LMFDB - Embedded newform 109.2.f.a.38.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [109,2,Mod(16,109)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(109, base_ring=CyclotomicField(18))

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

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

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

chi := DirichletCharacter("109.16");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 109 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	109.f (of order $9$, degree $6$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$0.870369382032$
Analytic rank:	$0$
Dimension:	$42$
Relative dimension:	$7$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			38.4
Character	$\chi$	$=$	109.38
Dual form			109.2.f.a.66.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0775572 + 0.134333i) q^{2} +(-0.124689 + 0.707146i) q^{3} +(0.987970 + 1.71121i) q^{4} +(-0.326444 + 0.118816i) q^{5} +(-0.0853226 - 0.0715941i) q^{6} +(-1.80571 + 0.657225i) q^{7} -0.616725 q^{8} +(2.33457 + 0.849714i) q^{9} +O(q^{10})$	\(q+(-0.0775572 + 0.134333i) q^{2} +(-0.124689 + 0.707146i) q^{3} +(0.987970 + 1.71121i) q^{4} +(-0.326444 + 0.118816i) q^{5} +(-0.0853226 - 0.0715941i) q^{6} +(-1.80571 + 0.657225i) q^{7} -0.616725 q^{8} +(2.33457 + 0.849714i) q^{9} +(0.00935720 - 0.0530673i) q^{10} +(-0.257155 - 1.45840i) q^{11} +(-1.33327 + 0.485270i) q^{12} +(2.58739 - 0.941734i) q^{13} +(0.0517589 - 0.293539i) q^{14} +(-0.0433163 - 0.245659i) q^{15} +(-1.92811 + 3.33958i) q^{16} +(1.05202 - 1.82214i) q^{17} +(-0.295207 + 0.247708i) q^{18} +(2.49619 - 4.32353i) q^{19} +(-0.525837 - 0.441230i) q^{20} +(-0.239602 - 1.35885i) q^{21} +(0.215855 + 0.0785647i) q^{22} +(-4.58193 - 7.93613i) q^{23} +(0.0768989 - 0.436115i) q^{24} +(-3.73777 + 3.13636i) q^{25} +(-0.0741650 + 0.420610i) q^{26} +(-1.96905 + 3.41049i) q^{27} +(-2.90864 - 2.44064i) q^{28} +(0.605232 - 3.43244i) q^{29} +(0.0363596 + 0.0132338i) q^{30} +(2.25849 + 0.822025i) q^{31} +(-0.915803 - 1.58622i) q^{32} +1.06336 q^{33} +(0.163183 + 0.282641i) q^{34} +(0.511375 - 0.429095i) q^{35} +(0.852442 + 4.83444i) q^{36} +(0.677419 + 0.246560i) q^{37} +(0.387195 + 0.670642i) q^{38} +(0.343324 + 1.94709i) q^{39} +(0.201327 - 0.0732769i) q^{40} +5.91541 q^{41} +(0.201121 + 0.0732022i) q^{42} +(-1.87080 + 3.24032i) q^{43} +(2.24157 - 1.88090i) q^{44} -0.863067 q^{45} +1.42145 q^{46} +(0.901240 - 0.756230i) q^{47} +(-2.12116 - 1.77986i) q^{48} +(-2.53366 + 2.12600i) q^{49} +(-0.131426 - 0.745354i) q^{50} +(1.15735 + 0.971130i) q^{51} +(4.16777 + 3.49718i) q^{52} +(-3.27696 + 1.19272i) q^{53} +(-0.305428 - 0.529017i) q^{54} +(0.257228 + 0.445531i) q^{55} +(1.11363 - 0.405327i) q^{56} +(2.74612 + 2.30427i) q^{57} +(0.414150 + 0.347513i) q^{58} +(1.63566 + 9.27628i) q^{59} +(0.377580 - 0.316827i) q^{60} +(6.88523 + 5.77739i) q^{61} +(-0.285587 + 0.239636i) q^{62} -4.77401 q^{63} -7.42832 q^{64} +(-0.732747 + 0.614848i) q^{65} +(-0.0824715 + 0.142845i) q^{66} +(-2.84013 - 1.03372i) q^{67} +4.15744 q^{68} +(6.18332 - 2.25054i) q^{69} +(0.0179808 + 0.101974i) q^{70} +(-3.65291 - 6.32702i) q^{71} +(-1.43979 - 0.524040i) q^{72} +(-0.306612 - 1.73888i) q^{73} +(-0.0856598 + 0.0718771i) q^{74} +(-1.75181 - 3.03422i) q^{75} +9.86465 q^{76} +(1.42284 + 2.46443i) q^{77} +(-0.288186 - 0.104891i) q^{78} +(-10.0981 - 3.67541i) q^{79} +(0.232624 - 1.31928i) q^{80} +(3.54328 + 2.97316i) q^{81} +(-0.458782 + 0.794634i) q^{82} +(-1.40952 + 7.99378i) q^{83} +(2.08856 - 1.75251i) q^{84} +(-0.126925 + 0.719825i) q^{85} +(-0.290188 - 0.502620i) q^{86} +(2.35177 + 0.855975i) q^{87} +(0.158594 + 0.899430i) q^{88} +(-5.19616 - 4.36010i) q^{89} +(0.0669370 - 0.115938i) q^{90} +(-4.05315 + 3.40100i) q^{91} +(9.05361 - 15.6813i) q^{92} +(-0.862901 + 1.49459i) q^{93} +(0.0316890 + 0.179717i) q^{94} +(-0.301163 + 1.70798i) q^{95} +(1.23588 - 0.449823i) q^{96} +(11.5063 - 4.18795i) q^{97} +(-0.0890876 - 0.505241i) q^{98} +(0.638874 - 3.62323i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 42 q - 6 q^{3} - 12 q^{4} - 6 q^{5} + 12 q^{6} + 3 q^{7} - 12 q^{8} - 12 q^{9}+O(q^{10}) $ 42 * q - 6 * q^3 - 12 * q^4 - 6 * q^5 + 12 * q^6 + 3 * q^7 - 12 * q^8 - 12 * q^9	\( 42 q - 6 q^{3} - 12 q^{4} - 6 q^{5} + 12 q^{6} + 3 q^{7} - 12 q^{8} - 12 q^{9} + 15 q^{10} - 15 q^{11} + 9 q^{12} - 30 q^{13} + 3 q^{14} + 6 q^{16} - 3 q^{17} - 27 q^{18} - 3 q^{19} - 30 q^{20} - 3 q^{21} - 18 q^{22} + 6 q^{23} - 12 q^{24} + 6 q^{25} + 15 q^{26} + 3 q^{27} + 66 q^{28} + 3 q^{30} + 6 q^{31} + 12 q^{32} + 24 q^{33} - 21 q^{34} - 54 q^{35} + 21 q^{36} - 24 q^{37} + 27 q^{38} + 18 q^{39} - 24 q^{40} - 30 q^{41} + 12 q^{42} + 9 q^{43} + 36 q^{44} + 12 q^{45} - 12 q^{46} - 42 q^{47} - 27 q^{48} + 15 q^{49} + 3 q^{50} - 12 q^{51} - 3 q^{52} + 3 q^{53} - 36 q^{54} + 21 q^{55} + 57 q^{56} - 15 q^{57} - 24 q^{58} + 18 q^{59} + 33 q^{60} + 6 q^{61} + 78 q^{62} - 48 q^{63} - 12 q^{64} + 3 q^{65} - 15 q^{66} - 6 q^{67} + 66 q^{68} + 15 q^{69} + 39 q^{70} + 15 q^{71} - 9 q^{72} + 66 q^{73} - 24 q^{74} + 24 q^{75} - 96 q^{76} - 39 q^{77} - 3 q^{78} + 18 q^{79} - 3 q^{80} - 15 q^{81} + 21 q^{82} + 21 q^{83} + 87 q^{84} + 120 q^{85} - 15 q^{86} + 12 q^{87} - 48 q^{88} + 15 q^{89} + 24 q^{90} + 63 q^{92} - 75 q^{93} - 30 q^{94} + 15 q^{95} - 21 q^{96} + 48 q^{97} - 126 q^{98} + 39 q^{99}+O(q^{100}) \) 42 * q - 6 * q^3 - 12 * q^4 - 6 * q^5 + 12 * q^6 + 3 * q^7 - 12 * q^8 - 12 * q^9 + 15 * q^10 - 15 * q^11 + 9 * q^12 - 30 * q^13 + 3 * q^14 + 6 * q^16 - 3 * q^17 - 27 * q^18 - 3 * q^19 - 30 * q^20 - 3 * q^21 - 18 * q^22 + 6 * q^23 - 12 * q^24 + 6 * q^25 + 15 * q^26 + 3 * q^27 + 66 * q^28 + 3 * q^30 + 6 * q^31 + 12 * q^32 + 24 * q^33 - 21 * q^34 - 54 * q^35 + 21 * q^36 - 24 * q^37 + 27 * q^38 + 18 * q^39 - 24 * q^40 - 30 * q^41 + 12 * q^42 + 9 * q^43 + 36 * q^44 + 12 * q^45 - 12 * q^46 - 42 * q^47 - 27 * q^48 + 15 * q^49 + 3 * q^50 - 12 * q^51 - 3 * q^52 + 3 * q^53 - 36 * q^54 + 21 * q^55 + 57 * q^56 - 15 * q^57 - 24 * q^58 + 18 * q^59 + 33 * q^60 + 6 * q^61 + 78 * q^62 - 48 * q^63 - 12 * q^64 + 3 * q^65 - 15 * q^66 - 6 * q^67 + 66 * q^68 + 15 * q^69 + 39 * q^70 + 15 * q^71 - 9 * q^72 + 66 * q^73 - 24 * q^74 + 24 * q^75 - 96 * q^76 - 39 * q^77 - 3 * q^78 + 18 * q^79 - 3 * q^80 - 15 * q^81 + 21 * q^82 + 21 * q^83 + 87 * q^84 + 120 * q^85 - 15 * q^86 + 12 * q^87 - 48 * q^88 + 15 * q^89 + 24 * q^90 + 63 * q^92 - 75 * q^93 - 30 * q^94 + 15 * q^95 - 21 * q^96 + 48 * q^97 - 126 * q^98 + 39 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/109\mathbb{Z}\right)^\times$.

$n$	$6$
$\chi(n)$	$e\left(\frac{2}{9}\right)$

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 $

$2$	−0.0775572	+	0.134333i	−0.0548412	+	0.0949878i	−0.892143	−	0.451754i	$-0.850799\pi$
$2$	−0.0775572	+	0.134333i	−0.0548412	+	0.0949878i	0.837302	+	0.546741i	$0.184132\pi$
$3$	−0.124689	+	0.707146i	−0.0719892	+	0.408271i	0.927424	+	0.374012i	$0.122018\pi$
$3$	−0.124689	+	0.707146i	−0.0719892	+	0.408271i	−0.999413	+	0.0342589i	$0.989093\pi$
$4$	0.987970	+	1.71121i	0.493985	+	0.855607i
$5$	−0.326444	+	0.118816i	−0.145990	+	0.0531362i	−0.413982	−	0.910285i	$-0.635862\pi$
$5$	−0.326444	+	0.118816i	−0.145990	+	0.0531362i	0.267991	+	0.963421i	$0.413640\pi$
$6$	−0.0853226	−	0.0715941i	−0.0348328	−	0.0292282i
$7$	−1.80571	+	0.657225i	−0.682495	+	0.248408i	−0.659918	−	0.751337i	$-0.729409\pi$
$7$	−1.80571	+	0.657225i	−0.682495	+	0.248408i	−0.0225763	+	0.999745i	$0.507187\pi$
$8$	−0.616725			−0.218045
$9$	2.33457	+	0.849714i	0.778190	+	0.283238i
$10$	0.00935720	−	0.0530673i	0.00295901	−	0.0167814i
$11$	−0.257155	−	1.45840i	−0.0775350	−	0.439723i	−0.998719	−	0.0505960i	$-0.983888\pi$
$11$	−0.257155	−	1.45840i	−0.0775350	−	0.439723i	0.921184	−	0.389127i	$-0.127223\pi$
$12$	−1.33327	+	0.485270i	−0.384881	+	0.140085i
$13$	2.58739	−	0.941734i	0.717614	−	0.261190i	0.0427012	−	0.999088i	$-0.486404\pi$
$13$	2.58739	−	0.941734i	0.717614	−	0.261190i	0.674912	+	0.737898i	$0.264181\pi$
$14$	0.0517589	−	0.293539i	0.0138331	−	0.0784516i
$15$	−0.0433163	−	0.245659i	−0.0111842	−	0.0634289i
$16$	−1.92811	+	3.33958i	−0.482027	+	0.834895i
$17$	1.05202	−	1.82214i	0.255151	−	0.441935i	−0.709785	−	0.704418i	$-0.751208\pi$
$17$	1.05202	−	1.82214i	0.255151	−	0.441935i	0.964937	+	0.262483i	$0.0845414\pi$
$18$	−0.295207	+	0.247708i	−0.0695810	+	0.0583854i
$19$	2.49619	−	4.32353i	0.572666	−	0.991886i	−0.423625	−	0.905838i	$-0.639243\pi$
$19$	2.49619	−	4.32353i	0.572666	−	0.991886i	0.996291	−	0.0860485i	$-0.0274240\pi$
$20$	−0.525837	−	0.441230i	−0.117581	−	0.0986619i
$21$	−0.239602	−	1.35885i	−0.0522854	−	0.296525i
$22$	0.215855	+	0.0785647i	0.0460204	+	0.0167501i
$23$	−4.58193	−	7.93613i	−0.955398	−	1.65480i	−0.733455	−	0.679738i	$-0.762094\pi$
$23$	−4.58193	−	7.93613i	−0.955398	−	1.65480i	−0.221943	−	0.975060i	$-0.571240\pi$
$24$	0.0768989	−	0.436115i	0.0156969	−	0.0890216i
$25$	−3.73777	+	3.13636i	−0.747555	+	0.627273i
$26$	−0.0741650	+	0.420610i	−0.0145449	+	0.0824885i
$27$	−1.96905	+	3.41049i	−0.378944	+	0.656350i
$28$	−2.90864	−	2.44064i	−0.549681	−	0.461237i
$29$	0.605232	−	3.43244i	0.112389	−	0.637388i	−0.875621	−	0.482998i	$-0.839548\pi$
$29$	0.605232	−	3.43244i	0.112389	−	0.637388i	0.988010	−	0.154390i	$-0.0493411\pi$
$30$	0.0363596	+	0.0132338i	0.00663833	+	0.00241615i
$31$	2.25849	+	0.822025i	0.405637	+	0.147640i	0.536777	−	0.843724i	$-0.319641\pi$
$31$	2.25849	+	0.822025i	0.405637	+	0.147640i	−0.131140	+	0.991364i	$0.541864\pi$
$32$	−0.915803	−	1.58622i	−0.161893	−	0.280406i
$33$	1.06336			0.185108
$34$	0.163183	+	0.282641i	0.0279856	+	0.0484725i
$35$	0.511375	−	0.429095i	0.0864382	−	0.0725303i
$36$	0.852442	+	4.83444i	0.142074	+	0.805740i
$37$	0.677419	+	0.246560i	0.111367	+	0.0405342i	0.397103	−	0.917774i	$-0.370016\pi$
$37$	0.677419	+	0.246560i	0.111367	+	0.0405342i	−0.285736	+	0.958308i	$0.592238\pi$
$38$	0.387195	+	0.670642i	0.0628114	+	0.108792i
$39$	0.343324	+	1.94709i	0.0549759	+	0.311784i
$40$	0.201327	−	0.0732769i	0.0318325	−	0.0115861i
$41$	5.91541			0.923831			0.461916	−	0.886924i	$-0.347162\pi$
$41$	5.91541			0.923831			0.461916	+	0.886924i	$0.347162\pi$
$42$	0.201121	+	0.0732022i	0.0310337	+	0.0112953i
$43$	−1.87080	+	3.24032i	−0.285294	+	0.494144i	−0.972680	−	0.232148i	$-0.925425\pi$
$43$	−1.87080	+	3.24032i	−0.285294	+	0.494144i	0.687386	+	0.726292i	$0.258758\pi$
$44$	2.24157	−	1.88090i	0.337929	−	0.283556i
$45$	−0.863067			−0.128658
$46$	1.42145			0.209581
$47$	0.901240	−	0.756230i	0.131459	−	0.110308i	−0.574687	−	0.818373i	$-0.694876\pi$
$47$	0.901240	−	0.756230i	0.131459	−	0.110308i	0.706147	+	0.708066i	$0.250432\pi$
$48$	−2.12116	−	1.77986i	−0.306163	−	0.256901i
$49$	−2.53366	+	2.12600i	−0.361952	+	0.303714i
$50$	−0.131426	−	0.745354i	−0.0185864	−	0.105409i
$51$	1.15735	+	0.971130i	0.162061	+	0.135985i
$52$	4.16777	+	3.49718i	0.577966	+	0.484971i
$53$	−3.27696	+	1.19272i	−0.450125	+	0.163832i	−0.557128	−	0.830427i	$-0.688097\pi$
$53$	−3.27696	+	1.19272i	−0.450125	+	0.163832i	0.107003	+	0.994259i	$0.465875\pi$
$54$	−0.305428	−	0.529017i	−0.0415635	−	0.0719901i
$55$	0.257228	+	0.445531i	0.0346846	+	0.0600754i
$56$	1.11363	−	0.405327i	0.148815	−	0.0541641i
$57$	2.74612	+	2.30427i	0.363733	+	0.305208i
$58$	0.414150	+	0.347513i	0.0543805	+	0.0456307i
$59$	1.63566	+	9.27628i	0.212945	+	1.20767i	0.884438	+	0.466658i	$0.154542\pi$
$59$	1.63566	+	9.27628i	0.212945	+	1.20767i	−0.671493	+	0.741011i	$0.734347\pi$
$60$	0.377580	−	0.316827i	0.0487454	−	0.0409022i
$61$	6.88523	+	5.77739i	0.881563	+	0.739719i	0.966500	−	0.256667i	$-0.0826244\pi$
$61$	6.88523	+	5.77739i	0.881563	+	0.739719i	−0.0849369	+	0.996386i	$0.527069\pi$
$62$	−0.285587	+	0.239636i	−0.0362696	+	0.0304338i
$63$	−4.77401			−0.601469
$64$	−7.42832			−0.928540
$65$	−0.732747	+	0.614848i	−0.0908861	+	0.0762625i
$66$	−0.0824715	+	0.142845i	−0.0101515	+	0.0175830i
$67$	−2.84013	−	1.03372i	−0.346977	−	0.126289i	0.162652	−	0.986683i	$-0.447995\pi$
$67$	−2.84013	−	1.03372i	−0.346977	−	0.126289i	−0.509629	+	0.860394i	$0.670217\pi$
$68$	4.15744			0.504164
$69$	6.18332	−	2.25054i	0.744384	−	0.270934i
$70$	0.0179808	+	0.101974i	0.00214911	+	0.0121882i
$71$	−3.65291	−	6.32702i	−0.433520	−	0.750879i	0.563653	−	0.826012i	$-0.309395\pi$
$71$	−3.65291	−	6.32702i	−0.433520	−	0.750879i	−0.997174	+	0.0751321i	$0.976062\pi$
$72$	−1.43979	−	0.524040i	−0.169681	−	0.0617587i
$73$	−0.306612	−	1.73888i	−0.0358862	−	0.203521i	0.961593	−	0.274479i	$-0.0885054\pi$
$73$	−0.306612	−	1.73888i	−0.0358862	−	0.203521i	−0.997479	+	0.0709582i	$0.977394\pi$
$74$	−0.0856598	+	0.0718771i	−0.00995775	+	0.00835555i
$75$	−1.75181	−	3.03422i	−0.202282	−	0.350362i
$76$	9.86465			1.13155
$77$	1.42284	+	2.46443i	0.162148	+	0.280848i
$78$	−0.288186	−	0.104891i	−0.0326306	−	0.0118766i
$79$	−10.0981	−	3.67541i	−1.13613	−	0.413516i	−0.295614	−	0.955308i	$-0.595524\pi$
$79$	−10.0981	−	3.67541i	−1.13613	−	0.413516i	−0.840513	+	0.541791i	$0.817746\pi$
$80$	0.232624	−	1.31928i	0.0260082	−	0.147500i
$81$	3.54328	+	2.97316i	0.393697	+	0.330351i
$82$	−0.458782	+	0.794634i	−0.0506640	+	0.0877527i
$83$	−1.40952	+	7.99378i	−0.154715	+	0.877431i	0.804331	+	0.594181i	$0.202524\pi$
$83$	−1.40952	+	7.99378i	−0.154715	+	0.877431i	−0.959046	+	0.283250i	$0.908587\pi$
$84$	2.08856	−	1.75251i	0.227881	−	0.191215i
$85$	−0.126925	+	0.719825i	−0.0137669	+	0.0780760i
$86$	−0.290188	−	0.502620i	−0.0312917	−	0.0541989i
$87$	2.35177	+	0.855975i	0.252136	+	0.0917701i
$88$	0.158594	+	0.899430i	0.0169061	+	0.0958795i
$89$	−5.19616	−	4.36010i	−0.550792	−	0.462169i	0.324417	−	0.945914i	$-0.394832\pi$
$89$	−5.19616	−	4.36010i	−0.550792	−	0.462169i	−0.875209	+	0.483745i	$0.839276\pi$
$90$	0.0669370	−	0.115938i	0.00705578	−	0.0122210i
$91$	−4.05315	+	3.40100i	−0.424886	+	0.356521i
$92$	9.05361	−	15.6813i	0.943904	−	1.63489i
$93$	−0.862901	+	1.49459i	−0.0894787	+	0.154982i
$94$	0.0316890	+	0.179717i	0.00326847	+	0.0185364i
$95$	−0.301163	+	1.70798i	−0.0308987	+	0.175235i
$96$	1.23588	−	0.449823i	0.126136	−	0.0459098i
$97$	11.5063	−	4.18795i	1.16829	−	0.425222i	0.316237	−	0.948680i	$-0.397581\pi$
$97$	11.5063	−	4.18795i	1.16829	−	0.425222i	0.852051	+	0.523458i	$0.175358\pi$
$98$	−0.0890876	−	0.505241i	−0.00899921	−	0.0510371i
$99$	0.638874	−	3.62323i	0.0642092	−	0.364149i
$100$	−9.05980	−	3.29750i	−0.905980	−	0.329750i
$101$	−17.5967			−1.75094			−0.875470	−	0.483273i	$-0.839448\pi$
$101$	−17.5967			−1.75094			−0.875470	+	0.483273i	$0.839448\pi$
$102$	−0.220216	+	0.0801519i	−0.0218046	+	0.00793622i
$103$	−11.5837	−	9.71985i	−1.14137	−	0.957726i	−0.141890	−	0.989882i	$-0.545318\pi$
$103$	−11.5837	−	9.71985i	−1.14137	−	0.957726i	−0.999483	+	0.0321569i	$0.989762\pi$
$104$	−1.59571	+	0.580791i	−0.156472	+	0.0569513i
$105$	0.239670	+	0.415121i	0.0233894	+	0.0405116i
$106$	0.0939307	−	0.532707i	0.00912336	−	0.0517411i
$107$	−4.43762	+	7.68619i	−0.429001	+	0.743052i	−0.996785	−	0.0801260i	$-0.974468\pi$
$107$	−4.43762	+	7.68619i	−0.429001	+	0.743052i	0.567784	+	0.823178i	$0.307801\pi$
$108$	−7.78145			−0.748770
$109$	10.2640	−	1.91055i	0.983113	−	0.182997i
$109$	10.2640	−	1.91055i	0.983113	−	0.182997i
$110$	−0.0797994			−0.00760857
$111$	−0.258821	+	0.448291i	−0.0245662	+	0.0425499i
$112$	1.28675	−	7.29752i	0.121586	−	0.689551i
$113$	−6.70185	−	11.6079i	−0.630457	−	1.09198i	−0.987458	−	0.157879i	$-0.949534\pi$
$113$	−6.70185	−	11.6079i	−0.630457	−	1.09198i	0.357002	−	0.934104i	$-0.383799\pi$
$114$	−0.522521	+	0.190182i	−0.0489386	+	0.0178122i
$115$	2.43868	+	2.04630i	0.227409	+	0.190818i
$116$	6.47159	−	2.35547i	0.600872	−	0.218699i
$117$	6.84065			0.632418
$118$	−1.37297	−	0.499719i	−0.126392	−	0.0460029i
$119$	−0.702077	+	3.98168i	−0.0643593	+	0.365000i
$120$	0.0267143	+	0.151504i	0.00243867	+	0.0138304i
$121$	8.27583	−	3.01216i	0.752348	−	0.273832i
$122$	−1.31009	+	0.476835i	−0.118610	+	0.0431706i
$123$	−0.737586	+	4.18306i	−0.0665059	+	0.377174i
$124$	0.824664	+	4.67690i	0.0740570	+	0.419998i
$125$	1.71601	−	2.97222i	0.153485	−	0.265843i
$126$	0.370259	−	0.641307i	0.0329853	−	0.0571322i
$127$	−7.24869	+	6.08237i	−0.643217	+	0.539723i	−0.905004	−	0.425402i	$-0.860133\pi$
$127$	−7.24869	+	6.08237i	−0.643217	+	0.539723i	0.261787	+	0.965126i	$0.415688\pi$
$128$	2.40773	−	4.17030i	0.212815	−	0.368606i
$129$	−2.05811	−	1.72696i	−0.181206	−	0.152050i
$130$	−0.0257645	−	0.146118i	−0.00225970	−	0.0128154i
$131$	−1.24748	−	0.454046i	−0.108993	−	0.0396702i	0.286948	−	0.957946i	$-0.407359\pi$
$131$	−1.24748	−	0.454046i	−0.108993	−	0.0396702i	−0.395941	+	0.918276i	$0.629582\pi$
$132$	1.05057	+	1.81964i	0.0914405	+	0.158380i
$133$	−1.66587	+	9.44761i	−0.144449	+	0.819211i
$134$	0.359136	−	0.301350i	0.0310246	−	0.0260327i
$135$	0.237564	−	1.34729i	0.0204462	−	0.115956i
$136$	−0.648805	+	1.12376i	−0.0556345	+	0.0963619i
$137$	9.67171	+	8.11553i	0.826310	+	0.693356i	0.954441	−	0.298401i	$-0.0964533\pi$
$137$	9.67171	+	8.11553i	0.826310	+	0.693356i	−0.128131	+	0.991757i	$0.540898\pi$
$138$	−0.177239	+	1.00517i	−0.0150875	+	0.0855657i
$139$	12.6840	+	4.61660i	1.07584	+	0.391575i	0.818359	−	0.574708i	$-0.194884\pi$
$139$	12.6840	+	4.61660i	1.07584	+	0.391575i	0.257484	+	0.966283i	$0.417107\pi$
$140$	1.23950	+	0.451140i	0.104757	+	0.0381283i
$141$	0.422391	+	0.731602i	0.0355717	+	0.0616120i
$142$	1.13324			0.0950991
$143$	−2.03878	−	3.53127i	−0.170491	−	0.295300i
$144$	−7.33899	+	6.15814i	−0.611582	+	0.513179i
$145$	0.210254	+	1.19241i	0.0174607	+	0.0990244i
$146$	0.257369	+	0.0936748i	0.0213000	+	0.00775258i
$147$	−1.18747	−	2.05676i	−0.0979409	−	0.169639i
$148$	0.247352	+	1.40280i	0.0203322	+	0.115310i
$149$	−10.6434	+	3.87387i	−0.871940	+	0.317360i	−0.738952	−	0.673758i	$-0.764679\pi$
$149$	−10.6434	+	3.87387i	−0.871940	+	0.317360i	−0.132987	+	0.991118i	$0.542457\pi$
$150$	0.543462			0.0443735
$151$	9.69990	+	3.53047i	0.789366	+	0.287306i	0.705073	−	0.709135i	$-0.250914\pi$
$151$	9.69990	+	3.53047i	0.789366	+	0.287306i	0.0842937	+	0.996441i	$0.473137\pi$
$152$	−1.53946	+	2.66643i	−0.124867	+	0.216276i
$153$	4.00430	−	3.36001i	0.323729	−	0.271641i
$154$	−0.441406			−0.0355695
$155$	−0.834943			−0.0670642
$156$	−2.99269	+	2.51117i	−0.239607	+	0.201054i
$157$	−3.38786	−	2.84275i	−0.270381	−	0.226876i	0.497508	−	0.867459i	$-0.334248\pi$
$157$	−3.38786	−	2.84275i	−0.270381	−	0.226876i	−0.767889	+	0.640583i	$0.778693\pi$
$158$	1.27691	−	1.07146i	0.101586	−	0.0852404i
$159$	−0.434824	−	2.46601i	−0.0344838	−	0.195567i
$160$	0.487427	+	0.409000i	0.0385345	+	0.0323343i
$161$	13.4895	+	11.3190i	1.06312	+	0.892062i
$162$	−0.674200	+	0.245389i	−0.0529702	+	0.0192796i
$163$	−9.14195	−	15.8343i	−0.716053	−	1.24024i	−0.962552	−	0.271097i	$-0.912614\pi$
$163$	−9.14195	−	15.8343i	−0.716053	−	1.24024i	0.246499	−	0.969143i	$-0.420720\pi$
$164$	5.84424	+	10.1225i	0.456359	+	0.790437i
$165$	−0.347129	+	0.126345i	−0.0270240	+	0.00983592i
$166$	−0.964509	−	0.809320i	−0.0748604	−	0.0628154i
$167$	11.0140	+	9.24183i	0.852288	+	0.715155i	0.960292	−	0.278996i	$-0.0900016\pi$
$167$	11.0140	+	9.24183i	0.852288	+	0.715155i	−0.108004	+	0.994150i	$0.534446\pi$
$168$	0.147769	+	0.838038i	0.0114006	+	0.0646560i
$169$	−4.15084	+	3.48297i	−0.319295	+	0.267921i
$170$	−0.0868524	−	0.0728778i	−0.00666127	−	0.00558947i
$171$	9.50130	−	7.97253i	0.726582	−	0.609675i
$172$	−7.39317			−0.563724
$173$	−15.2333			−1.15816			−0.579081	−	0.815270i	$-0.696589\pi$
$173$	−15.2333			−1.15816			−0.579081	+	0.815270i	$0.696589\pi$
$174$	−0.297382	+	0.249533i	−0.0225445	+	0.0189171i
$175$	4.68804	−	8.11992i	0.354383	−	0.613809i
$176$	5.36625	+	1.95316i	0.404496	+	0.147225i
$177$	−6.76364			−0.508386
$178$	0.988704	−	0.359859i	0.0741065	−	0.0269726i
$179$	3.53530	+	20.0497i	0.264241	+	1.49858i	0.771189	+	0.636607i	$0.219662\pi$
$179$	3.53530	+	20.0497i	0.264241	+	1.49858i	−0.506948	+	0.861977i	$0.669226\pi$
$180$	−0.852684	−	1.47689i	−0.0635553	−	0.110081i
$181$	8.81481	+	3.20833i	0.655200	+	0.238473i	0.648163	−	0.761502i	$-0.275538\pi$
$181$	8.81481	+	3.20833i	0.655200	+	0.238473i	0.00703737	+	0.999975i	$0.497760\pi$
$182$	−0.142515	−	0.808244i	−0.0105639	−	0.0599110i
$183$	−4.94397	+	4.14849i	−0.365469	+	0.306665i
$184$	2.82579	+	4.89441i	0.208320	+	0.360821i
$185$	−0.250435			−0.0184123
$186$	−0.133848	−	0.231832i	−0.00981424	−	0.0169988i
$187$	−2.92794	−	1.06568i	−0.214112	−	0.0779304i
$188$	2.18447	+	0.795082i	0.159319	+	0.0579873i
$189$	1.31407	−	7.45247i	0.0955847	−	0.542088i
$190$	−0.206081	−	0.172922i	−0.0149507	−	0.0125451i
$191$	−1.34101	+	2.32269i	−0.0970319	+	0.168064i	−0.910455	−	0.413609i	$-0.864268\pi$
$191$	−1.34101	+	2.32269i	−0.0970319	+	0.168064i	0.813423	+	0.581673i	$0.197602\pi$
$192$	0.926230	−	5.25291i	0.0668449	−	0.379096i
$193$	9.52882	−	7.99563i	0.685899	−	0.575538i	−0.231824	−	0.972758i	$-0.574469\pi$
$193$	9.52882	−	7.99563i	0.685899	−	0.575538i	0.917723	+	0.397220i	$0.130025\pi$
$194$	−0.329816	+	1.87048i	−0.0236794	+	0.134293i
$195$	−0.343422	−	0.594824i	−0.0245929	−	0.0425962i
$196$	−6.14122	−	2.23522i	−0.438659	−	0.159659i
$197$	3.06488	+	17.3818i	0.218364	+	1.23840i	0.874973	+	0.484172i	$0.160879\pi$
$197$	3.06488	+	17.3818i	0.218364	+	1.23840i	−0.656609	+	0.754231i	$0.728010\pi$
$198$	0.437171	+	0.366830i	0.0310684	+	0.0260694i
$199$	8.21023	−	14.2205i	0.582008	−	1.00807i	−0.413233	−	0.910625i	$-0.635601\pi$
$199$	8.21023	−	14.2205i	0.582008	−	1.00807i	0.995241	−	0.0974420i	$-0.0310660\pi$
$200$	2.30518	−	1.93428i	0.163001	−	0.136774i
$201$	1.08513	−	1.87949i	0.0765389	−	0.132569i
$202$	1.36475	−	2.36382i	0.0960236	−	0.166318i
$203$	1.16301	+	6.59577i	0.0816274	+	0.462932i
$204$	−0.518387	+	2.93992i	−0.0362943	+	0.205835i
$205$	−1.93105	+	0.702845i	−0.134871	+	0.0490889i
$206$	2.20409	−	0.802224i	0.153566	−	0.0558936i
$207$	−3.95339	−	22.4208i	−0.274779	−	1.55835i
$208$	−1.84378	+	10.4566i	−0.127843	+	0.725033i
$209$	−6.94733	−	2.52862i	−0.480557	−	0.174908i
$210$	−0.0743525			−0.00513081
$211$	−1.59748	+	0.581436i	−0.109975	+	0.0400277i	−0.396422	−	0.918069i	$-0.629748\pi$
$211$	−1.59748	+	0.581436i	−0.109975	+	0.0400277i	0.286446	+	0.958096i	$0.407526\pi$
$212$	−5.27853	−	4.42921i	−0.362531	−	0.304200i
$213$	4.92961	−	1.79423i	0.337771	−	0.122939i
$214$	−0.688339	−	1.19224i	−0.0470539	−	0.0814997i
$215$	0.225710	−	1.28006i	0.0153933	−	0.0872997i
$216$	1.21436	−	2.10334i	0.0826269	−	0.143114i
$217$	−4.61844			−0.313520
$218$	−0.539398	+	1.52697i	−0.0365326	+	0.103420i
$219$	1.26788			0.0856752
$220$	−0.508266	+	0.880343i	−0.0342673	+	0.0593527i
$221$	1.00600	−	5.70532i	0.0676710	−	0.383782i
$222$	−0.0401468	−	0.0695363i	−0.00269448	−	0.00466697i
$223$	−18.6678	+	6.79453i	−1.25009	+	0.454996i	−0.880432	−	0.474172i	$-0.842747\pi$
$223$	−18.6678	+	6.79453i	−1.25009	+	0.454996i	−0.369658	+	0.929168i	$0.620525\pi$
$224$	2.69618	+	2.26236i	0.180146	+	0.151160i
$225$	−11.3911	+	4.14602i	−0.759407	+	0.276401i
$226$	2.07911			0.138300
$227$	16.9665	+	6.17529i	1.12610	+	0.409869i	0.836877	−	0.547392i	$-0.184379\pi$
$227$	16.9665	+	6.17529i	1.12610	+	0.409869i	0.289228	+	0.957260i	$0.406601\pi$
$228$	−1.23001	+	6.97575i	−0.0814596	+	0.461980i
$229$	−5.07519	−	28.7828i	−0.335378	−	1.90202i	−0.423467	−	0.905912i	$-0.639187\pi$
$229$	−5.07519	−	28.7828i	−0.335378	−	1.90202i	0.0880888	−	0.996113i	$-0.471924\pi$
$230$	−0.464023	+	0.168891i	−0.0305968	+	0.0111363i
$231$	−1.92013	+	0.698869i	−0.126335	+	0.0459822i
$232$	−0.373262	+	2.11687i	−0.0245058	+	0.138979i
$233$	−3.65817	−	20.7465i	−0.239655	−	1.35915i	−0.832586	−	0.553896i	$-0.813140\pi$
$233$	−3.65817	−	20.7465i	−0.239655	−	1.35915i	0.592931	−	0.805253i	$-0.297971\pi$
$234$	−0.530542	+	0.918925i	−0.0346826	+	0.0600720i
$235$	−0.204353	+	0.353949i	−0.0133305	+	0.0230891i
$236$	−14.2577	+	11.9636i	−0.928098	+	0.778767i
$237$	3.85818	−	6.68256i	0.250616	−	0.434079i
$238$	−0.480419	−	0.403120i	−0.0311410	−	0.0261304i
$239$	−2.58351	−	14.6518i	−0.167113	−	0.947745i	−0.946859	−	0.321649i	$-0.895763\pi$
$239$	−2.58351	−	14.6518i	−0.167113	−	0.947745i	0.779746	−	0.626096i	$-0.215348\pi$
$240$	0.903917	+	0.328999i	0.0583476	+	0.0212368i
$241$	−8.05022	−	13.9434i	−0.518560	−	0.898172i	−0.999767	−	0.0215655i	$-0.993135\pi$
$241$	−8.05022	−	13.9434i	−0.518560	−	0.898172i	0.481207	−	0.876607i	$-0.340198\pi$
$242$	−0.237218	+	1.34533i	−0.0152490	+	0.0864812i
$243$	−11.5945	+	9.72898i	−0.743790	+	0.624114i
$244$	−3.08396	+	17.4900i	−0.197430	+	1.11968i
$245$	0.574498	−	0.995060i	0.0367033	−	0.0635721i
$246$	−0.504718	−	0.423508i	−0.0321796	−	0.0270019i
$247$	2.38701	−	13.5374i	0.151882	−	0.861365i
$248$	−1.39287	−	0.506963i	−0.0884474	−	0.0321922i
$249$	−5.47702	−	1.99347i	−0.347092	−	0.126331i
$250$	0.266178	+	0.461034i	0.0168346	+	0.0291584i
$251$	10.6748			0.673789			0.336894	−	0.941542i	$-0.390623\pi$
$251$	10.6748			0.673789			0.336894	+	0.941542i	$0.390623\pi$
$252$	−4.71658	−	8.16935i	−0.297116	−	0.514621i
$253$	−10.3958	+	8.72307i	−0.653576	+	0.548415i
$254$	−0.254875	−	1.44547i	−0.0159923	−	0.0906968i
$255$	−0.493196	−	0.179509i	−0.0308851	−	0.0112413i
$256$	−7.05485	−	12.2194i	−0.440928	−	0.763710i
$257$	1.73952	+	9.86532i	0.108508	+	0.615382i	0.989761	+	0.142736i	$0.0455899\pi$
$257$	1.73952	+	9.86532i	0.108508	+	0.615382i	−0.881252	+	0.472646i	$0.843299\pi$
$258$	0.391609	−	0.142534i	0.0243805	−	0.00887378i
$259$	−1.38527			−0.0860763
$260$	−1.77607	−	0.646436i	−0.110147	−	0.0400902i
$261$	4.32955	−	7.49899i	0.267992	−	0.464176i
$262$	0.157744	−	0.132363i	0.00974548	−	0.00817743i
$263$	30.8246			1.90072			0.950362	−	0.311148i	$-0.100713\pi$
$263$	30.8246			1.90072			0.950362	+	0.311148i	$0.100713\pi$
$264$	−0.655803			−0.0403619
$265$	0.928032	−	0.778711i	0.0570085	−	0.0478358i
$266$	−1.13993	−	0.956511i	−0.0698933	−	0.0586474i
$267$	3.73113	−	3.13079i	0.228341	−	0.191601i
$268$	−1.03704	−	5.88136i	−0.0633474	−	0.359261i
$269$	8.43619	+	7.07880i	0.514364	+	0.431602i	0.862662	−	0.505782i	$-0.168796\pi$
$269$	8.43619	+	7.07880i	0.514364	+	0.431602i	−0.348298	+	0.937384i	$0.613240\pi$
$270$	0.162561	+	0.136405i	0.00989314	+	0.00830133i
$271$	6.14450	−	2.23641i	0.373252	−	0.135853i	−0.148581	−	0.988900i	$-0.547471\pi$
$271$	6.14450	−	2.23641i	0.373252	−	0.135853i	0.521833	+	0.853048i	$0.325248\pi$
$272$	4.05680	+	7.02658i	0.245980	+	0.426049i
$273$	−1.89962	−	3.29024i	−0.114970	−	0.199134i
$274$	−1.84029	+	0.669812i	−0.111176	+	0.0404648i
$275$	5.53525	+	4.64462i	0.333788	+	0.280081i
$276$	9.96010	+	8.35751i	0.599527	+	0.503063i
$277$	0.404397	+	2.29345i	0.0242978	+	0.137800i	0.994543	−	0.104323i	$-0.0332675\pi$
$277$	0.404397	+	2.29345i	0.0242978	+	0.137800i	−0.970246	+	0.242123i	$0.922156\pi$
$278$	−1.60390	+	1.34583i	−0.0961953	+	0.0807175i
$279$	4.57412	+	3.83815i	0.273846	+	0.229784i
$280$	−0.315378	+	0.264634i	−0.0188475	+	0.0158149i
$281$	−23.3003			−1.38998			−0.694990	−	0.719019i	$-0.744591\pi$
$281$	−23.3003			−1.38998			−0.694990	+	0.719019i	$0.744591\pi$
$282$	−0.131038			−0.00780318
$283$	10.4047	−	8.73056i	0.618494	−	0.518978i	−0.278836	−	0.960339i	$-0.589949\pi$
$283$	10.4047	−	8.73056i	0.618494	−	0.518978i	0.897330	+	0.441361i	$0.145504\pi$
$284$	7.21793	−	12.5018i	0.428305	−	0.741846i
$285$	−1.17024	−	0.425933i	−0.0693191	−	0.0252301i
$286$	0.632488			0.0373998
$287$	−10.6815	+	3.88775i	−0.630510	+	0.229487i
$288$	−0.790175	−	4.48130i	−0.0465615	−	0.264063i
$289$	6.28653	+	10.8886i	0.369796	+	0.640505i
$290$	−0.176487	−	0.0642360i	−0.0103637	−	0.00377207i
$291$	1.52679	+	8.65883i	0.0895017	+	0.507590i
$292$	2.67268	−	2.24264i	0.156407	−	0.131241i
$293$	11.9593	+	20.7142i	0.698672	+	1.21014i	0.968927	+	0.247347i	$0.0795588\pi$
$293$	11.9593	+	20.7142i	0.698672	+	1.21014i	−0.270255	+	0.962789i	$0.587108\pi$
$294$	0.368388			0.0214848
$295$	−1.63612	−	2.83385i	−0.0952588	−	0.164993i
$296$	−0.417781	−	0.152060i	−0.0242830	−	0.00883830i
$297$	5.48020	+	1.99463i	0.317993	+	0.115740i
$298$	0.305082	−	1.73020i	0.0176729	−	0.100228i
$299$	−19.3290	−	16.2189i	−1.11782	−	0.937965i
$300$	3.46147	−	5.99544i	0.199848	−	0.346147i
$301$	1.24850	−	7.08061i	0.0719625	−	0.408120i
$302$	−1.22656	+	1.02920i	−0.0705803	+	0.0592239i
$303$	2.19412	−	12.4435i	0.126049	−	0.714858i
$304$	9.62586	+	16.6725i	0.552081	+	0.956232i
$305$	−2.93409	−	1.06792i	−0.168006	−	0.0611490i
$306$	0.140798	+	0.798503i	0.00804887	+	0.0456474i
$307$	16.3157	+	13.6905i	0.931186	+	0.781358i	0.976030	−	0.217636i	$-0.0698345\pi$
$307$	16.3157	+	13.6905i	0.931186	+	0.781358i	−0.0448437	+	0.998994i	$0.514279\pi$
$308$	−2.81145	+	4.86957i	−0.160197	+	0.277469i
$309$	8.31771	−	6.97939i	0.473178	−	0.397044i
$310$	0.0647558	−	0.112160i	0.00367788	−	0.00637028i
$311$	−9.76160	+	16.9076i	−0.553530	+	0.958742i	0.444487	+	0.895785i	$0.353386\pi$
$311$	−9.76160	+	16.9076i	−0.553530	+	0.958742i	−0.998016	+	0.0629561i	$0.979947\pi$
$312$	−0.211737	−	1.20082i	−0.0119872	−	0.0679830i
$313$	−5.00368	+	28.3773i	−0.282825	+	1.60398i	0.430129	+	0.902767i	$0.358468\pi$
$313$	−5.00368	+	28.3773i	−0.282825	+	1.60398i	−0.712954	+	0.701211i	$0.752643\pi$
$314$	0.644628	−	0.234626i	0.0363785	−	0.0132407i
$315$	1.55845	−	0.567229i	0.0878087	−	0.0319597i
$316$	−3.68721	−	20.9112i	−0.207422	−	1.17635i
$317$	−4.22032	+	23.9346i	−0.237037	+	1.34430i	0.601245	+	0.799065i	$0.294672\pi$
$317$	−4.22032	+	23.9346i	−0.237037	+	1.34430i	−0.838282	+	0.545238i	$0.816439\pi$
$318$	0.364990	+	0.132846i	0.0204676	+	0.00744961i
$319$	−5.16149			−0.288988
$320$	2.42494	−	0.882604i	0.135558	−	0.0493391i
$321$	−4.88194	−	4.09643i	−0.272483	−	0.228641i
$322$	−2.56672	+	0.934209i	−0.143038	+	0.0520615i
$323$	−5.25207	−	9.09684i	−0.292233	−	0.506162i
$324$	−1.58707	+	9.00069i	−0.0881703	+	0.500039i
$325$	−6.71747	+	11.6350i	−0.372618	+	0.645393i
$326$	2.83610			0.157077
$327$	0.0712289	+	7.49638i	0.00393897	+	0.414551i
$328$	−3.64818			−0.201437
$329$	−1.13037	+	1.95785i	−0.0623191	+	0.107940i
$330$	0.00995010	−	0.0564298i	0.000547735	−	0.00310636i
$331$	16.2700	+	28.1804i	0.894279	+	1.54894i	0.834694	+	0.550714i	$0.185644\pi$
$331$	16.2700	+	28.1804i	0.894279	+	1.54894i	0.0595848	+	0.998223i	$0.481022\pi$
$332$	−15.0716	+	5.48562i	−0.827163	+	0.301063i
$333$	1.37197	+	1.15122i	0.0751838	+	0.0630867i
$334$	−2.09570	+	0.762771i	−0.114671	+	0.0417370i
$335$	1.04997			0.0573659
$336$	4.99997	+	1.81984i	0.272771	+	0.0992804i
$337$	−1.83374	+	10.3997i	−0.0998902	+	0.566506i	0.893248	+	0.449563i	$0.148420\pi$
$337$	−1.83374	+	10.3997i	−0.0998902	+	0.566506i	−0.993139	+	0.116942i	$0.962691\pi$
$338$	−0.145950	−	0.827724i	−0.00793864	−	0.0450223i
$339$	9.04416	−	3.29180i	0.491211	−	0.178786i
$340$	−1.35717	+	0.493971i	−0.0736030	+	0.0267893i
$341$	0.618055	−	3.50516i	0.0334696	−	0.189815i
$342$	0.334081	+	1.89466i	0.0180650	+	0.102452i
$343$	9.90340	−	17.1532i	0.534733	−	0.926185i
$344$	1.15377	−	1.99839i	0.0622070	−	0.107746i
$345$	−1.75111	+	1.46936i	−0.0942766	+	0.0791075i
$346$	1.18145	−	2.04633i	0.0635150	−	0.110011i
$347$	−0.826627	−	0.693622i	−0.0443756	−	0.0372356i	0.620330	−	0.784341i	$-0.286999\pi$
$347$	−0.826627	−	0.693622i	−0.0443756	−	0.0372356i	−0.664706	+	0.747105i	$0.731443\pi$
$348$	0.858723	+	4.87006i	0.0460324	+	0.261063i
$349$	3.02778	+	1.10202i	0.162073	+	0.0589898i	0.421783	−	0.906697i	$-0.361405\pi$
$349$	3.02778	+	1.10202i	0.162073	+	0.0589898i	−0.259709	+	0.965687i	$0.583627\pi$
$350$	0.727183	+	1.25952i	0.0388695	+	0.0673240i
$351$	−1.88293	+	10.6786i	−0.100503	+	0.569982i
$352$	−2.07783	+	1.74351i	−0.110749	+	0.0929292i
$353$	3.92471	−	22.2581i	0.208891	−	1.18468i	−0.682306	−	0.731066i	$-0.739023\pi$
$353$	3.92471	−	22.2581i	0.208891	−	1.18468i	0.891198	−	0.453615i	$-0.149866\pi$
$354$	0.524569	−	0.908579i	0.0278805	−	0.0482905i
$355$	1.94422	+	1.63140i	0.103189	+	0.0865856i
$356$	2.32741	−	13.1994i	0.123352	−	0.699566i
$357$	−2.72809	−	0.992942i	−0.144386	−	0.0525521i
$358$	−2.96752	−	1.08009i	−0.156838	−	0.0570845i
$359$	−10.9243	−	18.9214i	−0.576561	−	0.998633i	−0.995870	−	0.0907897i	$-0.971061\pi$
$359$	−10.9243	−	18.9214i	−0.576561	−	0.998633i	0.419309	−	0.907844i	$-0.362272\pi$
$360$	0.532275			0.0280534
$361$	−2.96195	−	5.13024i	−0.155892	−	0.270013i
$362$	−1.11464	+	0.935291i	−0.0585840	+	0.0491578i
$363$	1.09813	+	6.22780i	0.0576369	+	0.326875i
$364$	−9.82423	−	3.57573i	−0.514929	−	0.187419i
$365$	0.306699	+	0.531219i	0.0160534	+	0.0278053i
$366$	−0.173838	−	0.985884i	−0.00908665	−	0.0515330i
$367$	−8.39771	+	3.05652i	−0.438357	+	0.159549i	−0.551765	−	0.834000i	$-0.686045\pi$
$367$	−8.39771	+	3.05652i	−0.438357	+	0.159549i	0.113408	+	0.993548i	$0.463823\pi$
$368$	35.3378			1.84211
$369$	13.8099	+	5.02640i	0.718916	+	0.261664i
$370$	0.0194230	−	0.0336417i	0.00100975	−	0.00174895i
$371$	5.13336	−	4.30740i	0.266511	−	0.223629i
$372$	−3.41008			−0.176804
$373$	−9.69523			−0.502000			−0.251000	−	0.967987i	$-0.580759\pi$
$373$	−9.69523			−0.502000			−0.251000	+	0.967987i	$0.580759\pi$
$374$	0.370239	−	0.310667i	0.0191446	−	0.0160642i
$375$	1.88783	+	1.58408i	0.0974870	+	0.0818013i
$376$	−0.555818	+	0.466386i	−0.0286641	+	0.0240520i
$377$	−1.66647	−	9.45104i	−0.0858277	−	0.486753i
$378$	0.899197	+	0.754516i	0.0462497	+	0.0388081i
$379$	15.0265	+	12.6087i	0.771857	+	0.647665i	0.941184	−	0.337895i	$-0.109715\pi$
$379$	15.0265	+	12.6087i	0.771857	+	0.647665i	−0.169327	+	0.985560i	$0.554159\pi$
$380$	−3.22026	+	1.17208i	−0.165196	+	0.0601264i
$381$	−3.39730	−	5.88429i	−0.174049	−	0.301461i
$382$	−0.208009	−	0.360283i	−0.0106427	−	0.0184337i
$383$	17.2454	−	6.27682i	0.881200	−	0.320731i	0.138506	−	0.990362i	$-0.455770\pi$
$383$	17.2454	−	6.27682i	0.881200	−	0.320731i	0.742694	+	0.669631i	$0.233548\pi$
$384$	2.64880	+	2.22260i	0.135171	+	0.113422i
$385$	−0.757293	−	0.635444i	−0.0385952	−	0.0323852i
$386$	0.335048	+	1.90015i	0.0170535	+	0.0967152i
$387$	−7.12085	+	5.97510i	−0.361973	+	0.303731i
$388$	18.5344	+	15.5522i	0.940939	+	0.789542i
$389$	−10.3108	+	8.65179i	−0.522778	+	0.438663i	−0.865599	−	0.500738i	$-0.833062\pi$
$389$	−10.3108	+	8.65179i	−0.522778	+	0.438663i	0.342821	+	0.939401i	$0.388618\pi$
$390$	0.106539			0.00539483
$391$	−19.2810			−0.975084
$392$	1.56258	−	1.31116i	0.0789220	−	0.0662234i
$393$	0.476624	−	0.825537i	0.0240425	−	0.0416428i
$394$	−2.57266	−	0.936370i	−0.129609	−	0.0471736i
$395$	3.73317			0.187836
$396$	6.83132	−	2.48640i	0.343287	−	0.124946i
$397$	−0.222590	−	1.26237i	−0.0111714	−	0.0633564i	0.978712	−	0.205237i	$-0.0657964\pi$
$397$	−0.222590	−	1.26237i	−0.0111714	−	0.0633564i	−0.989884	+	0.141880i	$0.954685\pi$
$398$	1.27352	+	2.20581i	0.0638360	+	0.110567i
$399$	−6.47312	−	2.35602i	−0.324062	−	0.117949i
$400$	−3.26731	−	18.5298i	−0.163366	−	0.926492i
$401$	−14.3426	+	12.0349i	−0.716237	+	0.600995i	−0.926342	−	0.376684i	$-0.877064\pi$
$401$	−14.3426	+	12.0349i	−0.716237	+	0.600995i	0.210104	+	0.977679i	$0.432620\pi$
$402$	0.168319	+	0.291536i	0.00839497	+	0.0145405i
$403$	6.61774			0.329653
$404$	−17.3850	−	30.1118i	−0.864937	−	1.49812i
$405$	−1.50994	−	0.549574i	−0.0750296	−	0.0273085i
$406$	−0.976229	−	0.355318i	−0.0484494	−	0.0176341i
$407$	0.185381	−	1.05135i	0.00918900	−	0.0521134i
$408$	−0.713766	−	0.598921i	−0.0353367	−	0.0296510i
$409$	13.9899	−	24.2313i	0.691757	−	1.19816i	−0.279505	−	0.960144i	$-0.590170\pi$
$409$	13.9899	−	24.2313i	0.691757	−	1.19816i	0.971262	−	0.238014i	$-0.0764964\pi$
$410$	0.0553516	−	0.313915i	0.00273362	−	0.0155031i
$411$	−6.94482	+	5.82740i	−0.342563	+	0.287444i
$412$	5.18843	−	29.4251i	0.255616	−	1.44967i
$413$	−9.05013	−	15.6753i	−0.445328	−	0.771330i
$414$	3.31846	+	1.20782i	0.163094	+	0.0593612i
$415$	−0.489660	−	2.77700i	−0.0240364	−	0.136317i
$416$	−3.86333	−	3.24172i	−0.189416	−	0.158939i
$417$	−4.84616	+	8.39380i	−0.237318	+	0.411046i
$418$	0.878492	−	0.737142i	0.0429685	−	0.0360548i
$419$	11.8648	−	20.5504i	0.579634	−	1.00395i	−0.415887	−	0.909416i	$-0.636529\pi$
$419$	11.8648	−	20.5504i	0.579634	−	1.00395i	0.995521	−	0.0945389i	$-0.0301377\pi$
$420$	−0.473573	+	0.820253i	−0.0231080	+	0.0400243i
$421$	−0.411086	−	2.33138i	−0.0200351	−	0.113625i	0.973150	−	0.230171i	$-0.0739287\pi$
$421$	−0.411086	−	2.33138i	−0.0200351	−	0.113625i	−0.993185	+	0.116547i	$0.962818\pi$
$422$	0.0457902	−	0.259689i	0.00222903	−	0.0126415i
$423$	2.74659	−	0.999676i	0.133544	−	0.0486059i
$424$	2.02098	−	0.735578i	0.0981477	−	0.0357228i
$425$	1.78271	+	10.1103i	0.0864743	+	0.490420i
$426$	−0.141302	+	0.801364i	−0.00684611	+	0.0388262i
$427$	−16.2298	−	5.90715i	−0.785414	−	0.285867i
$428$	−17.5369			−0.847680
$429$	2.75134	−	1.00141i	0.132836	−	0.0483483i
$430$	0.154449	+	0.129598i	0.00744821	+	0.00624979i
$431$	−27.7731	+	10.1086i	−1.33778	+	0.486912i	−0.909113	−	0.416550i	$-0.863239\pi$
$431$	−27.7731	+	10.1086i	−1.33778	+	0.486912i	−0.428668	+	0.903462i	$0.641017\pi$
$432$	−7.59308	−	13.1516i	−0.365322	−	0.632757i
$433$	−5.30114	+	30.0643i	−0.254757	+	1.44480i	0.541940	+	0.840417i	$0.317690\pi$
$433$	−5.30114	+	30.0643i	−0.254757	+	1.44480i	−0.796697	+	0.604379i	$0.793421\pi$
$434$	0.358193	−	0.620409i	0.0171938	−	0.0297806i
$435$	−0.869426			−0.0416858
$436$	13.4099	+	15.6763i	0.642217	+	0.750761i
$437$	−45.7495			−2.18849
$438$	−0.0983329	+	0.170318i	−0.00469853	+	0.00813809i
$439$	−1.12009	+	6.35236i	−0.0534591	+	0.303181i	−0.999800	−	0.0199879i	$-0.993637\pi$
$439$	−1.12009	+	6.35236i	−0.0534591	+	0.303181i	0.946341	+	0.323169i	$0.104748\pi$
$440$	−0.158639	−	0.274770i	−0.00756280	−	0.0130992i
$441$	−7.72150	+	2.81040i	−0.367691	+	0.133828i
$442$	0.688390	+	0.577628i	0.0327434	+	0.0274750i
$443$	12.9399	−	4.70974i	0.614794	−	0.223767i	−0.0158058	−	0.999875i	$-0.505031\pi$
$443$	12.9399	−	4.70974i	0.614794	−	0.223767i	0.630599	+	0.776109i	$0.282809\pi$
$444$	−1.02283			−0.0485413
$445$	2.21431	+	0.805942i	0.104968	+	0.0382053i
$446$	0.535094	−	3.03467i	0.0253374	−	0.143696i
$447$	−1.41228	−	8.00946i	−0.0667987	−	0.378834i
$448$	13.4134	−	4.88208i	0.633724	−	0.230657i
$449$	−33.9061	+	12.3408i	−1.60013	+	0.582400i	−0.979454	−	0.201667i	$-0.935364\pi$
$449$	−33.9061	+	12.3408i	−1.60013	+	0.582400i	−0.620676	+	0.784067i	$0.713142\pi$
$450$	0.326514	−	1.85175i	0.0153920	−	0.0872926i
$451$	−1.52117	−	8.62700i	−0.0716293	−	0.406230i
$452$	13.2424	−	22.9366i	0.622872	−	1.07885i
$453$	−3.70603	+	6.41903i	−0.174125	+	0.301593i
$454$	−2.14542	+	1.80022i	−0.100689	+	0.0844885i
$455$	0.919036	−	1.59182i	0.0430851	−	0.0746255i
$456$	−1.69360	−	1.42110i	−0.0793102	−	0.0665492i
$457$	−4.78034	−	27.1107i	−0.223615	−	1.26818i	−0.865315	−	0.501228i	$-0.832882\pi$
$457$	−4.78034	−	27.1107i	−0.223615	−	1.26818i	0.641700	−	0.766955i	$-0.278229\pi$
$458$	4.26010	+	1.55055i	0.199062	+	0.0724525i
$459$	4.14294	+	7.17579i	0.193376	+	0.334937i
$460$	−1.09231	+	6.19479i	−0.0509292	+	0.288834i
$461$	11.5974	−	9.73141i	0.540147	−	0.453237i	−0.331441	−	0.943476i	$-0.607535\pi$
$461$	11.5974	−	9.73141i	0.540147	−	0.453237i	0.871588	+	0.490239i	$0.163090\pi$
$462$	0.0550385	−	0.312139i	0.00256062	−	0.0145220i
$463$	6.08844	−	10.5455i	0.282954	−	0.490090i	−0.689157	−	0.724612i	$-0.742019\pi$
$463$	6.08844	−	10.5455i	0.282954	−	0.490090i	0.972111	+	0.234522i	$0.0753524\pi$
$464$	10.2960	+	8.63933i	0.477978	+	0.401071i
$465$	0.104108	−	0.590427i	0.00482790	−	0.0273804i
$466$	3.07066	+	1.11763i	0.142246	+	0.0517732i
$467$	25.4708	+	9.27063i	1.17865	+	0.428993i	0.855725	−	0.517431i	$-0.173112\pi$
$467$	25.4708	+	9.27063i	1.17865	+	0.428993i	0.322925	+	0.946425i	$0.395334\pi$
$468$	6.75836	+	11.7058i	0.312405	+	0.541102i
$469$	5.80784			0.268181
$470$	−0.0316980	−	0.0549026i	−0.00146212	−	0.00253247i
$471$	2.43267	−	2.04125i	0.112092	−	0.0940560i
$472$	−1.00875	−	5.72092i	−0.0464316	−	0.263327i
$473$	5.20675	+	1.89510i	0.239407	+	0.0871368i
$474$	0.598459	+	1.03656i	0.0274881	+	0.0476108i
$475$	4.22997	+	23.9893i	0.194084	+	1.10071i
$476$	−7.50713	+	2.73237i	−0.344089	+	0.125238i
$477$	−8.66376			−0.396686
$478$	2.16859	+	0.789302i	0.0991889	+	0.0361018i
$479$	7.49917	−	12.9889i	0.342646	−	0.593480i	−0.642277	−	0.766472i	$-0.722010\pi$
$479$	7.49917	−	12.9889i	0.342646	−	0.593480i	0.984923	+	0.172993i	$0.0553436\pi$
$480$	−0.349999	+	0.293684i	−0.0159752	+	0.0134048i
$481$	1.98494			0.0905056
$482$	2.49741			0.113754
$483$	−9.68618	+	8.12767i	−0.440736	+	0.369822i
$484$	13.3307	+	11.1858i	0.605941	+	0.508445i
$485$	−3.25857	+	2.73427i	−0.147964	+	0.124157i
$486$	−0.407682	−	2.31208i	−0.0184929	−	0.104878i
$487$	0.332850	+	0.279294i	0.0150829	+	0.0126560i	0.650298	−	0.759679i	$-0.274644\pi$
$487$	0.332850	+	0.279294i	0.0150829	+	0.0126560i	−0.635215	+	0.772335i	$0.719089\pi$
$488$	−4.24629	−	3.56306i	−0.192221	−	0.161292i
$489$	12.3371	−	4.49033i	0.557902	−	0.203060i
$490$	0.0891129	+	0.154348i	0.00402571	+	0.00697274i
$491$	9.67818	+	16.7631i	0.436770	+	0.756508i	0.997438	−	0.0715325i	$-0.0227890\pi$
$491$	9.67818	+	16.7631i	0.436770	+	0.756508i	−0.560668	+	0.828041i	$0.689456\pi$
$492$	−7.88682	+	2.87057i	−0.355565	+	0.129415i
$493$	−5.61769	−	4.71380i	−0.253008	−	0.212299i
$494$	1.63339	+	1.37058i	0.0734898	+	0.0616653i
$495$	0.221942	+	1.25869i	0.00997553	+	0.0565740i
$496$	−7.09984	+	5.95747i	−0.318792	+	0.267498i
$497$	10.7544	+	9.02399i	0.482400	+	0.404781i
$498$	0.692571	−	0.581136i	0.0310348	−	0.0260413i
$499$	−13.1757			−0.589826			−0.294913	−	0.955524i	$-0.595291\pi$
$499$	−13.1757			−0.589826			−0.294913	+	0.955524i	$0.595291\pi$
$500$	6.78147			0.303277
$501$	−7.90865	+	6.63615i	−0.353332	+	0.296481i
$502$	−0.827909	+	1.43398i	−0.0369514	+	0.0640017i
$503$	20.1197	+	7.32296i	0.897092	+	0.326515i	0.749087	−	0.662472i	$-0.230493\pi$
$503$	20.1197	+	7.32296i	0.897092	+	0.326515i	0.148005	+	0.988987i	$0.452715\pi$
$504$	2.94425			0.131147
$505$	5.74435	−	2.09077i	0.255620	−	0.0930382i
$506$	−0.365531	−	2.07303i	−0.0162498	−	0.0921574i
$507$	−1.94540	−	3.36954i	−0.0863984	−	0.149646i
$508$	−17.5697	−	6.39486i	−0.779531	−	0.283726i
$509$	−6.65394	−	37.7364i	−0.294931	−	1.67264i	−0.667483	−	0.744625i	$-0.732628\pi$
$509$	−6.65394	−	37.7364i	−0.294931	−	1.67264i	0.372552	−	0.928011i	$-0.378483\pi$
$510$	0.0623648	−	0.0523303i	0.00276156	−	0.00231722i
$511$	1.69649	+	2.93841i	0.0750483	+	0.129988i
$512$	11.8195			0.522354
$513$	9.83025	+	17.0265i	0.434016	+	0.751738i
$514$	−1.46015	−	0.531451i	−0.0644045	−	0.0234413i
$515$	4.93630	+	1.79667i	0.217519	+	0.0791706i
$516$	0.921846	−	5.22805i	0.0405820	−	0.230152i
$517$	−1.33464	−	1.11990i	−0.0586974	−	0.0492530i
$518$	0.107437	−	0.186087i	0.00472053	−	0.00817620i
$519$	1.89942	−	10.7721i	0.0833752	−	0.472844i
$520$	0.451904	−	0.379192i	0.0198173	−	0.0166287i
$521$	5.71315	−	32.4009i	0.250298	−	1.41951i	−0.557562	−	0.830135i	$-0.688263\pi$
$521$	5.71315	−	32.4009i	0.250298	−	1.41951i	0.807860	−	0.589374i	$-0.200626\pi$
$522$	0.671575	+	1.16320i	0.0293940	+	0.0509120i
$523$	40.2663	+	14.6557i	1.76072	+	0.640851i	0.999966	−	0.00818550i	$-0.00260555\pi$
$523$	40.2663	+	14.6557i	1.76072	+	0.640851i	0.760757	+	0.649037i	$0.224828\pi$
$524$	−0.455504	−	2.58329i	−0.0198988	−	0.112852i
$525$	5.15743	+	4.32760i	0.225089	+	0.188872i
$526$	−2.39067	+	4.14075i	−0.104238	+	0.180545i
$527$	3.87382	−	3.25052i	0.168746	−	0.141595i
$528$	−2.05028	+	3.55119i	−0.0892270	+	0.154546i
$529$	−30.4881	+	52.8070i	−1.32557	+	2.29595i
$530$	0.0326311	+	0.185060i	0.00141740	+	0.00803849i
$531$	−4.06362	+	23.0460i	−0.176346	+	1.00011i
$532$	−17.8127	+	6.48329i	−0.772279	+	0.281086i
$533$	15.3055	−	5.57074i	0.662954	−	0.241296i
$534$	0.131192	+	0.744029i	0.00567725	+	0.0321973i
$535$	0.535395	−	3.03637i	0.0231471	−	0.131274i
$536$	1.75158	+	0.637523i	0.0756567	+	0.0275368i
$537$	−14.6189			−0.630851
$538$	−1.60520	+	0.584246i	−0.0692053	+	0.0251887i
$539$	3.75209	+	3.14838i	0.161614	+	0.135610i
$540$	2.54021	−	0.924561i	0.109313	−	0.0397868i
$541$	−17.7392	−	30.7252i	−0.762667	−	1.32098i	−0.941471	−	0.337093i	$-0.890556\pi$
$541$	−17.7392	−	30.7252i	−0.762667	−	1.32098i	0.178804	−	0.983885i	$-0.442777\pi$
$542$	−0.176126	+	0.998859i	−0.00756525	+	0.0429047i
$543$	−3.36787	+	5.83332i	−0.144529	+	0.250332i
$544$	−3.85375			−0.165228
$545$	−3.12362	+	1.84322i	−0.133801	+	0.0789547i
$546$	0.589317			0.0252204
$547$	−12.3847	+	21.4510i	−0.529532	+	0.917177i	0.469874	+	0.882733i	$0.344299\pi$
$547$	−12.3847	+	21.4510i	−0.529532	+	0.917177i	−0.999407	+	0.0344435i	$0.989034\pi$
$548$	−4.33205	+	24.5683i	−0.185056	+	1.04950i
$549$	11.1649	+	19.3382i	0.476507	+	0.825334i
$550$	−1.05322	+	0.383342i	−0.0449096	+	0.0163458i
$551$	−13.3295	−	11.1848i	−0.567855	−	0.476487i
$552$	−3.81341	+	1.38797i	−0.162310	+	0.0590758i
$553$	20.6498			0.878121
$554$	−0.339449	−	0.123549i	−0.0144218	−	0.00524911i
$555$	0.0312265	−	0.177094i	0.00132549	−	0.00751723i
$556$	4.63142	+	26.2661i	0.196416	+	1.11393i
$557$	33.1898	−	12.0801i	1.40630	−	0.511850i	0.476255	−	0.879307i	$-0.341994\pi$
$557$	33.1898	−	12.0801i	1.40630	−	0.511850i	0.930040	+	0.367457i	$0.119772\pi$
$558$	−0.870346	+	0.316780i	−0.0368447	+	0.0134104i
$559$	−1.78897	+	10.1458i	−0.0756655	+	0.429120i
$560$	0.447010	+	2.53512i	0.0188896	+	0.107128i
$561$	1.11868	−	1.93760i	0.0472305	−	0.0818056i
$562$	1.80711	−	3.13000i	0.0762282	−	0.132031i
$563$	−12.3660	+	10.3763i	−0.521163	+	0.437308i	−0.865037	−	0.501708i	$-0.832705\pi$
$563$	−12.3660	+	10.3763i	−0.521163	+	0.437308i	0.343874	+	0.939016i	$0.388261\pi$
$564$	−0.834619	+	1.44560i	−0.0351438	+	0.0608708i
$565$	3.56699	+	2.99306i	0.150064	+	0.125919i
$566$	0.365845	+	2.07481i	0.0153776	+	0.0872107i
$567$	−8.35217	−	3.03994i	−0.350758	−	0.127665i
$568$	2.25284	+	3.90204i	0.0945271	+	0.163726i
$569$	−0.441782	+	2.50547i	−0.0185205	+	0.105035i	−0.992667	−	0.120884i	$-0.961427\pi$
$569$	−0.441782	+	2.50547i	−0.0185205	+	0.105035i	0.974146	+	0.225918i	$0.0725383\pi$
$570$	0.147977	−	0.124168i	0.00619809	−	0.00520081i
$571$	3.39957	−	19.2799i	0.142268	−	0.806840i	−0.827253	−	0.561830i	$-0.810098\pi$
$571$	3.39957	−	19.2799i	0.142268	−	0.806840i	0.969520	−	0.245010i	$-0.0787914\pi$
$572$	4.02851	−	6.97758i	0.168440	−	0.291747i
$573$	−1.47527	−	1.23790i	−0.0616305	−	0.0517141i
$574$	0.306175	−	1.73640i	0.0127795	−	0.0724761i
$575$	42.0168	+	15.2929i	1.75222	+	0.637757i
$576$	−17.3419	−	6.31195i	−0.722581	−	0.262998i
$577$	10.7565	+	18.6308i	0.447799	+	0.775610i	0.998242	−	0.0592621i	$-0.0188748\pi$
$577$	10.7565	+	18.6308i	0.447799	+	0.775610i	−0.550444	+	0.834872i	$0.685541\pi$
$578$	−1.95026			−0.0811202
$579$	4.46594	+	7.73523i	0.185598	+	0.321465i
$580$	−1.83275	+	1.53786i	−0.0761007	+	0.0638561i
$581$	−2.70853	−	15.3608i	−0.112369	−	0.637274i
$582$	−1.28158	−	0.466457i	−0.0531232	−	0.0193353i
$583$	2.58214	+	4.47239i	0.106941	+	0.185228i
$584$	0.189096	+	1.07241i	0.00782483	+	0.0443768i
$585$	−2.23309	+	0.812779i	−0.0923270	+	0.0336043i
$586$	−3.71013			−0.153264
$587$	−9.85932	−	3.58850i	−0.406938	−	0.148113i	0.130438	−	0.991457i	$-0.458362\pi$
$587$	−9.85932	−	3.58850i	−0.406938	−	0.148113i	−0.537375	+	0.843343i	$0.680584\pi$
$588$	2.34637	−	4.06403i	0.0967627	−	0.167598i
$589$	9.19168	−	7.71274i	0.378737	−	0.317798i
$590$	0.507572			0.0208964
$591$	−12.6736			−0.521324
$592$	−2.12954	+	1.78690i	−0.0875237	+	0.0734411i
$593$	−29.4282	−	24.6932i	−1.20847	−	1.01403i	−0.999347	−	0.0361392i	$-0.988494\pi$
$593$	−29.4282	−	24.6932i	−1.20847	−	1.01403i	−0.209125	−	0.977889i	$-0.567062\pi$
$594$	−0.692973	+	0.581474i	−0.0284330	+	0.0238582i
$595$	−0.243898	−	1.38321i	−0.00999884	−	0.0567063i
$596$	−17.1444	−	14.3858i	−0.702260	−	0.589266i
$597$	9.03228	+	7.57898i	0.369666	+	0.310187i
$598$	3.67784	−	1.33862i	0.150398	−	0.0547404i
$599$	−17.4416	−	30.2097i	−0.712644	−	1.23434i	−0.963861	−	0.266405i	$-0.914164\pi$
$599$	−17.4416	−	30.2097i	−0.712644	−	1.23434i	0.251217	−	0.967931i	$-0.419169\pi$
$600$	1.08039	+	1.87128i	0.0441065	+	0.0763948i
$601$	−1.43114	+	0.520894i	−0.0583776	+	0.0212477i	−0.371044	−	0.928615i	$-0.621000\pi$
$601$	−1.43114	+	0.520894i	−0.0583776	+	0.0212477i	0.312666	+	0.949863i	$0.398778\pi$
$602$	0.854329	+	0.716867i	0.0348199	+	0.0292173i
$603$	−5.75211	−	4.82659i	−0.234244	−	0.196554i
$604$	3.54181	+	20.0866i	0.144114	+	0.817312i
$605$	−2.34371	+	1.96660i	−0.0952852	+	0.0799538i
$606$	1.50140	+	1.25982i	0.0609901	+	0.0511768i
$607$	17.2487	−	14.4734i	0.700103	−	0.587456i	−0.221700	−	0.975115i	$-0.571161\pi$
$607$	17.2487	−	14.4734i	0.700103	−	0.587456i	0.921803	+	0.387659i	$0.126716\pi$
$608$	−9.14408			−0.370841
$609$	−4.80919			−0.194878
$610$	0.371017	−	0.311320i	0.0150220	−	0.0126050i
$611$	1.61969	−	2.80539i	0.0655258	−	0.113494i
$612$	9.70583	+	3.53263i	0.392335	+	0.142798i
$613$	18.5887			0.750789			0.375394	−	0.926865i	$-0.377507\pi$
$613$	18.5887			0.750789			0.375394	+	0.926865i	$0.377507\pi$
$614$	−3.10449	+	1.12994i	−0.125287	+	0.0456007i
$615$	−0.256234	−	1.45317i	−0.0103323	−	0.0585976i
$616$	−0.877502	−	1.51988i	−0.0353556	−	0.0612376i
$617$	19.2635	+	7.01133i	0.775518	+	0.282266i	0.699303	−	0.714826i	$-0.253494\pi$
$617$	19.2635	+	7.01133i	0.775518	+	0.282266i	0.0762157	+	0.997091i	$0.475716\pi$
$618$	0.292464	+	1.65865i	0.0117646	+	0.0667205i
$619$	−11.7678	+	9.87440i	−0.472990	+	0.396886i	−0.847884	−	0.530182i	$-0.822124\pi$
$619$	−11.7678	+	9.87440i	−0.472990	+	0.396886i	0.374894	+	0.927068i	$0.377679\pi$
$620$	−0.824898	−	1.42877i	−0.0331287	−	0.0573806i
$621$	36.0882			1.44817
$622$	−1.51416	−	2.62261i	−0.0607125	−	0.105157i
$623$	12.2483	+	4.45803i	0.490719	+	0.178607i
$624$	−7.16443	−	2.60764i	−0.286807	−	0.104389i
$625$	4.02939	−	22.8518i	0.161175	−	0.914072i
$626$	−3.42393	−	2.87302i	−0.136848	−	0.114829i
$627$	2.65436	−	4.59749i	0.106005	−	0.183606i
$628$	1.51745	−	8.60591i	0.0605530	−	0.343413i
$629$	1.16192	−	0.974969i	0.0463289	−	0.0388746i
$630$	−0.0446714	+	0.253344i	−0.00177975	+	0.0100935i
$631$	−5.33058	−	9.23283i	−0.212207	−	0.367553i	0.740198	−	0.672389i	$-0.234732\pi$
$631$	−5.33058	−	9.23283i	−0.212207	−	0.367553i	−0.952405	+	0.304836i	$0.901398\pi$
$632$	6.22776	+	2.26672i	0.247727	+	0.0901653i
$633$	−0.211972	−	1.20215i	−0.00842513	−	0.0477813i
$634$	−2.88789	−	2.42323i	−0.114693	−	0.0962388i
$635$	1.64361	−	2.84682i	0.0652247	−	0.112973i
$636$	3.79028	−	3.18042i	0.150294	−	0.126112i
$637$	−4.55346	+	7.88683i	−0.180415	+	0.312487i
$638$	0.400311	−	0.693359i	0.0158485	−	0.0274503i
$639$	−3.15181	−	17.8748i	−0.124684	−	0.707116i
$640$	−0.290490	+	1.64745i	−0.0114826	+	0.0651211i
$641$	−20.2361	+	7.36536i	−0.799280	+	0.290914i	−0.709188	−	0.705019i	$-0.750938\pi$
$641$	−20.2361	+	7.36536i	−0.799280	+	0.290914i	−0.0900918	+	0.995933i	$0.528716\pi$
$642$	0.928915	−	0.338097i	0.0366614	−	0.0133436i
$643$	−3.73114	−	21.1603i	−0.147142	−	0.834482i	−0.965623	−	0.259948i	$-0.916294\pi$
$643$	−3.73114	−	21.1603i	−0.147142	−	0.834482i	0.818481	−	0.574534i	$-0.194817\pi$
$644$	−6.04205	+	34.2662i	−0.238090	+	1.35028i
$645$	0.877049	+	0.319220i	0.0345338	+	0.0125693i
$646$	1.62934			0.0641056
$647$	−10.6135	+	3.86301i	−0.417261	+	0.151871i	−0.542115	−	0.840305i	$-0.682376\pi$
$647$	−10.6135	+	3.86301i	−0.417261	+	0.151871i	0.124854	+	0.992175i	$0.460154\pi$
$648$	−2.18523	−	1.83362i	−0.0858438	−	0.0720315i
$649$	13.1079	−	4.77087i	0.514529	−	0.187273i
$650$	−1.04198	−	1.80475i	−0.0408696	−	0.0707883i
$651$	0.575869	−	3.26591i	0.0225701	−	0.128001i
$652$	18.0639	−	31.2877i	0.707439	−	1.22532i
$653$	−7.61102			−0.297842			−0.148921	−	0.988849i	$-0.547580\pi$
$653$	−7.61102			−0.297842			−0.148921	+	0.988849i	$0.547580\pi$
$654$	−1.01254	−	0.571830i	−0.0395933	−	0.0223603i
$655$	0.461181			0.0180198
$656$	−11.4055	+	19.7550i	−0.445312	+	0.771302i
$657$	0.761746	−	4.32008i	0.0297186	−	0.168542i
$658$	−0.175336	−	0.303691i	−0.00683531	−	0.0118391i
$659$	−2.73491	+	0.995426i	−0.106537	+	0.0387763i	−0.394739	−	0.918793i	$-0.629165\pi$
$659$	−2.73491	+	0.995426i	−0.106537	+	0.0387763i	0.288202	+	0.957570i	$0.406943\pi$
$660$	−0.559156	−	0.469187i	−0.0217651	−	0.0182631i
$661$	−30.2497	+	11.0100i	−1.17658	+	0.428239i	−0.854992	−	0.518641i	$-0.826438\pi$
$661$	−30.2497	+	11.0100i	−1.17658	+	0.428239i	−0.321586	+	0.946881i	$0.604216\pi$
$662$	−5.04742			−0.196173
$663$	3.90906	+	1.42278i	0.151815	+	0.0552563i
$664$	0.869286	−	4.92996i	0.0337348	−	0.191320i
$665$	−0.578714	−	3.28205i	−0.0224416	−	0.127272i
$666$	−0.261054	+	0.0950158i	−0.0101156	+	0.00368179i
$667$	−30.0134	+	10.9240i	−1.16212	+	0.422979i
$668$	−4.93327	+	27.9779i	−0.190874	+	1.08250i
$669$	−2.47706	−	14.0481i	−0.0957686	−	0.543131i
$670$	−0.0814325	+	0.141045i	−0.00314601	+	0.00544905i
$671$	6.65516	−	11.5271i	0.256919	−	0.444998i
$672$	−1.93600	+	1.62450i	−0.0746829	+	0.0626664i
$673$	2.88876	−	5.00348i	0.111354	−	0.192870i	−0.804963	−	0.593325i	$-0.797815\pi$
$673$	2.88876	−	5.00348i	0.111354	−	0.192870i	0.916316	+	0.400455i	$0.131148\pi$
$674$	−1.25480	−	1.05290i	−0.0483330	−	0.0405562i
$675$	−3.33669	−	18.9233i	−0.128429	−	0.728359i
$676$	−10.0610	−	3.66191i	−0.386962	−	0.140843i
$677$	−17.5713	−	30.4343i	−0.675319	−	1.16969i	−0.976375	−	0.216081i	$-0.930673\pi$
$677$	−17.5713	−	30.4343i	−0.675319	−	1.16969i	0.301056	−	0.953606i	$-0.402661\pi$
$678$	−0.259242	+	1.47023i	−0.00995611	+	0.0564639i
$679$	−18.0246	+	15.1245i	−0.691722	+	0.580423i
$680$	0.0782776	−	0.443935i	0.00300181	−	0.0170241i
$681$	−6.48237	+	11.2278i	−0.248405	+	0.430250i
$682$	0.422925	+	0.354876i	0.0161946	+	0.0135889i
$683$	5.53072	−	31.3663i	0.211627	−	1.20020i	−0.675037	−	0.737784i	$-0.735872\pi$
$683$	5.53072	−	31.3663i	0.211627	−	1.20020i	0.886664	−	0.462414i	$-0.153017\pi$
$684$	23.0297	+	8.38213i	0.880563	+	0.320499i
$685$	−4.12153	−	1.50011i	−0.157476	−	0.0573164i
$686$	1.53616	+	2.66071i	0.0586508	+	0.101586i
$687$	20.9865			0.800685
$688$	−7.21420	−	12.4954i	−0.275039	−	0.476381i
$689$	−7.35556	+	6.17205i	−0.280225	+	0.235136i
$690$	−0.0615718	−	0.349191i	−0.00234400	−	0.0132935i
$691$	−44.3203	−	16.1313i	−1.68602	−	0.613662i	−0.691907	−	0.721987i	$-0.743229\pi$
$691$	−44.3203	−	16.1313i	−1.68602	−	0.613662i	−0.994116	+	0.108325i	$0.965451\pi$
$692$	−15.0500	−	26.0674i	−0.572115	−	0.990932i
$693$	1.22766	+	6.96240i	0.0466349	+	0.264480i
$694$	0.157287	−	0.0572478i	0.00597054	−	0.00217310i
$695$	−4.68915			−0.177869
$696$	−1.45040	−	0.527901i	−0.0549772	−	0.0200100i
$697$	6.22310	−	10.7787i	0.235717	−	0.408273i
$698$	−0.382864	+	0.321261i	−0.0144916	+	0.0121599i
$699$	15.1270			0.572154
$700$	18.5266			0.700239
$701$	9.71206	−	8.14939i	0.366819	−	0.307798i	−0.440682	−	0.897663i	$-0.645264\pi$
$701$	9.71206	−	8.14939i	0.366819	−	0.307798i	0.807502	+	0.589865i	$0.200819\pi$
$702$	−1.28845	−	1.08114i	−0.0486296	−	0.0408051i
$703$	2.75698	−	2.31338i	0.103981	−	0.0872507i
$704$	1.91023	+	10.8334i	0.0719944	+	0.408300i
$705$	−0.224813	−	0.188641i	−0.00846696	−	0.00710462i
$706$	2.68561	+	2.25350i	0.101074	+	0.0848115i
$707$	31.7746	−	11.5650i	1.19501	−	0.434947i
$708$	−6.68227	−	11.5740i	−0.251135	−	0.434979i
$709$	−0.723605	−	1.25332i	−0.0271756	−	0.0470695i	0.852118	−	0.523350i	$-0.175318\pi$
$709$	−0.723605	−	1.25332i	−0.0271756	−	0.0470695i	−0.879293	+	0.476281i	$0.841985\pi$
$710$	−0.369939	+	0.134647i	−0.0138836	+	0.00505320i
$711$	−20.4517	−	17.1610i	−0.766999	−	0.643588i
$712$	3.20460	+	2.68898i	0.120098	+	0.100774i
$713$	−3.82456	−	21.6902i	−0.143231	−	0.812303i
$714$	0.344968	−	0.289462i	0.0129101	−	0.0108329i
$715$	1.08512	+	0.910524i	0.0405812	+	0.0340517i
$716$	−30.8165	+	25.8581i	−1.15167	+	0.966364i
$717$	10.6831			0.398967
$718$	3.38902			0.126477
$719$	−39.1493	+	32.8501i	−1.46002	+	1.22510i	−0.535187	+	0.844734i	$0.679759\pi$
$719$	−39.1493	+	32.8501i	−1.46002	+	1.22510i	−0.924834	+	0.380370i	$0.875797\pi$
$720$	1.66409	−	2.88228i	0.0620168	−	0.107416i
$721$	27.3049	+	9.93817i	1.01689	+	0.370117i
$722$	0.918881			0.0341972
$723$	10.8638	−	3.95409i	0.404029	−	0.147054i
$724$	3.21863	+	18.2538i	0.119619	+	0.678396i
$725$	8.50316	+	14.7279i	0.315799	+	0.546981i
$726$	−0.921768	−	0.335496i	−0.0342100	−	0.0124514i
$727$	−2.68925	−	15.2515i	−0.0997388	−	0.565647i	−0.993192	−	0.116490i	$-0.962836\pi$
$727$	−2.68925	−	15.2515i	−0.0997388	−	0.565647i	0.893453	−	0.449157i	$-0.148275\pi$
$728$	2.49968	−	2.09748i	0.0926444	−	0.0777378i
$729$	1.50403	+	2.60505i	0.0557047	+	0.0964833i
$730$	−0.0951469			−0.00352155
$731$	3.93622	+	6.81773i	0.145586	+	0.252163i
$732$	−11.9834	−	4.36162i	−0.442921	−	0.161210i
$733$	44.8827	+	16.3360i	1.65778	+	0.603383i	0.990012	−	0.140986i	$-0.0450271\pi$
$733$	44.8827	+	16.3360i	1.65778	+	0.603383i	0.667769	+	0.744369i	$0.267249\pi$
$734$	0.240712	−	1.36514i	0.00888483	−	0.0503884i
$735$	0.632019	+	0.530327i	0.0233124	+	0.0195614i
$736$	−8.39228	+	14.5359i	−0.309344	+	0.535799i
$737$	−0.777225	+	4.40786i	−0.0286294	+	0.162366i
$738$	−1.74627	+	1.46530i	−0.0642811	+	0.0539383i
$739$	−1.51117	+	8.57028i	−0.0555894	+	0.315263i	−0.999905	−	0.0137778i	$-0.995614\pi$
$739$	−1.51117	+	8.57028i	−0.0555894	+	0.315263i	0.944316	+	0.329041i	$0.106725\pi$
$740$	−0.247422	−	0.428548i	−0.00909542	−	0.0157537i
$741$	9.27530	+	3.37593i	0.340737	+	0.124018i
$742$	0.180497	+	1.02365i	0.00662625	+	0.0375793i
$743$	22.0307	+	18.4859i	0.808228	+	0.678184i	0.950184	−	0.311689i	$-0.100895\pi$
$743$	22.0307	+	18.4859i	0.808228	+	0.678184i	−0.141956	+	0.989873i	$0.545339\pi$
$744$	0.532173	−	0.921750i	0.0195104	−	0.0337930i
$745$	3.01419	−	2.52921i	0.110432	−	0.0926630i
$746$	0.751935	−	1.30239i	0.0275303	−	0.0476839i
$747$	−10.0830	+	17.4643i	−0.368919	+	0.638987i
$748$	−1.06910	−	6.06319i	−0.0390903	−	0.221692i
$749$	2.96151	−	16.7955i	0.108211	−	0.613696i
$750$	−0.359208	+	0.130741i	−0.0131164	+	0.00477399i
$751$	3.06171	−	1.11437i	0.111723	−	0.0406640i	−0.285554	−	0.958363i	$-0.592177\pi$
$751$	3.06171	−	1.11437i	0.111723	−	0.0406640i	0.397277	+	0.917699i	$0.369955\pi$
$752$	0.787804	+	4.46786i	0.0287283	+	0.162926i
$753$	−1.33103	+	7.54866i	−0.0485055	+	0.275089i
$754$	1.39883	+	0.509133i	0.0509425	+	0.0185415i
$755$	−3.58595			−0.130506
$756$	14.0510	−	5.11416i	0.511031	−	0.186000i
$757$	−1.40555	−	1.17940i	−0.0510855	−	0.0428658i	0.616887	−	0.787051i	$-0.288393\pi$
$757$	−1.40555	−	1.17940i	−0.0510855	−	0.0428658i	−0.667973	+	0.744186i	$0.732838\pi$
$758$	−2.85917	+	1.04065i	−0.103850	+	0.0377983i
$759$	−4.87225	−	8.43899i	−0.176852	−	0.306316i
$760$	0.185735	−	1.05335i	0.00673731	−	0.0382092i
$761$	22.4109	−	38.8168i	0.812394	−	1.40711i	−0.0987895	−	0.995108i	$-0.531497\pi$
$761$	22.4109	−	38.8168i	0.812394	−	1.40711i	0.911184	−	0.412000i	$-0.135170\pi$
$762$	1.05394			0.0381802
$763$	−17.2782	+	10.1957i	−0.625512	+	0.369108i
$764$	−5.29950			−0.191729
$765$	−0.907960	+	1.57263i	−0.0328274	+	0.0568587i
$766$	−0.494323	+	2.80344i	−0.0178606	+	0.101293i
$767$	12.9679	+	22.4610i	0.468243	+	0.811021i
$768$	9.52054	−	3.46519i	0.343543	−	0.125039i
$769$	−18.1590	−	15.2372i	−0.654830	−	0.549468i	0.253702	−	0.967282i	$-0.418352\pi$
$769$	−18.1590	−	15.2372i	−0.654830	−	0.549468i	−0.908532	+	0.417815i	$0.862796\pi$
$770$	0.144095	−	0.0524461i	0.00519281	−	0.00189003i
$771$	−7.19313			−0.259054
$772$	23.0964	+	8.40641i	0.831258	+	0.302553i
$773$	−7.79309	+	44.1968i	−0.280298	+	1.58965i	0.441316	+	0.897352i	$0.354512\pi$
$773$	−7.79309	+	44.1968i	−0.280298	+	1.58965i	−0.721614	+	0.692296i	$0.756599\pi$
$774$	−0.250380	−	1.41998i	−0.00899973	−	0.0510400i
$775$	−11.0199	+	4.01092i	−0.395847	+	0.144076i
$776$	−7.09623	+	2.58282i	−0.254740	+	0.0927177i
$777$	0.172728	−	0.979587i	0.00619657	−	0.0351425i
$778$	−0.362544	−	2.05609i	−0.0129978	−	0.0737144i
$779$	14.7660	−	25.5754i	0.529047	−	0.916335i
$780$	0.678581	−	1.17534i	0.0242971	−	0.0420838i
$781$	−8.28794	+	6.95441i	−0.296566	+	0.248848i
$782$	1.49538	−	2.59008i	0.0534748	−	0.0926210i
$783$	10.5146	+	8.82278i	0.375761	+	0.315301i
$784$	−2.21476	−	12.5605i	−0.0790986	−	0.448590i
$785$	1.44371	+	0.525469i	0.0515283	+	0.0187548i
$786$	0.0739312	+	0.128053i	0.00263704	+	0.00456749i
$787$	1.55491	−	8.81833i	0.0554265	−	0.314340i	−0.944472	−	0.328592i	$-0.893426\pi$
$787$	1.55491	−	8.81833i	0.0554265	−	0.314340i	0.999898	+	0.0142527i	$0.00453693\pi$
$788$	−26.7160	+	22.4174i	−0.951718	+	0.798586i
$789$	−3.84348	+	21.7975i	−0.136832	+	0.776010i
$790$	−0.289534	+	0.501488i	−0.0103012	+	0.0178421i
$791$	19.7306	+	16.5560i	0.701540	+	0.588662i
$792$	−0.394010	+	2.23454i	−0.0140005	+	0.0794009i
$793$	23.2555	+	8.46433i	0.825829	+	0.300577i
$794$	0.186841	+	0.0680046i	0.00663074	+	0.00241339i
$795$	0.434947	+	0.753351i	0.0154260	+	0.0267186i
$796$	32.4458			1.15001
$797$	5.56698	+	9.64229i	0.197192	+	0.341547i	0.947617	−	0.319409i	$-0.103484\pi$
$797$	5.56698	+	9.64229i	0.197192	+	0.341547i	−0.750425	+	0.660956i	$0.770151\pi$
$798$	0.818529	−	0.686828i	0.0289756	−	0.0243134i
$799$	−0.429842	−	2.43776i	−0.0152067	−	0.0862416i
$800$	8.39802	+	3.05663i	0.296915	+	0.108068i
$801$	−8.42596	−	14.5942i	−0.297717	−	0.515661i
$802$	−0.504310	−	2.86008i	−0.0178078	−	0.100993i
$803$	−2.45713	+	0.894324i	−0.0867104	+	0.0315600i
$804$	4.28829			0.151236
$805$	−5.74844	−	2.09226i	−0.202606	−	0.0737425i
$806$	−0.513253	+	0.888981i	−0.0180786	+	0.0313130i
$807$	−6.05765	+	5.08297i	−0.213239	+	0.178929i
$808$	10.8523			0.381784
$809$	8.13251			0.285924			0.142962	−	0.989728i	$-0.454337\pi$
$809$	8.13251			0.285924			0.142962	+	0.989728i	$0.454337\pi$
$810$	0.190933	−	0.160212i	0.00670869	−	0.00562926i
$811$	−24.1132	−	20.2333i	−0.846727	−	0.710489i	0.112339	−	0.993670i	$-0.464166\pi$
$811$	−24.1132	−	20.2333i	−0.846727	−	0.710489i	−0.959066	+	0.283181i	$0.908610\pi$
$812$	−10.1377	+	8.50658i	−0.355765	+	0.298522i
$813$	0.815321	+	4.62392i	0.0285946	+	0.162168i
$814$	0.126853	+	0.106442i	0.00444620	+	0.00373080i
$815$	4.86571	+	4.08282i	0.170438	+	0.143015i
$816$	−5.47466	+	1.99261i	−0.191651	+	0.0697554i
$817$	9.33974	+	16.1769i	0.326756	+	0.565958i
$818$	2.17004	+	3.75862i	0.0758736	+	0.131417i
$819$	−12.3522	+	4.49585i	−0.431622	+	0.157098i
$820$	−3.11054	−	2.61005i	−0.108625	−	0.0911470i
$821$	24.1352	+	20.2518i	0.842324	+	0.706794i	0.958085	−	0.286483i	$-0.0924862\pi$
$821$	24.1352	+	20.2518i	0.842324	+	0.706794i	−0.115761	+	0.993277i	$0.536931\pi$
$822$	−0.244191	−	1.38488i	−0.00851713	−	0.0483031i
$823$	−15.6581	+	13.1387i	−0.545806	+	0.457986i	−0.873518	−	0.486792i	$-0.838167\pi$
$823$	−15.6581	+	13.1387i	−0.545806	+	0.457986i	0.327712	+	0.944778i	$0.393723\pi$
$824$	7.14394	+	5.99448i	0.248871	+	0.208828i
$825$	−3.97461	+	3.33510i	−0.138378	+	0.116113i
$826$	2.80761			0.0976893
$827$	−44.1340			−1.53469			−0.767345	−	0.641235i	$-0.778423\pi$
$827$	−44.1340			−1.53469			−0.767345	+	0.641235i	$0.778423\pi$
$828$	34.4609	−	28.9161i	1.19760	−	1.00491i
$829$	16.4688	−	28.5248i	0.571985	−	0.990707i	−0.424377	−	0.905486i	$-0.639507\pi$
$829$	16.4688	−	28.5248i	0.571985	−	0.990707i	0.996362	−	0.0852217i	$-0.0271598\pi$
$830$	0.411019	+	0.149599i	0.0142667	+	0.00519265i
$831$	−1.67223			−0.0580089
$832$	−19.2200	+	6.99550i	−0.666333	+	0.242525i
$833$	1.20842	+	6.85329i	0.0418692	+	0.237452i
$834$	−0.751710	−	1.30200i	−0.0260296	−	0.0450846i
$835$	−4.69353	−	1.70831i	−0.162426	−	0.0591184i
$836$	−2.53674	−	14.3866i	−0.0877349	−	0.497570i
$837$	−7.25060	+	6.08397i	−0.250617	+	0.210293i
$838$	1.84040	+	3.18767i	0.0635756	+	0.110116i
$839$	−16.2568			−0.561247			−0.280623	−	0.959818i	$-0.590541\pi$
$839$	−16.2568			−0.561247			−0.280623	+	0.959818i	$0.590541\pi$
$840$	−0.147811	−	0.256015i	−0.00509995	−	0.00883337i
$841$	15.8358	+	5.76374i	0.546060	+	0.198750i
$842$	0.345064	+	0.125593i	0.0118917	+	0.00432823i
$843$	2.90529	−	16.4767i	0.100064	−	0.567489i
$844$	−2.57323	−	2.15919i	−0.0885741	−	0.0743225i
$845$	0.941186	−	1.63018i	0.0323778	−	0.0560800i
$846$	−0.0787281	+	0.446489i	−0.00270673	+	0.0153506i
$847$	−12.9641	+	10.8782i	−0.445451	+	0.373778i
$848$	2.33516	−	13.2434i	0.0801898	−	0.454779i
$849$	4.87643	+	8.44623i	0.167359	+	0.289874i
$850$	−1.49640	−	0.544647i	−0.0513263	−	0.0186812i
$851$	−1.14715	−	6.50580i	−0.0393237	−	0.223016i
$852$	7.94062	+	6.66297i	0.272041	+	0.228270i
$853$	−27.6763	+	47.9368i	−0.947620	+	1.64133i	−0.197201	+	0.980363i	$0.563185\pi$
$853$	−27.6763	+	47.9368i	−0.947620	+	1.64133i	−0.750419	+	0.660963i	$0.770148\pi$
$854$	2.05226	−	1.72205i	0.0702269	−	0.0589274i
$855$	−2.15438	+	3.73150i	−0.0736783	+	0.127614i
$856$	2.73679	−	4.74027i	0.0935417	−	0.162019i
$857$	2.67867	+	15.1915i	0.0915017	+	0.518932i	0.995763	+	0.0919532i	$0.0293110\pi$
$857$	2.67867	+	15.1915i	0.0915017	+	0.518932i	−0.904262	+	0.426979i	$0.859578\pi$
$858$	−0.0788643	+	0.447262i	−0.00269238	+	0.0152693i
$859$	28.0426	−	10.2067i	0.956800	−	0.348247i	0.184021	−	0.982922i	$-0.441089\pi$
$859$	28.0426	−	10.2067i	0.956800	−	0.348247i	0.772779	+	0.634676i	$0.218866\pi$
$860$	2.41346	−	0.878427i	0.0822982	−	0.0299541i
$861$	−1.41734	−	8.03815i	−0.0483029	−	0.273940i
$862$	0.796086	−	4.51483i	0.0271148	−	0.153776i
$863$	41.8405	+	15.2287i	1.42427	+	0.518391i	0.935282	−	0.353902i	$-0.115145\pi$
$863$	41.8405	+	15.2287i	1.42427	+	0.518391i	0.488984	+	0.872293i	$0.337368\pi$
$864$	7.21304			0.245393
$865$	4.97281	−	1.80996i	0.169081	−	0.0615403i
$866$	−3.62748	−	3.04382i	−0.123267	−	0.103433i
$867$	−8.48368	+	3.08781i	−0.288121	+	0.104867i
$868$	−4.56288	−	7.90314i	−0.154874	−	0.268250i
$869$	−2.76343	+	15.6722i	−0.0937430	+	0.531643i
$870$	0.0674303	−	0.116793i	0.00228610	−	0.00395964i
$871$	−8.32202			−0.281981
$872$	−6.33007	+	1.17828i	−0.214363	+	0.0399017i
$873$	30.4208			1.02959
$874$	3.54820	−	6.14566i	0.120020	−	0.207880i
$875$	−1.14520	+	6.49478i	−0.0387150	+	0.219564i
$876$	1.25262	+	2.16961i	0.0423222	+	0.0733043i
$877$	−17.4833	+	6.36342i	−0.590371	+	0.214877i	−0.619892	−	0.784687i	$-0.712824\pi$
$877$	−17.4833	+	6.36342i	−0.590371	+	0.214877i	0.0295217	+	0.999564i	$0.490602\pi$
$878$	−0.766460	−	0.643136i	−0.0258668	−	0.0217048i
$879$	−16.1392	+	5.87418i	−0.544360	+	0.198131i
$880$	−1.98385			−0.0668756
$881$	2.19934	+	0.800493i	0.0740975	+	0.0269693i	0.378803	−	0.925477i	$-0.376336\pi$
$881$	2.19934	+	0.800493i	0.0740975	+	0.0269693i	−0.304705	+	0.952447i	$0.598558\pi$
$882$	0.221329	−	1.25522i	0.00745254	−	0.0422654i
$883$	−1.50708	−	8.54710i	−0.0507174	−	0.287633i	0.948891	−	0.315603i	$-0.102207\pi$
$883$	−1.50708	−	8.54710i	−0.0507174	−	0.287633i	−0.999609	+	0.0279701i	$0.991096\pi$
$884$	10.7569	−	3.91520i	0.361795	−	0.131682i
$885$	2.20795	−	0.803629i	0.0742195	−	0.0270137i
$886$	−0.370909	+	2.10353i	−0.0124609	+	0.0706695i
$887$	7.08591	+	40.1862i	0.237922	+	1.34932i	0.836373	+	0.548161i	$0.184672\pi$
$887$	7.08591	+	40.1862i	0.237922	+	1.34932i	−0.598451	+	0.801159i	$0.704217\pi$
$888$	0.159621	−	0.276472i	0.00535654	−	0.00927780i
$889$	9.09155	−	15.7470i	0.304921	−	0.528138i
$890$	−0.280000	+	0.234948i	−0.00938562	+	0.00787547i
$891$	3.42488	−	5.93206i	0.114738	−	0.198731i
$892$	−30.0701	−	25.2319i	−1.00682	−	0.844825i
$893$	−1.01992	−	5.78424i	−0.0341302	−	0.193562i
$894$	1.18547	+	0.431475i	0.0396479	+	0.0144307i
$895$	−3.53630	−	6.12506i	−0.118206	−	0.204738i
$896$	−1.60683	+	9.11278i	−0.0536804	+	0.304437i
$897$	13.8793	−	11.6461i	0.463415	−	0.388851i
$898$	0.971885	−	5.51183i	0.0324322	−	0.183932i
$899$	4.18846	−	7.25463i	0.139693	−	0.241955i
$900$	−18.3488	−	15.3965i	−0.611627	−	0.513216i
$901$	−1.27411	+	7.22585i	−0.0424468	+	0.240728i
$902$	1.27687	+	0.464742i	0.0425151	+	0.0154742i
$903$	4.85135	+	1.76575i	0.161443	+	0.0587604i
$904$	4.13320	+	7.15891i	0.137468	+	0.238102i
$905$	−3.25875			−0.108324
$906$	−0.574859	−	0.995684i	−0.0190984	−	0.0330794i
$907$	−7.13228	+	5.98470i	−0.236824	+	0.198719i	−0.753474	−	0.657478i	$-0.771623\pi$
$907$	−7.13228	+	5.98470i	−0.236824	+	0.198719i	0.516650	+	0.856197i	$0.327179\pi$
$908$	6.19512	+	35.1343i	0.205592	+	1.16597i
$909$	−41.0808	−	14.9522i	−1.36256	−	0.495932i
$910$	0.142556	+	0.246914i	0.00472567	+	0.00818511i
$911$	2.16155	+	12.2588i	0.0716153	+	0.406151i	0.999450	+	0.0331592i	$0.0105568\pi$
$911$	2.16155	+	12.2588i	0.0716153	+	0.406151i	−0.927835	+	0.372992i	$0.878332\pi$
$912$	−12.9901	+	4.72801i	−0.430146	+	0.156560i
$913$	12.0206			0.397822
$914$	4.01261	+	1.46047i	0.132725	+	0.0483080i
$915$	1.12103	−	1.94167i	0.0370600	−	0.0641898i
$916$	44.2395	−	37.1213i	1.46171	−	1.22652i
$917$	2.55100			0.0842414
$918$	−1.28526			−0.0424199
$919$	17.9913	−	15.0965i	0.593479	−	0.497988i	−0.295863	−	0.955230i	$-0.595607\pi$
$919$	17.9913	−	15.0965i	0.593479	−	0.497988i	0.889342	+	0.457242i	$0.151163\pi$
$920$	−1.50400	−	1.26200i	−0.0495854	−	0.0416071i
$921$	−11.7156	+	9.83053i	−0.386041	+	0.323927i
$922$	0.407785	+	2.31266i	0.0134297	+	0.0761634i
$923$	−15.4099	−	12.9304i	−0.507222	−	0.425610i
$924$	−3.09294	−	2.59529i	−0.101750	−	0.0853786i
$925$	−3.30534	+	1.20305i	−0.108679	+	0.0395559i
$926$	0.944404	+	1.63576i	0.0310351	+	0.0537543i
$927$	−18.7838	−	32.5345i	−0.616940	−	1.06857i
$928$	−5.99887	+	2.18341i	−0.196922	+	0.0716739i
$929$	21.6765	+	18.1887i	0.711183	+	0.596753i	0.924931	−	0.380135i	$-0.124123\pi$
$929$	21.6765	+	18.1887i	0.711183	+	0.596753i	−0.213748	+	0.976889i	$0.568567\pi$
$930$	0.0712394	+	0.0597770i	0.00233603	+	0.00196016i
$931$	2.86730	+	16.2613i	0.0939720	+	0.532942i
$932$	31.8876	−	26.7568i	1.04451	−	0.876450i
$933$	−10.7390	−	9.01107i	−0.351578	−	0.295009i
$934$	−3.22080	+	2.70257i	−0.105388	+	0.0884308i
$935$	1.08243			0.0353992
$936$	−4.21880			−0.137896
$937$	−2.70880	+	2.27296i	−0.0884928	+	0.0742543i	−0.685961	−	0.727638i	$-0.740618\pi$
$937$	−2.70880	+	2.27296i	−0.0884928	+	0.0742543i	0.597468	+	0.801893i	$0.296173\pi$
$938$	−0.450440	+	0.780185i	−0.0147074	+	0.0254739i
$939$	−19.4430	−	7.07667i	−0.634498	−	0.230938i
$940$	−0.807577			−0.0263402
$941$	27.6861	−	10.0769i	0.902542	−	0.328499i	0.151271	−	0.988492i	$-0.451663\pi$
$941$	27.6861	−	10.0769i	0.902542	−	0.328499i	0.751271	+	0.659994i	$0.229441\pi$
$942$	0.0855365	+	0.485102i	0.00278693	+	0.0158055i
$943$	−27.1040	−	46.9454i	−0.882626	−	1.52875i
$944$	−34.1326	−	12.4233i	−1.11092	−	0.404343i
$945$	0.456502	+	2.58895i	0.0148500	+	0.0842186i
$946$	−0.658395	+	0.552459i	−0.0214063	+	0.0179620i
$947$	9.80429	+	16.9815i	0.318597	+	0.551825i	0.980195	−	0.198033i	$-0.0634552\pi$
$947$	9.80429	+	16.9815i	0.318597	+	0.551825i	−0.661599	+	0.749858i	$0.730122\pi$
$948$	15.2471			0.495201
$949$	−2.43089	−	4.21043i	−0.0789101	−	0.136676i
$950$	−3.55063	−	1.29232i	−0.115197	−	0.0419285i
$951$	−16.3991	−	5.96877i	−0.531776	−	0.193551i
$952$	0.432989	−	2.45560i	0.0140332	−	0.0795865i
$953$	−38.1797	−	32.0366i	−1.23676	−	1.03777i	−0.997770	−	0.0667465i	$-0.978738\pi$
$953$	−38.1797	−	32.0366i	−1.23676	−	1.03777i	−0.238993	−	0.971021i	$-0.576817\pi$
$954$	0.671937	−	1.16383i	0.0217548	−	0.0376803i
$955$	0.161791	−	0.917563i	0.00523544	−	0.0296917i
$956$	22.5199	−	18.8965i	0.728346	−	0.611155i
$957$	0.643581	−	3.64993i	0.0208040	−	0.117986i
$958$	1.16323	+	2.01477i	0.0375822	+	0.0650943i
$959$	−22.7980	−	8.29781i	−0.736187	−	0.267950i
$960$	0.321768	+	1.82484i	0.0103850	+	0.0588963i
$961$	−19.3223	−	16.2133i	−0.623300	−	0.523011i
$962$	−0.153947	+	0.266643i	−0.00496343	+	0.00859692i
$963$	−16.8910	+	14.1732i	−0.544305	+	0.456726i
$964$	15.9067	−	27.5513i	0.512322	−	0.887367i
$965$	−2.16062	+	3.74230i	−0.0695528	+	0.120469i
$966$	−0.340581	−	1.93153i	−0.0109580	−	0.0621460i
$967$	−9.50039	+	53.8794i	−0.305512	+	1.73264i	0.315573	+	0.948901i	$0.397803\pi$
$967$	−9.50039	+	53.8794i	−0.305512	+	1.73264i	−0.621085	+	0.783743i	$0.713308\pi$
$968$	−5.10391	+	1.85767i	−0.164046	+	0.0597079i
$969$	7.08768	−	2.57970i	0.227689	−	0.0828720i
$970$	−0.114577	−	0.649796i	−0.00367883	−	0.0208637i
$971$	2.02193	−	11.4669i	0.0648868	−	0.367991i	−0.935023	−	0.354586i	$-0.884622\pi$
$971$	2.02193	−	11.4669i	0.0648868	−	0.367991i	0.999910	−	0.0134052i	$-0.00426713\pi$
$972$	−28.1034	−	10.2288i	−0.901418	−	0.328089i
$973$	−25.9378			−0.831527
$974$	−0.0633334	+	0.0230515i	−0.00202933	+	0.000738616i
$975$	−7.39005	−	6.20099i	−0.236671	−	0.198591i
$976$	−32.5695	+	11.8543i	−1.04253	+	0.379448i
$977$	17.4132	+	30.1606i	0.557099	+	0.964924i	0.997737	+	0.0672387i	$0.0214189\pi$
$977$	17.4132	+	30.1606i	0.557099	+	0.964924i	−0.440638	+	0.897685i	$0.645248\pi$
$978$	−0.353630	+	2.00554i	−0.0113078	+	0.0641300i
$979$	−5.02253	+	8.69928i	−0.160521	+	0.278030i
$980$	2.27035			0.0725236
$981$	25.5855	+	4.26116i	0.816881	+	0.136048i
$982$	−3.00245			−0.0958120
$983$	4.14260	−	7.17519i	0.132128	−	0.228853i	−0.792368	−	0.610043i	$-0.791152\pi$
$983$	4.14260	−	7.17519i	0.132128	−	0.228853i	0.924497	+	0.381190i	$0.124486\pi$
$984$	0.454888	−	2.57980i	0.0145013	−	0.0822410i
$985$	−3.06575	−	5.31004i	−0.0976830	−	0.169192i
$986$	1.06891	−	0.389052i	0.0340411	−	0.0123899i
$987$	−1.24354	−	1.04346i	−0.0395824	−	0.0332136i
$988$	25.5237	−	9.28987i	0.812018	−	0.295550i
$989$	34.2874			1.09028
$990$	−0.186297	−	0.0678066i	−0.00592091	−	0.00215504i
$991$	4.71913	−	26.7635i	0.149908	−	0.850171i	−0.813386	−	0.581724i	$-0.802378\pi$
$991$	4.71913	−	26.7635i	0.149908	−	0.850171i	0.963294	−	0.268447i	$-0.0865105\pi$
$992$	−0.764426	−	4.33527i	−0.0242705	−	0.137645i
$993$	−21.9564	+	7.99147i	−0.696765	+	0.253602i
$994$	−2.04630	+	0.744792i	−0.0649046	+	0.0236234i
$995$	−0.990556	+	5.61772i	−0.0314027	+	0.178094i
$996$	−1.99987	−	11.3418i	−0.0633684	−	0.359380i
$997$	16.2094	−	28.0755i	0.513357	−	0.889161i	−0.486523	−	0.873668i	$-0.661735\pi$
$997$	16.2094	−	28.0755i	0.513357	−	0.889161i	0.999880	−	0.0154932i	$-0.00493183\pi$
$998$	1.02187	−	1.76993i	0.0323467	−	0.0560262i
$999$	−2.17476	+	1.82484i	−0.0688065	+	0.0577355i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	109.2.f.a.38.4	✓	42
3.2	odd	2		981.2.w.a.910.4		42
109.66	even	9	inner	109.2.f.a.66.4	yes	42
327.284	odd	18		981.2.w.a.829.4		42

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
109.2.f.a.38.4	✓	42	1.1	even	1	trivial
109.2.f.a.66.4	yes	42	109.66	even	9	inner
981.2.w.a.829.4		42	327.284	odd	18
981.2.w.a.910.4		42	3.2	odd	2

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:	\( N \)	\(=\)	\( 109 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	109.f (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.0775572 + 0.134333i) q^{2} +(-0.124689 + 0.707146i) q^{3} +(0.987970 + 1.71121i) q^{4} +(-0.326444 + 0.118816i) q^{5} +(-0.0853226 - 0.0715941i) q^{6} +(-1.80571 + 0.657225i) q^{7} -0.616725 q^{8} +(2.33457 + 0.849714i) q^{9} +O(q^{10})\)	\(q+(-0.0775572 + 0.134333i) q^{2} +(-0.124689 + 0.707146i) q^{3} +(0.987970 + 1.71121i) q^{4} +(-0.326444 + 0.118816i) q^{5} +(-0.0853226 - 0.0715941i) q^{6} +(-1.80571 + 0.657225i) q^{7} -0.616725 q^{8} +(2.33457 + 0.849714i) q^{9} +(0.00935720 - 0.0530673i) q^{10} +(-0.257155 - 1.45840i) q^{11} +(-1.33327 + 0.485270i) q^{12} +(2.58739 - 0.941734i) q^{13} +(0.0517589 - 0.293539i) q^{14} +(-0.0433163 - 0.245659i) q^{15} +(-1.92811 + 3.33958i) q^{16} +(1.05202 - 1.82214i) q^{17} +(-0.295207 + 0.247708i) q^{18} +(2.49619 - 4.32353i) q^{19} +(-0.525837 - 0.441230i) q^{20} +(-0.239602 - 1.35885i) q^{21} +(0.215855 + 0.0785647i) q^{22} +(-4.58193 - 7.93613i) q^{23} +(0.0768989 - 0.436115i) q^{24} +(-3.73777 + 3.13636i) q^{25} +(-0.0741650 + 0.420610i) q^{26} +(-1.96905 + 3.41049i) q^{27} +(-2.90864 - 2.44064i) q^{28} +(0.605232 - 3.43244i) q^{29} +(0.0363596 + 0.0132338i) q^{30} +(2.25849 + 0.822025i) q^{31} +(-0.915803 - 1.58622i) q^{32} +1.06336 q^{33} +(0.163183 + 0.282641i) q^{34} +(0.511375 - 0.429095i) q^{35} +(0.852442 + 4.83444i) q^{36} +(0.677419 + 0.246560i) q^{37} +(0.387195 + 0.670642i) q^{38} +(0.343324 + 1.94709i) q^{39} +(0.201327 - 0.0732769i) q^{40} +5.91541 q^{41} +(0.201121 + 0.0732022i) q^{42} +(-1.87080 + 3.24032i) q^{43} +(2.24157 - 1.88090i) q^{44} -0.863067 q^{45} +1.42145 q^{46} +(0.901240 - 0.756230i) q^{47} +(-2.12116 - 1.77986i) q^{48} +(-2.53366 + 2.12600i) q^{49} +(-0.131426 - 0.745354i) q^{50} +(1.15735 + 0.971130i) q^{51} +(4.16777 + 3.49718i) q^{52} +(-3.27696 + 1.19272i) q^{53} +(-0.305428 - 0.529017i) q^{54} +(0.257228 + 0.445531i) q^{55} +(1.11363 - 0.405327i) q^{56} +(2.74612 + 2.30427i) q^{57} +(0.414150 + 0.347513i) q^{58} +(1.63566 + 9.27628i) q^{59} +(0.377580 - 0.316827i) q^{60} +(6.88523 + 5.77739i) q^{61} +(-0.285587 + 0.239636i) q^{62} -4.77401 q^{63} -7.42832 q^{64} +(-0.732747 + 0.614848i) q^{65} +(-0.0824715 + 0.142845i) q^{66} +(-2.84013 - 1.03372i) q^{67} +4.15744 q^{68} +(6.18332 - 2.25054i) q^{69} +(0.0179808 + 0.101974i) q^{70} +(-3.65291 - 6.32702i) q^{71} +(-1.43979 - 0.524040i) q^{72} +(-0.306612 - 1.73888i) q^{73} +(-0.0856598 + 0.0718771i) q^{74} +(-1.75181 - 3.03422i) q^{75} +9.86465 q^{76} +(1.42284 + 2.46443i) q^{77} +(-0.288186 - 0.104891i) q^{78} +(-10.0981 - 3.67541i) q^{79} +(0.232624 - 1.31928i) q^{80} +(3.54328 + 2.97316i) q^{81} +(-0.458782 + 0.794634i) q^{82} +(-1.40952 + 7.99378i) q^{83} +(2.08856 - 1.75251i) q^{84} +(-0.126925 + 0.719825i) q^{85} +(-0.290188 - 0.502620i) q^{86} +(2.35177 + 0.855975i) q^{87} +(0.158594 + 0.899430i) q^{88} +(-5.19616 - 4.36010i) q^{89} +(0.0669370 - 0.115938i) q^{90} +(-4.05315 + 3.40100i) q^{91} +(9.05361 - 15.6813i) q^{92} +(-0.862901 + 1.49459i) q^{93} +(0.0316890 + 0.179717i) q^{94} +(-0.301163 + 1.70798i) q^{95} +(1.23588 - 0.449823i) q^{96} +(11.5063 - 4.18795i) q^{97} +(-0.0890876 - 0.505241i) q^{98} +(0.638874 - 3.62323i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 42 q - 6 q^{3} - 12 q^{4} - 6 q^{5} + 12 q^{6} + 3 q^{7} - 12 q^{8} - 12 q^{9}+O(q^{10}) \) 42 * q - 6 * q^3 - 12 * q^4 - 6 * q^5 + 12 * q^6 + 3 * q^7 - 12 * q^8 - 12 * q^9	\( 42 q - 6 q^{3} - 12 q^{4} - 6 q^{5} + 12 q^{6} + 3 q^{7} - 12 q^{8} - 12 q^{9} + 15 q^{10} - 15 q^{11} + 9 q^{12} - 30 q^{13} + 3 q^{14} + 6 q^{16} - 3 q^{17} - 27 q^{18} - 3 q^{19} - 30 q^{20} - 3 q^{21} - 18 q^{22} + 6 q^{23} - 12 q^{24} + 6 q^{25} + 15 q^{26} + 3 q^{27} + 66 q^{28} + 3 q^{30} + 6 q^{31} + 12 q^{32} + 24 q^{33} - 21 q^{34} - 54 q^{35} + 21 q^{36} - 24 q^{37} + 27 q^{38} + 18 q^{39} - 24 q^{40} - 30 q^{41} + 12 q^{42} + 9 q^{43} + 36 q^{44} + 12 q^{45} - 12 q^{46} - 42 q^{47} - 27 q^{48} + 15 q^{49} + 3 q^{50} - 12 q^{51} - 3 q^{52} + 3 q^{53} - 36 q^{54} + 21 q^{55} + 57 q^{56} - 15 q^{57} - 24 q^{58} + 18 q^{59} + 33 q^{60} + 6 q^{61} + 78 q^{62} - 48 q^{63} - 12 q^{64} + 3 q^{65} - 15 q^{66} - 6 q^{67} + 66 q^{68} + 15 q^{69} + 39 q^{70} + 15 q^{71} - 9 q^{72} + 66 q^{73} - 24 q^{74} + 24 q^{75} - 96 q^{76} - 39 q^{77} - 3 q^{78} + 18 q^{79} - 3 q^{80} - 15 q^{81} + 21 q^{82} + 21 q^{83} + 87 q^{84} + 120 q^{85} - 15 q^{86} + 12 q^{87} - 48 q^{88} + 15 q^{89} + 24 q^{90} + 63 q^{92} - 75 q^{93} - 30 q^{94} + 15 q^{95} - 21 q^{96} + 48 q^{97} - 126 q^{98} + 39 q^{99}+O(q^{100}) \) 42 * q - 6 * q^3 - 12 * q^4 - 6 * q^5 + 12 * q^6 + 3 * q^7 - 12 * q^8 - 12 * q^9 + 15 * q^10 - 15 * q^11 + 9 * q^12 - 30 * q^13 + 3 * q^14 + 6 * q^16 - 3 * q^17 - 27 * q^18 - 3 * q^19 - 30 * q^20 - 3 * q^21 - 18 * q^22 + 6 * q^23 - 12 * q^24 + 6 * q^25 + 15 * q^26 + 3 * q^27 + 66 * q^28 + 3 * q^30 + 6 * q^31 + 12 * q^32 + 24 * q^33 - 21 * q^34 - 54 * q^35 + 21 * q^36 - 24 * q^37 + 27 * q^38 + 18 * q^39 - 24 * q^40 - 30 * q^41 + 12 * q^42 + 9 * q^43 + 36 * q^44 + 12 * q^45 - 12 * q^46 - 42 * q^47 - 27 * q^48 + 15 * q^49 + 3 * q^50 - 12 * q^51 - 3 * q^52 + 3 * q^53 - 36 * q^54 + 21 * q^55 + 57 * q^56 - 15 * q^57 - 24 * q^58 + 18 * q^59 + 33 * q^60 + 6 * q^61 + 78 * q^62 - 48 * q^63 - 12 * q^64 + 3 * q^65 - 15 * q^66 - 6 * q^67 + 66 * q^68 + 15 * q^69 + 39 * q^70 + 15 * q^71 - 9 * q^72 + 66 * q^73 - 24 * q^74 + 24 * q^75 - 96 * q^76 - 39 * q^77 - 3 * q^78 + 18 * q^79 - 3 * q^80 - 15 * q^81 + 21 * q^82 + 21 * q^83 + 87 * q^84 + 120 * q^85 - 15 * q^86 + 12 * q^87 - 48 * q^88 + 15 * q^89 + 24 * q^90 + 63 * q^92 - 75 * q^93 - 30 * q^94 + 15 * q^95 - 21 * q^96 + 48 * q^97 - 126 * q^98 + 39 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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