LMFDB - Embedded newform 294.2.j.a.251.16

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			251.16
Character	$\chi$	$=$	294.251
Dual form			294.2.j.a.41.16

$q$-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} +(-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} + 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
$3$	0.351758	+	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	0.338599	−	0.940931i	$-0.390047\pi$
$5$	−0.415766	−	0.200223i	−0.185936	−	0.0895423i	−0.524536	+	0.851388i	$0.675761\pi$
$6$	−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	0.959693	−	0.281051i	$-0.0906829\pi$
$11$	2.98244	+	2.37842i	0.899240	+	0.717120i	−0.0604524	+	0.998171i	$0.519254\pi$
$12$	−1.57516	+	0.720324i	−0.454710	+	0.207940i
$13$	2.23965	+	1.78606i	0.621167	+	0.495364i	0.882766	−	0.469813i	$-0.155678\pi$
$13$	2.23965	+	1.78606i	0.621167	+	0.495364i	−0.261599	+	0.965177i	$0.584250\pi$
$14$	−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	0.671668	+	0.740852i	$0.265578\pi$
$17$	−1.05109	+	4.60514i	−0.254928	+	1.11691i	−0.926596	+	0.376059i	$0.877279\pi$
$18$	−2.89592	−	0.783349i	−0.682575	−	0.184637i
$19$		−	7.86219i		−	1.80371i	−0.432039	−	0.901855i	$-0.642206\pi$
$19$		−	7.86219i		−	1.80371i	0.432039	−	0.901855i	$-0.357794\pi$
$20$	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	0.488704	−	0.872450i	$-0.337470\pi$
$23$	6.27080	−	1.43127i	1.30755	−	0.298440i	0.818849	+	0.574009i	$0.194613\pi$
$24$	−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	0.914559	−	0.404453i	$-0.132538\pi$
$29$	8.41735	+	1.92120i	1.56306	+	0.356759i	0.648503	+	0.761212i	$0.275395\pi$
$30$	0.634692	−	0.485818i	0.115878	−	0.0886978i
$31$		−	2.28828i		−	0.410987i	−0.978658	−	0.205494i	$-0.934120\pi$
$31$		−	2.28828i		−	0.410987i	0.978658	−	0.205494i	$-0.0658800\pi$
$32$	−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	0.617364	+	0.786678i	$0.288201\pi$
$37$	−1.70432	+	7.46711i	−0.280188	+	1.22759i	−0.897552	+	0.440908i	$0.854657\pi$
$38$	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	0.135398	−	0.990791i	$-0.456769\pi$
$41$	−3.55254	−	1.71081i	−0.554814	−	0.267184i	−0.690212	+	0.723607i	$0.742483\pi$
$42$	1.04071	−	4.46284i	0.160585	−	0.688631i
$43$	9.76045	−	4.70038i	1.48845	−	0.716802i	0.499679	−	0.866211i	$-0.333451\pi$
$43$	9.76045	−	4.70038i	1.48845	−	0.716802i	0.988775	+	0.149409i	$0.0477371\pi$
$44$	−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	−0.952028	−	0.306012i	$-0.901005\pi$
$47$	−3.02912	+	3.79839i	−0.441842	+	0.554052i	0.510186	+	0.860064i	$0.329577\pi$
$48$	−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	−0.214556	−	0.976712i	$-0.568830\pi$
$53$	0.115863	−	0.0264450i	0.0159150	−	0.00363250i	0.230471	+	0.973079i	$0.425973\pi$
$54$	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	−0.00538074	−	0.999986i	$-0.501713\pi$
$59$	5.93818	−	2.85967i	0.773085	−	0.372298i	0.778465	+	0.627688i	$0.215998\pi$
$60$	0.799124	+	0.0158963i	0.103167	+	0.00205221i
$61$	−1.62969	−	0.371966i	−0.208660	−	0.0476254i	0.116913	−	0.993142i	$-0.462700\pi$
$61$	−1.62969	−	0.371966i	−0.208660	−	0.0476254i	−0.325573	+	0.945517i	$0.605557\pi$
$62$	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	−0.169257	−	0.985572i	$-0.554137\pi$
$71$	0.892081	−	0.203612i	0.105871	−	0.0241643i	0.275128	+	0.961408i	$0.411280\pi$
$72$	0.119306	−	2.99763i	0.0140603	−	0.353274i
$73$	−5.38845	+	4.29715i	−0.630671	+	0.502943i	−0.885863	−	0.463947i	$-0.846433\pi$
$73$	−5.38845	+	4.29715i	−0.630671	+	0.502943i	0.255192	+	0.966890i	$0.417861\pi$
$74$	−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	−0.976073	−	0.217444i	$-0.930228\pi$
$83$	−8.84503	−	11.0913i	−0.970868	−	1.21743i	0.00520460	−	0.999986i	$-0.498343\pi$
$84$	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	0.986555	−	0.163430i	$-0.0522559\pi$
$89$	5.73296	+	7.18891i	0.607693	+	0.762023i	−0.378862	+	0.925453i	$0.623684\pi$
$90$	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	$-0.734386\pi$
$97$		−	14.5946i		−	1.48186i	0.671584	−	0.740929i	$-0.265614\pi$
$98$	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	0.0242343	−	0.999706i	$-0.492285\pi$
$101$	−7.45960	−	3.59235i	−0.742258	−	0.357452i	−0.766492	+	0.642254i	$0.778000\pi$
$102$	−6.29381	−	5.22727i	−0.623180	−	0.517577i
$103$	−6.00798	+	12.4757i	−0.591984	+	1.22927i	0.362773	+	0.931878i	$0.381830\pi$
$103$	−6.00798	+	12.4757i	−0.591984	+	1.22927i	−0.954756	+	0.297389i	$0.903884\pi$
$104$	−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	0.0538401	−	0.998550i	$-0.482854\pi$
$107$	10.7510	−	8.57360i	1.03933	−	0.828842i	0.985494	+	0.169708i	$0.0542824\pi$
$108$	3.47624	−	3.86209i	0.334502	−	0.371630i
$109$	−8.04399	+	10.0868i	−0.770475	+	0.966145i	−0.999974	−	0.00716406i	$-0.997720\pi$
$109$	−8.04399	+	10.0868i	−0.770475	+	0.966145i	0.229500	+	0.973309i	$0.426291\pi$
$110$	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	−0.530637	−	0.847599i	$-0.678047\pi$
$113$	1.88827	−	1.50585i	0.177634	−	0.141658i	0.708271	+	0.705941i	$0.249476\pi$
$114$	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	−0.944519	−	0.328455i	$-0.893472\pi$
$127$	0.551916	−	2.41810i	0.0489746	−	0.214572i	0.993494	+	0.113884i	$0.0363291\pi$
$128$		−	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	−0.715009	−	0.699115i	$-0.753577\pi$
$131$	−7.03006	+	3.38550i	−0.614220	+	0.295793i	0.100789	+	0.994908i	$0.467863\pi$
$132$	−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	0.999784	+	0.0207615i	$0.00660908\pi$
$137$	4.59598	+	9.54365i	0.392661	+	0.815369i	−0.607123	+	0.794608i	$0.707677\pi$
$138$	−2.69456	+	10.8099i	−0.229376	+	0.920200i
$139$	−0.262752	+	0.545611i	−0.0222864	+	0.0462781i	−0.911815	−	0.410602i	$-0.865319\pi$
$139$	−0.262752	+	0.545611i	−0.0222864	+	0.0462781i	0.889529	+	0.456880i	$0.151033\pi$
$140$	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	0.589502	−	0.807767i	$-0.299324\pi$
$149$	−0.815837	−	0.650608i	−0.0668360	−	0.0532999i	−0.656338	+	0.754467i	$0.727895\pi$
$150$	8.11862	−	1.68388i	0.662883	−	0.137488i
$151$	−4.06723	−	17.8197i	−0.330987	−	1.45015i	−0.817224	−	0.576321i	$-0.804488\pi$
$151$	−4.06723	−	17.8197i	−0.330987	−	1.45015i	0.486237	−	0.873827i	$-0.338369\pi$
$152$	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	0.766712	−	0.641991i	$-0.221891\pi$
$157$	−2.67207	−	5.54860i	−0.213254	−	0.442827i	−0.979966	+	0.199165i	$0.936177\pi$
$158$	−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	−0.819784	−	0.572672i	$-0.805907\pi$
$163$	−11.2757	+	5.43007i	−0.883178	+	0.425316i	−0.0633939	+	0.997989i	$0.520192\pi$
$164$	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	−0.998214	−	0.0597332i	$-0.980975\pi$
$167$	−0.942554	+	4.12960i	−0.0729370	+	0.319558i	0.925277	+	0.379291i	$0.123832\pi$
$168$	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	0.938815	−	0.344421i	$-0.111925\pi$
$173$	−0.742706	−	3.25401i	−0.0564669	−	0.247398i	−0.995282	+	0.0970236i	$0.969068\pi$
$174$	−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	−0.687832	−	0.725870i	$-0.741438\pi$
$179$	−21.7074	−	4.95458i	−1.62249	−	0.370323i	−0.934658	+	0.355547i	$0.884295\pi$
$180$	0.254139	+	1.36087i	0.0189424	+	0.101433i
$181$	3.93065	−	3.13459i	0.292163	−	0.232992i	−0.466428	−	0.884559i	$-0.654460\pi$
$181$	3.93065	−	3.13459i	0.292163	−	0.232992i	0.758591	+	0.651567i	$0.225888\pi$
$182$	−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	−0.822460	−	0.568824i	$-0.807399\pi$
$191$	1.86656	−	3.87596i	0.135060	−	0.280455i	0.957519	+	0.288369i	$0.0931130\pi$
$192$	1.10663	−	1.33243i	0.0798645	−	0.0961596i
$193$	4.68747	+	2.25737i	0.337412	+	0.162489i	0.594915	−	0.803788i	$-0.297186\pi$
$193$	4.68747	+	2.25737i	0.337412	+	0.162489i	−0.257504	+	0.966277i	$0.582900\pi$
$194$	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	$0.304108\pi$
$197$			22.9212i			1.63307i	−0.577296	+	0.816535i	$0.695892\pi$
$198$	−6.77379	−	9.22401i	−0.481392	−	0.655522i
$199$	7.26888	−	15.0940i	0.515277	−	1.06998i	−0.467295	−	0.884101i	$-0.654771\pi$
$199$	7.26888	−	15.0940i	0.515277	−	1.06998i	0.982572	−	0.185882i	$-0.0595143\pi$
$200$	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	0.679150	−	0.733999i	$-0.262348\pi$
$211$	−2.72463	−	3.41658i	−0.187571	−	0.235207i	−0.866722	+	0.498792i	$0.833777\pi$
$212$	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	−0.000828224	−	1.00000i	$-0.500264\pi$
$223$	6.45575	−	1.47348i	0.432309	−	0.0986717i	0.433137	+	0.901328i	$0.357406\pi$
$224$	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	0.989897	−	0.141791i	$-0.0452862\pi$
$229$	3.96250	+	8.22821i	0.261849	+	0.543736i	−0.728047	+	0.685527i	$0.759572\pi$
$230$	−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	0.719717	−	0.694267i	$-0.244271\pi$
$233$	16.2860	+	3.71717i	1.06693	+	0.243520i	0.347212	+	0.937787i	$0.387128\pi$
$234$	−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	0.950534	−	0.310622i	$-0.100537\pi$
$239$	1.77835	+	3.69278i	0.115032	+	0.238866i	−0.835502	+	0.549488i	$0.814823\pi$
$240$	0.162324	+	0.782626i	0.0104780	+	0.0505183i
$241$	3.62965	−	0.828444i	0.233806	−	0.0533648i	−0.104012	−	0.994576i	$-0.533168\pi$
$241$	3.62965	−	0.828444i	0.233806	−	0.0533648i	0.337819	+	0.941211i	$0.390311\pi$
$242$	−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	−0.418375	−	0.908274i	$-0.637400\pi$
$251$	0.489376	−	0.235671i	0.0308892	−	0.0148754i	0.449265	+	0.893399i	$0.351686\pi$
$252$	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	−0.970172	−	0.242418i	$-0.922059\pi$
$257$	0.145948	−	0.639440i	0.00910399	−	0.0398872i	0.979276	+	0.202531i	$0.0649166\pi$
$258$	−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	$-0.850237\pi$
$263$		−	14.7034i		−	0.906653i	0.891345	−	0.453326i	$-0.149763\pi$
$264$	−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	0.309976	−	0.950744i	$-0.399679\pi$
$269$	−11.2497	−	14.1067i	−0.685908	−	0.860101i	−0.995883	+	0.0906435i	$0.971108\pi$
$270$	−1.16737	+	2.09450i	−0.0710437	+	0.127467i
$271$	10.3730	−	2.36757i	0.630116	−	0.143820i	0.104477	−	0.994527i	$-0.466683\pi$
$271$	10.3730	−	2.36757i	0.630116	−	0.143820i	0.525639	+	0.850707i	$0.323826\pi$
$272$	−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	−0.963129	−	0.269040i	$-0.913294\pi$
$277$	0.355370	−	1.55698i	0.0213521	−	0.0935496i	0.984481	+	0.175490i	$0.0561509\pi$
$278$	−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	−0.893585	−	0.448894i	$-0.851818\pi$
$281$	−25.6486	−	20.4541i	−1.53007	−	1.22019i	−0.636480	−	0.771293i	$-0.719610\pi$
$282$	−3.49957	−	7.65265i	−0.208396	−	0.455708i
$283$	21.5133	+	17.1563i	1.27883	+	1.01984i	0.998197	+	0.0600219i	$0.0191171\pi$
$283$	21.5133	+	17.1563i	1.27883	+	1.01984i	0.280637	+	0.959814i	$0.409454\pi$
$284$	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	0.653240	−	0.757151i	$-0.273409\pi$
$307$	1.05886	+	0.844413i	0.0604323	+	0.0481932i	−0.592808	+	0.805344i	$0.701981\pi$
$308$	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	−0.949938	−	0.312438i	$-0.898854\pi$
$311$	0.731657	−	3.20560i	0.0414885	−	0.181773i	0.991427	+	0.130665i	$0.0417114\pi$
$312$	−3.01579	−	3.93994i	−0.170735	−	0.223055i
$313$		−	25.3216i		−	1.43126i	−0.698479	−	0.715630i	$-0.746140\pi$
$313$		−	25.3216i		−	1.43126i	0.698479	−	0.715630i	$-0.253860\pi$
$314$	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	−0.864305	−	0.502969i	$-0.832241\pi$
$317$	−25.3676	+	5.78999i	−1.42479	+	0.325198i	−0.560481	+	0.828167i	$0.689384\pi$
$318$	−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	−0.806851	−	0.590755i	$-0.798830\pi$
$331$	3.20960	−	14.0622i	0.176416	−	0.772928i	0.983267	−	0.182173i	$-0.0583130\pi$
$332$	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	−0.337073	−	0.941479i	$-0.609437\pi$
$337$	3.46670	−	1.66947i	0.188843	−	0.0909420i	0.525916	+	0.850537i	$0.323723\pi$
$338$	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	−0.461624	−	0.887075i	$-0.652733\pi$
$347$	−9.17698	+	2.09459i	−0.492646	+	0.112443i	−0.0310216	+	0.999519i	$0.509876\pi$
$348$	−14.6426	+	3.03701i	−0.784924	+	0.162801i
$349$	2.10222	+	4.36531i	0.112529	+	0.233670i	0.949626	−	0.313385i	$-0.101463\pi$
$349$	2.10222	+	4.36531i	0.112529	+	0.233670i	−0.837097	+	0.547055i	$0.815749\pi$
$350$	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	−0.601233	−	0.799074i	$-0.705323\pi$
$353$	−6.60133	+	3.17903i	−0.351354	+	0.169203i	0.249879	+	0.968277i	$0.419609\pi$
$354$	−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	0.998387	+	0.0567778i	$0.0180826\pi$
$359$	7.96342	+	16.5362i	0.420293	+	0.872748i	−0.578093	+	0.815971i	$0.696203\pi$
$360$	−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	0.0506461	−	0.998717i	$-0.483872\pi$
$367$	19.8391	−	15.8212i	1.03559	−	0.825858i	0.984947	+	0.172859i	$0.0553005\pi$
$368$	−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	−0.432957	−	0.901415i	$-0.642530\pi$
$379$	10.5555	−	13.2362i	0.542200	−	0.679897i	0.975156	+	0.221518i	$0.0711012\pi$
$380$	−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	0.988467	+	0.151440i	$0.0483909\pi$
$383$	17.9295	+	22.4829i	0.916155	+	1.14882i	−0.0723117	+	0.997382i	$0.523038\pi$
$384$	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	−0.771752	−	0.635924i	$-0.780619\pi$
$389$	4.07505	−	8.46193i	0.206613	−	0.429037i	0.978365	+	0.206887i	$0.0663334\pi$
$390$	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	−0.999577	−	0.0290662i	$-0.990747\pi$
$397$	−7.04595	+	14.6311i	−0.353626	+	0.734312i	0.645951	+	0.763379i	$0.276461\pi$
$398$	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	−0.731633	−	0.681699i	$-0.761241\pi$
$401$	−4.60232	+	3.67023i	−0.229829	+	0.183282i	0.501804	+	0.864981i	$0.332670\pi$
$402$	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	0.0162238	−	0.999868i	$-0.494836\pi$
$409$	−8.14988	−	1.86016i	−0.402986	−	0.0919788i	−0.419209	+	0.907890i	$0.637693\pi$
$410$			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	−0.899977	−	0.435937i	$-0.856417\pi$
$419$	−5.69608	−	24.9562i	−0.278272	−	1.21919i	0.621706	−	0.783251i	$-0.286440\pi$
$420$	−2.06387	+	0.460868i	−0.100707	+	0.0224881i
$421$	−4.13020	+	18.0956i	−0.201293	+	0.881924i	0.768857	+	0.639421i	$0.220826\pi$
$421$	−4.13020	+	18.0956i	−0.201293	+	0.881924i	−0.970151	+	0.242504i	$0.922031\pi$
$422$		−	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	0.982107	+	0.188323i	$0.0603053\pi$
$431$	10.7334	+	22.2882i	0.517010	+	1.07358i	−0.465097	+	0.885260i	$0.653980\pi$
$432$	4.53880	+	2.52969i	0.218373	+	0.121710i
$433$	−6.40335	+	13.2967i	−0.307726	+	0.638999i	−0.996279	−	0.0861869i	$-0.972532\pi$
$433$	−6.40335	+	13.2967i	−0.307726	+	0.638999i	0.688553	+	0.725186i	$0.258246\pi$
$434$	−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	0.994630	−	0.103495i	$-0.0330027\pi$
$439$	23.3630	+	18.6314i	1.11506	+	0.889227i	0.120425	+	0.992722i	$0.461574\pi$
$440$	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	0.690974	−	0.722880i	$-0.257182\pi$
$443$	2.94611	+	2.34944i	0.139974	+	0.111625i	−0.551000	+	0.834505i	$0.685754\pi$
$444$	−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	−0.116276	+	0.993217i	$0.537096\pi$
$449$	−17.3820	+	36.0941i	−0.820307	+	1.70339i	−0.704031	+	0.710169i	$0.748619\pi$
$450$	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	−0.341579	−	0.939853i	$-0.610962\pi$
$457$	3.85346	−	1.85573i	0.180257	−	0.0868073i	0.521836	+	0.853046i	$0.325247\pi$
$458$	−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	0.843699	+	0.536816i	$0.180373\pi$
$461$	−3.20697	+	14.0506i	−0.149363	+	0.654403i	−0.993063	+	0.117587i	$0.962484\pi$
$462$	13.7184	−	10.8349i	0.638236	−	0.504086i
$463$	−4.83048	−	21.1637i	−0.224492	−	0.983562i	−0.954051	−	0.299644i	$-0.903132\pi$
$463$	−4.83048	−	21.1637i	−0.224492	−	0.983562i	0.729559	−	0.683918i	$-0.239725\pi$
$464$	−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	0.883002	+	0.469369i	$0.155518\pi$
$467$	6.29064	+	27.5611i	0.291096	+	1.27538i	−0.591906	+	0.806007i	$0.701624\pi$
$468$	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	−0.993224	−	0.116214i	$-0.962924\pi$
$479$	−14.4210	+	18.0833i	−0.658911	+	0.826248i	0.334313	+	0.942462i	$0.391496\pi$
$480$	−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	0.296227	−	0.955118i	$-0.404272\pi$
$487$	−5.86614	−	2.82499i	−0.265820	−	0.128012i	−0.562047	+	0.827105i	$0.689986\pi$
$488$	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	$0.266422\pi$
$491$			32.9112i			1.48526i	−0.669702	+	0.742630i	$0.733578\pi$
$492$	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	0.530993	−	0.847376i	$-0.321819\pi$
$499$	−9.23232	−	11.5770i	−0.413295	−	0.518256i	−0.944288	+	0.329120i	$0.893248\pi$
$500$	−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	−0.692070	−	0.721831i	$-0.743301\pi$
$503$	3.71544	−	4.65902i	0.165663	−	0.207735i	0.857733	+	0.514096i	$0.171872\pi$
$504$	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	0.942713	+	0.333606i	$0.108265\pi$
$523$	14.0820	+	29.2417i	0.615765	+	1.27865i	−0.326948	+	0.945042i	$0.606020\pi$
$524$	−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	−0.150633	−	0.988590i	$-0.548131\pi$
$541$	19.6935	−	24.6949i	0.846690	−	1.06172i	0.997323	−	0.0731260i	$-0.0232975\pi$
$542$	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	0.532854	−	0.846207i	$-0.321120\pi$
$547$	4.75925	+	2.29193i	0.203491	+	0.0979959i	−0.329363	+	0.944203i	$0.606834\pi$
$548$	−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	$-0.854742\pi$
$557$		−	20.8002i		−	0.881333i	0.897671	−	0.440666i	$-0.145258\pi$
$558$	−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	−0.997031	−	0.0770030i	$-0.975465\pi$
$563$	−20.1742	−	25.2977i	−0.850243	−	1.06617i	0.146788	−	0.989168i	$-0.453107\pi$
$564$	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	$-0.820384\pi$
$569$		−	25.5143i		−	1.06962i	0.844974	−	0.534808i	$-0.179616\pi$
$570$	−3.81959	−	4.99007i	−0.159985	−	0.209011i
$571$	4.98153	−	21.8255i	0.208470	−	0.913369i	−0.757115	−	0.653282i	$-0.773392\pi$
$571$	4.98153	−	21.8255i	0.208470	−	0.913369i	0.965585	−	0.260087i	$-0.0837512\pi$
$572$	−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	0.0344185	−	0.999408i	$-0.489042\pi$
$577$	−22.3940	−	17.8586i	−0.932273	−	0.743463i	−0.966691	+	0.255945i	$0.917614\pi$
$578$	−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	0.821848	−	0.569707i	$-0.192943\pi$
$593$	21.6448	+	10.4236i	0.888847	+	0.428046i	0.0669990	+	0.997753i	$0.478658\pi$
$594$	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	−0.992319	−	0.123707i	$-0.960522\pi$
$599$	−32.6425	−	26.0315i	−1.33374	−	1.06362i	−0.341417	−	0.939912i	$-0.610907\pi$
$600$	3.44823	+	7.54037i	0.140773	+	0.307835i
$601$	4.71968	+	3.76382i	0.192520	+	0.153529i	0.715006	−	0.699118i	$-0.246424\pi$
$601$	4.71968	+	3.76382i	0.192520	+	0.153529i	−0.522486	+	0.852648i	$0.674995\pi$
$602$	−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	$-0.864113\pi$
$607$		−	20.4023i		−	0.828102i	0.910254	−	0.414051i	$-0.135887\pi$
$608$	−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	0.463690	−	0.885998i	$-0.346525\pi$
$613$	−12.4605	−	15.6250i	−0.503275	−	0.631087i	−0.966965	+	0.254911i	$0.917954\pi$
$614$	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	0.541109	−	0.840952i	$-0.318004\pi$
$617$	16.4874	+	3.76313i	0.663757	+	0.151498i	0.122647	+	0.992450i	$0.460862\pi$
$618$	−14.5777	−	19.0449i	−0.586400	−	0.766097i
$619$		−	25.0375i		−	1.00634i	−0.864187	−	0.503171i	$-0.832167\pi$
$619$		−	25.0375i		−	1.00634i	0.864187	−	0.503171i	$-0.167833\pi$
$620$	−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	−0.864655	−	0.502365i	$-0.832463\pi$
$631$	−25.3959	+	12.2300i	−1.01099	+	0.486869i	−0.146339	+	0.989235i	$0.546749\pi$
$632$	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	−0.660180	−	0.751107i	$-0.729520\pi$
$641$	−23.5227	+	5.36890i	−0.929089	+	0.212059i	−0.268909	+	0.963166i	$0.586663\pi$
$642$	4.83702	+	23.3211i	0.190902	+	0.920410i
$643$	−11.5031	−	23.8865i	−0.453640	−	0.941993i	−0.994874	−	0.101121i	$-0.967757\pi$
$643$	−11.5031	−	23.8865i	−0.453640	−	0.941993i	0.541234	−	0.840872i	$-0.317957\pi$
$644$	−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	−0.539668	−	0.841878i	$-0.681450\pi$
$647$	−5.54352	+	2.66962i	−0.217938	+	0.104953i	0.321730	+	0.946832i	$0.395736\pi$
$648$	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	0.732737	−	0.680512i	$-0.238243\pi$
$653$	−6.54596	−	13.5928i	−0.256163	−	0.531929i	−0.988900	+	0.148584i	$0.952528\pi$
$654$	−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	0.133753	−	0.991015i	$-0.457297\pi$
$659$	17.5653	−	4.00916i	0.684245	−	0.156175i	0.550492	+	0.834840i	$0.314440\pi$
$660$	2.34554	+	1.94806i	0.0912998	+	0.0758282i
$661$	−36.7924	+	29.3410i	−1.43106	+	1.14123i	−0.464257	+	0.885701i	$0.653679\pi$
$661$	−36.7924	+	29.3410i	−1.43106	+	1.14123i	−0.966801	+	0.255530i	$0.917750\pi$
$662$	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	−0.684451	−	0.729059i	$-0.739958\pi$
$673$	4.63417	−	5.81106i	0.178634	−	0.224000i	0.863085	+	0.505059i	$0.168529\pi$
$674$	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	0.998934	−	0.0461575i	$-0.0146976\pi$
$677$	19.0370	+	23.8716i	0.731650	+	0.917460i	−0.267284	+	0.963618i	$0.586126\pi$
$678$	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	0.549035	+	0.835799i	$0.314995\pi$
$683$	−11.6751	+	24.2437i	−0.446737	+	0.927659i	−0.995772	+	0.0918596i	$0.970719\pi$
$684$	−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	−0.947105	−	0.320922i	$-0.896007\pi$
$691$	−2.77820	+	5.76899i	−0.105688	+	0.219463i	0.841418	+	0.540385i	$0.181721\pi$
$692$	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	−0.158812	−	0.987309i	$-0.550766\pi$
$701$	20.3446	−	16.2243i	0.768404	−	0.612782i	0.927216	+	0.374527i	$0.122195\pi$
$702$	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	−0.883964	−	0.467555i	$-0.845135\pi$
$709$	−7.73261	−	33.8788i	−0.290404	−	1.27234i	0.593560	−	0.804790i	$-0.297722\pi$
$710$	−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	−0.752417	−	0.658687i	$-0.771112\pi$
$719$	−18.9458	+	9.12382i	−0.706560	+	0.340261i	0.0458576	+	0.998948i	$0.485398\pi$
$720$	−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	0.573487	+	0.819215i	$0.305590\pi$
$727$	−11.4475	+	23.7710i	−0.424564	+	0.881617i	−0.998051	+	0.0624020i	$0.980124\pi$
$728$	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	0.664362	−	0.747411i	$-0.268703\pi$
$733$	2.26133	+	1.80335i	0.0835241	+	0.0666082i	−0.580838	+	0.814019i	$0.697275\pi$
$734$	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	0.806877	+	0.590719i	$0.201156\pi$
$739$	9.13971	+	40.0437i	0.336210	+	1.47303i	−0.470668	+	0.882311i	$0.655987\pi$
$740$	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	−0.250557	−	0.968102i	$-0.580614\pi$
$743$	18.0599	−	37.5019i	0.662555	−	1.37581i	0.913112	−	0.407708i	$-0.133672\pi$
$744$	−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	−0.371604	−	0.928391i	$-0.621192\pi$
$751$	3.35840	−	1.61732i	0.122550	−	0.0590168i	0.494154	+	0.869374i	$0.335478\pi$
$752$	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	0.824984	+	0.565156i	$0.191184\pi$
$757$	8.99451	+	39.4075i	0.326911	+	1.43229i	−0.498073	+	0.867135i	$0.665959\pi$
$758$	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	−0.993802	−	0.111162i	$-0.964543\pi$
$761$	−4.04548	−	17.7244i	−0.146649	−	0.642510i	0.847154	−	0.531348i	$-0.178314\pi$
$762$	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	−0.547143	−	0.837039i	$-0.684285\pi$
$769$	4.08086	−	3.25438i	0.147160	−	0.117356i	0.694302	+	0.719684i	$0.255713\pi$
$770$	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	−0.817956	−	0.575281i	$-0.804893\pi$
$773$	−2.08762	+	2.61780i	−0.0750866	+	0.0941556i	0.742870	+	0.669436i	$0.233464\pi$
$774$	−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	−0.703543	−	0.710653i	$-0.748400\pi$
$787$	8.15570	−	16.9355i	0.290719	−	0.603685i	0.994263	+	0.106967i	$0.0341141\pi$
$788$	−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	−0.0184370	+	0.999830i	$0.505869\pi$
$797$	−27.9234	+	35.0148i	−0.989097	+	1.24029i	−0.970660	+	0.240458i	$0.922702\pi$
$798$	−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	−0.371957	−	0.928250i	$-0.621313\pi$
$809$	12.8065	−	10.2128i	0.450251	−	0.359064i	0.822209	+	0.569186i	$0.192742\pi$
$810$	−3.96281	−	1.24305i	−0.139239	−	0.0436762i
$811$	−27.7535	+	6.33455i	−0.974556	+	0.222436i	−0.680011	−	0.733202i	$-0.738025\pi$
$811$	−27.7535	+	6.33455i	−0.974556	+	0.222436i	−0.294545	+	0.955638i	$0.595168\pi$
$812$	−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	0.508112	−	0.861291i	$-0.330343\pi$
$821$	16.9685	+	3.87296i	0.592206	+	0.135167i	0.0840934	+	0.996458i	$0.473201\pi$
$822$	−18.3434	−	0.364890i	−0.639799	−	0.0127270i
$823$	−11.6357	+	5.60345i	−0.405594	+	0.195324i	−0.625547	−	0.780187i	$-0.715124\pi$
$823$	−11.6357	+	5.60345i	−0.405594	+	0.195324i	0.219952	+	0.975511i	$0.429410\pi$
$824$	−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	0.695227	−	0.718790i	$-0.255304\pi$
$827$	−8.63339	−	17.9274i	−0.300212	−	0.623397i	−0.995440	+	0.0953925i	$0.969589\pi$
$828$	−14.5960	−	12.6214i	−0.507246	−	0.438625i
$829$	−39.6230	+	9.04369i	−1.37616	+	0.314100i	−0.845723	−	0.533622i	$-0.820831\pi$
$829$	−39.6230	+	9.04369i	−1.37616	+	0.314100i	−0.530440	+	0.847722i	$0.677973\pi$
$830$	−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	−0.924726	−	0.380633i	$-0.875706\pi$
$839$	−34.8655	+	16.7904i	−1.20369	+	0.579668i	−0.278966	+	0.960301i	$0.589992\pi$
$840$	−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	0.248609	−	0.968604i	$-0.420027\pi$
$853$	1.52854	+	0.348878i	0.0523361	+	0.0119454i	−0.196273	+	0.980549i	$0.562884\pi$
$854$	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	0.802603	−	0.596513i	$-0.203448\pi$
$857$	1.24271	+	1.55831i	0.0424502	+	0.0532309i	−0.760153	+	0.649744i	$0.774876\pi$
$858$	−18.3652	−	4.57786i	−0.626979	−	0.156285i
$859$	−53.2227	+	12.1477i	−1.81594	+	0.414476i	−0.989012	−	0.147837i	$-0.952769\pi$
$859$	−53.2227	+	12.1477i	−1.81594	+	0.414476i	−0.826925	+	0.562313i	$0.809912\pi$
$860$	−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	$0.0457550\pi$
$863$			8.41642i			0.286498i	−0.989687	+	0.143249i	$0.954245\pi$
$864$	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	0.250345	−	0.968157i	$-0.419456\pi$
$877$	−10.3798	−	4.99866i	−0.350502	−	0.168793i	−0.600847	+	0.799364i	$0.705170\pi$
$878$	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	−0.343385	−	0.939195i	$-0.611574\pi$
$887$	−38.4723	−	18.5273i	−1.29177	−	0.622086i	−0.948389	+	0.317109i	$0.897288\pi$
$888$	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	−0.992124	−	0.125262i	$-0.960023\pi$
$907$	−26.9083	−	33.7420i	−0.893477	−	1.12038i	0.0986471	−	0.995122i	$-0.468549\pi$
$908$	−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	0.257610	−	0.966249i	$-0.417065\pi$
$911$	2.12695	+	0.485461i	0.0704689	+	0.0160841i	−0.187141	+	0.982333i	$0.559922\pi$
$912$	−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	−0.882007	−	0.471236i	$-0.843808\pi$
$919$	3.55035	−	15.5551i	0.117115	−	0.513115i	0.999123	−	0.0418798i	$-0.0133347\pi$
$920$	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	0.0421711	−	0.999110i	$-0.486573\pi$
$929$	30.6882	−	38.4818i	1.00685	−	1.26255i	0.964677	−	0.263437i	$-0.0848560\pi$
$930$	−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	0.803051	−	0.595911i	$-0.203209\pi$
$937$	−5.00618	−	10.3954i	−0.163545	−	0.339604i	−0.966596	+	0.256306i	$0.917494\pi$
$938$	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	−0.714047	−	0.700098i	$-0.753140\pi$
$941$	−18.7701	+	9.03922i	−0.611889	+	0.294670i	0.102158	+	0.994768i	$0.467425\pi$
$942$	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	0.859886	−	0.510487i	$-0.170535\pi$
$947$	−2.31905	−	4.81555i	−0.0753590	−	0.156485i	−0.935245	+	0.354002i	$0.884820\pi$
$948$	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	−0.597985	−	0.801507i	$-0.704032\pi$
$953$	−24.3567	+	5.55925i	−0.788990	+	0.180082i	−0.191005	+	0.981589i	$0.561175\pi$
$954$	−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	−0.984382	−	0.176048i	$-0.943669\pi$
$967$	−18.4621	+	23.1508i	−0.593702	+	0.744478i	0.390680	+	0.920527i	$0.372240\pi$
$968$	−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	0.374916	−	0.927059i	$-0.377672\pi$
$971$	−19.0806	−	23.9263i	−0.612326	−	0.767833i	−0.987242	+	0.159226i	$0.949100\pi$
$972$	−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	−0.846137	−	0.532965i	$-0.821078\pi$
$977$	3.06662	−	6.36790i	0.0981099	−	0.203727i	0.944247	+	0.329238i	$0.106792\pi$
$978$	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	0.992811	+	0.119696i	$0.0381919\pi$
$983$	53.4691	+	25.7494i	1.70540	+	0.821277i	0.712589	+	0.701582i	$0.247522\pi$
$984$	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	−0.645558	−	0.763711i	$-0.723375\pi$
$991$	7.63885	−	9.57881i	0.242656	−	0.304281i	0.888214	+	0.459430i	$0.151946\pi$
$992$	−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	0.610805	−	0.791781i	$-0.290846\pi$
$997$	25.8154	+	5.89219i	0.817581	+	0.186608i	0.206776	+	0.978388i	$0.433703\pi$
$998$		−	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.251.16	yes	120
3.2	odd	2	inner	294.2.j.a.251.2	yes	120
49.41	odd	14	inner	294.2.j.a.41.2	✓	120
147.41	even	14	inner	294.2.j.a.41.16	yes	120

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
294.2.j.a.41.2	✓	120	49.41	odd	14	inner
294.2.j.a.41.16	yes	120	147.41	even	14	inner
294.2.j.a.251.2	yes	120	3.2	odd	2	inner
294.2.j.a.251.16	yes	120	1.1	even	1	trivial

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} +(-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})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 120 q + 20 q^{4} - 14 q^{6} + 4 q^{7} - 10 q^{9} + 12 q^{15} - 20 q^{16} - 8 q^{18} - 12 q^{21} - 10 q^{22} - 24 q^{25} + 42 q^{27} - 4 q^{28} + 8 q^{30} + 10 q^{36} - 58 q^{37} + 8 q^{39} - 14 q^{40} - 2 q^{42}+ \cdots - 224 q^{99}+O(q^{100}) \) 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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