LMFDB - Embedded newform 784.2.bg.a.65.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [784,2,Mod(65,784)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(784, base_ring=CyclotomicField(42))

chi = DirichletCharacter(H, H._module([0, 0, 20]))

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

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

chi := DirichletCharacter("784.65");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 784 = 2^{4} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	784.bg (of order $21$, degree $12$, 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:	$6.26027151847$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$2$ over $\Q(\zeta_{21})$
Twist minimal:	no (minimal twist has level 98)
Sato-Tate group:	$\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label			65.2
Character	$\chi$	$=$	784.65
Dual form			784.2.bg.a.193.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.250133 + 3.33779i) q^{3} +(-1.09780 + 0.748464i) q^{5} +(-2.60370 - 0.469838i) q^{7} +(-8.11181 + 1.22266i) q^{9} +O(q^{10})$	\(q+(0.250133 + 3.33779i) q^{3} +(-1.09780 + 0.748464i) q^{5} +(-2.60370 - 0.469838i) q^{7} +(-8.11181 + 1.22266i) q^{9} +(-0.295564 - 0.0445491i) q^{11} +(3.39549 - 4.25781i) q^{13} +(-2.77281 - 3.47700i) q^{15} +(-0.690967 + 0.213135i) q^{17} +(-1.81038 + 3.13567i) q^{19} +(0.916952 - 8.80813i) q^{21} +(-2.13330 - 0.658036i) q^{23} +(-1.18175 + 3.01105i) q^{25} +(-3.87558 - 16.9800i) q^{27} +(-0.535518 + 2.34626i) q^{29} +(-3.38607 - 5.86484i) q^{31} +(0.0747654 - 0.997674i) q^{33} +(3.20999 - 1.43299i) q^{35} +(0.514508 + 0.477393i) q^{37} +(15.0610 + 10.2684i) q^{39} +(0.720062 + 0.346764i) q^{41} +(-0.726755 + 0.349987i) q^{43} +(7.98999 - 7.41362i) q^{45} +(2.20031 + 5.60630i) q^{47} +(6.55850 + 2.44664i) q^{49} +(-0.884235 - 2.25299i) q^{51} +(-5.76259 + 5.34691i) q^{53} +(0.357812 - 0.172313i) q^{55} +(-10.9191 - 5.25834i) q^{57} +(-2.55068 - 1.73903i) q^{59} +(-2.39548 - 2.22268i) q^{61} +(21.6952 + 0.627804i) q^{63} +(-0.540735 + 7.21560i) q^{65} +(-2.72892 - 4.72662i) q^{67} +(1.66278 - 7.28511i) q^{69} +(1.75840 + 7.70404i) q^{71} +(-2.41794 + 6.16080i) q^{73} +(-10.3459 - 3.19127i) q^{75} +(0.748629 + 0.254860i) q^{77} +(5.31472 - 9.20536i) q^{79} +(32.1894 - 9.92912i) q^{81} +(-3.86302 - 4.84407i) q^{83} +(0.599016 - 0.751143i) q^{85} +(-7.96527 - 1.20057i) q^{87} +(-13.2822 + 2.00198i) q^{89} +(-10.8413 + 9.49072i) q^{91} +(18.7287 - 12.7690i) q^{93} +(-0.359510 - 4.79733i) q^{95} -18.0790 q^{97} +2.45203 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 7 q^{3} - 33 q^{9}+O(q^{10}) $ 24 * q - 7 * q^3 - 33 * q^9	$ 24 q - 7 q^{3} - 33 q^{9} + 7 q^{11} + 14 q^{13} + 7 q^{15} - 7 q^{17} + 7 q^{21} + 21 q^{23} + 4 q^{25} + 35 q^{27} - 11 q^{29} - 28 q^{31} + 14 q^{33} - 21 q^{35} - 24 q^{37} + 40 q^{39} + 28 q^{41} - 10 q^{43} + 7 q^{45} + 70 q^{47} + 84 q^{49} - 60 q^{51} + 26 q^{53} - 56 q^{55} - 33 q^{57} + 7 q^{59} + 14 q^{61} + 14 q^{63} + 36 q^{67} - 35 q^{69} - 7 q^{73} + 28 q^{75} - 91 q^{77} + 26 q^{79} + 55 q^{81} + 7 q^{83} + 49 q^{85} - 35 q^{87} - 56 q^{89} - 7 q^{91} + 72 q^{93} + 14 q^{95} - 126 q^{97} + 14 q^{99}+O(q^{100}) $ 24 * q - 7 * q^3 - 33 * q^9 + 7 * q^11 + 14 * q^13 + 7 * q^15 - 7 * q^17 + 7 * q^21 + 21 * q^23 + 4 * q^25 + 35 * q^27 - 11 * q^29 - 28 * q^31 + 14 * q^33 - 21 * q^35 - 24 * q^37 + 40 * q^39 + 28 * q^41 - 10 * q^43 + 7 * q^45 + 70 * q^47 + 84 * q^49 - 60 * q^51 + 26 * q^53 - 56 * q^55 - 33 * q^57 + 7 * q^59 + 14 * q^61 + 14 * q^63 + 36 * q^67 - 35 * q^69 - 7 * q^73 + 28 * q^75 - 91 * q^77 + 26 * q^79 + 55 * q^81 + 7 * q^83 + 49 * q^85 - 35 * q^87 - 56 * q^89 - 7 * q^91 + 72 * q^93 + 14 * q^95 - 126 * q^97 + 14 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/784\mathbb{Z}\right)^\times$.

$n$	$197$	$687$	$689$
$\chi(n)$	$1$	$1$	$e\left(\frac{10}{21}\right)$

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
$3$	0.250133	+	3.33779i	0.144414	+	1.92708i	0.329131	+	0.944284i	$0.393244\pi$
$3$	0.250133	+	3.33779i	0.144414	+	1.92708i	−0.184717	+	0.982792i	$0.559137\pi$
$4$		0			0
$5$	−1.09780	+	0.748464i	−0.490949	+	0.334723i	−0.783359	−	0.621570i	$-0.786495\pi$
$5$	−1.09780	+	0.748464i	−0.490949	+	0.334723i	0.292410	+	0.956293i	$0.405543\pi$
$6$		0			0
$7$	−2.60370	−	0.469838i	−0.984106	−	0.177582i
$7$	−2.60370	−	0.469838i	−0.984106	−	0.177582i
$8$		0			0
$9$	−8.11181	+	1.22266i	−2.70394	+	0.407553i
$10$		0			0
$11$	−0.295564	−	0.0445491i	−0.0891159	−	0.0134321i	0.104333	−	0.994542i	$-0.466729\pi$
$11$	−0.295564	−	0.0445491i	−0.0891159	−	0.0134321i	−0.193449	+	0.981110i	$0.561967\pi$
$12$		0			0
$13$	3.39549	−	4.25781i	0.941739	−	1.18090i	−0.0416023	−	0.999134i	$-0.513246\pi$
$13$	3.39549	−	4.25781i	0.941739	−	1.18090i	0.983341	−	0.181769i	$-0.0581823\pi$
$14$		0			0
$15$	−2.77281	−	3.47700i	−0.715937	−	0.897757i
$16$		0			0
$17$	−0.690967	+	0.213135i	−0.167584	+	0.0516929i	−0.377412	−	0.926046i	$-0.623186\pi$
$17$	−0.690967	+	0.213135i	−0.167584	+	0.0516929i	0.209828	+	0.977738i	$0.432710\pi$
$18$		0			0
$19$	−1.81038	+	3.13567i	−0.415330	+	0.719372i	−0.995463	−	0.0951493i	$-0.969667\pi$
$19$	−1.81038	+	3.13567i	−0.415330	+	0.719372i	0.580133	+	0.814522i	$0.303000\pi$
$20$		0			0
$21$	0.916952	−	8.80813i	0.200095	−	1.92209i
$22$		0			0
$23$	−2.13330	−	0.658036i	−0.444824	−	0.137210i	0.0642482	−	0.997934i	$-0.479535\pi$
$23$	−2.13330	−	0.658036i	−0.444824	−	0.137210i	−0.509072	+	0.860724i	$0.670011\pi$
$24$		0			0
$25$	−1.18175	+	3.01105i	−0.236350	+	0.602210i
$26$		0			0
$27$	−3.87558	−	16.9800i	−0.745855	−	3.26780i
$28$		0			0
$29$	−0.535518	+	2.34626i	−0.0994432	+	0.435689i	0.900556	+	0.434739i	$0.143159\pi$
$29$	−0.535518	+	2.34626i	−0.0994432	+	0.435689i	−1.00000		0.000949836i	$0.999698\pi$
$30$		0			0
$31$	−3.38607	−	5.86484i	−0.608156	−	1.05336i	−0.991544	−	0.129769i	$-0.958576\pi$
$31$	−3.38607	−	5.86484i	−0.608156	−	1.05336i	0.383389	−	0.923587i	$-0.374757\pi$
$32$		0			0
$33$	0.0747654	−	0.997674i	0.0130150	−	0.173673i
$34$		0			0
$35$	3.20999	−	1.43299i	0.542587	−	0.242219i
$36$		0			0
$37$	0.514508	+	0.477393i	0.0845845	+	0.0784830i	0.721332	−	0.692589i	$-0.243530\pi$
$37$	0.514508	+	0.477393i	0.0845845	+	0.0784830i	−0.636748	+	0.771072i	$0.719721\pi$
$38$		0			0
$39$	15.0610	+	10.2684i	2.41169	+	1.64426i
$40$		0			0
$41$	0.720062	+	0.346764i	0.112455	+	0.0541554i	0.489265	−	0.872135i	$-0.337265\pi$
$41$	0.720062	+	0.346764i	0.112455	+	0.0541554i	−0.376811	+	0.926290i	$0.622979\pi$
$42$		0			0
$43$	−0.726755	+	0.349987i	−0.110829	+	0.0533725i	−0.488477	−	0.872577i	$-0.662447\pi$
$43$	−0.726755	+	0.349987i	−0.110829	+	0.0533725i	0.377648	+	0.925949i	$0.376733\pi$
$44$		0			0
$45$	7.98999	−	7.41362i	1.19108	−	1.10516i
$46$		0			0
$47$	2.20031	+	5.60630i	0.320949	+	0.817764i	0.996741	+	0.0806714i	$0.0257064\pi$
$47$	2.20031	+	5.60630i	0.320949	+	0.817764i	−0.675792	+	0.737092i	$0.736198\pi$
$48$		0			0
$49$	6.55850	+	2.44664i	0.936929	+	0.349519i
$50$		0			0
$51$	−0.884235	−	2.25299i	−0.123818	−	0.315482i
$52$		0			0
$53$	−5.76259	+	5.34691i	−0.791553	+	0.734454i	−0.968297	−	0.249803i	$-0.919634\pi$
$53$	−5.76259	+	5.34691i	−0.791553	+	0.734454i	0.176744	+	0.984257i	$0.443444\pi$
$54$		0			0
$55$	0.357812	−	0.172313i	0.0482474	−	0.0232347i
$56$		0			0
$57$	−10.9191	−	5.25834i	−1.44626	−	0.696484i
$58$		0			0
$59$	−2.55068	−	1.73903i	−0.332071	−	0.226402i	0.385793	−	0.922585i	$-0.373928\pi$
$59$	−2.55068	−	1.73903i	−0.332071	−	0.226402i	−0.717864	+	0.696183i	$0.754880\pi$
$60$		0			0
$61$	−2.39548	−	2.22268i	−0.306710	−	0.284585i	0.511768	−	0.859124i	$-0.328991\pi$
$61$	−2.39548	−	2.22268i	−0.306710	−	0.284585i	−0.818477	+	0.574539i	$0.805181\pi$
$62$		0			0
$63$	21.6952	+	0.627804i	2.73333	+	0.0790959i
$64$		0			0
$65$	−0.540735	+	7.21560i	−0.0670699	+	0.894985i
$66$		0			0
$67$	−2.72892	−	4.72662i	−0.333390	−	0.577449i	0.649784	−	0.760119i	$-0.274859\pi$
$67$	−2.72892	−	4.72662i	−0.333390	−	0.577449i	−0.983174	+	0.182670i	$0.941526\pi$
$68$		0			0
$69$	1.66278	−	7.28511i	0.200175	−	0.877024i
$70$		0			0
$71$	1.75840	+	7.70404i	0.208683	+	0.914302i	0.965444	+	0.260610i	$0.0839236\pi$
$71$	1.75840	+	7.70404i	0.208683	+	0.914302i	−0.756761	+	0.653692i	$0.773219\pi$
$72$		0			0
$73$	−2.41794	+	6.16080i	−0.282998	+	0.721067i	0.716721	+	0.697360i	$0.245642\pi$
$73$	−2.41794	+	6.16080i	−0.282998	+	0.721067i	−0.999719	+	0.0237069i	$0.992453\pi$
$74$		0			0
$75$	−10.3459	−	3.19127i	−1.19464	−	0.368496i
$76$		0			0
$77$	0.748629	+	0.254860i	0.0853142	+	0.0290440i
$78$		0			0
$79$	5.31472	−	9.20536i	0.597953	−	1.03568i	−0.395170	−	0.918608i	$-0.629314\pi$
$79$	5.31472	−	9.20536i	0.597953	−	1.03568i	0.993123	−	0.117076i	$-0.0373522\pi$
$80$		0			0
$81$	32.1894	−	9.92912i	3.57660	−	1.10324i
$82$		0			0
$83$	−3.86302	−	4.84407i	−0.424021	−	0.531706i	0.523233	−	0.852190i	$-0.324726\pi$
$83$	−3.86302	−	4.84407i	−0.424021	−	0.531706i	−0.947254	+	0.320484i	$0.896154\pi$
$84$		0			0
$85$	0.599016	−	0.751143i	0.0649724	−	0.0814729i
$86$		0			0
$87$	−7.96527	−	1.20057i	−0.853967	−	0.128715i
$88$		0			0
$89$	−13.2822	+	2.00198i	−1.40791	+	0.212209i	−0.808625	−	0.588324i	$-0.799788\pi$
$89$	−13.2822	+	2.00198i	−1.40791	+	0.212209i	−0.599289	+	0.800533i	$0.704550\pi$
$90$		0			0
$91$	−10.8413	+	9.49072i	−1.13648	+	0.994898i
$92$		0			0
$93$	18.7287	−	12.7690i	1.94207	−	1.32408i
$94$		0			0
$95$	−0.359510	−	4.79733i	−0.0368850	−	0.492196i
$96$		0			0
$97$	−18.0790			−1.83565			−0.917824	−	0.396987i	$-0.870056\pi$
$97$	−18.0790			−1.83565			−0.917824	+	0.396987i	$0.870056\pi$
$98$		0			0
$99$	2.45203			0.246438
$100$		0			0
$101$	−0.872755	−	11.6461i	−0.0868423	−	1.15883i	−0.855020	−	0.518594i	$-0.826456\pi$
$101$	−0.872755	−	11.6461i	−0.0868423	−	1.15883i	0.768178	−	0.640236i	$-0.221164\pi$
$102$		0			0
$103$	−2.35344	+	1.60454i	−0.231891	+	0.158101i	−0.673691	−	0.739013i	$-0.735292\pi$
$103$	−2.35344	+	1.60454i	−0.231891	+	0.158101i	0.441801	+	0.897113i	$0.354340\pi$
$104$		0			0
$105$	5.58595	+	10.3558i	0.545132	+	1.01063i
$106$		0			0
$107$	−13.1785	+	1.98634i	−1.27401	+	0.192027i	−0.751003	−	0.660299i	$-0.770430\pi$
$107$	−13.1785	+	1.98634i	−1.27401	+	0.192027i	−0.523012	+	0.852325i	$0.675192\pi$
$108$		0			0
$109$	−4.98637	−	0.751575i	−0.477608	−	0.0719878i	−0.0941733	−	0.995556i	$-0.530021\pi$
$109$	−4.98637	−	0.751575i	−0.477608	−	0.0719878i	−0.383435	+	0.923568i	$0.625259\pi$
$110$		0			0
$111$	−1.46474	+	1.83673i	−0.139027	+	0.174335i
$112$		0			0
$113$	11.7224	+	14.6995i	1.10275	+	1.38281i	0.916370	+	0.400332i	$0.131105\pi$
$113$	11.7224	+	14.6995i	1.10275	+	1.38281i	0.186384	+	0.982477i	$0.440323\pi$
$114$		0			0
$115$	2.83444	−	0.874310i	0.264313	−	0.0815298i
$116$		0			0
$117$	−22.3377	+	38.6900i	−2.06512	+	3.57689i
$118$		0			0
$119$	1.89921	−	0.230297i	0.174100	−	0.0211113i
$120$		0			0
$121$	−10.4259	−	3.21597i	−0.947812	−	0.292361i
$122$		0			0
$123$	−0.977314	+	2.49016i	−0.0881215	+	0.224530i
$124$		0			0
$125$	−2.43462	−	10.6668i	−0.217759	−	0.954066i
$126$		0			0
$127$	−3.08483	+	13.5155i	−0.273735	+	1.19931i	0.631832	+	0.775105i	$0.282303\pi$
$127$	−3.08483	+	13.5155i	−0.273735	+	1.19931i	−0.905567	+	0.424204i	$0.860554\pi$
$128$		0			0
$129$	−1.34997	−	2.33822i	−0.118858	−	0.205868i
$130$		0			0
$131$	−0.498173	+	6.64766i	−0.0435256	+	0.580809i	0.932219	+	0.361895i	$0.117870\pi$
$131$	−0.498173	+	6.64766i	−0.0435256	+	0.580809i	−0.975744	+	0.218913i	$0.929749\pi$
$132$		0			0
$133$	6.18695	−	7.31376i	0.536476	−	0.634183i
$134$		0			0
$135$	16.9635	+	15.7398i	1.45999	+	1.35467i
$136$		0			0
$137$	−2.62144	−	1.78727i	−0.223965	−	0.152697i	0.446140	−	0.894963i	$-0.352798\pi$
$137$	−2.62144	−	1.78727i	−0.223965	−	0.152697i	−0.670105	+	0.742267i	$0.733751\pi$
$138$		0			0
$139$	14.0754	+	6.77834i	1.19386	+	0.574931i	0.921919	−	0.387384i	$-0.126621\pi$
$139$	14.0754	+	6.77834i	1.19386	+	0.574931i	0.271938	+	0.962315i	$0.412335\pi$
$140$		0			0
$141$	−18.1623	+	8.74651i	−1.52954	+	0.736589i
$142$		0			0
$143$	−1.19327	+	1.10719i	−0.0997858	+	0.0925877i
$144$		0			0
$145$	−1.16820	−	2.97653i	−0.0970138	−	0.247187i
$146$		0			0
$147$	−6.52587	+	22.5029i	−0.538245	+	1.85601i
$148$		0			0
$149$	8.29101	+	21.1251i	0.679226	+	1.73064i	0.682758	+	0.730645i	$0.260780\pi$
$149$	8.29101	+	21.1251i	0.679226	+	1.73064i	−0.00353200	+	0.999994i	$0.501124\pi$
$150$		0			0
$151$	−8.37807	+	7.77372i	−0.681798	+	0.632616i	−0.943049	−	0.332655i	$-0.892056\pi$
$151$	−8.37807	+	7.77372i	−0.681798	+	0.632616i	0.261251	+	0.965271i	$0.415865\pi$
$152$		0			0
$153$	5.34440	−	2.57373i	0.432069	−	0.208074i
$154$		0			0
$155$	8.10683	+	3.90404i	0.651156	+	0.313580i
$156$		0			0
$157$	−3.24073	−	2.20949i	−0.258638	−	0.176337i	0.427058	−	0.904224i	$-0.359550\pi$
$157$	−3.24073	−	2.20949i	−0.258638	−	0.176337i	−0.685697	+	0.727888i	$0.740502\pi$
$158$		0			0
$159$	−19.2883	−	17.8969i	−1.52966	−	1.41932i
$160$		0			0
$161$	5.24530	+	2.71563i	0.413388	+	0.214022i
$162$		0			0
$163$	−0.302107	+	4.03134i	−0.0236629	+	0.315759i	0.972795	+	0.231667i	$0.0744180\pi$
$163$	−0.302107	+	4.03134i	−0.0236629	+	0.315759i	−0.996458	+	0.0840919i	$0.973201\pi$
$164$		0			0
$165$	0.664646	+	1.15120i	0.0517426	+	0.0896209i
$166$		0			0
$167$	−1.64323	+	7.19945i	−0.127157	+	0.557110i	0.870708	+	0.491800i	$0.163661\pi$
$167$	−1.64323	+	7.19945i	−0.127157	+	0.557110i	−0.997865	+	0.0653101i	$0.979196\pi$
$168$		0			0
$169$	−3.70681	−	16.2406i	−0.285139	−	1.24928i
$170$		0			0
$171$	10.8516	−	27.6494i	0.829843	−	2.11441i
$172$		0			0
$173$	3.85238	+	1.18830i	0.292891	+	0.0903449i	0.437719	−	0.899112i	$-0.355787\pi$
$173$	3.85238	+	1.18830i	0.292891	+	0.0903449i	−0.144828	+	0.989457i	$0.546263\pi$
$174$		0			0
$175$	4.49163	−	7.28463i	0.339535	−	0.550667i
$176$		0			0
$177$	5.16650	−	8.94865i	0.388338	−	0.672621i
$178$		0			0
$179$	13.6820	−	4.22034i	1.02264	−	0.315443i	0.262314	−	0.964983i	$-0.415514\pi$
$179$	13.6820	−	4.22034i	1.02264	−	0.315443i	0.760328	+	0.649539i	$0.225038\pi$
$180$		0			0
$181$	−0.722086	−	0.905468i	−0.0536723	−	0.0673029i	0.754271	−	0.656563i	$-0.227991\pi$
$181$	−0.722086	−	0.905468i	−0.0536723	−	0.0673029i	−0.807943	+	0.589261i	$0.799419\pi$
$182$		0			0
$183$	6.81966	−	8.55158i	0.504124	−	0.632151i
$184$		0			0
$185$	−0.922136	−	0.138990i	−0.0677968	−	0.0102187i
$186$		0			0
$187$	0.213720	−	0.0322131i	0.0156287	−	0.00235565i
$188$		0			0
$189$	2.11298	+	46.0317i	0.153696	+	3.34832i
$190$		0			0
$191$	5.77864	−	3.93981i	0.418128	−	0.285075i	−0.335925	−	0.941889i	$-0.609049\pi$
$191$	5.77864	−	3.93981i	0.418128	−	0.285075i	0.754053	+	0.656814i	$0.228096\pi$
$192$		0			0
$193$	−0.129054	−	1.72211i	−0.00928951	−	0.123960i	0.990631	−	0.136566i	$-0.0436064\pi$
$193$	−0.129054	−	1.72211i	−0.00928951	−	0.123960i	−0.999921	+	0.0126057i	$0.995987\pi$
$194$		0			0
$195$	−24.2194			−1.73439
$196$		0			0
$197$	10.3457			0.737101			0.368550	−	0.929608i	$-0.379854\pi$
$197$	10.3457			0.737101			0.368550	+	0.929608i	$0.379854\pi$
$198$		0			0
$199$	−0.139778	−	1.86521i	−0.00990859	−	0.132221i	0.990056	−	0.140676i	$-0.0449276\pi$
$199$	−0.139778	−	1.86521i	−0.00990859	−	0.132221i	−0.999964	+	0.00845524i	$0.997309\pi$
$200$		0			0
$201$	15.0939	−	10.2908i	1.06464	−	0.725860i
$202$		0			0
$203$	2.49669	−	5.85734i	0.175233	−	0.411105i
$204$		0			0
$205$	−1.05002	+	0.158265i	−0.0733367	+	0.0110537i
$206$		0			0
$207$	18.1095	+	2.72956i	1.25869	+	0.189718i
$208$		0			0
$209$	0.674774	−	0.846140i	0.0466751	−	0.0585288i
$210$		0			0
$211$	−4.26780	−	5.35165i	−0.293808	−	0.368423i	0.612916	−	0.790148i	$-0.289996\pi$
$211$	−4.26780	−	5.35165i	−0.293808	−	0.368423i	−0.906724	+	0.421725i	$0.861425\pi$
$212$		0			0
$213$	−25.2747	+	7.79620i	−1.73179	+	0.534187i
$214$		0			0
$215$	0.535876	−	0.928164i	0.0365464	−	0.0633003i
$216$		0			0
$217$	6.06077	+	16.8612i	0.411432	+	1.14461i
$218$		0			0
$219$	−21.1683	−	6.52955i	−1.43042	−	0.441226i
$220$		0			0
$221$	−1.43868	+	3.66570i	−0.0967762	+	0.246582i
$222$		0			0
$223$	−5.74434	−	25.1676i	−0.384669	−	1.68535i	−0.682626	−	0.730768i	$-0.739162\pi$
$223$	−5.74434	−	25.1676i	−0.384669	−	1.68535i	0.297957	−	0.954579i	$-0.403695\pi$
$224$		0			0
$225$	5.90464	−	25.8699i	0.393643	−	1.72466i
$226$		0			0
$227$	13.0700	+	22.6379i	0.867485	+	1.50253i	0.864559	+	0.502532i	$0.167598\pi$
$227$	13.0700	+	22.6379i	0.867485	+	1.50253i	0.00292604	+	0.999996i	$0.499069\pi$
$228$		0			0
$229$	0.944682	−	12.6059i	0.0624263	−	0.833022i	−0.874841	−	0.484410i	$-0.839034\pi$
$229$	0.944682	−	12.6059i	0.0624263	−	0.833022i	0.937267	−	0.348611i	$-0.113347\pi$
$230$		0			0
$231$	−0.663412	+	2.56252i	−0.0436493	+	0.168601i
$232$		0			0
$233$	16.0492	+	14.8915i	1.05142	+	0.975574i	0.999733	−	0.0230892i	$-0.00735016\pi$
$233$	16.0492	+	14.8915i	1.05142	+	0.975574i	0.0516856	+	0.998663i	$0.483541\pi$
$234$		0			0
$235$	−6.61161	−	4.50772i	−0.431294	−	0.294051i
$236$		0			0
$237$	32.0550	+	15.4369i	2.08219	+	1.00273i
$238$		0			0
$239$	−13.6184	+	6.55827i	−0.880901	+	0.424219i	−0.818953	−	0.573860i	$-0.805445\pi$
$239$	−13.6184	+	6.55827i	−0.880901	+	0.424219i	−0.0619472	+	0.998079i	$0.519731\pi$
$240$		0			0
$241$	−13.0704	+	12.1276i	−0.841938	+	0.781204i	−0.977804	−	0.209523i	$-0.932809\pi$
$241$	−13.0704	+	12.1276i	−0.841938	+	0.781204i	0.135866	+	0.990727i	$0.456618\pi$
$242$		0			0
$243$	22.1039	+	56.3198i	1.41797	+	3.61292i
$244$		0			0
$245$	−9.03111	+	2.22290i	−0.576977	+	0.142016i
$246$		0			0
$247$	7.20396	+	18.3554i	0.458377	+	1.16793i
$248$		0			0
$249$	15.2022	−	14.1056i	0.963403	−	0.893907i
$250$		0			0
$251$	14.2489	−	6.86193i	0.899385	−	0.433121i	0.0737185	−	0.997279i	$-0.476513\pi$
$251$	14.2489	−	6.86193i	0.899385	−	0.433121i	0.825667	+	0.564158i	$0.190799\pi$
$252$		0			0
$253$	0.601211	+	0.289528i	0.0377978	+	0.0182025i
$254$		0			0
$255$	2.65699	+	1.81151i	0.166387	+	0.113441i
$256$		0			0
$257$	15.0904	+	14.0018i	0.941310	+	0.873408i	0.992119	−	0.125300i	$-0.0399894\pi$
$257$	15.0904	+	14.0018i	0.941310	+	0.873408i	−0.0508087	+	0.998708i	$0.516180\pi$
$258$		0			0
$259$	−1.11533	−	1.48472i	−0.0693030	−	0.0922563i
$260$		0			0
$261$	1.47535	−	19.6871i	0.0913217	−	1.21860i
$262$		0			0
$263$	9.10450	+	15.7695i	0.561408	+	0.972387i	0.997374	+	0.0724238i	$0.0230734\pi$
$263$	9.10450	+	15.7695i	0.561408	+	0.972387i	−0.435966	+	0.899963i	$0.643593\pi$
$264$		0			0
$265$	2.32418	−	10.1829i	0.142773	−	0.625531i
$266$		0			0
$267$	−10.0045	−	43.8326i	−0.612266	−	2.68251i
$268$		0			0
$269$	2.81799	−	7.18013i	0.171816	−	0.437780i	−0.818864	−	0.573987i	$-0.805396\pi$
$269$	2.81799	−	7.18013i	0.171816	−	0.437780i	0.990680	+	0.136207i	$0.0434912\pi$
$270$		0			0
$271$	10.2742	+	3.16917i	0.624113	+	0.192513i	0.590652	−	0.806927i	$-0.298871\pi$
$271$	10.2742	+	3.16917i	0.624113	+	0.192513i	0.0334614	+	0.999440i	$0.489347\pi$
$272$		0			0
$273$	−34.3898	−	33.8121i	−2.08137	−	2.04640i
$274$		0			0
$275$	0.483422	−	0.837311i	0.0291514	−	0.0504918i
$276$		0			0
$277$	2.19322	−	0.676520i	0.131778	−	0.0406481i	−0.228165	−	0.973623i	$-0.573272\pi$
$277$	2.19322	−	0.676520i	0.131778	−	0.0406481i	0.359943	+	0.932974i	$0.382796\pi$
$278$		0			0
$279$	34.6378	+	43.4344i	2.07371	+	2.60035i
$280$		0			0
$281$	−13.3488	+	16.7389i	−0.796323	+	0.998557i	0.203487	+	0.979078i	$0.434772\pi$
$281$	−13.3488	+	16.7389i	−0.796323	+	0.998557i	−0.999810	+	0.0194799i	$0.993799\pi$
$282$		0			0
$283$	−2.39691	−	0.361276i	−0.142482	−	0.0214757i	0.0774141	−	0.996999i	$-0.475334\pi$
$283$	−2.39691	−	0.361276i	−0.142482	−	0.0214757i	−0.219896	+	0.975523i	$0.570572\pi$
$284$		0			0
$285$	15.9226	−	2.39994i	0.943172	−	0.142160i
$286$		0			0
$287$	−1.71190	−	1.24118i	−0.101050	−	0.0732646i
$288$		0			0
$289$	−13.6141	+	9.28190i	−0.800826	+	0.545994i
$290$		0			0
$291$	−4.52217	−	60.3441i	−0.265094	−	3.53743i
$292$		0			0
$293$	5.69907			0.332943			0.166472	−	0.986046i	$-0.446763\pi$
$293$	5.69907			0.332943			0.166472	+	0.986046i	$0.446763\pi$
$294$		0			0
$295$	4.10173			0.238812
$296$		0			0
$297$	0.389036	+	5.19133i	0.0225742	+	0.301232i
$298$		0			0
$299$	−10.0454	+	6.84883i	−0.580940	+	0.396078i
$300$		0			0
$301$	2.05669	−	0.569803i	0.118546	−	0.0328429i
$302$		0			0
$303$	38.6540	−	5.82615i	2.22061	−	0.334704i
$304$		0			0
$305$	4.29334	+	0.647117i	0.245836	+	0.0370538i
$306$		0			0
$307$	14.9873	−	18.7935i	0.855372	−	1.07260i	−0.141209	−	0.989980i	$-0.545099\pi$
$307$	14.9873	−	18.7935i	0.855372	−	1.07260i	0.996581	−	0.0826223i	$-0.0263295\pi$
$308$		0			0
$309$	−5.94431	−	7.45393i	−0.338160	−	0.424039i
$310$		0			0
$311$	−24.7753	+	7.64217i	−1.40488	+	0.433348i	−0.902272	−	0.431167i	$-0.858102\pi$
$311$	−24.7753	+	7.64217i	−1.40488	+	0.433348i	−0.502607	+	0.864515i	$0.667626\pi$
$312$		0			0
$313$	8.12788	−	14.0779i	0.459415	−	0.795730i	−0.539515	−	0.841976i	$-0.681392\pi$
$313$	8.12788	−	14.0779i	0.459415	−	0.795730i	0.998930	+	0.0462456i	$0.0147257\pi$
$314$		0			0
$315$	−24.2867	+	15.5488i	−1.36840	+	0.876078i
$316$		0			0
$317$	−18.8965	−	5.82880i	−1.06133	−	0.327378i	−0.285541	−	0.958367i	$-0.592173\pi$
$317$	−18.8965	−	5.82880i	−1.06133	−	0.327378i	−0.775792	+	0.630989i	$0.782649\pi$
$318$		0			0
$319$	0.262803	−	0.669612i	0.0147142	−	0.0374911i
$320$		0			0
$321$	−9.92638	−	43.4903i	−0.554036	−	2.42739i
$322$		0			0
$323$	0.582592	−	2.55250i	0.0324163	−	0.142025i
$324$		0			0
$325$	8.80785	+	15.2556i	0.488572	+	0.846231i
$326$		0			0
$327$	1.26135	−	16.8315i	0.0697525	−	0.930783i
$328$		0			0
$329$	−3.09490	−	15.6309i	−0.170627	−	0.861761i
$330$		0			0
$331$	2.52212	+	2.34019i	0.138628	+	0.128628i	0.746439	−	0.665453i	$-0.231762\pi$
$331$	2.52212	+	2.34019i	0.138628	+	0.128628i	−0.607811	+	0.794082i	$0.707952\pi$
$332$		0			0
$333$	−4.75728	−	3.24346i	−0.260697	−	0.177740i
$334$		0			0
$335$	6.53350	+	3.14637i	0.356963	+	0.171904i
$336$		0			0
$337$	9.97406	−	4.80325i	0.543321	−	0.261650i	−0.142030	−	0.989862i	$-0.545363\pi$
$337$	9.97406	−	4.80325i	0.543321	−	0.261650i	0.685351	+	0.728213i	$0.259649\pi$
$338$		0			0
$339$	−46.1316	+	42.8039i	−2.50553	+	2.32479i
$340$		0			0
$341$	0.739526	+	1.88428i	0.0400476	+	0.102040i
$342$		0			0
$343$	−15.9269	−	9.45174i	−0.859969	−	0.510346i
$344$		0			0
$345$	3.62725	+	9.24209i	0.195285	+	0.497577i
$346$		0			0
$347$	−15.7640	+	14.6268i	−0.846255	+	0.785210i	−0.978552	−	0.206000i	$-0.933955\pi$
$347$	−15.7640	+	14.6268i	−0.846255	+	0.785210i	0.132297	+	0.991210i	$0.457765\pi$
$348$		0			0
$349$	−15.3047	+	7.37035i	−0.819241	+	0.394526i	−0.796069	−	0.605206i	$-0.793091\pi$
$349$	−15.3047	+	7.37035i	−0.819241	+	0.394526i	−0.0231720	+	0.999731i	$0.507377\pi$
$350$		0			0
$351$	−85.4571	−	41.1540i	−4.56136	−	2.19664i
$352$		0			0
$353$	10.6760	+	7.27879i	0.568228	+	0.387411i	0.813082	−	0.582149i	$-0.197788\pi$
$353$	10.6760	+	7.27879i	0.568228	+	0.387411i	−0.244855	+	0.969560i	$0.578740\pi$
$354$		0			0
$355$	−7.69656	−	7.14136i	−0.408491	−	0.379024i
$356$		0			0
$357$	1.24374	+	6.28157i	0.0658256	+	0.332456i
$358$		0			0
$359$	−0.628657	+	8.38885i	−0.0331793	+	0.442747i	0.955732	+	0.294239i	$0.0950661\pi$
$359$	−0.628657	+	8.38885i	−0.0331793	+	0.442747i	−0.988911	+	0.148508i	$0.952553\pi$
$360$		0			0
$361$	2.94504	+	5.10096i	0.155002	+	0.268472i
$362$		0			0
$363$	8.12638	−	35.6040i	0.426525	−	1.86873i
$364$		0			0
$365$	−1.95674	−	8.57303i	−0.102420	−	0.448733i
$366$		0			0
$367$	−4.77594	+	12.1689i	−0.249302	+	0.635211i	−0.999667	−	0.0258130i	$-0.991783\pi$
$367$	−4.77594	+	12.1689i	−0.249302	+	0.635211i	0.750365	+	0.661024i	$0.229878\pi$
$368$		0			0
$369$	−6.26498	−	1.93249i	−0.326142	−	0.100601i
$370$		0			0
$371$	17.5162	−	11.2142i	0.909398	−	0.582215i
$372$		0			0
$373$	2.01818	−	3.49559i	0.104498	−	0.180995i	−0.809035	−	0.587760i	$-0.800010\pi$
$373$	2.01818	−	3.49559i	0.104498	−	0.180995i	0.913533	+	0.406765i	$0.133343\pi$
$374$		0			0
$375$	34.9945	−	10.7944i	1.80711	−	0.557419i
$376$		0			0
$377$	8.17157	+	10.2468i	0.420857	+	0.527738i
$378$		0			0
$379$	8.85963	−	11.1096i	0.455089	−	0.570663i	−0.500361	−	0.865817i	$-0.666799\pi$
$379$	8.85963	−	11.1096i	0.455089	−	0.570663i	0.955450	+	0.295154i	$0.0953708\pi$
$380$		0			0
$381$	−45.8837	−	6.91585i	−2.35069	−	0.354310i
$382$		0			0
$383$	14.3881	−	2.16866i	0.735198	−	0.110813i	0.229238	−	0.973370i	$-0.426377\pi$
$383$	14.3881	−	2.16866i	0.735198	−	0.110813i	0.505960	+	0.862557i	$0.331139\pi$
$384$		0			0
$385$	−1.01259	+	0.280538i	−0.0516066	+	0.0142975i
$386$		0			0
$387$	5.46738	−	3.72760i	0.277923	−	0.189485i
$388$		0			0
$389$	−0.791381	−	10.5602i	−0.0401246	−	0.535426i	−0.980659	−	0.195726i	$-0.937294\pi$
$389$	−0.791381	−	10.5602i	−0.0401246	−	0.535426i	0.940534	−	0.339700i	$-0.110325\pi$
$390$		0			0
$391$	1.61429			0.0816382
$392$		0			0
$393$	−22.3131			−1.12555
$394$		0			0
$395$	1.05541	+	14.0835i	0.0531035	+	0.708617i
$396$		0			0
$397$	4.72977	−	3.22470i	0.237380	−	0.161843i	−0.438787	−	0.898591i	$-0.644592\pi$
$397$	4.72977	−	3.22470i	0.237380	−	0.161843i	0.676168	+	0.736748i	$0.263639\pi$
$398$		0			0
$399$	25.9594	+	18.8213i	1.29959	+	0.942245i
$400$		0			0
$401$	31.0464	−	4.67949i	1.55038	−	0.233683i	0.682662	−	0.730735i	$-0.260822\pi$
$401$	31.0464	−	4.67949i	1.55038	−	0.233683i	0.867721	+	0.497052i	$0.165584\pi$
$402$		0			0
$403$	−36.4687	−	5.49677i	−1.81664	−	0.273814i
$404$		0			0
$405$	−27.9058	+	34.9928i	−1.38665	+	1.73880i
$406$		0			0
$407$	−0.130802	−	0.164021i	−0.00648364	−	0.00813022i
$408$		0			0
$409$	−0.0437437	+	0.0134932i	−0.00216299	+	0.000667194i	−0.295836	−	0.955239i	$-0.595598\pi$
$409$	−0.0437437	+	0.0134932i	−0.00216299	+	0.000667194i	0.293673	+	0.955906i	$0.405122\pi$
$410$		0			0
$411$	5.30982	−	9.19688i	0.261914	−	0.453648i
$412$		0			0
$413$	5.82415	+	5.72631i	0.286588	+	0.281774i
$414$		0			0
$415$	7.86641	+	2.42647i	0.386147	+	0.119111i
$416$		0			0
$417$	−19.1040	+	48.6761i	−0.935526	+	2.38368i
$418$		0			0
$419$	1.80667	+	7.91555i	0.0882618	+	0.386700i	0.999694	−	0.0247509i	$-0.00787926\pi$
$419$	1.80667	+	7.91555i	0.0882618	+	0.386700i	−0.911432	+	0.411451i	$0.865022\pi$
$420$		0			0
$421$	4.20041	−	18.4032i	0.204715	−	0.896917i	−0.763303	−	0.646040i	$-0.776424\pi$
$421$	4.20041	−	18.4032i	0.204715	−	0.896917i	0.968019	−	0.250877i	$-0.0807190\pi$
$422$		0			0
$423$	−24.7031	−	42.7870i	−1.20111	−	2.08038i
$424$		0			0
$425$	0.174790	−	2.33241i	0.00847855	−	0.113138i
$426$		0			0
$427$	5.19281	+	6.91268i	0.251298	+	0.334528i
$428$		0			0
$429$	−3.99404	−	3.70593i	−0.192834	−	0.178924i
$430$		0			0
$431$	−9.68669	−	6.60427i	−0.466591	−	0.318117i	0.307102	−	0.951677i	$-0.400641\pi$
$431$	−9.68669	−	6.60427i	−0.466591	−	0.318117i	−0.773694	+	0.633560i	$0.781593\pi$
$432$		0			0
$433$	24.7751	+	11.9310i	1.19061	+	0.573370i	0.920986	−	0.389595i	$-0.127385\pi$
$433$	24.7751	+	11.9310i	1.19061	+	0.573370i	0.269628	+	0.962965i	$0.413099\pi$
$434$		0			0
$435$	9.64282	−	4.64374i	0.462338	−	0.222650i
$436$		0			0
$437$	5.92547	−	5.49803i	0.283454	−	0.263007i
$438$		0			0
$439$	−10.0899	−	25.7086i	−0.481564	−	1.22700i	−0.940883	−	0.338733i	$-0.890002\pi$
$439$	−10.0899	−	25.7086i	−0.481564	−	1.22700i	0.459319	−	0.888271i	$-0.348094\pi$
$440$		0			0
$441$	−56.1927	−	11.8278i	−2.67584	−	0.563230i
$442$		0			0
$443$	13.0337	+	33.2094i	0.619251	+	1.57782i	0.803734	+	0.594989i	$0.202844\pi$
$443$	13.0337	+	33.2094i	0.619251	+	1.57782i	−0.184483	+	0.982836i	$0.559061\pi$
$444$		0			0
$445$	13.0828	−	12.1390i	0.620183	−	0.575445i
$446$		0			0
$447$	−68.4375	+	32.9578i	−3.23698	+	1.55885i
$448$		0			0
$449$	−21.4257	−	10.3181i	−1.01114	−	0.486940i	−0.146436	−	0.989220i	$-0.546780\pi$
$449$	−21.4257	−	10.3181i	−1.01114	−	0.486940i	−0.864705	+	0.502280i	$0.832495\pi$
$450$		0			0
$451$	−0.197376	−	0.134569i	−0.00929409	−	0.00633661i
$452$		0			0
$453$	−28.0427	−	26.0198i	−1.31756	−	1.22252i
$454$		0			0
$455$	4.79808	−	18.5332i	0.224937	−	0.868850i
$456$		0			0
$457$	−1.84045	+	24.5591i	−0.0860925	+	1.14882i	0.772102	+	0.635499i	$0.219206\pi$
$457$	−1.84045	+	24.5591i	−0.0860925	+	1.14882i	−0.858194	+	0.513325i	$0.828413\pi$
$458$		0			0
$459$	6.29693	+	10.9066i	0.293916	+	0.509077i
$460$		0			0
$461$	−0.823066	+	3.60609i	−0.0383340	+	0.167952i	−0.990472	−	0.137718i	$-0.956023\pi$
$461$	−0.823066	+	3.60609i	−0.0383340	+	0.167952i	0.952138	+	0.305670i	$0.0988804\pi$
$462$		0			0
$463$	6.45908	+	28.2991i	0.300179	+	1.31517i	0.869858	+	0.493302i	$0.164210\pi$
$463$	6.45908	+	28.2991i	0.300179	+	1.31517i	−0.569679	+	0.821867i	$0.692932\pi$
$464$		0			0
$465$	−11.0031	+	28.0355i	−0.510257	+	1.30011i
$466$		0			0
$467$	2.35174	+	0.725416i	0.108826	+	0.0335683i	0.348690	−	0.937238i	$-0.386627\pi$
$467$	2.35174	+	0.725416i	0.108826	+	0.0335683i	−0.239864	+	0.970806i	$0.577103\pi$
$468$		0			0
$469$	4.88453	+	13.5889i	0.225547	+	0.627475i
$470$		0			0
$471$	6.56421	−	11.3695i	0.302463	−	0.523881i
$472$		0			0
$473$	0.230394	−	0.0710672i	0.0105935	−	0.00326767i
$474$		0			0
$475$	−7.30224	−	9.15672i	−0.335050	−	0.420139i
$476$		0			0
$477$	40.2076	−	50.4187i	1.84098	−	2.30852i
$478$		0			0
$479$	−23.6666	−	3.56717i	−1.08136	−	0.162988i	−0.415889	−	0.909415i	$-0.636530\pi$
$479$	−23.6666	−	3.56717i	−1.08136	−	0.162988i	−0.665467	+	0.746427i	$0.731768\pi$
$480$		0			0
$481$	3.77965	−	0.569691i	0.172337	−	0.0259757i
$482$		0			0
$483$	−7.75220	+	18.1870i	−0.352737	+	0.827537i
$484$		0			0
$485$	19.8471	−	13.5315i	0.901210	−	0.614434i
$486$		0			0
$487$	−1.65235	−	22.0491i	−0.0748751	−	0.999139i	−0.900482	−	0.434893i	$-0.856786\pi$
$487$	−1.65235	−	22.0491i	−0.0748751	−	0.999139i	0.825607	−	0.564246i	$-0.190833\pi$
$488$		0			0
$489$	−13.5313			−0.611909
$490$		0			0
$491$	35.2831			1.59230			0.796151	−	0.605098i	$-0.206866\pi$
$491$	35.2831			1.59230			0.796151	+	0.605098i	$0.206866\pi$
$492$		0			0
$493$	−0.130045	−	1.73532i	−0.00585691	−	0.0781551i
$494$		0			0
$495$	−2.69182	+	1.83525i	−0.120988	+	0.0824885i
$496$		0			0
$497$	−0.958684	−	20.8852i	−0.0430028	−	0.936828i
$498$		0			0
$499$	−7.70733	+	1.16169i	−0.345028	+	0.0520045i	−0.319270	−	0.947664i	$-0.603438\pi$
$499$	−7.70733	+	1.16169i	−0.345028	+	0.0520045i	−0.0257572	+	0.999668i	$0.508200\pi$
$500$		0			0
$501$	−24.4413	−	3.68393i	−1.09196	−	0.164586i
$502$		0			0
$503$	10.2937	−	12.9078i	0.458972	−	0.575532i	−0.497461	−	0.867487i	$-0.665734\pi$
$503$	10.2937	−	12.9078i	0.458972	−	0.575532i	0.956432	+	0.291954i	$0.0943055\pi$
$504$		0			0
$505$	9.67479	+	12.1318i	0.430523	+	0.539858i
$506$		0			0
$507$	53.2806	−	16.4349i	2.36627	−	0.729899i
$508$		0			0
$509$	14.8313	−	25.6885i	0.657384	−	1.13862i	−0.323906	−	0.946089i	$-0.604996\pi$
$509$	14.8313	−	25.6885i	0.657384	−	1.13862i	0.981290	−	0.192533i	$-0.0616704\pi$
$510$		0			0
$511$	9.19016	−	14.9048i	0.406549	−	0.659351i
$512$		0			0
$513$	60.2600	+	18.5877i	2.66054	+	0.820669i
$514$		0			0
$515$	1.38265	−	3.52292i	0.0609266	−	0.155239i
$516$		0			0
$517$	−0.400577	−	1.75504i	−0.0176174	−	0.0771867i
$518$		0			0
$519$	−3.00270	+	13.1557i	−0.131804	+	0.577471i
$520$		0			0
$521$	−18.6492	−	32.3014i	−0.817037	−	1.41515i	−0.907856	−	0.419282i	$-0.862282\pi$
$521$	−18.6492	−	32.3014i	−0.817037	−	1.41515i	0.0908186	−	0.995867i	$-0.471052\pi$
$522$		0			0
$523$	0.260421	−	3.47508i	0.0113874	−	0.151955i	−0.988612	−	0.150490i	$-0.951915\pi$
$523$	0.260421	−	3.47508i	0.0113874	−	0.151955i	0.999999	−	0.00146440i	$-0.000466132\pi$
$524$		0			0
$525$	25.4381	+	13.1700i	1.11021	+	0.574786i
$526$		0			0
$527$	3.58966	+	3.33072i	0.156368	+	0.145088i
$528$		0			0
$529$	−14.8855	−	10.1488i	−0.647197	−	0.441252i
$530$		0			0
$531$	22.8169	+	10.9880i	0.990169	+	0.476840i
$532$		0			0
$533$	3.92142	−	1.88845i	0.169855	−	0.0817980i
$534$		0			0
$535$	12.9806	−	12.0442i	0.561200	−	0.520718i
$536$		0			0
$537$	17.5090	+	44.6121i	0.755568	+	1.92515i
$538$		0			0
$539$	−1.82946	−	1.01531i	−0.0788005	−	0.0437326i
$540$		0			0
$541$	−12.1488	−	30.9547i	−0.522319	−	1.33085i	−0.912111	−	0.409944i	$-0.865548\pi$
$541$	−12.1488	−	30.9547i	−0.522319	−	1.33085i	0.389792	−	0.920903i	$-0.372547\pi$
$542$		0			0
$543$	2.84165	−	2.63666i	0.121947	−	0.113150i
$544$		0			0
$545$	6.03654	−	2.90705i	0.258577	−	0.124524i
$546$		0			0
$547$	22.1221	+	10.6534i	0.945871	+	0.455507i	0.842237	−	0.539108i	$-0.181239\pi$
$547$	22.1221	+	10.6534i	0.945871	+	0.455507i	0.103634	+	0.994615i	$0.466953\pi$
$548$		0			0
$549$	22.1492	+	15.1011i	0.945307	+	0.644499i
$550$		0			0
$551$	−6.38760	−	5.92683i	−0.272121	−	0.252491i
$552$		0			0
$553$	−18.1630	+	21.4709i	−0.772368	+	0.913037i
$554$		0			0
$555$	0.233262	−	3.11266i	0.00990142	−	0.132125i
$556$		0			0
$557$	−16.8497	−	29.1845i	−0.713944	−	1.23659i	−0.963366	−	0.268192i	$-0.913574\pi$
$557$	−16.8497	−	29.1845i	−0.713944	−	1.23659i	0.249422	−	0.968395i	$-0.419759\pi$
$558$		0			0
$559$	−0.977512	+	4.28276i	−0.0413444	+	0.181141i
$560$		0			0
$561$	0.160979	+	0.705295i	0.00679654	+	0.0297776i
$562$		0			0
$563$	4.70517	−	11.9886i	0.198299	−	0.505258i	−0.796788	−	0.604259i	$-0.793469\pi$
$563$	4.70517	−	11.9886i	0.198299	−	0.505258i	0.995087	+	0.0990005i	$0.0315645\pi$
$564$		0			0
$565$	−23.8709	−	7.36318i	−1.00425	−	0.309771i
$566$		0			0
$567$	−88.4767	+	10.7286i	−3.71567	+	0.450560i
$568$		0			0
$569$	6.65632	−	11.5291i	0.279048	−	0.483325i	−0.692101	−	0.721801i	$-0.743315\pi$
$569$	6.65632	−	11.5291i	0.279048	−	0.483325i	0.971148	+	0.238476i	$0.0766479\pi$
$570$		0			0
$571$	4.70143	−	1.45020i	0.196749	−	0.0606889i	−0.194815	−	0.980840i	$-0.562411\pi$
$571$	4.70143	−	1.45020i	0.196749	−	0.0606889i	0.391563	+	0.920151i	$0.371934\pi$
$572$		0			0
$573$	14.5957	+	18.3024i	0.609744	+	0.764595i
$574$		0			0
$575$	4.50240	−	5.64584i	0.187763	−	0.235448i
$576$		0			0
$577$	23.3469	+	3.51897i	0.971942	+	0.146497i	0.615772	−	0.787924i	$-0.288844\pi$
$577$	23.3469	+	3.51897i	0.971942	+	0.146497i	0.356170	+	0.934421i	$0.384082\pi$
$578$		0			0
$579$	5.71575	−	0.861511i	0.237539	−	0.0358032i
$580$		0			0
$581$	7.78221	+	14.4275i	0.322860	+	0.598553i
$582$		0			0
$583$	1.94141	−	1.32363i	0.0804052	−	0.0548193i
$584$		0			0
$585$	−4.43588	−	59.1927i	−0.183401	−	2.44732i
$586$		0			0
$587$	37.6167			1.55261			0.776303	−	0.630359i	$-0.217092\pi$
$587$	37.6167			1.55261			0.776303	+	0.630359i	$0.217092\pi$
$588$		0			0
$589$	24.5203			1.01034
$590$		0			0
$591$	2.58780	+	34.5318i	0.106448	+	1.42045i
$592$		0			0
$593$	−17.2791	+	11.7807i	−0.709568	+	0.483775i	−0.863527	−	0.504302i	$-0.831750\pi$
$593$	−17.2791	+	11.7807i	−0.709568	+	0.483775i	0.153960	+	0.988077i	$0.450797\pi$
$594$		0			0
$595$	−1.91257	+	1.67431i	−0.0784079	+	0.0686400i
$596$		0			0
$597$	6.19071	−	0.933099i	0.253369	−	0.0381892i
$598$		0			0
$599$	−27.6160	−	4.16245i	−1.12836	−	0.170073i	−0.441778	−	0.897125i	$-0.645652\pi$
$599$	−27.6160	−	4.16245i	−1.12836	−	0.170073i	−0.686583	+	0.727052i	$0.740890\pi$
$600$		0			0
$601$	5.09701	−	6.39144i	0.207911	−	0.260712i	−0.666932	−	0.745119i	$-0.732393\pi$
$601$	5.09701	−	6.39144i	0.207911	−	0.260712i	0.874843	+	0.484406i	$0.160964\pi$
$602$		0			0
$603$	27.9155	+	35.0049i	1.13681	+	1.42551i
$604$		0			0
$605$	13.8526	−	4.27295i	0.563187	−	0.173720i
$606$		0			0
$607$	−14.3459	+	24.8478i	−0.582282	+	1.00854i	0.412926	+	0.910765i	$0.364507\pi$
$607$	−14.3459	+	24.8478i	−0.582282	+	1.00854i	−0.995208	+	0.0977779i	$0.968827\pi$
$608$		0			0
$609$	20.1751	+	6.86832i	0.817537	+	0.278318i
$610$		0			0
$611$	31.3417	+	9.66763i	1.26795	+	0.391111i
$612$		0			0
$613$	−1.88864	+	4.81217i	−0.0762814	+	0.194362i	−0.963928	−	0.266164i	$-0.914244\pi$
$613$	−1.88864	+	4.81217i	−0.0762814	+	0.194362i	0.887646	+	0.460526i	$0.152339\pi$
$614$		0			0
$615$	−0.790902	−	3.46517i	−0.0318922	−	0.139729i
$616$		0			0
$617$	−10.3325	+	45.2698i	−0.415972	+	1.82249i	0.138590	+	0.990350i	$0.455743\pi$
$617$	−10.3325	+	45.2698i	−0.415972	+	1.82249i	−0.554562	+	0.832143i	$0.687114\pi$
$618$		0			0
$619$	0.828754	+	1.43544i	0.0333104	+	0.0576953i	0.882200	−	0.470875i	$-0.156062\pi$
$619$	0.828754	+	1.43544i	0.0333104	+	0.0576953i	−0.848890	+	0.528570i	$0.822728\pi$
$620$		0			0
$621$	−2.90569	+	38.7737i	−0.116601	+	1.55594i
$622$		0			0
$623$	35.5236	+	1.02796i	1.42322	+	0.0411845i
$624$		0			0
$625$	−1.19941	−	1.11289i	−0.0479763	−	0.0445155i
$626$		0			0
$627$	2.99303	+	2.04061i	0.119530	+	0.0814941i
$628$		0			0
$629$	−0.457257	−	0.220203i	−0.0182320	−	0.00878009i
$630$		0			0
$631$	36.0118	−	17.3424i	1.43361	−	0.690389i	0.453943	−	0.891031i	$-0.350017\pi$
$631$	36.0118	−	17.3424i	1.43361	−	0.690389i	0.979665	+	0.200641i	$0.0643025\pi$
$632$		0			0
$633$	16.7952	−	15.5837i	0.667549	−	0.619395i
$634$		0			0
$635$	−6.72938	−	17.1462i	−0.267047	−	0.680425i
$636$		0			0
$637$	32.6866	−	19.6173i	1.29509	−	0.777267i
$638$		0			0
$639$	−23.6832	−	60.3438i	−0.936893	−	2.38716i
$640$		0			0
$641$	−21.2112	+	19.6811i	−0.837790	+	0.777356i	−0.977075	−	0.212897i	$-0.931710\pi$
$641$	−21.2112	+	19.6811i	−0.837790	+	0.777356i	0.139284	+	0.990252i	$0.455520\pi$
$642$		0			0
$643$	−24.4367	+	11.7681i	−0.963690	+	0.464089i	−0.848466	−	0.529251i	$-0.822473\pi$
$643$	−24.4367	+	11.7681i	−0.963690	+	0.464089i	−0.115225	+	0.993339i	$0.536759\pi$
$644$		0			0
$645$	3.23206	+	1.55648i	0.127262	+	0.0612863i
$646$		0			0
$647$	4.30164	+	2.93281i	0.169115	+	0.115301i	0.644920	−	0.764250i	$-0.276891\pi$
$647$	4.30164	+	2.93281i	0.169115	+	0.115301i	−0.475805	+	0.879551i	$0.657843\pi$
$648$		0			0
$649$	0.676418	+	0.627624i	0.0265517	+	0.0246364i
$650$		0			0
$651$	−54.7632	+	24.4472i	−2.14634	+	0.958159i
$652$		0			0
$653$	−0.914533	+	12.2036i	−0.0357884	+	0.477564i	0.950299	+	0.311338i	$0.100777\pi$
$653$	−0.914533	+	12.2036i	−0.0357884	+	0.477564i	−0.986088	+	0.166226i	$0.946842\pi$
$654$		0			0
$655$	−4.42864	−	7.67063i	−0.173041	−	0.299716i
$656$		0			0
$657$	12.0813	−	52.9315i	0.471335	−	2.06505i
$658$		0			0
$659$	−9.58399	−	41.9902i	−0.373339	−	1.63571i	−0.717331	−	0.696733i	$-0.754636\pi$
$659$	−9.58399	−	41.9902i	−0.373339	−	1.63571i	0.343992	−	0.938973i	$-0.388221\pi$
$660$		0			0
$661$	−4.02072	+	10.2446i	−0.156388	+	0.398470i	−0.987497	−	0.157640i	$-0.949611\pi$
$661$	−4.02072	+	10.2446i	−0.156388	+	0.398470i	0.831109	+	0.556110i	$0.187707\pi$
$662$		0			0
$663$	−12.5952	−	3.88511i	−0.489158	−	0.150885i
$664$		0			0
$665$	−1.31791	+	12.6597i	−0.0511065	+	0.490923i
$666$		0			0
$667$	2.68634	−	4.65288i	0.104016	−	0.180160i
$668$		0			0
$669$	82.5674	−	25.4687i	3.19224	−	0.984676i
$670$		0			0
$671$	0.608999	+	0.763660i	0.0235101	+	0.0294808i
$672$		0			0
$673$	1.65836	−	2.07952i	0.0639251	−	0.0801596i	−0.748841	−	0.662750i	$-0.769389\pi$
$673$	1.65836	−	2.07952i	0.0639251	−	0.0801596i	0.812766	+	0.582590i	$0.197961\pi$
$674$		0			0
$675$	55.7076	+	8.39657i	2.14419	+	0.323184i
$676$		0			0
$677$	−21.6891	+	3.26910i	−0.833578	+	0.125642i	−0.551945	−	0.833881i	$-0.686114\pi$
$677$	−21.6891	+	3.26910i	−0.833578	+	0.125642i	−0.281633	+	0.959522i	$0.590876\pi$
$678$		0			0
$679$	47.0724	+	8.49423i	1.80647	+	0.325979i
$680$		0			0
$681$	−72.2913	+	49.2874i	−2.77021	+	1.88870i
$682$		0			0
$683$	2.86975	+	38.2941i	0.109808	+	1.46528i	0.731403	+	0.681945i	$0.238866\pi$
$683$	2.86975	+	38.2941i	0.109808	+	1.46528i	−0.621595	+	0.783339i	$0.713515\pi$
$684$		0			0
$685$	4.21551			0.161066
$686$		0			0
$687$	42.3122			1.61431
$688$		0			0
$689$	3.19928	+	42.6914i	0.121883	+	1.62641i
$690$		0			0
$691$	6.47743	−	4.41624i	0.246413	−	0.168002i	−0.433815	−	0.901002i	$-0.642833\pi$
$691$	6.47743	−	4.41624i	0.246413	−	0.168002i	0.680228	+	0.733000i	$0.261881\pi$
$692$		0			0
$693$	−6.38434	−	1.15206i	−0.242521	−	0.0437630i
$694$		0			0
$695$	−20.5252	+	3.09368i	−0.778565	+	0.117350i
$696$		0			0
$697$	−0.571447	−	0.0861318i	−0.0216451	−	0.00326247i
$698$		0			0
$699$	−45.6903	+	57.2938i	−1.72817	+	2.16705i
$700$		0			0
$701$	26.8169	+	33.6273i	1.01286	+	1.27009i	0.962479	+	0.271357i	$0.0874723\pi$
$701$	26.8169	+	33.6273i	1.01286	+	1.27009i	0.0503815	+	0.998730i	$0.483956\pi$
$702$		0			0
$703$	−2.42840	+	0.749063i	−0.0915890	+	0.0282515i
$704$		0			0
$705$	13.3921	−	23.1957i	0.504374	−	0.873601i
$706$		0			0
$707$	−3.19939	+	30.7330i	−0.120326	+	1.15583i
$708$		0			0
$709$	−2.91784	−	0.900035i	−0.109582	−	0.0338015i	0.239479	−	0.970901i	$-0.423023\pi$
$709$	−2.91784	−	0.900035i	−0.109582	−	0.0338015i	−0.349061	+	0.937100i	$0.613499\pi$
$710$		0			0
$711$	−31.8570	+	81.1702i	−1.19473	+	3.04412i
$712$		0			0
$713$	3.36422	+	14.7396i	0.125991	+	0.552003i
$714$		0			0
$715$	0.481270	−	2.10858i	0.0179985	−	0.0788565i
$716$		0			0
$717$	−25.2966	−	43.8149i	−0.944718	−	1.63630i
$718$		0			0
$719$	1.55623	−	20.7664i	0.0580375	−	0.774456i	−0.889932	−	0.456094i	$-0.849248\pi$
$719$	1.55623	−	20.7664i	0.0580375	−	0.774456i	0.947969	−	0.318362i	$-0.103133\pi$
$720$		0			0
$721$	6.88151	−	3.07202i	0.256281	−	0.114408i
$722$		0			0
$723$	−43.7486	−	40.5928i	−1.62703	−	1.50966i
$724$		0			0
$725$	−6.43185	−	4.38516i	−0.238873	−	0.162861i
$726$		0			0
$727$	−31.8424	−	15.3345i	−1.18097	−	0.568724i	−0.262775	−	0.964857i	$-0.584638\pi$
$727$	−31.8424	−	15.3345i	−1.18097	−	0.568724i	−0.918193	+	0.396133i	$0.870352\pi$
$728$		0			0
$729$	−91.4050	+	44.0183i	−3.38537	+	1.63031i
$730$		0			0
$731$	0.427569	−	0.396726i	0.0158142	−	0.0146735i
$732$		0			0
$733$	5.38724	+	13.7265i	0.198982	+	0.506999i	0.995183	−	0.0980338i	$-0.0312553\pi$
$733$	5.38724	+	13.7265i	0.198982	+	0.506999i	−0.796201	+	0.605033i	$0.793160\pi$
$734$		0			0
$735$	−9.67856	−	29.5880i	−0.356999	−	1.09137i
$736$		0			0
$737$	0.596003	+	1.51859i	0.0219540	+	0.0559380i
$738$		0			0
$739$	13.4551	−	12.4845i	0.494955	−	0.459251i	−0.392762	−	0.919640i	$-0.628480\pi$
$739$	13.4551	−	12.4845i	0.494955	−	0.459251i	0.887717	+	0.460389i	$0.152290\pi$
$740$		0			0
$741$	−59.4645	+	28.6366i	−2.18448	+	1.05199i
$742$		0			0
$743$	−13.0063	−	6.26349i	−0.477154	−	0.229785i	0.179818	−	0.983700i	$-0.442449\pi$
$743$	−13.0063	−	6.26349i	−0.477154	−	0.229785i	−0.656973	+	0.753915i	$0.728163\pi$
$744$		0			0
$745$	−24.9132	−	16.9856i	−0.912750	−	0.622303i
$746$		0			0
$747$	37.2587	+	34.5710i	1.36322	+	1.26489i
$748$		0			0
$749$	35.2461	+	1.01994i	1.28787	+	0.0372676i
$750$		0			0
$751$	−2.71039	+	36.1676i	−0.0989034	+	1.31977i	0.698188	+	0.715915i	$0.253990\pi$
$751$	−2.71039	+	36.1676i	−0.0989034	+	1.31977i	−0.797091	+	0.603859i	$0.793629\pi$
$752$		0			0
$753$	26.4678	+	45.8436i	0.964542	+	1.67064i
$754$		0			0
$755$	3.37906	−	14.8046i	0.122977	−	0.538796i
$756$		0			0
$757$	−9.74724	−	42.7054i	−0.354269	−	1.55216i	−0.767209	−	0.641397i	$-0.778355\pi$
$757$	−9.74724	−	42.7054i	−0.354269	−	1.55216i	0.412940	−	0.910758i	$-0.364502\pi$
$758$		0			0
$759$	−0.816002	+	2.07914i	−0.0296190	+	0.0754680i
$760$		0			0
$761$	−40.3601	−	12.4494i	−1.46305	−	0.451292i	−0.541884	−	0.840454i	$-0.682289\pi$
$761$	−40.3601	−	12.4494i	−1.46305	−	0.451292i	−0.921170	+	0.389161i	$0.872765\pi$
$762$		0			0
$763$	12.6299	+	4.29967i	0.457233	+	0.155658i
$764$		0			0
$765$	−3.94071	+	6.82552i	−0.142477	+	0.246777i
$766$		0			0
$767$	−16.0653	+	4.95548i	−0.580083	+	0.178932i
$768$		0			0
$769$	−14.2989	−	17.9303i	−0.515633	−	0.646583i	0.454042	−	0.890980i	$-0.349981\pi$
$769$	−14.2989	−	17.9303i	−0.515633	−	0.646583i	−0.969675	+	0.244397i	$0.921410\pi$
$770$		0			0
$771$	−42.9605	+	53.8708i	−1.54719	+	1.94011i
$772$		0			0
$773$	−10.3640	−	1.56213i	−0.372768	−	0.0561858i	−0.0400135	−	0.999199i	$-0.512740\pi$
$773$	−10.3640	−	1.56213i	−0.372768	−	0.0561858i	−0.332755	+	0.943013i	$0.607978\pi$
$774$		0			0
$775$	21.6608	−	3.26484i	0.778079	−	0.117277i
$776$		0			0
$777$	4.67672	−	4.09411i	0.167777	−	0.146875i
$778$		0			0
$779$	−2.39092	+	1.63010i	−0.0856638	+	0.0584046i
$780$		0			0
$781$	−0.176511	−	2.35537i	−0.00631605	−	0.0842818i
$782$		0			0
$783$	41.9149			1.49792
$784$		0			0
$785$	5.21138			0.186002
$786$		0			0
$787$	0.604248	+	8.06313i	0.0215391	+	0.287420i	0.997564	+	0.0697598i	$0.0222233\pi$
$787$	0.604248	+	8.06313i	0.0215391	+	0.287420i	−0.976025	+	0.217660i	$0.930158\pi$
$788$		0			0
$789$	−50.3579	+	34.3334i	−1.79279	+	1.22230i
$790$		0			0
$791$	−23.6153	−	43.7806i	−0.839664	−	1.55666i
$792$		0			0
$793$	−17.5976	+	2.65241i	−0.624908	+	0.0941897i
$794$		0			0
$795$	34.5698	+	5.21055i	1.22606	+	0.184799i
$796$		0			0
$797$	9.75145	−	12.2279i	0.345414	−	0.433135i	−0.578531	−	0.815660i	$-0.696374\pi$
$797$	9.75145	−	12.2279i	0.345414	−	0.433135i	0.923945	+	0.382525i	$0.124945\pi$
$798$		0			0
$799$	−2.71524	−	3.40481i	−0.0960584	−	0.120453i
$800$		0			0
$801$	105.295	−	32.4793i	3.72042	−	1.14760i
$802$		0			0
$803$	0.989112	−	1.71319i	0.0349050	−	0.0604573i
$804$		0			0
$805$	−7.79082	+	0.944710i	−0.274590	+	0.0332966i
$806$		0			0
$807$	24.6707	+	7.60989i	0.868448	+	0.267881i
$808$		0			0
$809$	9.28826	−	23.6661i	0.326558	−	0.832056i	−0.669456	−	0.742852i	$-0.733473\pi$
$809$	9.28826	−	23.6661i	0.326558	−	0.832056i	0.996013	−	0.0892037i	$-0.0284322\pi$
$810$		0			0
$811$	−3.76251	−	16.4846i	−0.132120	−	0.578854i	−0.997036	−	0.0769378i	$-0.975486\pi$
$811$	−3.76251	−	16.4846i	−0.132120	−	0.578854i	0.864916	−	0.501916i	$-0.167371\pi$
$812$		0			0
$813$	−8.00812	+	35.0859i	−0.280857	+	1.23052i
$814$		0			0
$815$	−2.68566	−	4.65170i	−0.0940746	−	0.162942i
$816$		0			0
$817$	0.218260	−	2.91248i	0.00763595	−	0.101895i
$818$		0			0
$819$	76.3387	−	90.2421i	2.66749	−	3.15331i
$820$		0			0
$821$	27.4817	+	25.4993i	0.959118	+	0.889932i	0.993991	−	0.109460i	$-0.0349122\pi$
$821$	27.4817	+	25.4993i	0.959118	+	0.889932i	−0.0348731	+	0.999392i	$0.511103\pi$
$822$		0			0
$823$	18.8243	+	12.8342i	0.656175	+	0.447372i	0.845092	−	0.534621i	$-0.179546\pi$
$823$	18.8243	+	12.8342i	0.656175	+	0.447372i	−0.188918	+	0.981993i	$0.560498\pi$
$824$		0			0
$825$	2.91569	+	1.40412i	0.101511	+	0.0488853i
$826$		0			0
$827$	−43.5630	+	20.9789i	−1.51484	+	0.729506i	−0.992386	−	0.123164i	$-0.960696\pi$
$827$	−43.5630	+	20.9789i	−1.51484	+	0.729506i	−0.522449	+	0.852670i	$0.674982\pi$
$828$		0			0
$829$	−33.7388	+	31.3050i	−1.17180	+	1.08727i	−0.177124	+	0.984189i	$0.556679\pi$
$829$	−33.7388	+	31.3050i	−1.17180	+	1.08727i	−0.994673	+	0.103080i	$0.967130\pi$
$830$		0			0
$831$	2.80668	+	7.15130i	0.0973626	+	0.248076i
$832$		0			0
$833$	−5.05317	−	0.292698i	−0.175082	−	0.0101414i
$834$		0			0
$835$	−3.58460	−	9.13341i	−0.124050	−	0.316075i
$836$		0			0
$837$	−86.4621	+	80.2251i	−2.98857	+	2.77298i
$838$		0			0
$839$	4.09292	−	1.97105i	0.141303	−	0.0680481i	−0.361896	−	0.932218i	$-0.617870\pi$
$839$	4.09292	−	1.97105i	0.141303	−	0.0680481i	0.503199	+	0.864170i	$0.332156\pi$
$840$		0			0
$841$	20.9100	+	10.0697i	0.721033	+	0.347231i
$842$		0			0
$843$	−59.2099	−	40.3686i	−2.03930	−	1.39037i
$844$		0			0
$845$	16.2248	+	15.0544i	0.558151	+	0.517888i
$846$		0			0
$847$	25.6350	+	13.2719i	0.880829	+	0.456029i
$848$		0			0
$849$	0.606319	−	8.09076i	0.0208088	−	0.277674i
$850$		0			0
$851$	−0.783457	−	1.35699i	−0.0268566	−	0.0465169i
$852$		0			0
$853$	10.6652	−	46.7274i	0.365170	−	1.59992i	−0.374687	−	0.927151i	$-0.622250\pi$
$853$	10.6652	−	46.7274i	0.365170	−	1.59992i	0.739857	−	0.672764i	$-0.234893\pi$
$854$		0			0
$855$	8.78177	+	38.4754i	0.300330	+	1.31583i
$856$		0			0
$857$	−11.0491	+	28.1527i	−0.377431	+	0.961679i	0.608354	+	0.793666i	$0.291830\pi$
$857$	−11.0491	+	28.1527i	−0.377431	+	0.961679i	−0.985785	+	0.168013i	$0.946265\pi$
$858$		0			0
$859$	−4.29843	−	1.32589i	−0.146661	−	0.0452388i	0.220556	−	0.975374i	$-0.429213\pi$
$859$	−4.29843	−	1.32589i	−0.146661	−	0.0452388i	−0.367216	+	0.930136i	$0.619689\pi$
$860$		0			0
$861$	3.71460	−	6.02444i	0.126593	−	0.205312i
$862$		0			0
$863$	−20.8380	+	36.0925i	−0.709335	+	1.22860i	0.255770	+	0.966738i	$0.417671\pi$
$863$	−20.8380	+	36.0925i	−0.709335	+	1.22860i	−0.965104	+	0.261866i	$0.915662\pi$
$864$		0			0
$865$	−5.11853	+	1.57886i	−0.174035	+	0.0536827i
$866$		0			0
$867$	−34.3864	−	43.1192i	−1.16782	−	1.46440i
$868$		0			0
$869$	−1.98093	+	2.48401i	−0.0671984	+	0.0842642i
$870$		0			0
$871$	−29.3911	−	4.42999i	−0.995878	−	0.150104i
$872$		0			0
$873$	146.654	−	22.1045i	4.96348	−	0.748124i
$874$		0			0
$875$	1.32736	+	28.9170i	0.0448731	+	0.977572i
$876$		0			0
$877$	−12.5238	+	8.53859i	−0.422899	+	0.288328i	−0.756010	−	0.654560i	$-0.772854\pi$
$877$	−12.5238	+	8.53859i	−0.422899	+	0.288328i	0.333111	+	0.942888i	$0.391902\pi$
$878$		0			0
$879$	1.42553	+	19.0223i	0.0480818	+	0.641607i
$880$		0			0
$881$	23.7680			0.800765			0.400383	−	0.916348i	$-0.368877\pi$
$881$	23.7680			0.800765			0.400383	+	0.916348i	$0.368877\pi$
$882$		0			0
$883$	−27.8993			−0.938886			−0.469443	−	0.882963i	$-0.655545\pi$
$883$	−27.8993			−0.938886			−0.469443	+	0.882963i	$0.655545\pi$
$884$		0			0
$885$	1.02598	+	13.6907i	0.0344879	+	0.460209i
$886$		0			0
$887$	−37.0770	+	25.2787i	−1.24492	+	0.848774i	−0.992901	−	0.118947i	$-0.962048\pi$
$887$	−37.0770	+	25.2787i	−1.24492	+	0.848774i	−0.252022	+	0.967721i	$0.581096\pi$
$888$		0			0
$889$	14.3821	−	33.7410i	0.482360	−	1.13164i
$890$		0			0
$891$	−9.95636	+	1.50068i	−0.333551	+	0.0502747i
$892$		0			0
$893$	−21.5629	−	3.25009i	−0.721576	−	0.108760i
$894$		0			0
$895$	−11.8613	+	14.8736i	−0.396479	+	0.497169i
$896$		0			0
$897$	−25.3726	−	31.8163i	−0.847168	−	1.06232i
$898$		0			0
$899$	15.5737	−	4.80386i	0.519413	−	0.160218i
$900$		0			0
$901$	2.84215	−	4.92275i	0.0946857	−	0.164000i
$902$		0			0
$903$	2.41633	+	6.72228i	0.0804105	+	0.223703i
$904$		0			0
$905$	1.47041	+	0.453562i	0.0488782	+	0.0150769i
$906$		0			0
$907$	−17.9558	+	45.7505i	−0.596211	+	1.51912i	0.240034	+	0.970764i	$0.422841\pi$
$907$	−17.9558	+	45.7505i	−0.596211	+	1.51912i	−0.836245	+	0.548356i	$0.815254\pi$
$908$		0			0
$909$	21.3188	+	93.4038i	0.707100	+	3.09801i
$910$		0			0
$911$	−7.21735	+	31.6213i	−0.239121	+	1.04766i	0.702684	+	0.711502i	$0.251985\pi$
$911$	−7.21735	+	31.6213i	−0.239121	+	1.04766i	−0.941806	+	0.336157i	$0.890873\pi$
$912$		0			0
$913$	0.925969	+	1.60383i	0.0306451	+	0.0530789i
$914$		0			0
$915$	−1.08604	+	14.4922i	−0.0359033	+	0.479096i
$916$		0			0
$917$	4.42042	−	17.0744i	0.145975	−	0.563848i
$918$		0			0
$919$	−39.5766	−	36.7217i	−1.30551	−	1.21134i	−0.962272	−	0.272091i	$-0.912285\pi$
$919$	−39.5766	−	36.7217i	−1.30551	−	1.21134i	−0.343241	−	0.939247i	$-0.611525\pi$
$920$		0			0
$921$	66.4777	+	45.3237i	2.19051	+	1.49347i
$922$		0			0
$923$	38.7730	+	18.6721i	1.27623	+	0.614599i
$924$		0			0
$925$	−2.04547	+	0.985048i	−0.0672548	+	0.0323882i
$926$		0			0
$927$	17.1288	−	15.8932i	0.562584	−	0.522001i
$928$		0			0
$929$	−14.2184	−	36.2279i	−0.466491	−	1.18860i	−0.949718	−	0.313105i	$-0.898631\pi$
$929$	−14.2184	−	36.2279i	−0.466491	−	1.18860i	0.483227	−	0.875495i	$-0.339464\pi$
$930$		0			0
$931$	−19.5452	+	16.1360i	−0.640569	+	0.528835i
$932$		0			0
$933$	−31.7051	−	80.7833i	−1.03798	−	2.64473i
$934$		0			0
$935$	−0.210510	+	0.195325i	−0.00688442	+	0.00638781i
$936$		0			0
$937$	3.36588	−	1.62092i	0.109958	−	0.0529532i	−0.378096	−	0.925766i	$-0.623421\pi$
$937$	3.36588	−	1.62092i	0.109958	−	0.0529532i	0.488054	+	0.872813i	$0.337707\pi$
$938$		0			0
$939$	49.0222	+	23.6078i	1.59978	+	0.770413i
$940$		0			0
$941$	37.1774	+	25.3471i	1.21195	+	0.826292i	0.988910	−	0.148518i	$-0.0474503\pi$
$941$	37.1774	+	25.3471i	1.21195	+	0.826292i	0.223038	+	0.974810i	$0.428403\pi$
$942$		0			0
$943$	−1.30793	−	1.21358i	−0.0425919	−	0.0395195i
$944$		0			0
$945$	−36.7727	−	48.9519i	−1.19622	−	1.59241i
$946$		0			0
$947$	2.02007	−	26.9559i	0.0656433	−	0.875949i	−0.863054	−	0.505111i	$-0.831451\pi$
$947$	2.02007	−	26.9559i	0.0656433	−	0.875949i	0.928698	−	0.370838i	$-0.120930\pi$
$948$		0			0
$949$	18.0214	+	31.2140i	0.585000	+	1.01325i
$950$		0			0
$951$	14.7287	−	64.5306i	0.477610	−	2.09255i
$952$		0			0
$953$	3.70605	+	16.2373i	0.120051	+	0.525977i	0.998813	+	0.0487162i	$0.0155130\pi$
$953$	3.70605	+	16.2373i	0.120051	+	0.525977i	−0.878762	+	0.477260i	$0.841630\pi$
$954$		0			0
$955$	−3.39496	+	8.65021i	−0.109858	+	0.279914i
$956$		0			0
$957$	2.30076	+	0.709691i	0.0743731	+	0.0229411i
$958$		0			0
$959$	5.98571	+	5.88516i	0.193289	+	0.190042i
$960$		0			0
$961$	−7.43090	+	12.8707i	−0.239706	+	0.415183i
$962$		0			0
$963$	104.473	−	32.2256i	3.36659	−	1.03846i
$964$		0			0
$965$	1.43061	+	1.79393i	0.0460529	+	0.0577486i
$966$		0			0
$967$	14.8398	−	18.6085i	0.477215	−	0.598409i	−0.483706	−	0.875230i	$-0.660710\pi$
$967$	14.8398	−	18.6085i	0.477215	−	0.598409i	0.960921	+	0.276822i	$0.0892811\pi$
$968$		0			0
$969$	8.66545	+	1.30611i	0.278374	+	0.0419582i
$970$		0			0
$971$	38.0328	−	5.73253i	1.22053	−	0.183966i	0.492994	−	0.870033i	$-0.335903\pi$
$971$	38.0328	−	5.73253i	1.22053	−	0.183966i	0.727538	+	0.686067i	$0.240664\pi$
$972$		0			0
$973$	−33.4633	−	24.2619i	−1.07278	−	0.777801i
$974$		0			0
$975$	−48.7170	+	33.2147i	−1.56019	+	1.06372i
$976$		0			0
$977$	−2.70685	−	36.1204i	−0.0865998	−	1.15559i	−0.856052	−	0.516890i	$-0.827090\pi$
$977$	−2.70685	−	36.1204i	−0.0865998	−	1.15559i	0.769452	−	0.638704i	$-0.220529\pi$
$978$		0			0
$979$	4.01494			0.128318
$980$		0			0
$981$	41.3674			1.32076
$982$		0			0
$983$	−1.92397	−	25.6736i	−0.0613652	−	0.818861i	−0.939958	−	0.341290i	$-0.889136\pi$
$983$	−1.92397	−	25.6736i	−0.0613652	−	0.818861i	0.878593	−	0.477571i	$-0.158483\pi$
$984$		0			0
$985$	−11.3575	+	7.74338i	−0.361879	+	0.246725i
$986$		0			0
$987$	51.3987	−	14.2399i	1.63604	−	0.453262i
$988$		0			0
$989$	1.78069	−	0.268396i	0.0566227	−	0.00853449i
$990$		0			0
$991$	36.9809	+	5.57398i	1.17474	+	0.177063i	0.707268	−	0.706946i	$-0.249928\pi$
$991$	36.9809	+	5.57398i	1.17474	+	0.177063i	0.467470	+	0.884009i	$0.345166\pi$
$992$		0			0
$993$	−7.18019	+	9.00368i	−0.227857	+	0.285723i
$994$		0			0
$995$	1.54949	+	1.94299i	0.0491220	+	0.0615971i
$996$		0			0
$997$	10.0011	−	3.08493i	0.316737	−	0.0977006i	−0.132310	−	0.991208i	$-0.542240\pi$
$997$	10.0011	−	3.08493i	0.316737	−	0.0977006i	0.449048	+	0.893508i	$0.351763\pi$
$998$		0			0
$999$	6.11213	−	10.5865i	0.193379	−	0.334943i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	784.2.bg.a.65.2		24
4.3	odd	2		98.2.g.a.65.1	✓	24
12.11	even	2		882.2.z.d.163.2		24
28.3	even	6		686.2.g.c.165.2		24
28.11	odd	6		686.2.g.a.165.1		24
28.19	even	6		686.2.e.e.295.1		24
28.23	odd	6		686.2.e.f.295.4		24
28.27	even	2		686.2.g.b.569.2		24
49.46	even	21	inner	784.2.bg.a.193.2		24
196.3	even	42		686.2.g.b.557.2		24
196.95	odd	42		98.2.g.a.95.1	yes	24
196.103	even	42		686.2.e.e.393.1		24
196.135	odd	42		4802.2.a.i.1.1		12
196.139	even	14		686.2.g.c.79.2		24
196.155	odd	14		686.2.g.a.79.1		24
196.159	even	42		4802.2.a.k.1.12		12
196.191	odd	42		686.2.e.f.393.4		24
588.95	even	42		882.2.z.d.487.2		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
98.2.g.a.65.1	✓	24	4.3	odd	2
98.2.g.a.95.1	yes	24	196.95	odd	42
686.2.e.e.295.1		24	28.19	even	6
686.2.e.e.393.1		24	196.103	even	42
686.2.e.f.295.4		24	28.23	odd	6
686.2.e.f.393.4		24	196.191	odd	42
686.2.g.a.79.1		24	196.155	odd	14
686.2.g.a.165.1		24	28.11	odd	6
686.2.g.b.557.2		24	196.3	even	42
686.2.g.b.569.2		24	28.27	even	2
686.2.g.c.79.2		24	196.139	even	14
686.2.g.c.165.2		24	28.3	even	6
784.2.bg.a.65.2		24	1.1	even	1	trivial
784.2.bg.a.193.2		24	49.46	even	21	inner
882.2.z.d.163.2		24	12.11	even	2
882.2.z.d.487.2		24	588.95	even	42
4802.2.a.i.1.1		12	196.135	odd	42
4802.2.a.k.1.12		12	196.159	even	42

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:	\( N \)	\(=\)	\( 784 = 2^{4} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	784.bg (of order \(21\), degree \(12\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.250133 + 3.33779i) q^{3} +(-1.09780 + 0.748464i) q^{5} +(-2.60370 - 0.469838i) q^{7} +(-8.11181 + 1.22266i) q^{9} +O(q^{10})\)	\(q+(0.250133 + 3.33779i) q^{3} +(-1.09780 + 0.748464i) q^{5} +(-2.60370 - 0.469838i) q^{7} +(-8.11181 + 1.22266i) q^{9} +(-0.295564 - 0.0445491i) q^{11} +(3.39549 - 4.25781i) q^{13} +(-2.77281 - 3.47700i) q^{15} +(-0.690967 + 0.213135i) q^{17} +(-1.81038 + 3.13567i) q^{19} +(0.916952 - 8.80813i) q^{21} +(-2.13330 - 0.658036i) q^{23} +(-1.18175 + 3.01105i) q^{25} +(-3.87558 - 16.9800i) q^{27} +(-0.535518 + 2.34626i) q^{29} +(-3.38607 - 5.86484i) q^{31} +(0.0747654 - 0.997674i) q^{33} +(3.20999 - 1.43299i) q^{35} +(0.514508 + 0.477393i) q^{37} +(15.0610 + 10.2684i) q^{39} +(0.720062 + 0.346764i) q^{41} +(-0.726755 + 0.349987i) q^{43} +(7.98999 - 7.41362i) q^{45} +(2.20031 + 5.60630i) q^{47} +(6.55850 + 2.44664i) q^{49} +(-0.884235 - 2.25299i) q^{51} +(-5.76259 + 5.34691i) q^{53} +(0.357812 - 0.172313i) q^{55} +(-10.9191 - 5.25834i) q^{57} +(-2.55068 - 1.73903i) q^{59} +(-2.39548 - 2.22268i) q^{61} +(21.6952 + 0.627804i) q^{63} +(-0.540735 + 7.21560i) q^{65} +(-2.72892 - 4.72662i) q^{67} +(1.66278 - 7.28511i) q^{69} +(1.75840 + 7.70404i) q^{71} +(-2.41794 + 6.16080i) q^{73} +(-10.3459 - 3.19127i) q^{75} +(0.748629 + 0.254860i) q^{77} +(5.31472 - 9.20536i) q^{79} +(32.1894 - 9.92912i) q^{81} +(-3.86302 - 4.84407i) q^{83} +(0.599016 - 0.751143i) q^{85} +(-7.96527 - 1.20057i) q^{87} +(-13.2822 + 2.00198i) q^{89} +(-10.8413 + 9.49072i) q^{91} +(18.7287 - 12.7690i) q^{93} +(-0.359510 - 4.79733i) q^{95} -18.0790 q^{97} +2.45203 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 7 q^{3} - 33 q^{9}+O(q^{10}) \) 24 * q - 7 * q^3 - 33 * q^9	\( 24 q - 7 q^{3} - 33 q^{9} + 7 q^{11} + 14 q^{13} + 7 q^{15} - 7 q^{17} + 7 q^{21} + 21 q^{23} + 4 q^{25} + 35 q^{27} - 11 q^{29} - 28 q^{31} + 14 q^{33} - 21 q^{35} - 24 q^{37} + 40 q^{39} + 28 q^{41} - 10 q^{43} + 7 q^{45} + 70 q^{47} + 84 q^{49} - 60 q^{51} + 26 q^{53} - 56 q^{55} - 33 q^{57} + 7 q^{59} + 14 q^{61} + 14 q^{63} + 36 q^{67} - 35 q^{69} - 7 q^{73} + 28 q^{75} - 91 q^{77} + 26 q^{79} + 55 q^{81} + 7 q^{83} + 49 q^{85} - 35 q^{87} - 56 q^{89} - 7 q^{91} + 72 q^{93} + 14 q^{95} - 126 q^{97} + 14 q^{99}+O(q^{100}) \) 24 * q - 7 * q^3 - 33 * q^9 + 7 * q^11 + 14 * q^13 + 7 * q^15 - 7 * q^17 + 7 * q^21 + 21 * q^23 + 4 * q^25 + 35 * q^27 - 11 * q^29 - 28 * q^31 + 14 * q^33 - 21 * q^35 - 24 * q^37 + 40 * q^39 + 28 * q^41 - 10 * q^43 + 7 * q^45 + 70 * q^47 + 84 * q^49 - 60 * q^51 + 26 * q^53 - 56 * q^55 - 33 * q^57 + 7 * q^59 + 14 * q^61 + 14 * q^63 + 36 * q^67 - 35 * q^69 - 7 * q^73 + 28 * q^75 - 91 * q^77 + 26 * q^79 + 55 * q^81 + 7 * q^83 + 49 * q^85 - 35 * q^87 - 56 * q^89 - 7 * q^91 + 72 * q^93 + 14 * q^95 - 126 * q^97 + 14 * q^99

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