LMFDB - Embedded newform 290.2.j.f.157.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [290,2,Mod(133,290)] 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([3, 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("290.133"); S:= CuspForms(chi, 2); N := Newforms(S);

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

Newform invariants

comment:select newform

sage:traces = [12,0,0,-12,6,0,-4,0,28,4,10] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(11)] == 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			157.4
Root			$1.64632i$ of defining polynomial
Character	$\chi$	$=$	290.157
Dual form			290.2.j.f.133.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

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

Character values

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

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

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 $

$2$			1.00000i			0.707107i
$2$			1.00000i			0.707107i
$3$	0.289618			0.167211			0.0836054	−	0.996499i	$-0.473356\pi$
$3$	0.289618			0.167211			0.0836054	+	0.996499i	$0.473356\pi$
$4$	−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	0.816462	−	0.577399i	$-0.195932\pi$
$7$	0.632503	+	0.632503i	0.239064	+	0.239064i	−0.577399	+	0.816462i	$0.695932\pi$
$8$		−	1.00000i		−	0.353553i
$9$	−2.91612			−0.972041
$10$	−1.60047	+	1.56156i	−0.506114	+	0.493810i
$11$	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	$0.505980\pi$
$12$	−0.289618			−0.0836054
$13$	0.198612	+	0.198612i	0.0550850	+	0.0550850i	0.734113	−	0.679028i	$-0.237598\pi$
$13$	0.198612	+	0.198612i	0.0550850	+	0.0550850i	−0.679028	+	0.734113i	$0.737598\pi$
$14$	−0.632503	+	0.632503i	−0.169044	+	0.169044i
$15$	0.452256	+	0.463525i	0.116772	+	0.119682i
$16$	1.00000			0.250000
$17$			0.476804i			0.115642i	0.998327	+	0.0578210i	$0.0184153\pi$
$17$			0.476804i			0.115642i	−0.998327	+	0.0578210i	$0.981585\pi$
$18$		−	2.91612i		−	0.687336i
$19$	1.79299	−	1.79299i	0.411341	−	0.411341i	−0.470865	−	0.882205i	$-0.656058\pi$
$19$	1.79299	−	1.79299i	0.411341	−	0.411341i	0.882205	+	0.470865i	$0.156058\pi$
$20$	−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	−0.984759	−	0.173923i	$-0.944356\pi$
$23$	−3.88864	+	3.88864i	−0.810837	+	0.810837i	0.173923	+	0.984759i	$0.444356\pi$
$24$		−	0.289618i		−	0.0591179i
$25$	−0.123035	+	4.99849i	−0.0246070	+	0.999697i
$26$	−0.198612	+	0.198612i	−0.0389510	+	0.0389510i
$27$	−1.71341			−0.329746
$28$	−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	$-0.505067\pi$
$32$			1.00000i			0.176777i
$33$	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
$37$	6.58530			1.08262			0.541308	−	0.840824i	$-0.317929\pi$
$37$	6.58530			1.08262			0.541308	+	0.840824i	$0.317929\pi$
$38$	1.79299	+	1.79299i	0.290862	+	0.290862i
$39$	0.0575215	+	0.0575215i	0.00921081	+	0.00921081i
$40$	1.60047	−	1.56156i	0.253057	−	0.246905i
$41$	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
$43$	−8.57318			−1.30740			−0.653699	−	0.756755i	$-0.726784\pi$
$43$	−8.57318			−1.30740			−0.653699	+	0.756755i	$0.726784\pi$
$44$	−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
$47$	−1.36150			−0.198595			−0.0992974	−	0.995058i	$-0.531660\pi$
$47$	−1.36150			−0.198595			−0.0992974	+	0.995058i	$0.531660\pi$
$48$	0.289618			0.0418027
$49$		−	6.19988i		−	0.885697i
$50$	−4.99849	−	0.123035i	−0.706893	−	0.0173998i
$51$			0.138091i			0.0193366i
$52$	−0.198612	−	0.198612i	−0.0275425	−	0.0275425i
$53$	5.65569	−	5.65569i	0.776869	−	0.776869i	−0.202428	−	0.979297i	$-0.564883\pi$
$53$	5.65569	−	5.65569i	0.776869	−	0.776869i	0.979297	+	0.202428i	$0.0648832\pi$
$54$		−	1.71341i		−	0.233166i
$55$	−0.126603	+	10.2884i	−0.0170712	+	1.38729i
$56$	0.632503	−	0.632503i	0.0845218	−	0.0845218i
$57$	0.519282	−	0.519282i	0.0687806	−	0.0687806i
$58$	0.918177	+	5.30631i	0.120563	+	0.696753i
$59$		−	9.89258i		−	1.28790i	−0.765066	−	0.643952i	$-0.777294\pi$
$59$		−	9.89258i		−	1.28790i	0.765066	−	0.643952i	$-0.222706\pi$
$60$	−0.452256	−	0.463525i	−0.0583860	−	0.0598409i
$61$	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	$-0.512531\pi$
$67$	7.85685	−	7.85685i	0.959867	−	0.959867i	0.999225	+	0.0393577i	$0.0125312\pi$
$68$		−	0.476804i		−	0.0578210i
$69$	−1.12622	+	1.12622i	−0.135581	+	0.135581i
$70$	−2.00000	−	0.0246107i	−0.239046	−	0.00294154i
$71$		−	8.63547i		−	1.02484i	−0.858734	−	0.512421i	$-0.828749\pi$
$71$		−	8.63547i		−	1.02484i	0.858734	−	0.512421i	$-0.171251\pi$
$72$			2.91612i			0.343668i
$73$			8.56068i			1.00195i	0.865461	+	0.500976i	$0.167026\pi$
$73$			8.56068i			1.00195i	−0.865461	+	0.500976i	$0.832974\pi$
$74$			6.58530i			0.765525i
$75$	−0.0356331	+	1.44765i	−0.00411456	+	0.167160i
$76$	−1.79299	+	1.79299i	−0.205670	+	0.205670i
$77$			4.11600i			0.469062i
$78$	−0.0575215	+	0.0575215i	−0.00651302	+	0.00651302i
$79$	−0.0428537	+	0.0428537i	−0.00482142	+	0.00482142i	−0.709513	−	0.704692i	$-0.751085\pi$
$79$	−0.0428537	+	0.0428537i	−0.00482142	+	0.00482142i	0.704692	+	0.709513i	$0.251085\pi$
$80$	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	−0.759856	−	0.650092i	$-0.774731\pi$
$83$	−1.00000	+	1.00000i	−0.109764	+	0.109764i	0.650092	+	0.759856i	$0.274731\pi$
$84$	−0.183184	−	0.183184i	−0.0199870	−	0.0199870i
$85$	−0.763113	+	0.744561i	−0.0827712	+	0.0807589i
$86$		−	8.57318i		−	0.924469i
$87$	1.53680	−	0.265920i	0.164762	−	0.0285096i
$88$	3.25374	−	3.25374i	0.346850	−	0.346850i
$89$	5.88779	−	5.88779i	0.624104	−	0.624104i	−0.322474	−	0.946578i	$-0.604514\pi$
$89$	5.88779	−	5.88779i	0.624104	−	0.624104i	0.946578	+	0.322474i	$0.104514\pi$
$90$	4.66718	−	4.55371i	0.491964	−	0.480003i
$91$			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
$95$	5.66951	+	0.0697654i	0.581680	+	0.00715778i
$96$			0.289618i			0.0295590i
$97$	−11.8026			−1.19838			−0.599188	−	0.800608i	$-0.704510\pi$
$97$	−11.8026			−1.19838			−0.599188	+	0.800608i	$0.704510\pi$
$98$	6.19988			0.626282
$99$	−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	$0.763556\pi$
$102$	−0.138091			−0.0136730
$103$	−10.9674	+	10.9674i	−1.08065	+	1.08065i	−0.0841981	+	0.996449i	$0.526833\pi$
$103$	−10.9674	+	10.9674i	−1.08065	+	1.08065i	−0.996449	+	0.0841981i	$0.973167\pi$
$104$	0.198612	−	0.198612i	0.0194755	−	0.0194755i
$105$	−0.00712770	+	0.579235i	−0.000695592	+	0.0565276i
$106$	5.65569	+	5.65569i	0.549330	+	0.549330i
$107$	0.674656	+	0.674656i	0.0652215	+	0.0652215i	0.738965	−	0.673744i	$-0.235315\pi$
$107$	0.674656	+	0.674656i	0.0652215	+	0.0652215i	−0.673744	+	0.738965i	$0.735315\pi$
$108$	1.71341			0.164873
$109$	−10.4345			−0.999445			−0.499723	−	0.866185i	$-0.666565\pi$
$109$	−10.4345			−0.999445			−0.499723	+	0.866185i	$0.666565\pi$
$110$	−10.2884	−	0.126603i	−0.980965	−	0.0120711i
$111$	1.90722			0.181025
$112$	0.632503	+	0.632503i	0.0597660	+	0.0597660i
$113$		−	3.11631i		−	0.293158i	−0.989199	−	0.146579i	$-0.953174\pi$
$113$		−	3.11631i		−	0.293158i	0.989199	−	0.146579i	$-0.0468262\pi$
$114$	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
$118$	9.89258			0.910686
$119$	−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
$127$		−	2.18915i		−	0.194255i	−0.995272	−	0.0971277i	$-0.969034\pi$
$127$		−	2.18915i		−	0.194255i	0.995272	−	0.0971277i	$-0.0309655\pi$
$128$		−	1.00000i		−	0.0883883i
$129$	−2.48294			−0.218611
$130$	−0.628018	−	0.00772799i	−0.0550808	−	0.000677790i
$131$	−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
$133$	2.26815			0.196673
$134$	7.85685	+	7.85685i	0.678729	+	0.678729i
$135$	−2.67560	−	2.74227i	−0.230279	−	0.236017i
$136$	0.476804			0.0408856
$137$			14.1260i			1.20687i	0.797413	+	0.603435i	$0.206202\pi$
$137$			14.1260i			1.20687i	−0.797413	+	0.603435i	$0.793798\pi$
$138$	−1.12622	−	1.12622i	−0.0958700	−	0.0958700i
$139$			2.52250i			0.213956i	0.994261	+	0.106978i	$0.0341174\pi$
$139$			2.52250i			0.213956i	−0.994261	+	0.106978i	$0.965883\pi$
$140$	0.0246107	−	2.00000i	0.00207999	−	0.169031i
$141$	−0.394314			−0.0332072
$142$	8.63547			0.724673
$143$			1.29246i			0.108081i
$144$	−2.91612			−0.243010
$145$	9.75567	+	7.05882i	0.810164	+	0.586203i
$146$	−8.56068			−0.708487
$147$		−	1.79559i		−	0.148098i
$148$	−6.58530			−0.541308
$149$	2.94004			0.240858			0.120429	−	0.992722i	$-0.461573\pi$
$149$	2.94004			0.240858			0.120429	+	0.992722i	$0.461573\pi$
$150$	−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
$153$		−	1.39042i		−	0.112409i
$154$	−4.11600			−0.331677
$155$	0.220063	−	17.8835i	0.0176759	−	1.43644i
$156$	−0.0575215	−	0.0575215i	−0.00460540	−	0.00460540i
$157$	−7.88212			−0.629061			−0.314531	−	0.949247i	$-0.601847\pi$
$157$	−7.88212			−0.629061			−0.314531	+	0.949247i	$0.601847\pi$
$158$	−0.0428537	−	0.0428537i	−0.00340926	−	0.00340926i
$159$	1.63799	−	1.63799i	0.129901	−	0.129901i
$160$	−1.60047	+	1.56156i	−0.126529	+	0.123452i
$161$	−4.91915			−0.387683
$162$			8.25213i			0.648349i
$163$			22.3121i			1.74762i	0.486266	+	0.873811i	$0.338359\pi$
$163$			22.3121i			1.74762i	−0.486266	+	0.873811i	$0.661641\pi$
$164$	−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	$-0.613367\pi$
$167$	7.60605	−	7.60605i	0.588574	−	0.588574i	0.937245	+	0.348671i	$0.113367\pi$
$168$	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
$172$	8.57318			0.653699
$173$	−2.00873	−	2.00873i	−0.152721	−	0.152721i	0.626611	−	0.779332i	$-0.284442\pi$
$173$	−2.00873	−	2.00873i	−0.152721	−	0.152721i	−0.779332	+	0.626611i	$0.784442\pi$
$174$	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
$177$		−	2.86506i		−	0.215351i
$178$	5.88779	+	5.88779i	0.441308	+	0.441308i
$179$	−23.6028			−1.76415			−0.882077	−	0.471106i	$-0.843855\pi$
$179$	−23.6028			−1.76415			−0.882077	+	0.471106i	$0.843855\pi$
$180$	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	$0.219152\pi$
$182$	−0.251245			−0.0186235
$183$	1.12622	+	1.12622i	0.0832524	+	0.0832524i
$184$	3.88864	+	3.88864i	0.286674	+	0.286674i
$185$	10.2834	+	10.5396i	0.756048	+	0.774886i
$186$	1.63799	−	1.63799i	0.120103	−	0.120103i
$187$	−1.55140	+	1.55140i	−0.113449	+	0.113449i
$188$	1.36150			0.0992974
$189$	−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	$0.635088\pi$
$192$	−0.289618			−0.0209013
$193$	−24.3879			−1.75548			−0.877741	−	0.479135i	$-0.840950\pi$
$193$	−24.3879			−1.75548			−0.877741	+	0.479135i	$0.840950\pi$
$194$		−	11.8026i		−	0.847380i
$195$	−0.00223816	+	0.181885i	−0.000160278	+	0.0130251i
$196$			6.19988i			0.442848i
$197$	2.47207	+	2.47207i	0.176128	+	0.176128i	0.789666	−	0.613538i	$-0.210254\pi$
$197$	2.47207	+	2.47207i	0.176128	+	0.176128i	−0.613538	+	0.789666i	$0.710254\pi$
$198$	9.48830	−	9.48830i	0.674304	−	0.674304i
$199$			11.3378i			0.803712i	0.915703	+	0.401856i	$0.131635\pi$
$199$			11.3378i			0.803712i	−0.915703	+	0.401856i	$0.868365\pi$
$200$	4.99849	+	0.123035i	0.353446	+	0.00869989i
$201$	2.27548	−	2.27548i	0.160500	−	0.160500i
$202$	0.605077	−	0.605077i	0.0425731	−	0.0425731i
$203$	3.93701	+	2.77551i	0.276324	+	0.194803i
$204$		−	0.138091i		−	0.00966830i
$205$	20.4895	+	0.252131i	1.43105	+	0.0176096i
$206$	−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
$213$		−	2.50099i		−	0.171365i
$214$	−0.674656	+	0.674656i	−0.0461185	+	0.0461185i
$215$	−13.3876	−	13.7211i	−0.913024	−	0.935775i
$216$			1.71341i			0.116583i
$217$		−	7.15449i		−	0.485678i
$218$		−	10.4345i		−	0.706715i
$219$			2.47932i			0.167537i
$220$	0.126603	−	10.2884i	0.00853558	−	0.693647i
$221$	−0.0946990	+	0.0946990i	−0.00637014	+	0.00637014i
$222$			1.90722i			0.128004i
$223$	10.2691	−	10.2691i	0.687668	−	0.687668i	−0.274048	−	0.961716i	$-0.588363\pi$
$223$	10.2691	−	10.2691i	0.687668	−	0.687668i	0.961716	+	0.274048i	$0.0883628\pi$
$224$	−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	0.217299	−	0.976105i	$-0.430275\pi$
$227$	−11.4326	−	11.4326i	−0.758806	−	0.758806i	−0.976105	+	0.217299i	$0.930275\pi$
$228$	−0.519282	+	0.519282i	−0.0343903	+	0.0343903i
$229$	11.1122	+	11.1122i	0.734316	+	0.734316i	0.971472	−	0.237156i	$-0.0762151\pi$
$229$	11.1122	+	11.1122i	0.734316	+	0.734316i	−0.237156	+	0.971472i	$0.576215\pi$
$230$	0.151307	−	12.2960i	0.00997689	−	0.810775i
$231$			1.19207i			0.0784322i
$232$	−0.918177	−	5.30631i	−0.0602813	−	0.348376i
$233$	14.5816	−	14.5816i	0.955273	−	0.955273i	−0.0437692	−	0.999042i	$-0.513937\pi$
$233$	14.5816	−	14.5816i	0.955273	−	0.955273i	0.999042	+	0.0437692i	$0.0139366\pi$
$234$	0.579176	−	0.579176i	0.0378619	−	0.0378619i
$235$	−2.12607	−	2.17904i	−0.138689	−	0.142145i
$236$			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	$0.0123660\pi$
$239$			1.20088i			0.0776785i	−0.999245	+	0.0388392i	$0.987634\pi$
$240$	0.452256	+	0.463525i	0.0291930	+	0.0299204i
$241$		−	22.6204i		−	1.45711i	−0.684987	−	0.728555i	$-0.740192\pi$
$241$		−	22.6204i		−	1.45711i	0.684987	−	0.728555i	$-0.259808\pi$
$242$	−10.1736			−0.653985
$243$	7.53020			0.483063
$244$	−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
$247$	0.712219			0.0453174
$248$	−5.65569	+	5.65569i	−0.359137	+	0.359137i
$249$	−0.289618	+	0.289618i	−0.0183538	+	0.0183538i
$250$	−7.60854	−	8.19207i	−0.481206	−	0.518112i
$251$	−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
$253$	−25.3052			−1.59092
$254$	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	0.734387	−	0.678731i	$-0.237470\pi$
$257$	0.892241	+	0.892241i	0.0556564	+	0.0556564i	−0.678731	+	0.734387i	$0.737470\pi$
$258$		−	2.48294i		−	0.154581i
$259$	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
$263$	20.3198			1.25297			0.626486	−	0.779433i	$-0.284493\pi$
$263$	20.3198			1.25297			0.626486	+	0.779433i	$0.284493\pi$
$264$	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	$0.0877118\pi$
$269$	20.2449	+	20.2449i	1.23436	+	1.23436i	0.272081	+	0.962274i	$0.412288\pi$
$270$	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	$0.299574\pi$
$272$			0.476804i			0.0289105i
$273$			0.0727650i			0.00440394i
$274$	−14.1260			−0.853385
$275$	−16.6641	+	15.8634i	−1.00488	+	0.956601i
$276$	1.12622	−	1.12622i	0.0677903	−	0.0677903i
$277$	1.15866	+	1.15866i	0.0696169	+	0.0696169i	0.741058	−	0.671441i	$-0.234324\pi$
$277$	1.15866	+	1.15866i	0.0696169	+	0.0696169i	−0.671441	+	0.741058i	$0.734324\pi$
$278$	−2.52250			−0.151290
$279$	16.4927	+	16.4927i	0.987392	+	0.987392i
$280$	2.00000	+	0.0246107i	0.119523	+	0.00147077i
$281$	−8.88875			−0.530258			−0.265129	−	0.964213i	$-0.585415\pi$
$281$	−8.88875			−0.530258			−0.265129	+	0.964213i	$0.585415\pi$
$282$		−	0.394314i		−	0.0234810i
$283$	−22.9390	−	22.9390i	−1.36358	−	1.36358i	−0.869301	−	0.494284i	$-0.835430\pi$
$283$	−22.9390	−	22.9390i	−1.36358	−	1.36358i	−0.494284	−	0.869301i	$-0.664570\pi$
$284$			8.63547i			0.512421i
$285$	1.64199	+	0.0202053i	0.0972631	+	0.00119686i
$286$	−1.29246			−0.0764248
$287$	8.19704			0.483856
$288$		−	2.91612i		−	0.171834i
$289$	16.7727			0.986627
$290$	−7.05882	+	9.75567i	−0.414508	+	0.572872i
$291$	−3.41825			−0.200382
$292$		−	8.56068i		−	0.500976i
$293$	15.7998			0.923035			0.461517	−	0.887131i	$-0.347305\pi$
$293$	15.7998			0.923035			0.461517	+	0.887131i	$0.347305\pi$
$294$	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
$298$			2.94004i			0.170312i
$299$	−1.54466			−0.0893299
$300$	0.0356331	−	1.44765i	0.00205728	−	0.0835801i
$301$	−5.42256	−	5.42256i	−0.312551	−	0.312551i
$302$	−10.8414			−0.623853
$303$	−0.175241	−	0.175241i	−0.0100673	−	0.0100673i
$304$	1.79299	−	1.79299i	0.102835	−	0.102835i
$305$	−0.151307	+	12.2960i	−0.00866381	+	0.704068i
$306$	1.39042			0.0794850
$307$		−	15.9584i		−	0.910794i	−0.890289	−	0.455397i	$-0.849497\pi$
$307$		−	15.9584i		−	0.910794i	0.890289	−	0.455397i	$-0.150503\pi$
$308$		−	4.11600i		−	0.234531i
$309$	−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	−0.924663	−	0.380786i	$-0.875653\pi$
$313$	−9.62217	+	9.62217i	−0.543877	+	0.543877i	0.380786	+	0.924663i	$0.375653\pi$
$314$		−	7.88212i		−	0.444814i
$315$	0.0717679	−	5.83224i	0.00404366	−	0.328610i
$316$	0.0428537	−	0.0428537i	0.00241071	−	0.00241071i
$317$	−22.6925			−1.27454			−0.637269	−	0.770641i	$-0.719936\pi$
$317$	−22.6925			−1.27454			−0.637269	+	0.770641i	$0.719936\pi$
$318$	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
$322$		−	4.91915i		−	0.274134i
$323$	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
$327$	−3.02202			−0.167118
$328$	−6.47983	−	6.47983i	−0.357789	−	0.357789i
$329$	−0.861152	−	0.861152i	−0.0474768	−	0.0474768i
$330$	−2.97971	−	0.0366665i	−0.164028	−	0.00201842i
$331$	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
$333$	−19.2035			−1.05235
$334$	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
$337$	−20.6557			−1.12519			−0.562593	−	0.826734i	$-0.690196\pi$
$337$	−20.6557			−1.12519			−0.562593	+	0.826734i	$0.690196\pi$
$338$	12.9211			0.702816
$339$		−	0.902538i		−	0.0490191i
$340$	0.763113	−	0.744561i	0.0413856	−	0.0403795i
$341$		−	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
$345$	−3.56114	−	0.0438212i	−0.191725	−	0.00235925i
$346$	2.00873	−	2.00873i	0.107990	−	0.107990i
$347$	−23.4372	+	23.4372i	−1.25818	+	1.25818i	−0.306213	+	0.951963i	$0.599062\pi$
$347$	−23.4372	+	23.4372i	−1.25818	+	1.25818i	−0.951963	+	0.306213i	$0.900938\pi$
$348$	−1.53680	+	0.265920i	−0.0823812	+	0.0142548i
$349$		−	25.2886i		−	1.35367i	−0.736136	−	0.676834i	$-0.763351\pi$
$349$		−	25.2886i		−	1.35367i	0.736136	−	0.676834i	$-0.236649\pi$
$350$	−3.08374	−	3.23938i	−0.164833	−	0.173152i
$351$	−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	$-0.166571\pi$
$353$	6.88469	+	6.88469i	0.366435	+	0.366435i	−0.499740	+	0.866175i	$0.666571\pi$
$354$	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
$358$		−	23.6028i		−	1.24745i
$359$	22.2072	−	22.2072i	1.17205	−	1.17205i	0.190330	−	0.981720i	$-0.439044\pi$
$359$	22.2072	−	22.2072i	1.17205	−	1.17205i	0.981720	−	0.190330i	$-0.0609559\pi$
$360$	−4.66718	+	4.55371i	−0.245982	+	0.240002i
$361$			12.5703i			0.661597i
$362$			20.7780i			1.09207i
$363$			2.94646i			0.154649i
$364$		−	0.251245i		−	0.0131688i
$365$	−13.7012	+	13.3681i	−0.717151	+	0.699716i
$366$	−1.12622	+	1.12622i	−0.0588683	+	0.0588683i
$367$			1.97873i			0.103289i	0.998666	+	0.0516445i	$0.0164463\pi$
$367$			1.97873i			0.103289i	−0.998666	+	0.0516445i	$0.983554\pi$
$368$	−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	−0.0146674	−	0.999892i	$-0.504669\pi$
$373$	19.0279	−	19.0279i	0.985225	−	0.985225i	0.999892	+	0.0146674i	$0.00466895\pi$
$374$	−1.55140	−	1.55140i	−0.0802208	−	0.0802208i
$375$	−2.37257	+	2.20357i	−0.122519	+	0.113792i
$376$			1.36150i			0.0702139i
$377$	1.23626	+	0.871535i	0.0636705	+	0.0448864i
$378$	1.08374	−	1.08374i	0.0557415	−	0.0557415i
$379$	−10.8552	+	10.8552i	−0.557595	+	0.557595i	−0.928622	−	0.371027i	$-0.879006\pi$
$379$	−10.8552	+	10.8552i	−0.557595	+	0.557595i	0.371027	+	0.928622i	$0.379006\pi$
$380$	−5.66951	−	0.0697654i	−0.290840	−	0.00357889i
$381$		−	0.634016i		−	0.0324816i
$382$	−6.90356	+	6.90356i	−0.353217	+	0.353217i
$383$	22.6747	+	22.6747i	1.15862	+	1.15862i	0.984772	+	0.173848i	$0.0556202\pi$
$383$	22.6747	+	22.6747i	1.15862	+	1.15862i	0.173848	+	0.984772i	$0.444380\pi$
$384$		−	0.289618i		−	0.0147795i
$385$	−6.58755	+	6.42740i	−0.335733	+	0.327571i
$386$		−	24.3879i		−	1.24131i
$387$	25.0004			1.27084
$388$	11.8026			0.599188
$389$	8.76850	+	8.76850i	0.444581	+	0.444581i	0.893548	−	0.448967i	$-0.148208\pi$
$389$	8.76850	+	8.76850i	0.444581	+	0.444581i	−0.448967	+	0.893548i	$0.648208\pi$
$390$	−0.181885	−	0.00223816i	−0.00921011	−	0.000113334i
$391$	−1.85412	−	1.85412i	−0.0937668	−	0.0937668i
$392$	−6.19988			−0.313141
$393$	−1.24090	+	1.24090i	−0.0625953	+	0.0625953i
$394$	−2.47207	+	2.47207i	−0.124541	+	0.124541i
$395$	−0.135505	−	0.00166744i	−0.00681801	−	8.38980e-5i
$396$	9.48830	+	9.48830i	0.476805	+	0.476805i
$397$	−18.3875	−	18.3875i	−0.922841	−	0.922841i	0.0743886	−	0.997229i	$-0.476299\pi$
$397$	−18.3875	−	18.3875i	−0.922841	−	0.922841i	−0.997229	+	0.0743886i	$0.976299\pi$
$398$	−11.3378			−0.568310
$399$	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
$403$		−	2.24657i		−	0.111910i
$404$	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
$408$	0.138091			0.00683652
$409$	−11.7879	+	11.7879i	−0.582876	+	0.582876i	−0.935693	−	0.352816i	$-0.885224\pi$
$409$	−11.7879	+	11.7879i	−0.582876	+	0.582876i	0.352816	+	0.935693i	$0.385224\pi$
$410$	−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
$417$			0.730562i			0.0357758i
$418$			11.6679i			0.570694i
$419$	−18.7077			−0.913929			−0.456964	−	0.889485i	$-0.651063\pi$
$419$	−18.7077			−0.913929			−0.456964	+	0.889485i	$0.651063\pi$
$420$	0.00712770	−	0.579235i	0.000347796	−	0.0282638i
$421$	−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
$423$	3.97029			0.193042
$424$	−5.65569	−	5.65569i	−0.274665	−	0.274665i
$425$	−2.38330	−	0.0586636i	−0.115607	−	0.00284560i
$426$	2.50099			0.121173
$427$			4.91915i			0.238054i
$428$	−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	$0.494191\pi$
$432$	−1.71341			−0.0824366
$433$		−	10.8919i		−	0.523431i	−0.965145	−	0.261716i	$-0.915712\pi$
$433$		−	10.8919i		−	0.523431i	0.965145	−	0.261716i	$-0.0842882\pi$
$434$	7.15449			0.343427
$435$	2.82541	+	2.04436i	0.135468	+	0.0980195i
$436$	10.4345			0.499723
$437$			13.9446i			0.667061i
$438$	−2.47932			−0.118467
$439$	−16.0340			−0.765261			−0.382631	−	0.923901i	$-0.624982\pi$
$439$	−16.0340			−0.765261			−0.382631	+	0.923901i	$0.624982\pi$
$440$	10.2884	+	0.126603i	0.490482	+	0.00603556i
$441$			18.0796i			0.860933i
$442$	−0.0946990	−	0.0946990i	−0.00450437	−	0.00450437i
$443$			21.8127i			1.03635i	0.855274	+	0.518176i	$0.173389\pi$
$443$			21.8127i			1.03635i	−0.855274	+	0.518176i	$0.826611\pi$
$444$	−1.90722			−0.0905125
$445$	18.6174	+	0.229094i	0.882550	+	0.0108601i
$446$	10.2691	+	10.2691i	0.486255	+	0.486255i
$447$	0.851488			0.0402740
$448$	−0.632503	−	0.632503i	−0.0298830	−	0.0298830i
$449$	−11.8820	+	11.8820i	−0.560748	+	0.560748i	−0.929520	−	0.368772i	$-0.879778\pi$
$449$	−11.8820	+	11.8820i	−0.560748	+	0.560748i	0.368772	+	0.929520i	$0.379778\pi$
$450$	14.5762	+	0.358785i	0.687128	+	0.0169133i
$451$	42.1674			1.98558
$452$			3.11631i			0.146579i
$453$			3.13986i			0.147524i
$454$	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	−0.211340	+	0.977413i	$0.567783\pi$
$457$	−25.4126	+	25.4126i	−1.18875	+	1.18875i	−0.977413	+	0.211340i	$0.932217\pi$
$458$	−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	$0.920736\pi$
$462$	−1.19207			−0.0554599
$463$	−3.00076	−	3.00076i	−0.139457	−	0.139457i	0.633932	−	0.773389i	$-0.281440\pi$
$463$	−3.00076	−	3.00076i	−0.139457	−	0.139457i	−0.773389	+	0.633932i	$0.781440\pi$
$464$	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
$467$			4.86798i			0.225263i	0.993637	+	0.112632i	$0.0359280\pi$
$467$			4.86798i			0.225263i	−0.993637	+	0.112632i	$0.964072\pi$
$468$	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
$472$	−9.89258			−0.455343
$473$	−27.8949	−	27.8949i	−1.28261	−	1.28261i
$474$	−0.0124112	−	0.0124112i	−0.000570065	−	0.000570065i
$475$	8.74165	+	9.18285i	0.401094	+	0.421338i
$476$	0.301580	−	0.301580i	0.0138229	−	0.0138229i
$477$	−16.4927	+	16.4927i	−0.755148	+	0.755148i
$478$	−1.20088			−0.0549270
$479$	−4.92833	−	4.92833i	−0.225181	−	0.225181i	0.585495	−	0.810676i	$-0.300900\pi$
$479$	−4.92833	−	4.92833i	−0.225181	−	0.225181i	−0.810676	+	0.585495i	$0.800900\pi$
$480$	−0.463525	+	0.452256i	−0.0211569	+	0.0206426i
$481$	1.30792	+	1.30792i	0.0596359	+	0.0596359i
$482$	22.6204			1.03033
$483$	−1.42467			−0.0648249
$484$		−	10.1736i		−	0.462437i
$485$	−18.4306	−	18.8898i	−0.836890	−	0.857743i
$486$			7.53020i			0.341577i
$487$	2.73756	+	2.73756i	0.124050	+	0.124050i	0.766406	−	0.642356i	$-0.222043\pi$
$487$	2.73756	+	2.73756i	0.124050	+	0.124050i	−0.642356	+	0.766406i	$0.722043\pi$
$488$	3.88864	−	3.88864i	0.176030	−	0.176030i
$489$			6.46199i			0.292221i
$490$	9.68151	+	9.92275i	0.437366	+	0.448264i
$491$	−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
$493$	0.437791	+	2.53007i	0.0197171	+	0.113949i
$494$			0.712219i			0.0320443i
$495$	0.369190	−	30.0024i	0.0165939	−	1.34851i
$496$	−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	$-0.579751\pi$
$499$	−11.0768			−0.495867			−0.247934	+	0.968777i	$0.579751\pi$
$500$	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
$503$		−	8.08426i		−	0.360459i	−0.983625	−	0.180230i	$-0.942316\pi$
$503$		−	8.08426i		−	0.360459i	0.983625	−	0.180230i	$-0.0576841\pi$
$504$	−1.84446	+	1.84446i	−0.0821586	+	0.0821586i
$505$	0.0235436	−	1.91328i	0.00104768	−	0.0851397i
$506$		−	25.3052i		−	1.12495i
$507$		−	3.74218i		−	0.166196i
$508$			2.18915i			0.0971277i
$509$			12.9806i			0.575354i	0.957728	+	0.287677i	$0.0928829\pi$
$509$			12.9806i			0.575354i	−0.957728	+	0.287677i	$0.907117\pi$
$510$	−0.215638	−	0.221011i	−0.00954860	−	0.00978653i
$511$	−5.41466	+	5.41466i	−0.239531	+	0.239531i
$512$			1.00000i			0.0441942i
$513$	−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
$520$	0.628018	+	0.00772799i	0.0275404	+	0.000338895i
$521$		−	18.4390i		−	0.807827i	−0.914797	−	0.403914i	$-0.867650\pi$
$521$		−	18.4390i		−	0.807827i	0.914797	−	0.403914i	$-0.132350\pi$
$522$	−2.67752	−	15.4739i	−0.117192	−	0.677272i
$523$	13.6216	−	13.6216i	0.595631	−	0.595631i	−0.343516	−	0.939147i	$-0.611618\pi$
$523$	13.6216	−	13.6216i	0.595631	−	0.595631i	0.939147	+	0.343516i	$0.111618\pi$
$524$	4.28463	−	4.28463i	0.187175	−	0.187175i
$525$	−0.938181	+	0.893105i	−0.0409456	+	0.0389783i
$526$			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
$530$	−0.220063	+	17.8835i	−0.00955894	+	0.776810i
$531$			28.8480i			1.25190i
$532$	−2.26815			−0.0983367
$533$	2.57394			0.111490
$534$	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
$537$	−6.83578			−0.294986
$538$	−20.2449	+	20.2449i	−0.872821	+	0.872821i
$539$	20.1728	−	20.1728i	0.868903	−	0.868903i
$540$	2.67560	+	2.74227i	0.115140	+	0.118009i
$541$	−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
$543$	6.01768			0.258244
$544$	−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	0.508877	−	0.860839i	$-0.330061\pi$
$547$	−8.23169	−	8.23169i	−0.351961	−	0.351961i	−0.860839	+	0.508877i	$0.830061\pi$
$548$		−	14.1260i		−	0.603435i
$549$	−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
$553$	−0.0542103			−0.00230526
$554$	−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	0.00300753	−	0.999995i	$-0.499043\pi$
$557$	23.6717	−	23.6717i	1.00300	−	1.00300i	0.999995	−	0.00300753i	$-0.000957328\pi$
$558$	−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
$562$		−	8.88875i		−	0.374949i
$563$		−	38.2332i		−	1.61134i	−0.592365	−	0.805670i	$-0.701806\pi$
$563$		−	38.2332i		−	1.61134i	0.592365	−	0.805670i	$-0.298194\pi$
$564$	0.394314			0.0166036
$565$	4.98757	−	4.86632i	0.209829	−	0.204728i
$566$	22.9390	−	22.9390i	0.964200	−	0.964200i
$567$	5.21950	+	5.21950i	0.219198	+	0.219198i
$568$	−8.63547			−0.362336
$569$	10.6612	+	10.6612i	0.446939	+	0.446939i	0.894336	−	0.447397i	$-0.147649\pi$
$569$	10.6612	+	10.6612i	0.446939	+	0.446939i	−0.447397	+	0.894336i	$0.647649\pi$
$570$	−0.0202053	+	1.64199i	−0.000846307	+	0.0687754i
$571$	−12.7145			−0.532085			−0.266042	−	0.963961i	$-0.585716\pi$
$571$	−12.7145			−0.532085			−0.266042	+	0.963961i	$0.585716\pi$
$572$		−	1.29246i		−	0.0540405i
$573$	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
$577$	24.2872			1.01109			0.505545	−	0.862800i	$-0.331291\pi$
$577$	24.2872			1.01109			0.505545	+	0.862800i	$0.331291\pi$
$578$			16.7727i			0.697651i
$579$	−7.06318			−0.293536
$580$	−9.75567	−	7.05882i	−0.405082	−	0.293102i
$581$	−1.26501			−0.0524813
$582$		−	3.41825i		−	0.141691i
$583$	36.8043			1.52428
$584$	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	0.811318	−	0.584605i	$-0.198750\pi$
$587$	5.49283	+	5.49283i	0.226714	+	0.226714i	−0.584605	+	0.811318i	$0.698750\pi$
$588$			1.79559i			0.0740490i
$589$	−20.2812			−0.835674
$590$	15.4479	+	15.8328i	0.635980	+	0.651827i
$591$	0.715956	+	0.715956i	0.0294505	+	0.0294505i
$592$	6.58530			0.270654
$593$	28.1924	+	28.1924i	1.15772	+	1.15772i	0.984964	+	0.172761i	$0.0552688\pi$
$593$	28.1924	+	28.1924i	1.15772	+	1.15772i	0.172761	+	0.984964i	$0.444731\pi$
$594$	5.57500	−	5.57500i	0.228745	−	0.228745i
$595$	−0.953609	−	0.0117345i	−0.0390941	−	0.000481068i
$596$	−2.94004			−0.120429
$597$			3.28361i			0.134389i
$598$		−	1.54466i		−	0.0631658i
$599$	−20.0950	+	20.0950i	−0.821059	+	0.821059i	−0.986260	−	0.165201i	$-0.947173\pi$
$599$	−20.0950	+	20.0950i	−0.821059	+	0.821059i	0.165201	+	0.986260i	$0.447173\pi$
$600$	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
$607$	37.1113			1.50630			0.753150	−	0.657849i	$-0.228533\pi$
$607$	37.1113			1.50630			0.753150	+	0.657849i	$0.228533\pi$
$608$	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
$612$			1.39042i			0.0562044i
$613$	−20.5386	−	20.5386i	−0.829547	−	0.829547i	0.157907	−	0.987454i	$-0.449525\pi$
$613$	−20.5386	−	20.5386i	−0.829547	−	0.829547i	−0.987454	+	0.157907i	$0.949525\pi$
$614$	15.9584			0.644028
$615$	5.93411	+	0.0730214i	0.239287	+	0.00294451i
$616$	4.11600			0.165838
$617$	1.48087			0.0596176			0.0298088	−	0.999556i	$-0.490510\pi$
$617$	1.48087			0.0596176			0.0298088	+	0.999556i	$0.490510\pi$
$618$	−3.17634	−	3.17634i	−0.127771	−	0.127771i
$619$	−31.9416	−	31.9416i	−1.28384	−	1.28384i	−0.938463	−	0.345380i	$-0.887750\pi$
$619$	−31.9416	−	31.9416i	−1.28384	−	1.28384i	−0.345380	−	0.938463i	$-0.612250\pi$
$620$	−0.220063	+	17.8835i	−0.00883795	+	0.718219i
$621$	6.66284	−	6.66284i	0.267371	−	0.267371i
$622$	5.09331	−	5.09331i	0.204223	−	0.204223i
$623$	7.44809			0.298402
$624$	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
$627$	3.37922			0.134953
$628$	7.88212			0.314531
$629$			3.13990i			0.125196i
$630$	5.83224	+	0.0717679i	0.232362	+	0.00285930i
$631$		−	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
$635$	3.50367	−	3.41849i	0.139039	−	0.135659i
$636$	−1.63799	+	1.63799i	−0.0649505	+	0.0649505i
$637$	1.23137	−	1.23137i	0.0487886	−	0.0487886i
$638$	−14.2778	+	20.2529i	−0.565265	+	0.801818i
$639$			25.1821i			0.996188i
$640$	1.60047	−	1.56156i	0.0632643	−	0.0617262i
$641$	−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	$-0.180222\pi$
$643$	7.79835	+	7.79835i	0.307537	+	0.307537i	−0.536417	+	0.843953i	$0.680222\pi$
$644$	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	$-0.597157\pi$
$647$	16.6166	−	16.6166i	0.653268	−	0.653268i	0.953778	+	0.300511i	$0.0971571\pi$
$648$		−	8.25213i		−	0.324174i
$649$	32.1879	−	32.1879i	1.26348	−	1.26348i
$650$	−0.968322	−	1.01719i	−0.0379807	−	0.0398977i
$651$		−	2.07207i		−	0.0812107i
$652$		−	22.3121i		−	0.873811i
$653$			45.8616i			1.79470i	0.441317	+	0.897352i	$0.354512\pi$
$653$			45.8616i			1.79470i	−0.441317	+	0.897352i	$0.645488\pi$
$654$		−	3.02202i		−	0.118170i
$655$	−13.5482	−	0.166715i	−0.529370	−	0.00651410i
$656$	6.47983	−	6.47983i	0.252995	−	0.252995i
$657$		−	24.9640i		−	0.973938i
$658$	0.861152	−	0.861152i	0.0335712	−	0.0335712i
$659$	8.87020	−	8.87020i	0.345534	−	0.345534i	−0.512909	−	0.858443i	$-0.671432\pi$
$659$	8.87020	−	8.87020i	0.345534	−	0.345534i	0.858443	+	0.512909i	$0.171432\pi$
$660$	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
$665$	3.54186	+	3.63011i	0.137347	+	0.140770i
$666$		−	19.2035i		−	0.744121i
$667$	−17.0639	+	24.2048i	−0.660715	+	0.937213i
$668$	−7.60605	+	7.60605i	−0.294287	+	0.294287i
$669$	2.97410	−	2.97410i	0.114985	−	0.114985i
$670$	−0.305710	+	24.8437i	−0.0118106	+	0.959795i
$671$			25.3052i			0.976897i
$672$	−0.183184	+	0.183184i	−0.00706648	+	0.00706648i
$673$	−28.6125	−	28.6125i	−1.10293	−	1.10293i	−0.994056	−	0.108874i	$-0.965275\pi$
$673$	−28.6125	−	28.6125i	−1.10293	−	1.10293i	−0.108874	−	0.994056i	$-0.534725\pi$
$674$		−	20.6557i		−	0.795626i
$675$	0.210810	−	8.56447i	0.00811407	−	0.329647i
$676$			12.9211i			0.496966i
$677$	1.01813			0.0391300			0.0195650	−	0.999809i	$-0.493772\pi$
$677$	1.01813			0.0391300			0.0195650	+	0.999809i	$0.493772\pi$
$678$	0.902538			0.0346618
$679$	−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
$682$	36.8043			1.40931
$683$	−13.6805	+	13.6805i	−0.523470	+	0.523470i	−0.918618	−	0.395147i	$-0.870694\pi$
$683$	−13.6805	+	13.6805i	−0.523470	+	0.523470i	0.395147	+	0.918618i	$0.370694\pi$
$684$	5.22859	−	5.22859i	0.199920	−	0.199920i
$685$	−22.6084	+	22.0587i	−0.863821	+	0.842820i
$686$	8.34897	+	8.34897i	0.318765	+	0.318765i
$687$	3.21829	+	3.21829i	0.122786	+	0.122786i
$688$	−8.57318			−0.326849
$689$	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
$693$		−	12.0028i		−	0.455947i
$694$	−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
$698$	25.2886			0.957188
$699$	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
$707$		−	0.765427i		−	0.0287868i
$708$			2.86506i			0.107676i
$709$	−33.5904			−1.26151			−0.630756	−	0.775981i	$-0.717255\pi$
$709$	−33.5904			−1.26151			−0.630756	+	0.775981i	$0.717255\pi$
$710$	13.4848	+	13.8209i	0.506077	+	0.518687i
$711$	0.124967	−	0.124967i	0.00468662	−	0.00468662i
$712$	−5.88779	−	5.88779i	−0.220654	−	0.220654i
$713$	43.9859			1.64728
$714$	−0.0873430	−	0.0873430i	−0.00326873	−	0.00326873i
$715$	−2.06855	+	2.01826i	−0.0773594	+	0.0754787i
$716$	23.6028			0.882077
$717$			0.347796i			0.0129887i
$718$	22.2072	+	22.2072i	0.828765	+	0.828765i
$719$		−	5.51139i		−	0.205540i	−0.994705	−	0.102770i	$-0.967229\pi$
$719$		−	5.51139i		−	0.205540i	0.994705	−	0.102770i	$-0.0327706\pi$
$720$	−4.55371	−	4.66718i	−0.169707	−	0.173935i
$721$	−13.8738			−0.516687
$722$	−12.5703			−0.467820
$723$		−	6.55127i		−	0.243645i
$724$	−20.7780			−0.772210
$725$	3.93663	+	26.6365i	0.146203	+	0.989255i
$726$	−2.94646			−0.109353
$727$			5.28028i			0.195835i	0.995195	+	0.0979173i	$0.0312181\pi$
$727$			5.28028i			0.195835i	−0.995195	+	0.0979173i	$0.968782\pi$
$728$	0.251245			0.00931177
$729$	−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
$733$		−	24.3366i		−	0.898892i	−0.893308	−	0.449446i	$-0.851621\pi$
$733$		−	24.3366i		−	0.898892i	0.893308	−	0.449446i	$-0.148379\pi$
$734$	−1.97873			−0.0730363
$735$	2.87380	−	2.80393i	0.106002	−	0.103425i
$736$	−3.88864	−	3.88864i	−0.143337	−	0.143337i
$737$	51.1283			1.88333
$738$	−18.8960	−	18.8960i	−0.695571	−	0.695571i
$739$	24.1899	−	24.1899i	0.889839	−	0.889839i	−0.104669	−	0.994507i	$-0.533378\pi$
$739$	24.1899	−	24.1899i	0.889839	−	0.889839i	0.994507	+	0.104669i	$0.0333782\pi$
$740$	−10.2834	−	10.5396i	−0.378024	−	0.387443i
$741$	0.206271			0.00757756
$742$			7.15449i			0.262650i
$743$			53.3731i			1.95807i	0.203694	+	0.979035i	$0.434705\pi$
$743$			53.3731i			1.95807i	−0.203694	+	0.979035i	$0.565295\pi$
$744$	−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	$0.898437\pi$
$752$	−1.36150			−0.0496487
$753$	−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
$757$			33.8919i			1.23182i	0.787815	+	0.615911i	$0.211212\pi$
$757$			33.8919i			1.23182i	−0.787815	+	0.615911i	$0.788788\pi$
$758$	−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	$0.119918\pi$
$762$	0.634016			0.0229680
$763$	−6.59987	−	6.59987i	−0.238931	−	0.238931i
$764$	−6.90356	−	6.90356i	−0.249762	−	0.249762i
$765$	2.22533	−	2.17123i	0.0804570	−	0.0785010i
$766$	−22.6747	+	22.6747i	−0.819269	+	0.819269i
$767$	1.96478	−	1.96478i	0.0709442	−	0.0709442i
$768$	0.289618			0.0104507
$769$	13.2848	+	13.2848i	0.479063	+	0.479063i	0.904832	−	0.425769i	$-0.139996\pi$
$769$	13.2848	+	13.2848i	0.479063	+	0.479063i	−0.425769	+	0.904832i	$0.639996\pi$
$770$	−6.42740	−	6.58755i	−0.231627	−	0.237399i
$771$	0.258409	+	0.258409i	0.00930636	+	0.00930636i
$772$	24.3879			0.877741
$773$	23.8909			0.859294			0.429647	−	0.902997i	$-0.358638\pi$
$773$	23.8909			0.859294			0.429647	+	0.902997i	$0.358638\pi$
$774$			25.0004i			0.898622i
$775$	28.9658	−	27.5741i	1.04048	−	0.990489i
$776$			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
$780$	0.00223816	−	0.181885i	8.01391e−5	−	0.00651253i
$781$	28.0976	−	28.0976i	1.00541	−	1.00541i
$782$	1.85412	−	1.85412i	0.0663032	−	0.0663032i
$783$	−9.09190	+	1.57322i	−0.324918	+	0.0562222i
$784$		−	6.19988i		−	0.221424i
$785$	−12.3084	−	12.6151i	−0.439307	−	0.450253i
$786$	−1.24090	−	1.24090i	−0.0442616	−	0.0442616i
$787$	18.3968	−	18.3968i	0.655776	−	0.655776i	−0.298602	−	0.954378i	$-0.596520\pi$
$787$	18.3968	−	18.3968i	0.655776	−	0.655776i	0.954378	+	0.298602i	$0.0965202\pi$
$788$	−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
$793$			1.54466i			0.0548524i
$794$	18.3875	−	18.3875i	0.652547	−	0.652547i
$795$	5.17938	+	0.0637342i	0.183694	+	0.00226042i
$796$		−	11.3378i		−	0.401856i
$797$			16.2394i			0.575228i	0.957746	+	0.287614i	$0.0928621\pi$
$797$			16.2394i			0.575228i	−0.957746	+	0.287614i	$0.907138\pi$
$798$			0.656896i			0.0232539i
$799$		−	0.649168i		−	0.0229659i
$800$	−4.99849	−	0.123035i	−0.176723	−	0.00434994i
$801$	−17.1695	+	17.1695i	−0.606655	+	0.606655i
$802$			5.87124i			0.207321i
$803$	−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	0.766277	−	0.642510i	$-0.222107\pi$
$809$	3.52028	+	3.52028i	0.123766	+	0.123766i	−0.642510	+	0.766277i	$0.722107\pi$
$810$	−13.2073	+	12.8862i	−0.464058	+	0.452776i
$811$			2.40718i			0.0845277i	0.999106	+	0.0422638i	$0.0134570\pi$
$811$			2.40718i			0.0845277i	−0.999106	+	0.0422638i	$0.986543\pi$
$812$	−3.93701	−	2.77551i	−0.138162	−	0.0974013i
$813$	−1.04585	+	1.04585i	−0.0366795	+	0.0366795i
$814$	−21.4268	+	21.4268i	−0.751010	+	0.751010i
$815$	−35.7100	+	34.8418i	−1.25087	+	1.22046i
$816$			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
$820$	−20.4895	−	0.252131i	−0.715524	−	0.00880478i
$821$			36.8938i			1.28760i	0.765193	+	0.643801i	$0.222643\pi$
$821$			36.8938i			1.28760i	−0.765193	+	0.643801i	$0.777357\pi$
$822$	−4.09115			−0.142695
$823$	21.2449			0.740550			0.370275	−	0.928922i	$-0.379264\pi$
$823$	21.2449			0.740550			0.370275	+	0.928922i	$0.379264\pi$
$824$	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
$827$	−17.7303			−0.616542			−0.308271	−	0.951299i	$-0.599750\pi$
$827$	−17.7303			−0.616542			−0.308271	+	0.951299i	$0.599750\pi$
$828$	−11.3397	+	11.3397i	−0.394083	+	0.394083i
$829$	−16.5417	+	16.5417i	−0.574516	+	0.574516i	−0.933387	−	0.358871i	$-0.883162\pi$
$829$	−16.5417	+	16.5417i	−0.574516	+	0.574516i	0.358871	+	0.933387i	$0.383162\pi$
$830$	0.0389100	−	3.16204i	0.00135059	−	0.109756i
$831$	0.335567	+	0.335567i	0.0116407	+	0.0116407i
$832$	−0.198612	−	0.198612i	−0.00688563	−	0.00688563i
$833$	2.95613			0.102424
$834$	−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
$838$		−	18.7077i		−	0.646245i
$839$	14.1762	+	14.1762i	0.489416	+	0.489416i	0.908122	−	0.418706i	$-0.137516\pi$
$839$	14.1762	+	14.1762i	0.489416	+	0.489416i	−0.418706	+	0.908122i	$0.637516\pi$
$840$	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
$843$	−2.57434			−0.0886649
$844$	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
$852$			2.50099i			0.0856823i
$853$			29.1166i			0.996932i	0.866909	+	0.498466i	$0.166103\pi$
$853$			29.1166i			0.996932i	−0.866909	+	0.498466i	$0.833897\pi$
$854$	−4.91915			−0.168330
$855$	−16.5330	−	0.203445i	−0.565416	−	0.00695766i
$856$	0.674656	−	0.674656i	0.0230593	−	0.0230593i
$857$	7.30296	+	7.30296i	0.249464	+	0.249464i	0.820751	−	0.571286i	$-0.193555\pi$
$857$	7.30296	+	7.30296i	0.249464	+	0.249464i	−0.571286	+	0.820751i	$0.693555\pi$
$858$	−0.374320			−0.0127791
$859$	13.3341	+	13.3341i	0.454953	+	0.454953i	0.896995	−	0.442042i	$-0.145746\pi$
$859$	13.3341	+	13.3341i	0.454953	+	0.454953i	−0.442042	+	0.896995i	$0.645746\pi$
$860$	13.3876	+	13.7211i	0.456512	+	0.467887i
$861$	2.37401			0.0809059
$862$			0.757725i			0.0258082i
$863$	−9.11507	−	9.11507i	−0.310280	−	0.310280i	0.534738	−	0.845018i	$-0.320410\pi$
$863$	−9.11507	−	9.11507i	−0.310280	−	0.310280i	−0.845018	+	0.534738i	$0.820410\pi$
$864$		−	1.71341i		−	0.0582915i
$865$	0.0781599	−	6.35170i	0.00265752	−	0.215964i
$866$	10.8919			0.370122
$867$	4.85766			0.164975
$868$			7.15449i			0.242839i
$869$	−0.278870			−0.00946001
$870$	−2.04436	+	2.82541i	−0.0693103	+	0.0957904i
$871$	3.12093			0.105749
$872$			10.4345i			0.353357i
$873$	34.4179			1.16487
$874$	−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	−0.965677	−	0.259747i	$-0.916361\pi$
$877$	−36.2899	−	36.2899i	−1.22542	−	1.22542i	−0.259747	−	0.965677i	$-0.583639\pi$
$878$		−	16.0340i		−	0.541122i
$879$	4.57590			0.154341
$880$	−0.126603	+	10.2884i	−0.00426779	+	0.346823i
$881$	−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	$-0.522744\pi$
$882$	−18.0796			−0.608772
$883$	5.18708	+	5.18708i	0.174559	+	0.174559i	0.788979	−	0.614420i	$-0.210610\pi$
$883$	5.18708	+	5.18708i	0.174559	+	0.174559i	−0.614420	+	0.788979i	$0.710610\pi$
$884$	0.0946990	−	0.0946990i	0.00318507	−	0.00318507i
$885$	4.58546	−	4.47398i	0.154139	−	0.150391i
$886$	−21.8127			−0.732812
$887$			45.5203i			1.52842i	0.644967	+	0.764211i	$0.276871\pi$
$887$			45.5203i			1.52842i	−0.644967	+	0.764211i	$0.723129\pi$
$888$		−	1.90722i		−	0.0640020i
$889$	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
$897$	−0.447360			−0.0149369
$898$	−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
$902$			42.1674i			1.40402i
$903$	−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
$907$	52.1407			1.73130			0.865652	−	0.500646i	$-0.166904\pi$
$907$	52.1407			1.73130			0.865652	+	0.500646i	$0.166904\pi$
$908$	11.4326	+	11.4326i	0.379403	+	0.379403i
$909$	1.76448	+	1.76448i	0.0585241	+	0.0585241i
$910$	−0.392336	−	0.402112i	−0.0130058	−	0.0133299i
$911$	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
$913$	−6.50748			−0.215366
$914$	−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
$917$	−5.42008			−0.178987
$918$	0.816963			0.0269638
$919$			1.29013i			0.0425574i	0.999774	+	0.0212787i	$0.00677373\pi$
$919$			1.29013i			0.0425574i	−0.999774	+	0.0212787i	$0.993226\pi$
$920$	−0.151307	+	12.2960i	−0.00498844	+	0.405388i
$921$		−	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
$925$	−0.810222	+	32.9165i	−0.0266399	+	1.08229i
$926$	3.00076	−	3.00076i	0.0986111	−	0.0986111i
$927$	31.9822	−	31.9822i	1.05043	−	1.05043i
$928$	0.918177	+	5.30631i	0.0301406	+	0.174188i
$929$		−	29.6911i		−	0.974134i	−0.873365	−	0.487067i	$-0.838067\pi$
$929$		−	29.6911i		−	0.974134i	0.873365	−	0.487067i	$-0.161933\pi$
$930$	5.17938	+	0.0637342i	0.169839	+	0.00208993i
$931$	−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	−0.00181196	+	0.999998i	$0.500577\pi$
$937$	−30.6659	+	30.6659i	−1.00181	+	1.00181i	−0.999998	+	0.00181196i	$0.999423\pi$
$938$			9.93897i			0.324519i
$939$	−2.78675	+	2.78675i	−0.0909421	+	0.0909421i
$940$	2.12607	+	2.17904i	0.0693446	+	0.0710725i
$941$		−	32.2353i		−	1.05084i	−0.850842	−	0.525421i	$-0.823908\pi$
$941$		−	32.2353i		−	1.05084i	0.850842	−	0.525421i	$-0.176092\pi$
$942$		−	2.28280i		−	0.0743776i
$943$			50.3954i			1.64110i
$944$		−	9.89258i		−	0.321976i
$945$	0.0421683	−	3.42683i	0.00137174	−	0.111475i
$946$	27.8949	−	27.8949i	0.906940	−	0.906940i
$947$		−	32.5015i		−	1.05616i	−0.849195	−	0.528079i	$-0.822913\pi$
$947$		−	32.5015i		−	1.05616i	0.849195	−	0.528079i	$-0.177087\pi$
$948$	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	−0.973602	−	0.228254i	$-0.926698\pi$
$953$	−23.0094	+	23.0094i	−0.745348	+	0.745348i	0.228254	+	0.973602i	$0.426698\pi$
$954$	−16.4927	−	16.4927i	−0.533971	−	0.533971i
$955$	−0.268618	+	21.8293i	−0.00869226	+	0.706380i
$956$		−	1.20088i		−	0.0388392i
$957$	5.86558	+	4.13511i	0.189607	+	0.133669i
$958$	4.92833	−	4.92833i	0.159227	−	0.159227i
$959$	−8.93477	+	8.93477i	−0.288519	+	0.288519i
$960$	−0.452256	−	0.463525i	−0.0145965	−	0.0149602i
$961$			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
$965$	−38.0833	−	39.0323i	−1.22595	−	1.25649i
$966$		−	1.42467i		−	0.0458381i
$967$	−0.317494			−0.0102099			−0.00510495	−	0.999987i	$-0.501625\pi$
$967$	−0.317494			−0.0102099			−0.00510495	+	0.999987i	$0.501625\pi$
$968$	10.1736			0.326993
$969$	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	$0.931836\pi$
$972$	−7.53020			−0.241531
$973$	−1.59549	+	1.59549i	−0.0511491	+	0.0511491i
$974$	−2.73756	+	2.73756i	−0.0877169	+	0.0877169i
$975$	−0.294597	+	0.280443i	−0.00943467	+	0.00898137i
$976$	3.88864	+	3.88864i	0.124472	+	0.124472i
$977$	24.5169	+	24.5169i	0.784365	+	0.784365i	0.980564	−	0.196199i	$-0.0628598\pi$
$977$	24.5169	+	24.5169i	0.784365	+	0.784365i	−0.196199	+	0.980564i	$0.562860\pi$
$978$	−6.46199			−0.206632
$979$	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
$983$		−	59.6952i		−	1.90398i	−0.306126	−	0.951991i	$-0.599033\pi$
$983$		−	59.6952i		−	1.90398i	0.306126	−	0.951991i	$-0.400967\pi$
$984$	−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
$988$	−0.712219			−0.0226587
$989$	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
$997$			27.2996i			0.864586i	0.901733	+	0.432293i	$0.142295\pi$
$997$			27.2996i			0.864586i	−0.901733	+	0.432293i	$0.857705\pi$
$998$		−	11.0768i		−	0.350631i
$999$	−11.2833			−0.356989

Twists

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

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

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

Introduction

L-functions

Modular forms

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Database

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