LMFDB - Embedded newform 912.2.cc.c.257.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [912,2,Mod(257,912)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("912.257"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(912, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([0, 0, 9, 17])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 912 = 2^{4} \cdot 3 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	912.cc (of order $18$, degree $6$, not minimal)

Newform invariants

comment:select newform

sage:traces = [18,0,-3,0,0,0,0,0,-3,0,0,0,-12] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(13)] == traces)

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

Self dual:	no
Analytic conductor:	$7.28235666434$
Analytic rank:	$0$
Dimension:	$18$
Relative dimension:	$3$ over $\Q(\zeta_{18})$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - x^{15} - 18 x^{14} + 36 x^{13} + 10 x^{12} + 18 x^{11} + 90 x^{10} - 567 x^{9} + 270 x^{8} + \cdots + 19683 $ x^18 - x^15 - 18x^14 + 36x^13 + 10x^12 + 18x^11 + 90x^10 - 567x^9 + 270x^8 + 162x^7 + 270x^6 + 2916x^5 - 4374x^4 - 729x^3 + 19683
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 114)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			257.2
Root			$0.0786547 + 1.73026i$ of defining polynomial
Character	$\chi$	$=$	912.257
Dual form			912.2.cc.c.401.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.517874 - 1.65282i) q^{3} +(-0.258510 + 0.710252i) q^{5} +(-0.777943 + 1.34744i) q^{7} +(-2.46361 + 1.71190i) q^{9} +(-0.832399 + 0.480586i) q^{11} +(0.416982 - 0.496940i) q^{13} +(1.30779 + 0.0594499i) q^{15} +(6.73013 - 1.18670i) q^{17} +(4.14364 + 1.35288i) q^{19} +(2.62994 + 0.587996i) q^{21} +(-0.400647 - 1.10077i) q^{23} +(3.39259 + 2.84672i) q^{25} +(4.10530 + 3.18535i) q^{27} +(1.39666 - 7.92086i) q^{29} +(2.63927 + 1.52379i) q^{31} +(1.22540 + 1.12692i) q^{33} +(-0.755913 - 0.900862i) q^{35} -4.12648i q^{37} +(-1.03729 - 0.431843i) q^{39} +(-4.09755 + 3.43825i) q^{41} +(7.34330 + 2.67274i) q^{43} +(-0.579012 - 2.19233i) q^{45} +(3.11004 + 0.548383i) q^{47} +(2.28961 + 3.96572i) q^{49} +(-5.44676 - 10.5091i) q^{51} +(-13.6276 + 4.96002i) q^{53} +(-0.126153 - 0.715449i) q^{55} +(0.0901766 - 7.54930i) q^{57} +(-2.02192 - 11.4669i) q^{59} +(10.1813 - 3.70568i) q^{61} +(-0.390129 - 4.65133i) q^{63} +(0.245158 + 0.424626i) q^{65} +(9.19012 + 1.62047i) q^{67} +(-1.61189 + 1.23226i) q^{69} +(-0.0322101 - 0.0117235i) q^{71} +(-3.04446 + 2.55461i) q^{73} +(2.94818 - 7.08158i) q^{75} -1.49547i q^{77} +(0.893115 + 1.06437i) q^{79} +(3.13878 - 8.43493i) q^{81} +(10.4856 + 6.05389i) q^{83} +(-0.896950 + 5.08686i) q^{85} +(-13.8150 + 1.79358i) q^{87} +(4.68075 + 3.92762i) q^{89} +(0.345207 + 0.948448i) q^{91} +(1.15173 - 5.15137i) q^{93} +(-2.03206 + 2.59329i) q^{95} +(9.54804 - 1.68358i) q^{97} +(1.22799 - 2.60896i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q - 3 q^{3} - 3 q^{9} - 12 q^{13} - 18 q^{15} + 6 q^{17} + 6 q^{19} - 18 q^{25} + 6 q^{27} - 6 q^{29} - 24 q^{33} + 24 q^{35} - 6 q^{39} + 3 q^{41} + 6 q^{43} - 54 q^{45} - 30 q^{47} + 21 q^{49} - 42 q^{51}+ \cdots + 102 q^{99}+O(q^{100}) $ 18 * q - 3 * q^3 - 3 * q^9 - 12 * q^13 - 18 * q^15 + 6 * q^17 + 6 * q^19 - 18 * q^25 + 6 * q^27 - 6 * q^29 - 24 * q^33 + 24 * q^35 - 6 * q^39 + 3 * q^41 + 6 * q^43 - 54 * q^45 - 30 * q^47 + 21 * q^49 - 42 * q^51 - 60 * q^53 - 30 * q^55 + 12 * q^57 - 3 * q^59 + 54 * q^61 + 18 * q^63 + 24 * q^65 + 15 * q^67 + 30 * q^69 - 36 * q^71 - 42 * q^73 + 6 * q^79 - 3 * q^81 - 36 * q^83 - 60 * q^89 + 18 * q^91 - 66 * q^93 - 6 * q^95 + 9 * q^97 + 102 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/912\mathbb{Z}\right)^\times$.

$n$	$97$	$229$	$305$	$799$
$\chi(n)$	$e\left(\frac{17}{18}\right)$	$1$	$-1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.517874	−	1.65282i	−0.298995	−	0.954255i
$3$	−0.517874	−	1.65282i	−0.298995	−	0.954255i
$4$		0			0
$5$	−0.258510	+	0.710252i	−0.115609	+	0.317634i	−0.983979	−	0.178283i	$-0.942946\pi$
$5$	−0.258510	+	0.710252i	−0.115609	+	0.317634i	0.868370	+	0.495917i	$0.165168\pi$
$6$		0			0
$7$	−0.777943	+	1.34744i	−0.294035	+	0.509283i	−0.974760	−	0.223256i	$-0.928331\pi$
$7$	−0.777943	+	1.34744i	−0.294035	+	0.509283i	0.680725	+	0.732539i	$0.261665\pi$
$8$		0			0
$9$	−2.46361	+	1.71190i	−0.821204	+	0.570634i
$10$		0			0
$11$	−0.832399	+	0.480586i	−0.250978	+	0.144902i	−0.620212	−	0.784434i	$-0.712953\pi$
$11$	−0.832399	+	0.480586i	−0.250978	+	0.144902i	0.369234	+	0.929336i	$0.379620\pi$
$12$		0			0
$13$	0.416982	−	0.496940i	0.115650	−	0.137826i	−0.705113	−	0.709095i	$-0.749104\pi$
$13$	0.416982	−	0.496940i	0.115650	−	0.137826i	0.820763	+	0.571268i	$0.193548\pi$
$14$		0			0
$15$	1.30779	+	0.0594499i	0.337671	+	0.0153499i
$16$		0			0
$17$	6.73013	−	1.18670i	1.63230	−	0.287818i	0.718968	−	0.695043i	$-0.244615\pi$
$17$	6.73013	−	1.18670i	1.63230	−	0.287818i	0.913328	+	0.407226i	$0.133504\pi$
$18$		0			0
$19$	4.14364	+	1.35288i	0.950615	+	0.310371i
$19$	4.14364	+	1.35288i	0.950615	+	0.310371i
$20$		0			0
$21$	2.62994	+	0.587996i	0.573901	+	0.128311i
$22$		0			0
$23$	−0.400647	−	1.10077i	−0.0835407	−	0.229526i	0.890888	−	0.454223i	$-0.150083\pi$
$23$	−0.400647	−	1.10077i	−0.0835407	−	0.229526i	−0.974429	+	0.224697i	$0.927861\pi$
$24$		0			0
$25$	3.39259	+	2.84672i	0.678519	+	0.569345i
$26$		0			0
$27$	4.10530	+	3.18535i	0.790066	+	0.613022i
$28$		0			0
$29$	1.39666	−	7.92086i	0.259354	−	1.47087i	−0.525292	−	0.850922i	$-0.676044\pi$
$29$	1.39666	−	7.92086i	0.259354	−	1.47087i	0.784645	−	0.619945i	$-0.212845\pi$
$30$		0			0
$31$	2.63927	+	1.52379i	0.474028	+	0.273680i	0.717924	−	0.696121i	$-0.245092\pi$
$31$	2.63927	+	1.52379i	0.474028	+	0.273680i	−0.243897	+	0.969801i	$0.578426\pi$
$32$		0			0
$33$	1.22540	+	1.12692i	0.213314	+	0.196172i
$34$		0			0
$35$	−0.755913	−	0.900862i	−0.127773	−	0.152273i
$36$		0			0
$37$		−	4.12648i		−	0.678389i	−0.940716	−	0.339195i	$-0.889846\pi$
$37$		−	4.12648i		−	0.678389i	0.940716	−	0.339195i	$-0.110154\pi$
$38$		0			0
$39$	−1.03729	−	0.431843i	−0.166100	−	0.0691502i
$40$		0			0
$41$	−4.09755	+	3.43825i	−0.639929	+	0.536964i	−0.903996	−	0.427540i	$-0.859380\pi$
$41$	−4.09755	+	3.43825i	−0.639929	+	0.536964i	0.264067	+	0.964504i	$0.414936\pi$
$42$		0			0
$43$	7.34330	+	2.67274i	1.11984	+	0.407589i	0.834595	−	0.550865i	$-0.185702\pi$
$43$	7.34330	+	2.67274i	1.11984	+	0.407589i	0.285248	+	0.958454i	$0.407924\pi$
$44$		0			0
$45$	−0.579012	−	2.19233i	−0.0863139	−	0.326813i
$46$		0			0
$47$	3.11004	+	0.548383i	0.453646	+	0.0799899i	0.395802	−	0.918336i	$-0.370467\pi$
$47$	3.11004	+	0.548383i	0.453646	+	0.0799899i	0.0578432	+	0.998326i	$0.481578\pi$
$48$		0			0
$49$	2.28961	+	3.96572i	0.327087	+	0.566531i
$50$		0			0
$51$	−5.44676	−	10.5091i	−0.762699	−	1.47157i
$52$		0			0
$53$	−13.6276	+	4.96002i	−1.87189	+	0.681312i	−0.905427	+	0.424503i	$0.860449\pi$
$53$	−13.6276	+	4.96002i	−1.87189	+	0.681312i	−0.966462	+	0.256809i	$0.917329\pi$
$54$		0			0
$55$	−0.126153	−	0.715449i	−0.0170105	−	0.0964711i
$56$		0			0
$57$	0.0901766	−	7.54930i	0.0119442	−	0.999929i
$58$		0			0
$59$	−2.02192	−	11.4669i	−0.263231	−	1.49286i	−0.774024	−	0.633156i	$-0.781759\pi$
$59$	−2.02192	−	11.4669i	−0.263231	−	1.49286i	0.510793	−	0.859704i	$-0.329352\pi$
$60$		0			0
$61$	10.1813	−	3.70568i	1.30358	−	0.474464i	0.405419	−	0.914131i	$-0.367126\pi$
$61$	10.1813	−	3.70568i	1.30358	−	0.474464i	0.898161	+	0.439667i	$0.144903\pi$
$62$		0			0
$63$	−0.390129	−	4.65133i	−0.0491517	−	0.586012i
$64$		0			0
$65$	0.245158	+	0.424626i	0.0304081	+	0.0526684i
$66$		0			0
$67$	9.19012	+	1.62047i	1.12275	+	0.197972i	0.704049	−	0.710151i	$-0.251374\pi$
$67$	9.19012	+	1.62047i	1.12275	+	0.197972i	0.418703	+	0.908123i	$0.362485\pi$
$68$		0			0
$69$	−1.61189	+	1.23226i	−0.194048	+	0.148346i
$70$		0			0
$71$	−0.0322101	−	0.0117235i	−0.00382263	−	0.00139132i	0.340108	−	0.940386i	$-0.389536\pi$
$71$	−0.0322101	−	0.0117235i	−0.00382263	−	0.00139132i	−0.343931	+	0.938995i	$0.611759\pi$
$72$		0			0
$73$	−3.04446	+	2.55461i	−0.356327	+	0.298994i	−0.803325	−	0.595541i	$-0.796938\pi$
$73$	−3.04446	+	2.55461i	−0.356327	+	0.298994i	0.446998	+	0.894535i	$0.352493\pi$
$74$		0			0
$75$	2.94818	−	7.08158i	0.340426	−	0.817711i
$76$		0			0
$77$		−	1.49547i		−	0.170425i
$78$		0			0
$79$	0.893115	+	1.06437i	0.100483	+	0.119751i	0.813943	−	0.580945i	$-0.197317\pi$
$79$	0.893115	+	1.06437i	0.100483	+	0.119751i	−0.713459	+	0.700697i	$0.752873\pi$
$80$		0			0
$81$	3.13878	−	8.43493i	0.348753	−	0.937215i
$82$		0			0
$83$	10.4856	+	6.05389i	1.15095	+	0.664500i	0.949118	−	0.314920i	$-0.101978\pi$
$83$	10.4856	+	6.05389i	1.15095	+	0.664500i	0.201830	+	0.979421i	$0.435311\pi$
$84$		0			0
$85$	−0.896950	+	5.08686i	−0.0972879	+	0.551747i
$86$		0			0
$87$	−13.8150	+	1.79358i	−1.48113	+	0.192292i
$88$		0			0
$89$	4.68075	+	3.92762i	0.496159	+	0.416327i	0.856227	−	0.516599i	$-0.172802\pi$
$89$	4.68075	+	3.92762i	0.496159	+	0.416327i	−0.360069	+	0.932926i	$0.617247\pi$
$90$		0			0
$91$	0.345207	+	0.948448i	0.0361875	+	0.0994243i
$92$		0			0
$93$	1.15173	−	5.15137i	0.119429	−	0.534172i
$94$		0			0
$95$	−2.03206	+	2.59329i	−0.208485	+	0.266066i
$96$		0			0
$97$	9.54804	−	1.68358i	0.969457	−	0.170941i	0.333571	−	0.942725i	$-0.391746\pi$
$97$	9.54804	−	1.68358i	0.969457	−	0.170941i	0.635885	+	0.771784i	$0.280635\pi$
$98$		0			0
$99$	1.22799	−	2.60896i	0.123418	−	0.262211i
$100$		0			0
$101$	12.0945	−	14.4137i	1.20345	−	1.43422i	0.332323	−	0.943166i	$-0.392168\pi$
$101$	12.0945	−	14.4137i	1.20345	−	1.43422i	0.871130	−	0.491053i	$-0.163388\pi$
$102$		0			0
$103$	−9.92876	+	5.73237i	−0.978310	+	0.564828i	−0.901759	−	0.432238i	$-0.857724\pi$
$103$	−9.92876	+	5.73237i	−0.978310	+	0.564828i	−0.0765505	+	0.997066i	$0.524391\pi$
$104$		0			0
$105$	−1.09749	+	1.71592i	−0.107104	+	0.167457i
$106$		0			0
$107$	1.17826	−	2.04080i	0.113906	−	0.197292i	−0.803436	−	0.595392i	$-0.796997\pi$
$107$	1.17826	−	2.04080i	0.113906	−	0.197292i	0.917342	+	0.398100i	$0.130330\pi$
$108$		0			0
$109$	−2.21678	+	6.09056i	−0.212329	+	0.583370i	−0.999441	−	0.0334410i	$-0.989353\pi$
$109$	−2.21678	+	6.09056i	−0.212329	+	0.583370i	0.787111	+	0.616811i	$0.211576\pi$
$110$		0			0
$111$	−6.82032	+	2.13700i	−0.647356	+	0.202835i
$112$		0			0
$113$	−10.0387			−0.944358			−0.472179	−	0.881503i	$-0.656532\pi$
$113$	−10.0387			−0.944358			−0.472179	+	0.881503i	$0.656532\pi$
$114$		0			0
$115$	0.885394			0.0825635
$116$		0			0
$117$	−0.176570	+	1.93810i	−0.0163239	+	0.179177i
$118$		0			0
$119$	−3.63665	+	9.99161i	−0.333371	+	0.915929i
$120$		0			0
$121$	−5.03807	+	8.72620i	−0.458007	+	0.793291i
$122$		0			0
$123$	7.80481	+	4.99192i	0.703736	+	0.450106i
$124$		0			0
$125$	−6.17177	+	3.56327i	−0.552020	+	0.318709i
$126$		0			0
$127$	−8.95146	+	10.6679i	−0.794313	+	0.946626i	−0.999485	−	0.0321003i	$-0.989780\pi$
$127$	−8.95146	+	10.6679i	−0.794313	+	0.946626i	0.205171	+	0.978726i	$0.434225\pi$
$128$		0			0
$129$	0.614653	−	13.5213i	0.0541172	−	1.19048i
$130$		0			0
$131$	−10.9610	+	1.93273i	−0.957671	+	0.168863i	−0.630575	−	0.776128i	$-0.717181\pi$
$131$	−10.9610	+	1.93273i	−0.957671	+	0.168863i	−0.327096	+	0.944991i	$0.606070\pi$
$132$		0			0
$133$	−5.04643	+	4.53083i	−0.437581	+	0.392873i
$134$		0			0
$135$	−3.32367	+	2.09235i	−0.286056	+	0.180081i
$136$		0			0
$137$	−1.69757	−	4.66403i	−0.145033	−	0.398475i	0.845812	−	0.533482i	$-0.179117\pi$
$137$	−1.69757	−	4.66403i	−0.145033	−	0.398475i	−0.990845	+	0.135007i	$0.956894\pi$
$138$		0			0
$139$	2.76202	+	2.31761i	0.234272	+	0.196577i	0.752364	−	0.658747i	$-0.228913\pi$
$139$	2.76202	+	2.31761i	0.234272	+	0.196577i	−0.518093	+	0.855325i	$0.673358\pi$
$140$		0			0
$141$	−0.704229	−	5.42432i	−0.0593068	−	0.456810i
$142$		0			0
$143$	−0.108273	+	0.614047i	−0.00905425	+	0.0513492i
$144$		0			0
$145$	5.26475	+	3.03961i	0.437214	+	0.252426i
$146$		0			0
$147$	5.36888	−	5.83805i	0.442818	−	0.481514i
$148$		0			0
$149$	12.3170	+	14.6788i	1.00904	+	1.20253i	0.979183	+	0.202978i	$0.0650620\pi$
$149$	12.3170	+	14.6788i	1.00904	+	1.20253i	0.0298610	+	0.999554i	$0.490494\pi$
$150$		0			0
$151$		−	19.2624i		−	1.56755i	−0.621042	−	0.783777i	$-0.713290\pi$
$151$		−	19.2624i		−	1.56755i	0.621042	−	0.783777i	$-0.286710\pi$
$152$		0			0
$153$	−14.5489	+	14.4449i	−1.17621	+	1.16780i
$154$		0			0
$155$	−1.76455	+	1.48063i	−0.141732	+	0.118927i
$156$		0			0
$157$	−0.200940	−	0.0731363i	−0.0160368	−	0.00583691i	0.333989	−	0.942577i	$-0.391605\pi$
$157$	−0.200940	−	0.0731363i	−0.0160368	−	0.00583691i	−0.350026	+	0.936740i	$0.613827\pi$
$158$		0			0
$159$	15.2554	+	19.9552i	1.20983	+	1.58255i
$160$		0			0
$161$	1.79490	+	0.316489i	0.141458	+	0.0249428i
$162$		0			0
$163$	−7.51668	−	13.0193i	−0.588752	−	1.01975i	−0.994396	−	0.105717i	$-0.966286\pi$
$163$	−7.51668	−	13.0193i	−0.588752	−	1.01975i	0.405645	−	0.914031i	$-0.367047\pi$
$164$		0			0
$165$	−1.11718	+	0.579020i	−0.0869720	+	0.0450767i
$166$		0			0
$167$	8.87982	−	3.23199i	0.687141	−	0.250099i	0.0252305	−	0.999682i	$-0.491968\pi$
$167$	8.87982	−	3.23199i	0.687141	−	0.250099i	0.661911	+	0.749583i	$0.269746\pi$
$168$		0			0
$169$	2.18435	+	12.3881i	0.168027	+	0.952929i
$170$		0			0
$171$	−12.5243	+	3.76054i	−0.957758	+	0.287575i
$172$		0			0
$173$	2.33529	+	13.2441i	0.177549	+	1.00693i	0.935161	+	0.354224i	$0.115255\pi$
$173$	2.33529	+	13.2441i	0.177549	+	1.00693i	−0.757612	+	0.652705i	$0.773634\pi$
$174$		0			0
$175$	−6.47502	+	2.35672i	−0.489466	+	0.178151i
$176$		0			0
$177$	−17.9056	+	9.28026i	−1.34586	+	0.697547i
$178$		0			0
$179$	−8.34644	−	14.4565i	−0.623842	−	1.08053i	−0.988764	−	0.149488i	$-0.952237\pi$
$179$	−8.34644	−	14.4565i	−0.623842	−	1.08053i	0.364921	−	0.931038i	$-0.381096\pi$
$180$		0			0
$181$	−10.0398	−	1.77029i	−0.746251	−	0.131584i	−0.212424	−	0.977178i	$-0.568136\pi$
$181$	−10.0398	−	1.77029i	−0.746251	−	0.131584i	−0.533828	+	0.845593i	$0.679247\pi$
$182$		0			0
$183$	−11.3974	−	14.9087i	−0.842523	−	1.10209i
$184$		0			0
$185$	2.93084	+	1.06674i	0.215480	+	0.0784281i
$186$		0			0
$187$	−5.03184	+	4.22221i	−0.367964	+	0.308759i
$188$		0			0
$189$	−7.48576	+	3.05361i	−0.544509	+	0.222118i
$190$		0			0
$191$			12.0667i			0.873115i	0.899676	+	0.436558i	$0.143802\pi$
$191$			12.0667i			0.873115i	−0.899676	+	0.436558i	$0.856198\pi$
$192$		0			0
$193$	−2.14990	−	2.56215i	−0.154753	−	0.184427i	0.683098	−	0.730327i	$-0.260632\pi$
$193$	−2.14990	−	2.56215i	−0.154753	−	0.184427i	−0.837850	+	0.545900i	$0.816188\pi$
$194$		0			0
$195$	0.574869	−	0.625104i	0.0411672	−	0.0447647i
$196$		0			0
$197$	5.15098	+	2.97392i	0.366992	+	0.211883i	0.672144	−	0.740421i	$-0.265374\pi$
$197$	5.15098	+	2.97392i	0.366992	+	0.211883i	−0.305151	+	0.952304i	$0.598707\pi$
$198$		0			0
$199$	−1.94088	+	11.0073i	−0.137585	+	0.780286i	0.835439	+	0.549583i	$0.185214\pi$
$199$	−1.94088	+	11.0073i	−0.137585	+	0.780286i	−0.973024	+	0.230703i	$0.925898\pi$
$200$		0			0
$201$	−2.08099	−	16.0288i	−0.146782	−	1.13058i
$202$		0			0
$203$	9.58634	+	8.04389i	0.672829	+	0.564571i
$204$		0			0
$205$	−1.38276	−	3.79911i	−0.0965764	−	0.265342i
$206$		0			0
$207$	2.87145	+	2.02600i	0.199579	+	0.140817i
$208$		0			0
$209$	−4.09933	+	0.865240i	−0.283557	+	0.0598499i
$210$		0			0
$211$	20.9377	−	3.69188i	1.44141	−	0.254159i	0.602364	−	0.798222i	$-0.294226\pi$
$211$	20.9377	−	3.69188i	1.44141	−	0.254159i	0.839045	+	0.544063i	$0.183115\pi$
$212$		0			0
$213$	−0.00269607	+	0.0593087i	−0.000184731	+	0.00406376i
$214$		0			0
$215$	−3.79664	+	4.52466i	−0.258928	+	0.308579i
$216$		0			0
$217$	−4.10641	+	2.37084i	−0.278761	+	0.160943i
$218$		0			0
$219$	5.79895	+	3.70898i	0.391856	+	0.250629i
$220$		0			0
$221$	2.21662	−	3.83930i	0.149106	−	0.258259i
$222$		0			0
$223$	−4.71184	+	12.9457i	−0.315528	+	0.866907i	0.675987	+	0.736914i	$0.263718\pi$
$223$	−4.71184	+	12.9457i	−0.315528	+	0.866907i	−0.991515	+	0.129993i	$0.958505\pi$
$224$		0			0
$225$	−13.2313	−	1.20544i	−0.882090	−	0.0803625i
$226$		0			0
$227$	−16.1886			−1.07448			−0.537238	−	0.843430i	$-0.680532\pi$
$227$	−16.1886			−1.07448			−0.537238	+	0.843430i	$0.680532\pi$
$228$		0			0
$229$	−25.6462			−1.69475			−0.847374	−	0.530997i	$-0.821817\pi$
$229$	−25.6462			−1.69475			−0.847374	+	0.530997i	$0.821817\pi$
$230$		0			0
$231$	−2.47174	+	0.774466i	−0.162629	+	0.0509561i
$232$		0			0
$233$	3.98107	−	10.9379i	0.260808	−	0.716565i	−0.738305	−	0.674467i	$-0.764374\pi$
$233$	3.98107	−	10.9379i	0.260808	−	0.716565i	0.999113	−	0.0420981i	$-0.0134042\pi$
$234$		0			0
$235$	−1.19347	+	2.06715i	−0.0778532	+	0.134846i
$236$		0			0
$237$	1.29669	−	2.02737i	0.0842293	−	0.131692i
$238$		0			0
$239$	13.1831	−	7.61128i	0.852746	−	0.492333i	−0.00883069	−	0.999961i	$-0.502811\pi$
$239$	13.1831	−	7.61128i	0.852746	−	0.492333i	0.861576	+	0.507628i	$0.169478\pi$
$240$		0			0
$241$	9.76016	−	11.6317i	0.628707	−	0.749264i	−0.353834	−	0.935308i	$-0.615122\pi$
$241$	9.76016	−	11.6317i	0.628707	−	0.749264i	0.982541	+	0.186044i	$0.0595666\pi$
$242$		0			0
$243$	−15.5669	−	0.819603i	−0.998617	−	0.0525776i
$244$		0			0
$245$	−3.40855	+	0.601019i	−0.217764	+	0.0383977i
$246$		0			0
$247$	2.40012	−	1.49501i	0.152716	−	0.0951254i
$248$		0			0
$249$	4.57573	−	20.4660i	0.289975	−	1.29698i
$250$		0			0
$251$	3.71032	+	10.1940i	0.234193	+	0.643441i	1.00000		0.000369965i	$0.000117763\pi$
$251$	3.71032	+	10.1940i	0.234193	+	0.643441i	−0.765807	+	0.643071i	$0.777660\pi$
$252$		0			0
$253$	0.862512	+	0.723733i	0.0542257	+	0.0455007i
$254$		0			0
$255$	8.87216	−	1.15186i	0.555596	−	0.0721320i
$256$		0			0
$257$	−0.00786014	+	0.0445771i	−0.000490302	+	0.00278064i	−0.985052	−	0.172258i	$-0.944894\pi$
$257$	−0.00786014	+	0.0445771i	−0.000490302	+	0.00278064i	0.984562	+	0.175038i	$0.0560049\pi$
$258$		0			0
$259$	5.56017	+	3.21017i	0.345492	+	0.199470i
$260$		0			0
$261$	10.1189	+	21.9049i	0.626345	+	1.35588i
$262$		0			0
$263$	3.52577	+	4.20185i	0.217408	+	0.259097i	0.863715	−	0.503981i	$-0.168132\pi$
$263$	3.52577	+	4.20185i	0.217408	+	0.259097i	−0.646307	+	0.763078i	$0.723687\pi$
$264$		0			0
$265$		−	10.9612i		−	0.673342i
$266$		0			0
$267$	4.06760	−	9.77044i	0.248933	−	0.597941i
$268$		0			0
$269$	1.50432	−	1.26228i	0.0917202	−	0.0769623i	−0.595775	−	0.803152i	$-0.703155\pi$
$269$	1.50432	−	1.26228i	0.0917202	−	0.0769623i	0.687495	+	0.726189i	$0.258710\pi$
$270$		0			0
$271$	−19.8494	−	7.22458i	−1.20576	−	0.438862i	−0.340531	−	0.940233i	$-0.610607\pi$
$271$	−19.8494	−	7.22458i	−1.20576	−	0.438862i	−0.865232	+	0.501371i	$0.832829\pi$
$272$		0			0
$273$	1.38884	−	1.06174i	0.0840563	−	0.0642594i
$274$		0			0
$275$	−4.19208	−	0.739177i	−0.252792	−	0.0445741i
$276$		0			0
$277$	−3.91899	−	6.78789i	−0.235469	−	0.407845i	0.723940	−	0.689863i	$-0.242329\pi$
$277$	−3.91899	−	6.78789i	−0.235469	−	0.407845i	−0.959409	+	0.282018i	$0.908996\pi$
$278$		0			0
$279$	−9.11072	+	0.764161i	−0.545445	+	0.0457491i
$280$		0			0
$281$	−11.0064	+	4.00600i	−0.656587	+	0.238978i	−0.648762	−	0.760991i	$-0.724713\pi$
$281$	−11.0064	+	4.00600i	−0.656587	+	0.238978i	−0.00782495	+	0.999969i	$0.502491\pi$
$282$		0			0
$283$	−1.21905	−	6.91356i	−0.0724648	−	0.410968i	−0.999364	−	0.0356581i	$-0.988647\pi$
$283$	−1.21905	−	6.91356i	−0.0724648	−	0.410968i	0.926899	−	0.375310i	$-0.122464\pi$
$284$		0			0
$285$	5.33859	+	2.01562i	0.316231	+	0.119395i
$286$		0			0
$287$	−1.44517	−	8.19595i	−0.0853055	−	0.483791i
$288$		0			0
$289$	27.9116	−	10.1590i	1.64186	−	0.597587i
$290$		0			0
$291$	−7.72733	−	14.9093i	−0.452984	−	0.873998i
$292$		0			0
$293$	−1.29095	−	2.23599i	−0.0754180	−	0.130628i	0.825850	−	0.563890i	$-0.190696\pi$
$293$	−1.29095	−	2.23599i	−0.0754180	−	0.130628i	−0.901268	+	0.433262i	$0.857362\pi$
$294$		0			0
$295$	8.66705	+	1.52824i	0.504615	+	0.0889773i
$296$		0			0
$297$	−4.94808	−	0.678535i	−0.287117	−	0.0393726i
$298$		0			0
$299$	−0.714078	−	0.259903i	−0.0412962	−	0.0150306i
$300$		0			0
$301$	−9.31401	+	7.81539i	−0.536851	+	0.450471i
$302$		0			0
$303$	−30.0867	−	12.5256i	−1.72844	−	0.719577i
$304$		0			0
$305$			8.18923i			0.468914i
$306$		0			0
$307$	1.26629	+	1.50910i	0.0722709	+	0.0861290i	0.800968	−	0.598707i	$-0.204318\pi$
$307$	1.26629	+	1.50910i	0.0722709	+	0.0861290i	−0.728698	+	0.684836i	$0.759874\pi$
$308$		0			0
$309$	14.6164	+	13.4418i	0.831499	+	0.764677i
$310$		0			0
$311$	−22.4909	−	12.9851i	−1.27534	−	0.736320i	−0.299355	−	0.954142i	$-0.596771\pi$
$311$	−22.4909	−	12.9851i	−1.27534	−	0.736320i	−0.975989	+	0.217822i	$0.930105\pi$
$312$		0			0
$313$	−2.32842	+	13.2051i	−0.131610	+	0.746398i	0.845551	+	0.533895i	$0.179272\pi$
$313$	−2.32842	+	13.2051i	−0.131610	+	0.746398i	−0.977161	+	0.212502i	$0.931839\pi$
$314$		0			0
$315$	3.40446	+	0.925326i	0.191820	+	0.0521362i
$316$		0			0
$317$	−23.3056	−	19.5557i	−1.30897	−	1.09836i	−0.988519	−	0.151095i	$-0.951720\pi$
$317$	−23.3056	−	19.5557i	−1.30897	−	1.09836i	−0.320454	−	0.947264i	$-0.603835\pi$
$318$		0			0
$319$	2.64407	+	7.26453i	0.148040	+	0.406736i
$320$		0			0
$321$	−3.98326	−	0.890567i	−0.222324	−	0.0497066i
$322$		0			0
$323$	29.4927	+	4.18776i	1.64102	+	0.233013i
$324$		0			0
$325$	2.82930	−	0.498882i	0.156941	−	0.0276730i
$326$		0			0
$327$	11.2146	+	0.509796i	0.620169	+	0.0281918i
$328$		0			0
$329$	−3.15834	+	3.76397i	−0.174125	+	0.207514i
$330$		0			0
$331$	9.22014	−	5.32325i	0.506785	−	0.292592i	−0.224726	−	0.974422i	$-0.572149\pi$
$331$	9.22014	−	5.32325i	0.506785	−	0.292592i	0.731511	+	0.681830i	$0.238815\pi$
$332$		0			0
$333$	7.06413	+	10.1660i	0.387112	+	0.557096i
$334$		0			0
$335$	−3.52668	+	6.10839i	−0.192683	+	0.333737i
$336$		0			0
$337$	−2.38138	+	6.54278i	−0.129722	+	0.356408i	−0.987501	−	0.157610i	$-0.949621\pi$
$337$	−2.38138	+	6.54278i	−0.129722	+	0.356408i	0.857780	+	0.514018i	$0.171843\pi$
$338$		0			0
$339$	5.19876	+	16.5921i	0.282358	+	0.901158i
$340$		0			0
$341$	−2.92924			−0.158627
$342$		0			0
$343$	−18.0159			−0.972770
$344$		0			0
$345$	−0.458523	−	1.46340i	−0.0246860	−	0.0787866i
$346$		0			0
$347$	9.63081	−	26.4604i	0.517009	−	1.42047i	−0.356790	−	0.934185i	$-0.616129\pi$
$347$	9.63081	−	26.4604i	0.517009	−	1.42047i	0.873799	−	0.486287i	$-0.161649\pi$
$348$		0			0
$349$	9.79155	−	16.9595i	0.524130	−	0.907819i	−0.475476	−	0.879729i	$-0.657724\pi$
$349$	9.79155	−	16.9595i	0.524130	−	0.907819i	0.999605	−	0.0280904i	$-0.00894261\pi$
$350$		0			0
$351$	3.29477	−	0.711853i	0.175862	−	0.0379959i
$352$		0			0
$353$	−3.55050	+	2.04988i	−0.188974	+	0.109104i	−0.591502	−	0.806303i	$-0.701465\pi$
$353$	−3.55050	+	2.04988i	−0.188974	+	0.109104i	0.402528	+	0.915408i	$0.368132\pi$
$354$		0			0
$355$	0.0166533	−	0.0198466i	0.000883864	−	0.00105335i
$356$		0			0
$357$	18.3976	+	0.836324i	0.973706	+	0.0442629i
$358$		0			0
$359$	5.52450	−	0.974118i	0.291572	−	0.0514120i	−0.0259490	−	0.999663i	$-0.508261\pi$
$359$	5.52450	−	0.974118i	0.291572	−	0.0514120i	0.317521	+	0.948251i	$0.397150\pi$
$360$		0			0
$361$	15.3395	+	11.2117i	0.807340	+	0.590087i
$362$		0			0
$363$	17.0319	+	3.80795i	0.893943	+	0.199865i
$364$		0			0
$365$	−1.02739	−	2.82273i	−0.0537760	−	0.147748i
$366$		0			0
$367$	2.28539	+	1.91767i	0.119296	+	0.100101i	0.700484	−	0.713668i	$-0.252967\pi$
$367$	2.28539	+	1.91767i	0.119296	+	0.100101i	−0.581188	+	0.813769i	$0.697412\pi$
$368$		0			0
$369$	4.20882	−	15.4851i	0.219103	−	0.806123i
$370$		0			0
$371$	3.91814	−	22.2209i	0.203420	−	1.15365i
$372$		0			0
$373$	−18.2415	−	10.5317i	−0.944510	−	0.545313i	−0.0531391	−	0.998587i	$-0.516923\pi$
$373$	−18.2415	−	10.5317i	−0.944510	−	0.545313i	−0.891371	+	0.453274i	$0.850256\pi$
$374$		0			0
$375$	9.08564	+	8.35548i	0.469180	+	0.431475i
$376$		0			0
$377$	−3.35381	−	3.99691i	−0.172730	−	0.205852i
$378$		0			0
$379$		−	9.54057i		−	0.490066i	−0.969515	−	0.245033i	$-0.921201\pi$
$379$		−	9.54057i		−	0.490066i	0.969515	−	0.245033i	$-0.0787988\pi$
$380$		0			0
$381$	22.2679	+	9.27048i	1.14082	+	0.474941i
$382$		0			0
$383$	−5.96084	+	5.00173i	−0.304584	+	0.255577i	−0.782249	−	0.622965i	$-0.785928\pi$
$383$	−5.96084	+	5.00173i	−0.304584	+	0.255577i	0.477665	+	0.878542i	$0.341483\pi$
$384$		0			0
$385$	1.06216	+	0.386595i	0.0541328	+	0.0197027i
$386$		0			0
$387$	−22.6665	+	5.98640i	−1.15220	+	0.304306i
$388$		0			0
$389$	9.63724	+	1.69931i	0.488627	+	0.0861582i	0.412533	−	0.910942i	$-0.364644\pi$
$389$	9.63724	+	1.69931i	0.488627	+	0.0861582i	0.0760939	+	0.997101i	$0.475755\pi$
$390$		0			0
$391$	−4.00269	−	6.93287i	−0.202425	−	0.350610i
$392$		0			0
$393$	8.87089	+	17.1157i	0.447477	+	0.863373i
$394$		0			0
$395$	−0.986853	+	0.359185i	−0.0496539	+	0.0180726i
$396$		0			0
$397$	−2.05329	−	11.6448i	−0.103052	−	0.584435i	−0.991981	−	0.126390i	$-0.959661\pi$
$397$	−2.05329	−	11.6448i	−0.103052	−	0.584435i	0.888929	−	0.458045i	$-0.151450\pi$
$398$		0			0
$399$	10.1020	+	5.99443i	0.505735	+	0.300097i
$400$		0			0
$401$	−3.59086	−	20.3648i	−0.179319	−	1.01697i	−0.933039	−	0.359774i	$-0.882854\pi$
$401$	−3.59086	−	20.3648i	−0.179319	−	1.01697i	0.753720	−	0.657195i	$-0.228257\pi$
$402$		0			0
$403$	1.85776	−	0.676169i	0.0925416	−	0.0336824i
$404$		0			0
$405$	5.17952	+	4.40984i	0.257372	+	0.219127i
$406$		0			0
$407$	1.98313	+	3.43488i	0.0982999	+	0.170260i
$408$		0			0
$409$	3.39761	+	0.599090i	0.168001	+	0.0296231i	0.257016	−	0.966407i	$-0.417261\pi$
$409$	3.39761	+	0.599090i	0.168001	+	0.0296231i	−0.0890148	+	0.996030i	$0.528372\pi$
$410$		0			0
$411$	−6.82966	+	5.22115i	−0.336882	+	0.257540i
$412$		0			0
$413$	17.0238	+	6.19617i	0.837688	+	0.304893i
$414$		0			0
$415$	−7.01043	+	5.88245i	−0.344128	+	0.288758i
$416$		0			0
$417$	2.40021	−	5.76535i	0.117539	−	0.282331i
$418$		0			0
$419$			25.3156i			1.23675i	0.785884	+	0.618374i	$0.212208\pi$
$419$			25.3156i			1.23675i	−0.785884	+	0.618374i	$0.787792\pi$
$420$		0			0
$421$	20.4536	+	24.3756i	0.996845	+	1.18799i	0.982150	+	0.188102i	$0.0602334\pi$
$421$	20.4536	+	24.3756i	0.996845	+	1.18799i	0.0146955	+	0.999892i	$0.495322\pi$
$422$		0			0
$423$	−8.60071	+	3.97307i	−0.418181	+	0.193178i
$424$		0			0
$425$	26.2108	+	15.1328i	1.27141	+	0.734049i
$426$		0			0
$427$	−2.92728	+	16.6014i	−0.141661	+	0.803400i
$428$		0			0
$429$	1.07098	−	0.139043i	0.0517074	−	0.00671308i
$430$		0			0
$431$	25.2345	+	21.1742i	1.21550	+	1.01993i	0.999048	+	0.0436350i	$0.0138938\pi$
$431$	25.2345	+	21.1742i	1.21550	+	1.01993i	0.216455	+	0.976293i	$0.430551\pi$
$432$		0			0
$433$	−5.46188	−	15.0064i	−0.262481	−	0.721161i	−0.998999	−	0.0447423i	$-0.985753\pi$
$433$	−5.46188	−	15.0064i	−0.262481	−	0.721161i	0.736517	−	0.676419i	$-0.236469\pi$
$434$		0			0
$435$	2.29744	−	10.2758i	0.110154	−	0.492688i
$436$		0			0
$437$	−0.170932	−	5.10321i	−0.00817679	−	0.244120i
$438$		0			0
$439$	30.5401	−	5.38505i	1.45760	−	0.257014i	0.612011	−	0.790849i	$-0.290361\pi$
$439$	30.5401	−	5.38505i	1.45760	−	0.257014i	0.845589	+	0.533835i	$0.179250\pi$
$440$		0			0
$441$	−12.4296	−	5.85041i	−0.591887	−	0.278591i
$442$		0			0
$443$	−12.5287	+	14.9311i	−0.595257	+	0.709400i	−0.976607	−	0.215031i	$-0.931015\pi$
$443$	−12.5287	+	14.9311i	−0.595257	+	0.709400i	0.381350	+	0.924431i	$0.375459\pi$
$444$		0			0
$445$	−3.99962	+	2.30918i	−0.189600	+	0.109466i
$446$		0			0
$447$	17.8827	−	27.9594i	0.845823	−	1.32244i
$448$		0			0
$449$	6.61607	−	11.4594i	0.312232	−	0.540801i	−0.666613	−	0.745404i	$-0.732257\pi$
$449$	6.61607	−	11.4594i	0.312232	−	0.540801i	0.978845	+	0.204602i	$0.0655901\pi$
$450$		0			0
$451$	1.75842	−	4.83122i	0.0828007	−	0.227493i
$452$		0			0
$453$	−31.8373	+	9.97551i	−1.49585	+	0.468690i
$454$		0			0
$455$	−0.762876			−0.0357642
$456$		0			0
$457$	−15.4038			−0.720559			−0.360279	−	0.932844i	$-0.617319\pi$
$457$	−15.4038			−0.720559			−0.360279	+	0.932844i	$0.617319\pi$
$458$		0			0
$459$	31.4093	+	16.5661i	1.46606	+	0.773238i
$460$		0			0
$461$	−5.65076	+	15.5253i	−0.263182	+	0.723087i	0.735766	+	0.677236i	$0.236822\pi$
$461$	−5.65076	+	15.5253i	−0.263182	+	0.723087i	−0.998948	+	0.0458511i	$0.985400\pi$
$462$		0			0
$463$	4.69170	−	8.12625i	0.218042	−	0.377659i	−0.736168	−	0.676799i	$-0.763366\pi$
$463$	4.69170	−	8.12625i	0.218042	−	0.377659i	0.954209	+	0.299140i	$0.0966998\pi$
$464$		0			0
$465$	3.36103	+	2.14970i	0.155864	+	0.0996899i
$466$		0			0
$467$	−18.5458	+	10.7074i	−0.858196	+	0.495480i	−0.863408	−	0.504507i	$-0.831674\pi$
$467$	−18.5458	+	10.7074i	−0.858196	+	0.495480i	0.00521153	+	0.999986i	$0.498341\pi$
$468$		0			0
$469$	−9.33287	+	11.1225i	−0.430952	+	0.513588i
$470$		0			0
$471$	−0.0168192	+	0.369993i	−0.000774989	+	0.0170484i
$472$		0			0
$473$	−7.39703	+	1.30430i	−0.340116	+	0.0599716i
$474$		0			0
$475$	10.2064	+	16.3855i	0.468302	+	0.751820i
$476$		0			0
$477$	25.0820	−	35.5486i	1.14842	−	1.62766i
$478$		0			0
$479$	−11.4165	−	31.3665i	−0.521632	−	1.43317i	−0.868703	−	0.495333i	$-0.835046\pi$
$479$	−11.4165	−	31.3665i	−0.521632	−	1.43317i	0.347071	−	0.937839i	$-0.387176\pi$
$480$		0			0
$481$	−2.05061	−	1.72067i	−0.0934998	−	0.0784557i
$482$		0			0
$483$	−0.406432	−	3.13054i	−0.0184933	−	0.142444i
$484$		0			0
$485$	−1.27250	+	7.21673i	−0.0577815	+	0.327695i
$486$		0			0
$487$	28.9750	+	16.7288i	1.31298	+	0.758052i	0.982589	−	0.185791i	$-0.0594846\pi$
$487$	28.9750	+	16.7288i	1.31298	+	0.758052i	0.330395	+	0.943843i	$0.392818\pi$
$488$		0			0
$489$	−17.6258	+	19.1660i	−0.797066	+	0.866718i
$490$		0			0
$491$	−0.635055	−	0.756829i	−0.0286596	−	0.0341552i	0.751524	−	0.659705i	$-0.229319\pi$
$491$	−0.635055	−	0.756829i	−0.0286596	−	0.0341552i	−0.780184	+	0.625550i	$0.784875\pi$
$492$		0			0
$493$		−	54.9658i		−	2.47554i
$494$		0			0
$495$	1.53557	+	1.54663i	0.0690188	+	0.0695158i
$496$		0			0
$497$	0.0408543	−	0.0342808i	0.00183256	−	0.00153770i
$498$		0			0
$499$	4.11402	+	1.49738i	0.184169	+	0.0670319i	0.432458	−	0.901654i	$-0.357646\pi$
$499$	4.11402	+	1.49738i	0.184169	+	0.0670319i	−0.248290	+	0.968686i	$0.579868\pi$
$500$		0			0
$501$	−9.94052	−	13.0030i	−0.444110	−	0.580930i
$502$		0			0
$503$	−31.7905	−	5.60552i	−1.41747	−	0.249938i	−0.588167	−	0.808740i	$-0.700150\pi$
$503$	−31.7905	−	5.60552i	−1.41747	−	0.249938i	−0.829301	+	0.558802i	$0.811261\pi$
$504$		0			0
$505$	7.11080	+	12.3163i	0.316426	+	0.548067i
$506$		0			0
$507$	19.3440	−	10.0258i	0.859097	−	0.445261i
$508$		0			0
$509$	21.2608	−	7.73831i	0.942370	−	0.342994i	0.175268	−	0.984521i	$-0.443921\pi$
$509$	21.2608	−	7.73831i	0.942370	−	0.342994i	0.767101	+	0.641526i	$0.221698\pi$
$510$		0			0
$511$	−1.07375	−	6.08956i	−0.0475000	−	0.269386i
$512$		0			0
$513$	12.7015	+	18.7529i	0.560785	+	0.827962i
$514$		0			0
$515$	−1.50474	−	8.53380i	−0.0663067	−	0.376044i
$516$		0			0
$517$	−2.85234	+	1.03817i	−0.125446	+	0.0456585i
$518$		0			0
$519$	20.6807	−	10.7186i	0.907781	−	0.470493i
$520$		0			0
$521$	4.86213	+	8.42145i	0.213014	+	0.368950i	0.952656	−	0.304049i	$-0.0983388\pi$
$521$	4.86213	+	8.42145i	0.213014	+	0.368950i	−0.739643	+	0.673000i	$0.765005\pi$
$522$		0			0
$523$	−33.5671	−	5.91879i	−1.46779	−	0.258810i	−0.618101	−	0.786099i	$-0.712098\pi$
$523$	−33.5671	−	5.91879i	−1.46779	−	0.258810i	−0.849686	+	0.527288i	$0.823209\pi$
$524$		0			0
$525$	7.24847	+	9.48155i	0.316349	+	0.413809i
$526$		0			0
$527$	19.5709	+	7.12324i	0.852523	+	0.310293i
$528$		0			0
$529$	16.5678	−	13.9021i	0.720341	−	0.604438i
$530$		0			0
$531$	24.6114	+	24.7886i	1.06804	+	1.07573i
$532$		0			0
$533$			3.46992i			0.150299i
$534$		0			0
$535$	1.14489	+	1.36443i	0.0494980	+	0.0589894i
$536$		0			0
$537$	−19.5715	+	21.2818i	−0.844572	+	0.918376i
$538$		0			0
$539$	−3.81174	−	2.20071i	−0.164183	−	0.0947911i
$540$		0			0
$541$	0.180608	−	1.02428i	0.00776495	−	0.0440372i	−0.980679	−	0.195623i	$-0.937327\pi$
$541$	0.180608	−	1.02428i	0.00776495	−	0.0440372i	0.988444	+	0.151586i	$0.0484381\pi$
$542$		0			0
$543$	2.27338	+	17.5107i	0.0975603	+	0.751457i
$544$		0			0
$545$	−3.75277	−	3.14895i	−0.160751	−	0.134886i
$546$		0			0
$547$	−8.86889	−	24.3671i	−0.379207	−	1.04186i	−0.971686	−	0.236276i	$-0.924073\pi$
$547$	−8.86889	−	24.3671i	−0.379207	−	1.04186i	0.592480	−	0.805586i	$-0.298149\pi$
$548$		0			0
$549$	−18.7390	+	26.5587i	−0.799760	+	1.13350i
$550$		0			0
$551$	16.5032	−	30.9317i	0.703060	−	1.31773i
$552$		0			0
$553$	−2.12897	+	0.375395i	−0.0905330	+	0.0159634i
$554$		0			0
$555$	0.245319	−	5.39658i	0.0104132	−	0.229072i
$556$		0			0
$557$	−2.42914	+	2.89494i	−0.102926	+	0.122662i	−0.815048	−	0.579393i	$-0.803290\pi$
$557$	−2.42914	+	2.89494i	−0.102926	+	0.122662i	0.712122	+	0.702055i	$0.247734\pi$
$558$		0			0
$559$	4.39021	−	2.53469i	0.185686	−	0.107206i
$560$		0			0
$561$	9.58440	+	6.13013i	0.404654	+	0.258814i
$562$		0			0
$563$	−5.99208	+	10.3786i	−0.252536	+	0.437406i	−0.964223	−	0.265091i	$-0.914598\pi$
$563$	−5.99208	+	10.3786i	−0.252536	+	0.437406i	0.711687	+	0.702496i	$0.247931\pi$
$564$		0			0
$565$	2.59510	−	7.12998i	0.109177	−	0.299960i
$566$		0			0
$567$	8.92374	+	10.7912i	0.374762	+	0.453188i
$568$		0			0
$569$	11.2148			0.470147			0.235074	−	0.971978i	$-0.424467\pi$
$569$	11.2148			0.470147			0.235074	+	0.971978i	$0.424467\pi$
$570$		0			0
$571$	−16.2525			−0.680144			−0.340072	−	0.940399i	$-0.610452\pi$
$571$	−16.2525			−0.680144			−0.340072	+	0.940399i	$0.610452\pi$
$572$		0			0
$573$	19.9440	−	6.24902i	0.833174	−	0.261057i
$574$		0			0
$575$	1.77435	−	4.87499i	0.0739956	−	0.203301i
$576$		0			0
$577$	−4.02000	+	6.96284i	−0.167355	+	0.289867i	−0.937489	−	0.348015i	$-0.886856\pi$
$577$	−4.02000	+	6.96284i	−0.167355	+	0.289867i	0.770134	+	0.637882i	$0.220189\pi$
$578$		0			0
$579$	−3.12138	+	4.88025i	−0.129720	+	0.202816i
$580$		0			0
$581$	−16.3145	+	9.41916i	−0.676838	+	0.390772i
$582$		0			0
$583$	8.95984	−	10.6779i	0.371079	−	0.442234i
$584$		0			0
$585$	−1.33089	−	0.626428i	−0.0550257	−	0.0258996i
$586$		0			0
$587$	19.5628	−	3.44945i	0.807444	−	0.142374i	0.245336	−	0.969438i	$-0.421102\pi$
$587$	19.5628	−	3.44945i	0.807444	−	0.142374i	0.562108	+	0.827064i	$0.309991\pi$
$588$		0			0
$589$	8.87470	+	9.88463i	0.365676	+	0.407289i
$590$		0			0
$591$	2.24779	−	10.0537i	0.0924617	−	0.413556i
$592$		0			0
$593$	−7.64203	−	20.9963i	−0.313821	−	0.862215i	−0.991876	−	0.127205i	$-0.959399\pi$
$593$	−7.64203	−	20.9963i	−0.313821	−	0.862215i	0.678056	−	0.735010i	$-0.262823\pi$
$594$		0			0
$595$	−6.15644	−	5.16587i	−0.252390	−	0.211780i
$596$		0			0
$597$	19.1982	−	2.49246i	0.785729	−	0.102010i
$598$		0			0
$599$	−2.89198	+	16.4012i	−0.118163	+	0.670136i	0.866972	+	0.498356i	$0.166063\pi$
$599$	−2.89198	+	16.4012i	−0.118163	+	0.670136i	−0.985135	+	0.171780i	$0.945048\pi$
$600$		0			0
$601$	17.9204	+	10.3464i	0.730990	+	0.422037i	0.818784	−	0.574101i	$-0.194648\pi$
$601$	17.9204	+	10.3464i	0.730990	+	0.422037i	−0.0877940	+	0.996139i	$0.527982\pi$
$602$		0			0
$603$	−25.4150	+	11.7404i	−1.03498	+	0.478106i
$604$		0			0
$605$	−4.89540	−	5.83411i	−0.199026	−	0.237191i
$606$		0			0
$607$		−	39.3916i		−	1.59886i	−0.600761	−	0.799428i	$-0.705136\pi$
$607$		−	39.3916i		−	1.59886i	0.600761	−	0.799428i	$-0.294864\pi$
$608$		0			0
$609$	8.33058	−	20.0102i	0.337572	−	0.810854i
$610$		0			0
$611$	1.56934	−	1.31683i	0.0634888	−	0.0532734i
$612$		0			0
$613$	−26.4005	−	9.60900i	−1.06631	−	0.388104i	−0.251512	−	0.967854i	$-0.580928\pi$
$613$	−26.4005	−	9.60900i	−1.06631	−	0.388104i	−0.814794	+	0.579750i	$0.803150\pi$
$614$		0			0
$615$	−5.56314	+	4.25292i	−0.224328	+	0.171494i
$616$		0			0
$617$	20.3648	+	3.59086i	0.819854	+	0.144562i	0.567817	−	0.823155i	$-0.307788\pi$
$617$	20.3648	+	3.59086i	0.819854	+	0.144562i	0.252038	+	0.967717i	$0.418899\pi$
$618$		0			0
$619$	−16.8830	−	29.2423i	−0.678586	−	1.17535i	−0.975407	−	0.220412i	$-0.929260\pi$
$619$	−16.8830	−	29.2423i	−0.678586	−	1.17535i	0.296821	−	0.954933i	$-0.404074\pi$
$620$		0			0
$621$	1.86156	−	5.79519i	0.0747019	−	0.232553i
$622$		0			0
$623$	−8.93358	+	3.25156i	−0.357916	+	0.130271i
$624$		0			0
$625$	2.90984	+	16.5025i	0.116394	+	0.660101i
$626$		0			0
$627$	3.55302	+	6.32736i	0.141894	+	0.252690i
$628$		0			0
$629$	−4.89690	−	27.7717i	−0.195252	−	1.10733i
$630$		0			0
$631$	35.0060	−	12.7411i	1.39357	−	0.507217i	0.467304	−	0.884096i	$-0.345225\pi$
$631$	35.0060	−	12.7411i	1.39357	−	0.507217i	0.926262	+	0.376880i	$0.123003\pi$
$632$		0			0
$633$	−16.9451	−	32.6942i	−0.673506	−	1.29948i
$634$		0			0
$635$	−5.26287	−	9.11556i	−0.208851	−	0.361740i
$636$		0			0
$637$	2.92545	+	0.515836i	0.115911	+	0.0204382i
$638$		0			0
$639$	0.0994226	−	0.0262583i	0.00393310	−	0.00103876i
$640$		0			0
$641$	−7.37099	−	2.68282i	−0.291137	−	0.105965i	0.192323	−	0.981332i	$-0.438398\pi$
$641$	−7.37099	−	2.68282i	−0.291137	−	0.105965i	−0.483460	+	0.875367i	$0.660620\pi$
$642$		0			0
$643$	−29.9819	+	25.1578i	−1.18237	+	0.992126i	−0.182410	+	0.983223i	$0.558390\pi$
$643$	−29.9819	+	25.1578i	−1.18237	+	0.992126i	−0.999960	+	0.00890393i	$0.997166\pi$
$644$		0			0
$645$	9.44461	+	3.93195i	0.371881	+	0.154820i
$646$		0			0
$647$		−	6.21339i		−	0.244274i	−0.992513	−	0.122137i	$-0.961025\pi$
$647$		−	6.21339i		−	0.244274i	0.992513	−	0.122137i	$-0.0389747\pi$
$648$		0			0
$649$	7.19386	+	8.57331i	0.282384	+	0.336532i
$650$		0			0
$651$	6.04516	+	5.55935i	0.236929	+	0.217888i
$652$		0			0
$653$	−23.3831	−	13.5002i	−0.915050	−	0.528304i	−0.0329976	−	0.999455i	$-0.510505\pi$
$653$	−23.3831	−	13.5002i	−0.915050	−	0.528304i	−0.882053	+	0.471151i	$0.843839\pi$
$654$		0			0
$655$	1.46082	−	8.28473i	0.0570790	−	0.323711i
$656$		0			0
$657$	3.12714	−	11.5054i	0.122001	−	0.448868i
$658$		0			0
$659$	−23.3482	−	19.5915i	−0.909517	−	0.763176i	0.0625097	−	0.998044i	$-0.480090\pi$
$659$	−23.3482	−	19.5915i	−0.909517	−	0.763176i	−0.972027	+	0.234869i	$0.924534\pi$
$660$		0			0
$661$	−11.2133	−	30.8082i	−0.436146	−	1.19830i	−0.941980	−	0.335670i	$-0.891037\pi$
$661$	−11.2133	−	30.8082i	−0.436146	−	1.19830i	0.505834	−	0.862631i	$-0.331185\pi$
$662$		0			0
$663$	−7.49360	−	1.67540i	−0.291027	−	0.0650671i
$664$		0			0
$665$	−1.91347	−	4.75550i	−0.0742013	−	0.184410i
$666$		0			0
$667$	−9.27861	+	1.63607i	−0.359269	+	0.0633489i
$668$		0			0
$669$	23.8370	+	1.08359i	0.921591	+	0.0418939i
$670$		0			0
$671$	−6.69399	+	7.97759i	−0.258419	+	0.307971i
$672$		0			0
$673$	26.7750	−	15.4586i	1.03210	−	0.595884i	0.114516	−	0.993421i	$-0.463468\pi$
$673$	26.7750	−	15.4586i	1.03210	−	0.595884i	0.917586	+	0.397537i	$0.130135\pi$
$674$		0			0
$675$	4.85980	+	22.4933i	0.187054	+	0.865766i
$676$		0			0
$677$	−19.6720	+	34.0729i	−0.756057	+	1.30953i	0.188791	+	0.982017i	$0.439543\pi$
$677$	−19.6720	+	34.0729i	−0.756057	+	1.30953i	−0.944847	+	0.327511i	$0.893790\pi$
$678$		0			0
$679$	−5.15932	+	14.1751i	−0.197996	+	0.543991i
$680$		0			0
$681$	8.38366	+	26.7568i	0.321263	+	1.02532i
$682$		0			0
$683$	−12.0176			−0.459840			−0.229920	−	0.973210i	$-0.573846\pi$
$683$	−12.0176			−0.459840			−0.229920	+	0.973210i	$0.573846\pi$
$684$		0			0
$685$	3.75147			0.143336
$686$		0			0
$687$	13.2815	+	42.3885i	0.506720	+	1.61722i
$688$		0			0
$689$	−3.21761	+	8.84031i	−0.122581	+	0.336789i
$690$		0			0
$691$	17.5214	−	30.3479i	0.666544	−	1.15449i	−0.312320	−	0.949977i	$-0.601106\pi$
$691$	17.5214	−	30.3479i	0.666544	−	1.15449i	0.978864	−	0.204512i	$-0.0655606\pi$
$692$		0			0
$693$	2.56010	+	3.68427i	0.0972503	+	0.139954i
$694$		0			0
$695$	−2.36010	+	1.36260i	−0.0895237	+	0.0516865i
$696$		0			0
$697$	−23.4968	+	28.0024i	−0.890006	+	1.06067i
$698$		0			0
$699$	−20.1400	−	0.915530i	−0.761766	−	0.0346285i
$700$		0			0
$701$	−2.95841	+	0.521647i	−0.111738	+	0.0197023i	−0.229237	−	0.973371i	$-0.573623\pi$
$701$	−2.95841	+	0.521647i	−0.111738	+	0.0197023i	0.117500	+	0.993073i	$0.462512\pi$
$702$		0			0
$703$	5.58262	−	17.0986i	0.210552	−	0.644887i
$704$		0			0
$705$	4.03468	+	0.902063i	0.151955	+	0.0339737i
$706$		0			0
$707$	10.0127	+	27.5097i	0.376567	+	1.03461i
$708$		0			0
$709$	2.36012	+	1.98037i	0.0886360	+	0.0743744i	0.686029	−	0.727574i	$-0.259352\pi$
$709$	2.36012	+	1.98037i	0.0886360	+	0.0743744i	−0.597393	+	0.801949i	$0.703797\pi$
$710$		0			0
$711$	−4.02239	−	1.09328i	−0.150852	−	0.0410011i
$712$		0			0
$713$	0.619918	−	3.51573i	0.0232161	−	0.131665i
$714$		0			0
$715$	−0.408138	−	0.235639i	−0.0152635	−	0.00881239i
$716$		0			0
$717$	−19.4073	−	17.8476i	−0.724777	−	0.666532i
$718$		0			0
$719$	−7.13781	−	8.50651i	−0.266195	−	0.317239i	0.616345	−	0.787476i	$-0.288613\pi$
$719$	−7.13781	−	8.50651i	−0.266195	−	0.317239i	−0.882540	+	0.470237i	$0.844168\pi$
$720$		0			0
$721$		−	17.8378i		−	0.664316i
$722$		0			0
$723$	−24.2796	−	10.1080i	−0.902969	−	0.375921i
$724$		0			0
$725$	27.2868	−	22.8964i	1.01341	−	0.850349i
$726$		0			0
$727$	−13.8709	−	5.04860i	−0.514444	−	0.187242i	0.0717355	−	0.997424i	$-0.477146\pi$
$727$	−13.8709	−	5.04860i	−0.514444	−	0.187242i	−0.586179	+	0.810182i	$0.699368\pi$
$728$		0			0
$729$	6.70703	+	26.1537i	0.248409	+	0.968655i
$730$		0			0
$731$	52.5931	+	9.27357i	1.94522	+	0.342996i
$732$		0			0
$733$	−18.1447	−	31.4276i	−0.670191	−	1.16080i	−0.977850	−	0.209308i	$-0.932879\pi$
$733$	−18.1447	−	31.4276i	−0.670191	−	1.16080i	0.307659	−	0.951497i	$-0.400454\pi$
$734$		0			0
$735$	2.75857	+	5.32245i	0.101751	+	0.196322i
$736$		0			0
$737$	−8.42862	+	3.06777i	−0.310472	+	0.113003i
$738$		0			0
$739$	2.94942	+	16.7270i	0.108496	+	0.615312i	0.989766	+	0.142699i	$0.0455780\pi$
$739$	2.94942	+	16.7270i	0.108496	+	0.615312i	−0.881270	+	0.472613i	$0.843311\pi$
$740$		0			0
$741$	−3.71394	−	3.19273i	−0.136435	−	0.117288i
$742$		0			0
$743$	4.59818	+	26.0776i	0.168691	+	0.956693i	0.945177	+	0.326559i	$0.105889\pi$
$743$	4.59818	+	26.0776i	0.168691	+	0.956693i	−0.776486	+	0.630134i	$0.783000\pi$
$744$		0			0
$745$	−13.6097	+	4.95352i	−0.498620	+	0.181483i
$746$		0			0
$747$	−36.1962	+	3.03595i	−1.32435	+	0.111080i
$748$		0			0
$749$	1.83324	+	3.17526i	0.0669850	+	0.116021i
$750$		0			0
$751$	−46.8929	−	8.26849i	−1.71115	−	0.301722i	−0.769581	−	0.638549i	$-0.779535\pi$
$751$	−46.8929	−	8.26849i	−1.71115	−	0.301722i	−0.941566	+	0.336827i	$0.890646\pi$
$752$		0			0
$753$	14.9274	−	11.4117i	0.543984	−	0.415866i
$754$		0			0
$755$	13.6812	+	4.97954i	0.497909	+	0.181224i
$756$		0			0
$757$	−12.6519	+	10.6162i	−0.459843	+	0.385854i	−0.843073	−	0.537799i	$-0.819256\pi$
$757$	−12.6519	+	10.6162i	−0.459843	+	0.385854i	0.383230	+	0.923653i	$0.374812\pi$
$758$		0			0
$759$	0.749527	−	1.80038i	0.0272061	−	0.0653496i
$760$		0			0
$761$		−	19.1974i		−	0.695906i	−0.937512	−	0.347953i	$-0.886877\pi$
$761$		−	19.1974i		−	0.695906i	0.937512	−	0.347953i	$-0.113123\pi$
$762$		0			0
$763$	−6.48211	−	7.72508i	−0.234668	−	0.279667i
$764$		0			0
$765$	−6.49847	−	14.0675i	−0.234953	−	0.508613i
$766$		0			0
$767$	−6.54145	−	3.77671i	−0.236198	−	0.136369i
$768$		0			0
$769$	−5.25863	+	29.8231i	−0.189631	+	1.07545i	0.730229	+	0.683203i	$0.239413\pi$
$769$	−5.25863	+	29.8231i	−0.189631	+	1.07545i	−0.919860	+	0.392248i	$0.871698\pi$
$770$		0			0
$771$	0.0777483	−	0.0100939i	0.00280004	−	0.000363524i
$772$		0			0
$773$	21.9958	+	18.4567i	0.791134	+	0.663840i	0.946026	−	0.324091i	$-0.105058\pi$
$773$	21.9958	+	18.4567i	0.791134	+	0.663840i	−0.154892	+	0.987931i	$0.549503\pi$
$774$		0			0
$775$	4.61619	+	12.6829i	0.165818	+	0.455582i
$776$		0			0
$777$	2.42635	−	10.8524i	0.0870449	−	0.389328i
$778$		0			0
$779$	−21.6303	+	8.70339i	−0.774985	+	0.311831i
$780$		0			0
$781$	0.0324458	−	0.00572106i	0.00116100	−	0.000204716i
$782$		0			0
$783$	30.9645	−	28.0687i	1.10658	−	1.00309i
$784$		0			0
$785$	0.103890	−	0.123812i	0.00370800	−	0.00441903i
$786$		0			0
$787$	−22.1812	+	12.8063i	−0.790673	+	0.456495i	−0.840200	−	0.542277i	$-0.817562\pi$
$787$	−22.1812	+	12.8063i	−0.790673	+	0.456495i	0.0495262	+	0.998773i	$0.484229\pi$
$788$		0			0
$789$	5.11899	−	8.00348i	0.182241	−	0.284932i
$790$		0			0
$791$	7.80951	−	13.5265i	0.277674	−	0.480946i
$792$		0			0
$793$	2.40391	−	6.60469i	0.0853653	−	0.234539i
$794$		0			0
$795$	−18.1169	+	5.67652i	−0.642540	+	0.201326i
$796$		0			0
$797$	−32.4074			−1.14793			−0.573965	−	0.818880i	$-0.694595\pi$
$797$	−32.4074			−1.14793			−0.573965	+	0.818880i	$0.694595\pi$
$798$		0			0
$799$	21.5817			0.763506
$800$		0			0
$801$	−18.2553	−	1.66314i	−0.645018	−	0.0587642i
$802$		0			0
$803$	1.30650	−	3.58957i	0.0461053	−	0.126673i
$804$		0			0
$805$	−0.688786	+	1.19301i	−0.0242765	+	0.0420482i
$806$		0			0
$807$	−2.86536	−	1.83267i	−0.100866	−	0.0645131i
$808$		0			0
$809$	−30.3938	+	17.5479i	−1.06859	+	0.616950i	−0.927796	−	0.373089i	$-0.878299\pi$
$809$	−30.3938	+	17.5479i	−1.06859	+	0.616950i	−0.140793	+	0.990039i	$0.544965\pi$
$810$		0			0
$811$	−14.0733	+	16.7719i	−0.494181	+	0.588942i	−0.954276	−	0.298928i	$-0.903371\pi$
$811$	−14.0733	+	16.7719i	−0.494181	+	0.588942i	0.460095	+	0.887870i	$0.347815\pi$
$812$		0			0
$813$	−1.66144	+	36.5488i	−0.0582694	+	1.28182i
$814$		0			0
$815$	11.1901	−	1.97312i	0.391972	−	0.0691152i
$816$		0			0
$817$	26.8121	+	21.0094i	0.938035	+	0.735027i
$818$		0			0
$819$	−2.47411	−	1.74565i	−0.0864522	−	0.0609979i
$820$		0			0
$821$	4.83332	+	13.2794i	0.168684	+	0.463455i	0.995015	−	0.0997301i	$-0.0317979\pi$
$821$	4.83332	+	13.2794i	0.168684	+	0.463455i	−0.826331	+	0.563185i	$0.809576\pi$
$822$		0			0
$823$	−11.4669	−	9.62189i	−0.399712	−	0.335398i	0.420670	−	0.907214i	$-0.361795\pi$
$823$	−11.4669	−	9.62189i	−0.399712	−	0.335398i	−0.820382	+	0.571815i	$0.806239\pi$
$824$		0			0
$825$	0.949245	+	7.31155i	0.0330485	+	0.254556i
$826$		0			0
$827$	−3.63051	+	20.5896i	−0.126245	+	0.715972i	0.854315	+	0.519755i	$0.173977\pi$
$827$	−3.63051	+	20.5896i	−0.126245	+	0.715972i	−0.980561	+	0.196217i	$0.937134\pi$
$828$		0			0
$829$	−12.1611	−	7.02120i	−0.422371	−	0.243856i	0.273720	−	0.961809i	$-0.411746\pi$
$829$	−12.1611	−	7.02120i	−0.422371	−	0.243856i	−0.696091	+	0.717953i	$0.745079\pi$
$830$		0			0
$831$	−9.18960	+	9.99265i	−0.318784	+	0.346641i
$832$		0			0
$833$	20.1155	+	23.9727i	0.696960	+	0.830605i
$834$		0			0
$835$			7.14241i			0.247173i
$836$		0			0
$837$	5.98122	+	14.6626i	0.206741	+	0.506815i
$838$		0			0
$839$	42.8654	−	35.9683i	1.47988	−	1.24176i	0.573563	−	0.819162i	$-0.305561\pi$
$839$	42.8654	−	35.9683i	1.47988	−	1.24176i	0.906315	−	0.422603i	$-0.138884\pi$
$840$		0			0
$841$	−33.5383	−	12.2070i	−1.15649	−	0.420929i
$842$		0			0
$843$	12.3211	+	16.1170i	0.424362	+	0.555098i
$844$		0			0
$845$	−9.36332	−	1.65101i	−0.322108	−	0.0567964i
$846$		0			0
$847$	−7.83867	−	13.5770i	−0.269340	−	0.466510i
$848$		0			0
$849$	−10.7955	+	5.59521i	−0.370502	+	0.192027i
$850$		0			0
$851$	−4.54230	+	1.65326i	−0.155708	+	0.0566731i
$852$		0			0
$853$	−7.55129	−	42.8255i	−0.258551	−	1.46632i	−0.786790	−	0.617221i	$-0.788259\pi$
$853$	−7.55129	−	42.8255i	−0.258551	−	1.46632i	0.528239	−	0.849096i	$-0.322853\pi$
$854$		0			0
$855$	0.566737	−	9.86755i	0.0193820	−	0.337463i
$856$		0			0
$857$	8.77792	+	49.7820i	0.299848	+	1.70052i	0.646817	+	0.762645i	$0.276100\pi$
$857$	8.77792	+	49.7820i	0.299848	+	1.70052i	−0.346969	+	0.937877i	$0.612789\pi$
$858$		0			0
$859$	−23.3783	+	8.50899i	−0.797656	+	0.290323i	−0.708515	−	0.705696i	$-0.750634\pi$
$859$	−23.3783	+	8.50899i	−0.797656	+	0.290323i	−0.0891412	+	0.996019i	$0.528412\pi$
$860$		0			0
$861$	−12.7980	+	6.63306i	−0.436154	+	0.226054i
$862$		0			0
$863$	16.9638	+	29.3822i	0.577455	+	1.00018i	0.995770	+	0.0918798i	$0.0292876\pi$
$863$	16.9638	+	29.3822i	0.577455	+	1.00018i	−0.418315	+	0.908302i	$0.637379\pi$
$864$		0			0
$865$	−10.0103	−	1.76509i	−0.340362	−	0.0600149i
$866$		0			0
$867$	−31.2456	−	40.8717i	−1.06116	−	1.38807i
$868$		0			0
$869$	−1.25495	−	0.456765i	−0.0425713	−	0.0154947i
$870$		0			0
$871$	4.63739	−	3.89123i	0.157132	−	0.131849i
$872$		0			0
$873$	−20.6406	+	20.4930i	−0.698577	+	0.693583i
$874$		0			0
$875$		−	11.0881i		−	0.374846i
$876$		0			0
$877$	19.1891	+	22.8687i	0.647971	+	0.772222i	0.985607	−	0.169055i	$-0.0540717\pi$
$877$	19.1891	+	22.8687i	0.647971	+	0.772222i	−0.337636	+	0.941277i	$0.609627\pi$
$878$		0			0
$879$	−3.02713	+	3.29166i	−0.102103	+	0.111025i
$880$		0			0
$881$	−9.59448	−	5.53938i	−0.323246	−	0.186626i	0.329592	−	0.944123i	$-0.393089\pi$
$881$	−9.59448	−	5.53938i	−0.323246	−	0.186626i	−0.652839	+	0.757497i	$0.726422\pi$
$882$		0			0
$883$	−9.62988	+	54.6138i	−0.324071	+	1.83790i	0.192051	+	0.981385i	$0.438486\pi$
$883$	−9.62988	+	54.6138i	−0.324071	+	1.83790i	−0.516122	+	0.856515i	$0.672625\pi$
$884$		0			0
$885$	−1.96255	−	15.1165i	−0.0659703	−	0.508135i
$886$		0			0
$887$	−19.9548	−	16.7441i	−0.670017	−	0.562211i	0.243054	−	0.970013i	$-0.421851\pi$
$887$	−19.9548	−	16.7441i	−0.670017	−	0.562211i	−0.913070	+	0.407802i	$0.866295\pi$
$888$		0			0
$889$	−7.41064	−	20.3606i	−0.248545	−	0.682871i
$890$		0			0
$891$	1.44099	+	8.52968i	0.0482749	+	0.285755i
$892$		0			0
$893$	12.1450	+	6.47980i	0.406416	+	0.216838i
$894$		0			0
$895$	12.4254	−	2.19093i	0.415334	−	0.0732346i
$896$		0			0
$897$	−0.0597702	+	1.31484i	−0.00199567	+	0.0439012i
$898$		0			0
$899$	15.7559	−	18.7771i	0.525488	−	0.626252i
$900$		0			0
$901$	−85.8291	+	49.5535i	−2.85938	+	1.65086i
$902$		0			0
$903$	17.7409	+	11.3470i	0.590380	+	0.377604i
$904$		0			0
$905$	3.85274	−	6.67314i	0.128069	−	0.221823i
$906$		0			0
$907$	−5.92780	+	16.2865i	−0.196830	+	0.540785i	−0.998365	−	0.0571627i	$-0.981795\pi$
$907$	−5.92780	+	16.2865i	−0.196830	+	0.540785i	0.801535	+	0.597947i	$0.204017\pi$
$908$		0			0
$909$	−5.12141	+	56.2145i	−0.169866	+	1.86452i
$910$		0			0
$911$	−35.0957			−1.16277			−0.581386	−	0.813628i	$-0.697489\pi$
$911$	−35.0957			−1.16277			−0.581386	+	0.813628i	$0.697489\pi$
$912$		0			0
$913$	−11.6376			−0.385150
$914$		0			0
$915$	13.5353	−	4.24099i	0.447463	−	0.140203i
$916$		0			0
$917$	5.92284	−	16.2729i	0.195589	−	0.537377i
$918$		0			0
$919$	15.0221	−	26.0190i	0.495533	−	0.858288i	−0.504454	−	0.863439i	$-0.668306\pi$
$919$	15.0221	−	26.0190i	0.495533	−	0.858288i	0.999987	+	0.00515052i	$0.00163947\pi$
$920$		0			0
$921$	1.83849	−	2.87447i	0.0605805	−	0.0947169i
$922$		0			0
$923$	−0.0192569	+	0.0111180i	−0.000633848	+	0.000365952i
$924$		0			0
$925$	11.7469	−	13.9995i	0.386237	−	0.460300i
$926$		0			0
$927$	14.6474	−	31.1194i	0.481083	−	1.02210i
$928$		0			0
$929$	32.1458	−	5.66817i	1.05467	−	0.185967i	0.380680	−	0.924707i	$-0.375690\pi$
$929$	32.1458	−	5.66817i	1.05467	−	0.185967i	0.673990	+	0.738740i	$0.264579\pi$
$930$		0			0
$931$	4.12218	+	19.5301i	0.135099	+	0.640072i
$932$		0			0
$933$	−9.81461	+	43.8981i	−0.321316	+	1.43716i
$934$		0			0
$935$	−1.69805	−	4.66536i	−0.0555322	−	0.152573i
$936$		0			0
$937$	−24.8914	−	20.8863i	−0.813165	−	0.682327i	0.138196	−	0.990405i	$-0.455870\pi$
$937$	−24.8914	−	20.8863i	−0.813165	−	0.682327i	−0.951361	+	0.308078i	$0.900314\pi$
$938$		0			0
$939$	23.0315	−	2.99013i	0.751604	−	0.0975794i
$940$		0			0
$941$	2.50659	−	14.2156i	0.0817126	−	0.463415i	−0.916305	−	0.400481i	$-0.868843\pi$
$941$	2.50659	−	14.2156i	0.0817126	−	0.463415i	0.998018	−	0.0629344i	$-0.0200459\pi$
$942$		0			0
$943$	5.42639	+	3.13293i	0.176708	+	0.102022i
$944$		0			0
$945$	−0.233687	−	6.10616i	−0.00760185	−	0.198633i
$946$		0			0
$947$	28.2988	+	33.7252i	0.919588	+	1.09592i	0.995109	+	0.0987786i	$0.0314936\pi$
$947$	28.2988	+	33.7252i	0.919588	+	1.09592i	−0.0755210	+	0.997144i	$0.524062\pi$
$948$		0			0
$949$			2.57814i			0.0836899i
$950$		0			0
$951$	−20.2527	+	48.6473i	−0.656738	+	1.57750i
$952$		0			0
$953$	15.8037	−	13.2609i	0.511932	−	0.429562i	−0.349877	−	0.936796i	$-0.613777\pi$
$953$	15.8037	−	13.2609i	0.511932	−	0.429562i	0.861808	+	0.507234i	$0.169332\pi$
$954$		0			0
$955$	−8.57039	−	3.11937i	−0.277331	−	0.100940i
$956$		0			0
$957$	10.6377	−	8.13228i	0.343866	−	0.262879i
$958$		0			0
$959$	7.60509	+	1.34098i	0.245581	+	0.0433026i
$960$		0			0
$961$	−10.8562	−	18.8034i	−0.350199	−	0.606562i
$962$		0			0
$963$	0.590883	+	7.04481i	0.0190409	+	0.227016i
$964$		0			0
$965$	2.37554	−	0.864625i	0.0764713	−	0.0278333i
$966$		0			0
$967$	7.05922	+	40.0348i	0.227009	+	1.28743i	0.858807	+	0.512300i	$0.171206\pi$
$967$	7.05922	+	40.0348i	0.227009	+	1.28743i	−0.631798	+	0.775133i	$0.717683\pi$
$968$		0			0
$969$	−8.35187	−	50.9147i	−0.268301	−	1.63562i
$970$		0			0
$971$	−0.764165	−	4.33380i	−0.0245232	−	0.139078i	0.970088	−	0.242754i	$-0.0780507\pi$
$971$	−0.764165	−	4.33380i	−0.0245232	−	0.139078i	−0.994611	+	0.103676i	$0.966940\pi$
$972$		0			0
$973$	−5.27154	+	1.91868i	−0.168998	+	0.0615101i
$974$		0			0
$975$	−2.28978	−	4.41796i	−0.0733317	−	0.141488i
$976$		0			0
$977$	0.538610	+	0.932899i	0.0172317	+	0.0298461i	0.874513	−	0.485003i	$-0.161181\pi$
$977$	0.538610	+	0.932899i	0.0172317	+	0.0298461i	−0.857281	+	0.514849i	$0.827848\pi$
$978$		0			0
$979$	−5.78381	−	1.01984i	−0.184851	−	0.0325943i
$980$		0			0
$981$	−4.96515	−	18.7997i	−0.158525	−	0.600228i
$982$		0			0
$983$	−4.78675	−	1.74223i	−0.152674	−	0.0555687i	0.264553	−	0.964371i	$-0.414776\pi$
$983$	−4.78675	−	1.74223i	−0.152674	−	0.0555687i	−0.417227	+	0.908803i	$0.636998\pi$
$984$		0			0
$985$	−3.44381	+	2.88970i	−0.109729	+	0.0920736i
$986$		0			0
$987$	7.85678	+	3.27091i	0.250084	+	0.104114i
$988$		0			0
$989$		−	9.15410i		−	0.291083i
$990$		0			0
$991$	7.72397	+	9.20507i	0.245360	+	0.292409i	0.874643	−	0.484768i	$-0.161096\pi$
$991$	7.72397	+	9.20507i	0.245360	+	0.292409i	−0.629283	+	0.777176i	$0.716651\pi$
$992$		0			0
$993$	−13.5732	−	12.4824i	−0.430734	−	0.396118i
$994$		0			0
$995$	−7.31621	−	4.22401i	−0.231939	−	0.133910i
$996$		0			0
$997$	−6.23994	+	35.3885i	−0.197621	+	1.12076i	0.711016	+	0.703176i	$0.248235\pi$
$997$	−6.23994	+	35.3885i	−0.197621	+	1.12076i	−0.908637	+	0.417588i	$0.862876\pi$
$998$		0			0
$999$	13.1443	−	16.9404i	0.415867	−	0.535972i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	912.2.cc.c.257.2		18
3.2	odd	2		912.2.cc.d.257.1		18
4.3	odd	2		114.2.l.b.29.2	yes	18
12.11	even	2		114.2.l.a.29.3	✓	18
19.2	odd	18		912.2.cc.d.401.1		18
57.2	even	18	inner	912.2.cc.c.401.2		18
76.59	even	18		114.2.l.a.59.3	yes	18
228.59	odd	18		114.2.l.b.59.2	yes	18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
114.2.l.a.29.3	✓	18	12.11	even	2
114.2.l.a.59.3	yes	18	76.59	even	18
114.2.l.b.29.2	yes	18	4.3	odd	2
114.2.l.b.59.2	yes	18	228.59	odd	18
912.2.cc.c.257.2		18	1.1	even	1	trivial
912.2.cc.c.401.2		18	57.2	even	18	inner
912.2.cc.d.257.1		18	3.2	odd	2
912.2.cc.d.401.1		18	19.2	odd	18

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 912 = 2^{4} \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	912.cc (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.517874 - 1.65282i) q^{3} +(-0.258510 + 0.710252i) q^{5} +(-0.777943 + 1.34744i) q^{7} +(-2.46361 + 1.71190i) q^{9} +(-0.832399 + 0.480586i) q^{11} +(0.416982 - 0.496940i) q^{13} +(1.30779 + 0.0594499i) q^{15} +(6.73013 - 1.18670i) q^{17} +(4.14364 + 1.35288i) q^{19} +(2.62994 + 0.587996i) q^{21} +(-0.400647 - 1.10077i) q^{23} +(3.39259 + 2.84672i) q^{25} +(4.10530 + 3.18535i) q^{27} +(1.39666 - 7.92086i) q^{29} +(2.63927 + 1.52379i) q^{31} +(1.22540 + 1.12692i) q^{33} +(-0.755913 - 0.900862i) q^{35} -4.12648i q^{37} +(-1.03729 - 0.431843i) q^{39} +(-4.09755 + 3.43825i) q^{41} +(7.34330 + 2.67274i) q^{43} +(-0.579012 - 2.19233i) q^{45} +(3.11004 + 0.548383i) q^{47} +(2.28961 + 3.96572i) q^{49} +(-5.44676 - 10.5091i) q^{51} +(-13.6276 + 4.96002i) q^{53} +(-0.126153 - 0.715449i) q^{55} +(0.0901766 - 7.54930i) q^{57} +(-2.02192 - 11.4669i) q^{59} +(10.1813 - 3.70568i) q^{61} +(-0.390129 - 4.65133i) q^{63} +(0.245158 + 0.424626i) q^{65} +(9.19012 + 1.62047i) q^{67} +(-1.61189 + 1.23226i) q^{69} +(-0.0322101 - 0.0117235i) q^{71} +(-3.04446 + 2.55461i) q^{73} +(2.94818 - 7.08158i) q^{75} -1.49547i q^{77} +(0.893115 + 1.06437i) q^{79} +(3.13878 - 8.43493i) q^{81} +(10.4856 + 6.05389i) q^{83} +(-0.896950 + 5.08686i) q^{85} +(-13.8150 + 1.79358i) q^{87} +(4.68075 + 3.92762i) q^{89} +(0.345207 + 0.948448i) q^{91} +(1.15173 - 5.15137i) q^{93} +(-2.03206 + 2.59329i) q^{95} +(9.54804 - 1.68358i) q^{97} +(1.22799 - 2.60896i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q - 3 q^{3} - 3 q^{9} - 12 q^{13} - 18 q^{15} + 6 q^{17} + 6 q^{19} - 18 q^{25} + 6 q^{27} - 6 q^{29} - 24 q^{33} + 24 q^{35} - 6 q^{39} + 3 q^{41} + 6 q^{43} - 54 q^{45} - 30 q^{47} + 21 q^{49} - 42 q^{51}+ \cdots + 102 q^{99}+O(q^{100}) \) 18 * q - 3 * q^3 - 3 * q^9 - 12 * q^13 - 18 * q^15 + 6 * q^17 + 6 * q^19 - 18 * q^25 + 6 * q^27 - 6 * q^29 - 24 * q^33 + 24 * q^35 - 6 * q^39 + 3 * q^41 + 6 * q^43 - 54 * q^45 - 30 * q^47 + 21 * q^49 - 42 * q^51 - 60 * q^53 - 30 * q^55 + 12 * q^57 - 3 * q^59 + 54 * q^61 + 18 * q^63 + 24 * q^65 + 15 * q^67 + 30 * q^69 - 36 * q^71 - 42 * q^73 + 6 * q^79 - 3 * q^81 - 36 * q^83 - 60 * q^89 + 18 * q^91 - 66 * q^93 - 6 * q^95 + 9 * q^97 + 102 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

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Groups

Database

Properties

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