LMFDB - Embedded newform 1320.2.bw.f.1081.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1320,2,Mod(361,1320)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1320, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 0, 0, 6]))

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

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

chi := DirichletCharacter("1320.361");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1320 = 2^{3} \cdot 3 \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1320.bw (of order $5$, degree $4$, 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:	$10.5402530668$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$3$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 2 x^{11} + 7 x^{10} + 15 x^{9} + 51 x^{8} + 175 x^{7} + 1103 x^{6} + 2884 x^{5} + 5561 x^{4} + \cdots + 25 $ x^12 - 2x^11 + 7x^10 + 15x^9 + 51x^8 + 175x^7 + 1103x^6 + 2884x^5 + 5561x^4 + 5670x^3 + 2840x^2 - 125*x + 25
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			1081.1
Root			$-1.70426 + 1.23822i$ of defining polynomial
Character	$\chi$	$=$	1320.1081
Dual form			1320.2.bw.f.961.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.309017 - 0.951057i) q^{3} +(-0.809017 - 0.587785i) q^{5} +(-0.341952 + 1.05242i) q^{7} +(-0.809017 + 0.587785i) q^{9} +O(q^{10})$	\(q+(-0.309017 - 0.951057i) q^{3} +(-0.809017 - 0.587785i) q^{5} +(-0.341952 + 1.05242i) q^{7} +(-0.809017 + 0.587785i) q^{9} +(-3.19786 + 0.879593i) q^{11} +(1.80262 - 1.30968i) q^{13} +(-0.309017 + 0.951057i) q^{15} +(3.07407 + 2.23344i) q^{17} +(2.01370 + 6.19752i) q^{19} +1.10658 q^{21} +3.83204 q^{23} +(0.309017 + 0.951057i) q^{25} +(0.809017 + 0.587785i) q^{27} +(2.70030 - 8.31068i) q^{29} +(8.82882 - 6.41452i) q^{31} +(1.82474 + 2.76954i) q^{33} +(0.895242 - 0.650431i) q^{35} +(-0.137272 + 0.422479i) q^{37} +(-1.80262 - 1.30968i) q^{39} +(-3.22886 - 9.93740i) q^{41} -0.960681 q^{43} +1.00000 q^{45} +(1.39373 + 4.28946i) q^{47} +(4.67246 + 3.39474i) q^{49} +(1.17419 - 3.61378i) q^{51} +(-5.56664 + 4.04440i) q^{53} +(3.10414 + 1.16805i) q^{55} +(5.27193 - 3.83028i) q^{57} +(0.0159796 - 0.0491803i) q^{59} +(7.09019 + 5.15133i) q^{61} +(-0.341952 - 1.05242i) q^{63} -2.22816 q^{65} -1.06587 q^{67} +(-1.18416 - 3.64448i) q^{69} +(10.9561 + 7.96008i) q^{71} +(4.30838 - 13.2598i) q^{73} +(0.809017 - 0.587785i) q^{75} +(0.167814 - 3.66627i) q^{77} +(-8.69719 + 6.31888i) q^{79} +(0.309017 - 0.951057i) q^{81} +(-4.49188 - 3.26354i) q^{83} +(-1.17419 - 3.61378i) q^{85} -8.73837 q^{87} +8.73964 q^{89} +(0.761924 + 2.34496i) q^{91} +(-8.82882 - 6.41452i) q^{93} +(2.01370 - 6.19752i) q^{95} +(11.9931 - 8.71347i) q^{97} +(2.07011 - 2.59126i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 3 q^{3} - 3 q^{5} - 3 q^{9}+O(q^{10}) $ 12 * q + 3 * q^3 - 3 * q^5 - 3 * q^9	$ 12 q + 3 q^{3} - 3 q^{5} - 3 q^{9} - 4 q^{11} + 3 q^{13} + 3 q^{15} + 12 q^{17} - 4 q^{19} - 10 q^{21} - 12 q^{23} - 3 q^{25} + 3 q^{27} + 16 q^{29} + 3 q^{31} + 4 q^{33} - 5 q^{35} - 19 q^{37} - 3 q^{39} + 22 q^{41} + 52 q^{43} + 12 q^{45} + 25 q^{47} - 11 q^{49} + 8 q^{51} - q^{53} - 4 q^{55} + 4 q^{57} - 9 q^{59} + 21 q^{61} - 12 q^{65} - 18 q^{67} - 8 q^{69} + 17 q^{71} + 37 q^{73} + 3 q^{75} - 13 q^{77} - 18 q^{79} - 3 q^{81} + 19 q^{83} - 8 q^{85} + 14 q^{87} + 2 q^{89} - 30 q^{91} - 3 q^{93} - 4 q^{95} + q^{97} + 6 q^{99}+O(q^{100}) $ 12 * q + 3 * q^3 - 3 * q^5 - 3 * q^9 - 4 * q^11 + 3 * q^13 + 3 * q^15 + 12 * q^17 - 4 * q^19 - 10 * q^21 - 12 * q^23 - 3 * q^25 + 3 * q^27 + 16 * q^29 + 3 * q^31 + 4 * q^33 - 5 * q^35 - 19 * q^37 - 3 * q^39 + 22 * q^41 + 52 * q^43 + 12 * q^45 + 25 * q^47 - 11 * q^49 + 8 * q^51 - q^53 - 4 * q^55 + 4 * q^57 - 9 * q^59 + 21 * q^61 - 12 * q^65 - 18 * q^67 - 8 * q^69 + 17 * q^71 + 37 * q^73 + 3 * q^75 - 13 * q^77 - 18 * q^79 - 3 * q^81 + 19 * q^83 - 8 * q^85 + 14 * q^87 + 2 * q^89 - 30 * q^91 - 3 * q^93 - 4 * q^95 + q^97 + 6 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1320\mathbb{Z}\right)^\times$.

$n$	$661$	$881$	$991$	$1057$	$1201$
$\chi(n)$	$1$	$1$	$1$	$1$	$e\left(\frac{4}{5}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	−0.309017	−	0.951057i	−0.178411	−	0.549093i
$3$	−0.309017	−	0.951057i	−0.178411	−	0.549093i
$4$		0			0
$5$	−0.809017	−	0.587785i	−0.361803	−	0.262866i
$5$	−0.809017	−	0.587785i	−0.361803	−	0.262866i
$6$		0			0
$7$	−0.341952	+	1.05242i	−0.129246	+	0.397777i	−0.994651	−	0.103296i	$-0.967061\pi$
$7$	−0.341952	+	1.05242i	−0.129246	+	0.397777i	0.865405	+	0.501073i	$0.167061\pi$
$8$		0			0
$9$	−0.809017	+	0.587785i	−0.269672	+	0.195928i
$10$		0			0
$11$	−3.19786	+	0.879593i	−0.964191	+	0.265207i
$11$	−3.19786	+	0.879593i	−0.964191	+	0.265207i
$12$		0			0
$13$	1.80262	−	1.30968i	0.499957	−	0.363240i	−0.309044	−	0.951048i	$-0.600009\pi$
$13$	1.80262	−	1.30968i	0.499957	−	0.363240i	0.809000	+	0.587808i	$0.200009\pi$
$14$		0			0
$15$	−0.309017	+	0.951057i	−0.0797878	+	0.245562i
$16$		0			0
$17$	3.07407	+	2.23344i	0.745571	+	0.541689i	0.894451	−	0.447167i	$-0.147567\pi$
$17$	3.07407	+	2.23344i	0.745571	+	0.541689i	−0.148880	+	0.988855i	$0.547567\pi$
$18$		0			0
$19$	2.01370	+	6.19752i	0.461974	+	1.42181i	0.862749	+	0.505633i	$0.168741\pi$
$19$	2.01370	+	6.19752i	0.461974	+	1.42181i	−0.400775	+	0.916176i	$0.631259\pi$
$20$		0			0
$21$	1.10658			0.241475
$22$		0			0
$23$	3.83204			0.799035			0.399517	−	0.916726i	$-0.369178\pi$
$23$	3.83204			0.799035			0.399517	+	0.916726i	$0.369178\pi$
$24$		0			0
$25$	0.309017	+	0.951057i	0.0618034	+	0.190211i
$26$		0			0
$27$	0.809017	+	0.587785i	0.155695	+	0.113119i
$28$		0			0
$29$	2.70030	−	8.31068i	0.501434	−	1.54326i	−0.305250	−	0.952272i	$-0.598740\pi$
$29$	2.70030	−	8.31068i	0.501434	−	1.54326i	0.806684	−	0.590983i	$-0.201260\pi$
$30$		0			0
$31$	8.82882	−	6.41452i	1.58570	−	1.15208i	0.675938	−	0.736959i	$-0.263739\pi$
$31$	8.82882	−	6.41452i	1.58570	−	1.15208i	0.909766	−	0.415122i	$-0.136261\pi$
$32$		0			0
$33$	1.82474	+	2.76954i	0.317646	+	0.482115i
$34$		0			0
$35$	0.895242	−	0.650431i	0.151323	−	0.109943i
$36$		0			0
$37$	−0.137272	+	0.422479i	−0.0225674	+	0.0694552i	−0.961706	−	0.274083i	$-0.911626\pi$
$37$	−0.137272	+	0.422479i	−0.0225674	+	0.0694552i	0.939139	+	0.343539i	$0.111626\pi$
$38$		0			0
$39$	−1.80262	−	1.30968i	−0.288650	−	0.209717i
$40$		0			0
$41$	−3.22886	−	9.93740i	−0.504263	−	1.55196i	−0.802007	−	0.597315i	$-0.796234\pi$
$41$	−3.22886	−	9.93740i	−0.504263	−	1.55196i	0.297744	−	0.954646i	$-0.403766\pi$
$42$		0			0
$43$	−0.960681			−0.146503			−0.0732513	−	0.997314i	$-0.523338\pi$
$43$	−0.960681			−0.146503			−0.0732513	+	0.997314i	$0.523338\pi$
$44$		0			0
$45$	1.00000			0.149071
$46$		0			0
$47$	1.39373	+	4.28946i	0.203297	+	0.625683i	0.999779	+	0.0210210i	$0.00669167\pi$
$47$	1.39373	+	4.28946i	0.203297	+	0.625683i	−0.796482	+	0.604662i	$0.793308\pi$
$48$		0			0
$49$	4.67246	+	3.39474i	0.667495	+	0.484963i
$50$		0			0
$51$	1.17419	−	3.61378i	0.164419	−	0.506031i
$52$		0			0
$53$	−5.56664	+	4.04440i	−0.764637	+	0.555541i	−0.900329	−	0.435210i	$-0.856674\pi$
$53$	−5.56664	+	4.04440i	−0.764637	+	0.555541i	0.135692	+	0.990751i	$0.456674\pi$
$54$		0			0
$55$	3.10414	+	1.16805i	0.418562	+	0.157500i
$56$		0			0
$57$	5.27193	−	3.83028i	0.698284	−	0.507333i
$58$		0			0
$59$	0.0159796	−	0.0491803i	0.00208037	−	0.00640272i	−0.950011	−	0.312217i	$-0.898929\pi$
$59$	0.0159796	−	0.0491803i	0.00208037	−	0.00640272i	0.952091	+	0.305814i	$0.0989285\pi$
$60$		0			0
$61$	7.09019	+	5.15133i	0.907806	+	0.659560i	0.940459	−	0.339907i	$-0.110396\pi$
$61$	7.09019	+	5.15133i	0.907806	+	0.659560i	−0.0326530	+	0.999467i	$0.510396\pi$
$62$		0			0
$63$	−0.341952	−	1.05242i	−0.0430819	−	0.132592i
$64$		0			0
$65$	−2.22816			−0.276369
$66$		0			0
$67$	−1.06587			−0.130217			−0.0651084	−	0.997878i	$-0.520739\pi$
$67$	−1.06587			−0.130217			−0.0651084	+	0.997878i	$0.520739\pi$
$68$		0			0
$69$	−1.18416	−	3.64448i	−0.142557	−	0.438744i
$70$		0			0
$71$	10.9561	+	7.96008i	1.30025	+	0.944687i	0.999958	−	0.00915994i	$-0.00291574\pi$
$71$	10.9561	+	7.96008i	1.30025	+	0.944687i	0.300292	+	0.953847i	$0.402916\pi$
$72$		0			0
$73$	4.30838	−	13.2598i	0.504258	−	1.55195i	−0.297757	−	0.954642i	$-0.596238\pi$
$73$	4.30838	−	13.2598i	0.504258	−	1.55195i	0.802015	−	0.597304i	$-0.203762\pi$
$74$		0			0
$75$	0.809017	−	0.587785i	0.0934172	−	0.0678716i
$76$		0			0
$77$	0.167814	−	3.66627i	0.0191241	−	0.417810i
$78$		0			0
$79$	−8.69719	+	6.31888i	−0.978511	+	0.710930i	−0.957375	−	0.288847i	$-0.906728\pi$
$79$	−8.69719	+	6.31888i	−0.978511	+	0.710930i	−0.0211354	+	0.999777i	$0.506728\pi$
$80$		0			0
$81$	0.309017	−	0.951057i	0.0343352	−	0.105673i
$82$		0			0
$83$	−4.49188	−	3.26354i	−0.493048	−	0.358220i	0.313308	−	0.949652i	$-0.398563\pi$
$83$	−4.49188	−	3.26354i	−0.493048	−	0.358220i	−0.806355	+	0.591432i	$0.798563\pi$
$84$		0			0
$85$	−1.17419	−	3.61378i	−0.127359	−	0.391970i
$86$		0			0
$87$	−8.73837			−0.936852
$88$		0			0
$89$	8.73964			0.926400			0.463200	−	0.886254i	$-0.346701\pi$
$89$	8.73964			0.926400			0.463200	+	0.886254i	$0.346701\pi$
$90$		0			0
$91$	0.761924	+	2.34496i	0.0798713	+	0.245819i
$92$		0			0
$93$	−8.82882	−	6.41452i	−0.915506	−	0.665154i
$94$		0			0
$95$	2.01370	−	6.19752i	0.206601	−	0.635852i
$96$		0			0
$97$	11.9931	−	8.71347i	1.21771	−	0.884719i	0.221803	−	0.975091i	$-0.428806\pi$
$97$	11.9931	−	8.71347i	1.21771	−	0.884719i	0.995908	+	0.0903722i	$0.0288057\pi$
$98$		0			0
$99$	2.07011	−	2.59126i	0.208054	−	0.260432i
$100$		0			0
$101$	−2.17751	+	1.58205i	−0.216670	+	0.157420i	−0.690826	−	0.723021i	$-0.742753\pi$
$101$	−2.17751	+	1.58205i	−0.216670	+	0.157420i	0.474156	+	0.880441i	$0.342753\pi$
$102$		0			0
$103$	−2.71176	+	8.34594i	−0.267198	+	0.822350i	0.723981	+	0.689819i	$0.242310\pi$
$103$	−2.71176	+	8.34594i	−0.267198	+	0.822350i	−0.991179	+	0.132530i	$0.957690\pi$
$104$		0			0
$105$	−0.895242	−	0.650431i	−0.0873666	−	0.0634756i
$106$		0			0
$107$	−2.30126	−	7.08256i	−0.222472	−	0.684697i	−0.998538	−	0.0540466i	$-0.982788\pi$
$107$	−2.30126	−	7.08256i	−0.222472	−	0.684697i	0.776067	−	0.630651i	$-0.217212\pi$
$108$		0			0
$109$	11.4530			1.09699			0.548497	−	0.836152i	$-0.315200\pi$
$109$	11.4530			1.09699			0.548497	+	0.836152i	$0.315200\pi$
$110$		0			0
$111$	0.444221			0.0421636
$112$		0			0
$113$	−4.72860	−	14.5531i	−0.444829	−	1.36904i	−0.882671	−	0.469991i	$-0.844257\pi$
$113$	−4.72860	−	14.5531i	−0.444829	−	1.36904i	0.437843	−	0.899052i	$-0.355743\pi$
$114$		0			0
$115$	−3.10018	−	2.25241i	−0.289093	−	0.210039i
$116$		0			0
$117$	−0.688539	+	2.11911i	−0.0636555	+	0.195911i
$118$		0			0
$119$	−3.40170	+	2.47148i	−0.311833	+	0.226560i
$120$		0			0
$121$	9.45263	−	5.62563i	0.859330	−	0.511421i
$122$		0			0
$123$	−8.45325	+	6.14165i	−0.762204	+	0.553774i
$124$		0			0
$125$	0.309017	−	0.951057i	0.0276393	−	0.0850651i
$126$		0			0
$127$	11.1228	+	8.08119i	0.986989	+	0.717090i	0.959260	−	0.282526i	$-0.0911723\pi$
$127$	11.1228	+	8.08119i	0.986989	+	0.717090i	0.0277295	+	0.999615i	$0.491172\pi$
$128$		0			0
$129$	0.296867	+	0.913662i	0.0261377	+	0.0804435i
$130$		0			0
$131$	22.3443			1.95223			0.976115	−	0.217256i	$-0.0697106\pi$
$131$	22.3443			1.95223			0.976115	+	0.217256i	$0.0697106\pi$
$132$		0			0
$133$	−7.21098			−0.625271
$134$		0			0
$135$	−0.309017	−	0.951057i	−0.0265959	−	0.0818539i
$136$		0			0
$137$	6.53469	+	4.74773i	0.558296	+	0.405626i	0.830835	−	0.556519i	$-0.187863\pi$
$137$	6.53469	+	4.74773i	0.558296	+	0.405626i	−0.272539	+	0.962145i	$0.587863\pi$
$138$		0			0
$139$	−1.40238	+	4.31608i	−0.118948	+	0.366085i	−0.992750	−	0.120197i	$-0.961647\pi$
$139$	−1.40238	+	4.31608i	−0.118948	+	0.366085i	0.873802	+	0.486282i	$0.161647\pi$
$140$		0			0
$141$	3.64884	−	2.65103i	0.307287	−	0.223257i
$142$		0			0
$143$	−4.61254	+	5.77375i	−0.385720	+	0.482825i
$144$		0			0
$145$	−7.06949	+	5.13628i	−0.587089	+	0.426545i
$146$		0			0
$147$	1.78472	−	5.49281i	0.147201	−	0.453039i
$148$		0			0
$149$	−3.14073	−	2.28187i	−0.257298	−	0.186938i	0.451657	−	0.892192i	$-0.350833\pi$
$149$	−3.14073	−	2.28187i	−0.257298	−	0.186938i	−0.708955	+	0.705254i	$0.750833\pi$
$150$		0			0
$151$	2.21912	+	6.82975i	0.180590	+	0.555797i	0.999845	−	0.0176319i	$-0.00561271\pi$
$151$	2.21912	+	6.82975i	0.180590	+	0.555797i	−0.819255	+	0.573429i	$0.805613\pi$
$152$		0			0
$153$	−3.79975			−0.307192
$154$		0			0
$155$	−10.9130			−0.876555
$156$		0			0
$157$	5.48749	+	16.8888i	0.437949	+	1.34787i	0.890034	+	0.455894i	$0.150680\pi$
$157$	5.48749	+	16.8888i	0.437949	+	1.34787i	−0.452085	+	0.891975i	$0.649320\pi$
$158$		0			0
$159$	5.56664	+	4.04440i	0.441463	+	0.320742i
$160$		0			0
$161$	−1.31037	+	4.03291i	−0.103272	+	0.317838i
$162$		0			0
$163$	−19.7332	+	14.3370i	−1.54562	+	1.12296i	−0.598936	+	0.800797i	$0.704410\pi$
$163$	−19.7332	+	14.3370i	−1.54562	+	1.12296i	−0.946684	+	0.322162i	$0.895590\pi$
$164$		0			0
$165$	0.151651	−	3.31316i	0.0118060	−	0.257929i
$166$		0			0
$167$	−10.3974	+	7.55419i	−0.804579	+	0.584561i	−0.912254	−	0.409626i	$-0.865659\pi$
$167$	−10.3974	+	7.55419i	−0.804579	+	0.584561i	0.107675	+	0.994186i	$0.465659\pi$
$168$		0			0
$169$	−2.48304	+	7.64203i	−0.191003	+	0.587848i
$170$		0			0
$171$	−5.27193	−	3.83028i	−0.403154	−	0.292909i
$172$		0			0
$173$	−1.54027	−	4.74047i	−0.117105	−	0.360411i	0.875276	−	0.483625i	$-0.160680\pi$
$173$	−1.54027	−	4.74047i	−0.117105	−	0.360411i	−0.992380	+	0.123214i	$0.960680\pi$
$174$		0			0
$175$	−1.10658			−0.0836495
$176$		0			0
$177$	−0.0517112			−0.00388685
$178$		0			0
$179$	−5.67289	−	17.4594i	−0.424012	−	1.30497i	−0.903937	−	0.427665i	$-0.859336\pi$
$179$	−5.67289	−	17.4594i	−0.424012	−	1.30497i	0.479925	−	0.877309i	$-0.340664\pi$
$180$		0			0
$181$	9.04671	+	6.57282i	0.672437	+	0.488554i	0.870840	−	0.491566i	$-0.163576\pi$
$181$	9.04671	+	6.57282i	0.672437	+	0.488554i	−0.198403	+	0.980121i	$0.563576\pi$
$182$		0			0
$183$	2.70821	−	8.33502i	0.200197	−	0.616142i
$184$		0			0
$185$	0.359382	−	0.261107i	0.0264223	−	0.0191969i
$186$		0			0
$187$	−11.7950	−	4.43830i	−0.862532	−	0.324561i
$188$		0			0
$189$	−0.895242	+	0.650431i	−0.0651192	+	0.0473119i
$190$		0			0
$191$	1.90191	−	5.85349i	0.137618	−	0.423544i	−0.858370	−	0.513031i	$-0.828523\pi$
$191$	1.90191	−	5.85349i	0.137618	−	0.423544i	0.995988	+	0.0894870i	$0.0285227\pi$
$192$		0			0
$193$	12.3180	+	8.94958i	0.886672	+	0.644205i	0.935008	−	0.354626i	$-0.115392\pi$
$193$	12.3180	+	8.94958i	0.886672	+	0.644205i	−0.0483361	+	0.998831i	$0.515392\pi$
$194$		0			0
$195$	0.688539	+	2.11911i	0.0493073	+	0.151752i
$196$		0			0
$197$	−20.9227			−1.49068			−0.745341	−	0.666683i	$-0.767713\pi$
$197$	−20.9227			−1.49068			−0.745341	+	0.666683i	$0.767713\pi$
$198$		0			0
$199$	10.8665			0.770309			0.385154	−	0.922852i	$-0.374148\pi$
$199$	10.8665			0.770309			0.385154	+	0.922852i	$0.374148\pi$
$200$		0			0
$201$	0.329372	+	1.01370i	0.0232321	+	0.0715011i
$202$		0			0
$203$	7.82295	+	5.68371i	0.549064	+	0.398918i
$204$		0			0
$205$	−3.22886	+	9.93740i	−0.225513	+	0.694058i
$206$		0			0
$207$	−3.10018	+	2.25241i	−0.215478	+	0.156554i
$208$		0			0
$209$	−11.8908	−	18.0476i	−0.822505	−	1.24838i
$210$		0			0
$211$	−6.81712	+	4.95293i	−0.469310	+	0.340973i	−0.797172	−	0.603752i	$-0.793672\pi$
$211$	−6.81712	+	4.95293i	−0.469310	+	0.340973i	0.327863	+	0.944725i	$0.393672\pi$
$212$		0			0
$213$	4.18486	−	12.8797i	0.286742	−	0.882501i
$214$		0			0
$215$	0.777208	+	0.564674i	0.0530051	+	0.0385105i
$216$		0			0
$217$	3.73173	+	11.4851i	0.253326	+	0.779658i
$218$		0			0
$219$	−13.9422			−0.942127
$220$		0			0
$221$	8.46646			0.569516
$222$		0			0
$223$	−4.02127	−	12.3762i	−0.269284	−	0.828772i	−0.990675	−	0.136244i	$-0.956497\pi$
$223$	−4.02127	−	12.3762i	−0.269284	−	0.828772i	0.721391	−	0.692528i	$-0.243503\pi$
$224$		0			0
$225$	−0.809017	−	0.587785i	−0.0539345	−	0.0391857i
$226$		0			0
$227$	−2.08557	+	6.41874i	−0.138424	+	0.426027i	−0.996107	−	0.0881530i	$-0.971904\pi$
$227$	−2.08557	+	6.41874i	−0.138424	+	0.426027i	0.857682	+	0.514180i	$0.171904\pi$
$228$		0			0
$229$	1.38700	−	1.00772i	0.0916556	−	0.0665917i	−0.541014	−	0.841014i	$-0.681959\pi$
$229$	1.38700	−	1.00772i	0.0916556	−	0.0665917i	0.632669	+	0.774422i	$0.281959\pi$
$230$		0			0
$231$	−3.53869	+	0.973340i	−0.232829	+	0.0640410i
$232$		0			0
$233$	−8.88550	+	6.45570i	−0.582109	+	0.422927i	−0.839484	−	0.543385i	$-0.817142\pi$
$233$	−8.88550	+	6.45570i	−0.582109	+	0.422927i	0.257375	+	0.966312i	$0.417142\pi$
$234$		0			0
$235$	1.39373	−	4.28946i	0.0909170	−	0.279814i
$236$		0			0
$237$	8.69719	+	6.31888i	0.564943	+	0.410455i
$238$		0			0
$239$	7.16906	+	22.0641i	0.463728	+	1.42721i	0.860575	+	0.509323i	$0.170104\pi$
$239$	7.16906	+	22.0641i	0.463728	+	1.42721i	−0.396848	+	0.917885i	$0.629896\pi$
$240$		0			0
$241$	−15.1111			−0.973389			−0.486695	−	0.873572i	$-0.661798\pi$
$241$	−15.1111			−0.973389			−0.486695	+	0.873572i	$0.661798\pi$
$242$		0			0
$243$	−1.00000			−0.0641500
$244$		0			0
$245$	−1.78472	−	5.49281i	−0.114022	−	0.350923i
$246$		0			0
$247$	11.7467	+	8.53448i	0.747425	+	0.543036i
$248$		0			0
$249$	−1.71574	+	5.28052i	−0.108731	+	0.334639i
$250$		0			0
$251$	3.25067	−	2.36175i	0.205180	−	0.149072i	−0.480450	−	0.877022i	$-0.659527\pi$
$251$	3.25067	−	2.36175i	0.205180	−	0.149072i	0.685630	+	0.727950i	$0.259527\pi$
$252$		0			0
$253$	−12.2543	+	3.37063i	−0.770422	+	0.211910i
$254$		0			0
$255$	−3.07407	+	2.23344i	−0.192505	+	0.139863i
$256$		0			0
$257$	−1.39278	+	4.28654i	−0.0868793	+	0.267387i	−0.985052	−	0.172255i	$-0.944895\pi$
$257$	−1.39278	+	4.28654i	−0.0868793	+	0.267387i	0.898173	+	0.439642i	$0.144895\pi$
$258$		0			0
$259$	−0.397685	−	0.288935i	−0.0247110	−	0.0179536i
$260$		0			0
$261$	2.70030	+	8.31068i	0.167145	+	0.514418i
$262$		0			0
$263$	−26.7731			−1.65090			−0.825450	−	0.564475i	$-0.809079\pi$
$263$	−26.7731			−1.65090			−0.825450	+	0.564475i	$0.809079\pi$
$264$		0			0
$265$	6.88074			0.422681
$266$		0			0
$267$	−2.70070	−	8.31189i	−0.165280	−	0.508680i
$268$		0			0
$269$	−12.2656	−	8.91151i	−0.747849	−	0.543344i	0.147310	−	0.989090i	$-0.452938\pi$
$269$	−12.2656	−	8.91151i	−0.747849	−	0.543344i	−0.895159	+	0.445746i	$0.852938\pi$
$270$		0			0
$271$	2.06344	−	6.35060i	0.125345	−	0.385771i	−0.868619	−	0.495481i	$-0.834992\pi$
$271$	2.06344	−	6.35060i	0.125345	−	0.385771i	0.993964	+	0.109709i	$0.0349919\pi$
$272$		0			0
$273$	1.99474	−	1.44926i	0.120727	−	0.0877135i
$274$		0			0
$275$	−1.82474	−	2.76954i	−0.110036	−	0.167009i
$276$		0			0
$277$	8.75516	−	6.36099i	0.526046	−	0.382195i	−0.292830	−	0.956164i	$-0.594597\pi$
$277$	8.75516	−	6.36099i	0.526046	−	0.382195i	0.818877	+	0.573969i	$0.194597\pi$
$278$		0			0
$279$	−3.37231	+	10.3789i	−0.201895	+	0.621369i
$280$		0			0
$281$	6.93178	+	5.03623i	0.413515	+	0.300437i	0.775023	−	0.631932i	$-0.217738\pi$
$281$	6.93178	+	5.03623i	0.413515	+	0.300437i	−0.361508	+	0.932369i	$0.617738\pi$
$282$		0			0
$283$	−8.02462	−	24.6972i	−0.477014	−	1.46810i	−0.843222	−	0.537565i	$-0.819344\pi$
$283$	−8.02462	−	24.6972i	−0.477014	−	1.46810i	0.366208	−	0.930533i	$-0.380656\pi$
$284$		0			0
$285$	−6.51646			−0.386002
$286$		0			0
$287$	11.5624			0.682508
$288$		0			0
$289$	−0.791660	−	2.43648i	−0.0465682	−	0.143322i
$290$		0			0
$291$	−11.9931	−	8.71347i	−0.703046	−	0.510793i
$292$		0			0
$293$	−9.63977	+	29.6682i	−0.563161	+	1.73323i	0.110190	+	0.993911i	$0.464854\pi$
$293$	−9.63977	+	29.6682i	−0.563161	+	1.73323i	−0.673352	+	0.739322i	$0.735146\pi$
$294$		0			0
$295$	−0.0418352	+	0.0303951i	−0.00243574	+	0.00176967i
$296$		0			0
$297$	−3.10414	−	1.16805i	−0.180120	−	0.0677771i
$298$		0			0
$299$	6.90770	−	5.01874i	0.399483	−	0.290241i
$300$		0			0
$301$	0.328507	−	1.01104i	0.0189348	−	0.0582754i
$302$		0			0
$303$	2.17751	+	1.58205i	0.125094	+	0.0908865i
$304$		0			0
$305$	−2.70821	−	8.33502i	−0.155072	−	0.477262i
$306$		0			0
$307$	−9.32197			−0.532033			−0.266017	−	0.963968i	$-0.585708\pi$
$307$	−9.32197			−0.532033			−0.266017	+	0.963968i	$0.585708\pi$
$308$		0			0
$309$	8.77544			0.499217
$310$		0			0
$311$	4.60086	+	14.1600i	0.260891	+	0.802939i	0.992612	+	0.121335i	$0.0387175\pi$
$311$	4.60086	+	14.1600i	0.260891	+	0.802939i	−0.731721	+	0.681605i	$0.761282\pi$
$312$		0			0
$313$	4.80734	+	3.49274i	0.271727	+	0.197421i	0.715301	−	0.698817i	$-0.246290\pi$
$313$	4.80734	+	3.49274i	0.271727	+	0.197421i	−0.443574	+	0.896238i	$0.646290\pi$
$314$		0			0
$315$	−0.341952	+	1.05242i	−0.0192668	+	0.0592971i
$316$		0			0
$317$	24.5964	−	17.8703i	1.38147	−	1.00370i	0.384731	−	0.923029i	$-0.374294\pi$
$317$	24.5964	−	17.8703i	1.38147	−	1.00370i	0.996741	−	0.0806690i	$-0.0257057\pi$
$318$		0			0
$319$	−1.32518	+	28.9516i	−0.0741958	+	1.62098i
$320$		0			0
$321$	−6.02479	+	4.37727i	−0.336271	+	0.244315i
$322$		0			0
$323$	−7.65155	+	23.5491i	−0.425744	+	1.31030i
$324$		0			0
$325$	1.80262	+	1.30968i	0.0999913	+	0.0726480i
$326$		0			0
$327$	−3.53916	−	10.8924i	−0.195716	−	0.602352i
$328$		0			0
$329$	−4.99091			−0.275158
$330$		0			0
$331$	33.2381			1.82693			0.913465	−	0.406918i	$-0.133397\pi$
$331$	33.2381			1.82693			0.913465	+	0.406918i	$0.133397\pi$
$332$		0			0
$333$	−0.137272	−	0.422479i	−0.00752245	−	0.0231517i
$334$		0			0
$335$	0.862307	+	0.626503i	0.0471128	+	0.0342295i
$336$		0			0
$337$	5.09800	−	15.6900i	0.277706	−	0.854690i	−0.710785	−	0.703409i	$-0.751660\pi$
$337$	5.09800	−	15.6900i	0.277706	−	0.854690i	0.988491	−	0.151281i	$-0.0483398\pi$
$338$		0			0
$339$	−12.3796	+	8.99432i	−0.672369	+	0.488505i
$340$		0			0
$341$	−22.5912	+	28.2785i	−1.22338	+	1.53137i
$342$		0			0
$343$	−11.4371	+	8.30957i	−0.617548	+	0.448675i
$344$		0			0
$345$	−1.18416	+	3.64448i	−0.0637533	+	0.196212i
$346$		0			0
$347$	−16.0058	−	11.6289i	−0.859239	−	0.624273i	0.0684392	−	0.997655i	$-0.478198\pi$
$347$	−16.0058	−	11.6289i	−0.859239	−	0.624273i	−0.927678	+	0.373382i	$0.878198\pi$
$348$		0			0
$349$	−2.90543	−	8.94199i	−0.155524	−	0.478654i	0.842690	−	0.538400i	$-0.180971\pi$
$349$	−2.90543	−	8.94199i	−0.155524	−	0.478654i	−0.998214	+	0.0597460i	$0.980971\pi$
$350$		0			0
$351$	2.22816			0.118930
$352$		0			0
$353$	−29.7719			−1.58460			−0.792299	−	0.610133i	$-0.791116\pi$
$353$	−29.7719			−1.58460			−0.792299	+	0.610133i	$0.791116\pi$
$354$		0			0
$355$	−4.18486	−	12.8797i	−0.222109	−	0.683582i
$356$		0			0
$357$	3.40170	+	2.47148i	0.180037	+	0.130805i
$358$		0			0
$359$	8.77810	−	27.0162i	0.463291	−	1.42586i	−0.397829	−	0.917460i	$-0.630236\pi$
$359$	8.77810	−	27.0162i	0.463291	−	1.42586i	0.861120	−	0.508402i	$-0.169764\pi$
$360$		0			0
$361$	−18.9830	+	13.7919i	−0.999104	+	0.725892i
$362$		0			0
$363$	−8.27132	−	7.25157i	−0.434132	−	0.380609i
$364$		0			0
$365$	−11.2795	+	8.19503i	−0.590395	+	0.428947i
$366$		0			0
$367$	−6.88788	+	21.1987i	−0.359544	+	1.10656i	0.593783	+	0.804625i	$0.297634\pi$
$367$	−6.88788	+	21.1987i	−0.359544	+	1.10656i	−0.953327	+	0.301939i	$0.902366\pi$
$368$		0			0
$369$	8.45325	+	6.14165i	0.440059	+	0.319721i
$370$		0			0
$371$	−2.35288	−	7.24143i	−0.122156	−	0.375956i
$372$		0			0
$373$	−15.1825			−0.786118			−0.393059	−	0.919513i	$-0.628583\pi$
$373$	−15.1825			−0.786118			−0.393059	+	0.919513i	$0.628583\pi$
$374$		0			0
$375$	−1.00000			−0.0516398
$376$		0			0
$377$	−6.01671	−	18.5175i	−0.309876	−	0.953702i
$378$		0			0
$379$	−12.1746	−	8.84538i	−0.625368	−	0.454357i	0.229424	−	0.973327i	$-0.426316\pi$
$379$	−12.1746	−	8.84538i	−0.625368	−	0.454357i	−0.854793	+	0.518970i	$0.826316\pi$
$380$		0			0
$381$	4.24853	−	13.0756i	0.217659	−	0.669885i
$382$		0			0
$383$	16.8178	−	12.2189i	0.859351	−	0.624355i	−0.0683575	−	0.997661i	$-0.521776\pi$
$383$	16.8178	−	12.2189i	0.859351	−	0.624355i	0.927708	+	0.373306i	$0.121776\pi$
$384$		0			0
$385$	−2.29074	+	2.86744i	−0.116747	+	0.146138i
$386$		0			0
$387$	0.777208	−	0.564674i	0.0395077	−	0.0287040i
$388$		0			0
$389$	−1.58007	+	4.86297i	−0.0801129	+	0.246562i	−0.983089	−	0.183129i	$-0.941377\pi$
$389$	−1.58007	+	4.86297i	−0.0801129	+	0.246562i	0.902976	+	0.429691i	$0.141377\pi$
$390$		0			0
$391$	11.7799	+	8.55862i	0.595737	+	0.432828i
$392$		0			0
$393$	−6.90476	−	21.2507i	−0.348299	−	1.07195i
$394$		0			0
$395$	10.7503			0.540907
$396$		0			0
$397$	0.518082			0.0260018			0.0130009	−	0.999915i	$-0.495862\pi$
$397$	0.518082			0.0260018			0.0130009	+	0.999915i	$0.495862\pi$
$398$		0			0
$399$	2.22832	+	6.85805i	0.111555	+	0.343332i
$400$		0			0
$401$	2.93211	+	2.13030i	0.146422	+	0.106382i	0.658585	−	0.752507i	$-0.271155\pi$
$401$	2.93211	+	2.13030i	0.146422	+	0.106382i	−0.512162	+	0.858889i	$0.671155\pi$
$402$		0			0
$403$	7.51405	−	23.1259i	0.374301	−	1.15198i
$404$		0			0
$405$	−0.809017	+	0.587785i	−0.0402004	+	0.0292073i
$406$		0			0
$407$	0.0673664	−	1.47177i	0.00333923	−	0.0729531i
$408$		0			0
$409$	−12.4532	+	9.04775i	−0.615769	+	0.447382i	−0.851441	−	0.524450i	$-0.824271\pi$
$409$	−12.4532	+	9.04775i	−0.615769	+	0.447382i	0.235672	+	0.971833i	$0.424271\pi$
$410$		0			0
$411$	2.49603	−	7.68199i	0.123120	−	0.378924i
$412$		0			0
$413$	0.0462940	+	0.0336346i	0.00227798	+	0.00165505i
$414$		0			0
$415$	1.71574	+	5.28052i	0.0842226	+	0.259210i
$416$		0			0
$417$	4.53820			0.222236
$418$		0			0
$419$	4.19096			0.204742			0.102371	−	0.994746i	$-0.467357\pi$
$419$	4.19096			0.204742			0.102371	+	0.994746i	$0.467357\pi$
$420$		0			0
$421$	−7.05175	−	21.7031i	−0.343681	−	1.05774i	−0.962286	−	0.272040i	$-0.912302\pi$
$421$	−7.05175	−	21.7031i	−0.343681	−	1.05774i	0.618605	−	0.785702i	$-0.287698\pi$
$422$		0			0
$423$	−3.64884	−	2.65103i	−0.177412	−	0.128898i
$424$		0			0
$425$	−1.17419	+	3.61378i	−0.0569565	+	0.175294i
$426$		0			0
$427$	−7.84586	+	5.70035i	−0.379688	+	0.275859i
$428$		0			0
$429$	6.91651	+	2.60260i	0.333932	+	0.125655i
$430$		0			0
$431$	−4.02019	+	2.92084i	−0.193646	+	0.140692i	−0.680383	−	0.732856i	$-0.738187\pi$
$431$	−4.02019	+	2.92084i	−0.193646	+	0.140692i	0.486738	+	0.873548i	$0.338187\pi$
$432$		0			0
$433$	−7.65791	+	23.5686i	−0.368016	+	1.13264i	0.580055	+	0.814577i	$0.303031\pi$
$433$	−7.65791	+	23.5686i	−0.368016	+	1.13264i	−0.948071	+	0.318059i	$0.896969\pi$
$434$		0			0
$435$	7.06949	+	5.13628i	0.338956	+	0.246266i
$436$		0			0
$437$	7.71656	+	23.7491i	0.369133	+	1.13607i
$438$		0			0
$439$	6.85914			0.327369			0.163684	−	0.986513i	$-0.447662\pi$
$439$	6.85914			0.327369			0.163684	+	0.986513i	$0.447662\pi$
$440$		0			0
$441$	−5.77548			−0.275023
$442$		0			0
$443$	1.69560	+	5.21853i	0.0805606	+	0.247940i	0.983222	−	0.182410i	$-0.0583900\pi$
$443$	1.69560	+	5.21853i	0.0805606	+	0.247940i	−0.902662	+	0.430350i	$0.858390\pi$
$444$		0			0
$445$	−7.07052	−	5.13703i	−0.335175	−	0.243519i
$446$		0			0
$447$	−1.19965	+	3.69215i	−0.0567415	+	0.174633i
$448$		0			0
$449$	21.7487	−	15.8013i	1.02638	−	0.745712i	0.0588023	−	0.998270i	$-0.481272\pi$
$449$	21.7487	−	15.8013i	1.02638	−	0.745712i	0.967582	+	0.252558i	$0.0812718\pi$
$450$		0			0
$451$	19.0663	+	28.9383i	0.897797	+	1.36265i
$452$		0			0
$453$	5.80973	−	4.22102i	0.272965	−	0.198321i
$454$		0			0
$455$	0.761924	−	2.34496i	0.0357195	−	0.109933i
$456$		0			0
$457$	24.4597	+	17.7710i	1.14418	+	0.831292i	0.987696	−	0.156389i	$-0.0499853\pi$
$457$	24.4597	+	17.7710i	1.14418	+	0.831292i	0.156480	+	0.987681i	$0.449985\pi$
$458$		0			0
$459$	1.17419	+	3.61378i	0.0548064	+	0.168677i
$460$		0			0
$461$	−30.3787			−1.41488			−0.707439	−	0.706775i	$-0.750149\pi$
$461$	−30.3787			−1.41488			−0.707439	+	0.706775i	$0.750149\pi$
$462$		0			0
$463$	−8.80417			−0.409164			−0.204582	−	0.978849i	$-0.565584\pi$
$463$	−8.80417			−0.409164			−0.204582	+	0.978849i	$0.565584\pi$
$464$		0			0
$465$	3.37231	+	10.3789i	0.156387	+	0.481310i
$466$		0			0
$467$	18.2921	+	13.2900i	0.846457	+	0.614987i	0.924167	−	0.381989i	$-0.124761\pi$
$467$	18.2921	+	13.2900i	0.846457	+	0.614987i	−0.0777099	+	0.996976i	$0.524761\pi$
$468$		0			0
$469$	0.364476	−	1.12174i	0.0168299	−	0.0517972i
$470$		0			0
$471$	14.3664	−	10.4378i	0.661970	−	0.480949i
$472$		0			0
$473$	3.07213	−	0.845009i	0.141256	−	0.0388535i
$474$		0			0
$475$	−5.27193	+	3.83028i	−0.241893	+	0.175745i
$476$		0			0
$477$	2.12627	−	6.54398i	0.0973551	−	0.299628i
$478$		0			0
$479$	−11.0978	−	8.06301i	−0.507071	−	0.368408i	0.304641	−	0.952467i	$-0.401464\pi$
$479$	−11.0978	−	8.06301i	−0.507071	−	0.368408i	−0.811711	+	0.584059i	$0.801464\pi$
$480$		0			0
$481$	0.305864	+	0.941352i	0.0139462	+	0.0429219i
$482$		0			0
$483$	4.24045			0.192947
$484$		0			0
$485$	−14.8242			−0.673134
$486$		0			0
$487$	−12.5568	−	38.6459i	−0.569004	−	1.75121i	−0.655744	−	0.754984i	$-0.727645\pi$
$487$	−12.5568	−	38.6459i	−0.569004	−	1.75121i	0.0867394	−	0.996231i	$-0.472355\pi$
$488$		0			0
$489$	19.7332	+	14.3370i	0.892364	+	0.648341i
$490$		0			0
$491$	3.79322	−	11.6743i	0.171186	−	0.526855i	−0.828253	−	0.560354i	$-0.810665\pi$
$491$	3.79322	−	11.6743i	0.171186	−	0.526855i	0.999439	+	0.0334989i	$0.0106650\pi$
$492$		0			0
$493$	26.8623	−	19.5166i	1.20982	−	0.878984i
$494$		0			0
$495$	−3.19786	+	0.879593i	−0.143733	+	0.0395348i
$496$		0			0
$497$	−12.1238	+	8.80846i	−0.543827	+	0.395113i
$498$		0			0
$499$	10.7223	−	32.9998i	0.479995	−	1.47727i	−0.359105	−	0.933297i	$-0.616918\pi$
$499$	10.7223	−	32.9998i	0.479995	−	1.47727i	0.839100	−	0.543977i	$-0.183082\pi$
$500$		0			0
$501$	10.3974	+	7.55419i	0.464524	+	0.337496i
$502$		0			0
$503$	−1.29862	−	3.99673i	−0.0579025	−	0.178206i	0.917922	−	0.396761i	$-0.129866\pi$
$503$	−1.29862	−	3.99673i	−0.0579025	−	0.178206i	−0.975825	+	0.218555i	$0.929866\pi$
$504$		0			0
$505$	2.69155			0.119772
$506$		0			0
$507$	8.03530			0.356860
$508$		0			0
$509$	−4.58050	−	14.0973i	−0.203027	−	0.624854i	−0.999789	−	0.0205596i	$-0.993455\pi$
$509$	−4.58050	−	14.0973i	−0.203027	−	0.624854i	0.796761	−	0.604294i	$-0.206545\pi$
$510$		0			0
$511$	12.4816	+	9.06845i	0.552156	+	0.401165i
$512$		0			0
$513$	−2.01370	+	6.19752i	−0.0889069	+	0.273627i
$514$		0			0
$515$	7.09948	−	5.15807i	0.312840	−	0.227292i
$516$		0			0
$517$	−8.22994	−	12.4912i	−0.361952	−	0.549362i
$518$		0			0
$519$	−4.03248	+	2.92977i	−0.177006	+	0.128603i
$520$		0			0
$521$	1.47741	−	4.54700i	0.0647266	−	0.199208i	−0.913463	−	0.406922i	$-0.866602\pi$
$521$	1.47741	−	4.54700i	0.0647266	−	0.199208i	0.978190	+	0.207714i	$0.0666022\pi$
$522$		0			0
$523$	−22.1019	−	16.0580i	−0.966450	−	0.702167i	−0.0118104	−	0.999930i	$-0.503759\pi$
$523$	−22.1019	−	16.0580i	−0.966450	−	0.702167i	−0.954640	+	0.297763i	$0.903759\pi$
$524$		0			0
$525$	0.341952	+	1.05242i	0.0149240	+	0.0459314i
$526$		0			0
$527$	41.4668			1.80632
$528$		0			0
$529$	−8.31550			−0.361544
$530$		0			0
$531$	0.0159796	+	0.0491803i	0.000693457	+	0.00213424i
$532$		0			0
$533$	−18.8352	−	13.6846i	−0.815843	−	0.592745i
$534$		0			0
$535$	−2.30126	+	7.08256i	−0.0994924	+	0.306206i
$536$		0			0
$537$	−14.8518	+	10.7905i	−0.640904	+	0.465644i
$538$		0			0
$539$	−17.9279	−	6.74605i	−0.772208	−	0.290573i
$540$		0			0
$541$	3.06811	−	2.22911i	0.131908	−	0.0958371i	−0.519875	−	0.854243i	$-0.674021\pi$
$541$	3.06811	−	2.22911i	0.131908	−	0.0958371i	0.651783	+	0.758406i	$0.274021\pi$
$542$		0			0
$543$	3.45554	−	10.6351i	0.148291	−	0.456394i
$544$		0			0
$545$	−9.26564	−	6.73188i	−0.396896	−	0.288362i
$546$		0			0
$547$	3.88450	+	11.9553i	0.166089	+	0.511170i	0.999115	−	0.0420642i	$-0.0133934\pi$
$547$	3.88450	+	11.9553i	0.166089	+	0.511170i	−0.833026	+	0.553234i	$0.813393\pi$
$548$		0			0
$549$	−8.76396			−0.374037
$550$		0			0
$551$	56.9432			2.42586
$552$		0			0
$553$	−3.67609	−	11.3138i	−0.156323	−	0.481114i
$554$		0			0
$555$	−0.359382	−	0.261107i	−0.0152549	−	0.0110834i
$556$		0			0
$557$	4.19927	−	12.9240i	0.177929	−	0.547609i	−0.821826	−	0.569738i	$-0.807045\pi$
$557$	4.19927	−	12.9240i	0.177929	−	0.547609i	0.999755	+	0.0221294i	$0.00704460\pi$
$558$		0			0
$559$	−1.73174	+	1.25819i	−0.0732449	+	0.0532156i
$560$		0			0
$561$	−0.576235	+	12.5892i	−0.0243287	+	0.531516i
$562$		0			0
$563$	−3.81609	+	2.77255i	−0.160829	+	0.116849i	−0.665289	−	0.746586i	$-0.731692\pi$
$563$	−3.81609	+	2.77255i	−0.160829	+	0.116849i	0.504460	+	0.863435i	$0.331692\pi$
$564$		0			0
$565$	−4.72860	+	14.5531i	−0.198934	+	0.612254i
$566$		0			0
$567$	0.895242	+	0.650431i	0.0375966	+	0.0273155i
$568$		0			0
$569$	−6.21359	−	19.1235i	−0.260487	−	0.801697i	−0.992699	−	0.120620i	$-0.961512\pi$
$569$	−6.21359	−	19.1235i	−0.260487	−	0.801697i	0.732211	−	0.681077i	$-0.238488\pi$
$570$		0			0
$571$	−8.48783			−0.355205			−0.177602	−	0.984102i	$-0.556834\pi$
$571$	−8.48783			−0.355205			−0.177602	+	0.984102i	$0.556834\pi$
$572$		0			0
$573$	−6.15472			−0.257117
$574$		0			0
$575$	1.18416	+	3.64448i	0.0493831	+	0.151985i
$576$		0			0
$577$	−20.0653	−	14.5783i	−0.835329	−	0.606902i	0.0857330	−	0.996318i	$-0.472677\pi$
$577$	−20.0653	−	14.5783i	−0.835329	−	0.606902i	−0.921062	+	0.389416i	$0.872677\pi$
$578$		0			0
$579$	4.70507	−	14.4807i	0.195536	−	0.601798i
$580$		0			0
$581$	4.97062	−	3.61137i	0.206216	−	0.149825i
$582$		0			0
$583$	14.2439	−	17.8298i	0.589923	−	0.738435i
$584$		0			0
$585$	1.80262	−	1.30968i	0.0745291	−	0.0541486i
$586$		0			0
$587$	0.817056	−	2.51464i	0.0337235	−	0.103790i	−0.932778	−	0.360452i	$-0.882623\pi$
$587$	0.817056	−	2.51464i	0.0337235	−	0.103790i	0.966501	+	0.256661i	$0.0826225\pi$
$588$		0			0
$589$	57.5327	+	41.7999i	2.37059	+	1.72234i
$590$		0			0
$591$	6.46548	+	19.8987i	0.265954	+	0.818523i
$592$		0			0
$593$	24.5935			1.00993			0.504966	−	0.863139i	$-0.331505\pi$
$593$	24.5935			1.00993			0.504966	+	0.863139i	$0.331505\pi$
$594$		0			0
$595$	4.20473			0.172377
$596$		0			0
$597$	−3.35795	−	10.3347i	−0.137432	−	0.422971i
$598$		0			0
$599$	22.5812	+	16.4062i	0.922643	+	0.670339i	0.944180	−	0.329429i	$-0.106856\pi$
$599$	22.5812	+	16.4062i	0.922643	+	0.670339i	−0.0215376	+	0.999768i	$0.506856\pi$
$600$		0			0
$601$	−9.30372	+	28.6339i	−0.379507	+	1.16800i	0.560881	+	0.827897i	$0.310463\pi$
$601$	−9.30372	+	28.6339i	−0.379507	+	1.16800i	−0.940387	+	0.340105i	$0.889537\pi$
$602$		0			0
$603$	0.862307	−	0.626503i	0.0351158	−	0.0255132i
$604$		0			0
$605$	−10.9540	−	1.00488i	−0.445344	−	0.0408544i
$606$		0			0
$607$	−2.91487	+	2.11778i	−0.118311	+	0.0859579i	−0.645367	−	0.763872i	$-0.723296\pi$
$607$	−2.91487	+	2.11778i	−0.118311	+	0.0859579i	0.527056	+	0.849830i	$0.323296\pi$
$608$		0			0
$609$	2.98810	−	9.19643i	0.121084	−	0.372658i
$610$		0			0
$611$	8.13019	+	5.90693i	0.328912	+	0.238969i
$612$		0			0
$613$	−1.15001	−	3.53937i	−0.0464486	−	0.142954i	0.925142	−	0.379620i	$-0.123945\pi$
$613$	−1.15001	−	3.53937i	−0.0464486	−	0.142954i	−0.971591	+	0.236666i	$0.923945\pi$
$614$		0			0
$615$	10.4488			0.421336
$616$		0			0
$617$	45.0167			1.81230			0.906151	−	0.422954i	$-0.139007\pi$
$617$	45.0167			1.81230			0.906151	+	0.422954i	$0.139007\pi$
$618$		0			0
$619$	−3.38386	−	10.4145i	−0.136009	−	0.418592i	0.859737	−	0.510737i	$-0.170628\pi$
$619$	−3.38386	−	10.4145i	−0.136009	−	0.418592i	−0.995746	+	0.0921453i	$0.970628\pi$
$620$		0			0
$621$	3.10018	+	2.25241i	0.124406	+	0.0903863i
$622$		0			0
$623$	−2.98854	+	9.19777i	−0.119733	+	0.368501i
$624$		0			0
$625$	−0.809017	+	0.587785i	−0.0323607	+	0.0235114i
$626$		0			0
$627$	−13.4898	+	16.8859i	−0.538731	+	0.674356i
$628$		0			0
$629$	−1.36556	+	0.992141i	−0.0544486	+	0.0395593i
$630$		0			0
$631$	12.6233	−	38.8506i	0.502526	−	1.54662i	−0.302364	−	0.953193i	$-0.597776\pi$
$631$	12.6233	−	38.8506i	0.502526	−	1.54662i	0.804890	−	0.593424i	$-0.202224\pi$
$632$		0			0
$633$	6.81712	+	4.95293i	0.270956	+	0.196861i
$634$		0			0
$635$	−4.24853	−	13.0756i	−0.168598	−	0.518891i
$636$		0			0
$637$	12.8687			0.509876
$638$		0			0
$639$	−13.5425			−0.535733
$640$		0			0
$641$	8.97489	+	27.6219i	0.354487	+	1.09100i	0.956306	+	0.292367i	$0.0944427\pi$
$641$	8.97489	+	27.6219i	0.354487	+	1.09100i	−0.601819	+	0.798632i	$0.705557\pi$
$642$		0			0
$643$	−10.7993	−	7.84616i	−0.425883	−	0.309422i	0.354117	−	0.935201i	$-0.384781\pi$
$643$	−10.7993	−	7.84616i	−0.425883	−	0.309422i	−0.780001	+	0.625779i	$0.784781\pi$
$644$		0			0
$645$	0.296867	−	0.913662i	0.0116891	−	0.0359754i
$646$		0			0
$647$	−11.4545	+	8.32217i	−0.450322	+	0.327178i	−0.789723	−	0.613464i	$-0.789776\pi$
$647$	−11.4545	+	8.32217i	−0.450322	+	0.327178i	0.339401	+	0.940642i	$0.389776\pi$
$648$		0			0
$649$	−0.00784204	+	0.171327i	−0.000307827	+	0.00672518i
$650$		0			0
$651$	9.76979	−	7.09817i	0.382908	−	0.278199i
$652$		0			0
$653$	−8.04687	+	24.7657i	−0.314898	+	0.969158i	0.660898	+	0.750476i	$0.270176\pi$
$653$	−8.04687	+	24.7657i	−0.314898	+	0.969158i	−0.975796	+	0.218682i	$0.929824\pi$
$654$		0			0
$655$	−18.0769	−	13.1336i	−0.706323	−	0.513174i
$656$		0			0
$657$	4.30838	+	13.2598i	0.168086	+	0.517315i
$658$		0			0
$659$	−18.7249			−0.729420			−0.364710	−	0.931121i	$-0.618832\pi$
$659$	−18.7249			−0.729420			−0.364710	+	0.931121i	$0.618832\pi$
$660$		0			0
$661$	−5.05605			−0.196658			−0.0983288	−	0.995154i	$-0.531350\pi$
$661$	−5.05605			−0.196658			−0.0983288	+	0.995154i	$0.531350\pi$
$662$		0			0
$663$	−2.61628	−	8.05208i	−0.101608	−	0.312717i
$664$		0			0
$665$	5.83381	+	4.23851i	0.226225	+	0.164362i
$666$		0			0
$667$	10.3477	−	31.8468i	0.400663	−	1.23311i
$668$		0			0
$669$	−10.5278	+	7.64891i	−0.407029	+	0.295724i
$670$		0			0
$671$	−27.2045	−	10.2367i	−1.05022	−	0.395185i
$672$		0			0
$673$	−20.4272	+	14.8412i	−0.787409	+	0.572086i	−0.907193	−	0.420714i	$-0.861780\pi$
$673$	−20.4272	+	14.8412i	−0.787409	+	0.572086i	0.119785	+	0.992800i	$0.461780\pi$
$674$		0			0
$675$	−0.309017	+	0.951057i	−0.0118941	+	0.0366062i
$676$		0			0
$677$	−1.44386	−	1.04902i	−0.0554920	−	0.0403173i	0.559693	−	0.828700i	$-0.310919\pi$
$677$	−1.44386	−	1.04902i	−0.0554920	−	0.0403173i	−0.615185	+	0.788382i	$0.710919\pi$
$678$		0			0
$679$	5.06918	+	15.6013i	0.194537	+	0.598724i
$680$		0			0
$681$	6.74906			0.258625
$682$		0			0
$683$	12.1772			0.465948			0.232974	−	0.972483i	$-0.425154\pi$
$683$	12.1772			0.465948			0.232974	+	0.972483i	$0.425154\pi$
$684$		0			0
$685$	−2.49603	−	7.68199i	−0.0953684	−	0.293514i
$686$		0			0
$687$	−1.38700	−	1.00772i	−0.0529174	−	0.0384467i
$688$		0			0
$689$	−4.73766	+	14.5810i	−0.180491	+	0.555493i
$690$		0			0
$691$	20.9470	−	15.2189i	0.796861	−	0.578953i	−0.113131	−	0.993580i	$-0.536088\pi$
$691$	20.9470	−	15.2189i	0.796861	−	0.578953i	0.909991	+	0.414627i	$0.136088\pi$
$692$		0			0
$693$	2.01922	+	3.06471i	0.0767037	+	0.116419i
$694$		0			0
$695$	3.67148	−	2.66749i	0.139267	−	0.101183i
$696$		0			0
$697$	12.2689	−	37.7597i	0.464716	−	1.43025i
$698$		0			0
$699$	8.88550	+	6.45570i	0.336081	+	0.244177i
$700$		0			0
$701$	13.3431	+	41.0657i	0.503960	+	1.55103i	0.802511	+	0.596637i	$0.203497\pi$
$701$	13.3431	+	41.0657i	0.503960	+	1.55103i	−0.298551	+	0.954394i	$0.596503\pi$
$702$		0			0
$703$	−2.89475			−0.109178
$704$		0			0
$705$	−4.51021			−0.169864
$706$		0			0
$707$	−0.920379	−	2.83264i	−0.0346144	−	0.106532i
$708$		0			0
$709$	16.4728	+	11.9682i	0.618651	+	0.449476i	0.852450	−	0.522809i	$-0.175116\pi$
$709$	16.4728	+	11.9682i	0.618651	+	0.449476i	−0.233799	+	0.972285i	$0.575116\pi$
$710$		0			0
$711$	3.32203	−	10.2242i	0.124586	−	0.383436i
$712$		0			0
$713$	33.8324	−	24.5807i	1.26703	−	0.920553i
$714$		0			0
$715$	7.12535	−	1.95987i	0.266473	−	0.0732951i
$716$		0			0
$717$	18.7688	−	13.6364i	0.700935	−	0.509259i
$718$		0			0
$719$	−8.14924	+	25.0808i	−0.303915	+	0.935355i	0.676164	+	0.736751i	$0.263641\pi$
$719$	−8.14924	+	25.0808i	−0.303915	+	0.935355i	−0.980080	+	0.198604i	$0.936359\pi$
$720$		0			0
$721$	−7.85614	−	5.70782i	−0.292578	−	0.212570i
$722$		0			0
$723$	4.66958	+	14.3715i	0.173663	+	0.534481i
$724$		0			0
$725$	8.73837			0.324535
$726$		0			0
$727$	−27.8838			−1.03415			−0.517076	−	0.855939i	$-0.672980\pi$
$727$	−27.8838			−1.03415			−0.517076	+	0.855939i	$0.672980\pi$
$728$		0			0
$729$	0.309017	+	0.951057i	0.0114451	+	0.0352243i
$730$		0			0
$731$	−2.95320	−	2.14562i	−0.109228	−	0.0793588i
$732$		0			0
$733$	5.98419	−	18.4175i	0.221031	−	0.680264i	−0.777639	−	0.628711i	$-0.783583\pi$
$733$	5.98419	−	18.4175i	0.221031	−	0.680264i	0.998670	−	0.0515531i	$-0.0164171\pi$
$734$		0			0
$735$	−4.67246	+	3.39474i	−0.172346	+	0.125217i
$736$		0			0
$737$	3.40850	−	0.937532i	0.125554	−	0.0345344i
$738$		0			0
$739$	14.6731	−	10.6606i	0.539758	−	0.392157i	−0.284237	−	0.958754i	$-0.591740\pi$
$739$	14.6731	−	10.6606i	0.539758	−	0.392157i	0.823995	+	0.566597i	$0.191740\pi$
$740$		0			0
$741$	4.48684	−	13.8091i	0.164828	−	0.507289i
$742$		0			0
$743$	43.8856	+	31.8848i	1.61001	+	1.16974i	0.863476	+	0.504389i	$0.168282\pi$
$743$	43.8856	+	31.8848i	1.61001	+	1.16974i	0.746532	+	0.665350i	$0.231718\pi$
$744$		0			0
$745$	1.19965	+	3.69215i	0.0439518	+	0.135270i
$746$		0			0
$747$	5.55227			0.203147
$748$		0			0
$749$	8.24075			0.301111
$750$		0			0
$751$	−6.95958	−	21.4194i	−0.253959	−	0.781605i	−0.994033	−	0.109080i	$-0.965210\pi$
$751$	−6.95958	−	21.4194i	−0.253959	−	0.781605i	0.740074	−	0.672525i	$-0.234790\pi$
$752$		0			0
$753$	−3.25067	−	2.36175i	−0.118461	−	0.0860670i
$754$		0			0
$755$	2.21912	−	6.82975i	0.0807621	−	0.248560i
$756$		0			0
$757$	6.17971	−	4.48982i	0.224605	−	0.163185i	−0.469792	−	0.882777i	$-0.655671\pi$
$757$	6.17971	−	4.48982i	0.224605	−	0.163185i	0.694397	+	0.719592i	$0.255671\pi$
$758$		0			0
$759$	6.99245	+	10.6130i	0.253810	+	0.385226i
$760$		0			0
$761$	−4.82367	+	3.50460i	−0.174858	+	0.127042i	−0.671772	−	0.740758i	$-0.734466\pi$
$761$	−4.82367	+	3.50460i	−0.174858	+	0.127042i	0.496914	+	0.867800i	$0.334466\pi$
$762$		0			0
$763$	−3.91636	+	12.0533i	−0.141782	+	0.436359i
$764$		0			0
$765$	3.07407	+	2.23344i	0.111143	+	0.0807502i
$766$		0			0
$767$	−0.0356052	−	0.109582i	−0.00128563	−	0.00395676i
$768$		0			0
$769$	−27.3541			−0.986415			−0.493208	−	0.869912i	$-0.664176\pi$
$769$	−27.3541			−0.986415			−0.493208	+	0.869912i	$0.664176\pi$
$770$		0			0
$771$	4.50713			0.162320
$772$		0			0
$773$	−0.275296	−	0.847273i	−0.00990170	−	0.0304743i	0.945984	−	0.324214i	$-0.105100\pi$
$773$	−0.275296	−	0.847273i	−0.00990170	−	0.0304743i	−0.955885	+	0.293740i	$0.905100\pi$
$774$		0			0
$775$	8.82882	+	6.41452i	0.317141	+	0.230416i
$776$		0			0
$777$	−0.151902	+	0.467507i	−0.00544946	+	0.0167717i
$778$		0			0
$779$	55.0853	−	40.0218i	1.97364	−	1.43393i
$780$		0			0
$781$	−42.0377	−	15.8183i	−1.50423	−	0.566023i
$782$		0			0
$783$	7.06949	−	5.13628i	0.252643	−	0.183556i
$784$		0			0
$785$	5.48749	−	16.8888i	0.195857	−	0.602785i
$786$		0			0
$787$	−7.42863	−	5.39722i	−0.264802	−	0.192390i	0.447459	−	0.894304i	$-0.352329\pi$
$787$	−7.42863	−	5.39722i	−0.264802	−	0.192390i	−0.712261	+	0.701914i	$0.752329\pi$
$788$		0			0
$789$	8.27334	+	25.4627i	0.294539	+	0.906497i
$790$		0			0
$791$	16.9329			0.602066
$792$		0			0
$793$	19.5275			0.693442
$794$		0			0
$795$	−2.12627	−	6.54398i	−0.0754109	−	0.232091i
$796$		0			0
$797$	41.8614	+	30.4141i	1.48281	+	1.07732i	0.976639	+	0.214888i	$0.0689386\pi$
$797$	41.8614	+	30.4141i	1.48281	+	1.07732i	0.506169	+	0.862435i	$0.331061\pi$
$798$		0			0
$799$	−5.29584	+	16.2989i	−0.187353	+	0.576614i
$800$		0			0
$801$	−7.07052	+	5.13703i	−0.249825	+	0.181508i
$802$		0			0
$803$	−2.11435	+	46.1927i	−0.0746137	+	1.63011i
$804$		0			0
$805$	3.43060	−	2.49248i	0.120913	−	0.0878482i
$806$		0			0
$807$	−4.68506	+	14.4191i	−0.164922	+	0.507577i
$808$		0			0
$809$	4.65032	+	3.37866i	0.163497	+	0.118787i	0.666525	−	0.745483i	$-0.267781\pi$
$809$	4.65032	+	3.37866i	0.163497	+	0.118787i	−0.503028	+	0.864270i	$0.667781\pi$
$810$		0			0
$811$	−8.52983	−	26.2521i	−0.299523	−	0.921836i	−0.981665	−	0.190616i	$-0.938951\pi$
$811$	−8.52983	−	26.2521i	−0.299523	−	0.921836i	0.682142	−	0.731220i	$-0.261049\pi$
$812$		0			0
$813$	−6.67742			−0.234187
$814$		0			0
$815$	24.3915			0.854398
$816$		0			0
$817$	−1.93452	−	5.95384i	−0.0676803	−	0.208299i
$818$		0			0
$819$	−1.99474	−	1.44926i	−0.0697019	−	0.0506414i
$820$		0			0
$821$	−9.39247	+	28.9070i	−0.327799	+	1.00886i	0.642362	+	0.766402i	$0.277955\pi$
$821$	−9.39247	+	28.9070i	−0.327799	+	1.00886i	−0.970161	+	0.242461i	$0.922045\pi$
$822$		0			0
$823$	6.11445	−	4.44241i	0.213136	−	0.154853i	−0.476095	−	0.879394i	$-0.657948\pi$
$823$	6.11445	−	4.44241i	0.213136	−	0.154853i	0.689232	+	0.724541i	$0.257948\pi$
$824$		0			0
$825$	−2.07011	+	2.59126i	−0.0720721	+	0.0902161i
$826$		0			0
$827$	−2.06668	+	1.50153i	−0.0718653	+	0.0522132i	−0.623138	−	0.782112i	$-0.714142\pi$
$827$	−2.06668	+	1.50153i	−0.0718653	+	0.0522132i	0.551273	+	0.834325i	$0.314142\pi$
$828$		0			0
$829$	5.55888	−	17.1085i	0.193068	−	0.594202i	−0.806926	−	0.590653i	$-0.798870\pi$
$829$	5.55888	−	17.1085i	0.193068	−	0.594202i	0.999994	−	0.00354925i	$-0.00112976\pi$
$830$		0			0
$831$	−8.75516	−	6.36099i	−0.303713	−	0.220660i
$832$		0			0
$833$	6.78151	+	20.8713i	0.234965	+	0.723149i
$834$		0			0
$835$	12.8520			0.444760
$836$		0			0
$837$	10.9130			0.377209
$838$		0			0
$839$	−8.92978	−	27.4830i	−0.308290	−	0.948819i	−0.978429	−	0.206584i	$-0.933765\pi$
$839$	−8.92978	−	27.4830i	−0.308290	−	0.948819i	0.670139	−	0.742236i	$-0.266235\pi$
$840$		0			0
$841$	−38.3143	−	27.8370i	−1.32118	−	0.959896i
$842$		0			0
$843$	2.64771	−	8.14880i	0.0911918	−	0.280660i
$844$		0			0
$845$	6.50070	−	4.72303i	0.223631	−	0.162477i
$846$		0			0
$847$	2.68818	+	11.8718i	0.0923670	+	0.407921i
$848$		0			0
$849$	−21.0087	+	15.2637i	−0.721018	+	0.523850i
$850$		0			0
$851$	−0.526031	+	1.61896i	−0.0180321	+	0.0554971i
$852$		0			0
$853$	31.4431	+	22.8448i	1.07659	+	0.782190i	0.977086	−	0.212847i	$-0.0682735\pi$
$853$	31.4431	+	22.8448i	1.07659	+	0.782190i	0.0995067	+	0.995037i	$0.468274\pi$
$854$		0			0
$855$	2.01370	+	6.19752i	0.0688670	+	0.211951i
$856$		0			0
$857$	−50.2254			−1.71567			−0.857833	−	0.513929i	$-0.828190\pi$
$857$	−50.2254			−1.71567			−0.857833	+	0.513929i	$0.828190\pi$
$858$		0			0
$859$	−44.9125			−1.53239			−0.766197	−	0.642605i	$-0.777854\pi$
$859$	−44.9125			−1.53239			−0.766197	+	0.642605i	$0.777854\pi$
$860$		0			0
$861$	−3.57299	−	10.9965i	−0.121767	−	0.374760i
$862$		0			0
$863$	14.1843	+	10.3055i	0.482839	+	0.350803i	0.802424	−	0.596755i	$-0.203544\pi$
$863$	14.1843	+	10.3055i	0.482839	+	0.350803i	−0.319585	+	0.947558i	$0.603544\pi$
$864$		0			0
$865$	−1.54027	+	4.74047i	−0.0523708	+	0.161181i
$866$		0			0
$867$	−2.07259	+	1.50583i	−0.0703889	+	0.0511406i
$868$		0			0
$869$	22.2544	−	27.8569i	0.754928	−	0.944980i
$870$		0			0
$871$	−1.92136	+	1.39595i	−0.0651027	+	0.0472999i
$872$		0			0
$873$	−4.58094	+	14.0987i	−0.155041	+	0.477169i
$874$		0			0
$875$	0.895242	+	0.650431i	0.0302647	+	0.0219886i
$876$		0			0
$877$	−2.59233	−	7.97836i	−0.0875366	−	0.269410i	0.897700	−	0.440607i	$-0.145237\pi$
$877$	−2.59233	−	7.97836i	−0.0875366	−	0.269410i	−0.985237	+	0.171197i	$0.945237\pi$
$878$		0			0
$879$	31.1950			1.05218
$880$		0			0
$881$	−49.1487			−1.65586			−0.827931	−	0.560829i	$-0.810482\pi$
$881$	−49.1487			−1.65586			−0.827931	+	0.560829i	$0.810482\pi$
$882$		0			0
$883$	−15.4008	−	47.3989i	−0.518279	−	1.59510i	−0.777235	−	0.629210i	$-0.783378\pi$
$883$	−15.4008	−	47.3989i	−0.518279	−	1.59510i	0.258956	−	0.965889i	$-0.416622\pi$
$884$		0			0
$885$	0.0418352	+	0.0303951i	0.00140628	+	0.00102172i
$886$		0			0
$887$	0.840425	−	2.58656i	0.0282187	−	0.0868482i	−0.935955	−	0.352119i	$-0.885461\pi$
$887$	0.840425	−	2.58656i	0.0282187	−	0.0868482i	0.964174	+	0.265271i	$0.0854613\pi$
$888$		0			0
$889$	−12.3083	+	8.94248i	−0.412806	+	0.299921i
$890$		0			0
$891$	−0.151651	+	3.31316i	−0.00508049	+	0.110995i
$892$		0			0
$893$	−23.7775	+	17.2754i	−0.795684	+	0.578098i
$894$		0			0
$895$	−5.67289	+	17.4594i	−0.189624	+	0.583602i
$896$		0			0
$897$	−6.90770	−	5.01874i	−0.230641	−	0.167571i
$898$		0			0
$899$	−29.4685	−	90.6947i	−0.982829	−	3.02484i
$900$		0			0
$901$	−26.1451			−0.871021
$902$		0			0
$903$	−1.06307			−0.0353768
$904$		0			0
$905$	−3.45554	−	10.6351i	−0.114866	−	0.353521i
$906$		0			0
$907$	21.9396	+	15.9401i	0.728494	+	0.529282i	0.889087	−	0.457739i	$-0.151341\pi$
$907$	21.9396	+	15.9401i	0.728494	+	0.529282i	−0.160593	+	0.987021i	$0.551341\pi$
$908$		0			0
$909$	0.831733	−	2.55981i	0.0275869	−	0.0849036i
$910$		0			0
$911$	19.3246	−	14.0402i	0.640254	−	0.465172i	−0.219684	−	0.975571i	$-0.570502\pi$
$911$	19.3246	−	14.0402i	0.640254	−	0.465172i	0.859937	+	0.510400i	$0.170502\pi$
$912$		0			0
$913$	17.2350	+	6.48532i	0.570395	+	0.214633i
$914$		0			0
$915$	−7.09019	+	5.15133i	−0.234395	+	0.170298i
$916$		0			0
$917$	−7.64067	+	23.5156i	−0.252317	+	0.776552i
$918$		0			0
$919$	−0.383627	−	0.278721i	−0.0126547	−	0.00919417i	0.581440	−	0.813589i	$-0.302490\pi$
$919$	−0.383627	−	0.278721i	−0.0126547	−	0.00919417i	−0.594095	+	0.804395i	$0.702490\pi$
$920$		0			0
$921$	2.88065	+	8.86572i	0.0949206	+	0.292135i
$922$		0			0
$923$	30.1748			0.993217
$924$		0			0
$925$	−0.444221			−0.0146059
$926$		0			0
$927$	−2.71176	−	8.34594i	−0.0890659	−	0.274117i
$928$		0			0
$929$	3.25078	+	2.36183i	0.106654	+	0.0774890i	0.639834	−	0.768513i	$-0.279003\pi$
$929$	3.25078	+	2.36183i	0.106654	+	0.0774890i	−0.533180	+	0.846002i	$0.679003\pi$
$930$		0			0
$931$	−11.6301	+	35.7937i	−0.381160	+	1.17309i
$932$		0			0
$933$	12.0452	−	8.75136i	0.394342	−	0.286507i
$934$		0			0
$935$	6.93355	+	10.5236i	0.226751	+	0.344157i
$936$		0			0
$937$	−17.5734	+	12.7678i	−0.574098	+	0.417107i	−0.836592	−	0.547827i	$-0.815455\pi$
$937$	−17.5734	+	12.7678i	−0.574098	+	0.417107i	0.262494	+	0.964934i	$0.415455\pi$
$938$		0			0
$939$	1.83624	−	5.65137i	0.0599235	−	0.184425i
$940$		0			0
$941$	21.6432	+	15.7247i	0.705548	+	0.512611i	0.881734	−	0.471746i	$-0.156376\pi$
$941$	21.6432	+	15.7247i	0.705548	+	0.512611i	−0.176186	+	0.984357i	$0.556376\pi$
$942$		0			0
$943$	−12.3731	−	38.0805i	−0.402923	−	1.24007i
$944$		0			0
$945$	1.10658			0.0359970
$946$		0			0
$947$	−54.8496			−1.78237			−0.891186	−	0.453637i	$-0.850126\pi$
$947$	−54.8496			−1.78237			−0.891186	+	0.453637i	$0.850126\pi$
$948$		0			0
$949$	−9.59976	−	29.5450i	−0.311621	−	0.959072i
$950$		0			0
$951$	−24.5964	−	17.8703i	−0.797593	−	0.579485i
$952$		0			0
$953$	−5.36700	+	16.5179i	−0.173854	+	0.535069i	−0.999579	−	0.0290043i	$-0.990766\pi$
$953$	−5.36700	+	16.5179i	−0.173854	+	0.535069i	0.825725	+	0.564073i	$0.190766\pi$
$954$		0			0
$955$	−4.97928	+	3.61766i	−0.161126	+	0.117065i
$956$		0			0
$957$	27.9441	−	7.68621i	0.903304	−	0.248460i
$958$		0			0
$959$	−7.23115	+	5.25374i	−0.233506	+	0.169652i
$960$		0			0
$961$	27.2226	−	83.7825i	0.878148	−	2.70266i
$962$		0			0
$963$	6.02479	+	4.37727i	0.194146	+	0.141055i
$964$		0			0
$965$	−4.70507	−	14.4807i	−0.151462	−	0.466151i
$966$		0			0
$967$	−19.9715			−0.642239			−0.321119	−	0.947039i	$-0.604059\pi$
$967$	−19.9715			−0.642239			−0.321119	+	0.947039i	$0.604059\pi$
$968$		0			0
$969$	24.7609			0.795436
$970$		0			0
$971$	−6.65196	−	20.4726i	−0.213472	−	0.656998i	−0.999259	−	0.0385006i	$-0.987742\pi$
$971$	−6.65196	−	20.4726i	−0.213472	−	0.656998i	0.785787	−	0.618497i	$-0.212258\pi$
$972$		0			0
$973$	−4.06278	−	2.95178i	−0.130247	−	0.0946299i
$974$		0			0
$975$	0.688539	−	2.11911i	0.0220509	−	0.0678657i
$976$		0			0
$977$	23.8920	−	17.3585i	0.764372	−	0.555349i	−0.135876	−	0.990726i	$-0.543385\pi$
$977$	23.8920	−	17.3585i	0.764372	−	0.555349i	0.900248	+	0.435377i	$0.143385\pi$
$978$		0			0
$979$	−27.9482	+	7.68733i	−0.893227	+	0.245688i
$980$		0			0
$981$	−9.26564	+	6.73188i	−0.295829	+	0.214932i
$982$		0			0
$983$	−13.1288	+	40.4063i	−0.418744	+	1.28876i	0.490115	+	0.871658i	$0.336955\pi$
$983$	−13.1288	+	40.4063i	−0.418744	+	1.28876i	−0.908859	+	0.417103i	$0.863045\pi$
$984$		0			0
$985$	16.9268	+	12.2981i	0.539334	+	0.391849i
$986$		0			0
$987$	1.54227	+	4.74663i	0.0490911	+	0.151087i
$988$		0			0
$989$	−3.68137			−0.117061
$990$		0			0
$991$	41.1872			1.30835			0.654177	−	0.756341i	$-0.273015\pi$
$991$	41.1872			1.30835			0.654177	+	0.756341i	$0.273015\pi$
$992$		0			0
$993$	−10.2711	−	31.6113i	−0.325944	−	1.00315i
$994$		0			0
$995$	−8.79122	−	6.38719i	−0.278700	−	0.202488i
$996$		0			0
$997$	0.929169	−	2.85969i	0.0294271	−	0.0905672i	−0.935264	−	0.353950i	$-0.884838\pi$
$997$	0.929169	−	2.85969i	0.0294271	−	0.0905672i	0.964691	+	0.263383i	$0.0848383\pi$
$998$		0			0
$999$	−0.359382	+	0.261107i	−0.0113704	+	0.00826105i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1320.2.bw.f.1081.1	yes	12
11.4	even	5	inner	1320.2.bw.f.961.1	✓	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1320.2.bw.f.961.1	✓	12	11.4	even	5	inner
1320.2.bw.f.1081.1	yes	12	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1320 = 2^{3} \cdot 3 \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1320.bw (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.309017 - 0.951057i) q^{3} +(-0.809017 - 0.587785i) q^{5} +(-0.341952 + 1.05242i) q^{7} +(-0.809017 + 0.587785i) q^{9} +O(q^{10})\)	\(q+(-0.309017 - 0.951057i) q^{3} +(-0.809017 - 0.587785i) q^{5} +(-0.341952 + 1.05242i) q^{7} +(-0.809017 + 0.587785i) q^{9} +(-3.19786 + 0.879593i) q^{11} +(1.80262 - 1.30968i) q^{13} +(-0.309017 + 0.951057i) q^{15} +(3.07407 + 2.23344i) q^{17} +(2.01370 + 6.19752i) q^{19} +1.10658 q^{21} +3.83204 q^{23} +(0.309017 + 0.951057i) q^{25} +(0.809017 + 0.587785i) q^{27} +(2.70030 - 8.31068i) q^{29} +(8.82882 - 6.41452i) q^{31} +(1.82474 + 2.76954i) q^{33} +(0.895242 - 0.650431i) q^{35} +(-0.137272 + 0.422479i) q^{37} +(-1.80262 - 1.30968i) q^{39} +(-3.22886 - 9.93740i) q^{41} -0.960681 q^{43} +1.00000 q^{45} +(1.39373 + 4.28946i) q^{47} +(4.67246 + 3.39474i) q^{49} +(1.17419 - 3.61378i) q^{51} +(-5.56664 + 4.04440i) q^{53} +(3.10414 + 1.16805i) q^{55} +(5.27193 - 3.83028i) q^{57} +(0.0159796 - 0.0491803i) q^{59} +(7.09019 + 5.15133i) q^{61} +(-0.341952 - 1.05242i) q^{63} -2.22816 q^{65} -1.06587 q^{67} +(-1.18416 - 3.64448i) q^{69} +(10.9561 + 7.96008i) q^{71} +(4.30838 - 13.2598i) q^{73} +(0.809017 - 0.587785i) q^{75} +(0.167814 - 3.66627i) q^{77} +(-8.69719 + 6.31888i) q^{79} +(0.309017 - 0.951057i) q^{81} +(-4.49188 - 3.26354i) q^{83} +(-1.17419 - 3.61378i) q^{85} -8.73837 q^{87} +8.73964 q^{89} +(0.761924 + 2.34496i) q^{91} +(-8.82882 - 6.41452i) q^{93} +(2.01370 - 6.19752i) q^{95} +(11.9931 - 8.71347i) q^{97} +(2.07011 - 2.59126i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 3 q^{3} - 3 q^{5} - 3 q^{9}+O(q^{10}) \) 12 * q + 3 * q^3 - 3 * q^5 - 3 * q^9	\( 12 q + 3 q^{3} - 3 q^{5} - 3 q^{9} - 4 q^{11} + 3 q^{13} + 3 q^{15} + 12 q^{17} - 4 q^{19} - 10 q^{21} - 12 q^{23} - 3 q^{25} + 3 q^{27} + 16 q^{29} + 3 q^{31} + 4 q^{33} - 5 q^{35} - 19 q^{37} - 3 q^{39} + 22 q^{41} + 52 q^{43} + 12 q^{45} + 25 q^{47} - 11 q^{49} + 8 q^{51} - q^{53} - 4 q^{55} + 4 q^{57} - 9 q^{59} + 21 q^{61} - 12 q^{65} - 18 q^{67} - 8 q^{69} + 17 q^{71} + 37 q^{73} + 3 q^{75} - 13 q^{77} - 18 q^{79} - 3 q^{81} + 19 q^{83} - 8 q^{85} + 14 q^{87} + 2 q^{89} - 30 q^{91} - 3 q^{93} - 4 q^{95} + q^{97} + 6 q^{99}+O(q^{100}) \) 12 * q + 3 * q^3 - 3 * q^5 - 3 * q^9 - 4 * q^11 + 3 * q^13 + 3 * q^15 + 12 * q^17 - 4 * q^19 - 10 * q^21 - 12 * q^23 - 3 * q^25 + 3 * q^27 + 16 * q^29 + 3 * q^31 + 4 * q^33 - 5 * q^35 - 19 * q^37 - 3 * q^39 + 22 * q^41 + 52 * q^43 + 12 * q^45 + 25 * q^47 - 11 * q^49 + 8 * q^51 - q^53 - 4 * q^55 + 4 * q^57 - 9 * q^59 + 21 * q^61 - 12 * q^65 - 18 * q^67 - 8 * q^69 + 17 * q^71 + 37 * q^73 + 3 * q^75 - 13 * q^77 - 18 * q^79 - 3 * q^81 + 19 * q^83 - 8 * q^85 + 14 * q^87 + 2 * q^89 - 30 * q^91 - 3 * q^93 - 4 * q^95 + q^97 + 6 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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