LMFDB - Embedded newform 1734.2.f.m.1483.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1734,2,Mod(829,1734)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1734, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("1734.829");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1734 = 2 \cdot 3 \cdot 17^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1734.f (of order $4$, degree $2$, not 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:	$13.8460597105$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(i)$
Coefficient field:	$\Q(\zeta_{16})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 1 $ x^8 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 102)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			1483.3
Root			$-0.382683 - 0.923880i$ of defining polynomial
Character	$\chi$	$=$	1734.1483
Dual form			1734.2.f.m.829.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} +(0.707107 - 0.707107i) q^{3} -1.00000 q^{4} +(-0.306563 + 0.306563i) q^{5} +(0.707107 + 0.707107i) q^{6} +(-2.41421 - 2.41421i) q^{7} -1.00000i q^{8} -1.00000i q^{9} +O(q^{10})$	\(q+1.00000i q^{2} +(0.707107 - 0.707107i) q^{3} -1.00000 q^{4} +(-0.306563 + 0.306563i) q^{5} +(0.707107 + 0.707107i) q^{6} +(-2.41421 - 2.41421i) q^{7} -1.00000i q^{8} -1.00000i q^{9} +(-0.306563 - 0.306563i) q^{10} +(-1.19891 - 1.19891i) q^{11} +(-0.707107 + 0.707107i) q^{12} +0.331821 q^{13} +(2.41421 - 2.41421i) q^{14} +0.433546i q^{15} +1.00000 q^{16} +1.00000 q^{18} +2.14386i q^{19} +(0.306563 - 0.306563i) q^{20} -3.41421 q^{21} +(1.19891 - 1.19891i) q^{22} +(1.33182 + 1.33182i) q^{23} +(-0.707107 - 0.707107i) q^{24} +4.81204i q^{25} +0.331821i q^{26} +(-0.707107 - 0.707107i) q^{27} +(2.41421 + 2.41421i) q^{28} +(-6.03780 + 6.03780i) q^{29} -0.433546 q^{30} +(1.82843 - 1.82843i) q^{31} +1.00000i q^{32} -1.69552 q^{33} +1.48022 q^{35} +1.00000i q^{36} +(-7.50548 + 7.50548i) q^{37} -2.14386 q^{38} +(0.234633 - 0.234633i) q^{39} +(0.306563 + 0.306563i) q^{40} +(-8.56854 - 8.56854i) q^{41} -3.41421i q^{42} +10.0933i q^{43} +(1.19891 + 1.19891i) q^{44} +(0.306563 + 0.306563i) q^{45} +(-1.33182 + 1.33182i) q^{46} -2.38009 q^{47} +(0.707107 - 0.707107i) q^{48} +4.65685i q^{49} -4.81204 q^{50} -0.331821 q^{52} -3.13066i q^{53} +(0.707107 - 0.707107i) q^{54} +0.735084 q^{55} +(-2.41421 + 2.41421i) q^{56} +(1.51594 + 1.51594i) q^{57} +(-6.03780 - 6.03780i) q^{58} +7.67459i q^{59} -0.433546i q^{60} +(-5.68506 - 5.68506i) q^{61} +(1.82843 + 1.82843i) q^{62} +(-2.41421 + 2.41421i) q^{63} -1.00000 q^{64} +(-0.101724 + 0.101724i) q^{65} -1.69552i q^{66} -15.7711 q^{67} +1.88348 q^{69} +1.48022i q^{70} +(0.160248 - 0.160248i) q^{71} -1.00000 q^{72} +(8.58333 - 8.58333i) q^{73} +(-7.50548 - 7.50548i) q^{74} +(3.40262 + 3.40262i) q^{75} -2.14386i q^{76} +5.78886i q^{77} +(0.234633 + 0.234633i) q^{78} +(8.86672 + 8.86672i) q^{79} +(-0.306563 + 0.306563i) q^{80} -1.00000 q^{81} +(8.56854 - 8.56854i) q^{82} -1.04373i q^{83} +3.41421 q^{84} -10.0933 q^{86} +8.53874i q^{87} +(-1.19891 + 1.19891i) q^{88} -13.8281 q^{89} +(-0.306563 + 0.306563i) q^{90} +(-0.801088 - 0.801088i) q^{91} +(-1.33182 - 1.33182i) q^{92} -2.58579i q^{93} -2.38009i q^{94} +(-0.657228 - 0.657228i) q^{95} +(0.707107 + 0.707107i) q^{96} +(2.65546 - 2.65546i) q^{97} -4.65685 q^{98} +(-1.19891 + 1.19891i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{4} + 8 q^{5} - 8 q^{7}+O(q^{10}) $ 8 * q - 8 * q^4 + 8 * q^5 - 8 * q^7	$ 8 q - 8 q^{4} + 8 q^{5} - 8 q^{7} + 8 q^{10} + 8 q^{14} + 8 q^{16} + 8 q^{18} - 8 q^{20} - 16 q^{21} + 8 q^{23} + 8 q^{28} - 24 q^{29} - 8 q^{31} + 16 q^{33} - 16 q^{35} - 40 q^{37} + 16 q^{38} + 8 q^{39} - 8 q^{40} - 32 q^{41} - 8 q^{45} - 8 q^{46} - 8 q^{50} + 32 q^{55} - 8 q^{56} - 24 q^{58} - 8 q^{61} - 8 q^{62} - 8 q^{63} - 8 q^{64} - 48 q^{67} + 16 q^{69} - 24 q^{71} - 8 q^{72} + 32 q^{73} - 40 q^{74} - 8 q^{75} + 8 q^{78} - 24 q^{79} + 8 q^{80} - 8 q^{81} + 32 q^{82} + 16 q^{84} - 32 q^{86} + 8 q^{90} - 16 q^{91} - 8 q^{92} - 48 q^{95} - 16 q^{97} + 8 q^{98}+O(q^{100}) $ 8 * q - 8 * q^4 + 8 * q^5 - 8 * q^7 + 8 * q^10 + 8 * q^14 + 8 * q^16 + 8 * q^18 - 8 * q^20 - 16 * q^21 + 8 * q^23 + 8 * q^28 - 24 * q^29 - 8 * q^31 + 16 * q^33 - 16 * q^35 - 40 * q^37 + 16 * q^38 + 8 * q^39 - 8 * q^40 - 32 * q^41 - 8 * q^45 - 8 * q^46 - 8 * q^50 + 32 * q^55 - 8 * q^56 - 24 * q^58 - 8 * q^61 - 8 * q^62 - 8 * q^63 - 8 * q^64 - 48 * q^67 + 16 * q^69 - 24 * q^71 - 8 * q^72 + 32 * q^73 - 40 * q^74 - 8 * q^75 + 8 * q^78 - 24 * q^79 + 8 * q^80 - 8 * q^81 + 32 * q^82 + 16 * q^84 - 32 * q^86 + 8 * q^90 - 16 * q^91 - 8 * q^92 - 48 * q^95 - 16 * q^97 + 8 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1734\mathbb{Z}\right)^\times$.

$n$	$1157$	$1159$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$			1.00000i			0.707107i
$2$			1.00000i			0.707107i
$3$	0.707107	−	0.707107i	0.408248	−	0.408248i
$3$	0.707107	−	0.707107i	0.408248	−	0.408248i
$4$	−1.00000			−0.500000
$5$	−0.306563	+	0.306563i	−0.137099	+	0.137099i	−0.772326	−	0.635227i	$-0.780907\pi$
$5$	−0.306563	+	0.306563i	−0.137099	+	0.137099i	0.635227	+	0.772326i	$0.280907\pi$
$6$	0.707107	+	0.707107i	0.288675	+	0.288675i
$7$	−2.41421	−	2.41421i	−0.912487	−	0.912487i	0.0839804	−	0.996467i	$-0.473237\pi$
$7$	−2.41421	−	2.41421i	−0.912487	−	0.912487i	−0.996467	+	0.0839804i	$0.973237\pi$
$8$		−	1.00000i		−	0.353553i
$9$		−	1.00000i		−	0.333333i
$10$	−0.306563	−	0.306563i	−0.0969437	−	0.0969437i
$11$	−1.19891	−	1.19891i	−0.361486	−	0.361486i	0.502874	−	0.864360i	$-0.332276\pi$
$11$	−1.19891	−	1.19891i	−0.361486	−	0.361486i	−0.864360	+	0.502874i	$0.832276\pi$
$12$	−0.707107	+	0.707107i	−0.204124	+	0.204124i
$13$	0.331821			0.0920307			0.0460153	−	0.998941i	$-0.485348\pi$
$13$	0.331821			0.0920307			0.0460153	+	0.998941i	$0.485348\pi$
$14$	2.41421	−	2.41421i	0.645226	−	0.645226i
$15$			0.433546i			0.111941i
$16$	1.00000			0.250000
$17$		0			0
$17$		0			0
$18$	1.00000			0.235702
$19$			2.14386i			0.491835i	0.969291	+	0.245918i	$0.0790893\pi$
$19$			2.14386i			0.491835i	−0.969291	+	0.245918i	$0.920911\pi$
$20$	0.306563	−	0.306563i	0.0685496	−	0.0685496i
$21$	−3.41421			−0.745042
$22$	1.19891	−	1.19891i	0.255609	−	0.255609i
$23$	1.33182	+	1.33182i	0.277704	+	0.277704i	0.832192	−	0.554488i	$-0.187086\pi$
$23$	1.33182	+	1.33182i	0.277704	+	0.277704i	−0.554488	+	0.832192i	$0.687086\pi$
$24$	−0.707107	−	0.707107i	−0.144338	−	0.144338i
$25$			4.81204i			0.962408i
$26$			0.331821i			0.0650755i
$27$	−0.707107	−	0.707107i	−0.136083	−	0.136083i
$28$	2.41421	+	2.41421i	0.456243	+	0.456243i
$29$	−6.03780	+	6.03780i	−1.12119	+	1.12119i	−0.129629	+	0.991563i	$0.541379\pi$
$29$	−6.03780	+	6.03780i	−1.12119	+	1.12119i	−0.991563	+	0.129629i	$0.958621\pi$
$30$	−0.433546			−0.0791542
$31$	1.82843	−	1.82843i	0.328395	−	0.328395i	−0.523581	−	0.851976i	$-0.675404\pi$
$31$	1.82843	−	1.82843i	0.328395	−	0.328395i	0.851976	+	0.523581i	$0.175404\pi$
$32$			1.00000i			0.176777i
$33$	−1.69552			−0.295152
$34$		0			0
$35$	1.48022			0.250202
$36$			1.00000i			0.166667i
$37$	−7.50548	+	7.50548i	−1.23389	+	1.23389i	−0.271436	+	0.962456i	$0.587499\pi$
$37$	−7.50548	+	7.50548i	−1.23389	+	1.23389i	−0.962456	+	0.271436i	$0.912501\pi$
$38$	−2.14386			−0.347780
$39$	0.234633	−	0.234633i	0.0375714	−	0.0375714i
$40$	0.306563	+	0.306563i	0.0484719	+	0.0484719i
$41$	−8.56854	−	8.56854i	−1.33818	−	1.33818i	−0.897822	−	0.440358i	$-0.854851\pi$
$41$	−8.56854	−	8.56854i	−1.33818	−	1.33818i	−0.440358	−	0.897822i	$-0.645149\pi$
$42$		−	3.41421i		−	0.526825i
$43$			10.0933i			1.53922i	0.638514	+	0.769610i	$0.279549\pi$
$43$			10.0933i			1.53922i	−0.638514	+	0.769610i	$0.720451\pi$
$44$	1.19891	+	1.19891i	0.180743	+	0.180743i
$45$	0.306563	+	0.306563i	0.0456997	+	0.0456997i
$46$	−1.33182	+	1.33182i	−0.196366	+	0.196366i
$47$	−2.38009			−0.347171			−0.173586	−	0.984819i	$-0.555535\pi$
$47$	−2.38009			−0.347171			−0.173586	+	0.984819i	$0.555535\pi$
$48$	0.707107	−	0.707107i	0.102062	−	0.102062i
$49$			4.65685i			0.665265i
$50$	−4.81204			−0.680525
$51$		0			0
$52$	−0.331821			−0.0460153
$53$		−	3.13066i		−	0.430029i	−0.976611	−	0.215014i	$-0.931020\pi$
$53$		−	3.13066i		−	0.430029i	0.976611	−	0.215014i	$-0.0689798\pi$
$54$	0.707107	−	0.707107i	0.0962250	−	0.0962250i
$55$	0.735084			0.0991187
$56$	−2.41421	+	2.41421i	−0.322613	+	0.322613i
$57$	1.51594	+	1.51594i	0.200791	+	0.200791i
$58$	−6.03780	−	6.03780i	−0.792802	−	0.792802i
$59$			7.67459i			0.999147i	0.866272	+	0.499573i	$0.166510\pi$
$59$			7.67459i			0.999147i	−0.866272	+	0.499573i	$0.833490\pi$
$60$		−	0.433546i		−	0.0559705i
$61$	−5.68506	−	5.68506i	−0.727897	−	0.727897i	0.242304	−	0.970200i	$-0.422097\pi$
$61$	−5.68506	−	5.68506i	−0.727897	−	0.727897i	−0.970200	+	0.242304i	$0.922097\pi$
$62$	1.82843	+	1.82843i	0.232210	+	0.232210i
$63$	−2.41421	+	2.41421i	−0.304162	+	0.304162i
$64$	−1.00000			−0.125000
$65$	−0.101724	+	0.101724i	−0.0126173	+	0.0126173i
$66$		−	1.69552i		−	0.208704i
$67$	−15.7711			−1.92675			−0.963375	−	0.268159i	$-0.913585\pi$
$67$	−15.7711			−1.92675			−0.963375	+	0.268159i	$0.913585\pi$
$68$		0			0
$69$	1.88348			0.226744
$70$			1.48022i			0.176920i
$71$	0.160248	−	0.160248i	0.0190180	−	0.0190180i	−0.697534	−	0.716552i	$-0.745719\pi$
$71$	0.160248	−	0.160248i	0.0190180	−	0.0190180i	0.716552	+	0.697534i	$0.245719\pi$
$72$	−1.00000			−0.117851
$73$	8.58333	−	8.58333i	1.00460	−	1.00460i	0.00461362	−	0.999989i	$-0.498531\pi$
$73$	8.58333	−	8.58333i	1.00460	−	1.00460i	0.999989	−	0.00461362i	$-0.00146857\pi$
$74$	−7.50548	−	7.50548i	−0.872494	−	0.872494i
$75$	3.40262	+	3.40262i	0.392901	+	0.392901i
$76$		−	2.14386i		−	0.245918i
$77$			5.78886i			0.659702i
$78$	0.234633	+	0.234633i	0.0265670	+	0.0265670i
$79$	8.86672	+	8.86672i	0.997584	+	0.997584i	0.999997	−	0.00241345i	$-0.000768227\pi$
$79$	8.86672	+	8.86672i	0.997584	+	0.997584i	−0.00241345	+	0.999997i	$0.500768\pi$
$80$	−0.306563	+	0.306563i	−0.0342748	+	0.0342748i
$81$	−1.00000			−0.111111
$82$	8.56854	−	8.56854i	0.946236	−	0.946236i
$83$		−	1.04373i		−	0.114564i	−0.998358	−	0.0572820i	$-0.981757\pi$
$83$		−	1.04373i		−	0.114564i	0.998358	−	0.0572820i	$-0.0182434\pi$
$84$	3.41421			0.372521
$85$		0			0
$86$	−10.0933			−1.08839
$87$			8.53874i			0.915449i
$88$	−1.19891	+	1.19891i	−0.127804	+	0.127804i
$89$	−13.8281			−1.46577			−0.732885	−	0.680352i	$-0.761827\pi$
$89$	−13.8281			−1.46577			−0.732885	+	0.680352i	$0.761827\pi$
$90$	−0.306563	+	0.306563i	−0.0323146	+	0.0323146i
$91$	−0.801088	−	0.801088i	−0.0839768	−	0.0839768i
$92$	−1.33182	−	1.33182i	−0.138852	−	0.138852i
$93$		−	2.58579i		−	0.268134i
$94$		−	2.38009i		−	0.245487i
$95$	−0.657228	−	0.657228i	−0.0674302	−	0.0674302i
$96$	0.707107	+	0.707107i	0.0721688	+	0.0721688i
$97$	2.65546	−	2.65546i	0.269621	−	0.269621i	−0.559326	−	0.828948i	$-0.688940\pi$
$97$	2.65546	−	2.65546i	0.269621	−	0.269621i	0.828948	+	0.559326i	$0.188940\pi$
$98$	−4.65685			−0.470413
$99$	−1.19891	+	1.19891i	−0.120495	+	0.120495i
$100$		−	4.81204i		−	0.481204i
$101$	0.636303			0.0633145			0.0316573	−	0.999499i	$-0.489921\pi$
$101$	0.636303			0.0633145			0.0316573	+	0.999499i	$0.489921\pi$
$102$		0			0
$103$	8.59955			0.847339			0.423669	−	0.905817i	$-0.360742\pi$
$103$	8.59955			0.847339			0.423669	+	0.905817i	$0.360742\pi$
$104$		−	0.331821i		−	0.0325378i
$105$	1.04667	−	1.04667i	0.102145	−	0.102145i
$106$	3.13066			0.304076
$107$	−1.53073	+	1.53073i	−0.147982	+	0.147982i	−0.777216	−	0.629234i	$-0.783369\pi$
$107$	−1.53073	+	1.53073i	−0.147982	+	0.147982i	0.629234	+	0.777216i	$0.283369\pi$
$108$	0.707107	+	0.707107i	0.0680414	+	0.0680414i
$109$	5.59588	+	5.59588i	0.535988	+	0.535988i	0.922348	−	0.386360i	$-0.126268\pi$
$109$	5.59588	+	5.59588i	0.535988	+	0.535988i	−0.386360	+	0.922348i	$0.626268\pi$
$110$			0.735084i			0.0700875i
$111$			10.6143i			1.00747i
$112$	−2.41421	−	2.41421i	−0.228122	−	0.228122i
$113$	−6.49709	−	6.49709i	−0.611195	−	0.611195i	0.332062	−	0.943257i	$-0.392256\pi$
$113$	−6.49709	−	6.49709i	−0.611195	−	0.611195i	−0.943257	+	0.332062i	$0.892256\pi$
$114$	−1.51594	+	1.51594i	−0.141981	+	0.141981i
$115$	−0.816574			−0.0761459
$116$	6.03780	−	6.03780i	0.560596	−	0.560596i
$117$		−	0.331821i		−	0.0306769i
$118$	−7.67459			−0.706504
$119$		0			0
$120$	0.433546			0.0395771
$121$		−	8.12522i		−	0.738656i
$122$	5.68506	−	5.68506i	0.514701	−	0.514701i
$123$	−12.1177			−1.09262
$124$	−1.82843	+	1.82843i	−0.164198	+	0.164198i
$125$	−3.00801	−	3.00801i	−0.269044	−	0.269044i
$126$	−2.41421	−	2.41421i	−0.215075	−	0.215075i
$127$			12.0843i			1.07231i	0.844121	+	0.536153i	$0.180123\pi$
$127$			12.0843i			1.07231i	−0.844121	+	0.536153i	$0.819877\pi$
$128$		−	1.00000i		−	0.0883883i
$129$	7.13707	+	7.13707i	0.628384	+	0.628384i
$130$	−0.101724	−	0.101724i	−0.00892180	−	0.00892180i
$131$	−0.634051	+	0.634051i	−0.0553973	+	0.0553973i	−0.734263	−	0.678865i	$-0.762472\pi$
$131$	−0.634051	+	0.634051i	−0.0553973	+	0.0553973i	0.678865	+	0.734263i	$0.262472\pi$
$132$	1.69552			0.147576
$133$	5.17574	−	5.17574i	0.448793	−	0.448793i
$134$		−	15.7711i		−	1.36242i
$135$	0.433546			0.0373137
$136$		0			0
$137$	12.6109			1.07742			0.538710	−	0.842491i	$-0.318912\pi$
$137$	12.6109			1.07742			0.538710	+	0.842491i	$0.318912\pi$
$138$			1.88348i			0.160332i
$139$	12.0524	−	12.0524i	1.02227	−	1.02227i	0.0225272	−	0.999746i	$-0.492829\pi$
$139$	12.0524	−	12.0524i	1.02227	−	1.02227i	0.999746	−	0.0225272i	$-0.00717125\pi$
$140$	−1.48022			−0.125101
$141$	−1.68297	+	1.68297i	−0.141732	+	0.141732i
$142$	0.160248	+	0.160248i	0.0134478	+	0.0134478i
$143$	−0.397825	−	0.397825i	−0.0332678	−	0.0332678i
$144$		−	1.00000i		−	0.0833333i
$145$		−	3.70193i		−	0.307429i
$146$	8.58333	+	8.58333i	0.710362	+	0.710362i
$147$	3.29289	+	3.29289i	0.271593	+	0.271593i
$148$	7.50548	−	7.50548i	0.616946	−	0.616946i
$149$	−17.5004			−1.43369			−0.716844	−	0.697234i	$-0.754414\pi$
$149$	−17.5004			−1.43369			−0.716844	+	0.697234i	$0.754414\pi$
$150$	−3.40262	+	3.40262i	−0.277823	+	0.277823i
$151$			9.64009i			0.784500i	0.919859	+	0.392250i	$0.128303\pi$
$151$			9.64009i			0.784500i	−0.919859	+	0.392250i	$0.871697\pi$
$152$	2.14386			0.173890
$153$		0			0
$154$	−5.78886			−0.466480
$155$			1.12106i			0.0900454i
$156$	−0.234633	+	0.234633i	−0.0187857	+	0.0187857i
$157$	4.78976			0.382265			0.191132	−	0.981564i	$-0.438784\pi$
$157$	4.78976			0.382265			0.191132	+	0.981564i	$0.438784\pi$
$158$	−8.86672	+	8.86672i	−0.705398	+	0.705398i
$159$	−2.21371	−	2.21371i	−0.175558	−	0.175558i
$160$	−0.306563	−	0.306563i	−0.0242359	−	0.0242359i
$161$		−	6.43060i		−	0.506802i
$162$		−	1.00000i		−	0.0785674i
$163$	−12.5899	−	12.5899i	−0.986121	−	0.986121i	0.0137841	−	0.999905i	$-0.495612\pi$
$163$	−12.5899	−	12.5899i	−0.986121	−	0.986121i	−0.999905	+	0.0137841i	$0.995612\pi$
$164$	8.56854	+	8.56854i	0.669090	+	0.669090i
$165$	0.519783	−	0.519783i	0.0404651	−	0.0404651i
$166$	1.04373			0.0810090
$167$	−12.4416	+	12.4416i	−0.962756	+	0.962756i	−0.999331	−	0.0365746i	$-0.988355\pi$
$167$	−12.4416	+	12.4416i	−0.962756	+	0.962756i	0.0365746	+	0.999331i	$0.488355\pi$
$168$			3.41421i			0.263412i
$169$	−12.8899			−0.991530
$170$		0			0
$171$	2.14386			0.163945
$172$		−	10.0933i		−	0.769610i
$173$	−13.6799	+	13.6799i	−1.04006	+	1.04006i	−0.0408971	+	0.999163i	$0.513022\pi$
$173$	−13.6799	+	13.6799i	−1.04006	+	1.04006i	−0.999163	+	0.0408971i	$0.986978\pi$
$174$	−8.53874			−0.647320
$175$	11.6173	−	11.6173i	0.878184	−	0.878184i
$176$	−1.19891	−	1.19891i	−0.0903714	−	0.0903714i
$177$	5.42676	+	5.42676i	0.407900	+	0.407900i
$178$		−	13.8281i		−	1.03646i
$179$			9.11933i			0.681611i	0.940134	+	0.340805i	$0.110700\pi$
$179$			9.11933i			0.681611i	−0.940134	+	0.340805i	$0.889300\pi$
$180$	−0.306563	−	0.306563i	−0.0228499	−	0.0228499i
$181$	−0.549204	−	0.549204i	−0.0408220	−	0.0408220i	0.686401	−	0.727223i	$-0.259189\pi$
$181$	−0.549204	−	0.549204i	−0.0408220	−	0.0408220i	−0.727223	+	0.686401i	$0.759189\pi$
$182$	0.801088	−	0.801088i	0.0593806	−	0.0593806i
$183$	−8.03988			−0.594325
$184$	1.33182	−	1.33182i	0.0981832	−	0.0981832i
$185$		−	4.60180i		−	0.338331i
$186$	2.58579			0.189599
$187$		0			0
$188$	2.38009			0.173586
$189$			3.41421i			0.248347i
$190$	0.657228	−	0.657228i	0.0476803	−	0.0476803i
$191$	13.4248			0.971384			0.485692	−	0.874130i	$-0.338568\pi$
$191$	13.4248			0.971384			0.485692	+	0.874130i	$0.338568\pi$
$192$	−0.707107	+	0.707107i	−0.0510310	+	0.0510310i
$193$	3.59850	+	3.59850i	0.259026	+	0.259026i	0.824658	−	0.565632i	$-0.191368\pi$
$193$	3.59850	+	3.59850i	0.259026	+	0.259026i	−0.565632	+	0.824658i	$0.691368\pi$
$194$	2.65546	+	2.65546i	0.190651	+	0.190651i
$195$			0.143860i			0.0103020i
$196$		−	4.65685i		−	0.332632i
$197$	2.93767	+	2.93767i	0.209300	+	0.209300i	0.803970	−	0.594670i	$-0.202717\pi$
$197$	2.93767	+	2.93767i	0.209300	+	0.209300i	−0.594670	+	0.803970i	$0.702717\pi$
$198$	−1.19891	−	1.19891i	−0.0852030	−	0.0852030i
$199$	7.57221	−	7.57221i	0.536780	−	0.536780i	−0.385802	−	0.922582i	$-0.626075\pi$
$199$	7.57221	−	7.57221i	0.536780	−	0.536780i	0.922582	+	0.385802i	$0.126075\pi$
$200$	4.81204			0.340262
$201$	−11.1519	+	11.1519i	−0.786592	+	0.786592i
$202$			0.636303i			0.0447701i
$203$	29.1531			2.04615
$204$		0			0
$205$	5.25359			0.366927
$206$			8.59955i			0.599159i
$207$	1.33182	−	1.33182i	0.0925680	−	0.0925680i
$208$	0.331821			0.0230077
$209$	2.57030	−	2.57030i	0.177791	−	0.177791i
$210$	1.04667	+	1.04667i	0.0722272	+	0.0722272i
$211$	3.33861	+	3.33861i	0.229839	+	0.229839i	0.812626	−	0.582786i	$-0.198037\pi$
$211$	3.33861	+	3.33861i	0.229839	+	0.229839i	−0.582786	+	0.812626i	$0.698037\pi$
$212$			3.13066i			0.215014i
$213$		−	0.226626i		−	0.0155281i
$214$	−1.53073	−	1.53073i	−0.104639	−	0.104639i
$215$	−3.09425	−	3.09425i	−0.211026	−	0.211026i
$216$	−0.707107	+	0.707107i	−0.0481125	+	0.0481125i
$217$	−8.82843			−0.599313
$218$	−5.59588	+	5.59588i	−0.379000	+	0.379000i
$219$		−	12.1387i		−	0.820255i
$220$	−0.735084			−0.0495594
$221$		0			0
$222$	−10.6143			−0.712388
$223$		−	15.6359i		−	1.04706i	−0.852007	−	0.523530i	$-0.824615\pi$
$223$		−	15.6359i		−	1.04706i	0.852007	−	0.523530i	$-0.175385\pi$
$224$	2.41421	−	2.41421i	0.161306	−	0.161306i
$225$	4.81204			0.320803
$226$	6.49709	−	6.49709i	0.432180	−	0.432180i
$227$	−7.82164	−	7.82164i	−0.519140	−	0.519140i	0.398171	−	0.917311i	$-0.369645\pi$
$227$	−7.82164	−	7.82164i	−0.519140	−	0.519140i	−0.917311	+	0.398171i	$0.869645\pi$
$228$	−1.51594	−	1.51594i	−0.100395	−	0.100395i
$229$			15.3852i			1.01668i	0.861157	+	0.508340i	$0.169741\pi$
$229$			15.3852i			1.01668i	−0.861157	+	0.508340i	$0.830259\pi$
$230$		−	0.816574i		−	0.0538433i
$231$	4.09334	+	4.09334i	0.269322	+	0.269322i
$232$	6.03780	+	6.03780i	0.396401	+	0.396401i
$233$	−7.33806	+	7.33806i	−0.480733	+	0.480733i	−0.905366	−	0.424633i	$-0.860403\pi$
$233$	−7.33806	+	7.33806i	−0.480733	+	0.480733i	0.424633	+	0.905366i	$0.360403\pi$
$234$	0.331821			0.0216918
$235$	0.729646	−	0.729646i	0.0475969	−	0.0475969i
$236$		−	7.67459i		−	0.499573i
$237$	12.5394			0.814524
$238$		0			0
$239$	−24.7803			−1.60291			−0.801454	−	0.598057i	$-0.795940\pi$
$239$	−24.7803			−1.60291			−0.801454	+	0.598057i	$0.795940\pi$
$240$			0.433546i			0.0279852i
$241$	−3.04422	+	3.04422i	−0.196095	+	0.196095i	−0.798324	−	0.602229i	$-0.794280\pi$
$241$	−3.04422	+	3.04422i	−0.196095	+	0.196095i	0.602229	+	0.798324i	$0.294280\pi$
$242$	8.12522			0.522309
$243$	−0.707107	+	0.707107i	−0.0453609	+	0.0453609i
$244$	5.68506	+	5.68506i	0.363948	+	0.363948i
$245$	−1.42762	−	1.42762i	−0.0912072	−	0.0912072i
$246$		−	12.1177i		−	0.772599i
$247$			0.711378i			0.0452639i
$248$	−1.82843	−	1.82843i	−0.116105	−	0.116105i
$249$	−0.738027	−	0.738027i	−0.0467706	−	0.0467706i
$250$	3.00801	−	3.00801i	0.190243	−	0.190243i
$251$	19.0639			1.20330			0.601652	−	0.798759i	$-0.294510\pi$
$251$	19.0639			1.20330			0.601652	+	0.798759i	$0.294510\pi$
$252$	2.41421	−	2.41421i	0.152081	−	0.152081i
$253$		−	3.19347i		−	0.200772i
$254$	−12.0843			−0.758235
$255$		0			0
$256$	1.00000			0.0625000
$257$		−	26.7594i		−	1.66921i	−0.550851	−	0.834603i	$-0.685697\pi$
$257$		−	26.7594i		−	1.66921i	0.550851	−	0.834603i	$-0.314303\pi$
$258$	−7.13707	+	7.13707i	−0.444335	+	0.444335i
$259$	36.2396			2.25182
$260$	0.101724	−	0.101724i	0.00630866	−	0.00630866i
$261$	6.03780	+	6.03780i	0.373731	+	0.373731i
$262$	−0.634051	−	0.634051i	−0.0391718	−	0.0391718i
$263$		−	27.5122i		−	1.69648i	−0.529614	−	0.848239i	$-0.677663\pi$
$263$		−	27.5122i		−	1.69648i	0.529614	−	0.848239i	$-0.322337\pi$
$264$			1.69552i			0.104352i
$265$	0.959743	+	0.959743i	0.0589566	+	0.0589566i
$266$	5.17574	+	5.17574i	0.317345	+	0.317345i
$267$	−9.77791	+	9.77791i	−0.598398	+	0.598398i
$268$	15.7711			0.963375
$269$	−7.08153	+	7.08153i	−0.431769	+	0.431769i	−0.889230	−	0.457461i	$-0.848759\pi$
$269$	−7.08153	+	7.08153i	−0.431769	+	0.431769i	0.457461	+	0.889230i	$0.348759\pi$
$270$			0.433546i			0.0263847i
$271$	9.20949			0.559437			0.279718	−	0.960082i	$-0.409759\pi$
$271$	9.20949			0.559437			0.279718	+	0.960082i	$0.409759\pi$
$272$		0			0
$273$	−1.13291			−0.0685668
$274$			12.6109i			0.761851i
$275$	5.76921	−	5.76921i	0.347897	−	0.347897i
$276$	−1.88348			−0.113372
$277$	5.91515	−	5.91515i	0.355407	−	0.355407i	−0.506710	−	0.862117i	$-0.669138\pi$
$277$	5.91515	−	5.91515i	0.355407	−	0.355407i	0.862117	+	0.506710i	$0.169138\pi$
$278$	12.0524	+	12.0524i	0.722857	+	0.722857i
$279$	−1.82843	−	1.82843i	−0.109465	−	0.109465i
$280$		−	1.48022i		−	0.0884599i
$281$		−	10.9996i		−	0.656183i	−0.944646	−	0.328091i	$-0.893595\pi$
$281$		−	10.9996i		−	0.656183i	0.944646	−	0.328091i	$-0.106405\pi$
$282$	−1.68297	−	1.68297i	−0.100220	−	0.100220i
$283$	−14.9469	−	14.9469i	−0.888498	−	0.888498i	0.105880	−	0.994379i	$-0.466234\pi$
$283$	−14.9469	−	14.9469i	−0.888498	−	0.888498i	−0.994379	+	0.105880i	$0.966234\pi$
$284$	−0.160248	+	0.160248i	−0.00950900	+	0.00950900i
$285$	−0.929461			−0.0550565
$286$	0.397825	−	0.397825i	0.0235239	−	0.0235239i
$287$			41.3725i			2.44214i
$288$	1.00000			0.0589256
$289$		0			0
$290$	3.70193			0.217385
$291$		−	3.75539i		−	0.220145i
$292$	−8.58333	+	8.58333i	−0.502301	+	0.502301i
$293$	−25.1277			−1.46797			−0.733987	−	0.679164i	$-0.762343\pi$
$293$	−25.1277			−1.46797			−0.733987	+	0.679164i	$0.762343\pi$
$294$	−3.29289	+	3.29289i	−0.192045	+	0.192045i
$295$	−2.35275	−	2.35275i	−0.136982	−	0.136982i
$296$	7.50548	+	7.50548i	0.436247	+	0.436247i
$297$			1.69552i			0.0983839i
$298$		−	17.5004i		−	1.01377i
$299$	0.441927	+	0.441927i	0.0255573	+	0.0255573i
$300$	−3.40262	−	3.40262i	−0.196451	−	0.196451i
$301$	24.3675	−	24.3675i	1.40452	−	1.40452i
$302$	−9.64009			−0.554725
$303$	0.449934	−	0.449934i	0.0258481	−	0.0258481i
$304$			2.14386i			0.122959i
$305$	3.48566			0.199588
$306$		0			0
$307$	15.3433			0.875688			0.437844	−	0.899051i	$-0.355742\pi$
$307$	15.3433			0.875688			0.437844	+	0.899051i	$0.355742\pi$
$308$		−	5.78886i		−	0.329851i
$309$	6.08080	−	6.08080i	0.345925	−	0.345925i
$310$	−1.12106			−0.0636717
$311$	−15.3318	+	15.3318i	−0.869388	+	0.869388i	−0.992405	−	0.123017i	$-0.960743\pi$
$311$	−15.3318	+	15.3318i	−0.869388	+	0.869388i	0.123017	+	0.992405i	$0.460743\pi$
$312$	−0.234633	−	0.234633i	−0.0132835	−	0.0132835i
$313$	5.93154	+	5.93154i	0.335271	+	0.335271i	0.854584	−	0.519313i	$-0.173812\pi$
$313$	5.93154	+	5.93154i	0.335271	+	0.335271i	−0.519313	+	0.854584i	$0.673812\pi$
$314$			4.78976i			0.270302i
$315$		−	1.48022i		−	0.0834008i
$316$	−8.86672	−	8.86672i	−0.498792	−	0.498792i
$317$	−16.9566	−	16.9566i	−0.952379	−	0.952379i	0.0465374	−	0.998917i	$-0.485181\pi$
$317$	−16.9566	−	16.9566i	−0.952379	−	0.952379i	−0.998917	+	0.0465374i	$0.985181\pi$
$318$	2.21371	−	2.21371i	0.124139	−	0.124139i
$319$	14.4776			0.810589
$320$	0.306563	−	0.306563i	0.0171374	−	0.0171374i
$321$			2.16478i			0.120826i
$322$	6.43060			0.358363
$323$		0			0
$324$	1.00000			0.0555556
$325$			1.59674i			0.0885710i
$326$	12.5899	−	12.5899i	0.697293	−	0.697293i
$327$	7.91376			0.437632
$328$	−8.56854	+	8.56854i	−0.473118	+	0.473118i
$329$	5.74603	+	5.74603i	0.316789	+	0.316789i
$330$	0.519783	+	0.519783i	0.0286131	+	0.0286131i
$331$			4.07733i			0.224110i	0.993702	+	0.112055i	$0.0357433\pi$
$331$			4.07733i			0.224110i	−0.993702	+	0.112055i	$0.964257\pi$
$332$			1.04373i			0.0572820i
$333$	7.50548	+	7.50548i	0.411298	+	0.411298i
$334$	−12.4416	−	12.4416i	−0.680771	−	0.680771i
$335$	4.83484	−	4.83484i	0.264156	−	0.264156i
$336$	−3.41421			−0.186261
$337$	7.08288	−	7.08288i	0.385829	−	0.385829i	−0.487368	−	0.873197i	$-0.662043\pi$
$337$	7.08288	−	7.08288i	0.385829	−	0.385829i	0.873197	+	0.487368i	$0.162043\pi$
$338$		−	12.8899i		−	0.701118i
$339$	−9.18828			−0.499039
$340$		0			0
$341$	−4.38425			−0.237420
$342$			2.14386i			0.115927i
$343$	−5.65685	+	5.65685i	−0.305441	+	0.305441i
$344$	10.0933			0.544197
$345$	−0.577405	+	0.577405i	−0.0310864	+	0.0310864i
$346$	−13.6799	−	13.6799i	−0.735434	−	0.735434i
$347$	6.11236	+	6.11236i	0.328129	+	0.328129i	0.851875	−	0.523746i	$-0.175466\pi$
$347$	6.11236	+	6.11236i	0.328129	+	0.328129i	−0.523746	+	0.851875i	$0.675466\pi$
$348$		−	8.53874i		−	0.457725i
$349$		−	20.8126i		−	1.11407i	−0.830488	−	0.557036i	$-0.811938\pi$
$349$		−	20.8126i		−	1.11407i	0.830488	−	0.557036i	$-0.188062\pi$
$350$	11.6173	+	11.6173i	0.620970	+	0.620970i
$351$	−0.234633	−	0.234633i	−0.0125238	−	0.0125238i
$352$	1.19891	−	1.19891i	0.0639022	−	0.0639022i
$353$	20.1049			1.07007			0.535037	−	0.844829i	$-0.320298\pi$
$353$	20.1049			1.07007			0.535037	+	0.844829i	$0.320298\pi$
$354$	−5.42676	+	5.42676i	−0.288429	+	0.288429i
$355$			0.0982525i			0.00521470i
$356$	13.8281			0.732885
$357$		0			0
$358$	−9.11933			−0.481972
$359$			25.3001i			1.33529i	0.744480	+	0.667645i	$0.232698\pi$
$359$			25.3001i			1.33529i	−0.744480	+	0.667645i	$0.767302\pi$
$360$	0.306563	−	0.306563i	0.0161573	−	0.0161573i
$361$	14.4039			0.758098
$362$	0.549204	−	0.549204i	0.0288655	−	0.0288655i
$363$	−5.74540	−	5.74540i	−0.301555	−	0.301555i
$364$	0.801088	+	0.801088i	0.0419884	+	0.0419884i
$365$			5.26266i			0.275460i
$366$		−	8.03988i		−	0.420251i
$367$	−7.29732	−	7.29732i	−0.380917	−	0.380917i	0.490515	−	0.871432i	$-0.336809\pi$
$367$	−7.29732	−	7.29732i	−0.380917	−	0.380917i	−0.871432	+	0.490515i	$0.836809\pi$
$368$	1.33182	+	1.33182i	0.0694260	+	0.0694260i
$369$	−8.56854	+	8.56854i	−0.446060	+	0.446060i
$370$	4.60180			0.239236
$371$	−7.55807	+	7.55807i	−0.392396	+	0.392396i
$372$			2.58579i			0.134067i
$373$	18.2719			0.946083			0.473041	−	0.881040i	$-0.343156\pi$
$373$	18.2719			0.946083			0.473041	+	0.881040i	$0.343156\pi$
$374$		0			0
$375$	−4.25397			−0.219674
$376$			2.38009i			0.122744i
$377$	−2.00347	+	2.00347i	−0.103184	+	0.103184i
$378$	−3.41421			−0.175608
$379$	−14.8011	+	14.8011i	−0.760281	+	0.760281i	−0.976373	−	0.216092i	$-0.930669\pi$
$379$	−14.8011	+	14.8011i	−0.760281	+	0.760281i	0.216092	+	0.976373i	$0.430669\pi$
$380$	0.657228	+	0.657228i	0.0337151	+	0.0337151i
$381$	8.54487	+	8.54487i	0.437767	+	0.437767i
$382$			13.4248i			0.686872i
$383$		−	22.9974i		−	1.17511i	−0.809184	−	0.587555i	$-0.800090\pi$
$383$		−	22.9974i		−	1.17511i	0.809184	−	0.587555i	$-0.199910\pi$
$384$	−0.707107	−	0.707107i	−0.0360844	−	0.0360844i
$385$	−1.77465	−	1.77465i	−0.0904446	−	0.0904446i
$386$	−3.59850	+	3.59850i	−0.183159	+	0.183159i
$387$	10.0933			0.513073
$388$	−2.65546	+	2.65546i	−0.134811	+	0.134811i
$389$		−	9.07748i		−	0.460247i	−0.973161	−	0.230123i	$-0.926087\pi$
$389$		−	9.07748i		−	0.460247i	0.973161	−	0.230123i	$-0.0739130\pi$
$390$	−0.143860			−0.00728462
$391$		0			0
$392$	4.65685			0.235207
$393$			0.896683i			0.0452317i
$394$	−2.93767	+	2.93767i	−0.147998	+	0.147998i
$395$	−5.43641			−0.273536
$396$	1.19891	−	1.19891i	0.0602476	−	0.0602476i
$397$	−5.52149	−	5.52149i	−0.277116	−	0.277116i	0.554841	−	0.831957i	$-0.312779\pi$
$397$	−5.52149	−	5.52149i	−0.277116	−	0.277116i	−0.831957	+	0.554841i	$0.812779\pi$
$398$	7.57221	+	7.57221i	0.379561	+	0.379561i
$399$		−	7.31959i		−	0.366438i
$400$			4.81204i			0.240602i
$401$	−12.2759	−	12.2759i	−0.613030	−	0.613030i	0.330705	−	0.943734i	$-0.392714\pi$
$401$	−12.2759	−	12.2759i	−0.613030	−	0.613030i	−0.943734	+	0.330705i	$0.892714\pi$
$402$	−11.1519	−	11.1519i	−0.556205	−	0.556205i
$403$	0.606711	−	0.606711i	0.0302224	−	0.0302224i
$404$	−0.636303			−0.0316573
$405$	0.306563	−	0.306563i	0.0152332	−	0.0152332i
$406$			29.1531i			1.44684i
$407$	17.9968			0.892069
$408$		0			0
$409$	4.42153			0.218631			0.109315	−	0.994007i	$-0.465134\pi$
$409$	4.42153			0.218631			0.109315	+	0.994007i	$0.465134\pi$
$410$			5.25359i			0.259456i
$411$	8.91723	−	8.91723i	0.439855	−	0.439855i
$412$	−8.59955			−0.423669
$413$	18.5281	−	18.5281i	0.911709	−	0.911709i
$414$	1.33182	+	1.33182i	0.0654554	+	0.0654554i
$415$	0.319968	+	0.319968i	0.0157066	+	0.0157066i
$416$			0.331821i			0.0162689i
$417$		−	17.0447i		−	0.834683i
$418$	2.57030	+	2.57030i	0.125717	+	0.125717i
$419$	−16.3811	−	16.3811i	−0.800267	−	0.800267i	0.182870	−	0.983137i	$-0.441461\pi$
$419$	−16.3811	−	16.3811i	−0.800267	−	0.800267i	−0.983137	+	0.182870i	$0.941461\pi$
$420$	−1.04667	+	1.04667i	−0.0510723	+	0.0510723i
$421$	20.0524			0.977295			0.488648	−	0.872481i	$-0.337490\pi$
$421$	20.0524			0.977295			0.488648	+	0.872481i	$0.337490\pi$
$422$	−3.33861	+	3.33861i	−0.162521	+	0.162521i
$423$			2.38009i			0.115724i
$424$	−3.13066			−0.152038
$425$		0			0
$426$	0.226626			0.0109800
$427$			27.4499i			1.32839i
$428$	1.53073	−	1.53073i	0.0739908	−	0.0739908i
$429$	−0.562609			−0.0271630
$430$	3.09425	−	3.09425i	0.149218	−	0.149218i
$431$	28.3880	+	28.3880i	1.36740	+	1.36740i	0.864123	+	0.503280i	$0.167874\pi$
$431$	28.3880	+	28.3880i	1.36740	+	1.36740i	0.503280	+	0.864123i	$0.332126\pi$
$432$	−0.707107	−	0.707107i	−0.0340207	−	0.0340207i
$433$			21.8499i			1.05004i	0.851090	+	0.525020i	$0.175942\pi$
$433$			21.8499i			1.05004i	−0.851090	+	0.525020i	$0.824058\pi$
$434$		−	8.82843i		−	0.423778i
$435$	−2.61766	−	2.61766i	−0.125507	−	0.125507i
$436$	−5.59588	−	5.59588i	−0.267994	−	0.267994i
$437$	−2.85524	+	2.85524i	−0.136585	+	0.136585i
$438$	12.1387			0.580008
$439$	−0.593103	+	0.593103i	−0.0283073	+	0.0283073i	−0.721119	−	0.692811i	$-0.756372\pi$
$439$	−0.593103	+	0.593103i	−0.0283073	+	0.0283073i	0.692811	+	0.721119i	$0.256372\pi$
$440$		−	0.735084i		−	0.0350438i
$441$	4.65685			0.221755
$442$		0			0
$443$	−3.21267			−0.152639			−0.0763194	−	0.997083i	$-0.524317\pi$
$443$	−3.21267			−0.152639			−0.0763194	+	0.997083i	$0.524317\pi$
$444$		−	10.6143i		−	0.503735i
$445$	4.23917	−	4.23917i	0.200956	−	0.200956i
$446$	15.6359			0.740383
$447$	−12.3746	+	12.3746i	−0.585301	+	0.585301i
$448$	2.41421	+	2.41421i	0.114061	+	0.114061i
$449$	20.3281	+	20.3281i	0.959342	+	0.959342i	0.999205	−	0.0398632i	$-0.0126922\pi$
$449$	20.3281	+	20.3281i	0.959342	+	0.959342i	−0.0398632	+	0.999205i	$0.512692\pi$
$450$			4.81204i			0.226842i
$451$			20.5458i			0.967466i
$452$	6.49709	+	6.49709i	0.305598	+	0.305598i
$453$	6.81657	+	6.81657i	0.320271	+	0.320271i
$454$	7.82164	−	7.82164i	0.367088	−	0.367088i
$455$	0.491168			0.0230263
$456$	1.51594	−	1.51594i	0.0709903	−	0.0709903i
$457$		−	7.45097i		−	0.348542i	−0.984698	−	0.174271i	$-0.944243\pi$
$457$		−	7.45097i		−	0.348542i	0.984698	−	0.174271i	$-0.0557568\pi$
$458$	−15.3852			−0.718901
$459$		0			0
$460$	0.816574			0.0380730
$461$			25.6378i			1.19407i	0.802214	+	0.597037i	$0.203655\pi$
$461$			25.6378i			1.19407i	−0.802214	+	0.597037i	$0.796345\pi$
$462$	−4.09334	+	4.09334i	−0.190440	+	0.190440i
$463$	10.7747			0.500744			0.250372	−	0.968150i	$-0.419447\pi$
$463$	10.7747			0.500744			0.250372	+	0.968150i	$0.419447\pi$
$464$	−6.03780	+	6.03780i	−0.280298	+	0.280298i
$465$	0.792706	+	0.792706i	0.0367609	+	0.0367609i
$466$	−7.33806	−	7.33806i	−0.339929	−	0.339929i
$467$		−	35.6492i		−	1.64965i	−0.565391	−	0.824823i	$-0.691275\pi$
$467$		−	35.6492i		−	1.64965i	0.565391	−	0.824823i	$-0.308725\pi$
$468$			0.331821i			0.0153384i
$469$	38.0749	+	38.0749i	1.75813	+	1.75813i
$470$	0.729646	+	0.729646i	0.0336561	+	0.0336561i
$471$	3.38687	−	3.38687i	0.156059	−	0.156059i
$472$	7.67459			0.353252
$473$	12.1010	−	12.1010i	0.556406	−	0.556406i
$474$			12.5394i			0.575955i
$475$	−10.3163			−0.473346
$476$		0			0
$477$	−3.13066			−0.143343
$478$		−	24.7803i		−	1.13343i
$479$	−9.94911	+	9.94911i	−0.454586	+	0.454586i	−0.896874	−	0.442287i	$-0.854167\pi$
$479$	−9.94911	+	9.94911i	−0.454586	+	0.454586i	0.442287	+	0.896874i	$0.354167\pi$
$480$	−0.433546			−0.0197886
$481$	−2.49048	+	2.49048i	−0.113556	+	0.113556i
$482$	−3.04422	−	3.04422i	−0.138660	−	0.138660i
$483$	−4.54712	−	4.54712i	−0.206901	−	0.206901i
$484$			8.12522i			0.369328i
$485$			1.62813i			0.0739297i
$486$	−0.707107	−	0.707107i	−0.0320750	−	0.0320750i
$487$	17.0643	+	17.0643i	0.773256	+	0.773256i	0.978674	−	0.205418i	$-0.0658554\pi$
$487$	17.0643	+	17.0643i	0.773256	+	0.773256i	−0.205418	+	0.978674i	$0.565855\pi$
$488$	−5.68506	+	5.68506i	−0.257350	+	0.257350i
$489$	−17.8049			−0.805164
$490$	1.42762	−	1.42762i	0.0644933	−	0.0644933i
$491$			26.5200i			1.19683i	0.801186	+	0.598416i	$0.204203\pi$
$491$			26.5200i			1.19683i	−0.801186	+	0.598416i	$0.795797\pi$
$492$	12.1177			0.546310
$493$		0			0
$494$	−0.711378			−0.0320064
$495$		−	0.735084i		−	0.0330396i
$496$	1.82843	−	1.82843i	0.0820988	−	0.0820988i
$497$	−0.773748			−0.0347073
$498$	0.738027	−	0.738027i	0.0330718	−	0.0330718i
$499$	−3.21024	−	3.21024i	−0.143710	−	0.143710i	0.631591	−	0.775301i	$-0.282402\pi$
$499$	−3.21024	−	3.21024i	−0.143710	−	0.143710i	−0.775301	+	0.631591i	$0.782402\pi$
$500$	3.00801	+	3.00801i	0.134522	+	0.134522i
$501$			17.5950i			0.786087i
$502$			19.0639i			0.850864i
$503$	2.82655	+	2.82655i	0.126030	+	0.126030i	0.767308	−	0.641279i	$-0.221596\pi$
$503$	2.82655	+	2.82655i	0.126030	+	0.126030i	−0.641279	+	0.767308i	$0.721596\pi$
$504$	2.41421	+	2.41421i	0.107538	+	0.107538i
$505$	−0.195067	+	0.195067i	−0.00868037	+	0.00868037i
$506$	3.19347			0.141967
$507$	−9.11453	+	9.11453i	−0.404791	+	0.404791i
$508$		−	12.0843i		−	0.536153i
$509$	−22.9751			−1.01835			−0.509176	−	0.860662i	$-0.670050\pi$
$509$	−22.9751			−1.01835			−0.509176	+	0.860662i	$0.670050\pi$
$510$		0			0
$511$	−41.4440			−1.83337
$512$			1.00000i			0.0441942i
$513$	1.51594	−	1.51594i	0.0669303	−	0.0669303i
$514$	26.7594			1.18031
$515$	−2.63630	+	2.63630i	−0.116169	+	0.116169i
$516$	−7.13707	−	7.13707i	−0.314192	−	0.314192i
$517$	2.85351	+	2.85351i	0.125497	+	0.125497i
$518$			36.2396i			1.59228i
$519$			19.3462i			0.849206i
$520$	0.101724	+	0.101724i	0.00446090	+	0.00446090i
$521$	11.9380	+	11.9380i	0.523011	+	0.523011i	0.918480	−	0.395468i	$-0.129418\pi$
$521$	11.9380	+	11.9380i	0.523011	+	0.523011i	−0.395468	+	0.918480i	$0.629418\pi$
$522$	−6.03780	+	6.03780i	−0.264267	+	0.264267i
$523$	15.5903			0.681717			0.340859	−	0.940115i	$-0.389282\pi$
$523$	15.5903			0.681717			0.340859	+	0.940115i	$0.389282\pi$
$524$	0.634051	−	0.634051i	0.0276986	−	0.0276986i
$525$		−	16.4293i		−	0.717035i
$526$	27.5122			1.19959
$527$		0			0
$528$	−1.69552			−0.0737880
$529$		−	19.4525i		−	0.845761i
$530$	−0.959743	+	0.959743i	−0.0416886	+	0.0416886i
$531$	7.67459			0.333049
$532$	−5.17574	+	5.17574i	−0.224397	+	0.224397i
$533$	−2.84322	−	2.84322i	−0.123154	−	0.123154i
$534$	−9.77791	−	9.77791i	−0.423132	−	0.423132i
$535$		−	0.938533i		−	0.0405763i
$536$			15.7711i			0.681209i
$537$	6.44834	+	6.44834i	0.278266	+	0.278266i
$538$	−7.08153	−	7.08153i	−0.305306	−	0.305306i
$539$	5.58316	−	5.58316i	0.240484	−	0.240484i
$540$	−0.433546			−0.0186568
$541$	−10.6989	+	10.6989i	−0.459984	+	0.459984i	−0.898650	−	0.438666i	$-0.855451\pi$
$541$	−10.6989	+	10.6989i	−0.459984	+	0.459984i	0.438666	+	0.898650i	$0.355451\pi$
$542$			9.20949i			0.395581i
$543$	−0.776691			−0.0333310
$544$		0			0
$545$	−3.43098			−0.146967
$546$		−	1.13291i		−	0.0484840i
$547$	−1.87163	+	1.87163i	−0.0800250	+	0.0800250i	−0.745986	−	0.665961i	$-0.768022\pi$
$547$	−1.87163	+	1.87163i	−0.0800250	+	0.0800250i	0.665961	+	0.745986i	$0.268022\pi$
$548$	−12.6109			−0.538710
$549$	−5.68506	+	5.68506i	−0.242632	+	0.242632i
$550$	5.76921	+	5.76921i	0.246000	+	0.246000i
$551$	−12.9442	−	12.9442i	−0.551441	−	0.551441i
$552$		−	1.88348i		−	0.0801662i
$553$		−	42.8123i		−	1.82056i
$554$	5.91515	+	5.91515i	0.251311	+	0.251311i
$555$	−3.25397	−	3.25397i	−0.138123	−	0.138123i
$556$	−12.0524	+	12.0524i	−0.511137	+	0.511137i
$557$	12.4900			0.529217			0.264609	−	0.964356i	$-0.414757\pi$
$557$	12.4900			0.529217			0.264609	+	0.964356i	$0.414757\pi$
$558$	1.82843	−	1.82843i	0.0774035	−	0.0774035i
$559$			3.34919i			0.141656i
$560$	1.48022			0.0625506
$561$		0			0
$562$	10.9996			0.463991
$563$			1.98226i			0.0835423i	0.999127	+	0.0417712i	$0.0133000\pi$
$563$			1.98226i			0.0835423i	−0.999127	+	0.0417712i	$0.986700\pi$
$564$	1.68297	−	1.68297i	0.0708660	−	0.0708660i
$565$	3.98354			0.167589
$566$	14.9469	−	14.9469i	0.628263	−	0.628263i
$567$	2.41421	+	2.41421i	0.101387	+	0.101387i
$568$	−0.160248	−	0.160248i	−0.00672388	−	0.00672388i
$569$		−	16.7666i		−	0.702892i	−0.936208	−	0.351446i	$-0.885690\pi$
$569$		−	16.7666i		−	0.702892i	0.936208	−	0.351446i	$-0.114310\pi$
$570$		−	0.929461i		−	0.0389308i
$571$	−21.3001	−	21.3001i	−0.891383	−	0.891383i	0.103271	−	0.994653i	$-0.467069\pi$
$571$	−21.3001	−	21.3001i	−0.891383	−	0.891383i	−0.994653	+	0.103271i	$0.967069\pi$
$572$	0.397825	+	0.397825i	0.0166339	+	0.0166339i
$573$	9.49276	−	9.49276i	0.396566	−	0.396566i
$574$	−41.3725			−1.72686
$575$	−6.40878	+	6.40878i	−0.267264	+	0.267264i
$576$			1.00000i			0.0416667i
$577$	−19.8204			−0.825132			−0.412566	−	0.910928i	$-0.635367\pi$
$577$	−19.8204			−0.825132			−0.412566	+	0.910928i	$0.635367\pi$
$578$		0			0
$579$	5.08905			0.211494
$580$			3.70193i			0.153714i
$581$	−2.51978	+	2.51978i	−0.104538	+	0.104538i
$582$	3.75539			0.155666
$583$	−3.75338	+	3.75338i	−0.155449	+	0.155449i
$584$	−8.58333	−	8.58333i	−0.355181	−	0.355181i
$585$	0.101724	+	0.101724i	0.00420578	+	0.00420578i
$586$		−	25.1277i		−	1.03801i
$587$		−	12.8612i		−	0.530839i	−0.964133	−	0.265419i	$-0.914490\pi$
$587$		−	12.8612i		−	0.530839i	0.964133	−	0.265419i	$-0.0855104\pi$
$588$	−3.29289	−	3.29289i	−0.135797	−	0.135797i
$589$	3.91989	+	3.91989i	0.161516	+	0.161516i
$590$	2.35275	−	2.35275i	0.0968610	−	0.0968610i
$591$	4.15449			0.170893
$592$	−7.50548	+	7.50548i	−0.308473	+	0.308473i
$593$		−	35.8300i		−	1.47136i	−0.677328	−	0.735681i	$-0.736862\pi$
$593$		−	35.8300i		−	1.47136i	0.677328	−	0.735681i	$-0.263138\pi$
$594$	−1.69552			−0.0695680
$595$		0			0
$596$	17.5004			0.716844
$597$		−	10.7087i		−	0.438279i
$598$	−0.441927	+	0.441927i	−0.0180717	+	0.0180717i
$599$	21.1148			0.862728			0.431364	−	0.902178i	$-0.358032\pi$
$599$	21.1148			0.862728			0.431364	+	0.902178i	$0.358032\pi$
$600$	3.40262	−	3.40262i	0.138912	−	0.138912i
$601$	10.7725	+	10.7725i	0.439420	+	0.439420i	0.891817	−	0.452397i	$-0.149431\pi$
$601$	10.7725	+	10.7725i	0.439420	+	0.439420i	−0.452397	+	0.891817i	$0.649431\pi$
$602$	24.3675	+	24.3675i	0.993145	+	0.993145i
$603$			15.7711i			0.642250i
$604$		−	9.64009i		−	0.392250i
$605$	2.49089	+	2.49089i	0.101269	+	0.101269i
$606$	0.449934	+	0.449934i	0.0182773	+	0.0182773i
$607$	−27.1421	+	27.1421i	−1.10167	+	1.10167i	−0.107455	+	0.994210i	$0.534270\pi$
$607$	−27.1421	+	27.1421i	−1.10167	+	1.10167i	−0.994210	+	0.107455i	$0.965730\pi$
$608$	−2.14386			−0.0869450
$609$	20.6143	−	20.6143i	0.835335	−	0.835335i
$610$			3.48566i			0.141130i
$611$	−0.789763			−0.0319504
$612$		0			0
$613$	−1.39554			−0.0563654			−0.0281827	−	0.999603i	$-0.508972\pi$
$613$	−1.39554			−0.0563654			−0.0281827	+	0.999603i	$0.508972\pi$
$614$			15.3433i			0.619205i
$615$	3.71485	−	3.71485i	0.149797	−	0.149797i
$616$	5.78886			0.233240
$617$	−5.95021	+	5.95021i	−0.239547	+	0.239547i	−0.816662	−	0.577116i	$-0.804178\pi$
$617$	−5.95021	+	5.95021i	−0.239547	+	0.239547i	0.577116	+	0.816662i	$0.304178\pi$
$618$	6.08080	+	6.08080i	0.244606	+	0.244606i
$619$	3.77828	+	3.77828i	0.151862	+	0.151862i	0.778949	−	0.627087i	$-0.215753\pi$
$619$	3.77828	+	3.77828i	0.151862	+	0.151862i	−0.627087	+	0.778949i	$0.715753\pi$
$620$		−	1.12106i		−	0.0450227i
$621$		−	1.88348i		−	0.0755814i
$622$	−15.3318	−	15.3318i	−0.614750	−	0.614750i
$623$	33.3839	+	33.3839i	1.33750	+	1.33750i
$624$	0.234633	−	0.234633i	0.00939284	−	0.00939284i
$625$	−22.2159			−0.888636
$626$	−5.93154	+	5.93154i	−0.237072	+	0.237072i
$627$		−	3.63495i		−	0.145166i
$628$	−4.78976			−0.191132
$629$		0			0
$630$	1.48022			0.0589733
$631$		−	1.46282i		−	0.0582340i	−0.999576	−	0.0291170i	$-0.990730\pi$
$631$		−	1.46282i		−	0.0582340i	0.999576	−	0.0291170i	$-0.00926953\pi$
$632$	8.86672	−	8.86672i	0.352699	−	0.352699i
$633$	4.72151			0.187663
$634$	16.9566	−	16.9566i	0.673434	−	0.673434i
$635$	−3.70459	−	3.70459i	−0.147012	−	0.147012i
$636$	2.21371	+	2.21371i	0.0877792	+	0.0877792i
$637$			1.54524i			0.0612248i
$638$			14.4776i			0.573173i
$639$	−0.160248	−	0.160248i	−0.00633933	−	0.00633933i
$640$	0.306563	+	0.306563i	0.0121180	+	0.0121180i
$641$	−0.338967	+	0.338967i	−0.0133884	+	0.0133884i	−0.713769	−	0.700381i	$-0.753013\pi$
$641$	−0.338967	+	0.338967i	−0.0133884	+	0.0133884i	0.700381	+	0.713769i	$0.253013\pi$
$642$	−2.16478			−0.0854372
$643$	22.7016	−	22.7016i	0.895262	−	0.895262i	−0.0997504	−	0.995012i	$-0.531804\pi$
$643$	22.7016	−	22.7016i	0.895262	−	0.895262i	0.995012	+	0.0997504i	$0.0318044\pi$
$644$			6.43060i			0.253401i
$645$	−4.37592			−0.172302
$646$		0			0
$647$	23.4802			0.923103			0.461551	−	0.887114i	$-0.347293\pi$
$647$	23.4802			0.923103			0.461551	+	0.887114i	$0.347293\pi$
$648$			1.00000i			0.0392837i
$649$	9.20116	−	9.20116i	0.361177	−	0.361177i
$650$	−1.59674			−0.0626292
$651$	−6.24264	+	6.24264i	−0.244668	+	0.244668i
$652$	12.5899	+	12.5899i	0.493060	+	0.493060i
$653$	−32.0806	−	32.0806i	−1.25541	−	1.25541i	−0.953260	−	0.302152i	$-0.902295\pi$
$653$	−32.0806	−	32.0806i	−1.25541	−	1.25541i	−0.302152	−	0.953260i	$-0.597705\pi$
$654$			7.91376i			0.309453i
$655$		−	0.388753i		−	0.0151898i
$656$	−8.56854	−	8.56854i	−0.334545	−	0.334545i
$657$	−8.58333	−	8.58333i	−0.334868	−	0.334868i
$658$	−5.74603	+	5.74603i	−0.224004	+	0.224004i
$659$	−12.8417			−0.500240			−0.250120	−	0.968215i	$-0.580470\pi$
$659$	−12.8417			−0.500240			−0.250120	+	0.968215i	$0.580470\pi$
$660$	−0.519783	+	0.519783i	−0.0202325	+	0.0202325i
$661$		−	27.1878i		−	1.05748i	−0.848783	−	0.528741i	$-0.822664\pi$
$661$		−	27.1878i		−	1.05748i	0.848783	−	0.528741i	$-0.177336\pi$
$662$	−4.07733			−0.158470
$663$		0			0
$664$	−1.04373			−0.0405045
$665$			3.17338i			0.123058i
$666$	−7.50548	+	7.50548i	−0.290831	+	0.290831i
$667$	−16.0825			−0.622719
$668$	12.4416	−	12.4416i	0.481378	−	0.481378i
$669$	−11.0563	−	11.0563i	−0.427460	−	0.427460i
$670$	4.83484	+	4.83484i	0.186786	+	0.186786i
$671$			13.6318i			0.526249i
$672$		−	3.41421i		−	0.131706i
$673$	11.7925	+	11.7925i	0.454569	+	0.454569i	0.896868	−	0.442299i	$-0.145837\pi$
$673$	11.7925	+	11.7925i	0.454569	+	0.454569i	−0.442299	+	0.896868i	$0.645837\pi$
$674$	7.08288	+	7.08288i	0.272822	+	0.272822i
$675$	3.40262	−	3.40262i	0.130967	−	0.130967i
$676$	12.8899			0.495765
$677$	−1.84048	+	1.84048i	−0.0707355	+	0.0707355i	−0.741589	−	0.670854i	$-0.765928\pi$
$677$	−1.84048	+	1.84048i	−0.0707355	+	0.0707355i	0.670854	+	0.741589i	$0.265928\pi$
$678$		−	9.18828i		−	0.352874i
$679$	−12.8217			−0.492052
$680$		0			0
$681$	−11.0615			−0.423876
$682$		−	4.38425i		−	0.167882i
$683$	8.65689	−	8.65689i	0.331247	−	0.331247i	−0.521813	−	0.853060i	$-0.674744\pi$
$683$	8.65689	−	8.65689i	0.331247	−	0.331247i	0.853060	+	0.521813i	$0.174744\pi$
$684$	−2.14386			−0.0819725
$685$	−3.86603	+	3.86603i	−0.147713	+	0.147713i
$686$	−5.65685	−	5.65685i	−0.215980	−	0.215980i
$687$	10.8789	+	10.8789i	0.415058	+	0.415058i
$688$			10.0933i			0.384805i
$689$		−	1.03882i		−	0.0395758i
$690$	−0.577405	−	0.577405i	−0.0219814	−	0.0219814i
$691$	11.0829	+	11.0829i	0.421614	+	0.421614i	0.885759	−	0.464145i	$-0.153638\pi$
$691$	11.0829	+	11.0829i	0.421614	+	0.421614i	−0.464145	+	0.885759i	$0.653638\pi$
$692$	13.6799	−	13.6799i	0.520030	−	0.520030i
$693$	5.78886			0.219901
$694$	−6.11236	+	6.11236i	−0.232022	+	0.232022i
$695$			7.38966i			0.280306i
$696$	8.53874			0.323660
$697$		0			0
$698$	20.8126			0.787768
$699$			10.3776i			0.392517i
$700$	−11.6173	+	11.6173i	−0.439092	+	0.439092i
$701$	−30.8222			−1.16414			−0.582070	−	0.813139i	$-0.697757\pi$
$701$	−30.8222			−1.16414			−0.582070	+	0.813139i	$0.697757\pi$
$702$	0.234633	−	0.234633i	0.00885566	−	0.00885566i
$703$	−16.0907	−	16.0907i	−0.606872	−	0.606872i
$704$	1.19891	+	1.19891i	0.0451857	+	0.0451857i
$705$		−	1.03188i		−	0.0388627i
$706$			20.1049i			0.756656i
$707$	−1.53617	−	1.53617i	−0.0577737	−	0.0577737i
$708$	−5.42676	−	5.42676i	−0.203950	−	0.203950i
$709$	0.279223	−	0.279223i	0.0104865	−	0.0104865i	−0.701844	−	0.712331i	$-0.747640\pi$
$709$	0.279223	−	0.279223i	0.0104865	−	0.0104865i	0.712331	+	0.701844i	$0.247640\pi$
$710$	−0.0982525			−0.00368735
$711$	8.86672	−	8.86672i	0.332528	−	0.332528i
$712$			13.8281i			0.518228i
$713$	4.87028			0.182393
$714$		0			0
$715$	0.243917			0.00912197
$716$		−	9.11933i		−	0.340805i
$717$	−17.5224	+	17.5224i	−0.654384	+	0.654384i
$718$	−25.3001			−0.944193
$719$	7.84617	−	7.84617i	0.292613	−	0.292613i	−0.545499	−	0.838112i	$-0.683660\pi$
$719$	7.84617	−	7.84617i	0.292613	−	0.292613i	0.838112	+	0.545499i	$0.183660\pi$
$720$	0.306563	+	0.306563i	0.0114249	+	0.0114249i
$721$	−20.7611	−	20.7611i	−0.773186	−	0.773186i
$722$			14.4039i			0.536056i
$723$			4.30517i			0.160111i
$724$	0.549204	+	0.549204i	0.0204110	+	0.0204110i
$725$	−29.0541	−	29.0541i	−1.07904	−	1.07904i
$726$	5.74540	−	5.74540i	0.213232	−	0.213232i
$727$	−27.2866			−1.01200			−0.506001	−	0.862533i	$-0.668877\pi$
$727$	−27.2866			−1.01200			−0.506001	+	0.862533i	$0.668877\pi$
$728$	−0.801088	+	0.801088i	−0.0296903	+	0.0296903i
$729$			1.00000i			0.0370370i
$730$	−5.26266			−0.194780
$731$		0			0
$732$	8.03988			0.297163
$733$		−	29.2870i		−	1.08174i	−0.841106	−	0.540870i	$-0.818095\pi$
$733$		−	29.2870i		−	1.08174i	0.841106	−	0.540870i	$-0.181905\pi$
$734$	7.29732	−	7.29732i	0.269349	−	0.269349i
$735$	−2.01896			−0.0744704
$736$	−1.33182	+	1.33182i	−0.0490916	+	0.0490916i
$737$	18.9082	+	18.9082i	0.696492	+	0.696492i
$738$	−8.56854	−	8.56854i	−0.315412	−	0.315412i
$739$		−	37.0534i		−	1.36303i	−0.731803	−	0.681516i	$-0.761321\pi$
$739$		−	37.0534i		−	1.36303i	0.731803	−	0.681516i	$-0.238679\pi$
$740$			4.60180i			0.169166i
$741$	0.503021	+	0.503021i	0.0184789	+	0.0184789i
$742$	−7.55807	−	7.55807i	−0.277466	−	0.277466i
$743$	10.2440	−	10.2440i	0.375816	−	0.375816i	−0.493774	−	0.869590i	$-0.664383\pi$
$743$	10.2440	−	10.2440i	0.375816	−	0.375816i	0.869590	+	0.493774i	$0.164383\pi$
$744$	−2.58579			−0.0947995
$745$	5.36497	−	5.36497i	0.196557	−	0.196557i
$746$			18.2719i			0.668981i
$747$	−1.04373			−0.0381880
$748$		0			0
$749$	7.39104			0.270063
$750$		−	4.25397i		−	0.155333i
$751$	31.0867	−	31.0867i	1.13437	−	1.13437i	0.144928	−	0.989442i	$-0.453705\pi$
$751$	31.0867	−	31.0867i	1.13437	−	1.13437i	0.989442	−	0.144928i	$-0.0462950\pi$
$752$	−2.38009			−0.0867928
$753$	13.4802	−	13.4802i	0.491246	−	0.491246i
$754$	−2.00347	−	2.00347i	−0.0729621	−	0.0729621i
$755$	−2.95530	−	2.95530i	−0.107554	−	0.107554i
$756$		−	3.41421i		−	0.124174i
$757$			37.8588i			1.37600i	0.725710	+	0.688001i	$0.241511\pi$
$757$			37.8588i			1.37600i	−0.725710	+	0.688001i	$0.758489\pi$
$758$	−14.8011	−	14.8011i	−0.537600	−	0.537600i
$759$	−2.25813	−	2.25813i	−0.0819648	−	0.0819648i
$760$	−0.657228	+	0.657228i	−0.0238402	+	0.0238402i
$761$	9.82880			0.356294			0.178147	−	0.984004i	$-0.442990\pi$
$761$	9.82880			0.356294			0.178147	+	0.984004i	$0.442990\pi$
$762$	−8.54487	+	8.54487i	−0.309548	+	0.309548i
$763$		−	27.0193i		−	0.978163i
$764$	−13.4248			−0.485692
$765$		0			0
$766$	22.9974			0.830929
$767$			2.54659i			0.0919522i
$768$	0.707107	−	0.707107i	0.0255155	−	0.0255155i
$769$	−41.1522			−1.48398			−0.741992	−	0.670408i	$-0.766119\pi$
$769$	−41.1522			−1.48398			−0.741992	+	0.670408i	$0.766119\pi$
$770$	1.77465	−	1.77465i	0.0639540	−	0.0639540i
$771$	−18.9218	−	18.9218i	−0.681451	−	0.681451i
$772$	−3.59850	−	3.59850i	−0.129513	−	0.129513i
$773$		−	21.7456i		−	0.782136i	−0.920362	−	0.391068i	$-0.872106\pi$
$773$		−	21.7456i		−	0.782136i	0.920362	−	0.391068i	$-0.127894\pi$
$774$			10.0933i			0.362798i
$775$	8.79846	+	8.79846i	0.316050	+	0.316050i
$776$	−2.65546	−	2.65546i	−0.0953256	−	0.0953256i
$777$	25.6253	−	25.6253i	0.919302	−	0.919302i
$778$	9.07748			0.325444
$779$	18.3697	−	18.3697i	0.658164	−	0.658164i
$780$		−	0.143860i		−	0.00515100i
$781$	−0.384248			−0.0137495
$782$		0			0
$783$	8.53874			0.305150
$784$			4.65685i			0.166316i
$785$	−1.46836	+	1.46836i	−0.0524082	+	0.0524082i
$786$	−0.896683			−0.0319836
$787$	−33.6597	+	33.6597i	−1.19984	+	1.19984i	−0.225626	+	0.974214i	$0.572443\pi$
$787$	−33.6597	+	33.6597i	−1.19984	+	1.19984i	−0.974214	+	0.225626i	$0.927557\pi$
$788$	−2.93767	−	2.93767i	−0.104650	−	0.104650i
$789$	−19.4541	−	19.4541i	−0.692584	−	0.692584i
$790$		−	5.43641i		−	0.193419i
$791$			31.3707i			1.11542i
$792$	1.19891	+	1.19891i	0.0426015	+	0.0426015i
$793$	−1.88642	−	1.88642i	−0.0669888	−	0.0669888i
$794$	5.52149	−	5.52149i	0.195950	−	0.195950i
$795$	1.35728			0.0481378
$796$	−7.57221	+	7.57221i	−0.268390	+	0.268390i
$797$		−	37.8984i		−	1.34243i	−0.741263	−	0.671215i	$-0.765773\pi$
$797$		−	37.8984i		−	1.34243i	0.741263	−	0.671215i	$-0.234227\pi$
$798$	7.31959			0.259111
$799$		0			0
$800$	−4.81204			−0.170131
$801$			13.8281i			0.488590i
$802$	12.2759	−	12.2759i	0.433477	−	0.433477i
$803$	−20.5813			−0.726299
$804$	11.1519	−	11.1519i	0.393296	−	0.393296i
$805$	1.97138	+	1.97138i	0.0694822	+	0.0694822i
$806$	0.606711	+	0.606711i	0.0213705	+	0.0213705i
$807$			10.0148i			0.352538i
$808$		−	0.636303i		−	0.0223851i
$809$	−27.2753	−	27.2753i	−0.958948	−	0.958948i	0.0402418	−	0.999190i	$-0.487187\pi$
$809$	−27.2753	−	27.2753i	−0.958948	−	0.958948i	−0.999190	+	0.0402418i	$0.987187\pi$
$810$	0.306563	+	0.306563i	0.0107715	+	0.0107715i
$811$	−13.7457	+	13.7457i	−0.482677	+	0.482677i	−0.905985	−	0.423309i	$-0.860869\pi$
$811$	−13.7457	+	13.7457i	−0.482677	+	0.482677i	0.423309	+	0.905985i	$0.360869\pi$
$812$	−29.1531			−1.02307
$813$	6.51209	−	6.51209i	0.228389	−	0.228389i
$814$			17.9968i			0.630788i
$815$	7.71922			0.270393
$816$		0			0
$817$	−21.6387			−0.757043
$818$			4.42153i			0.154595i
$819$	−0.801088	+	0.801088i	−0.0279923	+	0.0279923i
$820$	−5.25359			−0.183463
$821$	−0.163922	+	0.163922i	−0.00572093	+	0.00572093i	−0.709961	−	0.704241i	$-0.751288\pi$
$821$	−0.163922	+	0.163922i	−0.00572093	+	0.00572093i	0.704241	+	0.709961i	$0.251288\pi$
$822$	8.91723	+	8.91723i	0.311024	+	0.311024i
$823$	15.9050	+	15.9050i	0.554414	+	0.554414i	0.927712	−	0.373298i	$-0.121773\pi$
$823$	15.9050	+	15.9050i	0.554414	+	0.554414i	−0.373298	+	0.927712i	$0.621773\pi$
$824$		−	8.59955i		−	0.299579i
$825$		−	8.15890i		−	0.284056i
$826$	18.5281	+	18.5281i	0.644675	+	0.644675i
$827$	36.9902	+	36.9902i	1.28628	+	1.28628i	0.937032	+	0.349244i	$0.113561\pi$
$827$	36.9902	+	36.9902i	1.28628	+	1.28628i	0.349244	+	0.937032i	$0.386439\pi$
$828$	−1.33182	+	1.33182i	−0.0462840	+	0.0462840i
$829$	−23.3260			−0.810144			−0.405072	−	0.914285i	$-0.632754\pi$
$829$	−23.3260			−0.810144			−0.405072	+	0.914285i	$0.632754\pi$
$830$	−0.319968	+	0.319968i	−0.0111063	+	0.0111063i
$831$		−	8.36529i		−	0.290189i
$832$	−0.331821			−0.0115038
$833$		0			0
$834$	17.0447			0.590210
$835$		−	7.62824i		−	0.263986i
$836$	−2.57030	+	2.57030i	−0.0888957	+	0.0888957i
$837$	−2.58579			−0.0893779
$838$	16.3811	−	16.3811i	0.565874	−	0.565874i
$839$	−9.49019	−	9.49019i	−0.327638	−	0.327638i	0.524050	−	0.851688i	$-0.324421\pi$
$839$	−9.49019	−	9.49019i	−0.327638	−	0.327638i	−0.851688	+	0.524050i	$0.824421\pi$
$840$	−1.04667	−	1.04667i	−0.0361136	−	0.0361136i
$841$		−	43.9101i		−	1.51414i
$842$			20.0524i			0.691052i
$843$	−7.77791	−	7.77791i	−0.267885	−	0.267885i
$844$	−3.33861	−	3.33861i	−0.114920	−	0.114920i
$845$	3.95156	−	3.95156i	0.135938	−	0.135938i
$846$	−2.38009			−0.0818290
$847$	−19.6160	+	19.6160i	−0.674014	+	0.674014i
$848$		−	3.13066i		−	0.107507i
$849$	−21.1380			−0.725456
$850$		0			0
$851$	−19.9919			−0.685314
$852$			0.226626i			0.00776406i
$853$	−35.3094	+	35.3094i	−1.20897	+	1.20897i	−0.237609	+	0.971361i	$0.576364\pi$
$853$	−35.3094	+	35.3094i	−1.20897	+	1.20897i	−0.971361	+	0.237609i	$0.923636\pi$
$854$	−27.4499			−0.939315
$855$	−0.657228	+	0.657228i	−0.0224767	+	0.0224767i
$856$	1.53073	+	1.53073i	0.0523194	+	0.0523194i
$857$	−12.1453	−	12.1453i	−0.414875	−	0.414875i	0.468558	−	0.883433i	$-0.344774\pi$
$857$	−12.1453	−	12.1453i	−0.414875	−	0.414875i	−0.883433	+	0.468558i	$0.844774\pi$
$858$		−	0.562609i		−	0.0192072i
$859$		−	8.76362i		−	0.299011i	−0.988761	−	0.149505i	$-0.952232\pi$
$859$		−	8.76362i		−	0.299011i	0.988761	−	0.149505i	$-0.0477681\pi$
$860$	3.09425	+	3.09425i	0.105513	+	0.105513i
$861$	29.2548	+	29.2548i	0.997001	+	0.997001i
$862$	−28.3880	+	28.3880i	−0.966900	+	0.966900i
$863$	−35.9177			−1.22265			−0.611326	−	0.791379i	$-0.709364\pi$
$863$	−35.9177			−1.22265			−0.611326	+	0.791379i	$0.709364\pi$
$864$	0.707107	−	0.707107i	0.0240563	−	0.0240563i
$865$		−	8.38748i		−	0.285183i
$866$	−21.8499			−0.742490
$867$		0			0
$868$	8.82843			0.299656
$869$		−	21.2608i		−	0.721224i
$870$	2.61766	−	2.61766i	0.0887470	−	0.0887470i
$871$	−5.23320			−0.177320
$872$	5.59588	−	5.59588i	0.189500	−	0.189500i
$873$	−2.65546	−	2.65546i	−0.0898738	−	0.0898738i
$874$	−2.85524	−	2.85524i	−0.0965799	−	0.0965799i
$875$			14.5239i			0.490999i
$876$			12.1387i			0.410127i
$877$	−2.98766	−	2.98766i	−0.100886	−	0.100886i	0.654862	−	0.755748i	$-0.272727\pi$
$877$	−2.98766	−	2.98766i	−0.100886	−	0.100886i	−0.755748	+	0.654862i	$0.772727\pi$
$878$	−0.593103	−	0.593103i	−0.0200163	−	0.0200163i
$879$	−17.7679	+	17.7679i	−0.599298	+	0.599298i
$880$	0.735084			0.0247797
$881$	21.2102	−	21.2102i	0.714590	−	0.714590i	−0.252902	−	0.967492i	$-0.581385\pi$
$881$	21.2102	−	21.2102i	0.714590	−	0.714590i	0.967492	+	0.252902i	$0.0813849\pi$
$882$			4.65685i			0.156804i
$883$	13.9714			0.470175			0.235087	−	0.971974i	$-0.424462\pi$
$883$	13.9714			0.470175			0.235087	+	0.971974i	$0.424462\pi$
$884$		0			0
$885$	−3.32729			−0.111845
$886$		−	3.21267i		−	0.107932i
$887$	−15.5758	+	15.5758i	−0.522986	+	0.522986i	−0.918472	−	0.395486i	$-0.870576\pi$
$887$	−15.5758	+	15.5758i	−0.522986	+	0.522986i	0.395486	+	0.918472i	$0.370576\pi$
$888$	10.6143			0.356194
$889$	29.1740	−	29.1740i	0.978465	−	0.978465i
$890$	4.23917	+	4.23917i	0.142097	+	0.142097i
$891$	1.19891	+	1.19891i	0.0401651	+	0.0401651i
$892$			15.6359i			0.523530i
$893$		−	5.10257i		−	0.170751i
$894$	−12.3746	−	12.3746i	−0.413870	−	0.413870i
$895$	−2.79565	−	2.79565i	−0.0934483	−	0.0934483i
$896$	−2.41421	+	2.41421i	−0.0806532	+	0.0806532i
$897$	0.624979			0.0208674
$898$	−20.3281	+	20.3281i	−0.678357	+	0.678357i
$899$			22.0794i			0.736388i
$900$	−4.81204			−0.160401
$901$		0			0
$902$	−20.5458			−0.684102
$903$		−	34.4608i		−	1.14678i
$904$	−6.49709	+	6.49709i	−0.216090	+	0.216090i
$905$	0.336731			0.0111933
$906$	−6.81657	+	6.81657i	−0.226466	+	0.226466i
$907$	−19.0287	−	19.0287i	−0.631837	−	0.631837i	0.316691	−	0.948529i	$-0.397428\pi$
$907$	−19.0287	−	19.0287i	−0.631837	−	0.631837i	−0.948529	+	0.316691i	$0.897428\pi$
$908$	7.82164	+	7.82164i	0.259570	+	0.259570i
$909$		−	0.636303i		−	0.0211048i
$910$			0.491168i			0.0162820i
$911$	−25.0916	−	25.0916i	−0.831322	−	0.831322i	0.156375	−	0.987698i	$-0.450019\pi$
$911$	−25.0916	−	25.0916i	−0.831322	−	0.831322i	−0.987698	+	0.156375i	$0.950019\pi$
$912$	1.51594	+	1.51594i	0.0501977	+	0.0501977i
$913$	−1.25134	+	1.25134i	−0.0414133	+	0.0414133i
$914$	7.45097			0.246456
$915$	2.46473	−	2.46473i	0.0814815	−	0.0814815i
$916$		−	15.3852i		−	0.508340i
$917$	3.06147			0.101099
$918$		0			0
$919$	−38.6107			−1.27365			−0.636824	−	0.771009i	$-0.719752\pi$
$919$	−38.6107			−1.27365			−0.636824	+	0.771009i	$0.719752\pi$
$920$			0.816574i			0.0269217i
$921$	10.8494	−	10.8494i	0.357498	−	0.357498i
$922$	−25.6378			−0.844337
$923$	0.0531739	−	0.0531739i	0.00175024	−	0.00175024i
$924$	−4.09334	−	4.09334i	−0.134661	−	0.134661i
$925$	−36.1166	−	36.1166i	−1.18751	−	1.18751i
$926$			10.7747i			0.354079i
$927$		−	8.59955i		−	0.282446i
$928$	−6.03780	−	6.03780i	−0.198201	−	0.198201i
$929$	−16.1891	−	16.1891i	−0.531148	−	0.531148i	0.389766	−	0.920914i	$-0.372556\pi$
$929$	−16.1891	−	16.1891i	−0.531148	−	0.531148i	−0.920914	+	0.389766i	$0.872556\pi$
$930$	−0.792706	+	0.792706i	−0.0259939	+	0.0259939i
$931$	−9.98364			−0.327201
$932$	7.33806	−	7.33806i	0.240366	−	0.240366i
$933$			21.6825i			0.709852i
$934$	35.6492			1.16648
$935$		0			0
$936$	−0.331821			−0.0108459
$937$			39.6793i			1.29627i	0.761527	+	0.648133i	$0.224450\pi$
$937$			39.6793i			1.29627i	−0.761527	+	0.648133i	$0.775550\pi$
$938$	−38.0749	+	38.0749i	−1.24319	+	1.24319i
$939$	8.38847			0.273747
$940$	−0.729646	+	0.729646i	−0.0237984	+	0.0237984i
$941$	−37.2398	−	37.2398i	−1.21398	−	1.21398i	−0.969705	−	0.244279i	$-0.921449\pi$
$941$	−37.2398	−	37.2398i	−1.21398	−	1.21398i	−0.244279	−	0.969705i	$-0.578551\pi$
$942$	3.38687	+	3.38687i	0.110350	+	0.110350i
$943$		−	22.8235i		−	0.743236i
$944$			7.67459i			0.249787i
$945$	−1.04667	−	1.04667i	−0.0340482	−	0.0340482i
$946$	12.1010	+	12.1010i	0.393439	+	0.393439i
$947$	−1.07974	+	1.07974i	−0.0350867	+	0.0350867i	−0.724432	−	0.689346i	$-0.757898\pi$
$947$	−1.07974	+	1.07974i	−0.0350867	+	0.0350867i	0.689346	+	0.724432i	$0.257898\pi$
$948$	−12.5394			−0.407262
$949$	2.84813	−	2.84813i	0.0924543	−	0.0924543i
$950$		−	10.3163i		−	0.334706i
$951$	−23.9803			−0.777614
$952$		0			0
$953$	9.95360			0.322429			0.161214	−	0.986919i	$-0.448459\pi$
$953$	9.95360			0.322429			0.161214	+	0.986919i	$0.448459\pi$
$954$		−	3.13066i		−	0.101359i
$955$	−4.11554	+	4.11554i	−0.133176	+	0.133176i
$956$	24.7803			0.801454
$957$	10.2372	−	10.2372i	0.330922	−	0.330922i
$958$	−9.94911	−	9.94911i	−0.321441	−	0.321441i
$959$	−30.4453	−	30.4453i	−0.983131	−	0.983131i
$960$		−	0.433546i		−	0.0139926i
$961$			24.3137i			0.784313i
$962$	−2.49048	−	2.49048i	−0.0802962	−	0.0802962i
$963$	1.53073	+	1.53073i	0.0493272	+	0.0493272i
$964$	3.04422	−	3.04422i	0.0980476	−	0.0980476i
$965$	−2.20633			−0.0710244
$966$	4.54712	−	4.54712i	0.146301	−	0.146301i
$967$			5.88843i			0.189359i	0.995508	+	0.0946796i	$0.0301827\pi$
$967$			5.88843i			0.189359i	−0.995508	+	0.0946796i	$0.969817\pi$
$968$	−8.12522			−0.261154
$969$		0			0
$970$	−1.62813			−0.0522762
$971$			18.9670i			0.608681i	0.952563	+	0.304341i	$0.0984361\pi$
$971$			18.9670i			0.608681i	−0.952563	+	0.304341i	$0.901564\pi$
$972$	0.707107	−	0.707107i	0.0226805	−	0.0226805i
$973$	−58.1943			−1.86562
$974$	−17.0643	+	17.0643i	−0.546775	+	0.546775i
$975$	1.12906	+	1.12906i	0.0361590	+	0.0361590i
$976$	−5.68506	−	5.68506i	−0.181974	−	0.181974i
$977$		−	32.3172i		−	1.03392i	−0.856010	−	0.516959i	$-0.827064\pi$
$977$		−	32.3172i		−	1.03392i	0.856010	−	0.516959i	$-0.172936\pi$
$978$		−	17.8049i		−	0.569337i
$979$	16.5786	+	16.5786i	0.529855	+	0.529855i
$980$	1.42762	+	1.42762i	0.0456036	+	0.0456036i
$981$	5.59588	−	5.59588i	0.178663	−	0.178663i
$982$	−26.5200			−0.846288
$983$	22.9359	−	22.9359i	0.731542	−	0.731542i	−0.239383	−	0.970925i	$-0.576945\pi$
$983$	22.9359	−	22.9359i	0.731542	−	0.731542i	0.970925	+	0.239383i	$0.0769453\pi$
$984$			12.1177i			0.386299i
$985$	−1.80116			−0.0573898
$986$		0			0
$987$	8.12612			0.258657
$988$		−	0.711378i		−	0.0226320i
$989$	−13.4425	+	13.4425i	−0.427448	+	0.427448i
$990$	0.735084			0.0233625
$991$	−33.1640	+	33.1640i	−1.05349	+	1.05349i	−0.0550042	+	0.998486i	$0.517517\pi$
$991$	−33.1640	+	33.1640i	−1.05349	+	1.05349i	−0.998486	+	0.0550042i	$0.982483\pi$
$992$	1.82843	+	1.82843i	0.0580526	+	0.0580526i
$993$	2.88311	+	2.88311i	0.0914926	+	0.0914926i
$994$		−	0.773748i		−	0.0245418i
$995$			4.64272i			0.147184i
$996$	0.738027	+	0.738027i	0.0233853	+	0.0233853i
$997$	33.5572	+	33.5572i	1.06277	+	1.06277i	0.997893	+	0.0648741i	$0.0206646\pi$
$997$	33.5572	+	33.5572i	1.06277	+	1.06277i	0.0648741	+	0.997893i	$0.479335\pi$
$998$	3.21024	−	3.21024i	0.101618	−	0.101618i
$999$	10.6143			0.335823

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1734.2.f.m.1483.3		8
17.2	even	8		1734.2.b.k.577.3		8
17.4	even	4		1734.2.f.j.829.2		8
17.5	odd	16		102.2.h.a.49.2	yes	8
17.6	odd	16		102.2.h.a.25.2	✓	8
17.8	even	8		1734.2.a.v.1.3		4
17.9	even	8		1734.2.a.w.1.2		4
17.13	even	4	inner	1734.2.f.m.829.3		8
17.15	even	8		1734.2.b.k.577.6		8
17.16	even	2		1734.2.f.j.1483.2		8
51.5	even	16		306.2.l.d.253.2		8
51.8	odd	8		5202.2.a.br.1.2		4
51.23	even	16		306.2.l.d.127.2		8
51.26	odd	8		5202.2.a.bt.1.3		4
68.23	even	16		816.2.bq.b.433.1		8
68.39	even	16		816.2.bq.b.49.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
102.2.h.a.25.2	✓	8	17.6	odd	16
102.2.h.a.49.2	yes	8	17.5	odd	16
306.2.l.d.127.2		8	51.23	even	16
306.2.l.d.253.2		8	51.5	even	16
816.2.bq.b.49.1		8	68.39	even	16
816.2.bq.b.433.1		8	68.23	even	16
1734.2.a.v.1.3		4	17.8	even	8
1734.2.a.w.1.2		4	17.9	even	8
1734.2.b.k.577.3		8	17.2	even	8
1734.2.b.k.577.6		8	17.15	even	8
1734.2.f.j.829.2		8	17.4	even	4
1734.2.f.j.1483.2		8	17.16	even	2
1734.2.f.m.829.3		8	17.13	even	4	inner
1734.2.f.m.1483.3		8	1.1	even	1	trivial
5202.2.a.br.1.2		4	51.8	odd	8
5202.2.a.bt.1.3		4	51.26	odd	8

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:	\( N \)	\(=\)	\( 1734 = 2 \cdot 3 \cdot 17^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1734.f (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} +(0.707107 - 0.707107i) q^{3} -1.00000 q^{4} +(-0.306563 + 0.306563i) q^{5} +(0.707107 + 0.707107i) q^{6} +(-2.41421 - 2.41421i) q^{7} -1.00000i q^{8} -1.00000i q^{9} +O(q^{10})\)	\(q+1.00000i q^{2} +(0.707107 - 0.707107i) q^{3} -1.00000 q^{4} +(-0.306563 + 0.306563i) q^{5} +(0.707107 + 0.707107i) q^{6} +(-2.41421 - 2.41421i) q^{7} -1.00000i q^{8} -1.00000i q^{9} +(-0.306563 - 0.306563i) q^{10} +(-1.19891 - 1.19891i) q^{11} +(-0.707107 + 0.707107i) q^{12} +0.331821 q^{13} +(2.41421 - 2.41421i) q^{14} +0.433546i q^{15} +1.00000 q^{16} +1.00000 q^{18} +2.14386i q^{19} +(0.306563 - 0.306563i) q^{20} -3.41421 q^{21} +(1.19891 - 1.19891i) q^{22} +(1.33182 + 1.33182i) q^{23} +(-0.707107 - 0.707107i) q^{24} +4.81204i q^{25} +0.331821i q^{26} +(-0.707107 - 0.707107i) q^{27} +(2.41421 + 2.41421i) q^{28} +(-6.03780 + 6.03780i) q^{29} -0.433546 q^{30} +(1.82843 - 1.82843i) q^{31} +1.00000i q^{32} -1.69552 q^{33} +1.48022 q^{35} +1.00000i q^{36} +(-7.50548 + 7.50548i) q^{37} -2.14386 q^{38} +(0.234633 - 0.234633i) q^{39} +(0.306563 + 0.306563i) q^{40} +(-8.56854 - 8.56854i) q^{41} -3.41421i q^{42} +10.0933i q^{43} +(1.19891 + 1.19891i) q^{44} +(0.306563 + 0.306563i) q^{45} +(-1.33182 + 1.33182i) q^{46} -2.38009 q^{47} +(0.707107 - 0.707107i) q^{48} +4.65685i q^{49} -4.81204 q^{50} -0.331821 q^{52} -3.13066i q^{53} +(0.707107 - 0.707107i) q^{54} +0.735084 q^{55} +(-2.41421 + 2.41421i) q^{56} +(1.51594 + 1.51594i) q^{57} +(-6.03780 - 6.03780i) q^{58} +7.67459i q^{59} -0.433546i q^{60} +(-5.68506 - 5.68506i) q^{61} +(1.82843 + 1.82843i) q^{62} +(-2.41421 + 2.41421i) q^{63} -1.00000 q^{64} +(-0.101724 + 0.101724i) q^{65} -1.69552i q^{66} -15.7711 q^{67} +1.88348 q^{69} +1.48022i q^{70} +(0.160248 - 0.160248i) q^{71} -1.00000 q^{72} +(8.58333 - 8.58333i) q^{73} +(-7.50548 - 7.50548i) q^{74} +(3.40262 + 3.40262i) q^{75} -2.14386i q^{76} +5.78886i q^{77} +(0.234633 + 0.234633i) q^{78} +(8.86672 + 8.86672i) q^{79} +(-0.306563 + 0.306563i) q^{80} -1.00000 q^{81} +(8.56854 - 8.56854i) q^{82} -1.04373i q^{83} +3.41421 q^{84} -10.0933 q^{86} +8.53874i q^{87} +(-1.19891 + 1.19891i) q^{88} -13.8281 q^{89} +(-0.306563 + 0.306563i) q^{90} +(-0.801088 - 0.801088i) q^{91} +(-1.33182 - 1.33182i) q^{92} -2.58579i q^{93} -2.38009i q^{94} +(-0.657228 - 0.657228i) q^{95} +(0.707107 + 0.707107i) q^{96} +(2.65546 - 2.65546i) q^{97} -4.65685 q^{98} +(-1.19891 + 1.19891i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{4} + 8 q^{5} - 8 q^{7}+O(q^{10}) \) 8 * q - 8 * q^4 + 8 * q^5 - 8 * q^7	\( 8 q - 8 q^{4} + 8 q^{5} - 8 q^{7} + 8 q^{10} + 8 q^{14} + 8 q^{16} + 8 q^{18} - 8 q^{20} - 16 q^{21} + 8 q^{23} + 8 q^{28} - 24 q^{29} - 8 q^{31} + 16 q^{33} - 16 q^{35} - 40 q^{37} + 16 q^{38} + 8 q^{39} - 8 q^{40} - 32 q^{41} - 8 q^{45} - 8 q^{46} - 8 q^{50} + 32 q^{55} - 8 q^{56} - 24 q^{58} - 8 q^{61} - 8 q^{62} - 8 q^{63} - 8 q^{64} - 48 q^{67} + 16 q^{69} - 24 q^{71} - 8 q^{72} + 32 q^{73} - 40 q^{74} - 8 q^{75} + 8 q^{78} - 24 q^{79} + 8 q^{80} - 8 q^{81} + 32 q^{82} + 16 q^{84} - 32 q^{86} + 8 q^{90} - 16 q^{91} - 8 q^{92} - 48 q^{95} - 16 q^{97} + 8 q^{98}+O(q^{100}) \) 8 * q - 8 * q^4 + 8 * q^5 - 8 * q^7 + 8 * q^10 + 8 * q^14 + 8 * q^16 + 8 * q^18 - 8 * q^20 - 16 * q^21 + 8 * q^23 + 8 * q^28 - 24 * q^29 - 8 * q^31 + 16 * q^33 - 16 * q^35 - 40 * q^37 + 16 * q^38 + 8 * q^39 - 8 * q^40 - 32 * q^41 - 8 * q^45 - 8 * q^46 - 8 * q^50 + 32 * q^55 - 8 * q^56 - 24 * q^58 - 8 * q^61 - 8 * q^62 - 8 * q^63 - 8 * q^64 - 48 * q^67 + 16 * q^69 - 24 * q^71 - 8 * q^72 + 32 * q^73 - 40 * q^74 - 8 * q^75 + 8 * q^78 - 24 * q^79 + 8 * q^80 - 8 * q^81 + 32 * q^82 + 16 * q^84 - 32 * q^86 + 8 * q^90 - 16 * q^91 - 8 * q^92 - 48 * q^95 - 16 * q^97 + 8 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more