LMFDB - Embedded newform 1050.2.m.b.307.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1050,2,Mod(307,1050)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1050, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 1, 2]))

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

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

chi := DirichletCharacter("1050.307");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1050.m (of order $4$, degree $2$, 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:	$8.38429221223$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(i)$
Coefficient field:	8.0.1698758656.6
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 18x^{6} + 97x^{4} + 176x^{2} + 64 $ x^8 + 18x^6 + 97x^4 + 176*x^2 + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 210)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			307.1
Root			$0.692297i$ of defining polynomial
Character	$\chi$	$=$	1050.307
Dual form			1050.2.m.b.643.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 - 0.707107i) q^{2} +(-0.707107 - 0.707107i) q^{3} +1.00000i q^{4} +1.00000i q^{6} +(-1.47472 - 2.19663i) q^{7} +(0.707107 - 0.707107i) q^{8} +1.00000i q^{9} +O(q^{10})$	\(q+(-0.707107 - 0.707107i) q^{2} +(-0.707107 - 0.707107i) q^{3} +1.00000i q^{4} +1.00000i q^{6} +(-1.47472 - 2.19663i) q^{7} +(0.707107 - 0.707107i) q^{8} +1.00000i q^{9} +0.0296189 q^{11} +(0.707107 - 0.707107i) q^{12} +(0.585786 + 0.585786i) q^{13} +(-0.510472 + 2.59604i) q^{14} -1.00000 q^{16} +(-1.72192 + 1.72192i) q^{17} +(0.707107 - 0.707107i) q^{18} -5.77786 q^{19} +(-0.510472 + 2.59604i) q^{21} +(-0.0209438 - 0.0209438i) q^{22} +(0.393270 - 0.393270i) q^{23} -1.00000 q^{24} -0.828427i q^{26} +(0.707107 - 0.707107i) q^{27} +(2.19663 - 1.47472i) q^{28} -9.70636i q^{29} +6.39327i q^{31} +(0.707107 + 0.707107i) q^{32} +(-0.0209438 - 0.0209438i) q^{33} +2.43516 q^{34} -1.00000 q^{36} +(3.72192 + 3.72192i) q^{37} +(4.08557 + 4.08557i) q^{38} -0.828427i q^{39} +0.514280i q^{41} +(2.19663 - 1.47472i) q^{42} +(-7.16246 + 7.16246i) q^{43} +0.0296189i q^{44} -0.556167 q^{46} +(-7.77786 + 7.77786i) q^{47} +(0.707107 + 0.707107i) q^{48} +(-2.65041 + 6.47884i) q^{49} +2.43516 q^{51} +(-0.585786 + 0.585786i) q^{52} +(5.77786 - 5.77786i) q^{53} -1.00000 q^{54} +(-2.59604 - 0.510472i) q^{56} +(4.08557 + 4.08557i) q^{57} +(-6.86343 + 6.86343i) q^{58} -12.8070 q^{59} +10.7273i q^{61} +(4.52072 - 4.52072i) q^{62} +(2.19663 - 1.47472i) q^{63} -1.00000i q^{64} +0.0296189i q^{66} +(-2.39327 - 2.39327i) q^{67} +(-1.72192 - 1.72192i) q^{68} -0.556167 q^{69} +6.64818 q^{71} +(0.707107 + 0.707107i) q^{72} +(5.12745 + 5.12745i) q^{73} -5.26358i q^{74} -5.77786i q^{76} +(-0.0436796 - 0.0650620i) q^{77} +(-0.585786 + 0.585786i) q^{78} +9.86988i q^{79} -1.00000 q^{81} +(0.363651 - 0.363651i) q^{82} +(0.150629 + 0.150629i) q^{83} +(-2.59604 - 0.510472i) q^{84} +10.1292 q^{86} +(-6.86343 + 6.86343i) q^{87} +(0.0209438 - 0.0209438i) q^{88} +4.38416 q^{89} +(0.422889 - 2.15063i) q^{91} +(0.393270 + 0.393270i) q^{92} +(4.52072 - 4.52072i) q^{93} +10.9996 q^{94} -1.00000i q^{96} +(-2.47016 + 2.47016i) q^{97} +(6.45535 - 2.70711i) q^{98} +0.0296189i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 4 q^{7}+O(q^{10}) $ 8 * q - 4 * q^7	$ 8 q - 4 q^{7} + 8 q^{11} + 16 q^{13} - 8 q^{14} - 8 q^{16} - 12 q^{17} - 8 q^{19} - 8 q^{21} - 8 q^{22} - 16 q^{23} - 8 q^{24} + 8 q^{28} - 8 q^{33} + 16 q^{34} - 8 q^{36} + 28 q^{37} + 4 q^{38} + 8 q^{42} - 8 q^{46} - 24 q^{47} + 4 q^{49} + 16 q^{51} - 16 q^{52} + 8 q^{53} - 8 q^{54} + 4 q^{56} + 4 q^{57} + 12 q^{58} + 8 q^{59} + 4 q^{62} + 8 q^{63} - 12 q^{68} - 8 q^{69} + 8 q^{71} + 28 q^{73} + 44 q^{77} - 16 q^{78} - 8 q^{81} - 24 q^{82} + 16 q^{83} + 4 q^{84} + 8 q^{86} + 12 q^{87} + 8 q^{88} - 64 q^{89} - 8 q^{91} - 16 q^{92} + 4 q^{93} + 8 q^{94} + 28 q^{97}+O(q^{100}) $ 8 * q - 4 * q^7 + 8 * q^11 + 16 * q^13 - 8 * q^14 - 8 * q^16 - 12 * q^17 - 8 * q^19 - 8 * q^21 - 8 * q^22 - 16 * q^23 - 8 * q^24 + 8 * q^28 - 8 * q^33 + 16 * q^34 - 8 * q^36 + 28 * q^37 + 4 * q^38 + 8 * q^42 - 8 * q^46 - 24 * q^47 + 4 * q^49 + 16 * q^51 - 16 * q^52 + 8 * q^53 - 8 * q^54 + 4 * q^56 + 4 * q^57 + 12 * q^58 + 8 * q^59 + 4 * q^62 + 8 * q^63 - 12 * q^68 - 8 * q^69 + 8 * q^71 + 28 * q^73 + 44 * q^77 - 16 * q^78 - 8 * q^81 - 24 * q^82 + 16 * q^83 + 4 * q^84 + 8 * q^86 + 12 * q^87 + 8 * q^88 - 64 * q^89 - 8 * q^91 - 16 * q^92 + 4 * q^93 + 8 * q^94 + 28 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times$.

$n$	$127$	$451$	$701$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$	$1$

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 $

$2$	−0.707107	−	0.707107i	−0.500000	−	0.500000i
$2$	−0.707107	−	0.707107i	−0.500000	−	0.500000i
$3$	−0.707107	−	0.707107i	−0.408248	−	0.408248i
$3$	−0.707107	−	0.707107i	−0.408248	−	0.408248i
$4$			1.00000i			0.500000i
$5$		0			0
$5$		0			0
$6$			1.00000i			0.408248i
$7$	−1.47472	−	2.19663i	−0.557391	−	0.830250i
$7$	−1.47472	−	2.19663i	−0.557391	−	0.830250i
$8$	0.707107	−	0.707107i	0.250000	−	0.250000i
$9$			1.00000i			0.333333i
$10$		0			0
$11$	0.0296189			0.00893045			0.00446522	−	0.999990i	$-0.498579\pi$
$11$	0.0296189			0.00893045			0.00446522	+	0.999990i	$0.498579\pi$
$12$	0.707107	−	0.707107i	0.204124	−	0.204124i
$13$	0.585786	+	0.585786i	0.162468	+	0.162468i	0.783659	−	0.621191i	$-0.213351\pi$
$13$	0.585786	+	0.585786i	0.162468	+	0.162468i	−0.621191	+	0.783659i	$0.713351\pi$
$14$	−0.510472	+	2.59604i	−0.136429	+	0.693821i
$15$		0			0
$16$	−1.00000			−0.250000
$17$	−1.72192	+	1.72192i	−0.417626	+	0.417626i	−0.884385	−	0.466759i	$-0.845422\pi$
$17$	−1.72192	+	1.72192i	−0.417626	+	0.417626i	0.466759	+	0.884385i	$0.345422\pi$
$18$	0.707107	−	0.707107i	0.166667	−	0.166667i
$19$	−5.77786			−1.32553			−0.662767	−	0.748826i	$-0.730618\pi$
$19$	−5.77786			−1.32553			−0.662767	+	0.748826i	$0.730618\pi$
$20$		0			0
$21$	−0.510472	+	2.59604i	−0.111394	+	0.566502i
$22$	−0.0209438	−	0.0209438i	−0.00446522	−	0.00446522i
$23$	0.393270	−	0.393270i	0.0820024	−	0.0820024i	−0.664916	−	0.746918i	$-0.731533\pi$
$23$	0.393270	−	0.393270i	0.0820024	−	0.0820024i	0.746918	+	0.664916i	$0.231533\pi$
$24$	−1.00000			−0.204124
$25$		0			0
$26$		−	0.828427i		−	0.162468i
$27$	0.707107	−	0.707107i	0.136083	−	0.136083i
$28$	2.19663	−	1.47472i	0.415125	−	0.278696i
$29$		−	9.70636i		−	1.80243i	−0.433377	−	0.901213i	$-0.642678\pi$
$29$		−	9.70636i		−	1.80243i	0.433377	−	0.901213i	$-0.357322\pi$
$30$		0			0
$31$			6.39327i			1.14827i	0.818762	+	0.574133i	$0.194661\pi$
$31$			6.39327i			1.14827i	−0.818762	+	0.574133i	$0.805339\pi$
$32$	0.707107	+	0.707107i	0.125000	+	0.125000i
$33$	−0.0209438	−	0.0209438i	−0.00364584	−	0.00364584i
$34$	2.43516			0.417626
$35$		0			0
$36$	−1.00000			−0.166667
$37$	3.72192	+	3.72192i	0.611879	+	0.611879i	0.943435	−	0.331556i	$-0.107574\pi$
$37$	3.72192	+	3.72192i	0.611879	+	0.611879i	−0.331556	+	0.943435i	$0.607574\pi$
$38$	4.08557	+	4.08557i	0.662767	+	0.662767i
$39$		−	0.828427i		−	0.132655i
$40$		0			0
$41$			0.514280i			0.0803170i	0.999193	+	0.0401585i	$0.0127863\pi$
$41$			0.514280i			0.0803170i	−0.999193	+	0.0401585i	$0.987214\pi$
$42$	2.19663	−	1.47472i	0.338948	−	0.227554i
$43$	−7.16246	+	7.16246i	−1.09226	+	1.09226i	−0.0969783	+	0.995286i	$0.530918\pi$
$43$	−7.16246	+	7.16246i	−1.09226	+	1.09226i	−0.995286	+	0.0969783i	$0.969082\pi$
$44$			0.0296189i			0.00446522i
$45$		0			0
$46$	−0.556167			−0.0820024
$47$	−7.77786	+	7.77786i	−1.13452	+	1.13452i	−0.145101	+	0.989417i	$0.546351\pi$
$47$	−7.77786	+	7.77786i	−1.13452	+	1.13452i	−0.989417	+	0.145101i	$0.953649\pi$
$48$	0.707107	+	0.707107i	0.102062	+	0.102062i
$49$	−2.65041	+	6.47884i	−0.378630	+	0.925548i
$50$		0			0
$51$	2.43516			0.340990
$52$	−0.585786	+	0.585786i	−0.0812340	+	0.0812340i
$53$	5.77786	−	5.77786i	0.793651	−	0.793651i	−0.188435	−	0.982086i	$-0.560341\pi$
$53$	5.77786	−	5.77786i	0.793651	−	0.793651i	0.982086	+	0.188435i	$0.0603415\pi$
$54$	−1.00000			−0.136083
$55$		0			0
$56$	−2.59604	−	0.510472i	−0.346910	−	0.0682147i
$57$	4.08557	+	4.08557i	0.541147	+	0.541147i
$58$	−6.86343	+	6.86343i	−0.901213	+	0.901213i
$59$	−12.8070			−1.66734			−0.833668	−	0.552267i	$-0.813763\pi$
$59$	−12.8070			−1.66734			−0.833668	+	0.552267i	$0.813763\pi$
$60$		0			0
$61$			10.7273i			1.37349i	0.726898	+	0.686745i	$0.240961\pi$
$61$			10.7273i			1.37349i	−0.726898	+	0.686745i	$0.759039\pi$
$62$	4.52072	−	4.52072i	0.574133	−	0.574133i
$63$	2.19663	−	1.47472i	0.276750	−	0.185797i
$64$		−	1.00000i		−	0.125000i
$65$		0			0
$66$			0.0296189i			0.00364584i
$67$	−2.39327	−	2.39327i	−0.292384	−	0.292384i	0.545637	−	0.838022i	$-0.316288\pi$
$67$	−2.39327	−	2.39327i	−0.292384	−	0.292384i	−0.838022	+	0.545637i	$0.816288\pi$
$68$	−1.72192	−	1.72192i	−0.208813	−	0.208813i
$69$	−0.556167			−0.0669547
$70$		0			0
$71$	6.64818			0.788994			0.394497	−	0.918897i	$-0.370919\pi$
$71$	6.64818			0.788994			0.394497	+	0.918897i	$0.370919\pi$
$72$	0.707107	+	0.707107i	0.0833333	+	0.0833333i
$73$	5.12745	+	5.12745i	0.600123	+	0.600123i	0.940345	−	0.340222i	$-0.110502\pi$
$73$	5.12745	+	5.12745i	0.600123	+	0.600123i	−0.340222	+	0.940345i	$0.610502\pi$
$74$		−	5.26358i		−	0.611879i
$75$		0			0
$76$		−	5.77786i		−	0.662767i
$77$	−0.0436796	−	0.0650620i	−0.00497775	−	0.00741450i
$78$	−0.585786	+	0.585786i	−0.0663273	+	0.0663273i
$79$			9.86988i			1.11045i	0.831701	+	0.555224i	$0.187367\pi$
$79$			9.86988i			1.11045i	−0.831701	+	0.555224i	$0.812633\pi$
$80$		0			0
$81$	−1.00000			−0.111111
$82$	0.363651	−	0.363651i	0.0401585	−	0.0401585i
$83$	0.150629	+	0.150629i	0.0165337	+	0.0165337i	0.715325	−	0.698792i	$-0.246279\pi$
$83$	0.150629	+	0.150629i	0.0165337	+	0.0165337i	−0.698792	+	0.715325i	$0.746279\pi$
$84$	−2.59604	−	0.510472i	−0.283251	−	0.0556970i
$85$		0			0
$86$	10.1292			1.09226
$87$	−6.86343	+	6.86343i	−0.735837	+	0.735837i
$88$	0.0209438	−	0.0209438i	0.00223261	−	0.00223261i
$89$	4.38416			0.464720			0.232360	−	0.972630i	$-0.425355\pi$
$89$	4.38416			0.464720			0.232360	+	0.972630i	$0.425355\pi$
$90$		0			0
$91$	0.422889	−	2.15063i	0.0443308	−	0.225447i
$92$	0.393270	+	0.393270i	0.0410012	+	0.0410012i
$93$	4.52072	−	4.52072i	0.468777	−	0.468777i
$94$	10.9996			1.13452
$95$		0			0
$96$		−	1.00000i		−	0.102062i
$97$	−2.47016	+	2.47016i	−0.250807	+	0.250807i	−0.821301	−	0.570494i	$-0.806752\pi$
$97$	−2.47016	+	2.47016i	−0.250807	+	0.250807i	0.570494	+	0.821301i	$0.306752\pi$
$98$	6.45535	−	2.70711i	0.652089	−	0.273459i
$99$			0.0296189i			0.00297682i
$100$		0			0
$101$			12.7897i			1.27262i	0.771433	+	0.636311i	$0.219541\pi$
$101$			12.7897i			1.27262i	−0.771433	+	0.636311i	$0.780459\pi$
$102$	−1.72192	−	1.72192i	−0.170495	−	0.170495i
$103$	−8.06462	−	8.06462i	−0.794631	−	0.794631i	0.187612	−	0.982243i	$-0.439925\pi$
$103$	−8.06462	−	8.06462i	−0.794631	−	0.794631i	−0.982243	+	0.187612i	$0.939925\pi$
$104$	0.828427			0.0812340
$105$		0			0
$106$	−8.17113			−0.793651
$107$	1.22170	+	1.22170i	0.118106	+	0.118106i	0.763690	−	0.645584i	$-0.223386\pi$
$107$	1.22170	+	1.22170i	0.118106	+	0.118106i	−0.645584	+	0.763690i	$0.723386\pi$
$108$	0.707107	+	0.707107i	0.0680414	+	0.0680414i
$109$			14.8984i			1.42701i	0.700649	+	0.713506i	$0.252894\pi$
$109$			14.8984i			1.42701i	−0.700649	+	0.713506i	$0.747106\pi$
$110$		0			0
$111$		−	5.26358i		−	0.499597i
$112$	1.47472	+	2.19663i	0.139348	+	0.207562i
$113$	0.0715065	−	0.0715065i	0.00672676	−	0.00672676i	−0.703735	−	0.710462i	$-0.748486\pi$
$113$	0.0715065	−	0.0715065i	0.00672676	−	0.00672676i	0.710462	+	0.703735i	$0.248486\pi$
$114$		−	5.77786i		−	0.541147i
$115$		0			0
$116$	9.70636			0.901213
$117$	−0.585786	+	0.585786i	−0.0541560	+	0.0541560i
$118$	9.05595	+	9.05595i	0.833668	+	0.833668i
$119$	6.32176	+	1.24308i	0.579515	+	0.113953i
$120$		0			0
$121$	−10.9991			−0.999920
$122$	7.58535	−	7.58535i	0.686745	−	0.686745i
$123$	0.363651	−	0.363651i	0.0327893	−	0.0327893i
$124$	−6.39327			−0.574133
$125$		0			0
$126$	−2.59604	−	0.510472i	−0.231274	−	0.0454764i
$127$	−6.15663	−	6.15663i	−0.546313	−	0.546313i	0.379059	−	0.925372i	$-0.376248\pi$
$127$	−6.15663	−	6.15663i	−0.546313	−	0.546313i	−0.925372	+	0.379059i	$0.876248\pi$
$128$	−0.707107	+	0.707107i	−0.0625000	+	0.0625000i
$129$	10.1292			0.891830
$130$		0			0
$131$			4.52401i			0.395265i	0.980276	+	0.197632i	$0.0633253\pi$
$131$			4.52401i			0.395265i	−0.980276	+	0.197632i	$0.936675\pi$
$132$	0.0209438	−	0.0209438i	0.00182292	−	0.00182292i
$133$	8.52072	+	12.6919i	0.738841	+	1.10052i
$134$			3.38459i			0.292384i
$135$		0			0
$136$			2.43516i			0.208813i
$137$	−5.58535	−	5.58535i	−0.477188	−	0.477188i	0.427043	−	0.904231i	$-0.359555\pi$
$137$	−5.58535	−	5.58535i	−0.477188	−	0.477188i	−0.904231	+	0.427043i	$0.859555\pi$
$138$	0.393270	+	0.393270i	0.0334773	+	0.0334773i
$139$	16.6063			1.40853			0.704264	−	0.709939i	$-0.251277\pi$
$139$	16.6063			1.40853			0.704264	+	0.709939i	$0.251277\pi$
$140$		0			0
$141$	10.9996			0.926330
$142$	−4.70097	−	4.70097i	−0.394497	−	0.394497i
$143$	0.0173504	+	0.0173504i	0.00145091	+	0.00145091i
$144$		−	1.00000i		−	0.0833333i
$145$		0			0
$146$		−	7.25132i		−	0.600123i
$147$	6.45535	−	2.70711i	0.532428	−	0.223278i
$148$	−3.72192	+	3.72192i	−0.305940	+	0.305940i
$149$		−	7.80748i		−	0.639614i	−0.947483	−	0.319807i	$-0.896382\pi$
$149$		−	7.80748i		−	0.639614i	0.947483	−	0.319807i	$-0.103618\pi$
$150$		0			0
$151$	0.870315			0.0708252			0.0354126	−	0.999373i	$-0.488725\pi$
$151$	0.870315			0.0708252			0.0354126	+	0.999373i	$0.488725\pi$
$152$	−4.08557	+	4.08557i	−0.331383	+	0.331383i
$153$	−1.72192	−	1.72192i	−0.139209	−	0.139209i
$154$	−0.0151196	+	0.0768919i	−0.00121838	+	0.00619613i
$155$		0			0
$156$	0.828427			0.0663273
$157$	−15.8403	+	15.8403i	−1.26419	+	1.26419i	−0.315147	+	0.949043i	$0.602054\pi$
$157$	−15.8403	+	15.8403i	−1.26419	+	1.26419i	−0.949043	+	0.315147i	$0.897946\pi$
$158$	6.97906	−	6.97906i	0.555224	−	0.555224i
$159$	−8.17113			−0.648013
$160$		0			0
$161$	−1.44383	−	0.283908i	−0.113790	−	0.0223751i
$162$	0.707107	+	0.707107i	0.0555556	+	0.0555556i
$163$	−2.70742	+	2.70742i	−0.212061	+	0.212061i	−0.805143	−	0.593081i	$-0.797911\pi$
$163$	−2.70742	+	2.70742i	−0.212061	+	0.212061i	0.593081	+	0.805143i	$0.297911\pi$
$164$	−0.514280			−0.0401585
$165$		0			0
$166$		−	0.213022i		−	0.0165337i
$167$	13.7779	−	13.7779i	1.06616	−	1.06616i	0.0685129	−	0.997650i	$-0.478175\pi$
$167$	13.7779	−	13.7779i	1.06616	−	1.06616i	0.997650	−	0.0685129i	$-0.0218254\pi$
$168$	1.47472	+	2.19663i	0.113777	+	0.169474i
$169$		−	12.3137i		−	0.947208i
$170$		0			0
$171$		−	5.77786i		−	0.441844i
$172$	−7.16246	−	7.16246i	−0.546132	−	0.546132i
$173$	−10.3077	−	10.3077i	−0.783680	−	0.783680i	0.196770	−	0.980450i	$-0.436955\pi$
$173$	−10.3077	−	10.3077i	−0.783680	−	0.783680i	−0.980450	+	0.196770i	$0.936955\pi$
$174$	9.70636			0.735837
$175$		0			0
$176$	−0.0296189			−0.00223261
$177$	9.05595	+	9.05595i	0.680687	+	0.680687i
$178$	−3.10007	−	3.10007i	−0.232360	−	0.232360i
$179$		−	17.2422i		−	1.28874i	−0.764713	−	0.644371i	$-0.777119\pi$
$179$		−	17.2422i		−	1.28874i	0.764713	−	0.644371i	$-0.222881\pi$
$180$		0			0
$181$		−	22.4015i		−	1.66509i	−0.553957	−	0.832545i	$-0.686883\pi$
$181$		−	22.4015i		−	1.66509i	0.553957	−	0.832545i	$-0.313117\pi$
$182$	−1.81975	+	1.22170i	−0.134889	+	0.0905582i
$183$	7.58535	−	7.58535i	0.560725	−	0.560725i
$184$		−	0.556167i		−	0.0410012i
$185$		0			0
$186$	−6.39327			−0.468777
$187$	−0.0510013	+	0.0510013i	−0.00372959	+	0.00372959i
$188$	−7.77786	−	7.77786i	−0.567259	−	0.567259i
$189$	−2.59604	−	0.510472i	−0.188834	−	0.0371314i
$190$		0			0
$191$	−22.5644			−1.63270			−0.816351	−	0.577555i	$-0.804007\pi$
$191$	−22.5644			−1.63270			−0.816351	+	0.577555i	$0.804007\pi$
$192$	−0.707107	+	0.707107i	−0.0510310	+	0.0510310i
$193$	−4.94076	+	4.94076i	−0.355644	+	0.355644i	−0.862204	−	0.506561i	$-0.830917\pi$
$193$	−4.94076	+	4.94076i	−0.355644	+	0.355644i	0.506561	+	0.862204i	$0.330917\pi$
$194$	3.49334			0.250807
$195$		0			0
$196$	−6.47884	−	2.65041i	−0.462774	−	0.189315i
$197$	6.64818	+	6.64818i	0.473663	+	0.473663i	0.903098	−	0.429435i	$-0.141287\pi$
$197$	6.64818	+	6.64818i	0.473663	+	0.473663i	−0.429435	+	0.903098i	$0.641287\pi$
$198$	0.0209438	−	0.0209438i	0.00148841	−	0.00148841i
$199$	−12.2631			−0.869311			−0.434656	−	0.900597i	$-0.643130\pi$
$199$	−12.2631			−0.869311			−0.434656	+	0.900597i	$0.643130\pi$
$200$		0			0
$201$			3.38459i			0.238731i
$202$	9.04368	−	9.04368i	0.636311	−	0.636311i
$203$	−21.3213	+	14.3141i	−1.49646	+	1.00466i
$204$			2.43516i			0.170495i
$205$		0			0
$206$			11.4051i			0.794631i
$207$	0.393270	+	0.393270i	0.0273341	+	0.0273341i
$208$	−0.585786	−	0.585786i	−0.0406170	−	0.0406170i
$209$	−0.171134			−0.0118376
$210$		0			0
$211$	−4.62829			−0.318625			−0.159312	−	0.987228i	$-0.550928\pi$
$211$	−4.62829			−0.318625			−0.159312	+	0.987228i	$0.550928\pi$
$212$	5.77786	+	5.77786i	0.396825	+	0.396825i
$213$	−4.70097	−	4.70097i	−0.322105	−	0.322105i
$214$		−	1.72774i		−	0.118106i
$215$		0			0
$216$		−	1.00000i		−	0.0680414i
$217$	14.0437	−	9.42827i	0.953347	−	0.640033i
$218$	10.5348	−	10.5348i	0.713506	−	0.713506i
$219$		−	7.25132i		−	0.489999i
$220$		0			0
$221$	−2.01735			−0.135702
$222$	−3.72192	+	3.72192i	−0.249799	+	0.249799i
$223$	−18.2266	−	18.2266i	−1.22055	−	1.22055i	−0.967438	−	0.253108i	$-0.918547\pi$
$223$	−18.2266	−	18.2266i	−1.22055	−	1.22055i	−0.253108	−	0.967438i	$-0.581453\pi$
$224$	0.510472	−	2.59604i	0.0341073	−	0.173455i
$225$		0			0
$226$	−0.101125			−0.00672676
$227$	8.89844	−	8.89844i	0.590610	−	0.590610i	−0.347186	−	0.937796i	$-0.612863\pi$
$227$	8.89844	−	8.89844i	0.590610	−	0.590610i	0.937796	+	0.347186i	$0.112863\pi$
$228$	−4.08557	+	4.08557i	−0.270573	+	0.270573i
$229$	13.3137			0.879795			0.439897	−	0.898048i	$-0.355015\pi$
$229$	13.3137			0.879795			0.439897	+	0.898048i	$0.355015\pi$
$230$		0			0
$231$	−0.0151196	+	0.0768919i	−0.000994799	+	0.00505912i
$232$	−6.86343	−	6.86343i	−0.450606	−	0.450606i
$233$	2.18340	−	2.18340i	0.143039	−	0.143039i	−0.631961	−	0.775000i	$-0.717750\pi$
$233$	2.18340	−	2.18340i	0.143039	−	0.143039i	0.775000	+	0.631961i	$0.217750\pi$
$234$	0.828427			0.0541560
$235$		0			0
$236$		−	12.8070i		−	0.833668i
$237$	6.97906	−	6.97906i	0.453338	−	0.453338i
$238$	−3.59117	−	5.34915i	−0.232781	−	0.346734i
$239$			18.1201i			1.17209i	0.810277	+	0.586047i	$0.199317\pi$
$239$			18.1201i			1.17209i	−0.810277	+	0.586047i	$0.800683\pi$
$240$		0			0
$241$		−	19.6257i		−	1.26420i	−0.774885	−	0.632102i	$-0.782192\pi$
$241$		−	19.6257i		−	1.26420i	0.774885	−	0.632102i	$-0.217808\pi$
$242$	7.77755	+	7.77755i	0.499960	+	0.499960i
$243$	0.707107	+	0.707107i	0.0453609	+	0.0453609i
$244$	−10.7273			−0.686745
$245$		0			0
$246$	−0.514280			−0.0327893
$247$	−3.38459	−	3.38459i	−0.215357	−	0.215357i
$248$	4.52072	+	4.52072i	0.287066	+	0.287066i
$249$		−	0.213022i		−	0.0134997i
$250$		0			0
$251$		−	28.7478i		−	1.81455i	−0.420543	−	0.907273i	$-0.638160\pi$
$251$		−	28.7478i		−	1.81455i	0.420543	−	0.907273i	$-0.361840\pi$
$252$	1.47472	+	2.19663i	0.0928985	+	0.138375i
$253$	0.0116482	−	0.0116482i	0.000732318	−	0.000732318i
$254$			8.70680i			0.546313i
$255$		0			0
$256$	1.00000			0.0625000
$257$	−15.5789	+	15.5789i	−0.971785	+	0.971785i	−0.999613	−	0.0278275i	$-0.991141\pi$
$257$	−15.5789	+	15.5789i	−0.971785	+	0.971785i	0.0278275	+	0.999613i	$0.491141\pi$
$258$	−7.16246	−	7.16246i	−0.445915	−	0.445915i
$259$	2.68691	−	13.6645i	0.166957	−	0.849069i
$260$		0			0
$261$	9.70636			0.600808
$262$	3.19896	−	3.19896i	0.197632	−	0.197632i
$263$	−7.34271	+	7.34271i	−0.452771	+	0.452771i	−0.896273	−	0.443502i	$-0.853736\pi$
$263$	−7.34271	+	7.34271i	−0.452771	+	0.452771i	0.443502	+	0.896273i	$0.353736\pi$
$264$	−0.0296189			−0.00182292
$265$		0			0
$266$	2.94944	−	14.9996i	0.180842	−	0.919682i
$267$	−3.10007	−	3.10007i	−0.189721	−	0.189721i
$268$	2.39327	−	2.39327i	0.146192	−	0.146192i
$269$	−16.6069			−1.01254			−0.506271	−	0.862375i	$-0.668976\pi$
$269$	−16.6069			−1.01254			−0.506271	+	0.862375i	$0.668976\pi$
$270$		0			0
$271$			9.90353i			0.601596i	0.953688	+	0.300798i	$0.0972531\pi$
$271$			9.90353i			0.601596i	−0.953688	+	0.300798i	$0.902747\pi$
$272$	1.72192	−	1.72192i	0.104407	−	0.104407i
$273$	−1.81975	+	1.22170i	−0.110136	+	0.0739405i
$274$			7.89887i			0.477188i
$275$		0			0
$276$		−	0.556167i		−	0.0334773i
$277$	−2.93538	−	2.93538i	−0.176370	−	0.176370i	0.613402	−	0.789771i	$-0.289801\pi$
$277$	−2.93538	−	2.93538i	−0.176370	−	0.176370i	−0.789771	+	0.613402i	$0.789801\pi$
$278$	−11.7424	−	11.7424i	−0.704264	−	0.704264i
$279$	−6.39327			−0.382755
$280$		0			0
$281$	−4.70995			−0.280972			−0.140486	−	0.990083i	$-0.544867\pi$
$281$	−4.70995			−0.280972			−0.140486	+	0.990083i	$0.544867\pi$
$282$	−7.77786	−	7.77786i	−0.463165	−	0.463165i
$283$	−13.0588	−	13.0588i	−0.776265	−	0.776265i	0.202929	−	0.979194i	$-0.434954\pi$
$283$	−13.0588	−	13.0588i	−0.776265	−	0.776265i	−0.979194	+	0.202929i	$0.934954\pi$
$284$			6.64818i			0.394497i
$285$		0			0
$286$		−	0.0245371i		−	0.00145091i
$287$	1.12969	−	0.758418i	0.0666832	−	0.0447680i
$288$	−0.707107	+	0.707107i	−0.0416667	+	0.0416667i
$289$			11.0700i			0.651177i
$290$		0			0
$291$	3.49334			0.204783
$292$	−5.12745	+	5.12745i	−0.300062	+	0.300062i
$293$	16.8844	+	16.8844i	0.986396	+	0.986396i	0.999909	−	0.0135130i	$-0.00430144\pi$
$293$	16.8844	+	16.8844i	0.986396	+	0.986396i	−0.0135130	+	0.999909i	$0.504301\pi$
$294$	−6.47884	−	2.65041i	−0.377853	−	0.154575i
$295$		0			0
$296$	5.26358			0.305940
$297$	0.0209438	−	0.0209438i	0.00121528	−	0.00121528i
$298$	−5.52072	+	5.52072i	−0.319807	+	0.319807i
$299$	0.460744			0.0266455
$300$		0			0
$301$	26.2959	+	5.17070i	1.51567	+	0.298034i
$302$	−0.615405	−	0.615405i	−0.0354126	−	0.0354126i
$303$	9.04368	−	9.04368i	0.519546	−	0.519546i
$304$	5.77786			0.331383
$305$		0			0
$306$			2.43516i			0.139209i
$307$	11.5185	−	11.5185i	0.657395	−	0.657395i	−0.297368	−	0.954763i	$-0.596109\pi$
$307$	11.5185	−	11.5185i	0.657395	−	0.657395i	0.954763	+	0.297368i	$0.0961088\pi$
$308$	0.0650620	−	0.0436796i	0.00370725	−	0.00248888i
$309$			11.4051i			0.648813i
$310$		0			0
$311$		−	9.59762i		−	0.544231i	−0.962265	−	0.272115i	$-0.912277\pi$
$311$		−	9.59762i		−	0.544231i	0.962265	−	0.272115i	$-0.0877233\pi$
$312$	−0.585786	−	0.585786i	−0.0331636	−	0.0331636i
$313$	0.529400	+	0.529400i	0.0299234	+	0.0299234i	0.721910	−	0.691987i	$-0.243264\pi$
$313$	0.529400	+	0.529400i	0.0299234	+	0.0299234i	−0.691987	+	0.721910i	$0.743264\pi$
$314$	22.4015			1.26419
$315$		0			0
$316$	−9.86988			−0.555224
$317$	−19.8576	−	19.8576i	−1.11531	−	1.11531i	−0.992420	−	0.122895i	$-0.960782\pi$
$317$	−19.8576	−	19.8576i	−1.11531	−	1.11531i	−0.122895	−	0.992420i	$-0.539218\pi$
$318$	5.77786	+	5.77786i	0.324007	+	0.324007i
$319$		−	0.287492i		−	0.0160965i
$320$		0			0
$321$		−	1.72774i		−	0.0964331i
$322$	0.820191	+	1.22170i	0.0457074	+	0.0680825i
$323$	9.94900	−	9.94900i	0.553577	−	0.553577i
$324$		−	1.00000i		−	0.0555556i
$325$		0			0
$326$	3.82887			0.212061
$327$	10.5348	−	10.5348i	0.582575	−	0.582575i
$328$	0.363651	+	0.363651i	0.0200793	+	0.0200793i
$329$	28.5553	+	5.61497i	1.57430	+	0.309563i
$330$		0			0
$331$	4.64353			0.255231			0.127616	−	0.991824i	$-0.459268\pi$
$331$	4.64353			0.255231			0.127616	+	0.991824i	$0.459268\pi$
$332$	−0.150629	+	0.150629i	−0.00826685	+	0.00826685i
$333$	−3.72192	+	3.72192i	−0.203960	+	0.203960i
$334$	−19.4848			−1.06616
$335$		0			0
$336$	0.510472	−	2.59604i	0.0278485	−	0.141626i
$337$	−7.05924	−	7.05924i	−0.384541	−	0.384541i	0.488194	−	0.872735i	$-0.337656\pi$
$337$	−7.05924	−	7.05924i	−0.384541	−	0.384541i	−0.872735	+	0.488194i	$0.837656\pi$
$338$	−8.70711	+	8.70711i	−0.473604	+	0.473604i
$339$	−0.101125			−0.00549238
$340$		0			0
$341$			0.189362i			0.0102545i
$342$	−4.08557	+	4.08557i	−0.220922	+	0.220922i
$343$	18.1402	−	3.73248i	0.979481	−	0.201535i
$344$			10.1292i			0.546132i
$345$		0			0
$346$			14.5773i			0.783680i
$347$	23.4925	+	23.4925i	1.26114	+	1.26114i	0.950540	+	0.310601i	$0.100530\pi$
$347$	23.4925	+	23.4925i	1.26114	+	1.26114i	0.310601	+	0.950540i	$0.399470\pi$
$348$	−6.86343	−	6.86343i	−0.367919	−	0.367919i
$349$	20.1819			1.08031			0.540156	−	0.841565i	$-0.318365\pi$
$349$	20.1819			1.08031			0.540156	+	0.841565i	$0.318365\pi$
$350$		0			0
$351$	0.828427			0.0442182
$352$	0.0209438	+	0.0209438i	0.00111631	+	0.00111631i
$353$	−7.44966	−	7.44966i	−0.396505	−	0.396505i	0.480493	−	0.876998i	$-0.340458\pi$
$353$	−7.44966	−	7.44966i	−0.396505	−	0.396505i	−0.876998	+	0.480493i	$0.840458\pi$
$354$		−	12.8070i		−	0.680687i
$355$		0			0
$356$			4.38416i			0.232360i
$357$	−3.59117	−	5.34915i	−0.190065	−	0.283107i
$358$	−12.1921	+	12.1921i	−0.644371	+	0.644371i
$359$			16.6063i			0.876447i	0.898866	+	0.438223i	$0.144392\pi$
$359$			16.6063i			0.876447i	−0.898866	+	0.438223i	$0.855608\pi$
$360$		0			0
$361$	14.3837			0.757038
$362$	−15.8403	+	15.8403i	−0.832545	+	0.832545i
$363$	7.77755	+	7.77755i	0.408216	+	0.408216i
$364$	2.15063	+	0.422889i	0.112724	+	0.0221654i
$365$		0			0
$366$	−10.7273			−0.560725
$367$	−2.87317	+	2.87317i	−0.149978	+	0.149978i	−0.778108	−	0.628130i	$-0.783821\pi$
$367$	−2.87317	+	2.87317i	−0.149978	+	0.149978i	0.628130	+	0.778108i	$0.283821\pi$
$368$	−0.393270	+	0.393270i	−0.0205006	+	0.0205006i
$369$	−0.514280			−0.0267723
$370$		0			0
$371$	−21.2126	−	4.17113i	−1.10130	−	0.216554i
$372$	4.52072	+	4.52072i	0.234389	+	0.234389i
$373$	1.55078	−	1.55078i	0.0802964	−	0.0802964i	−0.665818	−	0.746114i	$-0.731917\pi$
$373$	1.55078	−	1.55078i	0.0802964	−	0.0802964i	0.746114	+	0.665818i	$0.231917\pi$
$374$	0.0721268			0.00372959
$375$		0			0
$376$			10.9996i			0.567259i
$377$	5.68585	−	5.68585i	0.292836	−	0.292836i
$378$	1.47472	+	2.19663i	0.0758513	+	0.112983i
$379$			6.92743i			0.355838i	0.984045	+	0.177919i	$0.0569366\pi$
$379$			6.92743i			0.355838i	−0.984045	+	0.177919i	$0.943063\pi$
$380$		0			0
$381$			8.70680i			0.446063i
$382$	15.9554	+	15.9554i	0.816351	+	0.816351i
$383$	−3.46372	−	3.46372i	−0.176988	−	0.176988i	0.613054	−	0.790041i	$-0.289941\pi$
$383$	−3.46372	−	3.46372i	−0.176988	−	0.176988i	−0.790041	+	0.613054i	$0.789941\pi$
$384$	1.00000			0.0510310
$385$		0			0
$386$	6.98729			0.355644
$387$	−7.16246	−	7.16246i	−0.364088	−	0.364088i
$388$	−2.47016	−	2.47016i	−0.125403	−	0.125403i
$389$		−	24.9198i		−	1.26348i	−0.775178	−	0.631742i	$-0.782340\pi$
$389$		−	24.9198i		−	1.26348i	0.775178	−	0.631742i	$-0.217660\pi$
$390$		0			0
$391$			1.35436i			0.0684927i
$392$	2.70711	+	6.45535i	0.136730	+	0.326045i
$393$	3.19896	−	3.19896i	0.161366	−	0.161366i
$394$		−	9.40194i		−	0.473663i
$395$		0			0
$396$	−0.0296189			−0.00148841
$397$	−13.6562	+	13.6562i	−0.685387	+	0.685387i	−0.961209	−	0.275822i	$-0.911050\pi$
$397$	−13.6562	+	13.6562i	−0.685387	+	0.685387i	0.275822	+	0.961209i	$0.411050\pi$
$398$	8.67135	+	8.67135i	0.434656	+	0.434656i
$399$	2.94944	−	14.9996i	0.147657	−	0.750917i
$400$		0			0
$401$	13.0125			0.649811			0.324905	−	0.945747i	$-0.394668\pi$
$401$	13.0125			0.649811			0.324905	+	0.945747i	$0.394668\pi$
$402$	2.39327	−	2.39327i	0.119365	−	0.119365i
$403$	−3.74509	+	3.74509i	−0.186556	+	0.186556i
$404$	−12.7897			−0.636311
$405$		0			0
$406$	25.1981	+	4.95482i	1.25056	+	0.245904i
$407$	0.110239	+	0.110239i	0.00546436	+	0.00546436i
$408$	1.72192	−	1.72192i	0.0852476	−	0.0852476i
$409$	−10.6154			−0.524898			−0.262449	−	0.964946i	$-0.584530\pi$
$409$	−10.6154			−0.524898			−0.262449	+	0.964946i	$0.584530\pi$
$410$		0			0
$411$			7.89887i			0.389623i
$412$	8.06462	−	8.06462i	0.397315	−	0.397315i
$413$	18.8868	+	28.1324i	0.929358	+	1.38430i
$414$		−	0.556167i		−	0.0273341i
$415$		0			0
$416$			0.828427i			0.0406170i
$417$	−11.7424	−	11.7424i	−0.575029	−	0.575029i
$418$	0.121010	+	0.121010i	0.00591880	+	0.00591880i
$419$	−9.83560			−0.480501			−0.240250	−	0.970711i	$-0.577230\pi$
$419$	−9.83560			−0.480501			−0.240250	+	0.970711i	$0.577230\pi$
$420$		0			0
$421$	−32.5963			−1.58865			−0.794323	−	0.607495i	$-0.792174\pi$
$421$	−32.5963			−1.58865			−0.794323	+	0.607495i	$0.792174\pi$
$422$	3.27270	+	3.27270i	0.159312	+	0.159312i
$423$	−7.77786	−	7.77786i	−0.378173	−	0.378173i
$424$		−	8.17113i		−	0.396825i
$425$		0			0
$426$			6.64818i			0.322105i
$427$	23.5640	−	15.8198i	1.14034	−	0.765571i
$428$	−1.22170	+	1.22170i	−0.0590530	+	0.0590530i
$429$		−	0.0245371i		−	0.00118466i
$430$		0			0
$431$	−29.3746			−1.41492			−0.707462	−	0.706751i	$-0.750160\pi$
$431$	−29.3746			−1.41492			−0.707462	+	0.706751i	$0.750160\pi$
$432$	−0.707107	+	0.707107i	−0.0340207	+	0.0340207i
$433$	17.1266	+	17.1266i	0.823051	+	0.823051i	0.986544	−	0.163494i	$-0.0522763\pi$
$433$	17.1266	+	17.1266i	0.823051	+	0.823051i	−0.163494	+	0.986544i	$0.552276\pi$
$434$	−16.5972	−	3.26358i	−0.796690	−	0.156657i
$435$		0			0
$436$	−14.8984			−0.713506
$437$	−2.27226	+	2.27226i	−0.108697	+	0.108697i
$438$	−5.12745	+	5.12745i	−0.244999	+	0.244999i
$439$	−2.29872			−0.109712			−0.0548561	−	0.998494i	$-0.517470\pi$
$439$	−2.29872			−0.109712			−0.0548561	+	0.998494i	$0.517470\pi$
$440$		0			0
$441$	−6.47884	−	2.65041i	−0.308516	−	0.126210i
$442$	1.42648	+	1.42648i	0.0678508	+	0.0678508i
$443$	1.39433	−	1.39433i	0.0662466	−	0.0662466i	−0.673207	−	0.739454i	$-0.735084\pi$
$443$	1.39433	−	1.39433i	0.0662466	−	0.0662466i	0.739454	+	0.673207i	$0.235084\pi$
$444$	5.26358			0.249799
$445$		0			0
$446$			25.7764i			1.22055i
$447$	−5.52072	+	5.52072i	−0.261121	+	0.261121i
$448$	−2.19663	+	1.47472i	−0.103781	+	0.0696739i
$449$		−	6.72730i		−	0.317481i	−0.987320	−	0.158740i	$-0.949257\pi$
$449$		−	6.72730i		−	0.317481i	0.987320	−	0.158740i	$-0.0507433\pi$
$450$		0			0
$451$			0.0152324i			0.000717267i
$452$	0.0715065	+	0.0715065i	0.00336338	+	0.00336338i
$453$	−0.615405	−	0.615405i	−0.0289143	−	0.0289143i
$454$	−12.5843			−0.590610
$455$		0			0
$456$	5.77786			0.270573
$457$	16.6569	+	16.6569i	0.779175	+	0.779175i	0.979690	−	0.200516i	$-0.0642618\pi$
$457$	16.6569	+	16.6569i	0.779175	+	0.779175i	−0.200516	+	0.979690i	$0.564262\pi$
$458$	−9.41421	−	9.41421i	−0.439897	−	0.439897i
$459$			2.43516i			0.113663i
$460$		0			0
$461$			11.5655i			0.538657i	0.963048	+	0.269329i	$0.0868018\pi$
$461$			11.5655i			0.538657i	−0.963048	+	0.269329i	$0.913198\pi$
$462$	0.0650620	−	0.0436796i	0.00302696	−	0.00203216i
$463$	12.4160	−	12.4160i	0.577021	−	0.577021i	−0.357061	−	0.934081i	$-0.616221\pi$
$463$	12.4160	−	12.4160i	0.577021	−	0.577021i	0.934081	+	0.357061i	$0.116221\pi$
$464$			9.70636i			0.450606i
$465$		0			0
$466$	−3.08780			−0.143039
$467$	6.14975	−	6.14975i	0.284577	−	0.284577i	−0.550355	−	0.834931i	$-0.685507\pi$
$467$	6.14975	−	6.14975i	0.284577	−	0.284577i	0.834931	+	0.550355i	$0.185507\pi$
$468$	−0.585786	−	0.585786i	−0.0270780	−	0.0270780i
$469$	−1.72774	+	8.78654i	−0.0797796	+	0.405725i
$470$		0			0
$471$	22.4015			1.03221
$472$	−9.05595	+	9.05595i	−0.416834	+	0.416834i
$473$	−0.212144	+	0.212144i	−0.00975441	+	0.00975441i
$474$	−9.86988			−0.453338
$475$		0			0
$476$	−1.24308	+	6.32176i	−0.0569764	+	0.289758i
$477$	5.77786	+	5.77786i	0.264550	+	0.264550i
$478$	12.8129	−	12.8129i	0.586047	−	0.586047i
$479$	−6.82843			−0.311999			−0.155999	−	0.987757i	$-0.549860\pi$
$479$	−6.82843			−0.311999			−0.155999	+	0.987757i	$0.549860\pi$
$480$		0			0
$481$			4.36050i			0.198822i
$482$	−13.8775	+	13.8775i	−0.632102	+	0.632102i
$483$	0.820191	+	1.22170i	0.0373200	+	0.0555891i
$484$		−	10.9991i		−	0.499960i
$485$		0			0
$486$		−	1.00000i		−	0.0453609i
$487$	21.7124	+	21.7124i	0.983881	+	0.983881i	0.999872	−	0.0159910i	$-0.00509032\pi$
$487$	21.7124	+	21.7124i	0.983881	+	0.983881i	−0.0159910	+	0.999872i	$0.505090\pi$
$488$	7.58535	+	7.58535i	0.343373	+	0.343373i
$489$	3.82887			0.173147
$490$		0			0
$491$	14.8991			0.672385			0.336192	−	0.941793i	$-0.390861\pi$
$491$	14.8991			0.672385			0.336192	+	0.941793i	$0.390861\pi$
$492$	0.363651	+	0.363651i	0.0163946	+	0.0163946i
$493$	16.7135	+	16.7135i	0.752740	+	0.752740i
$494$			4.78654i			0.215357i
$495$		0			0
$496$		−	6.39327i		−	0.287066i
$497$	−9.80419	−	14.6036i	−0.439778	−	0.655062i
$498$	−0.150629	+	0.150629i	−0.00674985	+	0.00674985i
$499$		−	32.7928i		−	1.46801i	−0.679144	−	0.734005i	$-0.737649\pi$
$499$		−	32.7928i		−	1.46801i	0.679144	−	0.734005i	$-0.262351\pi$
$500$		0			0
$501$	−19.4848			−0.870519
$502$	−20.3278	+	20.3278i	−0.907273	+	0.907273i
$503$	−4.33403	−	4.33403i	−0.193245	−	0.193245i	0.603852	−	0.797097i	$-0.293632\pi$
$503$	−4.33403	−	4.33403i	−0.193245	−	0.193245i	−0.797097	+	0.603852i	$0.793632\pi$
$504$	0.510472	−	2.59604i	0.0227382	−	0.115637i
$505$		0			0
$506$	−0.0164731			−0.000732318
$507$	−8.70711	+	8.70711i	−0.386696	+	0.386696i
$508$	6.15663	−	6.15663i	0.273157	−	0.273157i
$509$	12.2581			0.543329			0.271665	−	0.962392i	$-0.412426\pi$
$509$	12.2581			0.543329			0.271665	+	0.962392i	$0.412426\pi$
$510$		0			0
$511$	3.70159	−	18.8247i	0.163749	−	0.832756i
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$	−4.08557	+	4.08557i	−0.180382	+	0.180382i
$514$	22.0319			0.971785
$515$		0			0
$516$			10.1292i			0.445915i
$517$	−0.230372	+	0.230372i	−0.0101318	+	0.0101318i
$518$	−11.5622	+	7.76231i	−0.508013	+	0.341056i
$519$			14.5773i			0.639872i
$520$		0			0
$521$			10.1828i			0.446116i	0.974805	+	0.223058i	$0.0716039\pi$
$521$			10.1828i			0.446116i	−0.974805	+	0.223058i	$0.928396\pi$
$522$	−6.86343	−	6.86343i	−0.300404	−	0.300404i
$523$	7.86522	+	7.86522i	0.343922	+	0.343922i	0.857840	−	0.513917i	$-0.171806\pi$
$523$	7.86522	+	7.86522i	0.343922	+	0.343922i	−0.513917	+	0.857840i	$0.671806\pi$
$524$	−4.52401			−0.197632
$525$		0			0
$526$	10.3842			0.452771
$527$	−11.0087	−	11.0087i	−0.479545	−	0.479545i
$528$	0.0209438	+	0.0209438i	0.000911460	+	0.000911460i
$529$			22.6907i			0.986551i
$530$		0			0
$531$		−	12.8070i		−	0.555778i
$532$	−12.6919	+	8.52072i	−0.550262	+	0.369420i
$533$	−0.301258	+	0.301258i	−0.0130489	+	0.0130489i
$534$			4.38416i			0.189721i
$535$		0			0
$536$	−3.38459			−0.146192
$537$	−12.1921	+	12.1921i	−0.526127	+	0.526127i
$538$	11.7429	+	11.7429i	0.506271	+	0.506271i
$539$	−0.0785023	+	0.191896i	−0.00338133	+	0.00826556i
$540$		0			0
$541$	17.5312			0.753725			0.376862	−	0.926269i	$-0.377003\pi$
$541$	17.5312			0.753725			0.376862	+	0.926269i	$0.377003\pi$
$542$	7.00285	−	7.00285i	0.300798	−	0.300798i
$543$	−15.8403	+	15.8403i	−0.679770	+	0.679770i
$544$	−2.43516			−0.104407
$545$		0			0
$546$	2.15063	+	0.422889i	0.0920384	+	0.0180980i
$547$	−12.5889	−	12.5889i	−0.538264	−	0.538264i	0.384755	−	0.923019i	$-0.374286\pi$
$547$	−12.5889	−	12.5889i	−0.538264	−	0.538264i	−0.923019	+	0.384755i	$0.874286\pi$
$548$	5.58535	−	5.58535i	0.238594	−	0.238594i
$549$	−10.7273			−0.457830
$550$		0			0
$551$			56.0820i			2.38917i
$552$	−0.393270	+	0.393270i	−0.0167387	+	0.0167387i
$553$	21.6805	−	14.5553i	0.921949	−	0.618954i
$554$			4.15125i			0.176370i
$555$		0			0
$556$			16.6063i			0.704264i
$557$	−24.5752	−	24.5752i	−1.04128	−	1.04128i	−0.999110	−	0.0421733i	$-0.986572\pi$
$557$	−24.5752	−	24.5752i	−1.04128	−	1.04128i	−0.0421733	−	0.999110i	$-0.513428\pi$
$558$	4.52072	+	4.52072i	0.191378	+	0.191378i
$559$	−8.39134			−0.354916
$560$		0			0
$561$	0.0721268			0.00304520
$562$	3.33044	+	3.33044i	0.140486	+	0.140486i
$563$	6.28391	+	6.28391i	0.264835	+	0.264835i	0.827015	−	0.562180i	$-0.190037\pi$
$563$	6.28391	+	6.28391i	0.264835	+	0.264835i	−0.562180	+	0.827015i	$0.690037\pi$
$564$			10.9996i			0.463165i
$565$		0			0
$566$			18.4679i			0.776265i
$567$	1.47472	+	2.19663i	0.0619324	+	0.0922500i
$568$	4.70097	−	4.70097i	0.197248	−	0.197248i
$569$		−	15.0696i		−	0.631749i	−0.948801	−	0.315875i	$-0.897702\pi$
$569$		−	15.0696i		−	0.631749i	0.948801	−	0.315875i	$-0.102298\pi$
$570$		0			0
$571$	28.0757			1.17493			0.587466	−	0.809249i	$-0.300126\pi$
$571$	28.0757			1.17493			0.587466	+	0.809249i	$0.300126\pi$
$572$	−0.0173504	+	0.0173504i	−0.000725456	+	0.000725456i
$573$	15.9554	+	15.9554i	0.666548	+	0.666548i
$574$	−1.33509	−	0.262525i	−0.0557256	−	0.0109576i
$575$		0			0
$576$	1.00000			0.0416667
$577$	14.2455	−	14.2455i	0.593048	−	0.593048i	−0.345406	−	0.938453i	$-0.612259\pi$
$577$	14.2455	−	14.2455i	0.593048	−	0.593048i	0.938453	+	0.345406i	$0.112259\pi$
$578$	7.82768	−	7.82768i	0.325588	−	0.325588i
$579$	6.98729			0.290382
$580$		0			0
$581$	0.108742	−	0.553013i	0.00451136	−	0.0229428i
$582$	−2.47016	−	2.47016i	−0.102391	−	0.102391i
$583$	0.171134	−	0.171134i	0.00708766	−	0.00708766i
$584$	7.25132			0.300062
$585$		0			0
$586$		−	23.8781i		−	0.986396i
$587$	6.03786	−	6.03786i	0.249209	−	0.249209i	−0.571437	−	0.820646i	$-0.693614\pi$
$587$	6.03786	−	6.03786i	0.249209	−	0.249209i	0.820646	+	0.571437i	$0.193614\pi$
$588$	2.70711	+	6.45535i	0.111639	+	0.266214i
$589$		−	36.9394i		−	1.52206i
$590$		0			0
$591$		−	9.40194i		−	0.386744i
$592$	−3.72192	−	3.72192i	−0.152970	−	0.152970i
$593$	18.9043	+	18.9043i	0.776305	+	0.776305i	0.979200	−	0.202895i	$-0.0650352\pi$
$593$	18.9043	+	18.9043i	0.776305	+	0.776305i	−0.202895	+	0.979200i	$0.565035\pi$
$594$	−0.0296189			−0.00121528
$595$		0			0
$596$	7.80748			0.319807
$597$	8.67135	+	8.67135i	0.354895	+	0.354895i
$598$	−0.325795	−	0.325795i	−0.0133228	−	0.0133228i
$599$			24.1620i			0.987233i	0.869680	+	0.493617i	$0.164325\pi$
$599$			24.1620i			0.987233i	−0.869680	+	0.493617i	$0.835675\pi$
$600$		0			0
$601$			46.4416i			1.89439i	0.320652	+	0.947197i	$0.396098\pi$
$601$			46.4416i			1.89439i	−0.320652	+	0.947197i	$0.603902\pi$
$602$	−14.9378	−	22.2503i	−0.608819	−	0.906853i
$603$	2.39327	−	2.39327i	0.0974615	−	0.0974615i
$604$			0.870315i			0.0354126i
$605$		0			0
$606$	−12.7897			−0.519546
$607$	−24.4860	+	24.4860i	−0.993857	+	0.993857i	−0.999981	−	0.00612457i	$-0.998050\pi$
$607$	−24.4860	+	24.4860i	−0.993857	+	0.993857i	0.00612457	+	0.999981i	$0.498050\pi$
$608$	−4.08557	−	4.08557i	−0.165692	−	0.165692i
$609$	25.1981	+	4.95482i	1.02108	+	0.200780i
$610$		0			0
$611$	−9.11233			−0.368646
$612$	1.72192	−	1.72192i	0.0696043	−	0.0696043i
$613$	29.5909	−	29.5909i	1.19517	−	1.19517i	0.219569	−	0.975597i	$-0.429535\pi$
$613$	29.5909	−	29.5909i	1.19517	−	1.19517i	0.975597	−	0.219569i	$-0.0704650\pi$
$614$	−16.2896			−0.657395
$615$		0			0
$616$	−0.0768919	−	0.0151196i	−0.00309806	−	0.000609188i
$617$	30.3710	+	30.3710i	1.22269	+	1.22269i	0.966672	+	0.256019i	$0.0824110\pi$
$617$	30.3710	+	30.3710i	1.22269	+	1.22269i	0.256019	+	0.966672i	$0.417589\pi$
$618$	8.06462	−	8.06462i	0.324407	−	0.324407i
$619$	−41.0141			−1.64850			−0.824248	−	0.566229i	$-0.808402\pi$
$619$	−41.0141			−1.64850			−0.824248	+	0.566229i	$0.808402\pi$
$620$		0			0
$621$		−	0.556167i		−	0.0223182i
$622$	−6.78654	+	6.78654i	−0.272115	+	0.272115i
$623$	−6.46540	−	9.63039i	−0.259031	−	0.385833i
$624$			0.828427i			0.0331636i
$625$		0			0
$626$		−	0.748684i		−	0.0299234i
$627$	0.121010	+	0.121010i	0.00483268	+	0.00483268i
$628$	−15.8403	−	15.8403i	−0.632095	−	0.632095i
$629$	−12.8177			−0.511073
$630$		0			0
$631$	−4.08948			−0.162800			−0.0813998	−	0.996682i	$-0.525939\pi$
$631$	−4.08948			−0.162800			−0.0813998	+	0.996682i	$0.525939\pi$
$632$	6.97906	+	6.97906i	0.277612	+	0.277612i
$633$	3.27270	+	3.27270i	0.130078	+	0.130078i
$634$			28.0829i			1.11531i
$635$		0			0
$636$		−	8.17113i		−	0.324007i
$637$	−5.34779	+	2.24264i	−0.211887	+	0.0888567i
$638$	−0.203288	+	0.203288i	−0.00804823	+	0.00804823i
$639$			6.64818i			0.262998i
$640$		0			0
$641$	11.8151			0.466668			0.233334	−	0.972397i	$-0.425036\pi$
$641$	11.8151			0.466668			0.233334	+	0.972397i	$0.425036\pi$
$642$	−1.22170	+	1.22170i	−0.0482165	+	0.0482165i
$643$	6.35138	+	6.35138i	0.250474	+	0.250474i	0.821165	−	0.570691i	$-0.193325\pi$
$643$	6.35138	+	6.35138i	0.250474	+	0.250474i	−0.570691	+	0.821165i	$0.693325\pi$
$644$	0.283908	−	1.44383i	0.0111875	−	0.0568950i
$645$		0			0
$646$	−14.0700			−0.553577
$647$	−34.1901	+	34.1901i	−1.34415	+	1.34415i	−0.452274	+	0.891879i	$0.649387\pi$
$647$	−34.1901	+	34.1901i	−1.34415	+	1.34415i	−0.891879	+	0.452274i	$0.850613\pi$
$648$	−0.707107	+	0.707107i	−0.0277778	+	0.0277778i
$649$	−0.379331			−0.0148900
$650$		0			0
$651$	−16.5972	−	3.26358i	−0.650495	−	0.127910i
$652$	−2.70742	−	2.70742i	−0.106031	−	0.106031i
$653$	−30.0988	+	30.0988i	−1.17786	+	1.17786i	−0.197565	+	0.980290i	$0.563303\pi$
$653$	−30.0988	+	30.0988i	−1.17786	+	1.17786i	−0.980290	+	0.197565i	$0.936697\pi$
$654$	−14.8984			−0.582575
$655$		0			0
$656$		−	0.514280i		−	0.0200793i
$657$	−5.12745	+	5.12745i	−0.200041	+	0.200041i
$658$	−16.2213	−	24.1620i	−0.632370	−	0.941934i
$659$			27.3843i			1.06674i	0.845881	+	0.533371i	$0.179075\pi$
$659$			27.3843i			1.06674i	−0.845881	+	0.533371i	$0.820925\pi$
$660$		0			0
$661$		−	22.5855i		−	0.878475i	−0.898371	−	0.439238i	$-0.855249\pi$
$661$		−	22.5855i		−	0.878475i	0.898371	−	0.439238i	$-0.144751\pi$
$662$	−3.28347	−	3.28347i	−0.127616	−	0.127616i
$663$	1.42648	+	1.42648i	0.0554000	+	0.0554000i
$664$	0.213022			0.00826685
$665$		0			0
$666$	5.26358			0.203960
$667$	−3.81722	−	3.81722i	−0.147803	−	0.147803i
$668$	13.7779	+	13.7779i	0.533082	+	0.533082i
$669$			25.7764i			0.996572i
$670$		0			0
$671$			0.317731i			0.0122659i
$672$	−2.19663	+	1.47472i	−0.0847370	+	0.0568885i
$673$	−17.7447	+	17.7447i	−0.684006	+	0.684006i	−0.960900	−	0.276894i	$-0.910695\pi$
$673$	−17.7447	+	17.7447i	−0.684006	+	0.684006i	0.276894	+	0.960900i	$0.410695\pi$
$674$			9.98327i			0.384541i
$675$		0			0
$676$	12.3137			0.473604
$677$	18.4477	−	18.4477i	0.709003	−	0.709003i	−0.257322	−	0.966326i	$-0.582840\pi$
$677$	18.4477	−	18.4477i	0.709003	−	0.709003i	0.966326	+	0.257322i	$0.0828402\pi$
$678$	0.0715065	+	0.0715065i	0.00274619	+	0.00274619i
$679$	9.06884	+	1.78325i	0.348030	+	0.0684349i
$680$		0			0
$681$	−12.5843			−0.482231
$682$	0.133899	−	0.133899i	0.00512726	−	0.00512726i
$683$	−1.35560	+	1.35560i	−0.0518704	+	0.0518704i	−0.732566	−	0.680696i	$-0.761678\pi$
$683$	−1.35560	+	1.35560i	−0.0518704	+	0.0518704i	0.680696	+	0.732566i	$0.261678\pi$
$684$	5.77786			0.220922
$685$		0			0
$686$	−15.4664	−	10.1878i	−0.590508	−	0.388973i
$687$	−9.41421	−	9.41421i	−0.359175	−	0.359175i
$688$	7.16246	−	7.16246i	0.273066	−	0.273066i
$689$	6.76919			0.257886
$690$		0			0
$691$		−	4.24455i		−	0.161470i	−0.996736	−	0.0807352i	$-0.974273\pi$
$691$		−	4.24455i		−	0.161470i	0.996736	−	0.0807352i	$-0.0257268\pi$
$692$	10.3077	−	10.3077i	0.391840	−	0.391840i
$693$	0.0650620	−	0.0436796i	0.00247150	−	0.00165925i
$694$		−	33.2234i		−	1.26114i
$695$		0			0
$696$			9.70636i			0.367919i
$697$	−0.885547	−	0.885547i	−0.0335425	−	0.0335425i
$698$	−14.2708	−	14.2708i	−0.540156	−	0.540156i
$699$	−3.08780			−0.116791
$700$		0			0
$701$	11.1047			0.419419			0.209710	−	0.977764i	$-0.432748\pi$
$701$	11.1047			0.419419			0.209710	+	0.977764i	$0.432748\pi$
$702$	−0.585786	−	0.585786i	−0.0221091	−	0.0221091i
$703$	−21.5047	−	21.5047i	−0.811066	−	0.811066i
$704$		−	0.0296189i		−	0.00111631i
$705$		0			0
$706$			10.5354i			0.396505i
$707$	28.0943	−	18.8612i	1.05659	−	0.709348i
$708$	−9.05595	+	9.05595i	−0.340343	+	0.340343i
$709$		−	34.1694i		−	1.28326i	−0.767015	−	0.641629i	$-0.778259\pi$
$709$		−	34.1694i		−	1.28326i	0.767015	−	0.641629i	$-0.221741\pi$
$710$		0			0
$711$	−9.86988			−0.370149
$712$	3.10007	−	3.10007i	0.116180	−	0.116180i
$713$	2.51428	+	2.51428i	0.0941605	+	0.0941605i
$714$	−1.24308	+	6.32176i	−0.0465211	+	0.236586i
$715$		0			0
$716$	17.2422			0.644371
$717$	12.8129	−	12.8129i	0.478505	−	0.478505i
$718$	11.7424	−	11.7424i	0.438223	−	0.438223i
$719$	−27.7960			−1.03662			−0.518308	−	0.855194i	$-0.673438\pi$
$719$	−27.7960			−1.03662			−0.518308	+	0.855194i	$0.673438\pi$
$720$		0			0
$721$	−5.82198	+	29.6081i	−0.216822	+	1.10266i
$722$	−10.1708	−	10.1708i	−0.378519	−	0.378519i
$723$	−13.8775	+	13.8775i	−0.516109	+	0.516109i
$724$	22.4015			0.832545
$725$		0			0
$726$		−	10.9991i		−	0.408216i
$727$	9.37456	−	9.37456i	0.347683	−	0.347683i	−0.511563	−	0.859246i	$-0.670933\pi$
$727$	9.37456	−	9.37456i	0.347683	−	0.347683i	0.859246	+	0.511563i	$0.170933\pi$
$728$	−1.22170	−	1.81975i	−0.0452791	−	0.0674445i
$729$		−	1.00000i		−	0.0370370i
$730$		0			0
$731$		−	24.6663i		−	0.912316i
$732$	7.58535	+	7.58535i	0.280363	+	0.280363i
$733$	−8.54390	−	8.54390i	−0.315576	−	0.315576i	0.531489	−	0.847065i	$-0.321633\pi$
$733$	−8.54390	−	8.54390i	−0.315576	−	0.315576i	−0.847065	+	0.531489i	$0.821633\pi$
$734$	4.06327			0.149978
$735$		0			0
$736$	0.556167			0.0205006
$737$	−0.0708861	−	0.0708861i	−0.00261112	−	0.00261112i
$738$	0.363651	+	0.363651i	0.0133862	+	0.0133862i
$739$			24.4015i			0.897624i	0.893626	+	0.448812i	$0.148153\pi$
$739$			24.4015i			0.897624i	−0.893626	+	0.448812i	$0.851847\pi$
$740$		0			0
$741$			4.78654i			0.175838i
$742$	12.0501	+	17.9490i	0.442374	+	0.658928i
$743$	−16.3076	+	16.3076i	−0.598267	+	0.598267i	−0.939851	−	0.341584i	$-0.889036\pi$
$743$	−16.3076	+	16.3076i	−0.598267	+	0.598267i	0.341584	+	0.939851i	$0.389036\pi$
$744$		−	6.39327i		−	0.234389i
$745$		0			0
$746$	−2.19314			−0.0802964
$747$	−0.150629	+	0.150629i	−0.00551123	+	0.00551123i
$748$	−0.0510013	−	0.0510013i	−0.00186479	−	0.00186479i
$749$	0.881963	−	4.48528i	0.0322262	−	0.163889i
$750$		0			0
$751$	27.6503			1.00897			0.504486	−	0.863420i	$-0.331682\pi$
$751$	27.6503			1.00897			0.504486	+	0.863420i	$0.331682\pi$
$752$	7.77786	−	7.77786i	0.283630	−	0.283630i
$753$	−20.3278	+	20.3278i	−0.740785	+	0.740785i
$754$	−8.04101			−0.292836
$755$		0			0
$756$	0.510472	−	2.59604i	0.0185657	−	0.0944170i
$757$	20.2224	+	20.2224i	0.734997	+	0.734997i	0.971605	−	0.236608i	$-0.0760358\pi$
$757$	20.2224	+	20.2224i	0.734997	+	0.734997i	−0.236608	+	0.971605i	$0.576036\pi$
$758$	4.89844	−	4.89844i	0.177919	−	0.177919i
$759$	−0.0164731			−0.000597935
$760$		0			0
$761$		−	23.1354i		−	0.838657i	−0.907835	−	0.419329i	$-0.862266\pi$
$761$		−	23.1354i		−	0.838657i	0.907835	−	0.419329i	$-0.137734\pi$
$762$	6.15663	−	6.15663i	0.223031	−	0.223031i
$763$	32.7264	−	21.9710i	1.18478	−	0.795404i
$764$		−	22.5644i		−	0.816351i
$765$		0			0
$766$			4.89844i			0.176988i
$767$	−7.50219	−	7.50219i	−0.270888	−	0.270888i
$768$	−0.707107	−	0.707107i	−0.0255155	−	0.0255155i
$769$	−25.1546			−0.907098			−0.453549	−	0.891231i	$-0.649842\pi$
$769$	−25.1546			−0.907098			−0.453549	+	0.891231i	$0.649842\pi$
$770$		0			0
$771$	22.0319			0.793459
$772$	−4.94076	−	4.94076i	−0.177822	−	0.177822i
$773$	−23.0515	−	23.0515i	−0.829104	−	0.829104i	0.158289	−	0.987393i	$-0.449402\pi$
$773$	−23.0515	−	23.0515i	−0.829104	−	0.829104i	−0.987393	+	0.158289i	$0.949402\pi$
$774$			10.1292i			0.364088i
$775$		0			0
$776$			3.49334i			0.125403i
$777$	−11.5622	+	7.76231i	−0.414791	+	0.278471i
$778$	−17.6210	+	17.6210i	−0.631742	+	0.631742i
$779$		−	2.97144i		−	0.106463i
$780$		0			0
$781$	0.196912			0.00704607
$782$	0.957674	−	0.957674i	0.0342463	−	0.0342463i
$783$	−6.86343	−	6.86343i	−0.245279	−	0.245279i
$784$	2.65041	−	6.47884i	0.0946575	−	0.231387i
$785$		0			0
$786$	−4.52401			−0.161366
$787$	24.2320	−	24.2320i	0.863779	−	0.863779i	−0.127996	−	0.991775i	$-0.540855\pi$
$787$	24.2320	−	24.2320i	0.863779	−	0.863779i	0.991775	+	0.127996i	$0.0408545\pi$
$788$	−6.64818	+	6.64818i	−0.236832	+	0.236832i
$789$	10.3842			0.369686
$790$		0			0
$791$	−0.262525	−	0.0516217i	−0.00933433	−	0.00183546i
$792$	0.0209438	+	0.0209438i	0.000744204	+	0.000744204i
$793$	−6.28391	+	6.28391i	−0.223148	+	0.223148i
$794$	19.3128			0.685387
$795$		0			0
$796$		−	12.2631i		−	0.434656i
$797$	−17.5376	+	17.5376i	−0.621215	+	0.621215i	−0.945842	−	0.324627i	$-0.894761\pi$
$797$	−17.5376	+	17.5376i	−0.621215	+	0.621215i	0.324627	+	0.945842i	$0.394761\pi$
$798$	−12.6919	+	8.52072i	−0.449287	+	0.301630i
$799$		−	26.7857i		−	0.947609i
$800$		0			0
$801$			4.38416i			0.154907i
$802$	−9.20119	−	9.20119i	−0.324905	−	0.324905i
$803$	0.151870	+	0.151870i	0.00535937	+	0.00535937i
$804$	−3.38459			−0.119365
$805$		0			0
$806$	5.29636			0.186556
$807$	11.7429	+	11.7429i	0.413368	+	0.413368i
$808$	9.04368	+	9.04368i	0.318156	+	0.318156i
$809$		−	20.1011i		−	0.706718i	−0.935488	−	0.353359i	$-0.885039\pi$
$809$		−	20.1011i		−	0.706718i	0.935488	−	0.353359i	$-0.114961\pi$
$810$		0			0
$811$		−	27.6340i		−	0.970360i	−0.874414	−	0.485180i	$-0.838754\pi$
$811$		−	27.6340i		−	0.970360i	0.874414	−	0.485180i	$-0.161246\pi$
$812$	−14.3141	−	21.3213i	−0.502328	−	0.748232i
$813$	7.00285	−	7.00285i	0.245601	−	0.245601i
$814$		−	0.155902i		−	0.00546436i
$815$		0			0
$816$	−2.43516			−0.0852476
$817$	41.3837	−	41.3837i	1.44783	−	1.44783i
$818$	7.50623	+	7.50623i	0.262449	+	0.262449i
$819$	2.15063	+	0.422889i	0.0751491	+	0.0147769i
$820$		0			0
$821$	−6.07616			−0.212059			−0.106030	−	0.994363i	$-0.533814\pi$
$821$	−6.07616			−0.212059			−0.106030	+	0.994363i	$0.533814\pi$
$822$	5.58535	−	5.58535i	0.194811	−	0.194811i
$823$	13.2971	−	13.2971i	0.463507	−	0.463507i	−0.436296	−	0.899803i	$-0.643710\pi$
$823$	13.2971	−	13.2971i	0.463507	−	0.463507i	0.899803	+	0.436296i	$0.143710\pi$
$824$	−11.4051			−0.397315
$825$		0			0
$826$	6.53764	−	33.2476i	0.227473	−	1.15683i
$827$	−4.21364	−	4.21364i	−0.146523	−	0.146523i	0.630040	−	0.776563i	$-0.283038\pi$
$827$	−4.21364	−	4.21364i	−0.146523	−	0.146523i	−0.776563	+	0.630040i	$0.783038\pi$
$828$	−0.393270	+	0.393270i	−0.0136671	+	0.0136671i
$829$	25.3382			0.880034			0.440017	−	0.897990i	$-0.354972\pi$
$829$	25.3382			0.880034			0.440017	+	0.897990i	$0.354972\pi$
$830$		0			0
$831$			4.15125i			0.144005i
$832$	0.585786	−	0.585786i	0.0203085	−	0.0203085i
$833$	−6.59223	−	15.7198i	−0.228407	−	0.544659i
$834$			16.6063i			0.575029i
$835$		0			0
$836$		−	0.171134i		−	0.00591880i
$837$	4.52072	+	4.52072i	0.156259	+	0.156259i
$838$	6.95482	+	6.95482i	0.240250	+	0.240250i
$839$	8.27672			0.285744			0.142872	−	0.989741i	$-0.454366\pi$
$839$	8.27672			0.285744			0.142872	+	0.989741i	$0.454366\pi$
$840$		0			0
$841$	−65.2134			−2.24874
$842$	23.0491	+	23.0491i	0.794323	+	0.794323i
$843$	3.33044	+	3.33044i	0.114706	+	0.114706i
$844$		−	4.62829i		−	0.159312i
$845$		0			0
$846$			10.9996i			0.378173i
$847$	16.2206	+	24.1611i	0.557347	+	0.830184i
$848$	−5.77786	+	5.77786i	−0.198413	+	0.198413i
$849$			18.4679i			0.633818i
$850$		0			0
$851$	2.92743			0.100351
$852$	4.70097	−	4.70097i	0.161053	−	0.161053i
$853$	−30.3653	−	30.3653i	−1.03969	−	1.03969i	−0.999179	−	0.0405092i	$-0.987102\pi$
$853$	−30.3653	−	30.3653i	−1.03969	−	1.03969i	−0.0405092	−	0.999179i	$-0.512898\pi$
$854$	−27.8485	−	5.47599i	−0.952956	−	0.187384i
$855$		0			0
$856$	1.72774			0.0590530
$857$	−33.0766	+	33.0766i	−1.12988	+	1.12988i	−0.139680	+	0.990197i	$0.544607\pi$
$857$	−33.0766	+	33.0766i	−1.12988	+	1.12988i	−0.990197	+	0.139680i	$0.955393\pi$
$858$	−0.0173504	+	0.0173504i	−0.000592332	+	0.000592332i
$859$	1.87687			0.0640380			0.0320190	−	0.999487i	$-0.489806\pi$
$859$	1.87687			0.0640380			0.0320190	+	0.999487i	$0.489806\pi$
$860$		0			0
$861$	−1.33509	−	0.262525i	−0.0454998	−	0.00894684i
$862$	20.7710	+	20.7710i	0.707462	+	0.707462i
$863$	−10.8612	+	10.8612i	−0.369720	+	0.369720i	−0.867375	−	0.497655i	$-0.834194\pi$
$863$	−10.8612	+	10.8612i	−0.369720	+	0.369720i	0.497655	+	0.867375i	$0.334194\pi$
$864$	1.00000			0.0340207
$865$		0			0
$866$		−	24.2206i		−	0.823051i
$867$	7.82768	−	7.82768i	0.265842	−	0.265842i
$868$	9.42827	+	14.0437i	0.320016	+	0.476674i
$869$			0.292335i			0.00991680i
$870$		0			0
$871$		−	2.80389i		−	0.0950062i
$872$	10.5348	+	10.5348i	0.356753	+	0.356753i
$873$	−2.47016	−	2.47016i	−0.0836023	−	0.0836023i
$874$	3.21346			0.108697
$875$		0			0
$876$	7.25132			0.244999
$877$	5.90470	+	5.90470i	0.199388	+	0.199388i	0.799737	−	0.600350i	$-0.204972\pi$
$877$	5.90470	+	5.90470i	0.199388	+	0.199388i	−0.600350	+	0.799737i	$0.704972\pi$
$878$	1.62544	+	1.62544i	0.0548561	+	0.0548561i
$879$		−	23.8781i		−	0.805389i
$880$		0			0
$881$		−	6.76200i		−	0.227818i	−0.993491	−	0.113909i	$-0.963663\pi$
$881$		−	6.76200i		−	0.227818i	0.993491	−	0.113909i	$-0.0363372\pi$
$882$	2.70711	+	6.45535i	0.0911530	+	0.217363i
$883$	−24.6192	+	24.6192i	−0.828501	+	0.828501i	−0.987309	−	0.158808i	$-0.949235\pi$
$883$	−24.6192	+	24.6192i	−0.828501	+	0.828501i	0.158808	+	0.987309i	$0.449235\pi$
$884$		−	2.01735i		−	0.0678508i
$885$		0			0
$886$	−1.97188			−0.0662466
$887$	6.92132	−	6.92132i	0.232395	−	0.232395i	−0.581297	−	0.813692i	$-0.697454\pi$
$887$	6.92132	−	6.92132i	0.232395	−	0.232395i	0.813692	+	0.581297i	$0.197454\pi$
$888$	−3.72192	−	3.72192i	−0.124899	−	0.124899i
$889$	−4.44457	+	22.6032i	−0.149066	+	0.758086i
$890$		0			0
$891$	−0.0296189			−0.000992272
$892$	18.2266	−	18.2266i	0.610273	−	0.610273i
$893$	44.9394	−	44.9394i	1.50384	−	1.50384i
$894$	7.80748			0.261121
$895$		0			0
$896$	2.59604	+	0.510472i	0.0867276	+	0.0170537i
$897$	−0.325795	−	0.325795i	−0.0108780	−	0.0108780i
$898$	−4.75692	+	4.75692i	−0.158740	+	0.158740i
$899$	62.0554			2.06966
$900$		0			0
$901$			19.8980i			0.662898i
$902$	0.0107710	−	0.0107710i	0.000358634	−	0.000358634i
$903$	−14.9378	−	22.2503i	−0.497098	−	0.740442i
$904$		−	0.101125i		−	0.00336338i
$905$		0			0
$906$			0.870315i			0.0289143i
$907$	6.28050	+	6.28050i	0.208540	+	0.208540i	0.803647	−	0.595106i	$-0.202890\pi$
$907$	6.28050	+	6.28050i	0.208540	+	0.208540i	−0.595106	+	0.803647i	$0.702890\pi$
$908$	8.89844	+	8.89844i	0.295305	+	0.295305i
$909$	−12.7897			−0.424207
$910$		0			0
$911$	19.9873			0.662209			0.331104	−	0.943594i	$-0.392579\pi$
$911$	19.9873			0.662209			0.331104	+	0.943594i	$0.392579\pi$
$912$	−4.08557	−	4.08557i	−0.135287	−	0.135287i
$913$	0.00446148	+	0.00446148i	0.000147653	+	0.000147653i
$914$		−	23.5563i		−	0.779175i
$915$		0			0
$916$			13.3137i			0.439897i
$917$	9.93761	−	6.67165i	0.328169	−	0.220317i
$918$	1.72192	−	1.72192i	0.0568317	−	0.0568317i
$919$			9.34358i			0.308216i	0.988054	+	0.154108i	$0.0492504\pi$
$919$			9.34358i			0.308216i	−0.988054	+	0.154108i	$0.950750\pi$
$920$		0			0
$921$	−16.2896			−0.536761
$922$	8.17802	−	8.17802i	0.269329	−	0.269329i
$923$	3.89441	+	3.89441i	0.128186	+	0.128186i
$924$	−0.0768919	−	0.0151196i	−0.00252956	−	0.000497400i
$925$		0			0
$926$	−17.5589			−0.577021
$927$	8.06462	−	8.06462i	0.264877	−	0.264877i
$928$	6.86343	−	6.86343i	0.225303	−	0.225303i
$929$	13.8699			0.455056			0.227528	−	0.973772i	$-0.426936\pi$
$929$	13.8699			0.455056			0.227528	+	0.973772i	$0.426936\pi$
$930$		0			0
$931$	15.3137	−	37.4338i	0.501887	−	1.22684i
$932$	2.18340	+	2.18340i	0.0715197	+	0.0715197i
$933$	−6.78654	+	6.78654i	−0.222181	+	0.222181i
$934$	−8.69706			−0.284577
$935$		0			0
$936$			0.828427i			0.0270780i
$937$	−27.3569	+	27.3569i	−0.893713	+	0.893713i	−0.994870	−	0.101158i	$-0.967745\pi$
$937$	−27.3569	+	27.3569i	−0.893713	+	0.893713i	0.101158	+	0.994870i	$0.467745\pi$
$938$	7.43472	−	4.99132i	0.242752	−	0.162973i
$939$		−	0.748684i		−	0.0244324i
$940$		0			0
$941$		−	54.0397i		−	1.76164i	−0.473448	−	0.880822i	$-0.656991\pi$
$941$		−	54.0397i		−	1.76164i	0.473448	−	0.880822i	$-0.343009\pi$
$942$	−15.8403	−	15.8403i	−0.516103	−	0.516103i
$943$	0.202251	+	0.202251i	0.00658619	+	0.00658619i
$944$	12.8070			0.416834
$945$		0			0
$946$	0.300018			0.00975441
$947$	−27.2157	−	27.2157i	−0.884393	−	0.884393i	0.109585	−	0.993977i	$-0.465048\pi$
$947$	−27.2157	−	27.2157i	−0.884393	−	0.884393i	−0.993977	+	0.109585i	$0.965048\pi$
$948$	6.97906	+	6.97906i	0.226669	+	0.226669i
$949$			6.00719i			0.195002i
$950$		0			0
$951$			28.0829i			0.910650i
$952$	5.34915	−	3.59117i	0.173367	−	0.116391i
$953$	4.60945	−	4.60945i	0.149315	−	0.149315i	−0.628497	−	0.777812i	$-0.716330\pi$
$953$	4.60945	−	4.60945i	0.149315	−	0.149315i	0.777812	+	0.628497i	$0.216330\pi$
$954$		−	8.17113i		−	0.264550i
$955$		0			0
$956$	−18.1201			−0.586047
$957$	−0.203288	+	0.203288i	−0.00657135	+	0.00657135i
$958$	4.82843	+	4.82843i	0.155999	+	0.155999i
$959$	−4.03215	+	20.5058i	−0.130205	+	0.662166i
$960$		0			0
$961$	−9.87390			−0.318513
$962$	3.08334	−	3.08334i	0.0994108	−	0.0994108i
$963$	−1.22170	+	1.22170i	−0.0393686	+	0.0393686i
$964$	19.6257			0.632102
$965$		0			0
$966$	0.283908	−	1.44383i	0.00913459	−	0.0464545i
$967$	−31.1433	−	31.1433i	−1.00150	−	1.00150i	−0.999999	−	0.00150238i	$-0.999522\pi$
$967$	−31.1433	−	31.1433i	−1.00150	−	1.00150i	−0.00150238	−	0.999999i	$-0.500478\pi$
$968$	−7.77755	+	7.77755i	−0.249980	+	0.249980i
$969$	−14.0700			−0.451994
$970$		0			0
$971$			0.0615153i			0.00197412i	1.00000		0.000987061i	$0.000314191\pi$
$971$			0.0615153i			0.00197412i	−1.00000		0.000987061i	$0.999686\pi$
$972$	−0.707107	+	0.707107i	−0.0226805	+	0.0226805i
$973$	−24.4896	−	36.4780i	−0.785101	−	1.16943i
$974$		−	30.7059i		−	0.983881i
$975$		0			0
$976$		−	10.7273i		−	0.343373i
$977$	−0.822738	−	0.822738i	−0.0263217	−	0.0263217i	0.693823	−	0.720145i	$-0.255925\pi$
$977$	−0.822738	−	0.822738i	−0.0263217	−	0.0263217i	−0.720145	+	0.693823i	$0.755925\pi$
$978$	−2.70742	−	2.70742i	−0.0865736	−	0.0865736i
$979$	0.129854			0.00415015
$980$		0			0
$981$	−14.8984			−0.475670
$982$	−10.5352	−	10.5352i	−0.336192	−	0.336192i
$983$	−19.9374	−	19.9374i	−0.635903	−	0.635903i	0.313639	−	0.949542i	$-0.398452\pi$
$983$	−19.9374	−	19.9374i	−0.635903	−	0.635903i	−0.949542	+	0.313639i	$0.898452\pi$
$984$		−	0.514280i		−	0.0163946i
$985$		0			0
$986$		−	23.6365i		−	0.752740i
$987$	−16.2213	−	24.1620i	−0.516328	−	0.769086i
$988$	3.38459	−	3.38459i	0.107678	−	0.107678i
$989$			5.63356i			0.179137i
$990$		0			0
$991$	24.6283			0.782344			0.391172	−	0.920318i	$-0.372070\pi$
$991$	24.6283			0.782344			0.391172	+	0.920318i	$0.372070\pi$
$992$	−4.52072	+	4.52072i	−0.143533	+	0.143533i
$993$	−3.28347	−	3.28347i	−0.104198	−	0.104198i
$994$	−3.39371	+	17.2589i	−0.107642	+	0.547420i
$995$		0			0
$996$	0.213022			0.00674985
$997$	−31.1165	+	31.1165i	−0.985471	+	0.985471i	−0.999896	−	0.0144253i	$-0.995408\pi$
$997$	−31.1165	+	31.1165i	−0.985471	+	0.985471i	0.0144253	+	0.999896i	$0.495408\pi$
$998$	−23.1880	+	23.1880i	−0.734005	+	0.734005i
$999$	5.26358			0.166532

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1050.2.m.b.307.1		8
5.2	odd	4		210.2.m.b.13.3	yes	8
5.3	odd	4		1050.2.m.a.643.1		8
5.4	even	2		210.2.m.a.97.4	yes	8
7.6	odd	2		1050.2.m.a.307.1		8
15.2	even	4		630.2.p.c.433.2		8
15.14	odd	2		630.2.p.b.307.1		8
20.7	even	4		1680.2.cz.a.433.3		8
20.19	odd	2		1680.2.cz.b.97.2		8
35.13	even	4	inner	1050.2.m.b.643.1		8
35.27	even	4		210.2.m.a.13.4	✓	8
35.34	odd	2		210.2.m.b.97.3	yes	8
105.62	odd	4		630.2.p.b.433.1		8
105.104	even	2		630.2.p.c.307.2		8
140.27	odd	4		1680.2.cz.b.433.2		8
140.139	even	2		1680.2.cz.a.97.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.2.m.a.13.4	✓	8	35.27	even	4
210.2.m.a.97.4	yes	8	5.4	even	2
210.2.m.b.13.3	yes	8	5.2	odd	4
210.2.m.b.97.3	yes	8	35.34	odd	2
630.2.p.b.307.1		8	15.14	odd	2
630.2.p.b.433.1		8	105.62	odd	4
630.2.p.c.307.2		8	105.104	even	2
630.2.p.c.433.2		8	15.2	even	4
1050.2.m.a.307.1		8	7.6	odd	2
1050.2.m.a.643.1		8	5.3	odd	4
1050.2.m.b.307.1		8	1.1	even	1	trivial
1050.2.m.b.643.1		8	35.13	even	4	inner
1680.2.cz.a.97.3		8	140.139	even	2
1680.2.cz.a.433.3		8	20.7	even	4
1680.2.cz.b.97.2		8	20.19	odd	2
1680.2.cz.b.433.2		8	140.27	odd	4

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:	\( N \)	\(=\)	\( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1050.m (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 - 0.707107i) q^{2} +(-0.707107 - 0.707107i) q^{3} +1.00000i q^{4} +1.00000i q^{6} +(-1.47472 - 2.19663i) q^{7} +(0.707107 - 0.707107i) q^{8} +1.00000i q^{9} +O(q^{10})\)	\(q+(-0.707107 - 0.707107i) q^{2} +(-0.707107 - 0.707107i) q^{3} +1.00000i q^{4} +1.00000i q^{6} +(-1.47472 - 2.19663i) q^{7} +(0.707107 - 0.707107i) q^{8} +1.00000i q^{9} +0.0296189 q^{11} +(0.707107 - 0.707107i) q^{12} +(0.585786 + 0.585786i) q^{13} +(-0.510472 + 2.59604i) q^{14} -1.00000 q^{16} +(-1.72192 + 1.72192i) q^{17} +(0.707107 - 0.707107i) q^{18} -5.77786 q^{19} +(-0.510472 + 2.59604i) q^{21} +(-0.0209438 - 0.0209438i) q^{22} +(0.393270 - 0.393270i) q^{23} -1.00000 q^{24} -0.828427i q^{26} +(0.707107 - 0.707107i) q^{27} +(2.19663 - 1.47472i) q^{28} -9.70636i q^{29} +6.39327i q^{31} +(0.707107 + 0.707107i) q^{32} +(-0.0209438 - 0.0209438i) q^{33} +2.43516 q^{34} -1.00000 q^{36} +(3.72192 + 3.72192i) q^{37} +(4.08557 + 4.08557i) q^{38} -0.828427i q^{39} +0.514280i q^{41} +(2.19663 - 1.47472i) q^{42} +(-7.16246 + 7.16246i) q^{43} +0.0296189i q^{44} -0.556167 q^{46} +(-7.77786 + 7.77786i) q^{47} +(0.707107 + 0.707107i) q^{48} +(-2.65041 + 6.47884i) q^{49} +2.43516 q^{51} +(-0.585786 + 0.585786i) q^{52} +(5.77786 - 5.77786i) q^{53} -1.00000 q^{54} +(-2.59604 - 0.510472i) q^{56} +(4.08557 + 4.08557i) q^{57} +(-6.86343 + 6.86343i) q^{58} -12.8070 q^{59} +10.7273i q^{61} +(4.52072 - 4.52072i) q^{62} +(2.19663 - 1.47472i) q^{63} -1.00000i q^{64} +0.0296189i q^{66} +(-2.39327 - 2.39327i) q^{67} +(-1.72192 - 1.72192i) q^{68} -0.556167 q^{69} +6.64818 q^{71} +(0.707107 + 0.707107i) q^{72} +(5.12745 + 5.12745i) q^{73} -5.26358i q^{74} -5.77786i q^{76} +(-0.0436796 - 0.0650620i) q^{77} +(-0.585786 + 0.585786i) q^{78} +9.86988i q^{79} -1.00000 q^{81} +(0.363651 - 0.363651i) q^{82} +(0.150629 + 0.150629i) q^{83} +(-2.59604 - 0.510472i) q^{84} +10.1292 q^{86} +(-6.86343 + 6.86343i) q^{87} +(0.0209438 - 0.0209438i) q^{88} +4.38416 q^{89} +(0.422889 - 2.15063i) q^{91} +(0.393270 + 0.393270i) q^{92} +(4.52072 - 4.52072i) q^{93} +10.9996 q^{94} -1.00000i q^{96} +(-2.47016 + 2.47016i) q^{97} +(6.45535 - 2.70711i) q^{98} +0.0296189i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{7}+O(q^{10}) \) 8 * q - 4 * q^7	\( 8 q - 4 q^{7} + 8 q^{11} + 16 q^{13} - 8 q^{14} - 8 q^{16} - 12 q^{17} - 8 q^{19} - 8 q^{21} - 8 q^{22} - 16 q^{23} - 8 q^{24} + 8 q^{28} - 8 q^{33} + 16 q^{34} - 8 q^{36} + 28 q^{37} + 4 q^{38} + 8 q^{42} - 8 q^{46} - 24 q^{47} + 4 q^{49} + 16 q^{51} - 16 q^{52} + 8 q^{53} - 8 q^{54} + 4 q^{56} + 4 q^{57} + 12 q^{58} + 8 q^{59} + 4 q^{62} + 8 q^{63} - 12 q^{68} - 8 q^{69} + 8 q^{71} + 28 q^{73} + 44 q^{77} - 16 q^{78} - 8 q^{81} - 24 q^{82} + 16 q^{83} + 4 q^{84} + 8 q^{86} + 12 q^{87} + 8 q^{88} - 64 q^{89} - 8 q^{91} - 16 q^{92} + 4 q^{93} + 8 q^{94} + 28 q^{97}+O(q^{100}) \) 8 * q - 4 * q^7 + 8 * q^11 + 16 * q^13 - 8 * q^14 - 8 * q^16 - 12 * q^17 - 8 * q^19 - 8 * q^21 - 8 * q^22 - 16 * q^23 - 8 * q^24 + 8 * q^28 - 8 * q^33 + 16 * q^34 - 8 * q^36 + 28 * q^37 + 4 * q^38 + 8 * q^42 - 8 * q^46 - 24 * q^47 + 4 * q^49 + 16 * q^51 - 16 * q^52 + 8 * q^53 - 8 * q^54 + 4 * q^56 + 4 * q^57 + 12 * q^58 + 8 * q^59 + 4 * q^62 + 8 * q^63 - 12 * q^68 - 8 * q^69 + 8 * q^71 + 28 * q^73 + 44 * q^77 - 16 * q^78 - 8 * q^81 - 24 * q^82 + 16 * q^83 + 4 * q^84 + 8 * q^86 + 12 * q^87 + 8 * q^88 - 64 * q^89 - 8 * q^91 - 16 * q^92 + 4 * q^93 + 8 * q^94 + 28 * q^97

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