LMFDB - Embedded newform 136.2.s.c.11.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [136,2,Mod(3,136)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(136, base_ring=CyclotomicField(16))

chi = DirichletCharacter(H, H._module([8, 8, 1]))

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

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

chi := DirichletCharacter("136.3");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 136 = 2^{3} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	136.s (of order $16$, degree $8$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.08596546749$
Analytic rank:	$0$
Dimension:	$112$
Relative dimension:	$14$ over $\Q(\zeta_{16})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			11.3
Character	$\chi$	$=$	136.11
Dual form			136.2.s.c.99.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.06196 + 0.933944i) q^{2} +(-0.481682 - 2.42158i) q^{3} +(0.255498 - 1.98361i) q^{4} +(-1.60449 + 2.40128i) q^{5} +(2.77314 + 2.12174i) q^{6} +(-2.01574 - 3.01677i) q^{7} +(1.58126 + 2.34513i) q^{8} +(-2.86039 + 1.18481i) q^{9} +O(q^{10})$	\(q+(-1.06196 + 0.933944i) q^{2} +(-0.481682 - 2.42158i) q^{3} +(0.255498 - 1.98361i) q^{4} +(-1.60449 + 2.40128i) q^{5} +(2.77314 + 2.12174i) q^{6} +(-2.01574 - 3.01677i) q^{7} +(1.58126 + 2.34513i) q^{8} +(-2.86039 + 1.18481i) q^{9} +(-0.538771 - 4.04856i) q^{10} +(-5.34680 - 1.06354i) q^{11} +(-4.92654 + 0.336762i) q^{12} +(-2.08889 - 2.08889i) q^{13} +(4.95813 + 1.32109i) q^{14} +(6.58775 + 2.72874i) q^{15} +(-3.86944 - 1.01362i) q^{16} +(2.60353 - 3.19713i) q^{17} +(1.93106 - 3.92966i) q^{18} +(3.80825 + 1.57743i) q^{19} +(4.35328 + 3.79621i) q^{20} +(-6.33441 + 6.33441i) q^{21} +(6.67135 - 3.86417i) q^{22} +(2.21592 + 0.440773i) q^{23} +(4.91725 - 4.95874i) q^{24} +(-1.27837 - 3.08626i) q^{25} +(4.16922 + 0.267402i) q^{26} +(0.131766 + 0.197202i) q^{27} +(-6.49913 + 3.22768i) q^{28} +(-1.95181 - 1.30416i) q^{29} +(-9.54438 + 3.25479i) q^{30} +(0.157623 + 0.792425i) q^{31} +(5.05584 - 2.53742i) q^{32} +13.4600i q^{33} +(0.221114 + 5.82676i) q^{34} +10.4784 q^{35} +(1.61938 + 5.97662i) q^{36} +(3.93527 - 0.782774i) q^{37} +(-5.51742 + 1.88153i) q^{38} +(-4.05224 + 6.06460i) q^{39} +(-8.16843 + 0.0343157i) q^{40} +(0.618274 - 0.413117i) q^{41} +(0.810876 - 12.6428i) q^{42} +(0.542885 - 0.224870i) q^{43} +(-3.47576 + 10.3342i) q^{44} +(1.74438 - 8.76962i) q^{45} +(-2.76486 + 1.60146i) q^{46} +(-2.27684 - 2.27684i) q^{47} +(-0.590716 + 9.85840i) q^{48} +(-2.35891 + 5.69492i) q^{49} +(4.23997 + 2.08355i) q^{50} +(-8.99618 - 4.76464i) q^{51} +(-4.67727 + 3.60985i) q^{52} +(4.67028 - 11.2751i) q^{53} +(-0.324105 - 0.0863575i) q^{54} +(11.1327 - 11.1327i) q^{55} +(3.88732 - 9.49747i) q^{56} +(1.98550 - 9.98179i) q^{57} +(3.29075 - 0.437924i) q^{58} +(2.07442 + 5.00809i) q^{59} +(7.09591 - 12.3704i) q^{60} +(-3.19122 + 2.13230i) q^{61} +(-0.907469 - 0.694308i) q^{62} +(9.34011 + 6.24086i) q^{63} +(-2.99926 + 7.41650i) q^{64} +(8.36764 - 1.66443i) q^{65} +(-12.5709 - 14.2939i) q^{66} -9.67224i q^{67} +(-5.67668 - 5.98125i) q^{68} -5.57833i q^{69} +(-11.1276 + 9.78620i) q^{70} +(-12.0958 + 2.40601i) q^{71} +(-7.30154 - 4.83449i) q^{72} +(-1.21626 - 0.812676i) q^{73} +(-3.44801 + 4.50659i) q^{74} +(-6.85786 + 4.58228i) q^{75} +(4.10201 - 7.15106i) q^{76} +(7.56930 + 18.2739i) q^{77} +(-1.36070 - 10.2249i) q^{78} +(2.62293 - 13.1863i) q^{79} +(8.64246 - 7.66529i) q^{80} +(-6.15366 + 6.15366i) q^{81} +(-0.270751 + 1.01615i) q^{82} +(-4.77818 + 11.5355i) q^{83} +(10.9466 + 14.1834i) q^{84} +(3.49990 + 11.3816i) q^{85} +(-0.366503 + 0.745827i) q^{86} +(-2.21797 + 5.35465i) q^{87} +(-5.96051 - 14.2207i) q^{88} +(-0.639995 - 0.639995i) q^{89} +(6.33787 + 10.9421i) q^{90} +(-2.09105 + 10.5124i) q^{91} +(1.44049 - 4.28291i) q^{92} +(1.84299 - 0.763393i) q^{93} +(4.54433 + 0.291461i) q^{94} +(-9.89814 + 6.61373i) q^{95} +(-8.57988 - 11.0209i) q^{96} +(-2.21618 + 3.31675i) q^{97} +(-2.81368 - 8.25084i) q^{98} +(16.5540 - 3.29280i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 112 q - 8 q^{2} - 16 q^{3} - 8 q^{4} - 8 q^{6} - 8 q^{8} - 16 q^{9}+O(q^{10}) $ 112 * q - 8 * q^2 - 16 * q^3 - 8 * q^4 - 8 * q^6 - 8 * q^8 - 16 * q^9	$ 112 q - 8 q^{2} - 16 q^{3} - 8 q^{4} - 8 q^{6} - 8 q^{8} - 16 q^{9} - 8 q^{10} - 16 q^{11} + 24 q^{12} - 8 q^{14} - 16 q^{17} - 16 q^{18} - 16 q^{19} - 8 q^{20} - 8 q^{22} - 56 q^{24} - 16 q^{25} - 40 q^{26} + 32 q^{27} + 40 q^{28} - 72 q^{30} + 32 q^{32} - 72 q^{34} - 32 q^{35} + 56 q^{36} + 48 q^{38} + 56 q^{40} - 16 q^{41} - 56 q^{42} - 96 q^{43} + 24 q^{44} - 24 q^{46} + 16 q^{48} - 16 q^{49} - 16 q^{51} - 16 q^{52} - 24 q^{54} + 32 q^{56} + 32 q^{57} + 48 q^{58} - 16 q^{59} + 96 q^{60} + 48 q^{62} + 40 q^{64} + 64 q^{65} - 16 q^{66} + 80 q^{68} + 64 q^{70} + 96 q^{72} - 96 q^{73} + 40 q^{74} - 16 q^{75} + 48 q^{76} + 96 q^{78} + 8 q^{80} - 96 q^{81} + 32 q^{82} + 128 q^{83} + 64 q^{86} - 72 q^{88} - 16 q^{89} + 152 q^{90} - 16 q^{91} - 120 q^{92} + 88 q^{94} - 160 q^{96} - 16 q^{97} + 128 q^{98} + 48 q^{99}+O(q^{100}) $ 112 * q - 8 * q^2 - 16 * q^3 - 8 * q^4 - 8 * q^6 - 8 * q^8 - 16 * q^9 - 8 * q^10 - 16 * q^11 + 24 * q^12 - 8 * q^14 - 16 * q^17 - 16 * q^18 - 16 * q^19 - 8 * q^20 - 8 * q^22 - 56 * q^24 - 16 * q^25 - 40 * q^26 + 32 * q^27 + 40 * q^28 - 72 * q^30 + 32 * q^32 - 72 * q^34 - 32 * q^35 + 56 * q^36 + 48 * q^38 + 56 * q^40 - 16 * q^41 - 56 * q^42 - 96 * q^43 + 24 * q^44 - 24 * q^46 + 16 * q^48 - 16 * q^49 - 16 * q^51 - 16 * q^52 - 24 * q^54 + 32 * q^56 + 32 * q^57 + 48 * q^58 - 16 * q^59 + 96 * q^60 + 48 * q^62 + 40 * q^64 + 64 * q^65 - 16 * q^66 + 80 * q^68 + 64 * q^70 + 96 * q^72 - 96 * q^73 + 40 * q^74 - 16 * q^75 + 48 * q^76 + 96 * q^78 + 8 * q^80 - 96 * q^81 + 32 * q^82 + 128 * q^83 + 64 * q^86 - 72 * q^88 - 16 * q^89 + 152 * q^90 - 16 * q^91 - 120 * q^92 + 88 * q^94 - 160 * q^96 - 16 * q^97 + 128 * q^98 + 48 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/136\mathbb{Z}\right)^\times$.

$n$	$69$	$103$	$105$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{7}{16}\right)$

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 $

$2$	−1.06196	+	0.933944i	−0.750916	+	0.660398i
$2$	−1.06196	+	0.933944i	−0.750916	+	0.660398i
$3$	−0.481682	−	2.42158i	−0.278099	−	1.39810i	−0.826996	−	0.562209i	$-0.809952\pi$
$3$	−0.481682	−	2.42158i	−0.278099	−	1.39810i	0.548896	−	0.835890i	$-0.315048\pi$
$4$	0.255498	−	1.98361i	0.127749	−	0.991807i
$5$	−1.60449	+	2.40128i	−0.717549	+	1.07389i	0.276075	+	0.961136i	$0.410966\pi$
$5$	−1.60449	+	2.40128i	−0.717549	+	1.07389i	−0.993623	+	0.112751i	$0.964034\pi$
$6$	2.77314	+	2.12174i	1.13213	+	0.866198i
$7$	−2.01574	−	3.01677i	−0.761879	−	1.14023i	−0.986174	−	0.165712i	$-0.947008\pi$
$7$	−2.01574	−	3.01677i	−0.761879	−	1.14023i	0.224295	−	0.974521i	$-0.427992\pi$
$8$	1.58126	+	2.34513i	0.559058	+	0.829128i
$9$	−2.86039	+	1.18481i	−0.953462	+	0.394937i
$10$	−0.538771	−	4.04856i	−0.170374	−	1.28027i
$11$	−5.34680	−	1.06354i	−1.61212	−	0.320671i	−0.694917	−	0.719090i	$-0.744559\pi$
$11$	−5.34680	−	1.06354i	−1.61212	−	0.320671i	−0.917203	+	0.398419i	$0.869559\pi$
$12$	−4.92654	+	0.336762i	−1.42217	+	0.0972149i
$13$	−2.08889	−	2.08889i	−0.579355	−	0.579355i	0.355370	−	0.934726i	$-0.384355\pi$
$13$	−2.08889	−	2.08889i	−0.579355	−	0.579355i	−0.934726	+	0.355370i	$0.884355\pi$
$14$	4.95813	+	1.32109i	1.32511	+	0.353075i
$15$	6.58775	+	2.72874i	1.70095	+	0.704557i
$16$	−3.86944	−	1.01362i	−0.967360	−	0.253405i
$17$	2.60353	−	3.19713i	0.631448	−	0.775418i
$17$	2.60353	−	3.19713i	0.631448	−	0.775418i
$18$	1.93106	−	3.92966i	0.455154	−	0.926229i
$19$	3.80825	+	1.57743i	0.873672	+	0.361887i	0.774039	−	0.633137i	$-0.218233\pi$
$19$	3.80825	+	1.57743i	0.873672	+	0.361887i	0.0996328	+	0.995024i	$0.468233\pi$
$20$	4.35328	+	3.79621i	0.973422	+	0.848857i
$21$	−6.33441	+	6.33441i	−1.38228	+	1.38228i
$22$	6.67135	−	3.86417i	1.42234	−	0.823844i
$23$	2.21592	+	0.440773i	0.462051	+	0.0919076i	0.420626	−	0.907234i	$-0.361810\pi$
$23$	2.21592	+	0.440773i	0.462051	+	0.0919076i	0.0414246	+	0.999142i	$0.486810\pi$
$24$	4.91725	−	4.95874i	1.00373	−	1.01220i
$25$	−1.27837	−	3.08626i	−0.255675	−	0.617253i
$26$	4.16922	+	0.267402i	0.817652	+	0.0524419i
$27$	0.131766	+	0.197202i	0.0253584	+	0.0379515i
$28$	−6.49913	+	3.22768i	−1.22822	+	0.609973i
$29$	−1.95181	−	1.30416i	−0.362442	−	0.242176i	0.360993	−	0.932569i	$-0.382438\pi$
$29$	−1.95181	−	1.30416i	−0.362442	−	0.242176i	−0.723435	+	0.690392i	$0.757438\pi$
$30$	−9.54438	+	3.25479i	−1.74256	+	0.594241i
$31$	0.157623	+	0.792425i	0.0283099	+	0.142324i	0.992355	−	0.123414i	$-0.0393844\pi$
$31$	0.157623	+	0.792425i	0.0283099	+	0.142324i	−0.964045	+	0.265738i	$0.914384\pi$
$32$	5.05584	−	2.53742i	0.893754	−	0.448557i
$33$			13.4600i			2.34308i
$34$	0.221114	+	5.82676i	0.0379207	+	0.999281i
$35$	10.4784			1.77117
$36$	1.61938	+	5.97662i	0.269897	+	0.996103i
$37$	3.93527	−	0.782774i	0.646954	−	0.128687i	0.139303	−	0.990250i	$-0.455514\pi$
$37$	3.93527	−	0.782774i	0.646954	−	0.128687i	0.507651	+	0.861563i	$0.330514\pi$
$38$	−5.51742	+	1.88153i	−0.895044	+	0.305225i
$39$	−4.05224	+	6.06460i	−0.648878	+	0.971114i
$40$	−8.16843	+	0.0343157i	−1.29154	+	0.00542579i
$41$	0.618274	−	0.413117i	0.0965581	−	0.0645181i	−0.506354	−	0.862326i	$-0.669007\pi$
$41$	0.618274	−	0.413117i	0.0965581	−	0.0645181i	0.602912	+	0.797808i	$0.294007\pi$
$42$	0.810876	−	12.6428i	0.125121	−	1.95083i
$43$	0.542885	−	0.224870i	0.0827892	−	0.0342924i	−0.340905	−	0.940098i	$-0.610733\pi$
$43$	0.542885	−	0.224870i	0.0827892	−	0.0342924i	0.423694	+	0.905806i	$0.360733\pi$
$44$	−3.47576	+	10.3342i	−0.523990	+	1.55795i
$45$	1.74438	−	8.76962i	0.260038	−	1.30730i
$46$	−2.76486	+	1.60146i	−0.407657	+	0.236123i
$47$	−2.27684	−	2.27684i	−0.332111	−	0.332111i	0.521277	−	0.853388i	$-0.325456\pi$
$47$	−2.27684	−	2.27684i	−0.332111	−	0.332111i	−0.853388	+	0.521277i	$0.825456\pi$
$48$	−0.590716	+	9.85840i	−0.0852625	+	1.42294i
$49$	−2.35891	+	5.69492i	−0.336988	+	0.813560i
$50$	4.23997	+	2.08355i	0.599623	+	0.294658i
$51$	−8.99618	−	4.76464i	−1.25972	−	0.667183i
$52$	−4.67727	+	3.60985i	−0.648620	+	0.500596i
$53$	4.67028	−	11.2751i	0.641513	−	1.54875i	−0.183127	−	0.983089i	$-0.558622\pi$
$53$	4.67028	−	11.2751i	0.641513	−	1.54875i	0.824639	−	0.565659i	$-0.191378\pi$
$54$	−0.324105	−	0.0863575i	−0.0441052	−	0.0117518i
$55$	11.1327	−	11.1327i	1.50114	−	1.50114i
$56$	3.88732	−	9.49747i	0.519464	−	1.26915i
$57$	1.98550	−	9.98179i	0.262986	−	1.32212i
$58$	3.29075	−	0.437924i	0.432096	−	0.0575022i
$59$	2.07442	+	5.00809i	0.270066	+	0.651998i	0.999486	−	0.0320692i	$-0.0102097\pi$
$59$	2.07442	+	5.00809i	0.270066	+	0.651998i	−0.729419	+	0.684067i	$0.760210\pi$
$60$	7.09591	−	12.3704i	0.916079	−	1.59701i
$61$	−3.19122	+	2.13230i	−0.408593	+	0.273013i	−0.742836	−	0.669474i	$-0.766520\pi$
$61$	−3.19122	+	2.13230i	−0.408593	+	0.273013i	0.334242	+	0.942487i	$0.391520\pi$
$62$	−0.907469	−	0.694308i	−0.115249	−	0.0881773i
$63$	9.34011	+	6.24086i	1.17674	+	0.786275i
$64$	−2.99926	+	7.41650i	−0.374908	+	0.927062i
$65$	8.36764	−	1.66443i	1.03788	−	0.206447i
$66$	−12.5709	−	14.2939i	−1.54737	−	1.75946i
$67$		−	9.67224i		−	1.18165i	−0.806799	−	0.590826i	$-0.798802\pi$
$67$		−	9.67224i		−	1.18165i	0.806799	−	0.590826i	$-0.201198\pi$
$68$	−5.67668	−	5.98125i	−0.688398	−	0.725333i
$69$		−	5.57833i		−	0.671552i
$70$	−11.1276	+	9.78620i	−1.33000	+	1.16968i
$71$	−12.0958	+	2.40601i	−1.43551	+	0.285541i	−0.850710	−	0.525635i	$-0.823828\pi$
$71$	−12.0958	+	2.40601i	−1.43551	+	0.285541i	−0.584802	+	0.811176i	$0.698828\pi$
$72$	−7.30154	−	4.83449i	−0.860494	−	0.569750i
$73$	−1.21626	−	0.812676i	−0.142352	−	0.0951165i	0.482355	−	0.875976i	$-0.339782\pi$
$73$	−1.21626	−	0.812676i	−0.142352	−	0.0951165i	−0.624707	+	0.780859i	$0.714782\pi$
$74$	−3.44801	+	4.50659i	−0.400823	+	0.523881i
$75$	−6.85786	+	4.58228i	−0.791878	+	0.529116i
$76$	4.10201	−	7.15106i	0.470533	−	0.820283i
$77$	7.56930	+	18.2739i	0.862602	+	2.08251i
$78$	−1.36070	−	10.2249i	−0.154069	−	1.15774i
$79$	2.62293	−	13.1863i	0.295102	−	1.48358i	−0.494078	−	0.869418i	$-0.664494\pi$
$79$	2.62293	−	13.1863i	0.295102	−	1.48358i	0.789180	−	0.614162i	$-0.210506\pi$
$80$	8.64246	−	7.66529i	0.966256	−	0.857006i
$81$	−6.15366	+	6.15366i	−0.683740	+	0.683740i
$82$	−0.270751	+	1.01615i	−0.0298994	+	0.112214i
$83$	−4.77818	+	11.5355i	−0.524473	+	1.26619i	0.410626	+	0.911804i	$0.365310\pi$
$83$	−4.77818	+	11.5355i	−0.524473	+	1.26619i	−0.935099	+	0.354387i	$0.884690\pi$
$84$	10.9466	+	14.1834i	1.19437	+	1.54754i
$85$	3.49990	+	11.3816i	0.379618	+	1.23450i
$86$	−0.366503	+	0.745827i	−0.0395211	+	0.0804245i
$87$	−2.21797	+	5.35465i	−0.237791	+	0.574079i
$88$	−5.96051	−	14.2207i	−0.635392	−	1.51593i
$89$	−0.639995	−	0.639995i	−0.0678393	−	0.0678393i	0.672373	−	0.740212i	$-0.265275\pi$
$89$	−0.639995	−	0.639995i	−0.0678393	−	0.0678393i	−0.740212	+	0.672373i	$0.765275\pi$
$90$	6.33787	+	10.9421i	0.668070	+	1.15340i
$91$	−2.09105	+	10.5124i	−0.219201	+	1.10200i
$92$	1.44049	−	4.28291i	0.150181	−	0.446524i
$93$	1.84299	−	0.763393i	0.191110	−	0.0791602i
$94$	4.54433	+	0.291461i	0.468712	+	0.0300619i
$95$	−9.89814	+	6.61373i	−1.01553	+	0.678554i
$96$	−8.57988	−	11.0209i	−0.875680	−	1.12481i
$97$	−2.21618	+	3.31675i	−0.225019	+	0.336765i	−0.926751	−	0.375676i	$-0.877410\pi$
$97$	−2.21618	+	3.31675i	−0.225019	+	0.336765i	0.701732	+	0.712441i	$0.252410\pi$
$98$	−2.81368	−	8.25084i	−0.284224	−	0.833461i
$99$	16.5540	−	3.29280i	1.66374	−	0.330939i
$100$	−6.44858	+	1.74726i	−0.644858	+	0.174726i
$101$	2.26972			0.225846			0.112923	−	0.993604i	$-0.463979\pi$
$101$	2.26972			0.225846			0.112923	+	0.993604i	$0.463979\pi$
$102$	14.0034	−	3.34209i	1.38655	−	0.330916i
$103$		−	2.74572i		−	0.270543i	−0.990809	−	0.135272i	$-0.956809\pi$
$103$		−	2.74572i		−	0.270543i	0.990809	−	0.135272i	$-0.0431907\pi$
$104$	1.59565	−	8.20180i	0.156466	−	0.804253i
$105$	−5.04724	−	25.3742i	−0.492560	−	2.47627i
$106$	5.57064	+	16.3354i	0.541068	+	1.58663i
$107$	−4.36506	−	2.91664i	−0.421986	−	0.281962i	0.326392	−	0.945235i	$-0.394167\pi$
$107$	−4.36506	−	2.91664i	−0.421986	−	0.281962i	−0.748378	+	0.663272i	$0.769167\pi$
$108$	0.424839	−	0.210988i	0.0408801	−	0.0203024i
$109$	0.289398	+	0.433115i	0.0277193	+	0.0414849i	0.845070	−	0.534655i	$-0.179558\pi$
$109$	0.289398	+	0.433115i	0.0277193	+	0.0414849i	−0.817351	+	0.576140i	$0.804558\pi$
$110$	−1.42512	+	22.2198i	−0.135880	+	2.11858i
$111$	−3.79110	−	9.15252i	−0.359835	−	0.868718i
$112$	4.74194	+	13.7164i	0.448072	+	1.29608i
$113$	−1.52079	−	0.302504i	−0.143064	−	0.0284572i	0.123039	−	0.992402i	$-0.460736\pi$
$113$	−1.52079	−	0.302504i	−0.143064	−	0.0284572i	−0.266103	+	0.963945i	$0.585736\pi$
$114$	7.21392	+	12.4546i	0.675645	+	1.16648i
$115$	−4.61383	+	4.61383i	−0.430242	+	0.430242i
$116$	−3.08563	+	3.53843i	−0.286494	+	0.328535i
$117$	8.44999	+	3.50010i	0.781202	+	0.323584i
$118$	−6.88021	−	3.38098i	−0.633375	−	0.311244i
$119$	−14.8931	−	1.40965i	−1.36524	−	0.129222i
$120$	4.01768	+	19.7640i	0.366762	+	1.80419i
$121$	17.2945	+	7.16360i	1.57222	+	0.651236i
$122$	1.39748	−	5.24483i	0.126522	−	0.474844i
$123$	−1.29821	−	1.29821i	−0.117055	−	0.117055i
$124$	1.61214	−	0.110200i	0.144774	−	0.00989628i
$125$	−4.70041	−	0.934970i	−0.420418	−	0.0836263i
$126$	−15.7474	+	2.09562i	−1.40289	+	0.186693i
$127$	−6.47420	+	2.68170i	−0.574492	+	0.237962i	−0.650963	−	0.759109i	$-0.725635\pi$
$127$	−6.47420	+	2.68170i	−0.574492	+	0.237962i	0.0764710	+	0.997072i	$0.475635\pi$
$128$	−3.74151	−	10.6771i	−0.330706	−	0.943734i
$129$	−0.806039	−	1.20632i	−0.0709678	−	0.106211i
$130$	−7.33157	+	9.58245i	−0.643022	+	0.840436i
$131$	8.25979	−	12.3616i	0.721661	−	1.08004i	−0.271403	−	0.962466i	$-0.587488\pi$
$131$	8.25979	−	12.3616i	0.721661	−	1.08004i	0.993064	−	0.117576i	$-0.0375124\pi$
$132$	26.6994	+	3.43900i	2.32388	+	0.299326i
$133$	−2.91771	−	14.6683i	−0.252997	−	1.27190i
$134$	9.03333	+	10.2715i	0.780361	+	0.887321i
$135$	−0.684955			−0.0589516
$136$	11.6145	+	1.05012i	0.995938	+	0.0900471i
$137$	−8.82036			−0.753575			−0.376787	−	0.926300i	$-0.622971\pi$
$137$	−8.82036			−0.753575			−0.376787	+	0.926300i	$0.622971\pi$
$138$	5.20985	+	5.92394i	0.443492	+	0.504279i
$139$	−0.676960	−	3.40331i	−0.0574190	−	0.288665i	0.941398	−	0.337299i	$-0.109513\pi$
$139$	−0.676960	−	3.40331i	−0.0574190	−	0.288665i	−0.998817	+	0.0486339i	$0.984513\pi$
$140$	2.67720	−	20.7850i	0.226265	−	1.75665i
$141$	−4.41683	+	6.61025i	−0.371964	+	0.556683i
$142$	10.5982	−	13.8519i	0.889378	−	1.16243i
$143$	8.94727	+	13.3905i	0.748208	+	1.11977i
$144$	12.2690	−	1.68522i	1.02242	−	0.140435i
$145$	6.26331	−	2.59435i	0.520140	−	0.215449i
$146$	2.05060	−	0.272889i	0.169709	−	0.0225844i
$147$	14.9269	+	2.96915i	1.23115	+	0.244892i
$148$	−0.547267	−	8.00605i	−0.0449851	−	0.658093i
$149$	2.85005	+	2.85005i	0.233485	+	0.233485i	0.814146	−	0.580661i	$-0.197206\pi$
$149$	2.85005	+	2.85005i	0.233485	+	0.233485i	−0.580661	+	0.814146i	$0.697206\pi$
$150$	3.00315	−	11.2710i	0.245206	−	0.920276i
$151$	7.79880	+	3.23037i	0.634657	+	0.262884i	0.676730	−	0.736231i	$-0.263396\pi$
$151$	7.79880	+	3.23037i	0.634657	+	0.262884i	−0.0420733	+	0.999115i	$0.513396\pi$
$152$	2.32254	+	11.4252i	0.188383	+	0.926702i
$153$	−3.65909	+	12.2297i	−0.295820	+	0.988714i
$154$	−25.1051	−	12.3368i	−2.02302	−	0.994125i
$155$	−2.15574	−	0.892937i	−0.173153	−	0.0717224i
$156$	10.9945	+	9.58757i	0.880264	+	0.767620i
$157$	9.27110	−	9.27110i	0.739914	−	0.739914i	−0.232647	−	0.972561i	$-0.574739\pi$
$157$	9.27110	−	9.27110i	0.739914	−	0.739914i	0.972561	+	0.232647i	$0.0747387\pi$
$158$	9.52987	+	16.4530i	0.758156	+	1.30893i
$159$	−29.5530	−	5.87846i	−2.34371	−	0.466192i
$160$	−2.01895	+	16.2118i	−0.159612	+	1.28165i
$161$	−3.13701	−	7.57341i	−0.247231	−	0.596868i
$162$	0.787739	−	12.2821i	0.0618907	−	0.964972i
$163$	3.72722	+	5.57818i	0.291939	+	0.436917i	0.948227	−	0.317593i	$-0.102875\pi$
$163$	3.72722	+	5.57818i	0.291939	+	0.436917i	−0.656288	+	0.754510i	$0.727875\pi$
$164$	−0.661497	−	1.33197i	−0.0516543	−	0.104009i
$165$	−32.3213	−	21.5964i	−2.51621	−	1.68128i
$166$	−5.69934	−	16.7128i	−0.442354	−	1.29716i
$167$	1.49663	+	7.52404i	0.115812	+	0.582228i	0.994492	+	0.104815i	$0.0334252\pi$
$167$	1.49663	+	7.52404i	0.115812	+	0.582228i	−0.878679	+	0.477412i	$0.841575\pi$
$168$	−24.8713	−	4.83868i	−1.91886	−	0.373313i
$169$		−	4.27304i		−	0.328695i
$170$	−14.3465	−	8.81800i	−1.10032	−	0.676310i
$171$	−12.7620			−0.975936
$172$	−0.307350	−	1.13433i	−0.0234352	−	0.0864917i
$173$	22.4827	−	4.47208i	1.70933	−	0.340006i	0.758960	−	0.651137i	$-0.225708\pi$
$173$	22.4827	−	4.47208i	1.70933	−	0.340006i	0.950367	+	0.311131i	$0.100708\pi$
$174$	−2.64556	−	7.75786i	−0.200559	−	0.588122i
$175$	−6.73369	+	10.0777i	−0.509019	+	0.761801i
$176$	19.6111	+	9.53493i	1.47824	+	0.718723i
$177$	11.1283	−	7.43567i	0.836452	−	0.558899i
$178$	1.27737	+	0.0819267i	0.0957426	+	0.00614067i
$179$	−7.03803	+	2.91525i	−0.526047	+	0.217896i	−0.629871	−	0.776700i	$-0.716892\pi$
$179$	−7.03803	+	2.91525i	−0.526047	+	0.217896i	0.103824	+	0.994596i	$0.466892\pi$
$180$	−16.9498	−	5.70080i	−1.26337	−	0.424913i
$181$	−4.00334	+	20.1261i	−0.297566	+	1.49596i	0.485616	+	0.874172i	$0.338595\pi$
$181$	−4.00334	+	20.1261i	−0.297566	+	1.49596i	−0.783182	+	0.621792i	$0.786405\pi$
$182$	−7.59739	−	13.1166i	−0.563156	−	0.972268i
$183$	6.70069	+	6.70069i	0.495329	+	0.495329i
$184$	2.47026	+	5.89359i	0.182110	+	0.434481i
$185$	−4.43443	+	10.7057i	−0.326026	+	0.787095i
$186$	−1.24421	+	2.53194i	−0.0912300	+	0.185651i
$187$	−17.3208	+	14.3255i	−1.26662	+	1.04758i
$188$	−5.09809	+	3.93463i	−0.371816	+	0.286963i
$189$	0.329307	−	0.795017i	0.0239536	−	0.0578290i
$190$	4.33453	−	16.2678i	0.314460	−	1.18019i
$191$	−0.0339325	+	0.0339325i	−0.00245527	+	0.00245527i	−0.708333	−	0.705878i	$-0.750553\pi$
$191$	−0.0339325	+	0.0339325i	−0.00245527	+	0.00245527i	0.705878	+	0.708333i	$0.250553\pi$
$192$	19.4043	+	3.69055i	1.40039	+	0.266343i
$193$	2.34370	−	11.7826i	0.168703	−	0.848128i	−0.800018	−	0.599976i	$-0.795177\pi$
$193$	2.34370	−	11.7826i	0.168703	−	0.848128i	0.968721	−	0.248152i	$-0.0798232\pi$
$194$	−0.744172	−	5.59203i	−0.0534285	−	0.401484i
$195$	−8.06108	−	19.4612i	−0.577266	−	1.39364i
$196$	10.6938	+	6.13421i	0.763845	+	0.438158i
$197$	22.2035	−	14.8359i	1.58193	−	1.05701i	0.619678	−	0.784856i	$-0.287263\pi$
$197$	22.2035	−	14.8359i	1.58193	−	1.05701i	0.962253	−	0.272157i	$-0.0877369\pi$
$198$	−14.5043	+	18.9573i	−1.03078	+	1.34724i
$199$	20.1081	+	13.4358i	1.42543	+	0.952440i	0.998848	+	0.0479893i	$0.0152813\pi$
$199$	20.1081	+	13.4358i	1.42543	+	0.952440i	0.426579	+	0.904450i	$0.359719\pi$
$200$	5.21625	−	7.87812i	0.368845	−	0.557067i
$201$	−23.4221	+	4.65894i	−1.65207	+	0.328616i
$202$	−2.41034	+	2.11979i	−0.169591	+	0.149148i
$203$			8.51702i			0.597778i
$204$	−11.7497	+	16.6276i	−0.822644	+	1.16416i
$205$			2.14749i			0.149987i
$206$	2.56434	+	2.91583i	0.178666	+	0.203155i
$207$	−6.86061	+	1.36466i	−0.476846	+	0.0948505i
$208$	5.96551	+	10.2002i	0.413634	+	0.707256i
$209$	−18.6843	−	12.4844i	−1.29242	−	0.863566i
$210$	29.0580	+	22.2324i	2.00519	+	1.53418i
$211$	20.1331	−	13.4525i	1.38602	−	0.926109i	0.386026	−	0.922488i	$-0.373847\pi$
$211$	20.1331	−	13.4525i	1.38602	−	0.926109i	0.999993	−	0.00362115i	$-0.00115265\pi$
$212$	−21.1721	−	12.1448i	−1.45411	−	0.834107i
$213$	11.6527	+	28.1321i	0.798429	+	1.92758i
$214$	7.35948	−	0.979380i	0.503083	−	0.0669490i
$215$	−0.331074	+	1.66442i	−0.0225791	+	0.113513i
$216$	−0.254108	+	0.620836i	−0.0172899	+	0.0422425i
$217$	2.07284	−	2.07284i	0.140713	−	0.140713i
$218$	−0.711833	−	0.189667i	−0.0482114	−	0.0128459i
$219$	−1.38211	+	3.33671i	−0.0933943	+	0.225474i
$220$	−19.2387	−	24.9274i	−1.29707	−	1.68061i
$221$	−12.1170	+	1.23998i	−0.815075	+	0.0834102i
$222$	12.5739	+	6.17889i	0.843906	+	0.414700i
$223$	−0.834332	+	2.01426i	−0.0558710	+	0.134885i	−0.949350	−	0.314220i	$-0.898257\pi$
$223$	−0.834332	+	2.01426i	−0.0558710	+	0.134885i	0.893479	+	0.449105i	$0.148257\pi$
$224$	−17.8461	−	10.1375i	−1.19239	−	0.677341i
$225$	7.31328	+	7.31328i	0.487552	+	0.487552i
$226$	1.89753	−	1.09909i	0.126222	−	0.0731102i
$227$	3.01389	−	15.1518i	0.200039	−	1.00566i	−0.742061	−	0.670332i	$-0.766152\pi$
$227$	3.01389	−	15.1518i	0.200039	−	1.00566i	0.942100	−	0.335331i	$-0.108848\pi$
$228$	−19.2927	−	6.48880i	−1.27769	−	0.429731i
$229$	−3.87809	+	1.60636i	−0.256272	+	0.106151i	−0.507121	−	0.861875i	$-0.669290\pi$
$229$	−3.87809	+	1.60636i	−0.256272	+	0.106151i	0.250849	+	0.968026i	$0.419290\pi$
$230$	0.590624	−	9.20875i	0.0389446	−	0.607207i
$231$	40.6057	−	27.1319i	2.67166	−	1.78515i
$232$	−0.0278925	−	6.63946i	−0.00183123	−	0.435902i
$233$	−8.78749	+	13.1514i	−0.575688	+	0.861577i	−0.999014	−	0.0443999i	$-0.985862\pi$
$233$	−8.78749	+	13.1514i	−0.575688	+	0.861577i	0.423326	+	0.905977i	$0.360862\pi$
$234$	−12.2424	+	4.17487i	−0.800311	+	0.272919i
$235$	9.12049	−	1.81418i	0.594955	−	0.118344i
$236$	10.4641	−	2.83529i	0.681156	−	0.184561i
$237$	−33.1952			−2.15626
$238$	17.1323	−	12.4123i	1.11052	−	0.804570i
$239$		−	30.2002i		−	1.95349i	−0.214402	−	0.976746i	$-0.568780\pi$
$239$		−	30.2002i		−	1.95349i	0.214402	−	0.976746i	$-0.431220\pi$
$240$	−22.7250	−	17.2362i	−1.46689	−	1.11259i
$241$	4.38937	+	22.0668i	0.282744	+	1.42145i	0.817249	+	0.576285i	$0.195498\pi$
$241$	4.38937	+	22.0668i	0.282744	+	1.42145i	−0.534505	+	0.845165i	$0.679502\pi$
$242$	−25.0563	+	8.54463i	−1.61068	+	0.549269i
$243$	18.4573	+	12.3328i	1.18404	+	0.791147i
$244$	3.41431	+	6.87494i	0.218579	+	0.440123i
$245$	−9.89028	−	14.8019i	−0.631867	−	0.945656i
$246$	2.59109	+	0.166185i	0.165202	+	0.0105956i
$247$	−4.65995	−	11.2501i	−0.296505	−	0.715827i
$248$	−1.60910	+	1.62267i	−0.102178	+	0.103040i
$249$	30.2358	+	6.01427i	1.91612	+	0.381139i
$250$	5.86484	−	3.39702i	0.370925	−	0.214847i
$251$	−4.38141	+	4.38141i	−0.276552	+	0.276552i	−0.831731	−	0.555179i	$-0.812650\pi$
$251$	−4.38141	+	4.38141i	−0.276552	+	0.276552i	0.555179	+	0.831731i	$0.312650\pi$
$252$	14.7658	−	16.9326i	0.930160	−	1.06666i
$253$	−11.3793	−	4.71345i	−0.715409	−	0.296332i
$254$	4.37075	−	8.89438i	0.274245	−	0.558083i
$255$	25.8755	−	13.9576i	1.62039	−	0.874058i
$256$	13.9452	+	7.84427i	0.871572	+	0.490267i
$257$	−25.4051	−	10.5232i	−1.58473	−	0.656416i	−0.595576	−	0.803299i	$-0.703076\pi$
$257$	−25.4051	−	10.5232i	−1.58473	−	0.656416i	−0.989154	+	0.146883i	$0.953076\pi$
$258$	1.98262	+	0.528266i	0.123432	+	0.0328884i
$259$	−10.2939	−	10.2939i	−0.639635	−	0.639635i
$260$	−1.16366	−	17.0234i	−0.0721674	−	1.05575i
$261$	7.12811	+	1.41787i	0.441219	+	0.0877640i
$262$	2.77356	+	20.8417i	0.171351	+	1.28760i
$263$	−9.27535	+	3.84198i	−0.571943	+	0.236906i	−0.649861	−	0.760053i	$-0.725173\pi$
$263$	−9.27535	+	3.84198i	−0.571943	+	0.236906i	0.0779180	+	0.996960i	$0.475173\pi$
$264$	−31.5654	+	21.2837i	−1.94272	+	1.30992i
$265$	19.5812	+	29.3054i	1.20286	+	1.80021i
$266$	16.7979	+	12.8521i	1.02994	+	0.788014i
$267$	−1.24152	+	1.85807i	−0.0759800	+	0.113712i
$268$	−19.1860	−	2.47124i	−1.17197	−	0.150955i
$269$	1.84008	+	9.25073i	0.112192	+	0.564027i	0.995462	+	0.0951618i	$0.0303369\pi$
$269$	1.84008	+	9.25073i	0.112192	+	0.564027i	−0.883270	+	0.468865i	$0.844663\pi$
$270$	0.727392	−	0.639710i	0.0442677	−	0.0389315i
$271$	20.7098			1.25803			0.629016	−	0.777392i	$-0.283458\pi$
$271$	20.7098			1.25803			0.629016	+	0.777392i	$0.283458\pi$
$272$	−13.3149	+	9.73214i	−0.807332	+	0.590097i
$273$	26.4638			1.60166
$274$	9.36683	−	8.23773i	0.565871	−	0.497659i
$275$	3.55282	+	17.8612i	0.214243	+	1.07707i
$276$	−11.0653	−	1.42525i	−0.666050	−	0.0857901i
$277$	10.3999	−	15.5646i	0.624872	−	0.935187i	−0.375094	−	0.926987i	$-0.622390\pi$
$277$	10.3999	−	15.5646i	0.624872	−	0.935187i	0.999966	−	0.00820064i	$-0.00261037\pi$
$278$	3.89740	+	2.98192i	0.233750	+	0.178844i
$279$	−1.38974	−	2.07989i	−0.0832013	−	0.124520i
$280$	16.5690	+	24.5731i	0.990186	+	1.46852i
$281$	27.5270	−	11.4021i	1.64212	−	0.680190i	0.645614	−	0.763664i	$-0.276602\pi$
$281$	27.5270	−	11.4021i	1.64212	−	0.680190i	0.996510	+	0.0834739i	$0.0266015\pi$
$282$	−1.48313	−	11.1449i	−0.0883190	−	0.663666i
$283$	−10.7523	−	2.13877i	−0.639160	−	0.127137i	−0.135137	−	0.990827i	$-0.543147\pi$
$283$	−10.7523	−	2.13877i	−0.639160	−	0.127137i	−0.504023	+	0.863690i	$0.668147\pi$
$284$	1.68213	+	24.6082i	0.0998163	+	1.46023i
$285$	20.7834	+	20.7834i	1.23110	+	1.23110i
$286$	−22.0076	−	5.86390i	−1.30134	−	0.346740i
$287$	−2.49256	−	1.03245i	−0.147131	−	0.0609438i
$288$	−11.4553	+	13.2482i	−0.675009	+	0.780659i
$289$	−3.44331	−	16.6476i	−0.202548	−	0.979272i
$290$	−4.22838	+	8.60466i	−0.248299	+	0.505283i
$291$	9.09926	+	3.76904i	0.533408	+	0.220945i
$292$	−1.92278	+	2.20494i	−0.112522	+	0.129034i
$293$	−16.5027	+	16.5027i	−0.964096	+	0.964096i	−0.999377	−	0.0352815i	$-0.988767\pi$
$293$	−16.5027	+	16.5027i	−0.964096	+	0.964096i	0.0352815	+	0.999377i	$0.488767\pi$
$294$	−18.6248	+	10.7878i	−1.08622	+	0.629158i
$295$	−15.3542	−	3.05414i	−0.893957	−	0.177819i
$296$	8.05837	+	7.99095i	0.468383	+	0.464465i
$297$	−0.494794	−	1.19454i	−0.0287109	−	0.0693142i
$298$	−5.68841	−	0.364839i	−0.329521	−	0.0211345i
$299$	−3.70809	−	5.54955i	−0.214444	−	0.320939i
$300$	7.33729	+	14.7741i	0.423619	+	0.852983i
$301$	−1.77270	−	1.18448i	−0.102177	−	0.0682723i
$302$	−11.2990	+	3.85313i	−0.650182	+	0.221723i
$303$	−1.09328	−	5.49630i	−0.0628075	−	0.315754i
$304$	−13.1369	−	9.96388i	−0.753452	−	0.571468i
$305$		−	11.0843i		−	0.634683i
$306$	−7.53608	−	16.4048i	−0.430809	−	0.937800i
$307$	6.03152			0.344237			0.172119	−	0.985076i	$-0.444939\pi$
$307$	6.03152			0.344237			0.172119	+	0.985076i	$0.444939\pi$
$308$	38.1823	−	10.3456i	2.17564	−	0.589496i
$309$	−6.64897	+	1.32256i	−0.378247	+	0.0752379i
$310$	3.12325	−	1.06508i	0.177389	−	0.0604926i
$311$	−5.39342	+	8.07183i	−0.305833	+	0.457711i	−0.952270	−	0.305256i	$-0.901258\pi$
$311$	−5.39342	+	8.07183i	−0.305833	+	0.457711i	0.646437	+	0.762967i	$0.276258\pi$
$312$	−20.6299	+	0.0866666i	−1.16794	+	0.00490653i
$313$	−24.5109	+	16.3777i	−1.38544	+	0.925721i	−0.385444	+	0.922731i	$0.625952\pi$
$313$	−24.5109	+	16.3777i	−1.38544	+	0.925721i	−0.999996	+	0.00298974i	$0.999048\pi$
$314$	−1.18681	+	18.5042i	−0.0669754	+	1.04425i
$315$	−29.9722	+	12.4149i	−1.68874	+	0.699499i
$316$	−25.4865	−	8.57196i	−1.43372	−	0.482210i
$317$	5.22906	−	26.2882i	0.293693	−	1.47649i	−0.498855	−	0.866685i	$-0.666246\pi$
$317$	5.22906	−	26.2882i	0.293693	−	1.47649i	0.792548	−	0.609809i	$-0.208754\pi$
$318$	36.8741	−	21.3582i	2.06780	−	1.19771i
$319$	9.04891	+	9.04891i	0.506642	+	0.506642i
$320$	−12.9968	−	19.1018i	−0.726546	−	1.06782i
$321$	−4.96030	+	11.9752i	−0.276857	+	0.668392i
$322$	10.4045	+	5.11283i	0.579820	+	0.284927i
$323$	14.9581	−	8.06860i	0.832292	−	0.448949i
$324$	10.6342	+	13.7787i	0.590791	+	0.765485i
$325$	−3.77650	+	9.11727i	−0.209482	+	0.505735i
$326$	−9.16786	−	2.44276i	−0.507761	−	0.135292i
$327$	0.909424	−	0.909424i	0.0502912	−	0.0502912i
$328$	1.94646	+	0.796688i	0.107475	+	0.0439897i
$329$	−2.27918	+	11.4582i	−0.125655	+	0.631712i
$330$	54.4935	−	7.25185i	2.99977	−	0.399201i
$331$	1.63696	+	3.95198i	0.0899756	+	0.217220i	0.962461	−	0.271420i	$-0.0874931\pi$
$331$	1.63696	+	3.95198i	0.0899756	+	0.217220i	−0.872485	+	0.488640i	$0.837493\pi$
$332$	21.6612	+	12.4254i	1.18882	+	0.681931i
$333$	−10.3290	+	6.90159i	−0.566023	+	0.378205i
$334$	−8.61638	−	6.59243i	−0.471467	−	0.360722i
$335$	23.2258	+	15.5190i	1.26896	+	0.847893i
$336$	30.9313	−	18.0899i	1.68744	−	0.986887i
$337$	13.0051	−	2.58687i	0.708430	−	0.140916i	0.172292	−	0.985046i	$-0.444883\pi$
$337$	13.0051	−	2.58687i	0.708430	−	0.140916i	0.536138	+	0.844130i	$0.319883\pi$
$338$	3.99078	+	4.53778i	0.217070	+	0.246823i
$339$			3.82842i			0.207931i
$340$	23.4708	−	4.03448i	1.27288	−	0.218801i
$341$		−	4.40457i		−	0.238521i
$342$	13.5527	−	11.9190i	0.732846	−	0.644506i
$343$	−2.97443	+	0.591652i	−0.160604	+	0.0319462i
$344$	1.38579	+	0.917558i	0.0747168	+	0.0494714i
$345$	13.3952	+	8.95036i	0.721171	+	0.481871i
$346$	−19.6989	+	25.7467i	−1.05902	+	1.38415i
$347$	−0.788720	+	0.527006i	−0.0423407	+	0.0282911i	−0.576560	−	0.817054i	$-0.695605\pi$
$347$	−0.788720	+	0.527006i	−0.0423407	+	0.0282911i	0.534220	+	0.845346i	$0.320605\pi$
$348$	10.0549	+	5.76770i	0.538998	+	0.309181i
$349$	−10.8276	−	26.1402i	−0.579588	−	1.39925i	−0.893183	−	0.449693i	$-0.851533\pi$
$349$	−10.8276	−	26.1402i	−0.579588	−	1.39925i	0.313595	−	0.949557i	$-0.398467\pi$
$350$	−2.26111	−	16.9909i	−0.120861	−	0.908203i
$351$	0.136689	−	0.687180i	0.00729590	−	0.0366789i
$352$	−29.7312	+	8.18999i	−1.58468	+	0.436528i
$353$	0.497957	−	0.497957i	0.0265036	−	0.0265036i	−0.693731	−	0.720234i	$-0.744034\pi$
$353$	0.497957	−	0.497957i	0.0265036	−	0.0265036i	0.720234	+	0.693731i	$0.244034\pi$
$354$	−4.87322	+	18.2895i	−0.259009	+	0.972077i
$355$	13.6301	−	32.9060i	0.723410	−	1.74647i
$356$	−1.43302	+	1.10599i	−0.0759499	+	0.0586171i
$357$	3.76014	+	36.7437i	0.199008	+	1.94468i
$358$	4.75139	−	9.66898i	0.251119	−	0.511022i
$359$	−5.85096	+	14.1255i	−0.308802	+	0.745514i	0.690942	+	0.722910i	$0.257196\pi$
$359$	−5.85096	+	14.1255i	−0.308802	+	0.745514i	−0.999744	+	0.0226044i	$0.992804\pi$
$360$	23.3242	−	9.77620i	1.22929	−	0.515251i
$361$	−1.42055	−	1.42055i	−0.0747657	−	0.0747657i
$362$	−14.5453	−	25.1120i	−0.764485	−	1.31986i
$363$	9.01679	−	45.3304i	0.473259	−	2.37923i
$364$	20.3183	+	6.83372i	1.06497	+	0.358184i
$365$	3.90293	−	1.61665i	0.204289	−	0.0846192i
$366$	−13.3739	−	0.857765i	−0.699065	−	0.0448361i
$367$	−4.15911	+	2.77903i	−0.217104	+	0.145064i	−0.659367	−	0.751821i	$-0.729176\pi$
$367$	−4.15911	+	2.77903i	−0.217104	+	0.145064i	0.442263	+	0.896885i	$0.354176\pi$
$368$	−8.12759	−	3.95164i	−0.423680	−	0.205994i
$369$	−1.27904	+	1.91421i	−0.0665839	+	0.0996499i
$370$	−5.28932	−	15.5104i	−0.274978	−	0.806349i
$371$	−43.4284	+	8.63844i	−2.25469	+	0.448486i
$372$	−1.04340	−	3.85083i	−0.0540975	−	0.199656i
$373$	−8.83029			−0.457215			−0.228607	−	0.973519i	$-0.573417\pi$
$373$	−8.83029			−0.457215			−0.228607	+	0.973519i	$0.573417\pi$
$374$	5.01476	−	31.3897i	0.259307	−	1.62312i
$375$			11.8328i			0.611042i
$376$	1.73921	−	8.93973i	0.0896931	−	0.461032i
$377$	1.35288	+	6.80138i	0.0696768	+	0.350289i
$378$	0.392792	+	1.15183i	0.0202031	+	0.0592436i
$379$	−17.5567	−	11.7310i	−0.901828	−	0.602582i	0.0158646	−	0.999874i	$-0.494950\pi$
$379$	−17.5567	−	11.7310i	−0.901828	−	0.602582i	−0.917692	+	0.397292i	$0.869950\pi$
$380$	10.5901	+	21.3239i	0.543262	+	1.09389i
$381$	9.61245	+	14.3860i	0.492461	+	0.737020i
$382$	0.00434375	−	0.0677258i	0.000222245	−	0.00346515i
$383$	10.4020	+	25.1126i	0.531516	+	1.28319i	0.930519	+	0.366244i	$0.119356\pi$
$383$	10.4020	+	25.1126i	0.531516	+	1.28319i	−0.399002	+	0.916950i	$0.630644\pi$
$384$	−24.0533	+	14.2033i	−1.22746	+	0.724811i
$385$	−56.0257	−	11.1442i	−2.85533	−	0.567961i
$386$	8.51535	+	14.7014i	0.433420	+	0.748284i
$387$	−1.28643	+	1.28643i	−0.0653930	+	0.0653930i
$388$	6.01292	+	5.24347i	0.305260	+	0.266197i
$389$	−12.5223	−	5.18690i	−0.634904	−	0.262986i	0.0419309	−	0.999121i	$-0.486649\pi$
$389$	−12.5223	−	5.18690i	−0.634904	−	0.262986i	−0.676835	+	0.736134i	$0.736649\pi$
$390$	26.7361	+	13.1383i	1.35384	+	0.665283i
$391$	7.17841	−	5.93702i	0.363028	−	0.300248i
$392$	−17.0854	+	3.47317i	−0.862942	+	0.175422i
$393$	−33.9133	−	14.0473i	−1.71070	−	0.708595i
$394$	−9.72321	+	36.4918i	−0.489848	+	1.83843i
$395$	27.4557	+	27.4557i	1.38145	+	1.38145i
$396$	−2.30212	−	33.6780i	−0.115686	−	1.69239i
$397$	−26.7643	−	5.32376i	−1.34326	−	0.267192i	−0.529462	−	0.848334i	$-0.677606\pi$
$397$	−26.7643	−	5.32376i	−1.34326	−	0.267192i	−0.813802	+	0.581142i	$0.802606\pi$
$398$	−33.9022	+	4.51162i	−1.69936	+	0.226147i
$399$	−34.1151	+	14.1309i	−1.70789	+	0.707431i
$400$	1.81829	+	13.2379i	0.0909147	+	0.661895i
$401$	−14.5262	−	21.7400i	−0.725405	−	1.08565i	−0.992532	−	0.121984i	$-0.961074\pi$
$401$	−14.5262	−	21.7400i	−0.725405	−	1.08565i	0.267127	−	0.963661i	$-0.413926\pi$
$402$	20.5220	−	26.8225i	1.02355	−	1.33778i
$403$	1.32603	−	1.98455i	0.0660544	−	0.0988574i
$404$	0.579909	−	4.50225i	0.0288515	−	0.223995i
$405$	−4.90322	−	24.6502i	−0.243643	−	1.22488i
$406$	−7.95442	−	9.04469i	−0.394771	−	0.448881i
$407$	−21.8736			−1.08423
$408$	−3.05156	−	28.6313i	−0.151075	−	1.41746i
$409$	28.7868			1.42342			0.711708	−	0.702476i	$-0.247922\pi$
$409$	28.7868			1.42342			0.711708	+	0.702476i	$0.247922\pi$
$410$	−2.00564	−	2.28054i	−0.0990514	−	0.112628i
$411$	4.24861	+	21.3592i	0.209568	+	1.05357i
$412$	−5.44644	−	0.701525i	−0.268327	−	0.0345617i
$413$	10.9268	−	16.3531i	0.537671	−	0.804682i
$414$	6.01115	−	7.85664i	0.295432	−	0.386133i
$415$	−20.0336	−	29.9824i	−0.983411	−	1.47178i
$416$	−15.8615	−	5.26070i	−0.777675	−	0.257927i
$417$	−7.91530	+	3.27862i	−0.387614	+	0.160555i
$418$	31.5016	−	4.19215i	1.54079	−	0.205045i
$419$	15.6908	+	3.12109i	0.766544	+	0.152475i	0.562849	−	0.826559i	$-0.309705\pi$
$419$	15.6908	+	3.12109i	0.766544	+	0.152475i	0.203695	+	0.979034i	$0.434705\pi$
$420$	−51.6221	+	3.52872i	−2.51890	+	0.172184i
$421$	21.5059	+	21.5059i	1.04813	+	1.04813i	0.998781	+	0.0493525i	$0.0157158\pi$
$421$	21.5059	+	21.5059i	1.04813	+	1.04813i	0.0493525	+	0.998781i	$0.484284\pi$
$422$	−8.81657	+	33.0891i	−0.429184	+	1.61075i
$423$	9.21025	+	3.81501i	0.447818	+	0.185492i
$424$	33.8264	−	6.87634i	1.64275	−	0.333944i
$425$	−13.1955	−	3.94804i	−0.640074	−	0.191508i
$426$	−38.6484	−	18.9921i	−1.87252	−	0.920168i
$427$	12.8653	+	5.32900i	0.622597	+	0.257888i
$428$	−6.90075	+	7.91339i	−0.333560	+	0.382508i
$429$	28.1165	−	28.1165i	1.35748	−	1.35748i
$430$	−1.20289	−	2.07675i	−0.0580086	−	0.100150i
$431$	9.63371	+	1.91626i	0.464039	+	0.0923032i	0.421573	−	0.906795i	$-0.361478\pi$
$431$	9.63371	+	1.91626i	0.464039	+	0.0923032i	0.0424669	+	0.999098i	$0.486478\pi$
$432$	−0.309974	−	0.896622i	−0.0149136	−	0.0431388i
$433$	−0.923113	−	2.22859i	−0.0443620	−	0.107099i	0.900145	−	0.435590i	$-0.143460\pi$
$433$	−0.923113	−	2.22859i	−0.0443620	−	0.107099i	−0.944507	+	0.328490i	$0.893460\pi$
$434$	−0.265347	+	4.13717i	−0.0127371	+	0.198591i
$435$	−9.29934	−	13.9175i	−0.445869	−	0.667291i
$436$	0.933073	−	0.463394i	0.0446861	−	0.0221925i
$437$	7.74348	+	5.17403i	0.370421	+	0.247507i
$438$	−1.64856	−	4.83425i	−0.0787712	−	0.230989i
$439$	0.672936	+	3.38308i	0.0321175	+	0.161466i	0.993516	−	0.113696i	$-0.0362688\pi$
$439$	0.672936	+	3.38308i	0.0321175	+	0.161466i	−0.961398	+	0.275161i	$0.911269\pi$
$440$	43.7114	+	8.50401i	2.08386	+	0.405413i
$441$		−	19.0845i		−	0.908788i
$442$	11.7096	−	12.6334i	0.556969	−	0.600908i
$443$	4.84412			0.230151			0.115075	−	0.993357i	$-0.463289\pi$
$443$	4.84412			0.230151			0.115075	+	0.993357i	$0.463289\pi$
$444$	−19.1237	+	5.18162i	−0.907569	+	0.245909i
$445$	2.56367	−	0.509947i	0.121530	−	0.0241738i
$446$	−0.995179	−	2.91827i	−0.0471231	−	0.138184i
$447$	5.52880	−	8.27443i	0.261503	−	0.391367i
$448$	28.4196	−	5.90167i	1.34270	−	0.278827i
$449$	25.2554	−	16.8751i	1.19188	−	0.796386i	0.208509	−	0.978020i	$-0.433139\pi$
$449$	25.2554	−	16.8751i	1.19188	−	0.796386i	0.983366	+	0.181635i	$0.0581388\pi$
$450$	−14.5966	−	0.936183i	−0.688089	−	0.0441321i
$451$	−3.74515	+	1.55129i	−0.176352	+	0.0730476i
$452$	−0.988610	+	2.93937i	−0.0465003	+	0.138256i
$453$	4.06605	−	20.4414i	0.191040	−	0.960421i
$454$	10.9504	+	18.9054i	0.513926	+	0.887274i
$455$	−21.8882	−	21.8882i	−1.02613	−	1.02613i
$456$	26.5482	−	11.1275i	1.24323	−	0.521093i
$457$	12.3081	−	29.7143i	0.575746	−	1.38997i	−0.320852	−	0.947130i	$-0.603969\pi$
$457$	12.3081	−	29.7143i	0.575746	−	1.38997i	0.896598	−	0.442845i	$-0.146031\pi$
$458$	2.61811	−	5.32780i	0.122336	−	0.248952i
$459$	0.973538	+	0.0921467i	0.0454408	+	0.00430104i
$460$	7.97324	+	10.3309i	0.371754	+	0.481680i
$461$	6.11137	−	14.7542i	0.284635	−	0.687169i	−0.715297	−	0.698820i	$-0.753709\pi$
$461$	6.11137	−	14.7542i	0.284635	−	0.687169i	0.999932	+	0.0116510i	$0.00370871\pi$
$462$	−17.7818	+	66.7363i	−0.827285	+	3.10485i
$463$	−4.50568	+	4.50568i	−0.209397	+	0.209397i	−0.804011	−	0.594614i	$-0.797305\pi$
$463$	−4.50568	+	4.50568i	−0.209397	+	0.209397i	0.594614	+	0.804011i	$0.297305\pi$
$464$	6.23050	+	7.02476i	0.289244	+	0.326116i
$465$	−1.12394	+	5.65041i	−0.0521213	+	0.262031i
$466$	−2.95076	−	22.1732i	−0.136691	−	1.02716i
$467$	8.30089	+	20.0401i	0.384119	+	0.927346i	0.991160	+	0.132675i	$0.0423567\pi$
$467$	8.30089	+	20.0401i	0.384119	+	0.927346i	−0.607040	+	0.794671i	$0.707643\pi$
$468$	9.10180	−	15.8672i	0.420731	−	0.733463i
$469$	−29.1789	+	19.4967i	−1.34736	+	0.900276i
$470$	−7.99121	+	10.4446i	−0.368607	+	0.481773i
$471$	−26.9164	−	17.9850i	−1.24024	−	0.828704i
$472$	−8.46443	+	12.7838i	−0.389607	+	0.588424i
$473$	−3.14186	+	0.624954i	−0.144463	+	0.0287354i
$474$	35.2518	−	31.0024i	1.61917	−	1.42399i
$475$		−	13.7698i		−	0.631802i
$476$	−6.60134	+	29.1819i	−0.302572	+	1.33755i
$477$			37.7844i			1.73003i
$478$	28.2053	+	32.0713i	1.29008	+	1.46691i
$479$	5.94932	−	1.18339i	0.271831	−	0.0540706i	−0.0572923	−	0.998357i	$-0.518247\pi$
$479$	5.94932	−	1.18339i	0.271831	−	0.0540706i	0.329124	+	0.944287i	$0.393247\pi$
$480$	40.2306	−	2.91987i	1.83627	−	0.133273i
$481$	−9.85550	−	6.58523i	−0.449372	−	0.300261i
$482$	−25.2705	−	19.3346i	−1.15104	−	0.880666i
$483$	−16.8286	+	11.2445i	−0.765726	+	0.511642i
$484$	18.6285	−	32.4752i	0.846750	−	1.47615i
$485$	−4.40863	−	10.6434i	−0.200185	−	0.483290i
$486$	−31.1189	+	4.14123i	−1.41158	+	0.187850i
$487$	−4.94155	+	24.8428i	−0.223923	+	1.12574i	0.691232	+	0.722633i	$0.257068\pi$
$487$	−4.94155	+	24.8428i	−0.223923	+	1.12574i	−0.915155	+	0.403103i	$0.867932\pi$
$488$	−10.0467	−	4.11210i	−0.454791	−	0.186146i
$489$	11.7127	−	11.7127i	0.529665	−	0.529665i
$490$	24.3271	+	6.48194i	1.09899	+	0.292824i
$491$	7.03999	−	16.9960i	0.317710	−	0.767020i	−0.681665	−	0.731665i	$-0.738744\pi$
$491$	7.03999	−	16.9960i	0.317710	−	0.767020i	0.999375	−	0.0353554i	$-0.0112563\pi$
$492$	−2.90683	+	2.24345i	−0.131050	+	0.101143i
$493$	−9.25116	+	2.84479i	−0.416651	+	0.128123i
$494$	15.4556	+	7.59499i	0.695382	+	0.341715i
$495$	−18.6537	+	45.0341i	−0.838424	+	2.02413i
$496$	0.193303	−	3.22601i	0.00867955	−	0.144852i
$497$	31.6405	+	31.6405i	1.41927	+	1.41927i
$498$	−37.7260	+	21.8516i	−1.69054	+	0.979195i
$499$	−5.76769	+	28.9961i	−0.258197	+	1.29804i	0.606231	+	0.795289i	$0.292681\pi$
$499$	−5.76769	+	28.9961i	−0.258197	+	1.29804i	−0.864428	+	0.502756i	$0.832319\pi$
$500$	−3.05556	+	9.08491i	−0.136649	+	0.406290i
$501$	17.4992	−	7.24839i	0.781805	−	0.323834i
$502$	0.560871	−	8.74485i	0.0250329	−	0.390302i
$503$	12.1514	−	8.11928i	0.541802	−	0.362021i	−0.254355	−	0.967111i	$-0.581863\pi$
$503$	12.1514	−	8.11928i	0.541802	−	0.362021i	0.796157	+	0.605090i	$0.206863\pi$
$504$	0.133475	+	31.7722i	0.00594546	+	1.41524i
$505$	−3.64174	+	5.45024i	−0.162055	+	0.242533i
$506$	16.4864	−	5.62213i	0.732910	−	0.249934i
$507$	−10.3475	+	2.05825i	−0.459549	+	0.0914099i
$508$	3.66531	+	13.5275i	0.162622	+	0.600184i
$509$	1.17308			0.0519960			0.0259980	−	0.999662i	$-0.491724\pi$
$509$	1.17308			0.0519960			0.0259980	+	0.999662i	$0.491724\pi$
$510$	−14.4430	+	38.9886i	−0.639549	+	1.72644i
$511$			5.30731i			0.234782i
$512$	−22.1352	+	4.69373i	−0.978249	+	0.207435i
$513$	0.190726	+	0.958846i	0.00842077	+	0.0423341i
$514$	36.8072	−	12.5519i	1.62349	−	0.553639i
$515$	6.59325	+	4.40547i	0.290533	+	0.194128i
$516$	−2.59882	+	1.29066i	−0.114407	+	0.0568180i
$517$	9.75227	+	14.5953i	0.428904	+	0.641900i
$518$	20.5457	+	1.31774i	0.902725	+	0.0578983i
$519$	−21.6590	−	52.2895i	−0.950725	−	2.29525i
$520$	17.1347	+	16.9913i	0.751405	+	0.745118i
$521$	36.0147	+	7.16376i	1.57783	+	0.313850i	0.904824	−	0.425785i	$-0.140002\pi$
$521$	36.0147	+	7.16376i	1.57783	+	0.313850i	0.673007	+	0.739636i	$0.265002\pi$
$522$	−8.89395	+	5.15154i	−0.389278	+	0.225477i
$523$	−27.9023	+	27.9023i	−1.22008	+	1.22008i	−0.252478	+	0.967603i	$0.581245\pi$
$523$	−27.9023	+	27.9023i	−1.22008	+	1.22008i	−0.967603	+	0.252478i	$0.918755\pi$
$524$	−22.4104	−	19.5426i	−0.979001	−	0.853722i
$525$	27.6474	+	11.4519i	1.20663	+	0.499803i
$526$	6.26182	−	12.7427i	0.273028	−	0.555607i
$527$	2.94386	+	1.55916i	0.128237	+	0.0679179i
$528$	13.6433	−	52.0826i	0.593748	−	2.26660i
$529$	−16.5332	−	6.84828i	−0.718836	−	0.297751i
$530$	−48.1639	−	12.8332i	−2.09211	−	0.557440i
$531$	−11.8673	−	11.8673i	−0.514996	−	0.514996i
$532$	−29.8417	+	2.03988i	−1.29380	+	0.0884401i
$533$	−2.15447	−	0.428550i	−0.0933203	−	0.0185626i
$534$	−0.416892	−	3.13270i	−0.0180407	−	0.135565i
$535$	14.0074	−	5.80204i	0.605591	−	0.250844i
$536$	22.6826	−	15.2943i	0.979741	−	0.660612i
$537$	10.4496	+	15.6389i	0.450933	+	0.674869i
$538$	−10.5937	−	8.10532i	−0.456729	−	0.349445i
$539$	18.6694	−	27.9408i	0.804150	−	1.20349i
$540$	−0.175005	+	1.35869i	−0.00753100	+	0.0584686i
$541$	6.52747	+	32.8158i	0.280638	+	1.41086i	0.821720	+	0.569892i	$0.193015\pi$
$541$	6.52747	+	32.8158i	0.280638	+	1.41086i	−0.541082	+	0.840970i	$0.681985\pi$
$542$	−21.9929	+	19.3418i	−0.944676	+	0.830802i
$543$	50.6654			2.17426
$544$	5.05052	−	22.7704i	0.216539	−	0.976274i
$545$	−1.50437			−0.0644400
$546$	−28.1034	+	24.7157i	−1.20271	+	1.05773i
$547$	2.49041	+	12.5201i	0.106482	+	0.535322i	0.996797	+	0.0799761i	$0.0254844\pi$
$547$	2.49041	+	12.5201i	0.106482	+	0.535322i	−0.890315	+	0.455346i	$0.849516\pi$
$548$	−2.25359	+	17.4962i	−0.0962684	+	0.747400i
$549$	6.60173	−	9.88019i	0.281755	−	0.421676i
$550$	−20.4543	−	15.6497i	−0.872176	−	0.667305i
$551$	−5.37577	−	8.04540i	−0.229015	−	0.342746i
$552$	13.0819	−	8.82077i	0.556803	−	0.375437i
$553$	−45.0673	+	18.6675i	−1.91646	+	0.793823i
$554$	3.49220	+	26.2419i	0.148369	+	1.11491i
$555$	28.0606	+	5.58159i	1.19110	+	0.236925i
$556$	−6.92381	+	0.473288i	−0.293635	+	0.0200719i
$557$	19.1908	+	19.1908i	0.813139	+	0.813139i	0.985103	−	0.171964i	$-0.0550113\pi$
$557$	19.1908	+	19.1908i	0.813139	+	0.813139i	−0.171964	+	0.985103i	$0.555011\pi$
$558$	3.41833	+	0.910811i	0.144710	+	0.0385577i
$559$	−1.60376	−	0.664299i	−0.0678318	−	0.0280969i
$560$	−40.5454	−	10.6211i	−1.71336	−	0.448822i
$561$	43.0333	+	35.0434i	1.81687	+	1.47953i
$562$	−18.5836	+	37.8172i	−0.783901	+	1.59522i
$563$	−24.5691	−	10.1769i	−1.03547	−	0.428904i	−0.200783	−	0.979636i	$-0.564349\pi$
$563$	−24.5691	−	10.1769i	−1.03547	−	0.428904i	−0.834682	+	0.550732i	$0.814349\pi$
$564$	11.9837	+	10.4502i	0.504604	+	0.440032i
$565$	3.16649	−	3.16649i	0.133215	−	0.133215i
$566$	13.4160	−	7.77080i	0.563916	−	0.326631i
$567$	30.9684	+	6.16000i	1.30055	+	0.258696i
$568$	−24.7690	−	24.5618i	−1.03928	−	1.03059i
$569$	10.6587	+	25.7325i	0.446838	+	1.07876i	0.973500	+	0.228687i	$0.0734432\pi$
$569$	10.6587	+	25.7325i	0.446838	+	1.07876i	−0.526662	+	0.850075i	$0.676557\pi$
$570$	−41.4816	−	2.66052i	−1.73747	−	0.111437i
$571$	12.7249	+	19.0441i	0.532520	+	0.796972i	0.996021	−	0.0891243i	$-0.0284068\pi$
$571$	12.7249	+	19.0441i	0.532520	+	0.796972i	−0.463501	+	0.886097i	$0.653407\pi$
$572$	28.8476	−	14.3267i	1.20618	−	0.599028i
$573$	0.0985148	+	0.0658255i	0.00411552	+	0.00274990i
$574$	3.61124	−	1.23149i	0.150730	−	0.0514016i
$575$	−1.47243	−	7.40238i	−0.0614044	−	0.308701i
$576$	−0.208102	−	24.7676i	−0.00867091	−	1.03198i
$577$			1.06474i			0.0443258i	0.999754	+	0.0221629i	$0.00705525\pi$
$577$			1.06474i			0.0443258i	−0.999754	+	0.0221629i	$0.992945\pi$
$578$	19.2046	+	14.4632i	0.798806	+	0.601589i
$579$	−29.6613			−1.23268
$580$	−3.54592	−	13.0868i	−0.147236	−	0.543401i
$581$	44.4317	−	8.83801i	1.84334	−	0.366663i
$582$	−13.1831	+	4.49565i	−0.546456	+	0.186351i
$583$	−36.9626	+	55.3184i	−1.53083	+	2.29105i
$584$	−0.0173810	−	4.13732i	−0.000719229	−	0.171204i
$585$	−21.9626	+	14.6750i	−0.908043	+	0.606735i
$586$	2.11253	−	32.9376i	0.0872678	−	1.36064i
$587$	9.66819	−	4.00470i	0.399049	−	0.165292i	−0.174128	−	0.984723i	$-0.555711\pi$
$587$	9.66819	−	4.00470i	0.399049	−	0.165292i	0.573177	+	0.819431i	$0.305711\pi$
$588$	9.70346	−	28.8507i	0.400164	−	1.18978i
$589$	−0.649725	+	3.26639i	−0.0267715	+	0.134589i
$590$	19.1579	−	11.0966i	0.788718	−	0.456840i
$591$	−46.6212	−	46.6212i	−1.91774	−	1.91774i
$592$	−16.0207	−	0.959964i	−0.658448	−	0.0394543i
$593$	3.10552	−	7.49739i	0.127528	−	0.307881i	−0.847200	−	0.531274i	$-0.821713\pi$
$593$	3.10552	−	7.49739i	0.127528	−	0.307881i	0.974728	+	0.223393i	$0.0717134\pi$
$594$	1.64108	+	0.806437i	0.0673344	+	0.0330885i
$595$	27.2807	−	33.5007i	1.11840	−	1.37340i
$596$	6.38157	−	4.92521i	0.261399	−	0.201745i
$597$	22.8502	−	55.1652i	0.935195	−	2.25776i
$598$	9.12079	+	2.43022i	0.372977	+	0.0993793i
$599$	−21.2261	+	21.2261i	−0.867273	+	0.867273i	−0.992170	−	0.124896i	$-0.960140\pi$
$599$	−21.2261	+	21.2261i	−0.867273	+	0.867273i	0.124896	+	0.992170i	$0.460140\pi$
$600$	−21.5901	−	8.83682i	−0.881411	−	0.360762i
$601$	2.54095	−	12.7742i	0.103647	−	0.521071i	−0.893724	−	0.448617i	$-0.851917\pi$
$601$	2.54095	−	12.7742i	0.103647	−	0.521071i	0.997372	−	0.0724541i	$-0.0230831\pi$
$602$	2.98877	−	0.397737i	0.121813	−	0.0162106i
$603$	11.4598	+	27.6663i	0.466678	+	1.12666i
$604$	8.40037	−	14.6444i	0.341806	−	0.595874i
$605$	−44.9506	+	30.0350i	−1.82750	+	1.22110i
$606$	6.29426	+	4.81576i	0.255687	+	0.195627i
$607$	−15.5850	−	10.4136i	−0.632577	−	0.422674i	0.197516	−	0.980300i	$-0.436713\pi$
$607$	−15.5850	−	10.4136i	−0.632577	−	0.422674i	−0.830093	+	0.557626i	$0.811713\pi$
$608$	23.2565	−	1.68792i	0.943175	−	0.0684543i
$609$	20.6246	−	4.10249i	0.835752	−	0.166241i
$610$	10.3521	+	11.7710i	0.419144	+	0.476594i
$611$			9.51214i			0.384820i
$612$	23.3241	+	10.3829i	0.942822	+	0.419703i
$613$		−	3.44652i		−	0.139203i	−0.997575	−	0.0696017i	$-0.977827\pi$
$613$		−	3.44652i		−	0.139203i	0.997575	−	0.0696017i	$-0.0221728\pi$
$614$	−6.40521	+	5.63310i	−0.258493	+	0.227333i
$615$	5.20032	−	1.03441i	0.209697	−	0.0417114i
$616$	−30.8857	+	46.6467i	−1.24442	+	1.87945i
$617$	−24.7560	−	16.5414i	−0.996640	−	0.665933i	−0.0535824	−	0.998563i	$-0.517064\pi$
$617$	−24.7560	−	16.5414i	−0.996640	−	0.665933i	−0.943057	+	0.332630i	$0.892064\pi$
$618$	5.82571	−	7.61426i	0.234344	−	0.306291i
$619$	2.66044	−	1.77765i	0.106932	−	0.0714497i	−0.500954	−	0.865474i	$-0.667018\pi$
$619$	2.66044	−	1.77765i	0.106932	−	0.0714497i	0.607886	+	0.794024i	$0.292018\pi$
$620$	−2.32203	+	4.04801i	−0.0932550	+	0.162572i
$621$	0.205062	+	0.495063i	0.00822884	+	0.0198662i
$622$	−1.81106	−	13.6091i	−0.0726169	−	0.545674i
$623$	−0.640654	+	3.22079i	−0.0256673	+	0.129038i
$624$	21.8271	−	19.3592i	0.873783	−	0.774989i
$625$	21.5975	−	21.5975i	0.863900	−	0.863900i
$626$	10.7337	−	40.2842i	0.429004	−	1.61008i
$627$	−21.2322	+	51.2590i	−0.847931	+	2.04709i
$628$	−16.0215	−	20.7590i	−0.639328	−	0.828375i
$629$	7.74295	−	14.6196i	0.308731	−	0.582920i
$630$	20.2343	−	41.1764i	0.806154	−	1.64051i
$631$	15.0844	−	36.4170i	0.600501	−	1.44974i	−0.272566	−	0.962137i	$-0.587872\pi$
$631$	15.0844	−	36.4170i	0.600501	−	1.44974i	0.873067	−	0.487600i	$-0.162128\pi$
$632$	35.0712	−	14.6999i	1.39506	−	0.584730i
$633$	−42.2741	−	42.2741i	−1.68024	−	1.68024i
$634$	18.9987	+	32.8006i	0.754535	+	1.30268i
$635$	3.94824	−	19.8491i	0.156681	−	0.787689i
$636$	−19.2113	+	57.1198i	−0.761779	+	2.26495i
$637$	16.8236	−	6.96857i	0.666576	−	0.276105i
$638$	−18.0607	−	1.15836i	−0.715030	−	0.0458601i
$639$	31.7481	−	21.2134i	1.25594	−	0.839189i
$640$	31.6420	+	8.14688i	1.25076	+	0.322034i
$641$	−0.263797	+	0.394800i	−0.0104194	+	0.0155937i	−0.836643	−	0.547749i	$-0.815485\pi$
$641$	−0.263797	+	0.394800i	−0.0104194	+	0.0155937i	0.826223	+	0.563343i	$0.190485\pi$
$642$	−5.91657	−	17.3498i	−0.233508	−	0.684742i
$643$	19.3491	−	3.84877i	0.763053	−	0.151781i	0.201802	−	0.979426i	$-0.435320\pi$
$643$	19.3491	−	3.84877i	0.763053	−	0.151781i	0.561251	+	0.827646i	$0.310320\pi$
$644$	−15.8242	+	4.28762i	−0.623561	+	0.168956i
$645$	4.19000			0.164981
$646$	−8.34924	+	22.5385i	−0.328496	+	0.886767i
$647$		−	49.0540i		−	1.92851i	−0.264974	−	0.964256i	$-0.585363\pi$
$647$		−	49.0540i		−	1.92851i	0.264974	−	0.964256i	$-0.414637\pi$
$648$	−24.1616	−	4.70062i	−0.949159	−	0.184658i
$649$	−5.76517	−	28.9835i	−0.226303	−	1.13770i
$650$	−4.50454	−	13.2092i	−0.176683	−	0.518106i
$651$	−6.01799	−	4.02109i	−0.235863	−	0.157599i
$652$	12.0173	−	5.96815i	0.470632	−	0.233731i
$653$	−14.5462	−	21.7700i	−0.569238	−	0.851925i	0.429452	−	0.903090i	$-0.358707\pi$
$653$	−14.5462	−	21.7700i	−0.569238	−	0.851925i	−0.998690	+	0.0511648i	$0.983707\pi$
$654$	−0.116417	+	1.81512i	−0.00455225	+	0.0709767i
$655$	16.4311	+	39.6682i	0.642016	+	1.54996i
$656$	−2.81112	+	0.971840i	−0.109756	+	0.0379440i
$657$	4.44183	+	0.883534i	0.173292	+	0.0344699i
$658$	−8.28094	−	14.2967i	−0.322825	−	0.557345i
$659$	−2.07502	+	2.07502i	−0.0808315	+	0.0808315i	−0.746367	−	0.665535i	$-0.768203\pi$
$659$	−2.07502	+	2.07502i	−0.0808315	+	0.0808315i	0.665535	+	0.746367i	$0.268203\pi$
$660$	−51.0969	+	58.5950i	−1.98894	+	2.28081i
$661$	−10.7602	−	4.45704i	−0.418525	−	0.173359i	0.163475	−	0.986547i	$-0.447730\pi$
$661$	−10.7602	−	4.45704i	−0.418525	−	0.173359i	−0.582000	+	0.813189i	$0.697730\pi$
$662$	−5.42931	−	2.66799i	−0.211016	−	0.103694i
$663$	8.83923	+	28.7449i	0.343287	+	1.11636i
$664$	−34.6079	+	7.03520i	−1.34305	+	0.273019i
$665$	39.9042	+	16.5289i	1.54742	+	0.640962i
$666$	4.52319	−	16.9758i	0.175270	−	0.657800i
$667$	−3.75021	−	3.75021i	−0.145209	−	0.145209i
$668$	15.3072	−	1.04635i	0.592252	−	0.0404844i
$669$	5.27956	+	1.05017i	0.204120	+	0.0406019i
$670$	−39.1586	+	5.21113i	−1.51283	+	0.201323i
$671$	19.3306	−	8.00699i	0.746249	−	0.309106i
$672$	−15.9526	+	48.0988i	−0.615387	+	1.85545i
$673$	5.98216	+	8.95293i	0.230595	+	0.345110i	0.928665	−	0.370920i	$-0.120957\pi$
$673$	5.98216	+	8.95293i	0.230595	+	0.345110i	−0.698070	+	0.716030i	$0.745957\pi$
$674$	−11.3948	+	14.8931i	−0.438911	+	0.573662i
$675$	0.440171	−	0.658763i	0.0169422	−	0.0253558i
$676$	−8.47606	−	1.09175i	−0.326002	−	0.0419905i
$677$	4.78105	+	24.0359i	0.183751	+	0.923777i	0.957091	+	0.289786i	$0.0935842\pi$
$677$	4.78105	+	24.0359i	0.183751	+	0.923777i	−0.773341	+	0.633990i	$0.781416\pi$
$678$	−3.57553	−	4.06562i	−0.137318	−	0.156139i
$679$	14.4731			0.555428
$680$	−21.1570	+	26.2049i	−0.811334	+	1.00491i
$681$	−38.1431			−1.46165
$682$	4.11362	+	4.67746i	0.157519	+	0.179109i
$683$	−3.49956	−	17.5935i	−0.133907	−	0.673195i	−0.988171	−	0.153356i	$-0.950992\pi$
$683$	−3.49956	−	17.5935i	−0.133907	−	0.673195i	0.854264	−	0.519839i	$-0.174008\pi$
$684$	−3.26067	+	25.3149i	−0.124675	+	0.967939i
$685$	14.1522	−	21.1802i	0.540726	−	0.809254i
$686$	2.60615	−	3.40626i	0.0995031	−	0.130052i
$687$	5.75793	+	8.61736i	0.219679	+	0.328773i
$688$	−2.32860	+	0.319845i	−0.0887769	+	0.0121940i
$689$	−33.3081	+	13.7967i	−1.26894	+	0.525612i
$690$	−22.5842	+	3.00545i	−0.859766	+	0.114415i
$691$	−7.79929	−	1.55138i	−0.296699	−	0.0590171i	0.0444962	−	0.999010i	$-0.485832\pi$
$691$	−7.79929	−	1.55138i	−0.296699	−	0.0590171i	−0.341195	+	0.939992i	$0.610832\pi$
$692$	−3.12660	−	45.7396i	−0.118856	−	1.73876i
$693$	−43.3022	−	43.3022i	−1.64492	−	1.64492i
$694$	0.345391	−	1.29628i	0.0131109	−	0.0492060i
$695$	9.25848	+	3.83499i	0.351194	+	0.145469i
$696$	−16.0645	+	3.26565i	−0.608924	+	0.123784i
$697$	0.288901	−	3.05226i	0.0109429	−	0.115613i
$698$	35.9119	+	17.6473i	1.35928	+	0.667960i
$699$	36.0799	+	14.9448i	1.36467	+	0.565264i
$700$	18.2698	+	15.9319i	0.690532	+	0.602168i
$701$	9.89559	−	9.89559i	0.373751	−	0.373751i	−0.495090	−	0.868842i	$-0.664865\pi$
$701$	9.89559	−	9.89559i	0.373751	−	0.373751i	0.868842	+	0.495090i	$0.164865\pi$
$702$	0.496630	+	0.857414i	0.0187441	+	0.0323610i
$703$	16.2213	+	3.22661i	0.611796	+	0.121694i
$704$	23.9242	−	36.4647i	0.901678	−	1.37431i
$705$	−8.78635	−	21.2121i	−0.330913	−	0.798894i
$706$	−0.0637442	+	0.993871i	−0.00239904	+	0.0374048i
$707$	−4.57517	−	6.84723i	−0.172067	−	0.257517i
$708$	−11.9062	−	23.9740i	−0.447464	−	0.900997i
$709$	−19.6994	−	13.1627i	−0.739828	−	0.494337i	0.127646	−	0.991820i	$-0.459258\pi$
$709$	−19.6994	−	13.1627i	−0.739828	−	0.494337i	−0.867474	+	0.497483i	$0.834258\pi$
$710$	16.2578	+	47.6744i	0.610143	+	1.78919i
$711$	8.12074	+	40.8257i	0.304551	+	1.53108i
$712$	0.488875	−	2.51287i	0.0183214	−	0.0941737i
$713$			1.82542i			0.0683627i
$714$	−38.3097	−	35.5084i	−1.43370	−	1.32887i
$715$	−46.5102			−1.73938
$716$	3.98452	+	14.7056i	0.148908	+	0.549573i
$717$	−73.1322	+	14.5469i	−2.73117	+	0.543264i
$718$	−6.97894	−	20.4651i	−0.260452	−	0.763751i
$719$	11.4721	−	17.1693i	0.427838	−	0.640305i	−0.553443	−	0.832887i	$-0.686686\pi$
$719$	11.4721	−	17.1693i	0.427838	−	0.640305i	0.981281	+	0.192582i	$0.0616862\pi$
$720$	−15.6388	+	32.1654i	−0.582825	+	1.19873i
$721$	−8.28320	+	5.53466i	−0.308483	+	0.206121i
$722$	2.83527	+	0.181846i	0.105518	+	0.00676762i
$723$	51.3223	−	21.2584i	1.90870	−	0.790608i
$724$	38.8996	+	13.0833i	1.44569	+	0.486236i
$725$	−1.52984	+	7.69101i	−0.0568167	+	0.285637i
$726$	32.7607	+	56.5601i	1.21586	+	2.09914i
$727$	−6.45281	−	6.45281i	−0.239322	−	0.239322i	0.577248	−	0.816569i	$-0.304127\pi$
$727$	−6.45281	−	6.45281i	−0.239322	−	0.239322i	−0.816569	+	0.577248i	$0.804127\pi$
$728$	−27.9594	+	11.7190i	−1.03624	+	0.434336i
$729$	10.9832	−	26.5158i	0.406785	−	0.982067i
$730$	−2.63488	+	5.36193i	−0.0975213	+	0.198454i
$731$	0.694475	−	2.32113i	0.0256861	−	0.0858501i
$732$	15.0036	−	11.5796i	0.554548	−	0.427993i
$733$	−7.73031	+	18.6626i	−0.285526	+	0.689320i	−0.999946	−	0.0103971i	$-0.996690\pi$
$733$	−7.73031	+	18.6626i	−0.285526	+	0.689320i	0.714420	+	0.699717i	$0.246690\pi$
$734$	1.82133	−	6.83558i	0.0672266	−	0.252306i
$735$	−31.0799	+	31.0799i	−1.14640	+	1.14640i
$736$	12.3217	−	3.39424i	0.454186	−	0.125114i
$737$	−10.2869	+	51.7155i	−0.378921	+	1.90497i
$738$	−0.429488	−	3.22736i	−0.0158097	−	0.118801i
$739$	−9.05164	−	21.8526i	−0.332970	−	0.803861i	−0.998354	−	0.0573590i	$-0.981732\pi$
$739$	−9.05164	−	21.8526i	−0.332970	−	0.803861i	0.665384	−	0.746502i	$-0.268268\pi$
$740$	20.1029	+	11.5315i	0.738997	+	0.423905i
$741$	−24.9984	+	16.7034i	−0.918340	+	0.613615i
$742$	38.0512	−	49.7333i	1.39690	−	1.82577i
$743$	19.9854	+	13.3538i	0.733194	+	0.489905i	0.865252	−	0.501337i	$-0.167158\pi$
$743$	19.9854	+	13.3538i	0.733194	+	0.489905i	−0.132058	+	0.991242i	$0.542158\pi$
$744$	4.70450	+	3.11494i	0.172475	+	0.114199i
$745$	−11.4166	+	2.27091i	−0.418273	+	0.0831998i
$746$	9.37737	−	8.24699i	0.343330	−	0.301944i
$747$		−	38.6573i		−	1.41440i
$748$	23.9907	+	38.0179i	0.877188	+	1.39007i
$749$			19.0476i			0.695984i
$750$	−11.0511	−	12.5659i	−0.403531	−	0.458841i
$751$	−46.0147	+	9.15289i	−1.67910	+	0.333994i	−0.940407	−	0.340050i	$-0.889556\pi$
$751$	−46.0147	+	9.15289i	−1.67910	+	0.333994i	−0.738692	+	0.674043i	$0.764556\pi$
$752$	6.50224	+	11.1179i	0.237112	+	0.405429i
$753$	12.7204	+	8.49948i	0.463556	+	0.309738i
$754$	−7.78880	−	5.95925i	−0.283651	−	0.217023i
$755$	−20.2701	+	13.5440i	−0.737704	+	0.492918i
$756$	−1.49287	−	0.856343i	−0.0542951	−	0.0311449i
$757$	7.37387	+	17.8021i	0.268008	+	0.647028i	0.999389	−	0.0349405i	$-0.0111242\pi$
$757$	7.37387	+	17.8021i	0.268008	+	0.647028i	−0.731382	+	0.681968i	$0.761124\pi$
$758$	29.6006	−	3.93916i	1.07514	−	0.143077i
$759$	−5.93280	+	29.8262i	−0.215347	+	1.08262i
$760$	−31.1615	−	12.7544i	−1.13035	−	0.462652i
$761$	27.3046	−	27.3046i	0.989791	−	0.989791i	−0.0101571	−	0.999948i	$-0.503233\pi$
$761$	27.3046	−	27.3046i	0.989791	−	0.989791i	0.999948	+	0.0101571i	$0.00323315\pi$
$762$	−23.6438	−	6.29985i	−0.856523	−	0.228220i
$763$	0.723257	−	1.74610i	0.0261837	−	0.0632129i
$764$	0.0586392	+	0.0759786i	0.00212149	+	0.00274881i
$765$	−23.4961	−	28.4089i	−0.849502	−	1.02713i
$766$	−34.5002	−	16.9536i	−1.24654	−	0.612558i
$767$	6.12813	−	14.7946i	0.221274	−	0.534202i
$768$	12.2784	−	37.5477i	0.443058	−	1.35489i
$769$	−3.82336	−	3.82336i	−0.137874	−	0.137874i	0.634801	−	0.772675i	$-0.281082\pi$
$769$	−3.82336	−	3.82336i	−0.137874	−	0.137874i	−0.772675	+	0.634801i	$0.781082\pi$
$770$	69.9049	−	40.4902i	2.51920	−	1.45917i
$771$	−13.2454	+	66.5894i	−0.477023	+	2.39816i
$772$	−22.7732	−	7.65941i	−0.819627	−	0.275668i
$773$	−24.3972	+	10.1057i	−0.877508	+	0.363476i	−0.775530	−	0.631311i	$-0.782517\pi$
$773$	−24.3972	+	10.1057i	−0.877508	+	0.363476i	−0.101978	+	0.994787i	$0.532517\pi$
$774$	0.164678	−	2.56759i	0.00591923	−	0.0922901i
$775$	2.24413	−	1.49948i	0.0806116	−	0.0538629i
$776$	−11.2826	+	0.0473982i	−0.405020	+	0.00170150i
$777$	−19.9692	+	29.8860i	−0.716391	+	1.07215i
$778$	18.1424	−	6.18685i	0.650435	−	0.221809i
$779$	3.00620	−	0.597971i	0.107708	−	0.0214245i
$780$	−40.6630	+	11.0178i	−1.45597	+	0.394499i
$781$	67.2329			2.40578
$782$	−2.07831	+	13.0091i	−0.0743202	+	0.465204i
$783$		−	0.556745i		−	0.0198964i
$784$	14.9002	−	19.6451i	0.532148	−	0.701612i
$785$	7.38719	+	37.1379i	0.263660	+	1.32551i
$786$	49.1338	−	16.7555i	1.75255	−	0.597647i
$787$	−1.34940	−	0.901637i	−0.0481008	−	0.0321399i	0.531287	−	0.847192i	$-0.321708\pi$
$787$	−1.34940	−	0.901637i	−0.0481008	−	0.0321399i	−0.579388	+	0.815052i	$0.696708\pi$
$788$	−23.7557	−	47.8336i	−0.846262	−	1.70400i
$789$	13.7714	+	20.6104i	0.490275	+	0.733749i
$790$	−54.7988	−	3.51465i	−1.94966	−	0.125046i
$791$	2.15294	+	5.19765i	0.0765496	+	0.184807i
$792$	33.8981	+	33.6145i	1.20452	+	1.19444i
$793$	11.1203	+	2.21196i	0.394892	+	0.0785489i
$794$	33.3946	−	19.3428i	1.18513	−	0.686450i
$795$	61.5333	−	61.5333i	2.18236	−	2.18236i
$796$	31.7890	−	36.4539i	1.12673	−	1.29207i
$797$	−13.1747	−	5.45715i	−0.466673	−	0.193302i	0.136941	−	0.990579i	$-0.456273\pi$
$797$	−13.1747	−	5.45715i	−0.466673	−	0.193302i	−0.603614	+	0.797277i	$0.706273\pi$
$798$	23.0312	−	46.8680i	0.815295	−	1.65911i
$799$	−13.2071	+	1.35154i	−0.467235	+	0.0478142i
$800$	−14.2944	−	12.3599i	−0.505383	−	0.436988i
$801$	2.58891	+	1.07236i	0.0914745	+	0.0378900i
$802$	35.7302	+	9.52026i	1.26168	+	0.336172i
$803$	5.63875	+	5.63875i	0.198987	+	0.198987i
$804$	3.25724	+	47.6507i	0.114874	+	1.68051i
$805$	23.2192	+	4.61859i	0.818369	+	0.162784i
$806$	0.445269	+	3.34594i	0.0156839	+	0.117856i
$807$	21.5150	−	8.91181i	0.757365	−	0.313711i
$808$	3.58901	+	5.32279i	0.126261	+	0.187255i
$809$	−6.66298	−	9.97186i	−0.234258	−	0.350592i	0.695652	−	0.718379i	$-0.255116\pi$
$809$	−6.66298	−	9.97186i	−0.234258	−	0.350592i	−0.929910	+	0.367787i	$0.880116\pi$
$810$	28.2289	+	21.5980i	0.991862	+	0.758878i
$811$	−21.2027	+	31.7321i	−0.744527	+	1.11426i	0.244945	+	0.969537i	$0.421230\pi$
$811$	−21.2027	+	31.7321i	−0.744527	+	1.11426i	−0.989472	+	0.144726i	$0.953770\pi$
$812$	16.8945	+	2.17608i	0.592880	+	0.0763655i
$813$	−9.97555	−	50.1505i	−0.349858	−	1.75885i
$814$	23.2288	−	20.4287i	0.814169	−	0.716026i
$815$	−19.3751			−0.678680
$816$	29.9807	+	27.5552i	1.04953	+	0.964625i
$817$	2.42216			0.0847406
$818$	−30.5703	+	26.8853i	−1.06887	+	0.940021i
$819$	−6.47400	−	32.5470i	−0.226220	−	1.13728i
$820$	4.25979	+	0.548680i	0.148758	+	0.0191607i
$821$	−17.7868	+	26.6198i	−0.620763	+	0.929038i	0.379230	+	0.925303i	$0.376189\pi$
$821$	−17.7868	+	26.6198i	−0.620763	+	0.929038i	−0.999993	+	0.00373538i	$0.998811\pi$
$822$	−24.4601	−	18.7146i	−0.853145	−	0.652745i
$823$	23.5034	+	35.1754i	0.819278	+	1.22614i	0.971323	+	0.237763i	$0.0764142\pi$
$823$	23.5034	+	35.1754i	0.819278	+	1.22614i	−0.152045	+	0.988374i	$0.548586\pi$
$824$	6.43906	−	4.34168i	0.224315	−	0.151250i
$825$	41.5411	−	17.2069i	1.44627	−	0.599066i
$826$	3.66910	+	27.5712i	0.127664	+	0.959325i
$827$	−38.0196	−	7.56257i	−1.32207	−	0.262976i	−0.516914	−	0.856037i	$-0.672919\pi$
$827$	−38.0196	−	7.56257i	−1.32207	−	0.262976i	−0.805158	+	0.593061i	$0.797919\pi$
$828$	0.954086	+	13.9575i	0.0331568	+	0.485056i
$829$	6.65292	+	6.65292i	0.231066	+	0.231066i	0.813137	−	0.582072i	$-0.197758\pi$
$829$	6.65292	+	6.65292i	0.231066	+	0.231066i	−0.582072	+	0.813137i	$0.697758\pi$
$830$	49.2767	+	13.1297i	1.71042	+	0.455739i
$831$	−42.7004	−	17.6871i	−1.48126	−	0.613558i
$832$	21.7574	−	9.22714i	0.754303	−	0.319894i
$833$	12.0659	+	22.3686i	0.418060	+	0.775027i
$834$	5.34364	−	10.8742i	0.185035	−	0.376543i
$835$	−20.4687	−	8.47841i	−0.708348	−	0.293407i
$836$	−29.5381	+	33.8726i	−1.02160	+	1.17151i
$837$	−0.135498	+	0.135498i	−0.00468351	+	0.00468351i
$838$	−19.5778	+	11.3398i	−0.676304	+	0.391728i
$839$	43.3377	+	8.62041i	1.49618	+	0.297610i	0.874256	−	0.485464i	$-0.161349\pi$
$839$	43.3377	+	8.62041i	1.49618	+	0.297610i	0.621928	+	0.783074i	$0.286349\pi$
$840$	51.5248	−	51.9595i	1.77777	−	1.79277i
$841$	−8.98908	−	21.7016i	−0.309968	−	0.748330i
$842$	−42.9236	−	2.75300i	−1.47925	−	0.0948748i
$843$	−40.8703	−	61.1667i	−1.40765	−	2.10669i
$844$	−21.5406	−	43.3734i	−0.741458	−	1.49297i
$845$	10.2608	+	6.85604i	0.352982	+	0.235855i
$846$	−13.3439	+	4.55048i	−0.458772	+	0.156449i
$847$	−13.2502	−	66.6134i	−0.455283	−	2.28886i
$848$	−29.5000	+	38.8943i	−1.01303	+	1.33564i
$849$			27.0678i			0.928966i
$850$	17.7002	−	8.13118i	0.607114	−	0.278897i
$851$	9.06526			0.310753
$852$	58.7804	−	15.9267i	2.01378	−	0.545641i
$853$	−10.4221	+	2.07308i	−0.356846	+	0.0709811i	−0.370258	−	0.928929i	$-0.620731\pi$
$853$	−10.4221	+	2.07308i	−0.356846	+	0.0709811i	0.0134121	+	0.999910i	$0.495731\pi$
$854$	−18.6394	+	6.35635i	−0.637827	+	0.217510i
$855$	20.4765	−	30.6452i	0.700281	−	1.04804i
$856$	−0.0623791	−	14.8486i	−0.00213207	−	0.507514i
$857$	10.8273	−	7.23454i	0.369852	−	0.247127i	−0.356729	−	0.934208i	$-0.616108\pi$
$857$	10.8273	−	7.23454i	0.369852	−	0.247127i	0.726581	+	0.687081i	$0.241108\pi$
$858$	−3.59923	+	56.1177i	−0.122876	+	1.91583i
$859$	16.2075	−	6.71335i	0.552992	−	0.229057i	−0.0886478	−	0.996063i	$-0.528255\pi$
$859$	16.2075	−	6.71335i	0.552992	−	0.229057i	0.641639	+	0.767006i	$0.278255\pi$
$860$	3.21698	+	1.08198i	0.109698	+	0.0368952i
$861$	−1.29954	+	6.53325i	−0.0442883	+	0.222653i
$862$	−12.0203	+	6.96236i	−0.409411	+	0.237139i
$863$	−15.8347	−	15.8347i	−0.539019	−	0.539019i	0.384221	−	0.923241i	$-0.374470\pi$
$863$	−15.8347	−	15.8347i	−0.539019	−	0.539019i	−0.923241	+	0.384221i	$0.874470\pi$
$864$	1.16657	+	0.662675i	0.0396876	+	0.0225446i
$865$	−25.3344	+	61.1627i	−0.861397	+	2.07960i
$866$	3.06169	+	1.50453i	0.104040	+	0.0511260i
$867$	−38.6550	+	16.3571i	−1.31279	+	0.555516i
$868$	−3.58210	−	4.64131i	−0.121584	−	0.157536i
$869$	−28.0485	+	67.7151i	−0.951481	+	2.29708i
$870$	22.8736	+	6.09465i	0.775488	+	0.206628i
$871$	−20.2043	+	20.2043i	−0.684596	+	0.684596i
$872$	−0.558098	+	1.36354i	−0.0188996	+	0.0461753i
$873$	2.40941	−	12.1129i	0.0815463	−	0.409961i
$874$	−13.0555	+	1.73739i	−0.441608	+	0.0587681i
$875$	6.65423	+	16.0647i	0.224954	+	0.543087i
$876$	6.26561	+	3.59409i	0.211695	+	0.121433i
$877$	−25.2373	+	16.8630i	−0.852203	+	0.569424i	−0.903173	−	0.429276i	$-0.858769\pi$
$877$	−25.2373	+	16.8630i	−0.852203	+	0.569424i	0.0509704	+	0.998700i	$0.483769\pi$
$878$	−3.87423	−	2.96419i	−0.130749	−	0.100037i
$879$	47.9115	+	32.0135i	1.61602	+	1.07979i
$880$	−54.3618	+	31.7931i	−1.83254	+	1.07175i
$881$	−24.7217	+	4.91746i	−0.832896	+	0.165673i	−0.593078	−	0.805145i	$-0.702088\pi$
$881$	−24.7217	+	4.91746i	−0.832896	+	0.165673i	−0.239818	+	0.970818i	$0.577088\pi$
$882$	17.8239	+	20.2669i	0.600162	+	0.682423i
$883$		−	27.0151i		−	0.909129i	−0.890714	−	0.454565i	$-0.849795\pi$
$883$		−	27.0151i		−	0.909129i	0.890714	−	0.454565i	$-0.150205\pi$
$884$	−0.636216	+	24.3522i	−0.0213983	+	0.819052i
$885$			38.6526i			1.29929i
$886$	−5.14424	+	4.52413i	−0.172824	+	0.151991i
$887$	43.2941	−	8.61174i	1.45367	−	0.289154i	0.595850	−	0.803096i	$-0.296815\pi$
$887$	43.2941	−	8.61174i	1.45367	−	0.289154i	0.857825	+	0.513942i	$0.171815\pi$
$888$	15.4691	−	23.3631i	0.519110	−	0.784014i
$889$	21.1404	+	14.1256i	0.709026	+	0.473756i
$890$	−2.24625	+	2.93587i	−0.0752943	+	0.0984105i
$891$	39.4471	−	26.3577i	1.32153	−	0.883016i
$892$	3.78233	+	2.16963i	0.126642	+	0.0726446i
$893$	−5.07921	−	12.2623i	−0.169969	−	0.410342i
$894$	1.85652	+	13.9507i	0.0620912	+	0.466580i
$895$	4.29209	−	21.5778i	0.143469	−	0.721266i
$896$	−24.6685	+	32.8096i	−0.824118	+	1.09609i
$897$	−11.6525	+	11.6525i	−0.389067	+	0.389067i
$898$	−11.0597	+	41.5077i	−0.369067	+	1.38513i
$899$	0.725797	−	1.75223i	0.0242067	−	0.0584401i
$900$	16.3752	−	12.6382i	0.545841	−	0.421273i
$901$	−23.8887	−	44.2864i	−0.795846	−	1.47539i
$902$	2.52836	−	5.14517i	0.0841853	−	0.171315i
$903$	−2.01443	+	4.86327i	−0.0670362	+	0.161840i
$904$	−1.69535	−	4.04479i	−0.0563864	−	0.134528i
$905$	−41.9053	−	41.9053i	−1.39298	−	1.39298i
$906$	14.7732	+	25.5053i	0.490805	+	0.847357i
$907$	−4.69407	+	23.5987i	−0.155864	+	0.783581i	0.821201	+	0.570639i	$0.193304\pi$
$907$	−4.69407	+	23.5987i	−0.155864	+	0.783581i	−0.977065	+	0.212942i	$0.931696\pi$
$908$	−29.2854	−	9.84966i	−0.971869	−	0.326872i
$909$	−6.49227	+	2.68919i	−0.215335	+	0.0891947i
$910$	43.6866	+	2.80194i	1.44820	+	0.0928834i
$911$	−11.7646	+	7.86089i	−0.389780	+	0.260443i	−0.734983	−	0.678085i	$-0.762810\pi$
$911$	−11.7646	+	7.86089i	−0.389780	+	0.260443i	0.345203	+	0.938528i	$0.387810\pi$
$912$	−17.8005	+	36.6114i	−0.589434	+	1.21233i
$913$	37.8165	−	56.5964i	1.25154	−	1.87307i
$914$	14.6809	+	43.0503i	0.485600	+	1.42398i
$915$	−26.8414	+	5.33909i	−0.887350	+	0.176505i
$916$	2.19555	+	8.10306i	0.0725430	+	0.267733i
$917$	−53.9419			−1.78132
$918$	−1.11991	+	0.811374i	−0.0369626	+	0.0267793i
$919$		−	40.2310i		−	1.32710i	−0.748133	−	0.663549i	$-0.769049\pi$
$919$		−	40.2310i		−	1.32710i	0.748133	−	0.663549i	$-0.230951\pi$
$920$	−18.1157	−	3.52439i	−0.597257	−	0.116196i
$921$	−2.90527	−	14.6058i	−0.0957321	−	0.481278i
$922$	7.28955	+	21.3759i	0.240068	+	0.703979i
$923$	30.2928	+	20.2410i	0.997101	+	0.666241i
$924$	−43.4444	−	87.4781i	−1.42922	−	2.87782i
$925$	−7.44659	−	11.1446i	−0.244842	−	0.366432i
$926$	0.576778	−	8.99288i	0.0189541	−	0.295524i
$927$	3.25315	+	7.85381i	0.106848	+	0.257953i
$928$	−13.1772	−	1.64104i	−0.432564	−	0.0538698i
$929$	0.519648	+	0.103364i	0.0170491	+	0.00339127i	0.203607	−	0.979053i	$-0.434733\pi$
$929$	0.519648	+	0.103364i	0.0170491	+	0.00339127i	−0.186558	+	0.982444i	$0.559733\pi$
$930$	−4.08359	−	7.05017i	−0.133906	−	0.231184i
$931$	−17.9667	+	17.9667i	−0.588834	+	0.588834i
$932$	23.8421	+	20.7911i	0.780975	+	0.681036i
$933$	22.1445	+	9.17254i	0.724978	+	0.300296i
$934$	−27.5315	−	13.5291i	−0.900859	−	0.442687i
$935$	−6.60847	−	64.5772i	−0.216120	−	2.11190i
$936$	5.15341	+	25.3509i	0.168444	+	0.828619i
$937$	46.2877	+	19.1730i	1.51215	+	0.626354i	0.976001	−	0.217768i	$-0.0698775\pi$
$937$	46.2877	+	19.1730i	1.51215	+	0.626354i	0.536152	+	0.844122i	$0.319878\pi$
$938$	12.7779	−	47.9562i	0.417212	−	1.56582i
$939$	51.4663	+	51.4663i	1.67954	+	1.67954i
$940$	−1.26836	−	18.5550i	−0.0413694	−	0.605198i
$941$	−7.08534	−	1.40936i	−0.230976	−	0.0459439i	0.0782454	−	0.996934i	$-0.475068\pi$
$941$	−7.08534	−	1.40936i	−0.230976	−	0.0459439i	−0.309221	+	0.950990i	$0.600068\pi$
$942$	45.3810	−	6.03918i	1.47859	−	0.196767i
$943$	1.55214	−	0.642915i	0.0505445	−	0.0209362i
$944$	−2.95055	−	21.4812i	−0.0960322	−	0.699153i
$945$	1.38069	+	2.06635i	0.0449140	+	0.0672185i
$946$	2.75284	−	3.59799i	0.0895025	−	0.116981i
$947$	−11.4457	+	17.1297i	−0.371934	+	0.556639i	−0.969472	−	0.245202i	$-0.921146\pi$
$947$	−11.4457	+	17.1297i	−0.371934	+	0.556639i	0.597538	+	0.801841i	$0.296146\pi$
$948$	−8.48130	+	65.8464i	−0.275460	+	2.13859i
$949$	0.843035	+	4.23822i	0.0273661	+	0.137579i
$950$	12.8602	+	14.6229i	0.417241	+	0.474430i
$951$	−66.1778			−2.14596
$952$	−20.2439	−	37.1552i	−0.656110	−	1.20421i
$953$	14.3416			0.464569			0.232285	−	0.972648i	$-0.425380\pi$
$953$	14.3416			0.464569			0.232285	+	0.972648i	$0.425380\pi$
$954$	−35.2885	−	40.1254i	−1.14251	−	1.29911i
$955$	−0.0270373	−	0.135926i	−0.000874907	−	0.00439846i
$956$	−59.9056	−	7.71610i	−1.93749	−	0.249557i
$957$	17.5539	−	26.2713i	0.567439	−	0.849232i
$958$	−5.21269	+	6.81304i	−0.168414	+	0.220119i
$959$	17.7796	+	26.6090i	0.574133	+	0.859251i
$960$	−39.9961	+	40.6739i	−1.29087	+	1.31274i
$961$	28.0372	−	11.6134i	0.904425	−	0.374625i
$962$	16.6163	−	2.21126i	0.535732	−	0.0712938i
$963$	15.9414	+	3.17095i	0.513705	+	0.102182i
$964$	44.8936	−	3.06877i	1.44592	−	0.0988386i
$965$	24.5329	+	24.5329i	0.789741	+	0.789741i
$966$	7.36946	−	27.6581i	0.237109	−	0.889884i
$967$	41.5733	+	17.2202i	1.33691	+	0.553765i	0.932618	−	0.360866i	$-0.117519\pi$
$967$	41.5733	+	17.2202i	1.33691	+	0.553765i	0.404289	+	0.914631i	$0.367519\pi$
$968$	10.5474	+	51.8852i	0.339006	+	1.66765i
$969$	−26.7438	−	32.3358i	−0.859135	−	1.03877i
$970$	14.6221	+	7.18537i	0.469486	+	0.230708i
$971$	8.48386	+	3.51413i	0.272260	+	0.112774i	0.514636	−	0.857408i	$-0.327927\pi$
$971$	8.48386	+	3.51413i	0.272260	+	0.112774i	−0.242376	+	0.970182i	$0.577927\pi$
$972$	29.1792	−	33.4611i	0.935925	−	1.07327i
$973$	−8.90243	+	8.90243i	−0.285399	+	0.285399i
$974$	−17.9541	−	30.9971i	−0.575287	−	0.993211i
$975$	23.8972	+	4.75346i	0.765324	+	0.152232i
$976$	14.5096	−	5.01614i	0.464440	−	0.160563i
$977$	−14.5121	−	35.0353i	−0.464283	−	1.12088i	−0.966622	−	0.256208i	$-0.917527\pi$
$977$	−14.5121	−	35.0353i	−0.464283	−	1.12088i	0.502338	−	0.864671i	$-0.332473\pi$
$978$	−1.49936	+	23.3773i	−0.0479441	+	0.747524i
$979$	2.74126	+	4.10259i	0.0876111	+	0.131119i
$980$	−31.8881	+	15.8366i	−1.01863	+	0.505883i
$981$	−1.34095	−	0.895994i	−0.0428132	−	0.0286069i
$982$	8.39719	+	24.6240i	0.267965	+	0.785783i
$983$	0.794731	+	3.99538i	0.0253480	+	0.127433i	0.991387	−	0.130962i	$-0.0418065\pi$
$983$	0.794731	+	3.99538i	0.0253480	+	0.127433i	−0.966039	+	0.258395i	$0.916806\pi$
$984$	0.991666	−	5.09726i	0.0316132	−	0.162495i
$985$			77.1208i			2.45727i
$986$	7.16744	−	11.6611i	0.228258	−	0.371365i
$987$	28.8448			0.918140
$988$	−23.5065	+	6.36915i	−0.747841	+	0.202630i
$989$	1.30211	−	0.259005i	0.0414046	−	0.00823588i
$990$	−22.2499	−	65.2458i	−0.707148	−	2.07365i
$991$	−5.27196	+	7.89004i	−0.167469	+	0.250635i	−0.905706	−	0.423906i	$-0.860659\pi$
$991$	−5.27196	+	7.89004i	−0.167469	+	0.250635i	0.738237	+	0.674542i	$0.235659\pi$
$992$	2.80763	+	3.60641i	0.0891424	+	0.114504i
$993$	8.78153	−	5.86763i	0.278673	−	0.186204i
$994$	−63.1512	−	4.05035i	−2.00304	−	0.128469i
$995$	−64.5264	+	26.7277i	−2.04563	+	0.847326i
$996$	19.6552	−	58.4395i	0.622798	−	1.85173i
$997$	0.0547743	−	0.275369i	0.00173472	−	0.00872102i	−0.979908	−	0.199449i	$-0.936085\pi$
$997$	0.0547743	−	0.275369i	0.00173472	−	0.00872102i	0.981643	+	0.190728i	$0.0610848\pi$
$998$	−20.9557	−	36.1793i	−0.663342	−	1.14524i
$999$	0.672900	+	0.672900i	0.0212896	+	0.0212896i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	136.2.s.c.11.3	✓	112
4.3	odd	2		544.2.cc.c.79.11		112
8.3	odd	2	inner	136.2.s.c.11.8	yes	112
8.5	even	2		544.2.cc.c.79.12		112
17.14	odd	16	inner	136.2.s.c.99.8	yes	112
68.31	even	16		544.2.cc.c.303.12		112
136.99	even	16	inner	136.2.s.c.99.3	yes	112
136.133	odd	16		544.2.cc.c.303.11		112

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
136.2.s.c.11.3	✓	112	1.1	even	1	trivial
136.2.s.c.11.8	yes	112	8.3	odd	2	inner
136.2.s.c.99.3	yes	112	136.99	even	16	inner
136.2.s.c.99.8	yes	112	17.14	odd	16	inner
544.2.cc.c.79.11		112	4.3	odd	2
544.2.cc.c.79.12		112	8.5	even	2
544.2.cc.c.303.11		112	136.133	odd	16
544.2.cc.c.303.12		112	68.31	even	16

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:	\( N \)	\(=\)	\( 136 = 2^{3} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	136.s (of order \(16\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.06196 + 0.933944i) q^{2} +(-0.481682 - 2.42158i) q^{3} +(0.255498 - 1.98361i) q^{4} +(-1.60449 + 2.40128i) q^{5} +(2.77314 + 2.12174i) q^{6} +(-2.01574 - 3.01677i) q^{7} +(1.58126 + 2.34513i) q^{8} +(-2.86039 + 1.18481i) q^{9} +O(q^{10})\)	\(q+(-1.06196 + 0.933944i) q^{2} +(-0.481682 - 2.42158i) q^{3} +(0.255498 - 1.98361i) q^{4} +(-1.60449 + 2.40128i) q^{5} +(2.77314 + 2.12174i) q^{6} +(-2.01574 - 3.01677i) q^{7} +(1.58126 + 2.34513i) q^{8} +(-2.86039 + 1.18481i) q^{9} +(-0.538771 - 4.04856i) q^{10} +(-5.34680 - 1.06354i) q^{11} +(-4.92654 + 0.336762i) q^{12} +(-2.08889 - 2.08889i) q^{13} +(4.95813 + 1.32109i) q^{14} +(6.58775 + 2.72874i) q^{15} +(-3.86944 - 1.01362i) q^{16} +(2.60353 - 3.19713i) q^{17} +(1.93106 - 3.92966i) q^{18} +(3.80825 + 1.57743i) q^{19} +(4.35328 + 3.79621i) q^{20} +(-6.33441 + 6.33441i) q^{21} +(6.67135 - 3.86417i) q^{22} +(2.21592 + 0.440773i) q^{23} +(4.91725 - 4.95874i) q^{24} +(-1.27837 - 3.08626i) q^{25} +(4.16922 + 0.267402i) q^{26} +(0.131766 + 0.197202i) q^{27} +(-6.49913 + 3.22768i) q^{28} +(-1.95181 - 1.30416i) q^{29} +(-9.54438 + 3.25479i) q^{30} +(0.157623 + 0.792425i) q^{31} +(5.05584 - 2.53742i) q^{32} +13.4600i q^{33} +(0.221114 + 5.82676i) q^{34} +10.4784 q^{35} +(1.61938 + 5.97662i) q^{36} +(3.93527 - 0.782774i) q^{37} +(-5.51742 + 1.88153i) q^{38} +(-4.05224 + 6.06460i) q^{39} +(-8.16843 + 0.0343157i) q^{40} +(0.618274 - 0.413117i) q^{41} +(0.810876 - 12.6428i) q^{42} +(0.542885 - 0.224870i) q^{43} +(-3.47576 + 10.3342i) q^{44} +(1.74438 - 8.76962i) q^{45} +(-2.76486 + 1.60146i) q^{46} +(-2.27684 - 2.27684i) q^{47} +(-0.590716 + 9.85840i) q^{48} +(-2.35891 + 5.69492i) q^{49} +(4.23997 + 2.08355i) q^{50} +(-8.99618 - 4.76464i) q^{51} +(-4.67727 + 3.60985i) q^{52} +(4.67028 - 11.2751i) q^{53} +(-0.324105 - 0.0863575i) q^{54} +(11.1327 - 11.1327i) q^{55} +(3.88732 - 9.49747i) q^{56} +(1.98550 - 9.98179i) q^{57} +(3.29075 - 0.437924i) q^{58} +(2.07442 + 5.00809i) q^{59} +(7.09591 - 12.3704i) q^{60} +(-3.19122 + 2.13230i) q^{61} +(-0.907469 - 0.694308i) q^{62} +(9.34011 + 6.24086i) q^{63} +(-2.99926 + 7.41650i) q^{64} +(8.36764 - 1.66443i) q^{65} +(-12.5709 - 14.2939i) q^{66} -9.67224i q^{67} +(-5.67668 - 5.98125i) q^{68} -5.57833i q^{69} +(-11.1276 + 9.78620i) q^{70} +(-12.0958 + 2.40601i) q^{71} +(-7.30154 - 4.83449i) q^{72} +(-1.21626 - 0.812676i) q^{73} +(-3.44801 + 4.50659i) q^{74} +(-6.85786 + 4.58228i) q^{75} +(4.10201 - 7.15106i) q^{76} +(7.56930 + 18.2739i) q^{77} +(-1.36070 - 10.2249i) q^{78} +(2.62293 - 13.1863i) q^{79} +(8.64246 - 7.66529i) q^{80} +(-6.15366 + 6.15366i) q^{81} +(-0.270751 + 1.01615i) q^{82} +(-4.77818 + 11.5355i) q^{83} +(10.9466 + 14.1834i) q^{84} +(3.49990 + 11.3816i) q^{85} +(-0.366503 + 0.745827i) q^{86} +(-2.21797 + 5.35465i) q^{87} +(-5.96051 - 14.2207i) q^{88} +(-0.639995 - 0.639995i) q^{89} +(6.33787 + 10.9421i) q^{90} +(-2.09105 + 10.5124i) q^{91} +(1.44049 - 4.28291i) q^{92} +(1.84299 - 0.763393i) q^{93} +(4.54433 + 0.291461i) q^{94} +(-9.89814 + 6.61373i) q^{95} +(-8.57988 - 11.0209i) q^{96} +(-2.21618 + 3.31675i) q^{97} +(-2.81368 - 8.25084i) q^{98} +(16.5540 - 3.29280i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 112 q - 8 q^{2} - 16 q^{3} - 8 q^{4} - 8 q^{6} - 8 q^{8} - 16 q^{9}+O(q^{10}) \) 112 * q - 8 * q^2 - 16 * q^3 - 8 * q^4 - 8 * q^6 - 8 * q^8 - 16 * q^9	\( 112 q - 8 q^{2} - 16 q^{3} - 8 q^{4} - 8 q^{6} - 8 q^{8} - 16 q^{9} - 8 q^{10} - 16 q^{11} + 24 q^{12} - 8 q^{14} - 16 q^{17} - 16 q^{18} - 16 q^{19} - 8 q^{20} - 8 q^{22} - 56 q^{24} - 16 q^{25} - 40 q^{26} + 32 q^{27} + 40 q^{28} - 72 q^{30} + 32 q^{32} - 72 q^{34} - 32 q^{35} + 56 q^{36} + 48 q^{38} + 56 q^{40} - 16 q^{41} - 56 q^{42} - 96 q^{43} + 24 q^{44} - 24 q^{46} + 16 q^{48} - 16 q^{49} - 16 q^{51} - 16 q^{52} - 24 q^{54} + 32 q^{56} + 32 q^{57} + 48 q^{58} - 16 q^{59} + 96 q^{60} + 48 q^{62} + 40 q^{64} + 64 q^{65} - 16 q^{66} + 80 q^{68} + 64 q^{70} + 96 q^{72} - 96 q^{73} + 40 q^{74} - 16 q^{75} + 48 q^{76} + 96 q^{78} + 8 q^{80} - 96 q^{81} + 32 q^{82} + 128 q^{83} + 64 q^{86} - 72 q^{88} - 16 q^{89} + 152 q^{90} - 16 q^{91} - 120 q^{92} + 88 q^{94} - 160 q^{96} - 16 q^{97} + 128 q^{98} + 48 q^{99}+O(q^{100}) \) 112 * q - 8 * q^2 - 16 * q^3 - 8 * q^4 - 8 * q^6 - 8 * q^8 - 16 * q^9 - 8 * q^10 - 16 * q^11 + 24 * q^12 - 8 * q^14 - 16 * q^17 - 16 * q^18 - 16 * q^19 - 8 * q^20 - 8 * q^22 - 56 * q^24 - 16 * q^25 - 40 * q^26 + 32 * q^27 + 40 * q^28 - 72 * q^30 + 32 * q^32 - 72 * q^34 - 32 * q^35 + 56 * q^36 + 48 * q^38 + 56 * q^40 - 16 * q^41 - 56 * q^42 - 96 * q^43 + 24 * q^44 - 24 * q^46 + 16 * q^48 - 16 * q^49 - 16 * q^51 - 16 * q^52 - 24 * q^54 + 32 * q^56 + 32 * q^57 + 48 * q^58 - 16 * q^59 + 96 * q^60 + 48 * q^62 + 40 * q^64 + 64 * q^65 - 16 * q^66 + 80 * q^68 + 64 * q^70 + 96 * q^72 - 96 * q^73 + 40 * q^74 - 16 * q^75 + 48 * q^76 + 96 * q^78 + 8 * q^80 - 96 * q^81 + 32 * q^82 + 128 * q^83 + 64 * q^86 - 72 * q^88 - 16 * q^89 + 152 * q^90 - 16 * q^91 - 120 * q^92 + 88 * q^94 - 160 * q^96 - 16 * q^97 + 128 * q^98 + 48 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more