LMFDB - Embedded newform 690.2.i.d.47.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [690,2,Mod(47,690)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(690, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("690.47");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 690 = 2 \cdot 3 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	690.i (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:	$5.50967773947$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(i)$
Coefficient field:	8.0.40960000.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 7x^{4} + 1 $ x^8 + 7*x^4 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			47.1
Root			$1.14412 + 1.14412i$ of defining polynomial
Character	$\chi$	$=$	690.47
Dual form			690.2.i.d.323.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 + 0.707107i) q^{2} +(-1.70711 + 0.292893i) q^{3} -1.00000i q^{4} -2.23607i q^{5} +(1.00000 - 1.41421i) q^{6} +(0.707107 + 0.707107i) q^{8} +(2.82843 - 1.00000i) q^{9} +O(q^{10})$	\(q+(-0.707107 + 0.707107i) q^{2} +(-1.70711 + 0.292893i) q^{3} -1.00000i q^{4} -2.23607i q^{5} +(1.00000 - 1.41421i) q^{6} +(0.707107 + 0.707107i) q^{8} +(2.82843 - 1.00000i) q^{9} +(1.58114 + 1.58114i) q^{10} -2.82843i q^{11} +(0.292893 + 1.70711i) q^{12} +(-2.16228 + 2.16228i) q^{13} +(0.654929 + 3.81721i) q^{15} -1.00000 q^{16} +(0.821854 - 0.821854i) q^{17} +(-1.29289 + 2.70711i) q^{18} +1.16228i q^{19} -2.23607 q^{20} +(2.00000 + 2.00000i) q^{22} +(0.707107 + 0.707107i) q^{23} +(-1.41421 - 1.00000i) q^{24} -5.00000 q^{25} -3.05792i q^{26} +(-4.53553 + 2.53553i) q^{27} -4.47214 q^{29} +(-3.16228 - 2.23607i) q^{30} -2.32456 q^{31} +(0.707107 - 0.707107i) q^{32} +(0.828427 + 4.82843i) q^{33} +1.16228i q^{34} +(-1.00000 - 2.82843i) q^{36} +(-1.16228 - 1.16228i) q^{37} +(-0.821854 - 0.821854i) q^{38} +(3.05792 - 4.32456i) q^{39} +(1.58114 - 1.58114i) q^{40} -11.7727i q^{41} +(-9.16228 + 9.16228i) q^{43} -2.82843 q^{44} +(-2.23607 - 6.32456i) q^{45} -1.00000 q^{46} +(-0.229495 + 0.229495i) q^{47} +(1.70711 - 0.292893i) q^{48} -7.00000i q^{49} +(3.53553 - 3.53553i) q^{50} +(-1.16228 + 1.64371i) q^{51} +(2.16228 + 2.16228i) q^{52} +(-6.70820 - 6.70820i) q^{53} +(1.41421 - 5.00000i) q^{54} -6.32456 q^{55} +(-0.340423 - 1.98413i) q^{57} +(3.16228 - 3.16228i) q^{58} -9.89949 q^{59} +(3.81721 - 0.654929i) q^{60} +8.00000 q^{61} +(1.64371 - 1.64371i) q^{62} +1.00000i q^{64} +(4.83500 + 4.83500i) q^{65} +(-4.00000 - 2.82843i) q^{66} +(-1.16228 - 1.16228i) q^{67} +(-0.821854 - 0.821854i) q^{68} +(-1.41421 - 1.00000i) q^{69} +5.88635i q^{71} +(2.70711 + 1.29289i) q^{72} +(5.32456 - 5.32456i) q^{73} +1.64371 q^{74} +(8.53553 - 1.46447i) q^{75} +1.16228 q^{76} +(0.895645 + 5.22020i) q^{78} +3.16228i q^{79} +2.23607i q^{80} +(7.00000 - 5.65685i) q^{81} +(8.32456 + 8.32456i) q^{82} +(-3.05792 - 3.05792i) q^{83} +(-1.83772 - 1.83772i) q^{85} -12.9574i q^{86} +(7.63441 - 1.30986i) q^{87} +(2.00000 - 2.00000i) q^{88} -17.4296 q^{89} +(6.05327 + 2.89100i) q^{90} +(0.707107 - 0.707107i) q^{92} +(3.96826 - 0.680846i) q^{93} -0.324555i q^{94} +2.59893 q^{95} +(-1.00000 + 1.41421i) q^{96} +(-5.16228 - 5.16228i) q^{97} +(4.94975 + 4.94975i) q^{98} +(-2.82843 - 8.00000i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{3} + 8 q^{6}+O(q^{10}) $ 8 * q - 8 * q^3 + 8 * q^6	$ 8 q - 8 q^{3} + 8 q^{6} + 8 q^{12} + 8 q^{13} - 8 q^{16} - 16 q^{18} + 16 q^{22} - 40 q^{25} - 8 q^{27} + 32 q^{31} - 16 q^{33} - 8 q^{36} + 16 q^{37} - 48 q^{43} - 8 q^{46} + 8 q^{48} + 16 q^{51} - 8 q^{52} + 16 q^{57} + 64 q^{61} - 32 q^{66} + 16 q^{67} + 16 q^{72} - 8 q^{73} + 40 q^{75} - 16 q^{76} + 8 q^{78} + 56 q^{81} + 16 q^{82} - 40 q^{85} + 16 q^{88} - 32 q^{93} - 8 q^{96} - 16 q^{97}+O(q^{100}) $ 8 * q - 8 * q^3 + 8 * q^6 + 8 * q^12 + 8 * q^13 - 8 * q^16 - 16 * q^18 + 16 * q^22 - 40 * q^25 - 8 * q^27 + 32 * q^31 - 16 * q^33 - 8 * q^36 + 16 * q^37 - 48 * q^43 - 8 * q^46 + 8 * q^48 + 16 * q^51 - 8 * q^52 + 16 * q^57 + 64 * q^61 - 32 * q^66 + 16 * q^67 + 16 * q^72 - 8 * q^73 + 40 * q^75 - 16 * q^76 + 8 * q^78 + 56 * q^81 + 16 * q^82 - 40 * q^85 + 16 * q^88 - 32 * q^93 - 8 * q^96 - 16 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/690\mathbb{Z}\right)^\times$.

$n$	$277$	$461$	$511$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$	$1$

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
$3$	−1.70711	+	0.292893i	−0.985599	+	0.169102i
$3$	−1.70711	+	0.292893i	−0.985599	+	0.169102i
$4$		−	1.00000i		−	0.500000i
$5$		−	2.23607i		−	1.00000i
$5$		−	2.23607i		−	1.00000i
$6$	1.00000	−	1.41421i	0.408248	−	0.577350i
$7$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$7$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$	2.82843	−	1.00000i	0.942809	−	0.333333i
$10$	1.58114	+	1.58114i	0.500000	+	0.500000i
$11$		−	2.82843i		−	0.852803i	−0.904534	−	0.426401i	$-0.859781\pi$
$11$		−	2.82843i		−	0.852803i	0.904534	−	0.426401i	$-0.140219\pi$
$12$	0.292893	+	1.70711i	0.0845510	+	0.492799i
$13$	−2.16228	+	2.16228i	−0.599708	+	0.599708i	−0.940235	−	0.340527i	$-0.889395\pi$
$13$	−2.16228	+	2.16228i	−0.599708	+	0.599708i	0.340527	+	0.940235i	$0.389395\pi$
$14$		0			0
$15$	0.654929	+	3.81721i	0.169102	+	0.985599i
$16$	−1.00000			−0.250000
$17$	0.821854	−	0.821854i	0.199329	−	0.199329i	−0.600383	−	0.799712i	$-0.704985\pi$
$17$	0.821854	−	0.821854i	0.199329	−	0.199329i	0.799712	+	0.600383i	$0.204985\pi$
$18$	−1.29289	+	2.70711i	−0.304738	+	0.638071i
$19$			1.16228i			0.266645i	0.991073	+	0.133322i	$0.0425646\pi$
$19$			1.16228i			0.266645i	−0.991073	+	0.133322i	$0.957435\pi$
$20$	−2.23607			−0.500000
$21$		0			0
$22$	2.00000	+	2.00000i	0.426401	+	0.426401i
$23$	0.707107	+	0.707107i	0.147442	+	0.147442i
$23$	0.707107	+	0.707107i	0.147442	+	0.147442i
$24$	−1.41421	−	1.00000i	−0.288675	−	0.204124i
$25$	−5.00000			−1.00000
$26$		−	3.05792i		−	0.599708i
$27$	−4.53553	+	2.53553i	−0.872864	+	0.487964i
$28$		0			0
$29$	−4.47214			−0.830455			−0.415227	−	0.909718i	$-0.636298\pi$
$29$	−4.47214			−0.830455			−0.415227	+	0.909718i	$0.636298\pi$
$30$	−3.16228	−	2.23607i	−0.577350	−	0.408248i
$31$	−2.32456			−0.417502			−0.208751	−	0.977969i	$-0.566940\pi$
$31$	−2.32456			−0.417502			−0.208751	+	0.977969i	$0.566940\pi$
$32$	0.707107	−	0.707107i	0.125000	−	0.125000i
$33$	0.828427	+	4.82843i	0.144211	+	0.840521i
$34$			1.16228i			0.199329i
$35$		0			0
$36$	−1.00000	−	2.82843i	−0.166667	−	0.471405i
$37$	−1.16228	−	1.16228i	−0.191077	−	0.191077i	0.605084	−	0.796161i	$-0.293139\pi$
$37$	−1.16228	−	1.16228i	−0.191077	−	0.191077i	−0.796161	+	0.605084i	$0.793139\pi$
$38$	−0.821854	−	0.821854i	−0.133322	−	0.133322i
$39$	3.05792	−	4.32456i	0.489659	−	0.692483i
$40$	1.58114	−	1.58114i	0.250000	−	0.250000i
$41$		−	11.7727i		−	1.83859i	−0.393573	−	0.919293i	$-0.628761\pi$
$41$		−	11.7727i		−	1.83859i	0.393573	−	0.919293i	$-0.371239\pi$
$42$		0			0
$43$	−9.16228	+	9.16228i	−1.39723	+	1.39723i	−0.589374	+	0.807861i	$0.700625\pi$
$43$	−9.16228	+	9.16228i	−1.39723	+	1.39723i	−0.807861	+	0.589374i	$0.799375\pi$
$44$	−2.82843			−0.426401
$45$	−2.23607	−	6.32456i	−0.333333	−	0.942809i
$46$	−1.00000			−0.147442
$47$	−0.229495	+	0.229495i	−0.0334753	+	0.0334753i	−0.723646	−	0.690171i	$-0.757535\pi$
$47$	−0.229495	+	0.229495i	−0.0334753	+	0.0334753i	0.690171	+	0.723646i	$0.257535\pi$
$48$	1.70711	−	0.292893i	0.246400	−	0.0422755i
$49$		−	7.00000i		−	1.00000i
$50$	3.53553	−	3.53553i	0.500000	−	0.500000i
$51$	−1.16228	+	1.64371i	−0.162751	+	0.230165i
$52$	2.16228	+	2.16228i	0.299854	+	0.299854i
$53$	−6.70820	−	6.70820i	−0.921443	−	0.921443i	0.0756888	−	0.997131i	$-0.475884\pi$
$53$	−6.70820	−	6.70820i	−0.921443	−	0.921443i	−0.997131	+	0.0756888i	$0.975884\pi$
$54$	1.41421	−	5.00000i	0.192450	−	0.680414i
$55$	−6.32456			−0.852803
$56$		0			0
$57$	−0.340423	−	1.98413i	−0.0450902	−	0.262805i
$58$	3.16228	−	3.16228i	0.415227	−	0.415227i
$59$	−9.89949			−1.28880			−0.644402	−	0.764687i	$-0.722894\pi$
$59$	−9.89949			−1.28880			−0.644402	+	0.764687i	$0.722894\pi$
$60$	3.81721	−	0.654929i	0.492799	−	0.0845510i
$61$	8.00000			1.02430			0.512148	−	0.858898i	$-0.328850\pi$
$61$	8.00000			1.02430			0.512148	+	0.858898i	$0.328850\pi$
$62$	1.64371	−	1.64371i	0.208751	−	0.208751i
$63$		0			0
$64$			1.00000i			0.125000i
$65$	4.83500	+	4.83500i	0.599708	+	0.599708i
$66$	−4.00000	−	2.82843i	−0.492366	−	0.348155i
$67$	−1.16228	−	1.16228i	−0.141995	−	0.141995i	0.632536	−	0.774531i	$-0.282014\pi$
$67$	−1.16228	−	1.16228i	−0.141995	−	0.141995i	−0.774531	+	0.632536i	$0.782014\pi$
$68$	−0.821854	−	0.821854i	−0.0996645	−	0.0996645i
$69$	−1.41421	−	1.00000i	−0.170251	−	0.120386i
$70$		0			0
$71$			5.88635i			0.698581i	0.937014	+	0.349291i	$0.113577\pi$
$71$			5.88635i			0.698581i	−0.937014	+	0.349291i	$0.886423\pi$
$72$	2.70711	+	1.29289i	0.319036	+	0.152369i
$73$	5.32456	−	5.32456i	0.623192	−	0.623192i	−0.323154	−	0.946346i	$-0.604743\pi$
$73$	5.32456	−	5.32456i	0.623192	−	0.623192i	0.946346	+	0.323154i	$0.104743\pi$
$74$	1.64371			0.191077
$75$	8.53553	−	1.46447i	0.985599	−	0.169102i
$76$	1.16228			0.133322
$77$		0			0
$78$	0.895645	+	5.22020i	0.101412	+	0.591071i
$79$			3.16228i			0.355784i	0.984050	+	0.177892i	$0.0569278\pi$
$79$			3.16228i			0.355784i	−0.984050	+	0.177892i	$0.943072\pi$
$80$			2.23607i			0.250000i
$81$	7.00000	−	5.65685i	0.777778	−	0.628539i
$82$	8.32456	+	8.32456i	0.919293	+	0.919293i
$83$	−3.05792	−	3.05792i	−0.335651	−	0.335651i	0.519077	−	0.854728i	$-0.326276\pi$
$83$	−3.05792	−	3.05792i	−0.335651	−	0.335651i	−0.854728	+	0.519077i	$0.826276\pi$
$84$		0			0
$85$	−1.83772	−	1.83772i	−0.199329	−	0.199329i
$86$		−	12.9574i		−	1.39723i
$87$	7.63441	−	1.30986i	0.818495	−	0.140432i
$88$	2.00000	−	2.00000i	0.213201	−	0.213201i
$89$	−17.4296			−1.84753			−0.923764	−	0.382961i	$-0.874904\pi$
$89$	−17.4296			−1.84753			−0.923764	+	0.382961i	$0.874904\pi$
$90$	6.05327	+	2.89100i	0.638071	+	0.304738i
$91$		0			0
$92$	0.707107	−	0.707107i	0.0737210	−	0.0737210i
$93$	3.96826	−	0.680846i	0.411490	−	0.0706005i
$94$		−	0.324555i		−	0.0334753i
$95$	2.59893			0.266645
$96$	−1.00000	+	1.41421i	−0.102062	+	0.144338i
$97$	−5.16228	−	5.16228i	−0.524150	−	0.524150i	0.394672	−	0.918822i	$-0.370858\pi$
$97$	−5.16228	−	5.16228i	−0.524150	−	0.524150i	−0.918822	+	0.394672i	$0.870858\pi$
$98$	4.94975	+	4.94975i	0.500000	+	0.500000i
$99$	−2.82843	−	8.00000i	−0.284268	−	0.804030i
$100$			5.00000i			0.500000i
$101$			7.30056i			0.726433i	0.931705	+	0.363217i	$0.118321\pi$
$101$			7.30056i			0.726433i	−0.931705	+	0.363217i	$0.881679\pi$
$102$	−0.340423	−	1.98413i	−0.0337069	−	0.196458i
$103$	−4.83772	+	4.83772i	−0.476675	+	0.476675i	−0.904067	−	0.427392i	$-0.859433\pi$
$103$	−4.83772	+	4.83772i	−0.476675	+	0.476675i	0.427392	+	0.904067i	$0.359433\pi$
$104$	−3.05792			−0.299854
$105$		0			0
$106$	9.48683			0.921443
$107$	−7.53006	+	7.53006i	−0.727958	+	0.727958i	−0.970213	−	0.242255i	$-0.922113\pi$
$107$	−7.53006	+	7.53006i	−0.727958	+	0.727958i	0.242255	+	0.970213i	$0.422113\pi$
$108$	2.53553	+	4.53553i	0.243982	+	0.436432i
$109$			1.67544i			0.160478i	0.996776	+	0.0802392i	$0.0255684\pi$
$109$			1.67544i			0.160478i	−0.996776	+	0.0802392i	$0.974432\pi$
$110$	4.47214	−	4.47214i	0.426401	−	0.426401i
$111$	2.32456	+	1.64371i	0.220637	+	0.156014i
$112$		0			0
$113$	−0.362864	−	0.362864i	−0.0341354	−	0.0341354i	0.689833	−	0.723968i	$-0.257684\pi$
$113$	−0.362864	−	0.362864i	−0.0341354	−	0.0341354i	−0.723968	+	0.689833i	$0.757684\pi$
$114$	1.64371	+	1.16228i	0.153947	+	0.108857i
$115$	1.58114	−	1.58114i	0.147442	−	0.147442i
$116$			4.47214i			0.415227i
$117$	−3.95357	+	8.27812i	−0.365507	+	0.765313i
$118$	7.00000	−	7.00000i	0.644402	−	0.644402i
$119$		0			0
$120$	−2.23607	+	3.16228i	−0.204124	+	0.288675i
$121$	3.00000			0.272727
$122$	−5.65685	+	5.65685i	−0.512148	+	0.512148i
$123$	3.44814	+	20.0973i	0.310909	+	1.81211i
$124$			2.32456i			0.208751i
$125$			11.1803i			1.00000i
$126$		0			0
$127$	1.16228	+	1.16228i	0.103135	+	0.103135i	0.756792	−	0.653656i	$-0.226766\pi$
$127$	1.16228	+	1.16228i	0.103135	+	0.103135i	−0.653656	+	0.756792i	$0.726766\pi$
$128$	−0.707107	−	0.707107i	−0.0625000	−	0.0625000i
$129$	12.9574	−	18.3246i	1.14084	−	1.61339i
$130$	−6.83772			−0.599708
$131$			10.3585i			0.905025i	0.891758	+	0.452513i	$0.149472\pi$
$131$			10.3585i			0.905025i	−0.891758	+	0.452513i	$0.850528\pi$
$132$	4.82843	−	0.828427i	0.420261	−	0.0721053i
$133$		0			0
$134$	1.64371			0.141995
$135$	5.66963	+	10.1418i	0.487964	+	0.872864i
$136$	1.16228			0.0996645
$137$	−0.821854	+	0.821854i	−0.0702158	+	0.0702158i	−0.741343	−	0.671127i	$-0.765811\pi$
$137$	−0.821854	+	0.821854i	−0.0702158	+	0.0702158i	0.671127	+	0.741343i	$0.265811\pi$
$138$	1.70711	−	0.292893i	0.145319	−	0.0249327i
$139$		−	10.3246i		−	0.875717i	−0.899044	−	0.437859i	$-0.855737\pi$
$139$		−	10.3246i		−	0.875717i	0.899044	−	0.437859i	$-0.144263\pi$
$140$		0			0
$141$	0.324555	−	0.458991i	0.0273325	−	0.0386540i
$142$	−4.16228	−	4.16228i	−0.349291	−	0.349291i
$143$	6.11584	+	6.11584i	0.511433	+	0.511433i
$144$	−2.82843	+	1.00000i	−0.235702	+	0.0833333i
$145$			10.0000i			0.830455i
$146$			7.53006i			0.623192i
$147$	2.05025	+	11.9497i	0.169102	+	0.985599i
$148$	−1.16228	+	1.16228i	−0.0955386	+	0.0955386i
$149$	−7.75955			−0.635687			−0.317844	−	0.948143i	$-0.602959\pi$
$149$	−7.75955			−0.635687			−0.317844	+	0.948143i	$0.602959\pi$
$150$	−5.00000	+	7.07107i	−0.408248	+	0.577350i
$151$	−10.3246			−0.840200			−0.420100	−	0.907478i	$-0.638005\pi$
$151$	−10.3246			−0.840200			−0.420100	+	0.907478i	$0.638005\pi$
$152$	−0.821854	+	0.821854i	−0.0666612	+	0.0666612i
$153$	1.50270	−	3.14641i	0.121486	−	0.254372i
$154$		0			0
$155$			5.19786i			0.417502i
$156$	−4.32456	−	3.05792i	−0.346242	−	0.244830i
$157$	9.48683	+	9.48683i	0.757132	+	0.757132i	0.975799	−	0.218668i	$-0.0701711\pi$
$157$	9.48683	+	9.48683i	0.757132	+	0.757132i	−0.218668	+	0.975799i	$0.570171\pi$
$158$	−2.23607	−	2.23607i	−0.177892	−	0.177892i
$159$	13.4164	+	9.48683i	1.06399	+	0.752355i
$160$	−1.58114	−	1.58114i	−0.125000	−	0.125000i
$161$		0			0
$162$	−0.949747	+	8.94975i	−0.0746192	+	0.703159i
$163$	−8.64911	+	8.64911i	−0.677451	+	0.677451i	−0.959423	−	0.281972i	$-0.909011\pi$
$163$	−8.64911	+	8.64911i	−0.677451	+	0.677451i	0.281972	+	0.959423i	$0.409011\pi$
$164$	−11.7727			−0.919293
$165$	10.7967	−	1.85242i	0.840521	−	0.144211i
$166$	4.32456			0.335651
$167$	14.6011	−	14.6011i	1.12987	−	1.12987i	0.139671	−	0.990198i	$-0.455395\pi$
$167$	14.6011	−	14.6011i	1.12987	−	1.12987i	0.990198	−	0.139671i	$-0.0446045\pi$
$168$		0			0
$169$			3.64911i			0.280701i
$170$	2.59893			0.199329
$171$	1.16228	+	3.28742i	0.0888816	+	0.251395i
$172$	9.16228	+	9.16228i	0.698617	+	0.698617i
$173$	−8.71478	−	8.71478i	−0.662572	−	0.662572i	0.293413	−	0.955986i	$-0.405209\pi$
$173$	−8.71478	−	8.71478i	−0.662572	−	0.662572i	−0.955986	+	0.293413i	$0.905209\pi$
$174$	−4.47214	+	6.32456i	−0.339032	+	0.479463i
$175$		0			0
$176$			2.82843i			0.213201i
$177$	16.8995	−	2.89949i	1.27024	−	0.217939i
$178$	12.3246	−	12.3246i	0.923764	−	0.923764i
$179$	13.1869			0.985636			0.492818	−	0.870132i	$-0.335967\pi$
$179$	13.1869			0.985636			0.492818	+	0.870132i	$0.335967\pi$
$180$	−6.32456	+	2.23607i	−0.471405	+	0.166667i
$181$	22.3246			1.65937			0.829686	−	0.558231i	$-0.188520\pi$
$181$	22.3246			1.65937			0.829686	+	0.558231i	$0.188520\pi$
$182$		0			0
$183$	−13.6569	+	2.34315i	−1.00954	+	0.173210i
$184$			1.00000i			0.0737210i
$185$	−2.59893	+	2.59893i	−0.191077	+	0.191077i
$186$	−2.32456	+	3.28742i	−0.170445	+	0.241045i
$187$	−2.32456	−	2.32456i	−0.169988	−	0.169988i
$188$	0.229495	+	0.229495i	0.0167377	+	0.0167377i
$189$		0			0
$190$	−1.83772	+	1.83772i	−0.133322	+	0.133322i
$191$		−	17.4296i		−	1.26116i	−0.776125	−	0.630579i	$-0.782817\pi$
$191$		−	17.4296i		−	1.26116i	0.776125	−	0.630579i	$-0.217183\pi$
$192$	−0.292893	−	1.70711i	−0.0211377	−	0.123200i
$193$	3.00000	−	3.00000i	0.215945	−	0.215945i	−0.590842	−	0.806787i	$-0.701204\pi$
$193$	3.00000	−	3.00000i	0.215945	−	0.215945i	0.806787	+	0.590842i	$0.201204\pi$
$194$	7.30056			0.524150
$195$	−9.67000	−	6.83772i	−0.692483	−	0.489659i
$196$	−7.00000			−0.500000
$197$	2.59893	−	2.59893i	0.185166	−	0.185166i	−0.608436	−	0.793603i	$-0.708203\pi$
$197$	2.59893	−	2.59893i	0.185166	−	0.185166i	0.793603	+	0.608436i	$0.208203\pi$
$198$	7.65685	+	3.65685i	0.544149	+	0.259881i
$199$		−	15.1623i		−	1.07483i	−0.843319	−	0.537413i	$-0.819402\pi$
$199$		−	15.1623i		−	1.07483i	0.843319	−	0.537413i	$-0.180598\pi$
$200$	−3.53553	−	3.53553i	−0.250000	−	0.250000i
$201$	2.32456	+	1.64371i	0.163961	+	0.115938i
$202$	−5.16228	−	5.16228i	−0.363217	−	0.363217i
$203$		0			0
$204$	1.64371	+	1.16228i	0.115083	+	0.0813757i
$205$	−26.3246			−1.83859
$206$		−	6.84157i		−	0.476675i
$207$	2.70711	+	1.29289i	0.188157	+	0.0898623i
$208$	2.16228	−	2.16228i	0.149927	−	0.149927i
$209$	3.28742			0.227395
$210$		0			0
$211$	1.67544			0.115342			0.0576712	−	0.998336i	$-0.481633\pi$
$211$	1.67544			0.115342			0.0576712	+	0.998336i	$0.481633\pi$
$212$	−6.70820	+	6.70820i	−0.460721	+	0.460721i
$213$	−1.72407	−	10.0486i	−0.118131	−	0.688521i
$214$		−	10.6491i		−	0.727958i
$215$	20.4875	+	20.4875i	1.39723	+	1.39723i
$216$	−5.00000	−	1.41421i	−0.340207	−	0.0962250i
$217$		0			0
$218$	−1.18472	−	1.18472i	−0.0802392	−	0.0802392i
$219$	−7.53006	+	10.6491i	−0.508834	+	0.719600i
$220$			6.32456i			0.426401i
$221$			3.55415i			0.239078i
$222$	−2.80599	+	0.481431i	−0.188325	+	0.0323115i
$223$	6.83772	−	6.83772i	0.457888	−	0.457888i	−0.440074	−	0.897962i	$-0.645048\pi$
$223$	6.83772	−	6.83772i	0.457888	−	0.457888i	0.897962	+	0.440074i	$0.145048\pi$
$224$		0			0
$225$	−14.1421	+	5.00000i	−0.942809	+	0.333333i
$226$	0.513167			0.0341354
$227$	4.24264	−	4.24264i	0.281594	−	0.281594i	−0.552151	−	0.833744i	$-0.686193\pi$
$227$	4.24264	−	4.24264i	0.281594	−	0.281594i	0.833744	+	0.552151i	$0.186193\pi$
$228$	−1.98413	+	0.340423i	−0.131402	+	0.0225451i
$229$		−	25.2982i		−	1.67175i	−0.548917	−	0.835877i	$-0.684960\pi$
$229$		−	25.2982i		−	1.67175i	0.548917	−	0.835877i	$-0.315040\pi$
$230$			2.23607i			0.147442i
$231$		0			0
$232$	−3.16228	−	3.16228i	−0.207614	−	0.207614i
$233$	−3.05792	−	3.05792i	−0.200331	−	0.200331i	0.599811	−	0.800142i	$-0.295243\pi$
$233$	−3.05792	−	3.05792i	−0.200331	−	0.200331i	−0.800142	+	0.599811i	$0.795243\pi$
$234$	−3.05792	−	8.64911i	−0.199903	−	0.565410i
$235$	0.513167	+	0.513167i	0.0334753	+	0.0334753i
$236$			9.89949i			0.644402i
$237$	−0.926210	−	5.39835i	−0.0601638	−	0.350660i
$238$		0			0
$239$	20.4875			1.32522			0.662612	−	0.748963i	$-0.269448\pi$
$239$	20.4875			1.32522			0.662612	+	0.748963i	$0.269448\pi$
$240$	−0.654929	−	3.81721i	−0.0422755	−	0.246400i
$241$	−4.32456			−0.278569			−0.139285	−	0.990252i	$-0.544480\pi$
$241$	−4.32456			−0.278569			−0.139285	+	0.990252i	$0.544480\pi$
$242$	−2.12132	+	2.12132i	−0.136364	+	0.136364i
$243$	−10.2929	+	11.7071i	−0.660289	+	0.751011i
$244$		−	8.00000i		−	0.512148i
$245$	−15.6525			−1.00000
$246$	−16.6491	−	11.7727i	−1.06151	−	0.750600i
$247$	−2.51317	−	2.51317i	−0.159909	−	0.159909i
$248$	−1.64371	−	1.64371i	−0.104376	−	0.104376i
$249$	6.11584	+	4.32456i	0.387576	+	0.274058i
$250$	−7.90569	−	7.90569i	−0.500000	−	0.500000i
$251$			5.65685i			0.357057i	0.983935	+	0.178529i	$0.0571337\pi$
$251$			5.65685i			0.357057i	−0.983935	+	0.178529i	$0.942866\pi$
$252$		0			0
$253$	2.00000	−	2.00000i	0.125739	−	0.125739i
$254$	−1.64371			−0.103135
$255$	3.67544	+	2.59893i	0.230165	+	0.162751i
$256$	1.00000			0.0625000
$257$	19.3028	−	19.3028i	1.20407	−	1.20407i	0.231156	−	0.972917i	$-0.425749\pi$
$257$	19.3028	−	19.3028i	1.20407	−	1.20407i	0.972917	−	0.231156i	$-0.0742509\pi$
$258$	3.79514	+	22.1197i	0.236275	+	1.37711i
$259$		0			0
$260$	4.83500	−	4.83500i	0.299854	−	0.299854i
$261$	−12.6491	+	4.47214i	−0.782960	+	0.276818i
$262$	−7.32456	−	7.32456i	−0.452513	−	0.452513i
$263$	0.458991	+	0.458991i	0.0283026	+	0.0283026i	0.721116	−	0.692814i	$-0.243629\pi$
$263$	0.458991	+	0.458991i	0.0283026	+	0.0283026i	−0.692814	+	0.721116i	$0.743629\pi$
$264$	−2.82843	+	4.00000i	−0.174078	+	0.246183i
$265$	−15.0000	+	15.0000i	−0.921443	+	0.921443i
$266$		0			0
$267$	29.7541	−	5.10500i	1.82092	−	0.312421i
$268$	−1.16228	+	1.16228i	−0.0709974	+	0.0709974i
$269$	−9.67000			−0.589590			−0.294795	−	0.955560i	$-0.595251\pi$
$269$	−9.67000			−0.589590			−0.294795	+	0.955560i	$0.595251\pi$
$270$	−11.1803	−	3.16228i	−0.680414	−	0.192450i
$271$	30.9737			1.88152			0.940758	−	0.339078i	$-0.110115\pi$
$271$	30.9737			1.88152			0.940758	+	0.339078i	$0.110115\pi$
$272$	−0.821854	+	0.821854i	−0.0498322	+	0.0498322i
$273$		0			0
$274$		−	1.16228i		−	0.0702158i
$275$			14.1421i			0.852803i
$276$	−1.00000	+	1.41421i	−0.0601929	+	0.0851257i
$277$	−2.16228	−	2.16228i	−0.129919	−	0.129919i	0.639157	−	0.769076i	$-0.279283\pi$
$277$	−2.16228	−	2.16228i	−0.129919	−	0.129919i	−0.769076	+	0.639157i	$0.779283\pi$
$278$	7.30056	+	7.30056i	0.437859	+	0.437859i
$279$	−6.57484	+	2.32456i	−0.393625	+	0.139167i
$280$		0			0
$281$			24.7301i			1.47528i	0.675197	+	0.737638i	$0.264059\pi$
$281$			24.7301i			1.47528i	−0.675197	+	0.737638i	$0.735941\pi$
$282$	0.0950601	+	0.554051i	0.00566074	+	0.0329932i
$283$	8.64911	−	8.64911i	0.514136	−	0.514136i	−0.401655	−	0.915791i	$-0.631565\pi$
$283$	8.64911	−	8.64911i	0.514136	−	0.514136i	0.915791	+	0.401655i	$0.131565\pi$
$284$	5.88635			0.349291
$285$	−4.43665	+	0.761210i	−0.262805	+	0.0450902i
$286$	−8.64911			−0.511433
$287$		0			0
$288$	1.29289	−	2.70711i	0.0761845	−	0.159518i
$289$			15.6491i			0.920536i
$290$	−7.07107	−	7.07107i	−0.415227	−	0.415227i
$291$	10.3246	+	7.30056i	0.605236	+	0.427967i
$292$	−5.32456	−	5.32456i	−0.311596	−	0.311596i
$293$	−22.4940	−	22.4940i	−1.31412	−	1.31412i	−0.918352	−	0.395764i	$-0.870480\pi$
$293$	−22.4940	−	22.4940i	−1.31412	−	1.31412i	−0.395764	−	0.918352i	$-0.629520\pi$
$294$	−9.89949	−	7.00000i	−0.577350	−	0.408248i
$295$			22.1359i			1.28880i
$296$		−	1.64371i		−	0.0955386i
$297$	7.17157	+	12.8284i	0.416137	+	0.744381i
$298$	5.48683	−	5.48683i	0.317844	−	0.317844i
$299$	−3.05792			−0.176844
$300$	−1.46447	−	8.53553i	−0.0845510	−	0.492799i
$301$		0			0
$302$	7.30056	−	7.30056i	0.420100	−	0.420100i
$303$	−2.13829	−	12.4628i	−0.122841	−	0.715971i
$304$		−	1.16228i		−	0.0666612i
$305$		−	17.8885i		−	1.02430i
$306$	1.16228	+	3.28742i	0.0664430	+	0.187929i
$307$	−10.3246	−	10.3246i	−0.589253	−	0.589253i	0.348176	−	0.937429i	$-0.386801\pi$
$307$	−10.3246	−	10.3246i	−0.589253	−	0.589253i	−0.937429	+	0.348176i	$0.886801\pi$
$308$		0			0
$309$	6.84157	−	9.67544i	0.389203	−	0.550417i
$310$	−3.67544	−	3.67544i	−0.208751	−	0.208751i
$311$		−	18.1180i		−	1.02738i	−0.857976	−	0.513690i	$-0.828278\pi$
$311$		−	18.1180i		−	1.02738i	0.857976	−	0.513690i	$-0.171722\pi$
$312$	5.22020	−	0.895645i	0.295536	−	0.0507059i
$313$	−2.83772	+	2.83772i	−0.160398	+	0.160398i	−0.782743	−	0.622345i	$-0.786180\pi$
$313$	−2.83772	+	2.83772i	−0.160398	+	0.160398i	0.622345	+	0.782743i	$0.286180\pi$
$314$	−13.4164			−0.757132
$315$		0			0
$316$	3.16228			0.177892
$317$	11.5432	−	11.5432i	0.648331	−	0.648331i	−0.304259	−	0.952589i	$-0.598409\pi$
$317$	11.5432	−	11.5432i	0.648331	−	0.648331i	0.952589	+	0.304259i	$0.0984087\pi$
$318$	−16.1950	+	2.77863i	−0.908173	+	0.155818i
$319$			12.6491i			0.708214i
$320$	2.23607			0.125000
$321$	10.6491	−	15.0601i	0.594375	−	0.840574i
$322$		0			0
$323$	0.955223	+	0.955223i	0.0531500	+	0.0531500i
$324$	−5.65685	−	7.00000i	−0.314270	−	0.388889i
$325$	10.8114	−	10.8114i	0.599708	−	0.599708i
$326$		−	12.2317i		−	0.677451i
$327$	−0.490726	−	2.86016i	−0.0271372	−	0.158167i
$328$	8.32456	−	8.32456i	0.459647	−	0.459647i
$329$		0			0
$330$	−6.32456	+	8.94427i	−0.348155	+	0.492366i
$331$	−34.9737			−1.92233			−0.961163	−	0.275980i	$-0.910998\pi$
$331$	−34.9737			−1.92233			−0.961163	+	0.275980i	$0.910998\pi$
$332$	−3.05792	+	3.05792i	−0.167825	+	0.167825i
$333$	−4.44970	−	2.12514i	−0.243842	−	0.116457i
$334$			20.6491i			1.12987i
$335$	−2.59893	+	2.59893i	−0.141995	+	0.141995i
$336$		0			0
$337$	9.48683	+	9.48683i	0.516781	+	0.516781i	0.916596	−	0.399815i	$-0.130926\pi$
$337$	9.48683	+	9.48683i	0.516781	+	0.516781i	−0.399815	+	0.916596i	$0.630926\pi$
$338$	−2.58031	−	2.58031i	−0.140350	−	0.140350i
$339$	0.725728	+	0.513167i	0.0394161	+	0.0278714i
$340$	−1.83772	+	1.83772i	−0.0996645	+	0.0996645i
$341$			6.57484i			0.356047i
$342$	−3.14641	−	1.50270i	−0.170138	−	0.0812568i
$343$		0			0
$344$	−12.9574			−0.698617
$345$	−2.23607	+	3.16228i	−0.120386	+	0.170251i
$346$	12.3246			0.662572
$347$	18.8438	−	18.8438i	1.01159	−	1.01159i	0.0116543	−	0.999932i	$-0.496290\pi$
$347$	18.8438	−	18.8438i	1.01159	−	1.01159i	0.999932	−	0.0116543i	$-0.00370977\pi$
$348$	−1.30986	−	7.63441i	−0.0702158	−	0.409248i
$349$			14.0000i			0.749403i	0.927146	+	0.374701i	$0.122255\pi$
$349$			14.0000i			0.749403i	−0.927146	+	0.374701i	$0.877745\pi$
$350$		0			0
$351$	4.32456	−	15.2896i	0.230828	−	0.816099i
$352$	−2.00000	−	2.00000i	−0.106600	−	0.106600i
$353$	9.17377	+	9.17377i	0.488270	+	0.488270i	0.907760	−	0.419490i	$-0.137791\pi$
$353$	9.17377	+	9.17377i	0.488270	+	0.488270i	−0.419490	+	0.907760i	$0.637791\pi$
$354$	−9.89949	+	14.0000i	−0.526152	+	0.744092i
$355$	13.1623			0.698581
$356$			17.4296i			0.923764i
$357$		0			0
$358$	−9.32456	+	9.32456i	−0.492818	+	0.492818i
$359$	−19.7990			−1.04495			−0.522475	−	0.852654i	$-0.674991\pi$
$359$	−19.7990			−1.04495			−0.522475	+	0.852654i	$0.674991\pi$
$360$	2.89100	−	6.05327i	0.152369	−	0.319036i
$361$	17.6491			0.928901
$362$	−15.7858	+	15.7858i	−0.829686	+	0.829686i
$363$	−5.12132	+	0.878680i	−0.268800	+	0.0461187i
$364$		0			0
$365$	−11.9061	−	11.9061i	−0.623192	−	0.623192i
$366$	8.00000	−	11.3137i	0.418167	−	0.591377i
$367$	−17.4868	−	17.4868i	−0.912805	−	0.912805i	0.0836869	−	0.996492i	$-0.473330\pi$
$367$	−17.4868	−	17.4868i	−0.912805	−	0.912805i	−0.996492	+	0.0836869i	$0.973330\pi$
$368$	−0.707107	−	0.707107i	−0.0368605	−	0.0368605i
$369$	−11.7727	−	33.2982i	−0.612862	−	1.73344i
$370$		−	3.67544i		−	0.191077i
$371$		0			0
$372$	−0.680846	−	3.96826i	−0.0353002	−	0.205745i
$373$	−5.48683	+	5.48683i	−0.284097	+	0.284097i	−0.834741	−	0.550643i	$-0.814382\pi$
$373$	−5.48683	+	5.48683i	−0.284097	+	0.284097i	0.550643	+	0.834741i	$0.314382\pi$
$374$	3.28742			0.169988
$375$	−3.27465	−	19.0860i	−0.169102	−	0.985599i
$376$	−0.324555			−0.0167377
$377$	9.67000	−	9.67000i	0.498030	−	0.498030i
$378$		0			0
$379$			15.4868i			0.795505i	0.917493	+	0.397753i	$0.130210\pi$
$379$			15.4868i			0.795505i	−0.917493	+	0.397753i	$0.869790\pi$
$380$		−	2.59893i		−	0.133322i
$381$	−2.32456	−	1.64371i	−0.119091	−	0.0842098i
$382$	12.3246	+	12.3246i	0.630579	+	0.630579i
$383$	−15.7858	−	15.7858i	−0.806619	−	0.806619i	0.177502	−	0.984121i	$-0.443199\pi$
$383$	−15.7858	−	15.7858i	−0.806619	−	0.806619i	−0.984121	+	0.177502i	$0.943199\pi$
$384$	1.41421	+	1.00000i	0.0721688	+	0.0510310i
$385$		0			0
$386$			4.24264i			0.215945i
$387$	−16.7526	+	35.0771i	−0.851580	+	1.78307i
$388$	−5.16228	+	5.16228i	−0.262075	+	0.262075i
$389$	21.4427			1.08719			0.543594	−	0.839348i	$-0.317063\pi$
$389$	21.4427			1.08719			0.543594	+	0.839348i	$0.317063\pi$
$390$	11.6727	−	2.00272i	0.591071	−	0.101412i
$391$	1.16228			0.0587789
$392$	4.94975	−	4.94975i	0.250000	−	0.250000i
$393$	−3.03393	−	17.6830i	−0.153042	−	0.891991i
$394$			3.67544i			0.185166i
$395$	7.07107			0.355784
$396$	−8.00000	+	2.82843i	−0.402015	+	0.142134i
$397$	−24.8114	−	24.8114i	−1.24525	−	1.24525i	−0.957795	−	0.287453i	$-0.907191\pi$
$397$	−24.8114	−	24.8114i	−1.24525	−	1.24525i	−0.287453	−	0.957795i	$-0.592809\pi$
$398$	10.7213	+	10.7213i	0.537413	+	0.537413i
$399$		0			0
$400$	5.00000			0.250000
$401$			19.7990i			0.988714i	0.869259	+	0.494357i	$0.164597\pi$
$401$			19.7990i			0.988714i	−0.869259	+	0.494357i	$0.835403\pi$
$402$	−2.80599	+	0.481431i	−0.139950	+	0.0240116i
$403$	5.02633	−	5.02633i	0.250380	−	0.250380i
$404$	7.30056			0.363217
$405$	−12.6491	−	15.6525i	−0.628539	−	0.777778i
$406$		0			0
$407$	−3.28742	+	3.28742i	−0.162951	+	0.162951i
$408$	−1.98413	+	0.340423i	−0.0982292	+	0.0168535i
$409$		−	20.0000i		−	0.988936i	−0.869196	−	0.494468i	$-0.835363\pi$
$409$		−	20.0000i		−	0.988936i	0.869196	−	0.494468i	$-0.164637\pi$
$410$	18.6143	−	18.6143i	0.919293	−	0.919293i
$411$	1.16228	−	1.64371i	0.0573309	−	0.0810782i
$412$	4.83772	+	4.83772i	0.238337	+	0.238337i
$413$		0			0
$414$	−2.82843	+	1.00000i	−0.139010	+	0.0491473i
$415$	−6.83772	+	6.83772i	−0.335651	+	0.335651i
$416$			3.05792i			0.149927i
$417$	3.02399	+	17.6251i	0.148086	+	0.863106i
$418$	−2.32456	+	2.32456i	−0.113698	+	0.113698i
$419$	9.40326			0.459379			0.229690	−	0.973264i	$-0.426229\pi$
$419$	9.40326			0.459379			0.229690	+	0.973264i	$0.426229\pi$
$420$		0			0
$421$	36.6491			1.78617			0.893084	−	0.449890i	$-0.148537\pi$
$421$	36.6491			1.78617			0.893084	+	0.449890i	$0.148537\pi$
$422$	−1.18472	+	1.18472i	−0.0576712	+	0.0576712i
$423$	−0.419615	+	0.878606i	−0.0204024	+	0.0427193i
$424$		−	9.48683i		−	0.460721i
$425$	−4.10927	+	4.10927i	−0.199329	+	0.199329i
$426$	8.32456	+	5.88635i	0.403326	+	0.285195i
$427$		0			0
$428$	7.53006	+	7.53006i	0.363979	+	0.363979i
$429$	−12.2317	−	8.64911i	−0.590552	−	0.417583i
$430$	−28.9737			−1.39723
$431$		−	11.7727i		−	0.567071i	−0.958962	−	0.283535i	$-0.908493\pi$
$431$		−	11.7727i		−	0.567071i	0.958962	−	0.283535i	$-0.0915074\pi$
$432$	4.53553	−	2.53553i	0.218216	−	0.121991i
$433$	−28.1359	+	28.1359i	−1.35213	+	1.35213i	−0.468849	+	0.883279i	$0.655331\pi$
$433$	−28.1359	+	28.1359i	−1.35213	+	1.35213i	−0.883279	+	0.468849i	$0.844669\pi$
$434$		0			0
$435$	−2.92893	−	17.0711i	−0.140432	−	0.818495i
$436$	1.67544			0.0802392
$437$	−0.821854	+	0.821854i	−0.0393146	+	0.0393146i
$438$	−2.20550	−	12.8546i	−0.105383	−	0.614217i
$439$			36.6491i			1.74917i	0.484875	+	0.874583i	$0.338865\pi$
$439$			36.6491i			1.74917i	−0.484875	+	0.874583i	$0.661135\pi$
$440$	−4.47214	−	4.47214i	−0.213201	−	0.213201i
$441$	−7.00000	−	19.7990i	−0.333333	−	0.942809i
$442$	−2.51317	−	2.51317i	−0.119539	−	0.119539i
$443$	−11.3137	−	11.3137i	−0.537531	−	0.537531i	0.385272	−	0.922803i	$-0.374107\pi$
$443$	−11.3137	−	11.3137i	−0.537531	−	0.537531i	−0.922803	+	0.385272i	$0.874107\pi$
$444$	1.64371	−	2.32456i	0.0780070	−	0.110319i
$445$			38.9737i			1.84753i
$446$			9.67000i			0.457888i
$447$	13.2464	−	2.27272i	0.626533	−	0.107496i
$448$		0			0
$449$	5.65685			0.266963			0.133482	−	0.991051i	$-0.457384\pi$
$449$	5.65685			0.266963			0.133482	+	0.991051i	$0.457384\pi$
$450$	6.46447	−	13.5355i	0.304738	−	0.638071i
$451$	−33.2982			−1.56795
$452$	−0.362864	+	0.362864i	−0.0170677	+	0.0170677i
$453$	17.6251	−	3.02399i	0.828100	−	0.142080i
$454$			6.00000i			0.281594i
$455$		0			0
$456$	1.16228	−	1.64371i	0.0544286	−	0.0769737i
$457$	−12.8377	−	12.8377i	−0.600523	−	0.600523i	0.339928	−	0.940451i	$-0.389597\pi$
$457$	−12.8377	−	12.8377i	−0.600523	−	0.600523i	−0.940451	+	0.339928i	$0.889597\pi$
$458$	17.8885	+	17.8885i	0.835877	+	0.835877i
$459$	−1.64371	+	5.81139i	−0.0767218	+	0.271252i
$460$	−1.58114	−	1.58114i	−0.0737210	−	0.0737210i
$461$		−	12.9574i		−	0.603487i	−0.953389	−	0.301744i	$-0.902431\pi$
$461$		−	12.9574i		−	0.603487i	0.953389	−	0.301744i	$-0.0975686\pi$
$462$		0			0
$463$	18.1359	−	18.1359i	0.842849	−	0.842849i	−0.146380	−	0.989228i	$-0.546762\pi$
$463$	18.1359	−	18.1359i	0.842849	−	0.842849i	0.989228	+	0.146380i	$0.0467621\pi$
$464$	4.47214			0.207614
$465$	−1.52242	−	8.87331i	−0.0706005	−	0.411490i
$466$	4.32456			0.200331
$467$	−13.1869	+	13.1869i	−0.610218	+	0.610218i	−0.943003	−	0.332785i	$-0.892012\pi$
$467$	−13.1869	+	13.1869i	−0.610218	+	0.610218i	0.332785	+	0.943003i	$0.392012\pi$
$468$	8.27812	+	3.95357i	0.382656	+	0.182754i
$469$		0			0
$470$	−0.725728			−0.0334753
$471$	−18.9737	−	13.4164i	−0.874260	−	0.618195i
$472$	−7.00000	−	7.00000i	−0.322201	−	0.322201i
$473$	25.9148	+	25.9148i	1.19157	+	1.19157i
$474$	4.47214	+	3.16228i	0.205412	+	0.145248i
$475$		−	5.81139i		−	0.266645i
$476$		0			0
$477$	−25.6819	−	12.2655i	−1.17589	−	0.561597i
$478$	−14.4868	+	14.4868i	−0.662612	+	0.662612i
$479$	28.2843			1.29234			0.646171	−	0.763193i	$-0.276369\pi$
$479$	28.2843			1.29234			0.646171	+	0.763193i	$0.276369\pi$
$480$	3.16228	+	2.23607i	0.144338	+	0.102062i
$481$	5.02633			0.229181
$482$	3.05792	−	3.05792i	0.139285	−	0.139285i
$483$		0			0
$484$		−	3.00000i		−	0.136364i
$485$	−11.5432	+	11.5432i	−0.524150	+	0.524150i
$486$	−1.00000	−	15.5563i	−0.0453609	−	0.705650i
$487$	−16.8377	−	16.8377i	−0.762990	−	0.762990i	0.213872	−	0.976862i	$-0.431393\pi$
$487$	−16.8377	−	16.8377i	−0.762990	−	0.762990i	−0.976862	+	0.213872i	$0.931393\pi$
$488$	5.65685	+	5.65685i	0.256074	+	0.256074i
$489$	12.2317	−	17.2982i	0.553136	−	0.782253i
$490$	11.0680	−	11.0680i	0.500000	−	0.500000i
$491$		−	9.89949i		−	0.446758i	−0.974732	−	0.223379i	$-0.928291\pi$
$491$		−	9.89949i		−	0.446758i	0.974732	−	0.223379i	$-0.0717087\pi$
$492$	20.0973	−	3.44814i	0.906054	−	0.155454i
$493$	−3.67544	+	3.67544i	−0.165534	+	0.165534i
$494$	3.55415			0.159909
$495$	−17.8885	+	6.32456i	−0.804030	+	0.284268i
$496$	2.32456			0.104376
$497$		0			0
$498$	−7.38248	+	1.26663i	−0.330817	+	0.0567592i
$499$			40.6491i			1.81970i	0.414933	+	0.909852i	$0.363805\pi$
$499$			40.6491i			1.81970i	−0.414933	+	0.909852i	$0.636195\pi$
$500$	11.1803			0.500000
$501$	−20.6491	+	29.2023i	−0.922534	+	1.30466i
$502$	−4.00000	−	4.00000i	−0.178529	−	0.178529i
$503$	6.84157	+	6.84157i	0.305051	+	0.305051i	0.842986	−	0.537935i	$-0.180796\pi$
$503$	6.84157	+	6.84157i	0.305051	+	0.305051i	−0.537935	+	0.842986i	$0.680796\pi$
$504$		0			0
$505$	16.3246			0.726433
$506$			2.82843i			0.125739i
$507$	−1.06880	−	6.22942i	−0.0474671	−	0.276658i
$508$	1.16228	−	1.16228i	0.0515677	−	0.0515677i
$509$	−18.1553			−0.804719			−0.402359	−	0.915482i	$-0.631810\pi$
$509$	−18.1553			−0.804719			−0.402359	+	0.915482i	$0.631810\pi$
$510$	−4.43665	+	0.761210i	−0.196458	+	0.0337069i
$511$		0			0
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$	−2.94699	−	5.27155i	−0.130113	−	0.232745i
$514$			27.2982i			1.20407i
$515$	10.8175	+	10.8175i	0.476675	+	0.476675i
$516$	−18.3246	−	12.9574i	−0.806694	−	0.570418i
$517$	0.649111	+	0.649111i	0.0285479	+	0.0285479i
$518$		0			0
$519$	17.4296	+	12.3246i	0.765072	+	0.540988i
$520$			6.83772i			0.299854i
$521$			26.3738i			1.15546i	0.816229	+	0.577729i	$0.196061\pi$
$521$			26.3738i			1.15546i	−0.816229	+	0.577729i	$0.803939\pi$
$522$	5.78199	−	12.1065i	0.253071	−	0.529889i
$523$	29.2982	−	29.2982i	1.28112	−	1.28112i	0.341092	−	0.940030i	$-0.389203\pi$
$523$	29.2982	−	29.2982i	1.28112	−	1.28112i	0.940030	−	0.341092i	$-0.110797\pi$
$524$	10.3585			0.452513
$525$		0			0
$526$	−0.649111			−0.0283026
$527$	−1.91045	+	1.91045i	−0.0832203	+	0.0832203i
$528$	−0.828427	−	4.82843i	−0.0360527	−	0.210130i
$529$			1.00000i			0.0434783i
$530$		−	21.2132i		−	0.921443i
$531$	−28.0000	+	9.89949i	−1.21510	+	0.429601i
$532$		0			0
$533$	25.4558	+	25.4558i	1.10262	+	1.10262i
$534$	−17.4296	+	24.6491i	−0.754251	+	1.06667i
$535$	16.8377	+	16.8377i	0.727958	+	0.727958i
$536$		−	1.64371i		−	0.0709974i
$537$	−22.5115	+	3.86236i	−0.971442	+	0.166673i
$538$	6.83772	−	6.83772i	0.294795	−	0.294795i
$539$	−19.7990			−0.852803
$540$	10.1418	−	5.66963i	0.436432	−	0.243982i
$541$	13.6754			0.587953			0.293977	−	0.955813i	$-0.405021\pi$
$541$	13.6754			0.587953			0.293977	+	0.955813i	$0.405021\pi$
$542$	−21.9017	+	21.9017i	−0.940758	+	0.940758i
$543$	−38.1104	+	6.53871i	−1.63547	+	0.280603i
$544$		−	1.16228i		−	0.0498322i
$545$	3.74641			0.160478
$546$		0			0
$547$	−6.32456	−	6.32456i	−0.270418	−	0.270418i	0.558850	−	0.829269i	$-0.311243\pi$
$547$	−6.32456	−	6.32456i	−0.270418	−	0.270418i	−0.829269	+	0.558850i	$0.811243\pi$
$548$	0.821854	+	0.821854i	0.0351079	+	0.0351079i
$549$	22.6274	−	8.00000i	0.965715	−	0.341432i
$550$	−10.0000	−	10.0000i	−0.426401	−	0.426401i
$551$		−	5.19786i		−	0.221436i
$552$	−0.292893	−	1.70711i	−0.0124664	−	0.0726593i
$553$		0			0
$554$	3.05792			0.129919
$555$	3.67544	−	5.19786i	0.156014	−	0.220637i
$556$	−10.3246			−0.437859
$557$	17.5629	−	17.5629i	0.744165	−	0.744165i	−0.229212	−	0.973377i	$-0.573615\pi$
$557$	17.5629	−	17.5629i	0.744165	−	0.744165i	0.973377	+	0.229212i	$0.0736148\pi$
$558$	3.00540	−	6.29282i	0.127229	−	0.266396i
$559$		−	39.6228i		−	1.67586i
$560$		0			0
$561$	4.64911	+	3.28742i	0.196286	+	0.138795i
$562$	−17.4868	−	17.4868i	−0.737638	−	0.737638i
$563$	5.88635	+	5.88635i	0.248080	+	0.248080i	0.820182	−	0.572102i	$-0.193872\pi$
$563$	5.88635	+	5.88635i	0.248080	+	0.248080i	−0.572102	+	0.820182i	$0.693872\pi$
$564$	−0.458991	−	0.324555i	−0.0193270	−	0.0136662i
$565$	−0.811388	+	0.811388i	−0.0341354	+	0.0341354i
$566$			12.2317i			0.514136i
$567$		0			0
$568$	−4.16228	+	4.16228i	−0.174645	+	0.174645i
$569$	−10.1290			−0.424629			−0.212315	−	0.977201i	$-0.568100\pi$
$569$	−10.1290			−0.424629			−0.212315	+	0.977201i	$0.568100\pi$
$570$	2.59893	−	3.67544i	0.108857	−	0.153947i
$571$	−10.8377			−0.453545			−0.226772	−	0.973948i	$-0.572817\pi$
$571$	−10.8377			−0.453545			−0.226772	+	0.973948i	$0.572817\pi$
$572$	6.11584	−	6.11584i	0.255716	−	0.255716i
$573$	5.10500	+	29.7541i	0.213264	+	1.24300i
$574$		0			0
$575$	−3.53553	−	3.53553i	−0.147442	−	0.147442i
$576$	1.00000	+	2.82843i	0.0416667	+	0.117851i
$577$	−6.67544	−	6.67544i	−0.277902	−	0.277902i	0.554369	−	0.832271i	$-0.312960\pi$
$577$	−6.67544	−	6.67544i	−0.277902	−	0.277902i	−0.832271	+	0.554369i	$0.812960\pi$
$578$	−11.0656	−	11.0656i	−0.460268	−	0.460268i
$579$	−4.24264	+	6.00000i	−0.176318	+	0.249351i
$580$	10.0000			0.415227
$581$		0			0
$582$	−12.4628	+	2.13829i	−0.516601	+	0.0886348i
$583$	−18.9737	+	18.9737i	−0.785809	+	0.785809i
$584$	7.53006			0.311596
$585$	18.5104	+	8.84044i	0.765313	+	0.365507i
$586$	31.8114			1.31412
$587$	−7.07107	+	7.07107i	−0.291854	+	0.291854i	−0.837812	−	0.545958i	$-0.816166\pi$
$587$	−7.07107	+	7.07107i	−0.291854	+	0.291854i	0.545958	+	0.837812i	$0.316166\pi$
$588$	11.9497	−	2.05025i	0.492799	−	0.0845510i
$589$		−	2.70178i		−	0.111325i
$590$	−15.6525	−	15.6525i	−0.644402	−	0.644402i
$591$	−3.67544	+	5.19786i	−0.151188	+	0.213812i
$592$	1.16228	+	1.16228i	0.0477693	+	0.0477693i
$593$	27.7880	+	27.7880i	1.14112	+	1.14112i	0.988246	+	0.152872i	$0.0488522\pi$
$593$	27.7880	+	27.7880i	1.14112	+	1.14112i	0.152872	+	0.988246i	$0.451148\pi$
$594$	−14.1421	−	4.00000i	−0.580259	−	0.164122i
$595$		0			0
$596$			7.75955i			0.317844i
$597$	4.44093	+	25.8836i	0.181755	+	1.05935i
$598$	2.16228	−	2.16228i	0.0884221	−	0.0884221i
$599$	17.2001			0.702775			0.351388	−	0.936230i	$-0.385710\pi$
$599$	17.2001			0.702775			0.351388	+	0.936230i	$0.385710\pi$
$600$	7.07107	+	5.00000i	0.288675	+	0.204124i
$601$	−9.35089			−0.381431			−0.190715	−	0.981645i	$-0.561081\pi$
$601$	−9.35089			−0.381431			−0.190715	+	0.981645i	$0.561081\pi$
$602$		0			0
$603$	−4.44970	−	2.12514i	−0.181206	−	0.0865424i
$604$			10.3246i			0.420100i
$605$		−	6.70820i		−	0.272727i
$606$	10.3246	+	7.30056i	0.419406	+	0.296565i
$607$	7.16228	+	7.16228i	0.290708	+	0.290708i	0.837360	−	0.546652i	$-0.184098\pi$
$607$	7.16228	+	7.16228i	0.290708	+	0.290708i	−0.546652	+	0.837360i	$0.684098\pi$
$608$	0.821854	+	0.821854i	0.0333306	+	0.0333306i
$609$		0			0
$610$	12.6491	+	12.6491i	0.512148	+	0.512148i
$611$		−	0.992465i		−	0.0401508i
$612$	−3.14641	−	1.50270i	−0.127186	−	0.0607431i
$613$	30.4605	−	30.4605i	1.23029	−	1.23029i	0.266435	−	0.963853i	$-0.414154\pi$
$613$	30.4605	−	30.4605i	1.23029	−	1.23029i	0.963853	−	0.266435i	$-0.0858458\pi$
$614$	14.6011			0.589253
$615$	44.9388	−	7.71028i	1.81211	−	0.310909i
$616$		0			0
$617$	−12.1356	+	12.1356i	−0.488559	+	0.488559i	−0.907851	−	0.419292i	$-0.862278\pi$
$617$	−12.1356	+	12.1356i	−0.488559	+	0.488559i	0.419292	+	0.907851i	$0.362278\pi$
$618$	2.00385	+	11.6793i	0.0806067	+	0.469810i
$619$		−	38.4605i		−	1.54586i	−0.634493	−	0.772929i	$-0.718791\pi$
$619$		−	38.4605i		−	1.54586i	0.634493	−	0.772929i	$-0.281209\pi$
$620$	5.19786			0.208751
$621$	−5.00000	−	1.41421i	−0.200643	−	0.0567504i
$622$	12.8114	+	12.8114i	0.513690	+	0.513690i
$623$		0			0
$624$	−3.05792	+	4.32456i	−0.122415	+	0.173121i
$625$	25.0000			1.00000
$626$		−	4.01315i		−	0.160398i
$627$	−5.61197	+	0.962862i	−0.224121	+	0.0384530i
$628$	9.48683	−	9.48683i	0.378566	−	0.378566i
$629$	−1.91045			−0.0761745
$630$		0			0
$631$	3.81139			0.151729			0.0758645	−	0.997118i	$-0.475828\pi$
$631$	3.81139			0.151729			0.0758645	+	0.997118i	$0.475828\pi$
$632$	−2.23607	+	2.23607i	−0.0889460	+	0.0889460i
$633$	−2.86016	+	0.490726i	−0.113681	+	0.0195046i
$634$			16.3246i			0.648331i
$635$	2.59893	−	2.59893i	0.103135	−	0.103135i
$636$	9.48683	−	13.4164i	0.376177	−	0.531995i
$637$	15.1359	+	15.1359i	0.599708	+	0.599708i
$638$	−8.94427	−	8.94427i	−0.354107	−	0.354107i
$639$	5.88635	+	16.6491i	0.232860	+	0.658629i
$640$	−1.58114	+	1.58114i	−0.0625000	+	0.0625000i
$641$			28.7433i			1.13529i	0.823273	+	0.567645i	$0.192145\pi$
$641$			28.7433i			1.13529i	−0.823273	+	0.567645i	$0.807855\pi$
$642$	3.11905	+	18.1792i	0.123099	+	0.717475i
$643$	1.16228	−	1.16228i	0.0458358	−	0.0458358i	−0.683817	−	0.729653i	$-0.739682\pi$
$643$	1.16228	−	1.16228i	0.0458358	−	0.0458358i	0.729653	+	0.683817i	$0.239682\pi$
$644$		0			0
$645$	−40.9750	−	28.9737i	−1.61339	−	1.14084i
$646$	−1.35089			−0.0531500
$647$	−28.5138	+	28.5138i	−1.12099	+	1.12099i	−0.129399	+	0.991593i	$0.541305\pi$
$647$	−28.5138	+	28.5138i	−1.12099	+	1.12099i	−0.991593	+	0.129399i	$0.958695\pi$
$648$	8.94975	+	0.949747i	0.351579	+	0.0373096i
$649$			28.0000i			1.09910i
$650$			15.2896i			0.599708i
$651$		0			0
$652$	8.64911	+	8.64911i	0.338725	+	0.338725i
$653$	9.17377	+	9.17377i	0.358997	+	0.358997i	0.863443	−	0.504446i	$-0.168303\pi$
$653$	9.17377	+	9.17377i	0.358997	+	0.358997i	−0.504446	+	0.863443i	$0.668303\pi$
$654$	2.36944	+	1.67544i	0.0926523	+	0.0655151i
$655$	23.1623			0.905025
$656$			11.7727i			0.459647i
$657$	9.73556	−	20.3847i	0.379820	−	0.795282i
$658$		0			0
$659$	−8.94427			−0.348419			−0.174210	−	0.984709i	$-0.555737\pi$
$659$	−8.94427			−0.348419			−0.174210	+	0.984709i	$0.555737\pi$
$660$	−1.85242	−	10.7967i	−0.0721053	−	0.420261i
$661$	−7.35089			−0.285916			−0.142958	−	0.989729i	$-0.545661\pi$
$661$	−7.35089			−0.285916			−0.142958	+	0.989729i	$0.545661\pi$
$662$	24.7301	−	24.7301i	0.961163	−	0.961163i
$663$	−1.04099	−	6.06732i	−0.0404286	−	0.235635i
$664$		−	4.32456i		−	0.167825i
$665$		0			0
$666$	4.64911	−	1.64371i	0.180149	−	0.0636924i
$667$	−3.16228	−	3.16228i	−0.122444	−	0.122444i
$668$	−14.6011	−	14.6011i	−0.564935	−	0.564935i
$669$	−9.67000	+	13.6754i	−0.373864	+	0.528723i
$670$		−	3.67544i		−	0.141995i
$671$		−	22.6274i		−	0.873522i
$672$		0			0
$673$	18.6754	−	18.6754i	0.719885	−	0.719885i	−0.248696	−	0.968582i	$-0.580002\pi$
$673$	18.6754	−	18.6754i	0.719885	−	0.719885i	0.968582	+	0.248696i	$0.0800020\pi$
$674$	−13.4164			−0.516781
$675$	22.6777	−	12.6777i	0.872864	−	0.487964i
$676$	3.64911			0.140350
$677$	−14.4678	+	14.4678i	−0.556041	+	0.556041i	−0.928178	−	0.372137i	$-0.878625\pi$
$677$	−14.4678	+	14.4678i	−0.556041	+	0.556041i	0.372137	+	0.928178i	$0.378625\pi$
$678$	−0.876031	+	0.150303i	−0.0336438	+	0.00577236i
$679$		0			0
$680$		−	2.59893i		−	0.0996645i
$681$	−6.00000	+	8.48528i	−0.229920	+	0.325157i
$682$	−4.64911	−	4.64911i	−0.178024	−	0.178024i
$683$	22.5902	+	22.5902i	0.864389	+	0.864389i	0.991844	−	0.127455i	$-0.0406809\pi$
$683$	22.5902	+	22.5902i	0.864389	+	0.864389i	−0.127455	+	0.991844i	$0.540681\pi$
$684$	3.28742	−	1.16228i	0.125698	−	0.0444408i
$685$	1.83772	+	1.83772i	0.0702158	+	0.0702158i
$686$		0			0
$687$	7.40968	+	43.1868i	0.282697	+	1.64768i
$688$	9.16228	−	9.16228i	0.349309	−	0.349309i
$689$	29.0100			1.10519
$690$	−0.654929	−	3.81721i	−0.0249327	−	0.145319i
$691$	12.6491			0.481195			0.240597	−	0.970625i	$-0.422657\pi$
$691$	12.6491			0.481195			0.240597	+	0.970625i	$0.422657\pi$
$692$	−8.71478	+	8.71478i	−0.331286	+	0.331286i
$693$		0			0
$694$			26.6491i			1.01159i
$695$	−23.0864			−0.875717
$696$	6.32456	+	4.47214i	0.239732	+	0.169516i
$697$	−9.67544	−	9.67544i	−0.366484	−	0.366484i
$698$	−9.89949	−	9.89949i	−0.374701	−	0.374701i
$699$	6.11584	+	4.32456i	0.231322	+	0.163570i
$700$		0			0
$701$			8.02629i			0.303149i	0.988446	+	0.151574i	$0.0484343\pi$
$701$			8.02629i			0.303149i	−0.988446	+	0.151574i	$0.951566\pi$
$702$	7.75347	+	13.8693i	0.292636	+	0.523463i
$703$	1.35089	−	1.35089i	0.0509498	−	0.0509498i
$704$	2.82843			0.106600
$705$	−1.02633	−	0.725728i	−0.0386540	−	0.0273325i
$706$	−12.9737			−0.488270
$707$		0			0
$708$	−2.89949	−	16.8995i	−0.108970	−	0.635122i
$709$			49.9473i			1.87581i	0.346890	+	0.937906i	$0.387238\pi$
$709$			49.9473i			1.87581i	−0.346890	+	0.937906i	$0.612762\pi$
$710$	−9.30714	+	9.30714i	−0.349291	+	0.349291i
$711$	3.16228	+	8.94427i	0.118595	+	0.335436i
$712$	−12.3246	−	12.3246i	−0.461882	−	0.461882i
$713$	−1.64371	−	1.64371i	−0.0615574	−	0.0615574i
$714$		0			0
$715$	13.6754	−	13.6754i	0.511433	−	0.511433i
$716$		−	13.1869i		−	0.492818i
$717$	−34.9743	+	6.00064i	−1.30614	+	0.224098i
$718$	14.0000	−	14.0000i	0.522475	−	0.522475i
$719$	−50.1487			−1.87023			−0.935116	−	0.354342i	$-0.884705\pi$
$719$	−50.1487			−1.87023			−0.935116	+	0.354342i	$0.884705\pi$
$720$	2.23607	+	6.32456i	0.0833333	+	0.235702i
$721$		0			0
$722$	−12.4798	+	12.4798i	−0.464450	+	0.464450i
$723$	7.38248	−	1.26663i	0.274557	−	0.0471066i
$724$		−	22.3246i		−	0.829686i
$725$	22.3607			0.830455
$726$	3.00000	−	4.24264i	0.111340	−	0.157459i
$727$	26.3246	+	26.3246i	0.976324	+	0.976324i	0.999726	−	0.0234024i	$-0.00744990\pi$
$727$	26.3246	+	26.3246i	0.976324	+	0.976324i	−0.0234024	+	0.999726i	$0.507450\pi$
$728$		0			0
$729$	14.1421	−	23.0000i	0.523783	−	0.851852i
$730$	16.8377			0.623192
$731$			15.0601i			0.557019i
$732$	2.34315	+	13.6569i	0.0866052	+	0.504772i
$733$	−2.18861	+	2.18861i	−0.0808382	+	0.0808382i	−0.746370	−	0.665532i	$-0.768205\pi$
$733$	−2.18861	+	2.18861i	−0.0808382	+	0.0808382i	0.665532	+	0.746370i	$0.268205\pi$
$734$	24.7301			0.912805
$735$	26.7204	−	4.58450i	0.985599	−	0.169102i
$736$	1.00000			0.0368605
$737$	−3.28742	+	3.28742i	−0.121094	+	0.121094i
$738$	31.8700	+	15.2208i	1.17315	+	0.560287i
$739$		−	36.2719i		−	1.33428i	−0.744931	−	0.667141i	$-0.767518\pi$
$739$		−	36.2719i		−	1.33428i	0.744931	−	0.667141i	$-0.232482\pi$
$740$	2.59893	+	2.59893i	0.0955386	+	0.0955386i
$741$	5.02633	+	3.55415i	0.184647	+	0.130565i
$742$		0			0
$743$	−10.5880	−	10.5880i	−0.388435	−	0.388435i	0.485694	−	0.874129i	$-0.338567\pi$
$743$	−10.5880	−	10.5880i	−0.388435	−	0.388435i	−0.874129	+	0.485694i	$0.838567\pi$
$744$	3.28742	+	2.32456i	0.120523	+	0.0852223i
$745$			17.3509i			0.635687i
$746$		−	7.75955i		−	0.284097i
$747$	−11.7070	−	5.59119i	−0.428338	−	0.204571i
$748$	−2.32456	+	2.32456i	−0.0849942	+	0.0849942i
$749$		0			0
$750$	15.8114	+	11.1803i	0.577350	+	0.408248i
$751$	28.4605			1.03854			0.519269	−	0.854611i	$-0.326204\pi$
$751$	28.4605			1.03854			0.519269	+	0.854611i	$0.326204\pi$
$752$	0.229495	−	0.229495i	0.00836883	−	0.00836883i
$753$	−1.65685	−	9.65685i	−0.0603791	−	0.351915i
$754$			13.6754i			0.498030i
$755$			23.0864i			0.840200i
$756$		0			0
$757$	−9.48683	−	9.48683i	−0.344805	−	0.344805i	0.513365	−	0.858170i	$-0.328399\pi$
$757$	−9.48683	−	9.48683i	−0.344805	−	0.344805i	−0.858170	+	0.513365i	$0.828399\pi$
$758$	−10.9508	−	10.9508i	−0.397753	−	0.397753i
$759$	−2.82843	+	4.00000i	−0.102665	+	0.145191i
$760$	1.83772	+	1.83772i	0.0666612	+	0.0666612i
$761$		−	32.4897i		−	1.17775i	−0.808224	−	0.588875i	$-0.799571\pi$
$761$		−	32.4897i		−	1.17775i	0.808224	−	0.588875i	$-0.200429\pi$
$762$	2.80599	−	0.481431i	0.101650	−	0.0174404i
$763$		0			0
$764$	−17.4296			−0.630579
$765$	−7.03559	−	3.36014i	−0.254372	−	0.121486i
$766$	22.3246			0.806619
$767$	21.4055	−	21.4055i	0.772906	−	0.772906i
$768$	−1.70711	+	0.292893i	−0.0615999	+	0.0105689i
$769$			16.3246i			0.588679i	0.955701	+	0.294339i	$0.0950996\pi$
$769$			16.3246i			0.588679i	−0.955701	+	0.294339i	$0.904900\pi$
$770$		0			0
$771$	−27.2982	+	38.6055i	−0.983121	+	1.39034i
$772$	−3.00000	−	3.00000i	−0.107972	−	0.107972i
$773$	−22.0351	−	22.0351i	−0.792546	−	0.792546i	0.189361	−	0.981907i	$-0.439358\pi$
$773$	−22.0351	−	22.0351i	−0.792546	−	0.792546i	−0.981907	+	0.189361i	$0.939358\pi$
$774$	−12.9574	−	36.6491i	−0.465745	−	1.31733i
$775$	11.6228			0.417502
$776$		−	7.30056i		−	0.262075i
$777$		0			0
$778$	−15.1623	+	15.1623i	−0.543594	+	0.543594i
$779$	13.6831			0.490250
$780$	−6.83772	+	9.67000i	−0.244830	+	0.346242i
$781$	16.6491			0.595752
$782$	−0.821854	+	0.821854i	−0.0293895	+	0.0293895i
$783$	20.2835	−	11.3393i	0.724874	−	0.405232i
$784$			7.00000i			0.250000i
$785$	21.2132	−	21.2132i	0.757132	−	0.757132i
$786$	14.6491	+	10.3585i	0.522516	+	0.369475i
$787$	−36.1359	−	36.1359i	−1.28811	−	1.28811i	−0.935935	−	0.352172i	$-0.885443\pi$
$787$	−36.1359	−	36.1359i	−1.28811	−	1.28811i	−0.352172	−	0.935935i	$-0.614557\pi$
$788$	−2.59893	−	2.59893i	−0.0925831	−	0.0925831i
$789$	−0.917981	−	0.649111i	−0.0326810	−	0.0231090i
$790$	−5.00000	+	5.00000i	−0.177892	+	0.177892i
$791$		0			0
$792$	3.65685	−	7.65685i	0.129941	−	0.272074i
$793$	−17.2982	+	17.2982i	−0.614278	+	0.614278i
$794$	35.0886			1.24525
$795$	21.2132	−	30.0000i	0.752355	−	1.06399i
$796$	−15.1623			−0.537413
$797$	16.3782	−	16.3782i	0.580146	−	0.580146i	−0.354797	−	0.934943i	$-0.615450\pi$
$797$	16.3782	−	16.3782i	0.580146	−	0.580146i	0.934943	+	0.354797i	$0.115450\pi$
$798$		0			0
$799$			0.377223i			0.0133452i
$800$	−3.53553	+	3.53553i	−0.125000	+	0.125000i
$801$	−49.2982	+	17.4296i	−1.74187	+	0.615843i
$802$	−14.0000	−	14.0000i	−0.494357	−	0.494357i
$803$	−15.0601	−	15.0601i	−0.531460	−	0.531460i
$804$	1.64371	−	2.32456i	0.0579691	−	0.0819807i
$805$		0			0
$806$			7.10831i			0.250380i
$807$	16.5077	−	2.83228i	0.581099	−	0.0997009i
$808$	−5.16228	+	5.16228i	−0.181608	+	0.181608i
$809$	−22.1684			−0.779400			−0.389700	−	0.920942i	$-0.627421\pi$
$809$	−22.1684			−0.779400			−0.389700	+	0.920942i	$0.627421\pi$
$810$	20.0122	+	2.12370i	0.703159	+	0.0746192i
$811$	−52.6491			−1.84876			−0.924380	−	0.381473i	$-0.875417\pi$
$811$	−52.6491			−1.84876			−0.924380	+	0.381473i	$0.875417\pi$
$812$		0			0
$813$	−52.8754	+	9.07198i	−1.85442	+	0.318168i
$814$		−	4.64911i		−	0.162951i
$815$	19.3400	+	19.3400i	0.677451	+	0.677451i
$816$	1.16228	−	1.64371i	0.0406879	−	0.0575413i
$817$	−10.6491	−	10.6491i	−0.372565	−	0.372565i
$818$	14.1421	+	14.1421i	0.494468	+	0.494468i
$819$		0			0
$820$			26.3246i			0.919293i
$821$			44.9881i			1.57010i	0.619435	+	0.785048i	$0.287362\pi$
$821$			44.9881i			1.57010i	−0.619435	+	0.785048i	$0.712638\pi$
$822$	0.340423	+	1.98413i	0.0118736	+	0.0692046i
$823$	−0.188612	+	0.188612i	−0.00657459	+	0.00657459i	−0.710386	−	0.703812i	$-0.751480\pi$
$823$	−0.188612	+	0.188612i	−0.00657459	+	0.00657459i	0.703812	+	0.710386i	$0.251480\pi$
$824$	−6.84157			−0.238337
$825$	−4.14214	−	24.1421i	−0.144211	−	0.840521i
$826$		0			0
$827$	−30.1575	+	30.1575i	−1.04868	+	1.04868i	−0.0499252	+	0.998753i	$0.515898\pi$
$827$	−30.1575	+	30.1575i	−1.04868	+	1.04868i	−0.998753	+	0.0499252i	$0.984102\pi$
$828$	1.29289	−	2.70711i	0.0449311	−	0.0940785i
$829$		−	42.3246i		−	1.46999i	−0.678071	−	0.734996i	$-0.737184\pi$
$829$		−	42.3246i		−	1.46999i	0.678071	−	0.734996i	$-0.262816\pi$
$830$		−	9.67000i		−	0.335651i
$831$	4.32456	+	3.05792i	0.150017	+	0.106078i
$832$	−2.16228	−	2.16228i	−0.0749635	−	0.0749635i
$833$	−5.75298	−	5.75298i	−0.199329	−	0.199329i
$834$	−14.6011	−	10.3246i	−0.505596	−	0.357510i
$835$	−32.6491	−	32.6491i	−1.12987	−	1.12987i
$836$		−	3.28742i		−	0.113698i
$837$	10.5431	−	5.89399i	0.364423	−	0.203726i
$838$	−6.64911	+	6.64911i	−0.229690	+	0.229690i
$839$	20.7170			0.715229			0.357615	−	0.933869i	$-0.383590\pi$
$839$	20.7170			0.715229			0.357615	+	0.933869i	$0.383590\pi$
$840$		0			0
$841$	−9.00000			−0.310345
$842$	−25.9148	+	25.9148i	−0.893084	+	0.893084i
$843$	−7.24328	−	42.2169i	−0.249472	−	1.45403i
$844$		−	1.67544i		−	0.0576712i
$845$	8.15966			0.280701
$846$	−0.324555	−	0.917981i	−0.0111584	−	0.0315608i
$847$		0			0
$848$	6.70820	+	6.70820i	0.230361	+	0.230361i
$849$	−12.2317	+	17.2982i	−0.419790	+	0.593673i
$850$		−	5.81139i		−	0.199329i
$851$		−	1.64371i		−	0.0563456i
$852$	−10.0486	+	1.72407i	−0.344260	+	0.0590657i
$853$	24.1623	−	24.1623i	0.827301	−	0.827301i	−0.159842	−	0.987143i	$-0.551098\pi$
$853$	24.1623	−	24.1623i	0.827301	−	0.827301i	0.987143	+	0.159842i	$0.0510985\pi$
$854$		0			0
$855$	7.35089	−	2.59893i	0.251395	−	0.0888816i
$856$	−10.6491			−0.363979
$857$	7.07107	−	7.07107i	0.241543	−	0.241543i	−0.575945	−	0.817488i	$-0.695366\pi$
$857$	7.07107	−	7.07107i	0.241543	−	0.241543i	0.817488	+	0.575945i	$0.195366\pi$
$858$	14.7650	−	2.53327i	0.504067	−	0.0864843i
$859$		−	30.3246i		−	1.03466i	−0.855786	−	0.517330i	$-0.826926\pi$
$859$		−	30.3246i		−	1.03466i	0.855786	−	0.517330i	$-0.173074\pi$
$860$	20.4875	−	20.4875i	0.698617	−	0.698617i
$861$		0			0
$862$	8.32456	+	8.32456i	0.283535	+	0.283535i
$863$	11.3137	+	11.3137i	0.385123	+	0.385123i	0.872944	−	0.487821i	$-0.162208\pi$
$863$	11.3137	+	11.3137i	0.385123	+	0.385123i	−0.487821	+	0.872944i	$0.662208\pi$
$864$	−1.41421	+	5.00000i	−0.0481125	+	0.170103i
$865$	−19.4868	+	19.4868i	−0.662572	+	0.662572i
$866$		−	39.7902i		−	1.35213i
$867$	−4.58352	−	26.7147i	−0.155664	−	0.907279i
$868$		0			0
$869$	8.94427			0.303414
$870$	14.1421	+	10.0000i	0.479463	+	0.339032i
$871$	5.02633			0.170311
$872$	−1.18472	+	1.18472i	−0.0401196	+	0.0401196i
$873$	−19.7634	−	9.43885i	−0.668890	−	0.319457i
$874$		−	1.16228i		−	0.0393146i
$875$		0			0
$876$	10.6491	+	7.53006i	0.359800	+	0.254417i
$877$	−0.811388	−	0.811388i	−0.0273986	−	0.0273986i	0.693275	−	0.720673i	$-0.256167\pi$
$877$	−0.811388	−	0.811388i	−0.0273986	−	0.0273986i	−0.720673	+	0.693275i	$0.756167\pi$
$878$	−25.9148	−	25.9148i	−0.874583	−	0.874583i
$879$	44.9881	+	31.8114i	1.51741	+	1.07297i
$880$	6.32456			0.213201
$881$		−	45.9061i		−	1.54662i	−0.634031	−	0.773308i	$-0.718601\pi$
$881$		−	45.9061i		−	1.54662i	0.634031	−	0.773308i	$-0.281399\pi$
$882$	18.9497	+	9.05025i	0.638071	+	0.304738i
$883$	−9.67544	+	9.67544i	−0.325605	+	0.325605i	−0.850912	−	0.525308i	$-0.823950\pi$
$883$	−9.67544	+	9.67544i	−0.325605	+	0.325605i	0.525308	+	0.850912i	$0.323950\pi$
$884$	3.55415			0.119539
$885$	−6.48347	−	37.7884i	−0.217939	−	1.27024i
$886$	16.0000			0.537531
$887$	−31.5717	+	31.5717i	−1.06007	+	1.06007i	−0.0619972	+	0.998076i	$0.519747\pi$
$887$	−31.5717	+	31.5717i	−1.06007	+	1.06007i	−0.998076	+	0.0619972i	$0.980253\pi$
$888$	0.481431	+	2.80599i	0.0161558	+	0.0941627i
$889$		0			0
$890$	−27.5585	−	27.5585i	−0.923764	−	0.923764i
$891$	−16.0000	−	19.7990i	−0.536020	−	0.663291i
$892$	−6.83772	−	6.83772i	−0.228944	−	0.228944i
$893$	−0.266737	−	0.266737i	−0.00892602	−	0.00892602i
$894$	−7.75955	+	10.9737i	−0.259518	+	0.367014i
$895$		−	29.4868i		−	0.985636i
$896$		0			0
$897$	5.22020	−	0.895645i	0.174297	−	0.0299047i
$898$	−4.00000	+	4.00000i	−0.133482	+	0.133482i
$899$	10.3957			0.346717
$900$	5.00000	+	14.1421i	0.166667	+	0.471405i
$901$	−11.0263			−0.367340
$902$	23.5454	−	23.5454i	0.783976	−	0.783976i
$903$		0			0
$904$		−	0.513167i		−	0.0170677i
$905$		−	49.9192i		−	1.65937i
$906$	−10.3246	+	14.6011i	−0.343010	+	0.485090i
$907$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$907$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$908$	−4.24264	−	4.24264i	−0.140797	−	0.140797i
$909$	7.30056	+	20.6491i	0.242144	+	0.684888i
$910$		0			0
$911$			14.6011i			0.483757i	0.970307	+	0.241878i	$0.0777635\pi$
$911$			14.6011i			0.483757i	−0.970307	+	0.241878i	$0.922236\pi$
$912$	0.340423	+	1.98413i	0.0112725	+	0.0657012i
$913$	−8.64911	+	8.64911i	−0.286244	+	0.286244i
$914$	18.1553			0.600523
$915$	5.23943	+	30.5377i	0.173210	+	1.00954i
$916$	−25.2982			−0.835877
$917$		0			0
$918$	−2.94699	−	5.27155i	−0.0972653	−	0.173987i
$919$		−	26.1359i		−	0.862145i	−0.902317	−	0.431073i	$-0.858135\pi$
$919$		−	26.1359i		−	0.862145i	0.902317	−	0.431073i	$-0.141865\pi$
$920$	2.23607			0.0737210
$921$	20.6491	+	14.6011i	0.680411	+	0.481123i
$922$	9.16228	+	9.16228i	0.301744	+	0.301744i
$923$	−12.7279	−	12.7279i	−0.418945	−	0.418945i
$924$		0			0
$925$	5.81139	+	5.81139i	0.191077	+	0.191077i
$926$			25.6481i			0.842849i
$927$	−8.84542	+	18.5209i	−0.290522	+	0.608305i
$928$	−3.16228	+	3.16228i	−0.103807	+	0.103807i
$929$	20.2580			0.664643			0.332321	−	0.943166i	$-0.392168\pi$
$929$	20.2580			0.664643			0.332321	+	0.943166i	$0.392168\pi$
$930$	7.35089	+	5.19786i	0.241045	+	0.170445i
$931$	8.13594			0.266645
$932$	−3.05792	+	3.05792i	−0.100166	+	0.100166i
$933$	5.30665	+	30.9294i	0.173732	+	1.01258i
$934$		−	18.6491i		−	0.610218i
$935$	−5.19786	+	5.19786i	−0.169988	+	0.169988i
$936$	−8.64911	+	3.05792i	−0.282705	+	0.0999513i
$937$	−1.81139	−	1.81139i	−0.0591755	−	0.0591755i	0.676900	−	0.736075i	$-0.263323\pi$
$937$	−1.81139	−	1.81139i	−0.0591755	−	0.0591755i	−0.736075	+	0.676900i	$0.763323\pi$
$938$		0			0
$939$	4.01315	−	5.67544i	0.130964	−	0.185211i
$940$	0.513167	−	0.513167i	0.0167377	−	0.0167377i
$941$		−	56.3018i		−	1.83539i	−0.397290	−	0.917693i	$-0.630049\pi$
$941$		−	56.3018i		−	1.83539i	0.397290	−	0.917693i	$-0.369951\pi$
$942$	22.9032	−	3.92957i	0.746228	−	0.128032i
$943$	8.32456	−	8.32456i	0.271085	−	0.271085i
$944$	9.89949			0.322201
$945$		0			0
$946$	−36.6491			−1.19157
$947$	−35.3181	+	35.3181i	−1.14768	+	1.14768i	−0.160677	+	0.987007i	$0.551368\pi$
$947$	−35.3181	+	35.3181i	−1.14768	+	1.14768i	−0.987007	+	0.160677i	$0.948632\pi$
$948$	−5.39835	+	0.926210i	−0.175330	+	0.0300819i
$949$			23.0263i			0.747466i
$950$	4.10927	+	4.10927i	0.133322	+	0.133322i
$951$	−16.3246	+	23.0864i	−0.529360	+	0.748628i
$952$		0			0
$953$	−41.7968	−	41.7968i	−1.35393	−	1.35393i	−0.881214	−	0.472717i	$-0.843273\pi$
$953$	−41.7968	−	41.7968i	−1.35393	−	1.35393i	−0.472717	−	0.881214i	$-0.656727\pi$
$954$	26.8328	−	9.48683i	0.868744	−	0.307148i
$955$	−38.9737			−1.26116
$956$		−	20.4875i		−	0.662612i
$957$	−3.70484	−	21.5934i	−0.119760	−	0.698015i
$958$	−20.0000	+	20.0000i	−0.646171	+	0.646171i
$959$		0			0
$960$	−3.81721	+	0.654929i	−0.123200	+	0.0211377i
$961$	−25.5964			−0.825692
$962$	−3.55415	+	3.55415i	−0.114591	+	0.114591i
$963$	−13.7682	+	28.8283i	−0.443673	+	0.928978i
$964$			4.32456i			0.139285i
$965$	−6.70820	−	6.70820i	−0.215945	−	0.215945i
$966$		0			0
$967$	28.8377	+	28.8377i	0.927359	+	0.927359i	0.997535	−	0.0701760i	$-0.0223561\pi$
$967$	28.8377	+	28.8377i	0.927359	+	0.927359i	−0.0701760	+	0.997535i	$0.522356\pi$
$968$	2.12132	+	2.12132i	0.0681818	+	0.0681818i
$969$	−1.91045	−	1.35089i	−0.0613724	−	0.0433968i
$970$		−	16.3246i		−	0.524150i
$971$		−	7.03383i		−	0.225726i	−0.993611	−	0.112863i	$-0.963998\pi$
$971$		−	7.03383i		−	0.225726i	0.993611	−	0.112863i	$-0.0360022\pi$
$972$	11.7071	+	10.2929i	0.375506	+	0.330145i
$973$		0			0
$974$	23.8121			0.762990
$975$	−15.2896	+	21.6228i	−0.489659	+	0.692483i
$976$	−8.00000			−0.256074
$977$	8.58141	−	8.58141i	0.274544	−	0.274544i	−0.556383	−	0.830926i	$-0.687811\pi$
$977$	8.58141	−	8.58141i	0.274544	−	0.274544i	0.830926	+	0.556383i	$0.187811\pi$
$978$	3.58258	+	20.8808i	0.114558	+	0.667694i
$979$			49.2982i			1.57558i
$980$			15.6525i			0.500000i
$981$	1.67544	+	4.73887i	0.0534928	+	0.151301i
$982$	7.00000	+	7.00000i	0.223379	+	0.223379i
$983$	−14.1421	−	14.1421i	−0.451064	−	0.451064i	0.444644	−	0.895708i	$-0.353330\pi$
$983$	−14.1421	−	14.1421i	−0.451064	−	0.451064i	−0.895708	+	0.444644i	$0.853330\pi$
$984$	−11.7727	+	16.6491i	−0.375300	+	0.530754i
$985$	−5.81139	−	5.81139i	−0.185166	−	0.185166i
$986$		−	5.19786i		−	0.165534i
$987$		0			0
$988$	−2.51317	+	2.51317i	−0.0799545	+	0.0799545i
$989$	−12.9574			−0.412022
$990$	8.17697	−	17.1212i	0.259881	−	0.544149i
$991$	−25.2982			−0.803624			−0.401812	−	0.915722i	$-0.631620\pi$
$991$	−25.2982			−0.803624			−0.401812	+	0.915722i	$0.631620\pi$
$992$	−1.64371	+	1.64371i	−0.0521878	+	0.0521878i
$993$	59.7038	−	10.2435i	1.89464	−	0.325069i
$994$		0			0
$995$	−33.9039			−1.07483
$996$	4.32456	−	6.11584i	0.137029	−	0.193788i
$997$	37.4605	+	37.4605i	1.18639	+	1.18639i	0.978059	+	0.208327i	$0.0668017\pi$
$997$	37.4605	+	37.4605i	1.18639	+	1.18639i	0.208327	+	0.978059i	$0.433198\pi$
$998$	−28.7433	−	28.7433i	−0.909852	−	0.909852i
$999$	8.21854	+	2.32456i	0.260023	+	0.0735457i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	690.2.i.d.47.1	✓	8
3.2	odd	2	inner	690.2.i.d.47.4	yes	8
5.3	odd	4	inner	690.2.i.d.323.3	yes	8
15.8	even	4	inner	690.2.i.d.323.2	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.2.i.d.47.1	✓	8	1.1	even	1	trivial
690.2.i.d.47.4	yes	8	3.2	odd	2	inner
690.2.i.d.323.2	yes	8	15.8	even	4	inner
690.2.i.d.323.3	yes	8	5.3	odd	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	690.i (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 + 0.707107i) q^{2} +(-1.70711 + 0.292893i) q^{3} -1.00000i q^{4} -2.23607i q^{5} +(1.00000 - 1.41421i) q^{6} +(0.707107 + 0.707107i) q^{8} +(2.82843 - 1.00000i) q^{9} +O(q^{10})\)	\(q+(-0.707107 + 0.707107i) q^{2} +(-1.70711 + 0.292893i) q^{3} -1.00000i q^{4} -2.23607i q^{5} +(1.00000 - 1.41421i) q^{6} +(0.707107 + 0.707107i) q^{8} +(2.82843 - 1.00000i) q^{9} +(1.58114 + 1.58114i) q^{10} -2.82843i q^{11} +(0.292893 + 1.70711i) q^{12} +(-2.16228 + 2.16228i) q^{13} +(0.654929 + 3.81721i) q^{15} -1.00000 q^{16} +(0.821854 - 0.821854i) q^{17} +(-1.29289 + 2.70711i) q^{18} +1.16228i q^{19} -2.23607 q^{20} +(2.00000 + 2.00000i) q^{22} +(0.707107 + 0.707107i) q^{23} +(-1.41421 - 1.00000i) q^{24} -5.00000 q^{25} -3.05792i q^{26} +(-4.53553 + 2.53553i) q^{27} -4.47214 q^{29} +(-3.16228 - 2.23607i) q^{30} -2.32456 q^{31} +(0.707107 - 0.707107i) q^{32} +(0.828427 + 4.82843i) q^{33} +1.16228i q^{34} +(-1.00000 - 2.82843i) q^{36} +(-1.16228 - 1.16228i) q^{37} +(-0.821854 - 0.821854i) q^{38} +(3.05792 - 4.32456i) q^{39} +(1.58114 - 1.58114i) q^{40} -11.7727i q^{41} +(-9.16228 + 9.16228i) q^{43} -2.82843 q^{44} +(-2.23607 - 6.32456i) q^{45} -1.00000 q^{46} +(-0.229495 + 0.229495i) q^{47} +(1.70711 - 0.292893i) q^{48} -7.00000i q^{49} +(3.53553 - 3.53553i) q^{50} +(-1.16228 + 1.64371i) q^{51} +(2.16228 + 2.16228i) q^{52} +(-6.70820 - 6.70820i) q^{53} +(1.41421 - 5.00000i) q^{54} -6.32456 q^{55} +(-0.340423 - 1.98413i) q^{57} +(3.16228 - 3.16228i) q^{58} -9.89949 q^{59} +(3.81721 - 0.654929i) q^{60} +8.00000 q^{61} +(1.64371 - 1.64371i) q^{62} +1.00000i q^{64} +(4.83500 + 4.83500i) q^{65} +(-4.00000 - 2.82843i) q^{66} +(-1.16228 - 1.16228i) q^{67} +(-0.821854 - 0.821854i) q^{68} +(-1.41421 - 1.00000i) q^{69} +5.88635i q^{71} +(2.70711 + 1.29289i) q^{72} +(5.32456 - 5.32456i) q^{73} +1.64371 q^{74} +(8.53553 - 1.46447i) q^{75} +1.16228 q^{76} +(0.895645 + 5.22020i) q^{78} +3.16228i q^{79} +2.23607i q^{80} +(7.00000 - 5.65685i) q^{81} +(8.32456 + 8.32456i) q^{82} +(-3.05792 - 3.05792i) q^{83} +(-1.83772 - 1.83772i) q^{85} -12.9574i q^{86} +(7.63441 - 1.30986i) q^{87} +(2.00000 - 2.00000i) q^{88} -17.4296 q^{89} +(6.05327 + 2.89100i) q^{90} +(0.707107 - 0.707107i) q^{92} +(3.96826 - 0.680846i) q^{93} -0.324555i q^{94} +2.59893 q^{95} +(-1.00000 + 1.41421i) q^{96} +(-5.16228 - 5.16228i) q^{97} +(4.94975 + 4.94975i) q^{98} +(-2.82843 - 8.00000i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{3} + 8 q^{6}+O(q^{10}) \) 8 * q - 8 * q^3 + 8 * q^6	\( 8 q - 8 q^{3} + 8 q^{6} + 8 q^{12} + 8 q^{13} - 8 q^{16} - 16 q^{18} + 16 q^{22} - 40 q^{25} - 8 q^{27} + 32 q^{31} - 16 q^{33} - 8 q^{36} + 16 q^{37} - 48 q^{43} - 8 q^{46} + 8 q^{48} + 16 q^{51} - 8 q^{52} + 16 q^{57} + 64 q^{61} - 32 q^{66} + 16 q^{67} + 16 q^{72} - 8 q^{73} + 40 q^{75} - 16 q^{76} + 8 q^{78} + 56 q^{81} + 16 q^{82} - 40 q^{85} + 16 q^{88} - 32 q^{93} - 8 q^{96} - 16 q^{97}+O(q^{100}) \) 8 * q - 8 * q^3 + 8 * q^6 + 8 * q^12 + 8 * q^13 - 8 * q^16 - 16 * q^18 + 16 * q^22 - 40 * q^25 - 8 * q^27 + 32 * q^31 - 16 * q^33 - 8 * q^36 + 16 * q^37 - 48 * q^43 - 8 * q^46 + 8 * q^48 + 16 * q^51 - 8 * q^52 + 16 * q^57 + 64 * q^61 - 32 * q^66 + 16 * q^67 + 16 * q^72 - 8 * q^73 + 40 * q^75 - 16 * q^76 + 8 * q^78 + 56 * q^81 + 16 * q^82 - 40 * q^85 + 16 * q^88 - 32 * q^93 - 8 * q^96 - 16 * q^97

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