LMFDB - Embedded newform 966.2.y.c.25.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [966,2,Mod(25,966)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(966, base_ring=CyclotomicField(66))

chi = DirichletCharacter(H, H._module([0, 44, 6]))

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

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

chi := DirichletCharacter("966.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 966 = 2 \cdot 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	966.y (of order $33$, degree $20$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.71354883526$
Analytic rank:	$0$
Dimension:	$160$
Relative dimension:	$8$ over $\Q(\zeta_{33})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{33}]$

Embedding invariants

Embedding label			25.1
Character	$\chi$	$=$	966.25
Dual form			966.2.y.c.541.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.0475819 - 0.998867i) q^{2} +(-0.928368 - 0.371662i) q^{3} +(-0.995472 - 0.0950560i) q^{4} +(-0.835382 - 3.44349i) q^{5} +(-0.415415 + 0.909632i) q^{6} +(0.912603 - 2.48338i) q^{7} +(-0.142315 + 0.989821i) q^{8} +(0.723734 + 0.690079i) q^{9} +O(q^{10})$	\(q+(0.0475819 - 0.998867i) q^{2} +(-0.928368 - 0.371662i) q^{3} +(-0.995472 - 0.0950560i) q^{4} +(-0.835382 - 3.44349i) q^{5} +(-0.415415 + 0.909632i) q^{6} +(0.912603 - 2.48338i) q^{7} +(-0.142315 + 0.989821i) q^{8} +(0.723734 + 0.690079i) q^{9} +(-3.47934 + 0.670588i) q^{10} +(0.0646978 + 1.35817i) q^{11} +(0.888835 + 0.458227i) q^{12} +(-3.15220 - 3.63784i) q^{13} +(-2.43714 - 1.02973i) q^{14} +(-0.504274 + 3.50731i) q^{15} +(0.981929 + 0.189251i) q^{16} +(-2.34802 - 3.29734i) q^{17} +(0.723734 - 0.690079i) q^{18} +(2.93100 - 4.11601i) q^{19} +(0.504274 + 3.50731i) q^{20} +(-1.77021 + 1.96631i) q^{21} +1.35971 q^{22} +(4.77097 + 0.487734i) q^{23} +(0.500000 - 0.866025i) q^{24} +(-6.71559 + 3.46213i) q^{25} +(-3.78370 + 2.97554i) q^{26} +(-0.415415 - 0.909632i) q^{27} +(-1.14453 + 2.38538i) q^{28} +(-2.53928 + 5.56025i) q^{29} +(3.47934 + 0.670588i) q^{30} +(-2.69118 - 2.11636i) q^{31} +(0.235759 - 0.971812i) q^{32} +(0.444719 - 1.28493i) q^{33} +(-3.40533 + 2.18847i) q^{34} +(-9.31385 - 1.06797i) q^{35} +(-0.654861 - 0.755750i) q^{36} +(2.88000 + 2.74608i) q^{37} +(-3.97188 - 3.12352i) q^{38} +(1.57436 + 4.54880i) q^{39} +(3.52733 - 0.336819i) q^{40} +(7.82560 + 2.29780i) q^{41} +(1.87985 + 1.86176i) q^{42} +(-0.827810 - 5.75754i) q^{43} +(0.0646978 - 1.35817i) q^{44} +(1.77169 - 3.06865i) q^{45} +(0.714193 - 4.74235i) q^{46} +(6.49658 + 11.2524i) q^{47} +(-0.841254 - 0.540641i) q^{48} +(-5.33431 - 4.53267i) q^{49} +(3.13866 + 6.87271i) q^{50} +(0.954333 + 3.93382i) q^{51} +(2.79213 + 3.92100i) q^{52} +(3.19261 + 9.22445i) q^{53} +(-0.928368 + 0.371662i) q^{54} +(4.62281 - 1.35738i) q^{55} +(2.32822 + 1.25673i) q^{56} +(-4.25081 + 2.73183i) q^{57} +(5.43313 + 2.80097i) q^{58} +(-10.1242 + 1.95128i) q^{59} +(0.835382 - 3.44349i) q^{60} +(-7.06672 + 2.82909i) q^{61} +(-2.24202 + 2.58743i) q^{62} +(2.37421 - 1.16754i) q^{63} +(-0.959493 - 0.281733i) q^{64} +(-9.89356 + 13.8936i) q^{65} +(-1.26231 - 0.505354i) q^{66} +(-4.57338 + 2.35774i) q^{67} +(2.02396 + 3.50560i) q^{68} +(-4.24794 - 2.22599i) q^{69} +(-1.50993 + 9.25249i) q^{70} +(-11.9508 - 7.68030i) q^{71} +(-0.786053 + 0.618159i) q^{72} +(2.51771 + 0.240412i) q^{73} +(2.88000 - 2.74608i) q^{74} +(7.52128 - 0.718195i) q^{75} +(-3.30898 + 3.81876i) q^{76} +(3.43190 + 1.07880i) q^{77} +(4.61856 - 1.35613i) q^{78} +(3.20155 - 9.25028i) q^{79} +(-0.168600 - 3.53936i) q^{80} +(0.0475819 + 0.998867i) q^{81} +(2.66756 - 7.70740i) q^{82} +(-7.99567 + 2.34774i) q^{83} +(1.94910 - 1.78913i) q^{84} +(-9.39286 + 10.8399i) q^{85} +(-5.79041 + 0.552917i) q^{86} +(4.42392 - 4.21820i) q^{87} +(-1.35356 - 0.129249i) q^{88} +(8.00784 - 6.29744i) q^{89} +(-2.98087 - 1.91569i) q^{90} +(-11.9108 + 4.50821i) q^{91} +(-4.70300 - 0.939035i) q^{92} +(1.71183 + 2.96497i) q^{93} +(11.5488 - 5.95381i) q^{94} +(-16.6219 - 6.65442i) q^{95} +(-0.580057 + 0.814576i) q^{96} +(8.74848 + 2.56879i) q^{97} +(-4.78135 + 5.11260i) q^{98} +(-0.890423 + 1.02760i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 160 q + 8 q^{2} - 8 q^{3} + 8 q^{4} + 2 q^{5} + 16 q^{6} - 2 q^{7} - 16 q^{8} + 8 q^{9}+O(q^{10}) $ 160 * q + 8 * q^2 - 8 * q^3 + 8 * q^4 + 2 * q^5 + 16 * q^6 - 2 * q^7 - 16 * q^8 + 8 * q^9	\( 160 q + 8 q^{2} - 8 q^{3} + 8 q^{4} + 2 q^{5} + 16 q^{6} - 2 q^{7} - 16 q^{8} + 8 q^{9} + 2 q^{10} + 8 q^{11} - 8 q^{12} - 4 q^{13} + 9 q^{14} - 18 q^{15} + 8 q^{16} - 21 q^{17} + 8 q^{18} + 4 q^{19} + 18 q^{20} - 15 q^{21} + 116 q^{22} + 14 q^{23} + 80 q^{24} + 2 q^{25} + 2 q^{26} + 16 q^{27} - 18 q^{28} - 46 q^{29} - 2 q^{30} + q^{31} + 8 q^{32} - 8 q^{33} - 68 q^{34} - 84 q^{35} - 16 q^{36} + 19 q^{37} - 7 q^{38} - 2 q^{39} - 9 q^{40} + 38 q^{41} + 2 q^{42} + 28 q^{43} + 8 q^{44} + 24 q^{45} - 8 q^{46} - 26 q^{47} + 16 q^{48} - 6 q^{49} - 4 q^{50} + 21 q^{51} + 2 q^{52} - 20 q^{53} - 8 q^{54} + 46 q^{55} - 2 q^{56} - 14 q^{57} - 21 q^{58} + 36 q^{59} - 2 q^{60} + 40 q^{61} - 24 q^{62} - 2 q^{63} - 16 q^{64} - 10 q^{65} - 8 q^{66} + 6 q^{67} + 34 q^{68} + 6 q^{69} - 20 q^{70} + 132 q^{71} + 8 q^{72} - 36 q^{73} + 19 q^{74} - 2 q^{75} - 8 q^{76} - 75 q^{77} - 18 q^{78} + 34 q^{79} + 2 q^{80} + 8 q^{81} + 47 q^{82} + 74 q^{83} + 13 q^{84} + 2 q^{85} + 30 q^{86} + 10 q^{87} - 3 q^{88} - 12 q^{89} - 4 q^{90} - 30 q^{91} - 50 q^{92} + 10 q^{93} - 4 q^{94} + 27 q^{95} - 8 q^{96} + 24 q^{97} + 7 q^{98} - 16 q^{99}+O(q^{100}) \) 160 * q + 8 * q^2 - 8 * q^3 + 8 * q^4 + 2 * q^5 + 16 * q^6 - 2 * q^7 - 16 * q^8 + 8 * q^9 + 2 * q^10 + 8 * q^11 - 8 * q^12 - 4 * q^13 + 9 * q^14 - 18 * q^15 + 8 * q^16 - 21 * q^17 + 8 * q^18 + 4 * q^19 + 18 * q^20 - 15 * q^21 + 116 * q^22 + 14 * q^23 + 80 * q^24 + 2 * q^25 + 2 * q^26 + 16 * q^27 - 18 * q^28 - 46 * q^29 - 2 * q^30 + q^31 + 8 * q^32 - 8 * q^33 - 68 * q^34 - 84 * q^35 - 16 * q^36 + 19 * q^37 - 7 * q^38 - 2 * q^39 - 9 * q^40 + 38 * q^41 + 2 * q^42 + 28 * q^43 + 8 * q^44 + 24 * q^45 - 8 * q^46 - 26 * q^47 + 16 * q^48 - 6 * q^49 - 4 * q^50 + 21 * q^51 + 2 * q^52 - 20 * q^53 - 8 * q^54 + 46 * q^55 - 2 * q^56 - 14 * q^57 - 21 * q^58 + 36 * q^59 - 2 * q^60 + 40 * q^61 - 24 * q^62 - 2 * q^63 - 16 * q^64 - 10 * q^65 - 8 * q^66 + 6 * q^67 + 34 * q^68 + 6 * q^69 - 20 * q^70 + 132 * q^71 + 8 * q^72 - 36 * q^73 + 19 * q^74 - 2 * q^75 - 8 * q^76 - 75 * q^77 - 18 * q^78 + 34 * q^79 + 2 * q^80 + 8 * q^81 + 47 * q^82 + 74 * q^83 + 13 * q^84 + 2 * q^85 + 30 * q^86 + 10 * q^87 - 3 * q^88 - 12 * q^89 - 4 * q^90 - 30 * q^91 - 50 * q^92 + 10 * q^93 - 4 * q^94 + 27 * q^95 - 8 * q^96 + 24 * q^97 + 7 * q^98 - 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/966\mathbb{Z}\right)^\times$.

$n$	$323$	$829$	$925$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{11}\right)$

Coefficient data

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

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

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

$2$	0.0475819	−	0.998867i	0.0336455	−	0.706306i
$2$	0.0475819	−	0.998867i	0.0336455	−	0.706306i
$3$	−0.928368	−	0.371662i	−0.535993	−	0.214579i
$3$	−0.928368	−	0.371662i	−0.535993	−	0.214579i
$4$	−0.995472	−	0.0950560i	−0.497736	−	0.0475280i
$5$	−0.835382	−	3.44349i	−0.373594	−	1.53998i	−0.779702	−	0.626151i	$-0.784629\pi$
$5$	−0.835382	−	3.44349i	−0.373594	−	1.53998i	0.406108	−	0.913825i	$-0.366886\pi$
$6$	−0.415415	+	0.909632i	−0.169592	+	0.371356i
$7$	0.912603	−	2.48338i	0.344931	−	0.938628i
$7$	0.912603	−	2.48338i	0.344931	−	0.938628i
$8$	−0.142315	+	0.989821i	−0.0503159	+	0.349955i
$9$	0.723734	+	0.690079i	0.241245	+	0.230026i
$10$	−3.47934	+	0.670588i	−1.10026	+	0.212058i
$11$	0.0646978	+	1.35817i	0.0195071	+	0.409505i	0.987410	+	0.158181i	$0.0505629\pi$
$11$	0.0646978	+	1.35817i	0.0195071	+	0.409505i	−0.967903	+	0.251324i	$0.919134\pi$
$12$	0.888835	+	0.458227i	0.256585	+	0.132279i
$13$	−3.15220	−	3.63784i	−0.874264	−	1.00895i	−0.999858	−	0.0168723i	$-0.994629\pi$
$13$	−3.15220	−	3.63784i	−0.874264	−	1.00895i	0.125594	−	0.992082i	$-0.459916\pi$
$14$	−2.43714	−	1.02973i	−0.651353	−	0.275208i
$15$	−0.504274	+	3.50731i	−0.130203	+	0.905583i
$16$	0.981929	+	0.189251i	0.245482	+	0.0473128i
$17$	−2.34802	−	3.29734i	−0.569479	−	0.799722i	0.424940	−	0.905222i	$-0.360295\pi$
$17$	−2.34802	−	3.29734i	−0.569479	−	0.799722i	−0.994419	+	0.105500i	$0.966356\pi$
$18$	0.723734	−	0.690079i	0.170586	−	0.162653i
$19$	2.93100	−	4.11601i	0.672417	−	0.944277i	−0.327583	−	0.944822i	$-0.606234\pi$
$19$	2.93100	−	4.11601i	0.672417	−	0.944277i	1.00000		0.000545339i	$0.000173587\pi$
$20$	0.504274	+	3.50731i	0.112759	+	0.784258i
$21$	−1.77021	+	1.96631i	−0.386291	+	0.429083i
$22$	1.35971			0.289892
$23$	4.77097	+	0.487734i	0.994815	+	0.101700i
$23$	4.77097	+	0.487734i	0.994815	+	0.101700i
$24$	0.500000	−	0.866025i	0.102062	−	0.176777i
$25$	−6.71559	+	3.46213i	−1.34312	+	0.692425i
$26$	−3.78370	+	2.97554i	−0.742045	+	0.583551i
$27$	−0.415415	−	0.909632i	−0.0799467	−	0.175059i
$28$	−1.14453	+	2.38538i	−0.216296	+	0.450795i
$29$	−2.53928	+	5.56025i	−0.471533	+	1.03251i	0.513173	+	0.858285i	$0.328470\pi$
$29$	−2.53928	+	5.56025i	−0.471533	+	1.03251i	−0.984705	+	0.174227i	$0.944257\pi$
$30$	3.47934	+	0.670588i	0.635238	+	0.122432i
$31$	−2.69118	−	2.11636i	−0.483349	−	0.380110i	0.346543	−	0.938034i	$-0.387356\pi$
$31$	−2.69118	−	2.11636i	−0.483349	−	0.380110i	−0.829892	+	0.557924i	$0.811598\pi$
$32$	0.235759	−	0.971812i	0.0416767	−	0.171794i
$33$	0.444719	−	1.28493i	0.0774156	−	0.223678i
$34$	−3.40533	+	2.18847i	−0.584009	+	0.375320i
$35$	−9.31385	−	1.06797i	−1.57433	−	0.180520i
$36$	−0.654861	−	0.755750i	−0.109143	−	0.125958i
$37$	2.88000	+	2.74608i	0.473469	+	0.451452i	0.888852	−	0.458195i	$-0.151504\pi$
$37$	2.88000	+	2.74608i	0.473469	+	0.451452i	−0.415382	+	0.909647i	$0.636352\pi$
$38$	−3.97188	−	3.12352i	−0.644325	−	0.506702i
$39$	1.57436	+	4.54880i	0.252099	+	0.728392i
$40$	3.52733	−	0.336819i	0.557720	−	0.0532558i
$41$	7.82560	+	2.29780i	1.22215	+	0.358857i	0.828283	−	0.560309i	$-0.189318\pi$
$41$	7.82560	+	2.29780i	1.22215	+	0.358857i	0.393870	+	0.919166i	$0.371136\pi$
$42$	1.87985	+	1.86176i	0.290067	+	0.287276i
$43$	−0.827810	−	5.75754i	−0.126240	−	0.878017i	−0.950260	−	0.311457i	$-0.899183\pi$
$43$	−0.827810	−	5.75754i	−0.126240	−	0.878017i	0.824020	−	0.566560i	$-0.191726\pi$
$44$	0.0646978	−	1.35817i	0.00975356	−	0.204752i
$45$	1.77169	−	3.06865i	0.264107	−	0.457447i
$46$	0.714193	−	4.74235i	0.105302	−	0.699222i
$47$	6.49658	+	11.2524i	0.947623	+	1.64133i	0.750411	+	0.660971i	$0.229855\pi$
$47$	6.49658	+	11.2524i	0.947623	+	1.64133i	0.197212	+	0.980361i	$0.436811\pi$
$48$	−0.841254	−	0.540641i	−0.121424	−	0.0780348i
$49$	−5.33431	−	4.53267i	−0.762045	−	0.647524i
$50$	3.13866	+	6.87271i	0.443874	+	0.971949i
$51$	0.954333	+	3.93382i	0.133633	+	0.550844i
$52$	2.79213	+	3.92100i	0.387199	+	0.543745i
$53$	3.19261	+	9.22445i	0.438539	+	1.26708i	0.920452	+	0.390856i	$0.127821\pi$
$53$	3.19261	+	9.22445i	0.438539	+	1.26708i	−0.481913	+	0.876219i	$0.660058\pi$
$54$	−0.928368	+	0.371662i	−0.126335	+	0.0505769i
$55$	4.62281	−	1.35738i	0.623340	−	0.183029i
$56$	2.32822	+	1.25673i	0.311122	+	0.167938i
$57$	−4.25081	+	2.73183i	−0.563033	+	0.361840i
$58$	5.43313	+	2.80097i	0.713405	+	0.367786i
$59$	−10.1242	+	1.95128i	−1.31806	+	0.254035i	−0.799324	−	0.600900i	$-0.794809\pi$
$59$	−10.1242	+	1.95128i	−1.31806	+	0.254035i	−0.518735	+	0.854935i	$0.673597\pi$
$60$	0.835382	−	3.44349i	0.107847	−	0.444553i
$61$	−7.06672	+	2.82909i	−0.904801	+	0.362228i	−0.776947	−	0.629566i	$-0.783233\pi$
$61$	−7.06672	+	2.82909i	−0.904801	+	0.362228i	−0.127853	+	0.991793i	$0.540809\pi$
$62$	−2.24202	+	2.58743i	−0.284737	+	0.328604i
$63$	2.37421	−	1.16754i	0.299122	−	0.147096i
$64$	−0.959493	−	0.281733i	−0.119937	−	0.0352166i
$65$	−9.89356	+	13.8936i	−1.22714	+	1.72328i
$66$	−1.26231	−	0.505354i	−0.155380	−	0.0622048i
$67$	−4.57338	+	2.35774i	−0.558727	+	0.288044i	−0.714368	−	0.699770i	$-0.753286\pi$
$67$	−4.57338	+	2.35774i	−0.558727	+	0.288044i	0.155641	+	0.987814i	$0.450256\pi$
$68$	2.02396	+	3.50560i	0.245441	+	0.425117i
$69$	−4.24794	−	2.22599i	−0.511392	−	0.267977i
$70$	−1.50993	+	9.25249i	−0.180471	+	1.10588i
$71$	−11.9508	−	7.68030i	−1.41830	−	0.911484i	−0.999995	−	0.00317575i	$-0.998989\pi$
$71$	−11.9508	−	7.68030i	−1.41830	−	0.911484i	−0.418302	−	0.908308i	$-0.637375\pi$
$72$	−0.786053	+	0.618159i	−0.0926372	+	0.0728507i
$73$	2.51771	+	0.240412i	0.294675	+	0.0281381i	0.241347	−	0.970439i	$-0.422411\pi$
$73$	2.51771	+	0.240412i	0.294675	+	0.0281381i	0.0533286	+	0.998577i	$0.483017\pi$
$74$	2.88000	−	2.74608i	0.334793	−	0.319225i
$75$	7.52128	−	0.718195i	0.868482	−	0.0829300i
$76$	−3.30898	+	3.81876i	−0.379566	+	0.438042i
$77$	3.43190	+	1.07880i	0.391101	+	0.122941i
$78$	4.61856	−	1.35613i	0.522949	−	0.153552i
$79$	3.20155	−	9.25028i	0.360203	−	1.04074i	−0.608722	−	0.793383i	$-0.708318\pi$
$79$	3.20155	−	9.25028i	0.360203	−	1.04074i	0.968925	−	0.247354i	$-0.0795611\pi$
$80$	−0.168600	−	3.53936i	−0.0188501	−	0.395712i
$81$	0.0475819	+	0.998867i	0.00528688	+	0.110985i
$82$	2.66756	−	7.70740i	0.294583	−	0.851140i
$83$	−7.99567	+	2.34774i	−0.877639	+	0.257698i	−0.689361	−	0.724418i	$-0.742109\pi$
$83$	−7.99567	+	2.34774i	−0.877639	+	0.257698i	−0.188278	+	0.982116i	$0.560291\pi$
$84$	1.94910	−	1.78913i	0.212664	−	0.195211i
$85$	−9.39286	+	10.8399i	−1.01880	+	1.17576i
$86$	−5.79041	+	0.552917i	−0.624396	+	0.0596226i
$87$	4.42392	−	4.21820i	0.474294	−	0.452239i
$88$	−1.35356	−	0.129249i	−0.144290	−	0.0137780i
$89$	8.00784	−	6.29744i	0.848830	−	0.667527i	−0.0958951	−	0.995391i	$-0.530571\pi$
$89$	8.00784	−	6.29744i	0.848830	−	0.667527i	0.944725	+	0.327864i	$0.106329\pi$
$90$	−2.98087	−	1.91569i	−0.314212	−	0.201932i
$91$	−11.9108	+	4.50821i	−1.24859	+	0.472588i
$92$	−4.70300	−	0.939035i	−0.490322	−	0.0979011i
$93$	1.71183	+	2.96497i	0.177508	+	0.307453i
$94$	11.5488	−	5.95381i	1.19117	−	0.614089i
$95$	−16.6219	−	6.65442i	−1.70537	−	0.682729i
$96$	−0.580057	+	0.814576i	−0.0592018	+	0.0831373i
$97$	8.74848	+	2.56879i	0.888274	+	0.260821i	0.693869	−	0.720101i	$-0.255904\pi$
$97$	8.74848	+	2.56879i	0.888274	+	0.260821i	0.194404	+	0.980922i	$0.437723\pi$
$98$	−4.78135	+	5.11260i	−0.482990	+	0.516450i
$99$	−0.890423	+	1.02760i	−0.0894909	+	0.103278i
$100$	7.01427	−	2.80809i	0.701427	−	0.280809i
$101$	−1.07463	+	4.42970i	−0.106930	+	0.440771i	−0.999957	−	0.00923092i	$-0.997062\pi$
$101$	−1.07463	+	4.42970i	−0.106930	+	0.440771i	0.893027	+	0.450002i	$0.148577\pi$
$102$	3.97477	−	0.766074i	0.393561	−	0.0758526i
$103$	−4.09304	−	2.11011i	−0.403300	−	0.207915i	0.244629	−	0.969617i	$-0.421334\pi$
$103$	−4.09304	−	2.11011i	−0.403300	−	0.207915i	−0.647928	+	0.761702i	$0.724364\pi$
$104$	4.04941	−	2.60240i	0.397078	−	0.255186i
$105$	8.24976	+	4.45308i	0.805094	+	0.434576i
$106$	9.36591	−	2.75008i	0.909698	−	0.267111i
$107$	17.1464	−	6.86440i	1.65761	−	0.663606i	0.661353	−	0.750074i	$-0.269982\pi$
$107$	17.1464	−	6.86440i	1.65761	−	0.663606i	0.996255	+	0.0864683i	$0.0275581\pi$
$108$	0.327068	+	0.945001i	0.0314721	+	0.0909327i
$109$	−8.47464	−	11.9010i	−0.811723	−	1.13991i	−0.987830	−	0.155535i	$-0.950290\pi$
$109$	−8.47464	−	11.9010i	−0.811723	−	1.13991i	0.176107	−	0.984371i	$-0.443649\pi$
$110$	−1.13588	−	4.68216i	−0.108302	−	0.446426i
$111$	−1.65309	−	3.61976i	−0.156904	−	0.343572i
$112$	1.36609	−	2.26579i	0.129084	−	0.214097i
$113$	7.33789	+	4.71578i	0.690291	+	0.443623i	0.838189	−	0.545380i	$-0.183615\pi$
$113$	7.33789	+	4.71578i	0.690291	+	0.443623i	−0.147898	+	0.989003i	$0.547251\pi$
$114$	2.52647	+	4.37598i	0.236626	+	0.409848i
$115$	−2.30607	−	16.8362i	−0.215042	−	1.56999i
$116$	3.05632	−	5.29370i	0.283772	−	0.491508i
$117$	0.229038	−	4.80809i	0.0211745	−	0.444508i
$118$	1.46734	+	10.2056i	0.135080	+	0.939501i
$119$	−10.3313	+	2.82187i	−0.947073	+	0.258680i
$120$	−3.39984	−	0.998283i	−0.310362	−	0.0911304i
$121$	9.10974	−	0.869875i	0.828158	−	0.0790795i
$122$	2.48963	+	7.19333i	0.225401	+	0.651253i
$123$	−6.41103	−	5.04169i	−0.578063	−	0.454594i
$124$	2.47782	+	2.36259i	0.222515	+	0.212167i
$125$	5.92980	+	6.84335i	0.530377	+	0.612088i
$126$	−1.05324	−	2.42707i	−0.0938304	−	0.216221i
$127$	1.80251	−	1.15840i	0.159947	−	0.102792i	−0.458219	−	0.888839i	$-0.651512\pi$
$127$	1.80251	−	1.15840i	0.159947	−	0.102792i	0.618166	+	0.786048i	$0.287876\pi$
$128$	−0.327068	+	0.945001i	−0.0289090	+	0.0835271i
$129$	−1.37135	+	5.65278i	−0.120741	+	0.497700i
$130$	13.4071	+	10.5434i	1.17588	+	0.924720i
$131$	−17.0299	−	3.28225i	−1.48791	−	0.286772i	−0.620439	−	0.784254i	$-0.713046\pi$
$131$	−17.0299	−	3.28225i	−1.48791	−	0.286772i	−0.867474	+	0.497483i	$0.834258\pi$
$132$	−0.564845	+	1.23684i	−0.0491635	+	0.107653i
$133$	−7.54676	−	11.0350i	−0.654387	−	0.956860i
$134$	2.13746	+	4.68038i	0.184648	+	0.404323i
$135$	−2.78528	+	2.19037i	−0.239719	+	0.188517i
$136$	3.59793	−	1.85486i	0.308520	−	0.159053i
$137$	8.24453	−	14.2799i	0.704378	−	1.22002i	−0.262538	−	0.964922i	$-0.584560\pi$
$137$	8.24453	−	14.2799i	0.704378	−	1.22002i	0.966916	−	0.255096i	$-0.0821072\pi$
$138$	−2.42559	+	4.13721i	−0.206480	+	0.352183i
$139$	16.9563			1.43821			0.719106	−	0.694901i	$-0.244552\pi$
$139$	16.9563			1.43821			0.719106	+	0.694901i	$0.244552\pi$
$140$	9.17016	+	1.94847i	0.775020	+	0.164676i
$141$	−1.84912	−	12.8609i	−0.155724	−	1.08308i
$142$	−8.24024	+	11.5718i	−0.691506	+	0.971084i
$143$	4.73687	−	4.51660i	0.396117	−	0.377697i
$144$	0.580057	+	0.814576i	0.0483381	+	0.0678813i
$145$	21.2679	+	4.09906i	1.76621	+	0.340408i
$146$	0.359937	−	2.50342i	0.0297886	−	0.207184i
$147$	3.26758	+	6.19055i	0.269506	+	0.510588i
$148$	−2.60593	−	3.00740i	−0.214206	−	0.247207i
$149$	4.41402	+	2.27559i	0.361611	+	0.186423i	0.629451	−	0.777040i	$-0.283280\pi$
$149$	4.41402	+	2.27559i	0.361611	+	0.186423i	−0.267840	+	0.963463i	$0.586310\pi$
$150$	−0.359505	−	7.54693i	−0.0293534	−	0.616204i
$151$	−13.7267	+	2.64560i	−1.11706	+	0.215296i	−0.714185	−	0.699957i	$-0.753202\pi$
$151$	−13.7267	+	2.64560i	−1.11706	+	0.215296i	−0.402878	+	0.915254i	$0.631990\pi$
$152$	3.65699	+	3.48693i	0.296621	+	0.282828i
$153$	0.576079	−	4.00672i	0.0465732	−	0.323924i
$154$	1.24088	−	3.37668i	0.0999928	−	0.272101i
$155$	−5.03952	+	11.0350i	−0.404784	+	0.886353i
$156$	−1.13484	−	4.67786i	−0.0908596	−	0.374529i
$157$	10.6896	+	1.02073i	0.853123	+	0.0814633i	0.512448	−	0.858718i	$-0.328739\pi$
$157$	10.6896	+	1.02073i	0.853123	+	0.0814633i	0.340674	+	0.940181i	$0.389345\pi$
$158$	−9.08746	−	3.63807i	−0.722960	−	0.289429i
$159$	0.464462	−	9.75026i	0.0368342	−	0.773246i
$160$	−3.54337			−0.280128
$161$	5.56522	−	11.4030i	0.438601	−	0.898682i
$162$	1.00000			0.0785674
$163$	0.143112	−	3.00430i	0.0112094	−	0.235315i	−0.986309	−	0.164908i	$-0.947267\pi$
$163$	0.143112	−	3.00430i	0.0112094	−	0.235315i	0.997518	−	0.0704067i	$-0.0224297\pi$
$164$	−7.57175	−	3.03127i	−0.591254	−	0.236702i
$165$	−4.79616	−	0.457977i	−0.373380	−	0.0356535i
$166$	1.96463	+	8.09832i	0.152485	+	0.628552i
$167$	1.97344	−	4.32123i	0.152709	−	0.334387i	−0.817780	−	0.575531i	$-0.804795\pi$
$167$	1.97344	−	4.32123i	0.152709	−	0.334387i	0.970489	+	0.241144i	$0.0775226\pi$
$168$	−1.69437	−	2.03203i	−0.130723	−	0.156774i
$169$	−1.44737	+	10.0667i	−0.111336	+	0.774362i
$170$	10.3807	+	9.89800i	0.796165	+	0.759142i
$171$	4.96163	−	0.956276i	0.379425	−	0.0731283i
$172$	0.276772	+	5.81016i	0.0211037	+	0.443021i
$173$	−12.0726	−	6.22386i	−0.917863	−	0.473192i	−0.0665111	−	0.997786i	$-0.521187\pi$
$173$	−12.0726	−	6.22386i	−0.917863	−	0.473192i	−0.851352	+	0.524594i	$0.824217\pi$
$174$	−4.00293	−	4.61962i	−0.303461	−	0.350213i
$175$	2.46910	+	19.8369i	0.186646	+	1.49953i
$176$	−0.193507	+	1.34587i	−0.0145862	+	0.101449i
$177$	10.1242	+	1.95128i	0.760982	+	0.146667i
$178$	−5.90928	−	8.29842i	−0.442919	−	0.621993i
$179$	12.0144	−	11.4557i	0.897996	−	0.856237i	−0.0922264	−	0.995738i	$-0.529398\pi$
$179$	12.0144	−	11.4557i	0.897996	−	0.856237i	0.990222	+	0.139501i	$0.0445499\pi$
$180$	−2.05536	+	2.88635i	−0.153197	+	0.215136i
$181$	0.661759	+	4.60264i	0.0491882	+	0.342111i	0.999523	+	0.0308820i	$0.00983160\pi$
$181$	0.661759	+	4.60264i	0.0491882	+	0.342111i	−0.950335	+	0.311229i	$0.899259\pi$
$182$	3.93636	+	12.1118i	0.291782	+	0.897789i
$183$	7.61198			0.562694
$184$	−1.16175	+	4.65299i	−0.0856453	+	0.343023i
$185$	7.05019	−	12.2113i	0.518340	−	0.897791i
$186$	3.04307	−	1.56881i	0.223129	−	0.115031i
$187$	4.32645	−	3.40235i	0.316381	−	0.248805i
$188$	−5.39755	−	11.8190i	−0.393657	−	0.861989i
$189$	−2.63807	+	0.201499i	−0.191891	+	0.0146569i
$190$	−7.43779	+	16.2865i	−0.539594	+	1.18155i
$191$	−8.43885	−	1.62646i	−0.610614	−	0.117686i	−0.125436	−	0.992102i	$-0.540033\pi$
$191$	−8.43885	−	1.62646i	−0.610614	−	0.117686i	−0.485178	+	0.874416i	$0.661245\pi$
$192$	0.786053	+	0.618159i	0.0567285	+	0.0446118i
$193$	1.87317	−	7.72130i	0.134834	−	0.555792i	−0.863814	−	0.503810i	$-0.831931\pi$
$193$	1.87317	−	7.72130i	0.134834	−	0.555792i	0.998648	−	0.0519815i	$-0.0165537\pi$
$194$	2.98215	−	8.61634i	0.214106	−	0.618617i
$195$	14.3486	−	9.22127i	1.02752	−	0.660349i
$196$	4.87930	+	5.01921i	0.348522	+	0.358515i
$197$	−7.04705	−	8.13273i	−0.502081	−	0.579433i	0.446972	−	0.894548i	$-0.352502\pi$
$197$	−7.04705	−	8.13273i	−0.502081	−	0.579433i	−0.949053	+	0.315115i	$0.897957\pi$
$198$	0.984071	+	0.938310i	0.0699349	+	0.0666828i
$199$	6.40612	+	5.03782i	0.454117	+	0.357122i	0.818867	−	0.573984i	$-0.194603\pi$
$199$	6.40612	+	5.03782i	0.454117	+	0.357122i	−0.364749	+	0.931106i	$0.618845\pi$
$200$	−2.47116	−	7.13994i	−0.174737	−	0.504870i
$201$	5.12206	−	0.489097i	0.361282	−	0.0344983i
$202$	4.37355	+	1.28419i	0.307722	+	0.0903552i
$203$	11.4908	+	11.3803i	0.806499	+	0.798740i
$204$	−0.576079	−	4.00672i	−0.0403336	−	0.280526i
$205$	1.37510	−	28.8669i	0.0960412	−	2.01615i
$206$	−2.30248	+	3.98800i	−0.160421	+	0.277857i
$207$	3.11634	+	3.64533i	0.216600	+	0.253368i
$208$	−2.40677	−	4.16865i	−0.166880	−	0.289044i
$209$	5.77988	+	3.71450i	0.399803	+	0.256938i
$210$	4.84058	−	8.02853i	0.334031	−	0.554021i
$211$	3.64916	+	7.99055i	0.251219	+	0.550092i	0.992662	−	0.120923i	$-0.0385855\pi$
$211$	3.64916	+	7.99055i	0.251219	+	0.550092i	−0.741443	+	0.671016i	$0.765858\pi$
$212$	−2.30132	−	9.48616i	−0.158055	−	0.651512i
$213$	8.24024	+	11.5718i	0.564612	+	0.792887i
$214$	−6.04076	−	17.4536i	−0.412938	−	1.19311i
$215$	−19.1345	+	7.66030i	−1.30496	+	0.522428i
$216$	0.959493	−	0.281733i	0.0652852	−	0.0191695i
$217$	−7.71170	+	4.75180i	−0.523504	+	0.322573i
$218$	−12.2907	+	7.89877i	−0.832433	+	0.534972i
$219$	−2.24801	−	1.15893i	−0.151906	−	0.0783131i
$220$	−4.73090	+	0.911807i	−0.318958	+	0.0614740i
$221$	−4.59373	+	18.9356i	−0.309008	+	1.27375i
$222$	−3.69432	+	1.47898i	−0.247946	+	0.0992627i
$223$	9.73288	−	11.2323i	0.651762	−	0.752174i	−0.329646	−	0.944105i	$-0.606929\pi$
$223$	9.73288	−	11.2323i	0.651762	−	0.752174i	0.981408	+	0.191931i	$0.0614749\pi$
$224$	−2.19822	−	1.47236i	−0.146875	−	0.0983759i
$225$	−7.24944	−	2.12863i	−0.483296	−	0.141908i
$226$	5.05959	−	7.10519i	0.336559	−	0.472630i
$227$	−19.5558	−	7.82896i	−1.29796	−	0.519626i	−0.383219	−	0.923658i	$-0.625184\pi$
$227$	−19.5558	−	7.82896i	−1.29796	−	0.519626i	−0.914745	+	0.404031i	$0.867609\pi$
$228$	4.49124	−	2.31539i	0.297439	−	0.153341i
$229$	−11.9237	−	20.6525i	−0.787942	−	1.36476i	−0.927226	−	0.374503i	$-0.877813\pi$
$229$	−11.9237	−	20.6525i	−0.787942	−	1.36476i	0.139283	−	0.990253i	$-0.455520\pi$
$230$	−16.9269	+	1.50236i	−1.11613	+	0.0990626i
$231$	−2.78511	−	2.27703i	−0.183247	−	0.149818i
$232$	−5.14228	−	3.30474i	−0.337607	−	0.216967i
$233$	−3.88267	+	3.05337i	−0.254362	+	0.200033i	−0.737195	−	0.675680i	$-0.763850\pi$
$233$	−3.88267	+	3.05337i	−0.254362	+	0.200033i	0.482833	+	0.875712i	$0.339608\pi$
$234$	−4.79175	−	0.457557i	−0.313246	−	0.0299114i
$235$	33.3204	−	31.7710i	2.17358	−	2.07251i
$236$	10.2638	−	0.980079i	0.668120	−	0.0637977i
$237$	−6.41020	+	7.39776i	−0.416387	+	0.480536i
$238$	2.32709	+	10.4539i	0.150843	+	0.677626i
$239$	−23.2658	+	6.83145i	−1.50494	+	0.441890i	−0.927274	−	0.374384i	$-0.877854\pi$
$239$	−23.2658	+	6.83145i	−1.50494	+	0.441890i	−0.577665	+	0.816274i	$0.696036\pi$
$240$	−1.15892	+	3.34849i	−0.0748082	+	0.216144i
$241$	0.593677	+	12.4628i	0.0382421	+	0.802800i	0.933787	+	0.357829i	$0.116483\pi$
$241$	0.593677	+	12.4628i	0.0382421	+	0.802800i	−0.895545	+	0.444971i	$0.853214\pi$
$242$	−0.435431	−	9.14081i	−0.0279905	−	0.587594i
$243$	0.327068	−	0.945001i	0.0209814	−	0.0606218i
$244$	7.30364	−	2.14454i	0.467568	−	0.137290i
$245$	−11.1520	+	22.1552i	−0.712476	+	1.41544i
$246$	−5.34103	+	6.16388i	−0.340532	+	0.392994i
$247$	−24.2125	+	2.31201i	−1.54060	+	0.147110i
$248$	2.47782	−	2.36259i	0.157342	−	0.150025i
$249$	8.29549	+	0.792123i	0.525705	+	0.0501988i
$250$	7.11775	−	5.59746i	0.450166	−	0.354015i
$251$	1.15853	+	0.744541i	0.0731256	+	0.0469950i	0.576693	−	0.816961i	$-0.304343\pi$
$251$	1.15853	+	0.744541i	0.0731256	+	0.0469950i	−0.503567	+	0.863956i	$0.667979\pi$
$252$	−2.47444	+	0.936566i	−0.155875	+	0.0589981i
$253$	−0.353756	+	6.51135i	−0.0222405	+	0.409365i
$254$	−1.07132	−	1.85559i	−0.0672208	−	0.116430i
$255$	12.7488	−	6.57248i	0.798362	−	0.411584i
$256$	0.928368	+	0.371662i	0.0580230	+	0.0232289i
$257$	−7.33407	+	10.2993i	−0.457487	+	0.642450i	−0.977308	−	0.211825i	$-0.932059\pi$
$257$	−7.33407	+	10.2993i	−0.457487	+	0.642450i	0.519821	+	0.854275i	$0.325999\pi$
$258$	5.58113	+	1.63877i	0.347466	+	0.102025i
$259$	9.44784	−	4.64605i	0.587060	−	0.288692i
$260$	11.1694	−	12.8902i	0.692698	−	0.799417i
$261$	−5.67478	+	2.27184i	−0.351260	+	0.140623i
$262$	−4.08885	+	16.8545i	−0.252610	+	1.04127i
$263$	24.2714	−	4.67794i	1.49664	−	0.288454i	0.625786	−	0.779995i	$-0.284778\pi$
$263$	24.2714	−	4.67794i	1.49664	−	0.288454i	0.870855	+	0.491541i	$0.163566\pi$
$264$	1.20856	+	0.623057i	0.0743818	+	0.0383465i
$265$	29.0973	−	18.6997i	1.78743	−	1.14871i
$266$	−11.3816	+	7.01314i	−0.697853	+	0.430003i
$267$	−9.77475	+	2.87012i	−0.598205	+	0.175649i
$268$	4.77678	−	1.91234i	0.291789	−	0.116815i
$269$	2.37362	+	6.85812i	0.144722	+	0.418147i	0.993944	−	0.109890i	$-0.0350497\pi$
$269$	2.37362	+	6.85812i	0.144722	+	0.418147i	−0.849222	+	0.528036i	$0.822929\pi$
$270$	2.05536	+	2.88635i	0.125085	+	0.175657i
$271$	−5.00044	−	20.6121i	−0.303755	−	1.25210i	−0.895168	−	0.445728i	$-0.852945\pi$
$271$	−5.00044	−	20.6121i	−0.303755	−	1.25210i	0.591413	−	0.806369i	$-0.298570\pi$
$272$	−1.68157	−	3.68212i	−0.101960	−	0.223261i
$273$	12.7332	+	0.241532i	0.770646	+	0.0146182i
$274$	−13.8715	−	8.91466i	−0.838007	−	0.538554i
$275$	−5.13665	−	8.89694i	−0.309752	−	0.536506i
$276$	4.01711	+	2.61970i	0.241802	+	0.157687i
$277$	−12.4158	+	21.5049i	−0.745995	+	1.29210i	0.203733	+	0.979026i	$0.434693\pi$
$277$	−12.4158	+	21.5049i	−0.745995	+	1.29210i	−0.949728	+	0.313075i	$0.898641\pi$
$278$	0.806812	−	16.9371i	0.0483893	−	1.01582i
$279$	−0.487237	−	3.38881i	−0.0291701	−	0.202883i
$280$	2.38260	−	9.06706i	0.142388	−	0.541861i
$281$	−13.6990	−	4.02238i	−0.817213	−	0.239955i	−0.153697	−	0.988118i	$-0.549118\pi$
$281$	−13.6990	−	4.02238i	−0.817213	−	0.239955i	−0.663515	+	0.748163i	$0.730936\pi$
$282$	−12.9343	+	1.23508i	−0.770228	+	0.0735478i
$283$	−9.26416	−	26.7670i	−0.550697	−	1.59114i	−0.785347	−	0.619055i	$-0.787516\pi$
$283$	−9.26416	−	26.7670i	−0.550697	−	1.59114i	0.234650	−	0.972080i	$-0.424606\pi$
$284$	11.1666	+	8.78152i	0.662616	+	0.521087i
$285$	12.9581	+	12.3555i	0.767570	+	0.731877i
$286$	−4.28609	−	4.94641i	−0.253442	−	0.292488i
$287$	12.8480	−	17.3369i	0.758392	−	1.02337i
$288$	0.841254	−	0.540641i	0.0495713	−	0.0318576i
$289$	0.200932	−	0.580556i	0.0118195	−	0.0341503i
$290$	5.10639	−	21.0488i	0.299857	−	1.23603i
$291$	−7.16709	−	5.63626i	−0.420142	−	0.330403i
$292$	−2.48346	−	0.478647i	−0.145333	−	0.0280107i
$293$	3.58146	−	7.84229i	0.209231	−	0.458152i	−0.775700	−	0.631102i	$-0.782603\pi$
$293$	3.58146	−	7.84229i	0.209231	−	0.458152i	0.984931	+	0.172951i	$0.0553301\pi$
$294$	6.33902	−	2.96932i	0.369699	−	0.173174i
$295$	15.1768	+	33.2326i	0.883627	+	1.93487i
$296$	−3.12799	+	2.45988i	−0.181811	+	0.142978i
$297$	1.20856	−	0.623057i	0.0701279	−	0.0361534i
$298$	2.48304	−	4.30075i	0.143839	−	0.249136i
$299$	−13.2648	−	18.8934i	−0.767120	−	1.09263i
$300$	−7.55549			−0.436216
$301$	−15.0536	−	3.19859i	−0.867675	−	0.184363i
$302$	1.98947	+	13.8370i	0.114481	+	0.796232i
$303$	2.64401	−	3.71299i	0.151894	−	0.213306i
$304$	3.65699	−	3.48693i	0.209743	−	0.199989i
$305$	15.6453	+	21.9708i	0.895850	+	1.25804i
$306$	−3.97477	−	0.766074i	−0.227222	−	0.0437935i
$307$	0.980222	−	6.81759i	0.0559442	−	0.389101i	−0.942541	−	0.334089i	$-0.891571\pi$
$307$	0.980222	−	6.81759i	0.0559442	−	0.389101i	0.998486	−	0.0550115i	$-0.0175196\pi$
$308$	−3.31381	−	1.40014i	−0.188822	−	0.0797805i
$309$	3.01560	+	3.48019i	0.171552	+	0.197981i
$310$	10.7827	+	5.55888i	0.612417	+	0.315723i
$311$	0.880615	+	18.4864i	0.0499351	+	1.04827i	0.875273	+	0.483628i	$0.160681\pi$
$311$	0.880615	+	18.4864i	0.0499351	+	1.04827i	−0.825338	+	0.564639i	$0.809016\pi$
$312$	−4.72656	+	0.910970i	−0.267589	+	0.0515735i
$313$	−2.92762	−	2.79148i	−0.165479	−	0.157784i	0.602815	−	0.797881i	$-0.294046\pi$
$313$	−2.92762	−	2.79148i	−0.165479	−	0.157784i	−0.768294	+	0.640097i	$0.778894\pi$
$314$	1.52821	−	10.6289i	0.0862418	−	0.599825i
$315$	−6.00377	−	7.20022i	−0.338274	−	0.405687i
$316$	−4.06635	+	8.90406i	−0.228750	+	0.500893i
$317$	0.221198	+	0.911792i	0.0124237	+	0.0512113i	0.977686	−	0.210071i	$-0.0673697\pi$
$317$	0.221198	+	0.911792i	0.0124237	+	0.0512113i	−0.965262	+	0.261283i	$0.915855\pi$
$318$	−9.71711	−	0.927872i	−0.544909	−	0.0520325i
$319$	−7.71607	−	3.08905i	−0.432017	−	0.172954i
$320$	−0.168600	+	3.53936i	−0.00942505	+	0.197856i
$321$	−18.4694			−1.03086
$322$	−11.1253	−	6.10150i	−0.619987	−	0.340023i
$323$	−20.4539			−1.13809
$324$	0.0475819	−	0.998867i	0.00264344	−	0.0554926i
$325$	33.7635	+	13.5169i	1.87286	+	0.749782i
$326$	−2.99409	−	0.285901i	−0.165827	−	0.0158346i
$327$	3.44444	+	14.1982i	0.190478	+	0.785161i
$328$	−3.38812	+	7.41894i	−0.187077	+	0.409642i
$329$	33.8727	−	5.86447i	1.86747	−	0.323319i
$330$	−0.685669	+	4.76893i	−0.0377448	+	0.262521i
$331$	−2.17213	−	2.07112i	−0.119391	−	0.113839i	0.628032	−	0.778187i	$-0.283861\pi$
$331$	−2.17213	−	2.07112i	−0.119391	−	0.113839i	−0.747423	+	0.664348i	$0.768709\pi$
$332$	8.18263	−	1.57707i	0.449080	−	0.0865531i
$333$	0.189346	+	3.97486i	0.0103761	+	0.217821i
$334$	−4.22244	−	2.17682i	−0.231042	−	0.119110i
$335$	11.9394	+	13.7788i	0.652317	+	0.752814i
$336$	−2.11034	+	1.59576i	−0.115129	+	0.0870558i
$337$	−3.02402	+	21.0325i	−0.164729	+	1.14572i	0.724841	+	0.688916i	$0.241913\pi$
$337$	−3.02402	+	21.0325i	−0.164729	+	1.14572i	−0.889570	+	0.456799i	$0.848996\pi$
$338$	9.98643	+	1.92473i	0.543190	+	0.104691i
$339$	−5.05959	−	7.10519i	−0.274799	−	0.385901i
$340$	10.3807	−	9.89800i	0.562974	−	0.536795i
$341$	2.70028	−	3.79201i	0.146228	−	0.205349i
$342$	−0.719109	−	5.00151i	−0.0388850	−	0.270451i
$343$	−16.1244	+	9.11058i	−0.870638	+	0.491925i
$344$	5.81675			0.313618
$345$	−4.11651	+	16.4873i	−0.221625	+	0.887646i
$346$	−6.79125	+	11.7628i	−0.365100	+	0.632372i
$347$	−14.1745	+	7.30747i	−0.760928	+	0.392286i	−0.794589	−	0.607148i	$-0.792314\pi$
$347$	−14.1745	+	7.30747i	−0.760928	+	0.392286i	0.0336612	+	0.999433i	$0.489283\pi$
$348$	−4.80486	+	3.77858i	−0.257567	+	0.202553i
$349$	−10.6430	−	23.3050i	−0.569709	−	1.24749i	−0.946952	−	0.321374i	$-0.895855\pi$
$349$	−10.6430	−	23.3050i	−0.569709	−	1.24749i	0.377244	−	0.926114i	$-0.376872\pi$
$350$	19.9319	−	1.52242i	1.06540	−	0.0813770i
$351$	−1.99962	+	4.37856i	−0.106732	+	0.233710i
$352$	1.33514	+	0.257327i	0.0711633	+	0.0137156i
$353$	9.22165	+	7.25199i	0.490819	+	0.385984i	0.832670	−	0.553770i	$-0.186811\pi$
$353$	9.22165	+	7.25199i	0.490819	+	0.385984i	−0.341851	+	0.939754i	$0.611054\pi$
$354$	2.43080	−	10.0199i	0.129196	−	0.532551i
$355$	−16.4636	+	47.5684i	−0.873796	+	2.52467i
$356$	−8.57019	+	5.50773i	−0.454219	+	0.291909i
$357$	10.6401	+	1.22004i	0.563132	+	0.0645715i
$358$	−10.8710	−	12.5458i	−0.574552	−	0.663068i
$359$	−19.4493	−	18.5449i	−1.02650	−	0.978761i	−0.0267133	−	0.999643i	$-0.508504\pi$
$359$	−19.4493	−	18.5449i	−1.02650	−	0.978761i	−0.999782	+	0.0208818i	$0.993353\pi$
$360$	2.78528	+	2.19037i	0.146797	+	0.115443i
$361$	−2.13649	−	6.17299i	−0.112447	−	0.324894i
$362$	4.62891	−	0.442007i	0.243290	−	0.0232314i
$363$	−8.78049	−	2.57819i	−0.460856	−	0.135320i
$364$	12.2854	−	3.35560i	0.643931	−	0.175881i
$365$	−1.27539	−	8.87054i	−0.0667570	−	0.464305i
$366$	0.362193	−	7.60336i	0.0189321	−	0.397434i
$367$	9.40116	−	16.2833i	0.490737	−	0.849981i	−0.509206	−	0.860644i	$-0.670061\pi$
$367$	9.40116	−	16.2833i	0.490737	−	0.849981i	0.999943	+	0.0106635i	$0.00339436\pi$
$368$	4.59244	+	1.38183i	0.239398	+	0.0720329i
$369$	4.07799	+	7.06328i	0.212292	+	0.367700i
$370$	−11.8620	−	7.62324i	−0.616676	−	0.396313i
$371$	25.8214	+	0.489798i	1.34058	+	0.0254290i
$372$	−1.42224	−	3.11427i	−0.0737396	−	0.161467i
$373$	1.68697	+	6.95377i	0.0873478	+	0.360052i	0.998665	−	0.0516522i	$-0.0164487\pi$
$373$	1.68697	+	6.95377i	0.0873478	+	0.360052i	−0.911317	+	0.411705i	$0.864934\pi$
$374$	−3.19264	−	4.48344i	−0.165087	−	0.231833i
$375$	−2.96162	−	8.55703i	−0.152937	−	0.441883i
$376$	−12.0624	+	4.82907i	−0.622072	+	0.249040i
$377$	28.2316	−	8.28955i	1.45400	−	0.426933i
$378$	0.0757466	+	2.64467i	0.00389599	+	0.136027i
$379$	6.91826	−	4.44610i	0.355367	−	0.228381i	−0.350760	−	0.936465i	$-0.614077\pi$
$379$	6.91826	−	4.44610i	0.355367	−	0.228381i	0.706128	+	0.708085i	$0.250440\pi$
$380$	15.9141	+	8.20430i	0.816377	+	0.420872i
$381$	−2.10393	+	0.405498i	−0.107787	+	0.0207743i
$382$	−2.02615	+	8.35190i	−0.103667	+	0.427320i
$383$	11.3790	−	4.55547i	0.581441	−	0.232774i	−0.0622485	−	0.998061i	$-0.519827\pi$
$383$	11.3790	−	4.55547i	0.581441	−	0.232774i	0.643689	+	0.765287i	$0.277403\pi$
$384$	0.654861	−	0.755750i	0.0334182	−	0.0385667i
$385$	0.847905	−	12.7189i	0.0432132	−	0.648216i
$386$	−7.62343	−	2.23844i	−0.388022	−	0.113934i
$387$	3.37405	−	4.73818i	0.171512	−	0.240855i
$388$	−8.46469	−	3.38875i	−0.429729	−	0.172038i
$389$	−13.1321	+	6.77007i	−0.665824	+	0.343256i	−0.757783	−	0.652507i	$-0.773717\pi$
$389$	−13.1321	+	6.77007i	−0.665824	+	0.343256i	0.0919591	+	0.995763i	$0.470687\pi$
$390$	−8.52809	−	14.7711i	−0.431837	−	0.747963i
$391$	−9.59412	−	16.8767i	−0.485195	−	0.853491i
$392$	5.24569	−	4.63495i	0.264947	−	0.234100i
$393$	14.5902	+	9.37653i	0.735977	+	0.472983i
$394$	−8.45883	+	6.65210i	−0.426150	+	0.335128i
$395$	−34.5278	−	3.29700i	−1.73728	−	0.165890i
$396$	0.984071	−	0.938310i	0.0494514	−	0.0471518i
$397$	−12.6237	+	1.20541i	−0.633563	+	0.0604979i	−0.406896	−	0.913474i	$-0.633389\pi$
$397$	−12.6237	+	1.20541i	−0.633563	+	0.0604979i	−0.226667	+	0.973972i	$0.572783\pi$
$398$	5.33693	−	6.15915i	0.267516	−	0.308730i
$399$	2.90486	+	13.0494i	0.145425	+	0.653289i
$400$	−7.24944	+	2.12863i	−0.362472	+	0.106431i
$401$	−10.3322	+	29.8529i	−0.515964	+	1.49078i	0.322896	+	0.946435i	$0.395344\pi$
$401$	−10.3322	+	29.8529i	−0.515964	+	1.49078i	−0.838860	+	0.544347i	$0.816778\pi$
$402$	−0.244826	−	5.13953i	−0.0122108	−	0.256336i
$403$	0.784147	+	16.4613i	0.0390611	+	0.819994i
$404$	1.49084	−	4.30749i	0.0741719	−	0.214306i
$405$	3.39984	−	0.998283i	0.168939	−	0.0496051i
$406$	11.9142	−	10.9363i	0.591290	−	0.542761i
$407$	−3.54332	+	4.08921i	−0.175636	+	0.202695i
$408$	−4.02959	+	0.384779i	−0.199494	+	0.0190494i
$409$	−0.530104	+	0.505453i	−0.0262119	+	0.0249930i	−0.703072	−	0.711119i	$-0.748189\pi$
$409$	−0.530104	+	0.505453i	−0.0262119	+	0.0249930i	0.676860	+	0.736112i	$0.263340\pi$
$410$	−28.7688	−	2.74709i	−1.42079	−	0.135669i
$411$	−12.9613	+	10.1929i	−0.639333	+	0.502777i
$412$	3.87393	+	2.48962i	0.190855	+	0.122655i
$413$	−4.39361	+	26.9230i	−0.216196	+	1.32479i
$414$	3.78949	−	2.93935i	0.186243	−	0.144461i
$415$	14.7639	+	25.5718i	0.724729	+	1.25527i
$416$	−4.27845	+	2.20569i	−0.209768	+	0.108143i
$417$	−15.7417	−	6.30201i	−0.770872	−	0.308611i
$418$	3.98531	−	5.59659i	0.194928	−	0.273738i
$419$	9.79365	+	2.87568i	0.478451	+	0.140486i	0.512061	−	0.858949i	$-0.328882\pi$
$419$	9.79365	+	2.87568i	0.478451	+	0.140486i	−0.0336098	+	0.999435i	$0.510700\pi$
$420$	−7.78911	−	5.21711i	−0.380070	−	0.254569i
$421$	−4.82789	+	5.57168i	−0.235297	+	0.271547i	−0.861102	−	0.508432i	$-0.830225\pi$
$421$	−4.82789	+	5.57168i	−0.235297	+	0.271547i	0.625805	+	0.779980i	$0.284771\pi$
$422$	8.15514	−	3.26482i	0.396986	−	0.158929i
$423$	−3.06325	+	12.6269i	−0.148940	+	0.613941i
$424$	−9.58491	+	1.84734i	−0.465485	+	0.0897148i
$425$	27.1842	+	14.0144i	1.31863	+	0.679799i
$426$	11.9508	−	7.68030i	0.579017	−	0.372112i
$427$	0.576582	+	20.1312i	0.0279028	+	0.974215i
$428$	−17.7213	+	5.20344i	−0.856591	+	0.251518i
$429$	−6.07621	+	2.43255i	−0.293362	+	0.117444i
$430$	6.74117	+	19.4773i	0.325088	+	0.939280i
$431$	−6.75116	−	9.48067i	−0.325192	−	0.456668i	0.619323	−	0.785136i	$-0.287407\pi$
$431$	−6.75116	−	9.48067i	−0.325192	−	0.456668i	−0.944515	+	0.328468i	$0.893468\pi$
$432$	−0.235759	−	0.971812i	−0.0113430	−	0.0467563i
$433$	3.47732	+	7.61426i	0.167109	+	0.365918i	0.974597	−	0.223966i	$-0.0719005\pi$
$433$	3.47732	+	7.61426i	0.167109	+	0.365918i	−0.807488	+	0.589884i	$0.799173\pi$
$434$	4.37948	+	7.92907i	0.210222	+	0.380607i
$435$	−18.2210	−	11.7099i	−0.873630	−	0.561448i
$436$	7.30501	+	12.6526i	0.349846	+	0.605952i
$437$	15.9912	−	18.2078i	0.764963	−	0.870997i
$438$	−1.26458	+	2.19032i	−0.0604240	+	0.104657i
$439$	−1.31756	+	27.6589i	−0.0628835	+	1.32009i	0.718277	+	0.695757i	$0.244931\pi$
$439$	−1.31756	+	27.6589i	−0.0628835	+	1.32009i	−0.781160	+	0.624330i	$0.785372\pi$
$440$	0.685669	+	4.76893i	0.0326880	+	0.227350i
$441$	−0.732723	−	6.96155i	−0.0348916	−	0.331502i
$442$	18.6956	+	5.48952i	0.889258	+	0.261110i
$443$	41.4535	−	3.95833i	1.96952	−	0.188066i	0.970851	−	0.239685i	$-0.0770441\pi$
$443$	41.4535	−	3.95833i	1.96952	−	0.188066i	0.998667	+	0.0516188i	$0.0164381\pi$
$444$	1.30152	+	3.76050i	0.0617676	+	0.178466i
$445$	−28.3748	−	22.3142i	−1.34509	−	1.05779i
$446$	−10.7565	−	10.2563i	−0.509336	−	0.485651i
$447$	−3.25209	−	3.75311i	−0.153818	−	0.177516i
$448$	−1.57528	+	2.12567i	−0.0744252	+	0.100429i
$449$	22.4141	−	14.4047i	1.05779	−	0.679798i	0.108463	−	0.994100i	$-0.465407\pi$
$449$	22.4141	−	14.4047i	1.05779	−	0.679798i	0.949323	+	0.314303i	$0.101771\pi$
$450$	−2.47116	+	7.13994i	−0.116492	+	0.336580i
$451$	−2.61452	+	10.7772i	−0.123113	+	0.507478i
$452$	−6.85640	−	5.39193i	−0.322498	−	0.253615i
$453$	13.7267	+	2.64560i	0.644937	+	0.124301i
$454$	−8.75059	+	19.1611i	−0.410686	+	0.899276i
$455$	25.4740	+	37.2487i	1.19424	+	1.74625i
$456$	−2.09907	−	4.59632i	−0.0982979	−	0.215242i
$457$	−5.70288	+	4.48479i	−0.266769	+	0.209790i	−0.742579	−	0.669759i	$-0.766398\pi$
$457$	−5.70288	+	4.48479i	−0.266769	+	0.209790i	0.475810	+	0.879548i	$0.342155\pi$
$458$	−21.1965	+	10.9275i	−0.990446	+	0.510610i
$459$	−2.02396	+	3.50560i	−0.0944704	+	0.163627i
$460$	0.695244	+	16.9792i	0.0324159	+	0.791659i
$461$	29.7565			1.38590			0.692949	−	0.720987i	$-0.256311\pi$
$461$	29.7565			1.38590			0.692949	+	0.720987i	$0.256311\pi$
$462$	−2.40698	+	2.67361i	−0.111983	+	0.124388i
$463$	−2.54084	−	17.6719i	−0.118083	−	0.821284i	−0.959663	−	0.281152i	$-0.909283\pi$
$463$	−2.54084	−	17.6719i	−0.118083	−	0.821284i	0.841580	−	0.540132i	$-0.181626\pi$
$464$	−3.54568	+	4.97921i	−0.164604	+	0.231154i
$465$	8.77983	−	8.37155i	0.407155	−	0.388221i
$466$	2.86516	+	4.02356i	0.132726	+	0.186388i
$467$	8.52235	+	1.64255i	0.394367	+	0.0760081i	0.382580	−	0.923922i	$-0.375036\pi$
$467$	8.52235	+	1.64255i	0.394367	+	0.0760081i	0.0117876	+	0.999931i	$0.496248\pi$
$468$	−0.685039	+	4.76455i	−0.0316659	+	0.220241i
$469$	1.68148	+	13.5091i	0.0776434	+	0.623792i
$470$	−30.1495	−	34.7944i	−1.39069	−	1.60495i
$471$	−9.54451	−	4.92054i	−0.439788	−	0.226726i
$472$	−0.490595	−	10.2989i	−0.0225815	−	0.474043i
$473$	7.76618	−	1.49681i	0.357090	−	0.0688234i
$474$	7.08438	+	6.75494i	0.325396	+	0.310265i
$475$	−5.43322	+	37.7889i	−0.249293	+	1.73387i
$476$	10.5528	−	1.82703i	0.483687	−	0.0837419i
$477$	−4.05500	+	8.87920i	−0.185666	+	0.406551i
$478$	5.71668	+	23.5645i	0.261475	+	1.07781i
$479$	0.901771	+	0.0861087i	0.0412030	+	0.00393441i	0.115637	−	0.993292i	$-0.463109\pi$
$479$	0.901771	+	0.0861087i	0.0412030	+	0.00393441i	−0.0744342	+	0.997226i	$0.523715\pi$
$480$	3.28955	+	1.31694i	0.150147	+	0.0601097i
$481$	0.911425	−	19.1332i	0.0415574	−	0.872397i
$482$	12.4769			0.568309
$483$	−9.40464	+	8.51779i	−0.427926	+	0.387573i
$484$	−9.15118			−0.415963
$485$	1.53727	−	32.2712i	0.0698037	−	1.46536i
$486$	−0.928368	−	0.371662i	−0.0421116	−	0.0168590i
$487$	35.0946	+	3.35113i	1.59029	+	0.151854i	0.852335	−	0.522996i	$-0.175186\pi$
$487$	35.0946	+	3.35113i	1.59029	+	0.151854i	0.737954	+	0.674851i	$0.235792\pi$
$488$	−1.79459	−	7.39741i	−0.0812374	−	0.334865i
$489$	−1.24945	+	2.73590i	−0.0565019	+	0.123722i
$490$	21.5994	+	12.1936i	0.975763	+	0.550850i
$491$	3.50829	−	24.4007i	0.158327	−	1.10119i	−0.743389	−	0.668860i	$-0.766783\pi$
$491$	3.50829	−	24.4007i	0.158327	−	1.10119i	0.901716	−	0.432329i	$-0.142308\pi$
$492$	5.90276	+	5.62827i	0.266117	+	0.253742i
$493$	24.2963	−	4.68273i	1.09425	−	0.210900i
$494$	1.15732	+	24.2950i	0.0520701	+	1.09309i
$495$	4.28238	+	2.20772i	0.192479	+	0.0992297i
$496$	−2.24202	−	2.58743i	−0.100670	−	0.116179i
$497$	−29.9794	+	22.6692i	−1.34476	+	1.01685i
$498$	1.18594	−	8.24841i	0.0531433	−	0.369620i
$499$	−12.8880	−	2.48396i	−0.576947	−	0.111198i	−0.107574	−	0.994197i	$-0.534308\pi$
$499$	−12.8880	−	2.48396i	−0.576947	−	0.111198i	−0.469374	+	0.883000i	$0.655520\pi$
$500$	−5.25244	−	7.37603i	−0.234896	−	0.329866i
$501$	−3.43812	+	3.27824i	−0.153604	+	0.146461i
$502$	0.798822	−	1.12179i	0.0356532	−	0.0500679i
$503$	2.09962	+	14.6031i	0.0936172	+	0.651122i	0.981558	+	0.191164i	$0.0612264\pi$
$503$	2.09962	+	14.6031i	0.0936172	+	0.651122i	−0.887941	+	0.459958i	$0.847865\pi$
$504$	0.817767	+	2.51620i	0.0364262	+	0.112080i
$505$	16.1513			0.718726
$506$	6.48715	+	0.663178i	0.288389	+	0.0294819i
$507$	5.08511	−	8.80767i	0.225838	−	0.391162i
$508$	−1.90446	+	0.981817i	−0.0844967	+	0.0435611i
$509$	13.2707	−	10.4362i	0.588213	−	0.462576i	−0.279153	−	0.960247i	$-0.590054\pi$
$509$	13.2707	−	10.4362i	0.588213	−	0.462576i	0.867366	+	0.497671i	$0.165811\pi$
$510$	−5.95842	−	13.0471i	−0.263843	−	0.577736i
$511$	2.89470	−	6.03302i	0.128054	−	0.266885i
$512$	0.415415	−	0.909632i	0.0183589	−	0.0402004i
$513$	−4.96163	−	0.956276i	−0.219061	−	0.0422206i
$514$	9.93862	+	7.81582i	0.438374	+	0.344741i
$515$	−3.84689	+	15.8571i	−0.169514	+	0.698747i
$516$	1.90247	−	5.49683i	0.0837517	−	0.241985i
$517$	−14.8624	+	9.55149i	−0.653648	+	0.420074i
$518$	−4.19124	−	9.65821i	−0.184153	−	0.424357i
$519$	8.89465	+	10.2650i	0.390432	+	0.450582i
$520$	−12.3441	−	11.7701i	−0.541326	−	0.516154i
$521$	10.6322	+	8.36126i	0.465806	+	0.366314i	0.823304	−	0.567600i	$-0.192128\pi$
$521$	10.6322	+	8.36126i	0.465806	+	0.366314i	−0.357499	+	0.933914i	$0.616370\pi$
$522$	1.99925	+	5.77645i	0.0875047	+	0.252828i
$523$	−11.5995	+	1.10761i	−0.507209	+	0.0484326i	−0.345524	−	0.938410i	$-0.612299\pi$
$523$	−11.5995	+	1.10761i	−0.507209	+	0.0484326i	−0.161685	+	0.986842i	$0.551693\pi$
$524$	16.6408	+	4.88619i	0.726958	+	0.213454i
$525$	5.08039	−	19.3336i	0.221726	−	0.843787i
$526$	−3.51776	−	24.4665i	−0.153381	−	1.06679i
$527$	−0.659423	+	13.8430i	−0.0287249	+	0.603010i
$528$	0.679857	−	1.17755i	0.0295870	−	0.0512461i
$529$	22.5242	+	4.65392i	0.979314	+	0.202345i
$530$	−17.2940	−	29.9541i	−0.751203	−	1.30112i
$531$	−8.67377	−	5.57430i	−0.376410	−	0.241904i
$532$	6.46364	+	11.7024i	0.280234	+	0.507365i
$533$	−16.3088	−	35.7114i	−0.706415	−	1.54683i
$534$	2.40177	+	9.90024i	0.103935	+	0.428425i
$535$	−37.9613	−	53.3092i	−1.64121	−	2.30476i
$536$	−1.68288	−	4.86237i	−0.0726894	−	0.210022i
$537$	−15.4114	+	6.16979i	−0.665051	+	0.266246i
$538$	6.96329	−	2.04461i	0.300209	−	0.0881492i
$539$	5.81103	−	7.53818i	0.250299	−	0.324692i
$540$	2.98087	−	1.91569i	0.128276	−	0.0824383i
$541$	7.86339	+	4.05386i	0.338074	+	0.174289i	0.618901	−	0.785469i	$-0.287578\pi$
$541$	7.86339	+	4.05386i	0.338074	+	0.174289i	−0.280827	+	0.959758i	$0.590609\pi$
$542$	−20.8267	+	4.01402i	−0.894583	+	0.172417i
$543$	1.09627	−	4.51889i	0.0470455	−	0.193924i
$544$	−3.75796	+	1.50446i	−0.161121	+	0.0645032i
$545$	−33.9013	+	39.1242i	−1.45217	+	1.67590i
$546$	0.847126	−	12.7072i	0.0362536	−	0.543820i
$547$	29.2585	+	8.59107i	1.25100	+	0.367328i	0.839139	−	0.543918i	$-0.183060\pi$
$547$	29.2585	+	8.59107i	1.25100	+	0.367328i	0.411864	+	0.911245i	$0.364878\pi$
$548$	−9.56459	+	13.4316i	−0.408579	+	0.573769i
$549$	−7.06672	−	2.82909i	−0.301600	−	0.120743i
$550$	−9.13127	+	4.70750i	−0.389359	+	0.200728i
$551$	15.4434	+	26.7488i	0.657912	+	1.13954i
$552$	2.80787	−	3.88791i	0.119511	−	0.165480i
$553$	−20.0502	−	16.3925i	−0.852620	−	0.697079i
$554$	20.8897	+	13.4250i	0.887520	+	0.570374i
$555$	−11.0836	+	8.71627i	−0.470474	+	0.369985i
$556$	−16.8795	−	1.61180i	−0.715850	−	0.0683554i
$557$	−5.62842	+	5.36668i	−0.238484	+	0.227394i	−0.799890	−	0.600147i	$-0.795109\pi$
$557$	−5.62842	+	5.36668i	−0.238484	+	0.227394i	0.561406	+	0.827540i	$0.310260\pi$
$558$	−3.40815	+	0.325439i	−0.144279	+	0.0137769i
$559$	−18.3356	+	21.1604i	−0.775512	+	0.894988i
$560$	−8.94342	−	2.81133i	−0.377929	−	0.118800i
$561$	−5.28106	+	1.55066i	−0.222967	+	0.0654689i
$562$	−4.66965	+	13.4921i	−0.196977	+	0.569129i
$563$	−1.77329	−	37.2259i	−0.0747353	−	1.56889i	−0.655740	−	0.754986i	$-0.727643\pi$
$563$	−1.77329	−	37.2259i	−0.0747353	−	1.56889i	0.581005	−	0.813900i	$-0.302660\pi$
$564$	0.618239	+	12.9784i	0.0260326	+	0.546491i
$565$	10.1088	−	29.2074i	0.425280	−	1.22877i
$566$	−27.1775	+	7.98004i	−1.14236	+	0.335426i
$567$	2.52399	+	0.793405i	0.105997	+	0.0333199i
$568$	9.30290	−	10.7361i	0.390341	−	0.450477i
$569$	19.7434	−	1.88527i	0.827688	−	0.0790347i	0.327392	−	0.944889i	$-0.393830\pi$
$569$	19.7434	−	1.88527i	0.827688	−	0.0790347i	0.500297	+	0.865854i	$0.333224\pi$
$570$	12.9581	−	12.3555i	0.542754	−	0.517515i
$571$	−33.0901	−	3.15972i	−1.38478	−	0.132230i	−0.624091	−	0.781351i	$-0.714531\pi$
$571$	−33.0901	−	3.15972i	−1.38478	−	0.132230i	−0.760685	+	0.649121i	$0.775137\pi$
$572$	−5.14475	+	4.04588i	−0.215113	+	0.169167i
$573$	7.22987	+	4.64635i	0.302032	+	0.194104i
$574$	−16.7060	−	13.6583i	−0.697293	−	0.570088i
$575$	−33.7284	+	13.2423i	−1.40657	+	0.552241i
$576$	−0.500000	−	0.866025i	−0.0208333	−	0.0360844i
$577$	−5.38389	+	2.77559i	−0.224134	+	0.115549i	−0.566637	−	0.823968i	$-0.691756\pi$
$577$	−5.38389	+	2.77559i	−0.224134	+	0.115549i	0.342503	+	0.939517i	$0.388725\pi$
$578$	−0.570338	−	0.228329i	−0.0237229	−	0.00949722i
$579$	−4.60871	+	6.47202i	−0.191531	+	0.268968i
$580$	−20.7820	−	6.10214i	−0.862925	−	0.253378i
$581$	−1.46655	+	21.9988i	−0.0608426	+	0.912665i
$582$	−5.97090	+	6.89079i	−0.247502	+	0.285632i
$583$	−12.3218	+	4.93292i	−0.510319	+	0.204301i
$584$	−0.596272	+	2.45787i	−0.0246739	+	0.101707i
$585$	−16.7480	+	3.22790i	−0.692443	+	0.133457i
$586$	−7.66300	−	3.95055i	−0.316556	−	0.163196i
$587$	25.3178	−	16.2708i	1.04498	−	0.671567i	0.0987653	−	0.995111i	$-0.468511\pi$
$587$	25.3178	−	16.2708i	1.04498	−	0.671567i	0.946213	+	0.323544i	$0.104874\pi$
$588$	−2.66434	−	6.47312i	−0.109875	−	0.266947i
$589$	−16.5988	+	4.87385i	−0.683942	+	0.200823i
$590$	33.9171	−	13.5783i	1.39634	−	0.559011i
$591$	3.51962	+	10.1693i	0.144778	+	0.418309i
$592$	2.30826	+	3.24150i	0.0948688	+	0.133225i
$593$	4.29416	+	17.7008i	0.176340	+	0.726883i	0.989462	+	0.144790i	$0.0462507\pi$
$593$	4.29416	+	17.7008i	0.176340	+	0.726883i	−0.813122	+	0.582093i	$0.802234\pi$
$594$	−0.564845	−	1.23684i	−0.0231759	−	0.0507481i
$595$	18.3477	+	33.2185i	0.752182	+	1.36183i
$596$	−4.17773	−	2.68486i	−0.171126	−	0.109976i
$597$	−4.07486	−	7.05787i	−0.166773	−	0.288859i
$598$	−19.5032	+	12.3507i	−0.797545	+	0.505059i
$599$	−8.78868	+	15.2224i	−0.359096	+	0.621972i	−0.987810	−	0.155665i	$-0.950248\pi$
$599$	−8.78868	+	15.2224i	−0.359096	+	0.621972i	0.628714	+	0.777636i	$0.283581\pi$
$600$	−0.359505	+	7.54693i	−0.0146767	+	0.308102i
$601$	−0.470552	−	3.27276i	−0.0191942	−	0.133499i	0.977971	−	0.208740i	$-0.0669363\pi$
$601$	−0.470552	−	3.27276i	−0.0191942	−	0.133499i	−0.997165	+	0.0752415i	$0.976027\pi$
$602$	−3.91124	+	14.8844i	−0.159410	+	0.606641i
$603$	−4.93693	−	1.44961i	−0.201048	−	0.0590329i
$604$	13.9160	−	1.32882i	0.566235	−	0.0540689i
$605$	−10.6055	−	30.6426i	−0.431176	−	1.24580i
$606$	−3.58298	−	2.81768i	−0.145548	−	0.114461i
$607$	−22.7022	−	21.6465i	−0.921455	−	0.878606i	0.0714583	−	0.997444i	$-0.477235\pi$
$607$	−22.7022	−	21.6465i	−0.921455	−	0.878606i	−0.992914	+	0.118838i	$0.962083\pi$
$608$	−3.30898	−	3.81876i	−0.134197	−	0.154871i
$609$	−6.43810	−	14.8358i	−0.260885	−	0.601177i
$610$	22.6904	−	14.5822i	0.918706	−	0.590416i
$611$	20.4559	−	59.1033i	0.827556	−	2.39107i
$612$	−0.954333	+	3.93382i	−0.0385766	+	0.159015i
$613$	28.2526	+	22.2181i	1.14111	+	0.897379i	0.995759	−	0.0920010i	$-0.0293263\pi$
$613$	28.2526	+	22.2181i	1.14111	+	0.897379i	0.145351	+	0.989380i	$0.453569\pi$
$614$	−6.76323	−	1.30351i	−0.272942	−	0.0526052i
$615$	−12.0054	+	26.2881i	−0.484103	+	1.06004i
$616$	−1.55623	+	3.24344i	−0.0627024	+	0.130682i
$617$	6.77771	+	14.8411i	0.272860	+	0.597481i	0.995607	−	0.0936323i	$-0.0298478\pi$
$617$	6.77771	+	14.8411i	0.272860	+	0.597481i	−0.722746	+	0.691113i	$0.757121\pi$
$618$	3.61974	−	2.84659i	0.145607	−	0.114507i
$619$	−33.8413	+	17.4464i	−1.36020	+	0.701230i	−0.975125	−	0.221657i	$-0.928854\pi$
$619$	−33.8413	+	17.4464i	−1.36020	+	0.701230i	−0.385071	+	0.922887i	$0.625823\pi$
$620$	6.06565	−	10.5060i	0.243602	−	0.421931i
$621$	−1.53827	−	4.54244i	−0.0617287	−	0.182282i
$622$	18.5074			0.742077
$623$	−8.33093	−	25.6335i	−0.333772	−	1.02699i
$624$	0.685039	+	4.76455i	0.0274235	+	0.190735i
$625$	−3.30170	+	4.63659i	−0.132068	+	0.185464i
$626$	−2.92762	+	2.79148i	−0.117011	+	0.111570i
$627$	−3.98531	−	5.59659i	−0.159158	−	0.223506i
$628$	−10.5442	−	2.03222i	−0.420758	−	0.0810945i
$629$	2.29243	−	15.9442i	0.0914051	−	0.635737i
$630$	−7.47774	+	5.65437i	−0.297920	+	0.225275i
$631$	1.13729	+	1.31251i	0.0452749	+	0.0522500i	0.777935	−	0.628344i	$-0.216267\pi$
$631$	1.13729	+	1.31251i	0.0452749	+	0.0522500i	−0.732660	+	0.680594i	$0.761722\pi$
$632$	8.70049	+	4.48542i	0.346087	+	0.178420i
$633$	−0.417978	−	8.77443i	−0.0166131	−	0.348752i
$634$	0.921284	−	0.177563i	0.0365889	−	0.00705192i
$635$	−5.49473	−	5.23921i	−0.218052	−	0.207912i
$636$	−1.38918	+	9.66196i	−0.0550846	+	0.383122i
$637$	0.325723	+	33.6932i	0.0129056	+	1.33498i
$638$	−3.45270	+	7.56035i	−0.136694	+	0.299317i
$639$	−3.34917	−	13.8055i	−0.132491	−	0.546136i
$640$	3.52733	+	0.336819i	0.139430	+	0.0133139i
$641$	26.0067	+	10.4115i	1.02720	+	0.411230i	0.823206	−	0.567742i	$-0.192183\pi$
$641$	26.0067	+	10.4115i	1.02720	+	0.411230i	0.203995	+	0.978972i	$0.434607\pi$
$642$	−0.878811	+	18.4485i	−0.0346839	+	0.728105i
$643$	26.0323			1.02661			0.513307	−	0.858205i	$-0.328420\pi$
$643$	26.0323			1.02661			0.513307	+	0.858205i	$0.328420\pi$
$644$	−6.62395	+	10.8224i	−0.261020	+	0.426460i
$645$	20.6109			0.811554
$646$	−0.973237	+	20.4308i	−0.0382915	+	0.803837i
$647$	−41.2126	−	16.4990i	−1.62023	−	0.648644i	−0.628601	−	0.777728i	$-0.716372\pi$
$647$	−41.2126	−	16.4990i	−1.62023	−	0.648644i	−0.991634	+	0.129084i	$0.958796\pi$
$648$	−0.995472	−	0.0950560i	−0.0391058	−	0.00373415i
$649$	−3.30519	−	13.6242i	−0.129740	−	0.534796i
$650$	15.1081	−	33.0821i	0.592589	−	1.29759i
$651$	8.92536	−	1.54527i	0.349813	−	0.0605639i
$652$	−0.428041	+	2.97709i	−0.0167634	+	0.116592i
$653$	0.525487	+	0.501051i	0.0205639	+	0.0196076i	0.700291	−	0.713857i	$-0.253053\pi$
$653$	0.525487	+	0.501051i	0.0205639	+	0.0196076i	−0.679727	+	0.733465i	$0.737902\pi$
$654$	14.3460	−	2.76496i	0.560973	−	0.108119i
$655$	2.92410	+	61.3844i	0.114254	+	2.39849i
$656$	7.24932	+	3.73728i	0.283038	+	0.145916i
$657$	1.65625	+	1.91141i	0.0646164	+	0.0745713i
$658$	−4.24610	−	34.1134i	−0.165530	−	1.32988i
$659$	0.376356	−	2.61761i	0.0146607	−	0.101968i	−0.981177	−	0.193110i	$-0.938143\pi$
$659$	0.376356	−	2.61761i	0.0146607	−	0.101968i	0.995838	+	0.0911421i	$0.0290517\pi$
$660$	4.73090	+	0.911807i	0.184150	+	0.0354920i
$661$	18.0015	+	25.2796i	0.700178	+	0.983262i	0.999576	+	0.0291335i	$0.00927479\pi$
$661$	18.0015	+	25.2796i	0.700178	+	0.983262i	−0.299398	+	0.954128i	$0.596786\pi$
$662$	−2.17213	+	2.07112i	−0.0844221	+	0.0804963i
$663$	11.3023	−	15.8719i	0.438946	−	0.616413i
$664$	−1.18594	−	8.24841i	−0.0460235	−	0.320100i
$665$	−31.6946	+	35.2057i	−1.22907	+	1.36522i
$666$	3.97937			0.154197
$667$	−14.8267	+	25.2893i	−0.574094	+	0.979205i
$668$	−2.37526	+	4.11408i	−0.0919017	+	0.159178i
$669$	−13.2103	+	6.81040i	−0.510741	+	0.263305i
$670$	14.3313	−	11.2702i	0.553665	−	0.435407i
$671$	−4.29959	−	9.41479i	−0.165984	−	0.363454i
$672$	1.49354	+	2.18388i	0.0576144	+	0.0842451i
$673$	9.82268	−	21.5087i	0.378637	−	0.829099i	−0.620360	−	0.784317i	$-0.713014\pi$
$673$	9.82268	−	21.5087i	0.378637	−	0.829099i	0.998997	−	0.0447816i	$-0.0142592\pi$
$674$	20.8648	+	4.02136i	0.803683	+	0.154897i
$675$	5.93902	+	4.67049i	0.228593	+	0.179767i
$676$	2.39772	−	9.88354i	0.0922200	−	0.380136i
$677$	−14.5220	+	41.9587i	−0.558127	+	1.61260i	0.213790	+	0.976880i	$0.431419\pi$
$677$	−14.5220	+	41.9587i	−0.558127	+	1.61260i	−0.771917	+	0.635723i	$0.780702\pi$
$678$	−7.33789	+	4.71578i	−0.281810	+	0.181108i
$679$	14.3631	−	19.3815i	0.551207	−	0.743793i
$680$	−9.39286	−	10.8399i	−0.360200	−	0.415693i
$681$	15.2452	+	14.5363i	0.584199	+	0.557033i
$682$	−3.65923	−	2.87765i	−0.140119	−	0.110191i
$683$	−5.11989	−	14.7929i	−0.195907	−	0.566036i	0.803671	−	0.595073i	$-0.202877\pi$
$683$	−5.11989	−	14.7929i	−0.195907	−	0.566036i	−0.999578	+	0.0290374i	$0.990756\pi$
$684$	−5.03007	+	0.480313i	−0.192329	+	0.0183652i
$685$	−56.0602	−	16.4608i	−2.14195	−	0.628933i
$686$	8.33303	+	16.5397i	0.318156	+	0.631488i
$687$	3.39385	+	23.6047i	0.129483	+	0.900576i
$688$	0.276772	−	5.81016i	0.0105518	−	0.221510i
$689$	23.4933	−	40.6915i	0.895022	−	1.55022i
$690$	16.2727	+	4.89634i	0.619493	+	0.186401i
$691$	−1.14074	−	1.97582i	−0.0433959	−	0.0751639i	0.843512	−	0.537111i	$-0.180484\pi$
$691$	−1.14074	−	1.97582i	−0.0433959	−	0.0751639i	−0.886908	+	0.461947i	$0.847151\pi$
$692$	11.4263	+	7.34325i	0.434364	+	0.279149i
$693$	1.73932	+	3.14905i	0.0660714	+	0.119622i
$694$	6.62474	+	14.5062i	0.251472	+	0.550646i
$695$	−14.1650	−	58.3887i	−0.537307	−	2.21481i
$696$	3.54568	+	4.97921i	0.134399	+	0.188736i
$697$	−10.7981	−	31.1990i	−0.409006	−	1.18174i
$698$	−23.7850	+	9.52209i	−0.900276	+	0.360416i
$699$	4.73937	−	1.39160i	0.179259	−	0.0526353i
$700$	−0.572303	−	19.9818i	−0.0216310	−	0.755239i
$701$	12.1671	−	7.81935i	0.459547	−	0.295333i	−0.290310	−	0.956933i	$-0.593759\pi$
$701$	12.1671	−	7.81935i	0.459547	−	0.295333i	0.749857	+	0.661600i	$0.230122\pi$
$702$	4.27845	+	2.20569i	0.161480	+	0.0832486i
$703$	19.7441	−	3.80537i	0.744665	−	0.143522i
$704$	0.320565	−	1.32139i	0.0120817	−	0.0498016i
$705$	−42.7417	+	17.1112i	−1.60975	+	0.644445i
$706$	7.68256	−	8.86614i	0.289137	−	0.333682i
$707$	10.0199	+	6.71127i	0.376837	+	0.252403i
$708$	−9.89289	−	2.90481i	−0.371797	−	0.109170i
$709$	−10.6894	+	15.0111i	−0.401448	+	0.563755i	−0.964975	−	0.262343i	$-0.915505\pi$
$709$	−10.6894	+	15.0111i	−0.401448	+	0.563755i	0.563526	+	0.826098i	$0.309444\pi$
$710$	46.7311	+	18.7083i	1.75379	+	0.702111i
$711$	8.70049	−	4.48542i	0.326294	−	0.168216i
$712$	5.09370	+	8.82255i	0.190895	+	0.330639i
$713$	−11.8073	−	11.4097i	−0.442186	−	0.427296i
$714$	1.72493	−	10.5700i	0.0645541	−	0.395571i
$715$	−19.5100	−	12.5383i	−0.729631	−	0.468905i
$716$	−13.0489	+	10.2618i	−0.487660	+	0.383500i
$717$	24.1382	+	2.30492i	0.901458	+	0.0860788i
$718$	−19.4493	+	18.5449i	−0.725842	+	0.692089i
$719$	15.8277	−	1.51136i	0.590273	−	0.0563642i	0.204354	−	0.978897i	$-0.434491\pi$
$719$	15.8277	−	1.51136i	0.590273	−	0.0563642i	0.385919	+	0.922533i	$0.373885\pi$
$720$	2.32042	−	2.67790i	0.0864768	−	0.0997995i
$721$	−8.97552	+	8.23887i	−0.334266	+	0.306832i
$722$	−6.26766	+	1.84035i	−0.233258	+	0.0684907i
$723$	4.08081	−	11.7907i	0.151767	−	0.438502i
$724$	−0.221254	−	4.64470i	−0.00822285	−	0.172619i
$725$	−2.19752	−	46.1317i	−0.0816139	−	1.71329i
$726$	−2.99306	+	8.64787i	−0.111083	+	0.320953i
$727$	7.16731	−	2.10451i	0.265821	−	0.0780520i	−0.146106	−	0.989269i	$-0.546674\pi$
$727$	7.16731	−	2.10451i	0.265821	−	0.0780520i	0.411927	+	0.911217i	$0.364856\pi$
$728$	−2.76723	−	12.4312i	−0.102560	−	0.460730i
$729$	−0.654861	+	0.755750i	−0.0242541	+	0.0279907i
$730$	−8.92118	+	0.851869i	−0.330188	+	0.0315291i
$731$	−17.0408	+	16.2484i	−0.630279	+	0.600969i
$732$	−7.57751	−	0.723565i	−0.280073	−	0.0267437i
$733$	−29.7179	+	23.3704i	−1.09766	+	0.863206i	−0.991365	−	0.131129i	$-0.958140\pi$
$733$	−29.7179	+	23.3704i	−1.09766	+	0.863206i	−0.106290	+	0.994335i	$0.533897\pi$
$734$	−15.8175	−	10.1653i	−0.583835	−	0.375208i
$735$	18.5874	−	16.4234i	0.685607	−	0.605785i
$736$	1.59878	−	4.52149i	0.0589319	−	0.166664i
$737$	−3.49811	−	6.05890i	−0.128854	−	0.223182i
$738$	7.24932	−	3.73728i	0.266851	−	0.137571i
$739$	1.78086	+	0.712948i	0.0655099	+	0.0262262i	0.404186	−	0.914677i	$-0.367555\pi$
$739$	1.78086	+	0.712948i	0.0655099	+	0.0262262i	−0.338676	+	0.940903i	$0.609979\pi$
$740$	−8.17902	+	11.4858i	−0.300667	+	0.422227i
$741$	23.3373	+	6.85246i	0.857319	+	0.251732i
$742$	1.71787	−	25.7688i	0.0630651	−	0.946003i
$743$	14.7877	−	17.0660i	0.542509	−	0.626089i	−0.416612	−	0.909084i	$-0.636783\pi$
$743$	14.7877	−	17.0660i	0.542509	−	0.626089i	0.959121	+	0.282995i	$0.0913280\pi$
$744$	−3.17841	+	1.27244i	−0.116526	+	0.0466501i
$745$	4.14857	−	17.1006i	0.151992	−	0.626519i
$746$	7.02616	−	1.35418i	0.257246	−	0.0495801i
$747$	−7.40687	−	3.81850i	−0.271003	−	0.139712i
$748$	−4.63027	+	2.97569i	−0.169299	+	0.108802i
$749$	−1.39900	−	48.8455i	−0.0511183	−	1.78478i
$750$	−8.68826	+	2.55110i	−0.317250	+	0.0931531i
$751$	30.4446	−	12.1882i	1.11094	−	0.444752i	0.257674	−	0.966232i	$-0.417044\pi$
$751$	30.4446	−	12.1882i	1.11094	−	0.444752i	0.853264	+	0.521480i	$0.174620\pi$
$752$	4.24965	+	12.2785i	0.154969	+	0.447752i
$753$	−0.798822	−	1.12179i	−0.0291107	−	0.0408803i
$754$	−6.93684	−	28.5941i	−0.252625	−	1.04133i
$755$	20.5771	+	45.0577i	0.748879	+	1.63982i
$756$	2.64528	+	0.0501775i	0.0962077	+	0.00182494i
$757$	20.5806	+	13.2263i	0.748014	+	0.480720i	0.858280	−	0.513183i	$-0.171534\pi$
$757$	20.5806	+	13.2263i	0.748014	+	0.480720i	−0.110265	+	0.993902i	$0.535170\pi$
$758$	−4.11188	−	7.12198i	−0.149350	−	0.258682i
$759$	2.74844	−	5.91345i	0.0997621	−	0.214645i
$760$	8.95223	−	15.5057i	0.324732	−	0.562452i
$761$	−1.26482	+	26.5518i	−0.0458497	+	0.962503i	0.852365	+	0.522947i	$0.175167\pi$
$761$	−1.26482	+	26.5518i	−0.0458497	+	0.962503i	−0.898215	+	0.439556i	$0.855136\pi$
$762$	0.304930	+	2.12084i	0.0110465	+	0.0768298i
$763$	−37.2886	+	10.1849i	−1.34994	+	0.368717i
$764$	8.24603	+	2.42125i	0.298331	+	0.0875979i
$765$	−14.2783	+	1.36342i	−0.516235	+	0.0492944i
$766$	−4.00888	−	11.5829i	−0.144847	−	0.418507i
$767$	39.0120	+	30.6794i	1.40864	+	1.10777i
$768$	−0.723734	−	0.690079i	−0.0261155	−	0.0249011i
$769$	−14.3337	−	16.5420i	−0.516888	−	0.596520i	0.435961	−	0.899966i	$-0.356409\pi$
$769$	−14.3337	−	16.5420i	−0.516888	−	0.596520i	−0.952849	+	0.303445i	$0.901863\pi$
$770$	−12.6642	−	1.45214i	−0.456385	−	0.0523313i
$771$	10.6366	−	6.83570i	0.383066	−	0.246182i
$772$	−2.59864	+	7.50828i	−0.0935272	+	0.270229i
$773$	−9.40757	+	38.7785i	−0.338367	+	1.39477i	0.507628	+	0.861576i	$0.330522\pi$
$773$	−9.40757	+	38.7785i	−0.338367	+	1.39477i	−0.845995	+	0.533191i	$0.820993\pi$
$774$	−4.57227	−	3.59568i	−0.164347	−	0.129244i
$775$	25.3999	+	4.89544i	0.912393	+	0.175849i
$776$	−3.78768	+	8.29386i	−0.135970	+	0.297732i
$777$	−10.4978	+	0.801839i	−0.376608	+	0.0287658i
$778$	6.13755	+	13.4394i	0.220042	+	0.481824i
$779$	32.3946	−	25.4754i	1.16066	−	0.912750i
$780$	−15.1601	+	7.81560i	−0.542820	+	0.279843i
$781$	9.65799	−	16.7281i	0.345590	−	0.598580i
$782$	−17.3141	+	8.78023i	−0.619151	+	0.313980i
$783$	6.11264			0.218448
$784$	−4.38010	−	5.46028i	−0.156432	−	0.195010i
$785$	−5.41501	−	37.6622i	−0.193270	−	1.34422i
$786$	10.0601	−	14.1275i	0.358833	−	0.503911i
$787$	4.18994	−	3.99510i	0.149355	−	0.142410i	−0.611718	−	0.791076i	$-0.709521\pi$
$787$	4.18994	−	3.99510i	0.149355	−	0.142410i	0.761073	+	0.648666i	$0.224673\pi$
$788$	6.24207	+	8.76577i	0.222365	+	0.312268i
$789$	−24.2714	−	4.67794i	−0.864086	−	0.166539i
$790$	−4.93616	+	34.3318i	−0.175621	+	1.22147i
$791$	18.4076	−	13.9191i	0.654500	−	0.494907i
$792$	−0.890423	−	1.02760i	−0.0316398	−	0.0365143i
$793$	32.5675	+	16.7897i	1.15651	+	0.596220i
$794$	0.603390	+	12.6667i	0.0214135	+	0.449525i
$795$	−33.9629	+	6.54582i	−1.20454	+	0.232156i
$796$	−5.89823	−	5.62395i	−0.209057	−	0.199336i
$797$	−2.69057	+	18.7133i	−0.0953048	+	0.662859i	0.885032	+	0.465529i	$0.154136\pi$
$797$	−2.69057	+	18.7133i	−0.0953048	+	0.662859i	−0.980337	+	0.197330i	$0.936773\pi$
$798$	13.1729	−	2.28065i	0.466314	−	0.0807342i
$799$	21.8489	−	47.8423i	0.772957	−	1.69254i
$800$	1.78127	+	7.34251i	0.0629776	+	0.259597i
$801$	10.1413	+	0.968375i	0.358324	+	0.0342158i
$802$	29.3274	+	11.7409i	1.03559	+	0.414587i
$803$	−0.163631	+	3.43504i	−0.00577441	+	0.121220i
$804$	−5.14536			−0.181463
$805$	−43.9152	−	9.63794i	−1.54781	−	0.339693i
$806$	16.4799			0.580481
$807$	0.345314	−	7.24904i	0.0121556	−	0.255178i
$808$	−4.23167	−	1.69411i	−0.148870	−	0.0595984i
$809$	−5.88769	−	0.562206i	−0.207000	−	0.0197661i	−0.00895913	−	0.999960i	$-0.502852\pi$
$809$	−5.88769	−	0.562206i	−0.207000	−	0.0197661i	−0.198041	+	0.980194i	$0.563458\pi$
$810$	−0.835382	−	3.44349i	−0.0293523	−	0.120992i
$811$	10.2214	−	22.3817i	0.358922	−	0.785929i	−0.640910	−	0.767616i	$-0.721443\pi$
$811$	10.2214	−	22.3817i	0.358922	−	0.785929i	0.999832	−	0.0183137i	$-0.00582975\pi$
$812$	−10.3570	−	12.4210i	−0.363461	−	0.435893i
$813$	−3.01850	+	20.9941i	−0.105863	+	0.736295i
$814$	3.91598	+	3.73388i	0.137255	+	0.130872i
$815$	−10.4648	+	2.01693i	−0.366567	+	0.0706500i
$816$	0.192608	+	4.04334i	0.00674262	+	0.141545i
$817$	−26.1244	−	13.4681i	−0.913977	−	0.471188i
$818$	0.479657	+	0.553554i	0.0167708	+	0.0193546i
$819$	−11.7313	−	4.95667i	−0.409924	−	0.173200i
$820$	−4.11285	+	28.6055i	−0.143627	+	0.998948i
$821$	−21.4577	−	4.13564i	−0.748881	−	0.144335i	−0.199489	−	0.979900i	$-0.563928\pi$
$821$	−21.4577	−	4.13564i	−0.748881	−	0.144335i	−0.549391	+	0.835565i	$0.685140\pi$
$822$	9.56459	+	13.4316i	0.333603	+	0.468481i
$823$	11.6395	−	11.0982i	0.405726	−	0.386859i	−0.459552	−	0.888151i	$-0.651990\pi$
$823$	11.6395	−	11.0982i	0.405726	−	0.386859i	0.865278	+	0.501292i	$0.167142\pi$
$824$	2.67113	−	3.75108i	0.0930533	−	0.130675i
$825$	1.46204	+	10.1687i	0.0509018	+	0.354030i
$826$	26.6834	+	5.66968i	0.928435	+	0.197274i
$827$	34.5142			1.20018			0.600088	−	0.799934i	$-0.295132\pi$
$827$	34.5142			1.20018			0.600088	+	0.799934i	$0.295132\pi$
$828$	−2.75571	−	3.92505i	−0.0957677	−	0.136405i
$829$	26.3244	−	45.5951i	0.914283	−	1.58358i	0.106336	−	0.994330i	$-0.466088\pi$
$829$	26.3244	−	45.5951i	0.914283	−	1.58358i	0.807948	−	0.589254i	$-0.200578\pi$
$830$	26.2453	−	13.5304i	0.910987	−	0.469647i
$831$	19.5190	−	15.3499i	0.677107	−	0.532483i
$832$	1.99962	+	4.37856i	0.0693243	+	0.151799i
$833$	−2.42065	+	28.2319i	−0.0838707	+	0.978176i
$834$	−7.04389	+	15.4240i	−0.243910	+	0.534088i
$835$	−16.5287	−	3.18565i	−0.571999	−	0.110244i
$836$	−5.40062	−	4.24710i	−0.186784	−	0.146889i
$837$	−0.807158	+	3.32715i	−0.0278994	+	0.115003i
$838$	3.33842	−	9.64573i	0.115324	−	0.333206i
$839$	−19.5495	+	12.5637i	−0.674924	+	0.433747i	−0.832698	−	0.553728i	$-0.813205\pi$
$839$	−19.5495	+	12.5637i	−0.674924	+	0.433747i	0.157773	+	0.987475i	$0.449568\pi$
$840$	−5.58182	+	7.53205i	−0.192591	+	0.259880i
$841$	−5.47748	−	6.32135i	−0.188879	−	0.217977i
$842$	5.33565	+	5.08753i	0.183879	+	0.175328i
$843$	11.2227	+	8.82565i	0.386531	+	0.303971i
$844$	−2.87309	−	8.30125i	−0.0988958	−	0.285741i
$845$	35.8737	−	3.42552i	1.23409	−	0.117842i
$846$	12.4668	+	3.66060i	0.428619	+	0.125854i
$847$	6.15335	−	23.4168i	0.211432	−	0.804610i
$848$	1.38918	+	9.66196i	0.0477046	+	0.331793i
$849$	−1.34775	+	28.2928i	−0.0462547	+	0.971006i
$850$	15.2920	−	26.4865i	0.524512	−	0.908481i
$851$	12.4010	+	14.5061i	0.425102	+	0.497263i
$852$	−7.10296	−	12.3027i	−0.243343	−	0.421483i
$853$	−35.1332	−	22.5787i	−1.20294	−	0.773080i	−0.223475	−	0.974710i	$-0.571740\pi$
$853$	−35.1332	−	22.5787i	−1.20294	−	0.773080i	−0.979462	+	0.201629i	$0.935376\pi$
$854$	20.1358	+	0.381950i	0.689032	+	0.0130701i
$855$	−7.43779	−	16.2865i	−0.254367	−	0.556986i
$856$	4.35433	+	17.9488i	0.148828	+	0.613478i
$857$	0.371178	+	0.521247i	0.0126792	+	0.0178055i	0.820867	−	0.571120i	$-0.193491\pi$
$857$	0.371178	+	0.521247i	0.0126792	+	0.0178055i	−0.808188	+	0.588925i	$0.799551\pi$
$858$	2.14067	+	6.18507i	0.0730814	+	0.211155i
$859$	22.5634	−	9.03303i	0.769854	−	0.308203i	0.0467174	−	0.998908i	$-0.485124\pi$
$859$	22.5634	−	9.03303i	0.769854	−	0.308203i	0.723136	+	0.690705i	$0.242700\pi$
$860$	19.7760	−	5.80676i	0.674357	−	0.198009i
$861$	−18.3711	+	11.3199i	−0.626087	+	0.385783i
$862$	−9.79117	+	6.29240i	−0.333488	+	0.214320i
$863$	33.4672	+	17.2535i	1.13924	+	0.587317i	0.921380	−	0.388664i	$-0.127063\pi$
$863$	33.4672	+	17.2535i	1.13924	+	0.587317i	0.217856	+	0.975981i	$0.430094\pi$
$864$	−0.981929	+	0.189251i	−0.0334059	+	0.00643846i
$865$	−11.3466	+	46.7712i	−0.385795	+	1.59027i
$866$	7.77110	−	3.11108i	0.264073	−	0.105719i
$867$	−0.402310	+	0.464290i	−0.0136632	+	0.0157681i
$868$	8.12847	−	3.99724i	0.275898	−	0.135675i
$869$	12.7706	+	3.74979i	0.433213	+	0.127203i
$870$	−12.5637	+	17.6432i	−0.425948	+	0.598160i
$871$	22.9933	+	9.20512i	0.779097	+	0.311904i
$872$	12.9859	−	6.69470i	0.439758	−	0.226711i
$873$	4.55891	+	7.89626i	0.154296	+	0.267248i
$874$	−17.4263	−	16.8394i	−0.589452	−	0.569603i
$875$	22.4062	−	8.48066i	0.757467	−	0.286699i
$876$	2.12767	+	1.36737i	0.0718871	+	0.0461991i
$877$	3.70731	−	2.91546i	0.125187	−	0.0984482i	−0.553602	−	0.832781i	$-0.686747\pi$
$877$	3.70731	−	2.91546i	0.125187	−	0.0984482i	0.678790	+	0.734333i	$0.262505\pi$
$878$	27.5649	+	2.63213i	0.930270	+	0.0888300i
$879$	−6.23959	+	5.94944i	−0.210456	+	0.200670i
$880$	4.79616	−	0.457977i	0.161678	−	0.0154384i
$881$	−37.6102	+	43.4044i	−1.26712	+	1.46233i	−0.442371	+	0.896832i	$0.645862\pi$
$881$	−37.6102	+	43.4044i	−1.26712	+	1.46233i	−0.824748	+	0.565501i	$0.808683\pi$
$882$	−6.98852	+	0.400649i	−0.235316	+	0.0134906i
$883$	−35.1819	+	10.3303i	−1.18396	+	0.347643i	−0.813701	−	0.581284i	$-0.802551\pi$
$883$	−35.1819	+	10.3303i	−1.18396	+	0.347643i	−0.370263	+	0.928927i	$0.620732\pi$
$884$	6.37287	−	18.4132i	0.214343	−	0.619303i
$885$	−1.73836	−	36.4927i	−0.0584344	−	1.22669i
$886$	−1.98141	−	41.5949i	−0.0665668	−	1.39741i
$887$	−3.71465	+	10.7328i	−0.124726	+	0.360372i	−0.990026	−	0.140882i	$-0.955006\pi$
$887$	−3.71465	+	10.7328i	−0.124726	+	0.360372i	0.865301	+	0.501253i	$0.167128\pi$
$888$	3.81817	−	1.12112i	0.128130	−	0.0376222i
$889$	−1.23177	−	5.53347i	−0.0413123	−	0.185586i
$890$	−23.6390	+	27.2809i	−0.792382	+	0.914457i
$891$	−1.35356	+	0.129249i	−0.0453459	+	0.00433000i
$892$	−10.7565	+	10.2563i	−0.360155	+	0.343407i
$893$	65.3564	+	6.24078i	2.18707	+	0.208840i
$894$	−3.90360	+	3.06982i	−0.130556	+	0.102670i
$895$	−49.4841	−	31.8015i	−1.65407	−	1.06301i
$896$	2.04831	+	1.67464i	0.0684292	+	0.0559459i
$897$	5.29260	+	22.4701i	0.176715	+	0.750253i
$898$	−13.3218	−	23.0741i	−0.444556	−	0.769993i
$899$	18.6012	−	9.58957i	0.620384	−	0.319830i
$900$	7.01427	+	2.80809i	0.233809	+	0.0936031i
$901$	22.9198	−	32.1864i	0.763569	−	1.07228i
$902$	10.6406	+	3.12436i	0.354292	+	0.104030i
$903$	12.7865	+	8.56432i	0.425508	+	0.285003i
$904$	−5.71207	+	6.59208i	−0.189981	+	0.219249i
$905$	15.2963	−	6.12372i	0.508467	−	0.203559i
$906$	3.29575	−	13.5853i	0.109494	−	0.451340i
$907$	−40.3842	+	7.78341i	−1.34093	+	0.258444i	−0.808734	−	0.588174i	$-0.799847\pi$
$907$	−40.3842	+	7.78341i	−1.34093	+	0.258444i	−0.532201	+	0.846618i	$0.678635\pi$
$908$	18.7231	+	9.65241i	0.621346	+	0.320326i
$909$	−3.83459	+	2.46434i	−0.127185	+	0.0817370i
$910$	38.4186	−	23.6728i	1.27357	−	0.784747i
$911$	15.4571	−	4.53861i	0.512117	−	0.150371i	−0.0154567	−	0.999881i	$-0.504920\pi$
$911$	15.4571	−	4.53861i	0.512117	−	0.150371i	0.527573	+	0.849510i	$0.323102\pi$
$912$	−4.69099	+	1.87799i	−0.155334	+	0.0621865i
$913$	−3.70594	−	10.7076i	−0.122649	−	0.354370i
$914$	4.20836	+	5.90981i	0.139200	+	0.195479i
$915$	−6.35891	−	26.2118i	−0.210219	−	0.866535i
$916$	9.90659	+	21.6924i	0.327323	+	0.716737i
$917$	−23.6926	+	39.2964i	−0.782400	+	1.29768i
$918$	3.40533	+	2.18847i	0.112393	+	0.0722303i
$919$	−5.04704	−	8.74174i	−0.166487	−	0.288363i	0.770696	−	0.637204i	$-0.219909\pi$
$919$	−5.04704	−	8.74174i	−0.166487	−	0.288363i	−0.937182	+	0.348840i	$0.886576\pi$
$920$	16.9930	+	0.113446i	0.560244	+	0.00374020i
$921$	−3.44385	+	5.96492i	−0.113479	+	0.196551i
$922$	1.41587	−	29.7228i	0.0466292	−	0.978868i
$923$	9.73161	+	67.6848i	0.320320	+	2.22787i
$924$	2.55606	+	2.53147i	0.0840881	+	0.0832791i
$925$	−28.8482	−	8.47059i	−0.948522	−	0.278511i
$926$	−17.7728	+	1.69710i	−0.584051	+	0.0557701i
$927$	−1.50613	−	4.35168i	−0.0494679	−	0.142928i
$928$	4.80486	+	3.77858i	0.157727	+	0.124038i
$929$	−33.1132	−	31.5734i	−1.08641	−	1.03589i	−0.999212	−	0.0396975i	$-0.987361\pi$
$929$	−33.1132	−	31.5734i	−1.08641	−	1.03589i	−0.0871969	−	0.996191i	$-0.527791\pi$
$930$	−7.94431	−	9.16822i	−0.260504	−	0.300638i
$931$	−34.2914	+	8.67083i	−1.12385	+	0.284175i
$932$	4.15533	−	2.67047i	0.136112	−	0.0874741i
$933$	6.05316	−	17.4895i	0.198172	−	0.572579i
$934$	2.04620	−	8.43455i	0.0669537	−	0.275987i
$935$	−15.3302	−	12.0558i	−0.501351	−	0.394267i
$936$	4.72656	+	0.910970i	0.154492	+	0.0297760i
$937$	7.19099	−	15.7461i	0.234919	−	0.514402i	−0.755053	−	0.655664i	$-0.772389\pi$
$937$	7.19099	−	15.7461i	0.234919	−	0.514402i	0.989972	+	0.141262i	$0.0451161\pi$
$938$	13.5738	−	1.03679i	0.443200	−	0.0338522i
$939$	1.68042	+	3.67961i	0.0548385	+	0.120079i
$940$	−36.1896	+	28.4598i	−1.18037	+	0.928256i
$941$	−33.2365	+	17.1346i	−1.08348	+	0.558572i	−0.905017	−	0.425375i	$-0.860142\pi$
$941$	−33.2365	+	17.1346i	−1.08348	+	0.558572i	−0.178462	+	0.983947i	$0.557112\pi$
$942$	−5.36911	+	9.29957i	−0.174935	+	0.302996i
$943$	36.2150	+	14.7796i	1.17932	+	0.481289i
$944$	−10.3105			−0.335579
$945$	2.89765	+	8.91583i	0.0942607	+	0.290032i
$946$	−1.12558	−	7.82861i	−0.0365959	−	0.254530i
$947$	14.3471	−	20.1477i	0.466218	−	0.654711i	−0.512795	−	0.858511i	$-0.671390\pi$
$947$	14.3471	−	20.1477i	0.466218	−	0.654711i	0.979013	+	0.203800i	$0.0653292\pi$
$948$	7.08438	−	6.75494i	0.230090	−	0.219390i
$949$	−7.06175	−	9.91683i	−0.229234	−	0.321914i
$950$	37.4876	+	7.22513i	1.21626	+	0.234414i
$951$	0.133525	−	0.928689i	0.00432986	−	0.0301148i
$952$	−1.32284	−	10.6278i	−0.0428735	−	0.344448i
$953$	−31.5718	−	36.4358i	−1.02271	−	1.18027i	−0.983475	−	0.181043i	$-0.942053\pi$
$953$	−31.5718	−	36.4358i	−1.02271	−	1.18027i	−0.0392371	−	0.999230i	$-0.512493\pi$
$954$	8.67620	+	4.47289i	0.280902	+	0.144815i
$955$	1.44898	+	30.4178i	0.0468879	+	0.984297i
$956$	23.8098	−	4.58897i	0.770065	−	0.148418i
$957$	6.01527	+	5.73555i	0.194446	+	0.185404i
$958$	0.128919	−	0.896653i	0.00416519	−	0.0289695i
$959$	−27.9385	−	33.5062i	−0.902181	−	1.08197i
$960$	1.47197	−	3.22317i	0.0475076	−	0.104027i
$961$	−4.54510	−	18.7351i	−0.146616	−	0.604359i
$962$	−19.0681	−	1.82079i	−0.614781	−	0.0587045i
$963$	17.1464	+	6.86440i	0.552536	+	0.221202i
$964$	0.593677	−	12.4628i	0.0191210	−	0.401400i
$965$	−28.1530			−0.906279
$966$	8.06065	+	9.79928i	0.259347	+	0.315287i
$967$	19.8297			0.637679			0.318839	−	0.947809i	$-0.396707\pi$
$967$	19.8297			0.637679			0.318839	+	0.947809i	$0.396707\pi$
$968$	−0.435431	+	9.14081i	−0.0139953	+	0.293797i
$969$	18.9888	+	7.60195i	0.610007	+	0.244210i
$970$	−32.1615	−	3.07105i	−1.03264	−	0.0986056i
$971$	−2.04378	−	8.42459i	−0.0655881	−	0.270358i	0.929570	−	0.368646i	$-0.120179\pi$
$971$	−2.04378	−	8.42459i	−0.0655881	−	0.270358i	−0.995158	+	0.0982880i	$0.968663\pi$
$972$	−0.415415	+	0.909632i	−0.0133244	+	0.0291765i
$973$	15.4743	−	42.1088i	0.496084	−	1.34995i
$974$	5.01720	−	34.8954i	0.160762	−	1.11812i
$975$	−26.3213	−	25.0973i	−0.842955	−	0.803756i
$976$	−7.47442	+	1.44058i	−0.239250	+	0.0461117i
$977$	0.189681	+	3.98189i	0.00606843	+	0.127392i	0.999869	+	0.0162110i	$0.00516033\pi$
$977$	0.189681	+	3.98189i	0.00606843	+	0.127392i	−0.993800	+	0.111181i	$0.964537\pi$
$978$	2.67335	+	1.37821i	0.0854845	+	0.0440703i
$979$	9.07110	+	10.4686i	0.289914	+	0.334578i
$980$	13.2075	−	20.9948i	0.421898	−	0.670654i
$981$	2.07922	−	14.4613i	0.0663844	−	0.461714i
$982$	−24.2062	−	4.66535i	−0.772449	−	0.148877i
$983$	−8.15967	−	11.4587i	−0.260253	−	0.365474i	0.663688	−	0.748010i	$-0.268990\pi$
$983$	−8.15967	−	11.4587i	−0.260253	−	0.365474i	−0.923941	+	0.382535i	$0.875051\pi$
$984$	5.90276	−	5.62827i	0.188173	−	0.179423i
$985$	−22.1180	+	31.0604i	−0.704738	+	0.989666i
$986$	−3.52136	−	24.4916i	−0.112143	−	0.779972i
$987$	−33.6260	−	7.14484i	−1.07033	−	0.227423i
$988$	24.3226			0.773805
$989$	−1.14130	−	27.8728i	−0.0362913	−	0.886303i
$990$	2.40899	−	4.17249i	0.0765626	−	0.132610i
$991$	28.8000	−	14.8474i	0.914861	−	0.471643i	0.0645440	−	0.997915i	$-0.479441\pi$
$991$	28.8000	−	14.8474i	0.914861	−	0.471643i	0.850317	+	0.526271i	$0.176410\pi$
$992$	−2.69118	+	2.11636i	−0.0854449	+	0.0671946i
$993$	1.24678	+	2.73006i	0.0395652	+	0.0866358i
$994$	21.2171	+	31.0241i	0.672964	+	0.984024i
$995$	11.9962	−	26.2679i	0.380304	−	0.832749i
$996$	−8.18263	−	1.57707i	−0.259277	−	0.0499715i
$997$	−9.61602	−	7.56212i	−0.304542	−	0.239495i	0.454178	−	0.890911i	$-0.349933\pi$
$997$	−9.61602	−	7.56212i	−0.304542	−	0.239495i	−0.758721	+	0.651416i	$0.774175\pi$
$998$	−3.09439	+	12.7552i	−0.0979511	+	0.403760i
$999$	1.30152	−	3.76050i	0.0411784	−	0.118977i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	966.2.y.c.25.1	✓	160
7.2	even	3	inner	966.2.y.c.163.1	yes	160
23.12	even	11	inner	966.2.y.c.403.1	yes	160
161.58	even	33	inner	966.2.y.c.541.1	yes	160

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.2.y.c.25.1	✓	160	1.1	even	1	trivial
966.2.y.c.163.1	yes	160	7.2	even	3	inner
966.2.y.c.403.1	yes	160	23.12	even	11	inner
966.2.y.c.541.1	yes	160	161.58	even	33	inner

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:	\( N \)	\(=\)	\( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	966.y (of order \(33\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(0.0475819 - 0.998867i) q^{2} +(-0.928368 - 0.371662i) q^{3} +(-0.995472 - 0.0950560i) q^{4} +(-0.835382 - 3.44349i) q^{5} +(-0.415415 + 0.909632i) q^{6} +(0.912603 - 2.48338i) q^{7} +(-0.142315 + 0.989821i) q^{8} +(0.723734 + 0.690079i) q^{9} +O(q^{10})\)	\(q+(0.0475819 - 0.998867i) q^{2} +(-0.928368 - 0.371662i) q^{3} +(-0.995472 - 0.0950560i) q^{4} +(-0.835382 - 3.44349i) q^{5} +(-0.415415 + 0.909632i) q^{6} +(0.912603 - 2.48338i) q^{7} +(-0.142315 + 0.989821i) q^{8} +(0.723734 + 0.690079i) q^{9} +(-3.47934 + 0.670588i) q^{10} +(0.0646978 + 1.35817i) q^{11} +(0.888835 + 0.458227i) q^{12} +(-3.15220 - 3.63784i) q^{13} +(-2.43714 - 1.02973i) q^{14} +(-0.504274 + 3.50731i) q^{15} +(0.981929 + 0.189251i) q^{16} +(-2.34802 - 3.29734i) q^{17} +(0.723734 - 0.690079i) q^{18} +(2.93100 - 4.11601i) q^{19} +(0.504274 + 3.50731i) q^{20} +(-1.77021 + 1.96631i) q^{21} +1.35971 q^{22} +(4.77097 + 0.487734i) q^{23} +(0.500000 - 0.866025i) q^{24} +(-6.71559 + 3.46213i) q^{25} +(-3.78370 + 2.97554i) q^{26} +(-0.415415 - 0.909632i) q^{27} +(-1.14453 + 2.38538i) q^{28} +(-2.53928 + 5.56025i) q^{29} +(3.47934 + 0.670588i) q^{30} +(-2.69118 - 2.11636i) q^{31} +(0.235759 - 0.971812i) q^{32} +(0.444719 - 1.28493i) q^{33} +(-3.40533 + 2.18847i) q^{34} +(-9.31385 - 1.06797i) q^{35} +(-0.654861 - 0.755750i) q^{36} +(2.88000 + 2.74608i) q^{37} +(-3.97188 - 3.12352i) q^{38} +(1.57436 + 4.54880i) q^{39} +(3.52733 - 0.336819i) q^{40} +(7.82560 + 2.29780i) q^{41} +(1.87985 + 1.86176i) q^{42} +(-0.827810 - 5.75754i) q^{43} +(0.0646978 - 1.35817i) q^{44} +(1.77169 - 3.06865i) q^{45} +(0.714193 - 4.74235i) q^{46} +(6.49658 + 11.2524i) q^{47} +(-0.841254 - 0.540641i) q^{48} +(-5.33431 - 4.53267i) q^{49} +(3.13866 + 6.87271i) q^{50} +(0.954333 + 3.93382i) q^{51} +(2.79213 + 3.92100i) q^{52} +(3.19261 + 9.22445i) q^{53} +(-0.928368 + 0.371662i) q^{54} +(4.62281 - 1.35738i) q^{55} +(2.32822 + 1.25673i) q^{56} +(-4.25081 + 2.73183i) q^{57} +(5.43313 + 2.80097i) q^{58} +(-10.1242 + 1.95128i) q^{59} +(0.835382 - 3.44349i) q^{60} +(-7.06672 + 2.82909i) q^{61} +(-2.24202 + 2.58743i) q^{62} +(2.37421 - 1.16754i) q^{63} +(-0.959493 - 0.281733i) q^{64} +(-9.89356 + 13.8936i) q^{65} +(-1.26231 - 0.505354i) q^{66} +(-4.57338 + 2.35774i) q^{67} +(2.02396 + 3.50560i) q^{68} +(-4.24794 - 2.22599i) q^{69} +(-1.50993 + 9.25249i) q^{70} +(-11.9508 - 7.68030i) q^{71} +(-0.786053 + 0.618159i) q^{72} +(2.51771 + 0.240412i) q^{73} +(2.88000 - 2.74608i) q^{74} +(7.52128 - 0.718195i) q^{75} +(-3.30898 + 3.81876i) q^{76} +(3.43190 + 1.07880i) q^{77} +(4.61856 - 1.35613i) q^{78} +(3.20155 - 9.25028i) q^{79} +(-0.168600 - 3.53936i) q^{80} +(0.0475819 + 0.998867i) q^{81} +(2.66756 - 7.70740i) q^{82} +(-7.99567 + 2.34774i) q^{83} +(1.94910 - 1.78913i) q^{84} +(-9.39286 + 10.8399i) q^{85} +(-5.79041 + 0.552917i) q^{86} +(4.42392 - 4.21820i) q^{87} +(-1.35356 - 0.129249i) q^{88} +(8.00784 - 6.29744i) q^{89} +(-2.98087 - 1.91569i) q^{90} +(-11.9108 + 4.50821i) q^{91} +(-4.70300 - 0.939035i) q^{92} +(1.71183 + 2.96497i) q^{93} +(11.5488 - 5.95381i) q^{94} +(-16.6219 - 6.65442i) q^{95} +(-0.580057 + 0.814576i) q^{96} +(8.74848 + 2.56879i) q^{97} +(-4.78135 + 5.11260i) q^{98} +(-0.890423 + 1.02760i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 160 q + 8 q^{2} - 8 q^{3} + 8 q^{4} + 2 q^{5} + 16 q^{6} - 2 q^{7} - 16 q^{8} + 8 q^{9}+O(q^{10}) \) 160 * q + 8 * q^2 - 8 * q^3 + 8 * q^4 + 2 * q^5 + 16 * q^6 - 2 * q^7 - 16 * q^8 + 8 * q^9	\( 160 q + 8 q^{2} - 8 q^{3} + 8 q^{4} + 2 q^{5} + 16 q^{6} - 2 q^{7} - 16 q^{8} + 8 q^{9} + 2 q^{10} + 8 q^{11} - 8 q^{12} - 4 q^{13} + 9 q^{14} - 18 q^{15} + 8 q^{16} - 21 q^{17} + 8 q^{18} + 4 q^{19} + 18 q^{20} - 15 q^{21} + 116 q^{22} + 14 q^{23} + 80 q^{24} + 2 q^{25} + 2 q^{26} + 16 q^{27} - 18 q^{28} - 46 q^{29} - 2 q^{30} + q^{31} + 8 q^{32} - 8 q^{33} - 68 q^{34} - 84 q^{35} - 16 q^{36} + 19 q^{37} - 7 q^{38} - 2 q^{39} - 9 q^{40} + 38 q^{41} + 2 q^{42} + 28 q^{43} + 8 q^{44} + 24 q^{45} - 8 q^{46} - 26 q^{47} + 16 q^{48} - 6 q^{49} - 4 q^{50} + 21 q^{51} + 2 q^{52} - 20 q^{53} - 8 q^{54} + 46 q^{55} - 2 q^{56} - 14 q^{57} - 21 q^{58} + 36 q^{59} - 2 q^{60} + 40 q^{61} - 24 q^{62} - 2 q^{63} - 16 q^{64} - 10 q^{65} - 8 q^{66} + 6 q^{67} + 34 q^{68} + 6 q^{69} - 20 q^{70} + 132 q^{71} + 8 q^{72} - 36 q^{73} + 19 q^{74} - 2 q^{75} - 8 q^{76} - 75 q^{77} - 18 q^{78} + 34 q^{79} + 2 q^{80} + 8 q^{81} + 47 q^{82} + 74 q^{83} + 13 q^{84} + 2 q^{85} + 30 q^{86} + 10 q^{87} - 3 q^{88} - 12 q^{89} - 4 q^{90} - 30 q^{91} - 50 q^{92} + 10 q^{93} - 4 q^{94} + 27 q^{95} - 8 q^{96} + 24 q^{97} + 7 q^{98} - 16 q^{99}+O(q^{100}) \) 160 * q + 8 * q^2 - 8 * q^3 + 8 * q^4 + 2 * q^5 + 16 * q^6 - 2 * q^7 - 16 * q^8 + 8 * q^9 + 2 * q^10 + 8 * q^11 - 8 * q^12 - 4 * q^13 + 9 * q^14 - 18 * q^15 + 8 * q^16 - 21 * q^17 + 8 * q^18 + 4 * q^19 + 18 * q^20 - 15 * q^21 + 116 * q^22 + 14 * q^23 + 80 * q^24 + 2 * q^25 + 2 * q^26 + 16 * q^27 - 18 * q^28 - 46 * q^29 - 2 * q^30 + q^31 + 8 * q^32 - 8 * q^33 - 68 * q^34 - 84 * q^35 - 16 * q^36 + 19 * q^37 - 7 * q^38 - 2 * q^39 - 9 * q^40 + 38 * q^41 + 2 * q^42 + 28 * q^43 + 8 * q^44 + 24 * q^45 - 8 * q^46 - 26 * q^47 + 16 * q^48 - 6 * q^49 - 4 * q^50 + 21 * q^51 + 2 * q^52 - 20 * q^53 - 8 * q^54 + 46 * q^55 - 2 * q^56 - 14 * q^57 - 21 * q^58 + 36 * q^59 - 2 * q^60 + 40 * q^61 - 24 * q^62 - 2 * q^63 - 16 * q^64 - 10 * q^65 - 8 * q^66 + 6 * q^67 + 34 * q^68 + 6 * q^69 - 20 * q^70 + 132 * q^71 + 8 * q^72 - 36 * q^73 + 19 * q^74 - 2 * q^75 - 8 * q^76 - 75 * q^77 - 18 * q^78 + 34 * q^79 + 2 * q^80 + 8 * q^81 + 47 * q^82 + 74 * q^83 + 13 * q^84 + 2 * q^85 + 30 * q^86 + 10 * q^87 - 3 * q^88 - 12 * q^89 - 4 * q^90 - 30 * q^91 - 50 * q^92 + 10 * q^93 - 4 * q^94 + 27 * q^95 - 8 * q^96 + 24 * q^97 + 7 * q^98 - 16 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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