LMFDB - Embedded newform 322.2.i.d.141.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [322,2,Mod(29,322)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(322, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 18]))

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

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

chi := DirichletCharacter("322.29");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 322 = 2 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	322.i (of order $11$, degree $10$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.57118294509$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$4$ over $\Q(\zeta_{11})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			141.3
Character	$\chi$	$=$	322.141
Dual form			322.2.i.d.169.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.142315 - 0.989821i) q^{2} +(0.128569 - 0.281527i) q^{3} +(-0.959493 + 0.281733i) q^{4} +(-1.69136 + 1.95194i) q^{5} +(-0.296959 - 0.0871950i) q^{6} +(-0.841254 + 0.540641i) q^{7} +(0.415415 + 0.909632i) q^{8} +(1.90185 + 2.19486i) q^{9} +O(q^{10})$	\(q+(-0.142315 - 0.989821i) q^{2} +(0.128569 - 0.281527i) q^{3} +(-0.959493 + 0.281733i) q^{4} +(-1.69136 + 1.95194i) q^{5} +(-0.296959 - 0.0871950i) q^{6} +(-0.841254 + 0.540641i) q^{7} +(0.415415 + 0.909632i) q^{8} +(1.90185 + 2.19486i) q^{9} +(2.17278 + 1.39636i) q^{10} +(0.223366 - 1.55354i) q^{11} +(-0.0440458 + 0.306345i) q^{12} +(5.87583 + 3.77617i) q^{13} +(0.654861 + 0.755750i) q^{14} +(0.332066 + 0.727124i) q^{15} +(0.841254 - 0.540641i) q^{16} +(3.24670 + 0.953318i) q^{17} +(1.90185 - 2.19486i) q^{18} +(-2.78645 + 0.818176i) q^{19} +(1.07293 - 2.34938i) q^{20} +(0.0440458 + 0.306345i) q^{21} -1.56952 q^{22} +(-3.55335 + 3.22082i) q^{23} +0.309496 q^{24} +(-0.237776 - 1.65377i) q^{25} +(2.90151 - 6.35343i) q^{26} +(1.75331 - 0.514818i) q^{27} +(0.654861 - 0.755750i) q^{28} +(-4.89082 - 1.43608i) q^{29} +(0.672465 - 0.432167i) q^{30} +(2.08555 + 4.56673i) q^{31} +(-0.654861 - 0.755750i) q^{32} +(-0.408647 - 0.262621i) q^{33} +(0.481561 - 3.34933i) q^{34} +(0.367568 - 2.55649i) q^{35} +(-2.44318 - 1.57014i) q^{36} +(-1.70330 - 1.96571i) q^{37} +(1.20640 + 2.64165i) q^{38} +(1.81854 - 1.16871i) q^{39} +(-2.47816 - 0.727654i) q^{40} +(2.81451 - 3.24811i) q^{41} +(0.296959 - 0.0871950i) q^{42} +(0.433199 - 0.948573i) q^{43} +(0.223366 + 1.55354i) q^{44} -7.50095 q^{45} +(3.69373 + 3.05881i) q^{46} -4.35535 q^{47} +(-0.0440458 - 0.306345i) q^{48} +(0.415415 - 0.909632i) q^{49} +(-1.60309 + 0.470711i) q^{50} +(0.685811 - 0.791468i) q^{51} +(-6.70169 - 1.96779i) q^{52} +(3.30701 - 2.12529i) q^{53} +(-0.759100 - 1.66220i) q^{54} +(2.65463 + 3.06360i) q^{55} +(-0.841254 - 0.540641i) q^{56} +(-0.127913 + 0.889654i) q^{57} +(-0.725421 + 5.04542i) q^{58} +(5.95911 + 3.82969i) q^{59} +(-0.523470 - 0.604116i) q^{60} +(3.26598 + 7.15149i) q^{61} +(4.22344 - 2.71424i) q^{62} +(-2.78657 - 0.818211i) q^{63} +(-0.654861 + 0.755750i) q^{64} +(-17.3090 + 5.08238i) q^{65} +(-0.201792 + 0.441862i) q^{66} +(-1.24794 - 8.67964i) q^{67} -3.38377 q^{68} +(0.449897 + 1.41446i) q^{69} -2.58278 q^{70} +(-1.40316 - 9.75920i) q^{71} +(-1.20645 + 2.64176i) q^{72} +(4.37444 - 1.28445i) q^{73} +(-1.70330 + 1.96571i) q^{74} +(-0.496151 - 0.145683i) q^{75} +(2.44307 - 1.57007i) q^{76} +(0.652002 + 1.42769i) q^{77} +(-1.41562 - 1.63371i) q^{78} +(-0.936623 - 0.601931i) q^{79} +(-0.367568 + 2.55649i) q^{80} +(-1.15945 + 8.06416i) q^{81} +(-3.61560 - 2.32360i) q^{82} +(-5.51811 - 6.36824i) q^{83} +(-0.128569 - 0.281527i) q^{84} +(-7.35218 + 4.72496i) q^{85} +(-1.00057 - 0.293794i) q^{86} +(-1.03310 + 1.19226i) q^{87} +(1.50594 - 0.442185i) q^{88} +(-5.26207 + 11.5223i) q^{89} +(1.06750 + 7.42460i) q^{90} -6.98462 q^{91} +(2.50201 - 4.09145i) q^{92} +1.55380 q^{93} +(0.619831 + 4.31102i) q^{94} +(3.11587 - 6.82281i) q^{95} +(-0.296959 + 0.0871950i) q^{96} +(7.73192 - 8.92312i) q^{97} +(-0.959493 - 0.281733i) q^{98} +(3.83462 - 2.46436i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 4 q^{2} - 4 q^{4} + 9 q^{5} + 4 q^{7} - 4 q^{8} - 8 q^{9}+O(q^{10}) $ 40 * q - 4 * q^2 - 4 * q^4 + 9 * q^5 + 4 * q^7 - 4 * q^8 - 8 * q^9	\( 40 q - 4 q^{2} - 4 q^{4} + 9 q^{5} + 4 q^{7} - 4 q^{8} - 8 q^{9} - 2 q^{10} + 6 q^{11} + 2 q^{13} + 4 q^{14} - 3 q^{15} - 4 q^{16} - 13 q^{17} - 8 q^{18} - 22 q^{19} - 2 q^{20} - 16 q^{22} - 9 q^{23} + 22 q^{24} - 15 q^{25} - 9 q^{26} + 21 q^{27} + 4 q^{28} - 10 q^{29} - 14 q^{30} - 2 q^{31} - 4 q^{32} + 8 q^{33} - 2 q^{34} + 13 q^{35} - 8 q^{36} - 45 q^{37} + 11 q^{38} - 22 q^{39} + 9 q^{40} + 21 q^{41} + 31 q^{43} + 6 q^{44} + 2 q^{45} - 9 q^{46} + 64 q^{47} - 4 q^{49} + 7 q^{50} + 65 q^{51} + 2 q^{52} + 69 q^{53} + 21 q^{54} - 74 q^{55} + 4 q^{56} - 68 q^{57} + 12 q^{58} + 48 q^{59} - 3 q^{60} + 6 q^{61} - 13 q^{62} + 8 q^{63} - 4 q^{64} - 64 q^{65} - 69 q^{66} + 31 q^{67} - 2 q^{68} - 62 q^{69} + 2 q^{70} - 57 q^{71} - 19 q^{72} + 70 q^{73} - 45 q^{74} - 11 q^{75} + 22 q^{76} - 6 q^{77} + 33 q^{78} + 34 q^{79} - 13 q^{80} + 30 q^{81} - 12 q^{82} - 56 q^{83} - 17 q^{85} + 42 q^{86} - 3 q^{87} + 6 q^{88} + 16 q^{89} + 46 q^{90} - 46 q^{91} + 24 q^{92} + 48 q^{93} + 9 q^{94} - 42 q^{95} - 36 q^{97} - 4 q^{98} + 112 q^{99}+O(q^{100}) \) 40 * q - 4 * q^2 - 4 * q^4 + 9 * q^5 + 4 * q^7 - 4 * q^8 - 8 * q^9 - 2 * q^10 + 6 * q^11 + 2 * q^13 + 4 * q^14 - 3 * q^15 - 4 * q^16 - 13 * q^17 - 8 * q^18 - 22 * q^19 - 2 * q^20 - 16 * q^22 - 9 * q^23 + 22 * q^24 - 15 * q^25 - 9 * q^26 + 21 * q^27 + 4 * q^28 - 10 * q^29 - 14 * q^30 - 2 * q^31 - 4 * q^32 + 8 * q^33 - 2 * q^34 + 13 * q^35 - 8 * q^36 - 45 * q^37 + 11 * q^38 - 22 * q^39 + 9 * q^40 + 21 * q^41 + 31 * q^43 + 6 * q^44 + 2 * q^45 - 9 * q^46 + 64 * q^47 - 4 * q^49 + 7 * q^50 + 65 * q^51 + 2 * q^52 + 69 * q^53 + 21 * q^54 - 74 * q^55 + 4 * q^56 - 68 * q^57 + 12 * q^58 + 48 * q^59 - 3 * q^60 + 6 * q^61 - 13 * q^62 + 8 * q^63 - 4 * q^64 - 64 * q^65 - 69 * q^66 + 31 * q^67 - 2 * q^68 - 62 * q^69 + 2 * q^70 - 57 * q^71 - 19 * q^72 + 70 * q^73 - 45 * q^74 - 11 * q^75 + 22 * q^76 - 6 * q^77 + 33 * q^78 + 34 * q^79 - 13 * q^80 + 30 * q^81 - 12 * q^82 - 56 * q^83 - 17 * q^85 + 42 * q^86 - 3 * q^87 + 6 * q^88 + 16 * q^89 + 46 * q^90 - 46 * q^91 + 24 * q^92 + 48 * q^93 + 9 * q^94 - 42 * q^95 - 36 * q^97 - 4 * q^98 + 112 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$185$	$281$
$\chi(n)$	$1$	$e\left(\frac{8}{11}\right)$

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 $

$2$	−0.142315	−	0.989821i	−0.100632	−	0.699909i
$2$	−0.142315	−	0.989821i	−0.100632	−	0.699909i
$3$	0.128569	−	0.281527i	0.0742294	−	0.162540i	−0.868880	−	0.495024i	$-0.835159\pi$
$3$	0.128569	−	0.281527i	0.0742294	−	0.162540i	0.943109	+	0.332484i	$0.107887\pi$
$4$	−0.959493	+	0.281733i	−0.479746	+	0.140866i
$5$	−1.69136	+	1.95194i	−0.756401	+	0.872933i	−0.995172	−	0.0981427i	$-0.968710\pi$
$5$	−1.69136	+	1.95194i	−0.756401	+	0.872933i	0.238772	+	0.971076i	$0.423255\pi$
$6$	−0.296959	−	0.0871950i	−0.121233	−	0.0355972i
$7$	−0.841254	+	0.540641i	−0.317964	+	0.204343i
$7$	−0.841254	+	0.540641i	−0.317964	+	0.204343i
$8$	0.415415	+	0.909632i	0.146871	+	0.321603i
$9$	1.90185	+	2.19486i	0.633952	+	0.731619i
$10$	2.17278	+	1.39636i	0.687092	+	0.441567i
$11$	0.223366	−	1.55354i	0.0673474	−	0.468411i	−0.928041	−	0.372479i	$-0.878508\pi$
$11$	0.223366	−	1.55354i	0.0673474	−	0.468411i	0.995388	−	0.0959319i	$-0.0305831\pi$
$12$	−0.0440458	+	0.306345i	−0.0127149	+	0.0884343i
$13$	5.87583	+	3.77617i	1.62966	+	1.04732i	0.949265	+	0.314478i	$0.101829\pi$
$13$	5.87583	+	3.77617i	1.62966	+	1.04732i	0.680398	+	0.732843i	$0.261807\pi$
$14$	0.654861	+	0.755750i	0.175019	+	0.201983i
$15$	0.332066	+	0.727124i	0.0857392	+	0.187743i
$16$	0.841254	−	0.540641i	0.210313	−	0.135160i
$17$	3.24670	+	0.953318i	0.787441	+	0.231214i	0.650642	−	0.759385i	$-0.274500\pi$
$17$	3.24670	+	0.953318i	0.787441	+	0.231214i	0.136800	+	0.990599i	$0.456318\pi$
$18$	1.90185	−	2.19486i	0.448271	−	0.517333i
$19$	−2.78645	+	0.818176i	−0.639256	+	0.187702i	−0.585269	−	0.810839i	$-0.699011\pi$
$19$	−2.78645	+	0.818176i	−0.639256	+	0.187702i	−0.0539868	+	0.998542i	$0.517193\pi$
$20$	1.07293	−	2.34938i	0.239914	−	0.525338i
$21$	0.0440458	+	0.306345i	0.00961159	+	0.0668501i
$22$	−1.56952			−0.334623
$23$	−3.55335	+	3.22082i	−0.740925	+	0.671588i
$23$	−3.55335	+	3.22082i	−0.740925	+	0.671588i
$24$	0.309496			0.0631755
$25$	−0.237776	−	1.65377i	−0.0475551	−	0.330753i
$26$	2.90151	−	6.35343i	0.569034	−	1.24601i
$27$	1.75331	−	0.514818i	0.337424	−	0.0990767i
$28$	0.654861	−	0.755750i	0.123757	−	0.142823i
$29$	−4.89082	−	1.43608i	−0.908203	−	0.266672i	−0.205919	−	0.978569i	$-0.566018\pi$
$29$	−4.89082	−	1.43608i	−0.908203	−	0.266672i	−0.702284	+	0.711897i	$0.747836\pi$
$30$	0.672465	−	0.432167i	0.122775	−	0.0789025i
$31$	2.08555	+	4.56673i	0.374577	+	0.820208i	0.999227	+	0.0393040i	$0.0125141\pi$
$31$	2.08555	+	4.56673i	0.374577	+	0.820208i	−0.624651	+	0.780904i	$0.714759\pi$
$32$	−0.654861	−	0.755750i	−0.115764	−	0.133599i
$33$	−0.408647	−	0.262621i	−0.0711363	−	0.0457165i
$34$	0.481561	−	3.34933i	0.0825870	−	0.574405i
$35$	0.367568	−	2.55649i	0.0621304	−	0.432126i
$36$	−2.44318	−	1.57014i	−0.407196	−	0.261689i
$37$	−1.70330	−	1.96571i	−0.280021	−	0.323162i	0.598264	−	0.801299i	$-0.295857\pi$
$37$	−1.70330	−	1.96571i	−0.280021	−	0.323162i	−0.878285	+	0.478138i	$0.841312\pi$
$38$	1.20640	+	2.64165i	0.195704	+	0.428532i
$39$	1.81854	−	1.16871i	0.291200	−	0.187143i
$40$	−2.47816	−	0.727654i	−0.391832	−	0.115052i
$41$	2.81451	−	3.24811i	0.439552	−	0.507270i	−0.492142	−	0.870515i	$-0.663786\pi$
$41$	2.81451	−	3.24811i	0.439552	−	0.507270i	0.931694	+	0.363245i	$0.118331\pi$
$42$	0.296959	−	0.0871950i	0.0458218	−	0.0134545i
$43$	0.433199	−	0.948573i	0.0660622	−	0.144656i	−0.873721	−	0.486428i	$-0.838300\pi$
$43$	0.433199	−	0.948573i	0.0660622	−	0.144656i	0.939783	+	0.341772i	$0.111027\pi$
$44$	0.223366	+	1.55354i	0.0336737	+	0.234206i
$45$	−7.50095			−1.11818
$46$	3.69373	+	3.05881i	0.544611	+	0.450997i
$47$	−4.35535			−0.635293			−0.317647	−	0.948209i	$-0.602893\pi$
$47$	−4.35535			−0.635293			−0.317647	+	0.948209i	$0.602893\pi$
$48$	−0.0440458	−	0.306345i	−0.00635747	−	0.0442172i
$49$	0.415415	−	0.909632i	0.0593450	−	0.129947i
$50$	−1.60309	+	0.470711i	−0.226712	+	0.0665685i
$51$	0.685811	−	0.791468i	0.0960328	−	0.110828i
$52$	−6.70169	−	1.96779i	−0.929357	−	0.272884i
$53$	3.30701	−	2.12529i	0.454253	−	0.291931i	−0.293437	−	0.955978i	$-0.594799\pi$
$53$	3.30701	−	2.12529i	0.454253	−	0.291931i	0.747690	+	0.664048i	$0.231163\pi$
$54$	−0.759100	−	1.66220i	−0.103300	−	0.226196i
$55$	2.65463	+	3.06360i	0.357950	+	0.413096i
$56$	−0.841254	−	0.540641i	−0.112417	−	0.0722462i
$57$	−0.127913	+	0.889654i	−0.0169425	+	0.117838i
$58$	−0.725421	+	5.04542i	−0.0952525	+	0.662496i
$59$	5.95911	+	3.82969i	0.775810	+	0.498583i	0.867641	−	0.497192i	$-0.165636\pi$
$59$	5.95911	+	3.82969i	0.775810	+	0.498583i	−0.0918308	+	0.995775i	$0.529272\pi$
$60$	−0.523470	−	0.604116i	−0.0675797	−	0.0779911i
$61$	3.26598	+	7.15149i	0.418165	+	0.915654i	0.995101	+	0.0988646i	$0.0315211\pi$
$61$	3.26598	+	7.15149i	0.418165	+	0.915654i	−0.576936	+	0.816790i	$0.695752\pi$
$62$	4.22344	−	2.71424i	0.536377	−	0.344709i
$63$	−2.78657	−	0.818211i	−0.351075	−	0.103085i
$64$	−0.654861	+	0.755750i	−0.0818576	+	0.0944687i
$65$	−17.3090	+	5.08238i	−2.14692	+	0.630392i
$66$	−0.201792	+	0.441862i	−0.0248389	+	0.0543895i
$67$	−1.24794	−	8.67964i	−0.152461	−	1.06039i	−0.912078	−	0.410017i	$-0.865523\pi$
$67$	−1.24794	−	8.67964i	−0.152461	−	1.06039i	0.759617	−	0.650370i	$-0.225386\pi$
$68$	−3.38377			−0.410343
$69$	0.449897	+	1.41446i	0.0541612	+	0.170281i
$70$	−2.58278			−0.308702
$71$	−1.40316	−	9.75920i	−0.166525	−	1.15820i	−0.886000	−	0.463686i	$-0.846527\pi$
$71$	−1.40316	−	9.75920i	−0.166525	−	1.15820i	0.719475	−	0.694518i	$-0.244382\pi$
$72$	−1.20645	+	2.64176i	−0.142182	+	0.311335i
$73$	4.37444	−	1.28445i	0.511989	−	0.150334i	−0.0155254	−	0.999879i	$-0.504942\pi$
$73$	4.37444	−	1.28445i	0.511989	−	0.150334i	0.527515	+	0.849546i	$0.323124\pi$
$74$	−1.70330	+	1.96571i	−0.198005	+	0.228510i
$75$	−0.496151	−	0.145683i	−0.0572905	−	0.0168220i
$76$	2.44307	−	1.57007i	0.280240	−	0.180099i
$77$	0.652002	+	1.42769i	0.0743025	+	0.162700i
$78$	−1.41562	−	1.63371i	−0.160287	−	0.184981i
$79$	−0.936623	−	0.601931i	−0.105378	−	0.0677225i	0.486890	−	0.873463i	$-0.338131\pi$
$79$	−0.936623	−	0.601931i	−0.105378	−	0.0677225i	−0.592269	+	0.805741i	$0.701768\pi$
$80$	−0.367568	+	2.55649i	−0.0410954	+	0.285825i
$81$	−1.15945	+	8.06416i	−0.128828	+	0.896018i
$82$	−3.61560	−	2.32360i	−0.399276	−	0.256599i
$83$	−5.51811	−	6.36824i	−0.605692	−	0.699006i	0.367233	−	0.930129i	$-0.380305\pi$
$83$	−5.51811	−	6.36824i	−0.605692	−	0.699006i	−0.972924	+	0.231124i	$0.925760\pi$
$84$	−0.128569	−	0.281527i	−0.0140280	−	0.0307171i
$85$	−7.35218	+	4.72496i	−0.797455	+	0.512493i
$86$	−1.00057	−	0.293794i	−0.107894	−	0.0316806i
$87$	−1.03310	+	1.19226i	−0.110760	+	0.127824i
$88$	1.50594	−	0.442185i	0.160534	−	0.0471370i
$89$	−5.26207	+	11.5223i	−0.557779	+	1.22136i	0.395275	+	0.918563i	$0.370649\pi$
$89$	−5.26207	+	11.5223i	−0.557779	+	1.22136i	−0.953054	+	0.302802i	$0.902078\pi$
$90$	1.06750	+	7.42460i	0.112524	+	0.782622i
$91$	−6.98462			−0.732187
$92$	2.50201	−	4.09145i	0.260852	−	0.426563i
$93$	1.55380			0.161121
$94$	0.619831	+	4.31102i	0.0639307	+	0.444648i
$95$	3.11587	−	6.82281i	0.319682	−	0.700006i
$96$	−0.296959	+	0.0871950i	−0.0303082	+	0.00889930i
$97$	7.73192	−	8.92312i	0.785058	−	0.906005i	−0.212406	−	0.977182i	$-0.568130\pi$
$97$	7.73192	−	8.92312i	0.785058	−	0.906005i	0.997464	+	0.0711763i	$0.0226753\pi$
$98$	−0.959493	−	0.281733i	−0.0969234	−	0.0284593i
$99$	3.83462	−	2.46436i	0.385393	−	0.247677i
$100$	0.694063	+	1.51979i	0.0694063	+	0.151979i
$101$	−5.77795	−	6.66811i	−0.574928	−	0.663502i	0.391579	−	0.920145i	$-0.371929\pi$
$101$	−5.77795	−	6.66811i	−0.574928	−	0.663502i	−0.966506	+	0.256643i	$0.917384\pi$
$102$	−0.881013	−	0.566193i	−0.0872333	−	0.0560615i
$103$	0.128275	−	0.892176i	0.0126394	−	0.0879087i	−0.982525	−	0.186129i	$-0.940406\pi$
$103$	0.128275	−	0.892176i	0.0126394	−	0.0879087i	0.995165	+	0.0982201i	$0.0313149\pi$
$104$	−0.994014	+	6.91352i	−0.0974711	+	0.677927i
$105$	−0.672465	−	0.432167i	−0.0656258	−	0.0421752i
$106$	−2.57429	−	2.97089i	−0.250037	−	0.288558i
$107$	−6.85915	−	15.0194i	−0.663099	−	1.45198i	−0.879606	−	0.475703i	$-0.842194\pi$
$107$	−6.85915	−	15.0194i	−0.663099	−	1.45198i	0.216507	−	0.976281i	$-0.430534\pi$
$108$	−1.53725	+	0.987928i	−0.147922	+	0.0950634i
$109$	14.1236	+	4.14707i	1.35280	+	0.397217i	0.876218	−	0.481915i	$-0.160058\pi$
$109$	14.1236	+	4.14707i	1.35280	+	0.397217i	0.476579	+	0.879132i	$0.341877\pi$
$110$	2.65463	−	3.06360i	0.253109	−	0.292103i
$111$	−0.772394	+	0.226795i	−0.0733124	+	0.0215265i
$112$	−0.415415	+	0.909632i	−0.0392530	+	0.0859521i
$113$	−1.40387	−	9.76415i	−0.132065	−	0.918534i	−0.942857	−	0.333199i	$-0.891872\pi$
$113$	−1.40387	−	9.76415i	−0.132065	−	0.918534i	0.810791	−	0.585335i	$-0.199037\pi$
$114$	0.898803			0.0841806
$115$	−0.276831	−	12.3835i	−0.0258146	−	1.15477i
$116$	5.09730			0.473272
$117$	2.88683	+	20.0783i	0.266887	+	1.85624i
$118$	2.94264	−	6.44347i	0.270892	−	0.593170i
$119$	−3.24670	+	0.953318i	−0.297625	+	0.0873906i
$120$	−0.523470	+	0.604116i	−0.0477860	+	0.0551480i
$121$	8.19082	+	2.40504i	0.744620	+	0.218640i
$122$	6.61390	−	4.25050i	0.598794	−	0.384822i
$123$	−0.552573	−	1.20997i	−0.0498239	−	0.109099i
$124$	−3.28767	−	3.79417i	−0.295241	−	0.340727i
$125$	−7.23367	−	4.64880i	−0.646999	−	0.415801i
$126$	−0.413313	+	2.87465i	−0.0368208	+	0.256094i
$127$	−2.85688	+	19.8700i	−0.253507	+	1.76318i	0.323299	+	0.946297i	$0.395208\pi$
$127$	−2.85688	+	19.8700i	−0.253507	+	1.76318i	−0.576805	+	0.816882i	$0.695701\pi$
$128$	0.841254	+	0.540641i	0.0743570	+	0.0477863i
$129$	−0.211353	−	0.243915i	−0.0186086	−	0.0214755i
$130$	7.49398	+	16.4095i	0.657266	+	1.43921i
$131$	10.9920	−	7.06415i	0.960379	−	0.617198i	0.0362759	−	0.999342i	$-0.488451\pi$
$131$	10.9920	−	7.06415i	0.960379	−	0.617198i	0.924103	+	0.382144i	$0.124814\pi$
$132$	0.466083	+	0.136854i	0.0405673	+	0.0119116i
$133$	1.90177	−	2.19476i	0.164905	−	0.190310i
$134$	−8.41369	+	2.47048i	−0.726832	+	0.213417i
$135$	−1.96059	+	4.29309i	−0.168741	+	0.369491i
$136$	0.481561	+	3.34933i	0.0412935	+	0.287203i
$137$	−14.3628			−1.22710			−0.613549	−	0.789657i	$-0.710259\pi$
$137$	−14.3628			−1.22710			−0.613549	+	0.789657i	$0.710259\pi$
$138$	1.33604	−	0.646617i	0.113731	−	0.0550437i
$139$	18.5193			1.57079			0.785394	−	0.618997i	$-0.212461\pi$
$139$	18.5193			1.57079			0.785394	+	0.618997i	$0.212461\pi$
$140$	0.367568	+	2.55649i	0.0310652	+	0.216063i
$141$	−0.559964	+	1.22615i	−0.0471575	+	0.103260i
$142$	−9.46018	+	2.77776i	−0.793880	+	0.233104i
$143$	7.17890	−	8.28490i	0.600330	−	0.692818i
$144$	2.78657	+	0.818211i	0.232214	+	0.0681843i
$145$	11.0753	−	7.11766i	0.919753	−	0.591089i
$146$	−1.89393	−	4.14712i	−0.156742	−	0.343218i
$147$	−0.202677	−	0.233901i	−0.0167165	−	0.0192918i
$148$	2.18811	+	1.40621i	0.179862	+	0.115590i
$149$	−0.641165	+	4.45940i	−0.0525263	+	0.365329i	0.946558	+	0.322535i	$0.104535\pi$
$149$	−0.641165	+	4.45940i	−0.0525263	+	0.365329i	−0.999084	+	0.0427938i	$0.986374\pi$
$150$	−0.0735905	+	0.511833i	−0.00600864	+	0.0417910i
$151$	8.21713	+	5.28083i	0.668701	+	0.429748i	0.830457	−	0.557083i	$-0.188079\pi$
$151$	8.21713	+	5.28083i	0.668701	+	0.429748i	−0.161756	+	0.986831i	$0.551716\pi$
$152$	−1.90177	−	2.19476i	−0.154254	−	0.178019i
$153$	4.08236	+	8.93913i	0.330039	+	0.722686i
$154$	1.32036	−	0.848546i	0.106398	−	0.0683778i
$155$	−12.4414	−	3.65312i	−0.999317	−	0.293426i
$156$	−1.41562	+	1.63371i	−0.113340	+	0.130801i
$157$	−2.41150	+	0.708081i	−0.192459	+	0.0565110i	−0.376541	−	0.926400i	$-0.622887\pi$
$157$	−2.41150	+	0.708081i	−0.192459	+	0.0565110i	0.184083	+	0.982911i	$0.441069\pi$
$158$	−0.462509	+	1.01275i	−0.0367952	+	0.0805703i
$159$	−0.173146	−	1.20426i	−0.0137314	−	0.0955040i
$160$	2.58278			0.204187
$161$	1.24796	−	4.63061i	0.0983533	−	0.364944i
$162$	8.14709			0.640096
$163$	−3.38115	−	23.5164i	−0.264832	−	1.84195i	−0.495121	−	0.868824i	$-0.664876\pi$
$163$	−3.38115	−	23.5164i	−0.264832	−	1.84195i	0.230289	−	0.973122i	$-0.426033\pi$
$164$	−1.78540	+	3.90948i	−0.139416	+	0.305279i
$165$	1.20379	−	0.353465i	0.0937150	−	0.0275172i
$166$	−5.51811	+	6.36824i	−0.428289	+	0.494272i
$167$	22.8990	+	6.72376i	1.77198	+	0.520300i	0.994134	−	0.108156i	$-0.0344947\pi$
$167$	22.8990	+	6.72376i	1.77198	+	0.520300i	0.777845	+	0.628456i	$0.216313\pi$
$168$	−0.260364	+	0.167326i	−0.0200875	+	0.0129095i
$169$	14.8656	+	32.5510i	1.14350	+	2.50393i
$170$	5.72319	+	6.60491i	0.438948	+	0.506573i
$171$	−7.09521	−	4.55981i	−0.542584	−	0.348698i
$172$	−0.148407	+	1.03220i	−0.0113160	+	0.0787042i
$173$	0.539942	−	3.75538i	0.0410510	−	0.285516i	−0.958947	−	0.283585i	$-0.908476\pi$
$173$	0.539942	−	3.75538i	0.0410510	−	0.285516i	0.999998	−	0.00193120i	$-0.000614720\pi$
$174$	1.32716	+	0.852911i	0.100611	+	0.0646590i
$175$	1.09412	+	1.26268i	0.0827079	+	0.0954500i
$176$	−0.652002	−	1.42769i	−0.0491465	−	0.107616i
$177$	1.84432	−	1.18527i	0.138627	−	0.0890904i
$178$	12.1539	+	3.56871i	0.910975	+	0.267486i
$179$	6.01036	−	6.93633i	0.449236	−	0.518446i	−0.485284	−	0.874356i	$-0.661284\pi$
$179$	6.01036	−	6.93633i	0.449236	−	0.518446i	0.934520	+	0.355911i	$0.115829\pi$
$180$	7.19711	−	2.11326i	0.536441	−	0.157513i
$181$	9.43201	−	20.6532i	0.701075	−	1.53514i	−0.137587	−	0.990490i	$-0.543935\pi$
$181$	9.43201	−	20.6532i	0.701075	−	1.53514i	0.838662	−	0.544651i	$-0.183338\pi$
$182$	0.994014	+	6.91352i	0.0736812	+	0.512464i
$183$	2.43324			0.179870
$184$	−4.40588	−	1.89427i	−0.324806	−	0.139647i
$185$	6.71785			0.493907
$186$	−0.221128	−	1.53798i	−0.0162139	−	0.112770i
$187$	2.20623	−	4.83096i	0.161335	−	0.353275i
$188$	4.17893	−	1.22704i	0.304780	−	0.0894914i
$189$	−1.19665	+	1.38100i	−0.0870432	+	0.100453i
$190$	−7.19680	−	2.11317i	−0.522111	−	0.153306i
$191$	13.4522	−	8.64524i	0.973371	−	0.625547i	0.0457032	−	0.998955i	$-0.485447\pi$
$191$	13.4522	−	8.64524i	0.973371	−	0.625547i	0.927667	+	0.373408i	$0.121811\pi$
$192$	0.128569	+	0.281527i	0.00927868	+	0.0203175i
$193$	−15.9672	−	18.4272i	−1.14935	−	1.32642i	−0.937043	−	0.349214i	$-0.886449\pi$
$193$	−15.9672	−	18.4272i	−1.14935	−	1.32642i	−0.212304	−	0.977204i	$-0.568097\pi$
$194$	−9.93266	−	6.38333i	−0.713123	−	0.458297i
$195$	−0.794576	+	5.52640i	−0.0569008	+	0.395753i
$196$	−0.142315	+	0.989821i	−0.0101653	+	0.0707015i
$197$	0.200069	+	0.128576i	0.0142543	+	0.00916069i	0.547749	−	0.836643i	$-0.315485\pi$
$197$	0.200069	+	0.128576i	0.0142543	+	0.00916069i	−0.533494	+	0.845804i	$0.679121\pi$
$198$	−2.98500	−	3.44487i	−0.212135	−	0.244816i
$199$	6.24993	+	13.6854i	0.443046	+	0.970135i	0.991029	+	0.133646i	$0.0426685\pi$
$199$	6.24993	+	13.6854i	0.443046	+	0.970135i	−0.547983	+	0.836489i	$0.684604\pi$
$200$	1.40554	−	0.903287i	0.0993868	−	0.0638720i
$201$	−2.60400	−	0.764604i	−0.183672	−	0.0539310i
$202$	−5.77795	+	6.66811i	−0.406535	+	0.469167i
$203$	4.89082	−	1.43608i	0.343268	−	0.100793i
$204$	−0.435049	+	0.952624i	−0.0304595	+	0.0666970i
$205$	1.57976	+	10.9875i	0.110335	+	0.767399i
$206$	−0.901350			−0.0628000
$207$	−13.8272	−	1.67357i	−0.961057	−	0.116321i
$208$	6.98462			0.484296
$209$	0.648674	+	4.51163i	0.0448697	+	0.312076i
$210$	−0.332066	+	0.727124i	−0.0229148	+	0.0501763i
$211$	−10.6272	+	3.12044i	−0.731608	+	0.214820i	−0.626258	−	0.779616i	$-0.715415\pi$
$211$	−10.6272	+	3.12044i	−0.731608	+	0.214820i	−0.105350	+	0.994435i	$0.533596\pi$
$212$	−2.57429	+	2.97089i	−0.176803	+	0.204042i
$213$	−2.92788	−	0.859704i	−0.200615	−	0.0589060i
$214$	−13.8904	+	8.92682i	−0.949529	+	0.610225i
$215$	1.11886	+	2.44996i	0.0763056	+	0.167086i
$216$	1.19665	+	1.38100i	0.0814214	+	0.0939653i
$217$	−4.22344	−	2.71424i	−0.286706	−	0.184255i
$218$	2.09486	−	14.5700i	0.141882	−	0.986808i
$219$	0.200810	−	1.39666i	0.0135695	−	0.0943778i
$220$	−3.41021	−	2.19161i	−0.229917	−	0.147758i
$221$	15.4772	+	17.8616i	1.04111	+	1.20150i
$222$	0.334410	+	0.732256i	0.0224441	+	0.0491458i
$223$	−9.67120	+	6.21530i	−0.647631	+	0.416207i	−0.822800	−	0.568331i	$-0.807589\pi$
$223$	−9.67120	+	6.21530i	−0.647631	+	0.416207i	0.175169	+	0.984538i	$0.443953\pi$
$224$	0.959493	+	0.281733i	0.0641088	+	0.0188240i
$225$	3.17756	−	3.66710i	0.211838	−	0.244474i
$226$	−9.46497	+	2.77917i	−0.629600	+	0.184867i
$227$	−3.98082	+	8.71679i	−0.264217	+	0.578553i	−0.994517	−	0.104572i	$-0.966653\pi$
$227$	−3.98082	+	8.71679i	−0.264217	+	0.578553i	0.730301	+	0.683126i	$0.239380\pi$
$228$	−0.127913	−	0.889654i	−0.00847124	−	0.0589188i
$229$	−19.1674			−1.26662			−0.633309	−	0.773899i	$-0.718304\pi$
$229$	−19.1674			−1.26662			−0.633309	+	0.773899i	$0.718304\pi$
$230$	−12.2181	+	2.03637i	−0.805635	+	0.134274i
$231$	0.485760			0.0319606
$232$	−0.725421	−	5.04542i	−0.0476262	−	0.331248i
$233$	−6.57244	+	14.3916i	−0.430575	+	0.942828i	0.562658	+	0.826690i	$0.309779\pi$
$233$	−6.57244	+	14.3916i	−0.430575	+	0.942828i	−0.993233	+	0.116138i	$0.962949\pi$
$234$	19.4631	−	5.71489i	1.27234	−	0.373594i
$235$	7.36648	−	8.50137i	0.480536	−	0.554568i
$236$	−6.79667	−	1.99568i	−0.442425	−	0.129908i
$237$	−0.289881	+	0.186295i	−0.0188298	+	0.0121012i
$238$	1.40567	+	3.07799i	0.0911160	+	0.199516i
$239$	−0.344892	−	0.398027i	−0.0223092	−	0.0257462i	0.744485	−	0.667639i	$-0.232695\pi$
$239$	−0.344892	−	0.398027i	−0.0223092	−	0.0257462i	−0.766795	+	0.641893i	$0.778149\pi$
$240$	0.672465	+	0.432167i	0.0434074	+	0.0278963i
$241$	2.99237	−	20.8124i	0.192755	−	1.34064i	−0.631918	−	0.775035i	$-0.717732\pi$
$241$	2.99237	−	20.8124i	0.192755	−	1.34064i	0.824674	−	0.565609i	$-0.191359\pi$
$242$	1.21489	−	8.44972i	0.0780958	−	0.543168i
$243$	6.73295	+	4.32700i	0.431919	+	0.277577i
$244$	−5.14849	−	5.94167i	−0.329598	−	0.380377i
$245$	1.07293	+	2.34938i	0.0685468	+	0.150097i
$246$	−1.11901	+	0.719145i	−0.0713456	+	0.0458510i
$247$	−19.4623	−	5.71464i	−1.23836	−	0.363614i
$248$	−3.28767	+	3.79417i	−0.208767	+	0.240930i
$249$	−2.50229	+	0.734740i	−0.158576	+	0.0465622i
$250$	−3.57202	+	7.82163i	−0.225914	+	0.494683i
$251$	2.63668	+	18.3385i	0.166426	+	1.15752i	0.886198	+	0.463307i	$0.153337\pi$
$251$	2.63668	+	18.3385i	0.166426	+	1.15752i	−0.719772	+	0.694211i	$0.755754\pi$
$252$	2.90421			0.182948
$253$	4.20999	+	6.23971i	0.264680	+	0.392287i
$254$	20.0743			1.25958
$255$	0.384941	+	2.67732i	0.0241059	+	0.167660i
$256$	0.415415	−	0.909632i	0.0259634	−	0.0568520i
$257$	−6.14200	+	1.80345i	−0.383127	+	0.112496i	−0.467624	−	0.883927i	$-0.654890\pi$
$257$	−6.14200	+	1.80345i	−0.383127	+	0.112496i	0.0844967	+	0.996424i	$0.473072\pi$
$258$	−0.211353	+	0.243915i	−0.0131583	+	0.0151855i
$259$	2.49565	+	0.732790i	0.155072	+	0.0455334i
$260$	15.1760	−	9.75303i	0.941176	−	0.604857i
$261$	−6.14965	−	13.4659i	−0.380654	−	0.833516i
$262$	−8.55658	−	9.87482i	−0.528627	−	0.610068i
$263$	−2.06434	−	1.32667i	−0.127292	−	0.0818059i	0.475445	−	0.879745i	$-0.342287\pi$
$263$	−2.06434	−	1.32667i	−0.127292	−	0.0818059i	−0.602738	+	0.797940i	$0.705923\pi$
$264$	0.0691308	−	0.480815i	0.00425471	−	0.0295921i
$265$	−1.44493	+	10.0497i	−0.0887614	+	0.617349i
$266$	−2.44307	−	1.57007i	−0.149794	−	0.0962671i
$267$	2.56731	+	2.96283i	0.157117	+	0.181322i
$268$	3.64273	+	7.97647i	0.222515	+	0.487240i
$269$	−2.26590	+	1.45621i	−0.138155	+	0.0887865i	−0.607892	−	0.794019i	$-0.707985\pi$
$269$	−2.26590	+	1.45621i	−0.138155	+	0.0887865i	0.469738	+	0.882806i	$0.344348\pi$
$270$	4.52842	+	1.32966i	0.275591	+	0.0809207i
$271$	−1.55581	+	1.79551i	−0.0945090	+	0.109069i	−0.801034	−	0.598619i	$-0.795716\pi$
$271$	−1.55581	+	1.79551i	−0.0945090	+	0.109069i	0.706525	+	0.707688i	$0.250262\pi$
$272$	3.24670	−	0.953318i	0.196860	−	0.0578034i
$273$	−0.898006	+	1.96636i	−0.0543498	+	0.119009i
$274$	2.04404	+	14.2166i	0.123485	+	0.858858i
$275$	−2.62231			−0.158131
$276$	−0.830174	−	1.23042i	−0.0499706	−	0.0740624i
$277$	3.55469			0.213581			0.106790	−	0.994282i	$-0.465943\pi$
$277$	3.55469			0.213581			0.106790	+	0.994282i	$0.465943\pi$
$278$	−2.63557	−	18.3308i	−0.158071	−	1.09941i
$279$	−6.05689	+	13.2627i	−0.362617	+	0.794020i
$280$	2.47816	−	0.727654i	0.148099	−	0.0434857i
$281$	8.92450	−	10.2994i	0.532391	−	0.614412i	−0.424299	−	0.905522i	$-0.639479\pi$
$281$	8.92450	−	10.2994i	0.532391	−	0.614412i	0.956689	+	0.291111i	$0.0940248\pi$
$282$	1.29336	+	0.379765i	0.0770185	+	0.0226147i
$283$	−8.96500	+	5.76146i	−0.532914	+	0.342483i	−0.779262	−	0.626698i	$-0.784406\pi$
$283$	−8.96500	+	5.76146i	−0.532914	+	0.342483i	0.246348	+	0.969181i	$0.420769\pi$
$284$	4.09581	+	8.96857i	0.243041	+	0.532187i
$285$	−1.52020	−	1.75441i	−0.0900490	−	0.103922i
$286$	−9.22223	−	5.92677i	−0.545322	−	0.350457i
$287$	−0.611650	+	4.25412i	−0.0361046	+	0.251113i
$288$	0.413313	−	2.87465i	0.0243547	−	0.169390i
$289$	−4.66904	−	3.00061i	−0.274649	−	0.176506i
$290$	−8.62139	−	9.94961i	−0.506265	−	0.584261i
$291$	−1.51801	−	3.32398i	−0.0889875	−	0.194855i
$292$	−3.83537	+	2.46484i	−0.224448	+	0.144244i
$293$	−20.9102	−	6.13978i	−1.22159	−	0.358690i	−0.393518	−	0.919317i	$-0.628742\pi$
$293$	−20.9102	−	6.13978i	−1.22159	−	0.358690i	−0.828068	+	0.560627i	$0.810560\pi$
$294$	−0.202677	+	0.233901i	−0.0118203	+	0.0136414i
$295$	−17.5543	+	5.15442i	−1.02205	+	0.300102i
$296$	1.08050	−	2.36597i	0.0628028	−	0.137519i
$297$	−0.408163	−	2.83883i	−0.0236840	−	0.164726i
$298$	4.50526			0.260983
$299$	−33.0413	+	5.50695i	−1.91083	+	0.318475i
$300$	0.517097			0.0298546
$301$	0.148407	+	1.03220i	0.00855406	+	0.0594948i
$302$	4.05766	−	8.88503i	0.233492	−	0.511276i
$303$	−2.62012	+	0.769337i	−0.150522	+	0.0441973i
$304$	−1.90177	+	2.19476i	−0.109074	+	0.125878i
$305$	−19.4832	−	5.72079i	−1.11561	−	0.327571i
$306$	8.26716	−	5.31298i	0.472602	−	0.303723i
$307$	−6.08642	−	13.3274i	−0.347371	−	0.760636i	−0.999996	−	0.00295449i	$-0.999060\pi$
$307$	−6.08642	−	13.3274i	−0.347371	−	0.760636i	0.652625	−	0.757681i	$-0.273668\pi$
$308$	−1.02782	−	1.18616i	−0.0585653	−	0.0675879i
$309$	−0.234679	−	0.150819i	−0.0133504	−	0.00857981i
$310$	−1.84534	+	12.8347i	−0.104809	+	0.728959i
$311$	1.65901	−	11.5386i	0.0940735	−	0.654296i	−0.887158	−	0.461465i	$-0.847324\pi$
$311$	1.65901	−	11.5386i	0.0940735	−	0.654296i	0.981232	−	0.192831i	$-0.0617669\pi$
$312$	1.81854	+	1.16871i	0.102955	+	0.0661650i
$313$	9.39697	+	10.8447i	0.531148	+	0.612978i	0.956387	−	0.292104i	$-0.0943553\pi$
$313$	9.39697	+	10.8447i	0.531148	+	0.612978i	−0.425239	+	0.905081i	$0.639810\pi$
$314$	1.04407	+	2.28619i	0.0589200	+	0.129017i
$315$	6.31020	−	4.05532i	0.355540	−	0.228491i
$316$	1.06827	+	0.313671i	0.0600947	+	0.0176454i
$317$	19.1571	−	22.1085i	1.07597	−	1.24174i	0.107078	−	0.994251i	$-0.465850\pi$
$317$	19.1571	−	22.1085i	1.07597	−	1.24174i	0.968892	−	0.247485i	$-0.0796041\pi$
$318$	−1.16736	+	0.342768i	−0.0654624	+	0.0192215i
$319$	−3.32345	+	7.27734i	−0.186077	+	0.407453i
$320$	−0.367568	−	2.55649i	−0.0205477	−	0.142912i
$321$	−5.11026			−0.285227
$322$	−4.76108	−	0.576255i	−0.265325	−	0.0321135i
$323$	−9.82677			−0.546776
$324$	−1.15945	−	8.06416i	−0.0644140	−	0.448009i
$325$	4.84777	−	10.6151i	0.268906	−	0.588821i
$326$	−22.7958	+	6.69346i	−1.26255	+	0.370717i
$327$	2.98337	−	3.44300i	0.164981	−	0.190398i
$328$	4.12377	+	1.21085i	0.227697	+	0.0668580i
$329$	3.66395	−	2.35468i	0.202000	−	0.129818i
$330$	−0.521185	−	1.14123i	−0.0286903	−	0.0628229i
$331$	−6.93947	−	8.00857i	−0.381428	−	0.440191i	0.532277	−	0.846570i	$-0.321337\pi$
$331$	−6.93947	−	8.00857i	−0.381428	−	0.440191i	−0.913704	+	0.406379i	$0.866791\pi$
$332$	7.08873	+	4.55565i	0.389045	+	0.250024i
$333$	1.07503	−	7.47701i	0.0589114	−	0.409737i
$334$	3.39645	−	23.6228i	0.185845	−	1.29258i
$335$	19.0528	+	12.2445i	1.04097	+	0.668990i
$336$	0.202677	+	0.233901i	0.0110569	+	0.0127604i
$337$	10.6715	+	23.3673i	0.581313	+	1.27290i	0.940551	+	0.339651i	$0.110309\pi$
$337$	10.6715	+	23.3673i	0.581313	+	1.27290i	−0.359239	+	0.933246i	$0.616964\pi$
$338$	30.1041	−	19.3468i	1.63745	−	1.05232i
$339$	−2.92937	−	0.860140i	−0.159101	−	0.0467164i
$340$	5.72319	−	6.60491i	0.310383	−	0.358202i
$341$	7.56045	−	2.21995i	0.409421	−	0.120217i
$342$	−3.50365	+	7.67192i	−0.189455	+	0.414850i
$343$	0.142315	+	0.989821i	0.00768428	+	0.0534453i
$344$	1.04281			0.0562245
$345$	−3.52188	−	1.51420i	−0.189612	−	0.0815218i
$346$	−3.79400			−0.203967
$347$	−0.689508	−	4.79563i	−0.0370147	−	0.257443i	0.962909	−	0.269828i	$-0.0869668\pi$
$347$	−0.689508	−	4.79563i	−0.0370147	−	0.257443i	−0.999923	+	0.0123847i	$0.996058\pi$
$348$	0.655355	−	1.43503i	0.0351307	−	0.0769256i
$349$	−13.8392	+	4.06356i	−0.740797	+	0.217518i	−0.630292	−	0.776358i	$-0.717065\pi$
$349$	−13.8392	+	4.06356i	−0.740797	+	0.217518i	−0.110505	+	0.993876i	$0.535247\pi$
$350$	1.09412	−	1.26268i	0.0584833	−	0.0674933i
$351$	12.2462	+	3.59580i	0.653653	+	0.191930i
$352$	−1.32036	+	0.848546i	−0.0703756	+	0.0452277i
$353$	3.53908	+	7.74950i	0.188366	+	0.412464i	0.980128	−	0.198366i	$-0.0635633\pi$
$353$	3.53908	+	7.74950i	0.188366	+	0.412464i	−0.791762	+	0.610830i	$0.790836\pi$
$354$	−1.43568	−	1.65686i	−0.0763056	−	0.0880613i
$355$	21.4226	+	13.7675i	1.13699	+	0.730702i
$356$	1.80271	−	12.5381i	0.0955432	−	0.664518i
$357$	−0.149041	+	1.03660i	−0.00788809	+	0.0548628i
$358$	−7.72109	−	4.96204i	−0.408072	−	0.262252i
$359$	8.63063	+	9.96027i	0.455507	+	0.525683i	0.936324	−	0.351138i	$-0.114205\pi$
$359$	8.63063	+	9.96027i	0.455507	+	0.525683i	−0.480817	+	0.876821i	$0.659660\pi$
$360$	−3.11601	−	6.82311i	−0.164228	−	0.359609i
$361$	−8.88892	+	5.71256i	−0.467838	+	0.300661i
$362$	−21.7853	−	6.39674i	−1.14501	−	0.336205i
$363$	1.73017	−	1.99672i	0.0908104	−	0.104801i
$364$	6.70169	−	1.96779i	0.351264	−	0.103140i
$365$	−4.89160	+	10.7111i	−0.256038	+	0.560645i
$366$	−0.346286	−	2.40848i	−0.0181007	−	0.125893i
$367$	−15.4410			−0.806016			−0.403008	−	0.915197i	$-0.632035\pi$
$367$	−15.4410			−0.806016			−0.403008	+	0.915197i	$0.632035\pi$
$368$	−1.24796	+	4.63061i	−0.0650546	+	0.241387i
$369$	12.4819			0.649783
$370$	−0.956050	−	6.64948i	−0.0497027	−	0.345690i
$371$	−1.63302	+	3.57581i	−0.0847821	+	0.185647i
$372$	−1.49086	+	0.437755i	−0.0772973	+	0.0226965i
$373$	14.1946	−	16.3815i	0.734971	−	0.848202i	−0.258051	−	0.966131i	$-0.583080\pi$
$373$	14.1946	−	16.3815i	0.734971	−	0.848202i	0.993022	+	0.117930i	$0.0376257\pi$
$374$	−5.09577	−	1.49625i	−0.263496	−	0.0773693i
$375$	−2.23879	+	1.43878i	−0.115611	+	0.0742984i
$376$	−1.80928	−	3.96177i	−0.0933064	−	0.204313i
$377$	−23.3148	−	26.9067i	−1.20077	−	1.38577i
$378$	1.53725	+	0.987928i	0.0790674	+	0.0508135i
$379$	3.82013	−	26.5696i	0.196227	−	1.36479i	−0.618883	−	0.785483i	$-0.712415\pi$
$379$	3.82013	−	26.5696i	0.196227	−	1.36479i	0.815110	−	0.579306i	$-0.196676\pi$
$380$	−1.06745	+	7.42428i	−0.0547591	+	0.380858i
$381$	5.22664	+	3.35896i	0.267769	+	0.172085i
$382$	−10.4717	−	12.0850i	−0.535778	−	0.618321i
$383$	−0.621466	−	1.36082i	−0.0317554	−	0.0695347i	0.893090	−	0.449879i	$-0.148533\pi$
$383$	−0.621466	−	1.36082i	−0.0317554	−	0.0695347i	−0.924845	+	0.380344i	$0.875806\pi$
$384$	0.260364	−	0.167326i	0.0132867	−	0.00853882i
$385$	−3.88952	−	1.14207i	−0.198229	−	0.0582051i
$386$	−15.9672	+	18.4272i	−0.812711	+	0.937919i
$387$	2.90586	−	0.853239i	0.147713	−	0.0433726i
$388$	−4.90479	+	10.7400i	−0.249003	+	0.545241i
$389$	3.85446	+	26.8083i	0.195429	+	1.35924i	0.817343	+	0.576151i	$0.195446\pi$
$389$	3.85446	+	26.8083i	0.195429	+	1.35924i	−0.621914	+	0.783085i	$0.713645\pi$
$390$	5.58323			0.282718
$391$	−14.6072	+	7.06958i	−0.738715	+	0.357524i
$392$	1.00000			0.0505076
$393$	−0.575514	−	4.00279i	−0.0290309	−	0.201914i
$394$	0.0987950	−	0.216331i	0.00497722	−	0.0108986i
$395$	2.75910	−	0.810145i	0.138825	−	0.0407628i
$396$	−2.98500	+	3.44487i	−0.150002	+	0.173111i
$397$	16.2059	+	4.75848i	0.813351	+	0.238821i	0.661850	−	0.749636i	$-0.269771\pi$
$397$	16.2059	+	4.75848i	0.813351	+	0.238821i	0.151500	+	0.988457i	$0.451590\pi$
$398$	12.6567	−	8.13396i	0.634422	−	0.407718i
$399$	−0.373376	−	0.817580i	−0.0186922	−	0.0409302i
$400$	−1.09412	−	1.26268i	−0.0547061	−	0.0631342i
$401$	26.0809	+	16.7612i	1.30242	+	0.837012i	0.993473	−	0.114068i	$-0.0363883\pi$
$401$	26.0809	+	16.7612i	1.30242	+	0.837012i	0.308943	+	0.951080i	$0.400025\pi$
$402$	−0.386233	+	2.68631i	−0.0192636	+	0.133981i
$403$	−4.99036	+	34.7087i	−0.248588	+	1.72896i
$404$	7.42253	+	4.77017i	0.369285	+	0.237325i
$405$	−13.7797	−	15.9026i	−0.684718	−	0.790207i
$406$	−2.11749	−	4.63667i	−0.105089	−	0.230114i
$407$	−3.43428	+	2.20708i	−0.170231	+	0.109401i
$408$	1.00484	+	0.295048i	0.0497470	+	0.0146071i
$409$	0.784563	−	0.905434i	0.0387942	−	0.0447708i	−0.736021	−	0.676959i	$-0.763298\pi$
$409$	0.784563	−	0.905434i	0.0387942	−	0.0447708i	0.774815	+	0.632188i	$0.217843\pi$
$410$	10.6508	−	3.12736i	0.526006	−	0.154449i
$411$	−1.84662	+	4.04352i	−0.0910868	+	0.199452i
$412$	0.128275	+	0.892176i	0.00631968	+	0.0439543i
$413$	−7.08360			−0.348561
$414$	0.311282	+	13.9246i	0.0152987	+	0.684358i
$415$	21.7636			1.06833
$416$	−0.994014	−	6.91352i	−0.0487356	−	0.338963i
$417$	2.38101	−	5.21369i	0.116599	−	0.255315i
$418$	4.37339	−	1.28414i	0.213909	−	0.0628095i
$419$	−25.2152	+	29.0999i	−1.23184	+	1.42162i	−0.359201	+	0.933260i	$0.616951\pi$
$419$	−25.2152	+	29.0999i	−1.23184	+	1.42162i	−0.872641	+	0.488361i	$0.837595\pi$
$420$	0.766981	+	0.225206i	0.0374248	+	0.0109889i
$421$	−0.333928	+	0.214603i	−0.0162747	+	0.0104591i	−0.548753	−	0.835985i	$-0.684897\pi$
$421$	−0.333928	+	0.214603i	−0.0162747	+	0.0104591i	0.532478	+	0.846444i	$0.321261\pi$
$422$	4.60109	+	10.0750i	0.223977	+	0.490442i
$423$	−8.28324	−	9.55937i	−0.402745	−	0.464793i
$424$	3.30701	+	2.12529i	0.160603	+	0.103213i
$425$	0.804578	−	5.59596i	0.0390278	−	0.271444i
$426$	−0.434272	+	3.02043i	−0.0210406	+	0.146340i
$427$	−6.61390	−	4.25050i	−0.320069	−	0.205696i
$428$	10.8128	+	12.4786i	0.522655	+	0.603176i
$429$	−1.40944	−	3.08624i	−0.0680483	−	0.149005i
$430$	2.26579	−	1.45614i	0.109266	−	0.0702211i
$431$	23.4761	+	6.89321i	1.13080	+	0.332034i	0.793024	−	0.609191i	$-0.208506\pi$
$431$	23.4761	+	6.89321i	1.13080	+	0.332034i	0.337780	+	0.941225i	$0.390324\pi$
$432$	1.19665	−	1.38100i	0.0575736	−	0.0664435i
$433$	15.3248	−	4.49975i	0.736461	−	0.216244i	0.108071	−	0.994143i	$-0.465533\pi$
$433$	15.3248	−	4.49975i	0.736461	−	0.216244i	0.628390	+	0.777899i	$0.283714\pi$
$434$	−2.08555	+	4.56673i	−0.100110	+	0.219210i
$435$	−0.579873	−	4.03311i	−0.0278028	−	0.193373i
$436$	−14.7199			−0.704954
$437$	7.26605	−	11.8819i	0.347582	−	0.568390i
$438$	−1.41103			−0.0674215
$439$	4.39979	+	30.6012i	0.209990	+	1.46052i	0.773179	+	0.634187i	$0.218665\pi$
$439$	4.39979	+	30.6012i	0.209990	+	1.46052i	−0.563189	+	0.826328i	$0.690426\pi$
$440$	−1.68398	+	3.68740i	−0.0802806	+	0.175790i
$441$	2.78657	−	0.818211i	0.132694	−	0.0389624i
$442$	15.4772	−	17.8616i	0.736175	−	0.849592i
$443$	23.2947	+	6.83993i	1.10676	+	0.324975i	0.783536	−	0.621347i	$-0.213414\pi$
$443$	23.2947	+	6.83993i	1.10676	+	0.324975i	0.323227	+	0.946322i	$0.395232\pi$
$444$	0.677211	−	0.435217i	0.0321390	−	0.0206545i
$445$	−13.5908	−	29.7597i	−0.644266	−	1.41074i
$446$	7.52839	+	8.68823i	0.356480	+	0.411400i
$447$	1.17301	+	0.753847i	0.0554814	+	0.0356558i
$448$	0.142315	−	0.989821i	0.00672374	−	0.0467647i
$449$	3.01728	−	20.9857i	0.142394	−	0.990375i	−0.785853	−	0.618413i	$-0.787776\pi$
$449$	3.01728	−	20.9857i	0.142394	−	0.990375i	0.928248	−	0.371962i	$-0.121315\pi$
$450$	−4.08199	−	2.62334i	−0.192427	−	0.123665i
$451$	−4.41742	−	5.09797i	−0.208008	−	0.240054i
$452$	4.09788	+	8.97311i	0.192748	+	0.422060i
$453$	2.54317	−	1.63439i	0.119488	−	0.0767905i
$454$	9.19459	+	2.69978i	0.431524	+	0.126707i
$455$	11.8135	−	13.6335i	0.553827	−	0.639150i
$456$	−0.862395	+	0.253222i	−0.0403853	+	0.0118582i
$457$	−14.0054	+	30.6676i	−0.655147	+	1.43457i	0.231829	+	0.972756i	$0.425529\pi$
$457$	−14.0054	+	30.6676i	−0.655147	+	1.43457i	−0.886976	+	0.461815i	$0.847198\pi$
$458$	2.72781	+	18.9723i	0.127462	+	0.886518i
$459$	6.18326			0.288610
$460$	3.75445	+	11.8039i	0.175052	+	0.550359i
$461$	−35.3529			−1.64655			−0.823274	−	0.567644i	$-0.807855\pi$
$461$	−35.3529			−1.64655			−0.823274	+	0.567644i	$0.807855\pi$
$462$	−0.0691308	−	0.480815i	−0.00321626	−	0.0223695i
$463$	15.5193	−	33.9825i	0.721243	−	1.57930i	−0.0909110	−	0.995859i	$-0.528978\pi$
$463$	15.5193	−	33.9825i	0.721243	−	1.57930i	0.812154	−	0.583443i	$-0.198295\pi$
$464$	−4.89082	+	1.43608i	−0.227051	+	0.0666681i
$465$	−2.62803	+	3.03291i	−0.121872	+	0.140648i
$466$	15.1805	+	4.45740i	0.703223	+	0.206485i
$467$	30.1948	−	19.4050i	1.39725	−	0.897958i	0.397443	−	0.917627i	$-0.369898\pi$
$467$	30.1948	−	19.4050i	1.39725	−	0.897958i	0.999807	+	0.0196690i	$0.00626123\pi$
$468$	−8.42661	−	18.4517i	−0.389520	−	0.852931i
$469$	5.74241	+	6.62709i	0.265160	+	0.306011i
$470$	−9.46320	−	6.08163i	−0.436505	−	0.280525i
$471$	−0.110701	+	0.769941i	−0.00510082	+	0.0354770i
$472$	−1.00810	+	7.01150i	−0.0464017	+	0.322731i
$473$	−1.37689	−	0.884873i	−0.0633094	−	0.0406865i
$474$	0.225653	+	0.260418i	0.0103646	+	0.0119614i
$475$	2.01562	+	4.41359i	0.0924830	+	0.202510i
$476$	2.84661	−	1.82940i	0.130474	−	0.0838506i
$477$	10.9542	+	3.21643i	0.501556	+	0.147270i
$478$	−0.344892	+	0.398027i	−0.0157750	+	0.0182053i
$479$	−35.0034	+	10.2779i	−1.59935	+	0.469610i	−0.955364	−	0.295431i	$-0.904537\pi$
$479$	−35.0034	+	10.2779i	−1.59935	+	0.469610i	−0.643982	+	0.765041i	$0.722719\pi$
$480$	0.332066	−	0.727124i	0.0151567	−	0.0331885i
$481$	−2.58544	−	17.9822i	−0.117886	−	0.819916i
$482$	−21.0264			−0.957727
$483$	−1.14319	−	0.946690i	−0.0520171	−	0.0430759i
$484$	−8.53661			−0.388028
$485$	4.33987	+	30.1845i	0.197063	+	1.37061i
$486$	3.32476	−	7.28022i	0.150814	−	0.330237i
$487$	9.62044	−	2.82482i	0.435944	−	0.128005i	−0.0563945	−	0.998409i	$-0.517960\pi$
$487$	9.62044	−	2.82482i	0.435944	−	0.128005i	0.492338	+	0.870404i	$0.336142\pi$
$488$	−5.14849	+	5.94167i	−0.233061	+	0.268967i
$489$	−7.05522	−	2.07160i	−0.319048	−	0.0936809i
$490$	2.17278	−	1.39636i	0.0981560	−	0.0630810i
$491$	14.6405	+	32.0583i	0.660718	+	1.44677i	0.881852	+	0.471526i	$0.156297\pi$
$491$	14.6405	+	32.0583i	0.660718	+	1.44677i	−0.221134	+	0.975243i	$0.570976\pi$
$492$	0.871077	+	1.00528i	0.0392712	+	0.0453214i
$493$	−14.5100	−	9.32502i	−0.653498	−	0.419978i
$494$	−2.88670	+	20.0775i	−0.129879	+	0.903328i
$495$	−1.67546	+	11.6531i	−0.0753062	+	0.523766i
$496$	4.22344	+	2.71424i	0.189638	+	0.121873i
$497$	6.45664	+	7.45136i	0.289620	+	0.334239i
$498$	1.08337	+	2.37226i	0.0485472	+	0.106303i
$499$	−11.7878	+	7.57553i	−0.527692	+	0.339127i	−0.777208	−	0.629243i	$-0.783365\pi$
$499$	−11.7878	+	7.57553i	−0.527692	+	0.339127i	0.249516	+	0.968371i	$0.419728\pi$
$500$	8.25037	+	2.42253i	0.368968	+	0.108339i
$501$	4.83703	−	5.58223i	0.216102	−	0.249396i
$502$	17.7766	−	5.21969i	0.793410	−	0.232966i
$503$	3.60415	−	7.89198i	0.160701	−	0.351886i	−0.812104	−	0.583513i	$-0.801678\pi$
$503$	3.60415	−	7.89198i	0.160701	−	0.351886i	0.972805	+	0.231627i	$0.0744049\pi$
$504$	−0.413313	−	2.87465i	−0.0184104	−	0.128047i
$505$	22.7884			1.01407
$506$	5.57706	−	5.05514i	0.247930	−	0.224728i
$507$	11.0753			0.491869
$508$	−2.85688	−	19.8700i	−0.126753	−	0.881589i
$509$	−4.04141	+	8.84946i	−0.179132	+	0.392245i	−0.977804	−	0.209522i	$-0.932809\pi$
$509$	−4.04141	+	8.84946i	−0.179132	+	0.392245i	0.798671	+	0.601767i	$0.205537\pi$
$510$	2.59529	−	0.762045i	0.114921	−	0.0337439i
$511$	−2.98559	+	3.44555i	−0.132075	+	0.152422i
$512$	−0.959493	−	0.281733i	−0.0424040	−	0.0124509i
$513$	−4.46430	+	2.86903i	−0.197104	+	0.126671i
$514$	2.65920	+	5.82283i	0.117292	+	0.256834i
$515$	1.52451	+	1.75938i	0.0671780	+	0.0775275i
$516$	0.271511	+	0.174489i	0.0119526	+	0.00768146i
$517$	−0.972837	+	6.76623i	−0.0427853	+	0.297578i
$518$	0.370163	−	2.57454i	0.0162640	−	0.113119i
$519$	−0.987821	−	0.634834i	−0.0433606	−	0.0278661i
$520$	−11.8135	−	13.6335i	−0.518057	−	0.597870i
$521$	12.6819	+	27.7695i	0.555604	+	1.21660i	0.954115	+	0.299439i	$0.0967995\pi$
$521$	12.6819	+	27.7695i	0.555604	+	1.21660i	−0.398512	+	0.917163i	$0.630473\pi$
$522$	−12.4536	+	8.00345i	−0.545080	+	0.350302i
$523$	−37.7455	−	11.0831i	−1.65049	−	0.484629i	−0.681522	−	0.731797i	$-0.738682\pi$
$523$	−37.7455	−	11.0831i	−1.65049	−	0.484629i	−0.968973	+	0.247168i	$0.920500\pi$
$524$	−8.55658	+	9.87482i	−0.373796	+	0.431383i
$525$	0.496151	−	0.145683i	0.0216538	−	0.00635812i
$526$	−1.01938	+	2.23213i	−0.0444471	+	0.0973255i
$527$	2.41763	+	16.8150i	0.105314	+	0.732473i
$528$	−0.485760			−0.0211400
$529$	2.25263	−	22.8894i	0.0979403	−	0.995192i
$530$	10.1531			0.441021
$531$	2.92774	+	20.3629i	0.127053	+	0.883674i
$532$	−1.20640	+	2.64165i	−0.0523041	+	0.114530i
$533$	28.8030	−	8.45732i	1.24760	−	0.366327i
$534$	2.56731	−	2.96283i	0.111098	−	0.128214i
$535$	40.9183	+	12.0147i	1.76905	+	0.519441i
$536$	7.37686	−	4.74082i	0.318632	−	0.204772i
$537$	−1.18002	−	2.58388i	−0.0509215	−	0.111503i
$538$	1.76386	+	2.03560i	0.0760453	+	0.0877609i
$539$	−1.32036	−	0.848546i	−0.0568721	−	0.0365495i
$540$	0.671668	−	4.67156i	0.0289040	−	0.201032i
$541$	1.05341	−	7.32665i	0.0452898	−	0.314997i	−0.954566	−	0.298000i	$-0.903680\pi$
$541$	1.05341	−	7.32665i	0.0452898	−	0.314997i	0.999856	−	0.0169970i	$-0.00541059\pi$
$542$	1.99865	+	1.28445i	0.0858492	+	0.0551719i
$543$	−4.60178	−	5.31073i	−0.197481	−	0.227905i
$544$	−1.40567	−	3.07799i	−0.0602676	−	0.131968i
$545$	−31.9830	+	20.5542i	−1.37000	+	0.880446i
$546$	2.07414	+	0.609024i	0.0887652	+	0.0260638i
$547$	23.7332	−	27.3896i	1.01476	−	1.17109i	0.0295793	−	0.999562i	$-0.490583\pi$
$547$	23.7332	−	27.3896i	1.01476	−	1.17109i	0.985179	−	0.171531i	$-0.0548713\pi$
$548$	13.7810	−	4.04647i	0.588696	−	0.172857i
$549$	−9.48509	+	20.7694i	−0.404814	+	0.886418i
$550$	0.373193	+	2.59562i	0.0159130	+	0.110677i
$551$	14.8030			0.630629
$552$	−1.09975	+	0.996830i	−0.0468084	+	0.0424279i
$553$	1.11337			0.0473451
$554$	−0.505885	−	3.51851i	−0.0214930	−	0.149487i
$555$	0.863709	−	1.89126i	0.0366624	−	0.0802795i
$556$	−17.7691	+	5.21749i	−0.753580	+	0.221271i
$557$	−0.622198	+	0.718055i	−0.0263634	+	0.0304250i	−0.768778	−	0.639516i	$-0.779135\pi$
$557$	−0.622198	+	0.718055i	−0.0263634	+	0.0304250i	0.742415	+	0.669941i	$0.233680\pi$
$558$	13.9897	+	4.10776i	0.592233	+	0.173895i
$559$	6.12738	−	3.93783i	0.259160	−	0.166552i
$560$	−1.07293	−	2.34938i	−0.0453394	−	0.0992795i
$561$	−1.07639	−	1.24222i	−0.0454454	−	0.0524468i
$562$	−11.4647	−	7.36790i	−0.483608	−	0.310796i
$563$	−2.99628	+	20.8396i	−0.126278	+	0.878283i	0.823936	+	0.566683i	$0.191774\pi$
$563$	−2.99628	+	20.8396i	−0.126278	+	0.878283i	−0.950214	+	0.311599i	$0.899135\pi$
$564$	0.191835	−	1.33424i	0.00807771	−	0.0561817i
$565$	21.4335	+	13.7745i	0.901713	+	0.579495i
$566$	6.97867	+	8.05381i	0.293335	+	0.338527i
$567$	−3.38442	−	7.41085i	−0.142132	−	0.311226i
$568$	8.29439	−	5.33048i	0.348025	−	0.223662i
$569$	16.7171	+	4.90859i	0.700818	+	0.205779i	0.612682	−	0.790330i	$-0.290091\pi$
$569$	16.7171	+	4.90859i	0.700818	+	0.205779i	0.0881364	+	0.996108i	$0.471909\pi$
$570$	−1.52020	+	1.75441i	−0.0636743	+	0.0734840i
$571$	−38.4230	+	11.2820i	−1.60795	+	0.472137i	−0.957744	−	0.287621i	$-0.907136\pi$
$571$	−38.4230	+	11.2820i	−1.60795	+	0.472137i	−0.650206	+	0.759758i	$0.725318\pi$
$572$	−4.55398	+	9.97183i	−0.190412	+	0.416943i
$573$	−0.704324	−	4.89868i	−0.0294236	−	0.204645i
$574$	4.29787			0.179390
$575$	6.17138	+	5.11058i	0.257364	+	0.213126i
$576$	−2.90421			−0.121009
$577$	−5.11814	−	35.5975i	−0.213071	−	1.48194i	−0.762820	−	0.646611i	$-0.776186\pi$
$577$	−5.11814	−	35.5975i	−0.213071	−	1.48194i	0.549749	−	0.835330i	$-0.314724\pi$
$578$	−2.30559	+	5.04854i	−0.0959000	+	0.209992i
$579$	−7.24065	+	2.12605i	−0.300911	+	0.0883555i
$580$	−8.62139	+	9.94961i	−0.357984	+	0.413135i
$581$	8.08507	+	2.37399i	0.335425	+	0.0984897i
$582$	−3.07412	+	1.97561i	−0.127426	+	0.0818918i
$583$	−2.56305	−	5.61230i	−0.106151	−	0.232438i
$584$	2.98559	+	3.44555i	0.123544	+	0.142578i
$585$	−44.0743	−	28.3249i	−1.82225	−	1.17109i
$586$	−3.10146	+	21.5711i	−0.128120	+	0.891095i
$587$	3.15015	−	21.9098i	0.130021	−	0.904314i	−0.815501	−	0.578756i	$-0.803539\pi$
$587$	3.15015	−	21.9098i	0.130021	−	0.904314i	0.945522	−	0.325559i	$-0.105552\pi$
$588$	0.260364	+	0.167326i	0.0107372	+	0.00690041i
$589$	−9.54768	−	11.0186i	−0.393405	−	0.454014i
$590$	7.60019	+	16.6421i	0.312895	+	0.685144i
$591$	0.0619205	−	0.0397939i	0.00254707	−	0.00163690i
$592$	−2.49565	−	0.732790i	−0.102571	−	0.0301175i
$593$	18.2335	−	21.0425i	0.748759	−	0.864114i	−0.245688	−	0.969349i	$-0.579014\pi$
$593$	18.2335	−	21.0425i	0.748759	−	0.864114i	0.994447	+	0.105235i	$0.0335595\pi$
$594$	−2.75185	+	0.808017i	−0.112910	+	0.0331533i
$595$	3.63054	−	7.94977i	0.148838	−	0.325909i
$596$	−0.641165	−	4.45940i	−0.0262632	−	0.182664i
$597$	4.65637			0.190573
$598$	10.1532	+	31.9212i	0.415193	+	1.30536i
$599$	11.1956			0.457441			0.228721	−	0.973492i	$-0.426546\pi$
$599$	11.1956			0.457441			0.228721	+	0.973492i	$0.426546\pi$
$600$	−0.0735905	−	0.511833i	−0.00300432	−	0.0208955i
$601$	11.3098	−	24.7649i	0.461335	−	1.01018i	−0.525846	−	0.850580i	$-0.676251\pi$
$601$	11.3098	−	24.7649i	0.461335	−	1.01018i	0.987181	−	0.159603i	$-0.0510214\pi$
$602$	1.00057	−	0.293794i	0.0407801	−	0.0119741i
$603$	16.6772	−	19.2465i	0.679147	−	0.783777i
$604$	−9.37206	−	2.75189i	−0.381344	−	0.111973i
$605$	−18.5481	+	11.9202i	−0.754089	+	0.484624i
$606$	1.13439	+	2.48396i	0.0460814	+	0.100904i
$607$	8.76092	+	10.1106i	0.355595	+	0.410378i	0.905159	−	0.425073i	$-0.139752\pi$
$607$	8.76092	+	10.1106i	0.355595	+	0.410378i	−0.549564	+	0.835452i	$0.685206\pi$
$608$	2.44307	+	1.57007i	0.0990797	+	0.0636747i
$609$	0.224515	−	1.56153i	0.00909780	−	0.0632766i
$610$	−2.88981	+	20.0991i	−0.117005	+	0.813787i
$611$	−25.5913	−	16.4465i	−1.03531	−	0.665356i
$612$	−6.43544	−	7.42689i	−0.260137	−	0.300214i
$613$	−15.1240	−	33.1168i	−0.610851	−	1.33758i	−0.921990	−	0.387213i	$-0.873438\pi$
$613$	−15.1240	−	33.1168i	−0.610851	−	1.33758i	0.311139	−	0.950364i	$-0.399289\pi$
$614$	−12.3256	+	7.92116i	−0.497419	+	0.319672i
$615$	3.29638	+	0.967905i	0.132923	+	0.0390297i
$616$	−1.02782	+	1.18616i	−0.0414119	+	0.0477919i
$617$	−18.4644	+	5.42165i	−0.743350	+	0.218267i	−0.631412	−	0.775448i	$-0.717524\pi$
$617$	−18.4644	+	5.42165i	−0.743350	+	0.218267i	−0.111939	+	0.993715i	$0.535706\pi$
$618$	−0.115886	+	0.253755i	−0.00466161	+	0.0102075i
$619$	−0.492404	−	3.42474i	−0.0197914	−	0.137652i	0.977530	−	0.210796i	$-0.0676057\pi$
$619$	−0.492404	−	3.42474i	−0.0197914	−	0.137652i	−0.997321	+	0.0731444i	$0.976697\pi$
$620$	12.9666			0.520753
$621$	−4.57199	+	7.47642i	−0.183468	+	0.300019i
$622$	−11.6573			−0.467415
$623$	−1.80271	−	12.5381i	−0.0722239	−	0.502328i
$624$	0.898006	−	1.96636i	0.0359490	−	0.0787174i
$625$	29.3244	−	8.61042i	1.17298	−	0.344417i
$626$	9.39697	−	10.8447i	0.375578	−	0.433441i
$627$	1.35355	+	0.397437i	0.0540554	+	0.0158721i
$628$	2.11433	−	1.35880i	0.0843709	−	0.0542219i
$629$	−3.65616	−	8.00588i	−0.145781	−	0.319215i
$630$	−4.91208	−	5.66884i	−0.195702	−	0.225852i
$631$	12.0652	+	7.75380i	0.480306	+	0.308674i	0.758296	−	0.651910i	$-0.226032\pi$
$631$	12.0652	+	7.75380i	0.480306	+	0.308674i	−0.277990	+	0.960584i	$0.589668\pi$
$632$	0.158448	−	1.10203i	0.00630274	−	0.0438365i
$633$	−0.487846	+	3.39305i	−0.0193901	+	0.134861i
$634$	−24.6098	−	15.8157i	−0.977379	−	0.628124i
$635$	−33.9530	−	39.1839i	−1.34738	−	1.55496i
$636$	0.505412	+	1.10670i	0.0200409	+	0.0438834i
$637$	5.87583	−	3.77617i	0.232809	−	0.149617i
$638$	7.67624	+	2.25395i	0.303905	+	0.0892346i
$639$	18.7514	−	21.6403i	0.741796	−	0.856078i
$640$	−2.47816	+	0.727654i	−0.0979580	+	0.0287631i
$641$	9.06852	−	19.8573i	0.358185	−	0.784316i	−0.641665	−	0.766985i	$-0.721756\pi$
$641$	9.06852	−	19.8573i	0.358185	−	0.784316i	0.999850	−	0.0173307i	$-0.00551681\pi$
$642$	0.727266	+	5.05824i	0.0287029	+	0.199633i
$643$	−5.42084			−0.213777			−0.106889	−	0.994271i	$-0.534089\pi$
$643$	−5.42084			−0.213777			−0.106889	+	0.994271i	$0.534089\pi$
$644$	0.107183	+	4.79463i	0.00422361	+	0.188935i
$645$	0.833581			0.0328222
$646$	1.39849	+	9.72674i	0.0550230	+	0.382694i
$647$	−16.0960	+	35.2454i	−0.632800	+	1.38564i	0.273034	+	0.962005i	$0.411973\pi$
$647$	−16.0960	+	35.2454i	−0.632800	+	1.38564i	−0.905833	+	0.423634i	$0.860754\pi$
$648$	−7.81707	+	2.29530i	−0.307084	+	0.0901679i
$649$	7.28065	−	8.40231i	0.285790	−	0.329820i
$650$	−11.1970	−	3.28773i	−0.439182	−	0.128955i
$651$	−1.30714	+	0.840045i	−0.0512307	+	0.0329240i
$652$	9.86952	+	21.6112i	0.386520	+	0.846361i
$653$	−31.0901	−	35.8799i	−1.21665	−	1.40409i	−0.888130	−	0.459592i	$-0.847996\pi$
$653$	−31.0901	−	35.8799i	−1.21665	−	1.40409i	−0.328520	−	0.944497i	$-0.606550\pi$
$654$	−3.83253	−	2.46302i	−0.149864	−	0.0963116i
$655$	−4.80274	+	33.4038i	−0.187659	+	1.30520i
$656$	0.611650	−	4.25412i	0.0238809	−	0.166096i
$657$	11.1387	+	7.15843i	0.434564	+	0.279277i
$658$	−2.85215	−	3.29155i	−0.111188	−	0.128318i
$659$	−14.5427	−	31.8440i	−0.566503	−	1.24047i	−0.948639	−	0.316362i	$-0.897539\pi$
$659$	−14.5427	−	31.8440i	−0.566503	−	1.24047i	0.382136	−	0.924106i	$-0.375189\pi$
$660$	−1.05545	+	0.678294i	−0.0410832	+	0.0264026i
$661$	−11.7750	−	3.45745i	−0.457994	−	0.134479i	0.0445940	−	0.999005i	$-0.485801\pi$
$661$	−11.7750	−	3.45745i	−0.457994	−	0.134479i	−0.502588	+	0.864526i	$0.667619\pi$
$662$	−6.93947	+	8.00857i	−0.269710	+	0.311262i
$663$	7.01843	−	2.06080i	0.272573	−	0.0800347i
$664$	3.50045	−	7.66492i	0.135844	−	0.297456i
$665$	1.06745	+	7.42428i	0.0413940	+	0.287901i
$666$	−7.55390			−0.292708
$667$	22.0042	−	10.6496i	0.852004	−	0.412354i
$668$	−23.8657			−0.923393
$669$	0.506359	+	3.52180i	0.0195770	+	0.136161i
$670$	9.40839	−	20.6015i	0.363478	−	0.795905i
$671$	11.8397	−	3.47644i	0.457065	−	0.134206i
$672$	0.202677	−	0.233901i	0.00781842	−	0.00902294i
$673$	−46.4834	−	13.6488i	−1.79180	−	0.526121i	−0.795044	−	0.606552i	$-0.792552\pi$
$673$	−46.4834	−	13.6488i	−1.79180	−	0.526121i	−0.996760	+	0.0804313i	$0.974370\pi$
$674$	21.6107	−	13.8884i	0.832414	−	0.534960i
$675$	−1.26828	−	2.77715i	−0.0488162	−	0.106893i
$676$	−23.4341	−	27.0444i	−0.901311	−	1.04017i
$677$	8.56762	+	5.50607i	0.329280	+	0.211616i	0.694826	−	0.719178i	$-0.255481\pi$
$677$	8.56762	+	5.50607i	0.329280	+	0.211616i	−0.365546	+	0.930793i	$0.619118\pi$
$678$	−0.434492	+	3.02196i	−0.0166866	+	0.116058i
$679$	−1.68031	+	11.6868i	−0.0644843	+	0.448498i
$680$	−7.35218	−	4.72496i	−0.281943	−	0.181194i
$681$	1.94220	+	2.24142i	0.0744253	+	0.0858914i
$682$	−3.27332	−	7.16757i	−0.125342	−	0.274460i
$683$	−13.7889	+	8.86159i	−0.527618	+	0.339079i	−0.777179	−	0.629280i	$-0.783350\pi$
$683$	−13.7889	+	8.86159i	−0.527618	+	0.339079i	0.249561	+	0.968359i	$0.419714\pi$
$684$	8.09245	+	2.37616i	0.309422	+	0.0908546i
$685$	24.2927	−	28.0353i	0.928178	−	1.07117i
$686$	0.959493	−	0.281733i	0.0366336	−	0.0107566i
$687$	−2.46434	+	5.39614i	−0.0940203	+	0.205876i
$688$	−0.148407	−	1.03220i	−0.00565798	−	0.0393521i
$689$	27.4569			1.04602
$690$	−0.997572	+	3.70153i	−0.0379769	+	0.140915i
$691$	−4.98404			−0.189602			−0.0948008	−	0.995496i	$-0.530221\pi$
$691$	−4.98404			−0.189602			−0.0948008	+	0.995496i	$0.530221\pi$
$692$	0.539942	+	3.75538i	0.0205255	+	0.142758i
$693$	−1.89355	+	4.14630i	−0.0719301	+	0.157505i
$694$	−4.64869	+	1.36498i	−0.176462	+	0.0518139i
$695$	−31.3229	+	36.1485i	−1.18814	+	1.37119i
$696$	−1.51369	−	0.444459i	−0.0573762	−	0.0168472i
$697$	12.2344	−	7.86254i	0.463409	−	0.297815i
$698$	5.99173	+	13.1201i	0.226790	+	0.496602i
$699$	3.20662	+	3.70064i	0.121286	+	0.139971i
$700$	−1.40554	−	0.903287i	−0.0531245	−	0.0341410i
$701$	1.22155	−	8.49608i	0.0461374	−	0.320892i	−0.953662	−	0.300879i	$-0.902720\pi$
$701$	1.22155	−	8.49608i	0.0461374	−	0.320892i	0.999800	−	0.0200135i	$-0.00637092\pi$
$702$	1.81639	−	12.6333i	0.0685552	−	0.476812i
$703$	6.35447	+	4.08377i	0.239663	+	0.154022i
$704$	1.02782	+	1.18616i	0.0387373	+	0.0447052i
$705$	−1.44627	−	3.16688i	−0.0544695	−	0.119272i
$706$	7.16695	−	4.60592i	0.269732	−	0.173346i
$707$	8.46578	+	2.48578i	0.318388	+	0.0934873i
$708$	−1.43568	+	1.65686i	−0.0539562	+	0.0622688i
$709$	47.2162	−	13.8639i	1.77324	−	0.520671i	0.778923	−	0.627119i	$-0.215766\pi$
$709$	47.2162	−	13.8639i	1.77324	−	0.520671i	0.994318	+	0.106448i	$0.0339479\pi$
$710$	10.5786	−	23.1639i	0.397007	−	0.869325i
$711$	−0.460168	−	3.20054i	−0.0172576	−	0.120030i
$712$	−12.6670			−0.474717
$713$	−22.1193	−	9.50999i	−0.828375	−	0.356152i
$714$	1.04726			0.0391928
$715$	4.02946	+	28.0255i	0.150693	+	1.04810i
$716$	−3.81271	+	8.34867i	−0.142488	+	0.312005i
$717$	−0.156398	+	0.0459226i	−0.00584079	+	0.00171501i
$718$	8.63063	−	9.96027i	0.322092	−	0.371714i
$719$	−36.6626	−	10.7651i	−1.36728	−	0.401470i	−0.485958	−	0.873982i	$-0.661529\pi$
$719$	−36.6626	−	10.7651i	−1.36728	−	0.401470i	−0.881325	+	0.472511i	$0.843348\pi$
$720$	−6.31020	+	4.05532i	−0.235167	+	0.151133i
$721$	0.374434	+	0.819897i	0.0139447	+	0.0305346i
$722$	6.91944	+	7.98546i	0.257515	+	0.297188i
$723$	−5.47453	−	3.51826i	−0.203600	−	0.130846i
$724$	−3.23126	+	22.4739i	−0.120089	+	0.835236i
$725$	−1.21201	+	8.42974i	−0.0450130	+	0.313073i
$726$	−2.22263	−	1.42840i	−0.0824895	−	0.0530128i
$727$	16.4705	+	19.0080i	0.610858	+	0.704967i	0.973944	−	0.226788i	$-0.0728225\pi$
$727$	16.4705	+	19.0080i	0.610858	+	0.704967i	−0.363087	+	0.931755i	$0.618277\pi$
$728$	−2.90151	−	6.35343i	−0.107537	−	0.235474i
$729$	−18.4775	+	11.8748i	−0.684351	+	0.439806i
$730$	11.2982	+	3.31746i	0.418166	+	0.122785i
$731$	2.31076	−	2.66676i	0.0854666	−	0.0986337i
$732$	−2.33468	+	0.685524i	−0.0862922	+	0.0253377i
$733$	−0.543788	+	1.19073i	−0.0200853	+	0.0439806i	−0.919409	−	0.393303i	$-0.871332\pi$
$733$	−0.543788	+	1.19073i	−0.0200853	+	0.0439806i	0.899324	+	0.437284i	$0.144060\pi$
$734$	2.19749	+	15.2839i	0.0811108	+	0.564138i
$735$	0.799360			0.0294849
$736$	4.76108	+	0.576255i	0.175496	+	0.0212411i
$737$	−13.7630			−0.506965
$738$	−1.77636	−	12.3549i	−0.0653888	−	0.454789i
$739$	−5.73162	+	12.5505i	−0.210841	+	0.461678i	−0.985275	−	0.170977i	$-0.945308\pi$
$739$	−5.73162	+	12.5505i	−0.210841	+	0.461678i	0.774434	+	0.632655i	$0.218035\pi$
$740$	−6.44573	+	1.89264i	−0.236950	+	0.0695748i
$741$	−4.11108	+	4.74444i	−0.151024	+	0.174291i
$742$	3.77182	+	1.10751i	0.138468	+	0.0406578i
$743$	−23.5405	+	15.1286i	−0.863617	+	0.555013i	−0.895794	−	0.444469i	$-0.853392\pi$
$743$	−23.5405	+	15.1286i	−0.863617	+	0.555013i	0.0321772	+	0.999482i	$0.489756\pi$
$744$	0.645470	+	1.41338i	0.0236641	+	0.0518171i
$745$	−7.62003	−	8.79399i	−0.279176	−	0.322187i
$746$	−18.2349	−	11.7188i	−0.667626	−	0.429057i
$747$	3.48273	−	24.2229i	0.127427	−	0.886271i
$748$	−0.755819	+	5.25684i	−0.0276355	+	0.192209i
$749$	13.8904	+	8.92682i	0.507545	+	0.326179i
$750$	1.74275	+	2.01124i	0.0636363	+	0.0734401i
$751$	−14.3444	−	31.4099i	−0.523436	−	1.14616i	−0.968122	−	0.250479i	$-0.919412\pi$
$751$	−14.3444	−	31.4099i	−0.523436	−	1.14616i	0.444686	−	0.895686i	$-0.353315\pi$
$752$	−3.66395	+	2.35468i	−0.133611	+	0.0858664i
$753$	5.50179	+	1.61547i	0.200496	+	0.0588711i
$754$	−23.3148	+	26.9067i	−0.849075	+	0.979884i
$755$	−24.2060	+	7.10752i	−0.880947	+	0.258669i
$756$	0.759100	−	1.66220i	0.0276082	−	0.0604535i
$757$	−0.881322	−	6.12973i	−0.0320322	−	0.222789i	0.967517	−	0.252805i	$-0.0813531\pi$
$757$	−0.881322	−	6.12973i	−0.0320322	−	0.222789i	−0.999549	+	0.0300164i	$0.990444\pi$
$758$	−26.8428			−0.974975
$759$	2.29792	−	0.382992i	0.0834093	−	0.0139017i
$760$	7.50063			0.272076
$761$	−1.14383	−	7.95551i	−0.0414638	−	0.288387i	−0.999994	−	0.00339685i	$-0.998919\pi$
$761$	−1.14383	−	7.95551i	−0.0414638	−	0.288387i	0.958530	−	0.284990i	$-0.0919903\pi$
$762$	2.58094	−	5.65147i	0.0934976	−	0.204731i
$763$	−14.1236	+	4.14707i	−0.511309	+	0.150134i
$764$	−10.4717	+	12.0850i	−0.378853	+	0.437219i
$765$	−24.3534	−	7.15080i	−0.880498	−	0.258538i
$766$	−1.25853	+	0.808805i	−0.0454724	+	0.0292233i
$767$	20.5532	+	45.0052i	0.742132	+	1.62504i
$768$	−0.202677	−	0.233901i	−0.00731346	−	0.00844018i
$769$	−19.7283	−	12.6786i	−0.711419	−	0.457201i	0.134223	−	0.990951i	$-0.457146\pi$
$769$	−19.7283	−	12.6786i	−0.711419	−	0.457201i	−0.845642	+	0.533750i	$0.820782\pi$
$770$	−0.576906	+	4.01247i	−0.0207902	+	0.144599i
$771$	−0.281950	+	1.96101i	−0.0101542	+	0.0706240i
$772$	20.5120	+	13.1823i	0.738243	+	0.474440i
$773$	23.8486	+	27.5228i	0.857775	+	0.989925i	1.00000		9.06851e-5i	$2.88660e-5\pi$
$773$	23.8486	+	27.5228i	0.857775	+	0.989925i	−0.142225	+	0.989834i	$0.545426\pi$
$774$	−1.25810	−	2.75486i	−0.0452215	−	0.0990213i
$775$	7.05640	−	4.53487i	0.253473	−	0.162897i
$776$	11.3287	+	3.32641i	0.406677	+	0.119411i
$777$	0.527165	−	0.608380i	0.0189119	−	0.0218255i
$778$	25.9869	−	7.63045i	0.931676	−	0.273565i
$779$	−5.18495	+	11.3535i	−0.185770	+	0.406780i
$780$	−0.794576	−	5.52640i	−0.0284504	−	0.197877i
$781$	−15.4748			−0.553731
$782$	9.07643	+	13.4524i	0.324573	+	0.481056i
$783$	−9.31444			−0.332871
$784$	−0.142315	−	0.989821i	−0.00508267	−	0.0353508i
$785$	2.69660	−	5.90472i	0.0962457	−	0.210749i
$786$	−3.88014	+	1.13931i	−0.138400	+	0.0406379i
$787$	8.89006	−	10.2597i	0.316896	−	0.365718i	−0.574846	−	0.818262i	$-0.694938\pi$
$787$	8.89006	−	10.2597i	0.316896	−	0.365718i	0.891742	+	0.452544i	$0.149483\pi$
$788$	−0.228189	−	0.0670023i	−0.00812889	−	0.00238686i
$789$	−0.638903	+	0.410598i	−0.0227456	+	0.0146177i
$790$	−1.19456	−	2.61572i	−0.0425005	−	0.0930632i
$791$	6.45991	+	7.45513i	0.229688	+	0.265074i
$792$	3.83462	+	2.46436i	0.136257	+	0.0875672i
$793$	−7.81490	+	54.3538i	−0.277515	+	1.93016i
$794$	2.40371	−	16.7181i	0.0853044	−	0.593305i
$795$	2.64349	+	1.69887i	0.0937551	+	0.0602527i
$796$	−9.85240	−	11.3703i	−0.349209	−	0.403009i
$797$	−1.23414	−	2.70240i	−0.0437156	−	0.0957239i	0.886514	−	0.462702i	$-0.153120\pi$
$797$	−1.23414	−	2.70240i	−0.0437156	−	0.0957239i	−0.930230	+	0.366978i	$0.880393\pi$
$798$	−0.756121	+	0.485929i	−0.0267664	+	0.0172017i
$799$	−14.1405	−	4.15204i	−0.500256	−	0.146888i
$800$	−1.09412	+	1.26268i	−0.0386831	+	0.0446426i
$801$	−35.2976	+	10.3643i	−1.24718	+	0.366205i
$802$	12.8789	−	28.2008i	0.454768	−	0.995803i
$803$	−1.01835	−	7.08279i	−0.0359368	−	0.249946i
$804$	2.71394			0.0957131
$805$	6.92791	+	10.2680i	0.244177	+	0.361899i
$806$	35.0656			1.23513
$807$	0.118637	+	0.825137i	0.00417621	+	0.0290462i
$808$	3.66528	−	8.02585i	0.128944	−	0.282348i
$809$	33.6838	−	9.89045i	1.18426	−	0.347730i	0.370444	−	0.928855i	$-0.379205\pi$
$809$	33.6838	−	9.89045i	1.18426	−	0.347730i	0.813814	+	0.581125i	$0.197387\pi$
$810$	−13.7797	+	15.9026i	−0.484169	+	0.558761i
$811$	7.64170	+	2.24381i	0.268337	+	0.0787907i	0.413133	−	0.910671i	$-0.364435\pi$
$811$	7.64170	+	2.24381i	0.268337	+	0.0787907i	−0.144796	+	0.989461i	$0.546253\pi$
$812$	−4.28812	+	2.75581i	−0.150484	+	0.0967099i
$813$	0.305454	+	0.668851i	0.0107127	+	0.0234576i
$814$	2.67336	+	3.08523i	0.0937014	+	0.108137i
$815$	51.6213	+	33.1750i	1.80821	+	1.16207i
$816$	0.149041	−	1.03660i	0.00521748	−	0.0362884i
$817$	−0.430988	+	2.99759i	−0.0150784	+	0.104872i
$818$	−1.00787	−	0.647721i	−0.0352395	−	0.0226470i
$819$	−13.2837	−	15.3302i	−0.464171	−	0.535682i
$820$	−4.61130	−	10.0973i	−0.161034	−	0.352614i
$821$	31.0290	−	19.9411i	1.08292	−	0.695950i	0.127690	−	0.991814i	$-0.459244\pi$
$821$	31.0290	−	19.9411i	1.08292	−	0.695950i	0.955230	+	0.295864i	$0.0956075\pi$
$822$	4.26517	+	1.25237i	0.148765	+	0.0436813i
$823$	−25.1820	+	29.0616i	−0.877789	+	1.01302i	0.122001	+	0.992530i	$0.461069\pi$
$823$	−25.1820	+	29.0616i	−0.877789	+	1.01302i	−0.999790	+	0.0204926i	$0.993477\pi$
$824$	0.864839	−	0.253940i	0.0301281	−	0.00884641i
$825$	−0.337148	+	0.738251i	−0.0117380	+	0.0257026i
$826$	1.00810	+	7.01150i	0.0350764	+	0.243961i
$827$	−13.5926			−0.472662			−0.236331	−	0.971673i	$-0.575945\pi$
$827$	−13.5926			−0.472662			−0.236331	+	0.971673i	$0.575945\pi$
$828$	13.7386	−	2.28980i	0.477449	−	0.0795759i
$829$	15.9994			0.555683			0.277842	−	0.960627i	$-0.410381\pi$
$829$	15.9994			0.555683			0.277842	+	0.960627i	$0.410381\pi$
$830$	−3.09728	−	21.5420i	−0.107508	−	0.747735i
$831$	0.457024	−	1.00074i	0.0158540	−	0.0347154i
$832$	−6.70169	+	1.96779i	−0.232339	+	0.0682210i
$833$	2.21590	−	2.55728i	0.0767763	−	0.0886046i
$834$	−5.49947	−	1.61479i	−0.190431	−	0.0559157i
$835$	−51.8549	+	33.3251i	−1.79451	+	1.15326i
$836$	−1.89347	−	4.14612i	−0.0654870	−	0.143397i
$837$	6.00765	+	6.93320i	0.207655	+	0.239646i
$838$	32.3922	+	20.8172i	1.11897	+	0.719118i
$839$	−3.01994	+	21.0041i	−0.104260	+	0.725143i	0.868896	+	0.494995i	$0.164830\pi$
$839$	−3.01994	+	21.0041i	−0.104260	+	0.725143i	−0.973156	+	0.230148i	$0.926079\pi$
$840$	0.113761	−	0.791224i	0.00392512	−	0.0272998i
$841$	−2.53852	−	1.63141i	−0.0875351	−	0.0562554i
$842$	0.259941	+	0.299988i	0.00895817	+	0.0103383i
$843$	−1.75215	−	3.83668i	−0.0603473	−	0.132142i
$844$	9.31762	−	5.98807i	0.320726	−	0.206118i
$845$	−88.6807	−	26.0390i	−3.05071	−	0.895769i
$846$	−8.28324	+	9.55937i	−0.284784	+	0.328658i
$847$	−8.19082	+	2.40504i	−0.281440	+	0.0826382i
$848$	1.63302	−	3.57581i	0.0560781	−	0.122794i
$849$	0.469384	+	3.26464i	0.0161092	+	0.112042i
$850$	−5.65351			−0.193914
$851$	12.3836	+	1.49885i	0.424506	+	0.0513798i
$852$	3.05149			0.104542
$853$	0.179501	+	1.24846i	0.00614601	+	0.0427465i	0.992664	−	0.120908i	$-0.0385807\pi$
$853$	0.179501	+	1.24846i	0.00614601	+	0.0427465i	−0.986518	+	0.163655i	$0.947672\pi$
$854$	−3.26598	+	7.15149i	−0.111759	+	0.244719i
$855$	20.9010	−	6.13710i	0.714800	−	0.209884i
$856$	10.8128	−	12.4786i	0.369573	−	0.426510i
$857$	−9.45841	−	2.77724i	−0.323093	−	0.0948687i	0.116164	−	0.993230i	$-0.462940\pi$
$857$	−9.45841	−	2.77724i	−0.323093	−	0.0948687i	−0.439257	+	0.898361i	$0.644758\pi$
$858$	−2.85424	+	1.83431i	−0.0974422	+	0.0626223i
$859$	−0.246981	−	0.540813i	−0.00842688	−	0.0184523i	0.905372	−	0.424620i	$-0.139592\pi$
$859$	−0.246981	−	0.540813i	−0.00842688	−	0.0184523i	−0.913799	+	0.406167i	$0.866865\pi$
$860$	−1.76377	−	2.03550i	−0.0601441	−	0.0694100i
$861$	1.11901	+	0.719145i	0.0381358	+	0.0245084i
$862$	3.48205	−	24.2182i	0.118599	−	0.824874i
$863$	1.73837	−	12.0906i	0.0591747	−	0.411569i	−0.938606	−	0.344990i	$-0.887882\pi$
$863$	1.73837	−	12.0906i	0.0591747	−	0.411569i	0.997781	−	0.0665791i	$-0.0212085\pi$
$864$	−1.53725	−	0.987928i	−0.0522982	−	0.0336100i
$865$	6.41703	+	7.40564i	0.218185	+	0.251799i
$866$	−6.63489	−	14.5284i	−0.225463	−	0.493695i
$867$	−1.44505	+	0.928675i	−0.0490764	+	0.0315395i
$868$	4.81705	+	1.41441i	0.163501	+	0.0480083i
$869$	−1.14434	+	1.32063i	−0.0388189	+	0.0447994i
$870$	−3.90953	+	1.14794i	−0.132545	+	0.0389189i
$871$	25.4431	−	55.7126i	0.862106	−	1.88775i
$872$	2.09486	+	14.5700i	0.0709408	+	0.493404i
$873$	34.2900			1.16054
$874$	−12.7951	−	5.50111i	−0.432799	−	0.186078i
$875$	8.59868			0.290688
$876$	0.200810	+	1.39666i	0.00678474	+	0.0471889i
$877$	−6.55155	+	14.3459i	−0.221230	+	0.484426i	−0.987406	−	0.158204i	$-0.949430\pi$
$877$	−6.55155	+	14.3459i	−0.221230	+	0.484426i	0.766176	+	0.642630i	$0.222157\pi$
$878$	29.6636	−	8.71001i	1.00110	−	0.293949i
$879$	−4.41692	+	5.09740i	−0.148979	+	0.171931i
$880$	3.88952	+	1.14207i	0.131116	+	0.0384991i
$881$	9.94408	−	6.39067i	0.335025	−	0.215307i	−0.362302	−	0.932061i	$-0.618009\pi$
$881$	9.94408	−	6.39067i	0.335025	−	0.215307i	0.697327	+	0.716753i	$0.254373\pi$
$882$	−1.20645	−	2.64176i	−0.0406234	−	0.0889528i
$883$	−7.56183	−	8.72682i	−0.254476	−	0.293681i	0.614109	−	0.789221i	$-0.289516\pi$
$883$	−7.56183	−	8.72682i	−0.254476	−	0.293681i	−0.868585	+	0.495540i	$0.834970\pi$
$884$	−19.8825	−	12.7777i	−0.668720	−	0.429760i
$885$	−0.805837	+	5.60472i	−0.0270879	+	0.188401i
$886$	3.45513	−	24.0310i	0.116077	−	0.807336i
$887$	−2.39055	−	1.53631i	−0.0802667	−	0.0515843i	0.499892	−	0.866088i	$-0.333373\pi$
$887$	−2.39055	−	1.53631i	−0.0802667	−	0.0515843i	−0.580159	+	0.814504i	$0.697009\pi$
$888$	−0.527165	−	0.608380i	−0.0176905	−	0.0204159i
$889$	−8.33918	−	18.2603i	−0.279687	−	0.612430i
$890$	−27.5226	+	17.6877i	−0.922560	+	0.592893i
$891$	12.2690	+	3.60252i	0.411029	+	0.120689i
$892$	7.52839	−	8.68823i	0.252069	−	0.290903i
$893$	12.1360	−	3.56344i	0.406115	−	0.119246i
$894$	0.579238	−	1.26835i	0.0193726	−	0.0424201i
$895$	3.37357	+	23.4637i	0.112766	+	0.784305i
$896$	−1.00000			−0.0334077
$897$	−2.69773	+	10.0100i	−0.0900747	+	0.334225i
$898$	−21.2015			−0.707503
$899$	−3.64191	−	25.3301i	−0.121465	−	0.844805i
$900$	−2.01571	+	4.41378i	−0.0671903	+	0.147126i
$901$	12.7630	−	3.74754i	0.425196	−	0.124849i
$902$	−4.41742	+	5.09797i	−0.147084	+	0.169744i
$903$	0.309672	+	0.0909278i	0.0103052	+	0.00302589i
$904$	8.29859	−	5.33318i	0.276007	−	0.177379i
$905$	24.3608	+	53.3428i	0.809781	+	1.77317i
$906$	−1.97969	−	2.28468i	−0.0657707	−	0.0759035i
$907$	46.6224	+	29.9624i	1.54807	+	0.994886i	0.985798	+	0.167935i	$0.0537100\pi$
$907$	46.6224	+	29.9624i	1.54807	+	0.994886i	0.562275	+	0.826951i	$0.309926\pi$
$908$	1.36377	−	9.48522i	0.0452583	−	0.314778i
$909$	3.64673	−	25.3636i	0.120954	−	0.841256i
$910$	−15.1760	−	9.75303i	−0.503080	−	0.323310i
$911$	7.74485	+	8.93803i	0.256598	+	0.296130i	0.869402	−	0.494105i	$-0.164504\pi$
$911$	7.74485	+	8.93803i	0.256598	+	0.296130i	−0.612804	+	0.790235i	$0.709959\pi$
$912$	0.373376	+	0.817580i	0.0123637	+	0.0270728i
$913$	−11.1259	+	7.15019i	−0.368214	+	0.236637i
$914$	32.3487	+	9.49843i	1.07000	+	0.314180i
$915$	−4.11550	+	4.74954i	−0.136054	+	0.157015i
$916$	18.3910	−	5.40008i	0.607655	−	0.178424i
$917$	−5.42792	+	11.8855i	−0.179246	+	0.392493i
$918$	−0.879970	−	6.12032i	−0.0290433	−	0.202001i
$919$	−45.0429			−1.48583			−0.742913	−	0.669387i	$-0.766557\pi$
$919$	−45.0429			−1.48583			−0.742913	+	0.669387i	$0.766557\pi$
$920$	11.1494	−	5.39611i	0.367586	−	0.177904i
$921$	−4.53456			−0.149419
$922$	5.03124	+	34.9930i	0.165695	+	1.15243i
$923$	28.6076	−	62.6420i	0.941632	−	2.06189i
$924$	−0.466083	+	0.136854i	−0.0153330	+	0.00450217i
$925$	−2.84583	+	3.28426i	−0.0935702	+	0.107986i
$926$	−35.8453	−	10.5251i	−1.17795	−	0.345877i
$927$	2.20216	−	1.41524i	0.0723284	−	0.0464826i
$928$	2.11749	+	4.63667i	0.0695102	+	0.152206i
$929$	18.1939	+	20.9969i	0.596924	+	0.688887i	0.971155	−	0.238448i	$-0.0766388\pi$
$929$	18.1939	+	20.9969i	0.596924	+	0.688887i	−0.374231	+	0.927335i	$0.622093\pi$
$930$	3.37605	+	2.16966i	0.110705	+	0.0711458i
$931$	−0.413295	+	2.87453i	−0.0135452	+	0.0942089i
$932$	2.25162	−	15.6603i	0.0737542	−	0.512972i
$933$	−3.03514	−	1.95057i	−0.0993661	−	0.0638587i
$934$	−23.5047	−	27.1259i	−0.769097	−	0.887585i
$935$	5.69820	+	12.4773i	0.186351	+	0.408052i
$936$	−17.0647	+	10.9668i	−0.557776	+	0.358461i
$937$	14.7357	+	4.32680i	0.481395	+	0.141350i	0.513421	−	0.858137i	$-0.328378\pi$
$937$	14.7357	+	4.32680i	0.481395	+	0.141350i	−0.0320264	+	0.999487i	$0.510196\pi$
$938$	5.74241	−	6.62709i	0.187496	−	0.216382i
$939$	4.26123	−	1.25121i	0.139060	−	0.0408317i
$940$	−4.67297	+	10.2324i	−0.152416	+	0.333744i
$941$	−1.55631	−	10.8244i	−0.0507342	−	0.352864i	−0.999337	−	0.0363964i	$-0.988412\pi$
$941$	−1.55631	−	10.8244i	−0.0507342	−	0.352864i	0.948603	−	0.316468i	$-0.102497\pi$
$942$	0.777858			0.0253440
$943$	0.460659	+	20.6067i	0.0150011	+	0.671047i
$944$	7.08360			0.230552
$945$	−0.671668	−	4.67156i	−0.0218494	−	0.151966i
$946$	−0.679914	+	1.48880i	−0.0221059	+	0.0484052i
$947$	36.6753	−	10.7688i	1.19179	−	0.349940i	0.375080	−	0.926992i	$-0.377615\pi$
$947$	36.6753	−	10.7688i	1.19179	−	0.349940i	0.816707	+	0.577052i	$0.195797\pi$
$948$	0.225653	−	0.260418i	0.00732887	−	0.00845797i
$949$	30.5538	+	8.97140i	0.991818	+	0.291224i
$950$	4.08182	−	2.62322i	0.132432	−	0.0851087i
$951$	−3.76112	−	8.23571i	−0.121963	−	0.267061i
$952$	−2.21590	−	2.55728i	−0.0718177	−	0.0828820i
$953$	21.2490	+	13.6559i	0.688322	+	0.442358i	0.837489	−	0.546454i	$-0.184023\pi$
$953$	21.2490	+	13.6559i	0.688322	+	0.442358i	−0.149167	+	0.988812i	$0.547659\pi$
$954$	1.62475	−	11.3004i	0.0526033	−	0.365864i
$955$	−5.87768	+	40.8802i	−0.190197	+	1.32285i
$956$	0.443059	+	0.284737i	0.0143295	+	0.00920904i
$957$	1.62148	+	1.87128i	0.0524149	+	0.0604900i
$958$	15.1548	+	33.1844i	0.489630	+	1.07214i
$959$	12.0828	−	7.76513i	0.390173	−	0.250749i
$960$	−0.766981	−	0.225206i	−0.0247542	−	0.00726849i
$961$	3.79523	−	4.37992i	0.122427	−	0.141288i
$962$	−17.4312	+	5.11826i	−0.562004	+	0.165019i
$963$	19.9204	−	43.6197i	0.641927	−	1.40562i
$964$	2.99237	+	20.8124i	0.0963777	+	0.670322i
$965$	62.9751			2.02724
$966$	−0.774360	+	1.26629i	−0.0249146	+	0.0407421i
$967$	−16.2119			−0.521339			−0.260669	−	0.965428i	$-0.583943\pi$
$967$	−16.2119			−0.521339			−0.260669	+	0.965428i	$0.583943\pi$
$968$	1.21489	+	8.44972i	0.0390479	+	0.271584i
$969$	−1.26342	+	2.76650i	−0.0405869	+	0.0888729i
$970$	29.2596	−	8.59140i	0.939469	−	0.275853i
$971$	19.1627	−	22.1149i	0.614960	−	0.709701i	−0.359782	−	0.933036i	$-0.617149\pi$
$971$	19.1627	−	22.1149i	0.614960	−	0.709701i	0.974742	+	0.223335i	$0.0716944\pi$
$972$	−7.67928	−	2.25484i	−0.246313	−	0.0723240i
$973$	−15.5794	+	10.0123i	−0.499454	+	0.320979i
$974$	−4.16520	−	9.12051i	−0.133461	−	0.292240i
$975$	−2.36517	−	2.72956i	−0.0757462	−	0.0874158i
$976$	6.61390	+	4.25050i	0.211706	+	0.136055i
$977$	−2.37189	+	16.4968i	−0.0758834	+	0.527781i	0.916054	+	0.401054i	$0.131356\pi$
$977$	−2.37189	+	16.4968i	−0.0758834	+	0.527781i	−0.991938	+	0.126727i	$0.959553\pi$
$978$	−1.04645	+	7.27822i	−0.0334618	+	0.232732i
$979$	16.7251	+	10.7486i	0.534536	+	0.343525i
$980$	−1.69136	−	1.95194i	−0.0540286	−	0.0623524i
$981$	17.7588	+	38.8864i	0.566996	+	1.24155i
$982$	29.6484	−	19.0539i	0.946119	−	0.608033i
$983$	19.0838	+	5.60350i	0.608677	+	0.178724i	0.571523	−	0.820586i	$-0.306353\pi$
$983$	19.0838	+	5.60350i	0.608677	+	0.178724i	0.0371539	+	0.999310i	$0.488171\pi$
$984$	0.871077	−	1.00528i	0.0277689	−	0.0320471i
$985$	−0.589362	+	0.173052i	−0.0187787	+	0.00551391i
$986$	−7.16512	+	15.6894i	−0.228184	+	0.499653i
$987$	−0.191835	−	1.33424i	−0.00610618	−	0.0424694i
$988$	20.2839			0.645318
$989$	1.51588	+	4.76587i	0.0482021	+	0.151546i
$990$	11.7729			0.374167
$991$	−1.81093	−	12.5953i	−0.0575262	−	0.400104i	−0.998158	−	0.0606740i	$-0.980675\pi$
$991$	−1.81093	−	12.5953i	−0.0575262	−	0.400104i	0.940631	−	0.339430i	$-0.110234\pi$
$992$	2.08555	−	4.56673i	0.0662164	−	0.144994i
$993$	−3.14683	+	0.923993i	−0.0998617	+	0.0293220i
$994$	6.45664	−	7.45136i	0.204792	−	0.236343i
$995$	−37.2840	−	10.9476i	−1.18198	−	0.347062i
$996$	2.19393	−	1.40995i	0.0695174	−	0.0446761i
$997$	−19.9359	−	43.6536i	−0.631378	−	1.38252i	−0.906948	−	0.421243i	$-0.861594\pi$
$997$	−19.9359	−	43.6536i	−0.631378	−	1.38252i	0.275570	−	0.961281i	$-0.411133\pi$
$998$	9.17599	+	10.5897i	0.290461	+	0.335210i
$999$	−3.99840	−	2.56961i	−0.126504	−	0.0812990i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	322.2.i.d.141.3	✓	40
23.8	even	11	inner	322.2.i.d.169.3	yes	40
23.10	odd	22		7406.2.a.bv.1.11		20
23.13	even	11		7406.2.a.bu.1.11		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
322.2.i.d.141.3	✓	40	1.1	even	1	trivial
322.2.i.d.169.3	yes	40	23.8	even	11	inner
7406.2.a.bu.1.11		20	23.13	even	11
7406.2.a.bv.1.11		20	23.10	odd	22

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 322 = 2 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	322.i (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.142315 - 0.989821i) q^{2} +(0.128569 - 0.281527i) q^{3} +(-0.959493 + 0.281733i) q^{4} +(-1.69136 + 1.95194i) q^{5} +(-0.296959 - 0.0871950i) q^{6} +(-0.841254 + 0.540641i) q^{7} +(0.415415 + 0.909632i) q^{8} +(1.90185 + 2.19486i) q^{9} +O(q^{10})\)	\(q+(-0.142315 - 0.989821i) q^{2} +(0.128569 - 0.281527i) q^{3} +(-0.959493 + 0.281733i) q^{4} +(-1.69136 + 1.95194i) q^{5} +(-0.296959 - 0.0871950i) q^{6} +(-0.841254 + 0.540641i) q^{7} +(0.415415 + 0.909632i) q^{8} +(1.90185 + 2.19486i) q^{9} +(2.17278 + 1.39636i) q^{10} +(0.223366 - 1.55354i) q^{11} +(-0.0440458 + 0.306345i) q^{12} +(5.87583 + 3.77617i) q^{13} +(0.654861 + 0.755750i) q^{14} +(0.332066 + 0.727124i) q^{15} +(0.841254 - 0.540641i) q^{16} +(3.24670 + 0.953318i) q^{17} +(1.90185 - 2.19486i) q^{18} +(-2.78645 + 0.818176i) q^{19} +(1.07293 - 2.34938i) q^{20} +(0.0440458 + 0.306345i) q^{21} -1.56952 q^{22} +(-3.55335 + 3.22082i) q^{23} +0.309496 q^{24} +(-0.237776 - 1.65377i) q^{25} +(2.90151 - 6.35343i) q^{26} +(1.75331 - 0.514818i) q^{27} +(0.654861 - 0.755750i) q^{28} +(-4.89082 - 1.43608i) q^{29} +(0.672465 - 0.432167i) q^{30} +(2.08555 + 4.56673i) q^{31} +(-0.654861 - 0.755750i) q^{32} +(-0.408647 - 0.262621i) q^{33} +(0.481561 - 3.34933i) q^{34} +(0.367568 - 2.55649i) q^{35} +(-2.44318 - 1.57014i) q^{36} +(-1.70330 - 1.96571i) q^{37} +(1.20640 + 2.64165i) q^{38} +(1.81854 - 1.16871i) q^{39} +(-2.47816 - 0.727654i) q^{40} +(2.81451 - 3.24811i) q^{41} +(0.296959 - 0.0871950i) q^{42} +(0.433199 - 0.948573i) q^{43} +(0.223366 + 1.55354i) q^{44} -7.50095 q^{45} +(3.69373 + 3.05881i) q^{46} -4.35535 q^{47} +(-0.0440458 - 0.306345i) q^{48} +(0.415415 - 0.909632i) q^{49} +(-1.60309 + 0.470711i) q^{50} +(0.685811 - 0.791468i) q^{51} +(-6.70169 - 1.96779i) q^{52} +(3.30701 - 2.12529i) q^{53} +(-0.759100 - 1.66220i) q^{54} +(2.65463 + 3.06360i) q^{55} +(-0.841254 - 0.540641i) q^{56} +(-0.127913 + 0.889654i) q^{57} +(-0.725421 + 5.04542i) q^{58} +(5.95911 + 3.82969i) q^{59} +(-0.523470 - 0.604116i) q^{60} +(3.26598 + 7.15149i) q^{61} +(4.22344 - 2.71424i) q^{62} +(-2.78657 - 0.818211i) q^{63} +(-0.654861 + 0.755750i) q^{64} +(-17.3090 + 5.08238i) q^{65} +(-0.201792 + 0.441862i) q^{66} +(-1.24794 - 8.67964i) q^{67} -3.38377 q^{68} +(0.449897 + 1.41446i) q^{69} -2.58278 q^{70} +(-1.40316 - 9.75920i) q^{71} +(-1.20645 + 2.64176i) q^{72} +(4.37444 - 1.28445i) q^{73} +(-1.70330 + 1.96571i) q^{74} +(-0.496151 - 0.145683i) q^{75} +(2.44307 - 1.57007i) q^{76} +(0.652002 + 1.42769i) q^{77} +(-1.41562 - 1.63371i) q^{78} +(-0.936623 - 0.601931i) q^{79} +(-0.367568 + 2.55649i) q^{80} +(-1.15945 + 8.06416i) q^{81} +(-3.61560 - 2.32360i) q^{82} +(-5.51811 - 6.36824i) q^{83} +(-0.128569 - 0.281527i) q^{84} +(-7.35218 + 4.72496i) q^{85} +(-1.00057 - 0.293794i) q^{86} +(-1.03310 + 1.19226i) q^{87} +(1.50594 - 0.442185i) q^{88} +(-5.26207 + 11.5223i) q^{89} +(1.06750 + 7.42460i) q^{90} -6.98462 q^{91} +(2.50201 - 4.09145i) q^{92} +1.55380 q^{93} +(0.619831 + 4.31102i) q^{94} +(3.11587 - 6.82281i) q^{95} +(-0.296959 + 0.0871950i) q^{96} +(7.73192 - 8.92312i) q^{97} +(-0.959493 - 0.281733i) q^{98} +(3.83462 - 2.46436i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 4 q^{2} - 4 q^{4} + 9 q^{5} + 4 q^{7} - 4 q^{8} - 8 q^{9}+O(q^{10}) \) 40 * q - 4 * q^2 - 4 * q^4 + 9 * q^5 + 4 * q^7 - 4 * q^8 - 8 * q^9	\( 40 q - 4 q^{2} - 4 q^{4} + 9 q^{5} + 4 q^{7} - 4 q^{8} - 8 q^{9} - 2 q^{10} + 6 q^{11} + 2 q^{13} + 4 q^{14} - 3 q^{15} - 4 q^{16} - 13 q^{17} - 8 q^{18} - 22 q^{19} - 2 q^{20} - 16 q^{22} - 9 q^{23} + 22 q^{24} - 15 q^{25} - 9 q^{26} + 21 q^{27} + 4 q^{28} - 10 q^{29} - 14 q^{30} - 2 q^{31} - 4 q^{32} + 8 q^{33} - 2 q^{34} + 13 q^{35} - 8 q^{36} - 45 q^{37} + 11 q^{38} - 22 q^{39} + 9 q^{40} + 21 q^{41} + 31 q^{43} + 6 q^{44} + 2 q^{45} - 9 q^{46} + 64 q^{47} - 4 q^{49} + 7 q^{50} + 65 q^{51} + 2 q^{52} + 69 q^{53} + 21 q^{54} - 74 q^{55} + 4 q^{56} - 68 q^{57} + 12 q^{58} + 48 q^{59} - 3 q^{60} + 6 q^{61} - 13 q^{62} + 8 q^{63} - 4 q^{64} - 64 q^{65} - 69 q^{66} + 31 q^{67} - 2 q^{68} - 62 q^{69} + 2 q^{70} - 57 q^{71} - 19 q^{72} + 70 q^{73} - 45 q^{74} - 11 q^{75} + 22 q^{76} - 6 q^{77} + 33 q^{78} + 34 q^{79} - 13 q^{80} + 30 q^{81} - 12 q^{82} - 56 q^{83} - 17 q^{85} + 42 q^{86} - 3 q^{87} + 6 q^{88} + 16 q^{89} + 46 q^{90} - 46 q^{91} + 24 q^{92} + 48 q^{93} + 9 q^{94} - 42 q^{95} - 36 q^{97} - 4 q^{98} + 112 q^{99}+O(q^{100}) \) 40 * q - 4 * q^2 - 4 * q^4 + 9 * q^5 + 4 * q^7 - 4 * q^8 - 8 * q^9 - 2 * q^10 + 6 * q^11 + 2 * q^13 + 4 * q^14 - 3 * q^15 - 4 * q^16 - 13 * q^17 - 8 * q^18 - 22 * q^19 - 2 * q^20 - 16 * q^22 - 9 * q^23 + 22 * q^24 - 15 * q^25 - 9 * q^26 + 21 * q^27 + 4 * q^28 - 10 * q^29 - 14 * q^30 - 2 * q^31 - 4 * q^32 + 8 * q^33 - 2 * q^34 + 13 * q^35 - 8 * q^36 - 45 * q^37 + 11 * q^38 - 22 * q^39 + 9 * q^40 + 21 * q^41 + 31 * q^43 + 6 * q^44 + 2 * q^45 - 9 * q^46 + 64 * q^47 - 4 * q^49 + 7 * q^50 + 65 * q^51 + 2 * q^52 + 69 * q^53 + 21 * q^54 - 74 * q^55 + 4 * q^56 - 68 * q^57 + 12 * q^58 + 48 * q^59 - 3 * q^60 + 6 * q^61 - 13 * q^62 + 8 * q^63 - 4 * q^64 - 64 * q^65 - 69 * q^66 + 31 * q^67 - 2 * q^68 - 62 * q^69 + 2 * q^70 - 57 * q^71 - 19 * q^72 + 70 * q^73 - 45 * q^74 - 11 * q^75 + 22 * q^76 - 6 * q^77 + 33 * q^78 + 34 * q^79 - 13 * q^80 + 30 * q^81 - 12 * q^82 - 56 * q^83 - 17 * q^85 + 42 * q^86 - 3 * q^87 + 6 * q^88 + 16 * q^89 + 46 * q^90 - 46 * q^91 + 24 * q^92 + 48 * q^93 + 9 * q^94 - 42 * q^95 - 36 * q^97 - 4 * q^98 + 112 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more