LMFDB - Embedded newform 294.2.j.a.41.16

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			41.16
Character	$\chi$	$=$	294.41
Dual form			294.2.j.a.251.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.781831 - 0.623490i) q^{2} +(0.351758 - 1.69596i) q^{3} +(0.222521 - 0.974928i) q^{4} +(-0.415766 + 0.200223i) q^{5} +(-0.782396 - 1.54527i) q^{6} +(-2.57018 - 0.627843i) q^{7} +(-0.433884 - 0.900969i) q^{8} +(-2.75253 - 1.19313i) q^{9} +O(q^{10})$	\(q+(0.781831 - 0.623490i) q^{2} +(0.351758 - 1.69596i) q^{3} +(0.222521 - 0.974928i) q^{4} +(-0.415766 + 0.200223i) q^{5} +(-0.782396 - 1.54527i) q^{6} +(-2.57018 - 0.627843i) q^{7} +(-0.433884 - 0.900969i) q^{8} +(-2.75253 - 1.19313i) q^{9} +(-0.200223 + 0.415766i) q^{10} +(2.98244 - 2.37842i) q^{11} +(-1.57516 - 0.720324i) q^{12} +(2.23965 - 1.78606i) q^{13} +(-2.40090 + 1.11161i) q^{14} +(0.193320 + 0.775551i) q^{15} +(-0.900969 - 0.433884i) q^{16} +(-1.05109 - 4.60514i) q^{17} +(-2.89592 + 0.783349i) q^{18} +7.86219i q^{19} +(0.102686 + 0.449896i) q^{20} +(-1.96887 + 4.13806i) q^{21} +(0.848848 - 3.71905i) q^{22} +(6.27080 + 1.43127i) q^{23} +(-1.68063 + 0.418925i) q^{24} +(-2.98468 + 3.74267i) q^{25} +(0.637438 - 2.79280i) q^{26} +(-2.99172 + 4.24848i) q^{27} +(-1.18402 + 2.36603i) q^{28} +(8.41735 - 1.92120i) q^{29} +(0.634692 + 0.485818i) q^{30} +2.28828i q^{31} +(-0.974928 + 0.222521i) q^{32} +(-2.98460 - 5.89472i) q^{33} +(-3.69304 - 2.94510i) q^{34} +(1.19430 - 0.253572i) q^{35} +(-1.77571 + 2.41802i) q^{36} +(-1.70432 - 7.46711i) q^{37} +(4.90199 + 6.14691i) q^{38} +(-2.24127 - 4.42661i) q^{39} +(0.360789 + 0.287719i) q^{40} +(-3.55254 + 1.71081i) q^{41} +(1.04071 + 4.46284i) q^{42} +(9.76045 + 4.70038i) q^{43} +(-1.65513 - 3.43692i) q^{44} +(1.38330 - 0.0550556i) q^{45} +(5.79509 - 2.79077i) q^{46} +(-3.02912 - 3.79839i) q^{47} +(-1.05277 + 1.37538i) q^{48} +(6.21163 + 3.22734i) q^{49} +4.78705i q^{50} +(-8.17985 + 0.162715i) q^{51} +(-1.24291 - 2.58093i) q^{52} +(0.115863 + 0.0264450i) q^{53} +(0.309864 + 5.18691i) q^{54} +(-0.763787 + 1.58602i) q^{55} +(0.549491 + 2.58806i) q^{56} +(13.3339 + 2.76558i) q^{57} +(5.38309 - 6.75019i) q^{58} +(5.93818 + 2.85967i) q^{59} +(0.799124 - 0.0158963i) q^{60} +(-1.62969 + 0.371966i) q^{61} +(1.42672 + 1.78905i) q^{62} +(6.32540 + 4.79472i) q^{63} +(-0.623490 + 0.781831i) q^{64} +(-0.573561 + 1.19101i) q^{65} +(-6.00875 - 2.74781i) q^{66} -3.96394 q^{67} -4.72357 q^{68} +(4.63317 - 10.1315i) q^{69} +(0.775644 - 0.942885i) q^{70} +(0.892081 + 0.203612i) q^{71} +(0.119306 + 2.99763i) q^{72} +(-5.38845 - 4.29715i) q^{73} +(-5.98816 - 4.77540i) q^{74} +(5.29751 + 6.37839i) q^{75} +(7.66507 + 1.74950i) q^{76} +(-9.15868 + 4.24045i) q^{77} +(-4.51224 - 2.06345i) q^{78} -0.975332 q^{79} +0.461466 q^{80} +(6.15288 + 6.56826i) q^{81} +(-1.71081 + 3.55254i) q^{82} +(-8.84503 + 11.0913i) q^{83} +(3.59619 + 2.84031i) q^{84} +(1.35906 + 1.70421i) q^{85} +(10.5617 - 2.41063i) q^{86} +(-0.297413 - 14.9512i) q^{87} +(-3.43692 - 1.65513i) q^{88} +(5.73296 - 7.18891i) q^{89} +(1.04718 - 0.905519i) q^{90} +(-6.87766 + 3.18434i) q^{91} +(2.79077 - 5.79509i) q^{92} +(3.88082 + 0.804920i) q^{93} +(-4.73652 - 1.08108i) q^{94} +(-1.57419 - 3.26883i) q^{95} +(0.0344474 + 1.73171i) q^{96} +14.5946i q^{97} +(6.86866 - 1.34965i) q^{98} +(-11.0470 + 2.98823i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 120 q + 20 q^{4} - 14 q^{6} + 4 q^{7} - 10 q^{9}+O(q^{10}) $ 120 * q + 20 * q^4 - 14 * q^6 + 4 * q^7 - 10 * q^9	$ 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}+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

Display 100 coefficients 10 coefficients

Character values

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

$n$	$197$	$199$
$\chi(n)$	$-1$	$e\left(\frac{5}{14}\right)$

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
$3$	0.351758	−	1.69596i	0.203087	−	0.979161i
$3$	0.351758	−	1.69596i	0.203087	−	0.979161i
$4$	0.222521	−	0.974928i	0.111260	−	0.487464i
$5$	−0.415766	+	0.200223i	−0.185936	+	0.0895423i	−0.524536	−	0.851388i	$-0.675761\pi$
$5$	−0.415766	+	0.200223i	−0.185936	+	0.0895423i	0.338599	+	0.940931i	$0.390047\pi$
$6$	−0.782396	−	1.54527i	−0.319412	−	0.630853i
$7$	−2.57018	−	0.627843i	−0.971436	−	0.237302i
$7$	−2.57018	−	0.627843i	−0.971436	−	0.237302i
$8$	−0.433884	−	0.900969i	−0.153401	−	0.318541i
$9$	−2.75253	−	1.19313i	−0.917511	−	0.397710i
$10$	−0.200223	+	0.415766i	−0.0633159	+	0.131477i
$11$	2.98244	−	2.37842i	0.899240	−	0.717120i	−0.0604524	−	0.998171i	$-0.519254\pi$
$11$	2.98244	−	2.37842i	0.899240	−	0.717120i	0.959693	+	0.281051i	$0.0906829\pi$
$12$	−1.57516	−	0.720324i	−0.454710	−	0.207940i
$13$	2.23965	−	1.78606i	0.621167	−	0.495364i	−0.261599	−	0.965177i	$-0.584250\pi$
$13$	2.23965	−	1.78606i	0.621167	−	0.495364i	0.882766	+	0.469813i	$0.155678\pi$
$14$	−2.40090	+	1.11161i	−0.641667	+	0.297091i
$15$	0.193320	+	0.775551i	0.0499149	+	0.200247i
$16$	−0.900969	−	0.433884i	−0.225242	−	0.108471i
$17$	−1.05109	−	4.60514i	−0.254928	−	1.11691i	−0.926596	−	0.376059i	$-0.877279\pi$
$17$	−1.05109	−	4.60514i	−0.254928	−	1.11691i	0.671668	−	0.740852i	$-0.265578\pi$
$18$	−2.89592	+	0.783349i	−0.682575	+	0.184637i
$19$			7.86219i			1.80371i	0.432039	+	0.901855i	$0.357794\pi$
$19$			7.86219i			1.80371i	−0.432039	+	0.901855i	$0.642206\pi$
$20$	0.102686	+	0.449896i	0.0229613	+	0.100600i
$21$	−1.96887	+	4.13806i	−0.429643	+	0.902999i
$22$	0.848848	−	3.71905i	0.180975	−	0.792903i
$23$	6.27080	+	1.43127i	1.30755	+	0.298440i	0.818849	−	0.574009i	$-0.194613\pi$
$23$	6.27080	+	1.43127i	1.30755	+	0.298440i	0.488704	+	0.872450i	$0.337470\pi$
$24$	−1.68063	+	0.418925i	−0.343056	+	0.0855127i
$25$	−2.98468	+	3.74267i	−0.596935	+	0.748533i
$26$	0.637438	−	2.79280i	0.125012	−	0.547712i
$27$	−2.99172	+	4.24848i	−0.575757	+	0.817621i
$28$	−1.18402	+	2.36603i	−0.223759	+	0.447138i
$29$	8.41735	−	1.92120i	1.56306	−	0.356759i	0.648503	−	0.761212i	$-0.275395\pi$
$29$	8.41735	−	1.92120i	1.56306	−	0.356759i	0.914559	+	0.404453i	$0.132538\pi$
$30$	0.634692	+	0.485818i	0.115878	+	0.0886978i
$31$			2.28828i			0.410987i	0.978658	+	0.205494i	$0.0658800\pi$
$31$			2.28828i			0.410987i	−0.978658	+	0.205494i	$0.934120\pi$
$32$	−0.974928	+	0.222521i	−0.172345	+	0.0393365i
$33$	−2.98460	−	5.89472i	−0.519552	−	1.02614i
$34$	−3.69304	−	2.94510i	−0.633351	−	0.505080i
$35$	1.19430	−	0.253572i	0.201874	−	0.0428614i
$36$	−1.77571	+	2.41802i	−0.295952	+	0.403004i
$37$	−1.70432	−	7.46711i	−0.280188	−	1.22759i	−0.897552	−	0.440908i	$-0.854657\pi$
$37$	−1.70432	−	7.46711i	−0.280188	−	1.22759i	0.617364	−	0.786678i	$-0.288201\pi$
$38$	4.90199	+	6.14691i	0.795208	+	0.997160i
$39$	−2.24127	−	4.42661i	−0.358890	−	0.708824i
$40$	0.360789	+	0.287719i	0.0570457	+	0.0454924i
$41$	−3.55254	+	1.71081i	−0.554814	+	0.267184i	−0.690212	−	0.723607i	$-0.742483\pi$
$41$	−3.55254	+	1.71081i	−0.554814	+	0.267184i	0.135398	+	0.990791i	$0.456769\pi$
$42$	1.04071	+	4.46284i	0.160585	+	0.688631i
$43$	9.76045	+	4.70038i	1.48845	+	0.716802i	0.988775	−	0.149409i	$-0.0477371\pi$
$43$	9.76045	+	4.70038i	1.48845	+	0.716802i	0.499679	+	0.866211i	$0.333451\pi$
$44$	−1.65513	−	3.43692i	−0.249520	−	0.518134i
$45$	1.38330	−	0.0550556i	0.206211	−	0.00820720i
$46$	5.79509	−	2.79077i	0.854440	−	0.411477i
$47$	−3.02912	−	3.79839i	−0.441842	−	0.554052i	0.510186	−	0.860064i	$-0.329577\pi$
$47$	−3.02912	−	3.79839i	−0.441842	−	0.554052i	−0.952028	+	0.306012i	$0.901005\pi$
$48$	−1.05277	+	1.37538i	−0.151954	+	0.198519i
$49$	6.21163	+	3.22734i	0.887375	+	0.461048i
$50$			4.78705i			0.676991i
$51$	−8.17985	+	0.162715i	−1.14541	+	0.0227847i
$52$	−1.24291	−	2.58093i	−0.172361	−	0.357911i
$53$	0.115863	+	0.0264450i	0.0159150	+	0.00363250i	0.230471	−	0.973079i	$-0.425973\pi$
$53$	0.115863	+	0.0264450i	0.0159150	+	0.00363250i	−0.214556	+	0.976712i	$0.568830\pi$
$54$	0.309864	+	5.18691i	0.0421671	+	0.705848i
$55$	−0.763787	+	1.58602i	−0.102989	+	0.213859i
$56$	0.549491	+	2.58806i	0.0734289	+	0.345844i
$57$	13.3339	+	2.76558i	1.76612	+	0.366311i
$58$	5.38309	−	6.75019i	0.706835	−	0.886343i
$59$	5.93818	+	2.85967i	0.773085	+	0.372298i	0.778465	−	0.627688i	$-0.215998\pi$
$59$	5.93818	+	2.85967i	0.773085	+	0.372298i	−0.00538074	+	0.999986i	$0.501713\pi$
$60$	0.799124	−	0.0158963i	0.103167	−	0.00205221i
$61$	−1.62969	+	0.371966i	−0.208660	+	0.0476254i	−0.325573	−	0.945517i	$-0.605557\pi$
$61$	−1.62969	+	0.371966i	−0.208660	+	0.0476254i	0.116913	+	0.993142i	$0.462700\pi$
$62$	1.42672	+	1.78905i	0.181194	+	0.227210i
$63$	6.32540	+	4.79472i	0.796926	+	0.604078i
$64$	−0.623490	+	0.781831i	−0.0779362	+	0.0977289i
$65$	−0.573561	+	1.19101i	−0.0711415	+	0.147727i
$66$	−6.00875	−	2.74781i	−0.739626	−	0.338232i
$67$	−3.96394			−0.484272			−0.242136	−	0.970242i	$-0.577848\pi$
$67$	−3.96394			−0.484272			−0.242136	+	0.970242i	$0.577848\pi$
$68$	−4.72357			−0.572817
$69$	4.63317	−	10.1315i	0.557769	−	1.21969i
$70$	0.775644	−	0.942885i	0.0927072	−	0.112696i
$71$	0.892081	+	0.203612i	0.105871	+	0.0241643i	0.275128	−	0.961408i	$-0.411280\pi$
$71$	0.892081	+	0.203612i	0.105871	+	0.0241643i	−0.169257	+	0.985572i	$0.554137\pi$
$72$	0.119306	+	2.99763i	0.0140603	+	0.353274i
$73$	−5.38845	−	4.29715i	−0.630671	−	0.502943i	0.255192	−	0.966890i	$-0.417861\pi$
$73$	−5.38845	−	4.29715i	−0.630671	−	0.502943i	−0.885863	+	0.463947i	$0.846433\pi$
$74$	−5.98816	−	4.77540i	−0.696109	−	0.555129i
$75$	5.29751	+	6.37839i	0.611704	+	0.736513i
$76$	7.66507	+	1.74950i	0.879243	+	0.200682i
$77$	−9.15868	+	4.24045i	−1.04373	+	0.483245i
$78$	−4.51224	−	2.06345i	−0.510910	−	0.233640i
$79$	−0.975332			−0.109733			−0.0548667	−	0.998494i	$-0.517473\pi$
$79$	−0.975332			−0.109733			−0.0548667	+	0.998494i	$0.517473\pi$
$80$	0.461466			0.0515935
$81$	6.15288	+	6.56826i	0.683653	+	0.729807i
$82$	−1.71081	+	3.55254i	−0.188928	+	0.392313i
$83$	−8.84503	+	11.0913i	−0.970868	+	1.21743i	0.00520460	+	0.999986i	$0.498343\pi$
$83$	−8.84503	+	11.0913i	−0.970868	+	1.21743i	−0.976073	+	0.217444i	$0.930228\pi$
$84$	3.59619	+	2.84031i	0.392377	+	0.309904i
$85$	1.35906	+	1.70421i	0.147411	+	0.184848i
$86$	10.5617	−	2.41063i	1.13889	−	0.259945i
$87$	−0.297413	−	14.9512i	−0.0318860	−	1.60294i
$88$	−3.43692	−	1.65513i	−0.366376	−	0.176438i
$89$	5.73296	−	7.18891i	0.607693	−	0.762023i	−0.378862	−	0.925453i	$-0.623684\pi$
$89$	5.73296	−	7.18891i	0.607693	−	0.762023i	0.986555	+	0.163430i	$0.0522559\pi$
$90$	1.04718	−	0.905519i	0.110383	−	0.0954501i
$91$	−6.87766	+	3.18434i	−0.720975	+	0.333810i
$92$	2.79077	−	5.79509i	0.290958	−	0.604180i
$93$	3.88082	+	0.804920i	0.402423	+	0.0834663i
$94$	−4.73652	−	1.08108i	−0.488534	−	0.111505i
$95$	−1.57419	−	3.26883i	−0.161508	−	0.335375i
$96$	0.0344474	+	1.73171i	0.00351578	+	0.176742i
$97$			14.5946i			1.48186i	0.671584	+	0.740929i	$0.265614\pi$
$97$			14.5946i			1.48186i	−0.671584	+	0.740929i	$0.734386\pi$
$98$	6.86866	−	1.34965i	0.693839	−	0.136335i
$99$	−11.0470	+	2.98823i	−1.11027	+	0.300329i
$100$	2.98468	+	3.74267i	0.298468	+	0.374267i
$101$	−7.45960	+	3.59235i	−0.742258	+	0.357452i	−0.766492	−	0.642254i	$-0.778000\pi$
$101$	−7.45960	+	3.59235i	−0.742258	+	0.357452i	0.0242343	+	0.999706i	$0.492285\pi$
$102$	−6.29381	+	5.22727i	−0.623180	+	0.517577i
$103$	−6.00798	−	12.4757i	−0.591984	−	1.22927i	−0.954756	−	0.297389i	$-0.903884\pi$
$103$	−6.00798	−	12.4757i	−0.591984	−	1.22927i	0.362773	−	0.931878i	$-0.381830\pi$
$104$	−2.58093	−	1.24291i	−0.253081	−	0.121877i
$105$	−0.00994134	−	2.11468i	−0.000970175	−	0.206372i
$106$	0.107074	−	0.0515640i	0.0103999	−	0.00500834i
$107$	10.7510	+	8.57360i	1.03933	+	0.828842i	0.985494	−	0.169708i	$-0.0542824\pi$
$107$	10.7510	+	8.57360i	1.03933	+	0.828842i	0.0538401	+	0.998550i	$0.482854\pi$
$108$	3.47624	+	3.86209i	0.334502	+	0.371630i
$109$	−8.04399	−	10.0868i	−0.770475	−	0.966145i	0.229500	−	0.973309i	$-0.426291\pi$
$109$	−8.04399	−	10.0868i	−0.770475	−	0.966145i	−0.999974	+	0.00716406i	$0.997720\pi$
$110$	0.391714	+	1.71621i	0.0373485	+	0.163634i
$111$	−13.2634	+	0.263838i	−1.25891	+	0.0250424i
$112$	2.04324	+	1.68083i	0.193068	+	0.158823i
$113$	1.88827	+	1.50585i	0.177634	+	0.141658i	0.708271	−	0.705941i	$-0.249476\pi$
$113$	1.88827	+	1.50585i	0.177634	+	0.141658i	−0.530637	+	0.847599i	$0.678047\pi$
$114$	12.1492	−	6.15135i	1.13788	−	0.576126i
$115$	−2.89376	+	0.660482i	−0.269845	+	0.0615903i
$116$		−	8.63381i		−	0.801629i
$117$	−8.29571	+	2.24400i	−0.766939	+	0.207458i
$118$	6.42563	−	1.46661i	0.591527	−	0.135012i
$119$	−0.189809	+	12.4960i	−0.0173998	+	1.14550i
$120$	0.614869	−	0.510674i	0.0561296	−	0.0466180i
$121$	0.790360	−	3.46279i	0.0718509	−	0.314799i
$122$	−1.04223	+	1.30691i	−0.0943587	+	0.118322i
$123$	1.65183	+	6.62675i	0.148941	+	0.597514i
$124$	2.23091	+	0.509190i	0.200342	+	0.0457266i
$125$	1.00499	−	4.40315i	0.0898892	−	0.393830i
$126$	7.93485	−	0.195162i	0.706893	−	0.0173864i
$127$	0.551916	+	2.41810i	0.0489746	+	0.214572i	0.993494	−	0.113884i	$-0.0363291\pi$
$127$	0.551916	+	2.41810i	0.0489746	+	0.214572i	−0.944519	+	0.328455i	$0.893472\pi$
$128$			1.00000i			0.0883883i
$129$	11.4050	−	14.8999i	1.00415	−	1.31186i
$130$	0.294156	+	1.28878i	0.0257992	+	0.113034i
$131$	−7.03006	−	3.38550i	−0.614220	−	0.295793i	0.100789	−	0.994908i	$-0.467863\pi$
$131$	−7.03006	−	3.38550i	−0.614220	−	0.295793i	−0.715009	+	0.699115i	$0.753577\pi$
$132$	−6.41106	+	1.59807i	−0.558011	+	0.139094i
$133$	4.93622	−	20.2072i	0.428025	−	1.75219i
$134$	−3.09913	+	2.47148i	−0.267724	+	0.213503i
$135$	0.393215	−	2.36539i	0.0338426	−	0.203580i
$136$	−3.69304	+	2.94510i	−0.316675	+	0.252540i
$137$	4.59598	−	9.54365i	0.392661	−	0.815369i	−0.607123	−	0.794608i	$-0.707677\pi$
$137$	4.59598	−	9.54365i	0.392661	−	0.815369i	0.999784	−	0.0207615i	$-0.00660908\pi$
$138$	−2.69456	−	10.8099i	−0.229376	−	0.920200i
$139$	−0.262752	−	0.545611i	−0.0222864	−	0.0462781i	0.889529	−	0.456880i	$-0.151033\pi$
$139$	−0.262752	−	0.545611i	−0.0222864	−	0.0462781i	−0.911815	+	0.410602i	$0.865319\pi$
$140$	0.0185433	−	1.22078i	0.00156719	−	0.103175i
$141$	−7.50742	+	3.80113i	−0.632239	+	0.320113i
$142$	0.824407	−	0.397013i	0.0691827	−	0.0333166i
$143$	2.43163	−	10.6536i	0.203343	−	0.890903i
$144$	1.96227	+	2.26925i	0.163522	+	0.189104i
$145$	−3.11498	+	2.48411i	−0.258685	+	0.206295i
$146$	−6.89209			−0.570393
$147$	7.65841	−	9.39940i	0.631655	−	0.775250i
$148$	−7.65914			−0.629578
$149$	−0.815837	+	0.650608i	−0.0668360	+	0.0532999i	−0.656338	−	0.754467i	$-0.727895\pi$
$149$	−0.815837	+	0.650608i	−0.0668360	+	0.0532999i	0.589502	+	0.807767i	$0.299324\pi$
$150$	8.11862	+	1.68388i	0.662883	+	0.137488i
$151$	−4.06723	+	17.8197i	−0.330987	+	1.45015i	0.486237	+	0.873827i	$0.338369\pi$
$151$	−4.06723	+	17.8197i	−0.330987	+	1.45015i	−0.817224	+	0.576321i	$0.804488\pi$
$152$	7.08359	−	3.41128i	0.574555	−	0.276691i
$153$	−2.60137	+	13.9299i	−0.210308	+	1.12617i
$154$	−4.51667	+	9.02567i	−0.363963	+	0.727309i
$155$	−0.458166	−	0.951390i	−0.0368007	−	0.0764175i
$156$	−4.81435	+	1.20006i	−0.385457	+	0.0960817i
$157$	−2.67207	+	5.54860i	−0.213254	+	0.442827i	−0.979966	−	0.199165i	$-0.936177\pi$
$157$	−2.67207	+	5.54860i	−0.213254	+	0.442827i	0.766712	+	0.641991i	$0.221891\pi$
$158$	−0.762545	+	0.608109i	−0.0606648	+	0.0483786i
$159$	0.0856054	−	0.187197i	0.00678895	−	0.0148457i
$160$	0.360789	−	0.287719i	0.0285228	−	0.0227462i
$161$	−15.2185	−	7.61570i	−1.19938	−	0.600201i
$162$	8.90576	+	1.29902i	0.699703	+	0.102061i
$163$	−11.2757	−	5.43007i	−0.883178	−	0.425316i	−0.0633939	−	0.997989i	$-0.520192\pi$
$163$	−11.2757	−	5.43007i	−0.883178	−	0.425316i	−0.819784	+	0.572672i	$0.805907\pi$
$164$	0.877406	+	3.84417i	0.0685139	+	0.300179i
$165$	2.42115	+	1.85324i	0.188486	+	0.144275i
$166$			14.1863i			1.10107i
$167$	−0.942554	−	4.12960i	−0.0729370	−	0.319558i	0.925277	−	0.379291i	$-0.123832\pi$
$167$	−0.942554	−	4.12960i	−0.0729370	−	0.319558i	−0.998214	+	0.0597332i	$0.980975\pi$
$168$	4.58253	−	0.0215429i	0.353549	−	0.00166207i
$169$	−1.06676	+	4.67377i	−0.0820582	+	0.359520i
$170$	2.12512	+	0.485044i	0.162989	+	0.0372012i
$171$	9.38062	−	21.6409i	0.717354	−	1.65492i
$172$	6.75444	−	8.46980i	0.515021	−	0.645816i
$173$	−0.742706	+	3.25401i	−0.0564669	+	0.247398i	−0.995282	−	0.0970236i	$-0.969068\pi$
$173$	−0.742706	+	3.25401i	−0.0564669	+	0.247398i	0.938815	+	0.344421i	$0.111925\pi$
$174$	−9.55448	−	11.5039i	−0.724323	−	0.872110i
$175$	10.0210	−	7.74541i	0.757513	−	0.585498i
$176$	−3.71905	+	0.848848i	−0.280334	+	0.0639843i
$177$	6.93868	−	9.06497i	0.521543	−	0.681365i
$178$		−	9.19496i		−	0.689191i
$179$	−21.7074	+	4.95458i	−1.62249	+	0.370323i	−0.934658	−	0.355547i	$-0.884295\pi$
$179$	−21.7074	+	4.95458i	−1.62249	+	0.370323i	−0.687832	+	0.725870i	$0.741438\pi$
$180$	0.254139	−	1.36087i	0.0189424	−	0.101433i
$181$	3.93065	+	3.13459i	0.292163	+	0.232992i	0.758591	−	0.651567i	$-0.225888\pi$
$181$	3.93065	+	3.13459i	0.292163	+	0.232992i	−0.466428	+	0.884559i	$0.654460\pi$
$182$	−3.39177	+	6.77777i	−0.251414	+	0.502402i
$183$	0.0575824	+	2.89472i	0.00425661	+	0.213984i
$184$	−1.43127	−	6.27080i	−0.105515	−	0.462290i
$185$	2.20368	+	2.76333i	0.162018	+	0.203164i
$186$	3.53601	−	1.79034i	0.259273	−	0.131274i
$187$	−14.0878	−	11.2346i	−1.03020	−	0.821558i
$188$	−4.37720	+	2.10795i	−0.319240	+	0.153738i
$189$	10.3566	−	9.04102i	0.753334	−	0.657638i
$190$	−3.26883	−	1.57419i	−0.237146	−	0.114204i
$191$	1.86656	+	3.87596i	0.135060	+	0.280455i	0.957519	−	0.288369i	$-0.0931130\pi$
$191$	1.86656	+	3.87596i	0.135060	+	0.280455i	−0.822460	+	0.568824i	$0.807399\pi$
$192$	1.10663	+	1.33243i	0.0798645	+	0.0961596i
$193$	4.68747	−	2.25737i	0.337412	−	0.162489i	−0.257504	−	0.966277i	$-0.582900\pi$
$193$	4.68747	−	2.25737i	0.337412	−	0.162489i	0.594915	+	0.803788i	$0.297186\pi$
$194$	9.09959	+	11.4105i	0.653312	+	0.819228i
$195$	1.81815	+	1.39168i	0.130200	+	0.0996604i
$196$	4.52864	−	5.33774i	0.323474	−	0.381267i
$197$		−	22.9212i		−	1.63307i	−0.577296	−	0.816535i	$-0.695892\pi$
$197$		−	22.9212i		−	1.63307i	0.577296	−	0.816535i	$-0.304108\pi$
$198$	−6.77379	+	9.22401i	−0.481392	+	0.655522i
$199$	7.26888	+	15.0940i	0.515277	+	1.06998i	0.982572	+	0.185882i	$0.0595143\pi$
$199$	7.26888	+	15.0940i	0.515277	+	1.06998i	−0.467295	+	0.884101i	$0.654771\pi$
$200$	4.66703	+	1.06522i	0.330009	+	0.0753223i
$201$	−1.39435	+	6.72267i	−0.0983496	+	0.474181i
$202$	−3.59235	+	7.45960i	−0.252757	+	0.524855i
$203$	−22.8403	−	0.346936i	−1.60307	−	0.0243501i
$204$	−1.66155	+	8.01097i	−0.116332	+	0.560880i
$205$	1.13448	−	1.42260i	0.0792358	−	0.0993586i
$206$	−12.4757	−	6.00798i	−0.869223	−	0.418596i
$207$	−15.5529	−	11.4215i	−1.08100	−	0.793850i
$208$	−2.79280	+	0.637438i	−0.193646	+	0.0441983i
$209$	18.6996	+	23.4485i	1.29348	+	1.62197i
$210$	−1.32625	−	1.64712i	−0.0915202	−	0.113662i
$211$	−2.72463	+	3.41658i	−0.187571	+	0.235207i	−0.866722	−	0.498792i	$-0.833777\pi$
$211$	−2.72463	+	3.41658i	−0.187571	+	0.235207i	0.679150	+	0.733999i	$0.262348\pi$
$212$	0.0515640	−	0.107074i	0.00354143	−	0.00735385i
$213$	0.659112	−	1.44131i	0.0451616	−	0.0987568i
$214$	13.7510			0.939999
$215$	−4.99919			−0.340942
$216$	5.12581	+	0.852100i	0.348767	+	0.0579781i
$217$	1.43668	−	5.88129i	0.0975283	−	0.399248i
$218$	−12.5781	−	2.87087i	−0.851896	−	0.194440i
$219$	−9.18320	+	7.62702i	−0.620543	+	0.515386i
$220$	1.37630	+	1.09756i	0.0927899	+	0.0739974i
$221$	−10.5791	−	8.43659i	−0.711630	−	0.567506i
$222$	−10.2052	+	8.47587i	−0.684931	+	0.568863i
$223$	6.45575	+	1.47348i	0.432309	+	0.0986717i	0.433137	−	0.901328i	$-0.357406\pi$
$223$	6.45575	+	1.47348i	0.432309	+	0.0986717i	−0.000828224		1.00000i	$0.500264\pi$
$224$	2.64545	+	0.0401834i	0.176756	+	0.00268487i
$225$	12.6809	−	6.74070i	0.845394	−	0.449380i
$226$	2.41519			0.160656
$227$	−3.52186			−0.233754			−0.116877	−	0.993146i	$-0.537288\pi$
$227$	−3.52186			−0.233754			−0.116877	+	0.993146i	$0.537288\pi$
$228$	5.66332	−	12.3842i	0.375063	−	0.820165i
$229$	3.96250	−	8.22821i	0.261849	−	0.543736i	−0.728047	−	0.685527i	$-0.759572\pi$
$229$	3.96250	−	8.22821i	0.261849	−	0.543736i	0.989897	+	0.141791i	$0.0452862\pi$
$230$	−1.85063	+	2.32062i	−0.122027	+	0.153017i
$231$	3.96999	+	17.0243i	0.261206	+	1.12012i
$232$	−5.38309	−	6.75019i	−0.353417	−	0.443171i
$233$	16.2860	−	3.71717i	1.06693	−	0.243520i	0.347212	−	0.937787i	$-0.387128\pi$
$233$	16.2860	−	3.71717i	1.06693	−	0.243520i	0.719717	+	0.694267i	$0.244271\pi$
$234$	−5.08674	+	6.92672i	−0.332531	+	0.452814i
$235$	2.01993	+	0.972746i	0.131766	+	0.0634550i
$236$	4.10934	−	5.15296i	0.267496	−	0.335429i
$237$	−0.343080	+	1.65412i	−0.0222855	+	0.107447i
$238$	7.64270	+	9.88808i	0.495403	+	0.640949i
$239$	1.77835	−	3.69278i	0.115032	−	0.238866i	−0.835502	−	0.549488i	$-0.814823\pi$
$239$	1.77835	−	3.69278i	0.115032	−	0.238866i	0.950534	+	0.310622i	$0.100537\pi$
$240$	0.162324	−	0.782626i	0.0104780	−	0.0505183i
$241$	3.62965	+	0.828444i	0.233806	+	0.0533648i	0.337819	−	0.941211i	$-0.390311\pi$
$241$	3.62965	+	0.828444i	0.233806	+	0.0533648i	−0.104012	+	0.994576i	$0.533168\pi$
$242$	−1.54109	−	3.20010i	−0.0990649	−	0.205710i
$243$	13.3038	−	8.12457i	0.853440	−	0.521192i
$244$			1.67160i			0.107013i
$245$	−3.22877	−	0.0981104i	−0.206279	−	0.00626805i
$246$	5.42316	+	4.15110i	0.345768	+	0.264664i
$247$	14.0423	+	17.6085i	0.893493	+	1.12040i
$248$	2.06167	−	0.992848i	0.130916	−	0.0630459i
$249$	15.6991	+	18.9022i	0.994889	+	1.19788i
$250$	−1.95959	−	4.06913i	−0.123935	−	0.257354i
$251$	0.489376	+	0.235671i	0.0308892	+	0.0148754i	0.449265	−	0.893399i	$-0.351686\pi$
$251$	0.489376	+	0.235671i	0.0308892	+	0.0148754i	−0.418375	+	0.908274i	$0.637400\pi$
$252$	6.08204	−	5.09988i	0.383132	−	0.321263i
$253$	22.1065	−	10.6459i	1.38982	−	0.669303i
$254$	1.93917	+	1.54643i	0.121674	+	0.0970320i
$255$	3.36833	−	1.70544i	0.210933	−	0.106799i
$256$	0.623490	+	0.781831i	0.0389681	+	0.0488645i
$257$	0.145948	+	0.639440i	0.00910399	+	0.0398872i	0.979276	−	0.202531i	$-0.0649166\pi$
$257$	0.145948	+	0.639440i	0.00910399	+	0.0398872i	−0.970172	+	0.242418i	$0.922059\pi$
$258$	−0.373179	−	18.7601i	−0.0232331	−	1.16795i
$259$	−0.307770	+	20.2618i	−0.0191239	+	1.25901i
$260$	1.03352	+	0.824206i	0.0640963	+	0.0511151i
$261$	−25.4613	−	4.75481i	−1.57601	−	0.294316i
$262$	−7.60715	+	1.73628i	−0.469971	+	0.107268i
$263$			14.7034i			0.906653i	0.891345	+	0.453326i	$0.149763\pi$
$263$			14.7034i			0.906653i	−0.891345	+	0.453326i	$0.850237\pi$
$264$	−4.01599	+	5.24665i	−0.247167	+	0.322909i
$265$	−0.0534669	+	0.0122035i	−0.00328445	+	0.000749654i
$266$	−8.73970	−	18.8763i	−0.535866	−	1.15738i
$267$	−10.1755	−	12.2516i	−0.622728	−	0.749786i
$268$	−0.882060	+	3.86456i	−0.0538804	+	0.236065i
$269$	−11.2497	+	14.1067i	−0.685908	+	0.860101i	−0.995883	−	0.0906435i	$-0.971108\pi$
$269$	−11.2497	+	14.1067i	−0.685908	+	0.860101i	0.309976	+	0.950744i	$0.399679\pi$
$270$	−1.16737	−	2.09450i	−0.0710437	−	0.127467i
$271$	10.3730	+	2.36757i	0.630116	+	0.143820i	0.525639	−	0.850707i	$-0.323826\pi$
$271$	10.3730	+	2.36757i	0.630116	+	0.143820i	0.104477	+	0.994527i	$0.466683\pi$
$272$	−1.05109	+	4.60514i	−0.0637319	+	0.279228i
$273$	2.98124	+	12.7843i	0.180433	+	0.773743i
$274$	−2.35709	−	10.3271i	−0.142397	−	0.623881i
$275$			18.2611i			1.10119i
$276$	−8.84655	−	6.77149i	−0.532500	−	0.407596i
$277$	0.355370	+	1.55698i	0.0213521	+	0.0935496i	0.984481	−	0.175490i	$-0.0561509\pi$
$277$	0.355370	+	1.55698i	0.0213521	+	0.0935496i	−0.963129	+	0.269040i	$0.913294\pi$
$278$	−0.545611	−	0.262752i	−0.0327236	−	0.0157588i
$279$	2.73022	−	6.29857i	0.163454	−	0.377085i
$280$	−0.746648	−	0.966008i	−0.0446208	−	0.0577300i
$281$	−25.6486	+	20.4541i	−1.53007	+	1.22019i	−0.636480	+	0.771293i	$0.719610\pi$
$281$	−25.6486	+	20.4541i	−1.53007	+	1.22019i	−0.893585	+	0.448894i	$0.851818\pi$
$282$	−3.49957	+	7.65265i	−0.208396	+	0.455708i
$283$	21.5133	−	17.1563i	1.27883	−	1.01984i	0.280637	−	0.959814i	$-0.409454\pi$
$283$	21.5133	−	17.1563i	1.27883	−	1.01984i	0.998197	−	0.0600219i	$-0.0191171\pi$
$284$	0.397013	−	0.824407i	0.0235584	−	0.0489195i
$285$	−6.09753	+	1.51992i	−0.361187	+	0.0900320i
$286$	−4.74132	−	9.84545i	−0.280360	−	0.582174i
$287$	10.2048	−	2.16666i	0.602370	−	0.127894i
$288$	2.94902	+	0.550720i	0.173773	+	0.0324515i
$289$	−4.78607	+	2.30485i	−0.281534	+	0.135579i
$290$	−0.886570	+	3.88432i	−0.0520612	+	0.228095i
$291$	24.7518	+	5.13376i	1.45098	+	0.300946i
$292$	−5.38845	+	4.29715i	−0.315335	+	0.251472i
$293$	33.7686			1.97278			0.986392	−	0.164411i	$-0.0525725\pi$
$293$	33.7686			1.97278			0.986392	+	0.164411i	$0.0525725\pi$
$294$	0.127151	−	12.1237i	0.00741558	−	0.707068i
$295$	−3.04147			−0.177081
$296$	−5.98816	+	4.77540i	−0.348055	+	0.277564i
$297$	1.18203	+	19.7864i	0.0685885	+	1.14812i
$298$	−0.232199	+	1.01733i	−0.0134510	+	0.0589325i
$299$	16.6007	−	7.99449i	0.960045	−	0.462333i
$300$	7.39728	−	3.74537i	0.427082	−	0.216239i
$301$	−22.1350	−	18.2088i	−1.27584	−	1.04954i
$302$	7.93052	+	16.4679i	0.456350	+	0.947621i
$303$	3.46850	+	13.9148i	0.199260	+	0.799384i
$304$	3.41128	−	7.08359i	0.195650	−	0.406272i
$305$	0.603095	−	0.480952i	0.0345331	−	0.0275392i
$306$	6.65132	+	12.5128i	0.380231	+	0.715307i
$307$	1.05886	−	0.844413i	0.0604323	−	0.0481932i	−0.592808	−	0.805344i	$-0.701981\pi$
$307$	1.05886	−	0.844413i	0.0604323	−	0.0481932i	0.653240	+	0.757151i	$0.273409\pi$
$308$	2.09614	+	9.87265i	0.119439	+	0.562546i
$309$	−23.2716	+	5.80085i	−1.32387	+	0.329999i
$310$	−0.951390	−	0.458166i	−0.0540353	−	0.0260221i
$311$	0.731657	+	3.20560i	0.0414885	+	0.181773i	0.991427	−	0.130665i	$-0.0417114\pi$
$311$	0.731657	+	3.20560i	0.0414885	+	0.181773i	−0.949938	+	0.312438i	$0.898854\pi$
$312$	−3.01579	+	3.93994i	−0.170735	+	0.223055i
$313$			25.3216i			1.43126i	0.698479	+	0.715630i	$0.253860\pi$
$313$			25.3216i			1.43126i	−0.698479	+	0.715630i	$0.746140\pi$
$314$	1.37039	+	6.00408i	0.0773357	+	0.338830i
$315$	−3.58990	−	0.726994i	−0.202268	−	0.0409615i
$316$	−0.217032	+	0.950878i	−0.0122090	+	0.0534911i
$317$	−25.3676	−	5.78999i	−1.42479	−	0.325198i	−0.560481	−	0.828167i	$-0.689384\pi$
$317$	−25.3676	−	5.78999i	−1.42479	−	0.325198i	−0.864305	+	0.502969i	$0.832241\pi$
$318$	−0.0497863	−	0.199730i	−0.00279188	−	0.0112003i
$319$	20.5348	−	25.7499i	1.14973	−	1.44172i
$320$	0.102686	−	0.449896i	0.00574031	−	0.0251500i
$321$	18.3222	−	15.2173i	1.02264	−	0.849348i
$322$	−16.6466	+	3.53437i	−0.927678	+	0.196962i
$323$	36.2065	−	8.26390i	2.01458	−	0.459816i
$324$	7.77273	−	4.53704i	0.431818	−	0.252058i
$325$			13.7131i			0.760664i
$326$	−12.2013	+	2.78486i	−0.675766	+	0.154239i
$327$	−19.9364	+	10.0941i	−1.10248	+	0.558207i
$328$	3.08278	+	2.45844i	0.170218	+	0.135744i
$329$	5.40057	+	11.6643i	0.297743	+	0.643076i
$330$	3.04841	−	0.0606395i	0.167809	−	0.00333810i
$331$	3.20960	+	14.0622i	0.176416	+	0.772928i	0.983267	+	0.182173i	$0.0583130\pi$
$331$	3.20960	+	14.0622i	0.176416	+	0.772928i	−0.806851	+	0.590755i	$0.798830\pi$
$332$	8.84503	+	11.0913i	0.485434	+	0.608715i
$333$	−4.21804	+	22.5869i	−0.231147	+	1.23776i
$334$	−3.31168	−	2.64098i	−0.181207	−	0.144508i
$335$	1.64807	−	0.793670i	0.0900439	−	0.0433628i
$336$	3.56933	−	2.87400i	0.194723	−	0.156790i
$337$	3.46670	+	1.66947i	0.188843	+	0.0909420i	0.525916	−	0.850537i	$-0.323723\pi$
$337$	3.46670	+	1.66947i	0.188843	+	0.0909420i	−0.337073	+	0.941479i	$0.609437\pi$
$338$	2.08002	+	4.31921i	0.113138	+	0.234934i
$339$	3.21807	−	2.67274i	0.174781	−	0.145163i
$340$	1.96390	−	0.945766i	0.106508	−	0.0512914i
$341$	5.44249	+	6.82467i	0.294727	+	0.369576i
$342$	−6.15884	−	22.7683i	−0.333032	−	1.23117i
$343$	−13.9387	−	12.1948i	−0.752620	−	0.658455i
$344$		−	10.8333i		−	0.584091i
$345$	0.102246	+	5.14002i	0.00550475	+	0.276730i
$346$	1.44817	+	3.00716i	0.0778541	+	0.161666i
$347$	−9.17698	−	2.09459i	−0.492646	−	0.112443i	−0.0310216	−	0.999519i	$-0.509876\pi$
$347$	−9.17698	−	2.09459i	−0.492646	−	0.112443i	−0.461624	+	0.887075i	$0.652733\pi$
$348$	−14.6426	−	3.03701i	−0.784924	−	0.162801i
$349$	2.10222	−	4.36531i	0.112529	−	0.233670i	−0.837097	−	0.547055i	$-0.815749\pi$
$349$	2.10222	−	4.36531i	0.112529	−	0.233670i	0.949626	+	0.313385i	$0.101463\pi$
$350$	3.00552	−	12.3036i	0.160652	−	0.657653i
$351$	0.887641	+	14.8585i	0.0473788	+	0.793088i
$352$	−2.37842	+	2.98244i	−0.126770	+	0.158965i
$353$	−6.60133	−	3.17903i	−0.351354	−	0.169203i	0.249879	−	0.968277i	$-0.419609\pi$
$353$	−6.60133	−	3.17903i	−0.351354	−	0.169203i	−0.601233	+	0.799074i	$0.705323\pi$
$354$	−0.227039	−	11.4135i	−0.0120670	−	0.606619i
$355$	−0.411665	+	0.0939598i	−0.0218489	+	0.00498687i
$356$	−5.73296	−	7.18891i	−0.303846	−	0.381011i
$357$	21.1258	+	4.71746i	1.11810	+	0.249674i
$358$	−13.8824	+	17.4080i	−0.733709	+	0.920042i
$359$	7.96342	−	16.5362i	0.420293	−	0.872748i	−0.578093	−	0.815971i	$-0.696203\pi$
$359$	7.96342	−	16.5362i	0.420293	−	0.872748i	0.998387	−	0.0567778i	$-0.0180826\pi$
$360$	−0.649796	−	1.22242i	−0.0342473	−	0.0644275i
$361$	−42.8140			−2.25337
$362$	5.02748			0.264239
$363$	−5.59473	−	2.55848i	−0.293647	−	0.134285i
$364$	1.57408	+	7.41381i	0.0825044	+	0.388589i
$365$	3.10072	+	0.707720i	0.162299	+	0.0370438i
$366$	1.84985	+	2.22728i	0.0966933	+	0.116422i
$367$	19.8391	+	15.8212i	1.03559	+	0.825858i	0.984947	−	0.172859i	$-0.0553005\pi$
$367$	19.8391	+	15.8212i	1.03559	+	0.825858i	0.0506461	+	0.998717i	$0.483872\pi$
$368$	−5.02879	−	4.01033i	−0.262144	−	0.209053i
$369$	11.8197	−	0.470426i	0.615310	−	0.0244894i
$370$	3.44582	+	0.786485i	0.179140	+	0.0408874i
$371$	−0.281186	−	0.140712i	−0.0145984	−	0.00730542i
$372$	1.64830	−	3.60441i	0.0854606	−	0.186880i
$373$	−11.8224			−0.612143			−0.306071	−	0.952009i	$-0.599015\pi$
$373$	−11.8224			−0.612143			−0.306071	+	0.952009i	$0.599015\pi$
$374$	−18.0190			−0.931738
$375$	−7.11404	−	3.25326i	−0.367368	−	0.167998i
$376$	−2.10795	+	4.37720i	−0.108709	+	0.225737i
$377$	15.4205	−	19.3367i	0.794197	−	0.995891i
$378$	2.46016	−	13.5258i	0.126537	−	0.695693i
$379$	10.5555	+	13.2362i	0.542200	+	0.679897i	0.975156	−	0.221518i	$-0.0711012\pi$
$379$	10.5555	+	13.2362i	0.542200	+	0.679897i	−0.432957	+	0.901415i	$0.642530\pi$
$380$	−3.53717	+	0.807335i	−0.181453	+	0.0414154i
$381$	4.29514	−	0.0854396i	0.220047	−	0.00437720i
$382$	3.87596	+	1.86656i	0.198311	+	0.0955017i
$383$	17.9295	−	22.4829i	0.916155	−	1.14882i	−0.0723117	−	0.997382i	$-0.523038\pi$
$383$	17.9295	−	22.4829i	0.916155	−	1.14882i	0.988467	−	0.151440i	$-0.0483909\pi$
$384$	1.69596	+	0.351758i	0.0865464	+	0.0179506i
$385$	2.95884	−	3.59681i	0.150796	−	0.183311i
$386$	2.25737	−	4.68747i	0.114897	−	0.238586i
$387$	−21.2578	−	24.5834i	−1.08059	−	1.24965i
$388$	14.2287	+	3.24760i	0.722352	+	0.164872i
$389$	4.07505	+	8.46193i	0.206613	+	0.429037i	0.978365	−	0.206887i	$-0.0663334\pi$
$389$	4.07505	+	8.46193i	0.206613	+	0.429037i	−0.771752	+	0.635924i	$0.780619\pi$
$390$	2.28919	−	0.0455369i	0.115917	−	0.00230585i
$391$		−	30.3823i		−	1.53650i
$392$	0.212606	−	6.99677i	0.0107382	−	0.353390i
$393$	−8.21454	+	10.7318i	−0.414369	+	0.541348i
$394$	−14.2911	−	17.9205i	−0.719978	−	0.902823i
$395$	0.405510	−	0.195283i	0.0204034	−	0.00982578i
$396$	0.455115	+	11.4350i	0.0228704	+	0.574631i
$397$	−7.04595	−	14.6311i	−0.353626	−	0.734312i	0.645951	−	0.763379i	$-0.276461\pi$
$397$	−7.04595	−	14.6311i	−0.353626	−	0.734312i	−0.999577	+	0.0290662i	$0.990747\pi$
$398$	15.0940	+	7.26888i	0.756593	+	0.364356i
$399$	−32.5342	−	15.4797i	−1.62875	−	0.774952i
$400$	4.31298	−	2.07702i	0.215649	−	0.103851i
$401$	−4.60232	−	3.67023i	−0.229829	−	0.183282i	0.501804	−	0.864981i	$-0.332670\pi$
$401$	−4.60232	−	3.67023i	−0.229829	−	0.183282i	−0.731633	+	0.681699i	$0.761241\pi$
$402$	3.10137	+	6.12535i	0.154682	+	0.305505i
$403$	4.08701	+	5.12495i	0.203588	+	0.255292i
$404$	1.84237	+	8.07194i	0.0916613	+	0.401594i
$405$	−3.87328	−	1.49892i	−0.192465	−	0.0744819i
$406$	−18.0736	+	13.9694i	−0.896976	+	0.693292i
$407$	−22.8430	−	18.2167i	−1.13228	−	0.902966i
$408$	3.69571	+	7.29919i	0.182965	+	0.361364i
$409$	−8.14988	+	1.86016i	−0.402986	+	0.0919788i	−0.419209	−	0.907890i	$-0.637693\pi$
$409$	−8.14988	+	1.86016i	−0.402986	+	0.0919788i	0.0162238	+	0.999868i	$0.494836\pi$
$410$		−	1.81957i		−	0.0898622i
$411$	−14.5689	−	11.1516i	−0.718633	−	0.550069i
$412$	−13.4998	+	3.08124i	−0.665088	+	0.151802i
$413$	−13.4667	−	11.0781i	−0.662655	−	0.545118i
$414$	−19.2809	+	0.767383i	−0.947607	+	0.0377148i
$415$	1.45673	−	6.38237i	0.0715083	−	0.313298i
$416$	−1.78606	+	2.23965i	−0.0875688	+	0.109808i
$417$	−1.01776	+	0.253694i	−0.0498398	+	0.0124234i
$418$	29.2398	+	6.67380i	1.43017	+	0.326426i
$419$	−5.69608	+	24.9562i	−0.278272	+	1.21919i	0.621706	+	0.783251i	$0.286440\pi$
$419$	−5.69608	+	24.9562i	−0.278272	+	1.21919i	−0.899977	+	0.435937i	$0.856417\pi$
$420$	−2.06387	−	0.460868i	−0.100707	−	0.0224881i
$421$	−4.13020	−	18.0956i	−0.201293	−	0.881924i	−0.970151	−	0.242504i	$-0.922031\pi$
$421$	−4.13020	−	18.0956i	−0.201293	−	0.881924i	0.768857	−	0.639421i	$-0.220826\pi$
$422$			4.36997i			0.212727i
$423$	3.80577	+	14.0693i	0.185043	+	0.684074i
$424$	−0.0264450	−	0.115863i	−0.00128428	−	0.00562682i
$425$	20.3727	+	9.81097i	0.988220	+	0.475902i
$426$	−0.383326	−	1.53781i	−0.0185722	−	0.0745071i
$427$	4.42213	+	0.0671706i	0.214002	+	0.00325061i
$428$	10.7510	−	8.57360i	0.519667	−	0.414421i
$429$	−17.2128	−	7.87143i	−0.831041	−	0.380036i
$430$	−3.90852	+	3.11694i	−0.188486	+	0.150312i
$431$	10.7334	−	22.2882i	0.517010	−	1.07358i	−0.465097	−	0.885260i	$-0.653980\pi$
$431$	10.7334	−	22.2882i	0.517010	−	1.07358i	0.982107	−	0.188323i	$-0.0603053\pi$
$432$	4.53880	−	2.52969i	0.218373	−	0.121710i
$433$	−6.40335	−	13.2967i	−0.307726	−	0.638999i	0.688553	−	0.725186i	$-0.258246\pi$
$433$	−6.40335	−	13.2967i	−0.307726	−	0.638999i	−0.996279	+	0.0861869i	$0.972532\pi$
$434$	−2.54368	−	5.49393i	−0.122101	−	0.263717i
$435$	3.11723	+	6.15668i	0.149460	+	0.295190i
$436$	−11.6239	+	5.59778i	−0.556684	+	0.268085i
$437$	−11.2529	+	49.3022i	−0.538300	+	2.35845i
$438$	−2.42434	+	11.6887i	−0.115840	+	0.558507i
$439$	23.3630	−	18.6314i	1.11506	−	0.889227i	0.120425	−	0.992722i	$-0.461574\pi$
$439$	23.3630	−	18.6314i	1.11506	−	0.889227i	0.994630	+	0.103495i	$0.0330027\pi$
$440$	1.76035			0.0839213
$441$	−13.2471	−	16.2946i	−0.630813	−	0.775935i
$442$	−13.5312			−0.643615
$443$	2.94611	−	2.34944i	0.139974	−	0.111625i	−0.551000	−	0.834505i	$-0.685754\pi$
$443$	2.94611	−	2.34944i	0.139974	−	0.111625i	0.690974	+	0.722880i	$0.257182\pi$
$444$	−2.69416	+	12.9896i	−0.127859	+	0.616458i
$445$	−0.944192	+	4.13678i	−0.0447590	+	0.196102i
$446$	5.96601	−	2.87308i	0.282499	−	0.136044i
$447$	0.816426	+	1.61248i	0.0386156	+	0.0762677i
$448$	2.09335	−	1.61799i	0.0989014	−	0.0764429i
$449$	−17.3820	−	36.0941i	−0.820307	−	1.70339i	−0.704031	−	0.710169i	$-0.748619\pi$
$449$	−17.3820	−	36.0941i	−0.820307	−	1.70339i	−0.116276	−	0.993217i	$-0.537096\pi$
$450$	5.71158	−	13.1765i	0.269246	−	0.621147i
$451$	−6.52622	+	13.5518i	−0.307308	+	0.638131i
$452$	1.88827	−	1.50585i	0.0888169	−	0.0708291i
$453$	28.7908	+	13.1661i	1.35271	+	0.618596i
$454$	−2.75350	+	2.19585i	−0.129228	+	0.103056i
$455$	2.22192	−	2.70101i	0.104165	−	0.126625i
$456$	−3.29367	−	13.2134i	−0.154240	−	0.618774i
$457$	3.85346	+	1.85573i	0.180257	+	0.0868073i	0.521836	−	0.853046i	$-0.325247\pi$
$457$	3.85346	+	1.85573i	0.180257	+	0.0868073i	−0.341579	+	0.939853i	$0.610962\pi$
$458$	−2.03220	−	8.90366i	−0.0949585	−	0.416041i
$459$	22.7094	+	9.31175i	1.05999	+	0.434635i
$460$			2.96818i			0.138392i
$461$	−3.20697	−	14.0506i	−0.149363	−	0.654403i	−0.993063	−	0.117587i	$-0.962484\pi$
$461$	−3.20697	−	14.0506i	−0.149363	−	0.654403i	0.843699	−	0.536816i	$-0.180373\pi$
$462$	13.7184	+	10.8349i	0.638236	+	0.504086i
$463$	−4.83048	+	21.1637i	−0.224492	+	0.983562i	0.729559	+	0.683918i	$0.239725\pi$
$463$	−4.83048	+	21.1637i	−0.224492	+	0.983562i	−0.954051	+	0.299644i	$0.903132\pi$
$464$	−8.41735	−	1.92120i	−0.390765	−	0.0891897i
$465$	−1.77468	+	0.442370i	−0.0822988	+	0.0205144i
$466$	10.4153	−	13.0603i	0.482478	−	0.605008i
$467$	6.29064	−	27.5611i	0.291096	−	1.27538i	−0.591906	−	0.806007i	$-0.701624\pi$
$467$	6.29064	−	27.5611i	0.291096	−	1.27538i	0.883002	−	0.469369i	$-0.155518\pi$
$468$	0.341766	+	8.58706i	0.0157981	+	0.396937i
$469$	10.1880	+	2.48873i	0.470440	+	0.114919i
$470$	2.18574	−	0.498881i	0.100821	−	0.0230117i
$471$	8.47026	+	6.48347i	0.390289	+	0.298742i
$472$		−	6.59088i		−	0.303370i
$473$	40.2895	−	9.19581i	1.85251	−	0.422824i
$474$	0.763096	+	1.50715i	0.0350502	+	0.0692257i
$475$	−29.4255	−	23.4661i	−1.35014	−	1.07670i
$476$	12.1404	+	2.96566i	0.556455	+	0.135931i
$477$	−0.287365	−	0.211031i	−0.0131575	−	0.00966244i
$478$	−0.912041	−	3.99591i	−0.0417158	−	0.182769i
$479$	−14.4210	−	18.0833i	−0.658911	−	0.826248i	0.334313	−	0.942462i	$-0.391496\pi$
$479$	−14.4210	−	18.0833i	−0.658911	−	0.826248i	−0.993224	+	0.116214i	$0.962924\pi$
$480$	−0.361049	−	0.713089i	−0.0164796	−	0.0325479i
$481$	−17.1538	−	13.6797i	−0.782146	−	0.623740i
$482$	3.35430	−	1.61535i	0.152784	−	0.0735770i
$483$	−18.2691	+	23.1310i	−0.831273	+	1.05250i
$484$	−3.20010	−	1.54109i	−0.145459	−	0.0700495i
$485$	−2.92217	−	6.06795i	−0.132689	−	0.275531i
$486$	5.33575	−	14.6468i	0.242034	−	0.664394i
$487$	−5.86614	+	2.82499i	−0.265820	+	0.128012i	−0.562047	−	0.827105i	$-0.689986\pi$
$487$	−5.86614	+	2.82499i	−0.265820	+	0.128012i	0.296227	+	0.955118i	$0.404272\pi$
$488$	1.04223	+	1.30691i	0.0471794	+	0.0591610i
$489$	−13.1755	+	17.2130i	−0.595815	+	0.778397i
$490$	−2.58553	+	1.93640i	−0.116802	+	0.0874776i
$491$		−	32.9112i		−	1.48526i	−0.669702	−	0.742630i	$-0.733578\pi$
$491$		−	32.9112i		−	1.48526i	0.669702	−	0.742630i	$-0.266422\pi$
$492$	6.82817	−	0.135827i	0.307838	−	0.00612356i
$493$	−17.6948	−	36.7437i	−0.796936	−	1.65485i
$494$	21.9575	+	5.01165i	0.987914	+	0.225485i
$495$	3.99468	−	3.45427i	0.179547	−	0.155258i
$496$	0.992848	−	2.06167i	0.0445802	−	0.0925717i
$497$	−2.16497	−	1.08340i	−0.0971122	−	0.0485973i
$498$	24.0594	+	4.99015i	1.07813	+	0.223614i
$499$	−9.23232	+	11.5770i	−0.413295	+	0.518256i	−0.944288	−	0.329120i	$-0.893248\pi$
$499$	−9.23232	+	11.5770i	−0.413295	+	0.518256i	0.530993	+	0.847376i	$0.321819\pi$
$500$	−4.06913	−	1.95959i	−0.181977	−	0.0876354i
$501$	−7.33517	+	0.145913i	−0.327711	+	0.00651889i
$502$	0.529549	−	0.120866i	0.0236349	−	0.00539451i
$503$	3.71544	+	4.65902i	0.165663	+	0.207735i	0.857733	−	0.514096i	$-0.171872\pi$
$503$	3.71544	+	4.65902i	0.165663	+	0.207735i	−0.692070	+	0.721831i	$0.743301\pi$
$504$	1.57540	−	7.77934i	0.0701740	−	0.346519i
$505$	2.38218	−	2.98716i	0.106006	−	0.132927i
$506$	10.6459	−	22.1065i	0.473269	−	0.982753i
$507$	7.55126	+	3.45320i	0.335363	+	0.153362i
$508$	2.48029			0.110045
$509$	−29.8331			−1.32233			−0.661165	−	0.750240i	$-0.729938\pi$
$509$	−29.8331			−1.32233			−0.661165	+	0.750240i	$0.729938\pi$
$510$	1.57014	−	3.43349i	0.0695269	−	0.152037i
$511$	11.1513	+	14.4275i	0.493306	+	0.638237i
$512$	0.974928	+	0.222521i	0.0430861	+	0.00983413i
$513$	−33.4024	−	23.5215i	−1.47475	−	1.03850i
$514$	0.512791	+	0.408937i	0.0226183	+	0.0180375i
$515$	4.99583	+	3.98404i	0.220143	+	0.175558i
$516$	−11.9885	−	14.4345i	−0.527763	−	0.635445i
$517$	−18.0683	−	4.12398i	−0.794644	−	0.181372i
$518$	12.3924	+	16.0332i	0.544492	+	0.704460i
$519$	5.25740	+	2.40422i	0.230774	+	0.105534i
$520$	1.32192			0.0579702
$521$	25.6625			1.12430			0.562148	−	0.827037i	$-0.309975\pi$
$521$	25.6625			1.12430			0.562148	+	0.827037i	$0.309975\pi$
$522$	−22.8710	+	12.1574i	−1.00104	+	0.532114i
$523$	14.0820	−	29.2417i	0.615765	−	1.27865i	−0.326948	−	0.945042i	$-0.606020\pi$
$523$	14.0820	−	29.2417i	0.615765	−	1.27865i	0.942713	−	0.333606i	$-0.108265\pi$
$524$	−4.86496	+	6.10046i	−0.212527	+	0.266500i
$525$	−9.61092	−	19.7196i	−0.419455	−	0.860634i
$526$	9.16744	+	11.4956i	0.399719	+	0.501232i
$527$	10.5379	−	2.40520i	0.459036	−	0.104772i
$528$	0.131406	+	6.60593i	0.00571872	+	0.287486i
$529$	16.5522	+	7.97110i	0.719659	+	0.346570i
$530$	−0.0341934	+	0.0428772i	−0.00148527	+	0.00186246i
$531$	−12.9331	−	14.9564i	−0.561247	−	0.649051i
$532$	−18.6022	−	9.30899i	−0.806506	−	0.403596i
$533$	−4.90083	+	10.1767i	−0.212279	+	0.440801i
$534$	−15.5942	−	3.23440i	−0.674829	−	0.139966i
$535$	−6.18652	−	1.41203i	−0.267466	−	0.0610475i
$536$	1.71989	+	3.57139i	0.0742879	+	0.154260i
$537$	0.766996	+	38.5577i	0.0330983	+	1.66389i
$538$			18.0432i			0.777895i
$539$	26.2018	−	5.14850i	1.12859	−	0.221762i
$540$	−2.21858	−	0.909705i	−0.0954726	−	0.0391475i
$541$	19.6935	+	24.6949i	0.846690	+	1.06172i	0.997323	+	0.0731260i	$0.0232975\pi$
$541$	19.6935	+	24.6949i	0.846690	+	1.06172i	−0.150633	+	0.988590i	$0.548131\pi$
$542$	9.58611	−	4.61643i	0.411759	−	0.198293i
$543$	6.69875	−	5.56359i	0.287471	−	0.238756i
$544$	2.04948	+	4.25579i	0.0878708	+	0.182466i
$545$	5.36404	+	2.58318i	0.229770	+	0.110651i
$546$	10.3017	+	8.13642i	0.440873	+	0.348207i
$547$	4.75925	−	2.29193i	0.203491	−	0.0979959i	−0.329363	−	0.944203i	$-0.606834\pi$
$547$	4.75925	−	2.29193i	0.203491	−	0.0979959i	0.532854	+	0.846207i	$0.321120\pi$
$548$	−8.28167	−	6.60441i	−0.353775	−	0.282126i
$549$	4.92958	+	0.920584i	0.210389	+	0.0392896i
$550$	11.3856	+	14.2771i	0.485484	+	0.608778i
$551$	15.1049	+	66.1788i	0.643489	+	2.81931i
$552$	−11.1385	+	0.221568i	−0.474085	+	0.00943058i
$553$	2.50678	+	0.612355i	0.106599	+	0.0260400i
$554$	1.24860	+	0.995724i	0.0530478	+	0.0423042i
$555$	5.46165	−	2.76533i	0.231834	−	0.117382i
$556$	−0.590399	+	0.134755i	−0.0250385	+	0.00571488i
$557$			20.8002i			0.881333i	0.897671	+	0.440666i	$0.145258\pi$
$557$			20.8002i			0.881333i	−0.897671	+	0.440666i	$0.854742\pi$
$558$	−1.79252	−	6.62668i	−0.0758836	−	0.280530i
$559$	30.2551	−	6.90554i	1.27966	−	0.292073i
$560$	−1.18605	−	0.289728i	−0.0501197	−	0.0122433i
$561$	−24.0089	+	19.9404i	−1.01366	+	0.841884i
$562$	−7.29997	+	31.9832i	−0.307931	+	1.34913i
$563$	−20.1742	+	25.2977i	−0.850243	+	1.06617i	0.146788	+	0.989168i	$0.453107\pi$
$563$	−20.1742	+	25.2977i	−0.850243	+	1.06617i	−0.997031	+	0.0770030i	$0.975465\pi$
$564$	2.03527	+	8.16502i	0.0857005	+	0.343810i
$565$	−1.08659	−	0.248006i	−0.0457130	−	0.0104337i
$566$	6.12301	−	26.8267i	0.257369	−	1.12761i
$567$	−11.6902	−	20.7446i	−0.490940	−	0.871193i
$568$	−0.203612	−	0.892081i	−0.00854335	−	0.0374309i
$569$			25.5143i			1.06962i	0.844974	+	0.534808i	$0.179616\pi$
$569$			25.5143i			1.06962i	−0.844974	+	0.534808i	$0.820384\pi$
$570$	−3.81959	+	4.99007i	−0.159985	+	0.209011i
$571$	4.98153	+	21.8255i	0.208470	+	0.913369i	0.965585	+	0.260087i	$0.0837512\pi$
$571$	4.98153	+	21.8255i	0.208470	+	0.913369i	−0.757115	+	0.653282i	$0.773392\pi$
$572$	−9.84545	−	4.74132i	−0.411659	−	0.198245i
$573$	7.23003	−	1.80221i	0.302039	−	0.0752885i
$574$	6.62754	−	8.05654i	0.276628	−	0.336274i
$575$	−24.0731	+	19.1976i	−1.00392	+	0.800597i
$576$	2.64900	−	1.40811i	0.110375	−	0.0586713i
$577$	−22.3940	+	17.8586i	−0.932273	+	0.743463i	−0.966691	−	0.255945i	$-0.917614\pi$
$577$	−22.3940	+	17.8586i	−0.932273	+	0.743463i	0.0344185	+	0.999408i	$0.489042\pi$
$578$	−2.30485	+	4.78607i	−0.0958692	+	0.199074i
$579$	−2.17954	−	8.74380i	−0.0905787	−	0.363380i
$580$	1.72868	+	3.58965i	0.0717797	+	0.149052i
$581$	29.6969	−	22.9534i	1.23204	−	0.952266i
$582$	22.5526	−	11.4188i	0.934835	−	0.473323i
$583$	0.408453	−	0.196701i	0.0169164	−	0.00814651i
$584$	−1.53363	+	6.71929i	−0.0634622	+	0.278046i
$585$	2.99978	−	2.59397i	0.124026	−	0.107247i
$586$	26.4014	−	21.0544i	1.09063	−	0.869749i
$587$	−4.90144			−0.202304			−0.101152	−	0.994871i	$-0.532253\pi$
$587$	−4.90144			−0.202304			−0.101152	+	0.994871i	$0.532253\pi$
$588$	−7.45959	−	9.55796i	−0.307628	−	0.394164i
$589$	−17.9909			−0.741302
$590$	−2.37791	+	1.89632i	−0.0978972	+	0.0780704i
$591$	−38.8734	−	8.06271i	−1.59904	−	0.331656i
$592$	−1.70432	+	7.46711i	−0.0700471	+	0.306896i
$593$	21.6448	−	10.4236i	0.888847	−	0.428046i	0.0669990	−	0.997753i	$-0.478658\pi$
$593$	21.6448	−	10.4236i	0.888847	−	0.428046i	0.821848	+	0.569707i	$0.192943\pi$
$594$	13.2608	+	14.7327i	0.544097	+	0.604489i
$595$	−2.42306	−	5.23340i	−0.0993356	−	0.214549i
$596$	0.452755	+	0.940156i	0.0185456	+	0.0385103i
$597$	28.1556	−	7.01827i	1.15233	−	0.287239i
$598$	7.99449	−	16.6007i	0.326919	−	0.678854i
$599$	−32.6425	+	26.0315i	−1.33374	+	1.06362i	−0.341417	+	0.939912i	$0.610907\pi$
$599$	−32.6425	+	26.0315i	−1.33374	+	1.06362i	−0.992319	+	0.123707i	$0.960522\pi$
$600$	3.44823	−	7.54037i	0.140773	−	0.307835i
$601$	4.71968	−	3.76382i	0.192520	−	0.153529i	−0.522486	−	0.852648i	$-0.674995\pi$
$601$	4.71968	−	3.76382i	0.192520	−	0.153529i	0.715006	+	0.699118i	$0.246424\pi$
$602$	−28.6589	−	0.435318i	−1.16805	−	0.0177422i
$603$	10.9109	+	4.72950i	0.444325	+	0.192600i
$604$	16.4679	+	7.93052i	0.670069	+	0.322688i
$605$	0.364724	+	1.59796i	0.0148281	+	0.0649664i
$606$	11.3875	+	8.71644i	0.462586	+	0.354081i
$607$			20.4023i			0.828102i	0.910254	+	0.414051i	$0.135887\pi$
$607$			20.4023i			0.828102i	−0.910254	+	0.414051i	$0.864113\pi$
$608$	−1.74950	−	7.66507i	−0.0709517	−	0.310860i
$609$	−8.62263	+	38.6141i	−0.349407	+	1.56472i
$610$	0.171650	−	0.752047i	0.00694989	−	0.0304495i
$611$	−13.5683	−	3.09688i	−0.548915	−	0.125286i
$612$	13.0018	+	5.63584i	0.525566	+	0.227815i
$613$	−12.4605	+	15.6250i	−0.503275	+	0.631087i	−0.966965	−	0.254911i	$-0.917954\pi$
$613$	−12.4605	+	15.6250i	−0.503275	+	0.631087i	0.463690	+	0.885998i	$0.346525\pi$
$614$	0.301367	−	1.32038i	0.0121622	−	0.0532861i
$615$	−2.01360	−	2.42445i	−0.0811962	−	0.0977631i
$616$	7.79432	+	6.41182i	0.314042	+	0.258340i
$617$	16.4874	−	3.76313i	0.663757	−	0.151498i	0.122647	−	0.992450i	$-0.460862\pi$
$617$	16.4874	−	3.76313i	0.663757	−	0.151498i	0.541109	+	0.840952i	$0.318004\pi$
$618$	−14.5777	+	19.0449i	−0.586400	+	0.766097i
$619$			25.0375i			1.00634i	0.864187	+	0.503171i	$0.167833\pi$
$619$			25.0375i			1.00634i	−0.864187	+	0.503171i	$0.832167\pi$
$620$	−1.02949	+	0.234974i	−0.0413453	+	0.00943678i
$621$	−24.8412	+	22.3594i	−0.996844	+	0.897253i
$622$	2.57069	+	2.05006i	0.103075	+	0.0821998i
$623$	−19.2482	+	14.8774i	−0.771165	+	0.596049i
$624$	0.0986788	+	4.96068i	0.00395031	+	0.198586i
$625$	−4.86232	−	21.3032i	−0.194493	−	0.852129i
$626$	15.7877	+	19.7972i	0.631005	+	0.791256i
$627$	46.3454	−	23.4655i	1.85086	−	0.937120i
$628$	4.81490	+	3.83975i	0.192135	+	0.153223i
$629$	−32.5957	+	15.6973i	−1.29968	+	0.625891i
$630$	−3.25997	+	1.66988i	−0.129880	+	0.0665296i
$631$	−25.3959	−	12.2300i	−1.01099	−	0.486869i	−0.146339	−	0.989235i	$-0.546749\pi$
$631$	−25.3959	−	12.2300i	−1.01099	−	0.486869i	−0.864655	+	0.502365i	$0.832463\pi$
$632$	0.423181	+	0.878744i	0.0168332	+	0.0349545i
$633$	4.83596	+	5.82266i	0.192212	+	0.231430i
$634$	−23.4432	+	11.2896i	−0.931048	+	0.448369i
$635$	−0.713627	−	0.894860i	−0.0283194	−	0.0355114i
$636$	−0.163454	−	0.125114i	−0.00648139	−	0.00496110i
$637$	19.6761	−	3.86624i	0.779595	−	0.153186i
$638$		−	32.9353i		−	1.30392i
$639$	−2.21255	−	1.62482i	−0.0875270	−	0.0642768i
$640$	−0.200223	−	0.415766i	−0.00791449	−	0.0164346i
$641$	−23.5227	−	5.36890i	−0.929089	−	0.212059i	−0.268909	−	0.963166i	$-0.586663\pi$
$641$	−23.5227	−	5.36890i	−0.929089	−	0.212059i	−0.660180	+	0.751107i	$0.729520\pi$
$642$	4.83702	−	23.3211i	0.190902	−	0.920410i
$643$	−11.5031	+	23.8865i	−0.453640	+	0.941993i	0.541234	+	0.840872i	$0.317957\pi$
$643$	−11.5031	+	23.8865i	−0.453640	+	0.941993i	−0.994874	+	0.101121i	$0.967757\pi$
$644$	−10.8112	+	13.1423i	−0.426020	+	0.517877i
$645$	−1.75850	+	8.47840i	−0.0692410	+	0.333837i
$646$	23.1549	−	29.0354i	0.911018	−	1.14238i
$647$	−5.54352	−	2.66962i	−0.217938	−	0.104953i	0.321730	−	0.946832i	$-0.395736\pi$
$647$	−5.54352	−	2.66962i	−0.217938	−	0.104953i	−0.539668	+	0.841878i	$0.681450\pi$
$648$	3.24817	−	8.39341i	0.127600	−	0.329724i
$649$	24.5118	−	5.59465i	0.962171	−	0.219609i
$650$	8.54996	+	10.7213i	0.335357	+	0.420524i
$651$	−9.46904	−	4.50534i	−0.371121	−	0.176578i
$652$	−7.80300	+	9.78466i	−0.305589	+	0.383197i
$653$	−6.54596	+	13.5928i	−0.256163	+	0.531929i	−0.988900	−	0.148584i	$-0.952528\pi$
$653$	−6.54596	+	13.5928i	−0.256163	+	0.531929i	0.732737	+	0.680512i	$0.238243\pi$
$654$	−9.29330	+	20.3220i	−0.363397	+	0.794655i
$655$	3.60072			0.140692
$656$	3.94302			0.153949
$657$	9.70484	+	18.2572i	0.378622	+	0.712280i
$658$	11.4949	+	5.75235i	0.448119	+	0.224250i
$659$	17.5653	+	4.00916i	0.684245	+	0.156175i	0.550492	−	0.834840i	$-0.314440\pi$
$659$	17.5653	+	4.00916i	0.684245	+	0.156175i	0.133753	+	0.991015i	$0.457297\pi$
$660$	2.34554	−	1.94806i	0.0912998	−	0.0758282i
$661$	−36.7924	−	29.3410i	−1.43106	−	1.14123i	−0.966801	−	0.255530i	$-0.917750\pi$
$661$	−36.7924	−	29.3410i	−1.43106	−	1.14123i	−0.464257	−	0.885701i	$-0.653679\pi$
$662$	11.2770	+	8.99311i	0.438293	+	0.349527i
$663$	−18.0294	+	14.9741i	−0.700203	+	0.581547i
$664$	13.8306	+	3.15675i	0.536733	+	0.122506i
$665$	1.99363	+	9.38983i	0.0773095	+	0.364122i
$666$	10.7849	+	20.2891i	0.417908	+	0.786186i
$667$	55.5333			2.15026
$668$	−4.23580			−0.163888
$669$	4.76982	−	10.4304i	0.184412	−	0.403261i
$670$	0.793670	−	1.64807i	0.0306622	−	0.0636706i
$671$	−3.97577	+	4.98545i	−0.153483	+	0.192461i
$672$	0.998705	−	4.47243i	0.0385259	−	0.172528i
$673$	4.63417	+	5.81106i	0.178634	+	0.224000i	0.863085	−	0.505059i	$-0.168529\pi$
$673$	4.63417	+	5.81106i	0.178634	+	0.224000i	−0.684451	+	0.729059i	$0.739958\pi$
$674$	3.75127	−	0.856203i	0.144494	−	0.0329797i
$675$	−6.97133	−	23.8774i	−0.268327	−	0.919040i
$676$	4.31921	+	2.08002i	0.166123	+	0.0800008i
$677$	19.0370	−	23.8716i	0.731650	−	0.917460i	−0.267284	−	0.963618i	$-0.586126\pi$
$677$	19.0370	−	23.8716i	0.731650	−	0.917460i	0.998934	+	0.0461575i	$0.0146976\pi$
$678$	0.849562	−	4.09606i	0.0326272	−	0.157308i
$679$	9.16312	−	37.5107i	0.351648	−	1.43953i
$680$	0.945766	−	1.96390i	0.0362685	−	0.0753122i
$681$	−1.23884	+	5.97293i	−0.0474725	+	0.228883i
$682$	8.51022	+	1.94240i	0.325873	+	0.0743784i
$683$	−11.6751	−	24.2437i	−0.446737	−	0.927659i	−0.995772	−	0.0918596i	$-0.970719\pi$
$683$	−11.6751	−	24.2437i	−0.446737	−	0.927659i	0.549035	−	0.835799i	$-0.314995\pi$
$684$	−19.0110	−	13.9610i	−0.726902	−	0.533812i
$685$			4.88815i			0.186767i
$686$	−18.5010	−	0.843592i	−0.706373	−	0.0322085i
$687$	−12.5609	−	9.61456i	−0.479226	−	0.366818i
$688$	−6.75444	−	8.46980i	−0.257511	−	0.322908i
$689$	0.306725	−	0.147711i	0.0116853	−	0.00562735i
$690$	3.28469	+	3.95488i	0.125046	+	0.150560i
$691$	−2.77820	−	5.76899i	−0.105688	−	0.219463i	0.841418	−	0.540385i	$-0.181721\pi$
$691$	−2.77820	−	5.76899i	−0.105688	−	0.219463i	−0.947105	+	0.320922i	$0.896007\pi$
$692$	3.00716	+	1.44817i	0.114315	+	0.0550512i
$693$	30.2690	−	0.744484i	1.14982	−	0.0282806i
$694$	−8.48080	+	4.08414i	−0.321927	+	0.155032i
$695$	0.218487	+	0.174238i	0.00828769	+	0.00660922i
$696$	−13.3416	+	6.75506i	−0.505711	+	0.256050i
$697$	11.6126	+	14.5617i	0.439859	+	0.551565i
$698$	−1.07814	−	4.72365i	−0.0408083	−	0.178793i
$699$	−0.575437	−	28.9278i	−0.0217650	−	1.09415i
$700$	−5.32134	−	11.4932i	−0.201128	−	0.434403i
$701$	20.3446	+	16.2243i	0.768404	+	0.612782i	0.927216	−	0.374527i	$-0.122195\pi$
$701$	20.3446	+	16.2243i	0.768404	+	0.612782i	−0.158812	+	0.987309i	$0.550766\pi$
$702$	9.95811	+	11.0634i	0.375845	+	0.417562i
$703$	58.7078	−	13.3997i	2.21421	−	0.505379i
$704$			3.81469i			0.143771i
$705$	2.36026	−	3.08354i	0.0888925	−	0.116133i
$706$	−7.14323	+	1.63039i	−0.268839	+	0.0613607i
$707$	21.4279	−	4.54953i	0.805880	−	0.171103i
$708$	−7.29369	−	8.78186i	−0.274114	−	0.330042i
$709$	−7.73261	+	33.8788i	−0.290404	+	1.27234i	0.593560	+	0.804790i	$0.297722\pi$
$709$	−7.73261	+	33.8788i	−0.290404	+	1.27234i	−0.883964	+	0.467555i	$0.845135\pi$
$710$	−0.263270	+	0.330130i	−0.00988033	+	0.0123895i
$711$	2.68463	+	1.16370i	0.100682	+	0.0436421i
$712$	−8.96442	−	2.04607i	−0.335956	−	0.0766798i
$713$	−3.27515	+	14.3494i	−0.122655	+	0.537388i
$714$	19.4581	−	9.48348i	0.728202	−	0.354910i
$715$	1.12211	+	4.91630i	0.0419646	+	0.183859i
$716$			22.2657i			0.832108i
$717$	−5.63724	−	4.31496i	−0.210527	−	0.161145i
$718$	−4.08411	−	17.8937i	−0.152418	−	0.667785i
$719$	−18.9458	−	9.12382i	−0.706560	−	0.340261i	0.0458576	−	0.998948i	$-0.485398\pi$
$719$	−18.9458	−	9.12382i	−0.706560	−	0.340261i	−0.752417	+	0.658687i	$0.771112\pi$
$720$	−1.27020	−	0.550589i	−0.0473376	−	0.0205192i
$721$	7.60879	+	35.8368i	0.283366	+	1.33463i
$722$	−33.4733	+	26.6941i	−1.24575	+	0.993451i
$723$	2.68176	−	5.86432i	0.0997358	−	0.218096i
$724$	3.93065	−	3.13459i	0.146081	−	0.116496i
$725$	−17.9326	+	37.2375i	−0.666001	+	1.38297i
$726$	−5.96932	+	1.48796i	−0.221542	+	0.0552233i
$727$	−11.4475	−	23.7710i	−0.424564	−	0.881617i	−0.998051	−	0.0624020i	$-0.980124\pi$
$727$	−11.4475	−	23.7710i	−0.424564	−	0.881617i	0.573487	−	0.819215i	$-0.305590\pi$
$728$	5.85310	+	4.81492i	0.216930	+	0.178453i
$729$	−9.09921	−	25.4206i	−0.337008	−	0.941502i
$730$	2.86550	−	1.37995i	0.106057	−	0.0510743i
$731$	11.3868	−	49.8888i	0.421156	−	1.84520i
$732$	2.83496	+	0.587998i	0.104783	+	0.0217330i
$733$	2.26133	−	1.80335i	0.0835241	−	0.0666082i	−0.580838	−	0.814019i	$-0.697275\pi$
$733$	2.26133	−	1.80335i	0.0835241	−	0.0666082i	0.664362	+	0.747411i	$0.268703\pi$
$734$	25.3752			0.936614
$735$	−1.30214	+	5.44134i	−0.0480300	+	0.200707i
$736$	−6.43207			−0.237089
$737$	−11.8222	+	9.42791i	−0.435477	+	0.347282i
$738$	8.94772	−	7.73727i	0.329370	−	0.284813i
$739$	9.13971	−	40.0437i	0.336210	−	1.47303i	−0.470668	−	0.882311i	$-0.655987\pi$
$739$	9.13971	−	40.0437i	0.336210	−	1.47303i	0.806877	−	0.590719i	$-0.201156\pi$
$740$	3.18441	−	1.53353i	0.117061	−	0.0563738i
$741$	34.8028	−	17.6213i	1.27851	−	0.647333i
$742$	−0.307573	+	0.0653031i	−0.0112913	+	0.00239735i
$743$	18.0599	+	37.5019i	0.662555	+	1.37581i	0.913112	+	0.407708i	$0.133672\pi$
$743$	18.0599	+	37.5019i	0.662555	+	1.37581i	−0.250557	+	0.968102i	$0.580614\pi$
$744$	−0.958618	−	3.84574i	−0.0351447	−	0.140992i
$745$	0.208931	−	0.433850i	0.00765465	−	0.0158950i
$746$	−9.24315	+	7.37117i	−0.338416	+	0.269878i
$747$	37.5796	−	19.9759i	1.37497	−	0.730882i
$748$	−14.0878	+	11.2346i	−0.515101	+	0.410779i
$749$	−22.2490	−	28.7856i	−0.812961	−	1.05180i
$750$	−7.59036	+	1.89203i	−0.277161	+	0.0690871i
$751$	3.35840	+	1.61732i	0.122550	+	0.0590168i	0.494154	−	0.869374i	$-0.335478\pi$
$751$	3.35840	+	1.61732i	0.122550	+	0.0590168i	−0.371604	+	0.928391i	$0.621192\pi$
$752$	1.08108	+	4.73652i	0.0394229	+	0.172723i
$753$	0.571830	−	0.747062i	0.0208386	−	0.0272244i
$754$		−	24.7326i		−	0.900708i
$755$	−1.87689	−	8.22319i	−0.0683070	−	0.299273i
$756$	−6.50978	−	12.1088i	−0.236758	−	0.440392i
$757$	8.99451	−	39.4075i	0.326911	−	1.43229i	−0.498073	−	0.867135i	$-0.665959\pi$
$757$	8.99451	−	39.4075i	0.326911	−	1.43229i	0.824984	−	0.565156i	$-0.191184\pi$
$758$	16.5052	+	3.76721i	0.599497	+	0.136831i
$759$	−10.2789	−	41.2364i	−0.373100	−	1.49679i
$760$	−2.26210	+	2.83659i	−0.0820551	+	0.102894i
$761$	−4.04548	+	17.7244i	−0.146649	+	0.642510i	0.847154	+	0.531348i	$0.178314\pi$
$761$	−4.04548	+	17.7244i	−0.146649	+	0.642510i	−0.993802	+	0.111162i	$0.964543\pi$
$762$	3.30480	−	2.74477i	0.119720	−	0.0994327i
$763$	14.3415	+	30.9754i	0.519198	+	1.12138i
$764$	4.19413	−	0.957283i	0.151738	−	0.0346333i
$765$	−1.70752	−	6.31244i	−0.0617355	−	0.228227i
$766$		−	28.7567i		−	1.03902i
$767$	18.4070	−	4.20127i	0.664638	−	0.151699i
$768$	1.54527	−	0.782396i	0.0557601	−	0.0282323i
$769$	4.08086	+	3.25438i	0.147160	+	0.117356i	0.694302	−	0.719684i	$-0.255713\pi$
$769$	4.08086	+	3.25438i	0.147160	+	0.117356i	−0.547143	+	0.837039i	$0.684285\pi$
$770$	0.0707368	−	4.65691i	0.00254918	−	0.167823i
$771$	1.13580	−	0.0225936i	0.0409049	−	0.000813687i
$772$	−1.15771	−	5.07226i	−0.0416669	−	0.182555i
$773$	−2.08762	−	2.61780i	−0.0750866	−	0.0941556i	0.742870	−	0.669436i	$-0.233464\pi$
$773$	−2.08762	−	2.61780i	−0.0750866	−	0.0941556i	−0.817956	+	0.575281i	$0.804893\pi$
$774$	−31.9475	−	5.96610i	−1.14833	−	0.214447i
$775$	−8.56427	−	6.82978i	−0.307638	−	0.245333i
$776$	13.1493	−	6.33236i	0.472032	−	0.227319i
$777$	34.2549	+	7.64922i	1.22889	+	0.274414i
$778$	8.46193	+	4.07505i	0.303375	+	0.146098i
$779$	−13.4507	−	27.9308i	−0.481923	−	1.00072i
$780$	1.76137	−	1.46289i	0.0630670	−	0.0523797i
$781$	3.14485	−	1.51448i	0.112532	−	0.0541924i
$782$	−18.9431	−	23.7539i	−0.677403	−	0.849437i
$783$	−17.0202	+	41.5087i	−0.608251	+	1.48340i
$784$	−4.19619	−	5.60285i	−0.149864	−	0.200102i
$785$		−	2.84193i		−	0.101433i
$786$	0.268786	+	13.5121i	0.00958728	+	0.481962i
$787$	8.15570	+	16.9355i	0.290719	+	0.603685i	0.994263	−	0.106967i	$-0.0341141\pi$
$787$	8.15570	+	16.9355i	0.290719	+	0.603685i	−0.703543	+	0.710653i	$0.748400\pi$
$788$	−22.3465	−	5.10045i	−0.796062	−	0.181696i
$789$	24.9364	+	5.17204i	0.887759	+	0.184130i
$790$	0.195283	−	0.405510i	0.00694787	−	0.0144274i
$791$	−3.90776	−	5.05584i	−0.138944	−	0.179765i
$792$	7.48544	+	8.65649i	0.265983	+	0.307595i
$793$	−2.98558	+	3.74380i	−0.106021	+	0.132946i
$794$	−14.6311	−	7.04595i	−0.519237	−	0.250052i
$795$	0.00188917	+	0.0949703i	6.70018e−5	+	0.00336825i
$796$	16.3330	−	3.72790i	0.578908	−	0.132132i
$797$	−27.9234	−	35.0148i	−0.989097	−	1.24029i	−0.970660	−	0.240458i	$-0.922702\pi$
$797$	−27.9234	−	35.0148i	−0.989097	−	1.24029i	−0.0184370	−	0.999830i	$-0.505869\pi$
$798$	−35.0877	+	8.18226i	−1.24209	+	0.289649i
$799$	−14.3083	+	17.9420i	−0.506190	+	0.634742i
$800$	2.07702	−	4.31298i	0.0734338	−	0.152487i
$801$	−24.3575	+	12.9475i	−0.860629	+	0.457479i
$802$	−5.88659			−0.207863
$803$	−26.2912			−0.927795
$804$	6.24385	+	2.85532i	0.220203	+	0.100699i
$805$	7.85216	+	0.119272i	0.276752	+	0.00420377i
$806$	6.39070	+	1.45864i	0.225103	+	0.0513783i
$807$	19.9672	+	24.0412i	0.702878	+	0.846289i
$808$	6.47320	+	5.16220i	0.227726	+	0.181606i
$809$	12.8065	+	10.2128i	0.450251	+	0.359064i	0.822209	−	0.569186i	$-0.192742\pi$
$809$	12.8065	+	10.2128i	0.450251	+	0.359064i	−0.371957	+	0.928250i	$0.621313\pi$
$810$	−3.96281	+	1.24305i	−0.139239	+	0.0436762i
$811$	−27.7535	−	6.33455i	−0.974556	−	0.222436i	−0.294545	−	0.955638i	$-0.595168\pi$
$811$	−27.7535	−	6.33455i	−0.974556	−	0.222436i	−0.680011	+	0.733202i	$0.738025\pi$
$812$	−5.42068	+	22.1904i	−0.190229	+	0.778732i
$813$	7.66409	−	16.7594i	0.268791	−	0.587777i
$814$	−29.2172			−1.02406
$815$	5.77527			0.202299
$816$	7.44039	+	3.40250i	0.260466	+	0.119111i
$817$	−36.9553	+	76.7385i	−1.29290	+	2.68474i
$818$	−5.21204	+	6.53570i	−0.182235	+	0.228515i
$819$	22.7303	−	0.559066i	0.794262	−	0.0195353i
$820$	−1.13448	−	1.42260i	−0.0396179	−	0.0496793i
$821$	16.9685	−	3.87296i	0.592206	−	0.135167i	0.0840934	−	0.996458i	$-0.473201\pi$
$821$	16.9685	−	3.87296i	0.592206	−	0.135167i	0.508112	+	0.861291i	$0.330343\pi$
$822$	−18.3434	+	0.364890i	−0.639799	+	0.0127270i
$823$	−11.6357	−	5.60345i	−0.405594	−	0.195324i	0.219952	−	0.975511i	$-0.429410\pi$
$823$	−11.6357	−	5.60345i	−0.405594	−	0.195324i	−0.625547	+	0.780187i	$0.715124\pi$
$824$	−8.63345	+	10.8260i	−0.300760	+	0.377142i
$825$	30.9700	+	6.42348i	1.07824	+	0.223637i
$826$	−17.4358	−	0.264844i	−0.606669	−	0.00921510i
$827$	−8.63339	+	17.9274i	−0.300212	+	0.623397i	−0.995440	−	0.0953925i	$-0.969589\pi$
$827$	−8.63339	+	17.9274i	−0.300212	+	0.623397i	0.695227	+	0.718790i	$0.255304\pi$
$828$	−14.5960	+	12.6214i	−0.507246	+	0.438625i
$829$	−39.6230	−	9.04369i	−1.37616	−	0.314100i	−0.530440	−	0.847722i	$-0.677973\pi$
$829$	−39.6230	−	9.04369i	−1.37616	−	0.314100i	−0.845723	+	0.533622i	$0.820831\pi$
$830$	−2.84042	−	5.89820i	−0.0985925	−	0.204729i
$831$	2.76557	−	0.0550132i	0.0959365	−	0.00190839i
$832$			2.86462i			0.0993128i
$833$	8.33334	−	31.9977i	0.288733	−	1.10865i
$834$	−0.637539	+	0.832907i	−0.0220762	+	0.0288412i
$835$	1.21872	+	1.52823i	0.0421756	+	0.0528865i
$836$	27.0217	−	13.0130i	0.934564	−	0.450062i
$837$	−9.72172	−	6.84590i	−0.336032	−	0.236629i
$838$	11.1065	+	23.0630i	0.383669	+	0.796697i
$839$	−34.8655	−	16.7904i	−1.20369	−	0.579668i	−0.278966	−	0.960301i	$-0.589992\pi$
$839$	−34.8655	−	16.7904i	−1.20369	−	0.579668i	−0.924726	+	0.380633i	$0.875706\pi$
$840$	−1.90095	+	0.926482i	−0.0655889	+	0.0319667i
$841$	41.0326	−	19.7603i	1.41492	−	0.681388i
$842$	−14.5115	−	11.5726i	−0.500100	−	0.398817i
$843$	25.6671	+	50.6937i	0.884022	+	1.74598i
$844$	2.72463	+	3.41658i	0.0937857	+	0.117604i
$845$	−0.492272	−	2.15678i	−0.0169347	−	0.0741956i
$846$	11.7476	+	8.62699i	0.403889	+	0.296602i
$847$	−4.20546	+	8.40377i	−0.144501	+	0.288757i
$848$	−0.0929151	−	0.0740973i	−0.00319072	−	0.00254451i
$849$	−21.5289	−	42.5205i	−0.738868	−	1.45930i
$850$	22.0450	−	5.03164i	0.756139	−	0.172584i
$851$		−	49.2641i		−	1.68875i
$852$	−1.25850	−	0.963308i	−0.0431157	−	0.0330024i
$853$	1.52854	−	0.348878i	0.0523361	−	0.0119454i	−0.196273	−	0.980549i	$-0.562884\pi$
$853$	1.52854	−	0.348878i	0.0523361	−	0.0119454i	0.248609	+	0.968604i	$0.420027\pi$
$854$	3.49924	−	2.70464i	0.119742	−	0.0925508i
$855$	0.432857	+	10.8758i	0.0148034	+	0.371944i
$856$	3.05988	−	13.4062i	0.104585	−	0.458215i
$857$	1.24271	−	1.55831i	0.0424502	−	0.0532309i	−0.760153	−	0.649744i	$-0.774876\pi$
$857$	1.24271	−	1.55831i	0.0424502	−	0.0532309i	0.802603	+	0.596513i	$0.203448\pi$
$858$	−18.3652	+	4.57786i	−0.626979	+	0.156285i
$859$	−53.2227	−	12.1477i	−1.81594	−	0.414476i	−0.826925	−	0.562313i	$-0.809912\pi$
$859$	−53.2227	−	12.1477i	−1.81594	−	0.414476i	−0.989012	+	0.147837i	$0.952769\pi$
$860$	−1.11242	+	4.87385i	−0.0379334	+	0.166197i
$861$	−0.0849444	−	18.0690i	−0.00289490	−	0.615790i
$862$	−5.50472	−	24.1178i	−0.187492	−	0.821454i
$863$		−	8.41642i		−	0.286498i	−0.989687	−	0.143249i	$-0.954245\pi$
$863$		−	8.41642i		−	0.286498i	0.989687	−	0.143249i	$-0.0457550\pi$
$864$	1.97134	−	4.80768i	0.0670662	−	0.163561i
$865$	−0.342734	−	1.50161i	−0.0116533	−	0.0510564i
$866$	−13.2967	−	6.40335i	−0.451840	−	0.217595i
$867$	2.22539	+	8.92772i	0.0755782	+	0.303201i
$868$	−5.41414	−	2.70937i	−0.183768	−	0.0919620i
$869$	−2.90887	+	2.31975i	−0.0986767	+	0.0786921i
$870$	6.27578	+	2.86992i	0.212769	+	0.0972995i
$871$	−8.87784	+	7.07984i	−0.300814	+	0.239891i
$872$	−5.59778	+	11.6239i	−0.189565	+	0.393635i
$873$	17.4133	−	40.1721i	0.589350	−	1.35962i
$874$	21.9416	+	45.5621i	0.742184	+	1.54116i
$875$	−5.34750	+	10.6859i	−0.180778	+	0.361250i
$876$	5.39234	+	10.6501i	0.182190	+	0.359835i
$877$	−10.3798	+	4.99866i	−0.350502	+	0.168793i	−0.600847	−	0.799364i	$-0.705170\pi$
$877$	−10.3798	+	4.99866i	−0.350502	+	0.168793i	0.250345	+	0.968157i	$0.419456\pi$
$878$	6.64946	−	29.1332i	0.224408	−	0.983197i
$879$	11.8784	−	57.2701i	0.400647	−	1.93167i
$880$	1.37630	−	1.09756i	0.0463949	−	0.0369987i
$881$	−2.74219			−0.0923867			−0.0461934	−	0.998933i	$-0.514709\pi$
$881$	−2.74219			−0.0923867			−0.0461934	+	0.998933i	$0.514709\pi$
$882$	−20.5165	−	4.48024i	−0.690827	−	0.150858i
$883$	−41.6420			−1.40137			−0.700683	−	0.713473i	$-0.747121\pi$
$883$	−41.6420			−1.40137			−0.700683	+	0.713473i	$0.747121\pi$
$884$	−10.5791	+	8.43659i	−0.355815	+	0.283753i
$885$	−1.06986	+	5.15819i	−0.0359629	+	0.173391i
$886$	0.838506	−	3.67374i	0.0281702	−	0.123422i
$887$	−38.4723	+	18.5273i	−1.29177	+	0.622086i	−0.948389	−	0.317109i	$-0.897288\pi$
$887$	−38.4723	+	18.5273i	−1.29177	+	0.622086i	−0.343385	+	0.939195i	$0.611574\pi$
$888$	5.99248	+	11.8354i	0.201095	+	0.397171i
$889$	0.0996664	−	6.56147i	0.00334271	−	0.220065i
$890$	1.84104	+	3.82296i	0.0617118	+	0.128146i
$891$	33.9727	+	4.95535i	1.13813	+	0.166010i
$892$	2.87308	−	5.96601i	0.0961978	−	0.199757i
$893$	29.8637	−	23.8155i	0.999350	−	0.796955i
$894$	1.64367	+	0.751654i	0.0549726	+	0.0251391i
$895$	8.03321	−	6.40627i	0.268521	−	0.214138i
$896$	0.627843	−	2.57018i	0.0209748	−	0.0858636i
$897$	−7.71887	−	30.9662i	−0.257726	−	1.03393i
$898$	−36.0941	−	17.3820i	−1.20448	−	0.580045i
$899$	4.39625	+	19.2613i	0.146623	+	0.642399i
$900$	−3.74993	−	13.8629i	−0.124998	−	0.462097i
$901$		−	0.561363i		−	0.0187017i
$902$	3.34703	+	14.6643i	0.111444	+	0.488267i
$903$	−38.6676	+	31.1348i	−1.28678	+	1.03610i
$904$	0.537431	−	2.35464i	0.0178747	−	0.0783141i
$905$	−2.26185	−	0.516251i	−0.0751863	−	0.0171608i
$906$	30.7184	−	7.65711i	1.02055	−	0.254390i
$907$	−26.9083	+	33.7420i	−0.893477	+	1.12038i	0.0986471	+	0.995122i	$0.468549\pi$
$907$	−26.9083	+	33.7420i	−0.893477	+	1.12038i	−0.992124	+	0.125262i	$0.960023\pi$
$908$	−0.783689	+	3.43356i	−0.0260076	+	0.113947i
$909$	24.8189	−	0.987796i	0.823192	−	0.0327631i
$910$	0.0531194	−	3.49708i	0.00176089	−	0.115927i
$911$	2.12695	−	0.485461i	0.0704689	−	0.0160841i	−0.187141	−	0.982333i	$-0.559922\pi$
$911$	2.12695	−	0.485461i	0.0704689	−	0.0160841i	0.257610	+	0.966249i	$0.417065\pi$
$912$	−10.8135	−	8.27708i	−0.358071	−	0.274081i
$913$			54.1164i			1.79099i
$914$	4.16978	−	0.951725i	0.137924	−	0.0314803i
$915$	−0.603530	−	1.19200i	−0.0199521	−	0.0394063i
$916$	−7.14018	−	5.69410i	−0.235918	−	0.188138i
$917$	15.9430	+	13.1151i	0.526483	+	0.433099i
$918$	23.5607	−	6.87889i	0.777620	−	0.227037i
$919$	3.55035	+	15.5551i	0.117115	+	0.513115i	0.999123	+	0.0418798i	$0.0133347\pi$
$919$	3.55035	+	15.5551i	0.117115	+	0.513115i	−0.882007	+	0.471236i	$0.843808\pi$
$920$	1.85063	+	2.32062i	0.0610135	+	0.0765085i
$921$	−1.05962	−	2.09281i	−0.0349158	−	0.0689604i
$922$	−11.2677	−	8.98572i	−0.371083	−	0.295929i
$923$	2.36161	−	1.13729i	0.0777334	−	0.0374344i
$924$	17.4809	−	0.0821796i	0.575080	−	0.00270351i
$925$	33.0337	+	15.9082i	1.08614	+	0.523059i
$926$	9.41875	+	19.5582i	0.309519	+	0.642723i
$927$	1.65203	+	41.5081i	0.0542596	+	1.36330i
$928$	−7.77880	+	3.74607i	−0.255352	+	0.122971i
$929$	30.6882	+	38.4818i	1.00685	+	1.26255i	0.964677	+	0.263437i	$0.0848560\pi$
$929$	30.6882	+	38.4818i	1.00685	+	1.26255i	0.0421711	+	0.999110i	$0.486573\pi$
$930$	−1.11169	+	1.45235i	−0.0364537	+	0.0476245i
$931$	−25.3739	+	48.8370i	−0.831597	+	1.60057i
$932$		−	16.7048i		−	0.547184i
$933$	5.69392	−	0.113265i	0.186411	−	0.00370811i
$934$	−12.2658	−	25.4703i	−0.401351	−	0.833413i
$935$	8.10666	+	1.85029i	0.265116	+	0.0605110i
$936$	5.62115	+	6.50054i	0.183733	+	0.212477i
$937$	−5.00618	+	10.3954i	−0.163545	+	0.339604i	−0.966596	−	0.256306i	$-0.917494\pi$
$937$	−5.00618	+	10.3954i	−0.163545	+	0.339604i	0.803051	+	0.595911i	$0.203209\pi$
$938$	9.51702	−	4.40636i	0.310742	−	0.143873i
$939$	42.9443	+	8.90706i	1.40143	+	0.290671i
$940$	1.39783	−	1.75283i	0.0455923	−	0.0571710i
$941$	−18.7701	−	9.03922i	−0.611889	−	0.294670i	0.102158	−	0.994768i	$-0.467425\pi$
$941$	−18.7701	−	9.03922i	−0.611889	−	0.294670i	−0.714047	+	0.700098i	$0.753140\pi$
$942$	10.6647	−	0.212144i	0.347475	−	0.00691202i
$943$	−24.7259	+	5.64353i	−0.805187	+	0.183779i
$944$	−4.10934	−	5.15296i	−0.133748	−	0.167714i
$945$	−2.49572	+	5.83259i	−0.0811859	+	0.189734i
$946$	25.7661	−	32.3096i	0.837727	−	1.05048i
$947$	−2.31905	+	4.81555i	−0.0753590	+	0.156485i	−0.935245	−	0.354002i	$-0.884820\pi$
$947$	−2.31905	+	4.81555i	−0.0753590	+	0.156485i	0.859886	+	0.510487i	$0.170535\pi$
$948$	1.53630	+	0.702555i	0.0498969	+	0.0228179i
$949$	−19.7432			−0.640892
$950$	−37.6367			−1.22110
$951$	−18.7428	+	40.9856i	−0.607777	+	1.32905i
$952$	11.3408	−	5.25078i	0.367558	−	0.170179i
$953$	−24.3567	−	5.55925i	−0.788990	−	0.180082i	−0.191005	−	0.981589i	$-0.561175\pi$
$953$	−24.3567	−	5.55925i	−0.788990	−	0.180082i	−0.597985	+	0.801507i	$0.704032\pi$
$954$	−0.356247	+	0.0141787i	−0.0115339	+	0.000459051i
$955$	−1.55211	−	1.23777i	−0.0502251	−	0.0400532i
$956$	−3.20447	−	2.55548i	−0.103640	−	0.0826502i
$957$	−36.4473	−	43.8839i	−1.17818	−	1.41856i
$958$	−22.5495	−	5.14679i	−0.728543	−	0.166285i
$959$	−17.8044	+	21.6433i	−0.574934	+	0.698899i
$960$	−0.726883	−	0.332405i	−0.0234601	−	0.0107283i
$961$	25.7638			0.831089
$962$	−21.9405			−0.707391
$963$	−19.3629	−	36.4264i	−0.623962	−	1.17383i
$964$	1.61535	−	3.35430i	0.0520268	−	0.108035i
$965$	−1.49692	+	1.87708i	−0.0481875	+	0.0604252i
$966$	0.138566	+	29.4751i	0.00445828	+	0.948346i
$967$	−18.4621	−	23.1508i	−0.593702	−	0.744478i	0.390680	−	0.920527i	$-0.372240\pi$
$967$	−18.4621	−	23.1508i	−0.593702	−	0.744478i	−0.984382	+	0.176048i	$0.943669\pi$
$968$	−3.46279	+	0.790360i	−0.111298	+	0.0254031i
$969$	−1.27930	−	64.3115i	−0.0410969	−	2.06598i
$970$	−6.06795	−	2.92217i	−0.194830	−	0.0938252i
$971$	−19.0806	+	23.9263i	−0.612326	+	0.767833i	−0.987242	−	0.159226i	$-0.949100\pi$
$971$	−19.0806	+	23.9263i	−0.612326	+	0.767833i	0.374916	+	0.927059i	$0.377672\pi$
$972$	−4.96050	−	14.7781i	−0.159108	−	0.474009i
$973$	0.332762	+	1.56728i	0.0106679	+	0.0502448i
$974$	−2.82499	+	5.86614i	−0.0905184	+	0.187963i
$975$	23.2568	+	4.82368i	0.744813	+	0.154481i
$976$	1.62969	+	0.371966i	0.0521651	+	0.0119063i
$977$	3.06662	+	6.36790i	0.0981099	+	0.203727i	0.944247	−	0.329238i	$-0.106792\pi$
$977$	3.06662	+	6.36790i	0.0981099	+	0.203727i	−0.846137	+	0.532965i	$0.821078\pi$
$978$	0.431111	+	21.6724i	0.0137854	+	0.693007i
$979$		−	35.0759i		−	1.12103i
$980$	−0.814120	+	3.12599i	−0.0260061	+	0.0998560i
$981$	10.1064	+	37.3619i	0.322673	+	1.19287i
$982$	−20.5198	−	25.7310i	−0.654812	−	0.821109i
$983$	53.4691	−	25.7494i	1.70540	−	0.821277i	0.712589	−	0.701582i	$-0.247522\pi$
$983$	53.4691	−	25.7494i	1.70540	−	0.821277i	0.992811	−	0.119696i	$-0.0381919\pi$
$984$	5.25379	−	4.36349i	0.167485	−	0.139103i
$985$	4.58935	+	9.52987i	0.146229	+	0.303647i
$986$	−36.7437	−	17.6948i	−1.17016	−	0.563519i
$987$	21.6819	−	5.05611i	0.690143	−	0.160938i
$988$	20.2918	−	9.77200i	0.645567	−	0.310889i
$989$	54.4783	+	43.4450i	1.73231	+	1.38147i
$990$	0.969459	−	5.19130i	0.0308114	−	0.164990i
$991$	7.63885	+	9.57881i	0.242656	+	0.304281i	0.888214	−	0.459430i	$-0.151946\pi$
$991$	7.63885	+	9.57881i	0.242656	+	0.304281i	−0.645558	+	0.763711i	$0.723375\pi$
$992$	−0.509190	−	2.23091i	−0.0161668	−	0.0708314i
$993$	24.9779	−	0.496864i	0.792648	−	0.0157675i
$994$	−2.36813	+	0.502797i	−0.0751126	+	0.0159477i
$995$	−6.04431	−	4.82018i	−0.191618	−	0.152810i
$996$	21.9217	−	11.0993i	0.694615	−	0.351696i
$997$	25.8154	−	5.89219i	0.817581	−	0.186608i	0.206776	−	0.978388i	$-0.433703\pi$
$997$	25.8154	−	5.89219i	0.817581	−	0.186608i	0.610805	+	0.791781i	$0.290846\pi$
$998$			14.8075i			0.468723i
$999$	36.8227	+	15.0987i	1.16502	+	0.477703i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	294.2.j.a.41.16	yes	120
3.2	odd	2	inner	294.2.j.a.41.2	✓	120
49.6	odd	14	inner	294.2.j.a.251.2	yes	120
147.104	even	14	inner	294.2.j.a.251.16	yes	120

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
294.2.j.a.41.2	✓	120	3.2	odd	2	inner
294.2.j.a.41.16	yes	120	1.1	even	1	trivial
294.2.j.a.251.2	yes	120	49.6	odd	14	inner
294.2.j.a.251.16	yes	120	147.104	even	14	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)

\(f(q)\)	\(=\)	\(q+(0.781831 - 0.623490i) q^{2} +(0.351758 - 1.69596i) q^{3} +(0.222521 - 0.974928i) q^{4} +(-0.415766 + 0.200223i) q^{5} +(-0.782396 - 1.54527i) q^{6} +(-2.57018 - 0.627843i) q^{7} +(-0.433884 - 0.900969i) q^{8} +(-2.75253 - 1.19313i) q^{9} +O(q^{10})\)	\(q+(0.781831 - 0.623490i) q^{2} +(0.351758 - 1.69596i) q^{3} +(0.222521 - 0.974928i) q^{4} +(-0.415766 + 0.200223i) q^{5} +(-0.782396 - 1.54527i) q^{6} +(-2.57018 - 0.627843i) q^{7} +(-0.433884 - 0.900969i) q^{8} +(-2.75253 - 1.19313i) q^{9} +(-0.200223 + 0.415766i) q^{10} +(2.98244 - 2.37842i) q^{11} +(-1.57516 - 0.720324i) q^{12} +(2.23965 - 1.78606i) q^{13} +(-2.40090 + 1.11161i) q^{14} +(0.193320 + 0.775551i) q^{15} +(-0.900969 - 0.433884i) q^{16} +(-1.05109 - 4.60514i) q^{17} +(-2.89592 + 0.783349i) q^{18} +7.86219i q^{19} +(0.102686 + 0.449896i) q^{20} +(-1.96887 + 4.13806i) q^{21} +(0.848848 - 3.71905i) q^{22} +(6.27080 + 1.43127i) q^{23} +(-1.68063 + 0.418925i) q^{24} +(-2.98468 + 3.74267i) q^{25} +(0.637438 - 2.79280i) q^{26} +(-2.99172 + 4.24848i) q^{27} +(-1.18402 + 2.36603i) q^{28} +(8.41735 - 1.92120i) q^{29} +(0.634692 + 0.485818i) q^{30} +2.28828i q^{31} +(-0.974928 + 0.222521i) q^{32} +(-2.98460 - 5.89472i) q^{33} +(-3.69304 - 2.94510i) q^{34} +(1.19430 - 0.253572i) q^{35} +(-1.77571 + 2.41802i) q^{36} +(-1.70432 - 7.46711i) q^{37} +(4.90199 + 6.14691i) q^{38} +(-2.24127 - 4.42661i) q^{39} +(0.360789 + 0.287719i) q^{40} +(-3.55254 + 1.71081i) q^{41} +(1.04071 + 4.46284i) q^{42} +(9.76045 + 4.70038i) q^{43} +(-1.65513 - 3.43692i) q^{44} +(1.38330 - 0.0550556i) q^{45} +(5.79509 - 2.79077i) q^{46} +(-3.02912 - 3.79839i) q^{47} +(-1.05277 + 1.37538i) q^{48} +(6.21163 + 3.22734i) q^{49} +4.78705i q^{50} +(-8.17985 + 0.162715i) q^{51} +(-1.24291 - 2.58093i) q^{52} +(0.115863 + 0.0264450i) q^{53} +(0.309864 + 5.18691i) q^{54} +(-0.763787 + 1.58602i) q^{55} +(0.549491 + 2.58806i) q^{56} +(13.3339 + 2.76558i) q^{57} +(5.38309 - 6.75019i) q^{58} +(5.93818 + 2.85967i) q^{59} +(0.799124 - 0.0158963i) q^{60} +(-1.62969 + 0.371966i) q^{61} +(1.42672 + 1.78905i) q^{62} +(6.32540 + 4.79472i) q^{63} +(-0.623490 + 0.781831i) q^{64} +(-0.573561 + 1.19101i) q^{65} +(-6.00875 - 2.74781i) q^{66} -3.96394 q^{67} -4.72357 q^{68} +(4.63317 - 10.1315i) q^{69} +(0.775644 - 0.942885i) q^{70} +(0.892081 + 0.203612i) q^{71} +(0.119306 + 2.99763i) q^{72} +(-5.38845 - 4.29715i) q^{73} +(-5.98816 - 4.77540i) q^{74} +(5.29751 + 6.37839i) q^{75} +(7.66507 + 1.74950i) q^{76} +(-9.15868 + 4.24045i) q^{77} +(-4.51224 - 2.06345i) q^{78} -0.975332 q^{79} +0.461466 q^{80} +(6.15288 + 6.56826i) q^{81} +(-1.71081 + 3.55254i) q^{82} +(-8.84503 + 11.0913i) q^{83} +(3.59619 + 2.84031i) q^{84} +(1.35906 + 1.70421i) q^{85} +(10.5617 - 2.41063i) q^{86} +(-0.297413 - 14.9512i) q^{87} +(-3.43692 - 1.65513i) q^{88} +(5.73296 - 7.18891i) q^{89} +(1.04718 - 0.905519i) q^{90} +(-6.87766 + 3.18434i) q^{91} +(2.79077 - 5.79509i) q^{92} +(3.88082 + 0.804920i) q^{93} +(-4.73652 - 1.08108i) q^{94} +(-1.57419 - 3.26883i) q^{95} +(0.0344474 + 1.73171i) q^{96} +14.5946i q^{97} +(6.86866 - 1.34965i) q^{98} +(-11.0470 + 2.98823i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 120 q + 20 q^{4} - 14 q^{6} + 4 q^{7} - 10 q^{9}+O(q^{10}) \) 120 * q + 20 * q^4 - 14 * q^6 + 4 * q^7 - 10 * q^9	\( 120 q + 20 q^{4} - 14 q^{6} + 4 q^{7} - 10 q^{9} + 12 q^{15} - 20 q^{16} - 8 q^{18} - 12 q^{21} - 10 q^{22} - 24 q^{25} + 42 q^{27} - 4 q^{28} + 8 q^{30} + 10 q^{36} - 58 q^{37} + 8 q^{39} - 14 q^{40} - 2 q^{42} - 12 q^{43} + 14 q^{45} - 60 q^{46} - 36 q^{49} - 24 q^{51} - 42 q^{52} - 14 q^{55} + 34 q^{57} + 50 q^{58} - 12 q^{60} - 154 q^{61} + 20 q^{64} - 28 q^{67} + 28 q^{69} - 38 q^{70} + 8 q^{72} - 84 q^{75} - 16 q^{78} + 16 q^{79} + 22 q^{81} - 30 q^{84} - 32 q^{85} - 56 q^{87} - 4 q^{88} - 42 q^{90} + 88 q^{91} + 14 q^{93} + 112 q^{94} - 224 q^{99}+O(q^{100}) \) 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

Varieties

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Database

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