LMFDB - Embedded newform 432.2.u.f.241.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [432,2,Mod(49,432)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(432, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 0, 14]))

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

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

chi := DirichletCharacter("432.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 432 = 2^{4} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	432.u (of order $9$, degree $6$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$3.44953736732$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$5$ over $\Q(\zeta_{9})$
Twist minimal:	no (minimal twist has level 216)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			241.2
Character	$\chi$	$=$	432.241
Dual form			432.2.u.f.337.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.485722 + 1.66255i) q^{3} +(-0.582934 + 0.489140i) q^{5} +(-3.39455 + 1.23552i) q^{7} +(-2.52815 - 1.61507i) q^{9} +O(q^{10})$	\(q+(-0.485722 + 1.66255i) q^{3} +(-0.582934 + 0.489140i) q^{5} +(-3.39455 + 1.23552i) q^{7} +(-2.52815 - 1.61507i) q^{9} +(-1.22326 - 1.02644i) q^{11} +(-0.872331 - 4.94723i) q^{13} +(-0.530076 - 1.20674i) q^{15} +(-0.153076 - 0.265135i) q^{17} +(0.463380 - 0.802597i) q^{19} +(-0.405300 - 6.24373i) q^{21} +(1.41468 + 0.514902i) q^{23} +(-0.767686 + 4.35377i) q^{25} +(3.91312 - 3.41870i) q^{27} +(-0.935202 + 5.30379i) q^{29} +(-8.64694 - 3.14723i) q^{31} +(2.30067 - 1.53517i) q^{33} +(1.37446 - 2.38064i) q^{35} +(-3.04343 - 5.27138i) q^{37} +(8.64874 + 0.952685i) q^{39} +(2.06526 + 11.7127i) q^{41} +(-5.66013 - 4.74941i) q^{43} +(2.26374 - 0.295137i) q^{45} +(-7.10890 + 2.58743i) q^{47} +(4.63418 - 3.88853i) q^{49} +(0.515153 - 0.125715i) q^{51} -10.5700 q^{53} +1.21515 q^{55} +(1.10928 + 1.16023i) q^{57} +(9.36544 - 7.85854i) q^{59} +(-5.59403 + 2.03606i) q^{61} +(10.5774 + 2.35889i) q^{63} +(2.92840 + 2.45722i) q^{65} +(0.432933 + 2.45528i) q^{67} +(-1.54319 + 2.10188i) q^{69} +(5.68591 + 9.84828i) q^{71} +(-4.80611 + 8.32442i) q^{73} +(-6.86547 - 3.39104i) q^{75} +(5.42059 + 1.97293i) q^{77} +(0.450963 - 2.55754i) q^{79} +(3.78307 + 8.16629i) q^{81} +(-2.82744 + 16.0352i) q^{83} +(0.218922 + 0.0796810i) q^{85} +(-8.36358 - 4.13099i) q^{87} +(4.62758 - 8.01520i) q^{89} +(9.07356 + 15.7159i) q^{91} +(9.43243 - 12.8473i) q^{93} +(0.122462 + 0.694519i) q^{95} +(2.67734 + 2.24656i) q^{97} +(1.43481 + 4.57064i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q - 3 q^{7} - 6 q^{9}+O(q^{10}) $ 30 * q - 3 * q^7 - 6 * q^9	$ 30 q - 3 q^{7} - 6 q^{9} + 3 q^{11} - 12 q^{13} - 15 q^{15} + 6 q^{17} + 9 q^{19} + 30 q^{21} + 12 q^{23} + 24 q^{25} + 15 q^{27} - 9 q^{29} - 27 q^{31} - 30 q^{33} + 18 q^{35} - 15 q^{37} + 21 q^{39} - 15 q^{41} + 30 q^{43} + 15 q^{45} + 18 q^{47} + 15 q^{49} + 6 q^{51} - 18 q^{53} - 54 q^{55} - 72 q^{57} + 12 q^{59} + 6 q^{61} + 54 q^{63} - 54 q^{65} + 45 q^{67} + 9 q^{69} - 36 q^{73} - 69 q^{75} + 12 q^{77} - 45 q^{79} - 30 q^{81} + 3 q^{83} + 57 q^{85} + 60 q^{87} + 36 q^{89} + 39 q^{91} + 30 q^{93} - 51 q^{95} - 84 q^{97} - 162 q^{99}+O(q^{100}) $ 30 * q - 3 * q^7 - 6 * q^9 + 3 * q^11 - 12 * q^13 - 15 * q^15 + 6 * q^17 + 9 * q^19 + 30 * q^21 + 12 * q^23 + 24 * q^25 + 15 * q^27 - 9 * q^29 - 27 * q^31 - 30 * q^33 + 18 * q^35 - 15 * q^37 + 21 * q^39 - 15 * q^41 + 30 * q^43 + 15 * q^45 + 18 * q^47 + 15 * q^49 + 6 * q^51 - 18 * q^53 - 54 * q^55 - 72 * q^57 + 12 * q^59 + 6 * q^61 + 54 * q^63 - 54 * q^65 + 45 * q^67 + 9 * q^69 - 36 * q^73 - 69 * q^75 + 12 * q^77 - 45 * q^79 - 30 * q^81 + 3 * q^83 + 57 * q^85 + 60 * q^87 + 36 * q^89 + 39 * q^91 + 30 * q^93 - 51 * q^95 - 84 * q^97 - 162 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/432\mathbb{Z}\right)^\times$.

$n$	$271$	$325$	$353$
$\chi(n)$	$1$	$1$	$e\left(\frac{5}{9}\right)$

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
$3$	−0.485722	+	1.66255i	−0.280432	+	0.959874i
$3$	−0.485722	+	1.66255i	−0.280432	+	0.959874i
$4$		0			0
$5$	−0.582934	+	0.489140i	−0.260696	+	0.218750i	−0.763762	−	0.645498i	$-0.776650\pi$
$5$	−0.582934	+	0.489140i	−0.260696	+	0.218750i	0.503066	+	0.864248i	$0.332205\pi$
$6$		0			0
$7$	−3.39455	+	1.23552i	−1.28302	+	0.466981i	−0.891430	−	0.453159i	$-0.850297\pi$
$7$	−3.39455	+	1.23552i	−1.28302	+	0.466981i	−0.391590	+	0.920140i	$0.628075\pi$
$8$		0			0
$9$	−2.52815	−	1.61507i	−0.842716	−	0.538358i
$10$		0			0
$11$	−1.22326	−	1.02644i	−0.368826	−	0.309482i	0.439471	−	0.898257i	$-0.355166\pi$
$11$	−1.22326	−	1.02644i	−0.368826	−	0.309482i	−0.808297	+	0.588775i	$0.799610\pi$
$12$		0			0
$13$	−0.872331	−	4.94723i	−0.241941	−	1.37212i	−0.827491	−	0.561479i	$-0.810232\pi$
$13$	−0.872331	−	4.94723i	−0.241941	−	1.37212i	0.585550	−	0.810637i	$-0.300879\pi$
$14$		0			0
$15$	−0.530076	−	1.20674i	−0.136865	−	0.311580i
$16$		0			0
$17$	−0.153076	−	0.265135i	−0.0371264	−	0.0643048i	0.846865	−	0.531808i	$-0.178487\pi$
$17$	−0.153076	−	0.265135i	−0.0371264	−	0.0643048i	−0.883992	+	0.467503i	$0.845154\pi$
$18$		0			0
$19$	0.463380	−	0.802597i	0.106307	−	0.184128i	−0.807965	−	0.589231i	$-0.799431\pi$
$19$	0.463380	−	0.802597i	0.106307	−	0.184128i	0.914271	+	0.405102i	$0.132764\pi$
$20$		0			0
$21$	−0.405300	−	6.24373i	−0.0884437	−	1.36249i
$22$		0			0
$23$	1.41468	+	0.514902i	0.294981	+	0.107364i	0.485272	−	0.874363i	$-0.338721\pi$
$23$	1.41468	+	0.514902i	0.294981	+	0.107364i	−0.190290	+	0.981728i	$0.560943\pi$
$24$		0			0
$25$	−0.767686	+	4.35377i	−0.153537	+	0.870753i
$26$		0			0
$27$	3.91312	−	3.41870i	0.753080	−	0.657929i
$28$		0			0
$29$	−0.935202	+	5.30379i	−0.173663	+	0.984890i	0.766014	+	0.642824i	$0.222237\pi$
$29$	−0.935202	+	5.30379i	−0.173663	+	0.984890i	−0.939676	+	0.342065i	$0.888874\pi$
$30$		0			0
$31$	−8.64694	−	3.14723i	−1.55304	−	0.565259i	−0.583909	−	0.811819i	$-0.698477\pi$
$31$	−8.64694	−	3.14723i	−1.55304	−	0.565259i	−0.969127	+	0.246560i	$0.920700\pi$
$32$		0			0
$33$	2.30067	−	1.53517i	0.400494	−	0.267238i
$34$		0			0
$35$	1.37446	−	2.38064i	0.232326	−	0.402401i
$36$		0			0
$37$	−3.04343	−	5.27138i	−0.500338	−	0.866610i	−1.00000		0.000389867i	$-0.999876\pi$
$37$	−3.04343	−	5.27138i	−0.500338	−	0.866610i	0.499662	−	0.866220i	$-0.333457\pi$
$38$		0			0
$39$	8.64874	+	0.952685i	1.38491	+	0.152552i
$40$		0			0
$41$	2.06526	+	11.7127i	0.322539	+	1.82921i	0.526431	+	0.850218i	$0.323530\pi$
$41$	2.06526	+	11.7127i	0.322539	+	1.82921i	−0.203892	+	0.978993i	$0.565359\pi$
$42$		0			0
$43$	−5.66013	−	4.74941i	−0.863162	−	0.724279i	0.0994852	−	0.995039i	$-0.468280\pi$
$43$	−5.66013	−	4.74941i	−0.863162	−	0.724279i	−0.962647	+	0.270760i	$0.912725\pi$
$44$		0			0
$45$	2.26374	−	0.295137i	0.337459	−	0.0439964i
$46$		0			0
$47$	−7.10890	+	2.58743i	−1.03694	+	0.377415i	−0.803719	−	0.595008i	$-0.797149\pi$
$47$	−7.10890	+	2.58743i	−1.03694	+	0.377415i	−0.233221	+	0.972424i	$0.574926\pi$
$48$		0			0
$49$	4.63418	−	3.88853i	0.662025	−	0.555505i
$50$		0			0
$51$	0.515153	−	0.125715i	0.0721359	−	0.0176036i
$52$		0			0
$53$	−10.5700			−1.45190			−0.725950	−	0.687748i	$-0.758599\pi$
$53$	−10.5700			−1.45190			−0.725950	+	0.687748i	$0.758599\pi$
$54$		0			0
$55$	1.21515			0.163851
$56$		0			0
$57$	1.10928	+	1.16023i	0.146928	+	0.153676i
$58$		0			0
$59$	9.36544	−	7.85854i	1.21928	−	1.02309i	0.220414	−	0.975406i	$-0.429259\pi$
$59$	9.36544	−	7.85854i	1.21928	−	1.02309i	0.998862	−	0.0476877i	$-0.0151852\pi$
$60$		0			0
$61$	−5.59403	+	2.03606i	−0.716242	+	0.260691i	−0.674330	−	0.738430i	$-0.735567\pi$
$61$	−5.59403	+	2.03606i	−0.716242	+	0.260691i	−0.0419125	+	0.999121i	$0.513345\pi$
$62$		0			0
$63$	10.5774	+	2.35889i	1.33263	+	0.297192i
$64$		0			0
$65$	2.92840	+	2.45722i	0.363224	+	0.304781i
$66$		0			0
$67$	0.432933	+	2.45528i	0.0528911	+	0.299961i	0.999766	−	0.0216423i	$-0.00688951\pi$
$67$	0.432933	+	2.45528i	0.0528911	+	0.299961i	−0.946875	+	0.321603i	$0.895778\pi$
$68$		0			0
$69$	−1.54319	+	2.10188i	−0.185778	+	0.253037i
$70$		0			0
$71$	5.68591	+	9.84828i	0.674793	+	1.16878i	0.976529	+	0.215385i	$0.0691006\pi$
$71$	5.68591	+	9.84828i	0.674793	+	1.16878i	−0.301736	+	0.953392i	$0.597566\pi$
$72$		0			0
$73$	−4.80611	+	8.32442i	−0.562512	+	0.974300i	0.434764	+	0.900544i	$0.356832\pi$
$73$	−4.80611	+	8.32442i	−0.562512	+	0.974300i	−0.997276	+	0.0737555i	$0.976502\pi$
$74$		0			0
$75$	−6.86547	−	3.39104i	−0.792757	−	0.391563i
$76$		0			0
$77$	5.42059	+	1.97293i	0.617734	+	0.224837i
$78$		0			0
$79$	0.450963	−	2.55754i	0.0507373	−	0.287745i	−0.948873	−	0.315658i	$-0.897775\pi$
$79$	0.450963	−	2.55754i	0.0507373	−	0.287745i	0.999610	+	0.0279124i	$0.00888595\pi$
$80$		0			0
$81$	3.78307	+	8.16629i	0.420341	+	0.907366i
$82$		0			0
$83$	−2.82744	+	16.0352i	−0.310352	+	1.76009i	0.286824	+	0.957983i	$0.407401\pi$
$83$	−2.82744	+	16.0352i	−0.310352	+	1.76009i	−0.597176	+	0.802110i	$0.703711\pi$
$84$		0			0
$85$	0.218922	+	0.0796810i	0.0237454	+	0.00864261i
$86$		0			0
$87$	−8.36358	−	4.13099i	−0.896669	−	0.442888i
$88$		0			0
$89$	4.62758	−	8.01520i	0.490522	−	0.849610i	−0.509418	−	0.860519i	$-0.670139\pi$
$89$	4.62758	−	8.01520i	0.490522	−	0.849610i	0.999940	+	0.0109095i	$0.00347267\pi$
$90$		0			0
$91$	9.07356	+	15.7159i	0.951168	+	1.64747i
$92$		0			0
$93$	9.43243	−	12.8473i	0.978098	−	1.33220i
$94$		0			0
$95$	0.122462	+	0.694519i	0.0125644	+	0.0712561i
$96$		0			0
$97$	2.67734	+	2.24656i	0.271843	+	0.228103i	0.768510	−	0.639838i	$-0.220999\pi$
$97$	2.67734	+	2.24656i	0.271843	+	0.228103i	−0.496667	+	0.867941i	$0.665443\pi$
$98$		0			0
$99$	1.43481	+	4.57064i	0.144204	+	0.459366i
$100$		0			0
$101$	12.0821	−	4.39753i	1.20222	−	0.437571i	0.338219	−	0.941067i	$-0.390175\pi$
$101$	12.0821	−	4.39753i	1.20222	−	0.437571i	0.863997	+	0.503496i	$0.167953\pi$
$102$		0			0
$103$	−1.62003	+	1.35936i	−0.159626	+	0.133942i	−0.719102	−	0.694904i	$-0.755447\pi$
$103$	−1.62003	+	1.35936i	−0.159626	+	0.133942i	0.559476	+	0.828846i	$0.311002\pi$
$104$		0			0
$105$	3.29032	+	3.44144i	0.321103	+	0.335850i
$106$		0			0
$107$	−9.09507			−0.879253			−0.439627	−	0.898181i	$-0.644889\pi$
$107$	−9.09507			−0.879253			−0.439627	+	0.898181i	$0.644889\pi$
$108$		0			0
$109$	0.0570954			0.00546874			0.00273437	−	0.999996i	$-0.499130\pi$
$109$	0.0570954			0.00546874			0.00273437	+	0.999996i	$0.499130\pi$
$110$		0			0
$111$	10.2422	−	2.49944i	0.972147	−	0.237236i
$112$		0			0
$113$	1.49384	−	1.25348i	0.140528	−	0.117917i	−0.569814	−	0.821774i	$-0.692985\pi$
$113$	1.49384	−	1.25348i	0.140528	−	0.117917i	0.710342	+	0.703857i	$0.248540\pi$
$114$		0			0
$115$	−1.07653	+	0.391823i	−0.100386	+	0.0365377i
$116$		0			0
$117$	−5.78477	+	13.9162i	−0.534802	+	1.28656i
$118$		0			0
$119$	0.847204	+	0.710888i	0.0776630	+	0.0651670i
$120$		0			0
$121$	−1.46734	−	8.32169i	−0.133394	−	0.756517i
$122$		0			0
$123$	−20.4760	−	2.25550i	−1.84626	−	0.203372i
$124$		0			0
$125$	−3.58451	−	6.20855i	−0.320608	−	0.555309i
$126$		0			0
$127$	8.62416	−	14.9375i	0.765271	−	1.32549i	−0.174833	−	0.984598i	$-0.555938\pi$
$127$	8.62416	−	14.9375i	0.765271	−	1.32549i	0.940103	−	0.340889i	$-0.110728\pi$
$128$		0			0
$129$	10.6454	−	7.10336i	0.937274	−	0.625416i
$130$		0			0
$131$	6.82592	+	2.48443i	0.596384	+	0.217066i	0.622535	−	0.782592i	$-0.286103\pi$
$131$	6.82592	+	2.48443i	0.596384	+	0.217066i	−0.0261512	+	0.999658i	$0.508325\pi$
$132$		0			0
$133$	−0.581345	+	3.29697i	−0.0504090	+	0.285884i
$134$		0			0
$135$	−0.608870	+	3.90694i	−0.0524031	+	0.336256i
$136$		0			0
$137$	−2.13029	+	12.0815i	−0.182003	+	1.03219i	0.747742	+	0.663989i	$0.231138\pi$
$137$	−2.13029	+	12.0815i	−0.182003	+	1.03219i	−0.929746	+	0.368203i	$0.879973\pi$
$138$		0			0
$139$	9.81439	+	3.57214i	0.832445	+	0.302985i	0.722862	−	0.690992i	$-0.242826\pi$
$139$	9.81439	+	3.57214i	0.832445	+	0.302985i	0.109583	+	0.993978i	$0.465048\pi$
$140$		0			0
$141$	−0.848783	−	13.0757i	−0.0714804	−	1.10117i
$142$		0			0
$143$	−4.01093	+	6.94714i	−0.335411	+	0.580949i
$144$		0			0
$145$	−2.04914	−	3.54921i	−0.170171	−	0.294746i
$146$		0			0
$147$	4.21397	+	9.59330i	0.347562	+	0.791242i
$148$		0			0
$149$	−3.30192	−	18.7261i	−0.270504	−	1.53410i	−0.752892	−	0.658144i	$-0.771342\pi$
$149$	−3.30192	−	18.7261i	−0.270504	−	1.53410i	0.482388	−	0.875958i	$-0.339769\pi$
$150$		0			0
$151$	−5.90771	−	4.95716i	−0.480763	−	0.403408i	0.369939	−	0.929056i	$-0.379379\pi$
$151$	−5.90771	−	4.95716i	−0.480763	−	0.403408i	−0.850702	+	0.525648i	$0.823823\pi$
$152$		0			0
$153$	−0.0412144	+	0.917531i	−0.00333199	+	0.0741780i
$154$		0			0
$155$	6.58003	−	2.39494i	0.528521	−	0.192366i
$156$		0			0
$157$	8.22005	−	6.89744i	0.656031	−	0.550476i	−0.252863	−	0.967502i	$-0.581372\pi$
$157$	8.22005	−	6.89744i	0.656031	−	0.550476i	0.908894	+	0.417027i	$0.136928\pi$
$158$		0			0
$159$	5.13407	−	17.5731i	0.407158	−	1.39364i
$160$		0			0
$161$	−5.43838			−0.428604
$162$		0			0
$163$	4.83928			0.379042			0.189521	−	0.981877i	$-0.439306\pi$
$163$	4.83928			0.379042			0.189521	+	0.981877i	$0.439306\pi$
$164$		0			0
$165$	−0.590225	+	2.02025i	−0.0459490	+	0.157276i
$166$		0			0
$167$	−4.87580	+	4.09129i	−0.377301	+	0.316593i	−0.811642	−	0.584155i	$-0.801426\pi$
$167$	−4.87580	+	4.09129i	−0.377301	+	0.316593i	0.434341	+	0.900749i	$0.356981\pi$
$168$		0			0
$169$	−11.4982	+	4.18499i	−0.884474	+	0.321922i
$170$		0			0
$171$	−2.46775	+	1.28069i	−0.188713	+	0.0979370i
$172$		0			0
$173$	−1.14072	−	0.957181i	−0.0867276	−	0.0727731i	0.598393	−	0.801203i	$-0.295806\pi$
$173$	−1.14072	−	0.957181i	−0.0867276	−	0.0727731i	−0.685121	+	0.728430i	$0.740251\pi$
$174$		0			0
$175$	−2.77320	−	15.7276i	−0.209634	−	1.18889i
$176$		0			0
$177$	8.51621	+	19.3876i	0.640118	+	1.45726i
$178$		0			0
$179$	−5.08789	−	8.81248i	−0.380287	−	0.658676i	0.610816	−	0.791772i	$-0.290841\pi$
$179$	−5.08789	−	8.81248i	−0.380287	−	0.658676i	−0.991103	+	0.133096i	$0.957508\pi$
$180$		0			0
$181$	−8.87219	+	15.3671i	−0.659465	+	1.14223i	0.321289	+	0.946981i	$0.395884\pi$
$181$	−8.87219	+	15.3671i	−0.659465	+	1.14223i	−0.980754	+	0.195246i	$0.937450\pi$
$182$		0			0
$183$	−0.667911	−	10.2893i	−0.0493734	−	0.760608i
$184$		0			0
$185$	4.35257	+	1.58420i	0.320007	+	0.116473i
$186$		0			0
$187$	−0.0848930	+	0.481452i	−0.00620799	+	0.0352073i
$188$		0			0
$189$	−9.05943	+	16.4397i	−0.658977	+	1.19581i
$190$		0			0
$191$	−2.99652	+	16.9941i	−0.216821	+	1.22965i	0.660898	+	0.750476i	$0.270176\pi$
$191$	−2.99652	+	16.9941i	−0.216821	+	1.22965i	−0.877719	+	0.479176i	$0.840935\pi$
$192$		0			0
$193$	−19.8891	−	7.23903i	−1.43165	−	0.521077i	−0.494243	−	0.869324i	$-0.664555\pi$
$193$	−19.8891	−	7.23903i	−1.43165	−	0.521077i	−0.937403	+	0.348247i	$0.886777\pi$
$194$		0			0
$195$	−5.50764	+	3.67509i	−0.394411	+	0.263179i
$196$		0			0
$197$	0.328212	−	0.568479i	0.0233841	−	0.0405025i	−0.854097	−	0.520115i	$-0.825889\pi$
$197$	0.328212	−	0.568479i	0.0233841	−	0.0405025i	0.877481	+	0.479612i	$0.159223\pi$
$198$		0			0
$199$	8.34016	+	14.4456i	0.591218	+	1.02402i	0.994069	+	0.108754i	$0.0346860\pi$
$199$	8.34016	+	14.4456i	0.591218	+	1.02402i	−0.402851	+	0.915266i	$0.631981\pi$
$200$		0			0
$201$	−4.29232	−	0.472812i	−0.302757	−	0.0333496i
$202$		0			0
$203$	−3.37833	−	19.1595i	−0.237112	−	1.34473i
$204$		0			0
$205$	−6.93304	−	5.81751i	−0.484225	−	0.406313i
$206$		0			0
$207$	−2.74492	−	3.58656i	−0.190785	−	0.249283i
$208$		0			0
$209$	−1.39065	+	0.506154i	−0.0961931	+	0.0350114i
$210$		0			0
$211$	3.72146	−	3.12267i	0.256196	−	0.214974i	−0.505639	−	0.862745i	$-0.668743\pi$
$211$	3.72146	−	3.12267i	0.256196	−	0.214974i	0.761835	+	0.647771i	$0.224299\pi$
$212$		0			0
$213$	−19.1350	+	4.66959i	−1.31111	+	0.319955i
$214$		0			0
$215$	5.62261			0.383459
$216$		0			0
$217$	33.2409			2.25654
$218$		0			0
$219$	−11.5053	−	12.0337i	−0.777459	−	0.813165i
$220$		0			0
$221$	−1.17815	+	0.988589i	−0.0792512	+	0.0664997i
$222$		0			0
$223$	−10.5728	+	3.84819i	−0.708007	+	0.257694i	−0.670826	−	0.741615i	$-0.734060\pi$
$223$	−10.5728	+	3.84819i	−0.708007	+	0.257694i	−0.0371816	+	0.999309i	$0.511838\pi$
$224$		0			0
$225$	8.97248	−	9.76710i	0.598165	−	0.651140i
$226$		0			0
$227$	−18.6574	−	15.6554i	−1.23833	−	1.03908i	−0.997652	−	0.0684801i	$-0.978185\pi$
$227$	−18.6574	−	15.6554i	−1.23833	−	1.03908i	−0.240680	−	0.970604i	$-0.577371\pi$
$228$		0			0
$229$	2.37423	+	13.4649i	0.156894	+	0.889788i	0.957034	+	0.289975i	$0.0936470\pi$
$229$	2.37423	+	13.4649i	0.156894	+	0.889788i	−0.800141	+	0.599812i	$0.795242\pi$
$230$		0			0
$231$	−5.91300	+	8.05371i	−0.389047	+	0.529896i
$232$		0			0
$233$	−13.2925	−	23.0234i	−0.870824	−	1.50831i	−0.861146	−	0.508357i	$-0.830253\pi$
$233$	−13.2925	−	23.0234i	−0.870824	−	1.50831i	−0.00967740	−	0.999953i	$-0.503080\pi$
$234$		0			0
$235$	2.87841	−	4.98555i	0.187767	−	0.325221i
$236$		0			0
$237$	4.03299	+	1.99200i	0.261971	+	0.129394i
$238$		0			0
$239$	8.03370	+	2.92403i	0.519657	+	0.189140i	0.588514	−	0.808487i	$-0.299713\pi$
$239$	8.03370	+	2.92403i	0.519657	+	0.189140i	−0.0688575	+	0.997627i	$0.521935\pi$
$240$		0			0
$241$	−3.32047	+	18.8313i	−0.213890	+	1.21303i	0.668932	+	0.743324i	$0.266752\pi$
$241$	−3.32047	+	18.8313i	−0.213890	+	1.21303i	−0.882822	+	0.469708i	$0.844359\pi$
$242$		0			0
$243$	−15.4144	+	2.32300i	−0.988834	+	0.149021i
$244$		0			0
$245$	−0.799382	+	4.53352i	−0.0510706	+	0.289636i
$246$		0			0
$247$	−4.37486	−	1.59232i	−0.278365	−	0.101317i
$248$		0			0
$249$	−25.2860	−	12.4894i	−1.60244	−	0.791485i
$250$		0			0
$251$	13.4200	−	23.2441i	0.847063	−	1.46716i	−0.0367543	−	0.999324i	$-0.511702\pi$
$251$	13.4200	−	23.2441i	0.847063	−	1.46716i	0.883817	−	0.467832i	$-0.154965\pi$
$252$		0			0
$253$	−1.20201	−	2.08194i	−0.0755695	−	0.130890i
$254$		0			0
$255$	−0.238809	+	0.325266i	−0.0149548	+	0.0203689i
$256$		0			0
$257$	1.33137	+	7.55056i	0.0830485	+	0.470991i	0.997761	+	0.0668853i	$0.0213062\pi$
$257$	1.33137	+	7.55056i	0.0830485	+	0.470991i	−0.914712	+	0.404106i	$0.867583\pi$
$258$		0			0
$259$	16.8440	+	14.1338i	1.04663	+	0.878230i
$260$		0			0
$261$	10.9303	−	11.8984i	0.676571	−	0.736490i
$262$		0			0
$263$	−0.220059	+	0.0800950i	−0.0135694	+	0.00493887i	−0.348796	−	0.937199i	$-0.613409\pi$
$263$	−0.220059	+	0.0800950i	−0.0135694	+	0.00493887i	0.335227	+	0.942138i	$0.391187\pi$
$264$		0			0
$265$	6.16161	−	5.17020i	0.378505	−	0.317603i
$266$		0			0
$267$	11.0780	+	11.5867i	0.677960	+	0.709097i
$268$		0			0
$269$	5.50541			0.335671			0.167835	−	0.985815i	$-0.446322\pi$
$269$	5.50541			0.335671			0.167835	+	0.985815i	$0.446322\pi$
$270$		0			0
$271$	−16.8819			−1.02550			−0.512751	−	0.858538i	$-0.671373\pi$
$271$	−16.8819			−1.02550			−0.512751	+	0.858538i	$0.671373\pi$
$272$		0			0
$273$	−30.5357	+	7.45171i	−1.84810	+	0.450998i
$274$		0			0
$275$	5.40794	−	4.53780i	0.326111	−	0.273640i
$276$		0			0
$277$	13.7575	−	5.00733i	0.826610	−	0.300861i	0.106143	−	0.994351i	$-0.466150\pi$
$277$	13.7575	−	5.00733i	0.826610	−	0.300861i	0.720467	+	0.693490i	$0.243928\pi$
$278$		0			0
$279$	16.7777	+	21.9221i	1.00446	+	1.31244i
$280$		0			0
$281$	−25.2094	−	21.1532i	−1.50387	−	1.26189i	−0.874739	−	0.484594i	$-0.838967\pi$
$281$	−25.2094	−	21.1532i	−1.50387	−	1.26189i	−0.629128	−	0.777301i	$-0.716588\pi$
$282$		0			0
$283$	−0.183931	−	1.04313i	−0.0109336	−	0.0620074i	0.978853	−	0.204566i	$-0.0655782\pi$
$283$	−0.183931	−	1.04313i	−0.0109336	−	0.0620074i	−0.989786	+	0.142558i	$0.954467\pi$
$284$		0			0
$285$	−1.21416	−	0.133743i	−0.0719204	−	0.00792225i
$286$		0			0
$287$	−21.4818	−	37.2076i	−1.26803	−	2.19629i
$288$		0			0
$289$	8.45314	−	14.6413i	0.497243	−	0.861251i
$290$		0			0
$291$	−5.03545	+	3.36001i	−0.295184	+	0.196967i
$292$		0			0
$293$	11.7187	+	4.26527i	0.684616	+	0.249180i	0.660828	−	0.750537i	$-0.270205\pi$
$293$	11.7187	+	4.26527i	0.684616	+	0.249180i	0.0237881	+	0.999717i	$0.492427\pi$
$294$		0			0
$295$	−1.61551	+	9.16202i	−0.0940587	+	0.533433i
$296$		0			0
$297$	−8.29583	+	0.165386i	−0.481373	+	0.00959669i
$298$		0			0
$299$	1.31327	−	7.44792i	0.0759484	−	0.430725i
$300$		0			0
$301$	25.0816	+	9.12895i	1.44568	+	0.526184i
$302$		0			0
$303$	1.44257	+	22.2231i	0.0828736	+	1.27669i
$304$		0			0
$305$	2.26503	−	3.92315i	0.129695	−	0.224639i
$306$		0			0
$307$	10.0121	+	17.3414i	0.571418	+	0.989725i	0.996421	+	0.0845330i	$0.0269398\pi$
$307$	10.0121	+	17.3414i	0.571418	+	0.989725i	−0.425003	+	0.905192i	$0.639727\pi$
$308$		0			0
$309$	−1.47313	−	3.35365i	−0.0838033	−	0.190782i
$310$		0			0
$311$	2.67087	+	15.1472i	0.151451	+	0.858921i	0.961959	+	0.273193i	$0.0880799\pi$
$311$	2.67087	+	15.1472i	0.151451	+	0.858921i	−0.810508	+	0.585727i	$0.800809\pi$
$312$		0			0
$313$	3.41111	+	2.86226i	0.192807	+	0.161785i	0.734081	−	0.679062i	$-0.237613\pi$
$313$	3.41111	+	2.86226i	0.192807	+	0.161785i	−0.541274	+	0.840847i	$0.682058\pi$
$314$		0			0
$315$	−7.31975	+	3.79875i	−0.412421	+	0.214035i
$316$		0			0
$317$	−11.7908	+	4.29150i	−0.662237	+	0.241034i	−0.651202	−	0.758905i	$-0.725735\pi$
$317$	−11.7908	+	4.29150i	−0.662237	+	0.241034i	−0.0110349	+	0.999939i	$0.503513\pi$
$318$		0			0
$319$	6.58800	−	5.52799i	0.368857	−	0.309508i
$320$		0			0
$321$	4.41767	−	15.1210i	0.246570	−	0.843972i
$322$		0			0
$323$	−0.283729			−0.0157871
$324$		0			0
$325$	22.2088			1.23192
$326$		0			0
$327$	−0.0277325	+	0.0949239i	−0.00153361	+	0.00524931i
$328$		0			0
$329$	20.9347	−	17.5663i	1.15417	−	0.968463i
$330$		0			0
$331$	0.151779	−	0.0552431i	0.00834253	−	0.00303643i	−0.337846	−	0.941202i	$-0.609698\pi$
$331$	0.151779	−	0.0552431i	0.00834253	−	0.00303643i	0.346188	+	0.938165i	$0.387476\pi$
$332$		0			0
$333$	−0.819419	+	18.2422i	−0.0449039	+	0.999667i
$334$		0			0
$335$	−1.45335	−	1.21950i	−0.0794049	−	0.0666286i
$336$		0			0
$337$	−3.30323	−	18.7335i	−0.179938	−	1.02048i	−0.932288	−	0.361717i	$-0.882191\pi$
$337$	−3.30323	−	18.7335i	−0.179938	−	1.02048i	0.752350	−	0.658764i	$-0.228920\pi$
$338$		0			0
$339$	1.35838	+	3.09242i	0.0737772	+	0.167957i
$340$		0			0
$341$	7.34702	+	12.7254i	0.397863	+	0.689119i
$342$		0			0
$343$	1.71682	−	2.97362i	0.0926997	−	0.160561i
$344$		0			0
$345$	−0.128534	−	1.98009i	−0.00692004	−	0.106605i
$346$		0			0
$347$	−0.993773	−	0.361704i	−0.0533485	−	0.0194173i	0.315208	−	0.949023i	$-0.397926\pi$
$347$	−0.993773	−	0.361704i	−0.0533485	−	0.0194173i	−0.368557	+	0.929605i	$0.620148\pi$
$348$		0			0
$349$	5.42535	−	30.7687i	0.290412	−	1.64701i	−0.394874	−	0.918735i	$-0.629212\pi$
$349$	5.42535	−	30.7687i	0.290412	−	1.64701i	0.685286	−	0.728274i	$-0.259677\pi$
$350$		0			0
$351$	−20.3266	−	16.3769i	−1.08496	−	0.874133i
$352$		0			0
$353$	−2.95822	+	16.7769i	−0.157450	+	0.892945i	0.799061	+	0.601250i	$0.205330\pi$
$353$	−2.95822	+	16.7769i	−0.157450	+	0.892945i	−0.956511	+	0.291695i	$0.905781\pi$
$354$		0			0
$355$	−8.13170	−	2.95970i	−0.431586	−	0.157084i
$356$		0			0
$357$	−1.59339	+	1.06323i	−0.0843313	+	0.0562718i
$358$		0			0
$359$	−9.73277	+	16.8576i	−0.513676	+	0.889713i	0.486198	+	0.873848i	$0.338383\pi$
$359$	−9.73277	+	16.8576i	−0.513676	+	0.889713i	−0.999874	+	0.0158641i	$0.994950\pi$
$360$		0			0
$361$	9.07056	+	15.7107i	0.477398	+	0.826877i
$362$		0			0
$363$	14.5480	+	1.60250i	0.763569	+	0.0841095i
$364$		0			0
$365$	−1.27016	−	7.20345i	−0.0664834	−	0.377046i
$366$		0			0
$367$	−2.36256	−	1.98243i	−0.123325	−	0.103482i	0.579039	−	0.815300i	$-0.303428\pi$
$367$	−2.36256	−	1.98243i	−0.123325	−	0.103482i	−0.702364	+	0.711818i	$0.747872\pi$
$368$		0			0
$369$	13.6955	−	32.9469i	0.712961	−	1.71515i
$370$		0			0
$371$	35.8804	−	13.0594i	1.86282	−	0.678010i
$372$		0			0
$373$	−16.3367	+	13.7081i	−0.845882	+	0.709779i	−0.958879	−	0.283816i	$-0.908399\pi$
$373$	−16.3367	+	13.7081i	−0.845882	+	0.709779i	0.112997	+	0.993595i	$0.463955\pi$
$374$		0			0
$375$	12.0631	−	2.94380i	0.622936	−	0.152017i
$376$		0			0
$377$	27.0549			1.39340
$378$		0			0
$379$	−17.1690			−0.881913			−0.440957	−	0.897528i	$-0.645361\pi$
$379$	−17.1690			−0.881913			−0.440957	+	0.897528i	$0.645361\pi$
$380$		0			0
$381$	20.6454	+	21.5936i	1.05770	+	1.10627i
$382$		0			0
$383$	6.79612	−	5.70262i	0.347265	−	0.291390i	−0.452426	−	0.891802i	$-0.649441\pi$
$383$	6.79612	−	5.70262i	0.347265	−	0.291390i	0.799691	+	0.600412i	$0.204997\pi$
$384$		0			0
$385$	−4.12489	+	1.50134i	−0.210224	+	0.0765153i
$386$		0			0
$387$	6.63900	+	21.1487i	0.337479	+	1.07505i
$388$		0			0
$389$	5.51259	+	4.62561i	0.279499	+	0.234528i	0.771750	−	0.635925i	$-0.219381\pi$
$389$	5.51259	+	4.62561i	0.279499	+	0.234528i	−0.492251	+	0.870453i	$0.663826\pi$
$390$		0			0
$391$	−0.0800350	−	0.453901i	−0.00404755	−	0.0229548i
$392$		0			0
$393$	−7.44599	+	10.1417i	−0.375601	+	0.511581i
$394$		0			0
$395$	0.988112	+	1.71146i	0.0497173	+	0.0861129i
$396$		0			0
$397$	−8.96150	+	15.5218i	−0.449765	+	0.779016i	−0.998370	−	0.0570657i	$-0.981826\pi$
$397$	−8.96150	+	15.5218i	−0.449765	+	0.779016i	0.548606	+	0.836081i	$0.315159\pi$
$398$		0			0
$399$	−5.19901	−	2.56793i	−0.260276	−	0.128557i
$400$		0			0
$401$	−17.6056	−	6.40792i	−0.879182	−	0.319996i	−0.137302	−	0.990529i	$-0.543843\pi$
$401$	−17.6056	−	6.40792i	−0.879182	−	0.319996i	−0.741880	+	0.670533i	$0.766065\pi$
$402$		0			0
$403$	−8.02709	+	45.5239i	−0.399858	+	2.26771i
$404$		0			0
$405$	−6.19974	−	2.90996i	−0.308068	−	0.144597i
$406$		0			0
$407$	−1.68783	+	9.57216i	−0.0836626	+	0.474474i
$408$		0			0
$409$	0.658114	+	0.239534i	0.0325417	+	0.0118442i	0.358240	−	0.933630i	$-0.383377\pi$
$409$	0.658114	+	0.239534i	0.0325417	+	0.0118442i	−0.325698	+	0.945474i	$0.605599\pi$
$410$		0			0
$411$	−19.0514	−	9.40996i	−0.939734	−	0.464159i
$412$		0			0
$413$	−22.0821	+	38.2474i	−1.08659	+	1.88203i
$414$		0			0
$415$	−6.19525	−	10.7305i	−0.304113	−	0.526739i
$416$		0			0
$417$	−10.7059	+	14.5818i	−0.524272	+	0.714076i
$418$		0			0
$419$	3.12089	+	17.6995i	0.152466	+	0.864676i	0.961066	+	0.276318i	$0.0891142\pi$
$419$	3.12089	+	17.6995i	0.152466	+	0.864676i	−0.808601	+	0.588358i	$0.799775\pi$
$420$		0			0
$421$	5.14228	+	4.31488i	0.250619	+	0.210294i	0.759439	−	0.650579i	$-0.225474\pi$
$421$	5.14228	+	4.31488i	0.250619	+	0.210294i	−0.508820	+	0.860873i	$0.669918\pi$
$422$		0			0
$423$	22.1513	+	4.94000i	1.07703	+	0.240191i
$424$		0			0
$425$	1.27185	−	0.462916i	0.0616939	−	0.0224547i
$426$		0			0
$427$	16.4736	−	13.8230i	0.797215	−	0.668943i
$428$		0			0
$429$	−9.60177	−	10.0428i	−0.463578	−	0.484869i
$430$		0			0
$431$	−1.52743			−0.0735739			−0.0367869	−	0.999323i	$-0.511712\pi$
$431$	−1.52743			−0.0735739			−0.0367869	+	0.999323i	$0.511712\pi$
$432$		0			0
$433$	24.1194			1.15910			0.579552	−	0.814935i	$-0.303227\pi$
$433$	24.1194			1.15910			0.579552	+	0.814935i	$0.303227\pi$
$434$		0			0
$435$	6.89605	−	1.68286i	0.330640	−	0.0806872i
$436$		0			0
$437$	1.06879	−	0.896824i	0.0511273	−	0.0429009i
$438$		0			0
$439$	2.44512	−	0.889952i	0.116699	−	0.0424751i	−0.283010	−	0.959117i	$-0.591333\pi$
$439$	2.44512	−	0.889952i	0.116699	−	0.0424751i	0.399710	+	0.916642i	$0.369111\pi$
$440$		0			0
$441$	−17.9962	+	2.34626i	−0.856960	+	0.111727i
$442$		0			0
$443$	−2.66172	−	2.23345i	−0.126462	−	0.106114i	0.577363	−	0.816487i	$-0.304082\pi$
$443$	−2.66172	−	2.23345i	−0.126462	−	0.106114i	−0.703825	+	0.710373i	$0.748526\pi$
$444$		0			0
$445$	1.22298	+	6.93587i	0.0579749	+	0.328792i
$446$		0			0
$447$	32.7369	+	3.60607i	1.54840	+	0.170561i
$448$		0			0
$449$	11.3550	+	19.6675i	0.535876	+	0.928165i	0.999120	+	0.0419341i	$0.0133519\pi$
$449$	11.3550	+	19.6675i	0.535876	+	0.928165i	−0.463244	+	0.886231i	$0.653315\pi$
$450$		0			0
$451$	9.49596	−	16.4475i	0.447147	−	0.774481i
$452$		0			0
$453$	11.1110	−	7.41407i	0.522042	−	0.348344i
$454$		0			0
$455$	−12.9766	−	4.72308i	−0.608350	−	0.221421i
$456$		0			0
$457$	1.20716	−	6.84612i	0.0564683	−	0.320248i	−0.943469	−	0.331461i	$-0.892458\pi$
$457$	1.20716	−	6.84612i	0.0564683	−	0.320248i	0.999937	+	0.0112135i	$0.00356945\pi$
$458$		0			0
$459$	−1.50542	−	0.514186i	−0.0702671	−	0.0240001i
$460$		0			0
$461$	−4.30041	+	24.3888i	−0.200290	+	1.13590i	0.704392	+	0.709812i	$0.251220\pi$
$461$	−4.30041	+	24.3888i	−0.200290	+	1.13590i	−0.904681	+	0.426089i	$0.859891\pi$
$462$		0			0
$463$	25.3216	+	9.21630i	1.17679	+	0.428318i	0.855069	−	0.518515i	$-0.173515\pi$
$463$	25.3216	+	9.21630i	1.17679	+	0.428318i	0.321725	+	0.946833i	$0.395737\pi$
$464$		0			0
$465$	0.785637	+	12.1029i	0.0364331	+	0.561259i
$466$		0			0
$467$	−1.26382	+	2.18900i	−0.0584826	+	0.101295i	−0.893784	−	0.448497i	$-0.851960\pi$
$467$	−1.26382	+	2.18900i	−0.0584826	+	0.101295i	0.835302	+	0.549792i	$0.185293\pi$
$468$		0			0
$469$	−4.50315	−	7.79969i	−0.207936	−	0.360156i
$470$		0			0
$471$	7.47468	+	17.0165i	0.344415	+	0.784078i
$472$		0			0
$473$	2.04883	+	11.6195i	0.0942055	+	0.534266i
$474$		0			0
$475$	3.13859	+	2.63359i	0.144008	+	0.120837i
$476$		0			0
$477$	26.7225	+	17.0713i	1.22354	+	0.781641i
$478$		0			0
$479$	37.2207	−	13.5472i	1.70066	−	0.618989i	0.704759	−	0.709447i	$-0.251055\pi$
$479$	37.2207	−	13.5472i	1.70066	−	0.618989i	0.995900	+	0.0904575i	$0.0288329\pi$
$480$		0			0
$481$	−23.4239	+	19.6550i	−1.06804	+	0.896190i
$482$		0			0
$483$	2.64154	−	9.04158i	0.120194	−	0.411406i
$484$		0			0
$485$	−2.65959			−0.120766
$486$		0			0
$487$	−21.4892			−0.973767			−0.486883	−	0.873467i	$-0.661866\pi$
$487$	−21.4892			−0.973767			−0.486883	+	0.873467i	$0.661866\pi$
$488$		0			0
$489$	−2.35055	+	8.04555i	−0.106295	+	0.363833i
$490$		0			0
$491$	−17.9959	+	15.1003i	−0.812143	+	0.681469i	−0.951118	−	0.308827i	$-0.900064\pi$
$491$	−17.9959	+	15.1003i	−0.812143	+	0.681469i	0.138975	+	0.990296i	$0.455619\pi$
$492$		0			0
$493$	1.54938	−	0.563928i	0.0697806	−	0.0253981i
$494$		0			0
$495$	−3.07208	−	1.96256i	−0.138080	−	0.0882104i
$496$		0			0
$497$	−31.4688	−	26.4055i	−1.41157	−	1.18445i
$498$		0			0
$499$	0.199454	+	1.13116i	0.00892880	+	0.0506378i	0.988947	−	0.148272i	$-0.0473711\pi$
$499$	0.199454	+	1.13116i	0.00892880	+	0.0506378i	−0.980018	+	0.198910i	$0.936260\pi$
$500$		0			0
$501$	−4.43368	−	10.0935i	−0.198082	−	0.450944i
$502$		0			0
$503$	−1.61381	−	2.79520i	−0.0719562	−	0.124632i	0.827802	−	0.561020i	$-0.189591\pi$
$503$	−1.61381	−	2.79520i	−0.0719562	−	0.124632i	−0.899759	+	0.436388i	$0.856258\pi$
$504$		0			0
$505$	−4.89208	+	8.47333i	−0.217695	+	0.377058i
$506$		0			0
$507$	−1.37285	−	21.1490i	−0.0609703	−	0.939261i
$508$		0			0
$509$	−13.5489	−	4.93139i	−0.600544	−	0.218580i	0.0238169	−	0.999716i	$-0.492418\pi$
$509$	−13.5489	−	4.93139i	−0.600544	−	0.218580i	−0.624360	+	0.781136i	$0.714640\pi$
$510$		0			0
$511$	6.02963	−	34.1957i	0.266735	−	1.51273i
$512$		0			0
$513$	−0.930578	−	4.72481i	−0.0410860	−	0.208606i
$514$		0			0
$515$	0.279450	−	1.58484i	0.0123140	−	0.0698363i
$516$		0			0
$517$	11.3519	+	4.13174i	0.499254	+	0.181714i
$518$		0			0
$519$	2.14544	−	1.43159i	0.0941742	−	0.0628397i
$520$		0			0
$521$	9.16224	−	15.8695i	0.401405	−	0.695254i	−0.592491	−	0.805577i	$-0.701855\pi$
$521$	9.16224	−	15.8695i	0.401405	−	0.695254i	0.993896	+	0.110323i	$0.0351886\pi$
$522$		0			0
$523$	−9.35270	−	16.1993i	−0.408965	−	0.708348i	0.585809	−	0.810449i	$-0.300777\pi$
$523$	−9.35270	−	16.1993i	−0.408965	−	0.708348i	−0.994774	+	0.102101i	$0.967444\pi$
$524$		0			0
$525$	27.4949	+	3.02865i	1.19998	+	0.132181i
$526$		0			0
$527$	0.489197	+	2.77438i	0.0213098	+	0.120854i
$528$		0			0
$529$	−15.8828	−	13.3273i	−0.690558	−	0.579447i
$530$		0			0
$531$	−36.3693	+	4.74167i	−1.57829	+	0.205771i
$532$		0			0
$533$	56.1437	−	20.4346i	2.43185	−	0.885123i
$534$		0			0
$535$	5.30183	−	4.44876i	0.229218	−	0.192337i
$536$		0			0
$537$	17.1225	−	4.17846i	0.738890	−	0.180314i
$538$		0			0
$539$	−9.66013			−0.416091
$540$		0			0
$541$	−31.9104			−1.37194			−0.685968	−	0.727632i	$-0.740621\pi$
$541$	−31.9104			−1.37194			−0.685968	+	0.727632i	$0.740621\pi$
$542$		0			0
$543$	−21.2391	−	22.2146i	−0.911459	−	0.953320i
$544$		0			0
$545$	−0.0332829	+	0.0279276i	−0.00142568	+	0.00119629i
$546$		0			0
$547$	21.7829	−	7.92832i	0.931368	−	0.338990i	0.168616	−	0.985682i	$-0.446070\pi$
$547$	21.7829	−	7.92832i	0.931368	−	0.338990i	0.762752	+	0.646691i	$0.223848\pi$
$548$		0			0
$549$	17.4309	+	3.88731i	0.743934	+	0.165906i
$550$		0			0
$551$	3.82346	+	3.20826i	0.162885	+	0.136676i
$552$		0			0
$553$	1.62906	+	9.23886i	0.0692747	+	0.392876i
$554$		0			0
$555$	−4.74796	+	6.46688i	−0.201540	+	0.274504i
$556$		0			0
$557$	1.70738	+	2.95727i	0.0723441	+	0.125304i	0.899928	−	0.436038i	$-0.143619\pi$
$557$	1.70738	+	2.95727i	0.0723441	+	0.125304i	−0.827584	+	0.561342i	$0.810285\pi$
$558$		0			0
$559$	−18.5590	+	32.1450i	−0.784960	+	1.35959i
$560$		0			0
$561$	−0.759204	−	0.374991i	−0.0320536	−	0.0158321i
$562$		0			0
$563$	−18.6394	−	6.78419i	−0.785558	−	0.285920i	−0.0820694	−	0.996627i	$-0.526153\pi$
$563$	−18.6394	−	6.78419i	−0.785558	−	0.285920i	−0.703488	+	0.710707i	$0.748375\pi$
$564$		0			0
$565$	−0.257683	+	1.46139i	−0.0108408	+	0.0614812i
$566$		0			0
$567$	−22.9314	−	23.0469i	−0.963029	−	0.967878i
$568$		0			0
$569$	1.44130	−	8.17403i	0.0604225	−	0.342673i	−0.939577	−	0.342337i	$-0.888782\pi$
$569$	1.44130	−	8.17403i	0.0604225	−	0.342673i	1.00000		0.000336694i	$-0.000107173\pi$
$570$		0			0
$571$	−2.97310	−	1.08212i	−0.124420	−	0.0452853i	0.279060	−	0.960274i	$-0.409977\pi$
$571$	−2.97310	−	1.08212i	−0.124420	−	0.0452853i	−0.403480	+	0.914988i	$0.632199\pi$
$572$		0			0
$573$	−26.7981	−	13.2363i	−1.11951	−	0.552954i
$574$		0			0
$575$	−3.32779	+	5.76391i	−0.138779	+	0.240372i
$576$		0			0
$577$	−22.4390	−	38.8656i	−0.934149	−	1.61799i	−0.776144	−	0.630556i	$-0.782827\pi$
$577$	−22.4390	−	38.8656i	−0.934149	−	1.61799i	−0.158006	−	0.987438i	$-0.550506\pi$
$578$		0			0
$579$	21.6958	−	29.5504i	0.901647	−	1.22807i
$580$		0			0
$581$	−10.2139	−	57.9257i	−0.423743	−	2.40316i
$582$		0			0
$583$	12.9298	+	10.8494i	0.535499	+	0.449337i
$584$		0			0
$585$	−3.43484	−	10.9418i	−0.142013	−	0.452388i
$586$		0			0
$587$	−17.0715	+	6.21350i	−0.704614	+	0.256459i	−0.669380	−	0.742920i	$-0.733440\pi$
$587$	−17.0715	+	6.21350i	−0.704614	+	0.256459i	−0.0352346	+	0.999379i	$0.511218\pi$
$588$		0			0
$589$	−6.53277	+	5.48165i	−0.269178	+	0.225867i
$590$		0			0
$591$	0.785706	+	0.821791i	0.0323196	+	0.0338040i
$592$		0			0
$593$	−0.302129			−0.0124070			−0.00620348	−	0.999981i	$-0.501975\pi$
$593$	−0.302129			−0.0124070			−0.00620348	+	0.999981i	$0.501975\pi$
$594$		0			0
$595$	−0.841588			−0.0345017
$596$		0			0
$597$	−28.0675	+	6.84940i	−1.14873	+	0.280327i
$598$		0			0
$599$	−1.92101	+	1.61192i	−0.0784905	+	0.0658614i	−0.681189	−	0.732108i	$-0.738537\pi$
$599$	−1.92101	+	1.61192i	−0.0784905	+	0.0658614i	0.602698	+	0.797969i	$0.294092\pi$
$600$		0			0
$601$	−9.87941	+	3.59581i	−0.402990	+	0.146676i	−0.535560	−	0.844497i	$-0.679899\pi$
$601$	−9.87941	+	3.59581i	−0.402990	+	0.146676i	0.132570	+	0.991174i	$0.457677\pi$
$602$		0			0
$603$	2.87095	−	6.90654i	0.116914	−	0.281256i
$604$		0			0
$605$	4.92583	+	4.13327i	0.200264	+	0.168041i
$606$		0			0
$607$	1.74872	+	9.91750i	0.0709784	+	0.402539i	0.999510	+	0.0312864i	$0.00996040\pi$
$607$	1.74872	+	9.91750i	0.0709784	+	0.402539i	−0.928532	+	0.371252i	$0.878928\pi$
$608$		0			0
$609$	33.4945	+	3.68952i	1.35727	+	0.149507i
$610$		0			0
$611$	19.0019	+	32.9123i	0.768736	+	1.33149i
$612$		0			0
$613$	0.863403	−	1.49546i	0.0348725	−	0.0604010i	−0.848062	−	0.529896i	$-0.822231\pi$
$613$	0.863403	−	1.49546i	0.0348725	−	0.0604010i	0.882935	+	0.469495i	$0.155564\pi$
$614$		0			0
$615$	13.0394	−	8.70084i	0.525801	−	0.350852i
$616$		0			0
$617$	19.3449	+	7.04097i	0.778796	+	0.283459i	0.700671	−	0.713485i	$-0.252884\pi$
$617$	19.3449	+	7.04097i	0.778796	+	0.283459i	0.0781256	+	0.996944i	$0.475106\pi$
$618$		0			0
$619$	6.06773	−	34.4118i	0.243883	−	1.38313i	−0.579190	−	0.815192i	$-0.696631\pi$
$619$	6.06773	−	34.4118i	0.243883	−	1.38313i	0.823073	−	0.567936i	$-0.192258\pi$
$620$		0			0
$621$	7.29611	−	2.82150i	0.292783	−	0.113223i
$622$		0			0
$623$	−5.80565	+	32.9255i	−0.232598	+	1.31913i
$624$		0			0
$625$	−15.6452	−	5.69438i	−0.625808	−	0.227775i
$626$		0			0
$627$	−0.166039	−	2.55787i	−0.00663097	−	0.102152i
$628$		0			0
$629$	−0.931754	+	1.61384i	−0.0371515	+	0.0643482i
$630$		0			0
$631$	−7.80338	−	13.5159i	−0.310648	−	0.538058i	0.667855	−	0.744291i	$-0.267213\pi$
$631$	−7.80338	−	13.5159i	−0.310648	−	0.538058i	−0.978503	+	0.206234i	$0.933879\pi$
$632$		0			0
$633$	3.38401	+	7.70386i	0.134502	+	0.306201i
$634$		0			0
$635$	2.27920	+	12.9260i	0.0904474	+	0.512953i
$636$		0			0
$637$	−23.2800	−	19.5343i	−0.922388	−	0.773976i
$638$		0			0
$639$	1.53088	−	34.0811i	0.0605608	−	1.34823i
$640$		0			0
$641$	−23.5190	+	8.56022i	−0.928945	+	0.338108i	−0.761791	−	0.647823i	$-0.775680\pi$
$641$	−23.5190	+	8.56022i	−0.928945	+	0.338108i	−0.167154	+	0.985931i	$0.553458\pi$
$642$		0			0
$643$	−30.7439	+	25.7972i	−1.21242	+	1.01734i	−0.213234	+	0.977001i	$0.568400\pi$
$643$	−30.7439	+	25.7972i	−1.21242	+	1.01734i	−0.999186	+	0.0403397i	$0.987156\pi$
$644$		0			0
$645$	−2.73102	+	9.34788i	−0.107534	+	0.368072i
$646$		0			0
$647$	10.7038			0.420809			0.210405	−	0.977614i	$-0.432522\pi$
$647$	10.7038			0.420809			0.210405	+	0.977614i	$0.432522\pi$
$648$		0			0
$649$	−19.5226			−0.766331
$650$		0			0
$651$	−16.1459	+	55.2647i	−0.632806	+	2.16600i
$652$		0			0
$653$	−2.78157	+	2.33402i	−0.108851	+	0.0913371i	−0.695589	−	0.718440i	$-0.744856\pi$
$653$	−2.78157	+	2.33402i	−0.108851	+	0.0913371i	0.586738	+	0.809777i	$0.300412\pi$
$654$		0			0
$655$	−5.19430	+	1.89057i	−0.202958	+	0.0738707i
$656$		0			0
$657$	25.5951	−	13.2832i	0.998560	−	0.518225i
$658$		0			0
$659$	3.49986	+	2.93673i	0.136335	+	0.114399i	0.708405	−	0.705806i	$-0.249415\pi$
$659$	3.49986	+	2.93673i	0.136335	+	0.114399i	−0.572070	+	0.820205i	$0.693859\pi$
$660$		0			0
$661$	4.32919	+	24.5520i	0.168386	+	0.954964i	0.945504	+	0.325609i	$0.105569\pi$
$661$	4.32919	+	24.5520i	0.168386	+	0.954964i	−0.777119	+	0.629354i	$0.783319\pi$
$662$		0			0
$663$	−1.07132	−	2.43892i	−0.0416068	−	0.0947198i
$664$		0			0
$665$	−1.27379	−	2.20628i	−0.0493956	−	0.0855557i
$666$		0			0
$667$	−4.05394	+	7.02164i	−0.156969	+	0.271879i
$668$		0			0
$669$	−1.26236	−	19.4470i	−0.0488058	−	0.751863i
$670$		0			0
$671$	8.93283	+	3.25128i	0.344848	+	0.125514i
$672$		0			0
$673$	1.61422	−	9.15468i	0.0622235	−	0.352887i	−0.937761	−	0.347282i	$-0.887105\pi$
$673$	1.61422	−	9.15468i	0.0622235	−	0.352887i	0.999984	−	0.00560507i	$-0.00178416\pi$
$674$		0			0
$675$	11.8802	+	19.6613i	0.457268	+	0.756763i
$676$		0			0
$677$	0.132305	−	0.750342i	0.00508491	−	0.0288380i	−0.982160	−	0.188049i	$-0.939784\pi$
$677$	0.132305	−	0.750342i	0.00508491	−	0.0288380i	0.987245	+	0.159211i	$0.0508949\pi$
$678$		0			0
$679$	−11.8640	−	4.31815i	−0.455300	−	0.165716i
$680$		0			0
$681$	35.0902	−	23.4146i	1.34466	−	0.897251i
$682$		0			0
$683$	−5.94471	+	10.2965i	−0.227468	+	0.393986i	−0.957057	−	0.289900i	$-0.906378\pi$
$683$	−5.94471	+	10.2965i	−0.227468	+	0.393986i	0.729589	+	0.683886i	$0.239711\pi$
$684$		0			0
$685$	−4.66772	−	8.08473i	−0.178344	−	0.308902i
$686$		0			0
$687$	−23.5393	−	2.59293i	−0.898082	−	0.0989265i
$688$		0			0
$689$	9.22052	+	52.2922i	0.351274	+	1.99217i
$690$		0			0
$691$	−15.4783	−	12.9878i	−0.588821	−	0.494079i	0.299010	−	0.954250i	$-0.403344\pi$
$691$	−15.4783	−	12.9878i	−0.588821	−	0.494079i	−0.887830	+	0.460171i	$0.847788\pi$
$692$		0			0
$693$	−10.5176	−	13.7425i	−0.399532	−	0.522036i
$694$		0			0
$695$	−7.46842	+	2.71828i	−0.283293	+	0.103110i
$696$		0			0
$697$	2.78930	−	2.34050i	0.105652	−	0.0886528i
$698$		0			0
$699$	44.7340	−	10.9166i	1.69199	−	0.412903i
$700$		0			0
$701$	−15.3255			−0.578837			−0.289418	−	0.957203i	$-0.593462\pi$
$701$	−15.3255			−0.578837			−0.289418	+	0.957203i	$0.593462\pi$
$702$		0			0
$703$	−5.64106			−0.212757
$704$		0			0
$705$	6.89062	+	7.20709i	0.259516	+	0.271435i
$706$		0			0
$707$	−35.5802	+	29.8553i	−1.33813	+	1.12283i
$708$		0			0
$709$	27.3536	−	9.95588i	1.02728	−	0.373901i	0.227238	−	0.973839i	$-0.427030\pi$
$709$	27.3536	−	9.95588i	1.02728	−	0.373901i	0.800046	+	0.599938i	$0.204808\pi$
$710$		0			0
$711$	−5.27071	+	5.73750i	−0.197667	+	0.215173i
$712$		0			0
$713$	−10.6121	−	8.90465i	−0.397428	−	0.333482i
$714$		0			0
$715$	−1.06001	−	6.01163i	−0.0396423	−	0.224822i
$716$		0			0
$717$	−8.76348	+	11.9362i	−0.327278	+	0.445764i
$718$		0			0
$719$	6.90583	+	11.9612i	0.257544	+	0.446079i	0.965583	−	0.260094i	$-0.0837534\pi$
$719$	6.90583	+	11.9612i	0.257544	+	0.446079i	−0.708039	+	0.706173i	$0.750420\pi$
$720$		0			0
$721$	3.81975	−	6.61600i	0.142255	−	0.246393i
$722$		0			0
$723$	−29.6952	−	14.6672i	−1.10438	−	0.545480i
$724$		0			0
$725$	−22.3735	−	8.14330i	−0.830932	−	0.302434i
$726$		0			0
$727$	−0.378999	+	2.14941i	−0.0140563	+	0.0797172i	−0.991029	−	0.133647i	$-0.957331\pi$
$727$	−0.378999	+	2.14941i	−0.0140563	+	0.0797172i	0.976973	+	0.213364i	$0.0684422\pi$
$728$		0			0
$729$	3.62500	−	26.7555i	0.134259	−	0.990946i
$730$		0			0
$731$	−0.392808	+	2.22772i	−0.0145285	+	0.0823953i
$732$		0			0
$733$	−38.8875	−	14.1539i	−1.43634	−	0.522786i	−0.497600	−	0.867407i	$-0.665785\pi$
$733$	−38.8875	−	14.1539i	−1.43634	−	0.522786i	−0.938742	+	0.344621i	$0.888007\pi$
$734$		0			0
$735$	−7.14893	−	3.53104i	−0.263692	−	0.130244i
$736$		0			0
$737$	1.99060	−	3.44782i	0.0733248	−	0.127002i
$738$		0			0
$739$	−18.0145	−	31.2020i	−0.662674	−	1.14779i	−0.979910	−	0.199439i	$-0.936088\pi$
$739$	−18.0145	−	31.2020i	−0.662674	−	1.14779i	0.317236	−	0.948347i	$-0.397245\pi$
$740$		0			0
$741$	4.77227	−	6.50000i	0.175314	−	0.238783i
$742$		0			0
$743$	−1.19334	−	6.76776i	−0.0437793	−	0.248285i	0.955062	−	0.296405i	$-0.0957880\pi$
$743$	−1.19334	−	6.76776i	−0.0437793	−	0.248285i	−0.998842	+	0.0481205i	$0.984677\pi$
$744$		0			0
$745$	11.0845	+	9.30099i	0.406104	+	0.340762i
$746$		0			0
$747$	33.0463	−	35.9729i	1.20910	−	1.31618i
$748$		0			0
$749$	30.8737	−	11.2371i	1.12810	−	0.410595i
$750$		0			0
$751$	−4.05658	+	3.40388i	−0.148027	+	0.124209i	−0.713794	−	0.700356i	$-0.753025\pi$
$751$	−4.05658	+	3.40388i	−0.148027	+	0.124209i	0.565767	+	0.824565i	$0.308580\pi$
$752$		0			0
$753$	32.1262	+	33.6016i	1.17074	+	1.22451i
$754$		0			0
$755$	5.86856			0.213579
$756$		0			0
$757$	−41.1017			−1.49387			−0.746933	−	0.664899i	$-0.768475\pi$
$757$	−41.1017			−1.49387			−0.746933	+	0.664899i	$0.768475\pi$
$758$		0			0
$759$	4.04517	−	0.987155i	0.146830	−	0.0358315i
$760$		0			0
$761$	−40.2528	+	33.7761i	−1.45916	+	1.22438i	−0.533627	+	0.845720i	$0.679171\pi$
$761$	−40.2528	+	33.7761i	−1.45916	+	1.22438i	−0.925535	+	0.378662i	$0.876384\pi$
$762$		0			0
$763$	−0.193813	+	0.0705422i	−0.00701651	+	0.00255380i
$764$		0			0
$765$	−0.424776	−	0.555020i	−0.0153578	−	0.0200668i
$766$		0			0
$767$	−47.0478	−	39.4778i	−1.69880	−	1.42546i
$768$		0			0
$769$	−2.01356	−	11.4195i	−0.0726108	−	0.411796i	−0.999349	−	0.0360877i	$-0.988510\pi$
$769$	−2.01356	−	11.4195i	−0.0726108	−	0.411796i	0.926738	−	0.375709i	$-0.122601\pi$
$770$		0			0
$771$	−13.1999	−	1.45401i	−0.475382	−	0.0523648i
$772$		0			0
$773$	11.9274	+	20.6589i	0.428999	+	0.743049i	0.996785	−	0.0801280i	$-0.0255329\pi$
$773$	11.9274	+	20.6589i	0.428999	+	0.743049i	−0.567785	+	0.823177i	$0.692200\pi$
$774$		0			0
$775$	20.3404	−	35.2307i	0.730650	−	1.26552i
$776$		0			0
$777$	−31.6796	+	21.1389i	−1.13650	+	0.758353i
$778$		0			0
$779$	10.3576	+	3.76984i	0.371098	+	0.135069i
$780$		0			0
$781$	3.15329	−	17.8832i	0.112834	−	0.639912i
$782$		0			0
$783$	14.4725	+	23.9515i	0.517205	+	0.855958i
$784$		0			0
$785$	−1.41793	+	8.04151i	−0.0506083	+	0.287014i
$786$		0			0
$787$	6.31279	+	2.29767i	0.225027	+	0.0819030i	0.452073	−	0.891981i	$-0.350685\pi$
$787$	6.31279	+	2.29767i	0.225027	+	0.0819030i	−0.227046	+	0.973884i	$0.572907\pi$
$788$		0			0
$789$	−0.0262745	−	0.404764i	−0.000935395	−	0.0144100i
$790$		0			0
$791$	−3.52222	+	6.10066i	−0.125236	+	0.216914i
$792$		0			0
$793$	14.9527	+	25.8989i	0.530986	+	0.919696i
$794$		0			0
$795$	5.60290	+	12.7553i	0.198714	+	0.452383i
$796$		0			0
$797$	4.43166	+	25.1332i	0.156978	+	0.890264i	0.956956	+	0.290235i	$0.0937334\pi$
$797$	4.43166	+	25.1332i	0.156978	+	0.890264i	−0.799978	+	0.600029i	$0.795156\pi$
$798$		0			0
$799$	1.77422	+	1.48875i	0.0627675	+	0.0526682i
$800$		0			0
$801$	−24.6444	+	12.7897i	−0.870765	+	0.451903i
$802$		0			0
$803$	14.4236	−	5.24976i	0.508998	−	0.185260i
$804$		0			0
$805$	3.17022	−	2.66013i	0.111735	−	0.0937572i
$806$		0			0
$807$	−2.67410	+	9.15302i	−0.0941327	+	0.322202i
$808$		0			0
$809$	43.0128			1.51225			0.756124	−	0.654428i	$-0.227091\pi$
$809$	43.0128			1.51225			0.756124	+	0.654428i	$0.227091\pi$
$810$		0			0
$811$	13.1743			0.462614			0.231307	−	0.972881i	$-0.425700\pi$
$811$	13.1743			0.462614			0.231307	+	0.972881i	$0.425700\pi$
$812$		0			0
$813$	8.19990	−	28.0670i	0.287583	−	0.984352i
$814$		0			0
$815$	−2.82099	+	2.36709i	−0.0988148	+	0.0829155i
$816$		0			0
$817$	−6.43465	+	2.34202i	−0.225120	+	0.0819370i
$818$		0			0
$819$	2.44298	−	54.3865i	0.0853647	−	1.90042i
$820$		0			0
$821$	−13.1427	−	11.0280i	−0.458683	−	0.384881i	0.383963	−	0.923348i	$-0.374559\pi$
$821$	−13.1427	−	11.0280i	−0.458683	−	0.384881i	−0.842646	+	0.538468i	$0.819003\pi$
$822$		0			0
$823$	0.334058	+	1.89453i	0.0116445	+	0.0660393i	0.990076	−	0.140531i	$-0.0448809\pi$
$823$	0.334058	+	1.89453i	0.0116445	+	0.0660393i	−0.978432	+	0.206570i	$0.933770\pi$
$824$		0			0
$825$	4.91757	+	11.1951i	0.171208	+	0.389763i
$826$		0			0
$827$	19.1936	+	33.2443i	0.667428	+	1.15602i	0.978621	+	0.205672i	$0.0659381\pi$
$827$	19.1936	+	33.2443i	0.667428	+	1.15602i	−0.311193	+	0.950347i	$0.600729\pi$
$828$		0			0
$829$	0.0698066	−	0.120909i	0.00242449	−	0.00419933i	−0.864811	−	0.502098i	$-0.832562\pi$
$829$	0.0698066	−	0.120909i	0.00242449	−	0.00419933i	0.867235	+	0.497899i	$0.165895\pi$
$830$		0			0
$831$	1.64261	+	25.3048i	0.0569815	+	0.877812i
$832$		0			0
$833$	−1.74037	−	0.633443i	−0.0603002	−	0.0219475i
$834$		0			0
$835$	0.841062	−	4.76990i	0.0291062	−	0.165069i
$836$		0			0
$837$	−44.5959	+	17.2458i	−1.54146	+	0.596102i
$838$		0			0
$839$	3.89949	−	22.1151i	0.134625	−	0.763499i	−0.840494	−	0.541820i	$-0.817735\pi$
$839$	3.89949	−	22.1151i	0.134625	−	0.763499i	0.975120	−	0.221678i	$-0.0711535\pi$
$840$		0			0
$841$	−0.00452481	−	0.00164690i	−0.000156028	−	5.67895e-5i
$842$		0			0
$843$	47.4131	−	31.6374i	1.63299	−	1.08965i
$844$		0			0
$845$	4.65563	−	8.06379i	0.160159	−	0.277403i
$846$		0			0
$847$	15.2625	+	26.4355i	0.524427	+	0.908334i
$848$		0			0
$849$	1.82359	+	0.200874i	0.0625854	+	0.00689397i
$850$		0			0
$851$	−1.59124	−	9.02440i	−0.0545472	−	0.309352i
$852$		0			0
$853$	22.9492	+	19.2566i	0.785764	+	0.659334i	0.944693	−	0.327956i	$-0.106360\pi$
$853$	22.9492	+	19.2566i	0.785764	+	0.659334i	−0.158929	+	0.987290i	$0.550804\pi$
$854$		0			0
$855$	0.812096	−	1.95363i	0.0277731	−	0.0668128i
$856$		0			0
$857$	12.6304	−	4.59709i	0.431446	−	0.157033i	−0.117163	−	0.993113i	$-0.537380\pi$
$857$	12.6304	−	4.59709i	0.431446	−	0.157033i	0.548609	+	0.836079i	$0.315158\pi$
$858$		0			0
$859$	−26.9921	+	22.6490i	−0.920957	+	0.772775i	−0.974172	−	0.225808i	$-0.927498\pi$
$859$	−26.9921	+	22.6490i	−0.920957	+	0.772775i	0.0532147	+	0.998583i	$0.483053\pi$
$860$		0			0
$861$	72.2937	−	17.6421i	2.46376	−	0.601240i
$862$		0			0
$863$	30.8606			1.05051			0.525253	−	0.850946i	$-0.323971\pi$
$863$	30.8606			1.05051			0.525253	+	0.850946i	$0.323971\pi$
$864$		0			0
$865$	1.13316			0.0385287
$866$		0			0
$867$	20.2360	+	21.1653i	0.687249	+	0.718813i
$868$		0			0
$869$	−3.17679	+	2.66565i	−0.107765	+	0.0904258i
$870$		0			0
$871$	11.7692	−	4.28364i	0.398784	−	0.145146i
$872$		0			0
$873$	−3.14036	−	10.0037i	−0.106285	−	0.338575i
$874$		0			0
$875$	19.8386	+	16.6465i	0.670666	+	0.562755i
$876$		0			0
$877$	1.02509	+	5.81358i	0.0346149	+	0.196311i	0.997211	−	0.0746282i	$-0.0237770\pi$
$877$	1.02509	+	5.81358i	0.0346149	+	0.196311i	−0.962597	+	0.270939i	$0.912666\pi$
$878$		0			0
$879$	−12.7833	+	17.4113i	−0.431170	+	0.587268i
$880$		0			0
$881$	20.0656	+	34.7547i	0.676028	+	1.17091i	0.976167	+	0.217019i	$0.0696333\pi$
$881$	20.0656	+	34.7547i	0.676028	+	1.17091i	−0.300140	+	0.953895i	$0.597033\pi$
$882$		0			0
$883$	−5.14988	+	8.91985i	−0.173307	+	0.300177i	−0.939574	−	0.342346i	$-0.888779\pi$
$883$	−5.14988	+	8.91985i	−0.173307	+	0.300177i	0.766267	+	0.642522i	$0.222112\pi$
$884$		0			0
$885$	−14.4476	−	7.13606i	−0.485652	−	0.239876i
$886$		0			0
$887$	−5.26720	−	1.91710i	−0.176855	−	0.0643700i	0.252075	−	0.967708i	$-0.418887\pi$
$887$	−5.26720	−	1.91710i	−0.176855	−	0.0643700i	−0.428930	+	0.903338i	$0.641109\pi$
$888$		0			0
$889$	−10.8197	+	61.3614i	−0.362880	+	2.05799i
$890$		0			0
$891$	3.75450	−	13.8726i	0.125781	−	0.464749i
$892$		0			0
$893$	−1.21746	+	6.90455i	−0.0407407	+	0.231052i
$894$		0			0
$895$	7.27644	+	2.64841i	0.243225	+	0.0885265i
$896$		0			0
$897$	11.7447	+	5.80100i	0.392143	+	0.193690i
$898$		0			0
$899$	24.7789	−	42.9183i	0.826422	−	1.43140i
$900$		0			0
$901$	1.61801	+	2.80248i	0.0539038	+	0.0933641i
$902$		0			0
$903$	−27.3600	+	37.2653i	−0.910484	+	1.24011i
$904$		0			0
$905$	−2.34475	−	13.2978i	−0.0779422	−	0.442032i
$906$		0			0
$907$	−23.0153	−	19.3122i	−0.764211	−	0.641250i	0.175008	−	0.984567i	$-0.444005\pi$
$907$	−23.0153	−	19.3122i	−0.764211	−	0.641250i	−0.939219	+	0.343317i	$0.888449\pi$
$908$		0			0
$909$	−37.6478	−	8.39591i	−1.24870	−	0.278475i
$910$		0			0
$911$	44.5982	−	16.2324i	1.47760	−	0.537804i	0.527451	−	0.849585i	$-0.323148\pi$
$911$	44.5982	−	16.2324i	1.47760	−	0.537804i	0.950154	+	0.311781i	$0.100926\pi$
$912$		0			0
$913$	19.9178	−	16.7130i	0.659184	−	0.553121i
$914$		0			0
$915$	5.42226	+	5.67129i	0.179255	+	0.187487i
$916$		0			0
$917$	−26.2405			−0.866538
$918$		0			0
$919$	48.6623			1.60522			0.802611	−	0.596503i	$-0.203444\pi$
$919$	48.6623			1.60522			0.802611	+	0.596503i	$0.203444\pi$
$920$		0			0
$921$	−33.6940	+	8.22246i	−1.11026	+	0.270939i
$922$		0			0
$923$	43.7618	−	36.7205i	1.44044	−	1.20867i
$924$		0			0
$925$	25.2868	−	9.20363i	0.831424	−	0.302614i
$926$		0			0
$927$	6.29114	−	0.820210i	0.206628	−	0.0269392i
$928$		0			0
$929$	24.2574	+	20.3544i	0.795859	+	0.667805i	0.947188	−	0.320679i	$-0.103911\pi$
$929$	24.2574	+	20.3544i	0.795859	+	0.667805i	−0.151329	+	0.988483i	$0.548355\pi$
$930$		0			0
$931$	−0.973544	−	5.52124i	−0.0319066	−	0.180951i
$932$		0			0
$933$	−26.4803	−	2.91689i	−0.866927	−	0.0954947i
$934$		0			0
$935$	−0.186010	−	0.322179i	−0.00608319	−	0.0105364i
$936$		0			0
$937$	27.2925	−	47.2720i	0.891607	−	1.54431i	0.0536586	−	0.998559i	$-0.482912\pi$
$937$	27.2925	−	47.2720i	0.891607	−	1.54431i	0.837948	−	0.545749i	$-0.183755\pi$
$938$		0			0
$939$	−6.41550	+	4.28088i	−0.209362	+	0.139701i
$940$		0			0
$941$	−20.0304	−	7.29047i	−0.652973	−	0.237663i	−0.00577333	−	0.999983i	$-0.501838\pi$
$941$	−20.0304	−	7.29047i	−0.652973	−	0.237663i	−0.647200	+	0.762321i	$0.724060\pi$
$942$		0			0
$943$	−3.10919	+	17.6331i	−0.101249	+	0.574212i
$944$		0			0
$945$	−2.76025	−	14.0146i	−0.0897909	−	0.455894i
$946$		0			0
$947$	2.85757	−	16.2061i	0.0928585	−	0.526627i	−0.902524	−	0.430640i	$-0.858288\pi$
$947$	2.85757	−	16.2061i	0.0928585	−	0.526627i	0.995383	−	0.0959874i	$-0.0306008\pi$
$948$		0			0
$949$	45.3754	+	16.5153i	1.47295	+	0.536109i
$950$		0			0
$951$	−1.40779	−	21.6873i	−0.0456506	−	0.703257i
$952$		0			0
$953$	6.43216	−	11.1408i	0.208358	−	0.360887i	−0.742839	−	0.669470i	$-0.766521\pi$
$953$	6.43216	−	11.1408i	0.208358	−	0.360887i	0.951197	+	0.308583i	$0.0998547\pi$
$954$		0			0
$955$	−6.56573	−	11.3722i	−0.212462	−	0.367995i
$956$		0			0
$957$	5.99062	+	13.6379i	0.193649	+	0.440852i
$958$		0			0
$959$	−7.69549	−	43.6433i	−0.248500	−	1.40931i
$960$		0			0
$961$	41.1171	+	34.5014i	1.32636	+	1.11295i
$962$		0			0
$963$	22.9937	+	14.6892i	0.740961	+	0.473353i
$964$		0			0
$965$	15.1349	−	5.50866i	0.487210	−	0.177330i
$966$		0			0
$967$	−44.6721	+	37.4843i	−1.43656	+	1.20541i	−0.494850	+	0.868978i	$0.664777\pi$
$967$	−44.6721	+	37.4843i	−1.43656	+	1.20541i	−0.941706	+	0.336436i	$0.890778\pi$
$968$		0			0
$969$	0.137813	−	0.471714i	0.00442721	−	0.0151536i
$970$		0			0
$971$	−54.5295			−1.74994			−0.874968	−	0.484181i	$-0.839118\pi$
$971$	−54.5295			−1.74994			−0.874968	+	0.484181i	$0.839118\pi$
$972$		0			0
$973$	−37.7289			−1.20953
$974$		0			0
$975$	−10.7873	+	36.9232i	−0.345470	+	1.18249i
$976$		0			0
$977$	−30.1945	+	25.3362i	−0.966007	+	0.810576i	−0.981920	−	0.189298i	$-0.939379\pi$
$977$	−30.1945	+	25.3362i	−0.966007	+	0.810576i	0.0159131	+	0.999873i	$0.494934\pi$
$978$		0			0
$979$	−13.8878	+	5.05475i	−0.443857	+	0.161551i
$980$		0			0
$981$	−0.144346	−	0.0922132i	−0.00460860	−	0.00294414i
$982$		0			0
$983$	−24.6204	−	20.6590i	−0.785269	−	0.658919i	0.159300	−	0.987230i	$-0.449076\pi$
$983$	−24.6204	−	20.6590i	−0.785269	−	0.658919i	−0.944570	+	0.328311i	$0.893521\pi$
$984$		0			0
$985$	0.0867401	+	0.491927i	0.00276377	+	0.0156741i
$986$		0			0
$987$	19.0365	+	43.3374i	0.605937	+	1.37944i
$988$		0			0
$989$	−5.56180	−	9.63331i	−0.176855	−	0.306322i
$990$		0			0
$991$	−18.8935	+	32.7245i	−0.600172	+	1.03953i	0.392622	+	0.919700i	$0.371568\pi$
$991$	−18.8935	+	32.7245i	−0.600172	+	1.03953i	−0.992795	+	0.119829i	$0.961765\pi$
$992$		0			0
$993$	0.0181220	+	0.279173i	0.000575084	+	0.00885929i
$994$		0			0
$995$	−11.9277	−	4.34132i	−0.378133	−	0.137629i
$996$		0			0
$997$	6.89259	−	39.0898i	0.218290	−	1.23799i	−0.656814	−	0.754052i	$-0.728096\pi$
$997$	6.89259	−	39.0898i	0.218290	−	1.23799i	0.875105	−	0.483934i	$-0.160792\pi$
$998$		0			0
$999$	−29.9306	−	10.2230i	−0.946962	−	0.323440i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	432.2.u.f.241.2		30
4.3	odd	2		216.2.q.b.25.4	✓	30
12.11	even	2		648.2.q.b.73.3		30
27.13	even	9	inner	432.2.u.f.337.2		30
108.11	even	18		5832.2.a.l.1.8		15
108.43	odd	18		5832.2.a.k.1.8		15
108.67	odd	18		216.2.q.b.121.4	yes	30
108.95	even	18		648.2.q.b.577.3		30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
216.2.q.b.25.4	✓	30	4.3	odd	2
216.2.q.b.121.4	yes	30	108.67	odd	18
432.2.u.f.241.2		30	1.1	even	1	trivial
432.2.u.f.337.2		30	27.13	even	9	inner
648.2.q.b.73.3		30	12.11	even	2
648.2.q.b.577.3		30	108.95	even	18
5832.2.a.k.1.8		15	108.43	odd	18
5832.2.a.l.1.8		15	108.11	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 432 = 2^{4} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	432.u (of order \(9\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.485722 + 1.66255i) q^{3} +(-0.582934 + 0.489140i) q^{5} +(-3.39455 + 1.23552i) q^{7} +(-2.52815 - 1.61507i) q^{9} +O(q^{10})\)	\(q+(-0.485722 + 1.66255i) q^{3} +(-0.582934 + 0.489140i) q^{5} +(-3.39455 + 1.23552i) q^{7} +(-2.52815 - 1.61507i) q^{9} +(-1.22326 - 1.02644i) q^{11} +(-0.872331 - 4.94723i) q^{13} +(-0.530076 - 1.20674i) q^{15} +(-0.153076 - 0.265135i) q^{17} +(0.463380 - 0.802597i) q^{19} +(-0.405300 - 6.24373i) q^{21} +(1.41468 + 0.514902i) q^{23} +(-0.767686 + 4.35377i) q^{25} +(3.91312 - 3.41870i) q^{27} +(-0.935202 + 5.30379i) q^{29} +(-8.64694 - 3.14723i) q^{31} +(2.30067 - 1.53517i) q^{33} +(1.37446 - 2.38064i) q^{35} +(-3.04343 - 5.27138i) q^{37} +(8.64874 + 0.952685i) q^{39} +(2.06526 + 11.7127i) q^{41} +(-5.66013 - 4.74941i) q^{43} +(2.26374 - 0.295137i) q^{45} +(-7.10890 + 2.58743i) q^{47} +(4.63418 - 3.88853i) q^{49} +(0.515153 - 0.125715i) q^{51} -10.5700 q^{53} +1.21515 q^{55} +(1.10928 + 1.16023i) q^{57} +(9.36544 - 7.85854i) q^{59} +(-5.59403 + 2.03606i) q^{61} +(10.5774 + 2.35889i) q^{63} +(2.92840 + 2.45722i) q^{65} +(0.432933 + 2.45528i) q^{67} +(-1.54319 + 2.10188i) q^{69} +(5.68591 + 9.84828i) q^{71} +(-4.80611 + 8.32442i) q^{73} +(-6.86547 - 3.39104i) q^{75} +(5.42059 + 1.97293i) q^{77} +(0.450963 - 2.55754i) q^{79} +(3.78307 + 8.16629i) q^{81} +(-2.82744 + 16.0352i) q^{83} +(0.218922 + 0.0796810i) q^{85} +(-8.36358 - 4.13099i) q^{87} +(4.62758 - 8.01520i) q^{89} +(9.07356 + 15.7159i) q^{91} +(9.43243 - 12.8473i) q^{93} +(0.122462 + 0.694519i) q^{95} +(2.67734 + 2.24656i) q^{97} +(1.43481 + 4.57064i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q - 3 q^{7} - 6 q^{9}+O(q^{10}) \) 30 * q - 3 * q^7 - 6 * q^9	\( 30 q - 3 q^{7} - 6 q^{9} + 3 q^{11} - 12 q^{13} - 15 q^{15} + 6 q^{17} + 9 q^{19} + 30 q^{21} + 12 q^{23} + 24 q^{25} + 15 q^{27} - 9 q^{29} - 27 q^{31} - 30 q^{33} + 18 q^{35} - 15 q^{37} + 21 q^{39} - 15 q^{41} + 30 q^{43} + 15 q^{45} + 18 q^{47} + 15 q^{49} + 6 q^{51} - 18 q^{53} - 54 q^{55} - 72 q^{57} + 12 q^{59} + 6 q^{61} + 54 q^{63} - 54 q^{65} + 45 q^{67} + 9 q^{69} - 36 q^{73} - 69 q^{75} + 12 q^{77} - 45 q^{79} - 30 q^{81} + 3 q^{83} + 57 q^{85} + 60 q^{87} + 36 q^{89} + 39 q^{91} + 30 q^{93} - 51 q^{95} - 84 q^{97} - 162 q^{99}+O(q^{100}) \) 30 * q - 3 * q^7 - 6 * q^9 + 3 * q^11 - 12 * q^13 - 15 * q^15 + 6 * q^17 + 9 * q^19 + 30 * q^21 + 12 * q^23 + 24 * q^25 + 15 * q^27 - 9 * q^29 - 27 * q^31 - 30 * q^33 + 18 * q^35 - 15 * q^37 + 21 * q^39 - 15 * q^41 + 30 * q^43 + 15 * q^45 + 18 * q^47 + 15 * q^49 + 6 * q^51 - 18 * q^53 - 54 * q^55 - 72 * q^57 + 12 * q^59 + 6 * q^61 + 54 * q^63 - 54 * q^65 + 45 * q^67 + 9 * q^69 - 36 * q^73 - 69 * q^75 + 12 * q^77 - 45 * q^79 - 30 * q^81 + 3 * q^83 + 57 * q^85 + 60 * q^87 + 36 * q^89 + 39 * q^91 + 30 * q^93 - 51 * q^95 - 84 * q^97 - 162 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more