$	−79.7972	−	11.3942i	−2.93142	−	0.418575i
$742$	−1.51218	+	0.366022i	−0.0555140	+	0.0134371i
$743$	36.9867	−	31.0355i	1.35691	−	1.13858i	0.379987	−	0.924992i	$-0.375928\pi$
$743$	36.9867	−	31.0355i	1.35691	−	1.13858i	0.976923	−	0.213591i	$-0.0685161\pi$
$744$	−5.35349	−	13.3349i	−0.196269	−	0.488881i
$745$	8.45132	+	7.09150i	0.309632	+	0.259812i
$746$	−11.5313	+	19.9727i	−0.422189	+	0.731253i
$747$	32.9712	+	9.61182i	1.20635	+	0.351678i
$748$	−1.68373	+	2.91630i	−0.0615632	+	0.106631i
$749$	−6.03013	−	13.7980i	−0.220336	−	0.504170i
$750$	−11.9036	−	6.36297i	−0.434660	−	0.232343i
$751$	−35.4782	+	29.7697i	−1.29462	+	1.08631i	−0.303569	+	0.952810i	$0.598178\pi$
$751$	−35.4782	+	29.7697i	−1.29462	+	1.08631i	−0.991048	+	0.133503i	$0.957377\pi$
$752$	−8.41542	+	7.06138i	−0.306879	+	0.257502i
$753$	−16.5453	+	50.5418i	−0.602942	+	1.84184i
$754$	0.842910	−	0.306794i	0.0306970	−	0.0111728i
$755$	−17.4365			−0.634580
$756$	−8.69414	−	10.6495i	−0.316203	−	0.387319i
$757$	−10.2663			−0.373136			−0.186568	−	0.982442i	$-0.559736\pi$
$757$	−10.2663			−0.373136			−0.186568	+	0.982442i	$0.559736\pi$
$758$	−8.27624	+	3.01230i	−0.300606	+	0.109412i
$759$	5.17182	+	5.76941i	0.187725	+	0.209416i
$760$	−4.88803	+	4.10154i	−0.177307	+	0.148779i
$761$	21.9819	−	18.4450i	0.796842	−	0.668630i	−0.150587	−	0.988597i	$-0.548116\pi$
$761$	21.9819	−	18.4450i	0.796842	−	0.668630i	0.947429	+	0.319967i	$0.103672\pi$
$762$	0.123061	+	3.76169i	0.00445804	+	0.136272i
$763$	−17.1109	−	1.91728i	−0.619456	−	0.0694102i
$764$	5.72911	−	9.92311i	0.207272	−	0.359006i
$765$	1.70325	+	2.54934i	0.0615811	+	0.0921714i
$766$	−6.09678	+	10.5599i	−0.220286	+	0.381546i
$767$	−56.2021	−	47.1591i	−2.02934	−	1.70282i
$768$	−1.71466	−	0.244834i	−0.0618724	−	0.00883470i
$769$	−12.9496	+	10.8660i	−0.466976	+	0.391840i	−0.845690	−	0.533674i	$-0.820811\pi$
$769$	−12.9496	+	10.8660i	−0.466976	+	0.391840i	0.378714	+	0.925514i	$0.376366\pi$
$770$	1.72849	−	5.87543i	0.0622904	−	0.211736i
$771$	0.669204	+	1.66690i	0.0241008	+	0.0600321i
$772$	0.500795	−	2.84015i	0.0180240	−	0.102219i
$773$	−13.5515	+	23.4718i	−0.487413	+	0.844223i	−0.999895	−	0.0144743i	$-0.995393\pi$
$773$	−13.5515	+	23.4718i	−0.487413	+	0.844223i	0.512483	+	0.858698i	$0.328726\pi$
$774$	−8.44170	+	17.1161i	−0.303431	+	0.615227i
$775$	17.8263	+	30.8761i	0.640340	+	1.10910i
$776$	1.56334	−	8.86616i	0.0561208	−	0.318277i
$777$	−0.0255918	+	0.0561051i	−0.000918100	+	0.00201276i
$778$	−5.01413	−	1.82500i	−0.179765	−	0.0654293i
$779$	−82.0305	−	29.8567i	−2.93905	−	1.06973i
$780$	−5.92373	−	6.60819i	−0.212103	−	0.236611i
$781$	−5.28032	+	29.9462i	−0.188945	+	1.07156i
$782$	−0.987505	+	1.71041i	−0.0353131	+	0.0611641i
$783$	−0.760236	−	0.0582143i	−0.0271686	−	0.00208041i
$784$	−6.94460	+	0.878948i	−0.248021	+	0.0313910i
$785$	4.31072	+	3.61712i	0.153856	+	0.129101i
$786$	29.3077	−	6.16207i	1.04537	−	0.219794i
$787$	−15.1572	+	12.7184i	−0.540295	+	0.453362i	−0.871639	−	0.490148i	$-0.836943\pi$
$787$	−15.1572	+	12.7184i	−0.540295	+	0.453362i	0.331343	+	0.943510i	$0.392498\pi$
$788$	−1.33879	−	7.59264i	−0.0476923	−	0.270477i
$789$	−2.98352	+	1.85518i	−0.106216	+	0.0660462i
$790$	0.0182301	−	0.103388i	0.000648596	−	0.00367837i
$791$	−39.7106	+	26.3903i	−1.41195	+	0.938332i
$792$	−5.98523	+	5.72910i	−0.212676	+	0.203575i
$793$	−30.1534			−1.07078
$794$	−17.0962	−	14.3454i	−0.606721	−	0.509099i
$795$	0.845136	+	0.120676i	0.0299739	+	0.00427994i
$796$	1.62891	+	9.23802i	0.0577353	+	0.327433i
$797$	−21.2713	+	17.8487i	−0.753466	+	0.632233i	−0.936417	−	0.350889i	$-0.885880\pi$
$797$	−21.2713	+	17.8487i	−0.753466	+	0.632233i	0.182951	+	0.983122i	$0.441435\pi$
$798$	31.4934	−	15.0083i	1.11485	−	0.531289i
$799$	−12.5871	+	4.58132i	−0.445299	+	0.162075i
$800$	4.29748			0.151939
$801$	−11.9241	−	8.74396i	−0.421319	−	0.308953i
$802$	−6.80151			−0.240170
$803$	−10.7203	−	8.99537i	−0.378310	−	0.317440i
$804$	2.63275	−	1.63707i	0.0928498	−	0.0577349i
$805$	1.01376	−	3.44593i	0.0357302	−	0.121453i
$806$	8.80658	+	49.9446i	0.310199	+	1.75922i
$807$	−13.2930	−	14.8289i	−0.467935	−	0.522003i
$808$	0.508931	−	2.88629i	0.0179041	−	0.101539i
$809$	5.81235	+	10.0673i	0.204351	+	0.353947i	0.949926	−	0.312475i	$-0.101158\pi$
$809$	5.81235	+	10.0673i	0.204351	+	0.353947i	−0.745574	+	0.666422i	$0.767825\pi$
$810$	2.26773	+	7.19455i	0.0796799	+	0.252791i
$811$	16.7983			0.589870			0.294935	−	0.955517i	$-0.404702\pi$
$811$	16.7983			0.589870			0.294935	+	0.955517i	$0.404702\pi$
$812$	−0.230345	+	0.312508i	−0.00808351	+	0.0109669i
$813$	10.2652	−	31.3577i	0.360017	−	1.09976i
$814$	0.0349228	+	0.0127109i	0.00122404	+	0.000445515i
$815$	0.654341	+	3.71095i	0.0229206	+	0.129989i
$816$	−1.86253	−	0.995594i	−0.0652014	−	0.0348528i
$817$	−37.0995	−	31.1302i	−1.29795	−	1.08911i
$818$	−7.14675	+	12.3785i	−0.249880	+	0.432805i
$819$	22.2948	+	43.0955i	0.779045	+	1.50588i
$820$	−4.80550	−	8.32337i	−0.167815	−	0.290665i
$821$	−9.32811	+	52.9024i	−0.325553	+	1.84630i	0.180204	+	0.983629i	$0.442324\pi$
$821$	−9.32811	+	52.9024i	−0.325553	+	1.84630i	−0.505758	+	0.862676i	$0.668787\pi$
$822$	1.54223	+	3.84150i	0.0537913	+	0.133988i
$823$	−25.3431	−	9.22413i	−0.883404	−	0.321533i	−0.139822	−	0.990177i	$-0.544653\pi$
$823$	−25.3431	−	9.22413i	−0.883404	−	0.321533i	−0.743583	+	0.668644i	$0.766875\pi$
$824$	2.22234	+	12.6035i	0.0774188	+	0.439064i
$825$	12.6918	−	16.1712i	0.441872	−	0.563009i
$826$	31.5558	+	3.53583i	1.09797	+	0.123027i
$827$	4.21459	+	7.29988i	0.146556	+	0.253842i	0.929952	−	0.367680i	$-0.119848\pi$
$827$	4.21459	+	7.29988i	0.146556	+	0.253842i	−0.783397	+	0.621522i	$0.786515\pi$
$828$	−3.51033	+	3.36011i	−0.121992	+	0.116772i
$829$	47.9427			1.66512			0.832559	−	0.553936i	$-0.186875\pi$
$829$	47.9427			1.66512			0.832559	+	0.553936i	$0.186875\pi$
$830$	−9.01655	+	3.28176i	−0.312969	+	0.113911i
$831$	−5.28358	+	3.28538i	−0.183285	+	0.113968i
$832$	5.74441	+	2.09079i	0.199151	+	0.0724852i
$833$	−8.32356	−	1.88903i	−0.288394	−	0.0654511i
$834$	−15.0516	−	16.7908i	−0.521194	−	0.581416i
$835$	9.42675	−	3.43106i	0.326226	−	0.118737i
$836$	−10.5125	−	18.2082i	−0.363582	−	0.629743i
$837$	10.7051	−	41.7578i	0.370024	−	1.44336i
$838$	−8.55377	+	14.8156i	−0.295485	+	0.511795i
$839$	36.4230	+	30.5625i	1.25746	+	1.05514i	0.995948	+	0.0899365i	$0.0286664\pi$
$839$	36.4230	+	30.5625i	1.25746	+	1.05514i	0.261515	+	0.965200i	$0.415778\pi$
$840$	3.71828	+	0.962971i	0.128293	+	0.0332257i
$841$	−5.03206	−	28.5382i	−0.173519	−	0.984077i
$842$	7.56402	−	6.34696i	0.260673	−	0.218731i
$843$	4.51862	−	2.80972i	0.155630	−	0.0967719i
$844$	−18.1064	+	6.59019i	−0.623248	+	0.226844i
$845$	10.2129	+	17.6892i	0.351334	+	0.608528i
$846$	−32.8862	+	2.15401i	−1.13065	+	0.0740563i
$847$	−7.99321	−	3.96670i	−0.274650	−	0.136298i
$848$	−0.552592	+	0.201127i	−0.0189761	+	0.00690674i
$849$	−24.4456	−	3.49056i	−0.838971	−	0.119796i
$850$	4.92398	+	1.79218i	0.168891	+	0.0614714i
$851$	0.0204822	+	0.00745490i	0.000702120	+	0.000255551i
$852$	−18.8791	−	2.69573i	−0.646789	−	0.0923543i
$853$	−26.0799	+	9.49231i	−0.892959	+	0.325010i	−0.747428	−	0.664343i	$-0.768711\pi$
$853$	−26.0799	+	9.49231i	−0.892959	+	0.325010i	−0.145531	+	0.989354i	$0.546489\pi$
$854$	10.8692	−	7.22327i	0.371935	−	0.247175i
$855$	−19.1017	+	1.25114i	−0.653264	+	0.0427880i
$856$	−2.84573	−	4.92894i	−0.0972649	−	0.168468i
$857$	13.1400	−	4.78258i	0.448855	−	0.163370i	−0.107695	−	0.994184i	$-0.534347\pi$
$857$	13.1400	−	4.78258i	0.448855	−	0.163370i	0.556550	+	0.830814i	$0.312125\pi$
$858$	24.8326	−	15.4411i	0.847771	−	0.527152i
$859$	21.1212	−	17.7228i	0.720646	−	0.604694i	−0.206918	−	0.978358i	$-0.566343\pi$
$859$	21.1212	−	17.7228i	0.720646	−	0.604694i	0.927564	+	0.373664i	$0.121899\pi$
$860$	−0.925898	−	5.25103i	−0.0315729	−	0.179059i
$861$	14.0253	+	50.6408i	0.477980	+	1.72583i
$862$	−1.18237	−	0.992124i	−0.0402716	−	0.0337919i
$863$	−3.72691	+	6.45519i	−0.126865	+	0.219737i	−0.922461	−	0.386091i	$-0.873825\pi$
$863$	−3.72691	+	6.45519i	−0.126865	+	0.219737i	0.795595	+	0.605829i	$0.207158\pi$
$864$	−3.71385	−	3.63418i	−0.126348	−	0.123637i
$865$	4.01966	+	6.96226i	0.136673	+	0.236724i
$866$	−5.81737	+	2.11735i	−0.197682	+	0.0719505i
$867$	17.9353	+	20.0077i	0.609116	+	0.679497i
$868$	−15.1387	−	15.8935i	−0.513842	−	0.539462i
$869$	0.325057	+	0.118311i	0.0110268	+	0.00401343i
$870$	0.180902	−	0.112486i	0.00613315	−	0.00381365i
$871$	−10.2820	+	3.74233i	−0.348391	+	0.126804i
$872$	−6.50779			−0.220381
$873$	19.5110	−	18.6761i	0.660348	−	0.632090i
$874$	−6.16556	−	10.6791i	−0.208553	−	0.361225i
$875$	−20.4896	−	2.29587i	−0.692676	−	0.0776145i
$876$	5.41865	−	6.90414i	0.183079	−	0.233269i
$877$	−5.10655	−	28.9607i	−0.172436	−	0.977933i	−0.941062	−	0.338235i	$-0.890170\pi$
$877$	−5.10655	−	28.9607i	−0.172436	−	0.977933i	0.768626	−	0.639699i	$-0.220941\pi$
$878$	8.72045	+	3.17398i	0.294301	+	0.107117i
$879$	13.5134	+	33.6602i	0.455796	+	1.13533i
$880$	0.401962	−	2.27964i	0.0135501	−	0.0768466i
$881$	18.3782	+	31.8319i	0.619176	+	1.07244i	0.989636	+	0.143596i	$0.0458665\pi$
$881$	18.3782	+	31.8319i	0.619176	+	1.07244i	−0.370461	+	0.928848i	$0.620800\pi$
$882$	−18.3600	−	10.1936i	−0.618215	−	0.343235i
$883$	8.75991	−	15.1726i	0.294794	−	0.510599i	−0.680143	−	0.733080i	$-0.738082\pi$
$883$	8.75991	−	15.1726i	0.294794	−	0.510599i	0.974937	+	0.222481i	$0.0714155\pi$
$884$	5.70992	+	4.79120i	0.192046	+	0.161145i
$885$	−15.3657	−	8.21360i	−0.516514	−	0.276097i
$886$	0.476695	+	2.70347i	0.0160149	+	0.0908249i
$887$	27.9150	+	10.1602i	0.937293	+	0.341147i	0.765096	−	0.643916i	$-0.222691\pi$
$887$	27.9150	+	10.1602i	0.937293	+	0.341147i	0.172197	+	0.985063i	$0.444914\pi$
$888$	−0.00725130	+	0.0221510i	−0.000243338	+	0.000743338i
$889$	2.30228	+	5.26804i	0.0772160	+	0.176684i
$890$	4.13119			0.138478
$891$	−24.6434	+	3.24214i	−0.825586	+	0.108616i
$892$	5.63643	+	9.76259i	0.188722	+	0.326876i
$893$	14.5225	−	82.3614i	0.485978	−	2.75612i
$894$	−15.2176	−	16.9760i	−0.508954	−	0.567762i
$895$	2.36088	+	13.3892i	0.0789154	+	0.447551i
$896$	−2.57149	+	0.622427i	−0.0859076	+	0.0207938i
$897$	14.5643	−	9.05621i	0.486288	−	0.302378i
$898$	19.3332	+	16.2225i	0.645156	+	0.541351i
$899$	−1.21735			−0.0406008
$900$	10.3967	+	7.62389i	0.346557	+	0.254130i
$901$	−0.717028			−0.0238877
$902$	29.7584	−	10.8312i	0.990847	−	0.360639i
$903$	−2.29721	+	29.0617i	−0.0764464	+	0.967112i
$904$	−13.8052	+	11.5839i	−0.459152	+	0.385275i
$905$	0.962984	+	5.46136i	0.0320107	+	0.181542i
$906$	35.6704	+	5.09334i	1.18507	+	0.169215i
$907$	−38.1227	−	31.9888i	−1.26584	−	1.06217i	−0.995034	−	0.0995373i	$-0.968264\pi$
$907$	−38.1227	−	31.9888i	−1.26584	−	1.06217i	−0.270811	−	0.962633i	$-0.587292\pi$
$908$	19.4624			0.645882
$909$	6.35162	−	6.07981i	0.210670	−	0.201654i
$910$	−12.1431	−	6.02615i	−0.402541	−	0.199765i
$911$	−3.88199	+	22.0158i	−0.128616	+	0.729417i	0.850478	+	0.526010i	$0.176313\pi$
$911$	−3.88199	+	22.0158i	−0.128616	+	0.729417i	−0.979094	+	0.203407i	$0.934799\pi$
$912$	11.1977	−	6.96282i	0.370792	−	0.230562i
$913$	−5.49010	−	31.1359i	−0.181696	−	1.03045i
$914$	8.13204	−	6.82359i	0.268984	−	0.225704i
$915$	−7.00767	+	1.47339i	−0.231666	+	0.0487088i
$916$	−1.92384	−	1.61429i	−0.0635655	−	0.0533377i
$917$	38.1008	−	25.3205i	1.25820	−	0.836157i
$918$	−2.73970	−	5.71278i	−0.0904237	−	0.188550i
$919$	−0.523622	+	0.906941i	−0.0172727	+	0.0299172i	−0.874533	−	0.484967i	$-0.838832\pi$
$919$	−0.523622	+	0.906941i	−0.0172727	+	0.0299172i	0.857260	+	0.514884i	$0.172165\pi$
$920$	0.235750	−	1.33701i	0.00777245	−	0.0440798i
$921$	6.26597	+	6.98998i	0.206471	+	0.230328i
$922$	8.20384	+	2.98595i	0.270179	+	0.0983371i
$923$	63.2484	+	23.0205i	2.08185	+	0.757730i
$924$	−5.25228	+	11.5146i	−0.172787	+	0.378803i
$925$	0.0100420	−	0.0569512i	0.000330180	−	0.00187255i
$926$	11.4597	+	19.8489i	0.376591	+	0.652274i
$927$	−16.9827	+	34.4336i	−0.557784	+	1.13095i
$928$	−0.0733679	+	0.127077i	−0.00240842	+	0.00417150i
$929$	−1.37352	+	7.78963i	−0.0450638	+	0.255570i	−0.999014	−	0.0443954i	$-0.985864\pi$
$929$	−1.37352	+	7.78963i	−0.0450638	+	0.255570i	0.953950	+	0.299965i	$0.0969750\pi$
$930$	4.48711	+	11.1768i	0.147138	+	0.366503i
$931$	36.1986	−	39.1091i	1.18636	−	1.28175i
$932$	18.6485	−	15.6480i	0.610852	−	0.512566i
$933$	24.2649	+	3.46476i	0.794396	+	0.113431i
$934$	−19.5037	−	16.3656i	−0.638181	−	0.535497i
$935$	1.41124	−	2.44434i	0.0461526	−	0.0799386i
$936$	10.1880	+	15.2489i	0.333007	+	0.498427i
$937$	21.6150	−	37.4382i	0.706130	−	1.22305i	−0.260153	−	0.965568i	$-0.583773\pi$
$937$	21.6150	−	37.4382i	0.706130	−	1.22305i	0.966282	−	0.257485i	$-0.0828938\pi$
$938$	2.80979	−	3.81203i	0.0917428	−	0.124467i
$939$	0.469271	+	14.3445i	0.0153141	+	0.468115i
$940$	7.05351	−	5.91860i	0.230060	−	0.193043i
$941$	−32.5237	+	27.2907i	−1.06024	+	0.889650i	−0.994133	−	0.108162i	$-0.965503\pi$
$941$	−32.5237	+	27.2907i	−1.06024	+	0.889650i	−0.0661104	+	0.997812i	$0.521059\pi$
$942$	−7.76197	−	8.65884i	−0.252899	−	0.282120i
$943$	17.4533	−	6.35248i	0.568357	−	0.206865i
$944$	12.0016			0.390619
$945$	7.28712	+	8.92604i	0.237050	+	0.290364i
$946$	17.5691			0.571220
$947$	32.1080	−	11.6863i	1.04337	−	0.379755i	0.237213	−	0.971458i	$-0.423766\pi$
$947$	32.1080	−	11.6863i	1.04337	−	0.379755i	0.806156	+	0.591702i	$0.201544\pi$
$948$	−0.0674941	+	0.206178i	−0.00219211	+	0.00669636i
$949$	−23.7290	+	19.9110i	−0.770276	+	0.646338i
$950$	−25.0621	+	21.0296i	−0.813123	+	0.682292i
$951$	−2.55605	−	1.36631i	−0.0828856	−	0.0443057i
$952$	−3.20595	−	0.359227i	−0.103905	−	0.0116426i
$953$	8.29834	−	14.3732i	0.268810	−	0.465592i	−0.699745	−	0.714393i	$-0.746703\pi$
$953$	8.29834	−	14.3732i	0.268810	−	0.465592i	0.968555	+	0.248801i	$0.0800364\pi$
$954$	−1.69367	−	0.493741i	−0.0548346	−	0.0159855i
$955$	−4.80194	+	8.31721i	−0.155387	+	0.269138i
$956$	14.7432	+	12.3710i	0.476829	+	0.400107i
$957$	0.261505	+	0.651378i	0.00845327	+	0.0210561i
$958$	5.23471	−	4.39244i	0.169126	−	0.141913i
$959$	4.36114	+	4.57858i	0.140829	+	0.147850i
$960$	1.43717	+	0.205212i	0.0463844	+	0.00662318i
$961$	6.56850	−	37.2518i	0.211887	−	1.20167i
$962$	0.0411308	−	0.0712407i	0.00132611	−	0.00229689i
$963$	1.85959	−	16.9728i	0.0599243	−	0.546941i
$964$	−6.51222	−	11.2795i	−0.209744	−	0.363288i
$965$	−0.419749	+	2.38052i	−0.0135122	+	0.0766315i
$966$	−3.08046	+	6.75332i	−0.0991120	+	0.217284i
$967$	53.1758	+	19.3544i	1.71002	+	0.622396i	0.996902	−	0.0786493i	$-0.0250607\pi$
$967$	53.1758	+	19.3544i	1.71002	+	0.622396i	0.713117	+	0.701045i	$0.247283\pi$
$968$	−3.16931	−	1.15353i	−0.101865	−	0.0370760i
$969$	15.7338	−	3.30811i	0.505444	−	0.106272i
$970$	−1.31034	+	7.43131i	−0.0420725	+	0.238605i
$971$	−15.8717	+	27.4906i	−0.509347	+	0.882215i	0.490594	+	0.871388i	$0.336780\pi$
$971$	−15.8717	+	27.4906i	−0.509347	+	0.882215i	−0.999941	+	0.0108271i	$0.996554\pi$
$972$	−2.53758	−	15.3805i	−0.0813929	−	0.493331i
$973$	−30.8545	−	15.3118i	−0.989150	−	0.490875i
$974$	−11.1369	−	9.34499i	−0.356850	−	0.299433i
$975$	−30.3724	−	33.8819i	−0.972696	−	1.08509i
$976$	3.77860	−	3.17062i	0.120950	−	0.101489i
$977$	−6.19365	−	35.1259i	−0.198152	−	1.12378i	−0.907857	−	0.419279i	$-0.862283\pi$
$977$	−6.19365	−	35.1259i	−0.198152	−	1.12378i	0.709705	−	0.704499i	$-0.248828\pi$
$978$	−0.254607	−	7.78274i	−0.00814145	−	0.248865i
$979$	−2.36375	+	13.4055i	−0.0755457	+	0.428441i
$980$	5.82072	−	0.736703i	0.185936	−	0.0235331i
$981$	−15.7440	−	11.5451i	−0.502667	−	0.368605i
$982$	16.1653			0.515854
$983$	20.9411	+	17.5716i	0.667916	+	0.560448i	0.912448	−	0.409193i	$-0.134190\pi$
$983$	20.9411	+	17.5716i	0.667916	+	0.560448i	−0.244532	+	0.969641i	$0.578634\pi$
$984$	7.39943	+	18.4311i	0.235885	+	0.587562i
$985$	1.12212	+	6.36388i	0.0357539	+	0.202770i
$986$	−0.137059	+	0.115006i	−0.00436484	+	0.00366254i
$987$	−45.4455	+	21.6573i	−1.44655	+	0.689359i
$988$	−43.7316	+	15.9170i	−1.39129	+	0.506388i
$989$	10.3042			0.327656
$990$	5.01661	−	4.80193i	0.159438	−	0.152615i
$991$	10.9744			0.348613			0.174307	−	0.984691i	$-0.444232\pi$
$991$	10.9744			0.348613			0.174307	+	0.984691i	$0.444232\pi$
$992$	−6.35524	−	5.33268i	−0.201779	−	0.169313i
$993$	35.0320	+	18.7260i	1.11171	+	0.594251i
$994$	−28.3133	+	6.85319i	−0.898042	+	0.217370i
$995$	−1.36530	−	7.74299i	−0.0432828	−	0.245469i
$996$	19.4041	−	4.07978i	0.614841	−	0.129273i
$997$	−6.43523	+	36.4960i	−0.203806	+	1.15584i	0.695502	+	0.718524i	$0.255182\pi$
$997$	−6.43523	+	36.4960i	−0.203806	+	1.15584i	−0.899308	+	0.437316i	$0.855929\pi$
$998$	17.6077	+	30.4974i	0.557361	+	0.965377i
$999$	−0.0568394	+	0.0407248i	−0.00179832	+	0.00128847i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	378.2.v.a.205.12	✓	72
7.4	even	3		378.2.w.b.151.4	yes	72
27.22	even	9		378.2.w.b.373.4	yes	72
189.130	even	9	inner	378.2.v.a.319.12	yes	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
378.2.v.a.205.12	✓	72	1.1	even	1	trivial
378.2.v.a.319.12	yes	72	189.130	even	9	inner
378.2.w.b.151.4	yes	72	7.4	even	3
378.2.w.b.373.4	yes	72	27.22	even	9

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:	\( N \)	\(=\)	\( 378 = 2 \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	378.v (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.939693 - 0.342020i) q^{2} +(1.69499 - 0.356379i) q^{3} +(0.766044 - 0.642788i) q^{4} +(-0.642072 + 0.538762i) q^{5} +(1.47088 - 0.914608i) q^{6} +(1.56979 - 2.12973i) q^{7} +(0.500000 - 0.866025i) q^{8} +(2.74599 - 1.20812i) q^{9} +O(q^{10})\)	\(q+(0.939693 - 0.342020i) q^{2} +(1.69499 - 0.356379i) q^{3} +(0.766044 - 0.642788i) q^{4} +(-0.642072 + 0.538762i) q^{5} +(1.47088 - 0.914608i) q^{6} +(1.56979 - 2.12973i) q^{7} +(0.500000 - 0.866025i) q^{8} +(2.74599 - 1.20812i) q^{9} +(-0.419082 + 0.725872i) q^{10} +(-2.11563 - 1.77522i) q^{11} +(1.06936 - 1.36252i) q^{12} +(-4.68288 + 3.92941i) q^{13} +(0.746710 - 2.53819i) q^{14} +(-0.896302 + 1.14202i) q^{15} +(0.173648 - 0.984808i) q^{16} +(0.609659 - 1.05596i) q^{17} +(2.16718 - 2.07444i) q^{18} +(3.80645 + 6.59297i) q^{19} +(-0.145546 + 0.825431i) q^{20} +(1.90179 - 4.16932i) q^{21} +(-2.59520 - 0.944576i) q^{22} +(-1.52208 - 0.553993i) q^{23} +(0.538862 - 1.64609i) q^{24} +(-0.746250 + 4.23219i) q^{25} +(-3.05653 + 5.29407i) q^{26} +(4.22388 - 3.02636i) q^{27} +(-0.166435 - 2.64051i) q^{28} +(-0.112406 - 0.0943199i) q^{29} +(-0.451655 + 1.37970i) q^{30} +(6.35524 - 5.33268i) q^{31} +(-0.173648 - 0.984808i) q^{32} +(-4.21862 - 2.25502i) q^{33} +(0.211732 - 1.20079i) q^{34} +(0.139500 + 2.21318i) q^{35} +(1.32699 - 2.69056i) q^{36} -0.0134567 q^{37} +(5.83182 + 4.89348i) q^{38} +(-6.53709 + 8.32919i) q^{39} +(0.145546 + 0.825431i) q^{40} +(-8.78401 + 7.37066i) q^{41} +(0.361108 - 4.56833i) q^{42} +(-5.97791 + 2.17578i) q^{43} -2.76176 q^{44} +(-1.11223 + 2.25513i) q^{45} -1.61977 q^{46} +(-8.41542 - 7.06138i) q^{47} +(-0.0566326 - 1.73112i) q^{48} +(-2.07151 - 6.68647i) q^{49} +(0.746250 + 4.23219i) q^{50} +(0.657045 - 2.00711i) q^{51} +(-1.06152 + 6.02020i) q^{52} +(-0.294028 - 0.509272i) q^{53} +(2.93407 - 4.28850i) q^{54} +2.31481 q^{55} +(-1.05951 - 2.42434i) q^{56} +(8.80150 + 9.81848i) q^{57} +(-0.137887 - 0.0501866i) q^{58} +(2.08406 + 11.8193i) q^{59} +(0.0474675 + 1.45097i) q^{60} +(3.77860 + 3.17062i) q^{61} +(4.14809 - 7.18470i) q^{62} +(1.73766 - 7.74471i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(0.889732 - 5.04592i) q^{65} +(-4.73547 - 0.676173i) q^{66} +(1.68197 + 0.612185i) q^{67} +(-0.211732 - 1.20079i) q^{68} +(-2.77735 - 0.396574i) q^{69} +(0.888041 + 2.03200i) q^{70} +(-5.50522 - 9.53532i) q^{71} +(0.326733 - 2.98215i) q^{72} +5.06718 q^{73} +(-0.0126451 + 0.00460246i) q^{74} +(0.243378 + 7.43947i) q^{75} +(7.15379 + 2.60377i) q^{76} +(-7.10184 + 1.71899i) q^{77} +(-3.29410 + 10.0627i) q^{78} +(-0.117699 + 0.0428391i) q^{79} +(0.419082 + 0.725872i) q^{80} +(6.08090 - 6.63496i) q^{81} +(-5.73336 + 9.93047i) q^{82} +(8.76959 + 7.35856i) q^{83} +(-1.22313 - 4.41633i) q^{84} +(0.177467 + 1.00646i) q^{85} +(-4.87324 + 4.08913i) q^{86} +(-0.224141 - 0.119812i) q^{87} +(-2.59520 + 0.944576i) q^{88} +(-2.46443 - 4.26851i) q^{89} +(-0.273856 + 2.49954i) q^{90} +(1.01743 + 16.1416i) q^{91} +(-1.52208 + 0.553993i) q^{92} +(8.87162 - 11.3037i) q^{93} +(-10.3230 - 3.75728i) q^{94} +(-5.99606 - 2.18239i) q^{95} +(-0.645297 - 1.60736i) q^{96} +(8.45999 - 3.07919i) q^{97} +(-4.23349 - 5.57473i) q^{98} +(-7.95417 - 2.31881i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q + 3 q^{6} - 6 q^{7} + 36 q^{8}+O(q^{10}) \) 72 * q + 3 * q^6 - 6 * q^7 + 36 * q^8	\( 72 q + 3 q^{6} - 6 q^{7} + 36 q^{8} + 6 q^{10} + 12 q^{11} + 12 q^{13} - 3 q^{14} - 6 q^{15} - 12 q^{17} + 18 q^{19} + 6 q^{22} + 12 q^{23} - 6 q^{25} - 18 q^{26} + 6 q^{27} + 3 q^{29} + 15 q^{30} - 9 q^{31} - 18 q^{33} - 9 q^{34} - 18 q^{35} - 3 q^{36} - 48 q^{39} - 6 q^{41} + 36 q^{42} - 24 q^{43} - 45 q^{45} - 27 q^{47} + 6 q^{48} + 48 q^{49} + 6 q^{50} + 15 q^{51} - 6 q^{52} - 15 q^{53} - 63 q^{54} - 72 q^{55} - 3 q^{56} + 57 q^{57} - 3 q^{58} - 30 q^{59} + 21 q^{60} + 9 q^{61} - 24 q^{62} - 21 q^{63} - 36 q^{64} + 45 q^{65} + 6 q^{67} + 9 q^{68} - 39 q^{69} + 15 q^{70} + 12 q^{71} - 60 q^{73} - 18 q^{74} + 42 q^{75} + 3 q^{77} + 6 q^{78} - 27 q^{79} - 6 q^{80} + 12 q^{81} + 33 q^{82} + 18 q^{83} - 21 q^{84} + 51 q^{85} - 12 q^{86} - 117 q^{87} + 6 q^{88} - 36 q^{89} - 69 q^{90} - 3 q^{91} + 12 q^{92} - 30 q^{93} - 27 q^{94} + 3 q^{95} + 48 q^{97} - 12 q^{98} + 90 q^{99}+O(q^{100}) \) 72 * q + 3 * q^6 - 6 * q^7 + 36 * q^8 + 6 * q^10 + 12 * q^11 + 12 * q^13 - 3 * q^14 - 6 * q^15 - 12 * q^17 + 18 * q^19 + 6 * q^22 + 12 * q^23 - 6 * q^25 - 18 * q^26 + 6 * q^27 + 3 * q^29 + 15 * q^30 - 9 * q^31 - 18 * q^33 - 9 * q^34 - 18 * q^35 - 3 * q^36 - 48 * q^39 - 6 * q^41 + 36 * q^42 - 24 * q^43 - 45 * q^45 - 27 * q^47 + 6 * q^48 + 48 * q^49 + 6 * q^50 + 15 * q^51 - 6 * q^52 - 15 * q^53 - 63 * q^54 - 72 * q^55 - 3 * q^56 + 57 * q^57 - 3 * q^58 - 30 * q^59 + 21 * q^60 + 9 * q^61 - 24 * q^62 - 21 * q^63 - 36 * q^64 + 45 * q^65 + 6 * q^67 + 9 * q^68 - 39 * q^69 + 15 * q^70 + 12 * q^71 - 60 * q^73 - 18 * q^74 + 42 * q^75 + 3 * q^77 + 6 * q^78 - 27 * q^79 - 6 * q^80 + 12 * q^81 + 33 * q^82 + 18 * q^83 - 21 * q^84 + 51 * q^85 - 12 * q^86 - 117 * q^87 + 6 * q^88 - 36 * q^89 - 69 * q^90 - 3 * q^91 + 12 * q^92 - 30 * q^93 - 27 * q^94 + 3 * q^95 + 48 * q^97 - 12 * q^98 + 90 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more