LMFDB - Embedded newform 693.2.m.g.190.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [693,2,Mod(64,693)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(693, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 6]))

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

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

chi := DirichletCharacter("693.64");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 693 = 3^{2} \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	693.m (of order $5$, degree $4$, 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:	$5.53363286007$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{5})$
Coefficient field:	8.0.159390625.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} + 6x^{6} - 11x^{5} + 21x^{4} - 5x^{3} + 10x^{2} + 25x + 25 $ x^8 - x^7 + 6x^6 - 11x^5 + 21x^4 - 5x^3 + 10x^2 + 25x + 25
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 77)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			190.2
Root			$-0.762262 + 2.34600i$ of defining polynomial
Character	$\chi$	$=$	693.190
Dual form			693.2.m.g.631.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.99563 - 1.44991i) q^{2} +(1.26226 - 3.88484i) q^{4} +(-2.80464 - 2.03769i) q^{5} +(-0.309017 + 0.951057i) q^{7} +(-1.58914 - 4.89086i) q^{8} +O(q^{10})$	\(q+(1.99563 - 1.44991i) q^{2} +(1.26226 - 3.88484i) q^{4} +(-2.80464 - 2.03769i) q^{5} +(-0.309017 + 0.951057i) q^{7} +(-1.58914 - 4.89086i) q^{8} -8.55150 q^{10} +(-2.91998 - 1.57281i) q^{11} +(0.528896 - 0.384266i) q^{13} +(0.762262 + 2.34600i) q^{14} +(-3.65334 - 2.65431i) q^{16} +(-0.919977 - 0.668402i) q^{17} +(-1.87759 - 5.77864i) q^{19} +(-11.4563 + 8.32350i) q^{20} +(-8.10762 + 1.09495i) q^{22} +6.66708 q^{23} +(2.16875 + 6.67473i) q^{25} +(0.498330 - 1.53370i) q^{26} +(3.30464 + 2.40097i) q^{28} +(1.41331 - 4.34973i) q^{29} +(-2.26226 + 1.64363i) q^{31} -0.854102 q^{32} -2.80505 q^{34} +(2.80464 - 2.03769i) q^{35} +(-0.135893 + 0.418235i) q^{37} +(-12.1255 - 8.80968i) q^{38} +(-5.50911 + 16.9553i) q^{40} +(1.82417 + 5.61423i) q^{41} +8.70820 q^{43} +(-9.79590 + 9.35835i) q^{44} +(13.3050 - 9.66666i) q^{46} +(0.186864 + 0.575107i) q^{47} +(-0.809017 - 0.587785i) q^{49} +(14.0058 + 10.1758i) q^{50} +(-0.825206 - 2.53972i) q^{52} +(7.94654 - 5.77350i) q^{53} +(4.98459 + 10.3612i) q^{55} +5.14256 q^{56} +(-3.48626 - 10.7296i) q^{58} +(-0.523492 + 1.61114i) q^{59} +(-5.54839 - 4.03114i) q^{61} +(-2.13152 + 6.56015i) q^{62} +(5.60222 - 4.07025i) q^{64} -2.26638 q^{65} -6.17828 q^{67} +(-3.75789 + 2.73027i) q^{68} +(2.64256 - 8.13296i) q^{70} +(-4.38234 - 3.18395i) q^{71} +(2.07103 - 6.37396i) q^{73} +(0.335211 + 1.03167i) q^{74} -24.8191 q^{76} +(2.39815 - 2.29104i) q^{77} +(-2.14693 + 1.55984i) q^{79} +(4.83766 + 14.8888i) q^{80} +(11.7805 + 8.55903i) q^{82} +(5.41765 + 3.93615i) q^{83} +(1.21821 + 3.74926i) q^{85} +(17.3783 - 12.6261i) q^{86} +(-3.05216 + 16.7806i) q^{88} +0.698213 q^{89} +(0.202020 + 0.621755i) q^{91} +(8.41560 - 25.9006i) q^{92} +(1.20676 + 0.876765i) q^{94} +(-6.50911 + 20.0330i) q^{95} +(12.0209 - 8.73372i) q^{97} -2.46673 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + q^{2} + 3 q^{4} - 3 q^{5} + 2 q^{7} - 3 q^{8}+O(q^{10}) $ 8 * q + q^2 + 3 * q^4 - 3 * q^5 + 2 * q^7 - 3 * q^8	$ 8 q + q^{2} + 3 q^{4} - 3 q^{5} + 2 q^{7} - 3 q^{8} - 28 q^{10} - 5 q^{11} + 5 q^{13} - q^{14} - 3 q^{16} + 11 q^{17} - 9 q^{19} - 21 q^{20} - q^{22} + 16 q^{23} + 5 q^{25} - 21 q^{26} + 7 q^{28} + 9 q^{29} - 11 q^{31} + 20 q^{32} - 24 q^{34} + 3 q^{35} + 6 q^{37} - 35 q^{38} - 16 q^{40} + 22 q^{41} + 16 q^{43} - 29 q^{44} + 29 q^{46} - 7 q^{47} - 2 q^{49} + 34 q^{50} + 21 q^{52} - 2 q^{53} + 26 q^{55} + 18 q^{56} - 39 q^{58} - 25 q^{59} + 7 q^{61} + 5 q^{62} + q^{64} - 24 q^{65} - 30 q^{67} - 8 q^{68} - 2 q^{70} + 14 q^{71} + 3 q^{73} + 9 q^{74} - 52 q^{76} + 5 q^{77} - 9 q^{79} + 33 q^{80} + 31 q^{82} - 23 q^{83} - 10 q^{85} + 17 q^{86} - 7 q^{88} + 34 q^{89} + 5 q^{91} + 34 q^{92} - 30 q^{94} - 24 q^{95} + 30 q^{97} - 4 q^{98}+O(q^{100}) $ 8 * q + q^2 + 3 * q^4 - 3 * q^5 + 2 * q^7 - 3 * q^8 - 28 * q^10 - 5 * q^11 + 5 * q^13 - q^14 - 3 * q^16 + 11 * q^17 - 9 * q^19 - 21 * q^20 - q^22 + 16 * q^23 + 5 * q^25 - 21 * q^26 + 7 * q^28 + 9 * q^29 - 11 * q^31 + 20 * q^32 - 24 * q^34 + 3 * q^35 + 6 * q^37 - 35 * q^38 - 16 * q^40 + 22 * q^41 + 16 * q^43 - 29 * q^44 + 29 * q^46 - 7 * q^47 - 2 * q^49 + 34 * q^50 + 21 * q^52 - 2 * q^53 + 26 * q^55 + 18 * q^56 - 39 * q^58 - 25 * q^59 + 7 * q^61 + 5 * q^62 + q^64 - 24 * q^65 - 30 * q^67 - 8 * q^68 - 2 * q^70 + 14 * q^71 + 3 * q^73 + 9 * q^74 - 52 * q^76 + 5 * q^77 - 9 * q^79 + 33 * q^80 + 31 * q^82 - 23 * q^83 - 10 * q^85 + 17 * q^86 - 7 * q^88 + 34 * q^89 + 5 * q^91 + 34 * q^92 - 30 * q^94 - 24 * q^95 + 30 * q^97 - 4 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/693\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$442$
$\chi(n)$	$1$	$1$	$e\left(\frac{4}{5}\right)$

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 $

$2$	1.99563	−	1.44991i	1.41112	−	1.02524i	0.417964	−	0.908464i	$-0.362744\pi$
$2$	1.99563	−	1.44991i	1.41112	−	1.02524i	0.993158	−	0.116777i	$-0.0372561\pi$
$3$		0			0
$3$		0			0
$4$	1.26226	−	3.88484i	0.631131	−	1.94242i
$5$	−2.80464	−	2.03769i	−1.25428	−	0.911284i	−0.255813	−	0.966726i	$-0.582343\pi$
$5$	−2.80464	−	2.03769i	−1.25428	−	0.911284i	−0.998462	+	0.0554418i	$0.982343\pi$
$6$		0			0
$7$	−0.309017	+	0.951057i	−0.116797	+	0.359466i
$7$	−0.309017	+	0.951057i	−0.116797	+	0.359466i
$8$	−1.58914	−	4.89086i	−0.561845	−	1.72918i
$9$		0			0
$10$	−8.55150			−2.70422
$11$	−2.91998	−	1.57281i	−0.880406	−	0.474220i
$11$	−2.91998	−	1.57281i	−0.880406	−	0.474220i
$12$		0			0
$13$	0.528896	−	0.384266i	0.146689	−	0.106576i	−0.512020	−	0.858973i	$-0.671103\pi$
$13$	0.528896	−	0.384266i	0.146689	−	0.106576i	0.658709	+	0.752397i	$0.271103\pi$
$14$	0.762262	+	2.34600i	0.203723	+	0.626995i
$15$		0			0
$16$	−3.65334	−	2.65431i	−0.913336	−	0.663577i
$17$	−0.919977	−	0.668402i	−0.223127	−	0.162111i	0.470606	−	0.882343i	$-0.344035\pi$
$17$	−0.919977	−	0.668402i	−0.223127	−	0.162111i	−0.693733	+	0.720232i	$0.744035\pi$
$18$		0			0
$19$	−1.87759	−	5.77864i	−0.430750	−	1.32571i	−0.897380	−	0.441259i	$-0.854532\pi$
$19$	−1.87759	−	5.77864i	−0.430750	−	1.32571i	0.466630	−	0.884452i	$-0.345468\pi$
$20$	−11.4563	+	8.32350i	−2.56171	+	1.86119i
$21$		0			0
$22$	−8.10762	+	1.09495i	−1.72855	+	0.233445i
$23$	6.66708			1.39018			0.695091	−	0.718921i	$-0.255364\pi$
$23$	6.66708			1.39018			0.695091	+	0.718921i	$0.255364\pi$
$24$		0			0
$25$	2.16875	+	6.67473i	0.433750	+	1.33495i
$26$	0.498330	−	1.53370i	0.0977306	−	0.300784i
$27$		0			0
$28$	3.30464	+	2.40097i	0.624519	+	0.453740i
$29$	1.41331	−	4.34973i	0.262445	−	0.807724i	−0.729826	−	0.683633i	$-0.760399\pi$
$29$	1.41331	−	4.34973i	0.262445	−	0.807724i	0.992271	−	0.124090i	$-0.0396013\pi$
$30$		0			0
$31$	−2.26226	+	1.64363i	−0.406314	+	0.295205i	−0.772108	−	0.635491i	$-0.780798\pi$
$31$	−2.26226	+	1.64363i	−0.406314	+	0.295205i	0.365794	+	0.930696i	$0.380798\pi$
$32$	−0.854102			−0.150985
$33$		0			0
$34$	−2.80505			−0.481063
$35$	2.80464	−	2.03769i	0.474072	−	0.344433i
$36$		0			0
$37$	−0.135893	+	0.418235i	−0.0223406	+	0.0687574i	−0.961605	−	0.274436i	$-0.911509\pi$
$37$	−0.135893	+	0.418235i	−0.0223406	+	0.0687574i	0.939265	+	0.343194i	$0.111509\pi$
$38$	−12.1255	−	8.80968i	−1.96701	−	1.42912i
$39$		0			0
$40$	−5.50911	+	16.9553i	−0.871068	+	2.68087i
$41$	1.82417	+	5.61423i	0.284888	+	0.876795i	0.986432	+	0.164169i	$0.0524943\pi$
$41$	1.82417	+	5.61423i	0.284888	+	0.876795i	−0.701544	+	0.712626i	$0.747506\pi$
$42$		0			0
$43$	8.70820			1.32799			0.663994	−	0.747738i	$-0.268860\pi$
$43$	8.70820			1.32799			0.663994	+	0.747738i	$0.268860\pi$
$44$	−9.79590	+	9.35835i	−1.47679	+	1.41082i
$45$		0			0
$46$	13.3050	−	9.66666i	1.96172	−	1.42527i
$47$	0.186864	+	0.575107i	0.0272569	+	0.0838880i	0.963760	−	0.266772i	$-0.0859572\pi$
$47$	0.186864	+	0.575107i	0.0272569	+	0.0838880i	−0.936503	+	0.350660i	$0.885957\pi$
$48$		0			0
$49$	−0.809017	−	0.587785i	−0.115574	−	0.0839693i
$50$	14.0058	+	10.1758i	1.98072	+	1.43907i
$51$		0			0
$52$	−0.825206	−	2.53972i	−0.114435	−	0.352196i
$53$	7.94654	−	5.77350i	1.09154	−	0.793051i	0.111883	−	0.993721i	$-0.464312\pi$
$53$	7.94654	−	5.77350i	1.09154	−	0.793051i	0.979659	+	0.200670i	$0.0643120\pi$
$54$		0			0
$55$	4.98459	+	10.3612i	0.672122	+	1.39710i
$56$	5.14256			0.687203
$57$		0			0
$58$	−3.48626	−	10.7296i	−0.457768	−	1.40887i
$59$	−0.523492	+	1.61114i	−0.0681529	+	0.209753i	−0.979333	−	0.202256i	$-0.935173\pi$
$59$	−0.523492	+	1.61114i	−0.0681529	+	0.209753i	0.911180	+	0.412009i	$0.135173\pi$
$60$		0			0
$61$	−5.54839	−	4.03114i	−0.710398	−	0.516134i	0.172904	−	0.984939i	$-0.444685\pi$
$61$	−5.54839	−	4.03114i	−0.710398	−	0.516134i	−0.883302	+	0.468804i	$0.844685\pi$
$62$	−2.13152	+	6.56015i	−0.270703	+	0.833139i
$63$		0			0
$64$	5.60222	−	4.07025i	0.700277	−	0.508781i
$65$	−2.26638			−0.281110
$66$		0			0
$67$	−6.17828			−0.754797			−0.377398	−	0.926051i	$-0.623181\pi$
$67$	−6.17828			−0.754797			−0.377398	+	0.926051i	$0.623181\pi$
$68$	−3.75789	+	2.73027i	−0.455711	+	0.331093i
$69$		0			0
$70$	2.64256	−	8.13296i	0.315846	−	0.972074i
$71$	−4.38234	−	3.18395i	−0.520088	−	0.377866i	0.296549	−	0.955018i	$-0.404164\pi$
$71$	−4.38234	−	3.18395i	−0.520088	−	0.377866i	−0.816637	+	0.577152i	$0.804164\pi$
$72$		0			0
$73$	2.07103	−	6.37396i	0.242395	−	0.746016i	−0.753659	−	0.657266i	$-0.771713\pi$
$73$	2.07103	−	6.37396i	0.242395	−	0.746016i	0.996054	−	0.0887500i	$-0.0282872\pi$
$74$	0.335211	+	1.03167i	0.0389675	+	0.119930i
$75$		0			0
$76$	−24.8191			−2.84695
$77$	2.39815	−	2.29104i	0.273295	−	0.261088i
$78$		0			0
$79$	−2.14693	+	1.55984i	−0.241549	+	0.175495i	−0.701973	−	0.712204i	$-0.747697\pi$
$79$	−2.14693	+	1.55984i	−0.241549	+	0.175495i	0.460424	+	0.887699i	$0.347697\pi$
$80$	4.83766	+	14.8888i	0.540867	+	1.66462i
$81$		0			0
$82$	11.7805	+	8.55903i	1.30094	+	0.945187i
$83$	5.41765	+	3.93615i	0.594664	+	0.432049i	0.843981	−	0.536373i	$-0.180206\pi$
$83$	5.41765	+	3.93615i	0.594664	+	0.432049i	−0.249317	+	0.968422i	$0.580206\pi$
$84$		0			0
$85$	1.21821	+	3.74926i	0.132133	+	0.406665i
$86$	17.3783	−	12.6261i	1.87395	−	1.36151i
$87$		0			0
$88$	−3.05216	+	16.7806i	−0.325361	+	1.78882i
$89$	0.698213			0.0740105			0.0370052	−	0.999315i	$-0.488218\pi$
$89$	0.698213			0.0740105			0.0370052	+	0.999315i	$0.488218\pi$
$90$		0			0
$91$	0.202020	+	0.621755i	0.0211775	+	0.0651776i
$92$	8.41560	−	25.9006i	0.877387	−	2.70032i
$93$		0			0
$94$	1.20676	+	0.876765i	0.124468	+	0.0904314i
$95$	−6.50911	+	20.0330i	−0.667821	+	2.05534i
$96$		0			0
$97$	12.0209	−	8.73372i	1.22054	−	0.886775i	0.224396	−	0.974498i	$-0.427959\pi$
$97$	12.0209	−	8.73372i	1.22054	−	0.886775i	0.996145	+	0.0877234i	$0.0279592\pi$
$98$	−2.46673			−0.249178
$99$		0			0
$100$	28.6678			2.86678
$101$	6.97340	−	5.06647i	0.693879	−	0.504133i	−0.184054	−	0.982916i	$-0.558922\pi$
$101$	6.97340	−	5.06647i	0.693879	−	0.504133i	0.877933	+	0.478784i	$0.158922\pi$
$102$		0			0
$103$	−0.288300	+	0.887296i	−0.0284070	+	0.0874279i	−0.964255	−	0.264976i	$-0.914636\pi$
$103$	−0.288300	+	0.887296i	−0.0284070	+	0.0874279i	0.935848	+	0.352404i	$0.114636\pi$
$104$	−2.71988	−	1.97611i	−0.266706	−	0.193773i
$105$		0			0
$106$	7.48729	−	23.0435i	0.727230	−	2.23818i
$107$	−2.04635	−	6.29801i	−0.197828	−	0.608851i	−0.999932	−	0.0116671i	$-0.996286\pi$
$107$	−2.04635	−	6.29801i	−0.197828	−	0.608851i	0.802104	−	0.597184i	$-0.203714\pi$
$108$		0			0
$109$	−4.12507			−0.395110			−0.197555	−	0.980292i	$-0.563300\pi$
$109$	−4.12507			−0.395110			−0.197555	+	0.980292i	$0.563300\pi$
$110$	24.9702	+	13.4499i	2.38081	+	1.28240i
$111$		0			0
$112$	3.65334	−	2.65431i	0.345208	−	0.250809i
$113$	5.81749	+	17.9044i	0.547264	+	1.68430i	0.715546	+	0.698566i	$0.246178\pi$
$113$	5.81749	+	17.9044i	0.547264	+	1.68430i	−0.168282	+	0.985739i	$0.553822\pi$
$114$		0			0
$115$	−18.6988	−	13.5855i	−1.74367	−	1.26685i
$116$	−15.1140	−	10.9810i	−1.40330	−	1.01956i
$117$		0			0
$118$	1.29131	+	3.97426i	0.118875	+	0.365860i
$119$	0.919977	−	0.668402i	0.0843341	−	0.0612723i
$120$		0			0
$121$	6.05253	+	9.18514i	0.550230	+	0.835013i
$122$	−16.9173			−1.53162
$123$		0			0
$124$	3.52968	+	10.8632i	0.316974	+	0.975546i
$125$	2.16209	−	6.65422i	0.193383	−	0.595171i
$126$		0			0
$127$	6.44491	+	4.68250i	0.571893	+	0.415505i	0.835792	−	0.549045i	$-0.185009\pi$
$127$	6.44491	+	4.68250i	0.571893	+	0.415505i	−0.263899	+	0.964550i	$0.585009\pi$
$128$	5.80631	−	17.8700i	0.513211	−	1.57950i
$129$		0			0
$130$	−4.52285	+	3.28605i	−0.396681	+	0.288205i
$131$	4.80505			0.419819			0.209910	−	0.977721i	$-0.432683\pi$
$131$	4.80505			0.419819			0.209910	+	0.977721i	$0.432683\pi$
$132$		0			0
$133$	6.07602			0.526858
$134$	−12.3295	+	8.95793i	−1.06511	+	0.773848i
$135$		0			0
$136$	−1.80709	+	5.56166i	−0.154957	+	0.476909i
$137$	−17.6995	−	12.8594i	−1.51217	−	1.09865i	−0.965204	−	0.261496i	$-0.915784\pi$
$137$	−17.6995	−	12.8594i	−1.51217	−	1.09865i	−0.546962	−	0.837157i	$-0.684216\pi$
$138$		0			0
$139$	−6.12278	+	18.8440i	−0.519327	+	1.59832i	0.255941	+	0.966692i	$0.417615\pi$
$139$	−6.12278	+	18.8440i	−0.519327	+	1.59832i	−0.775268	+	0.631632i	$0.782385\pi$
$140$	−4.37592	−	13.4677i	−0.369833	−	1.13823i
$141$		0			0
$142$	−13.3620			−1.12131
$143$	−2.14874	+	0.290193i	−0.179687	+	0.0242671i
$144$		0			0
$145$	−12.8272	+	9.31954i	−1.06524	+	0.773946i
$146$	−5.10867	−	15.7229i	−0.422796	−	1.30123i
$147$		0			0
$148$	1.45325	+	1.05584i	0.119456	+	0.0867899i
$149$	2.55820	+	1.85864i	0.209576	+	0.152266i	0.687622	−	0.726069i	$-0.258655\pi$
$149$	2.55820	+	1.85864i	0.209576	+	0.152266i	−0.478046	+	0.878335i	$0.658655\pi$
$150$		0			0
$151$	2.75892	+	8.49109i	0.224518	+	0.690995i	0.998340	+	0.0575923i	$0.0183423\pi$
$151$	2.75892	+	8.49109i	0.224518	+	0.690995i	−0.773822	+	0.633403i	$0.781658\pi$
$152$	−25.2788	+	18.3661i	−2.05038	+	1.48969i
$153$		0			0
$154$	1.46403	−	8.04916i	0.117975	−	0.648620i
$155$	9.69406			0.778645
$156$		0			0
$157$	0.352179	+	1.08390i	0.0281070	+	0.0865044i	0.964126	−	0.265445i	$-0.0855189\pi$
$157$	0.352179	+	1.08390i	0.0281070	+	0.0865044i	−0.936019	+	0.351949i	$0.885519\pi$
$158$	−2.02285	+	6.22570i	−0.160930	+	0.495290i
$159$		0			0
$160$	2.39545	+	1.74040i	0.189377	+	0.137591i
$161$	−2.06024	+	6.34077i	−0.162370	+	0.499723i
$162$		0			0
$163$	4.09951	−	2.97847i	0.321099	−	0.233292i	−0.415545	−	0.909572i	$-0.636409\pi$
$163$	4.09951	−	2.97847i	0.321099	−	0.233292i	0.736644	+	0.676281i	$0.236409\pi$
$164$	24.1130			1.88291
$165$		0			0
$166$	16.5187			1.28210
$167$	−15.9432	+	11.5834i	−1.23372	+	0.896351i	−0.997164	−	0.0752658i	$-0.976019\pi$
$167$	−15.9432	+	11.5834i	−1.23372	+	0.896351i	−0.236558	+	0.971617i	$0.576019\pi$
$168$		0			0
$169$	−3.88515	+	11.9573i	−0.298858	+	0.919789i
$170$	7.86718	+	5.71584i	0.603385	+	0.438385i
$171$		0			0
$172$	10.9920	−	33.8300i	0.838135	−	2.57951i
$173$	4.44824	+	13.6903i	0.338193	+	1.04085i	0.965128	+	0.261779i	$0.0843093\pi$
$173$	4.44824	+	13.6903i	0.338193	+	1.04085i	−0.626935	+	0.779072i	$0.715691\pi$
$174$		0			0
$175$	−7.01823			−0.530528
$176$	6.49295	+	13.4965i	0.489424	+	1.01734i
$177$		0			0
$178$	1.39337	−	1.01235i	0.104438	−	0.0758785i
$179$	1.44132	+	4.43592i	0.107729	+	0.331556i	0.990361	−	0.138508i	$-0.0442307\pi$
$179$	1.44132	+	4.43592i	0.107729	+	0.331556i	−0.882632	+	0.470064i	$0.844231\pi$
$180$		0			0
$181$	−8.01578	−	5.82381i	−0.595808	−	0.432880i	0.248580	−	0.968611i	$-0.420036\pi$
$181$	−8.01578	−	5.82381i	−0.595808	−	0.432880i	−0.844389	+	0.535731i	$0.820036\pi$
$182$	1.30464	+	0.947880i	0.0967067	+	0.0702615i
$183$		0			0
$184$	−10.5949	−	32.6078i	−0.781067	−	2.40388i
$185$	1.23337	−	0.896093i	0.0906789	−	0.0658821i
$186$		0			0
$187$	1.63504	+	3.39867i	0.119566	+	0.248535i
$188$	2.47007			0.180148
$189$		0			0
$190$	16.0562	+	49.4160i	1.16484	+	3.58502i
$191$	−3.07254	+	9.45631i	−0.222321	+	0.684234i	0.776231	+	0.630448i	$0.217129\pi$
$191$	−3.07254	+	9.45631i	−0.222321	+	0.684234i	−0.998552	+	0.0537861i	$0.982871\pi$
$192$		0			0
$193$	−2.99874	−	2.17871i	−0.215854	−	0.156827i	0.474604	−	0.880199i	$-0.342591\pi$
$193$	−2.99874	−	2.17871i	−0.215854	−	0.156827i	−0.690458	+	0.723372i	$0.742591\pi$
$194$	11.3262	−	34.8585i	0.813175	−	2.50269i
$195$		0			0
$196$	−3.30464	+	2.40097i	−0.236046	+	0.171498i
$197$	−5.91982			−0.421770			−0.210885	−	0.977511i	$-0.567635\pi$
$197$	−5.91982			−0.421770			−0.210885	+	0.977511i	$0.567635\pi$
$198$		0			0
$199$	11.4842			0.814095			0.407047	−	0.913407i	$-0.366558\pi$
$199$	11.4842			0.814095			0.407047	+	0.913407i	$0.366558\pi$
$200$	29.1988	−	21.2141i	2.06466	−	1.50007i
$201$		0			0
$202$	6.57039	−	20.2216i	0.462291	−	1.42279i
$203$	3.70010	+	2.68828i	0.259696	+	0.188680i
$204$		0			0
$205$	6.32392	−	19.4630i	0.441682	−	1.35936i
$206$	0.711159	+	2.18872i	0.0495488	+	0.152495i
$207$		0			0
$208$	−2.95220			−0.204698
$209$	−3.60618	+	19.8266i	−0.249445	+	1.37143i
$210$		0			0
$211$	−7.05857	+	5.12835i	−0.485932	+	0.353050i	−0.803618	−	0.595146i	$-0.797094\pi$
$211$	−7.05857	+	5.12835i	−0.485932	+	0.353050i	0.317686	+	0.948196i	$0.397094\pi$
$212$	−12.3985	−	38.1587i	−0.851534	−	2.62075i
$213$		0			0
$214$	−13.2153	−	9.60146i	−0.903378	−	0.656342i
$215$	−24.4234	−	17.7447i	−1.66566	−	1.21018i
$216$		0			0
$217$	−0.864107	−	2.65945i	−0.0586594	−	0.180535i
$218$	−8.23210	+	5.98097i	−0.557548	+	0.405083i
$219$		0			0
$220$	46.5435	−	6.28581i	3.13796	−	0.423789i
$221$	−0.743416			−0.0500076
$222$		0			0
$223$	3.19302	+	9.82712i	0.213821	+	0.658072i	0.999235	+	0.0391023i	$0.0124498\pi$
$223$	3.19302	+	9.82712i	0.213821	+	0.658072i	−0.785415	+	0.618970i	$0.787550\pi$
$224$	0.263932	−	0.812299i	0.0176347	−	0.0542740i
$225$		0			0
$226$	37.5693	+	27.2957i	2.49907	+	1.81568i
$227$	4.10033	−	12.6195i	0.272149	−	0.837587i	−0.717811	−	0.696238i	$-0.754856\pi$
$227$	4.10033	−	12.6195i	0.272149	−	0.837587i	0.989960	−	0.141349i	$-0.0451441\pi$
$228$		0			0
$229$	2.01949	−	1.46725i	0.133452	−	0.0969583i	−0.519057	−	0.854740i	$-0.673717\pi$
$229$	2.01949	−	1.46725i	0.133452	−	0.0969583i	0.652508	+	0.757781i	$0.273717\pi$
$230$	−57.0135			−3.75936
$231$		0			0
$232$	−23.5199			−1.54415
$233$	−7.76971	+	5.64502i	−0.509010	+	0.369818i	−0.812448	−	0.583034i	$-0.801866\pi$
$233$	−7.76971	+	5.64502i	−0.509010	+	0.369818i	0.303438	+	0.952851i	$0.401866\pi$
$234$		0			0
$235$	0.647806	−	1.99374i	0.0422582	−	0.130057i
$236$	5.59825	+	4.06737i	0.364415	+	0.264763i
$237$		0			0
$238$	0.866809	−	2.66776i	0.0561869	−	0.172925i
$239$	−1.71914	−	5.29098i	−0.111202	−	0.342245i	0.879934	−	0.475096i	$-0.157587\pi$
$239$	−1.71914	−	5.29098i	−0.111202	−	0.342245i	−0.991136	+	0.132851i	$0.957587\pi$
$240$		0			0
$241$	15.0208			0.967572			0.483786	−	0.875186i	$-0.339261\pi$
$241$	15.0208			0.967572			0.483786	+	0.875186i	$0.339261\pi$
$242$	25.3962	+	9.55452i	1.63253	+	0.614188i
$243$		0			0
$244$	−22.6639	+	16.4663i	−1.45090	+	1.05414i
$245$	1.07128	+	3.29706i	0.0684415	+	0.210641i
$246$		0			0
$247$	−3.21358	−	2.33481i	−0.204475	−	0.148560i
$248$	11.6338	+	8.45246i	0.738748	+	0.536732i
$249$		0			0
$250$	−5.33329	−	16.4142i	−0.337307	−	1.03812i
$251$	22.3394	−	16.2305i	1.41005	−	1.02446i	0.416738	−	0.909027i	$-0.363173\pi$
$251$	22.3394	−	16.2305i	1.41005	−	1.02446i	0.993315	−	0.115436i	$-0.0368266\pi$
$252$		0			0
$253$	−19.4677	−	10.4861i	−1.22393	−	0.659253i
$254$	19.6508			1.23300
$255$		0			0
$256$	−10.0429	−	30.9089i	−0.627682	−	1.93181i
$257$	8.79709	−	27.0747i	0.548747	−	1.68887i	−0.163162	−	0.986599i	$-0.552169\pi$
$257$	8.79709	−	27.0747i	0.548747	−	1.68887i	0.711909	−	0.702271i	$-0.247831\pi$
$258$		0			0
$259$	−0.355772	−	0.258483i	−0.0221066	−	0.0160614i
$260$	−2.86077	+	8.80454i	−0.177417	+	0.546034i
$261$		0			0
$262$	9.58910	−	6.96689i	0.592417	−	0.430416i
$263$	−14.1803			−0.874397			−0.437199	−	0.899365i	$-0.644029\pi$
$263$	−14.1803			−0.874397			−0.437199	+	0.899365i	$0.644029\pi$
$264$		0			0
$265$	−34.0519			−2.09179
$266$	12.1255	−	8.80968i	0.743461	−	0.540156i
$267$		0			0
$268$	−7.79860	+	24.0016i	−0.476375	+	1.46613i
$269$	−19.5731	−	14.2207i	−1.19339	−	0.867050i	−0.199774	−	0.979842i	$-0.564021\pi$
$269$	−19.5731	−	14.2207i	−1.19339	−	0.867050i	−0.993619	+	0.112792i	$0.964021\pi$
$270$		0			0
$271$	2.30210	−	7.08513i	0.139843	−	0.430391i	−0.856469	−	0.516198i	$-0.827347\pi$
$271$	2.30210	−	7.08513i	0.139843	−	0.430391i	0.996312	+	0.0858070i	$0.0273468\pi$
$272$	1.58684	+	4.88381i	0.0962166	+	0.296124i
$273$		0			0
$274$	−53.9665			−3.26024
$275$	4.16539	−	22.9011i	0.251182	−	1.38099i
$276$		0			0
$277$	15.5242	−	11.2790i	0.932761	−	0.677690i	−0.0139064	−	0.999903i	$-0.504427\pi$
$277$	15.5242	−	11.2790i	0.932761	−	0.677690i	0.946667	+	0.322213i	$0.104427\pi$
$278$	15.1032	+	46.4830i	0.905833	+	2.78787i
$279$		0			0
$280$	−14.4230	−	10.4790i	−0.861942	−	0.626238i
$281$	−1.53764	−	1.11716i	−0.0917279	−	0.0666442i	0.540976	−	0.841038i	$-0.318055\pi$
$281$	−1.53764	−	1.11716i	−0.0917279	−	0.0666442i	−0.632704	+	0.774394i	$0.718055\pi$
$282$		0			0
$283$	2.24092	+	6.89685i	0.133209	+	0.409975i	0.995307	−	0.0967663i	$-0.0308499\pi$
$283$	2.24092	+	6.89685i	0.133209	+	0.409975i	−0.862098	+	0.506741i	$0.830850\pi$
$284$	−17.9008	+	13.0057i	−1.06222	+	0.771747i
$285$		0			0
$286$	−3.86734	+	3.69460i	−0.228680	+	0.218466i
$287$	−5.90315			−0.348452
$288$		0			0
$289$	−4.85369	−	14.9381i	−0.285511	−	0.878714i
$290$	−12.0859	+	37.1967i	−0.709710	+	2.18426i
$291$		0			0
$292$	−22.1477	−	16.0912i	−1.29609	−	0.941668i
$293$	1.01078	−	3.11088i	0.0590507	−	0.181739i	−0.917180	−	0.398473i	$-0.869540\pi$
$293$	1.01078	−	3.11088i	0.0590507	−	0.181739i	0.976231	+	0.216734i	$0.0695403\pi$
$294$		0			0
$295$	4.75122	−	3.45197i	0.276627	−	0.200981i
$296$	2.26148			0.131446
$297$		0			0
$298$	7.80008			0.451846
$299$	3.52619	−	2.56193i	0.203925	−	0.148160i
$300$		0			0
$301$	−2.69098	+	8.28199i	−0.155106	+	0.477366i
$302$	17.8171	+	12.9449i	1.02526	+	0.744894i
$303$		0			0
$304$	−8.47880	+	26.0951i	−0.486293	+	1.49665i
$305$	7.34703	+	22.6118i	0.420690	+	1.29475i
$306$		0			0
$307$	31.6121			1.80420			0.902099	−	0.431530i	$-0.142026\pi$
$307$	31.6121			1.80420			0.902099	+	0.431530i	$0.142026\pi$
$308$	−5.87322	−	12.2083i	−0.334658	−	0.695635i
$309$		0			0
$310$	19.3457	−	14.0555i	1.09876	−	0.798298i
$311$	2.79298	+	8.59592i	0.158376	+	0.487430i	0.998487	−	0.0549835i	$-0.0175106\pi$
$311$	2.79298	+	8.59592i	0.158376	+	0.487430i	−0.840112	+	0.542414i	$0.817511\pi$
$312$		0			0
$313$	−11.7300	−	8.52232i	−0.663017	−	0.481710i	0.204664	−	0.978832i	$-0.434390\pi$
$313$	−11.7300	−	8.52232i	−0.663017	−	0.481710i	−0.867680	+	0.497122i	$0.834390\pi$
$314$	2.27437	+	1.65243i	0.128350	+	0.0932518i
$315$		0			0
$316$	3.34973	+	10.3094i	0.188437	+	0.579950i
$317$	−14.9000	+	10.8255i	−0.836865	+	0.608018i	−0.921493	−	0.388394i	$-0.873030\pi$
$317$	−14.9000	+	10.8255i	−0.836865	+	0.608018i	0.0846278	+	0.996413i	$0.473030\pi$
$318$		0			0
$319$	−10.9681	+	10.4782i	−0.614098	+	0.586668i
$320$	−24.0061			−1.34198
$321$		0			0
$322$	5.08206	+	15.6410i	0.283212	+	0.871638i
$323$	−2.13511	+	6.57120i	−0.118801	+	0.365632i
$324$		0			0
$325$	3.71191	+	2.69686i	0.205900	+	0.149595i
$326$	3.86259	−	11.8878i	0.213929	−	0.658407i
$327$		0			0
$328$	24.5596	−	17.8436i	1.35608	−	0.985246i
$329$	−0.604703			−0.0333384
$330$		0			0
$331$	−6.47653			−0.355982			−0.177991	−	0.984032i	$-0.556960\pi$
$331$	−6.47653			−0.355982			−0.177991	+	0.984032i	$0.556960\pi$
$332$	22.1298	−	16.0782i	1.21453	−	0.882409i
$333$		0			0
$334$	−15.0218	+	46.2324i	−0.821957	+	2.52972i
$335$	17.3279	+	12.5894i	0.946723	+	0.687834i
$336$		0			0
$337$	1.93346	−	5.95059i	0.105322	−	0.324149i	−0.884484	−	0.466571i	$-0.845489\pi$
$337$	1.93346	−	5.95059i	0.105322	−	0.324149i	0.989806	+	0.142422i	$0.0454891\pi$
$338$	9.58362	+	29.4954i	0.521280	+	1.60434i
$339$		0			0
$340$	16.1030			0.873308
$341$	9.19087	−	1.24125i	0.497714	−	0.0672174i
$342$		0			0
$343$	0.809017	−	0.587785i	0.0436828	−	0.0317374i
$344$	−13.8385	−	42.5906i	−0.746124	−	2.29633i
$345$		0			0
$346$	28.7266	+	20.8711i	1.54435	+	1.12204i
$347$	18.3773	+	13.3519i	0.986547	+	0.716768i	0.959162	−	0.282857i	$-0.0912822\pi$
$347$	18.3773	+	13.3519i	0.986547	+	0.716768i	0.0273845	+	0.999625i	$0.491282\pi$
$348$		0			0
$349$	9.17597	+	28.2407i	0.491178	+	1.51169i	0.822829	+	0.568289i	$0.192394\pi$
$349$	9.17597	+	28.2407i	0.491178	+	1.51169i	−0.331651	+	0.943402i	$0.607606\pi$
$350$	−14.0058	+	10.1758i	−0.748640	+	0.543919i
$351$		0			0
$352$	2.49396	+	1.34334i	0.132928	+	0.0716003i
$353$	6.82506			0.363262			0.181631	−	0.983367i	$-0.441862\pi$
$353$	6.82506			0.363262			0.181631	+	0.983367i	$0.441862\pi$
$354$		0			0
$355$	5.80297	+	17.8597i	0.307990	+	0.947896i
$356$	0.881328	−	2.71245i	0.0467103	−	0.143760i
$357$		0			0
$358$	9.30801	+	6.76266i	0.491944	+	0.357418i
$359$	2.24337	−	6.90439i	0.118401	−	0.364400i	−0.874241	−	0.485493i	$-0.838640\pi$
$359$	2.24337	−	6.90439i	0.118401	−	0.364400i	0.992641	+	0.121094i	$0.0386401\pi$
$360$		0			0
$361$	−14.4960	+	10.5320i	−0.762947	+	0.554314i
$362$	−24.4405			−1.28456
$363$		0			0
$364$	2.67042			0.139968
$365$	−18.7967	+	13.6566i	−0.983863	+	0.714818i
$366$		0			0
$367$	−11.2286	+	34.5582i	−0.586130	+	1.80392i	0.00855584	+	0.999963i	$0.497277\pi$
$367$	−11.2286	+	34.5582i	−0.586130	+	1.80392i	−0.594686	+	0.803958i	$0.702723\pi$
$368$	−24.3571	−	17.6965i	−1.26970	−	0.922494i
$369$		0			0
$370$	1.16209	−	3.57654i	0.0604140	−	0.185935i
$371$	3.03531	+	9.34172i	0.157585	+	0.484998i
$372$		0			0
$373$	−14.2913			−0.739977			−0.369989	−	0.929036i	$-0.620638\pi$
$373$	−14.2913			−0.739977			−0.369989	+	0.929036i	$0.620638\pi$
$374$	8.19069	+	4.41182i	0.423531	+	0.228130i
$375$		0			0
$376$	2.51582	−	1.82785i	0.129743	−	0.0942641i
$377$	−0.923955	−	2.84364i	−0.0475861	−	0.146455i
$378$		0			0
$379$	2.05917	+	1.49608i	0.105773	+	0.0768482i	0.639414	−	0.768862i	$-0.279177\pi$
$379$	2.05917	+	1.49608i	0.105773	+	0.0768482i	−0.533642	+	0.845711i	$0.679177\pi$
$380$	69.6088	+	50.5738i	3.57086	+	2.59438i
$381$		0			0
$382$	7.57913	+	23.3262i	0.387782	+	1.19347i
$383$	−18.7180	+	13.5994i	−0.956444	+	0.694897i	−0.952322	−	0.305094i	$-0.901312\pi$
$383$	−18.7180	+	13.5994i	−0.956444	+	0.694897i	−0.00412192	+	0.999992i	$0.501312\pi$
$384$		0			0
$385$	−11.3944	+	1.53884i	−0.580713	+	0.0784266i
$386$	−9.14330			−0.465382
$387$		0			0
$388$	−18.7556	−	57.7237i	−0.952169	−	2.93048i
$389$	−9.35130	+	28.7804i	−0.474130	+	1.45922i	0.372998	+	0.927832i	$0.378330\pi$
$389$	−9.35130	+	28.7804i	−0.474130	+	1.45922i	−0.847128	+	0.531390i	$0.821670\pi$
$390$		0			0
$391$	−6.13356	−	4.45629i	−0.310188	−	0.225364i
$392$	−1.58914	+	4.89086i	−0.0802636	+	0.247026i
$393$		0			0
$394$	−11.8138	+	8.58320i	−0.595169	+	0.432415i
$395$	9.19985			0.462894
$396$		0			0
$397$	−22.6740			−1.13798			−0.568989	−	0.822345i	$-0.692665\pi$
$397$	−22.6740			−1.13798			−0.568989	+	0.822345i	$0.692665\pi$
$398$	22.9182	−	16.6511i	1.14879	−	0.834643i
$399$		0			0
$400$	9.79361	−	30.1416i	0.489680	−	1.50708i
$401$	−13.1211	−	9.53304i	−0.655237	−	0.476057i	0.209814	−	0.977741i	$-0.432714\pi$
$401$	−13.1211	−	9.53304i	−0.655237	−	0.476057i	−0.865051	+	0.501684i	$0.832714\pi$
$402$		0			0
$403$	−0.564911	+	1.73862i	−0.0281402	+	0.0866068i
$404$	−10.8802	−	33.4858i	−0.541309	−	1.66598i
$405$		0			0
$406$	11.2818			0.559905
$407$	1.05461	−	1.00750i	0.0522750	−	0.0499401i
$408$		0			0
$409$	28.3653	−	20.6086i	1.40257	−	1.01903i	0.408222	−	0.912883i	$-0.366149\pi$
$409$	28.3653	−	20.6086i	1.40257	−	1.01903i	0.994351	−	0.106146i	$-0.0338512\pi$
$410$	−15.5994	−	48.0101i	−0.770400	−	2.37105i
$411$		0			0
$412$	3.08310	+	2.24000i	0.151893	+	0.110357i
$413$	−1.37052	−	0.995741i	−0.0674389	−	0.0489972i
$414$		0			0
$415$	−7.17390	−	22.0790i	−0.352153	−	1.08382i
$416$	−0.451731	+	0.328202i	−0.0221479	+	0.0160914i
$417$		0			0
$418$	21.5502	+	44.7951i	1.05405	+	2.19100i
$419$	−28.2633			−1.38075			−0.690376	−	0.723451i	$-0.742555\pi$
$419$	−28.2633			−1.38075			−0.690376	+	0.723451i	$0.742555\pi$
$420$		0			0
$421$	−4.26279	−	13.1195i	−0.207756	−	0.639406i	−0.999589	−	0.0286688i	$-0.990873\pi$
$421$	−4.26279	−	13.1195i	−0.207756	−	0.639406i	0.791833	−	0.610737i	$-0.209127\pi$
$422$	−6.65064	+	20.4686i	−0.323748	+	0.996394i
$423$		0			0
$424$	−40.8656	−	29.6906i	−1.98461	−	1.44190i
$425$	2.46621	−	7.59020i	0.119629	−	0.368179i
$426$		0			0
$427$	5.54839	−	4.03114i	0.268505	−	0.195080i
$428$	−27.0498			−1.30750
$429$		0			0
$430$	−74.4682			−3.59117
$431$	22.7900	−	16.5579i	1.09776	−	0.797568i	0.117065	−	0.993124i	$-0.462651\pi$
$431$	22.7900	−	16.5579i	1.09776	−	0.797568i	0.980692	+	0.195557i	$0.0626514\pi$
$432$		0			0
$433$	4.38165	−	13.4853i	0.210569	−	0.648064i	−0.788870	−	0.614560i	$-0.789333\pi$
$433$	4.38165	−	13.4853i	0.210569	−	0.648064i	0.999439	−	0.0335038i	$-0.0106666\pi$
$434$	−5.58039	−	4.05439i	−0.267867	−	0.194617i
$435$		0			0
$436$	−5.20692	+	16.0252i	−0.249366	+	0.767470i
$437$	−12.5181	−	38.5267i	−0.598821	−	1.84298i
$438$		0			0
$439$	28.0185			1.33725			0.668625	−	0.743599i	$-0.266883\pi$
$439$	28.0185			1.33725			0.668625	+	0.743599i	$0.266883\pi$
$440$	42.7540	−	40.8443i	2.03822	−	1.94718i
$441$		0			0
$442$	−1.48358	+	1.07789i	−0.0705668	+	0.0512698i
$443$	−5.35743	−	16.4885i	−0.254539	−	0.783391i	−0.993920	−	0.110103i	$-0.964882\pi$
$443$	−5.35743	−	16.4885i	−0.254539	−	0.783391i	0.739381	−	0.673287i	$-0.235118\pi$
$444$		0			0
$445$	−1.95824	−	1.42274i	−0.0928295	−	0.0674446i
$446$	20.6205	+	14.9817i	0.976409	+	0.709403i
$447$		0			0
$448$	2.13986	+	6.58580i	0.101099	+	0.311150i
$449$	−23.8834	+	17.3523i	−1.12713	+	0.818906i	−0.985274	−	0.170982i	$-0.945306\pi$
$449$	−23.8834	+	17.3523i	−1.12713	+	0.818906i	−0.141853	+	0.989888i	$0.545306\pi$
$450$		0			0
$451$	3.50358	−	19.2625i	0.164977	−	0.907036i
$452$	76.8990			3.61702
$453$		0			0
$454$	−10.1144	−	31.1290i	−0.474693	−	1.46096i
$455$	0.700350	−	2.15546i	0.0328329	−	0.101049i
$456$		0			0
$457$	−7.84524	−	5.69990i	−0.366985	−	0.266630i	0.388975	−	0.921248i	$-0.372829\pi$
$457$	−7.84524	−	5.69990i	−0.366985	−	0.266630i	−0.755960	+	0.654618i	$0.772829\pi$
$458$	1.90278	−	5.85615i	0.0889110	−	0.273640i
$459$		0			0
$460$	−76.3802	+	55.4935i	−3.56125	+	2.58740i
$461$	19.2216			0.895240			0.447620	−	0.894224i	$-0.352272\pi$
$461$	19.2216			0.895240			0.447620	+	0.894224i	$0.352272\pi$
$462$		0			0
$463$	20.5327			0.954235			0.477117	−	0.878840i	$-0.341682\pi$
$463$	20.5327			0.954235			0.477117	+	0.878840i	$0.341682\pi$
$464$	−16.7088	+	12.1397i	−0.775688	+	0.563570i
$465$		0			0
$466$	−7.32068	+	22.5307i	−0.339124	+	1.04372i
$467$	27.2408	+	19.7916i	1.26055	+	0.915845i	0.998785	−	0.0492858i	$-0.0156945\pi$
$467$	27.2408	+	19.7916i	1.26055	+	0.915845i	0.261768	+	0.965131i	$0.415695\pi$
$468$		0			0
$469$	1.90919	−	5.87589i	0.0881583	−	0.271323i
$470$	−1.59796	−	4.91803i	−0.0737086	−	0.226852i
$471$		0			0
$472$	8.71178			0.400992
$473$	−25.4278	−	13.6964i	−1.16917	−	0.629759i
$474$		0			0
$475$	34.4988	−	25.0649i	1.58292	−	1.15006i
$476$	−1.43539	−	4.41766i	−0.0657908	−	0.202483i
$477$		0			0
$478$	−11.1022	−	8.06623i	−0.507804	−	0.368941i
$479$	11.4644	+	8.32937i	0.523822	+	0.380579i	0.818042	−	0.575159i	$-0.195060\pi$
$479$	11.4644	+	8.32937i	0.523822	+	0.380579i	−0.294220	+	0.955738i	$0.595060\pi$
$480$		0			0
$481$	0.0888401	+	0.273422i	0.00405076	+	0.0124670i
$482$	29.9758	−	21.7787i	1.36536	−	0.991993i
$483$		0			0
$484$	43.3227	−	11.9191i	1.96921	−	0.541776i
$485$	−51.5111			−2.33900
$486$		0			0
$487$	8.57259	+	26.3837i	0.388461	+	1.19556i	0.933938	+	0.357434i	$0.116348\pi$
$487$	8.57259	+	26.3837i	0.388461	+	1.19556i	−0.545477	+	0.838126i	$0.683652\pi$
$488$	−10.8986	+	33.5424i	−0.493356	+	1.51839i
$489$		0			0
$490$	6.91831	+	5.02644i	0.312537	+	0.227072i
$491$	1.06393	−	3.27444i	0.0480145	−	0.147774i	−0.924175	−	0.381970i	$-0.875246\pi$
$491$	1.06393	−	3.27444i	0.0480145	−	0.147774i	0.972189	+	0.234196i	$0.0752458\pi$
$492$		0			0
$493$	−4.20758	+	3.05699i	−0.189500	+	0.137680i
$494$	−9.79837			−0.440850
$495$		0			0
$496$	12.6275			0.566992
$497$	4.38234	−	3.18395i	0.196575	−	0.142820i
$498$		0			0
$499$	−0.800117	+	2.46251i	−0.0358181	+	0.110237i	−0.967367	−	0.253379i	$-0.918458\pi$
$499$	−0.800117	+	2.46251i	−0.0358181	+	0.110237i	0.931549	+	0.363616i	$0.118458\pi$
$500$	−23.1215	−	16.7987i	−1.03402	−	0.751262i
$501$		0			0
$502$	21.0484	−	64.7803i	0.939435	−	2.89129i
$503$	7.07731	+	21.7817i	0.315561	+	0.971198i	0.975523	+	0.219899i	$0.0705727\pi$
$503$	7.07731	+	21.7817i	0.315561	+	0.971198i	−0.659961	+	0.751300i	$0.729427\pi$
$504$		0			0
$505$	−29.8818			−1.32972
$506$	−54.0542	+	7.30014i	−2.40300	+	0.324531i
$507$		0			0
$508$	26.3259	−	19.1269i	1.16803	−	0.848620i
$509$	7.44685	+	22.9191i	0.330076	+	1.01587i	0.969097	+	0.246680i	$0.0793397\pi$
$509$	7.44685	+	22.9191i	0.330076	+	1.01587i	−0.639021	+	0.769189i	$0.720660\pi$
$510$		0			0
$511$	5.42202	+	3.93933i	0.239856	+	0.174266i
$512$	−34.4547	−	25.0328i	−1.52270	−	1.10631i
$513$		0			0
$514$	−21.7001	−	66.7859i	−0.957149	−	2.94580i
$515$	2.61662	−	1.90108i	0.115302	−	0.0837717i
$516$		0			0
$517$	0.358897	−	1.97320i	0.0157843	−	0.0867813i
$518$	−1.08477			−0.0476619
$519$		0			0
$520$	3.60159	+	11.0846i	0.157940	+	0.486090i
$521$	10.3538	−	31.8658i	0.453610	−	1.39607i	−0.419150	−	0.907917i	$-0.637672\pi$
$521$	10.3538	−	31.8658i	0.453610	−	1.39607i	0.872760	−	0.488150i	$-0.162328\pi$
$522$		0			0
$523$	25.2068	+	18.3138i	1.10222	+	0.800808i	0.981421	−	0.191869i	$-0.0614548\pi$
$523$	25.2068	+	18.3138i	1.10222	+	0.800808i	0.120798	+	0.992677i	$0.461455\pi$
$524$	6.06524	−	18.6669i	0.264961	−	0.815466i
$525$		0			0
$526$	−28.2987	+	20.5602i	−1.23388	+	0.896467i
$527$	3.17983			0.138516
$528$		0			0
$529$	21.4500			0.932608
$530$	−67.9548	+	49.3721i	−2.95177	+	2.14459i
$531$		0			0
$532$	7.66953	−	23.6044i	0.332516	−	1.02338i
$533$	3.12215	+	2.26838i	0.135235	+	0.0982543i
$534$		0			0
$535$	−7.09413	+	21.8335i	−0.306706	+	0.943944i
$536$	9.81813	+	30.2171i	0.424079	+	1.30518i
$537$		0			0
$538$	−59.6793			−2.57296
$539$	1.43784	+	2.98875i	0.0619320	+	0.128735i
$540$		0			0
$541$	−18.2896	+	13.2881i	−0.786330	+	0.571302i	−0.906872	−	0.421406i	$-0.861537\pi$
$541$	−18.2896	+	13.2881i	−0.786330	+	0.571302i	0.120542	+	0.992708i	$0.461537\pi$
$542$	−5.67866	−	17.4771i	−0.243919	−	0.750707i
$543$		0			0
$544$	0.785754	+	0.570884i	0.0336889	+	0.0244764i
$545$	11.5694	+	8.40563i	0.495577	+	0.360058i
$546$		0			0
$547$	−8.48072	−	26.1010i	−0.362610	−	1.11600i	−0.951464	−	0.307759i	$-0.900421\pi$
$547$	−8.48072	−	26.1010i	−0.362610	−	1.11600i	0.588855	−	0.808239i	$-0.299579\pi$
$548$	−72.2981	+	52.5277i	−3.08842	+	2.24387i
$549$		0			0
$550$	−24.8919	−	51.7415i	−1.06140	−	2.20627i
$551$	−27.7891			−1.18386
$552$		0			0
$553$	−0.820054	−	2.52387i	−0.0348723	−	0.107326i
$554$	14.6271	−	45.0174i	0.621444	−	1.91261i
$555$		0			0
$556$	65.4773	+	47.5721i	2.77686	+	2.01750i
$557$	9.34788	−	28.7698i	0.396082	−	1.21902i	−0.532033	−	0.846724i	$-0.678572\pi$
$557$	9.34788	−	28.7698i	0.396082	−	1.21902i	0.928115	−	0.372293i	$-0.121428\pi$
$558$		0			0
$559$	4.60574	−	3.34626i	0.194802	−	0.141532i
$560$	−15.6550			−0.661544
$561$		0			0
$562$	−4.68834			−0.197766
$563$	6.03716	−	4.38625i	0.254436	−	0.184858i	−0.453255	−	0.891381i	$-0.649737\pi$
$563$	6.03716	−	4.38625i	0.254436	−	0.184858i	0.707690	+	0.706523i	$0.249737\pi$
$564$		0			0
$565$	20.1677	−	62.0698i	0.848461	−	2.61129i
$566$	14.4718	+	10.5144i	0.608297	+	0.441954i
$567$		0			0
$568$	−8.60815	+	26.4932i	−0.361190	+	1.11163i
$569$	−11.0159	−	33.9036i	−0.461812	−	1.42131i	−0.862948	−	0.505293i	$-0.831384\pi$
$569$	−11.0159	−	33.9036i	−0.461812	−	1.42131i	0.401136	−	0.916019i	$-0.368616\pi$
$570$		0			0
$571$	25.8902			1.08347			0.541737	−	0.840548i	$-0.317767\pi$
$571$	25.8902			1.08347			0.541737	+	0.840548i	$0.317767\pi$
$572$	−1.58492	+	8.71382i	−0.0662689	+	0.364343i
$573$		0			0
$574$	−11.7805	+	8.55903i	−0.491708	+	0.357247i
$575$	14.4592	+	44.5010i	0.602992	+	1.85582i
$576$		0			0
$577$	−6.60467	−	4.79857i	−0.274956	−	0.199767i	0.441758	−	0.897134i	$-0.354355\pi$
$577$	−6.60467	−	4.79857i	−0.274956	−	0.199767i	−0.716714	+	0.697367i	$0.754355\pi$
$578$	−31.3451	−	22.7735i	−1.30378	−	0.947254i
$579$		0			0
$580$	20.0136	+	61.5955i	0.831020	+	2.55762i
$581$	−5.41765	+	3.93615i	−0.224762	+	0.163299i
$582$		0			0
$583$	−32.2843	+	4.36008i	−1.33708	+	0.180576i
$584$	−34.4653			−1.42619
$585$		0			0
$586$	−2.49333	−	7.67370i	−0.102999	−	0.316997i
$587$	3.85140	−	11.8534i	0.158964	−	0.489242i	−0.839577	−	0.543241i	$-0.817197\pi$
$587$	3.85140	−	11.8534i	0.158964	−	0.489242i	0.998541	+	0.0539994i	$0.0171969\pi$
$588$		0			0
$589$	13.7456	+	9.98673i	0.566376	+	0.411496i
$590$	4.47664	−	13.7777i	0.184300	−	0.567218i
$591$		0			0
$592$	1.60659	−	1.16725i	0.0660304	−	0.0479739i
$593$	23.6707			0.972037			0.486019	−	0.873948i	$-0.338449\pi$
$593$	23.6707			0.972037			0.486019	+	0.873948i	$0.338449\pi$
$594$		0			0
$595$	−3.94221			−0.161615
$596$	10.4497	−	7.59212i	0.428034	−	0.310985i
$597$		0			0
$598$	3.32241	−	10.2253i	0.135863	−	0.418144i
$599$	31.5362	+	22.9124i	1.28853	+	0.936175i	0.999775	−	0.0212271i	$-0.00675731\pi$
$599$	31.5362	+	22.9124i	1.28853	+	0.936175i	0.288759	+	0.957402i	$0.406757\pi$
$600$		0			0
$601$	9.44078	−	29.0557i	0.385097	−	1.18521i	−0.551312	−	0.834299i	$-0.685873\pi$
$601$	9.44078	−	29.0557i	0.385097	−	1.18521i	0.936410	−	0.350909i	$-0.114127\pi$
$602$	6.63793	+	20.4295i	0.270542	+	0.832643i
$603$		0			0
$604$	36.4690			1.48390
$605$	1.74132	−	38.0943i	0.0707946	−	1.54875i
$606$		0			0
$607$	−30.4330	+	22.1109i	−1.23524	+	0.897454i	−0.997272	−	0.0738195i	$-0.976481\pi$
$607$	−30.4330	+	22.1109i	−1.23524	+	0.897454i	−0.237967	+	0.971273i	$0.576481\pi$
$608$	1.60366	+	4.93555i	0.0650369	+	0.200163i
$609$		0			0
$610$	47.4470	+	34.4723i	1.92107	+	1.39574i
$611$	0.319825	+	0.232367i	0.0129387	+	0.00940055i
$612$		0			0
$613$	5.44711	+	16.7645i	0.220007	+	0.677111i	0.998760	+	0.0497807i	$0.0158522\pi$
$613$	5.44711	+	16.7645i	0.220007	+	0.677111i	−0.778754	+	0.627330i	$0.784148\pi$
$614$	63.0860	−	45.8346i	2.54594	−	1.84974i
$615$		0			0
$616$	−15.0162	−	8.08827i	−0.605018	−	0.325886i
$617$	44.4849			1.79089			0.895447	−	0.445168i	$-0.146856\pi$
$617$	44.4849			1.79089			0.895447	+	0.445168i	$0.146856\pi$
$618$		0			0
$619$	−1.91722	−	5.90058i	−0.0770594	−	0.237164i	0.905105	−	0.425188i	$-0.139792\pi$
$619$	−1.91722	−	5.90058i	−0.0770594	−	0.237164i	−0.982165	+	0.188023i	$0.939792\pi$
$620$	12.2364	−	37.6599i	0.491427	−	1.51246i
$621$		0			0
$622$	18.0371	+	13.1047i	0.723220	+	0.525450i
$623$	−0.215760	+	0.664040i	−0.00864423	+	0.0266042i
$624$		0			0
$625$	8.76619	−	6.36901i	0.350647	−	0.254760i
$626$	−35.7652			−1.42947
$627$		0			0
$628$	4.65531			0.185767
$629$	0.404567	−	0.293935i	0.0161312	−	0.0117200i
$630$		0			0
$631$	13.8457	−	42.6128i	0.551190	−	1.69639i	−0.154609	−	0.987976i	$-0.549412\pi$
$631$	13.8457	−	42.6128i	0.551190	−	1.69639i	0.705799	−	0.708412i	$-0.250588\pi$
$632$	11.0407	+	8.02155i	0.439176	+	0.319080i
$633$		0			0
$634$	−14.0389	+	43.2072i	−0.557554	+	1.71598i
$635$	−8.53418	−	26.2655i	−0.338669	−	1.04231i
$636$		0			0
$637$	−0.653752			−0.0259026
$638$	−6.69585	+	36.8134i	−0.265091	+	1.45746i
$639$		0			0
$640$	−52.6982	+	38.2875i	−2.08308	+	1.51345i
$641$	3.17534	+	9.77271i	0.125419	+	0.385999i	0.993977	−	0.109588i	$-0.0349531\pi$
$641$	3.17534	+	9.77271i	0.125419	+	0.385999i	−0.868559	+	0.495587i	$0.834953\pi$
$642$		0			0
$643$	13.3039	+	9.66588i	0.524656	+	0.381185i	0.818355	−	0.574713i	$-0.194886\pi$
$643$	13.3039	+	9.66588i	0.524656	+	0.381185i	−0.293699	+	0.955898i	$0.594886\pi$
$644$	22.0323	+	16.0074i	0.868196	+	0.630781i
$645$		0			0
$646$	5.26675	+	16.2094i	0.207218	+	0.637750i
$647$	−21.8181	+	15.8518i	−0.857758	+	0.623197i	−0.927274	−	0.374383i	$-0.877854\pi$
$647$	−21.8181	+	15.8518i	−0.857758	+	0.623197i	0.0695163	+	0.997581i	$0.477854\pi$
$648$		0			0
$649$	4.06261	−	3.88115i	0.159471	−	0.152348i
$650$	11.3178			0.443921
$651$		0			0
$652$	−6.39623	−	19.6856i	−0.250496	−	0.770947i
$653$	−2.19588	+	6.75823i	−0.0859315	+	0.264470i	−0.984784	−	0.173780i	$-0.944402\pi$
$653$	−2.19588	+	6.75823i	−0.0859315	+	0.264470i	0.898853	+	0.438250i	$0.144402\pi$
$654$		0			0
$655$	−13.4765	−	9.79123i	−0.526569	−	0.382575i
$656$	8.23757	−	25.3526i	0.321623	−	0.989854i
$657$		0			0
$658$	−1.20676	+	0.876765i	−0.0470445	+	0.0341798i
$659$	32.6279			1.27100			0.635502	−	0.772099i	$-0.280793\pi$
$659$	32.6279			1.27100			0.635502	+	0.772099i	$0.280793\pi$
$660$		0			0
$661$	−33.8165			−1.31531			−0.657654	−	0.753320i	$-0.728451\pi$
$661$	−33.8165			−1.31531			−0.657654	+	0.753320i	$0.728451\pi$
$662$	−12.9247	+	9.39038i	−0.502334	+	0.364967i
$663$		0			0
$664$	10.6418	−	32.7520i	0.412981	−	1.27103i
$665$	−17.0411	−	12.3811i	−0.660825	−	0.480117i
$666$		0			0
$667$	9.42266	−	29.0000i	0.364847	−	1.12288i
$668$	24.8752	+	76.5581i	0.962452	+	2.96212i
$669$		0			0
$670$	52.8335			2.04114
$671$	9.86094	+	20.4974i	0.380677	+	0.791293i
$672$		0			0
$673$	−19.2138	+	13.9596i	−0.740638	+	0.538105i	−0.892911	−	0.450234i	$-0.851341\pi$
$673$	−19.2138	+	13.9596i	−0.740638	+	0.538105i	0.152273	+	0.988338i	$0.451341\pi$
$674$	−4.76934	−	14.6785i	−0.183708	−	0.565395i
$675$		0			0
$676$	41.5480	+	30.1864i	1.59800	+	1.16102i
$677$	−36.9164	−	26.8213i	−1.41881	−	1.03083i	−0.991966	−	0.126502i	$-0.959625\pi$
$677$	−36.9164	−	26.8213i	−1.41881	−	1.03083i	−0.426845	−	0.904325i	$-0.640375\pi$
$678$		0			0
$679$	4.59159	+	14.1315i	0.176209	+	0.542315i
$680$	16.4012	−	11.9162i	0.628958	−	0.456965i
$681$		0			0
$682$	16.5419	−	15.8030i	0.633421	−	0.605128i
$683$	28.8727			1.10478			0.552392	−	0.833585i	$-0.313715\pi$
$683$	28.8727			1.10478			0.552392	+	0.833585i	$0.313715\pi$
$684$		0			0
$685$	23.4372	+	72.1322i	0.895488	+	2.75603i
$686$	0.762262	−	2.34600i	0.0291033	−	0.0895707i
$687$		0			0
$688$	−31.8141	−	23.1143i	−1.21290	−	0.881223i
$689$	1.98434	−	6.10716i	0.0755973	−	0.232664i
$690$		0			0
$691$	21.8948	−	15.9075i	0.832918	−	0.605150i	−0.0874654	−	0.996168i	$-0.527877\pi$
$691$	21.8948	−	15.9075i	0.832918	−	0.605150i	0.920383	+	0.391017i	$0.127877\pi$
$692$	58.7994			2.23522
$693$		0			0
$694$	56.0334			2.12700
$695$	55.5705	−	40.3743i	2.10791	−	1.53148i
$696$		0			0
$697$	2.07437	−	6.38424i	0.0785722	−	0.241820i
$698$	59.2583	+	43.0537i	2.24296	+	1.62961i
$699$		0			0
$700$	−8.85884	+	27.2647i	−0.334833	+	1.03051i
$701$	−11.9020	−	36.6305i	−0.449531	−	1.38352i	−0.877437	−	0.479692i	$-0.840748\pi$
$701$	−11.9020	−	36.6305i	−0.449531	−	1.38352i	0.427905	−	0.903823i	$-0.359252\pi$
$702$		0			0
$703$	2.67198			0.100776
$704$	−22.7601	+	3.07380i	−0.857802	+	0.115848i
$705$		0			0
$706$	13.6203	−	9.89572i	0.512606	−	0.372430i
$707$	2.66360	+	8.19772i	0.100175	+	0.308307i
$708$		0			0
$709$	1.53280	+	1.11364i	0.0575654	+	0.0418237i	0.616196	−	0.787593i	$-0.288673\pi$
$709$	1.53280	+	1.11364i	0.0575654	+	0.0418237i	−0.558630	+	0.829417i	$0.688673\pi$
$710$	37.4755	+	27.2276i	1.40643	+	1.02183i
$711$		0			0
$712$	−1.10956	−	3.41487i	−0.0415824	−	0.127978i
$713$	−15.0827	+	10.9582i	−0.564851	+	0.410388i
$714$		0			0
$715$	6.61778	+	3.56459i	0.247491	+	0.133308i
$716$	19.0522			0.712013
$717$		0			0
$718$	−5.53379	−	17.0313i	−0.206519	−	0.635601i
$719$	−4.50461	+	13.8638i	−0.167994	+	0.517031i	−0.999244	−	0.0388664i	$-0.987625\pi$
$719$	−4.50461	+	13.8638i	−0.167994	+	0.517031i	0.831251	+	0.555898i	$0.187625\pi$
$720$		0			0
$721$	−0.754779	−	0.548379i	−0.0281094	−	0.0204227i
$722$	−13.6582	+	42.0357i	−0.508307	+	1.56441i
$723$		0			0
$724$	−32.7426	+	23.7889i	−1.21687	+	0.884107i
$725$	32.0984			1.19210
$726$		0			0
$727$	4.04780			0.150125			0.0750623	−	0.997179i	$-0.476084\pi$
$727$	4.04780			0.150125			0.0750623	+	0.997179i	$0.476084\pi$
$728$	2.71988	−	1.97611i	0.100805	−	0.0732394i
$729$		0			0
$730$	−17.7104	+	54.5069i	−0.655490	+	2.01739i
$731$	−8.01135	−	5.82058i	−0.296310	−	0.215282i
$732$		0			0
$733$	−7.26226	+	22.3509i	−0.268238	+	0.825551i	0.722692	+	0.691170i	$0.242905\pi$
$733$	−7.26226	+	22.3509i	−0.268238	+	0.825551i	−0.990930	+	0.134381i	$0.957095\pi$
$734$	27.6980	+	85.2457i	1.02235	+	3.14648i
$735$		0			0
$736$	−5.69437			−0.209897
$737$	18.0404	+	9.71726i	0.664527	+	0.357940i
$738$		0			0
$739$	26.4376	−	19.2080i	0.972522	−	0.706578i	0.0164968	−	0.999864i	$-0.494749\pi$
$739$	26.4376	−	19.2080i	0.972522	−	0.706578i	0.956025	+	0.293286i	$0.0947487\pi$
$740$	−1.92435	−	5.92254i	−0.0707405	−	0.217717i
$741$		0			0
$742$	19.6020	+	14.2417i	0.719612	+	0.522828i
$743$	−14.6479	−	10.6423i	−0.537379	−	0.390429i	0.285731	−	0.958310i	$-0.407763\pi$
$743$	−14.6479	−	10.6423i	−0.537379	−	0.390429i	−0.823111	+	0.567881i	$0.807763\pi$
$744$		0			0
$745$	−3.38750	−	10.4257i	−0.124108	−	0.381967i
$746$	−28.5202	+	20.7211i	−1.04420	+	0.758655i
$747$		0			0
$748$	15.2671	−	2.06186i	0.558222	−	0.0753892i
$749$	6.62212			0.241967
$750$		0			0
$751$	2.82552	+	8.69605i	0.103105	+	0.317323i	0.989281	−	0.146025i	$-0.0466479\pi$
$751$	2.82552	+	8.69605i	0.103105	+	0.317323i	−0.886176	+	0.463348i	$0.846648\pi$
$752$	0.843835	−	2.59706i	0.0307715	−	0.0947049i
$753$		0			0
$754$	−5.96689	−	4.33520i	−0.217301	−	0.157879i
$755$	9.56444	−	29.4363i	0.348086	−	1.07130i
$756$		0			0
$757$	−38.3077	+	27.8322i	−1.39232	+	1.01158i	−0.396710	+	0.917944i	$0.629848\pi$
$757$	−38.3077	+	27.8322i	−1.39232	+	1.01158i	−0.995607	+	0.0936338i	$0.970152\pi$
$758$	6.27851			0.228046
$759$		0			0
$760$	108.323			3.92927
$761$	2.78972	−	2.02685i	0.101127	−	0.0734732i	−0.536073	−	0.844172i	$-0.680093\pi$
$761$	2.78972	−	2.02685i	0.101127	−	0.0734732i	0.637200	+	0.770699i	$0.280093\pi$
$762$		0			0
$763$	1.27472	−	3.92317i	0.0461478	−	0.142028i
$764$	32.8579	+	23.8727i	1.18876	+	0.863683i
$765$		0			0
$766$	−17.6362	+	54.2787i	−0.637223	+	1.96117i
$767$	0.342234	+	1.05329i	0.0123573	+	0.0380320i
$768$		0			0
$769$	34.9787			1.26137			0.630683	−	0.776041i	$-0.282775\pi$
$769$	34.9787			1.26137			0.630683	+	0.776041i	$0.282775\pi$
$770$	−20.5078	+	19.5918i	−0.739050	+	0.706040i
$771$		0			0
$772$	−12.2491	+	8.89953i	−0.440856	+	0.320301i
$773$	−7.84266	−	24.1372i	−0.282081	−	0.868155i	−0.987258	−	0.159125i	$-0.949133\pi$
$773$	−7.84266	−	24.1372i	−0.282081	−	0.868155i	0.705178	−	0.709031i	$-0.250867\pi$
$774$		0			0
$775$	−15.8771	−	11.5354i	−0.570321	−	0.414363i
$776$	−61.8183	−	44.9137i	−2.21915	−	1.61231i
$777$		0			0
$778$	23.0672	+	70.9934i	0.826998	+	2.54524i
$779$	29.0176	−	21.0825i	1.03966	−	0.755358i
$780$		0			0
$781$	7.78856	+	16.1897i	0.278697	+	0.579312i
$782$	−18.7015			−0.668765
$783$		0			0
$784$	1.39545	+	4.29476i	0.0498376	+	0.153384i
$785$	1.22091	−	3.75758i	0.0435762	−	0.134114i
$786$		0			0
$787$	−24.0725	−	17.4897i	−0.858090	−	0.623439i	0.0692745	−	0.997598i	$-0.477932\pi$
$787$	−24.0725	−	17.4897i	−0.858090	−	0.623439i	−0.927365	+	0.374159i	$0.877932\pi$
$788$	−7.47236	+	22.9976i	−0.266192	+	0.819255i
$789$		0			0
$790$	18.3595	−	13.3389i	0.653201	−	0.474578i
$791$	−18.8258			−0.669369
$792$		0			0
$793$	−4.48355			−0.159215
$794$	−45.2490	+	32.8753i	−1.60583	+	1.16670i
$795$		0			0
$796$	14.4961	−	44.6144i	0.513800	−	1.58132i
$797$	−5.05094	−	3.66972i	−0.178913	−	0.129988i	0.494724	−	0.869050i	$-0.335269\pi$
$797$	−5.05094	−	3.66972i	−0.178913	−	0.129988i	−0.673638	+	0.739062i	$0.735269\pi$
$798$		0			0
$799$	0.212493	−	0.653985i	0.00751745	−	0.0231363i
$800$	−1.85234	−	5.70090i	−0.0654899	−	0.201557i
$801$		0			0
$802$	−40.0069			−1.41269
$803$	−16.0724	+	15.3545i	−0.567182	+	0.541848i
$804$		0			0
$805$	18.6988	−	13.5855i	0.659046	−	0.478825i
$806$	1.39349	+	4.28871i	0.0490834	+	0.151063i
$807$		0			0
$808$	−35.8611	−	26.0546i	−1.26159	−	0.916598i
$809$	31.7022	+	23.0330i	1.11459	+	0.809796i	0.983380	−	0.181559i	$-0.0581142\pi$
$809$	31.7022	+	23.0330i	1.11459	+	0.809796i	0.131209	+	0.991355i	$0.458114\pi$
$810$		0			0
$811$	−3.82591	−	11.7749i	−0.134346	−	0.413474i	0.861142	−	0.508365i	$-0.169750\pi$
$811$	−3.82591	−	11.7749i	−0.134346	−	0.413474i	−0.995488	+	0.0948906i	$0.969750\pi$
$812$	15.1140	−	10.9810i	0.530399	−	0.385357i
$813$		0			0
$814$	0.643819	−	3.53969i	0.0225659	−	0.124066i
$815$	−17.5669			−0.615341
$816$		0			0
$817$	−16.3505	−	50.3216i	−0.572031	−	1.76053i
$818$	26.7260	−	82.2541i	0.934452	−	2.87595i
$819$		0			0
$820$	−67.6284	−	49.1349i	−2.36168	−	1.71586i
$821$	−14.7397	+	45.3642i	−0.514420	+	1.58322i	0.269916	+	0.962884i	$0.413004\pi$
$821$	−14.7397	+	45.3642i	−0.514420	+	1.58322i	−0.784335	+	0.620337i	$0.786996\pi$
$822$		0			0
$823$	11.7475	−	8.53507i	0.409493	−	0.297514i	−0.363904	−	0.931437i	$-0.618556\pi$
$823$	11.7475	−	8.53507i	0.409493	−	0.297514i	0.773396	+	0.633923i	$0.218556\pi$
$824$	4.79779			0.167139
$825$		0			0
$826$	−4.17878			−0.145398
$827$	−25.0287	+	18.1844i	−0.870335	+	0.632335i	−0.930677	−	0.365843i	$-0.880781\pi$
$827$	−25.0287	+	18.1844i	−0.870335	+	0.632335i	0.0603420	+	0.998178i	$0.480781\pi$
$828$		0			0
$829$	0.0265154	−	0.0816061i	0.000920918	−	0.00283430i	−0.950595	−	0.310434i	$-0.899526\pi$
$829$	0.0265154	−	0.0816061i	0.000920918	−	0.00283430i	0.951516	+	0.307600i	$0.0995257\pi$
$830$	−46.3290	−	33.6600i	−1.60810	−	1.16835i
$831$		0			0
$832$	1.39893	−	4.30548i	0.0484993	−	0.149266i
$833$	0.351400	+	1.08150i	0.0121753	+	0.0374717i
$834$		0			0
$835$	68.3185			2.36426
$836$	72.4713	+	39.0358i	2.50647	+	1.35008i
$837$		0			0
$838$	−56.4030	+	40.9792i	−1.94841	+	1.41560i
$839$	−3.30355	−	10.1673i	−0.114051	−	0.351014i	0.877697	−	0.479217i	$-0.159079\pi$
$839$	−3.30355	−	10.1673i	−0.114051	−	0.351014i	−0.991748	+	0.128203i	$0.959079\pi$
$840$		0			0
$841$	6.53883	+	4.75074i	0.225477	+	0.163819i
$842$	−27.5290	−	20.0010i	−0.948713	−	0.689281i
$843$		0			0
$844$	11.0131	+	33.8948i	0.379086	+	1.16671i
$845$	35.2617	−	25.6191i	1.21304	−	0.881325i
$846$		0			0
$847$	−10.6059	+	2.91793i	−0.364424	+	0.100261i
$848$	−44.3561			−1.52319
$849$		0			0
$850$	−6.08347	−	18.7230i	−0.208661	−	0.642193i
$851$	−0.906008	+	2.78841i	−0.0310576	+	0.0955854i
$852$		0			0
$853$	−17.1514	−	12.4612i	−0.587252	−	0.426664i	0.254079	−	0.967183i	$-0.418228\pi$
$853$	−17.1514	−	12.4612i	−0.587252	−	0.426664i	−0.841331	+	0.540520i	$0.818228\pi$
$854$	5.22773	−	16.0893i	0.178889	−	0.550565i
$855$		0			0
$856$	−27.5508	+	20.0168i	−0.941666	+	0.684160i
$857$	9.45359			0.322929			0.161464	−	0.986879i	$-0.448378\pi$
$857$	9.45359			0.322929			0.161464	+	0.986879i	$0.448378\pi$
$858$		0			0
$859$	−38.8261			−1.32473			−0.662365	−	0.749181i	$-0.730447\pi$
$859$	−38.8261			−1.32473			−0.662365	+	0.749181i	$0.730447\pi$
$860$	−99.7640	+	72.4828i	−3.40192	+	2.47164i
$861$		0			0
$862$	21.4730	−	66.0869i	0.731372	−	2.25093i
$863$	−30.4228	−	22.1034i	−1.03560	−	0.752410i	−0.0661810	−	0.997808i	$-0.521081\pi$
$863$	−30.4228	−	22.1034i	−1.03560	−	0.752410i	−0.969423	+	0.245398i	$0.921081\pi$
$864$		0			0
$865$	15.4208	−	47.4605i	0.524324	−	1.61370i
$866$	−10.8084	−	33.2647i	−0.367283	−	1.13038i
$867$		0			0
$868$	−11.4223			−0.387697
$869$	8.72231	−	1.17797i	0.295884	−	0.0399599i
$870$		0			0
$871$	−3.26767	+	2.37410i	−0.110721	+	0.0804433i
$872$	6.55530	+	20.1752i	0.221991	+	0.683217i
$873$		0			0
$874$	−80.8416	−	58.7348i	−2.73451	−	1.98674i
$875$	5.66042	+	4.11253i	0.191357	+	0.139029i
$876$		0			0
$877$	6.80103	+	20.9314i	0.229654	+	0.706804i	0.997786	+	0.0665113i	$0.0211869\pi$
$877$	6.80103	+	20.9314i	0.229654	+	0.706804i	−0.768131	+	0.640293i	$0.778813\pi$
$878$	55.9145	−	40.6243i	1.88702	−	1.37100i
$879$		0			0
$880$	9.29140	−	51.0836i	0.313213	−	1.72203i
$881$	6.92969			0.233467			0.116734	−	0.993163i	$-0.462758\pi$
$881$	6.92969			0.233467			0.116734	+	0.993163i	$0.462758\pi$
$882$		0			0
$883$	13.0834	+	40.2666i	0.440292	+	1.35508i	0.887566	+	0.460681i	$0.152395\pi$
$883$	13.0834	+	40.2666i	0.440292	+	1.35508i	−0.447274	+	0.894397i	$0.647605\pi$
$884$	−0.938386	+	2.88806i	−0.0315613	+	0.0971358i
$885$		0			0
$886$	−34.5982	−	25.1371i	−1.16235	−	0.844496i
$887$	−2.48959	+	7.66216i	−0.0835921	+	0.257270i	−0.984113	−	0.177542i	$-0.943185\pi$
$887$	−2.48959	+	7.66216i	−0.0835921	+	0.257270i	0.900521	+	0.434812i	$0.143185\pi$
$888$		0			0
$889$	−6.44491	+	4.68250i	−0.216155	+	0.157046i
$890$	−5.97077			−0.200141
$891$		0			0
$892$	42.2072			1.41320
$893$	2.97248	−	2.15964i	0.0994703	−	0.0722694i
$894$		0			0
$895$	4.99666	−	15.3781i	0.167020	−	0.514034i
$896$	15.2011	+	11.0443i	0.507834	+	0.368963i
$897$		0			0
$898$	−22.5031	+	69.2575i	−0.750939	+	2.31115i
$899$	3.95206	+	12.1632i	0.131808	+	0.405665i
$900$		0			0
$901$	−11.1697			−0.372115
$902$	−20.9370	−	43.5207i	−0.697127	−	1.44908i
$903$		0			0
$904$	78.3232	−	56.9051i	2.60499	−	1.89264i
$905$	10.6143	+	32.6674i	0.352831	+	1.08590i
$906$		0			0
$907$	−2.34153	−	1.70122i	−0.0777492	−	0.0564881i	0.548232	−	0.836327i	$-0.315301\pi$
$907$	−2.34153	−	1.70122i	−0.0777492	−	0.0564881i	−0.625981	+	0.779838i	$0.715301\pi$
$908$	−43.8492	−	31.8583i	−1.45519	−	1.05725i
$909$		0			0
$910$	−1.72758	−	5.31693i	−0.0572686	−	0.176255i
$911$	−16.3826	+	11.9026i	−0.542779	+	0.394352i	−0.825116	−	0.564963i	$-0.808890\pi$
$911$	−16.3826	+	11.9026i	−0.542779	+	0.394352i	0.282337	+	0.959315i	$0.408890\pi$
$912$		0			0
$913$	−9.62858	−	20.0144i	−0.318659	−	0.662380i
$914$	−23.9205			−0.791220
$915$		0			0
$916$	−3.15089	−	9.69745i	−0.104108	−	0.320413i
$917$	−1.48484	+	4.56988i	−0.0490338	+	0.150911i
$918$		0			0
$919$	−15.1498	−	11.0069i	−0.499744	−	0.363085i	0.309175	−	0.951005i	$-0.399947\pi$
$919$	−15.1498	−	11.0069i	−0.499744	−	0.363085i	−0.808919	+	0.587920i	$0.799947\pi$
$920$	−36.7297	+	113.042i	−1.21094	+	3.72690i
$921$		0			0
$922$	38.3592	−	27.8696i	1.26329	−	0.917836i
$923$	−3.54128			−0.116563
$924$		0			0
$925$	−3.08632			−0.101478
$926$	40.9756	−	29.7705i	1.34654	−	0.978320i
$927$		0			0
$928$	−1.20711	+	3.71511i	−0.0396254	+	0.121954i
$929$	−36.6243	−	26.6091i	−1.20160	−	0.873016i	−0.207162	−	0.978307i	$-0.566423\pi$
$929$	−36.6243	−	26.6091i	−1.20160	−	0.873016i	−0.994441	+	0.105291i	$0.966423\pi$
$930$		0			0
$931$	−1.87759	+	5.77864i	−0.0615357	+	0.189387i
$932$	12.1226	+	37.3096i	0.397090	+	1.22212i
$933$		0			0
$934$	83.0584			2.71775
$935$	2.33974	−	12.8638i	0.0765177	−	0.420690i
$936$		0			0
$937$	−23.8336	+	17.3161i	−0.778609	+	0.565692i	−0.904561	−	0.426344i	$-0.859801\pi$
$937$	−23.8336	+	17.3161i	−0.778609	+	0.565692i	0.125952	+	0.992036i	$0.459801\pi$
$938$	−4.70947	−	14.4942i	−0.153769	−	0.473254i
$939$		0			0
$940$	−6.92767	−	5.03325i	−0.225956	−	0.164167i
$941$	47.1128	+	34.2294i	1.53583	+	1.11585i	0.952882	+	0.303340i	$0.0981017\pi$
$941$	47.1128	+	34.2294i	1.53583	+	1.11585i	0.582950	+	0.812508i	$0.301898\pi$
$942$		0			0
$943$	12.1619	+	37.4305i	0.396046	+	1.21891i
$944$	6.18897	−	4.49655i	0.201434	−	0.146350i
$945$		0			0
$946$	−70.6028	+	9.53508i	−2.29550	+	0.310012i
$947$	−45.3642			−1.47414			−0.737069	−	0.675818i	$-0.763791\pi$
$947$	−45.3642			−1.47414			−0.737069	+	0.675818i	$0.763791\pi$
$948$		0			0
$949$	−1.35394	−	4.16699i	−0.0439506	−	0.135266i
$950$	32.5051	−	100.040i	1.05460	−	3.24574i
$951$		0			0
$952$	−4.73103	−	3.43730i	−0.153334	−	0.111403i
$953$	12.7740	−	39.3143i	0.413790	−	1.27352i	−0.499538	−	0.866292i	$-0.666497\pi$
$953$	12.7740	−	39.3143i	0.413790	−	1.27352i	0.913328	−	0.407224i	$-0.133503\pi$
$954$		0			0
$955$	27.8864	−	20.2607i	0.902384	−	0.655620i
$956$	−22.7247			−0.734968
$957$		0			0
$958$	34.9555			1.12936
$959$	17.6995	−	12.8594i	0.571545	−	0.415252i
$960$		0			0
$961$	−7.16322	+	22.0461i	−0.231071	+	0.711165i
$962$	0.573728	+	0.416838i	0.0184977	+	0.0134394i
$963$		0			0
$964$	18.9601	−	58.3533i	0.610665	−	1.87943i
$965$	3.97085	+	12.2210i	0.127826	+	0.393409i
$966$		0			0
$967$	−6.52818			−0.209932			−0.104966	−	0.994476i	$-0.533473\pi$
$967$	−6.52818			−0.209932			−0.104966	+	0.994476i	$0.533473\pi$
$968$	35.3050	−	44.1986i	1.13475	−	1.42060i
$969$		0			0
$970$	−102.797	+	74.6864i	−3.30061	+	2.39803i
$971$	−8.91783	−	27.4462i	−0.286187	−	0.880792i	−0.986040	−	0.166506i	$-0.946752\pi$
$971$	−8.91783	−	27.4462i	−0.286187	−	0.880792i	0.699854	−	0.714286i	$-0.253248\pi$
$972$		0			0
$973$	−16.0296	−	11.6462i	−0.513887	−	0.373360i
$974$	55.3617	+	40.2226i	1.77390	+	1.28882i
$975$		0			0
$976$	9.57027	+	29.4543i	0.306337	+	0.942808i
$977$	−7.26864	+	5.28097i	−0.232544	+	0.168953i	−0.697955	−	0.716141i	$-0.745907\pi$
$977$	−7.26864	+	5.28097i	−0.232544	+	0.168953i	0.465411	+	0.885095i	$0.345907\pi$
$978$		0			0
$979$	−2.03877	−	1.09816i	−0.0651593	−	0.0350973i
$980$	14.1608			0.452350
$981$		0			0
$982$	−2.62443	−	8.07717i	−0.0837490	−	0.257753i
$983$	−11.3971	+	35.0768i	−0.363512	+	1.11877i	0.587396	+	0.809300i	$0.300153\pi$
$983$	−11.3971	+	35.0768i	−0.363512	+	1.11877i	−0.950908	+	0.309475i	$0.899847\pi$
$984$		0			0
$985$	16.6030	+	12.0628i	0.529015	+	0.384352i
$986$	−3.96441	+	12.2012i	−0.126253	+	0.388566i
$987$		0			0
$988$	−13.1267	+	9.53713i	−0.417617	+	0.303417i
$989$	58.0583			1.84615
$990$		0			0
$991$	−2.98352			−0.0947746			−0.0473873	−	0.998877i	$-0.515089\pi$
$991$	−2.98352			−0.0947746			−0.0473873	+	0.998877i	$0.515089\pi$
$992$	1.93220	−	1.40383i	0.0613475	−	0.0445716i
$993$		0			0
$994$	4.12907	−	12.7080i	0.130966	−	0.403072i
$995$	−32.2092	−	23.4013i	−1.02110	−	0.741872i
$996$		0			0
$997$	19.4234	−	59.7790i	0.615144	−	1.89322i	0.215707	−	0.976458i	$-0.430795\pi$
$997$	19.4234	−	59.7790i	0.615144	−	1.89322i	0.399437	−	0.916760i	$-0.369205\pi$
$998$	1.97367	+	6.07434i	0.0624755	+	0.192280i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	693.2.m.g.190.2		8
3.2	odd	2		77.2.f.a.36.1	yes	8
11.2	odd	10		7623.2.a.co.1.4		4
11.4	even	5	inner	693.2.m.g.631.2		8
11.9	even	5		7623.2.a.ch.1.1		4
21.2	odd	6		539.2.q.c.410.2		16
21.5	even	6		539.2.q.b.410.2		16
21.11	odd	6		539.2.q.c.520.1		16
21.17	even	6		539.2.q.b.520.1		16
21.20	even	2		539.2.f.d.344.1		8
33.2	even	10		847.2.a.k.1.1		4
33.5	odd	10		847.2.f.p.372.2		8
33.8	even	10		847.2.f.s.148.1		8
33.14	odd	10		847.2.f.p.148.2		8
33.17	even	10		847.2.f.s.372.1		8
33.20	odd	10		847.2.a.l.1.4		4
33.26	odd	10		77.2.f.a.15.1	✓	8
33.29	even	10		847.2.f.q.323.2		8
33.32	even	2		847.2.f.q.729.2		8
231.20	even	10		5929.2.a.bi.1.4		4
231.26	even	30		539.2.q.b.312.1		16
231.59	even	30		539.2.q.b.422.2		16
231.125	even	10		539.2.f.d.246.1		8
231.158	odd	30		539.2.q.c.422.2		16
231.167	odd	10		5929.2.a.bb.1.1		4
231.191	odd	30		539.2.q.c.312.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
77.2.f.a.15.1	✓	8	33.26	odd	10
77.2.f.a.36.1	yes	8	3.2	odd	2
539.2.f.d.246.1		8	231.125	even	10
539.2.f.d.344.1		8	21.20	even	2
539.2.q.b.312.1		16	231.26	even	30
539.2.q.b.410.2		16	21.5	even	6
539.2.q.b.422.2		16	231.59	even	30
539.2.q.b.520.1		16	21.17	even	6
539.2.q.c.312.1		16	231.191	odd	30
539.2.q.c.410.2		16	21.2	odd	6
539.2.q.c.422.2		16	231.158	odd	30
539.2.q.c.520.1		16	21.11	odd	6
693.2.m.g.190.2		8	1.1	even	1	trivial
693.2.m.g.631.2		8	11.4	even	5	inner
847.2.a.k.1.1		4	33.2	even	10
847.2.a.l.1.4		4	33.20	odd	10
847.2.f.p.148.2		8	33.14	odd	10
847.2.f.p.372.2		8	33.5	odd	10
847.2.f.q.323.2		8	33.29	even	10
847.2.f.q.729.2		8	33.32	even	2
847.2.f.s.148.1		8	33.8	even	10
847.2.f.s.372.1		8	33.17	even	10
5929.2.a.bb.1.1		4	231.167	odd	10
5929.2.a.bi.1.4		4	231.20	even	10
7623.2.a.ch.1.1		4	11.9	even	5
7623.2.a.co.1.4		4	11.2	odd	10

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:	\( N \)	\(=\)	\( 693 = 3^{2} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	693.m (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.99563 - 1.44991i) q^{2} +(1.26226 - 3.88484i) q^{4} +(-2.80464 - 2.03769i) q^{5} +(-0.309017 + 0.951057i) q^{7} +(-1.58914 - 4.89086i) q^{8} +O(q^{10})\)	\(q+(1.99563 - 1.44991i) q^{2} +(1.26226 - 3.88484i) q^{4} +(-2.80464 - 2.03769i) q^{5} +(-0.309017 + 0.951057i) q^{7} +(-1.58914 - 4.89086i) q^{8} -8.55150 q^{10} +(-2.91998 - 1.57281i) q^{11} +(0.528896 - 0.384266i) q^{13} +(0.762262 + 2.34600i) q^{14} +(-3.65334 - 2.65431i) q^{16} +(-0.919977 - 0.668402i) q^{17} +(-1.87759 - 5.77864i) q^{19} +(-11.4563 + 8.32350i) q^{20} +(-8.10762 + 1.09495i) q^{22} +6.66708 q^{23} +(2.16875 + 6.67473i) q^{25} +(0.498330 - 1.53370i) q^{26} +(3.30464 + 2.40097i) q^{28} +(1.41331 - 4.34973i) q^{29} +(-2.26226 + 1.64363i) q^{31} -0.854102 q^{32} -2.80505 q^{34} +(2.80464 - 2.03769i) q^{35} +(-0.135893 + 0.418235i) q^{37} +(-12.1255 - 8.80968i) q^{38} +(-5.50911 + 16.9553i) q^{40} +(1.82417 + 5.61423i) q^{41} +8.70820 q^{43} +(-9.79590 + 9.35835i) q^{44} +(13.3050 - 9.66666i) q^{46} +(0.186864 + 0.575107i) q^{47} +(-0.809017 - 0.587785i) q^{49} +(14.0058 + 10.1758i) q^{50} +(-0.825206 - 2.53972i) q^{52} +(7.94654 - 5.77350i) q^{53} +(4.98459 + 10.3612i) q^{55} +5.14256 q^{56} +(-3.48626 - 10.7296i) q^{58} +(-0.523492 + 1.61114i) q^{59} +(-5.54839 - 4.03114i) q^{61} +(-2.13152 + 6.56015i) q^{62} +(5.60222 - 4.07025i) q^{64} -2.26638 q^{65} -6.17828 q^{67} +(-3.75789 + 2.73027i) q^{68} +(2.64256 - 8.13296i) q^{70} +(-4.38234 - 3.18395i) q^{71} +(2.07103 - 6.37396i) q^{73} +(0.335211 + 1.03167i) q^{74} -24.8191 q^{76} +(2.39815 - 2.29104i) q^{77} +(-2.14693 + 1.55984i) q^{79} +(4.83766 + 14.8888i) q^{80} +(11.7805 + 8.55903i) q^{82} +(5.41765 + 3.93615i) q^{83} +(1.21821 + 3.74926i) q^{85} +(17.3783 - 12.6261i) q^{86} +(-3.05216 + 16.7806i) q^{88} +0.698213 q^{89} +(0.202020 + 0.621755i) q^{91} +(8.41560 - 25.9006i) q^{92} +(1.20676 + 0.876765i) q^{94} +(-6.50911 + 20.0330i) q^{95} +(12.0209 - 8.73372i) q^{97} -2.46673 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + q^{2} + 3 q^{4} - 3 q^{5} + 2 q^{7} - 3 q^{8}+O(q^{10}) \) 8 * q + q^2 + 3 * q^4 - 3 * q^5 + 2 * q^7 - 3 * q^8	\( 8 q + q^{2} + 3 q^{4} - 3 q^{5} + 2 q^{7} - 3 q^{8} - 28 q^{10} - 5 q^{11} + 5 q^{13} - q^{14} - 3 q^{16} + 11 q^{17} - 9 q^{19} - 21 q^{20} - q^{22} + 16 q^{23} + 5 q^{25} - 21 q^{26} + 7 q^{28} + 9 q^{29} - 11 q^{31} + 20 q^{32} - 24 q^{34} + 3 q^{35} + 6 q^{37} - 35 q^{38} - 16 q^{40} + 22 q^{41} + 16 q^{43} - 29 q^{44} + 29 q^{46} - 7 q^{47} - 2 q^{49} + 34 q^{50} + 21 q^{52} - 2 q^{53} + 26 q^{55} + 18 q^{56} - 39 q^{58} - 25 q^{59} + 7 q^{61} + 5 q^{62} + q^{64} - 24 q^{65} - 30 q^{67} - 8 q^{68} - 2 q^{70} + 14 q^{71} + 3 q^{73} + 9 q^{74} - 52 q^{76} + 5 q^{77} - 9 q^{79} + 33 q^{80} + 31 q^{82} - 23 q^{83} - 10 q^{85} + 17 q^{86} - 7 q^{88} + 34 q^{89} + 5 q^{91} + 34 q^{92} - 30 q^{94} - 24 q^{95} + 30 q^{97} - 4 q^{98}+O(q^{100}) \) 8 * q + q^2 + 3 * q^4 - 3 * q^5 + 2 * q^7 - 3 * q^8 - 28 * q^10 - 5 * q^11 + 5 * q^13 - q^14 - 3 * q^16 + 11 * q^17 - 9 * q^19 - 21 * q^20 - q^22 + 16 * q^23 + 5 * q^25 - 21 * q^26 + 7 * q^28 + 9 * q^29 - 11 * q^31 + 20 * q^32 - 24 * q^34 + 3 * q^35 + 6 * q^37 - 35 * q^38 - 16 * q^40 + 22 * q^41 + 16 * q^43 - 29 * q^44 + 29 * q^46 - 7 * q^47 - 2 * q^49 + 34 * q^50 + 21 * q^52 - 2 * q^53 + 26 * q^55 + 18 * q^56 - 39 * q^58 - 25 * q^59 + 7 * q^61 + 5 * q^62 + q^64 - 24 * q^65 - 30 * q^67 - 8 * q^68 - 2 * q^70 + 14 * q^71 + 3 * q^73 + 9 * q^74 - 52 * q^76 + 5 * q^77 - 9 * q^79 + 33 * q^80 + 31 * q^82 - 23 * q^83 - 10 * q^85 + 17 * q^86 - 7 * q^88 + 34 * q^89 + 5 * q^91 + 34 * q^92 - 30 * q^94 - 24 * q^95 + 30 * q^97 - 4 * q^98

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