LMFDB - Embedded newform 37.2.f.a.16.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [37,2,Mod(7,37)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(37, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([16]))

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

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

chi := DirichletCharacter("37.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	37.f (of order $9$, degree $6$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$0.295446487479$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\Q(\zeta_{18})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{3} + 1 $ x^6 - x^3 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			16.1
Root			$-0.173648 - 0.984808i$ of defining polynomial
Character	$\chi$	$=$	37.16
Dual form			37.2.f.a.7.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.76604 - 0.642788i) q^{2} +(1.26604 - 0.460802i) q^{3} +(1.17365 + 0.984808i) q^{4} +(0.532089 - 3.01763i) q^{5} -2.53209 q^{6} +(-0.613341 + 3.47843i) q^{7} +(0.439693 + 0.761570i) q^{8} +(-0.907604 + 0.761570i) q^{9} +O(q^{10})$	\(q+(-1.76604 - 0.642788i) q^{2} +(1.26604 - 0.460802i) q^{3} +(1.17365 + 0.984808i) q^{4} +(0.532089 - 3.01763i) q^{5} -2.53209 q^{6} +(-0.613341 + 3.47843i) q^{7} +(0.439693 + 0.761570i) q^{8} +(-0.907604 + 0.761570i) q^{9} +(-2.87939 + 4.98724i) q^{10} +(0.173648 + 0.300767i) q^{11} +(1.93969 + 0.705990i) q^{12} +(-0.141559 - 0.118782i) q^{13} +(3.31908 - 5.74881i) q^{14} +(-0.716881 - 4.06564i) q^{15} +(-0.819078 - 4.64522i) q^{16} +(-4.44356 + 3.72859i) q^{17} +(2.09240 - 0.761570i) q^{18} +(6.31180 - 2.29731i) q^{19} +(3.59627 - 3.01763i) q^{20} +(0.826352 + 4.68647i) q^{21} +(-0.113341 - 0.642788i) q^{22} +(0.266044 - 0.460802i) q^{23} +(0.907604 + 0.761570i) q^{24} +(-4.12449 - 1.50119i) q^{25} +(0.173648 + 0.300767i) q^{26} +(-2.81908 + 4.88279i) q^{27} +(-4.14543 + 3.47843i) q^{28} +(-4.03209 - 6.98378i) q^{29} +(-1.34730 + 7.64090i) q^{30} -2.75877 q^{31} +(-1.23396 + 6.99811i) q^{32} +(0.358441 + 0.300767i) q^{33} +(10.2442 - 3.72859i) q^{34} +(10.1702 + 3.70167i) q^{35} -1.81521 q^{36} +(-1.52094 - 5.88954i) q^{37} -12.6236 q^{38} +(-0.233956 - 0.0851529i) q^{39} +(2.53209 - 0.921605i) q^{40} +(1.70574 + 1.43128i) q^{41} +(1.55303 - 8.80769i) q^{42} -1.14290 q^{43} +(-0.0923963 + 0.524005i) q^{44} +(1.81521 + 3.14403i) q^{45} +(-0.766044 + 0.642788i) q^{46} +(0.620615 - 1.07494i) q^{47} +(-3.17752 - 5.50362i) q^{48} +(-5.14543 - 1.87278i) q^{49} +(6.31908 + 5.30234i) q^{50} +(-3.90760 + 6.76817i) q^{51} +(-0.0491630 - 0.278817i) q^{52} +(0.0675813 + 0.383273i) q^{53} +(8.11721 - 6.81115i) q^{54} +(1.00000 - 0.363970i) q^{55} +(-2.91875 + 1.06234i) q^{56} +(6.93242 - 5.81699i) q^{57} +(2.63176 + 14.9254i) q^{58} +(0.724155 + 4.10689i) q^{59} +(3.16250 - 5.47762i) q^{60} +(-7.07398 - 5.93577i) q^{61} +(4.87211 + 1.77330i) q^{62} +(-2.09240 - 3.62414i) q^{63} +(1.96064 - 3.39592i) q^{64} +(-0.433763 + 0.363970i) q^{65} +(-0.439693 - 0.761570i) q^{66} +(-0.354570 + 2.01087i) q^{67} -8.88713 q^{68} +(0.124485 - 0.705990i) q^{69} +(-15.5817 - 13.0746i) q^{70} +(12.7417 - 4.63760i) q^{71} +(-0.979055 - 0.356347i) q^{72} +10.0077 q^{73} +(-1.09967 + 11.3788i) q^{74} -5.91353 q^{75} +(9.67024 + 3.51968i) q^{76} +(-1.15270 + 0.419550i) q^{77} +(0.358441 + 0.300767i) q^{78} +(-1.32295 + 7.50281i) q^{79} -14.4534 q^{80} +(-0.701867 + 3.98048i) q^{81} +(-2.09240 - 3.62414i) q^{82} +(-0.401674 + 0.337044i) q^{83} +(-3.64543 + 6.31407i) q^{84} +(8.88713 + 15.3930i) q^{85} +(2.01842 + 0.734644i) q^{86} +(-8.32295 - 6.98378i) q^{87} +(-0.152704 + 0.264490i) q^{88} +(1.75490 + 9.95253i) q^{89} +(-1.18479 - 6.71929i) q^{90} +(0.500000 - 0.419550i) q^{91} +(0.766044 - 0.278817i) q^{92} +(-3.49273 + 1.27125i) q^{93} +(-1.78699 + 1.49946i) q^{94} +(-3.57398 - 20.2690i) q^{95} +(1.66250 + 9.42853i) q^{96} +(1.53936 - 2.66625i) q^{97} +(7.88326 + 6.61484i) q^{98} +(-0.386659 - 0.140732i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 6 q^{2} + 3 q^{3} + 6 q^{4} - 6 q^{5} - 6 q^{6} + 3 q^{7} - 3 q^{8} - 9 q^{9}+O(q^{10}) $ 6 * q - 6 * q^2 + 3 * q^3 + 6 * q^4 - 6 * q^5 - 6 * q^6 + 3 * q^7 - 3 * q^8 - 9 * q^9	\( 6 q - 6 q^{2} + 3 q^{3} + 6 q^{4} - 6 q^{5} - 6 q^{6} + 3 q^{7} - 3 q^{8} - 9 q^{9} - 6 q^{10} + 6 q^{12} - 9 q^{13} + 3 q^{14} + 12 q^{15} + 12 q^{16} + 3 q^{17} + 9 q^{18} + 3 q^{19} - 6 q^{20} + 6 q^{21} + 6 q^{22} - 3 q^{23} + 9 q^{24} - 12 q^{25} - 9 q^{28} - 15 q^{29} - 6 q^{30} + 6 q^{31} - 12 q^{32} - 6 q^{33} + 3 q^{34} + 18 q^{35} - 18 q^{36} - 6 q^{37} - 6 q^{38} - 6 q^{39} + 6 q^{40} - 3 q^{42} - 6 q^{43} + 3 q^{44} + 18 q^{45} + 15 q^{47} + 6 q^{48} - 15 q^{49} + 21 q^{50} - 27 q^{51} - 12 q^{52} + 24 q^{53} + 18 q^{54} + 6 q^{55} - 15 q^{56} + 18 q^{57} + 21 q^{58} + 6 q^{59} + 24 q^{60} - 27 q^{61} - 9 q^{63} + 3 q^{64} + 30 q^{65} + 3 q^{66} - 18 q^{67} + 6 q^{68} - 12 q^{69} - 30 q^{70} + 33 q^{71} - 9 q^{72} + 12 q^{73} - 21 q^{74} - 66 q^{75} + 15 q^{76} - 9 q^{77} - 6 q^{78} + 33 q^{79} - 60 q^{80} - 18 q^{81} - 9 q^{82} + 21 q^{83} - 6 q^{84} - 6 q^{85} + 24 q^{86} - 9 q^{87} - 3 q^{88} + 12 q^{89} + 3 q^{91} - 3 q^{93} - 3 q^{94} - 6 q^{95} + 15 q^{96} + 18 q^{97} + 12 q^{98} - 9 q^{99}+O(q^{100}) \) 6 * q - 6 * q^2 + 3 * q^3 + 6 * q^4 - 6 * q^5 - 6 * q^6 + 3 * q^7 - 3 * q^8 - 9 * q^9 - 6 * q^10 + 6 * q^12 - 9 * q^13 + 3 * q^14 + 12 * q^15 + 12 * q^16 + 3 * q^17 + 9 * q^18 + 3 * q^19 - 6 * q^20 + 6 * q^21 + 6 * q^22 - 3 * q^23 + 9 * q^24 - 12 * q^25 - 9 * q^28 - 15 * q^29 - 6 * q^30 + 6 * q^31 - 12 * q^32 - 6 * q^33 + 3 * q^34 + 18 * q^35 - 18 * q^36 - 6 * q^37 - 6 * q^38 - 6 * q^39 + 6 * q^40 - 3 * q^42 - 6 * q^43 + 3 * q^44 + 18 * q^45 + 15 * q^47 + 6 * q^48 - 15 * q^49 + 21 * q^50 - 27 * q^51 - 12 * q^52 + 24 * q^53 + 18 * q^54 + 6 * q^55 - 15 * q^56 + 18 * q^57 + 21 * q^58 + 6 * q^59 + 24 * q^60 - 27 * q^61 - 9 * q^63 + 3 * q^64 + 30 * q^65 + 3 * q^66 - 18 * q^67 + 6 * q^68 - 12 * q^69 - 30 * q^70 + 33 * q^71 - 9 * q^72 + 12 * q^73 - 21 * q^74 - 66 * q^75 + 15 * q^76 - 9 * q^77 - 6 * q^78 + 33 * q^79 - 60 * q^80 - 18 * q^81 - 9 * q^82 + 21 * q^83 - 6 * q^84 - 6 * q^85 + 24 * q^86 - 9 * q^87 - 3 * q^88 + 12 * q^89 + 3 * q^91 - 3 * q^93 - 3 * q^94 - 6 * q^95 + 15 * q^96 + 18 * q^97 + 12 * q^98 - 9 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/37\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{9}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.76604	−	0.642788i	−1.24878	−	0.454519i	−0.368792	−	0.929512i	$-0.620229\pi$
$2$	−1.76604	−	0.642788i	−1.24878	−	0.454519i	−0.879990	+	0.474992i	$0.842451\pi$
$3$	1.26604	−	0.460802i	0.730951	−	0.266044i	0.0503837	−	0.998730i	$-0.483956\pi$
$3$	1.26604	−	0.460802i	0.730951	−	0.266044i	0.680567	+	0.732685i	$0.261733\pi$
$4$	1.17365	+	0.984808i	0.586824	+	0.492404i
$5$	0.532089	−	3.01763i	0.237957	−	1.34952i	−0.598338	−	0.801244i	$-0.704172\pi$
$5$	0.532089	−	3.01763i	0.237957	−	1.34952i	0.836295	−	0.548279i	$-0.184717\pi$
$6$	−2.53209			−1.03372
$7$	−0.613341	+	3.47843i	−0.231821	+	1.31472i	0.617385	+	0.786661i	$0.288192\pi$
$7$	−0.613341	+	3.47843i	−0.231821	+	1.31472i	−0.849206	+	0.528061i	$0.822919\pi$
$8$	0.439693	+	0.761570i	0.155455	+	0.269256i
$9$	−0.907604	+	0.761570i	−0.302535	+	0.253857i
$10$	−2.87939	+	4.98724i	−0.910542	+	1.57710i
$11$	0.173648	+	0.300767i	0.0523569	+	0.0906848i	0.891016	−	0.453972i	$-0.149993\pi$
$11$	0.173648	+	0.300767i	0.0523569	+	0.0906848i	−0.838659	+	0.544657i	$0.816660\pi$
$12$	1.93969	+	0.705990i	0.559941	+	0.203802i
$13$	−0.141559	−	0.118782i	−0.0392615	−	0.0329443i	0.622946	−	0.782265i	$-0.285936\pi$
$13$	−0.141559	−	0.118782i	−0.0392615	−	0.0329443i	−0.662207	+	0.749321i	$0.730380\pi$
$14$	3.31908	−	5.74881i	0.887061	−	1.53643i
$15$	−0.716881	−	4.06564i	−0.185098	−	1.04974i
$16$	−0.819078	−	4.64522i	−0.204769	−	1.16131i
$17$	−4.44356	+	3.72859i	−1.07772	+	0.904316i	−0.995730	−	0.0923165i	$-0.970573\pi$
$17$	−4.44356	+	3.72859i	−1.07772	+	0.904316i	−0.0819926	+	0.996633i	$0.526128\pi$
$18$	2.09240	−	0.761570i	0.493183	−	0.179504i
$19$	6.31180	−	2.29731i	1.44803	−	0.527039i	0.505988	−	0.862541i	$-0.331128\pi$
$19$	6.31180	−	2.29731i	1.44803	−	0.527039i	0.942040	+	0.335502i	$0.108906\pi$
$20$	3.59627	−	3.01763i	0.804150	−	0.674762i
$21$	0.826352	+	4.68647i	0.180325	+	1.02267i
$22$	−0.113341	−	0.642788i	−0.0241643	−	0.137043i
$23$	0.266044	−	0.460802i	0.0554741	−	0.0960840i	−0.836955	−	0.547272i	$-0.815666\pi$
$23$	0.266044	−	0.460802i	0.0554741	−	0.0960840i	0.892429	+	0.451188i	$0.149000\pi$
$24$	0.907604	+	0.761570i	0.185264	+	0.155455i
$25$	−4.12449	−	1.50119i	−0.824897	−	0.300238i
$26$	0.173648	+	0.300767i	0.0340552	+	0.0589854i
$27$	−2.81908	+	4.88279i	−0.542532	+	0.939693i
$28$	−4.14543	+	3.47843i	−0.783413	+	0.657361i
$29$	−4.03209	−	6.98378i	−0.748740	−	1.29686i	−0.948427	−	0.316996i	$-0.897326\pi$
$29$	−4.03209	−	6.98378i	−0.748740	−	1.29686i	0.199687	−	0.979860i	$-0.436008\pi$
$30$	−1.34730	+	7.64090i	−0.245982	+	1.39503i
$31$	−2.75877			−0.495490			−0.247745	−	0.968825i	$-0.579689\pi$
$31$	−2.75877			−0.495490			−0.247745	+	0.968825i	$0.579689\pi$
$32$	−1.23396	+	6.99811i	−0.218135	+	1.23710i
$33$	0.358441	+	0.300767i	0.0623965	+	0.0523569i
$34$	10.2442	−	3.72859i	1.75687	−	0.639448i
$35$	10.1702	+	3.70167i	1.71909	+	0.625696i
$36$	−1.81521			−0.302535
$37$	−1.52094	−	5.88954i	−0.250042	−	0.968235i
$37$	−1.52094	−	5.88954i	−0.250042	−	0.968235i
$38$	−12.6236			−2.04782
$39$	−0.233956	−	0.0851529i	−0.0374629	−	0.0136354i
$40$	2.53209	−	0.921605i	0.400358	−	0.145719i
$41$	1.70574	+	1.43128i	0.266391	+	0.223529i	0.766192	−	0.642611i	$-0.222149\pi$
$41$	1.70574	+	1.43128i	0.266391	+	0.223529i	−0.499801	+	0.866140i	$0.666593\pi$
$42$	1.55303	−	8.80769i	0.239638	−	1.35906i
$43$	−1.14290			−0.174291			−0.0871456	−	0.996196i	$-0.527775\pi$
$43$	−1.14290			−0.174291			−0.0871456	+	0.996196i	$0.527775\pi$
$44$	−0.0923963	+	0.524005i	−0.0139293	+	0.0789968i
$45$	1.81521	+	3.14403i	0.270595	+	0.468685i
$46$	−0.766044	+	0.642788i	−0.112947	+	0.0947739i
$47$	0.620615	−	1.07494i	0.0905260	−	0.156796i	−0.817207	−	0.576345i	$-0.804479\pi$
$47$	0.620615	−	1.07494i	0.0905260	−	0.156796i	0.907733	+	0.419549i	$0.137812\pi$
$48$	−3.17752	−	5.50362i	−0.458635	−	0.794380i
$49$	−5.14543	−	1.87278i	−0.735061	−	0.267540i
$50$	6.31908	+	5.30234i	0.893653	+	0.749864i
$51$	−3.90760	+	6.76817i	−0.547174	+	0.947733i
$52$	−0.0491630	−	0.278817i	−0.00681769	−	0.0386650i
$53$	0.0675813	+	0.383273i	0.00928301	+	0.0526466i	0.989097	−	0.147263i	$-0.0470463\pi$
$53$	0.0675813	+	0.383273i	0.00928301	+	0.0526466i	−0.979814	+	0.199909i	$0.935935\pi$
$54$	8.11721	−	6.81115i	1.10461	−	0.926880i
$55$	1.00000	−	0.363970i	0.134840	−	0.0490777i
$56$	−2.91875	+	1.06234i	−0.390034	+	0.141961i
$57$	6.93242	−	5.81699i	0.918221	−	0.770479i
$58$	2.63176	+	14.9254i	0.345567	+	1.95981i
$59$	0.724155	+	4.10689i	0.0942770	+	0.534671i	0.994967	+	0.100208i	$0.0319508\pi$
$59$	0.724155	+	4.10689i	0.0942770	+	0.534671i	−0.900690	+	0.434463i	$0.856938\pi$
$60$	3.16250	−	5.47762i	0.408277	−	0.707157i
$61$	−7.07398	−	5.93577i	−0.905730	−	0.759998i	0.0655718	−	0.997848i	$-0.479113\pi$
$61$	−7.07398	−	5.93577i	−0.905730	−	0.759998i	−0.971302	+	0.237850i	$0.923557\pi$
$62$	4.87211	+	1.77330i	0.618759	+	0.225210i
$63$	−2.09240	−	3.62414i	−0.263617	−	0.456598i
$64$	1.96064	−	3.39592i	0.245080	−	0.424490i
$65$	−0.433763	+	0.363970i	−0.0538017	+	0.0451450i
$66$	−0.439693	−	0.761570i	−0.0541224	−	0.0937428i
$67$	−0.354570	+	2.01087i	−0.0433177	+	0.245667i	−0.998776	−	0.0494588i	$-0.984250\pi$
$67$	−0.354570	+	2.01087i	−0.0433177	+	0.245667i	0.955459	+	0.295125i	$0.0953615\pi$
$68$	−8.88713			−1.07772
$69$	0.124485	−	0.705990i	0.0149863	−	0.0849913i
$70$	−15.5817	−	13.0746i	−1.86237	−	1.56272i
$71$	12.7417	−	4.63760i	1.51216	−	0.550382i	0.552985	−	0.833191i	$-0.313489\pi$
$71$	12.7417	−	4.63760i	1.51216	−	0.550382i	0.959176	+	0.282810i	$0.0912664\pi$
$72$	−0.979055	−	0.356347i	−0.115383	−	0.0419959i
$73$	10.0077			1.17132			0.585659	−	0.810558i	$-0.300836\pi$
$73$	10.0077			1.17132			0.585659	+	0.810558i	$0.300836\pi$
$74$	−1.09967	+	11.3788i	−0.127834	+	1.32276i
$75$	−5.91353			−0.682836
$76$	9.67024	+	3.51968i	1.10925	+	0.403735i
$77$	−1.15270	+	0.419550i	−0.131363	+	0.0478121i
$78$	0.358441	+	0.300767i	0.0405854	+	0.0340552i
$79$	−1.32295	+	7.50281i	−0.148843	+	0.844132i	0.815357	+	0.578958i	$0.196541\pi$
$79$	−1.32295	+	7.50281i	−0.148843	+	0.844132i	−0.964201	+	0.265174i	$0.914571\pi$
$80$	−14.4534			−1.61594
$81$	−0.701867	+	3.98048i	−0.0779852	+	0.442276i
$82$	−2.09240	−	3.62414i	−0.231067	−	0.400219i
$83$	−0.401674	+	0.337044i	−0.0440894	+	0.0369954i	−0.664566	−	0.747229i	$-0.731384\pi$
$83$	−0.401674	+	0.337044i	−0.0440894	+	0.0369954i	0.620477	+	0.784225i	$0.286939\pi$
$84$	−3.64543	+	6.31407i	−0.397749	+	0.688921i
$85$	8.88713	+	15.3930i	0.963944	+	1.66960i
$86$	2.01842	+	0.734644i	0.217652	+	0.0792187i
$87$	−8.32295	−	6.98378i	−0.892314	−	0.748740i
$88$	−0.152704	+	0.264490i	−0.0162783	+	0.0281948i
$89$	1.75490	+	9.95253i	0.186019	+	1.05497i	0.924639	+	0.380844i	$0.124367\pi$
$89$	1.75490	+	9.95253i	0.186019	+	1.05497i	−0.738620	+	0.674122i	$0.764522\pi$
$90$	−1.18479	−	6.71929i	−0.124888	−	0.708276i
$91$	0.500000	−	0.419550i	0.0524142	−	0.0439808i
$92$	0.766044	−	0.278817i	0.0798657	−	0.0290687i
$93$	−3.49273	+	1.27125i	−0.362179	+	0.131822i
$94$	−1.78699	+	1.49946i	−0.184314	+	0.154658i
$95$	−3.57398	−	20.2690i	−0.366682	−	2.07956i
$96$	1.66250	+	9.42853i	0.169679	+	0.962295i
$97$	1.53936	−	2.66625i	0.156299	−	0.270717i	−0.777233	−	0.629213i	$-0.783377\pi$
$97$	1.53936	−	2.66625i	0.156299	−	0.270717i	0.933531	+	0.358496i	$0.116710\pi$
$98$	7.88326	+	6.61484i	0.796329	+	0.668199i
$99$	−0.386659	−	0.140732i	−0.0388607	−	0.0141441i
$100$	−3.36231	−	5.82369i	−0.336231	−	0.582369i
$101$	0.286989	−	0.497079i	0.0285565	−	0.0494613i	−0.851394	−	0.524527i	$-0.824242\pi$
$101$	0.286989	−	0.497079i	0.0285565	−	0.0494613i	0.879950	+	0.475065i	$0.157576\pi$
$102$	11.2515	−	9.44113i	1.11406	−	0.934811i
$103$	−1.01367	−	1.75573i	−0.0998799	−	0.172997i	0.811755	−	0.583998i	$-0.198513\pi$
$103$	−1.01367	−	1.75573i	−0.0998799	−	0.172997i	−0.911635	+	0.411001i	$0.865179\pi$
$104$	0.0282185	−	0.160035i	0.00276705	−	0.0156927i
$105$	14.5817			1.42303
$106$	0.127011	−	0.720317i	0.0123364	−	0.0699634i
$107$	4.25284	+	3.56856i	0.411138	+	0.344985i	0.824780	−	0.565454i	$-0.191299\pi$
$107$	4.25284	+	3.56856i	0.411138	+	0.344985i	−0.413642	+	0.910440i	$0.635744\pi$
$108$	−8.11721	+	2.95442i	−0.781079	+	0.284290i
$109$	2.38666	+	0.868673i	0.228600	+	0.0832038i	0.453781	−	0.891113i	$-0.350075\pi$
$109$	2.38666	+	0.868673i	0.228600	+	0.0832038i	−0.225180	+	0.974317i	$0.572297\pi$
$110$	−2.00000			−0.190693
$111$	−4.63950	−	6.75557i	−0.440362	−	0.641210i
$112$	16.6604			1.57426
$113$	−5.83750	−	2.12467i	−0.549145	−	0.199873i	0.0525213	−	0.998620i	$-0.483274\pi$
$113$	−5.83750	−	2.12467i	−0.549145	−	0.199873i	−0.601667	+	0.798747i	$0.705496\pi$
$114$	−15.9820	+	5.81699i	−1.49686	+	0.544811i
$115$	−1.24897	−	1.04801i	−0.116467	−	0.0977275i
$116$	2.14543	−	12.1673i	0.199198	−	1.12971i
$117$	0.218941			0.0202411
$118$	1.36097	−	7.71843i	0.125287	−	0.710539i
$119$	−10.2442	−	17.7435i	−0.939086	−	1.62655i
$120$	2.78106	−	2.33359i	0.253875	−	0.213026i
$121$	5.43969	−	9.42182i	0.494518	−	0.856529i
$122$	8.67752	+	15.0299i	0.785626	+	1.36074i
$123$	2.81908	+	1.02606i	0.254188	+	0.0925168i
$124$	−3.23783	−	2.71686i	−0.290765	−	0.243981i
$125$	0.935822	−	1.62089i	0.0837025	−	0.144977i
$126$	1.36571	+	7.74535i	0.121668	+	0.690011i
$127$	0.475652	+	2.69756i	0.0422073	+	0.239369i	0.998612	−	0.0526763i	$-0.0167752\pi$
$127$	0.475652	+	2.69756i	0.0422073	+	0.239369i	−0.956404	+	0.292046i	$0.905664\pi$
$128$	5.24170	−	4.39831i	0.463305	−	0.388759i
$129$	−1.44697	+	0.526653i	−0.127398	+	0.0463692i
$130$	1.00000	−	0.363970i	0.0877058	−	0.0319223i
$131$	−6.53596	+	5.48432i	−0.571049	+	0.479167i	−0.881994	−	0.471261i	$-0.843799\pi$
$131$	−6.53596	+	5.48432i	−0.571049	+	0.479167i	0.310945	+	0.950428i	$0.399355\pi$
$132$	0.124485	+	0.705990i	0.0108350	+	0.0614486i
$133$	4.11974	+	23.3642i	0.357227	+	2.02593i
$134$	1.91875	−	3.32337i	0.165755	−	0.287095i
$135$	13.2344	+	11.1050i	1.13904	+	0.955766i
$136$	−4.79339	−	1.74465i	−0.411029	−	0.149602i
$137$	−1.16978	−	2.02611i	−0.0999409	−	0.173103i	0.811719	−	0.584048i	$-0.198532\pi$
$137$	−1.16978	−	2.02611i	−0.0999409	−	0.173103i	−0.911660	+	0.410945i	$0.865199\pi$
$138$	−0.673648	+	1.16679i	−0.0573447	+	0.0993240i
$139$	−15.1480	+	12.7106i	−1.28483	+	1.07810i	−0.292274	+	0.956335i	$0.594412\pi$
$139$	−15.1480	+	12.7106i	−1.28483	+	1.07810i	−0.992559	+	0.121768i	$0.961144\pi$
$140$	8.29086	+	14.3602i	0.700706	+	1.21366i
$141$	0.290393	−	1.64690i	0.0244555	−	0.138694i
$142$	−25.4834			−2.13852
$143$	0.0111444	−	0.0632028i	0.000931938	−	0.00528528i
$144$	4.28106	+	3.59224i	0.356755	+	0.299353i
$145$	−23.2199	+	8.45134i	−1.92831	+	0.701846i
$146$	−17.6741	−	6.43285i	−1.46272	−	0.532387i
$147$	−7.37733			−0.608472
$148$	4.01501	−	8.41009i	0.330032	−	0.691305i
$149$	2.00505			0.164260			0.0821301	−	0.996622i	$-0.473828\pi$
$149$	2.00505			0.164260			0.0821301	+	0.996622i	$0.473828\pi$
$150$	10.4436	+	3.80115i	0.852713	+	0.310362i
$151$	−3.02569	+	1.10126i	−0.246227	+	0.0896194i	−0.462186	−	0.886783i	$-0.652935\pi$
$151$	−3.02569	+	1.10126i	−0.246227	+	0.0896194i	0.215958	+	0.976403i	$0.430712\pi$
$152$	4.52481	+	3.79677i	0.367011	+	0.307959i
$153$	1.19341	−	6.76817i	0.0964815	−	0.547174i
$154$	2.30541			0.185775
$155$	−1.46791	+	8.32494i	−0.117905	+	0.668675i
$156$	−0.190722	−	0.330341i	−0.0152700	−	0.0264484i
$157$	12.0287	−	10.0933i	0.959994	−	0.805530i	−0.0209584	−	0.999780i	$-0.506672\pi$
$157$	12.0287	−	10.0933i	0.959994	−	0.805530i	0.980952	+	0.194250i	$0.0622273\pi$
$158$	7.15910	−	12.3999i	0.569547	−	0.986485i
$159$	0.262174	+	0.454099i	0.0207918	+	0.0360124i
$160$	20.4611	+	7.44723i	1.61759	+	0.588755i
$161$	1.43969	+	1.20805i	0.113464	+	0.0952073i
$162$	3.79813	−	6.57856i	0.298410	−	0.516860i
$163$	−2.65018	−	15.0299i	−0.207578	−	1.17723i	−0.893331	−	0.449399i	$-0.851638\pi$
$163$	−2.65018	−	15.0299i	−0.207578	−	1.17723i	0.685753	−	0.727834i	$-0.259473\pi$
$164$	0.592396	+	3.35965i	0.0462584	+	0.262344i
$165$	1.09833	−	0.921605i	0.0855046	−	0.0717469i
$166$	0.926022	−	0.337044i	0.0718732	−	0.0261597i
$167$	−19.5462	+	7.11424i	−1.51253	+	0.550517i	−0.959270	−	0.282490i	$-0.908839\pi$
$167$	−19.5462	+	7.11424i	−1.51253	+	0.550517i	−0.553262	+	0.833007i	$0.686617\pi$
$168$	−3.20574	+	2.68993i	−0.247328	+	0.207533i
$169$	−2.25150	−	12.7689i	−0.173192	−	0.982221i
$170$	−5.80066	−	32.8972i	−0.444890	−	2.52310i
$171$	−3.97906	+	6.89193i	−0.304286	+	0.527039i
$172$	−1.34137	−	1.12554i	−0.102278	−	0.0858216i
$173$	18.0214	+	6.55926i	1.37014	+	0.498691i	0.919175	−	0.393849i	$-0.128857\pi$
$173$	18.0214	+	6.55926i	1.37014	+	0.498691i	0.450967	+	0.892540i	$0.351079\pi$
$174$	10.2096	+	17.6836i	0.773988	+	1.34059i
$175$	7.75150	−	13.4260i	0.585958	−	1.01491i
$176$	1.25490	−	1.05299i	0.0945917	−	0.0793718i
$177$	2.80928	+	4.86581i	0.211158	+	0.365737i
$178$	3.29813	−	18.7046i	0.247206	−	1.40197i
$179$	17.2567			1.28983			0.644914	−	0.764256i	$-0.276893\pi$
$179$	17.2567			1.28983			0.644914	+	0.764256i	$0.276893\pi$
$180$	−0.965852	+	5.47762i	−0.0719903	+	0.408277i
$181$	−2.91669	−	2.44739i	−0.216796	−	0.181913i	0.527922	−	0.849293i	$-0.322971\pi$
$181$	−2.91669	−	2.44739i	−0.216796	−	0.181913i	−0.744718	+	0.667380i	$0.767416\pi$
$182$	−1.15270	+	0.419550i	−0.0854441	+	0.0310991i
$183$	−11.6912	−	4.25524i	−0.864238	−	0.314557i
$184$	0.467911			0.0344949
$185$	−18.5817	+	1.45588i	−1.36616	+	0.107038i
$186$	6.98545			0.512198
$187$	−1.89306	−	0.689016i	−0.138434	−	0.0503858i
$188$	1.78699	−	0.650411i	0.130330	−	0.0474361i
$189$	−15.2554	−	12.8008i	−1.10966	−	0.931119i
$190$	−6.71688	+	38.0933i	−0.487294	+	2.76358i
$191$	22.9736			1.66231			0.831155	−	0.556040i	$-0.187680\pi$
$191$	22.9736			1.66231			0.831155	+	0.556040i	$0.187680\pi$
$192$	0.917404	−	5.20286i	0.0662079	−	0.375484i
$193$	13.0496	+	22.6026i	0.939333	+	1.62697i	0.766719	+	0.641983i	$0.221888\pi$
$193$	13.0496	+	22.6026i	0.939333	+	1.62697i	0.172614	+	0.984990i	$0.444779\pi$
$194$	−4.43242	+	3.71924i	−0.318229	+	0.267026i
$195$	−0.381445	+	0.660681i	−0.0273158	+	0.0473124i
$196$	−4.19459	−	7.26525i	−0.299614	−	0.518946i
$197$	−15.1211	−	5.50362i	−1.07733	−	0.392117i	−0.258418	−	0.966033i	$-0.583201\pi$
$197$	−15.1211	−	5.50362i	−1.07733	−	0.392117i	−0.818914	+	0.573916i	$0.805424\pi$
$198$	0.592396	+	0.497079i	0.0420998	+	0.0353259i
$199$	−7.13088	+	12.3510i	−0.505495	+	0.875543i	0.494485	+	0.869186i	$0.335357\pi$
$199$	−7.13088	+	12.3510i	−0.505495	+	0.875543i	−0.999980	+	0.00635652i	$0.997977\pi$
$200$	−0.670245	−	3.80115i	−0.0473935	−	0.268782i
$201$	0.477711	+	2.70924i	0.0336952	+	0.191095i
$202$	−0.826352	+	0.693392i	−0.0581419	+	0.0487869i
$203$	26.7656	−	9.74189i	1.87858	−	0.683747i
$204$	−11.2515	+	4.09521i	−0.787762	+	0.286722i
$205$	5.22668	−	4.38571i	0.365047	−	0.306311i
$206$	0.661626	+	3.75227i	0.0460977	+	0.261433i
$207$	0.109470	+	0.620838i	0.00760872	+	0.0431512i
$208$	−0.435822	+	0.754866i	−0.0302188	+	0.0523406i
$209$	1.78699	+	1.49946i	0.123609	+	0.103720i
$210$	−25.7520	−	9.37295i	−1.77705	−	0.646795i
$211$	4.99020	+	8.64328i	0.343540	+	0.595028i	0.985087	−	0.172055i	$-0.0550407\pi$
$211$	4.99020	+	8.64328i	0.343540	+	0.595028i	−0.641548	+	0.767083i	$0.721707\pi$
$212$	−0.298133	+	0.516382i	−0.0204759	+	0.0354653i
$213$	13.9945	−	11.7428i	0.958890	−	0.804604i
$214$	−5.21688	−	9.03590i	−0.356619	−	0.617682i
$215$	−0.608126	+	3.44886i	−0.0414739	+	0.235210i
$216$	−4.95811			−0.337357
$217$	1.69207	−	9.59619i	0.114865	−	0.651432i
$218$	−3.65657	−	3.06823i	−0.247654	−	0.207807i
$219$	12.6702	−	4.61159i	0.856176	−	0.311623i
$220$	1.53209	+	0.557635i	0.103293	+	0.0375957i
$221$	1.07192			0.0721050
$222$	3.85117	+	14.9128i	0.258473	+	1.00088i
$223$	−11.6040			−0.777062			−0.388531	−	0.921436i	$-0.627017\pi$
$223$	−11.6040			−0.777062			−0.388531	+	0.921436i	$0.627017\pi$
$224$	−23.5856	−	8.58445i	−1.57588	−	0.573573i
$225$	4.88666	−	1.77860i	0.325777	−	0.118573i
$226$	8.94356	+	7.50454i	0.594917	+	0.499195i
$227$	0.113341	−	0.642788i	0.00752269	−	0.0426633i	−0.980815	−	0.194939i	$-0.937549\pi$
$227$	0.113341	−	0.642788i	0.00752269	−	0.0426633i	0.988338	+	0.152276i	$0.0486602\pi$
$228$	13.8648			0.918221
$229$	−1.74422	+	9.89198i	−0.115261	+	0.653680i	0.871359	+	0.490646i	$0.163239\pi$
$229$	−1.74422	+	9.89198i	−0.115261	+	0.653680i	−0.986620	+	0.163034i	$0.947872\pi$
$230$	1.53209	+	2.65366i	0.101023	+	0.174977i
$231$	−1.26604	+	1.06234i	−0.0832996	+	0.0698967i
$232$	3.54576	−	6.14144i	0.232791	−	0.403205i
$233$	−11.1604	−	19.3305i	−0.731145	−	1.26638i	−0.956394	−	0.292079i	$-0.905653\pi$
$233$	−11.1604	−	19.3305i	−0.731145	−	1.26638i	0.225249	−	0.974301i	$-0.427680\pi$
$234$	−0.386659	−	0.140732i	−0.0252767	−	0.00919997i
$235$	−2.91353	−	2.44474i	−0.190058	−	0.159478i
$236$	−3.19459	+	5.53320i	−0.207950	+	0.360180i
$237$	1.78240	+	10.1085i	0.115780	+	0.656618i
$238$	6.68644	+	37.9207i	0.433418	+	2.45803i
$239$	−1.73396	+	1.45496i	−0.112160	+	0.0941136i	−0.697143	−	0.716932i	$-0.745546\pi$
$239$	−1.73396	+	1.45496i	−0.112160	+	0.0941136i	0.584983	+	0.811046i	$0.301101\pi$
$240$	−18.2986	+	6.66015i	−1.18117	+	0.429911i
$241$	24.4304	−	8.89192i	1.57370	−	0.572779i	0.599876	−	0.800093i	$-0.295216\pi$
$241$	24.4304	−	8.89192i	1.57370	−	0.572779i	0.973822	+	0.227314i	$0.0729943\pi$
$242$	−15.6630	+	13.1428i	−1.00685	+	0.844851i
$243$	−1.99154	−	11.2946i	−0.127758	−	0.724549i
$244$	−2.45677	−	13.9330i	−0.157278	−	0.891970i
$245$	−8.38919	+	14.5305i	−0.535965	+	0.928319i
$246$	−4.31908	−	3.62414i	−0.275374	−	0.231067i
$247$	−1.16637	−	0.424525i	−0.0742146	−	0.0270119i
$248$	−1.21301	−	2.10100i	−0.0770263	−	0.133413i
$249$	−0.353226	+	0.611806i	−0.0223848	+	0.0387716i
$250$	−2.69459	+	2.26103i	−0.170421	+	0.143000i
$251$	2.72534	+	4.72042i	0.172022	+	0.297950i	0.939127	−	0.343571i	$-0.111637\pi$
$251$	2.72534	+	4.72042i	0.172022	+	0.297950i	−0.767105	+	0.641522i	$0.778303\pi$
$252$	1.11334	−	6.31407i	0.0701339	−	0.397749i
$253$	0.184793			0.0116178
$254$	0.893933	−	5.06975i	0.0560904	−	0.318104i
$255$	18.3446	+	15.3930i	1.14878	+	0.963944i
$256$	−19.4538	+	7.08062i	−1.21586	+	0.442538i
$257$	−11.4042	−	4.15079i	−0.711374	−	0.258919i	−0.0391150	−	0.999235i	$-0.512454\pi$
$257$	−11.4042	−	4.15079i	−0.711374	−	0.258919i	−0.672259	+	0.740316i	$0.734676\pi$
$258$	2.89393			0.180168
$259$	21.4192	−	1.67820i	1.33093	−	0.104278i
$260$	−0.867526			−0.0538017
$261$	8.97818	+	3.26779i	0.555735	+	0.202271i
$262$	15.0680	−	5.48432i	0.930907	−	0.338822i
$263$	−6.25284	−	5.24676i	−0.385567	−	0.323529i	0.429316	−	0.903154i	$-0.358755\pi$
$263$	−6.25284	−	5.24676i	−0.385567	−	0.323529i	−0.814883	+	0.579625i	$0.803199\pi$
$264$	−0.0714517	+	0.405223i	−0.00439755	+	0.0249397i
$265$	1.19253			0.0732567
$266$	7.74257	−	43.9103i	0.474728	−	2.69231i
$267$	6.80793	+	11.7917i	0.416639	+	0.721640i
$268$	−2.39646	+	2.01087i	−0.146387	+	0.122833i
$269$	−8.70620	+	15.0796i	−0.530827	+	0.919419i	0.468526	+	0.883450i	$0.344785\pi$
$269$	−8.70620	+	15.0796i	−0.530827	+	0.919419i	−0.999353	+	0.0359691i	$0.988548\pi$
$270$	−16.2344	−	28.1188i	−0.987995	−	1.71126i
$271$	−10.5642	−	3.84505i	−0.641728	−	0.233570i	0.000599869	−	1.00000i	$-0.499809\pi$
$271$	−10.5642	−	3.84505i	−0.641728	−	0.233570i	−0.642328	+	0.766430i	$0.722031\pi$
$272$	20.9598	+	17.5873i	1.27087	+	1.06639i
$273$	0.439693	−	0.761570i	0.0266114	−	0.0460923i
$274$	0.763518	+	4.33013i	0.0461258	+	0.261593i
$275$	−0.264700	−	1.50119i	−0.0159620	−	0.0905252i
$276$	0.841367	−	0.705990i	0.0506443	−	0.0424956i
$277$	−21.3332	+	7.76466i	−1.28179	+	0.466533i	−0.891023	−	0.453957i	$-0.850012\pi$
$277$	−21.3332	+	7.76466i	−1.28179	+	0.466533i	−0.390765	+	0.920490i	$0.627790\pi$
$278$	34.9222	−	12.7106i	2.09449	−	0.762334i
$279$	2.50387	−	2.10100i	0.149903	−	0.125783i
$280$	1.65270	+	9.37295i	0.0987679	+	0.560141i
$281$	−0.0564370	−	0.320070i	−0.00336675	−	0.0190938i	0.983078	−	0.183187i	$-0.0586414\pi$
$281$	−0.0564370	−	0.320070i	−0.00336675	−	0.0190938i	−0.986445	+	0.164093i	$0.947530\pi$
$282$	−1.57145	+	2.72183i	−0.0935786	+	0.162083i
$283$	−19.8457	−	16.6525i	−1.17970	−	0.989890i	−0.999981	−	0.00617260i	$-0.998035\pi$
$283$	−19.8457	−	16.6525i	−1.17970	−	0.989890i	−0.179724	−	0.983717i	$-0.557520\pi$
$284$	19.5214	+	7.10521i	1.15838	+	0.421617i
$285$	−13.8648	−	24.0146i	−0.821282	−	1.42250i
$286$	−0.0603074	+	0.104455i	−0.00356605	+	0.00617658i
$287$	−6.02481	+	5.05542i	−0.355634	+	0.298412i
$288$	−4.20961	−	7.29125i	−0.248053	−	0.429641i
$289$	2.89083	−	16.3947i	0.170049	−	0.964396i
$290$	46.4397			2.72704
$291$	0.720285	−	4.08494i	0.0422239	−	0.239463i
$292$	11.7456	+	9.85570i	0.687357	+	0.576761i
$293$	−9.04488	+	3.29207i	−0.528408	+	0.192325i	−0.592427	−	0.805624i	$-0.701830\pi$
$293$	−9.04488	+	3.29207i	−0.528408	+	0.192325i	0.0640195	+	0.997949i	$0.479608\pi$
$294$	13.0287	+	4.74205i	0.759848	+	0.276562i
$295$	12.7784			0.743986
$296$	3.81655	−	3.74789i	0.221833	−	0.217842i
$297$	−1.95811			−0.113621
$298$	−3.54101	−	1.28882i	−0.205125	−	0.0746595i
$299$	−0.0923963	+	0.0336295i	−0.00534341	+	0.00194484i
$300$	−6.94041	−	5.82369i	−0.400705	−	0.336231i
$301$	0.700989	−	3.97551i	0.0404044	−	0.229144i
$302$	6.05138			0.348218
$303$	0.134285	−	0.761570i	0.00771449	−	0.0437511i
$304$	−15.8414	−	27.4381i	−0.908565	−	1.57368i
$305$	−21.6759	+	18.1883i	−1.24116	+	1.04146i
$306$	−6.45811	+	11.1858i	−0.369186	+	0.639448i
$307$	−4.28833	−	7.42761i	−0.244748	−	0.423916i	0.717313	−	0.696751i	$-0.245372\pi$
$307$	−4.28833	−	7.42761i	−0.244748	−	0.423916i	−0.962061	+	0.272835i	$0.912039\pi$
$308$	−1.76604	−	0.642788i	−0.100630	−	0.0366262i
$309$	−2.09240	−	1.75573i	−0.119032	−	0.0998799i
$310$	7.94356	−	13.7587i	0.451164	−	0.781439i
$311$	0.595389	+	3.37662i	0.0337614	+	0.191471i	0.997024	−	0.0770904i	$-0.0245630\pi$
$311$	0.595389	+	3.37662i	0.0337614	+	0.191471i	−0.963263	+	0.268561i	$0.913452\pi$
$312$	−0.0380187	−	0.215615i	−0.00215238	−	0.0122068i
$313$	−17.0214	+	14.2827i	−0.962107	+	0.807304i	−0.981295	−	0.192512i	$-0.938336\pi$
$313$	−17.0214	+	14.2827i	−0.962107	+	0.807304i	0.0191875	+	0.999816i	$0.493892\pi$
$314$	−27.7310	+	10.0933i	−1.56495	+	0.569596i
$315$	−12.0496	+	4.38571i	−0.678920	+	0.247107i
$316$	−8.94150	+	7.50281i	−0.502999	+	0.422066i
$317$	2.72193	+	15.4369i	0.152879	+	0.867020i	0.960699	+	0.277591i	$0.0895361\pi$
$317$	2.72193	+	15.4369i	0.152879	+	0.867020i	−0.807820	+	0.589429i	$0.799353\pi$
$318$	−0.171122	−	0.970481i	−0.00959604	−	0.0544219i
$319$	1.40033	−	2.42544i	0.0784034	−	0.135799i
$320$	−9.20439	−	7.72340i	−0.514541	−	0.431751i
$321$	7.02869	+	2.55823i	0.392303	+	0.142787i
$322$	−1.76604	−	3.05888i	−0.0984178	−	0.170465i
$323$	−19.4812	+	33.7424i	−1.08396	+	1.87748i
$324$	−4.74376	+	3.98048i	−0.263542	+	0.221138i
$325$	0.405544	+	0.702423i	0.0224956	+	0.0389634i
$326$	−4.98070	+	28.2470i	−0.275856	+	1.56446i
$327$	3.42190			0.189232
$328$	−0.340022	+	1.92836i	−0.0187746	+	0.106476i
$329$	3.35844	+	2.81807i	0.185157	+	0.155365i
$330$	−2.53209	+	0.921605i	−0.139387	+	0.0507327i
$331$	24.3910	+	8.87760i	1.34065	+	0.487957i	0.910017	−	0.414570i	$-0.136068\pi$
$331$	24.3910	+	8.87760i	1.34065	+	0.487957i	0.430633	+	0.902527i	$0.358290\pi$
$332$	−0.803348			−0.0440894
$333$	5.86571	+	4.18707i	0.321439	+	0.229450i
$334$	39.0925			2.13904
$335$	5.87939	+	2.13992i	0.321225	+	0.116916i
$336$	21.0929	−	7.67717i	1.15071	−	0.418824i
$337$	10.6434	+	8.93085i	0.579781	+	0.486494i	0.884875	−	0.465828i	$-0.154243\pi$
$337$	10.6434	+	8.93085i	0.579781	+	0.486494i	−0.305094	+	0.952322i	$0.598688\pi$
$338$	−4.23143	+	23.9976i	−0.230159	+	1.30530i
$339$	−8.36959			−0.454573
$340$	−4.72874	+	26.8180i	−0.256452	+	1.45441i
$341$	−0.479055	−	0.829748i	−0.0259423	−	0.0449334i
$342$	11.4572	−	9.61376i	0.619536	−	0.519853i
$343$	−2.69207	+	4.66280i	−0.145358	+	0.251767i
$344$	−0.502526	−	0.870401i	−0.0270944	−	0.0469289i
$345$	−2.06418	−	0.751299i	−0.111132	−	0.0404486i
$346$	−27.6104	−	23.1679i	−1.48434	−	1.24551i
$347$	3.12314	−	5.40944i	0.167659	−	0.290394i	−0.769937	−	0.638119i	$-0.779713\pi$
$347$	3.12314	−	5.40944i	0.167659	−	0.290394i	0.937596	+	0.347726i	$0.113046\pi$
$348$	−2.89053	−	16.3930i	−0.154949	−	0.878757i
$349$	−3.77972	−	21.4358i	−0.202324	−	1.14743i	−0.901596	−	0.432579i	$-0.857604\pi$
$349$	−3.77972	−	21.4358i	−0.202324	−	1.14743i	0.699273	−	0.714855i	$-0.253507\pi$
$350$	−22.3195	+	18.7283i	−1.19303	+	1.00107i
$351$	0.979055	−	0.356347i	0.0522581	−	0.0190204i
$352$	−2.31908	+	0.844075i	−0.123607	+	0.0449894i
$353$	3.03730	−	2.54860i	0.161659	−	0.135648i	−0.558370	−	0.829592i	$-0.688573\pi$
$353$	3.03730	−	2.54860i	0.161659	−	0.135648i	0.720029	+	0.693944i	$0.244128\pi$
$354$	−1.83363	−	10.3990i	−0.0974561	−	0.552701i
$355$	−7.21482	−	40.9173i	−0.382923	−	2.17166i
$356$	−7.74170	+	13.4090i	−0.410309	+	0.710676i
$357$	−21.1459	−	17.7435i	−1.11916	−	0.939086i
$358$	−30.4761	−	11.0924i	−1.61071	−	0.586252i
$359$	13.9213	+	24.1124i	0.734737	+	1.27260i	0.954839	+	0.297125i	$0.0960277\pi$
$359$	13.9213	+	24.1124i	0.734737	+	1.27260i	−0.220102	+	0.975477i	$0.570639\pi$
$360$	−1.59627	+	2.76481i	−0.0841306	+	0.145719i
$361$	20.0064	−	16.7874i	1.05297	−	0.883545i
$362$	3.57785	+	6.19702i	0.188048	+	0.325708i
$363$	2.54529	−	14.4351i	0.133593	−	0.757645i
$364$	1.00000			0.0524142
$365$	5.32501	−	30.1996i	0.278724	−	1.58072i
$366$	17.9119	+	15.0299i	0.936272	+	0.785626i
$367$	9.35029	−	3.40323i	0.488081	−	0.177647i	−0.0862444	−	0.996274i	$-0.527487\pi$
$367$	9.35029	−	3.40323i	0.488081	−	0.177647i	0.574326	+	0.818627i	$0.305264\pi$
$368$	−2.35844	−	0.858402i	−0.122942	−	0.0447473i
$369$	−2.63816			−0.137337
$370$	33.7520	+	9.37295i	1.75468	+	0.487276i
$371$	−1.37464			−0.0713676
$372$	−5.35117	−	1.94767i	−0.277445	−	0.100982i
$373$	3.28446	−	1.19545i	0.170063	−	0.0618979i	−0.255585	−	0.966786i	$-0.582268\pi$
$373$	3.28446	−	1.19545i	0.170063	−	0.0618979i	0.425649	+	0.904889i	$0.360046\pi$
$374$	2.90033	+	2.43367i	0.149972	+	0.125842i
$375$	0.437882	−	2.48335i	0.0226121	−	0.128240i
$376$	1.09152			0.0562908
$377$	−0.258770	+	1.46756i	−0.0133274	+	0.0755832i
$378$	18.7135	+	32.4127i	0.962517	+	1.66713i
$379$	−14.0706	+	11.8066i	−0.722757	+	0.606465i	−0.928146	−	0.372215i	$-0.878598\pi$
$379$	−14.0706	+	11.8066i	−0.722757	+	0.606465i	0.205390	+	0.978680i	$0.434154\pi$
$380$	15.7665	−	27.3084i	0.808805	−	1.40089i
$381$	1.84524	+	3.19604i	0.0945344	+	0.163738i
$382$	−40.5724	−	14.7671i	−2.07586	−	0.755553i
$383$	8.11128	+	6.80617i	0.414467	+	0.347779i	0.826054	−	0.563591i	$-0.190581\pi$
$383$	8.11128	+	6.80617i	0.414467	+	0.347779i	−0.411587	+	0.911371i	$0.635025\pi$
$384$	4.60947	−	7.98384i	0.235226	−	0.407423i
$385$	0.652704	+	3.70167i	0.0332649	+	0.188654i
$386$	−8.51754	−	48.3054i	−0.433531	−	2.45868i
$387$	1.03730	−	0.870401i	0.0527291	−	0.0442450i
$388$	4.43242	−	1.61327i	0.225022	−	0.0819013i
$389$	6.27972	−	2.28563i	0.318394	−	0.115886i	−0.177879	−	0.984052i	$-0.556924\pi$
$389$	6.27972	−	2.28563i	0.318394	−	0.115886i	0.496273	+	0.868166i	$0.334701\pi$
$390$	1.09833	−	0.921605i	0.0556159	−	0.0466673i
$391$	0.535959	+	3.03958i	0.0271046	+	0.153718i
$392$	−0.836152	−	4.74205i	−0.0422321	−	0.239510i
$393$	−5.74763	+	9.95518i	−0.289929	+	0.502172i
$394$	23.1668	+	19.4393i	1.16713	+	0.979337i
$395$	21.9368	+	7.98433i	1.10376	+	0.401735i
$396$	−0.315207	−	0.545955i	−0.0158398	−	0.0274353i
$397$	16.8097	−	29.1153i	0.843657	−	1.46126i	−0.0431256	−	0.999070i	$-0.513732\pi$
$397$	16.8097	−	29.1153i	0.843657	−	1.46126i	0.886783	−	0.462187i	$-0.152935\pi$
$398$	20.5326	−	17.2289i	1.02920	−	0.863605i
$399$	15.9820	+	27.6817i	0.800103	+	1.38582i
$400$	−3.59508	+	20.3887i	−0.179754	+	1.01944i
$401$	−5.97359			−0.298307			−0.149153	−	0.988814i	$-0.547655\pi$
$401$	−5.97359			−0.298307			−0.149153	+	0.988814i	$0.547655\pi$
$402$	0.897804	−	5.09170i	0.0447784	−	0.253951i
$403$	0.390530	+	0.327693i	0.0194537	+	0.0163236i
$404$	0.826352	−	0.300767i	0.0411125	−	0.0149637i
$405$	11.6382	+	4.23594i	0.578305	+	0.210486i
$406$	−53.5313			−2.65671
$407$	1.50727	−	1.48016i	0.0747128	−	0.0733688i
$408$	−6.87258			−0.340243
$409$	−25.7977	−	9.38960i	−1.27562	−	0.464286i	−0.386636	−	0.922233i	$-0.626363\pi$
$409$	−25.7977	−	9.38960i	−1.27562	−	0.464286i	−0.888980	+	0.457947i	$0.848585\pi$
$410$	−12.0496	+	4.38571i	−0.595089	+	0.216595i
$411$	−2.41463	−	2.02611i	−0.119105	−	0.0999409i
$412$	0.539363	−	3.05888i	0.0265725	−	0.150700i
$413$	−14.7297			−0.724800
$414$	0.205737	−	1.16679i	0.0101114	−	0.0573447i
$415$	0.803348	+	1.39144i	0.0394348	+	0.0683031i
$416$	1.00593	−	0.844075i	0.0493198	−	0.0413842i
$417$	−13.3209	+	23.0725i	−0.652327	+	1.12986i
$418$	−2.19207	−	3.79677i	−0.107217	−	0.185706i
$419$	12.7875	+	4.65425i	0.624708	+	0.227375i	0.634926	−	0.772573i	$-0.281030\pi$
$419$	12.7875	+	4.65425i	0.624708	+	0.227375i	−0.0102183	+	0.999948i	$0.503253\pi$
$420$	17.1138	+	14.3602i	0.835068	+	0.700706i
$421$	−16.8366	+	29.1619i	−0.820567	+	1.42126i	0.0846943	+	0.996407i	$0.473009\pi$
$421$	−16.8366	+	29.1619i	−0.820567	+	1.42126i	−0.905261	+	0.424856i	$0.860325\pi$
$422$	−3.25712	−	18.4721i	−0.158554	−	0.899206i
$423$	0.255367	+	1.44826i	0.0124164	+	0.0704167i
$424$	−0.262174	+	0.219990i	−0.0127323	+	0.0106837i
$425$	23.9247	−	8.70789i	1.16052	−	0.422395i
$426$	−32.2631	+	11.7428i	−1.56315	+	0.568941i
$427$	24.9859	−	20.9657i	1.20915	−	1.01460i
$428$	1.47700	+	8.37646i	0.0713933	+	0.404892i
$429$	−0.0150147	−	0.0851529i	−0.000724919	−	0.00411122i
$430$	3.29086	−	5.69994i	0.158699	−	0.274875i
$431$	−14.1500	−	11.8733i	−0.681582	−	0.571915i	0.234886	−	0.972023i	$-0.424528\pi$
$431$	−14.1500	−	11.8733i	−0.681582	−	0.571915i	−0.916468	+	0.400108i	$0.868973\pi$
$432$	24.9907	+	9.09586i	1.20236	+	0.437625i
$433$	7.51501	+	13.0164i	0.361149	+	0.625528i	0.988150	−	0.153490i	$-0.0490514\pi$
$433$	7.51501	+	13.0164i	0.361149	+	0.625528i	−0.627002	+	0.779018i	$0.715718\pi$
$434$	−9.15657	+	15.8597i	−0.439530	+	0.761288i
$435$	−25.5030	+	21.3996i	−1.22277	+	1.02603i
$436$	1.94562	+	3.36992i	0.0931784	+	0.161390i
$437$	0.620615	−	3.51968i	0.0296880	−	0.168369i
$438$	−25.3405			−1.21082
$439$	−4.33615	+	24.5915i	−0.206953	+	1.17369i	0.687383	+	0.726295i	$0.258759\pi$
$439$	−4.33615	+	24.5915i	−0.206953	+	1.17369i	−0.894336	+	0.447395i	$0.852352\pi$
$440$	0.716881	+	0.601535i	0.0341760	+	0.0286771i
$441$	6.09627	−	2.21886i	0.290298	−	0.105660i
$442$	−1.89306	−	0.689016i	−0.0900435	−	0.0327731i
$443$	−35.6732			−1.69489			−0.847443	−	0.530886i	$-0.821859\pi$
$443$	−35.6732			−1.69489			−0.847443	+	0.530886i	$0.821859\pi$
$444$	1.20780	−	12.4977i	0.0573195	−	0.593114i
$445$	30.9668			1.46797
$446$	20.4932	+	7.45891i	0.970381	+	0.353190i
$447$	2.53849	−	0.923933i	0.120066	−	0.0437005i
$448$	10.6099	+	8.90279i	0.501272	+	0.420618i
$449$	5.21987	−	29.6034i	0.246341	−	1.39707i	−0.571016	−	0.820939i	$-0.693451\pi$
$449$	5.21987	−	29.6034i	0.246341	−	1.39707i	0.817357	−	0.576131i	$-0.195438\pi$
$450$	−9.77332			−0.460719
$451$	−0.134285	+	0.761570i	−0.00632325	+	0.0358609i
$452$	−4.75877	−	8.24243i	−0.223834	−	0.387691i
$453$	−3.32320	+	2.78849i	−0.156137	+	0.131015i
$454$	−0.613341	+	1.06234i	−0.0287855	+	0.0498580i
$455$	−1.00000	−	1.73205i	−0.0468807	−	0.0811998i
$456$	7.47818	+	2.72183i	0.350198	+	0.127462i
$457$	−3.87140	−	3.24849i	−0.181096	−	0.151958i	0.547733	−	0.836653i	$-0.315491\pi$
$457$	−3.87140	−	3.24849i	−0.181096	−	0.151958i	−0.728830	+	0.684695i	$0.759935\pi$
$458$	9.43882	−	16.3485i	0.441047	−	0.763916i
$459$	−5.67917	−	32.2082i	−0.265081	−	1.50335i
$460$	−0.433763	−	2.45999i	−0.0202243	−	0.114698i
$461$	−13.9743	+	11.7258i	−0.650848	+	0.546127i	−0.907328	−	0.420423i	$-0.861882\pi$
$461$	−13.9743	+	11.7258i	−0.650848	+	0.546127i	0.256480	+	0.966550i	$0.417437\pi$
$462$	2.91875	−	1.06234i	0.135792	−	0.0494244i
$463$	−9.79086	+	3.56358i	−0.455020	+	0.165614i	−0.559354	−	0.828929i	$-0.688951\pi$
$463$	−9.79086	+	3.56358i	−0.455020	+	0.165614i	0.104335	+	0.994542i	$0.466729\pi$
$464$	−29.1386	+	24.4502i	−1.35273	+	1.13507i
$465$	1.97771	+	11.2162i	0.0917142	+	0.520137i
$466$	7.28446	+	41.3122i	0.337446	+	1.91375i
$467$	10.4213	−	18.0502i	0.482239	−	0.835263i	−0.517553	−	0.855651i	$-0.673157\pi$
$467$	10.4213	−	18.0502i	0.482239	−	0.835263i	0.999792	+	0.0203886i	$0.00649033\pi$
$468$	0.256959	+	0.215615i	0.0118780	+	0.00996679i
$469$	−6.77719	−	2.46669i	−0.312942	−	0.113901i
$470$	3.57398	+	6.19031i	0.164855	+	0.285538i
$471$	10.5778	−	18.3214i	0.487402	−	0.844204i
$472$	−2.80928	+	2.35726i	−0.129307	+	0.108502i
$473$	−0.198463	−	0.343748i	−0.00912534	−	0.0158056i
$474$	3.34982	−	18.9978i	0.153862	−	0.872597i
$475$	−29.4816			−1.35271
$476$	5.45084	−	30.9132i	0.249839	−	1.41691i
$477$	−0.353226	−	0.296392i	−0.0161731	−	0.0135709i
$478$	3.99747	−	1.45496i	0.182840	−	0.0665484i
$479$	7.21126	+	2.62468i	0.329491	+	0.119925i	0.501468	−	0.865176i	$-0.332793\pi$
$479$	7.21126	+	2.62468i	0.329491	+	0.119925i	−0.171978	+	0.985101i	$0.555016\pi$
$480$	29.3364			1.33902
$481$	−0.484270	+	1.01438i	−0.0220808	+	0.0462518i
$482$	−48.8607			−2.22554
$483$	2.37939	+	0.866025i	0.108266	+	0.0394055i
$484$	15.6630	−	5.70086i	0.711953	−	0.259130i
$485$	−7.22668	−	6.06391i	−0.328147	−	0.275348i
$486$	−3.74288	+	21.2269i	−0.169780	+	0.962873i
$487$	33.3678			1.51204			0.756020	−	0.654548i	$-0.227141\pi$
$487$	33.3678			1.51204			0.756020	+	0.654548i	$0.227141\pi$
$488$	1.41013	−	7.99724i	0.0638336	−	0.362018i
$489$	−10.2811	−	17.8073i	−0.464926	−	0.805275i
$490$	24.1557	−	20.2690i	1.09124	−	0.915662i
$491$	17.2606	−	29.8962i	0.778959	−	1.34920i	−0.153583	−	0.988136i	$-0.549081\pi$
$491$	17.2606	−	29.8962i	0.778959	−	1.34920i	0.932542	−	0.361061i	$-0.117585\pi$
$492$	2.29813	+	3.98048i	0.103608	+	0.179454i
$493$	43.9565	+	15.9989i	1.97970	+	0.720553i
$494$	1.78699	+	1.49946i	0.0804004	+	0.0674640i
$495$	−0.630415	+	1.09191i	−0.0283350	+	0.0490777i
$496$	2.25965	+	12.8151i	0.101461	+	0.575415i
$497$	8.31655	+	47.1655i	0.373048	+	2.11566i
$498$	1.01707	−	0.853427i	0.0455762	−	0.0382430i
$499$	−27.4577	+	9.99379i	−1.22918	+	0.447383i	−0.873315	−	0.487156i	$-0.838034\pi$
$499$	−27.4577	+	9.99379i	−1.22918	+	0.447383i	−0.355860	+	0.934539i	$0.615812\pi$
$500$	2.69459	−	0.980752i	0.120506	−	0.0438605i
$501$	−21.4681	+	18.0139i	−0.959125	+	0.804802i
$502$	−1.77884	−	10.0883i	−0.0793934	−	0.450262i
$503$	−2.64022	−	14.9734i	−0.117721	−	0.667631i	−0.985367	−	0.170448i	$-0.945479\pi$
$503$	−2.64022	−	14.9734i	−0.117721	−	0.667631i	0.867645	−	0.497184i	$-0.165632\pi$
$504$	1.84002	−	3.18701i	0.0819611	−	0.141961i
$505$	−1.34730	−	1.13052i	−0.0599539	−	0.0503073i
$506$	−0.326352	−	0.118782i	−0.0145081	−	0.00528052i
$507$	−8.73442	−	15.1285i	−0.387909	−	0.671879i
$508$	−2.09833	+	3.63441i	−0.0930982	+	0.161251i
$509$	2.21554	−	1.85906i	0.0982020	−	0.0824012i	−0.592365	−	0.805670i	$-0.701806\pi$
$509$	2.21554	−	1.85906i	0.0982020	−	0.0824012i	0.690567	+	0.723269i	$0.257361\pi$
$510$	−22.5030	−	38.9763i	−0.996449	−	1.72590i
$511$	−6.13816	+	34.8112i	−0.271536	+	1.53996i
$512$	25.2226			1.11469
$513$	−6.57620	+	37.2955i	−0.290346	+	1.64664i
$514$	17.4722	+	14.6610i	0.770668	+	0.646667i
$515$	−5.83750	+	2.12467i	−0.257231	+	0.0936244i
$516$	−2.21688	−	0.806879i	−0.0975928	−	0.0355209i
$517$	0.431074			0.0189586
$518$	−38.9060	−	10.8042i	−1.70943	−	0.474711i
$519$	25.8384			1.13418
$520$	−0.467911	−	0.170306i	−0.0205193	−	0.00746840i
$521$	4.18479	−	1.52314i	0.183339	−	0.0667300i	−0.248719	−	0.968576i	$-0.580010\pi$
$521$	4.18479	−	1.52314i	0.183339	−	0.0667300i	0.432058	+	0.901846i	$0.357787\pi$
$522$	−13.7554	−	11.5421i	−0.602056	−	0.505185i
$523$	−3.25150	+	18.4402i	−0.142178	+	0.806332i	0.827412	+	0.561596i	$0.189812\pi$
$523$	−3.25150	+	18.4402i	−0.142178	+	0.806332i	−0.969590	+	0.244736i	$0.921299\pi$
$524$	−13.0719			−0.571049
$525$	3.62701	−	20.5698i	0.158296	−	0.897740i
$526$	7.67024	+	13.2853i	0.334439	+	0.579265i
$527$	12.2588	−	10.2863i	0.534000	−	0.448080i
$528$	1.10354	−	1.91139i	0.0480254	−	0.0831825i
$529$	11.3584	+	19.6734i	0.493845	+	0.855365i
$530$	−2.10607	−	0.766546i	−0.0914817	−	0.0332966i
$531$	−3.78493	−	3.17593i	−0.164252	−	0.137824i
$532$	−18.1741	+	31.4785i	−0.787948	+	1.36477i
$533$	−0.0714517	−	0.405223i	−0.00309492	−	0.0175522i
$534$	−4.44356	−	25.2007i	−0.192292	−	1.09054i
$535$	13.0315	−	10.9347i	0.563399	−	0.472748i
$536$	−1.68732	+	0.614134i	−0.0728811	+	0.0265265i
$537$	21.8478	−	7.95194i	0.942801	−	0.343151i
$538$	25.0685	−	21.0350i	1.08078	−	0.906882i
$539$	−0.330222	−	1.87278i	−0.0142237	−	0.0806665i
$540$	4.59627	+	26.0667i	0.197792	+	1.12173i
$541$	17.5988	−	30.4820i	0.756631	−	1.31052i	−0.187928	−	0.982183i	$-0.560177\pi$
$541$	17.5988	−	30.4820i	0.756631	−	1.31052i	0.944559	−	0.328341i	$-0.106489\pi$
$542$	16.1853	+	13.5810i	0.695216	+	0.583356i
$543$	−4.82042	−	1.75449i	−0.206864	−	0.0752924i
$544$	−20.6099	−	35.6975i	−0.883644	−	1.53052i
$545$	3.89124	−	6.73983i	0.166683	−	0.288703i
$546$	−1.26604	+	1.06234i	−0.0541817	+	0.0454638i
$547$	−17.9093	−	31.0197i	−0.765744	−	1.32631i	−0.939852	−	0.341582i	$-0.889037\pi$
$547$	−17.9093	−	31.0197i	−0.765744	−	1.32631i	0.174108	−	0.984727i	$-0.444296\pi$
$548$	0.622426	−	3.52995i	0.0265887	−	0.150792i
$549$	10.9409			0.466945
$550$	−0.497474	+	2.82131i	−0.0212124	+	0.120301i
$551$	−41.4937	−	34.8173i	−1.76769	−	1.48327i
$552$	0.592396	−	0.215615i	0.0252141	−	0.00917717i
$553$	−25.2866	−	9.20356i	−1.07529	−	0.391375i
$554$	42.6664			1.81272
$555$	−22.8544	+	10.4057i	−0.970116	+	0.441698i
$556$	−30.2959			−1.28483
$557$	37.9239	+	13.8032i	1.60689	+	0.584858i	0.980821	−	0.194913i	$-0.0624423\pi$
$557$	37.9239	+	13.8032i	1.60689	+	0.584858i	0.626065	+	0.779771i	$0.284665\pi$
$558$	−5.77244	+	2.10100i	−0.244367	+	0.0889423i
$559$	0.161789	+	0.135757i	0.00684293	+	0.00574190i
$560$	8.86484	−	50.2750i	0.374608	−	2.12451i
$561$	−2.71419			−0.114593
$562$	−0.106067	+	0.601535i	−0.00447416	+	0.0253742i
$563$	−0.202333	−	0.350452i	−0.00852734	−	0.0147698i	0.861730	−	0.507367i	$-0.169381\pi$
$563$	−0.202333	−	0.350452i	−0.00852734	−	0.0147698i	−0.870258	+	0.492597i	$0.836048\pi$
$564$	1.96270	−	1.64690i	0.0826444	−	0.0693469i
$565$	−9.51754	+	16.4849i	−0.400406	+	0.693523i
$566$	24.3444	+	42.1657i	1.02327	+	1.77236i
$567$	−13.4153	−	4.88279i	−0.563392	−	0.205058i
$568$	9.13429	+	7.66458i	0.383266	+	0.321598i
$569$	11.7562	−	20.3624i	0.492847	−	0.853637i	−0.507119	−	0.861876i	$-0.669289\pi$
$569$	11.7562	−	20.3624i	0.492847	−	0.853637i	0.999966	+	0.00823952i	$0.00262275\pi$
$570$	9.04963	+	51.3230i	0.379047	+	2.14968i
$571$	2.43494	+	13.8093i	0.101899	+	0.577899i	0.992414	+	0.122944i	$0.0392336\pi$
$571$	2.43494	+	13.8093i	0.101899	+	0.577899i	−0.890514	+	0.454955i	$0.849655\pi$
$572$	0.0753221	−	0.0632028i	0.00314938	−	0.00264264i
$573$	29.0856	−	10.5863i	1.21507	−	0.442249i
$574$	13.8897	−	5.05542i	0.579743	−	0.211009i
$575$	−1.78905	+	1.50119i	−0.0746085	+	0.0626039i
$576$	0.806751	+	4.57531i	0.0336146	+	0.190638i
$577$	2.71260	+	15.3839i	0.112927	+	0.640441i	0.987756	+	0.156009i	$0.0498628\pi$
$577$	2.71260	+	15.3839i	0.112927	+	0.640441i	−0.874829	+	0.484432i	$0.839026\pi$
$578$	−15.6437	+	27.0956i	−0.650691	+	1.12703i
$579$	26.9368	+	22.6026i	1.11945	+	0.939333i
$580$	−35.5749	−	12.9482i	−1.47717	−	0.537645i
$581$	−0.926022	−	1.60392i	−0.0384179	−	0.0665417i
$582$	−3.89780	+	6.75119i	−0.161569	+	0.279846i
$583$	−0.103541	+	0.0868809i	−0.00428821	+	0.00359824i
$584$	4.40033	+	7.62159i	0.182087	+	0.315384i
$585$	0.116496	−	0.660681i	0.00481652	−	0.0273158i
$586$	18.0898			0.747281
$587$	1.71167	−	9.70735i	0.0706481	−	0.400665i	−0.928892	−	0.370350i	$-0.879238\pi$
$587$	1.71167	−	9.70735i	0.0706481	−	0.400665i	0.999540	−	0.0303151i	$-0.00965109\pi$
$588$	−8.65839	−	7.26525i	−0.357066	−	0.299614i
$589$	−17.4128	+	6.33775i	−0.717483	+	0.261142i
$590$	−22.5672	−	8.21378i	−0.929076	−	0.338156i
$591$	−21.6800			−0.891798
$592$	−26.1125	+	11.8891i	−1.07322	+	0.488640i
$593$	−35.0925			−1.44107			−0.720537	−	0.693416i	$-0.756105\pi$
$593$	−35.0925			−1.44107			−0.720537	+	0.693416i	$0.756105\pi$
$594$	3.45811	+	1.25865i	0.141888	+	0.0516430i
$595$	−58.9941	+	21.4721i	−2.41852	+	0.880271i
$596$	2.35323	+	1.97459i	0.0963919	+	0.0808824i
$597$	−3.33662	+	18.9229i	−0.136559	+	0.774463i
$598$	0.184793			0.00755673
$599$	−4.82770	+	27.3792i	−0.197254	+	1.11868i	0.711917	+	0.702263i	$0.247827\pi$
$599$	−4.82770	+	27.3792i	−0.197254	+	1.11868i	−0.909172	+	0.416422i	$0.863284\pi$
$600$	−2.60014	−	4.50357i	−0.106150	−	0.183857i
$601$	−17.6441	+	14.8051i	−0.719717	+	0.603914i	−0.927307	−	0.374301i	$-0.877883\pi$
$601$	−17.6441	+	14.8051i	−0.719717	+	0.603914i	0.207590	+	0.978216i	$0.433438\pi$
$602$	−3.79339	+	6.57034i	−0.154607	+	0.267787i
$603$	−1.20961	−	2.09510i	−0.0492590	−	0.0853191i
$604$	−4.63563	−	1.68723i	−0.188621	−	0.0686525i
$605$	−25.5371	−	21.4282i	−1.03823	−	0.871180i
$606$	−0.726682	+	1.25865i	−0.0295194	+	0.0511291i
$607$	6.55169	+	37.1565i	0.265925	+	1.50813i	0.766389	+	0.642377i	$0.222052\pi$
$607$	6.55169	+	37.1565i	0.265925	+	1.50813i	−0.500464	+	0.865758i	$0.666837\pi$
$608$	8.28833	+	47.0055i	0.336136	+	1.90632i
$609$	29.3974	−	24.6673i	1.19124	−	0.999571i
$610$	49.9718	−	18.1883i	2.02330	−	0.736421i
$611$	−0.215537	+	0.0784491i	−0.00871970	+	0.00317371i
$612$	8.06599	−	6.76817i	0.326048	−	0.273587i
$613$	−4.22122	−	23.9397i	−0.170493	−	0.966916i	−0.943218	−	0.332175i	$-0.892218\pi$
$613$	−4.22122	−	23.9397i	−0.170493	−	0.966916i	0.772724	−	0.634742i	$-0.218893\pi$
$614$	2.79901	+	15.8740i	0.112959	+	0.640622i
$615$	4.59627	−	7.96097i	0.185339	−	0.321017i
$616$	−0.826352	−	0.693392i	−0.0332947	−	0.0279375i
$617$	−2.83022	−	1.03012i	−0.113940	−	0.0414709i	0.284421	−	0.958700i	$-0.408199\pi$
$617$	−2.83022	−	1.03012i	−0.113940	−	0.0414709i	−0.398361	+	0.917229i	$0.630421\pi$
$618$	2.56670	+	4.44566i	0.103248	+	0.178831i
$619$	14.0993	−	24.4206i	0.566697	−	0.981548i	−0.430192	−	0.902737i	$-0.641554\pi$
$619$	14.0993	−	24.4206i	0.566697	−	0.981548i	0.996890	−	0.0788110i	$-0.0251124\pi$
$620$	−9.92127	+	8.32494i	−0.398448	+	0.334338i
$621$	1.50000	+	2.59808i	0.0601929	+	0.104257i
$622$	1.11897	−	6.34597i	0.0448664	−	0.254450i
$623$	−35.6955			−1.43011
$624$	−0.203926	+	1.15652i	−0.00816358	+	0.0462979i
$625$	−21.2049	−	17.7930i	−0.848194	−	0.711720i
$626$	39.2413	−	14.2827i	1.56840	−	0.570850i
$627$	2.95336	+	1.07494i	0.117946	+	0.0429288i
$628$	24.0574			0.959994
$629$	28.7181	+	20.4996i	1.14507	+	0.817372i
$630$	24.0993			0.960137
$631$	−10.3238	−	3.75757i	−0.410985	−	0.149586i	0.128250	−	0.991742i	$-0.459064\pi$
$631$	−10.3238	−	3.75757i	−0.410985	−	0.149586i	−0.539235	+	0.842156i	$0.681286\pi$
$632$	−6.29561	+	2.29141i	−0.250426	+	0.0911475i
$633$	10.3007	+	8.64328i	0.409414	+	0.343540i
$634$	5.11556	−	29.0118i	0.203165	−	1.15221i
$635$	8.39330			0.333078
$636$	−0.139500	+	0.791143i	−0.00553153	+	0.0313709i
$637$	0.505930	+	0.876296i	0.0200457	+	0.0347201i
$638$	−4.03209	+	3.38332i	−0.159632	+	0.133947i
$639$	−8.03256	+	13.9128i	−0.317763	+	0.550382i
$640$	−10.4834	−	18.1578i	−0.414392	−	0.717749i
$641$	13.2255	+	4.81369i	0.522376	+	0.190129i	0.589731	−	0.807600i	$-0.299234\pi$
$641$	13.2255	+	4.81369i	0.522376	+	0.190129i	−0.0673551	+	0.997729i	$0.521456\pi$
$642$	−10.7686	−	9.03590i	−0.425002	−	0.356619i
$643$	8.17071	−	14.1521i	0.322221	−	0.558104i	−0.658725	−	0.752384i	$-0.728904\pi$
$643$	8.17071	−	14.1521i	0.322221	−	0.558104i	0.980946	+	0.194280i	$0.0622371\pi$
$644$	0.500000	+	2.83564i	0.0197028	+	0.111740i
$645$	0.819326	+	4.64663i	0.0322609	+	0.182961i
$646$	56.0938	−	47.0683i	2.20698	−	1.85188i
$647$	−28.3606	+	10.3224i	−1.11497	+	0.405815i	−0.832814	−	0.553554i	$-0.813271\pi$
$647$	−28.3606	+	10.3224i	−1.11497	+	0.405815i	−0.282155	+	0.959369i	$0.591049\pi$
$648$	−3.34002	+	1.21567i	−0.131208	+	0.0477560i
$649$	−1.10947	+	0.930956i	−0.0435505	+	0.0365432i
$650$	−0.264700	−	1.50119i	−0.0103824	−	0.0588815i
$651$	−2.27972	−	12.9289i	−0.0893491	−	0.506724i
$652$	11.6912	−	20.2497i	0.457862	−	0.793041i
$653$	9.64022	+	8.08910i	0.377251	+	0.316551i	0.811622	−	0.584183i	$-0.198585\pi$
$653$	9.64022	+	8.08910i	0.377251	+	0.316551i	−0.434371	+	0.900734i	$0.643029\pi$
$654$	−6.04323	−	2.19956i	−0.236309	−	0.0860095i
$655$	13.0719	+	22.6412i	0.510762	+	0.884666i
$656$	5.25150	−	9.09586i	0.205036	−	0.355134i
$657$	−9.08306	+	7.62159i	−0.354364	+	0.297347i
$658$	−4.11974	−	7.13559i	−0.160604	−	0.278174i
$659$	5.68361	−	32.2334i	0.221402	−	1.25563i	−0.648043	−	0.761604i	$-0.724412\pi$
$659$	5.68361	−	32.2334i	0.221402	−	1.25563i	0.869445	−	0.494030i	$-0.164477\pi$
$660$	2.19665			0.0855046
$661$	−1.99226	+	11.2987i	−0.0774899	+	0.439467i	0.921236	+	0.389004i	$0.127181\pi$
$661$	−1.99226	+	11.2987i	−0.0774899	+	0.439467i	−0.998726	+	0.0504630i	$0.983930\pi$
$662$	−37.3692	−	31.3565i	−1.45239	−	1.21870i
$663$	1.35710	−	0.493943i	0.0527053	−	0.0191831i
$664$	−0.433296	−	0.157707i	−0.0168151	−	0.00612021i
$665$	72.6965			2.81905
$666$	−7.66772	−	11.1650i	−0.297118	−	0.432633i
$667$	−4.29086			−0.166143
$668$	−29.9466	−	10.8997i	−1.15867	−	0.421720i
$669$	−14.6912	+	5.34716i	−0.567994	+	0.206733i
$670$	−9.00774	−	7.55839i	−0.347999	−	0.292006i
$671$	0.556904	−	3.15836i	0.0214990	−	0.121927i
$672$	−33.8161			−1.30449
$673$	3.78729	−	21.4788i	0.145989	−	0.827947i	−0.820578	−	0.571535i	$-0.806348\pi$
$673$	3.78729	−	21.4788i	0.145989	−	0.827947i	0.966567	−	0.256413i	$-0.0825406\pi$
$674$	−13.0560	−	22.6137i	−0.502899	−	0.871047i
$675$	18.9572	−	15.9070i	0.729664	−	0.612261i
$676$	9.93242	−	17.2035i	0.382016	−	0.661671i
$677$	7.41488	+	12.8429i	0.284977	+	0.493594i	0.972604	−	0.232470i	$-0.0746807\pi$
$677$	7.41488	+	12.8429i	0.284977	+	0.493594i	−0.687627	+	0.726064i	$0.741347\pi$
$678$	14.7811	+	5.37987i	0.567663	+	0.206612i
$679$	8.33022	+	6.98989i	0.319685	+	0.268247i
$680$	−7.81521	+	13.5363i	−0.299700	+	0.519095i
$681$	−0.152704	−	0.866025i	−0.00585162	−	0.0331862i
$682$	0.312681	+	1.77330i	0.0119732	+	0.0679033i
$683$	17.3425	−	14.5521i	0.663594	−	0.556822i	−0.247568	−	0.968871i	$-0.579631\pi$
$683$	17.3425	−	14.5521i	0.663594	−	0.556822i	0.911162	+	0.412049i	$0.135187\pi$
$684$	−11.4572	+	4.17009i	−0.438078	+	0.159447i
$685$	−6.73648	+	2.45188i	−0.257388	+	0.0936815i
$686$	7.75150	−	6.50428i	0.295954	−	0.248334i
$687$	2.34998	+	13.3274i	0.0896575	+	0.508473i
$688$	0.936127	+	5.30904i	0.0356895	+	0.202405i
$689$	0.0359593	−	0.0622833i	0.00136994	−	0.00237280i
$690$	3.16250	+	2.65366i	0.120394	+	0.101023i
$691$	28.0202	+	10.1985i	1.06594	+	0.387970i	0.814657	−	0.579943i	$-0.196925\pi$
$691$	28.0202	+	10.1985i	1.06594	+	0.387970i	0.251283	+	0.967914i	$0.419148\pi$
$692$	14.6912	+	25.4459i	0.558475	+	0.967307i
$693$	0.726682	−	1.25865i	0.0276044	−	0.0478121i
$694$	−8.99273	+	7.54579i	−0.341359	+	0.286434i
$695$	30.2959	+	52.4741i	1.14919	+	1.99045i
$696$	1.65910	−	9.40923i	0.0628880	−	0.356656i
$697$	−12.9162			−0.489237
$698$	−7.10354	+	40.2862i	−0.268873	+	1.52485i
$699$	−23.0371	−	19.3305i	−0.871345	−	0.731145i
$700$	22.3195	−	8.12365i	0.843599	−	0.307045i
$701$	−19.8212	−	7.21432i	−0.748636	−	0.272481i	−0.0606044	−	0.998162i	$-0.519303\pi$
$701$	−19.8212	−	7.21432i	−0.748636	−	0.272481i	−0.688032	+	0.725681i	$0.741525\pi$
$702$	−1.95811			−0.0739041
$703$	−23.1300	−	33.6796i	−0.872365	−	1.27025i
$704$	1.36184			0.0513264
$705$	−4.81521	−	1.75259i	−0.181351	−	0.0660064i
$706$	−7.00222	+	2.54860i	−0.263532	+	0.0959178i
$707$	1.55303	+	1.30315i	0.0584078	+	0.0490100i
$708$	−1.49479	+	8.47735i	−0.0561775	+	0.318598i
$709$	−40.7939			−1.53205			−0.766023	−	0.642814i	$-0.777767\pi$
$709$	−40.7939			−1.53205			−0.766023	+	0.642814i	$0.777767\pi$
$710$	−13.5594	+	76.8993i	−0.508876	+	2.88598i
$711$	−4.51320	−	7.81710i	−0.169258	−	0.293164i
$712$	−6.80793	+	5.71253i	−0.255138	+	0.214086i
$713$	−0.733956	+	1.27125i	−0.0274869	+	0.0476086i
$714$	25.9393	+	44.9282i	0.970753	+	1.68139i
$715$	−0.184793	−	0.0672590i	−0.00691085	−	0.00251534i
$716$	20.2533	+	16.9945i	0.756902	+	0.635116i
$717$	−1.52481	+	2.64106i	−0.0569453	+	0.0986321i
$718$	−9.08647	−	51.5319i	−0.339104	−	1.92315i
$719$	−6.97162	−	39.5380i	−0.259998	−	1.47452i	−0.782911	−	0.622134i	$-0.786266\pi$
$719$	−6.97162	−	39.5380i	−0.259998	−	1.47452i	0.522914	−	0.852386i	$-0.324845\pi$
$720$	13.1179	−	11.0072i	0.488876	−	0.410216i
$721$	6.72890	−	2.44912i	0.250597	−	0.0912100i
$722$	−46.1229	+	16.7874i	−1.71652	+	0.624761i
$723$	26.8325	−	22.5151i	0.997911	−	0.837347i
$724$	−1.01296	−	5.74476i	−0.0376462	−	0.213502i
$725$	6.14631	+	34.8574i	0.228268	+	1.29457i
$726$	−13.7738	+	23.8569i	−0.511193	+	0.885412i
$727$	22.8143	+	19.1435i	0.846137	+	0.709993i	0.958935	−	0.283625i	$-0.0915371\pi$
$727$	22.8143	+	19.1435i	0.846137	+	0.709993i	−0.112799	+	0.993618i	$0.535981\pi$
$728$	0.539363	+	0.196312i	0.0199901	+	0.00727581i
$729$	−13.7888	−	23.8829i	−0.510696	−	0.884552i
$730$	−28.8161	+	49.9110i	−1.06653	+	1.84729i
$731$	5.07856	−	4.26142i	0.187837	−	0.157614i
$732$	−9.53074	−	16.5077i	−0.352266	−	0.610143i
$733$	−2.70187	+	15.3230i	−0.0997957	+	0.565970i	0.893376	+	0.449309i	$0.148330\pi$
$733$	−2.70187	+	15.3230i	−0.0997957	+	0.565970i	−0.993172	+	0.116660i	$0.962781\pi$
$734$	−18.7006			−0.690251
$735$	−3.92539	+	22.2620i	−0.144790	+	0.821147i
$736$	2.89646	+	2.43042i	0.106765	+	0.0895864i
$737$	−0.666374	+	0.242540i	−0.0245462	+	0.00893409i
$738$	4.65910	+	1.69577i	0.171504	+	0.0624223i
$739$	18.3482			0.674951			0.337475	−	0.941334i	$-0.390427\pi$
$739$	18.3482			0.674951			0.337475	+	0.941334i	$0.390427\pi$
$740$	−23.2422	−	16.5907i	−0.854399	−	0.609887i
$741$	−1.67230			−0.0614336
$742$	2.42767	+	0.883600i	0.0891226	+	0.0324380i
$743$	22.7682	−	8.28693i	0.835283	−	0.304018i	0.111258	−	0.993792i	$-0.464512\pi$
$743$	22.7682	−	8.28693i	0.835283	−	0.304018i	0.724025	+	0.689774i	$0.242290\pi$
$744$	−2.50387	−	2.10100i	−0.0917963	−	0.0770263i
$745$	1.06687	−	6.05050i	0.0390870	−	0.221673i
$746$	−6.56893			−0.240505
$747$	0.107878	−	0.611806i	0.00394704	−	0.0223848i
$748$	−1.54323	−	2.67296i	−0.0564262	−	0.0977330i
$749$	−15.0214	+	12.6045i	−0.548870	+	0.460557i
$750$	−2.36959	+	4.10424i	−0.0865250	+	0.149866i
$751$	−4.18345	−	7.24595i	−0.152656	−	0.264408i	0.779547	−	0.626344i	$-0.215449\pi$
$751$	−4.18345	−	7.24595i	−0.152656	−	0.264408i	−0.932203	+	0.361936i	$0.882116\pi$
$752$	−5.50165	−	2.00244i	−0.200624	−	0.0730213i
$753$	5.62558	+	4.72042i	0.205008	+	0.172022i
$754$	1.40033	−	2.42544i	0.0509970	−	0.0883294i
$755$	1.71326	+	9.71638i	0.0623519	+	0.353615i
$756$	−5.29813	−	30.0472i	−0.192691	−	1.09281i
$757$	4.30722	−	3.61419i	0.156549	−	0.131360i	−0.561149	−	0.827715i	$-0.689641\pi$
$757$	4.30722	−	3.61419i	0.156549	−	0.131360i	0.717697	+	0.696355i	$0.245196\pi$
$758$	32.4384	−	11.8066i	1.17822	−	0.428836i
$759$	0.233956	−	0.0851529i	0.00849205	−	0.00309085i
$760$	13.8648	−	11.6340i	0.502931	−	0.422009i
$761$	−0.395115	−	2.24081i	−0.0143229	−	0.0812293i	0.976808	−	0.214115i	$-0.0686868\pi$
$761$	−0.395115	−	2.24081i	−0.0143229	−	0.0812293i	−0.991131	+	0.132886i	$0.957576\pi$
$762$	−1.20439	−	6.83045i	−0.0436306	−	0.247441i
$763$	−4.48545	+	7.76903i	−0.162384	+	0.281258i
$764$	26.9629	+	22.6246i	0.975484	+	0.818528i
$765$	−19.7888	−	7.20253i	−0.715466	−	0.260408i
$766$	−9.94996	−	17.2338i	−0.359507	−	0.622684i
$767$	0.385315	−	0.667385i	0.0139129	−	0.0240979i
$768$	−21.3666	+	17.9287i	−0.771003	+	0.646948i
$769$	6.93969	+	12.0199i	0.250252	+	0.433449i	0.963595	−	0.267366i	$-0.0861533\pi$
$769$	6.93969	+	12.0199i	0.250252	+	0.433449i	−0.713343	+	0.700815i	$0.752820\pi$
$770$	1.22668	−	6.95686i	0.0442065	−	0.250708i
$771$	−16.3509			−0.588864
$772$	−6.94356	+	39.3789i	−0.249904	+	1.41728i
$773$	21.9538	+	18.4215i	0.789624	+	0.662574i	0.945652	−	0.325179i	$-0.105425\pi$
$773$	21.9538	+	18.4215i	0.789624	+	0.662574i	−0.156028	+	0.987753i	$0.549869\pi$
$774$	−2.39141	+	0.870401i	−0.0859573	+	0.0312859i
$775$	11.3785	+	4.14144i	0.408728	+	0.148765i
$776$	2.70739			0.0971895
$777$	26.3444	−	11.9947i	0.945099	−	0.430308i
$778$	−12.5594			−0.450277
$779$	14.0544	+	5.11538i	0.503550	+	0.183277i
$780$	−1.09833	+	0.399758i	−0.0393264	+	0.0143136i
$781$	3.60741	+	3.02698i	0.129083	+	0.108314i
$782$	1.00727	−	5.71253i	0.0360200	−	0.204280i
$783$	45.4671			1.62486
$784$	−4.48499	+	25.4356i	−0.160178	+	0.908415i
$785$	−24.0574	−	41.6686i	−0.858644	−	1.48722i
$786$	16.5496	−	13.8868i	0.590306	−	0.495325i
$787$	18.9650	−	32.8483i	0.676028	−	1.17092i	−0.300139	−	0.953896i	$-0.597033\pi$
$787$	18.9650	−	32.8483i	0.676028	−	1.17092i	0.976167	−	0.217020i	$-0.0696336\pi$
$788$	−12.3268	−	21.3507i	−0.439125	−	0.760586i
$789$	−10.3341	−	3.76130i	−0.367903	−	0.133906i
$790$	−33.6091	−	28.2013i	−1.19576	−	1.00336i
$791$	10.9709	−	19.0022i	0.390080	−	0.675639i
$792$	−0.0628336	−	0.356347i	−0.00223269	−	0.0126622i
$793$	0.296322	+	1.68053i	0.0105227	+	0.0596773i
$794$	−48.4017	+	40.6139i	−1.71771	+	1.44133i
$795$	1.50980	−	0.549522i	0.0535471	−	0.0194895i
$796$	−20.5326	+	7.47324i	−0.727757	+	0.264882i
$797$	0.880729	−	0.739020i	0.0311970	−	0.0261774i	−0.627056	−	0.778974i	$-0.715740\pi$
$797$	0.880729	−	0.739020i	0.0311970	−	0.0261774i	0.658253	+	0.752797i	$0.271296\pi$
$798$	−10.4315	−	59.1602i	−0.369273	−	2.09425i
$799$	1.25026	+	7.09057i	0.0442310	+	0.250846i
$800$	15.5949	−	27.0112i	0.551364	−	0.954990i
$801$	−9.17230	−	7.69648i	−0.324087	−	0.271942i
$802$	10.5496	+	3.83975i	0.372520	+	0.135586i
$803$	1.73783	+	3.01000i	0.0613265	+	0.106221i
$804$	−2.10741	+	3.65014i	−0.0743227	+	0.128731i
$805$	4.41147	−	3.70167i	0.155484	−	0.130467i
$806$	−0.479055	−	0.829748i	−0.0168740	−	0.0292266i
$807$	−4.07373	+	23.1033i	−0.143402	+	0.813274i
$808$	0.504748			0.0177570
$809$	7.32872	−	41.5632i	0.257664	−	1.46128i	−0.531477	−	0.847073i	$-0.678363\pi$
$809$	7.32872	−	41.5632i	0.257664	−	1.46128i	0.789141	−	0.614212i	$-0.210526\pi$
$810$	−17.8307	−	14.9617i	−0.626507	−	0.525701i
$811$	−25.8033	+	9.39165i	−0.906078	+	0.329785i	−0.752686	−	0.658380i	$-0.771242\pi$
$811$	−25.8033	+	9.39165i	−0.906078	+	0.329785i	−0.153392	+	0.988165i	$0.549020\pi$
$812$	41.0073	+	14.9254i	1.43908	+	0.523781i
$813$	−15.1465			−0.531212
$814$	−3.61334	+	1.64517i	−0.126648	+	0.0576632i
$815$	−46.7648			−1.63810
$816$	34.6403	+	12.6080i	1.21265	+	0.441369i
$817$	−7.21378	+	2.62560i	−0.252378	+	0.0918582i
$818$	39.5244	+	33.1649i	1.38194	+	1.15958i
$819$	−0.134285	+	0.761570i	−0.00469231	+	0.0266114i
$820$	10.4534			0.365047
$821$	5.96555	−	33.8323i	0.208199	−	1.18076i	−0.684127	−	0.729363i	$-0.739816\pi$
$821$	5.96555	−	33.8323i	0.208199	−	1.18076i	0.892326	−	0.451392i	$-0.149072\pi$
$822$	2.96198	+	5.13030i	0.103311	+	0.178940i
$823$	32.3448	−	27.1405i	1.12747	−	0.946059i	0.128512	−	0.991708i	$-0.458980\pi$
$823$	32.3448	−	27.1405i	1.12747	−	0.946059i	0.998958	+	0.0456485i	$0.0145354\pi$
$824$	0.891407	−	1.54396i	0.0310536	−	0.0537865i
$825$	−1.02687	−	1.77860i	−0.0357512	−	0.0619229i
$826$	26.0133	+	9.46805i	0.905117	+	0.329436i
$827$	39.4734	+	33.1221i	1.37263	+	1.15177i	0.971852	+	0.235593i	$0.0757031\pi$
$827$	39.4734	+	33.1221i	1.37263	+	1.15177i	0.400774	+	0.916177i	$0.368741\pi$
$828$	−0.482926	+	0.836452i	−0.0167828	+	0.0290687i
$829$	3.96791	+	22.5031i	0.137811	+	0.781566i	0.972861	+	0.231392i	$0.0743278\pi$
$829$	3.96791	+	22.5031i	0.137811	+	0.781566i	−0.835049	+	0.550175i	$0.814561\pi$
$830$	−0.524348	−	2.97373i	−0.0182004	−	0.103220i
$831$	−23.4308	+	19.6608i	−0.812806	+	0.682026i
$832$	−0.680922	+	0.247835i	−0.0236067	+	0.00859215i
$833$	29.8469	−	10.8634i	1.03413	−	0.376394i
$834$	38.3560	−	32.1845i	1.32816	−	1.11446i
$835$	11.0678	+	62.7686i	0.383017	+	2.17220i
$836$	0.620615	+	3.51968i	0.0214644	+	0.121731i
$837$	7.77719	−	13.4705i	0.268819	−	0.465608i
$838$	−19.5915	−	16.4392i	−0.676778	−	0.567884i
$839$	−40.1609	−	14.6174i	−1.38651	−	0.504648i	−0.462364	−	0.886690i	$-0.652999\pi$
$839$	−40.1609	−	14.6174i	−1.38651	−	0.504648i	−0.924145	+	0.382042i	$0.875221\pi$
$840$	6.41147	+	11.1050i	0.221217	+	0.383159i
$841$	−18.0155	+	31.2037i	−0.621224	+	1.07599i
$842$	48.4791	−	40.6788i	1.67070	−	1.40188i
$843$	−0.218941	−	0.379217i	−0.00754072	−	0.0130609i
$844$	−2.65523	+	15.0586i	−0.0913968	+	0.518337i
$845$	−39.7297			−1.36674
$846$	0.479933	−	2.72183i	0.0165004	−	0.0935786i
$847$	29.4368	+	24.7004i	1.01146	+	0.848715i
$848$	1.72503	−	0.627861i	0.0592379	−	0.0215608i
$849$	−32.7991	−	11.9379i	−1.12566	−	0.409707i
$850$	−47.8495			−1.64122
$851$	−3.11856	−	0.866025i	−0.106903	−	0.0296870i
$852$	27.9891			0.958890
$853$	10.9684	+	3.99216i	0.375550	+	0.136689i	0.522897	−	0.852396i	$-0.324851\pi$
$853$	10.9684	+	3.99216i	0.375550	+	0.136689i	−0.147347	+	0.989085i	$0.547073\pi$
$854$	−57.6027	+	20.9657i	−1.97112	+	0.717431i
$855$	18.6800	+	15.6744i	0.638844	+	0.536054i
$856$	−0.847763	+	4.80790i	−0.0289759	+	0.164331i
$857$	−37.8489			−1.29289			−0.646446	−	0.762960i	$-0.723746\pi$
$857$	−37.8489			−1.29289			−0.646446	+	0.762960i	$0.723746\pi$
$858$	−0.0282185	+	0.160035i	−0.000963363	+	0.00546351i
$859$	17.5282	+	30.3598i	0.598055	+	1.03586i	0.993108	+	0.117203i	$0.0373929\pi$
$859$	17.5282	+	30.3598i	0.598055	+	1.03586i	−0.395053	+	0.918658i	$0.629274\pi$
$860$	−4.11019	+	3.44886i	−0.140156	+	0.117605i
$861$	−5.29813	+	9.17664i	−0.180560	+	0.312739i
$862$	17.3576	+	30.0642i	0.591201	+	1.02399i
$863$	−14.2157	−	5.17409i	−0.483908	−	0.176128i	0.0885343	−	0.996073i	$-0.471782\pi$
$863$	−14.2157	−	5.17409i	−0.483908	−	0.176128i	−0.572442	+	0.819945i	$0.694004\pi$
$864$	−30.6917	−	25.7534i	−1.04415	−	0.876147i
$865$	29.3824	−	50.8918i	0.999031	−	1.73037i
$866$	−4.90508	−	27.8181i	−0.166681	−	0.945297i
$867$	−3.89481	−	22.0886i	−0.132275	−	0.750167i
$868$	11.4363	−	9.59619i	0.388173	−	0.325716i
$869$	−2.48633	+	0.904950i	−0.0843429	+	0.0306983i
$870$	58.7948	−	21.3996i	1.99333	−	0.725513i
$871$	0.289048	−	0.242540i	0.00979403	−	0.00821817i
$872$	0.387841	+	2.19956i	0.0131340	+	0.0744864i
$873$	0.633408	+	3.59224i	0.0214376	+	0.121579i
$874$	−3.35844	+	5.81699i	−0.113601	+	0.196763i
$875$	5.06418	+	4.24935i	0.171200	+	0.143654i
$876$	19.4119	+	7.06537i	0.655869	+	0.238717i
$877$	−26.2494	−	45.4654i	−0.886381	−	1.53526i	−0.844123	−	0.536149i	$-0.819878\pi$
$877$	−26.2494	−	45.4654i	−0.886381	−	1.53526i	−0.0422574	−	0.999107i	$-0.513455\pi$
$878$	23.4650	−	40.6425i	0.791905	−	1.37162i
$879$	−9.93423	+	8.33581i	−0.335073	+	0.281160i
$880$	−2.50980	−	4.34710i	−0.0846053	−	0.146541i
$881$	−7.88191	+	44.7005i	−0.265548	+	1.50600i	0.501921	+	0.864914i	$0.332627\pi$
$881$	−7.88191	+	44.7005i	−0.265548	+	1.50600i	−0.767469	+	0.641086i	$0.778484\pi$
$882$	−12.1925			−0.410544
$883$	−4.21419	+	23.8999i	−0.141819	+	0.804295i	0.828048	+	0.560658i	$0.189452\pi$
$883$	−4.21419	+	23.8999i	−0.141819	+	0.804295i	−0.969866	+	0.243637i	$0.921659\pi$
$884$	1.25806	+	1.05563i	0.0423130	+	0.0355048i
$885$	16.1780	−	5.88831i	0.543817	−	0.197933i
$886$	63.0005	+	22.9303i	2.11654	+	0.770359i
$887$	−51.3360			−1.72370			−0.861848	−	0.507167i	$-0.830693\pi$
$887$	−51.3360			−1.72370			−0.861848	+	0.507167i	$0.830693\pi$
$888$	3.10488	−	6.50368i	0.104193	−	0.218249i
$889$	−9.67499			−0.324489
$890$	−54.6887	−	19.9051i	−1.83317	−	0.667219i
$891$	−1.31908	+	0.480105i	−0.0441908	+	0.0160841i
$892$	−13.6190	−	11.4277i	−0.455999	−	0.382628i
$893$	1.44774	−	8.21053i	0.0484467	−	0.274755i
$894$	−5.07697			−0.169799
$895$	9.18210	−	52.0743i	0.306924	−	1.74065i
$896$	12.0842	+	20.9305i	0.403706	+	0.699240i
$897$	−0.101481	+	0.0851529i	−0.00338836	+	0.00284317i
$898$	−28.2472	+	48.9256i	−0.942622	+	1.63267i
$899$	11.1236	+	19.2667i	0.370993	+	0.642579i
$900$	7.48680	+	2.72497i	0.249560	+	0.0908324i
$901$	−1.72937	−	1.45111i	−0.0576137	−	0.0483436i
$902$	0.726682	−	1.25865i	0.0241959	−	0.0419084i
$903$	−0.944440	−	5.35619i	−0.0314290	−	0.178243i
$904$	−0.948615	−	5.37987i	−0.0315505	−	0.178932i
$905$	−8.93725	+	7.49925i	−0.297084	+	0.249283i
$906$	7.66132	−	2.78849i	0.254530	−	0.0926415i
$907$	−37.2371	+	13.5532i	−1.23644	+	0.450027i	−0.875798	−	0.482678i	$-0.839664\pi$
$907$	−37.2371	+	13.5532i	−1.23644	+	0.450027i	−0.360640	+	0.932705i	$0.617442\pi$
$908$	0.766044	−	0.642788i	0.0254221	−	0.0213317i
$909$	0.118089	+	0.669713i	0.00391675	+	0.0222130i
$910$	0.652704	+	3.70167i	0.0216369	+	0.122709i
$911$	6.33868	−	10.9789i	0.210010	−	0.363748i	−0.741708	−	0.670723i	$-0.765984\pi$
$911$	6.33868	−	10.9789i	0.210010	−	0.363748i	0.951717	+	0.306976i	$0.0993171\pi$
$912$	−32.6994	−	27.4381i	−1.08279	−	0.908565i
$913$	−0.171122	−	0.0622833i	−0.00566331	−	0.00206128i
$914$	4.74897	+	8.22546i	0.157082	+	0.272074i
$915$	−19.0615	+	33.0155i	−0.630153	+	1.09146i
$916$	−11.7888	+	9.89198i	−0.389513	+	0.326840i
$917$	−15.0680	−	26.0986i	−0.497591	−	0.861853i
$918$	−10.6733	+	60.5315i	−0.352273	+	1.99784i
$919$	50.0901			1.65232			0.826160	−	0.563436i	$-0.190521\pi$
$919$	50.0901			1.65232			0.826160	+	0.563436i	$0.190521\pi$
$920$	0.248970	−	1.41198i	0.00820831	−	0.0465516i
$921$	−8.85188	−	7.42761i	−0.291679	−	0.244748i
$922$	32.2165	−	11.7258i	1.06099	−	0.386170i
$923$	−2.35457	−	0.856994i	−0.0775016	−	0.0282083i
$924$	−2.53209			−0.0832996
$925$	−2.56821	+	26.5746i	−0.0844422	+	0.873766i
$926$	19.5817			0.643495
$927$	2.25712	+	0.821525i	0.0741336	+	0.0269824i
$928$	53.8487	−	19.5993i	1.76767	−	0.643379i
$929$	−10.2954	−	8.63890i	−0.337783	−	0.283433i	0.458079	−	0.888911i	$-0.348538\pi$
$929$	−10.2954	−	8.63890i	−0.337783	−	0.283433i	−0.795862	+	0.605478i	$0.792982\pi$
$930$	3.71688	−	21.0795i	0.121881	−	0.691223i
$931$	−36.7793			−1.20539
$932$	5.93835	−	33.6780i	0.194517	−	1.10316i
$933$	2.30974	+	4.00059i	0.0756176	+	0.130974i
$934$	−30.0069	+	25.1787i	−0.981855	+	0.823874i
$935$	−3.08647	+	5.34592i	−0.100938	+	0.174830i
$936$	0.0962667	+	0.166739i	0.00314657	+	0.00545003i
$937$	35.6857	+	12.9885i	1.16580	+	0.424317i	0.851167	−	0.524895i	$-0.175896\pi$
$937$	35.6857	+	12.9885i	1.16580	+	0.424317i	0.314635	+	0.949213i	$0.398118\pi$
$938$	10.3833	+	8.71259i	0.339025	+	0.284476i
$939$	−14.9684	+	25.9260i	−0.488475	+	0.846063i
$940$	−1.01186	−	5.73854i	−0.0330032	−	0.187171i
$941$	5.19294	+	29.4506i	0.169285	+	0.960064i	0.944535	+	0.328410i	$0.106513\pi$
$941$	5.19294	+	29.4506i	0.169285	+	0.960064i	−0.775250	+	0.631654i	$0.782376\pi$
$942$	−30.4577	+	25.5570i	−0.992366	+	0.832694i
$943$	1.11334	−	0.405223i	0.0362554	−	0.0131959i
$944$	18.4843	−	6.72772i	0.601612	−	0.218969i
$945$	−46.7452	+	39.2238i	−1.52062	+	1.27595i
$946$	0.129538	+	0.734644i	0.00421163	+	0.0238853i
$947$	0.0312115	+	0.177009i	0.00101424	+	0.00575203i	0.985311	−	0.170771i	$-0.0546260\pi$
$947$	0.0312115	+	0.177009i	0.00101424	+	0.00575203i	−0.984296	+	0.176523i	$0.943515\pi$
$948$	−7.86303	+	13.6192i	−0.255379	+	0.442330i
$949$	−1.41669	−	1.18874i	−0.0459877	−	0.0385882i
$950$	52.0659	+	18.9504i	1.68924	+	0.614833i
$951$	10.5594	+	18.2895i	0.342413	+	0.593077i
$952$	9.00862	−	15.6034i	0.291971	−	0.505709i
$953$	7.50316	−	6.29589i	0.243051	−	0.203944i	−0.513122	−	0.858316i	$-0.671511\pi$
$953$	7.50316	−	6.29589i	0.243051	−	0.203944i	0.756173	+	0.654372i	$0.227067\pi$
$954$	0.433296	+	0.750491i	0.0140285	+	0.0242980i
$955$	12.2240	−	69.3257i	0.395559	−	2.24333i
$956$	−3.46791			−0.112160
$957$	0.655230	−	3.71599i	0.0211806	−	0.120121i
$958$	−11.0483	−	9.27061i	−0.356954	−	0.299520i
$959$	7.76517	−	2.82629i	0.250750	−	0.0912657i
$960$	−15.2121	−	5.53676i	−0.490970	−	0.178698i
$961$	−23.3892			−0.754490
$962$	1.50727	−	1.48016i	0.0485965	−	0.0477222i
$963$	−6.57760			−0.211960
$964$	37.4295	+	13.6232i	1.20552	+	0.438774i
$965$	75.1498	−	27.3523i	2.41916	−	0.880502i
$966$	−3.64543	−	3.05888i	−0.117290	−	0.0984178i
$967$	4.70945	−	26.7086i	0.151446	−	0.858890i	−0.810518	−	0.585713i	$-0.800814\pi$
$967$	4.70945	−	26.7086i	0.151446	−	0.858890i	0.961964	−	0.273177i	$-0.0880745\pi$
$968$	9.56717			0.307501
$969$	−9.11546	+	51.6963i	−0.292831	+	1.66073i
$970$	8.86484	+	15.3543i	0.284633	+	0.492998i
$971$	−3.24485	+	2.72275i	−0.104132	+	0.0873773i	−0.693367	−	0.720584i	$-0.743874\pi$
$971$	−3.24485	+	2.72275i	−0.104132	+	0.0873773i	0.589235	+	0.807962i	$0.299429\pi$
$972$	8.78564	−	15.2172i	0.281800	−	0.488091i
$973$	−34.9222	−	60.4870i	−1.11955	−	1.93913i
$974$	−58.9291	−	21.4484i	−1.88821	−	0.687252i
$975$	0.837116	+	0.702423i	0.0268092	+	0.0224956i
$976$	−21.7788	+	37.7221i	−0.697124	+	1.20745i
$977$	−6.39811	−	36.2855i	−0.204694	−	1.16088i	−0.897921	−	0.440156i	$-0.854923\pi$
$977$	−6.39811	−	36.2855i	−0.204694	−	1.16088i	0.693228	−	0.720719i	$-0.256188\pi$
$978$	6.71048	+	38.0571i	0.214578	+	1.21693i
$979$	−2.68866	+	2.25606i	−0.0859300	+	0.0721039i
$980$	−24.1557	+	8.79195i	−0.771625	+	0.280849i
$981$	−2.82770	+	1.02920i	−0.0902814	+	0.0328597i
$982$	−49.6999	+	41.7031i	−1.58599	+	1.33080i
$983$	8.49629	+	48.1849i	0.270990	+	1.53686i	0.751419	+	0.659825i	$0.229370\pi$
$983$	8.49629	+	48.1849i	0.270990	+	1.53686i	−0.480430	+	0.877033i	$0.659519\pi$
$984$	0.458111	+	2.59808i	0.0146040	+	0.0828236i
$985$	−24.6536	+	42.7014i	−0.785530	+	1.36058i
$986$	−67.3453	−	56.5094i	−2.14471	−	1.79963i
$987$	5.55051	+	2.02022i	0.176675	+	0.0643043i
$988$	−0.950837	−	1.64690i	−0.0302502	−	0.0523948i
$989$	−0.304063	+	0.526653i	−0.00966864	+	0.0167466i
$990$	1.81521	−	1.52314i	0.0576911	−	0.0484086i
$991$	−23.8243	−	41.2649i	−0.756804	−	1.31082i	−0.944473	−	0.328590i	$-0.893427\pi$
$991$	−23.8243	−	41.2649i	−0.756804	−	1.31082i	0.187669	−	0.982232i	$-0.439907\pi$
$992$	3.40420	−	19.3062i	0.108083	−	0.612972i
$993$	34.9709			1.10977
$994$	15.6300	−	88.6422i	0.495754	−	2.81156i
$995$	33.4766	+	28.0902i	1.06128	+	0.890519i
$996$	−1.01707	+	0.370185i	−0.0322272	+	0.0117298i
$997$	8.29591	+	3.01946i	0.262734	+	0.0956274i	0.470029	−	0.882651i	$-0.344244\pi$
$997$	8.29591	+	3.01946i	0.262734	+	0.0956274i	−0.207294	+	0.978279i	$0.566466\pi$
$998$	54.9154			1.73832
$999$	33.0450	+	9.17664i	1.04550	+	0.290336i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	37.2.f.a.16.1	yes	6
3.2	odd	2		333.2.x.c.127.1		6
4.3	odd	2		592.2.bc.a.497.1		6
5.2	odd	4		925.2.bc.a.349.2		12
5.3	odd	4		925.2.bc.a.349.1		12
5.4	even	2		925.2.p.b.201.1		6
37.7	even	9	inner	37.2.f.a.7.1	✓	6
37.9	even	9		1369.2.a.j.1.3		3
37.17	odd	36		1369.2.b.f.1368.1		6
37.20	odd	36		1369.2.b.f.1368.6		6
37.28	even	18		1369.2.a.k.1.1		3
111.44	odd	18		333.2.x.c.118.1		6
148.7	odd	18		592.2.bc.a.81.1		6
185.7	odd	36		925.2.bc.a.599.1		12
185.44	even	18		925.2.p.b.451.1		6
185.118	odd	36		925.2.bc.a.599.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
37.2.f.a.7.1	✓	6	37.7	even	9	inner
37.2.f.a.16.1	yes	6	1.1	even	1	trivial
333.2.x.c.118.1		6	111.44	odd	18
333.2.x.c.127.1		6	3.2	odd	2
592.2.bc.a.81.1		6	148.7	odd	18
592.2.bc.a.497.1		6	4.3	odd	2
925.2.p.b.201.1		6	5.4	even	2
925.2.p.b.451.1		6	185.44	even	18
925.2.bc.a.349.1		12	5.3	odd	4
925.2.bc.a.349.2		12	5.2	odd	4
925.2.bc.a.599.1		12	185.7	odd	36
925.2.bc.a.599.2		12	185.118	odd	36
1369.2.a.j.1.3		3	37.9	even	9
1369.2.a.k.1.1		3	37.28	even	18
1369.2.b.f.1368.1		6	37.17	odd	36
1369.2.b.f.1368.6		6	37.20	odd	36

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:	\( N \)	\(=\)	\( 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	37.f (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.76604 - 0.642788i) q^{2} +(1.26604 - 0.460802i) q^{3} +(1.17365 + 0.984808i) q^{4} +(0.532089 - 3.01763i) q^{5} -2.53209 q^{6} +(-0.613341 + 3.47843i) q^{7} +(0.439693 + 0.761570i) q^{8} +(-0.907604 + 0.761570i) q^{9} +O(q^{10})\)	\(q+(-1.76604 - 0.642788i) q^{2} +(1.26604 - 0.460802i) q^{3} +(1.17365 + 0.984808i) q^{4} +(0.532089 - 3.01763i) q^{5} -2.53209 q^{6} +(-0.613341 + 3.47843i) q^{7} +(0.439693 + 0.761570i) q^{8} +(-0.907604 + 0.761570i) q^{9} +(-2.87939 + 4.98724i) q^{10} +(0.173648 + 0.300767i) q^{11} +(1.93969 + 0.705990i) q^{12} +(-0.141559 - 0.118782i) q^{13} +(3.31908 - 5.74881i) q^{14} +(-0.716881 - 4.06564i) q^{15} +(-0.819078 - 4.64522i) q^{16} +(-4.44356 + 3.72859i) q^{17} +(2.09240 - 0.761570i) q^{18} +(6.31180 - 2.29731i) q^{19} +(3.59627 - 3.01763i) q^{20} +(0.826352 + 4.68647i) q^{21} +(-0.113341 - 0.642788i) q^{22} +(0.266044 - 0.460802i) q^{23} +(0.907604 + 0.761570i) q^{24} +(-4.12449 - 1.50119i) q^{25} +(0.173648 + 0.300767i) q^{26} +(-2.81908 + 4.88279i) q^{27} +(-4.14543 + 3.47843i) q^{28} +(-4.03209 - 6.98378i) q^{29} +(-1.34730 + 7.64090i) q^{30} -2.75877 q^{31} +(-1.23396 + 6.99811i) q^{32} +(0.358441 + 0.300767i) q^{33} +(10.2442 - 3.72859i) q^{34} +(10.1702 + 3.70167i) q^{35} -1.81521 q^{36} +(-1.52094 - 5.88954i) q^{37} -12.6236 q^{38} +(-0.233956 - 0.0851529i) q^{39} +(2.53209 - 0.921605i) q^{40} +(1.70574 + 1.43128i) q^{41} +(1.55303 - 8.80769i) q^{42} -1.14290 q^{43} +(-0.0923963 + 0.524005i) q^{44} +(1.81521 + 3.14403i) q^{45} +(-0.766044 + 0.642788i) q^{46} +(0.620615 - 1.07494i) q^{47} +(-3.17752 - 5.50362i) q^{48} +(-5.14543 - 1.87278i) q^{49} +(6.31908 + 5.30234i) q^{50} +(-3.90760 + 6.76817i) q^{51} +(-0.0491630 - 0.278817i) q^{52} +(0.0675813 + 0.383273i) q^{53} +(8.11721 - 6.81115i) q^{54} +(1.00000 - 0.363970i) q^{55} +(-2.91875 + 1.06234i) q^{56} +(6.93242 - 5.81699i) q^{57} +(2.63176 + 14.9254i) q^{58} +(0.724155 + 4.10689i) q^{59} +(3.16250 - 5.47762i) q^{60} +(-7.07398 - 5.93577i) q^{61} +(4.87211 + 1.77330i) q^{62} +(-2.09240 - 3.62414i) q^{63} +(1.96064 - 3.39592i) q^{64} +(-0.433763 + 0.363970i) q^{65} +(-0.439693 - 0.761570i) q^{66} +(-0.354570 + 2.01087i) q^{67} -8.88713 q^{68} +(0.124485 - 0.705990i) q^{69} +(-15.5817 - 13.0746i) q^{70} +(12.7417 - 4.63760i) q^{71} +(-0.979055 - 0.356347i) q^{72} +10.0077 q^{73} +(-1.09967 + 11.3788i) q^{74} -5.91353 q^{75} +(9.67024 + 3.51968i) q^{76} +(-1.15270 + 0.419550i) q^{77} +(0.358441 + 0.300767i) q^{78} +(-1.32295 + 7.50281i) q^{79} -14.4534 q^{80} +(-0.701867 + 3.98048i) q^{81} +(-2.09240 - 3.62414i) q^{82} +(-0.401674 + 0.337044i) q^{83} +(-3.64543 + 6.31407i) q^{84} +(8.88713 + 15.3930i) q^{85} +(2.01842 + 0.734644i) q^{86} +(-8.32295 - 6.98378i) q^{87} +(-0.152704 + 0.264490i) q^{88} +(1.75490 + 9.95253i) q^{89} +(-1.18479 - 6.71929i) q^{90} +(0.500000 - 0.419550i) q^{91} +(0.766044 - 0.278817i) q^{92} +(-3.49273 + 1.27125i) q^{93} +(-1.78699 + 1.49946i) q^{94} +(-3.57398 - 20.2690i) q^{95} +(1.66250 + 9.42853i) q^{96} +(1.53936 - 2.66625i) q^{97} +(7.88326 + 6.61484i) q^{98} +(-0.386659 - 0.140732i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 6 q^{2} + 3 q^{3} + 6 q^{4} - 6 q^{5} - 6 q^{6} + 3 q^{7} - 3 q^{8} - 9 q^{9}+O(q^{10}) \) 6 * q - 6 * q^2 + 3 * q^3 + 6 * q^4 - 6 * q^5 - 6 * q^6 + 3 * q^7 - 3 * q^8 - 9 * q^9	\( 6 q - 6 q^{2} + 3 q^{3} + 6 q^{4} - 6 q^{5} - 6 q^{6} + 3 q^{7} - 3 q^{8} - 9 q^{9} - 6 q^{10} + 6 q^{12} - 9 q^{13} + 3 q^{14} + 12 q^{15} + 12 q^{16} + 3 q^{17} + 9 q^{18} + 3 q^{19} - 6 q^{20} + 6 q^{21} + 6 q^{22} - 3 q^{23} + 9 q^{24} - 12 q^{25} - 9 q^{28} - 15 q^{29} - 6 q^{30} + 6 q^{31} - 12 q^{32} - 6 q^{33} + 3 q^{34} + 18 q^{35} - 18 q^{36} - 6 q^{37} - 6 q^{38} - 6 q^{39} + 6 q^{40} - 3 q^{42} - 6 q^{43} + 3 q^{44} + 18 q^{45} + 15 q^{47} + 6 q^{48} - 15 q^{49} + 21 q^{50} - 27 q^{51} - 12 q^{52} + 24 q^{53} + 18 q^{54} + 6 q^{55} - 15 q^{56} + 18 q^{57} + 21 q^{58} + 6 q^{59} + 24 q^{60} - 27 q^{61} - 9 q^{63} + 3 q^{64} + 30 q^{65} + 3 q^{66} - 18 q^{67} + 6 q^{68} - 12 q^{69} - 30 q^{70} + 33 q^{71} - 9 q^{72} + 12 q^{73} - 21 q^{74} - 66 q^{75} + 15 q^{76} - 9 q^{77} - 6 q^{78} + 33 q^{79} - 60 q^{80} - 18 q^{81} - 9 q^{82} + 21 q^{83} - 6 q^{84} - 6 q^{85} + 24 q^{86} - 9 q^{87} - 3 q^{88} + 12 q^{89} + 3 q^{91} - 3 q^{93} - 3 q^{94} - 6 q^{95} + 15 q^{96} + 18 q^{97} + 12 q^{98} - 9 q^{99}+O(q^{100}) \) 6 * q - 6 * q^2 + 3 * q^3 + 6 * q^4 - 6 * q^5 - 6 * q^6 + 3 * q^7 - 3 * q^8 - 9 * q^9 - 6 * q^10 + 6 * q^12 - 9 * q^13 + 3 * q^14 + 12 * q^15 + 12 * q^16 + 3 * q^17 + 9 * q^18 + 3 * q^19 - 6 * q^20 + 6 * q^21 + 6 * q^22 - 3 * q^23 + 9 * q^24 - 12 * q^25 - 9 * q^28 - 15 * q^29 - 6 * q^30 + 6 * q^31 - 12 * q^32 - 6 * q^33 + 3 * q^34 + 18 * q^35 - 18 * q^36 - 6 * q^37 - 6 * q^38 - 6 * q^39 + 6 * q^40 - 3 * q^42 - 6 * q^43 + 3 * q^44 + 18 * q^45 + 15 * q^47 + 6 * q^48 - 15 * q^49 + 21 * q^50 - 27 * q^51 - 12 * q^52 + 24 * q^53 + 18 * q^54 + 6 * q^55 - 15 * q^56 + 18 * q^57 + 21 * q^58 + 6 * q^59 + 24 * q^60 - 27 * q^61 - 9 * q^63 + 3 * q^64 + 30 * q^65 + 3 * q^66 - 18 * q^67 + 6 * q^68 - 12 * q^69 - 30 * q^70 + 33 * q^71 - 9 * q^72 + 12 * q^73 - 21 * q^74 - 66 * q^75 + 15 * q^76 - 9 * q^77 - 6 * q^78 + 33 * q^79 - 60 * q^80 - 18 * q^81 - 9 * q^82 + 21 * q^83 - 6 * q^84 - 6 * q^85 + 24 * q^86 - 9 * q^87 - 3 * q^88 + 12 * q^89 + 3 * q^91 - 3 * q^93 - 3 * q^94 - 6 * q^95 + 15 * q^96 + 18 * q^97 + 12 * q^98 - 9 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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