LMFDB - Embedded newform 1155.2.c.f.694.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1155,2,Mod(694,1155)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1155, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1, 0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("1155.694");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1155 = 3 \cdot 5 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1155.c (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$9.22272143346$
Analytic rank:	$0$
Dimension:	$20$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 33 x^{18} + 456 x^{16} + 3426 x^{14} + 15210 x^{12} + 40640 x^{10} + 63865 x^{8} + 55281 x^{6} + \cdots + 4 $ x^20 + 33x^18 + 456x^16 + 3426x^14 + 15210x^12 + 40640x^10 + 63865x^8 + 55281x^6 + 22984x^4 + 3428*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			694.16
Root			$1.93467i$ of defining polynomial
Character	$\chi$	$=$	1155.694
Dual form			1155.2.c.f.694.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.93467i q^{2} -1.00000i q^{3} -1.74296 q^{4} +(1.72871 + 1.41829i) q^{5} +1.93467 q^{6} -1.00000i q^{7} +0.497289i q^{8} -1.00000 q^{9} +O(q^{10})$	\(q+1.93467i q^{2} -1.00000i q^{3} -1.74296 q^{4} +(1.72871 + 1.41829i) q^{5} +1.93467 q^{6} -1.00000i q^{7} +0.497289i q^{8} -1.00000 q^{9} +(-2.74393 + 3.34450i) q^{10} +1.00000 q^{11} +1.74296i q^{12} -0.486284i q^{13} +1.93467 q^{14} +(1.41829 - 1.72871i) q^{15} -4.44801 q^{16} +4.43871i q^{17} -1.93467i q^{18} -3.34908 q^{19} +(-3.01308 - 2.47202i) q^{20} -1.00000 q^{21} +1.93467i q^{22} +5.94604i q^{23} +0.497289 q^{24} +(0.976909 + 4.90364i) q^{25} +0.940801 q^{26} +1.00000i q^{27} +1.74296i q^{28} +3.07793 q^{29} +(3.34450 + 2.74393i) q^{30} +6.58078 q^{31} -7.61087i q^{32} -1.00000i q^{33} -8.58745 q^{34} +(1.41829 - 1.72871i) q^{35} +1.74296 q^{36} +6.41028i q^{37} -6.47938i q^{38} -0.486284 q^{39} +(-0.705299 + 0.859670i) q^{40} +8.83019 q^{41} -1.93467i q^{42} -5.13533i q^{43} -1.74296 q^{44} +(-1.72871 - 1.41829i) q^{45} -11.5036 q^{46} +11.8075i q^{47} +4.44801i q^{48} -1.00000 q^{49} +(-9.48693 + 1.89000i) q^{50} +4.43871 q^{51} +0.847574i q^{52} -6.16737i q^{53} -1.93467 q^{54} +(1.72871 + 1.41829i) q^{55} +0.497289 q^{56} +3.34908i q^{57} +5.95479i q^{58} -8.45061 q^{59} +(-2.47202 + 3.01308i) q^{60} +2.24120 q^{61} +12.7317i q^{62} +1.00000i q^{63} +5.82852 q^{64} +(0.689692 - 0.840646i) q^{65} +1.93467 q^{66} -6.81402i q^{67} -7.73649i q^{68} +5.94604 q^{69} +(3.34450 + 2.74393i) q^{70} +3.62954 q^{71} -0.497289i q^{72} +15.7313i q^{73} -12.4018 q^{74} +(4.90364 - 0.976909i) q^{75} +5.83732 q^{76} -1.00000i q^{77} -0.940801i q^{78} -12.0868 q^{79} +(-7.68934 - 6.30857i) q^{80} +1.00000 q^{81} +17.0835i q^{82} -14.0401i q^{83} +1.74296 q^{84} +(-6.29537 + 7.67326i) q^{85} +9.93518 q^{86} -3.07793i q^{87} +0.497289i q^{88} +3.85548 q^{89} +(2.74393 - 3.34450i) q^{90} -0.486284 q^{91} -10.3637i q^{92} -6.58078i q^{93} -22.8436 q^{94} +(-5.78961 - 4.74997i) q^{95} -7.61087 q^{96} -3.75732i q^{97} -1.93467i q^{98} -1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 26 q^{4} - 2 q^{5} + 6 q^{6} - 20 q^{9}+O(q^{10}) $ 20 * q - 26 * q^4 - 2 * q^5 + 6 * q^6 - 20 * q^9	$ 20 q - 26 q^{4} - 2 q^{5} + 6 q^{6} - 20 q^{9} + 2 q^{10} + 20 q^{11} + 6 q^{14} - 2 q^{15} + 38 q^{16} - 34 q^{19} + 4 q^{20} - 20 q^{21} - 18 q^{24} - 4 q^{25} + 28 q^{26} - 10 q^{29} - 6 q^{30} + 12 q^{31} - 32 q^{34} - 2 q^{35} + 26 q^{36} - 2 q^{40} + 52 q^{41} - 26 q^{44} + 2 q^{45} + 40 q^{46} - 20 q^{49} + 6 q^{50} + 6 q^{51} - 6 q^{54} - 2 q^{55} - 18 q^{56} - 14 q^{59} - 28 q^{60} + 78 q^{61} - 26 q^{64} - 4 q^{65} + 6 q^{66} - 18 q^{69} - 6 q^{70} - 8 q^{74} - 8 q^{75} + 84 q^{76} - 52 q^{79} - 40 q^{80} + 20 q^{81} + 26 q^{84} - 24 q^{85} + 4 q^{86} - 10 q^{89} - 2 q^{90} - 96 q^{94} - 30 q^{95} + 62 q^{96} - 20 q^{99}+O(q^{100}) $ 20 * q - 26 * q^4 - 2 * q^5 + 6 * q^6 - 20 * q^9 + 2 * q^10 + 20 * q^11 + 6 * q^14 - 2 * q^15 + 38 * q^16 - 34 * q^19 + 4 * q^20 - 20 * q^21 - 18 * q^24 - 4 * q^25 + 28 * q^26 - 10 * q^29 - 6 * q^30 + 12 * q^31 - 32 * q^34 - 2 * q^35 + 26 * q^36 - 2 * q^40 + 52 * q^41 - 26 * q^44 + 2 * q^45 + 40 * q^46 - 20 * q^49 + 6 * q^50 + 6 * q^51 - 6 * q^54 - 2 * q^55 - 18 * q^56 - 14 * q^59 - 28 * q^60 + 78 * q^61 - 26 * q^64 - 4 * q^65 + 6 * q^66 - 18 * q^69 - 6 * q^70 - 8 * q^74 - 8 * q^75 + 84 * q^76 - 52 * q^79 - 40 * q^80 + 20 * q^81 + 26 * q^84 - 24 * q^85 + 4 * q^86 - 10 * q^89 - 2 * q^90 - 96 * q^94 - 30 * q^95 + 62 * q^96 - 20 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1155\mathbb{Z}\right)^\times$.

$n$	$211$	$232$	$386$	$661$
$\chi(n)$	$1$	$-1$	$1$	$1$

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 $

$2$			1.93467i			1.36802i	0.729472	+	0.684010i	$0.239766\pi$
$2$			1.93467i			1.36802i	−0.729472	+	0.684010i	$0.760234\pi$
$3$		−	1.00000i		−	0.577350i
$3$		−	1.00000i		−	0.577350i
$4$	−1.74296			−0.871480
$5$	1.72871	+	1.41829i	0.773105	+	0.634278i
$5$	1.72871	+	1.41829i	0.773105	+	0.634278i
$6$	1.93467			0.789827
$7$		−	1.00000i		−	0.377964i
$7$		−	1.00000i		−	0.377964i
$8$			0.497289i			0.175818i
$9$	−1.00000			−0.333333
$10$	−2.74393	+	3.34450i	−0.867706	+	1.05762i
$11$	1.00000			0.301511
$11$	1.00000			0.301511
$12$			1.74296i			0.503149i
$13$		−	0.486284i		−	0.134871i	−0.997724	−	0.0674355i	$-0.978518\pi$
$13$		−	0.486284i		−	0.134871i	0.997724	−	0.0674355i	$-0.0214817\pi$
$14$	1.93467			0.517063
$15$	1.41829	−	1.72871i	0.366201	−	0.446352i
$16$	−4.44801			−1.11200
$17$			4.43871i			1.07654i	0.842771	+	0.538272i	$0.180923\pi$
$17$			4.43871i			1.07654i	−0.842771	+	0.538272i	$0.819077\pi$
$18$		−	1.93467i		−	0.456007i
$19$	−3.34908			−0.768333			−0.384166	−	0.923264i	$-0.625511\pi$
$19$	−3.34908			−0.768333			−0.384166	+	0.923264i	$0.625511\pi$
$20$	−3.01308	−	2.47202i	−0.673745	−	0.552761i
$21$	−1.00000			−0.218218
$22$			1.93467i			0.412474i
$23$			5.94604i			1.23983i	0.784667	+	0.619917i	$0.212834\pi$
$23$			5.94604i			1.23983i	−0.784667	+	0.619917i	$0.787166\pi$
$24$	0.497289			0.101509
$25$	0.976909	+	4.90364i	0.195382	+	0.980727i
$26$	0.940801			0.184506
$27$			1.00000i			0.192450i
$28$			1.74296i			0.329388i
$29$	3.07793			0.571557			0.285778	−	0.958296i	$-0.407748\pi$
$29$	3.07793			0.571557			0.285778	+	0.958296i	$0.407748\pi$
$30$	3.34450	+	2.74393i	0.610619	+	0.500970i
$31$	6.58078			1.18194			0.590972	−	0.806692i	$-0.298744\pi$
$31$	6.58078			1.18194			0.590972	+	0.806692i	$0.298744\pi$
$32$		−	7.61087i		−	1.34542i
$33$		−	1.00000i		−	0.174078i
$34$	−8.58745			−1.47274
$35$	1.41829	−	1.72871i	0.239735	−	0.292206i
$36$	1.74296			0.290493
$37$			6.41028i			1.05384i	0.849914	+	0.526922i	$0.176654\pi$
$37$			6.41028i			1.05384i	−0.849914	+	0.526922i	$0.823346\pi$
$38$		−	6.47938i		−	1.05109i
$39$	−0.486284			−0.0778678
$40$	−0.705299	+	0.859670i	−0.111518	+	0.135926i
$41$	8.83019			1.37904			0.689522	−	0.724265i	$-0.257821\pi$
$41$	8.83019			1.37904			0.689522	+	0.724265i	$0.257821\pi$
$42$		−	1.93467i		−	0.298527i
$43$		−	5.13533i		−	0.783130i	−0.920150	−	0.391565i	$-0.871934\pi$
$43$		−	5.13533i		−	0.783130i	0.920150	−	0.391565i	$-0.128066\pi$
$44$	−1.74296			−0.262761
$45$	−1.72871	−	1.41829i	−0.257702	−	0.211426i
$46$	−11.5036			−1.69612
$47$			11.8075i			1.72229i	0.508356	+	0.861147i	$0.330253\pi$
$47$			11.8075i			1.72229i	−0.508356	+	0.861147i	$0.669747\pi$
$48$			4.44801i			0.642015i
$49$	−1.00000			−0.142857
$50$	−9.48693	+	1.89000i	−1.34165	+	0.267286i
$51$	4.43871			0.621543
$52$			0.847574i			0.117537i
$53$		−	6.16737i		−	0.847154i	−0.905860	−	0.423577i	$-0.860774\pi$
$53$		−	6.16737i		−	0.847154i	0.905860	−	0.423577i	$-0.139226\pi$
$54$	−1.93467			−0.263276
$55$	1.72871	+	1.41829i	0.233100	+	0.191242i
$56$	0.497289			0.0664530
$57$			3.34908i			0.443597i
$58$			5.95479i			0.781902i
$59$	−8.45061			−1.10018			−0.550088	−	0.835107i	$-0.685406\pi$
$59$	−8.45061			−1.10018			−0.550088	+	0.835107i	$0.685406\pi$
$60$	−2.47202	+	3.01308i	−0.319137	+	0.388987i
$61$	2.24120			0.286957			0.143478	−	0.989653i	$-0.454171\pi$
$61$	2.24120			0.286957			0.143478	+	0.989653i	$0.454171\pi$
$62$			12.7317i			1.61692i
$63$			1.00000i			0.125988i
$64$	5.82852			0.728565
$65$	0.689692	−	0.840646i	0.0855457	−	0.104269i
$66$	1.93467			0.238142
$67$		−	6.81402i		−	0.832466i	−0.909258	−	0.416233i	$-0.863350\pi$
$67$		−	6.81402i		−	0.832466i	0.909258	−	0.416233i	$-0.136650\pi$
$68$		−	7.73649i		−	0.938187i
$69$	5.94604			0.715819
$70$	3.34450	+	2.74393i	0.399744	+	0.327962i
$71$	3.62954			0.430747			0.215373	−	0.976532i	$-0.430903\pi$
$71$	3.62954			0.430747			0.215373	+	0.976532i	$0.430903\pi$
$72$		−	0.497289i		−	0.0586060i
$73$			15.7313i			1.84121i	0.390500	+	0.920603i	$0.372302\pi$
$73$			15.7313i			1.84121i	−0.390500	+	0.920603i	$0.627698\pi$
$74$	−12.4018			−1.44168
$75$	4.90364	−	0.976909i	0.566223	−	0.112804i
$76$	5.83732			0.669586
$77$		−	1.00000i		−	0.113961i
$78$		−	0.940801i		−	0.106525i
$79$	−12.0868			−1.35987			−0.679935	−	0.733273i	$-0.737992\pi$
$79$	−12.0868			−1.35987			−0.679935	+	0.733273i	$0.737992\pi$
$80$	−7.68934	−	6.30857i	−0.859695	−	0.705319i
$81$	1.00000			0.111111
$82$			17.0835i			1.88656i
$83$		−	14.0401i		−	1.54110i	−0.637381	−	0.770549i	$-0.719982\pi$
$83$		−	14.0401i		−	1.54110i	0.637381	−	0.770549i	$-0.280018\pi$
$84$	1.74296			0.190173
$85$	−6.29537	+	7.67326i	−0.682829	+	0.832282i
$86$	9.93518			1.07134
$87$		−	3.07793i		−	0.329989i
$88$			0.497289i			0.0530111i
$89$	3.85548			0.408680			0.204340	−	0.978900i	$-0.434495\pi$
$89$	3.85548			0.408680			0.204340	+	0.978900i	$0.434495\pi$
$90$	2.74393	−	3.34450i	0.289235	−	0.352541i
$91$	−0.486284			−0.0509764
$92$		−	10.3637i		−	1.08049i
$93$		−	6.58078i		−	0.682396i
$94$	−22.8436			−2.35613
$95$	−5.78961	−	4.74997i	−0.594002	−	0.487337i
$96$	−7.61087			−0.776781
$97$		−	3.75732i		−	0.381498i	−0.981639	−	0.190749i	$-0.938908\pi$
$97$		−	3.75732i		−	0.381498i	0.981639	−	0.190749i	$-0.0610917\pi$
$98$		−	1.93467i		−	0.195431i
$99$	−1.00000			−0.100504
$100$	−1.70271	−	8.54684i	−0.170271	−	0.854684i
$101$	−5.90144			−0.587216			−0.293608	−	0.955926i	$-0.594856\pi$
$101$	−5.90144			−0.587216			−0.293608	+	0.955926i	$0.594856\pi$
$102$			8.58745i			0.850284i
$103$			8.72066i			0.859273i	0.903002	+	0.429636i	$0.141358\pi$
$103$			8.72066i			0.859273i	−0.903002	+	0.429636i	$0.858642\pi$
$104$	0.241824			0.0237127
$105$	−1.72871	−	1.41829i	−0.168705	−	0.138411i
$106$	11.9318			1.15892
$107$		−	8.67192i		−	0.838346i	−0.907906	−	0.419173i	$-0.862320\pi$
$107$		−	8.67192i		−	0.838346i	0.907906	−	0.419173i	$-0.137680\pi$
$108$		−	1.74296i		−	0.167716i
$109$	−4.62309			−0.442812			−0.221406	−	0.975182i	$-0.571065\pi$
$109$	−4.62309			−0.442812			−0.221406	+	0.975182i	$0.571065\pi$
$110$	−2.74393	+	3.34450i	−0.261623	+	0.318885i
$111$	6.41028			0.608437
$112$			4.44801i			0.420297i
$113$			8.75247i			0.823363i	0.911328	+	0.411682i	$0.135058\pi$
$113$			8.75247i			0.823363i	−0.911328	+	0.411682i	$0.864942\pi$
$114$	−6.47938			−0.606850
$115$	−8.43320	+	10.2790i	−0.786400	+	0.958522i
$116$	−5.36471			−0.498100
$117$			0.486284i			0.0449570i
$118$		−	16.3492i		−	1.50506i
$119$	4.43871			0.406896
$120$	0.859670	+	0.705299i	0.0784768	+	0.0643847i
$121$	1.00000			0.0909091
$122$			4.33600i			0.392563i
$123$		−	8.83019i		−	0.796192i
$124$	−11.4700			−1.03004
$125$	−5.26598	+	9.86253i	−0.471003	+	0.882131i
$126$	−1.93467			−0.172354
$127$		−	9.85804i		−	0.874760i	−0.899277	−	0.437380i	$-0.855907\pi$
$127$		−	9.85804i		−	0.874760i	0.899277	−	0.437380i	$-0.144093\pi$
$128$		−	3.94545i		−	0.348732i
$129$	−5.13533			−0.452140
$130$	1.62638	+	1.33433i	0.142643	+	0.117028i
$131$	−12.0688			−1.05446			−0.527229	−	0.849723i	$-0.676769\pi$
$131$	−12.0688			−1.05446			−0.527229	+	0.849723i	$0.676769\pi$
$132$			1.74296i			0.151705i
$133$			3.34908i			0.290402i
$134$	13.1829			1.13883
$135$	−1.41829	+	1.72871i	−0.122067	+	0.148784i
$136$	−2.20732			−0.189276
$137$		−	7.24704i		−	0.619157i	−0.950874	−	0.309578i	$-0.899812\pi$
$137$		−	7.24704i		−	0.619157i	0.950874	−	0.309578i	$-0.100188\pi$
$138$			11.5036i			0.979254i
$139$	10.9343			0.927439			0.463719	−	0.885982i	$-0.346515\pi$
$139$	10.9343			0.927439			0.463719	+	0.885982i	$0.346515\pi$
$140$	−2.47202	+	3.01308i	−0.208924	+	0.254652i
$141$	11.8075			0.994367
$142$			7.02197i			0.589271i
$143$		−	0.486284i		−	0.0406651i
$144$	4.44801			0.370668
$145$	5.32086	+	4.36539i	0.441873	+	0.362526i
$146$	−30.4349			−2.51881
$147$			1.00000i			0.0824786i
$148$		−	11.1729i		−	0.918404i
$149$	13.6541			1.11858			0.559292	−	0.828971i	$-0.311073\pi$
$149$	13.6541			1.11858			0.559292	+	0.828971i	$0.311073\pi$
$150$	1.89000	+	9.48693i	0.154318	+	0.774605i
$151$	10.2594			0.834901			0.417451	−	0.908700i	$-0.362924\pi$
$151$	10.2594			0.834901			0.417451	+	0.908700i	$0.362924\pi$
$152$		−	1.66546i		−	0.135087i
$153$		−	4.43871i		−	0.358848i
$154$	1.93467			0.155900
$155$	11.3763	+	9.33346i	0.913766	+	0.749681i
$156$	0.847574			0.0678602
$157$			1.39955i			0.111696i	0.998439	+	0.0558482i	$0.0177863\pi$
$157$			1.39955i			0.111696i	−0.998439	+	0.0558482i	$0.982214\pi$
$158$		−	23.3840i		−	1.86033i
$159$	−6.16737			−0.489104
$160$	10.7944	−	13.1570i	0.853374	−	1.04015i
$161$	5.94604			0.468613
$162$			1.93467i			0.152002i
$163$		−	22.3092i		−	1.74739i	−0.486476	−	0.873694i	$-0.661718\pi$
$163$		−	22.3092i		−	1.74739i	0.486476	−	0.873694i	$-0.338282\pi$
$164$	−15.3907			−1.20181
$165$	1.41829	−	1.72871i	0.110414	−	0.134580i
$166$	27.1629			2.10825
$167$		−	22.8901i		−	1.77129i	−0.464362	−	0.885645i	$-0.653716\pi$
$167$		−	22.8901i		−	1.77129i	0.464362	−	0.885645i	$-0.346284\pi$
$168$		−	0.497289i		−	0.0383666i
$169$	12.7635			0.981810
$170$	−14.8452	−	12.1795i	−1.13858	−	0.934124i
$171$	3.34908			0.256111
$172$			8.95067i			0.682482i
$173$		−	23.3388i		−	1.77441i	−0.461372	−	0.887207i	$-0.652643\pi$
$173$		−	23.3388i		−	1.77441i	0.461372	−	0.887207i	$-0.347357\pi$
$174$	5.95479			0.451431
$175$	4.90364	−	0.976909i	0.370680	−	0.0738474i
$176$	−4.44801			−0.335281
$177$			8.45061i			0.635187i
$178$			7.45910i			0.559083i
$179$	17.3105			1.29385			0.646925	−	0.762554i	$-0.276055\pi$
$179$	17.3105			1.29385			0.646925	+	0.762554i	$0.276055\pi$
$180$	3.01308	+	2.47202i	0.224582	+	0.184254i
$181$	−14.4204			−1.07186			−0.535932	−	0.844261i	$-0.680040\pi$
$181$	−14.4204			−1.07186			−0.535932	+	0.844261i	$0.680040\pi$
$182$		−	0.940801i		−	0.0697368i
$183$		−	2.24120i		−	0.165674i
$184$	−2.95690			−0.217985
$185$	−9.09164	+	11.0816i	−0.668431	+	0.814732i
$186$	12.7317			0.933531
$187$			4.43871i			0.324590i
$188$		−	20.5799i		−	1.50094i
$189$	1.00000			0.0727393
$190$	9.18964	−	11.2010i	0.666687	−	0.812606i
$191$	7.77969			0.562918			0.281459	−	0.959573i	$-0.409182\pi$
$191$	7.77969			0.562918			0.281459	+	0.959573i	$0.409182\pi$
$192$		−	5.82852i		−	0.420637i
$193$		−	20.0940i		−	1.44640i	−0.690639	−	0.723199i	$-0.742671\pi$
$193$		−	20.0940i		−	1.44640i	0.690639	−	0.723199i	$-0.257329\pi$
$194$	7.26919			0.521897
$195$	−0.840646	−	0.689692i	−0.0601999	−	0.0493898i
$196$	1.74296			0.124497
$197$			15.0464i			1.07201i	0.844214	+	0.536007i	$0.180068\pi$
$197$			15.0464i			1.07201i	−0.844214	+	0.536007i	$0.819932\pi$
$198$		−	1.93467i		−	0.137491i
$199$	4.97921			0.352967			0.176483	−	0.984304i	$-0.443528\pi$
$199$	4.97921			0.352967			0.176483	+	0.984304i	$0.443528\pi$
$200$	−2.43852	+	0.485806i	−0.172430	+	0.0343517i
$201$	−6.81402			−0.480624
$202$		−	11.4174i		−	0.803323i
$203$		−	3.07793i		−	0.216028i
$204$	−7.73649			−0.541663
$205$	15.2649	+	12.5238i	1.06615	+	0.874698i
$206$	−16.8716			−1.17550
$207$		−	5.94604i		−	0.413278i
$208$			2.16300i			0.149977i
$209$	−3.34908			−0.231661
$210$	2.74393	−	3.34450i	0.189349	−	0.230792i
$211$	10.6017			0.729851			0.364925	−	0.931037i	$-0.381094\pi$
$211$	10.6017			0.729851			0.364925	+	0.931037i	$0.381094\pi$
$212$			10.7495i			0.738277i
$213$		−	3.62954i		−	0.248692i
$214$	16.7773			1.14687
$215$	7.28338	−	8.87751i	0.496722	−	0.605441i
$216$	−0.497289			−0.0338362
$217$		−	6.58078i		−	0.446733i
$218$		−	8.94417i		−	0.605776i
$219$	15.7313			1.06302
$220$	−3.01308	−	2.47202i	−0.203142	−	0.166664i
$221$	2.15847			0.145195
$222$			12.4018i			0.832354i
$223$			18.8820i			1.26443i	0.774792	+	0.632216i	$0.217855\pi$
$223$			18.8820i			1.26443i	−0.774792	+	0.632216i	$0.782145\pi$
$224$	−7.61087			−0.508523
$225$	−0.976909	−	4.90364i	−0.0651273	−	0.326909i
$226$	−16.9332			−1.12638
$227$		−	6.81354i		−	0.452231i	−0.974101	−	0.226115i	$-0.927397\pi$
$227$		−	6.81354i		−	0.452231i	0.974101	−	0.226115i	$-0.0726026\pi$
$228$		−	5.83732i		−	0.386586i
$229$	−6.79478			−0.449012			−0.224506	−	0.974473i	$-0.572077\pi$
$229$	−6.79478			−0.449012			−0.224506	+	0.974473i	$0.572077\pi$
$230$	−19.8865	−	16.3155i	−1.31128	−	1.07581i
$231$	−1.00000			−0.0657952
$232$			1.53062i			0.100490i
$233$		−	9.13907i		−	0.598720i	−0.954140	−	0.299360i	$-0.903227\pi$
$233$		−	9.13907i		−	0.598720i	0.954140	−	0.299360i	$-0.0967732\pi$
$234$	−0.940801			−0.0615021
$235$	−16.7464	+	20.4117i	−1.09241	+	1.33151i
$236$	14.7291			0.958781
$237$			12.0868i			0.785121i
$238$			8.58745i			0.556642i
$239$	−14.0062			−0.905986			−0.452993	−	0.891514i	$-0.649644\pi$
$239$	−14.0062			−0.905986			−0.452993	+	0.891514i	$0.649644\pi$
$240$	−6.30857	+	7.68934i	−0.407216	+	0.496345i
$241$	23.4924			1.51328			0.756638	−	0.653834i	$-0.226840\pi$
$241$	23.4924			1.51328			0.756638	+	0.653834i	$0.226840\pi$
$242$			1.93467i			0.124365i
$243$		−	1.00000i		−	0.0641500i
$244$	−3.90633			−0.250077
$245$	−1.72871	−	1.41829i	−0.110444	−	0.0906112i
$246$	17.0835			1.08921
$247$			1.62861i			0.103626i
$248$			3.27255i			0.207807i
$249$	−14.0401			−0.889753
$250$	−19.0808	−	10.1879i	−1.20677	−	0.644342i
$251$	25.0394			1.58047			0.790237	−	0.612801i	$-0.209957\pi$
$251$	25.0394			1.58047			0.790237	+	0.612801i	$0.209957\pi$
$252$		−	1.74296i		−	0.109796i
$253$			5.94604i			0.373824i
$254$	19.0721			1.19669
$255$	7.67326	+	6.29537i	0.480518	+	0.394232i
$256$	19.2902			1.20564
$257$			21.1389i			1.31861i	0.751875	+	0.659306i	$0.229150\pi$
$257$			21.1389i			1.31861i	−0.751875	+	0.659306i	$0.770850\pi$
$258$		−	9.93518i		−	0.618537i
$259$	6.41028			0.398316
$260$	−1.20210	+	1.46521i	−0.0745514	+	0.0908687i
$261$	−3.07793			−0.190519
$262$		−	23.3492i		−	1.44252i
$263$		−	8.42987i		−	0.519808i	−0.965634	−	0.259904i	$-0.916309\pi$
$263$		−	8.42987i		−	0.519808i	0.965634	−	0.259904i	$-0.0836909\pi$
$264$	0.497289			0.0306060
$265$	8.74712	−	10.6616i	0.537331	−	0.654938i
$266$	−6.47938			−0.397276
$267$		−	3.85548i		−	0.235952i
$268$			11.8766i			0.725477i
$269$	−7.45515			−0.454548			−0.227274	−	0.973831i	$-0.572981\pi$
$269$	−7.45515			−0.454548			−0.227274	+	0.973831i	$0.572981\pi$
$270$	−3.34450	−	2.74393i	−0.203540	−	0.166990i
$271$	−15.1635			−0.921117			−0.460558	−	0.887629i	$-0.652351\pi$
$271$	−15.1635			−0.921117			−0.460558	+	0.887629i	$0.652351\pi$
$272$		−	19.7434i		−	1.19712i
$273$			0.486284i			0.0294312i
$274$	14.0207			0.847019
$275$	0.976909	+	4.90364i	0.0589098	+	0.295700i
$276$	−10.3637			−0.623822
$277$			1.30255i			0.0782627i	0.999234	+	0.0391313i	$0.0124591\pi$
$277$			1.30255i			0.0782627i	−0.999234	+	0.0391313i	$0.987541\pi$
$278$			21.1544i			1.26876i
$279$	−6.58078			−0.393981
$280$	0.859670	+	0.705299i	0.0513751	+	0.0421497i
$281$	3.63058			0.216582			0.108291	−	0.994119i	$-0.465462\pi$
$281$	3.63058			0.216582			0.108291	+	0.994119i	$0.465462\pi$
$282$			22.8436i			1.36031i
$283$			17.9821i			1.06892i	0.845193	+	0.534462i	$0.179486\pi$
$283$			17.9821i			1.06892i	−0.845193	+	0.534462i	$0.820514\pi$
$284$	−6.32614			−0.375387
$285$	−4.74997	+	5.78961i	−0.281364	+	0.342947i
$286$	0.940801			0.0556307
$287$		−	8.83019i		−	0.521230i
$288$			7.61087i			0.448475i
$289$	−2.70212			−0.158948
$290$	−8.44561	+	10.2941i	−0.495943	+	0.604492i
$291$	−3.75732			−0.220258
$292$		−	27.4190i		−	1.60457i
$293$			6.41942i			0.375026i	0.982262	+	0.187513i	$0.0600427\pi$
$293$			6.41942i			0.375026i	−0.982262	+	0.187513i	$0.939957\pi$
$294$	−1.93467			−0.112832
$295$	−14.6087	−	11.9854i	−0.850551	−	0.697818i
$296$	−3.18776			−0.185285
$297$			1.00000i			0.0580259i
$298$			26.4161i			1.53025i
$299$	2.89146			0.167218
$300$	−8.54684	+	1.70271i	−0.493452	+	0.0983062i
$301$	−5.13533			−0.295995
$302$			19.8487i			1.14216i
$303$			5.90144i			0.339029i
$304$	14.8968			0.854388
$305$	3.87440	+	3.17867i	0.221848	+	0.182010i
$306$	8.58745			0.490912
$307$		−	22.0523i		−	1.25859i	−0.777166	−	0.629296i	$-0.783343\pi$
$307$		−	22.0523i		−	1.25859i	0.777166	−	0.629296i	$-0.216657\pi$
$308$			1.74296i			0.0993144i
$309$	8.72066			0.496101
$310$	−18.0572	+	22.0094i	−1.02558	+	1.25005i
$311$	−12.2369			−0.693889			−0.346944	−	0.937886i	$-0.612781\pi$
$311$	−12.2369			−0.693889			−0.346944	+	0.937886i	$0.612781\pi$
$312$		−	0.241824i		−	0.0136906i
$313$			11.1695i			0.631337i	0.948870	+	0.315668i	$0.102229\pi$
$313$			11.1695i			0.631337i	−0.948870	+	0.315668i	$0.897771\pi$
$314$	−2.70768			−0.152803
$315$	−1.41829	+	1.72871i	−0.0799116	+	0.0974020i
$316$	21.0668			1.18510
$317$			5.54264i			0.311306i	0.987812	+	0.155653i	$0.0497481\pi$
$317$			5.54264i			0.311306i	−0.987812	+	0.155653i	$0.950252\pi$
$318$		−	11.9318i		−	0.669105i
$319$	3.07793			0.172331
$320$	10.0759	+	8.26653i	0.563257	+	0.462113i
$321$	−8.67192			−0.484019
$322$			11.5036i			0.641073i
$323$		−	14.8656i		−	0.827144i
$324$	−1.74296			−0.0968311
$325$	2.38456	−	0.475055i	0.132272	−	0.0263513i
$326$	43.1609			2.39046
$327$			4.62309i			0.255658i
$328$			4.39115i			0.242461i
$329$	11.8075			0.650966
$330$	3.34450	+	2.74393i	0.184109	+	0.151048i
$331$	19.0431			1.04670			0.523352	−	0.852116i	$-0.324681\pi$
$331$	19.0431			1.04670			0.523352	+	0.852116i	$0.324681\pi$
$332$			24.4713i			1.34304i
$333$		−	6.41028i		−	0.351281i
$334$	44.2849			2.42316
$335$	9.66426	−	11.7795i	0.528015	−	0.643583i
$336$	4.44801			0.242659
$337$		−	7.60541i		−	0.414293i	−0.978310	−	0.207146i	$-0.933582\pi$
$337$		−	7.60541i		−	0.414293i	0.978310	−	0.207146i	$-0.0664177\pi$
$338$			24.6933i			1.34314i
$339$	8.75247			0.475369
$340$	10.9726	−	13.3742i	0.595072	−	0.725317i
$341$	6.58078			0.356369
$342$			6.47938i			0.350365i
$343$			1.00000i			0.0539949i
$344$	2.55374			0.137688
$345$	10.2790	+	8.43320i	0.553403	+	0.454028i
$346$	45.1529			2.42743
$347$		−	10.7126i		−	0.575081i	−0.957768	−	0.287541i	$-0.907162\pi$
$347$		−	10.7126i		−	0.575081i	0.957768	−	0.287541i	$-0.0928376\pi$
$348$			5.36471i			0.287578i
$349$	−18.3427			−0.981862			−0.490931	−	0.871199i	$-0.663343\pi$
$349$	−18.3427			−0.981862			−0.490931	+	0.871199i	$0.663343\pi$
$350$	1.89000	+	9.48693i	0.101025	+	0.507098i
$351$	0.486284			0.0259559
$352$		−	7.61087i		−	0.405661i
$353$			25.7112i			1.36847i	0.729263	+	0.684233i	$0.239863\pi$
$353$			25.7112i			1.36847i	−0.729263	+	0.684233i	$0.760137\pi$
$354$	−16.3492			−0.868949
$355$	6.27444	+	5.14774i	0.333012	+	0.273213i
$356$	−6.71995			−0.356157
$357$		−	4.43871i		−	0.234921i
$358$			33.4902i			1.77001i
$359$	32.0751			1.69286			0.846430	−	0.532501i	$-0.178748\pi$
$359$	32.0751			1.69286			0.846430	+	0.532501i	$0.178748\pi$
$360$	0.705299	−	0.859670i	0.0371725	−	0.0453086i
$361$	−7.78364			−0.409665
$362$		−	27.8988i		−	1.46633i
$363$		−	1.00000i		−	0.0524864i
$364$	0.847574			0.0444249
$365$	−22.3115	+	27.1949i	−1.16784	+	1.42345i
$366$	4.33600			0.226646
$367$		−	5.24372i		−	0.273720i	−0.990590	−	0.136860i	$-0.956299\pi$
$367$		−	5.24372i		−	0.273720i	0.990590	−	0.136860i	$-0.0437011\pi$
$368$		−	26.4480i		−	1.37870i
$369$	−8.83019			−0.459681
$370$	−21.4392	−	17.5893i	−1.11457	−	0.914427i
$371$	−6.16737			−0.320194
$372$			11.4700i			0.594694i
$373$			3.51383i			0.181939i	0.995854	+	0.0909697i	$0.0289966\pi$
$373$			3.51383i			0.181939i	−0.995854	+	0.0909697i	$0.971003\pi$
$374$	−8.58745			−0.444046
$375$	9.86253	+	5.26598i	0.509299	+	0.271934i
$376$	−5.87171			−0.302810
$377$		−	1.49675i		−	0.0770864i
$378$			1.93467i			0.0995088i
$379$	−24.2240			−1.24430			−0.622152	−	0.782897i	$-0.713741\pi$
$379$	−24.2240			−1.24430			−0.622152	+	0.782897i	$0.713741\pi$
$380$	10.0911	+	8.27901i	0.517660	+	0.424704i
$381$	−9.85804			−0.505043
$382$			15.0511i			0.770084i
$383$		−	28.9965i		−	1.48165i	−0.671696	−	0.740827i	$-0.734434\pi$
$383$		−	28.9965i		−	1.48165i	0.671696	−	0.740827i	$-0.265566\pi$
$384$	−3.94545			−0.201341
$385$	1.41829	−	1.72871i	0.0722827	−	0.0881035i
$386$	38.8754			1.97870
$387$			5.13533i			0.261043i
$388$			6.54886i			0.332468i
$389$	32.4101			1.64326			0.821629	−	0.570022i	$-0.193065\pi$
$389$	32.4101			1.64326			0.821629	+	0.570022i	$0.193065\pi$
$390$	1.33433	−	1.62638i	0.0675663	−	0.0823547i
$391$	−26.3927			−1.33474
$392$		−	0.497289i		−	0.0251169i
$393$			12.0688i			0.608791i
$394$	−29.1099			−1.46654
$395$	−20.8946	−	17.1426i	−1.05132	−	0.862536i
$396$	1.74296			0.0875870
$397$		−	25.8259i		−	1.29616i	−0.761571	−	0.648081i	$-0.775572\pi$
$397$		−	25.8259i		−	1.29616i	0.761571	−	0.648081i	$-0.224428\pi$
$398$			9.63315i			0.482866i
$399$	3.34908			0.167664
$400$	−4.34530	−	21.8114i	−0.217265	−	1.09057i
$401$	−5.03699			−0.251535			−0.125768	−	0.992060i	$-0.540139\pi$
$401$	−5.03699			−0.251535			−0.125768	+	0.992060i	$0.540139\pi$
$402$		−	13.1829i		−	0.657504i
$403$		−	3.20013i		−	0.159410i
$404$	10.2860			0.511747
$405$	1.72871	+	1.41829i	0.0859005	+	0.0704754i
$406$	5.95479			0.295531
$407$			6.41028i			0.317746i
$408$			2.20732i			0.109279i
$409$	−32.8699			−1.62531			−0.812657	−	0.582742i	$-0.801980\pi$
$409$	−32.8699			−1.62531			−0.812657	+	0.582742i	$0.801980\pi$
$410$	−24.2294	+	29.5326i	−1.19660	+	1.45851i
$411$	−7.24704			−0.357470
$412$		−	15.1998i		−	0.748839i
$413$			8.45061i			0.415827i
$414$	11.5036			0.565373
$415$	19.9129	−	24.2713i	0.977485	−	1.19143i
$416$	−3.70104			−0.181459
$417$		−	10.9343i		−	0.535457i
$418$		−	6.47938i		−	0.316917i
$419$	10.7301			0.524198			0.262099	−	0.965041i	$-0.415585\pi$
$419$	10.7301			0.524198			0.262099	+	0.965041i	$0.415585\pi$
$420$	3.01308	+	2.47202i	0.147023	+	0.120622i
$421$	12.5222			0.610295			0.305148	−	0.952305i	$-0.401294\pi$
$421$	12.5222			0.610295			0.305148	+	0.952305i	$0.401294\pi$
$422$			20.5108i			0.998451i
$423$		−	11.8075i		−	0.574098i
$424$	3.06696			0.148945
$425$	−21.7658	+	4.33621i	−1.05580	+	0.210337i
$426$	7.02197			0.340216
$427$		−	2.24120i		−	0.108459i
$428$			15.1148i			0.730602i
$429$	−0.486284			−0.0234780
$430$	17.1751	+	14.0910i	0.828256	+	0.679526i
$431$	6.16368			0.296894			0.148447	−	0.988920i	$-0.452573\pi$
$431$	6.16368			0.296894			0.148447	+	0.988920i	$0.452573\pi$
$432$		−	4.44801i		−	0.214005i
$433$		−	17.0602i		−	0.819861i	−0.912117	−	0.409931i	$-0.865553\pi$
$433$		−	17.0602i		−	0.819861i	0.912117	−	0.409931i	$-0.134447\pi$
$434$	12.7317			0.611140
$435$	4.36539	−	5.32086i	0.209305	−	0.255116i
$436$	8.05786			0.385902
$437$		−	19.9138i		−	0.952605i
$438$			30.4349i			1.45423i
$439$	4.91619			0.234637			0.117319	−	0.993094i	$-0.462570\pi$
$439$	4.91619			0.234637			0.117319	+	0.993094i	$0.462570\pi$
$440$	−0.705299	+	0.859670i	−0.0336238	+	0.0409832i
$441$	1.00000			0.0476190
$442$			4.17594i			0.198629i
$443$			32.9476i			1.56539i	0.622407	+	0.782694i	$0.286155\pi$
$443$			32.9476i			1.56539i	−0.622407	+	0.782694i	$0.713845\pi$
$444$	−11.1729			−0.530241
$445$	6.66503	+	5.46819i	0.315953	+	0.259217i
$446$	−36.5305			−1.72977
$447$		−	13.6541i		−	0.645815i
$448$		−	5.82852i		−	0.275372i
$449$	−8.54536			−0.403280			−0.201640	−	0.979460i	$-0.564627\pi$
$449$	−8.54536			−0.403280			−0.201640	+	0.979460i	$0.564627\pi$
$450$	9.48693	−	1.89000i	0.447218	−	0.0890954i
$451$	8.83019			0.415797
$452$		−	15.2552i		−	0.717544i
$453$		−	10.2594i		−	0.482030i
$454$	13.1820			0.618661
$455$	−0.840646	−	0.689692i	−0.0394101	−	0.0323332i
$456$	−1.66546			−0.0779924
$457$		−	28.4943i		−	1.33291i	−0.745546	−	0.666455i	$-0.767811\pi$
$457$		−	28.4943i		−	1.33291i	0.745546	−	0.666455i	$-0.232189\pi$
$458$		−	13.1457i		−	0.614257i
$459$	−4.43871			−0.207181
$460$	14.6987	−	17.9159i	0.685332	−	0.835332i
$461$	−10.3390			−0.481534			−0.240767	−	0.970583i	$-0.577399\pi$
$461$	−10.3390			−0.481534			−0.240767	+	0.970583i	$0.577399\pi$
$462$		−	1.93467i		−	0.0900091i
$463$		−	10.8486i		−	0.504176i	−0.967704	−	0.252088i	$-0.918883\pi$
$463$		−	10.8486i		−	0.504176i	0.967704	−	0.252088i	$-0.0811172\pi$
$464$	−13.6907			−0.635573
$465$	9.33346	−	11.3763i	0.432829	−	0.527563i
$466$	17.6811			0.819062
$467$		−	11.7458i		−	0.543531i	−0.962364	−	0.271765i	$-0.912393\pi$
$467$		−	11.7458i		−	0.543531i	0.962364	−	0.271765i	$-0.0876074\pi$
$468$		−	0.847574i		−	0.0391791i
$469$	−6.81402			−0.314642
$470$	−39.4900	−	32.3988i	−1.82154	−	1.49444i
$471$	1.39955			0.0644880
$472$		−	4.20239i		−	0.193431i
$473$		−	5.13533i		−	0.236123i
$474$	−23.3840			−1.07406
$475$	−3.27175	−	16.4227i	−0.150118	−	0.753525i
$476$	−7.73649			−0.354601
$477$			6.16737i			0.282385i
$478$		−	27.0974i		−	1.23941i
$479$	0.768060			0.0350936			0.0175468	−	0.999846i	$-0.494414\pi$
$479$	0.768060			0.0350936			0.0175468	+	0.999846i	$0.494414\pi$
$480$	−13.1570	−	10.7944i	−0.600533	−	0.492695i
$481$	3.11722			0.142133
$482$			45.4501i			2.07019i
$483$		−	5.94604i		−	0.270554i
$484$	−1.74296			−0.0792254
$485$	5.32897	−	6.49534i	0.241976	−	0.294938i
$486$	1.93467			0.0877586
$487$		−	35.9798i		−	1.63040i	−0.579181	−	0.815199i	$-0.696627\pi$
$487$		−	35.9798i		−	1.63040i	0.579181	−	0.815199i	$-0.303373\pi$
$488$			1.11452i			0.0504522i
$489$	−22.3092			−1.00886
$490$	2.74393	−	3.34450i	0.123958	−	0.151089i
$491$	5.27263			0.237951			0.118975	−	0.992897i	$-0.462039\pi$
$491$	5.27263			0.237951			0.118975	+	0.992897i	$0.462039\pi$
$492$			15.3907i			0.693865i
$493$			13.6620i			0.615307i
$494$	−3.15082			−0.141762
$495$	−1.72871	−	1.41829i	−0.0776999	−	0.0637474i
$496$	−29.2714			−1.31432
$497$		−	3.62954i		−	0.162807i
$498$		−	27.1629i		−	1.21720i
$499$	−13.3312			−0.596785			−0.298393	−	0.954443i	$-0.596450\pi$
$499$	−13.3312			−0.596785			−0.298393	+	0.954443i	$0.596450\pi$
$500$	9.17839	−	17.1900i	0.410470	−	0.768760i
$501$	−22.8901			−1.02266
$502$			48.4431i			2.16212i
$503$			32.1241i			1.43234i	0.697925	+	0.716171i	$0.254107\pi$
$503$			32.1241i			1.43234i	−0.697925	+	0.716171i	$0.745893\pi$
$504$	−0.497289			−0.0221510
$505$	−10.2019	−	8.36996i	−0.453979	−	0.372458i
$506$	−11.5036			−0.511399
$507$		−	12.7635i		−	0.566848i
$508$			17.1822i			0.762336i
$509$	−27.5924			−1.22301			−0.611506	−	0.791240i	$-0.709436\pi$
$509$	−27.5924			−1.22301			−0.611506	+	0.791240i	$0.709436\pi$
$510$	−12.1795	+	14.8452i	−0.539317	+	0.657359i
$511$	15.7313			0.695910
$512$			29.4293i			1.30061i
$513$		−	3.34908i		−	0.147866i
$514$	−40.8970			−1.80389
$515$	−12.3684	+	15.0755i	−0.545018	+	0.664308i
$516$	8.95067			0.394031
$517$			11.8075i			0.519291i
$518$			12.4018i			0.544904i
$519$	−23.3388			−1.02446
$520$	0.418044	+	0.342976i	0.0183324	+	0.0150405i
$521$	44.8079			1.96307			0.981535	−	0.191282i	$-0.0612644\pi$
$521$	44.8079			1.96307			0.981535	+	0.191282i	$0.0612644\pi$
$522$		−	5.95479i		−	0.260634i
$523$			8.83094i			0.386150i	0.981184	+	0.193075i	$0.0618461\pi$
$523$			8.83094i			0.386150i	−0.981184	+	0.193075i	$0.938154\pi$
$524$	21.0355			0.918939
$525$	−0.976909	−	4.90364i	−0.0426358	−	0.214012i
$526$	16.3090			0.711108
$527$			29.2102i			1.27242i
$528$			4.44801i			0.193575i
$529$	−12.3553			−0.537189
$530$	20.6268	+	16.9228i	0.895969	+	0.735080i
$531$	8.45061			0.366725
$532$		−	5.83732i		−	0.253080i
$533$		−	4.29398i		−	0.185993i
$534$	7.45910			0.322787
$535$	12.2993	−	14.9913i	0.531745	−	0.648130i
$536$	3.38854			0.146362
$537$		−	17.3105i		−	0.747004i
$538$		−	14.4233i		−	0.621831i
$539$	−1.00000			−0.0430730
$540$	2.47202	−	3.01308i	0.106379	−	0.129662i
$541$	−24.8432			−1.06809			−0.534046	−	0.845455i	$-0.679329\pi$
$541$	−24.8432			−1.06809			−0.534046	+	0.845455i	$0.679329\pi$
$542$		−	29.3364i		−	1.26011i
$543$			14.4204i			0.618841i
$544$	33.7824			1.44841
$545$	−7.99201	−	6.55688i	−0.342340	−	0.280866i
$546$	−0.940801			−0.0402626
$547$		−	16.2122i		−	0.693184i	−0.938016	−	0.346592i	$-0.887339\pi$
$547$		−	16.2122i		−	0.693184i	0.938016	−	0.346592i	$-0.112661\pi$
$548$			12.6313i			0.539583i
$549$	−2.24120			−0.0956522
$550$	−9.48693	+	1.89000i	−0.404524	+	0.0805899i
$551$	−10.3082			−0.439146
$552$			2.95690i			0.125854i
$553$			12.0868i			0.513982i
$554$	−2.52001			−0.107065
$555$	11.0816	+	9.09164i	0.470386	+	0.385919i
$556$	−19.0581			−0.808244
$557$		−	35.0671i		−	1.48584i	−0.669379	−	0.742921i	$-0.733440\pi$
$557$		−	35.0671i		−	1.48584i	0.669379	−	0.742921i	$-0.266560\pi$
$558$		−	12.7317i		−	0.538974i
$559$	−2.49723			−0.105621
$560$	−6.30857	+	7.68934i	−0.266586	+	0.324934i
$561$	4.43871			0.187402
$562$			7.02398i			0.296289i
$563$			19.0651i			0.803498i	0.915750	+	0.401749i	$0.131598\pi$
$563$			19.0651i			0.803498i	−0.915750	+	0.401749i	$0.868402\pi$
$564$	−20.5799			−0.866571
$565$	−12.4135	+	15.1305i	−0.522241	+	0.636546i
$566$	−34.7894			−1.46231
$567$		−	1.00000i		−	0.0419961i
$568$			1.80493i			0.0757331i
$569$	8.66471			0.363244			0.181622	−	0.983368i	$-0.441865\pi$
$569$	8.66471			0.363244			0.181622	+	0.983368i	$0.441865\pi$
$570$	−11.2010	−	9.18964i	−0.469158	−	0.384912i
$571$	−11.6051			−0.485660			−0.242830	−	0.970069i	$-0.578076\pi$
$571$	−11.6051			−0.485660			−0.242830	+	0.970069i	$0.578076\pi$
$572$			0.847574i			0.0354388i
$573$		−	7.77969i		−	0.325001i
$574$	17.0835			0.713053
$575$	−29.1572	+	5.80874i	−1.21594	+	0.242241i
$576$	−5.82852			−0.242855
$577$		−	16.6250i		−	0.692109i	−0.938214	−	0.346055i	$-0.887521\pi$
$577$		−	16.6250i		−	0.692109i	0.938214	−	0.346055i	$-0.112479\pi$
$578$		−	5.22772i		−	0.217445i
$579$	−20.0940			−0.835079
$580$	−9.27405	−	7.60871i	−0.385084	−	0.315934i
$581$	−14.0401			−0.582480
$582$		−	7.26919i		−	0.301318i
$583$		−	6.16737i		−	0.255426i
$584$	−7.82298			−0.323717
$585$	−0.689692	+	0.840646i	−0.0285152	+	0.0347565i
$586$	−12.4195			−0.513044
$587$		−	16.7067i		−	0.689559i	−0.938684	−	0.344780i	$-0.887954\pi$
$587$		−	16.7067i		−	0.689559i	0.938684	−	0.344780i	$-0.112046\pi$
$588$		−	1.74296i		−	0.0718785i
$589$	−22.0396			−0.908126
$590$	23.1879	−	28.2631i	0.954629	−	1.16357i
$591$	15.0464			0.618927
$592$		−	28.5130i		−	1.17188i
$593$			11.9860i			0.492206i	0.969244	+	0.246103i	$0.0791502\pi$
$593$			11.9860i			0.492206i	−0.969244	+	0.246103i	$0.920850\pi$
$594$	−1.93467			−0.0793806
$595$	7.67326	+	6.29537i	0.314573	+	0.258085i
$596$	−23.7985			−0.974824
$597$		−	4.97921i		−	0.203786i
$598$			5.59403i			0.228757i
$599$	41.1344			1.68070			0.840352	−	0.542040i	$-0.182348\pi$
$599$	41.1344			1.68070			0.840352	+	0.542040i	$0.182348\pi$
$600$	0.485806	+	2.43852i	0.0198329	+	0.0995523i
$601$	−41.4222			−1.68965			−0.844823	−	0.535046i	$-0.820294\pi$
$601$	−41.4222			−1.68965			−0.844823	+	0.535046i	$0.820294\pi$
$602$		−	9.93518i		−	0.404928i
$603$			6.81402i			0.277489i
$604$	−17.8818			−0.727599
$605$	1.72871	+	1.41829i	0.0702822	+	0.0576617i
$606$	−11.4174			−0.463799
$607$			4.60439i			0.186886i	0.995625	+	0.0934431i	$0.0297873\pi$
$607$			4.60439i			0.186886i	−0.995625	+	0.0934431i	$0.970213\pi$
$608$			25.4894i			1.03373i
$609$	−3.07793			−0.124724
$610$	−6.14970	+	7.49570i	−0.248994	+	0.303492i
$611$	5.74178			0.232287
$612$			7.73649i			0.312729i
$613$			31.5006i			1.27230i	0.771566	+	0.636149i	$0.219474\pi$
$613$			31.5006i			1.27230i	−0.771566	+	0.636149i	$0.780526\pi$
$614$	42.6640			1.72178
$615$	12.5238	−	15.2649i	0.505007	−	0.615539i
$616$	0.497289			0.0200363
$617$			34.0672i			1.37149i	0.727840	+	0.685747i	$0.240524\pi$
$617$			34.0672i			1.37149i	−0.727840	+	0.685747i	$0.759476\pi$
$618$			16.8716i			0.678677i
$619$	−4.56364			−0.183428			−0.0917141	−	0.995785i	$-0.529235\pi$
$619$	−4.56364			−0.183428			−0.0917141	+	0.995785i	$0.529235\pi$
$620$	−19.8284	−	16.2678i	−0.796329	−	0.653332i
$621$	−5.94604			−0.238606
$622$		−	23.6743i		−	0.949254i
$623$		−	3.85548i		−	0.154467i
$624$	2.16300			0.0865892
$625$	−23.0913	+	9.58081i	−0.923652	+	0.383233i
$626$	−21.6093			−0.863681
$627$			3.34908i			0.133750i
$628$		−	2.43936i		−	0.0973412i
$629$	−28.4534			−1.13451
$630$	−3.34450	−	2.74393i	−0.133248	−	0.109321i
$631$	−15.3660			−0.611710			−0.305855	−	0.952078i	$-0.598942\pi$
$631$	−15.3660			−0.611710			−0.305855	+	0.952078i	$0.598942\pi$
$632$		−	6.01062i		−	0.239090i
$633$		−	10.6017i		−	0.421380i
$634$	−10.7232			−0.425873
$635$	13.9816	−	17.0417i	0.554841	−	0.676281i
$636$	10.7495			0.426245
$637$			0.486284i			0.0192673i
$638$			5.95479i			0.235752i
$639$	−3.62954			−0.143582
$640$	5.59580	−	6.82056i	0.221193	−	0.269606i
$641$	6.78313			0.267918			0.133959	−	0.990987i	$-0.457231\pi$
$641$	6.78313			0.267918			0.133959	+	0.990987i	$0.457231\pi$
$642$		−	16.7773i		−	0.662149i
$643$			2.87222i			0.113269i	0.998395	+	0.0566347i	$0.0180371\pi$
$643$			2.87222i			0.113269i	−0.998395	+	0.0566347i	$0.981963\pi$
$644$	−10.3637			−0.408387
$645$	−8.87751	−	7.28338i	−0.349552	−	0.286783i
$646$	28.7601			1.13155
$647$			1.17219i			0.0460836i	0.999735	+	0.0230418i	$0.00733508\pi$
$647$			1.17219i			0.0460836i	−0.999735	+	0.0230418i	$0.992665\pi$
$648$			0.497289i			0.0195353i
$649$	−8.45061			−0.331716
$650$	0.919077	+	4.61334i	0.0360492	+	0.180950i
$651$	−6.58078			−0.257921
$652$			38.8840i			1.52281i
$653$			16.7681i			0.656185i	0.944646	+	0.328092i	$0.106406\pi$
$653$			16.7681i			0.656185i	−0.944646	+	0.328092i	$0.893594\pi$
$654$	−8.94417			−0.349745
$655$	−20.8635	−	17.1171i	−0.815206	−	0.668820i
$656$	−39.2768			−1.53350
$657$		−	15.7313i		−	0.613735i
$658$			22.8436i			0.890535i
$659$	−28.4282			−1.10740			−0.553702	−	0.832715i	$-0.686785\pi$
$659$	−28.4282			−1.10740			−0.553702	+	0.832715i	$0.686785\pi$
$660$	−2.47202	+	3.01308i	−0.0962233	+	0.117284i
$661$	23.0786			0.897654			0.448827	−	0.893619i	$-0.351842\pi$
$661$	23.0786			0.897654			0.448827	+	0.893619i	$0.351842\pi$
$662$			36.8422i			1.43191i
$663$		−	2.15847i		−	0.0838281i
$664$	6.98196			0.270953
$665$	−4.74997	+	5.78961i	−0.184196	+	0.224511i
$666$	12.4018			0.480560
$667$			18.3015i			0.708636i
$668$			39.8966i			1.54364i
$669$	18.8820			0.730021
$670$	22.7895	+	18.6972i	0.880435	+	0.722335i
$671$	2.24120			0.0865207
$672$			7.61087i			0.293596i
$673$		−	26.2090i		−	1.01028i	−0.863036	−	0.505142i	$-0.831440\pi$
$673$		−	26.2090i		−	1.01028i	0.863036	−	0.505142i	$-0.168560\pi$
$674$	14.7140			0.566761
$675$	−4.90364	+	0.976909i	−0.188741	+	0.0376013i
$676$	−22.2463			−0.855628
$677$		−	2.51096i		−	0.0965040i	−0.998835	−	0.0482520i	$-0.984635\pi$
$677$		−	2.51096i		−	0.0965040i	0.998835	−	0.0482520i	$-0.0153651\pi$
$678$			16.9332i			0.650314i
$679$	−3.75732			−0.144193
$680$	−3.81582	−	3.13062i	−0.146330	−	0.120054i
$681$	−6.81354			−0.261096
$682$			12.7317i			0.487521i
$683$		−	34.2884i		−	1.31201i	−0.754757	−	0.656004i	$-0.772245\pi$
$683$		−	34.2884i		−	1.31201i	0.754757	−	0.656004i	$-0.227755\pi$
$684$	−5.83732			−0.223195
$685$	10.2784	−	12.5281i	0.392718	−	0.478673i
$686$	−1.93467			−0.0738662
$687$			6.79478i			0.259237i
$688$			22.8420i			0.870842i
$689$	−2.99909			−0.114256
$690$	−16.3155	+	19.8865i	−0.621120	+	0.757066i
$691$	−21.5128			−0.818384			−0.409192	−	0.912448i	$-0.634189\pi$
$691$	−21.5128			−0.818384			−0.409192	+	0.912448i	$0.634189\pi$
$692$			40.6785i			1.54637i
$693$			1.00000i			0.0379869i
$694$	20.7253			0.786723
$695$	18.9024	+	15.5081i	0.717007	+	0.588254i
$696$	1.53062			0.0580180
$697$			39.1946i			1.48460i
$698$		−	35.4871i		−	1.34321i
$699$	−9.13907			−0.345671
$700$	−8.54684	+	1.70271i	−0.323040	+	0.0643565i
$701$	38.8130			1.46595			0.732973	−	0.680257i	$-0.238132\pi$
$701$	38.8130			1.46595			0.732973	+	0.680257i	$0.238132\pi$
$702$			0.940801i			0.0355082i
$703$		−	21.4686i		−	0.809703i
$704$	5.82852			0.219671
$705$	20.4117	+	16.7464i	0.768750	+	0.630705i
$706$	−49.7427			−1.87209
$707$			5.90144i			0.221947i
$708$		−	14.7291i		−	0.553553i
$709$	24.6621			0.926206			0.463103	−	0.886304i	$-0.346736\pi$
$709$	24.6621			0.926206			0.463103	+	0.886304i	$0.346736\pi$
$710$	−9.95919	+	12.1390i	−0.373762	+	0.455568i
$711$	12.0868			0.453290
$712$			1.91729i			0.0718534i
$713$			39.1296i			1.46541i
$714$	8.58745			0.321377
$715$	0.689692	−	0.840646i	0.0257930	−	0.0314384i
$716$	−30.1715			−1.12756
$717$			14.0062i			0.523071i
$718$			62.0548i			2.31587i
$719$	34.7777			1.29699			0.648494	−	0.761219i	$-0.275399\pi$
$719$	34.7777			1.29699			0.648494	+	0.761219i	$0.275399\pi$
$720$	7.68934	+	6.30857i	0.286565	+	0.235106i
$721$	8.72066			0.324775
$722$		−	15.0588i		−	0.560430i
$723$		−	23.4924i		−	0.873691i
$724$	25.1343			0.934107
$725$	3.00686	+	15.0930i	0.111672	+	0.560542i
$726$	1.93467			0.0718025
$727$		−	11.2866i		−	0.418598i	−0.977852	−	0.209299i	$-0.932882\pi$
$727$		−	11.2866i		−	0.418598i	0.977852	−	0.209299i	$-0.0671182\pi$
$728$		−	0.241824i		−	0.00896258i
$729$	−1.00000			−0.0370370
$730$	−52.6132	−	43.1655i	−1.94730	−	1.59763i
$731$	22.7942			0.843074
$732$			3.90633i			0.144382i
$733$			37.2301i			1.37512i	0.726126	+	0.687562i	$0.241319\pi$
$733$			37.2301i			1.37512i	−0.726126	+	0.687562i	$0.758681\pi$
$734$	10.1449			0.374455
$735$	−1.41829	+	1.72871i	−0.0523144	+	0.0637646i
$736$	45.2545			1.66810
$737$		−	6.81402i		−	0.250998i
$738$		−	17.0835i		−	0.628854i
$739$	−50.7940			−1.86849			−0.934243	−	0.356638i	$-0.883923\pi$
$739$	−50.7940			−1.86849			−0.934243	+	0.356638i	$0.883923\pi$
$740$	15.8464	−	19.3147i	0.582524	−	0.710022i
$741$	1.62861			0.0598283
$742$		−	11.9318i		−	0.438032i
$743$			32.1426i			1.17920i	0.807697	+	0.589598i	$0.200714\pi$
$743$			32.1426i			1.17920i	−0.807697	+	0.589598i	$0.799286\pi$
$744$	3.27255			0.119977
$745$	23.6040	+	19.3654i	0.864783	+	0.709494i
$746$	−6.79812			−0.248897
$747$			14.0401i			0.513699i
$748$		−	7.73649i		−	0.282874i
$749$	−8.67192			−0.316865
$750$	−10.1879	+	19.0808i	−0.372011	+	0.696731i
$751$	−18.4830			−0.674454			−0.337227	−	0.941423i	$-0.609489\pi$
$751$	−18.4830			−0.674454			−0.337227	+	0.941423i	$0.609489\pi$
$752$		−	52.5197i		−	1.91520i
$753$		−	25.0394i		−	0.912487i
$754$	2.89572			0.105456
$755$	17.7356	+	14.5509i	0.645466	+	0.529560i
$756$	−1.74296			−0.0633908
$757$		−	44.8916i		−	1.63161i	−0.578326	−	0.815806i	$-0.696294\pi$
$757$		−	44.8916i		−	1.63161i	0.578326	−	0.815806i	$-0.303706\pi$
$758$		−	46.8655i		−	1.70223i
$759$	5.94604			0.215827
$760$	2.36211	−	2.87911i	0.0856826	−	0.104436i
$761$	46.5228			1.68645			0.843225	−	0.537561i	$-0.180654\pi$
$761$	46.5228			1.68645			0.843225	+	0.537561i	$0.180654\pi$
$762$		−	19.0721i		−	0.690909i
$763$			4.62309i			0.167367i
$764$	−13.5597			−0.490572
$765$	6.29537	−	7.67326i	0.227610	−	0.277427i
$766$	56.0988			2.02693
$767$			4.10940i			0.148382i
$768$		−	19.2902i		−	0.696075i
$769$	−32.6184			−1.17625			−0.588125	−	0.808770i	$-0.700134\pi$
$769$	−32.6184			−1.17625			−0.588125	+	0.808770i	$0.700134\pi$
$770$	3.34450	+	2.74393i	0.120527	+	0.0988843i
$771$	21.1389			0.761301
$772$			35.0231i			1.26051i
$773$			5.94071i			0.213673i	0.994277	+	0.106836i	$0.0340721\pi$
$773$			5.94071i			0.213673i	−0.994277	+	0.106836i	$0.965928\pi$
$774$	−9.93518			−0.357113
$775$	6.42883	+	32.2698i	0.230930	+	1.15916i
$776$	1.86847			0.0670743
$777$		−	6.41028i		−	0.229968i
$778$			62.7030i			2.24801i
$779$	−29.5731			−1.05956
$780$	1.46521	+	1.20210i	0.0524630	+	0.0430423i
$781$	3.62954			0.129875
$782$		−	51.0613i		−	1.82595i
$783$			3.07793i			0.109996i
$784$	4.44801			0.158858
$785$	−1.98497	+	2.41943i	−0.0708467	+	0.0863531i
$786$	−23.3492			−0.832839
$787$			48.3411i			1.72317i	0.507609	+	0.861587i	$0.330529\pi$
$787$			48.3411i			1.72317i	−0.507609	+	0.861587i	$0.669471\pi$
$788$		−	26.2253i		−	0.934239i
$789$	−8.42987			−0.300111
$790$	33.1652	−	40.4242i	1.17997	−	1.43823i
$791$	8.75247			0.311202
$792$		−	0.497289i		−	0.0176704i
$793$		−	1.08986i		−	0.0387021i
$794$	49.9646			1.77318
$795$	−10.6616	−	8.74712i	−0.378129	−	0.310228i
$796$	−8.67857			−0.307604
$797$			34.4700i			1.22099i	0.792020	+	0.610495i	$0.209029\pi$
$797$			34.4700i			1.22099i	−0.792020	+	0.610495i	$0.790971\pi$
$798$			6.47938i			0.229368i
$799$	−52.4098			−1.85413
$800$	37.3209	−	7.43513i	1.31949	−	0.262871i
$801$	−3.85548			−0.136227
$802$		−	9.74494i		−	0.344106i
$803$			15.7313i			0.555145i
$804$	11.8766			0.418854
$805$	10.2790	+	8.43320i	0.362287	+	0.297231i
$806$	6.19121			0.218076
$807$			7.45515i			0.262434i
$808$		−	2.93472i		−	0.103243i
$809$	−40.3713			−1.41938			−0.709689	−	0.704515i	$-0.751165\pi$
$809$	−40.3713			−1.41938			−0.709689	+	0.704515i	$0.751165\pi$
$810$	−2.74393	+	3.34450i	−0.0964118	+	0.117514i
$811$	34.3907			1.20762			0.603810	−	0.797128i	$-0.293648\pi$
$811$	34.3907			1.20762			0.603810	+	0.797128i	$0.293648\pi$
$812$			5.36471i			0.188264i
$813$			15.1635i			0.531807i
$814$	−12.4018			−0.434683
$815$	31.6409	−	38.5662i	1.10833	−	1.35091i
$816$	−19.7434			−0.691158
$817$			17.1986i			0.601704i
$818$		−	63.5926i		−	2.22346i
$819$	0.486284			0.0169921
$820$	−26.6061	−	21.8284i	−0.929125	−	0.762282i
$821$	11.5642			0.403594			0.201797	−	0.979427i	$-0.435322\pi$
$821$	11.5642			0.403594			0.201797	+	0.979427i	$0.435322\pi$
$822$		−	14.0207i		−	0.489027i
$823$			5.31479i			0.185262i	0.995701	+	0.0926309i	$0.0295277\pi$
$823$			5.31479i			0.185262i	−0.995701	+	0.0926309i	$0.970472\pi$
$824$	−4.33669			−0.151076
$825$	4.90364	−	0.976909i	0.170723	−	0.0340116i
$826$	−16.3492			−0.568860
$827$		−	15.4919i		−	0.538705i	−0.963042	−	0.269353i	$-0.913190\pi$
$827$		−	15.4919i		−	0.538705i	0.963042	−	0.269353i	$-0.0868097\pi$
$828$			10.3637i			0.360164i
$829$	14.3417			0.498109			0.249054	−	0.968489i	$-0.419880\pi$
$829$	14.3417			0.498109			0.249054	+	0.968489i	$0.419880\pi$
$830$	46.9570	+	38.5249i	1.62990	+	1.33722i
$831$	1.30255			0.0451850
$832$		−	2.83432i		−	0.0982623i
$833$		−	4.43871i		−	0.153792i
$834$	21.1544			0.732516
$835$	32.4648	−	39.5705i	1.12349	−	1.36939i
$836$	5.83732			0.201888
$837$			6.58078i			0.227465i
$838$			20.7592i			0.717113i
$839$	−16.0582			−0.554390			−0.277195	−	0.960814i	$-0.589405\pi$
$839$	−16.0582			−0.554390			−0.277195	+	0.960814i	$0.589405\pi$
$840$	0.705299	−	0.859670i	0.0243351	−	0.0296614i
$841$	−19.5264			−0.673323
$842$			24.2264i			0.834897i
$843$		−	3.63058i		−	0.125044i
$844$	−18.4783			−0.636050
$845$	22.0645	+	18.1024i	0.759042	+	0.622741i
$846$	22.8436			0.785378
$847$		−	1.00000i		−	0.0343604i
$848$			27.4325i			0.942037i
$849$	17.9821			0.617143
$850$	−8.38916	−	42.1097i	−0.287746	−	1.44435i
$851$	−38.1158			−1.30659
$852$			6.32614i			0.216730i
$853$			50.9375i			1.74407i	0.489446	+	0.872034i	$0.337199\pi$
$853$			50.9375i			1.74407i	−0.489446	+	0.872034i	$0.662801\pi$
$854$	4.33600			0.148375
$855$	5.78961	+	4.74997i	0.198001	+	0.162446i
$856$	4.31245			0.147396
$857$		−	31.1131i		−	1.06280i	−0.847120	−	0.531402i	$-0.821665\pi$
$857$		−	31.1131i		−	1.06280i	0.847120	−	0.531402i	$-0.178335\pi$
$858$		−	0.940801i		−	0.0321184i
$859$	35.1265			1.19850			0.599251	−	0.800561i	$-0.295465\pi$
$859$	35.1265			1.19850			0.599251	+	0.800561i	$0.295465\pi$
$860$	−12.6946	+	15.4731i	−0.432884	+	0.527630i
$861$	−8.83019			−0.300932
$862$			11.9247i			0.406157i
$863$		−	22.0086i		−	0.749182i	−0.927190	−	0.374591i	$-0.877783\pi$
$863$		−	22.0086i		−	0.749182i	0.927190	−	0.374591i	$-0.122217\pi$
$864$	7.61087			0.258927
$865$	33.1011	−	40.3461i	1.12547	−	1.37181i
$866$	33.0059			1.12159
$867$			2.70212i			0.0917689i
$868$			11.4700i			0.389319i
$869$	−12.0868			−0.410016
$870$	10.2941	+	8.44561i	0.349004	+	0.286333i
$871$	−3.31355			−0.112275
$872$		−	2.29901i		−	0.0778543i
$873$			3.75732i			0.127166i
$874$	38.5266			1.30318
$875$	9.86253	+	5.26598i	0.333414	+	0.178023i
$876$	−27.4190			−0.926401
$877$		−	5.85632i		−	0.197754i	−0.995100	−	0.0988770i	$-0.968475\pi$
$877$		−	5.85632i		−	0.197754i	0.995100	−	0.0988770i	$-0.0315250\pi$
$878$			9.51123i			0.320988i
$879$	6.41942			0.216522
$880$	−7.68934	−	6.30857i	−0.259208	−	0.212662i
$881$	−8.00704			−0.269764			−0.134882	−	0.990862i	$-0.543066\pi$
$881$	−8.00704			−0.269764			−0.134882	+	0.990862i	$0.543066\pi$
$882$			1.93467i			0.0651438i
$883$			19.3149i			0.649997i	0.945715	+	0.324999i	$0.105364\pi$
$883$			19.3149i			0.649997i	−0.945715	+	0.324999i	$0.894636\pi$
$884$	−3.76213			−0.126534
$885$	−11.9854	+	14.6087i	−0.402885	+	0.491066i
$886$	−63.7428			−2.14148
$887$			34.9065i			1.17204i	0.810295	+	0.586022i	$0.199307\pi$
$887$			34.9065i			1.17204i	−0.810295	+	0.586022i	$0.800693\pi$
$888$			3.18776i			0.106974i
$889$	−9.85804			−0.330628
$890$	−10.5792	+	12.8947i	−0.354614	+	0.432230i
$891$	1.00000			0.0335013
$892$		−	32.9106i		−	1.10193i
$893$		−	39.5442i		−	1.32329i
$894$	26.4161			0.883488
$895$	29.9250	+	24.5513i	1.00028	+	0.820661i
$896$	−3.94545			−0.131808
$897$		−	2.89146i		−	0.0965431i
$898$		−	16.5325i		−	0.551696i
$899$	20.2552			0.675548
$900$	1.70271	+	8.54684i	0.0567571	+	0.284895i
$901$	27.3752			0.911999
$902$			17.0835i			0.568819i
$903$			5.13533i			0.170893i
$904$	−4.35250			−0.144762
$905$	−24.9288	−	20.4524i	−0.828663	−	0.679860i
$906$	19.8487			0.659427
$907$			24.6238i			0.817620i	0.912620	+	0.408810i	$0.134056\pi$
$907$			24.6238i			0.817620i	−0.912620	+	0.408810i	$0.865944\pi$
$908$			11.8757i			0.394110i
$909$	5.90144			0.195739
$910$	1.33433	−	1.62638i	0.0442325	−	0.0539138i
$911$	16.1533			0.535181			0.267591	−	0.963533i	$-0.413772\pi$
$911$	16.1533			0.535181			0.267591	+	0.963533i	$0.413772\pi$
$912$		−	14.8968i		−	0.493281i
$913$		−	14.0401i		−	0.464658i
$914$	55.1272			1.82345
$915$	3.17867	−	3.87440i	0.105084	−	0.128084i
$916$	11.8430			0.391305
$917$			12.0688i			0.398548i
$918$		−	8.58745i		−	0.283428i
$919$	19.2320			0.634404			0.317202	−	0.948358i	$-0.397257\pi$
$919$	19.2320			0.634404			0.317202	+	0.948358i	$0.397257\pi$
$920$	−5.11163	−	4.19373i	−0.168525	−	0.138263i
$921$	−22.0523			−0.726648
$922$		−	20.0025i		−	0.658748i
$923$		−	1.76499i		−	0.0580952i
$924$	1.74296			0.0573392
$925$	−31.4337	+	6.26226i	−1.03353	+	0.205902i
$926$	20.9884			0.689723
$927$		−	8.72066i		−	0.286424i
$928$		−	23.4257i		−	0.768987i
$929$	−47.6195			−1.56234			−0.781172	−	0.624316i	$-0.785378\pi$
$929$	−47.6195			−1.56234			−0.781172	+	0.624316i	$0.785378\pi$
$930$	22.0094	+	18.0572i	0.721717	+	0.592119i
$931$	3.34908			0.109762
$932$			15.9290i			0.521773i
$933$			12.2369i			0.400617i
$934$	22.7243			0.743561
$935$	−6.29537	+	7.67326i	−0.205881	+	0.250942i
$936$	−0.241824			−0.00790425
$937$			2.92896i			0.0956849i	0.998855	+	0.0478424i	$0.0152345\pi$
$937$			2.92896i			0.0956849i	−0.998855	+	0.0478424i	$0.984765\pi$
$938$		−	13.1829i		−	0.430437i
$939$	11.1695			0.364502
$940$	29.1883	−	35.5768i	0.952017	−	1.16039i
$941$	21.8097			0.710977			0.355489	−	0.934681i	$-0.384314\pi$
$941$	21.8097			0.710977			0.355489	+	0.934681i	$0.384314\pi$
$942$			2.70768i			0.0882209i
$943$			52.5046i			1.70979i
$944$	37.5884			1.22340
$945$	1.72871	+	1.41829i	0.0562351	+	0.0461370i
$946$	9.93518			0.323020
$947$			39.5244i			1.28437i	0.766550	+	0.642185i	$0.221972\pi$
$947$			39.5244i			1.28437i	−0.766550	+	0.642185i	$0.778028\pi$
$948$		−	21.0668i		−	0.684217i
$949$	7.64987			0.248325
$950$	31.7725	−	6.32977i	1.03084	−	0.205365i
$951$	5.54264			0.179733
$952$			2.20732i			0.0715396i
$953$		−	12.6794i		−	0.410725i	−0.978686	−	0.205362i	$-0.934163\pi$
$953$		−	12.6794i		−	0.410725i	0.978686	−	0.205362i	$-0.0658373\pi$
$954$	−11.9318			−0.386308
$955$	13.4489	+	11.0338i	0.435195	+	0.357047i
$956$	24.4123			0.789549
$957$		−	3.07793i		−	0.0994953i
$958$			1.48595i			0.0480087i
$959$	−7.24704			−0.234019
$960$	8.26653	−	10.0759i	0.266801	−	0.325197i
$961$	12.3067			0.396991
$962$			6.03080i			0.194441i
$963$			8.67192i			0.279449i
$964$	−40.9463			−1.31879
$965$	28.4991	−	34.7368i	0.917420	−	1.11822i
$966$	11.5036			0.370123
$967$			24.0642i			0.773854i	0.922110	+	0.386927i	$0.126463\pi$
$967$			24.0642i			0.773854i	−0.922110	+	0.386927i	$0.873537\pi$
$968$			0.497289i			0.0159835i
$969$	−14.8656			−0.477552
$970$	12.5664	+	10.3098i	0.403481	+	0.331028i
$971$	−43.8969			−1.40872			−0.704360	−	0.709843i	$-0.748766\pi$
$971$	−43.8969			−1.40872			−0.704360	+	0.709843i	$0.748766\pi$
$972$			1.74296i			0.0559055i
$973$		−	10.9343i		−	0.350539i
$974$	69.6091			2.23042
$975$	−0.475055	−	2.38456i	−0.0152139	−	0.0763670i
$976$	−9.96889			−0.319097
$977$			2.88099i			0.0921711i	0.998937	+	0.0460855i	$0.0146747\pi$
$977$			2.88099i			0.0921711i	−0.998937	+	0.0460855i	$0.985325\pi$
$978$		−	43.1609i		−	1.38013i
$979$	3.85548			0.123222
$980$	3.01308	+	2.47202i	0.0962493	+	0.0789658i
$981$	4.62309			0.147604
$982$			10.2008i			0.325521i
$983$			43.3176i			1.38162i	0.723037	+	0.690809i	$0.242745\pi$
$983$			43.3176i			1.38162i	−0.723037	+	0.690809i	$0.757255\pi$
$984$	4.39115			0.139985
$985$	−21.3402	+	26.0110i	−0.679955	+	0.828779i
$986$	−26.4315			−0.841752
$987$		−	11.8075i		−	0.375835i
$988$		−	2.83860i		−	0.0903077i
$989$	30.5348			0.970951
$990$	2.74393	−	3.34450i	0.0872077	−	0.106295i
$991$	−59.9488			−1.90434			−0.952169	−	0.305573i	$-0.901152\pi$
$991$	−59.9488			−1.90434			−0.952169	+	0.305573i	$0.901152\pi$
$992$		−	50.0855i		−	1.59022i
$993$		−	19.0431i		−	0.604315i
$994$	7.02197			0.222723
$995$	8.60764	+	7.06196i	0.272880	+	0.223879i
$996$	24.4713			0.775402
$997$		−	30.1058i		−	0.953460i	−0.879050	−	0.476730i	$-0.841822\pi$
$997$		−	30.1058i		−	0.953460i	0.879050	−	0.476730i	$-0.158178\pi$
$998$		−	25.7915i		−	0.816414i
$999$	−6.41028			−0.202812

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1155.2.c.f.694.16	yes	20
5.2	odd	4		5775.2.a.cn.1.3		10
5.3	odd	4		5775.2.a.co.1.8		10
5.4	even	2	inner	1155.2.c.f.694.5	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1155.2.c.f.694.5	✓	20	5.4	even	2	inner
1155.2.c.f.694.16	yes	20	1.1	even	1	trivial
5775.2.a.cn.1.3		10	5.2	odd	4
5775.2.a.co.1.8		10	5.3	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1155 = 3 \cdot 5 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1155.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.93467i q^{2} -1.00000i q^{3} -1.74296 q^{4} +(1.72871 + 1.41829i) q^{5} +1.93467 q^{6} -1.00000i q^{7} +0.497289i q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q+1.93467i q^{2} -1.00000i q^{3} -1.74296 q^{4} +(1.72871 + 1.41829i) q^{5} +1.93467 q^{6} -1.00000i q^{7} +0.497289i q^{8} -1.00000 q^{9} +(-2.74393 + 3.34450i) q^{10} +1.00000 q^{11} +1.74296i q^{12} -0.486284i q^{13} +1.93467 q^{14} +(1.41829 - 1.72871i) q^{15} -4.44801 q^{16} +4.43871i q^{17} -1.93467i q^{18} -3.34908 q^{19} +(-3.01308 - 2.47202i) q^{20} -1.00000 q^{21} +1.93467i q^{22} +5.94604i q^{23} +0.497289 q^{24} +(0.976909 + 4.90364i) q^{25} +0.940801 q^{26} +1.00000i q^{27} +1.74296i q^{28} +3.07793 q^{29} +(3.34450 + 2.74393i) q^{30} +6.58078 q^{31} -7.61087i q^{32} -1.00000i q^{33} -8.58745 q^{34} +(1.41829 - 1.72871i) q^{35} +1.74296 q^{36} +6.41028i q^{37} -6.47938i q^{38} -0.486284 q^{39} +(-0.705299 + 0.859670i) q^{40} +8.83019 q^{41} -1.93467i q^{42} -5.13533i q^{43} -1.74296 q^{44} +(-1.72871 - 1.41829i) q^{45} -11.5036 q^{46} +11.8075i q^{47} +4.44801i q^{48} -1.00000 q^{49} +(-9.48693 + 1.89000i) q^{50} +4.43871 q^{51} +0.847574i q^{52} -6.16737i q^{53} -1.93467 q^{54} +(1.72871 + 1.41829i) q^{55} +0.497289 q^{56} +3.34908i q^{57} +5.95479i q^{58} -8.45061 q^{59} +(-2.47202 + 3.01308i) q^{60} +2.24120 q^{61} +12.7317i q^{62} +1.00000i q^{63} +5.82852 q^{64} +(0.689692 - 0.840646i) q^{65} +1.93467 q^{66} -6.81402i q^{67} -7.73649i q^{68} +5.94604 q^{69} +(3.34450 + 2.74393i) q^{70} +3.62954 q^{71} -0.497289i q^{72} +15.7313i q^{73} -12.4018 q^{74} +(4.90364 - 0.976909i) q^{75} +5.83732 q^{76} -1.00000i q^{77} -0.940801i q^{78} -12.0868 q^{79} +(-7.68934 - 6.30857i) q^{80} +1.00000 q^{81} +17.0835i q^{82} -14.0401i q^{83} +1.74296 q^{84} +(-6.29537 + 7.67326i) q^{85} +9.93518 q^{86} -3.07793i q^{87} +0.497289i q^{88} +3.85548 q^{89} +(2.74393 - 3.34450i) q^{90} -0.486284 q^{91} -10.3637i q^{92} -6.58078i q^{93} -22.8436 q^{94} +(-5.78961 - 4.74997i) q^{95} -7.61087 q^{96} -3.75732i q^{97} -1.93467i q^{98} -1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 26 q^{4} - 2 q^{5} + 6 q^{6} - 20 q^{9}+O(q^{10}) \) 20 * q - 26 * q^4 - 2 * q^5 + 6 * q^6 - 20 * q^9	\( 20 q - 26 q^{4} - 2 q^{5} + 6 q^{6} - 20 q^{9} + 2 q^{10} + 20 q^{11} + 6 q^{14} - 2 q^{15} + 38 q^{16} - 34 q^{19} + 4 q^{20} - 20 q^{21} - 18 q^{24} - 4 q^{25} + 28 q^{26} - 10 q^{29} - 6 q^{30} + 12 q^{31} - 32 q^{34} - 2 q^{35} + 26 q^{36} - 2 q^{40} + 52 q^{41} - 26 q^{44} + 2 q^{45} + 40 q^{46} - 20 q^{49} + 6 q^{50} + 6 q^{51} - 6 q^{54} - 2 q^{55} - 18 q^{56} - 14 q^{59} - 28 q^{60} + 78 q^{61} - 26 q^{64} - 4 q^{65} + 6 q^{66} - 18 q^{69} - 6 q^{70} - 8 q^{74} - 8 q^{75} + 84 q^{76} - 52 q^{79} - 40 q^{80} + 20 q^{81} + 26 q^{84} - 24 q^{85} + 4 q^{86} - 10 q^{89} - 2 q^{90} - 96 q^{94} - 30 q^{95} + 62 q^{96} - 20 q^{99}+O(q^{100}) \) 20 * q - 26 * q^4 - 2 * q^5 + 6 * q^6 - 20 * q^9 + 2 * q^10 + 20 * q^11 + 6 * q^14 - 2 * q^15 + 38 * q^16 - 34 * q^19 + 4 * q^20 - 20 * q^21 - 18 * q^24 - 4 * q^25 + 28 * q^26 - 10 * q^29 - 6 * q^30 + 12 * q^31 - 32 * q^34 - 2 * q^35 + 26 * q^36 - 2 * q^40 + 52 * q^41 - 26 * q^44 + 2 * q^45 + 40 * q^46 - 20 * q^49 + 6 * q^50 + 6 * q^51 - 6 * q^54 - 2 * q^55 - 18 * q^56 - 14 * q^59 - 28 * q^60 + 78 * q^61 - 26 * q^64 - 4 * q^65 + 6 * q^66 - 18 * q^69 - 6 * q^70 - 8 * q^74 - 8 * q^75 + 84 * q^76 - 52 * q^79 - 40 * q^80 + 20 * q^81 + 26 * q^84 - 24 * q^85 + 4 * q^86 - 10 * q^89 - 2 * q^90 - 96 * q^94 - 30 * q^95 + 62 * q^96 - 20 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more