LMFDB - Embedded newform 798.2.bp.b.613.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [798,2,Mod(289,798)]

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, 6, 2]))

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

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

chi := DirichletCharacter("798.289");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 798 = 2 \cdot 3 \cdot 7 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	798.bp (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:	$12$
Relative dimension:	$2$ over $\Q(\zeta_{9})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 30x^{10} + 393x^{8} - 2717x^{6} + 10056x^{4} - 18960x^{2} + 18496 $ x^12 - 30x^10 + 393x^8 - 2717x^6 + 10056x^4 - 18960*x^2 + 18496
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			613.2
Root			$-1.35206 + 0.642788i$ of defining polynomial
Character	$\chi$	$=$	798.613
Dual form			798.2.bp.b.289.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.766044 - 0.642788i) q^{2} +(0.766044 + 0.642788i) q^{3} +(0.173648 + 0.984808i) q^{4} +(0.101760 - 0.577108i) q^{5} +(-0.173648 - 0.984808i) q^{6} +(-0.500000 - 2.59808i) q^{7} +(0.500000 - 0.866025i) q^{8} +(0.173648 + 0.984808i) q^{9} +O(q^{10})$	\(q+(-0.766044 - 0.642788i) q^{2} +(0.766044 + 0.642788i) q^{3} +(0.173648 + 0.984808i) q^{4} +(0.101760 - 0.577108i) q^{5} +(-0.173648 - 0.984808i) q^{6} +(-0.500000 - 2.59808i) q^{7} +(0.500000 - 0.866025i) q^{8} +(0.173648 + 0.984808i) q^{9} +(-0.448910 + 0.376681i) q^{10} +(-1.40635 - 2.43586i) q^{11} +(-0.500000 + 0.866025i) q^{12} +(-0.176849 - 1.00296i) q^{13} +(-1.28699 + 2.31164i) q^{14} +(0.448910 - 0.376681i) q^{15} +(-0.939693 + 0.342020i) q^{16} +(0.498743 - 2.82851i) q^{17} +(0.500000 - 0.866025i) q^{18} +(-4.18119 + 1.23193i) q^{19} +0.586011 q^{20} +(1.28699 - 2.31164i) q^{21} +(-0.488419 + 2.76996i) q^{22} +(-5.82625 - 2.12058i) q^{23} +(0.939693 - 0.342020i) q^{24} +(4.37576 + 1.59265i) q^{25} +(-0.509218 + 0.881991i) q^{26} +(-0.500000 + 0.866025i) q^{27} +(2.47178 - 0.943555i) q^{28} +(-2.17266 - 0.790785i) q^{29} -0.586011 q^{30} -1.37683 q^{31} +(0.939693 + 0.342020i) q^{32} +(0.488419 - 2.76996i) q^{33} +(-2.20019 + 1.84618i) q^{34} +(-1.55025 + 0.0241745i) q^{35} +(-0.939693 + 0.342020i) q^{36} +(-3.41514 - 5.91520i) q^{37} +(3.99485 + 1.74390i) q^{38} +(0.509218 - 0.881991i) q^{39} +(-0.448910 - 0.376681i) q^{40} +(1.53502 - 8.70551i) q^{41} +(-2.47178 + 0.943555i) q^{42} +(7.01269 + 5.88435i) q^{43} +(2.15465 - 1.80796i) q^{44} +0.586011 q^{45} +(3.10008 + 5.36950i) q^{46} +(0.0272348 + 0.154456i) q^{47} +(-0.939693 - 0.342020i) q^{48} +(-6.50000 + 2.59808i) q^{49} +(-2.32830 - 4.03273i) q^{50} +(2.20019 - 1.84618i) q^{51} +(0.957016 - 0.348325i) q^{52} +(-1.29688 - 7.35495i) q^{53} +(0.939693 - 0.342020i) q^{54} +(-1.54887 + 0.563741i) q^{55} +(-2.50000 - 0.866025i) q^{56} +(-3.99485 - 1.74390i) q^{57} +(1.15605 + 2.00234i) q^{58} +(1.64083 - 9.30558i) q^{59} +(0.448910 + 0.376681i) q^{60} +(3.69235 + 1.34391i) q^{61} +(1.05471 + 0.885007i) q^{62} +(2.47178 - 0.943555i) q^{63} +(-0.500000 - 0.866025i) q^{64} -0.596814 q^{65} +(-2.15465 + 1.80796i) q^{66} +(11.1012 - 9.31500i) q^{67} +2.87214 q^{68} +(-3.10008 - 5.36950i) q^{69} +(1.20310 + 0.977963i) q^{70} +(0.573369 + 0.481114i) q^{71} +(0.939693 + 0.342020i) q^{72} +(9.22700 + 7.74237i) q^{73} +(-1.18607 + 6.72652i) q^{74} +(2.32830 + 4.03273i) q^{75} +(-1.93927 - 3.90374i) q^{76} +(-5.62538 + 4.87173i) q^{77} +(-0.957016 + 0.348325i) q^{78} +(-6.75312 + 2.45794i) q^{79} +(0.101760 + 0.577108i) q^{80} +(-0.939693 + 0.342020i) q^{81} +(-6.77168 + 5.68212i) q^{82} +(-8.23139 - 14.2572i) q^{83} +(2.50000 + 0.866025i) q^{84} +(-1.58160 - 0.575657i) q^{85} +(-1.58965 - 9.01535i) q^{86} +(-1.15605 - 2.00234i) q^{87} -2.81269 q^{88} +(-8.82233 + 7.40282i) q^{89} +(-0.448910 - 0.376681i) q^{90} +(-2.51735 + 0.960950i) q^{91} +(1.07665 - 6.10597i) q^{92} +(-1.05471 - 0.885007i) q^{93} +(0.0784195 - 0.135827i) q^{94} +(0.285482 + 2.53836i) q^{95} +(0.500000 + 0.866025i) q^{96} +(1.18097 - 0.429837i) q^{97} +(6.64930 + 2.18788i) q^{98} +(2.15465 - 1.80796i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 3 q^{5} - 6 q^{7} + 6 q^{8}+O(q^{10}) $ 12 * q + 3 * q^5 - 6 * q^7 + 6 * q^8	$ 12 q + 3 q^{5} - 6 q^{7} + 6 q^{8} + 6 q^{10} - 6 q^{12} + 12 q^{13} - 6 q^{15} - 18 q^{17} + 6 q^{18} - 3 q^{19} - 21 q^{22} - 3 q^{23} + 21 q^{25} - 6 q^{26} - 6 q^{27} - 12 q^{29} - 6 q^{31} + 21 q^{33} - 9 q^{34} + 12 q^{35} - 3 q^{37} + 3 q^{38} + 6 q^{39} + 6 q^{40} - 24 q^{41} - 21 q^{43} - 6 q^{44} - 6 q^{46} + 18 q^{47} - 78 q^{49} + 6 q^{50} + 9 q^{51} - 15 q^{52} + 36 q^{53} + 30 q^{55} - 30 q^{56} - 3 q^{57} + 15 q^{58} - 33 q^{59} - 6 q^{60} + 33 q^{62} - 6 q^{64} + 24 q^{65} + 6 q^{66} + 51 q^{67} - 6 q^{68} + 6 q^{69} - 3 q^{70} + 6 q^{71} - 3 q^{73} - 6 q^{75} + 9 q^{76} + 15 q^{78} + 30 q^{79} + 3 q^{80} - 3 q^{82} - 27 q^{83} + 30 q^{84} - 36 q^{85} + 3 q^{86} - 15 q^{87} + 12 q^{89} + 6 q^{90} + 21 q^{91} - 3 q^{92} - 33 q^{93} + 6 q^{94} + 21 q^{95} + 6 q^{96} + 30 q^{97} - 6 q^{99}+O(q^{100}) $ 12 * q + 3 * q^5 - 6 * q^7 + 6 * q^8 + 6 * q^10 - 6 * q^12 + 12 * q^13 - 6 * q^15 - 18 * q^17 + 6 * q^18 - 3 * q^19 - 21 * q^22 - 3 * q^23 + 21 * q^25 - 6 * q^26 - 6 * q^27 - 12 * q^29 - 6 * q^31 + 21 * q^33 - 9 * q^34 + 12 * q^35 - 3 * q^37 + 3 * q^38 + 6 * q^39 + 6 * q^40 - 24 * q^41 - 21 * q^43 - 6 * q^44 - 6 * q^46 + 18 * q^47 - 78 * q^49 + 6 * q^50 + 9 * q^51 - 15 * q^52 + 36 * q^53 + 30 * q^55 - 30 * q^56 - 3 * q^57 + 15 * q^58 - 33 * q^59 - 6 * q^60 + 33 * q^62 - 6 * q^64 + 24 * q^65 + 6 * q^66 + 51 * q^67 - 6 * q^68 + 6 * q^69 - 3 * q^70 + 6 * q^71 - 3 * q^73 - 6 * q^75 + 9 * q^76 + 15 * q^78 + 30 * q^79 + 3 * q^80 - 3 * q^82 - 27 * q^83 + 30 * q^84 - 36 * q^85 + 3 * q^86 - 15 * q^87 + 12 * q^89 + 6 * q^90 + 21 * q^91 - 3 * q^92 - 33 * q^93 + 6 * q^94 + 21 * q^95 + 6 * q^96 + 30 * q^97 - 6 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$115$	$211$	$533$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{8}{9}\right)$	$1$

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
$3$	0.766044	+	0.642788i	0.442276	+	0.371114i
$3$	0.766044	+	0.642788i	0.442276	+	0.371114i
$4$	0.173648	+	0.984808i	0.0868241	+	0.492404i
$5$	0.101760	−	0.577108i	0.0455083	−	0.258091i	−0.953562	−	0.301196i	$-0.902614\pi$
$5$	0.101760	−	0.577108i	0.0455083	−	0.258091i	0.999071	+	0.0431056i	$0.0137252\pi$
$6$	−0.173648	−	0.984808i	−0.0708916	−	0.402046i
$7$	−0.500000	−	2.59808i	−0.188982	−	0.981981i
$7$	−0.500000	−	2.59808i	−0.188982	−	0.981981i
$8$	0.500000	−	0.866025i	0.176777	−	0.306186i
$9$	0.173648	+	0.984808i	0.0578827	+	0.328269i
$10$	−0.448910	+	0.376681i	−0.141958	+	0.119117i
$11$	−1.40635	−	2.43586i	−0.424029	−	0.734440i	0.572300	−	0.820044i	$-0.306051\pi$
$11$	−1.40635	−	2.43586i	−0.424029	−	0.734440i	−0.996329	+	0.0856040i	$0.972718\pi$
$12$	−0.500000	+	0.866025i	−0.144338	+	0.250000i
$13$	−0.176849	−	1.00296i	−0.0490492	−	0.278172i	0.950412	−	0.310994i	$-0.100662\pi$
$13$	−0.176849	−	1.00296i	−0.0490492	−	0.278172i	−0.999461	+	0.0328217i	$0.989551\pi$
$14$	−1.28699	+	2.31164i	−0.343962	+	0.617811i
$15$	0.448910	−	0.376681i	0.115908	−	0.0972585i
$16$	−0.939693	+	0.342020i	−0.234923	+	0.0855050i
$17$	0.498743	−	2.82851i	0.120963	−	0.686014i	−0.862661	−	0.505782i	$-0.831204\pi$
$17$	0.498743	−	2.82851i	0.120963	−	0.686014i	0.983624	−	0.180232i	$-0.0576849\pi$
$18$	0.500000	−	0.866025i	0.117851	−	0.204124i
$19$	−4.18119	+	1.23193i	−0.959231	+	0.282625i
$19$	−4.18119	+	1.23193i	−0.959231	+	0.282625i
$20$	0.586011			0.131036
$21$	1.28699	−	2.31164i	0.280844	−	0.504440i
$22$	−0.488419	+	2.76996i	−0.104131	+	0.590558i
$23$	−5.82625	−	2.12058i	−1.21486	−	0.442172i	−0.346471	−	0.938061i	$-0.612620\pi$
$23$	−5.82625	−	2.12058i	−1.21486	−	0.442172i	−0.868386	+	0.495889i	$0.834842\pi$
$24$	0.939693	−	0.342020i	0.191814	−	0.0698146i
$25$	4.37576	+	1.59265i	0.875153	+	0.318530i
$26$	−0.509218	+	0.881991i	−0.0998658	+	0.172973i
$27$	−0.500000	+	0.866025i	−0.0962250	+	0.166667i
$28$	2.47178	−	0.943555i	0.467123	−	0.178315i
$29$	−2.17266	−	0.790785i	−0.403454	−	0.146845i	0.132319	−	0.991207i	$-0.457758\pi$
$29$	−2.17266	−	0.790785i	−0.403454	−	0.146845i	−0.535773	+	0.844362i	$0.679980\pi$
$30$	−0.586011			−0.106990
$31$	−1.37683			−0.247285			−0.123643	−	0.992327i	$-0.539458\pi$
$31$	−1.37683			−0.247285			−0.123643	+	0.992327i	$0.539458\pi$
$32$	0.939693	+	0.342020i	0.166116	+	0.0604612i
$33$	0.488419	−	2.76996i	0.0850228	−	0.482188i
$34$	−2.20019	+	1.84618i	−0.377329	+	0.316617i
$35$	−1.55025	+	0.0241745i	−0.262040	+	0.00408624i
$36$	−0.939693	+	0.342020i	−0.156615	+	0.0570034i
$37$	−3.41514	−	5.91520i	−0.561446	−	0.972454i	−0.997371	−	0.0724702i	$-0.976912\pi$
$37$	−3.41514	−	5.91520i	−0.561446	−	0.972454i	0.435924	−	0.899983i	$-0.356422\pi$
$38$	3.99485	+	1.74390i	0.648050	+	0.282898i
$39$	0.509218	−	0.881991i	0.0815401	−	0.141232i
$40$	−0.448910	−	0.376681i	−0.0709790	−	0.0595584i
$41$	1.53502	−	8.70551i	0.239729	−	1.35957i	−0.592692	−	0.805429i	$-0.701935\pi$
$41$	1.53502	−	8.70551i	0.239729	−	1.35957i	0.832421	−	0.554143i	$-0.186954\pi$
$42$	−2.47178	+	0.943555i	−0.381404	+	0.145594i
$43$	7.01269	+	5.88435i	1.06943	+	0.897355i	0.995000	−	0.0998716i	$-0.0318432\pi$
$43$	7.01269	+	5.88435i	1.06943	+	0.897355i	0.0744256	+	0.997227i	$0.476288\pi$
$44$	2.15465	−	1.80796i	0.324825	−	0.272561i
$45$	0.586011			0.0873573
$46$	3.10008	+	5.36950i	0.457082	+	0.791690i
$47$	0.0272348	+	0.154456i	0.00397261	+	0.0225298i	0.986730	−	0.162372i	$-0.0519144\pi$
$47$	0.0272348	+	0.154456i	0.00397261	+	0.0225298i	−0.982757	+	0.184902i	$0.940803\pi$
$48$	−0.939693	−	0.342020i	−0.135633	−	0.0493664i
$49$	−6.50000	+	2.59808i	−0.928571	+	0.371154i
$50$	−2.32830	−	4.03273i	−0.329271	−	0.570314i
$51$	2.20019	−	1.84618i	0.308088	−	0.258517i
$52$	0.957016	−	0.348325i	0.132714	−	0.0483041i
$53$	−1.29688	−	7.35495i	−0.178140	−	1.01028i	−0.934457	−	0.356075i	$-0.884115\pi$
$53$	−1.29688	−	7.35495i	−0.178140	−	1.01028i	0.756318	−	0.654205i	$-0.226996\pi$
$54$	0.939693	−	0.342020i	0.127876	−	0.0465430i
$55$	−1.54887	+	0.563741i	−0.208849	+	0.0760148i
$56$	−2.50000	−	0.866025i	−0.334077	−	0.115728i
$57$	−3.99485	−	1.74390i	−0.529131	−	0.230985i
$58$	1.15605	+	2.00234i	0.151797	+	0.262920i
$59$	1.64083	−	9.30558i	0.213617	−	1.21148i	−0.669673	−	0.742656i	$-0.733566\pi$
$59$	1.64083	−	9.30558i	0.213617	−	1.21148i	0.883290	−	0.468827i	$-0.155323\pi$
$60$	0.448910	+	0.376681i	0.0579541	+	0.0486292i
$61$	3.69235	+	1.34391i	0.472757	+	0.172070i	0.567401	−	0.823442i	$-0.307949\pi$
$61$	3.69235	+	1.34391i	0.472757	+	0.172070i	−0.0946438	+	0.995511i	$0.530171\pi$
$62$	1.05471	+	0.885007i	0.133948	+	0.112396i
$63$	2.47178	−	0.943555i	0.311415	−	0.118877i
$64$	−0.500000	−	0.866025i	−0.0625000	−	0.108253i
$65$	−0.596814			−0.0740257
$66$	−2.15465	+	1.80796i	−0.265219	+	0.222545i
$67$	11.1012	−	9.31500i	1.35623	−	1.13801i	0.379098	−	0.925356i	$-0.376234\pi$
$67$	11.1012	−	9.31500i	1.35623	−	1.13801i	0.977128	−	0.212652i	$-0.0682102\pi$
$68$	2.87214			0.348299
$69$	−3.10008	−	5.36950i	−0.373206	−	0.646412i
$70$	1.20310	+	0.977963i	0.143798	+	0.116889i
$71$	0.573369	+	0.481114i	0.0680464	+	0.0570977i	0.676177	−	0.736740i	$-0.263636\pi$
$71$	0.573369	+	0.481114i	0.0680464	+	0.0570977i	−0.608130	+	0.793837i	$0.708080\pi$
$72$	0.939693	+	0.342020i	0.110744	+	0.0403075i
$73$	9.22700	+	7.74237i	1.07994	+	0.906176i	0.995916	−	0.0902879i	$-0.0287787\pi$
$73$	9.22700	+	7.74237i	1.07994	+	0.906176i	0.0840227	+	0.996464i	$0.473223\pi$
$74$	−1.18607	+	6.72652i	−0.137878	+	0.781942i
$75$	2.32830	+	4.03273i	0.268848	+	0.465659i
$76$	−1.93927	−	3.90374i	−0.222450	−	0.447790i
$77$	−5.62538	+	4.87173i	−0.641072	+	0.555185i
$78$	−0.957016	+	0.348325i	−0.108361	+	0.0394401i
$79$	−6.75312	+	2.45794i	−0.759785	+	0.276539i	−0.692717	−	0.721209i	$-0.743587\pi$
$79$	−6.75312	+	2.45794i	−0.759785	+	0.276539i	−0.0670680	+	0.997748i	$0.521364\pi$
$80$	0.101760	+	0.577108i	0.0113771	+	0.0645226i
$81$	−0.939693	+	0.342020i	−0.104410	+	0.0380022i
$82$	−6.77168	+	5.68212i	−0.747808	+	0.627485i
$83$	−8.23139	−	14.2572i	−0.903512	−	1.56493i	−0.822902	−	0.568184i	$-0.807646\pi$
$83$	−8.23139	−	14.2572i	−0.903512	−	1.56493i	−0.0806107	−	0.996746i	$-0.525687\pi$
$84$	2.50000	+	0.866025i	0.272772	+	0.0944911i
$85$	−1.58160	−	0.575657i	−0.171549	−	0.0624387i
$86$	−1.58965	−	9.01535i	−0.171416	−	0.972150i
$87$	−1.15605	−	2.00234i	−0.123942	−	0.214673i
$88$	−2.81269			−0.299834
$89$	−8.82233	+	7.40282i	−0.935165	+	0.784697i	−0.976737	−	0.214439i	$-0.931208\pi$
$89$	−8.82233	+	7.40282i	−0.935165	+	0.784697i	0.0415722	+	0.999136i	$0.486763\pi$
$90$	−0.448910	−	0.376681i	−0.0473193	−	0.0397056i
$91$	−2.51735	+	0.960950i	−0.263890	+	0.100735i
$92$	1.07665	−	6.10597i	0.112248	−	0.636591i
$93$	−1.05471	−	0.885007i	−0.109368	−	0.0917710i
$94$	0.0784195	−	0.135827i	0.00808836	−	0.0140094i
$95$	0.285482	+	2.53836i	0.0292898	+	0.260430i
$96$	0.500000	+	0.866025i	0.0510310	+	0.0883883i
$97$	1.18097	−	0.429837i	0.119909	−	0.0436433i	−0.281369	−	0.959600i	$-0.590788\pi$
$97$	1.18097	−	0.429837i	0.119909	−	0.0436433i	0.401278	+	0.915956i	$0.368566\pi$
$98$	6.64930	+	2.18788i	0.671681	+	0.221009i
$99$	2.15465	−	1.80796i	0.216550	−	0.181707i
$100$	−0.808609	+	4.58585i	−0.0808609	+	0.458585i
$101$	12.6204	+	4.59345i	1.25578	+	0.457065i	0.882350	−	0.470595i	$-0.155961\pi$
$101$	12.6204	+	4.59345i	1.25578	+	0.457065i	0.373427	+	0.927660i	$0.378183\pi$
$102$	−2.87214			−0.284385
$103$	−7.68085			−0.756816			−0.378408	−	0.925639i	$-0.623528\pi$
$103$	−7.68085			−0.756816			−0.378408	+	0.925639i	$0.623528\pi$
$104$	−0.957016	−	0.348325i	−0.0938432	−	0.0341561i
$105$	−1.20310	−	0.977963i	−0.117411	−	0.0954394i
$106$	−3.73421	+	6.46783i	−0.362698	+	0.628211i
$107$	−7.87970	+	13.6480i	−0.761760	+	1.31941i	0.180183	+	0.983633i	$0.442331\pi$
$107$	−7.87970	+	13.6480i	−0.761760	+	1.31941i	−0.941943	+	0.335773i	$0.891002\pi$
$108$	−0.939693	−	0.342020i	−0.0904220	−	0.0329109i
$109$	−11.3641	+	4.13620i	−1.08849	+	0.396177i	−0.823060	−	0.567955i	$-0.807735\pi$
$109$	−11.3641	+	4.13620i	−1.08849	+	0.396177i	−0.265426	+	0.964131i	$0.585513\pi$
$110$	1.54887	+	0.563741i	0.147679	+	0.0537506i
$111$	1.18607	−	6.72652i	0.112577	−	0.638453i
$112$	1.35844	+	2.27038i	0.128361	+	0.214531i
$113$	15.5274			1.46069			0.730347	−	0.683077i	$-0.239358\pi$
$113$	15.5274			1.46069			0.730347	+	0.683077i	$0.239358\pi$
$114$	1.93927	+	3.90374i	0.181630	+	0.365619i
$115$	−1.81668	+	3.14659i	−0.169406	+	0.293421i
$116$	0.401492	−	2.27698i	0.0372776	−	0.211412i
$117$	0.957016	−	0.348325i	0.0884762	−	0.0322027i
$118$	−7.23846	+	6.07379i	−0.666354	+	0.559137i
$119$	−7.59805	+	0.118484i	−0.696512	+	0.0108614i
$120$	−0.101760	−	0.577108i	−0.00928935	−	0.0526825i
$121$	1.54438	−	2.67495i	0.140398	−	0.243177i
$122$	−1.96466	−	3.40289i	−0.177872	−	0.308083i
$123$	6.77168	−	5.68212i	0.610582	−	0.512339i
$124$	−0.239083	−	1.35591i	−0.0214703	−	0.121764i
$125$	2.82943	−	4.90072i	0.253072	−	0.438334i
$126$	−2.50000	−	0.866025i	−0.222718	−	0.0771517i
$127$	2.02522	+	11.4856i	0.179709	+	1.01918i	0.932567	+	0.360997i	$0.117564\pi$
$127$	2.02522	+	11.4856i	0.179709	+	1.01918i	−0.752858	+	0.658183i	$0.771325\pi$
$128$	−0.173648	+	0.984808i	−0.0153485	+	0.0870455i
$129$	1.58965	+	9.01535i	0.139961	+	0.793757i
$130$	0.457186	+	0.383625i	0.0400979	+	0.0336461i
$131$	−2.81154	−	2.35916i	−0.245645	−	0.206121i	0.511649	−	0.859194i	$-0.329035\pi$
$131$	−2.81154	−	2.35916i	−0.245645	−	0.206121i	−0.757294	+	0.653074i	$0.773479\pi$
$132$	2.81269			0.244813
$133$	5.29125	+	10.2471i	0.458810	+	0.888535i
$134$	−14.4916			−1.25188
$135$	0.448910	+	0.376681i	0.0386361	+	0.0324195i
$136$	−2.20019	−	1.84618i	−0.188665	−	0.158308i
$137$	−1.26455	−	7.17160i	−0.108038	−	0.612711i	−0.989964	−	0.141323i	$-0.954864\pi$
$137$	−1.26455	−	7.17160i	−0.108038	−	0.612711i	0.881926	−	0.471388i	$-0.156247\pi$
$138$	−1.07665	+	6.10597i	−0.0916503	+	0.519775i
$139$	0.448066	+	2.54111i	0.0380045	+	0.215534i	0.997896	−	0.0648382i	$-0.0206531\pi$
$139$	0.448066	+	2.54111i	0.0380045	+	0.215534i	−0.959891	+	0.280372i	$0.909542\pi$
$140$	−0.293005	−	1.52250i	−0.0247635	−	0.128675i
$141$	−0.0784195	+	0.135827i	−0.00660412	+	0.0114387i
$142$	−0.129972	−	0.737109i	−0.0109070	−	0.0618568i
$143$	−2.19437	+	1.84129i	−0.183502	+	0.153977i
$144$	−0.500000	−	0.866025i	−0.0416667	−	0.0721688i
$145$	−0.677458	+	1.17339i	−0.0562598	+	0.0974449i
$146$	−2.09159	−	11.8620i	−0.173101	−	0.981706i
$147$	−6.64930	−	2.18788i	−0.548425	−	0.180453i
$148$	5.23230	−	4.39043i	0.430093	−	0.360891i
$149$	11.1197	−	4.04723i	0.910959	−	0.331562i	0.156323	−	0.987706i	$-0.450036\pi$
$149$	11.1197	−	4.04723i	0.910959	−	0.331562i	0.754636	+	0.656144i	$0.227814\pi$
$150$	0.808609	−	4.58585i	0.0660226	−	0.374433i
$151$	−3.36098	+	5.82139i	−0.273513	+	0.473738i	−0.969759	−	0.244065i	$-0.921519\pi$
$151$	−3.36098	+	5.82139i	−0.273513	+	0.473738i	0.696246	+	0.717803i	$0.254852\pi$
$152$	−1.02371	+	4.23698i	−0.0830338	+	0.343665i
$153$	2.87214			0.232199
$154$	7.44078	−	0.116031i	0.599595	−	0.00935005i
$155$	−0.140106	+	0.794578i	−0.0112535	+	0.0638220i
$156$	0.957016	+	0.348325i	0.0766226	+	0.0278884i
$157$	2.42555	−	0.882829i	0.193580	−	0.0704574i	−0.243411	−	0.969923i	$-0.578266\pi$
$157$	2.42555	−	0.882829i	0.193580	−	0.0704574i	0.436991	+	0.899466i	$0.356044\pi$
$158$	6.75312	+	2.45794i	0.537249	+	0.195543i
$159$	3.73421	−	6.46783i	0.296142	−	0.512933i
$160$	0.293005	−	0.507500i	0.0231641	−	0.0401214i
$161$	−2.59631	+	16.1973i	−0.204618	+	1.27653i
$162$	0.939693	+	0.342020i	0.0738292	+	0.0268716i
$163$	0.934079			0.0731628			0.0365814	−	0.999331i	$-0.488353\pi$
$163$	0.934079			0.0731628			0.0365814	+	0.999331i	$0.488353\pi$
$164$	8.83981			0.690273
$165$	−1.54887	−	0.563741i	−0.120579	−	0.0438872i
$166$	−2.85873	+	16.2127i	−0.221881	+	1.25835i
$167$	1.39888	−	1.17380i	0.108249	−	0.0908314i	−0.587057	−	0.809546i	$-0.699714\pi$
$167$	1.39888	−	1.17380i	0.108249	−	0.0908314i	0.695306	+	0.718714i	$0.255269\pi$
$168$	−1.35844	−	2.27038i	−0.104806	−	0.175164i
$169$	11.2413	−	4.09151i	0.864719	−	0.314732i
$170$	0.841554	+	1.45761i	0.0645442	+	0.111794i
$171$	−1.93927	−	3.90374i	−0.148300	−	0.298527i
$172$	−4.57721	+	7.92796i	−0.349009	+	0.604502i
$173$	15.1304	+	12.6959i	1.15035	+	0.965254i	0.999728	−	0.0233376i	$-0.00742925\pi$
$173$	15.1304	+	12.6959i	1.15035	+	0.965254i	0.150618	+	0.988592i	$0.451874\pi$
$174$	−0.401492	+	2.27698i	−0.0304370	+	0.172617i
$175$	1.94994	−	12.1649i	0.147402	−	0.919580i
$176$	2.15465	+	1.80796i	0.162413	+	0.136280i
$177$	7.23846	−	6.07379i	0.544076	−	0.456534i
$178$	11.5167			0.863216
$179$	3.90211	+	6.75865i	0.291657	+	0.505166i	0.974202	−	0.225679i	$-0.0724599\pi$
$179$	3.90211	+	6.75865i	0.291657	+	0.505166i	−0.682544	+	0.730844i	$0.739127\pi$
$180$	0.101760	+	0.577108i	0.00758472	+	0.0430151i
$181$	−13.5187	−	4.92041i	−1.00484	−	0.365732i	−0.213390	−	0.976967i	$-0.568451\pi$
$181$	−13.5187	−	4.92041i	−1.00484	−	0.365732i	−0.791449	+	0.611235i	$0.790673\pi$
$182$	2.54609	+	0.881991i	0.188729	+	0.0653775i
$183$	1.96466	+	3.40289i	0.145232	+	0.251549i
$184$	−4.74960	+	3.98539i	−0.350145	+	0.293807i
$185$	−3.76124	+	1.36898i	−0.276532	+	0.100649i
$186$	0.239083	+	1.35591i	0.0175304	+	0.0994201i
$187$	−7.59127	+	2.76299i	−0.555128	+	0.202050i
$188$	−0.147381	+	0.0536421i	−0.0107488	+	0.00391225i
$189$	2.50000	+	0.866025i	0.181848	+	0.0629941i
$190$	1.41293	−	2.12800i	0.102505	−	0.154381i
$191$	4.34340	+	7.52299i	0.314278	+	0.544345i	0.979284	−	0.202493i	$-0.0649044\pi$
$191$	4.34340	+	7.52299i	0.314278	+	0.544345i	−0.665006	+	0.746838i	$0.731571\pi$
$192$	0.173648	−	0.984808i	0.0125320	−	0.0710724i
$193$	18.0648	+	15.1582i	1.30033	+	1.09111i	0.990087	+	0.140454i	$0.0448563\pi$
$193$	18.0648	+	15.1582i	1.30033	+	1.09111i	0.310247	+	0.950656i	$0.399588\pi$
$194$	−1.18097	−	0.429837i	−0.0847885	−	0.0308605i
$195$	−0.457186	−	0.383625i	−0.0327398	−	0.0274719i
$196$	−3.68732	−	5.95010i	−0.263380	−	0.425007i
$197$	3.15388	+	5.46267i	0.224704	+	0.389199i	0.956231	−	0.292614i	$-0.0945250\pi$
$197$	3.15388	+	5.46267i	0.224704	+	0.389199i	−0.731526	+	0.681813i	$0.761192\pi$
$198$	−2.81269			−0.199889
$199$	10.3730	−	8.70396i	0.735321	−	0.617007i	−0.196256	−	0.980553i	$-0.562878\pi$
$199$	10.3730	−	8.70396i	0.735321	−	0.617007i	0.931577	+	0.363545i	$0.118434\pi$
$200$	3.56716	−	2.99320i	0.252236	−	0.211651i
$201$	14.4916			1.02216
$202$	−6.71517	−	11.6310i	−0.472478	−	0.818356i
$203$	−0.968188	+	6.04014i	−0.0679535	+	0.423935i
$204$	2.20019	+	1.84618i	0.154044	+	0.129258i
$205$	−4.86782	−	1.77174i	−0.339983	−	0.123744i
$206$	5.88387	+	4.93715i	0.409949	+	0.343988i
$207$	1.07665	−	6.10597i	0.0748322	−	0.424394i
$208$	0.509218	+	0.881991i	0.0353079	+	0.0611551i
$209$	8.88102	+	8.45228i	0.614313	+	0.584656i
$210$	0.293005	+	1.52250i	0.0202193	+	0.105063i
$211$	22.7674	−	8.28667i	1.56737	−	0.570478i	0.594963	−	0.803753i	$-0.297167\pi$
$211$	22.7674	−	8.28667i	1.56737	−	0.570478i	0.972411	+	0.233275i	$0.0749443\pi$
$212$	7.01801	−	2.55435i	0.481999	−	0.175433i
$213$	0.129972	+	0.737109i	0.00890555	+	0.0505059i
$214$	14.8090	−	5.39003i	1.01232	−	0.368455i
$215$	4.10952	−	3.44829i	0.280267	−	0.235172i
$216$	0.500000	+	0.866025i	0.0340207	+	0.0589256i
$217$	0.688413	+	3.57710i	0.0467325	+	0.242829i
$218$	11.3641	+	4.13620i	0.769676	+	0.280139i
$219$	2.09159	+	11.8620i	0.141337	+	0.801560i
$220$	−0.824134	−	1.42744i	−0.0555631	−	0.0962381i
$221$	−2.92509			−0.196763
$222$	−5.23230	+	4.39043i	−0.351169	+	0.294666i
$223$	−10.2961	−	8.63942i	−0.689475	−	0.578538i	0.229283	−	0.973360i	$-0.426362\pi$
$223$	−10.2961	−	8.63942i	−0.689475	−	0.578538i	−0.918758	+	0.394822i	$0.870806\pi$
$224$	0.418748	−	2.61240i	0.0279788	−	0.174549i
$225$	−0.808609	+	4.58585i	−0.0539072	+	0.305723i
$226$	−11.8947	−	9.98081i	−0.791221	−	0.663914i
$227$	−2.12289	+	3.67695i	−0.140901	+	0.244048i	−0.927836	−	0.372988i	$-0.878333\pi$
$227$	−2.12289	+	3.67695i	−0.140901	+	0.244048i	0.786935	+	0.617036i	$0.211667\pi$
$228$	1.02371	−	4.23698i	0.0677968	−	0.280601i
$229$	9.45689	+	16.3798i	0.624929	+	1.08241i	0.988555	+	0.150863i	$0.0482053\pi$
$229$	9.45689	+	16.3798i	0.624929	+	1.08241i	−0.363626	+	0.931545i	$0.618461\pi$
$230$	3.41425	−	1.24268i	0.225129	−	0.0819401i
$231$	−7.44078	+	0.116031i	−0.489567	+	0.00763429i
$232$	−1.77117	+	1.48619i	−0.116283	+	0.0975732i
$233$	−0.800047	+	4.53729i	−0.0524128	+	0.297248i	−0.999735	−	0.0230353i	$-0.992667\pi$
$233$	−0.800047	+	4.53729i	−0.0524128	+	0.297248i	0.947322	+	0.320283i	$0.103778\pi$
$234$	−0.957016	−	0.348325i	−0.0625621	−	0.0227707i
$235$	0.0919094			0.00599551
$236$	9.44914			0.615086
$237$	−6.75312	−	2.45794i	−0.438662	−	0.159660i
$238$	5.89661	+	4.79317i	0.382220	+	0.310695i
$239$	−9.52851	+	16.5039i	−0.616348	+	1.06755i	0.373798	+	0.927510i	$0.378055\pi$
$239$	−9.52851	+	16.5039i	−0.616348	+	1.06755i	−0.990146	+	0.140036i	$0.955278\pi$
$240$	−0.293005	+	0.507500i	−0.0189134	+	0.0327590i
$241$	−13.9445	−	5.07540i	−0.898247	−	0.326935i	−0.148697	−	0.988883i	$-0.547508\pi$
$241$	−13.9445	−	5.07540i	−0.898247	−	0.326935i	−0.749550	+	0.661948i	$0.769730\pi$
$242$	−2.90249	+	1.05642i	−0.186579	+	0.0679092i
$243$	−0.939693	−	0.342020i	−0.0602813	−	0.0219406i
$244$	−0.682319	+	3.86962i	−0.0436810	+	0.247727i
$245$	0.837933	+	4.01558i	0.0535335	+	0.256546i
$246$	−8.83981			−0.563606
$247$	1.97502	+	3.97571i	0.125668	+	0.252968i
$248$	−0.688413	+	1.19237i	−0.0437143	+	0.0757154i
$249$	2.85873	−	16.2127i	0.181165	−	1.02744i
$250$	−5.31760	+	1.93545i	−0.336314	+	0.122408i
$251$	6.76220	−	5.67416i	0.426827	−	0.358150i	−0.403926	−	0.914792i	$-0.632355\pi$
$251$	6.76220	−	5.67416i	0.426827	−	0.358150i	0.830753	+	0.556642i	$0.187910\pi$
$252$	1.35844	+	2.27038i	0.0855737	+	0.143021i
$253$	3.02828	+	17.1742i	0.190386	+	1.07973i
$254$	5.83138	−	10.1002i	0.365893	−	0.633746i
$255$	−0.841554	−	1.45761i	−0.0527001	−	0.0912793i
$256$	0.766044	−	0.642788i	0.0478778	−	0.0401742i
$257$	−0.549157	−	3.11442i	−0.0342555	−	0.194272i	0.962878	−	0.269938i	$-0.0870031\pi$
$257$	−0.549157	−	3.11442i	−0.0342555	−	0.194272i	−0.997133	+	0.0756652i	$0.975892\pi$
$258$	4.57721	−	7.92796i	0.284965	−	0.493573i
$259$	−13.6606	+	11.8304i	−0.848827	+	0.735106i
$260$	−0.103636	−	0.587747i	−0.00642721	−	0.0364505i
$261$	0.401492	−	2.27698i	0.0248517	−	0.140941i
$262$	0.637324	+	3.61444i	0.0393740	+	0.223301i
$263$	12.0042	+	10.0727i	0.740208	+	0.621109i	0.932894	−	0.360152i	$-0.117275\pi$
$263$	12.0042	+	10.0727i	0.740208	+	0.621109i	−0.192685	+	0.981261i	$0.561720\pi$
$264$	−2.15465	−	1.80796i	−0.132609	−	0.111272i
$265$	−4.37657			−0.268851
$266$	2.53336	−	11.2509i	0.155330	−	0.689835i
$267$	−11.5167			−0.704813
$268$	11.1012	+	9.31500i	0.678113	+	0.569004i
$269$	−9.64348	−	8.09184i	−0.587973	−	0.493368i	0.299581	−	0.954071i	$-0.403153\pi$
$269$	−9.64348	−	8.09184i	−0.587973	−	0.493368i	−0.887555	+	0.460703i	$0.847597\pi$
$270$	−0.101760	−	0.577108i	−0.00619290	−	0.0351217i
$271$	3.57494	−	20.2745i	0.217162	−	1.23159i	−0.659953	−	0.751306i	$-0.729424\pi$
$271$	3.57494	−	20.2745i	0.217162	−	1.23159i	0.877115	−	0.480280i	$-0.159465\pi$
$272$	0.498743	+	2.82851i	0.0302407	+	0.171504i
$273$	−2.54609	−	0.881991i	−0.154096	−	0.0533805i
$274$	−3.64112	+	6.30660i	−0.219968	+	0.380996i
$275$	−2.27437	−	12.8986i	−0.137150	−	0.777814i
$276$	4.74960	−	3.98539i	0.285892	−	0.239892i
$277$	3.65200	+	6.32546i	0.219428	+	0.380060i	0.954633	−	0.297784i	$-0.0962477\pi$
$277$	3.65200	+	6.32546i	0.219428	+	0.380060i	−0.735205	+	0.677844i	$0.762914\pi$
$278$	1.29016	−	2.23462i	0.0773784	−	0.134023i
$279$	−0.239083	−	1.35591i	−0.0143136	−	0.0811762i
$280$	−0.754190	+	1.35464i	−0.0450714	+	0.0809554i
$281$	−14.8319	+	12.4454i	−0.884795	+	0.742431i	−0.967159	−	0.254171i	$-0.918197\pi$
$281$	−14.8319	+	12.4454i	−0.884795	+	0.742431i	0.0823642	+	0.996602i	$0.473753\pi$
$282$	0.147381	−	0.0536421i	0.00877638	−	0.00319434i
$283$	−2.17019	+	12.3078i	−0.129004	+	0.731620i	0.849844	+	0.527034i	$0.176696\pi$
$283$	−2.17019	+	12.3078i	−0.129004	+	0.731620i	−0.978849	+	0.204586i	$0.934415\pi$
$284$	−0.374240	+	0.648203i	−0.0222071	+	0.0384638i
$285$	−1.41293	+	2.12800i	−0.0836950	+	0.126052i
$286$	2.86455			0.169384
$287$	−23.3851	+	0.364666i	−1.38038	+	0.0215255i
$288$	−0.173648	+	0.984808i	−0.0102323	+	0.0580304i
$289$	8.22305	+	2.99295i	0.483709	+	0.176056i
$290$	1.27321	−	0.463409i	0.0747652	−	0.0272123i
$291$	1.18097	+	0.429837i	0.0692296	+	0.0251975i
$292$	−6.02250	+	10.4313i	−0.352440	+	0.610444i
$293$	0.363191	−	0.629065i	0.0212178	−	0.0367504i	−0.855222	−	0.518263i	$-0.826579\pi$
$293$	0.363191	−	0.629065i	0.0212178	−	0.0367504i	0.876439	+	0.481512i	$0.159912\pi$
$294$	3.68732	+	5.95010i	0.215049	+	0.347017i
$295$	−5.20336	−	1.89387i	−0.302951	−	0.110265i
$296$	−6.83029			−0.397002
$297$	2.81269			0.163209
$298$	−11.1197	−	4.04723i	−0.644145	−	0.234450i
$299$	−1.09650	+	6.21854i	−0.0634120	+	0.359627i
$300$	−3.56716	+	2.99320i	−0.205950	+	0.172812i
$301$	11.7816	−	21.1617i	0.679083	−	1.21974i
$302$	6.31658	−	2.29905i	0.363478	−	0.132295i
$303$	6.71517	+	11.6310i	0.385777	+	0.668185i
$304$	3.50769	−	2.58769i	0.201180	−	0.148414i
$305$	1.15131	−	1.99413i	0.0659239	−	0.114184i
$306$	−2.20019	−	1.84618i	−0.125776	−	0.105539i
$307$	−1.75798	+	9.97002i	−0.100333	+	0.569019i	0.892649	+	0.450753i	$0.148845\pi$
$307$	−1.75798	+	9.97002i	−0.100333	+	0.569019i	−0.992982	+	0.118266i	$0.962267\pi$
$308$	−5.77455	−	4.69396i	−0.329036	−	0.267463i
$309$	−5.88387	−	4.93715i	−0.334722	−	0.280865i
$310$	0.618072	−	0.518624i	0.0351041	−	0.0294559i
$311$	−28.5877			−1.62106			−0.810531	−	0.585696i	$-0.800821\pi$
$311$	−28.5877			−1.62106			−0.810531	+	0.585696i	$0.800821\pi$
$312$	−0.509218	−	0.881991i	−0.0288288	−	0.0499329i
$313$	−5.46591	−	30.9987i	−0.308952	−	1.75215i	−0.604295	−	0.796761i	$-0.706545\pi$
$313$	−5.46591	−	30.9987i	−0.308952	−	1.75215i	0.295343	−	0.955391i	$-0.404566\pi$
$314$	−2.42555	−	0.882829i	−0.136882	−	0.0498209i
$315$	−0.293005	−	1.52250i	−0.0165090	−	0.0857832i
$316$	−3.59326	−	6.22371i	−0.202137	−	0.350111i
$317$	12.4999	−	10.4886i	0.702063	−	0.589101i	−0.220297	−	0.975433i	$-0.570703\pi$
$317$	12.4999	−	10.4886i	0.702063	−	0.589101i	0.922360	+	0.386332i	$0.126258\pi$
$318$	−7.01801	+	2.55435i	−0.393550	+	0.143241i
$319$	1.12927	+	6.40443i	0.0632272	+	0.358579i
$320$	−0.550670	+	0.200428i	−0.0307834	+	0.0112042i
$321$	−14.8090	+	5.39003i	−0.826558	+	0.300842i
$322$	12.4003	−	10.7390i	0.691043	−	0.598461i
$323$	1.39920	+	12.4409i	0.0778534	+	0.692233i
$324$	−0.500000	−	0.866025i	−0.0277778	−	0.0481125i
$325$	0.823516	−	4.67039i	0.0456804	−	0.259067i
$326$	−0.715546	−	0.600415i	−0.0396304	−	0.0332539i
$327$	−11.3641	−	4.13620i	−0.628438	−	0.228733i
$328$	−6.77168	−	5.68212i	−0.373904	−	0.313743i
$329$	0.387672	−	0.147986i	0.0213730	−	0.00815875i
$330$	0.824134	+	1.42744i	0.0453671	+	0.0785781i
$331$	10.3855			0.570836			0.285418	−	0.958403i	$-0.407868\pi$
$331$	10.3855			0.570836			0.285418	+	0.958403i	$0.407868\pi$
$332$	12.6112	−	10.5821i	0.692131	−	0.580767i
$333$	5.23230	−	4.39043i	0.286729	−	0.240594i
$334$	−1.82611			−0.0999203
$335$	−4.24611	−	7.35448i	−0.231990	−	0.401818i
$336$	−0.418748	+	2.61240i	−0.0228446	+	0.142518i
$337$	2.56896	+	2.15562i	0.139940	+	0.117424i	0.710071	−	0.704130i	$-0.248663\pi$
$337$	2.56896	+	2.15562i	0.139940	+	0.117424i	−0.570130	+	0.821554i	$0.693107\pi$
$338$	−11.2413	−	4.09151i	−0.611449	−	0.222549i
$339$	11.8947	+	9.98081i	0.646030	+	0.542083i
$340$	0.292269	−	1.65754i	0.0158505	−	0.0898926i
$341$	1.93630	+	3.35376i	0.104856	+	0.181616i
$342$	−1.02371	+	4.23698i	−0.0553558	+	0.229110i
$343$	10.0000	+	15.5885i	0.539949	+	0.841698i
$344$	8.60234	−	3.13100i	0.463807	−	0.168812i
$345$	−3.41425	+	1.24268i	−0.183817	+	0.0669038i
$346$	−3.42979	−	19.4513i	−0.184387	−	1.04571i
$347$	5.44387	−	1.98141i	0.292242	−	0.106367i	−0.191739	−	0.981446i	$-0.561413\pi$
$347$	5.44387	−	1.98141i	0.292242	−	0.106367i	0.483981	+	0.875079i	$0.339190\pi$
$348$	1.77117	−	1.48619i	0.0949448	−	0.0796681i
$349$	−17.1539	−	29.7113i	−0.918225	−	1.59041i	−0.802110	−	0.597176i	$-0.796289\pi$
$349$	−17.1539	−	29.7113i	−0.918225	−	1.59041i	−0.116114	−	0.993236i	$-0.537044\pi$
$350$	−9.31318	+	8.06545i	−0.497811	+	0.431117i
$351$	0.957016	+	0.348325i	0.0510818	+	0.0185922i
$352$	−0.488419	−	2.76996i	−0.0260328	−	0.147639i
$353$	12.7941	+	22.1600i	0.680960	+	1.17946i	0.974688	+	0.223569i	$0.0717707\pi$
$353$	12.7941	+	22.1600i	0.680960	+	1.17946i	−0.293728	+	0.955889i	$0.594896\pi$
$354$	−9.44914			−0.502216
$355$	0.336001	−	0.281938i	0.0178331	−	0.0149637i
$356$	−8.82233	−	7.40282i	−0.467583	−	0.392348i
$357$	−5.89661	−	4.79317i	−0.312082	−	0.253682i
$358$	1.35519	−	7.68566i	0.0716240	−	0.406200i
$359$	−24.9573	−	20.9417i	−1.31720	−	1.10526i	−0.986891	−	0.161387i	$-0.948403\pi$
$359$	−24.9573	−	20.9417i	−1.31720	−	1.10526i	−0.330307	−	0.943874i	$-0.607152\pi$
$360$	0.293005	−	0.507500i	0.0154427	−	0.0267476i
$361$	15.9647	−	10.3019i	0.840246	−	0.542205i
$362$	7.19317	+	12.4589i	0.378064	+	0.654827i
$363$	2.90249	−	1.05642i	0.152341	−	0.0554476i
$364$	−1.38348	−	2.31224i	−0.0725143	−	0.121194i
$365$	5.40712	−	4.53711i	0.283022	−	0.237483i
$366$	0.682319	−	3.86962i	0.0356654	−	0.202268i
$367$	−8.49066	−	3.09035i	−0.443209	−	0.161315i	0.110769	−	0.993846i	$-0.464669\pi$
$367$	−8.49066	−	3.09035i	−0.443209	−	0.161315i	−0.553978	+	0.832531i	$0.686891\pi$
$368$	6.20017			0.323206
$369$	8.83981			0.460182
$370$	3.76124	+	1.36898i	0.195537	+	0.0711698i
$371$	−18.4603	+	7.04686i	−0.958410	+	0.365855i
$372$	0.688413	−	1.19237i	0.0356926	−	0.0618213i
$373$	10.6800	−	18.4983i	0.552990	−	0.957806i	−0.445067	−	0.895497i	$-0.646820\pi$
$373$	10.6800	−	18.4983i	0.552990	−	0.957806i	0.998057	−	0.0623092i	$-0.0198465\pi$
$374$	7.59127	+	2.76299i	0.392535	+	0.142871i
$375$	5.31760	−	1.93545i	0.274599	−	0.0999460i
$376$	0.147381	+	0.0536421i	0.00760057	+	0.00276638i
$377$	−0.408894	+	2.31895i	−0.0210591	+	0.119432i
$378$	−1.35844	−	2.27038i	−0.0698707	−	0.116776i
$379$	5.36933			0.275804			0.137902	−	0.990446i	$-0.455964\pi$
$379$	5.36933			0.275804			0.137902	+	0.990446i	$0.455964\pi$
$380$	−2.45022	+	0.721926i	−0.125694	+	0.0370340i
$381$	−5.83138	+	10.1002i	−0.298751	+	0.517451i
$382$	1.50845	−	8.55483i	0.0771789	−	0.437703i
$383$	−26.4737	+	9.63565i	−1.35274	+	0.492359i	−0.913803	−	0.406157i	$-0.866869\pi$
$383$	−26.4737	+	9.63565i	−1.35274	+	0.492359i	−0.438941	+	0.898516i	$0.644646\pi$
$384$	−0.766044	+	0.642788i	−0.0390920	+	0.0328021i
$385$	2.23907	+	3.74220i	0.114114	+	0.190720i
$386$	−4.09496	−	23.2237i	−0.208428	−	1.18205i
$387$	−4.57721	+	7.92796i	−0.232673	+	0.403001i
$388$	0.628380	+	1.08839i	0.0319012	+	0.0552544i
$389$	16.9768	−	14.2452i	0.860759	−	0.722262i	−0.101373	−	0.994849i	$-0.532323\pi$
$389$	16.9768	−	14.2452i	0.860759	−	0.722262i	0.962131	+	0.272586i	$0.0878790\pi$
$390$	0.103636	+	0.587747i	0.00524780	+	0.0297617i
$391$	−8.90388	+	15.4220i	−0.450289	+	0.779923i
$392$	−1.00000	+	6.92820i	−0.0505076	+	0.349927i
$393$	−0.637324	−	3.61444i	−0.0321487	−	0.182325i
$394$	1.09533	−	6.21192i	0.0551819	−	0.312952i
$395$	0.731298	+	4.14740i	0.0367956	+	0.208678i
$396$	2.15465	+	1.80796i	0.108275	+	0.0908536i
$397$	−14.4921	−	12.1603i	−0.727339	−	0.610310i	0.202066	−	0.979372i	$-0.435234\pi$
$397$	−14.4921	−	12.1603i	−0.727339	−	0.610310i	−0.929405	+	0.369062i	$0.879679\pi$
$398$	−13.5410			−0.678747
$399$	−2.53336	+	11.2509i	−0.126827	+	0.563248i
$400$	−4.65659			−0.232830
$401$	−3.62610	−	3.04266i	−0.181079	−	0.151943i	0.547743	−	0.836647i	$-0.315487\pi$
$401$	−3.62610	−	3.04266i	−0.181079	−	0.151943i	−0.728822	+	0.684704i	$0.759932\pi$
$402$	−11.1012	−	9.31500i	−0.553677	−	0.464590i
$403$	0.243491	+	1.38091i	0.0121292	+	0.0687879i
$404$	−2.33215	+	13.2263i	−0.116029	+	0.658033i
$405$	0.101760	+	0.577108i	0.00505648	+	0.0286767i
$406$	4.62420	−	4.00468i	0.229495	−	0.198749i
$407$	−9.60575	+	16.6376i	−0.476139	+	0.824698i
$408$	−0.498743	−	2.82851i	−0.0246914	−	0.140032i
$409$	0.566573	−	0.475412i	0.0280153	−	0.0235076i	−0.628673	−	0.777670i	$-0.716401\pi$
$409$	0.566573	−	0.475412i	0.0280153	−	0.0235076i	0.656688	+	0.754163i	$0.271957\pi$
$410$	2.59011	+	4.48620i	0.127916	+	0.221558i
$411$	3.64112	−	6.30660i	0.179603	−	0.311082i
$412$	−1.33377	−	7.56416i	−0.0657099	−	0.372659i
$413$	−24.9970	+	0.389802i	−1.23002	+	0.0191809i
$414$	−4.74960	+	3.98539i	−0.233430	+	0.195871i
$415$	−9.06556	+	3.29959i	−0.445011	+	0.161971i
$416$	0.176849	−	1.00296i	0.00867076	−	0.0491743i
$417$	−1.29016	+	2.23462i	−0.0631792	+	0.109430i
$418$	−1.37024	−	12.1834i	−0.0670204	−	0.595911i
$419$	−9.39306			−0.458881			−0.229440	−	0.973323i	$-0.573690\pi$
$419$	−9.39306			−0.458881			−0.229440	+	0.973323i	$0.573690\pi$
$420$	0.754190	−	1.35464i	0.0368007	−	0.0660998i
$421$	3.64930	−	20.6962i	0.177856	−	1.00867i	−0.756940	−	0.653485i	$-0.773306\pi$
$421$	3.64930	−	20.6962i	0.177856	−	1.00867i	0.934796	−	0.355186i	$-0.115582\pi$
$422$	−22.7674	−	8.28667i	−1.10830	−	0.403389i
$423$	−0.147381	+	0.0536421i	−0.00716589	+	0.00260817i
$424$	−7.01801	−	2.55435i	−0.340825	−	0.124050i
$425$	6.68720	−	11.5826i	0.324377	−	0.561837i
$426$	0.374240	−	0.648203i	0.0181320	−	0.0314055i
$427$	1.64539	−	10.2650i	0.0796262	−	0.496756i
$428$	−14.8090	−	5.39003i	−0.715820	−	0.260537i
$429$	−2.86455			−0.138302
$430$	−5.36459			−0.258704
$431$	−23.7586	−	8.64741i	−1.14441	−	0.416531i	−0.300905	−	0.953654i	$-0.597289\pi$
$431$	−23.7586	−	8.64741i	−1.14441	−	0.416531i	−0.843504	+	0.537123i	$0.819511\pi$
$432$	0.173648	−	0.984808i	0.00835465	−	0.0473816i
$433$	−16.2038	+	13.5966i	−0.778706	+	0.653412i	−0.942922	−	0.333013i	$-0.891935\pi$
$433$	−16.2038	+	13.5966i	−0.778706	+	0.653412i	0.164217	+	0.986424i	$0.447490\pi$
$434$	1.77196	−	3.18272i	0.0850568	−	0.152776i
$435$	−1.27321	+	0.463409i	−0.0610455	+	0.0222187i
$436$	−6.04673	−	10.4732i	−0.289586	−	0.501577i
$437$	26.9731	+	1.68900i	1.29030	+	0.0807959i
$438$	6.02250	−	10.4313i	0.287766	−	0.498425i
$439$	−10.9438	−	9.18295i	−0.522320	−	0.438278i	0.343120	−	0.939292i	$-0.388516\pi$
$439$	−10.9438	−	9.18295i	−0.522320	−	0.438278i	−0.865439	+	0.501013i	$0.832961\pi$
$440$	−0.286219	+	1.62323i	−0.0136449	+	0.0773843i
$441$	−3.68732	−	5.95010i	−0.175587	−	0.283338i
$442$	2.24075	+	1.88021i	0.106582	+	0.0894326i
$443$	17.7503	−	14.8942i	0.843341	−	0.707647i	−0.114972	−	0.993369i	$-0.536678\pi$
$443$	17.7503	−	14.8942i	0.843341	−	0.707647i	0.958313	+	0.285722i	$0.0922334\pi$
$444$	6.83029			0.324151
$445$	3.37447	+	5.84475i	0.159965	+	0.277068i
$446$	2.33393	+	13.2364i	0.110515	+	0.626759i
$447$	11.1197	+	4.04723i	0.525942	+	0.191427i
$448$	−2.00000	+	1.73205i	−0.0944911	+	0.0818317i
$449$	17.9099	+	31.0209i	0.845223	+	1.46397i	0.885428	+	0.464777i	$0.153865\pi$
$449$	17.9099	+	31.0209i	0.845223	+	1.46397i	−0.0402053	+	0.999191i	$0.512801\pi$
$450$	3.56716	−	2.99320i	0.168157	−	0.141101i
$451$	−23.3642	+	8.50387i	−1.10018	+	0.400432i
$452$	2.69630	+	15.2915i	0.126823	+	0.719251i
$453$	−6.31658	+	2.29905i	−0.296779	+	0.108019i
$454$	3.98972	−	1.45214i	0.187247	−	0.0681523i
$455$	0.298407	+	1.55057i	0.0139895	+	0.0726918i
$456$	−3.50769	+	2.58769i	−0.164262	+	0.121180i
$457$	14.6670	+	25.4040i	0.686095	+	1.18835i	0.973091	+	0.230419i	$0.0740097\pi$
$457$	14.6670	+	25.4040i	0.686095	+	1.18835i	−0.286997	+	0.957931i	$0.592657\pi$
$458$	3.28434	−	18.6264i	0.153467	−	0.870356i
$459$	2.20019	+	1.84618i	0.102696	+	0.0861722i
$460$	−3.41425	−	1.24268i	−0.159190	−	0.0579404i
$461$	10.0390	+	8.42371i	0.467562	+	0.392331i	0.845905	−	0.533334i	$-0.179061\pi$
$461$	10.0390	+	8.42371i	0.467562	+	0.392331i	−0.378342	+	0.925666i	$0.623506\pi$
$462$	5.77455	+	4.69396i	0.268656	+	0.218383i
$463$	−8.27675	−	14.3357i	−0.384653	−	0.666239i	0.607068	−	0.794650i	$-0.292346\pi$
$463$	−8.27675	−	14.3357i	−0.384653	−	0.666239i	−0.991721	+	0.128411i	$0.959012\pi$
$464$	2.31210			0.107337
$465$	−0.618072	+	0.518624i	−0.0286624	+	0.0240506i
$466$	3.52939	−	2.96151i	0.163496	−	0.137189i
$467$	−18.9543			−0.877102			−0.438551	−	0.898706i	$-0.644508\pi$
$467$	−18.9543			−0.877102			−0.438551	+	0.898706i	$0.644508\pi$
$468$	0.509218	+	0.881991i	0.0235386	+	0.0407700i
$469$	−29.7517	−	24.1842i	−1.37381	−	1.11672i
$470$	−0.0704067	−	0.0590782i	−0.00324762	−	0.00272508i
$471$	2.42555	+	0.882829i	0.111764	+	0.0406786i
$472$	−7.23846	−	6.07379i	−0.333177	−	0.279569i
$473$	4.47119	−	25.3574i	0.205586	−	1.16593i
$474$	3.59326	+	6.22371i	0.165044	+	0.285864i
$475$	−20.2579	−	1.26851i	−0.929498	−	0.0582034i
$476$	−1.43607	−	7.46205i	−0.0658222	−	0.342022i
$477$	7.01801	−	2.55435i	0.321333	−	0.116956i
$478$	17.9077	−	6.51789i	0.819081	−	0.298121i
$479$	−3.95215	−	22.4138i	−0.180578	−	1.02411i	−0.931506	−	0.363726i	$-0.881504\pi$
$479$	−3.95215	−	22.4138i	−0.180578	−	1.02411i	0.750927	−	0.660385i	$-0.229607\pi$
$480$	0.550670	−	0.200428i	0.0251345	−	0.00914822i
$481$	−5.32877	+	4.47136i	−0.242971	+	0.203877i
$482$	7.41973	+	12.8514i	0.337960	+	0.585363i
$483$	−12.4003	+	10.7390i	−0.564235	+	0.488641i
$484$	2.90249	+	1.05642i	0.131931	+	0.0480190i
$485$	−0.127888	−	0.725286i	−0.00580707	−	0.0329335i
$486$	0.500000	+	0.866025i	0.0226805	+	0.0392837i
$487$	9.79638			0.443916			0.221958	−	0.975056i	$-0.428755\pi$
$487$	9.79638			0.443916			0.221958	+	0.975056i	$0.428755\pi$
$488$	3.01003	−	2.52572i	0.136258	−	0.114334i
$489$	0.715546	+	0.600415i	0.0323581	+	0.0271517i
$490$	1.93927	−	3.61473i	0.0876074	−	0.163297i
$491$	0.604724	−	3.42956i	0.0272908	−	0.154774i	−0.968117	−	0.250498i	$-0.919406\pi$
$491$	0.604724	−	3.42956i	0.0272908	−	0.154774i	0.995408	+	0.0957243i	$0.0305167\pi$
$492$	6.77168	+	5.68212i	0.305291	+	0.256170i
$493$	−3.32034	+	5.75100i	−0.149541	+	0.259012i
$494$	1.04258	−	4.31509i	0.0469080	−	0.194145i
$495$	−0.824134	−	1.42744i	−0.0370421	−	0.0641588i
$496$	1.29379	−	0.470902i	0.0580931	−	0.0211441i
$497$	0.963286	−	1.73021i	0.0432093	−	0.0776107i
$498$	−12.6112	+	10.5821i	−0.565122	+	0.474194i
$499$	1.94350	−	11.0221i	0.0870031	−	0.493419i	−0.909903	−	0.414820i	$-0.863844\pi$
$499$	1.94350	−	11.0221i	0.0870031	−	0.493419i	0.996906	−	0.0785985i	$-0.0250445\pi$
$500$	5.31760	+	1.93545i	0.237810	+	0.0865558i
$501$	1.82611			0.0815846
$502$	−8.82743			−0.393988
$503$	26.3483	+	9.58999i	1.17481	+	0.427597i	0.854367	−	0.519670i	$-0.173945\pi$
$503$	26.3483	+	9.58999i	1.17481	+	0.427597i	0.320445	+	0.947267i	$0.396167\pi$
$504$	0.418748	−	2.61240i	0.0186525	−	0.116366i
$505$	3.93516	−	6.81590i	0.175112	−	0.303304i
$506$	8.71958	−	15.1028i	0.387633	−	0.671399i
$507$	11.2413	+	4.09151i	0.499246	+	0.181711i
$508$	−10.9594	+	3.98890i	−0.486245	+	0.176979i
$509$	18.2712	+	6.65018i	0.809857	+	0.294764i	0.713565	−	0.700589i	$-0.247079\pi$
$509$	18.2712	+	6.65018i	0.809857	+	0.294764i	0.0962923	+	0.995353i	$0.469302\pi$
$510$	−0.292269	+	1.65754i	−0.0129419	+	0.0733970i
$511$	15.5018	−	27.8436i	0.685758	−	1.23173i
$512$	−1.00000			−0.0441942
$513$	1.02371	−	4.23698i	0.0451979	−	0.187067i
$514$	−1.58123	+	2.73878i	−0.0697453	+	0.120802i
$515$	−0.781601	+	4.43268i	−0.0344415	+	0.195327i
$516$	−8.60234	+	3.13100i	−0.378697	+	0.137834i
$517$	0.337933	−	0.283559i	0.0148623	−	0.0124709i
$518$	18.0690	−	0.281768i	0.793908	−	0.0123802i
$519$	3.42979	+	19.4513i	0.150551	+	0.853818i
$520$	−0.298407	+	0.516856i	−0.0130860	+	0.0226657i
$521$	−5.12918	−	8.88401i	−0.224714	−	0.389215i	0.731520	−	0.681820i	$-0.238811\pi$
$521$	−5.12918	−	8.88401i	−0.224714	−	0.389215i	−0.956233	+	0.292605i	$0.905478\pi$
$522$	−1.77117	+	1.48619i	−0.0775221	+	0.0650488i
$523$	−0.0850954	−	0.482600i	−0.00372096	−	0.0211026i	0.982891	−	0.184190i	$-0.0589660\pi$
$523$	−0.0850954	−	0.482600i	−0.00372096	−	0.0211026i	−0.986612	+	0.163087i	$0.947855\pi$
$524$	1.83510	−	3.17849i	0.0801667	−	0.138853i
$525$	9.31318	−	8.06545i	0.406461	−	0.352005i
$526$	−2.72112	−	15.4323i	−0.118647	−	0.672878i
$527$	−0.686682	+	3.89437i	−0.0299123	+	0.169641i
$528$	0.488419	+	2.76996i	0.0212557	+	0.120547i
$529$	11.8293	+	9.92596i	0.514317	+	0.431563i
$530$	3.35265	+	2.81320i	0.145630	+	0.122198i
$531$	9.44914			0.410058
$532$	−9.17259	+	6.99025i	−0.397682	+	0.303066i
$533$	−9.00277			−0.389953
$534$	8.82233	+	7.40282i	0.381780	+	0.320351i
$535$	7.07456	+	5.93626i	0.305860	+	0.256647i
$536$	−2.51644	−	14.2714i	−0.108693	−	0.616431i
$537$	−1.35519	+	7.68566i	−0.0584807	+	0.331661i
$538$	2.18600	+	12.3974i	0.0942451	+	0.534491i
$539$	15.4698	+	12.1793i	0.666332	+	0.524600i
$540$	−0.293005	+	0.507500i	−0.0126089	+	0.0218393i
$541$	−7.79320	−	44.1974i	−0.335056	−	1.90020i	−0.426681	−	0.904402i	$-0.640317\pi$
$541$	−7.79320	−	44.1974i	−0.335056	−	1.90020i	0.0916256	−	0.995794i	$-0.470794\pi$
$542$	−15.7707	+	13.2332i	−0.677411	+	0.568415i
$543$	−7.19317	−	12.4589i	−0.308688	−	0.534664i
$544$	1.43607	−	2.48735i	0.0615711	−	0.106644i
$545$	1.23063	+	6.97923i	0.0527142	+	0.298957i
$546$	1.38348	+	2.31224i	0.0592077	+	0.0989547i
$547$	15.7997	−	13.2575i	0.675546	−	0.566850i	−0.239155	−	0.970981i	$-0.576870\pi$
$547$	15.7997	−	13.2575i	0.675546	−	0.566850i	0.914701	+	0.404131i	$0.132426\pi$
$548$	6.84306	−	2.49067i	0.292321	−	0.106396i
$549$	−0.682319	+	3.86962i	−0.0291207	+	0.165151i
$550$	−6.54878	+	11.3428i	−0.279241	+	0.483659i
$551$	10.0585	+	0.629845i	0.428507	+	0.0268323i
$552$	−6.20017			−0.263897
$553$	9.76246	+	16.3162i	0.415142	+	0.693834i
$554$	1.26833	−	7.19304i	0.0538861	−	0.305603i
$555$	−3.76124	−	1.36898i	−0.159656	−	0.0581099i
$556$	−2.42470	+	0.882519i	−0.102830	+	0.0374271i
$557$	18.4450	+	6.71344i	0.781541	+	0.284458i	0.701815	−	0.712359i	$-0.252373\pi$
$557$	18.4450	+	6.71344i	0.781541	+	0.284458i	0.0797260	+	0.996817i	$0.474595\pi$
$558$	−0.688413	+	1.19237i	−0.0291429	+	0.0504769i
$559$	4.66159	−	8.07412i	0.197164	−	0.341499i
$560$	1.44849	−	0.552934i	0.0612099	−	0.0233657i
$561$	−7.59127	−	2.76299i	−0.320504	−	0.116654i
$562$	19.3616			0.816721
$563$	−37.1467			−1.56555			−0.782774	−	0.622306i	$-0.786196\pi$
$563$	−37.1467			−1.56555			−0.782774	+	0.622306i	$0.786196\pi$
$564$	−0.147381	−	0.0536421i	−0.00620584	−	0.00225874i
$565$	1.58006	−	8.96098i	0.0664737	−	0.376991i
$566$	9.57374	−	8.03332i	0.402414	−	0.337666i
$567$	1.35844	+	2.27038i	0.0570491	+	0.0953471i
$568$	0.703341	−	0.255995i	0.0295115	−	0.0107413i
$569$	15.0802	+	26.1197i	0.632195	+	1.09499i	0.987102	+	0.160093i	$0.0511793\pi$
$569$	15.0802	+	26.1197i	0.632195	+	1.09499i	−0.354907	+	0.934902i	$0.615487\pi$
$570$	2.45022	−	0.721926i	0.102629	−	0.0302382i
$571$	−12.2643	+	21.2424i	−0.513246	+	0.888968i	0.486636	+	0.873605i	$0.338224\pi$
$571$	−12.2643	+	21.2424i	−0.513246	+	0.888968i	−0.999882	+	0.0153629i	$0.995110\pi$
$572$	−2.19437	−	1.84129i	−0.0917512	−	0.0769884i
$573$	−1.50845	+	8.55483i	−0.0630163	+	0.357383i
$574$	18.1484	+	14.7523i	0.757500	+	0.615749i
$575$	−22.1170	−	18.5583i	−0.922341	−	0.773936i
$576$	0.766044	−	0.642788i	0.0319185	−	0.0267828i
$577$	4.91367			0.204559			0.102279	−	0.994756i	$-0.467386\pi$
$577$	4.91367			0.204559			0.102279	+	0.994756i	$0.467386\pi$
$578$	−4.37540	−	7.57841i	−0.181992	−	0.315220i
$579$	4.09496	+	23.2237i	0.170181	+	0.965144i
$580$	−1.27321	−	0.463409i	−0.0528670	−	0.0192420i
$581$	−32.9256	+	28.5144i	−1.36598	+	1.18298i
$582$	−0.628380	−	1.08839i	−0.0260472	−	0.0451150i
$583$	−16.0918	+	13.5026i	−0.666454	+	0.559221i
$584$	11.3186	−	4.11963i	0.468367	−	0.170471i
$585$	−0.103636	−	0.587747i	−0.00428481	−	0.0243004i
$586$	−0.682576	+	0.248437i	−0.0281969	+	0.0102628i
$587$	27.2027	−	9.90098i	1.12278	−	0.408657i	0.287111	−	0.957897i	$-0.407305\pi$
$587$	27.2027	−	9.90098i	1.12278	−	0.408657i	0.835665	+	0.549240i	$0.185083\pi$
$588$	1.00000	−	6.92820i	0.0412393	−	0.285714i
$589$	5.75677	−	1.69616i	0.237204	−	0.0698890i
$590$	2.76865	+	4.79544i	0.113983	+	0.197425i
$591$	−1.09533	+	6.21192i	−0.0450558	+	0.255524i
$592$	5.23230	+	4.39043i	0.215046	+	0.180445i
$593$	4.45322	+	1.62084i	0.182872	+	0.0665599i	0.431833	−	0.901954i	$-0.357867\pi$
$593$	4.45322	+	1.62084i	0.182872	+	0.0665599i	−0.248961	+	0.968513i	$0.580089\pi$
$594$	−2.15465	−	1.80796i	−0.0884063	−	0.0741817i
$595$	−0.704798	+	4.39696i	−0.0288939	+	0.180258i
$596$	5.91665	+	10.2479i	0.242356	+	0.419772i
$597$	13.5410			0.554195
$598$	4.83716	−	4.05886i	0.197806	−	0.165979i
$599$	19.3243	−	16.2150i	0.789570	−	0.662528i	−0.156069	−	0.987746i	$-0.549882\pi$
$599$	19.3243	−	16.2150i	0.789570	−	0.662528i	0.945639	+	0.325219i	$0.105438\pi$
$600$	4.65659			0.190105
$601$	−0.357997	−	0.620069i	−0.0146030	−	0.0252931i	0.858632	−	0.512593i	$-0.171315\pi$
$601$	−0.357997	−	0.620069i	−0.0146030	−	0.0252931i	−0.873235	+	0.487300i	$0.837982\pi$
$602$	−22.6277	+	8.63770i	−0.922238	+	0.352046i
$603$	11.1012	+	9.31500i	0.452075	+	0.379336i
$604$	−6.31658	−	2.29905i	−0.257018	−	0.0935469i
$605$	−1.38658	−	1.16348i	−0.0563724	−	0.0473020i
$606$	2.33215	−	13.2263i	0.0947373	−	0.537282i
$607$	−6.02557	−	10.4366i	−0.244570	−	0.423608i	0.717440	−	0.696620i	$-0.245314\pi$
$607$	−6.02557	−	10.4366i	−0.244570	−	0.423608i	−0.962011	+	0.273012i	$0.911980\pi$
$608$	−4.35038	−	0.272412i	−0.176431	−	0.0110478i
$609$	−4.62420	+	4.00468i	−0.187382	+	0.162278i
$610$	−2.16376	+	0.787544i	−0.0876080	+	0.0318867i
$611$	0.150098	−	0.0546310i	0.00607230	−	0.00221014i
$612$	0.498743	+	2.82851i	0.0201605	+	0.114336i
$613$	9.41558	−	3.42699i	0.380292	−	0.138415i	−0.144799	−	0.989461i	$-0.546254\pi$
$613$	9.41558	−	3.42699i	0.380292	−	0.138415i	0.525091	+	0.851046i	$0.324031\pi$
$614$	7.75530	−	6.50747i	0.312978	−	0.262620i
$615$	−2.59011	−	4.48620i	−0.104443	−	0.180901i
$616$	1.40635	+	7.30759i	0.0566633	+	0.294431i
$617$	14.8119	+	5.39110i	0.596306	+	0.217038i	0.622501	−	0.782619i	$-0.286117\pi$
$617$	14.8119	+	5.39110i	0.596306	+	0.217038i	−0.0261947	+	0.999657i	$0.508339\pi$
$618$	1.33377	+	7.56416i	0.0536519	+	0.304275i
$619$	−0.691819	−	1.19827i	−0.0278066	−	0.0481624i	0.851787	−	0.523888i	$-0.175519\pi$
$619$	−0.691819	−	1.19827i	−0.0278066	−	0.0481624i	−0.879594	+	0.475725i	$0.842186\pi$
$620$	−0.806835			−0.0324033
$621$	4.74960	−	3.98539i	0.190595	−	0.159928i
$622$	21.8995	+	18.3758i	0.878089	+	0.736804i
$623$	23.6442	+	19.2197i	0.947287	+	0.770020i
$624$	−0.176849	+	1.00296i	−0.00707964	+	0.0401507i
$625$	15.2955	+	12.8344i	0.611818	+	0.513376i
$626$	−15.7385	+	27.2598i	−0.629036	+	1.08952i
$627$	1.37024	+	12.1834i	0.0547219	+	0.486559i
$628$	1.29061	+	2.23540i	0.0515009	+	0.0892022i
$629$	−18.4345	+	6.70960i	−0.735031	+	0.267529i
$630$	−0.754190	+	1.35464i	−0.0300476	+	0.0539703i
$631$	30.6262	−	25.6984i	1.21921	−	1.02304i	0.220344	−	0.975422i	$-0.429282\pi$
$631$	30.6262	−	25.6984i	1.21921	−	1.02304i	0.998866	−	0.0476160i	$-0.0151624\pi$
$632$	−1.24793	+	7.07734i	−0.0496398	+	0.281522i
$633$	22.7674	+	8.28667i	0.904924	+	0.329365i
$634$	−16.3174			−0.648048
$635$	6.83450			0.271219
$636$	7.01801	+	2.55435i	0.278282	+	0.101286i
$637$	3.75530	+	6.05979i	0.148790	+	0.240098i
$638$	3.25161	−	5.63196i	0.128733	−	0.222972i
$639$	−0.374240	+	0.648203i	−0.0148047	+	0.0256425i
$640$	0.550670	+	0.200428i	0.0217671	+	0.00792259i
$641$	−15.1506	+	5.51437i	−0.598413	+	0.217804i	−0.623426	−	0.781883i	$-0.714260\pi$
$641$	−15.1506	+	5.51437i	−0.598413	+	0.217804i	0.0250128	+	0.999687i	$0.492037\pi$
$642$	14.8090	+	5.39003i	0.584464	+	0.212728i
$643$	−1.21183	+	6.87265i	−0.0477901	+	0.271031i	−0.999334	−	0.0364808i	$-0.988385\pi$
$643$	−1.21183	+	6.87265i	−0.0477901	+	0.271031i	0.951544	+	0.307512i	$0.0994963\pi$
$644$	−16.4021	+	0.255773i	−0.646333	+	0.0100789i
$645$	5.36459			0.211231
$646$	6.92504	−	10.4297i	0.272462	−	0.410351i
$647$	−7.83521	+	13.5710i	−0.308034	+	0.533531i	−0.977932	−	0.208922i	$-0.933004\pi$
$647$	−7.83521	+	13.5710i	−0.308034	+	0.533531i	0.669898	+	0.742453i	$0.266338\pi$
$648$	−0.173648	+	0.984808i	−0.00682154	+	0.0386869i
$649$	−24.9747	+	9.09004i	−0.980342	+	0.356815i
$650$	−3.63292	+	3.04838i	−0.142495	+	0.119567i
$651$	−1.77196	+	3.18272i	−0.0694486	+	0.124741i
$652$	0.162201	+	0.919889i	0.00635229	+	0.0360256i
$653$	−4.25658	+	7.37261i	−0.166573	+	0.288512i	−0.937213	−	0.348758i	$-0.886603\pi$
$653$	−4.25658	+	7.37261i	−0.166573	+	0.288512i	0.770640	+	0.637271i	$0.219937\pi$
$654$	6.04673	+	10.4732i	0.236446	+	0.409536i
$655$	−1.64759	+	1.38249i	−0.0643767	+	0.0540185i
$656$	1.53502	+	8.70551i	0.0599323	+	0.339893i
$657$	−6.02250	+	10.4313i	−0.234960	+	0.406963i
$658$	−0.392098	−	0.135827i	−0.0152856	−	0.00529507i
$659$	−2.58984	−	14.6877i	−0.100886	−	0.572151i	−0.992784	−	0.119915i	$-0.961738\pi$
$659$	−2.58984	−	14.6877i	−0.100886	−	0.572151i	0.891898	−	0.452236i	$-0.149373\pi$
$660$	0.286219	−	1.62323i	0.0111411	−	0.0631840i
$661$	−5.64143	−	31.9942i	−0.219426	−	1.24443i	−0.873058	−	0.487616i	$-0.837867\pi$
$661$	−5.64143	−	31.9942i	−0.219426	−	1.24443i	0.653632	−	0.756812i	$-0.273244\pi$
$662$	−7.95572	−	6.67564i	−0.309208	−	0.259456i
$663$	−2.24075	−	1.88021i	−0.0870236	−	0.0730214i
$664$	−16.4628			−0.638880
$665$	6.45211	−	2.01088i	0.250202	−	0.0779787i
$666$	−6.83029			−0.264668
$667$	10.9816	+	9.21462i	0.425208	+	0.356792i
$668$	1.39888	+	1.17380i	0.0541243	+	0.0454157i
$669$	−2.33393	−	13.2364i	−0.0902348	−	0.511747i
$670$	−1.47466	+	8.36320i	−0.0569710	+	0.323099i
$671$	−1.91915	−	10.8841i	−0.0740881	−	0.420174i
$672$	2.00000	−	1.73205i	0.0771517	−	0.0668153i
$673$	6.74503	−	11.6827i	0.260002	−	0.450336i	−0.706240	−	0.707972i	$-0.749610\pi$
$673$	6.74503	−	11.6827i	0.260002	−	0.450336i	0.966242	+	0.257636i	$0.0829436\pi$
$674$	−0.582336	−	3.30259i	−0.0224308	−	0.127211i
$675$	−3.56716	+	2.99320i	−0.137300	+	0.115208i
$676$	5.98139	+	10.3601i	0.230054	+	0.398465i
$677$	−3.07246	+	5.32165i	−0.118084	+	0.204528i	−0.919008	−	0.394238i	$-0.871009\pi$
$677$	−3.07246	+	5.32165i	−0.118084	+	0.204528i	0.800924	+	0.598766i	$0.204342\pi$
$678$	−2.69630	−	15.2915i	−0.103551	−	0.587266i
$679$	−1.70723	−	2.85333i	−0.0655176	−	0.109501i
$680$	−1.28934	+	1.08188i	−0.0494437	+	0.0414882i
$681$	−3.98972	+	1.45214i	−0.152886	+	0.0556461i
$682$	0.672468	−	3.81376i	0.0257501	−	0.146036i
$683$	4.57211	−	7.91913i	0.174947	−	0.303017i	−0.765196	−	0.643797i	$-0.777358\pi$
$683$	4.57211	−	7.91913i	0.174947	−	0.303017i	0.940143	+	0.340780i	$0.110691\pi$
$684$	3.50769	−	2.58769i	0.134120	−	0.0989428i
$685$	−4.26747			−0.163052
$686$	2.35962	−	18.3693i	0.0900908	−	0.701344i
$687$	−3.28434	+	18.6264i	−0.125306	+	0.710643i
$688$	−8.60234	−	3.13100i	−0.327961	−	0.119368i
$689$	−7.14739	+	2.60144i	−0.272294	+	0.0991069i
$690$	3.41425	+	1.24268i	0.129978	+	0.0473082i
$691$	17.6723	−	30.6093i	0.672285	−	1.16443i	−0.304969	−	0.952362i	$-0.598646\pi$
$691$	17.6723	−	30.6093i	0.672285	−	1.16443i	0.977254	−	0.212070i	$-0.0680205\pi$
$692$	−9.87569	+	17.1052i	−0.375417	+	0.650242i
$693$	−5.77455	−	4.69396i	−0.219357	−	0.178309i
$694$	−5.44387	−	1.98141i	−0.206646	−	0.0752132i
$695$	1.51209			0.0573569
$696$	−2.31210			−0.0876400
$697$	−23.8580	−	8.68362i	−0.903688	−	0.328915i
$698$	−5.95747	+	33.7865i	−0.225494	+	1.27884i
$699$	−3.52939	+	2.96151i	−0.133494	+	0.112014i
$700$	12.3187	−	0.192097i	0.465603	−	0.00726058i
$701$	18.0760	−	6.57911i	0.682720	−	0.248490i	0.0227048	−	0.999742i	$-0.492772\pi$
$701$	18.0760	−	6.57911i	0.682720	−	0.248490i	0.660015	+	0.751253i	$0.270550\pi$
$702$	−0.509218	−	0.881991i	−0.0192192	−	0.0332886i
$703$	21.5665	+	20.5254i	0.813396	+	0.774128i
$704$	−1.40635	+	2.43586i	−0.0530037	+	0.0918050i
$705$	0.0704067	+	0.0590782i	0.00265167	+	0.00222501i
$706$	4.44334	−	25.1994i	0.167227	−	0.948393i
$707$	5.62393	−	35.0855i	0.211510	−	1.31953i
$708$	7.23846	+	6.07379i	0.272038	+	0.228267i
$709$	−10.9927	+	9.22397i	−0.412840	+	0.346414i	−0.825431	−	0.564503i	$-0.809068\pi$
$709$	−10.9927	+	9.22397i	−0.412840	+	0.346414i	0.412592	+	0.910916i	$0.364624\pi$
$710$	−0.438618			−0.0164610
$711$	−3.59326	−	6.22371i	−0.134758	−	0.233407i
$712$	1.99986	+	11.3418i	0.0749479	+	0.425051i
$713$	8.02174	+	2.91967i	0.300416	+	0.109343i
$714$	1.43607	+	7.46205i	0.0537436	+	0.279260i
$715$	0.839328	+	1.45376i	0.0313891	+	0.0543675i
$716$	−5.97838	+	5.01646i	−0.223423	+	0.187474i
$717$	−17.9077	+	6.51789i	−0.668777	+	0.243415i
$718$	5.65737	+	32.0845i	0.211131	+	1.19738i
$719$	4.71687	−	1.71680i	0.175910	−	0.0640258i	−0.252564	−	0.967580i	$-0.581274\pi$
$719$	4.71687	−	1.71680i	0.175910	−	0.0640258i	0.428473	+	0.903554i	$0.359052\pi$
$720$	−0.550670	+	0.200428i	−0.0205223	+	0.00746949i
$721$	3.84042	+	19.9554i	0.143025	+	0.743179i
$722$	−18.8516	−	2.37019i	−0.701583	−	0.0882095i
$723$	−7.41973	−	12.8514i	−0.275943	−	0.477947i
$724$	2.49816	−	14.1678i	0.0928434	−	0.526541i
$725$	−8.24763	−	6.92058i	−0.306309	−	0.257024i
$726$	−2.90249	−	1.05642i	−0.107721	−	0.0392074i
$727$	27.6783	+	23.2249i	1.02653	+	0.861362i	0.990434	−	0.137986i	$-0.0440629\pi$
$727$	27.6783	+	23.2249i	1.02653	+	0.861362i	0.0360973	+	0.999348i	$0.488507\pi$
$728$	−0.426468	+	2.66056i	−0.0158060	+	0.0986071i
$729$	−0.500000	−	0.866025i	−0.0185185	−	0.0320750i
$730$	−7.05850			−0.261247
$731$	20.1415	−	16.9007i	0.744959	−	0.625095i
$732$	−3.01003	+	2.52572i	−0.111254	+	0.0933532i
$733$	47.6852			1.76129			0.880646	−	0.473775i	$-0.157109\pi$
$733$	47.6852			1.76129			0.880646	+	0.473775i	$0.157109\pi$
$734$	4.51779	+	7.82504i	0.166755	+	0.288827i
$735$	−1.93927	+	3.61473i	−0.0715312	+	0.133331i
$736$	−4.74960	−	3.98539i	−0.175073	−	0.146903i
$737$	−38.3022	−	13.9409i	−1.41088	−	0.513518i
$738$	−6.77168	−	5.68212i	−0.249269	−	0.209162i
$739$	−6.27023	+	35.5602i	−0.230654	+	1.30810i	0.620921	+	0.783873i	$0.286759\pi$
$739$	−6.27023	+	35.5602i	−0.230654	+	1.30810i	−0.851576	+	0.524232i	$0.824352\pi$
$740$	−2.00131	−	3.46637i	−0.0735697	−	0.127426i
$741$	−1.04258	+	4.31509i	−0.0383002	+	0.158519i
$742$	18.6710	+	6.46783i	0.685435	+	0.237442i
$743$	−1.10155	+	0.400932i	−0.0404120	+	0.0147088i	−0.362147	−	0.932121i	$-0.617956\pi$
$743$	−1.10155	+	0.400932i	−0.0404120	+	0.0147088i	0.321735	+	0.946830i	$0.395734\pi$
$744$	−1.29379	+	0.470902i	−0.0474328	+	0.0172641i
$745$	−1.20415	−	6.82910i	−0.0441168	−	0.250199i
$746$	−20.0718	+	7.30556i	−0.734883	+	0.267475i
$747$	12.6112	−	10.5821i	0.461420	−	0.387178i
$748$	−4.03923	−	6.99615i	−0.147689	−	0.255805i
$749$	39.3985	+	13.6480i	1.43959	+	0.498689i
$750$	−5.31760	−	1.93545i	−0.194171	−	0.0706725i
$751$	2.43101	+	13.7869i	0.0887087	+	0.503092i	0.996495	+	0.0836581i	$0.0266604\pi$
$751$	2.43101	+	13.7869i	0.0887087	+	0.503092i	−0.907786	+	0.419434i	$0.862229\pi$
$752$	−0.0784195	−	0.135827i	−0.00285967	−	0.00495309i
$753$	8.82743			0.321689
$754$	1.80382	−	1.51359i	0.0656914	−	0.0551217i
$755$	3.01756	+	2.53203i	0.109820	+	0.0921501i
$756$	−0.418748	+	2.61240i	−0.0152297	+	0.0950122i
$757$	−1.38554	+	7.85779i	−0.0503583	+	0.285596i	−0.999579	−	0.0290149i	$-0.990763\pi$
$757$	−1.38554	+	7.85779i	−0.0503583	+	0.285596i	0.949221	+	0.314611i	$0.101874\pi$
$758$	−4.11314	−	3.45134i	−0.149396	−	0.125358i
$759$	−8.71958	+	15.1028i	−0.316501	+	0.548195i
$760$	2.34102	+	1.02194i	0.0849179	+	0.0370698i
$761$	3.26597	+	5.65682i	0.118391	+	0.205060i	0.919130	−	0.393954i	$-0.128893\pi$
$761$	3.26597	+	5.65682i	0.118391	+	0.205060i	−0.800739	+	0.599013i	$0.795560\pi$
$762$	10.9594	−	3.98890i	0.397017	−	0.144502i
$763$	16.4282	+	27.4568i	0.594742	+	0.994002i
$764$	−6.65448	+	5.58377i	−0.240751	+	0.202014i
$765$	0.292269	−	1.65754i	0.0105670	−	0.0599284i
$766$	26.4737	+	9.63565i	0.956535	+	0.348150i
$767$	−9.62334			−0.347479
$768$	1.00000			0.0360844
$769$	47.6400	+	17.3396i	1.71794	+	0.625280i	0.997658	−	0.0683974i	$-0.0217886\pi$
$769$	47.6400	+	17.3396i	1.71794	+	0.625280i	0.720285	+	0.693678i	$0.244011\pi$
$770$	0.690209	−	4.30594i	0.0248734	−	0.155175i
$771$	1.58123	−	2.73878i	0.0569468	−	0.0986347i
$772$	−11.7910	+	20.4226i	−0.424367	+	0.735024i
$773$	−36.6148	−	13.3267i	−1.31694	−	0.479327i	−0.414464	−	0.910066i	$-0.636031\pi$
$773$	−36.6148	−	13.3267i	−1.31694	−	0.479327i	−0.902477	+	0.430738i	$0.858253\pi$
$774$	8.60234	−	3.13100i	0.309205	−	0.112541i
$775$	−6.02467	−	2.19280i	−0.216413	−	0.0787677i
$776$	0.218234	−	1.23767i	0.00783414	−	0.0444296i
$777$	−18.0690	+	0.281768i	−0.648224	+	0.0101084i
$778$	−22.1617			−0.794534
$779$	4.30641	+	38.2904i	0.154293	+	1.37190i
$780$	0.298407	−	0.516856i	0.0106847	−	0.0185064i
$781$	0.365572	−	2.07326i	0.0130812	−	0.0741871i
$782$	16.7338	−	6.09061i	0.598400	−	0.217800i
$783$	1.77117	−	1.48619i	0.0632965	−	0.0531121i
$784$	5.21941	−	4.66452i	0.186407	−	0.166590i
$785$	−0.262664	−	1.48964i	−0.00937489	−	0.0531676i
$786$	−1.83510	+	3.17849i	−0.0654559	+	0.113373i
$787$	−17.8795	−	30.9682i	−0.637335	−	1.10390i	−0.986015	−	0.166655i	$-0.946703\pi$
$787$	−17.8795	−	30.9682i	−0.637335	−	1.10390i	0.348680	−	0.937242i	$-0.386630\pi$
$788$	−4.83202	+	4.05455i	−0.172134	+	0.144437i
$789$	2.72112	+	15.4323i	0.0968745	+	0.549403i
$790$	2.10569	−	3.64716i	0.0749171	−	0.129760i
$791$	−7.76369	−	40.3413i	−0.276045	−	1.43437i
$792$	−0.488419	−	2.76996i	−0.0173552	−	0.0984263i
$793$	0.694898	−	3.94096i	0.0246765	−	0.139948i
$794$	3.28510	+	18.6307i	0.116584	+	0.661179i
$795$	−3.35265	−	2.81320i	−0.118906	−	0.0997741i
$796$	10.3730	+	8.70396i	0.367660	+	0.308504i
$797$	14.1899			0.502632			0.251316	−	0.967905i	$-0.419137\pi$
$797$	14.1899			0.502632			0.251316	+	0.967905i	$0.419137\pi$
$798$	9.17259	−	6.99025i	0.324706	−	0.247452i
$799$	0.450464			0.0159363
$800$	3.56716	+	2.99320i	0.126118	+	0.105826i
$801$	−8.82233	−	7.40282i	−0.311722	−	0.261566i
$802$	0.821970	+	4.66162i	0.0290248	+	0.164608i
$803$	5.88300	−	33.3642i	0.207607	−	1.17740i
$804$	2.51644	+	14.2714i	0.0887478	+	0.503314i
$805$	9.08341	+	3.14659i	0.320148	+	0.110903i
$806$	0.701105	−	1.21435i	0.0246954	−	0.0427736i
$807$	−2.18600	−	12.3974i	−0.0769508	−	0.436410i
$808$	10.2882	−	8.63286i	0.361939	−	0.303703i
$809$	−10.4218	−	18.0511i	−0.366410	−	0.634642i	0.622591	−	0.782547i	$-0.286080\pi$
$809$	−10.4218	−	18.0511i	−0.366410	−	0.634642i	−0.989001	+	0.147906i	$0.952747\pi$
$810$	0.293005	−	0.507500i	0.0102952	−	0.0178317i
$811$	−5.13876	−	29.1434i	−0.180446	−	1.02336i	−0.931668	−	0.363312i	$-0.881646\pi$
$811$	−5.13876	−	29.1434i	−0.180446	−	1.02336i	0.751221	−	0.660051i	$-0.229465\pi$
$812$	−6.11650	+	0.0953804i	−0.214647	+	0.00334719i
$813$	15.7707	−	13.2332i	0.553104	−	0.464109i
$814$	18.0529	−	6.57072i	0.632754	−	0.230304i
$815$	0.0950517	−	0.539065i	0.00332951	−	0.0188826i
$816$	−1.43607	+	2.48735i	−0.0502726	+	0.0870746i
$817$	−36.5705	−	15.9644i	−1.27944	−	0.558524i
$818$	−0.739609			−0.0258598
$819$	−1.38348	−	2.31224i	−0.0483429	−	0.0807962i
$820$	0.899536	−	5.10152i	0.0314132	−	0.178153i
$821$	35.1250	+	12.7845i	1.22587	+	0.446181i	0.872182	−	0.489182i	$-0.162705\pi$
$821$	35.1250	+	12.7845i	1.22587	+	0.446181i	0.353689	+	0.935363i	$0.384927\pi$
$822$	−6.84306	+	2.49067i	−0.238679	+	0.0868721i
$823$	−3.91632	−	1.42542i	−0.136514	−	0.0496871i	0.272860	−	0.962054i	$-0.412031\pi$
$823$	−3.91632	−	1.42542i	−0.136514	−	0.0496871i	−0.409374	+	0.912367i	$0.634253\pi$
$824$	−3.84042	+	6.65181i	−0.133787	+	0.231727i
$825$	6.54878	−	11.3428i	0.227999	−	0.394906i
$826$	19.3994	+	15.7692i	0.674991	+	0.548680i
$827$	−31.4540	−	11.4483i	−1.09376	−	0.398097i	−0.268750	−	0.963210i	$-0.586610\pi$
$827$	−31.4540	−	11.4483i	−1.09376	−	0.398097i	−0.825014	+	0.565113i	$0.808833\pi$
$828$	6.20017			0.215471
$829$	−35.4925			−1.23271			−0.616353	−	0.787470i	$-0.711391\pi$
$829$	−35.4925			−1.23271			−0.616353	+	0.787470i	$0.711391\pi$
$830$	9.06556	+	3.29959i	0.314670	+	0.114531i
$831$	−1.26833	+	7.19304i	−0.0439978	+	0.249524i
$832$	−0.780167	+	0.654638i	−0.0270474	+	0.0226955i
$833$	4.10686	+	19.6811i	0.142294	+	0.681909i
$834$	2.42470	−	0.882519i	0.0839605	−	0.0305591i
$835$	−0.535060	−	0.926751i	−0.0185165	−	0.0320716i
$836$	−6.78170	+	10.2138i	−0.234550	+	0.353252i
$837$	0.688413	−	1.19237i	0.0237950	−	0.0412142i
$838$	7.19550	+	6.03774i	0.248564	+	0.208570i
$839$	2.20204	−	12.4884i	0.0760228	−	0.431147i	−0.922912	−	0.385010i	$-0.874198\pi$
$839$	2.20204	−	12.4884i	0.0760228	−	0.431147i	0.998935	−	0.0461366i	$-0.0146910\pi$
$840$	−1.44849	+	0.552934i	−0.0499777	+	0.0190780i
$841$	−18.1202	−	15.2046i	−0.624833	−	0.524297i
$842$	−16.0988	+	13.5085i	−0.554800	+	0.465533i
$843$	−19.3616			−0.666850
$844$	12.1143	+	20.9826i	0.416991	+	0.722250i
$845$	−1.21733	−	6.90382i	−0.0418774	−	0.237499i
$846$	0.147381	+	0.0536421i	0.00506705	+	0.00184425i
$847$	−7.72190	−	2.67495i	−0.265328	−	0.0919122i
$848$	3.73421	+	6.46783i	0.128233	+	0.222106i
$849$	−9.57374	+	8.03332i	−0.328570	+	0.275703i
$850$	−12.5678	+	4.57431i	−0.431073	+	0.156898i
$851$	7.35381	+	41.7055i	0.252085	+	1.42965i
$852$	−0.703341	+	0.255995i	−0.0240961	+	0.00877026i
$853$	−32.1538	+	11.7030i	−1.10092	+	0.400704i	−0.827657	−	0.561234i	$-0.810327\pi$
$853$	−32.1538	+	11.7030i	−1.10092	+	0.400704i	−0.273268	+	0.961938i	$0.588104\pi$
$854$	−7.85864	+	6.80578i	−0.268917	+	0.232889i
$855$	−2.45022	+	0.721926i	−0.0837958	+	0.0246894i
$856$	7.87970	+	13.6480i	0.269323	+	0.466481i
$857$	7.26848	−	41.2216i	0.248287	−	1.40810i	−0.564448	−	0.825469i	$-0.690911\pi$
$857$	7.26848	−	41.2216i	0.248287	−	1.40810i	0.812734	−	0.582634i	$-0.197978\pi$
$858$	2.19437	+	1.84129i	0.0749145	+	0.0628608i
$859$	−23.2805	−	8.47340i	−0.794320	−	0.289109i	−0.0871892	−	0.996192i	$-0.527788\pi$
$859$	−23.2805	−	8.47340i	−0.794320	−	0.289109i	−0.707131	+	0.707083i	$0.750011\pi$
$860$	4.10952	+	3.44829i	0.140133	+	0.117586i
$861$	−18.1484	−	14.7523i	−0.618496	−	0.502757i
$862$	12.6417	+	21.8960i	0.430577	+	0.745781i
$863$	23.0675			0.785226			0.392613	−	0.919704i	$-0.371571\pi$
$863$	23.0675			0.785226			0.392613	+	0.919704i	$0.371571\pi$
$864$	−0.766044	+	0.642788i	−0.0260614	+	0.0218681i
$865$	8.86660	−	7.43996i	0.301473	−	0.252966i
$866$	21.1526			0.718794
$867$	4.37540	+	7.57841i	0.148596	+	0.257376i
$868$	−3.40321	+	1.29911i	−0.115513	+	0.0440947i
$869$	15.4844	+	12.9930i	0.525273	+	0.440756i
$870$	1.27321	+	0.463409i	0.0431657	+	0.0157110i
$871$	−11.3058	−	9.48673i	−0.383084	−	0.321446i
$872$	−2.10001	+	11.9097i	−0.0711152	+	0.403314i
$873$	0.628380	+	1.08839i	0.0212674	+	0.0368363i
$874$	−19.5769	−	18.6318i	−0.662198	−	0.630230i
$875$	−14.1472	−	4.90072i	−0.478262	−	0.165675i
$876$	−11.3186	+	4.11963i	−0.382420	+	0.139189i
$877$	32.7768	−	11.9298i	1.10679	−	0.402840i	0.276978	−	0.960876i	$-0.410667\pi$
$877$	32.7768	−	11.9298i	1.10679	−	0.402840i	0.829817	+	0.558036i	$0.188445\pi$
$878$	2.48076	+	14.0691i	0.0837216	+	0.474809i
$879$	0.682576	−	0.248437i	0.0230227	−	0.00837958i
$880$	1.26265	−	1.05949i	0.0425638	−	0.0357153i
$881$	1.11216	+	1.92631i	0.0374696	+	0.0648992i	0.884152	−	0.467199i	$-0.154737\pi$
$881$	1.11216	+	1.92631i	0.0374696	+	0.0648992i	−0.846682	+	0.532098i	$0.821404\pi$
$882$	−1.00000	+	6.92820i	−0.0336718	+	0.233285i
$883$	−15.1753	−	5.52337i	−0.510691	−	0.185876i	0.0738056	−	0.997273i	$-0.476486\pi$
$883$	−15.1753	−	5.52337i	−0.510691	−	0.185876i	−0.584496	+	0.811396i	$0.698708\pi$
$884$	−0.507937	−	2.88065i	−0.0170838	−	0.0968869i
$885$	−2.76865	−	4.79544i	−0.0930671	−	0.161197i
$886$	−23.1713			−0.778456
$887$	34.7640	−	29.1705i	1.16726	−	0.979449i	0.167282	−	0.985909i	$-0.446501\pi$
$887$	34.7640	−	29.1705i	1.16726	−	0.979449i	0.999979	+	0.00646032i	$0.00205640\pi$
$888$	−5.23230	−	4.39043i	−0.175585	−	0.147333i
$889$	28.8278	−	11.0045i	0.966853	−	0.369077i
$890$	1.17194	−	6.64640i	0.0392835	−	0.222788i
$891$	2.15465	+	1.80796i	0.0721834	+	0.0605691i
$892$	6.72027	−	11.6399i	0.225011	−	0.389731i
$893$	−0.304154	−	0.612260i	−0.0101781	−	0.0204885i
$894$	−5.91665	−	10.2479i	−0.197882	−	0.342742i
$895$	4.29755	−	1.56418i	0.143651	−	0.0522848i
$896$	2.64543	−	0.0412527i	0.0883776	−	0.00137816i
$897$	−4.83716	+	4.05886i	−0.161508	+	0.135521i
$898$	6.22006	−	35.2757i	0.207566	−	1.17717i
$899$	2.99138	+	1.08877i	0.0997682	+	0.0363127i
$900$	−4.65659			−0.155220
$901$	−21.4503			−0.714615
$902$	23.3642	+	8.50387i	0.777943	+	0.283148i
$903$	22.6277	−	8.63770i	0.753004	−	0.287445i
$904$	7.76369	−	13.4471i	0.258217	−	0.447244i
$905$	−4.21527	+	7.30107i	−0.140120	+	0.242696i
$906$	6.31658	+	2.29905i	0.209854	+	0.0763807i
$907$	−32.5265	+	11.8387i	−1.08002	+	0.393097i	−0.819917	−	0.572483i	$-0.805980\pi$
$907$	−32.5265	+	11.8387i	−1.08002	+	0.393097i	−0.260108	+	0.965580i	$0.583758\pi$
$908$	−3.98972	−	1.45214i	−0.132404	−	0.0481909i
$909$	−2.33215	+	13.2263i	−0.0773527	+	0.438689i
$910$	0.768093	−	1.37962i	0.0254620	−	0.0457339i
$911$	−40.8979			−1.35501			−0.677504	−	0.735519i	$-0.736938\pi$
$911$	−40.8979			−1.35501			−0.677504	+	0.735519i	$0.736938\pi$
$912$	4.35038	+	0.272412i	0.144055	+	0.00902048i
$913$	−23.1524	+	40.1011i	−0.766232	+	1.32715i
$914$	5.09380	−	28.8884i	0.168488	−	0.955543i
$915$	2.16376	−	0.787544i	0.0715316	−	0.0260354i
$916$	−14.4888	+	12.1575i	−0.478723	+	0.401696i
$917$	−4.72351	+	8.48417i	−0.155984	+	0.280172i
$918$	−0.498743	−	2.82851i	−0.0164610	−	0.0933547i
$919$	−14.7886	+	25.6146i	−0.487831	+	0.844949i	−0.999902	−	0.0139946i	$-0.995545\pi$
$919$	−14.7886	+	25.6146i	−0.487831	+	0.844949i	0.512071	+	0.858943i	$0.328879\pi$
$920$	1.81668	+	3.14659i	0.0598942	+	0.103740i
$921$	−7.75530	+	6.50747i	−0.255546	+	0.214428i
$922$	−2.27565	−	12.9059i	−0.0749447	−	0.425032i
$923$	0.381139	−	0.660153i	0.0125454	−	0.0217292i
$924$	−1.40635	−	7.30759i	−0.0462654	−	0.240402i
$925$	−5.52303	−	31.3227i	−0.181596	−	1.02988i
$926$	−2.87448	+	16.3020i	−0.0944614	+	0.535717i
$927$	−1.33377	−	7.56416i	−0.0438066	−	0.248440i
$928$	−1.77117	−	1.48619i	−0.0581416	−	0.0487866i
$929$	−5.82634	−	4.88888i	−0.191156	−	0.160399i	0.542187	−	0.840258i	$-0.317596\pi$
$929$	−5.82634	−	4.88888i	−0.191156	−	0.160399i	−0.733343	+	0.679859i	$0.762041\pi$
$930$	0.806835			0.0264572
$931$	23.9771	−	18.8706i	0.785817	−	0.618459i
$932$	−4.60729			−0.150917
$933$	−21.8995	−	18.3758i	−0.716957	−	0.601598i
$934$	14.5199	+	12.1836i	0.475104	+	0.398660i
$935$	0.822062	+	4.66214i	0.0268843	+	0.152468i
$936$	0.176849	−	1.00296i	0.00578051	−	0.0327829i
$937$	9.25422	+	52.4833i	0.302322	+	1.71456i	0.635848	+	0.771814i	$0.280650\pi$
$937$	9.25422	+	52.4833i	0.302322	+	1.71456i	−0.333526	+	0.942741i	$0.608238\pi$
$938$	7.24579	+	37.6502i	0.236583	+	1.22932i
$939$	15.7385	−	27.2598i	0.513606	−	0.889591i
$940$	0.0159599	+	0.0905131i	0.000520555	+	0.00295221i
$941$	−18.8940	+	15.8540i	−0.615928	+	0.516825i	−0.896520	−	0.443002i	$-0.853913\pi$
$941$	−18.8940	+	15.8540i	−0.615928	+	0.516825i	0.280593	+	0.959827i	$0.409469\pi$
$942$	−1.29061	−	2.23540i	−0.0420503	−	0.0728333i
$943$	−27.4041	+	47.4653i	−0.892401	+	1.54568i
$944$	1.64083	+	9.30558i	0.0534043	+	0.302871i
$945$	0.754190	−	1.35464i	0.0245338	−	0.0440666i
$946$	−19.7246	+	16.5509i	−0.641301	+	0.538115i
$947$	21.6325	−	7.87358i	0.702961	−	0.255857i	0.0342864	−	0.999412i	$-0.489084\pi$
$947$	21.6325	−	7.87358i	0.702961	−	0.255857i	0.668675	+	0.743555i	$0.266862\pi$
$948$	1.24793	−	7.07734i	0.0405308	−	0.229861i
$949$	6.13352	−	10.6236i	0.199103	−	0.344856i
$950$	14.7031	+	13.9933i	0.477031	+	0.454002i
$951$	16.3174			0.529129
$952$	−3.69642	+	6.63935i	−0.119802	+	0.215183i
$953$	−5.40443	+	30.6501i	−0.175067	+	0.992853i	0.763000	+	0.646398i	$0.223726\pi$
$953$	−5.40443	+	30.6501i	−0.175067	+	0.992853i	−0.938067	+	0.346454i	$0.887386\pi$
$954$	−7.01801	−	2.55435i	−0.227216	−	0.0827000i
$955$	4.78356	−	1.74107i	0.154792	−	0.0563398i
$956$	−17.9077	−	6.51789i	−0.579178	−	0.210803i
$957$	−3.25161	+	5.63196i	−0.105110	+	0.182055i
$958$	−11.3798	+	19.7103i	−0.367664	+	0.636812i
$959$	−18.0001	+	6.87119i	−0.581253	+	0.221882i
$960$	−0.550670	−	0.200428i	−0.0177728	−	0.00646877i
$961$	−29.1043			−0.938850
$962$	6.95621			0.224277
$963$	−14.8090	−	5.39003i	−0.477213	−	0.173691i
$964$	2.57685	−	14.6140i	0.0829946	−	0.470686i
$965$	10.5862	−	8.88286i	0.340781	−	0.285949i
$966$	16.4021	−	0.255773i	0.527729	−	0.00822937i
$967$	48.6505	−	17.7073i	1.56449	−	0.569429i	0.592733	−	0.805399i	$-0.298049\pi$
$967$	48.6505	−	17.7073i	1.56449	−	0.569429i	0.971760	+	0.235970i	$0.0758266\pi$
$968$	−1.54438	−	2.67495i	−0.0496383	−	0.0859760i
$969$	−6.92504	+	10.4297i	−0.222464	+	0.335050i
$970$	−0.368237	+	0.637806i	−0.0118234	+	0.0204787i
$971$	−35.8483	−	30.0803i	−1.15043	−	0.965321i	−0.150696	−	0.988580i	$-0.548151\pi$
$971$	−35.8483	−	30.0803i	−1.15043	−	0.965321i	−0.999729	+	0.0232589i	$0.992596\pi$
$972$	0.173648	−	0.984808i	0.00556977	−	0.0315877i
$973$	6.37797	−	2.43467i	0.204468	−	0.0780518i
$974$	−7.50446	−	6.29699i	−0.240458	−	0.201769i
$975$	3.63292	−	3.04838i	0.116346	−	0.0976263i
$976$	−3.92932			−0.125774
$977$	17.0045	+	29.4526i	0.544022	+	0.942273i	0.998668	+	0.0516009i	$0.0164324\pi$
$977$	17.0045	+	29.4526i	0.544022	+	0.942273i	−0.454646	+	0.890672i	$0.650234\pi$
$978$	−0.162201	−	0.919889i	−0.00518662	−	0.0294148i
$979$	30.4395	+	11.0791i	0.972851	+	0.354089i
$980$	−3.80907	+	1.52250i	−0.121676	+	0.0486345i
$981$	−6.04673	−	10.4732i	−0.193057	−	0.334385i
$982$	−2.66772	+	2.23849i	−0.0851305	+	0.0714330i
$983$	17.7781	−	6.47071i	0.567035	−	0.206384i	−0.0425643	−	0.999094i	$-0.513553\pi$
$983$	17.7781	−	6.47071i	0.567035	−	0.206384i	0.609599	+	0.792710i	$0.291331\pi$
$984$	−1.53502	−	8.70551i	−0.0489345	−	0.277522i
$985$	3.47349	−	1.26425i	0.110675	−	0.0402823i
$986$	6.24020	−	2.27125i	0.198729	−	0.0723313i
$987$	0.392098	+	0.135827i	0.0124806	+	0.00432341i
$988$	−3.57235	+	2.63539i	−0.113652	+	0.0838431i
$989$	−28.3795	−	49.1547i	−0.902415	−	1.56303i
$990$	−0.286219	+	1.62323i	−0.00909663	+	0.0515896i
$991$	40.4527	+	33.9439i	1.28502	+	1.07826i	0.992531	+	0.121995i	$0.0389292\pi$
$991$	40.4527	+	33.9439i	1.28502	+	1.07826i	0.292493	+	0.956268i	$0.405515\pi$
$992$	−1.29379	−	0.470902i	−0.0410780	−	0.0149512i
$993$	7.95572	+	6.67564i	0.252467	+	0.211845i
$994$	−1.85008	+	0.706232i	−0.0586810	+	0.0224003i
$995$	−3.96757	−	6.87204i	−0.125781	−	0.217858i
$996$	16.4628			0.521643
$997$	0.598356	−	0.502080i	0.0189501	−	0.0159010i	−0.633263	−	0.773936i	$-0.718285\pi$
$997$	0.598356	−	0.502080i	0.0189501	−	0.0159010i	0.652213	+	0.758035i	$0.273841\pi$
$998$	−8.57371	+	7.19419i	−0.271396	+	0.227728i
$999$	6.83029			0.216101

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	798.2.bp.b.613.2	yes	12
7.2	even	3		798.2.bq.b.499.1	yes	12
19.4	even	9		798.2.bq.b.403.1	yes	12
133.23	even	9	inner	798.2.bp.b.289.2	✓	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
798.2.bp.b.289.2	✓	12	133.23	even	9	inner
798.2.bp.b.613.2	yes	12	1.1	even	1	trivial
798.2.bq.b.403.1	yes	12	19.4	even	9
798.2.bq.b.499.1	yes	12	7.2	even	3

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.bp (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.766044 - 0.642788i) q^{2} +(0.766044 + 0.642788i) q^{3} +(0.173648 + 0.984808i) q^{4} +(0.101760 - 0.577108i) q^{5} +(-0.173648 - 0.984808i) q^{6} +(-0.500000 - 2.59808i) q^{7} +(0.500000 - 0.866025i) q^{8} +(0.173648 + 0.984808i) q^{9} +O(q^{10})\)	\(q+(-0.766044 - 0.642788i) q^{2} +(0.766044 + 0.642788i) q^{3} +(0.173648 + 0.984808i) q^{4} +(0.101760 - 0.577108i) q^{5} +(-0.173648 - 0.984808i) q^{6} +(-0.500000 - 2.59808i) q^{7} +(0.500000 - 0.866025i) q^{8} +(0.173648 + 0.984808i) q^{9} +(-0.448910 + 0.376681i) q^{10} +(-1.40635 - 2.43586i) q^{11} +(-0.500000 + 0.866025i) q^{12} +(-0.176849 - 1.00296i) q^{13} +(-1.28699 + 2.31164i) q^{14} +(0.448910 - 0.376681i) q^{15} +(-0.939693 + 0.342020i) q^{16} +(0.498743 - 2.82851i) q^{17} +(0.500000 - 0.866025i) q^{18} +(-4.18119 + 1.23193i) q^{19} +0.586011 q^{20} +(1.28699 - 2.31164i) q^{21} +(-0.488419 + 2.76996i) q^{22} +(-5.82625 - 2.12058i) q^{23} +(0.939693 - 0.342020i) q^{24} +(4.37576 + 1.59265i) q^{25} +(-0.509218 + 0.881991i) q^{26} +(-0.500000 + 0.866025i) q^{27} +(2.47178 - 0.943555i) q^{28} +(-2.17266 - 0.790785i) q^{29} -0.586011 q^{30} -1.37683 q^{31} +(0.939693 + 0.342020i) q^{32} +(0.488419 - 2.76996i) q^{33} +(-2.20019 + 1.84618i) q^{34} +(-1.55025 + 0.0241745i) q^{35} +(-0.939693 + 0.342020i) q^{36} +(-3.41514 - 5.91520i) q^{37} +(3.99485 + 1.74390i) q^{38} +(0.509218 - 0.881991i) q^{39} +(-0.448910 - 0.376681i) q^{40} +(1.53502 - 8.70551i) q^{41} +(-2.47178 + 0.943555i) q^{42} +(7.01269 + 5.88435i) q^{43} +(2.15465 - 1.80796i) q^{44} +0.586011 q^{45} +(3.10008 + 5.36950i) q^{46} +(0.0272348 + 0.154456i) q^{47} +(-0.939693 - 0.342020i) q^{48} +(-6.50000 + 2.59808i) q^{49} +(-2.32830 - 4.03273i) q^{50} +(2.20019 - 1.84618i) q^{51} +(0.957016 - 0.348325i) q^{52} +(-1.29688 - 7.35495i) q^{53} +(0.939693 - 0.342020i) q^{54} +(-1.54887 + 0.563741i) q^{55} +(-2.50000 - 0.866025i) q^{56} +(-3.99485 - 1.74390i) q^{57} +(1.15605 + 2.00234i) q^{58} +(1.64083 - 9.30558i) q^{59} +(0.448910 + 0.376681i) q^{60} +(3.69235 + 1.34391i) q^{61} +(1.05471 + 0.885007i) q^{62} +(2.47178 - 0.943555i) q^{63} +(-0.500000 - 0.866025i) q^{64} -0.596814 q^{65} +(-2.15465 + 1.80796i) q^{66} +(11.1012 - 9.31500i) q^{67} +2.87214 q^{68} +(-3.10008 - 5.36950i) q^{69} +(1.20310 + 0.977963i) q^{70} +(0.573369 + 0.481114i) q^{71} +(0.939693 + 0.342020i) q^{72} +(9.22700 + 7.74237i) q^{73} +(-1.18607 + 6.72652i) q^{74} +(2.32830 + 4.03273i) q^{75} +(-1.93927 - 3.90374i) q^{76} +(-5.62538 + 4.87173i) q^{77} +(-0.957016 + 0.348325i) q^{78} +(-6.75312 + 2.45794i) q^{79} +(0.101760 + 0.577108i) q^{80} +(-0.939693 + 0.342020i) q^{81} +(-6.77168 + 5.68212i) q^{82} +(-8.23139 - 14.2572i) q^{83} +(2.50000 + 0.866025i) q^{84} +(-1.58160 - 0.575657i) q^{85} +(-1.58965 - 9.01535i) q^{86} +(-1.15605 - 2.00234i) q^{87} -2.81269 q^{88} +(-8.82233 + 7.40282i) q^{89} +(-0.448910 - 0.376681i) q^{90} +(-2.51735 + 0.960950i) q^{91} +(1.07665 - 6.10597i) q^{92} +(-1.05471 - 0.885007i) q^{93} +(0.0784195 - 0.135827i) q^{94} +(0.285482 + 2.53836i) q^{95} +(0.500000 + 0.866025i) q^{96} +(1.18097 - 0.429837i) q^{97} +(6.64930 + 2.18788i) q^{98} +(2.15465 - 1.80796i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 3 q^{5} - 6 q^{7} + 6 q^{8}+O(q^{10}) \) 12 * q + 3 * q^5 - 6 * q^7 + 6 * q^8	\( 12 q + 3 q^{5} - 6 q^{7} + 6 q^{8} + 6 q^{10} - 6 q^{12} + 12 q^{13} - 6 q^{15} - 18 q^{17} + 6 q^{18} - 3 q^{19} - 21 q^{22} - 3 q^{23} + 21 q^{25} - 6 q^{26} - 6 q^{27} - 12 q^{29} - 6 q^{31} + 21 q^{33} - 9 q^{34} + 12 q^{35} - 3 q^{37} + 3 q^{38} + 6 q^{39} + 6 q^{40} - 24 q^{41} - 21 q^{43} - 6 q^{44} - 6 q^{46} + 18 q^{47} - 78 q^{49} + 6 q^{50} + 9 q^{51} - 15 q^{52} + 36 q^{53} + 30 q^{55} - 30 q^{56} - 3 q^{57} + 15 q^{58} - 33 q^{59} - 6 q^{60} + 33 q^{62} - 6 q^{64} + 24 q^{65} + 6 q^{66} + 51 q^{67} - 6 q^{68} + 6 q^{69} - 3 q^{70} + 6 q^{71} - 3 q^{73} - 6 q^{75} + 9 q^{76} + 15 q^{78} + 30 q^{79} + 3 q^{80} - 3 q^{82} - 27 q^{83} + 30 q^{84} - 36 q^{85} + 3 q^{86} - 15 q^{87} + 12 q^{89} + 6 q^{90} + 21 q^{91} - 3 q^{92} - 33 q^{93} + 6 q^{94} + 21 q^{95} + 6 q^{96} + 30 q^{97} - 6 q^{99}+O(q^{100}) \) 12 * q + 3 * q^5 - 6 * q^7 + 6 * q^8 + 6 * q^10 - 6 * q^12 + 12 * q^13 - 6 * q^15 - 18 * q^17 + 6 * q^18 - 3 * q^19 - 21 * q^22 - 3 * q^23 + 21 * q^25 - 6 * q^26 - 6 * q^27 - 12 * q^29 - 6 * q^31 + 21 * q^33 - 9 * q^34 + 12 * q^35 - 3 * q^37 + 3 * q^38 + 6 * q^39 + 6 * q^40 - 24 * q^41 - 21 * q^43 - 6 * q^44 - 6 * q^46 + 18 * q^47 - 78 * q^49 + 6 * q^50 + 9 * q^51 - 15 * q^52 + 36 * q^53 + 30 * q^55 - 30 * q^56 - 3 * q^57 + 15 * q^58 - 33 * q^59 - 6 * q^60 + 33 * q^62 - 6 * q^64 + 24 * q^65 + 6 * q^66 + 51 * q^67 - 6 * q^68 + 6 * q^69 - 3 * q^70 + 6 * q^71 - 3 * q^73 - 6 * q^75 + 9 * q^76 + 15 * q^78 + 30 * q^79 + 3 * q^80 - 3 * q^82 - 27 * q^83 + 30 * q^84 - 36 * q^85 + 3 * q^86 - 15 * q^87 + 12 * q^89 + 6 * q^90 + 21 * q^91 - 3 * q^92 - 33 * q^93 + 6 * q^94 + 21 * q^95 + 6 * q^96 + 30 * q^97 - 6 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

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Database

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