LMFDB - Embedded newform 112.2.w.c.109.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [112,2,Mod(37,112)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(112, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([0, 3, 4])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("112.37"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 112 = 2^{4} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	112.w (of order $12$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [48,-4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$0.894324502638$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$12$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			109.1
Character	$\chi$	$=$	112.109
Dual form			112.2.w.c.37.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.40462 - 0.164410i) q^{2} +(-0.839165 + 0.224854i) q^{3} +(1.94594 + 0.461868i) q^{4} +(-3.16320 - 0.847576i) q^{5} +(1.21568 - 0.177868i) q^{6} +(0.654939 - 2.56341i) q^{7} +(-2.65738 - 0.968682i) q^{8} +(-1.94444 + 1.12262i) q^{9} +(4.30375 + 1.71059i) q^{10} +(-0.769121 - 2.87040i) q^{11} +(-1.73682 + 0.0499683i) q^{12} +(-3.63293 - 3.63293i) q^{13} +(-1.34139 + 3.49295i) q^{14} +2.84503 q^{15} +(3.57336 + 1.79753i) q^{16} +(-1.81856 + 3.14984i) q^{17} +(2.91577 - 1.25718i) q^{18} +(-0.429496 + 1.60290i) q^{19} +(-5.76392 - 3.11031i) q^{20} +(0.0267897 + 2.29839i) q^{21} +(0.608405 + 4.15828i) q^{22} +(5.33698 - 3.08131i) q^{23} +(2.44779 + 0.215363i) q^{24} +(4.95730 + 2.86210i) q^{25} +(4.50561 + 5.70019i) q^{26} +(3.22221 - 3.22221i) q^{27} +(2.45843 - 4.68574i) q^{28} +(5.10266 + 5.10266i) q^{29} +(-3.99619 - 0.467750i) q^{30} +(-1.00761 + 1.74523i) q^{31} +(-4.72369 - 3.11235i) q^{32} +(1.29084 + 2.23580i) q^{33} +(3.07226 - 4.12535i) q^{34} +(-4.24438 + 7.55345i) q^{35} +(-4.30226 + 1.28648i) q^{36} +(-5.57162 - 1.49291i) q^{37} +(0.866812 - 2.18086i) q^{38} +(3.86550 + 2.23175i) q^{39} +(7.58478 + 5.31646i) q^{40} -3.71244i q^{41} +(0.340248 - 3.23278i) q^{42} +(-2.91640 + 2.91640i) q^{43} +(-0.170919 - 5.94085i) q^{44} +(7.10214 - 1.90301i) q^{45} +(-8.00305 + 3.45063i) q^{46} +(-5.06565 - 8.77396i) q^{47} +(-3.40282 - 0.704944i) q^{48} +(-6.14211 - 3.35775i) q^{49} +(-6.49259 - 4.83520i) q^{50} +(0.817820 - 3.05215i) q^{51} +(-5.39152 - 8.74739i) q^{52} +(-0.986836 - 3.68292i) q^{53} +(-5.05576 + 3.99624i) q^{54} +9.73153i q^{55} +(-4.22354 + 6.17751i) q^{56} -1.44167i q^{57} +(-6.32839 - 8.00624i) q^{58} +(0.977963 + 3.64981i) q^{59} +(5.53625 + 1.31403i) q^{60} +(1.75433 - 6.54724i) q^{61} +(1.70224 - 2.28573i) q^{62} +(1.60425 + 5.71963i) q^{63} +(6.12331 + 5.14831i) q^{64} +(8.41248 + 14.5708i) q^{65} +(-1.44556 - 3.35269i) q^{66} +(5.88390 - 1.57659i) q^{67} +(-4.99362 + 5.28946i) q^{68} +(-3.78577 + 3.78577i) q^{69} +(7.20362 - 9.91194i) q^{70} -9.55168i q^{71} +(6.25456 - 1.09969i) q^{72} +(0.990000 + 0.571577i) q^{73} +(7.58058 + 3.01301i) q^{74} +(-4.80355 - 1.28711i) q^{75} +(-1.57610 + 2.92078i) q^{76} +(-7.86173 + 0.0916354i) q^{77} +(-5.06266 - 3.77030i) q^{78} +(0.120696 + 0.209052i) q^{79} +(-9.77969 - 8.71464i) q^{80} +(1.38842 - 2.40481i) q^{81} +(-0.610362 + 5.21459i) q^{82} +(-0.459183 - 0.459183i) q^{83} +(-1.00942 + 4.48490i) q^{84} +(8.42219 - 8.42219i) q^{85} +(4.57593 - 3.61696i) q^{86} +(-5.42932 - 3.13462i) q^{87} +(-0.736657 + 8.37277i) q^{88} +(-3.76823 + 2.17559i) q^{89} +(-10.2887 + 1.50536i) q^{90} +(-11.6920 + 6.93333i) q^{91} +(11.8086 - 3.53106i) q^{92} +(0.453128 - 1.69110i) q^{93} +(5.67281 + 13.1570i) q^{94} +(2.71716 - 4.70626i) q^{95} +(4.66378 + 1.54964i) q^{96} +6.80176 q^{97} +(8.07531 + 5.72620i) q^{98} +(4.71788 + 4.71788i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 4 q^{2} - 4 q^{4} + 4 q^{5} - 4 q^{6} - 4 q^{8} - 2 q^{10} - 4 q^{11} + 2 q^{12} - 24 q^{13} - 34 q^{14} - 40 q^{15} + 16 q^{16} + 8 q^{17} + 18 q^{18} - 4 q^{19} - 16 q^{20} - 8 q^{21} + 18 q^{24}+ \cdots - 24 q^{99}+O(q^{100}) $ 48 * q - 4 * q^2 - 4 * q^4 + 4 * q^5 - 4 * q^6 - 4 * q^8 - 2 * q^10 - 4 * q^11 + 2 * q^12 - 24 * q^13 - 34 * q^14 - 40 * q^15 + 16 * q^16 + 8 * q^17 + 18 * q^18 - 4 * q^19 - 16 * q^20 - 8 * q^21 + 18 * q^24 - 10 * q^26 - 24 * q^27 - 10 * q^28 + 24 * q^29 - 4 * q^30 + 28 * q^31 + 16 * q^32 + 16 * q^33 - 44 * q^34 + 28 * q^35 - 72 * q^36 - 24 * q^37 + 20 * q^38 + 26 * q^40 + 6 * q^42 - 40 * q^43 + 6 * q^44 - 28 * q^45 - 14 * q^46 - 20 * q^47 + 56 * q^48 + 56 * q^50 + 24 * q^51 - 16 * q^52 - 16 * q^53 + 64 * q^54 + 40 * q^56 - 6 * q^58 - 20 * q^59 + 46 * q^60 + 8 * q^61 + 24 * q^62 - 16 * q^63 + 80 * q^64 + 8 * q^65 - 20 * q^66 + 48 * q^67 - 40 * q^69 + 82 * q^70 - 32 * q^72 - 8 * q^74 - 4 * q^75 - 36 * q^76 - 20 * q^77 + 116 * q^78 - 36 * q^79 - 28 * q^80 + 2 * q^82 - 8 * q^83 + 28 * q^84 - 20 * q^86 - 42 * q^88 - 20 * q^90 + 64 * q^91 + 76 * q^92 + 8 * q^93 - 72 * q^94 - 4 * q^95 - 120 * q^96 - 48 * q^97 - 2 * q^98 - 24 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/112\mathbb{Z}\right)^\times$.

$n$	$15$	$17$	$85$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−1.40462	−	0.164410i	−0.993219	−	0.116255i
$2$	−1.40462	−	0.164410i	−0.993219	−	0.116255i
$3$	−0.839165	+	0.224854i	−0.484492	+	0.129819i	−0.492794	−	0.870146i	$-0.664024\pi$
$3$	−0.839165	+	0.224854i	−0.484492	+	0.129819i	0.00830125	+	0.999966i	$0.497358\pi$
$4$	1.94594	+	0.461868i	0.972969	+	0.230934i
$5$	−3.16320	−	0.847576i	−1.41462	−	0.379048i	−0.531051	−	0.847340i	$-0.678203\pi$
$5$	−3.16320	−	0.847576i	−1.41462	−	0.379048i	−0.883574	+	0.468292i	$0.844869\pi$
$6$	1.21568	−	0.177868i	0.496299	−	0.0726143i
$7$	0.654939	−	2.56341i	0.247544	−	0.968877i
$7$	0.654939	−	2.56341i	0.247544	−	0.968877i
$8$	−2.65738	−	0.968682i	−0.939525	−	0.342481i
$9$	−1.94444	+	1.12262i	−0.648146	+	0.374207i
$10$	4.30375	+	1.71059i	1.36097	+	0.540935i
$11$	−0.769121	−	2.87040i	−0.231899	−	0.865458i	−0.979522	−	0.201335i	$-0.935472\pi$
$11$	−0.769121	−	2.87040i	−0.231899	−	0.865458i	0.747624	−	0.664123i	$-0.231195\pi$
$12$	−1.73682	+	0.0499683i	−0.501376	+	0.0144246i
$13$	−3.63293	−	3.63293i	−1.00759	−	1.00759i	−0.999971	−	0.00762179i	$-0.997574\pi$
$13$	−3.63293	−	3.63293i	−1.00759	−	1.00759i	−0.00762179	−	0.999971i	$-0.502426\pi$
$14$	−1.34139	+	3.49295i	−0.358502	+	0.933529i
$15$	2.84503			0.734583
$16$	3.57336	+	1.79753i	0.893339	+	0.449383i
$17$	−1.81856	+	3.14984i	−0.441066	+	0.763948i	−0.997769	−	0.0667634i	$-0.978733\pi$
$17$	−1.81856	+	3.14984i	−0.441066	+	0.763948i	0.556703	+	0.830711i	$0.312066\pi$
$18$	2.91577	−	1.25718i	0.687254	−	0.296319i
$19$	−0.429496	+	1.60290i	−0.0985331	+	0.367730i	−0.997531	−	0.0702216i	$-0.977629\pi$
$19$	−0.429496	+	1.60290i	−0.0985331	+	0.367730i	0.898998	+	0.437952i	$0.144296\pi$
$20$	−5.76392	−	3.11031i	−1.28885	−	0.695486i
$21$	0.0267897	+	2.29839i	0.00584600	+	0.501549i
$22$	0.608405	+	4.15828i	0.129712	+	0.886549i
$23$	5.33698	−	3.08131i	1.11284	−	0.642497i	0.173275	−	0.984874i	$-0.444565\pi$
$23$	5.33698	−	3.08131i	1.11284	−	0.642497i	0.939563	+	0.342377i	$0.111232\pi$
$24$	2.44779	+	0.215363i	0.499653	+	0.0439608i
$25$	4.95730	+	2.86210i	0.991461	+	0.572420i
$26$	4.50561	+	5.70019i	0.883623	+	1.11790i
$27$	3.22221	−	3.22221i	0.620115	−	0.620115i
$28$	2.45843	−	4.68574i	0.464599	−	0.885521i
$29$	5.10266	+	5.10266i	0.947539	+	0.947539i	0.998691	−	0.0511514i	$-0.0162891\pi$
$29$	5.10266	+	5.10266i	0.947539	+	0.947539i	−0.0511514	+	0.998691i	$0.516289\pi$
$30$	−3.99619	−	0.467750i	−0.729602	−	0.0853990i
$31$	−1.00761	+	1.74523i	−0.180972	+	0.313452i	−0.942212	−	0.335018i	$-0.891258\pi$
$31$	−1.00761	+	1.74523i	−0.180972	+	0.313452i	0.761240	+	0.648470i	$0.224591\pi$
$32$	−4.72369	−	3.11235i	−0.835039	−	0.550191i
$33$	1.29084	+	2.23580i	0.224706	+	0.389203i
$34$	3.07226	−	4.12535i	0.526888	−	0.707492i
$35$	−4.24438	+	7.55345i	−0.717432	+	1.27677i
$36$	−4.30226	+	1.28648i	−0.717043	+	0.214413i
$37$	−5.57162	−	1.49291i	−0.915969	−	0.245433i	−0.230107	−	0.973165i	$-0.573908\pi$
$37$	−5.57162	−	1.49291i	−0.915969	−	0.245433i	−0.685861	+	0.727732i	$0.740574\pi$
$38$	0.866812	−	2.18086i	0.140616	−	0.353782i
$39$	3.86550	+	2.23175i	0.618976	+	0.357366i
$40$	7.58478	+	5.31646i	1.19926	+	0.840606i
$41$		−	3.71244i		−	0.579786i	−0.957059	−	0.289893i	$-0.906380\pi$
$41$		−	3.71244i		−	0.579786i	0.957059	−	0.289893i	$-0.0936198\pi$
$42$	0.340248	−	3.23278i	0.0525014	−	0.498828i
$43$	−2.91640	+	2.91640i	−0.444747	+	0.444747i	−0.893604	−	0.448857i	$-0.851831\pi$
$43$	−2.91640	+	2.91640i	−0.444747	+	0.444747i	0.448857	+	0.893604i	$0.351831\pi$
$44$	−0.170919	−	5.94085i	−0.0257669	−	0.895617i
$45$	7.10214	−	1.90301i	1.05872	−	0.283685i
$46$	−8.00305	+	3.45063i	−1.17999	+	0.508767i
$47$	−5.06565	−	8.77396i	−0.738900	−	1.27981i	−0.952991	−	0.302999i	$-0.902012\pi$
$47$	−5.06565	−	8.77396i	−0.738900	−	1.27981i	0.214090	−	0.976814i	$-0.431321\pi$
$48$	−3.40282	−	0.704944i	−0.491155	−	0.101750i
$49$	−6.14211	−	3.35775i	−0.877444	−	0.479678i
$50$	−6.49259	−	4.83520i	−0.918191	−	0.683801i
$51$	0.817820	−	3.05215i	0.114518	−	0.427386i
$52$	−5.39152	−	8.74739i	−0.747670	−	1.21304i
$53$	−0.986836	−	3.68292i	−0.135552	−	0.505888i	−0.999995	−	0.00315690i	$-0.998995\pi$
$53$	−0.986836	−	3.68292i	−0.135552	−	0.505888i	0.864443	−	0.502731i	$-0.167672\pi$
$54$	−5.05576	+	3.99624i	−0.688002	+	0.543819i
$55$			9.73153i			1.31220i
$56$	−4.22354	+	6.17751i	−0.564395	+	0.825505i
$57$		−	1.44167i		−	0.190954i
$58$	−6.32839	−	8.00624i	−0.830958	−	1.05127i
$59$	0.977963	+	3.64981i	0.127320	+	0.475164i	0.999912	−	0.0132857i	$-0.00422909\pi$
$59$	0.977963	+	3.64981i	0.127320	+	0.475164i	−0.872592	+	0.488450i	$0.837562\pi$
$60$	5.53625	+	1.31403i	0.714727	+	0.169640i
$61$	1.75433	−	6.54724i	0.224619	−	0.838288i	−0.757938	−	0.652326i	$-0.773793\pi$
$61$	1.75433	−	6.54724i	0.224619	−	0.838288i	0.982557	−	0.185962i	$-0.0595402\pi$
$62$	1.70224	−	2.28573i	0.216185	−	0.290288i
$63$	1.60425	+	5.71963i	0.202116	+	0.720606i
$64$	6.12331	+	5.14831i	0.765414	+	0.643538i
$65$	8.41248	+	14.5708i	1.04344	+	1.80729i
$66$	−1.44556	−	3.35269i	−0.177936	−	0.412687i
$67$	5.88390	−	1.57659i	0.718833	−	0.192611i	0.119182	−	0.992872i	$-0.461973\pi$
$67$	5.88390	−	1.57659i	0.718833	−	0.192611i	0.599651	+	0.800262i	$0.295306\pi$
$68$	−4.99362	+	5.28946i	−0.605565	+	0.641441i
$69$	−3.78577	+	3.78577i	−0.455753	+	0.455753i
$70$	7.20362	−	9.91194i	0.860998	−	1.18470i
$71$		−	9.55168i		−	1.13358i	−0.823864	−	0.566788i	$-0.808186\pi$
$71$		−	9.55168i		−	1.13358i	0.823864	−	0.566788i	$-0.191814\pi$
$72$	6.25456	−	1.09969i	0.737108	−	0.129599i
$73$	0.990000	+	0.571577i	0.115871	+	0.0668980i	0.556815	−	0.830636i	$-0.312023\pi$
$73$	0.990000	+	0.571577i	0.115871	+	0.0668980i	−0.440945	+	0.897534i	$0.645356\pi$
$74$	7.58058	+	3.01301i	0.881225	+	0.350255i
$75$	−4.80355	−	1.28711i	−0.554666	−	0.148622i
$76$	−1.57610	+	2.92078i	−0.180791	+	0.335036i
$77$	−7.86173	+	0.0916354i	−0.895927	+	0.0104428i
$78$	−5.06266	−	3.77030i	−0.573233	−	0.426902i
$79$	0.120696	+	0.209052i	0.0135794	+	0.0235202i	0.872735	−	0.488194i	$-0.162344\pi$
$79$	0.120696	+	0.209052i	0.0135794	+	0.0235202i	−0.859156	+	0.511714i	$0.829011\pi$
$80$	−9.77969	−	8.71464i	−1.09340	−	0.974326i
$81$	1.38842	−	2.40481i	0.154269	−	0.267201i
$82$	−0.610362	+	5.21459i	−0.0674032	+	0.575855i
$83$	−0.459183	−	0.459183i	−0.0504018	−	0.0504018i	0.681457	−	0.731858i	$-0.261347\pi$
$83$	−0.459183	−	0.459183i	−0.0504018	−	0.0504018i	−0.731858	+	0.681457i	$0.761347\pi$
$84$	−1.00942	+	4.48490i	−0.110137	+	0.489342i
$85$	8.42219	−	8.42219i	0.913515	−	0.913515i
$86$	4.57593	−	3.61696i	0.493435	−	0.390027i
$87$	−5.42932	−	3.13462i	−0.582085	−	0.336067i
$88$	−0.736657	+	8.37277i	−0.0785279	+	0.892540i
$89$	−3.76823	+	2.17559i	−0.399432	+	0.230612i	−0.686239	−	0.727376i	$-0.740739\pi$
$89$	−3.76823	+	2.17559i	−0.399432	+	0.230612i	0.286807	+	0.957988i	$0.407406\pi$
$90$	−10.2887	+	1.50536i	−1.08453	+	0.158679i
$91$	−11.6920	+	6.93333i	−1.22566	+	0.726810i
$92$	11.8086	−	3.53106i	1.23113	−	0.368138i
$93$	0.453128	−	1.69110i	0.0469872	−	0.175359i
$94$	5.67281	+	13.1570i	0.585105	+	1.35704i
$95$	2.71716	−	4.70626i	0.278775	−	0.482852i
$96$	4.66378	+	1.54964i	0.475995	+	0.158159i
$97$	6.80176			0.690614			0.345307	−	0.938490i	$-0.387775\pi$
$97$	6.80176			0.690614			0.345307	+	0.938490i	$0.387775\pi$
$98$	8.07531	+	5.72620i	0.815730	+	0.578433i
$99$	4.71788	+	4.71788i	0.474165	+	0.474165i
$100$	8.32470	+	7.85909i	0.832470	+	0.785909i
$101$	−0.824407	−	3.07673i	−0.0820316	−	0.306146i	0.912704	−	0.408621i	$-0.133990\pi$
$101$	−0.824407	−	3.07673i	−0.0820316	−	0.306146i	−0.994736	+	0.102475i	$0.967324\pi$
$102$	−1.65053	+	4.15266i	−0.163427	+	0.411175i
$103$	3.25557	−	1.87960i	0.320781	−	0.185203i	−0.330960	−	0.943645i	$-0.607372\pi$
$103$	3.25557	−	1.87960i	0.320781	−	0.185203i	0.651741	+	0.758442i	$0.274039\pi$
$104$	6.13491	+	13.1732i	0.601577	+	1.29174i
$105$	1.86332	−	7.29296i	0.181841	−	0.711720i
$106$	0.780626	+	5.33537i	0.0758211	+	0.518217i
$107$	−0.366346	−	0.0981620i	−0.0354160	−	0.00948968i	0.241068	−	0.970508i	$-0.422502\pi$
$107$	−0.366346	−	0.0981620i	−0.0354160	−	0.00948968i	−0.276484	+	0.961019i	$0.589169\pi$
$108$	7.75847	−	4.78200i	0.746559	−	0.460148i
$109$	−9.65655	+	2.58746i	−0.924929	+	0.247834i	−0.689691	−	0.724104i	$-0.742254\pi$
$109$	−9.65655	+	2.58746i	−0.924929	+	0.247834i	−0.235238	+	0.971938i	$0.575587\pi$
$110$	1.59996	−	13.6691i	0.152550	−	1.30330i
$111$	5.01120			0.475642
$112$	6.94814	−	7.98269i	0.656537	−	0.754294i
$113$	2.62015			0.246483			0.123242	−	0.992377i	$-0.460671\pi$
$113$	2.62015			0.246483			0.123242	+	0.992377i	$0.460671\pi$
$114$	−0.237025	+	2.02501i	−0.0221994	+	0.189659i
$115$	−19.4936	+	5.22328i	−1.81778	+	0.487074i
$116$	7.57271	+	12.2862i	0.703108	+	1.14075i
$117$	11.1424	+	2.98560i	1.03012	+	0.276018i
$118$	−0.773607	−	5.28739i	−0.0712163	−	0.486744i
$119$	6.88327	+	6.72466i	0.630989	+	0.616449i
$120$	−7.56031	−	2.75592i	−0.690159	−	0.251580i
$121$	1.87863	−	1.08463i	0.170785	−	0.0986027i
$122$	−3.54060	+	8.90799i	−0.320551	+	0.806491i
$123$	0.834757	+	3.11535i	0.0752675	+	0.280902i
$124$	−2.76680	+	2.93072i	−0.248466	+	0.263187i
$125$	−1.67697	−	1.67697i	−0.149993	−	0.149993i
$126$	−1.31300	−	8.29769i	−0.116972	−	0.739217i
$127$	−12.8840			−1.14327			−0.571635	−	0.820508i	$-0.693691\pi$
$127$	−12.8840			−1.14327			−0.571635	+	0.820508i	$0.693691\pi$
$128$	−7.75452	−	8.23817i	−0.685409	−	0.728158i
$129$	1.79158	−	3.10311i	0.157740	−	0.273213i
$130$	−9.42079	−	21.8497i	−0.826258	−	1.91634i
$131$	2.40496	−	8.97544i	0.210122	−	0.784188i	−0.777704	−	0.628630i	$-0.783616\pi$
$131$	2.40496	−	8.97544i	0.210122	−	0.784188i	0.987827	−	0.155557i	$-0.0497174\pi$
$132$	1.47925	+	4.94693i	0.128752	+	0.430575i
$133$	3.82759	+	2.15077i	0.331894	+	0.186496i
$134$	−8.52388	+	1.24714i	−0.736351	+	0.107737i
$135$	−12.9236	+	7.46143i	−1.11228	+	0.642177i
$136$	7.88379	−	6.60871i	0.676030	−	0.566692i
$137$	−10.2211	−	5.90118i	−0.873251	−	0.504172i	−0.00482362	−	0.999988i	$-0.501535\pi$
$137$	−10.2211	−	5.90118i	−0.873251	−	0.504172i	−0.868427	+	0.495817i	$0.834869\pi$
$138$	5.94000	−	4.69516i	0.505646	−	0.399679i
$139$	8.15708	−	8.15708i	0.691874	−	0.691874i	−0.270770	−	0.962644i	$-0.587278\pi$
$139$	8.15708	−	8.15708i	0.691874	−	0.691874i	0.962644	+	0.270770i	$0.0872782\pi$
$140$	−11.7480	+	12.7382i	−0.992887	+	1.07658i
$141$	6.22377	+	6.22377i	0.524136	+	0.524136i
$142$	−1.57039	+	13.4165i	−0.131784	+	1.12589i
$143$	−7.63379	+	13.2221i	−0.638370	+	1.10569i
$144$	−8.96611	+	0.516338i	−0.747176	+	0.0430282i
$145$	−11.8158	−	20.4656i	−0.981250	−	1.69958i
$146$	−1.29660	−	0.965616i	−0.107308	−	0.0799149i
$147$	5.90925	+	1.43663i	0.487387	+	0.118491i
$148$	−10.1525	−	5.47846i	−0.834531	−	0.450327i
$149$	11.3488	+	3.04089i	0.929727	+	0.249119i	0.691738	−	0.722148i	$-0.256845\pi$
$149$	11.3488	+	3.04089i	0.929727	+	0.249119i	0.237989	+	0.971268i	$0.423512\pi$
$150$	6.53557	+	2.59765i	0.533627	+	0.212097i
$151$	−16.9805	−	9.80371i	−1.38186	−	0.797815i	−0.389476	−	0.921036i	$-0.627344\pi$
$151$	−16.9805	−	9.80371i	−1.38186	−	0.797815i	−0.992379	+	0.123222i	$0.960677\pi$
$152$	2.69403	−	3.84347i	0.218515	−	0.311746i
$153$		−	8.16622i		−	0.660199i
$154$	11.0578	+	1.16383i	0.891066	+	0.0937842i
$155$	4.66647	−	4.66647i	0.374820	−	0.374820i
$156$	6.49126	+	6.12820i	0.519717	+	0.490649i
$157$	5.22347	−	1.39962i	0.416878	−	0.111702i	−0.0442821	−	0.999019i	$-0.514100\pi$
$157$	5.22347	−	1.39962i	0.416878	−	0.111702i	0.461160	+	0.887317i	$0.347433\pi$
$158$	−0.135163	−	0.313484i	−0.0107530	−	0.0249394i
$159$	1.65624	+	2.86869i	0.131348	+	0.227502i
$160$	12.3040	+	13.8487i	0.972718	+	1.09483i
$161$	−4.40325	−	15.6989i	−0.347025	−	1.23725i
$162$	−2.34558	+	3.14959i	−0.184286	+	0.247455i
$163$	2.91941	−	10.8954i	0.228666	−	0.853394i	−0.752236	−	0.658893i	$-0.771025\pi$
$163$	2.91941	−	10.8954i	0.228666	−	0.853394i	0.980902	−	0.194500i	$-0.0623085\pi$
$164$	1.71466	−	7.22419i	0.133892	−	0.564114i
$165$	−2.18817	−	8.16636i	−0.170349	−	0.635750i
$166$	0.569485	+	0.720473i	0.0442006	+	0.0559195i
$167$			21.8111i			1.68779i	0.536508	+	0.843895i	$0.319743\pi$
$167$			21.8111i			1.68779i	−0.536508	+	0.843895i	$0.680257\pi$
$168$	2.15522	−	6.13364i	0.166278	−	0.473220i
$169$			13.3963i			1.03049i
$170$	−13.2147	+	10.4453i	−1.01352	+	0.801120i
$171$	−0.964322	−	3.59890i	−0.0737435	−	0.275215i
$172$	−7.02213	+	4.32815i	−0.535432	+	0.330018i
$173$	−5.87840	+	21.9385i	−0.446927	+	1.66795i	0.263872	+	0.964558i	$0.415000\pi$
$173$	−5.87840	+	21.9385i	−0.446927	+	1.66795i	−0.710799	+	0.703396i	$0.751666\pi$
$174$	7.11080	+	5.29560i	0.539068	+	0.401458i
$175$	10.5835	−	10.8331i	0.800034	−	0.818904i
$176$	2.41129	−	11.6395i	0.181758	−	0.877359i
$177$	−1.64135	−	2.84289i	−0.123371	−	0.213685i
$178$	5.65064	−	2.43635i	0.423533	−	0.182612i
$179$	20.7936	−	5.57162i	1.55418	−	0.416443i	0.623368	−	0.781929i	$-0.285764\pi$
$179$	20.7936	−	5.57162i	1.55418	−	0.416443i	0.930817	+	0.365486i	$0.119097\pi$
$180$	14.6993	−	0.422899i	1.09562	−	0.0315210i
$181$	−11.8484	+	11.8484i	−0.880684	+	0.880684i	−0.993604	−	0.112920i	$-0.963980\pi$
$181$	−11.8484	+	11.8484i	−0.880684	+	0.880684i	0.112920	+	0.993604i	$0.463980\pi$
$182$	17.5628	−	7.81644i	1.30184	−	0.579393i
$183$			5.88869i			0.435304i
$184$	−17.1672	+	3.01836i	−1.26558	+	0.222517i
$185$	16.3588	+	9.44474i	1.20272	+	0.694391i
$186$	−0.914508	+	2.30086i	−0.0670550	+	0.168707i
$187$	10.4400	+	2.79739i	0.763448	+	0.204565i
$188$	−5.80503	−	19.4132i	−0.423375	−	1.41586i
$189$	−6.14949	−	10.3702i	−0.447310	−	0.754321i
$190$	−4.59034	+	6.16380i	−0.333018	+	0.447169i
$191$	−3.94400	−	6.83120i	−0.285377	−	0.494288i	0.687323	−	0.726352i	$-0.258786\pi$
$191$	−3.94400	−	6.83120i	−0.285377	−	0.494288i	−0.972701	+	0.232063i	$0.925452\pi$
$192$	−6.29609	−	2.94343i	−0.454381	−	0.212424i
$193$	−12.4404	+	21.5474i	−0.895478	+	1.55101i	−0.0622664	+	0.998060i	$0.519833\pi$
$193$	−12.4404	+	21.5474i	−0.895478	+	1.55101i	−0.833212	+	0.552954i	$0.813500\pi$
$194$	−9.55392	−	1.11828i	−0.685931	−	0.0802875i
$195$	−10.3358	−	10.3358i	−0.740160	−	0.740160i
$196$	−10.4013	−	9.37081i	−0.742953	−	0.669344i
$197$	−7.75408	+	7.75408i	−0.552455	+	0.552455i	−0.927149	−	0.374694i	$-0.877748\pi$
$197$	−7.75408	+	7.75408i	−0.552455	+	0.552455i	0.374694	+	0.927149i	$0.377748\pi$
$198$	−5.85118	−	7.40251i	−0.415825	−	0.526074i
$199$	−9.91354	−	5.72359i	−0.702753	−	0.405734i	0.105619	−	0.994407i	$-0.466318\pi$
$199$	−9.91354	−	5.72359i	−0.702753	−	0.405734i	−0.808372	+	0.588672i	$0.799651\pi$
$200$	−10.4010	−	12.4077i	−0.735459	−	0.877359i
$201$	−4.58307	+	2.64603i	−0.323264	+	0.186637i
$202$	0.652139	+	4.45719i	0.0458843	+	0.313607i
$203$	16.4221	−	9.73826i	1.15261	−	0.683492i
$204$	3.00112	−	5.56157i	0.210120	−	0.389387i
$205$	−3.14658	+	11.7432i	−0.219767	+	0.820180i
$206$	−4.88188	+	2.10489i	−0.340137	+	0.146655i
$207$	−6.91828	+	11.9828i	−0.480854	+	0.832863i
$208$	−6.45144	−	19.5120i	−0.447327	−	1.35292i
$209$	4.93130			0.341105
$210$	−3.81629	+	9.93752i	−0.263349	+	0.685754i
$211$	−8.69524	−	8.69524i	−0.598605	−	0.598605i	0.341336	−	0.939941i	$-0.389120\pi$
$211$	−8.69524	−	8.69524i	−0.598605	−	0.598605i	−0.939941	+	0.341336i	$0.889120\pi$
$212$	−0.219300	−	7.62253i	−0.0150616	−	0.523518i
$213$	2.14773	+	8.01544i	0.147160	+	0.549209i
$214$	0.498439	+	0.198112i	0.0340726	+	0.0135426i
$215$	11.6970	−	6.75328i	0.797730	−	0.460570i
$216$	−11.6839	+	5.44134i	−0.794991	+	0.370236i
$217$	3.81380	+	3.72592i	0.258898	+	0.252932i
$218$	13.9892	−	2.04679i	0.947470	−	0.138626i
$219$	−0.959295	−	0.257042i	−0.0648231	−	0.0173693i
$220$	−4.49468	+	18.9370i	−0.303031	+	1.27673i
$221$	18.0498	−	4.83644i	1.21416	−	0.325334i
$222$	−7.03885	−	0.823889i	−0.472417	−	0.0552958i
$223$	21.9483			1.46976			0.734882	−	0.678195i	$-0.237238\pi$
$223$	21.9483			1.46976			0.734882	+	0.678195i	$0.237238\pi$
$224$	−11.0720	+	10.0703i	−0.739776	+	0.672853i
$225$	−12.8522			−0.856814
$226$	−3.68033	−	0.430779i	−0.244812	−	0.0286550i
$227$	23.8284	−	6.38481i	1.58155	−	0.423774i	0.642143	−	0.766585i	$-0.278045\pi$
$227$	23.8284	−	6.38481i	1.58155	−	0.423774i	0.939405	+	0.342810i	$0.111379\pi$
$228$	0.665862	−	2.80541i	0.0440978	−	0.185793i
$229$	9.19018	+	2.46250i	0.607304	+	0.162727i	0.549350	−	0.835592i	$-0.314875\pi$
$229$	9.19018	+	2.46250i	0.607304	+	0.162727i	0.0579547	+	0.998319i	$0.481542\pi$
$230$	28.2399	−	4.13182i	1.86208	−	0.272444i
$231$	6.57669	−	1.84464i	0.432714	−	0.121368i
$232$	−8.61684	−	18.5025i	−0.565723	−	1.21475i
$233$	−19.2584	+	11.1188i	−1.26166	+	0.728418i	−0.973395	−	0.229133i	$-0.926411\pi$
$233$	−19.2584	+	11.1188i	−1.26166	+	0.728418i	−0.288262	+	0.957552i	$0.593077\pi$
$234$	−15.1600	−	6.02556i	−0.991042	−	0.393903i
$235$	8.58704	+	32.0473i	0.560157	+	2.09053i
$236$	0.217329	+	7.55399i	0.0141469	+	0.491723i
$237$	−0.148290	−	0.148290i	−0.00963250	−	0.00963250i
$238$	−8.56281	−	10.5773i	−0.555045	−	0.685624i
$239$	14.9579			0.967548			0.483774	−	0.875193i	$-0.339266\pi$
$239$	14.9579			0.967548			0.483774	+	0.875193i	$0.339266\pi$
$240$	10.1663	+	5.11403i	0.656231	+	0.330109i
$241$	12.1750	−	21.0877i	0.784262	−	1.35838i	−0.145178	−	0.989406i	$-0.546375\pi$
$241$	12.1750	−	21.0877i	0.784262	−	1.35838i	0.929439	−	0.368975i	$-0.120291\pi$
$242$	−2.81710	+	1.21463i	−0.181090	+	0.0780795i
$243$	−4.16262	+	15.5351i	−0.267032	+	0.996577i
$244$	6.43777	−	11.9303i	0.412136	−	0.763757i
$245$	16.5828	+	15.8271i	1.05943	+	1.01116i
$246$	−0.660325	−	4.51315i	−0.0421008	−	0.287748i
$247$	7.38355	−	4.26289i	0.469804	−	0.271241i
$248$	4.36816	−	3.66168i	0.277378	−	0.232517i
$249$	0.488579	+	0.282081i	0.0309624	+	0.0178762i
$250$	2.07981	+	2.63123i	0.131539	+	0.166414i
$251$	−3.50509	+	3.50509i	−0.221239	+	0.221239i	−0.809020	−	0.587781i	$-0.800002\pi$
$251$	−3.50509	+	3.50509i	−0.221239	+	0.221239i	0.587781	+	0.809020i	$0.300002\pi$
$252$	0.480057	+	11.8710i	0.0302407	+	0.747803i
$253$	−12.9494	−	12.9494i	−0.814120	−	0.814120i
$254$	18.0972	+	2.11825i	1.13552	+	0.132911i
$255$	−5.17385	+	8.96137i	−0.323999	+	0.561183i
$256$	9.53776	+	12.8464i	0.596110	+	0.802903i
$257$	−3.24853	−	5.62661i	−0.202638	−	0.350978i	0.746740	−	0.665116i	$-0.231618\pi$
$257$	−3.24853	−	5.62661i	−0.202638	−	0.350978i	−0.949377	+	0.314138i	$0.898285\pi$
$258$	−3.02668	+	4.06415i	−0.188433	+	0.253023i
$259$	−7.47601	+	13.3046i	−0.464536	+	0.826705i
$260$	9.64038	+	32.2394i	0.597871	+	1.99940i
$261$	−15.6501	−	4.19344i	−0.968719	−	0.259568i
$262$	−4.85372	+	12.2117i	−0.299864	+	0.754442i
$263$	−21.4222	−	12.3681i	−1.32095	−	0.762650i	−0.337069	−	0.941480i	$-0.609436\pi$
$263$	−21.4222	−	12.3681i	−1.32095	−	0.762650i	−0.983880	+	0.178829i	$0.942769\pi$
$264$	−1.26447	−	7.19178i	−0.0778228	−	0.442623i
$265$			12.4862i			0.767023i
$266$	−5.02272	−	3.65032i	−0.307963	−	0.223816i
$267$	2.67298	−	2.67298i	0.163584	−	0.163584i
$268$	12.1779	−	0.350358i	0.743883	−	0.0214015i
$269$	1.44745	−	0.387844i	0.0882528	−	0.0236473i	−0.214422	−	0.976741i	$-0.568787\pi$
$269$	1.44745	−	0.387844i	0.0882528	−	0.0236473i	0.302675	+	0.953094i	$0.402120\pi$
$270$	19.3795	−	8.35574i	1.17940	−	0.508514i
$271$	3.68123	+	6.37608i	0.223619	+	0.387320i	0.955904	−	0.293679i	$-0.0948795\pi$
$271$	3.68123	+	6.37608i	0.223619	+	0.387320i	−0.732285	+	0.680998i	$0.761546\pi$
$272$	−12.1603	+	7.98658i	−0.737327	+	0.484257i
$273$	8.25255	−	8.44720i	0.499467	−	0.511248i
$274$	13.3866	+	9.96939i	0.808717	+	0.602273i
$275$	4.40260	−	16.4307i	0.265487	−	0.990811i
$276$	−9.11539	+	5.61835i	−0.548682	+	0.338185i
$277$	−1.17214	−	4.37447i	−0.0704268	−	0.262836i	0.921731	−	0.387831i	$-0.126775\pi$
$277$	−1.17214	−	4.37447i	−0.0704268	−	0.262836i	−0.992157	+	0.124994i	$0.960109\pi$
$278$	−12.7987	+	10.1165i	−0.767617	+	0.606749i
$279$		−	4.52464i		−	0.270883i
$280$	18.5958	−	15.9609i	1.11131	−	0.953847i
$281$		−	9.72875i		−	0.580369i	−0.956971	−	0.290184i	$-0.906283\pi$
$281$		−	9.72875i		−	0.580369i	0.956971	−	0.290184i	$-0.0937166\pi$
$282$	−7.71881	−	9.76531i	−0.459649	−	0.581516i
$283$	1.04114	+	3.88559i	0.0618893	+	0.230974i	0.989942	−	0.141475i	$-0.0451846\pi$
$283$	1.04114	+	3.88559i	0.0618893	+	0.230974i	−0.928052	+	0.372450i	$0.878518\pi$
$284$	4.41161	−	18.5870i	0.261781	−	1.10293i
$285$	−1.22193	+	4.56029i	−0.0723807	+	0.270128i
$286$	12.8965	−	17.3170i	0.762583	−	1.02398i
$287$	−9.51650	−	2.43142i	−0.561742	−	0.143522i
$288$	12.6789	+	0.748855i	0.747112	+	0.0441267i
$289$	1.88568	+	3.26609i	0.110922	+	0.192123i
$290$	13.2320	+	30.6891i	0.777012	+	1.80213i
$291$	−5.70780	+	1.52940i	−0.334597	+	0.0896551i
$292$	1.66249	+	1.56950i	0.0972896	+	0.0918481i
$293$	1.88131	−	1.88131i	0.109908	−	0.109908i	−0.650014	−	0.759922i	$-0.725237\pi$
$293$	1.88131	−	1.88131i	0.109908	−	0.109908i	0.759922	+	0.650014i	$0.225237\pi$
$294$	−8.06408	−	2.98946i	−0.470307	−	0.174349i
$295$		−	12.3740i		−	0.720440i
$296$	13.3597	+	9.36435i	0.776519	+	0.544292i
$297$	−11.7273	−	6.77077i	−0.680488	−	0.392880i
$298$	−15.4408	−	6.13715i	−0.894461	−	0.355516i
$299$	−30.5830	−	8.19470i	−1.76866	−	0.473912i
$300$	−8.75295	−	4.72324i	−0.505352	−	0.272696i
$301$	5.56586	+	9.38598i	0.320811	+	0.540999i
$302$	22.2394	+	16.5623i	1.27974	+	0.953053i
$303$	1.38363	+	2.39651i	0.0794874	+	0.137676i
$304$	−4.41601	+	4.95570i	−0.253275	+	0.284229i
$305$	−11.0986	+	19.2233i	−0.635502	+	1.10072i
$306$	−1.34260	+	11.4705i	−0.0767516	+	0.655723i
$307$	3.98977	+	3.98977i	0.227708	+	0.227708i	0.811735	−	0.584026i	$-0.198524\pi$
$307$	3.98977	+	3.98977i	0.227708	+	0.227708i	−0.584026	+	0.811735i	$0.698524\pi$
$308$	−15.3408	−	3.45276i	−0.874121	−	0.196739i
$309$	−2.30933	+	2.30933i	−0.131373	+	0.131373i
$310$	−7.32185	+	5.78743i	−0.415853	+	0.328704i
$311$	−0.699829	−	0.404047i	−0.0396837	−	0.0229114i	0.480027	−	0.877254i	$-0.340627\pi$
$311$	−0.699829	−	0.404047i	−0.0396837	−	0.0229114i	−0.519711	+	0.854342i	$0.673960\pi$
$312$	−8.11025	−	9.67505i	−0.459152	−	0.547742i
$313$	20.1745	−	11.6478i	1.14033	−	0.658371i	0.193819	−	0.981037i	$-0.437913\pi$
$313$	20.1745	−	11.6478i	1.14033	−	0.658371i	0.946513	+	0.322666i	$0.104579\pi$
$314$	−7.56712	+	1.10716i	−0.427037	+	0.0624805i
$315$	−0.226731	−	19.4520i	−0.0127748	−	1.09600i
$316$	0.138313	+	0.462549i	0.00778073	+	0.0260204i
$317$	−0.808194	+	3.01622i	−0.0453927	+	0.169408i	−0.984901	−	0.173118i	$-0.944616\pi$
$317$	−0.808194	+	3.01622i	−0.0453927	+	0.169408i	0.939508	+	0.342526i	$0.111282\pi$
$318$	−1.85475	−	4.30173i	−0.104009	−	0.241229i
$319$	10.7221	−	18.5712i	0.600322	−	1.03979i
$320$	−15.0057	−	21.4751i	−0.838842	−	1.20049i
$321$	0.329497			0.0183907
$322$	3.60386	+	22.7750i	0.200835	+	1.26920i
$323$	−4.26781	−	4.26781i	−0.237467	−	0.237467i
$324$	3.81248	−	4.03835i	0.211805	−	0.224353i
$325$	−7.61172	−	28.4073i	−0.422222	−	1.57575i
$326$	−5.89199	+	14.8240i	−0.326327	+	0.821023i
$327$	7.52164	−	4.34262i	0.415948	−	0.240147i
$328$	−3.59618	+	9.86537i	−0.198566	+	0.544724i
$329$	−25.8089	+	7.23891i	−1.42289	+	0.399094i
$330$	1.73093	+	11.8304i	0.0952845	+	0.651244i
$331$	15.2162	+	4.07718i	0.836360	+	0.224102i	0.651486	−	0.758660i	$-0.274146\pi$
$331$	15.2162	+	4.07718i	0.836360	+	0.224102i	0.184874	+	0.982762i	$0.440812\pi$
$332$	−0.681460	−	1.10562i	−0.0374000	−	0.0606789i
$333$	12.5096	−	3.35195i	0.685524	−	0.183686i
$334$	3.58595	−	30.6363i	0.196214	−	1.67635i
$335$	−19.9482			−1.08989
$336$	−4.03570	+	8.26112i	−0.220165	+	0.450681i
$337$	−5.36065			−0.292013			−0.146007	−	0.989284i	$-0.546642\pi$
$337$	−5.36065			−0.292013			−0.146007	+	0.989284i	$0.546642\pi$
$338$	2.20248	−	18.8168i	0.119799	−	1.02350i
$339$	−2.19874	+	0.589151i	−0.119419	+	0.0319983i
$340$	20.2790	−	12.4991i	1.09978	−	0.677861i
$341$	5.78447	+	1.54994i	0.313247	+	0.0839341i
$342$	0.762816	+	5.21364i	0.0412484	+	0.281922i
$343$	−12.6300	+	13.5456i	−0.681955	+	0.731394i
$344$	10.5750	−	4.92491i	0.570168	−	0.265534i
$345$	15.1838	−	8.76640i	0.817471	−	0.471967i
$346$	11.8639	−	29.8489i	0.637805	−	1.60469i
$347$	−4.29752	−	16.0386i	−0.230703	−	0.860995i	−0.980039	−	0.198805i	$-0.936294\pi$
$347$	−4.29752	−	16.0386i	−0.230703	−	0.860995i	0.749336	−	0.662190i	$-0.230373\pi$
$348$	−9.11735	−	8.60741i	−0.488741	−	0.461406i
$349$	−22.2799	−	22.2799i	−1.19262	−	1.19262i	−0.976330	−	0.216286i	$-0.930606\pi$
$349$	−22.2799	−	22.2799i	−1.19262	−	1.19262i	−0.216286	−	0.976330i	$-0.569394\pi$
$350$	−16.6468	+	13.4764i	−0.889811	+	0.720344i
$351$	−23.4121			−1.24965
$352$	−5.30060	+	15.9527i	−0.282523	+	0.850280i
$353$	−6.84373	+	11.8537i	−0.364255	+	0.630908i	−0.988656	−	0.150196i	$-0.952010\pi$
$353$	−6.84373	+	11.8537i	−0.364255	+	0.630908i	0.624401	+	0.781104i	$0.285343\pi$
$354$	1.83807	+	4.26305i	0.0976926	+	0.226579i
$355$	−8.09577	+	30.2138i	−0.429679	+	1.60358i
$356$	−8.33758	+	2.49314i	−0.441891	+	0.132136i
$357$	−7.28827	−	4.09537i	−0.385736	−	0.216750i
$358$	−30.1232	+	4.40737i	−1.59206	+	0.232937i
$359$	−5.47529	+	3.16116i	−0.288974	+	0.166840i	−0.637479	−	0.770467i	$-0.720023\pi$
$359$	−5.47529	+	3.16116i	−0.288974	+	0.166840i	0.348505	+	0.937307i	$0.386690\pi$
$360$	−20.7165	−	1.82269i	−1.09185	−	0.0960642i
$361$	14.0697	+	8.12312i	0.740508	+	0.427533i
$362$	18.5905	−	14.6945i	0.977096	−	0.772328i
$363$	−1.33260	+	1.33260i	−0.0699434	+	0.0699434i
$364$	−25.9542	+	8.09167i	−1.36037	+	0.424119i
$365$	−2.64711	−	2.64711i	−0.138556	−	0.138556i
$366$	0.968157	−	8.27139i	0.0506064	−	0.432353i
$367$	18.6164	−	32.2445i	0.971768	−	1.68315i	0.281555	−	0.959545i	$-0.409150\pi$
$367$	18.6164	−	32.2445i	0.971768	−	1.68315i	0.690213	−	0.723606i	$-0.257517\pi$
$368$	24.6097	−	1.41722i	1.28287	−	0.0738775i
$369$	4.16767	+	7.21861i	0.216960	+	0.375786i
$370$	−21.4251	−	15.9559i	−1.11384	−	0.829505i
$371$	−10.0871	+	0.117575i	−0.523699	+	0.00610417i
$372$	1.66282	−	3.08149i	0.0862134	−	0.159768i
$373$	−4.17538	−	1.11879i	−0.216193	−	0.0579287i	0.149097	−	0.988823i	$-0.452363\pi$
$373$	−4.17538	−	1.11879i	−0.216193	−	0.0579287i	−0.365290	+	0.930894i	$0.619030\pi$
$374$	−14.2043	−	5.64571i	−0.734489	−	0.291933i
$375$	1.78433	+	1.03019i	0.0921426	+	0.0531985i
$376$	4.96217	+	28.2227i	0.255904	+	1.45548i
$377$		−	37.0752i		−	1.90947i
$378$	6.93277	+	15.5773i	0.356583	+	0.801208i
$379$	−11.5118	+	11.5118i	−0.591323	+	0.591323i	−0.937989	−	0.346666i	$-0.887314\pi$
$379$	−11.5118	+	11.5118i	−0.591323	+	0.591323i	0.346666	+	0.937989i	$0.387314\pi$
$380$	7.46109	−	7.90312i	0.382746	−	0.405422i
$381$	10.8118	−	2.89701i	0.553906	−	0.148419i
$382$	4.41672	+	10.2437i	0.225979	+	0.524113i
$383$	9.86334	+	17.0838i	0.503993	+	0.872942i	0.999989	+	0.00461719i	$0.00146970\pi$
$383$	9.86334	+	17.0838i	0.503993	+	0.872942i	−0.495996	+	0.868325i	$0.665197\pi$
$384$	8.35971	+	5.16955i	0.426605	+	0.263808i
$385$	24.9459	+	6.37355i	1.27136	+	0.324826i
$386$	21.0167	−	28.2206i	1.06972	−	1.43639i
$387$	2.39674	−	8.94477i	0.121833	−	0.454688i
$388$	13.2358	+	3.14151i	0.671947	+	0.159486i
$389$	−1.53689	−	5.73576i	−0.0779236	−	0.290815i	0.915957	−	0.401277i	$-0.131434\pi$
$389$	−1.53689	−	5.73576i	−0.0779236	−	0.290815i	−0.993880	+	0.110462i	$0.964767\pi$
$390$	12.8186	+	16.2172i	0.649094	+	0.821189i
$391$			22.4142i			1.13353i
$392$	13.0693	+	14.8726i	0.660100	+	0.751177i
$393$			8.07264i			0.407211i
$394$	12.1664	−	9.61672i	0.612935	−	0.484483i
$395$	−0.204599	−	0.763573i	−0.0102945	−	0.0384195i
$396$	7.00167	+	11.3597i	0.351847	+	0.570848i
$397$	−6.61855	+	24.7008i	−0.332175	+	1.23970i	0.574724	+	0.818348i	$0.305110\pi$
$397$	−6.61855	+	24.7008i	−0.332175	+	1.23970i	−0.906899	+	0.421348i	$0.861557\pi$
$398$	12.9838	+	9.66937i	0.650819	+	0.484682i
$399$	−3.69559	−	0.944207i	−0.185011	−	0.0472695i
$400$	12.5695	+	19.1382i	0.628475	+	0.956911i
$401$	−1.80147	−	3.12023i	−0.0899610	−	0.155817i	0.817533	−	0.575881i	$-0.195341\pi$
$401$	−1.80147	−	3.12023i	−0.0899610	−	0.155817i	−0.907494	+	0.420064i	$0.862008\pi$
$402$	6.87252	−	2.96318i	0.342770	−	0.147790i
$403$	10.0008	−	2.67972i	0.498177	−	0.133486i
$404$	−0.183205	−	6.36790i	−0.00911476	−	0.316815i
$405$	−6.43010	+	6.43010i	−0.319514	+	0.319514i
$406$	−24.6680	+	10.9786i	−1.22425	+	0.544861i
$407$			17.1410i			0.849648i
$408$	−5.12981	+	7.31850i	−0.253964	+	0.362320i
$409$	−13.2778	−	7.66595i	−0.656546	−	0.379057i	0.134414	−	0.990925i	$-0.457085\pi$
$409$	−13.2778	−	7.66595i	−0.656546	−	0.379057i	−0.790959	+	0.611869i	$0.790418\pi$
$410$	6.35046	−	15.9774i	0.313627	−	0.789070i
$411$	9.90413	+	2.65380i	0.488535	+	0.130902i
$412$	7.20327	−	2.15395i	0.354880	−	0.106118i
$413$	9.99645	−	0.116517i	0.491893	−	0.00573345i
$414$	11.6877	−	15.6939i	0.574418	−	0.771314i
$415$	1.06329	+	1.84168i	0.0521950	+	0.0904044i
$416$	5.85388	+	28.4678i	0.287010	+	1.39575i
$417$	−5.01099	+	8.67929i	−0.245389	+	0.425027i
$418$	−6.92662	−	0.810753i	−0.338792	−	0.0396552i
$419$	−17.2949	−	17.2949i	−0.844910	−	0.844910i	0.144583	−	0.989493i	$-0.453816\pi$
$419$	−17.2949	−	17.2949i	−0.844910	−	0.844910i	−0.989493	+	0.144583i	$0.953816\pi$
$420$	6.99428	−	13.3311i	0.341286	−	0.650489i
$421$	18.2430	−	18.2430i	0.889111	−	0.889111i	−0.105327	−	0.994438i	$-0.533589\pi$
$421$	18.2430	−	18.2430i	0.889111	−	0.889111i	0.994438	+	0.105327i	$0.0335888\pi$
$422$	10.7840	+	13.6431i	0.524955	+	0.664137i
$423$	19.6997	+	11.3736i	0.957830	+	0.553003i
$424$	−0.945183	+	10.7428i	−0.0459021	+	0.521719i
$425$	−18.0303	+	10.4098i	−0.874598	+	0.504950i
$426$	−1.69894	−	11.6118i	−0.0823138	−	0.562593i
$427$	−15.6343	−	8.78510i	−0.756595	−	0.425141i
$428$	−0.667549	−	0.360221i	−0.0322672	−	0.0174119i
$429$	3.43297	−	12.8120i	0.165745	−	0.618571i
$430$	−17.5402	+	7.56271i	−0.845865	+	0.364707i
$431$	−16.8098	+	29.1154i	−0.809698	+	1.40244i	0.103375	+	0.994642i	$0.467036\pi$
$431$	−16.8098	+	29.1154i	−0.809698	+	1.40244i	−0.913073	+	0.407796i	$0.866297\pi$
$432$	17.3062	−	5.72209i	0.832643	−	0.275304i
$433$	26.5511			1.27596			0.637982	−	0.770051i	$-0.279769\pi$
$433$	26.5511			1.27596			0.637982	+	0.770051i	$0.279769\pi$
$434$	−4.74438	−	5.86055i	−0.227738	−	0.281315i
$435$	14.5172	+	14.5172i	0.696046	+	0.696046i
$436$	−19.9861	+	0.575001i	−0.957161	+	0.0275375i
$437$	2.64682	+	9.87805i	0.126614	+	0.472531i
$438$	1.30519	+	0.518765i	0.0623643	+	0.0247876i
$439$	16.9833	−	9.80529i	0.810567	−	0.467981i	−0.0365859	−	0.999331i	$-0.511648\pi$
$439$	16.9833	−	9.80529i	0.810567	−	0.467981i	0.847153	+	0.531350i	$0.178315\pi$
$440$	9.42675	−	25.8603i	0.449403	−	1.23284i
$441$	15.7124	−	0.366334i	0.748211	−	0.0174445i
$442$	−26.1484	+	3.82581i	−1.24375	+	0.181975i
$443$	−6.58948	−	1.76565i	−0.313076	−	0.0838883i	0.0988599	−	0.995101i	$-0.468480\pi$
$443$	−6.58948	−	1.76565i	−0.313076	−	0.0838883i	−0.411935	+	0.911213i	$0.635147\pi$
$444$	9.75148	+	2.31451i	0.462785	+	0.109842i
$445$	13.7636	−	3.68795i	0.652459	−	0.174826i
$446$	−30.8291	−	3.60850i	−1.45980	−	0.170868i
$447$	−10.2072			−0.482786
$448$	17.2076	−	12.3247i	0.812982	−	0.582288i
$449$	6.32412			0.298454			0.149227	−	0.988803i	$-0.452322\pi$
$449$	6.32412			0.298454			0.149227	+	0.988803i	$0.452322\pi$
$450$	18.0525	+	2.11303i	0.851005	+	0.0996091i
$451$	−10.6562	+	2.85532i	−0.501781	+	0.134452i
$452$	5.09866	+	1.21016i	0.239821	+	0.0569213i
$453$	16.4539	+	4.40880i	0.773070	+	0.207144i
$454$	−34.5197	+	5.05063i	−1.62009	+	0.237038i
$455$	42.8607	−	12.0216i	2.00934	−	0.563582i
$456$	−1.39652	+	3.83107i	−0.0653981	+	0.179406i
$457$	34.2066	−	19.7492i	1.60012	−	0.923829i	0.608657	−	0.793433i	$-0.291709\pi$
$457$	34.2066	−	19.7492i	1.60012	−	0.923829i	0.991462	−	0.130396i	$-0.0416248\pi$
$458$	−12.5039	−	4.96985i	−0.584269	−	0.232226i
$459$	4.28966	+	16.0092i	0.200224	+	0.747248i
$460$	−40.3457	+	1.16075i	−1.88113	+	0.0541202i
$461$	−1.26773	−	1.26773i	−0.0590440	−	0.0590440i	0.676968	−	0.736012i	$-0.263293\pi$
$461$	−1.26773	−	1.26773i	−0.0590440	−	0.0590440i	−0.736012	+	0.676968i	$0.763293\pi$
$462$	−9.54105	+	1.50975i	−0.443890	+	0.0702399i
$463$	−14.4427			−0.671208			−0.335604	−	0.942003i	$-0.608940\pi$
$463$	−14.4427			−0.671208			−0.335604	+	0.942003i	$0.608940\pi$
$464$	9.06142	+	27.4058i	0.420666	+	1.27228i
$465$	−2.86667	+	4.96521i	−0.132939	+	0.230256i
$466$	28.8788	−	12.4515i	1.33778	−	0.576805i
$467$	−4.49607	+	16.7796i	−0.208053	+	0.776465i	0.780444	+	0.625226i	$0.214993\pi$
$467$	−4.49607	+	16.7796i	−0.208053	+	0.776465i	−0.988497	+	0.151240i	$0.951674\pi$
$468$	20.3035	+	10.9561i	0.938528	+	0.506446i
$469$	−0.187839	−	16.1154i	−0.00867361	−	0.744140i
$470$	−6.79269	−	46.4262i	−0.313323	−	2.14148i
$471$	−4.06864	+	2.34903i	−0.187473	+	0.108238i
$472$	0.936684	−	10.6463i	0.0431144	−	0.490033i
$473$	10.6143	+	6.12817i	0.488046	+	0.281773i
$474$	0.183912	+	0.232673i	0.00844736	+	0.0106870i
$475$	−6.71680	+	6.71680i	−0.308188	+	0.308188i
$476$	10.2885	+	16.2649i	0.471574	+	0.745502i
$477$	6.05337	+	6.05337i	0.277165	+	0.277165i
$478$	−21.0103	−	2.45923i	−0.960988	−	0.112483i
$479$	2.39344	−	4.14556i	0.109359	−	0.189416i	−0.806152	−	0.591709i	$-0.798453\pi$
$479$	2.39344	−	4.14556i	0.109359	−	0.189416i	0.915511	+	0.402293i	$0.131787\pi$
$480$	−13.4390	−	8.85472i	−0.613405	−	0.404161i
$481$	14.8177	+	25.6649i	0.675627	+	1.17022i
$482$	−20.5684	+	27.6187i	−0.936863	+	1.25800i
$483$	7.22502	+	12.1839i	0.328750	+	0.554387i
$484$	4.15666	−	1.24294i	0.188939	−	0.0564974i
$485$	−21.5153	−	5.76501i	−0.976960	−	0.261776i
$486$	8.40104	−	21.1366i	0.381079	−	0.958776i
$487$	23.2700	+	13.4349i	1.05446	+	0.608795i	0.923896	−	0.382644i	$-0.124987\pi$
$487$	23.2700	+	13.4349i	1.05446	+	0.608795i	0.130568	+	0.991439i	$0.458320\pi$
$488$	−11.0041	+	15.6991i	−0.498132	+	0.710665i
$489$			9.79948i			0.443148i
$490$	−20.6904	−	24.9575i	−0.934698	−	1.12747i
$491$	−11.7576	+	11.7576i	−0.530611	+	0.530611i	−0.920754	−	0.390143i	$-0.872426\pi$
$491$	−11.7576	+	11.7576i	−0.530611	+	0.530611i	0.390143	+	0.920754i	$0.372426\pi$
$492$	0.185504	+	6.44784i	0.00836319	+	0.290691i
$493$	−25.3520	+	6.79306i	−1.14180	+	0.305944i
$494$	−11.0720	+	4.77384i	−0.498151	+	0.214785i
$495$	−10.9248	−	18.9223i	−0.491034	−	0.850496i
$496$	−6.73764	+	4.42511i	−0.302529	+	0.198693i
$497$	−24.4848	−	6.25576i	−1.09829	−	0.280609i
$498$	−0.639893	−	0.476545i	−0.0286743	−	0.0213545i
$499$	−5.10099	+	19.0371i	−0.228352	+	0.852220i	0.752682	+	0.658384i	$0.228760\pi$
$499$	−5.10099	+	19.0371i	−0.228352	+	0.852220i	−0.981034	+	0.193836i	$0.937907\pi$
$500$	−2.48875	−	4.03783i	−0.111300	−	0.180577i
$501$	−4.90430	−	18.3031i	−0.219108	−	0.817721i
$502$	5.49961	−	4.34707i	0.245460	−	0.194019i
$503$		−	23.6387i		−	1.05400i	−0.849866	−	0.526999i	$-0.823317\pi$
$503$		−	23.6387i		−	1.05400i	0.849866	−	0.526999i	$-0.176683\pi$
$504$	1.27741	−	16.7532i	0.0569002	−	0.746248i
$505$			10.4311i			0.464176i
$506$	16.0600	+	20.3180i	0.713954	+	0.903245i
$507$	−3.01221	−	11.2417i	−0.133777	−	0.499263i
$508$	−25.0715	−	5.95070i	−1.11237	−	0.264020i
$509$	8.81005	−	32.8795i	0.390498	−	1.45736i	−0.438816	−	0.898577i	$-0.644602\pi$
$509$	8.81005	−	32.8795i	0.390498	−	1.45736i	0.829314	−	0.558783i	$-0.188731\pi$
$510$	8.74065	−	11.7367i	0.387043	−	0.519711i
$511$	2.11357	−	2.16342i	0.0934989	−	0.0957043i
$512$	−11.2849	−	19.6125i	−0.498726	−	0.866760i
$513$	3.78096	+	6.54881i	0.166933	+	0.289137i
$514$	3.63789	+	8.43737i	0.160460	+	0.372156i
$515$	−11.8911	+	3.18622i	−0.523985	+	0.140401i
$516$	4.91953	−	5.21098i	0.216570	−	0.229401i
$517$	−21.2887	+	21.2887i	−0.936274	+	0.936274i
$518$	12.6884	−	17.4588i	0.557495	−	0.767095i
$519$		−	19.7318i		−	0.866131i
$520$	−8.24063	−	46.8693i	−0.361376	−	2.05535i
$521$	15.2768	+	8.82007i	0.669289	+	0.386414i	0.795807	−	0.605550i	$-0.207047\pi$
$521$	15.2768	+	8.82007i	0.669289	+	0.386414i	−0.126518	+	0.991964i	$0.540380\pi$
$522$	21.2931	+	8.46325i	0.931975	+	0.370426i
$523$	−13.8896	−	3.72172i	−0.607352	−	0.162739i	−0.0579803	−	0.998318i	$-0.518466\pi$
$523$	−13.8896	−	3.72172i	−0.607352	−	0.162739i	−0.549371	+	0.835578i	$0.685133\pi$
$524$	8.82537	−	16.3549i	0.385538	−	0.714466i
$525$	−6.44541	+	11.4705i	−0.281301	+	0.500613i
$526$	28.0567	+	20.8946i	1.22333	+	0.911046i
$527$	−3.66479	−	6.34760i	−0.159641	−	0.276506i
$528$	0.593708	+	10.3096i	0.0258378	+	0.448669i
$529$	7.48891	−	12.9712i	0.325605	−	0.563964i
$530$	2.05286	−	17.5385i	0.0891704	−	0.761822i
$531$	−5.99894	−	5.99894i	−0.260332	−	0.260332i
$532$	6.45489	+	5.95311i	0.279855	+	0.258100i
$533$	−13.4870	+	13.4870i	−0.584189	+	0.584189i
$534$	−4.19400	+	3.31507i	−0.181492	+	0.143457i
$535$	1.07562	+	0.621012i	0.0465033	+	0.0268487i
$536$	−17.1630	−	1.51004i	−0.741327	−	0.0652238i
$537$	−16.1964	+	9.35102i	−0.698928	+	0.403526i
$538$	−2.09689	+	0.306800i	−0.0904035	+	0.0132271i
$539$	−4.91405	+	20.2128i	−0.211663	+	0.870628i
$540$	−28.5947	+	8.55050i	−1.23052	+	0.367955i
$541$	7.69386	−	28.7139i	0.330785	−	1.23451i	−0.577582	−	0.816332i	$-0.696004\pi$
$541$	7.69386	−	28.7139i	0.330785	−	1.23451i	0.908367	−	0.418173i	$-0.137330\pi$
$542$	−4.12246	−	9.56123i	−0.177075	−	0.410690i
$543$	7.27860	−	12.6069i	0.312355	−	0.541014i
$544$	18.3937	−	9.21887i	0.788624	−	0.395256i
$545$	32.7386			1.40237
$546$	−12.9805	+	10.5083i	−0.555516	+	0.449716i
$547$	27.6503	+	27.6503i	1.18224	+	1.18224i	0.979163	+	0.203076i	$0.0650940\pi$
$547$	27.6503	+	27.6503i	1.18224	+	1.18224i	0.203076	+	0.979163i	$0.434906\pi$
$548$	−17.1641	−	16.2041i	−0.733216	−	0.692207i
$549$	3.93889	+	14.7001i	0.168108	+	0.627387i
$550$	−8.88538	+	22.3552i	−0.378874	+	0.953229i
$551$	−10.3706	+	5.98748i	−0.441803	+	0.255075i
$552$	13.7274	−	6.39301i	0.584277	−	0.272105i
$553$	0.614935	−	0.172478i	0.0261497	−	0.00733449i
$554$	0.927205	+	6.33720i	0.0393932	+	0.269242i
$555$	−15.8514	−	4.24737i	−0.672855	−	0.180291i
$556$	19.6407	−	12.1057i	0.832950	−	0.513396i
$557$	−6.35511	+	1.70285i	−0.269275	+	0.0721519i	−0.390930	−	0.920421i	$-0.627846\pi$
$557$	−6.35511	+	1.70285i	−0.269275	+	0.0721519i	0.121655	+	0.992572i	$0.461180\pi$
$558$	−0.743895	+	6.35542i	−0.0314916	+	0.269047i
$559$	21.1901			0.896247
$560$	−28.7443	+	19.3618i	−1.21467	+	0.818184i
$561$	−9.38988			−0.396441
$562$	−1.59950	+	13.6652i	−0.0674709	+	0.576433i
$563$	25.7157	−	6.89049i	1.08379	−	0.290399i	0.327640	−	0.944803i	$-0.393747\pi$
$563$	25.7157	−	6.89049i	1.08379	−	0.290399i	0.756146	+	0.654403i	$0.227080\pi$
$564$	9.23652	+	14.9856i	0.388928	+	0.631009i
$565$	−8.28807	−	2.22078i	−0.348682	−	0.0934289i
$566$	−0.823582	−	5.62896i	−0.0346178	−	0.236603i
$567$	−5.25518	−	5.13409i	−0.220697	−	0.215611i
$568$	−9.25253	+	25.3824i	−0.388228	+	1.06502i
$569$	−2.20198	+	1.27132i	−0.0923119	+	0.0532963i	−0.545445	−	0.838146i	$-0.683639\pi$
$569$	−2.20198	+	1.27132i	−0.0923119	+	0.0532963i	0.453133	+	0.891443i	$0.350306\pi$
$570$	2.46610	−	6.20460i	0.103294	−	0.259882i
$571$	−10.3843	−	38.7549i	−0.434571	−	1.62184i	−0.742091	−	0.670299i	$-0.766166\pi$
$571$	−10.3843	−	38.7549i	−0.434571	−	1.62184i	0.307521	−	0.951541i	$-0.400501\pi$
$572$	−20.9618	+	22.2036i	−0.876455	+	0.928380i
$573$	4.84569	+	4.84569i	0.202431	+	0.202431i
$574$	12.9674	+	4.97984i	0.541247	+	0.207855i
$575$	35.2760			1.47111
$576$	−17.6860	−	3.13639i	−0.736916	−	0.130683i
$577$	−17.3756	+	30.0953i	−0.723354	+	1.25289i	0.236294	+	0.971682i	$0.424067\pi$
$577$	−17.3756	+	30.0953i	−0.723354	+	1.25289i	−0.959648	+	0.281204i	$0.909266\pi$
$578$	−2.11169	−	4.89765i	−0.0878348	−	0.203715i
$579$	5.59453	−	20.8791i	0.232501	−	0.867705i
$580$	−13.5405	−	45.2821i	−0.562237	−	1.88024i
$581$	−1.47781	+	0.876335i	−0.0613098	+	0.0363565i
$582$	8.26877	−	1.20982i	0.342751	−	0.0501485i
$583$	−9.81246	+	5.66523i	−0.406391	+	0.234630i
$584$	−2.07713	−	2.47789i	−0.0859521	−	0.102536i
$585$	−32.7151	−	18.8881i	−1.35260	−	0.780925i
$586$	−2.95185	+	2.33323i	−0.121940	+	0.0963850i
$587$	20.1643	−	20.1643i	0.832268	−	0.832268i	−0.155559	−	0.987827i	$-0.549718\pi$
$587$	20.1643	−	20.1643i	0.832268	−	0.832268i	0.987827	+	0.155559i	$0.0497178\pi$
$588$	10.8355	+	5.52489i	0.446849	+	0.227842i
$589$	−2.36466	−	2.36466i	−0.0974341	−	0.0974341i
$590$	−2.03440	+	17.3808i	−0.0837548	+	0.715555i
$591$	4.76342	−	8.25049i	0.195941	−	0.339380i
$592$	−17.2258	−	15.3499i	−0.707977	−	0.630876i
$593$	−4.20461	−	7.28261i	−0.172663	−	0.299061i	0.766687	−	0.642021i	$-0.221904\pi$
$593$	−4.20461	−	7.28261i	−0.172663	−	0.299061i	−0.939350	+	0.342960i	$0.888570\pi$
$594$	15.3593	+	11.4385i	0.630199	+	0.469326i
$595$	−16.0735	−	27.1055i	−0.658949	−	1.11122i
$596$	20.6795	+	11.1590i	0.847065	+	0.457091i
$597$	9.60607	+	2.57394i	0.393150	+	0.105344i
$598$	41.6104	+	16.5386i	1.70157	+	0.676314i
$599$	−3.08368	−	1.78037i	−0.125996	−	0.0727438i	0.435677	−	0.900103i	$-0.356509\pi$
$599$	−3.08368	−	1.78037i	−0.125996	−	0.0727438i	−0.561673	+	0.827359i	$0.689842\pi$
$600$	11.5181	+	8.07344i	0.470223	+	0.329597i
$601$			45.3712i			1.85073i	0.379076	+	0.925365i	$0.376242\pi$
$601$			45.3712i			1.85073i	−0.379076	+	0.925365i	$0.623758\pi$
$602$	−6.27479	−	14.0989i	−0.255741	−	0.574627i
$603$	−9.67096	+	9.67096i	−0.393832	+	0.393832i
$604$	−28.5150	−	26.9202i	−1.16026	−	1.09537i
$605$	−6.86180	+	1.83861i	−0.278972	+	0.0747502i
$606$	−1.54947	−	3.59368i	−0.0629428	−	0.145983i
$607$	2.45090	+	4.24508i	0.0994789	+	0.172302i	0.911469	−	0.411369i	$-0.134949\pi$
$607$	2.45090	+	4.24508i	0.0994789	+	0.172302i	−0.811990	+	0.583671i	$0.801616\pi$
$608$	7.01759	−	6.23486i	0.284601	−	0.252857i
$609$	−11.5912	+	11.8646i	−0.469699	+	0.480777i
$610$	18.7498	−	25.1768i	0.759158	−	1.01938i
$611$	−13.4720	+	50.2783i	−0.545020	+	2.03404i
$612$	3.77171	−	15.8910i	0.152462	−	0.642354i
$613$	−2.06747	−	7.71591i	−0.0835045	−	0.311643i	0.911522	−	0.411251i	$-0.134908\pi$
$613$	−2.06747	−	7.71591i	−0.0835045	−	0.311643i	−0.995027	+	0.0996077i	$0.968241\pi$
$614$	−4.94817	−	6.26008i	−0.199692	−	0.252636i
$615$		−	10.5620i		−	0.425901i
$616$	20.9803	+	7.37200i	0.845322	+	0.297026i
$617$		−	40.2966i		−	1.62228i	−0.584852	−	0.811140i	$-0.698847\pi$
$617$		−	40.2966i		−	1.62228i	0.584852	−	0.811140i	$-0.301153\pi$
$618$	3.62341	−	2.86406i	0.145755	−	0.115209i
$619$	5.20932	+	19.4415i	0.209380	+	0.781418i	0.988070	+	0.154008i	$0.0492183\pi$
$619$	5.20932	+	19.4415i	0.209380	+	0.781418i	−0.778689	+	0.627410i	$0.784115\pi$
$620$	11.2360	−	6.92538i	0.451247	−	0.278130i
$621$	7.26826	−	27.1255i	0.291665	−	1.08851i
$622$	0.916568	+	0.682592i	0.0367510	+	0.0273695i
$623$	3.10896	+	11.0844i	0.124558	+	0.444086i
$624$	9.80118	+	14.9232i	0.392361	+	0.597406i
$625$	−10.4273	−	18.0606i	−0.417091	−	0.722422i
$626$	−30.2526	+	13.0439i	−1.20914	+	0.521337i
$627$	−4.13817	+	1.10882i	−0.165263	+	0.0442820i
$628$	10.8110	−	0.311032i	0.431405	−	0.0124115i
$629$	14.8348	−	14.8348i	0.591500	−	0.591500i
$630$	−2.87963	+	27.3601i	−0.114727	+	1.09005i
$631$		−	15.2886i		−	0.608631i	−0.952571	−	0.304315i	$-0.901572\pi$
$631$		−	15.2886i		−	0.608631i	0.952571	−	0.304315i	$-0.0984277\pi$
$632$	−0.118231	−	0.672447i	−0.00470297	−	0.0267485i
$633$	9.25190	+	5.34159i	0.367730	+	0.212309i
$634$	1.63110	−	4.10378i	0.0647794	−	0.162982i
$635$	40.7546	+	10.9202i	1.61730	+	0.433354i
$636$	1.89798	+	6.34725i	0.0752599	+	0.251685i
$637$	10.1154	+	34.5123i	0.400786	+	1.36743i
$638$	−18.1138	+	24.3228i	−0.717133	+	0.962948i
$639$	10.7229	+	18.5726i	0.424192	+	0.734722i
$640$	17.5466	+	32.6315i	0.693591	+	1.28987i
$641$	6.18366	−	10.7104i	0.244240	−	0.423036i	−0.717678	−	0.696375i	$-0.754795\pi$
$641$	6.18366	−	10.7104i	0.244240	−	0.423036i	0.961918	+	0.273340i	$0.0881283\pi$
$642$	−0.462819	−	0.0541725i	−0.0182660	−	0.00213802i
$643$	−29.2082	−	29.2082i	−1.15186	−	1.15186i	−0.986180	−	0.165677i	$-0.947019\pi$
$643$	−29.2082	−	29.2082i	−1.15186	−	1.15186i	−0.165677	−	0.986180i	$-0.552981\pi$
$644$	−1.31763	−	32.5829i	−0.0519220	−	1.28394i
$645$	−8.29724	+	8.29724i	−0.326703	+	0.326703i
$646$	5.29300	+	6.69634i	0.208250	+	0.263464i
$647$	−12.4455	−	7.18540i	−0.489282	−	0.282487i	0.234994	−	0.971997i	$-0.424493\pi$
$647$	−12.4455	−	7.18540i	−0.489282	−	0.282487i	−0.724277	+	0.689509i	$0.757826\pi$
$648$	−6.01905	+	5.04556i	−0.236451	+	0.198208i
$649$	9.72423	−	5.61429i	0.381710	−	0.220380i
$650$	6.02117	+	41.1531i	0.236170	+	1.61416i
$651$	−4.03820	−	2.26912i	−0.158270	−	0.0889337i
$652$	10.7132	−	19.8534i	0.419563	−	0.777519i
$653$	3.79601	−	14.1669i	0.148549	−	0.554393i	−0.851022	−	0.525129i	$-0.824017\pi$
$653$	3.79601	−	14.1669i	0.148549	−	0.554393i	0.999572	−	0.0292641i	$-0.00931639\pi$
$654$	−11.2790	+	4.86312i	−0.441046	+	0.190163i
$655$	−15.2147	+	26.3527i	−0.594489	+	1.02968i
$656$	6.67324	−	13.2659i	0.260546	−	0.517946i
$657$	−2.56666			−0.100135
$658$	37.4420	−	5.92472i	1.45964	−	0.230969i
$659$	−30.0445	−	30.0445i	−1.17037	−	1.17037i	−0.982122	−	0.188248i	$-0.939719\pi$
$659$	−30.0445	−	30.0445i	−1.17037	−	1.17037i	−0.188248	−	0.982122i	$-0.560281\pi$
$660$	−0.486268	−	16.9019i	−0.0189279	−	0.657905i
$661$	−0.717370	−	2.67726i	−0.0279025	−	0.104133i	0.950570	−	0.310509i	$-0.100500\pi$
$661$	−0.717370	−	2.67726i	−0.0279025	−	0.104133i	−0.978473	+	0.206376i	$0.933833\pi$
$662$	−20.7028	−	8.22860i	−0.804636	−	0.319814i
$663$	−14.0593	+	8.11714i	−0.546018	+	0.315244i
$664$	0.775420	+	1.66502i	0.0300921	+	0.0646154i
$665$	−10.2845	−	10.0475i	−0.398815	−	0.389625i
$666$	−18.1224	+	2.65152i	−0.702230	+	0.102744i
$667$	42.9556	+	11.5099i	1.66325	+	0.445666i
$668$	−10.0738	+	42.4430i	−0.389768	+	1.64217i
$669$	−18.4182	+	4.93515i	−0.712089	+	0.190804i
$670$	28.0197	+	3.27968i	1.08250	+	0.126705i
$671$	−20.1425			−0.777592
$672$	7.02685	−	10.9403i	0.271066	−	0.422030i
$673$	−4.79538			−0.184848			−0.0924242	−	0.995720i	$-0.529462\pi$
$673$	−4.79538			−0.184848			−0.0924242	+	0.995720i	$0.529462\pi$
$674$	7.52969	+	0.881342i	0.290033	+	0.0339480i
$675$	25.1958	−	6.75119i	0.969786	−	0.259854i
$676$	−6.18733	+	26.0684i	−0.237974	+	1.00263i
$677$	−48.0358	−	12.8711i	−1.84616	−	0.494678i	−0.846855	−	0.531824i	$-0.821507\pi$
$677$	−48.0358	−	12.8711i	−1.84616	−	0.494678i	−0.999310	+	0.0371454i	$0.988174\pi$
$678$	3.18527	−	0.466042i	0.122330	−	0.0178982i
$679$	4.45474	−	17.4357i	0.170957	−	0.669120i
$680$	−30.5394	+	14.2225i	−1.17113	+	0.545409i
$681$	−18.5603	+	10.7158i	−0.711234	+	0.410631i
$682$	−7.87018	−	3.12811i	−0.301365	−	0.119782i
$683$	−1.06566	−	3.97711i	−0.0407764	−	0.152180i	0.942536	−	0.334105i	$-0.108434\pi$
$683$	−1.06566	−	3.97711i	−0.0407764	−	0.152180i	−0.983312	+	0.181925i	$0.941767\pi$
$684$	−0.214297	−	7.44863i	−0.00819386	−	0.284805i
$685$	27.3298	+	27.3298i	1.04422	+	1.04422i
$686$	19.9674	−	16.9500i	0.762359	−	0.647154i
$687$	−8.26579			−0.315360
$688$	−15.6637	+	5.17902i	−0.597172	+	0.197448i
$689$	−9.79469	+	16.9649i	−0.373148	+	0.646311i
$690$	−22.7689	+	9.81713i	−0.866797	+	0.373732i
$691$	9.19198	−	34.3049i	0.349679	−	1.30502i	−0.537370	−	0.843347i	$-0.680582\pi$
$691$	9.19198	−	34.3049i	0.349679	−	1.30502i	0.887049	−	0.461674i	$-0.152751\pi$
$692$	−21.5717	+	39.9759i	−0.820033	+	1.51966i
$693$	15.1838	−	9.00392i	0.576783	−	0.342031i
$694$	3.39951	+	23.2347i	0.129043	+	0.881977i
$695$	−32.7162	+	18.8887i	−1.24100	+	0.716489i
$696$	11.3913	+	13.5892i	0.431787	+	0.515096i
$697$	11.6936	+	6.75130i	0.442927	+	0.255724i
$698$	27.6319	+	34.9579i	1.04588	+	1.32318i
$699$	13.6608	−	13.6608i	0.516701	−	0.516701i
$700$	25.5982	−	16.1924i	0.967521	−	0.612014i
$701$	15.7687	+	15.7687i	0.595575	+	0.595575i	0.939132	−	0.343557i	$-0.111632\pi$
$701$	15.7687	+	15.7687i	0.595575	+	0.595575i	−0.343557	+	0.939132i	$0.611632\pi$
$702$	32.8853	+	3.84918i	1.24117	+	0.145278i
$703$	4.78597	−	8.28955i	0.180506	−	0.312646i
$704$	10.0681	−	21.5360i	0.379457	−	0.811669i
$705$	−14.4119	−	24.9621i	−0.542783	−	0.940129i
$706$	11.5617	−	15.5248i	0.435131	−	0.584283i
$707$	−8.42685	+	0.0982224i	−0.316924	+	0.00369403i
$708$	−1.88092	−	6.29018i	−0.0706892	−	0.236400i
$709$	11.1596	+	2.99021i	0.419108	+	0.112300i	0.462209	−	0.886771i	$-0.347057\pi$
$709$	11.1596	+	2.99021i	0.419108	+	0.112300i	−0.0431009	+	0.999071i	$0.513724\pi$
$710$	16.3390	−	41.1081i	0.613190	−	1.54276i
$711$	−0.469373	−	0.270993i	−0.0176029	−	0.0101630i
$712$	12.1211	−	2.13115i	0.454256	−	0.0798681i
$713$			12.4190i			0.465095i
$714$	9.56396	+	6.95072i	0.357922	+	0.260124i
$715$	35.3539	−	35.3539i	1.32216	−	1.32216i
$716$	43.0364	−	1.23816i	1.60834	−	0.0462721i
$717$	−12.5522	+	3.36335i	−0.468770	+	0.125607i
$718$	8.21044	−	3.54005i	0.306411	−	0.132113i
$719$	−14.4263	−	24.9871i	−0.538011	−	0.931863i	−0.999011	−	0.0444624i	$-0.985842\pi$
$719$	−14.4263	−	24.9871i	−0.538011	−	0.931863i	0.461000	−	0.887400i	$-0.347491\pi$
$720$	28.7992	+	5.96618i	1.07328	+	0.222347i
$721$	−2.68599	−	9.57638i	−0.100032	−	0.356643i
$722$	−18.4271	−	13.7231i	−0.685784	−	0.510722i
$723$	−5.47519	+	20.4337i	−0.203625	+	0.759938i
$724$	−28.5286	+	17.5839i	−1.06026	+	0.653499i
$725$	10.6911	+	39.8997i	0.397057	+	1.48184i
$726$	2.09090	−	1.65271i	0.0776005	−	0.0613379i
$727$		−	19.1342i		−	0.709648i	−0.934933	−	0.354824i	$-0.884541\pi$
$727$		−	19.1342i		−	0.709648i	0.934933	−	0.354824i	$-0.115459\pi$
$728$	37.7863	−	7.09863i	1.40045	−	0.263093i
$729$		−	5.64199i		−	0.208963i
$730$	3.28298	+	4.15340i	0.121509	+	0.153724i
$731$	−3.88254	−	14.4898i	−0.143601	−	0.535926i
$732$	−2.71979	+	11.4590i	−0.100526	+	0.423538i
$733$	−2.99140	+	11.1641i	−0.110490	+	0.412354i	−0.998910	−	0.0466772i	$-0.985137\pi$
$733$	−2.99140	+	11.1641i	−0.110490	+	0.412354i	0.888420	+	0.459031i	$0.151803\pi$
$734$	−31.4504	+	42.2308i	−1.16085	+	1.55877i
$735$	−17.4745	−	9.55288i	−0.644555	−	0.352363i
$736$	−34.8004	−	2.05541i	−1.28276	−	0.0757636i
$737$	−9.05087	−	15.6766i	−0.333393	−	0.577453i
$738$	−4.66720	−	10.8246i	−0.171802	−	0.398461i
$739$	8.01230	−	2.14689i	0.294737	−	0.0789746i	−0.108420	−	0.994105i	$-0.534579\pi$
$739$	8.01230	−	2.14689i	0.294737	−	0.0789746i	0.403158	+	0.915130i	$0.367913\pi$
$740$	27.4710	+	25.9345i	1.00985	+	0.953371i
$741$	−5.23749	+	5.23749i	−0.192404	+	0.192404i
$742$	14.1880	+	1.49328i	0.520857	+	0.0548199i
$743$			9.24326i			0.339102i	0.985521	+	0.169551i	$0.0542318\pi$
$743$			9.24326i			0.339102i	−0.985521	+	0.169551i	$0.945768\pi$
$744$	−2.84227	+	4.05495i	−0.104203	+	0.148662i
$745$	−33.3210	−	19.2379i	−1.22079	−	0.704821i
$746$	5.68090	+	2.25795i	0.207993	+	0.0826695i
$747$	1.40834	+	0.377363i	0.0515284	+	0.0138070i
$748$	19.0236	+	10.2654i	0.695570	+	0.375341i
$749$	−0.491563	+	0.874803i	−0.0179613	+	0.0319646i
$750$	−2.33695	−	1.74038i	−0.0853332	−	0.0635499i
$751$	10.3379	+	17.9057i	0.377234	+	0.653388i	0.990659	−	0.136365i	$-0.0435421\pi$
$751$	10.3379	+	17.9057i	0.377234	+	0.653388i	−0.613425	+	0.789753i	$0.710209\pi$
$752$	−2.32989	−	40.4581i	−0.0849624	−	1.47536i
$753$	2.15322	−	3.72949i	0.0784677	−	0.135910i
$754$	−6.09551	+	52.0767i	−0.221986	+	1.89652i
$755$	45.4034	+	45.4034i	1.65240	+	1.65240i
$756$	−7.17688	−	23.0200i	−0.261021	−	0.837230i
$757$	19.3612	−	19.3612i	0.703694	−	0.703694i	−0.261508	−	0.965201i	$-0.584220\pi$
$757$	19.3612	−	19.3612i	0.703694	−	0.703694i	0.965201	+	0.261508i	$0.0842197\pi$
$758$	18.0624	−	14.2771i	0.656057	−	0.518569i
$759$	13.7784	+	7.95495i	0.500123	+	0.288746i
$760$	−11.7794	+	9.87424i	−0.427283	+	0.358176i
$761$	15.2778	−	8.82065i	0.553821	−	0.319748i	−0.196841	−	0.980435i	$-0.563068\pi$
$761$	15.2778	−	8.82065i	0.553821	−	0.319748i	0.750662	+	0.660687i	$0.229735\pi$
$762$	−15.6628	+	2.29165i	−0.567404	+	0.0830178i
$763$	0.308278	+	26.4483i	0.0111604	+	0.957492i
$764$	−4.51966	−	15.1147i	−0.163516	−	0.546831i
$765$	−6.92149	+	25.8313i	−0.250247	+	0.933934i
$766$	−11.0455	−	25.6180i	−0.399092	−	0.925615i
$767$	9.70662	−	16.8124i	0.350486	−	0.607059i
$768$	−10.8923	−	8.63570i	−0.393043	−	0.311614i
$769$	−33.4127			−1.20489			−0.602447	−	0.798159i	$-0.705807\pi$
$769$	−33.4127			−1.20489			−0.602447	+	0.798159i	$0.705807\pi$
$770$	−33.9917	−	13.0538i	−1.22498	−	0.470426i
$771$	3.99122	+	3.99122i	0.143740	+	0.143740i
$772$	−34.1603	+	36.1841i	−1.22945	+	1.30229i
$773$	−3.46760	−	12.9412i	−0.124721	−	0.465464i	0.875109	−	0.483926i	$-0.160790\pi$
$773$	−3.46760	−	12.9412i	−0.124721	−	0.465464i	−0.999830	+	0.0184619i	$0.994123\pi$
$774$	−4.83713	+	12.1700i	−0.173867	+	0.437441i
$775$	−9.99003	+	5.76774i	−0.358852	+	0.207183i
$776$	−18.0748	−	6.58874i	−0.648849	−	0.236522i
$777$	3.28203	−	12.8457i	0.117742	−	0.460838i
$778$	1.21574	+	8.30927i	0.0435865	+	0.297902i
$779$	5.95068	+	1.59448i	0.213205	+	0.0571281i
$780$	−15.3390	−	24.8865i	−0.549225	−	0.891081i
$781$	−27.4171	+	7.34640i	−0.981062	+	0.262875i
$782$	3.68511	−	31.4835i	0.131779	−	1.12585i
$783$	32.8837			1.17517
$784$	−15.9123	−	23.0391i	−0.568296	−	0.822824i
$785$	−17.7091			−0.632066
$786$	1.32722	−	11.3390i	0.0473404	−	0.404450i
$787$	9.30456	−	2.49315i	0.331672	−	0.0888712i	−0.0891401	−	0.996019i	$-0.528412\pi$
$787$	9.30456	−	2.49315i	0.331672	−	0.0888712i	0.420812	+	0.907148i	$0.361745\pi$
$788$	−18.6703	+	11.5076i	−0.665102	+	0.409941i
$789$	20.7578	+	5.56203i	0.738997	+	0.198014i
$790$	0.161846	+	1.10617i	0.00575821	+	0.0393558i
$791$	1.71604	−	6.71652i	0.0610154	−	0.238812i
$792$	−7.96706	−	17.1073i	−0.283097	−	0.607882i
$793$	−30.1590	+	17.4123i	−1.07098	+	0.618329i
$794$	13.3576	−	33.6071i	0.474044	−	1.19267i
$795$	−2.80758	−	10.4780i	−0.0995744	−	0.371617i
$796$	−16.6476	−	15.7165i	−0.590059	−	0.557056i
$797$	3.47475	+	3.47475i	0.123082	+	0.123082i	0.765965	−	0.642883i	$-0.222262\pi$
$797$	3.47475	+	3.47475i	0.123082	+	0.123082i	−0.642883	+	0.765965i	$0.722262\pi$
$798$	5.03568	+	1.93385i	0.178261	+	0.0684574i
$799$	36.8487			1.30361
$800$	−14.5089	−	28.9486i	−0.512967	−	1.02349i
$801$	4.88472	−	8.46059i	0.172593	−	0.298940i
$802$	2.01739	+	4.67893i	0.0712365	+	0.165219i
$803$	0.879223	−	3.28131i	0.0310271	−	0.115795i
$804$	−10.1405	+	3.03225i	−0.357627	+	0.106939i
$805$	0.622318	+	53.3909i	0.0219338	+	1.88178i
$806$	−14.4880	+	2.11976i	−0.510318	+	0.0746654i
$807$	−1.12744	+	0.650930i	−0.0396879	+	0.0229138i
$808$	−0.789610	+	8.97462i	−0.0277784	+	0.315726i
$809$	38.9261	+	22.4740i	1.36857	+	0.790144i	0.990745	−	0.135734i	$-0.0433391\pi$
$809$	38.9261	+	22.4740i	1.36857	+	0.790144i	0.377824	+	0.925877i	$0.376672\pi$
$810$	10.0891	−	7.97471i	0.354493	−	0.280203i
$811$	−23.3543	+	23.3543i	−0.820080	+	0.820080i	−0.986119	−	0.166039i	$-0.946902\pi$
$811$	−23.3543	+	23.3543i	−0.820080	+	0.820080i	0.166039	+	0.986119i	$0.446902\pi$
$812$	36.4542	−	11.3652i	1.27929	−	0.398841i
$813$	−4.52285	−	4.52285i	−0.158623	−	0.158623i
$814$	2.81815	−	24.0767i	0.0987760	−	0.843887i
$815$	−18.4694	+	31.9899i	−0.646953	+	1.12056i
$816$	8.40869	−	9.43635i	0.294363	−	0.330338i
$817$	−3.42212	−	5.92728i	−0.119725	−	0.207369i
$818$	17.3900	+	12.9508i	0.608026	+	0.452813i
$819$	14.9509	−	26.6071i	0.522426	−	0.929728i
$820$	−11.5468	+	21.3982i	−0.403233	+	0.747259i
$821$	31.0690	+	8.32491i	1.08432	+	0.290541i	0.756362	−	0.654153i	$-0.226975\pi$
$821$	31.0690	+	8.32491i	1.08432	+	0.290541i	0.327953	+	0.944694i	$0.393641\pi$
$822$	−13.4753	−	5.35593i	−0.470004	−	0.186810i
$823$	5.60251	+	3.23461i	0.195291	+	0.112751i	0.594457	−	0.804127i	$-0.297367\pi$
$823$	5.60251	+	3.23461i	0.195291	+	0.112751i	−0.399166	+	0.916879i	$0.630700\pi$
$824$	−10.4720	+	1.84121i	−0.364810	+	0.0641415i
$825$			14.7781i			0.514506i
$826$	−14.0604	−	1.47985i	−0.489224	−	0.0514905i
$827$	0.313180	−	0.313180i	0.0108903	−	0.0108903i	−0.701641	−	0.712531i	$-0.747549\pi$
$827$	0.313180	−	0.313180i	0.0108903	−	0.0108903i	0.712531	+	0.701641i	$0.247549\pi$
$828$	−18.9970	+	20.1225i	−0.660192	+	0.699305i
$829$	−27.5710	+	7.38763i	−0.957581	+	0.256583i	−0.703576	−	0.710620i	$-0.748415\pi$
$829$	−27.5710	+	7.38763i	−0.957581	+	0.256583i	−0.254005	+	0.967203i	$0.581748\pi$
$830$	−1.19074	−	2.76168i	−0.0413311	−	0.0958593i
$831$	1.96723	+	3.40735i	0.0682425	+	0.118200i
$832$	−3.54213	−	40.9490i	−0.122801	−	1.41965i
$833$	21.7462	−	13.2404i	0.753460	−	0.458752i
$834$	8.46552	−	11.3673i	0.293137	−	0.393617i
$835$	18.4865	−	68.9927i	0.639753	−	2.38759i
$836$	9.59600	+	2.27761i	0.331885	+	0.0787727i
$837$	2.37677	+	8.87022i	0.0821531	+	0.306600i
$838$	21.4493	+	27.1362i	0.740955	+	0.937406i
$839$			49.1079i			1.69539i	0.530482	+	0.847696i	$0.322011\pi$
$839$			49.1079i			1.69539i	−0.530482	+	0.847696i	$0.677989\pi$
$840$	−12.0161	+	17.5752i	−0.414595	+	0.606402i
$841$			23.0742i			0.795662i
$842$	−28.6239	+	22.6253i	−0.986446	+	0.779718i
$843$	2.18755	+	8.16403i	0.0753431	+	0.281184i
$844$	−12.9044	−	20.9365i	−0.444186	−	0.720662i
$845$	11.3544	−	42.3752i	0.390603	−	1.45775i
$846$	−25.8007	−	19.2145i	−0.887046	−	0.660606i
$847$	−1.54996	−	5.52607i	−0.0532572	−	0.189878i
$848$	3.09385	−	14.9343i	0.106243	−	0.512845i
$849$	−1.74738	−	3.02655i	−0.0599698	−	0.103871i
$850$	27.0373	−	11.6575i	0.927371	−	0.399849i
$851$	−34.3357	+	9.20023i	−1.17701	+	0.315380i
$852$	0.477281	+	16.5895i	0.0163514	+	0.568348i
$853$	4.33966	−	4.33966i	0.148587	−	0.148587i	−0.628899	−	0.777487i	$-0.716494\pi$
$853$	4.33966	−	4.33966i	0.148587	−	0.148587i	0.777487	+	0.628899i	$0.216494\pi$
$854$	20.5159	+	14.9102i	0.702040	+	0.510216i
$855$			12.2014i			0.417278i
$856$	0.878431	+	0.615726i	0.0300242	+	0.0210451i
$857$	−14.0065	−	8.08667i	−0.478454	−	0.276235i	0.241318	−	0.970446i	$-0.422420\pi$
$857$	−14.0065	−	8.08667i	−0.478454	−	0.276235i	−0.719772	+	0.694211i	$0.755754\pi$
$858$	−6.92846	+	17.4317i	−0.236534	+	0.595107i
$859$	−43.0148	−	11.5258i	−1.46765	−	0.393254i	−0.565522	−	0.824733i	$-0.691325\pi$
$859$	−43.0148	−	11.5258i	−1.46765	−	0.393254i	−0.902123	+	0.431479i	$0.857992\pi$
$860$	25.8808	−	7.73899i	0.882528	−	0.263897i
$861$	8.53264	−	0.0994554i	0.290791	−	0.00338943i
$862$	28.3983	−	38.1325i	0.967249	−	1.29880i
$863$	−2.85176	−	4.93940i	−0.0970752	−	0.168139i	0.813398	−	0.581708i	$-0.197615\pi$
$863$	−2.85176	−	4.93940i	−0.0970752	−	0.168139i	−0.910473	+	0.413569i	$0.864282\pi$
$864$	−25.2494	+	5.19208i	−0.859002	+	0.176638i
$865$	37.1891	−	64.4134i	1.26447	−	2.19012i
$866$	−37.2943	−	4.36526i	−1.26731	−	0.148338i
$867$	−2.31679	−	2.31679i	−0.0786822	−	0.0786822i
$868$	5.70055	+	9.01189i	0.193489	+	0.305883i
$869$	0.507233	−	0.507233i	0.0172067	−	0.0172067i
$870$	−18.0044	−	22.7780i	−0.610407	−	0.772245i
$871$	−27.1034	−	15.6482i	−0.918364	−	0.530218i
$872$	28.1675	+	2.47825i	0.953872	+	0.0839241i
$873$	−13.2256	+	7.63580i	−0.447619	+	0.258433i
$874$	−2.09374	−	14.3101i	−0.0708217	−	0.484047i
$875$	−5.39708	+	3.20045i	−0.182455	+	0.108195i
$876$	−1.74801	−	0.943255i	−0.0590598	−	0.0318696i
$877$	4.09303	−	15.2754i	0.138212	−	0.515814i	−0.861752	−	0.507330i	$-0.830633\pi$
$877$	4.09303	−	15.2754i	0.138212	−	0.515814i	0.999964	−	0.00848425i	$-0.00270065\pi$
$878$	−25.4672	+	10.9805i	−0.859476	+	0.370575i
$879$	−1.15571	+	2.00176i	−0.0389813	+	0.0675175i
$880$	−17.4927	+	34.7742i	−0.589680	+	1.17224i
$881$	20.6047			0.694190			0.347095	−	0.937830i	$-0.387168\pi$
$881$	20.6047			0.694190			0.347095	+	0.937830i	$0.387168\pi$
$882$	−22.1303	−	2.06871i	−0.745165	−	0.0696572i
$883$	3.92964	+	3.92964i	0.132243	+	0.132243i	0.770130	−	0.637887i	$-0.220191\pi$
$883$	3.92964	+	3.92964i	0.132243	+	0.132243i	−0.637887	+	0.770130i	$0.720191\pi$
$884$	37.3577	−	1.07478i	1.25647	−	0.0361488i
$885$	2.78233	+	10.3838i	0.0935270	+	0.349048i
$886$	8.96545	+	3.56344i	0.301200	+	0.119716i
$887$	−16.0874	+	9.28808i	−0.540163	+	0.311863i	−0.745145	−	0.666903i	$-0.767620\pi$
$887$	−16.0874	+	9.28808i	−0.540163	+	0.311863i	0.204982	+	0.978766i	$0.434286\pi$
$888$	−13.3166	−	4.85425i	−0.446877	−	0.162898i
$889$	−8.43823	+	33.0269i	−0.283009	+	1.10769i
$890$	−19.9391	+	2.91732i	−0.668359	+	0.0977887i
$891$	−7.97063	−	2.13573i	−0.267026	−	0.0715495i
$892$	42.7100	+	10.1372i	1.43004	+	0.339418i
$893$	16.2394	−	4.35135i	0.543432	−	0.145612i
$894$	14.3373	+	1.67817i	0.479512	+	0.0561264i
$895$	−70.4965			−2.35644
$896$	−26.1965	+	14.4825i	−0.875164	+	0.483826i
$897$	27.5068			0.918426
$898$	−8.88301	−	1.03975i	−0.296430	−	0.0346968i
$899$	−14.0468	+	3.76382i	−0.468486	+	0.125530i
$900$	−25.0096	−	5.93602i	−0.833654	−	0.197867i
$901$	13.3952	+	3.58924i	0.446260	+	0.119575i
$902$	15.4374	−	2.25867i	0.514009	−	0.0752055i
$903$	−6.78115	−	6.62489i	−0.225663	−	0.220463i
$904$	−6.96274	−	2.53810i	−0.231577	−	0.0844158i
$905$	47.5212	−	27.4364i	1.57966	−	0.912016i
$906$	−22.3867	−	8.89788i	−0.743747	−	0.295612i
$907$	7.38295	+	27.5535i	0.245147	+	0.914900i	0.973310	+	0.229496i	$0.0737078\pi$
$907$	7.38295	+	27.5535i	0.245147	+	0.914900i	−0.728163	+	0.685404i	$0.759626\pi$
$908$	49.3176	−	1.41887i	1.63666	−	0.0470868i
$909$	5.05701	+	5.05701i	0.167730	+	0.167730i
$910$	−62.1796	+	9.83913i	−2.06123	+	0.326164i
$911$	40.6520			1.34686			0.673431	−	0.739250i	$-0.264820\pi$
$911$	40.6520			1.34686			0.673431	+	0.739250i	$0.264820\pi$
$912$	2.59145	−	5.15161i	0.0858116	−	0.170587i
$913$	−0.964870	+	1.67120i	−0.0319325	+	0.0553088i
$914$	−51.2944	+	22.1163i	−1.69667	+	0.731543i
$915$	4.99111	−	18.6271i	0.165001	−	0.615792i
$916$	16.7462	+	9.03653i	0.553310	+	0.298575i
$917$	−21.4326	−	12.0433i	−0.707767	−	0.397703i
$918$	−3.39329	−	23.1922i	−0.111995	−	0.765458i
$919$	23.3547	−	13.4838i	0.770400	−	0.444790i	−0.0626175	−	0.998038i	$-0.519945\pi$
$919$	23.3547	−	13.4838i	0.770400	−	0.444790i	0.833017	+	0.553247i	$0.186611\pi$
$920$	56.8615	+	5.00282i	1.87467	+	0.164938i
$921$	−4.24519	−	2.45096i	−0.139884	−	0.0807619i
$922$	1.57225	+	1.98911i	0.0517794	+	0.0655078i
$923$	−34.7005	+	34.7005i	−1.14218	+	1.14218i
$924$	13.6498	−	0.551991i	0.449046	−	0.0181592i
$925$	−23.3473	−	23.3473i	−0.767656	−	0.767656i
$926$	20.2865	+	2.37451i	0.666657	+	0.0780314i
$927$	−4.22017	+	7.30954i	−0.138608	+	0.240077i
$928$	−8.22212	−	39.9846i	−0.269904	−	1.31256i
$929$	−7.81601	−	13.5377i	−0.256435	−	0.444159i	0.708849	−	0.705360i	$-0.249215\pi$
$929$	−7.81601	−	13.5377i	−0.256435	−	0.444159i	−0.965284	+	0.261201i	$0.915881\pi$
$930$	4.84292	−	6.50295i	0.158806	−	0.213240i
$931$	8.02015	−	8.40305i	0.262850	−	0.275399i
$932$	−42.6110	+	12.7417i	−1.39577	+	0.417369i
$933$	0.678124	+	0.181703i	0.0222008	+	0.00594868i
$934$	9.07401	−	22.8298i	0.296911	−	0.747013i
$935$	−30.6527	−	17.6974i	−1.00245	−	0.578766i
$936$	−26.7175	−	18.7273i	−0.873288	−	0.612121i
$937$		−	47.9244i		−	1.56562i	−0.622260	−	0.782811i	$-0.713785\pi$
$937$		−	47.9244i		−	1.56562i	0.622260	−	0.782811i	$-0.286215\pi$
$938$	−2.38568	+	22.6670i	−0.0778953	+	0.740103i
$939$	−14.3107	+	14.3107i	−0.467013	+	0.467013i
$940$	1.90826	+	66.3281i	0.0622406	+	2.16338i
$941$	−10.4101	+	2.78937i	−0.339359	+	0.0909309i	−0.424474	−	0.905440i	$-0.639541\pi$
$941$	−10.4101	+	2.78937i	−0.339359	+	0.0909309i	0.0851151	+	0.996371i	$0.472874\pi$
$942$	6.10112	−	2.63058i	0.198785	−	0.0857090i
$943$	−11.4392	−	19.8132i	−0.372511	−	0.645208i
$944$	−3.06604	+	14.8000i	−0.0997910	+	0.481698i
$945$	10.6625	+	38.0151i	0.346852	+	1.23663i
$946$	−13.9016	−	10.3529i	−0.451979	−	0.336601i
$947$	−7.18339	+	26.8088i	−0.233429	+	0.871168i	0.745422	+	0.666593i	$0.232248\pi$
$947$	−7.18339	+	26.8088i	−0.233429	+	0.871168i	−0.978851	+	0.204575i	$0.934419\pi$
$948$	−0.220074	−	0.357055i	−0.00714766	−	0.0115966i
$949$	−1.52010	−	5.67309i	−0.0493446	−	0.184156i
$950$	10.5389	−	8.33028i	0.341927	−	0.270270i
$951$		−	2.71283i		−	0.0879696i
$952$	−11.7774	−	24.5377i	−0.381708	−	0.795270i
$953$			3.58597i			0.116161i	0.998312	+	0.0580805i	$0.0184980\pi$
$953$			3.58597i			0.116161i	−0.998312	+	0.0580805i	$0.981502\pi$
$954$	−7.50747	−	9.49794i	−0.243063	−	0.307507i
$955$	6.68567	+	24.9513i	0.216343	+	0.807404i
$956$	29.1072	+	6.90859i	0.941395	+	0.223440i
$957$	−4.82181	+	17.9952i	−0.155867	+	0.581703i
$958$	−4.04346	+	5.42945i	−0.130638	+	0.175418i
$959$	−21.8213	+	22.3360i	−0.704648	+	0.721268i
$960$	17.4210	+	14.6471i	0.562260	+	0.472732i
$961$	13.4695	+	23.3298i	0.434499	+	0.752574i
$962$	−16.5937	−	38.4857i	−0.535001	−	1.24083i
$963$	0.822535	−	0.220398i	0.0265058	−	0.00710221i
$964$	33.4316	−	35.4122i	1.07676	−	1.14055i
$965$	57.6144	−	57.6144i	1.85467	−	1.85467i
$966$	−8.14528	−	18.3017i	−0.262070	−	0.588847i
$967$			51.9947i			1.67204i	0.548703	+	0.836018i	$0.315122\pi$
$967$			51.9947i			1.67204i	−0.548703	+	0.836018i	$0.684878\pi$
$968$	−6.04290	+	1.06247i	−0.194226	+	0.0341492i
$969$	4.54103	+	2.62177i	0.145879	+	0.0842233i
$970$	29.2731	+	11.6350i	0.939903	+	0.373577i
$971$	47.9206	+	12.8403i	1.53785	+	0.412064i	0.925569	−	0.378579i	$-0.123587\pi$
$971$	47.9206	+	12.8403i	1.53785	+	0.412064i	0.612277	+	0.790644i	$0.290254\pi$
$972$	−15.2754	+	28.3078i	−0.489958	+	0.907973i
$973$	−15.5675	−	26.2523i	−0.499072	−	0.841610i
$974$	−30.4768	−	22.6968i	−0.976538	−	0.727254i
$975$	12.7750	+	22.1269i	0.409127	+	0.708629i
$976$	18.0377	−	20.2422i	0.577373	−	0.647936i
$977$	−2.83541	+	4.91108i	−0.0907129	+	0.157119i	−0.907811	−	0.419379i	$-0.862248\pi$
$977$	−2.83541	+	4.91108i	−0.0907129	+	0.157119i	0.817098	+	0.576498i	$0.195581\pi$
$978$	1.61113	−	13.7646i	0.0515182	−	0.440143i
$979$	9.14303	+	9.14303i	0.292213	+	0.292213i
$980$	24.9590	+	38.4577i	0.797286	+	1.22848i
$981$	15.8718	−	15.8718i	0.506748	−	0.506748i
$982$	18.4480	−	14.5819i	0.588699	−	0.465327i
$983$	40.4834	+	23.3731i	1.29122	+	0.745486i	0.978870	−	0.204482i	$-0.0655510\pi$
$983$	40.4834	+	23.3731i	1.29122	+	0.745486i	0.312349	+	0.949968i	$0.398884\pi$
$984$	0.799523	−	9.08729i	0.0254879	−	0.289692i
$985$	31.0998	−	17.9555i	0.990923	−	0.572110i
$986$	36.7269	−	5.37357i	1.16962	−	0.171129i
$987$	20.0303	−	11.8779i	0.637570	−	0.378077i
$988$	16.3368	−	4.88511i	0.519744	−	0.155416i
$989$	−6.57845	+	24.5511i	−0.209182	+	0.780679i
$990$	12.2342	+	28.3749i	0.388830	+	0.901814i
$991$	−7.20690	+	12.4827i	−0.228935	+	0.396527i	−0.957493	−	0.288457i	$-0.906858\pi$
$991$	−7.20690	+	12.4827i	−0.228935	+	0.396527i	0.728558	+	0.684984i	$0.240191\pi$
$992$	10.1914	−	5.10788i	0.323577	−	0.162175i
$993$	−13.6857			−0.434303
$994$	33.3635	+	12.8125i	1.05823	+	0.406389i
$995$	26.5073	+	26.5073i	0.840339	+	0.840339i
$996$	0.820461	+	0.774572i	0.0259973	+	0.0245432i
$997$	14.7190	+	54.9322i	0.466156	+	1.73972i	0.653027	+	0.757334i	$0.273499\pi$
$997$	14.7190	+	54.9322i	0.466156	+	1.73972i	−0.186871	+	0.982384i	$0.559835\pi$
$998$	10.2949	−	25.9014i	0.325878	−	0.819894i
$999$	−22.7634	+	13.1425i	−0.720203	+	0.415809i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	112.2.w.c.109.1	yes	48
4.3	odd	2		448.2.ba.c.81.8		48
7.2	even	3	inner	112.2.w.c.93.9	yes	48
7.3	odd	6		784.2.m.k.589.8		24
7.4	even	3		784.2.m.j.589.8		24
7.5	odd	6		784.2.x.o.765.9		48
7.6	odd	2		784.2.x.o.557.1		48
8.3	odd	2		896.2.ba.e.417.5		48
8.5	even	2		896.2.ba.f.417.8		48
16.3	odd	4		896.2.ba.e.865.8		48
16.5	even	4	inner	112.2.w.c.53.9	yes	48
16.11	odd	4		448.2.ba.c.305.5		48
16.13	even	4		896.2.ba.f.865.5		48
28.23	odd	6		448.2.ba.c.401.5		48
56.37	even	6		896.2.ba.f.289.5		48
56.51	odd	6		896.2.ba.e.289.8		48
112.5	odd	12		784.2.x.o.373.1		48
112.37	even	12	inner	112.2.w.c.37.1	✓	48
112.51	odd	12		896.2.ba.e.737.5		48
112.53	even	12		784.2.m.j.197.8		24
112.69	odd	4		784.2.x.o.165.9		48
112.93	even	12		896.2.ba.f.737.8		48
112.101	odd	12		784.2.m.k.197.8		24
112.107	odd	12		448.2.ba.c.177.8		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
112.2.w.c.37.1	✓	48	112.37	even	12	inner
112.2.w.c.53.9	yes	48	16.5	even	4	inner
112.2.w.c.93.9	yes	48	7.2	even	3	inner
112.2.w.c.109.1	yes	48	1.1	even	1	trivial
448.2.ba.c.81.8		48	4.3	odd	2
448.2.ba.c.177.8		48	112.107	odd	12
448.2.ba.c.305.5		48	16.11	odd	4
448.2.ba.c.401.5		48	28.23	odd	6
784.2.m.j.197.8		24	112.53	even	12
784.2.m.j.589.8		24	7.4	even	3
784.2.m.k.197.8		24	112.101	odd	12
784.2.m.k.589.8		24	7.3	odd	6
784.2.x.o.165.9		48	112.69	odd	4
784.2.x.o.373.1		48	112.5	odd	12
784.2.x.o.557.1		48	7.6	odd	2
784.2.x.o.765.9		48	7.5	odd	6
896.2.ba.e.289.8		48	56.51	odd	6
896.2.ba.e.417.5		48	8.3	odd	2
896.2.ba.e.737.5		48	112.51	odd	12
896.2.ba.e.865.8		48	16.3	odd	4
896.2.ba.f.289.5		48	56.37	even	6
896.2.ba.f.417.8		48	8.5	even	2
896.2.ba.f.737.8		48	112.93	even	12
896.2.ba.f.865.5		48	16.13	even	4

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 112 = 2^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	112.w (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.40462 - 0.164410i) q^{2} +(-0.839165 + 0.224854i) q^{3} +(1.94594 + 0.461868i) q^{4} +(-3.16320 - 0.847576i) q^{5} +(1.21568 - 0.177868i) q^{6} +(0.654939 - 2.56341i) q^{7} +(-2.65738 - 0.968682i) q^{8} +(-1.94444 + 1.12262i) q^{9} +(4.30375 + 1.71059i) q^{10} +(-0.769121 - 2.87040i) q^{11} +(-1.73682 + 0.0499683i) q^{12} +(-3.63293 - 3.63293i) q^{13} +(-1.34139 + 3.49295i) q^{14} +2.84503 q^{15} +(3.57336 + 1.79753i) q^{16} +(-1.81856 + 3.14984i) q^{17} +(2.91577 - 1.25718i) q^{18} +(-0.429496 + 1.60290i) q^{19} +(-5.76392 - 3.11031i) q^{20} +(0.0267897 + 2.29839i) q^{21} +(0.608405 + 4.15828i) q^{22} +(5.33698 - 3.08131i) q^{23} +(2.44779 + 0.215363i) q^{24} +(4.95730 + 2.86210i) q^{25} +(4.50561 + 5.70019i) q^{26} +(3.22221 - 3.22221i) q^{27} +(2.45843 - 4.68574i) q^{28} +(5.10266 + 5.10266i) q^{29} +(-3.99619 - 0.467750i) q^{30} +(-1.00761 + 1.74523i) q^{31} +(-4.72369 - 3.11235i) q^{32} +(1.29084 + 2.23580i) q^{33} +(3.07226 - 4.12535i) q^{34} +(-4.24438 + 7.55345i) q^{35} +(-4.30226 + 1.28648i) q^{36} +(-5.57162 - 1.49291i) q^{37} +(0.866812 - 2.18086i) q^{38} +(3.86550 + 2.23175i) q^{39} +(7.58478 + 5.31646i) q^{40} -3.71244i q^{41} +(0.340248 - 3.23278i) q^{42} +(-2.91640 + 2.91640i) q^{43} +(-0.170919 - 5.94085i) q^{44} +(7.10214 - 1.90301i) q^{45} +(-8.00305 + 3.45063i) q^{46} +(-5.06565 - 8.77396i) q^{47} +(-3.40282 - 0.704944i) q^{48} +(-6.14211 - 3.35775i) q^{49} +(-6.49259 - 4.83520i) q^{50} +(0.817820 - 3.05215i) q^{51} +(-5.39152 - 8.74739i) q^{52} +(-0.986836 - 3.68292i) q^{53} +(-5.05576 + 3.99624i) q^{54} +9.73153i q^{55} +(-4.22354 + 6.17751i) q^{56} -1.44167i q^{57} +(-6.32839 - 8.00624i) q^{58} +(0.977963 + 3.64981i) q^{59} +(5.53625 + 1.31403i) q^{60} +(1.75433 - 6.54724i) q^{61} +(1.70224 - 2.28573i) q^{62} +(1.60425 + 5.71963i) q^{63} +(6.12331 + 5.14831i) q^{64} +(8.41248 + 14.5708i) q^{65} +(-1.44556 - 3.35269i) q^{66} +(5.88390 - 1.57659i) q^{67} +(-4.99362 + 5.28946i) q^{68} +(-3.78577 + 3.78577i) q^{69} +(7.20362 - 9.91194i) q^{70} -9.55168i q^{71} +(6.25456 - 1.09969i) q^{72} +(0.990000 + 0.571577i) q^{73} +(7.58058 + 3.01301i) q^{74} +(-4.80355 - 1.28711i) q^{75} +(-1.57610 + 2.92078i) q^{76} +(-7.86173 + 0.0916354i) q^{77} +(-5.06266 - 3.77030i) q^{78} +(0.120696 + 0.209052i) q^{79} +(-9.77969 - 8.71464i) q^{80} +(1.38842 - 2.40481i) q^{81} +(-0.610362 + 5.21459i) q^{82} +(-0.459183 - 0.459183i) q^{83} +(-1.00942 + 4.48490i) q^{84} +(8.42219 - 8.42219i) q^{85} +(4.57593 - 3.61696i) q^{86} +(-5.42932 - 3.13462i) q^{87} +(-0.736657 + 8.37277i) q^{88} +(-3.76823 + 2.17559i) q^{89} +(-10.2887 + 1.50536i) q^{90} +(-11.6920 + 6.93333i) q^{91} +(11.8086 - 3.53106i) q^{92} +(0.453128 - 1.69110i) q^{93} +(5.67281 + 13.1570i) q^{94} +(2.71716 - 4.70626i) q^{95} +(4.66378 + 1.54964i) q^{96} +6.80176 q^{97} +(8.07531 + 5.72620i) q^{98} +(4.71788 + 4.71788i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 4 q^{2} - 4 q^{4} + 4 q^{5} - 4 q^{6} - 4 q^{8} - 2 q^{10} - 4 q^{11} + 2 q^{12} - 24 q^{13} - 34 q^{14} - 40 q^{15} + 16 q^{16} + 8 q^{17} + 18 q^{18} - 4 q^{19} - 16 q^{20} - 8 q^{21} + 18 q^{24}+ \cdots - 24 q^{99}+O(q^{100}) \) 48 * q - 4 * q^2 - 4 * q^4 + 4 * q^5 - 4 * q^6 - 4 * q^8 - 2 * q^10 - 4 * q^11 + 2 * q^12 - 24 * q^13 - 34 * q^14 - 40 * q^15 + 16 * q^16 + 8 * q^17 + 18 * q^18 - 4 * q^19 - 16 * q^20 - 8 * q^21 + 18 * q^24 - 10 * q^26 - 24 * q^27 - 10 * q^28 + 24 * q^29 - 4 * q^30 + 28 * q^31 + 16 * q^32 + 16 * q^33 - 44 * q^34 + 28 * q^35 - 72 * q^36 - 24 * q^37 + 20 * q^38 + 26 * q^40 + 6 * q^42 - 40 * q^43 + 6 * q^44 - 28 * q^45 - 14 * q^46 - 20 * q^47 + 56 * q^48 + 56 * q^50 + 24 * q^51 - 16 * q^52 - 16 * q^53 + 64 * q^54 + 40 * q^56 - 6 * q^58 - 20 * q^59 + 46 * q^60 + 8 * q^61 + 24 * q^62 - 16 * q^63 + 80 * q^64 + 8 * q^65 - 20 * q^66 + 48 * q^67 - 40 * q^69 + 82 * q^70 - 32 * q^72 - 8 * q^74 - 4 * q^75 - 36 * q^76 - 20 * q^77 + 116 * q^78 - 36 * q^79 - 28 * q^80 + 2 * q^82 - 8 * q^83 + 28 * q^84 - 20 * q^86 - 42 * q^88 - 20 * q^90 + 64 * q^91 + 76 * q^92 + 8 * q^93 - 72 * q^94 - 4 * q^95 - 120 * q^96 - 48 * q^97 - 2 * q^98 - 24 * q^99

Introduction

L-functions

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