LMFDB - Embedded newform 1450.2.j.h.1293.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1450,2,Mod(157,1450)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1450, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([1, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1450.157"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 1450 = 2 \cdot 5^{2} \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1450.j (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [12,0,0,-12,0,0,4,0,28,0,10] 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:	$11.5783082931$
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:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 290)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			1293.3
Root			$1.64632i$ of defining polynomial
Character	$\chi$	$=$	1450.1293
Dual form			1450.2.j.h.157.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.00000i q^{2} -0.289618 q^{3} -1.00000 q^{4} -0.289618i q^{6} +(-0.632503 + 0.632503i) q^{7} -1.00000i q^{8} -2.91612 q^{9} +(3.25374 - 3.25374i) q^{11} +0.289618 q^{12} +(-0.198612 + 0.198612i) q^{13} +(-0.632503 - 0.632503i) q^{14} +1.00000 q^{16} +0.476804i q^{17} -2.91612i q^{18} +(1.79299 + 1.79299i) q^{19} +(0.183184 - 0.183184i) q^{21} +(3.25374 + 3.25374i) q^{22} +(3.88864 + 3.88864i) q^{23} +0.289618i q^{24} +(-0.198612 - 0.198612i) q^{26} +1.71341 q^{27} +(0.632503 - 0.632503i) q^{28} +(5.30631 + 0.918177i) q^{29} +(-5.65569 + 5.65569i) q^{31} +1.00000i q^{32} +(-0.942340 + 0.942340i) q^{33} -0.476804 q^{34} +2.91612 q^{36} -6.58530 q^{37} +(-1.79299 + 1.79299i) q^{38} +(0.0575215 - 0.0575215i) q^{39} +(6.47983 + 6.47983i) q^{41} +(0.183184 + 0.183184i) q^{42} +8.57318 q^{43} +(-3.25374 + 3.25374i) q^{44} +(-3.88864 + 3.88864i) q^{46} +1.36150 q^{47} -0.289618 q^{48} +6.19988i q^{49} -0.138091i q^{51} +(0.198612 - 0.198612i) q^{52} +(-5.65569 - 5.65569i) q^{53} +1.71341i q^{54} +(0.632503 + 0.632503i) q^{56} +(-0.519282 - 0.519282i) q^{57} +(-0.918177 + 5.30631i) q^{58} +9.89258i q^{59} +(3.88864 - 3.88864i) q^{61} +(-5.65569 - 5.65569i) q^{62} +(1.84446 - 1.84446i) q^{63} -1.00000 q^{64} +(-0.942340 - 0.942340i) q^{66} +(-7.85685 - 7.85685i) q^{67} -0.476804i q^{68} +(-1.12622 - 1.12622i) q^{69} +8.63547i q^{71} +2.91612i q^{72} +8.56068i q^{73} -6.58530i q^{74} +(-1.79299 - 1.79299i) q^{76} +4.11600i q^{77} +(0.0575215 + 0.0575215i) q^{78} +(-0.0428537 - 0.0428537i) q^{79} +8.25213 q^{81} +(-6.47983 + 6.47983i) q^{82} +(1.00000 + 1.00000i) q^{83} +(-0.183184 + 0.183184i) q^{84} +8.57318i q^{86} +(-1.53680 - 0.265920i) q^{87} +(-3.25374 - 3.25374i) q^{88} +(5.88779 + 5.88779i) q^{89} -0.251245i q^{91} +(-3.88864 - 3.88864i) q^{92} +(1.63799 - 1.63799i) q^{93} +1.36150i q^{94} -0.289618i q^{96} +11.8026 q^{97} -6.19988 q^{98} +(-9.48830 + 9.48830i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 12 q^{4} + 4 q^{7} + 28 q^{9} + 10 q^{11} - 2 q^{13} + 4 q^{14} + 12 q^{16} - 16 q^{19} - 16 q^{21} + 10 q^{22} - 4 q^{23} - 2 q^{26} - 12 q^{27} - 4 q^{28} + 20 q^{29} + 18 q^{31} + 6 q^{33} - 28 q^{36}+ \cdots + 36 q^{99}+O(q^{100}) $ 12 * q - 12 * q^4 + 4 * q^7 + 28 * q^9 + 10 * q^11 - 2 * q^13 + 4 * q^14 + 12 * q^16 - 16 * q^19 - 16 * q^21 + 10 * q^22 - 4 * q^23 - 2 * q^26 - 12 * q^27 - 4 * q^28 + 20 * q^29 + 18 * q^31 + 6 * q^33 - 28 * q^36 + 16 * q^38 - 38 * q^39 + 36 * q^41 - 16 * q^42 + 12 * q^43 - 10 * q^44 + 4 * q^46 - 20 * q^47 + 2 * q^52 + 18 * q^53 - 4 * q^56 + 32 * q^57 - 16 * q^58 - 4 * q^61 + 18 * q^62 + 24 * q^63 - 12 * q^64 + 6 * q^66 + 12 * q^67 + 12 * q^69 + 16 * q^76 - 38 * q^78 + 30 * q^79 + 44 * q^81 - 36 * q^82 + 12 * q^83 + 16 * q^84 + 16 * q^87 - 10 * q^88 + 20 * q^89 + 4 * q^92 - 2 * q^93 - 76 * q^97 - 16 * q^98 + 36 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1450\mathbb{Z}\right)^\times$.

$n$	$901$	$1277$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{3}{4}\right)$

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 $

$2$			1.00000i			0.707107i
$2$			1.00000i			0.707107i
$3$	−0.289618			−0.167211			−0.0836054	−	0.996499i	$-0.526644\pi$
$3$	−0.289618			−0.167211			−0.0836054	+	0.996499i	$0.526644\pi$
$4$	−1.00000			−0.500000
$5$		0			0
$5$		0			0
$6$		−	0.289618i		−	0.118236i
$7$	−0.632503	+	0.632503i	−0.239064	+	0.239064i	−0.816462	−	0.577399i	$-0.804068\pi$
$7$	−0.632503	+	0.632503i	−0.239064	+	0.239064i	0.577399	+	0.816462i	$0.304068\pi$
$8$		−	1.00000i		−	0.353553i
$9$	−2.91612			−0.972041
$10$		0			0
$11$	3.25374	−	3.25374i	0.981039	−	0.981039i	−0.0187847	−	0.999824i	$-0.505980\pi$
$11$	3.25374	−	3.25374i	0.981039	−	0.981039i	0.999824	+	0.0187847i	$0.00597971\pi$
$12$	0.289618			0.0836054
$13$	−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			0
$16$	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	0.882205	−	0.470865i	$-0.156058\pi$
$19$	1.79299	+	1.79299i	0.411341	+	0.411341i	−0.470865	+	0.882205i	$0.656058\pi$
$20$		0			0
$21$	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	$-0.0556442\pi$
$23$	3.88864	+	3.88864i	0.810837	+	0.810837i	−0.173923	+	0.984759i	$0.555644\pi$
$24$			0.289618i			0.0591179i
$25$		0			0
$26$	−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			0
$31$	−5.65569	+	5.65569i	−1.01579	+	1.01579i	−0.0159192	+	0.999873i	$0.505067\pi$
$31$	−5.65569	+	5.65569i	−1.01579	+	1.01579i	−0.999873	+	0.0159192i	$0.994933\pi$
$32$			1.00000i			0.176777i
$33$	−0.942340	+	0.942340i	−0.164040	+	0.164040i
$34$	−0.476804			−0.0817713
$35$		0			0
$36$	2.91612			0.486020
$37$	−6.58530			−1.08262			−0.541308	−	0.840824i	$-0.682071\pi$
$37$	−6.58530			−1.08262			−0.541308	+	0.840824i	$0.682071\pi$
$38$	−1.79299	+	1.79299i	−0.290862	+	0.290862i
$39$	0.0575215	−	0.0575215i	0.00921081	−	0.00921081i
$40$		0			0
$41$	6.47983	+	6.47983i	1.01198	+	1.01198i	0.999927	+	0.0120528i	$0.00383661\pi$
$41$	6.47983	+	6.47983i	1.01198	+	1.01198i	0.0120528	+	0.999927i	$0.496163\pi$
$42$	0.183184	+	0.183184i	0.0282659	+	0.0282659i
$43$	8.57318			1.30740			0.653699	−	0.756755i	$-0.273216\pi$
$43$	8.57318			1.30740			0.653699	+	0.756755i	$0.273216\pi$
$44$	−3.25374	+	3.25374i	−0.490519	+	0.490519i
$45$		0			0
$46$	−3.88864	+	3.88864i	−0.573348	+	0.573348i
$47$	1.36150			0.198595			0.0992974	−	0.995058i	$-0.468340\pi$
$47$	1.36150			0.198595			0.0992974	+	0.995058i	$0.468340\pi$
$48$	−0.289618			−0.0418027
$49$			6.19988i			0.885697i
$50$		0			0
$51$		−	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	$-0.435117\pi$
$53$	−5.65569	−	5.65569i	−0.776869	−	0.776869i	−0.979297	+	0.202428i	$0.935117\pi$
$54$			1.71341i			0.233166i
$55$		0			0
$56$	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	$0.222706\pi$
$59$			9.89258i			1.28790i	−0.765066	+	0.643952i	$0.777294\pi$
$60$		0			0
$61$	3.88864	−	3.88864i	0.497889	−	0.497889i	−0.412891	−	0.910780i	$-0.635481\pi$
$61$	3.88864	−	3.88864i	0.497889	−	0.497889i	0.910780	+	0.412891i	$0.135481\pi$
$62$	−5.65569	−	5.65569i	−0.718274	−	0.718274i
$63$	1.84446	−	1.84446i	0.232380	−	0.232380i
$64$	−1.00000			−0.125000
$65$		0			0
$66$	−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	$0.987469\pi$
$68$		−	0.476804i		−	0.0578210i
$69$	−1.12622	−	1.12622i	−0.135581	−	0.135581i
$70$		0			0
$71$			8.63547i			1.02484i	0.858734	+	0.512421i	$0.171251\pi$
$71$			8.63547i			1.02484i	−0.858734	+	0.512421i	$0.828749\pi$
$72$			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			0
$76$	−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	0.704692	−	0.709513i	$-0.251085\pi$
$79$	−0.0428537	−	0.0428537i	−0.00482142	−	0.00482142i	−0.709513	+	0.704692i	$0.751085\pi$
$80$		0			0
$81$	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	$-0.225269\pi$
$83$	1.00000	+	1.00000i	0.109764	+	0.109764i	−0.650092	+	0.759856i	$0.725269\pi$
$84$	−0.183184	+	0.183184i	−0.0199870	+	0.0199870i
$85$		0			0
$86$			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	0.946578	−	0.322474i	$-0.104514\pi$
$89$	5.88779	+	5.88779i	0.624104	+	0.624104i	−0.322474	+	0.946578i	$0.604514\pi$
$90$		0			0
$91$		−	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			0
$96$		−	0.289618i		−	0.0295590i
$97$	11.8026			1.19838			0.599188	−	0.800608i	$-0.295490\pi$
$97$	11.8026			1.19838			0.599188	+	0.800608i	$0.295490\pi$
$98$	−6.19988			−0.626282
$99$	−9.48830	+	9.48830i	−0.953610	+	0.953610i
$100$		0			0
$101$	−0.605077	+	0.605077i	−0.0602074	+	0.0602074i	−0.736569	−	0.676362i	$-0.763556\pi$
$101$	−0.605077	+	0.605077i	−0.0602074	+	0.0602074i	0.676362	+	0.736569i	$0.263556\pi$
$102$	0.138091			0.0136730
$103$	10.9674	+	10.9674i	1.08065	+	1.08065i	0.996449	+	0.0841981i	$0.0268328\pi$
$103$	10.9674	+	10.9674i	1.08065	+	1.08065i	0.0841981	+	0.996449i	$0.473167\pi$
$104$	0.198612	+	0.198612i	0.0194755	+	0.0194755i
$105$		0			0
$106$	5.65569	−	5.65569i	0.549330	−	0.549330i
$107$	−0.674656	+	0.674656i	−0.0652215	+	0.0652215i	−0.738965	−	0.673744i	$-0.764685\pi$
$107$	−0.674656	+	0.674656i	−0.0652215	+	0.0652215i	0.673744	+	0.738965i	$0.264685\pi$
$108$	−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	$0.666565\pi$
$110$		0			0
$111$	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
$115$		0			0
$116$	−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			0
$121$		−	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
$125$		0			0
$126$	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			0
$131$	−4.28463	−	4.28463i	−0.374350	−	0.374350i	0.494709	−	0.869059i	$-0.335275\pi$
$131$	−4.28463	−	4.28463i	−0.374350	−	0.374350i	−0.869059	+	0.494709i	$0.835275\pi$
$132$	0.942340	−	0.942340i	0.0820201	−	0.0820201i
$133$	−2.26815			−0.196673
$134$	7.85685	−	7.85685i	0.678729	−	0.678729i
$135$		0			0
$136$	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	$-0.965883\pi$
$139$		−	2.52250i		−	0.213956i	0.994261	−	0.106978i	$-0.0341174\pi$
$140$		0			0
$141$	−0.394314			−0.0332072
$142$	−8.63547			−0.724673
$143$			1.29246i			0.108081i
$144$	−2.91612			−0.243010
$145$		0			0
$146$	−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	$0.461573\pi$
$150$		0			0
$151$		−	10.8414i		−	0.882262i	−0.897443	−	0.441131i	$-0.854577\pi$
$151$		−	10.8414i		−	0.882262i	0.897443	−	0.441131i	$-0.145423\pi$
$152$	1.79299	−	1.79299i	0.145431	−	0.145431i
$153$		−	1.39042i		−	0.112409i
$154$	−4.11600			−0.331677
$155$		0			0
$156$	−0.0575215	+	0.0575215i	−0.00460540	+	0.00460540i
$157$	7.88212			0.629061			0.314531	−	0.949247i	$-0.398153\pi$
$157$	7.88212			0.629061			0.314531	+	0.949247i	$0.398153\pi$
$158$	0.0428537	−	0.0428537i	0.00340926	−	0.00340926i
$159$	1.63799	+	1.63799i	0.129901	+	0.129901i
$160$		0			0
$161$	−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			0
$166$	−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			0
$171$	−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	$-0.715558\pi$
$173$	2.00873	−	2.00873i	0.152721	−	0.152721i	0.779332	+	0.626611i	$0.215558\pi$
$174$	0.265920	−	1.53680i	0.0201594	−	0.116505i
$175$		0			0
$176$	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	$0.843855\pi$
$180$		0			0
$181$	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
$185$		0			0
$186$	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			0
$191$	6.90356	−	6.90356i	0.499524	−	0.499524i	−0.411766	−	0.911290i	$-0.635088\pi$
$191$	6.90356	−	6.90356i	0.499524	−	0.499524i	0.911290	+	0.411766i	$0.135088\pi$
$192$	0.289618			0.0209013
$193$	24.3879			1.75548			0.877741	−	0.479135i	$-0.159050\pi$
$193$	24.3879			1.75548			0.877741	+	0.479135i	$0.159050\pi$
$194$			11.8026i			0.847380i
$195$		0			0
$196$		−	6.19988i		−	0.442848i
$197$	−2.47207	+	2.47207i	−0.176128	+	0.176128i	−0.789666	−	0.613538i	$-0.789746\pi$
$197$	−2.47207	+	2.47207i	−0.176128	+	0.176128i	0.613538	+	0.789666i	$0.289746\pi$
$198$	−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			0
$201$	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
$205$		0			0
$206$	−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			0
$211$	−11.8850	−	11.8850i	−0.818199	−	0.818199i	0.167648	−	0.985847i	$-0.446383\pi$
$211$	−11.8850	−	11.8850i	−0.818199	−	0.818199i	−0.985847	+	0.167648i	$0.946383\pi$
$212$	5.65569	+	5.65569i	0.388435	+	0.388435i
$213$		−	2.50099i		−	0.171365i
$214$	−0.674656	−	0.674656i	−0.0461185	−	0.0461185i
$215$		0			0
$216$		−	1.71341i		−	0.116583i
$217$		−	7.15449i		−	0.485678i
$218$		−	10.4345i		−	0.706715i
$219$		−	2.47932i		−	0.167537i
$220$		0			0
$221$	−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	$-0.411637\pi$
$223$	−10.2691	−	10.2691i	−0.687668	−	0.687668i	−0.961716	+	0.274048i	$0.911637\pi$
$224$	−0.632503	−	0.632503i	−0.0422609	−	0.0422609i
$225$		0			0
$226$	3.11631			0.207294
$227$	11.4326	−	11.4326i	0.758806	−	0.758806i	−0.217299	−	0.976105i	$-0.569725\pi$
$227$	11.4326	−	11.4326i	0.758806	−	0.758806i	0.976105	+	0.217299i	$0.0697246\pi$
$228$	0.519282	+	0.519282i	0.0343903	+	0.0343903i
$229$	11.1122	−	11.1122i	0.734316	−	0.734316i	−0.237156	−	0.971472i	$-0.576215\pi$
$229$	11.1122	−	11.1122i	0.734316	−	0.734316i	0.971472	+	0.237156i	$0.0762151\pi$
$230$		0			0
$231$		−	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	$-0.486063\pi$
$233$	−14.5816	−	14.5816i	−0.955273	−	0.955273i	−0.999042	+	0.0437692i	$0.986063\pi$
$234$	0.579176	+	0.579176i	0.0378619	+	0.0378619i
$235$		0			0
$236$		−	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			0
$241$			22.6204i			1.45711i	0.684987	+	0.728555i	$0.259808\pi$
$241$			22.6204i			1.45711i	−0.684987	+	0.728555i	$0.740192\pi$
$242$	10.1736			0.653985
$243$	−7.53020			−0.483063
$244$	−3.88864	+	3.88864i	−0.248944	+	0.248944i
$245$		0			0
$246$	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
$250$		0			0
$251$	−4.26661	+	4.26661i	−0.269306	+	0.269306i	−0.828821	−	0.559514i	$-0.810988\pi$
$251$	−4.26661	+	4.26661i	−0.269306	+	0.269306i	0.559514	+	0.828821i	$0.310988\pi$
$252$	−1.84446	+	1.84446i	−0.116190	+	0.116190i
$253$	25.3052			1.59092
$254$	2.18915			0.137359
$255$		0			0
$256$	1.00000			0.0625000
$257$	−0.892241	+	0.892241i	−0.0556564	+	0.0556564i	−0.734387	−	0.678731i	$-0.762530\pi$
$257$	−0.892241	+	0.892241i	−0.0556564	+	0.0556564i	0.678731	+	0.734387i	$0.262530\pi$
$258$		−	2.48294i		−	0.154581i
$259$	4.16522	−	4.16522i	0.258814	−	0.258814i
$260$		0			0
$261$	−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	$-0.715507\pi$
$263$	−20.3198			−1.25297			−0.626486	+	0.779433i	$0.715507\pi$
$264$	0.942340	+	0.942340i	0.0579970	+	0.0579970i
$265$		0			0
$266$		−	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	0.272081	−	0.962274i	$-0.412288\pi$
$269$	20.2449	−	20.2449i	1.23436	−	1.23436i	0.962274	−	0.272081i	$-0.0877118\pi$
$270$		0			0
$271$	−3.61114	−	3.61114i	−0.219361	−	0.219361i	0.588868	−	0.808229i	$-0.299574\pi$
$271$	−3.61114	−	3.61114i	−0.219361	−	0.219361i	−0.808229	+	0.588868i	$0.799574\pi$
$272$			0.476804i			0.0289105i
$273$			0.0727650i			0.00440394i
$274$	−14.1260			−0.853385
$275$		0			0
$276$	1.12622	+	1.12622i	0.0677903	+	0.0677903i
$277$	−1.15866	+	1.15866i	−0.0696169	+	0.0696169i	−0.741058	−	0.671441i	$-0.765676\pi$
$277$	−1.15866	+	1.15866i	−0.0696169	+	0.0696169i	0.671441	+	0.741058i	$0.265676\pi$
$278$	2.52250			0.151290
$279$	16.4927	−	16.4927i	0.987392	−	0.987392i
$280$		0			0
$281$	−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	0.494284	−	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
$285$		0			0
$286$	−1.29246			−0.0764248
$287$	−8.19704			−0.483856
$288$		−	2.91612i		−	0.171834i
$289$	16.7727			0.986627
$290$		0			0
$291$	−3.41825			−0.200382
$292$		−	8.56068i		−	0.500976i
$293$	−15.7998			−0.923035			−0.461517	−	0.887131i	$-0.652695\pi$
$293$	−15.7998			−0.923035			−0.461517	+	0.887131i	$0.652695\pi$
$294$	1.79559			0.104721
$295$		0			0
$296$			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			0
$301$	−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			0
$306$	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
$310$		0			0
$311$	−5.09331	+	5.09331i	−0.288815	+	0.288815i	−0.836612	−	0.547797i	$-0.815467\pi$
$311$	−5.09331	+	5.09331i	−0.288815	+	0.288815i	0.547797	+	0.836612i	$0.315467\pi$
$312$	−0.0575215	−	0.0575215i	−0.00325651	−	0.00325651i
$313$	9.62217	+	9.62217i	0.543877	+	0.543877i	0.924663	−	0.380786i	$-0.124347\pi$
$313$	9.62217	+	9.62217i	0.543877	+	0.543877i	−0.380786	+	0.924663i	$0.624347\pi$
$314$			7.88212i			0.444814i
$315$		0			0
$316$	0.0428537	+	0.0428537i	0.00241071	+	0.00241071i
$317$	22.6925			1.27454			0.637269	−	0.770641i	$-0.280064\pi$
$317$	22.6925			1.27454			0.637269	+	0.770641i	$0.280064\pi$
$318$	−1.63799	+	1.63799i	−0.0918538	+	0.0918538i
$319$	20.2529	−	14.2778i	1.13394	−	0.799406i
$320$		0			0
$321$	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
$325$		0			0
$326$	−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
$330$		0			0
$331$	3.40255	+	3.40255i	0.187021	+	0.187021i	0.794407	−	0.607386i	$-0.207782\pi$
$331$	3.40255	+	3.40255i	0.187021	+	0.187021i	−0.607386	+	0.794407i	$0.707782\pi$
$332$	−1.00000	−	1.00000i	−0.0548821	−	0.0548821i
$333$	19.2035			1.05235
$334$	7.60605	−	7.60605i	0.416185	−	0.416185i
$335$		0			0
$336$	0.183184	−	0.183184i	0.00999351	−	0.00999351i
$337$	20.6557			1.12519			0.562593	−	0.826734i	$-0.309804\pi$
$337$	20.6557			1.12519			0.562593	+	0.826734i	$0.309804\pi$
$338$	−12.9211			−0.702816
$339$			0.902538i			0.0490191i
$340$		0			0
$341$			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			0
$346$	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	$0.400938\pi$
$348$	1.53680	+	0.265920i	0.0823812	+	0.0142548i
$349$			25.2886i			1.35367i	0.736136	+	0.676834i	$0.236649\pi$
$349$			25.2886i			1.35367i	−0.736136	+	0.676834i	$0.763351\pi$
$350$		0			0
$351$	−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
$355$		0			0
$356$	−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	0.981720	+	0.190330i	$0.0609559\pi$
$359$	22.2072	+	22.2072i	1.17205	+	1.17205i	0.190330	+	0.981720i	$0.439044\pi$
$360$		0			0
$361$		−	12.5703i		−	0.661597i
$362$			20.7780i			1.09207i
$363$			2.94646i			0.154649i
$364$			0.251245i			0.0131688i
$365$		0			0
$366$	−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
$370$		0			0
$371$	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	$-0.495331\pi$
$373$	−19.0279	−	19.0279i	−0.985225	−	0.985225i	−0.999892	+	0.0146674i	$0.995331\pi$
$374$	−1.55140	+	1.55140i	−0.0802208	+	0.0802208i
$375$		0			0
$376$		−	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	0.371027	−	0.928622i	$-0.379006\pi$
$379$	−10.8552	−	10.8552i	−0.557595	−	0.557595i	−0.928622	+	0.371027i	$0.879006\pi$
$380$		0			0
$381$			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
$385$		0			0
$386$			24.3879i			1.24131i
$387$	−25.0004			−1.27084
$388$	−11.8026			−0.599188
$389$	8.76850	−	8.76850i	0.444581	−	0.444581i	−0.448967	−	0.893548i	$-0.648208\pi$
$389$	8.76850	−	8.76850i	0.444581	−	0.444581i	0.893548	+	0.448967i	$0.148208\pi$
$390$		0			0
$391$	−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			0
$396$	9.48830	−	9.48830i	0.476805	−	0.476805i
$397$	18.3875	−	18.3875i	0.922841	−	0.922841i	−0.0743886	−	0.997229i	$-0.523701\pi$
$397$	18.3875	−	18.3875i	0.922841	−	0.922841i	0.997229	+	0.0743886i	$0.0237005\pi$
$398$	11.3378			0.568310
$399$	0.656896			0.0328859
$400$		0			0
$401$	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
$405$		0			0
$406$	−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	0.352816	−	0.935693i	$-0.385224\pi$
$409$	−11.7879	−	11.7879i	−0.582876	−	0.582876i	−0.935693	+	0.352816i	$0.885224\pi$
$410$		0			0
$411$		−	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
$415$		0			0
$416$	−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			0
$421$	−4.16276	−	4.16276i	−0.202880	−	0.202880i	0.598353	−	0.801233i	$-0.295822\pi$
$421$	−4.16276	−	4.16276i	−0.202880	−	0.202880i	−0.801233	+	0.598353i	$0.795822\pi$
$422$	11.8850	−	11.8850i	0.578554	−	0.578554i
$423$	−3.97029			−0.193042
$424$	−5.65569	+	5.65569i	−0.274665	+	0.274665i
$425$		0			0
$426$	2.50099			0.121173
$427$			4.91915i			0.238054i
$428$	0.674656	−	0.674656i	0.0326107	−	0.0326107i
$429$		−	0.374320i		−	0.0180723i
$430$		0			0
$431$	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
$435$		0			0
$436$	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	$0.624982\pi$
$440$		0			0
$441$		−	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
$445$		0			0
$446$	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	0.368772	−	0.929520i	$-0.379778\pi$
$449$	−11.8820	−	11.8820i	−0.560748	−	0.560748i	−0.929520	+	0.368772i	$0.879778\pi$
$450$		0			0
$451$	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			0
$456$	−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
$460$		0			0
$461$	−26.1001	−	26.1001i	−1.21560	−	1.21560i	−0.969156	−	0.246449i	$-0.920736\pi$
$461$	−26.1001	−	26.1001i	−1.21560	−	1.21560i	−0.246449	−	0.969156i	$-0.579264\pi$
$462$	1.19207			0.0554599
$463$	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			0
$466$	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
$470$		0			0
$471$	−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
$475$		0			0
$476$	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	−0.810676	−	0.585495i	$-0.800900\pi$
$479$	−4.92833	+	4.92833i	−0.225181	+	0.225181i	0.585495	+	0.810676i	$0.300900\pi$
$480$		0			0
$481$	1.30792	−	1.30792i	0.0596359	−	0.0596359i
$482$	−22.6204			−1.03033
$483$	1.42467			0.0648249
$484$			10.1736i			0.462437i
$485$		0			0
$486$		−	7.53020i		−	0.341577i
$487$	−2.73756	+	2.73756i	−0.124050	+	0.124050i	−0.766406	−	0.642356i	$-0.777957\pi$
$487$	−2.73756	+	2.73756i	−0.124050	+	0.124050i	0.642356	+	0.766406i	$0.277957\pi$
$488$	−3.88864	−	3.88864i	−0.176030	−	0.176030i
$489$		−	6.46199i		−	0.292221i
$490$		0			0
$491$	−16.0568	−	16.0568i	−0.724631	−	0.724631i	0.244914	−	0.969545i	$-0.421240\pi$
$491$	−16.0568	−	16.0568i	−0.724631	−	0.724631i	−0.969545	+	0.244914i	$0.921240\pi$
$492$	1.87667	+	1.87667i	0.0846070	+	0.0846070i
$493$	−0.437791	+	2.53007i	−0.0197171	+	0.113949i
$494$		−	0.712219i		−	0.0320443i
$495$		0			0
$496$	−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	$0.579751\pi$
$500$		0			0
$501$	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			0
$506$			25.3052i			1.12495i
$507$		−	3.74218i		−	0.166196i
$508$			2.18915i			0.0971277i
$509$		−	12.9806i		−	0.575354i	−0.957728	−	0.287677i	$-0.907117\pi$
$509$		−	12.9806i		−	0.575354i	0.957728	−	0.287677i	$-0.0928829\pi$
$510$		0			0
$511$	−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
$515$		0			0
$516$	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			0
$521$			18.4390i			0.807827i	0.914797	+	0.403914i	$0.132350\pi$
$521$			18.4390i			0.807827i	−0.914797	+	0.403914i	$0.867650\pi$
$522$	2.67752	−	15.4739i	0.117192	−	0.677272i
$523$	−13.6216	−	13.6216i	−0.595631	−	0.595631i	0.343516	−	0.939147i	$-0.388382\pi$
$523$	−13.6216	−	13.6216i	−0.595631	−	0.595631i	−0.939147	+	0.343516i	$0.888382\pi$
$524$	4.28463	+	4.28463i	0.187175	+	0.187175i
$525$		0			0
$526$		−	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			0
$531$		−	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			0
$536$	−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
$540$		0			0
$541$	−16.5747	+	16.5747i	−0.712602	+	0.712602i	−0.967079	−	0.254477i	$-0.918097\pi$
$541$	−16.5747	+	16.5747i	−0.712602	+	0.712602i	0.254477	+	0.967079i	$0.418097\pi$
$542$	3.61114	−	3.61114i	0.155112	−	0.155112i
$543$	−6.01768			−0.258244
$544$	−0.476804			−0.0204428
$545$		0			0
$546$	−0.0727650			−0.00311406
$547$	8.23169	−	8.23169i	0.351961	−	0.351961i	−0.508877	−	0.860839i	$-0.669939\pi$
$547$	8.23169	−	8.23169i	0.351961	−	0.351961i	0.860839	+	0.508877i	$0.169939\pi$
$548$		−	14.1260i		−	0.603435i
$549$	−11.3397	+	11.3397i	−0.483968	+	0.483968i
$550$		0			0
$551$	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
$555$		0			0
$556$			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			0
$561$	−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
$565$		0			0
$566$	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	−0.447397	−	0.894336i	$-0.647649\pi$
$569$	10.6612	−	10.6612i	0.446939	−	0.446939i	0.894336	+	0.447397i	$0.147649\pi$
$570$		0			0
$571$	−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
$575$		0			0
$576$	2.91612			0.121505
$577$	−24.2872			−1.01109			−0.505545	−	0.862800i	$-0.668709\pi$
$577$	−24.2872			−1.01109			−0.505545	+	0.862800i	$0.668709\pi$
$578$			16.7727i			0.697651i
$579$	−7.06318			−0.293536
$580$		0			0
$581$	−1.26501			−0.0524813
$582$		−	3.41825i		−	0.141691i
$583$	−36.8043			−1.52428
$584$	8.56068			0.354244
$585$		0			0
$586$		−	15.7998i		−	0.652684i
$587$	−5.49283	+	5.49283i	−0.226714	+	0.226714i	−0.811318	−	0.584605i	$-0.801250\pi$
$587$	−5.49283	+	5.49283i	−0.226714	+	0.226714i	0.584605	+	0.811318i	$0.301250\pi$
$588$			1.79559i			0.0740490i
$589$	−20.2812			−0.835674
$590$		0			0
$591$	0.715956	−	0.715956i	0.0294505	−	0.0294505i
$592$	−6.58530			−0.270654
$593$	−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			0
$596$	−2.94004			−0.120429
$597$			3.28361i			0.134389i
$598$		−	1.54466i		−	0.0631658i
$599$	−20.0950	−	20.0950i	−0.821059	−	0.821059i	0.165201	−	0.986260i	$-0.447173\pi$
$599$	−20.0950	−	20.0950i	−0.821059	−	0.821059i	−0.986260	+	0.165201i	$0.947173\pi$
$600$		0			0
$601$	−2.21091	+	2.21091i	−0.0901848	+	0.0901848i	−0.750760	−	0.660575i	$-0.770313\pi$
$601$	−2.21091	+	2.21091i	−0.0901848	+	0.0901848i	0.660575	+	0.750760i	$0.270313\pi$
$602$	−5.42256	−	5.42256i	−0.221007	−	0.221007i
$603$	22.9115	+	22.9115i	0.933030	+	0.933030i
$604$			10.8414i			0.441131i
$605$		0			0
$606$	0.175241	+	0.175241i	0.00711868	+	0.00711868i
$607$	−37.1113			−1.50630			−0.753150	−	0.657849i	$-0.771467\pi$
$607$	−37.1113			−1.50630			−0.753150	+	0.657849i	$0.771467\pi$
$608$	−1.79299	+	1.79299i	−0.0727155	+	0.0727155i
$609$	1.14023	−	0.803837i	0.0462043	−	0.0325731i
$610$		0			0
$611$	−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	$-0.550475\pi$
$613$	20.5386	−	20.5386i	0.829547	−	0.829547i	0.987454	+	0.157907i	$0.0504745\pi$
$614$	15.9584			0.644028
$615$		0			0
$616$	4.11600			0.165838
$617$	−1.48087			−0.0596176			−0.0298088	−	0.999556i	$-0.509490\pi$
$617$	−1.48087			−0.0596176			−0.0298088	+	0.999556i	$0.509490\pi$
$618$	3.17634	−	3.17634i	0.127771	−	0.127771i
$619$	−31.9416	+	31.9416i	−1.28384	+	1.28384i	−0.345380	+	0.938463i	$0.612250\pi$
$619$	−31.9416	+	31.9416i	−1.28384	+	1.28384i	−0.938463	+	0.345380i	$0.887750\pi$
$620$		0			0
$621$	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
$625$		0			0
$626$	−9.62217	+	9.62217i	−0.384579	+	0.384579i
$627$	−3.37922			−0.134953
$628$	−7.88212			−0.314531
$629$		−	3.13990i		−	0.125196i
$630$		0			0
$631$			32.1454i			1.27969i	0.768505	+	0.639844i	$0.221001\pi$
$631$			32.1454i			1.27969i	−0.768505	+	0.639844i	$0.778999\pi$
$632$	−0.0428537	+	0.0428537i	−0.00170463	+	0.00170463i
$633$	3.44211	+	3.44211i	0.136812	+	0.136812i
$634$			22.6925i			0.901235i
$635$		0			0
$636$	−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
$640$		0			0
$641$	−30.2409	+	30.2409i	−1.19444	+	1.19444i	−0.218636	+	0.975806i	$0.570161\pi$
$641$	−30.2409	+	30.2409i	−1.19444	+	1.19444i	−0.975806	+	0.218636i	$0.929839\pi$
$642$	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
$645$		0			0
$646$	−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	$0.902843\pi$
$648$		−	8.25213i		−	0.324174i
$649$	32.1879	+	32.1879i	1.26348	+	1.26348i
$650$		0			0
$651$			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
$655$		0			0
$656$	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	0.858443	−	0.512909i	$-0.171432\pi$
$659$	8.87020	+	8.87020i	0.345534	+	0.345534i	−0.512909	+	0.858443i	$0.671432\pi$
$660$		0			0
$661$	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
$665$		0			0
$666$			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			0
$671$		−	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
$675$		0			0
$676$		−	12.9211i		−	0.496966i
$677$	−1.01813			−0.0391300			−0.0195650	−	0.999809i	$-0.506228\pi$
$677$	−1.01813			−0.0391300			−0.0195650	+	0.999809i	$0.506228\pi$
$678$	−0.902538			−0.0346618
$679$	−7.46521	+	7.46521i	−0.286489	+	0.286489i
$680$		0			0
$681$	−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	$-0.129306\pi$
$683$	13.6805	+	13.6805i	0.523470	+	0.523470i	−0.395147	+	0.918618i	$0.629306\pi$
$684$	5.22859	+	5.22859i	0.199920	+	0.199920i
$685$		0			0
$686$	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			0
$691$	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
$695$		0			0
$696$	−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
$700$		0			0
$701$			22.9970i			0.868586i	0.900772	+	0.434293i	$0.143002\pi$
$701$			22.9970i			0.868586i	−0.900772	+	0.434293i	$0.856998\pi$
$702$	−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			0
$706$	−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	$0.717255\pi$
$710$		0			0
$711$	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
$715$		0			0
$716$	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	$0.0327706\pi$
$719$			5.51139i			0.205540i	−0.994705	+	0.102770i	$0.967229\pi$
$720$		0			0
$721$	−13.8738			−0.516687
$722$	12.5703			0.467820
$723$		−	6.55127i		−	0.243645i
$724$	−20.7780			−0.772210
$725$		0			0
$726$	−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
$730$		0			0
$731$			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
$735$		0			0
$736$	−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	0.994507	−	0.104669i	$-0.0333782\pi$
$739$	24.1899	+	24.1899i	0.889839	+	0.889839i	−0.104669	+	0.994507i	$0.533378\pi$
$740$		0			0
$741$	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
$745$		0			0
$746$	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
$750$		0			0
$751$	−34.6175	−	34.6175i	−1.26321	−	1.26321i	−0.949528	−	0.313682i	$-0.898437\pi$
$751$	−34.6175	−	34.6175i	−1.26321	−	1.26321i	−0.313682	−	0.949528i	$-0.601563\pi$
$752$	1.36150			0.0496487
$753$	1.23569	−	1.23569i	0.0450309	−	0.0450309i
$754$	−0.871535	−	1.23626i	−0.0317394	−	0.0450218i
$755$		0			0
$756$	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			0
$761$	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
$765$		0			0
$766$	−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	−0.425769	−	0.904832i	$-0.639996\pi$
$769$	13.2848	−	13.2848i	0.479063	−	0.479063i	0.904832	+	0.425769i	$0.139996\pi$
$770$		0			0
$771$	0.258409	−	0.258409i	0.00930636	−	0.00930636i
$772$	−24.3879			−0.877741
$773$	−23.8909			−0.859294			−0.429647	−	0.902997i	$-0.641362\pi$
$773$	−23.8909			−0.859294			−0.429647	+	0.902997i	$0.641362\pi$
$774$		−	25.0004i		−	0.898622i
$775$		0			0
$776$		−	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			0
$781$	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
$785$		0			0
$786$	−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			0
$791$	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
$795$		0			0
$796$			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
$800$		0			0
$801$	−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
$805$		0			0
$806$	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	$-0.722107\pi$
$809$	3.52028	−	3.52028i	0.123766	−	0.123766i	0.766277	+	0.642510i	$0.222107\pi$
$810$		0			0
$811$		−	2.40718i		−	0.0845277i	−0.999106	−	0.0422638i	$-0.986543\pi$
$811$		−	2.40718i		−	0.0845277i	0.999106	−	0.0422638i	$-0.0134570\pi$
$812$	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
$815$		0			0
$816$		−	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			0
$821$		−	36.8938i		−	1.28760i	−0.765193	−	0.643801i	$-0.777357\pi$
$821$		−	36.8938i		−	1.28760i	0.765193	−	0.643801i	$-0.222643\pi$
$822$	4.09115			0.142695
$823$	−21.2449			−0.740550			−0.370275	−	0.928922i	$-0.620736\pi$
$823$	−21.2449			−0.740550			−0.370275	+	0.928922i	$0.620736\pi$
$824$	10.9674	−	10.9674i	0.382066	−	0.382066i
$825$		0			0
$826$	6.25709	−	6.25709i	0.217712	−	0.217712i
$827$	17.7303			0.616542			0.308271	−	0.951299i	$-0.400250\pi$
$827$	17.7303			0.616542			0.308271	+	0.951299i	$0.400250\pi$
$828$	11.3397	+	11.3397i	0.394083	+	0.394083i
$829$	−16.5417	−	16.5417i	−0.574516	−	0.574516i	0.358871	−	0.933387i	$-0.383162\pi$
$829$	−16.5417	−	16.5417i	−0.574516	−	0.574516i	−0.933387	+	0.358871i	$0.883162\pi$
$830$		0			0
$831$	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
$835$		0			0
$836$	−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	−0.418706	−	0.908122i	$-0.637516\pi$
$839$	14.1762	−	14.1762i	0.489416	−	0.489416i	0.908122	+	0.418706i	$0.137516\pi$
$840$		0			0
$841$	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
$845$		0			0
$846$		−	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			0
$851$	−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
$855$		0			0
$856$	0.674656	+	0.674656i	0.0230593	+	0.0230593i
$857$	−7.30296	+	7.30296i	−0.249464	+	0.249464i	−0.820751	−	0.571286i	$-0.806445\pi$
$857$	−7.30296	+	7.30296i	−0.249464	+	0.249464i	0.571286	+	0.820751i	$0.306445\pi$
$858$	0.374320			0.0127791
$859$	13.3341	−	13.3341i	0.454953	−	0.454953i	−0.442042	−	0.896995i	$-0.645746\pi$
$859$	13.3341	−	13.3341i	0.454953	−	0.454953i	0.896995	+	0.442042i	$0.145746\pi$
$860$		0			0
$861$	2.37401			0.0809059
$862$			0.757725i			0.0258082i
$863$	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			0
$866$	10.8919			0.370122
$867$	−4.85766			−0.164975
$868$			7.15449i			0.242839i
$869$	−0.278870			−0.00946001
$870$		0			0
$871$	3.12093			0.105749
$872$			10.4345i			0.353357i
$873$	−34.4179			−1.16487
$874$	−13.9446			−0.471683
$875$		0			0
$876$			2.47932i			0.0837686i
$877$	36.2899	−	36.2899i	1.22542	−	1.22542i	0.259747	−	0.965677i	$-0.416361\pi$
$877$	36.2899	−	36.2899i	1.22542	−	1.22542i	0.965677	−	0.259747i	$-0.0836390\pi$
$878$		−	16.0340i		−	0.541122i
$879$	4.57590			0.154341
$880$		0			0
$881$	−31.7249	+	31.7249i	−1.06884	+	1.06884i	−0.0713908	+	0.997448i	$0.522744\pi$
$881$	−31.7249	+	31.7249i	−1.06884	+	1.06884i	−0.997448	+	0.0713908i	$0.977256\pi$
$882$	18.0796			0.608772
$883$	−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
$885$		0			0
$886$	−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			0
$891$	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
$895$		0			0
$896$	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			0
$901$	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
$905$		0			0
$906$	−3.13986			−0.104315
$907$	−52.1407			−1.73130			−0.865652	−	0.500646i	$-0.833096\pi$
$907$	−52.1407			−1.73130			−0.865652	+	0.500646i	$0.833096\pi$
$908$	−11.4326	+	11.4326i	−0.379403	+	0.379403i
$909$	1.76448	−	1.76448i	0.0585241	−	0.0585241i
$910$		0			0
$911$	22.5889	+	22.5889i	0.748403	+	0.748403i	0.974179	−	0.225776i	$-0.0724918\pi$
$911$	22.5889	+	22.5889i	0.748403	+	0.748403i	−0.225776	+	0.974179i	$0.572492\pi$
$912$	−0.519282	−	0.519282i	−0.0171952	−	0.0171952i
$913$	6.50748			0.215366
$914$	−25.4126	+	25.4126i	−0.840575	+	0.840575i
$915$		0			0
$916$	−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	$-0.993226\pi$
$919$		−	1.29013i		−	0.0425574i	0.999774	−	0.0212787i	$-0.00677373\pi$
$920$		0			0
$921$			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			0
$926$	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	$0.161933\pi$
$929$			29.6911i			0.974134i	−0.873365	+	0.487067i	$0.838067\pi$
$930$		0			0
$931$	−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
$935$		0			0
$936$	−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	$0.499423\pi$
$938$			9.93897i			0.324519i
$939$	−2.78675	−	2.78675i	−0.0909421	−	0.0909421i
$940$		0			0
$941$			32.2353i			1.05084i	0.850842	+	0.525421i	$0.176092\pi$
$941$			32.2353i			1.05084i	−0.850842	+	0.525421i	$0.823908\pi$
$942$		−	2.28280i		−	0.0743776i
$943$			50.3954i			1.64110i
$944$			9.89258i			0.321976i
$945$		0			0
$946$	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
$950$		0			0
$951$	−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	$-0.0733015\pi$
$953$	23.0094	+	23.0094i	0.745348	+	0.745348i	−0.228254	+	0.973602i	$0.573302\pi$
$954$	−16.4927	+	16.4927i	−0.533971	+	0.533971i
$955$		0			0
$956$			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			0
$961$		−	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
$965$		0			0
$966$			1.42467i			0.0458381i
$967$	0.317494			0.0102099			0.00510495	−	0.999987i	$-0.498375\pi$
$967$	0.317494			0.0102099			0.00510495	+	0.999987i	$0.498375\pi$
$968$	−10.1736			−0.326993
$969$	0.247596	−	0.247596i	0.00795393	−	0.00795393i
$970$		0			0
$971$	−23.8271	+	23.8271i	−0.764647	+	0.764647i	−0.977159	−	0.212512i	$-0.931836\pi$
$971$	−23.8271	+	23.8271i	−0.764647	+	0.764647i	0.212512	+	0.977159i	$0.431836\pi$
$972$	7.53020			0.241531
$973$	1.59549	+	1.59549i	0.0511491	+	0.0511491i
$974$	−2.73756	−	2.73756i	−0.0877169	−	0.0877169i
$975$		0			0
$976$	3.88864	−	3.88864i	0.124472	−	0.124472i
$977$	−24.5169	+	24.5169i	−0.784365	+	0.784365i	−0.980564	−	0.196199i	$-0.937140\pi$
$977$	−24.5169	+	24.5169i	−0.784365	+	0.784365i	0.196199	+	0.980564i	$0.437140\pi$
$978$	6.46199			0.206632
$979$	38.3146			1.22454
$980$		0			0
$981$	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			0
$986$	−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
$990$		0			0
$991$		−	5.66996i		−	0.180112i	−0.995937	−	0.0900561i	$-0.971295\pi$
$991$		−	5.66996i		−	0.180112i	0.995937	−	0.0900561i	$-0.0287046\pi$
$992$	−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
$995$		0			0
$996$	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	1450.2.j.h.1293.3		12
5.2	odd	4		1450.2.e.h.307.4		12
5.3	odd	4		290.2.e.f.17.3	✓	12
5.4	even	2		290.2.j.f.133.4	yes	12
29.12	odd	4		1450.2.e.h.1143.3		12
145.12	even	4	inner	1450.2.j.h.157.3		12
145.99	odd	4		290.2.e.f.273.4	yes	12
145.128	even	4		290.2.j.f.157.4	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
290.2.e.f.17.3	✓	12	5.3	odd	4
290.2.e.f.273.4	yes	12	145.99	odd	4
290.2.j.f.133.4	yes	12	5.4	even	2
290.2.j.f.157.4	yes	12	145.128	even	4
1450.2.e.h.307.4		12	5.2	odd	4
1450.2.e.h.1143.3		12	29.12	odd	4
1450.2.j.h.157.3		12	145.12	even	4	inner
1450.2.j.h.1293.3		12	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 1450 = 2 \cdot 5^{2} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1450.j (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} -0.289618 q^{3} -1.00000 q^{4} -0.289618i q^{6} +(-0.632503 + 0.632503i) q^{7} -1.00000i q^{8} -2.91612 q^{9} +(3.25374 - 3.25374i) q^{11} +0.289618 q^{12} +(-0.198612 + 0.198612i) q^{13} +(-0.632503 - 0.632503i) q^{14} +1.00000 q^{16} +0.476804i q^{17} -2.91612i q^{18} +(1.79299 + 1.79299i) q^{19} +(0.183184 - 0.183184i) q^{21} +(3.25374 + 3.25374i) q^{22} +(3.88864 + 3.88864i) q^{23} +0.289618i q^{24} +(-0.198612 - 0.198612i) q^{26} +1.71341 q^{27} +(0.632503 - 0.632503i) q^{28} +(5.30631 + 0.918177i) q^{29} +(-5.65569 + 5.65569i) q^{31} +1.00000i q^{32} +(-0.942340 + 0.942340i) q^{33} -0.476804 q^{34} +2.91612 q^{36} -6.58530 q^{37} +(-1.79299 + 1.79299i) q^{38} +(0.0575215 - 0.0575215i) q^{39} +(6.47983 + 6.47983i) q^{41} +(0.183184 + 0.183184i) q^{42} +8.57318 q^{43} +(-3.25374 + 3.25374i) q^{44} +(-3.88864 + 3.88864i) q^{46} +1.36150 q^{47} -0.289618 q^{48} +6.19988i q^{49} -0.138091i q^{51} +(0.198612 - 0.198612i) q^{52} +(-5.65569 - 5.65569i) q^{53} +1.71341i q^{54} +(0.632503 + 0.632503i) q^{56} +(-0.519282 - 0.519282i) q^{57} +(-0.918177 + 5.30631i) q^{58} +9.89258i q^{59} +(3.88864 - 3.88864i) q^{61} +(-5.65569 - 5.65569i) q^{62} +(1.84446 - 1.84446i) q^{63} -1.00000 q^{64} +(-0.942340 - 0.942340i) q^{66} +(-7.85685 - 7.85685i) q^{67} -0.476804i q^{68} +(-1.12622 - 1.12622i) q^{69} +8.63547i q^{71} +2.91612i q^{72} +8.56068i q^{73} -6.58530i q^{74} +(-1.79299 - 1.79299i) q^{76} +4.11600i q^{77} +(0.0575215 + 0.0575215i) q^{78} +(-0.0428537 - 0.0428537i) q^{79} +8.25213 q^{81} +(-6.47983 + 6.47983i) q^{82} +(1.00000 + 1.00000i) q^{83} +(-0.183184 + 0.183184i) q^{84} +8.57318i q^{86} +(-1.53680 - 0.265920i) q^{87} +(-3.25374 - 3.25374i) q^{88} +(5.88779 + 5.88779i) q^{89} -0.251245i q^{91} +(-3.88864 - 3.88864i) q^{92} +(1.63799 - 1.63799i) q^{93} +1.36150i q^{94} -0.289618i q^{96} +11.8026 q^{97} -6.19988 q^{98} +(-9.48830 + 9.48830i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 12 q^{4} + 4 q^{7} + 28 q^{9} + 10 q^{11} - 2 q^{13} + 4 q^{14} + 12 q^{16} - 16 q^{19} - 16 q^{21} + 10 q^{22} - 4 q^{23} - 2 q^{26} - 12 q^{27} - 4 q^{28} + 20 q^{29} + 18 q^{31} + 6 q^{33} - 28 q^{36}+ \cdots + 36 q^{99}+O(q^{100}) \) 12 * q - 12 * q^4 + 4 * q^7 + 28 * q^9 + 10 * q^11 - 2 * q^13 + 4 * q^14 + 12 * q^16 - 16 * q^19 - 16 * q^21 + 10 * q^22 - 4 * q^23 - 2 * q^26 - 12 * q^27 - 4 * q^28 + 20 * q^29 + 18 * q^31 + 6 * q^33 - 28 * q^36 + 16 * q^38 - 38 * q^39 + 36 * q^41 - 16 * q^42 + 12 * q^43 - 10 * q^44 + 4 * q^46 - 20 * q^47 + 2 * q^52 + 18 * q^53 - 4 * q^56 + 32 * q^57 - 16 * q^58 - 4 * q^61 + 18 * q^62 + 24 * q^63 - 12 * q^64 + 6 * q^66 + 12 * q^67 + 12 * q^69 + 16 * q^76 - 38 * q^78 + 30 * q^79 + 44 * q^81 - 36 * q^82 + 12 * q^83 + 16 * q^84 + 16 * q^87 - 10 * q^88 + 20 * q^89 + 4 * q^92 - 2 * q^93 - 76 * q^97 - 16 * q^98 + 36 * q^99

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