LMFDB - Embedded newform 1155.2.c.e.694.9

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} + 15194 x^{12} + 40320 x^{10} + 61593 x^{8} + 48545 x^{6} + \cdots + 100 $ x^20 + 33x^18 + 456x^16 + 3426x^14 + 15194x^12 + 40320x^10 + 61593x^8 + 48545x^6 + 15624x^4 + 2116*x^2 + 100
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			694.9
Root			$-0.437361i$ of defining polynomial
Character	$\chi$	$=$	1155.694
Dual form			1155.2.c.e.694.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.437361i q^{2} -1.00000i q^{3} +1.80872 q^{4} +(0.978157 - 2.01077i) q^{5} -0.437361 q^{6} +1.00000i q^{7} -1.66578i q^{8} -1.00000 q^{9} +O(q^{10})$	\(q-0.437361i q^{2} -1.00000i q^{3} +1.80872 q^{4} +(0.978157 - 2.01077i) q^{5} -0.437361 q^{6} +1.00000i q^{7} -1.66578i q^{8} -1.00000 q^{9} +(-0.879433 - 0.427807i) q^{10} -1.00000 q^{11} -1.80872i q^{12} +0.0257972i q^{13} +0.437361 q^{14} +(-2.01077 - 0.978157i) q^{15} +2.88888 q^{16} -1.73932i q^{17} +0.437361i q^{18} -2.62891 q^{19} +(1.76921 - 3.63692i) q^{20} +1.00000 q^{21} +0.437361i q^{22} -8.28038i q^{23} -1.66578 q^{24} +(-3.08642 - 3.93370i) q^{25} +0.0112827 q^{26} +1.00000i q^{27} +1.80872i q^{28} +4.93063 q^{29} +(-0.427807 + 0.879433i) q^{30} +1.90570 q^{31} -4.59505i q^{32} +1.00000i q^{33} -0.760710 q^{34} +(2.01077 + 0.978157i) q^{35} -1.80872 q^{36} -3.18596i q^{37} +1.14978i q^{38} +0.0257972 q^{39} +(-3.34951 - 1.62940i) q^{40} -2.07074 q^{41} -0.437361i q^{42} +3.85880i q^{43} -1.80872 q^{44} +(-0.978157 + 2.01077i) q^{45} -3.62151 q^{46} +10.1019i q^{47} -2.88888i q^{48} -1.00000 q^{49} +(-1.72045 + 1.34988i) q^{50} -1.73932 q^{51} +0.0466597i q^{52} -10.9173i q^{53} +0.437361 q^{54} +(-0.978157 + 2.01077i) q^{55} +1.66578 q^{56} +2.62891i q^{57} -2.15647i q^{58} +7.00705 q^{59} +(-3.63692 - 1.76921i) q^{60} -1.71290 q^{61} -0.833477i q^{62} -1.00000i q^{63} +3.76807 q^{64} +(0.0518722 + 0.0252337i) q^{65} +0.437361 q^{66} +7.39906i q^{67} -3.14593i q^{68} -8.28038 q^{69} +(0.427807 - 0.879433i) q^{70} +2.36851 q^{71} +1.66578i q^{72} +11.0792i q^{73} -1.39341 q^{74} +(-3.93370 + 3.08642i) q^{75} -4.75494 q^{76} -1.00000i q^{77} -0.0112827i q^{78} +8.85469 q^{79} +(2.82578 - 5.80889i) q^{80} +1.00000 q^{81} +0.905660i q^{82} +9.51268i q^{83} +1.80872 q^{84} +(-3.49738 - 1.70133i) q^{85} +1.68769 q^{86} -4.93063i q^{87} +1.66578i q^{88} -9.48265 q^{89} +(0.879433 + 0.427807i) q^{90} -0.0257972 q^{91} -14.9769i q^{92} -1.90570i q^{93} +4.41819 q^{94} +(-2.57148 + 5.28613i) q^{95} -4.59505 q^{96} -0.755716i q^{97} +0.437361i q^{98} +1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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} + 2 q^{19} + 4 q^{20} + 20 q^{21} - 18 q^{24} + 12 q^{25} + 20 q^{26} - 38 q^{29} + 6 q^{30} + 20 q^{31} - 32 q^{34} - 2 q^{35} + 26 q^{36} + 2 q^{40} + 12 q^{41} + 26 q^{44} + 2 q^{45} + 8 q^{46} - 20 q^{49} - 6 q^{50} + 26 q^{51} - 6 q^{54} + 2 q^{55} + 18 q^{56} - 22 q^{59} + 16 q^{60} + 34 q^{61} - 26 q^{64} - 28 q^{65} - 6 q^{66} - 26 q^{69} - 6 q^{70} + 72 q^{71} - 72 q^{74} - 8 q^{75} + 44 q^{76} + 4 q^{79} - 8 q^{80} + 20 q^{81} - 26 q^{84} - 16 q^{85} + 52 q^{86} + 6 q^{89} + 2 q^{90} + 16 q^{94} + 14 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 + 2 * q^19 + 4 * q^20 + 20 * q^21 - 18 * q^24 + 12 * q^25 + 20 * q^26 - 38 * q^29 + 6 * q^30 + 20 * q^31 - 32 * q^34 - 2 * q^35 + 26 * q^36 + 2 * q^40 + 12 * q^41 + 26 * q^44 + 2 * q^45 + 8 * q^46 - 20 * q^49 - 6 * q^50 + 26 * q^51 - 6 * q^54 + 2 * q^55 + 18 * q^56 - 22 * q^59 + 16 * q^60 + 34 * q^61 - 26 * q^64 - 28 * q^65 - 6 * q^66 - 26 * q^69 - 6 * q^70 + 72 * q^71 - 72 * q^74 - 8 * q^75 + 44 * q^76 + 4 * q^79 - 8 * q^80 + 20 * q^81 - 26 * q^84 - 16 * q^85 + 52 * q^86 + 6 * q^89 + 2 * q^90 + 16 * q^94 + 14 * 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 $

$2$		−	0.437361i		−	0.309261i	−0.987972	−	0.154630i	$-0.950581\pi$
$2$		−	0.437361i		−	0.309261i	0.987972	−	0.154630i	$-0.0494187\pi$
$3$		−	1.00000i		−	0.577350i
$3$		−	1.00000i		−	0.577350i
$4$	1.80872			0.904358
$5$	0.978157	−	2.01077i	0.437445	−	0.899245i
$5$	0.978157	−	2.01077i	0.437445	−	0.899245i
$6$	−0.437361			−0.178552
$7$			1.00000i			0.377964i
$7$			1.00000i			0.377964i
$8$		−	1.66578i		−	0.588943i
$9$	−1.00000			−0.333333
$10$	−0.879433	−	0.427807i	−0.278101	−	0.135285i
$11$	−1.00000			−0.301511
$11$	−1.00000			−0.301511
$12$		−	1.80872i		−	0.522131i
$13$			0.0257972i			0.00715484i	0.999994	+	0.00357742i	$0.00113873\pi$
$13$			0.0257972i			0.00715484i	−0.999994	+	0.00357742i	$0.998861\pi$
$14$	0.437361			0.116890
$15$	−2.01077	−	0.978157i	−0.519179	−	0.252559i
$16$	2.88888			0.722221
$17$		−	1.73932i		−	0.421847i	−0.977503	−	0.210923i	$-0.932353\pi$
$17$		−	1.73932i		−	0.421847i	0.977503	−	0.210923i	$-0.0676471\pi$
$18$			0.437361i			0.103087i
$19$	−2.62891			−0.603112			−0.301556	−	0.953448i	$-0.597506\pi$
$19$	−2.62891			−0.603112			−0.301556	+	0.953448i	$0.597506\pi$
$20$	1.76921	−	3.63692i	0.395607	−	0.813239i
$21$	1.00000			0.218218
$22$			0.437361i			0.0932456i
$23$		−	8.28038i		−	1.72658i	−0.504710	−	0.863289i	$-0.668400\pi$
$23$		−	8.28038i		−	1.72658i	0.504710	−	0.863289i	$-0.331600\pi$
$24$	−1.66578			−0.340026
$25$	−3.08642	−	3.93370i	−0.617284	−	0.786740i
$26$	0.0112827			0.00221271
$27$			1.00000i			0.192450i
$28$			1.80872i			0.341815i
$29$	4.93063			0.915596			0.457798	−	0.889056i	$-0.348638\pi$
$29$	4.93063			0.915596			0.457798	+	0.889056i	$0.348638\pi$
$30$	−0.427807	+	0.879433i	−0.0781066	+	0.160562i
$31$	1.90570			0.342273			0.171137	−	0.985247i	$-0.445256\pi$
$31$	1.90570			0.342273			0.171137	+	0.985247i	$0.445256\pi$
$32$		−	4.59505i		−	0.812298i
$33$			1.00000i			0.174078i
$34$	−0.760710			−0.130461
$35$	2.01077	+	0.978157i	0.339883	+	0.165339i
$36$	−1.80872			−0.301453
$37$		−	3.18596i		−	0.523768i	−0.965099	−	0.261884i	$-0.915656\pi$
$37$		−	3.18596i		−	0.523768i	0.965099	−	0.261884i	$-0.0843438\pi$
$38$			1.14978i			0.186519i
$39$	0.0257972			0.00413085
$40$	−3.34951	−	1.62940i	−0.529604	−	0.257630i
$41$	−2.07074			−0.323395			−0.161698	−	0.986840i	$-0.551697\pi$
$41$	−2.07074			−0.323395			−0.161698	+	0.986840i	$0.551697\pi$
$42$		−	0.437361i		−	0.0674862i
$43$			3.85880i			0.588461i	0.955734	+	0.294231i	$0.0950634\pi$
$43$			3.85880i			0.588461i	−0.955734	+	0.294231i	$0.904937\pi$
$44$	−1.80872			−0.272674
$45$	−0.978157	+	2.01077i	−0.145815	+	0.299748i
$46$	−3.62151			−0.533963
$47$			10.1019i			1.47352i	0.676155	+	0.736759i	$0.263645\pi$
$47$			10.1019i			1.47352i	−0.676155	+	0.736759i	$0.736355\pi$
$48$		−	2.88888i		−	0.416974i
$49$	−1.00000			−0.142857
$50$	−1.72045	+	1.34988i	−0.243308	+	0.190902i
$51$	−1.73932			−0.243553
$52$			0.0466597i			0.00647054i
$53$		−	10.9173i		−	1.49961i	−0.661658	−	0.749806i	$-0.730147\pi$
$53$		−	10.9173i		−	1.49961i	0.661658	−	0.749806i	$-0.269853\pi$
$54$	0.437361			0.0595173
$55$	−0.978157	+	2.01077i	−0.131895	+	0.271133i
$56$	1.66578			0.222600
$57$			2.62891i			0.348207i
$58$		−	2.15647i		−	0.283158i
$59$	7.00705			0.912240			0.456120	−	0.889918i	$-0.349239\pi$
$59$	7.00705			0.912240			0.456120	+	0.889918i	$0.349239\pi$
$60$	−3.63692	−	1.76921i	−0.469524	−	0.228404i
$61$	−1.71290			−0.219314			−0.109657	−	0.993969i	$-0.534975\pi$
$61$	−1.71290			−0.219314			−0.109657	+	0.993969i	$0.534975\pi$
$62$		−	0.833477i		−	0.105852i
$63$		−	1.00000i		−	0.125988i
$64$	3.76807			0.471009
$65$	0.0518722	+	0.0252337i	0.00643396	+	0.00312985i
$66$	0.437361			0.0538354
$67$			7.39906i			0.903939i	0.892033	+	0.451969i	$0.149278\pi$
$67$			7.39906i			0.903939i	−0.892033	+	0.451969i	$0.850722\pi$
$68$		−	3.14593i		−	0.381501i
$69$	−8.28038			−0.996840
$70$	0.427807	−	0.879433i	0.0511327	−	0.105112i
$71$	2.36851			0.281090			0.140545	−	0.990074i	$-0.455115\pi$
$71$	2.36851			0.281090			0.140545	+	0.990074i	$0.455115\pi$
$72$			1.66578i			0.196314i
$73$			11.0792i			1.29672i	0.761335	+	0.648359i	$0.224544\pi$
$73$			11.0792i			1.29672i	−0.761335	+	0.648359i	$0.775456\pi$
$74$	−1.39341			−0.161981
$75$	−3.93370	+	3.08642i	−0.454225	+	0.356389i
$76$	−4.75494			−0.545429
$77$		−	1.00000i		−	0.113961i
$78$		−	0.0112827i		−	0.00127751i
$79$	8.85469			0.996231			0.498115	−	0.867111i	$-0.334026\pi$
$79$	8.85469			0.996231			0.498115	+	0.867111i	$0.334026\pi$
$80$	2.82578	−	5.80889i	0.315932	−	0.649454i
$81$	1.00000			0.111111
$82$			0.905660i			0.100013i
$83$			9.51268i			1.04415i	0.852899	+	0.522076i	$0.174842\pi$
$83$			9.51268i			1.04415i	−0.852899	+	0.522076i	$0.825158\pi$
$84$	1.80872			0.197347
$85$	−3.49738	−	1.70133i	−0.379344	−	0.184535i
$86$	1.68769			0.181988
$87$		−	4.93063i		−	0.528619i
$88$			1.66578i			0.177573i
$89$	−9.48265			−1.00516			−0.502580	−	0.864531i	$-0.667616\pi$
$89$	−9.48265			−1.00516			−0.502580	+	0.864531i	$0.667616\pi$
$90$	0.879433	+	0.427807i	0.0927004	+	0.0450948i
$91$	−0.0257972			−0.00270428
$92$		−	14.9769i		−	1.56144i
$93$		−	1.90570i		−	0.197612i
$94$	4.41819			0.455701
$95$	−2.57148	+	5.28613i	−0.263828	+	0.542346i
$96$	−4.59505			−0.468980
$97$		−	0.755716i		−	0.0767314i	−0.999264	−	0.0383657i	$-0.987785\pi$
$97$		−	0.755716i		−	0.0767314i	0.999264	−	0.0383657i	$-0.0122152\pi$
$98$			0.437361i			0.0441801i
$99$	1.00000			0.100504
$100$	−5.58246	−	7.11495i	−0.558246	−	0.711495i
$101$	10.9386			1.08844			0.544218	−	0.838944i	$-0.316827\pi$
$101$	10.9386			1.08844			0.544218	+	0.838944i	$0.316827\pi$
$102$			0.760710i			0.0753215i
$103$		−	9.47623i		−	0.933721i	−0.884331	−	0.466860i	$-0.845385\pi$
$103$		−	9.47623i		−	0.933721i	0.884331	−	0.466860i	$-0.154615\pi$
$104$	0.0429725			0.00421380
$105$	0.978157	−	2.01077i	0.0954583	−	0.196231i
$106$	−4.77481			−0.463771
$107$		−	5.34487i		−	0.516708i	−0.966050	−	0.258354i	$-0.916820\pi$
$107$		−	5.34487i		−	0.516708i	0.966050	−	0.258354i	$-0.0831801\pi$
$108$			1.80872i			0.174044i
$109$	−16.5202			−1.58234			−0.791172	−	0.611594i	$-0.790529\pi$
$109$	−16.5202			−1.58234			−0.791172	+	0.611594i	$0.790529\pi$
$110$	0.879433	+	0.427807i	0.0838507	+	0.0407898i
$111$	−3.18596			−0.302398
$112$			2.88888i			0.272974i
$113$			5.05846i			0.475860i	0.971282	+	0.237930i	$0.0764689\pi$
$113$			5.05846i			0.475860i	−0.971282	+	0.237930i	$0.923531\pi$
$114$	1.14978			0.107687
$115$	−16.6500	−	8.09951i	−1.55262	−	0.755283i
$116$	8.91811			0.828026
$117$		−	0.0257972i		−	0.00238495i
$118$		−	3.06461i		−	0.282120i
$119$	1.73932			0.159443
$120$	−1.62940	+	3.34951i	−0.148743	+	0.305767i
$121$	1.00000			0.0909091
$122$			0.749155i			0.0678253i
$123$			2.07074i			0.186712i
$124$	3.44686			0.309537
$125$	−10.9288	+	2.35831i	−0.977500	+	0.210934i
$126$	−0.437361			−0.0389632
$127$			9.34124i			0.828901i	0.910072	+	0.414450i	$0.136026\pi$
$127$			9.34124i			0.828901i	−0.910072	+	0.414450i	$0.863974\pi$
$128$		−	10.8381i		−	0.957962i
$129$	3.85880			0.339748
$130$	0.0110362	−	0.0226869i	0.000967940	−	0.00198977i
$131$	4.71375			0.411842			0.205921	−	0.978569i	$-0.433981\pi$
$131$	4.71375			0.411842			0.205921	+	0.978569i	$0.433981\pi$
$132$			1.80872i			0.157428i
$133$		−	2.62891i		−	0.227955i
$134$	3.23606			0.279553
$135$	2.01077	+	0.978157i	0.173060	+	0.0841863i
$136$	−2.89733			−0.248444
$137$		−	1.06035i		−	0.0905920i	−0.998974	−	0.0452960i	$-0.985577\pi$
$137$		−	1.06035i		−	0.0905920i	0.998974	−	0.0452960i	$-0.0144231\pi$
$138$			3.62151i			0.308284i
$139$	−14.8517			−1.25970			−0.629852	−	0.776716i	$-0.716884\pi$
$139$	−14.8517			−1.25970			−0.629852	+	0.776716i	$0.716884\pi$
$140$	3.63692	+	1.76921i	0.307376	+	0.149525i
$141$	10.1019			0.850736
$142$		−	1.03589i		−	0.0869301i
$143$		−	0.0257972i		−	0.00215727i
$144$	−2.88888			−0.240740
$145$	4.82293	−	9.91439i	0.400523	−	0.823345i
$146$	4.84559			0.401024
$147$			1.00000i			0.0824786i
$148$		−	5.76249i		−	0.473674i
$149$	15.5241			1.27178			0.635892	−	0.771778i	$-0.280632\pi$
$149$	15.5241			1.27178			0.635892	+	0.771778i	$0.280632\pi$
$150$	1.34988	+	1.72045i	0.110217	+	0.140474i
$151$	16.5877			1.34989			0.674943	−	0.737870i	$-0.264168\pi$
$151$	16.5877			1.34989			0.674943	+	0.737870i	$0.264168\pi$
$152$			4.37919i			0.355199i
$153$			1.73932i			0.140616i
$154$	−0.437361			−0.0352435
$155$	1.86407	−	3.83192i	0.149726	−	0.307788i
$156$	0.0466597			0.00373577
$157$		−	0.0195881i		−	0.00156330i	−1.00000		0.000781652i	$-0.999751\pi$
$157$		−	0.0195881i		−	0.00156330i	1.00000		0.000781652i	$-0.000248807\pi$
$158$		−	3.87270i		−	0.308095i
$159$	−10.9173			−0.865801
$160$	−9.23960	−	4.49468i	−0.730455	−	0.355335i
$161$	8.28038			0.652585
$162$		−	0.437361i		−	0.0343623i
$163$		−	0.512887i		−	0.0401724i	−0.999798	−	0.0200862i	$-0.993606\pi$
$163$		−	0.512887i		−	0.0401724i	0.999798	−	0.0200862i	$-0.00639406\pi$
$164$	−3.74538			−0.292465
$165$	2.01077	+	0.978157i	0.156538	+	0.0761494i
$166$	4.16047			0.322915
$167$			16.7502i			1.29617i	0.761568	+	0.648085i	$0.224430\pi$
$167$			16.7502i			1.29617i	−0.761568	+	0.648085i	$0.775570\pi$
$168$		−	1.66578i		−	0.128518i
$169$	12.9993			0.999949
$170$	−0.744094	+	1.52962i	−0.0570694	+	0.117316i
$171$	2.62891			0.201037
$172$			6.97947i			0.532179i
$173$		−	3.91073i		−	0.297327i	−0.988888	−	0.148664i	$-0.952503\pi$
$173$		−	3.91073i		−	0.297327i	0.988888	−	0.148664i	$-0.0474972\pi$
$174$	−2.15647			−0.163481
$175$	3.93370	−	3.08642i	0.297360	−	0.233311i
$176$	−2.88888			−0.217758
$177$		−	7.00705i		−	0.526682i
$178$			4.14734i			0.310856i
$179$	−3.41672			−0.255377			−0.127689	−	0.991814i	$-0.540756\pi$
$179$	−3.41672			−0.255377			−0.127689	+	0.991814i	$0.540756\pi$
$180$	−1.76921	+	3.63692i	−0.131869	+	0.271080i
$181$	2.93257			0.217977			0.108988	−	0.994043i	$-0.465239\pi$
$181$	2.93257			0.217977			0.108988	+	0.994043i	$0.465239\pi$
$182$			0.0112827i			0.000836327i
$183$			1.71290i			0.126621i
$184$	−13.7933			−1.01686
$185$	−6.40624	−	3.11637i	−0.470996	−	0.229120i
$186$	−0.833477			−0.0611135
$187$			1.73932i			0.127192i
$188$			18.2715i			1.33259i
$189$	−1.00000			−0.0727393
$190$	2.31195	+	1.12467i	0.167726	+	0.0815918i
$191$	11.6978			0.846426			0.423213	−	0.906030i	$-0.360902\pi$
$191$	11.6978			0.846426			0.423213	+	0.906030i	$0.360902\pi$
$192$		−	3.76807i		−	0.271937i
$193$			19.3725i			1.39446i	0.716846	+	0.697232i	$0.245585\pi$
$193$			19.3725i			1.39446i	−0.716846	+	0.697232i	$0.754415\pi$
$194$	−0.330521			−0.0237300
$195$	0.0252337	−	0.0518722i	0.00180702	−	0.00371465i
$196$	−1.80872			−0.129194
$197$		−	12.6669i		−	0.902481i	−0.892402	−	0.451241i	$-0.850982\pi$
$197$		−	12.6669i		−	0.902481i	0.892402	−	0.451241i	$-0.149018\pi$
$198$		−	0.437361i		−	0.0310819i
$199$	−12.8379			−0.910058			−0.455029	−	0.890477i	$-0.650371\pi$
$199$	−12.8379			−0.910058			−0.455029	+	0.890477i	$0.650371\pi$
$200$	−6.55269	+	5.14130i	−0.463345	+	0.363545i
$201$	7.39906			0.521889
$202$		−	4.78413i		−	0.336610i
$203$			4.93063i			0.346063i
$204$	−3.14593			−0.220259
$205$	−2.02551	+	4.16379i	−0.141468	+	0.290812i
$206$	−4.14453			−0.288763
$207$			8.28038i			0.575526i
$208$			0.0745250i			0.00516738i
$209$	2.62891			0.181845
$210$	−0.879433	−	0.427807i	−0.0606867	−	0.0295215i
$211$	7.36203			0.506823			0.253412	−	0.967359i	$-0.418447\pi$
$211$	7.36203			0.506823			0.253412	+	0.967359i	$0.418447\pi$
$212$		−	19.7464i		−	1.35619i
$213$		−	2.36851i		−	0.162287i
$214$	−2.33764			−0.159797
$215$	7.75917	+	3.77451i	0.529171	+	0.257419i
$216$	1.66578			0.113342
$217$			1.90570i			0.129367i
$218$			7.22527i			0.489357i
$219$	11.0792			0.748660
$220$	−1.76921	+	3.63692i	−0.119280	+	0.245201i
$221$	0.0448695			0.00301825
$222$			1.39341i			0.0935197i
$223$			21.2820i			1.42515i	0.701598	+	0.712573i	$0.252470\pi$
$223$			21.2820i			1.42515i	−0.701598	+	0.712573i	$0.747530\pi$
$224$	4.59505			0.307020
$225$	3.08642	+	3.93370i	0.205761	+	0.262247i
$226$	2.21237			0.147165
$227$			10.4419i			0.693051i	0.938041	+	0.346525i	$0.112639\pi$
$227$			10.4419i			0.693051i	−0.938041	+	0.346525i	$0.887361\pi$
$228$			4.75494i			0.314904i
$229$	13.9313			0.920606			0.460303	−	0.887762i	$-0.347741\pi$
$229$	13.9313			0.920606			0.460303	+	0.887762i	$0.347741\pi$
$230$	−3.54241	+	7.28204i	−0.233579	+	0.480164i
$231$	−1.00000			−0.0657952
$232$		−	8.21336i		−	0.539234i
$233$			17.8902i			1.17202i	0.810302	+	0.586012i	$0.199303\pi$
$233$			17.8902i			1.17202i	−0.810302	+	0.586012i	$0.800697\pi$
$234$	−0.0112827			−0.000737571
$235$	20.3127	+	9.88127i	1.32505	+	0.644583i
$236$	12.6738			0.824991
$237$		−	8.85469i		−	0.575174i
$238$		−	0.760710i		−	0.0493095i
$239$	−26.5267			−1.71587			−0.857935	−	0.513758i	$-0.828253\pi$
$239$	−26.5267			−1.71587			−0.857935	+	0.513758i	$0.828253\pi$
$240$	−5.80889	−	2.82578i	−0.374962	−	0.182403i
$241$	11.7385			0.756143			0.378072	−	0.925776i	$-0.376587\pi$
$241$	11.7385			0.756143			0.378072	+	0.925776i	$0.376587\pi$
$242$		−	0.437361i		−	0.0281146i
$243$		−	1.00000i		−	0.0641500i
$244$	−3.09815			−0.198339
$245$	−0.978157	+	2.01077i	−0.0624921	+	0.128464i
$246$	0.905660			0.0577428
$247$		−	0.0678183i		−	0.00431518i
$248$		−	3.17448i		−	0.201579i
$249$	9.51268			0.602842
$250$	1.03143	+	4.77982i	0.0652336	+	0.302302i
$251$	18.3852			1.16046			0.580231	−	0.814452i	$-0.302962\pi$
$251$	18.3852			1.16046			0.580231	+	0.814452i	$0.302962\pi$
$252$		−	1.80872i		−	0.113938i
$253$			8.28038i			0.520583i
$254$	4.08549			0.256346
$255$	−1.70133	+	3.49738i	−0.106541	+	0.219014i
$256$	2.79598			0.174749
$257$			1.53575i			0.0957973i	0.998852	+	0.0478986i	$0.0152524\pi$
$257$			1.53575i			0.0957973i	−0.998852	+	0.0478986i	$0.984748\pi$
$258$		−	1.68769i		−	0.105071i
$259$	3.18596			0.197966
$260$	0.0938221	+	0.0456405i	0.00581860	+	0.00283050i
$261$	−4.93063			−0.305199
$262$		−	2.06161i		−	0.127367i
$263$		−	14.0623i		−	0.867121i	−0.901125	−	0.433560i	$-0.857257\pi$
$263$		−	14.0623i		−	0.867121i	0.901125	−	0.433560i	$-0.142743\pi$
$264$	1.66578			0.102522
$265$	−21.9523	−	10.6789i	−1.34852	−	0.655997i
$266$	−1.14978			−0.0704976
$267$			9.48265i			0.580329i
$268$			13.3828i			0.817484i
$269$	−12.3826			−0.754982			−0.377491	−	0.926013i	$-0.623213\pi$
$269$	−12.3826			−0.754982			−0.377491	+	0.926013i	$0.623213\pi$
$270$	0.427807	−	0.879433i	0.0260355	−	0.0535206i
$271$	4.80521			0.291896			0.145948	−	0.989292i	$-0.453377\pi$
$271$	4.80521			0.291896			0.145948	+	0.989292i	$0.453377\pi$
$272$		−	5.02469i		−	0.304667i
$273$			0.0257972i			0.00156132i
$274$	−0.463756			−0.0280166
$275$	3.08642	+	3.93370i	0.186118	+	0.237211i
$276$	−14.9769			−0.901500
$277$			19.8713i			1.19395i	0.802260	+	0.596974i	$0.203631\pi$
$277$			19.8713i			1.19395i	−0.802260	+	0.596974i	$0.796369\pi$
$278$			6.49554i			0.389577i
$279$	−1.90570			−0.114091
$280$	1.62940	−	3.34951i	0.0973750	−	0.200172i
$281$	27.2198			1.62379			0.811897	−	0.583800i	$-0.198435\pi$
$281$	27.2198			1.62379			0.811897	+	0.583800i	$0.198435\pi$
$282$		−	4.41819i		−	0.263099i
$283$			17.3650i			1.03224i	0.856516	+	0.516121i	$0.172624\pi$
$283$			17.3650i			1.03224i	−0.856516	+	0.516121i	$0.827376\pi$
$284$	4.28395			0.254206
$285$	5.28613	+	2.57148i	0.313124	+	0.152321i
$286$	−0.0112827			−0.000667158
$287$		−	2.07074i		−	0.122232i
$288$			4.59505i			0.270766i
$289$	13.9748			0.822045
$290$	−4.33616	−	2.10936i	−0.254628	−	0.123866i
$291$	−0.755716			−0.0443009
$292$			20.0390i			1.17270i
$293$			5.96726i			0.348611i	0.984692	+	0.174306i	$0.0557680\pi$
$293$			5.96726i			0.348611i	−0.984692	+	0.174306i	$0.944232\pi$
$294$	0.437361			0.0255074
$295$	6.85399	−	14.0896i	0.399055	−	0.820327i
$296$	−5.30711			−0.308470
$297$		−	1.00000i		−	0.0580259i
$298$		−	6.78963i		−	0.393313i
$299$	0.213610			0.0123534
$300$	−7.11495	+	5.58246i	−0.410782	+	0.322303i
$301$	−3.85880			−0.222417
$302$		−	7.25480i		−	0.417467i
$303$		−	10.9386i		−	0.628408i
$304$	−7.59460			−0.435580
$305$	−1.67548	+	3.44425i	−0.0959380	+	0.197217i
$306$	0.760710			0.0434869
$307$			7.18932i			0.410316i	0.978729	+	0.205158i	$0.0657708\pi$
$307$			7.18932i			0.410316i	−0.978729	+	0.205158i	$0.934229\pi$
$308$		−	1.80872i		−	0.103061i
$309$	−9.47623			−0.539084
$310$	−1.67593	−	0.815271i	−0.0951866	−	0.0463043i
$311$	10.9338			0.619999			0.309999	−	0.950737i	$-0.399671\pi$
$311$	10.9338			0.619999			0.309999	+	0.950737i	$0.399671\pi$
$312$		−	0.0429725i		−	0.00243284i
$313$		−	6.26466i		−	0.354100i	−0.984202	−	0.177050i	$-0.943345\pi$
$313$		−	6.26466i		−	0.354100i	0.984202	−	0.177050i	$-0.0566554\pi$
$314$	−0.00856708			−0.000483468
$315$	−2.01077	−	0.978157i	−0.113294	−	0.0551129i
$316$	16.0156			0.900949
$317$			3.52327i			0.197887i	0.995093	+	0.0989433i	$0.0315463\pi$
$317$			3.52327i			0.197887i	−0.995093	+	0.0989433i	$0.968454\pi$
$318$			4.77481i			0.267758i
$319$	−4.93063			−0.276063
$320$	3.68576	−	7.57674i	0.206041	−	0.423553i
$321$	−5.34487			−0.298321
$322$		−	3.62151i		−	0.201819i
$323$			4.57251i			0.254421i
$324$	1.80872			0.100484
$325$	0.101478	−	0.0796209i	0.00562901	−	0.00441657i
$326$	−0.224316			−0.0124237
$327$			16.5202i			0.913566i
$328$			3.44940i			0.190461i
$329$	−10.1019			−0.556937
$330$	0.427807	−	0.879433i	0.0235500	−	0.0484112i
$331$	17.0628			0.937856			0.468928	−	0.883236i	$-0.344640\pi$
$331$	17.0628			0.937856			0.468928	+	0.883236i	$0.344640\pi$
$332$			17.2057i			0.944287i
$333$			3.18596i			0.174589i
$334$	7.32588			0.400854
$335$	14.8778	+	7.23744i	0.812863	+	0.395423i
$336$	2.88888			0.157602
$337$		−	8.61745i		−	0.469423i	−0.972065	−	0.234711i	$-0.924586\pi$
$337$		−	8.61745i		−	0.469423i	0.972065	−	0.234711i	$-0.0754145\pi$
$338$		−	5.68540i		−	0.309245i
$339$	5.05846			0.274738
$340$	−6.32576	−	3.07722i	−0.343063	−	0.166885i
$341$	−1.90570			−0.103199
$342$		−	1.14978i		−	0.0621730i
$343$		−	1.00000i		−	0.0539949i
$344$	6.42792			0.346570
$345$	−8.09951	+	16.6500i	−0.436063	+	0.896404i
$346$	−1.71040			−0.0919516
$347$			7.64356i			0.410328i	0.978728	+	0.205164i	$0.0657728\pi$
$347$			7.64356i			0.410328i	−0.978728	+	0.205164i	$0.934227\pi$
$348$		−	8.91811i		−	0.478061i
$349$	−6.84409			−0.366356			−0.183178	−	0.983080i	$-0.558638\pi$
$349$	−6.84409			−0.366356			−0.183178	+	0.983080i	$0.558638\pi$
$350$	−1.34988	−	1.72045i	−0.0721541	−	0.0919618i
$351$	−0.0257972			−0.00137695
$352$			4.59505i			0.244917i
$353$		−	18.2214i		−	0.969827i	−0.874562	−	0.484914i	$-0.838851\pi$
$353$		−	18.2214i		−	0.969827i	0.874562	−	0.484914i	$-0.161149\pi$
$354$	−3.06461			−0.162882
$355$	2.31677	−	4.76253i	0.122961	−	0.252769i
$356$	−17.1514			−0.909024
$357$		−	1.73932i		−	0.0920546i
$358$			1.49434i			0.0789782i
$359$	8.69863			0.459096			0.229548	−	0.973297i	$-0.426275\pi$
$359$	8.69863			0.459096			0.229548	+	0.973297i	$0.426275\pi$
$360$	3.34951	+	1.62940i	0.176535	+	0.0858767i
$361$	−12.0889			−0.636255
$362$		−	1.28259i		−	0.0674116i
$363$		−	1.00000i		−	0.0524864i
$364$	−0.0466597			−0.00244563
$365$	22.2777	+	10.8372i	1.16607	+	0.567243i
$366$	0.749155			0.0391590
$367$			13.4591i			0.702557i	0.936271	+	0.351278i	$0.114253\pi$
$367$			13.4591i			0.702557i	−0.936271	+	0.351278i	$0.885747\pi$
$368$		−	23.9210i		−	1.24697i
$369$	2.07074			0.107798
$370$	−1.36298	+	2.80184i	−0.0708577	+	0.145661i
$371$	10.9173			0.566800
$372$		−	3.44686i		−	0.178712i
$373$		−	15.3062i		−	0.792525i	−0.918137	−	0.396263i	$-0.870307\pi$
$373$		−	15.3062i		−	0.792525i	0.918137	−	0.396263i	$-0.129693\pi$
$374$	0.760710			0.0393354
$375$	2.35831	+	10.9288i	0.121783	+	0.564360i
$376$	16.8276			0.867818
$377$			0.127196i			0.00655095i
$378$			0.437361i			0.0224954i
$379$	−2.21901			−0.113983			−0.0569916	−	0.998375i	$-0.518151\pi$
$379$	−2.21901			−0.113983			−0.0569916	+	0.998375i	$0.518151\pi$
$380$	−4.65108	+	9.56111i	−0.238595	+	0.490475i
$381$	9.34124			0.478566
$382$		−	5.11618i		−	0.261766i
$383$		−	29.2940i		−	1.49686i	−0.663216	−	0.748428i	$-0.730809\pi$
$383$		−	29.2940i		−	1.49686i	0.663216	−	0.748428i	$-0.269191\pi$
$384$	−10.8381			−0.553080
$385$	−2.01077	−	0.978157i	−0.102479	−	0.0498515i
$386$	8.47277			0.431253
$387$		−	3.85880i		−	0.196154i
$388$		−	1.36688i		−	0.0693926i
$389$	−26.1981			−1.32830			−0.664148	−	0.747601i	$-0.731205\pi$
$389$	−26.1981			−1.32830			−0.664148	+	0.747601i	$0.731205\pi$
$390$	−0.0226869	−	0.0110362i	−0.00114879	−	0.000558840i
$391$	−14.4022			−0.728352
$392$			1.66578i			0.0841347i
$393$		−	4.71375i		−	0.237777i
$394$	−5.54002			−0.279102
$395$	8.66128	−	17.8048i	0.435796	−	0.895856i
$396$	1.80872			0.0908914
$397$		−	30.3740i		−	1.52443i	−0.647324	−	0.762215i	$-0.724112\pi$
$397$		−	30.3740i		−	1.52443i	0.647324	−	0.762215i	$-0.275888\pi$
$398$			5.61481i			0.281445i
$399$	−2.62891			−0.131610
$400$	−8.91631	−	11.3640i	−0.445815	−	0.568200i
$401$	18.2717			0.912444			0.456222	−	0.889866i	$-0.349202\pi$
$401$	18.2717			0.912444			0.456222	+	0.889866i	$0.349202\pi$
$402$		−	3.23606i		−	0.161400i
$403$			0.0491616i			0.00244891i
$404$	19.7849			0.984335
$405$	0.978157	−	2.01077i	0.0486050	−	0.0999161i
$406$	2.15647			0.107024
$407$			3.18596i			0.157922i
$408$			2.89733i			0.143439i
$409$	−37.0325			−1.83114			−0.915570	−	0.402159i	$-0.868260\pi$
$409$	−37.0325			−1.83114			−0.915570	+	0.402159i	$0.868260\pi$
$410$	1.82108	+	0.885877i	0.0899366	+	0.0437504i
$411$	−1.06035			−0.0523033
$412$		−	17.1398i		−	0.844418i
$413$			7.00705i			0.344794i
$414$	3.62151			0.177988
$415$	19.1278	+	9.30489i	0.938949	+	0.456759i
$416$	0.118539			0.00581186
$417$			14.8517i			0.727290i
$418$		−	1.14978i		−	0.0562376i
$419$	−39.7187			−1.94039			−0.970194	−	0.242330i	$-0.922088\pi$
$419$	−39.7187			−1.94039			−0.970194	+	0.242330i	$0.922088\pi$
$420$	1.76921	−	3.63692i	0.0863285	−	0.177463i
$421$	21.4636			1.04607			0.523037	−	0.852310i	$-0.324799\pi$
$421$	21.4636			1.04607			0.523037	+	0.852310i	$0.324799\pi$
$422$		−	3.21986i		−	0.156741i
$423$		−	10.1019i		−	0.491173i
$424$	−18.1859			−0.883186
$425$	−6.84197	+	5.36827i	−0.331884	+	0.260399i
$426$	−1.03589			−0.0501891
$427$		−	1.71290i		−	0.0828931i
$428$		−	9.66735i		−	0.467289i
$429$	−0.0257972			−0.00124550
$430$	1.65082	−	3.39356i	0.0796097	−	0.163652i
$431$	−21.0475			−1.01382			−0.506911	−	0.861998i	$-0.669213\pi$
$431$	−21.0475			−1.01382			−0.506911	+	0.861998i	$0.669213\pi$
$432$			2.88888i			0.138991i
$433$		−	6.40458i		−	0.307784i	−0.988088	−	0.153892i	$-0.950819\pi$
$433$		−	6.40458i		−	0.307784i	0.988088	−	0.153892i	$-0.0491808\pi$
$434$	0.833477			0.0400082
$435$	−9.91439	−	4.82293i	−0.475359	−	0.231242i
$436$	−29.8803			−1.43100
$437$			21.7683i			1.04132i
$438$		−	4.84559i		−	0.231531i
$439$	30.1740			1.44013			0.720064	−	0.693907i	$-0.244112\pi$
$439$	30.1740			1.44013			0.720064	+	0.693907i	$0.244112\pi$
$440$	3.34951	+	1.62940i	0.159682	+	0.0776784i
$441$	1.00000			0.0476190
$442$		−	0.0196242i		−	0.000933426i
$443$			23.9132i			1.13615i	0.822977	+	0.568075i	$0.192312\pi$
$443$			23.9132i			1.13615i	−0.822977	+	0.568075i	$0.807688\pi$
$444$	−5.76249			−0.273476
$445$	−9.27552	+	19.0675i	−0.439702	+	0.903885i
$446$	9.30790			0.440742
$447$		−	15.5241i		−	0.734265i
$448$			3.76807i			0.178025i
$449$	−37.1653			−1.75394			−0.876969	−	0.480548i	$-0.840438\pi$
$449$	−37.1653			−1.75394			−0.876969	+	0.480548i	$0.840438\pi$
$450$	1.72045	−	1.34988i	0.0811026	−	0.0636339i
$451$	2.07074			0.0975073
$452$			9.14932i			0.430348i
$453$		−	16.5877i		−	0.779357i
$454$	4.56686			0.214333
$455$	−0.0252337	+	0.0518722i	−0.00118297	+	0.00243181i
$456$	4.37919			0.205074
$457$		−	33.7866i		−	1.58047i	−0.612804	−	0.790235i	$-0.709958\pi$
$457$		−	33.7866i		−	1.58047i	0.612804	−	0.790235i	$-0.290042\pi$
$458$		−	6.09300i		−	0.284707i
$459$	1.73932			0.0811845
$460$	−30.1151	−	14.6497i	−1.40412	−	0.683046i
$461$	−39.8493			−1.85597			−0.927985	−	0.372619i	$-0.878460\pi$
$461$	−39.8493			−1.85597			−0.927985	+	0.372619i	$0.878460\pi$
$462$			0.437361i			0.0203479i
$463$			21.5789i			1.00285i	0.865200	+	0.501427i	$0.167192\pi$
$463$			21.5789i			1.00285i	−0.865200	+	0.501427i	$0.832808\pi$
$464$	14.2440			0.661262
$465$	−3.83192	−	1.86407i	−0.177701	−	0.0864442i
$466$	7.82446			0.362461
$467$		−	13.6268i		−	0.630571i	−0.948997	−	0.315286i	$-0.897900\pi$
$467$		−	13.6268i		−	0.630571i	0.948997	−	0.315286i	$-0.102100\pi$
$468$		−	0.0466597i		−	0.00215685i
$469$	−7.39906			−0.341657
$470$	4.32168	−	8.88397i	0.199344	−	0.409787i
$471$	−0.0195881			−0.000902574
$472$		−	11.6722i		−	0.537257i
$473$		−	3.85880i		−	0.177428i
$474$	−3.87270			−0.177879
$475$	8.11391	+	10.3413i	0.372292	+	0.474493i
$476$	3.14593			0.144194
$477$			10.9173i			0.499871i
$478$			11.6017i			0.530651i
$479$	17.1083			0.781698			0.390849	−	0.920455i	$-0.372181\pi$
$479$	17.1083			0.781698			0.390849	+	0.920455i	$0.372181\pi$
$480$	−4.49468	+	9.23960i	−0.205153	+	0.421728i
$481$	0.0821887			0.00374748
$482$		−	5.13396i		−	0.233845i
$483$		−	8.28038i		−	0.376770i
$484$	1.80872			0.0822143
$485$	−1.51957	−	0.739209i	−0.0690003	−	0.0335658i
$486$	−0.437361			−0.0198391
$487$			32.9977i			1.49527i	0.664111	+	0.747634i	$0.268810\pi$
$487$			32.9977i			1.49527i	−0.664111	+	0.747634i	$0.731190\pi$
$488$			2.85332i			0.129164i
$489$	−0.512887			−0.0231935
$490$	0.879433	+	0.427807i	0.0397287	+	0.0193264i
$491$	26.9846			1.21780			0.608898	−	0.793248i	$-0.291612\pi$
$491$	26.9846			1.21780			0.608898	+	0.793248i	$0.291612\pi$
$492$			3.74538i			0.168855i
$493$		−	8.57595i		−	0.386241i
$494$	−0.0296611			−0.00133451
$495$	0.978157	−	2.01077i	0.0439649	−	0.0903775i
$496$	5.50534			0.247197
$497$			2.36851i			0.106242i
$498$		−	4.16047i		−	0.186435i
$499$	23.6494			1.05869			0.529346	−	0.848406i	$-0.322437\pi$
$499$	23.6494			1.05869			0.529346	+	0.848406i	$0.322437\pi$
$500$	−19.7671	+	4.26552i	−0.884010	+	0.190760i
$501$	16.7502			0.748344
$502$		−	8.04096i		−	0.358886i
$503$		−	2.38267i		−	0.106238i	−0.998588	−	0.0531189i	$-0.983084\pi$
$503$		−	2.38267i		−	0.106238i	0.998588	−	0.0531189i	$-0.0169162\pi$
$504$	−1.66578			−0.0741999
$505$	10.6997	−	21.9951i	0.476130	−	0.978770i
$506$	3.62151			0.160996
$507$		−	12.9993i		−	0.577321i
$508$			16.8956i			0.749623i
$509$	11.9399			0.529226			0.264613	−	0.964355i	$-0.414756\pi$
$509$	11.9399			0.529226			0.264613	+	0.964355i	$0.414756\pi$
$510$	1.52962	+	0.744094i	0.0677325	+	0.0329490i
$511$	−11.0792			−0.490113
$512$		−	22.8991i		−	1.01201i
$513$		−	2.62891i		−	0.116069i
$514$	0.671675			0.0296263
$515$	−19.0545	−	9.26924i	−0.839644	−	0.408451i
$516$	6.97947			0.307254
$517$		−	10.1019i		−	0.444282i
$518$		−	1.39341i		−	0.0612230i
$519$	−3.91073			−0.171662
$520$	0.0420338	−	0.0864079i	0.00184330	−	0.00378924i
$521$	−35.5144			−1.55592			−0.777958	−	0.628316i	$-0.783744\pi$
$521$	−35.5144			−1.55592			−0.777958	+	0.628316i	$0.783744\pi$
$522$			2.15647i			0.0943859i
$523$			2.23505i			0.0977319i	0.998805	+	0.0488660i	$0.0155607\pi$
$523$			2.23505i			0.0977319i	−0.998805	+	0.0488660i	$0.984439\pi$
$524$	8.52583			0.372453
$525$	−3.08642	−	3.93370i	−0.134702	−	0.171681i
$526$	−6.15031			−0.268166
$527$		−	3.31462i		−	0.144387i
$528$			2.88888i			0.125723i
$529$	−45.5647			−1.98107
$530$	−4.67052	+	9.60107i	−0.202874	+	0.417044i
$531$	−7.00705			−0.304080
$532$		−	4.75494i		−	0.206153i
$533$		−	0.0534192i		−	0.00231384i
$534$	4.14734			0.179473
$535$	−10.7473	−	5.22812i	−0.464647	−	0.226031i
$536$	12.3252			0.532368
$537$			3.41672i			0.147442i
$538$			5.41568i			0.233486i
$539$	1.00000			0.0430730
$540$	3.63692	+	1.76921i	0.156508	+	0.0761345i
$541$	37.4515			1.61017			0.805083	−	0.593163i	$-0.202121\pi$
$541$	37.4515			1.61017			0.805083	+	0.593163i	$0.202121\pi$
$542$		−	2.10161i		−	0.0902719i
$543$		−	2.93257i		−	0.125849i
$544$	−7.99226			−0.342665
$545$	−16.1593	+	33.2183i	−0.692188	+	1.42291i
$546$	0.0112827			0.000482853
$547$		−	14.1039i		−	0.603038i	−0.953460	−	0.301519i	$-0.902506\pi$
$547$		−	14.1039i		−	0.603038i	0.953460	−	0.301519i	$-0.0974938\pi$
$548$		−	1.91788i		−	0.0819276i
$549$	1.71290			0.0731048
$550$	1.72045	−	1.34988i	0.0733601	−	0.0575590i
$551$	−12.9622			−0.552207
$552$			13.7933i			0.587082i
$553$			8.85469i			0.376540i
$554$	8.69091			0.369242
$555$	−3.11637	+	6.40624i	−0.132282	+	0.271930i
$556$	−26.8625			−1.13922
$557$		−	35.1520i		−	1.48944i	−0.667377	−	0.744720i	$-0.732583\pi$
$557$		−	35.1520i		−	1.48944i	0.667377	−	0.744720i	$-0.267417\pi$
$558$			0.833477i			0.0352839i
$559$	−0.0995460			−0.00421035
$560$	5.80889	+	2.82578i	0.245470	+	0.119411i
$561$	1.73932			0.0734341
$562$		−	11.9049i		−	0.502176i
$563$		−	0.837376i		−	0.0352912i	−0.999844	−	0.0176456i	$-0.994383\pi$
$563$		−	0.837376i		−	0.0352912i	0.999844	−	0.0176456i	$-0.00561706\pi$
$564$	18.2715			0.769370
$565$	10.1714	+	4.94797i	0.427915	+	0.208163i
$566$	7.59477			0.319232
$567$			1.00000i			0.0419961i
$568$		−	3.94542i		−	0.165546i
$569$	−41.1209			−1.72388			−0.861939	−	0.507012i	$-0.830750\pi$
$569$	−41.1209			−1.72388			−0.861939	+	0.507012i	$0.830750\pi$
$570$	1.12467	−	2.31195i	0.0471070	−	0.0968368i
$571$	−23.1499			−0.968795			−0.484398	−	0.874848i	$-0.660961\pi$
$571$	−23.1499			−0.968795			−0.484398	+	0.874848i	$0.660961\pi$
$572$		−	0.0466597i		−	0.00195094i
$573$		−	11.6978i		−	0.488684i
$574$	−0.905660			−0.0378015
$575$	−32.5725	+	25.5567i	−1.35837	+	1.06579i
$576$	−3.76807			−0.157003
$577$		−	41.6966i		−	1.73585i	−0.496694	−	0.867926i	$-0.665453\pi$
$577$		−	41.6966i		−	1.73585i	0.496694	−	0.867926i	$-0.334547\pi$
$578$		−	6.11201i		−	0.254226i
$579$	19.3725			0.805094
$580$	8.72331	−	17.9323i	0.362216	−	0.744599i
$581$	−9.51268			−0.394652
$582$			0.330521i			0.0137005i
$583$			10.9173i			0.452150i
$584$	18.4555			0.763693
$585$	−0.0518722	−	0.0252337i	−0.00214465	−	0.00104328i
$586$	2.60985			0.107812
$587$			34.7195i			1.43303i	0.697572	+	0.716514i	$0.254264\pi$
$587$			34.7195i			1.43303i	−0.697572	+	0.716514i	$0.745736\pi$
$588$			1.80872i			0.0745902i
$589$	−5.00990			−0.206429
$590$	−6.16223	−	2.99767i	−0.253695	−	0.123412i
$591$	−12.6669			−0.521048
$592$		−	9.20386i		−	0.378276i
$593$		−	29.2291i		−	1.20029i	−0.799889	−	0.600147i	$-0.795109\pi$
$593$		−	29.2291i		−	1.20029i	0.799889	−	0.600147i	$-0.204891\pi$
$594$	−0.437361			−0.0179451
$595$	1.70133	−	3.49738i	0.0697476	−	0.143378i
$596$	28.0787			1.15015
$597$			12.8379i			0.525422i
$598$		−	0.0934247i		−	0.00382042i
$599$	−14.2643			−0.582823			−0.291412	−	0.956598i	$-0.594125\pi$
$599$	−14.2643			−0.582823			−0.291412	+	0.956598i	$0.594125\pi$
$600$	5.14130	+	6.55269i	0.209893	+	0.267513i
$601$	−12.8690			−0.524936			−0.262468	−	0.964941i	$-0.584536\pi$
$601$	−12.8690			−0.524936			−0.262468	+	0.964941i	$0.584536\pi$
$602$			1.68769i			0.0687850i
$603$		−	7.39906i		−	0.301313i
$604$	30.0024			1.22078
$605$	0.978157	−	2.01077i	0.0397677	−	0.0817496i
$606$	−4.78413			−0.194342
$607$			30.2146i			1.22637i	0.789938	+	0.613186i	$0.210112\pi$
$607$			30.2146i			1.22637i	−0.789938	+	0.613186i	$0.789888\pi$
$608$			12.0800i			0.489907i
$609$	4.93063			0.199799
$610$	1.50638	+	0.732791i	0.0609916	+	0.0296699i
$611$	−0.260601			−0.0105428
$612$			3.14593i			0.127167i
$613$		−	21.5477i		−	0.870302i	−0.900357	−	0.435151i	$-0.856695\pi$
$613$		−	21.5477i		−	0.870302i	0.900357	−	0.435151i	$-0.143305\pi$
$614$	3.14432			0.126895
$615$	4.16379	+	2.02551i	0.167900	+	0.0816763i
$616$	−1.66578			−0.0671163
$617$			36.2211i			1.45821i	0.684404	+	0.729103i	$0.260062\pi$
$617$			36.2211i			1.45821i	−0.684404	+	0.729103i	$0.739938\pi$
$618$			4.14453i			0.166717i
$619$	34.2672			1.37732			0.688658	−	0.725086i	$-0.258200\pi$
$619$	34.2672			1.37732			0.688658	+	0.725086i	$0.258200\pi$
$620$	3.37157	−	6.93086i	0.135406	−	0.278350i
$621$	8.28038			0.332280
$622$		−	4.78201i		−	0.191741i
$623$		−	9.48265i		−	0.379914i
$624$	0.0745250			0.00298339
$625$	−5.94803	+	24.2821i	−0.237921	+	0.971284i
$626$	−2.73992			−0.109509
$627$		−	2.62891i		−	0.104988i
$628$		−	0.0354294i		−	0.00141379i
$629$	−5.54140			−0.220950
$630$	−0.427807	+	0.879433i	−0.0170442	+	0.0350375i
$631$	6.62987			0.263931			0.131966	−	0.991254i	$-0.457871\pi$
$631$	6.62987			0.263931			0.131966	+	0.991254i	$0.457871\pi$
$632$		−	14.7500i		−	0.586723i
$633$		−	7.36203i		−	0.292615i
$634$	1.54094			0.0611986
$635$	18.7831	+	9.13719i	0.745385	+	0.362598i
$636$	−19.7464			−0.782994
$637$		−	0.0257972i		−	0.00102212i
$638$			2.15647i			0.0853753i
$639$	−2.36851			−0.0936966
$640$	−21.7930	−	10.6014i	−0.861443	−	0.419056i
$641$	1.02086			0.0403217			0.0201609	−	0.999797i	$-0.493582\pi$
$641$	1.02086			0.0403217			0.0201609	+	0.999797i	$0.493582\pi$
$642$			2.33764i			0.0922591i
$643$			15.9759i			0.630027i	0.949087	+	0.315013i	$0.102009\pi$
$643$			15.9759i			0.630027i	−0.949087	+	0.315013i	$0.897991\pi$
$644$	14.9769			0.590171
$645$	3.77451	−	7.75917i	0.148621	−	0.305517i
$646$	1.99984			0.0786825
$647$		−	0.879073i		−	0.0345599i	−0.999851	−	0.0172800i	$-0.994499\pi$
$647$		−	0.879073i		−	0.0345599i	0.999851	−	0.0172800i	$-0.00550066\pi$
$648$		−	1.66578i		−	0.0654381i
$649$	−7.00705			−0.275051
$650$	−0.0348230	−	0.0443826i	−0.00136587	−	0.00174083i
$651$	1.90570			0.0746902
$652$		−	0.927666i		−	0.0363302i
$653$		−	16.5372i		−	0.647152i	−0.946202	−	0.323576i	$-0.895115\pi$
$653$		−	16.5372i		−	0.647152i	0.946202	−	0.323576i	$-0.104885\pi$
$654$	7.22527			0.282530
$655$	4.61079	−	9.47829i	0.180158	−	0.370347i
$656$	−5.98212			−0.233563
$657$		−	11.0792i		−	0.432239i
$658$			4.41819i			0.172239i
$659$	10.2423			0.398984			0.199492	−	0.979899i	$-0.436071\pi$
$659$	10.2423			0.398984			0.199492	+	0.979899i	$0.436071\pi$
$660$	3.63692	+	1.76921i	0.141567	+	0.0688663i
$661$	22.7201			0.883708			0.441854	−	0.897087i	$-0.354321\pi$
$661$	22.7201			0.883708			0.441854	+	0.897087i	$0.354321\pi$
$662$		−	7.46259i		−	0.290042i
$663$		−	0.0448695i		−	0.00174259i
$664$	15.8461			0.614946
$665$	−5.28613	−	2.57148i	−0.204988	−	0.0997178i
$666$	1.39341			0.0539937
$667$		−	40.8275i		−	1.58085i
$668$			30.2964i			1.17220i
$669$	21.2820			0.822809
$670$	3.16537	−	6.50698i	0.122289	−	0.251386i
$671$	1.71290			0.0661258
$672$		−	4.59505i		−	0.177258i
$673$		−	15.0702i		−	0.580912i	−0.956888	−	0.290456i	$-0.906193\pi$
$673$		−	15.0702i		−	0.580912i	0.956888	−	0.290456i	$-0.0938070\pi$
$674$	−3.76894			−0.145174
$675$	3.93370	−	3.08642i	0.151408	−	0.118796i
$676$	23.5121			0.904312
$677$		−	27.9338i		−	1.07358i	−0.843715	−	0.536791i	$-0.819636\pi$
$677$		−	27.9338i		−	1.07358i	0.843715	−	0.536791i	$-0.180364\pi$
$678$		−	2.21237i		−	0.0849657i
$679$	0.755716			0.0290017
$680$	−2.83404	+	5.82587i	−0.108680	+	0.223412i
$681$	10.4419			0.400133
$682$			0.833477i			0.0319155i
$683$		−	32.5701i		−	1.24626i	−0.782118	−	0.623130i	$-0.785861\pi$
$683$		−	32.5701i		−	1.24626i	0.782118	−	0.623130i	$-0.214139\pi$
$684$	4.75494			0.181810
$685$	−2.13213	−	1.03719i	−0.0814644	−	0.0396290i
$686$	−0.437361			−0.0166985
$687$		−	13.9313i		−	0.531512i
$688$			11.1476i			0.424999i
$689$	0.281636			0.0107295
$690$	7.28204	+	3.54241i	0.277223	+	0.134857i
$691$	−31.8400			−1.21125			−0.605626	−	0.795750i	$-0.707077\pi$
$691$	−31.8400			−1.21125			−0.605626	+	0.795750i	$0.707077\pi$
$692$		−	7.07340i		−	0.268890i
$693$			1.00000i			0.0379869i
$694$	3.34299			0.126898
$695$	−14.5273	+	29.8634i	−0.551051	+	1.13278i
$696$	−8.21336			−0.311327
$697$			3.60168i			0.136423i
$698$			2.99334i			0.113299i
$699$	17.8902			0.676669
$700$	7.11495	−	5.58246i	0.268920	−	0.210997i
$701$	−23.3301			−0.881167			−0.440584	−	0.897712i	$-0.645228\pi$
$701$	−23.3301			−0.881167			−0.440584	+	0.897712i	$0.645228\pi$
$702$			0.0112827i			0.000425837i
$703$			8.37558i			0.315891i
$704$	−3.76807			−0.142015
$705$	9.88127	−	20.3127i	0.372150	−	0.765020i
$706$	−7.96932			−0.299929
$707$			10.9386i			0.411390i
$708$		−	12.6738i		−	0.476309i
$709$	3.93346			0.147724			0.0738621	−	0.997268i	$-0.476468\pi$
$709$	3.93346			0.147724			0.0738621	+	0.997268i	$0.476468\pi$
$710$	−2.08294	−	1.01326i	−0.0781715	−	0.0380271i
$711$	−8.85469			−0.332077
$712$			15.7960i			0.591982i
$713$		−	15.7799i		−	0.590962i
$714$	−0.760710			−0.0284689
$715$	−0.0518722	−	0.0252337i	−0.00193991	−	0.000943685i
$716$	−6.17987			−0.230953
$717$			26.5267i			0.990658i
$718$		−	3.80444i		−	0.141980i
$719$	−27.2732			−1.01712			−0.508560	−	0.861026i	$-0.669822\pi$
$719$	−27.2732			−1.01712			−0.508560	+	0.861026i	$0.669822\pi$
$720$	−2.82578	+	5.80889i	−0.105311	+	0.216485i
$721$	9.47623			0.352913
$722$			5.28719i			0.196769i
$723$		−	11.7385i		−	0.436560i
$724$	5.30419			0.197129
$725$	−15.2180	−	19.3956i	−0.565183	−	0.720336i
$726$	−0.437361			−0.0162320
$727$		−	51.5190i		−	1.91073i	−0.295422	−	0.955367i	$-0.595460\pi$
$727$		−	51.5190i		−	1.91073i	0.295422	−	0.955367i	$-0.404540\pi$
$728$			0.0429725i			0.00159267i
$729$	−1.00000			−0.0370370
$730$	4.73975	−	9.74338i	0.175426	−	0.360619i
$731$	6.71168			0.248241
$732$			3.09815i			0.114511i
$733$			23.1428i			0.854800i	0.904063	+	0.427400i	$0.140570\pi$
$733$			23.1428i			0.854800i	−0.904063	+	0.427400i	$0.859430\pi$
$734$	5.88646			0.217273
$735$	2.01077	+	0.978157i	0.0741685	+	0.0360798i
$736$	−38.0488			−1.40250
$737$		−	7.39906i		−	0.272548i
$738$		−	0.905660i		−	0.0333378i
$739$	31.4244			1.15596			0.577982	−	0.816049i	$-0.303840\pi$
$739$	31.4244			1.15596			0.577982	+	0.816049i	$0.303840\pi$
$740$	−11.5871	−	5.63662i	−0.425949	−	0.207206i
$741$	−0.0678183			−0.00249137
$742$		−	4.77481i		−	0.175289i
$743$		−	29.8588i		−	1.09541i	−0.836670	−	0.547707i	$-0.815501\pi$
$743$		−	29.8588i		−	1.09541i	0.836670	−	0.547707i	$-0.184499\pi$
$744$	−3.17448			−0.116382
$745$	15.1850	−	31.2155i	0.556335	−	1.14365i
$746$	−6.69433			−0.245097
$747$		−	9.51268i		−	0.348051i
$748$			3.14593i			0.115027i
$749$	5.34487			0.195297
$750$	4.77982	−	1.03143i	0.174534	−	0.0376626i
$751$	−2.27149			−0.0828879			−0.0414439	−	0.999141i	$-0.513196\pi$
$751$	−2.27149			−0.0828879			−0.0414439	+	0.999141i	$0.513196\pi$
$752$			29.1833i			1.06421i
$753$		−	18.3852i		−	0.669993i
$754$	0.0556307			0.00202595
$755$	16.2253	−	33.3540i	0.590501	−	1.21388i
$756$	−1.80872			−0.0657824
$757$		−	21.5578i		−	0.783533i	−0.920065	−	0.391766i	$-0.871864\pi$
$757$		−	21.5578i		−	0.783533i	0.920065	−	0.391766i	$-0.128136\pi$
$758$			0.970510i			0.0352505i
$759$	8.28038			0.300559
$760$	8.80555	+	4.28353i	0.319411	+	0.155380i
$761$	−18.9626			−0.687394			−0.343697	−	0.939081i	$-0.611679\pi$
$761$	−18.9626			−0.687394			−0.343697	+	0.939081i	$0.611679\pi$
$762$		−	4.08549i		−	0.148002i
$763$		−	16.5202i		−	0.598070i
$764$	21.1581			0.765472
$765$	3.49738	+	1.70133i	0.126448	+	0.0615116i
$766$	−12.8121			−0.462919
$767$			0.180762i			0.00652693i
$768$		−	2.79598i		−	0.100891i
$769$	−27.0273			−0.974631			−0.487315	−	0.873226i	$-0.662024\pi$
$769$	−27.0273			−0.974631			−0.487315	+	0.873226i	$0.662024\pi$
$770$	−0.427807	+	0.879433i	−0.0154171	+	0.0316926i
$771$	1.53575			0.0553086
$772$			35.0394i			1.26109i
$773$			45.5894i			1.63974i	0.572553	+	0.819868i	$0.305953\pi$
$773$			45.5894i			1.63974i	−0.572553	+	0.819868i	$0.694047\pi$
$774$	−1.68769			−0.0606626
$775$	−5.88178	−	7.49644i	−0.211280	−	0.269280i
$776$	−1.25886			−0.0451904
$777$		−	3.18596i		−	0.114296i
$778$			11.4580i			0.410790i
$779$	5.44378			0.195044
$780$	0.0456405	−	0.0938221i	0.00163419	−	0.00335937i
$781$	−2.36851			−0.0847518
$782$			6.29897i			0.225251i
$783$			4.93063i			0.176206i
$784$	−2.88888			−0.103174
$785$	−0.0393873	−	0.0191603i	−0.00140579	−	0.000683859i
$786$	−2.06161			−0.0735352
$787$			28.1716i			1.00421i	0.864807	+	0.502105i	$0.167441\pi$
$787$			28.1716i			1.00421i	−0.864807	+	0.502105i	$0.832559\pi$
$788$		−	22.9109i		−	0.816166i
$789$	−14.0623			−0.500632
$790$	−7.78711	−	3.78810i	−0.277053	−	0.134775i
$791$	−5.05846			−0.179858
$792$		−	1.66578i		−	0.0591910i
$793$		−	0.0441880i		−	0.00156916i
$794$	−13.2844			−0.471446
$795$	−10.6789	+	21.9523i	−0.378740	+	0.778568i
$796$	−23.2202			−0.823018
$797$			38.3583i			1.35872i	0.733804	+	0.679361i	$0.237743\pi$
$797$			38.3583i			1.35872i	−0.733804	+	0.679361i	$0.762257\pi$
$798$			1.14978i			0.0407018i
$799$	17.5705			0.621599
$800$	−18.0756	+	14.1822i	−0.639067	+	0.501418i
$801$	9.48265			0.335053
$802$		−	7.99132i		−	0.282183i
$803$		−	11.0792i		−	0.390975i
$804$	13.3828			0.471975
$805$	8.09951	−	16.6500i	0.285470	−	0.586834i
$806$	0.0215013			0.000757352
$807$			12.3826i			0.435889i
$808$		−	18.2214i		−	0.641026i
$809$	−52.4122			−1.84271			−0.921357	−	0.388717i	$-0.872918\pi$
$809$	−52.4122			−1.84271			−0.921357	+	0.388717i	$0.872918\pi$
$810$	−0.879433	−	0.427807i	−0.0309001	−	0.0150316i
$811$	29.2676			1.02773			0.513863	−	0.857872i	$-0.328214\pi$
$811$	29.2676			1.02773			0.513863	+	0.857872i	$0.328214\pi$
$812$			8.91811i			0.312964i
$813$		−	4.80521i		−	0.168526i
$814$	1.39341			0.0488391
$815$	−1.03130	−	0.501683i	−0.0361248	−	0.0175732i
$816$	−5.02469			−0.175899
$817$		−	10.1444i		−	0.354908i
$818$			16.1966i			0.566300i
$819$	0.0257972			0.000901426
$820$	−3.66357	+	7.53111i	−0.127937	+	0.262998i
$821$	−41.1927			−1.43764			−0.718818	−	0.695199i	$-0.755316\pi$
$821$	−41.1927			−1.43764			−0.718818	+	0.695199i	$0.755316\pi$
$822$			0.463756i			0.0161754i
$823$			21.4531i			0.747809i	0.927467	+	0.373905i	$0.121981\pi$
$823$			21.4531i			0.747809i	−0.927467	+	0.373905i	$0.878019\pi$
$824$	−15.7853			−0.549908
$825$	3.93370	−	3.08642i	0.136954	−	0.107455i
$826$	3.06461			0.106631
$827$			12.4824i			0.434056i	0.976165	+	0.217028i	$0.0696363\pi$
$827$			12.4824i			0.434056i	−0.976165	+	0.217028i	$0.930364\pi$
$828$			14.9769i			0.520482i
$829$	46.2552			1.60651			0.803255	−	0.595635i	$-0.203099\pi$
$829$	46.2552			1.60651			0.803255	+	0.595635i	$0.203099\pi$
$830$	4.06959	−	8.36577i	0.141258	−	0.290380i
$831$	19.8713			0.689327
$832$			0.0972056i			0.00337000i
$833$			1.73932i			0.0602638i
$834$	6.49554			0.224922
$835$	33.6809	+	16.3843i	1.16557	+	0.567003i
$836$	4.75494			0.164453
$837$			1.90570i			0.0658705i
$838$			17.3714i			0.600086i
$839$	−43.5378			−1.50309			−0.751547	−	0.659680i	$-0.770692\pi$
$839$	−43.5378			−1.50309			−0.751547	+	0.659680i	$0.770692\pi$
$840$	−3.34951	−	1.62940i	−0.115569	−	0.0562195i
$841$	−4.68885			−0.161684
$842$		−	9.38735i		−	0.323509i
$843$		−	27.2198i		−	0.937498i
$844$	13.3158			0.458350
$845$	12.7154	−	26.1387i	0.437423	−	0.899199i
$846$	−4.41819			−0.151900
$847$			1.00000i			0.0343604i
$848$		−	31.5389i		−	1.08305i
$849$	17.3650			0.595965
$850$	2.34787	+	2.99241i	0.0805313	+	0.102639i
$851$	−26.3809			−0.904327
$852$		−	4.28395i		−	0.146766i
$853$			49.9931i			1.71173i	0.517200	+	0.855865i	$0.326974\pi$
$853$			49.9931i			1.71173i	−0.517200	+	0.855865i	$0.673026\pi$
$854$	−0.749155			−0.0256356
$855$	2.57148	−	5.28613i	0.0879428	−	0.180782i
$856$	−8.90339			−0.304312
$857$			10.7203i			0.366199i	0.983094	+	0.183099i	$0.0586130\pi$
$857$			10.7203i			0.366199i	−0.983094	+	0.183099i	$0.941387\pi$
$858$			0.0112827i			0.000385184i
$859$	−2.41919			−0.0825418			−0.0412709	−	0.999148i	$-0.513141\pi$
$859$	−2.41919			−0.0825418			−0.0412709	+	0.999148i	$0.513141\pi$
$860$	14.0341	+	6.82701i	0.478560	+	0.232799i
$861$	−2.07074			−0.0705706
$862$			9.20535i			0.313536i
$863$			10.1189i			0.344451i	0.985058	+	0.172226i	$0.0550958\pi$
$863$			10.1189i			0.344451i	−0.985058	+	0.172226i	$0.944904\pi$
$864$	4.59505			0.156327
$865$	−7.86359	−	3.82531i	−0.267370	−	0.130064i
$866$	−2.80111			−0.0951856
$867$		−	13.9748i		−	0.474608i
$868$			3.44686i			0.116994i
$869$	−8.85469			−0.300375
$870$	−2.10936	+	4.33616i	−0.0715140	+	0.147010i
$871$	−0.190875			−0.00646754
$872$			27.5190i			0.931910i
$873$			0.755716i			0.0255771i
$874$	9.52062			0.322040
$875$	−2.35831	−	10.9288i	−0.0797256	−	0.369460i
$876$	20.0390			0.677057
$877$		−	38.2969i		−	1.29320i	−0.762831	−	0.646598i	$-0.776191\pi$
$877$		−	38.2969i		−	1.29320i	0.762831	−	0.646598i	$-0.223809\pi$
$878$		−	13.1969i		−	0.445375i
$879$	5.96726			0.201271
$880$	−2.82578	+	5.80889i	−0.0952570	+	0.195818i
$881$	−30.1330			−1.01521			−0.507603	−	0.861591i	$-0.669469\pi$
$881$	−30.1330			−1.01521			−0.507603	+	0.861591i	$0.669469\pi$
$882$		−	0.437361i		−	0.0147267i
$883$			27.4676i			0.924358i	0.886787	+	0.462179i	$0.152932\pi$
$883$			27.4676i			0.924358i	−0.886787	+	0.462179i	$0.847068\pi$
$884$	0.0811562			0.00272958
$885$	−14.0896	−	6.85399i	−0.473616	−	0.230394i
$886$	10.4587			0.351366
$887$			40.2212i			1.35049i	0.737591	+	0.675247i	$0.235963\pi$
$887$			40.2212i			1.35049i	−0.737591	+	0.675247i	$0.764037\pi$
$888$			5.30711i			0.178095i
$889$	−9.34124			−0.313295
$890$	8.33936	+	4.05675i	0.279536	+	0.135982i
$891$	−1.00000			−0.0335013
$892$			38.4930i			1.28884i
$893$		−	26.5570i		−	0.888697i
$894$	−6.78963			−0.227079
$895$	−3.34208	+	6.87024i	−0.111714	+	0.229647i
$896$	10.8381			0.362076
$897$		−	0.213610i		−	0.00713224i
$898$			16.2546i			0.542424i
$899$	9.39629			0.313384
$900$	5.58246	+	7.11495i	0.186082	+	0.237165i
$901$	−18.9887			−0.632607
$902$		−	0.905660i		−	0.0301552i
$903$			3.85880i			0.128413i
$904$	8.42630			0.280255
$905$	2.86852	−	5.89674i	0.0953527	−	0.196014i
$906$	−7.25480			−0.241024
$907$		−	36.0929i		−	1.19845i	−0.800582	−	0.599223i	$-0.795476\pi$
$907$		−	36.0929i		−	1.19845i	0.800582	−	0.599223i	$-0.204524\pi$
$908$			18.8864i			0.626766i
$909$	−10.9386			−0.362812
$910$	0.0226869	+	0.0110362i	0.000752063	+	0.000365847i
$911$	−32.8345			−1.08786			−0.543928	−	0.839132i	$-0.683064\pi$
$911$	−32.8345			−1.08786			−0.543928	+	0.839132i	$0.683064\pi$
$912$			7.59460i			0.251482i
$913$		−	9.51268i		−	0.314824i
$914$	−14.7769			−0.488777
$915$	3.44425	+	1.67548i	0.113864	+	0.0553898i
$916$	25.1978			0.832557
$917$			4.71375i			0.155662i
$918$		−	0.760710i		−	0.0251072i
$919$	−47.5464			−1.56841			−0.784206	−	0.620500i	$-0.786930\pi$
$919$	−47.5464			−1.56841			−0.784206	+	0.620500i	$0.786930\pi$
$920$	−13.4920	+	27.7352i	−0.444819	+	0.914403i
$921$	7.18932			0.236896
$922$			17.4285i			0.573978i
$923$			0.0611007i			0.00201115i
$924$	−1.80872			−0.0595024
$925$	−12.5326	+	9.83320i	−0.412070	+	0.323314i
$926$	9.43775			0.310144
$927$			9.47623i			0.311240i
$928$		−	22.6565i		−	0.743736i
$929$	−40.5411			−1.33011			−0.665054	−	0.746795i	$-0.731592\pi$
$929$	−40.5411			−1.33011			−0.665054	+	0.746795i	$0.731592\pi$
$930$	−0.815271	+	1.67593i	−0.0267338	+	0.0549560i
$931$	2.62891			0.0861589
$932$			32.3582i			1.05993i
$933$		−	10.9338i		−	0.357957i
$934$	−5.95981			−0.195011
$935$	3.49738	+	1.70133i	0.114376	+	0.0556393i
$936$	−0.0429725			−0.00140460
$937$		−	16.8775i		−	0.551365i	−0.961249	−	0.275683i	$-0.911096\pi$
$937$		−	16.8775i		−	0.551365i	0.961249	−	0.275683i	$-0.0889039\pi$
$938$			3.23606i			0.105661i
$939$	−6.26466			−0.204439
$940$	36.7399	+	17.8724i	1.19832	+	0.582934i
$941$	10.2428			0.333906			0.166953	−	0.985965i	$-0.446607\pi$
$941$	10.2428			0.333906			0.166953	+	0.985965i	$0.446607\pi$
$942$			0.00856708i			0.000279131i
$943$			17.1465i			0.558367i
$944$	20.2425			0.658839
$945$	−0.978157	+	2.01077i	−0.0318194	+	0.0654105i
$946$	−1.68769			−0.0548714
$947$		−	43.8469i		−	1.42483i	−0.701757	−	0.712416i	$-0.747601\pi$
$947$		−	43.8469i		−	1.42483i	0.701757	−	0.712416i	$-0.252399\pi$
$948$		−	16.0156i		−	0.520163i
$949$	−0.285811			−0.00927781
$950$	4.52289	−	3.54870i	0.146742	−	0.115135i
$951$	3.52327			0.114250
$952$		−	2.89733i		−	0.0939029i
$953$			48.4706i			1.57012i	0.619422	+	0.785058i	$0.287367\pi$
$953$			48.4706i			1.57012i	−0.619422	+	0.785058i	$0.712633\pi$
$954$	4.77481			0.154590
$955$	11.4423	−	23.5217i	0.370265	−	0.761144i
$956$	−47.9793			−1.55176
$957$			4.93063i			0.159385i
$958$		−	7.48250i		−	0.241749i
$959$	1.06035			0.0342406
$960$	−7.57674	−	3.68576i	−0.244538	−	0.118958i
$961$	−27.3683			−0.882849
$962$		−	0.0359461i		−	0.00115895i
$963$			5.34487i			0.172236i
$964$	21.2316			0.683824
$965$	38.9537	+	18.9493i	1.25396	+	0.610001i
$966$	−3.62151			−0.116520
$967$		−	48.0624i		−	1.54558i	−0.634661	−	0.772791i	$-0.718860\pi$
$967$		−	48.0624i		−	1.54558i	0.634661	−	0.772791i	$-0.281140\pi$
$968$		−	1.66578i		−	0.0535403i
$969$	4.57251			0.146890
$970$	−0.323301	+	0.664602i	−0.0103806	+	0.0213391i
$971$	−7.93304			−0.254583			−0.127292	−	0.991865i	$-0.540628\pi$
$971$	−7.93304			−0.254583			−0.127292	+	0.991865i	$0.540628\pi$
$972$		−	1.80872i		−	0.0580146i
$973$		−	14.8517i		−	0.476123i
$974$	14.4319			0.462428
$975$	−0.0796209	−	0.101478i	−0.00254991	−	0.00324991i
$976$	−4.94837			−0.158393
$977$			20.2929i			0.649227i	0.945847	+	0.324614i	$0.105234\pi$
$977$			20.2929i			0.649227i	−0.945847	+	0.324614i	$0.894766\pi$
$978$			0.224316i			0.00717285i
$979$	9.48265			0.303067
$980$	−1.76921	+	3.63692i	−0.0565152	+	0.116177i
$981$	16.5202			0.527448
$982$		−	11.8020i		−	0.376617i
$983$			53.3231i			1.70074i	0.526184	+	0.850371i	$0.323622\pi$
$983$			53.3231i			1.70074i	−0.526184	+	0.850371i	$0.676378\pi$
$984$	3.44940			0.109963
$985$	−25.4703	−	12.3902i	−0.811552	−	0.394786i
$986$	−3.75078			−0.119449
$987$			10.1019i			0.321548i
$988$		−	0.122664i		−	0.00390246i
$989$	31.9523			1.01602
$990$	−0.879433	−	0.427807i	−0.0279502	−	0.0135966i
$991$	36.9618			1.17413			0.587065	−	0.809540i	$-0.300283\pi$
$991$	36.9618			1.17413			0.587065	+	0.809540i	$0.300283\pi$
$992$		−	8.75677i		−	0.278028i
$993$		−	17.0628i		−	0.541471i
$994$	1.03589			0.0328565
$995$	−12.5575	+	25.8142i	−0.398100	+	0.818365i
$996$	17.2057			0.545184
$997$			29.4173i			0.931654i	0.884876	+	0.465827i	$0.154243\pi$
$997$			29.4173i			0.931654i	−0.884876	+	0.465827i	$0.845757\pi$
$998$		−	10.3433i		−	0.327412i
$999$	3.18596			0.100799

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1155.2.c.e.694.9	✓	20
5.2	odd	4		5775.2.a.cm.1.7		10
5.3	odd	4		5775.2.a.cp.1.4		10
5.4	even	2	inner	1155.2.c.e.694.12	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1155.2.c.e.694.9	✓	20	1.1	even	1	trivial
1155.2.c.e.694.12	yes	20	5.4	even	2	inner
5775.2.a.cm.1.7		10	5.2	odd	4
5775.2.a.cp.1.4		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)

\(f(q)\)	\(=\)	\(q-0.437361i q^{2} -1.00000i q^{3} +1.80872 q^{4} +(0.978157 - 2.01077i) q^{5} -0.437361 q^{6} +1.00000i q^{7} -1.66578i q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q-0.437361i q^{2} -1.00000i q^{3} +1.80872 q^{4} +(0.978157 - 2.01077i) q^{5} -0.437361 q^{6} +1.00000i q^{7} -1.66578i q^{8} -1.00000 q^{9} +(-0.879433 - 0.427807i) q^{10} -1.00000 q^{11} -1.80872i q^{12} +0.0257972i q^{13} +0.437361 q^{14} +(-2.01077 - 0.978157i) q^{15} +2.88888 q^{16} -1.73932i q^{17} +0.437361i q^{18} -2.62891 q^{19} +(1.76921 - 3.63692i) q^{20} +1.00000 q^{21} +0.437361i q^{22} -8.28038i q^{23} -1.66578 q^{24} +(-3.08642 - 3.93370i) q^{25} +0.0112827 q^{26} +1.00000i q^{27} +1.80872i q^{28} +4.93063 q^{29} +(-0.427807 + 0.879433i) q^{30} +1.90570 q^{31} -4.59505i q^{32} +1.00000i q^{33} -0.760710 q^{34} +(2.01077 + 0.978157i) q^{35} -1.80872 q^{36} -3.18596i q^{37} +1.14978i q^{38} +0.0257972 q^{39} +(-3.34951 - 1.62940i) q^{40} -2.07074 q^{41} -0.437361i q^{42} +3.85880i q^{43} -1.80872 q^{44} +(-0.978157 + 2.01077i) q^{45} -3.62151 q^{46} +10.1019i q^{47} -2.88888i q^{48} -1.00000 q^{49} +(-1.72045 + 1.34988i) q^{50} -1.73932 q^{51} +0.0466597i q^{52} -10.9173i q^{53} +0.437361 q^{54} +(-0.978157 + 2.01077i) q^{55} +1.66578 q^{56} +2.62891i q^{57} -2.15647i q^{58} +7.00705 q^{59} +(-3.63692 - 1.76921i) q^{60} -1.71290 q^{61} -0.833477i q^{62} -1.00000i q^{63} +3.76807 q^{64} +(0.0518722 + 0.0252337i) q^{65} +0.437361 q^{66} +7.39906i q^{67} -3.14593i q^{68} -8.28038 q^{69} +(0.427807 - 0.879433i) q^{70} +2.36851 q^{71} +1.66578i q^{72} +11.0792i q^{73} -1.39341 q^{74} +(-3.93370 + 3.08642i) q^{75} -4.75494 q^{76} -1.00000i q^{77} -0.0112827i q^{78} +8.85469 q^{79} +(2.82578 - 5.80889i) q^{80} +1.00000 q^{81} +0.905660i q^{82} +9.51268i q^{83} +1.80872 q^{84} +(-3.49738 - 1.70133i) q^{85} +1.68769 q^{86} -4.93063i q^{87} +1.66578i q^{88} -9.48265 q^{89} +(0.879433 + 0.427807i) q^{90} -0.0257972 q^{91} -14.9769i q^{92} -1.90570i q^{93} +4.41819 q^{94} +(-2.57148 + 5.28613i) q^{95} -4.59505 q^{96} -0.755716i q^{97} +0.437361i q^{98} +1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 26 q^{4} - 2 q^{5} + 6 q^{6} - 20 q^{9}+O(q^{10}) \) 20 * q - 26 * q^4 - 2 * q^5 + 6 * q^6 - 20 * q^9	\( 20 q - 26 q^{4} - 2 q^{5} + 6 q^{6} - 20 q^{9} - 2 q^{10} - 20 q^{11} - 6 q^{14} + 2 q^{15} + 38 q^{16} + 2 q^{19} + 4 q^{20} + 20 q^{21} - 18 q^{24} + 12 q^{25} + 20 q^{26} - 38 q^{29} + 6 q^{30} + 20 q^{31} - 32 q^{34} - 2 q^{35} + 26 q^{36} + 2 q^{40} + 12 q^{41} + 26 q^{44} + 2 q^{45} + 8 q^{46} - 20 q^{49} - 6 q^{50} + 26 q^{51} - 6 q^{54} + 2 q^{55} + 18 q^{56} - 22 q^{59} + 16 q^{60} + 34 q^{61} - 26 q^{64} - 28 q^{65} - 6 q^{66} - 26 q^{69} - 6 q^{70} + 72 q^{71} - 72 q^{74} - 8 q^{75} + 44 q^{76} + 4 q^{79} - 8 q^{80} + 20 q^{81} - 26 q^{84} - 16 q^{85} + 52 q^{86} + 6 q^{89} + 2 q^{90} + 16 q^{94} + 14 q^{95} + 62 q^{96} + 20 q^{99}+O(q^{100}) \) 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 + 2 * q^19 + 4 * q^20 + 20 * q^21 - 18 * q^24 + 12 * q^25 + 20 * q^26 - 38 * q^29 + 6 * q^30 + 20 * q^31 - 32 * q^34 - 2 * q^35 + 26 * q^36 + 2 * q^40 + 12 * q^41 + 26 * q^44 + 2 * q^45 + 8 * q^46 - 20 * q^49 - 6 * q^50 + 26 * q^51 - 6 * q^54 + 2 * q^55 + 18 * q^56 - 22 * q^59 + 16 * q^60 + 34 * q^61 - 26 * q^64 - 28 * q^65 - 6 * q^66 - 26 * q^69 - 6 * q^70 + 72 * q^71 - 72 * q^74 - 8 * q^75 + 44 * q^76 + 4 * q^79 - 8 * q^80 + 20 * q^81 - 26 * q^84 - 16 * q^85 + 52 * q^86 + 6 * q^89 + 2 * q^90 + 16 * q^94 + 14 * q^95 + 62 * q^96 + 20 * q^99

Introduction

L-functions

Modular forms

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Database

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