LMFDB - Embedded newform 216.2.q.b.25.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [216,2,Mod(25,216)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(216, base_ring=CyclotomicField(18))

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

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

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

chi := DirichletCharacter("216.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 216 = 2^{3} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	216.q (of order $9$, degree $6$, 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:	$1.72476868366$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$5$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			25.4
Character	$\chi$	$=$	216.25
Dual form			216.2.q.b.121.4

$q$-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 $\left(\mathbb{Z}/216\mathbb{Z}\right)^\times$.

$n$	$55$	$109$	$137$
$\chi(n)$	$1$	$1$	$e\left(\frac{5}{9}\right)$

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	0.391590	−	0.920140i	$-0.371925\pi$
$7$	3.39455	−	1.23552i	1.28302	−	0.466981i	0.891430	+	0.453159i	$0.149703\pi$
$8$		0			0
$9$	−2.52815	−	1.61507i	−0.842716	−	0.538358i
$10$		0			0
$11$	1.22326	+	1.02644i	0.368826	+	0.309482i	0.808297	−	0.588775i	$-0.200390\pi$
$11$	1.22326	+	1.02644i	0.368826	+	0.309482i	−0.439471	+	0.898257i	$0.644834\pi$
$12$		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	−0.914271	−	0.405102i	$-0.867236\pi$
$19$	−0.463380	+	0.802597i	−0.106307	+	0.184128i	0.807965	+	0.589231i	$0.200569\pi$
$20$		0			0
$21$	−0.405300	−	6.24373i	−0.0884437	−	1.36249i
$22$		0			0
$23$	−1.41468	−	0.514902i	−0.294981	−	0.107364i	0.190290	−	0.981728i	$-0.439057\pi$
$23$	−1.41468	−	0.514902i	−0.294981	−	0.107364i	−0.485272	+	0.874363i	$0.661279\pi$
$24$		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	0.969127	−	0.246560i	$-0.0793003\pi$
$31$	8.64694	+	3.14723i	1.55304	+	0.565259i	0.583909	+	0.811819i	$0.301523\pi$
$32$		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	0.962647	−	0.270760i	$-0.0872751\pi$
$43$	5.66013	+	4.74941i	0.863162	+	0.724279i	−0.0994852	+	0.995039i	$0.531720\pi$
$44$		0			0
$45$	2.26374	−	0.295137i	0.337459	−	0.0439964i
$46$		0			0
$47$	7.10890	−	2.58743i	1.03694	−	0.377415i	0.233221	−	0.972424i	$-0.425074\pi$
$47$	7.10890	−	2.58743i	1.03694	−	0.377415i	0.803719	+	0.595008i	$0.202851\pi$
$48$		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	$0.570741\pi$
$59$	−9.36544	+	7.85854i	−1.21928	+	1.02309i	−0.998862	+	0.0476877i	$0.984815\pi$
$60$		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	0.946875	−	0.321603i	$-0.104222\pi$
$67$	−0.432933	−	2.45528i	−0.0528911	−	0.299961i	−0.999766	+	0.0216423i	$0.993110\pi$
$68$		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	$-0.930899\pi$
$71$	−5.68591	−	9.84828i	−0.674793	−	1.16878i	0.301736	−	0.953392i	$-0.402434\pi$
$72$		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	−0.999610	−	0.0279124i	$-0.991114\pi$
$79$	−0.450963	+	2.55754i	−0.0507373	+	0.287745i	0.948873	+	0.315658i	$0.102225\pi$
$80$		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	$-0.592599\pi$
$83$	2.82744	−	16.0352i	0.310352	−	1.76009i	0.597176	−	0.802110i	$-0.296289\pi$
$84$		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	−0.559476	−	0.828846i	$-0.688998\pi$
$103$	1.62003	−	1.35936i	0.159626	−	0.133942i	0.719102	+	0.694904i	$0.244553\pi$
$104$		0			0
$105$	3.29032	+	3.44144i	0.321103	+	0.335850i
$106$		0			0
$107$	9.09507			0.879253			0.439627	−	0.898181i	$-0.355111\pi$
$107$	9.09507			0.879253			0.439627	+	0.898181i	$0.355111\pi$
$108$		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	$0.444062\pi$
$127$	−8.62416	+	14.9375i	−0.765271	+	1.32549i	−0.940103	+	0.340889i	$0.889272\pi$
$128$		0			0
$129$	10.6454	−	7.10336i	0.937274	−	0.625416i
$130$		0			0
$131$	−6.82592	−	2.48443i	−0.596384	−	0.217066i	0.0261512	−	0.999658i	$-0.491675\pi$
$131$	−6.82592	−	2.48443i	−0.596384	−	0.217066i	−0.622535	+	0.782592i	$0.713897\pi$
$132$		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	−0.109583	−	0.993978i	$-0.534952\pi$
$139$	−9.81439	−	3.57214i	−0.832445	−	0.302985i	−0.722862	+	0.690992i	$0.757174\pi$
$140$		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	0.850702	−	0.525648i	$-0.176177\pi$
$151$	5.90771	+	4.95716i	0.480763	+	0.403408i	−0.369939	+	0.929056i	$0.620621\pi$
$152$		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	$-0.560694\pi$
$163$	−4.83928			−0.379042			−0.189521	+	0.981877i	$0.560694\pi$
$164$		0			0
$165$	−0.590225	+	2.02025i	−0.0459490	+	0.157276i
$166$		0			0
$167$	4.87580	−	4.09129i	0.377301	−	0.316593i	−0.434341	−	0.900749i	$-0.643019\pi$
$167$	4.87580	−	4.09129i	0.377301	−	0.316593i	0.811642	+	0.584155i	$0.198574\pi$
$168$		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	0.991103	−	0.133096i	$-0.0424920\pi$
$179$	5.08789	+	8.81248i	0.380287	+	0.658676i	−0.610816	+	0.791772i	$0.709159\pi$
$180$		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	$-0.729824\pi$
$191$	2.99652	−	16.9941i	0.216821	−	1.22965i	0.877719	−	0.479176i	$-0.159065\pi$
$192$		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	$-0.965314\pi$
$199$	−8.34016	−	14.4456i	−0.591218	−	1.02402i	0.402851	−	0.915266i	$-0.368019\pi$
$200$		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	−0.761835	−	0.647771i	$-0.775701\pi$
$211$	−3.72146	+	3.12267i	−0.256196	+	0.214974i	0.505639	+	0.862745i	$0.331257\pi$
$212$		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	0.0371816	−	0.999309i	$-0.488162\pi$
$223$	10.5728	−	3.84819i	0.708007	−	0.257694i	0.670826	+	0.741615i	$0.265940\pi$
$224$		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	$0.0218150\pi$
$227$	18.6574	+	15.6554i	1.23833	+	1.03908i	0.240680	+	0.970604i	$0.422629\pi$
$228$		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	0.0688575	−	0.997627i	$-0.478065\pi$
$239$	−8.03370	−	2.92403i	−0.519657	−	0.189140i	−0.588514	+	0.808487i	$0.700287\pi$
$240$		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	$0.488298\pi$
$251$	−13.4200	+	23.2441i	−0.847063	+	1.46716i	−0.883817	+	0.467832i	$0.845035\pi$
$252$		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	−0.335227	−	0.942138i	$-0.608813\pi$
$263$	0.220059	−	0.0800950i	0.0135694	−	0.00493887i	0.348796	+	0.937199i	$0.386591\pi$
$264$		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	$-0.328627\pi$
$271$	16.8819			1.02550			0.512751	+	0.858538i	$0.328627\pi$
$272$		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	0.989786	−	0.142558i	$-0.0455329\pi$
$283$	0.183931	+	1.04313i	0.0109336	+	0.0620074i	−0.978853	+	0.204566i	$0.934422\pi$
$284$		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	$-0.973060\pi$
$307$	−10.0121	−	17.3414i	−0.571418	−	0.989725i	0.425003	−	0.905192i	$-0.360273\pi$
$308$		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	$-0.911920\pi$
$311$	−2.67087	−	15.1472i	−0.151451	−	0.858921i	0.810508	−	0.585727i	$-0.199191\pi$
$312$		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	−0.346188	−	0.938165i	$-0.612524\pi$
$331$	−0.151779	+	0.0552431i	−0.00834253	+	0.00303643i	0.337846	+	0.941202i	$0.390302\pi$
$332$		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	0.368557	−	0.929605i	$-0.379852\pi$
$347$	0.993773	+	0.361704i	0.0533485	+	0.0194173i	−0.315208	+	0.949023i	$0.602074\pi$
$348$		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	$-0.661617\pi$
$359$	9.73277	−	16.8576i	0.513676	−	0.889713i	0.999874	−	0.0158641i	$-0.00504990\pi$
$360$		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	0.702364	−	0.711818i	$-0.252128\pi$
$367$	2.36256	+	1.98243i	0.123325	+	0.103482i	−0.579039	+	0.815300i	$0.696572\pi$
$368$		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	$-0.354639\pi$
$379$	17.1690			0.881913			0.440957	+	0.897528i	$0.354639\pi$
$380$		0			0
$381$	20.6454	+	21.5936i	1.05770	+	1.10627i
$382$		0			0
$383$	−6.79612	+	5.70262i	−0.347265	+	0.291390i	−0.799691	−	0.600412i	$-0.795003\pi$
$383$	−6.79612	+	5.70262i	−0.347265	+	0.291390i	0.452426	+	0.891802i	$0.350559\pi$
$384$		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	$-0.910886\pi$
$419$	−3.12089	−	17.6995i	−0.152466	−	0.864676i	0.808601	−	0.588358i	$-0.200225\pi$
$420$		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	$-0.488288\pi$
$431$	1.52743			0.0735739			0.0367869	+	0.999323i	$0.488288\pi$
$432$		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	−0.399710	−	0.916642i	$-0.630889\pi$
$439$	−2.44512	+	0.889952i	−0.116699	+	0.0424751i	0.283010	+	0.959117i	$0.408667\pi$
$440$		0			0
$441$	−17.9962	+	2.34626i	−0.856960	+	0.111727i
$442$		0			0
$443$	2.66172	+	2.23345i	0.126462	+	0.106114i	0.703825	−	0.710373i	$-0.251474\pi$
$443$	2.66172	+	2.23345i	0.126462	+	0.106114i	−0.577363	+	0.816487i	$0.695918\pi$
$444$		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	−0.321725	−	0.946833i	$-0.604263\pi$
$463$	−25.3216	−	9.21630i	−1.17679	−	0.428318i	−0.855069	+	0.518515i	$0.826485\pi$
$464$		0			0
$465$	0.785637	+	12.1029i	0.0364331	+	0.561259i
$466$		0			0
$467$	1.26382	−	2.18900i	0.0584826	−	0.101295i	−0.835302	−	0.549792i	$-0.814707\pi$
$467$	1.26382	−	2.18900i	0.0584826	−	0.101295i	0.893784	+	0.448497i	$0.148040\pi$
$468$		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	−0.995900	−	0.0904575i	$-0.971167\pi$
$479$	−37.2207	+	13.5472i	−1.70066	+	0.618989i	−0.704759	+	0.709447i	$0.748945\pi$
$480$		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	$-0.338134\pi$
$487$	21.4892			0.973767			0.486883	+	0.873467i	$0.338134\pi$
$488$		0			0
$489$	−2.35055	+	8.04555i	−0.106295	+	0.363833i
$490$		0			0
$491$	17.9959	−	15.1003i	0.812143	−	0.681469i	−0.138975	−	0.990296i	$-0.544381\pi$
$491$	17.9959	−	15.1003i	0.812143	−	0.681469i	0.951118	+	0.308827i	$0.0999363\pi$
$492$		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	0.980018	−	0.198910i	$-0.0637400\pi$
$499$	−0.199454	−	1.13116i	−0.00892880	−	0.0506378i	−0.988947	+	0.148272i	$0.952629\pi$
$500$		0			0
$501$	−4.43368	−	10.0935i	−0.198082	−	0.450944i
$502$		0			0
$503$	1.61381	+	2.79520i	0.0719562	+	0.124632i	0.899759	−	0.436388i	$-0.143742\pi$
$503$	1.61381	+	2.79520i	0.0719562	+	0.124632i	−0.827802	+	0.561020i	$0.810409\pi$
$504$		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	0.994774	−	0.102101i	$-0.0325565\pi$
$523$	9.35270	+	16.1993i	0.408965	+	0.708348i	−0.585809	+	0.810449i	$0.699223\pi$
$524$		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	−0.762752	−	0.646691i	$-0.776152\pi$
$547$	−21.7829	+	7.92832i	−0.931368	+	0.338990i	−0.168616	+	0.985682i	$0.553930\pi$
$548$		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	0.703488	−	0.710707i	$-0.251625\pi$
$563$	18.6394	+	6.78419i	0.785558	+	0.285920i	0.0820694	+	0.996627i	$0.473847\pi$
$564$		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	0.403480	−	0.914988i	$-0.367801\pi$
$571$	2.97310	+	1.08212i	0.124420	+	0.0452853i	−0.279060	+	0.960274i	$0.590023\pi$
$572$		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	0.0352346	−	0.999379i	$-0.488782\pi$
$587$	17.0715	−	6.21350i	0.704614	−	0.256459i	0.669380	+	0.742920i	$0.266560\pi$
$588$		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	−0.602698	−	0.797969i	$-0.705908\pi$
$599$	1.92101	−	1.61192i	0.0784905	−	0.0658614i	0.681189	+	0.732108i	$0.261463\pi$
$600$		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	$-0.990040\pi$
$607$	−1.74872	−	9.91750i	−0.0709784	−	0.402539i	0.928532	−	0.371252i	$-0.121072\pi$
$608$		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	$0.303369\pi$
$619$	−6.06773	+	34.4118i	−0.243883	+	1.38313i	−0.823073	+	0.567936i	$0.807742\pi$
$620$		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	0.978503	−	0.206234i	$-0.0661207\pi$
$631$	7.80338	+	13.5159i	0.310648	+	0.538058i	−0.667855	+	0.744291i	$0.732787\pi$
$632$		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	$-0.431600\pi$
$643$	30.7439	−	25.7972i	1.21242	−	1.01734i	0.999186	−	0.0403397i	$-0.0128440\pi$
$644$		0			0
$645$	−2.73102	+	9.34788i	−0.107534	+	0.368072i
$646$		0			0
$647$	−10.7038			−0.420809			−0.210405	−	0.977614i	$-0.567478\pi$
$647$	−10.7038			−0.420809			−0.210405	+	0.977614i	$0.567478\pi$
$648$		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	0.572070	−	0.820205i	$-0.306141\pi$
$659$	−3.49986	−	2.93673i	−0.136335	−	0.114399i	−0.708405	+	0.705806i	$0.750585\pi$
$660$		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	−0.729589	−	0.683886i	$-0.760289\pi$
$683$	5.94471	−	10.2965i	0.227468	−	0.393986i	0.957057	+	0.289900i	$0.0936220\pi$
$684$		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	0.887830	−	0.460171i	$-0.152212\pi$
$691$	15.4783	+	12.9878i	0.588821	+	0.494079i	−0.299010	+	0.954250i	$0.596656\pi$
$692$		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	0.708039	−	0.706173i	$-0.249580\pi$
$719$	−6.90583	−	11.9612i	−0.257544	−	0.446079i	−0.965583	+	0.260094i	$0.916247\pi$
$720$		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	−0.976973	−	0.213364i	$-0.931558\pi$
$727$	0.378999	−	2.14941i	0.0140563	−	0.0797172i	0.991029	+	0.133647i	$0.0426689\pi$
$728$		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	$0.0639120\pi$
$739$	18.0145	+	31.2020i	0.662674	+	1.14779i	−0.317236	+	0.948347i	$0.602755\pi$
$740$		0			0
$741$	4.77227	−	6.50000i	0.175314	−	0.238783i
$742$		0			0
$743$	1.19334	+	6.76776i	0.0437793	+	0.248285i	0.998842	−	0.0481205i	$-0.0153231\pi$
$743$	1.19334	+	6.76776i	0.0437793	+	0.248285i	−0.955062	+	0.296405i	$0.904212\pi$
$744$		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	−0.565767	−	0.824565i	$-0.691420\pi$
$751$	4.05658	−	3.40388i	0.148027	−	0.124209i	0.713794	+	0.700356i	$0.246975\pi$
$752$		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	0.227046	−	0.973884i	$-0.427093\pi$
$787$	−6.31279	−	2.29767i	−0.225027	−	0.0819030i	−0.452073	+	0.891981i	$0.649315\pi$
$788$		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	$-0.574300\pi$
$811$	−13.1743			−0.462614			−0.231307	+	0.972881i	$0.574300\pi$
$812$		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	0.978432	−	0.206570i	$-0.0662302\pi$
$823$	−0.334058	−	1.89453i	−0.0116445	−	0.0660393i	−0.990076	+	0.140531i	$0.955119\pi$
$824$		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	$-0.934062\pi$
$827$	−19.1936	−	33.2443i	−0.667428	−	1.15602i	0.311193	−	0.950347i	$-0.399271\pi$
$828$		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	$0.182265\pi$
$839$	−3.89949	+	22.1151i	−0.134625	+	0.763499i	−0.975120	+	0.221678i	$0.928846\pi$
$840$		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	−0.0532147	−	0.998583i	$-0.516947\pi$
$859$	26.9921	−	22.6490i	0.920957	−	0.772775i	0.974172	+	0.225808i	$0.0725023\pi$
$860$		0			0
$861$	72.2937	−	17.6421i	2.46376	−	0.601240i
$862$		0			0
$863$	−30.8606			−1.05051			−0.525253	−	0.850946i	$-0.676029\pi$
$863$	−30.8606			−1.05051			−0.525253	+	0.850946i	$0.676029\pi$
$864$		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	−0.766267	−	0.642522i	$-0.777888\pi$
$883$	5.14988	−	8.91985i	0.173307	−	0.300177i	0.939574	+	0.342346i	$0.111221\pi$
$884$		0			0
$885$	−14.4476	−	7.13606i	−0.485652	−	0.239876i
$886$		0			0
$887$	5.26720	+	1.91710i	0.176855	+	0.0643700i	0.428930	−	0.903338i	$-0.358891\pi$
$887$	5.26720	+	1.91710i	0.176855	+	0.0643700i	−0.252075	+	0.967708i	$0.581113\pi$
$888$		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	0.939219	−	0.343317i	$-0.111551\pi$
$907$	23.0153	+	19.3122i	0.764211	+	0.641250i	−0.175008	+	0.984567i	$0.555995\pi$
$908$		0			0
$909$	−37.6478	−	8.39591i	−1.24870	−	0.278475i
$910$		0			0
$911$	−44.5982	+	16.2324i	−1.47760	+	0.537804i	−0.950154	−	0.311781i	$-0.899074\pi$
$911$	−44.5982	+	16.2324i	−1.47760	+	0.537804i	−0.527451	+	0.849585i	$0.676852\pi$
$912$		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	$-0.796556\pi$
$919$	−48.6623			−1.60522			−0.802611	+	0.596503i	$0.796556\pi$
$920$		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	$0.141712\pi$
$947$	−2.85757	+	16.2061i	−0.0928585	+	0.526627i	−0.995383	+	0.0959874i	$0.969399\pi$
$948$		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	$-0.335223\pi$
$967$	44.6721	−	37.4843i	1.43656	−	1.20541i	0.941706	−	0.336436i	$-0.109222\pi$
$968$		0			0
$969$	0.137813	−	0.471714i	0.00442721	−	0.0151536i
$970$		0			0
$971$	54.5295			1.74994			0.874968	−	0.484181i	$-0.160882\pi$
$971$	54.5295			1.74994			0.874968	+	0.484181i	$0.160882\pi$
$972$		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	0.944570	−	0.328311i	$-0.106479\pi$
$983$	24.6204	+	20.6590i	0.785269	+	0.658919i	−0.159300	+	0.987230i	$0.550924\pi$
$984$		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	$-0.628432\pi$
$991$	18.8935	−	32.7245i	0.600172	−	1.03953i	0.992795	−	0.119829i	$-0.0382347\pi$
$992$		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	216.2.q.b.25.4	✓	30
3.2	odd	2		648.2.q.b.73.3		30
4.3	odd	2		432.2.u.f.241.2		30
27.11	odd	18		5832.2.a.l.1.8		15
27.13	even	9	inner	216.2.q.b.121.4	yes	30
27.14	odd	18		648.2.q.b.577.3		30
27.16	even	9		5832.2.a.k.1.8		15
108.67	odd	18		432.2.u.f.337.2		30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
216.2.q.b.25.4	✓	30	1.1	even	1	trivial
216.2.q.b.121.4	yes	30	27.13	even	9	inner
432.2.u.f.241.2		30	4.3	odd	2
432.2.u.f.337.2		30	108.67	odd	18
648.2.q.b.73.3		30	3.2	odd	2
648.2.q.b.577.3		30	27.14	odd	18
5832.2.a.k.1.8		15	27.16	even	9
5832.2.a.l.1.8		15	27.11	odd	18

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 216 = 2^{3} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	216.q (of order \(9\), degree \(6\), 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

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Representations

Groups

Database

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