LMFDB - Embedded newform 92.2.e.a.49.2

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			49.2
Root			$-0.115644 + 0.0743196i$ of defining polynomial
Character	$\chi$	$=$	92.49
Dual form			92.2.e.a.77.2

$q$-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 $\left(\mathbb{Z}/92\mathbb{Z}\right)^\times$.

$n$	$5$	$47$
$\chi(n)$	$e\left(\frac{8}{11}\right)$	$1$

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	−0.892431	−	0.451185i	$-0.851002\pi$
$3$	0.0571054	−	0.125043i	0.0329698	−	0.0721938i	0.925400	+	0.378991i	$0.123729\pi$
$4$		0			0
$5$	1.77577	−	2.04934i	0.794147	−	0.916495i	−0.203898	−	0.978992i	$-0.565361\pi$
$5$	1.77577	−	2.04934i	0.794147	−	0.916495i	0.998045	+	0.0624975i	$0.0199065\pi$
$6$		0			0
$7$	−0.600040	+	0.385622i	−0.226794	+	0.145752i	−0.649104	−	0.760700i	$-0.724856\pi$
$7$	−0.600040	+	0.385622i	−0.226794	+	0.145752i	0.422310	+	0.906452i	$0.361219\pi$
$8$		0			0
$9$	1.95221	+	2.25297i	0.650736	+	0.750989i
$10$		0			0
$11$	−0.176680	+	1.22883i	−0.0532709	+	0.370507i	0.945696	+	0.325054i	$0.105382\pi$
$11$	−0.176680	+	1.22883i	−0.0532709	+	0.370507i	−0.998966	+	0.0454536i	$0.985527\pi$
$12$		0			0
$13$	−3.37543	−	2.16925i	−0.936175	−	0.601643i	−0.0188670	−	0.999822i	$-0.506006\pi$
$13$	−3.37543	−	2.16925i	−0.936175	−	0.601643i	−0.917308	+	0.398179i	$0.869642\pi$
$14$		0			0
$15$	−0.154851	−	0.339076i	−0.0399823	−	0.0875491i
$16$		0			0
$17$	−1.87813	−	0.551470i	−0.455515	−	0.133751i	0.0459230	−	0.998945i	$-0.485377\pi$
$17$	−1.87813	−	0.551470i	−0.455515	−	0.133751i	−0.501438	+	0.865194i	$0.667195\pi$
$18$		0			0
$19$	−5.89961	+	1.73228i	−1.35346	+	0.397412i	−0.876454	−	0.481486i	$-0.840097\pi$
$19$	−5.89961	+	1.73228i	−1.35346	+	0.397412i	−0.477009	+	0.878898i	$0.658279\pi$
$20$		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	0.862212	−	0.506548i	$-0.169079\pi$
$29$	7.07444	+	2.07724i	1.31369	+	0.385734i	0.451479	+	0.892282i	$0.350897\pi$
$30$		0			0
$31$	−1.60018	−	3.50391i	−0.287401	−	0.629321i	0.709774	−	0.704429i	$-0.248797\pi$
$31$	−1.60018	−	3.50391i	−0.287401	−	0.629321i	−0.997175	+	0.0751086i	$0.976070\pi$
$32$		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	0.609643	−	0.792676i	$-0.291313\pi$
$37$	−1.59202	−	1.83729i	−0.261727	−	0.302049i	−0.871369	+	0.490628i	$0.836767\pi$
$38$		0			0
$39$	−0.464006	+	0.298198i	−0.0743004	+	0.0477499i
$40$		0			0
$41$	−2.23988	+	2.58496i	−0.349810	+	0.403703i	−0.903200	−	0.429220i	$-0.858789\pi$
$41$	−2.23988	+	2.58496i	−0.349810	+	0.403703i	0.553390	+	0.832922i	$0.313334\pi$
$42$		0			0
$43$	4.86900	−	10.6616i	0.742515	−	1.62588i	−0.0368584	−	0.999320i	$-0.511735\pi$
$43$	4.86900	−	10.6616i	0.742515	−	1.62588i	0.779373	−	0.626560i	$-0.215538\pi$
$44$		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	−0.00115923	−	0.999999i	$-0.500369\pi$
$53$	6.61027	−	4.24816i	0.907991	−	0.583530i	0.909150	+	0.416469i	$0.136733\pi$
$54$		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	0.963518	−	0.267643i	$-0.0862447\pi$
$59$	8.60536	+	5.53033i	1.12032	+	0.719987i	0.156804	+	0.987630i	$0.449881\pi$
$60$		0			0
$61$	−4.24909	−	9.30420i	−0.544040	−	1.19128i	−0.959510	−	0.281674i	$-0.909110\pi$
$61$	−4.24909	−	9.30420i	−0.544040	−	1.19128i	0.415470	−	0.909607i	$-0.363617\pi$
$62$		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	0.971280	+	0.237940i	$0.0764721\pi$
$67$	0.870750	+	6.05620i	0.106379	+	0.739883i	−0.864901	+	0.501943i	$0.832619\pi$
$68$		0			0
$69$	0.451098	+	0.480768i	0.0543058	+	0.0578777i
$70$		0			0
$71$	−2.12198	−	14.7587i	−0.251832	−	1.75153i	−0.587197	−	0.809444i	$-0.699769\pi$
$71$	−2.12198	−	14.7587i	−0.251832	−	1.75153i	0.335364	−	0.942088i	$-0.391141\pi$
$72$		0			0
$73$	−14.6335	+	4.29679i	−1.71273	+	0.502902i	−0.983429	−	0.181295i	$-0.941971\pi$
$73$	−14.6335	+	4.29679i	−1.71273	+	0.502902i	−0.729297	+	0.684197i	$0.760153\pi$
$74$		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	0.926996	−	0.375071i	$-0.122382\pi$
$79$	8.62961	+	5.54592i	0.970907	+	0.623964i	0.0439114	+	0.999035i	$0.486018\pi$
$80$		0			0
$81$	−1.25668	+	8.74041i	−0.139631	+	0.971156i
$82$		0			0
$83$	−7.65314	−	8.83219i	−0.840041	−	0.969459i	0.159803	−	0.987149i	$-0.448914\pi$
$83$	−7.65314	−	8.83219i	−0.840041	−	0.969459i	−0.999844	+	0.0176901i	$0.994369\pi$
$84$		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	−0.949900	−	0.312555i	$-0.898815\pi$
$89$	−0.864480	+	1.89295i	−0.0916347	+	0.200652i	0.858265	+	0.513207i	$0.171543\pi$
$90$		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	−0.784793	−	0.619757i	$-0.787231\pi$
$97$	−0.587549	+	0.678068i	−0.0596566	+	0.0688474i	0.725137	+	0.688605i	$0.241776\pi$
$98$		0			0
$99$	−3.11344	+	2.00089i	−0.312912	+	0.201097i
$100$		0			0
$101$	4.44390	+	5.12853i	0.442184	+	0.510308i	0.932467	−	0.361256i	$-0.117652\pi$
$101$	4.44390	+	5.12853i	0.442184	+	0.510308i	−0.490283	+	0.871564i	$0.663106\pi$
$102$		0			0
$103$	2.08664	−	14.5129i	0.205603	−	1.43000i	−0.581686	−	0.813414i	$-0.697607\pi$
$103$	2.08664	−	14.5129i	0.205603	−	1.43000i	0.787289	−	0.616585i	$-0.211484\pi$
$104$		0			0
$105$	0.223672	+	0.143745i	0.0218282	+	0.0140281i
$106$		0			0
$107$	−5.99449	−	13.1261i	−0.579509	−	1.26895i	−0.941578	−	0.336796i	$-0.890657\pi$
$107$	−5.99449	−	13.1261i	−0.579509	−	1.26895i	0.362068	−	0.932151i	$-0.382071\pi$
$108$		0			0
$109$	−2.17177	−	0.637688i	−0.208017	−	0.0610794i	0.176064	−	0.984379i	$-0.443664\pi$
$109$	−2.17177	−	0.637688i	−0.208017	−	0.0610794i	−0.384081	+	0.923299i	$0.625482\pi$
$110$		0			0
$111$	−0.320654	+	0.0941524i	−0.0304351	+	0.00893655i
$112$		0			0
$113$	−0.493869	−	3.43494i	−0.0464593	−	0.323132i	−0.999776	−	0.0211597i	$-0.993264\pi$
$113$	−0.493869	−	3.43494i	−0.0464593	−	0.323132i	0.953317	−	0.301972i	$-0.0976449\pi$
$114$		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	0.855908	+	0.517128i	$0.172999\pi$
$127$	−1.25115	+	8.70193i	−0.111021	+	0.772171i	−0.966930	+	0.255043i	$0.917910\pi$
$128$		0			0
$129$	−1.05512	−	1.21767i	−0.0928979	−	0.107210i
$130$		0			0
$131$	3.76585	−	2.42017i	0.329024	−	0.211451i	−0.365690	−	0.930737i	$-0.619167\pi$
$131$	3.76585	−	2.42017i	0.329024	−	0.211451i	0.694714	+	0.719286i	$0.255531\pi$
$132$		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	0.755442	+	0.655216i	$0.227422\pi$
$149$	−1.87975	+	13.0739i	−0.153995	+	1.07106i	−0.909437	+	0.415842i	$0.863487\pi$
$150$		0			0
$151$	−4.52981	−	2.91113i	−0.368631	−	0.236904i	0.343190	−	0.939266i	$-0.388493\pi$
$151$	−4.52981	−	2.91113i	−0.368631	−	0.236904i	−0.711820	+	0.702362i	$0.752129\pi$
$152$		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	−0.781758	−	0.623582i	$-0.785677\pi$
$157$	−13.8115	+	4.05543i	−1.10228	+	0.323659i	−0.320522	+	0.947241i	$0.603858\pi$
$158$		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	0.920538	+	0.390654i	$0.127751\pi$
$163$	1.88122	+	13.0841i	0.147348	+	1.02483i	−0.773190	+	0.634175i	$0.781340\pi$
$164$		0			0
$165$	0.444027	−	0.130378i	0.0345675	−	0.0101499i
$166$		0			0
$167$	8.68878	+	2.55125i	0.672358	+	0.197422i	0.600053	−	0.799961i	$-0.295146\pi$
$167$	8.68878	+	2.55125i	0.672358	+	0.197422i	0.0723051	+	0.997383i	$0.476964\pi$
$168$		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	−0.897803	−	0.440397i	$-0.854838\pi$
$173$	1.15360	−	8.02349i	0.0877068	−	0.610014i	0.985510	−	0.169617i	$-0.0542532\pi$
$174$		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	−0.999873	−	0.0159066i	$-0.994937\pi$
$179$	−11.2629	+	12.9981i	−0.841832	+	0.971526i	0.158042	+	0.987432i	$0.449482\pi$
$180$		0			0
$181$	5.37156	−	11.7621i	0.399265	−	0.874267i	−0.598080	−	0.801437i	$-0.704069\pi$
$181$	5.37156	−	11.7621i	0.399265	−	0.874267i	0.997344	−	0.0728309i	$-0.0232033\pi$
$182$		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	−0.981731	−	0.190272i	$-0.939063\pi$
$191$	−16.8121	+	10.8045i	−1.21648	+	0.781784i	−0.234748	+	0.972056i	$0.575427\pi$
$192$		0			0
$193$	6.95504	+	8.02655i	0.500635	+	0.577763i	0.948676	−	0.316249i	$-0.102424\pi$
$193$	6.95504	+	8.02655i	0.500635	+	0.577763i	−0.448041	+	0.894013i	$0.647878\pi$
$194$		0			0
$195$	−0.212855	+	1.48044i	−0.0152429	+	0.106016i
$196$		0			0
$197$	−6.26488	−	4.02620i	−0.446354	−	0.286855i	0.298092	−	0.954537i	$-0.403650\pi$
$197$	−6.26488	−	4.02620i	−0.446354	−	0.286855i	−0.744446	+	0.667683i	$0.767286\pi$
$198$		0			0
$199$	6.21716	+	13.6137i	0.440723	+	0.965048i	0.991465	+	0.130373i	$0.0416174\pi$
$199$	6.21716	+	13.6137i	0.440723	+	0.965048i	−0.550743	+	0.834675i	$0.685655\pi$
$200$		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	−0.247823	−	0.968805i	$-0.579715\pi$
$211$	0.980075	−	0.287776i	0.0674711	−	0.0198113i	0.315294	+	0.948994i	$0.397897\pi$
$212$		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	−0.955024	−	0.296527i	$-0.904171\pi$
$223$	−16.1581	+	10.3842i	−1.08202	+	0.695375i	−0.127001	+	0.991903i	$0.540535\pi$
$224$		0			0
$225$	4.59386	−	5.30159i	0.306257	−	0.353440i
$226$		0			0
$227$	−1.13417	+	2.48348i	−0.0752774	+	0.164835i	−0.943529	−	0.331289i	$-0.892516\pi$
$227$	−1.13417	+	2.48348i	−0.0752774	+	0.164835i	0.868252	+	0.496124i	$0.165244\pi$
$228$		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	−0.551800	−	0.833976i	$-0.686059\pi$
$233$	6.71370	−	14.7010i	0.439829	−	0.963092i	0.991630	−	0.129116i	$-0.0412138\pi$
$234$		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	0.689468	−	0.724317i	$-0.257845\pi$
$239$	−1.94170	−	2.24084i	−0.125598	−	0.144948i	−0.815066	+	0.579369i	$0.803299\pi$
$240$		0			0
$241$	−1.21176	+	8.42795i	−0.0780561	+	0.542892i	0.912846	+	0.408305i	$0.133880\pi$
$241$	−1.21176	+	8.42795i	−0.0780561	+	0.542892i	−0.990902	+	0.134587i	$0.957029\pi$
$242$		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	0.959976	−	0.280081i	$-0.0903614\pi$
$251$	−0.634071	−	4.41006i	−0.0400222	−	0.278360i	−0.999999	+	0.00172069i	$0.999452\pi$
$252$		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	0.272128	−	0.962261i	$-0.412272\pi$
$257$	16.3726	−	4.80743i	1.02129	−	0.299879i	0.749167	+	0.662382i	$0.230454\pi$
$258$		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	0.780060	−	0.625704i	$-0.215188\pi$
$263$	8.67540	+	5.57534i	0.534948	+	0.343790i	−0.245112	+	0.969495i	$0.578825\pi$
$264$		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	0.0691764	−	0.997604i	$-0.477963\pi$
$269$	16.4892	−	10.5970i	1.00537	−	0.646110i	0.936190	+	0.351495i	$0.114327\pi$
$270$		0			0
$271$	6.73812	−	7.77620i	0.409312	−	0.472371i	−0.513240	−	0.858245i	$-0.671555\pi$
$271$	6.73812	−	7.77620i	0.409312	−	0.472371i	0.922551	+	0.385875i	$0.126100\pi$
$272$		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	−0.887954	−	0.459933i	$-0.847873\pi$
$281$	−5.13508	+	5.92620i	−0.306333	+	0.353527i	0.581621	+	0.813460i	$0.302419\pi$
$282$		0			0
$283$	−5.18764	+	3.33389i	−0.308373	+	0.198179i	−0.685669	−	0.727913i	$-0.740490\pi$
$283$	−5.18764	+	3.33389i	−0.308373	+	0.198179i	0.377296	+	0.926093i	$0.376854\pi$
$284$		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	−0.195194	−	0.980765i	$-0.562534\pi$
$293$	−15.2282	−	4.47141i	−0.889643	−	0.261223i	−0.694449	+	0.719542i	$0.744352\pi$
$294$		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	0.985409	−	0.170201i	$-0.0544416\pi$
$307$	3.70533	+	8.11355i	0.211474	+	0.463065i	−0.773935	+	0.633265i	$0.781714\pi$
$308$		0			0
$309$	−1.69558	−	1.08968i	−0.0964583	−	0.0619900i
$310$		0			0
$311$	−0.892165	+	6.20514i	−0.0505900	+	0.351861i	0.948766	+	0.315979i	$0.102333\pi$
$311$	−0.892165	+	6.20514i	−0.0505900	+	0.351861i	−0.999356	+	0.0358818i	$0.988576\pi$
$312$		0			0
$313$	15.4592	+	17.8408i	0.873804	+	1.00842i	0.999865	+	0.0164014i	$0.00522095\pi$
$313$	15.4592	+	17.8408i	0.873804	+	1.00842i	−0.126061	+	0.992022i	$0.540234\pi$
$314$		0			0
$315$	−4.85059	+	3.11728i	−0.273300	+	0.175639i
$316$		0			0
$317$	−5.96538	+	6.88441i	−0.335049	+	0.386667i	−0.898127	−	0.439737i	$-0.855072\pi$
$317$	−5.96538	+	6.88441i	−0.335049	+	0.386667i	0.563078	+	0.826404i	$0.309617\pi$
$318$		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	−0.984608	−	0.174779i	$-0.944079\pi$
$331$	−18.5115	−	21.3634i	−1.01748	−	1.17424i	−0.0328758	−	0.999459i	$-0.510467\pi$
$332$		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	0.696837	−	0.717230i	$-0.254590\pi$
$337$	−5.53555	−	12.1212i	−0.301540	−	0.660282i	−0.998377	+	0.0569483i	$0.981863\pi$
$338$		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	0.249912	+	0.968269i	$0.419598\pi$
$347$	5.27014	+	36.6546i	0.282916	+	1.96772i	0.0330044	+	0.999455i	$0.489492\pi$
$348$		0			0
$349$	−17.4012	+	5.10944i	−0.931463	+	0.273502i	−0.712049	−	0.702130i	$-0.752233\pi$
$349$	−17.4012	+	5.10944i	−0.931463	+	0.273502i	−0.219414	+	0.975632i	$0.570414\pi$
$350$		0			0
$351$	−3.16533	−	0.929426i	−0.168953	−	0.0496091i
$352$		0			0
$353$	8.27976	+	18.1301i	0.440687	+	0.964970i	0.991472	+	0.130323i	$0.0416013\pi$
$353$	8.27976	+	18.1301i	0.440687	+	0.964970i	−0.550785	+	0.834647i	$0.685671\pi$
$354$		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	−0.954330	−	0.298755i	$-0.903429\pi$
$359$	−21.1116	−	24.3641i	−1.11423	−	1.28589i	−0.159899	−	0.987133i	$-0.551117\pi$
$360$		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	0.0477255	+	0.998860i	$0.484803\pi$
$373$	−18.3043	+	21.1243i	−0.947760	+	1.09377i	−0.995486	+	0.0949129i	$0.969743\pi$
$374$		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	−0.831883	−	0.554951i	$-0.812737\pi$
$379$	2.38775	−	16.6072i	0.122651	−	0.853053i	0.954534	−	0.298103i	$-0.0963538\pi$
$380$		0			0
$381$	1.01667	+	0.653374i	0.0520856	+	0.0334734i
$382$		0			0
$383$	8.14929	+	17.8445i	0.416409	+	0.911809i	0.995340	+	0.0964322i	$0.0307431\pi$
$383$	8.14929	+	17.8445i	0.416409	+	0.911809i	−0.578930	+	0.815377i	$0.696530\pi$
$384$		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	−0.985268	−	0.171016i	$-0.945295\pi$
$389$	−1.73743	−	12.0841i	−0.0880911	−	0.612687i	0.897177	−	0.441671i	$-0.145614\pi$
$390$		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	−0.394951	−	0.918702i	$-0.629238\pi$
$397$	−24.3859	−	7.16035i	−1.22389	−	0.359367i	−0.828942	+	0.559335i	$0.811057\pi$
$398$		0			0
$399$	−0.250444	−	0.548397i	−0.0125379	−	0.0274542i
$400$		0			0
$401$	30.2068	+	19.4127i	1.50845	+	0.969424i	0.993698	+	0.112087i	$0.0357536\pi$
$401$	30.2068	+	19.4127i	1.50845	+	0.969424i	0.514755	+	0.857337i	$0.327883\pi$
$402$		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	−0.255433	−	0.966827i	$-0.582218\pi$
$409$	14.9232	−	17.2223i	0.737905	−	0.851587i	0.993338	+	0.115239i	$0.0367635\pi$
$410$		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	−0.944426	−	0.328725i	$-0.893381\pi$
$419$	−9.92036	+	11.4487i	−0.484641	+	0.559306i	0.459784	+	0.888031i	$0.347927\pi$
$420$		0			0
$421$	1.52719	−	0.981463i	0.0744305	−	0.0478336i	−0.502896	−	0.864347i	$-0.667732\pi$
$421$	1.52719	−	0.981463i	0.0744305	−	0.0478336i	0.577327	+	0.816513i	$0.304096\pi$
$422$		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	0.829676	−	0.558246i	$-0.188525\pi$
$431$	25.4490	+	7.47249i	1.22583	+	0.359937i	0.396157	+	0.918183i	$0.370343\pi$
$432$		0			0
$433$	33.2893	−	9.77462i	1.59978	−	0.469738i	0.644296	−	0.764776i	$-0.277150\pi$
$433$	33.2893	−	9.77462i	1.59978	−	0.469738i	0.955486	+	0.295037i	$0.0953321\pi$
$434$		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	0.992658	−	0.120955i	$-0.0385957\pi$
$439$	0.128494	+	0.893693i	0.00613267	+	0.0426536i	−0.986525	+	0.163609i	$0.947687\pi$
$440$		0			0
$441$	−18.5672	+	5.45183i	−0.884154	+	0.259611i
$442$		0			0
$443$	5.19119	+	1.52427i	0.246641	+	0.0724202i	0.402716	−	0.915325i	$-0.368066\pi$
$443$	5.19119	+	1.52427i	0.246641	+	0.0724202i	−0.156076	+	0.987745i	$0.549884\pi$
$444$		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	−0.263974	−	0.964530i	$-0.585033\pi$
$449$	5.53148	−	38.4723i	0.261047	−	1.81562i	0.525021	−	0.851089i	$-0.324058\pi$
$450$		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	−0.966383	−	0.257105i	$-0.917231\pi$
$457$	−2.97640	+	6.51740i	−0.139230	+	0.304871i	0.827154	+	0.561976i	$0.189959\pi$
$458$		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	−0.428249	−	0.903661i	$-0.640870\pi$
$463$	11.5147	−	25.2138i	0.535135	−	1.17178i	0.963385	−	0.268122i	$-0.0864032\pi$
$464$		0			0
$465$	−0.940303	+	1.08517i	−0.0436055	+	0.0503234i
$466$		0			0
$467$	3.25500	−	2.09186i	0.150623	−	0.0967997i	−0.463158	−	0.886276i	$-0.653284\pi$
$467$	3.25500	−	2.09186i	0.150623	−	0.0967997i	0.613782	+	0.789476i	$0.289648\pi$
$468$		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	−0.0743780	−	0.997230i	$-0.523697\pi$
$479$	8.80246	−	2.58463i	0.402195	−	0.118095i	0.476573	+	0.879135i	$0.341879\pi$
$480$		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	−0.101823	−	0.994802i	$-0.532468\pi$
$487$	7.73151	−	2.27018i	0.350348	−	0.102872i	0.452172	+	0.891931i	$0.350649\pi$
$488$		0			0
$489$	1.74351	+	0.511941i	0.0788443	+	0.0231508i
$490$		0			0
$491$	−5.64284	−	12.3561i	−0.254658	−	0.557623i	0.738520	−	0.674231i	$-0.235525\pi$
$491$	−5.64284	−	12.3561i	−0.254658	−	0.557623i	−0.993178	+	0.116609i	$0.962798\pi$
$492$		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	−0.857210	−	0.514967i	$-0.827804\pi$
$499$	−16.6393	+	10.6934i	−0.744877	+	0.478703i	0.112333	+	0.993671i	$0.464168\pi$
$500$		0			0
$501$	0.815193	−	0.940783i	0.0364201	−	0.0420311i
$502$		0			0
$503$	−10.8916	+	23.8492i	−0.485631	+	1.06338i	0.495246	+	0.868753i	$0.335078\pi$
$503$	−10.8916	+	23.8492i	−0.485631	+	1.06338i	−0.980877	+	0.194631i	$0.937649\pi$
$504$		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	−0.662217	−	0.749312i	$-0.730384\pi$
$509$	7.61965	−	16.6847i	0.337735	−	0.739536i	0.999952	+	0.00977557i	$0.00311171\pi$
$510$		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	0.912708	+	0.408612i	$0.133987\pi$
$521$	14.2390	+	31.1790i	0.623820	+	1.36597i	−0.288888	+	0.957363i	$0.593286\pi$
$522$		0			0
$523$	−2.14481	−	0.629772i	−0.0937858	−	0.0275380i	0.234503	−	0.972115i	$-0.424654\pi$
$523$	−2.14481	−	0.629772i	−0.0937858	−	0.0275380i	−0.328289	+	0.944577i	$0.606472\pi$
$524$		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	−0.925284	−	0.379275i	$-0.876173\pi$
$541$	1.61359	−	11.2228i	0.0693738	−	0.482505i	0.994658	−	0.103230i	$-0.0329176\pi$
$542$		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	−0.968578	−	0.248710i	$-0.919993\pi$
$547$	−13.6716	+	15.7779i	−0.584556	+	0.674614i	0.384022	+	0.923324i	$0.374539\pi$
$548$		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	−0.460677	−	0.887568i	$-0.652393\pi$
$557$	11.4091	−	13.1668i	0.483419	−	0.557895i	0.944095	+	0.329673i	$0.106939\pi$
$558$		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	0.847797	+	0.530321i	$0.177929\pi$
$563$	−2.73027	+	18.9894i	−0.115067	+	0.800309i	−0.962864	+	0.269987i	$0.912980\pi$
$564$		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	0.0244456	−	0.999701i	$-0.492218\pi$
$569$	−11.8188	−	3.47030i	−0.495469	−	0.145483i	−0.519914	+	0.854218i	$0.674036\pi$
$570$		0			0
$571$	7.78356	−	2.28546i	0.325732	−	0.0956435i	−0.114778	−	0.993391i	$-0.536616\pi$
$571$	7.78356	−	2.28546i	0.325732	−	0.0956435i	0.440510	+	0.897748i	$0.354798\pi$
$572$		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	0.985516	+	0.169581i	$0.0542415\pi$
$577$	2.10655	+	14.6514i	0.0876969	+	0.609945i	−0.897819	+	0.440364i	$0.854849\pi$
$578$		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	−0.914907	−	0.403664i	$-0.867737\pi$
$587$	1.85745	−	12.9188i	0.0766650	−	0.533217i	0.991572	−	0.129553i	$-0.0413543\pi$
$588$		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	0.0276122	+	0.999619i	$0.491210\pi$
$593$	−23.5178	+	27.1410i	−0.965761	+	1.11455i	−0.993374	+	0.114929i	$0.963336\pi$
$594$		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	−0.551584	−	0.834119i	$-0.685976\pi$
$601$	10.7870	−	23.6203i	0.440012	−	0.963492i	0.991596	−	0.129373i	$-0.0412964\pi$
$602$		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	0.999674	+	0.0255396i	$0.00813038\pi$
$607$	21.7470	+	25.0974i	0.882685	+	1.01867i	−0.116989	+	0.993133i	$0.537324\pi$
$608$		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	0.991307	−	0.131571i	$-0.0420022\pi$
$613$	6.00907	+	13.1580i	0.242704	+	0.531448i	−0.748603	+	0.663019i	$0.769275\pi$
$614$		0			0
$615$	1.22335	+	0.359207i	0.0493300	+	0.0144846i
$616$		0			0
$617$	−32.7699	+	9.62212i	−1.31927	+	0.387372i	−0.864228	−	0.503100i	$-0.832193\pi$
$617$	−32.7699	+	9.62212i	−1.31927	+	0.387372i	−0.455039	+	0.890472i	$0.650375\pi$
$618$		0			0
$619$	−4.68738	−	32.6015i	−0.188402	−	1.31036i	−0.836146	−	0.548506i	$-0.815197\pi$
$619$	−4.68738	−	32.6015i	−0.188402	−	1.31036i	0.647745	−	0.761858i	$-0.275712\pi$
$620$		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	0.440979	−	0.897517i	$-0.354631\pi$
$631$	−4.82905	−	3.10344i	−0.192241	−	0.123546i	−0.633221	+	0.773971i	$0.718268\pi$
$632$		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	−0.998112	−	0.0614209i	$-0.980437\pi$
$641$	−7.54650	+	16.5245i	−0.298069	+	0.652680i	0.700043	+	0.714101i	$0.253164\pi$
$642$		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	−0.906686	−	0.421805i	$-0.861397\pi$
$647$	0.148701	−	0.325611i	0.00584606	−	0.0128011i	0.912533	+	0.409004i	$0.134124\pi$
$648$		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	0.575511	−	0.817794i	$-0.304803\pi$
$653$	−8.07152	−	9.31503i	−0.315863	−	0.364525i	−0.891374	+	0.453269i	$0.850258\pi$
$654$		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	0.998428	−	0.0560469i	$-0.0178496\pi$
$659$	7.75878	+	16.9894i	0.302239	+	0.661812i	−0.696189	+	0.717859i	$0.745122\pi$
$660$		0			0
$661$	−9.84343	−	2.89029i	−0.382865	−	0.112419i	0.0846357	−	0.996412i	$-0.473027\pi$
$661$	−9.84343	−	2.89029i	−0.382865	−	0.112419i	−0.467501	+	0.883993i	$0.654846\pi$
$662$		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	0.722914	−	0.690938i	$-0.242802\pi$
$673$	24.8402	+	7.29373i	0.957518	+	0.281153i	0.234604	+	0.972091i	$0.424621\pi$
$674$		0			0
$675$	−0.803729	−	1.75992i	−0.0309355	−	0.0677394i
$676$		0			0
$677$	28.6277	+	18.3979i	1.10025	+	0.707090i	0.959148	−	0.282905i	$-0.0912980\pi$
$677$	28.6277	+	18.3979i	1.10025	+	0.707090i	0.141105	+	0.989995i	$0.454934\pi$
$678$		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	0.281834	−	0.959463i	$-0.409057\pi$
$683$	33.2342	−	21.3583i	1.27167	−	0.817253i	0.989837	+	0.142210i	$0.0454208\pi$
$684$		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	−0.999875	−	0.0158251i	$-0.994963\pi$
$701$	−0.954302	+	6.63732i	−0.0360435	+	0.250688i	0.963831	+	0.266513i	$0.0858716\pi$
$702$		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	0.210097	−	0.977680i	$-0.432622\pi$
$709$	24.3748	−	7.15710i	0.915416	−	0.268791i	0.705319	+	0.708890i	$0.250804\pi$
$710$		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	0.316039	−	0.948746i	$-0.397647\pi$
$719$	1.84954	+	0.543073i	0.0689761	+	0.0202532i	−0.247062	+	0.969000i	$0.579465\pi$
$720$		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	0.848038	−	0.529935i	$-0.177784\pi$
$727$	5.46833	+	6.31079i	0.202809	+	0.234054i	−0.645229	+	0.763989i	$0.723238\pi$
$728$		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	−0.989843	−	0.142166i	$-0.954593\pi$
$733$	−6.34050	+	13.8838i	−0.234192	+	0.512808i	0.755651	+	0.654974i	$0.227321\pi$
$734$		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	−0.919674	−	0.392683i	$-0.871547\pi$
$739$	−0.561238	+	1.22894i	−0.0206455	+	0.0452073i	0.899028	+	0.437890i	$0.144274\pi$
$740$		0			0
$741$	2.22089	−	2.56304i	0.0815863	−	0.0941557i
$742$		0			0
$743$	−32.0633	+	20.6059i	−1.17629	+	0.755955i	−0.974701	−	0.223515i	$-0.928247\pi$
$743$	−32.0633	+	20.6059i	−1.17629	+	0.755955i	−0.201589	+	0.979470i	$0.564611\pi$
$744$		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	−0.999014	−	0.0443955i	$-0.985864\pi$
$751$	−10.3685	−	22.7038i	−0.378351	−	0.828473i	0.620663	−	0.784077i	$-0.286863\pi$
$752$		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	0.972025	+	0.234877i	$0.0754689\pi$
$757$	2.90397	+	20.1975i	0.105546	+	0.734092i	−0.866479	+	0.499214i	$0.833622\pi$
$758$		0			0
$759$	−0.670484	+	0.469383i	−0.0243370	+	0.0170375i
$760$		0			0
$761$	0.482325	+	3.35464i	0.0174843	+	0.121606i	0.996694	−	0.0812432i	$-0.0258891\pi$
$761$	0.482325	+	3.35464i	0.0174843	+	0.121606i	−0.979210	+	0.202849i	$0.934980\pi$
$762$		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	0.0890730	−	0.996025i	$-0.471610\pi$
$769$	−21.6284	−	13.8997i	−0.779941	−	0.501238i	−0.869014	+	0.494787i	$0.835246\pi$
$770$		0			0
$771$	0.333827	−	2.32181i	0.0120225	−	0.0836181i
$772$		0			0
$773$	−34.6287	−	39.9637i	−1.24551	−	1.43739i	−0.856490	−	0.516164i	$-0.827359\pi$
$773$	−34.6287	−	39.9637i	−1.24551	−	1.43739i	−0.389019	−	0.921230i	$-0.627186\pi$
$774$		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	−0.941859	−	0.336009i	$-0.890923\pi$
$787$	−13.3319	+	15.3858i	−0.475229	+	0.548444i	0.466630	+	0.884453i	$0.345468\pi$
$788$		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	−0.862145	−	0.506662i	$-0.830879\pi$
$797$	−19.2105	−	42.0651i	−0.680470	−	1.49002i	0.181675	−	0.983359i	$-0.441848\pi$
$798$		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	−0.936150	−	0.351601i	$-0.885637\pi$
$809$	−43.6200	+	12.8080i	−1.53360	+	0.450305i	−0.597449	+	0.801907i	$0.703819\pi$
$810$		0			0
$811$	12.4621	+	3.65921i	0.437605	+	0.128492i	0.493112	−	0.869966i	$-0.335859\pi$
$811$	12.4621	+	3.65921i	0.437605	+	0.128492i	−0.0555071	+	0.998458i	$0.517678\pi$
$812$		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	−0.954288	−	0.298889i	$-0.903384\pi$
$821$	−30.9119	+	19.8659i	−1.07883	+	0.693325i	−0.124547	+	0.992214i	$0.539748\pi$
$822$		0			0
$823$	−0.585875	+	0.676135i	−0.0204223	+	0.0235686i	−0.765869	−	0.642997i	$-0.777691\pi$
$823$	−0.585875	+	0.676135i	−0.0204223	+	0.0235686i	0.745447	+	0.666565i	$0.232236\pi$
$824$		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	0.925655	+	0.378369i	$0.123515\pi$
$839$	−2.00161	+	13.9215i	−0.0691033	+	0.480624i	−0.994758	+	0.102255i	$0.967394\pi$
$840$		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	−0.801773	−	0.597628i	$-0.796110\pi$
$853$	−5.86602	−	40.7991i	−0.200849	−	1.39693i	0.600925	−	0.799306i	$-0.294799\pi$
$854$		0			0
$855$	−47.6911	+	14.0034i	−1.63100	+	0.478905i
$856$		0			0
$857$	−12.5551	−	3.68650i	−0.428873	−	0.125928i	0.0601702	−	0.998188i	$-0.480836\pi$
$857$	−12.5551	−	3.68650i	−0.428873	−	0.125928i	−0.489043	+	0.872260i	$0.662654\pi$
$858$		0			0
$859$	17.5445	+	38.4171i	0.598610	+	1.31077i	0.930097	+	0.367314i	$0.119722\pi$
$859$	17.5445	+	38.4171i	0.598610	+	1.31077i	−0.331487	+	0.943460i	$0.607550\pi$
$860$		0			0
$861$	−0.282131	−	0.181314i	−0.00961499	−	0.00617918i
$862$		0			0
$863$	6.04438	−	42.0396i	0.205753	−	1.43104i	−0.581064	−	0.813858i	$-0.697364\pi$
$863$	6.04438	−	42.0396i	0.205753	−	1.43104i	0.786817	−	0.617186i	$-0.211727\pi$
$864$		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	−0.883261	−	0.468882i	$-0.844657\pi$
$877$	1.46617	−	3.21047i	0.0495092	−	0.108410i	0.932770	+	0.360472i	$0.117384\pi$
$878$		0			0
$879$	−1.42873	+	1.64885i	−0.0481900	+	0.0556142i
$880$		0			0
$881$	29.7859	−	19.1423i	1.00351	−	0.644919i	0.0678075	−	0.997698i	$-0.478400\pi$
$881$	29.7859	−	19.1423i	1.00351	−	0.644919i	0.935707	+	0.352779i	$0.114763\pi$
$882$		0			0
$883$	−18.4058	−	21.2414i	−0.619405	−	0.714831i	0.356189	−	0.934414i	$-0.384076\pi$
$883$	−18.4058	−	21.2414i	−0.619405	−	0.714831i	−0.975594	+	0.219583i	$0.929530\pi$
$884$		0			0
$885$	0.542655	−	3.77425i	0.0182411	−	0.126870i
$886$		0			0
$887$	39.1972	+	25.1905i	1.31611	+	0.845815i	0.994868	−	0.101181i	$-0.0322621\pi$
$887$	39.1972	+	25.1905i	1.31611	+	0.845815i	0.321246	+	0.946996i	$0.395898\pi$
$888$		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	0.565127	−	0.825004i	$-0.308827\pi$
$907$	1.48892	+	0.956870i	0.0494387	+	0.0317723i	−0.515688	+	0.856776i	$0.672464\pi$
$908$		0			0
$909$	−2.87900	+	20.0239i	−0.0954905	+	0.664151i
$910$		0			0
$911$	−10.2287	−	11.8046i	−0.338892	−	0.391102i	0.560566	−	0.828110i	$-0.310584\pi$
$911$	−10.2287	−	11.8046i	−0.338892	−	0.391102i	−0.899458	+	0.437008i	$0.856038\pi$
$912$		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	0.956867	−	0.290526i	$-0.0938302\pi$
$929$	16.2493	+	18.7527i	0.533122	+	0.615256i	−0.423745	+	0.905781i	$0.639285\pi$
$930$		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	0.658556	−	0.752532i	$-0.271168\pi$
$937$	24.6634	+	7.24183i	0.805718	+	0.236580i	0.147163	+	0.989112i	$0.452986\pi$
$938$		0			0
$939$	3.11368	−	0.914259i	0.101611	−	0.0298357i
$940$		0			0
$941$	−7.13691	−	49.6383i	−0.232657	−	1.61816i	−0.686534	−	0.727098i	$-0.740869\pi$
$941$	−7.13691	−	49.6383i	−0.232657	−	1.61816i	0.453878	−	0.891064i	$-0.350040\pi$
$942$		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	0.606458	−	0.795115i	$-0.292590\pi$
$947$	47.5915	−	13.9741i	1.54652	−	0.454098i	0.940057	+	0.341017i	$0.110772\pi$
$948$		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	0.928857	−	0.370438i	$-0.120792\pi$
$953$	30.1840	+	19.3981i	0.977756	+	0.628366i	0.0488989	+	0.998804i	$0.484429\pi$
$954$		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	−0.313394	+	0.949623i	$0.601466\pi$
$971$	−37.6657	+	43.4686i	−1.20875	+	1.39497i	−0.895357	+	0.445349i	$0.853079\pi$
$972$		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	−0.564270	−	0.825590i	$-0.690842\pi$
$977$	6.55581	−	45.5966i	0.209739	−	1.45877i	0.774009	−	0.633175i	$-0.218249\pi$
$978$		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	0.337535	−	0.941313i	$-0.390407\pi$
$983$	3.52958	+	1.03638i	0.112576	+	0.0330553i	−0.224959	+	0.974368i	$0.572225\pi$
$984$		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	−0.640064	−	0.768322i	$-0.721092\pi$
$991$	−7.63042	−	53.0707i	−0.242388	−	1.68585i	0.397676	−	0.917526i	$-0.369817\pi$
$992$		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	0.776668	−	0.629911i	$-0.216909\pi$
$997$	−6.56755	−	14.3809i	−0.207996	−	0.455448i	−0.984664	+	0.174462i	$0.944181\pi$
$998$		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.49.2	✓	20
3.2	odd	2		828.2.q.a.325.1		20
4.3	odd	2		368.2.m.d.49.1		20
23.8	even	11	inner	92.2.e.a.77.2	yes	20
23.10	odd	22		2116.2.a.i.1.6		10
23.13	even	11		2116.2.a.j.1.6		10
69.8	odd	22		828.2.q.a.721.1		20
92.31	odd	22		368.2.m.d.353.1		20
92.59	odd	22		8464.2.a.ce.1.5		10
92.79	even	22		8464.2.a.cd.1.5		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
92.2.e.a.49.2	✓	20	1.1	even	1	trivial
92.2.e.a.77.2	yes	20	23.8	even	11	inner
368.2.m.d.49.1		20	4.3	odd	2
368.2.m.d.353.1		20	92.31	odd	22
828.2.q.a.325.1		20	3.2	odd	2
828.2.q.a.721.1		20	69.8	odd	22
2116.2.a.i.1.6		10	23.10	odd	22
2116.2.a.j.1.6		10	23.13	even	11
8464.2.a.cd.1.5		10	92.79	even	22
8464.2.a.ce.1.5		10	92.59	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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Modular forms

Varieties

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Database

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