LMFDB - Embedded newform 798.2.bo.f.253.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [798,2,Mod(43,798)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(798, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 0, 16]))

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

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

chi := DirichletCharacter("798.43");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 798 = 2 \cdot 3 \cdot 7 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	798.bo (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:	$6.37206208130$
Analytic rank:	$0$
Dimension:	$18$
Relative dimension:	$3$ over $\Q(\zeta_{9})$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - 3 x^{17} + 27 x^{16} - 28 x^{15} + 333 x^{14} - 195 x^{13} + 2778 x^{12} + 519 x^{11} + \cdots + 1369 $ x^18 - 3x^17 + 27x^16 - 28x^15 + 333x^14 - 195x^13 + 2778x^12 + 519x^11 + 13116x^10 + 3193x^9 + 40191x^8 + 15663x^7 + 69675x^6 + 1134x^5 + 45822x^4 - 3079x^3 + 22776x^2 - 4995*x + 1369
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			253.2
Root			$0.125533 - 0.217429i$ of defining polynomial
Character	$\chi$	$=$	798.253
Dual form			798.2.bo.f.757.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.766044 - 0.642788i) q^{2} +(-0.939693 - 0.342020i) q^{3} +(0.173648 - 0.984808i) q^{4} +(0.130051 + 0.737556i) q^{5} +(-0.939693 + 0.342020i) q^{6} +(-0.500000 + 0.866025i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(0.766044 + 0.642788i) q^{9} +O(q^{10})$	\(q+(0.766044 - 0.642788i) q^{2} +(-0.939693 - 0.342020i) q^{3} +(0.173648 - 0.984808i) q^{4} +(0.130051 + 0.737556i) q^{5} +(-0.939693 + 0.342020i) q^{6} +(-0.500000 + 0.866025i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(0.766044 + 0.642788i) q^{9} +(0.573717 + 0.481406i) q^{10} +(0.411353 + 0.712484i) q^{11} +(-0.500000 + 0.866025i) q^{12} +(2.37677 - 0.865074i) q^{13} +(0.173648 + 0.984808i) q^{14} +(0.130051 - 0.737556i) q^{15} +(-0.939693 - 0.342020i) q^{16} +(4.68619 - 3.93218i) q^{17} +1.00000 q^{18} +(2.14057 - 3.79710i) q^{19} +0.748934 q^{20} +(0.766044 - 0.642788i) q^{21} +(0.773090 + 0.281382i) q^{22} +(-0.0151626 + 0.0859912i) q^{23} +(0.173648 + 0.984808i) q^{24} +(4.17139 - 1.51826i) q^{25} +(1.26465 - 2.19044i) q^{26} +(-0.500000 - 0.866025i) q^{27} +(0.766044 + 0.642788i) q^{28} +(1.82468 + 1.53109i) q^{29} +(-0.374467 - 0.648596i) q^{30} +(0.177343 - 0.307167i) q^{31} +(-0.939693 + 0.342020i) q^{32} +(-0.142861 - 0.810207i) q^{33} +(1.06227 - 6.02445i) q^{34} +(-0.703768 - 0.256151i) q^{35} +(0.766044 - 0.642788i) q^{36} -0.471849 q^{37} +(-0.800961 - 4.28468i) q^{38} -2.52931 q^{39} +(0.573717 - 0.481406i) q^{40} +(-0.844631 - 0.307421i) q^{41} +(0.173648 - 0.984808i) q^{42} +(-0.409857 - 2.32441i) q^{43} +(0.773090 - 0.281382i) q^{44} +(-0.374467 + 0.648596i) q^{45} +(0.0436589 + 0.0756194i) q^{46} +(-3.44550 - 2.89111i) q^{47} +(0.766044 + 0.642788i) q^{48} +(-0.500000 - 0.866025i) q^{49} +(2.21955 - 3.84437i) q^{50} +(-5.74846 + 2.09227i) q^{51} +(-0.439209 - 2.49088i) q^{52} +(-0.886252 + 5.02618i) q^{53} +(-0.939693 - 0.342020i) q^{54} +(-0.472000 + 0.396055i) q^{55} +1.00000 q^{56} +(-3.31016 + 2.83599i) q^{57} +2.38195 q^{58} +(3.93546 - 3.30225i) q^{59} +(-0.703768 - 0.256151i) q^{60} +(1.89162 - 10.7279i) q^{61} +(-0.0615905 - 0.349297i) q^{62} +(-0.939693 + 0.342020i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(0.947142 + 1.64050i) q^{65} +(-0.630229 - 0.528825i) q^{66} +(11.5351 + 9.67913i) q^{67} +(-3.05869 - 5.29781i) q^{68} +(0.0436589 - 0.0756194i) q^{69} +(-0.703768 + 0.256151i) q^{70} +(2.02278 + 11.4717i) q^{71} +(0.173648 - 0.984808i) q^{72} +(2.42721 + 0.883432i) q^{73} +(-0.361457 + 0.303299i) q^{74} -4.43910 q^{75} +(-3.36771 - 2.76741i) q^{76} -0.822706 q^{77} +(-1.93756 + 1.62581i) q^{78} +(-14.3224 - 5.21292i) q^{79} +(0.130051 - 0.737556i) q^{80} +(0.173648 + 0.984808i) q^{81} +(-0.844631 + 0.307421i) q^{82} +(-0.971697 + 1.68303i) q^{83} +(-0.500000 - 0.866025i) q^{84} +(3.50965 + 2.94494i) q^{85} +(-1.80807 - 1.51715i) q^{86} +(-1.19098 - 2.06283i) q^{87} +(0.411353 - 0.712484i) q^{88} +(5.18954 - 1.88884i) q^{89} +(0.130051 + 0.737556i) q^{90} +(-0.439209 + 2.49088i) q^{91} +(0.0820519 + 0.0298644i) q^{92} +(-0.271705 + 0.227988i) q^{93} -4.49778 q^{94} +(3.07896 + 1.08497i) q^{95} +1.00000 q^{96} +(8.83211 - 7.41102i) q^{97} +(-0.939693 - 0.342020i) q^{98} +(-0.142861 + 0.810207i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q - 9 q^{7} - 9 q^{8}+O(q^{10}) $ 18 * q - 9 * q^7 - 9 * q^8	$ 18 q - 9 q^{7} - 9 q^{8} - 9 q^{11} - 9 q^{12} + 3 q^{13} - 6 q^{17} + 18 q^{18} + 3 q^{19} + 12 q^{20} - 6 q^{22} - 3 q^{23} - 12 q^{25} - 15 q^{26} - 9 q^{27} - 3 q^{29} - 6 q^{30} - 15 q^{31} + 3 q^{33} - 6 q^{34} - 3 q^{38} + 30 q^{39} - 24 q^{43} - 6 q^{44} - 6 q^{45} - 6 q^{46} - 9 q^{49} - 3 q^{50} + 12 q^{51} + 3 q^{52} - 39 q^{53} - 48 q^{55} + 18 q^{56} + 15 q^{57} + 24 q^{58} + 30 q^{59} + 21 q^{61} - 9 q^{64} - 12 q^{65} + 3 q^{66} + 3 q^{67} - 12 q^{68} - 6 q^{69} + 33 q^{71} + 3 q^{73} - 3 q^{74} + 6 q^{75} + 3 q^{76} + 18 q^{77} - 6 q^{78} - 3 q^{79} + 30 q^{83} - 9 q^{84} - 24 q^{85} - 6 q^{86} - 12 q^{87} - 9 q^{88} + 12 q^{89} + 3 q^{91} - 3 q^{92} + 9 q^{93} + 18 q^{94} - 24 q^{95} + 18 q^{96} + 63 q^{97} + 3 q^{99}+O(q^{100}) $ 18 * q - 9 * q^7 - 9 * q^8 - 9 * q^11 - 9 * q^12 + 3 * q^13 - 6 * q^17 + 18 * q^18 + 3 * q^19 + 12 * q^20 - 6 * q^22 - 3 * q^23 - 12 * q^25 - 15 * q^26 - 9 * q^27 - 3 * q^29 - 6 * q^30 - 15 * q^31 + 3 * q^33 - 6 * q^34 - 3 * q^38 + 30 * q^39 - 24 * q^43 - 6 * q^44 - 6 * q^45 - 6 * q^46 - 9 * q^49 - 3 * q^50 + 12 * q^51 + 3 * q^52 - 39 * q^53 - 48 * q^55 + 18 * q^56 + 15 * q^57 + 24 * q^58 + 30 * q^59 + 21 * q^61 - 9 * q^64 - 12 * q^65 + 3 * q^66 + 3 * q^67 - 12 * q^68 - 6 * q^69 + 33 * q^71 + 3 * q^73 - 3 * q^74 + 6 * q^75 + 3 * q^76 + 18 * q^77 - 6 * q^78 - 3 * q^79 + 30 * q^83 - 9 * q^84 - 24 * q^85 - 6 * q^86 - 12 * q^87 - 9 * q^88 + 12 * q^89 + 3 * q^91 - 3 * q^92 + 9 * q^93 + 18 * q^94 - 24 * q^95 + 18 * q^96 + 63 * q^97 + 3 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/798\mathbb{Z}\right)^\times$.

$n$	$115$	$211$	$533$
$\chi(n)$	$1$	$e\left(\frac{7}{9}\right)$	$1$

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 $

$2$	0.766044	−	0.642788i	0.541675	−	0.454519i
$2$	0.766044	−	0.642788i	0.541675	−	0.454519i
$3$	−0.939693	−	0.342020i	−0.542532	−	0.197465i
$3$	−0.939693	−	0.342020i	−0.542532	−	0.197465i
$4$	0.173648	−	0.984808i	0.0868241	−	0.492404i
$5$	0.130051	+	0.737556i	0.0581606	+	0.329845i	0.999980	−	0.00627326i	$-0.00199685\pi$
$5$	0.130051	+	0.737556i	0.0581606	+	0.329845i	−0.941820	+	0.336118i	$0.890886\pi$
$6$	−0.939693	+	0.342020i	−0.383628	+	0.139629i
$7$	−0.500000	+	0.866025i	−0.188982	+	0.327327i
$7$	−0.500000	+	0.866025i	−0.188982	+	0.327327i
$8$	−0.500000	−	0.866025i	−0.176777	−	0.306186i
$9$	0.766044	+	0.642788i	0.255348	+	0.214263i
$10$	0.573717	+	0.481406i	0.181425	+	0.152234i
$11$	0.411353	+	0.712484i	0.124028	+	0.214822i	0.921352	−	0.388728i	$-0.127086\pi$
$11$	0.411353	+	0.712484i	0.124028	+	0.214822i	−0.797325	+	0.603550i	$0.793752\pi$
$12$	−0.500000	+	0.866025i	−0.144338	+	0.250000i
$13$	2.37677	−	0.865074i	0.659198	−	0.239928i	0.00930769	−	0.999957i	$-0.497037\pi$
$13$	2.37677	−	0.865074i	0.659198	−	0.239928i	0.649890	+	0.760028i	$0.274815\pi$
$14$	0.173648	+	0.984808i	0.0464094	+	0.263201i
$15$	0.130051	−	0.737556i	0.0335790	−	0.190436i
$16$	−0.939693	−	0.342020i	−0.234923	−	0.0855050i
$17$	4.68619	−	3.93218i	1.13657	−	0.953693i	0.137246	−	0.990537i	$-0.456175\pi$
$17$	4.68619	−	3.93218i	1.13657	−	0.953693i	0.999321	+	0.0368436i	$0.0117303\pi$
$18$	1.00000			0.235702
$19$	2.14057	−	3.79710i	0.491079	−	0.871115i
$19$	2.14057	−	3.79710i	0.491079	−	0.871115i
$20$	0.748934			0.167467
$21$	0.766044	−	0.642788i	0.167165	−	0.140268i
$22$	0.773090	+	0.281382i	0.164823	+	0.0599908i
$23$	−0.0151626	+	0.0859912i	−0.00316162	+	0.0179304i	−0.986348	−	0.164676i	$-0.947342\pi$
$23$	−0.0151626	+	0.0859912i	−0.00316162	+	0.0179304i	0.983186	+	0.182606i	$0.0584533\pi$
$24$	0.173648	+	0.984808i	0.0354458	+	0.201023i
$25$	4.17139	−	1.51826i	0.834277	−	0.303652i
$26$	1.26465	−	2.19044i	0.248019	−	0.429581i
$27$	−0.500000	−	0.866025i	−0.0962250	−	0.166667i
$28$	0.766044	+	0.642788i	0.144769	+	0.121475i
$29$	1.82468	+	1.53109i	0.338835	+	0.284316i	0.796288	−	0.604917i	$-0.206794\pi$
$29$	1.82468	+	1.53109i	0.338835	+	0.284316i	−0.457453	+	0.889234i	$0.651238\pi$
$30$	−0.374467	−	0.648596i	−0.0683680	−	0.118417i
$31$	0.177343	−	0.307167i	0.0318517	−	0.0551688i	−0.849660	−	0.527331i	$-0.823193\pi$
$31$	0.177343	−	0.307167i	0.0318517	−	0.0551688i	0.881512	+	0.472162i	$0.156526\pi$
$32$	−0.939693	+	0.342020i	−0.166116	+	0.0604612i
$33$	−0.142861	−	0.810207i	−0.0248690	−	0.141039i
$34$	1.06227	−	6.02445i	0.182178	−	1.03318i
$35$	−0.703768	−	0.256151i	−0.118959	−	0.0432974i
$36$	0.766044	−	0.642788i	0.127674	−	0.107131i
$37$	−0.471849			−0.0775715			−0.0387858	−	0.999248i	$-0.512349\pi$
$37$	−0.471849			−0.0775715			−0.0387858	+	0.999248i	$0.512349\pi$
$38$	−0.800961	−	4.28468i	−0.129933	−	0.695066i
$39$	−2.52931			−0.405013
$40$	0.573717	−	0.481406i	0.0907126	−	0.0761169i
$41$	−0.844631	−	0.307421i	−0.131909	−	0.0480110i	0.275222	−	0.961381i	$-0.411249\pi$
$41$	−0.844631	−	0.307421i	−0.131909	−	0.0480110i	−0.407131	+	0.913370i	$0.633471\pi$
$42$	0.173648	−	0.984808i	0.0267945	−	0.151959i
$43$	−0.409857	−	2.32441i	−0.0625026	−	0.354470i	−0.999979	−	0.00642193i	$-0.997956\pi$
$43$	−0.409857	−	2.32441i	−0.0625026	−	0.354470i	0.937477	−	0.348048i	$-0.113155\pi$
$44$	0.773090	−	0.281382i	0.116548	−	0.0424199i
$45$	−0.374467	+	0.648596i	−0.0558223	+	0.0966870i
$46$	0.0436589	+	0.0756194i	0.00643715	+	0.0111495i
$47$	−3.44550	−	2.89111i	−0.502577	−	0.421712i	0.355931	−	0.934512i	$-0.384164\pi$
$47$	−3.44550	−	2.89111i	−0.502577	−	0.421712i	−0.858508	+	0.512800i	$0.828608\pi$
$48$	0.766044	+	0.642788i	0.110569	+	0.0927784i
$49$	−0.500000	−	0.866025i	−0.0714286	−	0.123718i
$50$	2.21955	−	3.84437i	0.313892	−	0.543676i
$51$	−5.74846	+	2.09227i	−0.804945	+	0.292976i
$52$	−0.439209	−	2.49088i	−0.0609074	−	0.345423i
$53$	−0.886252	+	5.02618i	−0.121736	+	0.690399i	0.861457	+	0.507831i	$0.169552\pi$
$53$	−0.886252	+	5.02618i	−0.121736	+	0.690399i	−0.983193	+	0.182569i	$0.941559\pi$
$54$	−0.939693	−	0.342020i	−0.127876	−	0.0465430i
$55$	−0.472000	+	0.396055i	−0.0636445	+	0.0534041i
$56$	1.00000			0.133631
$57$	−3.31016	+	2.83599i	−0.438441	+	0.375636i
$58$	2.38195			0.312766
$59$	3.93546	−	3.30225i	0.512354	−	0.429916i	−0.349603	−	0.936898i	$-0.613683\pi$
$59$	3.93546	−	3.30225i	0.512354	−	0.429916i	0.861956	+	0.506982i	$0.169239\pi$
$60$	−0.703768	−	0.256151i	−0.0908561	−	0.0330689i
$61$	1.89162	−	10.7279i	0.242197	−	1.37357i	−0.584717	−	0.811238i	$-0.698794\pi$
$61$	1.89162	−	10.7279i	0.242197	−	1.37357i	0.826913	−	0.562329i	$-0.190095\pi$
$62$	−0.0615905	−	0.349297i	−0.00782200	−	0.0443608i
$63$	−0.939693	+	0.342020i	−0.118390	+	0.0430905i
$64$	−0.500000	+	0.866025i	−0.0625000	+	0.108253i
$65$	0.947142	+	1.64050i	0.117479	+	0.203479i
$66$	−0.630229	−	0.528825i	−0.0775758	−	0.0650938i
$67$	11.5351	+	9.67913i	1.40924	+	1.18249i	0.956817	+	0.290692i	$0.0938854\pi$
$67$	11.5351	+	9.67913i	1.40924	+	1.18249i	0.452425	+	0.891803i	$0.350559\pi$
$68$	−3.05869	−	5.29781i	−0.370921	−	0.642454i
$69$	0.0436589	−	0.0756194i	0.00525591	−	0.00910351i
$70$	−0.703768	+	0.256151i	−0.0841164	+	0.0306159i
$71$	2.02278	+	11.4717i	0.240059	+	1.36144i	0.831692	+	0.555237i	$0.187372\pi$
$71$	2.02278	+	11.4717i	0.240059	+	1.36144i	−0.591633	+	0.806207i	$0.701517\pi$
$72$	0.173648	−	0.984808i	0.0204646	−	0.116061i
$73$	2.42721	+	0.883432i	0.284083	+	0.103398i	0.480132	−	0.877196i	$-0.340589\pi$
$73$	2.42721	+	0.883432i	0.284083	+	0.103398i	−0.196049	+	0.980594i	$0.562811\pi$
$74$	−0.361457	+	0.303299i	−0.0420186	+	0.0352578i
$75$	−4.43910			−0.512583
$76$	−3.36771	−	2.76741i	−0.386303	−	0.317443i
$77$	−0.822706			−0.0937560
$78$	−1.93756	+	1.62581i	−0.219386	+	0.184086i
$79$	−14.3224	−	5.21292i	−1.61139	−	0.586499i	−0.629678	−	0.776857i	$-0.716813\pi$
$79$	−14.3224	−	5.21292i	−1.61139	−	0.586499i	−0.981715	+	0.190358i	$0.939035\pi$
$80$	0.130051	−	0.737556i	0.0145402	−	0.0824613i
$81$	0.173648	+	0.984808i	0.0192942	+	0.109423i
$82$	−0.844631	+	0.307421i	−0.0932739	+	0.0339489i
$83$	−0.971697	+	1.68303i	−0.106658	+	0.184736i	−0.914414	−	0.404780i	$-0.867348\pi$
$83$	−0.971697	+	1.68303i	−0.106658	+	0.184736i	0.807757	+	0.589516i	$0.200682\pi$
$84$	−0.500000	−	0.866025i	−0.0545545	−	0.0944911i
$85$	3.50965	+	2.94494i	0.380675	+	0.319424i
$86$	−1.80807	−	1.51715i	−0.194969	−	0.163599i
$87$	−1.19098	−	2.06283i	−0.127686	−	0.221159i
$88$	0.411353	−	0.712484i	0.0438504	−	0.0759510i
$89$	5.18954	−	1.88884i	0.550090	−	0.200216i	−0.0519965	−	0.998647i	$-0.516558\pi$
$89$	5.18954	−	1.88884i	0.550090	−	0.200216i	0.602086	+	0.798431i	$0.294336\pi$
$90$	0.130051	+	0.737556i	0.0137086	+	0.0777453i
$91$	−0.439209	+	2.49088i	−0.0460417	+	0.261115i
$92$	0.0820519	+	0.0298644i	0.00855450	+	0.00311358i
$93$	−0.271705	+	0.227988i	−0.0281745	+	0.0236412i
$94$	−4.49778			−0.463910
$95$	3.07896	+	1.08497i	0.315895	+	0.111316i
$96$	1.00000			0.102062
$97$	8.83211	−	7.41102i	0.896765	−	0.752475i	−0.0727901	−	0.997347i	$-0.523190\pi$
$97$	8.83211	−	7.41102i	0.896765	−	0.752475i	0.969555	+	0.244872i	$0.0787459\pi$
$98$	−0.939693	−	0.342020i	−0.0949233	−	0.0345493i
$99$	−0.142861	+	0.810207i	−0.0143581	+	0.0814288i
$100$	−0.770841	−	4.37166i	−0.0770841	−	0.437166i
$101$	−14.3530	+	5.22408i	−1.42818	+	0.519816i	−0.936410	−	0.350909i	$-0.885873\pi$
$101$	−14.3530	+	5.22408i	−1.42818	+	0.519816i	−0.491772	+	0.870724i	$0.663651\pi$
$102$	−3.05869	+	5.29781i	−0.302856	+	0.524561i
$103$	−2.15636	−	3.73492i	−0.212472	−	0.368013i	0.740015	−	0.672590i	$-0.234818\pi$
$103$	−2.15636	−	3.73492i	−0.212472	−	0.368013i	−0.952488	+	0.304577i	$0.901485\pi$
$104$	−1.93756	−	1.62581i	−0.189993	−	0.159423i
$105$	0.573717	+	0.481406i	0.0559890	+	0.0469804i
$106$	2.55186	+	4.41995i	0.247859	+	0.429304i
$107$	−7.71284	+	13.3590i	−0.745629	+	1.29147i	0.204272	+	0.978914i	$0.434517\pi$
$107$	−7.71284	+	13.3590i	−0.745629	+	1.29147i	−0.949901	+	0.312552i	$0.898816\pi$
$108$	−0.939693	+	0.342020i	−0.0904220	+	0.0329109i
$109$	1.53388	+	8.69906i	0.146919	+	0.833219i	0.965806	+	0.259264i	$0.0834801\pi$
$109$	1.53388	+	8.69906i	0.146919	+	0.833219i	−0.818887	+	0.573954i	$0.805409\pi$
$110$	−0.106994	+	0.606792i	−0.0102015	+	0.0578553i
$111$	0.443393	+	0.161382i	0.0420850	+	0.0153177i
$112$	0.766044	−	0.642788i	0.0723844	−	0.0607377i
$113$	2.83131			0.266347			0.133174	−	0.991093i	$-0.457483\pi$
$113$	2.83131			0.266347			0.133174	+	0.991093i	$0.457483\pi$
$114$	−0.712789	+	4.30022i	−0.0667588	+	0.402753i
$115$	−0.0653953			−0.00609814
$116$	1.82468	−	1.53109i	0.169417	−	0.142158i
$117$	2.37677	+	0.865074i	0.219733	+	0.0799761i
$118$	0.892097	−	5.05933i	0.0821242	−	0.465749i
$119$	1.06227	+	6.02445i	0.0973784	+	0.552260i
$120$	−0.703768	+	0.256151i	−0.0642449	+	0.0233832i
$121$	5.16158	−	8.94011i	0.469234	−	0.812738i
$122$	−5.44670	−	9.43396i	−0.493121	−	0.854110i
$123$	0.688549	+	0.577762i	0.0620844	+	0.0520950i
$124$	−0.271705	−	0.227988i	−0.0243998	−	0.0204739i
$125$	3.53463	+	6.12216i	0.316147	+	0.547583i
$126$	−0.500000	+	0.866025i	−0.0445435	+	0.0771517i
$127$	2.17056	−	0.790020i	0.192606	−	0.0701029i	−0.243916	−	0.969796i	$-0.578432\pi$
$127$	2.17056	−	0.790020i	0.192606	−	0.0701029i	0.436522	+	0.899693i	$0.356210\pi$
$128$	0.173648	+	0.984808i	0.0153485	+	0.0870455i
$129$	−0.409857	+	2.32441i	−0.0360859	+	0.204653i
$130$	1.78005	+	0.647883i	0.156120	+	0.0568231i
$131$	−9.98585	+	8.37912i	−0.872467	+	0.732087i	−0.964616	−	0.263658i	$-0.915071\pi$
$131$	−9.98585	+	8.37912i	−0.872467	+	0.732087i	0.0921487	+	0.995745i	$0.470626\pi$
$132$	−0.822706			−0.0716073
$133$	2.21810	+	3.75234i	0.192334	+	0.325369i
$134$	15.0581			1.30082
$135$	0.573717	−	0.481406i	0.0493777	−	0.0414328i
$136$	−5.74846	−	2.09227i	−0.492926	−	0.179411i
$137$	−1.87410	+	10.6286i	−0.160115	+	0.908060i	0.793843	+	0.608122i	$0.208077\pi$
$137$	−1.87410	+	10.6286i	−0.160115	+	0.908060i	−0.953959	+	0.299937i	$0.903034\pi$
$138$	−0.0151626	−	0.0859912i	−0.00129072	−	0.00732006i
$139$	−5.90067	+	2.14767i	−0.500488	+	0.182163i	−0.579914	−	0.814678i	$-0.696914\pi$
$139$	−5.90067	+	2.14767i	−0.500488	+	0.182163i	0.0794252	+	0.996841i	$0.474692\pi$
$140$	−0.374467	+	0.648596i	−0.0316483	+	0.0548164i
$141$	2.24889	+	3.89519i	0.189391	+	0.328034i
$142$	8.92342	+	7.48764i	0.748837	+	0.628349i
$143$	1.59404	+	1.33756i	0.133301	+	0.111852i
$144$	−0.500000	−	0.866025i	−0.0416667	−	0.0721688i
$145$	−0.891963	+	1.54493i	−0.0740735	+	0.128299i
$146$	2.42721	−	0.883432i	0.200877	−	0.0731133i
$147$	0.173648	+	0.984808i	0.0143223	+	0.0812256i
$148$	−0.0819357	+	0.464681i	−0.00673508	+	0.0381965i
$149$	0.0354871	+	0.0129163i	0.00290722	+	0.00105814i	0.343473	−	0.939162i	$-0.388396\pi$
$149$	0.0354871	+	0.0129163i	0.00290722	+	0.00105814i	−0.340566	+	0.940221i	$0.610619\pi$
$150$	−3.40055	+	2.85340i	−0.277653	+	0.232979i
$151$	1.35626			0.110371			0.0551853	−	0.998476i	$-0.482425\pi$
$151$	1.35626			0.110371			0.0551853	+	0.998476i	$0.482425\pi$
$152$	−4.35867	+	0.0447662i	−0.353535	+	0.00363102i
$153$	6.11738			0.494561
$154$	−0.630229	+	0.528825i	−0.0507853	+	0.0426139i
$155$	0.249616	+	0.0908530i	0.0200497	+	0.00729748i
$156$	−0.439209	+	2.49088i	−0.0351649	+	0.199430i
$157$	0.483705	+	2.74323i	0.0386039	+	0.218933i	0.998007	−	0.0631054i	$-0.0201004\pi$
$157$	0.483705	+	2.74323i	0.0386039	+	0.218933i	−0.959403	+	0.282039i	$0.908989\pi$
$158$	−14.3224	+	5.21292i	−1.13943	+	0.414717i
$159$	2.55186	−	4.41995i	0.202376	−	0.350525i
$160$	−0.374467	−	0.648596i	−0.0296042	−	0.0512760i
$161$	−0.0668893	−	0.0561268i	−0.00527162	−	0.00442341i
$162$	0.766044	+	0.642788i	0.0601861	+	0.0505022i
$163$	−9.82357	−	17.0149i	−0.769441	−	1.33271i	−0.937866	−	0.346997i	$-0.887201\pi$
$163$	−9.82357	−	17.0149i	−0.769441	−	1.33271i	0.168425	−	0.985715i	$-0.446132\pi$
$164$	−0.449419	+	0.778416i	−0.0350937	+	0.0607841i
$165$	0.578994	−	0.210737i	0.0450746	−	0.0164058i
$166$	0.337467	+	1.91387i	0.0261925	+	0.148545i
$167$	−3.69772	+	20.9708i	−0.286138	+	1.62277i	0.415053	+	0.909797i	$0.363763\pi$
$167$	−3.69772	+	20.9708i	−0.286138	+	1.62277i	−0.701191	+	0.712973i	$0.747348\pi$
$168$	−0.939693	−	0.342020i	−0.0724989	−	0.0263874i
$169$	−5.05789	+	4.24408i	−0.389069	+	0.326467i
$170$	4.58152			0.351386
$171$	4.08050	−	1.53282i	0.312043	−	0.117218i
$172$	−2.36027			−0.179969
$173$	−5.21489	+	4.37581i	−0.396480	+	0.332687i	−0.819131	−	0.573606i	$-0.805544\pi$
$173$	−5.21489	+	4.37581i	−0.396480	+	0.332687i	0.422651	+	0.906293i	$0.361100\pi$
$174$	−2.23830	−	0.814676i	−0.169685	−	0.0617604i
$175$	−0.770841	+	4.37166i	−0.0582701	+	0.330466i
$176$	−0.142861	−	0.810207i	−0.0107686	−	0.0610716i
$177$	−4.82756	+	1.75709i	−0.362862	+	0.132071i
$178$	2.76130	−	4.78271i	0.206968	−	0.358479i
$179$	2.73674	+	4.74018i	0.204554	+	0.354297i	0.949990	−	0.312279i	$-0.101092\pi$
$179$	2.73674	+	4.74018i	0.204554	+	0.354297i	−0.745437	+	0.666576i	$0.767759\pi$
$180$	0.573717	+	0.481406i	0.0427623	+	0.0358819i
$181$	10.1129	+	8.48577i	0.751690	+	0.630742i	0.935949	−	0.352135i	$-0.114544\pi$
$181$	10.1129	+	8.48577i	0.751690	+	0.630742i	−0.184260	+	0.982878i	$0.558989\pi$
$182$	1.26465	+	2.19044i	0.0937423	+	0.162366i
$183$	−5.44670	+	9.43396i	−0.402631	+	0.697378i
$184$	0.0820519	−	0.0298644i	0.00604894	−	0.00220164i
$185$	−0.0613645	−	0.348015i	−0.00451161	−	0.0255866i
$186$	−0.0615905	+	0.349297i	−0.00451604	+	0.0256117i
$187$	4.72929	+	1.72132i	0.345840	+	0.125875i
$188$	−3.44550	+	2.89111i	−0.251289	+	0.210856i
$189$	1.00000			0.0727393
$190$	3.05603	−	1.14798i	0.221707	−	0.0832833i
$191$	−14.9761			−1.08363			−0.541816	−	0.840497i	$-0.682263\pi$
$191$	−14.9761			−1.08363			−0.541816	+	0.840497i	$0.682263\pi$
$192$	0.766044	−	0.642788i	0.0552845	−	0.0463892i
$193$	−0.732484	−	0.266603i	−0.0527254	−	0.0191905i	0.315523	−	0.948918i	$-0.397820\pi$
$193$	−0.732484	−	0.266603i	−0.0527254	−	0.0191905i	−0.368248	+	0.929728i	$0.620042\pi$
$194$	2.00208	−	11.3543i	0.143741	−	0.815195i
$195$	−0.328939	−	1.86551i	−0.0235558	−	0.133592i
$196$	−0.939693	+	0.342020i	−0.0671209	+	0.0244300i
$197$	5.61483	−	9.72517i	0.400040	−	0.692889i	−0.593690	−	0.804694i	$-0.702330\pi$
$197$	5.61483	−	9.72517i	0.400040	−	0.692889i	0.993730	+	0.111804i	$0.0356629\pi$
$198$	0.411353	+	0.712484i	0.0292336	+	0.0506340i
$199$	−13.6167	−	11.4258i	−0.965261	−	0.809951i	0.0165395	−	0.999863i	$-0.494735\pi$
$199$	−13.6167	−	11.4258i	−0.965261	−	0.809951i	−0.981801	+	0.189913i	$0.939180\pi$
$200$	−3.40055	−	2.85340i	−0.240455	−	0.201766i
$201$	−7.52903	−	13.0407i	−0.531057	−	0.919817i
$202$	−7.63710	+	13.2278i	−0.537344	+	0.930708i
$203$	−2.23830	+	0.814676i	−0.157098	+	0.0571790i
$204$	1.06227	+	6.02445i	0.0743740	+	0.421796i
$205$	0.116895	−	0.662943i	0.00816429	−	0.0463020i
$206$	−4.05263	−	1.47504i	−0.282360	−	0.102771i
$207$	−0.0668893	+	0.0561268i	−0.00464913	+	0.00390108i
$208$	−2.52931			−0.175376
$209$	3.58590	−	0.0368294i	0.248042	−	0.00254754i
$210$	0.748934			0.0516814
$211$	2.78243	−	2.33474i	0.191551	−	0.160730i	−0.541969	−	0.840399i	$-0.682321\pi$
$211$	2.78243	−	2.33474i	0.191551	−	0.160730i	0.733519	+	0.679669i	$0.237876\pi$
$212$	4.79593	+	1.74558i	0.329386	+	0.119887i
$213$	2.02278	−	11.4717i	0.138598	−	0.786030i
$214$	2.67864	+	15.1913i	0.183108	+	1.03846i
$215$	1.66108	−	0.604585i	0.113285	−	0.0412323i
$216$	−0.500000	+	0.866025i	−0.0340207	+	0.0589256i
$217$	0.177343	+	0.307167i	0.0120388	+	0.0208518i
$218$	6.76666	+	5.67791i	0.458296	+	0.384556i
$219$	−1.97868	−	1.66031i	−0.133707	−	0.112193i
$220$	0.308076	+	0.533604i	0.0207705	+	0.0359756i
$221$	7.73637	−	13.3998i	0.520405	−	0.901367i
$222$	0.443393	−	0.161382i	0.0297586	−	0.0108312i
$223$	0.711937	+	4.03759i	0.0476748	+	0.270377i	0.999322	−	0.0368156i	$-0.0117214\pi$
$223$	0.711937	+	4.03759i	0.0476748	+	0.270377i	−0.951647	+	0.307193i	$0.900610\pi$
$224$	0.173648	−	0.984808i	0.0116024	−	0.0658002i
$225$	4.17139	+	1.51826i	0.278092	+	0.101217i
$226$	2.16891	−	1.81993i	0.144274	−	0.121060i
$227$	−7.80803			−0.518237			−0.259119	−	0.965846i	$-0.583432\pi$
$227$	−7.80803			−0.518237			−0.259119	+	0.965846i	$0.583432\pi$
$228$	2.21810	+	3.75234i	0.146897	+	0.248504i
$229$	16.4397			1.08637			0.543183	−	0.839614i	$-0.317219\pi$
$229$	16.4397			1.08637			0.543183	+	0.839614i	$0.317219\pi$
$230$	−0.0500957	+	0.0420353i	−0.00330321	+	0.00277172i
$231$	0.773090	+	0.281382i	0.0508656	+	0.0185136i
$232$	0.413622	−	2.34577i	0.0271556	−	0.154007i
$233$	1.36305	+	7.73025i	0.0892965	+	0.506426i	0.996347	+	0.0854028i	$0.0272177\pi$
$233$	1.36305	+	7.73025i	0.0892965	+	0.506426i	−0.907050	+	0.421023i	$0.861671\pi$
$234$	2.37677	−	0.865074i	0.155374	−	0.0565516i
$235$	1.68427	−	2.91724i	0.109870	−	0.190300i
$236$	−2.56869	−	4.44910i	−0.167208	−	0.289612i
$237$	11.6757	+	9.79708i	0.758418	+	0.636389i
$238$	4.68619	+	3.93218i	0.303760	+	0.254885i
$239$	−5.94581	−	10.2984i	−0.384603	−	0.666151i	0.607111	−	0.794617i	$-0.292328\pi$
$239$	−5.94581	−	10.2984i	−0.384603	−	0.666151i	−0.991714	+	0.128466i	$0.958995\pi$
$240$	−0.374467	+	0.648596i	−0.0241718	+	0.0418667i
$241$	1.44934	−	0.527517i	0.0933603	−	0.0339804i	−0.294918	−	0.955523i	$-0.595292\pi$
$241$	1.44934	−	0.527517i	0.0933603	−	0.0339804i	0.388278	+	0.921542i	$0.373070\pi$
$242$	−1.79260	−	10.1663i	−0.115233	−	0.653516i
$243$	0.173648	−	0.984808i	0.0111395	−	0.0631754i
$244$	−10.2364	−	3.72576i	−0.655321	−	0.238517i
$245$	0.573717	−	0.481406i	0.0366534	−	0.0307559i
$246$	0.898838			0.0573078
$247$	1.80286	−	10.8766i	0.114713	−	0.692061i
$248$	−0.354686			−0.0225226
$249$	1.48873	−	1.24919i	0.0943441	−	0.0791641i
$250$	6.64294	+	2.41783i	0.420136	+	0.152917i
$251$	−0.174147	+	0.987635i	−0.0109920	+	0.0623390i	−0.989810	−	0.142392i	$-0.954521\pi$
$251$	−0.174147	+	0.987635i	−0.0109920	+	0.0623390i	0.978818	+	0.204731i	$0.0656318\pi$
$252$	0.173648	+	0.984808i	0.0109388	+	0.0620371i
$253$	−0.0675045	+	0.0245696i	−0.00424397	+	0.00154468i
$254$	1.15493	−	2.00040i	0.0724669	−	0.125516i
$255$	−2.29076	−	3.96771i	−0.143453	−	0.248468i
$256$	0.766044	+	0.642788i	0.0478778	+	0.0401742i
$257$	−7.82202	−	6.56345i	−0.487924	−	0.409417i	0.365357	−	0.930867i	$-0.380947\pi$
$257$	−7.82202	−	6.56345i	−0.487924	−	0.409417i	−0.853282	+	0.521450i	$0.825391\pi$
$258$	1.18014	+	2.04405i	0.0734720	+	0.127257i
$259$	0.235925	−	0.408633i	0.0146596	−	0.0253912i
$260$	1.78005	−	0.647883i	0.110394	−	0.0401800i
$261$	0.413622	+	2.34577i	0.0256025	+	0.145199i
$262$	−2.26361	+	12.8376i	−0.139846	+	0.793107i
$263$	−2.63402	−	0.958705i	−0.162421	−	0.0591163i	0.259530	−	0.965735i	$-0.416432\pi$
$263$	−2.63402	−	0.958705i	−0.162421	−	0.0591163i	−0.421951	+	0.906619i	$0.638655\pi$
$264$	−0.630229	+	0.528825i	−0.0387879	+	0.0325469i
$265$	−3.82235			−0.234805
$266$	4.11112	+	1.44869i	0.252069	+	0.0888246i
$267$	−5.52259			−0.337977
$268$	11.5351	−	9.67913i	0.704621	−	0.591247i
$269$	−19.6248	−	7.14284i	−1.19654	−	0.435506i	−0.334527	−	0.942386i	$-0.608577\pi$
$269$	−19.6248	−	7.14284i	−1.19654	−	0.435506i	−0.862017	+	0.506880i	$0.830799\pi$
$270$	0.130051	−	0.737556i	0.00791466	−	0.0448862i
$271$	−4.50584	−	25.5539i	−0.273710	−	1.55229i	−0.743029	−	0.669259i	$-0.766612\pi$
$271$	−4.50584	−	25.5539i	−0.273710	−	1.55229i	0.469319	−	0.883029i	$-0.344499\pi$
$272$	−5.74846	+	2.09227i	−0.348552	+	0.126862i
$273$	1.26465	−	2.19044i	0.0765403	−	0.132572i
$274$	5.39626	+	9.34660i	0.326000	+	0.564649i
$275$	2.79765	+	2.34751i	0.168705	+	0.141560i
$276$	−0.0668893	−	0.0561268i	−0.00402626	−	0.00337844i
$277$	8.19629	+	14.1964i	0.492468	+	0.852979i	0.999962	−	0.00867603i	$-0.00276170\pi$
$277$	8.19629	+	14.1964i	0.492468	+	0.852979i	−0.507495	+	0.861655i	$0.669428\pi$
$278$	−3.13968	+	5.43809i	−0.188306	+	0.326155i
$279$	0.333295	−	0.121310i	0.0199539	−	0.00726262i
$280$	0.130051	+	0.737556i	0.00777204	+	0.0440774i
$281$	−2.59704	+	14.7286i	−0.154927	+	0.878633i	0.803926	+	0.594729i	$0.202741\pi$
$281$	−2.59704	+	14.7286i	−0.154927	+	0.878633i	−0.958853	+	0.283904i	$0.908370\pi$
$282$	4.22653	+	1.53833i	0.251686	+	0.0916062i
$283$	−3.18802	+	2.67506i	−0.189508	+	0.159016i	−0.732605	−	0.680654i	$-0.761696\pi$
$283$	−3.18802	+	2.67506i	−0.189508	+	0.159016i	0.543097	+	0.839670i	$0.317251\pi$
$284$	11.6487			0.691223
$285$	−2.52219	−	2.07261i	−0.149402	−	0.122771i
$286$	2.08087			0.123045
$287$	0.688549	−	0.577762i	0.0406438	−	0.0341042i
$288$	−0.939693	−	0.342020i	−0.0553719	−	0.0201537i
$289$	3.54631	−	20.1121i	0.208606	−	1.18307i
$290$	0.309776	+	1.75682i	0.0181906	+	0.103164i
$291$	−10.8342	+	3.94332i	−0.635112	+	0.231162i
$292$	1.29149	−	2.23693i	0.0755788	−	0.130906i
$293$	−4.50617	−	7.80491i	−0.263253	−	0.455968i	0.703851	−	0.710347i	$-0.251462\pi$
$293$	−4.50617	−	7.80491i	−0.263253	−	0.455968i	−0.967104	+	0.254379i	$0.918129\pi$
$294$	0.766044	+	0.642788i	0.0446766	+	0.0374881i
$295$	2.94740	+	2.47316i	0.171604	+	0.143993i
$296$	0.235925	+	0.408633i	0.0137128	+	0.0237513i
$297$	0.411353	−	0.712484i	0.0238691	−	0.0413425i
$298$	0.0354871	−	0.0129163i	0.00205571	−	0.000748219i
$299$	0.0383508	+	0.217498i	0.00221788	+	0.0125782i
$300$	−0.770841	+	4.37166i	−0.0445045	+	0.252398i
$301$	2.21793	+	0.807260i	0.127839	+	0.0465297i
$302$	1.03895	−	0.871785i	0.0597850	−	0.0501656i
$303$	15.2742			0.877480
$304$	−3.31016	+	2.83599i	−0.189851	+	0.162655i
$305$	8.15844			0.467151
$306$	4.68619	−	3.93218i	0.267892	−	0.224788i
$307$	12.2992	+	4.47653i	0.701951	+	0.255489i	0.668243	−	0.743943i	$-0.267046\pi$
$307$	12.2992	+	4.47653i	0.701951	+	0.255489i	0.0337071	+	0.999432i	$0.489269\pi$
$308$	−0.142861	+	0.810207i	−0.00814028	+	0.0461658i
$309$	0.748895	+	4.24720i	0.0426032	+	0.241615i
$310$	0.249616	−	0.0908530i	0.0141773	−	0.00516010i
$311$	16.6125	−	28.7737i	0.942010	−	1.63161i	0.180380	−	0.983597i	$-0.442267\pi$
$311$	16.6125	−	28.7737i	0.942010	−	1.63161i	0.761630	−	0.648012i	$-0.224399\pi$
$312$	1.26465	+	2.19044i	0.0715969	+	0.124009i
$313$	9.71973	+	8.15582i	0.549392	+	0.460994i	0.874735	−	0.484602i	$-0.161035\pi$
$313$	9.71973	+	8.15582i	0.549392	+	0.460994i	−0.325343	+	0.945596i	$0.605480\pi$
$314$	2.13385	+	1.79051i	0.120420	+	0.101045i
$315$	−0.374467	−	0.648596i	−0.0210988	−	0.0365443i
$316$	−7.62077	+	13.1996i	−0.428702	+	0.742534i
$317$	−21.5422	+	7.84073i	−1.20993	+	0.440379i	−0.866680	−	0.498864i	$-0.833751\pi$
$317$	−21.5422	+	7.84073i	−1.20993	+	0.440379i	−0.343252	+	0.939243i	$0.611528\pi$
$318$	−0.886252	−	5.02618i	−0.0496985	−	0.281854i
$319$	−0.340289	+	1.92987i	−0.0190525	+	0.108052i
$320$	−0.703768	−	0.256151i	−0.0393418	−	0.0143193i
$321$	11.8168	−	9.91544i	0.659547	−	0.553426i
$322$	−0.0873178			−0.00486603
$323$	−4.89979	−	26.2110i	−0.272631	−	1.45842i
$324$	1.00000			0.0555556
$325$	8.60102	−	7.21711i	0.477099	−	0.400334i
$326$	−18.4623	−	6.71972i	−1.02253	−	0.372171i
$327$	1.53388	−	8.69906i	0.0848237	−	0.481059i
$328$	0.156081	+	0.885182i	0.00861816	+	0.0488760i
$329$	4.22653	−	1.53833i	0.233016	−	0.0848109i
$330$	0.308076	−	0.533604i	0.0169590	−	0.0293739i
$331$	−3.90678	−	6.76674i	−0.214736	−	0.371934i	0.738455	−	0.674303i	$-0.235556\pi$
$331$	−3.90678	−	6.76674i	−0.214736	−	0.371934i	−0.953191	+	0.302369i	$0.902222\pi$
$332$	1.48873	+	1.24919i	0.0817044	+	0.0685582i
$333$	−0.361457	−	0.303299i	−0.0198077	−	0.0166207i
$334$	10.6472	+	18.4414i	0.582587	+	1.00907i
$335$	−5.63875	+	9.76660i	−0.308078	+	0.533606i
$336$	−0.939693	+	0.342020i	−0.0512644	+	0.0186587i
$337$	2.77901	+	15.7606i	0.151382	+	0.858532i	0.962019	+	0.272983i	$0.0880101\pi$
$337$	2.77901	+	15.7606i	0.151382	+	0.858532i	−0.810637	+	0.585550i	$0.800879\pi$
$338$	−1.14653	+	6.50230i	−0.0623631	+	0.353679i
$339$	−2.66056	−	0.968366i	−0.144502	−	0.0525944i
$340$	3.50965	−	2.94494i	0.190337	−	0.159712i
$341$	0.291802			0.0158020
$342$	2.14057	−	3.79710i	0.115749	−	0.205324i
$343$	1.00000			0.0539949
$344$	−1.80807	+	1.51715i	−0.0974847	+	0.0817994i
$345$	0.0614515	+	0.0223665i	0.00330844	+	0.00120417i
$346$	−1.18212	+	6.70413i	−0.0635511	+	0.360416i
$347$	6.03811	+	34.2438i	0.324143	+	1.83831i	0.515631	+	0.856811i	$0.327558\pi$
$347$	6.03811	+	34.2438i	0.324143	+	1.83831i	−0.191488	+	0.981495i	$0.561331\pi$
$348$	−2.23830	+	0.814676i	−0.119986	+	0.0436712i
$349$	6.84422	−	11.8545i	0.366363	−	0.634559i	−0.622631	−	0.782516i	$-0.713936\pi$
$349$	6.84422	−	11.8545i	0.366363	−	0.634559i	0.988994	+	0.147956i	$0.0472695\pi$
$350$	2.21955	+	3.84437i	0.118640	+	0.205490i
$351$	−1.93756	−	1.62581i	−0.103419	−	0.0867791i
$352$	−0.630229	−	0.528825i	−0.0335913	−	0.0281865i
$353$	−14.5392	−	25.1826i	−0.773841	−	1.34033i	−0.935443	−	0.353477i	$-0.884999\pi$
$353$	−14.5392	−	25.1826i	−0.773841	−	1.34033i	0.161602	−	0.986856i	$-0.448334\pi$
$354$	−2.56869	+	4.44910i	−0.136524	+	0.236467i
$355$	−8.19799	+	2.98382i	−0.435104	+	0.158365i
$356$	−0.958988	−	5.43869i	−0.0508263	−	0.288250i
$357$	1.06227	−	6.02445i	0.0562214	−	0.318848i
$358$	5.14339	+	1.87204i	0.271837	+	0.0989405i
$359$	5.21497	−	4.37588i	0.275236	−	0.230950i	−0.494712	−	0.869057i	$-0.664727\pi$
$359$	5.21497	−	4.37588i	0.275236	−	0.230950i	0.769948	+	0.638107i	$0.220282\pi$
$360$	0.748934			0.0394723
$361$	−9.83596	−	16.2559i	−0.517682	−	0.855573i
$362$	13.2015			0.693856
$363$	−7.90800	+	6.63560i	−0.415062	+	0.348278i
$364$	2.37677	+	0.865074i	0.124577	+	0.0453422i
$365$	−0.335920	+	1.90509i	−0.0175828	+	0.0997172i
$366$	1.89162	+	10.7279i	0.0988765	+	0.560756i
$367$	−20.8397	+	7.58505i	−1.08783	+	0.395936i	−0.822815	−	0.568309i	$-0.807598\pi$
$367$	−20.8397	+	7.58505i	−1.08783	+	0.395936i	−0.265011	+	0.964245i	$0.585376\pi$
$368$	0.0436589	−	0.0756194i	0.00227588	−	0.00394193i
$369$	−0.449419	−	0.778416i	−0.0233958	−	0.0405227i
$370$	−0.270708	−	0.227151i	−0.0140734	−	0.0118090i
$371$	−3.90968	−	3.28061i	−0.202980	−	0.170321i
$372$	0.177343	+	0.307167i	0.00919480	+	0.0159259i
$373$	5.37022	−	9.30150i	0.278060	−	0.481614i	−0.692843	−	0.721089i	$-0.743642\pi$
$373$	5.37022	−	9.30150i	0.278060	−	0.481614i	0.970902	+	0.239475i	$0.0769754\pi$
$374$	4.72929	−	1.72132i	0.244546	−	0.0890074i
$375$	−1.22756	−	6.96187i	−0.0633912	−	0.359509i
$376$	−0.781031	+	4.42944i	−0.0402786	+	0.228431i
$377$	5.66136	+	2.06057i	0.291575	+	0.106125i
$378$	0.766044	−	0.642788i	0.0394011	−	0.0330614i
$379$	−26.6152			−1.36713			−0.683567	−	0.729888i	$-0.739572\pi$
$379$	−26.6152			−1.36713			−0.683567	+	0.729888i	$0.739572\pi$
$380$	1.60314	−	2.84378i	0.0822395	−	0.145883i
$381$	−2.30986			−0.118338
$382$	−11.4724	+	9.62645i	−0.586977	+	0.492532i
$383$	−11.5416	−	4.20080i	−0.589749	−	0.214651i	0.0298703	−	0.999554i	$-0.490491\pi$
$383$	−11.5416	−	4.20080i	−0.589749	−	0.214651i	−0.619619	+	0.784903i	$0.712713\pi$
$384$	0.173648	−	0.984808i	0.00886145	−	0.0502558i
$385$	−0.106994	−	0.606792i	−0.00545291	−	0.0309250i
$386$	−0.732484	+	0.266603i	−0.0372825	+	0.0135697i
$387$	1.18014	−	2.04405i	0.0599897	−	0.103905i
$388$	−5.76475	−	9.98485i	−0.292661	−	0.506904i
$389$	8.37600	+	7.02830i	0.424680	+	0.356349i	0.829940	−	0.557853i	$-0.188375\pi$
$389$	8.37600	+	7.02830i	0.424680	+	0.356349i	−0.405260	+	0.914201i	$0.632819\pi$
$390$	−1.45111	−	1.21762i	−0.0734796	−	0.0616567i
$391$	0.267078	+	0.462593i	0.0135067	+	0.0233943i
$392$	−0.500000	+	0.866025i	−0.0252538	+	0.0437409i
$393$	12.2495	−	4.45844i	0.617903	−	0.224898i
$394$	−1.95001	−	11.0591i	−0.0982401	−	0.557147i
$395$	1.98218	−	11.2415i	0.0997343	−	0.565621i
$396$	0.773090	+	0.281382i	0.0388493	+	0.0141400i
$397$	−28.0351	+	23.5243i	−1.40704	+	1.18065i	−0.449172	+	0.893445i	$0.648281\pi$
$397$	−28.0351	+	23.5243i	−1.40704	+	1.18065i	−0.957870	+	0.287203i	$0.907274\pi$
$398$	−17.7753			−0.890996
$399$	−0.800961	−	4.28468i	−0.0400982	−	0.214502i
$400$	−4.43910			−0.221955
$401$	9.57303	−	8.03272i	0.478054	−	0.401135i	−0.371668	−	0.928366i	$-0.621214\pi$
$401$	9.57303	−	8.03272i	0.478054	−	0.401135i	0.849722	+	0.527231i	$0.176770\pi$
$402$	−14.1499	−	5.15016i	−0.705735	−	0.256867i
$403$	0.155781	−	0.883480i	0.00776002	−	0.0440093i
$404$	2.65234	+	15.0421i	0.131959	+	0.748375i
$405$	−0.703768	+	0.256151i	−0.0349705	+	0.0127282i
$406$	−1.19098	+	2.06283i	−0.0591072	+	0.102377i
$407$	−0.194096	−	0.336185i	−0.00962100	−	0.0166641i
$408$	4.68619	+	3.93218i	0.232001	+	0.194672i
$409$	14.9324	+	12.5298i	0.738361	+	0.619558i	0.932397	−	0.361436i	$-0.117713\pi$
$409$	14.9324	+	12.5298i	0.738361	+	0.619558i	−0.194036	+	0.980994i	$0.562158\pi$
$410$	−0.336585	−	0.582983i	−0.0166228	−	0.0287915i
$411$	5.39626	−	9.34660i	0.266178	−	0.461034i
$412$	−4.05263	+	1.47504i	−0.199659	+	0.0726698i
$413$	0.892097	+	5.05933i	0.0438972	+	0.248954i
$414$	−0.0151626	+	0.0859912i	−0.000745200	+	0.00422624i
$415$	−1.36770	−	0.497801i	−0.0671377	−	0.0244361i
$416$	−1.93756	+	1.62581i	−0.0949967	+	0.0797117i
$417$	6.27936			0.307502
$418$	2.72329	−	2.33319i	0.133200	−	0.114120i
$419$	14.6132			0.713902			0.356951	−	0.934123i	$-0.383816\pi$
$419$	14.6132			0.713902			0.356951	+	0.934123i	$0.383816\pi$
$420$	0.573717	−	0.481406i	0.0279945	−	0.0234902i
$421$	−16.1430	−	5.87557i	−0.786761	−	0.286358i	−0.0827720	−	0.996569i	$-0.526377\pi$
$421$	−16.1430	−	5.87557i	−0.786761	−	0.286358i	−0.703989	+	0.710211i	$0.748600\pi$
$422$	0.630727	−	3.57703i	0.0307033	−	0.174127i
$423$	−0.781031	−	4.42944i	−0.0379750	−	0.215367i
$424$	4.79593	−	1.74558i	0.232911	−	0.0847726i
$425$	13.5778	−	23.5175i	0.658622	−	1.14077i
$426$	−5.82435	−	10.0881i	−0.282191	−	0.488769i
$427$	8.34482	+	7.00214i	0.403834	+	0.338857i
$428$	11.8168	+	9.91544i	0.571185	+	0.479281i
$429$	−1.04044	−	1.80209i	−0.0502328	−	0.0870057i
$430$	0.883844	−	1.53086i	0.0426227	−	0.0738247i
$431$	6.84354	−	2.49084i	0.329642	−	0.119980i	−0.171897	−	0.985115i	$-0.554990\pi$
$431$	6.84354	−	2.49084i	0.329642	−	0.119980i	0.501539	+	0.865135i	$0.332767\pi$
$432$	0.173648	+	0.984808i	0.00835465	+	0.0473816i
$433$	1.87603	−	10.6395i	0.0901563	−	0.511302i	−0.905968	−	0.423346i	$-0.860855\pi$
$433$	1.87603	−	10.6395i	0.0901563	−	0.511302i	0.996124	−	0.0879559i	$-0.0280335\pi$
$434$	0.333295	+	0.121310i	0.0159987	+	0.00582305i
$435$	1.36657	−	1.14669i	0.0655219	−	0.0549794i
$436$	8.83325			0.423036
$437$	0.294061	+	0.241644i	0.0140668	+	0.0115594i
$438$	−2.58298			−0.123420
$439$	−20.1999	+	16.9497i	−0.964088	+	0.808966i	−0.981613	−	0.190881i	$-0.938866\pi$
$439$	−20.1999	+	16.9497i	−0.964088	+	0.808966i	0.0175255	+	0.999846i	$0.494421\pi$
$440$	0.578994	+	0.210737i	0.0276025	+	0.0100465i
$441$	0.173648	−	0.984808i	0.00826896	−	0.0468956i
$442$	−2.68681	−	15.2377i	−0.127799	−	0.724782i
$443$	11.8795	−	4.32379i	0.564413	−	0.205429i	−0.0440258	−	0.999030i	$-0.514018\pi$
$443$	11.8795	−	4.32379i	0.564413	−	0.205429i	0.608439	+	0.793601i	$0.291796\pi$
$444$	0.235925	−	0.408633i	0.0111965	−	0.0193929i
$445$	2.06803	+	3.58193i	0.0980340	+	0.169800i
$446$	3.14069	+	2.63535i	0.148716	+	0.124788i
$447$	−0.0289294	−	0.0242746i	−0.00136831	−	0.00114815i
$448$	−0.500000	−	0.866025i	−0.0236228	−	0.0409159i
$449$	13.7464	−	23.8094i	0.648732	−	1.12364i	−0.334694	−	0.942327i	$-0.608633\pi$
$449$	13.7464	−	23.8094i	0.648732	−	1.12364i	0.983426	−	0.181310i	$-0.0580337\pi$
$450$	4.17139	−	1.51826i	0.196641	−	0.0715715i
$451$	−0.128409	−	0.728244i	−0.00604655	−	0.0342917i
$452$	0.491652	−	2.78830i	0.0231254	−	0.131151i
$453$	−1.27446	−	0.463867i	−0.0598795	−	0.0217944i
$454$	−5.98130	+	5.01890i	−0.280716	+	0.235549i
$455$	−1.89428			−0.0888054
$456$	4.11112	+	1.44869i	0.192521	+	0.0678409i
$457$	−34.6873			−1.62260			−0.811301	−	0.584629i	$-0.801240\pi$
$457$	−34.6873			−1.62260			−0.811301	+	0.584629i	$0.801240\pi$
$458$	12.5935	−	10.5672i	0.588458	−	0.493775i
$459$	−5.74846	−	2.09227i	−0.268315	−	0.0976587i
$460$	−0.0113558	+	0.0644018i	−0.000529466	+	0.00300275i
$461$	3.83667	+	21.7588i	0.178691	+	1.01341i	0.933796	+	0.357805i	$0.116475\pi$
$461$	3.83667	+	21.7588i	0.178691	+	1.01341i	−0.755105	+	0.655604i	$0.772414\pi$
$462$	0.773090	−	0.281382i	0.0359674	−	0.0130911i
$463$	11.8535	−	20.5309i	0.550879	−	0.954151i	−0.447332	−	0.894368i	$-0.647626\pi$
$463$	11.8535	−	20.5309i	0.550879	−	0.954151i	0.998211	−	0.0597831i	$-0.0190409\pi$
$464$	−1.19098	−	2.06283i	−0.0552897	−	0.0957646i
$465$	−0.203489	−	0.170748i	−0.00943658	−	0.00791823i
$466$	6.01307	+	5.04556i	0.278550	+	0.233731i
$467$	8.83472	+	15.3022i	0.408822	+	0.708101i	0.994758	−	0.102257i	$-0.0326063\pi$
$467$	8.83472	+	15.3022i	0.408822	+	0.708101i	−0.585936	+	0.810357i	$0.699273\pi$
$468$	1.26465	−	2.19044i	0.0584586	−	0.101253i
$469$	−14.1499	+	5.15016i	−0.653384	+	0.237812i
$470$	−0.584941	−	3.31736i	−0.0269813	−	0.153019i
$471$	0.483705	−	2.74323i	0.0222880	−	0.126401i
$472$	−4.82756	−	1.75709i	−0.222206	−	0.0808765i
$473$	1.48751	−	1.24817i	0.0683958	−	0.0573909i
$474$	15.2415			0.700067
$475$	3.16414	−	19.0891i	0.145181	−	0.875869i
$476$	6.11738			0.280390
$477$	−3.90968	+	3.28061i	−0.179012	+	0.150209i
$478$	−11.1745	−	4.06717i	−0.511108	−	0.186028i
$479$	3.95340	−	22.4209i	0.180636	−	1.02444i	−0.750800	−	0.660529i	$-0.770332\pi$
$479$	3.95340	−	22.4209i	0.180636	−	1.02444i	0.931436	−	0.363906i	$-0.118557\pi$
$480$	0.130051	+	0.737556i	0.00593599	+	0.0336647i
$481$	−1.12148	+	0.408184i	−0.0511350	+	0.0186116i
$482$	0.771179	−	1.33572i	0.0351262	−	0.0608404i
$483$	0.0436589	+	0.0756194i	0.00198655	+	0.00344080i
$484$	−7.90800	−	6.63560i	−0.359454	−	0.301618i
$485$	6.61467	+	5.55037i	0.300357	+	0.252029i
$486$	−0.500000	−	0.866025i	−0.0226805	−	0.0392837i
$487$	−2.59750	+	4.49900i	−0.117704	+	0.203869i	−0.918857	−	0.394590i	$-0.870887\pi$
$487$	−2.59750	+	4.49900i	−0.117704	+	0.203869i	0.801153	+	0.598459i	$0.204220\pi$
$488$	−10.2364	+	3.72576i	−0.463382	+	0.168657i
$489$	3.41169	+	19.3487i	0.154282	+	0.874977i
$490$	0.130051	−	0.737556i	0.00587511	−	0.0333194i
$491$	−2.19825	−	0.800096i	−0.0992055	−	0.0361078i	0.291941	−	0.956436i	$-0.405699\pi$
$491$	−2.19825	−	0.800096i	−0.0992055	−	0.0361078i	−0.391146	+	0.920329i	$0.627921\pi$
$492$	0.688549	−	0.577762i	0.0310422	−	0.0260475i
$493$	14.5713			0.656259
$494$	−5.61026	−	9.49081i	−0.252418	−	0.427012i
$495$	−0.616152			−0.0276940
$496$	−0.271705	+	0.227988i	−0.0121999	+	0.0102369i
$497$	−10.9462	−	3.98409i	−0.491004	−	0.178711i
$498$	0.337467	−	1.91387i	0.0151222	−	0.0857625i
$499$	−4.59349	−	26.0510i	−0.205633	−	1.16620i	−0.896441	−	0.443164i	$-0.853856\pi$
$499$	−4.59349	−	26.0510i	−0.205633	−	1.16620i	0.690808	−	0.723039i	$-0.257255\pi$
$500$	6.64294	−	2.41783i	0.297081	−	0.108129i
$501$	10.6472	−	18.4414i	0.475680	−	0.823902i
$502$	0.501435	+	0.868511i	0.0223802	+	0.0387636i
$503$	22.1574	+	18.5923i	0.987951	+	0.828989i	0.985270	−	0.171007i	$-0.0547021\pi$
$503$	22.1574	+	18.5923i	0.987951	+	0.828989i	0.00268132	+	0.999996i	$0.499147\pi$
$504$	0.766044	+	0.642788i	0.0341223	+	0.0286320i
$505$	−5.71968	−	9.90678i	−0.254523	−	0.440846i
$506$	−0.0359184	+	0.0622125i	−0.00159677	+	0.00276568i
$507$	6.20442	−	2.25823i	0.275548	−	0.100291i
$508$	−0.401104	−	2.27477i	−0.0177961	−	0.100927i
$509$	−3.82153	+	21.6730i	−0.169386	+	0.960638i	0.775039	+	0.631913i	$0.217730\pi$
$509$	−3.82153	+	21.6730i	−0.169386	+	0.960638i	−0.944426	+	0.328725i	$0.893381\pi$
$510$	−4.30522	−	1.56697i	−0.190638	−	0.0693867i
$511$	−1.97868	+	1.66031i	−0.0875316	+	0.0734477i
$512$	1.00000			0.0441942
$513$	−4.35867	+	0.0447662i	−0.192440	+	0.00197648i
$514$	−10.2109			−0.450384
$515$	2.47428	−	2.07617i	0.109030	−	0.0914868i
$516$	2.21793	+	0.807260i	0.0976389	+	0.0355376i
$517$	0.642558	−	3.64413i	0.0282597	−	0.160269i
$518$	−0.0819357	−	0.464681i	−0.00360005	−	0.0204169i
$519$	6.39701	−	2.32832i	0.280797	−	0.102202i
$520$	0.947142	−	1.64050i	0.0415349	−	0.0719406i
$521$	0.389177	+	0.674074i	0.0170501	+	0.0295317i	0.874425	−	0.485161i	$-0.161239\pi$
$521$	0.389177	+	0.674074i	0.0170501	+	0.0295317i	−0.857374	+	0.514693i	$0.827906\pi$
$522$	1.82468	+	1.53109i	0.0798642	+	0.0670140i
$523$	31.5690	+	26.4895i	1.38041	+	1.15830i	0.969059	+	0.246830i	$0.0793889\pi$
$523$	31.5690	+	26.4895i	1.38041	+	1.15830i	0.411355	+	0.911475i	$0.365056\pi$
$524$	6.51780	+	11.2892i	0.284731	+	0.493169i
$525$	2.21955	−	3.84437i	0.0968690	−	0.167782i
$526$	−2.63402	+	0.958705i	−0.114849	+	0.0418015i
$527$	−0.376773	−	2.13678i	−0.0164125	−	0.0930798i
$528$	−0.142861	+	0.810207i	−0.00621724	+	0.0352597i
$529$	21.6058	+	7.86386i	0.939381	+	0.341907i
$530$	−2.92809	+	2.45696i	−0.127188	+	0.106724i
$531$	5.13738			0.222943
$532$	4.08050	−	1.53282i	0.176912	−	0.0664561i
$533$	−2.27344			−0.0984734
$534$	−4.23055	+	3.54985i	−0.183074	+	0.153617i
$535$	−10.8561	−	3.95130i	−0.469350	−	0.170830i
$536$	2.61480	−	14.8293i	0.112942	−	0.640528i
$537$	−0.950461	−	5.39033i	−0.0410154	−	0.232610i
$538$	−19.6248	+	7.14284i	−0.846084	+	0.307950i
$539$	0.411353	−	0.712484i	0.0177182	−	0.0306889i
$540$	−0.374467	−	0.648596i	−0.0161145	−	0.0279111i
$541$	−3.82810	−	3.21216i	−0.164583	−	0.138102i	0.556777	−	0.830662i	$-0.312038\pi$
$541$	−3.82810	−	3.21216i	−0.164583	−	0.138102i	−0.721359	+	0.692561i	$0.756482\pi$
$542$	−19.8774	−	16.6791i	−0.853807	−	0.716429i
$543$	−6.60076	−	11.4328i	−0.283266	−	0.490630i
$544$	−3.05869	+	5.29781i	−0.131140	+	0.227142i
$545$	−6.21656	+	2.26264i	−0.266288	+	0.0969210i
$546$	−0.439209	−	2.49088i	−0.0187964	−	0.106600i
$547$	−7.32057	+	41.5170i	−0.313005	+	1.77514i	0.270189	+	0.962807i	$0.412914\pi$
$547$	−7.32057	+	41.5170i	−0.313005	+	1.77514i	−0.583194	+	0.812333i	$0.698197\pi$
$548$	10.1417	+	3.69126i	0.433230	+	0.157683i
$549$	8.34482	−	7.00214i	0.356148	−	0.298844i
$550$	3.65207			0.155725
$551$	9.71956	−	3.65110i	0.414067	−	0.155542i
$552$	−0.0873178			−0.00371649
$553$	11.6757	−	9.79708i	0.496501	−	0.416614i
$554$	15.4040	+	5.60659i	0.654453	+	0.238201i
$555$	−0.0613645	+	0.348015i	−0.00260478	+	0.0147724i
$556$	1.09040	+	6.18397i	0.0462433	+	0.262259i
$557$	14.6133	−	5.31881i	0.619185	−	0.225365i	−0.0133322	−	0.999911i	$-0.504244\pi$
$557$	14.6133	−	5.31881i	0.619185	−	0.225365i	0.632517	+	0.774546i	$0.282022\pi$
$558$	0.177343	−	0.307167i	0.00750752	−	0.0130034i
$559$	−2.98492	−	5.17004i	−0.126249	−	0.218669i
$560$	0.573717	+	0.481406i	0.0242440	+	0.0203431i
$561$	−3.85535	−	3.23503i	−0.162773	−	0.136583i
$562$	7.47789	+	12.9521i	0.315436	+	0.546351i
$563$	15.7432	−	27.2681i	0.663498	−	1.14921i	−0.316192	−	0.948695i	$-0.602404\pi$
$563$	15.7432	−	27.2681i	0.663498	−	1.14921i	0.979690	−	0.200518i	$-0.0642624\pi$
$564$	4.22653	−	1.53833i	0.177969	−	0.0647754i
$565$	0.368215	+	2.08825i	0.0154909	+	0.0878534i
$566$	−0.722665	+	4.09844i	−0.0303759	+	0.172270i
$567$	−0.939693	−	0.342020i	−0.0394634	−	0.0143635i
$568$	8.92342	−	7.48764i	0.374419	−	0.314174i
$569$	−15.9460			−0.668491			−0.334246	−	0.942486i	$-0.608482\pi$
$569$	−15.9460			−0.668491			−0.334246	+	0.942486i	$0.608482\pi$
$570$	−3.26436	+	0.0335269i	−0.136729	+	0.00140429i
$571$	−25.3825			−1.06223			−0.531113	−	0.847301i	$-0.678226\pi$
$571$	−25.3825			−1.06223			−0.531113	+	0.847301i	$0.678226\pi$
$572$	1.59404	−	1.33756i	0.0666503	−	0.0559262i
$573$	14.0729	+	5.12213i	0.587905	+	0.213980i
$574$	0.156081	−	0.885182i	0.00651472	−	0.0369468i
$575$	0.0673081	+	0.381723i	0.00280694	+	0.0159190i
$576$	−0.939693	+	0.342020i	−0.0391539	+	0.0142508i
$577$	−6.49475	+	11.2492i	−0.270380	+	0.468312i	−0.968959	−	0.247221i	$-0.920483\pi$
$577$	−6.49475	+	11.2492i	−0.270380	+	0.468312i	0.698579	+	0.715533i	$0.253816\pi$
$578$	−10.2112	−	17.6863i	−0.424730	−	0.735653i
$579$	0.597127	+	0.501049i	0.0248157	+	0.0208229i
$580$	1.36657	+	1.14669i	0.0567436	+	0.0476135i
$581$	−0.971697	−	1.68303i	−0.0403128	−	0.0698238i
$582$	−5.76475	+	9.98485i	−0.238957	+	0.413885i
$583$	−3.94564	+	1.43609i	−0.163412	+	0.0594770i
$584$	−0.448530	−	2.54374i	−0.0185603	−	0.105261i
$585$	−0.328939	+	1.86551i	−0.0136000	+	0.0771292i
$586$	−8.46883	−	3.08240i	−0.349844	−	0.127333i
$587$	4.22701	−	3.54689i	0.174468	−	0.146396i	−0.551373	−	0.834259i	$-0.685896\pi$
$587$	4.22701	−	3.54689i	0.174468	−	0.146396i	0.725840	+	0.687864i	$0.241451\pi$
$588$	1.00000			0.0412393
$589$	−0.786729	−	1.33090i	−0.0324166	−	0.0548388i
$590$	3.84756			0.158402
$591$	−8.60242	+	7.21828i	−0.353856	+	0.296921i
$592$	0.443393	+	0.161382i	0.0182233	+	0.00663276i
$593$	3.45691	−	19.6051i	0.141958	−	0.805086i	−0.827801	−	0.561022i	$-0.810408\pi$
$593$	3.45691	−	19.6051i	0.141958	−	0.805086i	0.969759	−	0.244064i	$-0.0784806\pi$
$594$	−0.142861	−	0.810207i	−0.00586167	−	0.0332432i
$595$	−4.30522	+	1.56697i	−0.176497	+	0.0642396i
$596$	0.0188823	−	0.0327051i	0.000773450	−	0.00133965i
$597$	8.88766	+	15.3939i	0.363748	+	0.630030i
$598$	0.169184	+	0.141962i	0.00691843	+	0.00580525i
$599$	8.50657	+	7.13786i	0.347569	+	0.291645i	0.799813	−	0.600249i	$-0.204932\pi$
$599$	8.50657	+	7.13786i	0.347569	+	0.291645i	−0.452244	+	0.891894i	$0.649376\pi$
$600$	2.21955	+	3.84437i	0.0906127	+	0.156946i
$601$	10.6390	−	18.4273i	0.433975	−	0.751666i	−0.563237	−	0.826296i	$-0.690444\pi$
$601$	10.6390	−	18.4273i	0.433975	−	0.751666i	0.997211	+	0.0746294i	$0.0237774\pi$
$602$	2.21793	−	0.807260i	0.0903960	−	0.0329015i
$603$	2.61480	+	14.8293i	0.106483	+	0.603895i
$604$	0.235511	−	1.33565i	0.00958282	−	0.0543469i
$605$	7.26511	+	2.64428i	0.295369	+	0.107505i
$606$	11.7007	−	9.81806i	0.475309	−	0.398832i
$607$	−6.54064			−0.265476			−0.132738	−	0.991151i	$-0.542377\pi$
$607$	−6.54064			−0.265476			−0.132738	+	0.991151i	$0.542377\pi$
$608$	−0.712789	+	4.30022i	−0.0289074	+	0.174397i
$609$	2.38195			0.0965216
$610$	6.24973	−	5.24414i	0.253044	−	0.212329i
$611$	−10.6902	−	3.89091i	−0.432478	−	0.157409i
$612$	1.06227	−	6.02445i	0.0429398	−	0.243524i
$613$	0.916361	+	5.19694i	0.0370115	+	0.209903i	0.997705	−	0.0677080i	$-0.0215686\pi$
$613$	0.916361	+	5.19694i	0.0370115	+	0.209903i	−0.960694	+	0.277611i	$0.910458\pi$
$614$	12.2992	−	4.47653i	0.496354	−	0.180658i
$615$	−0.336585	+	0.582983i	−0.0135724	+	0.0235081i
$616$	0.411353	+	0.712484i	0.0165739	+	0.0287068i
$617$	15.4569	+	12.9699i	0.622270	+	0.522147i	0.898516	−	0.438940i	$-0.144646\pi$
$617$	15.4569	+	12.9699i	0.622270	+	0.522147i	−0.276246	+	0.961087i	$0.589091\pi$
$618$	3.30373	+	2.77216i	0.132896	+	0.111513i
$619$	0.260972	+	0.452016i	0.0104893	+	0.0181681i	0.871222	−	0.490888i	$-0.163328\pi$
$619$	0.260972	+	0.452016i	0.0104893	+	0.0181681i	−0.860733	+	0.509057i	$0.829994\pi$
$620$	0.132818	−	0.230048i	0.00533410	−	0.00923894i
$621$	0.0820519	−	0.0298644i	0.00329263	−	0.00119842i
$622$	−5.76947	−	32.7203i	−0.231335	−	1.31196i
$623$	−0.958988	+	5.43869i	−0.0384210	+	0.217897i
$624$	2.37677	+	0.865074i	0.0951470	+	0.0346307i
$625$	12.9470	−	10.8638i	0.517879	−	0.434552i
$626$	12.6882			0.507123
$627$	−3.38224	−	1.19184i	−0.135074	−	0.0475976i
$628$	2.78555			0.111155
$629$	−2.21117	+	1.85540i	−0.0881653	+	0.0739794i
$630$	−0.703768	−	0.256151i	−0.0280388	−	0.0102053i
$631$	−1.65297	+	9.37447i	−0.0658038	+	0.373192i	0.934067	+	0.357099i	$0.116234\pi$
$631$	−1.65297	+	9.37447i	−0.0658038	+	0.373192i	−0.999870	+	0.0160932i	$0.994877\pi$
$632$	2.64667	+	15.0100i	0.105279	+	0.597065i
$633$	−3.41316	+	1.24229i	−0.135661	+	0.0493766i
$634$	−11.4624	+	19.8534i	−0.455229	+	0.788480i
$635$	0.864968	+	1.49817i	0.0343252	+	0.0594530i
$636$	−3.90968	−	3.28061i	−0.155029	−	0.130085i
$637$	−1.93756	−	1.62581i	−0.0767690	−	0.0644168i
$638$	0.979823	+	1.69710i	0.0387916	+	0.0671890i
$639$	−5.82435	+	10.0881i	−0.230408	+	0.399078i
$640$	−0.703768	+	0.256151i	−0.0278189	+	0.0101252i
$641$	−4.61883	−	26.1947i	−0.182433	−	1.03463i	−0.929210	−	0.369553i	$-0.879511\pi$
$641$	−4.61883	−	26.1947i	−0.182433	−	1.03463i	0.746777	−	0.665075i	$-0.231600\pi$
$642$	2.67864	−	15.1913i	0.105718	−	0.599554i
$643$	17.3605	+	6.31871i	0.684632	+	0.249186i	0.660835	−	0.750531i	$-0.270202\pi$
$643$	17.3605	+	6.31871i	0.684632	+	0.249186i	0.0237970	+	0.999717i	$0.492424\pi$
$644$	−0.0668893	+	0.0561268i	−0.00263581	+	0.00221171i
$645$	−1.76769			−0.0696026
$646$	−20.6016	−	16.9293i	−0.810558	−	0.666074i
$647$	28.0640			1.10331			0.551656	−	0.834072i	$-0.313996\pi$
$647$	28.0640			1.10331			0.551656	+	0.834072i	$0.313996\pi$
$648$	0.766044	−	0.642788i	0.0300931	−	0.0252511i
$649$	3.97166	+	1.44557i	0.155901	+	0.0567434i
$650$	1.94969	−	11.0573i	0.0764733	−	0.433701i
$651$	−0.0615905	−	0.349297i	−0.00241392	−	0.0136900i
$652$	−18.4623	+	6.71972i	−0.723038	+	0.263164i
$653$	−1.27797	+	2.21351i	−0.0500108	+	0.0866213i	−0.889947	−	0.456064i	$-0.849259\pi$
$653$	−1.27797	+	2.21351i	−0.0500108	+	0.0866213i	0.839936	+	0.542685i	$0.182592\pi$
$654$	−4.41663	−	7.64982i	−0.172704	−	0.299132i
$655$	−7.47874	−	6.27541i	−0.292219	−	0.245201i
$656$	0.688549	+	0.577762i	0.0268833	+	0.0225578i
$657$	1.29149	+	2.23693i	0.0503859	+	0.0872709i
$658$	2.24889	−	3.89519i	0.0876708	−	0.151850i
$659$	−22.0889	+	8.03969i	−0.860460	+	0.313182i	−0.734298	−	0.678828i	$-0.762488\pi$
$659$	−22.0889	+	8.03969i	−0.860460	+	0.313182i	−0.126163	+	0.992010i	$0.540266\pi$
$660$	−0.106994	−	0.606792i	−0.00416473	−	0.0236193i
$661$	−8.74280	+	49.5829i	−0.340055	+	1.92855i	0.0300220	+	0.999549i	$0.490442\pi$
$661$	−8.74280	+	49.5829i	−0.340055	+	1.92855i	−0.370077	+	0.929001i	$0.620669\pi$
$662$	−7.34234	−	2.67239i	−0.285368	−	0.103866i
$663$	−11.8528	+	9.94568i	−0.460325	+	0.386258i
$664$	1.94339			0.0754183
$665$	−2.47909	+	2.12397i	−0.0961351	+	0.0823641i
$666$	−0.471849			−0.0182838
$667$	−0.159327	+	0.133691i	−0.00616917	+	0.00517655i
$668$	20.0101	+	7.28309i	0.774215	+	0.281791i
$669$	0.711937	−	4.03759i	0.0275251	−	0.156102i
$670$	1.95832	+	11.1062i	0.0756564	+	0.429069i
$671$	8.42158	−	3.06520i	0.325111	−	0.118331i
$672$	−0.500000	+	0.866025i	−0.0192879	+	0.0334077i
$673$	1.83552	+	3.17922i	0.0707543	+	0.122550i	0.899232	−	0.437472i	$-0.144126\pi$
$673$	1.83552	+	3.17922i	0.0707543	+	0.122550i	−0.828478	+	0.560022i	$0.810793\pi$
$674$	12.2595	+	10.2870i	0.472220	+	0.396239i
$675$	−3.40055	−	2.85340i	−0.130887	−	0.109827i
$676$	3.30130	+	5.71803i	0.126973	+	0.219924i
$677$	−20.1914	+	34.9726i	−0.776020	+	1.34411i	0.158200	+	0.987407i	$0.449431\pi$
$677$	−20.1914	+	34.9726i	−0.776020	+	1.34411i	−0.934220	+	0.356698i	$0.883902\pi$
$678$	−2.66056	+	0.968366i	−0.102178	+	0.0371899i
$679$	2.00208	+	11.3543i	0.0768327	+	0.435740i
$680$	0.795572	−	4.51192i	0.0305088	−	0.173024i
$681$	7.33715	+	2.67050i	0.281160	+	0.102334i
$682$	0.223533	−	0.187567i	0.00855953	−	0.00718230i
$683$	42.7647			1.63634			0.818172	−	0.574973i	$-0.194987\pi$
$683$	42.7647			1.63634			0.818172	+	0.574973i	$0.194987\pi$
$684$	−0.800961	−	4.28468i	−0.0306255	−	0.163829i
$685$	−8.08289			−0.308832
$686$	0.766044	−	0.642788i	0.0292477	−	0.0245417i
$687$	−15.4483	−	5.62271i	−0.589388	−	0.214520i
$688$	−0.409857	+	2.32441i	−0.0156256	+	0.0886174i
$689$	2.24160	+	12.7128i	0.0853983	+	0.484318i
$690$	0.0614515	−	0.0223665i	0.00233942	−	0.000851478i
$691$	−12.4443	+	21.5542i	−0.473405	+	0.819962i	−0.999537	−	0.0304413i	$-0.990309\pi$
$691$	−12.4443	+	21.5542i	−0.473405	+	0.819962i	0.526131	+	0.850403i	$0.323642\pi$
$692$	3.40378	+	5.89551i	0.129392	+	0.224114i
$693$	−0.630229	−	0.528825i	−0.0239404	−	0.0200884i
$694$	26.6370	+	22.3511i	1.01113	+	0.848435i
$695$	−2.35142	−	4.07277i	−0.0891943	−	0.154489i
$696$	−1.19098	+	2.06283i	−0.0451439	+	0.0781914i
$697$	−5.16693	+	1.88061i	−0.195712	+	0.0712332i
$698$	−2.37697	−	13.4805i	−0.0899698	−	0.510244i
$699$	1.36305	−	7.73025i	0.0515554	−	0.292385i
$700$	4.17139	+	1.51826i	0.157664	+	0.0573849i
$701$	−3.42694	+	2.87554i	−0.129434	+	0.108608i	−0.705207	−	0.709002i	$-0.749146\pi$
$701$	−3.42694	+	2.87554i	−0.129434	+	0.108608i	0.575773	+	0.817610i	$0.304701\pi$
$702$	−2.52931			−0.0954625
$703$	−1.01002	+	1.79166i	−0.0380938	+	0.0675737i
$704$	−0.822706			−0.0310069
$705$	−2.58045	+	2.16526i	−0.0971854	+	0.0815482i
$706$	−27.3247	−	9.94537i	−1.02838	−	0.374299i
$707$	2.65234	−	15.0421i	0.0997514	−	0.565718i
$708$	0.892097	+	5.05933i	0.0335271	+	0.190141i
$709$	−35.4924	+	12.9182i	−1.33294	+	0.485152i	−0.907583	−	0.419872i	$-0.862075\pi$
$709$	−35.4924	+	12.9182i	−1.33294	+	0.485152i	−0.425360	+	0.905024i	$0.639853\pi$
$710$	−4.36206	+	7.55530i	−0.163705	+	0.283546i
$711$	−7.62077	−	13.1996i	−0.285801	−	0.495022i
$712$	−4.23055	−	3.54985i	−0.158547	−	0.133036i
$713$	0.0237247	+	0.0199074i	0.000888496	+	0.000745537i
$714$	−3.05869	−	5.29781i	−0.114469	−	0.198266i
$715$	−0.779219	+	1.34965i	−0.0291411	+	0.0504739i
$716$	5.14339	−	1.87204i	0.192218	−	0.0699615i
$717$	2.06496	+	11.7110i	0.0771173	+	0.437354i
$718$	1.18214	−	6.70424i	0.0441170	−	0.250200i
$719$	20.1723	+	7.34213i	0.752301	+	0.273815i	0.689574	−	0.724216i	$-0.257798\pi$
$719$	20.1723	+	7.34213i	0.752301	+	0.273815i	0.0627273	+	0.998031i	$0.480020\pi$
$720$	0.573717	−	0.481406i	0.0213812	−	0.0179409i
$721$	4.31272			0.160614
$722$	−17.9839	−	6.13030i	−0.669290	−	0.228146i
$723$	−1.54236			−0.0573609
$724$	10.1129	−	8.48577i	0.375845	−	0.315371i
$725$	9.93605	+	3.61643i	0.369016	+	0.134311i
$726$	−1.79260	+	10.1663i	−0.0665295	+	0.377308i
$727$	3.46122	+	19.6296i	0.128370	+	0.728020i	0.979249	+	0.202659i	$0.0649584\pi$
$727$	3.46122	+	19.6296i	0.128370	+	0.728020i	−0.850880	+	0.525361i	$0.823930\pi$
$728$	2.37677	−	0.865074i	0.0880890	−	0.0320618i
$729$	−0.500000	+	0.866025i	−0.0185185	+	0.0320750i
$730$	0.967242	+	1.67531i	0.0357992	+	0.0620061i
$731$	−11.0607	−	9.28101i	−0.409094	−	0.343270i
$732$	8.34482	+	7.00214i	0.308434	+	0.258807i
$733$	−6.50564	−	11.2681i	−0.240291	−	0.416197i	0.720506	−	0.693449i	$-0.243910\pi$
$733$	−6.50564	−	11.2681i	−0.240291	−	0.416197i	−0.960797	+	0.277252i	$0.910576\pi$
$734$	−11.0886	+	19.2060i	−0.409288	+	0.708907i
$735$	−0.703768	+	0.256151i	−0.0259589	+	0.00944826i
$736$	−0.0151626	−	0.0859912i	−0.000558900	−	0.00316968i
$737$	−2.15121	+	12.2001i	−0.0792410	+	0.449398i
$738$	−0.844631	−	0.307421i	−0.0310913	−	0.0113163i
$739$	−39.7986	+	33.3950i	−1.46402	+	1.22846i	−0.542534	+	0.840034i	$0.682535\pi$
$739$	−39.7986	+	33.3950i	−1.46402	+	1.22846i	−0.921482	+	0.388422i	$0.873020\pi$
$740$	−0.353384			−0.0129907
$741$	−5.41415	+	9.60403i	−0.198894	+	0.352813i
$742$	−5.10372			−0.187363
$743$	−24.3903	+	20.4659i	−0.894792	+	0.750820i	−0.969165	−	0.246411i	$-0.920749\pi$
$743$	−24.3903	+	20.4659i	−0.894792	+	0.750820i	0.0743734	+	0.997230i	$0.476304\pi$
$744$	0.333295	+	0.121310i	0.0122192	+	0.00444743i
$745$	−0.00491133	+	0.0278535i	−0.000179937	+	0.00102047i
$746$	−1.86506	−	10.5773i	−0.0682847	−	0.387262i
$747$	−1.82619	+	0.664680i	−0.0668169	+	0.0243194i
$748$	2.51640	−	4.35854i	0.0920088	−	0.159364i
$749$	−7.71284	−	13.3590i	−0.281821	−	0.488128i
$750$	−5.41537	−	4.54404i	−0.197741	−	0.165925i
$751$	−6.65224	−	5.58189i	−0.242744	−	0.203686i	0.513297	−	0.858211i	$-0.328424\pi$
$751$	−6.65224	−	5.58189i	−0.242744	−	0.203686i	−0.756040	+	0.654525i	$0.772869\pi$
$752$	2.24889	+	3.89519i	0.0820085	+	0.142043i
$753$	0.501435	−	0.868511i	0.0182733	−	0.0316503i
$754$	5.66136	−	2.06057i	0.206174	−	0.0750414i
$755$	0.176383	+	1.00032i	0.00641922	+	0.0364052i
$756$	0.173648	−	0.984808i	0.00631552	−	0.0358171i
$757$	14.6824	+	5.34394i	0.533639	+	0.194229i	0.594763	−	0.803901i	$-0.297246\pi$
$757$	14.6824	+	5.34394i	0.533639	+	0.194229i	−0.0611232	+	0.998130i	$0.519468\pi$
$758$	−20.3885	+	17.1079i	−0.740542	+	0.621389i
$759$	0.0718368			0.00260751
$760$	−0.599867	−	3.20894i	−0.0217595	−	0.116401i
$761$	−12.9601			−0.469805			−0.234902	−	0.972019i	$-0.575477\pi$
$761$	−12.9601			−0.469805			−0.234902	+	0.972019i	$0.575477\pi$
$762$	−1.76946	+	1.48475i	−0.0641007	+	0.0537869i
$763$	−8.30054	−	3.02115i	−0.300500	−	0.109373i
$764$	−2.60057	+	14.7486i	−0.0940854	+	0.533585i
$765$	0.795572	+	4.51192i	0.0287640	+	0.163129i
$766$	−11.5416	+	4.20080i	−0.417015	+	0.151781i
$767$	6.49701	−	11.2531i	0.234593	−	0.406328i
$768$	−0.500000	−	0.866025i	−0.0180422	−	0.0312500i
$769$	20.3666	+	17.0896i	0.734439	+	0.616268i	0.931338	−	0.364156i	$-0.118643\pi$
$769$	20.3666	+	17.0896i	0.734439	+	0.616268i	−0.196899	+	0.980424i	$0.563087\pi$
$770$	−0.472000	−	0.396055i	−0.0170097	−	0.0142728i
$771$	5.10546	+	8.84292i	0.183869	+	0.318470i
$772$	−0.389747	+	0.675061i	−0.0140273	+	0.0242960i
$773$	−24.0590	+	8.75675i	−0.865341	+	0.314958i	−0.736279	−	0.676678i	$-0.763419\pi$
$773$	−24.0590	+	8.75675i	−0.865341	+	0.314958i	−0.129062	+	0.991636i	$0.541197\pi$
$774$	−0.409857	−	2.32441i	−0.0147320	−	0.0835493i
$775$	0.273406	−	1.55056i	0.00982104	−	0.0556979i
$776$	−10.8342	−	3.94332i	−0.388925	−	0.141557i
$777$	−0.361457	+	0.303299i	−0.0129672	+	0.0108808i
$778$	10.9341			0.392006
$779$	−2.97530	+	2.54910i	−0.106601	+	0.0913308i
$780$	−1.89428			−0.0678263
$781$	−7.34135	+	6.16012i	−0.262694	+	0.220427i
$782$	0.501943	+	0.182692i	0.0179494	+	0.00653306i
$783$	0.413622	−	2.34577i	0.0147816	−	0.0838308i
$784$	0.173648	+	0.984808i	0.00620172	+	0.0351717i
$785$	−1.96038	+	0.713520i	−0.0699689	+	0.0254666i
$786$	6.51780	−	11.2892i	0.232482	−	0.402671i
$787$	21.0031	+	36.3785i	0.748680	+	1.29675i	0.948456	+	0.316910i	$0.102645\pi$
$787$	21.0031	+	36.3785i	0.748680	+	1.29675i	−0.199775	+	0.979842i	$0.564021\pi$
$788$	−8.60242	−	7.21828i	−0.306448	−	0.257141i
$789$	2.14727	+	1.80178i	0.0764449	+	0.0641449i
$790$	−5.70746	−	9.88561i	−0.203062	−	0.351714i
$791$	−1.41566	+	2.45199i	−0.0503349	+	0.0871827i
$792$	0.773090	−	0.281382i	0.0274706	−	0.00999847i
$793$	−4.78448	−	27.1341i	−0.169902	−	0.963562i
$794$	−6.35504	+	36.0412i	−0.225532	+	1.27906i
$795$	3.59184	+	1.30732i	0.127389	+	0.0463659i
$796$	−13.6167	+	11.4258i	−0.482631	+	0.404975i
$797$	−10.9853			−0.389120			−0.194560	−	0.980891i	$-0.562328\pi$
$797$	−10.9853			−0.389120			−0.194560	+	0.980891i	$0.562328\pi$
$798$	−3.36771	−	2.76741i	−0.119216	−	0.0979651i
$799$	−27.5146			−0.973397
$800$	−3.40055	+	2.85340i	−0.120227	+	0.100883i
$801$	5.18954	+	1.88884i	0.183363	+	0.0667388i
$802$	2.17003	−	12.3068i	0.0766264	−	0.434570i
$803$	0.369008	+	2.09275i	0.0130220	+	0.0738515i
$804$	−14.1499	+	5.15016i	−0.499030	+	0.181632i
$805$	0.0326976	−	0.0566340i	0.00115244	−	0.00199609i
$806$	−0.448554	−	0.776919i	−0.0157997	−	0.0273658i
$807$	15.9983	+	13.4241i	0.563166	+	0.472552i
$808$	11.7007	+	9.81806i	0.411630	+	0.345398i
$809$	−14.3069	−	24.7802i	−0.503003	−	0.871227i	−0.999994	−	0.00347092i	$-0.998895\pi$
$809$	−14.3069	−	24.7802i	−0.503003	−	0.871227i	0.496991	−	0.867756i	$-0.334438\pi$
$810$	−0.374467	+	0.648596i	−0.0131574	+	0.0227893i
$811$	2.39675	−	0.872344i	0.0841611	−	0.0306321i	−0.299596	−	0.954066i	$-0.596852\pi$
$811$	2.39675	−	0.872344i	0.0841611	−	0.0306321i	0.383758	+	0.923434i	$0.374630\pi$
$812$	0.413622	+	2.34577i	0.0145153	+	0.0823203i
$813$	−4.50584	+	25.5539i	−0.158027	+	0.896214i
$814$	−0.364782	−	0.132770i	−0.0127856	−	0.00465358i
$815$	11.2719	−	9.45825i	0.394837	−	0.331308i
$816$	6.11738			0.214151
$817$	−9.70336	−	3.41929i	−0.339477	−	0.119626i
$818$	19.4929			0.681553
$819$	−1.93756	+	1.62581i	−0.0677039	+	0.0568103i
$820$	−0.632573	−	0.230238i	−0.0220904	−	0.00804025i
$821$	1.68533	−	9.55798i	0.0588184	−	0.333576i	−0.941172	−	0.337928i	$-0.890274\pi$
$821$	1.68533	−	9.55798i	0.0588184	−	0.333576i	0.999991	+	0.00435183i	$0.00138523\pi$
$822$	−1.87410	−	10.6286i	−0.0653668	−	0.370714i
$823$	3.98732	−	1.45126i	0.138989	−	0.0505879i	−0.271589	−	0.962413i	$-0.587549\pi$
$823$	3.98732	−	1.45126i	0.138989	−	0.0505879i	0.410578	+	0.911825i	$0.365327\pi$
$824$	−2.15636	+	3.73492i	−0.0751203	+	0.130112i
$825$	−1.82604	−	3.16279i	−0.0635744	−	0.110114i
$826$	3.93546	+	3.30225i	0.136932	+	0.114900i
$827$	12.4277	+	10.4281i	0.432154	+	0.362620i	0.832764	−	0.553628i	$-0.186757\pi$
$827$	12.4277	+	10.4281i	0.432154	+	0.362620i	−0.400610	+	0.916249i	$0.631202\pi$
$828$	0.0436589	+	0.0756194i	0.00151725	+	0.00262796i
$829$	−17.3478	+	30.0472i	−0.602513	+	1.04358i	0.389926	+	0.920846i	$0.372501\pi$
$829$	−17.3478	+	30.0472i	−0.602513	+	1.04358i	−0.992439	+	0.122737i	$0.960833\pi$
$830$	−1.36770	+	0.497801i	−0.0474735	+	0.0172789i
$831$	−2.84654	−	16.1435i	−0.0987455	−	0.560013i
$832$	−0.439209	+	2.49088i	−0.0152268	+	0.0863557i
$833$	−5.74846	−	2.09227i	−0.199172	−	0.0724928i
$834$	4.81027	−	4.03630i	0.166566	−	0.139766i
$835$	−15.9480			−0.551905
$836$	0.586415	−	3.53782i	0.0202816	−	0.122358i
$837$	−0.354686			−0.0122597
$838$	11.1944	−	9.39319i	0.386703	−	0.324482i
$839$	−32.5013	−	11.8295i	−1.12207	−	0.408400i	−0.286662	−	0.958032i	$-0.592546\pi$
$839$	−32.5013	−	11.8295i	−1.12207	−	0.408400i	−0.835407	+	0.549632i	$0.814768\pi$
$840$	0.130051	−	0.737556i	0.00448719	−	0.0254481i
$841$	−4.05057	−	22.9719i	−0.139675	−	0.792135i
$842$	−16.1430	+	5.87557i	−0.556324	+	0.202485i
$843$	7.47789	−	12.9521i	0.257552	−	0.446094i
$844$	−1.81611	−	3.14559i	−0.0625129	−	0.108276i
$845$	−3.78803	−	3.17853i	−0.130312	−	0.109345i
$846$	−3.44550	−	2.89111i	−0.118459	−	0.0993986i
$847$	5.16158	+	8.94011i	0.177354	+	0.307186i
$848$	2.55186	−	4.41995i	0.0876313	−	0.151782i
$849$	3.91068	−	1.42337i	0.134214	−	0.0488500i
$850$	−4.71553	−	26.7431i	−0.161741	−	0.917281i
$851$	0.00715445	−	0.0405749i	0.000245251	−	0.00139089i
$852$	−10.9462	−	3.98409i	−0.375011	−	0.136493i
$853$	−16.2763	+	13.6574i	−0.557289	+	0.467621i	−0.877400	−	0.479759i	$-0.840724\pi$
$853$	−16.2763	+	13.6574i	−0.557289	+	0.467621i	0.320111	+	0.947380i	$0.396280\pi$
$854$	10.8934			0.372764
$855$	1.66121	+	2.81025i	0.0568123	+	0.0961086i
$856$	15.4257			0.527239
$857$	−25.3582	+	21.2780i	−0.866219	+	0.726844i	−0.963299	−	0.268432i	$-0.913494\pi$
$857$	−25.3582	+	21.2780i	−0.866219	+	0.726844i	0.0970793	+	0.995277i	$0.469050\pi$
$858$	−1.95538	−	0.711701i	−0.0667557	−	0.0242971i
$859$	−3.23295	+	18.3350i	−0.110307	+	0.625582i	0.878660	+	0.477447i	$0.158438\pi$
$859$	−3.23295	+	18.3350i	−0.110307	+	0.625582i	−0.988967	+	0.148134i	$0.952673\pi$
$860$	−0.306956	−	1.74083i	−0.0104671	−	0.0593619i
$861$	−0.844631	+	0.307421i	−0.0287849	+	0.0104769i
$862$	3.64137	−	6.30704i	0.124026	−	0.214819i
$863$	25.7754	+	44.6442i	0.877403	+	1.51971i	0.854180	+	0.519977i	$0.174059\pi$
$863$	25.7754	+	44.6442i	0.877403	+	1.51971i	0.0232228	+	0.999730i	$0.492607\pi$
$864$	0.766044	+	0.642788i	0.0260614	+	0.0218681i
$865$	−3.90561	−	3.27719i	−0.132795	−	0.111428i
$866$	−5.40182	−	9.35623i	−0.183561	−	0.317937i
$867$	−10.2112	+	17.6863i	−0.346790	+	0.600658i
$868$	0.333295	−	0.121310i	0.0113128	−	0.00411752i
$869$	−2.17743	−	12.3488i	−0.0738642	−	0.418904i
$870$	0.309776	−	1.75682i	0.0105024	−	0.0595619i
$871$	35.7895	+	13.0263i	1.21268	+	0.441380i
$872$	6.76666	−	5.67791i	0.229148	−	0.192278i
$873$	11.5295			0.390215
$874$	0.380589	−	0.00390889i	0.0128736	−	0.000132220i
$875$	−7.06926			−0.238985
$876$	−1.97868	+	1.66031i	−0.0668534	+	0.0560966i
$877$	44.4754	+	16.1877i	1.50183	+	0.546620i	0.956533	−	0.291625i	$-0.0941958\pi$
$877$	44.4754	+	16.1877i	1.50183	+	0.546620i	0.545294	+	0.838245i	$0.316418\pi$
$878$	−4.57894	+	25.9685i	−0.154532	+	0.876393i
$879$	1.56498	+	8.87542i	0.0527853	+	0.299360i
$880$	0.578994	−	0.210737i	0.0195179	−	0.00710393i
$881$	28.8179	−	49.9140i	0.970899	−	1.68165i	0.278045	−	0.960568i	$-0.410314\pi$
$881$	28.8179	−	49.9140i	0.970899	−	1.68165i	0.692854	−	0.721078i	$-0.256353\pi$
$882$	−0.500000	−	0.866025i	−0.0168359	−	0.0291606i
$883$	−32.5062	−	27.2759i	−1.09392	−	0.917907i	−0.0969179	−	0.995292i	$-0.530898\pi$
$883$	−32.5062	−	27.2759i	−1.09392	−	0.917907i	−0.997001	+	0.0773852i	$0.975343\pi$
$884$	−11.8528	−	9.94568i	−0.398653	−	0.334510i
$885$	−1.92378	−	3.33209i	−0.0646672	−	0.112007i
$886$	6.32096	−	10.9482i	0.212357	−	0.367813i
$887$	−48.6670	+	17.7133i	−1.63408	+	0.594756i	−0.985989	−	0.166809i	$-0.946654\pi$
$887$	−48.6670	+	17.7133i	−1.63408	+	0.594756i	−0.648089	+	0.761565i	$0.724431\pi$
$888$	−0.0819357	−	0.464681i	−0.00274958	−	0.0155937i
$889$	−0.401104	+	2.27477i	−0.0134526	+	0.0762934i
$890$	3.88662	+	1.41462i	0.130280	+	0.0474180i
$891$	−0.630229	+	0.528825i	−0.0211135	+	0.0177163i
$892$	4.09988			0.137274
$893$	−18.3532	+	6.89428i	−0.614165	+	0.230708i
$894$	−0.0377646			−0.00126304
$895$	−3.14023	+	2.63497i	−0.104966	+	0.0880772i
$896$	−0.939693	−	0.342020i	−0.0313929	−	0.0114261i
$897$	0.0383508	−	0.217498i	0.00128050	−	0.00726205i
$898$	−4.77407	−	27.0751i	−0.159313	−	0.903508i
$899$	0.793894	−	0.288954i	0.0264779	−	0.00963715i
$900$	2.21955	−	3.84437i	0.0739850	−	0.128146i
$901$	15.6107	+	27.0385i	0.520068	+	0.900784i
$902$	−0.566473	−	0.475328i	−0.0188615	−	0.0158267i
$903$	−1.80807	−	1.51715i	−0.0601689	−	0.0504877i
$904$	−1.41566	−	2.45199i	−0.0470840	−	0.0815519i
$905$	−4.94353	+	8.56245i	−0.164329	+	0.284626i
$906$	−1.27446	+	0.463867i	−0.0423412	+	0.0154109i
$907$	4.94637	+	28.0522i	0.164241	+	0.931459i	0.949843	+	0.312727i	$0.101242\pi$
$907$	4.94637	+	28.0522i	0.164241	+	0.931459i	−0.785602	+	0.618732i	$0.787646\pi$
$908$	−1.35585	+	7.68941i	−0.0449955	+	0.255182i
$909$	−14.3530	−	5.22408i	−0.476061	−	0.173272i
$910$	−1.45111	+	1.21762i	−0.0481037	+	0.0403638i
$911$	21.0748			0.698240			0.349120	−	0.937078i	$-0.386480\pi$
$911$	21.0748			0.698240			0.349120	+	0.937078i	$0.386480\pi$
$912$	4.08050	−	1.53282i	0.135119	−	0.0507567i
$913$	−1.59884			−0.0529139
$914$	−26.5720	+	22.2965i	−0.878923	+	0.737504i
$915$	−7.66642	−	2.79035i	−0.253444	−	0.0922461i
$916$	2.85473	−	16.1900i	0.0943228	−	0.534931i
$917$	−2.26361	−	12.8376i	−0.0747509	−	0.423933i
$918$	−5.74846	+	2.09227i	−0.189727	+	0.0690552i
$919$	19.8512	−	34.3832i	0.654830	−	1.13420i	−0.327107	−	0.944987i	$-0.606074\pi$
$919$	19.8512	−	34.3832i	0.654830	−	1.13420i	0.981936	−	0.189211i	$-0.0605930\pi$
$920$	0.0326976	+	0.0566340i	0.00107801	+	0.00186717i
$921$	−10.0264	−	8.41313i	−0.330380	−	0.277222i
$922$	16.9254	+	14.2021i	0.557407	+	0.467720i
$923$	14.7316	+	25.5158i	0.484896	+	0.839864i
$924$	0.411353	−	0.712484i	0.0135325	−	0.0234390i
$925$	−1.96827	+	0.716390i	−0.0647162	+	0.0235548i
$926$	−4.11668	−	23.3469i	−0.135283	−	0.767225i
$927$	0.748895	−	4.24720i	0.0245969	−	0.139496i
$928$	−2.23830	−	0.814676i	−0.0734759	−	0.0267431i
$929$	−34.7829	+	29.1863i	−1.14119	+	0.957571i	−0.999477	−	0.0323368i	$-0.989705\pi$
$929$	−34.7829	+	29.1863i	−1.14119	+	0.957571i	−0.141712	+	0.989908i	$0.545261\pi$
$930$	−0.265636			−0.00871056
$931$	−4.35867	+	0.0447662i	−0.142850	+	0.00146715i
$932$	7.84950			0.257119
$933$	−25.4519	+	21.3567i	−0.833257	+	0.699185i
$934$	16.6038	+	6.04331i	0.543294	+	0.197743i
$935$	−0.654522	+	3.71198i	−0.0214052	+	0.121395i
$936$	−0.439209	−	2.49088i	−0.0143560	−	0.0814170i
$937$	−14.5829	+	5.30775i	−0.476404	+	0.173397i	−0.569051	−	0.822302i	$-0.692689\pi$
$937$	−14.5829	+	5.30775i	−0.476404	+	0.173397i	0.0926473	+	0.995699i	$0.470467\pi$
$938$	−7.52903	+	13.0407i	−0.245831	+	0.425793i
$939$	−6.34410	−	10.9883i	−0.207032	−	0.358590i
$940$	−2.58045	−	2.16526i	−0.0841650	−	0.0706228i
$941$	−9.48054	−	7.95511i	−0.309057	−	0.259329i	0.475045	−	0.879961i	$-0.342432\pi$
$941$	−9.48054	−	7.95511i	−0.309057	−	0.259329i	−0.784102	+	0.620632i	$0.786876\pi$
$942$	−1.39277	−	2.41235i	−0.0453790	−	0.0785988i
$943$	0.0392423	−	0.0679696i	0.00127790	−	0.00221339i
$944$	−4.82756	+	1.75709i	−0.157124	+	0.0571883i
$945$	0.130051	+	0.737556i	0.00423056	+	0.0239927i
$946$	0.337191	−	1.91231i	0.0109630	−	0.0621745i
$947$	36.9388	+	13.4446i	1.20035	+	0.436891i	0.863346	−	0.504612i	$-0.168364\pi$
$947$	36.9388	+	13.4446i	1.20035	+	0.436891i	0.337003	+	0.941504i	$0.390587\pi$
$948$	11.6757	−	9.79708i	0.379209	−	0.318194i
$949$	6.53315			0.212075
$950$	−9.84638	−	16.6570i	−0.319459	−	0.540424i
$951$	22.9248			0.743386
$952$	4.68619	−	3.93218i	0.151880	−	0.127443i
$953$	−15.8433	−	5.76649i	−0.513215	−	0.186795i	0.0724133	−	0.997375i	$-0.476930\pi$
$953$	−15.8433	−	5.76649i	−0.513215	−	0.186795i	−0.585628	+	0.810580i	$0.699152\pi$
$954$	−0.886252	+	5.02618i	−0.0286935	+	0.162729i
$955$	−1.94766	−	11.0457i	−0.0630247	−	0.357431i
$956$	−11.1745	+	4.06717i	−0.361408	+	0.131542i
$957$	0.979823	−	1.69710i	0.0316732	−	0.0548596i
$958$	−11.3834	−	19.7166i	−0.367780	−	0.637013i
$959$	−8.26756	−	6.93730i	−0.266973	−	0.224017i
$960$	0.573717	+	0.481406i	0.0185166	+	0.0155373i
$961$	15.4371	+	26.7378i	0.497971	+	0.862511i
$962$	−0.596726	+	1.03356i	−0.0192392	+	0.0333233i
$963$	−14.4954	+	5.27589i	−0.467108	+	0.170013i
$964$	−0.267828	−	1.51893i	−0.00862614	−	0.0489213i
$965$	0.101374	−	0.574920i	0.00326334	−	0.0185073i
$966$	0.0820519	+	0.0298644i	0.00263998	+	0.000960873i
$967$	27.1607	−	22.7905i	0.873429	−	0.732894i	−0.0913886	−	0.995815i	$-0.529131\pi$
$967$	27.1607	−	22.7905i	0.873429	−	0.732894i	0.964817	+	0.262922i	$0.0846861\pi$
$968$	−10.3232			−0.331799
$969$	−4.36040	+	26.3061i	−0.140076	+	0.845074i
$970$	8.63484			0.277248
$971$	11.1849	−	9.38524i	0.358940	−	0.301187i	−0.445428	−	0.895318i	$-0.646948\pi$
$971$	11.1849	−	9.38524i	0.358940	−	0.301187i	0.804368	+	0.594131i	$0.202504\pi$
$972$	−0.939693	−	0.342020i	−0.0301407	−	0.0109703i
$973$	1.09040	−	6.18397i	0.0349566	−	0.198249i
$974$	0.902103	+	5.11608i	0.0289052	+	0.163930i
$975$	−10.5507	+	3.84015i	−0.337893	+	0.122983i
$976$	−5.44670	+	9.43396i	−0.174345	+	0.301974i
$977$	4.70493	+	8.14918i	0.150524	+	0.260715i	0.931420	−	0.363945i	$-0.118571\pi$
$977$	4.70493	+	8.14918i	0.150524	+	0.260715i	−0.780896	+	0.624661i	$0.785237\pi$
$978$	15.0506	+	12.6289i	0.481265	+	0.403829i
$979$	3.48050	+	2.92048i	0.111237	+	0.0933391i
$980$	−0.374467	−	0.648596i	−0.0119619	−	0.0207186i
$981$	−4.41663	+	7.64982i	−0.141012	+	0.244240i
$982$	−2.19825	+	0.800096i	−0.0701489	+	0.0255321i
$983$	7.58469	+	43.0149i	0.241914	+	1.37196i	0.827552	+	0.561390i	$0.189733\pi$
$983$	7.58469	+	43.0149i	0.241914	+	1.37196i	−0.585637	+	0.810573i	$0.699156\pi$
$984$	0.156081	−	0.885182i	0.00497570	−	0.0282186i
$985$	7.90307	+	2.87648i	0.251813	+	0.0916524i
$986$	11.1623	−	9.36627i	0.355479	−	0.298283i
$987$	−4.49778			−0.143166
$988$	−10.3983	−	3.66417i	−0.330813	−	0.116573i
$989$	0.206094			0.00655340
$990$	−0.472000	+	0.396055i	−0.0150011	+	0.0125875i
$991$	4.23641	+	1.54193i	0.134574	+	0.0489809i	0.408429	−	0.912790i	$-0.366077\pi$
$991$	4.23641	+	1.54193i	0.134574	+	0.0489809i	−0.273855	+	0.961771i	$0.588299\pi$
$992$	−0.0615905	+	0.349297i	−0.00195550	+	0.0110902i
$993$	1.35681	+	7.69485i	0.0430571	+	0.244189i
$994$	−10.9462	+	3.98409i	−0.347192	+	0.126368i
$995$	6.65628	−	11.5290i	0.211018	−	0.365494i
$996$	−0.971697	−	1.68303i	−0.0307894	−	0.0533288i
$997$	27.3388	+	22.9400i	0.865830	+	0.726518i	0.963216	−	0.268729i	$-0.0866036\pi$
$997$	27.3388	+	22.9400i	0.865830	+	0.726518i	−0.0973858	+	0.995247i	$0.531048\pi$
$998$	−20.2641	−	17.0036i	−0.641448	−	0.538239i
$999$	0.235925	+	0.408633i	0.00746432	+	0.0129286i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	798.2.bo.f.253.2	✓	18
19.16	even	9	inner	798.2.bo.f.757.2	yes	18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
798.2.bo.f.253.2	✓	18	1.1	even	1	trivial
798.2.bo.f.757.2	yes	18	19.16	even	9	inner

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:	\( N \)	\(=\)	\( 798 = 2 \cdot 3 \cdot 7 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	798.bo (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.766044 - 0.642788i) q^{2} +(-0.939693 - 0.342020i) q^{3} +(0.173648 - 0.984808i) q^{4} +(0.130051 + 0.737556i) q^{5} +(-0.939693 + 0.342020i) q^{6} +(-0.500000 + 0.866025i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(0.766044 + 0.642788i) q^{9} +O(q^{10})\)	\(q+(0.766044 - 0.642788i) q^{2} +(-0.939693 - 0.342020i) q^{3} +(0.173648 - 0.984808i) q^{4} +(0.130051 + 0.737556i) q^{5} +(-0.939693 + 0.342020i) q^{6} +(-0.500000 + 0.866025i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(0.766044 + 0.642788i) q^{9} +(0.573717 + 0.481406i) q^{10} +(0.411353 + 0.712484i) q^{11} +(-0.500000 + 0.866025i) q^{12} +(2.37677 - 0.865074i) q^{13} +(0.173648 + 0.984808i) q^{14} +(0.130051 - 0.737556i) q^{15} +(-0.939693 - 0.342020i) q^{16} +(4.68619 - 3.93218i) q^{17} +1.00000 q^{18} +(2.14057 - 3.79710i) q^{19} +0.748934 q^{20} +(0.766044 - 0.642788i) q^{21} +(0.773090 + 0.281382i) q^{22} +(-0.0151626 + 0.0859912i) q^{23} +(0.173648 + 0.984808i) q^{24} +(4.17139 - 1.51826i) q^{25} +(1.26465 - 2.19044i) q^{26} +(-0.500000 - 0.866025i) q^{27} +(0.766044 + 0.642788i) q^{28} +(1.82468 + 1.53109i) q^{29} +(-0.374467 - 0.648596i) q^{30} +(0.177343 - 0.307167i) q^{31} +(-0.939693 + 0.342020i) q^{32} +(-0.142861 - 0.810207i) q^{33} +(1.06227 - 6.02445i) q^{34} +(-0.703768 - 0.256151i) q^{35} +(0.766044 - 0.642788i) q^{36} -0.471849 q^{37} +(-0.800961 - 4.28468i) q^{38} -2.52931 q^{39} +(0.573717 - 0.481406i) q^{40} +(-0.844631 - 0.307421i) q^{41} +(0.173648 - 0.984808i) q^{42} +(-0.409857 - 2.32441i) q^{43} +(0.773090 - 0.281382i) q^{44} +(-0.374467 + 0.648596i) q^{45} +(0.0436589 + 0.0756194i) q^{46} +(-3.44550 - 2.89111i) q^{47} +(0.766044 + 0.642788i) q^{48} +(-0.500000 - 0.866025i) q^{49} +(2.21955 - 3.84437i) q^{50} +(-5.74846 + 2.09227i) q^{51} +(-0.439209 - 2.49088i) q^{52} +(-0.886252 + 5.02618i) q^{53} +(-0.939693 - 0.342020i) q^{54} +(-0.472000 + 0.396055i) q^{55} +1.00000 q^{56} +(-3.31016 + 2.83599i) q^{57} +2.38195 q^{58} +(3.93546 - 3.30225i) q^{59} +(-0.703768 - 0.256151i) q^{60} +(1.89162 - 10.7279i) q^{61} +(-0.0615905 - 0.349297i) q^{62} +(-0.939693 + 0.342020i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(0.947142 + 1.64050i) q^{65} +(-0.630229 - 0.528825i) q^{66} +(11.5351 + 9.67913i) q^{67} +(-3.05869 - 5.29781i) q^{68} +(0.0436589 - 0.0756194i) q^{69} +(-0.703768 + 0.256151i) q^{70} +(2.02278 + 11.4717i) q^{71} +(0.173648 - 0.984808i) q^{72} +(2.42721 + 0.883432i) q^{73} +(-0.361457 + 0.303299i) q^{74} -4.43910 q^{75} +(-3.36771 - 2.76741i) q^{76} -0.822706 q^{77} +(-1.93756 + 1.62581i) q^{78} +(-14.3224 - 5.21292i) q^{79} +(0.130051 - 0.737556i) q^{80} +(0.173648 + 0.984808i) q^{81} +(-0.844631 + 0.307421i) q^{82} +(-0.971697 + 1.68303i) q^{83} +(-0.500000 - 0.866025i) q^{84} +(3.50965 + 2.94494i) q^{85} +(-1.80807 - 1.51715i) q^{86} +(-1.19098 - 2.06283i) q^{87} +(0.411353 - 0.712484i) q^{88} +(5.18954 - 1.88884i) q^{89} +(0.130051 + 0.737556i) q^{90} +(-0.439209 + 2.49088i) q^{91} +(0.0820519 + 0.0298644i) q^{92} +(-0.271705 + 0.227988i) q^{93} -4.49778 q^{94} +(3.07896 + 1.08497i) q^{95} +1.00000 q^{96} +(8.83211 - 7.41102i) q^{97} +(-0.939693 - 0.342020i) q^{98} +(-0.142861 + 0.810207i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q - 9 q^{7} - 9 q^{8}+O(q^{10}) \) 18 * q - 9 * q^7 - 9 * q^8	\( 18 q - 9 q^{7} - 9 q^{8} - 9 q^{11} - 9 q^{12} + 3 q^{13} - 6 q^{17} + 18 q^{18} + 3 q^{19} + 12 q^{20} - 6 q^{22} - 3 q^{23} - 12 q^{25} - 15 q^{26} - 9 q^{27} - 3 q^{29} - 6 q^{30} - 15 q^{31} + 3 q^{33} - 6 q^{34} - 3 q^{38} + 30 q^{39} - 24 q^{43} - 6 q^{44} - 6 q^{45} - 6 q^{46} - 9 q^{49} - 3 q^{50} + 12 q^{51} + 3 q^{52} - 39 q^{53} - 48 q^{55} + 18 q^{56} + 15 q^{57} + 24 q^{58} + 30 q^{59} + 21 q^{61} - 9 q^{64} - 12 q^{65} + 3 q^{66} + 3 q^{67} - 12 q^{68} - 6 q^{69} + 33 q^{71} + 3 q^{73} - 3 q^{74} + 6 q^{75} + 3 q^{76} + 18 q^{77} - 6 q^{78} - 3 q^{79} + 30 q^{83} - 9 q^{84} - 24 q^{85} - 6 q^{86} - 12 q^{87} - 9 q^{88} + 12 q^{89} + 3 q^{91} - 3 q^{92} + 9 q^{93} + 18 q^{94} - 24 q^{95} + 18 q^{96} + 63 q^{97} + 3 q^{99}+O(q^{100}) \) 18 * q - 9 * q^7 - 9 * q^8 - 9 * q^11 - 9 * q^12 + 3 * q^13 - 6 * q^17 + 18 * q^18 + 3 * q^19 + 12 * q^20 - 6 * q^22 - 3 * q^23 - 12 * q^25 - 15 * q^26 - 9 * q^27 - 3 * q^29 - 6 * q^30 - 15 * q^31 + 3 * q^33 - 6 * q^34 - 3 * q^38 + 30 * q^39 - 24 * q^43 - 6 * q^44 - 6 * q^45 - 6 * q^46 - 9 * q^49 - 3 * q^50 + 12 * q^51 + 3 * q^52 - 39 * q^53 - 48 * q^55 + 18 * q^56 + 15 * q^57 + 24 * q^58 + 30 * q^59 + 21 * q^61 - 9 * q^64 - 12 * q^65 + 3 * q^66 + 3 * q^67 - 12 * q^68 - 6 * q^69 + 33 * q^71 + 3 * q^73 - 3 * q^74 + 6 * q^75 + 3 * q^76 + 18 * q^77 - 6 * q^78 - 3 * q^79 + 30 * q^83 - 9 * q^84 - 24 * q^85 - 6 * q^86 - 12 * q^87 - 9 * q^88 + 12 * q^89 + 3 * q^91 - 3 * q^92 + 9 * q^93 + 18 * q^94 - 24 * q^95 + 18 * q^96 + 63 * q^97 + 3 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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