LMFDB - Embedded newform 98.2.g.a.95.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [98,2,Mod(9,98)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(98, base_ring=CyclotomicField(42))

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

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

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

chi := DirichletCharacter("98.9");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 98 = 2 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	98.g (of order $21$, degree $12$, 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:	$0.782533939809$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$2$ over $\Q(\zeta_{21})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label			95.1
Character	$\chi$	$=$	98.95
Dual form			98.2.g.a.65.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.365341 + 0.930874i) q^{2} +(-0.250133 + 3.33779i) q^{3} +(-0.733052 - 0.680173i) q^{4} +(-1.09780 - 0.748464i) q^{5} +(-3.01568 - 1.45228i) q^{6} +(2.60370 - 0.469838i) q^{7} +(0.900969 - 0.433884i) q^{8} +(-8.11181 - 1.22266i) q^{9} +O(q^{10})$	\(q+(-0.365341 + 0.930874i) q^{2} +(-0.250133 + 3.33779i) q^{3} +(-0.733052 - 0.680173i) q^{4} +(-1.09780 - 0.748464i) q^{5} +(-3.01568 - 1.45228i) q^{6} +(2.60370 - 0.469838i) q^{7} +(0.900969 - 0.433884i) q^{8} +(-8.11181 - 1.22266i) q^{9} +(1.09780 - 0.748464i) q^{10} +(0.295564 - 0.0445491i) q^{11} +(2.45364 - 2.27664i) q^{12} +(3.39549 + 4.25781i) q^{13} +(-0.513878 + 2.59537i) q^{14} +(2.77281 - 3.47700i) q^{15} +(0.0747301 + 0.997204i) q^{16} +(-0.690967 - 0.213135i) q^{17} +(4.10172 - 7.10438i) q^{18} +(1.81038 + 3.13567i) q^{19} +(0.295656 + 1.29535i) q^{20} +(0.916952 + 8.80813i) q^{21} +(-0.0665120 + 0.291408i) q^{22} +(2.13330 - 0.658036i) q^{23} +(1.22285 + 3.11578i) q^{24} +(-1.18175 - 3.01105i) q^{25} +(-5.20399 + 1.60522i) q^{26} +(3.87558 - 16.9800i) q^{27} +(-2.22822 - 1.42655i) q^{28} +(-0.535518 - 2.34626i) q^{29} +(2.22362 + 3.85143i) q^{30} +(3.38607 - 5.86484i) q^{31} +(-0.955573 - 0.294755i) q^{32} +(0.0747654 + 0.997674i) q^{33} +(0.450841 - 0.565336i) q^{34} +(-3.20999 - 1.43299i) q^{35} +(5.11476 + 6.41370i) q^{36} +(0.514508 - 0.477393i) q^{37} +(-3.58032 + 0.539646i) q^{38} +(-15.0610 + 10.2684i) q^{39} +(-1.31383 - 0.198027i) q^{40} +(0.720062 - 0.346764i) q^{41} +(-8.53426 - 2.36441i) q^{42} +(0.726755 + 0.349987i) q^{43} +(-0.246965 - 0.168378i) q^{44} +(7.98999 + 7.41362i) q^{45} +(-0.166834 + 2.22624i) q^{46} +(-2.20031 + 5.60630i) q^{47} -3.34715 q^{48} +(6.55850 - 2.44664i) q^{49} +3.23465 q^{50} +(0.884235 - 2.25299i) q^{51} +(0.406976 - 5.43071i) q^{52} +(-5.76259 - 5.34691i) q^{53} +(14.3903 + 9.81117i) q^{54} +(-0.357812 - 0.172313i) q^{55} +(2.14200 - 1.55301i) q^{56} +(-10.9191 + 5.25834i) q^{57} +(2.37972 + 0.358685i) q^{58} +(2.55068 - 1.73903i) q^{59} +(-4.39757 + 0.662828i) q^{60} +(-2.39548 + 2.22268i) q^{61} +(4.22236 + 5.29467i) q^{62} +(-21.6952 + 0.627804i) q^{63} +(0.623490 - 0.781831i) q^{64} +(-0.540735 - 7.21560i) q^{65} +(-0.956024 - 0.294894i) q^{66} +(2.72892 - 4.72662i) q^{67} +(0.361546 + 0.626216i) q^{68} +(1.66278 + 7.28511i) q^{69} +(2.50667 - 2.46456i) q^{70} +(-1.75840 + 7.70404i) q^{71} +(-7.83898 + 2.41800i) q^{72} +(-2.41794 - 6.16080i) q^{73} +(0.256422 + 0.653353i) q^{74} +(10.3459 - 3.19127i) q^{75} +(0.805695 - 3.52998i) q^{76} +(0.748629 - 0.254860i) q^{77} +(-4.05620 - 17.7714i) q^{78} +(-5.31472 - 9.20536i) q^{79} +(0.664333 - 1.15066i) q^{80} +(32.1894 + 9.92912i) q^{81} +(0.0597250 + 0.796974i) q^{82} +(3.86302 - 4.84407i) q^{83} +(5.31888 - 7.08050i) q^{84} +(0.599016 + 0.751143i) q^{85} +(-0.591307 + 0.548653i) q^{86} +(7.96527 - 1.20057i) q^{87} +(0.246965 - 0.168378i) q^{88} +(-13.2822 - 2.00198i) q^{89} +(-9.82022 + 4.72917i) q^{90} +(10.8413 + 9.49072i) q^{91} +(-2.01140 - 0.968638i) q^{92} +(18.7287 + 12.7690i) q^{93} +(-4.41490 - 4.09643i) q^{94} +(0.359510 - 4.79733i) q^{95} +(1.22285 - 3.11578i) q^{96} -18.0790 q^{97} +(-0.118581 + 6.99900i) q^{98} -2.45203 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 2 q^{2} + 7 q^{3} + 2 q^{4} - 7 q^{6} + 4 q^{8} - 33 q^{9}+O(q^{10}) $ 24 * q - 2 * q^2 + 7 * q^3 + 2 * q^4 - 7 * q^6 + 4 * q^8 - 33 * q^9	$ 24 q - 2 q^{2} + 7 q^{3} + 2 q^{4} - 7 q^{6} + 4 q^{8} - 33 q^{9} - 7 q^{11} + 14 q^{13} - 7 q^{15} + 2 q^{16} - 7 q^{17} + 5 q^{18} - 7 q^{20} + 7 q^{21} - 7 q^{22} - 21 q^{23} + 4 q^{25} - 7 q^{26} - 35 q^{27} - 14 q^{28} - 11 q^{29} + 28 q^{31} - 2 q^{32} + 14 q^{33} + 7 q^{34} + 21 q^{35} + 3 q^{36} - 24 q^{37} - 7 q^{38} - 40 q^{39} + 14 q^{40} + 28 q^{41} - 21 q^{42} + 10 q^{43} + 21 q^{44} + 7 q^{45} + 42 q^{46} - 70 q^{47} - 14 q^{48} + 84 q^{49} + 8 q^{50} + 60 q^{51} - 7 q^{52} + 26 q^{53} + 63 q^{54} + 56 q^{55} + 21 q^{56} - 33 q^{57} - 30 q^{58} - 7 q^{59} + 14 q^{60} + 14 q^{61} + 28 q^{62} - 14 q^{63} - 4 q^{64} - 21 q^{66} - 36 q^{67} - 14 q^{68} - 35 q^{69} + 14 q^{70} - 2 q^{72} - 7 q^{73} - 11 q^{74} - 28 q^{75} - 91 q^{77} - 24 q^{78} - 26 q^{79} + 55 q^{81} + 14 q^{82} - 7 q^{83} - 21 q^{84} + 49 q^{85} - 16 q^{86} + 35 q^{87} - 21 q^{88} - 56 q^{89} - 21 q^{90} + 7 q^{91} + 21 q^{92} + 72 q^{93} - 35 q^{94} - 14 q^{95} - 126 q^{97} - 56 q^{98} - 14 q^{99}+O(q^{100}) $ 24 * q - 2 * q^2 + 7 * q^3 + 2 * q^4 - 7 * q^6 + 4 * q^8 - 33 * q^9 - 7 * q^11 + 14 * q^13 - 7 * q^15 + 2 * q^16 - 7 * q^17 + 5 * q^18 - 7 * q^20 + 7 * q^21 - 7 * q^22 - 21 * q^23 + 4 * q^25 - 7 * q^26 - 35 * q^27 - 14 * q^28 - 11 * q^29 + 28 * q^31 - 2 * q^32 + 14 * q^33 + 7 * q^34 + 21 * q^35 + 3 * q^36 - 24 * q^37 - 7 * q^38 - 40 * q^39 + 14 * q^40 + 28 * q^41 - 21 * q^42 + 10 * q^43 + 21 * q^44 + 7 * q^45 + 42 * q^46 - 70 * q^47 - 14 * q^48 + 84 * q^49 + 8 * q^50 + 60 * q^51 - 7 * q^52 + 26 * q^53 + 63 * q^54 + 56 * q^55 + 21 * q^56 - 33 * q^57 - 30 * q^58 - 7 * q^59 + 14 * q^60 + 14 * q^61 + 28 * q^62 - 14 * q^63 - 4 * q^64 - 21 * q^66 - 36 * q^67 - 14 * q^68 - 35 * q^69 + 14 * q^70 - 2 * q^72 - 7 * q^73 - 11 * q^74 - 28 * q^75 - 91 * q^77 - 24 * q^78 - 26 * q^79 + 55 * q^81 + 14 * q^82 - 7 * q^83 - 21 * q^84 + 49 * q^85 - 16 * q^86 + 35 * q^87 - 21 * q^88 - 56 * q^89 - 21 * q^90 + 7 * q^91 + 21 * q^92 + 72 * q^93 - 35 * q^94 - 14 * q^95 - 126 * q^97 - 56 * q^98 - 14 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/98\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{11}{21}\right)$

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 $

$2$	−0.365341	+	0.930874i	−0.258335	+	0.658227i
$2$	−0.365341	+	0.930874i	−0.258335	+	0.658227i
$3$	−0.250133	+	3.33779i	−0.144414	+	1.92708i	0.184717	+	0.982792i	$0.440863\pi$
$3$	−0.250133	+	3.33779i	−0.144414	+	1.92708i	−0.329131	+	0.944284i	$0.606756\pi$
$4$	−0.733052	−	0.680173i	−0.366526	−	0.340086i
$5$	−1.09780	−	0.748464i	−0.490949	−	0.334723i	0.292410	−	0.956293i	$-0.405543\pi$
$5$	−1.09780	−	0.748464i	−0.490949	−	0.334723i	−0.783359	+	0.621570i	$0.786495\pi$
$6$	−3.01568	−	1.45228i	−1.23115	−	0.592889i
$7$	2.60370	−	0.469838i	0.984106	−	0.177582i
$7$	2.60370	−	0.469838i	0.984106	−	0.177582i
$8$	0.900969	−	0.433884i	0.318541	−	0.153401i
$9$	−8.11181	−	1.22266i	−2.70394	−	0.407553i
$10$	1.09780	−	0.748464i	0.347153	−	0.236685i
$11$	0.295564	−	0.0445491i	0.0891159	−	0.0134321i	−0.104333	−	0.994542i	$-0.533271\pi$
$11$	0.295564	−	0.0445491i	0.0891159	−	0.0134321i	0.193449	+	0.981110i	$0.438033\pi$
$12$	2.45364	−	2.27664i	0.708304	−	0.657210i
$13$	3.39549	+	4.25781i	0.941739	+	1.18090i	0.983341	+	0.181769i	$0.0581823\pi$
$13$	3.39549	+	4.25781i	0.941739	+	1.18090i	−0.0416023	+	0.999134i	$0.513246\pi$
$14$	−0.513878	+	2.59537i	−0.137340	+	0.693641i
$15$	2.77281	−	3.47700i	0.715937	−	0.897757i
$16$	0.0747301	+	0.997204i	0.0186825	+	0.249301i
$17$	−0.690967	−	0.213135i	−0.167584	−	0.0516929i	0.209828	−	0.977738i	$-0.432710\pi$
$17$	−0.690967	−	0.213135i	−0.167584	−	0.0516929i	−0.377412	+	0.926046i	$0.623186\pi$
$18$	4.10172	−	7.10438i	0.966784	−	1.67452i
$19$	1.81038	+	3.13567i	0.415330	+	0.719372i	0.995463	−	0.0951493i	$-0.0303328\pi$
$19$	1.81038	+	3.13567i	0.415330	+	0.719372i	−0.580133	+	0.814522i	$0.697000\pi$
$20$	0.295656	+	1.29535i	0.0661107	+	0.289650i
$21$	0.916952	+	8.80813i	0.200095	+	1.92209i
$22$	−0.0665120	+	0.291408i	−0.0141804	+	0.0621285i
$23$	2.13330	−	0.658036i	0.444824	−	0.137210i	−0.0642482	−	0.997934i	$-0.520465\pi$
$23$	2.13330	−	0.658036i	0.444824	−	0.137210i	0.509072	+	0.860724i	$0.329989\pi$
$24$	1.22285	+	3.11578i	0.249614	+	0.636005i
$25$	−1.18175	−	3.01105i	−0.236350	−	0.602210i
$26$	−5.20399	+	1.60522i	−1.02059	+	0.314809i
$27$	3.87558	−	16.9800i	0.745855	−	3.26780i
$28$	−2.22822	−	1.42655i	−0.421094	−	0.269593i
$29$	−0.535518	−	2.34626i	−0.0994432	−	0.435689i	−1.00000		0.000949836i	$-0.999698\pi$
$29$	−0.535518	−	2.34626i	−0.0994432	−	0.435689i	0.900556	−	0.434739i	$-0.143159\pi$
$30$	2.22362	+	3.85143i	0.405976	+	0.703171i
$31$	3.38607	−	5.86484i	0.608156	−	1.05336i	−0.383389	−	0.923587i	$-0.625243\pi$
$31$	3.38607	−	5.86484i	0.608156	−	1.05336i	0.991544	−	0.129769i	$-0.0414236\pi$
$32$	−0.955573	−	0.294755i	−0.168923	−	0.0521058i
$33$	0.0747654	+	0.997674i	0.0130150	+	0.173673i
$34$	0.450841	−	0.565336i	0.0773185	−	0.0969543i
$35$	−3.20999	−	1.43299i	−0.542587	−	0.242219i
$36$	5.11476	+	6.41370i	0.852459	+	1.06895i
$37$	0.514508	−	0.477393i	0.0845845	−	0.0784830i	−0.636748	−	0.771072i	$-0.719721\pi$
$37$	0.514508	−	0.477393i	0.0845845	−	0.0784830i	0.721332	+	0.692589i	$0.243530\pi$
$38$	−3.58032	+	0.539646i	−0.580805	+	0.0875422i
$39$	−15.0610	+	10.2684i	−2.41169	+	1.64426i
$40$	−1.31383	−	0.198027i	−0.207734	−	0.0313109i
$41$	0.720062	−	0.346764i	0.112455	−	0.0541554i	−0.376811	−	0.926290i	$-0.622979\pi$
$41$	0.720062	−	0.346764i	0.112455	−	0.0541554i	0.489265	+	0.872135i	$0.337265\pi$
$42$	−8.53426	−	2.36441i	−1.31687	−	0.364836i
$43$	0.726755	+	0.349987i	0.110829	+	0.0533725i	0.488477	−	0.872577i	$-0.337553\pi$
$43$	0.726755	+	0.349987i	0.110829	+	0.0533725i	−0.377648	+	0.925949i	$0.623267\pi$
$44$	−0.246965	−	0.168378i	−0.0372313	−	0.0253839i
$45$	7.98999	+	7.41362i	1.19108	+	1.10516i
$46$	−0.166834	+	2.22624i	−0.0245983	+	0.328241i
$47$	−2.20031	+	5.60630i	−0.320949	+	0.817764i	0.675792	+	0.737092i	$0.263802\pi$
$47$	−2.20031	+	5.60630i	−0.320949	+	0.817764i	−0.996741	+	0.0806714i	$0.974294\pi$
$48$	−3.34715			−0.483120
$49$	6.55850	−	2.44664i	0.936929	−	0.349519i
$50$	3.23465			0.457448
$51$	0.884235	−	2.25299i	0.123818	−	0.315482i
$52$	0.406976	−	5.43071i	0.0564374	−	0.753104i
$53$	−5.76259	−	5.34691i	−0.791553	−	0.734454i	0.176744	−	0.984257i	$-0.443444\pi$
$53$	−5.76259	−	5.34691i	−0.791553	−	0.734454i	−0.968297	+	0.249803i	$0.919634\pi$
$54$	14.3903	+	9.81117i	1.95828	+	1.33513i
$55$	−0.357812	−	0.172313i	−0.0482474	−	0.0232347i
$56$	2.14200	−	1.55301i	0.286236	−	0.207530i
$57$	−10.9191	+	5.25834i	−1.44626	+	0.696484i
$58$	2.37972	+	0.358685i	0.312472	+	0.0470976i
$59$	2.55068	−	1.73903i	0.332071	−	0.226402i	−0.385793	−	0.922585i	$-0.626072\pi$
$59$	2.55068	−	1.73903i	0.332071	−	0.226402i	0.717864	+	0.696183i	$0.245120\pi$
$60$	−4.39757	+	0.662828i	−0.567724	+	0.0855707i
$61$	−2.39548	+	2.22268i	−0.306710	+	0.284585i	−0.818477	−	0.574539i	$-0.805181\pi$
$61$	−2.39548	+	2.22268i	−0.306710	+	0.284585i	0.511768	+	0.859124i	$0.328991\pi$
$62$	4.22236	+	5.29467i	0.536240	+	0.672423i
$63$	−21.6952	+	0.627804i	−2.73333	+	0.0790959i
$64$	0.623490	−	0.781831i	0.0779362	−	0.0977289i
$65$	−0.540735	−	7.21560i	−0.0670699	−	0.894985i
$66$	−0.956024	−	0.294894i	−0.117678	−	0.0362990i
$67$	2.72892	−	4.72662i	0.333390	−	0.577449i	−0.649784	−	0.760119i	$-0.725141\pi$
$67$	2.72892	−	4.72662i	0.333390	−	0.577449i	0.983174	+	0.182670i	$0.0584740\pi$
$68$	0.361546	+	0.626216i	0.0438439	+	0.0759399i
$69$	1.66278	+	7.28511i	0.200175	+	0.877024i
$70$	2.50667	−	2.46456i	0.299605	−	0.294571i
$71$	−1.75840	+	7.70404i	−0.208683	+	0.914302i	0.756761	+	0.653692i	$0.226781\pi$
$71$	−1.75840	+	7.70404i	−0.208683	+	0.914302i	−0.965444	+	0.260610i	$0.916076\pi$
$72$	−7.83898	+	2.41800i	−0.923832	+	0.284964i
$73$	−2.41794	−	6.16080i	−0.282998	−	0.721067i	−0.999719	−	0.0237069i	$-0.992453\pi$
$73$	−2.41794	−	6.16080i	−0.282998	−	0.721067i	0.716721	−	0.697360i	$-0.245642\pi$
$74$	0.256422	+	0.653353i	0.0298085	+	0.0759507i
$75$	10.3459	−	3.19127i	1.19464	−	0.368496i
$76$	0.805695	−	3.52998i	0.0924196	−	0.404917i
$77$	0.748629	−	0.254860i	0.0853142	−	0.0290440i
$78$	−4.05620	−	17.7714i	−0.459274	−	2.01221i
$79$	−5.31472	−	9.20536i	−0.597953	−	1.03568i	−0.993123	−	0.117076i	$-0.962648\pi$
$79$	−5.31472	−	9.20536i	−0.597953	−	1.03568i	0.395170	−	0.918608i	$-0.370686\pi$
$80$	0.664333	−	1.15066i	0.0742747	−	0.128647i
$81$	32.1894	+	9.92912i	3.57660	+	1.10324i
$82$	0.0597250	+	0.796974i	0.00659552	+	0.0880111i
$83$	3.86302	−	4.84407i	0.424021	−	0.531706i	−0.523233	−	0.852190i	$-0.675274\pi$
$83$	3.86302	−	4.84407i	0.424021	−	0.531706i	0.947254	+	0.320484i	$0.103846\pi$
$84$	5.31888	−	7.08050i	0.580337	−	0.772546i
$85$	0.599016	+	0.751143i	0.0649724	+	0.0814729i
$86$	−0.591307	+	0.548653i	−0.0637623	+	0.0591628i
$87$	7.96527	−	1.20057i	0.853967	−	0.128715i
$88$	0.246965	−	0.168378i	0.0263265	−	0.0179491i
$89$	−13.2822	−	2.00198i	−1.40791	−	0.212209i	−0.599289	−	0.800533i	$-0.704550\pi$
$89$	−13.2822	−	2.00198i	−1.40791	−	0.212209i	−0.808625	+	0.588324i	$0.799788\pi$
$90$	−9.82022	+	4.72917i	−1.03514	+	0.498498i
$91$	10.8413	+	9.49072i	1.13648	+	0.994898i
$92$	−2.01140	−	0.968638i	−0.209703	−	0.100987i
$93$	18.7287	+	12.7690i	1.94207	+	1.32408i
$94$	−4.41490	−	4.09643i	−0.455362	−	0.422514i
$95$	0.359510	−	4.79733i	0.0368850	−	0.492196i
$96$	1.22285	−	3.11578i	0.124807	−	0.318003i
$97$	−18.0790			−1.83565			−0.917824	−	0.396987i	$-0.870056\pi$
$97$	−18.0790			−1.83565			−0.917824	+	0.396987i	$0.870056\pi$
$98$	−0.118581	+	6.99900i	−0.0119785	+	0.707005i
$99$	−2.45203			−0.246438
$100$	−1.18175	+	3.01105i	−0.118175	+	0.301105i
$101$	−0.872755	+	11.6461i	−0.0868423	+	1.15883i	0.768178	+	0.640236i	$0.221164\pi$
$101$	−0.872755	+	11.6461i	−0.0868423	+	1.15883i	−0.855020	+	0.518594i	$0.826456\pi$
$102$	1.77421	+	1.64622i	0.175672	+	0.163000i
$103$	2.35344	+	1.60454i	0.231891	+	0.158101i	0.673691	−	0.739013i	$-0.264708\pi$
$103$	2.35344	+	1.60454i	0.231891	+	0.158101i	−0.441801	+	0.897113i	$0.645660\pi$
$104$	4.90662	+	2.36290i	0.481134	+	0.231702i
$105$	5.58595	−	10.3558i	0.545132	−	1.01063i
$106$	7.08261	−	3.41080i	0.687923	−	0.331286i
$107$	13.1785	+	1.98634i	1.27401	+	0.192027i	0.751003	−	0.660299i	$-0.229570\pi$
$107$	13.1785	+	1.98634i	1.27401	+	0.192027i	0.523012	+	0.852325i	$0.324808\pi$
$108$	−14.3903	+	9.81117i	−1.38471	+	0.944080i
$109$	−4.98637	+	0.751575i	−0.477608	+	0.0719878i	−0.383435	−	0.923568i	$-0.625259\pi$
$109$	−4.98637	+	0.751575i	−0.477608	+	0.0719878i	−0.0941733	+	0.995556i	$0.530021\pi$
$110$	0.291125	−	0.270125i	0.0277577	−	0.0257554i
$111$	1.46474	+	1.83673i	0.139027	+	0.174335i
$112$	0.663099	+	2.56131i	0.0626570	+	0.242021i
$113$	11.7224	−	14.6995i	1.10275	−	1.38281i	0.186384	−	0.982477i	$-0.440323\pi$
$113$	11.7224	−	14.6995i	1.10275	−	1.38281i	0.916370	−	0.400332i	$-0.131105\pi$
$114$	−0.905672	−	12.0854i	−0.0848240	−	1.13190i
$115$	−2.83444	−	0.874310i	−0.264313	−	0.0815298i
$116$	−1.20330	+	2.08417i	−0.111723	+	0.193511i
$117$	−22.3377	−	38.6900i	−2.06512	−	3.57689i
$118$	0.686945	+	3.00970i	0.0632384	+	0.277066i
$119$	−1.89921	−	0.230297i	−0.174100	−	0.0211113i
$120$	0.989606	−	4.33575i	0.0903382	−	0.395798i
$121$	−10.4259	+	3.21597i	−0.947812	+	0.292361i
$122$	−1.19387	−	3.04193i	−0.108088	−	0.275403i
$123$	0.977314	+	2.49016i	0.0881215	+	0.224530i
$124$	−6.47127	+	1.99612i	−0.581137	+	0.179257i
$125$	−2.43462	+	10.6668i	−0.217759	+	0.954066i
$126$	7.34173	−	20.4248i	0.654053	−	1.81959i
$127$	3.08483	+	13.5155i	0.273735	+	1.19931i	0.905567	+	0.424204i	$0.139446\pi$
$127$	3.08483	+	13.5155i	0.273735	+	1.19931i	−0.631832	+	0.775105i	$0.717697\pi$
$128$	0.500000	+	0.866025i	0.0441942	+	0.0765466i
$129$	−1.34997	+	2.33822i	−0.118858	+	0.205868i
$130$	6.91437	+	2.13280i	0.606430	+	0.187059i
$131$	0.498173	+	6.64766i	0.0435256	+	0.580809i	0.975744	+	0.218913i	$0.0702512\pi$
$131$	0.498173	+	6.64766i	0.0435256	+	0.580809i	−0.932219	+	0.361895i	$0.882130\pi$
$132$	0.623784	−	0.782200i	0.0542934	−	0.0680818i
$133$	6.18695	+	7.31376i	0.536476	+	0.634183i
$134$	3.40290	+	4.26711i	0.293966	+	0.368622i
$135$	−16.9635	+	15.7398i	−1.45999	+	1.35467i
$136$	−0.715016	+	0.107771i	−0.0613121	+	0.00924131i
$137$	−2.62144	+	1.78727i	−0.223965	+	0.152697i	−0.670105	−	0.742267i	$-0.733751\pi$
$137$	−2.62144	+	1.78727i	−0.223965	+	0.152697i	0.446140	+	0.894963i	$0.352798\pi$
$138$	−7.38900	−	1.11371i	−0.628993	−	0.0948055i
$139$	−14.0754	+	6.77834i	−1.19386	+	0.574931i	−0.921919	−	0.387384i	$-0.873379\pi$
$139$	−14.0754	+	6.77834i	−1.19386	+	0.574931i	−0.271938	+	0.962315i	$0.587665\pi$
$140$	1.37841	+	3.23380i	0.116497	+	0.273306i
$141$	−18.1623	−	8.74651i	−1.52954	−	0.736589i
$142$	−6.52908	−	4.45145i	−0.547908	−	0.373557i
$143$	1.19327	+	1.10719i	0.0997858	+	0.0925877i
$144$	0.613043	−	8.18049i	0.0510869	−	0.681708i
$145$	−1.16820	+	2.97653i	−0.0970138	+	0.247187i
$146$	6.61830			0.547734
$147$	6.52587	+	22.5029i	0.538245	+	1.85601i
$148$	−0.701871			−0.0576934
$149$	8.29101	−	21.1251i	0.679226	−	1.73064i	−0.00353200	−	0.999994i	$-0.501124\pi$
$149$	8.29101	−	21.1251i	0.679226	−	1.73064i	0.682758	−	0.730645i	$-0.260780\pi$
$150$	−0.809092	+	10.7966i	−0.0660621	+	0.881538i
$151$	8.37807	+	7.77372i	0.681798	+	0.632616i	0.943049	−	0.332655i	$-0.107944\pi$
$151$	8.37807	+	7.77372i	0.681798	+	0.632616i	−0.261251	+	0.965271i	$0.584135\pi$
$152$	2.99161	+	2.03965i	0.242652	+	0.165437i
$153$	5.34440	+	2.57373i	0.432069	+	0.208074i
$154$	−0.0362626	+	0.789990i	−0.00292212	+	0.0636592i
$155$	−8.10683	+	3.90404i	−0.651156	+	0.313580i
$156$	18.0248	+	2.71680i	1.44314	+	0.217518i
$157$	−3.24073	+	2.20949i	−0.258638	+	0.176337i	−0.685697	−	0.727888i	$-0.740502\pi$
$157$	−3.24073	+	2.20949i	−0.258638	+	0.176337i	0.427058	+	0.904224i	$0.359550\pi$
$158$	10.5107	−	1.58424i	0.836188	−	0.126035i
$159$	19.2883	−	17.8969i	1.52966	−	1.41932i
$160$	0.828409	+	1.03879i	0.0654915	+	0.0821238i
$161$	5.24530	−	2.71563i	0.413388	−	0.214022i
$162$	−21.0029	+	26.3368i	−1.65014	+	2.06921i
$163$	0.302107	+	4.03134i	0.0236629	+	0.315759i	0.996458	+	0.0840919i	$0.0267989\pi$
$163$	0.302107	+	4.03134i	0.0236629	+	0.315759i	−0.972795	+	0.231667i	$0.925582\pi$
$164$	−0.763702	−	0.235571i	−0.0596351	−	0.0183950i
$165$	0.664646	−	1.15120i	0.0517426	−	0.0896209i
$166$	3.09790	+	5.36572i	0.240444	+	0.416461i
$167$	1.64323	+	7.19945i	0.127157	+	0.557110i	0.997865	+	0.0653101i	$0.0208037\pi$
$167$	1.64323	+	7.19945i	0.127157	+	0.557110i	−0.870708	+	0.491800i	$0.836339\pi$
$168$	4.64785	+	7.53800i	0.358590	+	0.581570i
$169$	−3.70681	+	16.2406i	−0.285139	+	1.24928i
$170$	−0.918064	+	0.283185i	−0.0704123	+	0.0217193i
$171$	−10.8516	−	27.6494i	−0.829843	−	2.11441i
$172$	−0.294698	−	0.750878i	−0.0224705	−	0.0572539i
$173$	3.85238	−	1.18830i	0.292891	−	0.0903449i	−0.144828	−	0.989457i	$-0.546263\pi$
$173$	3.85238	−	1.18830i	0.292891	−	0.0903449i	0.437719	+	0.899112i	$0.355787\pi$
$174$	−1.79246	+	7.85328i	−0.135886	+	0.595356i
$175$	−4.49163	−	7.28463i	−0.339535	−	0.550667i
$176$	0.0665120	+	0.291408i	0.00501353	+	0.0219657i
$177$	5.16650	+	8.94865i	0.388338	+	0.672621i
$178$	6.71613	−	11.6327i	0.503395	−	0.871906i
$179$	−13.6820	−	4.22034i	−1.02264	−	0.315443i	−0.262314	−	0.964983i	$-0.584486\pi$
$179$	−13.6820	−	4.22034i	−1.02264	−	0.315443i	−0.760328	+	0.649539i	$0.774962\pi$
$180$	−0.814529	−	10.8691i	−0.0607114	−	0.810138i
$181$	−0.722086	+	0.905468i	−0.0536723	+	0.0673029i	−0.807943	−	0.589261i	$-0.799419\pi$
$181$	−0.722086	+	0.905468i	−0.0536723	+	0.0673029i	0.754271	+	0.656563i	$0.227991\pi$
$182$	−12.7954	+	6.62454i	−0.948461	+	0.491044i
$183$	−6.81966	−	8.55158i	−0.504124	−	0.632151i
$184$	1.63653	−	1.51847i	0.120646	−	0.111943i
$185$	−0.922136	+	0.138990i	−0.0677968	+	0.0102187i
$186$	−18.7287	+	12.7690i	−1.37325	+	0.936267i
$187$	−0.213720	−	0.0322131i	−0.0156287	−	0.00235565i
$188$	5.42620	−	2.61312i	0.395746	−	0.190581i
$189$	2.11298	−	46.0317i	0.153696	−	3.34832i
$190$	4.33436	+	2.08732i	0.314448	+	0.151430i
$191$	−5.77864	−	3.93981i	−0.418128	−	0.285075i	0.335925	−	0.941889i	$-0.390951\pi$
$191$	−5.77864	−	3.93981i	−0.418128	−	0.285075i	−0.754053	+	0.656814i	$0.771904\pi$
$192$	2.45364	+	2.27664i	0.177076	+	0.164302i
$193$	−0.129054	+	1.72211i	−0.00928951	+	0.123960i	−0.999921	−	0.0126057i	$-0.995987\pi$
$193$	−0.129054	+	1.72211i	−0.00928951	+	0.123960i	0.990631	+	0.136566i	$0.0436064\pi$
$194$	6.60502	−	16.8293i	0.474213	−	1.20827i
$195$	24.2194			1.73439
$196$	−6.47186	−	2.66740i	−0.462276	−	0.190529i
$197$	10.3457			0.737101			0.368550	−	0.929608i	$-0.379854\pi$
$197$	10.3457			0.737101			0.368550	+	0.929608i	$0.379854\pi$
$198$	0.895825	−	2.28253i	0.0636635	−	0.162212i
$199$	0.139778	−	1.86521i	0.00990859	−	0.132221i	−0.990056	−	0.140676i	$-0.955072\pi$
$199$	0.139778	−	1.86521i	0.00990859	−	0.132221i	0.999964	+	0.00845524i	$0.00269142\pi$
$200$	−2.37116	−	2.20012i	−0.167667	−	0.155572i
$201$	15.0939	+	10.2908i	1.06464	+	0.725860i
$202$	−10.5222	−	5.06722i	−0.740339	−	0.356529i
$203$	−2.49669	−	5.85734i	−0.175233	−	0.411105i
$204$	−2.18061	+	1.05013i	−0.152674	+	0.0735237i
$205$	−1.05002	−	0.158265i	−0.0733367	−	0.0110537i
$206$	−2.35344	+	1.60454i	−0.163972	+	0.111794i
$207$	−18.1095	+	2.72956i	−1.25869	+	0.189718i
$208$	−3.99216	+	3.70418i	−0.276806	+	0.256839i
$209$	0.674774	+	0.846140i	0.0466751	+	0.0585288i
$210$	7.59920	+	8.98322i	0.524394	+	0.619901i
$211$	4.26780	−	5.35165i	0.293808	−	0.368423i	−0.612916	−	0.790148i	$-0.710004\pi$
$211$	4.26780	−	5.35165i	0.293808	−	0.368423i	0.906724	+	0.421725i	$0.138575\pi$
$212$	0.587461	+	7.83912i	0.0403470	+	0.538393i
$213$	−25.2747	−	7.79620i	−1.73179	−	0.534187i
$214$	−6.66368	+	11.5418i	−0.455520	+	0.788984i
$215$	−0.535876	−	0.928164i	−0.0365464	−	0.0633003i
$216$	−3.87558	−	16.9800i	−0.263700	−	1.15534i
$217$	6.06077	−	16.8612i	0.411432	−	1.14461i
$218$	1.12211	−	4.91627i	0.0759986	−	0.332972i
$219$	21.1683	−	6.52955i	1.43042	−	0.441226i
$220$	0.145092	+	0.369688i	0.00978210	+	0.0249244i
$221$	−1.43868	−	3.66570i	−0.0967762	−	0.246582i
$222$	−2.24490	+	0.692459i	−0.150668	+	0.0464748i
$223$	5.74434	−	25.1676i	0.384669	−	1.68535i	−0.297957	−	0.954579i	$-0.596305\pi$
$223$	5.74434	−	25.1676i	0.384669	−	1.68535i	0.682626	−	0.730768i	$-0.260838\pi$
$224$	−2.62651	−	0.318489i	−0.175491	−	0.0212799i
$225$	5.90464	+	25.8699i	0.393643	+	1.72466i
$226$	9.40066	+	16.2824i	0.625323	+	1.08309i
$227$	−13.0700	+	22.6379i	−0.867485	+	1.50253i	−0.00292604	+	0.999996i	$0.500931\pi$
$227$	−13.0700	+	22.6379i	−0.867485	+	1.50253i	−0.864559	+	0.502532i	$0.832402\pi$
$228$	11.5808	+	3.57221i	0.766958	+	0.236575i
$229$	0.944682	+	12.6059i	0.0624263	+	0.833022i	0.937267	+	0.348611i	$0.113347\pi$
$229$	0.944682	+	12.6059i	0.0624263	+	0.833022i	−0.874841	+	0.484410i	$0.839034\pi$
$230$	1.84941	−	2.31909i	0.121946	−	0.152916i
$231$	0.663412	+	2.56252i	0.0436493	+	0.168601i
$232$	−1.50049	−	1.88155i	−0.0985119	−	0.123530i
$233$	16.0492	−	14.8915i	1.05142	−	0.975574i	0.0516856	−	0.998663i	$-0.483541\pi$
$233$	16.0492	−	14.8915i	1.05142	−	0.975574i	0.999733	+	0.0230892i	$0.00735016\pi$
$234$	44.1764	−	6.65852i	2.88790	−	0.435281i
$235$	6.61161	−	4.50772i	0.431294	−	0.294051i
$236$	−3.05262	−	0.460109i	−0.198709	−	0.0299505i
$237$	32.0550	−	15.4369i	2.08219	−	1.00273i
$238$	0.908237	−	1.68379i	0.0588722	−	0.109144i
$239$	13.6184	+	6.55827i	0.880901	+	0.424219i	0.818953	−	0.573860i	$-0.194555\pi$
$239$	13.6184	+	6.55827i	0.880901	+	0.424219i	0.0619472	+	0.998079i	$0.480269\pi$
$240$	3.67449	+	2.50522i	0.237187	+	0.161711i
$241$	−13.0704	−	12.1276i	−0.841938	−	0.781204i	0.135866	−	0.990727i	$-0.456618\pi$
$241$	−13.0704	−	12.1276i	−0.841938	−	0.781204i	−0.977804	+	0.209523i	$0.932809\pi$
$242$	0.815354	−	10.8801i	0.0524130	−	0.699402i
$243$	−22.1039	+	56.3198i	−1.41797	+	3.61292i
$244$	3.26782			0.209201
$245$	−9.03111	−	2.22290i	−0.576977	−	0.142016i
$246$	−2.67507			−0.170557
$247$	−7.20396	+	18.3554i	−0.458377	+	1.16793i
$248$	0.506082	−	6.75320i	0.0321362	−	0.428828i
$249$	15.2022	+	14.1056i	0.963403	+	0.893907i
$250$	−9.03996	−	6.16334i	−0.571737	−	0.389804i
$251$	−14.2489	−	6.86193i	−0.899385	−	0.433121i	−0.0737185	−	0.997279i	$-0.523487\pi$
$251$	−14.2489	−	6.86193i	−0.899385	−	0.433121i	−0.825667	+	0.564158i	$0.809201\pi$
$252$	16.3307	+	14.2962i	1.02874	+	0.900579i
$253$	0.601211	−	0.289528i	0.0377978	−	0.0182025i
$254$	−13.7083	−	2.06619i	−0.860133	−	0.129644i
$255$	−2.65699	+	1.81151i	−0.166387	+	0.113441i
$256$	−0.988831	+	0.149042i	−0.0618019	+	0.00931514i
$257$	15.0904	−	14.0018i	0.941310	−	0.873408i	−0.0508087	−	0.998708i	$-0.516180\pi$
$257$	15.0904	−	14.0018i	0.941310	−	0.873408i	0.992119	+	0.125300i	$0.0399894\pi$
$258$	−1.68338	−	2.11090i	−0.104803	−	0.131419i
$259$	1.11533	−	1.48472i	0.0693030	−	0.0922563i
$260$	−4.51147	+	5.65720i	−0.279789	+	0.350845i
$261$	1.47535	+	19.6871i	0.0913217	+	1.21860i
$262$	−6.37013	−	1.96493i	−0.393548	−	0.121394i
$263$	−9.10450	+	15.7695i	−0.561408	+	0.972387i	0.435966	+	0.899963i	$0.356407\pi$
$263$	−9.10450	+	15.7695i	−0.561408	+	0.972387i	−0.997374	+	0.0724238i	$0.976927\pi$
$264$	0.500236	+	0.866434i	0.0307874	+	0.0533253i
$265$	2.32418	+	10.1829i	0.142773	+	0.625531i
$266$	−9.06853	+	3.08725i	−0.556027	+	0.189291i
$267$	10.0045	−	43.8326i	0.612266	−	2.68251i
$268$	−5.21536	+	1.60872i	−0.318579	+	0.0982685i
$269$	2.81799	+	7.18013i	0.171816	+	0.437780i	0.990680	−	0.136207i	$-0.0434912\pi$
$269$	2.81799	+	7.18013i	0.171816	+	0.437780i	−0.818864	+	0.573987i	$0.805396\pi$
$270$	−8.45434	−	21.5413i	−0.514515	−	1.31096i
$271$	−10.2742	+	3.16917i	−0.624113	+	0.192513i	−0.590652	−	0.806927i	$-0.701129\pi$
$271$	−10.2742	+	3.16917i	−0.624113	+	0.192513i	−0.0334614	+	0.999440i	$0.510653\pi$
$272$	0.160903	−	0.704963i	0.00975618	−	0.0427446i
$273$	−34.3898	+	33.8121i	−2.08137	+	2.04640i
$274$	−0.706001	−	3.09319i	−0.0426511	−	0.186866i
$275$	−0.483422	−	0.837311i	−0.0291514	−	0.0504918i
$276$	3.73623	−	6.47134i	0.224895	−	0.389529i
$277$	2.19322	+	0.676520i	0.131778	+	0.0406481i	0.359943	−	0.932974i	$-0.382796\pi$
$277$	2.19322	+	0.676520i	0.131778	+	0.0406481i	−0.228165	+	0.973623i	$0.573272\pi$
$278$	−1.16747	−	15.5788i	−0.0700201	−	0.934354i
$279$	−34.6378	+	43.4344i	−2.07371	+	2.60035i
$280$	−3.51385	+	0.101682i	−0.209993	+	0.00607666i
$281$	−13.3488	−	16.7389i	−0.796323	−	0.998557i	−0.999810	−	0.0194799i	$-0.993799\pi$
$281$	−13.3488	−	16.7389i	−0.796323	−	0.998557i	0.203487	−	0.979078i	$-0.434772\pi$
$282$	14.7773	−	13.7114i	0.879978	−	0.816500i
$283$	2.39691	−	0.361276i	0.142482	−	0.0214757i	−0.0774141	−	0.996999i	$-0.524666\pi$
$283$	2.39691	−	0.361276i	0.142482	−	0.0214757i	0.219896	+	0.975523i	$0.429428\pi$
$284$	6.52908	−	4.45145i	0.387429	−	0.264145i
$285$	15.9226	+	2.39994i	0.943172	+	0.142160i
$286$	−1.46660	+	0.706278i	−0.0867219	+	0.0417631i
$287$	1.71190	−	1.24118i	0.101050	−	0.0732646i
$288$	7.39104	+	3.55934i	0.435521	+	0.209736i
$289$	−13.6141	−	9.28190i	−0.800826	−	0.545994i
$290$	−2.34398	−	2.17489i	−0.137643	−	0.127714i
$291$	4.52217	−	60.3441i	0.265094	−	3.53743i
$292$	−2.41794	+	6.16080i	−0.141499	+	0.360533i
$293$	5.69907			0.332943			0.166472	−	0.986046i	$-0.446763\pi$
$293$	5.69907			0.332943			0.166472	+	0.986046i	$0.446763\pi$
$294$	−23.3315	−	2.14648i	−1.36072	−	0.125185i
$295$	−4.10173			−0.238812
$296$	0.256422	−	0.653353i	0.0149042	−	0.0379754i
$297$	0.389036	−	5.19133i	0.0225742	−	0.301232i
$298$	16.6358	+	15.4358i	0.963686	+	0.894169i
$299$	10.0454	+	6.84883i	0.580940	+	0.396078i
$300$	−9.75466	−	4.69760i	−0.563186	−	0.271216i
$301$	2.05669	+	0.569803i	0.118546	+	0.0328429i
$302$	−10.2972	+	4.95887i	−0.592537	+	0.285351i
$303$	−38.6540	−	5.82615i	−2.22061	−	0.334704i
$304$	−2.99161	+	2.03965i	−0.171581	+	0.116982i
$305$	4.29334	−	0.647117i	0.245836	−	0.0370538i
$306$	−4.34834	+	4.03467i	−0.248578	+	0.230647i
$307$	−14.9873	−	18.7935i	−0.855372	−	1.07260i	−0.996581	−	0.0826223i	$-0.973671\pi$
$307$	−14.9873	−	18.7935i	−0.855372	−	1.07260i	0.141209	−	0.989980i	$-0.454901\pi$
$308$	−0.722132	−	0.322371i	−0.0411473	−	0.0183688i
$309$	−5.94431	+	7.45393i	−0.338160	+	0.424039i
$310$	−0.672414	−	8.97274i	−0.0381905	−	0.509617i
$311$	24.7753	+	7.64217i	1.40488	+	0.433348i	0.902272	−	0.431167i	$-0.141898\pi$
$311$	24.7753	+	7.64217i	1.40488	+	0.433348i	0.502607	+	0.864515i	$0.332374\pi$
$312$	−9.11420	+	15.7863i	−0.515990	+	0.893720i
$313$	8.12788	+	14.0779i	0.459415	+	0.795730i	0.998930	−	0.0462456i	$-0.0147257\pi$
$313$	8.12788	+	14.0779i	0.459415	+	0.795730i	−0.539515	+	0.841976i	$0.681392\pi$
$314$	−0.872786	−	3.82393i	−0.0492542	−	0.215797i
$315$	24.2867	+	15.5488i	1.36840	+	0.876078i
$316$	−2.36527	+	10.3629i	−0.133057	+	0.582961i
$317$	−18.8965	+	5.82880i	−1.06133	+	0.327378i	−0.775792	−	0.630989i	$-0.782649\pi$
$317$	−18.8965	+	5.82880i	−1.06133	+	0.327378i	−0.285541	+	0.958367i	$0.592173\pi$
$318$	9.61296	+	24.4934i	0.539068	+	1.37352i
$319$	−0.262803	−	0.669612i	−0.0147142	−	0.0374911i
$320$	−1.26964	+	0.391631i	−0.0709749	+	0.0218928i
$321$	−9.92638	+	43.4903i	−0.554036	+	2.42739i
$322$	0.611588	+	5.87485i	0.0340825	+	0.327392i
$323$	−0.582592	−	2.55250i	−0.0324163	−	0.142025i
$324$	−16.8430	−	29.1729i	−0.935722	−	1.62072i
$325$	8.80785	−	15.2556i	0.488572	−	0.846231i
$326$	−3.86304	−	1.19159i	−0.213954	−	0.0659961i
$327$	−1.26135	−	16.8315i	−0.0697525	−	0.930783i
$328$	0.498299	−	0.624847i	0.0275139	−	0.0345014i
$329$	−3.09490	+	15.6309i	−0.170627	+	0.861761i
$330$	0.828800	+	1.03928i	0.0456240	+	0.0572106i
$331$	−2.52212	+	2.34019i	−0.138628	+	0.128628i	−0.746439	−	0.665453i	$-0.768238\pi$
$331$	−2.52212	+	2.34019i	−0.138628	+	0.128628i	0.607811	+	0.794082i	$0.292048\pi$
$332$	−6.12660	+	0.923436i	−0.336241	+	0.0506801i
$333$	−4.75728	+	3.24346i	−0.260697	+	0.177740i
$334$	−7.30211	−	1.10062i	−0.399554	−	0.0602231i
$335$	−6.53350	+	3.14637i	−0.356963	+	0.171904i
$336$	−8.71498	+	1.57262i	−0.475441	+	0.0857935i
$337$	9.97406	+	4.80325i	0.543321	+	0.261650i	0.685351	−	0.728213i	$-0.259649\pi$
$337$	9.97406	+	4.80325i	0.543321	+	0.261650i	−0.142030	+	0.989862i	$0.545363\pi$
$338$	−13.7637	−	9.38393i	−0.748647	−	0.510419i
$339$	46.1316	+	42.8039i	2.50553	+	2.32479i
$340$	0.0717968	−	0.958061i	0.00389373	−	0.0519582i
$341$	0.739526	−	1.88428i	0.0400476	−	0.102040i
$342$	29.7027			1.60614
$343$	15.9269	−	9.45174i	0.859969	−	0.510346i
$344$	0.806638			0.0434910
$345$	3.62725	−	9.24209i	0.195285	−	0.497577i
$346$	−0.301274	+	4.02022i	−0.0161966	+	0.216128i
$347$	15.7640	+	14.6268i	0.846255	+	0.785210i	0.978552	−	0.206000i	$-0.0660447\pi$
$347$	15.7640	+	14.6268i	0.846255	+	0.785210i	−0.132297	+	0.991210i	$0.542235\pi$
$348$	−6.65556	−	4.53768i	−0.356775	−	0.243245i
$349$	−15.3047	−	7.37035i	−0.819241	−	0.394526i	−0.0231720	−	0.999731i	$-0.507377\pi$
$349$	−15.3047	−	7.37035i	−0.819241	−	0.394526i	−0.796069	+	0.605206i	$0.793091\pi$
$350$	8.42205	−	1.51976i	0.450178	−	0.0812347i
$351$	85.4571	−	41.1540i	4.56136	−	2.19664i
$352$	−0.295564	−	0.0445491i	−0.0157536	−	0.00237447i
$353$	10.6760	−	7.27879i	0.568228	−	0.387411i	−0.244855	−	0.969560i	$-0.578740\pi$
$353$	10.6760	−	7.27879i	0.568228	−	0.387411i	0.813082	+	0.582149i	$0.197788\pi$
$354$	−10.2176	+	1.54005i	−0.543059	+	0.0818530i
$355$	7.69656	−	7.14136i	0.408491	−	0.379024i
$356$	8.37488	+	10.5018i	0.443868	+	0.556593i
$357$	1.24374	−	6.28157i	0.0658256	−	0.332456i
$358$	8.92721	−	11.1944i	0.471818	−	0.591641i
$359$	0.628657	+	8.38885i	0.0331793	+	0.442747i	0.988911	+	0.148508i	$0.0474470\pi$
$359$	0.628657	+	8.38885i	0.0331793	+	0.442747i	−0.955732	+	0.294239i	$0.904934\pi$
$360$	10.4154	+	3.21272i	0.548939	+	0.169325i
$361$	2.94504	−	5.10096i	0.155002	−	0.268472i
$362$	−0.579068	−	1.00298i	−0.0304352	−	0.0527152i
$363$	−8.12638	−	35.6040i	−0.426525	−	1.86873i
$364$	−1.49191	−	14.3312i	−0.0781976	−	0.751157i
$365$	−1.95674	+	8.57303i	−0.102420	+	0.448733i
$366$	10.4519	−	3.22400i	0.546332	−	0.168521i
$367$	4.77594	+	12.1689i	0.249302	+	0.635211i	0.999667	−	0.0258130i	$-0.00821745\pi$
$367$	4.77594	+	12.1689i	0.249302	+	0.635211i	−0.750365	+	0.661024i	$0.770122\pi$
$368$	0.815617	+	2.07816i	0.0425170	+	0.108332i
$369$	−6.26498	+	1.93249i	−0.326142	+	0.100601i
$370$	0.207512	−	0.909171i	0.0107880	−	0.0472655i
$371$	−17.5162	−	11.2142i	−0.909398	−	0.582215i
$372$	−5.04396	−	22.0990i	−0.261517	−	1.14578i
$373$	2.01818	+	3.49559i	0.104498	+	0.180995i	0.913533	−	0.406765i	$-0.133343\pi$
$373$	2.01818	+	3.49559i	0.104498	+	0.180995i	−0.809035	+	0.587760i	$0.800010\pi$
$374$	0.108067	−	0.187177i	0.00558801	−	0.00967872i
$375$	−34.9945	−	10.7944i	−1.80711	−	0.557419i
$376$	0.450071	+	6.00579i	0.0232107	+	0.309725i
$377$	8.17157	−	10.2468i	0.420857	−	0.527738i
$378$	42.0778	+	18.7842i	2.16425	+	0.966155i
$379$	−8.85963	−	11.1096i	−0.455089	−	0.570663i	0.500361	−	0.865817i	$-0.333201\pi$
$379$	−8.85963	−	11.1096i	−0.455089	−	0.570663i	−0.955450	+	0.295154i	$0.904629\pi$
$380$	−3.52655	+	3.27216i	−0.180908	+	0.167858i
$381$	−45.8837	+	6.91585i	−2.35069	+	0.354310i
$382$	5.77864	−	3.93981i	0.295661	−	0.201578i
$383$	−14.3881	−	2.16866i	−0.735198	−	0.110813i	−0.229238	−	0.973370i	$-0.573623\pi$
$383$	−14.3881	−	2.16866i	−0.735198	−	0.110813i	−0.505960	+	0.862557i	$0.668861\pi$
$384$	−3.01568	+	1.45228i	−0.153893	+	0.0741111i
$385$	−1.01259	−	0.280538i	−0.0516066	−	0.0142975i
$386$	−1.55591	−	0.749289i	−0.0791940	−	0.0381378i
$387$	−5.46738	−	3.72760i	−0.277923	−	0.189485i
$388$	13.2529	+	12.2969i	0.672813	+	0.624279i
$389$	−0.791381	+	10.5602i	−0.0401246	+	0.535426i	0.940534	+	0.339700i	$0.110325\pi$
$389$	−0.791381	+	10.5602i	−0.0401246	+	0.535426i	−0.980659	+	0.195726i	$0.937294\pi$
$390$	−8.84835	+	22.5452i	−0.448054	+	1.14162i
$391$	−1.61429			−0.0816382
$392$	4.84745	−	5.04997i	0.244833	−	0.255062i
$393$	−22.3131			−1.12555
$394$	−3.77971	+	9.63054i	−0.190419	+	0.485180i
$395$	−1.05541	+	14.0835i	−0.0531035	+	0.708617i
$396$	1.79746	+	1.66780i	0.0903258	+	0.0838101i
$397$	4.72977	+	3.22470i	0.237380	+	0.161843i	0.676168	−	0.736748i	$-0.263639\pi$
$397$	4.72977	+	3.22470i	0.237380	+	0.161843i	−0.438787	+	0.898591i	$0.644592\pi$
$398$	1.68520	+	0.811552i	0.0844717	+	0.0406794i
$399$	−25.9594	+	18.8213i	−1.29959	+	0.942245i
$400$	2.91432	−	1.40346i	0.145716	−	0.0701730i
$401$	31.0464	+	4.67949i	1.55038	+	0.233683i	0.867721	−	0.497052i	$-0.165584\pi$
$401$	31.0464	+	4.67949i	1.55038	+	0.233683i	0.682662	+	0.730735i	$0.260822\pi$
$402$	−15.0939	+	10.2908i	−0.752815	+	0.513261i
$403$	36.4687	−	5.49677i	1.81664	−	0.273814i
$404$	8.56114	−	7.94357i	0.425932	−	0.395208i
$405$	−27.9058	−	34.9928i	−1.38665	−	1.73880i
$406$	6.36459	−	0.184175i	0.315869	−	0.00914047i
$407$	0.130802	−	0.164021i	0.00648364	−	0.00813022i
$408$	−0.180869	−	2.41353i	−0.00895436	−	0.119488i
$409$	−0.0437437	−	0.0134932i	−0.00216299	−	0.000667194i	0.293673	−	0.955906i	$-0.405122\pi$
$409$	−0.0437437	−	0.0134932i	−0.00216299	−	0.000667194i	−0.295836	+	0.955239i	$0.595598\pi$
$410$	0.530941	−	0.919616i	0.0262213	−	0.0454166i
$411$	−5.30982	−	9.19688i	−0.261914	−	0.453648i
$412$	−0.633822	−	2.77696i	−0.0312262	−	0.136811i
$413$	5.82415	−	5.72631i	0.286588	−	0.281774i
$414$	4.07525	−	17.8548i	0.200288	−	0.877518i
$415$	−7.86641	+	2.42647i	−0.386147	+	0.119111i
$416$	−1.98963	−	5.06948i	−0.0975494	−	0.248552i
$417$	−19.1040	−	48.6761i	−0.935526	−	2.38368i
$418$	−1.03417	+	0.319000i	−0.0505830	+	0.0156028i
$419$	−1.80667	+	7.91555i	−0.0882618	+	0.386700i	−0.999694	−	0.0247509i	$-0.992121\pi$
$419$	−1.80667	+	7.91555i	−0.0882618	+	0.386700i	0.911432	+	0.411451i	$0.134978\pi$
$420$	−11.1385	+	3.79195i	−0.543505	+	0.185028i
$421$	4.20041	+	18.4032i	0.204715	+	0.896917i	0.968019	+	0.250877i	$0.0807190\pi$
$421$	4.20041	+	18.4032i	0.204715	+	0.896917i	−0.763303	+	0.646040i	$0.776424\pi$
$422$	3.42251	+	5.92796i	0.166605	+	0.288569i
$423$	24.7031	−	42.7870i	1.20111	−	2.08038i
$424$	−7.51185	−	2.31710i	−0.364808	−	0.112528i
$425$	0.174790	+	2.33241i	0.00847855	+	0.113138i
$426$	16.4912	−	20.6793i	0.798999	−	1.00191i
$427$	−5.19281	+	6.91268i	−0.251298	+	0.334528i
$428$	−8.30948	−	10.4198i	−0.401654	−	0.503658i
$429$	−3.99404	+	3.70593i	−0.192834	+	0.178924i
$430$	1.05978	−	0.159736i	0.0511072	−	0.00770317i
$431$	9.68669	−	6.60427i	0.466591	−	0.318117i	−0.307102	−	0.951677i	$-0.599359\pi$
$431$	9.68669	−	6.60427i	0.466591	−	0.318117i	0.773694	+	0.633560i	$0.218407\pi$
$432$	17.2222	+	2.59582i	0.828601	+	0.124892i
$433$	24.7751	−	11.9310i	1.19061	−	0.573370i	0.269628	−	0.962965i	$-0.413099\pi$
$433$	24.7751	−	11.9310i	1.19061	−	0.573370i	0.920986	+	0.389595i	$0.127385\pi$
$434$	13.4814	+	11.8019i	0.647127	+	0.566509i
$435$	−9.64282	−	4.64374i	−0.462338	−	0.222650i
$436$	4.16647	+	2.84065i	0.199538	+	0.136043i
$437$	5.92547	+	5.49803i	0.283454	+	0.263007i
$438$	−1.65545	+	22.0905i	−0.0791007	+	1.05553i
$439$	10.0899	−	25.7086i	0.481564	−	1.22700i	−0.459319	−	0.888271i	$-0.651906\pi$
$439$	10.0899	−	25.7086i	0.481564	−	1.22700i	0.940883	−	0.338733i	$-0.109998\pi$
$440$	−0.397141			−0.0189330
$441$	−56.1927	+	11.8278i	−2.67584	+	0.563230i
$442$	3.93792			0.187308
$443$	−13.0337	+	33.2094i	−0.619251	+	1.57782i	0.184483	+	0.982836i	$0.440939\pi$
$443$	−13.0337	+	33.2094i	−0.619251	+	1.57782i	−0.803734	+	0.594989i	$0.797156\pi$
$444$	0.175561	−	2.34270i	0.00833176	−	0.111180i
$445$	13.0828	+	12.1390i	0.620183	+	0.575445i
$446$	21.3292	+	14.5420i	1.00997	+	0.688584i
$447$	68.4375	+	32.9578i	3.23698	+	1.55885i
$448$	1.25605	−	2.32859i	0.0593426	−	0.110016i
$449$	−21.4257	+	10.3181i	−1.01114	+	0.486940i	−0.864705	−	0.502280i	$-0.832495\pi$
$449$	−21.4257	+	10.3181i	−1.01114	+	0.486940i	−0.146436	+	0.989220i	$0.546780\pi$
$450$	−26.2388	−	3.95487i	−1.23691	−	0.186434i
$451$	0.197376	−	0.134569i	0.00929409	−	0.00633661i
$452$	−18.5913	+	2.80219i	−0.874462	+	0.131804i
$453$	−28.0427	+	26.0198i	−1.31756	+	1.22252i
$454$	−16.2980	−	20.4370i	−0.764903	−	0.959158i
$455$	−4.79808	−	18.5332i	−0.224937	−	0.868850i
$456$	−7.55622	+	9.47520i	−0.353853	+	0.443717i
$457$	−1.84045	−	24.5591i	−0.0860925	−	1.14882i	−0.858194	−	0.513325i	$-0.828413\pi$
$457$	−1.84045	−	24.5591i	−0.0860925	−	1.14882i	0.772102	−	0.635499i	$-0.219206\pi$
$458$	−12.0796	−	3.72607i	−0.564444	−	0.174108i
$459$	−6.29693	+	10.9066i	−0.293916	+	0.509077i
$460$	1.48311	+	2.56882i	0.0691504	+	0.119772i
$461$	−0.823066	−	3.60609i	−0.0383340	−	0.167952i	0.952138	−	0.305670i	$-0.0988804\pi$
$461$	−0.823066	−	3.60609i	−0.0383340	−	0.167952i	−0.990472	+	0.137718i	$0.956023\pi$
$462$	−2.62775	−	0.318639i	−0.122254	−	0.0148244i
$463$	−6.45908	+	28.2991i	−0.300179	+	1.31517i	0.569679	+	0.821867i	$0.307068\pi$
$463$	−6.45908	+	28.2991i	−0.300179	+	1.31517i	−0.869858	+	0.493302i	$0.835790\pi$
$464$	2.29968	−	0.709357i	0.106760	−	0.0329311i
$465$	−11.0031	−	28.0355i	−0.510257	−	1.30011i
$466$	7.99867	+	20.3803i	0.370531	+	0.944098i
$467$	−2.35174	+	0.725416i	−0.108826	+	0.0335683i	−0.348690	−	0.937238i	$-0.613373\pi$
$467$	−2.35174	+	0.725416i	−0.108826	+	0.0335683i	0.239864	+	0.970806i	$0.422897\pi$
$468$	−9.94121	+	43.5553i	−0.459533	+	2.01334i
$469$	4.88453	−	13.5889i	0.225547	−	0.627475i
$470$	1.78063	+	7.80143i	0.0821341	+	0.359853i
$471$	−6.56421	−	11.3695i	−0.302463	−	0.523881i
$472$	1.54355	−	2.67351i	0.0710477	−	0.123058i
$473$	0.230394	+	0.0710672i	0.0105935	+	0.00326767i
$474$	2.65877	+	35.4789i	0.122121	+	1.62960i
$475$	7.30224	−	9.15672i	0.335050	−	0.420139i
$476$	1.23558	+	1.46061i	0.0566326	+	0.0669470i
$477$	40.2076	+	50.4187i	1.84098	+	2.30852i
$478$	−11.0803	+	10.2810i	−0.506800	+	0.470242i
$479$	23.6666	−	3.56717i	1.08136	−	0.162988i	0.415889	−	0.909415i	$-0.363470\pi$
$479$	23.6666	−	3.56717i	1.08136	−	0.162988i	0.665467	+	0.746427i	$0.268232\pi$
$480$	−3.67449	+	2.50522i	−0.167717	+	0.114347i
$481$	3.77965	+	0.569691i	0.172337	+	0.0259757i
$482$	16.0644	−	7.73619i	0.731712	−	0.352374i
$483$	7.75220	+	18.1870i	0.352737	+	0.827537i
$484$	9.83016	+	4.73396i	0.446826	+	0.215180i
$485$	19.8471	+	13.5315i	0.901210	+	0.614434i
$486$	−44.3512	−	41.1519i	−2.01181	−	1.86669i
$487$	1.65235	−	22.0491i	0.0748751	−	0.999139i	−0.825607	−	0.564246i	$-0.809167\pi$
$487$	1.65235	−	22.0491i	0.0748751	−	0.999139i	0.900482	−	0.434893i	$-0.143214\pi$
$488$	−1.19387	+	3.04193i	−0.0540439	+	0.137702i
$489$	−13.5313			−0.611909
$490$	5.36867	−	7.59471i	0.242532	−	0.343094i
$491$	−35.2831			−1.59230			−0.796151	−	0.605098i	$-0.793134\pi$
$491$	−35.2831			−1.59230			−0.796151	+	0.605098i	$0.793134\pi$
$492$	0.977314	−	2.49016i	0.0440607	−	0.112265i
$493$	−0.130045	+	1.73532i	−0.00585691	+	0.0781551i
$494$	−14.4546	−	13.4120i	−0.650345	−	0.603432i
$495$	2.69182	+	1.83525i	0.120988	+	0.0824885i
$496$	6.10148	+	2.93832i	0.273965	+	0.131934i
$497$	−0.958684	+	20.8852i	−0.0430028	+	0.936828i
$498$	−18.6845	+	8.99800i	−0.837275	+	0.403210i
$499$	7.70733	+	1.16169i	0.345028	+	0.0520045i	0.319270	−	0.947664i	$-0.396562\pi$
$499$	7.70733	+	1.16169i	0.345028	+	0.0520045i	0.0257572	+	0.999668i	$0.491800\pi$
$500$	9.03996	−	6.16334i	0.404279	−	0.275633i
$501$	−24.4413	+	3.68393i	−1.09196	+	0.164586i
$502$	11.5933	−	10.7570i	0.517435	−	0.480109i
$503$	−10.2937	−	12.9078i	−0.458972	−	0.575532i	0.497461	−	0.867487i	$-0.334266\pi$
$503$	−10.2937	−	12.9078i	−0.458972	−	0.575532i	−0.956432	+	0.291954i	$0.905694\pi$
$504$	−19.2743	+	9.97881i	−0.858544	+	0.444491i
$505$	9.67479	−	12.1318i	0.430523	−	0.539858i
$506$	0.0498670	+	0.665428i	0.00221686	+	0.0295819i
$507$	−53.2806	−	16.4349i	−2.36627	−	0.729899i
$508$	6.93156	−	12.0058i	0.307538	−	0.532672i
$509$	14.8313	+	25.6885i	0.657384	+	1.13862i	0.981290	+	0.192533i	$0.0616704\pi$
$509$	14.8313	+	25.6885i	0.657384	+	1.13862i	−0.323906	+	0.946089i	$0.604996\pi$
$510$	−0.715576	−	3.13514i	−0.0316862	−	0.138826i
$511$	−9.19016	−	14.9048i	−0.406549	−	0.659351i
$512$	0.222521	−	0.974928i	0.00983413	−	0.0430861i
$513$	60.2600	−	18.5877i	2.66054	−	0.820669i
$514$	7.52078	+	19.1626i	0.331728	+	0.845228i
$515$	−1.38265	−	3.52292i	−0.0609266	−	0.155239i
$516$	2.57999	−	0.795821i	0.113578	−	0.0350341i
$517$	−0.400577	+	1.75504i	−0.0176174	+	0.0771867i
$518$	0.974617	+	1.58066i	0.0428222	+	0.0694501i
$519$	3.00270	+	13.1557i	0.131804	+	0.577471i
$520$	−3.61792	−	6.26642i	−0.158656	−	0.274800i
$521$	−18.6492	+	32.3014i	−0.817037	+	1.41515i	0.0908186	+	0.995867i	$0.471052\pi$
$521$	−18.6492	+	32.3014i	−0.817037	+	1.41515i	−0.907856	+	0.419282i	$0.862282\pi$
$522$	−18.8653	−	5.81916i	−0.825710	−	0.254698i
$523$	−0.260421	−	3.47508i	−0.0113874	−	0.151955i	−0.999999	−	0.00146440i	$-0.999534\pi$
$523$	−0.260421	−	3.47508i	−0.0113874	−	0.151955i	0.988612	−	0.150490i	$-0.0480852\pi$
$524$	4.15637	−	5.21192i	0.181572	−	0.227684i
$525$	25.4381	−	13.1700i	1.11021	−	0.574786i
$526$	−11.3531	−	14.2364i	−0.495020	−	0.620736i
$527$	−3.58966	+	3.33072i	−0.156368	+	0.145088i
$528$	−0.989297	+	0.149113i	−0.0430536	+	0.00648929i
$529$	−14.8855	+	10.1488i	−0.647197	+	0.441252i
$530$	−10.3281	−	1.55671i	−0.448625	−	0.0676193i
$531$	−22.8169	+	10.9880i	−0.990169	+	0.476840i
$532$	0.439267	−	9.56956i	0.0190447	−	0.414893i
$533$	3.92142	+	1.88845i	0.169855	+	0.0817980i
$534$	37.1476	+	25.3268i	1.60753	+	1.09600i
$535$	−12.9806	−	12.0442i	−0.561200	−	0.520718i
$536$	0.407864	−	5.44257i	0.0176171	−	0.235083i
$537$	17.5090	−	44.6121i	0.755568	−	1.92515i
$538$	−7.71332			−0.332545
$539$	1.82946	−	1.01531i	0.0788005	−	0.0437326i
$540$	23.1409			0.995828
$541$	−12.1488	+	30.9547i	−0.522319	+	1.33085i	0.389792	+	0.920903i	$0.372547\pi$
$541$	−12.1488	+	30.9547i	−0.522319	+	1.33085i	−0.912111	+	0.409944i	$0.865548\pi$
$542$	0.803489	−	10.7218i	0.0345128	−	0.460541i
$543$	−2.84165	−	2.63666i	−0.121947	−	0.113150i
$544$	0.597447	+	0.407332i	0.0256153	+	0.0174642i
$545$	6.03654	+	2.90705i	0.258577	+	0.124524i
$546$	−18.9108	−	44.3655i	−0.809307	−	1.89867i
$547$	−22.1221	+	10.6534i	−0.945871	+	0.455507i	−0.842237	−	0.539108i	$-0.818761\pi$
$547$	−22.1221	+	10.6534i	−0.945871	+	0.455507i	−0.103634	+	0.994615i	$0.533047\pi$
$548$	3.13730	+	0.472872i	0.134019	+	0.0202001i
$549$	22.1492	−	15.1011i	0.945307	−	0.644499i
$550$	0.956045	−	0.144101i	0.0407659	−	0.00614447i
$551$	6.38760	−	5.92683i	0.272121	−	0.252491i
$552$	4.65900	+	5.84220i	0.198300	+	0.248661i
$553$	−18.1630	−	21.4709i	−0.772368	−	0.913037i
$554$	−1.43103	+	1.79445i	−0.0607986	+	0.0762390i
$555$	−0.233262	−	3.11266i	−0.00990142	−	0.132125i
$556$	14.9284	+	4.60480i	0.633106	+	0.195287i
$557$	−16.8497	+	29.1845i	−0.713944	+	1.23659i	0.249422	+	0.968395i	$0.419759\pi$
$557$	−16.8497	+	29.1845i	−0.713944	+	1.23659i	−0.963366	+	0.268192i	$0.913574\pi$
$558$	−27.7774	−	48.1118i	−1.17591	−	2.03674i
$559$	0.977512	+	4.28276i	0.0413444	+	0.181141i
$560$	1.18910	−	3.30810i	0.0502486	−	0.139793i
$561$	0.160979	−	0.705295i	0.00679654	−	0.0297776i
$562$	20.4586	−	6.31066i	0.862996	−	0.266199i
$563$	−4.70517	−	11.9886i	−0.198299	−	0.505258i	0.796788	−	0.604259i	$-0.206531\pi$
$563$	−4.70517	−	11.9886i	−0.198299	−	0.505258i	−0.995087	+	0.0990005i	$0.968435\pi$
$564$	7.36478	+	18.7652i	0.310113	+	0.790156i
$565$	−23.8709	+	7.36318i	−1.00425	+	0.309771i
$566$	−0.539388	+	2.36321i	−0.0226722	+	0.0993332i
$567$	88.4767	+	10.7286i	3.71567	+	0.450560i
$568$	1.75840	+	7.70404i	0.0737807	+	0.323255i
$569$	6.65632	+	11.5291i	0.279048	+	0.483325i	0.971148	−	0.238476i	$-0.0766479\pi$
$569$	6.65632	+	11.5291i	0.279048	+	0.483325i	−0.692101	+	0.721801i	$0.743315\pi$
$570$	−8.05121	+	13.9451i	−0.337228	+	0.584096i
$571$	−4.70143	−	1.45020i	−0.196749	−	0.0606889i	0.194815	−	0.980840i	$-0.437589\pi$
$571$	−4.70143	−	1.45020i	−0.196749	−	0.0606889i	−0.391563	+	0.920151i	$0.628066\pi$
$572$	−0.121646	−	1.62325i	−0.00508627	−	0.0678716i
$573$	14.5957	−	18.3024i	0.609744	−	0.764595i
$574$	0.529955	+	2.04702i	0.0221199	+	0.0854410i
$575$	−4.50240	−	5.64584i	−0.187763	−	0.235448i
$576$	−6.01354	+	5.57975i	−0.250564	+	0.232490i
$577$	23.3469	−	3.51897i	0.971942	−	0.146497i	0.356170	−	0.934421i	$-0.384082\pi$
$577$	23.3469	−	3.51897i	0.971942	−	0.146497i	0.615772	+	0.787924i	$0.288844\pi$
$578$	13.6141	−	9.28190i	0.566270	−	0.386076i
$579$	−5.71575	−	0.861511i	−0.237539	−	0.0358032i
$580$	2.88090	−	1.38737i	0.119623	−	0.0576074i
$581$	7.78221	−	14.4275i	0.322860	−	0.598553i
$582$	54.5206	+	26.2557i	2.25995	+	1.08834i
$583$	−1.94141	−	1.32363i	−0.0804052	−	0.0548193i
$584$	−4.85155	−	4.50158i	−0.200759	−	0.186277i
$585$	−4.43588	+	59.1927i	−0.183401	+	2.44732i
$586$	−2.08210	+	5.30511i	−0.0860109	+	0.219152i
$587$	−37.6167			−1.55261			−0.776303	−	0.630359i	$-0.782908\pi$
$587$	−37.6167			−1.55261			−0.776303	+	0.630359i	$0.782908\pi$
$588$	10.5221	−	20.9345i	0.433923	−	0.863325i
$589$	24.5203			1.01034
$590$	1.49853	−	3.81819i	0.0616935	−	0.157192i
$591$	−2.58780	+	34.5318i	−0.106448	+	1.42045i
$592$	0.514508	+	0.477393i	0.0211461	+	0.0196207i
$593$	−17.2791	−	11.7807i	−0.709568	−	0.483775i	0.153960	−	0.988077i	$-0.450797\pi$
$593$	−17.2791	−	11.7807i	−0.709568	−	0.483775i	−0.863527	+	0.504302i	$0.831750\pi$
$594$	4.69034	+	2.25875i	0.192447	+	0.0926776i
$595$	1.91257	+	1.67431i	0.0784079	+	0.0686400i
$596$	−20.4465	+	9.84651i	−0.837520	+	0.403329i
$597$	6.19071	+	0.933099i	0.253369	+	0.0381892i
$598$	−10.0454	+	6.84883i	−0.410786	+	0.280069i
$599$	27.6160	−	4.16245i	1.12836	−	0.170073i	0.441778	−	0.897125i	$-0.354348\pi$
$599$	27.6160	−	4.16245i	1.12836	−	0.170073i	0.686583	+	0.727052i	$0.259110\pi$
$600$	7.93665	−	7.36413i	0.324012	−	0.300640i
$601$	5.09701	+	6.39144i	0.207911	+	0.260712i	0.874843	−	0.484406i	$-0.160964\pi$
$601$	5.09701	+	6.39144i	0.207911	+	0.260712i	−0.666932	+	0.745119i	$0.732393\pi$
$602$	−1.28181	+	1.70635i	−0.0522426	+	0.0695455i
$603$	−27.9155	+	35.0049i	−1.13681	+	1.42551i
$604$	−0.854093	−	11.3971i	−0.0347525	−	0.463740i
$605$	13.8526	+	4.27295i	0.563187	+	0.173720i
$606$	19.5453	−	33.8534i	0.793973	−	1.37520i
$607$	14.3459	+	24.8478i	0.582282	+	1.00854i	0.995208	+	0.0977779i	$0.0311735\pi$
$607$	14.3459	+	24.8478i	0.582282	+	1.00854i	−0.412926	+	0.910765i	$0.635493\pi$
$608$	−0.805695	−	3.52998i	−0.0326753	−	0.143160i
$609$	20.1751	−	6.86832i	0.817537	−	0.278318i
$610$	−0.966150	+	4.23298i	−0.0391183	+	0.171388i
$611$	−31.3417	+	9.66763i	−1.26795	+	0.391111i
$612$	−2.16714	−	5.52179i	−0.0876016	−	0.223205i
$613$	−1.88864	−	4.81217i	−0.0762814	−	0.194362i	0.887646	−	0.460526i	$-0.152339\pi$
$613$	−1.88864	−	4.81217i	−0.0762814	−	0.194362i	−0.963928	+	0.266164i	$0.914244\pi$
$614$	22.9699	−	7.08526i	0.926988	−	0.285938i
$615$	0.790902	−	3.46517i	0.0318922	−	0.139729i
$616$	0.563912	−	0.554438i	0.0227206	−	0.0223390i
$617$	−10.3325	−	45.2698i	−0.415972	−	1.82249i	−0.554562	−	0.832143i	$-0.687114\pi$
$617$	−10.3325	−	45.2698i	−0.415972	−	1.82249i	0.138590	−	0.990350i	$-0.455743\pi$
$618$	−4.76697	−	8.25663i	−0.191756	−	0.332130i
$619$	−0.828754	+	1.43544i	−0.0333104	+	0.0576953i	−0.882200	−	0.470875i	$-0.843938\pi$
$619$	−0.828754	+	1.43544i	−0.0333104	+	0.0576953i	0.848890	+	0.528570i	$0.177272\pi$
$620$	8.59815	+	2.65218i	0.345310	+	0.106514i
$621$	−2.90569	−	38.7737i	−0.116601	−	1.55594i
$622$	−16.1653	+	20.2707i	−0.648171	+	0.812781i
$623$	−35.5236	+	1.02796i	−1.42322	+	0.0411845i
$624$	−11.3652	−	14.2515i	−0.454973	−	0.570518i
$625$	−1.19941	+	1.11289i	−0.0479763	+	0.0445155i
$626$	−16.0742	+	2.42280i	−0.642454	+	0.0968344i
$627$	−2.99303	+	2.04061i	−0.119530	+	0.0814941i
$628$	3.87846	+	0.584583i	0.154767	+	0.0233274i
$629$	−0.457257	+	0.220203i	−0.0182320	+	0.00878009i
$630$	−23.3469	+	16.9272i	−0.930165	+	0.674398i
$631$	−36.0118	−	17.3424i	−1.43361	−	0.690389i	−0.453943	−	0.891031i	$-0.649983\pi$
$631$	−36.0118	−	17.3424i	−1.43361	−	0.690389i	−0.979665	+	0.200641i	$0.935697\pi$
$632$	−8.78245	−	5.98777i	−0.349347	−	0.238181i
$633$	16.7952	+	15.5837i	0.667549	+	0.619395i
$634$	1.47779	−	19.7197i	0.0586906	−	0.783171i
$635$	6.72938	−	17.1462i	0.267047	−	0.680425i
$636$	−26.3123			−1.04335
$637$	32.6866	+	19.6173i	1.29509	+	0.777267i
$638$	0.719337			0.0284788
$639$	23.6832	−	60.3438i	0.936893	−	2.38716i
$640$	0.0992913	−	1.32495i	0.00392483	−	0.0523733i
$641$	−21.2112	−	19.6811i	−0.837790	−	0.777356i	0.139284	−	0.990252i	$-0.455520\pi$
$641$	−21.2112	−	19.6811i	−0.837790	−	0.777356i	−0.977075	+	0.212897i	$0.931710\pi$
$642$	−36.8575	−	25.1290i	−1.45465	−	0.991762i
$643$	24.4367	+	11.7681i	0.963690	+	0.464089i	0.848466	−	0.529251i	$-0.177527\pi$
$643$	24.4367	+	11.7681i	0.963690	+	0.464089i	0.115225	+	0.993339i	$0.463241\pi$
$644$	−5.69218	−	1.57701i	−0.224303	−	0.0621429i
$645$	3.23206	−	1.55648i	0.127262	−	0.0612863i
$646$	2.58890	+	0.390214i	0.101859	+	0.0153528i
$647$	−4.30164	+	2.93281i	−0.169115	+	0.115301i	−0.644920	−	0.764250i	$-0.723109\pi$
$647$	−4.30164	+	2.93281i	−0.169115	+	0.115301i	0.475805	+	0.879551i	$0.342157\pi$
$648$	33.3098	−	5.02064i	1.30853	−	0.197229i
$649$	0.676418	−	0.627624i	0.0265517	−	0.0246364i
$650$	10.9832	+	13.7725i	0.430797	+	0.540202i
$651$	54.7632	+	24.4472i	2.14634	+	0.958159i
$652$	2.52055	−	3.16067i	0.0987123	−	0.123781i
$653$	−0.914533	−	12.2036i	−0.0357884	−	0.477564i	−0.986088	−	0.166226i	$-0.946842\pi$
$653$	−0.914533	−	12.2036i	−0.0357884	−	0.477564i	0.950299	−	0.311338i	$-0.100777\pi$
$654$	16.1288	+	4.97508i	0.630686	+	0.194541i
$655$	4.42864	−	7.67063i	0.173041	−	0.299716i
$656$	0.399604	+	0.692135i	0.0156019	+	0.0270233i
$657$	12.0813	+	52.9315i	0.471335	+	2.06505i
$658$	−13.4197	−	8.59158i	−0.523155	−	0.334934i
$659$	9.58399	−	41.9902i	0.373339	−	1.63571i	−0.343992	−	0.938973i	$-0.611779\pi$
$659$	9.58399	−	41.9902i	0.373339	−	1.63571i	0.717331	−	0.696733i	$-0.245364\pi$
$660$	−1.27024	+	0.391816i	−0.0494439	+	0.0152514i
$661$	−4.02072	−	10.2446i	−0.156388	−	0.398470i	0.831109	−	0.556110i	$-0.187707\pi$
$661$	−4.02072	−	10.2446i	−0.156388	−	0.398470i	−0.987497	+	0.157640i	$0.949611\pi$
$662$	−1.25698	−	3.20274i	−0.0488541	−	0.124478i
$663$	12.5952	−	3.88511i	0.489158	−	0.150885i
$664$	1.37869	−	6.04046i	0.0535037	−	0.234415i
$665$	−1.31791	−	12.6597i	−0.0511065	−	0.490923i
$666$	−1.28122	−	5.61339i	−0.0496463	−	0.217514i
$667$	−2.68634	−	4.65288i	−0.104016	−	0.180160i
$668$	3.69230	−	6.39525i	0.142859	−	0.247439i
$669$	82.5674	+	25.4687i	3.19224	+	0.984676i
$670$	−0.541915	−	7.23136i	−0.0209360	−	0.279372i
$671$	−0.608999	+	0.763660i	−0.0235101	+	0.0294808i
$672$	1.72003	−	8.68709i	0.0663515	−	0.335112i
$673$	1.65836	+	2.07952i	0.0639251	+	0.0801596i	0.812766	−	0.582590i	$-0.197961\pi$
$673$	1.65836	+	2.07952i	0.0639251	+	0.0801596i	−0.748841	+	0.662750i	$0.769389\pi$
$674$	−8.11515	+	7.52976i	−0.312584	+	0.290036i
$675$	−55.7076	+	8.39657i	−2.14419	+	0.323184i
$676$	13.7637	−	9.38393i	0.529373	−	0.360920i
$677$	−21.6891	−	3.26910i	−0.833578	−	0.125642i	−0.281633	−	0.959522i	$-0.590876\pi$
$677$	−21.6891	−	3.26910i	−0.833578	−	0.125642i	−0.551945	+	0.833881i	$0.686114\pi$
$678$	−56.6988	+	27.3047i	−2.17750	+	1.04863i
$679$	−47.0724	+	8.49423i	−1.80647	+	0.325979i
$680$	0.865604	+	0.416853i	0.0331944	+	0.0159856i
$681$	−72.2913	−	49.2874i	−2.77021	−	1.88870i
$682$	1.48385	+	1.37681i	0.0568195	+	0.0527208i
$683$	−2.86975	+	38.2941i	−0.109808	+	1.46528i	0.621595	+	0.783339i	$0.286485\pi$
$683$	−2.86975	+	38.2941i	−0.109808	+	1.46528i	−0.731403	+	0.681945i	$0.761134\pi$
$684$	−10.8516	+	27.6494i	−0.414921	+	1.05720i
$685$	4.21551			0.161066
$686$	2.97965	+	18.2790i	0.113763	+	0.697895i
$687$	−42.3122			−1.61431
$688$	−0.294698	+	0.750878i	−0.0112352	+	0.0286269i
$689$	3.19928	−	42.6914i	0.121883	−	1.62641i
$690$	7.27803	+	6.75303i	0.277070	+	0.257083i
$691$	−6.47743	−	4.41624i	−0.246413	−	0.168002i	0.433815	−	0.901002i	$-0.357167\pi$
$691$	−6.47743	−	4.41624i	−0.246413	−	0.168002i	−0.680228	+	0.733000i	$0.738119\pi$
$692$	−3.63225	−	1.74920i	−0.138077	−	0.0664945i
$693$	−6.38434	+	1.15206i	−0.242521	+	0.0437630i
$694$	−19.3750	+	9.33050i	−0.735464	+	0.354181i
$695$	20.5252	+	3.09368i	0.778565	+	0.117350i
$696$	6.65556	−	4.53768i	0.252278	−	0.172000i
$697$	−0.571447	+	0.0861318i	−0.0216451	+	0.00326247i
$698$	12.4523	−	11.5540i	0.471326	−	0.437327i
$699$	45.6903	+	57.2938i	1.72817	+	2.16705i
$700$	−1.66221	+	8.39510i	−0.0628258	+	0.317305i
$701$	26.8169	−	33.6273i	1.01286	−	1.27009i	0.0503815	−	0.998730i	$-0.483956\pi$
$701$	26.8169	−	33.6273i	1.01286	−	1.27009i	0.962479	−	0.271357i	$-0.0874723\pi$
$702$	7.08816	+	94.5850i	0.267526	+	3.56988i
$703$	2.42840	+	0.749063i	0.0915890	+	0.0282515i
$704$	0.149451	−	0.258857i	0.00563265	−	0.00975604i
$705$	13.3921	+	23.1957i	0.504374	+	0.873601i
$706$	2.87525	+	12.5973i	0.108211	+	0.474105i
$707$	3.19939	+	30.7330i	0.120326	+	1.15583i
$708$	2.29931	−	10.0739i	0.0864134	−	0.378602i
$709$	−2.91784	+	0.900035i	−0.109582	+	0.0338015i	−0.349061	−	0.937100i	$-0.613499\pi$
$709$	−2.91784	+	0.900035i	−0.109582	+	0.0338015i	0.239479	+	0.970901i	$0.423023\pi$
$710$	3.83584	+	9.77356i	0.143956	+	0.366795i
$711$	31.8570	+	81.1702i	1.19473	+	3.04412i
$712$	−12.8355	+	3.95923i	−0.481031	+	0.148378i
$713$	3.36422	−	14.7396i	0.125991	−	0.552003i
$714$	5.39296	+	3.45268i	0.201826	+	0.129213i
$715$	−0.481270	−	2.10858i	−0.0179985	−	0.0788565i
$716$	7.15907	+	12.3999i	0.267547	+	0.463405i
$717$	−25.2966	+	43.8149i	−0.944718	+	1.63630i
$718$	−8.03863	−	2.47959i	−0.299999	−	0.0925375i
$719$	−1.55623	−	20.7664i	−0.0580375	−	0.774456i	−0.947969	−	0.318362i	$-0.896867\pi$
$719$	−1.55623	−	20.7664i	−0.0580375	−	0.774456i	0.889932	−	0.456094i	$-0.150752\pi$
$720$	−6.79580	+	8.52166i	−0.253265	+	0.317584i
$721$	6.88151	+	3.07202i	0.256281	+	0.114408i
$722$	3.67241	+	4.60505i	0.136673	+	0.171382i
$723$	43.7486	−	40.5928i	1.62703	−	1.50966i
$724$	1.14520	−	0.172611i	0.0425611	−	0.00641505i
$725$	−6.43185	+	4.38516i	−0.238873	+	0.162861i
$726$	36.1117	+	5.44297i	1.34023	+	0.202008i
$727$	31.8424	−	15.3345i	1.18097	−	0.568724i	0.262775	−	0.964857i	$-0.415362\pi$
$727$	31.8424	−	15.3345i	1.18097	−	0.568724i	0.918193	+	0.396133i	$0.129648\pi$
$728$	13.8856	+	3.84697i	0.514633	+	0.142578i
$729$	−91.4050	−	44.0183i	−3.38537	−	1.63031i
$730$	−7.26553	−	4.95356i	−0.268909	−	0.183339i
$731$	−0.427569	−	0.396726i	−0.0158142	−	0.0146735i
$732$	−0.817389	+	10.9073i	−0.0302116	+	0.403145i
$733$	5.38724	−	13.7265i	0.198982	−	0.506999i	−0.796201	−	0.605033i	$-0.793160\pi$
$733$	5.38724	−	13.7265i	0.198982	−	0.506999i	0.995183	+	0.0980338i	$0.0312553\pi$
$734$	−13.0725			−0.482516
$735$	9.67856	−	29.5880i	0.356999	−	1.09137i
$736$	−2.23248			−0.0822904
$737$	0.596003	−	1.51859i	0.0219540	−	0.0559380i
$738$	0.489950	−	6.53792i	0.0180353	−	0.240664i
$739$	−13.4551	−	12.4845i	−0.494955	−	0.459251i	0.392762	−	0.919640i	$-0.371520\pi$
$739$	−13.4551	−	12.4845i	−0.494955	−	0.459251i	−0.887717	+	0.460389i	$0.847710\pi$
$740$	0.770510	+	0.525325i	0.0283245	+	0.0193113i
$741$	−59.4645	−	28.6366i	−2.18448	−	1.05199i
$742$	16.8385	−	12.2084i	0.618159	−	0.448184i
$743$	13.0063	−	6.26349i	0.477154	−	0.229785i	−0.179818	−	0.983700i	$-0.557551\pi$
$743$	13.0063	−	6.26349i	0.477154	−	0.229785i	0.656973	+	0.753915i	$0.271837\pi$
$744$	22.4142	+	3.37840i	0.821744	+	0.123858i
$745$	−24.9132	+	16.9856i	−0.912750	+	0.622303i
$746$	−3.99128	+	0.601589i	−0.146131	+	0.0220257i
$747$	−37.2587	+	34.5710i	−1.36322	+	1.26489i
$748$	0.134757	+	0.168980i	0.00492721	+	0.00617853i
$749$	35.2461	−	1.01994i	1.28787	−	0.0372676i
$750$	22.8331	−	28.6319i	0.833748	−	1.04549i
$751$	2.71039	+	36.1676i	0.0989034	+	1.31977i	0.797091	+	0.603859i	$0.206371\pi$
$751$	2.71039	+	36.1676i	0.0989034	+	1.31977i	−0.698188	+	0.715915i	$0.746010\pi$
$752$	−5.75506	−	1.77520i	−0.209865	−	0.0647349i
$753$	26.4678	−	45.8436i	0.964542	−	1.67064i
$754$	6.55309	+	11.3503i	0.238649	+	0.413353i
$755$	−3.37906	−	14.8046i	−0.122977	−	0.538796i
$756$	−32.8585	+	32.3065i	−1.19505	+	1.17497i
$757$	−9.74724	+	42.7054i	−0.354269	+	1.55216i	0.412940	+	0.910758i	$0.364502\pi$
$757$	−9.74724	+	42.7054i	−0.354269	+	1.55216i	−0.767209	+	0.641397i	$0.778355\pi$
$758$	13.5784	−	4.18840i	0.493191	−	0.152129i
$759$	0.816002	+	2.07914i	0.0296190	+	0.0754680i
$760$	−1.75758	−	4.47823i	−0.0637540	−	0.162442i
$761$	−40.3601	+	12.4494i	−1.46305	+	0.451292i	−0.921170	−	0.389161i	$-0.872765\pi$
$761$	−40.3601	+	12.4494i	−1.46305	+	0.451292i	−0.541884	+	0.840454i	$0.682289\pi$
$762$	10.3254	−	45.2386i	0.374050	−	1.63882i
$763$	−12.6299	+	4.29967i	−0.457233	+	0.155658i
$764$	1.55629	+	6.81856i	0.0563047	+	0.246687i
$765$	−3.94071	−	6.82552i	−0.142477	−	0.246777i
$766$	7.27531	−	12.6012i	0.262868	−	0.455300i
$767$	16.0653	+	4.95548i	0.580083	+	0.178932i
$768$	−0.250133	−	3.33779i	−0.00902590	−	0.120442i
$769$	−14.2989	+	17.9303i	−0.515633	+	0.646583i	−0.969675	−	0.244397i	$-0.921410\pi$
$769$	−14.2989	+	17.9303i	−0.515633	+	0.646583i	0.454042	+	0.890980i	$0.349981\pi$
$770$	0.631088	−	0.840105i	0.0227428	−	0.0302753i
$771$	42.9605	+	53.8708i	1.54719	+	1.94011i
$772$	1.26593	−	1.17461i	0.0455619	−	0.0422753i
$773$	−10.3640	+	1.56213i	−0.372768	+	0.0561858i	−0.332755	−	0.943013i	$-0.607978\pi$
$773$	−10.3640	+	1.56213i	−0.372768	+	0.0561858i	−0.0400135	+	0.999199i	$0.512740\pi$
$774$	5.46738	−	3.72760i	0.196521	−	0.133986i
$775$	−21.6608	−	3.26484i	−0.778079	−	0.117277i
$776$	−16.2887	+	7.84420i	−0.584729	+	0.281590i
$777$	4.67672	+	4.09411i	0.167777	+	0.146875i
$778$	−9.54113	−	4.59477i	−0.342066	−	0.164730i
$779$	2.39092	+	1.63010i	0.0856638	+	0.0584046i
$780$	−17.7541	−	16.4734i	−0.635699	−	0.589842i
$781$	−0.176511	+	2.35537i	−0.00631605	+	0.0842818i
$782$	0.589767	−	1.50270i	0.0210900	−	0.0537365i
$783$	−41.9149			−1.49792
$784$	2.92991	+	6.35733i	0.104640	+	0.227047i
$785$	5.21138			0.186002
$786$	8.15190	−	20.7707i	0.290769	−	0.740866i
$787$	−0.604248	+	8.06313i	−0.0215391	+	0.287420i	0.976025	+	0.217660i	$0.0698423\pi$
$787$	−0.604248	+	8.06313i	−0.0215391	+	0.287420i	−0.997564	+	0.0697598i	$0.977777\pi$
$788$	−7.58393	−	7.03686i	−0.270166	−	0.250678i
$789$	−50.3579	−	34.3334i	−1.79279	−	1.22230i
$790$	−12.7244	−	6.12773i	−0.452712	−	0.218015i
$791$	23.6153	−	43.7806i	0.839664	−	1.55666i
$792$	−2.20920	+	1.06389i	−0.0785004	+	0.0378038i
$793$	−17.5976	−	2.65241i	−0.624908	−	0.0941897i
$794$	−4.72977	+	3.22470i	−0.167853	+	0.114440i
$795$	−34.5698	+	5.21055i	−1.22606	+	0.184799i
$796$	−1.37113	+	1.27222i	−0.0485983	+	0.0450926i
$797$	9.75145	+	12.2279i	0.345414	+	0.433135i	0.923945	−	0.382525i	$-0.124945\pi$
$797$	9.75145	+	12.2279i	0.345414	+	0.433135i	−0.578531	+	0.815660i	$0.696374\pi$
$798$	−8.03626	−	31.0411i	−0.284481	−	1.09884i
$799$	2.71524	−	3.40481i	0.0960584	−	0.120453i
$800$	0.241726	+	3.22560i	0.00854629	+	0.114042i
$801$	105.295	+	32.4793i	3.72042	+	1.14760i
$802$	−15.6985	+	27.1907i	−0.554334	+	0.960135i
$803$	−0.989112	−	1.71319i	−0.0349050	−	0.0604573i
$804$	−4.06506	−	17.8102i	−0.143364	−	0.628117i
$805$	−7.79082	−	0.944710i	−0.274590	−	0.0332966i
$806$	−8.20671	+	35.9560i	−0.289069	+	1.26649i
$807$	−24.6707	+	7.60989i	−0.868448	+	0.267881i
$808$	4.26673	+	10.8714i	0.150103	+	0.382456i
$809$	9.28826	+	23.6661i	0.326558	+	0.832056i	0.996013	+	0.0892037i	$0.0284322\pi$
$809$	9.28826	+	23.6661i	0.326558	+	0.832056i	−0.669456	+	0.742852i	$0.733473\pi$
$810$	42.7690	−	13.1925i	1.50275	−	0.463537i
$811$	3.76251	−	16.4846i	0.132120	−	0.578854i	−0.864916	−	0.501916i	$-0.832629\pi$
$811$	3.76251	−	16.4846i	0.132120	−	0.578854i	0.997036	−	0.0769378i	$-0.0245143\pi$
$812$	−2.15380	+	5.99192i	−0.0755836	+	0.210275i
$813$	−8.00812	−	35.0859i	−0.280857	−	1.23052i
$814$	0.104895	+	0.181684i	0.00367658	+	0.00636803i
$815$	2.68566	−	4.65170i	0.0940746	−	0.162942i
$816$	2.31277	+	0.713396i	0.0809632	+	0.0249738i
$817$	0.218260	+	2.91248i	0.00763595	+	0.101895i
$818$	0.0285418	−	0.0357903i	0.000997941	−	0.00125138i
$819$	−76.3387	−	90.2421i	−2.66749	−	3.15331i
$820$	0.662072	+	0.830212i	0.0231206	+	0.0289923i
$821$	27.4817	−	25.4993i	0.959118	−	0.889932i	−0.0348731	−	0.999392i	$-0.511103\pi$
$821$	27.4817	−	25.4993i	0.959118	−	0.889932i	0.993991	+	0.109460i	$0.0349122\pi$
$822$	10.5010	−	1.58277i	0.366265	−	0.0552056i
$823$	−18.8243	+	12.8342i	−0.656175	+	0.447372i	−0.845092	−	0.534621i	$-0.820454\pi$
$823$	−18.8243	+	12.8342i	−0.656175	+	0.447372i	0.188918	+	0.981993i	$0.439502\pi$
$824$	2.81656	+	0.424528i	0.0981194	+	0.0147891i
$825$	2.91569	−	1.40412i	0.101511	−	0.0488853i
$826$	3.20267	+	7.51361i	0.111435	+	0.261432i
$827$	43.5630	+	20.9789i	1.51484	+	0.729506i	0.992386	−	0.123164i	$-0.0393041\pi$
$827$	43.5630	+	20.9789i	1.51484	+	0.729506i	0.522449	+	0.852670i	$0.325018\pi$
$828$	15.1318	+	10.3167i	0.525865	+	0.358529i
$829$	−33.7388	−	31.3050i	−1.17180	−	1.08727i	−0.994673	−	0.103080i	$-0.967130\pi$
$829$	−33.7388	−	31.3050i	−1.17180	−	1.08727i	−0.177124	−	0.984189i	$-0.556679\pi$
$830$	0.615189	−	8.20913i	0.0213535	−	0.284943i
$831$	−2.80668	+	7.15130i	−0.0973626	+	0.248076i
$832$	5.44594			0.188804
$833$	−5.05317	+	0.292698i	−0.175082	+	0.0101414i
$834$	52.2908			1.81068
$835$	3.58460	−	9.13341i	0.124050	−	0.316075i
$836$	0.0808770	−	1.07923i	0.00279719	−	0.0373259i
$837$	−86.4621	−	80.2251i	−2.98857	−	2.77298i
$838$	−6.70833	−	4.57366i	−0.231735	−	0.157995i
$839$	−4.09292	−	1.97105i	−0.141303	−	0.0680481i	0.361896	−	0.932218i	$-0.382130\pi$
$839$	−4.09292	−	1.97105i	−0.141303	−	0.0680481i	−0.503199	+	0.864170i	$0.667844\pi$
$840$	0.539536	−	11.7539i	0.0186158	−	0.405549i
$841$	20.9100	−	10.0697i	0.721033	−	0.347231i
$842$	−18.6656	−	2.81339i	−0.643260	−	0.0969559i
$843$	59.2099	−	40.3686i	2.03930	−	1.39037i
$844$	−6.76857	+	1.02020i	−0.232984	+	0.0351166i
$845$	16.2248	−	15.0544i	0.558151	−	0.517888i
$846$	30.8043	+	38.6273i	1.05907	+	1.32803i
$847$	−25.6350	+	13.2719i	−0.880829	+	0.456029i
$848$	4.90132	−	6.14605i	0.168312	−	0.211056i
$849$	0.606319	+	8.09076i	0.0208088	+	0.277674i
$850$	−2.23503	−	0.689417i	−0.0766611	−	0.0236468i
$851$	0.783457	−	1.35699i	0.0268566	−	0.0465169i
$852$	13.2249	+	22.9062i	0.453077	+	0.784752i
$853$	10.6652	+	46.7274i	0.365170	+	1.59992i	0.739857	+	0.672764i	$0.234893\pi$
$853$	10.6652	+	46.7274i	0.365170	+	1.59992i	−0.374687	+	0.927151i	$0.622250\pi$
$854$	−4.53769	−	7.35934i	−0.155276	−	0.251831i
$855$	−8.78177	+	38.4754i	−0.300330	+	1.31583i
$856$	12.7353	−	3.92831i	0.435283	−	0.134267i
$857$	−11.0491	−	28.1527i	−0.377431	−	0.961679i	−0.985785	−	0.168013i	$-0.946265\pi$
$857$	−11.0491	−	28.1527i	−0.377431	−	0.961679i	0.608354	−	0.793666i	$-0.291830\pi$
$858$	−1.99056	−	5.07187i	−0.0679567	−	0.173151i
$859$	4.29843	−	1.32589i	0.146661	−	0.0452388i	−0.220556	−	0.975374i	$-0.570787\pi$
$859$	4.29843	−	1.32589i	0.146661	−	0.0452388i	0.367216	+	0.930136i	$0.380311\pi$
$860$	−0.238487	+	1.04488i	−0.00813234	+	0.0356301i
$861$	3.71460	+	6.02444i	0.126593	+	0.205312i
$862$	2.60880	+	11.4299i	0.0888560	+	0.389304i
$863$	20.8380	+	36.0925i	0.709335	+	1.22860i	0.965104	+	0.261866i	$0.0843378\pi$
$863$	20.8380	+	36.0925i	0.709335	+	1.22860i	−0.255770	+	0.966738i	$0.582329\pi$
$864$	−8.70834	+	15.0833i	−0.296264	+	0.513144i
$865$	−5.11853	−	1.57886i	−0.174035	−	0.0536827i
$866$	2.05495	+	27.4214i	0.0698300	+	0.931816i
$867$	34.3864	−	43.1192i	1.16782	−	1.46440i
$868$	−15.9114	+	8.23775i	−0.540067	+	0.279607i
$869$	−1.98093	−	2.48401i	−0.0671984	−	0.0842642i
$870$	7.84565	−	7.27970i	0.265993	−	0.246805i
$871$	29.3911	−	4.42999i	0.995878	−	0.150104i
$872$	−4.16647	+	2.84065i	−0.141095	+	0.0961966i
$873$	146.654	+	22.1045i	4.96348	+	0.748124i
$874$	−7.28279	+	3.50721i	−0.246344	+	0.118633i
$875$	−1.32736	+	28.9170i	−0.0448731	+	0.977572i
$876$	−19.9587	−	9.61159i	−0.674341	−	0.324745i
$877$	−12.5238	−	8.53859i	−0.422899	−	0.288328i	0.333111	−	0.942888i	$-0.391902\pi$
$877$	−12.5238	−	8.53859i	−0.422899	−	0.288328i	−0.756010	+	0.654560i	$0.772854\pi$
$878$	20.2452	+	18.7848i	0.683243	+	0.633957i
$879$	−1.42553	+	19.0223i	−0.0480818	+	0.641607i
$880$	0.145092	−	0.369688i	0.00489105	−	0.0124622i
$881$	23.7680			0.800765			0.400383	−	0.916348i	$-0.368877\pi$
$881$	23.7680			0.800765			0.400383	+	0.916348i	$0.368877\pi$
$882$	9.51928	−	56.6295i	0.320531	−	1.90681i
$883$	27.8993			0.938886			0.469443	−	0.882963i	$-0.344455\pi$
$883$	27.8993			0.938886			0.469443	+	0.882963i	$0.344455\pi$
$884$	−1.43868	+	3.66570i	−0.0483881	+	0.123291i
$885$	1.02598	−	13.6907i	0.0344879	−	0.460209i
$886$	−26.1520	−	24.2655i	−0.878593	−	0.815215i
$887$	37.0770	+	25.2787i	1.24492	+	0.848774i	0.992901	−	0.118947i	$-0.0379520\pi$
$887$	37.0770	+	25.2787i	1.24492	+	0.848774i	0.252022	+	0.967721i	$0.418904\pi$
$888$	2.11662	+	1.01931i	0.0710290	+	0.0342058i
$889$	14.3821	+	33.7410i	0.482360	+	1.13164i
$890$	−16.0796	+	7.74352i	−0.538989	+	0.259563i
$891$	9.95636	+	1.50068i	0.333551	+	0.0502747i
$892$	−21.3292	+	14.5420i	−0.714155	+	0.486903i
$893$	−21.5629	+	3.25009i	−0.721576	+	0.108760i
$894$	−55.6825	+	51.6658i	−1.86230	+	1.72796i
$895$	11.8613	+	14.8736i	0.396479	+	0.497169i
$896$	1.70874	+	2.01995i	0.0570851	+	0.0674818i
$897$	−25.3726	+	31.8163i	−0.847168	+	1.06232i
$898$	−1.77714	−	23.7142i	−0.0593038	−	0.791354i
$899$	−15.5737	−	4.80386i	−0.519413	−	0.160218i
$900$	13.2676	−	22.9802i	0.442254	−	0.766006i
$901$	2.84215	+	4.92275i	0.0946857	+	0.164000i
$902$	0.0531570	+	0.232896i	0.00176993	+	0.00775459i
$903$	−2.41633	+	6.72228i	−0.0804105	+	0.223703i
$904$	4.18369	−	18.3299i	0.139147	−	0.609645i
$905$	1.47041	−	0.453562i	0.0488782	−	0.0150769i
$906$	−13.9760	−	35.6103i	−0.464322	−	1.18307i
$907$	17.9558	+	45.7505i	0.596211	+	1.51912i	0.836245	+	0.548356i	$0.184746\pi$
$907$	17.9558	+	45.7505i	0.596211	+	1.51912i	−0.240034	+	0.970764i	$0.577159\pi$
$908$	24.9786	−	7.70489i	0.828945	−	0.255696i
$909$	21.3188	−	93.4038i	0.707100	−	3.09801i
$910$	19.0050	+	2.30453i	0.630010	+	0.0763946i
$911$	7.21735	+	31.6213i	0.239121	+	1.04766i	0.941806	+	0.336157i	$0.109127\pi$
$911$	7.21735	+	31.6213i	0.239121	+	1.04766i	−0.702684	+	0.711502i	$0.748015\pi$
$912$	−6.05962	−	10.4956i	−0.200654	−	0.347543i
$913$	0.925969	−	1.60383i	0.0306451	−	0.0530789i
$914$	23.5338	+	7.25921i	0.778428	+	0.240113i
$915$	1.08604	+	14.4922i	0.0359033	+	0.479096i
$916$	7.88169	−	9.88333i	0.260418	−	0.326554i
$917$	4.42042	+	17.0744i	0.145975	+	0.563848i
$918$	−7.85215	−	9.84628i	−0.259159	−	0.324976i
$919$	39.5766	−	36.7217i	1.30551	−	1.21134i	0.343241	−	0.939247i	$-0.388475\pi$
$919$	39.5766	−	36.7217i	1.30551	−	1.21134i	0.962272	−	0.272091i	$-0.0877152\pi$
$920$	−2.93309	+	0.442093i	−0.0967012	+	0.0145754i
$921$	66.4777	−	45.3237i	2.19051	−	1.49347i
$922$	3.65751	+	0.551281i	0.120454	+	0.0181555i
$923$	−38.7730	+	18.6721i	−1.27623	+	0.614599i
$924$	1.25664	−	2.32969i	0.0413404	−	0.0766413i
$925$	−2.04547	−	0.985048i	−0.0672548	−	0.0323882i
$926$	−23.9831	−	16.3514i	−0.788134	−	0.537340i
$927$	−17.1288	−	15.8932i	−0.562584	−	0.522001i
$928$	−0.179845	+	2.39987i	−0.00590371	+	0.0787795i
$929$	−14.2184	+	36.2279i	−0.466491	+	1.18860i	0.483227	+	0.875495i	$0.339464\pi$
$929$	−14.2184	+	36.2279i	−0.466491	+	1.18860i	−0.949718	+	0.313105i	$0.898631\pi$
$930$	30.1173			0.987587
$931$	19.5452	+	16.1360i	0.640569	+	0.528835i
$932$	−21.8937			−0.717152
$933$	−31.7051	+	80.7833i	−1.03798	+	2.64473i
$934$	0.183917	−	2.45420i	0.00601794	−	0.0803039i
$935$	0.210510	+	0.195325i	0.00688442	+	0.00638781i
$936$	−36.9125	−	25.1665i	−1.20652	−	0.822594i
$937$	3.36588	+	1.62092i	0.109958	+	0.0529532i	0.488054	−	0.872813i	$-0.337707\pi$
$937$	3.36588	+	1.62092i	0.109958	+	0.0529532i	−0.378096	+	0.925766i	$0.623421\pi$
$938$	10.8650	+	9.51145i	0.354755	+	0.310560i
$939$	−49.0222	+	23.6078i	−1.59978	+	0.770413i
$940$	−7.91268	−	1.19264i	−0.258083	−	0.0388998i
$941$	37.1774	−	25.3471i	1.21195	−	0.826292i	0.223038	−	0.974810i	$-0.428403\pi$
$941$	37.1774	−	25.3471i	1.21195	−	0.826292i	0.988910	+	0.148518i	$0.0474503\pi$
$942$	12.9818	−	1.95669i	0.422970	−	0.0637524i
$943$	1.30793	−	1.21358i	0.0425919	−	0.0395195i
$944$	1.92478	+	2.41359i	0.0626462	+	0.0785558i
$945$	−36.7727	+	48.9519i	−1.19622	+	1.59241i
$946$	−0.150327	+	0.188504i	−0.00488755	+	0.00612880i
$947$	−2.02007	−	26.9559i	−0.0656433	−	0.875949i	−0.928698	−	0.370838i	$-0.879070\pi$
$947$	−2.02007	−	26.9559i	−0.0656433	−	0.875949i	0.863054	−	0.505111i	$-0.168549\pi$
$948$	−33.9977	−	10.4869i	−1.10419	−	0.340599i
$949$	18.0214	−	31.2140i	0.585000	−	1.01325i
$950$	5.85594	+	10.1428i	0.189992	+	0.329076i
$951$	−14.7287	−	64.5306i	−0.477610	−	2.09255i
$952$	−1.81105	+	0.616546i	−0.0586965	+	0.0199824i
$953$	3.70605	−	16.2373i	0.120051	−	0.525977i	−0.878762	−	0.477260i	$-0.841630\pi$
$953$	3.70605	−	16.2373i	0.120051	−	0.525977i	0.998813	−	0.0487162i	$-0.0155130\pi$
$954$	−61.6230	+	19.0082i	−1.99512	+	0.615412i
$955$	3.39496	+	8.65021i	0.109858	+	0.279914i
$956$	−5.52223	−	14.0704i	−0.178602	−	0.455070i
$957$	2.30076	−	0.709691i	0.0743731	−	0.0229411i
$958$	−5.32581	+	23.3339i	−0.172069	+	0.753884i
$959$	−5.98571	+	5.88516i	−0.193289	+	0.190042i
$960$	−0.989606	−	4.33575i	−0.0319394	−	0.139936i
$961$	−7.43090	−	12.8707i	−0.239706	−	0.415183i
$962$	−1.91117	+	3.31025i	−0.0616187	+	0.106727i
$963$	−104.473	−	32.2256i	−3.36659	−	1.03846i
$964$	1.33245	+	17.7802i	0.0429152	+	0.572663i
$965$	1.43061	−	1.79393i	0.0460529	−	0.0577486i
$966$	−19.7620	+	0.571863i	−0.635832	+	0.0183994i
$967$	−14.8398	−	18.6085i	−0.477215	−	0.598409i	0.483706	−	0.875230i	$-0.339290\pi$
$967$	−14.8398	−	18.6085i	−0.477215	−	0.598409i	−0.960921	+	0.276822i	$0.910719\pi$
$968$	−7.99808	+	7.42113i	−0.257068	+	0.238524i
$969$	8.66545	−	1.30611i	0.278374	−	0.0419582i
$970$	−19.8471	+	13.5315i	−0.637251	+	0.434471i
$971$	−38.0328	−	5.73253i	−1.22053	−	0.183966i	−0.492994	−	0.870033i	$-0.664097\pi$
$971$	−38.0328	−	5.73253i	−1.22053	−	0.183966i	−0.727538	+	0.686067i	$0.759336\pi$
$972$	54.5105	−	26.2509i	1.74843	−	0.841998i
$973$	−33.4633	+	24.2619i	−1.07278	+	0.777801i
$974$	19.9212	+	9.59356i	0.638318	+	0.307398i
$975$	48.7170	+	33.2147i	1.56019	+	1.06372i
$976$	−2.39548	−	2.22268i	−0.0766774	−	0.0711463i
$977$	−2.70685	+	36.1204i	−0.0865998	+	1.15559i	0.769452	+	0.638704i	$0.220529\pi$
$977$	−2.70685	+	36.1204i	−0.0865998	+	1.15559i	−0.856052	+	0.516890i	$0.827090\pi$
$978$	4.94356	−	12.5960i	0.158078	−	0.402775i
$979$	−4.01494			−0.128318
$980$	5.10832	+	7.77222i	0.163179	+	0.248274i
$981$	41.3674			1.32076
$982$	12.8903	−	32.8441i	0.411348	−	1.04810i
$983$	1.92397	−	25.6736i	0.0613652	−	0.818861i	−0.878593	−	0.477571i	$-0.841517\pi$
$983$	1.92397	−	25.6736i	0.0613652	−	0.818861i	0.939958	−	0.341290i	$-0.110864\pi$
$984$	1.96097	+	1.81951i	0.0625134	+	0.0580039i
$985$	−11.3575	−	7.74338i	−0.361879	−	0.246725i
$986$	−1.56786	−	0.755040i	−0.0499308	−	0.0240454i
$987$	−51.3987	−	14.2399i	−1.63604	−	0.453262i
$988$	17.7657	−	8.55551i	0.565203	−	0.272187i
$989$	1.78069	+	0.268396i	0.0566227	+	0.00853449i
$990$	−2.69182	+	1.83525i	−0.0855517	+	0.0583282i
$991$	−36.9809	+	5.57398i	−1.17474	+	0.177063i	−0.707268	−	0.706946i	$-0.750072\pi$
$991$	−36.9809	+	5.57398i	−1.17474	+	0.177063i	−0.467470	+	0.884009i	$0.654834\pi$
$992$	−4.96433	+	4.60622i	−0.157617	+	0.146248i
$993$	−7.18019	−	9.00368i	−0.227857	−	0.285723i
$994$	−19.0912	−	8.52263i	−0.605537	−	0.270321i
$995$	−1.54949	+	1.94299i	−0.0491220	+	0.0615971i
$996$	−1.54977	−	20.6803i	−0.0491065	−	0.655280i
$997$	10.0011	+	3.08493i	0.316737	+	0.0977006i	0.449048	−	0.893508i	$-0.351763\pi$
$997$	10.0011	+	3.08493i	0.316737	+	0.0977006i	−0.132310	+	0.991208i	$0.542240\pi$
$998$	−3.89719	+	6.75014i	−0.123364	+	0.213672i
$999$	−6.11213	−	10.5865i	−0.193379	−	0.334943i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	98.2.g.a.95.1	yes	24
3.2	odd	2		882.2.z.d.487.2		24
4.3	odd	2		784.2.bg.a.193.2		24
7.2	even	3		686.2.g.a.79.1		24
7.3	odd	6		686.2.e.e.393.1		24
7.4	even	3		686.2.e.f.393.4		24
7.5	odd	6		686.2.g.c.79.2		24
7.6	odd	2		686.2.g.b.557.2		24
49.4	even	21		4802.2.a.i.1.1		12
49.6	odd	14		686.2.g.c.165.2		24
49.10	odd	42		686.2.e.e.295.1		24
49.16	even	21	inner	98.2.g.a.65.1	✓	24
49.33	odd	42		686.2.g.b.569.2		24
49.39	even	21		686.2.e.f.295.4		24
49.43	even	7		686.2.g.a.165.1		24
49.45	odd	42		4802.2.a.k.1.12		12
147.65	odd	42		882.2.z.d.163.2		24
196.163	odd	42		784.2.bg.a.65.2		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
98.2.g.a.65.1	✓	24	49.16	even	21	inner
98.2.g.a.95.1	yes	24	1.1	even	1	trivial
686.2.e.e.295.1		24	49.10	odd	42
686.2.e.e.393.1		24	7.3	odd	6
686.2.e.f.295.4		24	49.39	even	21
686.2.e.f.393.4		24	7.4	even	3
686.2.g.a.79.1		24	7.2	even	3
686.2.g.a.165.1		24	49.43	even	7
686.2.g.b.557.2		24	7.6	odd	2
686.2.g.b.569.2		24	49.33	odd	42
686.2.g.c.79.2		24	7.5	odd	6
686.2.g.c.165.2		24	49.6	odd	14
784.2.bg.a.65.2		24	196.163	odd	42
784.2.bg.a.193.2		24	4.3	odd	2
882.2.z.d.163.2		24	147.65	odd	42
882.2.z.d.487.2		24	3.2	odd	2
4802.2.a.i.1.1		12	49.4	even	21
4802.2.a.k.1.12		12	49.45	odd	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:	\( N \)	\(=\)	\( 98 = 2 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	98.g (of order \(21\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.365341 + 0.930874i) q^{2} +(-0.250133 + 3.33779i) q^{3} +(-0.733052 - 0.680173i) q^{4} +(-1.09780 - 0.748464i) q^{5} +(-3.01568 - 1.45228i) q^{6} +(2.60370 - 0.469838i) q^{7} +(0.900969 - 0.433884i) q^{8} +(-8.11181 - 1.22266i) q^{9} +O(q^{10})\)	\(q+(-0.365341 + 0.930874i) q^{2} +(-0.250133 + 3.33779i) q^{3} +(-0.733052 - 0.680173i) q^{4} +(-1.09780 - 0.748464i) q^{5} +(-3.01568 - 1.45228i) q^{6} +(2.60370 - 0.469838i) q^{7} +(0.900969 - 0.433884i) q^{8} +(-8.11181 - 1.22266i) q^{9} +(1.09780 - 0.748464i) q^{10} +(0.295564 - 0.0445491i) q^{11} +(2.45364 - 2.27664i) q^{12} +(3.39549 + 4.25781i) q^{13} +(-0.513878 + 2.59537i) q^{14} +(2.77281 - 3.47700i) q^{15} +(0.0747301 + 0.997204i) q^{16} +(-0.690967 - 0.213135i) q^{17} +(4.10172 - 7.10438i) q^{18} +(1.81038 + 3.13567i) q^{19} +(0.295656 + 1.29535i) q^{20} +(0.916952 + 8.80813i) q^{21} +(-0.0665120 + 0.291408i) q^{22} +(2.13330 - 0.658036i) q^{23} +(1.22285 + 3.11578i) q^{24} +(-1.18175 - 3.01105i) q^{25} +(-5.20399 + 1.60522i) q^{26} +(3.87558 - 16.9800i) q^{27} +(-2.22822 - 1.42655i) q^{28} +(-0.535518 - 2.34626i) q^{29} +(2.22362 + 3.85143i) q^{30} +(3.38607 - 5.86484i) q^{31} +(-0.955573 - 0.294755i) q^{32} +(0.0747654 + 0.997674i) q^{33} +(0.450841 - 0.565336i) q^{34} +(-3.20999 - 1.43299i) q^{35} +(5.11476 + 6.41370i) q^{36} +(0.514508 - 0.477393i) q^{37} +(-3.58032 + 0.539646i) q^{38} +(-15.0610 + 10.2684i) q^{39} +(-1.31383 - 0.198027i) q^{40} +(0.720062 - 0.346764i) q^{41} +(-8.53426 - 2.36441i) q^{42} +(0.726755 + 0.349987i) q^{43} +(-0.246965 - 0.168378i) q^{44} +(7.98999 + 7.41362i) q^{45} +(-0.166834 + 2.22624i) q^{46} +(-2.20031 + 5.60630i) q^{47} -3.34715 q^{48} +(6.55850 - 2.44664i) q^{49} +3.23465 q^{50} +(0.884235 - 2.25299i) q^{51} +(0.406976 - 5.43071i) q^{52} +(-5.76259 - 5.34691i) q^{53} +(14.3903 + 9.81117i) q^{54} +(-0.357812 - 0.172313i) q^{55} +(2.14200 - 1.55301i) q^{56} +(-10.9191 + 5.25834i) q^{57} +(2.37972 + 0.358685i) q^{58} +(2.55068 - 1.73903i) q^{59} +(-4.39757 + 0.662828i) q^{60} +(-2.39548 + 2.22268i) q^{61} +(4.22236 + 5.29467i) q^{62} +(-21.6952 + 0.627804i) q^{63} +(0.623490 - 0.781831i) q^{64} +(-0.540735 - 7.21560i) q^{65} +(-0.956024 - 0.294894i) q^{66} +(2.72892 - 4.72662i) q^{67} +(0.361546 + 0.626216i) q^{68} +(1.66278 + 7.28511i) q^{69} +(2.50667 - 2.46456i) q^{70} +(-1.75840 + 7.70404i) q^{71} +(-7.83898 + 2.41800i) q^{72} +(-2.41794 - 6.16080i) q^{73} +(0.256422 + 0.653353i) q^{74} +(10.3459 - 3.19127i) q^{75} +(0.805695 - 3.52998i) q^{76} +(0.748629 - 0.254860i) q^{77} +(-4.05620 - 17.7714i) q^{78} +(-5.31472 - 9.20536i) q^{79} +(0.664333 - 1.15066i) q^{80} +(32.1894 + 9.92912i) q^{81} +(0.0597250 + 0.796974i) q^{82} +(3.86302 - 4.84407i) q^{83} +(5.31888 - 7.08050i) q^{84} +(0.599016 + 0.751143i) q^{85} +(-0.591307 + 0.548653i) q^{86} +(7.96527 - 1.20057i) q^{87} +(0.246965 - 0.168378i) q^{88} +(-13.2822 - 2.00198i) q^{89} +(-9.82022 + 4.72917i) q^{90} +(10.8413 + 9.49072i) q^{91} +(-2.01140 - 0.968638i) q^{92} +(18.7287 + 12.7690i) q^{93} +(-4.41490 - 4.09643i) q^{94} +(0.359510 - 4.79733i) q^{95} +(1.22285 - 3.11578i) q^{96} -18.0790 q^{97} +(-0.118581 + 6.99900i) q^{98} -2.45203 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 2 q^{2} + 7 q^{3} + 2 q^{4} - 7 q^{6} + 4 q^{8} - 33 q^{9}+O(q^{10}) \) 24 * q - 2 * q^2 + 7 * q^3 + 2 * q^4 - 7 * q^6 + 4 * q^8 - 33 * q^9	\( 24 q - 2 q^{2} + 7 q^{3} + 2 q^{4} - 7 q^{6} + 4 q^{8} - 33 q^{9} - 7 q^{11} + 14 q^{13} - 7 q^{15} + 2 q^{16} - 7 q^{17} + 5 q^{18} - 7 q^{20} + 7 q^{21} - 7 q^{22} - 21 q^{23} + 4 q^{25} - 7 q^{26} - 35 q^{27} - 14 q^{28} - 11 q^{29} + 28 q^{31} - 2 q^{32} + 14 q^{33} + 7 q^{34} + 21 q^{35} + 3 q^{36} - 24 q^{37} - 7 q^{38} - 40 q^{39} + 14 q^{40} + 28 q^{41} - 21 q^{42} + 10 q^{43} + 21 q^{44} + 7 q^{45} + 42 q^{46} - 70 q^{47} - 14 q^{48} + 84 q^{49} + 8 q^{50} + 60 q^{51} - 7 q^{52} + 26 q^{53} + 63 q^{54} + 56 q^{55} + 21 q^{56} - 33 q^{57} - 30 q^{58} - 7 q^{59} + 14 q^{60} + 14 q^{61} + 28 q^{62} - 14 q^{63} - 4 q^{64} - 21 q^{66} - 36 q^{67} - 14 q^{68} - 35 q^{69} + 14 q^{70} - 2 q^{72} - 7 q^{73} - 11 q^{74} - 28 q^{75} - 91 q^{77} - 24 q^{78} - 26 q^{79} + 55 q^{81} + 14 q^{82} - 7 q^{83} - 21 q^{84} + 49 q^{85} - 16 q^{86} + 35 q^{87} - 21 q^{88} - 56 q^{89} - 21 q^{90} + 7 q^{91} + 21 q^{92} + 72 q^{93} - 35 q^{94} - 14 q^{95} - 126 q^{97} - 56 q^{98} - 14 q^{99}+O(q^{100}) \) 24 * q - 2 * q^2 + 7 * q^3 + 2 * q^4 - 7 * q^6 + 4 * q^8 - 33 * q^9 - 7 * q^11 + 14 * q^13 - 7 * q^15 + 2 * q^16 - 7 * q^17 + 5 * q^18 - 7 * q^20 + 7 * q^21 - 7 * q^22 - 21 * q^23 + 4 * q^25 - 7 * q^26 - 35 * q^27 - 14 * q^28 - 11 * q^29 + 28 * q^31 - 2 * q^32 + 14 * q^33 + 7 * q^34 + 21 * q^35 + 3 * q^36 - 24 * q^37 - 7 * q^38 - 40 * q^39 + 14 * q^40 + 28 * q^41 - 21 * q^42 + 10 * q^43 + 21 * q^44 + 7 * q^45 + 42 * q^46 - 70 * q^47 - 14 * q^48 + 84 * q^49 + 8 * q^50 + 60 * q^51 - 7 * q^52 + 26 * q^53 + 63 * q^54 + 56 * q^55 + 21 * q^56 - 33 * q^57 - 30 * q^58 - 7 * q^59 + 14 * q^60 + 14 * q^61 + 28 * q^62 - 14 * q^63 - 4 * q^64 - 21 * q^66 - 36 * q^67 - 14 * q^68 - 35 * q^69 + 14 * q^70 - 2 * q^72 - 7 * q^73 - 11 * q^74 - 28 * q^75 - 91 * q^77 - 24 * q^78 - 26 * q^79 + 55 * q^81 + 14 * q^82 - 7 * q^83 - 21 * q^84 + 49 * q^85 - 16 * q^86 + 35 * q^87 - 21 * q^88 - 56 * q^89 - 21 * q^90 + 7 * q^91 + 21 * q^92 + 72 * q^93 - 35 * q^94 - 14 * q^95 - 126 * q^97 - 56 * q^98 - 14 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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