LMFDB - Embedded newform 112.2.w.c.93.9

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			93.9
Character	$\chi$	$=$	112.93
Dual form			112.2.w.c.53.9

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.559929 + 1.29865i) q^{2} +(0.224854 - 0.839165i) q^{3} +(-1.37296 + 1.45430i) q^{4} +(0.847576 + 3.16320i) 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} +(-3.63329 + 2.87187i) q^{10} +(2.87040 + 0.769121i) q^{11} +(0.911683 + 1.47914i) q^{12} +(-3.63293 - 3.63293i) q^{13} +(2.96224 - 2.28586i) q^{14} +2.84503 q^{15} +(-0.229970 - 3.99338i) q^{16} +(-1.81856 - 3.14984i) q^{17} +(-0.369139 + 3.15372i) q^{18} +(1.60290 - 0.429496i) q^{19} +(-5.76392 - 3.11031i) q^{20} +(-2.29839 - 0.0267897i) q^{21} +(0.608405 + 4.15828i) q^{22} +(-5.33698 - 3.08131i) q^{23} +(-1.41041 + 2.01217i) q^{24} +(-4.95730 + 2.86210i) q^{25} +(2.68370 - 6.75207i) q^{26} +(3.22221 - 3.22221i) q^{27} +(4.62716 + 2.56698i) q^{28} +(5.10266 + 5.10266i) q^{29} +(1.59301 + 3.69468i) q^{30} +(-1.00761 - 1.74523i) q^{31} +(5.05722 - 2.53466i) q^{32} +(1.29084 - 2.23580i) q^{33} +(3.07226 - 4.12535i) q^{34} +(7.55345 - 4.24438i) q^{35} +(-4.30226 + 1.28648i) q^{36} +(1.49291 + 5.57162i) q^{37} +(1.45527 + 1.84111i) q^{38} +(-3.86550 + 2.23175i) q^{39} +(0.811801 - 9.22684i) q^{40} -3.71244i q^{41} +(-1.25214 - 2.99979i) q^{42} +(-2.91640 + 2.91640i) q^{43} +(-5.05947 + 3.11845i) q^{44} +(-1.90301 + 7.10214i) q^{45} +(1.01319 - 8.65616i) 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} +(-3.05215 + 0.817820i) q^{51} +(10.2712 - 0.295503i) q^{52} +(3.68292 + 0.986836i) q^{53} +(5.98872 + 2.38030i) q^{54} +9.73153i q^{55} +(-0.742706 + 7.44637i) q^{56} -1.44167i q^{57} +(-3.76941 + 9.48367i) q^{58} +(-3.64981 - 0.977963i) q^{59} +(-3.90610 + 4.13752i) q^{60} +(-6.54724 + 1.75433i) 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} +(3.62629 + 0.424453i) q^{66} +(-1.57659 + 5.88390i) q^{67} +(7.07761 + 1.67987i) q^{68} +(-3.78577 + 3.78577i) q^{69} +(9.74134 + 7.43270i) q^{70} -9.55168i q^{71} +(-4.07964 - 4.86677i) q^{72} +(-0.990000 + 0.571577i) q^{73} +(-6.39963 + 5.05847i) q^{74} +(1.28711 + 4.80355i) q^{75} +(-1.57610 + 2.92078i) q^{76} +(0.0916354 - 7.86173i) q^{77} +(-5.06266 - 3.77030i) q^{78} +(0.120696 - 0.209052i) q^{79} +(12.4369 - 4.11214i) q^{80} +(1.38842 + 2.40481i) q^{81} +(4.82115 - 2.07871i) q^{82} +(-0.459183 - 0.459183i) q^{83} +(3.19455 - 3.30576i) q^{84} +(8.42219 - 8.42219i) q^{85} +(-5.42035 - 2.15439i) q^{86} +(5.42932 - 3.13462i) q^{87} +(-6.88270 - 4.82435i) q^{88} +(3.76823 + 2.17559i) q^{89} +(-10.2887 + 1.50536i) q^{90} +(-6.93333 + 11.6920i) q^{91} +(11.8086 - 3.53106i) q^{92} +(-1.69110 + 0.453128i) q^{93} +(-14.2307 - 1.66568i) q^{94} +(2.71716 + 4.70626i) q^{95} +(-0.989865 - 4.81377i) q^{96} +6.80176 q^{97} +(-7.79967 - 6.09632i) 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 $\left(\mathbb{Z}/112\mathbb{Z}\right)^\times$.

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

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 $

$2$	0.559929	+	1.29865i	0.395930	+	0.918281i
$2$	0.559929	+	1.29865i	0.395930	+	0.918281i
$3$	0.224854	−	0.839165i	0.129819	−	0.484492i	−0.870146	−	0.492794i	$-0.835976\pi$
$3$	0.224854	−	0.839165i	0.129819	−	0.484492i	0.999966	+	0.00830125i	$0.00264240\pi$
$4$	−1.37296	+	1.45430i	−0.686479	+	0.727149i
$5$	0.847576	+	3.16320i	0.379048	+	1.41462i	0.847340	+	0.531051i	$0.178203\pi$
$5$	0.847576	+	3.16320i	0.379048	+	1.41462i	−0.468292	+	0.883574i	$0.655131\pi$
$6$	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
$10$	−3.63329	+	2.87187i	−1.14895	+	0.908164i
$11$	2.87040	+	0.769121i	0.865458	+	0.231899i	0.664123	−	0.747624i	$-0.268805\pi$
$11$	2.87040	+	0.769121i	0.865458	+	0.231899i	0.201335	+	0.979522i	$0.435472\pi$
$12$	0.911683	+	1.47914i	0.263180	+	0.426992i
$13$	−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	$-0.502426\pi$
$14$	2.96224	−	2.28586i	0.791691	−	0.610922i
$15$	2.84503			0.734583
$16$	−0.229970	−	3.99338i	−0.0574925	−	0.998346i
$17$	−1.81856	−	3.14984i	−0.441066	−	0.763948i	0.556703	−	0.830711i	$-0.312066\pi$
$17$	−1.81856	−	3.14984i	−0.441066	−	0.763948i	−0.997769	+	0.0667634i	$0.978733\pi$
$18$	−0.369139	+	3.15372i	−0.0870070	+	0.743339i
$19$	1.60290	−	0.429496i	0.367730	−	0.0985331i	−0.0702216	−	0.997531i	$-0.522371\pi$
$19$	1.60290	−	0.429496i	0.367730	−	0.0985331i	0.437952	+	0.898998i	$0.355704\pi$
$20$	−5.76392	−	3.11031i	−1.28885	−	0.695486i
$21$	−2.29839	−	0.0267897i	−0.501549	−	0.00584600i
$22$	0.608405	+	4.15828i	0.129712	+	0.886549i
$23$	−5.33698	−	3.08131i	−1.11284	−	0.642497i	−0.173275	−	0.984874i	$-0.555435\pi$
$23$	−5.33698	−	3.08131i	−1.11284	−	0.642497i	−0.939563	+	0.342377i	$0.888768\pi$
$24$	−1.41041	+	2.01217i	−0.287898	+	0.410732i
$25$	−4.95730	+	2.86210i	−0.991461	+	0.572420i
$26$	2.68370	−	6.75207i	0.526317	−	1.32419i
$27$	3.22221	−	3.22221i	0.620115	−	0.620115i
$28$	4.62716	+	2.56698i	0.874452	+	0.485113i
$29$	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	$0.516289\pi$
$30$	1.59301	+	3.69468i	0.290843	+	0.674553i
$31$	−1.00761	−	1.74523i	−0.180972	−	0.313452i	0.761240	−	0.648470i	$-0.224591\pi$
$31$	−1.00761	−	1.74523i	−0.180972	−	0.313452i	−0.942212	+	0.335018i	$0.891258\pi$
$32$	5.05722	−	2.53466i	0.893999	−	0.448069i
$33$	1.29084	−	2.23580i	0.224706	−	0.389203i
$34$	3.07226	−	4.12535i	0.526888	−	0.707492i
$35$	7.55345	−	4.24438i	1.27677	−	0.717432i
$36$	−4.30226	+	1.28648i	−0.717043	+	0.214413i
$37$	1.49291	+	5.57162i	0.245433	+	0.915969i	0.973165	+	0.230107i	$0.0739077\pi$
$37$	1.49291	+	5.57162i	0.245433	+	0.915969i	−0.727732	+	0.685861i	$0.759426\pi$
$38$	1.45527	+	1.84111i	0.236076	+	0.298668i
$39$	−3.86550	+	2.23175i	−0.618976	+	0.357366i
$40$	0.811801	−	9.22684i	0.128357	−	1.45889i
$41$		−	3.71244i		−	0.579786i	−0.957059	−	0.289893i	$-0.906380\pi$
$41$		−	3.71244i		−	0.579786i	0.957059	−	0.289893i	$-0.0936198\pi$
$42$	−1.25214	−	2.99979i	−0.193210	−	0.462878i
$43$	−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	$0.351831\pi$
$44$	−5.05947	+	3.11845i	−0.762744	+	0.470124i
$45$	−1.90301	+	7.10214i	−0.283685	+	1.05872i
$46$	1.01319	−	8.65616i	0.149387	−	1.27628i
$47$	−5.06565	+	8.77396i	−0.738900	+	1.27981i	0.214090	+	0.976814i	$0.431321\pi$
$47$	−5.06565	+	8.77396i	−0.738900	+	1.27981i	−0.952991	+	0.302999i	$0.902012\pi$
$48$	−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
$51$	−3.05215	+	0.817820i	−0.427386	+	0.114518i
$52$	10.2712	−	0.295503i	1.42436	−	0.0409789i
$53$	3.68292	+	0.986836i	0.505888	+	0.135552i	0.502731	−	0.864443i	$-0.332328\pi$
$53$	3.68292	+	0.986836i	0.505888	+	0.135552i	0.00315690	+	0.999995i	$0.498995\pi$
$54$	5.98872	+	2.38030i	0.814962	+	0.323918i
$55$			9.73153i			1.31220i
$56$	−0.742706	+	7.44637i	−0.0992483	+	0.995063i
$57$		−	1.44167i		−	0.190954i
$58$	−3.76941	+	9.48367i	−0.494948	+	1.24527i
$59$	−3.64981	−	0.977963i	−0.475164	−	0.127320i	0.0132857	−	0.999912i	$-0.495771\pi$
$59$	−3.64981	−	0.977963i	−0.475164	−	0.127320i	−0.488450	+	0.872592i	$0.662438\pi$
$60$	−3.90610	+	4.13752i	−0.504276	+	0.534151i
$61$	−6.54724	+	1.75433i	−0.838288	+	0.224619i	−0.652326	−	0.757938i	$-0.726207\pi$
$61$	−6.54724	+	1.75433i	−0.838288	+	0.224619i	−0.185962	+	0.982557i	$0.559540\pi$
$62$	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
$66$	3.62629	+	0.424453i	0.446365	+	0.0522466i
$67$	−1.57659	+	5.88390i	−0.192611	+	0.718833i	0.800262	+	0.599651i	$0.204694\pi$
$67$	−1.57659	+	5.88390i	−0.192611	+	0.718833i	−0.992872	+	0.119182i	$0.961973\pi$
$68$	7.07761	+	1.67987i	0.858287	+	0.203714i
$69$	−3.78577	+	3.78577i	−0.455753	+	0.455753i
$70$	9.74134	+	7.43270i	1.16431	+	0.888377i
$71$		−	9.55168i		−	1.13358i	−0.823864	−	0.566788i	$-0.808186\pi$
$71$		−	9.55168i		−	1.13358i	0.823864	−	0.566788i	$-0.191814\pi$
$72$	−4.07964	−	4.86677i	−0.480790	−	0.573554i
$73$	−0.990000	+	0.571577i	−0.115871	+	0.0668980i	−0.556815	−	0.830636i	$-0.687977\pi$
$73$	−0.990000	+	0.571577i	−0.115871	+	0.0668980i	0.440945	+	0.897534i	$0.354644\pi$
$74$	−6.39963	+	5.05847i	−0.743942	+	0.588036i
$75$	1.28711	+	4.80355i	0.148622	+	0.554666i
$76$	−1.57610	+	2.92078i	−0.180791	+	0.335036i
$77$	0.0916354	−	7.86173i	0.0104428	−	0.895927i
$78$	−5.06266	−	3.77030i	−0.573233	−	0.426902i
$79$	0.120696	−	0.209052i	0.0135794	−	0.0235202i	−0.859156	−	0.511714i	$-0.829011\pi$
$79$	0.120696	−	0.209052i	0.0135794	−	0.0235202i	0.872735	+	0.488194i	$0.162344\pi$
$80$	12.4369	−	4.11214i	1.39049	−	0.459751i
$81$	1.38842	+	2.40481i	0.154269	+	0.267201i
$82$	4.82115	−	2.07871i	0.532407	−	0.229555i
$83$	−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	$0.761347\pi$
$84$	3.19455	−	3.30576i	0.348554	−	0.360688i
$85$	8.42219	−	8.42219i	0.913515	−	0.913515i
$86$	−5.42035	−	2.15439i	−0.584491	−	0.232314i
$87$	5.42932	−	3.13462i	0.582085	−	0.336067i
$88$	−6.88270	−	4.82435i	−0.733698	−	0.514277i
$89$	3.76823	+	2.17559i	0.399432	+	0.230612i	0.686239	−	0.727376i	$-0.259261\pi$
$89$	3.76823	+	2.17559i	0.399432	+	0.230612i	−0.286807	+	0.957988i	$0.592594\pi$
$90$	−10.2887	+	1.50536i	−1.08453	+	0.158679i
$91$	−6.93333	+	11.6920i	−0.726810	+	1.22566i
$92$	11.8086	−	3.53106i	1.23113	−	0.368138i
$93$	−1.69110	+	0.453128i	−0.175359	+	0.0469872i
$94$	−14.2307	−	1.66568i	−1.46778	−	0.171802i
$95$	2.71716	+	4.70626i	0.278775	+	0.482852i
$96$	−0.989865	−	4.81377i	−0.101028	−	0.491304i
$97$	6.80176			0.690614			0.345307	−	0.938490i	$-0.387775\pi$
$97$	6.80176			0.690614			0.345307	+	0.938490i	$0.387775\pi$
$98$	−7.79967	−	6.09632i	−0.787886	−	0.615821i
$99$	4.71788	+	4.71788i	0.474165	+	0.474165i
$100$	2.64382	−	11.1389i	0.264382	−	1.11389i
$101$	3.07673	+	0.824407i	0.306146	+	0.0820316i	0.408621	−	0.912704i	$-0.366010\pi$
$101$	3.07673	+	0.824407i	0.306146	+	0.0820316i	−0.102475	+	0.994736i	$0.532676\pi$
$102$	−2.77104	−	3.50573i	−0.274374	−	0.347119i
$103$	−3.25557	−	1.87960i	−0.320781	−	0.185203i	0.330960	−	0.943645i	$-0.392628\pi$
$103$	−3.25557	−	1.87960i	−0.320781	−	0.185203i	−0.651741	+	0.758442i	$0.725961\pi$
$104$	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
$107$	0.0981620	+	0.366346i	0.00948968	+	0.0354160i	0.970508	−	0.241068i	$-0.0774975\pi$
$107$	0.0981620	+	0.366346i	0.00948968	+	0.0354160i	−0.961019	+	0.276484i	$0.910831\pi$
$108$	0.262096	+	9.11003i	0.0252202	+	0.876613i
$109$	2.58746	−	9.65655i	0.247834	−	0.924929i	−0.724104	−	0.689691i	$-0.757746\pi$
$109$	2.58746	−	9.65655i	0.247834	−	0.924929i	0.971938	−	0.235238i	$-0.0755870\pi$
$110$	−12.6378	+	5.44897i	−1.20497	+	0.519539i
$111$	5.01120			0.475642
$112$	−10.0861	+	3.20493i	−0.953042	+	0.302837i
$113$	2.62015			0.246483			0.123242	−	0.992377i	$-0.460671\pi$
$113$	2.62015			0.246483			0.123242	+	0.992377i	$0.460671\pi$
$114$	1.87222	−	0.807234i	0.175350	−	0.0756044i
$115$	5.22328	−	19.4936i	0.487074	−	1.81778i
$116$	−14.4265	+	0.415051i	−1.33947	+	0.0385365i
$117$	−2.98560	−	11.1424i	−0.276018	−	1.03012i
$118$	−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
$122$	−5.94424	−	7.52024i	−0.538166	−	0.680851i
$123$	−3.11535	−	0.834757i	−0.280902	−	0.0752675i
$124$	3.92148	+	0.930762i	0.352160	+	0.0835849i
$125$	−1.67697	−	1.67697i	−0.149993	−	0.149993i
$126$	8.32604	−	1.11924i	0.741742	−	0.0997098i
$127$	−12.8840			−1.14327			−0.571635	−	0.820508i	$-0.693691\pi$
$127$	−12.8840			−1.14327			−0.571635	+	0.820508i	$0.693691\pi$
$128$	−3.25720	+	10.8347i	−0.287899	+	0.957661i
$129$	1.79158	+	3.10311i	0.157740	+	0.273213i
$130$	23.6328	+	2.76619i	2.07273	+	0.242611i
$131$	−8.97544	+	2.40496i	−0.784188	+	0.210122i	−0.628630	−	0.777704i	$-0.716384\pi$
$131$	−8.97544	+	2.40496i	−0.784188	+	0.210122i	−0.155557	+	0.987827i	$0.549717\pi$
$132$	1.47925	+	4.94693i	0.128752	+	0.430575i
$133$	−2.15077	−	3.82759i	−0.186496	−	0.331894i
$134$	−8.52388	+	1.24714i	−0.736351	+	0.107737i
$135$	12.9236	+	7.46143i	1.11228	+	0.642177i
$136$	1.78141	+	10.1319i	0.152755	+	0.868805i
$137$	10.2211	−	5.90118i	0.873251	−	0.504172i	0.00482362	−	0.999988i	$-0.498465\pi$
$137$	10.2211	−	5.90118i	0.873251	−	0.504172i	0.868427	+	0.495817i	$0.165131\pi$
$138$	−7.03613	−	2.79661i	−0.598955	−	0.238063i
$139$	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	$0.0872782\pi$
$140$	−4.19798	+	16.8123i	−0.354794	+	1.42090i
$141$	6.22377	+	6.22377i	0.524136	+	0.524136i
$142$	12.4042	−	5.34826i	1.04094	−	0.448816i
$143$	−7.63379	−	13.2221i	−0.638370	−	1.10569i
$144$	4.03589	−	8.02305i	0.336325	−	0.668588i
$145$	−11.8158	+	20.4656i	−0.981250	+	1.69958i
$146$	−1.29660	−	0.965616i	−0.107308	−	0.0799149i
$147$	1.43663	+	5.90925i	0.118491	+	0.487387i
$148$	−10.1525	−	5.47846i	−0.834531	−	0.450327i
$149$	−3.04089	−	11.3488i	−0.249119	−	0.929727i	−0.971268	−	0.237989i	$-0.923512\pi$
$149$	−3.04089	−	11.3488i	−0.249119	−	0.929727i	0.722148	−	0.691738i	$-0.243155\pi$
$150$	−5.51742	+	4.36115i	−0.450495	+	0.356086i
$151$	16.9805	−	9.80371i	1.38186	−	0.797815i	0.389476	−	0.921036i	$-0.372656\pi$
$151$	16.9805	−	9.80371i	1.38186	−	0.797815i	0.992379	+	0.123222i	$0.0393227\pi$
$152$	−4.67556	−	0.411367i	−0.379238	−	0.0333663i
$153$		−	8.16622i		−	0.660199i
$154$	10.2609	−	4.28301i	0.826847	−	0.345135i
$155$	4.66647	−	4.66647i	0.374820	−	0.374820i
$156$	2.06155	−	8.68570i	0.165056	−	0.695412i
$157$	−1.39962	+	5.22347i	−0.111702	+	0.416878i	−0.999019	−	0.0442821i	$-0.985900\pi$
$157$	−1.39962	+	5.22347i	−0.111702	+	0.416878i	0.887317	+	0.461160i	$0.152567\pi$
$158$	0.339066	+	0.0396873i	0.0269747	+	0.00315735i
$159$	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
$163$	−10.8954	+	2.91941i	−0.853394	+	0.228666i	−0.658893	−	0.752236i	$-0.728975\pi$
$163$	−10.8954	+	2.91941i	−0.853394	+	0.228666i	−0.194500	+	0.980902i	$0.562308\pi$
$164$	5.39900	+	5.09703i	0.421591	+	0.398011i
$165$	8.16636	+	2.18817i	0.635750	+	0.170349i
$166$	0.339205	−	0.853425i	0.0263274	−	0.0662386i
$167$			21.8111i			1.68779i	0.536508	+	0.843895i	$0.319743\pi$
$167$			21.8111i			1.68779i	−0.536508	+	0.843895i	$0.680257\pi$
$168$	6.08173	+	2.29760i	0.469216	+	0.177263i
$169$			13.3963i			1.03049i
$170$	15.6533	+	6.22161i	1.20055	+	0.477176i
$171$	3.59890	+	0.964322i	0.275215	+	0.0737435i
$172$	−0.237221	−	8.24541i	−0.0180879	−	0.628707i
$173$	21.9385	−	5.87840i	1.66795	−	0.446927i	0.703396	−	0.710799i	$-0.251666\pi$
$173$	21.9385	−	5.87840i	1.66795	−	0.446927i	0.964558	+	0.263872i	$0.0849996\pi$
$174$	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
$178$	−0.715375	+	6.11177i	−0.0536197	+	0.458096i
$179$	−5.57162	+	20.7936i	−0.416443	+	1.55418i	0.365486	+	0.930817i	$0.380903\pi$
$179$	−5.57162	+	20.7936i	−0.416443	+	1.55418i	−0.781929	+	0.623368i	$0.785764\pi$
$180$	−7.71588	−	12.5185i	−0.575108	−	0.933074i
$181$	−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	$0.463980\pi$
$182$	−19.0660	−	2.45723i	−1.41326	−	0.182142i
$183$			5.88869i			0.435304i
$184$	11.1976	+	13.3580i	0.825496	+	0.984767i
$185$	−16.3588	+	9.44474i	−1.20272	+	0.694391i
$186$	−1.53535	−	1.94242i	−0.112577	−	0.142425i
$187$	−2.79739	−	10.4400i	−0.204565	−	0.763448i
$188$	−5.80503	−	19.4132i	−0.423375	−	1.41586i
$189$	−10.3702	−	6.14949i	−0.754321	−	0.447310i
$190$	−4.59034	+	6.16380i	−0.333018	+	0.447169i
$191$	−3.94400	+	6.83120i	−0.285377	+	0.494288i	−0.972701	−	0.232063i	$-0.925452\pi$
$191$	−3.94400	+	6.83120i	−0.285377	+	0.494288i	0.687323	+	0.726352i	$0.258786\pi$
$192$	5.69713	−	3.98086i	0.411155	−	0.287294i
$193$	−12.4404	−	21.5474i	−0.895478	−	1.55101i	−0.833212	−	0.552954i	$-0.813500\pi$
$193$	−12.4404	−	21.5474i	−0.895478	−	1.55101i	−0.0622664	−	0.998060i	$-0.519833\pi$
$194$	3.80851	+	8.83307i	0.273435	+	0.634178i
$195$	−10.3358	−	10.3358i	−0.740160	−	0.740160i
$196$	3.54969	−	13.5425i	0.253550	−	0.967322i
$197$	−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	$0.377748\pi$
$198$	−3.48517	+	8.76853i	−0.247680	+	0.623152i
$199$	9.91354	−	5.72359i	0.702753	−	0.405734i	−0.105619	−	0.994407i	$-0.533682\pi$
$199$	9.91354	−	5.72359i	0.702753	−	0.405734i	0.808372	+	0.588672i	$0.200349\pi$
$200$	15.9459	−	2.80363i	1.12754	−	0.198247i
$201$	4.58307	+	2.64603i	0.323264	+	0.186637i
$202$	0.652139	+	4.45719i	0.0458843	+	0.313607i
$203$	9.73826	−	16.4221i	0.683492	−	1.15261i
$204$	3.00112	−	5.56157i	0.210120	−	0.389387i
$205$	11.7432	−	3.14658i	0.820180	−	0.219767i
$206$	0.618050	−	5.28028i	0.0430616	−	0.367894i
$207$	−6.91828	−	11.9828i	−0.480854	−	0.832863i
$208$	−13.6722	+	15.3431i	−0.947997	+	1.06386i
$209$	4.93130			0.341105
$210$	8.42764	−	6.50333i	0.581563	−	0.448772i
$211$	−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	$0.889120\pi$
$212$	−6.49166	+	4.00119i	−0.445849	+	0.274803i
$213$	−8.01544	−	2.14773i	−0.549209	−	0.147160i
$214$	−0.420789	+	0.332605i	−0.0287646	+	0.0227364i
$215$	−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
$219$	0.257042	+	0.959295i	0.0173693	+	0.0648231i
$220$	−14.1525	−	13.3610i	−0.954165	−	0.900797i
$221$	−4.83644	+	18.0498i	−0.325334	+	1.21416i
$222$	2.80592	+	6.50777i	0.188321	+	0.436773i
$223$	21.9483			1.46976			0.734882	−	0.678195i	$-0.237238\pi$
$223$	21.9483			1.46976			0.734882	+	0.678195i	$0.237238\pi$
$224$	−9.80954	−	11.3037i	−0.655427	−	0.755258i
$225$	−12.8522			−0.856814
$226$	1.46710	+	3.40265i	0.0975901	+	0.226341i
$227$	−6.38481	+	23.8284i	−0.423774	+	1.58155i	0.342810	+	0.939405i	$0.388621\pi$
$227$	−6.38481	+	23.8284i	−0.423774	+	1.58155i	−0.766585	+	0.642143i	$0.778045\pi$
$228$	2.09662	+	1.97936i	0.138852	+	0.131086i
$229$	−2.46250	−	9.19018i	−0.162727	−	0.607304i	−0.998319	−	0.0579547i	$-0.981542\pi$
$229$	−2.46250	−	9.19018i	−0.162727	−	0.607304i	0.835592	−	0.549350i	$-0.185125\pi$
$230$	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	$-0.0735892\pi$
$233$	19.2584	+	11.1188i	1.26166	+	0.728418i	0.288262	+	0.957552i	$0.406923\pi$
$234$	12.7983	−	10.1162i	0.836651	−	0.661316i
$235$	−32.0473	−	8.58704i	−2.09053	−	0.560157i
$236$	6.43328	−	3.96521i	0.418771	−	0.258113i
$237$	−0.148290	−	0.148290i	−0.00963250	−	0.00963250i
$238$	−12.5871	−	5.17360i	−0.815900	−	0.335354i
$239$	14.9579			0.967548			0.483774	−	0.875193i	$-0.339266\pi$
$239$	14.9579			0.967548			0.483774	+	0.875193i	$0.339266\pi$
$240$	−0.654270	−	11.3613i	−0.0422330	−	0.733368i
$241$	12.1750	+	21.0877i	0.784262	+	1.35838i	0.929439	+	0.368975i	$0.120291\pi$
$241$	12.1750	+	21.0877i	0.784262	+	1.35838i	−0.145178	+	0.989406i	$0.546375\pi$
$242$	0.356647	−	3.04699i	0.0229261	−	0.195868i
$243$	15.5351	−	4.16262i	0.996577	−	0.267032i
$244$	6.43777	−	11.9303i	0.412136	−	0.763757i
$245$	−15.8271	−	16.5828i	−1.01116	−	1.05943i
$246$	−0.660325	−	4.51315i	−0.0421008	−	0.287748i
$247$	−7.38355	−	4.26289i	−0.469804	−	0.271241i
$248$	0.987023	+	5.61378i	0.0626761	+	0.356475i
$249$	−0.488579	+	0.282081i	−0.0309624	+	0.0178762i
$250$	1.23881	−	3.11678i	0.0783491	−	0.197123i
$251$	−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	$0.300002\pi$
$252$	6.11549	+	10.1859i	0.385239	+	0.641650i
$253$	−12.9494	−	12.9494i	−0.814120	−	0.814120i
$254$	−7.21413	−	16.7317i	−0.452655	−	1.04984i
$255$	−5.17385	−	8.96137i	−0.323999	−	0.561183i
$256$	−15.8942	+	1.83672i	−0.993389	+	0.114795i
$257$	−3.24853	+	5.62661i	−0.202638	+	0.350978i	−0.949377	−	0.314138i	$-0.898285\pi$
$257$	−3.24853	+	5.62661i	−0.202638	+	0.350978i	0.746740	+	0.665116i	$0.231618\pi$
$258$	−3.02668	+	4.06415i	−0.188433	+	0.253023i
$259$	13.3046	−	7.47601i	0.826705	−	0.464536i
$260$	9.64038	+	32.2394i	0.597871	+	1.99940i
$261$	4.19344	+	15.6501i	0.259568	+	0.968719i
$262$	−8.14880	−	10.3093i	−0.503435	−	0.636911i
$263$	21.4222	−	12.3681i	1.32095	−	0.762650i	0.337069	−	0.941480i	$-0.390564\pi$
$263$	21.4222	−	12.3681i	1.32095	−	0.762650i	0.983880	+	0.178829i	$0.0572310\pi$
$264$	−5.59603	+	4.69095i	−0.344412	+	0.288708i
$265$			12.4862i			0.767023i
$266$	3.76640	−	4.93627i	0.230933	−	0.302662i
$267$	2.67298	−	2.67298i	0.163584	−	0.163584i
$268$	−6.39236	−	10.3712i	−0.390476	−	0.633521i
$269$	−0.387844	+	1.44745i	−0.0236473	+	0.0882528i	−0.976741	−	0.214422i	$-0.931213\pi$
$269$	−0.387844	+	1.44745i	−0.0236473	+	0.0882528i	0.953094	+	0.302675i	$0.0978797\pi$
$270$	−2.45346	+	20.9610i	−0.149313	+	1.27565i
$271$	3.68123	−	6.37608i	0.223619	−	0.387320i	−0.732285	−	0.680998i	$-0.761546\pi$
$271$	3.68123	−	6.37608i	0.223619	−	0.387320i	0.955904	+	0.293679i	$0.0948795\pi$
$272$	−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
$275$	−16.4307	+	4.40260i	−0.990811	+	0.265487i
$276$	−0.307935	−	10.7033i	−0.0185355	−	0.644265i
$277$	4.37447	+	1.17214i	0.262836	+	0.0704268i	0.387831	−	0.921731i	$-0.373225\pi$
$277$	4.37447	+	1.17214i	0.262836	+	0.0704268i	−0.124994	+	0.992157i	$0.539891\pi$
$278$	15.1605	+	6.02576i	0.909269	+	0.361401i
$279$		−	4.52464i		−	0.270883i
$280$	−24.1838	+	3.96204i	−1.44526	+	0.236777i
$281$		−	9.72875i		−	0.580369i	−0.956971	−	0.290184i	$-0.906283\pi$
$281$		−	9.72875i		−	0.580369i	0.956971	−	0.290184i	$-0.0937166\pi$
$282$	−4.59760	+	11.5673i	−0.273783	+	0.688825i
$283$	−3.88559	−	1.04114i	−0.230974	−	0.0618893i	0.141475	−	0.989942i	$-0.454815\pi$
$283$	−3.88559	−	1.04114i	−0.230974	−	0.0618893i	−0.372450	+	0.928052i	$0.621482\pi$
$284$	13.8910	+	13.1141i	0.824279	+	0.778176i
$285$	4.56029	−	1.22193i	0.270128	−	0.0723807i
$286$	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
$290$	−33.1936	−	3.88527i	−1.94919	−	0.228151i
$291$	1.52940	−	5.70780i	0.0896551	−	0.334597i
$292$	0.527985	−	2.22451i	0.0308980	−	0.130179i
$293$	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	$0.225237\pi$
$294$	−6.86961	+	5.17443i	−0.400644	+	0.301779i
$295$		−	12.3740i		−	0.720440i
$296$	1.42990	−	16.2521i	0.0831111	−	0.944631i
$297$	11.7273	−	6.77077i	0.680488	−	0.392880i
$298$	13.0353	−	10.3035i	0.755116	−	0.596868i
$299$	8.19470	+	30.5830i	0.473912	+	1.76866i
$300$	−8.75295	−	4.72324i	−0.505352	−	0.272696i
$301$	9.38598	+	5.56586i	0.540999	+	0.320811i
$302$	22.2394	+	16.5623i	1.27974	+	0.953053i
$303$	1.38363	−	2.39651i	0.0794874	−	0.137676i
$304$	−2.08376	−	6.30222i	−0.119512	−	0.361457i
$305$	−11.0986	−	19.2233i	−0.635502	−	1.10072i
$306$	10.6050	−	4.57250i	0.606248	−	0.261393i
$307$	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	$0.698524\pi$
$308$	11.3075	+	10.9271i	0.644304	+	0.622629i
$309$	−2.30933	+	2.30933i	−0.131373	+	0.131373i
$310$	8.67298	+	3.44720i	0.492592	+	0.195788i
$311$	0.699829	−	0.404047i	0.0396837	−	0.0229114i	−0.480027	−	0.877254i	$-0.659373\pi$
$311$	0.699829	−	0.404047i	0.0396837	−	0.0229114i	0.519711	+	0.854342i	$0.326040\pi$
$312$	12.4340	−	2.18616i	0.703934	−	0.123767i
$313$	−20.1745	−	11.6478i	−1.14033	−	0.658371i	−0.193819	−	0.981037i	$-0.562087\pi$
$313$	−20.1745	−	11.6478i	−1.14033	−	0.658371i	−0.946513	+	0.322666i	$0.895421\pi$
$314$	−7.56712	+	1.10716i	−0.427037	+	0.0624805i
$315$	19.4520	+	0.226731i	1.09600	+	0.0127748i
$316$	0.138313	+	0.462549i	0.00778073	+	0.0260204i
$317$	3.01622	−	0.808194i	0.169408	−	0.0453927i	−0.173118	−	0.984901i	$-0.555384\pi$
$317$	3.01622	−	0.808194i	0.169408	−	0.0453927i	0.342526	+	0.939508i	$0.388718\pi$
$318$	4.65278	+	0.544603i	0.260915	+	0.0305398i
$319$	10.7221	+	18.5712i	0.600322	+	1.03979i
$320$	−11.0951	+	23.7328i	−0.620237	+	1.32671i
$321$	0.329497			0.0183907
$322$	−22.8528	+	3.07202i	−1.27354	+	0.171197i
$323$	−4.26781	−	4.26781i	−0.237467	−	0.237467i
$324$	−5.40356	−	1.28253i	−0.300198	−	0.0712518i
$325$	28.4073	+	7.61172i	1.57575	+	0.422222i
$326$	−9.89193	−	12.5146i	−0.547864	−	0.693119i
$327$	−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
$331$	−4.07718	−	15.2162i	−0.224102	−	0.836360i	−0.982762	−	0.184874i	$-0.940812\pi$
$331$	−4.07718	−	15.2162i	−0.224102	−	0.836360i	0.758660	−	0.651486i	$-0.225854\pi$
$332$	1.29823	−	0.0373500i	0.0712495	−	0.00204985i
$333$	−3.35195	+	12.5096i	−0.183686	+	0.685524i
$334$	−28.3248	+	12.2126i	−1.54987	+	0.668246i
$335$	−19.9482			−1.08989
$336$	0.421578	+	9.18451i	0.0229990	+	0.501056i
$337$	−5.36065			−0.292013			−0.146007	−	0.989284i	$-0.546642\pi$
$337$	−5.36065			−0.292013			−0.146007	+	0.989284i	$0.546642\pi$
$338$	−17.3971	+	7.50099i	−0.946276	+	0.408000i
$339$	0.589151	−	2.19874i	0.0319983	−	0.119419i
$340$	0.685063	+	23.8117i	0.0371528	+	1.29137i
$341$	−1.54994	−	5.78447i	−0.0839341	−	0.313247i
$342$	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
$346$	19.9180	+	25.1988i	1.07080	+	1.35470i
$347$	16.0386	+	4.29752i	0.860995	+	0.230703i	0.662190	−	0.749336i	$-0.269627\pi$
$347$	16.0386	+	4.29752i	0.860995	+	0.230703i	0.198805	+	0.980039i	$0.436294\pi$
$348$	−2.89556	+	12.1996i	−0.155218	+	0.653965i
$349$	−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	$-0.569394\pi$
$350$	−8.14235	+	19.8099i	−0.435227	+	1.05888i
$351$	−23.4121			−1.24965
$352$	16.4657	−	3.38587i	0.877625	−	0.180468i
$353$	−6.84373	−	11.8537i	−0.364255	−	0.630908i	0.624401	−	0.781104i	$-0.285343\pi$
$353$	−6.84373	−	11.8537i	−0.364255	−	0.630908i	−0.988656	+	0.150196i	$0.952010\pi$
$354$	−4.61095	−	0.539706i	−0.245069	−	0.0286851i
$355$	30.2138	−	8.09577i	1.60358	−	0.429679i
$356$	−8.33758	+	2.49314i	−0.441891	+	0.132136i
$357$	4.09537	+	7.28827i	0.216750	+	0.385736i
$358$	−30.1232	+	4.40737i	−1.59206	+	0.232937i
$359$	5.47529	+	3.16116i	0.288974	+	0.166840i	0.637479	−	0.770467i	$-0.279977\pi$
$359$	5.47529	+	3.16116i	0.288974	+	0.166840i	−0.348505	+	0.937307i	$0.613310\pi$
$360$	11.9367	−	17.0297i	0.629121	−	0.897542i
$361$	−14.0697	+	8.12312i	−0.740508	+	0.427533i
$362$	−22.0211	−	8.75259i	−1.15740	−	0.460026i
$363$	−1.33260	+	1.33260i	−0.0699434	+	0.0699434i
$364$	−7.48451	−	26.1358i	−0.392295	−	1.36989i
$365$	−2.64711	−	2.64711i	−0.138556	−	0.138556i
$366$	−7.64731	+	3.29725i	−0.399732	+	0.172350i
$367$	18.6164	+	32.2445i	0.971768	+	1.68315i	0.690213	+	0.723606i	$0.257517\pi$
$367$	18.6164	+	32.2445i	0.971768	+	1.68315i	0.281555	+	0.959545i	$0.409150\pi$
$368$	−11.0775	+	22.0212i	−0.577454	+	1.14794i
$369$	4.16767	−	7.21861i	0.216960	−	0.375786i
$370$	−21.4251	−	15.9559i	−1.11384	−	0.829505i
$371$	0.117575	−	10.0871i	0.00610417	−	0.523699i
$372$	1.66282	−	3.08149i	0.0862134	−	0.159768i
$373$	1.11879	+	4.17538i	0.0579287	+	0.216193i	0.988823	−	0.149097i	$-0.0476366\pi$
$373$	1.11879	+	4.17538i	0.0579287	+	0.216193i	−0.930894	+	0.365290i	$0.880970\pi$
$374$	11.9915	−	9.47847i	0.620066	−	0.490120i
$375$	−1.78433	+	1.03019i	−0.0921426	+	0.0531985i
$376$	21.9605	−	18.4087i	1.13253	−	0.949357i
$377$		−	37.0752i		−	1.90947i
$378$	2.17943	−	16.9105i	0.112098	−	0.869782i
$379$	−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	$0.387314\pi$
$380$	−10.5749	−	2.50994i	−0.542479	−	0.128757i
$381$	−2.89701	+	10.8118i	−0.148419	+	0.553906i
$382$	−11.0797	−	1.29686i	−0.566885	−	0.0663532i
$383$	9.86334	−	17.0838i	0.503993	−	0.872942i	−0.495996	−	0.868325i	$-0.665197\pi$
$383$	9.86334	−	17.0838i	0.503993	−	0.872942i	0.999989	−	0.00461719i	$-0.00146970\pi$
$384$	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
$387$	−8.94477	+	2.39674i	−0.454688	+	0.121833i
$388$	−9.33854	+	9.89179i	−0.474092	+	0.502180i
$389$	5.73576	+	1.53689i	0.290815	+	0.0779236i	0.401277	−	0.915957i	$-0.368566\pi$
$389$	5.73576	+	1.53689i	0.290815	+	0.0779236i	−0.110462	+	0.993880i	$0.535233\pi$
$390$	7.63520	−	19.2098i	0.386623	−	0.972726i
$391$			22.4142i			1.13353i
$392$	19.5745	−	2.97306i	0.988661	−	0.150162i
$393$			8.07264i			0.407211i
$394$	−14.4115	−	5.72806i	−0.726042	−	0.288575i
$395$	0.763573	+	0.204599i	0.0384195	+	0.0102945i
$396$	−13.3387	+	0.383753i	−0.670293	+	0.0192843i
$397$	24.7008	−	6.61855i	1.23970	−	0.332175i	0.421348	−	0.906899i	$-0.361557\pi$
$397$	24.7008	−	6.61855i	1.23970	−	0.332175i	0.818348	+	0.574724i	$0.194890\pi$
$398$	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	−0.907494	−	0.420064i	$-0.862008\pi$
$401$	−1.80147	+	3.12023i	−0.0899610	+	0.155817i	0.817533	+	0.575881i	$0.195341\pi$
$402$	−0.870067	+	7.43337i	−0.0433950	+	0.370743i
$403$	−2.67972	+	10.0008i	−0.133486	+	0.498177i
$404$	−5.42316	+	3.34261i	−0.269812	+	0.166301i
$405$	−6.43010	+	6.43010i	−0.319514	+	0.319514i
$406$	26.7792	+	3.45132i	1.32903	+	0.171286i
$407$			17.1410i			0.849648i
$408$	8.90291	+	0.783301i	0.440760	+	0.0387792i
$409$	13.2778	−	7.66595i	0.656546	−	0.379057i	−0.134414	−	0.990925i	$-0.542915\pi$
$409$	13.2778	−	7.66595i	0.656546	−	0.379057i	0.790959	+	0.611869i	$0.209582\pi$
$410$	10.6616	+	13.4884i	0.526541	+	0.666144i
$411$	−2.65380	−	9.90413i	−0.130902	−	0.488535i
$412$	7.20327	−	2.15395i	0.354880	−	0.106118i
$413$	−0.116517	+	9.99645i	−0.00573345	+	0.491893i
$414$	11.6877	−	15.6939i	0.574418	−	0.771314i
$415$	1.06329	−	1.84168i	0.0521950	−	0.0904044i
$416$	−27.5808	−	9.16428i	−1.35226	−	0.449316i
$417$	−5.01099	−	8.67929i	−0.245389	−	0.425027i
$418$	2.76118	+	6.40401i	0.135054	+	0.313230i
$419$	−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	$0.953816\pi$
$420$	13.1644	+	7.30311i	0.642357	+	0.356355i
$421$	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	$0.0335888\pi$
$422$	6.42331	−	16.1607i	0.312682	−	0.786693i
$423$	−19.6997	+	11.3736i	−0.957830	+	0.553003i
$424$	−8.83099	−	6.18998i	−0.428871	−	0.300612i
$425$	18.0303	+	10.4098i	0.874598	+	0.504950i
$426$	−1.69894	−	11.6118i	−0.0823138	−	0.562593i
$427$	8.78510	+	15.6343i	0.425141	+	0.756595i
$428$	−0.667549	−	0.360221i	−0.0322672	−	0.0174119i
$429$	−12.8120	+	3.43297i	−0.618571	+	0.165745i
$430$	2.22061	−	18.9716i	0.107087	−	0.914894i
$431$	−16.8098	−	29.1154i	−0.809698	−	1.40244i	−0.913073	−	0.407796i	$-0.866297\pi$
$431$	−16.8098	−	29.1154i	−0.809698	−	1.40244i	0.103375	−	0.994642i	$-0.467036\pi$
$432$	−13.6085	−	12.1265i	−0.654742	−	0.583438i
$433$	26.5511			1.27596			0.637982	−	0.770051i	$-0.279769\pi$
$433$	26.5511			1.27596			0.637982	+	0.770051i	$0.279769\pi$
$434$	−6.97411	−	2.86653i	−0.334768	−	0.137598i
$435$	14.5172	+	14.5172i	0.696046	+	0.696046i
$436$	10.4910	+	17.0210i	0.502429	+	0.815157i
$437$	−9.87805	−	2.64682i	−0.472531	−	0.126614i
$438$	−1.10186	+	0.870944i	−0.0526488	+	0.0416153i
$439$	−16.9833	−	9.80529i	−0.810567	−	0.467981i	0.0365859	−	0.999331i	$-0.488352\pi$
$439$	−16.9833	−	9.80529i	−0.810567	−	0.467981i	−0.847153	+	0.531350i	$0.821685\pi$
$440$	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
$443$	1.76565	+	6.58948i	0.0838883	+	0.313076i	0.995101	−	0.0988599i	$-0.0315196\pi$
$443$	1.76565	+	6.58948i	0.0838883	+	0.313076i	−0.911213	+	0.411935i	$0.864853\pi$
$444$	−6.88017	+	7.28778i	−0.326518	+	0.345863i
$445$	−3.68795	+	13.7636i	−0.174826	+	0.652459i
$446$	12.2895	+	28.5030i	0.581923	+	1.34966i
$447$	−10.2072			−0.482786
$448$	9.18681	−	19.0684i	0.434036	−	0.900896i
$449$	6.32412			0.298454			0.149227	−	0.988803i	$-0.452322\pi$
$449$	6.32412			0.298454			0.149227	+	0.988803i	$0.452322\pi$
$450$	−7.19633	−	16.6905i	−0.339238	−	0.786796i
$451$	2.85532	−	10.6562i	0.134452	−	0.501781i
$452$	−3.59736	+	3.81049i	−0.169206	+	0.179230i
$453$	−4.40880	−	16.4539i	−0.207144	−	0.773070i
$454$	−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	−0.991462	−	0.130396i	$-0.958375\pi$
$457$	−34.2066	−	19.7492i	−1.60012	−	0.923829i	−0.608657	−	0.793433i	$-0.708291\pi$
$458$	10.5560	−	8.34377i	0.493248	−	0.389879i
$459$	−16.0092	−	4.28966i	−0.747248	−	0.200224i
$460$	21.1781	+	34.3601i	0.987435	+	1.60205i
$461$	−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	$0.763293\pi$
$462$	−1.28695	−	9.57365i	−0.0598744	−	0.445406i
$463$	−14.4427			−0.671208			−0.335604	−	0.942003i	$-0.608940\pi$
$463$	−14.4427			−0.671208			−0.335604	+	0.942003i	$0.608940\pi$
$464$	19.2034	−	21.5503i	0.891496	−	1.00045i
$465$	−2.86667	−	4.96521i	−0.132939	−	0.230256i
$466$	−3.65608	+	31.2355i	−0.169365	+	1.44696i
$467$	16.7796	−	4.49607i	0.776465	−	0.208053i	0.151240	−	0.988497i	$-0.451674\pi$
$467$	16.7796	−	4.49607i	0.776465	−	0.208053i	0.625226	+	0.780444i	$0.285007\pi$
$468$	20.3035	+	10.9561i	0.938528	+	0.506446i
$469$	16.1154	+	0.187839i	0.744140	+	0.00867361i
$470$	−6.79269	−	46.4262i	−0.313323	−	2.14148i
$471$	4.06864	+	2.34903i	0.187473	+	0.108238i
$472$	8.75158	+	6.13432i	0.402824	+	0.282355i
$473$	−10.6143	+	6.12817i	−0.488046	+	0.281773i
$474$	0.109545	−	0.275609i	0.00503155	−	0.0126591i
$475$	−6.71680	+	6.71680i	−0.308188	+	0.308188i
$476$	−0.329217	−	19.2430i	−0.0150896	−	0.882002i
$477$	6.05337	+	6.05337i	0.277165	+	0.277165i
$478$	8.37539	+	19.4251i	0.383081	+	0.888481i
$479$	2.39344	+	4.14556i	0.109359	+	0.189416i	0.915511	−	0.402293i	$-0.131787\pi$
$479$	2.39344	+	4.14556i	0.109359	+	0.189416i	−0.806152	+	0.591709i	$0.798453\pi$
$480$	14.3879	−	7.21118i	0.656716	−	0.329144i
$481$	14.8177	−	25.6649i	0.675627	−	1.17022i
$482$	−20.5684	+	27.6187i	−0.936863	+	1.25800i
$483$	12.1839	+	7.22502i	0.554387	+	0.328750i
$484$	4.15666	−	1.24294i	0.188939	−	0.0564974i
$485$	5.76501	+	21.5153i	0.261776	+	0.976960i
$486$	14.1043	+	17.8438i	0.639785	+	0.809412i
$487$	−23.2700	+	13.4349i	−1.05446	+	0.608795i	−0.923896	−	0.382644i	$-0.875013\pi$
$487$	−23.2700	+	13.4349i	−1.05446	+	0.608795i	−0.130568	+	0.991439i	$0.541680\pi$
$488$	19.0979	+	1.68028i	0.864520	+	0.0760627i
$489$			9.79948i			0.443148i
$490$	12.6731	−	29.8390i	0.572510	−	1.34799i
$491$	−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	$0.372426\pi$
$492$	5.49124	−	3.38457i	0.247564	−	0.152588i
$493$	6.79306	−	25.3520i	0.305944	−	1.14180i
$494$	1.40172	−	11.9755i	0.0630664	−	0.538804i
$495$	−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
$499$	19.0371	−	5.10099i	0.852220	−	0.228352i	0.193836	−	0.981034i	$-0.437907\pi$
$499$	19.0371	−	5.10099i	0.852220	−	0.228352i	0.658384	+	0.752682i	$0.271240\pi$
$500$	4.74124	−	0.136406i	0.212035	−	0.00610024i
$501$	18.3031	+	4.90430i	0.817721	+	0.219108i
$502$	−6.51447	−	2.58927i	−0.290755	−	0.115565i
$503$		−	23.6387i		−	1.05400i	−0.849866	−	0.526999i	$-0.823317\pi$
$503$		−	23.6387i		−	1.05400i	0.849866	−	0.526999i	$-0.176683\pi$
$504$	−9.80359	+	13.6452i	−0.436687	+	0.607806i
$505$			10.4311i			0.464176i
$506$	9.56590	−	24.0674i	0.425256	−	1.06992i
$507$	11.2417	+	3.01221i	0.499263	+	0.133777i
$508$	17.6892	−	18.7372i	0.784831	−	0.831328i
$509$	−32.8795	+	8.81005i	−1.45736	+	0.390498i	−0.898577	−	0.438816i	$-0.855398\pi$
$509$	−32.8795	+	8.81005i	−1.45736	+	0.390498i	−0.558783	+	0.829314i	$0.688731\pi$
$510$	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
$514$	−9.12592	−	1.06818i	−0.402527	−	0.0471153i
$515$	3.18622	−	11.8911i	0.140401	−	0.523985i
$516$	−6.97261	−	1.65494i	−0.306952	−	0.0728549i
$517$	−21.2887	+	21.2887i	−0.936274	+	0.936274i
$518$	17.1583	+	13.0919i	0.753892	+	0.575224i
$519$		−	19.7318i		−	0.866131i
$520$	−36.4697	+	30.5712i	−1.59930	+	1.34064i
$521$	−15.2768	+	8.82007i	−0.669289	+	0.386414i	−0.795807	−	0.605550i	$-0.792953\pi$
$521$	−15.2768	+	8.82007i	−0.669289	+	0.386414i	0.126518	+	0.991964i	$0.459620\pi$
$522$	−17.9759	+	14.2088i	−0.786786	+	0.621901i
$523$	3.72172	+	13.8896i	0.162739	+	0.607352i	0.998318	+	0.0579803i	$0.0184661\pi$
$523$	3.72172	+	13.8896i	0.162739	+	0.607352i	−0.835578	+	0.549371i	$0.814867\pi$
$524$	8.82537	−	16.3549i	0.385538	−	0.714466i
$525$	11.4705	−	6.44541i	0.500613	−	0.281301i
$526$	28.0567	+	20.8946i	1.22333	+	0.911046i
$527$	−3.66479	+	6.34760i	−0.159641	+	0.276506i
$528$	−9.22526	−	4.64065i	−0.401478	−	0.201958i
$529$	7.48891	+	12.9712i	0.325605	+	0.563964i
$530$	−16.2152	+	6.99140i	−0.704342	+	0.303687i
$531$	−5.99894	−	5.99894i	−0.260332	−	0.260332i
$532$	8.51938	+	2.12726i	0.369362	+	0.0922283i
$533$	−13.4870	+	13.4870i	−0.584189	+	0.584189i
$534$	4.96793	+	1.97457i	0.214983	+	0.0854481i
$535$	−1.07562	+	0.621012i	−0.0465033	+	0.0268487i
$536$	9.88921	−	14.1085i	0.427149	−	0.609396i
$537$	16.1964	+	9.35102i	0.698928	+	0.403526i
$538$	−2.09689	+	0.306800i	−0.0904035	+	0.0132271i
$539$	−20.2128	+	4.91405i	−0.870628	+	0.211663i
$540$	−28.5947	+	8.55050i	−1.23052	+	0.367955i
$541$	−28.7139	+	7.69386i	−1.23451	+	0.330785i	−0.816332	−	0.577582i	$-0.803996\pi$
$541$	−28.7139	+	7.69386i	−1.23451	+	0.330785i	−0.418173	+	0.908367i	$0.637330\pi$
$542$	10.3415	+	1.21046i	0.444206	+	0.0519937i
$543$	7.27860	+	12.6069i	0.312355	+	0.541014i
$544$	−17.1806	−	11.3200i	−0.736614	−	0.485341i
$545$	32.7386			1.40237
$546$	−6.34907	+	15.4470i	−0.271715	+	0.661069i
$547$	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	$0.434906\pi$
$548$	−5.45112	+	22.9667i	−0.232860	+	0.981087i
$549$	−14.7001	−	3.93889i	−0.627387	−	0.168108i
$550$	−14.9175	−	18.8726i	−0.636083	−	0.804729i
$551$	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
$555$	4.24737	+	15.8514i	0.180291	+	0.672855i
$556$	0.663499	+	23.0622i	0.0281386	+	0.978054i
$557$	1.70285	−	6.35511i	0.0721519	−	0.269275i	−0.920421	−	0.390930i	$-0.872154\pi$
$557$	1.70285	−	6.35511i	0.0721519	−	0.269275i	0.992572	+	0.121655i	$0.0388202\pi$
$558$	5.87591	−	2.53348i	0.248747	−	0.107251i
$559$	21.1901			0.896247
$560$	−18.6865	−	29.1877i	−0.789649	−	1.23341i
$561$	−9.38988			−0.396441
$562$	12.6342	−	5.44741i	0.532941	−	0.229785i
$563$	−6.89049	+	25.7157i	−0.290399	+	1.08379i	0.654403	+	0.756146i	$0.272920\pi$
$563$	−6.89049	+	25.7157i	−0.290399	+	1.08379i	−0.944803	+	0.327640i	$0.893747\pi$
$564$	−17.5962	+	0.506243i	−0.740934	+	0.0213167i
$565$	2.22078	+	8.28807i	0.0934289	+	0.348682i
$566$	−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	$-0.316361\pi$
$569$	2.20198	+	1.27132i	0.0923119	+	0.0532963i	−0.453133	+	0.891443i	$0.649694\pi$
$570$	4.14029	+	5.23801i	0.173418	+	0.219396i
$571$	38.7549	+	10.3843i	1.62184	+	0.434571i	0.951541	−	0.307521i	$-0.0994993\pi$
$571$	38.7549	+	10.3843i	1.62184	+	0.434571i	0.670299	+	0.742091i	$0.266166\pi$
$572$	29.7098	+	7.05160i	1.24223	+	0.294842i
$573$	4.84569	+	4.84569i	0.202431	+	0.202431i
$574$	−8.48612	−	10.9971i	−0.354204	−	0.459012i
$575$	35.2760			1.47111
$576$	6.12680	+	16.8847i	0.255283	+	0.703530i
$577$	−17.3756	−	30.0953i	−0.723354	−	1.25289i	−0.959648	−	0.281204i	$-0.909266\pi$
$577$	−17.3756	−	30.0953i	−0.723354	−	1.25289i	0.236294	−	0.971682i	$-0.424067\pi$
$578$	5.29734	+	0.620047i	0.220340	+	0.0257906i
$579$	−20.8791	+	5.59453i	−0.867705	+	0.232501i
$580$	−13.5405	−	45.2821i	−0.562237	−	1.88024i
$581$	−0.876335	+	1.47781i	−0.0363565	+	0.0613098i
$582$	8.26877	−	1.20982i	0.342751	−	0.0501485i
$583$	9.81246	+	5.66523i	0.406391	+	0.234630i
$584$	3.18448	−	0.559900i	0.131775	−	0.0231688i
$585$	32.7151	−	18.8881i	1.35260	−	0.780925i
$586$	3.49656	+	1.38976i	0.144442	+	0.0574103i
$587$	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	$0.0497178\pi$
$588$	−10.5662	−	6.02387i	−0.435745	−	0.248420i
$589$	−2.36466	−	2.36466i	−0.0974341	−	0.0974341i
$590$	16.0694	−	6.92854i	0.661566	−	0.285244i
$591$	4.76342	+	8.25049i	0.195941	+	0.339380i
$592$	21.9063	−	7.24307i	0.900343	−	0.297688i
$593$	−4.20461	+	7.28261i	−0.172663	+	0.299061i	−0.939350	−	0.342960i	$-0.888570\pi$
$593$	−4.20461	+	7.28261i	−0.172663	+	0.299061i	0.766687	+	0.642021i	$0.221904\pi$
$594$	15.3593	+	11.4385i	0.630199	+	0.469326i
$595$	−27.1055	−	16.0735i	−1.11122	−	0.658949i
$596$	20.6795	+	11.1590i	0.847065	+	0.457091i
$597$	−2.57394	−	9.60607i	−0.105344	−	0.393150i
$598$	−35.1280	+	27.7663i	−1.43649	+	1.13545i
$599$	3.08368	−	1.78037i	0.125996	−	0.0727438i	−0.435677	−	0.900103i	$-0.643491\pi$
$599$	3.08368	−	1.78037i	0.125996	−	0.0727438i	0.561673	+	0.827359i	$0.310158\pi$
$600$	1.23278	−	14.0116i	0.0503280	−	0.572023i
$601$			45.3712i			1.85073i	0.379076	+	0.925365i	$0.376242\pi$
$601$			45.3712i			1.85073i	−0.379076	+	0.925365i	$0.623758\pi$
$602$	−1.97259	+	15.3055i	−0.0803967	+	0.623808i
$603$	−9.67096	+	9.67096i	−0.393832	+	0.393832i
$604$	−9.05603	+	38.1548i	−0.368485	+	1.55250i
$605$	1.83861	−	6.86180i	0.0747502	−	0.278972i
$606$	3.88696	+	0.454964i	0.157897	+	0.0184816i
$607$	2.45090	−	4.24508i	0.0994789	−	0.172302i	−0.811990	−	0.583671i	$-0.801616\pi$
$607$	2.45090	−	4.24508i	0.0994789	−	0.172302i	0.911469	+	0.411369i	$0.134949\pi$
$608$	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
$611$	50.2783	−	13.4720i	2.03404	−	0.545020i
$612$	11.8761	+	11.2119i	0.480064	+	0.453213i
$613$	7.71591	+	2.06747i	0.311643	+	0.0835045i	0.411251	−	0.911522i	$-0.365092\pi$
$613$	7.71591	+	2.06747i	0.311643	+	0.0835045i	−0.0996077	+	0.995027i	$0.531759\pi$
$614$	−2.94731	+	7.41528i	−0.118944	+	0.299256i
$615$		−	10.5620i		−	0.425901i
$616$	−7.85902	+	20.8028i	−0.316649	+	0.838169i
$617$		−	40.2966i		−	1.62228i	−0.584852	−	0.811140i	$-0.698847\pi$
$617$		−	40.2966i		−	1.62228i	0.584852	−	0.811140i	$-0.301153\pi$
$618$	−4.29205	−	1.70594i	−0.172652	−	0.0686228i
$619$	−19.4415	−	5.20932i	−0.781418	−	0.209380i	−0.154008	−	0.988070i	$-0.549218\pi$
$619$	−19.4415	−	5.20932i	−0.781418	−	0.209380i	−0.627410	+	0.778689i	$0.715885\pi$
$620$	0.379572	+	13.1933i	0.0152440	+	0.529856i
$621$	−27.1255	+	7.26826i	−1.08851	+	0.291665i
$622$	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
$626$	3.83001	−	32.7215i	0.153078	−	1.30781i
$627$	1.10882	−	4.13817i	0.0442820	−	0.165263i
$628$	−5.67485	−	9.20707i	−0.226451	−	0.367402i
$629$	14.8348	−	14.8348i	0.591500	−	0.591500i
$630$	10.5973	+	25.3883i	0.422207	+	1.01149i
$631$		−	15.2886i		−	0.608631i	−0.952571	−	0.304315i	$-0.901572\pi$
$631$		−	15.2886i		−	0.608631i	0.952571	−	0.304315i	$-0.0984277\pi$
$632$	−0.523241	+	0.438615i	−0.0208134	+	0.0174471i
$633$	−9.25190	+	5.34159i	−0.367730	+	0.212309i
$634$	2.73843	+	3.46447i	0.108757	+	0.137592i
$635$	−10.9202	−	40.7546i	−0.433354	−	1.61730i
$636$	1.89798	+	6.34725i	0.0752599	+	0.251685i
$637$	34.5123	+	10.1154i	1.36743	+	0.400786i
$638$	−18.1138	+	24.3228i	−0.717133	+	0.962948i
$639$	10.7229	−	18.5726i	0.424192	−	0.734722i
$640$	−37.0330	−	1.11994i	−1.46386	−	0.0442694i
$641$	6.18366	+	10.7104i	0.244240	+	0.423036i	0.961918	−	0.273340i	$-0.0881283\pi$
$641$	6.18366	+	10.7104i	0.244240	+	0.423036i	−0.717678	+	0.696375i	$0.754795\pi$
$642$	0.184495	+	0.427899i	0.00728143	+	0.0168878i
$643$	−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	$-0.552981\pi$
$644$	−16.7854	−	27.9576i	−0.661439	−	1.10168i
$645$	−8.29724	+	8.29724i	−0.326703	+	0.326703i
$646$	3.15270	−	7.93205i	0.124041	−	0.312082i
$647$	12.4455	−	7.18540i	0.489282	−	0.282487i	−0.234994	−	0.971997i	$-0.575507\pi$
$647$	12.4455	−	7.18540i	0.489282	−	0.282487i	0.724277	+	0.689509i	$0.242174\pi$
$648$	−1.36006	−	7.73543i	−0.0534281	−	0.303876i
$649$	−9.72423	−	5.61429i	−0.381710	−	0.220380i
$650$	6.02117	+	41.1531i	0.236170	+	1.61416i
$651$	2.26912	+	4.03820i	0.0889337	+	0.158270i
$652$	10.7132	−	19.8534i	0.419563	−	0.777519i
$653$	−14.1669	+	3.79601i	−0.554393	+	0.148549i	−0.525129	−	0.851022i	$-0.675983\pi$
$653$	−14.1669	+	3.79601i	−0.554393	+	0.148549i	−0.0292641	+	0.999572i	$0.509316\pi$
$654$	1.42794	−	12.1995i	0.0558368	−	0.477038i
$655$	−15.2147	−	26.3527i	−0.594489	−	1.02968i
$656$	−14.8252	+	0.853750i	−0.578827	+	0.0333333i
$657$	−2.56666			−0.100135
$658$	5.05039	+	37.5699i	0.196885	+	1.46463i
$659$	−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	$-0.560281\pi$
$660$	−14.3943	+	8.87206i	−0.560299	+	0.345345i
$661$	2.67726	+	0.717370i	0.104133	+	0.0279025i	0.310509	−	0.950570i	$-0.399500\pi$
$661$	2.67726	+	0.717370i	0.104133	+	0.0279025i	−0.206376	+	0.978473i	$0.566167\pi$
$662$	17.4776	−	13.8148i	0.679285	−	0.536928i
$663$	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
$667$	−11.5099	−	42.9556i	−0.445666	−	1.66325i
$668$	−31.7198	−	29.9457i	−1.22728	−	1.15863i
$669$	4.93515	−	18.4182i	0.190804	−	0.712089i
$670$	−11.1696	−	25.9057i	−0.431519	−	1.00082i
$671$	−20.1425			−0.777592
$672$	−11.6914	+	5.69015i	−0.451004	+	0.219502i
$673$	−4.79538			−0.184848			−0.0924242	−	0.995720i	$-0.529462\pi$
$673$	−4.79538			−0.184848			−0.0924242	+	0.995720i	$0.529462\pi$
$674$	−3.00158	−	6.96158i	−0.115617	−	0.268150i
$675$	−6.75119	+	25.1958i	−0.259854	+	0.969786i
$676$	−19.4823	−	18.3926i	−0.749317	−	0.707407i
$677$	12.8711	+	48.0358i	0.494678	+	1.84616i	0.531824	+	0.846855i	$0.321507\pi$
$677$	12.8711	+	48.0358i	0.494678	+	1.84616i	−0.0371454	+	0.999310i	$0.511826\pi$
$678$	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
$682$	6.64411	−	5.25172i	0.254416	−	0.201099i
$683$	3.97711	+	1.06566i	0.152180	+	0.0407764i	0.334105	−	0.942536i	$-0.391566\pi$
$683$	3.97711	+	1.06566i	0.152180	+	0.0407764i	−0.181925	+	0.983312i	$0.558233\pi$
$684$	−6.34355	+	3.90990i	−0.242552	+	0.149499i
$685$	27.3298	+	27.3298i	1.04422	+	1.04422i
$686$	−10.5190	+	23.9864i	−0.401619	+	0.915807i
$687$	−8.26579			−0.315360
$688$	12.3170	+	10.9756i	0.469581	+	0.418442i
$689$	−9.79469	−	16.9649i	−0.373148	−	0.646311i
$690$	2.88256	−	24.6270i	0.109737	−	0.937534i
$691$	−34.3049	+	9.19198i	−1.30502	+	0.349679i	−0.843347	−	0.537370i	$-0.819418\pi$
$691$	−34.3049	+	9.19198i	−1.30502	+	0.349679i	−0.461674	+	0.887049i	$0.652751\pi$
$692$	−21.5717	+	39.9759i	−0.820033	+	1.51966i
$693$	9.00392	−	15.1838i	0.342031	−	0.576783i
$694$	3.39951	+	23.2347i	0.129043	+	0.881977i
$695$	32.7162	+	18.8887i	1.24100	+	0.716489i
$696$	−17.4642	+	3.07059i	−0.661979	+	0.116390i
$697$	−11.6936	+	6.75130i	−0.442927	+	0.255724i
$698$	16.4585	−	41.4089i	0.622964	−	1.56735i
$699$	13.6608	−	13.6608i	0.516701	−	0.516701i
$700$	−30.2852	+	0.518131i	−1.14467	+	0.0195835i
$701$	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	$0.611632\pi$
$702$	−13.1091	−	30.4041i	−0.494773	−	1.14753i
$703$	4.78597	+	8.28955i	0.180506	+	0.312646i
$704$	13.6167	+	19.4873i	0.513198	+	0.734454i
$705$	−14.4119	+	24.9621i	−0.542783	+	0.940129i
$706$	11.5617	−	15.5248i	0.435131	−	0.584283i
$707$	0.0982224	−	8.42685i	0.00369403	−	0.316924i
$708$	−1.88092	−	6.29018i	−0.0706892	−	0.236400i
$709$	−2.99021	−	11.1596i	−0.112300	−	0.419108i	0.886771	−	0.462209i	$-0.152943\pi$
$709$	−2.99021	−	11.1596i	−0.112300	−	0.419108i	−0.999071	+	0.0431009i	$0.986276\pi$
$710$	27.4311	+	34.7040i	1.02947	+	1.30242i
$711$	0.469373	−	0.270993i	0.0176029	−	0.0101630i
$712$	−7.90616	−	9.43158i	−0.296296	−	0.353463i
$713$			12.4190i			0.465095i
$714$	−7.17176	+	9.39935i	−0.268396	+	0.351762i
$715$	35.3539	−	35.3539i	1.32216	−	1.32216i
$716$	−22.5905	−	36.6515i	−0.844245	−	1.36973i
$717$	3.36335	−	12.5522i	0.125607	−	0.468770i
$718$	−1.03945	+	8.88048i	−0.0387919	+	0.331416i
$719$	−14.4263	+	24.9871i	−0.538011	+	0.931863i	0.461000	+	0.887400i	$0.347491\pi$
$719$	−14.4263	+	24.9871i	−0.538011	+	0.931863i	−0.999011	+	0.0444624i	$0.985842\pi$
$720$	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
$723$	20.4337	−	5.47519i	0.759938	−	0.203625i
$724$	−0.963751	−	33.4984i	−0.0358175	−	1.24496i
$725$	−39.8997	−	10.6911i	−1.48184	−	0.397057i
$726$	−2.47674	−	0.984414i	−0.0919204	−	0.0365350i
$727$		−	19.1342i		−	0.709648i	−0.934933	−	0.354824i	$-0.884541\pi$
$727$		−	19.1342i		−	0.709648i	0.934933	−	0.354824i	$-0.115459\pi$
$728$	29.7503	−	24.3539i	1.10262	−	0.902616i
$729$		−	5.64199i		−	0.208963i
$730$	1.95546	−	4.91985i	0.0723749	−	0.182092i
$731$	14.4898	+	3.88254i	0.535926	+	0.143601i
$732$	−8.56391	−	8.08492i	−0.316531	−	0.298827i
$733$	11.1641	−	2.99140i	0.412354	−	0.110490i	−0.0466772	−	0.998910i	$-0.514863\pi$
$733$	11.1641	−	2.99140i	0.412354	−	0.110490i	0.459031	+	0.888420i	$0.348197\pi$
$734$	−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
$738$	11.7080	+	1.37041i	0.430978	+	0.0504455i
$739$	−2.14689	+	8.01230i	−0.0789746	+	0.294737i	−0.994105	−	0.108420i	$-0.965421\pi$
$739$	−2.14689	+	8.01230i	−0.0789746	+	0.294737i	0.915130	+	0.403158i	$0.132087\pi$
$740$	8.72444	−	36.7578i	0.320717	−	1.35124i
$741$	−5.23749	+	5.23749i	−0.192404	+	0.192404i
$742$	13.1655	−	5.49540i	0.483319	−	0.201743i
$743$			9.24326i			0.339102i	0.985521	+	0.169551i	$0.0542318\pi$
$743$			9.24326i			0.339102i	−0.985521	+	0.169551i	$0.945768\pi$
$744$	4.93282	+	0.434002i	0.180846	+	0.0159113i
$745$	33.3210	−	19.2379i	1.22079	−	0.704821i
$746$	−4.79589	+	3.79083i	−0.175590	+	0.138792i
$747$	−0.377363	−	1.40834i	−0.0138070	−	0.0515284i
$748$	19.0236	+	10.2654i	0.695570	+	0.375341i
$749$	0.874803	−	0.491563i	0.0319646	−	0.0179613i
$750$	−2.33695	−	1.74038i	−0.0853332	−	0.0635499i
$751$	10.3379	−	17.9057i	0.377234	−	0.653388i	−0.613425	−	0.789753i	$-0.710209\pi$
$751$	10.3379	−	17.9057i	0.377234	−	0.653388i	0.990659	+	0.136365i	$0.0435421\pi$
$752$	36.2027	+	18.2113i	1.32018	+	0.664099i
$753$	2.15322	+	3.72949i	0.0784677	+	0.135910i
$754$	48.1475	−	20.7595i	1.75343	−	0.756015i
$755$	45.4034	+	45.4034i	1.65240	+	1.65240i
$756$	23.1811	−	6.63837i	0.843087	−	0.241435i
$757$	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	$0.0842197\pi$
$758$	−21.3956	−	8.50397i	−0.777122	−	0.308878i
$759$	−13.7784	+	7.95495i	−0.500123	+	0.288746i
$760$	−2.66165	−	15.1384i	−0.0965483	−	0.549126i
$761$	−15.2778	−	8.82065i	−0.553821	−	0.319748i	0.196841	−	0.980435i	$-0.436932\pi$
$761$	−15.2778	−	8.82065i	−0.553821	−	0.319748i	−0.750662	+	0.660687i	$0.770265\pi$
$762$	−15.6628	+	2.29165i	−0.567404	+	0.0830178i
$763$	−26.4483	−	0.308278i	−0.957492	−	0.0111604i
$764$	−4.51966	−	15.1147i	−0.163516	−	0.546831i
$765$	25.8313	−	6.92149i	0.933934	−	0.250247i
$766$	27.7086	+	3.24326i	1.00115	+	0.117184i
$767$	9.70662	+	16.8124i	0.350486	+	0.607059i
$768$	−2.03257	+	13.7509i	−0.0733440	+	0.496192i
$769$	−33.4127			−1.20489			−0.602447	−	0.798159i	$-0.705807\pi$
$769$	−33.4127			−1.20489			−0.602447	+	0.798159i	$0.705807\pi$
$770$	22.2449	+	28.8271i	0.801651	+	1.03886i
$771$	3.99122	+	3.99122i	0.143740	+	0.143740i
$772$	48.4164	+	11.4916i	1.74255	+	0.413592i
$773$	12.9412	+	3.46760i	0.465464	+	0.124721i	0.483926	−	0.875109i	$-0.339210\pi$
$773$	12.9412	+	3.46760i	0.465464	+	0.124721i	−0.0184619	+	0.999830i	$0.505877\pi$
$774$	−8.12096	−	10.2741i	−0.291902	−	0.369294i
$775$	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
$779$	−1.59448	−	5.95068i	−0.0571281	−	0.213205i
$780$	29.2219	−	0.840714i	1.04631	−	0.0301024i
$781$	7.34640	−	27.4171i	0.262875	−	0.981062i
$782$	−29.1081	+	12.5503i	−1.04090	+	0.448800i
$783$	32.8837			1.17517
$784$	14.8213	+	23.7556i	0.529331	+	0.848415i
$785$	−17.7091			−0.632066
$786$	−10.4835	+	4.52011i	−0.373934	+	0.161227i
$787$	−2.49315	+	9.30456i	−0.0888712	+	0.331672i	−0.996019	−	0.0891401i	$-0.971588\pi$
$787$	−2.49315	+	9.30456i	−0.0888712	+	0.331672i	0.907148	+	0.420812i	$0.138255\pi$
$788$	−0.630719	−	21.9228i	−0.0224684	−	0.780966i
$789$	−5.56203	−	20.7578i	−0.198014	−	0.738997i
$790$	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
$794$	22.4258	+	28.3716i	0.795863	+	1.00687i
$795$	10.4780	+	2.80758i	0.371617	+	0.0995744i
$796$	−5.28708	+	22.2755i	−0.187396	+	0.789534i
$797$	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	$0.722262\pi$
$798$	−3.29546	−	4.27057i	−0.116658	−	0.151177i
$799$	36.8487			1.30361
$800$	−17.8157	+	27.0394i	−0.629881	+	0.955986i
$801$	4.88472	+	8.46059i	0.172593	+	0.298940i
$802$	−5.06077	−	0.592357i	−0.178702	−	0.0209169i
$803$	−3.28131	+	0.879223i	−0.115795	+	0.0310271i
$804$	−10.1405	+	3.03225i	−0.357627	+	0.106939i
$805$	−53.3909	−	0.622318i	−1.88178	−	0.0219338i
$806$	−14.4880	+	2.11976i	−0.510318	+	0.0746654i
$807$	1.12744	+	0.650930i	0.0396879	+	0.0229138i
$808$	−7.37745	−	5.17113i	−0.259538	−	0.181920i
$809$	−38.9261	+	22.4740i	−1.36857	+	0.790144i	−0.990745	−	0.135734i	$-0.956661\pi$
$809$	−38.9261	+	22.4740i	−1.36857	+	0.790144i	−0.377824	+	0.925877i	$0.623328\pi$
$810$	−11.9508	−	4.75002i	−0.419909	−	0.166899i
$811$	−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	$0.446902\pi$
$812$	10.5124	+	36.7092i	0.368914	+	1.28824i
$813$	−4.52285	−	4.52285i	−0.158623	−	0.158623i
$814$	−22.2601	+	9.59775i	−0.780215	+	0.336401i
$815$	−18.4694	−	31.9899i	−0.646953	−	1.12056i
$816$	3.96777	+	12.0003i	0.138900	+	0.420095i
$817$	−3.42212	+	5.92728i	−0.119725	+	0.207369i
$818$	17.3900	+	12.9508i	0.608026	+	0.452813i
$819$	−26.6071	+	14.9509i	−0.929728	+	0.522426i
$820$	−11.5468	+	21.3982i	−0.403233	+	0.747259i
$821$	−8.32491	−	31.0690i	−0.290541	−	1.08432i	−0.944694	−	0.327953i	$-0.893641\pi$
$821$	−8.32491	−	31.0690i	−0.290541	−	1.08432i	0.654153	−	0.756362i	$-0.273025\pi$
$822$	11.3760	−	8.99196i	0.396784	−	0.313631i
$823$	−5.60251	+	3.23461i	−0.195291	+	0.112751i	−0.594457	−	0.804127i	$-0.702633\pi$
$823$	−5.60251	+	3.23461i	−0.195291	+	0.112751i	0.399166	+	0.916879i	$0.369300\pi$
$824$	6.83054	+	8.14843i	0.237953	+	0.283864i
$825$			14.7781i			0.514506i
$826$	−13.0471	+	5.44599i	−0.453966	+	0.189490i
$827$	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	$0.247549\pi$
$828$	26.9251	+	6.39066i	0.935712	+	0.222091i
$829$	7.38763	−	27.5710i	0.256583	−	0.957581i	−0.710620	−	0.703576i	$-0.751585\pi$
$829$	7.38763	−	27.5710i	0.256583	−	0.957581i	0.967203	−	0.254005i	$-0.0817479\pi$
$830$	2.98705	+	0.349631i	0.103682	+	0.0121359i
$831$	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
$835$	−68.9927	+	18.4865i	−2.38759	+	0.639753i
$836$	−6.77047	+	7.17158i	−0.234162	+	0.248034i
$837$	−8.87022	−	2.37677i	−0.306600	−	0.0821531i
$838$	12.7760	−	32.1438i	0.441339	−	1.11039i
$839$			49.1079i			1.69539i	0.530482	+	0.847696i	$0.322011\pi$
$839$			49.1079i			1.69539i	−0.530482	+	0.847696i	$0.677989\pi$
$840$	−2.11302	+	21.1851i	−0.0729060	+	0.730956i
$841$			23.0742i			0.795662i
$842$	33.9060	+	13.4764i	1.16848	+	0.464428i
$843$	−8.16403	−	2.18755i	−0.281184	−	0.0753431i
$844$	24.5837	−	0.707273i	0.846205	−	0.0243453i
$845$	−42.3752	+	11.3544i	−1.45775	+	0.390603i
$846$	−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
$850$	−3.42294	+	29.2437i	−0.117406	+	1.00305i
$851$	9.20023	−	34.3357i	0.315380	−	1.17701i
$852$	14.1283	−	8.70810i	0.484028	−	0.298334i
$853$	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	$0.216494\pi$
$854$	−15.3843	+	20.1628i	−0.526441	+	0.689957i
$855$			12.2014i			0.417278i
$856$	0.0940187	−	1.06861i	0.00321349	−	0.0365242i
$857$	14.0065	−	8.08667i	0.478454	−	0.276235i	−0.241318	−	0.970446i	$-0.577580\pi$
$857$	14.0065	−	8.08667i	0.478454	−	0.276235i	0.719772	+	0.694211i	$0.244246\pi$
$858$	−11.6320	−	14.7161i	−0.397111	−	0.502398i
$859$	11.5258	+	43.0148i	0.393254	+	1.46765i	0.824733	+	0.565522i	$0.191325\pi$
$859$	11.5258	+	43.0148i	0.393254	+	1.46765i	−0.431479	+	0.902123i	$0.642008\pi$
$860$	25.8808	−	7.73899i	0.882528	−	0.263897i
$861$	−0.0994554	+	8.53264i	−0.00338943	+	0.290791i
$862$	28.3983	−	38.1325i	0.967249	−	1.29880i
$863$	−2.85176	+	4.93940i	−0.0970752	+	0.168139i	−0.910473	−	0.413569i	$-0.864282\pi$
$863$	−2.85176	+	4.93940i	−0.0970752	+	0.168139i	0.813398	+	0.581708i	$0.197615\pi$
$864$	8.12823	−	24.4627i	0.276528	−	0.832237i
$865$	37.1891	+	64.4134i	1.26447	+	2.19012i
$866$	14.8667	+	34.4805i	0.505192	+	1.17169i
$867$	−2.31679	−	2.31679i	−0.0786822	−	0.0786822i
$868$	−0.182409	−	10.6619i	−0.00619136	−	0.361890i
$869$	0.507233	−	0.507233i	0.0172067	−	0.0172067i
$870$	−10.7241	+	26.9813i	−0.363580	+	0.914751i
$871$	27.1034	−	15.6482i	0.918364	−	0.530218i
$872$	−16.2300	+	23.1547i	−0.549617	+	0.784116i
$873$	13.2256	+	7.63580i	0.447619	+	0.258433i
$874$	−2.09374	−	14.3101i	−0.0708217	−	0.484047i
$875$	−3.20045	+	5.39708i	−0.108195	+	0.182455i
$876$	−1.74801	−	0.943255i	−0.0590598	−	0.0318696i
$877$	−15.2754	+	4.09303i	−0.515814	+	0.138212i	−0.507330	−	0.861752i	$-0.669367\pi$
$877$	−15.2754	+	4.09303i	−0.515814	+	0.138212i	−0.00848425	+	0.999964i	$0.502701\pi$
$878$	3.22417	−	27.5455i	0.108810	−	0.929615i
$879$	−1.15571	−	2.00176i	−0.0389813	−	0.0675175i
$880$	38.8617	−	2.23796i	1.31003	−	0.0754415i
$881$	20.6047			0.694190			0.347095	−	0.937830i	$-0.387168\pi$
$881$	20.6047			0.694190			0.347095	+	0.937830i	$0.387168\pi$
$882$	−8.32211	−	20.6100i	−0.280220	−	0.693974i
$883$	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	$0.720191\pi$
$884$	−19.6096	−	31.8153i	−0.659543	−	1.07006i
$885$	−10.3838	−	2.78233i	−0.349048	−	0.0935270i
$886$	−7.56876	+	5.98259i	−0.254277	+	0.200989i
$887$	16.0874	+	9.28808i	0.540163	+	0.311863i	0.745145	−	0.666903i	$-0.232380\pi$
$887$	16.0874	+	9.28808i	0.540163	+	0.311863i	−0.204982	+	0.978766i	$0.565714\pi$
$888$	−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
$891$	2.13573	+	7.97063i	0.0715495	+	0.267026i
$892$	−30.1340	+	31.9193i	−1.00896	+	1.06874i
$893$	−4.35135	+	16.2394i	−0.145612	+	0.543432i
$894$	−5.71533	−	13.2556i	−0.191149	−	0.443333i
$895$	−70.4965			−2.35644
$896$	29.9070	+	1.25347i	0.999123	+	0.0418755i
$897$	27.5068			0.918426
$898$	3.54106	+	8.21278i	0.118167	+	0.274064i
$899$	3.76382	−	14.0468i	0.125530	−	0.468486i
$900$	17.6456	−	18.6910i	0.588185	−	0.623032i
$901$	−3.58924	−	13.3952i	−0.119575	−	0.446260i
$902$	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
$906$	18.8991	−	14.9385i	0.627881	−	0.496297i
$907$	−27.5535	−	7.38295i	−0.914900	−	0.245147i	−0.229496	−	0.973310i	$-0.573708\pi$
$907$	−27.5535	−	7.38295i	−0.914900	−	0.245147i	−0.685404	+	0.728163i	$0.740374\pi$
$908$	−25.8876	−	42.0008i	−0.859109	−	1.39385i
$909$	5.05701	+	5.05701i	0.167730	+	0.167730i
$910$	−8.38714	−	62.3921i	−0.278031	−	2.06828i
$911$	40.6520			1.34686			0.673431	−	0.739250i	$-0.264820\pi$
$911$	40.6520			1.34686			0.673431	+	0.739250i	$0.264820\pi$
$912$	−5.75715	+	0.331541i	−0.190638	+	0.0109784i
$913$	−0.964870	−	1.67120i	−0.0319325	−	0.0553088i
$914$	6.49392	−	55.4804i	0.214800	−	1.83513i
$915$	−18.6271	+	4.99111i	−0.615792	+	0.165001i
$916$	16.7462	+	9.03653i	0.553310	+	0.298575i
$917$	12.0433	+	21.4326i	0.397703	+	0.707767i
$918$	−3.39329	−	23.1922i	−0.111995	−	0.765458i
$919$	−23.3547	−	13.4838i	−0.770400	−	0.444790i	0.0626175	−	0.998038i	$-0.480055\pi$
$919$	−23.3547	−	13.4838i	−0.770400	−	0.444790i	−0.833017	+	0.553247i	$0.813389\pi$
$920$	−32.7633	+	46.7421i	−1.08017	+	1.54104i
$921$	4.24519	−	2.45096i	0.139884	−	0.0807619i
$922$	0.936491	−	2.35617i	0.0308417	−	0.0775962i
$923$	−34.7005	+	34.7005i	−1.14218	+	1.14218i
$924$	11.7122	−	7.03186i	0.385302	−	0.231331i
$925$	−23.3473	−	23.3473i	−0.767656	−	0.767656i
$926$	−8.08687	−	18.7559i	−0.265751	−	0.616357i
$927$	−4.22017	−	7.30954i	−0.138608	−	0.240077i
$928$	38.7388	+	12.8718i	1.27166	+	0.422536i
$929$	−7.81601	+	13.5377i	−0.256435	+	0.444159i	−0.965284	−	0.261201i	$-0.915881\pi$
$929$	−7.81601	+	13.5377i	−0.256435	+	0.444159i	0.708849	+	0.705360i	$0.249215\pi$
$930$	4.84292	−	6.50295i	0.158806	−	0.213240i
$931$	−8.40305	+	8.02015i	−0.275399	+	0.262850i
$932$	−42.6110	+	12.7417i	−1.39577	+	0.417369i
$933$	−0.181703	−	0.678124i	−0.00594868	−	0.0222008i
$934$	15.2342	+	19.2732i	0.498477	+	0.630639i
$935$	30.6527	−	17.6974i	1.00245	−	0.578766i
$936$	−2.85958	+	32.5017i	−0.0934682	+	1.06235i
$937$		−	47.9244i		−	1.56562i	−0.622260	−	0.782811i	$-0.713785\pi$
$937$		−	47.9244i		−	1.56562i	0.622260	−	0.782811i	$-0.286215\pi$
$938$	8.77955	+	21.0334i	0.286662	+	0.686764i
$939$	−14.3107	+	14.3107i	−0.467013	+	0.467013i
$940$	56.4877	−	34.8167i	1.84243	−	1.13559i
$941$	2.78937	−	10.4101i	0.0909309	−	0.339359i	−0.905440	−	0.424474i	$-0.860459\pi$
$941$	2.78937	−	10.4101i	0.0909309	−	0.339359i	0.996371	+	0.0851151i	$0.0271258\pi$
$942$	−0.772407	+	6.59901i	−0.0251664	+	0.215007i
$943$	−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
$947$	26.8088	−	7.18339i	0.871168	−	0.233429i	0.204575	−	0.978851i	$-0.434419\pi$
$947$	26.8088	−	7.18339i	0.871168	−	0.233429i	0.666593	+	0.745422i	$0.267752\pi$
$948$	0.419255	−	0.0120620i	0.0136168	−	0.000391755i
$949$	5.67309	+	1.52010i	0.184156	+	0.0493446i
$950$	−12.4837	−	4.96181i	−0.405024	−	0.160982i
$951$		−	2.71283i		−	0.0879696i
$952$	24.8055	−	11.2023i	0.803951	−	0.363067i
$953$			3.58597i			0.116161i	0.998312	+	0.0580805i	$0.0184980\pi$
$953$			3.58597i			0.116161i	−0.998312	+	0.0580805i	$0.981502\pi$
$954$	−4.47172	+	11.2506i	−0.144777	+	0.364253i
$955$	−24.9513	−	6.68567i	−0.807404	−	0.216343i
$956$	−20.5366	+	21.7533i	−0.664202	+	0.703552i
$957$	17.9952	−	4.82181i	0.581703	−	0.155867i
$958$	−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
$962$	41.6265	+	4.87233i	1.34209	+	0.157090i
$963$	−0.220398	+	0.822535i	−0.00710221	+	0.0265058i
$964$	−47.3837	−	11.2465i	−1.52613	−	0.362225i
$965$	57.6144	−	57.6144i	1.85467	−	1.85467i
$966$	−2.56061	+	19.8681i	−0.0823862	+	0.639245i
$967$			51.9947i			1.67204i	0.548703	+	0.836018i	$0.315122\pi$
$967$			51.9947i			1.67204i	−0.548703	+	0.836018i	$0.684878\pi$
$968$	3.94158	+	4.70207i	0.126687	+	0.151130i
$969$	−4.54103	+	2.62177i	−0.145879	+	0.0842233i
$970$	−24.7128	+	19.5338i	−0.793479	+	0.627191i
$971$	−12.8403	−	47.9206i	−0.412064	−	1.53785i	−0.790644	−	0.612277i	$-0.790254\pi$
$971$	−12.8403	−	47.9206i	−0.412064	−	1.53785i	0.378579	−	0.925569i	$-0.376413\pi$
$972$	−15.2754	+	28.3078i	−0.489958	+	0.907973i
$973$	−26.2523	−	15.5675i	−0.841610	−	0.499072i
$974$	−30.4768	−	22.6968i	−0.976538	−	0.727254i
$975$	12.7750	−	22.1269i	0.409127	−	0.708629i
$976$	8.51137	+	25.7422i	0.272442	+	0.823988i
$977$	−2.83541	−	4.91108i	−0.0907129	−	0.157119i	0.817098	−	0.576498i	$-0.195581\pi$
$977$	−2.83541	−	4.91108i	−0.0907129	−	0.157119i	−0.907811	+	0.419379i	$0.862248\pi$
$978$	−12.7261	+	5.48702i	−0.406934	+	0.175455i
$979$	9.14303	+	9.14303i	0.292213	+	0.292213i
$980$	45.8463	−	0.249928i	1.46451	−	0.00798364i
$981$	15.8718	−	15.8718i	0.506748	−	0.506748i
$982$	−21.8523	−	8.68549i	−0.697335	−	0.277165i
$983$	−40.4834	+	23.3731i	−1.29122	+	0.745486i	−0.978870	−	0.204482i	$-0.934449\pi$
$983$	−40.4834	+	23.3731i	−1.29122	+	0.745486i	−0.312349	+	0.949968i	$0.601116\pi$
$984$	7.47006	+	5.23605i	0.238137	+	0.166919i
$985$	−31.0998	−	17.9555i	−0.990923	−	0.572110i
$986$	36.7269	−	5.37357i	1.16962	−	0.171129i
$987$	11.8779	−	20.0303i	0.378077	−	0.637570i
$988$	16.3368	−	4.88511i	0.519744	−	0.155416i
$989$	24.5511	−	6.57845i	0.780679	−	0.209182i
$990$	−30.6905	−	3.59229i	−0.975409	−	0.114170i
$991$	−7.20690	−	12.4827i	−0.228935	−	0.396527i	0.728558	−	0.684984i	$-0.240191\pi$
$991$	−7.20690	−	12.4827i	−0.228935	−	0.396527i	−0.957493	+	0.288457i	$0.906858\pi$
$992$	−9.51925	−	6.27205i	−0.302236	−	0.199138i
$993$	−13.6857			−0.434303
$994$	−21.8338	−	28.2943i	−0.692526	−	0.897442i
$995$	26.5073	+	26.5073i	0.840339	+	0.840339i
$996$	0.260568	−	1.09783i	0.00825642	−	0.0347859i
$997$	−54.9322	−	14.7190i	−1.73972	−	0.466156i	−0.757334	−	0.653027i	$-0.773499\pi$
$997$	−54.9322	−	14.7190i	−1.73972	−	0.466156i	−0.982384	+	0.186871i	$0.940165\pi$
$998$	17.2838	+	21.8663i	0.547110	+	0.692166i
$999$	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.93.9	yes	48
4.3	odd	2		448.2.ba.c.401.5		48
7.2	even	3		784.2.m.j.589.8		24
7.3	odd	6		784.2.x.o.557.1		48
7.4	even	3	inner	112.2.w.c.109.1	yes	48
7.5	odd	6		784.2.m.k.589.8		24
7.6	odd	2		784.2.x.o.765.9		48
8.3	odd	2		896.2.ba.e.289.8		48
8.5	even	2		896.2.ba.f.289.5		48
16.3	odd	4		896.2.ba.e.737.5		48
16.5	even	4	inner	112.2.w.c.37.1	✓	48
16.11	odd	4		448.2.ba.c.177.8		48
16.13	even	4		896.2.ba.f.737.8		48
28.11	odd	6		448.2.ba.c.81.8		48
56.11	odd	6		896.2.ba.e.417.5		48
56.53	even	6		896.2.ba.f.417.8		48
112.5	odd	12		784.2.m.k.197.8		24
112.11	odd	12		448.2.ba.c.305.5		48
112.37	even	12		784.2.m.j.197.8		24
112.53	even	12	inner	112.2.w.c.53.9	yes	48
112.67	odd	12		896.2.ba.e.865.8		48
112.69	odd	4		784.2.x.o.373.1		48
112.101	odd	12		784.2.x.o.165.9		48
112.109	even	12		896.2.ba.f.865.5		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
112.2.w.c.37.1	✓	48	16.5	even	4	inner
112.2.w.c.53.9	yes	48	112.53	even	12	inner
112.2.w.c.93.9	yes	48	1.1	even	1	trivial
112.2.w.c.109.1	yes	48	7.4	even	3	inner
448.2.ba.c.81.8		48	28.11	odd	6
448.2.ba.c.177.8		48	16.11	odd	4
448.2.ba.c.305.5		48	112.11	odd	12
448.2.ba.c.401.5		48	4.3	odd	2
784.2.m.j.197.8		24	112.37	even	12
784.2.m.j.589.8		24	7.2	even	3
784.2.m.k.197.8		24	112.5	odd	12
784.2.m.k.589.8		24	7.5	odd	6
784.2.x.o.165.9		48	112.101	odd	12
784.2.x.o.373.1		48	112.69	odd	4
784.2.x.o.557.1		48	7.3	odd	6
784.2.x.o.765.9		48	7.6	odd	2
896.2.ba.e.289.8		48	8.3	odd	2
896.2.ba.e.417.5		48	56.11	odd	6
896.2.ba.e.737.5		48	16.3	odd	4
896.2.ba.e.865.8		48	112.67	odd	12
896.2.ba.f.289.5		48	8.5	even	2
896.2.ba.f.417.8		48	56.53	even	6
896.2.ba.f.737.8		48	16.13	even	4
896.2.ba.f.865.5		48	112.109	even	12

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+(0.559929 + 1.29865i) q^{2} +(0.224854 - 0.839165i) q^{3} +(-1.37296 + 1.45430i) q^{4} +(0.847576 + 3.16320i) 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} +(-3.63329 + 2.87187i) q^{10} +(2.87040 + 0.769121i) q^{11} +(0.911683 + 1.47914i) q^{12} +(-3.63293 - 3.63293i) q^{13} +(2.96224 - 2.28586i) q^{14} +2.84503 q^{15} +(-0.229970 - 3.99338i) q^{16} +(-1.81856 - 3.14984i) q^{17} +(-0.369139 + 3.15372i) q^{18} +(1.60290 - 0.429496i) q^{19} +(-5.76392 - 3.11031i) q^{20} +(-2.29839 - 0.0267897i) q^{21} +(0.608405 + 4.15828i) q^{22} +(-5.33698 - 3.08131i) q^{23} +(-1.41041 + 2.01217i) q^{24} +(-4.95730 + 2.86210i) q^{25} +(2.68370 - 6.75207i) q^{26} +(3.22221 - 3.22221i) q^{27} +(4.62716 + 2.56698i) q^{28} +(5.10266 + 5.10266i) q^{29} +(1.59301 + 3.69468i) q^{30} +(-1.00761 - 1.74523i) q^{31} +(5.05722 - 2.53466i) q^{32} +(1.29084 - 2.23580i) q^{33} +(3.07226 - 4.12535i) q^{34} +(7.55345 - 4.24438i) q^{35} +(-4.30226 + 1.28648i) q^{36} +(1.49291 + 5.57162i) q^{37} +(1.45527 + 1.84111i) q^{38} +(-3.86550 + 2.23175i) q^{39} +(0.811801 - 9.22684i) q^{40} -3.71244i q^{41} +(-1.25214 - 2.99979i) q^{42} +(-2.91640 + 2.91640i) q^{43} +(-5.05947 + 3.11845i) q^{44} +(-1.90301 + 7.10214i) q^{45} +(1.01319 - 8.65616i) 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} +(-3.05215 + 0.817820i) q^{51} +(10.2712 - 0.295503i) q^{52} +(3.68292 + 0.986836i) q^{53} +(5.98872 + 2.38030i) q^{54} +9.73153i q^{55} +(-0.742706 + 7.44637i) q^{56} -1.44167i q^{57} +(-3.76941 + 9.48367i) q^{58} +(-3.64981 - 0.977963i) q^{59} +(-3.90610 + 4.13752i) q^{60} +(-6.54724 + 1.75433i) 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} +(3.62629 + 0.424453i) q^{66} +(-1.57659 + 5.88390i) q^{67} +(7.07761 + 1.67987i) q^{68} +(-3.78577 + 3.78577i) q^{69} +(9.74134 + 7.43270i) q^{70} -9.55168i q^{71} +(-4.07964 - 4.86677i) q^{72} +(-0.990000 + 0.571577i) q^{73} +(-6.39963 + 5.05847i) q^{74} +(1.28711 + 4.80355i) q^{75} +(-1.57610 + 2.92078i) q^{76} +(0.0916354 - 7.86173i) q^{77} +(-5.06266 - 3.77030i) q^{78} +(0.120696 - 0.209052i) q^{79} +(12.4369 - 4.11214i) q^{80} +(1.38842 + 2.40481i) q^{81} +(4.82115 - 2.07871i) q^{82} +(-0.459183 - 0.459183i) q^{83} +(3.19455 - 3.30576i) q^{84} +(8.42219 - 8.42219i) q^{85} +(-5.42035 - 2.15439i) q^{86} +(5.42932 - 3.13462i) q^{87} +(-6.88270 - 4.82435i) q^{88} +(3.76823 + 2.17559i) q^{89} +(-10.2887 + 1.50536i) q^{90} +(-6.93333 + 11.6920i) q^{91} +(11.8086 - 3.53106i) q^{92} +(-1.69110 + 0.453128i) q^{93} +(-14.2307 - 1.66568i) q^{94} +(2.71716 + 4.70626i) q^{95} +(-0.989865 - 4.81377i) q^{96} +6.80176 q^{97} +(-7.79967 - 6.09632i) 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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