LMFDB - Embedded newform 92.2.e.a.77.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [92,2,Mod(9,92)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(92, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 10]))

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

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

chi := DirichletCharacter("92.9");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 92 = 2^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	92.e (of order $11$, degree $10$, 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:	$0.734623698596$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$2$ over $\Q(\zeta_{11})$
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} - 9 x^{19} + 51 x^{18} - 200 x^{17} + 633 x^{16} - 1688 x^{15} + 3957 x^{14} - 8161 x^{13} + \cdots + 529 $ x^20 - 9x^19 + 51x^18 - 200x^17 + 633x^16 - 1688x^15 + 3957x^14 - 8161x^13 + 14788x^12 - 23925x^11 + 35080x^10 - 43945x^9 + 57269x^8 - 57348x^7 + 52821x^6 - 34986x^5 + 26231x^4 + 96928x^3 + 49370x^2 + 8165*x + 529
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			77.2
Root			$-0.115644 - 0.0743196i$ of defining polynomial
Character	$\chi$	$=$	92.77
Dual form			92.2.e.a.49.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.0571054 + 0.125043i) q^{3} +(1.77577 + 2.04934i) q^{5} +(-0.600040 - 0.385622i) q^{7} +(1.95221 - 2.25297i) q^{9} +O(q^{10})$	\(q+(0.0571054 + 0.125043i) q^{3} +(1.77577 + 2.04934i) q^{5} +(-0.600040 - 0.385622i) q^{7} +(1.95221 - 2.25297i) q^{9} +(-0.176680 - 1.22883i) q^{11} +(-3.37543 + 2.16925i) q^{13} +(-0.154851 + 0.339076i) q^{15} +(-1.87813 + 0.551470i) q^{17} +(-5.89961 - 1.73228i) q^{19} +(0.0139540 - 0.0970521i) q^{21} +(-1.81812 - 4.43784i) q^{23} +(-0.334890 + 2.32921i) q^{25} +(0.788892 + 0.231640i) q^{27} +(7.07444 - 2.07724i) q^{29} +(-1.60018 + 3.50391i) q^{31} +(0.143568 - 0.0922656i) q^{33} +(-0.275258 - 1.91446i) q^{35} +(-1.59202 + 1.83729i) q^{37} +(-0.464006 - 0.298198i) q^{39} +(-2.23988 - 2.58496i) q^{41} +(4.86900 + 10.6616i) q^{43} +8.08377 q^{45} +5.43590 q^{47} +(-2.69656 - 5.90465i) q^{49} +(-0.176209 - 0.203356i) q^{51} +(6.61027 + 4.24816i) q^{53} +(2.20456 - 2.54420i) q^{55} +(-0.120289 - 0.836629i) q^{57} +(8.60536 - 5.53033i) q^{59} +(-4.24909 + 9.30420i) q^{61} +(-2.04020 + 0.599056i) q^{63} +(-10.4395 - 3.06532i) q^{65} +(0.870750 - 6.05620i) q^{67} +(0.451098 - 0.480768i) q^{69} +(-2.12198 + 14.7587i) q^{71} +(-14.6335 - 4.29679i) q^{73} +(-0.310376 + 0.0911346i) q^{75} +(-0.367851 + 0.805481i) q^{77} +(8.62961 - 5.54592i) q^{79} +(-1.25668 - 8.74041i) q^{81} +(-7.65314 + 8.83219i) q^{83} +(-4.46528 - 2.86966i) q^{85} +(0.663734 + 0.765990i) q^{87} +(-0.864480 - 1.89295i) q^{89} +2.86190 q^{91} -0.529519 q^{93} +(-6.92629 - 15.1665i) q^{95} +(-0.587549 - 0.678068i) q^{97} +(-3.11344 - 2.00089i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 2 q^{3} + 2 q^{5} + 2 q^{7} - 4 q^{9}+O(q^{10}) $ 20 * q + 2 * q^3 + 2 * q^5 + 2 * q^7 - 4 * q^9	$ 20 q + 2 q^{3} + 2 q^{5} + 2 q^{7} - 4 q^{9} - 2 q^{11} + 6 q^{13} - 17 q^{15} - 9 q^{17} - 11 q^{19} - 47 q^{21} - 22 q^{23} - 16 q^{25} - 19 q^{27} - q^{29} - 13 q^{31} - 5 q^{33} + 14 q^{35} + 34 q^{37} + 30 q^{39} + 28 q^{41} + 44 q^{43} + 78 q^{45} + 26 q^{47} + 60 q^{49} + 62 q^{51} + 14 q^{53} + 26 q^{55} + 3 q^{57} - 10 q^{59} - 56 q^{61} - 27 q^{63} - 87 q^{65} - 44 q^{67} - 51 q^{69} - 37 q^{71} - 12 q^{73} - 53 q^{75} - 47 q^{77} - 6 q^{79} - 10 q^{81} - 25 q^{83} + 8 q^{85} + 48 q^{87} + 10 q^{89} + 26 q^{91} - 14 q^{93} + 29 q^{95} - q^{97} - q^{99}+O(q^{100}) $ 20 * q + 2 * q^3 + 2 * q^5 + 2 * q^7 - 4 * q^9 - 2 * q^11 + 6 * q^13 - 17 * q^15 - 9 * q^17 - 11 * q^19 - 47 * q^21 - 22 * q^23 - 16 * q^25 - 19 * q^27 - q^29 - 13 * q^31 - 5 * q^33 + 14 * q^35 + 34 * q^37 + 30 * q^39 + 28 * q^41 + 44 * q^43 + 78 * q^45 + 26 * q^47 + 60 * q^49 + 62 * q^51 + 14 * q^53 + 26 * q^55 + 3 * q^57 - 10 * q^59 - 56 * q^61 - 27 * q^63 - 87 * q^65 - 44 * q^67 - 51 * q^69 - 37 * q^71 - 12 * q^73 - 53 * q^75 - 47 * q^77 - 6 * q^79 - 10 * q^81 - 25 * q^83 + 8 * q^85 + 48 * q^87 + 10 * q^89 + 26 * q^91 - 14 * q^93 + 29 * q^95 - q^97 - q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/92\mathbb{Z}\right)^\times$.

$n$	$5$	$47$
$\chi(n)$	$e\left(\frac{3}{11}\right)$	$1$

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			0
$2$		0			0
$3$	0.0571054	+	0.125043i	0.0329698	+	0.0721938i	0.925400	−	0.378991i	$-0.123729\pi$
$3$	0.0571054	+	0.125043i	0.0329698	+	0.0721938i	−0.892431	+	0.451185i	$0.851002\pi$
$4$		0			0
$5$	1.77577	+	2.04934i	0.794147	+	0.916495i	0.998045	−	0.0624975i	$-0.0199065\pi$
$5$	1.77577	+	2.04934i	0.794147	+	0.916495i	−0.203898	+	0.978992i	$0.565361\pi$
$6$		0			0
$7$	−0.600040	−	0.385622i	−0.226794	−	0.145752i	0.422310	−	0.906452i	$-0.361219\pi$
$7$	−0.600040	−	0.385622i	−0.226794	−	0.145752i	−0.649104	+	0.760700i	$0.724856\pi$
$8$		0			0
$9$	1.95221	−	2.25297i	0.650736	−	0.750989i
$10$		0			0
$11$	−0.176680	−	1.22883i	−0.0532709	−	0.370507i	−0.998966	−	0.0454536i	$-0.985527\pi$
$11$	−0.176680	−	1.22883i	−0.0532709	−	0.370507i	0.945696	−	0.325054i	$-0.105382\pi$
$12$		0			0
$13$	−3.37543	+	2.16925i	−0.936175	+	0.601643i	−0.917308	−	0.398179i	$-0.869642\pi$
$13$	−3.37543	+	2.16925i	−0.936175	+	0.601643i	−0.0188670	+	0.999822i	$0.506006\pi$
$14$		0			0
$15$	−0.154851	+	0.339076i	−0.0399823	+	0.0875491i
$16$		0			0
$17$	−1.87813	+	0.551470i	−0.455515	+	0.133751i	−0.501438	−	0.865194i	$-0.667195\pi$
$17$	−1.87813	+	0.551470i	−0.455515	+	0.133751i	0.0459230	+	0.998945i	$0.485377\pi$
$18$		0			0
$19$	−5.89961	−	1.73228i	−1.35346	−	0.397412i	−0.477009	−	0.878898i	$-0.658279\pi$
$19$	−5.89961	−	1.73228i	−1.35346	−	0.397412i	−0.876454	+	0.481486i	$0.840097\pi$
$20$		0			0
$21$	0.0139540	−	0.0970521i	0.00304501	−	0.0211785i
$22$		0			0
$23$	−1.81812	−	4.43784i	−0.379104	−	0.925354i
$23$	−1.81812	−	4.43784i	−0.379104	−	0.925354i
$24$		0			0
$25$	−0.334890	+	2.32921i	−0.0669779	+	0.465842i
$26$		0			0
$27$	0.788892	+	0.231640i	0.151822	+	0.0445791i
$28$		0			0
$29$	7.07444	−	2.07724i	1.31369	−	0.385734i	0.451479	−	0.892282i	$-0.350897\pi$
$29$	7.07444	−	2.07724i	1.31369	−	0.385734i	0.862212	+	0.506548i	$0.169079\pi$
$30$		0			0
$31$	−1.60018	+	3.50391i	−0.287401	+	0.629321i	−0.997175	−	0.0751086i	$-0.976070\pi$
$31$	−1.60018	+	3.50391i	−0.287401	+	0.629321i	0.709774	+	0.704429i	$0.248797\pi$
$32$		0			0
$33$	0.143568	−	0.0922656i	0.0249920	−	0.0160614i
$34$		0			0
$35$	−0.275258	−	1.91446i	−0.0465272	−	0.323603i
$36$		0			0
$37$	−1.59202	+	1.83729i	−0.261727	+	0.302049i	−0.871369	−	0.490628i	$-0.836767\pi$
$37$	−1.59202	+	1.83729i	−0.261727	+	0.302049i	0.609643	+	0.792676i	$0.291313\pi$
$38$		0			0
$39$	−0.464006	−	0.298198i	−0.0743004	−	0.0477499i
$40$		0			0
$41$	−2.23988	−	2.58496i	−0.349810	−	0.403703i	0.553390	−	0.832922i	$-0.313334\pi$
$41$	−2.23988	−	2.58496i	−0.349810	−	0.403703i	−0.903200	+	0.429220i	$0.858789\pi$
$42$		0			0
$43$	4.86900	+	10.6616i	0.742515	+	1.62588i	0.779373	+	0.626560i	$0.215538\pi$
$43$	4.86900	+	10.6616i	0.742515	+	1.62588i	−0.0368584	+	0.999320i	$0.511735\pi$
$44$		0			0
$45$	8.08377			1.20506
$46$		0			0
$47$	5.43590			0.792908			0.396454	−	0.918055i	$-0.370241\pi$
$47$	5.43590			0.792908			0.396454	+	0.918055i	$0.370241\pi$
$48$		0			0
$49$	−2.69656	−	5.90465i	−0.385223	−	0.843521i
$50$		0			0
$51$	−0.176209	−	0.203356i	−0.0246742	−	0.0284756i
$52$		0			0
$53$	6.61027	+	4.24816i	0.907991	+	0.583530i	0.909150	−	0.416469i	$-0.136733\pi$
$53$	6.61027	+	4.24816i	0.907991	+	0.583530i	−0.00115923	+	0.999999i	$0.500369\pi$
$54$		0			0
$55$	2.20456	−	2.54420i	0.297263	−	0.343060i
$56$		0			0
$57$	−0.120289	−	0.836629i	−0.0159327	−	0.110814i
$58$		0			0
$59$	8.60536	−	5.53033i	1.12032	−	0.719987i	0.156804	−	0.987630i	$-0.449881\pi$
$59$	8.60536	−	5.53033i	1.12032	−	0.719987i	0.963518	+	0.267643i	$0.0862447\pi$
$60$		0			0
$61$	−4.24909	+	9.30420i	−0.544040	+	1.19128i	0.415470	+	0.909607i	$0.363617\pi$
$61$	−4.24909	+	9.30420i	−0.544040	+	1.19128i	−0.959510	+	0.281674i	$0.909110\pi$
$62$		0			0
$63$	−2.04020	+	0.599056i	−0.257041	+	0.0754739i
$64$		0			0
$65$	−10.4395	−	3.06532i	−1.29486	−	0.380206i
$66$		0			0
$67$	0.870750	−	6.05620i	0.106379	−	0.739883i	−0.864901	−	0.501943i	$-0.832619\pi$
$67$	0.870750	−	6.05620i	0.106379	−	0.739883i	0.971280	−	0.237940i	$-0.0764721\pi$
$68$		0			0
$69$	0.451098	−	0.480768i	0.0543058	−	0.0578777i
$70$		0			0
$71$	−2.12198	+	14.7587i	−0.251832	+	1.75153i	0.335364	+	0.942088i	$0.391141\pi$
$71$	−2.12198	+	14.7587i	−0.251832	+	1.75153i	−0.587197	+	0.809444i	$0.699769\pi$
$72$		0			0
$73$	−14.6335	−	4.29679i	−1.71273	−	0.502902i	−0.729297	−	0.684197i	$-0.760153\pi$
$73$	−14.6335	−	4.29679i	−1.71273	−	0.502902i	−0.983429	+	0.181295i	$0.941971\pi$
$74$		0			0
$75$	−0.310376	+	0.0911346i	−0.0358391	+	0.0105233i
$76$		0			0
$77$	−0.367851	+	0.805481i	−0.0419205	+	0.0917931i
$78$		0			0
$79$	8.62961	−	5.54592i	0.970907	−	0.623964i	0.0439114	−	0.999035i	$-0.486018\pi$
$79$	8.62961	−	5.54592i	0.970907	−	0.623964i	0.926996	+	0.375071i	$0.122382\pi$
$80$		0			0
$81$	−1.25668	−	8.74041i	−0.139631	−	0.971156i
$82$		0			0
$83$	−7.65314	+	8.83219i	−0.840041	+	0.969459i	−0.999844	−	0.0176901i	$-0.994369\pi$
$83$	−7.65314	+	8.83219i	−0.840041	+	0.969459i	0.159803	+	0.987149i	$0.448914\pi$
$84$		0			0
$85$	−4.46528	−	2.86966i	−0.484328	−	0.311259i
$86$		0			0
$87$	0.663734	+	0.765990i	0.0711597	+	0.0821227i
$88$		0			0
$89$	−0.864480	−	1.89295i	−0.0916347	−	0.200652i	0.858265	−	0.513207i	$-0.171543\pi$
$89$	−0.864480	−	1.89295i	−0.0916347	−	0.200652i	−0.949900	+	0.312555i	$0.898815\pi$
$90$		0			0
$91$	2.86190			0.300009
$92$		0			0
$93$	−0.529519			−0.0549086
$94$		0			0
$95$	−6.92629	−	15.1665i	−0.710622	−	1.55605i
$96$		0			0
$97$	−0.587549	−	0.678068i	−0.0596566	−	0.0688474i	0.725137	−	0.688605i	$-0.241776\pi$
$97$	−0.587549	−	0.678068i	−0.0596566	−	0.0688474i	−0.784793	+	0.619757i	$0.787231\pi$
$98$		0			0
$99$	−3.11344	−	2.00089i	−0.312912	−	0.201097i
$100$		0			0
$101$	4.44390	−	5.12853i	0.442184	−	0.510308i	−0.490283	−	0.871564i	$-0.663106\pi$
$101$	4.44390	−	5.12853i	0.442184	−	0.510308i	0.932467	+	0.361256i	$0.117652\pi$
$102$		0			0
$103$	2.08664	+	14.5129i	0.205603	+	1.43000i	0.787289	+	0.616585i	$0.211484\pi$
$103$	2.08664	+	14.5129i	0.205603	+	1.43000i	−0.581686	+	0.813414i	$0.697607\pi$
$104$		0			0
$105$	0.223672	−	0.143745i	0.0218282	−	0.0140281i
$106$		0			0
$107$	−5.99449	+	13.1261i	−0.579509	+	1.26895i	0.362068	+	0.932151i	$0.382071\pi$
$107$	−5.99449	+	13.1261i	−0.579509	+	1.26895i	−0.941578	+	0.336796i	$0.890657\pi$
$108$		0			0
$109$	−2.17177	+	0.637688i	−0.208017	+	0.0610794i	−0.384081	−	0.923299i	$-0.625482\pi$
$109$	−2.17177	+	0.637688i	−0.208017	+	0.0610794i	0.176064	+	0.984379i	$0.443664\pi$
$110$		0			0
$111$	−0.320654	−	0.0941524i	−0.0304351	−	0.00893655i
$112$		0			0
$113$	−0.493869	+	3.43494i	−0.0464593	+	0.323132i	0.953317	+	0.301972i	$0.0976449\pi$
$113$	−0.493869	+	3.43494i	−0.0464593	+	0.323132i	−0.999776	+	0.0211597i	$0.993264\pi$
$114$		0			0
$115$	5.86611	−	11.6065i	0.547018	−	1.08231i
$116$		0			0
$117$	−1.70227	+	11.8396i	−0.157375	+	1.09457i
$118$		0			0
$119$	1.33961	+	0.393346i	0.122802	+	0.0360580i
$120$		0			0
$121$	9.07561	−	2.66484i	0.825055	−	0.242258i
$122$		0			0
$123$	0.195323	−	0.427697i	0.0176116	−	0.0385641i
$124$		0			0
$125$	6.03798	−	3.88037i	0.540053	−	0.347071i
$126$		0			0
$127$	−1.25115	−	8.70193i	−0.111021	−	0.772171i	−0.966930	−	0.255043i	$-0.917910\pi$
$127$	−1.25115	−	8.70193i	−0.111021	−	0.772171i	0.855908	−	0.517128i	$-0.172999\pi$
$128$		0			0
$129$	−1.05512	+	1.21767i	−0.0928979	+	0.107210i
$130$		0			0
$131$	3.76585	+	2.42017i	0.329024	+	0.211451i	0.694714	−	0.719286i	$-0.255531\pi$
$131$	3.76585	+	2.42017i	0.329024	+	0.211451i	−0.365690	+	0.930737i	$0.619167\pi$
$132$		0			0
$133$	2.87199	+	3.31446i	0.249033	+	0.287400i
$134$		0			0
$135$	0.926179	+	2.02805i	0.0797128	+	0.174547i
$136$		0			0
$137$	8.03333			0.686334			0.343167	−	0.939274i	$-0.388500\pi$
$137$	8.03333			0.686334			0.343167	+	0.939274i	$0.388500\pi$
$138$		0			0
$139$	16.0205			1.35884			0.679422	−	0.733748i	$-0.262231\pi$
$139$	16.0205			1.35884			0.679422	+	0.733748i	$0.262231\pi$
$140$		0			0
$141$	0.310419	+	0.679723i	0.0261420	+	0.0572430i
$142$		0			0
$143$	3.26202	+	3.76457i	0.272784	+	0.314810i
$144$		0			0
$145$	16.8195	+	10.8093i	1.39679	+	0.897660i
$146$		0			0
$147$	0.584348	−	0.674374i	0.0481962	−	0.0556214i
$148$		0			0
$149$	−1.87975	−	13.0739i	−0.153995	−	1.07106i	−0.909437	−	0.415842i	$-0.863487\pi$
$149$	−1.87975	−	13.0739i	−0.153995	−	1.07106i	0.755442	−	0.655216i	$-0.227422\pi$
$150$		0			0
$151$	−4.52981	+	2.91113i	−0.368631	+	0.236904i	−0.711820	−	0.702362i	$-0.752129\pi$
$151$	−4.52981	+	2.91113i	−0.368631	+	0.236904i	0.343190	+	0.939266i	$0.388493\pi$
$152$		0			0
$153$	−2.42406	+	5.30796i	−0.195974	+	0.429123i
$154$		0			0
$155$	−10.0223	+	2.94280i	−0.805008	+	0.236372i
$156$		0			0
$157$	−13.8115	−	4.05543i	−1.10228	−	0.323659i	−0.320522	−	0.947241i	$-0.603858\pi$
$157$	−13.8115	−	4.05543i	−1.10228	−	0.323659i	−0.781758	+	0.623582i	$0.785677\pi$
$158$		0			0
$159$	−0.153722	+	1.06916i	−0.0121910	+	0.0847901i
$160$		0			0
$161$	−0.620387	+	3.36399i	−0.0488933	+	0.265120i
$162$		0			0
$163$	1.88122	−	13.0841i	0.147348	−	1.02483i	−0.773190	−	0.634175i	$-0.781340\pi$
$163$	1.88122	−	13.0841i	0.147348	−	1.02483i	0.920538	−	0.390654i	$-0.127751\pi$
$164$		0			0
$165$	0.444027	+	0.130378i	0.0345675	+	0.0101499i
$166$		0			0
$167$	8.68878	−	2.55125i	0.672358	−	0.197422i	0.0723051	−	0.997383i	$-0.476964\pi$
$167$	8.68878	−	2.55125i	0.672358	−	0.197422i	0.600053	+	0.799961i	$0.295146\pi$
$168$		0			0
$169$	1.28744	−	2.81910i	0.0990339	−	0.216854i
$170$		0			0
$171$	−15.4200	+	9.90985i	−1.17920	+	0.757825i
$172$		0			0
$173$	1.15360	+	8.02349i	0.0877068	+	0.610014i	0.985510	+	0.169617i	$0.0542532\pi$
$173$	1.15360	+	8.02349i	0.0877068	+	0.610014i	−0.897803	+	0.440397i	$0.854838\pi$
$174$		0			0
$175$	1.09914	−	1.26848i	0.0830873	−	0.0958879i
$176$		0			0
$177$	1.18294	+	0.760231i	0.0889154	+	0.0571424i
$178$		0			0
$179$	−11.2629	−	12.9981i	−0.841832	−	0.971526i	0.158042	−	0.987432i	$-0.449482\pi$
$179$	−11.2629	−	12.9981i	−0.841832	−	0.971526i	−0.999873	+	0.0159066i	$0.994937\pi$
$180$		0			0
$181$	5.37156	+	11.7621i	0.399265	+	0.874267i	0.997344	+	0.0728309i	$0.0232033\pi$
$181$	5.37156	+	11.7621i	0.399265	+	0.874267i	−0.598080	+	0.801437i	$0.704069\pi$
$182$		0			0
$183$	−1.40607			−0.103940
$184$		0			0
$185$	−6.59230			−0.484675
$186$		0			0
$187$	1.00949	+	2.21048i	0.0738215	+	0.161646i
$188$		0			0
$189$	−0.384042	−	0.443208i	−0.0279349	−	0.0322386i
$190$		0			0
$191$	−16.8121	−	10.8045i	−1.21648	−	0.781784i	−0.234748	−	0.972056i	$-0.575427\pi$
$191$	−16.8121	−	10.8045i	−1.21648	−	0.781784i	−0.981731	+	0.190272i	$0.939063\pi$
$192$		0			0
$193$	6.95504	−	8.02655i	0.500635	−	0.577763i	−0.448041	−	0.894013i	$-0.647878\pi$
$193$	6.95504	−	8.02655i	0.500635	−	0.577763i	0.948676	+	0.316249i	$0.102424\pi$
$194$		0			0
$195$	−0.212855	−	1.48044i	−0.0152429	−	0.106016i
$196$		0			0
$197$	−6.26488	+	4.02620i	−0.446354	+	0.286855i	−0.744446	−	0.667683i	$-0.767286\pi$
$197$	−6.26488	+	4.02620i	−0.446354	+	0.286855i	0.298092	+	0.954537i	$0.403650\pi$
$198$		0			0
$199$	6.21716	−	13.6137i	0.440723	−	0.965048i	−0.550743	−	0.834675i	$-0.685655\pi$
$199$	6.21716	−	13.6137i	0.440723	−	0.965048i	0.991465	−	0.130373i	$-0.0416174\pi$
$200$		0			0
$201$	0.807012	−	0.236960i	0.0569222	−	0.0167139i
$202$		0			0
$203$	−5.04598	−	1.48163i	−0.354158	−	0.103990i
$204$		0			0
$205$	1.31997	−	9.18057i	0.0921904	−	0.641199i
$206$		0			0
$207$	−13.5477	−	4.56743i	−0.941627	−	0.317458i
$208$		0			0
$209$	−1.08634	+	7.55570i	−0.0751441	+	0.522638i
$210$		0			0
$211$	0.980075	+	0.287776i	0.0674711	+	0.0198113i	0.315294	−	0.948994i	$-0.397897\pi$
$211$	0.980075	+	0.287776i	0.0674711	+	0.0198113i	−0.247823	+	0.968805i	$0.579715\pi$
$212$		0			0
$213$	−1.96665	+	0.577460i	−0.134753	+	0.0395669i
$214$		0			0
$215$	−13.2031	+	28.9108i	−0.900445	+	1.97170i
$216$		0			0
$217$	2.31136	−	1.48542i	0.156905	−	0.100837i
$218$		0			0
$219$	−0.298368	−	2.07520i	−0.0201619	−	0.140229i
$220$		0			0
$221$	5.14323	−	5.93560i	0.345971	−	0.399272i
$222$		0			0
$223$	−16.1581	−	10.3842i	−1.08202	−	0.695375i	−0.127001	−	0.991903i	$-0.540535\pi$
$223$	−16.1581	−	10.3842i	−1.08202	−	0.695375i	−0.955024	+	0.296527i	$0.904171\pi$
$224$		0			0
$225$	4.59386	+	5.30159i	0.306257	+	0.353440i
$226$		0			0
$227$	−1.13417	−	2.48348i	−0.0752774	−	0.164835i	0.868252	−	0.496124i	$-0.165244\pi$
$227$	−1.13417	−	2.48348i	−0.0752774	−	0.164835i	−0.943529	+	0.331289i	$0.892516\pi$
$228$		0			0
$229$	−9.38133			−0.619936			−0.309968	−	0.950747i	$-0.600318\pi$
$229$	−9.38133			−0.619936			−0.309968	+	0.950747i	$0.600318\pi$
$230$		0			0
$231$	−0.121726			−0.00800900
$232$		0			0
$233$	6.71370	+	14.7010i	0.439829	+	0.963092i	0.991630	+	0.129116i	$0.0412138\pi$
$233$	6.71370	+	14.7010i	0.439829	+	0.963092i	−0.551800	+	0.833976i	$0.686059\pi$
$234$		0			0
$235$	9.65290	+	11.1400i	0.629685	+	0.726696i
$236$		0			0
$237$	1.18628	+	0.762374i	0.0770570	+	0.0495215i
$238$		0			0
$239$	−1.94170	+	2.24084i	−0.125598	+	0.144948i	−0.815066	−	0.579369i	$-0.803299\pi$
$239$	−1.94170	+	2.24084i	−0.125598	+	0.144948i	0.689468	+	0.724317i	$0.257845\pi$
$240$		0			0
$241$	−1.21176	−	8.42795i	−0.0780561	−	0.542892i	−0.990902	−	0.134587i	$-0.957029\pi$
$241$	−1.21176	−	8.42795i	−0.0780561	−	0.542892i	0.912846	−	0.408305i	$-0.133880\pi$
$242$		0			0
$243$	3.09619	−	1.98980i	0.198621	−	0.127646i
$244$		0			0
$245$	7.31219	−	16.0115i	0.467159	−	1.02293i
$246$		0			0
$247$	23.6714	−	6.95056i	1.50618	−	0.442254i
$248$		0			0
$249$	−1.54144	−	0.452608i	−0.0976849	−	0.0286829i
$250$		0			0
$251$	−0.634071	+	4.41006i	−0.0400222	+	0.278360i	−0.999999	−	0.00172069i	$-0.999452\pi$
$251$	−0.634071	+	4.41006i	−0.0400222	+	0.278360i	0.959976	+	0.280081i	$0.0903614\pi$
$252$		0			0
$253$	−5.13215	+	3.01824i	−0.322655	+	0.189755i
$254$		0			0
$255$	0.103840	−	0.722227i	0.00650274	−	0.0452276i
$256$		0			0
$257$	16.3726	+	4.80743i	1.02129	+	0.299879i	0.749167	−	0.662382i	$-0.230454\pi$
$257$	16.3726	+	4.80743i	1.02129	+	0.299879i	0.272128	+	0.962261i	$0.412272\pi$
$258$		0			0
$259$	1.66378	−	0.488529i	0.103382	−	0.0303557i
$260$		0			0
$261$	9.13081	−	19.9937i	0.565183	−	1.23758i
$262$		0			0
$263$	8.67540	−	5.57534i	0.534948	−	0.343790i	−0.245112	−	0.969495i	$-0.578825\pi$
$263$	8.67540	−	5.57534i	0.534948	−	0.343790i	0.780060	+	0.625704i	$0.215188\pi$
$264$		0			0
$265$	3.03235	+	21.0905i	0.186276	+	1.29558i
$266$		0			0
$267$	0.187334	−	0.216195i	0.0114646	−	0.0132309i
$268$		0			0
$269$	16.4892	+	10.5970i	1.00537	+	0.646110i	0.936190	−	0.351495i	$-0.114327\pi$
$269$	16.4892	+	10.5970i	1.00537	+	0.646110i	0.0691764	+	0.997604i	$0.477963\pi$
$270$		0			0
$271$	6.73812	+	7.77620i	0.409312	+	0.472371i	0.922551	−	0.385875i	$-0.126100\pi$
$271$	6.73812	+	7.77620i	0.409312	+	0.472371i	−0.513240	+	0.858245i	$0.671555\pi$
$272$		0			0
$273$	0.163430	+	0.357862i	0.00989123	+	0.0216588i
$274$		0			0
$275$	2.92138			0.176166
$276$		0			0
$277$	−13.3823			−0.804063			−0.402031	−	0.915626i	$-0.631696\pi$
$277$	−13.3823			−0.804063			−0.402031	+	0.915626i	$0.631696\pi$
$278$		0			0
$279$	4.77031	+	10.4455i	0.285591	+	0.625357i
$280$		0			0
$281$	−5.13508	−	5.92620i	−0.306333	−	0.353527i	0.581621	−	0.813460i	$-0.302419\pi$
$281$	−5.13508	−	5.92620i	−0.306333	−	0.353527i	−0.887954	+	0.459933i	$0.847873\pi$
$282$		0			0
$283$	−5.18764	−	3.33389i	−0.308373	−	0.198179i	0.377296	−	0.926093i	$-0.376854\pi$
$283$	−5.18764	−	3.33389i	−0.308373	−	0.198179i	−0.685669	+	0.727913i	$0.740490\pi$
$284$		0			0
$285$	1.50094	−	1.73217i	0.0889077	−	0.102605i
$286$		0			0
$287$	0.347199	+	2.41483i	0.0204945	+	0.142543i
$288$		0			0
$289$	−11.0780	+	7.11942i	−0.651649	+	0.418790i
$290$		0			0
$291$	0.0512356	−	0.112190i	0.00300349	−	0.00657672i
$292$		0			0
$293$	−15.2282	+	4.47141i	−0.889643	+	0.261223i	−0.694449	−	0.719542i	$-0.744352\pi$
$293$	−15.2282	+	4.47141i	−0.889643	+	0.261223i	−0.195194	+	0.980765i	$0.562534\pi$
$294$		0			0
$295$	26.6146	+	7.81477i	1.54956	+	0.454993i
$296$		0			0
$297$	0.145265	−	1.01034i	0.00842916	−	0.0586261i
$298$		0			0
$299$	15.7637	+	11.0356i	0.911640	+	0.638208i
$300$		0			0
$301$	1.18976	−	8.27499i	0.0685768	−	0.476962i
$302$		0			0
$303$	0.895058	+	0.262813i	0.0514198	+	0.0150982i
$304$		0			0
$305$	−26.6129	+	7.81425i	−1.52385	+	0.447443i
$306$		0			0
$307$	3.70533	−	8.11355i	0.211474	−	0.463065i	−0.773935	−	0.633265i	$-0.781714\pi$
$307$	3.70533	−	8.11355i	0.211474	−	0.463065i	0.985409	+	0.170201i	$0.0544416\pi$
$308$		0			0
$309$	−1.69558	+	1.08968i	−0.0964583	+	0.0619900i
$310$		0			0
$311$	−0.892165	−	6.20514i	−0.0505900	−	0.351861i	−0.999356	−	0.0358818i	$-0.988576\pi$
$311$	−0.892165	−	6.20514i	−0.0505900	−	0.351861i	0.948766	−	0.315979i	$-0.102333\pi$
$312$		0			0
$313$	15.4592	−	17.8408i	0.873804	−	1.00842i	−0.126061	−	0.992022i	$-0.540234\pi$
$313$	15.4592	−	17.8408i	0.873804	−	1.00842i	0.999865	−	0.0164014i	$-0.00522095\pi$
$314$		0			0
$315$	−4.85059	−	3.11728i	−0.273300	−	0.175639i
$316$		0			0
$317$	−5.96538	−	6.88441i	−0.335049	−	0.386667i	0.563078	−	0.826404i	$-0.309617\pi$
$317$	−5.96538	−	6.88441i	−0.335049	−	0.386667i	−0.898127	+	0.439737i	$0.855072\pi$
$318$		0			0
$319$	−3.80250	−	8.32630i	−0.212899	−	0.466184i
$320$		0			0
$321$	−1.98365			−0.110716
$322$		0			0
$323$	12.0356			0.669676
$324$		0			0
$325$	−3.92225	−	8.58853i	−0.217567	−	0.476406i
$326$		0			0
$327$	−0.203758	−	0.235149i	−0.0112678	−	0.0130038i
$328$		0			0
$329$	−3.26176	−	2.09620i	−0.179827	−	0.115568i
$330$		0			0
$331$	−18.5115	+	21.3634i	−1.01748	+	1.17424i	−0.0328758	+	0.999459i	$0.510467\pi$
$331$	−18.5115	+	21.3634i	−1.01748	+	1.17424i	−0.984608	+	0.174779i	$0.944079\pi$
$332$		0			0
$333$	1.03140	+	7.17354i	0.0565203	+	0.393108i
$334$		0			0
$335$	13.9575	−	8.96993i	0.762579	−	0.490080i
$336$		0			0
$337$	−5.53555	+	12.1212i	−0.301540	+	0.660282i	−0.998377	−	0.0569483i	$-0.981863\pi$
$337$	−5.53555	+	12.1212i	−0.301540	+	0.660282i	0.696837	+	0.717230i	$0.254590\pi$
$338$		0			0
$339$	−0.457718	+	0.134398i	−0.0248599	+	0.00729951i
$340$		0			0
$341$	4.58844	+	1.34729i	0.248478	+	0.0729597i
$342$		0			0
$343$	−1.36948	+	9.52494i	−0.0739449	+	0.514298i
$344$		0			0
$345$	1.78630	+	0.0707232i	0.0961714	+	0.00380761i
$346$		0			0
$347$	5.27014	−	36.6546i	0.282916	−	1.96772i	0.0330044	−	0.999455i	$-0.489492\pi$
$347$	5.27014	−	36.6546i	0.282916	−	1.96772i	0.249912	−	0.968269i	$-0.419598\pi$
$348$		0			0
$349$	−17.4012	−	5.10944i	−0.931463	−	0.273502i	−0.219414	−	0.975632i	$-0.570414\pi$
$349$	−17.4012	−	5.10944i	−0.931463	−	0.273502i	−0.712049	+	0.702130i	$0.752233\pi$
$350$		0			0
$351$	−3.16533	+	0.929426i	−0.168953	+	0.0496091i
$352$		0			0
$353$	8.27976	−	18.1301i	0.440687	−	0.964970i	−0.550785	−	0.834647i	$-0.685671\pi$
$353$	8.27976	−	18.1301i	0.440687	−	0.964970i	0.991472	−	0.130323i	$-0.0416013\pi$
$354$		0			0
$355$	−34.0137	+	21.8593i	−1.80526	+	1.16017i
$356$		0			0
$357$	0.0273139	+	0.189972i	0.00144560	+	0.0100544i
$358$		0			0
$359$	−21.1116	+	24.3641i	−1.11423	+	1.28589i	−0.159899	+	0.987133i	$0.551117\pi$
$359$	−21.1116	+	24.3641i	−1.11423	+	1.28589i	−0.954330	+	0.298755i	$0.903429\pi$
$360$		0			0
$361$	15.8207	+	10.1674i	0.832671	+	0.535125i
$362$		0			0
$363$	0.851486	+	0.982667i	0.0446914	+	0.0515766i
$364$		0			0
$365$	−17.1801	−	37.6193i	−0.899250	−	1.96908i
$366$		0			0
$367$	−23.7295			−1.23867			−0.619335	−	0.785127i	$-0.712598\pi$
$367$	−23.7295			−1.23867			−0.619335	+	0.785127i	$0.712598\pi$
$368$		0			0
$369$	−10.1965			−0.530810
$370$		0			0
$371$	−2.32824	−	5.09814i	−0.120876	−	0.264682i
$372$		0			0
$373$	−18.3043	−	21.1243i	−0.947760	−	1.09377i	−0.995486	−	0.0949129i	$-0.969743\pi$
$373$	−18.3043	−	21.1243i	−0.947760	−	1.09377i	0.0477255	−	0.998860i	$-0.484803\pi$
$374$		0			0
$375$	0.830016	+	0.533419i	0.0428618	+	0.0275456i
$376$		0			0
$377$	−19.3732	+	22.3578i	−0.997770	+	1.15149i
$378$		0			0
$379$	2.38775	+	16.6072i	0.122651	+	0.853053i	0.954534	+	0.298103i	$0.0963538\pi$
$379$	2.38775	+	16.6072i	0.122651	+	0.853053i	−0.831883	+	0.554951i	$0.812737\pi$
$380$		0			0
$381$	1.01667	−	0.653374i	0.0520856	−	0.0334734i
$382$		0			0
$383$	8.14929	−	17.8445i	0.416409	−	0.911809i	−0.578930	−	0.815377i	$-0.696530\pi$
$383$	8.14929	−	17.8445i	0.416409	−	0.911809i	0.995340	−	0.0964322i	$-0.0307431\pi$
$384$		0			0
$385$	−2.30393	+	0.676494i	−0.117419	+	0.0344773i
$386$		0			0
$387$	33.5256	+	9.84399i	1.70420	+	0.500398i
$388$		0			0
$389$	−1.73743	+	12.0841i	−0.0880911	+	0.612687i	0.897177	+	0.441671i	$0.145614\pi$
$389$	−1.73743	+	12.0841i	−0.0880911	+	0.612687i	−0.985268	+	0.171016i	$0.945295\pi$
$390$		0			0
$391$	5.86201	+	7.33223i	0.296455	+	0.370807i
$392$		0			0
$393$	−0.0875752	+	0.609099i	−0.00441758	+	0.0307250i
$394$		0			0
$395$	26.6897	+	7.83680i	1.34290	+	0.394312i
$396$		0			0
$397$	−24.3859	+	7.16035i	−1.22389	+	0.359367i	−0.828942	−	0.559335i	$-0.811057\pi$
$397$	−24.3859	+	7.16035i	−1.22389	+	0.359367i	−0.394951	+	0.918702i	$0.629238\pi$
$398$		0			0
$399$	−0.250444	+	0.548397i	−0.0125379	+	0.0274542i
$400$		0			0
$401$	30.2068	−	19.4127i	1.50845	−	0.969424i	0.514755	−	0.857337i	$-0.327883\pi$
$401$	30.2068	−	19.4127i	1.50845	−	0.969424i	0.993698	−	0.112087i	$-0.0357536\pi$
$402$		0			0
$403$	−2.19958	−	15.2984i	−0.109569	−	0.762067i
$404$		0			0
$405$	15.6805	−	18.0963i	0.779172	−	0.899212i
$406$		0			0
$407$	2.53900	+	1.63172i	0.125854	+	0.0808812i
$408$		0			0
$409$	14.9232	+	17.2223i	0.737905	+	0.851587i	0.993338	−	0.115239i	$-0.0367635\pi$
$409$	14.9232	+	17.2223i	0.737905	+	0.851587i	−0.255433	+	0.966827i	$0.582218\pi$
$410$		0			0
$411$	0.458746	+	1.00451i	0.0226283	+	0.0495490i
$412$		0			0
$413$	−7.29617			−0.359021
$414$		0			0
$415$	−31.6904			−1.55562
$416$		0			0
$417$	0.914858	+	2.00326i	0.0448008	+	0.0981000i
$418$		0			0
$419$	−9.92036	−	11.4487i	−0.484641	−	0.559306i	0.459784	−	0.888031i	$-0.347927\pi$
$419$	−9.92036	−	11.4487i	−0.484641	−	0.559306i	−0.944426	+	0.328725i	$0.893381\pi$
$420$		0			0
$421$	1.52719	+	0.981463i	0.0744305	+	0.0478336i	0.577327	−	0.816513i	$-0.304096\pi$
$421$	1.52719	+	0.981463i	0.0744305	+	0.0478336i	−0.502896	+	0.864347i	$0.667732\pi$
$422$		0			0
$423$	10.6120	−	12.2469i	0.515974	−	0.595465i
$424$		0			0
$425$	−0.655521	−	4.55925i	−0.0317974	−	0.221156i
$426$		0			0
$427$	6.13753	−	3.94435i	0.297016	−	0.190880i
$428$		0			0
$429$	−0.284456	+	0.622871i	−0.0137337	+	0.0300725i
$430$		0			0
$431$	25.4490	−	7.47249i	1.22583	−	0.359937i	0.396157	−	0.918183i	$-0.370343\pi$
$431$	25.4490	−	7.47249i	1.22583	−	0.359937i	0.829676	+	0.558246i	$0.188525\pi$
$432$		0			0
$433$	33.2893	+	9.77462i	1.59978	+	0.469738i	0.955486	−	0.295037i	$-0.0953321\pi$
$433$	33.2893	+	9.77462i	1.59978	+	0.469738i	0.644296	+	0.764776i	$0.277150\pi$
$434$		0			0
$435$	−0.391140	+	2.72044i	−0.0187537	+	0.130435i
$436$		0			0
$437$	3.03860	+	29.3310i	0.145356	+	1.40309i
$438$		0			0
$439$	0.128494	−	0.893693i	0.00613267	−	0.0426536i	−0.986525	−	0.163609i	$-0.947687\pi$
$439$	0.128494	−	0.893693i	0.00613267	−	0.0426536i	0.992658	+	0.120955i	$0.0385957\pi$
$440$		0			0
$441$	−18.5672	−	5.45183i	−0.884154	−	0.259611i
$442$		0			0
$443$	5.19119	−	1.52427i	0.246641	−	0.0724202i	−0.156076	−	0.987745i	$-0.549884\pi$
$443$	5.19119	−	1.52427i	0.246641	−	0.0724202i	0.402716	+	0.915325i	$0.368066\pi$
$444$		0			0
$445$	2.34418	−	5.13305i	0.111125	−	0.243330i
$446$		0			0
$447$	1.52746	−	0.981641i	0.0722466	−	0.0464300i
$448$		0			0
$449$	5.53148	+	38.4723i	0.261047	+	1.81562i	0.525021	+	0.851089i	$0.324058\pi$
$449$	5.53148	+	38.4723i	0.261047	+	1.81562i	−0.263974	+	0.964530i	$0.585033\pi$
$450$		0			0
$451$	−2.78074	+	3.20915i	−0.130940	+	0.151113i
$452$		0			0
$453$	−0.622694	−	0.400181i	−0.0292567	−	0.0188021i
$454$		0			0
$455$	5.08207	+	5.86503i	0.238251	+	0.274957i
$456$		0			0
$457$	−2.97640	−	6.51740i	−0.139230	−	0.304871i	0.827154	−	0.561976i	$-0.189959\pi$
$457$	−2.97640	−	6.51740i	−0.139230	−	0.304871i	−0.966383	+	0.257105i	$0.917231\pi$
$458$		0			0
$459$	−1.60939			−0.0751198
$460$		0			0
$461$	−11.5403			−0.537483			−0.268742	−	0.963212i	$-0.586608\pi$
$461$	−11.5403			−0.537483			−0.268742	+	0.963212i	$0.586608\pi$
$462$		0			0
$463$	11.5147	+	25.2138i	0.535135	+	1.17178i	0.963385	+	0.268122i	$0.0864032\pi$
$463$	11.5147	+	25.2138i	0.535135	+	1.17178i	−0.428249	+	0.903661i	$0.640870\pi$
$464$		0			0
$465$	−0.940303	−	1.08517i	−0.0436055	−	0.0503234i
$466$		0			0
$467$	3.25500	+	2.09186i	0.150623	+	0.0967997i	0.613782	−	0.789476i	$-0.289648\pi$
$467$	3.25500	+	2.09186i	0.150623	+	0.0967997i	−0.463158	+	0.886276i	$0.653284\pi$
$468$		0			0
$469$	−2.85789	+	3.29818i	−0.131965	+	0.152296i
$470$		0			0
$471$	−0.281608	−	1.95863i	−0.0129758	−	0.0902487i
$472$		0			0
$473$	12.2411	−	7.86688i	0.562846	−	0.361719i
$474$		0			0
$475$	6.01056	−	13.1613i	0.275783	−	0.603881i
$476$		0			0
$477$	22.4756	−	6.59943i	1.02909	−	0.302167i
$478$		0			0
$479$	8.80246	+	2.58463i	0.402195	+	0.118095i	0.476573	−	0.879135i	$-0.341879\pi$
$479$	8.80246	+	2.58463i	0.402195	+	0.118095i	−0.0743780	+	0.997230i	$0.523697\pi$
$480$		0			0
$481$	1.38820	−	9.65513i	0.0632964	−	0.440236i
$482$		0			0
$483$	−0.456072	+	0.114527i	−0.0207520	+	0.00521114i
$484$		0			0
$485$	0.346244	−	2.40818i	0.0157221	−	0.109350i
$486$		0			0
$487$	7.73151	+	2.27018i	0.350348	+	0.102872i	0.452172	−	0.891931i	$-0.350649\pi$
$487$	7.73151	+	2.27018i	0.350348	+	0.102872i	−0.101823	+	0.994802i	$0.532468\pi$
$488$		0			0
$489$	1.74351	−	0.511941i	0.0788443	−	0.0231508i
$490$		0			0
$491$	−5.64284	+	12.3561i	−0.254658	+	0.557623i	−0.993178	−	0.116609i	$-0.962798\pi$
$491$	−5.64284	+	12.3561i	−0.254658	+	0.557623i	0.738520	+	0.674231i	$0.235525\pi$
$492$		0			0
$493$	−12.1412	+	7.80268i	−0.546813	+	0.351415i
$494$		0			0
$495$	−1.42824	−	9.93361i	−0.0641945	−	0.446483i
$496$		0			0
$497$	6.96455	−	8.03751i	0.312403	−	0.360532i
$498$		0			0
$499$	−16.6393	−	10.6934i	−0.744877	−	0.478703i	0.112333	−	0.993671i	$-0.464168\pi$
$499$	−16.6393	−	10.6934i	−0.744877	−	0.478703i	−0.857210	+	0.514967i	$0.827804\pi$
$500$		0			0
$501$	0.815193	+	0.940783i	0.0364201	+	0.0420311i
$502$		0			0
$503$	−10.8916	−	23.8492i	−0.485631	−	1.06338i	−0.980877	−	0.194631i	$-0.937649\pi$
$503$	−10.8916	−	23.8492i	−0.485631	−	1.06338i	0.495246	−	0.868753i	$-0.335078\pi$
$504$		0			0
$505$	18.4014			0.818853
$506$		0			0
$507$	0.426029			0.0189206
$508$		0			0
$509$	7.61965	+	16.6847i	0.337735	+	0.739536i	0.999952	−	0.00977557i	$-0.00311171\pi$
$509$	7.61965	+	16.6847i	0.337735	+	0.739536i	−0.662217	+	0.749312i	$0.730384\pi$
$510$		0			0
$511$	7.12377	+	8.22127i	0.315137	+	0.363687i
$512$		0			0
$513$	−4.25289	−	2.73317i	−0.187770	−	0.120672i
$514$		0			0
$515$	−26.0365	+	30.0478i	−1.14731	+	1.32406i
$516$		0			0
$517$	−0.960413	−	6.67982i	−0.0422389	−	0.293778i
$518$		0			0
$519$	−0.937406	+	0.602434i	−0.0411476	+	0.0264439i
$520$		0			0
$521$	14.2390	−	31.1790i	0.623820	−	1.36597i	−0.288888	−	0.957363i	$-0.593286\pi$
$521$	14.2390	−	31.1790i	0.623820	−	1.36597i	0.912708	−	0.408612i	$-0.133987\pi$
$522$		0			0
$523$	−2.14481	+	0.629772i	−0.0937858	+	0.0275380i	−0.328289	−	0.944577i	$-0.606472\pi$
$523$	−2.14481	+	0.629772i	−0.0937858	+	0.0275380i	0.234503	+	0.972115i	$0.424654\pi$
$524$		0			0
$525$	0.221381	+	0.0650035i	0.00966188	+	0.00283698i
$526$		0			0
$527$	1.07306	−	7.46326i	0.0467430	−	0.325105i
$528$		0			0
$529$	−16.3889	+	16.1370i	−0.712560	+	0.701611i
$530$		0			0
$531$	4.33979	−	30.1839i	0.188331	−	1.30987i
$532$		0			0
$533$	13.1680	+	3.86647i	0.570368	+	0.167475i
$534$		0			0
$535$	−37.5447	+	11.0241i	−1.62320	+	0.476614i
$536$		0			0
$537$	0.982155	−	2.15062i	0.0423831	−	0.0928060i
$538$		0			0
$539$	−6.77940	+	4.35686i	−0.292010	+	0.187663i
$540$		0			0
$541$	1.61359	+	11.2228i	0.0693738	+	0.482505i	0.994658	+	0.103230i	$0.0329176\pi$
$541$	1.61359	+	11.2228i	0.0693738	+	0.482505i	−0.925284	+	0.379275i	$0.876173\pi$
$542$		0			0
$543$	−1.16402	+	1.34335i	−0.0499530	+	0.0576488i
$544$		0			0
$545$	−5.16339	−	3.31831i	−0.221175	−	0.142141i
$546$		0			0
$547$	−13.6716	−	15.7779i	−0.584556	−	0.674614i	0.384022	−	0.923324i	$-0.374539\pi$
$547$	−13.6716	−	15.7779i	−0.584556	−	0.674614i	−0.968578	+	0.248710i	$0.919993\pi$
$548$		0			0
$549$	12.6670	+	27.7368i	0.540613	+	1.18378i
$550$		0			0
$551$	−45.3348			−1.93133
$552$		0			0
$553$	−7.31674			−0.311140
$554$		0			0
$555$	−0.376455	−	0.824323i	−0.0159796	−	0.0349905i
$556$		0			0
$557$	11.4091	+	13.1668i	0.483419	+	0.557895i	0.944095	−	0.329673i	$-0.106939\pi$
$557$	11.4091	+	13.1668i	0.483419	+	0.557895i	−0.460677	+	0.887568i	$0.652393\pi$
$558$		0			0
$559$	−39.5627	−	25.4254i	−1.67332	−	1.07538i
$560$		0			0
$561$	−0.218758	+	0.252461i	−0.00923599	+	0.0106589i
$562$		0			0
$563$	−2.73027	−	18.9894i	−0.115067	−	0.800309i	−0.962864	−	0.269987i	$-0.912980\pi$
$563$	−2.73027	−	18.9894i	−0.115067	−	0.800309i	0.847797	−	0.530321i	$-0.177929\pi$
$564$		0			0
$565$	−7.91637	+	5.08754i	−0.333044	+	0.214034i
$566$		0			0
$567$	−2.61644	+	5.72920i	−0.109880	+	0.240604i
$568$		0			0
$569$	−11.8188	+	3.47030i	−0.495469	+	0.145483i	−0.519914	−	0.854218i	$-0.674036\pi$
$569$	−11.8188	+	3.47030i	−0.495469	+	0.145483i	0.0244456	+	0.999701i	$0.492218\pi$
$570$		0			0
$571$	7.78356	+	2.28546i	0.325732	+	0.0956435i	0.440510	−	0.897748i	$-0.354798\pi$
$571$	7.78356	+	2.28546i	0.325732	+	0.0956435i	−0.114778	+	0.993391i	$0.536616\pi$
$572$		0			0
$573$	0.390966	−	2.71923i	0.0163329	−	0.113598i
$574$		0			0
$575$	10.9455	−	2.74859i	0.456460	−	0.114624i
$576$		0			0
$577$	2.10655	−	14.6514i	0.0876969	−	0.609945i	−0.897819	−	0.440364i	$-0.854849\pi$
$577$	2.10655	−	14.6514i	0.0876969	−	0.609945i	0.985516	−	0.169581i	$-0.0542415\pi$
$578$		0			0
$579$	1.40084	+	0.411323i	0.0582168	+	0.0170940i
$580$		0			0
$581$	7.99808	−	2.34845i	0.331816	−	0.0974300i
$582$		0			0
$583$	4.05239	−	8.87349i	0.167833	−	0.367502i
$584$		0			0
$585$	−27.2862	+	17.5358i	−1.12814	+	0.725014i
$586$		0			0
$587$	1.85745	+	12.9188i	0.0766650	+	0.533217i	0.991572	+	0.129553i	$0.0413543\pi$
$587$	1.85745	+	12.9188i	0.0766650	+	0.533217i	−0.914907	+	0.403664i	$0.867737\pi$
$588$		0			0
$589$	15.5102	−	17.8997i	0.639086	−	0.737545i
$590$		0			0
$591$	−0.861207	−	0.553464i	−0.0354253	−	0.0227665i
$592$		0			0
$593$	−23.5178	−	27.1410i	−0.965761	−	1.11455i	−0.993374	−	0.114929i	$-0.963336\pi$
$593$	−23.5178	−	27.1410i	−0.965761	−	1.11455i	0.0276122	−	0.999619i	$-0.491210\pi$
$594$		0			0
$595$	1.57274	+	3.44382i	0.0644761	+	0.141183i
$596$		0			0
$597$	2.05733			0.0842010
$598$		0			0
$599$	11.6332			0.475320			0.237660	−	0.971348i	$-0.423620\pi$
$599$	11.6332			0.475320			0.237660	+	0.971348i	$0.423620\pi$
$600$		0			0
$601$	10.7870	+	23.6203i	0.440012	+	0.963492i	0.991596	+	0.129373i	$0.0412964\pi$
$601$	10.7870	+	23.6203i	0.440012	+	0.963492i	−0.551584	+	0.834119i	$0.685976\pi$
$602$		0			0
$603$	−11.9445	−	13.7847i	−0.486419	−	0.561358i
$604$		0			0
$605$	21.5773	+	13.8669i	0.877243	+	0.563770i
$606$		0			0
$607$	21.7470	−	25.0974i	0.882685	−	1.01867i	−0.116989	−	0.993133i	$-0.537324\pi$
$607$	21.7470	−	25.0974i	0.882685	−	1.01867i	0.999674	−	0.0255396i	$-0.00813038\pi$
$608$		0			0
$609$	−0.102884	−	0.715575i	−0.00416908	−	0.0289966i
$610$		0			0
$611$	−18.3485	+	11.7919i	−0.742300	+	0.477047i
$612$		0			0
$613$	6.00907	−	13.1580i	0.242704	−	0.531448i	−0.748603	−	0.663019i	$-0.769275\pi$
$613$	6.00907	−	13.1580i	0.242704	−	0.531448i	0.991307	+	0.131571i	$0.0420022\pi$
$614$		0			0
$615$	1.22335	−	0.359207i	0.0493300	−	0.0144846i
$616$		0			0
$617$	−32.7699	−	9.62212i	−1.31927	−	0.387372i	−0.455039	−	0.890472i	$-0.650375\pi$
$617$	−32.7699	−	9.62212i	−1.31927	−	0.387372i	−0.864228	+	0.503100i	$0.832193\pi$
$618$		0			0
$619$	−4.68738	+	32.6015i	−0.188402	+	1.31036i	0.647745	+	0.761858i	$0.275712\pi$
$619$	−4.68738	+	32.6015i	−0.188402	+	1.31036i	−0.836146	+	0.548506i	$0.815197\pi$
$620$		0			0
$621$	−0.406319	−	3.92213i	−0.0163050	−	0.157390i
$622$		0			0
$623$	−0.211240	+	1.46921i	−0.00846315	+	0.0588625i
$624$		0			0
$625$	29.9635	+	8.79807i	1.19854	+	0.351923i
$626$		0			0
$627$	−1.00683	+	0.295631i	−0.0402087	+	0.0118063i
$628$		0			0
$629$	1.97682	−	4.32863i	0.0788209	−	0.172594i
$630$		0			0
$631$	−4.82905	+	3.10344i	−0.192241	+	0.123546i	−0.633221	−	0.773971i	$-0.718268\pi$
$631$	−4.82905	+	3.10344i	−0.192241	+	0.123546i	0.440979	+	0.897517i	$0.354631\pi$
$632$		0			0
$633$	0.0199831	+	0.138985i	0.000794256	+	0.00552417i
$634$		0			0
$635$	15.6115	−	18.0166i	0.619523	−	0.714968i
$636$		0			0
$637$	21.9107	+	14.0812i	0.868135	+	0.557916i
$638$		0			0
$639$	29.1083	+	33.5927i	1.15151	+	1.32891i
$640$		0			0
$641$	−7.54650	−	16.5245i	−0.298069	−	0.652680i	0.700043	−	0.714101i	$-0.253164\pi$
$641$	−7.54650	−	16.5245i	−0.298069	−	0.652680i	−0.998112	+	0.0614209i	$0.980437\pi$
$642$		0			0
$643$	19.9591			0.787109			0.393554	−	0.919301i	$-0.371245\pi$
$643$	19.9591			0.787109			0.393554	+	0.919301i	$0.371245\pi$
$644$		0			0
$645$	−4.36907			−0.172032
$646$		0			0
$647$	0.148701	+	0.325611i	0.00584606	+	0.0128011i	0.912533	−	0.409004i	$-0.134124\pi$
$647$	0.148701	+	0.325611i	0.00584606	+	0.0128011i	−0.906686	+	0.421805i	$0.861397\pi$
$648$		0			0
$649$	−8.31624	−	9.59746i	−0.326441	−	0.376733i
$650$		0			0
$651$	0.317733	+	0.204194i	0.0124529	+	0.00800301i
$652$		0			0
$653$	−8.07152	+	9.31503i	−0.315863	+	0.364525i	−0.891374	−	0.453269i	$-0.850258\pi$
$653$	−8.07152	+	9.31503i	−0.315863	+	0.364525i	0.575511	+	0.817794i	$0.304803\pi$
$654$		0			0
$655$	1.72752	+	12.0152i	0.0674999	+	0.469472i
$656$		0			0
$657$	−38.2482	+	24.5807i	−1.49221	+	0.958983i
$658$		0			0
$659$	7.75878	−	16.9894i	0.302239	−	0.661812i	−0.696189	−	0.717859i	$-0.745122\pi$
$659$	7.75878	−	16.9894i	0.302239	−	0.661812i	0.998428	+	0.0560469i	$0.0178496\pi$
$660$		0			0
$661$	−9.84343	+	2.89029i	−0.382865	+	0.112419i	−0.467501	−	0.883993i	$-0.654846\pi$
$661$	−9.84343	+	2.89029i	−0.382865	+	0.112419i	0.0846357	+	0.996412i	$0.473027\pi$
$662$		0			0
$663$	1.03591	+	0.304171i	0.0402315	+	0.0118130i
$664$		0			0
$665$	−1.69247	+	11.7714i	−0.0656313	+	0.456476i
$666$		0			0
$667$	−22.0806	−	27.6186i	−0.854966	−	1.06940i
$668$		0			0
$669$	0.375757	−	2.61345i	0.0145276	−	0.101042i
$670$		0			0
$671$	12.1840	+	3.57756i	0.470360	+	0.138110i
$672$		0			0
$673$	24.8402	−	7.29373i	0.957518	−	0.281153i	0.234604	−	0.972091i	$-0.424621\pi$
$673$	24.8402	−	7.29373i	0.957518	−	0.281153i	0.722914	+	0.690938i	$0.242802\pi$
$674$		0			0
$675$	−0.803729	+	1.75992i	−0.0309355	+	0.0677394i
$676$		0			0
$677$	28.6277	−	18.3979i	1.10025	−	0.707090i	0.141105	−	0.989995i	$-0.454934\pi$
$677$	28.6277	−	18.3979i	1.10025	−	0.707090i	0.959148	+	0.282905i	$0.0912980\pi$
$678$		0			0
$679$	0.0910749	+	0.633440i	0.00349513	+	0.0243092i
$680$		0			0
$681$	0.245776	−	0.283640i	0.00941815	−	0.0108691i
$682$		0			0
$683$	33.2342	+	21.3583i	1.27167	+	0.817253i	0.989837	−	0.142210i	$-0.0454208\pi$
$683$	33.2342	+	21.3583i	1.27167	+	0.817253i	0.281834	+	0.959463i	$0.409057\pi$
$684$		0			0
$685$	14.2653	+	16.4631i	0.545050	+	0.629021i
$686$		0			0
$687$	−0.535724	−	1.17307i	−0.0204392	−	0.0447555i
$688$		0			0
$689$	−31.5278			−1.20111
$690$		0			0
$691$	25.0115			0.951484			0.475742	−	0.879585i	$-0.342180\pi$
$691$	25.0115			0.951484			0.475742	+	0.879585i	$0.342180\pi$
$692$		0			0
$693$	1.09660	+	2.40122i	0.0416564	+	0.0912149i
$694$		0			0
$695$	28.4487	+	32.8316i	1.07912	+	1.24537i
$696$		0			0
$697$	5.63232	+	3.61967i	0.213339	+	0.137105i
$698$		0			0
$699$	−1.45487	+	1.67901i	−0.0550282	+	0.0635059i
$700$		0			0
$701$	−0.954302	−	6.63732i	−0.0360435	−	0.250688i	0.963831	−	0.266513i	$-0.0858716\pi$
$701$	−0.954302	−	6.63732i	−0.0360435	−	0.250688i	−0.999875	+	0.0158251i	$0.994963\pi$
$702$		0			0
$703$	12.5750	−	8.08146i	0.474275	−	0.304798i
$704$		0			0
$705$	−0.841755	+	1.84319i	−0.0317023	+	0.0694184i
$706$		0			0
$707$	−4.64419	+	1.36366i	−0.174663	+	0.0512856i
$708$		0			0
$709$	24.3748	+	7.15710i	0.915416	+	0.268791i	0.705319	−	0.708890i	$-0.250804\pi$
$709$	24.3748	+	7.15710i	0.915416	+	0.268791i	0.210097	+	0.977680i	$0.432622\pi$
$710$		0			0
$711$	4.35203	−	30.2690i	0.163214	−	1.13518i
$712$		0			0
$713$	18.4591	+	0.730832i	0.691299	+	0.0273699i
$714$		0			0
$715$	−1.92232	+	13.3700i	−0.0718906	+	0.500010i
$716$		0			0
$717$	−0.391083	−	0.114832i	−0.0146053	−	0.00428849i
$718$		0			0
$719$	1.84954	−	0.543073i	0.0689761	−	0.0202532i	−0.247062	−	0.969000i	$-0.579465\pi$
$719$	1.84954	−	0.543073i	0.0689761	−	0.0202532i	0.316039	+	0.948746i	$0.397647\pi$
$720$		0			0
$721$	4.34443	−	9.51297i	0.161795	−	0.354282i
$722$		0			0
$723$	0.984660	−	0.632803i	0.0366199	−	0.0235342i
$724$		0			0
$725$	2.46918	+	17.1735i	0.0917029	+	0.637807i
$726$		0			0
$727$	5.46833	−	6.31079i	0.202809	−	0.234054i	−0.645229	−	0.763989i	$-0.723238\pi$
$727$	5.46833	−	6.31079i	0.202809	−	0.234054i	0.848038	+	0.529935i	$0.177784\pi$
$728$		0			0
$729$	−21.8599	−	14.0485i	−0.809626	−	0.520315i
$730$		0			0
$731$	−15.0242	−	17.3388i	−0.555690	−	0.641300i
$732$		0			0
$733$	−6.34050	−	13.8838i	−0.234192	−	0.512808i	0.755651	−	0.654974i	$-0.227321\pi$
$733$	−6.34050	−	13.8838i	−0.234192	−	0.512808i	−0.989843	+	0.142166i	$0.954593\pi$
$734$		0			0
$735$	2.41969			0.0892516
$736$		0			0
$737$	−7.59591			−0.279799
$738$		0			0
$739$	−0.561238	−	1.22894i	−0.0206455	−	0.0452073i	0.899028	−	0.437890i	$-0.144274\pi$
$739$	−0.561238	−	1.22894i	−0.0206455	−	0.0452073i	−0.919674	+	0.392683i	$0.871547\pi$
$740$		0			0
$741$	2.22089	+	2.56304i	0.0815863	+	0.0941557i
$742$		0			0
$743$	−32.0633	−	20.6059i	−1.17629	−	0.755955i	−0.201589	−	0.979470i	$-0.564611\pi$
$743$	−32.0633	−	20.6059i	−1.17629	−	0.755955i	−0.974701	+	0.223515i	$0.928247\pi$
$744$		0			0
$745$	23.4550	−	27.0685i	0.859325	−	0.991713i
$746$		0			0
$747$	4.95813	+	34.4845i	0.181408	+	1.26172i
$748$		0			0
$749$	8.65865	−	5.56458i	0.316380	−	0.203325i
$750$		0			0
$751$	−10.3685	+	22.7038i	−0.378351	+	0.828473i	0.620663	+	0.784077i	$0.286863\pi$
$751$	−10.3685	+	22.7038i	−0.378351	+	0.828473i	−0.999014	+	0.0443955i	$0.985864\pi$
$752$		0			0
$753$	−0.587657	+	0.172552i	−0.0214154	+	0.00628813i
$754$		0			0
$755$	−14.0098	−	4.11365i	−0.509869	−	0.149711i
$756$		0			0
$757$	2.90397	−	20.1975i	0.105546	−	0.734092i	−0.866479	−	0.499214i	$-0.833622\pi$
$757$	2.90397	−	20.1975i	0.105546	−	0.734092i	0.972025	−	0.234877i	$-0.0754689\pi$
$758$		0			0
$759$	−0.670484	−	0.469383i	−0.0243370	−	0.0170375i
$760$		0			0
$761$	0.482325	−	3.35464i	0.0174843	−	0.121606i	−0.979210	−	0.202849i	$-0.934980\pi$
$761$	0.482325	−	3.35464i	0.0174843	−	0.121606i	0.996694	+	0.0812432i	$0.0258891\pi$
$762$		0			0
$763$	1.54905	+	0.454843i	0.0560795	+	0.0164664i
$764$		0			0
$765$	−15.1824	+	4.45796i	−0.548921	+	0.161178i
$766$		0			0
$767$	−17.0501	+	37.3344i	−0.615642	+	1.34807i
$768$		0			0
$769$	−21.6284	+	13.8997i	−0.779941	+	0.501238i	−0.869014	−	0.494787i	$-0.835246\pi$
$769$	−21.6284	+	13.8997i	−0.779941	+	0.501238i	0.0890730	+	0.996025i	$0.471610\pi$
$770$		0			0
$771$	0.333827	+	2.32181i	0.0120225	+	0.0836181i
$772$		0			0
$773$	−34.6287	+	39.9637i	−1.24551	+	1.43739i	−0.389019	+	0.921230i	$0.627186\pi$
$773$	−34.6287	+	39.9637i	−1.24551	+	1.43739i	−0.856490	+	0.516164i	$0.827359\pi$
$774$		0			0
$775$	−7.62545	−	4.90058i	−0.273914	−	0.176034i
$776$		0			0
$777$	0.156098	+	0.180146i	0.00559998	+	0.00646272i
$778$		0			0
$779$	8.73653	+	19.1303i	0.313019	+	0.685415i
$780$		0			0
$781$	18.5109			0.662371
$782$		0			0
$783$	6.06214			0.216643
$784$		0			0
$785$	−16.2151	−	35.5061i	−0.578741	−	1.26727i
$786$		0			0
$787$	−13.3319	−	15.3858i	−0.475229	−	0.548444i	0.466630	−	0.884453i	$-0.345468\pi$
$787$	−13.3319	−	15.3858i	−0.475229	−	0.548444i	−0.941859	+	0.336009i	$0.890923\pi$
$788$		0			0
$789$	1.19257	+	0.766419i	0.0424566	+	0.0272852i
$790$		0			0
$791$	1.62093	−	1.87065i	0.0576336	−	0.0665128i
$792$		0			0
$793$	−5.84070	−	40.6230i	−0.207409	−	1.44256i
$794$		0			0
$795$	−2.46406	+	1.58355i	−0.0873911	+	0.0561629i
$796$		0			0
$797$	−19.2105	+	42.0651i	−0.680470	+	1.49002i	0.181675	+	0.983359i	$0.441848\pi$
$797$	−19.2105	+	42.0651i	−0.680470	+	1.49002i	−0.862145	+	0.506662i	$0.830879\pi$
$798$		0			0
$799$	−10.2094	+	2.99774i	−0.361181	+	0.106052i
$800$		0			0
$801$	−5.95239	−	1.74778i	−0.210317	−	0.0617548i
$802$		0			0
$803$	−2.69460	+	18.7413i	−0.0950903	+	0.661368i
$804$		0			0
$805$	−7.99564	+	4.70228i	−0.281809	+	0.165733i
$806$		0			0
$807$	−0.383459	+	2.66701i	−0.0134984	+	0.0938833i
$808$		0			0
$809$	−43.6200	−	12.8080i	−1.53360	−	0.450305i	−0.597449	−	0.801907i	$-0.703819\pi$
$809$	−43.6200	−	12.8080i	−1.53360	−	0.450305i	−0.936150	+	0.351601i	$0.885637\pi$
$810$		0			0
$811$	12.4621	−	3.65921i	0.437605	−	0.128492i	−0.0555071	−	0.998458i	$-0.517678\pi$
$811$	12.4621	−	3.65921i	0.437605	−	0.128492i	0.493112	+	0.869966i	$0.335859\pi$
$812$		0			0
$813$	−0.587579	+	1.28662i	−0.0206073	+	0.0451237i
$814$		0			0
$815$	30.1545	−	19.3791i	1.05627	−	0.678821i
$816$		0			0
$817$	−10.2562	−	71.3338i	−0.358821	−	2.49565i
$818$		0			0
$819$	5.58703	−	6.44778i	0.195227	−	0.225304i
$820$		0			0
$821$	−30.9119	−	19.8659i	−1.07883	−	0.693325i	−0.124547	−	0.992214i	$-0.539748\pi$
$821$	−30.9119	−	19.8659i	−1.07883	−	0.693325i	−0.954288	+	0.298889i	$0.903384\pi$
$822$		0			0
$823$	−0.585875	−	0.676135i	−0.0204223	−	0.0235686i	0.745447	−	0.666565i	$-0.232236\pi$
$823$	−0.585875	−	0.676135i	−0.0204223	−	0.0235686i	−0.765869	+	0.642997i	$0.777691\pi$
$824$		0			0
$825$	0.166826	+	0.365299i	0.00580815	+	0.0127181i
$826$		0			0
$827$	4.91804			0.171017			0.0855085	−	0.996337i	$-0.472749\pi$
$827$	4.91804			0.171017			0.0855085	+	0.996337i	$0.472749\pi$
$828$		0			0
$829$	8.16941			0.283735			0.141868	−	0.989886i	$-0.454689\pi$
$829$	8.16941			0.283735			0.141868	+	0.989886i	$0.454689\pi$
$830$		0			0
$831$	−0.764199	−	1.67336i	−0.0265098	−	0.0580483i
$832$		0			0
$833$	8.32074	+	9.60265i	0.288297	+	0.332712i
$834$		0			0
$835$	20.6576	+	13.2759i	0.714887	+	0.459430i
$836$		0			0
$837$	−2.07402	+	2.39354i	−0.0716885	+	0.0827329i
$838$		0			0
$839$	−2.00161	−	13.9215i	−0.0691033	−	0.480624i	−0.994758	−	0.102255i	$-0.967394\pi$
$839$	−2.00161	−	13.9215i	−0.0691033	−	0.480624i	0.925655	−	0.378369i	$-0.123515\pi$
$840$		0			0
$841$	21.3364	−	13.7121i	0.735738	−	0.472830i
$842$		0			0
$843$	0.447791	−	0.980525i	0.0154227	−	0.0337711i
$844$		0			0
$845$	8.06350	−	2.36766i	0.277393	−	0.0814499i
$846$		0			0
$847$	−6.47335	−	1.90075i	−0.222427	−	0.0653104i
$848$		0			0
$849$	0.120639	−	0.839062i	0.00414032	−	0.0287965i
$850$		0			0
$851$	11.0481	+	3.72473i	0.378723	+	0.127682i
$852$		0			0
$853$	−5.86602	+	40.7991i	−0.200849	+	1.39693i	0.600925	+	0.799306i	$0.294799\pi$
$853$	−5.86602	+	40.7991i	−0.200849	+	1.39693i	−0.801773	+	0.597628i	$0.796110\pi$
$854$		0			0
$855$	−47.6911	−	14.0034i	−1.63100	−	0.478905i
$856$		0			0
$857$	−12.5551	+	3.68650i	−0.428873	+	0.125928i	−0.489043	−	0.872260i	$-0.662654\pi$
$857$	−12.5551	+	3.68650i	−0.428873	+	0.125928i	0.0601702	+	0.998188i	$0.480836\pi$
$858$		0			0
$859$	17.5445	−	38.4171i	0.598610	−	1.31077i	−0.331487	−	0.943460i	$-0.607550\pi$
$859$	17.5445	−	38.4171i	0.598610	−	1.31077i	0.930097	−	0.367314i	$-0.119722\pi$
$860$		0			0
$861$	−0.282131	+	0.181314i	−0.00961499	+	0.00617918i
$862$		0			0
$863$	6.04438	+	42.0396i	0.205753	+	1.43104i	0.786817	+	0.617186i	$0.211727\pi$
$863$	6.04438	+	42.0396i	0.205753	+	1.43104i	−0.581064	+	0.813858i	$0.697364\pi$
$864$		0			0
$865$	−14.3944	+	16.6120i	−0.489423	+	0.564824i
$866$		0			0
$867$	−1.52285	−	0.978677i	−0.0517188	−	0.0332376i
$868$		0			0
$869$	−8.33969	−	9.62451i	−0.282904	−	0.326489i
$870$		0			0
$871$	10.1983	+	22.3311i	0.345556	+	0.756662i
$872$		0			0
$873$	−2.67468			−0.0905243
$874$		0			0
$875$	−5.11939			−0.173067
$876$		0			0
$877$	1.46617	+	3.21047i	0.0495092	+	0.108410i	0.932770	−	0.360472i	$-0.117384\pi$
$877$	1.46617	+	3.21047i	0.0495092	+	0.108410i	−0.883261	+	0.468882i	$0.844657\pi$
$878$		0			0
$879$	−1.42873	−	1.64885i	−0.0481900	−	0.0556142i
$880$		0			0
$881$	29.7859	+	19.1423i	1.00351	+	0.644919i	0.935707	−	0.352779i	$-0.114763\pi$
$881$	29.7859	+	19.1423i	1.00351	+	0.644919i	0.0678075	+	0.997698i	$0.478400\pi$
$882$		0			0
$883$	−18.4058	+	21.2414i	−0.619405	+	0.714831i	−0.975594	−	0.219583i	$-0.929530\pi$
$883$	−18.4058	+	21.2414i	−0.619405	+	0.714831i	0.356189	+	0.934414i	$0.384076\pi$
$884$		0			0
$885$	0.542655	+	3.77425i	0.0182411	+	0.126870i
$886$		0			0
$887$	39.1972	−	25.1905i	1.31611	−	0.845815i	0.321246	−	0.946996i	$-0.395898\pi$
$887$	39.1972	−	25.1905i	1.31611	−	0.845815i	0.994868	+	0.101181i	$0.0322621\pi$
$888$		0			0
$889$	−2.60492	+	5.70398i	−0.0873662	+	0.191305i
$890$		0			0
$891$	−10.5185	+	3.08850i	−0.352382	+	0.103469i
$892$		0			0
$893$	−32.0697	−	9.41651i	−1.07317	−	0.315111i
$894$		0			0
$895$	6.63728	−	46.1633i	0.221860	−	1.54307i
$896$		0			0
$897$	−0.479740	+	2.60134i	−0.0160180	+	0.0868563i
$898$		0			0
$899$	−4.04192	+	28.1122i	−0.134806	+	0.937593i
$900$		0			0
$901$	−14.7577	−	4.33326i	−0.491651	−	0.144362i
$902$		0			0
$903$	1.10267	−	0.323774i	0.0366947	−	0.0107745i
$904$		0			0
$905$	−14.5659	+	31.8949i	−0.484187	+	1.06022i
$906$		0			0
$907$	1.48892	−	0.956870i	0.0494387	−	0.0317723i	−0.515688	−	0.856776i	$-0.672464\pi$
$907$	1.48892	−	0.956870i	0.0494387	−	0.0317723i	0.565127	+	0.825004i	$0.308827\pi$
$908$		0			0
$909$	−2.87900	−	20.0239i	−0.0954905	−	0.664151i
$910$		0			0
$911$	−10.2287	+	11.8046i	−0.338892	+	0.391102i	−0.899458	−	0.437008i	$-0.856038\pi$
$911$	−10.2287	+	11.8046i	−0.338892	+	0.391102i	0.560566	+	0.828110i	$0.310584\pi$
$912$		0			0
$913$	12.2054	+	7.84397i	0.403941	+	0.259597i
$914$		0			0
$915$	−2.49686	−	2.88153i	−0.0825436	−	0.0952604i
$916$		0			0
$917$	−1.32639	−	2.90439i	−0.0438013	−	0.0959115i
$918$		0			0
$919$	55.1708			1.81992			0.909959	−	0.414699i	$-0.136113\pi$
$919$	55.1708			1.81992			0.909959	+	0.414699i	$0.136113\pi$
$920$		0			0
$921$	1.22614			0.0404026
$922$		0			0
$923$	−24.8527	−	54.4199i	−0.818038	−	1.79125i
$924$		0			0
$925$	−3.74628	−	4.32344i	−0.123177	−	0.142154i
$926$		0			0
$927$	36.7706	+	23.6311i	1.20771	+	0.776146i
$928$		0			0
$929$	16.2493	−	18.7527i	0.533122	−	0.615256i	−0.423745	−	0.905781i	$-0.639285\pi$
$929$	16.2493	−	18.7527i	0.533122	−	0.615256i	0.956867	+	0.290526i	$0.0938302\pi$
$930$		0			0
$931$	5.68015	+	39.5063i	0.186159	+	1.29477i
$932$		0			0
$933$	0.724964	−	0.465906i	0.0237343	−	0.0152531i
$934$		0			0
$935$	−2.73741	+	5.99410i	−0.0895230	+	0.196028i
$936$		0			0
$937$	24.6634	−	7.24183i	0.805718	−	0.236580i	0.147163	−	0.989112i	$-0.452986\pi$
$937$	24.6634	−	7.24183i	0.805718	−	0.236580i	0.658556	+	0.752532i	$0.271168\pi$
$938$		0			0
$939$	3.11368	+	0.914259i	0.101611	+	0.0298357i
$940$		0			0
$941$	−7.13691	+	49.6383i	−0.232657	+	1.61816i	0.453878	+	0.891064i	$0.350040\pi$
$941$	−7.13691	+	49.6383i	−0.232657	+	1.61816i	−0.686534	+	0.727098i	$0.740869\pi$
$942$		0			0
$943$	−7.39927	+	14.6400i	−0.240953	+	0.476744i
$944$		0			0
$945$	0.226317	−	1.57407i	0.00736208	−	0.0512044i
$946$		0			0
$947$	47.5915	+	13.9741i	1.54652	+	0.454098i	0.940057	−	0.341017i	$-0.110772\pi$
$947$	47.5915	+	13.9741i	1.54652	+	0.454098i	0.606458	+	0.795115i	$0.292590\pi$
$948$		0			0
$949$	58.7153	−	17.2404i	1.90598	−	0.559646i
$950$		0			0
$951$	0.520194	−	1.13907i	0.0168685	−	0.0369368i
$952$		0			0
$953$	30.1840	−	19.3981i	0.977756	−	0.628366i	0.0488989	−	0.998804i	$-0.484429\pi$
$953$	30.1840	−	19.3981i	0.977756	−	0.628366i	0.928857	+	0.370438i	$0.120792\pi$
$954$		0			0
$955$	−7.71226	−	53.6400i	−0.249563	−	1.73575i
$956$		0			0
$957$	0.824006	−	0.950953i	0.0266363	−	0.0307400i
$958$		0			0
$959$	−4.82032	−	3.09783i	−0.155656	−	0.100034i
$960$		0			0
$961$	10.5839	+	12.2145i	0.341416	+	0.394015i
$962$		0			0
$963$	17.8702	+	39.1303i	0.575859	+	1.26095i
$964$		0			0
$965$	28.7997			0.927095
$966$		0			0
$967$	−11.9602			−0.384615			−0.192307	−	0.981335i	$-0.561597\pi$
$967$	−11.9602			−0.384615			−0.192307	+	0.981335i	$0.561597\pi$
$968$		0			0
$969$	0.687295	+	1.50497i	0.0220791	+	0.0483465i
$970$		0			0
$971$	−37.6657	−	43.4686i	−1.20875	−	1.39497i	−0.895357	−	0.445349i	$-0.853079\pi$
$971$	−37.6657	−	43.4686i	−1.20875	−	1.39497i	−0.313394	−	0.949623i	$-0.601466\pi$
$972$		0			0
$973$	−9.61296	−	6.17787i	−0.308177	−	0.198053i
$974$		0			0
$975$	0.849957	−	0.980902i	0.0272204	−	0.0314140i
$976$		0			0
$977$	6.55581	+	45.5966i	0.209739	+	1.45877i	0.774009	+	0.633175i	$0.218249\pi$
$977$	6.55581	+	45.5966i	0.209739	+	1.45877i	−0.564270	+	0.825590i	$0.690842\pi$
$978$		0			0
$979$	−2.17338	+	1.39675i	−0.0694615	+	0.0446402i
$980$		0			0
$981$	−2.80305	+	6.13781i	−0.0894944	+	0.195965i
$982$		0			0
$983$	3.52958	−	1.03638i	0.112576	−	0.0330553i	−0.224959	−	0.974368i	$-0.572225\pi$
$983$	3.52958	−	1.03638i	0.112576	−	0.0330553i	0.337535	+	0.941313i	$0.390407\pi$
$984$		0			0
$985$	−19.3760	−	5.68932i	−0.617372	−	0.181277i
$986$		0			0
$987$	0.0758525	−	0.527566i	0.00241441	−	0.0167926i
$988$		0			0
$989$	38.4621	−	40.9919i	1.22302	−	1.30347i
$990$		0			0
$991$	−7.63042	+	53.0707i	−0.242388	+	1.68585i	0.397676	+	0.917526i	$0.369817\pi$
$991$	−7.63042	+	53.0707i	−0.242388	+	1.68585i	−0.640064	+	0.768322i	$0.721092\pi$
$992$		0			0
$993$	−3.72845	−	1.09477i	−0.118319	−	0.0347416i
$994$		0			0
$995$	38.9393	−	11.4336i	1.23446	−	0.362470i
$996$		0			0
$997$	−6.56755	+	14.3809i	−0.207996	+	0.455448i	−0.984664	−	0.174462i	$-0.944181\pi$
$997$	−6.56755	+	14.3809i	−0.207996	+	0.455448i	0.776668	+	0.629911i	$0.216909\pi$
$998$		0			0
$999$	−1.68152	+	1.08065i	−0.0532010	+	0.0341902i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	92.2.e.a.77.2	yes	20
3.2	odd	2		828.2.q.a.721.1		20
4.3	odd	2		368.2.m.d.353.1		20
23.3	even	11	inner	92.2.e.a.49.2	✓	20
23.7	odd	22		2116.2.a.i.1.6		10
23.16	even	11		2116.2.a.j.1.6		10
69.26	odd	22		828.2.q.a.325.1		20
92.3	odd	22		368.2.m.d.49.1		20
92.7	even	22		8464.2.a.cd.1.5		10
92.39	odd	22		8464.2.a.ce.1.5		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
92.2.e.a.49.2	✓	20	23.3	even	11	inner
92.2.e.a.77.2	yes	20	1.1	even	1	trivial
368.2.m.d.49.1		20	92.3	odd	22
368.2.m.d.353.1		20	4.3	odd	2
828.2.q.a.325.1		20	69.26	odd	22
828.2.q.a.721.1		20	3.2	odd	2
2116.2.a.i.1.6		10	23.7	odd	22
2116.2.a.j.1.6		10	23.16	even	11
8464.2.a.cd.1.5		10	92.7	even	22
8464.2.a.ce.1.5		10	92.39	odd	22

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:	\( N \)	\(=\)	\( 92 = 2^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	92.e (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(0.0571054 + 0.125043i) q^{3} +(1.77577 + 2.04934i) q^{5} +(-0.600040 - 0.385622i) q^{7} +(1.95221 - 2.25297i) q^{9} +O(q^{10})\)	\(q+(0.0571054 + 0.125043i) q^{3} +(1.77577 + 2.04934i) q^{5} +(-0.600040 - 0.385622i) q^{7} +(1.95221 - 2.25297i) q^{9} +(-0.176680 - 1.22883i) q^{11} +(-3.37543 + 2.16925i) q^{13} +(-0.154851 + 0.339076i) q^{15} +(-1.87813 + 0.551470i) q^{17} +(-5.89961 - 1.73228i) q^{19} +(0.0139540 - 0.0970521i) q^{21} +(-1.81812 - 4.43784i) q^{23} +(-0.334890 + 2.32921i) q^{25} +(0.788892 + 0.231640i) q^{27} +(7.07444 - 2.07724i) q^{29} +(-1.60018 + 3.50391i) q^{31} +(0.143568 - 0.0922656i) q^{33} +(-0.275258 - 1.91446i) q^{35} +(-1.59202 + 1.83729i) q^{37} +(-0.464006 - 0.298198i) q^{39} +(-2.23988 - 2.58496i) q^{41} +(4.86900 + 10.6616i) q^{43} +8.08377 q^{45} +5.43590 q^{47} +(-2.69656 - 5.90465i) q^{49} +(-0.176209 - 0.203356i) q^{51} +(6.61027 + 4.24816i) q^{53} +(2.20456 - 2.54420i) q^{55} +(-0.120289 - 0.836629i) q^{57} +(8.60536 - 5.53033i) q^{59} +(-4.24909 + 9.30420i) q^{61} +(-2.04020 + 0.599056i) q^{63} +(-10.4395 - 3.06532i) q^{65} +(0.870750 - 6.05620i) q^{67} +(0.451098 - 0.480768i) q^{69} +(-2.12198 + 14.7587i) q^{71} +(-14.6335 - 4.29679i) q^{73} +(-0.310376 + 0.0911346i) q^{75} +(-0.367851 + 0.805481i) q^{77} +(8.62961 - 5.54592i) q^{79} +(-1.25668 - 8.74041i) q^{81} +(-7.65314 + 8.83219i) q^{83} +(-4.46528 - 2.86966i) q^{85} +(0.663734 + 0.765990i) q^{87} +(-0.864480 - 1.89295i) q^{89} +2.86190 q^{91} -0.529519 q^{93} +(-6.92629 - 15.1665i) q^{95} +(-0.587549 - 0.678068i) q^{97} +(-3.11344 - 2.00089i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 2 q^{3} + 2 q^{5} + 2 q^{7} - 4 q^{9}+O(q^{10}) \) 20 * q + 2 * q^3 + 2 * q^5 + 2 * q^7 - 4 * q^9	\( 20 q + 2 q^{3} + 2 q^{5} + 2 q^{7} - 4 q^{9} - 2 q^{11} + 6 q^{13} - 17 q^{15} - 9 q^{17} - 11 q^{19} - 47 q^{21} - 22 q^{23} - 16 q^{25} - 19 q^{27} - q^{29} - 13 q^{31} - 5 q^{33} + 14 q^{35} + 34 q^{37} + 30 q^{39} + 28 q^{41} + 44 q^{43} + 78 q^{45} + 26 q^{47} + 60 q^{49} + 62 q^{51} + 14 q^{53} + 26 q^{55} + 3 q^{57} - 10 q^{59} - 56 q^{61} - 27 q^{63} - 87 q^{65} - 44 q^{67} - 51 q^{69} - 37 q^{71} - 12 q^{73} - 53 q^{75} - 47 q^{77} - 6 q^{79} - 10 q^{81} - 25 q^{83} + 8 q^{85} + 48 q^{87} + 10 q^{89} + 26 q^{91} - 14 q^{93} + 29 q^{95} - q^{97} - q^{99}+O(q^{100}) \) 20 * q + 2 * q^3 + 2 * q^5 + 2 * q^7 - 4 * q^9 - 2 * q^11 + 6 * q^13 - 17 * q^15 - 9 * q^17 - 11 * q^19 - 47 * q^21 - 22 * q^23 - 16 * q^25 - 19 * q^27 - q^29 - 13 * q^31 - 5 * q^33 + 14 * q^35 + 34 * q^37 + 30 * q^39 + 28 * q^41 + 44 * q^43 + 78 * q^45 + 26 * q^47 + 60 * q^49 + 62 * q^51 + 14 * q^53 + 26 * q^55 + 3 * q^57 - 10 * q^59 - 56 * q^61 - 27 * q^63 - 87 * q^65 - 44 * q^67 - 51 * q^69 - 37 * q^71 - 12 * q^73 - 53 * q^75 - 47 * q^77 - 6 * q^79 - 10 * q^81 - 25 * q^83 + 8 * q^85 + 48 * q^87 + 10 * q^89 + 26 * q^91 - 14 * q^93 + 29 * q^95 - q^97 - q^99

Introduction

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Varieties

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Database

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