LMFDB - Embedded newform 152.2.q.b.137.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [152,2,Mod(9,152)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(152, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([0, 0, 8])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("152.9"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 152 = 2^{3} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	152.q (of order $9$, degree $6$, minimal)

Newform invariants

comment:select newform

sage:traces = [6,0,9] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$1.21372611072$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\Q(\zeta_{18})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{3} + 1 $ x^6 - x^3 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			137.1
Root			$0.939693 + 0.342020i$ of defining polynomial
Character	$\chi$	$=$	152.137
Dual form			152.2.q.b.81.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.560307 + 3.17766i) q^{3} +(-1.93969 + 1.62760i) q^{5} +(1.93969 - 3.35965i) q^{7} +(-6.96451 + 2.53487i) q^{9} +(1.17365 + 2.03282i) q^{11} +(0.145430 - 0.824773i) q^{13} +(-6.25877 - 5.25173i) q^{15} +(0.900330 + 0.327693i) q^{17} +(4.35844 + 0.0632028i) q^{19} +(11.7626 + 4.28125i) q^{21} +(3.34730 + 2.80872i) q^{23} +(0.245100 - 1.39003i) q^{25} +(-7.11721 - 12.3274i) q^{27} +(3.25877 - 1.18610i) q^{29} +(2.31908 - 4.01676i) q^{31} +(-5.80200 + 4.86846i) q^{33} +(1.70574 + 9.67372i) q^{35} -6.22668 q^{37} +2.70233 q^{39} +(-1.63176 - 9.25417i) q^{41} +(-3.42855 + 2.87689i) q^{43} +(9.38326 - 16.2523i) q^{45} +(6.73783 - 2.45237i) q^{47} +(-4.02481 - 6.97118i) q^{49} +(-0.536837 + 3.04455i) q^{51} +(-3.24376 - 2.72183i) q^{53} +(-5.58512 - 2.03282i) q^{55} +(2.24123 + 13.8851i) q^{57} +(-7.92514 - 2.88452i) q^{59} +(-4.89440 - 4.10689i) q^{61} +(-4.99273 + 28.3152i) q^{63} +(1.06031 + 1.83651i) q^{65} +(12.7442 - 4.63852i) q^{67} +(-7.04963 + 12.2103i) q^{69} +(-6.53983 + 5.48757i) q^{71} +(1.54664 + 8.77141i) q^{73} +4.55438 q^{75} +9.10607 q^{77} +(-0.647956 - 3.67474i) q^{79} +(18.1518 - 15.2312i) q^{81} +(1.23396 - 2.13727i) q^{83} +(-2.27972 + 0.829748i) q^{85} +(5.59492 + 9.69069i) q^{87} +(-0.396459 + 2.24843i) q^{89} +(-2.48886 - 2.08840i) q^{91} +(14.0633 + 5.11862i) q^{93} +(-8.55690 + 6.97118i) q^{95} +(0.166374 + 0.0605553i) q^{97} +(-13.3268 - 11.1825i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 9 q^{3} - 6 q^{5} + 6 q^{7} - 9 q^{9} + 6 q^{11} - 15 q^{13} - 15 q^{15} - 9 q^{17} + 18 q^{19} + 24 q^{21} + 18 q^{23} - 12 q^{27} - 3 q^{29} - 3 q^{31} + 3 q^{33} - 24 q^{37} - 36 q^{39} - 15 q^{41}+ \cdots - 15 q^{99}+O(q^{100}) $ 6 * q + 9 * q^3 - 6 * q^5 + 6 * q^7 - 9 * q^9 + 6 * q^11 - 15 * q^13 - 15 * q^15 - 9 * q^17 + 18 * q^19 + 24 * q^21 + 18 * q^23 - 12 * q^27 - 3 * q^29 - 3 * q^31 + 3 * q^33 - 24 * q^37 - 36 * q^39 - 15 * q^41 - 21 * q^43 + 21 * q^45 + 21 * q^47 + 3 * q^49 - 27 * q^51 - 27 * q^53 - 12 * q^55 + 36 * q^57 - 6 * q^59 + 12 * q^61 - 12 * q^63 + 12 * q^65 + 18 * q^67 + 12 * q^69 + 18 * q^71 + 36 * q^73 + 6 * q^75 + 30 * q^77 + 27 * q^79 + 54 * q^81 + 12 * q^83 + 12 * q^85 + 15 * q^87 - 12 * q^89 - 21 * q^91 + 9 * q^93 - 15 * q^95 - 18 * q^97 - 15 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/152\mathbb{Z}\right)^\times$.

$n$	$39$	$77$	$97$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{9}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.560307	+	3.17766i	0.323494	+	1.83462i	0.520056	+	0.854132i	$0.325911\pi$
$3$	0.560307	+	3.17766i	0.323494	+	1.83462i	−0.196562	+	0.980491i	$0.562978\pi$
$4$		0			0
$5$	−1.93969	+	1.62760i	−0.867457	+	0.727883i	−0.963561	−	0.267489i	$-0.913806\pi$
$5$	−1.93969	+	1.62760i	−0.867457	+	0.727883i	0.0961041	+	0.995371i	$0.469362\pi$
$6$		0			0
$7$	1.93969	−	3.35965i	0.733135	−	1.26983i	−0.222402	−	0.974955i	$-0.571390\pi$
$7$	1.93969	−	3.35965i	0.733135	−	1.26983i	0.955537	−	0.294872i	$-0.0952770\pi$
$8$		0			0
$9$	−6.96451	+	2.53487i	−2.32150	+	0.844958i
$10$		0			0
$11$	1.17365	+	2.03282i	0.353868	+	0.612918i	0.986924	−	0.161189i	$-0.0515328\pi$
$11$	1.17365	+	2.03282i	0.353868	+	0.612918i	−0.633055	+	0.774107i	$0.718199\pi$
$12$		0			0
$13$	0.145430	−	0.824773i	0.0403349	−	0.228751i	−0.957976	−	0.286848i	$-0.907392\pi$
$13$	0.145430	−	0.824773i	0.0403349	−	0.228751i	0.998311	+	0.0580977i	$0.0185035\pi$
$14$		0			0
$15$	−6.25877	−	5.25173i	−1.61601	−	1.35599i
$16$		0			0
$17$	0.900330	+	0.327693i	0.218362	+	0.0794773i	0.448885	−	0.893590i	$-0.351821\pi$
$17$	0.900330	+	0.327693i	0.218362	+	0.0794773i	−0.230523	+	0.973067i	$0.574044\pi$
$18$		0			0
$19$	4.35844	+	0.0632028i	0.999895	+	0.0144997i
$19$	4.35844	+	0.0632028i	0.999895	+	0.0144997i
$20$		0			0
$21$	11.7626	+	4.28125i	2.56682	+	0.934246i
$22$		0			0
$23$	3.34730	+	2.80872i	0.697960	+	0.585658i	0.921192	−	0.389108i	$-0.127217\pi$
$23$	3.34730	+	2.80872i	0.697960	+	0.585658i	−0.223233	+	0.974765i	$0.571661\pi$
$24$		0			0
$25$	0.245100	−	1.39003i	0.0490200	−	0.278006i
$26$		0			0
$27$	−7.11721	−	12.3274i	−1.36971	−	2.37240i
$28$		0			0
$29$	3.25877	−	1.18610i	0.605138	−	0.220252i	−0.0212363	−	0.999774i	$-0.506760\pi$
$29$	3.25877	−	1.18610i	0.605138	−	0.220252i	0.626375	+	0.779522i	$0.284538\pi$
$30$		0			0
$31$	2.31908	−	4.01676i	0.416519	−	0.721432i	−0.579068	−	0.815279i	$-0.696583\pi$
$31$	2.31908	−	4.01676i	0.416519	−	0.721432i	0.995587	+	0.0938478i	$0.0299167\pi$
$32$		0			0
$33$	−5.80200	+	4.86846i	−1.01000	+	0.847490i
$34$		0			0
$35$	1.70574	+	9.67372i	0.288322	+	1.63516i
$36$		0			0
$37$	−6.22668			−1.02366			−0.511830	−	0.859087i	$-0.671032\pi$
$37$	−6.22668			−1.02366			−0.511830	+	0.859087i	$0.671032\pi$
$38$		0			0
$39$	2.70233			0.432720
$40$		0			0
$41$	−1.63176	−	9.25417i	−0.254838	−	1.44526i	−0.796488	−	0.604654i	$-0.793311\pi$
$41$	−1.63176	−	9.25417i	−0.254838	−	1.44526i	0.541650	−	0.840604i	$-0.317800\pi$
$42$		0			0
$43$	−3.42855	+	2.87689i	−0.522849	+	0.438722i	−0.865624	−	0.500695i	$-0.833078\pi$
$43$	−3.42855	+	2.87689i	−0.522849	+	0.438722i	0.342775	+	0.939418i	$0.388633\pi$
$44$		0			0
$45$	9.38326	−	16.2523i	1.39877	−	2.42275i
$46$		0			0
$47$	6.73783	−	2.45237i	0.982813	−	0.357715i	0.199880	−	0.979820i	$-0.435945\pi$
$47$	6.73783	−	2.45237i	0.982813	−	0.357715i	0.782933	+	0.622106i	$0.213723\pi$
$48$		0			0
$49$	−4.02481	−	6.97118i	−0.574974	−	0.995883i
$50$		0			0
$51$	−0.536837	+	3.04455i	−0.0751722	+	0.426323i
$52$		0			0
$53$	−3.24376	−	2.72183i	−0.445564	−	0.373873i	0.392223	−	0.919870i	$-0.371706\pi$
$53$	−3.24376	−	2.72183i	−0.445564	−	0.373873i	−0.837787	+	0.545998i	$0.816151\pi$
$54$		0			0
$55$	−5.58512	−	2.03282i	−0.753098	−	0.274105i
$56$		0			0
$57$	2.24123	+	13.8851i	0.296858	+	1.83912i
$58$		0			0
$59$	−7.92514	−	2.88452i	−1.03177	−	0.375532i	−0.230013	−	0.973188i	$-0.573877\pi$
$59$	−7.92514	−	2.88452i	−1.03177	−	0.375532i	−0.801753	+	0.597655i	$0.796099\pi$
$60$		0			0
$61$	−4.89440	−	4.10689i	−0.626664	−	0.525833i	0.273227	−	0.961950i	$-0.411909\pi$
$61$	−4.89440	−	4.10689i	−0.626664	−	0.525833i	−0.899890	+	0.436116i	$0.856354\pi$
$62$		0			0
$63$	−4.99273	+	28.3152i	−0.629024	+	3.56737i
$64$		0			0
$65$	1.06031	+	1.83651i	0.131515	+	0.227791i
$66$		0			0
$67$	12.7442	−	4.63852i	1.55695	−	0.566685i	0.586919	−	0.809646i	$-0.300341\pi$
$67$	12.7442	−	4.63852i	1.55695	−	0.566685i	0.970036	+	0.242961i	$0.0781187\pi$
$68$		0			0
$69$	−7.04963	+	12.2103i	−0.848676	+	1.46995i
$70$		0			0
$71$	−6.53983	+	5.48757i	−0.776135	+	0.651255i	−0.942272	−	0.334848i	$-0.891315\pi$
$71$	−6.53983	+	5.48757i	−0.776135	+	0.651255i	0.166137	+	0.986103i	$0.446871\pi$
$72$		0			0
$73$	1.54664	+	8.77141i	0.181020	+	1.02662i	0.930963	+	0.365114i	$0.118970\pi$
$73$	1.54664	+	8.77141i	0.181020	+	1.02662i	−0.749943	+	0.661503i	$0.769919\pi$
$74$		0			0
$75$	4.55438			0.525894
$76$		0			0
$77$	9.10607			1.03773
$78$		0			0
$79$	−0.647956	−	3.67474i	−0.0729007	−	0.413441i	−0.999317	−	0.0369409i	$-0.988239\pi$
$79$	−0.647956	−	3.67474i	−0.0729007	−	0.413441i	0.926417	−	0.376500i	$-0.122872\pi$
$80$		0			0
$81$	18.1518	−	15.2312i	2.01687	−	1.69235i
$82$		0			0
$83$	1.23396	−	2.13727i	0.135444	−	0.234596i	−0.790323	−	0.612691i	$-0.790087\pi$
$83$	1.23396	−	2.13727i	0.135444	−	0.234596i	0.925767	+	0.378094i	$0.123421\pi$
$84$		0			0
$85$	−2.27972	+	0.829748i	−0.247270	+	0.0899989i
$86$		0			0
$87$	5.59492	+	9.69069i	0.599839	+	1.03895i
$88$		0			0
$89$	−0.396459	+	2.24843i	−0.0420246	+	0.238333i	−0.998584	−	0.0532055i	$-0.983056\pi$
$89$	−0.396459	+	2.24843i	−0.0420246	+	0.238333i	0.956559	+	0.291539i	$0.0941673\pi$
$90$		0			0
$91$	−2.48886	−	2.08840i	−0.260903	−	0.218924i
$92$		0			0
$93$	14.0633	+	5.11862i	1.45830	+	0.530776i
$94$		0			0
$95$	−8.55690	+	6.97118i	−0.877920	+	0.715228i
$96$		0			0
$97$	0.166374	+	0.0605553i	0.0168927	+	0.00614846i	0.350453	−	0.936580i	$-0.386028\pi$
$97$	0.166374	+	0.0605553i	0.0168927	+	0.00614846i	−0.333560	+	0.942729i	$0.608250\pi$
$98$		0			0
$99$	−13.3268	−	11.1825i	−1.33940	−	1.12389i
$100$		0			0
$101$	−0.680922	+	3.86170i	−0.0677543	+	0.384254i	0.932008	+	0.362438i	$0.118056\pi$
$101$	−0.680922	+	3.86170i	−0.0677543	+	0.384254i	−0.999762	+	0.0218153i	$0.993055\pi$
$102$		0			0
$103$	−5.87211	−	10.1708i	−0.578596	−	1.00216i	−0.995641	−	0.0932721i	$-0.970267\pi$
$103$	−5.87211	−	10.1708i	−0.578596	−	1.00216i	0.417044	−	0.908886i	$-0.363066\pi$
$104$		0			0
$105$	−29.7841	+	10.8405i	−2.90663	+	1.05793i
$106$		0			0
$107$	−8.04576	+	13.9357i	−0.777813	+	1.34721i	0.155387	+	0.987854i	$0.450338\pi$
$107$	−8.04576	+	13.9357i	−0.777813	+	1.34721i	−0.933200	+	0.359358i	$0.882996\pi$
$108$		0			0
$109$	8.14337	−	6.83310i	0.779993	−	0.654492i	−0.163254	−	0.986584i	$-0.552199\pi$
$109$	8.14337	−	6.83310i	0.779993	−	0.654492i	0.943247	+	0.332092i	$0.107754\pi$
$110$		0			0
$111$	−3.48886	−	19.7863i	−0.331148	−	1.87803i
$112$		0			0
$113$	−5.61856			−0.528549			−0.264275	−	0.964447i	$-0.585133\pi$
$113$	−5.61856			−0.528549			−0.264275	+	0.964447i	$0.585133\pi$
$114$		0			0
$115$	−11.0642			−1.03174
$116$		0			0
$117$	1.07785	+	6.11278i	0.0996471	+	0.565127i
$118$		0			0
$119$	2.84730	−	2.38917i	0.261011	−	0.219014i
$120$		0			0
$121$	2.74510	−	4.75465i	0.249555	−	0.432241i
$122$		0			0
$123$	28.4923	−	10.3704i	2.56907	−	0.935063i
$124$		0			0
$125$	−4.54323	−	7.86911i	−0.406359	−	0.703835i
$126$		0			0
$127$	−1.03209	+	5.85327i	−0.0915831	+	0.519393i	0.904158	+	0.427198i	$0.140499\pi$
$127$	−1.03209	+	5.85327i	−0.0915831	+	0.519393i	−0.995741	+	0.0921950i	$0.970612\pi$
$128$		0			0
$129$	−11.0628	−	9.28282i	−0.974028	−	0.817307i
$130$		0			0
$131$	−4.23783	−	1.54244i	−0.370261	−	0.134764i	0.150187	−	0.988658i	$-0.452013\pi$
$131$	−4.23783	−	1.54244i	−0.370261	−	0.134764i	−0.520447	+	0.853894i	$0.674235\pi$
$132$		0			0
$133$	8.66637	−	14.5202i	0.751470	−	1.25906i
$134$		0			0
$135$	33.8692	+	12.3274i	2.91499	+	1.06097i
$136$		0			0
$137$	−5.24376	−	4.40003i	−0.448004	−	0.375920i	0.390690	−	0.920522i	$-0.372236\pi$
$137$	−5.24376	−	4.40003i	−0.448004	−	0.375920i	−0.838695	+	0.544602i	$0.816681\pi$
$138$		0			0
$139$	2.93717	−	16.6575i	0.249127	−	1.41287i	−0.561582	−	0.827421i	$-0.689807\pi$
$139$	2.93717	−	16.6575i	0.249127	−	1.41287i	0.810709	−	0.585449i	$-0.199082\pi$
$140$		0			0
$141$	11.5680	+	20.0364i	0.974205	+	1.68737i
$142$		0			0
$143$	1.84730	−	0.672361i	0.154479	−	0.0562256i
$144$		0			0
$145$	−4.39053	+	7.60462i	−0.364614	+	0.631529i
$146$		0			0
$147$	19.8969	−	16.6955i	1.64107	−	1.37702i
$148$		0			0
$149$	0.00134417	+	0.00762319i	0.000110119	+	0.000624516i	0.984863	−	0.173336i	$-0.0554546\pi$
$149$	0.00134417	+	0.00762319i	0.000110119	+	0.000624516i	−0.984753	+	0.173960i	$0.944344\pi$
$150$		0			0
$151$	−5.44831			−0.443377			−0.221689	−	0.975118i	$-0.571157\pi$
$151$	−5.44831			−0.443377			−0.221689	+	0.975118i	$0.571157\pi$
$152$		0			0
$153$	−7.10101			−0.574083
$154$		0			0
$155$	2.03936	+	11.5658i	0.163806	+	0.928988i
$156$		0			0
$157$	−18.0758	+	15.1674i	−1.44261	+	1.21049i	−0.504843	+	0.863211i	$0.668450\pi$
$157$	−18.0758	+	15.1674i	−1.44261	+	1.21049i	−0.937762	+	0.347278i	$0.887106\pi$
$158$		0			0
$159$	6.83157	−	11.8326i	0.541778	−	0.938388i
$160$		0			0
$161$	15.9290	−	5.79769i	1.25538	−	0.456922i
$162$		0			0
$163$	9.97431	+	17.2760i	0.781248	+	1.35316i	0.931215	+	0.364470i	$0.118750\pi$
$163$	9.97431	+	17.2760i	0.781248	+	1.35316i	−0.149967	+	0.988691i	$0.547917\pi$
$164$		0			0
$165$	3.33022	−	18.8866i	0.259257	−	1.47032i
$166$		0			0
$167$	−0.418748	−	0.351371i	−0.0324037	−	0.0271899i	0.626442	−	0.779468i	$-0.284511\pi$
$167$	−0.418748	−	0.351371i	−0.0324037	−	0.0271899i	−0.658846	+	0.752278i	$0.728955\pi$
$168$		0			0
$169$	11.5569	+	4.20637i	0.888993	+	0.323567i
$170$		0			0
$171$	−30.5146	+	10.6079i	−2.33351	+	0.811208i
$172$		0			0
$173$	−10.6750	−	3.88538i	−0.811605	−	0.295400i	−0.0973181	−	0.995253i	$-0.531026\pi$
$173$	−10.6750	−	3.88538i	−0.811605	−	0.295400i	−0.714287	+	0.699853i	$0.753249\pi$
$174$		0			0
$175$	−4.19459	−	3.51968i	−0.317081	−	0.266063i
$176$		0			0
$177$	4.72550	−	26.7996i	0.355190	−	2.01438i
$178$		0			0
$179$	0.922618	+	1.59802i	0.0689597	+	0.119442i	0.898444	−	0.439089i	$-0.144699\pi$
$179$	0.922618	+	1.59802i	0.0689597	+	0.119442i	−0.829484	+	0.558531i	$0.811365\pi$
$180$		0			0
$181$	4.30541	−	1.56704i	0.320018	−	0.116477i	−0.177016	−	0.984208i	$-0.556644\pi$
$181$	4.30541	−	1.56704i	0.320018	−	0.116477i	0.497034	+	0.867731i	$0.334422\pi$
$182$		0			0
$183$	10.3079	−	17.8539i	0.761984	−	1.31980i
$184$		0			0
$185$	12.0778	−	10.1345i	0.887981	−	0.745105i
$186$		0			0
$187$	0.390530	+	2.21480i	0.0285584	+	0.161962i
$188$		0			0
$189$	−55.2208			−4.01672
$190$		0			0
$191$	2.08647			0.150971			0.0754857	−	0.997147i	$-0.475949\pi$
$191$	2.08647			0.150971			0.0754857	+	0.997147i	$0.475949\pi$
$192$		0			0
$193$	4.36871	+	24.7762i	0.314466	+	1.78343i	0.575196	+	0.818016i	$0.304926\pi$
$193$	4.36871	+	24.7762i	0.314466	+	1.78343i	−0.260729	+	0.965412i	$0.583963\pi$
$194$		0			0
$195$	−5.24170	+	4.39831i	−0.375366	+	0.314969i
$196$		0			0
$197$	−12.4153	+	21.5040i	−0.884557	+	1.53210i	−0.0383357	+	0.999265i	$0.512206\pi$
$197$	−12.4153	+	21.5040i	−0.884557	+	1.53210i	−0.846221	+	0.532832i	$0.821128\pi$
$198$		0			0
$199$	−11.6750	+	4.24935i	−0.827618	+	0.301228i	−0.720881	−	0.693059i	$-0.756263\pi$
$199$	−11.6750	+	4.24935i	−0.827618	+	0.301228i	−0.106737	+	0.994287i	$0.534040\pi$
$200$		0			0
$201$	21.8803	+	37.8978i	1.54332	+	2.67311i
$202$		0			0
$203$	2.33615	−	13.2490i	0.163966	−	0.929896i
$204$		0			0
$205$	18.2271	+	15.2944i	1.27304	+	1.06821i
$206$		0			0
$207$	−30.4320	−	11.0763i	−2.11517	−	0.769859i
$208$		0			0
$209$	4.98680	+	8.93410i	0.344944	+	0.617984i
$210$		0			0
$211$	1.73396	+	0.631108i	0.119370	+	0.0434473i	0.401015	−	0.916072i	$-0.368658\pi$
$211$	1.73396	+	0.631108i	0.119370	+	0.0434473i	−0.281644	+	0.959519i	$0.590880\pi$
$212$		0			0
$213$	−21.1019	−	17.7066i	−1.44588	−	1.21324i
$214$		0			0
$215$	1.96791	−	11.1606i	0.134210	−	0.761145i
$216$		0			0
$217$	−8.99660	−	15.5826i	−0.610729	−	1.05781i
$218$		0			0
$219$	−27.0060	+	9.82938i	−1.82490	+	0.664208i
$220$		0			0
$221$	0.401207	−	0.694911i	0.0269881	−	0.0467448i
$222$		0			0
$223$	10.9474	−	9.18599i	0.733094	−	0.615139i	−0.197879	−	0.980226i	$-0.563405\pi$
$223$	10.9474	−	9.18599i	0.733094	−	0.615139i	0.930973	+	0.365087i	$0.118961\pi$
$224$		0			0
$225$	1.81655	+	10.3022i	0.121103	+	0.686812i
$226$		0			0
$227$	16.7023			1.10857			0.554286	−	0.832326i	$-0.312991\pi$
$227$	16.7023			1.10857			0.554286	+	0.832326i	$0.312991\pi$
$228$		0			0
$229$	5.32501			0.351886			0.175943	−	0.984400i	$-0.443702\pi$
$229$	5.32501			0.351886			0.175943	+	0.984400i	$0.443702\pi$
$230$		0			0
$231$	5.10220	+	28.9360i	0.335700	+	1.90385i
$232$		0			0
$233$	22.5915	−	18.9565i	1.48002	−	1.24188i	0.573856	−	0.818956i	$-0.305447\pi$
$233$	22.5915	−	18.9565i	1.48002	−	1.24188i	0.906163	−	0.422928i	$-0.138998\pi$
$234$		0			0
$235$	−9.07785	+	15.7233i	−0.592174	+	1.02567i
$236$		0			0
$237$	11.3140	−	4.11797i	0.734925	−	0.267491i
$238$		0			0
$239$	−9.33022	−	16.1604i	−0.603522	−	1.04533i	−0.992283	−	0.123992i	$-0.960430\pi$
$239$	−9.33022	−	16.1604i	−0.603522	−	1.04533i	0.388761	−	0.921339i	$-0.372903\pi$
$240$		0			0
$241$	−1.87464	+	10.6316i	−0.120756	+	0.684841i	0.862982	+	0.505234i	$0.168594\pi$
$241$	−1.87464	+	10.6316i	−0.120756	+	0.684841i	−0.983738	+	0.179607i	$0.942517\pi$
$242$		0			0
$243$	25.8576	+	21.6971i	1.65876	+	1.39187i
$244$		0			0
$245$	19.1532	+	6.97118i	1.22365	+	0.445373i
$246$		0			0
$247$	0.685975	−	3.58553i	0.0436475	−	0.228142i
$248$		0			0
$249$	7.48293	+	2.72356i	0.474211	+	0.172599i
$250$		0			0
$251$	8.11721	+	6.81115i	0.512354	+	0.429916i	0.861957	−	0.506982i	$-0.169239\pi$
$251$	8.11721	+	6.81115i	0.512354	+	0.429916i	−0.349603	+	0.936898i	$0.613683\pi$
$252$		0			0
$253$	−1.78106	+	10.1009i	−0.111974	+	0.635037i
$254$		0			0
$255$	−3.91400	−	6.77925i	−0.245104	−	0.424533i
$256$		0			0
$257$	−1.76352	+	0.641868i	−0.110005	+	0.0400386i	−0.396436	−	0.918062i	$-0.629753\pi$
$257$	−1.76352	+	0.641868i	−0.110005	+	0.0400386i	0.286431	+	0.958101i	$0.407531\pi$
$258$		0			0
$259$	−12.0778	+	20.9194i	−0.750481	+	1.29987i
$260$		0			0
$261$	−19.6891	+	16.5211i	−1.21873	+	1.02263i
$262$		0			0
$263$	1.44104	+	8.17253i	0.0888581	+	0.503940i	0.996457	+	0.0841015i	$0.0268020\pi$
$263$	1.44104	+	8.17253i	0.0888581	+	0.503940i	−0.907599	+	0.419838i	$0.862087\pi$
$264$		0			0
$265$	10.7219			0.658643
$266$		0			0
$267$	−7.36690			−0.450847
$268$		0			0
$269$	−2.51872	−	14.2844i	−0.153569	−	0.870935i	−0.960082	−	0.279718i	$-0.909759\pi$
$269$	−2.51872	−	14.2844i	−0.153569	−	0.870935i	0.806513	−	0.591216i	$-0.201352\pi$
$270$		0			0
$271$	11.6702	−	9.79250i	0.708917	−	0.594852i	−0.215378	−	0.976531i	$-0.569098\pi$
$271$	11.6702	−	9.79250i	0.708917	−	0.594852i	0.924295	+	0.381679i	$0.124654\pi$
$272$		0			0
$273$	5.24170	−	9.07888i	0.317242	−	0.549479i
$274$		0			0
$275$	3.11334	−	1.13316i	0.187742	−	0.0683323i
$276$		0			0
$277$	−1.40895	−	2.44037i	−0.0846555	−	0.146628i	0.820589	−	0.571519i	$-0.193646\pi$
$277$	−1.40895	−	2.44037i	−0.0846555	−	0.146628i	−0.905244	+	0.424891i	$0.860312\pi$
$278$		0			0
$279$	−5.96926	+	33.8533i	−0.357370	+	2.02675i
$280$		0			0
$281$	−5.97178	−	5.01092i	−0.356247	−	0.298926i	0.447046	−	0.894511i	$-0.352476\pi$
$281$	−5.97178	−	5.01092i	−0.356247	−	0.298926i	−0.803293	+	0.595585i	$0.796920\pi$
$282$		0			0
$283$	19.6621	+	7.15642i	1.16879	+	0.425405i	0.852230	−	0.523168i	$-0.175250\pi$
$283$	19.6621	+	7.15642i	1.16879	+	0.425405i	0.316560	+	0.948572i	$0.397472\pi$
$284$		0			0
$285$	−26.9466	−	23.2849i	−1.59618	−	1.37928i
$286$		0			0
$287$	−34.2558	−	12.4681i	−2.02206	−	0.735969i
$288$		0			0
$289$	−12.3195	−	10.3373i	−0.724679	−	0.608078i
$290$		0			0
$291$	−0.0992034	+	0.562610i	−0.00581541	+	0.0329808i
$292$		0			0
$293$	−13.9304	−	24.1281i	−0.813820	−	1.40958i	−0.910172	−	0.414231i	$-0.864051\pi$
$293$	−13.9304	−	24.1281i	−0.813820	−	1.40958i	0.0963516	−	0.995347i	$-0.469283\pi$
$294$		0			0
$295$	20.0672	−	7.30385i	1.16836	−	0.425247i
$296$		0			0
$297$	16.7062	−	28.9360i	0.969392	−	1.67904i
$298$		0			0
$299$	2.80335	−	2.35229i	0.162122	−	0.136036i
$300$		0			0
$301$	3.01501	+	17.0990i	0.173783	+	0.985570i
$302$		0			0
$303$	−12.6527			−0.726879
$304$		0			0
$305$	16.1780			0.926349
$306$		0			0
$307$	2.42380	+	13.7461i	0.138334	+	0.784529i	0.972480	+	0.232986i	$0.0748496\pi$
$307$	2.42380	+	13.7461i	0.138334	+	0.784529i	−0.834147	+	0.551543i	$0.814039\pi$
$308$		0			0
$309$	29.0292	−	24.3584i	1.65141	−	1.38570i
$310$		0			0
$311$	2.48886	−	4.31082i	0.141130	−	0.244444i	−0.786792	−	0.617218i	$-0.788260\pi$
$311$	2.48886	−	4.31082i	0.141130	−	0.244444i	0.927922	+	0.372773i	$0.121593\pi$
$312$		0			0
$313$	−1.75965	+	0.640459i	−0.0994612	+	0.0362009i	−0.391271	−	0.920275i	$-0.627965\pi$
$313$	−1.75965	+	0.640459i	−0.0994612	+	0.0362009i	0.291810	+	0.956476i	$0.405742\pi$
$314$		0			0
$315$	−36.4013	−	63.0488i	−2.05098	−	3.55240i
$316$		0			0
$317$	−5.24510	+	29.7464i	−0.294594	+	1.67073i	0.374253	+	0.927327i	$0.377899\pi$
$317$	−5.24510	+	29.7464i	−0.294594	+	1.67073i	−0.668847	+	0.743400i	$0.733212\pi$
$318$		0			0
$319$	6.23577	+	5.23243i	0.349136	+	0.292960i
$320$		0			0
$321$	−48.7909	−	17.7584i	−2.72324	−	0.991180i
$322$		0			0
$323$	3.90332	+	1.48513i	0.217187	+	0.0826351i
$324$		0			0
$325$	−1.11081	−	0.404303i	−0.0616169	−	0.0224267i
$326$		0			0
$327$	26.2761	+	22.0482i	1.45307	+	1.21927i
$328$		0			0
$329$	4.83022	−	27.3936i	0.266299	−	1.51026i
$330$		0			0
$331$	−4.86959	−	8.43437i	−0.267657	−	0.463595i	0.700600	−	0.713555i	$-0.252916\pi$
$331$	−4.86959	−	8.43437i	−0.267657	−	0.463595i	−0.968256	+	0.249960i	$0.919583\pi$
$332$		0			0
$333$	43.3658	−	15.7838i	2.37643	−	0.864950i
$334$		0			0
$335$	−17.1702	+	29.7397i	−0.938111	+	1.62486i
$336$		0			0
$337$	−14.0458	+	11.7858i	−0.765121	+	0.642013i	−0.939454	−	0.342674i	$-0.888667\pi$
$337$	−14.0458	+	11.7858i	−0.765121	+	0.642013i	0.174333	+	0.984687i	$0.444223\pi$
$338$		0			0
$339$	−3.14812	−	17.8539i	−0.170982	−	0.969689i
$340$		0			0
$341$	10.8871			0.589571
$342$		0			0
$343$	−4.07192			−0.219863
$344$		0			0
$345$	−6.19934	−	35.1582i	−0.333761	−	1.89285i
$346$		0			0
$347$	2.61721	−	2.19610i	0.140499	−	0.117893i	−0.569829	−	0.821763i	$-0.692991\pi$
$347$	2.61721	−	2.19610i	0.140499	−	0.117893i	0.710329	+	0.703870i	$0.248546\pi$
$348$		0			0
$349$	−3.45218	+	5.97935i	−0.184791	+	0.320067i	−0.943506	−	0.331355i	$-0.892494\pi$
$349$	−3.45218	+	5.97935i	−0.184791	+	0.320067i	0.758715	+	0.651423i	$0.225827\pi$
$350$		0			0
$351$	−11.2023	+	4.07732i	−0.597936	+	0.217631i
$352$		0			0
$353$	16.5903	+	28.7353i	0.883015	+	1.52943i	0.847973	+	0.530040i	$0.177823\pi$
$353$	16.5903	+	28.7353i	0.883015	+	1.52943i	0.0350420	+	0.999386i	$0.488843\pi$
$354$		0			0
$355$	3.75372	−	21.2884i	0.199227	−	1.12987i
$356$		0			0
$357$	9.18732	+	7.70908i	0.486244	+	0.408008i
$358$		0			0
$359$	18.5680	+	6.75822i	0.979984	+	0.356685i	0.781834	−	0.623487i	$-0.214284\pi$
$359$	18.5680	+	6.75822i	0.979984	+	0.356685i	0.198150	+	0.980172i	$0.436507\pi$
$360$		0			0
$361$	18.9920	+	0.550931i	0.999580	+	0.0289964i
$362$		0			0
$363$	16.6468	+	6.05893i	0.873729	+	0.318011i
$364$		0			0
$365$	−17.2763	−	14.4965i	−0.904283	−	0.758784i
$366$		0			0
$367$	−4.41581	+	25.0433i	−0.230503	+	1.30725i	0.621376	+	0.783512i	$0.286574\pi$
$367$	−4.41581	+	25.0433i	−0.230503	+	1.30725i	−0.851880	+	0.523738i	$0.824537\pi$
$368$		0			0
$369$	34.8225	+	60.3144i	1.81279	+	3.13984i
$370$		0			0
$371$	−15.4363	+	5.61835i	−0.801412	+	0.291690i
$372$		0			0
$373$	4.44222	−	7.69415i	0.230009	−	0.398388i	−0.727801	−	0.685788i	$-0.759458\pi$
$373$	4.44222	−	7.69415i	0.230009	−	0.398388i	0.957811	+	0.287400i	$0.0927910\pi$
$374$		0			0
$375$	22.4598	−	18.8460i	1.15982	−	0.973202i
$376$		0			0
$377$	−0.504337	−	2.86024i	−0.0259747	−	0.147310i
$378$		0			0
$379$	−11.3327			−0.582124			−0.291062	−	0.956704i	$-0.594009\pi$
$379$	−11.3327			−0.582124			−0.291062	+	0.956704i	$0.594009\pi$
$380$		0			0
$381$	−19.1780			−0.982518
$382$		0			0
$383$	−6.42309	−	36.4271i	−0.328204	−	1.86134i	−0.486128	−	0.873888i	$-0.661591\pi$
$383$	−6.42309	−	36.4271i	−0.328204	−	1.86134i	0.157923	−	0.987451i	$-0.449520\pi$
$384$		0			0
$385$	−17.6630	+	14.8210i	−0.900188	+	0.755348i
$386$		0			0
$387$	16.5856	−	28.7271i	0.843093	−	1.46028i
$388$		0			0
$389$	−16.9500	+	6.16928i	−0.859397	+	0.312795i	−0.733866	−	0.679295i	$-0.762286\pi$
$389$	−16.9500	+	6.16928i	−0.859397	+	0.312795i	−0.125531	+	0.992090i	$0.540064\pi$
$390$		0			0
$391$	2.09327	+	3.62566i	0.105861	+	0.183357i
$392$		0			0
$393$	2.52687	−	14.3306i	0.127464	−	0.722884i
$394$		0			0
$395$	7.23783	+	6.07326i	0.364175	+	0.305579i
$396$		0			0
$397$	6.16297	+	2.24314i	0.309311	+	0.112580i	0.492012	−	0.870589i	$-0.336262\pi$
$397$	6.16297	+	2.24314i	0.309311	+	0.112580i	−0.182701	+	0.983169i	$0.558484\pi$
$398$		0			0
$399$	50.9962	+	19.4030i	2.55300	+	0.971366i
$400$		0			0
$401$	−26.5929	−	9.67901i	−1.32798	−	0.483347i	−0.421976	−	0.906607i	$-0.638663\pi$
$401$	−26.5929	−	9.67901i	−1.32798	−	0.483347i	−0.906008	+	0.423260i	$0.860886\pi$
$402$		0			0
$403$	−2.97565	−	2.49687i	−0.148228	−	0.124378i
$404$		0			0
$405$	−10.4187	+	59.0877i	−0.517712	+	2.93609i
$406$		0			0
$407$	−7.30793	−	12.6577i	−0.362241	−	0.627419i
$408$		0			0
$409$	−18.4153	+	6.70264i	−0.910580	+	0.331424i	−0.754485	−	0.656318i	$-0.772113\pi$
$409$	−18.4153	+	6.70264i	−0.910580	+	0.331424i	−0.156096	+	0.987742i	$0.549891\pi$
$410$		0			0
$411$	11.0437	−	19.1282i	0.544746	−	0.943527i
$412$		0			0
$413$	−25.0633	+	21.0306i	−1.23328	+	1.03485i
$414$		0			0
$415$	1.08512	+	6.15403i	0.0532666	+	0.302090i
$416$		0			0
$417$	54.5776			2.67268
$418$		0			0
$419$	−7.94450			−0.388114			−0.194057	−	0.980990i	$-0.562165\pi$
$419$	−7.94450			−0.388114			−0.194057	+	0.980990i	$0.562165\pi$
$420$		0			0
$421$	−2.26857	−	12.8657i	−0.110563	−	0.627036i	−0.988852	−	0.148904i	$-0.952425\pi$
$421$	−2.26857	−	12.8657i	−0.110563	−	0.627036i	0.878288	−	0.478132i	$-0.158686\pi$
$422$		0			0
$423$	−40.7092	+	34.1591i	−1.97935	+	1.66087i
$424$		0			0
$425$	0.676174	−	1.17117i	0.0327993	−	0.0568100i
$426$		0			0
$427$	−23.2913	+	8.47735i	−1.12715	+	0.410248i
$428$		0			0
$429$	3.17159	+	5.49335i	0.153126	+	0.265222i
$430$		0			0
$431$	2.09879	−	11.9028i	0.101095	−	0.573340i	−0.891613	−	0.452798i	$-0.850426\pi$
$431$	2.09879	−	11.9028i	0.101095	−	0.573340i	0.992708	−	0.120542i	$-0.0384631\pi$
$432$		0			0
$433$	−16.0929	−	13.5035i	−0.773374	−	0.648938i	0.168197	−	0.985753i	$-0.446206\pi$
$433$	−16.0929	−	13.5035i	−0.773374	−	0.648938i	−0.941571	+	0.336816i	$0.890650\pi$
$434$		0			0
$435$	−26.6250	−	9.69069i	−1.27657	−	0.464633i
$436$		0			0
$437$	14.4115	+	12.4532i	0.689394	+	0.595716i
$438$		0			0
$439$	2.84477	+	1.03541i	0.135773	+	0.0494175i	0.409013	−	0.912528i	$-0.365873\pi$
$439$	2.84477	+	1.03541i	0.135773	+	0.0494175i	−0.273240	+	0.961946i	$0.588095\pi$
$440$		0			0
$441$	45.7019	+	38.3485i	2.17628	+	1.82612i
$442$		0			0
$443$	1.48680	−	8.43204i	0.0706398	−	0.400618i	−0.928901	−	0.370327i	$-0.879246\pi$
$443$	1.48680	−	8.43204i	0.0706398	−	0.400618i	0.999541	−	0.0302910i	$-0.00964338\pi$
$444$		0			0
$445$	−2.89053	−	5.00654i	−0.137024	−	0.237333i
$446$		0			0
$447$	−0.0234708	+	0.00854266i	−0.00111013	+	0.000404054i
$448$		0			0
$449$	11.5312	−	19.9726i	0.544192	−	0.942567i	−0.454466	−	0.890764i	$-0.650170\pi$
$449$	11.5312	−	19.9726i	0.544192	−	0.942567i	0.998657	−	0.0518032i	$-0.0164968\pi$
$450$		0			0
$451$	16.8969	−	14.1782i	0.795645	−	0.667626i
$452$		0			0
$453$	−3.05273	−	17.3129i	−0.143430	−	0.813430i
$454$		0			0
$455$	8.22668			0.385673
$456$		0			0
$457$	−25.4953			−1.19262			−0.596309	−	0.802755i	$-0.703367\pi$
$457$	−25.4953			−1.19262			−0.596309	+	0.802755i	$0.703367\pi$
$458$		0			0
$459$	−2.36824	−	13.4310i	−0.110540	−	0.626904i
$460$		0			0
$461$	−27.6446	+	23.1965i	−1.28754	+	1.08037i	−0.295377	+	0.955381i	$0.595445\pi$
$461$	−27.6446	+	23.1965i	−1.28754	+	1.08037i	−0.992158	+	0.124990i	$0.960110\pi$
$462$		0			0
$463$	−20.7695	+	35.9738i	−0.965241	+	1.67185i	−0.256274	+	0.966604i	$0.582495\pi$
$463$	−20.7695	+	35.9738i	−0.965241	+	1.67185i	−0.708967	+	0.705242i	$0.750838\pi$
$464$		0			0
$465$	−35.6095	+	12.9608i	−1.65135	+	0.601043i
$466$		0			0
$467$	−3.25537	−	5.63846i	−0.150640	−	0.260917i	0.780823	−	0.624753i	$-0.214800\pi$
$467$	−3.25537	−	5.63846i	−0.150640	−	0.260917i	−0.931463	+	0.363836i	$0.881467\pi$
$468$		0			0
$469$	9.13610	−	51.8134i	0.421866	−	2.39252i
$470$		0			0
$471$	−58.3248	−	48.9403i	−2.68747	−	2.25505i
$472$		0			0
$473$	−9.87211	−	3.59315i	−0.453920	−	0.165213i
$474$		0			0
$475$	1.15611	−	6.04288i	0.0530458	−	0.277266i
$476$		0			0
$477$	29.4907	+	10.7337i	1.35028	+	0.491463i
$478$		0			0
$479$	14.0856	+	11.8192i	0.643587	+	0.540034i	0.905117	−	0.425162i	$-0.139783\pi$
$479$	14.0856	+	11.8192i	0.643587	+	0.540034i	−0.261530	+	0.965195i	$0.584227\pi$
$480$		0			0
$481$	−0.905544	+	5.13560i	−0.0412893	+	0.234163i
$482$		0			0
$483$	27.3482	+	47.3685i	1.24439	+	2.15534i
$484$		0			0
$485$	−0.421274	+	0.153331i	−0.0191291	+	0.00696242i
$486$		0			0
$487$	−16.8662	+	29.2131i	−0.764280	+	1.32377i	0.176347	+	0.984328i	$0.443572\pi$
$487$	−16.8662	+	29.2131i	−0.764280	+	1.32377i	−0.940627	+	0.339443i	$0.889761\pi$
$488$		0			0
$489$	−49.3086	+	41.3748i	−2.22981	+	1.87104i
$490$		0			0
$491$	2.41859	+	13.7165i	0.109149	+	0.619016i	0.989482	+	0.144659i	$0.0462084\pi$
$491$	2.41859	+	13.7165i	0.109149	+	0.619016i	−0.880332	+	0.474357i	$0.842680\pi$
$492$		0			0
$493$	3.32264			0.149644
$494$		0			0
$495$	44.0506			1.97993
$496$		0			0
$497$	5.75103	+	32.6157i	0.257969	+	1.46301i
$498$		0			0
$499$	−25.9978	+	21.8147i	−1.16382	+	0.976561i	−0.999951	−	0.00992074i	$-0.996842\pi$
$499$	−25.9978	+	21.8147i	−1.16382	+	0.976561i	−0.163870	+	0.986482i	$0.552398\pi$
$500$		0			0
$501$	0.881911	−	1.52752i	0.0394009	−	0.0682444i
$502$		0			0
$503$	8.25372	−	3.00411i	0.368015	−	0.133947i	−0.151391	−	0.988474i	$-0.548375\pi$
$503$	8.25372	−	3.00411i	0.368015	−	0.133947i	0.519406	+	0.854527i	$0.326153\pi$
$504$		0			0
$505$	−4.96451	−	8.59878i	−0.220918	−	0.382641i
$506$		0			0
$507$	−6.89100	+	39.0808i	−0.306040	+	1.73564i
$508$		0			0
$509$	−18.6327	−	15.6347i	−0.825880	−	0.692995i	0.128461	−	0.991715i	$-0.458996\pi$
$509$	−18.6327	−	15.6347i	−0.825880	−	0.692995i	−0.954341	+	0.298719i	$0.903441\pi$
$510$		0			0
$511$	32.4688	+	11.8177i	1.43634	+	0.522784i
$512$		0			0
$513$	−30.2408	−	54.1779i	−1.33516	−	2.39201i
$514$		0			0
$515$	27.9440	+	10.1708i	1.23136	+	0.448179i
$516$		0			0
$517$	12.8931	+	10.8186i	0.567036	+	0.475800i
$518$		0			0
$519$	6.36514	−	36.0985i	0.279399	−	1.58455i
$520$		0			0
$521$	−2.06418	−	3.57526i	−0.0904333	−	0.156635i	0.817260	−	0.576269i	$-0.195492\pi$
$521$	−2.06418	−	3.57526i	−0.0904333	−	0.156635i	−0.907694	+	0.419634i	$0.862159\pi$
$522$		0			0
$523$	36.4752	−	13.2759i	1.59495	−	0.580515i	0.616565	−	0.787304i	$-0.288524\pi$
$523$	36.4752	−	13.2759i	1.59495	−	0.580515i	0.978386	+	0.206789i	$0.0663014\pi$
$524$		0			0
$525$	8.83409	−	15.3011i	0.385551	−	0.667795i
$526$		0			0
$527$	3.40420	−	2.85646i	0.148289	−	0.124429i
$528$		0			0
$529$	−0.678396	−	3.84737i	−0.0294955	−	0.167277i
$530$		0			0
$531$	62.5066			2.71256
$532$		0			0
$533$	−7.86989			−0.340883
$534$		0			0
$535$	−7.07532	−	40.1261i	−0.305893	−	1.73480i
$536$		0			0
$537$	−4.56102	+	3.82715i	−0.196823	+	0.165154i
$538$		0			0
$539$	9.44743	−	16.3634i	0.406930	−	0.704823i
$540$		0			0
$541$	34.7622	−	12.6524i	1.49455	−	0.543970i	0.539903	−	0.841727i	$-0.318461\pi$
$541$	34.7622	−	12.6524i	1.49455	−	0.543970i	0.954642	+	0.297757i	$0.0962386\pi$
$542$		0			0
$543$	7.39187	+	12.8031i	0.317216	+	0.549434i
$544$		0			0
$545$	−4.67412	+	26.5082i	−0.200217	+	1.13549i
$546$		0			0
$547$	−17.9394	−	15.0530i	−0.767035	−	0.643619i	0.172913	−	0.984937i	$-0.444682\pi$
$547$	−17.9394	−	15.0530i	−0.767035	−	0.643619i	−0.939948	+	0.341318i	$0.889127\pi$
$548$		0			0
$549$	44.4975	+	16.1958i	1.89911	+	0.691219i
$550$		0			0
$551$	14.2781	−	4.96356i	0.608268	−	0.211455i
$552$		0			0
$553$	−13.6027	−	4.95096i	−0.578444	−	0.210536i
$554$		0			0
$555$	38.9714	+	32.7009i	1.65424	+	1.38807i
$556$		0			0
$557$	−3.35086	+	19.0037i	−0.141981	+	0.805212i	0.827761	+	0.561080i	$0.189614\pi$
$557$	−3.35086	+	19.0037i	−0.141981	+	0.805212i	−0.969742	+	0.244132i	$0.921497\pi$
$558$		0			0
$559$	1.87417	+	3.24616i	0.0792690	+	0.137298i
$560$		0			0
$561$	−6.81908	+	2.48194i	−0.287902	+	0.104788i
$562$		0			0
$563$	7.93763	−	13.7484i	0.334531	−	0.579425i	−0.648863	−	0.760905i	$-0.724755\pi$
$563$	7.93763	−	13.7484i	0.334531	−	0.579425i	0.983395	+	0.181480i	$0.0580887\pi$
$564$		0			0
$565$	10.8983	−	9.14473i	0.458494	−	0.384722i
$566$		0			0
$567$	−15.9624	−	90.5275i	−0.670360	−	3.80180i
$568$		0			0
$569$	11.8571			0.497075			0.248538	−	0.968622i	$-0.420050\pi$
$569$	11.8571			0.497075			0.248538	+	0.968622i	$0.420050\pi$
$570$		0			0
$571$	12.0291			0.503402			0.251701	−	0.967805i	$-0.419010\pi$
$571$	12.0291			0.503402			0.251701	+	0.967805i	$0.419010\pi$
$572$		0			0
$573$	1.16906	+	6.63008i	0.0488383	+	0.276976i
$574$		0			0
$575$	4.72462	−	3.96443i	0.197030	−	0.165328i
$576$		0			0
$577$	14.1163	−	24.4502i	0.587671	−	1.01788i	−0.406866	−	0.913488i	$-0.633378\pi$
$577$	14.1163	−	24.4502i	0.587671	−	1.01788i	0.994537	−	0.104388i	$-0.0332883\pi$
$578$		0			0
$579$	−76.2825	+	27.7645i	−3.17019	+	1.15386i
$580$		0			0
$581$	−4.78699	−	8.29131i	−0.198598	−	0.343981i
$582$		0			0
$583$	1.72597	−	9.78844i	0.0714822	−	0.405396i
$584$		0			0
$585$	−12.0398	−	10.1026i	−0.497786	−	0.417692i
$586$		0			0
$587$	−29.4069	−	10.7032i	−1.21375	−	0.441770i	−0.345748	−	0.938327i	$-0.612375\pi$
$587$	−29.4069	−	10.7032i	−1.21375	−	0.441770i	−0.868004	+	0.496558i	$0.834597\pi$
$588$		0			0
$589$	10.3614	−	17.3602i	0.426935	−	0.715316i
$590$		0			0
$591$	−75.2889	−	27.4029i	−3.09697	−	1.12720i
$592$		0			0
$593$	−8.83481	−	7.41328i	−0.362802	−	0.304427i	0.443104	−	0.896470i	$-0.353877\pi$
$593$	−8.83481	−	7.41328i	−0.362802	−	0.304427i	−0.805906	+	0.592043i	$0.798322\pi$
$594$		0			0
$595$	−1.63429	+	9.26849i	−0.0669992	+	0.379971i
$596$		0			0
$597$	−20.0446	−	34.7182i	−0.820370	−	1.42092i
$598$		0			0
$599$	2.53374	−	0.922205i	0.103526	−	0.0376803i	−0.289738	−	0.957106i	$-0.593568\pi$
$599$	2.53374	−	0.922205i	0.103526	−	0.0376803i	0.393264	+	0.919426i	$0.371346\pi$
$600$		0			0
$601$	−2.88026	+	4.98876i	−0.117488	+	0.203496i	−0.918772	−	0.394789i	$-0.870818\pi$
$601$	−2.88026	+	4.98876i	−0.117488	+	0.203496i	0.801283	+	0.598285i	$0.204151\pi$
$602$		0			0
$603$	−76.9992	+	64.6100i	−3.13565	+	2.63112i
$604$		0			0
$605$	2.41400	+	13.6905i	0.0981431	+	0.556597i
$606$		0			0
$607$	−11.7510			−0.476960			−0.238480	−	0.971147i	$-0.576649\pi$
$607$	−11.7510			−0.476960			−0.238480	+	0.971147i	$0.576649\pi$
$608$		0			0
$609$	43.4097			1.75905
$610$		0			0
$611$	−1.04277	−	5.91382i	−0.0421858	−	0.239248i
$612$		0			0
$613$	−10.9554	+	9.19269i	−0.442485	+	0.371289i	−0.836638	−	0.547755i	$-0.815482\pi$
$613$	−10.9554	+	9.19269i	−0.442485	+	0.371289i	0.394153	+	0.919045i	$0.371038\pi$
$614$		0			0
$615$	−38.3876	+	66.4893i	−1.54794	+	2.68111i
$616$		0			0
$617$	29.4440	−	10.7168i	1.18537	−	0.431440i	0.327276	−	0.944929i	$-0.393869\pi$
$617$	29.4440	−	10.7168i	1.18537	−	0.431440i	0.858096	+	0.513489i	$0.171647\pi$
$618$		0			0
$619$	−7.65776	−	13.2636i	−0.307791	−	0.533110i	0.670088	−	0.742282i	$-0.266256\pi$
$619$	−7.65776	−	13.2636i	−0.307791	−	0.533110i	−0.977879	+	0.209172i	$0.932923\pi$
$620$		0			0
$621$	10.8007	−	61.2536i	0.433416	−	2.45802i
$622$		0			0
$623$	6.78493	+	5.69323i	0.271832	+	0.228095i
$624$		0			0
$625$	28.2520	+	10.2829i	1.13008	+	0.411315i
$626$		0			0
$627$	−25.5954	+	20.8522i	−1.02218	+	0.832756i
$628$		0			0
$629$	−5.60607	−	2.04044i	−0.223529	−	0.0813577i
$630$		0			0
$631$	1.55438	+	1.30428i	0.0618788	+	0.0519225i	0.673203	−	0.739458i	$-0.264918\pi$
$631$	1.55438	+	1.30428i	0.0618788	+	0.0519225i	−0.611324	+	0.791381i	$0.709363\pi$
$632$		0			0
$633$	−1.03390	+	5.86354i	−0.0410938	+	0.233055i
$634$		0			0
$635$	−7.52481	−	13.0334i	−0.298613	−	0.517213i
$636$		0			0
$637$	−6.33497	+	2.30574i	−0.251001	+	0.0913568i
$638$		0			0
$639$	31.6364	−	54.7959i	1.25152	−	2.16769i
$640$		0			0
$641$	−2.97178	+	2.49362i	−0.117378	+	0.0984921i	−0.699588	−	0.714547i	$-0.746633\pi$
$641$	−2.97178	+	2.49362i	−0.117378	+	0.0984921i	0.582209	+	0.813039i	$0.302188\pi$
$642$		0			0
$643$	−3.01872	−	17.1200i	−0.119047	−	0.675148i	−0.984667	−	0.174446i	$-0.944186\pi$
$643$	−3.01872	−	17.1200i	−0.119047	−	0.675148i	0.865620	−	0.500702i	$-0.166925\pi$
$644$		0			0
$645$	36.5672			1.43983
$646$		0			0
$647$	27.3414			1.07490			0.537451	−	0.843295i	$-0.319387\pi$
$647$	27.3414			1.07490			0.537451	+	0.843295i	$0.319387\pi$
$648$		0			0
$649$	−3.43763	−	19.4958i	−0.134939	−	0.765277i
$650$		0			0
$651$	44.4752	−	37.3192i	1.74312	−	1.46265i
$652$		0			0
$653$	−14.5351	+	25.1755i	−0.568802	+	0.985193i	0.427883	+	0.903834i	$0.359259\pi$
$653$	−14.5351	+	25.1755i	−0.568802	+	0.985193i	−0.996685	+	0.0813594i	$0.974074\pi$
$654$		0			0
$655$	10.7306	−	3.90560i	0.419277	−	0.152604i
$656$		0			0
$657$	−33.0060	−	57.1680i	−1.28769	−	2.23034i
$658$		0			0
$659$	5.58125	−	31.6529i	0.217415	−	1.23302i	−0.659252	−	0.751922i	$-0.729127\pi$
$659$	5.58125	−	31.6529i	0.217415	−	1.23302i	0.876667	−	0.481098i	$-0.159762\pi$
$660$		0			0
$661$	29.7290	+	24.9456i	1.15632	+	0.970270i	0.999848	−	0.0174123i	$-0.00554278\pi$
$661$	29.7290	+	24.9456i	1.15632	+	0.970270i	0.156474	+	0.987682i	$0.449987\pi$
$662$		0			0
$663$	2.43299	+	0.885536i	0.0944896	+	0.0343914i
$664$		0			0
$665$	6.82295	+	42.2701i	0.264583	+	1.63917i
$666$		0			0
$667$	14.2395	+	5.18274i	0.551355	+	0.200677i
$668$		0			0
$669$	35.3239	+	29.6403i	1.36570	+	1.14596i
$670$		0			0
$671$	2.60426	−	14.7695i	0.100536	−	0.570169i
$672$		0			0
$673$	−5.58512	−	9.67372i	−0.215291	−	0.372894i	0.738072	−	0.674722i	$-0.235737\pi$
$673$	−5.58512	−	9.67372i	−0.215291	−	0.372894i	−0.953362	+	0.301828i	$0.902403\pi$
$674$		0			0
$675$	−18.8799	+	6.87170i	−0.726686	+	0.264492i
$676$		0			0
$677$	14.3466	−	24.8490i	0.551384	−	0.955025i	−0.446791	−	0.894638i	$-0.647433\pi$
$677$	14.3466	−	24.8490i	0.551384	−	0.955025i	0.998175	−	0.0603867i	$-0.0192334\pi$
$678$		0			0
$679$	0.526159	−	0.441500i	0.0201921	−	0.0169432i
$680$		0			0
$681$	9.35844	+	53.0744i	0.358616	+	2.03381i
$682$		0			0
$683$	−12.3550			−0.472752			−0.236376	−	0.971662i	$-0.575960\pi$
$683$	−12.3550			−0.472752			−0.236376	+	0.971662i	$0.575960\pi$
$684$		0			0
$685$	17.3327			0.662250
$686$		0			0
$687$	2.98364	+	16.9211i	0.113833	+	0.645579i
$688$		0			0
$689$	−2.71663	+	2.27953i	−0.103495	+	0.0868430i
$690$		0			0
$691$	−5.34998	+	9.26645i	−0.203523	+	0.352512i	−0.949661	−	0.313279i	$-0.898573\pi$
$691$	−5.34998	+	9.26645i	−0.203523	+	0.352512i	0.746138	+	0.665791i	$0.231906\pi$
$692$		0			0
$693$	−63.4193	+	23.0827i	−2.40910	+	0.876840i
$694$		0			0
$695$	21.4145	+	37.0909i	0.812297	+	1.40694i
$696$		0			0
$697$	1.56341	−	8.86652i	0.0592182	−	0.335843i
$698$		0			0
$699$	72.8956	+	61.1667i	2.75717	+	2.31354i
$700$		0			0
$701$	−18.6065	−	6.77222i	−0.702759	−	0.255783i	−0.0341706	−	0.999416i	$-0.510879\pi$
$701$	−18.6065	−	6.77222i	−0.702759	−	0.255783i	−0.668588	+	0.743633i	$0.733101\pi$
$702$		0			0
$703$	−27.1386	−	0.393544i	−1.02355	−	0.0148428i
$704$		0			0
$705$	−55.0497	−	20.0364i	−2.07329	−	0.754616i
$706$		0			0
$707$	11.6532	+	9.77817i	0.438263	+	0.367746i
$708$		0			0
$709$	2.06893	−	11.7335i	0.0777001	−	0.440659i	−0.920994	−	0.389576i	$-0.872622\pi$
$709$	2.06893	−	11.7335i	0.0777001	−	0.440659i	0.998694	−	0.0510832i	$-0.0162674\pi$
$710$		0			0
$711$	13.8277	+	23.9503i	0.518579	+	0.898205i
$712$		0			0
$713$	19.0446	−	6.93166i	0.713225	−	0.259593i
$714$		0			0
$715$	−2.48886	+	4.31082i	−0.0930779	+	0.161216i
$716$		0			0
$717$	46.1245	−	38.7031i	1.72255	−	1.44539i
$718$		0			0
$719$	8.13799	+	46.1529i	0.303496	+	1.72121i	0.630501	+	0.776188i	$0.282849\pi$
$719$	8.13799	+	46.1529i	0.303496	+	1.72121i	−0.327005	+	0.945023i	$0.606039\pi$
$720$		0			0
$721$	−45.5604			−1.69676
$722$		0			0
$723$	−34.8340			−1.29549
$724$		0			0
$725$	−0.849985	−	4.82050i	−0.0315676	−	0.179029i
$726$		0			0
$727$	−12.5496	+	10.5304i	−0.465440	+	0.390551i	−0.845128	−	0.534564i	$-0.820476\pi$
$727$	−12.5496	+	10.5304i	−0.465440	+	0.390551i	0.379688	+	0.925115i	$0.376031\pi$
$728$		0			0
$729$	−18.9145	+	32.7608i	−0.700536	+	1.21336i
$730$		0			0
$731$	−4.02956	+	1.46664i	−0.149039	+	0.0542457i
$732$		0			0
$733$	−13.3503	−	23.1234i	−0.493104	−	0.854082i	0.506864	−	0.862026i	$-0.330805\pi$
$733$	−13.3503	−	23.1234i	−0.493104	−	0.854082i	−0.999968	+	0.00794438i	$0.997471\pi$
$734$		0			0
$735$	−11.4204	+	64.7683i	−0.421248	+	2.38901i
$736$		0			0
$737$	24.3865	+	20.4627i	0.898288	+	0.753753i
$738$		0			0
$739$	12.3598	+	4.49859i	0.454662	+	0.165483i	0.559192	−	0.829038i	$-0.311112\pi$
$739$	12.3598	+	4.49859i	0.454662	+	0.165483i	−0.104530	+	0.994522i	$0.533334\pi$
$740$		0			0
$741$	11.7780	+	0.170795i	0.432674	+	0.00627431i
$742$		0			0
$743$	−1.08765	−	0.395872i	−0.0399020	−	0.0145231i	0.321992	−	0.946742i	$-0.395648\pi$
$743$	−1.08765	−	0.395872i	−0.0399020	−	0.0145231i	−0.361894	+	0.932219i	$0.617870\pi$
$744$		0			0
$745$	−0.0150147	−	0.0125989i	−0.000550098	−	0.000461587i
$746$		0			0
$747$	−3.17617	+	18.0130i	−0.116210	+	0.659060i
$748$		0			0
$749$	31.2126	+	54.0618i	1.14048	+	1.97538i
$750$		0			0
$751$	43.1045	−	15.6887i	1.57290	−	0.572490i	0.599259	−	0.800555i	$-0.295462\pi$
$751$	43.1045	−	15.6887i	1.57290	−	0.572490i	0.973646	+	0.228065i	$0.0732399\pi$
$752$		0			0
$753$	−17.0954	+	29.6101i	−0.622991	+	1.07905i
$754$		0			0
$755$	10.5680	−	8.86765i	0.384611	−	0.322727i
$756$		0			0
$757$	−8.20398	−	46.5271i	−0.298179	−	1.69106i	−0.653994	−	0.756500i	$-0.726908\pi$
$757$	−8.20398	−	46.5271i	−0.298179	−	1.69106i	0.355815	−	0.934556i	$-0.384203\pi$
$758$		0			0
$759$	−33.0951			−1.20128
$760$		0			0
$761$	−18.9495			−0.686921			−0.343460	−	0.939167i	$-0.611599\pi$
$761$	−18.9495			−0.686921			−0.343460	+	0.939167i	$0.611599\pi$
$762$		0			0
$763$	−7.16116	−	40.6130i	−0.259251	−	1.47029i
$764$		0			0
$765$	13.7738	−	11.5576i	0.497992	−	0.417865i
$766$		0			0
$767$	−3.53162	+	6.11695i	−0.127519	+	0.220870i
$768$		0			0
$769$	47.3858	−	17.2470i	1.70878	−	0.621944i	0.712001	−	0.702178i	$-0.247789\pi$
$769$	47.3858	−	17.2470i	1.70878	−	0.621944i	0.996776	+	0.0802345i	$0.0255669\pi$
$770$		0			0
$771$	−3.02775	−	5.24422i	−0.109042	−	0.188866i
$772$		0			0
$773$	−7.31299	+	41.4740i	−0.263030	+	1.49172i	0.511557	+	0.859249i	$0.329069\pi$
$773$	−7.31299	+	41.4740i	−0.263030	+	1.49172i	−0.774587	+	0.632467i	$0.782042\pi$
$774$		0			0
$775$	−5.01501	−	4.20810i	−0.180145	−	0.151159i
$776$		0			0
$777$	−73.2422	−	26.6580i	−2.62755	−	0.956350i
$778$		0			0
$779$	−6.52704	−	40.4369i	−0.233855	−	1.44880i
$780$		0			0
$781$	−18.8307	−	6.85381i	−0.673815	−	0.245249i
$782$		0			0
$783$	−37.8148	−	31.7304i	−1.35139	−	1.13395i
$784$		0			0
$785$	10.3751	−	58.8401i	0.370303	−	2.10009i
$786$		0			0
$787$	4.57832	+	7.92987i	0.163199	+	0.282669i	0.936014	−	0.351962i	$-0.114485\pi$
$787$	4.57832	+	7.92987i	0.163199	+	0.282669i	−0.772815	+	0.634631i	$0.781152\pi$
$788$		0			0
$789$	−25.1621	+	9.15825i	−0.895794	+	0.326042i
$790$		0			0
$791$	−10.8983	+	18.8764i	−0.387498	+	0.671166i
$792$		0			0
$793$	−4.09904	+	3.43950i	−0.145561	+	0.122140i
$794$		0			0
$795$	6.00758	+	34.0707i	0.213067	+	1.20836i
$796$		0			0
$797$	31.8708			1.12892			0.564461	−	0.825460i	$-0.309084\pi$
$797$	31.8708			1.12892			0.564461	+	0.825460i	$0.309084\pi$
$798$		0			0
$799$	6.86989			0.243039
$800$		0			0
$801$	−2.93835	−	16.6642i	−0.103821	−	0.588801i
$802$		0			0
$803$	−16.0155	+	13.4386i	−0.565174	+	0.474237i
$804$		0			0
$805$	−21.4611	+	37.1717i	−0.756405	+	1.31013i
$806$		0			0
$807$	43.9797	−	16.0073i	1.54816	−	0.563484i
$808$		0			0
$809$	−7.05051	−	12.2118i	−0.247883	−	0.429345i	0.715055	−	0.699068i	$-0.246401\pi$
$809$	−7.05051	−	12.2118i	−0.247883	−	0.429345i	−0.962938	+	0.269722i	$0.913068\pi$
$810$		0			0
$811$	2.76423	−	15.6767i	0.0970654	−	0.550485i	−0.897030	−	0.441971i	$-0.854280\pi$
$811$	2.76423	−	15.6767i	0.0970654	−	0.550485i	0.994095	−	0.108514i	$-0.0346094\pi$
$812$		0			0
$813$	37.6562	+	31.5973i	1.32066	+	1.10816i
$814$		0			0
$815$	−47.4654	−	17.2760i	−1.66264	−	0.605152i
$816$		0			0
$817$	−15.1250	+	12.3221i	−0.529155	+	0.431095i
$818$		0			0
$819$	22.6275	+	8.23573i	0.790668	+	0.287780i
$820$		0			0
$821$	13.3680	+	11.2171i	0.466546	+	0.391479i	0.845533	−	0.533923i	$-0.179283\pi$
$821$	13.3680	+	11.2171i	0.466546	+	0.391479i	−0.378987	+	0.925402i	$0.623727\pi$
$822$		0			0
$823$	−5.44949	+	30.9056i	−0.189957	+	1.07730i	0.729461	+	0.684022i	$0.239771\pi$
$823$	−5.44949	+	30.9056i	−0.189957	+	1.07730i	−0.919419	+	0.393280i	$0.871340\pi$
$824$		0			0
$825$	5.34524	+	9.25822i	0.186097	+	0.322330i
$826$		0			0
$827$	−17.0021	+	6.18826i	−0.591221	+	0.215187i	−0.620267	−	0.784391i	$-0.712976\pi$
$827$	−17.0021	+	6.18826i	−0.591221	+	0.215187i	0.0290451	+	0.999578i	$0.490753\pi$
$828$		0			0
$829$	−10.3145	+	17.8652i	−0.358237	+	0.620485i	−0.987666	−	0.156573i	$-0.949955\pi$
$829$	−10.3145	+	17.8652i	−0.358237	+	0.620485i	0.629429	+	0.777058i	$0.283289\pi$
$830$		0			0
$831$	6.96522	−	5.84452i	0.241621	−	0.202744i
$832$		0			0
$833$	−1.33925	−	7.59527i	−0.0464023	−	0.263160i
$834$		0			0
$835$	1.38413			0.0478999
$836$		0			0
$837$	−66.0215			−2.28204
$838$		0			0
$839$	8.44760	+	47.9087i	0.291643	+	1.65399i	0.680540	+	0.732711i	$0.261745\pi$
$839$	8.44760	+	47.9087i	0.291643	+	1.65399i	−0.388897	+	0.921281i	$0.627144\pi$
$840$		0			0
$841$	−13.0025	+	10.9104i	−0.448363	+	0.376221i
$842$		0			0
$843$	12.5770	−	21.7840i	0.433174	−	0.750279i
$844$		0			0
$845$	−29.2631	+	10.6509i	−1.00668	+	0.366402i
$846$		0			0
$847$	−10.6493	−	18.4451i	−0.365914	−	0.633782i
$848$		0			0
$849$	−11.7239	+	66.4893i	−0.402362	+	2.28191i
$850$		0			0
$851$	−20.8425	−	17.4890i	−0.714473	−	0.599514i
$852$		0			0
$853$	29.3748	+	10.6916i	1.00577	+	0.366072i	0.791809	−	0.610769i	$-0.209140\pi$
$853$	29.3748	+	10.6916i	1.00577	+	0.366072i	0.213965	+	0.976841i	$0.431362\pi$
$854$		0			0
$855$	41.9236	−	70.2415i	1.43376	−	2.40221i
$856$		0			0
$857$	12.2049	+	4.44221i	0.416910	+	0.151743i	0.541954	−	0.840408i	$-0.317685\pi$
$857$	12.2049	+	4.44221i	0.416910	+	0.151743i	−0.125044	+	0.992151i	$0.539907\pi$
$858$		0			0
$859$	−33.7380	−	28.3096i	−1.15113	−	0.965910i	−0.151382	−	0.988475i	$-0.548372\pi$
$859$	−33.7380	−	28.3096i	−1.15113	−	0.965910i	−0.999745	+	0.0225649i	$0.992817\pi$
$860$		0			0
$861$	20.4256	−	115.839i	0.696103	−	3.94780i
$862$		0			0
$863$	−0.625829	−	1.08397i	−0.0213035	−	0.0368987i	0.855177	−	0.518336i	$-0.173448\pi$
$863$	−0.625829	−	1.08397i	−0.0213035	−	0.0368987i	−0.876481	+	0.481437i	$0.840115\pi$
$864$		0			0
$865$	27.0300	−	9.83813i	0.919049	−	0.334506i
$866$		0			0
$867$	25.9458	−	44.9394i	0.881165	−	1.52622i
$868$		0			0
$869$	6.70961	−	5.63003i	0.227608	−	0.190986i
$870$		0			0
$871$	−1.97233	−	11.1857i	−0.0668300	−	0.379012i
$872$		0			0
$873$	−1.31221			−0.0444117
$874$		0			0
$875$	−35.2499			−1.19166
$876$		0			0
$877$	1.83124	+	10.3855i	0.0618367	+	0.350693i	0.999990	+	0.00447306i	$0.00142382\pi$
$877$	1.83124	+	10.3855i	0.0618367	+	0.350693i	−0.938153	+	0.346220i	$0.887465\pi$
$878$		0			0
$879$	68.8656	−	57.7851i	2.32278	−	1.94904i
$880$		0			0
$881$	5.34864	−	9.26412i	0.180200	−	0.312116i	−0.761748	−	0.647873i	$-0.775659\pi$
$881$	5.34864	−	9.26412i	0.180200	−	0.312116i	0.941949	+	0.335757i	$0.108992\pi$
$882$		0			0
$883$	26.9111	−	9.79483i	0.905629	−	0.329622i	0.153123	−	0.988207i	$-0.451067\pi$
$883$	26.9111	−	9.79483i	0.905629	−	0.329622i	0.752506	+	0.658585i	$0.228845\pi$
$884$		0			0
$885$	34.4530	+	59.6743i	1.15812	+	2.00593i
$886$		0			0
$887$	−2.78405	+	15.7891i	−0.0934793	+	0.530148i	0.901723	+	0.432313i	$0.142303\pi$
$887$	−2.78405	+	15.7891i	−0.0934793	+	0.530148i	−0.995203	+	0.0978342i	$0.968809\pi$
$888$		0			0
$889$	17.6630	+	14.8210i	0.592397	+	0.497080i
$890$		0			0
$891$	52.2661	+	19.0233i	1.75098	+	0.637305i
$892$		0			0
$893$	29.5214	−	10.2627i	0.987896	−	0.343427i
$894$		0			0
$895$	−4.39053	−	1.59802i	−0.146759	−	0.0534160i
$896$		0			0
$897$	9.04551	+	7.59008i	0.302021	+	0.253426i
$898$		0			0
$899$	2.79308	−	15.8403i	0.0931545	−	0.528305i
$900$		0			0
$901$	−2.02852	−	3.51351i	−0.0675799	−	0.117052i
$902$		0			0
$903$	−52.6455	+	19.1614i	−1.75193	+	0.637651i
$904$		0			0
$905$	−5.80066	+	10.0470i	−0.192820	+	0.333975i
$906$		0			0
$907$	7.70027	−	6.46130i	0.255683	−	0.214544i	−0.505932	−	0.862574i	$-0.668851\pi$
$907$	7.70027	−	6.46130i	0.255683	−	0.214544i	0.761615	+	0.648030i	$0.224407\pi$
$908$		0			0
$909$	−5.04664	−	28.6209i	−0.167386	−	0.949295i
$910$		0			0
$911$	−3.46379			−0.114761			−0.0573803	−	0.998352i	$-0.518275\pi$
$911$	−3.46379			−0.114761			−0.0573803	+	0.998352i	$0.518275\pi$
$912$		0			0
$913$	5.79292			0.191718
$914$		0			0
$915$	9.06464	+	51.4082i	0.299668	+	1.69950i
$916$		0			0
$917$	−13.4021	+	11.2457i	−0.442578	+	0.371367i
$918$		0			0
$919$	2.28400	−	3.95600i	0.0753421	−	0.130496i	−0.825893	−	0.563827i	$-0.809328\pi$
$919$	2.28400	−	3.95600i	0.0753421	−	0.130496i	0.901235	+	0.433331i	$0.142662\pi$
$920$		0			0
$921$	−42.3222	+	15.4040i	−1.39456	+	0.507580i
$922$		0			0
$923$	3.57491	+	6.19193i	0.117670	+	0.203810i
$924$		0			0
$925$	−1.52616	+	8.65528i	−0.0501798	+	0.284584i
$926$		0			0
$927$	66.6780	+	55.9495i	2.18999	+	1.83762i
$928$		0			0
$929$	33.6279	+	12.2396i	1.10330	+	0.401567i	0.828531	−	0.559944i	$-0.189177\pi$
$929$	33.6279	+	12.2396i	1.10330	+	0.401567i	0.274766	+	0.961511i	$0.411399\pi$
$930$		0			0
$931$	−17.1013	−	30.6379i	−0.560473	−	1.00412i
$932$		0			0
$933$	15.0929	+	5.49335i	0.494118	+	0.179844i
$934$		0			0
$935$	−4.36231	−	3.66041i	−0.142663	−	0.119708i
$936$		0			0
$937$	−6.70170	+	38.0073i	−0.218935	+	1.24164i	0.655011	+	0.755620i	$0.272664\pi$
$937$	−6.70170	+	38.0073i	−0.218935	+	1.24164i	−0.873946	+	0.486023i	$0.838447\pi$
$938$		0			0
$939$	−3.02111	−	5.23271i	−0.0985901	−	0.170763i
$940$		0			0
$941$	−11.0954	+	4.03839i	−0.361699	+	0.131648i	−0.516476	−	0.856302i	$-0.672756\pi$
$941$	−11.0954	+	4.03839i	−0.361699	+	0.131648i	0.154777	+	0.987949i	$0.450534\pi$
$942$		0			0
$943$	20.5303	−	35.5596i	0.668560	−	1.15798i
$944$		0			0
$945$	107.111	−	89.8771i	3.48433	−	2.92370i
$946$		0			0
$947$	−3.06267	−	17.3693i	−0.0995235	−	0.564426i	−0.993267	−	0.115847i	$-0.963042\pi$
$947$	−3.06267	−	17.3693i	−0.0995235	−	0.564426i	0.893744	−	0.448578i	$-0.148069\pi$
$948$		0			0
$949$	7.45935			0.242141
$950$		0			0
$951$	−97.4630			−3.16045
$952$		0			0
$953$	7.80082	+	44.2407i	0.252693	+	1.43310i	0.801925	+	0.597425i	$0.203809\pi$
$953$	7.80082	+	44.2407i	0.252693	+	1.43310i	−0.549231	+	0.835670i	$0.685079\pi$
$954$		0			0
$955$	−4.04710	+	3.39592i	−0.130961	+	0.109889i
$956$		0			0
$957$	−13.1329	+	22.7469i	−0.424528	+	0.735304i
$958$		0			0
$959$	−24.9538	+	9.08245i	−0.805801	+	0.293288i
$960$		0			0
$961$	4.74376	+	8.21643i	0.153024	+	0.265046i
$962$		0			0
$963$	20.7096	−	117.450i	0.667358	−	3.78477i
$964$		0			0
$965$	−48.7995	−	40.9477i	−1.57091	−	1.31815i
$966$		0			0
$967$	−25.4884	−	9.27704i	−0.819653	−	0.298329i	−0.102048	−	0.994779i	$-0.532540\pi$
$967$	−25.4884	−	9.27704i	−0.819653	−	0.298329i	−0.717605	+	0.696450i	$0.754762\pi$
$968$		0			0
$969$	−2.53219	+	13.2356i	−0.0813458	+	0.425188i
$970$		0			0
$971$	−48.0232	−	17.4790i	−1.54114	−	0.560929i	−0.574821	−	0.818280i	$-0.694928\pi$
$971$	−48.0232	−	17.4790i	−1.54114	−	0.560929i	−0.966318	+	0.257351i	$0.917150\pi$
$972$		0			0
$973$	−50.2661	−	42.1783i	−1.61146	−	1.35217i
$974$		0			0
$975$	0.662342	−	3.75633i	0.0212119	−	0.120299i
$976$		0			0
$977$	7.28106	+	12.6112i	0.232942	+	0.403467i	0.958673	−	0.284512i	$-0.0918315\pi$
$977$	7.28106	+	12.6112i	0.232942	+	0.403467i	−0.725731	+	0.687979i	$0.758498\pi$
$978$		0			0
$979$	−5.03596	+	1.83294i	−0.160950	+	0.0585810i
$980$		0			0
$981$	−39.3935	+	68.2316i	−1.25774	+	2.17847i
$982$		0			0
$983$	30.1132	−	25.2680i	0.960461	−	0.805923i	−0.0205668	−	0.999788i	$-0.506547\pi$
$983$	30.1132	−	25.2680i	0.960461	−	0.805923i	0.981028	+	0.193866i	$0.0621026\pi$
$984$		0			0
$985$	−10.9179	−	61.9183i	−0.347872	−	1.97288i
$986$		0			0
$987$	89.7538			2.85690
$988$		0			0
$989$	−19.5567			−0.621868
$990$		0			0
$991$	8.39709	+	47.6223i	0.266742	+	1.51277i	0.764028	+	0.645184i	$0.223219\pi$
$991$	8.39709	+	47.6223i	0.266742	+	1.51277i	−0.497285	+	0.867587i	$0.665670\pi$
$992$		0			0
$993$	24.0731	−	20.1997i	0.763937	−	0.641019i
$994$		0			0
$995$	15.7297	−	27.2446i	0.498664	−	0.863712i
$996$		0			0
$997$	−21.3414	+	7.76762i	−0.675888	+	0.246003i	−0.657081	−	0.753820i	$-0.728209\pi$
$997$	−21.3414	+	7.76762i	−0.675888	+	0.246003i	−0.0188070	+	0.999823i	$0.505987\pi$
$998$		0			0
$999$	44.3166	+	76.7586i	1.40212	+	2.42854i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	152.2.q.b.137.1	yes	6
4.3	odd	2		304.2.u.a.289.1		6
19.5	even	9	inner	152.2.q.b.81.1	✓	6
19.9	even	9		2888.2.a.s.1.3		3
19.10	odd	18		2888.2.a.m.1.1		3
76.43	odd	18		304.2.u.a.81.1		6
76.47	odd	18		5776.2.a.bj.1.1		3
76.67	even	18		5776.2.a.bs.1.3		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
152.2.q.b.81.1	✓	6	19.5	even	9	inner
152.2.q.b.137.1	yes	6	1.1	even	1	trivial
304.2.u.a.81.1		6	76.43	odd	18
304.2.u.a.289.1		6	4.3	odd	2
2888.2.a.m.1.1		3	19.10	odd	18
2888.2.a.s.1.3		3	19.9	even	9
5776.2.a.bj.1.1		3	76.47	odd	18
5776.2.a.bs.1.3		3	76.67	even	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:	\( N \)	\(=\)	\( 152 = 2^{3} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	152.q (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.560307 + 3.17766i) q^{3} +(-1.93969 + 1.62760i) q^{5} +(1.93969 - 3.35965i) q^{7} +(-6.96451 + 2.53487i) q^{9} +(1.17365 + 2.03282i) q^{11} +(0.145430 - 0.824773i) q^{13} +(-6.25877 - 5.25173i) q^{15} +(0.900330 + 0.327693i) q^{17} +(4.35844 + 0.0632028i) q^{19} +(11.7626 + 4.28125i) q^{21} +(3.34730 + 2.80872i) q^{23} +(0.245100 - 1.39003i) q^{25} +(-7.11721 - 12.3274i) q^{27} +(3.25877 - 1.18610i) q^{29} +(2.31908 - 4.01676i) q^{31} +(-5.80200 + 4.86846i) q^{33} +(1.70574 + 9.67372i) q^{35} -6.22668 q^{37} +2.70233 q^{39} +(-1.63176 - 9.25417i) q^{41} +(-3.42855 + 2.87689i) q^{43} +(9.38326 - 16.2523i) q^{45} +(6.73783 - 2.45237i) q^{47} +(-4.02481 - 6.97118i) q^{49} +(-0.536837 + 3.04455i) q^{51} +(-3.24376 - 2.72183i) q^{53} +(-5.58512 - 2.03282i) q^{55} +(2.24123 + 13.8851i) q^{57} +(-7.92514 - 2.88452i) q^{59} +(-4.89440 - 4.10689i) q^{61} +(-4.99273 + 28.3152i) q^{63} +(1.06031 + 1.83651i) q^{65} +(12.7442 - 4.63852i) q^{67} +(-7.04963 + 12.2103i) q^{69} +(-6.53983 + 5.48757i) q^{71} +(1.54664 + 8.77141i) q^{73} +4.55438 q^{75} +9.10607 q^{77} +(-0.647956 - 3.67474i) q^{79} +(18.1518 - 15.2312i) q^{81} +(1.23396 - 2.13727i) q^{83} +(-2.27972 + 0.829748i) q^{85} +(5.59492 + 9.69069i) q^{87} +(-0.396459 + 2.24843i) q^{89} +(-2.48886 - 2.08840i) q^{91} +(14.0633 + 5.11862i) q^{93} +(-8.55690 + 6.97118i) q^{95} +(0.166374 + 0.0605553i) q^{97} +(-13.3268 - 11.1825i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 9 q^{3} - 6 q^{5} + 6 q^{7} - 9 q^{9} + 6 q^{11} - 15 q^{13} - 15 q^{15} - 9 q^{17} + 18 q^{19} + 24 q^{21} + 18 q^{23} - 12 q^{27} - 3 q^{29} - 3 q^{31} + 3 q^{33} - 24 q^{37} - 36 q^{39} - 15 q^{41}+ \cdots - 15 q^{99}+O(q^{100}) \) 6 * q + 9 * q^3 - 6 * q^5 + 6 * q^7 - 9 * q^9 + 6 * q^11 - 15 * q^13 - 15 * q^15 - 9 * q^17 + 18 * q^19 + 24 * q^21 + 18 * q^23 - 12 * q^27 - 3 * q^29 - 3 * q^31 + 3 * q^33 - 24 * q^37 - 36 * q^39 - 15 * q^41 - 21 * q^43 + 21 * q^45 + 21 * q^47 + 3 * q^49 - 27 * q^51 - 27 * q^53 - 12 * q^55 + 36 * q^57 - 6 * q^59 + 12 * q^61 - 12 * q^63 + 12 * q^65 + 18 * q^67 + 12 * q^69 + 18 * q^71 + 36 * q^73 + 6 * q^75 + 30 * q^77 + 27 * q^79 + 54 * q^81 + 12 * q^83 + 12 * q^85 + 15 * q^87 - 12 * q^89 - 21 * q^91 + 9 * q^93 - 15 * q^95 - 18 * q^97 - 15 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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