LMFDB - Embedded newform 290.2.e.f.273.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [290,2,Mod(17,290)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(290, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([1, 3])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("290.17"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 290 = 2 \cdot 5 \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	290.e (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [12,12,0,12,-6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$2.31566165862$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 18x^{10} + 119x^{8} + 346x^{6} + 397x^{4} + 80x^{2} + 4 $ x^12 + 18x^10 + 119x^8 + 346x^6 + 397x^4 + 80*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			273.4
Root			$-1.64632i$ of defining polynomial
Character	$\chi$	$=$	290.273
Dual form			290.2.e.f.17.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.00000 q^{2} +0.289618i q^{3} +1.00000 q^{4} +(-1.56156 + 1.60047i) q^{5} +0.289618i q^{6} +(0.632503 - 0.632503i) q^{7} +1.00000 q^{8} +2.91612 q^{9} +(-1.56156 + 1.60047i) q^{10} +(3.25374 + 3.25374i) q^{11} +0.289618i q^{12} +(-0.198612 + 0.198612i) q^{13} +(0.632503 - 0.632503i) q^{14} +(-0.463525 - 0.452256i) q^{15} +1.00000 q^{16} +0.476804 q^{17} +2.91612 q^{18} +(-1.79299 + 1.79299i) q^{19} +(-1.56156 + 1.60047i) q^{20} +(0.183184 + 0.183184i) q^{21} +(3.25374 + 3.25374i) q^{22} +(-3.88864 - 3.88864i) q^{23} +0.289618i q^{24} +(-0.123035 - 4.99849i) q^{25} +(-0.198612 + 0.198612i) q^{26} +1.71341i q^{27} +(0.632503 - 0.632503i) q^{28} +(-5.30631 + 0.918177i) q^{29} +(-0.463525 - 0.452256i) q^{30} +(-5.65569 - 5.65569i) q^{31} +1.00000 q^{32} +(-0.942340 + 0.942340i) q^{33} +0.476804 q^{34} +(0.0246107 + 2.00000i) q^{35} +2.91612 q^{36} -6.58530i q^{37} +(-1.79299 + 1.79299i) q^{38} +(-0.0575215 - 0.0575215i) q^{39} +(-1.56156 + 1.60047i) q^{40} +(6.47983 - 6.47983i) q^{41} +(0.183184 + 0.183184i) q^{42} -8.57318i q^{43} +(3.25374 + 3.25374i) q^{44} +(-4.55371 + 4.66718i) q^{45} +(-3.88864 - 3.88864i) q^{46} +1.36150i q^{47} +0.289618i q^{48} +6.19988i q^{49} +(-0.123035 - 4.99849i) q^{50} +0.138091i q^{51} +(-0.198612 + 0.198612i) q^{52} +(5.65569 + 5.65569i) q^{53} +1.71341i q^{54} +(-10.2884 + 0.126603i) q^{55} +(0.632503 - 0.632503i) q^{56} +(-0.519282 - 0.519282i) q^{57} +(-5.30631 + 0.918177i) q^{58} +9.89258i q^{59} +(-0.463525 - 0.452256i) q^{60} +(3.88864 + 3.88864i) q^{61} +(-5.65569 - 5.65569i) q^{62} +(1.84446 - 1.84446i) q^{63} +1.00000 q^{64} +(-0.00772799 - 0.628018i) q^{65} +(-0.942340 + 0.942340i) q^{66} +(-7.85685 - 7.85685i) q^{67} +0.476804 q^{68} +(1.12622 - 1.12622i) q^{69} +(0.0246107 + 2.00000i) q^{70} -8.63547i q^{71} +2.91612 q^{72} -8.56068 q^{73} -6.58530i q^{74} +(1.44765 - 0.0356331i) q^{75} +(-1.79299 + 1.79299i) q^{76} +4.11600 q^{77} +(-0.0575215 - 0.0575215i) q^{78} +(0.0428537 - 0.0428537i) q^{79} +(-1.56156 + 1.60047i) q^{80} +8.25213 q^{81} +(6.47983 - 6.47983i) q^{82} +(-1.00000 - 1.00000i) q^{83} +(0.183184 + 0.183184i) q^{84} +(-0.744561 + 0.763113i) q^{85} -8.57318i q^{86} +(-0.265920 - 1.53680i) q^{87} +(3.25374 + 3.25374i) q^{88} +(-5.88779 + 5.88779i) q^{89} +(-4.55371 + 4.66718i) q^{90} +0.251245i q^{91} +(-3.88864 - 3.88864i) q^{92} +(1.63799 - 1.63799i) q^{93} +1.36150i q^{94} +(-0.0697654 - 5.66951i) q^{95} +0.289618i q^{96} +11.8026i q^{97} +6.19988i q^{98} +(9.48830 + 9.48830i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 12 q^{2} + 12 q^{4} - 6 q^{5} - 4 q^{7} + 12 q^{8} - 28 q^{9} - 6 q^{10} + 10 q^{11} - 2 q^{13} - 4 q^{14} - 16 q^{15} + 12 q^{16} - 28 q^{18} + 16 q^{19} - 6 q^{20} - 16 q^{21} + 10 q^{22} + 4 q^{23}+ \cdots - 36 q^{99}+O(q^{100}) $ 12 * q + 12 * q^2 + 12 * q^4 - 6 * q^5 - 4 * q^7 + 12 * q^8 - 28 * q^9 - 6 * q^10 + 10 * q^11 - 2 * q^13 - 4 * q^14 - 16 * q^15 + 12 * q^16 - 28 * q^18 + 16 * q^19 - 6 * q^20 - 16 * q^21 + 10 * q^22 + 4 * q^23 - 10 * q^25 - 2 * q^26 - 4 * q^28 - 20 * q^29 - 16 * q^30 + 18 * q^31 + 12 * q^32 + 6 * q^33 + 20 * q^35 - 28 * q^36 + 16 * q^38 + 38 * q^39 - 6 * q^40 + 36 * q^41 - 16 * q^42 + 10 * q^44 - 12 * q^45 + 4 * q^46 - 10 * q^50 - 2 * q^52 - 18 * q^53 + 18 * q^55 - 4 * q^56 + 32 * q^57 - 20 * q^58 - 16 * q^60 - 4 * q^61 + 18 * q^62 + 24 * q^63 + 12 * q^64 + 22 * q^65 + 6 * q^66 + 12 * q^67 - 12 * q^69 + 20 * q^70 - 28 * q^72 - 4 * q^73 - 32 * q^75 + 16 * q^76 - 72 * q^77 + 38 * q^78 - 30 * q^79 - 6 * q^80 + 44 * q^81 + 36 * q^82 - 12 * q^83 - 16 * q^84 - 58 * q^85 + 4 * q^87 + 10 * q^88 - 20 * q^89 - 12 * q^90 + 4 * q^92 - 2 * q^93 - 26 * q^95 - 36 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/290\mathbb{Z}\right)^\times$.

$n$	$31$	$117$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{3}{4}\right)$

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 $

$2$	1.00000			0.707107
$2$	1.00000			0.707107
$3$			0.289618i			0.167211i	0.996499	+	0.0836054i	$0.0266435\pi$
$3$			0.289618i			0.167211i	−0.996499	+	0.0836054i	$0.973356\pi$
$4$	1.00000			0.500000
$5$	−1.56156	+	1.60047i	−0.698353	+	0.715754i
$5$	−1.56156	+	1.60047i	−0.698353	+	0.715754i
$6$			0.289618i			0.118236i
$7$	0.632503	−	0.632503i	0.239064	−	0.239064i	−0.577399	−	0.816462i	$-0.695932\pi$
$7$	0.632503	−	0.632503i	0.239064	−	0.239064i	0.816462	+	0.577399i	$0.195932\pi$
$8$	1.00000			0.353553
$9$	2.91612			0.972041
$10$	−1.56156	+	1.60047i	−0.493810	+	0.506114i
$11$	3.25374	+	3.25374i	0.981039	+	0.981039i	0.999824	−	0.0187847i	$-0.00597971\pi$
$11$	3.25374	+	3.25374i	0.981039	+	0.981039i	−0.0187847	+	0.999824i	$0.505980\pi$
$12$			0.289618i			0.0836054i
$13$	−0.198612	+	0.198612i	−0.0550850	+	0.0550850i	−0.734113	−	0.679028i	$-0.762402\pi$
$13$	−0.198612	+	0.198612i	−0.0550850	+	0.0550850i	0.679028	+	0.734113i	$0.262402\pi$
$14$	0.632503	−	0.632503i	0.169044	−	0.169044i
$15$	−0.463525	−	0.452256i	−0.119682	−	0.116772i
$16$	1.00000			0.250000
$17$	0.476804			0.115642			0.0578210	−	0.998327i	$-0.481585\pi$
$17$	0.476804			0.115642			0.0578210	+	0.998327i	$0.481585\pi$
$18$	2.91612			0.687336
$19$	−1.79299	+	1.79299i	−0.411341	+	0.411341i	−0.882205	−	0.470865i	$-0.843942\pi$
$19$	−1.79299	+	1.79299i	−0.411341	+	0.411341i	0.470865	+	0.882205i	$0.343942\pi$
$20$	−1.56156	+	1.60047i	−0.349176	+	0.357877i
$21$	0.183184	+	0.183184i	0.0399740	+	0.0399740i
$22$	3.25374	+	3.25374i	0.693699	+	0.693699i
$23$	−3.88864	−	3.88864i	−0.810837	−	0.810837i	0.173923	−	0.984759i	$-0.444356\pi$
$23$	−3.88864	−	3.88864i	−0.810837	−	0.810837i	−0.984759	+	0.173923i	$0.944356\pi$
$24$			0.289618i			0.0591179i
$25$	−0.123035	−	4.99849i	−0.0246070	−	0.999697i
$26$	−0.198612	+	0.198612i	−0.0389510	+	0.0389510i
$27$			1.71341i			0.329746i
$28$	0.632503	−	0.632503i	0.119532	−	0.119532i
$29$	−5.30631	+	0.918177i	−0.985357	+	0.170501i
$29$	−5.30631	+	0.918177i	−0.985357	+	0.170501i
$30$	−0.463525	−	0.452256i	−0.0846278	−	0.0825703i
$31$	−5.65569	−	5.65569i	−1.01579	−	1.01579i	−0.999873	−	0.0159192i	$-0.994933\pi$
$31$	−5.65569	−	5.65569i	−1.01579	−	1.01579i	−0.0159192	−	0.999873i	$-0.505067\pi$
$32$	1.00000			0.176777
$33$	−0.942340	+	0.942340i	−0.164040	+	0.164040i
$34$	0.476804			0.0817713
$35$	0.0246107	+	2.00000i	0.00415997	+	0.338062i
$36$	2.91612			0.486020
$37$		−	6.58530i		−	1.08262i	−0.840824	−	0.541308i	$-0.817929\pi$
$37$		−	6.58530i		−	1.08262i	0.840824	−	0.541308i	$-0.182071\pi$
$38$	−1.79299	+	1.79299i	−0.290862	+	0.290862i
$39$	−0.0575215	−	0.0575215i	−0.00921081	−	0.00921081i
$40$	−1.56156	+	1.60047i	−0.246905	+	0.253057i
$41$	6.47983	−	6.47983i	1.01198	−	1.01198i	0.0120528	−	0.999927i	$-0.496163\pi$
$41$	6.47983	−	6.47983i	1.01198	−	1.01198i	0.999927	−	0.0120528i	$-0.00383661\pi$
$42$	0.183184	+	0.183184i	0.0282659	+	0.0282659i
$43$		−	8.57318i		−	1.30740i	−0.756755	−	0.653699i	$-0.773216\pi$
$43$		−	8.57318i		−	1.30740i	0.756755	−	0.653699i	$-0.226784\pi$
$44$	3.25374	+	3.25374i	0.490519	+	0.490519i
$45$	−4.55371	+	4.66718i	−0.678827	+	0.695742i
$46$	−3.88864	−	3.88864i	−0.573348	−	0.573348i
$47$			1.36150i			0.198595i	0.995058	+	0.0992974i	$0.0316595\pi$
$47$			1.36150i			0.198595i	−0.995058	+	0.0992974i	$0.968340\pi$
$48$			0.289618i			0.0418027i
$49$			6.19988i			0.885697i
$50$	−0.123035	−	4.99849i	−0.0173998	−	0.706893i
$51$			0.138091i			0.0193366i
$52$	−0.198612	+	0.198612i	−0.0275425	+	0.0275425i
$53$	5.65569	+	5.65569i	0.776869	+	0.776869i	0.979297	−	0.202428i	$-0.0648832\pi$
$53$	5.65569	+	5.65569i	0.776869	+	0.776869i	−0.202428	+	0.979297i	$0.564883\pi$
$54$			1.71341i			0.233166i
$55$	−10.2884	+	0.126603i	−1.38729	+	0.0170712i
$56$	0.632503	−	0.632503i	0.0845218	−	0.0845218i
$57$	−0.519282	−	0.519282i	−0.0687806	−	0.0687806i
$58$	−5.30631	+	0.918177i	−0.696753	+	0.120563i
$59$			9.89258i			1.28790i	0.765066	+	0.643952i	$0.222706\pi$
$59$			9.89258i			1.28790i	−0.765066	+	0.643952i	$0.777294\pi$
$60$	−0.463525	−	0.452256i	−0.0598409	−	0.0583860i
$61$	3.88864	+	3.88864i	0.497889	+	0.497889i	0.910780	−	0.412891i	$-0.135481\pi$
$61$	3.88864	+	3.88864i	0.497889	+	0.497889i	−0.412891	+	0.910780i	$0.635481\pi$
$62$	−5.65569	−	5.65569i	−0.718274	−	0.718274i
$63$	1.84446	−	1.84446i	0.232380	−	0.232380i
$64$	1.00000			0.125000
$65$	−0.00772799	−	0.628018i	−0.000958539	−	0.0778961i
$66$	−0.942340	+	0.942340i	−0.115994	+	0.115994i
$67$	−7.85685	−	7.85685i	−0.959867	−	0.959867i	0.0393577	−	0.999225i	$-0.487469\pi$
$67$	−7.85685	−	7.85685i	−0.959867	−	0.959867i	−0.999225	+	0.0393577i	$0.987469\pi$
$68$	0.476804			0.0578210
$69$	1.12622	−	1.12622i	0.135581	−	0.135581i
$70$	0.0246107	+	2.00000i	0.00294154	+	0.239046i
$71$		−	8.63547i		−	1.02484i	−0.858734	−	0.512421i	$-0.828749\pi$
$71$		−	8.63547i		−	1.02484i	0.858734	−	0.512421i	$-0.171251\pi$
$72$	2.91612			0.343668
$73$	−8.56068			−1.00195			−0.500976	−	0.865461i	$-0.667026\pi$
$73$	−8.56068			−1.00195			−0.500976	+	0.865461i	$0.667026\pi$
$74$		−	6.58530i		−	0.765525i
$75$	1.44765	−	0.0356331i	0.167160	−	0.00411456i
$76$	−1.79299	+	1.79299i	−0.205670	+	0.205670i
$77$	4.11600			0.469062
$78$	−0.0575215	−	0.0575215i	−0.00651302	−	0.00651302i
$79$	0.0428537	−	0.0428537i	0.00482142	−	0.00482142i	−0.704692	−	0.709513i	$-0.748915\pi$
$79$	0.0428537	−	0.0428537i	0.00482142	−	0.00482142i	0.709513	+	0.704692i	$0.248915\pi$
$80$	−1.56156	+	1.60047i	−0.174588	+	0.178938i
$81$	8.25213			0.916903
$82$	6.47983	−	6.47983i	0.715578	−	0.715578i
$83$	−1.00000	−	1.00000i	−0.109764	−	0.109764i	0.650092	−	0.759856i	$-0.274731\pi$
$83$	−1.00000	−	1.00000i	−0.109764	−	0.109764i	−0.759856	+	0.650092i	$0.774731\pi$
$84$	0.183184	+	0.183184i	0.0199870	+	0.0199870i
$85$	−0.744561	+	0.763113i	−0.0807589	+	0.0827712i
$86$		−	8.57318i		−	0.924469i
$87$	−0.265920	−	1.53680i	−0.0285096	−	0.164762i
$88$	3.25374	+	3.25374i	0.346850	+	0.346850i
$89$	−5.88779	+	5.88779i	−0.624104	+	0.624104i	−0.946578	−	0.322474i	$-0.895486\pi$
$89$	−5.88779	+	5.88779i	−0.624104	+	0.624104i	0.322474	+	0.946578i	$0.395486\pi$
$90$	−4.55371	+	4.66718i	−0.480003	+	0.491964i
$91$			0.251245i			0.0263377i
$92$	−3.88864	−	3.88864i	−0.405418	−	0.405418i
$93$	1.63799	−	1.63799i	0.169851	−	0.169851i
$94$			1.36150i			0.140428i
$95$	−0.0697654	−	5.66951i	−0.00715778	−	0.581680i
$96$			0.289618i			0.0295590i
$97$			11.8026i			1.19838i	0.800608	+	0.599188i	$0.204510\pi$
$97$			11.8026i			1.19838i	−0.800608	+	0.599188i	$0.795490\pi$
$98$			6.19988i			0.626282i
$99$	9.48830	+	9.48830i	0.953610	+	0.953610i
$100$	−0.123035	−	4.99849i	−0.0123035	−	0.499849i
$101$	−0.605077	−	0.605077i	−0.0602074	−	0.0602074i	0.676362	−	0.736569i	$-0.263556\pi$
$101$	−0.605077	−	0.605077i	−0.0602074	−	0.0602074i	−0.736569	+	0.676362i	$0.763556\pi$
$102$			0.138091i			0.0136730i
$103$	−10.9674	−	10.9674i	−1.08065	−	1.08065i	−0.996449	−	0.0841981i	$-0.973167\pi$
$103$	−10.9674	−	10.9674i	−1.08065	−	1.08065i	−0.0841981	−	0.996449i	$-0.526833\pi$
$104$	−0.198612	+	0.198612i	−0.0194755	+	0.0194755i
$105$	−0.579235	+	0.00712770i	−0.0565276	+	0.000695592i
$106$	5.65569	+	5.65569i	0.549330	+	0.549330i
$107$	0.674656	−	0.674656i	0.0652215	−	0.0652215i	−0.673744	−	0.738965i	$-0.735315\pi$
$107$	0.674656	−	0.674656i	0.0652215	−	0.0652215i	0.738965	+	0.673744i	$0.235315\pi$
$108$			1.71341i			0.164873i
$109$	10.4345			0.999445			0.499723	−	0.866185i	$-0.333435\pi$
$109$	10.4345			0.999445			0.499723	+	0.866185i	$0.333435\pi$
$110$	−10.2884	+	0.126603i	−0.980965	+	0.0120711i
$111$	1.90722			0.181025
$112$	0.632503	−	0.632503i	0.0597660	−	0.0597660i
$113$	3.11631			0.293158			0.146579	−	0.989199i	$-0.453174\pi$
$113$	3.11631			0.293158			0.146579	+	0.989199i	$0.453174\pi$
$114$	−0.519282	−	0.519282i	−0.0486353	−	0.0486353i
$115$	12.2960	−	0.151307i	1.14661	−	0.0141095i
$116$	−5.30631	+	0.918177i	−0.492679	+	0.0852506i
$117$	−0.579176	+	0.579176i	−0.0535449	+	0.0535449i
$118$			9.89258i			0.910686i
$119$	0.301580	−	0.301580i	0.0276458	−	0.0276458i
$120$	−0.463525	−	0.452256i	−0.0423139	−	0.0412852i
$121$			10.1736i			0.924874i
$122$	3.88864	+	3.88864i	0.352061	+	0.352061i
$123$	1.87667	+	1.87667i	0.169214	+	0.169214i
$124$	−5.65569	−	5.65569i	−0.507896	−	0.507896i
$125$	8.19207	+	7.60854i	0.732721	+	0.680529i
$126$	1.84446	−	1.84446i	0.164317	−	0.164317i
$127$	−2.18915			−0.194255			−0.0971277	−	0.995272i	$-0.530966\pi$
$127$	−2.18915			−0.194255			−0.0971277	+	0.995272i	$0.530966\pi$
$128$	1.00000			0.0883883
$129$	2.48294			0.218611
$130$	−0.00772799	−	0.628018i	−0.000677790	−	0.0550808i
$131$	−4.28463	+	4.28463i	−0.374350	+	0.374350i	−0.869059	−	0.494709i	$-0.835275\pi$
$131$	−4.28463	+	4.28463i	−0.374350	+	0.374350i	0.494709	+	0.869059i	$0.335275\pi$
$132$	−0.942340	+	0.942340i	−0.0820201	+	0.0820201i
$133$			2.26815i			0.196673i
$134$	−7.85685	−	7.85685i	−0.678729	−	0.678729i
$135$	−2.74227	−	2.67560i	−0.236017	−	0.230279i
$136$	0.476804			0.0408856
$137$	14.1260			1.20687			0.603435	−	0.797413i	$-0.293798\pi$
$137$	14.1260			1.20687			0.603435	+	0.797413i	$0.293798\pi$
$138$	1.12622	−	1.12622i	0.0958700	−	0.0958700i
$139$		−	2.52250i		−	0.213956i	−0.994261	−	0.106978i	$-0.965883\pi$
$139$		−	2.52250i		−	0.213956i	0.994261	−	0.106978i	$-0.0341174\pi$
$140$	0.0246107	+	2.00000i	0.00207999	+	0.169031i
$141$	−0.394314			−0.0332072
$142$		−	8.63547i		−	0.724673i
$143$	−1.29246			−0.108081
$144$	2.91612			0.243010
$145$	6.81663	−	9.92641i	0.566090	−	0.824343i
$146$	−8.56068			−0.708487
$147$	−1.79559			−0.148098
$148$		−	6.58530i		−	0.541308i
$149$	−2.94004			−0.240858			−0.120429	−	0.992722i	$-0.538427\pi$
$149$	−2.94004			−0.240858			−0.120429	+	0.992722i	$0.538427\pi$
$150$	1.44765	−	0.0356331i	0.118200	−	0.00290943i
$151$			10.8414i			0.882262i	0.897443	+	0.441131i	$0.145423\pi$
$151$			10.8414i			0.882262i	−0.897443	+	0.441131i	$0.854577\pi$
$152$	−1.79299	+	1.79299i	−0.145431	+	0.145431i
$153$	1.39042			0.112409
$154$	4.11600			0.331677
$155$	17.8835	−	0.220063i	1.43644	−	0.0176759i
$156$	−0.0575215	−	0.0575215i	−0.00460540	−	0.00460540i
$157$			7.88212i			0.629061i	0.949247	+	0.314531i	$0.101847\pi$
$157$			7.88212i			0.629061i	−0.949247	+	0.314531i	$0.898153\pi$
$158$	0.0428537	−	0.0428537i	0.00340926	−	0.00340926i
$159$	−1.63799	+	1.63799i	−0.129901	+	0.129901i
$160$	−1.56156	+	1.60047i	−0.123452	+	0.126529i
$161$	−4.91915			−0.387683
$162$	8.25213			0.648349
$163$	−22.3121			−1.74762			−0.873811	−	0.486266i	$-0.838359\pi$
$163$	−22.3121			−1.74762			−0.873811	+	0.486266i	$0.838359\pi$
$164$	6.47983	−	6.47983i	0.505990	−	0.505990i
$165$	−0.0366665	−	2.97971i	−0.00285448	−	0.231970i
$166$	−1.00000	−	1.00000i	−0.0776151	−	0.0776151i
$167$	−7.60605	−	7.60605i	−0.588574	−	0.588574i	0.348671	−	0.937245i	$-0.386633\pi$
$167$	−7.60605	−	7.60605i	−0.588574	−	0.588574i	−0.937245	+	0.348671i	$0.886633\pi$
$168$	0.183184	+	0.183184i	0.0141330	+	0.0141330i
$169$			12.9211i			0.993931i
$170$	−0.744561	+	0.763113i	−0.0571052	+	0.0585281i
$171$	−5.22859	+	5.22859i	−0.399840	+	0.399840i
$172$		−	8.57318i		−	0.653699i
$173$	2.00873	−	2.00873i	0.152721	−	0.152721i	−0.626611	−	0.779332i	$-0.715558\pi$
$173$	2.00873	−	2.00873i	0.152721	−	0.152721i	0.779332	+	0.626611i	$0.215558\pi$
$174$	−0.265920	−	1.53680i	−0.0201594	−	0.116505i
$175$	−3.23938	−	3.08374i	−0.244874	−	0.233109i
$176$	3.25374	+	3.25374i	0.245260	+	0.245260i
$177$	−2.86506			−0.215351
$178$	−5.88779	+	5.88779i	−0.441308	+	0.441308i
$179$	23.6028			1.76415			0.882077	−	0.471106i	$-0.156145\pi$
$179$	23.6028			1.76415			0.882077	+	0.471106i	$0.156145\pi$
$180$	−4.55371	+	4.66718i	−0.339414	+	0.347871i
$181$	20.7780			1.54442			0.772210	−	0.635368i	$-0.219152\pi$
$181$	20.7780			1.54442			0.772210	+	0.635368i	$0.219152\pi$
$182$			0.251245i			0.0186235i
$183$	−1.12622	+	1.12622i	−0.0832524	+	0.0832524i
$184$	−3.88864	−	3.88864i	−0.286674	−	0.286674i
$185$	10.5396	+	10.2834i	0.774886	+	0.756048i
$186$	1.63799	−	1.63799i	0.120103	−	0.120103i
$187$	1.55140	+	1.55140i	0.113449	+	0.113449i
$188$			1.36150i			0.0992974i
$189$	1.08374	+	1.08374i	0.0788304	+	0.0788304i
$190$	−0.0697654	−	5.66951i	−0.00506132	−	0.411310i
$191$	6.90356	+	6.90356i	0.499524	+	0.499524i	0.911290	−	0.411766i	$-0.135088\pi$
$191$	6.90356	+	6.90356i	0.499524	+	0.499524i	−0.411766	+	0.911290i	$0.635088\pi$
$192$			0.289618i			0.0209013i
$193$		−	24.3879i		−	1.75548i	−0.479135	−	0.877741i	$-0.659050\pi$
$193$		−	24.3879i		−	1.75548i	0.479135	−	0.877741i	$-0.340950\pi$
$194$			11.8026i			0.847380i
$195$	0.181885	−	0.00223816i	0.0130251	−	0.000160278i
$196$			6.19988i			0.442848i
$197$	2.47207	−	2.47207i	0.176128	−	0.176128i	−0.613538	−	0.789666i	$-0.710254\pi$
$197$	2.47207	−	2.47207i	0.176128	−	0.176128i	0.789666	+	0.613538i	$0.210254\pi$
$198$	9.48830	+	9.48830i	0.674304	+	0.674304i
$199$		−	11.3378i		−	0.803712i	−0.915703	−	0.401856i	$-0.868365\pi$
$199$		−	11.3378i		−	0.803712i	0.915703	−	0.401856i	$-0.131635\pi$
$200$	−0.123035	−	4.99849i	−0.00869989	−	0.353446i
$201$	2.27548	−	2.27548i	0.160500	−	0.160500i
$202$	−0.605077	−	0.605077i	−0.0425731	−	0.0425731i
$203$	−2.77551	+	3.93701i	−0.194803	+	0.276324i
$204$			0.138091i			0.00966830i
$205$	0.252131	+	20.4895i	0.0176096	+	1.43105i
$206$	−10.9674	−	10.9674i	−0.764133	−	0.764133i
$207$	−11.3397	−	11.3397i	−0.788166	−	0.788166i
$208$	−0.198612	+	0.198612i	−0.0137713	+	0.0137713i
$209$	−11.6679			−0.807083
$210$	−0.579235	+	0.00712770i	−0.0399710	+	0.000491858i
$211$	−11.8850	+	11.8850i	−0.818199	+	0.818199i	−0.985847	−	0.167648i	$-0.946383\pi$
$211$	−11.8850	+	11.8850i	−0.818199	+	0.818199i	0.167648	+	0.985847i	$0.446383\pi$
$212$	5.65569	+	5.65569i	0.388435	+	0.388435i
$213$	2.50099			0.171365
$214$	0.674656	−	0.674656i	0.0461185	−	0.0461185i
$215$	13.7211	+	13.3876i	0.935775	+	0.913024i
$216$			1.71341i			0.116583i
$217$	−7.15449			−0.485678
$218$	10.4345			0.706715
$219$		−	2.47932i		−	0.167537i
$220$	−10.2884	+	0.126603i	−0.693647	+	0.00853558i
$221$	−0.0946990	+	0.0946990i	−0.00637014	+	0.00637014i
$222$	1.90722			0.128004
$223$	10.2691	+	10.2691i	0.687668	+	0.687668i	0.961716	−	0.274048i	$-0.0883628\pi$
$223$	10.2691	+	10.2691i	0.687668	+	0.687668i	−0.274048	+	0.961716i	$0.588363\pi$
$224$	0.632503	−	0.632503i	0.0422609	−	0.0422609i
$225$	−0.358785	−	14.5762i	−0.0239190	−	0.971746i
$226$	3.11631			0.207294
$227$	−11.4326	+	11.4326i	−0.758806	+	0.758806i	−0.976105	−	0.217299i	$-0.930275\pi$
$227$	−11.4326	+	11.4326i	−0.758806	+	0.758806i	0.217299	+	0.976105i	$0.430275\pi$
$228$	−0.519282	−	0.519282i	−0.0343903	−	0.0343903i
$229$	−11.1122	−	11.1122i	−0.734316	−	0.734316i	0.237156	−	0.971472i	$-0.423785\pi$
$229$	−11.1122	−	11.1122i	−0.734316	−	0.734316i	−0.971472	+	0.237156i	$0.923785\pi$
$230$	12.2960	−	0.151307i	0.810775	−	0.00997689i
$231$			1.19207i			0.0784322i
$232$	−5.30631	+	0.918177i	−0.348376	+	0.0602813i
$233$	14.5816	+	14.5816i	0.955273	+	0.955273i	0.999042	−	0.0437692i	$-0.0139366\pi$
$233$	14.5816	+	14.5816i	0.955273	+	0.955273i	−0.0437692	+	0.999042i	$0.513937\pi$
$234$	−0.579176	+	0.579176i	−0.0378619	+	0.0378619i
$235$	−2.17904	−	2.12607i	−0.142145	−	0.138689i
$236$			9.89258i			0.643952i
$237$	0.0124112	+	0.0124112i	0.000806194	+	0.000806194i
$238$	0.301580	−	0.301580i	0.0195486	−	0.0195486i
$239$		−	1.20088i		−	0.0776785i	−0.999245	−	0.0388392i	$-0.987634\pi$
$239$		−	1.20088i		−	0.0776785i	0.999245	−	0.0388392i	$-0.0123660\pi$
$240$	−0.463525	−	0.452256i	−0.0299204	−	0.0291930i
$241$		−	22.6204i		−	1.45711i	−0.684987	−	0.728555i	$-0.740192\pi$
$241$		−	22.6204i		−	1.45711i	0.684987	−	0.728555i	$-0.259808\pi$
$242$			10.1736i			0.653985i
$243$			7.53020i			0.483063i
$244$	3.88864	+	3.88864i	0.248944	+	0.248944i
$245$	−9.92275	−	9.68151i	−0.633941	−	0.618529i
$246$	1.87667	+	1.87667i	0.119652	+	0.119652i
$247$		−	0.712219i		−	0.0453174i
$248$	−5.65569	−	5.65569i	−0.359137	−	0.359137i
$249$	0.289618	−	0.289618i	0.0183538	−	0.0183538i
$250$	8.19207	+	7.60854i	0.518112	+	0.481206i
$251$	−4.26661	−	4.26661i	−0.269306	−	0.269306i	0.559514	−	0.828821i	$-0.310988\pi$
$251$	−4.26661	−	4.26661i	−0.269306	−	0.269306i	−0.828821	+	0.559514i	$0.810988\pi$
$252$	1.84446	−	1.84446i	0.116190	−	0.116190i
$253$		−	25.3052i		−	1.59092i
$254$	−2.18915			−0.137359
$255$	−0.221011	−	0.215638i	−0.0138402	−	0.0135038i
$256$	1.00000			0.0625000
$257$	0.892241	−	0.892241i	0.0556564	−	0.0556564i	−0.678731	−	0.734387i	$-0.737470\pi$
$257$	0.892241	−	0.892241i	0.0556564	−	0.0556564i	0.734387	+	0.678731i	$0.237470\pi$
$258$	2.48294			0.154581
$259$	−4.16522	−	4.16522i	−0.258814	−	0.258814i
$260$	−0.00772799	−	0.628018i	−0.000479270	−	0.0389480i
$261$	−15.4739	+	2.67752i	−0.957807	+	0.165734i
$262$	−4.28463	+	4.28463i	−0.264705	+	0.264705i
$263$			20.3198i			1.25297i	0.779433	+	0.626486i	$0.215507\pi$
$263$			20.3198i			1.25297i	−0.779433	+	0.626486i	$0.784493\pi$
$264$	−0.942340	+	0.942340i	−0.0579970	+	0.0579970i
$265$	−17.8835	+	0.220063i	−1.09858	+	0.0135184i
$266$			2.26815i			0.139069i
$267$	−1.70521	−	1.70521i	−0.104357	−	0.104357i
$268$	−7.85685	−	7.85685i	−0.479934	−	0.479934i
$269$	−20.2449	−	20.2449i	−1.23436	−	1.23436i	−0.962274	−	0.272081i	$-0.912288\pi$
$269$	−20.2449	−	20.2449i	−1.23436	−	1.23436i	−0.272081	−	0.962274i	$-0.587712\pi$
$270$	−2.74227	−	2.67560i	−0.166889	−	0.162832i
$271$	−3.61114	+	3.61114i	−0.219361	+	0.219361i	−0.808229	−	0.588868i	$-0.799574\pi$
$271$	−3.61114	+	3.61114i	−0.219361	+	0.219361i	0.588868	+	0.808229i	$0.299574\pi$
$272$	0.476804			0.0289105
$273$	−0.0727650			−0.00440394
$274$	14.1260			0.853385
$275$	15.8634	−	16.6641i	0.956601	−	1.00488i
$276$	1.12622	−	1.12622i	0.0677903	−	0.0677903i
$277$	1.15866	−	1.15866i	0.0696169	−	0.0696169i	−0.671441	−	0.741058i	$-0.734324\pi$
$277$	1.15866	−	1.15866i	0.0696169	−	0.0696169i	0.741058	+	0.671441i	$0.234324\pi$
$278$		−	2.52250i		−	0.151290i
$279$	−16.4927	−	16.4927i	−0.987392	−	0.987392i
$280$	0.0246107	+	2.00000i	0.00147077	+	0.119523i
$281$	−8.88875			−0.530258			−0.265129	−	0.964213i	$-0.585415\pi$
$281$	−8.88875			−0.530258			−0.265129	+	0.964213i	$0.585415\pi$
$282$	−0.394314			−0.0234810
$283$	22.9390	−	22.9390i	1.36358	−	1.36358i	0.494284	−	0.869301i	$-0.335430\pi$
$283$	22.9390	−	22.9390i	1.36358	−	1.36358i	0.869301	−	0.494284i	$-0.164570\pi$
$284$		−	8.63547i		−	0.512421i
$285$	1.64199	−	0.0202053i	0.0972631	−	0.00119686i
$286$	−1.29246			−0.0764248
$287$		−	8.19704i		−	0.483856i
$288$	2.91612			0.171834
$289$	−16.7727			−0.986627
$290$	6.81663	−	9.92641i	0.400286	−	0.582899i
$291$	−3.41825			−0.200382
$292$	−8.56068			−0.500976
$293$			15.7998i			0.923035i	0.887131	+	0.461517i	$0.152695\pi$
$293$			15.7998i			0.923035i	−0.887131	+	0.461517i	$0.847305\pi$
$294$	−1.79559			−0.104721
$295$	−15.8328	−	15.4479i	−0.921822	−	0.899411i
$296$		−	6.58530i		−	0.382763i
$297$	−5.57500	+	5.57500i	−0.323494	+	0.323494i
$298$	−2.94004			−0.170312
$299$	1.54466			0.0893299
$300$	1.44765	−	0.0356331i	0.0835801	−	0.00205728i
$301$	−5.42256	−	5.42256i	−0.312551	−	0.312551i
$302$			10.8414i			0.623853i
$303$	0.175241	−	0.175241i	0.0100673	−	0.0100673i
$304$	−1.79299	+	1.79299i	−0.102835	+	0.102835i
$305$	−12.2960	+	0.151307i	−0.704068	+	0.00866381i
$306$	1.39042			0.0794850
$307$	−15.9584			−0.910794			−0.455397	−	0.890289i	$-0.650503\pi$
$307$	−15.9584			−0.910794			−0.455397	+	0.890289i	$0.650503\pi$
$308$	4.11600			0.234531
$309$	3.17634	−	3.17634i	0.180696	−	0.180696i
$310$	17.8835	−	0.220063i	1.01572	−	0.0124988i
$311$	−5.09331	−	5.09331i	−0.288815	−	0.288815i	0.547797	−	0.836612i	$-0.315467\pi$
$311$	−5.09331	−	5.09331i	−0.288815	−	0.288815i	−0.836612	+	0.547797i	$0.815467\pi$
$312$	−0.0575215	−	0.0575215i	−0.00325651	−	0.00325651i
$313$	−9.62217	−	9.62217i	−0.543877	−	0.543877i	0.380786	−	0.924663i	$-0.375653\pi$
$313$	−9.62217	−	9.62217i	−0.543877	−	0.543877i	−0.924663	+	0.380786i	$0.875653\pi$
$314$			7.88212i			0.444814i
$315$	0.0717679	+	5.83224i	0.00404366	+	0.328610i
$316$	0.0428537	−	0.0428537i	0.00241071	−	0.00241071i
$317$			22.6925i			1.27454i	0.770641	+	0.637269i	$0.219936\pi$
$317$			22.6925i			1.27454i	−0.770641	+	0.637269i	$0.780064\pi$
$318$	−1.63799	+	1.63799i	−0.0918538	+	0.0918538i
$319$	−20.2529	−	14.2778i	−1.13394	−	0.799406i
$320$	−1.56156	+	1.60047i	−0.0872941	+	0.0894692i
$321$	0.195392	+	0.195392i	0.0109057	+	0.0109057i
$322$	−4.91915			−0.274134
$323$	−0.854907	+	0.854907i	−0.0475683	+	0.0475683i
$324$	8.25213			0.458452
$325$	1.01719	+	0.968322i	0.0564238	+	0.0537128i
$326$	−22.3121			−1.23576
$327$			3.02202i			0.167118i
$328$	6.47983	−	6.47983i	0.357789	−	0.357789i
$329$	0.861152	+	0.861152i	0.0474768	+	0.0474768i
$330$	−0.0366665	−	2.97971i	−0.00201842	−	0.164028i
$331$	3.40255	−	3.40255i	0.187021	−	0.187021i	−0.607386	−	0.794407i	$-0.707782\pi$
$331$	3.40255	−	3.40255i	0.187021	−	0.187021i	0.794407	+	0.607386i	$0.207782\pi$
$332$	−1.00000	−	1.00000i	−0.0548821	−	0.0548821i
$333$		−	19.2035i		−	1.05235i
$334$	−7.60605	−	7.60605i	−0.416185	−	0.416185i
$335$	24.8437	−	0.305710i	1.35735	−	0.0167027i
$336$	0.183184	+	0.183184i	0.00999351	+	0.00999351i
$337$			20.6557i			1.12519i	0.826734	+	0.562593i	$0.190196\pi$
$337$			20.6557i			1.12519i	−0.826734	+	0.562593i	$0.809804\pi$
$338$			12.9211i			0.702816i
$339$			0.902538i			0.0490191i
$340$	−0.744561	+	0.763113i	−0.0403795	+	0.0413856i
$341$		−	36.8043i		−	1.99306i
$342$	−5.22859	+	5.22859i	−0.282730	+	0.282730i
$343$	8.34897	+	8.34897i	0.450802	+	0.450802i
$344$		−	8.57318i		−	0.462235i
$345$	0.0438212	+	3.56114i	0.00235925	+	0.191725i
$346$	2.00873	−	2.00873i	0.107990	−	0.107990i
$347$	23.4372	+	23.4372i	1.25818	+	1.25818i	0.951963	+	0.306213i	$0.0990621\pi$
$347$	23.4372	+	23.4372i	1.25818	+	1.25818i	0.306213	+	0.951963i	$0.400938\pi$
$348$	−0.265920	−	1.53680i	−0.0142548	−	0.0823812i
$349$			25.2886i			1.35367i	0.736136	+	0.676834i	$0.236649\pi$
$349$			25.2886i			1.35367i	−0.736136	+	0.676834i	$0.763351\pi$
$350$	−3.23938	−	3.08374i	−0.173152	−	0.164833i
$351$	−0.340304	−	0.340304i	−0.0181641	−	0.0181641i
$352$	3.25374	+	3.25374i	0.173425	+	0.173425i
$353$	−6.88469	+	6.88469i	−0.366435	+	0.366435i	−0.866175	−	0.499740i	$-0.833429\pi$
$353$	−6.88469	+	6.88469i	−0.366435	+	0.366435i	0.499740	+	0.866175i	$0.333429\pi$
$354$	−2.86506			−0.152276
$355$	13.8209	+	13.4848i	0.733535	+	0.715701i
$356$	−5.88779	+	5.88779i	−0.312052	+	0.312052i
$357$	0.0873430	+	0.0873430i	0.00462268	+	0.00462268i
$358$	23.6028			1.24745
$359$	−22.2072	+	22.2072i	−1.17205	+	1.17205i	−0.190330	+	0.981720i	$0.560956\pi$
$359$	−22.2072	+	22.2072i	−1.17205	+	1.17205i	−0.981720	+	0.190330i	$0.939044\pi$
$360$	−4.55371	+	4.66718i	−0.240002	+	0.245982i
$361$			12.5703i			0.661597i
$362$	20.7780			1.09207
$363$	−2.94646			−0.154649
$364$			0.251245i			0.0131688i
$365$	13.3681	−	13.7012i	0.699716	−	0.717151i
$366$	−1.12622	+	1.12622i	−0.0588683	+	0.0588683i
$367$	1.97873			0.103289			0.0516445	−	0.998666i	$-0.483554\pi$
$367$	1.97873			0.103289			0.0516445	+	0.998666i	$0.483554\pi$
$368$	−3.88864	−	3.88864i	−0.202709	−	0.202709i
$369$	18.8960	−	18.8960i	0.983686	−	0.983686i
$370$	10.5396	+	10.2834i	0.547927	+	0.534607i
$371$	7.15449			0.371443
$372$	1.63799	−	1.63799i	0.0849257	−	0.0849257i
$373$	19.0279	+	19.0279i	0.985225	+	0.985225i	0.999892	−	0.0146674i	$-0.00466895\pi$
$373$	19.0279	+	19.0279i	0.985225	+	0.985225i	−0.0146674	+	0.999892i	$0.504669\pi$
$374$	1.55140	+	1.55140i	0.0802208	+	0.0802208i
$375$	−2.20357	+	2.37257i	−0.113792	+	0.122519i
$376$			1.36150i			0.0702139i
$377$	0.871535	−	1.23626i	0.0448864	−	0.0636705i
$378$	1.08374	+	1.08374i	0.0557415	+	0.0557415i
$379$	10.8552	−	10.8552i	0.557595	−	0.557595i	−0.371027	−	0.928622i	$-0.620994\pi$
$379$	10.8552	−	10.8552i	0.557595	−	0.557595i	0.928622	+	0.371027i	$0.120994\pi$
$380$	−0.0697654	−	5.66951i	−0.00357889	−	0.290840i
$381$		−	0.634016i		−	0.0324816i
$382$	6.90356	+	6.90356i	0.353217	+	0.353217i
$383$	−22.6747	+	22.6747i	−1.15862	+	1.15862i	−0.173848	+	0.984772i	$0.555620\pi$
$383$	−22.6747	+	22.6747i	−1.15862	+	1.15862i	−0.984772	+	0.173848i	$0.944380\pi$
$384$			0.289618i			0.0147795i
$385$	−6.42740	+	6.58755i	−0.327571	+	0.335733i
$386$		−	24.3879i		−	1.24131i
$387$		−	25.0004i		−	1.27084i
$388$			11.8026i			0.599188i
$389$	−8.76850	−	8.76850i	−0.444581	−	0.444581i	0.448967	−	0.893548i	$-0.351792\pi$
$389$	−8.76850	−	8.76850i	−0.444581	−	0.444581i	−0.893548	+	0.448967i	$0.851792\pi$
$390$	0.181885	−	0.00223816i	0.00921011	−	0.000113334i
$391$	−1.85412	−	1.85412i	−0.0937668	−	0.0937668i
$392$			6.19988i			0.313141i
$393$	−1.24090	−	1.24090i	−0.0625953	−	0.0625953i
$394$	2.47207	−	2.47207i	0.124541	−	0.124541i
$395$	0.00166744	+	0.135505i	8.38980e−5	+	0.00681801i
$396$	9.48830	+	9.48830i	0.476805	+	0.476805i
$397$	−18.3875	+	18.3875i	−0.922841	+	0.922841i	−0.997229	−	0.0743886i	$-0.976299\pi$
$397$	−18.3875	+	18.3875i	−0.922841	+	0.922841i	0.0743886	+	0.997229i	$0.476299\pi$
$398$		−	11.3378i		−	0.568310i
$399$	−0.656896			−0.0328859
$400$	−0.123035	−	4.99849i	−0.00615175	−	0.249924i
$401$	5.87124			0.293196			0.146598	−	0.989196i	$-0.453168\pi$
$401$	5.87124			0.293196			0.146598	+	0.989196i	$0.453168\pi$
$402$	2.27548	−	2.27548i	0.113491	−	0.113491i
$403$	2.24657			0.111910
$404$	−0.605077	−	0.605077i	−0.0301037	−	0.0301037i
$405$	−12.8862	+	13.2073i	−0.640322	+	0.656277i
$406$	−2.77551	+	3.93701i	−0.137746	+	0.195391i
$407$	21.4268	−	21.4268i	1.06209	−	1.06209i
$408$			0.138091i			0.00683652i
$409$	11.7879	−	11.7879i	0.582876	−	0.582876i	−0.352816	−	0.935693i	$-0.614776\pi$
$409$	11.7879	−	11.7879i	0.582876	−	0.582876i	0.935693	+	0.352816i	$0.114776\pi$
$410$	0.252131	+	20.4895i	0.0124518	+	1.01190i
$411$			4.09115i			0.201802i
$412$	−10.9674	−	10.9674i	−0.540324	−	0.540324i
$413$	6.25709	+	6.25709i	0.307891	+	0.307891i
$414$	−11.3397	−	11.3397i	−0.557318	−	0.557318i
$415$	3.16204	−	0.0389100i	0.155218	−	0.00191002i
$416$	−0.198612	+	0.198612i	−0.00973774	+	0.00973774i
$417$	0.730562			0.0357758
$418$	−11.6679			−0.570694
$419$	18.7077			0.913929			0.456964	−	0.889485i	$-0.348937\pi$
$419$	18.7077			0.913929			0.456964	+	0.889485i	$0.348937\pi$
$420$	−0.579235	+	0.00712770i	−0.0282638	+	0.000347796i
$421$	−4.16276	+	4.16276i	−0.202880	+	0.202880i	−0.801233	−	0.598353i	$-0.795822\pi$
$421$	−4.16276	+	4.16276i	−0.202880	+	0.202880i	0.598353	+	0.801233i	$0.295822\pi$
$422$	−11.8850	+	11.8850i	−0.578554	+	0.578554i
$423$			3.97029i			0.193042i
$424$	5.65569	+	5.65569i	0.274665	+	0.274665i
$425$	−0.0586636	−	2.38330i	−0.00284560	−	0.115607i
$426$	2.50099			0.121173
$427$	4.91915			0.238054
$428$	0.674656	−	0.674656i	0.0326107	−	0.0326107i
$429$		−	0.374320i		−	0.0180723i
$430$	13.7211	+	13.3876i	0.661693	+	0.645606i
$431$	0.757725			0.0364983			0.0182492	−	0.999833i	$-0.494191\pi$
$431$	0.757725			0.0364983			0.0182492	+	0.999833i	$0.494191\pi$
$432$			1.71341i			0.0824366i
$433$	10.8919			0.523431			0.261716	−	0.965145i	$-0.415712\pi$
$433$	10.8919			0.523431			0.261716	+	0.965145i	$0.415712\pi$
$434$	−7.15449			−0.343427
$435$	2.87486	+	1.97422i	0.137839	+	0.0946564i
$436$	10.4345			0.499723
$437$	13.9446			0.667061
$438$		−	2.47932i		−	0.118467i
$439$	16.0340			0.765261			0.382631	−	0.923901i	$-0.375018\pi$
$439$	16.0340			0.765261			0.382631	+	0.923901i	$0.375018\pi$
$440$	−10.2884	+	0.126603i	−0.490482	+	0.00603556i
$441$			18.0796i			0.860933i
$442$	−0.0946990	+	0.0946990i	−0.00450437	+	0.00450437i
$443$	−21.8127			−1.03635			−0.518176	−	0.855274i	$-0.673389\pi$
$443$	−21.8127			−1.03635			−0.518176	+	0.855274i	$0.673389\pi$
$444$	1.90722			0.0905125
$445$	−0.229094	−	18.6174i	−0.0108601	−	0.882550i
$446$	10.2691	+	10.2691i	0.486255	+	0.486255i
$447$		−	0.851488i		−	0.0402740i
$448$	0.632503	−	0.632503i	0.0298830	−	0.0298830i
$449$	11.8820	−	11.8820i	0.560748	−	0.560748i	−0.368772	−	0.929520i	$-0.620222\pi$
$449$	11.8820	−	11.8820i	0.560748	−	0.560748i	0.929520	+	0.368772i	$0.120222\pi$
$450$	−0.358785	−	14.5762i	−0.0169133	−	0.687128i
$451$	42.1674			1.98558
$452$	3.11631			0.146579
$453$	−3.13986			−0.147524
$454$	−11.4326	+	11.4326i	−0.536557	+	0.536557i
$455$	−0.402112	−	0.392336i	−0.0188513	−	0.0183930i
$456$	−0.519282	−	0.519282i	−0.0243176	−	0.0243176i
$457$	25.4126	+	25.4126i	1.18875	+	1.18875i	0.977413	+	0.211340i	$0.0677828\pi$
$457$	25.4126	+	25.4126i	1.18875	+	1.18875i	0.211340	+	0.977413i	$0.432217\pi$
$458$	−11.1122	−	11.1122i	−0.519240	−	0.519240i
$459$			0.816963i			0.0381325i
$460$	12.2960	−	0.151307i	0.573305	−	0.00705473i
$461$	−26.1001	+	26.1001i	−1.21560	+	1.21560i	−0.246449	+	0.969156i	$0.579264\pi$
$461$	−26.1001	+	26.1001i	−1.21560	+	1.21560i	−0.969156	+	0.246449i	$0.920736\pi$
$462$			1.19207i			0.0554599i
$463$	3.00076	−	3.00076i	0.139457	−	0.139457i	−0.633932	−	0.773389i	$-0.718560\pi$
$463$	3.00076	−	3.00076i	0.139457	−	0.139457i	0.773389	+	0.633932i	$0.218560\pi$
$464$	−5.30631	+	0.918177i	−0.246339	+	0.0426253i
$465$	0.0637342	+	5.17938i	0.00295560	+	0.240188i
$466$	14.5816	+	14.5816i	0.675480	+	0.675480i
$467$	4.86798			0.225263			0.112632	−	0.993637i	$-0.464072\pi$
$467$	4.86798			0.225263			0.112632	+	0.993637i	$0.464072\pi$
$468$	−0.579176	+	0.579176i	−0.0267724	+	0.0267724i
$469$	−9.93897			−0.458939
$470$	−2.17904	−	2.12607i	−0.100512	−	0.0980681i
$471$	−2.28280			−0.105186
$472$			9.89258i			0.455343i
$473$	27.8949	−	27.8949i	1.28261	−	1.28261i
$474$	0.0124112	+	0.0124112i	0.000570065	+	0.000570065i
$475$	9.18285	+	8.74165i	0.421338	+	0.401094i
$476$	0.301580	−	0.301580i	0.0138229	−	0.0138229i
$477$	16.4927	+	16.4927i	0.755148	+	0.755148i
$478$		−	1.20088i		−	0.0549270i
$479$	4.92833	+	4.92833i	0.225181	+	0.225181i	0.810676	−	0.585495i	$-0.199100\pi$
$479$	4.92833	+	4.92833i	0.225181	+	0.225181i	−0.585495	+	0.810676i	$0.699100\pi$
$480$	−0.463525	−	0.452256i	−0.0211569	−	0.0206426i
$481$	1.30792	+	1.30792i	0.0596359	+	0.0596359i
$482$		−	22.6204i		−	1.03033i
$483$		−	1.42467i		−	0.0648249i
$484$			10.1736i			0.462437i
$485$	−18.8898	−	18.4306i	−0.857743	−	0.836890i
$486$			7.53020i			0.341577i
$487$	2.73756	−	2.73756i	0.124050	−	0.124050i	−0.642356	−	0.766406i	$-0.722043\pi$
$487$	2.73756	−	2.73756i	0.124050	−	0.124050i	0.766406	+	0.642356i	$0.222043\pi$
$488$	3.88864	+	3.88864i	0.176030	+	0.176030i
$489$		−	6.46199i		−	0.292221i
$490$	−9.92275	−	9.68151i	−0.448264	−	0.437366i
$491$	−16.0568	+	16.0568i	−0.724631	+	0.724631i	−0.969545	−	0.244914i	$-0.921240\pi$
$491$	−16.0568	+	16.0568i	−0.724631	+	0.724631i	0.244914	+	0.969545i	$0.421240\pi$
$492$	1.87667	+	1.87667i	0.0846070	+	0.0846070i
$493$	−2.53007	+	0.437791i	−0.113949	+	0.0197171i
$494$		−	0.712219i		−	0.0320443i
$495$	−30.0024	+	0.369190i	−1.34851	+	0.0165939i
$496$	−5.65569	−	5.65569i	−0.253948	−	0.253948i
$497$	−5.46197	−	5.46197i	−0.245003	−	0.245003i
$498$	0.289618	−	0.289618i	0.0129781	−	0.0129781i
$499$	11.0768			0.495867			0.247934	−	0.968777i	$-0.420249\pi$
$499$	11.0768			0.495867			0.247934	+	0.968777i	$0.420249\pi$
$500$	8.19207	+	7.60854i	0.366361	+	0.340264i
$501$	2.20285	−	2.20285i	0.0984159	−	0.0984159i
$502$	−4.26661	−	4.26661i	−0.190428	−	0.190428i
$503$	8.08426			0.360459			0.180230	−	0.983625i	$-0.442316\pi$
$503$	8.08426			0.360459			0.180230	+	0.983625i	$0.442316\pi$
$504$	1.84446	−	1.84446i	0.0821586	−	0.0821586i
$505$	1.91328	−	0.0235436i	0.0851397	−	0.00104768i
$506$		−	25.3052i		−	1.12495i
$507$	−3.74218			−0.166196
$508$	−2.18915			−0.0971277
$509$		−	12.9806i		−	0.575354i	−0.957728	−	0.287677i	$-0.907117\pi$
$509$		−	12.9806i		−	0.575354i	0.957728	−	0.287677i	$-0.0928829\pi$
$510$	−0.221011	−	0.215638i	−0.00978653	−	0.00954860i
$511$	−5.41466	+	5.41466i	−0.239531	+	0.239531i
$512$	1.00000			0.0441942
$513$	−3.07214	−	3.07214i	−0.135638	−	0.135638i
$514$	0.892241	−	0.892241i	0.0393550	−	0.0393550i
$515$	34.6792	−	0.426741i	1.52815	−	0.0188044i
$516$	2.48294			0.109305
$517$	−4.42996	+	4.42996i	−0.194829	+	0.194829i
$518$	−4.16522	−	4.16522i	−0.183009	−	0.183009i
$519$	0.581765	+	0.581765i	0.0255366	+	0.0255366i
$520$	−0.00772799	−	0.628018i	−0.000338895	−	0.0275404i
$521$		−	18.4390i		−	0.807827i	−0.914797	−	0.403914i	$-0.867650\pi$
$521$		−	18.4390i		−	0.807827i	0.914797	−	0.403914i	$-0.132350\pi$
$522$	−15.4739	+	2.67752i	−0.677272	+	0.117192i
$523$	13.6216	+	13.6216i	0.595631	+	0.595631i	0.939147	−	0.343516i	$-0.111618\pi$
$523$	13.6216	+	13.6216i	0.595631	+	0.595631i	−0.343516	+	0.939147i	$0.611618\pi$
$524$	−4.28463	+	4.28463i	−0.187175	+	0.187175i
$525$	0.893105	−	0.938181i	0.0389783	−	0.0409456i
$526$			20.3198i			0.885984i
$527$	−2.69666	−	2.69666i	−0.117468	−	0.117468i
$528$	−0.942340	+	0.942340i	−0.0410101	+	0.0410101i
$529$			7.24299i			0.314913i
$530$	−17.8835	+	0.220063i	−0.776810	+	0.00955894i
$531$			28.8480i			1.25190i
$532$			2.26815i			0.0983367i
$533$			2.57394i			0.111490i
$534$	−1.70521	−	1.70521i	−0.0737915	−	0.0737915i
$535$	0.0262509	+	2.13329i	0.00113493	+	0.0922301i
$536$	−7.85685	−	7.85685i	−0.339364	−	0.339364i
$537$			6.83578i			0.294986i
$538$	−20.2449	−	20.2449i	−0.872821	−	0.872821i
$539$	−20.1728	+	20.1728i	−0.868903	+	0.868903i
$540$	−2.74227	−	2.67560i	−0.118009	−	0.115140i
$541$	−16.5747	−	16.5747i	−0.712602	−	0.712602i	0.254477	−	0.967079i	$-0.418097\pi$
$541$	−16.5747	−	16.5747i	−0.712602	−	0.712602i	−0.967079	+	0.254477i	$0.918097\pi$
$542$	−3.61114	+	3.61114i	−0.155112	+	0.155112i
$543$			6.01768i			0.258244i
$544$	0.476804			0.0204428
$545$	−16.2942	+	16.7002i	−0.697965	+	0.715357i
$546$	−0.0727650			−0.00311406
$547$	−8.23169	+	8.23169i	−0.351961	+	0.351961i	−0.860839	−	0.508877i	$-0.830061\pi$
$547$	−8.23169	+	8.23169i	−0.351961	+	0.351961i	0.508877	+	0.860839i	$0.330061\pi$
$548$	14.1260			0.603435
$549$	11.3397	+	11.3397i	0.483968	+	0.483968i
$550$	15.8634	−	16.6641i	0.676419	−	0.710559i
$551$	7.86790	−	11.1605i	0.335184	−	0.475452i
$552$	1.12622	−	1.12622i	0.0479350	−	0.0479350i
$553$		−	0.0542103i		−	0.00230526i
$554$	1.15866	−	1.15866i	0.0492266	−	0.0492266i
$555$	−2.97824	+	3.05245i	−0.126419	+	0.129569i
$556$		−	2.52250i		−	0.106978i
$557$	−23.6717	−	23.6717i	−1.00300	−	1.00300i	−0.999995	−	0.00300753i	$-0.999043\pi$
$557$	−23.6717	−	23.6717i	−1.00300	−	1.00300i	−0.00300753	−	0.999995i	$-0.500957\pi$
$558$	−16.4927	−	16.4927i	−0.698191	−	0.698191i
$559$	1.70273	+	1.70273i	0.0720180	+	0.0720180i
$560$	0.0246107	+	2.00000i	0.00103999	+	0.0845154i
$561$	−0.449312	+	0.449312i	−0.0189700	+	0.0189700i
$562$	−8.88875			−0.374949
$563$	38.2332			1.61134			0.805670	−	0.592365i	$-0.201806\pi$
$563$	38.2332			1.61134			0.805670	+	0.592365i	$0.201806\pi$
$564$	−0.394314			−0.0166036
$565$	−4.86632	+	4.98757i	−0.204728	+	0.209829i
$566$	22.9390	−	22.9390i	0.964200	−	0.964200i
$567$	5.21950	−	5.21950i	0.219198	−	0.219198i
$568$		−	8.63547i		−	0.362336i
$569$	−10.6612	−	10.6612i	−0.446939	−	0.446939i	0.447397	−	0.894336i	$-0.352351\pi$
$569$	−10.6612	−	10.6612i	−0.446939	−	0.446939i	−0.894336	+	0.447397i	$0.852351\pi$
$570$	1.64199	−	0.0202053i	0.0687754	−	0.000846307i
$571$	−12.7145			−0.532085			−0.266042	−	0.963961i	$-0.585716\pi$
$571$	−12.7145			−0.532085			−0.266042	+	0.963961i	$0.585716\pi$
$572$	−1.29246			−0.0540405
$573$	−1.99939	+	1.99939i	−0.0835258	+	0.0835258i
$574$		−	8.19704i		−	0.342138i
$575$	−18.9589	+	19.9157i	−0.790639	+	0.830544i
$576$	2.91612			0.121505
$577$		−	24.2872i		−	1.01109i	−0.862800	−	0.505545i	$-0.831291\pi$
$577$		−	24.2872i		−	1.01109i	0.862800	−	0.505545i	$-0.168709\pi$
$578$	−16.7727			−0.697651
$579$	7.06318			0.293536
$580$	6.81663	−	9.92641i	0.283045	−	0.412172i
$581$	−1.26501			−0.0524813
$582$	−3.41825			−0.141691
$583$			36.8043i			1.52428i
$584$	−8.56068			−0.354244
$585$	−0.0225358	−	1.83138i	−0.000931739	−	0.0757181i
$586$			15.7998i			0.652684i
$587$	5.49283	−	5.49283i	0.226714	−	0.226714i	−0.584605	−	0.811318i	$-0.698750\pi$
$587$	5.49283	−	5.49283i	0.226714	−	0.226714i	0.811318	+	0.584605i	$0.198750\pi$
$588$	−1.79559			−0.0740490
$589$	20.2812			0.835674
$590$	−15.8328	−	15.4479i	−0.651827	−	0.635980i
$591$	0.715956	+	0.715956i	0.0294505	+	0.0294505i
$592$		−	6.58530i		−	0.270654i
$593$	−28.1924	+	28.1924i	−1.15772	+	1.15772i	−0.172761	+	0.984964i	$0.555269\pi$
$593$	−28.1924	+	28.1924i	−1.15772	+	1.15772i	−0.984964	+	0.172761i	$0.944731\pi$
$594$	−5.57500	+	5.57500i	−0.228745	+	0.228745i
$595$	0.0117345	+	0.953609i	0.000481068	+	0.0390941i
$596$	−2.94004			−0.120429
$597$	3.28361			0.134389
$598$	1.54466			0.0631658
$599$	20.0950	−	20.0950i	0.821059	−	0.821059i	−0.165201	−	0.986260i	$-0.552827\pi$
$599$	20.0950	−	20.0950i	0.821059	−	0.821059i	0.986260	+	0.165201i	$0.0528271\pi$
$600$	1.44765	−	0.0356331i	0.0591000	−	0.00145472i
$601$	−2.21091	−	2.21091i	−0.0901848	−	0.0901848i	0.660575	−	0.750760i	$-0.270313\pi$
$601$	−2.21091	−	2.21091i	−0.0901848	−	0.0901848i	−0.750760	+	0.660575i	$0.770313\pi$
$602$	−5.42256	−	5.42256i	−0.221007	−	0.221007i
$603$	−22.9115	−	22.9115i	−0.933030	−	0.933030i
$604$			10.8414i			0.441131i
$605$	−16.2826	−	15.8868i	−0.661982	−	0.645889i
$606$	0.175241	−	0.175241i	0.00711868	−	0.00711868i
$607$		−	37.1113i		−	1.50630i	−0.657849	−	0.753150i	$-0.728533\pi$
$607$		−	37.1113i		−	1.50630i	0.657849	−	0.753150i	$-0.271467\pi$
$608$	−1.79299	+	1.79299i	−0.0727155	+	0.0727155i
$609$	−1.14023	−	0.803837i	−0.0462043	−	0.0325731i
$610$	−12.2960	+	0.151307i	−0.497851	+	0.00612624i
$611$	−0.270409	−	0.270409i	−0.0109396	−	0.0109396i
$612$	1.39042			0.0562044
$613$	20.5386	−	20.5386i	0.829547	−	0.829547i	−0.157907	−	0.987454i	$-0.550475\pi$
$613$	20.5386	−	20.5386i	0.829547	−	0.829547i	0.987454	+	0.157907i	$0.0504745\pi$
$614$	−15.9584			−0.644028
$615$	−5.93411	+	0.0730214i	−0.239287	+	0.00294451i
$616$	4.11600			0.165838
$617$		−	1.48087i		−	0.0596176i	−0.999556	−	0.0298088i	$-0.990510\pi$
$617$		−	1.48087i		−	0.0596176i	0.999556	−	0.0298088i	$-0.00948984\pi$
$618$	3.17634	−	3.17634i	0.127771	−	0.127771i
$619$	31.9416	+	31.9416i	1.28384	+	1.28384i	0.938463	+	0.345380i	$0.112250\pi$
$619$	31.9416	+	31.9416i	1.28384	+	1.28384i	0.345380	+	0.938463i	$0.387750\pi$
$620$	17.8835	−	0.220063i	0.718219	−	0.00883795i
$621$	6.66284	−	6.66284i	0.267371	−	0.267371i
$622$	−5.09331	−	5.09331i	−0.204223	−	0.204223i
$623$			7.44809i			0.298402i
$624$	−0.0575215	−	0.0575215i	−0.00230270	−	0.00230270i
$625$	−24.9697	+	1.22998i	−0.998789	+	0.0491991i
$626$	−9.62217	−	9.62217i	−0.384579	−	0.384579i
$627$		−	3.37922i		−	0.134953i
$628$			7.88212i			0.314531i
$629$		−	3.13990i		−	0.125196i
$630$	0.0717679	+	5.83224i	0.00285930	+	0.232362i
$631$		−	32.1454i		−	1.27969i	−0.768505	−	0.639844i	$-0.778999\pi$
$631$		−	32.1454i		−	1.27969i	0.768505	−	0.639844i	$-0.221001\pi$
$632$	0.0428537	−	0.0428537i	0.00170463	−	0.00170463i
$633$	−3.44211	−	3.44211i	−0.136812	−	0.136812i
$634$			22.6925i			0.901235i
$635$	3.41849	−	3.50367i	0.135659	−	0.139039i
$636$	−1.63799	+	1.63799i	−0.0649505	+	0.0649505i
$637$	−1.23137	−	1.23137i	−0.0487886	−	0.0487886i
$638$	−20.2529	−	14.2778i	−0.801818	−	0.565265i
$639$		−	25.1821i		−	0.996188i
$640$	−1.56156	+	1.60047i	−0.0617262	+	0.0632643i
$641$	−30.2409	−	30.2409i	−1.19444	−	1.19444i	−0.975806	−	0.218636i	$-0.929839\pi$
$641$	−30.2409	−	30.2409i	−1.19444	−	1.19444i	−0.218636	−	0.975806i	$-0.570161\pi$
$642$	0.195392	+	0.195392i	0.00771152	+	0.00771152i
$643$	−7.79835	+	7.79835i	−0.307537	+	0.307537i	−0.843953	−	0.536417i	$-0.819778\pi$
$643$	−7.79835	+	7.79835i	−0.307537	+	0.307537i	0.536417	+	0.843953i	$0.319778\pi$
$644$	−4.91915			−0.193842
$645$	−3.87727	+	3.97389i	−0.152668	+	0.156472i
$646$	−0.854907	+	0.854907i	−0.0336359	+	0.0336359i
$647$	−16.6166	−	16.6166i	−0.653268	−	0.653268i	0.300511	−	0.953778i	$-0.402843\pi$
$647$	−16.6166	−	16.6166i	−0.653268	−	0.653268i	−0.953778	+	0.300511i	$0.902843\pi$
$648$	8.25213			0.324174
$649$	−32.1879	+	32.1879i	−1.26348	+	1.26348i
$650$	1.01719	+	0.968322i	0.0398977	+	0.0379807i
$651$		−	2.07207i		−	0.0812107i
$652$	−22.3121			−0.873811
$653$	−45.8616			−1.79470			−0.897352	−	0.441317i	$-0.854512\pi$
$653$	−45.8616			−1.79470			−0.897352	+	0.441317i	$0.854512\pi$
$654$			3.02202i			0.118170i
$655$	−0.166715	−	13.5482i	−0.00651410	−	0.529370i
$656$	6.47983	−	6.47983i	0.252995	−	0.252995i
$657$	−24.9640			−0.973938
$658$	0.861152	+	0.861152i	0.0335712	+	0.0335712i
$659$	−8.87020	+	8.87020i	−0.345534	+	0.345534i	−0.858443	−	0.512909i	$-0.828568\pi$
$659$	−8.87020	+	8.87020i	−0.345534	+	0.345534i	0.512909	+	0.858443i	$0.328568\pi$
$660$	−0.0366665	−	2.97971i	−0.00142724	−	0.115985i
$661$	25.4205			0.988743			0.494371	−	0.869251i	$-0.335398\pi$
$661$	25.4205			0.988743			0.494371	+	0.869251i	$0.335398\pi$
$662$	3.40255	−	3.40255i	0.132244	−	0.132244i
$663$	−0.0274265	−	0.0274265i	−0.00106516	−	0.00106516i
$664$	−1.00000	−	1.00000i	−0.0388075	−	0.0388075i
$665$	−3.63011	−	3.54186i	−0.140770	−	0.137347i
$666$		−	19.2035i		−	0.744121i
$667$	24.2048	+	17.0639i	0.937213	+	0.660715i
$668$	−7.60605	−	7.60605i	−0.294287	−	0.294287i
$669$	−2.97410	+	2.97410i	−0.114985	+	0.114985i
$670$	24.8437	−	0.305710i	0.959795	−	0.0118106i
$671$			25.3052i			0.976897i
$672$	0.183184	+	0.183184i	0.00706648	+	0.00706648i
$673$	28.6125	−	28.6125i	1.10293	−	1.10293i	0.108874	−	0.994056i	$-0.465275\pi$
$673$	28.6125	−	28.6125i	1.10293	−	1.10293i	0.994056	−	0.108874i	$-0.0347246\pi$
$674$			20.6557i			0.795626i
$675$	8.56447	−	0.210810i	0.329647	−	0.00811407i
$676$			12.9211i			0.496966i
$677$		−	1.01813i		−	0.0391300i	−0.999809	−	0.0195650i	$-0.993772\pi$
$677$		−	1.01813i		−	0.0391300i	0.999809	−	0.0195650i	$-0.00622813\pi$
$678$			0.902538i			0.0346618i
$679$	7.46521	+	7.46521i	0.286489	+	0.286489i
$680$	−0.744561	+	0.763113i	−0.0285526	+	0.0292640i
$681$	−3.31107	−	3.31107i	−0.126881	−	0.126881i
$682$		−	36.8043i		−	1.40931i
$683$	−13.6805	−	13.6805i	−0.523470	−	0.523470i	0.395147	−	0.918618i	$-0.370694\pi$
$683$	−13.6805	−	13.6805i	−0.523470	−	0.523470i	−0.918618	+	0.395147i	$0.870694\pi$
$684$	−5.22859	+	5.22859i	−0.199920	+	0.199920i
$685$	−22.0587	+	22.6084i	−0.842820	+	0.863821i
$686$	8.34897	+	8.34897i	0.318765	+	0.318765i
$687$	3.21829	−	3.21829i	0.122786	−	0.122786i
$688$		−	8.57318i		−	0.326849i
$689$	−2.24657			−0.0855877
$690$	0.0438212	+	3.56114i	0.00166824	+	0.135570i
$691$	39.6924			1.50997			0.754985	−	0.655742i	$-0.227644\pi$
$691$	39.6924			1.50997			0.754985	+	0.655742i	$0.227644\pi$
$692$	2.00873	−	2.00873i	0.0763606	−	0.0763606i
$693$	12.0028			0.455947
$694$	23.4372	+	23.4372i	0.889665	+	0.889665i
$695$	4.03720	+	3.93905i	0.153140	+	0.149417i
$696$	−0.265920	−	1.53680i	−0.0100797	−	0.0582523i
$697$	3.08961	−	3.08961i	0.117027	−	0.117027i
$698$			25.2886i			0.957188i
$699$	−4.22309	+	4.22309i	−0.159732	+	0.159732i
$700$	−3.23938	−	3.08374i	−0.122437	−	0.116554i
$701$		−	22.9970i		−	0.868586i	−0.900772	−	0.434293i	$-0.856998\pi$
$701$		−	22.9970i		−	0.868586i	0.900772	−	0.434293i	$-0.143002\pi$
$702$	−0.340304	−	0.340304i	−0.0128439	−	0.0128439i
$703$	11.8074	+	11.8074i	0.445324	+	0.445324i
$704$	3.25374	+	3.25374i	0.122630	+	0.122630i
$705$	0.615746	−	0.631089i	0.0231903	−	0.0237682i
$706$	−6.88469	+	6.88469i	−0.259109	+	0.259109i
$707$	−0.765427			−0.0287868
$708$	−2.86506			−0.107676
$709$	33.5904			1.26151			0.630756	−	0.775981i	$-0.282745\pi$
$709$	33.5904			1.26151			0.630756	+	0.775981i	$0.282745\pi$
$710$	13.8209	+	13.4848i	0.518687	+	0.506077i
$711$	0.124967	−	0.124967i	0.00468662	−	0.00468662i
$712$	−5.88779	+	5.88779i	−0.220654	+	0.220654i
$713$			43.9859i			1.64728i
$714$	0.0873430	+	0.0873430i	0.00326873	+	0.00326873i
$715$	2.01826	−	2.06855i	0.0754787	−	0.0773594i
$716$	23.6028			0.882077
$717$	0.347796			0.0129887
$718$	−22.2072	+	22.2072i	−0.828765	+	0.828765i
$719$			5.51139i			0.205540i	0.994705	+	0.102770i	$0.0327706\pi$
$719$			5.51139i			0.205540i	−0.994705	+	0.102770i	$0.967229\pi$
$720$	−4.55371	+	4.66718i	−0.169707	+	0.173935i
$721$	−13.8738			−0.516687
$722$			12.5703i			0.467820i
$723$	6.55127			0.243645
$724$	20.7780			0.772210
$725$	5.24236	+	26.4106i	0.194696	+	0.980864i
$726$	−2.94646			−0.109353
$727$	5.28028			0.195835			0.0979173	−	0.995195i	$-0.468782\pi$
$727$	5.28028			0.195835			0.0979173	+	0.995195i	$0.468782\pi$
$728$			0.251245i			0.00931177i
$729$	22.5755			0.836130
$730$	13.3681	−	13.7012i	0.494774	−	0.507102i
$731$		−	4.08773i		−	0.151190i
$732$	−1.12622	+	1.12622i	−0.0416262	+	0.0416262i
$733$	24.3366			0.898892			0.449446	−	0.893308i	$-0.351621\pi$
$733$	24.3366			0.898892			0.449446	+	0.893308i	$0.351621\pi$
$734$	1.97873			0.0730363
$735$	2.80393	−	2.87380i	0.103425	−	0.106002i
$736$	−3.88864	−	3.88864i	−0.143337	−	0.143337i
$737$		−	51.1283i		−	1.88333i
$738$	18.8960	−	18.8960i	0.695571	−	0.695571i
$739$	−24.1899	+	24.1899i	−0.889839	+	0.889839i	−0.994507	−	0.104669i	$-0.966622\pi$
$739$	−24.1899	+	24.1899i	−0.889839	+	0.889839i	0.104669	+	0.994507i	$0.466622\pi$
$740$	10.5396	+	10.2834i	0.387443	+	0.378024i
$741$	0.206271			0.00757756
$742$	7.15449			0.262650
$743$	−53.3731			−1.95807			−0.979035	−	0.203694i	$-0.934705\pi$
$743$	−53.3731			−1.95807			−0.979035	+	0.203694i	$0.934705\pi$
$744$	1.63799	−	1.63799i	0.0600516	−	0.0600516i
$745$	4.59106	−	4.70546i	0.168204	−	0.172395i
$746$	19.0279	+	19.0279i	0.696659	+	0.696659i
$747$	−2.91612	−	2.91612i	−0.106695	−	0.106695i
$748$	1.55140	+	1.55140i	0.0567247	+	0.0567247i
$749$		−	0.853445i		−	0.0311842i
$750$	−2.20357	+	2.37257i	−0.0804629	+	0.0866340i
$751$	−34.6175	+	34.6175i	−1.26321	+	1.26321i	−0.313682	+	0.949528i	$0.601563\pi$
$751$	−34.6175	+	34.6175i	−1.26321	+	1.26321i	−0.949528	+	0.313682i	$0.898437\pi$
$752$			1.36150i			0.0496487i
$753$	1.23569	−	1.23569i	0.0450309	−	0.0450309i
$754$	0.871535	−	1.23626i	0.0317394	−	0.0450218i
$755$	−17.3514	−	16.9296i	−0.631482	−	0.616130i
$756$	1.08374	+	1.08374i	0.0394152	+	0.0394152i
$757$	33.8919			1.23182			0.615911	−	0.787815i	$-0.288788\pi$
$757$	33.8919			1.23182			0.615911	+	0.787815i	$0.288788\pi$
$758$	10.8552	−	10.8552i	0.394279	−	0.394279i
$759$	7.32883			0.266020
$760$	−0.0697654	−	5.66951i	−0.00253066	−	0.205655i
$761$	51.3033			1.85974			0.929871	−	0.367886i	$-0.119918\pi$
$761$	51.3033			1.85974			0.929871	+	0.367886i	$0.119918\pi$
$762$		−	0.634016i		−	0.0229680i
$763$	6.59987	−	6.59987i	0.238931	−	0.238931i
$764$	6.90356	+	6.90356i	0.249762	+	0.249762i
$765$	−2.17123	+	2.22533i	−0.0785010	+	0.0804570i
$766$	−22.6747	+	22.6747i	−0.819269	+	0.819269i
$767$	−1.96478	−	1.96478i	−0.0709442	−	0.0709442i
$768$			0.289618i			0.0104507i
$769$	−13.2848	−	13.2848i	−0.479063	−	0.479063i	0.425769	−	0.904832i	$-0.360004\pi$
$769$	−13.2848	−	13.2848i	−0.479063	−	0.479063i	−0.904832	+	0.425769i	$0.860004\pi$
$770$	−6.42740	+	6.58755i	−0.231627	+	0.237399i
$771$	0.258409	+	0.258409i	0.00930636	+	0.00930636i
$772$		−	24.3879i		−	0.877741i
$773$			23.8909i			0.859294i	0.902997	+	0.429647i	$0.141362\pi$
$773$			23.8909i			0.859294i	−0.902997	+	0.429647i	$0.858638\pi$
$774$		−	25.0004i		−	0.898622i
$775$	−27.5741	+	28.9658i	−0.990489	+	1.04048i
$776$			11.8026i			0.423690i
$777$	1.20632	−	1.20632i	0.0432765	−	0.0432765i
$778$	−8.76850	−	8.76850i	−0.314366	−	0.314366i
$779$			23.2366i			0.832538i
$780$	0.181885	−	0.00223816i	0.00651253	−	8.01391e-5i
$781$	28.0976	−	28.0976i	1.00541	−	1.00541i
$782$	−1.85412	−	1.85412i	−0.0663032	−	0.0663032i
$783$	−1.57322	−	9.09190i	−0.0562222	−	0.324918i
$784$			6.19988i			0.221424i
$785$	−12.6151	−	12.3084i	−0.450253	−	0.439307i
$786$	−1.24090	−	1.24090i	−0.0442616	−	0.0442616i
$787$	−18.3968	−	18.3968i	−0.655776	−	0.655776i	0.298602	−	0.954378i	$-0.403480\pi$
$787$	−18.3968	−	18.3968i	−0.655776	−	0.655776i	−0.954378	+	0.298602i	$0.903480\pi$
$788$	2.47207	−	2.47207i	0.0880640	−	0.0880640i
$789$	−5.88496			−0.209510
$790$	0.00166744	+	0.135505i	5.93249e−5	+	0.00482106i
$791$	1.97108	−	1.97108i	0.0700834	−	0.0700834i
$792$	9.48830	+	9.48830i	0.337152	+	0.337152i
$793$	−1.54466			−0.0548524
$794$	−18.3875	+	18.3875i	−0.652547	+	0.652547i
$795$	−0.0637342	−	5.17938i	−0.00226042	−	0.183694i
$796$		−	11.3378i		−	0.401856i
$797$	16.2394			0.575228			0.287614	−	0.957746i	$-0.407138\pi$
$797$	16.2394			0.575228			0.287614	+	0.957746i	$0.407138\pi$
$798$	−0.656896			−0.0232539
$799$			0.649168i			0.0229659i
$800$	−0.123035	−	4.99849i	−0.00434994	−	0.176723i
$801$	−17.1695	+	17.1695i	−0.606655	+	0.606655i
$802$	5.87124			0.207321
$803$	−27.8542	−	27.8542i	−0.982954	−	0.982954i
$804$	2.27548	−	2.27548i	0.0802501	−	0.0802501i
$805$	7.68157	−	7.87298i	0.270740	−	0.277486i
$806$	2.24657			0.0791322
$807$	5.86329	−	5.86329i	0.206397	−	0.206397i
$808$	−0.605077	−	0.605077i	−0.0212865	−	0.0212865i
$809$	−3.52028	−	3.52028i	−0.123766	−	0.123766i	0.642510	−	0.766277i	$-0.277893\pi$
$809$	−3.52028	−	3.52028i	−0.123766	−	0.123766i	−0.766277	+	0.642510i	$0.777893\pi$
$810$	−12.8862	+	13.2073i	−0.452776	+	0.464058i
$811$			2.40718i			0.0845277i	0.999106	+	0.0422638i	$0.0134570\pi$
$811$			2.40718i			0.0845277i	−0.999106	+	0.0422638i	$0.986543\pi$
$812$	−2.77551	+	3.93701i	−0.0974013	+	0.138162i
$813$	−1.04585	−	1.04585i	−0.0366795	−	0.0366795i
$814$	21.4268	−	21.4268i	0.751010	−	0.751010i
$815$	34.8418	−	35.7100i	1.22046	−	1.25087i
$816$			0.138091i			0.00483415i
$817$	15.3716	+	15.3716i	0.537786	+	0.537786i
$818$	11.7879	−	11.7879i	0.412156	−	0.412156i
$819$			0.732662i			0.0256013i
$820$	0.252131	+	20.4895i	0.00880478	+	0.715524i
$821$			36.8938i			1.28760i	0.765193	+	0.643801i	$0.222643\pi$
$821$			36.8938i			1.28760i	−0.765193	+	0.643801i	$0.777357\pi$
$822$			4.09115i			0.142695i
$823$			21.2449i			0.740550i	0.928922	+	0.370275i	$0.120736\pi$
$823$			21.2449i			0.740550i	−0.928922	+	0.370275i	$0.879264\pi$
$824$	−10.9674	−	10.9674i	−0.382066	−	0.382066i
$825$	4.82621	+	4.59433i	0.168027	+	0.159954i
$826$	6.25709	+	6.25709i	0.217712	+	0.217712i
$827$			17.7303i			0.616542i	0.951299	+	0.308271i	$0.0997504\pi$
$827$			17.7303i			0.616542i	−0.951299	+	0.308271i	$0.900250\pi$
$828$	−11.3397	−	11.3397i	−0.394083	−	0.394083i
$829$	16.5417	−	16.5417i	0.574516	−	0.574516i	−0.358871	−	0.933387i	$-0.616838\pi$
$829$	16.5417	−	16.5417i	0.574516	−	0.574516i	0.933387	+	0.358871i	$0.116838\pi$
$830$	3.16204	−	0.0389100i	0.109756	−	0.00135059i
$831$	0.335567	+	0.335567i	0.0116407	+	0.0116407i
$832$	−0.198612	+	0.198612i	−0.00688563	+	0.00688563i
$833$			2.95613i			0.102424i
$834$	0.730562			0.0252973
$835$	24.0506	−	0.295952i	0.832306	−	0.0102418i
$836$	−11.6679			−0.403541
$837$	9.69054	−	9.69054i	0.334954	−	0.334954i
$838$	18.7077			0.646245
$839$	−14.1762	−	14.1762i	−0.489416	−	0.489416i	0.418706	−	0.908122i	$-0.362484\pi$
$839$	−14.1762	−	14.1762i	−0.489416	−	0.489416i	−0.908122	+	0.418706i	$0.862484\pi$
$840$	−0.579235	+	0.00712770i	−0.0199855	+	0.000245929i
$841$	27.3139	−	9.74427i	0.941859	−	0.336009i
$842$	−4.16276	+	4.16276i	−0.143458	+	0.143458i
$843$		−	2.57434i		−	0.0886649i
$844$	−11.8850	+	11.8850i	−0.409100	+	0.409100i
$845$	−20.6799	−	20.1771i	−0.711410	−	0.694115i
$846$			3.97029i			0.136501i
$847$	6.43485	+	6.43485i	0.221104	+	0.221104i
$848$	5.65569	+	5.65569i	0.194217	+	0.194217i
$849$	6.64355	+	6.64355i	0.228006	+	0.228006i
$850$	−0.0586636	−	2.38330i	−0.00201215	−	0.0817465i
$851$	−25.6078	+	25.6078i	−0.877825	+	0.877825i
$852$	2.50099			0.0856823
$853$	−29.1166			−0.996932			−0.498466	−	0.866909i	$-0.666103\pi$
$853$	−29.1166			−0.996932			−0.498466	+	0.866909i	$0.666103\pi$
$854$	4.91915			0.168330
$855$	−0.203445	−	16.5330i	−0.00695766	−	0.565416i
$856$	0.674656	−	0.674656i	0.0230593	−	0.0230593i
$857$	7.30296	−	7.30296i	0.249464	−	0.249464i	−0.571286	−	0.820751i	$-0.693555\pi$
$857$	7.30296	−	7.30296i	0.249464	−	0.249464i	0.820751	+	0.571286i	$0.193555\pi$
$858$		−	0.374320i		−	0.0127791i
$859$	−13.3341	−	13.3341i	−0.454953	−	0.454953i	0.442042	−	0.896995i	$-0.354254\pi$
$859$	−13.3341	−	13.3341i	−0.454953	−	0.454953i	−0.896995	+	0.442042i	$0.854254\pi$
$860$	13.7211	+	13.3876i	0.467887	+	0.456512i
$861$	2.37401			0.0809059
$862$	0.757725			0.0258082
$863$	9.11507	−	9.11507i	0.310280	−	0.310280i	−0.534738	−	0.845018i	$-0.679590\pi$
$863$	9.11507	−	9.11507i	0.310280	−	0.310280i	0.845018	+	0.534738i	$0.179590\pi$
$864$			1.71341i			0.0582915i
$865$	0.0781599	+	6.35170i	0.00265752	+	0.215964i
$866$	10.8919			0.370122
$867$		−	4.85766i		−	0.164975i
$868$	−7.15449			−0.242839
$869$	0.278870			0.00946001
$870$	2.87486	+	1.97422i	0.0974670	+	0.0669322i
$871$	3.12093			0.105749
$872$	10.4345			0.353357
$873$			34.4179i			1.16487i
$874$	13.9446			0.471683
$875$	9.99394	−	0.369086i	0.337857	−	0.0124774i
$876$		−	2.47932i		−	0.0837686i
$877$	−36.2899	+	36.2899i	−1.22542	+	1.22542i	−0.259747	+	0.965677i	$0.583639\pi$
$877$	−36.2899	+	36.2899i	−1.22542	+	1.22542i	−0.965677	+	0.259747i	$0.916361\pi$
$878$	16.0340			0.541122
$879$	−4.57590			−0.154341
$880$	−10.2884	+	0.126603i	−0.346823	+	0.00426779i
$881$	−31.7249	−	31.7249i	−1.06884	−	1.06884i	−0.997448	−	0.0713908i	$-0.977256\pi$
$881$	−31.7249	−	31.7249i	−1.06884	−	1.06884i	−0.0713908	−	0.997448i	$-0.522744\pi$
$882$			18.0796i			0.608772i
$883$	−5.18708	+	5.18708i	−0.174559	+	0.174559i	−0.788979	−	0.614420i	$-0.789390\pi$
$883$	−5.18708	+	5.18708i	−0.174559	+	0.174559i	0.614420	+	0.788979i	$0.289390\pi$
$884$	−0.0946990	+	0.0946990i	−0.00318507	+	0.00318507i
$885$	4.47398	−	4.58546i	0.150391	−	0.154139i
$886$	−21.8127			−0.732812
$887$	45.5203			1.52842			0.764211	−	0.644967i	$-0.223129\pi$
$887$	45.5203			1.52842			0.764211	+	0.644967i	$0.223129\pi$
$888$	1.90722			0.0640020
$889$	−1.38464	+	1.38464i	−0.0464394	+	0.0464394i
$890$	−0.229094	−	18.6174i	−0.00767925	−	0.624057i
$891$	26.8503	+	26.8503i	0.899518	+	0.899518i
$892$	10.2691	+	10.2691i	0.343834	+	0.343834i
$893$	−2.44116	−	2.44116i	−0.0816902	−	0.0816902i
$894$		−	0.851488i		−	0.0284780i
$895$	−36.8572	+	37.7756i	−1.23200	+	1.26270i
$896$	0.632503	−	0.632503i	0.0211305	−	0.0211305i
$897$			0.447360i			0.0149369i
$898$	11.8820	−	11.8820i	0.396509	−	0.396509i
$899$	35.2038	+	24.8179i	1.17411	+	0.827725i
$900$	−0.358785	−	14.5762i	−0.0119595	−	0.485873i
$901$	2.69666	+	2.69666i	0.0898387	+	0.0898387i
$902$	42.1674			1.40402
$903$	1.57047	−	1.57047i	0.0522620	−	0.0522620i
$904$	3.11631			0.103647
$905$	−32.4462	+	33.2547i	−1.07855	+	1.10542i
$906$	−3.13986			−0.104315
$907$		−	52.1407i		−	1.73130i	−0.500646	−	0.865652i	$-0.666904\pi$
$907$		−	52.1407i		−	1.73130i	0.500646	−	0.865652i	$-0.333096\pi$
$908$	−11.4326	+	11.4326i	−0.379403	+	0.379403i
$909$	−1.76448	−	1.76448i	−0.0585241	−	0.0585241i
$910$	−0.402112	−	0.392336i	−0.0133299	−	0.0130058i
$911$	22.5889	−	22.5889i	0.748403	−	0.748403i	−0.225776	−	0.974179i	$-0.572492\pi$
$911$	22.5889	−	22.5889i	0.748403	−	0.748403i	0.974179	+	0.225776i	$0.0724918\pi$
$912$	−0.519282	−	0.519282i	−0.0171952	−	0.0171952i
$913$		−	6.50748i		−	0.215366i
$914$	25.4126	+	25.4126i	0.840575	+	0.840575i
$915$	−0.0438212	−	3.56114i	−0.00144868	−	0.117728i
$916$	−11.1122	−	11.1122i	−0.367158	−	0.367158i
$917$			5.42008i			0.178987i
$918$			0.816963i			0.0269638i
$919$		−	1.29013i		−	0.0425574i	−0.999774	−	0.0212787i	$-0.993226\pi$
$919$		−	1.29013i		−	0.0425574i	0.999774	−	0.0212787i	$-0.00677373\pi$
$920$	12.2960	−	0.151307i	0.405388	−	0.00498844i
$921$		−	4.62183i		−	0.152295i
$922$	−26.1001	+	26.1001i	−0.859562	+	0.859562i
$923$	1.71511	+	1.71511i	0.0564534	+	0.0564534i
$924$			1.19207i			0.0392161i
$925$	−32.9165	+	0.810222i	−1.08229	+	0.0266399i
$926$	3.00076	−	3.00076i	0.0986111	−	0.0986111i
$927$	−31.9822	−	31.9822i	−1.05043	−	1.05043i
$928$	−5.30631	+	0.918177i	−0.174188	+	0.0301406i
$929$			29.6911i			0.974134i	0.873365	+	0.487067i	$0.161933\pi$
$929$			29.6911i			0.974134i	−0.873365	+	0.487067i	$0.838067\pi$
$930$	0.0637342	+	5.17938i	0.00208993	+	0.169839i
$931$	−11.1163	−	11.1163i	−0.364323	−	0.364323i
$932$	14.5816	+	14.5816i	0.477636	+	0.477636i
$933$	1.47511	−	1.47511i	0.0482930	−	0.0482930i
$934$	4.86798			0.159285
$935$	−4.90557	+	0.0603649i	−0.160429	+	0.00197414i
$936$	−0.579176	+	0.579176i	−0.0189310	+	0.0189310i
$937$	30.6659	+	30.6659i	1.00181	+	1.00181i	0.999998	+	0.00181196i	$0.000576765\pi$
$937$	30.6659	+	30.6659i	1.00181	+	1.00181i	0.00181196	+	0.999998i	$0.499423\pi$
$938$	−9.93897			−0.324519
$939$	2.78675	−	2.78675i	0.0909421	−	0.0909421i
$940$	−2.17904	−	2.12607i	−0.0710725	−	0.0693446i
$941$		−	32.2353i		−	1.05084i	−0.850842	−	0.525421i	$-0.823908\pi$
$941$		−	32.2353i		−	1.05084i	0.850842	−	0.525421i	$-0.176092\pi$
$942$	−2.28280			−0.0743776
$943$	−50.3954			−1.64110
$944$			9.89258i			0.321976i
$945$	−3.42683	+	0.0421683i	−0.111475	+	0.00137174i
$946$	27.8949	−	27.8949i	0.906940	−	0.906940i
$947$	−32.5015			−1.05616			−0.528079	−	0.849195i	$-0.677087\pi$
$947$	−32.5015			−1.05616			−0.528079	+	0.849195i	$0.677087\pi$
$948$	0.0124112	+	0.0124112i	0.000403097	+	0.000403097i
$949$	1.70025	−	1.70025i	0.0551925	−	0.0551925i
$950$	9.18285	+	8.74165i	0.297931	+	0.283617i
$951$	−6.57215			−0.213117
$952$	0.301580	−	0.301580i	0.00977428	−	0.00977428i
$953$	−23.0094	−	23.0094i	−0.745348	−	0.745348i	0.228254	−	0.973602i	$-0.426698\pi$
$953$	−23.0094	−	23.0094i	−0.745348	−	0.745348i	−0.973602	+	0.228254i	$0.926698\pi$
$954$	16.4927	+	16.4927i	0.533971	+	0.533971i
$955$	−21.8293	+	0.268618i	−0.706380	+	0.00869226i
$956$		−	1.20088i		−	0.0388392i
$957$	4.13511	−	5.86558i	0.133669	−	0.189607i
$958$	4.92833	+	4.92833i	0.159227	+	0.159227i
$959$	8.93477	−	8.93477i	0.288519	−	0.288519i
$960$	−0.463525	−	0.452256i	−0.0149602	−	0.0145965i
$961$			32.9737i			1.06367i
$962$	1.30792	+	1.30792i	0.0421689	+	0.0421689i
$963$	1.96738	−	1.96738i	0.0633979	−	0.0633979i
$964$		−	22.6204i		−	0.728555i
$965$	39.0323	+	38.0833i	1.25649	+	1.22595i
$966$		−	1.42467i		−	0.0458381i
$967$			0.317494i			0.0102099i	0.999987	+	0.00510495i	$0.00162496\pi$
$967$			0.317494i			0.0102099i	−0.999987	+	0.00510495i	$0.998375\pi$
$968$			10.1736i			0.326993i
$969$	−0.247596	−	0.247596i	−0.00795393	−	0.00795393i
$970$	−18.8898	−	18.4306i	−0.606516	−	0.591770i
$971$	−23.8271	−	23.8271i	−0.764647	−	0.764647i	0.212512	−	0.977159i	$-0.431836\pi$
$971$	−23.8271	−	23.8271i	−0.764647	−	0.764647i	−0.977159	+	0.212512i	$0.931836\pi$
$972$			7.53020i			0.241531i
$973$	−1.59549	−	1.59549i	−0.0511491	−	0.0511491i
$974$	2.73756	−	2.73756i	0.0877169	−	0.0877169i
$975$	−0.280443	+	0.294597i	−0.00898137	+	0.00943467i
$976$	3.88864	+	3.88864i	0.124472	+	0.124472i
$977$	24.5169	−	24.5169i	0.784365	−	0.784365i	−0.196199	−	0.980564i	$-0.562860\pi$
$977$	24.5169	−	24.5169i	0.784365	−	0.784365i	0.980564	+	0.196199i	$0.0628598\pi$
$978$		−	6.46199i		−	0.206632i
$979$	−38.3146			−1.22454
$980$	−9.92275	−	9.68151i	−0.316970	−	0.309264i
$981$	30.4283			0.971501
$982$	−16.0568	+	16.0568i	−0.512392	+	0.512392i
$983$	59.6952			1.90398			0.951991	−	0.306126i	$-0.0990330\pi$
$983$	59.6952			1.90398			0.951991	+	0.306126i	$0.0990330\pi$
$984$	1.87667	+	1.87667i	0.0598262	+	0.0598262i
$985$	0.0961885	+	7.81679i	0.00306482	+	0.249064i
$986$	−2.53007	+	0.437791i	−0.0805739	+	0.0139421i
$987$	−0.249405	+	0.249405i	−0.00793864	+	0.00793864i
$988$		−	0.712219i		−	0.0226587i
$989$	−33.3380	+	33.3380i	−1.06009	+	1.06009i
$990$	−30.0024	+	0.369190i	−0.953537	+	0.0117336i
$991$			5.66996i			0.180112i	0.995937	+	0.0900561i	$0.0287046\pi$
$991$			5.66996i			0.180112i	−0.995937	+	0.0900561i	$0.971295\pi$
$992$	−5.65569	−	5.65569i	−0.179568	−	0.179568i
$993$	0.985439	+	0.985439i	0.0312720	+	0.0312720i
$994$	−5.46197	−	5.46197i	−0.173243	−	0.173243i
$995$	18.1458	+	17.7046i	0.575260	+	0.561275i
$996$	0.289618	−	0.289618i	0.00917688	−	0.00917688i
$997$	27.2996			0.864586			0.432293	−	0.901733i	$-0.357705\pi$
$997$	27.2996			0.864586			0.432293	+	0.901733i	$0.357705\pi$
$998$	11.0768			0.350631
$999$	11.2833			0.356989

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	290.2.e.f.273.4	yes	12
5.2	odd	4		290.2.j.f.157.4	yes	12
5.3	odd	4		1450.2.j.h.157.3		12
5.4	even	2		1450.2.e.h.1143.3		12
29.17	odd	4		290.2.j.f.133.4	yes	12
145.17	even	4	inner	290.2.e.f.17.3	✓	12
145.104	odd	4		1450.2.j.h.1293.3		12
145.133	even	4		1450.2.e.h.307.4		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
290.2.e.f.17.3	✓	12	145.17	even	4	inner
290.2.e.f.273.4	yes	12	1.1	even	1	trivial
290.2.j.f.133.4	yes	12	29.17	odd	4
290.2.j.f.157.4	yes	12	5.2	odd	4
1450.2.e.h.307.4		12	145.133	even	4
1450.2.e.h.1143.3		12	5.4	even	2
1450.2.j.h.157.3		12	5.3	odd	4
1450.2.j.h.1293.3		12	145.104	odd	4

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 290 = 2 \cdot 5 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	290.e (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +0.289618i q^{3} +1.00000 q^{4} +(-1.56156 + 1.60047i) q^{5} +0.289618i q^{6} +(0.632503 - 0.632503i) q^{7} +1.00000 q^{8} +2.91612 q^{9} +(-1.56156 + 1.60047i) q^{10} +(3.25374 + 3.25374i) q^{11} +0.289618i q^{12} +(-0.198612 + 0.198612i) q^{13} +(0.632503 - 0.632503i) q^{14} +(-0.463525 - 0.452256i) q^{15} +1.00000 q^{16} +0.476804 q^{17} +2.91612 q^{18} +(-1.79299 + 1.79299i) q^{19} +(-1.56156 + 1.60047i) q^{20} +(0.183184 + 0.183184i) q^{21} +(3.25374 + 3.25374i) q^{22} +(-3.88864 - 3.88864i) q^{23} +0.289618i q^{24} +(-0.123035 - 4.99849i) q^{25} +(-0.198612 + 0.198612i) q^{26} +1.71341i q^{27} +(0.632503 - 0.632503i) q^{28} +(-5.30631 + 0.918177i) q^{29} +(-0.463525 - 0.452256i) q^{30} +(-5.65569 - 5.65569i) q^{31} +1.00000 q^{32} +(-0.942340 + 0.942340i) q^{33} +0.476804 q^{34} +(0.0246107 + 2.00000i) q^{35} +2.91612 q^{36} -6.58530i q^{37} +(-1.79299 + 1.79299i) q^{38} +(-0.0575215 - 0.0575215i) q^{39} +(-1.56156 + 1.60047i) q^{40} +(6.47983 - 6.47983i) q^{41} +(0.183184 + 0.183184i) q^{42} -8.57318i q^{43} +(3.25374 + 3.25374i) q^{44} +(-4.55371 + 4.66718i) q^{45} +(-3.88864 - 3.88864i) q^{46} +1.36150i q^{47} +0.289618i q^{48} +6.19988i q^{49} +(-0.123035 - 4.99849i) q^{50} +0.138091i q^{51} +(-0.198612 + 0.198612i) q^{52} +(5.65569 + 5.65569i) q^{53} +1.71341i q^{54} +(-10.2884 + 0.126603i) q^{55} +(0.632503 - 0.632503i) q^{56} +(-0.519282 - 0.519282i) q^{57} +(-5.30631 + 0.918177i) q^{58} +9.89258i q^{59} +(-0.463525 - 0.452256i) q^{60} +(3.88864 + 3.88864i) q^{61} +(-5.65569 - 5.65569i) q^{62} +(1.84446 - 1.84446i) q^{63} +1.00000 q^{64} +(-0.00772799 - 0.628018i) q^{65} +(-0.942340 + 0.942340i) q^{66} +(-7.85685 - 7.85685i) q^{67} +0.476804 q^{68} +(1.12622 - 1.12622i) q^{69} +(0.0246107 + 2.00000i) q^{70} -8.63547i q^{71} +2.91612 q^{72} -8.56068 q^{73} -6.58530i q^{74} +(1.44765 - 0.0356331i) q^{75} +(-1.79299 + 1.79299i) q^{76} +4.11600 q^{77} +(-0.0575215 - 0.0575215i) q^{78} +(0.0428537 - 0.0428537i) q^{79} +(-1.56156 + 1.60047i) q^{80} +8.25213 q^{81} +(6.47983 - 6.47983i) q^{82} +(-1.00000 - 1.00000i) q^{83} +(0.183184 + 0.183184i) q^{84} +(-0.744561 + 0.763113i) q^{85} -8.57318i q^{86} +(-0.265920 - 1.53680i) q^{87} +(3.25374 + 3.25374i) q^{88} +(-5.88779 + 5.88779i) q^{89} +(-4.55371 + 4.66718i) q^{90} +0.251245i q^{91} +(-3.88864 - 3.88864i) q^{92} +(1.63799 - 1.63799i) q^{93} +1.36150i q^{94} +(-0.0697654 - 5.66951i) q^{95} +0.289618i q^{96} +11.8026i q^{97} +6.19988i q^{98} +(9.48830 + 9.48830i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 12 q^{2} + 12 q^{4} - 6 q^{5} - 4 q^{7} + 12 q^{8} - 28 q^{9} - 6 q^{10} + 10 q^{11} - 2 q^{13} - 4 q^{14} - 16 q^{15} + 12 q^{16} - 28 q^{18} + 16 q^{19} - 6 q^{20} - 16 q^{21} + 10 q^{22} + 4 q^{23}+ \cdots - 36 q^{99}+O(q^{100}) \) 12 * q + 12 * q^2 + 12 * q^4 - 6 * q^5 - 4 * q^7 + 12 * q^8 - 28 * q^9 - 6 * q^10 + 10 * q^11 - 2 * q^13 - 4 * q^14 - 16 * q^15 + 12 * q^16 - 28 * q^18 + 16 * q^19 - 6 * q^20 - 16 * q^21 + 10 * q^22 + 4 * q^23 - 10 * q^25 - 2 * q^26 - 4 * q^28 - 20 * q^29 - 16 * q^30 + 18 * q^31 + 12 * q^32 + 6 * q^33 + 20 * q^35 - 28 * q^36 + 16 * q^38 + 38 * q^39 - 6 * q^40 + 36 * q^41 - 16 * q^42 + 10 * q^44 - 12 * q^45 + 4 * q^46 - 10 * q^50 - 2 * q^52 - 18 * q^53 + 18 * q^55 - 4 * q^56 + 32 * q^57 - 20 * q^58 - 16 * q^60 - 4 * q^61 + 18 * q^62 + 24 * q^63 + 12 * q^64 + 22 * q^65 + 6 * q^66 + 12 * q^67 - 12 * q^69 + 20 * q^70 - 28 * q^72 - 4 * q^73 - 32 * q^75 + 16 * q^76 - 72 * q^77 + 38 * q^78 - 30 * q^79 - 6 * q^80 + 44 * q^81 + 36 * q^82 - 12 * q^83 - 16 * q^84 - 58 * q^85 + 4 * q^87 + 10 * q^88 - 20 * q^89 - 12 * q^90 + 4 * q^92 - 2 * q^93 - 26 * q^95 - 36 * q^99

Introduction

L-functions

Modular forms

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