LMFDB - Embedded newform 513.2.h.c.235.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [513,2,Mod(235,513)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(513, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 2]))

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

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

chi := DirichletCharacter("513.235");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 513 = 3^{3} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	513.h (of order $3$, degree $2$, 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:	$4.09632562369$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{3})$
Twist minimal:	no (minimal twist has level 171)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			235.9
Character	$\chi$	$=$	513.235
Dual form			513.2.h.c.334.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.146534 q^{2} -1.97853 q^{4} +(1.28502 - 2.22572i) q^{5} +(-1.73898 + 3.01201i) q^{7} +0.582990 q^{8} +O(q^{10})$	\(q-0.146534 q^{2} -1.97853 q^{4} +(1.28502 - 2.22572i) q^{5} +(-1.73898 + 3.01201i) q^{7} +0.582990 q^{8} +(-0.188299 + 0.326143i) q^{10} +(-2.07935 + 3.60154i) q^{11} +4.59850 q^{13} +(0.254820 - 0.441362i) q^{14} +3.87163 q^{16} +(1.50797 + 2.61188i) q^{17} +(3.65690 - 2.37215i) q^{19} +(-2.54244 + 4.40364i) q^{20} +(0.304695 - 0.527748i) q^{22} +4.91882 q^{23} +(-0.802545 - 1.39005i) q^{25} -0.673837 q^{26} +(3.44063 - 5.95934i) q^{28} +(-1.85701 - 3.21644i) q^{29} +(3.31980 + 5.75007i) q^{31} -1.73330 q^{32} +(-0.220969 - 0.382729i) q^{34} +(4.46925 + 7.74097i) q^{35} -5.28491 q^{37} +(-0.535860 + 0.347600i) q^{38} +(0.749153 - 1.29757i) q^{40} +(1.26597 - 2.19272i) q^{41} +4.78072 q^{43} +(4.11405 - 7.12574i) q^{44} -0.720775 q^{46} +(4.85627 + 8.41131i) q^{47} +(-2.54812 - 4.41348i) q^{49} +(0.117600 + 0.203689i) q^{50} -9.09827 q^{52} +(-5.35547 + 9.27595i) q^{53} +(5.34400 + 9.25609i) q^{55} +(-1.01381 + 1.75597i) q^{56} +(0.272116 + 0.471318i) q^{58} +(-4.48107 + 7.76144i) q^{59} +(-0.472085 - 0.817675i) q^{61} +(-0.486464 - 0.842580i) q^{62} -7.48927 q^{64} +(5.90916 - 10.2350i) q^{65} +1.37716 q^{67} +(-2.98356 - 5.16768i) q^{68} +(-0.654897 - 1.13432i) q^{70} +(-4.45338 - 7.71347i) q^{71} +(-2.14771 - 3.71994i) q^{73} +0.774420 q^{74} +(-7.23528 + 4.69336i) q^{76} +(-7.23190 - 12.5260i) q^{77} +3.38521 q^{79} +(4.97511 - 8.61715i) q^{80} +(-0.185507 + 0.321308i) q^{82} +(-4.52640 + 7.83996i) q^{83} +7.75108 q^{85} -0.700538 q^{86} +(-1.21224 + 2.09966i) q^{88} +(3.96515 - 6.86783i) q^{89} +(-7.99672 + 13.8507i) q^{91} -9.73202 q^{92} +(-0.711609 - 1.23254i) q^{94} +(-0.580542 - 11.1875i) q^{95} +1.86067 q^{97} +(0.373387 + 0.646725i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 2 q^{2} + 34 q^{4} - 3 q^{5} + q^{7} + 36 q^{8}+O(q^{10}) $ 32 * q + 2 * q^2 + 34 * q^4 - 3 * q^5 + q^7 + 36 * q^8	$ 32 q + 2 q^{2} + 34 q^{4} - 3 q^{5} + q^{7} + 36 q^{8} - 8 q^{10} - 7 q^{11} + 8 q^{13} - q^{14} + 22 q^{16} + 7 q^{17} + 7 q^{19} + 3 q^{20} - 8 q^{22} + 10 q^{23} - 9 q^{25} + 4 q^{26} - 10 q^{28} - 10 q^{29} - 10 q^{31} + 34 q^{32} - 13 q^{34} + 3 q^{35} + 2 q^{37} + 46 q^{38} + 12 q^{40} - 6 q^{41} - 14 q^{43} - 20 q^{44} + 9 q^{47} - 13 q^{49} - q^{50} - 38 q^{52} - 16 q^{53} + 15 q^{55} + 6 q^{56} - 37 q^{59} - 12 q^{61} - 54 q^{62} - 64 q^{64} - 54 q^{65} + 22 q^{67} + 2 q^{68} + 24 q^{70} - 9 q^{71} - 10 q^{73} + 12 q^{74} - 40 q^{76} - 46 q^{77} + 16 q^{79} + 24 q^{80} + 7 q^{82} - 3 q^{83} + 54 q^{85} + 34 q^{86} + 9 q^{88} - 30 q^{89} - q^{91} - 34 q^{92} - 18 q^{94} - 3 q^{95} - 18 q^{98}+O(q^{100}) $ 32 * q + 2 * q^2 + 34 * q^4 - 3 * q^5 + q^7 + 36 * q^8 - 8 * q^10 - 7 * q^11 + 8 * q^13 - q^14 + 22 * q^16 + 7 * q^17 + 7 * q^19 + 3 * q^20 - 8 * q^22 + 10 * q^23 - 9 * q^25 + 4 * q^26 - 10 * q^28 - 10 * q^29 - 10 * q^31 + 34 * q^32 - 13 * q^34 + 3 * q^35 + 2 * q^37 + 46 * q^38 + 12 * q^40 - 6 * q^41 - 14 * q^43 - 20 * q^44 + 9 * q^47 - 13 * q^49 - q^50 - 38 * q^52 - 16 * q^53 + 15 * q^55 + 6 * q^56 - 37 * q^59 - 12 * q^61 - 54 * q^62 - 64 * q^64 - 54 * q^65 + 22 * q^67 + 2 * q^68 + 24 * q^70 - 9 * q^71 - 10 * q^73 + 12 * q^74 - 40 * q^76 - 46 * q^77 + 16 * q^79 + 24 * q^80 + 7 * q^82 - 3 * q^83 + 54 * q^85 + 34 * q^86 + 9 * q^88 - 30 * q^89 - q^91 - 34 * q^92 - 18 * q^94 - 3 * q^95 - 18 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/513\mathbb{Z}\right)^\times$.

$n$	$191$	$325$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−0.146534			−0.103615			−0.0518076	−	0.998657i	$-0.516498\pi$
$2$	−0.146534			−0.103615			−0.0518076	+	0.998657i	$0.516498\pi$
$3$		0			0
$3$		0			0
$4$	−1.97853			−0.989264
$5$	1.28502	−	2.22572i	0.574678	−	0.995371i	−0.421399	−	0.906875i	$-0.638461\pi$
$5$	1.28502	−	2.22572i	0.574678	−	0.995371i	0.996077	−	0.0884956i	$-0.0282059\pi$
$6$		0			0
$7$	−1.73898	+	3.01201i	−0.657274	+	1.13843i	0.324045	+	0.946042i	$0.394957\pi$
$7$	−1.73898	+	3.01201i	−0.657274	+	1.13843i	−0.981319	+	0.192390i	$0.938376\pi$
$8$	0.582990			0.206118
$9$		0			0
$10$	−0.188299	+	0.326143i	−0.0595454	+	0.103136i
$11$	−2.07935	+	3.60154i	−0.626947	+	1.08590i	0.361214	+	0.932483i	$0.382363\pi$
$11$	−2.07935	+	3.60154i	−0.626947	+	1.08590i	−0.988161	+	0.153421i	$0.950971\pi$
$12$		0			0
$13$	4.59850			1.27540			0.637698	−	0.770287i	$-0.279887\pi$
$13$	4.59850			1.27540			0.637698	+	0.770287i	$0.279887\pi$
$14$	0.254820	−	0.441362i	0.0681036	−	0.117959i
$15$		0			0
$16$	3.87163			0.967907
$17$	1.50797	+	2.61188i	0.365736	+	0.633474i	0.988894	−	0.148622i	$-0.0474838\pi$
$17$	1.50797	+	2.61188i	0.365736	+	0.633474i	−0.623158	+	0.782096i	$0.714150\pi$
$18$		0			0
$19$	3.65690	−	2.37215i	0.838951	−	0.544208i
$19$	3.65690	−	2.37215i	0.838951	−	0.544208i
$20$	−2.54244	+	4.40364i	−0.568508	+	0.984685i
$21$		0			0
$22$	0.304695	−	0.527748i	0.0649613	−	0.112516i
$23$	4.91882			1.02564			0.512822	−	0.858495i	$-0.328600\pi$
$23$	4.91882			1.02564			0.512822	+	0.858495i	$0.328600\pi$
$24$		0			0
$25$	−0.802545	−	1.39005i	−0.160509	−	0.278010i
$26$	−0.673837			−0.132150
$27$		0			0
$28$	3.44063	−	5.95934i	0.650217	−	1.12621i
$29$	−1.85701	−	3.21644i	−0.344839	−	0.597278i	0.640486	−	0.767970i	$-0.278733\pi$
$29$	−1.85701	−	3.21644i	−0.344839	−	0.597278i	−0.985324	+	0.170692i	$0.945400\pi$
$30$		0			0
$31$	3.31980	+	5.75007i	0.596254	+	1.03274i	0.993369	+	0.114973i	$0.0366782\pi$
$31$	3.31980	+	5.75007i	0.596254	+	1.03274i	−0.397115	+	0.917769i	$0.629988\pi$
$32$	−1.73330			−0.306408
$33$		0			0
$34$	−0.220969	−	0.382729i	−0.0378959	−	0.0656376i
$35$	4.46925	+	7.74097i	0.755441	+	1.30846i
$36$		0			0
$37$	−5.28491			−0.868834			−0.434417	−	0.900712i	$-0.643046\pi$
$37$	−5.28491			−0.868834			−0.434417	+	0.900712i	$0.643046\pi$
$38$	−0.535860	+	0.347600i	−0.0869280	+	0.0563882i
$39$		0			0
$40$	0.749153	−	1.29757i	0.118451	−	0.205164i
$41$	1.26597	−	2.19272i	0.197711	−	0.342445i	−0.750075	−	0.661353i	$-0.769983\pi$
$41$	1.26597	−	2.19272i	0.197711	−	0.342445i	0.947786	+	0.318908i	$0.103316\pi$
$42$		0			0
$43$	4.78072			0.729052			0.364526	−	0.931193i	$-0.381231\pi$
$43$	4.78072			0.729052			0.364526	+	0.931193i	$0.381231\pi$
$44$	4.11405	−	7.12574i	0.620216	−	1.07425i
$45$		0			0
$46$	−0.720775			−0.106272
$47$	4.85627	+	8.41131i	0.708360	+	1.22692i	0.965465	+	0.260532i	$0.0838981\pi$
$47$	4.85627	+	8.41131i	0.708360	+	1.22692i	−0.257105	+	0.966384i	$0.582769\pi$
$48$		0			0
$49$	−2.54812	−	4.41348i	−0.364017	−	0.630497i
$50$	0.117600	+	0.203689i	0.0166312	+	0.0288060i
$51$		0			0
$52$	−9.09827			−1.26170
$53$	−5.35547	+	9.27595i	−0.735631	+	1.27415i	0.218815	+	0.975766i	$0.429781\pi$
$53$	−5.35547	+	9.27595i	−0.735631	+	1.27415i	−0.954446	+	0.298384i	$0.903553\pi$
$54$		0			0
$55$	5.34400	+	9.25609i	0.720585	+	1.24809i
$56$	−1.01381	+	1.75597i	−0.135476	+	0.234651i
$57$		0			0
$58$	0.272116	+	0.471318i	0.0357305	+	0.0618871i
$59$	−4.48107	+	7.76144i	−0.583385	+	1.01045i	0.411689	+	0.911324i	$0.364939\pi$
$59$	−4.48107	+	7.76144i	−0.583385	+	1.01045i	−0.995075	+	0.0991287i	$0.968394\pi$
$60$		0			0
$61$	−0.472085	−	0.817675i	−0.0604443	−	0.104693i	0.834220	−	0.551432i	$-0.185918\pi$
$61$	−0.472085	−	0.817675i	−0.0604443	−	0.104693i	−0.894664	+	0.446740i	$0.852585\pi$
$62$	−0.486464	−	0.842580i	−0.0617810	−	0.107008i
$63$		0			0
$64$	−7.48927			−0.936158
$65$	5.90916	−	10.2350i	0.732941	−	1.26949i
$66$		0			0
$67$	1.37716			0.168247			0.0841236	−	0.996455i	$-0.473191\pi$
$67$	1.37716			0.168247			0.0841236	+	0.996455i	$0.473191\pi$
$68$	−2.98356	−	5.16768i	−0.361810	−	0.626673i
$69$		0			0
$70$	−0.654897	−	1.13432i	−0.0782752	−	0.135577i
$71$	−4.45338	−	7.71347i	−0.528519	−	0.915421i	−0.999447	−	0.0332496i	$-0.989414\pi$
$71$	−4.45338	−	7.71347i	−0.528519	−	0.915421i	0.470929	−	0.882171i	$-0.343919\pi$
$72$		0			0
$73$	−2.14771	−	3.71994i	−0.251370	−	0.435386i	0.712533	−	0.701638i	$-0.247548\pi$
$73$	−2.14771	−	3.71994i	−0.251370	−	0.435386i	−0.963903	+	0.266253i	$0.914214\pi$
$74$	0.774420			0.0900244
$75$		0			0
$76$	−7.23528	+	4.69336i	−0.829943	+	0.538365i
$77$	−7.23190	−	12.5260i	−0.824152	−	1.42747i
$78$		0			0
$79$	3.38521			0.380866			0.190433	−	0.981700i	$-0.439011\pi$
$79$	3.38521			0.380866			0.190433	+	0.981700i	$0.439011\pi$
$80$	4.97511	−	8.61715i	0.556235	−	0.963427i
$81$		0			0
$82$	−0.185507	+	0.321308i	−0.0204858	+	0.0354825i
$83$	−4.52640	+	7.83996i	−0.496837	+	0.860547i	−0.999993	−	0.00364819i	$-0.998839\pi$
$83$	−4.52640	+	7.83996i	−0.496837	+	0.860547i	0.503156	+	0.864196i	$0.332172\pi$
$84$		0			0
$85$	7.75108			0.840722
$86$	−0.700538			−0.0755409
$87$		0			0
$88$	−1.21224	+	2.09966i	−0.129225	+	0.223824i
$89$	3.96515	−	6.86783i	0.420305	−	0.727989i	−0.575665	−	0.817686i	$-0.695257\pi$
$89$	3.96515	−	6.86783i	0.420305	−	0.727989i	0.995969	+	0.0896971i	$0.0285899\pi$
$90$		0			0
$91$	−7.99672	+	13.8507i	−0.838284	+	1.45195i
$92$	−9.73202			−1.01463
$93$		0			0
$94$	−0.711609	−	1.23254i	−0.0733969	−	0.127127i
$95$	−0.580542	−	11.1875i	−0.0595624	−	1.14781i
$96$		0			0
$97$	1.86067			0.188923			0.0944613	−	0.995529i	$-0.469887\pi$
$97$	1.86067			0.188923			0.0944613	+	0.995529i	$0.469887\pi$
$98$	0.373387	+	0.646725i	0.0377177	+	0.0653291i
$99$		0			0
$100$	1.58786	+	2.75025i	0.158786	+	0.275025i
$101$	−4.94152	−	8.55897i	−0.491700	−	0.851649i	0.508255	−	0.861207i	$-0.330291\pi$
$101$	−4.94152	−	8.55897i	−0.491700	−	0.851649i	−0.999954	+	0.00955791i	$0.996958\pi$
$102$		0			0
$103$	−9.35247	−	16.1990i	−0.921527	−	1.59613i	−0.797054	−	0.603908i	$-0.793609\pi$
$103$	−9.35247	−	16.1990i	−0.921527	−	1.59613i	−0.124473	−	0.992223i	$-0.539724\pi$
$104$	2.68088			0.262882
$105$		0			0
$106$	0.784759	−	1.35924i	0.0762225	−	0.132021i
$107$	15.3037			1.47947			0.739733	−	0.672901i	$-0.234952\pi$
$107$	15.3037			1.47947			0.739733	+	0.672901i	$0.234952\pi$
$108$		0			0
$109$	1.64679	+	2.85232i	0.157734	+	0.273203i	0.934051	−	0.357139i	$-0.116248\pi$
$109$	1.64679	+	2.85232i	0.157734	+	0.273203i	−0.776317	+	0.630342i	$0.782915\pi$
$110$	−0.783079	−	1.35633i	−0.0746636	−	0.129321i
$111$		0			0
$112$	−6.73269	+	11.6614i	−0.636180	+	1.10190i
$113$	1.80784	+	3.13127i	0.170067	+	0.294565i	0.938443	−	0.345434i	$-0.112268\pi$
$113$	1.80784	+	3.13127i	0.170067	+	0.294565i	−0.768376	+	0.639999i	$0.778935\pi$
$114$		0			0
$115$	6.32077	−	10.9479i	0.589415	−	1.02090i
$116$	3.67415	+	6.36382i	0.341137	+	0.590866i
$117$		0			0
$118$	0.656629	−	1.13731i	0.0604476	−	0.104698i
$119$	−10.4893			−0.961556
$120$		0			0
$121$	−3.14738	−	5.45143i	−0.286126	−	0.495584i
$122$	0.0691765	+	0.119817i	0.00626295	+	0.0108477i
$123$		0			0
$124$	−6.56832	−	11.3767i	−0.589853	−	1.02165i
$125$	8.72504			0.780392
$126$		0			0
$127$	9.12699	−	15.8084i	0.809890	−	1.40277i	−0.103050	−	0.994676i	$-0.532860\pi$
$127$	9.12699	−	15.8084i	0.809890	−	1.40277i	0.912940	−	0.408094i	$-0.133806\pi$
$128$	4.56404			0.403408
$129$		0			0
$130$	−0.865893	+	1.49977i	−0.0759439	+	0.131539i
$131$	−10.7499	+	18.6193i	−0.939222	+	1.62678i	−0.172294	+	0.985046i	$0.555118\pi$
$131$	−10.7499	+	18.6193i	−0.939222	+	1.62678i	−0.766927	+	0.641734i	$0.778215\pi$
$132$		0			0
$133$	0.785633	+	15.1397i	0.0681230	+	1.31278i
$134$	−0.201801			−0.0174330
$135$		0			0
$136$	0.879131	+	1.52270i	0.0753849	+	0.130570i
$137$	−4.42082	−	7.65709i	−0.377696	−	0.654189i	0.613030	−	0.790059i	$-0.289950\pi$
$137$	−4.42082	−	7.65709i	−0.377696	−	0.654189i	−0.990727	+	0.135870i	$0.956617\pi$
$138$		0			0
$139$	−13.2894			−1.12720			−0.563598	−	0.826050i	$-0.690583\pi$
$139$	−13.2894			−1.12720			−0.563598	+	0.826050i	$0.690583\pi$
$140$	−8.84254	−	15.3157i	−0.747331	−	1.29441i
$141$		0			0
$142$	0.652571	+	1.13029i	0.0547626	+	0.0948515i
$143$	−9.56189	+	16.5617i	−0.799606	+	1.38496i
$144$		0			0
$145$	−9.54519			−0.792685
$146$	0.314712	+	0.545098i	0.0260458	+	0.0451126i
$147$		0			0
$148$	10.4563			0.859506
$149$	6.90739	−	11.9639i	0.565875	−	0.980125i	−0.431092	−	0.902308i	$-0.641872\pi$
$149$	6.90739	−	11.9639i	0.565875	−	0.980125i	0.996968	−	0.0778169i	$-0.0247950\pi$
$150$		0			0
$151$	−1.82757	+	3.16545i	−0.148726	+	0.257600i	−0.930757	−	0.365639i	$-0.880850\pi$
$151$	−1.82757	+	3.16545i	−0.148726	+	0.257600i	0.782031	+	0.623239i	$0.214184\pi$
$152$	2.13194	−	1.38294i	0.172923	−	0.112171i
$153$		0			0
$154$	1.05972	+	1.83549i	0.0853947	+	0.147908i
$155$	17.0640			1.37062
$156$		0			0
$157$	−2.27274	+	3.93650i	−0.181384	+	0.314167i	−0.942352	−	0.334623i	$-0.891391\pi$
$157$	−2.27274	+	3.93650i	−0.181384	+	0.314167i	0.760968	+	0.648789i	$0.224724\pi$
$158$	−0.496049			−0.0394635
$159$		0			0
$160$	−2.22733	+	3.85785i	−0.176086	+	0.304990i
$161$	−8.55374	+	14.8155i	−0.674129	+	1.16763i
$162$		0			0
$163$	−2.30348			−0.180422			−0.0902111	−	0.995923i	$-0.528754\pi$
$163$	−2.30348			−0.180422			−0.0902111	+	0.995923i	$0.528754\pi$
$164$	−2.50475	+	4.33835i	−0.195588	+	0.338769i
$165$		0			0
$166$	0.663272	−	1.14882i	0.0514799	−	0.0891658i
$167$	8.94204			0.691956			0.345978	−	0.938243i	$-0.387547\pi$
$167$	8.94204			0.691956			0.345978	+	0.938243i	$0.387547\pi$
$168$		0			0
$169$	8.14623			0.626633
$170$	−1.13580			−0.0871116
$171$		0			0
$172$	−9.45878			−0.721225
$173$	1.29491			0.0984498			0.0492249	−	0.998788i	$-0.484325\pi$
$173$	1.29491			0.0984498			0.0492249	+	0.998788i	$0.484325\pi$
$174$		0			0
$175$	5.58245			0.421993
$176$	−8.05046	+	13.9438i	−0.606827	+	1.05105i
$177$		0			0
$178$	−0.581029	+	1.00637i	−0.0435499	+	0.0754307i
$179$	−7.43054			−0.555385			−0.277692	−	0.960670i	$-0.589570\pi$
$179$	−7.43054			−0.555385			−0.277692	+	0.960670i	$0.589570\pi$
$180$		0			0
$181$	−0.306836	+	0.531455i	−0.0228069	+	0.0395027i	−0.877204	−	0.480119i	$-0.840594\pi$
$181$	−0.306836	+	0.531455i	−0.0228069	+	0.0395027i	0.854397	+	0.519621i	$0.173927\pi$
$182$	1.17179	−	2.02960i	0.0868590	−	0.150444i
$183$		0			0
$184$	2.86762			0.211404
$185$	−6.79121	+	11.7627i	−0.499300	+	0.864812i
$186$		0			0
$187$	−12.5424			−0.917190
$188$	−9.60827	−	16.6420i	−0.700755	−	1.21374i
$189$		0			0
$190$	0.0850692	+	1.63935i	0.00617157	+	0.118931i
$191$	2.82733	−	4.89708i	0.204578	−	0.354340i	−0.745420	−	0.666595i	$-0.767751\pi$
$191$	2.82733	−	4.89708i	0.204578	−	0.354340i	0.949998	+	0.312255i	$0.101084\pi$
$192$		0			0
$193$	−0.882469	+	1.52848i	−0.0635215	+	0.110022i	−0.896037	−	0.443979i	$-0.853566\pi$
$193$	−0.882469	+	1.52848i	−0.0635215	+	0.110022i	0.832516	+	0.554001i	$0.186900\pi$
$194$	−0.272652			−0.0195753
$195$		0			0
$196$	5.04153	+	8.73219i	0.360109	+	0.623728i
$197$	1.37197			0.0977491			0.0488745	−	0.998805i	$-0.484437\pi$
$197$	1.37197			0.0977491			0.0488745	+	0.998805i	$0.484437\pi$
$198$		0			0
$199$	12.3083	−	21.3186i	0.872513	−	1.51124i	0.0131236	−	0.999914i	$-0.495823\pi$
$199$	12.3083	−	21.3186i	0.872513	−	1.51124i	0.859389	−	0.511322i	$-0.170844\pi$
$200$	−0.467876	−	0.810384i	−0.0330838	−	0.0573028i
$201$		0			0
$202$	0.724101	+	1.25418i	0.0509476	+	0.0882438i
$203$	12.9173			0.906614
$204$		0			0
$205$	−3.25358	−	5.63537i	−0.227240	−	0.393591i
$206$	1.37046	+	2.37370i	0.0954842	+	0.165383i
$207$		0			0
$208$	17.8037			1.23446
$209$	0.939403	+	18.1030i	0.0649798	+	1.25221i
$210$		0			0
$211$	3.58264	−	6.20531i	0.246639	−	0.427191i	−0.715952	−	0.698149i	$-0.754007\pi$
$211$	3.58264	−	6.20531i	0.246639	−	0.427191i	0.962591	+	0.270958i	$0.0873405\pi$
$212$	10.5960	−	18.3527i	0.727733	−	1.26047i
$213$		0			0
$214$	−2.24252			−0.153295
$215$	6.14331	−	10.6405i	0.418970	−	0.725678i
$216$		0			0
$217$	−23.0923			−1.56761
$218$	−0.241311	−	0.417962i	−0.0163436	−	0.0283080i
$219$		0			0
$220$	−10.5733	−	18.3134i	−0.712849	−	1.23469i
$221$	6.93440	+	12.0107i	0.466459	+	0.807930i
$222$		0			0
$223$	1.21546			0.0813931			0.0406965	−	0.999172i	$-0.487042\pi$
$223$	1.21546			0.0813931			0.0406965	+	0.999172i	$0.487042\pi$
$224$	3.01419	−	5.22073i	0.201394	−	0.348824i
$225$		0			0
$226$	−0.264910	−	0.458837i	−0.0176215	−	0.0305214i
$227$	4.45999	−	7.72493i	0.296020	−	0.512722i	−0.679202	−	0.733952i	$-0.737674\pi$
$227$	4.45999	−	7.72493i	0.296020	−	0.512722i	0.975222	+	0.221230i	$0.0710072\pi$
$228$		0			0
$229$	6.50685	+	11.2702i	0.429985	+	0.744756i	0.996871	−	0.0790402i	$-0.0251856\pi$
$229$	6.50685	+	11.2702i	0.429985	+	0.744756i	−0.566887	+	0.823796i	$0.691852\pi$
$230$	−0.926209	+	1.60424i	−0.0610724	+	0.105780i
$231$		0			0
$232$	−1.08262	−	1.87515i	−0.0710775	−	0.123110i
$233$	−8.92397	−	15.4568i	−0.584629	−	1.01261i	−0.994922	−	0.100653i	$-0.967907\pi$
$233$	−8.92397	−	15.4568i	−0.584629	−	1.01261i	0.410293	−	0.911954i	$-0.365426\pi$
$234$		0			0
$235$	24.9616			1.62832
$236$	8.86592	−	15.3562i	0.577122	−	0.999605i
$237$		0			0
$238$	1.53704			0.0996318
$239$	3.30689	+	5.72770i	0.213905	+	0.370494i	0.952933	−	0.303180i	$-0.0980484\pi$
$239$	3.30689	+	5.72770i	0.213905	+	0.370494i	−0.739028	+	0.673674i	$0.764715\pi$
$240$		0			0
$241$	3.85952	+	6.68488i	0.248613	+	0.430611i	0.963141	−	0.268996i	$-0.0866918\pi$
$241$	3.85952	+	6.68488i	0.248613	+	0.430611i	−0.714528	+	0.699607i	$0.753358\pi$
$242$	0.461199	+	0.798820i	0.0296470	+	0.0513501i
$243$		0			0
$244$	0.934033	+	1.61779i	0.0597953	+	0.103569i
$245$	−13.0975			−0.836771
$246$		0			0
$247$	16.8163	−	10.9083i	1.06999	−	0.694080i
$248$	1.93541	+	3.35223i	0.122899	+	0.212867i
$249$		0			0
$250$	−1.27852			−0.0808605
$251$	−9.90854	+	17.1621i	−0.625422	+	1.08326i	0.363038	+	0.931775i	$0.381740\pi$
$251$	−9.90854	+	17.1621i	−0.625422	+	1.08326i	−0.988459	+	0.151487i	$0.951594\pi$
$252$		0			0
$253$	−10.2279	+	17.7153i	−0.643025	+	1.11375i
$254$	−1.33742	+	2.31647i	−0.0839169	+	0.145348i
$255$		0			0
$256$	14.3097			0.894359
$257$	19.0966			1.19121			0.595606	−	0.803277i	$-0.296912\pi$
$257$	19.0966			1.19121			0.595606	+	0.803277i	$0.296912\pi$
$258$		0			0
$259$	9.19037	−	15.9182i	0.571062	−	0.989108i
$260$	−11.6914	+	20.2502i	−0.725072	+	1.25586i
$261$		0			0
$262$	1.57522	−	2.72837i	0.0973177	−	0.168559i
$263$	−18.8451			−1.16204			−0.581020	−	0.813889i	$-0.697346\pi$
$263$	−18.8451			−1.16204			−0.581020	+	0.813889i	$0.697346\pi$
$264$		0			0
$265$	13.7638	+	23.8395i	0.845501	+	1.46445i
$266$	−0.115122	−	2.21849i	−0.00705858	−	0.136024i
$267$		0			0
$268$	−2.72475			−0.166441
$269$	−8.42218	−	14.5876i	−0.513509	−	0.889424i	−0.999877	−	0.0156702i	$-0.995012\pi$
$269$	−8.42218	−	14.5876i	−0.513509	−	0.889424i	0.486368	−	0.873754i	$-0.338322\pi$
$270$		0			0
$271$	10.1398	+	17.5626i	0.615946	+	1.06685i	0.990218	+	0.139531i	$0.0445596\pi$
$271$	10.1398	+	17.5626i	0.615946	+	1.06685i	−0.374271	+	0.927319i	$0.622107\pi$
$272$	5.83830	+	10.1122i	0.353999	+	0.613144i
$273$		0			0
$274$	0.647801	+	1.12202i	0.0391351	+	0.0677839i
$275$	6.67508			0.402523
$276$		0			0
$277$	−4.15551	+	7.19756i	−0.249681	+	0.432460i	−0.963437	−	0.267934i	$-0.913659\pi$
$277$	−4.15551	+	7.19756i	−0.249681	+	0.432460i	0.713756	+	0.700394i	$0.246992\pi$
$278$	1.94735			0.116795
$279$		0			0
$280$	2.60553	+	4.51291i	0.155710	+	0.269698i
$281$	6.21567	+	10.7659i	0.370796	+	0.642237i	0.989688	−	0.143238i	$-0.0457516\pi$
$281$	6.21567	+	10.7659i	0.370796	+	0.642237i	−0.618892	+	0.785476i	$0.712418\pi$
$282$		0			0
$283$	−14.6625	+	25.3963i	−0.871598	+	1.50965i	−0.0112550	+	0.999937i	$0.503583\pi$
$283$	−14.6625	+	25.3963i	−0.871598	+	1.50965i	−0.860343	+	0.509715i	$0.829751\pi$
$284$	8.81113	+	15.2613i	0.522844	+	0.905593i
$285$		0			0
$286$	1.40114	−	2.42685i	0.0828513	−	0.143503i
$287$	4.40299	+	7.62620i	0.259900	+	0.450160i
$288$		0			0
$289$	3.95205	−	6.84516i	0.232474	−	0.402656i
$290$	1.39870			0.0821342
$291$		0			0
$292$	4.24930	+	7.36000i	0.248671	+	0.430712i
$293$	−1.02728	−	1.77930i	−0.0600143	−	0.103948i	0.834457	−	0.551073i	$-0.185781\pi$
$293$	−1.02728	−	1.77930i	−0.0600143	−	0.103948i	−0.894472	+	0.447125i	$0.852448\pi$
$294$		0			0
$295$	11.5165	+	19.9472i	0.670517	+	1.16137i
$296$	−3.08105			−0.179082
$297$		0			0
$298$	−1.01217	+	1.75313i	−0.0586333	+	0.101556i
$299$	22.6192			1.30810
$300$		0			0
$301$	−8.31358	+	14.3995i	−0.479187	+	0.829976i
$302$	0.267802	−	0.463846i	0.0154102	−	0.0266913i
$303$		0			0
$304$	14.1582	−	9.18407i	0.812026	−	0.526742i
$305$	−2.42655			−0.138944
$306$		0			0
$307$	−5.53654	−	9.58957i	−0.315987	−	0.547306i	0.663660	−	0.748035i	$-0.269002\pi$
$307$	−5.53654	−	9.58957i	−0.315987	−	0.547306i	−0.979647	+	0.200729i	$0.935669\pi$
$308$	14.3085	+	24.7831i	0.815304	+	1.41215i
$309$		0			0
$310$	−2.50046			−0.142017
$311$	9.02794	+	15.6369i	0.511928	+	0.886685i	0.999904	+	0.0138280i	$0.00440174\pi$
$311$	9.02794	+	15.6369i	0.511928	+	0.886685i	−0.487977	+	0.872857i	$0.662265\pi$
$312$		0			0
$313$	−5.88811	−	10.1985i	−0.332815	−	0.576453i	0.650247	−	0.759723i	$-0.274665\pi$
$313$	−5.88811	−	10.1985i	−0.332815	−	0.576453i	−0.983063	+	0.183269i	$0.941332\pi$
$314$	0.333033	−	0.576831i	0.0187942	−	0.0325525i
$315$		0			0
$316$	−6.69773			−0.376777
$317$	2.95851	+	5.12429i	0.166166	+	0.287809i	0.937069	−	0.349144i	$-0.113528\pi$
$317$	2.95851	+	5.12429i	0.166166	+	0.287809i	−0.770902	+	0.636953i	$0.780194\pi$
$318$		0			0
$319$	15.4455			0.864783
$320$	−9.62385	+	16.6690i	−0.537989	+	0.931825i
$321$		0			0
$322$	1.25341	−	2.17098i	0.0698501	−	0.120984i
$323$	11.7103	+	5.97426i	0.651576	+	0.332417i
$324$		0			0
$325$	−3.69051	−	6.39214i	−0.204712	−	0.354572i
$326$	0.337538			0.0186945
$327$		0			0
$328$	0.738046	−	1.27833i	0.0407518	−	0.0705841i
$329$	−33.7799			−1.86235
$330$		0			0
$331$	5.39815	−	9.34987i	0.296709	−	0.513916i	−0.678672	−	0.734442i	$-0.737444\pi$
$331$	5.39815	−	9.34987i	0.296709	−	0.513916i	0.975381	+	0.220526i	$0.0707774\pi$
$332$	8.95561	−	15.5116i	0.491503	−	0.851308i
$333$		0			0
$334$	−1.31031			−0.0716972
$335$	1.76968	−	3.06517i	0.0966879	−	0.167468i
$336$		0			0
$337$	14.5238	−	25.1560i	0.791164	−	1.37034i	−0.134082	−	0.990970i	$-0.542809\pi$
$337$	14.5238	−	25.1560i	0.791164	−	1.37034i	0.925246	−	0.379366i	$-0.123858\pi$
$338$	−1.19370			−0.0649287
$339$		0			0
$340$	−15.3357			−0.831696
$341$	−27.6121			−1.49528
$342$		0			0
$343$	−6.62120			−0.357511
$344$	2.78711			0.150271
$345$		0			0
$346$	−0.189748			−0.0102009
$347$	6.12607	−	10.6107i	0.328865	−	0.569610i	−0.653422	−	0.756994i	$-0.726667\pi$
$347$	6.12607	−	10.6107i	0.328865	−	0.569610i	0.982287	+	0.187383i	$0.0600007\pi$
$348$		0			0
$349$	−3.55181	+	6.15191i	−0.190124	+	0.329304i	−0.945291	−	0.326228i	$-0.894222\pi$
$349$	−3.55181	+	6.15191i	−0.190124	+	0.329304i	0.755167	+	0.655532i	$0.227556\pi$
$350$	−0.818019			−0.0437249
$351$		0			0
$352$	3.60415	−	6.24256i	0.192102	−	0.332730i
$353$	17.7023	−	30.6613i	0.942200	−	1.63194i	0.180936	−	0.983495i	$-0.442087\pi$
$353$	17.7023	−	30.6613i	0.942200	−	1.63194i	0.761264	−	0.648443i	$-0.224579\pi$
$354$		0			0
$355$	−22.8907			−1.21491
$356$	−7.84515	+	13.5882i	−0.415792	+	0.720173i
$357$		0			0
$358$	1.08883			0.0575463
$359$	−7.86541	−	13.6233i	−0.415121	−	0.719010i	0.580320	−	0.814388i	$-0.302927\pi$
$359$	−7.86541	−	13.6233i	−0.415121	−	0.719010i	−0.995441	+	0.0953781i	$0.969594\pi$
$360$		0			0
$361$	7.74584	−	17.3494i	0.407676	−	0.913127i
$362$	0.0449619	−	0.0778762i	0.00236314	−	0.00409308i
$363$		0			0
$364$	15.8217	−	27.4040i	0.829284	−	1.43636i
$365$	−11.0394			−0.577827
$366$		0			0
$367$	−14.9741	−	25.9359i	−0.781641	−	1.35384i	−0.930986	−	0.365056i	$-0.881050\pi$
$367$	−14.9741	−	25.9359i	−0.781641	−	1.35384i	0.149345	−	0.988785i	$-0.452284\pi$
$368$	19.0438			0.992729
$369$		0			0
$370$	0.995143	−	1.72364i	0.0517350	−	0.0896077i
$371$	−18.6261	−	32.2614i	−0.967021	−	1.67493i
$372$		0			0
$373$	−5.46086	−	9.45848i	−0.282753	−	0.489742i	0.689309	−	0.724467i	$-0.257914\pi$
$373$	−5.46086	−	9.45848i	−0.282753	−	0.489742i	−0.972062	+	0.234726i	$0.924581\pi$
$374$	1.83789			0.0950348
$375$		0			0
$376$	2.83116	+	4.90371i	0.146006	+	0.252889i
$377$	−8.53948	−	14.7908i	−0.439806	−	0.761766i
$378$		0			0
$379$	−17.0217			−0.874348			−0.437174	−	0.899377i	$-0.644021\pi$
$379$	−17.0217			−0.874348			−0.437174	+	0.899377i	$0.644021\pi$
$380$	1.14862	+	22.1347i	0.0589229	+	1.13549i
$381$		0			0
$382$	−0.414300	+	0.717589i	−0.0211974	+	0.0367150i
$383$	−4.77558	+	8.27154i	−0.244021	+	0.422656i	−0.961856	−	0.273557i	$-0.911800\pi$
$383$	−4.77558	+	8.27154i	−0.244021	+	0.422656i	0.717835	+	0.696213i	$0.245133\pi$
$384$		0			0
$385$	−37.1725			−1.89449
$386$	0.129312	−	0.223974i	0.00658179	−	0.0114000i
$387$		0			0
$388$	−3.68139			−0.186894
$389$	8.88453	+	15.3884i	0.450463	+	0.780225i	0.998415	−	0.0562848i	$-0.0179255\pi$
$389$	8.88453	+	15.3884i	0.450463	+	0.780225i	−0.547951	+	0.836510i	$0.684592\pi$
$390$		0			0
$391$	7.41743	+	12.8474i	0.375116	+	0.649719i
$392$	−1.48553	−	2.57301i	−0.0750306	−	0.129957i
$393$		0			0
$394$	−0.201041			−0.0101283
$395$	4.35006	−	7.53452i	0.218875	−	0.379103i
$396$		0			0
$397$	−4.95146	−	8.57619i	−0.248507	−	0.430426i	0.714605	−	0.699528i	$-0.246607\pi$
$397$	−4.95146	−	8.57619i	−0.248507	−	0.430426i	−0.963112	+	0.269102i	$0.913273\pi$
$398$	−1.80359	+	3.12390i	−0.0904056	+	0.156587i
$399$		0			0
$400$	−3.10716	−	5.38175i	−0.155358	−	0.269088i
$401$	8.21244	−	14.2244i	0.410110	−	0.710331i	−0.584792	−	0.811184i	$-0.698824\pi$
$401$	8.21244	−	14.2244i	0.410110	−	0.710331i	0.994901	+	0.100853i	$0.0321570\pi$
$402$		0			0
$403$	15.2661	+	26.4417i	0.760460	+	1.31715i
$404$	9.77694	+	16.9342i	0.486421	+	0.842506i
$405$		0			0
$406$	−1.89282			−0.0939390
$407$	10.9892	−	19.0338i	0.544713	−	0.943471i
$408$		0			0
$409$	−28.0875			−1.38884			−0.694418	−	0.719572i	$-0.744338\pi$
$409$	−28.0875			−1.38884			−0.694418	+	0.719572i	$0.744338\pi$
$410$	0.476760	+	0.825773i	0.0235455	+	0.0407820i
$411$		0			0
$412$	18.5041	+	32.0501i	0.911633	+	1.57899i
$413$	−15.5850	−	26.9940i	−0.766888	−	1.32829i
$414$		0			0
$415$	11.6330	+	20.1490i	0.571043	+	0.989075i
$416$	−7.97061			−0.390791
$417$		0			0
$418$	−0.137654	−	2.65270i	−0.00673290	−	0.129748i
$419$	−2.35560	−	4.08002i	−0.115079	−	0.199322i	0.802733	−	0.596339i	$-0.203379\pi$
$419$	−2.35560	−	4.08002i	−0.115079	−	0.199322i	−0.917811	+	0.397017i	$0.870045\pi$
$420$		0			0
$421$	16.6902			0.813431			0.406716	−	0.913555i	$-0.366674\pi$
$421$	16.6902			0.813431			0.406716	+	0.913555i	$0.366674\pi$
$422$	−0.524978	+	0.909289i	−0.0255555	+	0.0442635i
$423$		0			0
$424$	−3.12219	+	5.40778i	−0.151627	+	0.262625i
$425$	2.42043	−	4.19230i	0.117408	−	0.203357i
$426$		0			0
$427$	3.28379			0.158914
$428$	−30.2788			−1.46358
$429$		0			0
$430$	−0.900204	+	1.55920i	−0.0434117	+	0.0751912i
$431$	−13.7404	+	23.7990i	−0.661850	+	1.14636i	0.318279	+	0.947997i	$0.396895\pi$
$431$	−13.7404	+	23.7990i	−0.661850	+	1.14636i	−0.980129	+	0.198360i	$0.936438\pi$
$432$		0			0
$433$	16.6749	−	28.8817i	0.801343	−	1.38797i	−0.117389	−	0.993086i	$-0.537452\pi$
$433$	16.6749	−	28.8817i	0.801343	−	1.38797i	0.918732	−	0.394881i	$-0.129214\pi$
$434$	3.38381			0.162428
$435$		0			0
$436$	−3.25822	−	5.64340i	−0.156040	−	0.270270i
$437$	17.9876	−	11.6682i	0.860465	−	0.558164i
$438$		0			0
$439$	−26.3194			−1.25616			−0.628078	−	0.778151i	$-0.716158\pi$
$439$	−26.3194			−1.25616			−0.628078	+	0.778151i	$0.716158\pi$
$440$	3.11550	+	5.39620i	0.148526	+	0.257254i
$441$		0			0
$442$	−1.01613	−	1.75998i	−0.0483322	−	0.0837138i
$443$	−14.2764	−	24.7275i	−0.678293	−	1.17484i	−0.975495	−	0.220024i	$-0.929387\pi$
$443$	−14.2764	−	24.7275i	−0.678293	−	1.17484i	0.297201	−	0.954815i	$-0.403947\pi$
$444$		0			0
$445$	−10.1906	−	17.6506i	−0.483079	−	0.836718i
$446$	−0.178106			−0.00843356
$447$		0			0
$448$	13.0237	−	22.5577i	0.615312	−	1.06575i
$449$	−29.8391			−1.40819			−0.704097	−	0.710104i	$-0.748648\pi$
$449$	−29.8391			−1.40819			−0.704097	+	0.710104i	$0.748648\pi$
$450$		0			0
$451$	5.26477	+	9.11885i	0.247908	+	0.429390i
$452$	−3.57686	−	6.19530i	−0.168241	−	0.291402i
$453$		0			0
$454$	−0.653540	+	1.13197i	−0.0306722	+	0.0531258i
$455$	20.5519	+	35.5969i	0.963486	+	1.66881i
$456$		0			0
$457$	−2.02990	+	3.51588i	−0.0949546	+	0.164466i	−0.909590	−	0.415508i	$-0.863604\pi$
$457$	−2.02990	+	3.51588i	−0.0949546	+	0.164466i	0.814635	+	0.579974i	$0.196937\pi$
$458$	−0.953475	−	1.65147i	−0.0445530	−	0.0771680i
$459$		0			0
$460$	−12.5058	+	21.6607i	−0.583087	+	1.00994i
$461$	16.7814			0.781586			0.390793	−	0.920479i	$-0.372201\pi$
$461$	16.7814			0.781586			0.390793	+	0.920479i	$0.372201\pi$
$462$		0			0
$463$	−0.887050	−	1.53642i	−0.0412247	−	0.0714033i	0.844677	−	0.535277i	$-0.179793\pi$
$463$	−0.887050	−	1.53642i	−0.0412247	−	0.0714033i	−0.885902	+	0.463873i	$0.846459\pi$
$464$	−7.18967	−	12.4529i	−0.333772	−	0.578110i
$465$		0			0
$466$	1.30767	+	2.26494i	0.0605764	+	0.104921i
$467$	−13.4739			−0.623496			−0.311748	−	0.950165i	$-0.600914\pi$
$467$	−13.4739			−0.623496			−0.311748	+	0.950165i	$0.600914\pi$
$468$		0			0
$469$	−2.39486	+	4.14802i	−0.110584	+	0.191538i
$470$	−3.65772			−0.168718
$471$		0			0
$472$	−2.61242	+	4.52484i	−0.120246	+	0.208273i
$473$	−9.94078	+	17.2179i	−0.457077	+	0.791681i
$474$		0			0
$475$	−6.23223	−	3.17952i	−0.285954	−	0.145886i
$476$	20.7534			0.951232
$477$		0			0
$478$	−0.484572	−	0.839303i	−0.0221638	−	0.0383888i
$479$	−10.2064	−	17.6780i	−0.466343	−	0.807729i	0.532918	−	0.846167i	$-0.321095\pi$
$479$	−10.2064	−	17.6780i	−0.466343	−	0.807729i	−0.999261	+	0.0384376i	$0.987762\pi$
$480$		0			0
$481$	−24.3027			−1.10811
$482$	−0.565551	−	0.979563i	−0.0257601	−	0.0446179i
$483$		0			0
$484$	6.22719	+	10.7858i	0.283054	+	0.490264i
$485$	2.39100	−	4.14133i	0.108570	−	0.188048i
$486$		0			0
$487$	23.6649			1.07236			0.536180	−	0.844104i	$-0.319867\pi$
$487$	23.6649			1.07236			0.536180	+	0.844104i	$0.319867\pi$
$488$	−0.275221	−	0.476696i	−0.0124587	−	0.0215790i
$489$		0			0
$490$	1.91923			0.0867022
$491$	2.03418	−	3.52330i	0.0918013	−	0.159005i	−0.816468	−	0.577391i	$-0.804071\pi$
$491$	2.03418	−	3.52330i	0.0918013	−	0.159005i	0.908269	+	0.418386i	$0.137404\pi$
$492$		0			0
$493$	5.60064	−	9.70060i	0.252240	−	0.436893i
$494$	−2.46416	+	1.59844i	−0.110868	+	0.0719172i
$495$		0			0
$496$	12.8530	+	22.2621i	0.577118	+	0.999598i
$497$	30.9774			1.38953
$498$		0			0
$499$	−13.6550	+	23.6512i	−0.611283	+	1.05877i	0.379742	+	0.925092i	$0.376013\pi$
$499$	−13.6550	+	23.6512i	−0.611283	+	1.05877i	−0.991025	+	0.133680i	$0.957321\pi$
$500$	−17.2627			−0.772013
$501$		0			0
$502$	1.45194	−	2.51483i	0.0648032	−	0.112242i
$503$	10.8699	−	18.8272i	0.484665	−	0.839465i	−0.515179	−	0.857082i	$-0.672275\pi$
$503$	10.8699	−	18.8272i	0.484665	−	0.839465i	0.999845	+	0.0176172i	$0.00560801\pi$
$504$		0			0
$505$	−25.3998			−1.13028
$506$	1.49874	−	2.59590i	0.0666272	−	0.115402i
$507$		0			0
$508$	−18.0580	+	31.2774i	−0.801195	+	1.38771i
$509$	26.1713			1.16002			0.580012	−	0.814608i	$-0.303048\pi$
$509$	26.1713			1.16002			0.580012	+	0.814608i	$0.303048\pi$
$510$		0			0
$511$	14.9393			0.660876
$512$	−11.2250			−0.496077
$513$		0			0
$514$	−2.79830			−0.123428
$515$	−48.0724			−2.11832
$516$		0			0
$517$	−40.3915			−1.77642
$518$	−1.34670	+	2.33256i	−0.0591707	+	0.102487i
$519$		0			0
$520$	3.44498	−	5.96688i	0.151072	−	0.261665i
$521$	30.4889			1.33574			0.667872	−	0.744276i	$-0.267205\pi$
$521$	30.4889			1.33574			0.667872	+	0.744276i	$0.267205\pi$
$522$		0			0
$523$	−10.8103	+	18.7241i	−0.472703	+	0.818746i	−0.999512	−	0.0312380i	$-0.990055\pi$
$523$	−10.8103	+	18.7241i	−0.472703	+	0.818746i	0.526809	+	0.849984i	$0.323388\pi$
$524$	21.2689	−	36.8389i	0.929138	−	1.60931i
$525$		0			0
$526$	2.76145			0.120405
$527$	−10.0123	+	17.3419i	−0.436144	+	0.755423i
$528$		0			0
$529$	1.19478			0.0519470
$530$	−2.01686	−	3.49330i	−0.0876068	−	0.151739i
$531$		0			0
$532$	−1.55440	−	29.9544i	−0.0673916	−	1.29869i
$533$	5.82155	−	10.0832i	0.252159	−	0.436753i
$534$		0			0
$535$	19.6656	−	34.0617i	0.850216	−	1.47262i
$536$	0.802872			0.0346788
$537$		0			0
$538$	1.23414	+	2.13759i	0.0532074	+	0.0921579i
$539$	21.1937			0.912879
$540$		0			0
$541$	−18.3616	+	31.8032i	−0.789427	+	1.36733i	0.136891	+	0.990586i	$0.456289\pi$
$541$	−18.3616	+	31.8032i	−0.789427	+	1.36733i	−0.926318	+	0.376742i	$0.877044\pi$
$542$	−1.48582	−	2.57352i	−0.0638214	−	0.110542i
$543$		0			0
$544$	−2.61377	−	4.52719i	−0.112065	−	0.194101i
$545$	8.46461			0.362584
$546$		0			0
$547$	−8.60656	−	14.9070i	−0.367990	−	0.637377i	0.621261	−	0.783604i	$-0.286621\pi$
$547$	−8.60656	−	14.9070i	−0.367990	−	0.637377i	−0.989251	+	0.146226i	$0.953287\pi$
$548$	8.74672	+	15.1498i	0.373641	+	0.647166i
$549$		0			0
$550$	−0.978127			−0.0417075
$551$	−14.4208	−	7.35710i	−0.614346	−	0.313423i
$552$		0			0
$553$	−5.88682	+	10.1963i	−0.250333	+	0.433590i
$554$	0.608924	−	1.05469i	0.0258707	−	0.0448094i
$555$		0			0
$556$	26.2935			1.11509
$557$	−8.67769	+	15.0302i	−0.367686	+	0.636850i	−0.989203	−	0.146550i	$-0.953183\pi$
$557$	−8.67769	+	15.0302i	−0.367686	+	0.636850i	0.621518	+	0.783400i	$0.286516\pi$
$558$		0			0
$559$	21.9841			0.929830
$560$	17.3033	+	29.9701i	0.731197	+	1.26647i
$561$		0			0
$562$	−0.910808	−	1.57757i	−0.0384201	−	0.0665456i
$563$	−8.34041	−	14.4460i	−0.351506	−	0.608827i	0.635007	−	0.772506i	$-0.280997\pi$
$563$	−8.34041	−	14.4460i	−0.351506	−	0.608827i	−0.986514	+	0.163679i	$0.947664\pi$
$564$		0			0
$565$	9.29242			0.390935
$566$	2.14856	−	3.72142i	0.0903108	−	0.156423i
$567$		0			0
$568$	−2.59627	−	4.49688i	−0.108937	−	0.188685i
$569$	−5.41399	+	9.37731i	−0.226966	+	0.393117i	−0.956908	−	0.290393i	$-0.906214\pi$
$569$	−5.41399	+	9.37731i	−0.226966	+	0.393117i	0.729941	+	0.683510i	$0.239547\pi$
$570$		0			0
$571$	−11.5342	−	19.9778i	−0.482691	−	0.836045i	0.517111	−	0.855918i	$-0.327007\pi$
$571$	−11.5342	−	19.9778i	−0.482691	−	0.836045i	−0.999803	+	0.0198726i	$0.993674\pi$
$572$	18.9185	−	32.7678i	0.791021	−	1.37009i
$573$		0			0
$574$	−0.645188	−	1.11750i	−0.0269296	−	0.0466435i
$575$	−3.94757	−	6.83740i	−0.164625	−	0.285139i
$576$		0			0
$577$	2.29118			0.0953830			0.0476915	−	0.998862i	$-0.484814\pi$
$577$	2.29118			0.0953830			0.0476915	+	0.998862i	$0.484814\pi$
$578$	−0.579110	+	1.00305i	−0.0240878	+	0.0417213i
$579$		0			0
$580$	18.8854			0.784174
$581$	−15.7427	−	27.2671i	−0.653116	−	1.13123i
$582$		0			0
$583$	−22.2718	−	38.5759i	−0.922403	−	1.59765i
$584$	−1.25209	−	2.16869i	−0.0518119	−	0.0897409i
$585$		0			0
$586$	0.150531	+	0.260728i	0.00621840	+	0.0107706i
$587$	−36.0643			−1.48853			−0.744267	−	0.667882i	$-0.767201\pi$
$587$	−36.0643			−1.48853			−0.744267	+	0.667882i	$0.767201\pi$
$588$		0			0
$589$	25.7802	+	13.1524i	1.06225	+	0.541934i
$590$	−1.68756	−	2.92294i	−0.0694758	−	0.120336i
$591$		0			0
$592$	−20.4612			−0.840951
$593$	3.95398	−	6.84849i	0.162370	−	0.281234i	−0.773348	−	0.633982i	$-0.781419\pi$
$593$	3.95398	−	6.84849i	0.162370	−	0.281234i	0.935718	+	0.352748i	$0.114753\pi$
$594$		0			0
$595$	−13.4790	+	23.3463i	−0.552585	+	0.957105i
$596$	−13.6665	+	23.6710i	−0.559800	+	0.969602i
$597$		0			0
$598$	−3.31448			−0.135539
$599$	32.0218			1.30837			0.654187	−	0.756333i	$-0.273011\pi$
$599$	32.0218			1.30837			0.654187	+	0.756333i	$0.273011\pi$
$600$		0			0
$601$	−16.6013	+	28.7542i	−0.677180	+	1.17291i	0.298646	+	0.954364i	$0.403465\pi$
$601$	−16.6013	+	28.7542i	−0.677180	+	1.17291i	−0.975827	+	0.218546i	$0.929868\pi$
$602$	1.21822	−	2.11002i	0.0496511	−	0.0859982i
$603$		0			0
$604$	3.61590	−	6.26293i	0.147129	−	0.254835i
$605$	−16.1778			−0.657721
$606$		0			0
$607$	19.9393	+	34.5360i	0.809313	+	1.40177i	0.913340	+	0.407197i	$0.133494\pi$
$607$	19.9393	+	34.5360i	0.809313	+	1.40177i	−0.104027	+	0.994574i	$0.533173\pi$
$608$	−6.33852	+	4.11165i	−0.257061	+	0.166750i
$609$		0			0
$610$	0.355572			0.0143967
$611$	22.3316	+	38.6794i	0.903439	+	1.56480i
$612$		0			0
$613$	−4.68793	−	8.11973i	−0.189344	−	0.327953i	0.755688	−	0.654932i	$-0.227303\pi$
$613$	−4.68793	−	8.11973i	−0.189344	−	0.327953i	−0.945032	+	0.326979i	$0.893969\pi$
$614$	0.811292	+	1.40520i	0.0327411	+	0.0567092i
$615$		0			0
$616$	−4.21613	−	7.30254i	−0.169873	−	0.294228i
$617$	−30.4124			−1.22436			−0.612179	−	0.790719i	$-0.709707\pi$
$617$	−30.4124			−1.22436			−0.612179	+	0.790719i	$0.709707\pi$
$618$		0			0
$619$	−11.8294	+	20.4890i	−0.475462	+	0.823524i	−0.999605	−	0.0281061i	$-0.991052\pi$
$619$	−11.8294	+	20.4890i	−0.475462	+	0.823524i	0.524143	+	0.851630i	$0.324386\pi$
$620$	−33.7617			−1.35590
$621$		0			0
$622$	−1.32290	−	2.29133i	−0.0530435	−	0.0918740i
$623$	13.7906	+	23.8861i	0.552510	+	0.956976i
$624$		0			0
$625$	15.2246	−	26.3697i	0.608983	−	1.05479i
$626$	0.862808	+	1.49443i	0.0344847	+	0.0597293i
$627$		0			0
$628$	4.49667	−	7.78847i	0.179437	−	0.310794i
$629$	−7.96949	−	13.8036i	−0.317764	−	0.550384i
$630$		0			0
$631$	9.85638	−	17.0717i	0.392376	−	0.679615i	−0.600386	−	0.799710i	$-0.704986\pi$
$631$	9.85638	−	17.0717i	0.392376	−	0.679615i	0.992762	+	0.120095i	$0.0383198\pi$
$632$	1.97354			0.0785033
$633$		0			0
$634$	−0.433522	−	0.750883i	−0.0172174	−	0.0298214i
$635$	−23.4567	−	40.6282i	−0.930851	−	1.61228i
$636$		0			0
$637$	−11.7175	−	20.2954i	−0.464266	−	0.804132i
$638$	−2.26329			−0.0896047
$639$		0			0
$640$	5.86488	−	10.1583i	0.231830	−	0.401541i
$641$	1.18538			0.0468197			0.0234098	−	0.999726i	$-0.492548\pi$
$641$	1.18538			0.0468197			0.0234098	+	0.999726i	$0.492548\pi$
$642$		0			0
$643$	13.9281	−	24.1242i	0.549272	−	0.951367i	−0.449052	−	0.893505i	$-0.648238\pi$
$643$	13.9281	−	24.1242i	0.549272	−	0.951367i	0.998325	−	0.0578619i	$-0.0184283\pi$
$644$	16.9238	−	29.3129i	0.666892	−	1.15509i
$645$		0			0
$646$	−1.71595	−	0.875433i	−0.0675132	−	0.0344434i
$647$	3.69287			0.145182			0.0725909	−	0.997362i	$-0.476873\pi$
$647$	3.69287			0.145182			0.0725909	+	0.997362i	$0.476873\pi$
$648$		0			0
$649$	−18.6354	−	32.2775i	−0.731504	−	1.26700i
$650$	0.540785	+	0.936667i	0.0212113	+	0.0367391i
$651$		0			0
$652$	4.55749			0.178485
$653$	−0.659445	−	1.14219i	−0.0258061	−	0.0446974i	0.852834	−	0.522182i	$-0.174882\pi$
$653$	−0.659445	−	1.14219i	−0.0258061	−	0.0446974i	−0.878640	+	0.477485i	$0.841549\pi$
$654$		0			0
$655$	27.6276	+	47.8524i	1.07950	+	1.86975i
$656$	4.90135	−	8.48939i	0.191366	−	0.331455i
$657$		0			0
$658$	4.94991			0.192967
$659$	−2.42873	−	4.20668i	−0.0946097	−	0.163869i	0.814836	−	0.579692i	$-0.196827\pi$
$659$	−2.42873	−	4.20668i	−0.0946097	−	0.163869i	−0.909446	+	0.415823i	$0.863494\pi$
$660$		0			0
$661$	30.2136			1.17517			0.587586	−	0.809162i	$-0.300078\pi$
$661$	30.2136			1.17517			0.587586	+	0.809162i	$0.300078\pi$
$662$	−0.791013	+	1.37008i	−0.0307436	+	0.0532495i
$663$		0			0
$664$	−2.63885	+	4.57062i	−0.102407	+	0.177374i
$665$	34.7063	+	17.7062i	1.34585	+	0.686618i
$666$		0			0
$667$	−9.13431	−	15.8211i	−0.353682	−	0.612595i
$668$	−17.6921			−0.684527
$669$		0			0
$670$	−0.259318	+	0.449152i	−0.0100183	+	0.0173523i
$671$	3.92652			0.151582
$672$		0			0
$673$	3.03772	−	5.26149i	0.117096	−	0.202815i	−0.801520	−	0.597968i	$-0.795975\pi$
$673$	3.03772	−	5.26149i	0.117096	−	0.202815i	0.918615	+	0.395153i	$0.129308\pi$
$674$	−2.12824	+	3.68622i	−0.0819767	+	0.141988i
$675$		0			0
$676$	−16.1175			−0.619905
$677$	−5.96003	+	10.3231i	−0.229062	+	0.396748i	−0.957531	−	0.288332i	$-0.906899\pi$
$677$	−5.96003	+	10.3231i	−0.229062	+	0.396748i	0.728468	+	0.685080i	$0.240233\pi$
$678$		0			0
$679$	−3.23568	+	5.60436i	−0.124174	+	0.215075i
$680$	4.51880			0.173288
$681$		0			0
$682$	4.04611			0.154934
$683$	0.0898958			0.00343977			0.00171988	−	0.999999i	$-0.499453\pi$
$683$	0.0898958			0.00343977			0.00171988	+	0.999999i	$0.499453\pi$
$684$		0			0
$685$	−22.7233			−0.868214
$686$	0.970231			0.0370436
$687$		0			0
$688$	18.5092			0.705655
$689$	−24.6272	+	42.6555i	−0.938220	+	1.62504i
$690$		0			0
$691$	3.96889	−	6.87432i	0.150984	−	0.261512i	−0.780606	−	0.625024i	$-0.785089\pi$
$691$	3.96889	−	6.87432i	0.150984	−	0.261512i	0.931589	+	0.363512i	$0.118423\pi$
$692$	−2.56201			−0.0973929
$693$		0			0
$694$	−0.897678	+	1.55482i	−0.0340754	+	0.0590203i
$695$	−17.0772	+	29.5785i	−0.647774	+	1.12198i
$696$		0			0
$697$	7.63616			0.289240
$698$	0.520461	−	0.901465i	0.0196997	−	0.0341209i
$699$		0			0
$700$	−11.0450			−0.417463
$701$	24.0605	+	41.6741i	0.908753	+	1.57401i	0.815798	+	0.578337i	$0.196298\pi$
$701$	24.0605	+	41.6741i	0.908753	+	1.57401i	0.0929554	+	0.995670i	$0.470369\pi$
$702$		0			0
$703$	−19.3264	+	12.5366i	−0.728909	+	0.472826i
$704$	15.5728	−	26.9729i	0.586922	−	1.01658i
$705$		0			0
$706$	−2.59399	+	4.49293i	−0.0976262	+	0.169094i
$707$	34.3729			1.29273
$708$		0			0
$709$	−11.3295	−	19.6232i	−0.425487	−	0.736965i	0.570979	−	0.820965i	$-0.306564\pi$
$709$	−11.3295	−	19.6232i	−0.425487	−	0.736965i	−0.996466	+	0.0839996i	$0.973231\pi$
$710$	3.35426			0.125883
$711$		0			0
$712$	2.31164	−	4.00388i	0.0866323	−	0.150052i
$713$	16.3295	+	28.2835i	0.611545	+	1.05923i
$714$		0			0
$715$	24.5744	+	42.5641i	0.919031	+	1.59181i
$716$	14.7015			0.549422
$717$		0			0
$718$	1.15255	+	1.99628i	0.0430128	+	0.0745004i
$719$	7.93724	+	13.7477i	0.296009	+	0.512703i	0.975219	−	0.221241i	$-0.0710108\pi$
$719$	7.93724	+	13.7477i	0.296009	+	0.512703i	−0.679210	+	0.733944i	$0.737677\pi$
$720$		0			0
$721$	65.0552			2.42278
$722$	−1.13503	+	2.54228i	−0.0422414	+	0.0946138i
$723$		0			0
$724$	0.607083	−	1.05150i	0.0225620	−	0.0390786i
$725$	−2.98067	+	5.16268i	−0.110699	+	0.191737i
$726$		0			0
$727$	19.7347			0.731921			0.365960	−	0.930630i	$-0.380741\pi$
$727$	19.7347			0.731921			0.365960	+	0.930630i	$0.380741\pi$
$728$	−4.66200	+	8.07483i	−0.172785	+	0.299273i
$729$		0			0
$730$	1.61764			0.0598717
$731$	7.20918	+	12.4867i	0.266641	+	0.461836i
$732$		0			0
$733$	−8.80378	−	15.2486i	−0.325175	−	0.563220i	0.656373	−	0.754437i	$-0.272090\pi$
$733$	−8.80378	−	15.2486i	−0.325175	−	0.563220i	−0.981548	+	0.191217i	$0.938757\pi$
$734$	2.19421	+	3.80049i	0.0809899	+	0.140279i
$735$		0			0
$736$	−8.52581			−0.314266
$737$	−2.86360	+	4.95990i	−0.105482	+	0.182700i
$738$		0			0
$739$	9.37525	+	16.2384i	0.344874	+	0.597339i	0.985331	−	0.170655i	$-0.0545883\pi$
$739$	9.37525	+	16.2384i	0.344874	+	0.597339i	−0.640457	+	0.767994i	$0.721255\pi$
$740$	13.4366	−	23.2729i	0.493939	−	0.855528i
$741$		0			0
$742$	2.72937	+	4.72740i	0.100198	+	0.173548i
$743$	10.7071	−	18.5452i	0.392804	−	0.680357i	−0.600014	−	0.799990i	$-0.704838\pi$
$743$	10.7071	−	18.5452i	0.392804	−	0.680357i	0.992818	+	0.119632i	$0.0381716\pi$
$744$		0			0
$745$	−17.7522	−	30.7478i	−0.650392	−	1.12651i
$746$	0.800202	+	1.38599i	0.0292975	+	0.0507447i
$747$		0			0
$748$	24.8155			0.907343
$749$	−26.6129	+	46.0949i	−0.972414	+	1.68427i
$750$		0			0
$751$	−32.2026			−1.17509			−0.587546	−	0.809191i	$-0.699906\pi$
$751$	−32.2026			−1.17509			−0.587546	+	0.809191i	$0.699906\pi$
$752$	18.8017	+	32.5655i	0.685627	+	1.18754i
$753$		0			0
$754$	1.25133	+	2.16736i	0.0455706	+	0.0789305i
$755$	4.69693	+	8.13532i	0.170939	+	0.296075i
$756$		0			0
$757$	13.3362	+	23.0990i	0.484713	+	0.839548i	0.999846	−	0.0175627i	$-0.00559065\pi$
$757$	13.3362	+	23.0990i	0.484713	+	0.839548i	−0.515133	+	0.857111i	$0.672257\pi$
$758$	2.49426			0.0905957
$759$		0			0
$760$	−0.338450	−	6.52219i	−0.0122769	−	0.236585i
$761$	−2.75558	−	4.77281i	−0.0998898	−	0.173014i	0.811749	−	0.584006i	$-0.198516\pi$
$761$	−2.75558	−	4.77281i	−0.0998898	−	0.173014i	−0.911639	+	0.410992i	$0.865182\pi$
$762$		0			0
$763$	−11.4549			−0.414697
$764$	−5.59395	+	9.68901i	−0.202382	+	0.350536i
$765$		0			0
$766$	0.699784	−	1.21206i	0.0252842	−	0.0437936i
$767$	−20.6062	+	35.6910i	−0.744047	+	1.28873i
$768$		0			0
$769$	17.0767			0.615802			0.307901	−	0.951418i	$-0.400373\pi$
$769$	17.0767			0.615802			0.307901	+	0.951418i	$0.400373\pi$
$770$	5.44704			0.196298
$771$		0			0
$772$	1.74599	−	3.02414i	0.0628395	−	0.108841i
$773$	24.4260	−	42.3071i	0.878542	−	1.52168i	0.0256018	−	0.999672i	$-0.491850\pi$
$773$	24.4260	−	42.3071i	0.878542	−	1.52168i	0.852941	−	0.522008i	$-0.174817\pi$
$774$		0			0
$775$	5.32858	−	9.22937i	0.191408	−	0.331529i
$776$	1.08475			0.0389404
$777$		0			0
$778$	−1.30189	−	2.25493i	−0.0466749	−	0.0808432i
$779$	−0.571935	−	11.0216i	−0.0204917	−	0.394890i
$780$		0			0
$781$	37.0405			1.32541
$782$	−1.08691	−	1.88258i	−0.0388677	−	0.0673208i
$783$		0			0
$784$	−9.86538	−	17.0873i	−0.352335	−	0.610262i
$785$	5.84102	+	10.1169i	0.208475	+	0.361089i
$786$		0			0
$787$	−14.3827	−	24.9115i	−0.512687	−	0.888000i	−0.999892	−	0.0147124i	$-0.995317\pi$
$787$	−14.3827	−	24.9115i	−0.512687	−	0.888000i	0.487205	−	0.873288i	$-0.338017\pi$
$788$	−2.71449			−0.0966996
$789$		0			0
$790$	−0.637432	+	1.10406i	−0.0226788	+	0.0392808i
$791$	−12.5752			−0.447122
$792$		0			0
$793$	−2.17088	−	3.76008i	−0.0770903	−	0.133524i
$794$	0.725558	+	1.25670i	0.0257491	+	0.0445987i
$795$		0			0
$796$	−24.3523	+	42.1795i	−0.863145	+	1.49501i
$797$	−4.94044	−	8.55709i	−0.174999	−	0.303108i	0.765162	−	0.643838i	$-0.222659\pi$
$797$	−4.94044	−	8.55709i	−0.174999	−	0.303108i	−0.940161	+	0.340730i	$0.889326\pi$
$798$		0			0
$799$	−14.6462	+	25.3680i	−0.518146	+	0.897456i
$800$	1.39106	+	2.40938i	0.0491812	+	0.0851844i
$801$		0			0
$802$	−1.20340	+	2.08435i	−0.0424936	+	0.0736011i
$803$	17.8633			0.630383
$804$		0			0
$805$	21.9834	+	38.0764i	0.774814	+	1.34202i
$806$	−2.23701	−	3.87461i	−0.0787952	−	0.136477i
$807$		0			0
$808$	−2.88086	−	4.98979i	−0.101348	−	0.175540i
$809$	−21.3112			−0.749262			−0.374631	−	0.927174i	$-0.622231\pi$
$809$	−21.3112			−0.749262			−0.374631	+	0.927174i	$0.622231\pi$
$810$		0			0
$811$	−4.62375	+	8.00857i	−0.162362	+	0.281219i	−0.935715	−	0.352756i	$-0.885244\pi$
$811$	−4.62375	+	8.00857i	−0.162362	+	0.281219i	0.773353	+	0.633975i	$0.218578\pi$
$812$	−25.5572			−0.896880
$813$		0			0
$814$	−1.61029	+	2.78910i	−0.0564406	+	0.0977580i
$815$	−2.96001	+	5.12689i	−0.103685	+	0.179587i
$816$		0			0
$817$	17.4826	−	11.3406i	0.611639	−	0.396756i
$818$	4.11577			0.143905
$819$		0			0
$820$	6.43730	+	11.1497i	0.224800	+	0.389366i
$821$	−22.6312	−	39.1984i	−0.789834	−	1.36803i	−0.926068	−	0.377357i	$-0.876833\pi$
$821$	−22.6312	−	39.1984i	−0.789834	−	1.36803i	0.136234	−	0.990677i	$-0.456500\pi$
$822$		0			0
$823$	33.5057			1.16794			0.583968	−	0.811777i	$-0.301499\pi$
$823$	33.5057			1.16794			0.583968	+	0.811777i	$0.301499\pi$
$824$	−5.45240	−	9.44383i	−0.189943	−	0.328991i
$825$		0			0
$826$	2.28373	+	3.95554i	0.0794612	+	0.137631i
$827$	7.94152	−	13.7551i	0.276154	−	0.478312i	−0.694272	−	0.719713i	$-0.744273\pi$
$827$	7.94152	−	13.7551i	0.276154	−	0.478312i	0.970426	+	0.241401i	$0.0776068\pi$
$828$		0			0
$829$	16.0447			0.557254			0.278627	−	0.960399i	$-0.410121\pi$
$829$	16.0447			0.557254			0.278627	+	0.960399i	$0.410121\pi$
$830$	−1.70463	−	2.95251i	−0.0591687	−	0.102483i
$831$		0			0
$832$	−34.4394			−1.19397
$833$	7.68498	−	13.3108i	0.266269	−	0.461191i
$834$		0			0
$835$	11.4907	−	19.9025i	0.397652	−	0.688753i
$836$	−1.85863	−	35.8173i	−0.0642822	−	1.23877i
$837$		0			0
$838$	0.345176	+	0.597862i	0.0119239	+	0.0206528i
$839$	54.0973			1.86765			0.933823	−	0.357734i	$-0.116451\pi$
$839$	54.0973			1.86765			0.933823	+	0.357734i	$0.116451\pi$
$840$		0			0
$841$	7.60300	−	13.1688i	0.262172	−	0.454096i
$842$	−2.44569			−0.0842839
$843$		0			0
$844$	−7.08834	+	12.2774i	−0.243991	+	0.422605i
$845$	10.4681	−	18.1312i	0.360112	−	0.623732i
$846$		0			0
$847$	21.8930			0.752252
$848$	−20.7344	+	35.9130i	−0.712022	+	1.23326i
$849$		0			0
$850$	−0.354675	+	0.614315i	−0.0121653	+	0.0210708i
$851$	−25.9955			−0.891115
$852$		0			0
$853$	−32.9540			−1.12832			−0.564162	−	0.825664i	$-0.690801\pi$
$853$	−32.9540			−1.12832			−0.564162	+	0.825664i	$0.690801\pi$
$854$	−0.481187			−0.0164659
$855$		0			0
$856$	8.92191			0.304945
$857$	41.6199			1.42171			0.710854	−	0.703340i	$-0.248309\pi$
$857$	41.6199			1.42171			0.710854	+	0.703340i	$0.248309\pi$
$858$		0			0
$859$	26.2960			0.897208			0.448604	−	0.893731i	$-0.351921\pi$
$859$	26.2960			0.897208			0.448604	+	0.893731i	$0.351921\pi$
$860$	−12.1547	+	21.0526i	−0.414472	+	0.717887i
$861$		0			0
$862$	2.01343	−	3.48736i	0.0685777	−	0.118780i
$863$	52.7542			1.79577			0.897886	−	0.440228i	$-0.145102\pi$
$863$	52.7542			1.79577			0.897886	+	0.440228i	$0.145102\pi$
$864$		0			0
$865$	1.66398	−	2.88209i	0.0565769	−	0.0979941i
$866$	−2.44344	+	4.23216i	−0.0830314	+	0.143815i
$867$		0			0
$868$	45.6888			1.55078
$869$	−7.03903	+	12.1920i	−0.238783	+	0.413584i
$870$		0			0
$871$	6.33288			0.214582
$872$	0.960061	+	1.66287i	0.0325118	+	0.0563120i
$873$		0			0
$874$	−2.63580	+	1.70978i	−0.0891573	+	0.0578343i
$875$	−15.1727	+	26.2799i	−0.512931	+	0.888422i
$876$		0			0
$877$	−1.19699	+	2.07324i	−0.0404193	+	0.0700083i	−0.885527	−	0.464587i	$-0.846203\pi$
$877$	−1.19699	+	2.07324i	−0.0404193	+	0.0700083i	0.845108	+	0.534596i	$0.179536\pi$
$878$	3.85668			0.130157
$879$		0			0
$880$	20.6900	+	35.8361i	0.697459	+	1.20804i
$881$	−44.3808			−1.49523			−0.747613	−	0.664135i	$-0.768800\pi$
$881$	−44.3808			−1.49523			−0.747613	+	0.664135i	$0.768800\pi$
$882$		0			0
$883$	1.13232	−	1.96123i	0.0381055	−	0.0660007i	−0.846344	−	0.532637i	$-0.821201\pi$
$883$	1.13232	−	1.96123i	0.0381055	−	0.0660007i	0.884449	+	0.466637i	$0.154534\pi$
$884$	−13.7199	−	23.7636i	−0.461451	−	0.799256i
$885$		0			0
$886$	2.09198	+	3.62342i	0.0702815	+	0.121731i
$887$	35.6418			1.19673			0.598367	−	0.801223i	$-0.295817\pi$
$887$	35.6418			1.19673			0.598367	+	0.801223i	$0.295817\pi$
$888$		0			0
$889$	31.7434	+	54.9811i	1.06464	+	1.84401i
$890$	1.49327	+	2.58641i	0.0500544	+	0.0866967i
$891$		0			0
$892$	−2.40482			−0.0805192
$893$	37.7118	+	19.2395i	1.26198	+	0.643827i
$894$		0			0
$895$	−9.54838	+	16.5383i	−0.319167	+	0.552814i
$896$	−7.93679	+	13.7469i	−0.265150	+	0.459253i
$897$		0			0
$898$	4.37244			0.145910
$899$	12.3298	−	21.3559i	0.411223	−	0.712259i
$900$		0			0
$901$	−32.3036			−1.07619
$902$	−0.771469	−	1.33622i	−0.0256871	−	0.0444913i
$903$		0			0
$904$	1.05395	+	1.82550i	0.0350539	+	0.0607151i
$905$	0.788579	+	1.36586i	0.0262132	+	0.0454027i
$906$		0			0
$907$	5.62882			0.186902			0.0934509	−	0.995624i	$-0.470210\pi$
$907$	5.62882			0.186902			0.0934509	+	0.995624i	$0.470210\pi$
$908$	−8.82422	+	15.2840i	−0.292842	+	0.507217i
$909$		0			0
$910$	−3.01155	−	5.21615i	−0.0998318	−	0.172914i
$911$	−10.5622	+	18.2942i	−0.349941	+	0.606115i	−0.986239	−	0.165328i	$-0.947132\pi$
$911$	−10.5622	+	18.2942i	−0.349941	+	0.606115i	0.636298	+	0.771444i	$0.280465\pi$
$912$		0			0
$913$	−18.8239	−	32.6040i	−0.622982	−	1.07904i
$914$	0.297449	−	0.515197i	0.00983874	−	0.0170412i
$915$		0			0
$916$	−12.8740	−	22.2984i	−0.425368	−	0.736760i
$917$	−37.3877	−	64.7574i	−1.23465	−	2.13848i
$918$		0			0
$919$	−60.0424			−1.98062			−0.990308	−	0.138887i	$-0.955647\pi$
$919$	−60.0424			−1.98062			−0.990308	+	0.138887i	$0.955647\pi$
$920$	3.68495	−	6.38251i	0.121489	−	0.210425i
$921$		0			0
$922$	−2.45904			−0.0809842
$923$	−20.4789	−	35.4704i	−0.674070	−	1.16752i
$924$		0			0
$925$	4.24138	+	7.34629i	0.139456	+	0.241544i
$926$	0.129983	+	0.225137i	0.00427151	+	0.00739846i
$927$		0			0
$928$	3.21877	+	5.57507i	0.105661	+	0.183011i
$929$	−7.39631			−0.242665			−0.121333	−	0.992612i	$-0.538717\pi$
$929$	−7.39631			−0.242665			−0.121333	+	0.992612i	$0.538717\pi$
$930$		0			0
$931$	−19.7876	−	10.0951i	−0.648514	−	0.330854i
$932$	17.6563	+	30.5817i	0.578352	+	1.00174i
$933$		0			0
$934$	1.97438			0.0646036
$935$	−16.1172	+	27.9158i	−0.527089	+	0.912944i
$936$		0			0
$937$	16.6488	−	28.8365i	0.543891	−	0.942048i	−0.454784	−	0.890602i	$-0.650284\pi$
$937$	16.6488	−	28.8365i	0.543891	−	0.942048i	0.998676	−	0.0514461i	$-0.0163830\pi$
$938$	0.350929	−	0.607826i	0.0114582	−	0.0198462i
$939$		0			0
$940$	−49.3872			−1.61083
$941$	−14.0828			−0.459086			−0.229543	−	0.973299i	$-0.573723\pi$
$941$	−14.0828			−0.459086			−0.229543	+	0.973299i	$0.573723\pi$
$942$		0			0
$943$	6.22706	−	10.7856i	0.202781	−	0.351227i
$944$	−17.3490	+	30.0494i	−0.564663	+	0.978024i
$945$		0			0
$946$	1.45666	−	2.52301i	0.0473602	−	0.0820302i
$947$	−36.9882			−1.20195			−0.600977	−	0.799266i	$-0.705222\pi$
$947$	−36.9882			−1.20195			−0.600977	+	0.799266i	$0.705222\pi$
$948$		0			0
$949$	−9.87624	−	17.1061i	−0.320596	−	0.555289i
$950$	0.913233	+	0.465907i	0.0296292	+	0.0151160i
$951$		0			0
$952$	−6.11518			−0.198194
$953$	−15.5969	−	27.0147i	−0.505235	−	0.875092i	−0.999982	−	0.00605517i	$-0.998073\pi$
$953$	−15.5969	−	27.0147i	−0.505235	−	0.875092i	0.494747	−	0.869037i	$-0.335261\pi$
$954$		0			0
$955$	−7.26634	−	12.5857i	−0.235133	−	0.407263i
$956$	−6.54277	−	11.3324i	−0.211608	−	0.366516i
$957$		0			0
$958$	1.49559	+	2.59043i	0.0483202	+	0.0836930i
$959$	30.7509			0.992999
$960$		0			0
$961$	−6.54217	+	11.3314i	−0.211038	+	0.365528i
$962$	3.56117			0.114817
$963$		0			0
$964$	−7.63617	−	13.2262i	−0.245944	−	0.425988i
$965$	2.26798	+	3.92825i	0.0730088	+	0.126455i
$966$		0			0
$967$	6.86587	−	11.8920i	0.220792	−	0.382422i	−0.734257	−	0.678872i	$-0.762469\pi$
$967$	6.86587	−	11.8920i	0.220792	−	0.382422i	0.955049	+	0.296449i	$0.0958026\pi$
$968$	−1.83489	−	3.17813i	−0.0589757	−	0.102149i
$969$		0			0
$970$	−0.350363	+	0.606846i	−0.0112495	+	0.0194846i
$971$	10.0476	+	17.4030i	0.322444	+	0.558489i	0.980992	−	0.194050i	$-0.0621624\pi$
$971$	10.0476	+	17.4030i	0.322444	+	0.558489i	−0.658548	+	0.752539i	$0.728829\pi$
$972$		0			0
$973$	23.1101	−	40.0279i	0.740876	−	1.28323i
$974$	−3.46772			−0.111113
$975$		0			0
$976$	−1.82774	−	3.16573i	−0.0585044	−	0.101333i
$977$	−22.4381	−	38.8639i	−0.717858	−	1.24337i	−0.961847	−	0.273588i	$-0.911789\pi$
$977$	−22.4381	−	38.8639i	−0.717858	−	1.24337i	0.243989	−	0.969778i	$-0.421544\pi$
$978$		0			0
$979$	16.4898	+	28.5612i	0.527018	+	0.912821i
$980$	25.9138			0.827787
$981$		0			0
$982$	−0.298077	+	0.516284i	−0.00951201	+	0.0164753i
$983$	40.9255			1.30532			0.652660	−	0.757651i	$-0.273653\pi$
$983$	40.9255			1.30532			0.652660	+	0.757651i	$0.273653\pi$
$984$		0			0
$985$	1.76301	−	3.05362i	0.0561742	−	0.0972966i
$986$	−0.820685	+	1.42147i	−0.0261359	+	0.0452687i
$987$		0			0
$988$	−33.2715	+	21.5824i	−1.05851	+	0.686628i
$989$	23.5155			0.747749
$990$		0			0
$991$	−3.01999	−	5.23077i	−0.0959330	−	0.166161i	0.814065	−	0.580774i	$-0.197250\pi$
$991$	−3.01999	−	5.23077i	−0.0959330	−	0.166161i	−0.909998	+	0.414613i	$0.863917\pi$
$992$	−5.75423	−	9.96662i	−0.182697	−	0.316440i
$993$		0			0
$994$	−4.53924			−0.143976
$995$	−31.6328	−	54.7896i	−1.00283	−	1.73695i
$996$		0			0
$997$	−21.2278	−	36.7676i	−0.672291	−	1.16444i	−0.977253	−	0.212078i	$-0.931977\pi$
$997$	−21.2278	−	36.7676i	−0.672291	−	1.16444i	0.304962	−	0.952365i	$-0.401356\pi$
$998$	2.00093	−	3.46570i	0.0633382	−	0.109705i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	513.2.h.c.235.9		32
3.2	odd	2		171.2.h.c.7.8	yes	32
9.4	even	3		513.2.g.c.64.8		32
9.5	odd	6		171.2.g.c.121.9	yes	32
19.11	even	3		513.2.g.c.505.8		32
57.11	odd	6		171.2.g.c.106.9	✓	32
171.49	even	3	inner	513.2.h.c.334.9		32
171.68	odd	6		171.2.h.c.49.8	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
171.2.g.c.106.9	✓	32	57.11	odd	6
171.2.g.c.121.9	yes	32	9.5	odd	6
171.2.h.c.7.8	yes	32	3.2	odd	2
171.2.h.c.49.8	yes	32	171.68	odd	6
513.2.g.c.64.8		32	9.4	even	3
513.2.g.c.505.8		32	19.11	even	3
513.2.h.c.235.9		32	1.1	even	1	trivial
513.2.h.c.334.9		32	171.49	even	3	inner

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:	\( N \)	\(=\)	\( 513 = 3^{3} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	513.h (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q-0.146534 q^{2} -1.97853 q^{4} +(1.28502 - 2.22572i) q^{5} +(-1.73898 + 3.01201i) q^{7} +0.582990 q^{8} +O(q^{10})\)	\(q-0.146534 q^{2} -1.97853 q^{4} +(1.28502 - 2.22572i) q^{5} +(-1.73898 + 3.01201i) q^{7} +0.582990 q^{8} +(-0.188299 + 0.326143i) q^{10} +(-2.07935 + 3.60154i) q^{11} +4.59850 q^{13} +(0.254820 - 0.441362i) q^{14} +3.87163 q^{16} +(1.50797 + 2.61188i) q^{17} +(3.65690 - 2.37215i) q^{19} +(-2.54244 + 4.40364i) q^{20} +(0.304695 - 0.527748i) q^{22} +4.91882 q^{23} +(-0.802545 - 1.39005i) q^{25} -0.673837 q^{26} +(3.44063 - 5.95934i) q^{28} +(-1.85701 - 3.21644i) q^{29} +(3.31980 + 5.75007i) q^{31} -1.73330 q^{32} +(-0.220969 - 0.382729i) q^{34} +(4.46925 + 7.74097i) q^{35} -5.28491 q^{37} +(-0.535860 + 0.347600i) q^{38} +(0.749153 - 1.29757i) q^{40} +(1.26597 - 2.19272i) q^{41} +4.78072 q^{43} +(4.11405 - 7.12574i) q^{44} -0.720775 q^{46} +(4.85627 + 8.41131i) q^{47} +(-2.54812 - 4.41348i) q^{49} +(0.117600 + 0.203689i) q^{50} -9.09827 q^{52} +(-5.35547 + 9.27595i) q^{53} +(5.34400 + 9.25609i) q^{55} +(-1.01381 + 1.75597i) q^{56} +(0.272116 + 0.471318i) q^{58} +(-4.48107 + 7.76144i) q^{59} +(-0.472085 - 0.817675i) q^{61} +(-0.486464 - 0.842580i) q^{62} -7.48927 q^{64} +(5.90916 - 10.2350i) q^{65} +1.37716 q^{67} +(-2.98356 - 5.16768i) q^{68} +(-0.654897 - 1.13432i) q^{70} +(-4.45338 - 7.71347i) q^{71} +(-2.14771 - 3.71994i) q^{73} +0.774420 q^{74} +(-7.23528 + 4.69336i) q^{76} +(-7.23190 - 12.5260i) q^{77} +3.38521 q^{79} +(4.97511 - 8.61715i) q^{80} +(-0.185507 + 0.321308i) q^{82} +(-4.52640 + 7.83996i) q^{83} +7.75108 q^{85} -0.700538 q^{86} +(-1.21224 + 2.09966i) q^{88} +(3.96515 - 6.86783i) q^{89} +(-7.99672 + 13.8507i) q^{91} -9.73202 q^{92} +(-0.711609 - 1.23254i) q^{94} +(-0.580542 - 11.1875i) q^{95} +1.86067 q^{97} +(0.373387 + 0.646725i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 2 q^{2} + 34 q^{4} - 3 q^{5} + q^{7} + 36 q^{8}+O(q^{10}) \) 32 * q + 2 * q^2 + 34 * q^4 - 3 * q^5 + q^7 + 36 * q^8	\( 32 q + 2 q^{2} + 34 q^{4} - 3 q^{5} + q^{7} + 36 q^{8} - 8 q^{10} - 7 q^{11} + 8 q^{13} - q^{14} + 22 q^{16} + 7 q^{17} + 7 q^{19} + 3 q^{20} - 8 q^{22} + 10 q^{23} - 9 q^{25} + 4 q^{26} - 10 q^{28} - 10 q^{29} - 10 q^{31} + 34 q^{32} - 13 q^{34} + 3 q^{35} + 2 q^{37} + 46 q^{38} + 12 q^{40} - 6 q^{41} - 14 q^{43} - 20 q^{44} + 9 q^{47} - 13 q^{49} - q^{50} - 38 q^{52} - 16 q^{53} + 15 q^{55} + 6 q^{56} - 37 q^{59} - 12 q^{61} - 54 q^{62} - 64 q^{64} - 54 q^{65} + 22 q^{67} + 2 q^{68} + 24 q^{70} - 9 q^{71} - 10 q^{73} + 12 q^{74} - 40 q^{76} - 46 q^{77} + 16 q^{79} + 24 q^{80} + 7 q^{82} - 3 q^{83} + 54 q^{85} + 34 q^{86} + 9 q^{88} - 30 q^{89} - q^{91} - 34 q^{92} - 18 q^{94} - 3 q^{95} - 18 q^{98}+O(q^{100}) \) 32 * q + 2 * q^2 + 34 * q^4 - 3 * q^5 + q^7 + 36 * q^8 - 8 * q^10 - 7 * q^11 + 8 * q^13 - q^14 + 22 * q^16 + 7 * q^17 + 7 * q^19 + 3 * q^20 - 8 * q^22 + 10 * q^23 - 9 * q^25 + 4 * q^26 - 10 * q^28 - 10 * q^29 - 10 * q^31 + 34 * q^32 - 13 * q^34 + 3 * q^35 + 2 * q^37 + 46 * q^38 + 12 * q^40 - 6 * q^41 - 14 * q^43 - 20 * q^44 + 9 * q^47 - 13 * q^49 - q^50 - 38 * q^52 - 16 * q^53 + 15 * q^55 + 6 * q^56 - 37 * q^59 - 12 * q^61 - 54 * q^62 - 64 * q^64 - 54 * q^65 + 22 * q^67 + 2 * q^68 + 24 * q^70 - 9 * q^71 - 10 * q^73 + 12 * q^74 - 40 * q^76 - 46 * q^77 + 16 * q^79 + 24 * q^80 + 7 * q^82 - 3 * q^83 + 54 * q^85 + 34 * q^86 + 9 * q^88 - 30 * q^89 - q^91 - 34 * q^92 - 18 * q^94 - 3 * q^95 - 18 * q^98

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