LMFDB - Embedded newform 294.2.j.a.41.2

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			41.2
Character	$\chi$	$=$	294.41
Dual form			294.2.j.a.251.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.781831 + 0.623490i) q^{2} +(-1.54527 - 0.782396i) q^{3} +(0.222521 - 0.974928i) q^{4} +(0.415766 - 0.200223i) q^{5} +(1.69596 - 0.351758i) q^{6} +(-2.57018 - 0.627843i) q^{7} +(0.433884 + 0.900969i) q^{8} +(1.77571 + 2.41802i) q^{9} +O(q^{10})$	\(q+(-0.781831 + 0.623490i) q^{2} +(-1.54527 - 0.782396i) q^{3} +(0.222521 - 0.974928i) q^{4} +(0.415766 - 0.200223i) q^{5} +(1.69596 - 0.351758i) q^{6} +(-2.57018 - 0.627843i) q^{7} +(0.433884 + 0.900969i) q^{8} +(1.77571 + 2.41802i) q^{9} +(-0.200223 + 0.415766i) q^{10} +(-2.98244 + 2.37842i) q^{11} +(-1.10663 + 1.33243i) q^{12} +(2.23965 - 1.78606i) q^{13} +(2.40090 - 1.11161i) q^{14} +(-0.799124 - 0.0158963i) 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} +(3.48039 + 2.98108i) q^{21} +(0.848848 - 3.71905i) q^{22} +(-6.27080 - 1.43127i) q^{23} +(0.0344474 - 1.73171i) q^{24} +(-2.98468 + 3.74267i) q^{25} +(-0.637438 + 2.79280i) q^{26} +(-0.852100 - 5.12581i) 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} +(6.46954 - 1.34185i) q^{33} +(-3.69304 - 2.94510i) q^{34} +(-1.19430 + 0.253572i) q^{35} +(2.75253 - 1.19313i) q^{36} +(-1.70432 - 7.46711i) q^{37} +(-4.90199 - 6.14691i) q^{38} +(-4.85827 + 1.00765i) q^{39} +(0.360789 + 0.287719i) q^{40} +(3.55254 - 1.71081i) q^{41} +(-4.57976 - 0.160715i) q^{42} +(9.76045 + 4.70038i) q^{43} +(1.65513 + 3.43692i) q^{44} +(1.22242 + 0.649796i) 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} +(1.97882 - 7.93856i) q^{51} +(-1.24291 - 2.58093i) q^{52} +(-0.115863 - 0.0264450i) q^{53} +(3.86209 + 3.47624i) q^{54} +(-0.763787 + 1.58602i) q^{55} +(-0.549491 - 2.58806i) q^{56} +(6.15135 - 12.1492i) q^{57} +(5.38309 - 6.75019i) q^{58} +(-5.93818 - 2.85967i) q^{59} +(-0.193320 + 0.775551i) q^{60} +(-1.62969 + 0.371966i) q^{61} +(-1.42672 - 1.78905i) q^{62} +(-3.04576 - 7.32962i) q^{63} +(-0.623490 + 0.781831i) q^{64} +(0.573561 - 1.19101i) q^{65} +(-4.22147 + 5.08279i) q^{66} -3.96394 q^{67} +4.72357 q^{68} +(8.57026 + 7.11795i) q^{69} +(0.775644 - 0.942885i) q^{70} +(-0.892081 - 0.203612i) q^{71} +(-1.40811 + 2.64900i) q^{72} +(-5.38845 - 4.29715i) q^{73} +(5.98816 + 4.77540i) q^{74} +(7.54037 - 3.44823i) q^{75} +(7.66507 + 1.74950i) q^{76} +(9.15868 - 4.24045i) q^{77} +(3.17009 - 3.81689i) q^{78} -0.975332 q^{79} -0.461466 q^{80} +(-2.69369 + 8.58743i) q^{81} +(-1.71081 + 3.55254i) q^{82} +(8.84503 - 11.0913i) q^{83} +(3.68080 - 2.72978i) q^{84} +(1.35906 + 1.70421i) q^{85} +(-10.5617 + 2.41063i) q^{86} +(14.5102 + 3.61692i) q^{87} +(-3.43692 - 1.65513i) q^{88} +(-5.73296 + 7.18891i) q^{89} +(-1.36087 + 0.254139i) q^{90} +(-6.87766 + 3.18434i) q^{91} +(-2.79077 + 5.79509i) q^{92} +(1.79034 - 3.53601i) q^{93} +(-4.73652 - 1.08108i) q^{94} +(1.57419 + 3.26883i) q^{95} +(-1.68063 - 0.418925i) 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
$3$	−1.54527	−	0.782396i	−0.892161	−	0.451717i
$3$	−1.54527	−	0.782396i	−0.892161	−	0.451717i
$4$	0.222521	−	0.974928i	0.111260	−	0.487464i
$5$	0.415766	−	0.200223i	0.185936	−	0.0895423i	−0.338599	−	0.940931i	$-0.609953\pi$
$5$	0.415766	−	0.200223i	0.185936	−	0.0895423i	0.524536	+	0.851388i	$0.324239\pi$
$6$	1.69596	−	0.351758i	0.692371	−	0.143604i
$7$	−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
$9$	1.77571	+	2.41802i	0.591904	+	0.806008i
$10$	−0.200223	+	0.415766i	−0.0633159	+	0.131477i
$11$	−2.98244	+	2.37842i	−0.899240	+	0.717120i	−0.959693	−	0.281051i	$-0.909317\pi$
$11$	−2.98244	+	2.37842i	−0.899240	+	0.717120i	0.0604524	+	0.998171i	$0.480746\pi$
$12$	−1.10663	+	1.33243i	−0.319458	+	0.384638i
$13$	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
$15$	−0.799124	−	0.0158963i	−0.206333	−	0.00410441i
$16$	−0.900969	−	0.433884i	−0.225242	−	0.108471i
$17$	1.05109	+	4.60514i	0.254928	+	1.11691i	0.926596	+	0.376059i	$0.122721\pi$
$17$	1.05109	+	4.60514i	0.254928	+	1.11691i	−0.671668	+	0.740852i	$0.734422\pi$
$18$	−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
$21$	3.48039	+	2.98108i	0.759484	+	0.650526i
$22$	0.848848	−	3.71905i	0.180975	−	0.792903i
$23$	−6.27080	−	1.43127i	−1.30755	−	0.298440i	−0.488704	−	0.872450i	$-0.662530\pi$
$23$	−6.27080	−	1.43127i	−1.30755	−	0.298440i	−0.818849	+	0.574009i	$0.805387\pi$
$24$	0.0344474	−	1.73171i	0.00703156	−	0.353483i
$25$	−2.98468	+	3.74267i	−0.596935	+	0.748533i
$26$	−0.637438	+	2.79280i	−0.125012	+	0.547712i
$27$	−0.852100	−	5.12581i	−0.163987	−	0.986463i
$28$	−1.18402	+	2.36603i	−0.223759	+	0.447138i
$29$	−8.41735	+	1.92120i	−1.56306	+	0.356759i	−0.914559	−	0.404453i	$-0.867462\pi$
$29$	−8.41735	+	1.92120i	−1.56306	+	0.356759i	−0.648503	+	0.761212i	$0.724605\pi$
$30$	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
$33$	6.46954	−	1.34185i	1.12620	−	0.233585i
$34$	−3.69304	−	2.94510i	−0.633351	−	0.505080i
$35$	−1.19430	+	0.253572i	−0.201874	+	0.0428614i
$36$	2.75253	−	1.19313i	0.458756	−	0.198855i
$37$	−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
$39$	−4.85827	+	1.00765i	−0.777945	+	0.161353i
$40$	0.360789	+	0.287719i	0.0570457	+	0.0454924i
$41$	3.55254	−	1.71081i	0.554814	−	0.267184i	−0.135398	−	0.990791i	$-0.543231\pi$
$41$	3.55254	−	1.71081i	0.554814	−	0.267184i	0.690212	+	0.723607i	$0.257517\pi$
$42$	−4.57976	−	0.160715i	−0.706672	−	0.0247988i
$43$	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
$45$	1.22242	+	0.649796i	0.182228	+	0.0968659i
$46$	5.79509	−	2.79077i	0.854440	−	0.411477i
$47$	3.02912	+	3.79839i	0.441842	+	0.554052i	0.952028	−	0.306012i	$-0.0989948\pi$
$47$	3.02912	+	3.79839i	0.441842	+	0.554052i	−0.510186	+	0.860064i	$0.670423\pi$
$48$	1.05277	+	1.37538i	0.151954	+	0.198519i
$49$	6.21163	+	3.22734i	0.887375	+	0.461048i
$50$		−	4.78705i		−	0.676991i
$51$	1.97882	−	7.93856i	0.277091	−	1.11162i
$52$	−1.24291	−	2.58093i	−0.172361	−	0.357911i
$53$	−0.115863	−	0.0264450i	−0.0159150	−	0.00363250i	0.214556	−	0.976712i	$-0.431170\pi$
$53$	−0.115863	−	0.0264450i	−0.0159150	−	0.00363250i	−0.230471	+	0.973079i	$0.574027\pi$
$54$	3.86209	+	3.47624i	0.525564	+	0.473057i
$55$	−0.763787	+	1.58602i	−0.102989	+	0.213859i
$56$	−0.549491	−	2.58806i	−0.0734289	−	0.345844i
$57$	6.15135	−	12.1492i	0.814766	−	1.60920i
$58$	5.38309	−	6.75019i	0.706835	−	0.886343i
$59$	−5.93818	−	2.85967i	−0.773085	−	0.372298i	0.00538074	−	0.999986i	$-0.498287\pi$
$59$	−5.93818	−	2.85967i	−0.773085	−	0.372298i	−0.778465	+	0.627688i	$0.784002\pi$
$60$	−0.193320	+	0.775551i	−0.0249575	+	0.100123i
$61$	−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
$63$	−3.04576	−	7.32962i	−0.383729	−	0.923446i
$64$	−0.623490	+	0.781831i	−0.0779362	+	0.0977289i
$65$	0.573561	−	1.19101i	0.0711415	−	0.147727i
$66$	−4.22147	+	5.08279i	−0.519626	+	0.625648i
$67$	−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
$69$	8.57026	+	7.11795i	1.03174	+	0.856900i
$70$	0.775644	−	0.942885i	0.0927072	−	0.112696i
$71$	−0.892081	−	0.203612i	−0.105871	−	0.0241643i	0.169257	−	0.985572i	$-0.445863\pi$
$71$	−0.892081	−	0.203612i	−0.105871	−	0.0241643i	−0.275128	+	0.961408i	$0.588720\pi$
$72$	−1.40811	+	2.64900i	−0.165948	+	0.312188i
$73$	−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
$75$	7.54037	−	3.44823i	0.870688	−	0.398167i
$76$	7.66507	+	1.74950i	0.879243	+	0.200682i
$77$	9.15868	−	4.24045i	1.04373	−	0.483245i
$78$	3.17009	−	3.81689i	0.358942	−	0.432178i
$79$	−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
$81$	−2.69369	+	8.58743i	−0.299299	+	0.954159i
$82$	−1.71081	+	3.55254i	−0.188928	+	0.392313i
$83$	8.84503	−	11.0913i	0.970868	−	1.21743i	−0.00520460	−	0.999986i	$-0.501657\pi$
$83$	8.84503	−	11.0913i	0.970868	−	1.21743i	0.976073	−	0.217444i	$-0.0697719\pi$
$84$	3.68080	−	2.72978i	0.401608	−	0.297843i
$85$	1.35906	+	1.70421i	0.147411	+	0.184848i
$86$	−10.5617	+	2.41063i	−1.13889	+	0.259945i
$87$	14.5102	+	3.61692i	1.55566	+	0.387775i
$88$	−3.43692	−	1.65513i	−0.366376	−	0.176438i
$89$	−5.73296	+	7.18891i	−0.607693	+	0.762023i	−0.986555	−	0.163430i	$-0.947744\pi$
$89$	−5.73296	+	7.18891i	−0.607693	+	0.762023i	0.378862	+	0.925453i	$0.376316\pi$
$90$	−1.36087	+	0.254139i	−0.143448	+	0.0267886i
$91$	−6.87766	+	3.18434i	−0.720975	+	0.333810i
$92$	−2.79077	+	5.79509i	−0.290958	+	0.604180i
$93$	1.79034	−	3.53601i	0.185650	−	0.366667i
$94$	−4.73652	−	1.08108i	−0.488534	−	0.111505i
$95$	1.57419	+	3.26883i	0.161508	+	0.335375i
$96$	−1.68063	−	0.418925i	−0.171528	−	0.0427564i
$97$			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	−0.0242343	−	0.999706i	$-0.507715\pi$
$101$	7.45960	−	3.59235i	0.742258	−	0.357452i	0.766492	+	0.642254i	$0.222000\pi$
$102$	3.40250	+	7.44039i	0.336898	+	0.736708i
$103$	−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
$105$	2.04391	+	0.542581i	0.199465	+	0.0529505i
$106$	0.107074	−	0.0515640i	0.0103999	−	0.00500834i
$107$	−10.7510	−	8.57360i	−1.03933	−	0.828842i	−0.0538401	−	0.998550i	$-0.517146\pi$
$107$	−10.7510	−	8.57360i	−1.03933	−	0.828842i	−0.985494	+	0.169708i	$0.945718\pi$
$108$	−5.18691	−	0.309864i	−0.499110	−	0.0298166i
$109$	−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
$111$	−3.20861	+	12.8721i	−0.304548	+	1.22177i
$112$	2.04324	+	1.68083i	0.193068	+	0.158823i
$113$	−1.88827	−	1.50585i	−0.177634	−	0.141658i	0.530637	−	0.847599i	$-0.321953\pi$
$113$	−1.88827	−	1.50585i	−0.177634	−	0.141658i	−0.708271	+	0.705941i	$0.750524\pi$
$114$	2.76558	+	13.3339i	0.259021	+	1.24884i
$115$	−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
$120$	−0.332405	−	0.726883i	−0.0303443	−	0.0663551i
$121$	0.790360	−	3.46279i	0.0718509	−	0.314799i
$122$	1.04223	−	1.30691i	0.0943587	−	0.118322i
$123$	−6.82817	−	0.135827i	−0.615675	−	0.0122471i
$124$	2.23091	+	0.509190i	0.200342	+	0.0457266i
$125$	−1.00499	+	4.40315i	−0.0898892	+	0.393830i
$126$	6.95121	+	3.83153i	0.619263	+	0.341340i
$127$	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	0.715009	−	0.699115i	$-0.246423\pi$
$131$	7.03006	+	3.38550i	0.614220	+	0.295793i	−0.100789	+	0.994908i	$0.532137\pi$
$132$	0.131406	−	6.60593i	0.0114374	−	0.574972i
$133$	4.93622	−	20.2072i	0.428025	−	1.75219i
$134$	3.09913	−	2.47148i	0.267724	−	0.213503i
$135$	−1.38058	−	1.96053i	−0.118821	−	0.168736i
$136$	−3.69304	+	2.94510i	−0.316675	+	0.252540i
$137$	−4.59598	+	9.54365i	−0.392661	+	0.815369i	0.607123	+	0.794608i	$0.292323\pi$
$137$	−4.59598	+	9.54365i	−0.392661	+	0.815369i	−0.999784	+	0.0207615i	$0.993391\pi$
$138$	−11.1385	−	0.221568i	−0.948169	−	0.0188612i
$139$	−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
$141$	−1.70895	−	8.23951i	−0.143920	−	0.693891i
$142$	0.824407	−	0.397013i	0.0691827	−	0.0333166i
$143$	−2.43163	+	10.6536i	−0.203343	+	0.890903i
$144$	−0.550720	−	2.94902i	−0.0458933	−	0.245752i
$145$	−3.11498	+	2.48411i	−0.258685	+	0.206295i
$146$	6.89209			0.570393
$147$	−7.07358	−	9.84706i	−0.583419	−	0.812171i
$148$	−7.65914			−0.629578
$149$	0.815837	−	0.650608i	0.0668360	−	0.0532999i	−0.589502	−	0.807767i	$-0.700676\pi$
$149$	0.815837	−	0.650608i	0.0668360	−	0.0532999i	0.656338	+	0.754467i	$0.272105\pi$
$150$	−3.74537	+	7.39728i	−0.305808	+	0.603985i
$151$	−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
$153$	−9.26891	+	10.7190i	−0.749347	+	0.866578i
$154$	−4.51667	+	9.02567i	−0.363963	+	0.727309i
$155$	0.458166	+	0.951390i	0.0368007	+	0.0764175i
$156$	−0.0986788	+	4.96068i	−0.00790063	+	0.397173i
$157$	−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
$159$	0.158349	+	0.131516i	0.0125579	+	0.0104299i
$160$	0.360789	−	0.287719i	0.0285228	−	0.0227462i
$161$	15.2185	+	7.61570i	1.19938	+	0.600201i
$162$	−3.24817	−	8.39341i	−0.255200	−	0.659449i
$163$	−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	0.998214	−	0.0597332i	$-0.0190250\pi$
$167$	0.942554	+	4.12960i	0.0729370	+	0.319558i	−0.925277	+	0.379291i	$0.876168\pi$
$168$	−1.17578	+	4.42917i	−0.0907132	+	0.341718i
$169$	−1.06676	+	4.67377i	−0.0820582	+	0.359520i
$170$	−2.12512	−	0.485044i	−0.162989	−	0.0372012i
$171$	−19.0110	+	13.9610i	−1.45380	+	1.06762i
$172$	6.75444	−	8.46980i	0.515021	−	0.645816i
$173$	0.742706	−	3.25401i	0.0564669	−	0.247398i	−0.938815	−	0.344421i	$-0.888075\pi$
$173$	0.742706	−	3.25401i	0.0564669	−	0.247398i	0.995282	+	0.0970236i	$0.0309322\pi$
$174$	−13.5996	+	6.21914i	−1.03099	+	0.471472i
$175$	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	$-0.258562\pi$
$179$	21.7074	−	4.95458i	1.62249	−	0.370323i	0.934658	+	0.355547i	$0.115705\pi$
$180$	0.905519	−	1.04718i	0.0674934	−	0.0780524i
$181$	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
$183$	2.80933	+	0.700276i	0.207672	+	0.0517659i
$184$	−1.43127	−	6.27080i	−0.105515	−	0.462290i
$185$	−2.20368	−	2.76333i	−0.162018	−	0.203164i
$186$	0.804920	+	3.88082i	0.0590196	+	0.284556i
$187$	−14.0878	−	11.2346i	−1.03020	−	0.821558i
$188$	4.37720	−	2.10795i	0.319240	−	0.153738i
$189$	−1.02815	+	13.7092i	−0.0747873	+	0.997200i
$190$	−3.26883	−	1.57419i	−0.237146	−	0.114204i
$191$	−1.86656	−	3.87596i	−0.135060	−	0.280455i	0.822460	−	0.568824i	$-0.192601\pi$
$191$	−1.86656	−	3.87596i	−0.135060	−	0.280455i	−0.957519	+	0.288369i	$0.906887\pi$
$192$	1.57516	−	0.720324i	0.113677	−	0.0519849i
$193$	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	$0.304108\pi$
$197$			22.9212i			1.63307i	−0.577296	+	0.816535i	$0.695892\pi$
$198$	10.5001	−	4.55142i	0.746206	−	0.323455i
$199$	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
$201$	6.12535	+	3.10137i	0.432049	+	0.218754i
$202$	−3.59235	+	7.45960i	−0.252757	+	0.524855i
$203$	22.8403	+	0.346936i	1.60307	+	0.0243501i
$204$	−7.29919	−	3.69571i	−0.511046	−	0.258751i
$205$	1.13448	−	1.42260i	0.0792358	−	0.0993586i
$206$	12.4757	+	6.00798i	0.869223	+	0.418596i
$207$	−7.67430	−	17.7045i	−0.533401	−	1.23055i
$208$	−2.79280	+	0.637438i	−0.193646	+	0.0441983i
$209$	−18.6996	−	23.4485i	−1.29348	−	1.62197i
$210$	−1.93629	+	0.850151i	−0.133617	+	0.0586660i
$211$	−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
$213$	1.21920	+	1.01260i	0.0835382	+	0.0693819i
$214$	13.7510			0.939999
$215$	4.99919			0.340942
$216$	4.24848	−	2.99172i	0.289073	−	0.203561i
$217$	1.43668	−	5.88129i	0.0975283	−	0.399248i
$218$	12.5781	+	2.87087i	0.851896	+	0.194440i
$219$	4.96454	+	10.8562i	0.335472	+	0.733591i
$220$	1.37630	+	1.09756i	0.0927899	+	0.0739974i
$221$	10.5791	+	8.43659i	0.711630	+	0.567506i
$222$	−5.51706	−	12.0644i	−0.370281	−	0.809709i
$223$	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
$225$	−14.3498	−	0.571123i	−0.956652	−	0.0380749i
$226$	2.41519			0.160656
$227$	3.52186			0.233754			0.116877	−	0.993146i	$-0.462712\pi$
$227$	3.52186			0.233754			0.116877	+	0.993146i	$0.462712\pi$
$228$	−10.4758	−	8.70057i	−0.693776	−	0.576209i
$229$	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
$231$	−17.4703	−	0.613077i	−1.14946	−	0.0403375i
$232$	−5.38309	−	6.75019i	−0.353417	−	0.443171i
$233$	−16.2860	+	3.71717i	−1.06693	+	0.243520i	−0.719717	−	0.694267i	$-0.755729\pi$
$233$	−16.2860	+	3.71717i	−1.06693	+	0.243520i	−0.347212	+	0.937787i	$0.612872\pi$
$234$	−7.88496	+	3.41786i	−0.515456	+	0.223433i
$235$	2.01993	+	0.972746i	0.131766	+	0.0634550i
$236$	−4.10934	+	5.15296i	−0.267496	+	0.335429i
$237$	1.50715	+	0.763096i	0.0978999	+	0.0495684i
$238$	7.64270	+	9.88808i	0.495403	+	0.640949i
$239$	−1.77835	+	3.69278i	−0.115032	+	0.238866i	−0.950534	−	0.310622i	$-0.899463\pi$
$239$	−1.77835	+	3.69278i	−0.115032	+	0.238866i	0.835502	+	0.549488i	$0.185177\pi$
$240$	0.713089	+	0.361049i	0.0460297	+	0.0233056i
$241$	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
$243$	10.8813	−	11.1624i	0.698033	−	0.716066i
$244$			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
$249$	−22.3458	+	10.2188i	−1.41610	+	0.647587i
$250$	−1.95959	−	4.06913i	−0.123935	−	0.257354i
$251$	−0.489376	−	0.235671i	−0.0308892	−	0.0148754i	0.418375	−	0.908274i	$-0.362600\pi$
$251$	−0.489376	−	0.235671i	−0.0308892	−	0.0148754i	−0.449265	+	0.893399i	$0.648314\pi$
$252$	−7.82360	+	1.33840i	−0.492840	+	0.0843112i
$253$	22.1065	−	10.6459i	1.38982	−	0.669303i
$254$	−1.93917	−	1.54643i	−0.121674	−	0.0970320i
$255$	−0.766750	−	3.69679i	−0.0480157	−	0.231502i
$256$	0.623490	+	0.781831i	0.0389681	+	0.0488645i
$257$	−0.145948	−	0.639440i	−0.00910399	−	0.0398872i	0.970172	−	0.242418i	$-0.0779405\pi$
$257$	−0.145948	−	0.639440i	−0.00910399	−	0.0398872i	−0.979276	+	0.202531i	$0.935083\pi$
$258$	18.2067	+	4.53833i	1.13350	+	0.282544i
$259$	−0.307770	+	20.2618i	−0.0191239	+	1.25901i
$260$	−1.03352	−	0.824206i	−0.0640963	−	0.0511151i
$261$	−19.5923	−	16.9418i	−1.21273	−	1.04867i
$262$	−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
$267$	14.4835	−	6.62335i	0.886379	−	0.405342i
$268$	−0.882060	+	3.86456i	−0.0538804	+	0.236065i
$269$	11.2497	−	14.1067i	0.685908	−	0.860101i	−0.309976	−	0.950744i	$-0.600321\pi$
$269$	11.2497	−	14.1067i	0.685908	−	0.860101i	0.995883	+	0.0906435i	$0.0288924\pi$
$270$	2.30175	+	0.672028i	0.140080	+	0.0408983i
$271$	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
$273$	13.1193	+	0.460387i	0.794013	+	0.0278639i
$274$	−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
$279$	−5.53312	+	4.06333i	−0.331259	+	0.243265i
$280$	−0.746648	−	0.966008i	−0.0446208	−	0.0577300i
$281$	25.6486	−	20.4541i	1.53007	−	1.22019i	0.636480	−	0.771293i	$-0.280390\pi$
$281$	25.6486	−	20.4541i	1.53007	−	1.22019i	0.893585	−	0.448894i	$-0.148182\pi$
$282$	6.47336	+	5.37639i	0.385483	+	0.320159i
$283$	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
$285$	0.124980	−	6.28287i	0.00740317	−	0.372165i
$286$	−4.74132	−	9.84545i	−0.280360	−	0.582174i
$287$	−10.2048	+	2.16666i	−0.602370	+	0.127894i
$288$	2.26925	+	1.96227i	0.133717	+	0.115628i
$289$	−4.78607	+	2.30485i	−0.281534	+	0.135579i
$290$	0.886570	−	3.88432i	0.0520612	−	0.228095i
$291$	11.4188	−	22.5526i	0.669380	−	1.32206i
$292$	−5.38845	+	4.29715i	−0.315335	+	0.251472i
$293$	−33.7686			−1.97278			−0.986392	−	0.164411i	$-0.947428\pi$
$293$	−33.7686			−1.97278			−0.986392	+	0.164411i	$0.947428\pi$
$294$	11.6699	+	3.28843i	0.680601	+	0.191785i
$295$	−3.04147			−0.177081
$296$	5.98816	−	4.77540i	0.348055	−	0.277564i
$297$	14.7327	+	13.2608i	0.854876	+	0.769469i
$298$	−0.232199	+	1.01733i	−0.0134510	+	0.0589325i
$299$	−16.6007	+	7.99449i	−0.960045	+	0.462333i
$300$	−1.68388	−	8.11862i	−0.0972189	−	0.468729i
$301$	−22.1350	−	18.2088i	−1.27584	−	1.04954i
$302$	−7.93052	−	16.4679i	−0.456350	−	0.947621i
$303$	−14.3377	−	0.285209i	−0.823681	−	0.0163848i
$304$	3.41128	−	7.08359i	0.195650	−	0.406272i
$305$	−0.603095	+	0.480952i	−0.0345331	+	0.0275392i
$306$	0.563550	−	14.1595i	0.0322160	−	0.809445i
$307$	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
$309$	−0.476993	+	23.9789i	−0.0271352	+	1.36411i
$310$	−0.951390	−	0.458166i	−0.0540353	−	0.0260221i
$311$	−0.731657	−	3.20560i	−0.0414885	−	0.181773i	0.949938	−	0.312438i	$-0.101146\pi$
$311$	−0.731657	−	3.20560i	−0.0414885	−	0.181773i	−0.991427	+	0.130665i	$0.958289\pi$
$312$	−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
$315$	−2.73388	−	2.43758i	−0.154037	−	0.137342i
$316$	−0.217032	+	0.950878i	−0.0122090	+	0.0534911i
$317$	25.3676	+	5.78999i	1.42479	+	0.325198i	0.864305	−	0.502969i	$-0.167759\pi$
$317$	25.3676	+	5.78999i	1.42479	+	0.325198i	0.560481	+	0.828167i	$0.310616\pi$
$318$	−0.205801	−	0.00409383i	−0.0115408	−	0.000229571i
$319$	20.5348	−	25.7499i	1.14973	−	1.44172i
$320$	−0.102686	+	0.449896i	−0.00574031	+	0.0251500i
$321$	9.90517	+	21.6600i	0.552853	+	1.20895i
$322$	−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
$327$	4.53822	+	21.8805i	0.250964	+	1.20999i
$328$	3.08278	+	2.45844i	0.170218	+	0.135744i
$329$	−5.40057	−	11.6643i	−0.297743	−	0.643076i
$330$	−0.737454	+	2.95849i	−0.0405955	+	0.162859i
$331$	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
$333$	15.0293	−	17.3805i	0.823600	−	0.952447i
$334$	−3.31168	−	2.64098i	−0.181207	−	0.144508i
$335$	−1.64807	+	0.793670i	−0.0900439	+	0.0433628i
$336$	−1.84228	−	4.19595i	−0.100505	−	0.228908i
$337$	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
$339$	1.73972	+	3.80432i	0.0944887	+	0.206622i
$340$	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
$345$	4.98840	+	1.24345i	0.268566	+	0.0669449i
$346$	1.44817	+	3.00716i	0.0778541	+	0.161666i
$347$	9.17698	+	2.09459i	0.492646	+	0.112443i	0.461624	−	0.887075i	$-0.347267\pi$
$347$	9.17698	+	2.09459i	0.492646	+	0.112443i	0.0310216	+	0.999519i	$0.490124\pi$
$348$	6.75506	−	13.3416i	0.362109	−	0.715183i
$349$	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
$351$	−11.0634	−	9.95811i	−0.590521	−	0.531525i
$352$	−2.37842	+	2.98244i	−0.126770	+	0.158965i
$353$	6.60133	+	3.17903i	0.351354	+	0.169203i	0.601233	−	0.799074i	$-0.294677\pi$
$353$	6.60133	+	3.17903i	0.351354	+	0.169203i	−0.249879	+	0.968277i	$0.580391\pi$
$354$	−11.0768	−	2.76108i	−0.588725	−	0.146750i
$355$	−0.411665	+	0.0939598i	−0.0218489	+	0.00498687i
$356$	5.73296	+	7.18891i	0.303846	+	0.381011i
$357$	−10.0701	+	19.1611i	−0.532966	+	1.01411i
$358$	−13.8824	+	17.4080i	−0.733709	+	0.920042i
$359$	−7.96342	+	16.5362i	−0.420293	+	0.872748i	0.578093	+	0.815971i	$0.303797\pi$
$359$	−7.96342	+	16.5362i	−0.420293	+	0.872748i	−0.998387	+	0.0567778i	$0.981917\pi$
$360$	−0.0550556	+	1.38330i	−0.00290168	+	0.0729065i
$361$	−42.8140			−2.25337
$362$	−5.02748			−0.264239
$363$	−3.93059	+	4.73257i	−0.206303	+	0.248396i
$364$	1.57408	+	7.41381i	0.0825044	+	0.388589i
$365$	−3.10072	−	0.707720i	−0.162299	−	0.0370438i
$366$	−2.63304	+	1.20409i	−0.137631	+	0.0629390i
$367$	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
$369$	10.4451	+	5.55222i	0.543750	+	0.289037i
$370$	3.44582	+	0.786485i	0.179140	+	0.0408874i
$371$	0.281186	+	0.140712i	0.0145984	+	0.00730542i
$372$	−3.04897	−	2.53229i	−0.158082	−	0.131293i
$373$	−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
$375$	4.99799	−	6.01776i	0.258095	−	0.310756i
$376$	−2.10795	+	4.37720i	−0.108709	+	0.225737i
$377$	−15.4205	+	19.3367i	−0.794197	+	0.995891i
$378$	−7.74372	−	11.3593i	−0.398294	−	0.584262i
$379$	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
$381$	1.03906	−	4.16844i	0.0532324	−	0.213555i
$382$	3.87596	+	1.86656i	0.198311	+	0.0955017i
$383$	−17.9295	+	22.4829i	−0.916155	+	1.14882i	0.0723117	+	0.997382i	$0.476962\pi$
$383$	−17.9295	+	22.4829i	−0.916155	+	1.14882i	−0.988467	+	0.151440i	$0.951609\pi$
$384$	−0.782396	+	1.54527i	−0.0399265	+	0.0788567i
$385$	2.95884	−	3.59681i	0.150796	−	0.183311i
$386$	−2.25737	+	4.68747i	−0.114897	+	0.238586i
$387$	5.96610	+	31.9475i	0.303274	+	1.62398i
$388$	14.2287	+	3.24760i	0.722352	+	0.164872i
$389$	−4.07505	−	8.46193i	−0.206613	−	0.429037i	0.771752	−	0.635924i	$-0.219381\pi$
$389$	−4.07505	−	8.46193i	−0.206613	−	0.429037i	−0.978365	+	0.206887i	$0.933667\pi$
$390$	0.553787	−	2.22166i	0.0280421	−	0.112498i
$391$		−	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
$396$	−5.37151	+	10.1051i	−0.269929	+	0.507801i
$397$	−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
$399$	−23.4378	+	27.3635i	−1.17336	+	1.36989i
$400$	4.31298	−	2.07702i	0.215649	−	0.103851i
$401$	4.60232	+	3.67023i	0.229829	+	0.183282i	0.731633	−	0.681699i	$-0.238759\pi$
$401$	4.60232	+	3.67023i	0.229829	+	0.183282i	−0.501804	+	0.864981i	$0.667330\pi$
$402$	−6.72267	+	1.39435i	−0.335296	+	0.0695437i
$403$	4.08701	+	5.12495i	0.203588	+	0.255292i
$404$	−1.84237	−	8.07194i	−0.0916613	−	0.401594i
$405$	0.599453	+	4.10970i	0.0297870	+	0.204213i
$406$	−18.0736	+	13.9694i	−0.896976	+	0.693292i
$407$	22.8430	+	18.2167i	1.13228	+	0.902966i
$408$	8.01097	−	1.66155i	0.396602	−	0.0822591i
$409$	−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
$414$	17.0386	+	9.05708i	0.837400	+	0.445131i
$415$	1.45673	−	6.38237i	0.0715083	−	0.313298i
$416$	1.78606	−	2.23965i	0.0875688	−	0.109808i
$417$	−0.0208608	+	1.04869i	−0.00102156	+	0.0513547i
$418$	29.2398	+	6.67380i	1.43017	+	0.326426i
$419$	5.69608	−	24.9562i	0.278272	−	1.21919i	−0.621706	−	0.783251i	$-0.713560\pi$
$419$	5.69608	−	24.9562i	0.278272	−	1.21919i	0.899977	−	0.435937i	$-0.143583\pi$
$420$	0.983790	−	1.87193i	0.0480041	−	0.0913409i
$421$	−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
$426$	−1.58455	−	0.0315202i	−0.0767718	−	0.00152716i
$427$	4.42213	+	0.0671706i	0.214002	+	0.00325061i
$428$	−10.7510	+	8.57360i	−0.519667	+	0.414421i
$429$	12.0929	−	14.5603i	0.583850	−	0.702976i
$430$	−3.90852	+	3.11694i	−0.188486	+	0.150312i
$431$	−10.7334	+	22.2882i	−0.517010	+	1.07358i	0.465097	+	0.885260i	$0.346020\pi$
$431$	−10.7334	+	22.2882i	−0.517010	+	1.07358i	−0.982107	+	0.188323i	$0.939695\pi$
$432$	−1.45629	+	4.98791i	−0.0700658	+	0.239981i
$433$	−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
$435$	6.75705	−	1.40148i	0.323976	−	0.0671956i
$436$	−11.6239	+	5.59778i	−0.556684	+	0.268085i
$437$	11.2529	−	49.3022i	0.538300	−	2.35845i
$438$	−10.6501	−	5.39234i	−0.508883	−	0.257656i
$439$	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
$441$	3.22628	+	20.7507i	0.153633	+	0.988128i
$442$	−13.5312			−0.643615
$443$	−2.94611	+	2.34944i	−0.139974	+	0.111625i	−0.690974	−	0.722880i	$-0.742818\pi$
$443$	−2.94611	+	2.34944i	−0.139974	+	0.111625i	0.551000	+	0.834505i	$0.314246\pi$
$444$	11.8354	+	5.99248i	0.561685	+	0.284391i
$445$	−0.944192	+	4.13678i	−0.0447590	+	0.196102i
$446$	−5.96601	+	2.87308i	−0.282499	+	0.136044i
$447$	−1.76972	+	0.367057i	−0.0837050	+	0.0173612i
$448$	2.09335	−	1.61799i	0.0989014	−	0.0764429i
$449$	17.3820	+	36.0941i	0.820307	+	1.70339i	0.704031	+	0.710169i	$0.251381\pi$
$449$	17.3820	+	36.0941i	0.820307	+	1.70339i	0.116276	+	0.993217i	$0.462904\pi$
$450$	11.5752	−	8.50042i	0.545660	−	0.400714i
$451$	−6.52622	+	13.5518i	−0.307308	+	0.638131i
$452$	−1.88827	+	1.50585i	−0.0888169	+	0.0708291i
$453$	20.2270	−	24.3541i	0.950350	−	1.14425i
$454$	−2.75350	+	2.19585i	−0.129228	+	0.103056i
$455$	−2.22192	+	2.70101i	−0.104165	+	0.126625i
$456$	13.6150	+	0.270832i	0.637582	+	0.0126829i
$457$	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	$0.0375160\pi$
$461$	3.20697	+	14.0506i	0.149363	+	0.654403i	−0.843699	+	0.536816i	$0.819627\pi$
$462$	14.0411	−	10.4133i	0.653252	−	0.484469i
$463$	−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
$465$	0.0363753	−	1.82862i	0.00168686	−	0.0848003i
$466$	10.4153	−	13.0603i	0.482478	−	0.605008i
$467$	−6.29064	+	27.5611i	−0.291096	+	1.27538i	0.591906	+	0.806007i	$0.298376\pi$
$467$	−6.29064	+	27.5611i	−0.291096	+	1.27538i	−0.883002	+	0.469369i	$0.844482\pi$
$468$	4.03370	−	7.58838i	0.186458	−	0.350773i
$469$	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
$474$	−1.65412	+	0.343080i	−0.0759762	+	0.0157582i
$475$	−29.4255	−	23.4661i	−1.35014	−	1.07670i
$476$	−12.1404	−	2.96566i	−0.556455	−	0.135931i
$477$	−0.141795	−	0.327119i	−0.00649235	−	0.0149778i
$478$	−0.912041	−	3.99591i	−0.0417158	−	0.182769i
$479$	14.4210	+	18.0833i	0.658911	+	0.826248i	0.993224	−	0.116214i	$-0.0370757\pi$
$479$	14.4210	+	18.0833i	0.658911	+	0.826248i	−0.334313	+	0.942462i	$0.608504\pi$
$480$	−0.782626	+	0.162324i	−0.0357218	+	0.00740905i
$481$	−17.1538	−	13.6797i	−0.782146	−	0.623740i
$482$	−3.35430	+	1.61535i	−0.152784	+	0.0735770i
$483$	−17.5581	−	23.6752i	−0.798923	−	1.07726i
$484$	−3.20010	−	1.54109i	−0.145459	−	0.0700495i
$485$	2.92217	+	6.06795i	0.132689	+	0.275531i
$486$	−1.54768	+	15.5114i	−0.0702043	+	0.703613i
$487$	−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	$0.266422\pi$
$491$			32.9112i			1.48526i	−0.669702	+	0.742630i	$0.733578\pi$
$492$	−1.65183	+	6.62675i	−0.0744703	+	0.298757i
$493$	−17.6948	−	36.7437i	−0.796936	−	1.65485i
$494$	−21.9575	−	5.01165i	−0.987914	−	0.225485i
$495$	−5.19130	+	0.969459i	−0.233332	+	0.0435740i
$496$	0.992848	−	2.06167i	0.0445802	−	0.0925717i
$497$	2.16497	+	1.08340i	0.0971122	+	0.0485973i
$498$	11.0993	−	21.9217i	0.497373	−	0.982335i
$499$	−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
$501$	1.77448	−	7.11879i	0.0792781	−	0.318044i
$502$	0.529549	−	0.120866i	0.0236349	−	0.00539451i
$503$	−3.71544	−	4.65902i	−0.165663	−	0.207735i	0.692070	−	0.721831i	$-0.256699\pi$
$503$	−3.71544	−	4.65902i	−0.165663	−	0.207735i	−0.857733	+	0.514096i	$0.828128\pi$
$504$	5.28226	−	5.92434i	0.235290	−	0.263891i
$505$	2.38218	−	2.98716i	0.106006	−	0.132927i
$506$	−10.6459	+	22.1065i	−0.473269	+	0.982753i
$507$	5.30516	−	6.38760i	0.235611	−	0.283683i
$508$	2.48029			0.110045
$509$	29.8331			1.32233			0.661165	−	0.750240i	$-0.270062\pi$
$509$	29.8331			1.32233			0.661165	+	0.750240i	$0.270062\pi$
$510$	2.90438	+	2.41221i	0.128608	+	0.106814i
$511$	11.1513	+	14.4275i	0.493306	+	0.638237i
$512$	−0.974928	−	0.222521i	−0.0430861	−	0.00983413i
$513$	40.3001	−	6.69937i	1.77929	−	0.295785i
$514$	0.512791	+	0.408937i	0.0226183	+	0.0180375i
$515$	−4.99583	−	3.98404i	−0.220143	−	0.175558i
$516$	−17.0642	+	7.80347i	−0.751208	+	0.343529i
$517$	−18.0683	−	4.12398i	−0.794644	−	0.181372i
$518$	−12.3924	−	16.0332i	−0.544492	−	0.704460i
$519$	−3.69361	+	4.44723i	−0.162131	+	0.195212i
$520$	1.32192			0.0579702
$521$	−25.6625			−1.12430			−0.562148	−	0.827037i	$-0.690025\pi$
$521$	−25.6625			−1.12430			−0.562148	+	0.827037i	$0.690025\pi$
$522$	25.8809	+	1.03006i	1.13278	+	0.0450847i
$523$	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
$525$	−21.5450	+	4.12838i	−0.940303	+	0.180177i
$526$	9.16744	+	11.4956i	0.399719	+	0.501232i
$527$	−10.5379	+	2.40520i	−0.459036	+	0.104772i
$528$	−6.41106	−	1.59807i	−0.279006	−	0.0695470i
$529$	16.5522	+	7.97110i	0.719659	+	0.346570i
$530$	0.0341934	−	0.0428772i	0.00148527	−	0.00186246i
$531$	−3.62973	−	19.4366i	−0.157517	−	0.843477i
$532$	−18.6022	−	9.30899i	−0.806506	−	0.403596i
$533$	4.90083	−	10.1767i	0.212279	−	0.440801i
$534$	−7.19410	+	14.2087i	−0.311319	+	0.614870i
$535$	−6.18652	−	1.41203i	−0.267466	−	0.0610475i
$536$	−1.71989	−	3.57139i	−0.0742879	−	0.154260i
$537$	−37.4203	−	9.32766i	−1.61480	−	0.402518i
$538$			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
$543$	−3.62142	−	7.91910i	−0.155410	−	0.339841i
$544$	2.04948	+	4.25579i	0.0878708	+	0.182466i
$545$	−5.36404	−	2.58318i	−0.229770	−	0.110651i
$546$	−10.5441	+	7.81978i	−0.451246	+	0.334656i
$547$	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
$549$	−3.79328	−	3.28013i	−0.161893	−	0.139992i
$550$	11.3856	+	14.2771i	0.485484	+	0.608778i
$551$	−15.1049	−	66.1788i	−0.643489	−	2.81931i
$552$	−2.69456	+	10.8099i	−0.114688	+	0.460100i
$553$	2.50678	+	0.612355i	0.106599	+	0.0260400i
$554$	−1.24860	−	0.995724i	−0.0530478	−	0.0423042i
$555$	1.24326	+	5.99424i	0.0527736	+	0.254441i
$556$	−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
$561$	12.9795	+	28.3828i	0.547994	+	1.19832i
$562$	−7.29997	+	31.9832i	−0.307931	+	1.34913i
$563$	20.1742	−	25.2977i	0.850243	−	1.06617i	−0.146788	−	0.989168i	$-0.546893\pi$
$563$	20.1742	−	25.2977i	0.850243	−	1.06617i	0.997031	−	0.0770030i	$-0.0245351\pi$
$564$	−8.41320	−	0.167357i	−0.354260	−	0.00704700i
$565$	−1.08659	−	0.248006i	−0.0457130	−	0.0104337i
$566$	−6.12301	+	26.8267i	−0.257369	+	1.12761i
$567$	12.3148	−	20.3800i	0.517174	−	0.855880i
$568$	−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	0.965585	+	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
$573$	−0.148193	+	7.44979i	−0.00619083	+	0.311219i
$574$	6.62754	−	8.05654i	0.276628	−	0.336274i
$575$	24.0731	−	19.1976i	1.00392	−	0.800597i
$576$	−2.99763	−	0.119306i	−0.124901	−	0.00497108i
$577$	−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
$579$	−9.00956	−	0.179220i	−0.374425	−	0.00744812i
$580$	1.72868	+	3.58965i	0.0717797	+	0.149052i
$581$	−29.6969	+	22.9534i	−1.23204	+	0.952266i
$582$	5.13376	+	24.7518i	0.212801	+	1.02600i
$583$	0.408453	−	0.196701i	0.0169164	−	0.00814651i
$584$	1.53363	−	6.71929i	0.0634622	−	0.278046i
$585$	3.89838	−	0.728010i	0.161178	−	0.0300995i
$586$	26.4014	−	21.0544i	1.09063	−	0.869749i
$587$	4.90144			0.202304			0.101152	−	0.994871i	$-0.467747\pi$
$587$	4.90144			0.202304			0.101152	+	0.994871i	$0.467747\pi$
$588$	−11.1742	+	4.70505i	−0.460816	+	0.194033i
$589$	−17.9909			−0.741302
$590$	2.37791	−	1.89632i	0.0978972	−	0.0780704i
$591$	17.9335	−	35.4195i	0.737685	−	1.45696i
$592$	−1.70432	+	7.46711i	−0.0700471	+	0.306896i
$593$	−21.6448	+	10.4236i	−0.888847	+	0.428046i	−0.821848	−	0.569707i	$-0.807057\pi$
$593$	−21.6448	+	10.4236i	−0.888847	+	0.428046i	−0.0669990	+	0.997753i	$0.521342\pi$
$594$	−19.7864	−	1.18203i	−0.811847	−	0.0484994i
$595$	−2.42306	−	5.23340i	−0.0993356	−	0.214549i
$596$	−0.452755	−	0.940156i	−0.0185456	−	0.0385103i
$597$	0.577100	−	29.0114i	0.0236191	−	1.18736i
$598$	7.99449	−	16.6007i	0.326919	−	0.678854i
$599$	32.6425	−	26.0315i	1.33374	−	1.06362i	0.341417	−	0.939912i	$-0.389093\pi$
$599$	32.6425	−	26.0315i	1.33374	−	1.06362i	0.992319	−	0.123707i	$-0.0394784\pi$
$600$	6.37839	+	5.29751i	0.260397	+	0.216270i
$601$	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
$603$	−7.03882	−	9.58491i	−0.286643	−	0.390328i
$604$	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
$609$	−35.0229	−	18.4063i	−1.41920	−	0.745859i
$610$	0.171650	−	0.752047i	0.00694989	−	0.0304495i
$611$	13.5683	+	3.09688i	0.548915	+	0.125286i
$612$	8.38771	+	11.4217i	0.339053	+	0.461696i
$613$	−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
$615$	−2.86612	+	1.31068i	−0.115573	+	0.0528518i
$616$	7.79432	+	6.41182i	0.314042	+	0.258340i
$617$	−16.4874	+	3.76313i	−0.663757	+	0.151498i	−0.541109	−	0.840952i	$-0.681996\pi$
$617$	−16.4874	+	3.76313i	−0.663757	+	0.151498i	−0.122647	+	0.992450i	$0.539138\pi$
$618$	−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
$621$	−1.99306	+	33.3625i	−0.0799789	+	1.33879i
$622$	2.57069	+	2.05006i	0.103075	+	0.0821998i
$623$	19.2482	−	14.8774i	0.771165	−	0.596049i
$624$	4.81435	+	1.20006i	0.192728	+	0.0480409i
$625$	−4.86232	−	21.3032i	−0.194493	−	0.852129i
$626$	−15.7877	−	19.7972i	−0.631005	−	0.791256i
$627$	10.5498	+	50.8648i	0.421320	+	2.03134i
$628$	4.81490	+	3.83975i	0.192135	+	0.153223i
$629$	32.5957	−	15.6973i	1.29968	−	0.625891i
$630$	3.65724	+	0.201232i	0.145708	+	0.00801729i
$631$	−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
$633$	6.88341	−	3.14779i	0.273591	−	0.125114i
$634$	−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
$639$	−1.09174	−	2.51863i	−0.0431886	−	0.0996354i
$640$	−0.200223	−	0.415766i	−0.00791449	−	0.0164346i
$641$	23.5227	+	5.36890i	0.929089	+	0.212059i	0.660180	−	0.751107i	$-0.270480\pi$
$641$	23.5227	+	5.36890i	0.929089	+	0.212059i	0.268909	+	0.963166i	$0.413337\pi$
$642$	−21.2490	−	10.7587i	−0.838630	−	0.424613i
$643$	−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
$645$	−7.72509	−	3.91135i	−0.304175	−	0.154009i
$646$	23.1549	−	29.0354i	0.911018	−	1.14238i
$647$	5.54352	+	2.66962i	0.217938	+	0.104953i	0.539668	−	0.841878i	$-0.318550\pi$
$647$	5.54352	+	2.66962i	0.217938	+	0.104953i	−0.321730	+	0.946832i	$0.604264\pi$
$648$	−8.90576	+	1.29902i	−0.349851	+	0.0510303i
$649$	24.5118	−	5.59465i	0.962171	−	0.219609i
$650$	−8.54996	−	10.7213i	−0.335357	−	0.420524i
$651$	−6.82156	+	7.96412i	−0.267358	+	0.312138i
$652$	−7.80300	+	9.78466i	−0.305589	+	0.383197i
$653$	6.54596	−	13.5928i	0.256163	−	0.531929i	−0.732737	−	0.680512i	$-0.761757\pi$
$653$	6.54596	−	13.5928i	0.256163	−	0.531929i	0.988900	+	0.148584i	$0.0474715\pi$
$654$	−17.1904	−	14.2773i	−0.672197	−	0.558287i
$655$	3.60072			0.140692
$656$	−3.94302			−0.153949
$657$	0.822267	−	20.6599i	0.0320797	−	0.806020i
$658$	11.4949	+	5.75235i	0.448119	+	0.224250i
$659$	−17.5653	−	4.00916i	−0.684245	−	0.156175i	−0.133753	−	0.991015i	$-0.542703\pi$
$659$	−17.5653	−	4.00916i	−0.684245	−	0.156175i	−0.550492	+	0.834840i	$0.685560\pi$
$660$	−1.26802	−	2.77283i	−0.0493577	−	0.107932i
$661$	−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
$663$	−9.74687	−	21.3139i	−0.378537	−	0.827762i
$664$	13.8306	+	3.15675i	0.536733	+	0.122506i
$665$	−1.99363	−	9.38983i	−0.0773095	−	0.364122i
$666$	−0.913781	+	22.9593i	−0.0354083	+	0.889653i
$667$	55.5333			2.15026
$668$	4.23580			0.163888
$669$	−8.82303	−	7.32788i	−0.341118	−	0.283312i
$670$	0.793670	−	1.64807i	0.0306622	−	0.0636706i
$671$	3.97577	−	4.98545i	0.153483	−	0.192461i
$672$	4.05649	+	2.13188i	0.156482	+	0.0822391i
$673$	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
$675$	21.7274	+	12.1098i	0.836289	+	0.466105i
$676$	4.31921	+	2.08002i	0.166123	+	0.0800008i
$677$	−19.0370	+	23.8716i	−0.731650	+	0.917460i	−0.998934	−	0.0461575i	$-0.985302\pi$
$677$	−19.0370	+	23.8716i	−0.731650	+	0.917460i	0.267284	+	0.963618i	$0.413874\pi$
$678$	−3.73212	−	1.88964i	−0.143331	−	0.0725711i
$679$	9.16312	−	37.5107i	0.351648	−	1.43953i
$680$	−0.945766	+	1.96390i	−0.0362685	+	0.0753122i
$681$	−5.44223	−	2.75549i	−0.208547	−	0.105591i
$682$	8.51022	+	1.94240i	0.325873	+	0.0743784i
$683$	11.6751	+	24.2437i	0.446737	+	0.927659i	0.995772	+	0.0918596i	$0.0292811\pi$
$683$	11.6751	+	24.2437i	0.446737	+	0.927659i	−0.549035	+	0.835799i	$0.685005\pi$
$684$	9.38062	+	21.6409i	0.358677	+	0.827462i
$685$			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
$690$	−4.67536	+	2.13805i	−0.177988	+	0.0813942i
$691$	−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
$693$	26.5167	+	14.6161i	1.00729	+	0.555220i
$694$	−8.48080	+	4.08414i	−0.321927	+	0.155032i
$695$	−0.218487	−	0.174238i	−0.00828769	−	0.00660922i
$696$	3.03701	+	14.6426i	0.115118	+	0.555025i
$697$	11.6126	+	14.5617i	0.439859	+	0.551565i
$698$	1.07814	+	4.72365i	0.0408083	+	0.178793i
$699$	28.0745	+	6.99806i	1.06188	+	0.264691i
$700$	−5.32134	−	11.4932i	−0.201128	−	0.434403i
$701$	−20.3446	−	16.2243i	−0.768404	−	0.612782i	0.158812	−	0.987309i	$-0.449234\pi$
$701$	−20.3446	−	16.2243i	−0.768404	−	0.612782i	−0.927216	+	0.374527i	$0.877805\pi$
$702$	14.8585	+	0.887641i	0.560798	+	0.0335018i
$703$	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
$708$	10.3817	−	4.74757i	0.390168	−	0.178424i
$709$	−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
$711$	−1.73191	−	2.35838i	−0.0649517	−	0.0884460i
$712$	−8.96442	−	2.04607i	−0.335956	−	0.0766798i
$713$	3.27515	−	14.3494i	0.122655	−	0.537388i
$714$	−4.07364	−	21.2594i	−0.152452	−	0.795612i
$715$	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	$-0.228888\pi$
$719$	18.9458	+	9.12382i	0.706560	+	0.340261i	−0.0458576	+	0.998948i	$0.514602\pi$
$720$	−0.819431	−	1.11584i	−0.0305384	−	0.0415848i
$721$	7.60879	+	35.8368i	0.283366	+	1.33463i
$722$	33.4733	−	26.6941i	1.24575	−	0.993451i
$723$	−4.96061	−	4.11999i	−0.184487	−	0.153224i
$724$	3.93065	−	3.13459i	0.146081	−	0.116496i
$725$	17.9326	−	37.2375i	0.666001	−	1.38297i
$726$	0.122352	−	6.15076i	0.00454091	−	0.228276i
$727$	−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
$729$	−25.5478	+	8.73541i	−0.946217	+	0.323534i
$730$	2.86550	−	1.37995i	0.106057	−	0.0510743i
$731$	−11.3868	+	49.8888i	−0.421156	+	1.84520i
$732$	1.30785	−	2.58307i	0.0483397	−	0.0954731i
$733$	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
$735$	−4.91256	−	2.67779i	−0.181202	−	0.0987716i
$736$	−6.43207			−0.237089
$737$	11.8222	−	9.42791i	0.435477	−	0.347282i
$738$	−11.6281	+	2.17150i	−0.428034	+	0.0799341i
$739$	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
$741$	−7.92234	−	38.1966i	−0.291035	−	1.40319i
$742$	−0.307573	+	0.0653031i	−0.0112913	+	0.00239735i
$743$	−18.0599	−	37.5019i	−0.662555	−	1.37581i	−0.913112	−	0.407708i	$-0.866328\pi$
$743$	−18.0599	−	37.5019i	−0.662555	−	1.37581i	0.250557	−	0.968102i	$-0.419386\pi$
$744$	3.96263	+	0.0788254i	0.145277	+	0.00288988i
$745$	0.208931	−	0.433850i	0.00765465	−	0.0158950i
$746$	9.24315	−	7.37117i	0.338416	−	0.269878i
$747$	42.5253	+	1.69251i	1.55592	+	0.0619258i
$748$	−14.0878	+	11.2346i	−0.515101	+	0.410779i
$749$	22.2490	+	28.7856i	0.812961	+	1.05180i
$750$	−0.155578	+	7.82107i	−0.00568091	+	0.285585i
$751$	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
$756$	13.1367	+	4.05297i	0.477778	+	0.147405i
$757$	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
$759$	−42.4898	−	0.845214i	−1.54228	−	0.0306793i
$760$	−2.26210	+	2.83659i	−0.0820551	+	0.102894i
$761$	4.04548	−	17.7244i	0.146649	−	0.642510i	−0.847154	−	0.531348i	$-0.821686\pi$
$761$	4.04548	−	17.7244i	0.146649	−	0.642510i	0.993802	−	0.111162i	$-0.0354572\pi$
$762$	1.78661	+	3.90686i	0.0647221	+	0.141530i
$763$	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
$768$	−0.351758	−	1.69596i	−0.0126930	−	0.0611975i
$769$	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
$771$	−0.274767	+	1.10230i	−0.00989548	+	0.0396982i
$772$	−1.15771	−	5.07226i	−0.0416669	−	0.182555i
$773$	2.08762	+	2.61780i	0.0750866	+	0.0941556i	0.817956	−	0.575281i	$-0.195107\pi$
$773$	2.08762	+	2.61780i	0.0750866	+	0.0941556i	−0.742870	+	0.669436i	$0.766536\pi$
$774$	−24.5834	−	21.2578i	−0.883634	−	0.764095i
$775$	−8.56427	−	6.82978i	−0.307638	−	0.245333i
$776$	−13.1493	+	6.33236i	−0.472032	+	0.227319i
$777$	16.3284	−	31.0692i	0.585777	−	1.11460i
$778$	8.46193	+	4.07505i	0.303375	+	0.146098i
$779$	13.4507	+	27.9308i	0.481923	+	1.00072i
$780$	0.952214	+	2.08224i	0.0340947	+	0.0745563i
$781$	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
$786$	13.1136	+	3.26878i	0.467745	+	0.116594i
$787$	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
$789$	−11.5039	+	22.7208i	−0.409550	+	0.808881i
$790$	0.195283	−	0.405510i	0.00694787	−	0.0144274i
$791$	3.90776	+	5.05584i	0.138944	+	0.179765i
$792$	−2.10083	−	11.2496i	−0.0746496	−	0.399737i
$793$	−2.98558	+	3.74380i	−0.106021	+	0.132946i
$794$	14.6311	+	7.04595i	0.519237	+	0.250052i
$795$	0.0921688	+	0.0229747i	0.00326889	+	0.000814828i
$796$	16.3330	−	3.72790i	0.578908	−	0.132132i
$797$	27.9234	+	35.0148i	0.989097	+	1.24029i	0.970660	+	0.240458i	$0.0772976\pi$
$797$	27.9234	+	35.0148i	0.989097	+	1.24029i	0.0184370	+	0.999830i	$0.494131\pi$
$798$	1.26357	−	36.0069i	0.0447299	−	1.27463i
$799$	−14.3083	+	17.9420i	−0.506190	+	0.634742i
$800$	−2.07702	+	4.31298i	−0.0734338	+	0.152487i
$801$	−27.5631	−	1.09701i	−0.973893	−	0.0387610i
$802$	−5.88659			−0.207863
$803$	26.2912			0.927795
$804$	4.38663	−	5.28166i	0.154705	−	0.186270i
$805$	7.85216	+	0.119272i	0.276752	+	0.00420377i
$806$	−6.39070	−	1.45864i	−0.225103	−	0.0513783i
$807$	−28.4209	+	12.9969i	−1.00046	+	0.457513i
$808$	6.47320	+	5.16220i	0.227726	+	0.181606i
$809$	−12.8065	−	10.2128i	−0.450251	−	0.359064i	0.371957	−	0.928250i	$-0.378687\pi$
$809$	−12.8065	−	10.2128i	−0.450251	−	0.359064i	−0.822209	+	0.569186i	$0.807258\pi$
$810$	−3.03103	−	2.83934i	−0.106500	−	0.0997644i
$811$	−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
$813$	−14.1767	−	11.7743i	−0.497199	−	0.412944i
$814$	−29.2172			−1.02406
$815$	−5.77527			−0.202299
$816$	−5.22727	+	6.29381i	−0.182991	+	0.220328i
$817$	−36.9553	+	76.7385i	−1.29290	+	2.68474i
$818$	5.21204	−	6.53570i	0.182235	−	0.228515i
$819$	−19.9126	−	10.9759i	−0.695802	−	0.383528i
$820$	−1.13448	−	1.42260i	−0.0396179	−	0.0496793i
$821$	−16.9685	+	3.87296i	−0.592206	+	0.135167i	−0.508112	−	0.861291i	$-0.669657\pi$
$821$	−16.9685	+	3.87296i	−0.592206	+	0.135167i	−0.0840934	+	0.996458i	$0.526799\pi$
$822$	−4.43753	+	17.8023i	−0.154777	+	0.620926i
$823$	−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
$825$	−14.2874	+	28.2183i	−0.497424	+	0.982435i
$826$	−17.4358	−	0.264844i	−0.606669	−	0.00921510i
$827$	8.63339	−	17.9274i	0.300212	−	0.623397i	−0.695227	−	0.718790i	$-0.744696\pi$
$827$	8.63339	−	17.9274i	0.300212	−	0.623397i	0.995440	+	0.0953925i	$0.0304106\pi$
$828$	−18.9683	+	3.54227i	−0.659194	+	0.123102i
$829$	−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
$831$	0.669030	−	2.68399i	0.0232084	−	0.0931065i
$832$			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
$837$	11.7293	−	1.94985i	0.405424	−	0.0673965i
$838$	11.1065	+	23.0630i	0.383669	+	0.796697i
$839$	34.8655	+	16.7904i	1.20369	+	0.579668i	0.924726	−	0.380633i	$-0.124294\pi$
$839$	34.8655	+	16.7904i	1.20369	+	0.579668i	0.278966	+	0.960301i	$0.410008\pi$
$840$	0.397971	+	2.07692i	0.0137313	+	0.0716605i
$841$	41.0326	−	19.7603i	1.41492	−	0.681388i
$842$	14.5115	+	11.5726i	0.500100	+	0.398817i
$843$	−55.6371	+	11.5397i	−1.91624	+	0.397447i
$844$	2.72463	+	3.41658i	0.0937857	+	0.117604i
$845$	0.492272	+	2.15678i	0.0169347	+	0.0741956i
$846$	−5.79662	−	13.3727i	−0.199292	−	0.459763i
$847$	−4.20546	+	8.40377i	−0.144501	+	0.288757i
$848$	0.0929151	+	0.0740973i	0.00319072	+	0.00254451i
$849$	−46.6669	+	9.67916i	−1.60160	+	0.332188i
$850$	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
$855$	−5.10882	+	9.61093i	−0.174718	+	0.328687i
$856$	3.05988	−	13.4062i	0.104585	−	0.458215i
$857$	−1.24271	+	1.55831i	−0.0424502	+	0.0532309i	−0.802603	−	0.596513i	$-0.796552\pi$
$857$	−1.24271	+	1.55831i	−0.0424502	+	0.0532309i	0.760153	+	0.649744i	$0.225124\pi$
$858$	−0.376429	+	18.9235i	−0.0128511	+	0.646036i
$859$	−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
$861$	17.4643	+	4.63612i	0.595183	+	0.157998i
$862$	−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
$867$	9.19908	+	0.182990i	0.312417	+	0.00621466i
$868$	−5.41414	−	2.70937i	−0.183768	−	0.0919620i
$869$	2.90887	−	2.31975i	0.0986767	−	0.0786921i
$870$	−4.40907	+	5.30867i	−0.149481	+	0.179981i
$871$	−8.87784	+	7.07984i	−0.300814	+	0.239891i
$872$	5.59778	−	11.6239i	0.189565	−	0.393635i
$873$	−35.2901	+	25.9158i	−1.19439	+	0.877118i
$874$	21.9416	+	45.5621i	0.742184	+	1.54116i
$875$	5.34750	−	10.6859i	0.180778	−	0.361250i
$876$	11.6887	−	2.42434i	0.394924	−	0.0819110i
$877$	−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
$879$	52.1816	+	26.4204i	1.76004	+	0.891139i
$880$	1.37630	−	1.09756i	0.0463949	−	0.0369987i
$881$	2.74219			0.0923867			0.0461934	−	0.998933i	$-0.485291\pi$
$881$	2.74219			0.0923867			0.0461934	+	0.998933i	$0.485291\pi$
$882$	−15.4603	−	14.2120i	−0.520574	−	0.478543i
$883$	−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
$885$	4.69988	+	2.37963i	0.157985	+	0.0799904i
$886$	0.838506	−	3.67374i	0.0281702	−	0.123422i
$887$	38.4723	−	18.5273i	1.29177	−	0.622086i	0.343385	−	0.939195i	$-0.388426\pi$
$887$	38.4723	−	18.5273i	1.29177	−	0.622086i	0.948389	+	0.317109i	$0.102712\pi$
$888$	−12.9896	+	2.69416i	−0.435901	+	0.0904101i
$889$	0.0996664	−	6.56147i	0.00334271	−	0.220065i
$890$	−1.84104	−	3.82296i	−0.0617118	−	0.128146i
$891$	−12.3907	−	32.0183i	−0.415106	−	1.07265i
$892$	2.87308	−	5.96601i	0.0961978	−	0.199757i
$893$	−29.8637	+	23.8155i	−0.999350	+	0.796955i
$894$	1.15477	−	1.39038i	0.0386212	−	0.0465013i
$895$	8.03321	−	6.40627i	0.268521	−	0.214138i
$896$	−0.627843	+	2.57018i	−0.0209748	+	0.0858636i
$897$	31.9075	+	0.634709i	1.06536	+	0.0211923i
$898$	−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
$903$	19.9580	+	45.4559i	0.664159	+	1.51268i
$904$	0.537431	−	2.35464i	0.0178747	−	0.0783141i
$905$	2.26185	+	0.516251i	0.0751863	+	0.0171608i
$906$	−0.629630	+	31.6521i	−0.0209181	+	1.05157i
$907$	−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
$909$	21.9325	+	11.6585i	0.727455	+	0.386688i
$910$	0.0531194	−	3.49708i	0.00176089	−	0.115927i
$911$	−2.12695	+	0.485461i	−0.0704689	+	0.0160841i	−0.257610	−	0.966249i	$-0.582935\pi$
$911$	−2.12695	+	0.485461i	−0.0704689	+	0.0160841i	0.187141	+	0.982333i	$0.440078\pi$
$912$	−10.8135	+	8.27708i	−0.358071	+	0.274081i
$913$			54.1164i			1.79099i
$914$	−4.16978	+	0.951725i	−0.137924	+	0.0314803i
$915$	1.30824	−	0.271341i	0.0432490	−	0.00897026i
$916$	−7.14018	−	5.69410i	−0.235918	−	0.188138i
$917$	−15.9430	−	13.1151i	−0.526483	−	0.433099i
$918$	−11.9492	+	21.4393i	−0.394382	+	0.707603i
$919$	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
$921$	−2.29689	+	0.476397i	−0.0756851	+	0.0156978i
$922$	−11.2677	−	8.98572i	−0.371083	−	0.295929i
$923$	−2.36161	+	1.13729i	−0.0777334	+	0.0374344i
$924$	−4.48522	+	16.8959i	−0.147553	+	0.555834i
$925$	33.0337	+	15.9082i	1.08614	+	0.523059i
$926$	−9.41875	−	19.5582i	−0.309519	−	0.642723i
$927$	19.4981	−	36.6807i	0.640402	−	1.20475i
$928$	−7.77880	+	3.74607i	−0.255352	+	0.122971i
$929$	−30.6882	−	38.4818i	−1.00685	−	1.26255i	−0.964677	−	0.263437i	$-0.915144\pi$
$929$	−30.6882	−	38.4818i	−1.00685	−	1.26255i	−0.0421711	−	0.999110i	$-0.513427\pi$
$930$	1.11169	+	1.45235i	0.0364537	+	0.0476245i
$931$	−25.3739	+	48.8370i	−0.831597	+	1.60057i
$932$			16.7048i			0.547184i
$933$	−1.37744	+	5.52596i	−0.0450954	+	0.180912i
$934$	−12.2658	−	25.4703i	−0.401351	−	0.833413i
$935$	−8.10666	−	1.85029i	−0.265116	−	0.0605110i
$936$	1.57760	+	8.44781i	0.0515656	+	0.276125i
$937$	−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
$939$	19.8115	−	39.1287i	0.646524	−	1.27692i
$940$	1.39783	−	1.75283i	0.0455923	−	0.0571710i
$941$	18.7701	+	9.03922i	0.611889	+	0.294670i	0.714047	−	0.700098i	$-0.246860\pi$
$941$	18.7701	+	9.03922i	0.611889	+	0.294670i	−0.102158	+	0.994768i	$0.532575\pi$
$942$	−2.57994	+	10.3501i	−0.0840591	+	0.337225i
$943$	−24.7259	+	5.64353i	−0.805187	+	0.183779i
$944$	4.10934	+	5.15296i	0.133748	+	0.167714i
$945$	2.31742	+	5.90570i	0.0753858	+	0.192112i
$946$	25.7661	−	32.3096i	0.837727	−	1.05048i
$947$	2.31905	−	4.81555i	0.0753590	−	0.156485i	−0.859886	−	0.510487i	$-0.829465\pi$
$947$	2.31905	−	4.81555i	0.0753590	−	0.156485i	0.935245	+	0.354002i	$0.115180\pi$
$948$	1.07934	−	1.29956i	0.0350552	−	0.0422077i
$949$	−19.7432			−0.640892
$950$	37.6367			1.22110
$951$	−34.6697	−	28.7946i	−1.12424	−	0.933729i
$952$	11.3408	−	5.25078i	0.367558	−	0.170179i
$953$	24.3567	+	5.55925i	0.788990	+	0.180082i	0.597985	−	0.801507i	$-0.295968\pi$
$953$	24.3567	+	5.55925i	0.788990	+	0.180082i	0.191005	+	0.981589i	$0.438825\pi$
$954$	0.314815	+	0.167344i	0.0101925	+	0.00541797i
$955$	−1.55211	−	1.23777i	−0.0502251	−	0.0400532i
$956$	3.20447	+	2.55548i	0.103640	+	0.0826502i
$957$	−51.8784	+	23.7241i	−1.67699	+	0.766891i
$958$	−22.5495	−	5.14679i	−0.728543	−	0.166285i
$959$	17.8044	−	21.6433i	0.574934	−	0.698899i
$960$	0.510674	−	0.614869i	0.0164819	−	0.0198448i
$961$	25.7638			0.831089
$962$	21.9405			0.707391
$963$	1.64057	−	41.2203i	0.0528668	−	1.32831i
$964$	1.61535	−	3.35430i	0.0520268	−	0.108035i
$965$	1.49692	−	1.87708i	0.0481875	−	0.0604252i
$966$	28.4887	+	7.56268i	0.916610	+	0.243325i
$967$	−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
$969$	62.4144	+	15.5579i	2.00504	+	0.499791i
$970$	−6.06795	−	2.92217i	−0.194830	−	0.0938252i
$971$	19.0806	−	23.9263i	0.612326	−	0.767833i	−0.374916	−	0.927059i	$-0.622328\pi$
$971$	19.0806	−	23.9263i	0.612326	−	0.767833i	0.987242	+	0.159226i	$0.0508999\pi$
$972$	−8.46120	−	13.0923i	−0.271393	−	0.419936i
$973$	0.332762	+	1.56728i	0.0106679	+	0.0502448i
$974$	2.82499	−	5.86614i	0.0905184	−	0.187963i
$975$	10.7291	−	21.1904i	0.343605	−	0.678635i
$976$	1.62969	+	0.371966i	0.0521651	+	0.0119063i
$977$	−3.06662	−	6.36790i	−0.0981099	−	0.203727i	0.846137	−	0.532965i	$-0.178922\pi$
$977$	−3.06662	−	6.36790i	−0.0981099	−	0.203727i	−0.944247	+	0.329238i	$0.893208\pi$
$978$	−21.0331	−	5.24287i	−0.672564	−	0.167648i
$979$		−	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	$0.752478\pi$
$983$	−53.4691	+	25.7494i	−1.70540	+	0.821277i	−0.992811	+	0.119696i	$0.961808\pi$
$984$	−2.84026	−	6.21090i	−0.0905440	−	0.197996i
$985$	4.58935	+	9.52987i	0.146229	+	0.303647i
$986$	36.7437	+	17.6948i	1.17016	+	0.563519i
$987$	−0.780805	+	22.2499i	−0.0248533	+	0.708224i
$988$	20.2918	−	9.77200i	0.645567	−	0.310889i
$989$	−54.4783	−	43.4450i	−1.73231	−	1.38147i
$990$	3.45427	−	3.99468i	0.109784	−	0.126959i
$991$	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
$993$	6.04250	−	24.2410i	0.191753	−	0.769266i
$994$	−2.36813	+	0.502797i	−0.0751126	+	0.0159477i
$995$	6.04431	+	4.82018i	0.191618	+	0.152810i
$996$	4.99015	+	24.0594i	0.158119	+	0.762351i
$997$	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.41.2	✓	120
3.2	odd	2	inner	294.2.j.a.41.16	yes	120
49.6	odd	14	inner	294.2.j.a.251.16	yes	120
147.104	even	14	inner	294.2.j.a.251.2	yes	120

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

\(f(q)\)	\(=\)	\(q+(-0.781831 + 0.623490i) q^{2} +(-1.54527 - 0.782396i) q^{3} +(0.222521 - 0.974928i) q^{4} +(0.415766 - 0.200223i) q^{5} +(1.69596 - 0.351758i) q^{6} +(-2.57018 - 0.627843i) q^{7} +(0.433884 + 0.900969i) q^{8} +(1.77571 + 2.41802i) q^{9} +O(q^{10})\)	\(q+(-0.781831 + 0.623490i) q^{2} +(-1.54527 - 0.782396i) q^{3} +(0.222521 - 0.974928i) q^{4} +(0.415766 - 0.200223i) q^{5} +(1.69596 - 0.351758i) q^{6} +(-2.57018 - 0.627843i) q^{7} +(0.433884 + 0.900969i) q^{8} +(1.77571 + 2.41802i) q^{9} +(-0.200223 + 0.415766i) q^{10} +(-2.98244 + 2.37842i) q^{11} +(-1.10663 + 1.33243i) q^{12} +(2.23965 - 1.78606i) q^{13} +(2.40090 - 1.11161i) q^{14} +(-0.799124 - 0.0158963i) 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} +(3.48039 + 2.98108i) q^{21} +(0.848848 - 3.71905i) q^{22} +(-6.27080 - 1.43127i) q^{23} +(0.0344474 - 1.73171i) q^{24} +(-2.98468 + 3.74267i) q^{25} +(-0.637438 + 2.79280i) q^{26} +(-0.852100 - 5.12581i) 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} +(6.46954 - 1.34185i) q^{33} +(-3.69304 - 2.94510i) q^{34} +(-1.19430 + 0.253572i) q^{35} +(2.75253 - 1.19313i) q^{36} +(-1.70432 - 7.46711i) q^{37} +(-4.90199 - 6.14691i) q^{38} +(-4.85827 + 1.00765i) q^{39} +(0.360789 + 0.287719i) q^{40} +(3.55254 - 1.71081i) q^{41} +(-4.57976 - 0.160715i) q^{42} +(9.76045 + 4.70038i) q^{43} +(1.65513 + 3.43692i) q^{44} +(1.22242 + 0.649796i) 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} +(1.97882 - 7.93856i) q^{51} +(-1.24291 - 2.58093i) q^{52} +(-0.115863 - 0.0264450i) q^{53} +(3.86209 + 3.47624i) q^{54} +(-0.763787 + 1.58602i) q^{55} +(-0.549491 - 2.58806i) q^{56} +(6.15135 - 12.1492i) q^{57} +(5.38309 - 6.75019i) q^{58} +(-5.93818 - 2.85967i) q^{59} +(-0.193320 + 0.775551i) q^{60} +(-1.62969 + 0.371966i) q^{61} +(-1.42672 - 1.78905i) q^{62} +(-3.04576 - 7.32962i) q^{63} +(-0.623490 + 0.781831i) q^{64} +(0.573561 - 1.19101i) q^{65} +(-4.22147 + 5.08279i) q^{66} -3.96394 q^{67} +4.72357 q^{68} +(8.57026 + 7.11795i) q^{69} +(0.775644 - 0.942885i) q^{70} +(-0.892081 - 0.203612i) q^{71} +(-1.40811 + 2.64900i) q^{72} +(-5.38845 - 4.29715i) q^{73} +(5.98816 + 4.77540i) q^{74} +(7.54037 - 3.44823i) q^{75} +(7.66507 + 1.74950i) q^{76} +(9.15868 - 4.24045i) q^{77} +(3.17009 - 3.81689i) q^{78} -0.975332 q^{79} -0.461466 q^{80} +(-2.69369 + 8.58743i) q^{81} +(-1.71081 + 3.55254i) q^{82} +(8.84503 - 11.0913i) q^{83} +(3.68080 - 2.72978i) q^{84} +(1.35906 + 1.70421i) q^{85} +(-10.5617 + 2.41063i) q^{86} +(14.5102 + 3.61692i) q^{87} +(-3.43692 - 1.65513i) q^{88} +(-5.73296 + 7.18891i) q^{89} +(-1.36087 + 0.254139i) q^{90} +(-6.87766 + 3.18434i) q^{91} +(-2.79077 + 5.79509i) q^{92} +(1.79034 - 3.53601i) q^{93} +(-4.73652 - 1.08108i) q^{94} +(1.57419 + 3.26883i) q^{95} +(-1.68063 - 0.418925i) 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

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Database

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