LMFDB - Embedded newform 294.2.j.a.251.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [294,2,Mod(41,294)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(294, base_ring=CyclotomicField(14))

chi = DirichletCharacter(H, H._module([7, 5]))

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

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

chi := DirichletCharacter("294.41");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 294 = 2 \cdot 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	294.j (of order $14$, 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:	$2.34760181943$
Analytic rank:	$0$
Dimension:	$120$
Relative dimension:	$20$ over $\Q(\zeta_{14})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{14}]$

Embedding invariants

Embedding label			251.4
Character	$\chi$	$=$	294.251
Dual form			294.2.j.a.41.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.781831 - 0.623490i) q^{2} +(-0.580532 + 1.63186i) q^{3} +(0.222521 + 0.974928i) q^{4} +(-3.14996 - 1.51694i) q^{5} +(1.47133 - 0.913887i) q^{6} +(2.47808 - 0.926885i) q^{7} +(0.433884 - 0.900969i) q^{8} +(-2.32596 - 1.89470i) q^{9} +(1.51694 + 3.14996i) q^{10} +(1.47826 + 1.17888i) q^{11} +(-1.72013 - 0.202853i) q^{12} +(-0.731696 - 0.583508i) q^{13} +(-2.51534 - 0.820391i) q^{14} +(4.30409 - 4.25967i) q^{15} +(-0.900969 + 0.433884i) q^{16} +(1.24123 - 5.43819i) q^{17} +(0.637185 + 2.93155i) q^{18} -6.71507i q^{19} +(0.777975 - 3.40853i) q^{20} +(0.0739439 + 4.58198i) q^{21} +(-0.420736 - 1.84336i) q^{22} +(5.84179 - 1.33335i) q^{23} +(1.21838 + 1.23108i) q^{24} +(4.50368 + 5.64743i) q^{25} +(0.208252 + 0.912410i) q^{26} +(4.44219 - 2.69572i) q^{27} +(1.45507 + 2.20970i) q^{28} +(0.519155 + 0.118494i) q^{29} +(-6.02094 + 0.646788i) q^{30} -5.34122i q^{31} +(0.974928 + 0.222521i) q^{32} +(-2.78195 + 1.72795i) q^{33} +(-4.36109 + 3.47785i) q^{34} +(-9.21188 - 0.839452i) q^{35} +(1.32962 - 2.68926i) q^{36} +(0.612916 - 2.68536i) q^{37} +(-4.18678 + 5.25005i) q^{38} +(1.37698 - 0.855284i) q^{39} +(-2.73343 + 2.17984i) q^{40} +(-1.61381 - 0.777171i) q^{41} +(2.79901 - 3.62844i) q^{42} +(-9.41518 + 4.53411i) q^{43} +(-0.820375 + 1.70353i) q^{44} +(4.45254 + 9.49657i) q^{45} +(-5.39863 - 2.59984i) q^{46} +(-7.08465 + 8.88387i) q^{47} +(-0.184998 - 1.72214i) q^{48} +(5.28177 - 4.59379i) q^{49} -7.22334i q^{50} +(8.15381 + 5.18257i) q^{51} +(0.406061 - 0.843194i) q^{52} +(-5.46957 + 1.24839i) q^{53} +(-5.15380 - 0.662060i) q^{54} +(-2.86818 - 5.95585i) q^{55} +(0.240105 - 2.63483i) q^{56} +(10.9581 + 3.89832i) q^{57} +(-0.332012 - 0.416330i) q^{58} +(0.981235 - 0.472538i) q^{59} +(5.11062 + 3.24831i) q^{60} +(4.27189 + 0.975031i) q^{61} +(-3.33020 + 4.17593i) q^{62} +(-7.52010 - 2.53932i) q^{63} +(-0.623490 - 0.781831i) q^{64} +(1.41966 + 2.94796i) q^{65} +(3.25237 + 0.383549i) q^{66} -9.15032 q^{67} +5.57804 q^{68} +(-1.21550 + 10.3071i) q^{69} +(6.67875 + 6.39982i) q^{70} +(5.70374 - 1.30184i) q^{71} +(-2.71626 + 1.27354i) q^{72} +(1.01364 - 0.808350i) q^{73} +(-2.15349 + 1.71735i) q^{74} +(-11.8304 + 4.07087i) q^{75} +(6.54671 - 1.49424i) q^{76} +(4.75594 + 1.55117i) q^{77} +(-1.60983 - 0.189845i) q^{78} +15.3224 q^{79} +3.49619 q^{80} +(1.82022 + 8.81401i) q^{81} +(0.777171 + 1.61381i) q^{82} +(-9.92846 - 12.4499i) q^{83} +(-4.45065 + 1.09168i) q^{84} +(-12.1592 + 15.2472i) q^{85} +(10.1881 + 2.32536i) q^{86} +(-0.494752 + 0.778401i) q^{87} +(1.70353 - 0.820375i) q^{88} +(-6.59006 - 8.26368i) q^{89} +(2.43988 - 10.2008i) q^{90} +(-2.35405 - 0.767783i) q^{91} +(2.59984 + 5.39863i) q^{92} +(8.71615 + 3.10075i) q^{93} +(11.0780 - 2.52848i) q^{94} +(-10.1864 + 21.1522i) q^{95} +(-0.929101 + 1.46177i) q^{96} +7.02844i q^{97} +(-6.99364 + 0.298440i) q^{98} +(-1.20477 - 5.54289i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 120 q + 20 q^{4} - 14 q^{6} + 4 q^{7} - 10 q^{9} + 12 q^{15} - 20 q^{16} - 8 q^{18} - 12 q^{21} - 10 q^{22} - 24 q^{25} + 42 q^{27} - 4 q^{28} + 8 q^{30} + 10 q^{36} - 58 q^{37} + 8 q^{39} - 14 q^{40} - 2 q^{42}+ \cdots - 224 q^{99}+O(q^{100}) $ 120 * q + 20 * q^4 - 14 * q^6 + 4 * q^7 - 10 * q^9 + 12 * q^15 - 20 * q^16 - 8 * q^18 - 12 * q^21 - 10 * q^22 - 24 * q^25 + 42 * q^27 - 4 * q^28 + 8 * q^30 + 10 * q^36 - 58 * q^37 + 8 * q^39 - 14 * q^40 - 2 * q^42 - 12 * q^43 + 14 * q^45 - 60 * q^46 - 36 * q^49 - 24 * q^51 - 42 * q^52 - 14 * q^55 + 34 * q^57 + 50 * q^58 - 12 * q^60 - 154 * q^61 + 20 * q^64 - 28 * q^67 + 28 * q^69 - 38 * q^70 + 8 * q^72 - 84 * q^75 - 16 * q^78 + 16 * q^79 + 22 * q^81 - 30 * q^84 - 32 * q^85 - 56 * q^87 - 4 * q^88 - 42 * q^90 + 88 * q^91 + 14 * q^93 + 112 * q^94 - 224 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/294\mathbb{Z}\right)^\times$.

$n$	$197$	$199$
$\chi(n)$	$-1$	$e\left(\frac{9}{14}\right)$

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 $

$2$	−0.781831	−	0.623490i	−0.552838	−	0.440874i
$2$	−0.781831	−	0.623490i	−0.552838	−	0.440874i
$3$	−0.580532	+	1.63186i	−0.335171	+	0.942157i
$3$	−0.580532	+	1.63186i	−0.335171	+	0.942157i
$4$	0.222521	+	0.974928i	0.111260	+	0.487464i
$5$	−3.14996	−	1.51694i	−1.40870	−	0.678396i	−0.433797	−	0.901010i	$-0.642827\pi$
$5$	−3.14996	−	1.51694i	−1.40870	−	0.678396i	−0.974907	+	0.222614i	$0.928541\pi$
$6$	1.47133	−	0.913887i	0.600668	−	0.373093i
$7$	2.47808	−	0.926885i	0.936627	−	0.350329i
$7$	2.47808	−	0.926885i	0.936627	−	0.350329i
$8$	0.433884	−	0.900969i	0.153401	−	0.318541i
$9$	−2.32596	−	1.89470i	−0.775321	−	0.631567i
$10$	1.51694	+	3.14996i	0.479698	+	0.996104i
$11$	1.47826	+	1.17888i	0.445713	+	0.355445i	0.820481	−	0.571674i	$-0.193706\pi$
$11$	1.47826	+	1.17888i	0.445713	+	0.355445i	−0.374767	+	0.927119i	$0.622277\pi$
$12$	−1.72013	−	0.202853i	−0.496559	−	0.0585587i
$13$	−0.731696	−	0.583508i	−0.202936	−	0.161836i	0.516749	−	0.856137i	$-0.327142\pi$
$13$	−0.731696	−	0.583508i	−0.202936	−	0.161836i	−0.719685	+	0.694301i	$0.755714\pi$
$14$	−2.51534	−	0.820391i	−0.672254	−	0.219259i
$15$	4.30409	−	4.25967i	1.11131	−	1.09984i
$16$	−0.900969	+	0.433884i	−0.225242	+	0.108471i
$17$	1.24123	−	5.43819i	0.301043	−	1.31895i	−0.567513	−	0.823364i	$-0.692094\pi$
$17$	1.24123	−	5.43819i	0.301043	−	1.31895i	0.868556	−	0.495591i	$-0.165048\pi$
$18$	0.637185	+	2.93155i	0.150186	+	0.690973i
$19$		−	6.71507i		−	1.54054i	−0.637716	−	0.770271i	$-0.720121\pi$
$19$		−	6.71507i		−	1.54054i	0.637716	−	0.770271i	$-0.279879\pi$
$20$	0.777975	−	3.40853i	0.173961	−	0.762171i
$21$	0.0739439	+	4.58198i	0.0161359	+	0.999870i
$22$	−0.420736	−	1.84336i	−0.0897012	−	0.393007i
$23$	5.84179	−	1.33335i	1.21810	−	0.278023i	0.435292	−	0.900289i	$-0.356645\pi$
$23$	5.84179	−	1.33335i	1.21810	−	0.278023i	0.782806	+	0.622266i	$0.213788\pi$
$24$	1.21838	+	1.23108i	0.248700	+	0.251293i
$25$	4.50368	+	5.64743i	0.900736	+	1.12949i
$26$	0.208252	+	0.912410i	0.0408415	+	0.178938i
$27$	4.44219	−	2.69572i	0.854900	−	0.518792i
$28$	1.45507	+	2.20970i	0.274982	+	0.417594i
$29$	0.519155	+	0.118494i	0.0964047	+	0.0220037i	0.270451	−	0.962734i	$-0.412827\pi$
$29$	0.519155	+	0.118494i	0.0964047	+	0.0220037i	−0.174046	+	0.984737i	$0.555684\pi$
$30$	−6.02094	+	0.646788i	−1.09927	+	0.118087i
$31$		−	5.34122i		−	0.959311i	−0.877457	−	0.479656i	$-0.840762\pi$
$31$		−	5.34122i		−	0.959311i	0.877457	−	0.479656i	$-0.159238\pi$
$32$	0.974928	+	0.222521i	0.172345	+	0.0393365i
$33$	−2.78195	+	1.72795i	−0.484275	+	0.300798i
$34$	−4.36109	+	3.47785i	−0.747921	+	0.596447i
$35$	−9.21188	−	0.839452i	−1.55709	−	0.141893i
$36$	1.32962	−	2.68926i	0.221603	−	0.448210i
$37$	0.612916	−	2.68536i	0.100763	−	0.441470i	−0.899229	−	0.437478i	$-0.855872\pi$
$37$	0.612916	−	2.68536i	0.100763	−	0.441470i	0.999992	−	0.00399278i	$-0.00127095\pi$
$38$	−4.18678	+	5.25005i	−0.679185	+	0.851671i
$39$	1.37698	−	0.855284i	0.220493	−	0.136955i
$40$	−2.73343	+	2.17984i	−0.432193	+	0.344663i
$41$	−1.61381	−	0.777171i	−0.252035	−	0.121374i	0.303601	−	0.952799i	$-0.401811\pi$
$41$	−1.61381	−	0.777171i	−0.252035	−	0.121374i	−0.555636	+	0.831425i	$0.687525\pi$
$42$	2.79901	−	3.62844i	0.431896	−	0.559880i
$43$	−9.41518	+	4.53411i	−1.43580	+	0.691445i	−0.980066	−	0.198670i	$-0.936338\pi$
$43$	−9.41518	+	4.53411i	−1.43580	+	0.691445i	−0.455735	+	0.890116i	$0.650623\pi$
$44$	−0.820375	+	1.70353i	−0.123676	+	0.256816i
$45$	4.45254	+	9.49657i	0.663746	+	1.41567i
$46$	−5.39863	−	2.59984i	−0.795984	−	0.383326i
$47$	−7.08465	+	8.88387i	−1.03340	+	1.29584i	−0.0791429	+	0.996863i	$0.525218\pi$
$47$	−7.08465	+	8.88387i	−1.03340	+	1.29584i	−0.954259	+	0.298982i	$0.903353\pi$
$48$	−0.184998	−	1.72214i	−0.0267021	−	0.248570i
$49$	5.28177	−	4.59379i	0.754539	−	0.656256i
$50$		−	7.22334i		−	1.02153i
$51$	8.15381	+	5.18257i	1.14176	+	0.725705i
$52$	0.406061	−	0.843194i	0.0563105	−	0.116930i
$53$	−5.46957	+	1.24839i	−0.751304	+	0.171480i	−0.580991	−	0.813910i	$-0.697335\pi$
$53$	−5.46957	+	1.24839i	−0.751304	+	0.171480i	−0.170313	+	0.985390i	$0.554478\pi$
$54$	−5.15380	−	0.662060i	−0.701344	−	0.0900950i
$55$	−2.86818	−	5.95585i	−0.386746	−	0.803086i
$56$	0.240105	−	2.63483i	0.0320854	−	0.352094i
$57$	10.9581	+	3.89832i	1.45143	+	0.516345i
$58$	−0.332012	−	0.416330i	−0.0435953	−	0.0546668i
$59$	0.981235	−	0.472538i	0.127746	−	0.0615192i	−0.368919	−	0.929462i	$-0.620272\pi$
$59$	0.981235	−	0.472538i	0.127746	−	0.0615192i	0.496665	+	0.867942i	$0.334558\pi$
$60$	5.11062	+	3.24831i	0.659779	+	0.419356i
$61$	4.27189	+	0.975031i	0.546960	+	0.124840i	0.487067	−	0.873365i	$-0.338067\pi$
$61$	4.27189	+	0.975031i	0.546960	+	0.124840i	0.0598930	+	0.998205i	$0.480924\pi$
$62$	−3.33020	+	4.17593i	−0.422935	+	0.530344i
$63$	−7.52010	−	2.53932i	−0.947443	−	0.319924i
$64$	−0.623490	−	0.781831i	−0.0779362	−	0.0977289i
$65$	1.41966	+	2.94796i	0.176088	+	0.365650i
$66$	3.25237	+	0.383549i	0.400339	+	0.0472116i
$67$	−9.15032			−1.11789			−0.558945	−	0.829205i	$-0.688794\pi$
$67$	−9.15032			−1.11789			−0.558945	+	0.829205i	$0.688794\pi$
$68$	5.57804			0.676437
$69$	−1.21550	+	10.3071i	−0.146329	+	1.24083i
$70$	6.67875	+	6.39982i	0.798263	+	0.764925i
$71$	5.70374	−	1.30184i	0.676909	−	0.154500i	0.129773	−	0.991544i	$-0.458575\pi$
$71$	5.70374	−	1.30184i	0.676909	−	0.154500i	0.547136	+	0.837044i	$0.315718\pi$
$72$	−2.71626	+	1.27354i	−0.320115	+	0.150088i
$73$	1.01364	−	0.808350i	0.118637	−	0.0946102i	−0.562374	−	0.826883i	$-0.690112\pi$
$73$	1.01364	−	0.808350i	0.118637	−	0.0946102i	0.681011	+	0.732273i	$0.261540\pi$
$74$	−2.15349	+	1.71735i	−0.250338	+	0.199638i
$75$	−11.8304	+	4.07087i	−1.36605	+	0.470064i
$76$	6.54671	−	1.49424i	0.750959	−	0.171402i
$77$	4.75594	+	1.55117i	0.541990	+	0.176772i
$78$	−1.60983	−	0.189845i	−0.182277	−	0.0214957i
$79$	15.3224			1.72390			0.861950	−	0.506993i	$-0.169243\pi$
$79$	15.3224			1.72390			0.861950	+	0.506993i	$0.169243\pi$
$80$	3.49619			0.390886
$81$	1.82022	+	8.81401i	0.202247	+	0.979335i
$82$	0.777171	+	1.61381i	0.0858242	+	0.178216i
$83$	−9.92846	−	12.4499i	−1.08979	−	1.36655i	−0.924886	−	0.380244i	$-0.875840\pi$
$83$	−9.92846	−	12.4499i	−1.08979	−	1.36655i	−0.164904	−	0.986310i	$-0.552731\pi$
$84$	−4.45065	+	1.09168i	−0.485605	+	0.119112i
$85$	−12.1592	+	15.2472i	−1.31885	+	1.65379i
$86$	10.1881	+	2.32536i	1.09861	+	0.250750i
$87$	−0.494752	+	0.778401i	−0.0530430	+	0.0834534i
$88$	1.70353	−	0.820375i	0.181596	−	0.0874522i
$89$	−6.59006	−	8.26368i	−0.698545	−	0.875948i	0.298369	−	0.954451i	$-0.403557\pi$
$89$	−6.59006	−	8.26368i	−0.698545	−	0.875948i	−0.996914	+	0.0785028i	$0.974986\pi$
$90$	2.43988	−	10.2008i	0.257186	−	1.07526i
$91$	−2.35405	−	0.767783i	−0.246771	−	0.0804855i
$92$	2.59984	+	5.39863i	0.271052	+	0.562846i
$93$	8.71615	+	3.10075i	0.903822	+	0.321533i
$94$	11.0780	−	2.52848i	1.14261	−	0.260793i
$95$	−10.1864	+	21.1522i	−1.04510	+	2.17017i
$96$	−0.929101	+	1.46177i	−0.0948260	+	0.149191i
$97$			7.02844i			0.713630i	0.934175	+	0.356815i	$0.116137\pi$
$97$			7.02844i			0.713630i	−0.934175	+	0.356815i	$0.883863\pi$
$98$	−6.99364	+	0.298440i	−0.706464	+	0.0301470i
$99$	−1.20477	−	5.54289i	−0.121084	−	0.557082i
$100$	−4.50368	+	5.64743i	−0.450368	+	0.564743i
$101$	14.8915	+	7.17135i	1.48176	+	0.713576i	0.987773	−	0.155896i	$-0.0498264\pi$
$101$	14.8915	+	7.17135i	1.48176	+	0.713576i	0.493982	+	0.869472i	$0.335541\pi$
$102$	−3.14363	−	9.13571i	−0.311266	−	0.904571i
$103$	0.0466493	−	0.0968682i	0.00459649	−	0.00954471i	−0.898658	−	0.438650i	$-0.855457\pi$
$103$	0.0466493	−	0.0968682i	0.00459649	−	0.00954471i	0.903254	+	0.429105i	$0.141171\pi$
$104$	−0.843194	+	0.406061i	−0.0826819	+	0.0398175i
$105$	6.71767	−	14.5452i	0.655577	−	1.41947i
$106$	5.05464	+	2.43419i	0.490951	+	0.236429i
$107$	9.83286	−	7.84144i	0.950578	−	0.758061i	−0.0197619	−	0.999805i	$-0.506291\pi$
$107$	9.83286	−	7.84144i	0.950578	−	0.758061i	0.970340	+	0.241744i	$0.0777194\pi$
$108$	3.61662	+	3.73096i	0.348009	+	0.359012i
$109$	−2.56680	+	3.21867i	−0.245855	+	0.308292i	−0.889413	−	0.457105i	$-0.848886\pi$
$109$	−2.56680	+	3.21867i	−0.245855	+	0.308292i	0.643558	+	0.765398i	$0.277458\pi$
$110$	−1.47097	+	6.44475i	−0.140252	+	0.614483i
$111$	4.02633	+	2.55913i	0.382162	+	0.242902i
$112$	−1.83051	+	1.91029i	−0.172967	+	0.180506i
$113$	−0.409927	+	0.326906i	−0.0385627	+	0.0307528i	−0.642582	−	0.766217i	$-0.722137\pi$
$113$	−0.409927	+	0.326906i	−0.0385627	+	0.0307528i	0.604019	+	0.796970i	$0.293565\pi$
$114$	−6.13682	−	9.88008i	−0.574765	−	0.925354i
$115$	−20.4240	−	4.66165i	−1.90455	−	0.434701i
$116$			0.532506i			0.0494419i
$117$	0.596326	+	2.74356i	0.0551303	+	0.253643i
$118$	−1.06178	−	0.242345i	−0.0977451	−	0.0223097i
$119$	−1.96470	−	14.6268i	−0.180104	−	1.34083i
$120$	−1.97036	−	5.72606i	−0.179868	−	0.522715i
$121$	−1.65222	−	7.23883i	−0.150201	−	0.658075i
$122$	−2.73198	−	3.42579i	−0.247342	−	0.310156i
$123$	2.20511	−	2.18235i	0.198828	−	0.196776i
$124$	5.20730	−	1.18853i	0.467630	−	0.106733i
$125$	−1.72970	−	7.57832i	−0.154709	−	0.677826i
$126$	4.29621	+	6.67402i	0.382737	+	0.594569i
$127$	2.25720	−	9.88945i	0.200294	−	0.877547i	−0.770463	−	0.637484i	$-0.779975\pi$
$127$	2.25720	−	9.88945i	0.200294	−	0.877547i	0.970758	−	0.240062i	$-0.0771678\pi$
$128$			1.00000i			0.0883883i
$129$	−1.93324	−	17.9965i	−0.170212	−	1.58450i
$130$	0.728087	−	3.18996i	0.0638575	−	0.279778i
$131$	4.46922	−	2.15226i	0.390477	−	0.188044i	−0.228335	−	0.973583i	$-0.573328\pi$
$131$	4.46922	−	2.15226i	0.390477	−	0.188044i	0.618813	+	0.785539i	$0.287614\pi$
$132$	−2.30367	−	2.32769i	−0.200509	−	0.202600i
$133$	−6.22410	−	16.6405i	−0.539698	−	1.44291i
$134$	7.15401	+	5.70513i	0.618012	+	0.492848i
$135$	−18.0820	+	1.75288i	−1.55625	+	0.150864i
$136$	−4.36109	−	3.47785i	−0.373960	−	0.298223i
$137$	−0.306633	−	0.636730i	−0.0261974	−	0.0543995i	0.887459	−	0.460886i	$-0.152468\pi$
$137$	−0.306633	−	0.636730i	−0.0261974	−	0.0543995i	−0.913657	+	0.406486i	$0.866754\pi$
$138$	7.37667	−	7.30054i	0.627944	−	0.621463i
$139$	2.79825	−	5.81062i	0.237344	−	0.492851i	−0.747942	−	0.663765i	$-0.768958\pi$
$139$	2.79825	−	5.81062i	0.237344	−	0.492851i	0.985286	+	0.170914i	$0.0546720\pi$
$140$	−1.23143	−	9.16771i	−0.104075	−	0.774813i
$141$	−10.3844	−	16.7186i	−0.874524	−	1.40796i
$142$	−5.27105	−	2.53840i	−0.442336	−	0.213018i
$143$	−0.393756	−	1.72516i	−0.0329275	−	0.144265i
$144$	2.91770	+	0.697868i	0.243142	+	0.0581557i
$145$	−1.45557	−	1.16078i	−0.120878	−	0.0963973i
$146$	−1.29649			−0.107299
$147$	4.43020	+	11.2860i	0.365397	+	0.930852i
$148$	2.75442			0.226412
$149$	8.44769	+	6.73681i	0.692062	+	0.551901i	0.905129	−	0.425137i	$-0.139774\pi$
$149$	8.44769	+	6.73681i	0.692062	+	0.551901i	−0.213067	+	0.977038i	$0.568345\pi$
$150$	11.7875	+	4.19338i	0.962446	+	0.342388i
$151$	−0.671380	−	2.94151i	−0.0546361	−	0.239377i	0.940235	−	0.340526i	$-0.110605\pi$
$151$	−0.671380	−	2.94151i	−0.0546361	−	0.239377i	−0.994871	+	0.101149i	$0.967748\pi$
$152$	−6.05007	−	2.91356i	−0.490725	−	0.236321i
$153$	−13.1908	+	10.2973i	−1.06641	+	0.832485i
$154$	−2.75120	−	4.17803i	−0.221698	−	0.336676i
$155$	−8.10231	+	16.8246i	−0.650793	+	1.35139i
$156$	1.14025	+	1.15214i	0.0912928	+	0.0922448i
$157$	9.20064	+	19.1053i	0.734291	+	1.52477i	0.847264	+	0.531172i	$0.178248\pi$
$157$	9.20064	+	19.1053i	0.734291	+	1.52477i	−0.112973	+	0.993598i	$0.536037\pi$
$158$	−11.9795	−	9.55333i	−0.953038	−	0.760022i
$159$	1.13805	−	9.65033i	0.0902535	−	0.765321i
$160$	−2.73343	−	2.17984i	−0.216097	−	0.172331i
$161$	13.2406	−	8.71882i	1.04350	−	0.687139i
$162$	4.07234	−	8.02596i	0.319953	−	0.630579i
$163$	−6.52790	+	3.14367i	−0.511305	+	0.246231i	−0.671702	−	0.740821i	$-0.734437\pi$
$163$	−6.52790	+	3.14367i	−0.511305	+	0.246231i	0.160398	+	0.987052i	$0.448722\pi$
$164$	0.398579	−	1.74629i	0.0311238	−	0.136362i
$165$	11.3842	−	1.22293i	0.886260	−	0.0952047i
$166$			15.9240i			1.23594i
$167$	−0.192314	+	0.842585i	−0.0148817	+	0.0652012i	−0.981824	−	0.189796i	$-0.939217\pi$
$167$	−0.192314	+	0.842585i	−0.0148817	+	0.0652012i	0.966942	+	0.254997i	$0.0820745\pi$
$168$	4.16030	+	1.92143i	0.320974	+	0.148241i
$169$	−2.69787	−	11.8202i	−0.207529	−	0.909243i
$170$	19.0129	−	4.33958i	1.45823	−	0.332831i
$171$	−12.7230	+	15.6190i	−0.972956	+	1.19442i
$172$	−6.51550	−	8.17018i	−0.496803	−	0.622971i
$173$	4.85722	+	21.2809i	0.369288	+	1.61795i	0.728740	+	0.684791i	$0.240106\pi$
$173$	4.85722	+	21.2809i	0.369288	+	1.61795i	−0.359452	+	0.933163i	$0.617036\pi$
$174$	0.872138	−	0.300106i	0.0661166	−	0.0227510i
$175$	16.3950	+	9.82041i	1.23935	+	0.742353i
$176$	−1.84336	−	0.420736i	−0.138949	−	0.0317142i
$177$	0.201479	+	1.87557i	0.0151441	+	0.140976i
$178$			10.5696i			0.792228i
$179$	4.81319	+	1.09858i	0.359755	+	0.0821116i	0.398578	−	0.917134i	$-0.369504\pi$
$179$	4.81319	+	1.09858i	0.359755	+	0.0821116i	−0.0388234	+	0.999246i	$0.512361\pi$
$180$	−8.26769	+	6.45409i	−0.616237	+	0.481060i
$181$	−18.5737	+	14.8120i	−1.38057	+	1.10097i	−0.397528	+	0.917590i	$0.630132\pi$
$181$	−18.5737	+	14.8120i	−1.38057	+	1.10097i	−0.983043	+	0.183378i	$0.941297\pi$
$182$	1.36176	+	2.06800i	0.100941	+	0.153290i
$183$	−4.07109	+	6.40511i	−0.300944	+	0.473479i
$184$	1.33335	−	5.84179i	0.0982959	−	0.430663i
$185$	−6.00419	+	7.52901i	−0.441437	+	0.553544i
$186$	−4.88127	−	7.85869i	−0.357912	−	0.576227i
$187$	8.24582	−	6.57582i	0.602994	−	0.480872i
$188$	−10.2376	−	4.93017i	−0.746654	−	0.359570i
$189$	8.50949	−	10.7976i	0.618974	−	0.785411i
$190$	21.1522	−	10.1864i	1.53454	−	0.738996i
$191$	6.99491	−	14.5251i	0.506134	−	1.05100i	−0.478777	−	0.877936i	$-0.658920\pi$
$191$	6.99491	−	14.5251i	0.506134	−	1.05100i	0.984911	−	0.173061i	$-0.0553659\pi$
$192$	1.63780	−	0.563572i	0.118198	−	0.0406723i
$193$	10.4512	+	5.03302i	0.752292	+	0.362285i	0.770408	−	0.637551i	$-0.220053\pi$
$193$	10.4512	+	5.03302i	0.752292	+	0.362285i	−0.0181163	+	0.999836i	$0.505767\pi$
$194$	4.38216	−	5.49506i	0.314621	−	0.394522i
$195$	−5.63484	+	0.605312i	−0.403519	+	0.0433473i
$196$	5.65392	+	4.12713i	0.403851	+	0.294795i
$197$		−	15.3394i		−	1.09289i	−0.837497	−	0.546443i	$-0.815982\pi$
$197$		−	15.3394i		−	1.09289i	0.837497	−	0.546443i	$-0.184018\pi$
$198$	−2.51401	+	5.08477i	−0.178663	+	0.361359i
$199$	−10.9339	+	22.7045i	−0.775085	+	1.60948i	0.0175977	+	0.999845i	$0.494398\pi$
$199$	−10.9339	+	22.7045i	−0.775085	+	1.60948i	−0.792682	+	0.609635i	$0.791316\pi$
$200$	7.04223	−	1.60734i	0.497961	−	0.113656i
$201$	5.31206	−	14.9321i	0.374684	−	1.05323i
$202$	−7.17135	−	14.8915i	−0.504574	−	1.04776i
$203$	1.39634	−	0.187560i	0.0980037	−	0.0131641i
$204$	−3.23824	+	9.10261i	−0.226722	+	0.637310i
$205$	3.90452	+	4.89611i	0.272703	+	0.341959i
$206$	−0.0968682	+	0.0466493i	−0.00674913	+	0.00325021i
$207$	−16.1141	−	7.96712i	−1.12001	−	0.553753i
$208$	0.912410	+	0.208252i	0.0632643	+	0.0144397i
$209$	7.91624	−	9.92665i	0.547577	−	0.686640i
$210$	−14.3209	+	7.18351i	−0.988234	+	0.495709i
$211$	5.21715	+	6.54210i	0.359163	+	0.450377i	0.928281	−	0.371880i	$-0.121287\pi$
$211$	5.21715	+	6.54210i	0.359163	+	0.450377i	−0.569118	+	0.822256i	$0.692715\pi$
$212$	−2.43419	−	5.05464i	−0.167181	−	0.347154i
$213$	−1.18678	+	10.0635i	−0.0813166	+	0.689539i
$214$	−12.5767			−0.859725
$215$	36.5354			2.49169
$216$	−0.501368	−	5.17191i	−0.0341138	−	0.351904i
$217$	−4.95069	−	13.2360i	−0.336075	−	0.898516i
$218$	4.01361	−	0.916081i	0.271836	−	0.0620448i
$219$	0.730668	+	2.12340i	0.0493740	+	0.143486i
$220$	5.16829	−	4.12157i	0.348446	−	0.277876i
$221$	−4.08143	+	3.25483i	−0.274547	+	0.218944i
$222$	−1.55231	−	4.51118i	−0.104185	−	0.302771i
$223$	−0.338200	+	0.0771919i	−0.0226475	+	0.00516915i	−0.233830	−	0.972278i	$-0.575126\pi$
$223$	−0.338200	+	0.0771919i	−0.0226475	+	0.00516915i	0.211182	+	0.977447i	$0.432269\pi$
$224$	2.62220	−	0.352221i	0.175203	−	0.0235337i
$225$	0.224803	−	21.6688i	0.0149868	−	1.44459i
$226$	0.524317			0.0348770
$227$	−12.4355			−0.825373			−0.412687	−	0.910873i	$-0.635410\pi$
$227$	−12.4355			−0.825373			−0.412687	+	0.910873i	$0.635410\pi$
$228$	−1.36217	+	11.5508i	−0.0902122	+	0.764970i
$229$	−1.56484	−	3.24941i	−0.103407	−	0.214727i	0.842845	−	0.538156i	$-0.180879\pi$
$229$	−1.56484	−	3.24941i	−0.103407	−	0.214727i	−0.946253	+	0.323428i	$0.895165\pi$
$230$	13.0616	+	16.3788i	0.861259	+	1.07998i
$231$	−5.29228	+	6.86054i	−0.348206	+	0.451391i
$232$	0.332012	−	0.416330i	0.0217977	−	0.0273334i
$233$	−12.4633	−	2.84467i	−0.816499	−	0.186361i	−0.206178	−	0.978515i	$-0.566103\pi$
$233$	−12.4633	−	2.84467i	−0.816499	−	0.186361i	−0.610321	+	0.792154i	$0.708960\pi$
$234$	1.24436	−	2.51681i	0.0813462	−	0.164529i
$235$	35.7926	−	17.2368i	2.33485	−	1.12441i
$236$	0.679036	+	0.851484i	0.0442015	+	0.0554269i
$237$	−8.89513	+	25.0040i	−0.577800	+	1.62419i
$238$	−7.58356	+	12.6606i	−0.491570	+	0.820667i
$239$	10.5814	+	21.9726i	0.684457	+	1.42129i	0.896060	+	0.443933i	$0.146417\pi$
$239$	10.5814	+	21.9726i	0.684457	+	1.42129i	−0.211603	+	0.977356i	$0.567868\pi$
$240$	−2.02965	+	5.70531i	−0.131013	+	0.368276i
$241$	0.779823	−	0.177990i	0.0502328	−	0.0114653i	−0.197331	−	0.980337i	$-0.563227\pi$
$241$	0.779823	−	0.177990i	0.0502328	−	0.0114653i	0.247563	+	0.968872i	$0.420370\pi$
$242$	−3.22158	+	6.68968i	−0.207091	+	0.430029i
$243$	−15.4400	−	2.14647i	−0.990475	−	0.137696i
$244$			4.38175i			0.280513i
$245$	−23.6059	+	6.45812i	−1.50812	+	0.412594i
$246$	−3.08470	+	0.331368i	−0.196673	+	0.0211272i
$247$	−3.91830	+	4.91339i	−0.249315	+	0.312632i
$248$	−4.81227	−	2.31747i	−0.305580	−	0.147159i
$249$	26.0803	−	8.97433i	1.65277	−	0.568725i
$250$	−3.37267	+	7.00342i	−0.213306	+	0.442935i
$251$	17.4679	−	8.41209i	1.10256	−	0.530967i	0.208100	−	0.978108i	$-0.433272\pi$
$251$	17.4679	−	8.41209i	1.10256	−	0.530967i	0.894464	+	0.447141i	$0.147558\pi$
$252$	0.802276	−	7.89660i	0.0505386	−	0.497439i
$253$	10.2076	+	4.91570i	0.641744	+	0.309048i
$254$	−7.93072	+	6.32454i	−0.497618	+	0.396837i
$255$	−17.8225	−	28.6937i	−1.11609	−	1.79687i
$256$	0.623490	−	0.781831i	0.0389681	−	0.0488645i
$257$	−5.63841	+	24.7035i	−0.351714	+	1.54096i	0.421507	+	0.906825i	$0.361501\pi$
$257$	−5.63841	+	24.7035i	−0.351714	+	1.54096i	−0.773222	+	0.634136i	$0.781356\pi$
$258$	−9.70916	+	15.2756i	−0.604466	+	0.951016i
$259$	−0.970164	−	7.22264i	−0.0602830	−	0.448793i
$260$	−2.55815	+	2.04005i	−0.158650	+	0.126519i
$261$	−0.983026	−	1.25926i	−0.0608478	−	0.0779460i
$262$	−4.83609	−	1.10381i	−0.298775	−	0.0681933i
$263$			15.8937i			0.980048i	0.871709	+	0.490024i	$0.163012\pi$
$263$			15.8937i			0.980048i	−0.871709	+	0.490024i	$0.836988\pi$
$264$	0.349788	+	3.25618i	0.0215280	+	0.200404i
$265$	19.1227	+	4.36462i	1.17470	+	0.268117i
$266$	−5.50898	+	16.8907i	−0.337777	+	1.03564i
$267$	17.3109	−	5.95676i	1.05941	−	0.364548i
$268$	−2.03614	−	8.92090i	−0.124377	−	0.544931i
$269$	−2.62574	−	3.29258i	−0.160094	−	0.200752i	0.695314	−	0.718706i	$-0.255265\pi$
$269$	−2.62574	−	3.29258i	−0.160094	−	0.200752i	−0.855408	+	0.517954i	$0.826694\pi$
$270$	15.2300	+	9.90347i	0.926865	+	0.602706i
$271$	9.72437	−	2.21952i	0.590714	−	0.134827i	0.0832931	−	0.996525i	$-0.473456\pi$
$271$	9.72437	−	2.21952i	0.590714	−	0.134827i	0.507421	+	0.861699i	$0.330599\pi$
$272$	1.24123	+	5.43819i	0.0752607	+	0.329739i
$273$	2.61952	−	3.39576i	0.158540	−	0.205521i
$274$	−0.157259	+	0.688998i	−0.00950038	+	0.0416239i
$275$			13.6577i			0.823589i
$276$	−10.3191	+	1.10851i	−0.621138	+	0.0667246i
$277$	3.14104	−	13.7618i	0.188727	−	0.826866i	−0.788562	−	0.614955i	$-0.789174\pi$
$277$	3.14104	−	13.7618i	0.188727	−	0.826866i	0.977289	−	0.211911i	$-0.0679687\pi$
$278$	−5.81062	+	2.79825i	−0.348498	+	0.167828i
$279$	−10.1200	+	12.4235i	−0.605869	+	0.743775i
$280$	−4.75320	+	7.93539i	−0.284058	+	0.474230i
$281$	14.2433	+	11.3587i	0.849684	+	0.677600i	0.948248	−	0.317530i	$-0.102854\pi$
$281$	14.2433	+	11.3587i	0.849684	+	0.677600i	−0.0985641	+	0.995131i	$0.531425\pi$
$282$	−2.30500	+	19.5457i	−0.137261	+	1.16393i
$283$	5.75856	+	4.59230i	0.342311	+	0.272984i	0.779522	−	0.626375i	$-0.215462\pi$
$283$	5.75856	+	4.59230i	0.342311	+	0.272984i	−0.437211	+	0.899359i	$0.644034\pi$
$284$	2.53840	+	5.27105i	0.150626	+	0.312779i
$285$	−28.6040	−	28.9023i	−1.69435	−	1.71202i
$286$	−0.767768	+	1.59429i	−0.0453990	+	0.0942721i
$287$	−4.71951	−	0.430075i	−0.278584	−	0.0253865i
$288$	−1.84604	−	2.36477i	−0.108779	−	0.139346i
$289$	−12.7168	−	6.12408i	−0.748046	−	0.360240i
$290$	0.414277	+	1.81506i	0.0243272	+	0.106584i
$291$	−11.4695	−	4.08024i	−0.672352	−	0.239188i
$292$	1.01364	+	0.808350i	0.0593187	+	0.0473051i
$293$	−6.26961			−0.366274			−0.183137	−	0.983087i	$-0.558625\pi$
$293$	−6.26961			−0.366274			−0.183137	+	0.983087i	$0.558625\pi$
$294$	3.57302	−	11.5859i	0.208383	−	0.675705i
$295$	−3.80766			−0.221691
$296$	−2.15349	−	1.71735i	−0.125169	−	0.0998191i
$297$	9.74466	+	1.25180i	0.565442	+	0.0726371i
$298$	−2.40434	−	10.5341i	−0.139280	−	0.610224i
$299$	−5.05244	−	2.43313i	−0.292190	−	0.140711i
$300$	−6.60132	−	10.6279i	−0.381127	−	0.613603i
$301$	−19.1290	+	19.9627i	−1.10258	+	1.15063i
$302$	−1.30909	+	2.71836i	−0.0753299	+	0.156424i
$303$	−20.3476	+	20.1376i	−1.16894	+	1.15688i
$304$	2.91356	+	6.05007i	0.167104	+	0.346995i
$305$	−11.9772	−	9.55151i	−0.685813	−	0.546918i
$306$	16.7332	+	0.173598i	0.956575	+	0.00992395i
$307$	9.18514	+	7.32491i	0.524224	+	0.418054i	0.849519	−	0.527558i	$-0.176892\pi$
$307$	9.18514	+	7.32491i	0.524224	+	0.418054i	−0.325295	+	0.945612i	$0.605464\pi$
$308$	−0.453983	+	4.98187i	−0.0258681	+	0.283868i
$309$	0.130994	+	0.132360i	0.00745201	+	0.00752972i
$310$	16.8246	−	8.10231i	0.955574	−	0.460180i
$311$	7.19171	−	31.5090i	0.407805	−	1.78671i	−0.186485	−	0.982458i	$-0.559710\pi$
$311$	7.19171	−	31.5090i	0.407805	−	1.78671i	0.594289	−	0.804251i	$-0.297433\pi$
$312$	−0.173135	−	1.61171i	−0.00980183	−	0.0912451i
$313$			3.86197i			0.218292i	0.994026	+	0.109146i	$0.0348116\pi$
$313$			3.86197i			0.218292i	−0.994026	+	0.109146i	$0.965188\pi$
$314$	4.71862	−	20.6736i	0.266287	−	1.16668i
$315$	19.8360	+	19.4063i	1.11763	+	1.09342i
$316$	3.40955	+	14.9382i	0.191802	+	0.840339i
$317$	−10.8251	+	2.47075i	−0.607996	+	0.138771i	−0.515425	−	0.856935i	$-0.672366\pi$
$317$	−10.8251	+	2.47075i	−0.607996	+	0.138771i	−0.0925714	+	0.995706i	$0.529509\pi$
$318$	−6.90665	+	6.83537i	−0.387306	+	0.383309i
$319$	0.627759	+	0.787184i	0.0351477	+	0.0440739i
$320$	0.777975	+	3.40853i	0.0434901	+	0.190543i
$321$	7.08788	+	20.5981i	0.395607	+	1.14967i
$322$	−15.7880	−	1.43871i	−0.879830	−	0.0801764i
$323$	−36.5178	−	8.33496i	−2.03191	−	0.463769i
$324$	−8.18799	+	3.73588i	−0.454888	+	0.207549i
$325$		−	6.76014i		−	0.374985i
$326$	7.06376	+	1.61226i	0.391226	+	0.0892947i
$327$	−3.76232	−	6.05721i	−0.208057	−	0.334965i
$328$	−1.40041	+	1.11679i	−0.0773249	+	0.0616646i
$329$	−9.32201	+	28.5816i	−0.513939	+	1.57575i
$330$	−9.66302	−	6.14182i	−0.531932	−	0.338096i
$331$	2.54914	−	11.1685i	0.140113	−	0.613877i	−0.855294	−	0.518144i	$-0.826623\pi$
$331$	2.54914	−	11.1685i	0.140113	−	0.613877i	0.995407	−	0.0957333i	$-0.0305196\pi$
$332$	9.92846	−	12.4499i	0.544895	−	0.683277i
$333$	−6.51357	+	5.08476i	−0.356942	+	0.278643i
$334$	0.675700	−	0.538853i	0.0369727	−	0.0294847i
$335$	28.8231	+	13.8805i	1.57477	+	0.758372i
$336$	−2.05467	−	4.09614i	−0.112091	−	0.223463i
$337$	−12.5010	+	6.02017i	−0.680973	+	0.327940i	−0.742194	−	0.670185i	$-0.766215\pi$
$337$	−12.5010	+	6.02017i	−0.680973	+	0.327940i	0.0612209	+	0.998124i	$0.480501\pi$
$338$	−5.26047	+	10.9235i	−0.286132	+	0.594159i
$339$	−0.295491	−	0.858726i	−0.0160488	−	0.0466396i
$340$	−17.5706	−	8.46155i	−0.952900	−	0.458892i
$341$	6.29664	−	7.89573i	0.340982	−	0.427578i
$342$	19.6856	−	4.27875i	1.06447	−	0.231368i
$343$	8.83074	−	16.2794i	0.476815	−	0.879004i
$344$			10.4501i			0.563429i
$345$	19.4640	−	30.6230i	1.04791	−	1.64869i
$346$	9.47088	−	19.6665i	0.509157	−	1.05728i
$347$	21.4836	−	4.90348i	1.15330	−	0.263233i	0.397226	−	0.917721i	$-0.369973\pi$
$347$	21.4836	−	4.90348i	1.15330	−	0.263233i	0.756072	+	0.654488i	$0.227116\pi$
$348$	−0.868978	−	0.309137i	−0.0465821	−	0.0165715i
$349$	−1.23408	−	2.56259i	−0.0660588	−	0.137173i	0.865325	−	0.501211i	$-0.167112\pi$
$349$	−1.23408	−	2.56259i	−0.0660588	−	0.137173i	−0.931384	+	0.364038i	$0.881398\pi$
$350$	−6.69520	−	17.9000i	−0.357874	−	0.956796i
$351$	−4.82331	−	0.619605i	−0.257449	−	0.0330721i
$352$	1.17888	+	1.47826i	0.0628343	+	0.0787917i
$353$	9.16301	−	4.41267i	0.487698	−	0.234863i	−0.173841	−	0.984774i	$-0.555618\pi$
$353$	9.16301	−	4.41267i	0.487698	−	0.234863i	0.661539	+	0.749911i	$0.269904\pi$
$354$	1.01187	−	1.59200i	0.0537805	−	0.0846137i
$355$	−19.9413	−	4.55148i	−1.05838	−	0.241568i
$356$	6.59006	−	8.26368i	0.349273	−	0.437974i
$357$	25.0095	+	5.28518i	1.32364	+	0.279721i
$358$	−3.07815	−	3.85988i	−0.162685	−	0.204001i
$359$	−1.98772	−	4.12754i	−0.104908	−	0.217843i	0.841907	−	0.539623i	$-0.181433\pi$
$359$	−1.98772	−	4.12754i	−0.104908	−	0.217843i	−0.946815	+	0.321780i	$0.895719\pi$
$360$	10.4880	+	0.108807i	0.552766	+	0.00573465i
$361$	−26.0922			−1.37327
$362$	23.7566			1.24862
$363$	12.7719	+	1.50618i	0.670354	+	0.0790541i
$364$	0.224708	−	2.46587i	0.0117779	−	0.129247i
$365$	−4.41914	+	1.00864i	−0.231308	+	0.0527946i
$366$	7.17643	−	2.46943i	0.375118	−	0.129079i
$367$	12.9265	−	10.3086i	0.674759	−	0.538103i	−0.225071	−	0.974342i	$-0.572261\pi$
$367$	12.9265	−	10.3086i	0.674759	−	0.538103i	0.899830	+	0.436240i	$0.143690\pi$
$368$	−4.68475	+	3.73597i	−0.244210	+	0.194751i
$369$	2.28116	+	4.86536i	0.118753	+	0.253281i
$370$	9.38853	−	2.14287i	0.488086	−	0.111402i
$371$	−12.3969	+	8.16328i	−0.643616	+	0.423817i
$372$	−1.08348	+	9.18760i	−0.0561760	+	0.476355i
$373$	−4.86997			−0.252158			−0.126079	−	0.992020i	$-0.540239\pi$
$373$	−4.86997			−0.252158			−0.126079	+	0.992020i	$0.540239\pi$
$374$	−10.5468			−0.545362
$375$	13.3709	+	1.57682i	0.690472	+	0.0814267i
$376$	4.93017	+	10.2376i	0.254254	+	0.527964i
$377$	−0.310722	−	0.389633i	−0.0160030	−	0.0200671i
$378$	−13.3852	+	3.13634i	−0.688460	+	0.161316i
$379$	−2.11183	+	2.64815i	−0.108477	+	0.136026i	−0.833106	−	0.553113i	$-0.813440\pi$
$379$	−2.11183	+	2.64815i	−0.108477	+	0.136026i	0.724629	+	0.689139i	$0.242011\pi$
$380$	−22.8885	−	5.22416i	−1.17416	−	0.267994i
$381$	14.8279	+	9.42459i	0.759654	+	0.482837i
$382$	−14.5251	+	6.99491i	−0.743168	+	0.357891i
$383$	−20.5992	−	25.8306i	−1.05257	−	1.31988i	−0.945496	−	0.325633i	$-0.894423\pi$
$383$	−20.5992	−	25.8306i	−1.05257	−	1.31988i	−0.107076	−	0.994251i	$-0.534149\pi$
$384$	−1.63186	−	0.580532i	−0.0832757	−	0.0296252i
$385$	−12.6280	−	12.1006i	−0.643581	−	0.616703i
$386$	−5.03302	−	10.4512i	−0.256174	−	0.531950i
$387$	30.4901	+	7.29276i	1.54990	+	0.370712i
$388$	−6.85223	+	1.56398i	−0.347869	+	0.0793988i
$389$	4.17306	−	8.66545i	0.211583	−	0.439356i	−0.767986	−	0.640467i	$-0.778741\pi$
$389$	4.17306	−	8.66545i	0.211583	−	0.439356i	0.979568	+	0.201111i	$0.0644552\pi$
$390$	4.78290	+	3.04001i	0.242192	+	0.153937i
$391$		−	33.4238i		−	1.69031i
$392$	−1.84719	−	6.75188i	−0.0932971	−	0.341021i
$393$	0.917674	+	8.54262i	0.0462905	+	0.430918i
$394$	−9.56394	+	11.9928i	−0.481825	+	0.604189i
$395$	−48.2648	−	23.2431i	−2.42846	−	1.16949i
$396$	5.13583	−	2.40797i	0.258085	−	0.121005i
$397$	−4.66293	+	9.68268i	−0.234026	+	0.485960i	−0.984599	−	0.174827i	$-0.944063\pi$
$397$	−4.66293	+	9.68268i	−0.234026	+	0.485960i	0.750573	+	0.660787i	$0.229778\pi$
$398$	22.7045	−	10.9339i	1.13807	−	0.548068i
$399$	30.7683	−	0.496538i	1.54034	−	0.0248580i
$400$	−6.50800	−	3.13409i	−0.325400	−	0.156704i
$401$	3.93361	−	3.13695i	0.196435	−	0.156652i	−0.520333	−	0.853964i	$-0.674192\pi$
$401$	3.93361	−	3.13695i	0.196435	−	0.156652i	0.716768	+	0.697312i	$0.245621\pi$
$402$	−13.4631	+	8.36236i	−0.671480	+	0.417076i
$403$	−3.11664	+	3.90815i	−0.155251	+	0.194679i
$404$	−3.67789	+	16.1139i	−0.182982	+	0.801695i
$405$	7.63671	−	30.5249i	0.379471	−	1.51680i
$406$	−1.20864	−	0.723962i	−0.0599839	−	0.0359297i
$407$	4.07176	−	3.24712i	0.201830	−	0.160954i
$408$	8.20714	−	5.09770i	0.406314	−	0.252374i
$409$	25.9226	+	5.91665i	1.28179	+	0.292560i	0.808577	−	0.588390i	$-0.200238\pi$
$409$	25.9226	+	5.91665i	1.28179	+	0.292560i	0.473210	+	0.880949i	$0.343095\pi$
$410$		−	6.26236i		−	0.309276i
$411$	1.21707	−	0.130741i	0.0600335	−	0.00644898i
$412$	0.104820	+	0.0239245i	0.00516411	+	0.00117867i
$413$	1.99359	−	2.08048i	0.0980983	−	0.102374i
$414$	7.63109	+	16.2759i	0.375048	+	0.799918i
$415$	12.3885	+	54.2775i	0.608127	+	2.66438i
$416$	−0.583508	−	0.731696i	−0.0286088	−	0.0358744i
$417$	7.85768	+	7.93962i	0.384792	+	0.388805i
$418$	−12.3783	+	2.82527i	−0.605444	+	0.138189i
$419$	1.32239	+	5.79375i	0.0646028	+	0.283043i	0.996903	−	0.0786423i	$-0.0250585\pi$
$419$	1.32239	+	5.79375i	0.0646028	+	0.283043i	−0.932300	+	0.361686i	$0.882201\pi$
$420$	15.6754	+	3.31263i	0.764879	+	0.161640i
$421$	0.130906	−	0.573538i	0.00637998	−	0.0279525i	−0.971638	−	0.236474i	$-0.924008\pi$
$421$	0.130906	−	0.573538i	0.00637998	−	0.0279525i	0.978018	+	0.208522i	$0.0668652\pi$
$422$		−	8.36766i		−	0.407331i
$423$	33.3109	−	7.24027i	1.61963	−	0.352034i
$424$	−1.24839	+	5.46957i	−0.0606274	+	0.265626i
$425$	36.3019	−	17.4821i	1.76090	−	0.848006i
$426$	7.20234	−	7.12801i	0.348955	−	0.345353i
$427$	11.4898	−	1.54334i	0.556032	−	0.0746876i
$428$	9.83286	+	7.84144i	0.475289	+	0.379030i
$429$	3.04381	+	0.358954i	0.146957	+	0.0173304i
$430$	−28.5645	−	22.7794i	−1.37750	−	1.09852i
$431$	−14.4900	−	30.0888i	−0.697958	−	1.44932i	−0.884338	−	0.466847i	$-0.845390\pi$
$431$	−14.4900	−	30.0888i	−0.697958	−	1.44932i	0.186380	−	0.982478i	$-0.440324\pi$
$432$	−2.83265	+	4.35616i	−0.136286	+	0.209586i
$433$	−14.3080	+	29.7109i	−0.687598	+	1.42781i	0.205821	+	0.978590i	$0.434013\pi$
$433$	−14.3080	+	29.7109i	−0.687598	+	1.42781i	−0.893420	+	0.449223i	$0.851701\pi$
$434$	−4.38189	+	13.4350i	−0.210337	+	0.644901i
$435$	2.73924	−	1.70142i	0.131336	−	0.0815769i
$436$	−3.70914	−	1.78623i	−0.177635	−	0.0855447i
$437$	−8.95354	−	39.2280i	−0.428306	−	1.87653i
$438$	0.752656	−	2.11570i	0.0359633	−	0.101092i
$439$	18.0534	+	14.3971i	0.861642	+	0.687136i	0.951110	−	0.308853i	$-0.0999453\pi$
$439$	18.0534	+	14.3971i	0.861642	+	0.687136i	−0.0894681	+	0.995990i	$0.528517\pi$
$440$	−6.61049			−0.315143
$441$	−20.9891	+	0.677619i	−0.999479	+	0.0322676i
$442$	5.22035			0.248307
$443$	19.7092	+	15.7176i	0.936414	+	0.746765i	0.967531	−	0.252751i	$-0.0813353\pi$
$443$	19.7092	+	15.7176i	0.936414	+	0.746765i	−0.0311178	+	0.999516i	$0.509907\pi$
$444$	−1.59903	+	4.49484i	−0.0758866	+	0.213316i
$445$	8.22292	+	36.0270i	0.389804	+	1.70784i
$446$	0.312544	+	0.150513i	0.0147994	+	0.00712700i
$447$	−15.8977	+	9.87455i	−0.751936	+	0.467050i
$448$	−2.26973	−	1.35954i	−0.107234	−	0.0642322i
$449$	−12.5440	+	26.0480i	−0.591990	+	1.22928i	0.362763	+	0.931881i	$0.381833\pi$
$449$	−12.5440	+	26.0480i	−0.591990	+	1.22928i	−0.954753	+	0.297399i	$0.903881\pi$
$450$	−13.6861	+	16.8012i	−0.645167	+	0.792017i
$451$	−1.46945	−	3.05135i	−0.0691938	−	0.143682i
$452$	−0.409927	−	0.326906i	−0.0192814	−	0.0153764i
$453$	5.18990	+	0.612040i	0.243843	+	0.0287561i
$454$	9.72247	+	7.75341i	0.456298	+	0.363886i
$455$	6.25047	+	5.98943i	0.293026	+	0.280789i
$456$	8.26680	−	8.18148i	0.387128	−	0.383133i
$457$	−1.14333	+	0.550596i	−0.0534825	+	0.0257558i	−0.460434	−	0.887694i	$-0.652306\pi$
$457$	−1.14333	+	0.550596i	−0.0534825	+	0.0257558i	0.406951	+	0.913450i	$0.366592\pi$
$458$	−0.802539	+	3.51615i	−0.0375002	+	0.164299i
$459$	−9.14607	−	27.5035i	−0.426902	−	1.28375i
$460$		−	20.9493i		−	0.976764i
$461$	−0.971716	+	4.25737i	−0.0452573	+	0.198285i	−0.992502	−	0.122225i	$-0.960997\pi$
$461$	−0.971716	+	4.25737i	−0.0452573	+	0.198285i	0.947245	+	0.320510i	$0.103854\pi$
$462$	8.41515	−	2.06411i	0.391508	−	0.0960310i
$463$	7.77329	+	34.0570i	0.361255	+	1.58276i	0.750013	+	0.661423i	$0.230047\pi$
$463$	7.77329	+	34.0570i	0.361255	+	1.58276i	−0.388758	+	0.921340i	$0.627096\pi$
$464$	−0.519155	+	0.118494i	−0.0241012	+	0.00550093i
$465$	−22.7518	−	22.9891i	−1.05509	−	1.06609i
$466$	7.97059	+	9.99481i	0.369231	+	0.463000i
$467$	−0.310204	−	1.35909i	−0.0143545	−	0.0628914i	0.967243	−	0.253851i	$-0.0816972\pi$
$467$	−0.310204	−	1.35909i	−0.0143545	−	0.0628914i	−0.981598	+	0.190959i	$0.938840\pi$
$468$	−2.54208	+	1.19187i	−0.117508	+	0.0550944i
$469$	−22.6752	+	8.48129i	−1.04704	+	0.391629i
$470$	−38.7308	−	8.84005i	−1.78652	−	0.407761i
$471$	−36.5186	+	3.92294i	−1.68269	+	0.180759i
$472$		−	1.08909i		−	0.0501294i
$473$	−19.2633	−	4.39672i	−0.885726	−	0.202161i
$474$	22.5442	−	14.0029i	1.03549	−	0.643175i
$475$	37.9229	−	30.2425i	1.74002	−	1.38762i
$476$	13.8228	−	5.17020i	0.633569	−	0.236976i
$477$	15.0874	+	7.45948i	0.690803	+	0.341546i
$478$	5.42678	−	23.7763i	0.248215	−	1.08750i
$479$	−17.4124	+	21.8344i	−0.795592	+	0.997641i	0.204233	+	0.978922i	$0.434530\pi$
$479$	−17.4124	+	21.8344i	−0.795592	+	0.997641i	−0.999825	+	0.0187185i	$0.994041\pi$
$480$	5.14405	−	3.19512i	0.234793	−	0.145837i
$481$	−2.01540	+	1.60723i	−0.0918942	+	0.0732832i
$482$	−0.720665	−	0.347054i	−0.0328254	−	0.0158079i
$483$	6.54135	+	26.6684i	0.297642	+	1.21345i
$484$	6.68968	−	3.22158i	0.304076	−	0.146436i
$485$	10.6617	−	22.1393i	0.484124	−	1.00529i
$486$	10.7332	+	11.3048i	0.486866	+	0.512798i
$487$	20.9148	+	10.0720i	0.947739	+	0.456407i	0.842893	−	0.538081i	$-0.180851\pi$
$487$	20.9148	+	10.0720i	0.947739	+	0.456407i	0.104846	+	0.994488i	$0.466565\pi$
$488$	2.73198	−	3.42579i	0.123671	−	0.155078i
$489$	−1.34039	−	12.4777i	−0.0606144	−	0.564259i
$490$	22.4824	+	9.66885i	1.01565	+	0.436794i
$491$		−	24.1230i		−	1.08865i	−0.838873	−	0.544327i	$-0.816785\pi$
$491$		−	24.1230i		−	1.08865i	0.838873	−	0.544327i	$-0.183215\pi$
$492$	2.61832	+	1.66420i	0.118043	+	0.0750281i
$493$	1.28878	−	2.67619i	0.0580439	−	0.120529i
$494$	6.12690	−	1.39842i	0.275662	−	0.0629181i
$495$	−4.61325	+	19.2874i	−0.207350	+	0.866906i
$496$	2.31747	+	4.81227i	0.104057	+	0.216077i
$497$	12.9277	−	8.51278i	0.579885	−	0.381850i
$498$	−25.9858	−	9.24441i	−1.16445	−	0.414252i
$499$	−16.0286	−	20.0992i	−0.717539	−	0.899765i	0.280657	−	0.959808i	$-0.409448\pi$
$499$	−16.0286	−	20.0992i	−0.717539	−	0.899765i	−0.998196	+	0.0600429i	$0.980876\pi$
$500$	7.00342	−	3.37267i	0.313203	−	0.150830i
$501$	−1.26334	−	0.802979i	−0.0564418	−	0.0358745i
$502$	−18.9018	−	4.31421i	−0.843629	−	0.192553i
$503$	−17.4154	+	21.8382i	−0.776512	+	0.973716i	−1.00000		0.000991148i	$-0.999685\pi$
$503$	−17.4154	+	21.8382i	−0.776512	+	0.973716i	0.223487	+	0.974707i	$0.428256\pi$
$504$	−5.55070	+	5.67360i	−0.247248	+	0.252722i
$505$	−36.0290	−	45.1789i	−1.60327	−	2.01043i
$506$	−4.91570	−	10.2076i	−0.218530	−	0.453782i
$507$	20.8551	+	2.45942i	0.926208	+	0.109227i
$508$	10.1438			0.450057
$509$	23.5371			1.04326			0.521631	−	0.853171i	$-0.325324\pi$
$509$	23.5371			1.04326			0.521631	+	0.853171i	$0.325324\pi$
$510$	−3.95602	+	33.5458i	−0.175176	+	1.48543i
$511$	1.76263	−	2.94268i	0.0779743	−	0.130177i
$512$	−0.974928	+	0.222521i	−0.0430861	+	0.00983413i
$513$	−18.1020	−	29.8296i	−0.799222	−	1.31701i
$514$	19.8107	−	15.7985i	0.873810	−	0.696841i
$515$	−0.293886	+	0.234367i	−0.0129502	+	0.0103274i
$516$	17.1151	−	5.88936i	0.753450	−	0.259265i
$517$	−20.9460	+	4.78078i	−0.921202	+	0.210258i
$518$	−3.74474	+	6.25178i	−0.164534	+	0.274687i
$519$	−37.5473	−	4.42791i	−1.64814	−	0.194364i
$520$	3.27199			0.143486
$521$	−8.87883			−0.388988			−0.194494	−	0.980904i	$-0.562307\pi$
$521$	−8.87883			−0.388988			−0.194494	+	0.980904i	$0.562307\pi$
$522$	−0.0165725	+	1.59743i	−0.000725358	+	0.0699177i
$523$	−1.67184	−	3.47161i	−0.0731044	−	0.151803i	0.861214	−	0.508243i	$-0.169705\pi$
$523$	−1.67184	−	3.47161i	−0.0731044	−	0.151803i	−0.934318	+	0.356440i	$0.883990\pi$
$524$	3.09279	+	3.87824i	0.135109	+	0.169422i
$525$	−25.5434	+	21.0534i	−1.11481	+	0.918844i
$526$	9.90957	−	12.4262i	0.432078	−	0.541808i
$527$	−29.0466	−	6.62969i	−1.26529	−	0.288794i
$528$	1.75672	−	2.76387i	0.0764513	−	0.120282i
$529$	11.6264	−	5.59899i	0.505497	−	0.243434i
$530$	−12.2294	−	15.3352i	−0.531211	−	0.666118i
$531$	−3.17764	−	0.760041i	−0.137898	−	0.0329830i
$532$	14.8383	−	9.77090i	0.643321	−	0.423622i
$533$	0.727335	+	1.51033i	0.0315044	+	0.0654195i
$534$	−17.2482	−	6.13602i	−0.746403	−	0.265531i
$535$	−42.8681	+	9.78436i	−1.85335	+	0.423015i
$536$	−3.97017	+	8.24415i	−0.171485	+	0.356093i
$537$	−4.58694	+	7.21671i	−0.197941	+	0.311424i
$538$			4.21137i			0.181565i
$539$	13.2234	−	0.564282i	0.569570	−	0.0243053i
$540$	−5.73254	−	17.2386i	−0.246689	−	0.741830i
$541$	−1.60716	+	2.01531i	−0.0690972	+	0.0866451i	−0.815179	−	0.579209i	$-0.803361\pi$
$541$	−1.60716	+	2.01531i	−0.0690972	+	0.0866451i	0.746082	+	0.665854i	$0.231933\pi$
$542$	−8.98667	−	4.32775i	−0.386011	−	0.185893i
$543$	−13.3886	−	38.9086i	−0.574559	−	1.66973i
$544$	2.42022	−	5.02564i	0.103766	−	0.215473i
$545$	12.9678	−	6.24498i	0.555481	−	0.267506i
$546$	−4.16525	+	1.02167i	−0.178256	+	0.0437235i
$547$	−2.74349	−	1.32120i	−0.117303	−	0.0564902i	0.374312	−	0.927303i	$-0.377879\pi$
$547$	−2.74349	−	1.32120i	−0.117303	−	0.0564902i	−0.491615	+	0.870813i	$0.663593\pi$
$548$	0.552534	−	0.440631i	0.0236031	−	0.0188228i
$549$	−8.08887	−	10.3618i	−0.345225	−	0.442233i
$550$	8.51542	−	10.6780i	0.363099	−	0.455311i
$551$	0.795694	−	3.48616i	0.0338977	−	0.148516i
$552$	8.75896	+	5.56720i	0.372806	+	0.236956i
$553$	37.9700	−	14.2021i	1.61465	−	0.603933i
$554$	−11.0361	+	8.80100i	−0.468879	+	0.373919i
$555$	−8.80070	−	14.1689i	−0.373569	−	0.601435i
$556$	6.28761	+	1.43511i	0.266654	+	0.0608620i
$557$		−	6.39084i		−	0.270789i	−0.990792	−	0.135394i	$-0.956770\pi$
$557$		−	6.39084i		−	0.270789i	0.990792	−	0.135394i	$-0.0432301\pi$
$558$	15.6581	−	3.40335i	0.662858	−	0.144075i
$559$	9.53474	+	2.17624i	0.403276	+	0.0920452i
$560$	8.66384	−	3.24056i	0.366114	−	0.136939i
$561$	5.94389	+	17.2735i	0.250951	+	0.729289i
$562$	−4.05386	−	17.7611i	−0.171002	−	0.749207i
$563$	6.82612	+	8.55968i	0.287686	+	0.360747i	0.904584	−	0.426296i	$-0.140182\pi$
$563$	6.82612	+	8.55968i	0.287686	+	0.360747i	−0.616897	+	0.787044i	$0.711611\pi$
$564$	13.9886	−	13.8443i	0.589028	−	0.582949i
$565$	1.78715	−	0.407906i	0.0751860	−	0.0171607i
$566$	−1.63897	−	7.18081i	−0.0688912	−	0.301832i
$567$	12.6802	+	20.1547i	0.532519	+	0.846418i
$568$	1.30184	−	5.70374i	0.0546240	−	0.239324i
$569$			36.1358i			1.51489i	0.652897	+	0.757447i	$0.273553\pi$
$569$			36.1358i			1.51489i	−0.652897	+	0.757447i	$0.726447\pi$
$570$	4.34322	+	40.4310i	0.181918	+	1.69347i
$571$	−7.19005	+	31.5016i	−0.300894	+	1.31830i	0.567887	+	0.823107i	$0.307761\pi$
$571$	−7.19005	+	31.5016i	−0.300894	+	1.31830i	−0.868781	+	0.495196i	$0.835096\pi$
$572$	1.59429	−	0.767768i	0.0666604	−	0.0321020i
$573$	19.6422	+	19.8470i	0.820564	+	0.829121i
$574$	3.42171	+	3.27881i	0.142819	+	0.136855i
$575$	33.8396	+	26.9861i	1.41121	+	1.12540i
$576$	−0.0311217	+	2.99984i	−0.00129674	+	0.124993i
$577$	10.6004	+	8.45354i	0.441300	+	0.351925i	0.818795	−	0.574087i	$-0.194643\pi$
$577$	10.6004	+	8.45354i	0.441300	+	0.351925i	−0.377494	+	0.926012i	$0.623214\pi$
$578$	6.12408	+	12.7168i	0.254728	+	0.528949i
$579$	−14.2804	+	14.1331i	−0.593475	+	0.587350i
$580$	0.807780	−	1.67737i	0.0335412	−	0.0696491i
$581$	−36.1431	−	21.6493i	−1.49947	−	0.898165i
$582$	6.42320	+	10.3412i	0.266250	+	0.428655i
$583$	−9.55717	−	4.60249i	−0.395818	−	0.190616i
$584$	−0.288497	−	1.26399i	−0.0119381	−	0.0523042i
$585$	2.28342	−	9.54670i	0.0944078	−	0.394707i
$586$	4.90177	+	3.90903i	0.202490	+	0.161481i
$587$	10.2207			0.421854			0.210927	−	0.977502i	$-0.432352\pi$
$587$	10.2207			0.421854			0.210927	+	0.977502i	$0.432352\pi$
$588$	−10.0172	+	6.83050i	−0.413102	+	0.281685i
$589$	−35.8667			−1.47786
$590$	2.97695	+	2.37404i	0.122559	+	0.0977376i
$591$	25.0318	+	8.90501i	1.02967	+	0.366303i
$592$	0.612916	+	2.68536i	0.0251907	+	0.110368i
$593$	7.72484	+	3.72009i	0.317221	+	0.152766i	0.585718	−	0.810515i	$-0.300813\pi$
$593$	7.72484	+	3.72009i	0.317221	+	0.152766i	−0.268497	+	0.963281i	$0.586527\pi$
$594$	−6.83819	−	7.05439i	−0.280574	−	0.289445i
$595$	−15.9992	+	49.0540i	−0.655902	+	2.01102i
$596$	−4.68811	+	9.73497i	−0.192033	+	0.398760i
$597$	−30.7032	−	31.0234i	−1.25660	−	1.26970i
$598$	2.43313	+	5.05244i	0.0994979	+	0.206610i
$599$	12.3013	+	9.80999i	0.502619	+	0.400825i	0.841711	−	0.539928i	$-0.181548\pi$
$599$	12.3013	+	9.80999i	0.502619	+	0.400825i	−0.339092	+	0.940753i	$0.610120\pi$
$600$	−1.46528	+	12.4251i	−0.0598197	+	0.507252i
$601$	−19.3083	−	15.3979i	−0.787603	−	0.628092i	0.144821	−	0.989458i	$-0.453739\pi$
$601$	−19.3083	−	15.3979i	−0.787603	−	0.628092i	−0.932424	+	0.361365i	$0.882311\pi$
$602$	27.4022	−	3.68073i	1.11683	−	0.150015i
$603$	21.2833	+	17.3371i	0.866723	+	0.706022i
$604$	2.71836	−	1.30909i	0.110609	−	0.0532663i
$605$	−5.77646	+	25.3083i	−0.234846	+	1.02893i
$606$	28.4641	−	3.05770i	1.15627	−	0.124210i
$607$		−	27.8162i		−	1.12903i	−0.825424	−	0.564513i	$-0.809064\pi$
$607$		−	27.8162i		−	1.12903i	0.825424	−	0.564513i	$-0.190936\pi$
$608$	1.49424	−	6.54671i	0.0605996	−	0.265504i
$609$	−0.504548	+	2.38752i	−0.0204453	+	0.0967472i
$610$	3.40889	+	14.9353i	0.138022	+	0.604714i
$611$	10.3676	−	2.36634i	0.419429	−	0.0957319i
$612$	−12.9743	−	10.5687i	−0.524456	−	0.427215i
$613$	9.11335	+	11.4278i	0.368085	+	0.461564i	0.931036	−	0.364926i	$-0.118906\pi$
$613$	9.11335	+	11.4278i	0.368085	+	0.461564i	−0.562952	+	0.826490i	$0.690334\pi$
$614$	−2.61423	−	11.4537i	−0.105502	−	0.462233i
$615$	−10.2565	+	3.52929i	−0.413582	+	0.142315i
$616$	3.46108	−	3.61193i	0.139451	−	0.145529i
$617$	23.6239	+	5.39201i	0.951063	+	0.217074i	0.669787	−	0.742553i	$-0.266385\pi$
$617$	23.6239	+	5.39201i	0.951063	+	0.217074i	0.281276	+	0.959627i	$0.409242\pi$
$618$	−0.0198902	−	0.185157i	−0.000800099	−	0.00744812i
$619$			28.5393i			1.14709i	0.819173	+	0.573546i	$0.194433\pi$
$619$			28.5393i			1.14709i	−0.819173	+	0.573546i	$0.805567\pi$
$620$	−18.2057	−	4.15534i	−0.731159	−	0.166882i
$621$	22.3560	−	21.6709i	0.897116	−	0.869621i
$622$	−25.2682	+	20.1507i	−1.01316	+	0.807971i
$623$	−23.9902	−	14.3698i	−0.961146	−	0.575715i
$624$	−0.869522	+	1.36803i	−0.0348087	+	0.0547651i
$625$	1.98935	−	8.71593i	0.0795742	−	0.348637i
$626$	2.40790	−	3.01941i	0.0962391	−	0.120680i
$627$	11.6033	+	18.6810i	0.463392	+	0.746046i
$628$	−16.5790	+	13.2213i	−0.661573	+	0.527587i
$629$	−13.8427	−	6.66631i	−0.551946	−	0.265803i
$630$	−3.40878	−	27.5400i	−0.135809	−	1.09722i
$631$	26.3497	−	12.6894i	1.04897	−	0.505156i	0.171695	−	0.985150i	$-0.445076\pi$
$631$	26.3497	−	12.6894i	1.04897	−	0.505156i	0.877272	+	0.479994i	$0.159361\pi$
$632$	6.64812	−	13.8050i	0.264448	−	0.549132i
$633$	−13.7045	+	4.71578i	−0.544707	+	0.187435i
$634$	10.0039	+	4.81761i	0.397304	+	0.191332i
$635$	−22.1118	+	27.7273i	−0.877480	+	1.10032i
$636$	9.66162	−	1.03788i	0.383108	−	0.0411547i
$637$	−6.54516	+	0.279303i	−0.259329	+	0.0110664i
$638$		−	1.00685i		−	0.0398614i
$639$	−15.7333	−	7.77884i	−0.622399	−	0.307726i
$640$	1.51694	−	3.14996i	0.0599623	−	0.124513i
$641$	−41.7094	+	9.51990i	−1.64742	+	0.376013i	−0.942745	−	0.333514i	$-0.891766\pi$
$641$	−41.7094	+	9.51990i	−1.64742	+	0.376013i	−0.704678	+	0.709528i	$0.748908\pi$
$642$	7.30118	−	20.5235i	0.288155	−	0.809997i
$643$	−2.21459	−	4.59865i	−0.0873350	−	0.181353i	0.852727	−	0.522357i	$-0.174947\pi$
$643$	−2.21459	−	4.59865i	−0.0873350	−	0.181353i	−0.940062	+	0.341004i	$0.889233\pi$
$644$	11.4465	+	10.9685i	0.451056	+	0.432219i
$645$	−21.2100	+	59.6208i	−0.835142	+	2.34757i
$646$	23.3540	+	29.2850i	0.918852	+	1.15220i
$647$	25.1785	−	12.1253i	0.989871	−	0.476697i	0.132382	−	0.991199i	$-0.457738\pi$
$647$	25.1785	−	12.1253i	0.989871	−	0.476697i	0.857489	+	0.514502i	$0.172023\pi$
$648$	8.73091	+	2.18430i	0.342983	+	0.0858073i
$649$	2.00759	+	0.458219i	0.0788047	+	0.0179867i
$650$	−4.21488	+	5.28529i	−0.165321	+	0.207306i
$651$	24.4734	−	0.394950i	0.959186	−	0.0154793i
$652$	−4.51745	−	5.66470i	−0.176917	−	0.221847i
$653$	−10.2505	−	21.2853i	−0.401131	−	0.832958i	−0.999496	−	0.0317341i	$-0.989897\pi$
$653$	−10.2505	−	21.2853i	−0.401131	−	0.832958i	0.598365	−	0.801224i	$-0.295817\pi$
$654$	−0.835112	+	7.08149i	−0.0326555	+	0.276908i
$655$	−17.3427			−0.677635
$656$	1.79120			0.0699345
$657$	−3.88927	−	0.0403491i	−0.151735	−	0.00157417i
$658$	25.1086	−	16.5338i	0.978834	−	0.644555i
$659$	−34.6272	+	7.90343i	−1.34888	+	0.307874i	−0.835124	−	0.550061i	$-0.814604\pi$
$659$	−34.6272	+	7.90343i	−1.34888	+	0.307874i	−0.513759	+	0.857935i	$0.671747\pi$
$660$	3.72549	+	10.8267i	0.145015	+	0.421427i
$661$	28.2365	−	22.5179i	1.09827	−	0.875844i	0.105330	−	0.994437i	$-0.466410\pi$
$661$	28.2365	−	22.5179i	1.09827	−	0.875844i	0.992943	+	0.118594i	$0.0378386\pi$
$662$	−8.95645	+	7.14253i	−0.348102	+	0.277602i
$663$	−2.94204	−	8.54988i	−0.114260	−	0.332050i
$664$	−15.5248	+	3.54343i	−0.602478	+	0.137512i
$665$	−5.63698	+	61.8584i	−0.218593	+	2.39877i
$666$	8.26281	+	0.0857222i	0.320177	+	0.00332167i
$667$	3.19079			0.123548
$668$	−0.864253			−0.0334390
$669$	0.0703693	−	0.596709i	0.00272063	−	0.0230701i
$670$	−13.8805	−	28.8231i	−0.536250	−	1.11353i
$671$	5.16554	+	6.47738i	0.199413	+	0.250057i
$672$	−0.947496	+	4.48355i	−0.0365505	+	0.172957i
$673$	18.7379	−	23.4966i	0.722294	−	0.905728i	−0.276171	−	0.961108i	$-0.589066\pi$
$673$	18.7379	−	23.4966i	0.722294	−	0.905728i	0.998465	+	0.0553805i	$0.0176372\pi$
$674$	13.5272	+	3.08749i	0.521048	+	0.118926i
$675$	35.2301	+	12.9463i	1.35601	+	0.498304i
$676$	10.9235	−	5.26047i	0.420134	−	0.202326i
$677$	20.0772	+	25.1760i	0.771630	+	0.967594i	0.999982	−	0.00598501i	$-0.00190510\pi$
$677$	20.0772	+	25.1760i	0.771630	+	0.967594i	−0.228352	+	0.973579i	$0.573334\pi$
$678$	−0.304383	+	0.855614i	−0.0116898	+	0.0328597i
$679$	6.51456	+	17.4171i	0.250006	+	0.668405i
$680$	8.46155	+	17.5706i	0.324486	+	0.673802i
$681$	7.21921	−	20.2931i	0.276641	−	0.777632i
$682$	−9.84582	+	2.24724i	−0.377016	+	0.0860514i
$683$	17.3665	−	36.0619i	0.664511	−	1.37987i	−0.247170	−	0.968972i	$-0.579501\pi$
$683$	17.3665	−	36.0619i	0.664511	−	1.37987i	0.911681	−	0.410899i	$-0.134785\pi$
$684$	−18.0586	−	8.92850i	−0.690486	−	0.341390i
$685$			2.47082i			0.0944050i
$686$	−17.0542	+	7.22185i	−0.651131	+	0.275732i
$687$	6.21104	−	0.667209i	0.236966	−	0.0254556i
$688$	6.51550	−	8.17018i	0.248401	−	0.311485i
$689$	4.73051	+	2.27809i	0.180218	+	0.0867885i
$690$	−34.3107	+	11.8064i	−1.30618	+	0.449463i
$691$	12.8577	−	26.6993i	0.489130	−	1.01569i	−0.499638	−	0.866234i	$-0.666534\pi$
$691$	12.8577	−	26.6993i	0.489130	−	1.01569i	0.988768	−	0.149455i	$-0.0477520\pi$
$692$	−19.6665	+	9.47088i	−0.747607	+	0.360029i
$693$	−8.12314	−	12.6190i	−0.308573	−	0.479358i
$694$	−19.8538	−	9.56109i	−0.753640	−	0.362934i
$695$	−17.6287	+	14.0584i	−0.668696	+	0.533267i
$696$	0.486650	+	0.783492i	0.0184464	+	0.0296982i
$697$	−6.22952	+	7.81157i	−0.235960	+	0.295884i
$698$	−0.632909	+	2.77295i	−0.0239559	+	0.104958i
$699$	11.8775	−	18.6870i	0.449248	−	0.706808i
$700$	−5.92596	+	18.1692i	−0.223980	+	0.686731i
$701$	−7.44619	+	5.93814i	−0.281239	+	0.224280i	−0.753942	−	0.656942i	$-0.771850\pi$
$701$	−7.44619	+	5.93814i	−0.281239	+	0.224280i	0.472703	+	0.881222i	$0.343278\pi$
$702$	3.38470	+	3.49171i	0.127747	+	0.131786i
$703$	−18.0324	−	4.11577i	−0.680104	−	0.155229i
$704$		−	1.89077i		−	0.0712611i
$705$	7.34938	+	68.4152i	0.276793	+	2.57667i
$706$	−9.91518	−	2.26308i	−0.373163	−	0.0851720i
$707$	43.5493	+	3.96852i	1.63784	+	0.149251i
$708$	−1.78371	+	0.613781i	−0.0670359	+	0.0230673i
$709$	9.17508	+	40.1987i	0.344577	+	1.50969i	0.789291	+	0.614020i	$0.210448\pi$
$709$	9.17508	+	40.1987i	0.344577	+	1.50969i	−0.444713	+	0.895673i	$0.646694\pi$
$710$	12.7530	+	15.9917i	0.478610	+	0.600159i
$711$	−35.6393	−	29.0313i	−1.33658	−	1.08876i
$712$	−10.3046	+	2.35197i	−0.386183	+	0.0881436i
$713$	−7.12172	−	31.2023i	−0.266710	−	1.16853i
$714$	−16.2579	−	19.7253i	−0.608438	−	0.738199i
$715$	−1.37665	+	6.03148i	−0.0514836	+	0.225565i
$716$			4.93697i			0.184503i
$717$	−41.9992	+	4.51168i	−1.56849	+	0.168492i
$718$	−1.01942	+	4.46637i	−0.0380444	+	0.166683i
$719$	13.2937	−	6.40189i	0.495770	−	0.238750i	−0.169254	−	0.985573i	$-0.554136\pi$
$719$	13.2937	−	6.40189i	0.495770	−	0.238750i	0.665024	+	0.746822i	$0.268421\pi$
$720$	−8.13201	−	6.62423i	−0.303062	−	0.246871i
$721$	0.0258150	−	0.283286i	0.000961401	−	0.0105501i
$722$	20.3997	+	16.2682i	0.759197	+	0.605440i
$723$	−0.162258	+	1.37589i	−0.00603443	+	0.0511701i
$724$	−18.5737	−	14.8120i	−0.690285	−	0.550484i
$725$	1.66892	+	3.46555i	0.0619822	+	0.128707i
$726$	−9.04642	−	9.14076i	−0.335744	−	0.339245i
$727$	4.49126	−	9.32620i	0.166572	−	0.345890i	−0.800929	−	0.598760i	$-0.795660\pi$
$727$	4.49126	−	9.32620i	0.166572	−	0.345890i	0.967500	+	0.252870i	$0.0813746\pi$
$728$	−1.71313	+	1.78779i	−0.0634929	+	0.0662601i
$729$	12.4662	−	23.9498i	0.461709	−	0.887031i
$730$	4.08390	+	1.96670i	0.151152	+	0.0727909i
$731$	12.9709	+	56.8294i	0.479748	+	2.10191i
$732$	−7.15042	−	2.54375i	−0.264287	−	0.0940196i
$733$	−25.1654	−	20.0687i	−0.929503	−	0.741254i	0.0366215	−	0.999329i	$-0.488340\pi$
$733$	−25.1654	−	20.0687i	−0.929503	−	0.741254i	−0.966125	+	0.258075i	$0.916912\pi$
$734$	−16.5337			−0.610268
$735$	3.16519	−	42.2707i	0.116750	−	1.55918i
$736$	5.99202			0.220869
$737$	−13.5266	−	10.7871i	−0.498258	−	0.397348i
$738$	1.25002	−	5.22618i	0.0460139	−	0.192378i
$739$	−0.272894	−	1.19563i	−0.0100386	−	0.0439818i	0.969661	−	0.244455i	$-0.0786091\pi$
$739$	−0.272894	−	1.19563i	−0.0100386	−	0.0439818i	−0.979699	+	0.200473i	$0.935752\pi$
$740$	−8.67630	−	4.17829i	−0.318947	−	0.153597i
$741$	−5.74329	−	9.24651i	−0.210985	−	0.339679i
$742$	14.7820	+	1.34704i	0.542665	+	0.0494515i
$743$	−3.78240	+	7.85423i	−0.138763	+	0.288144i	−0.958757	−	0.284229i	$-0.908263\pi$
$743$	−3.78240	+	7.85423i	−0.138763	+	0.288144i	0.819994	+	0.572372i	$0.193977\pi$
$744$	6.57547	−	6.50761i	0.241069	−	0.238581i
$745$	−16.3905	−	34.0353i	−0.600503	−	1.24696i
$746$	3.80750	+	3.03638i	0.139402	+	0.111170i
$747$	−0.495582	+	47.7695i	−0.0181324	+	1.74779i
$748$	8.24582	+	6.57582i	0.301497	+	0.240436i
$749$	17.0985	−	28.5457i	0.624766	−	1.04304i
$750$	−9.47069	−	9.56945i	−0.345821	−	0.349427i
$751$	−16.8476	+	8.11337i	−0.614777	+	0.296061i	−0.715239	−	0.698880i	$-0.753682\pi$
$751$	−16.8476	+	8.11337i	−0.614777	+	0.296061i	0.100462	+	0.994941i	$0.467968\pi$
$752$	2.52848	−	11.0780i	0.0922042	−	0.403973i
$753$	3.58672	+	33.3887i	0.130707	+	1.21675i
$754$			0.498359i			0.0181492i
$755$	−2.34727	+	10.2841i	−0.0854260	+	0.374276i
$756$	12.4204	+	5.89344i	0.451727	+	0.214342i
$757$	−3.31118	−	14.5072i	−0.120347	−	0.527274i	−0.998779	−	0.0494064i	$-0.984267\pi$
$757$	−3.31118	−	14.5072i	−0.120347	−	0.527274i	0.878432	−	0.477867i	$-0.158590\pi$
$758$	3.30219	−	0.753702i	0.119941	−	0.0273757i
$759$	−13.9476	+	13.8036i	−0.506265	+	0.501040i
$760$	14.6378	+	18.3552i	0.530968	+	0.665812i
$761$	−8.41521	−	36.8694i	−0.305051	−	1.33652i	−0.862396	−	0.506235i	$-0.831037\pi$
$761$	−8.41521	−	36.8694i	−0.305051	−	1.33652i	0.557345	−	0.830281i	$-0.311820\pi$
$762$	−5.71675	−	16.6135i	−0.207096	−	0.601842i
$763$	−3.37741	+	10.3552i	−0.122270	+	0.374885i
$764$	15.7174	+	3.58740i	0.568636	+	0.129788i
$765$	57.1708	−	12.4263i	2.06701	−	0.449275i
$766$			33.0386i			1.19373i
$767$	−0.993696	−	0.226805i	−0.0358803	−	0.00818944i
$768$	0.913887	+	1.47133i	0.0329771	+	0.0530920i
$769$	25.7798	−	20.5587i	0.929645	−	0.741367i	−0.0365092	−	0.999333i	$-0.511624\pi$
$769$	25.7798	−	20.5587i	0.929645	−	0.741367i	0.966154	+	0.257966i	$0.0830524\pi$
$770$	2.32835	+	17.3340i	0.0839080	+	0.624675i
$771$	−37.0395	−	23.5423i	−1.33394	−	0.847855i
$772$	−2.58123	+	11.3091i	−0.0929003	+	0.407023i
$773$	9.18431	−	11.5168i	0.330337	−	0.414229i	−0.588731	−	0.808329i	$-0.700372\pi$
$773$	9.18431	−	11.5168i	0.330337	−	0.414229i	0.919068	+	0.394100i	$0.128944\pi$
$774$	−19.2912	−	24.7120i	−0.693408	−	0.888255i
$775$	30.1642	−	24.0551i	1.08353	−	0.864086i
$776$	6.33241	+	3.04953i	0.227320	+	0.109472i
$777$	12.3496	+	2.60980i	0.443039	+	0.0936261i
$778$	−8.66545	+	4.17306i	−0.310672	+	0.149612i
$779$	−5.21876	+	10.8369i	−0.186981	+	0.388271i
$780$	−1.84401	−	5.35887i	−0.0660260	−	0.191878i
$781$	9.96634	+	4.79954i	0.356624	+	0.171741i
$782$	−20.8394	+	26.1318i	−0.745215	+	0.934470i
$783$	2.62561	−	0.873126i	0.0938318	−	0.0312030i
$784$	−2.76554	+	6.43054i	−0.0987693	+	0.229662i
$785$		−	74.1378i		−	2.64609i
$786$	4.60877	−	7.25105i	0.164389	−	0.258636i
$787$	18.5806	−	38.5829i	0.662325	−	1.37533i	−0.250954	−	0.967999i	$-0.580744\pi$
$787$	18.5806	−	38.5829i	0.662325	−	1.37533i	0.913280	−	0.407333i	$-0.133541\pi$
$788$	14.9548	−	3.41333i	0.532742	−	0.121595i
$789$	−25.9364	−	9.22682i	−0.923360	−	0.328483i
$790$	23.2431	+	48.2648i	0.826952	+	1.71718i
$791$	−0.712829	+	1.19006i	−0.0253453	+	0.0423135i
$792$	−5.51670	−	1.31951i	−0.196028	−	0.0468867i
$793$	−2.55679	−	3.20611i	−0.0907942	−	0.113852i
$794$	9.68268	−	4.66293i	0.343626	−	0.165481i
$795$	−18.2238	+	28.6718i	−0.646331	+	1.01688i
$796$	−24.5683	−	5.60755i	−0.870800	−	0.198754i
$797$	−15.6893	+	19.6738i	−0.555744	+	0.696881i	−0.977765	−	0.209705i	$-0.932750\pi$
$797$	−15.6893	+	19.6738i	−0.555744	+	0.696881i	0.422020	+	0.906586i	$0.361321\pi$
$798$	−24.3652	−	18.7955i	−0.862519	−	0.665354i
$799$	39.5185	+	49.5546i	1.39806	+	1.75312i
$800$	3.13409	+	6.50800i	0.110807	+	0.230093i
$801$	−0.328945	+	31.7072i	−0.0116227	+	1.12032i
$802$	−5.03127			−0.177660
$803$	2.45137			0.0865070
$804$	15.7397	+	1.85617i	0.555098	+	0.0654621i
$805$	−54.9332	+	7.37876i	−1.93614	+	0.260067i
$806$	4.87338	−	1.11232i	0.171658	−	0.0391797i
$807$	6.89737	−	2.37341i	0.242799	−	0.0835480i
$808$	12.9223	−	10.3052i	0.454606	−	0.362536i
$809$	20.2571	−	16.1545i	0.712202	−	0.567962i	−0.198962	−	0.980007i	$-0.563757\pi$
$809$	20.2571	−	16.1545i	0.712202	−	0.567962i	0.911163	+	0.412045i	$0.135185\pi$
$810$	−25.0026	+	19.1039i	−0.878502	+	0.671244i
$811$	9.44028	−	2.15468i	0.331493	−	0.0756612i	−0.0535350	−	0.998566i	$-0.517049\pi$
$811$	9.44028	−	2.15468i	0.331493	−	0.0756612i	0.385028	+	0.922905i	$0.374192\pi$
$812$	0.493572	+	1.31959i	0.0173210	+	0.0463086i
$813$	−2.02335	+	17.1574i	−0.0709620	+	0.601735i
$814$	−5.20797			−0.182539
$815$	25.3314			0.887319
$816$	−9.59497	−	1.13152i	−0.335891	−	0.0396113i
$817$	30.4469	+	63.2236i	1.06520	+	2.21191i
$818$	−16.5781	−	20.7883i	−0.579640	−	0.726845i
$819$	4.02071	+	6.24605i	0.140495	+	0.218255i
$820$	−3.90452	+	4.89611i	−0.136352	+	0.170980i
$821$	18.1075	+	4.13292i	0.631956	+	0.144240i	0.526488	−	0.850183i	$-0.323509\pi$
$821$	18.1075	+	4.13292i	0.631956	+	0.144240i	0.105468	+	0.994423i	$0.466366\pi$
$822$	−1.03306	−	0.656612i	−0.0360320	−	0.0229020i
$823$	−9.91019	+	4.77250i	−0.345448	+	0.166359i	−0.598560	−	0.801078i	$-0.704260\pi$
$823$	−9.91019	+	4.77250i	−0.345448	+	0.166359i	0.253112	+	0.967437i	$0.418546\pi$
$824$	−0.0670349	−	0.0840591i	−0.00233527	−	0.00292834i
$825$	−22.2875	−	7.92872i	−0.775950	−	0.276043i
$826$	−2.85581	+	0.383600i	−0.0993664	+	0.0133471i
$827$	3.97464	+	8.25342i	0.138212	+	0.287000i	0.958574	−	0.284845i	$-0.0919422\pi$
$827$	3.97464	+	8.25342i	0.138212	+	0.287000i	−0.820362	+	0.571845i	$0.806228\pi$
$828$	4.18164	−	17.4829i	0.145322	−	0.607574i
$829$	16.6757	−	3.80612i	0.579171	−	0.132192i	0.0771074	−	0.997023i	$-0.475432\pi$
$829$	16.6757	−	3.80612i	0.579171	−	0.132192i	0.502063	+	0.864831i	$0.332574\pi$
$830$	24.1558	−	50.1600i	0.838459	−	1.74108i
$831$	20.6339	+	13.1149i	0.715782	+	0.454952i
$832$			0.935874i			0.0324456i
$833$	−18.4260	−	34.4252i	−0.638423	−	1.19276i
$834$	−1.19311	−	11.1066i	−0.0413140	−	0.384591i
$835$	1.88393	−	2.36238i	0.0651962	−	0.0817534i
$836$	11.4393	+	5.50887i	0.395636	+	0.190528i
$837$	−14.3984	−	23.7267i	−0.497683	−	0.820116i
$838$	2.57846	−	5.35423i	0.0890715	−	0.184959i
$839$	−3.29152	+	1.58511i	−0.113636	+	0.0547242i	−0.489838	−	0.871813i	$-0.662944\pi$
$839$	−3.29152	+	1.58511i	−0.113636	+	0.0547242i	0.376202	+	0.926538i	$0.377230\pi$
$840$	−10.1901	−	12.3633i	−0.351592	−	0.426576i
$841$	−25.8726	−	12.4596i	−0.892159	−	0.429641i
$842$	−0.459942	+	0.366791i	−0.0158506	+	0.0126405i
$843$	−26.8045	+	16.6491i	−0.923195	+	0.573424i
$844$	−5.21715	+	6.54210i	−0.179582	+	0.225188i
$845$	−9.43228	+	41.3255i	−0.324480	+	1.42164i
$846$	−30.5577	−	15.1083i	−1.05060	−	0.519435i
$847$	−10.8039	−	16.4070i	−0.371226	−	0.563751i
$848$	4.38626	−	3.49792i	0.150625	−	0.120119i
$849$	−10.8370	+	6.73122i	−0.371926	+	0.231015i
$850$	−39.2819	−	8.96583i	−1.34736	−	0.307526i
$851$		−	16.5045i		−	0.565769i
$852$	−10.0753	+	1.08232i	−0.345173	+	0.0370795i
$853$	15.3949	+	3.51378i	0.527111	+	0.120310i	0.477791	−	0.878473i	$-0.341438\pi$
$853$	15.3949	+	3.51378i	0.527111	+	0.120310i	0.0493196	+	0.998783i	$0.484295\pi$
$854$	−9.94537	−	5.95716i	−0.340324	−	0.203850i
$855$	63.7702	−	29.8991i	2.18089	−	1.02253i
$856$	−2.79858	−	12.2614i	−0.0956534	−	0.419085i
$857$	11.8969	+	14.9183i	0.406391	+	0.509598i	0.942342	−	0.334651i	$-0.108618\pi$
$857$	11.8969	+	14.9183i	0.406391	+	0.509598i	−0.535951	+	0.844249i	$0.680047\pi$
$858$	−2.15594	−	2.17843i	−0.0736027	−	0.0743703i
$859$	29.7891	−	6.79917i	1.01639	−	0.231985i	0.318298	−	0.947991i	$-0.396889\pi$
$859$	29.7891	−	6.79917i	1.01639	−	0.231985i	0.698094	+	0.716006i	$0.254032\pi$
$860$	8.12989	+	35.6194i	0.277227	+	1.21461i
$861$	3.44165	−	7.45192i	0.117291	−	0.253961i
$862$	−7.43131	+	32.5587i	−0.253111	+	1.10895i
$863$		−	2.81501i		−	0.0958240i	−0.998852	−	0.0479120i	$-0.984743\pi$
$863$		−	2.81501i		−	0.0958240i	0.998852	−	0.0479120i	$-0.0152567\pi$
$864$	4.93067	−	1.63966i	0.167745	−	0.0557822i
$865$	16.9818	−	74.4019i	0.577397	−	2.52974i
$866$	29.7109	−	14.3080i	1.00962	−	0.486205i
$867$	17.3762	−	17.1968i	0.590126	−	0.584036i
$868$	11.8025	−	7.77185i	0.400602	−	0.263794i
$869$	22.6505	+	18.0632i	0.768365	+	0.612751i
$870$	−3.20244	−	0.377660i	−0.108573	−	0.0128039i
$871$	6.69525	+	5.33928i	0.226860	+	0.180915i
$872$	1.78623	+	3.70914i	0.0604892	+	0.125607i
$873$	13.3168	−	16.3479i	0.450705	−	0.553293i
$874$	−17.4581	+	36.2522i	−0.590530	+	1.22625i
$875$	−11.3106	−	17.1765i	−0.382367	−	0.580670i
$876$	−1.90757	+	1.18485i	−0.0644508	+	0.0400323i
$877$	7.64504	+	3.68166i	0.258155	+	0.124321i	0.558485	−	0.829514i	$-0.311383\pi$
$877$	7.64504	+	3.68166i	0.258155	+	0.124321i	−0.300331	+	0.953835i	$0.597097\pi$
$878$	−5.13827	−	22.5122i	−0.173408	−	0.759750i
$879$	3.63971	−	10.2311i	0.122764	−	0.345088i
$880$	5.16829	+	4.12157i	0.174223	+	0.138938i
$881$	49.1472			1.65581			0.827905	−	0.560868i	$-0.189533\pi$
$881$	49.1472			1.65581			0.827905	+	0.560868i	$0.189533\pi$
$882$	16.8324	+	12.5567i	0.566776	+	0.422806i
$883$	12.3776			0.416540			0.208270	−	0.978071i	$-0.433217\pi$
$883$	12.3776			0.416540			0.208270	+	0.978071i	$0.433217\pi$
$884$	−4.08143	−	3.25483i	−0.137273	−	0.109472i
$885$	2.21047	−	6.21359i	0.0743042	−	0.208867i
$886$	−5.60954	−	24.5770i	−0.188456	−	0.825681i
$887$	−23.2903	−	11.2160i	−0.782011	−	0.376597i	−0.000110765	−	1.00000i	$-0.500035\pi$
$887$	−23.2903	−	11.2160i	−0.782011	−	0.376597i	−0.781901	+	0.623403i	$0.785750\pi$
$888$	4.05266	−	2.51723i	0.135998	−	0.0844726i
$889$	−3.57285	−	26.5990i	−0.119829	−	0.892103i
$890$	16.0335	−	33.2939i	0.537444	−	1.11601i
$891$	−7.69986	+	15.1752i	−0.257955	+	0.508390i
$892$	−0.150513	−	0.312544i	−0.00503955	−	0.0104647i
$893$	59.6558	+	47.5739i	1.99630	+	1.59200i
$894$	18.5860	+	2.19183i	0.621609	+	0.0733058i
$895$	−13.4949	−	10.7618i	−0.451083	−	0.359727i
$896$	0.926885	+	2.47808i	0.0309650	+	0.0827869i
$897$	6.90364	−	6.83239i	0.230506	−	0.228127i
$898$	26.0480	−	12.5440i	0.869233	−	0.418600i
$899$	0.632901	−	2.77292i	0.0211084	−	0.0924821i
$900$	21.1756	−	4.60261i	0.705853	−	0.153420i
$901$			31.2941i			1.04256i
$902$	−0.753621	+	3.30183i	−0.0250928	+	0.109939i
$903$	−21.4714	−	42.8049i	−0.714523	−	1.42446i
$904$	0.116671	+	0.511171i	0.00388044	+	0.0170013i
$905$	80.9752	−	18.4821i	2.69171	−	0.614365i
$906$	−3.67603	−	3.71436i	−0.122128	−	0.123401i
$907$	−20.8470	−	26.1414i	−0.692215	−	0.868010i	0.304200	−	0.952608i	$-0.401611\pi$
$907$	−20.8470	−	26.1414i	−0.692215	−	0.868010i	−0.996415	+	0.0845982i	$0.973039\pi$
$908$	−2.76716	−	12.1237i	−0.0918314	−	0.402340i
$909$	−21.0494	−	44.8952i	−0.698166	−	1.48908i
$910$	−1.15246	−	8.57983i	−0.0382038	−	0.284419i
$911$	−44.8646	−	10.2400i	−1.48643	−	0.339268i	−0.599201	−	0.800598i	$-0.704515\pi$
$911$	−44.8646	−	10.2400i	−1.48643	−	0.339268i	−0.887228	+	0.461330i	$0.847372\pi$
$912$	−11.5643	+	1.24227i	−0.382933	+	0.0411358i
$913$		−	30.1087i		−	0.996451i
$914$	1.23718	+	0.282378i	0.0409222	+	0.00934023i
$915$	22.5399	−	14.0002i	0.745147	−	0.462833i
$916$	2.81974	−	2.24866i	0.0931667	−	0.0742980i
$917$	9.08019	−	9.47593i	0.299854	−	0.312923i
$918$	−9.99747	+	27.2056i	−0.329966	+	0.897918i
$919$	−6.75190	+	29.5820i	−0.222724	+	0.975820i	0.732692	+	0.680560i	$0.238263\pi$
$919$	−6.75190	+	29.5820i	−0.222724	+	0.975820i	−0.955417	+	0.295260i	$0.904594\pi$
$920$	−13.0616	+	16.3788i	−0.430630	+	0.539992i
$921$	−17.2855	+	10.7366i	−0.569578	+	0.353782i
$922$	3.41414	−	2.72269i	0.112439	−	0.0896670i
$923$	−4.93304	−	2.37563i	−0.162373	−	0.0781947i
$924$	−7.86618	−	3.63297i	−0.258778	−	0.119516i
$925$	17.9258	−	8.63259i	0.589396	−	0.283838i
$926$	15.1568	−	31.4734i	0.498083	−	1.03428i
$927$	−0.292041	+	0.136926i	−0.00959188	+	0.00449723i
$928$	0.479771	+	0.231046i	0.0157493	+	0.00758445i
$929$	−1.04602	+	1.31166i	−0.0343187	+	0.0430342i	−0.798695	−	0.601737i	$-0.794476\pi$
$929$	−1.04602	+	1.31166i	−0.0343187	+	0.0430342i	0.764376	+	0.644771i	$0.223047\pi$
$930$	3.45463	+	32.1591i	0.113282	+	1.05454i
$931$	−30.8476	−	35.4675i	−1.01099	−	1.16240i
$932$		−	12.7838i		−	0.418748i
$933$	47.2433	+	30.0279i	1.54668	+	0.983069i
$934$	−0.604854	+	1.25599i	−0.0197914	+	0.0410973i
$935$	−35.9491	+	8.20515i	−1.17566	+	0.268337i
$936$	2.73060	+	0.653117i	0.0892525	+	0.0213478i
$937$	−14.8287	−	30.7920i	−0.484431	−	1.00593i	−0.989725	−	0.142984i	$-0.954330\pi$
$937$	−14.8287	−	30.7920i	−0.484431	−	1.00593i	0.505294	−	0.862947i	$-0.331384\pi$
$938$	23.0162	+	7.50683i	0.751506	+	0.245107i
$939$	−6.30222	−	2.24200i	−0.205665	−	0.0731650i
$940$	24.7693	+	31.0597i	0.807884	+	1.01305i
$941$	−7.21806	+	3.47603i	−0.235302	+	0.113315i	−0.547820	−	0.836596i	$-0.684542\pi$
$941$	−7.21806	+	3.47603i	−0.235302	+	0.113315i	0.312518	+	0.949912i	$0.398828\pi$
$942$	30.9973	+	19.7019i	1.00995	+	0.641922i
$943$	−10.4638	−	2.38829i	−0.340748	−	0.0777735i
$944$	−0.679036	+	0.851484i	−0.0221007	+	0.0277134i
$945$	−43.1839	+	21.1037i	−1.40477	+	0.686502i
$946$	12.3193	+	15.4479i	0.400536	+	0.502256i
$947$	−3.81956	−	7.93140i	−0.124119	−	0.257736i	0.829646	−	0.558290i	$-0.188543\pi$
$947$	−3.81956	−	7.93140i	−0.124119	−	0.257736i	−0.953765	+	0.300555i	$0.902828\pi$
$948$	−26.3565	−	3.10819i	−0.856018	−	0.100949i
$949$	−1.21335			−0.0393872
$950$	−48.5052			−1.57372
$951$	2.25237	−	19.0994i	0.0730381	−	0.619340i
$952$	−14.0307	−	4.57617i	−0.454738	−	0.148315i
$953$	5.81440	−	1.32710i	0.188347	−	0.0429889i	−0.127307	−	0.991863i	$-0.540633\pi$
$953$	5.81440	−	1.32710i	0.188347	−	0.0429889i	0.315654	+	0.948874i	$0.397776\pi$
$954$	−7.14486	−	15.2389i	−0.231324	−	0.493377i
$955$	−44.0673	+	35.1425i	−1.42599	+	1.13719i
$956$	−19.0671	+	15.2055i	−0.616674	+	0.491781i
$957$	−1.64901	+	0.567431i	−0.0533050	+	0.0183424i
$958$	27.2271	−	6.21441i	0.879668	−	0.200778i
$959$	−1.35004	−	1.29365i	−0.0435950	−	0.0417743i
$960$	−6.01390	−	0.709213i	−0.194098	−	0.0228898i
$961$	2.47138			0.0797219
$962$	2.57779			0.0831113
$963$	−37.7281	−	0.391408i	−1.21577	−	0.0126130i
$964$	0.347054	+	0.720665i	0.0111779	+	0.0232111i
$965$	−25.2860	−	31.7076i	−0.813984	−	1.02070i
$966$	11.5132	−	24.9286i	0.370432	−	0.802066i
$967$	2.27991	−	2.85892i	0.0733169	−	0.0919365i	−0.743820	−	0.668379i	$-0.766988\pi$
$967$	2.27991	−	2.85892i	0.0733169	−	0.0919365i	0.817137	+	0.576443i	$0.195560\pi$
$968$	−7.23883	−	1.65222i	−0.232665	−	0.0531042i
$969$	34.8013	−	54.7534i	1.11798	−	1.75893i
$970$	−22.1393	+	10.6617i	−0.710850	+	0.342327i
$971$	−20.4671	−	25.6649i	−0.656819	−	0.823625i	0.336174	−	0.941800i	$-0.390867\pi$
$971$	−20.4671	−	25.6649i	−0.656819	−	0.823625i	−0.992993	+	0.118175i	$0.962296\pi$
$972$	−1.34306	−	15.5305i	−0.0430788	−	0.498141i
$973$	1.54851	−	16.9929i	0.0496429	−	0.544766i
$974$	−10.0720	−	20.9148i	−0.322729	−	0.670153i
$975$	11.0316	+	3.92448i	0.353295	+	0.125684i
$976$	−4.27189	+	0.975031i	−0.136740	+	0.0312100i
$977$	−15.4660	+	32.1155i	−0.494801	+	1.02747i	0.492751	+	0.870171i	$0.335991\pi$
$977$	−15.4660	+	32.1155i	−0.494801	+	1.02747i	−0.987552	+	0.157295i	$0.949723\pi$
$978$	−6.73173	+	10.5911i	−0.215257	+	0.338667i
$979$		−	19.9848i		−	0.638716i
$980$	−11.5490	−	21.5769i	−0.368919	−	0.689250i
$981$	12.0687	−	2.62318i	0.385324	−	0.0837518i
$982$	−15.0404	+	18.8601i	−0.479959	+	0.601850i
$983$	−25.3959	−	12.2300i	−0.810002	−	0.390077i	−0.0174252	−	0.999848i	$-0.505547\pi$
$983$	−25.3959	−	12.2300i	−0.810002	−	0.390077i	−0.792577	+	0.609772i	$0.791261\pi$
$984$	−1.00947	−	2.93362i	−0.0321807	−	0.0935204i
$985$	−23.2689	+	48.3184i	−0.741409	+	1.53955i
$986$	−2.67619	+	1.28878i	−0.0852271	+	0.0410432i
$987$	−41.2295	−	31.8048i	−1.31235	−	1.01236i
$988$	−5.66211	−	2.72673i	−0.180136	−	0.0867487i
$989$	−48.9559	+	39.0411i	−1.55671	+	1.24143i
$990$	15.6323	−	12.2032i	0.496827	−	0.387843i
$991$	−1.69684	+	2.12777i	−0.0539018	+	0.0675907i	−0.808052	−	0.589112i	$-0.799478\pi$
$991$	−1.69684	+	2.12777i	−0.0539018	+	0.0675907i	0.754150	+	0.656702i	$0.228049\pi$
$992$	1.18853	−	5.20730i	0.0377360	−	0.165332i
$993$	16.7456	+	10.6435i	0.531407	+	0.337762i
$994$	−15.4149	−	1.40471i	−0.488931	−	0.0445548i
$995$	68.8827	−	54.9322i	2.18373	−	1.74147i
$996$	14.5528	+	23.4295i	0.461122	+	0.742391i
$997$	56.3565	+	12.8630i	1.78483	+	0.407375i	0.982007	−	0.188844i	$-0.0604741\pi$
$997$	56.3565	+	12.8630i	1.78483	+	0.407375i	0.802821	+	0.596220i	$0.203331\pi$
$998$			25.7079i			0.813769i
$999$	−4.51630	−	13.5811i	−0.142889	−	0.429688i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	294.2.j.a.251.4	yes	120
3.2	odd	2	inner	294.2.j.a.251.14	yes	120
49.41	odd	14	inner	294.2.j.a.41.14	yes	120
147.41	even	14	inner	294.2.j.a.41.4	✓	120

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
294.2.j.a.41.4	✓	120	147.41	even	14	inner
294.2.j.a.41.14	yes	120	49.41	odd	14	inner
294.2.j.a.251.4	yes	120	1.1	even	1	trivial
294.2.j.a.251.14	yes	120	3.2	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 294 = 2 \cdot 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	294.j (of order \(14\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.781831 - 0.623490i) q^{2} +(-0.580532 + 1.63186i) q^{3} +(0.222521 + 0.974928i) q^{4} +(-3.14996 - 1.51694i) q^{5} +(1.47133 - 0.913887i) q^{6} +(2.47808 - 0.926885i) q^{7} +(0.433884 - 0.900969i) q^{8} +(-2.32596 - 1.89470i) q^{9} +(1.51694 + 3.14996i) q^{10} +(1.47826 + 1.17888i) q^{11} +(-1.72013 - 0.202853i) q^{12} +(-0.731696 - 0.583508i) q^{13} +(-2.51534 - 0.820391i) q^{14} +(4.30409 - 4.25967i) q^{15} +(-0.900969 + 0.433884i) q^{16} +(1.24123 - 5.43819i) q^{17} +(0.637185 + 2.93155i) q^{18} -6.71507i q^{19} +(0.777975 - 3.40853i) q^{20} +(0.0739439 + 4.58198i) q^{21} +(-0.420736 - 1.84336i) q^{22} +(5.84179 - 1.33335i) q^{23} +(1.21838 + 1.23108i) q^{24} +(4.50368 + 5.64743i) q^{25} +(0.208252 + 0.912410i) q^{26} +(4.44219 - 2.69572i) q^{27} +(1.45507 + 2.20970i) q^{28} +(0.519155 + 0.118494i) q^{29} +(-6.02094 + 0.646788i) q^{30} -5.34122i q^{31} +(0.974928 + 0.222521i) q^{32} +(-2.78195 + 1.72795i) q^{33} +(-4.36109 + 3.47785i) q^{34} +(-9.21188 - 0.839452i) q^{35} +(1.32962 - 2.68926i) q^{36} +(0.612916 - 2.68536i) q^{37} +(-4.18678 + 5.25005i) q^{38} +(1.37698 - 0.855284i) q^{39} +(-2.73343 + 2.17984i) q^{40} +(-1.61381 - 0.777171i) q^{41} +(2.79901 - 3.62844i) q^{42} +(-9.41518 + 4.53411i) q^{43} +(-0.820375 + 1.70353i) q^{44} +(4.45254 + 9.49657i) q^{45} +(-5.39863 - 2.59984i) q^{46} +(-7.08465 + 8.88387i) q^{47} +(-0.184998 - 1.72214i) q^{48} +(5.28177 - 4.59379i) q^{49} -7.22334i q^{50} +(8.15381 + 5.18257i) q^{51} +(0.406061 - 0.843194i) q^{52} +(-5.46957 + 1.24839i) q^{53} +(-5.15380 - 0.662060i) q^{54} +(-2.86818 - 5.95585i) q^{55} +(0.240105 - 2.63483i) q^{56} +(10.9581 + 3.89832i) q^{57} +(-0.332012 - 0.416330i) q^{58} +(0.981235 - 0.472538i) q^{59} +(5.11062 + 3.24831i) q^{60} +(4.27189 + 0.975031i) q^{61} +(-3.33020 + 4.17593i) q^{62} +(-7.52010 - 2.53932i) q^{63} +(-0.623490 - 0.781831i) q^{64} +(1.41966 + 2.94796i) q^{65} +(3.25237 + 0.383549i) q^{66} -9.15032 q^{67} +5.57804 q^{68} +(-1.21550 + 10.3071i) q^{69} +(6.67875 + 6.39982i) q^{70} +(5.70374 - 1.30184i) q^{71} +(-2.71626 + 1.27354i) q^{72} +(1.01364 - 0.808350i) q^{73} +(-2.15349 + 1.71735i) q^{74} +(-11.8304 + 4.07087i) q^{75} +(6.54671 - 1.49424i) q^{76} +(4.75594 + 1.55117i) q^{77} +(-1.60983 - 0.189845i) q^{78} +15.3224 q^{79} +3.49619 q^{80} +(1.82022 + 8.81401i) q^{81} +(0.777171 + 1.61381i) q^{82} +(-9.92846 - 12.4499i) q^{83} +(-4.45065 + 1.09168i) q^{84} +(-12.1592 + 15.2472i) q^{85} +(10.1881 + 2.32536i) q^{86} +(-0.494752 + 0.778401i) q^{87} +(1.70353 - 0.820375i) q^{88} +(-6.59006 - 8.26368i) q^{89} +(2.43988 - 10.2008i) q^{90} +(-2.35405 - 0.767783i) q^{91} +(2.59984 + 5.39863i) q^{92} +(8.71615 + 3.10075i) q^{93} +(11.0780 - 2.52848i) q^{94} +(-10.1864 + 21.1522i) q^{95} +(-0.929101 + 1.46177i) q^{96} +7.02844i q^{97} +(-6.99364 + 0.298440i) q^{98} +(-1.20477 - 5.54289i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 120 q + 20 q^{4} - 14 q^{6} + 4 q^{7} - 10 q^{9} + 12 q^{15} - 20 q^{16} - 8 q^{18} - 12 q^{21} - 10 q^{22} - 24 q^{25} + 42 q^{27} - 4 q^{28} + 8 q^{30} + 10 q^{36} - 58 q^{37} + 8 q^{39} - 14 q^{40} - 2 q^{42}+ \cdots - 224 q^{99}+O(q^{100}) \) 120 * q + 20 * q^4 - 14 * q^6 + 4 * q^7 - 10 * q^9 + 12 * q^15 - 20 * q^16 - 8 * q^18 - 12 * q^21 - 10 * q^22 - 24 * q^25 + 42 * q^27 - 4 * q^28 + 8 * q^30 + 10 * q^36 - 58 * q^37 + 8 * q^39 - 14 * q^40 - 2 * q^42 - 12 * q^43 + 14 * q^45 - 60 * q^46 - 36 * q^49 - 24 * q^51 - 42 * q^52 - 14 * q^55 + 34 * q^57 + 50 * q^58 - 12 * q^60 - 154 * q^61 + 20 * q^64 - 28 * q^67 + 28 * q^69 - 38 * q^70 + 8 * q^72 - 84 * q^75 - 16 * q^78 + 16 * q^79 + 22 * q^81 - 30 * q^84 - 32 * q^85 - 56 * q^87 - 4 * q^88 - 42 * q^90 + 88 * q^91 + 14 * q^93 + 112 * q^94 - 224 * q^99

Introduction

L-functions

Modular forms

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