LMFDB - Embedded newform 273.2.cd.e.242.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [273,2,Mod(44,273)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(273, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 4, 9]))

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

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

chi := DirichletCharacter("273.44");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 273 = 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	273.cd (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.17991597518$
Analytic rank:	$0$
Dimension:	$112$
Relative dimension:	$28$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			242.15
Character	$\chi$	$=$	273.242
Dual form			273.2.cd.e.44.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.246180 + 0.0659636i) q^{2} +(1.72740 - 0.126782i) q^{3} +(-1.67580 - 0.967522i) q^{4} +(2.71744 + 0.728135i) q^{5} +(0.433615 + 0.0827348i) q^{6} +(1.41179 + 2.23760i) q^{7} +(-0.709158 - 0.709158i) q^{8} +(2.96785 - 0.438007i) q^{9} +O(q^{10})$	\(q+(0.246180 + 0.0659636i) q^{2} +(1.72740 - 0.126782i) q^{3} +(-1.67580 - 0.967522i) q^{4} +(2.71744 + 0.728135i) q^{5} +(0.433615 + 0.0827348i) q^{6} +(1.41179 + 2.23760i) q^{7} +(-0.709158 - 0.709158i) q^{8} +(2.96785 - 0.438007i) q^{9} +(0.620947 + 0.358504i) q^{10} +(-3.10321 + 0.831504i) q^{11} +(-3.01744 - 1.45884i) q^{12} +(-3.47296 - 0.968803i) q^{13} +(0.199953 + 0.643978i) q^{14} +(4.78643 + 0.913262i) q^{15} +(1.80724 + 3.13024i) q^{16} +(3.96062 - 6.86000i) q^{17} +(0.759517 + 0.0879420i) q^{18} +(-0.0189720 + 0.0708044i) q^{19} +(-3.84939 - 3.84939i) q^{20} +(2.72242 + 3.68625i) q^{21} -0.818797 q^{22} +(1.44544 + 2.50358i) q^{23} +(-1.31491 - 1.13509i) q^{24} +(2.52416 + 1.45732i) q^{25} +(-0.791065 - 0.467588i) q^{26} +(5.07115 - 1.13288i) q^{27} +(-0.200944 - 5.11570i) q^{28} +0.0351243i q^{29} +(1.11808 + 0.540557i) q^{30} +(-8.23449 + 2.20642i) q^{31} +(0.757564 + 2.82727i) q^{32} +(-5.25509 + 1.82977i) q^{33} +(1.42753 - 1.42753i) q^{34} +(2.20717 + 7.10851i) q^{35} +(-5.39730 - 2.13745i) q^{36} +(-8.86476 - 2.37531i) q^{37} +(-0.00934103 + 0.0161791i) q^{38} +(-6.12203 - 1.23321i) q^{39} +(-1.41073 - 2.44345i) q^{40} +(-1.39282 + 1.39282i) q^{41} +(0.427045 + 1.08706i) q^{42} -0.378909i q^{43} +(6.00486 + 1.60900i) q^{44} +(8.38388 + 0.970742i) q^{45} +(0.190693 + 0.711676i) q^{46} +(-0.516348 + 1.92704i) q^{47} +(3.51870 + 5.17806i) q^{48} +(-3.01371 + 6.31804i) q^{49} +(0.525266 + 0.525266i) q^{50} +(5.97187 - 12.3521i) q^{51} +(4.88263 + 4.98368i) q^{52} +(-5.88649 - 3.39856i) q^{53} +(1.32314 + 0.0556184i) q^{54} -9.03824 q^{55} +(0.585631 - 2.58799i) q^{56} +(-0.0237956 + 0.124713i) q^{57} +(-0.00231692 + 0.00864688i) q^{58} +(8.27883 - 2.21831i) q^{59} +(-7.13748 - 6.16142i) q^{60} +(-4.83406 - 8.37284i) q^{61} -2.17271 q^{62} +(5.17006 + 6.02249i) q^{63} -6.48298i q^{64} +(-8.73212 - 5.16144i) q^{65} +(-1.41439 + 0.103809i) q^{66} +(-4.85879 + 1.30191i) q^{67} +(-13.2744 + 7.66398i) q^{68} +(2.81427 + 4.14143i) q^{69} +(0.0744576 + 1.89556i) q^{70} +(1.74479 - 1.74479i) q^{71} +(-2.41529 - 1.79406i) q^{72} +(2.08150 + 7.76825i) q^{73} +(-2.02564 - 1.16950i) q^{74} +(4.54500 + 2.19737i) q^{75} +(0.100298 - 0.100298i) q^{76} +(-6.24166 - 5.76984i) q^{77} +(-1.42577 - 0.707422i) q^{78} +(3.79033 + 6.56505i) q^{79} +(2.63183 + 9.82214i) q^{80} +(8.61630 - 2.59988i) q^{81} +(-0.434759 + 0.251008i) q^{82} +(3.46542 - 3.46542i) q^{83} +(-0.995690 - 8.81141i) q^{84} +(15.7578 - 15.7578i) q^{85} +(0.0249942 - 0.0932797i) q^{86} +(0.00445312 + 0.0606738i) q^{87} +(2.79034 + 1.61100i) q^{88} +(-3.92087 + 14.6329i) q^{89} +(1.99991 + 0.792008i) q^{90} +(-2.73529 - 9.13883i) q^{91} -5.59398i q^{92} +(-13.9446 + 4.85537i) q^{93} +(-0.254229 + 0.440337i) q^{94} +(-0.103110 + 0.178592i) q^{95} +(1.66707 + 4.78779i) q^{96} +(0.107635 + 0.107635i) q^{97} +(-1.15867 + 1.35658i) q^{98} +(-8.84568 + 3.82701i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 112 q - 12 q^{3} - 8 q^{6} - 4 q^{7} + 8 q^{9}+O(q^{10}) $ 112 * q - 12 * q^3 - 8 * q^6 - 4 * q^7 + 8 * q^9	$ 112 q - 12 q^{3} - 8 q^{6} - 4 q^{7} + 8 q^{9} - 48 q^{13} - 12 q^{15} + 40 q^{16} - 26 q^{18} + 40 q^{19} - 10 q^{21} + 16 q^{22} + 32 q^{24} - 24 q^{27} - 52 q^{28} - 12 q^{31} - 44 q^{33} + 16 q^{34} - 8 q^{37} - 42 q^{39} - 160 q^{40} - 80 q^{42} + 6 q^{45} + 32 q^{46} + 72 q^{48} - 12 q^{52} + 34 q^{54} - 48 q^{55} - 24 q^{57} - 28 q^{58} + 44 q^{60} + 78 q^{63} + 4 q^{66} + 24 q^{67} - 12 q^{70} - 26 q^{72} - 40 q^{73} + 112 q^{76} + 32 q^{78} + 48 q^{79} + 128 q^{81} - 150 q^{84} + 160 q^{85} - 48 q^{87} + 24 q^{91} + 10 q^{93} - 8 q^{94} - 106 q^{96} + 56 q^{97} - 36 q^{99}+O(q^{100}) $ 112 * q - 12 * q^3 - 8 * q^6 - 4 * q^7 + 8 * q^9 - 48 * q^13 - 12 * q^15 + 40 * q^16 - 26 * q^18 + 40 * q^19 - 10 * q^21 + 16 * q^22 + 32 * q^24 - 24 * q^27 - 52 * q^28 - 12 * q^31 - 44 * q^33 + 16 * q^34 - 8 * q^37 - 42 * q^39 - 160 * q^40 - 80 * q^42 + 6 * q^45 + 32 * q^46 + 72 * q^48 - 12 * q^52 + 34 * q^54 - 48 * q^55 - 24 * q^57 - 28 * q^58 + 44 * q^60 + 78 * q^63 + 4 * q^66 + 24 * q^67 - 12 * q^70 - 26 * q^72 - 40 * q^73 + 112 * q^76 + 32 * q^78 + 48 * q^79 + 128 * q^81 - 150 * q^84 + 160 * q^85 - 48 * q^87 + 24 * q^91 + 10 * q^93 - 8 * q^94 - 106 * q^96 + 56 * q^97 - 36 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/273\mathbb{Z}\right)^\times$.

$n$	$92$	$106$	$157$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	0.246180	+	0.0659636i	0.174075	+	0.0466433i	0.344804	−	0.938675i	$-0.387945\pi$
$2$	0.246180	+	0.0659636i	0.174075	+	0.0466433i	−0.170729	+	0.985318i	$0.554612\pi$
$3$	1.72740	−	0.126782i	0.997317	−	0.0731975i
$3$	1.72740	−	0.126782i	0.997317	−	0.0731975i
$4$	−1.67580	−	0.967522i	−0.837899	−	0.483761i
$5$	2.71744	+	0.728135i	1.21527	+	0.325632i	0.808830	−	0.588043i	$-0.200101\pi$
$5$	2.71744	+	0.728135i	1.21527	+	0.325632i	0.406445	+	0.913675i	$0.366768\pi$
$6$	0.433615	+	0.0827348i	0.177022	+	0.0337763i
$7$	1.41179	+	2.23760i	0.533606	+	0.845733i
$7$	1.41179	+	2.23760i	0.533606	+	0.845733i
$8$	−0.709158	−	0.709158i	−0.250725	−	0.250725i
$9$	2.96785	−	0.438007i	0.989284	−	0.146002i
$10$	0.620947	+	0.358504i	0.196361	+	0.113369i
$11$	−3.10321	+	0.831504i	−0.935654	+	0.250708i	−0.694264	−	0.719720i	$-0.744270\pi$
$11$	−3.10321	+	0.831504i	−0.935654	+	0.250708i	−0.241390	+	0.970428i	$0.577603\pi$
$12$	−3.01744	−	1.45884i	−0.871061	−	0.421131i
$13$	−3.47296	−	0.968803i	−0.963225	−	0.268698i
$13$	−3.47296	−	0.968803i	−0.963225	−	0.268698i
$14$	0.199953	+	0.643978i	0.0534398	+	0.172110i
$15$	4.78643	+	0.913262i	1.23585	+	0.235803i
$16$	1.80724	+	3.13024i	0.451811	+	0.782559i
$17$	3.96062	−	6.86000i	0.960592	−	1.66379i	0.239574	−	0.970878i	$-0.422992\pi$
$17$	3.96062	−	6.86000i	0.960592	−	1.66379i	0.721018	−	0.692916i	$-0.243674\pi$
$18$	0.759517	+	0.0879420i	0.179020	+	0.0207281i
$19$	−0.0189720	+	0.0708044i	−0.00435247	+	0.0162437i	−0.968068	−	0.250688i	$-0.919343\pi$
$19$	−0.0189720	+	0.0708044i	−0.00435247	+	0.0162437i	0.963715	+	0.266932i	$0.0860098\pi$
$20$	−3.84939	−	3.84939i	−0.860749	−	0.860749i
$21$	2.72242	+	3.68625i	0.594080	+	0.804406i
$22$	−0.818797			−0.174568
$23$	1.44544	+	2.50358i	0.301395	+	0.522032i	0.976452	−	0.215734i	$-0.0692143\pi$
$23$	1.44544	+	2.50358i	0.301395	+	0.522032i	−0.675057	+	0.737766i	$0.735881\pi$
$24$	−1.31491	−	1.13509i	−0.268405	−	0.231700i
$25$	2.52416	+	1.45732i	0.504832	+	0.291465i
$26$	−0.791065	−	0.467588i	−0.155141	−	0.0917016i
$27$	5.07115	−	1.13288i	0.975943	−	0.218024i
$28$	−0.200944	−	5.11570i	−0.0379749	−	0.966777i
$29$			0.0351243i			0.00652242i	0.999995	+	0.00326121i	$0.00103808\pi$
$29$			0.0351243i			0.00652242i	−0.999995	+	0.00326121i	$0.998962\pi$
$30$	1.11808	+	0.540557i	0.204132	+	0.0986917i
$31$	−8.23449	+	2.20642i	−1.47896	+	0.396286i	−0.905992	−	0.423294i	$-0.860874\pi$
$31$	−8.23449	+	2.20642i	−1.47896	+	0.396286i	−0.572966	+	0.819579i	$0.694207\pi$
$32$	0.757564	+	2.82727i	0.133920	+	0.499795i
$33$	−5.25509	+	1.82977i	−0.914793	+	0.318523i
$34$	1.42753	−	1.42753i	0.244820	−	0.244820i
$35$	2.20717	+	7.10851i	0.373080	+	1.20156i
$36$	−5.39730	−	2.13745i	−0.899550	−	0.356242i
$37$	−8.86476	−	2.37531i	−1.45736	−	0.390498i	−0.558781	−	0.829315i	$-0.688731\pi$
$37$	−8.86476	−	2.37531i	−1.45736	−	0.390498i	−0.898576	+	0.438817i	$0.855398\pi$
$38$	−0.00934103	+	0.0161791i	−0.00151532	+	0.00262460i
$39$	−6.12203	−	1.23321i	−0.980309	−	0.197471i
$40$	−1.41073	−	2.44345i	−0.223056	−	0.386344i
$41$	−1.39282	+	1.39282i	−0.217522	+	0.217522i	−0.807453	−	0.589931i	$-0.799155\pi$
$41$	−1.39282	+	1.39282i	−0.217522	+	0.217522i	0.589931	+	0.807453i	$0.299155\pi$
$42$	0.427045	+	1.08706i	0.0658945	+	0.167737i
$43$		−	0.378909i		−	0.0577831i	−0.999583	−	0.0288916i	$-0.990802\pi$
$43$		−	0.378909i		−	0.0577831i	0.999583	−	0.0288916i	$-0.00919775\pi$
$44$	6.00486	+	1.60900i	0.905266	+	0.242565i
$45$	8.38388	+	0.970742i	1.24980	+	0.144710i
$46$	0.190693	+	0.711676i	0.0281162	+	0.104931i
$47$	−0.516348	+	1.92704i	−0.0753171	+	0.281087i	−0.993305	−	0.115521i	$-0.963146\pi$
$47$	−0.516348	+	1.92704i	−0.0753171	+	0.281087i	0.917988	+	0.396608i	$0.129813\pi$
$48$	3.51870	+	5.17806i	0.507880	+	0.747388i
$49$	−3.01371	+	6.31804i	−0.430529	+	0.902577i
$50$	0.525266	+	0.525266i	0.0742838	+	0.0742838i
$51$	5.97187	−	12.3521i	0.836230	−	1.72964i
$52$	4.88263	+	4.98368i	0.677099	+	0.691112i
$53$	−5.88649	−	3.39856i	−0.808571	−	0.466829i	0.0378884	−	0.999282i	$-0.487937\pi$
$53$	−5.88649	−	3.39856i	−0.808571	−	0.466829i	−0.846459	+	0.532453i	$0.821270\pi$
$54$	1.32314	+	0.0556184i	0.180057	+	0.00756871i
$55$	−9.03824			−1.21872
$56$	0.585631	−	2.58799i	0.0782582	−	0.345835i
$57$	−0.0237956	+	0.124713i	−0.00315180	+	0.0165187i
$58$	−0.00231692	+	0.00864688i	−0.000304227	+	0.00113539i
$59$	8.27883	−	2.21831i	1.07781	−	0.288799i	0.324113	−	0.946018i	$-0.394934\pi$
$59$	8.27883	−	2.21831i	1.07781	−	0.288799i	0.753699	+	0.657219i	$0.228268\pi$
$60$	−7.13748	−	6.16142i	−0.921445	−	0.795436i
$61$	−4.83406	−	8.37284i	−0.618938	−	1.07203i	−0.989680	−	0.143297i	$-0.954230\pi$
$61$	−4.83406	−	8.37284i	−0.618938	−	1.07203i	0.370741	−	0.928736i	$-0.379104\pi$
$62$	−2.17271			−0.275934
$63$	5.17006	+	6.02249i	0.651367	+	0.758763i
$64$		−	6.48298i		−	0.810373i
$65$	−8.73212	−	5.16144i	−1.08309	−	0.640198i
$66$	−1.41439	+	0.103809i	−0.174100	+	0.0127779i
$67$	−4.85879	+	1.30191i	−0.593595	+	0.159053i	−0.543096	−	0.839671i	$-0.682748\pi$
$67$	−4.85879	+	1.30191i	−0.593595	+	0.159053i	−0.0504994	+	0.998724i	$0.516081\pi$
$68$	−13.2744	+	7.66398i	−1.60976	+	0.929394i
$69$	2.81427	+	4.14143i	0.338798	+	0.498570i
$70$	0.0744576	+	1.89556i	0.00889938	+	0.226563i
$71$	1.74479	−	1.74479i	0.207068	−	0.207068i	−0.595952	−	0.803020i	$-0.703225\pi$
$71$	1.74479	−	1.74479i	0.207068	−	0.207068i	0.803020	+	0.595952i	$0.203225\pi$
$72$	−2.41529	−	1.79406i	−0.284645	−	0.211432i
$73$	2.08150	+	7.76825i	0.243621	+	0.909205i	0.974072	+	0.226240i	$0.0726433\pi$
$73$	2.08150	+	7.76825i	0.243621	+	0.909205i	−0.730451	+	0.682965i	$0.760690\pi$
$74$	−2.02564	−	1.16950i	−0.235476	−	0.135952i
$75$	4.54500	+	2.19737i	0.524812	+	0.253730i
$76$	0.100298	−	0.100298i	0.0115050	−	0.0115050i
$77$	−6.24166	−	5.76984i	−0.711303	−	0.657535i
$78$	−1.42577	−	0.707422i	−0.161437	−	0.0800997i
$79$	3.79033	+	6.56505i	0.426446	+	0.738626i	0.996554	−	0.0829437i	$-0.0264322\pi$
$79$	3.79033	+	6.56505i	0.426446	+	0.738626i	−0.570108	+	0.821569i	$0.693099\pi$
$80$	2.63183	+	9.82214i	0.294248	+	1.09815i
$81$	8.61630	−	2.59988i	0.957367	−	0.288875i
$82$	−0.434759	+	0.251008i	−0.0480111	+	0.0277192i
$83$	3.46542	−	3.46542i	0.380379	−	0.380379i	−0.490860	−	0.871239i	$-0.663317\pi$
$83$	3.46542	−	3.46542i	0.380379	−	0.380379i	0.871239	+	0.490860i	$0.163317\pi$
$84$	−0.995690	−	8.81141i	−0.108639	−	0.961404i
$85$	15.7578	−	15.7578i	1.70917	−	1.70917i
$86$	0.0249942	−	0.0932797i	0.00269520	−	0.0100586i
$87$	0.00445312	+	0.0606738i	0.000477424	+	0.00650492i
$88$	2.79034	+	1.61100i	0.297451	+	0.171733i
$89$	−3.92087	+	14.6329i	−0.415611	+	1.55108i	0.367997	+	0.929827i	$0.380044\pi$
$89$	−3.92087	+	14.6329i	−0.415611	+	1.55108i	−0.783608	+	0.621255i	$0.786623\pi$
$90$	1.99991	+	0.792008i	0.210809	+	0.0834850i
$91$	−2.73529	−	9.13883i	−0.286736	−	0.958010i
$92$		−	5.59398i		−	0.583213i
$93$	−13.9446	+	4.85537i	−1.44598	+	0.503479i
$94$	−0.254229	+	0.440337i	−0.0262217	+	0.0454173i
$95$	−0.103110	+	0.178592i	−0.0105789	+	0.0183232i
$96$	1.66707	+	4.78779i	0.170144	+	0.488652i
$97$	0.107635	+	0.107635i	0.0109287	+	0.0109287i	0.712550	−	0.701621i	$-0.247540\pi$
$97$	0.107635	+	0.107635i	0.0109287	+	0.0109287i	−0.701621	+	0.712550i	$0.747540\pi$
$98$	−1.15867	+	1.35658i	−0.117044	+	0.137035i
$99$	−8.84568	+	3.82701i	−0.889024	+	0.384629i
$100$	−2.81999	−	4.88436i	−0.281999	−	0.488436i
$101$	−4.49533	+	7.78613i	−0.447302	+	0.774749i	−0.998209	−	0.0598169i	$-0.980948\pi$
$101$	−4.49533	+	7.78613i	−0.447302	+	0.774749i	0.550908	+	0.834566i	$0.314282\pi$
$102$	2.28494	−	2.64692i	0.226243	−	0.262084i
$103$	−4.35494	+	2.51432i	−0.429105	+	0.247744i	−0.698965	−	0.715156i	$-0.746356\pi$
$103$	−4.35494	+	2.51432i	−0.429105	+	0.247744i	0.269860	+	0.962899i	$0.413022\pi$
$104$	1.77584	+	3.14991i	0.174135	+	0.308874i
$105$	4.71391	+	11.9994i	0.460030	+	1.17103i
$106$	−1.22495	−	1.22495i	−0.118978	−	0.118978i
$107$	2.16952	−	1.25257i	0.209735	−	0.121091i	−0.391453	−	0.920198i	$-0.628028\pi$
$107$	2.16952	−	1.25257i	0.209735	−	0.121091i	0.601188	+	0.799107i	$0.294694\pi$
$108$	−9.59431	−	3.00797i	−0.923213	−	0.289442i
$109$	12.6799	−	3.39756i	1.21451	−	0.325427i	0.405980	−	0.913882i	$-0.366930\pi$
$109$	12.6799	−	3.39756i	1.21451	−	0.325427i	0.808530	+	0.588455i	$0.200264\pi$
$110$	−2.22503	−	0.596195i	−0.212148	−	0.0568450i
$111$	−15.6142	−	2.97922i	−1.48203	−	0.282775i
$112$	−4.45277	+	8.46312i	−0.420747	+	0.799690i
$113$		−	7.91460i		−	0.744543i	−0.928124	−	0.372272i	$-0.878579\pi$
$113$		−	7.91460i		−	0.744543i	0.928124	−	0.372272i	$-0.121421\pi$
$114$	−0.0140845	+	0.0291322i	−0.00131914	+	0.00272848i
$115$	2.10495	+	7.85579i	0.196288	+	0.732556i
$116$	0.0339835	−	0.0588612i	0.00315529	−	0.00546512i
$117$	−10.7316	−	1.35409i	−0.992133	−	0.125185i
$118$	2.18441			0.201091
$119$	20.9415	−	0.822580i	1.91970	−	0.0754058i
$120$	−2.74669	−	4.04198i	−0.250737	−	0.368981i
$121$	−0.587739	+	0.339331i	−0.0534308	+	0.0308483i
$122$	−0.637745	−	2.38010i	−0.0577387	−	0.215484i
$123$	−2.22938	+	2.58255i	−0.201016	+	0.232860i
$124$	15.9341	+	4.26953i	1.43092	+	0.383415i
$125$	−4.14840	−	4.14840i	−0.371044	−	0.371044i
$126$	0.875499	+	1.82365i	0.0779956	+	0.162464i
$127$		−	2.97209i		−	0.263730i	−0.991268	−	0.131865i	$-0.957903\pi$
$127$		−	2.97209i		−	0.263730i	0.991268	−	0.131865i	$-0.0420966\pi$
$128$	1.94277	−	7.25051i	0.171718	−	0.640861i
$129$	−0.0480388	−	0.654530i	−0.00422958	−	0.0576281i
$130$	−1.80920	−	1.84664i	−0.158678	−	0.161961i
$131$	13.0495	−	7.53413i	1.14014	−	0.658260i	0.193675	−	0.981066i	$-0.437959\pi$
$131$	13.0495	−	7.53413i	1.14014	−	0.658260i	0.946465	+	0.322806i	$0.104626\pi$
$132$	10.5768	+	2.01808i	0.920593	+	0.175651i
$133$	−0.185216	+	0.0575092i	−0.0160603	+	0.00498668i
$134$	−1.28201			−0.110749
$135$	14.6054	+	0.613941i	1.25704	+	0.0528396i
$136$	−7.67353	+	2.05612i	−0.658000	+	0.176310i
$137$	13.7675	−	3.68900i	1.17624	−	0.315173i	0.382807	−	0.923829i	$-0.374958\pi$
$137$	13.7675	−	3.68900i	1.17624	−	0.315173i	0.793434	+	0.608656i	$0.208291\pi$
$138$	0.419632	+	1.20518i	0.0357214	+	0.102591i
$139$	16.5108			1.40042			0.700212	−	0.713935i	$-0.253089\pi$
$139$	16.5108			1.40042			0.700212	+	0.713935i	$0.253089\pi$
$140$	3.17887	−	14.0479i	0.268663	−	1.18727i
$141$	−0.647629	+	3.39424i	−0.0545402	+	0.285846i
$142$	0.544624	−	0.314439i	0.0457038	−	0.0263871i
$143$	11.5829	+	0.118628i	0.968610	+	0.00992019i
$144$	6.73470	+	8.49850i	0.561225	+	0.708208i
$145$	−0.0255752	+	0.0954480i	−0.00212391	+	0.00792653i
$146$			2.04969i			0.169633i
$147$	−4.40488	+	11.2959i	−0.363308	+	0.931669i
$148$	12.5574	+	12.5574i	1.03221	+	1.03221i
$149$	9.06680	+	2.42944i	0.742781	+	0.199028i	0.610314	−	0.792160i	$-0.291043\pi$
$149$	9.06680	+	2.42944i	0.742781	+	0.199028i	0.132467	+	0.991187i	$0.457710\pi$
$150$	0.973941	+	0.840753i	0.0795219	+	0.0686472i
$151$	−2.42619	−	9.05465i	−0.197440	−	0.736857i	−0.991622	−	0.129176i	$-0.958767\pi$
$151$	−2.42619	−	9.05465i	−0.197440	−	0.736857i	0.794181	−	0.607681i	$-0.207900\pi$
$152$	0.0636657	−	0.0367574i	0.00516397	−	0.00298142i
$153$	8.74982	−	22.0942i	0.707381	−	1.78621i
$154$	−1.15597	−	1.83214i	−0.0931506	−	0.147638i
$155$	−23.9833			−1.92638
$156$	9.06612	+	7.98980i	0.725871	+	0.639696i
$157$	1.34007	−	2.32108i	0.106950	−	0.185242i	−0.807583	−	0.589753i	$-0.799225\pi$
$157$	1.34007	−	2.32108i	0.106950	−	0.185242i	0.914533	+	0.404511i	$0.132558\pi$
$158$	0.500048	+	1.86621i	0.0397817	+	0.148467i
$159$	−10.5992	−	5.12440i	−0.840573	−	0.406391i
$160$			8.23453i			0.650997i
$161$	−3.56135	+	6.76884i	−0.280673	+	0.533459i
$162$	2.29265	−	0.0716749i	0.180128	−	0.00563131i
$163$	−2.23644	−	0.599253i	−0.175172	−	0.0469372i	0.170167	−	0.985415i	$-0.445569\pi$
$163$	−2.23644	−	0.599253i	−0.175172	−	0.0469372i	−0.345339	+	0.938478i	$0.612236\pi$
$164$	3.68167	−	0.986500i	0.287490	−	0.0770327i
$165$	−15.6127	+	1.14588i	−1.21545	+	0.0892069i
$166$	1.08171	−	0.624523i	0.0839567	−	0.0484724i
$167$	13.5165	+	13.5165i	1.04594	+	1.04594i	0.998893	+	0.0470461i	$0.0149808\pi$
$167$	13.5165	+	13.5165i	1.04594	+	1.04594i	0.0470461	+	0.998893i	$0.485019\pi$
$168$	0.683511	−	4.54476i	0.0527340	−	0.350636i
$169$	11.1228	+	6.72922i	0.855603	+	0.517632i
$170$	4.91867	−	2.83980i	0.377245	−	0.217803i
$171$	−0.0252933	+	0.218447i	−0.00193422	+	0.0167051i
$172$	−0.366603	+	0.634975i	−0.0279532	+	0.0484164i
$173$	8.51466	+	14.7478i	0.647358	+	1.12126i	0.983752	+	0.179535i	$0.0574594\pi$
$173$	8.51466	+	14.7478i	0.647358	+	1.12126i	−0.336394	+	0.941721i	$0.609207\pi$
$174$	−0.00290600	+	0.0152304i	−0.000220303	+	0.00115461i
$175$	0.302671	+	7.70549i	0.0228798	+	0.582480i
$176$	−8.21107	−	8.21107i	−0.618932	−	0.618932i
$177$	14.0197	−	4.88152i	1.05378	−	0.366917i
$178$	−1.93048	+	3.34368i	−0.144695	+	0.250619i
$179$	6.29452	−	10.9024i	0.470474	−	0.814886i	−0.528955	−	0.848650i	$-0.677416\pi$
$179$	6.29452	−	10.9024i	0.470474	−	0.814886i	0.999430	+	0.0337640i	$0.0107494\pi$
$180$	−13.1105	−	9.73836i	−0.977197	−	0.725854i
$181$		−	11.8729i		−	0.882509i	−0.897382	−	0.441255i	$-0.854534\pi$
$181$		−	11.8729i		−	0.882509i	0.897382	−	0.441255i	$-0.145466\pi$
$182$	−0.0705410	−	2.43022i	−0.00522885	−	0.180140i
$183$	−9.41191	−	13.8504i	−0.695748	−	1.02385i
$184$	0.750386	−	2.80048i	0.0553192	−	0.206454i
$185$	−22.3599	−	12.9095i	−1.64393	−	0.949124i
$186$	−3.75314	+	0.275460i	−0.275194	+	0.0201977i
$187$	−6.58654	+	24.5813i	−0.481656	+	1.79756i
$188$	2.72975	−	2.72975i	0.199087	−	0.199087i
$189$	9.69434	+	9.74781i	0.705159	+	0.709049i
$190$	−0.0371643	+	0.0371643i	−0.00269618	+	0.00269618i
$191$	−18.3898	+	10.6174i	−1.33064	+	0.768246i	−0.985398	−	0.170267i	$-0.945537\pi$
$191$	−18.3898	+	10.6174i	−1.33064	+	0.768246i	−0.345243	+	0.938513i	$0.612203\pi$
$192$	−0.821924	−	11.1987i	−0.0593173	−	0.808199i
$193$	−1.57794	−	5.88894i	−0.113582	−	0.423895i	0.885595	−	0.464459i	$-0.153751\pi$
$193$	−1.57794	−	5.88894i	−0.113582	−	0.423895i	−0.999177	+	0.0405640i	$0.987085\pi$
$194$	0.0193976	+	0.0335976i	0.00139266	+	0.00241217i
$195$	−15.7383	−	7.80883i	−1.12704	−	0.559202i
$196$	11.1632	−	7.67192i	0.797372	−	0.547994i
$197$	3.24256	−	3.24256i	0.231023	−	0.231023i	−0.582097	−	0.813120i	$-0.697767\pi$
$197$	3.24256	−	3.24256i	0.231023	−	0.231023i	0.813120	+	0.582097i	$0.197767\pi$
$198$	−2.43007	+	0.358639i	−0.172697	+	0.0254873i
$199$	0.250546	+	0.144653i	0.0177607	+	0.0102542i	0.508854	−	0.860853i	$-0.330069\pi$
$199$	0.250546	+	0.144653i	0.0177607	+	0.0102542i	−0.491093	+	0.871107i	$0.663403\pi$
$200$	−0.756554	−	2.82350i	−0.0534965	−	0.199652i
$201$	−8.22803	+	2.86493i	−0.580361	+	0.202076i
$202$	−1.62026	+	1.62026i	−0.114001	+	0.114001i
$203$	−0.0785941	+	0.0495881i	−0.00551622	+	0.00348040i
$204$	−21.9586	+	14.9217i	−1.53741	+	1.04473i
$205$	−4.79906	+	2.77074i	−0.335181	+	0.193517i
$206$	−1.23795	+	0.331708i	−0.0862521	+	0.0231112i
$207$	5.38644	+	6.79714i	0.374383	+	0.472434i
$208$	−3.24389	−	12.6220i	−0.224923	−	0.875181i
$209$		−	0.235497i		−	0.0162896i
$210$	0.368941	+	3.26496i	0.0254594	+	0.225304i
$211$	0.580776			0.0399822			0.0199911	−	0.999800i	$-0.493636\pi$
$211$	0.580776			0.0399822			0.0199911	+	0.999800i	$0.493636\pi$
$212$	6.57637	+	11.3906i	0.451667	+	0.782310i
$213$	2.79275	−	3.23516i	0.191356	−	0.221670i
$214$	0.616715	−	0.165248i	0.0421577	−	0.0112961i
$215$	0.275897	−	1.02966i	0.0188160	−	0.0702224i
$216$	−4.39964	−	2.79285i	−0.299358	−	0.190030i
$217$	−16.5625	−	15.3105i	−1.12433	−	1.03934i
$218$	3.34564			0.226595
$219$	4.58046	+	13.1550i	0.309519	+	0.888933i
$220$	15.1463	+	8.74470i	1.02116	+	0.589567i
$221$	−20.4011	+	19.9874i	−1.37232	+	1.34450i
$222$	−3.64737	−	1.76339i	−0.244795	−	0.118351i
$223$	−0.0823082	−	0.0823082i	−0.00551176	−	0.00551176i	0.704346	−	0.709857i	$-0.251241\pi$
$223$	−0.0823082	−	0.0823082i	−0.00551176	−	0.00551176i	−0.709857	+	0.704346i	$0.751241\pi$
$224$	−5.25677	+	5.68663i	−0.351233	+	0.379954i
$225$	8.12965	+	3.21952i	0.541977	+	0.214635i
$226$	0.522076	−	1.94841i	0.0347280	−	0.129607i
$227$	1.82108	+	6.79638i	0.120870	+	0.451091i	0.999659	−	0.0261186i	$-0.00831475\pi$
$227$	1.82108	+	6.79638i	0.120870	+	0.451091i	−0.878789	+	0.477210i	$0.841648\pi$
$228$	0.160539	−	0.185971i	0.0106320	−	0.0123163i
$229$	2.32688	+	0.623485i	0.153764	+	0.0412010i	0.334880	−	0.942261i	$-0.391304\pi$
$229$	2.32688	+	0.623485i	0.153764	+	0.0412010i	−0.181116	+	0.983462i	$0.557971\pi$
$230$			2.07279i			0.136675i
$231$	−11.5134	−	9.17553i	−0.757524	−	0.603705i
$232$	0.0249087	−	0.0249087i	0.00163533	−	0.00163533i
$233$	−11.7794	−	20.4025i	−0.771693	−	1.33661i	−0.936635	−	0.350308i	$-0.886077\pi$
$233$	−11.7794	−	20.4025i	−0.771693	−	1.33661i	0.164942	−	0.986303i	$-0.447256\pi$
$234$	−2.55257	−	1.04124i	−0.166867	−	0.0680681i
$235$	−2.80629	+	4.86063i	−0.183062	+	0.317073i
$236$	−16.0199	−	4.29252i	−1.04281	−	0.279419i
$237$	7.37977	+	10.8600i	0.479367	+	0.705430i
$238$	5.20963	+	1.17887i	0.337690	+	0.0764151i
$239$	1.35327	−	1.35327i	0.0875359	−	0.0875359i	−0.661983	−	0.749519i	$-0.730285\pi$
$239$	1.35327	−	1.35327i	0.0875359	−	0.0875359i	0.749519	+	0.661983i	$0.230285\pi$
$240$	5.79151	+	16.6331i	0.373840	+	1.07366i
$241$	−4.54834	−	16.9746i	−0.292984	−	1.09343i	−0.942805	−	0.333345i	$-0.891823\pi$
$241$	−4.54834	−	16.9746i	−0.292984	−	1.09343i	0.649820	−	0.760088i	$-0.274844\pi$
$242$	−0.167073	+	0.0447671i	−0.0107399	+	0.00287774i
$243$	14.5542	−	5.58343i	0.933654	−	0.358177i
$244$			18.7083i			1.19767i
$245$	−12.7899	+	14.9745i	−0.817119	+	0.956685i
$246$	−0.719182	+	0.488713i	−0.0458534	+	0.0311592i
$247$	0.134484	−	0.227521i	0.00855704	−	0.0144768i
$248$	7.40426	+	4.27485i	0.470171	+	0.271453i
$249$	5.54682	−	6.42553i	0.351516	−	0.407201i
$250$	−0.747607	−	1.29489i	−0.0472828	−	0.0818963i
$251$	−21.1871			−1.33732			−0.668659	−	0.743569i	$-0.733131\pi$
$251$	−21.1871			−1.33732			−0.668659	+	0.743569i	$0.733131\pi$
$252$	−2.83709	−	15.0946i	−0.178720	−	0.950873i
$253$	−6.56725	−	6.56725i	−0.412879	−	0.412879i
$254$	0.196050	−	0.731668i	0.0123013	−	0.0459090i
$255$	25.2222	−	29.2178i	1.57948	−	1.82969i
$256$	−5.52644	+	9.57208i	−0.345403	+	0.598255i
$257$	−8.39438	−	14.5395i	−0.523627	−	0.906949i	−0.999622	−	0.0275005i	$-0.991245\pi$
$257$	−8.39438	−	14.5395i	−0.523627	−	0.906949i	0.475995	−	0.879448i	$-0.342088\pi$
$258$	0.0313490	−	0.164301i	0.00195170	−	0.0102289i
$259$	−7.20018	−	23.1892i	−0.447398	−	1.44091i
$260$	9.63945	+	17.0981i	0.597814	+	1.06038i
$261$	0.0153847	+	0.104244i	0.000952287	+	0.00645252i
$262$	3.70950	−	0.993957i	0.229174	−	0.0614069i
$263$	23.2847	+	13.4435i	1.43580	+	0.828959i	0.997554	−	0.0698972i	$-0.0222671\pi$
$263$	23.2847	+	13.4435i	1.43580	+	0.828959i	0.438244	+	0.898856i	$0.355600\pi$
$264$	5.02428	+	2.42909i	0.309223	+	0.149500i
$265$	−13.5215	−	13.5215i	−0.830622	−	0.830622i
$266$	−0.0493900	+	0.00194004i	−0.00302830	+	0.000118951i
$267$	−4.91774	+	25.7740i	−0.300961	+	1.57734i
$268$	9.40197	+	2.51925i	0.574317	+	0.153888i
$269$	−15.2291	−	8.79254i	−0.928536	−	0.536091i	−0.0421879	−	0.999110i	$-0.513433\pi$
$269$	−15.2291	−	8.79254i	−0.928536	−	0.536091i	−0.886348	+	0.463019i	$0.846766\pi$
$270$	3.55506	+	1.11457i	0.216354	+	0.0678304i
$271$	9.54880	+	2.55859i	0.580048	+	0.155424i	0.536901	−	0.843645i	$-0.319595\pi$
$271$	9.54880	+	2.55859i	0.580048	+	0.155424i	0.0431474	+	0.999069i	$0.486261\pi$
$272$	28.6312			1.73602
$273$	−5.88358	−	15.4397i	−0.356091	−	0.934451i
$274$	3.63263			0.219455
$275$	−9.04477	−	2.42354i	−0.545420	−	0.146145i
$276$	−0.709215	−	9.66307i	−0.0426897	−	0.581649i
$277$	6.45680	+	3.72783i	0.387951	+	0.223984i	0.681272	−	0.732030i	$-0.261427\pi$
$277$	6.45680	+	3.72783i	0.387951	+	0.223984i	−0.293321	+	0.956014i	$0.594760\pi$
$278$	4.06461	+	1.08911i	0.243779	+	0.0653205i
$279$	−23.4723	+	10.1551i	−1.40525	+	0.607970i
$280$	3.47582	−	6.60629i	0.207720	−	0.394801i
$281$	16.7345	+	16.7345i	0.998296	+	0.998296i	0.999999	−	0.00170209i	$-0.000541793\pi$
$281$	16.7345	+	16.7345i	0.998296	+	0.998296i	−0.00170209	+	0.999999i	$0.500542\pi$
$282$	−0.383329	+	0.792872i	−0.0228269	+	0.0472148i
$283$	21.7494	+	12.5570i	1.29287	+	0.746438i	0.979162	−	0.203082i	$-0.0650957\pi$
$283$	21.7494	+	12.5570i	1.29287	+	0.746438i	0.313707	+	0.949520i	$0.398429\pi$
$284$	−4.61203	+	1.23579i	−0.273674	+	0.0733307i
$285$	−0.155471	+	0.321574i	−0.00920931	+	0.0190484i
$286$	2.84365	+	0.793253i	0.168148	+	0.0469060i
$287$	−5.08294	−	1.15021i	−0.300036	−	0.0678945i
$288$	3.48670	+	8.05910i	0.205456	+	0.474887i
$289$	−22.8731	−	39.6173i	−1.34547	−	2.33043i
$290$	−0.0125922	+	0.0218103i	−0.000739439	+	0.00128075i
$291$	0.199576	+	0.172283i	0.0116993	+	0.0100994i
$292$	4.02779	−	15.0319i	0.235708	−	0.879676i
$293$	−8.13360	−	8.13360i	−0.475170	−	0.475170i	0.428413	−	0.903583i	$-0.359073\pi$
$293$	−8.13360	−	8.13360i	−0.475170	−	0.475170i	−0.903583	+	0.428413i	$0.859073\pi$
$294$	−1.82951	+	2.49026i	−0.106699	+	0.145235i
$295$	24.1124			1.40388
$296$	4.60205	+	7.97098i	0.267489	+	0.463304i
$297$	−14.7949	+	7.73226i	−0.858485	+	0.448671i
$298$	2.07181	+	1.19616i	0.120017	+	0.0692916i
$299$	−2.59448	−	10.0952i	−0.150043	−	0.583818i
$300$	−5.49050	−	8.07974i	−0.316994	−	0.466484i
$301$	0.847847	−	0.534940i	0.0488691	−	0.0308334i
$302$		−	2.38911i		−	0.137478i
$303$	−6.77811	+	14.0197i	−0.389392	+	0.805412i
$304$	−0.255922	+	0.0685740i	−0.0146781	+	0.00393299i
$305$	−7.03970	−	26.2725i	−0.403092	−	1.50436i
$306$	3.61144	−	4.86198i	0.206452	−	0.277941i
$307$	−14.1383	+	14.1383i	−0.806918	+	0.806918i	−0.984166	−	0.177248i	$-0.943280\pi$
$307$	−14.1383	+	14.1383i	−0.806918	+	0.806918i	0.177248	+	0.984166i	$0.443280\pi$
$308$	4.87730	+	15.7080i	0.277910	+	0.895048i
$309$	−7.20397	+	4.89538i	−0.409819	+	0.278488i
$310$	−5.90420	−	1.58202i	−0.335336	−	0.0898530i
$311$	−10.1078	+	17.5072i	−0.573160	+	0.992743i	0.423078	+	0.906093i	$0.360950\pi$
$311$	−10.1078	+	17.5072i	−0.573160	+	0.992743i	−0.996239	+	0.0866500i	$0.972384\pi$
$312$	3.46694	+	5.21602i	0.196277	+	0.295299i
$313$	13.0051	+	22.5254i	0.735090	+	1.27321i	0.954684	+	0.297621i	$0.0961933\pi$
$313$	13.0051	+	22.5254i	0.735090	+	1.27321i	−0.219594	+	0.975591i	$0.570473\pi$
$314$	0.483006	−	0.483006i	0.0272576	−	0.0272576i
$315$	9.66414	+	20.1303i	0.544512	+	1.13421i
$316$		−	14.6689i		−	0.825192i
$317$	6.64679	+	1.78100i	0.373321	+	0.100031i	0.440601	−	0.897703i	$-0.354765\pi$
$317$	6.64679	+	1.78100i	0.373321	+	0.100031i	−0.0672799	+	0.997734i	$0.521432\pi$
$318$	−2.27129	−	1.96068i	−0.127367	−	0.109950i
$319$	−0.0292060	−	0.108998i	−0.00163522	−	0.00610273i
$320$	4.72049	−	17.6171i	0.263883	−	0.984826i
$321$	3.58883	−	2.43875i	0.200309	−	0.136118i
$322$	−1.32323	+	1.43143i	−0.0737406	+	0.0797705i
$323$	0.410577	+	0.410577i	0.0228451	+	0.0228451i
$324$	−16.9546	−	3.97959i	−0.941923	−	0.221088i
$325$	−7.35443	−	7.50663i	−0.407950	−	0.416393i
$326$	−0.511038	−	0.295048i	−0.0283038	−	0.0163412i
$327$	21.4725	−	7.47653i	1.18743	−	0.413453i
$328$	1.97546			0.109076
$329$	−5.04091	+	1.56519i	−0.277915	+	0.0862917i
$330$	−3.91911	−	0.747777i	−0.215740	−	0.0411637i
$331$	−2.93997	+	10.9721i	−0.161595	+	0.603082i	0.836855	+	0.547425i	$0.184392\pi$
$331$	−2.93997	+	10.9721i	−0.161595	+	0.603082i	−0.998450	+	0.0556568i	$0.982275\pi$
$332$	−9.16020	+	2.45447i	−0.502731	+	0.134706i
$333$	−27.3497	−	3.16673i	−1.49875	−	0.173536i
$334$	2.43589	+	4.21909i	0.133286	+	0.230858i
$335$	−14.1514			−0.773174
$336$	−6.61877	+	15.1838i	−0.361083	+	0.828342i
$337$		−	0.687884i		−	0.0374714i	−0.999824	−	0.0187357i	$-0.994036\pi$
$337$		−	0.687884i		−	0.0374714i	0.999824	−	0.0187357i	$-0.00596411\pi$
$338$	2.29433	+	2.39030i	0.124795	+	0.130015i
$339$	−1.00343	−	13.6717i	−0.0544987	−	0.742546i
$340$	−41.6528	+	11.1608i	−2.25894	+	0.605281i
$341$	23.7187	−	13.6940i	1.28444	−	0.741573i
$342$	−0.0206362	+	0.0521088i	−0.00111588	+	0.00281772i
$343$	−18.3920	+	2.17626i	−0.993072	+	0.117507i
$344$	−0.268706	+	0.268706i	−0.0144877	+	0.0144877i
$345$	4.63208	+	13.3033i	0.249383	+	0.716223i
$346$	1.12332	+	4.19227i	0.0603899	+	0.225378i
$347$	1.84737	+	1.06658i	0.0991719	+	0.0572569i	0.548766	−	0.835976i	$-0.315098\pi$
$347$	1.84737	+	1.06658i	0.0991719	+	0.0572569i	−0.449594	+	0.893233i	$0.648431\pi$
$348$	0.0512408	−	0.105986i	0.00274679	−	0.00568142i
$349$	−18.9392	+	18.9392i	−1.01379	+	1.01379i	−0.0138872	+	0.999904i	$0.504421\pi$
$349$	−18.9392	+	18.9392i	−1.01379	+	1.01379i	−0.999904	+	0.0138872i	$0.995579\pi$
$350$	−0.433771	+	1.91690i	−0.0231860	+	0.102463i
$351$	−18.7094	−	0.978490i	−0.998635	−	0.0522279i
$352$	−4.70177	−	8.14370i	−0.250605	−	0.434061i
$353$	−3.14604	−	11.7412i	−0.167447	−	0.624920i	−0.997715	−	0.0675566i	$-0.978480\pi$
$353$	−3.14604	−	11.7412i	−0.167447	−	0.624920i	0.830269	−	0.557363i	$-0.188187\pi$
$354$	3.77335	−	0.276943i	0.200552	−	0.0147194i
$355$	6.01179	−	3.47091i	0.319073	−	0.184217i
$356$	20.7282	−	20.7282i	1.09859	−	1.09859i
$357$	36.0701	−	4.07593i	1.90903	−	0.215721i
$358$	2.26875	−	2.26875i	0.119907	−	0.119907i
$359$	−1.51841	+	5.66678i	−0.0801385	+	0.299081i	−0.994349	−	0.106158i	$-0.966145\pi$
$359$	−1.51841	+	5.66678i	−0.0801385	+	0.299081i	0.914211	+	0.405239i	$0.132812\pi$
$360$	−5.25709	−	6.63391i	−0.277073	−	0.349638i
$361$	16.4498	+	9.49731i	0.865780	+	0.499859i
$362$	0.783183	−	2.92288i	0.0411632	−	0.153623i
$363$	−0.972242	+	0.660677i	−0.0510295	+	0.0346766i
$364$	−4.25824	+	17.9613i	−0.223192	+	0.941427i
$365$			22.6253i			1.18426i
$366$	−1.40340	−	4.03053i	−0.0733567	−	0.210679i
$367$	−15.9432	+	27.6144i	−0.832228	+	1.44146i	0.0640399	+	0.997947i	$0.479602\pi$
$367$	−15.9432	+	27.6144i	−0.832228	+	1.44146i	−0.896268	+	0.443513i	$0.853732\pi$
$368$	−5.22453	+	9.04914i	−0.272347	+	0.471719i
$369$	−3.52362	+	4.74375i	−0.183432	+	0.246950i
$370$	−4.65299	−	4.65299i	−0.241897	−	0.241897i
$371$	−0.705847	−	17.9697i	−0.0366457	−	0.932938i
$372$	28.0659	+	5.35505i	1.45515	+	0.277647i
$373$	4.21830	+	7.30631i	0.218415	+	0.378307i	0.954324	−	0.298775i	$-0.0965779\pi$
$373$	4.21830	+	7.30631i	0.218415	+	0.378307i	−0.735908	+	0.677081i	$0.763245\pi$
$374$	−3.24295	+	5.61695i	−0.167689	+	0.290445i
$375$	−7.69190	−	6.64002i	−0.397208	−	0.342889i
$376$	1.73275	−	1.00040i	0.0893596	−	0.0515918i
$377$	0.0340285	−	0.121985i	0.00175256	−	0.00628255i
$378$	1.74355	+	3.03919i	0.0896784	+	0.156319i
$379$	−9.76263	−	9.76263i	−0.501473	−	0.501473i	0.410423	−	0.911895i	$-0.365381\pi$
$379$	−9.76263	−	9.76263i	−0.501473	−	0.501473i	−0.911895	+	0.410423i	$0.865381\pi$
$380$	0.345584	−	0.199523i	0.0177281	−	0.0102353i
$381$	−0.376807	−	5.13400i	−0.0193044	−	0.263023i
$382$	−5.22756	+	1.40072i	−0.267465	+	0.0716671i
$383$	−4.70284	−	1.26012i	−0.240304	−	0.0643892i	0.136657	−	0.990618i	$-0.456364\pi$
$383$	−4.70284	−	1.26012i	−0.240304	−	0.0643892i	−0.376961	+	0.926229i	$0.623031\pi$
$384$	2.43672	−	12.7709i	0.124348	−	0.651711i
$385$	−12.7601	−	20.2240i	−0.650314	−	1.03071i
$386$		−	1.55382i		−	0.0790875i
$387$	−0.165965	−	1.12455i	−0.00843647	−	0.0571639i
$388$	−0.0762353	−	0.284514i	−0.00387026	−	0.0144440i
$389$	12.7346	−	22.0570i	0.645670	−	1.11833i	−0.338476	−	0.940975i	$-0.609912\pi$
$389$	12.7346	−	22.0570i	0.645670	−	1.11833i	0.984146	−	0.177358i	$-0.0567551\pi$
$390$	−3.35934	−	2.96053i	−0.170107	−	0.149912i
$391$	22.8994			1.15807
$392$	6.61768	−	2.34329i	0.334243	−	0.118354i
$393$	21.5866	−	14.6689i	1.08890	−	0.739950i
$394$	1.01214	−	0.584362i	0.0509911	−	0.0294397i
$395$	5.51975	+	20.6000i	0.277729	+	1.03650i
$396$	18.5263	+	2.14510i	0.930981	+	0.107795i
$397$	4.20331	+	1.12627i	0.210958	+	0.0565260i	0.362750	−	0.931886i	$-0.381838\pi$
$397$	4.20331	+	1.12627i	0.210958	+	0.0565260i	−0.151792	+	0.988412i	$0.548504\pi$
$398$	0.0521374	+	0.0521374i	0.00261341	+	0.00261341i
$399$	−0.312653	+	0.122824i	−0.0156522	+	0.00614887i
$400$			10.5350i			0.526748i
$401$	8.64026	−	32.2459i	0.431474	−	1.61028i	−0.317891	−	0.948127i	$-0.602975\pi$
$401$	8.64026	−	32.2459i	0.431474	−	1.61028i	0.749366	−	0.662156i	$-0.230359\pi$
$402$	−2.21455	+	0.162536i	−0.110452	+	0.00810655i
$403$	30.7356	+	0.314784i	1.53105	+	0.0156805i
$404$	15.0665	−	8.69866i	0.749587	−	0.432774i
$405$	25.3073	−	0.791178i	1.25753	−	0.0393140i
$406$	−0.0226193	+	0.00702322i	−0.00112258	+	0.000348556i
$407$	29.4843			1.46148
$408$	−12.9946	+	4.52461i	−0.643329	+	0.224001i
$409$	−7.41551	+	1.98698i	−0.366674	+	0.0982499i	−0.437451	−	0.899242i	$-0.644119\pi$
$409$	−7.41551	+	1.98698i	−0.366674	+	0.0982499i	0.0707774	+	0.997492i	$0.477452\pi$
$410$	−1.36420	+	0.365536i	−0.0673730	+	0.0180525i
$411$	23.3144	−	8.11788i	1.15002	−	0.400425i
$412$	9.73066			0.479395
$413$	16.6516	+	15.3929i	0.819374	+	0.757437i
$414$	0.877668	+	2.02863i	0.0431350	+	0.0997015i
$415$	11.9403	−	6.89376i	0.586128	−	0.338401i
$416$	0.108080	−	10.5529i	0.00529903	−	0.517399i
$417$	28.5208	−	2.09326i	1.39667	−	0.102508i
$418$	0.0155342	−	0.0579745i	0.000759803	−	0.00283562i
$419$			18.1984i			0.889049i	0.895767	+	0.444525i	$0.146627\pi$
$419$			18.1984i			0.889049i	−0.895767	+	0.444525i	$0.853373\pi$
$420$	3.71017	−	24.6695i	0.181038	−	1.20375i
$421$	−15.6859	−	15.6859i	−0.764486	−	0.764486i	0.212644	−	0.977130i	$-0.431793\pi$
$421$	−15.6859	−	15.6859i	−0.764486	−	0.764486i	−0.977130	+	0.212644i	$0.931793\pi$
$422$	0.142975	+	0.0383101i	0.00695992	+	0.00186491i
$423$	−0.688390	+	5.94533i	−0.0334707	+	0.289072i
$424$	1.76433	+	6.58457i	0.0856834	+	0.319775i
$425$	19.9945	−	11.5438i	0.969875	−	0.559957i
$426$	0.900921	−	0.612211i	0.0436497	−	0.0296617i
$427$	11.9104	−	22.6374i	0.576385	−	1.09550i
$428$	−4.84756			−0.234316
$429$	20.0234	−	1.26358i	0.966738	−	0.0610062i
$430$	0.135840	−	0.235283i	0.00655081	−	0.0113463i
$431$	0.978180	+	3.65062i	0.0471173	+	0.175844i	0.985475	−	0.169823i	$-0.0543195\pi$
$431$	0.978180	+	3.65062i	0.0471173	+	0.175844i	−0.938357	+	0.345667i	$0.887653\pi$
$432$	12.7110	+	13.8265i	0.611558	+	0.665228i
$433$			11.0265i			0.529899i	0.964262	+	0.264949i	$0.0853553\pi$
$433$			11.0265i			0.529899i	−0.964262	+	0.264949i	$0.914645\pi$
$434$	−3.06740	−	4.86165i	−0.147240	−	0.233367i
$435$	−0.0320777	+	0.168120i	−0.00153801	+	0.00806073i
$436$	−24.5361	−	6.57442i	−1.17507	−	0.314858i
$437$	−0.204687	+	0.0548458i	−0.00979152	+	0.00262363i
$438$	0.259863	+	3.54064i	0.0124167	+	0.169178i
$439$	−23.7490	+	13.7115i	−1.13348	+	0.654415i	−0.944808	−	0.327625i	$-0.893752\pi$
$439$	−23.7490	+	13.7115i	−1.13348	+	0.654415i	−0.188672	+	0.982040i	$0.560418\pi$
$440$	6.40954	+	6.40954i	0.305563	+	0.305563i
$441$	−6.17689	+	20.0710i	−0.294138	+	0.955763i
$442$	−6.34077	+	3.57476i	−0.301599	+	0.170034i
$443$	−2.11034	+	1.21840i	−0.100265	+	0.0578881i	−0.549294	−	0.835629i	$-0.685103\pi$
$443$	−2.11034	+	1.21840i	−0.100265	+	0.0578881i	0.449029	+	0.893517i	$0.351770\pi$
$444$	23.2837	+	20.0996i	1.10500	+	0.953886i
$445$	−21.3094	+	36.9090i	−1.01016	+	1.74965i
$446$	−0.0148333	−	0.0256919i	−0.000702375	−	0.00121655i
$447$	15.9700	+	3.04712i	0.755357	+	0.144124i
$448$	14.5063	−	9.15260i	0.685359	−	0.432420i
$449$	7.28361	+	7.28361i	0.343735	+	0.343735i	0.857770	−	0.514035i	$-0.171850\pi$
$449$	7.28361	+	7.28361i	0.343735	+	0.343735i	−0.514035	+	0.857770i	$0.671850\pi$
$450$	1.78898	+	1.32884i	0.0843334	+	0.0626422i
$451$	3.16408	−	5.48035i	0.148991	−	0.258060i
$452$	−7.65756	+	13.2633i	−0.360181	+	0.623852i
$453$	−5.33897	−	15.3335i	−0.250847	−	0.720429i
$454$			1.79325i			0.0841616i
$455$	−0.778662	−	26.8259i	−0.0365043	−	1.25762i
$456$	0.105316	−	0.0715665i	0.00493188	−	0.00335141i
$457$	−1.35656	+	5.06276i	−0.0634573	+	0.236826i	−0.990369	−	0.138454i	$-0.955787\pi$
$457$	−1.35656	+	5.06276i	−0.0634573	+	0.236826i	0.926912	+	0.375280i	$0.122453\pi$
$458$	0.531702	+	0.306979i	0.0248448	+	0.0143442i
$459$	12.3133	−	39.2750i	0.574737	−	1.83320i
$460$	4.07318	−	15.2013i	0.189913	−	0.708764i
$461$	−23.7114	+	23.7114i	−1.10435	+	1.10435i	−0.110471	+	0.993879i	$0.535236\pi$
$461$	−23.7114	+	23.7114i	−1.10435	+	1.10435i	−0.993879	+	0.110471i	$0.964764\pi$
$462$	−2.22911	−	3.01829i	−0.103707	−	0.140424i
$463$	−8.98248	+	8.98248i	−0.417451	+	0.417451i	−0.884324	−	0.466873i	$-0.845380\pi$
$463$	−8.98248	+	8.98248i	−0.417451	+	0.417451i	0.466873	+	0.884324i	$0.345380\pi$
$464$	−0.109947	+	0.0634781i	−0.00510418	+	0.00294690i
$465$	−41.4288	+	3.04064i	−1.92122	+	0.141006i
$466$	−1.55402	−	5.79969i	−0.0719886	−	0.268665i
$467$	5.44419	+	9.42961i	0.251927	+	0.436350i	0.964056	−	0.265698i	$-0.0856024\pi$
$467$	5.44419	+	9.42961i	0.251927	+	0.436350i	−0.712129	+	0.702048i	$0.752269\pi$
$468$	16.6738	+	12.6522i	0.770748	+	0.584848i
$469$	−9.77273	−	9.03400i	−0.451263	−	0.417151i
$470$	−1.01148	+	1.01148i	−0.0466559	+	0.0466559i
$471$	2.02058	−	4.17934i	0.0931034	−	0.192574i
$472$	−7.44413	−	4.29787i	−0.342644	−	0.197825i
$473$	0.315064	+	1.17584i	0.0144867	+	0.0540650i
$474$	1.10039	+	3.16029i	0.0505424	+	0.145157i
$475$	−0.151073	+	0.151073i	−0.00693172	+	0.00693172i
$476$	−35.8896	−	18.8829i	−1.64500	−	0.865496i
$477$	−18.9588	−	7.50812i	−0.868065	−	0.343773i
$478$	0.422415	−	0.243881i	0.0193208	−	0.0111549i
$479$	4.04474	−	1.08378i	0.184809	−	0.0495194i	−0.165228	−	0.986255i	$-0.552836\pi$
$479$	4.04474	−	1.08378i	0.184809	−	0.0495194i	0.350036	+	0.936736i	$0.386169\pi$
$480$	1.04399	+	14.2244i	0.0476513	+	0.649251i
$481$	28.4857	+	16.8375i	1.29884	+	0.767726i
$482$		−	4.47884i		−	0.204005i
$483$	−5.29372	+	12.1440i	−0.240873	+	0.552573i
$484$	1.31324			0.0596928
$485$	0.214119	+	0.370865i	0.00972263	+	0.0168401i
$486$	3.95126	−	0.414478i	0.179233	−	0.0188011i
$487$	1.50609	−	0.403555i	0.0682473	−	0.0182868i	−0.224534	−	0.974466i	$-0.572086\pi$
$487$	1.50609	−	0.403555i	0.0682473	−	0.0182868i	0.292781	+	0.956179i	$0.405419\pi$
$488$	−2.50955	+	9.36578i	−0.113602	+	0.423969i
$489$	−3.93922	−	0.751613i	−0.178138	−	0.0339891i
$490$	−4.13639	+	2.84274i	−0.186863	+	0.128422i
$491$	−11.7480			−0.530180			−0.265090	−	0.964224i	$-0.585402\pi$
$491$	−11.7480			−0.530180			−0.265090	+	0.964224i	$0.585402\pi$
$492$	6.23466	−	2.17085i	0.281080	−	0.0978696i
$493$	0.240953	+	0.139114i	0.0108520	+	0.00626538i
$494$	0.0481154	−	0.0471398i	0.00216481	−	0.00212092i
$495$	−26.8242	+	3.95881i	−1.20566	+	0.177935i
$496$	−21.7884	−	21.7884i	−0.978326	−	0.978326i
$497$	6.36741	+	1.44087i	0.285617	+	0.0646317i
$498$	1.78937	−	1.21595i	0.0801834	−	0.0544878i
$499$	4.09542	−	15.2843i	0.183336	−	0.684221i	−0.811644	−	0.584152i	$-0.801427\pi$
$499$	4.09542	−	15.2843i	0.183336	−	0.684221i	0.994981	−	0.100068i	$-0.0319062\pi$
$500$	2.93821	+	10.9655i	0.131401	+	0.490394i
$501$	25.0621	+	21.6348i	1.11969	+	0.966573i
$502$	−5.21583	−	1.39758i	−0.232794	−	0.0623770i
$503$		−	22.3862i		−	0.998150i	−0.866559	−	0.499075i	$-0.833673\pi$
$503$		−	22.3862i		−	0.998150i	0.866559	−	0.499075i	$-0.166327\pi$
$504$	0.604507	−	7.93729i	0.0269269	−	0.353555i
$505$	−17.8851	+	17.8851i	−0.795878	+	0.795878i
$506$	−1.18352	−	2.04992i	−0.0526140	−	0.0911301i
$507$	20.0668	+	10.2139i	0.891197	+	0.453616i
$508$	−2.87556	+	4.98062i	−0.127583	+	0.220979i
$509$	−9.85480	−	2.64058i	−0.436806	−	0.117042i	0.0337131	−	0.999432i	$-0.489267\pi$
$509$	−9.85480	−	2.64058i	−0.436806	−	0.117042i	−0.470519	+	0.882390i	$0.655933\pi$
$510$	8.13651	−	5.52908i	0.360291	−	0.244832i
$511$	−14.4436	+	15.6247i	−0.638947	+	0.691195i
$512$	−12.6074	+	12.6074i	−0.557173	+	0.557173i
$513$	−0.0159966	+	0.380553i	−0.000706266	+	0.0168018i
$514$	−1.10745	−	4.13305i	−0.0488474	−	0.182301i
$515$	−13.6650	+	3.66153i	−0.602153	+	0.161347i
$516$	−0.552769	+	1.14334i	−0.0243343	+	0.0503326i
$517$		−	6.40936i		−	0.281883i
$518$	−0.242894	−	6.18366i	−0.0106721	−	0.271694i
$519$	16.5780	+	24.3960i	0.727695	+	1.07086i
$520$	2.53217	+	9.85273i	0.111043	+	0.432071i
$521$	−22.7900	−	13.1578i	−0.998447	−	0.576454i	−0.0906586	−	0.995882i	$-0.528897\pi$
$521$	−22.7900	−	13.1578i	−0.998447	−	0.576454i	−0.907788	+	0.419428i	$0.862231\pi$
$522$	−0.00308890	+	0.0266775i	−0.000135197	+	0.00116764i
$523$	−1.99759	−	3.45993i	−0.0873486	−	0.151292i	0.819041	−	0.573735i	$-0.194506\pi$
$523$	−1.99759	−	3.45993i	−0.0873486	−	0.151292i	−0.906390	+	0.422443i	$0.861173\pi$
$524$	−29.1578			−1.27376
$525$	1.49975	+	13.2721i	0.0654545	+	0.579243i
$526$	4.84545	+	4.84545i	0.211272	+	0.211272i
$527$	−17.4776	+	65.2274i	−0.761338	+	2.84135i
$528$	−15.2248	−	13.1428i	−0.662576	−	0.571968i
$529$	7.32140	−	12.6810i	0.318322	−	0.551350i
$530$	−2.43680	−	4.22066i	−0.105848	−	0.183334i
$531$	23.5987	−	10.2098i	1.02410	−	0.443067i
$532$	0.366027	+	0.0828273i	0.0158693	+	0.00359102i
$533$	6.18657	−	3.48783i	0.267970	−	0.151075i
$534$	−2.91079	+	6.02064i	−0.125962	+	0.260539i
$535$	6.80756	−	1.82408i	0.294317	−	0.0788619i
$536$	4.36891	+	2.52239i	0.188708	+	0.108951i
$537$	9.49095	−	19.6309i	0.409565	−	0.847137i
$538$	−3.16911	−	3.16911i	−0.136630	−	0.136630i
$539$	4.09871	−	22.1121i	0.176544	−	0.952437i
$540$	−23.8817	−	15.1599i	−1.02771	−	0.652379i
$541$	−3.29000	−	0.881552i	−0.141448	−	0.0379009i	0.187400	−	0.982284i	$-0.439994\pi$
$541$	−3.29000	−	0.881552i	−0.141448	−	0.0379009i	−0.328848	+	0.944383i	$0.606661\pi$
$542$	2.18195	+	1.25975i	0.0937226	+	0.0541108i
$543$	−1.50527	−	20.5094i	−0.0645975	−	0.880142i
$544$	22.3955	+	6.00085i	0.960198	+	0.257284i
$545$	36.9306			1.58193
$546$	−0.429961	−	4.18903i	−0.0184006	−	0.179274i
$547$	−5.84928			−0.250097			−0.125049	−	0.992151i	$-0.539909\pi$
$547$	−5.84928			−0.250097			−0.125049	+	0.992151i	$0.539909\pi$
$548$	−26.6408	−	7.13839i	−1.13804	−	0.304937i
$549$	−18.0142	−	22.7320i	−0.768825	−	0.970179i
$550$	−2.06677	−	1.19325i	−0.0881275	−	0.0508804i
$551$	−0.00248695		0.000666378i	−0.000105948		2.83886e-5i
$552$	0.941170	−	4.93269i	0.0400589	−	0.209949i
$553$	−9.33880	+	17.7497i	−0.397126	+	0.754794i
$554$	1.34363	+	1.34363i	0.0570854	+	0.0570854i
$555$	−40.2613	−	19.4651i	−1.70900	−	0.826247i
$556$	−27.6687	−	15.9745i	−1.17341	−	0.677471i
$557$	30.4609	−	8.16196i	1.29067	−	0.345833i	0.452754	−	0.891636i	$-0.350442\pi$
$557$	30.4609	−	8.16196i	1.29067	−	0.345833i	0.837914	+	0.545802i	$0.183775\pi$
$558$	−6.44828	+	0.951661i	−0.272977	+	0.0402870i
$559$	−0.367088	+	1.31593i	−0.0155262	+	0.0556581i
$560$	−18.2624	+	19.7558i	−0.771728	+	0.834834i
$561$	−8.26116	+	43.2969i	−0.348787	+	1.82800i
$562$	3.01582	+	5.22356i	0.127215	+	0.220343i
$563$	15.9085	−	27.5543i	0.670464	−	1.16128i	−0.307309	−	0.951610i	$-0.599429\pi$
$563$	15.9085	−	27.5543i	0.670464	−	1.16128i	0.977773	−	0.209667i	$-0.0672381\pi$
$564$	4.36930	−	5.06146i	0.183981	−	0.213126i
$565$	5.76290	−	21.5074i	0.242447	−	0.904825i
$566$	4.52596	+	4.52596i	0.190240	+	0.190240i
$567$	17.9819	+	15.6094i	0.755168	+	0.655531i
$568$	−2.47466			−0.103834
$569$	10.2235	+	17.7077i	0.428593	+	0.742345i	0.996748	−	0.0805766i	$-0.0256762\pi$
$569$	10.2235	+	17.7077i	0.428593	+	0.742345i	−0.568156	+	0.822921i	$0.692343\pi$
$570$	−0.0594860	+	0.0689095i	−0.00249159	+	0.00288630i
$571$	−30.0115	−	17.3271i	−1.25594	−	0.725118i	−0.283658	−	0.958926i	$-0.591548\pi$
$571$	−30.0115	−	17.3271i	−1.25594	−	0.725118i	−0.972283	+	0.233808i	$0.924881\pi$
$572$	−19.2958	−	11.4055i	−0.806798	−	0.476888i
$573$	−30.4206	+	20.6720i	−1.27084	+	0.863585i
$574$	−1.17544	−	0.618446i	−0.0490621	−	0.0258135i
$575$			8.42590i			0.351384i
$576$	−2.83959	−	19.2405i	−0.118316	−	0.801689i
$577$	3.27490	−	0.877506i	0.136336	−	0.0365310i	−0.190006	−	0.981783i	$-0.560851\pi$
$577$	3.27490	−	0.877506i	0.136336	−	0.0365310i	0.326342	+	0.945252i	$0.394184\pi$
$578$	−3.01758	−	11.2618i	−0.125515	−	0.468427i
$579$	−3.47234	−	9.97253i	−0.144306	−	0.414444i
$580$	0.135207	−	0.135207i	0.00561416	−	0.00561416i
$581$	12.6467	+	2.86178i	0.524671	+	0.118727i
$582$	0.0377670	+	0.0555773i	0.00156549	+	0.00230375i
$583$	21.0929	+	5.65184i	0.873580	+	0.234075i
$584$	4.03281	−	6.98502i	0.166879	−	0.289042i
$585$	−28.1764	−	11.4937i	−1.16495	−	0.475205i
$586$	−1.46580	−	2.53885i	−0.0605518	−	0.104879i
$587$	10.3142	−	10.3142i	0.425714	−	0.425714i	−0.461452	−	0.887165i	$-0.652671\pi$
$587$	10.3142	−	10.3142i	0.425714	−	0.425714i	0.887165	+	0.461452i	$0.152671\pi$
$588$	18.3107	−	14.6678i	0.755121	−	0.604890i
$589$		−	0.624899i		−	0.0257485i
$590$	5.93599	+	1.59054i	0.244381	+	0.0654816i
$591$	5.19012	−	6.01232i	0.213493	−	0.247314i
$592$	−8.58551	−	32.0415i	−0.352862	−	1.31690i
$593$	−9.51681	+	35.5172i	−0.390808	+	1.45852i	0.437995	+	0.898977i	$0.355689\pi$
$593$	−9.51681	+	35.5172i	−0.390808	+	1.45852i	−0.828804	+	0.559540i	$0.810978\pi$
$594$	−4.15224	+	0.927603i	−0.170369	+	0.0380600i
$595$	57.5062	+	13.0129i	2.35752	+	0.533478i
$596$	−12.8436	−	12.8436i	−0.526094	−	0.526094i
$597$	0.451133	+	0.218109i	0.0184637	+	0.00892661i
$598$	0.0272056	−	2.65636i	0.00111252	−	0.108627i
$599$	−9.82791	−	5.67415i	−0.401558	−	0.231839i	0.285598	−	0.958349i	$-0.407808\pi$
$599$	−9.82791	−	5.67415i	−0.401558	−	0.231839i	−0.687156	+	0.726510i	$0.741141\pi$
$600$	−1.66484	−	4.78141i	−0.0679670	−	0.195200i
$601$	−8.65978			−0.353240			−0.176620	−	0.984279i	$-0.556516\pi$
$601$	−8.65978			−0.353240			−0.176620	+	0.984279i	$0.556516\pi$
$602$	0.244009	−	0.0757642i	0.00994507	−	0.00308792i
$603$	−13.8499	+	5.99205i	−0.564012	+	0.244015i
$604$	−4.69478	+	17.5212i	−0.191028	+	0.712926i
$605$	−1.84422	+	0.494158i	−0.0749783	+	0.0200904i
$606$	−2.59342	+	3.00426i	−0.105351	+	0.122040i
$607$	11.7019	+	20.2683i	0.474965	+	0.822663i	0.999589	−	0.0286710i	$-0.00912751\pi$
$607$	11.7019	+	20.2683i	0.474965	+	0.822663i	−0.524624	+	0.851334i	$0.675794\pi$
$608$	−0.214556			−0.00870138
$609$	−0.129477	+	0.0956229i	−0.00524667	+	0.00387484i
$610$		−	6.93213i		−	0.280674i
$611$	3.66018	−	6.19228i	0.148075	−	0.250513i
$612$	−36.0396	+	28.5598i	−1.45681	+	1.15446i
$613$	26.7536	−	7.16861i	1.08057	−	0.289537i	0.325739	−	0.945460i	$-0.394387\pi$
$613$	26.7536	−	7.16861i	1.08057	−	0.289537i	0.754828	+	0.655922i	$0.227720\pi$
$614$	−4.41319	+	2.54796i	−0.178102	+	0.102827i
$615$	−7.93864	+	5.39462i	−0.320117	+	0.217532i
$616$	0.334588	+	8.51805i	0.0134809	+	0.343202i
$617$	−6.78902	+	6.78902i	−0.273316	+	0.273316i	−0.830433	−	0.557118i	$-0.811907\pi$
$617$	−6.78902	+	6.78902i	−0.273316	+	0.273316i	0.557118	+	0.830433i	$0.311907\pi$
$618$	−2.09639	+	0.729943i	−0.0843290	+	0.0293626i
$619$	9.77385	+	36.4765i	0.392844	+	1.46611i	0.825421	+	0.564517i	$0.190938\pi$
$619$	9.77385	+	36.4765i	0.392844	+	1.46611i	−0.432577	+	0.901597i	$0.642396\pi$
$620$	40.1911	+	23.2044i	1.61411	+	0.931910i
$621$	10.1663	+	11.0585i	0.407960	+	0.443762i
$622$	−3.64317	+	3.64317i	−0.146078	+	0.146078i
$623$	−38.2780	+	11.8852i	−1.53357	+	0.476170i
$624$	−7.20376	−	21.3921i	−0.288381	−	0.856369i
$625$	−15.5390	−	26.9144i	−0.621561	−	1.07658i
$626$	1.71572	+	6.40316i	0.0685740	+	0.255922i
$627$	−0.0298567	−	0.406798i	−0.00119236	−	0.0162459i
$628$	−4.49139	+	2.59310i	−0.179226	+	0.103476i
$629$	−51.4046	+	51.4046i	−2.04963	+	2.04963i
$630$	1.05125	+	5.59314i	0.0418828	+	0.222836i
$631$	−1.01075	+	1.01075i	−0.0402374	+	0.0402374i	−0.726939	−	0.686702i	$-0.759058\pi$
$631$	−1.01075	+	1.01075i	−0.0402374	+	0.0402374i	0.686702	+	0.726939i	$0.259058\pi$
$632$	1.96771	−	7.34360i	0.0782714	−	0.292113i
$633$	1.00323	−	0.0736318i	0.0398750	−	0.00292660i
$634$	1.51882	+	0.876893i	0.0603202	+	0.0348259i
$635$	2.16408	−	8.07647i	0.0858791	−	0.320505i
$636$	12.8042	+	18.8424i	0.507719	+	0.747151i
$637$	16.5874	−	19.0226i	0.657217	−	0.753702i
$638$		−	0.0287597i		−	0.00113861i
$639$	4.41405	−	5.94250i	0.174617	−	0.235082i
$640$	10.5587	−	18.2882i	0.417370	−	0.722905i
$641$	−3.32852	+	5.76517i	−0.131469	+	0.227711i	−0.924243	−	0.381805i	$-0.875303\pi$
$641$	−3.32852	+	5.76517i	−0.131469	+	0.227711i	0.792774	+	0.609515i	$0.208636\pi$
$642$	1.04437	−	0.363639i	0.0412178	−	0.0143517i
$643$	−16.9839	−	16.9839i	−0.669780	−	0.669780i	0.287885	−	0.957665i	$-0.407048\pi$
$643$	−16.9839	−	16.9839i	−0.669780	−	0.669780i	−0.957665	+	0.287885i	$0.907048\pi$
$644$	12.5171	−	7.89752i	0.493243	−	0.311206i
$645$	0.346044	−	1.81362i	0.0136255	−	0.0714113i
$646$	0.0739926	+	0.128159i	0.00291120	+	0.00504235i
$647$	13.0009	−	22.5183i	0.511120	−	0.885286i	−0.488797	−	0.872398i	$-0.662564\pi$
$647$	13.0009	−	22.5183i	0.511120	−	0.885286i	0.999917	−	0.0128882i	$-0.00410257\pi$
$648$	−7.95404	−	4.26659i	−0.312464	−	0.167608i
$649$	−23.8465	+	13.7678i	−0.936055	+	0.540432i
$650$	−1.31535	−	2.33310i	−0.0515921	−	0.0915119i
$651$	−30.5512	−	24.3476i	−1.19739	−	0.954257i
$652$	3.16804	+	3.16804i	0.124070	+	0.124070i
$653$	12.0001	−	6.92828i	0.469602	−	0.271125i	−0.246471	−	0.969150i	$-0.579271\pi$
$653$	12.0001	−	6.92828i	0.469602	−	0.271125i	0.716073	+	0.698025i	$0.245938\pi$
$654$	5.77927	−	0.424166i	0.225987	−	0.0165862i
$655$	40.9471	−	10.9717i	1.59993	−	0.428701i
$656$	−6.87702	−	1.84269i	−0.268502	−	0.0719450i
$657$	9.58012	+	22.1433i	0.373756	+	0.863893i
$658$	−1.34422	+	0.0528007i	−0.0524030	+	0.00205839i
$659$		−	25.9191i		−	1.00966i	−0.863218	−	0.504832i	$-0.831555\pi$
$659$		−	25.9191i		−	1.00966i	0.863218	−	0.504832i	$-0.168445\pi$
$660$	27.2724	+	13.1854i	1.06158	+	0.513239i
$661$	−7.46215	−	27.8491i	−0.290244	−	1.08320i	−0.944922	−	0.327297i	$-0.893862\pi$
$661$	−7.46215	−	27.8491i	−0.290244	−	1.08320i	0.654678	−	0.755908i	$-0.272804\pi$
$662$	−1.44752	+	2.50718i	−0.0562595	+	0.0974443i
$663$	−32.7068	+	37.1128i	−1.27023	+	1.44134i
$664$	−4.91505			−0.190741
$665$	−0.545189	+	0.0214150i	−0.0211415	+	0.000830437i
$666$	−6.52405	−	2.58367i	−0.252802	−	0.100115i
$667$	−0.0879363	+	0.0507701i	−0.00340491	+	0.00196583i
$668$	−9.57341	−	35.7285i	−0.370406	−	1.38238i
$669$	−0.152615	−	0.131744i	−0.00590043	−	0.00509353i
$670$	−3.48379	−	0.933479i	−0.134591	−	0.0360634i
$671$	21.9632	+	21.9632i	0.847879	+	0.847879i
$672$	−8.35961	+	10.4896i	−0.322479	+	0.404644i
$673$		−	4.97327i		−	0.191705i	−0.995396	−	0.0958527i	$-0.969442\pi$
$673$		−	4.97327i		−	0.191705i	0.995396	−	0.0958527i	$-0.0305578\pi$
$674$	0.0453753	−	0.169343i	0.00174779	−	0.00652285i
$675$	14.4514	+	4.53073i	0.556233	+	0.174388i
$676$	−12.1290	−	22.0384i	−0.466498	−	0.847631i
$677$	−4.21948	+	2.43612i	−0.162168	+	0.0936276i	−0.578888	−	0.815407i	$-0.696513\pi$
$677$	−4.21948	+	2.43612i	−0.162168	+	0.0936276i	0.416720	+	0.909035i	$0.363180\pi$
$678$	0.654813	−	3.43189i	0.0251479	−	0.131801i
$679$	−0.0888863	+	0.392802i	−0.00341114	+	0.0150744i
$680$	−22.3495			−0.857063
$681$	4.00741	+	11.5092i	0.153564	+	0.441034i
$682$	6.74238	−	1.80661i	0.258179	−	0.0691788i
$683$	7.72004	−	2.06858i	0.295399	−	0.0791519i	−0.108076	−	0.994143i	$-0.534469\pi$
$683$	7.72004	−	2.06858i	0.295399	−	0.0791519i	0.403475	+	0.914991i	$0.367802\pi$
$684$	0.253739	−	0.341601i	0.00970194	−	0.0130614i
$685$	40.0985			1.53209
$686$	−4.67128	−	0.677448i	−0.178350	−	0.0258651i
$687$	4.09851	+	0.782005i	0.156368	+	0.0298354i
$688$	1.18608	−	0.684781i	0.0452187	−	0.0261070i
$689$	17.1510	+	17.5059i	0.653400	+	0.666922i
$690$	0.262791	+	3.58054i	0.0100043	+	0.136309i
$691$	−2.85162	+	10.6424i	−0.108481	+	0.404856i	−0.998717	−	0.0506439i	$-0.983873\pi$
$691$	−2.85162	+	10.6424i	−0.108481	+	0.404856i	0.890236	+	0.455500i	$0.150539\pi$
$692$		−	32.9525i		−	1.25267i
$693$	−21.0515	−	14.3902i	−0.799682	−	0.546637i
$694$	0.384429	+	0.384429i	0.0145927	+	0.0145927i
$695$	44.8670	+	12.0221i	1.70190	+	0.456023i
$696$	0.0398694	−	0.0461853i	0.00151124	−	0.00175065i
$697$	4.03831	+	15.0712i	0.152962	+	0.570861i
$698$	−5.91173	+	3.41314i	−0.223762	+	0.129189i
$699$	−22.9344	−	33.7499i	−0.867459	−	1.27654i
$700$	6.94802	−	13.2057i	0.262610	−	0.499128i
$701$	39.3887			1.48769			0.743845	−	0.668352i	$-0.233000\pi$
$701$	39.3887			1.48769			0.743845	+	0.668352i	$0.233000\pi$
$702$	−4.54133	−	1.47503i	−0.171402	−	0.0556713i
$703$	0.336364	−	0.582600i	0.0126862	−	0.0219732i
$704$	5.39063	+	20.1181i	0.203167	+	0.758229i
$705$	−4.23136	+	8.75207i	−0.159362	+	0.329622i
$706$		−	3.09796i		−	0.116593i
$707$	−23.7687	+	0.933633i	−0.893914	+	0.0351129i
$708$	−28.2171	−	5.38389i	−1.06046	−	0.202339i
$709$	10.8943	+	2.91911i	0.409143	+	0.109630i	0.457520	−	0.889200i	$-0.348738\pi$
$709$	10.8943	+	2.91911i	0.409143	+	0.109630i	−0.0483762	+	0.998829i	$0.515405\pi$
$710$	1.70894	−	0.457908i	0.0641352	−	0.0171850i
$711$	14.1247	+	17.8239i	0.529717	+	0.668449i
$712$	13.1575	−	7.59651i	0.493099	−	0.284691i
$713$	−17.4264	−	17.4264i	−0.652625	−	0.652625i
$714$	9.14860	+	1.37591i	0.342378	+	0.0514920i
$715$	31.3894	+	8.75627i	1.17390	+	0.327466i
$716$	−21.0967	+	12.1802i	−0.788420	+	0.455195i
$717$	2.16608	−	2.50922i	0.0808936	−	0.0937085i
$718$	−0.747602	+	1.29488i	−0.0279003	+	0.0483247i
$719$	−7.72451	−	13.3792i	−0.288076	−	0.498962i	0.685275	−	0.728285i	$-0.259682\pi$
$719$	−7.72451	−	13.3792i	−0.288076	−	0.498962i	−0.973350	+	0.229323i	$0.926349\pi$
$720$	12.1131	+	27.9979i	0.451427	+	1.04342i
$721$	−11.7743	−	6.19491i	−0.438498	−	0.230711i
$722$	3.42314	+	3.42314i	0.127396	+	0.127396i
$723$	−10.0089	−	28.7454i	−0.372235	−	1.06905i
$724$	−11.4873	+	19.8967i	−0.426924	+	0.739453i
$725$	−0.0511874	+	0.0886592i	−0.00190105	+	0.00329272i
$726$	−0.282927	+	0.0985126i	−0.0105004	+	0.00365615i
$727$			49.2519i			1.82665i	0.407228	+	0.913327i	$0.366496\pi$
$727$			49.2519i			1.82665i	−0.407228	+	0.913327i	$0.633504\pi$
$728$	−4.54112	+	8.42062i	−0.168305	+	0.312089i
$729$	24.4331	−	11.4901i	0.904931	−	0.425558i
$730$	−1.49245	+	5.56990i	−0.0552380	+	0.206151i
$731$	−2.59932	−	1.50072i	−0.0961392	−	0.0555060i
$732$	2.37187	+	32.3167i	0.0876667	+	1.19446i
$733$	10.8707	−	40.5701i	0.401519	−	1.49849i	−0.408867	−	0.912594i	$-0.634076\pi$
$733$	10.8707	−	40.5701i	0.401519	−	1.49849i	0.810386	−	0.585896i	$-0.199257\pi$
$734$	−5.74644	+	5.74644i	−0.212105	+	0.212105i
$735$	−20.1949	+	27.4885i	−0.744901	+	1.01393i
$736$	−5.98327	+	5.98327i	−0.220546	+	0.220546i
$737$	13.9953	−	8.08020i	0.515524	−	0.297638i
$738$	−1.18036	+	0.935383i	−0.0434496	+	0.0344319i
$739$	0.964951	+	3.60124i	0.0354963	+	0.132474i	0.981400	−	0.191973i	$-0.0614886\pi$
$739$	0.964951	+	3.60124i	0.0354963	+	0.132474i	−0.945904	+	0.324447i	$0.894822\pi$
$740$	24.9804	+	43.2674i	0.918299	+	1.59054i
$741$	0.203464	−	0.410070i	0.00747442	−	0.0150643i
$742$	1.01158	−	4.47032i	0.0371362	−	0.164111i
$743$	18.6096	−	18.6096i	0.682720	−	0.682720i	−0.277892	−	0.960612i	$-0.589636\pi$
$743$	18.6096	−	18.6096i	0.682720	−	0.682720i	0.960612	+	0.277892i	$0.0896358\pi$
$744$	13.3321	+	6.44567i	0.488779	+	0.236310i
$745$	22.8695	+	13.2037i	0.837874	+	0.483746i
$746$	0.556509	+	2.07692i	0.0203752	+	0.0760414i
$747$	8.76697	−	11.8027i	0.320767	−	0.431839i
$748$	34.8207	−	34.8207i	1.27317	−	1.27317i
$749$	5.86565	+	3.08614i	0.214326	+	0.112765i
$750$	−1.45559	−	2.14202i	−0.0531506	−	0.0782156i
$751$	−35.5729	+	20.5380i	−1.29807	+	0.749442i	−0.980071	−	0.198648i	$-0.936345\pi$
$751$	−35.5729	+	20.5380i	−1.29807	+	0.749442i	−0.318001	+	0.948090i	$0.603012\pi$
$752$	−6.96525	+	1.86633i	−0.253997	+	0.0680582i
$753$	−36.5987	+	2.68614i	−1.33373	+	0.0978883i
$754$	0.0164237	−	0.0277856i	0.000598116	−	0.00101189i
$755$		−	26.3721i		−	0.959777i
$756$	−6.81452	−	25.7148i	−0.247842	−	0.935240i
$757$	−1.96778			−0.0715200			−0.0357600	−	0.999360i	$-0.511385\pi$
$757$	−1.96778			−0.0715200			−0.0357600	+	0.999360i	$0.511385\pi$
$758$	−1.75938	−	3.04734i	−0.0639036	−	0.110684i
$759$	−12.1769	−	10.5117i	−0.441993	−	0.381550i
$760$	0.199772	−	0.0535287i	0.00724648	−	0.00194169i
$761$	2.94311	−	10.9838i	0.106688	−	0.398164i	−0.891843	−	0.452344i	$-0.850588\pi$
$761$	2.94311	−	10.9838i	0.106688	−	0.398164i	0.998531	+	0.0541801i	$0.0172545\pi$
$762$	0.245895	−	1.28874i	0.00890785	−	0.0466862i
$763$	25.5036	+	23.5758i	0.923294	+	0.853502i
$764$	41.0902			1.48659
$765$	39.8647	−	53.6687i	1.44131	−	1.94040i
$766$	−1.07462	−	0.620433i	−0.0388276	−	0.0224171i
$767$	−30.9011	−	0.316479i	−1.11577	−	0.0114274i
$768$	−8.33284	+	17.2355i	−0.300685	+	0.621933i
$769$	−9.25147	−	9.25147i	−0.333617	−	0.333617i	0.520342	−	0.853958i	$-0.325805\pi$
$769$	−9.25147	−	9.25147i	−0.333617	−	0.333617i	−0.853958	+	0.520342i	$0.825805\pi$
$770$	−1.80723	−	5.82043i	−0.0651279	−	0.209754i
$771$	−16.3438	−	24.0513i	−0.588609	−	0.866188i
$772$	−3.05338	+	11.3954i	−0.109893	+	0.410128i
$773$	12.3225	+	45.9883i	0.443211	+	1.65409i	0.720617	+	0.693333i	$0.243859\pi$
$773$	12.3225	+	45.9883i	0.443211	+	1.65409i	−0.277406	+	0.960753i	$0.589475\pi$
$774$	0.0333220	−	0.287788i	0.00119774	−	0.0103443i
$775$	−24.0006	−	6.43095i	−0.862128	−	0.231007i
$776$		−	0.152661i		−	0.00548020i
$777$	−15.3776	−	39.1443i	−0.551668	−	1.40429i
$778$	4.58996	−	4.58996i	0.164558	−	0.164558i
$779$	−0.0721933	−	0.125042i	−0.00258659	−	0.00448011i
$780$	18.8190	+	28.3131i	0.673827	+	1.01377i
$781$	−3.96365	+	6.86525i	−0.141831	+	0.245658i
$782$	5.63736	+	1.51053i	0.201592	+	0.0540163i
$783$	0.0397918	+	0.178121i	0.00142204	+	0.00636551i
$784$	−25.2234	+	1.98461i	−0.900837	+	0.0708790i
$785$	5.33163	−	5.33163i	0.190294	−	0.190294i
$786$	6.28179	−	2.18726i	0.224064	−	0.0780171i
$787$	−12.0305	−	44.8985i	−0.428842	−	1.60046i	−0.755387	−	0.655278i	$-0.772551\pi$
$787$	−12.0305	−	44.8985i	−0.428842	−	1.60046i	0.326545	−	0.945181i	$-0.394115\pi$
$788$	−8.57113	+	2.29663i	−0.305334	+	0.0818140i
$789$	41.9265	+	20.2702i	1.49262	+	0.721638i
$790$			5.43540i			0.193383i
$791$	17.7097	−	11.1737i	0.629685	−	0.397293i
$792$	8.98694	+	3.55903i	0.319337	+	0.126465i
$793$	8.67685	+	33.7618i	0.308124	+	1.19892i
$794$	0.960475	+	0.554531i	0.0340860	+	0.0196796i
$795$	−25.0715	−	21.6429i	−0.889193	−	0.767594i
$796$	−0.279909	−	0.484817i	−0.00992112	−	0.0171839i
$797$	34.9166			1.23681			0.618405	−	0.785859i	$-0.287779\pi$
$797$	34.9166			1.23681			0.618405	+	0.785859i	$0.287779\pi$
$798$	−0.0850706	+	0.00961298i	−0.00301147	+	0.000340296i
$799$	11.1744	+	11.1744i	0.395322	+	0.395322i
$800$	−2.20803	+	8.24049i	−0.0780657	+	0.291345i
$801$	−5.22726	+	45.1456i	−0.184696	+	1.59514i
$802$	4.25411	−	7.36834i	0.150218	−	0.260185i
$803$	−12.9187	−	22.3758i	−0.455889	−	0.789624i
$804$	16.5604	+	3.15977i	0.584040	+	0.111436i
$805$	−14.6064	+	15.8008i	−0.514807	+	0.556903i
$806$	7.54572	+	2.10493i	0.265787	+	0.0741428i
$807$	−27.4216	−	13.2575i	−0.965286	−	0.466686i
$808$	8.70949	−	2.33370i	0.306399	−	0.0820993i
$809$	−33.6608	−	19.4340i	−1.18345	−	0.683265i	−0.226639	−	0.973979i	$-0.572774\pi$
$809$	−33.6608	−	19.4340i	−1.18345	−	0.683265i	−0.956810	+	0.290714i	$0.906107\pi$
$810$	6.28233	+	1.47459i	0.220739	+	0.0518118i
$811$	−13.7603	−	13.7603i	−0.483191	−	0.483191i	0.422958	−	0.906149i	$-0.360992\pi$
$811$	−13.7603	−	13.7603i	−0.483191	−	0.483191i	−0.906149	+	0.422958i	$0.860992\pi$
$812$	0.179685	−	0.00705803i	0.00630572	−	0.000247688i
$813$	16.8190	+	3.20911i	0.589869	+	0.112548i
$814$	7.25844	+	1.94489i	0.254408	+	0.0681685i
$815$	−5.64106	−	3.25687i	−0.197598	−	0.114083i
$816$	49.4577	−	3.62992i	1.73137	−	0.127073i
$817$	0.0268285	+	0.00718866i	0.000938609	+	0.000251499i
$818$	−1.95662			−0.0684115
$819$	−12.1208	−	25.9246i	−0.423535	−	0.905880i
$820$	10.7230			0.374464
$821$	−39.3761	−	10.5508i	−1.37424	−	0.368226i	−0.505213	−	0.862995i	$-0.668586\pi$
$821$	−39.3761	−	10.5508i	−1.37424	−	0.368226i	−0.869024	+	0.494769i	$0.835253\pi$
$822$	6.27502	−	0.460551i	0.218866	−	0.0160636i
$823$	19.6164	+	11.3255i	0.683783	+	0.394783i	0.801279	−	0.598291i	$-0.204153\pi$
$823$	19.6164	+	11.3255i	0.683783	+	0.394783i	−0.117496	+	0.993073i	$0.537487\pi$
$824$	4.87139	+	1.30528i	0.169703	+	0.0454718i
$825$	−15.9312	−	3.03972i	−0.554655	−	0.105830i
$826$	3.08392	+	4.88783i	0.107303	+	0.170069i
$827$	−40.4535	−	40.4535i	−1.40670	−	1.40670i	−0.776122	−	0.630583i	$-0.782816\pi$
$827$	−40.4535	−	40.4535i	−1.40670	−	1.40670i	−0.630583	−	0.776122i	$-0.717184\pi$
$828$	−2.45020	−	16.6021i	−0.0851504	−	0.576964i
$829$	17.0739	+	9.85760i	0.593000	+	0.342369i	0.766283	−	0.642503i	$-0.222104\pi$
$829$	17.0739	+	9.85760i	0.593000	+	0.342369i	−0.173283	+	0.984872i	$0.555437\pi$
$830$	3.39421	−	0.909475i	0.117815	−	0.0315683i
$831$	11.6261	+	5.62087i	0.403306	+	0.194986i
$832$	−6.28074	+	22.5151i	−0.217745	+	0.780571i
$833$	31.4056	+	45.6974i	1.08814	+	1.58332i
$834$	7.15931	+	1.36601i	0.247907	+	0.0473012i
$835$	26.8884	+	46.5721i	0.930512	+	1.61169i
$836$	−0.227848	+	0.394645i	−0.00788030	+	0.0136491i
$837$	−39.2587	+	20.5178i	−1.35698	+	0.709200i
$838$	−1.20043	+	4.48007i	−0.0414682	+	0.154761i
$839$	−22.8553	−	22.8553i	−0.789054	−	0.789054i	0.192285	−	0.981339i	$-0.438410\pi$
$839$	−22.8553	−	22.8553i	−0.789054	−	0.789054i	−0.981339	+	0.192285i	$0.938410\pi$
$840$	5.16659	−	11.8524i	0.178264	−	0.408947i
$841$	28.9988			0.999957
$842$	−2.82686	−	4.89626i	−0.0974199	−	0.168736i
$843$	31.0289	+	26.7856i	1.06869	+	0.922546i
$844$	−0.973263	−	0.561913i	−0.0335011	−	0.0193419i
$845$	25.3258	+	26.3852i	0.871235	+	0.907677i
$846$	−0.561643	+	1.41821i	−0.0193097	+	0.0487591i
$847$	−1.58905	−	0.836061i	−0.0546004	−	0.0287274i
$848$		−	24.5681i		−	0.843673i
$849$	39.1621	+	18.9336i	1.34404	+	0.649801i
$850$	5.68370	−	1.52294i	0.194949	−	0.0522365i
$851$	−6.86673	−	25.6270i	−0.235388	−	0.878481i
$852$	−7.81017	+	2.71943i	−0.267572	+	0.0931662i
$853$	7.93126	−	7.93126i	0.271561	−	0.271561i	−0.558167	−	0.829728i	$-0.688495\pi$
$853$	7.93126	−	7.93126i	0.271561	−	0.271561i	0.829728	+	0.558167i	$0.188495\pi$
$854$	4.42534	−	4.78721i	0.151432	−	0.163815i
$855$	−0.227792	+	0.575199i	−0.00779031	+	0.0196714i
$856$	−2.42680	−	0.650259i	−0.0829463	−	0.0222254i
$857$	1.60609	−	2.78183i	0.0548630	−	0.0950255i	−0.837290	−	0.546760i	$-0.815861\pi$
$857$	1.60609	−	2.78183i	0.0548630	−	0.0950255i	0.892153	+	0.451734i	$0.149194\pi$
$858$	5.01270	+	1.00975i	0.171131	+	0.0344722i
$859$	−12.6207	−	21.8597i	−0.430612	−	0.745842i	0.566314	−	0.824190i	$-0.308369\pi$
$859$	−12.6207	−	21.8597i	−0.430612	−	0.745842i	−0.996926	+	0.0783473i	$0.975036\pi$
$860$	−1.45857	+	1.45857i	−0.0497368	+	0.0497368i
$861$	−8.92612	−	1.34245i	−0.304201	−	0.0457505i
$862$			0.963232i			0.0328078i
$863$	−30.0171	−	8.04307i	−1.02180	−	0.273789i	−0.291245	−	0.956648i	$-0.594070\pi$
$863$	−30.0171	−	8.04307i	−1.02180	−	0.273789i	−0.730550	+	0.682859i	$0.760736\pi$
$864$	7.04469	+	13.4793i	0.239665	+	0.458574i
$865$	12.3997	+	46.2761i	0.421601	+	1.57344i
$866$	−0.727347	+	2.71449i	−0.0247162	+	0.0922423i
$867$	−44.5338	−	65.5352i	−1.51245	−	2.22569i
$868$	12.9421	+	41.6818i	0.439283	+	1.41477i
$869$	−17.2211	−	17.2211i	−0.584185	−	0.584185i
$870$	−0.0189867	+	0.0392717i	−0.000643708	+	0.00133144i
$871$	18.1356	+	0.185739i	0.614503	+	0.00629354i
$872$	−11.4014	−	6.58261i	−0.386101	−	0.222915i
$873$	0.366590	+	0.272300i	0.0124072	+	0.00921597i
$874$	−0.0540077			−0.00182684
$875$	3.42579	−	15.1391i	0.115813	−	0.511795i
$876$	5.05185	−	26.4768i	0.170686	−	0.894569i
$877$	−9.65506	+	36.0332i	−0.326028	+	1.21675i	0.587246	+	0.809408i	$0.300212\pi$
$877$	−9.65506	+	36.0332i	−0.326028	+	1.21675i	−0.913274	+	0.407345i	$0.866455\pi$
$878$	−6.75099	+	1.80892i	−0.227835	+	0.0610482i
$879$	−15.0812	−	13.0188i	−0.508676	−	0.439114i
$880$	−16.3343	−	28.2918i	−0.550629	−	0.953717i
$881$	−5.16207			−0.173915			−0.0869574	−	0.996212i	$-0.527714\pi$
$881$	−5.16207			−0.173915			−0.0869574	+	0.996212i	$0.527714\pi$
$882$	−2.84458	+	4.53363i	−0.0957821	+	0.152655i
$883$		−	23.2348i		−	0.781912i	−0.920409	−	0.390956i	$-0.872145\pi$
$883$		−	23.2348i		−	0.781912i	0.920409	−	0.390956i	$-0.127855\pi$
$884$	53.5263	−	13.7564i	1.80028	−	0.462677i
$885$	41.6519	−	3.05702i	1.40011	−	0.102761i
$886$	−0.599892	+	0.160741i	−0.0201538	+	0.00540019i
$887$	9.69044	−	5.59478i	0.325373	−	0.187854i	−0.328412	−	0.944535i	$-0.606513\pi$
$887$	9.69044	−	5.59478i	0.325373	−	0.187854i	0.653785	+	0.756680i	$0.273180\pi$
$888$	8.96017	+	13.1857i	0.300684	+	0.442481i
$889$	6.65035	−	4.19597i	0.223046	−	0.140728i
$890$	−7.68060	+	7.68060i	−0.257454	+	0.257454i
$891$	−24.5764	+	15.2325i	−0.823341	+	0.510307i
$892$	0.0582969	+	0.217567i	0.00195192	+	0.00728468i
$893$	−0.126647	−	0.0731195i	−0.00423807	−	0.00244685i
$894$	3.73050	+	1.80358i	0.124767	+	0.0603208i
$895$	25.0434	−	25.0434i	0.837109	−	0.837109i
$896$	18.9665	−	5.88905i	0.633627	−	0.196739i
$897$	−5.76160	−	17.1095i	−0.192374	−	0.571269i
$898$	1.31262	+	2.27353i	0.0438028	+	0.0758687i
$899$	−0.0774991	−	0.289231i	−0.00258474	−	0.00964638i
$900$	−10.5087	−	13.2609i	−0.350289	−	0.442029i
$901$	−46.6283	+	26.9209i	−1.55341	+	0.896864i
$902$	1.14044	−	1.14044i	0.0379724	−	0.0379724i
$903$	1.39675	−	1.03155i	0.0464811	−	0.0343278i
$904$	−5.61270	+	5.61270i	−0.186676	+	0.186676i
$905$	8.64511	−	32.2640i	0.287373	−	1.07249i
$906$	−0.302896	−	4.12696i	−0.0100630	−	0.137109i
$907$	−20.9166	−	12.0762i	−0.694524	−	0.400984i	0.110780	−	0.993845i	$-0.464665\pi$
$907$	−20.9166	−	12.0762i	−0.694524	−	0.400984i	−0.805305	+	0.592861i	$0.797998\pi$
$908$	3.52388	−	13.1513i	0.116944	−	0.436441i
$909$	−9.93109	+	25.0771i	−0.329393	+	0.831754i
$910$	1.57784	−	6.65534i	0.0523049	−	0.220622i
$911$			21.5718i			0.714706i	0.933969	+	0.357353i	$0.116321\pi$
$911$			21.5718i			0.714706i	−0.933969	+	0.357353i	$0.883679\pi$
$912$	−0.433386	+	0.150901i	−0.0143509	+	0.00499684i
$913$	−7.87242	+	13.6354i	−0.260539	+	0.451267i
$914$	−0.667916	+	1.15686i	−0.0220927	+	0.0382657i
$915$	−15.4913	−	44.4908i	−0.512126	−	1.47082i
$916$	−3.29614	−	3.29614i	−0.108908	−	0.108908i
$917$	35.2815	+	18.5630i	1.16510	+	0.613003i
$918$	5.62201	−	8.85648i	0.185554	−	0.292307i
$919$	−14.1452	−	24.5003i	−0.466608	−	0.808189i	0.532664	−	0.846327i	$-0.321191\pi$
$919$	−14.1452	−	24.5003i	−0.466608	−	0.808189i	−0.999273	+	0.0381373i	$0.987858\pi$
$920$	4.07825	−	7.06374i	0.134456	−	0.232885i
$921$	−22.6302	+	26.2151i	−0.745689	+	0.863818i
$922$	−7.40135	+	4.27317i	−0.243751	+	0.140729i
$923$	−7.74993	+	4.36922i	−0.255092	+	0.143814i
$924$	10.4166	+	26.5158i	0.342680	+	0.872305i
$925$	−18.9145	−	18.9145i	−0.621904	−	0.621904i
$926$	−2.80382	+	1.61879i	−0.0921392	+	0.0531966i
$927$	−11.8235	+	9.36963i	−0.388335	+	0.307739i
$928$	−0.0993058	+	0.0266089i	−0.00325987	+	0.000873480i
$929$	0.800524	+	0.214500i	0.0262643	+	0.00703751i	0.271927	−	0.962318i	$-0.412339\pi$
$929$	0.800524	+	0.214500i	0.0262643	+	0.00703751i	−0.245663	+	0.969355i	$0.579006\pi$
$930$	−10.3995	−	1.98425i	−0.341013	−	0.0650662i
$931$	−0.390169	−	0.333249i	−0.0127873	−	0.0109218i
$932$			45.5872i			1.49326i
$933$	−15.2407	+	31.5235i	−0.498957	+	1.03203i
$934$	0.718237	+	2.68050i	0.0235014	+	0.0877085i
$935$	−35.7970	+	62.0023i	−1.17069	+	2.02769i
$936$	6.65011	+	8.57063i	0.217366	+	0.280140i
$937$	38.9669			1.27299			0.636496	−	0.771280i	$-0.280383\pi$
$937$	38.9669			1.27299			0.636496	+	0.771280i	$0.280383\pi$
$938$	−1.80993	−	2.86863i	−0.0590963	−	0.0936641i
$939$	25.3208	+	37.2617i	0.826314	+	1.21599i
$940$	9.40554	−	5.43029i	0.306775	−	0.177117i
$941$	2.64634	+	9.87626i	0.0862681	+	0.321957i	0.995551	−	0.0942210i	$-0.0300360\pi$
$941$	2.64634	+	9.87626i	0.0862681	+	0.321957i	−0.909283	+	0.416178i	$0.863369\pi$
$942$	0.773110	−	0.895582i	0.0251893	−	0.0291796i
$943$	−5.50027	−	1.47379i	−0.179113	−	0.0479933i
$944$	21.9057	+	21.9057i	0.712969	+	0.712969i
$945$	19.2460	+	33.5479i	0.626073	+	1.09131i
$946$			0.310250i			0.0100871i
$947$	0.595716	−	2.22324i	0.0193582	−	0.0722457i	−0.955571	−	0.294761i	$-0.904760\pi$
$947$	0.595716	−	2.22324i	0.0193582	−	0.0722457i	0.974929	+	0.222515i	$0.0714267\pi$
$948$	−1.85975	−	25.3392i	−0.0604019	−	0.822978i
$949$	0.296961	−	28.9953i	0.00963976	−	0.941229i
$950$	−0.0471565	+	0.0272258i	−0.00152996	+	0.000883322i
$951$	11.7075	+	2.23382i	0.379642	+	0.0724366i
$952$	−15.4342	−	14.2675i	−0.500224	−	0.462412i
$953$	−10.6438			−0.344786			−0.172393	−	0.985028i	$-0.555150\pi$
$953$	−10.6438			−0.344786			−0.172393	+	0.985028i	$0.555150\pi$
$954$	−4.17201	−	3.09894i	−0.135074	−	0.100332i
$955$	−57.7041	+	15.4618i	−1.86726	+	0.500331i
$956$	−3.57713	+	0.958489i	−0.115693	+	0.0309998i
$957$	−0.0642695	−	0.184581i	−0.00207754	−	0.00596666i
$958$	1.06722			0.0344804
$959$	27.6914	+	25.5982i	0.894201	+	0.826608i
$960$	5.92067	−	31.0303i	0.191089	−	1.00150i
$961$	36.0917	−	20.8376i	1.16425	−	0.672180i
$962$	5.90194	+	6.02408i	0.190286	+	0.194224i
$963$	5.89017	−	4.66771i	0.189808	−	0.150415i
$964$	−8.80124	+	32.8467i	−0.283469	+	1.05792i
$965$		−	17.1518i		−	0.552135i
$966$	−2.10427	+	2.64042i	−0.0677038	+	0.0849542i
$967$	−13.4449	−	13.4449i	−0.432359	−	0.432359i	0.457071	−	0.889430i	$-0.348898\pi$
$967$	−13.4449	−	13.4449i	−0.432359	−	0.432359i	−0.889430	+	0.457071i	$0.848898\pi$
$968$	0.657439	+	0.176160i	0.0211309	+	0.00566201i
$969$	0.761287	+	0.657180i	0.0244561	+	0.0211117i
$970$	0.0282481	+	0.105423i	0.000906992	+	0.00338494i
$971$	−52.4109	+	30.2594i	−1.68195	+	0.971072i	−0.721579	+	0.692332i	$0.756583\pi$
$971$	−52.4109	+	30.2594i	−1.68195	+	0.971072i	−0.960367	+	0.278739i	$0.910083\pi$
$972$	−29.7920	−	4.72483i	−0.955579	−	0.151549i
$973$	23.3097	+	36.9445i	0.747275	+	1.18439i
$974$	0.397388			0.0127331
$975$	−13.6558	−	12.0346i	−0.437335	−	0.385415i
$976$	17.4727	−	30.2635i	0.559286	−	0.968712i
$977$	13.7503	+	51.3168i	0.439911	+	1.64177i	0.729034	+	0.684478i	$0.239970\pi$
$977$	13.7503	+	51.3168i	0.439911	+	1.64177i	−0.289123	+	0.957292i	$0.593364\pi$
$978$	−0.920176	−	0.444877i	−0.0294240	−	0.0142256i
$979$		−	48.6692i		−	1.55547i
$980$	35.9215	−	12.7196i	1.14747	−	0.406314i
$981$	36.1438	−	15.6373i	1.15398	−	0.499261i
$982$	−2.89212	−	0.774941i	−0.0922912	−	0.0247294i
$983$	43.1202	−	11.5540i	1.37532	−	0.368516i	0.505901	−	0.862592i	$-0.331160\pi$
$983$	43.1202	−	11.5540i	1.37532	−	0.368516i	0.869419	+	0.494076i	$0.164494\pi$
$984$	3.41242	−	0.250452i	0.108784	−	0.00798412i
$985$	11.1725	−	6.45044i	0.355985	−	0.205528i
$986$	0.0501411	+	0.0501411i	0.00159682	+	0.00159682i
$987$	−8.50926	+	3.34281i	−0.270853	+	0.106403i
$988$	−0.445500	+	0.251162i	−0.0141732	+	0.00799052i
$989$	0.948628	−	0.547691i	0.0301646	−	0.0174156i
$990$	−6.86470	−	0.794841i	−0.218174	−	0.0252617i
$991$	22.5217	−	39.0087i	0.715426	−	1.23915i	−0.247369	−	0.968921i	$-0.579566\pi$
$991$	22.5217	−	39.0087i	0.715426	−	1.23915i	0.962795	−	0.270232i	$-0.0871006\pi$
$992$	−12.4763	−	21.6096i	−0.396123	−	0.686106i
$993$	−3.68745	+	19.3260i	−0.117018	+	0.613292i
$994$	1.47248	+	0.774729i	0.0467043	+	0.0245729i
$995$	0.575516	+	0.575516i	0.0182451	+	0.0182451i
$996$	−15.5122	+	5.40121i	−0.491523	+	0.171144i
$997$	10.0403	−	17.3904i	0.317981	−	0.550759i	−0.662086	−	0.749428i	$-0.730329\pi$
$997$	10.0403	−	17.3904i	0.317981	−	0.550759i	0.980067	+	0.198669i	$0.0636619\pi$
$998$	2.01642	−	3.49254i	0.0638286	−	0.110554i
$999$	−47.6455	−	2.00278i	−1.50744	−	0.0633652i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	273.2.cd.e.242.15	yes	112
3.2	odd	2	inner	273.2.cd.e.242.14	yes	112
7.2	even	3	inner	273.2.cd.e.86.14	yes	112
13.5	odd	4	inner	273.2.cd.e.200.15	yes	112
21.2	odd	6	inner	273.2.cd.e.86.15	yes	112
39.5	even	4	inner	273.2.cd.e.200.14	yes	112
91.44	odd	12	inner	273.2.cd.e.44.14	✓	112
273.44	even	12	inner	273.2.cd.e.44.15	yes	112

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.cd.e.44.14	✓	112	91.44	odd	12	inner
273.2.cd.e.44.15	yes	112	273.44	even	12	inner
273.2.cd.e.86.14	yes	112	7.2	even	3	inner
273.2.cd.e.86.15	yes	112	21.2	odd	6	inner
273.2.cd.e.200.14	yes	112	39.5	even	4	inner
273.2.cd.e.200.15	yes	112	13.5	odd	4	inner
273.2.cd.e.242.14	yes	112	3.2	odd	2	inner
273.2.cd.e.242.15	yes	112	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 273 = 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	273.cd (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.246180 + 0.0659636i) q^{2} +(1.72740 - 0.126782i) q^{3} +(-1.67580 - 0.967522i) q^{4} +(2.71744 + 0.728135i) q^{5} +(0.433615 + 0.0827348i) q^{6} +(1.41179 + 2.23760i) q^{7} +(-0.709158 - 0.709158i) q^{8} +(2.96785 - 0.438007i) q^{9} +O(q^{10})\)	\(q+(0.246180 + 0.0659636i) q^{2} +(1.72740 - 0.126782i) q^{3} +(-1.67580 - 0.967522i) q^{4} +(2.71744 + 0.728135i) q^{5} +(0.433615 + 0.0827348i) q^{6} +(1.41179 + 2.23760i) q^{7} +(-0.709158 - 0.709158i) q^{8} +(2.96785 - 0.438007i) q^{9} +(0.620947 + 0.358504i) q^{10} +(-3.10321 + 0.831504i) q^{11} +(-3.01744 - 1.45884i) q^{12} +(-3.47296 - 0.968803i) q^{13} +(0.199953 + 0.643978i) q^{14} +(4.78643 + 0.913262i) q^{15} +(1.80724 + 3.13024i) q^{16} +(3.96062 - 6.86000i) q^{17} +(0.759517 + 0.0879420i) q^{18} +(-0.0189720 + 0.0708044i) q^{19} +(-3.84939 - 3.84939i) q^{20} +(2.72242 + 3.68625i) q^{21} -0.818797 q^{22} +(1.44544 + 2.50358i) q^{23} +(-1.31491 - 1.13509i) q^{24} +(2.52416 + 1.45732i) q^{25} +(-0.791065 - 0.467588i) q^{26} +(5.07115 - 1.13288i) q^{27} +(-0.200944 - 5.11570i) q^{28} +0.0351243i q^{29} +(1.11808 + 0.540557i) q^{30} +(-8.23449 + 2.20642i) q^{31} +(0.757564 + 2.82727i) q^{32} +(-5.25509 + 1.82977i) q^{33} +(1.42753 - 1.42753i) q^{34} +(2.20717 + 7.10851i) q^{35} +(-5.39730 - 2.13745i) q^{36} +(-8.86476 - 2.37531i) q^{37} +(-0.00934103 + 0.0161791i) q^{38} +(-6.12203 - 1.23321i) q^{39} +(-1.41073 - 2.44345i) q^{40} +(-1.39282 + 1.39282i) q^{41} +(0.427045 + 1.08706i) q^{42} -0.378909i q^{43} +(6.00486 + 1.60900i) q^{44} +(8.38388 + 0.970742i) q^{45} +(0.190693 + 0.711676i) q^{46} +(-0.516348 + 1.92704i) q^{47} +(3.51870 + 5.17806i) q^{48} +(-3.01371 + 6.31804i) q^{49} +(0.525266 + 0.525266i) q^{50} +(5.97187 - 12.3521i) q^{51} +(4.88263 + 4.98368i) q^{52} +(-5.88649 - 3.39856i) q^{53} +(1.32314 + 0.0556184i) q^{54} -9.03824 q^{55} +(0.585631 - 2.58799i) q^{56} +(-0.0237956 + 0.124713i) q^{57} +(-0.00231692 + 0.00864688i) q^{58} +(8.27883 - 2.21831i) q^{59} +(-7.13748 - 6.16142i) q^{60} +(-4.83406 - 8.37284i) q^{61} -2.17271 q^{62} +(5.17006 + 6.02249i) q^{63} -6.48298i q^{64} +(-8.73212 - 5.16144i) q^{65} +(-1.41439 + 0.103809i) q^{66} +(-4.85879 + 1.30191i) q^{67} +(-13.2744 + 7.66398i) q^{68} +(2.81427 + 4.14143i) q^{69} +(0.0744576 + 1.89556i) q^{70} +(1.74479 - 1.74479i) q^{71} +(-2.41529 - 1.79406i) q^{72} +(2.08150 + 7.76825i) q^{73} +(-2.02564 - 1.16950i) q^{74} +(4.54500 + 2.19737i) q^{75} +(0.100298 - 0.100298i) q^{76} +(-6.24166 - 5.76984i) q^{77} +(-1.42577 - 0.707422i) q^{78} +(3.79033 + 6.56505i) q^{79} +(2.63183 + 9.82214i) q^{80} +(8.61630 - 2.59988i) q^{81} +(-0.434759 + 0.251008i) q^{82} +(3.46542 - 3.46542i) q^{83} +(-0.995690 - 8.81141i) q^{84} +(15.7578 - 15.7578i) q^{85} +(0.0249942 - 0.0932797i) q^{86} +(0.00445312 + 0.0606738i) q^{87} +(2.79034 + 1.61100i) q^{88} +(-3.92087 + 14.6329i) q^{89} +(1.99991 + 0.792008i) q^{90} +(-2.73529 - 9.13883i) q^{91} -5.59398i q^{92} +(-13.9446 + 4.85537i) q^{93} +(-0.254229 + 0.440337i) q^{94} +(-0.103110 + 0.178592i) q^{95} +(1.66707 + 4.78779i) q^{96} +(0.107635 + 0.107635i) q^{97} +(-1.15867 + 1.35658i) q^{98} +(-8.84568 + 3.82701i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 112 q - 12 q^{3} - 8 q^{6} - 4 q^{7} + 8 q^{9}+O(q^{10}) \) 112 * q - 12 * q^3 - 8 * q^6 - 4 * q^7 + 8 * q^9	\( 112 q - 12 q^{3} - 8 q^{6} - 4 q^{7} + 8 q^{9} - 48 q^{13} - 12 q^{15} + 40 q^{16} - 26 q^{18} + 40 q^{19} - 10 q^{21} + 16 q^{22} + 32 q^{24} - 24 q^{27} - 52 q^{28} - 12 q^{31} - 44 q^{33} + 16 q^{34} - 8 q^{37} - 42 q^{39} - 160 q^{40} - 80 q^{42} + 6 q^{45} + 32 q^{46} + 72 q^{48} - 12 q^{52} + 34 q^{54} - 48 q^{55} - 24 q^{57} - 28 q^{58} + 44 q^{60} + 78 q^{63} + 4 q^{66} + 24 q^{67} - 12 q^{70} - 26 q^{72} - 40 q^{73} + 112 q^{76} + 32 q^{78} + 48 q^{79} + 128 q^{81} - 150 q^{84} + 160 q^{85} - 48 q^{87} + 24 q^{91} + 10 q^{93} - 8 q^{94} - 106 q^{96} + 56 q^{97} - 36 q^{99}+O(q^{100}) \) 112 * q - 12 * q^3 - 8 * q^6 - 4 * q^7 + 8 * q^9 - 48 * q^13 - 12 * q^15 + 40 * q^16 - 26 * q^18 + 40 * q^19 - 10 * q^21 + 16 * q^22 + 32 * q^24 - 24 * q^27 - 52 * q^28 - 12 * q^31 - 44 * q^33 + 16 * q^34 - 8 * q^37 - 42 * q^39 - 160 * q^40 - 80 * q^42 + 6 * q^45 + 32 * q^46 + 72 * q^48 - 12 * q^52 + 34 * q^54 - 48 * q^55 - 24 * q^57 - 28 * q^58 + 44 * q^60 + 78 * q^63 + 4 * q^66 + 24 * q^67 - 12 * q^70 - 26 * q^72 - 40 * q^73 + 112 * q^76 + 32 * q^78 + 48 * q^79 + 128 * q^81 - 150 * q^84 + 160 * q^85 - 48 * q^87 + 24 * q^91 + 10 * q^93 - 8 * q^94 - 106 * q^96 + 56 * q^97 - 36 * q^99

Introduction

L-functions

Modular forms

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