LMFDB - Embedded newform 804.2.e.b.535.25

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [804,2,Mod(535,804)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(804, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("804.535");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 804 = 2^{2} \cdot 3 \cdot 67 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	804.e (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$6.41997232251$
Analytic rank:	$0$
Dimension:	$34$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			535.25
Character	$\chi$	$=$	804.535
Dual form			804.2.e.b.535.26

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.946315 - 1.05095i) q^{2} +1.00000 q^{3} +(-0.208975 - 1.98905i) q^{4} -4.42921i q^{5} +(0.946315 - 1.05095i) q^{6} +2.81753 q^{7} +(-2.28814 - 1.66265i) q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+(0.946315 - 1.05095i) q^{2} +1.00000 q^{3} +(-0.208975 - 1.98905i) q^{4} -4.42921i q^{5} +(0.946315 - 1.05095i) q^{6} +2.81753 q^{7} +(-2.28814 - 1.66265i) q^{8} +1.00000 q^{9} +(-4.65486 - 4.19143i) q^{10} +4.49085 q^{11} +(-0.208975 - 1.98905i) q^{12} +6.44697i q^{13} +(2.66628 - 2.96108i) q^{14} -4.42921i q^{15} +(-3.91266 + 0.831325i) q^{16} +1.33300 q^{17} +(0.946315 - 1.05095i) q^{18} +1.70948i q^{19} +(-8.80993 + 0.925594i) q^{20} +2.81753 q^{21} +(4.24976 - 4.71965i) q^{22} +3.41301i q^{23} +(-2.28814 - 1.66265i) q^{24} -14.6179 q^{25} +(6.77542 + 6.10087i) q^{26} +1.00000 q^{27} +(-0.588795 - 5.60422i) q^{28} -3.13779 q^{29} +(-4.65486 - 4.19143i) q^{30} -8.45275 q^{31} +(-2.82893 + 4.89869i) q^{32} +4.49085 q^{33} +(1.26144 - 1.40092i) q^{34} -12.4794i q^{35} +(-0.208975 - 1.98905i) q^{36} +5.75928 q^{37} +(1.79658 + 1.61771i) q^{38} +6.44697i q^{39} +(-7.36422 + 10.1347i) q^{40} +5.15047i q^{41} +(2.66628 - 2.96108i) q^{42} -1.06496 q^{43} +(-0.938477 - 8.93254i) q^{44} -4.42921i q^{45} +(3.58689 + 3.22978i) q^{46} +4.52896i q^{47} +(-3.91266 + 0.831325i) q^{48} +0.938501 q^{49} +(-13.8331 + 15.3626i) q^{50} +1.33300 q^{51} +(12.8234 - 1.34726i) q^{52} +4.63647i q^{53} +(0.946315 - 1.05095i) q^{54} -19.8909i q^{55} +(-6.44692 - 4.68457i) q^{56} +1.70948i q^{57} +(-2.96934 + 3.29764i) q^{58} -10.2820i q^{59} +(-8.80993 + 0.925594i) q^{60} +9.66191i q^{61} +(-7.99897 + 8.88339i) q^{62} +2.81753 q^{63} +(2.47120 + 7.60876i) q^{64} +28.5550 q^{65} +(4.24976 - 4.71965i) q^{66} +(-6.48382 - 4.99600i) q^{67} +(-0.278565 - 2.65142i) q^{68} +3.41301i q^{69} +(-13.1152 - 11.8095i) q^{70} -0.479394i q^{71} +(-2.28814 - 1.66265i) q^{72} +3.68198 q^{73} +(5.45009 - 6.05269i) q^{74} -14.6179 q^{75} +(3.40026 - 0.357240i) q^{76} +12.6531 q^{77} +(6.77542 + 6.10087i) q^{78} +9.91224 q^{79} +(3.68211 + 17.3300i) q^{80} +1.00000 q^{81} +(5.41286 + 4.87397i) q^{82} -8.53248i q^{83} +(-0.588795 - 5.60422i) q^{84} -5.90416i q^{85} +(-1.00779 + 1.11921i) q^{86} -3.13779 q^{87} +(-10.2757 - 7.46671i) q^{88} -11.6876 q^{89} +(-4.65486 - 4.19143i) q^{90} +18.1646i q^{91} +(6.78865 - 0.713234i) q^{92} -8.45275 q^{93} +(4.75969 + 4.28582i) q^{94} +7.57166 q^{95} +(-2.82893 + 4.89869i) q^{96} -13.2311i q^{97} +(0.888118 - 0.986314i) q^{98} +4.49085 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 34 q + 34 q^{3} + 2 q^{4} + 4 q^{7} - 6 q^{8} + 34 q^{9}+O(q^{10}) $ 34 * q + 34 * q^3 + 2 * q^4 + 4 * q^7 - 6 * q^8 + 34 * q^9	$ 34 q + 34 q^{3} + 2 q^{4} + 4 q^{7} - 6 q^{8} + 34 q^{9} - 6 q^{10} + 2 q^{12} - 4 q^{14} + 2 q^{16} - 12 q^{20} + 4 q^{21} - 8 q^{22} - 6 q^{24} - 34 q^{25} + 10 q^{26} + 34 q^{27} - 8 q^{28} - 16 q^{29} - 6 q^{30} - 4 q^{31} + 2 q^{36} + 12 q^{37} + 26 q^{38} - 18 q^{40} - 4 q^{42} - 4 q^{43} + 26 q^{44} - 4 q^{46} + 2 q^{48} + 46 q^{49} - 18 q^{50} + 32 q^{52} + 14 q^{56} + 4 q^{58} - 12 q^{60} - 2 q^{62} + 4 q^{63} + 26 q^{64} - 8 q^{66} - 18 q^{67} - 34 q^{68} + 56 q^{70} - 6 q^{72} + 12 q^{73} + 22 q^{74} - 34 q^{75} - 32 q^{76} - 8 q^{77} + 10 q^{78} - 12 q^{79} - 2 q^{80} + 34 q^{81} + 26 q^{82} - 8 q^{84} + 6 q^{86} - 16 q^{87} - 28 q^{88} - 6 q^{90} - 46 q^{92} - 4 q^{93} + 32 q^{94} - 40 q^{95} - 40 q^{98}+O(q^{100}) $ 34 * q + 34 * q^3 + 2 * q^4 + 4 * q^7 - 6 * q^8 + 34 * q^9 - 6 * q^10 + 2 * q^12 - 4 * q^14 + 2 * q^16 - 12 * q^20 + 4 * q^21 - 8 * q^22 - 6 * q^24 - 34 * q^25 + 10 * q^26 + 34 * q^27 - 8 * q^28 - 16 * q^29 - 6 * q^30 - 4 * q^31 + 2 * q^36 + 12 * q^37 + 26 * q^38 - 18 * q^40 - 4 * q^42 - 4 * q^43 + 26 * q^44 - 4 * q^46 + 2 * q^48 + 46 * q^49 - 18 * q^50 + 32 * q^52 + 14 * q^56 + 4 * q^58 - 12 * q^60 - 2 * q^62 + 4 * q^63 + 26 * q^64 - 8 * q^66 - 18 * q^67 - 34 * q^68 + 56 * q^70 - 6 * q^72 + 12 * q^73 + 22 * q^74 - 34 * q^75 - 32 * q^76 - 8 * q^77 + 10 * q^78 - 12 * q^79 - 2 * q^80 + 34 * q^81 + 26 * q^82 - 8 * q^84 + 6 * q^86 - 16 * q^87 - 28 * q^88 - 6 * q^90 - 46 * q^92 - 4 * q^93 + 32 * q^94 - 40 * q^95 - 40 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/804\mathbb{Z}\right)^\times$.

$n$	$269$	$337$	$403$
$\chi(n)$	$1$	$-1$	$-1$

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 $

$2$	0.946315	−	1.05095i	0.669146	−	0.743131i
$2$	0.946315	−	1.05095i	0.669146	−	0.743131i
$3$	1.00000			0.577350
$3$	1.00000			0.577350
$4$	−0.208975	−	1.98905i	−0.104488	−	0.994526i
$5$		−	4.42921i		−	1.98080i	−0.138224	−	0.990401i	$-0.544139\pi$
$5$		−	4.42921i		−	1.98080i	0.138224	−	0.990401i	$-0.455861\pi$
$6$	0.946315	−	1.05095i	0.386332	−	0.429047i
$7$	2.81753			1.06493			0.532464	−	0.846453i	$-0.321266\pi$
$7$	2.81753			1.06493			0.532464	+	0.846453i	$0.321266\pi$
$8$	−2.28814	−	1.66265i	−0.808981	−	0.587835i
$9$	1.00000			0.333333
$10$	−4.65486	−	4.19143i	−1.47200	−	1.32545i
$11$	4.49085			1.35404			0.677022	−	0.735963i	$-0.263270\pi$
$11$	4.49085			1.35404			0.677022	+	0.735963i	$0.263270\pi$
$12$	−0.208975	−	1.98905i	−0.0603259	−	0.574190i
$13$			6.44697i			1.78807i	0.447998	+	0.894035i	$0.352137\pi$
$13$			6.44697i			1.78807i	−0.447998	+	0.894035i	$0.647863\pi$
$14$	2.66628	−	2.96108i	0.712592	−	0.791381i
$15$		−	4.42921i		−	1.14362i
$16$	−3.91266	+	0.831325i	−0.978165	+	0.207831i
$17$	1.33300			0.323301			0.161651	−	0.986848i	$-0.448318\pi$
$17$	1.33300			0.323301			0.161651	+	0.986848i	$0.448318\pi$
$18$	0.946315	−	1.05095i	0.223049	−	0.247710i
$19$			1.70948i			0.392183i	0.980586	+	0.196091i	$0.0628249\pi$
$19$			1.70948i			0.392183i	−0.980586	+	0.196091i	$0.937175\pi$
$20$	−8.80993	+	0.925594i	−1.96996	+	0.206969i
$21$	2.81753			0.614836
$22$	4.24976	−	4.71965i	0.906053	−	1.00623i
$23$			3.41301i			0.711661i	0.934551	+	0.355830i	$0.115802\pi$
$23$			3.41301i			0.711661i	−0.934551	+	0.355830i	$0.884198\pi$
$24$	−2.28814	−	1.66265i	−0.467065	−	0.339387i
$25$	−14.6179			−2.92358
$26$	6.77542	+	6.10087i	1.32877	+	1.19648i
$27$	1.00000			0.192450
$28$	−0.588795	−	5.60422i	−0.111272	−	1.05910i
$29$	−3.13779			−0.582672			−0.291336	−	0.956621i	$-0.594100\pi$
$29$	−3.13779			−0.582672			−0.291336	+	0.956621i	$0.594100\pi$
$30$	−4.65486	−	4.19143i	−0.849857	−	0.765246i
$31$	−8.45275			−1.51816			−0.759080	−	0.650998i	$-0.774351\pi$
$31$	−8.45275			−1.51816			−0.759080	+	0.650998i	$0.774351\pi$
$32$	−2.82893	+	4.89869i	−0.500089	+	0.865974i
$33$	4.49085			0.781757
$34$	1.26144	−	1.40092i	0.216336	−	0.240255i
$35$		−	12.4794i		−	2.10941i
$36$	−0.208975	−	1.98905i	−0.0348292	−	0.331509i
$37$	5.75928			0.946820			0.473410	−	0.880842i	$-0.343023\pi$
$37$	5.75928			0.946820			0.473410	+	0.880842i	$0.343023\pi$
$38$	1.79658	+	1.61771i	0.291443	+	0.262427i
$39$			6.44697i			1.03234i
$40$	−7.36422	+	10.1347i	−1.16438	+	1.60243i
$41$			5.15047i			0.804368i	0.915559	+	0.402184i	$0.131749\pi$
$41$			5.15047i			0.804368i	−0.915559	+	0.402184i	$0.868251\pi$
$42$	2.66628	−	2.96108i	0.411415	−	0.456904i
$43$	−1.06496			−0.162404			−0.0812022	−	0.996698i	$-0.525876\pi$
$43$	−1.06496			−0.162404			−0.0812022	+	0.996698i	$0.525876\pi$
$44$	−0.938477	−	8.93254i	−0.141481	−	1.34663i
$45$		−	4.42921i		−	0.660267i
$46$	3.58689	+	3.22978i	0.528857	+	0.476205i
$47$			4.52896i			0.660617i	0.943873	+	0.330308i	$0.107153\pi$
$47$			4.52896i			0.660617i	−0.943873	+	0.330308i	$0.892847\pi$
$48$	−3.91266	+	0.831325i	−0.564744	+	0.119991i
$49$	0.938501			0.134072
$50$	−13.8331	+	15.3626i	−1.95630	+	2.17260i
$51$	1.33300			0.186658
$52$	12.8234	−	1.34726i	1.77828	−	0.186831i
$53$			4.63647i			0.636869i	0.947945	+	0.318434i	$0.103157\pi$
$53$			4.63647i			0.636869i	−0.947945	+	0.318434i	$0.896843\pi$
$54$	0.946315	−	1.05095i	0.128777	−	0.143016i
$55$		−	19.8909i		−	2.68209i
$56$	−6.44692	−	4.68457i	−0.861506	−	0.626002i
$57$			1.70948i			0.226427i
$58$	−2.96934	+	3.29764i	−0.389893	+	0.433002i
$59$		−	10.2820i		−	1.33860i	−0.742991	−	0.669301i	$-0.766594\pi$
$59$		−	10.2820i		−	1.33860i	0.742991	−	0.669301i	$-0.233406\pi$
$60$	−8.80993	+	0.925594i	−1.13736	+	0.119494i
$61$			9.66191i			1.23708i	0.785753	+	0.618540i	$0.212276\pi$
$61$			9.66191i			1.23708i	−0.785753	+	0.618540i	$0.787724\pi$
$62$	−7.99897	+	8.88339i	−1.01587	+	1.12819i
$63$	2.81753			0.354976
$64$	2.47120	+	7.60876i	0.308900	+	0.951095i
$65$	28.5550			3.54181
$66$	4.24976	−	4.71965i	0.523110	−	0.580948i
$67$	−6.48382	−	4.99600i	−0.792125	−	0.610359i
$67$	−6.48382	−	4.99600i	−0.792125	−	0.610359i
$68$	−0.278565	−	2.65142i	−0.0337810	−	0.321531i
$69$			3.41301i			0.410878i
$70$	−13.1152	−	11.8095i	−1.56757	−	1.41150i
$71$		−	0.479394i		−	0.0568935i	−0.999595	−	0.0284468i	$-0.990944\pi$
$71$		−	0.479394i		−	0.0568935i	0.999595	−	0.0284468i	$-0.00905611\pi$
$72$	−2.28814	−	1.66265i	−0.269660	−	0.195945i
$73$	3.68198			0.430943			0.215471	−	0.976510i	$-0.430871\pi$
$73$	3.68198			0.430943			0.215471	+	0.976510i	$0.430871\pi$
$74$	5.45009	−	6.05269i	0.633560	−	0.703611i
$75$	−14.6179			−1.68793
$76$	3.40026	−	0.357240i	0.390036	−	0.0409782i
$77$	12.6531			1.44196
$78$	6.77542	+	6.10087i	0.767166	+	0.690787i
$79$	9.91224			1.11521			0.557607	−	0.830105i	$-0.311720\pi$
$79$	9.91224			1.11521			0.557607	+	0.830105i	$0.311720\pi$
$80$	3.68211	+	17.3300i	0.411673	+	1.93755i
$81$	1.00000			0.111111
$82$	5.41286	+	4.87397i	0.597751	+	0.538240i
$83$		−	8.53248i		−	0.936561i	−0.883580	−	0.468281i	$-0.844874\pi$
$83$		−	8.53248i		−	0.936561i	0.883580	−	0.468281i	$-0.155126\pi$
$84$	−0.588795	−	5.60422i	−0.0642428	−	0.611471i
$85$		−	5.90416i		−	0.640396i
$86$	−1.00779	+	1.11921i	−0.108672	+	0.120688i
$87$	−3.13779			−0.336406
$88$	−10.2757	−	7.46671i	−1.09540	−	0.795954i
$89$	−11.6876			−1.23888			−0.619441	−	0.785043i	$-0.712641\pi$
$89$	−11.6876			−1.23888			−0.619441	+	0.785043i	$0.712641\pi$
$90$	−4.65486	−	4.19143i	−0.490665	−	0.441815i
$91$			18.1646i			1.90416i
$92$	6.78865	−	0.713234i	0.707765	−	0.0743597i
$93$	−8.45275			−0.876510
$94$	4.75969	+	4.28582i	0.490925	+	0.442049i
$95$	7.57166			0.776836
$96$	−2.82893	+	4.89869i	−0.288727	+	0.499970i
$97$		−	13.2311i		−	1.34342i	−0.740814	−	0.671710i	$-0.765560\pi$
$97$		−	13.2311i		−	1.34342i	0.740814	−	0.671710i	$-0.234440\pi$
$98$	0.888118	−	0.986314i	0.0897135	−	0.0996328i
$99$	4.49085			0.451348
$100$	3.05477	+	29.0757i	0.305477	+	2.90757i
$101$			4.40366i			0.438180i	0.975705	+	0.219090i	$0.0703089\pi$
$101$			4.40366i			0.438180i	−0.975705	+	0.219090i	$0.929691\pi$
$102$	1.26144	−	1.40092i	0.124901	−	0.138711i
$103$			8.63164i			0.850501i	0.905076	+	0.425250i	$0.139814\pi$
$103$			8.63164i			0.850501i	−0.905076	+	0.425250i	$0.860186\pi$
$104$	10.7191	−	14.7516i	1.05109	−	1.44651i
$105$		−	12.4794i		−	1.21787i
$106$	4.87268	+	4.38757i	0.473277	+	0.426158i
$107$		−	4.97798i		−	0.481239i	−0.970620	−	0.240620i	$-0.922649\pi$
$107$		−	4.97798i		−	0.481239i	0.970620	−	0.240620i	$-0.0773506\pi$
$108$	−0.208975	−	1.98905i	−0.0201086	−	0.191397i
$109$			6.06886i			0.581291i	0.956831	+	0.290646i	$0.0938701\pi$
$109$			6.06886i			0.581291i	−0.956831	+	0.290646i	$0.906130\pi$
$110$	−20.9043	−	18.8231i	−1.99315	−	1.79471i
$111$	5.75928			0.546647
$112$	−11.0241	+	2.34229i	−1.04167	+	0.221325i
$113$		−	11.7654i		−	1.10679i	−0.832917	−	0.553397i	$-0.813331\pi$
$113$		−	11.7654i		−	1.10679i	0.832917	−	0.553397i	$-0.186669\pi$
$114$	1.79658	+	1.61771i	0.168265	+	0.151513i
$115$	15.1169			1.40966
$116$	0.655720	+	6.24122i	0.0608820	+	0.579483i
$117$			6.44697i			0.596023i
$118$	−10.8058	−	9.73001i	−0.994757	−	0.895720i
$119$	3.75579			0.344292
$120$	−7.36422	+	10.1347i	−0.672258	+	0.925164i
$121$	9.16777			0.833434
$122$	10.1541	+	9.14321i	0.919313	+	0.827787i
$123$			5.15047i			0.464402i
$124$	1.76642	+	16.8130i	0.158629	+	1.50985i
$125$			42.5996i			3.81022i
$126$	2.66628	−	2.96108i	0.237531	−	0.263794i
$127$		−	6.70864i		−	0.595296i	−0.954676	−	0.297648i	$-0.903798\pi$
$127$		−	6.70864i		−	0.595296i	0.954676	−	0.297648i	$-0.0962021\pi$
$128$	10.3349	+	4.60319i	0.913487	+	0.406868i
$129$	−1.06496			−0.0937643
$130$	27.0220	−	30.0098i	2.36999	−	2.63203i
$131$			2.95058i			0.257794i	0.991658	+	0.128897i	$0.0411436\pi$
$131$			2.95058i			0.257794i	−0.991658	+	0.128897i	$0.958856\pi$
$132$	−0.938477	−	8.93254i	−0.0816839	−	0.777478i
$133$			4.81653i			0.417646i
$134$	−11.3863	+	2.08636i	−0.983624	+	0.180234i
$135$		−	4.42921i		−	0.381206i
$136$	−3.05011	−	2.21632i	−0.261544	−	0.190048i
$137$		−	6.89136i		−	0.588769i	−0.955687	−	0.294384i	$-0.904885\pi$
$137$		−	6.89136i		−	0.588769i	0.955687	−	0.294384i	$-0.0951146\pi$
$138$	3.58689	+	3.22978i	0.305336	+	0.274937i
$139$	3.31586			0.281247			0.140624	−	0.990063i	$-0.455089\pi$
$139$	3.31586			0.281247			0.140624	+	0.990063i	$0.455089\pi$
$140$	−24.8223	+	2.60789i	−2.09786	+	0.220407i
$141$			4.52896i			0.381407i
$142$	−0.503817	−	0.453657i	−0.0422794	−	0.0380701i
$143$			28.9524i			2.42112i
$144$	−3.91266	+	0.831325i	−0.326055	+	0.0692771i
$145$			13.8979i			1.15416i
$146$	3.48431	−	3.86956i	0.288364	−	0.320247i
$147$	0.938501			0.0774063
$148$	−1.20355	−	11.4555i	−0.0989309	−	0.941637i
$149$	−19.2320			−1.57555			−0.787773	−	0.615966i	$-0.788766\pi$
$149$	−19.2320			−1.57555			−0.787773	+	0.615966i	$0.788766\pi$
$150$	−13.8331	+	15.3626i	−1.12947	+	1.25435i
$151$		−	11.1412i		−	0.906658i	−0.891343	−	0.453329i	$-0.850236\pi$
$151$		−	11.1412i		−	0.906658i	0.891343	−	0.453329i	$-0.149764\pi$
$152$	2.84227	−	3.91155i	0.230539	−	0.317268i
$153$	1.33300			0.107767
$154$	11.9739	−	13.2978i	0.964881	−	1.07156i
$155$			37.4390i			3.00717i
$156$	12.8234	−	1.34726i	1.02669	−	0.107867i
$157$	−10.8432			−0.865384			−0.432692	−	0.901542i	$-0.642436\pi$
$157$	−10.8432			−0.865384			−0.432692	+	0.901542i	$0.642436\pi$
$158$	9.38010	−	10.4172i	0.746241	−	0.828750i
$159$			4.63647i			0.367696i
$160$	21.6973	+	12.5299i	1.71532	+	0.990577i
$161$			9.61626i			0.757868i
$162$	0.946315	−	1.05095i	0.0743495	−	0.0825701i
$163$		−	17.2780i		−	1.35331i	−0.736299	−	0.676657i	$-0.763428\pi$
$163$		−	17.2780i		−	1.35331i	0.736299	−	0.676657i	$-0.236572\pi$
$164$	10.2446	−	1.07632i	0.799965	−	0.0840465i
$165$		−	19.8909i		−	1.54851i
$166$	−8.96718	−	8.07442i	−0.695988	−	0.626696i
$167$		−	12.4165i		−	0.960814i	−0.877046	−	0.480407i	$-0.840489\pi$
$167$		−	12.4165i		−	0.960814i	0.877046	−	0.480407i	$-0.159511\pi$
$168$	−6.44692	−	4.68457i	−0.497391	−	0.361422i
$169$	−28.5635			−2.19719
$170$	−6.20495	−	5.58719i	−0.475898	−	0.428518i
$171$			1.70948i			0.130728i
$172$	0.222550	+	2.11826i	0.0169692	+	0.161515i
$173$	18.7820			1.42797			0.713986	−	0.700160i	$-0.246888\pi$
$173$	18.7820			1.42797			0.713986	+	0.700160i	$0.246888\pi$
$174$	−2.96934	+	3.29764i	−0.225105	+	0.249994i
$175$	−41.1864			−3.11340
$176$	−17.5712	+	3.73336i	−1.32448	+	0.281413i
$177$		−	10.2820i		−	0.772843i
$178$	−11.0601	+	12.2830i	−0.828993	+	0.920652i
$179$	0.502646			0.0375695			0.0187848	−	0.999824i	$-0.494020\pi$
$179$	0.502646			0.0375695			0.0187848	+	0.999824i	$0.494020\pi$
$180$	−8.80993	+	0.925594i	−0.656653	+	0.0689897i
$181$	−15.4255			−1.14657			−0.573285	−	0.819356i	$-0.694331\pi$
$181$	−15.4255			−1.14657			−0.573285	+	0.819356i	$0.694331\pi$
$182$	19.0900	+	17.1894i	1.41504	+	1.27416i
$183$			9.66191i			0.714229i
$184$	5.67463	−	7.80945i	0.418339	−	0.575720i
$185$		−	25.5090i		−	1.87546i
$186$	−7.99897	+	8.88339i	−0.586513	+	0.651362i
$187$	5.98633			0.437764
$188$	9.00834	−	0.946440i	0.657001	−	0.0690262i
$189$	2.81753			0.204945
$190$	7.16518	−	7.95741i	0.519817	−	0.577291i
$191$	6.61535			0.478670			0.239335	−	0.970937i	$-0.423071\pi$
$191$	6.61535			0.478670			0.239335	+	0.970937i	$0.423071\pi$
$192$	2.47120	+	7.60876i	0.178343	+	0.549115i
$193$	−7.57636			−0.545358			−0.272679	−	0.962105i	$-0.587910\pi$
$193$	−7.57636			−0.545358			−0.272679	+	0.962105i	$0.587910\pi$
$194$	−13.9052	−	12.5208i	−0.998337	−	0.898944i
$195$	28.5550			2.04487
$196$	−0.196123	−	1.86673i	−0.0140088	−	0.133338i
$197$			7.80716i			0.556237i	0.960547	+	0.278119i	$0.0897108\pi$
$197$			7.80716i			0.556237i	−0.960547	+	0.278119i	$0.910289\pi$
$198$	4.24976	−	4.71965i	0.302018	−	0.335411i
$199$		−	6.41107i		−	0.454469i	−0.973840	−	0.227234i	$-0.927032\pi$
$199$		−	6.41107i		−	0.454469i	0.973840	−	0.227234i	$-0.0729684\pi$
$200$	33.4478	+	24.3044i	2.36512	+	1.71858i
$201$	−6.48382	−	4.99600i	−0.457334	−	0.352391i
$202$	4.62801	+	4.16725i	0.325626	+	0.293207i
$203$	−8.84082			−0.620504
$204$	−0.278565	−	2.65142i	−0.0195034	−	0.185636i
$205$	22.8125			1.59329
$206$	9.07139	+	8.16825i	0.632033	+	0.569109i
$207$			3.41301i			0.237220i
$208$	−5.35953	−	25.2248i	−0.371617	−	1.74903i
$209$			7.67705i			0.531033i
$210$	−13.1152	−	11.8095i	−0.905036	−	0.814932i
$211$			9.57658i			0.659279i	0.944107	+	0.329639i	$0.106927\pi$
$211$			9.57658i			0.659279i	−0.944107	+	0.329639i	$0.893073\pi$
$212$	9.22219	−	0.968908i	0.633383	−	0.0665449i
$213$		−	0.479394i		−	0.0328475i
$214$	−5.23158	−	4.71073i	−0.357624	−	0.322019i
$215$			4.71692i			0.321691i
$216$	−2.28814	−	1.66265i	−0.155688	−	0.113129i
$217$	−23.8159			−1.61673
$218$	6.37804	+	5.74305i	0.431976	+	0.388969i
$219$	3.68198			0.248805
$220$	−39.5641	+	4.15671i	−2.66741	+	0.280245i
$221$			8.59385i			0.578085i
$222$	5.45009	−	6.05269i	0.365786	−	0.406230i
$223$		−	20.5887i		−	1.37872i	−0.724418	−	0.689361i	$-0.757892\pi$
$223$		−	20.5887i		−	1.37872i	0.724418	−	0.689361i	$-0.242108\pi$
$224$	−7.97061	+	13.8022i	−0.532559	+	0.922200i
$225$	−14.6179			−0.974525
$226$	−12.3648	−	11.1338i	−0.822493	−	0.740607i
$227$			8.99211i			0.596827i	0.954437	+	0.298414i	$0.0964575\pi$
$227$			8.99211i			0.596827i	−0.954437	+	0.298414i	$0.903542\pi$
$228$	3.40026	−	0.357240i	0.225187	−	0.0236588i
$229$		−	2.72243i		−	0.179903i	−0.995946	−	0.0899515i	$-0.971329\pi$
$229$		−	2.72243i		−	0.179903i	0.995946	−	0.0899515i	$-0.0286712\pi$
$230$	14.3054	−	15.8871i	0.943268	−	1.04756i
$231$	12.6531			0.832515
$232$	7.17971	+	5.21704i	0.471371	+	0.342515i
$233$		−	18.8884i		−	1.23742i	−0.785620	−	0.618709i	$-0.787656\pi$
$233$		−	18.8884i		−	1.23742i	0.785620	−	0.618709i	$-0.212344\pi$
$234$	6.77542	+	6.10087i	0.442923	+	0.398826i
$235$	20.0597			1.30855
$236$	−20.4514	+	2.14868i	−1.33128	+	0.139867i
$237$	9.91224			0.643869
$238$	3.55416	−	3.94713i	0.230382	−	0.255854i
$239$	26.7279			1.72888			0.864441	−	0.502734i	$-0.167672\pi$
$239$	26.7279			1.72888			0.864441	+	0.502734i	$0.167672\pi$
$240$	3.68211	+	17.3300i	0.237679	+	1.11865i
$241$	12.0626			0.777023			0.388511	−	0.921444i	$-0.372989\pi$
$241$	12.0626			0.777023			0.388511	+	0.921444i	$0.372989\pi$
$242$	8.67560	−	9.63483i	0.557689	−	0.619351i
$243$	1.00000			0.0641500
$244$	19.2180	−	2.01910i	1.23031	−	0.129260i
$245$		−	4.15682i		−	0.265569i
$246$	5.41286	+	4.87397i	0.345112	+	0.310753i
$247$	−11.0210			−0.701250
$248$	19.3411	+	14.0540i	1.22816	+	0.892427i
$249$		−	8.53248i		−	0.540724i
$250$	44.7699	+	40.3126i	2.83150	+	2.54960i
$251$	25.4913			1.60900			0.804499	−	0.593955i	$-0.202434\pi$
$251$	25.4913			1.60900			0.804499	+	0.593955i	$0.202434\pi$
$252$	−0.588795	−	5.60422i	−0.0370906	−	0.353033i
$253$			15.3273i			0.963620i
$254$	−7.05042	−	6.34849i	−0.442383	−	0.398340i
$255$		−	5.90416i		−	0.369733i
$256$	14.6178	−	6.50538i	0.913612	−	0.406586i
$257$	12.9570			0.808235			0.404118	−	0.914707i	$-0.367579\pi$
$257$	12.9570			0.808235			0.404118	+	0.914707i	$0.367579\pi$
$258$	−1.00779	+	1.11921i	−0.0627420	+	0.0696791i
$259$	16.2270			1.00829
$260$	−5.96728	−	56.7974i	−0.370075	−	3.52242i
$261$	−3.13779			−0.194224
$262$	3.10090	+	2.79218i	0.191574	+	0.172502i
$263$		−	1.56509i		−	0.0965074i	−0.998835	−	0.0482537i	$-0.984634\pi$
$263$		−	1.56509i		−	0.0965074i	0.998835	−	0.0482537i	$-0.0153656\pi$
$264$	−10.2757	−	7.46671i	−0.632427	−	0.459544i
$265$	20.5359			1.26151
$266$	5.06192	+	4.55796i	0.310366	+	0.279466i
$267$	−11.6876			−0.715269
$268$	−8.58235	+	13.9407i	−0.524250	+	0.851564i
$269$	6.01649			0.366832			0.183416	−	0.983035i	$-0.441285\pi$
$269$	6.01649			0.366832			0.183416	+	0.983035i	$0.441285\pi$
$270$	−4.65486	−	4.19143i	−0.283286	−	0.255082i
$271$	25.6297			1.55689			0.778446	−	0.627712i	$-0.216008\pi$
$271$	25.6297			1.55689			0.778446	+	0.627712i	$0.216008\pi$
$272$	−5.21559	+	1.10816i	−0.316242	+	0.0671921i
$273$			18.1646i			1.09937i
$274$	−7.24245	−	6.52140i	−0.437532	−	0.393972i
$275$	−65.6468			−3.95865
$276$	6.78865	−	0.713234i	0.408629	−	0.0429316i
$277$	5.21072			0.313082			0.156541	−	0.987671i	$-0.449966\pi$
$277$	5.21072			0.313082			0.156541	+	0.987671i	$0.449966\pi$
$278$	3.13784	−	3.48479i	0.188195	−	0.209004i
$279$	−8.45275			−0.506053
$280$	−20.7489	+	28.5548i	−1.23999	+	1.70647i
$281$		−	24.6197i		−	1.46869i	−0.678778	−	0.734344i	$-0.737490\pi$
$281$		−	24.6197i		−	1.46869i	0.678778	−	0.734344i	$-0.262510\pi$
$282$	4.75969	+	4.28582i	0.283436	+	0.255217i
$283$		−	8.75201i		−	0.520253i	−0.965575	−	0.260126i	$-0.916236\pi$
$283$		−	8.75201i		−	0.520253i	0.965575	−	0.260126i	$-0.0837642\pi$
$284$	−0.953539	+	0.100181i	−0.0565821	+	0.00594467i
$285$	7.57166			0.448507
$286$	30.4274	+	27.3981i	1.79921	+	1.62008i
$287$			14.5116i			0.856594i
$288$	−2.82893	+	4.89869i	−0.166696	+	0.288658i
$289$	−15.2231			−0.895476
$290$	14.6060	+	13.1518i	0.857691	+	0.772300i
$291$		−	13.2311i		−	0.775624i
$292$	−0.769442	−	7.32364i	−0.0450282	−	0.428584i
$293$	−12.2547			−0.715929			−0.357965	−	0.933735i	$-0.616529\pi$
$293$	−12.2547			−0.715929			−0.357965	+	0.933735i	$0.616529\pi$
$294$	0.888118	−	0.986314i	0.0517961	−	0.0575230i
$295$	−45.5411			−2.65151
$296$	−13.1781	−	9.57566i	−0.765959	−	0.556574i
$297$	4.49085			0.260586
$298$	−18.1995	+	20.2118i	−1.05427	+	1.17084i
$299$	−22.0036			−1.27250
$300$	3.05477	+	29.0757i	0.176367	+	1.67869i
$301$	−3.00055			−0.172949
$302$	−11.7088	−	10.5431i	−0.673766	−	0.606686i
$303$			4.40366i			0.252984i
$304$	−1.42114	−	6.68863i	−0.0815078	−	0.383619i
$305$	42.7946			2.45041
$306$	1.26144	−	1.40092i	0.0721119	−	0.0800850i
$307$			20.6834i			1.18046i	0.807234	+	0.590232i	$0.200964\pi$
$307$			20.6834i			1.18046i	−0.807234	+	0.590232i	$0.799036\pi$
$308$	−2.64419	−	25.1678i	−0.150667	−	1.43407i
$309$			8.63164i			0.491037i
$310$	39.3464	+	35.4291i	2.23472	+	2.01224i
$311$	6.74222			0.382316			0.191158	−	0.981559i	$-0.438776\pi$
$311$	6.74222			0.382316			0.191158	+	0.981559i	$0.438776\pi$
$312$	10.7191	−	14.7516i	0.606847	−	0.835145i
$313$		−	6.93434i		−	0.391952i	−0.980609	−	0.195976i	$-0.937213\pi$
$313$		−	6.93434i		−	0.391952i	0.980609	−	0.195976i	$-0.0627875\pi$
$314$	−10.2611	+	11.3957i	−0.579068	+	0.643094i
$315$		−	12.4794i		−	0.703137i
$316$	−2.07141	−	19.7160i	−0.116526	−	1.10911i
$317$	−17.2122			−0.966732			−0.483366	−	0.875418i	$-0.660586\pi$
$317$	−17.2122			−0.966732			−0.483366	+	0.875418i	$0.660586\pi$
$318$	4.87268	+	4.38757i	0.273247	+	0.246042i
$319$	−14.0913			−0.788964
$320$	33.7008	−	10.9454i	1.88393	−	0.611869i
$321$		−	4.97798i		−	0.277843i
$322$	10.1062	+	9.10002i	0.563195	+	0.507124i
$323$			2.27875i			0.126793i
$324$	−0.208975	−	1.98905i	−0.0116097	−	0.110503i
$325$		−	94.2411i		−	5.22756i
$326$	−18.1582	−	16.3504i	−1.00569	−	0.905564i
$327$			6.06886i			0.335609i
$328$	8.56342	−	11.7850i	0.472836	−	0.650718i
$329$			12.7605i			0.703509i
$330$	−20.9043	−	18.8231i	−1.15074	−	1.03618i
$331$	−11.8004			−0.648611			−0.324306	−	0.945952i	$-0.605131\pi$
$331$	−11.8004			−0.648611			−0.324306	+	0.945952i	$0.605131\pi$
$332$	−16.9716	+	1.78308i	−0.931435	+	0.0978590i
$333$	5.75928			0.315607
$334$	−13.0490	−	11.7499i	−0.714011	−	0.642925i
$335$	−22.1283	+	28.7182i	−1.20900	+	1.56904i
$336$	−11.0241	+	2.34229i	−0.601411	+	0.127782i
$337$			26.7813i			1.45887i	0.684051	+	0.729434i	$0.260216\pi$
$337$			26.7813i			1.45887i	−0.684051	+	0.729434i	$0.739784\pi$
$338$	−27.0301	+	30.0187i	−1.47024	+	1.63280i
$339$		−	11.7654i		−	0.639008i
$340$	−11.7437	+	1.23382i	−0.636890	+	0.0669134i
$341$	−37.9601			−2.05565
$342$	1.79658	+	1.61771i	0.0971477	+	0.0874758i
$343$	−17.0785			−0.922151
$344$	2.43677	+	1.77065i	0.131382	+	0.0954670i
$345$	15.1169			0.813867
$346$	17.7737	−	19.7389i	0.955522	−	1.06117i
$347$	−11.4891			−0.616766			−0.308383	−	0.951262i	$-0.599788\pi$
$347$	−11.4891			−0.616766			−0.308383	+	0.951262i	$0.599788\pi$
$348$	0.655720	+	6.24122i	0.0351503	+	0.334565i
$349$	−16.4608			−0.881127			−0.440563	−	0.897722i	$-0.645221\pi$
$349$	−16.4608			−0.881127			−0.440563	+	0.897722i	$0.645221\pi$
$350$	−38.9753	+	43.2847i	−2.08332	+	2.31366i
$351$			6.44697i			0.344114i
$352$	−12.7043	+	21.9993i	−0.677142	+	1.17257i
$353$			3.89747i			0.207441i	0.994606	+	0.103721i	$0.0330748\pi$
$353$			3.89747i			0.207441i	−0.994606	+	0.103721i	$0.966925\pi$
$354$	−10.8058	−	9.73001i	−0.574323	−	0.517144i
$355$	−2.12333			−0.112695
$356$	2.44242	+	23.2472i	0.129448	+	1.23210i
$357$	3.75579			0.198777
$358$	0.475661	−	0.528253i	0.0251395	−	0.0279191i
$359$		−	29.8392i		−	1.57485i	−0.616408	−	0.787427i	$-0.711413\pi$
$359$		−	29.8392i		−	1.57485i	0.616408	−	0.787427i	$-0.288587\pi$
$360$	−7.36422	+	10.1347i	−0.388128	+	0.534144i
$361$	16.0777			0.846193
$362$	−14.5974	+	16.2114i	−0.767223	+	0.852052i
$363$	9.16777			0.481183
$364$	36.1303	−	3.79594i	1.89374	−	0.198962i
$365$		−	16.3082i		−	0.853612i
$366$	10.1541	+	9.14321i	0.530766	+	0.477923i
$367$	37.1530			1.93937			0.969686	−	0.244355i	$-0.0785764\pi$
$367$	37.1530			1.93937			0.969686	+	0.244355i	$0.0785764\pi$
$368$	−2.83732	−	13.3539i	−0.147905	−	0.696122i
$369$			5.15047i			0.268123i
$370$	−26.8086	−	24.1396i	−1.39371	−	1.25496i
$371$			13.0634i			0.678219i
$372$	1.76642	+	16.8130i	0.0915844	+	0.871712i
$373$			31.6985i			1.64129i	0.571441	+	0.820643i	$0.306384\pi$
$373$			31.6985i			1.64129i	−0.571441	+	0.820643i	$0.693616\pi$
$374$	5.66496	−	6.29131i	0.292928	−	0.325316i
$375$			42.5996i			2.19983i
$376$	7.53007	−	10.3629i	0.388334	−	0.534426i
$377$		−	20.2292i		−	1.04186i
$378$	2.66628	−	2.96108i	0.137138	−	0.152301i
$379$	−31.8816			−1.63765			−0.818823	−	0.574046i	$-0.805373\pi$
$379$	−31.8816			−1.63765			−0.818823	+	0.574046i	$0.805373\pi$
$380$	−1.58229	−	15.0604i	−0.0811698	−	0.772584i
$381$		−	6.70864i		−	0.343694i
$382$	6.26021	−	6.95238i	0.320300	−	0.355715i
$383$	−29.9214			−1.52891			−0.764457	−	0.644675i	$-0.776993\pi$
$383$	−29.9214			−1.52891			−0.764457	+	0.644675i	$0.776993\pi$
$384$	10.3349	+	4.60319i	0.527402	+	0.234905i
$385$		−	56.0434i		−	2.85623i
$386$	−7.16962	+	7.96234i	−0.364924	+	0.405273i
$387$	−1.06496			−0.0541348
$388$	−26.3174	+	2.76498i	−1.33607	+	0.140371i
$389$	28.6071			1.45044			0.725220	−	0.688518i	$-0.241738\pi$
$389$	28.6071			1.45044			0.725220	+	0.688518i	$0.241738\pi$
$390$	27.0220	−	30.0098i	1.36831	−	1.51960i
$391$			4.54955i			0.230081i
$392$	−2.14743	−	1.56040i	−0.108461	−	0.0788120i
$393$			2.95058i			0.148837i
$394$	8.20490	+	7.38803i	0.413357	+	0.372204i
$395$		−	43.9034i		−	2.20902i
$396$	−0.938477	−	8.93254i	−0.0471602	−	0.448877i
$397$	−26.0821			−1.30902			−0.654511	−	0.756053i	$-0.727125\pi$
$397$	−26.0821			−1.30902			−0.654511	+	0.756053i	$0.727125\pi$
$398$	−6.73769	−	6.06690i	−0.337730	−	0.304106i
$399$			4.81653i			0.241128i
$400$	57.1948	−	12.1522i	2.85974	−	0.607611i
$401$		−	1.63624i		−	0.0817100i	−0.999165	−	0.0408550i	$-0.986992\pi$
$401$		−	1.63624i		−	0.0817100i	0.999165	−	0.0408550i	$-0.0130082\pi$
$402$	−11.3863	+	2.08636i	−0.567895	+	0.104058i
$403$		−	54.4947i		−	2.71457i
$404$	8.75911	−	0.920255i	0.435782	−	0.0457844i
$405$		−	4.42921i		−	0.220089i
$406$	−8.36620	+	9.29123i	−0.415208	+	0.461116i
$407$	25.8641			1.28203
$408$	−3.05011	−	2.21632i	−0.151003	−	0.109724i
$409$		−	1.01269i		−	0.0500744i	−0.999687	−	0.0250372i	$-0.992030\pi$
$409$		−	1.01269i		−	0.0500744i	0.999687	−	0.0250372i	$-0.00797042\pi$
$410$	21.5878	−	23.9747i	1.06615	−	1.18403i
$411$		−	6.89136i		−	0.339926i
$412$	17.1688	−	1.80380i	0.845845	−	0.0888668i
$413$		−	28.9699i		−	1.42552i
$414$	3.58689	+	3.22978i	0.176286	+	0.158735i
$415$	−37.7921			−1.85514
$416$	−31.5817	−	18.2380i	−1.54842	−	0.894194i
$417$	3.31586			0.162378
$418$	8.06816	+	7.26491i	0.394627	+	0.355338i
$419$			9.62094i			0.470013i	0.971994	+	0.235007i	$0.0755112\pi$
$419$			9.62094i			0.470013i	−0.971994	+	0.235007i	$0.924489\pi$
$420$	−24.8223	+	2.60789i	−1.21120	+	0.127252i
$421$	10.2672			0.500393			0.250196	−	0.968195i	$-0.419505\pi$
$421$	10.2672			0.500393			0.250196	+	0.968195i	$0.419505\pi$
$422$	10.0645	+	9.06246i	0.489930	+	0.441154i
$423$			4.52896i			0.220206i
$424$	7.70883	−	10.6089i	0.374374	−	0.515215i
$425$	−19.4857			−0.945196
$426$	−0.503817	−	0.453657i	−0.0244100	−	0.0219798i
$427$			27.2228i			1.31740i
$428$	−9.90145	+	1.04027i	−0.478605	+	0.0502835i
$429$			28.9524i			1.39784i
$430$	4.95723	+	4.46369i	0.239059	+	0.215258i
$431$		−	6.49042i		−	0.312632i	−0.987707	−	0.156316i	$-0.950038\pi$
$431$		−	6.49042i		−	0.312632i	0.987707	−	0.156316i	$-0.0499619\pi$
$432$	−3.91266	+	0.831325i	−0.188248	+	0.0399971i
$433$			24.5663i			1.18058i	0.807192	+	0.590289i	$0.200986\pi$
$433$			24.5663i			1.18058i	−0.807192	+	0.590289i	$0.799014\pi$
$434$	−22.5374	+	25.0293i	−1.08183	+	1.20144i
$435$			13.8979i			0.666354i
$436$	12.0713	−	1.26824i	0.578109	−	0.0607377i
$437$	−5.83448			−0.279101
$438$	3.48431	−	3.86956i	0.166487	−	0.184895i
$439$			10.4351i			0.498042i	0.968498	+	0.249021i	$0.0801089\pi$
$439$			10.4351i			0.498042i	−0.968498	+	0.249021i	$0.919891\pi$
$440$	−33.0716	+	45.5133i	−1.57663	+	2.16976i
$441$	0.938501			0.0446905
$442$	9.03167	+	8.13249i	0.429593	+	0.386823i
$443$	2.65628			0.126204			0.0631018	−	0.998007i	$-0.479901\pi$
$443$	2.65628			0.126204			0.0631018	+	0.998007i	$0.479901\pi$
$444$	−1.20355	−	11.4555i	−0.0571178	−	0.543654i
$445$			51.7668i			2.45398i
$446$	−21.6376	−	19.4834i	−1.02457	−	0.922566i
$447$	−19.2320			−0.909642
$448$	6.96269	+	21.4379i	0.328956	+	1.01285i
$449$	−10.1088			−0.477063			−0.238531	−	0.971135i	$-0.576666\pi$
$449$	−10.1088			−0.477063			−0.238531	+	0.971135i	$0.576666\pi$
$450$	−13.8331	+	15.3626i	−0.652100	+	0.724200i
$451$			23.1300i			1.08915i
$452$	−23.4020	+	2.45867i	−1.10074	+	0.115646i
$453$		−	11.1412i		−	0.523459i
$454$	9.45022	+	8.50937i	0.443521	+	0.399365i
$455$	80.4547			3.77177
$456$	2.84227	−	3.91155i	0.133102	−	0.183175i
$457$	9.51702			0.445187			0.222594	−	0.974911i	$-0.428548\pi$
$457$	9.51702			0.445187			0.222594	+	0.974911i	$0.428548\pi$
$458$	−2.86112	−	2.57627i	−0.133691	−	0.120381i
$459$	1.33300			0.0622193
$460$	−3.15906	−	30.0683i	−0.147292	−	1.40194i
$461$	−38.4051			−1.78870			−0.894351	−	0.447366i	$-0.852362\pi$
$461$	−38.4051			−1.78870			−0.894351	+	0.447366i	$0.852362\pi$
$462$	11.9739	−	13.2978i	0.557074	−	0.618668i
$463$	−15.1386			−0.703549			−0.351774	−	0.936085i	$-0.614422\pi$
$463$	−15.1386			−0.703549			−0.351774	+	0.936085i	$0.614422\pi$
$464$	12.2771	−	2.60852i	0.569950	−	0.121098i
$465$			37.4390i			1.73619i
$466$	−19.8506	−	17.8743i	−0.919563	−	0.828013i
$467$			30.8798i			1.42895i	0.699662	+	0.714474i	$0.253334\pi$
$467$			30.8798i			1.42895i	−0.699662	+	0.714474i	$0.746666\pi$
$468$	12.8234	−	1.34726i	0.592760	−	0.0622770i
$469$	−18.2684	−	14.0764i	−0.843556	−	0.649988i
$470$	18.9828	−	21.0817i	0.875611	−	0.972425i
$471$	−10.8432			−0.499630
$472$	−17.0954	+	23.5267i	−0.786878	+	1.08290i
$473$	−4.78257			−0.219903
$474$	9.38010	−	10.4172i	0.430842	−	0.478479i
$475$		−	24.9890i		−	1.14658i
$476$	−0.784866	−	7.47046i	−0.0359743	−	0.342408i
$477$			4.63647i			0.212290i
$478$	25.2930	−	28.0896i	1.15687	−	1.28479i
$479$		−	25.5835i		−	1.16894i	−0.811416	−	0.584469i	$-0.801303\pi$
$479$		−	25.5835i		−	1.16894i	0.811416	−	0.584469i	$-0.198697\pi$
$480$	21.6973	+	12.5299i	0.990342	+	0.571910i
$481$			37.1299i			1.69298i
$482$	11.4151	−	12.6772i	0.519942	−	0.577430i
$483$			9.61626i			0.437555i
$484$	−1.91584	−	18.2352i	−0.0870835	−	0.828872i
$485$	−58.6035			−2.66105
$486$	0.946315	−	1.05095i	0.0429257	−	0.0476719i
$487$	−21.7976			−0.987745			−0.493872	−	0.869534i	$-0.664419\pi$
$487$	−21.7976			−0.987745			−0.493872	+	0.869534i	$0.664419\pi$
$488$	16.0644	−	22.1078i	0.727199	−	1.00077i
$489$		−	17.2780i		−	0.781336i
$490$	−4.36859	−	3.93366i	−0.197353	−	0.177705i
$491$		−	29.7112i		−	1.34085i	−0.741978	−	0.670424i	$-0.766112\pi$
$491$		−	29.7112i		−	1.34085i	0.741978	−	0.670424i	$-0.233888\pi$
$492$	10.2446	−	1.07632i	0.461860	−	0.0485243i
$493$	−4.18268			−0.188379
$494$	−10.4293	+	11.5825i	−0.469238	+	0.521121i
$495$		−	19.8909i		−	0.894031i
$496$	33.0727	−	7.02699i	1.48501	−	0.315521i
$497$		−	1.35071i		−	0.0605875i
$498$	−8.96718	−	8.07442i	−0.401829	−	0.361823i
$499$	13.0259			0.583120			0.291560	−	0.956552i	$-0.405826\pi$
$499$	13.0259			0.583120			0.291560	+	0.956552i	$0.405826\pi$
$500$	84.7328	−	8.90226i	3.78937	−	0.398121i
$501$		−	12.4165i		−	0.554726i
$502$	24.1228	−	26.7900i	1.07665	−	1.19570i
$503$	−14.1739			−0.631985			−0.315992	−	0.948762i	$-0.602337\pi$
$503$	−14.1739			−0.631985			−0.315992	+	0.948762i	$0.602337\pi$
$504$	−6.44692	−	4.68457i	−0.287169	−	0.208667i
$505$	19.5047			0.867949
$506$	16.1082	+	14.5045i	0.716096	+	0.644802i
$507$	−28.5635			−1.26855
$508$	−13.3438	+	1.40194i	−0.592037	+	0.0622010i
$509$	0.469183			0.0207962			0.0103981	−	0.999946i	$-0.496690\pi$
$509$	0.469183			0.0207962			0.0103981	+	0.999946i	$0.496690\pi$
$510$	−6.20495	−	5.58719i	−0.274760	−	0.247405i
$511$	10.3741			0.458923
$512$	6.99624	−	21.5187i	0.309193	−	0.950999i
$513$			1.70948i			0.0754756i
$514$	12.2614	−	13.6171i	0.540827	−	0.600625i
$515$	38.2313			1.68467
$516$	0.222550	+	2.11826i	0.00979720	+	0.0932510i
$517$			20.3389i			0.894504i
$518$	15.3558	−	17.0537i	0.674696	−	0.749295i
$519$	18.7820			0.824440
$520$	−65.3379	−	47.4769i	−2.86526	−	2.08200i
$521$			26.8304i			1.17546i	0.809056	+	0.587731i	$0.199979\pi$
$521$			26.8304i			1.17546i	−0.809056	+	0.587731i	$0.800021\pi$
$522$	−2.96934	+	3.29764i	−0.129964	+	0.144334i
$523$			6.00603i			0.262625i	0.991341	+	0.131313i	$0.0419192\pi$
$523$			6.00603i			0.262625i	−0.991341	+	0.131313i	$0.958081\pi$
$524$	5.86886	−	0.616599i	0.256383	−	0.0269362i
$525$	−41.1864			−1.79752
$526$	−1.64482	−	1.48107i	−0.0717177	−	0.0645775i
$527$	−11.2676			−0.490823
$528$	−17.5712	+	3.73336i	−0.764687	+	0.162474i
$529$	11.3514			0.493539
$530$	19.4334	−	21.5821i	0.844135	−	0.937468i
$531$		−	10.2820i		−	0.446201i
$532$	9.58034	−	1.00654i	0.415360	−	0.0436389i
$533$	−33.2049			−1.43827
$534$	−11.0601	+	12.2830i	−0.478619	+	0.531539i
$535$	−22.0485			−0.953239
$536$	6.52932	+	22.2119i	0.282024	+	0.959407i
$537$	0.502646			0.0216908
$538$	5.69349	−	6.32300i	0.245464	−	0.272604i
$539$	4.21467			0.181539
$540$	−8.80993	+	0.925594i	−0.379119	+	0.0398312i
$541$			19.1448i			0.823101i	0.911387	+	0.411550i	$0.135013\pi$
$541$			19.1448i			0.823101i	−0.911387	+	0.411550i	$0.864987\pi$
$542$	24.2537	−	26.9354i	1.04179	−	1.15697i
$543$	−15.4255			−0.661973
$544$	−3.77098	+	6.52998i	−0.161679	+	0.279970i
$545$	26.8802			1.15142
$546$	19.0900	+	17.1894i	0.816976	+	0.735639i
$547$	35.4826			1.51713			0.758563	−	0.651599i	$-0.225902\pi$
$547$	35.4826			1.51713			0.758563	+	0.651599i	$0.225902\pi$
$548$	−13.7073	+	1.44012i	−0.585546	+	0.0615190i
$549$			9.66191i			0.412360i
$550$	−62.1225	+	68.9912i	−2.64891	+	2.94180i
$551$		−	5.36400i		−	0.228514i
$552$	5.67463	−	7.80945i	0.241528	−	0.332392i
$553$	27.9281			1.18762
$554$	4.93098	−	5.47618i	0.209497	−	0.232661i
$555$		−	25.5090i		−	1.08280i
$556$	−0.692931	−	6.59541i	−0.0293868	−	0.279708i
$557$	18.7124			0.792870			0.396435	−	0.918063i	$-0.370247\pi$
$557$	18.7124			0.792870			0.396435	+	0.918063i	$0.370247\pi$
$558$	−7.99897	+	8.88339i	−0.338623	+	0.376064i
$559$		−	6.86575i		−	0.290390i
$560$	10.3745	+	48.8278i	0.438402	+	2.06335i
$561$	5.98633			0.252743
$562$	−25.8740	−	23.2980i	−1.09143	−	0.982766i
$563$	22.6150			0.953108			0.476554	−	0.879145i	$-0.341886\pi$
$563$	22.6150			0.953108			0.476554	+	0.879145i	$0.341886\pi$
$564$	9.00834	−	0.946440i	0.379320	−	0.0398523i
$565$	−52.1113			−2.19234
$566$	−9.19789	−	8.28216i	−0.386616	−	0.348125i
$567$	2.81753			0.118325
$568$	−0.797063	+	1.09692i	−0.0334440	+	0.0460258i
$569$	18.0974			0.758681			0.379341	−	0.925257i	$-0.376151\pi$
$569$	18.0974			0.758681			0.379341	+	0.925257i	$0.376151\pi$
$570$	7.16518	−	7.95741i	0.300116	−	0.333299i
$571$			12.8629i			0.538294i	0.963099	+	0.269147i	$0.0867417\pi$
$571$			12.8629i			0.538294i	−0.963099	+	0.269147i	$0.913258\pi$
$572$	57.5879	−	6.05034i	2.40787	−	0.252977i
$573$	6.61535			0.276360
$574$	15.2509	+	13.7326i	0.636562	+	0.573186i
$575$		−	49.8909i		−	2.08060i
$576$	2.47120	+	7.60876i	0.102967	+	0.317032i
$577$		−	22.5707i		−	0.939630i	−0.882765	−	0.469815i	$-0.844321\pi$
$577$		−	22.5707i		−	0.939630i	0.882765	−	0.469815i	$-0.155679\pi$
$578$	−14.4058	+	15.9987i	−0.599204	+	0.665456i
$579$	−7.57636			−0.314863
$580$	27.6437	−	2.90432i	1.14784	−	0.120595i
$581$		−	24.0406i		−	0.997370i
$582$	−13.9052	−	12.5208i	−0.576390	−	0.519005i
$583$			20.8217i			0.862348i
$584$	−8.42489	−	6.12183i	−0.348624	−	0.253323i
$585$	28.5550			1.18060
$586$	−11.5968	+	12.8791i	−0.479061	+	0.532029i
$587$	44.5937			1.84058			0.920290	−	0.391238i	$-0.127953\pi$
$587$	44.5937			1.84058			0.920290	+	0.391238i	$0.127953\pi$
$588$	−0.196123	−	1.86673i	−0.00808800	−	0.0769826i
$589$		−	14.4499i		−	0.595396i
$590$	−43.0963	+	47.8613i	−1.77424	+	1.97042i
$591$			7.80716i			0.321144i
$592$	−22.5341	+	4.78783i	−0.926145	+	0.196779i
$593$		−	9.87000i		−	0.405312i	−0.979250	−	0.202656i	$-0.935043\pi$
$593$		−	9.87000i		−	0.405312i	0.979250	−	0.202656i	$-0.0649573\pi$
$594$	4.24976	−	4.71965i	0.174370	−	0.193649i
$595$		−	16.6352i		−	0.681975i
$596$	4.01901	+	38.2534i	0.164625	+	1.56692i
$597$		−	6.41107i		−	0.262388i
$598$	−20.8223	+	23.1246i	−0.851487	+	0.945634i
$599$	−4.78024			−0.195315			−0.0976576	−	0.995220i	$-0.531135\pi$
$599$	−4.78024			−0.195315			−0.0976576	+	0.995220i	$0.531135\pi$
$600$	33.4478	+	24.3044i	1.36550	+	0.992223i
$601$	−7.77550			−0.317169			−0.158585	−	0.987345i	$-0.550693\pi$
$601$	−7.77550			−0.317169			−0.158585	+	0.987345i	$0.550693\pi$
$602$	−2.83947	+	3.15342i	−0.115728	+	0.128524i
$603$	−6.48382	−	4.99600i	−0.264042	−	0.203453i
$604$	−22.1604	+	2.32823i	−0.901695	+	0.0947345i
$605$		−	40.6060i		−	1.65087i
$606$	4.62801	+	4.16725i	0.188000	+	0.169283i
$607$			39.5661i			1.60594i	0.596020	+	0.802969i	$0.296748\pi$
$607$			39.5661i			1.60594i	−0.596020	+	0.802969i	$0.703252\pi$
$608$	−8.37423	−	4.83601i	−0.339620	−	0.196126i
$609$	−8.84082			−0.358248
$610$	40.4972	−	44.9748i	1.63968	−	1.82098i
$611$	−29.1981			−1.18123
$612$	−0.278565	−	2.65142i	−0.0112603	−	0.107177i
$613$	−5.66134			−0.228659			−0.114330	−	0.993443i	$-0.536472\pi$
$613$	−5.66134			−0.228659			−0.114330	+	0.993443i	$0.536472\pi$
$614$	21.7371	+	19.5730i	0.877240	+	0.789903i
$615$	22.8125			0.919889
$616$	−28.9522	−	21.0377i	−1.16652	−	0.847634i
$617$	−6.40871			−0.258005			−0.129003	−	0.991644i	$-0.541178\pi$
$617$	−6.40871			−0.258005			−0.129003	+	0.991644i	$0.541178\pi$
$618$	9.07139	+	8.16825i	0.364905	+	0.328575i
$619$			35.6982i			1.43483i	0.696645	+	0.717416i	$0.254675\pi$
$619$			35.6982i			1.43483i	−0.696645	+	0.717416i	$0.745325\pi$
$620$	74.4681	−	7.82382i	2.99071	−	0.314212i
$621$			3.41301i			0.136959i
$622$	6.38027	−	7.08571i	0.255825	−	0.284111i
$623$	−32.9302			−1.31932
$624$	−5.35953	−	25.2248i	−0.214553	−	1.00980i
$625$	115.593			4.62372
$626$	−7.28762	−	6.56207i	−0.291272	−	0.262273i
$627$			7.67705i			0.306592i
$628$	2.26597	+	21.5678i	0.0904219	+	0.860647i
$629$	7.67715			0.306108
$630$	−13.1152	−	11.8095i	−0.522523	−	0.470501i
$631$	−3.22001			−0.128187			−0.0640934	−	0.997944i	$-0.520416\pi$
$631$	−3.22001			−0.128187			−0.0640934	+	0.997944i	$0.520416\pi$
$632$	−22.6806	−	16.4806i	−0.902187	−	0.655562i
$633$			9.57658i			0.380635i
$634$	−16.2881	+	18.0891i	−0.646885	+	0.718409i
$635$	−29.7140			−1.17916
$636$	9.22219	−	0.968908i	0.365684	−	0.0384197i
$637$			6.05049i			0.239729i
$638$	−13.3349	+	14.8092i	−0.527932	+	0.586303i
$639$		−	0.479394i		−	0.0189645i
$640$	20.3885	−	45.7755i	0.805925	−	1.80944i
$641$		−	19.1452i		−	0.756189i	−0.925767	−	0.378095i	$-0.876579\pi$
$641$		−	19.1452i		−	0.756189i	0.925767	−	0.378095i	$-0.123421\pi$
$642$	−5.23158	−	4.71073i	−0.206474	−	0.185918i
$643$			15.3290i			0.604516i	0.953226	+	0.302258i	$0.0977405\pi$
$643$			15.3290i			0.604516i	−0.953226	+	0.302258i	$0.902260\pi$
$644$	19.1273	−	2.00956i	0.753719	−	0.0791878i
$645$			4.71692i			0.185728i
$646$	2.39485	+	2.15642i	0.0942239	+	0.0848431i
$647$	−5.79937			−0.227997			−0.113998	−	0.993481i	$-0.536366\pi$
$647$	−5.79937			−0.227997			−0.113998	+	0.993481i	$0.536366\pi$
$648$	−2.28814	−	1.66265i	−0.0898868	−	0.0653150i
$649$		−	46.1750i		−	1.81253i
$650$	−99.0423	−	89.1818i	−3.88476	−	3.49800i
$651$	−23.8159			−0.933420
$652$	−34.3667	+	3.61066i	−1.34591	+	0.141404i
$653$		−	26.4803i		−	1.03626i	−0.855303	−	0.518128i	$-0.826629\pi$
$653$		−	26.4803i		−	1.03626i	0.855303	−	0.518128i	$-0.173371\pi$
$654$	6.37804	+	5.74305i	0.249401	+	0.224571i
$655$	13.0687			0.510638
$656$	−4.28171	−	20.1520i	−0.167173	−	0.786804i
$657$	3.68198			0.143648
$658$	13.4106	+	12.0755i	0.522800	+	0.470750i
$659$		−	21.1839i		−	0.825206i	−0.910911	−	0.412603i	$-0.864620\pi$
$659$		−	21.1839i		−	0.825206i	0.910911	−	0.412603i	$-0.135380\pi$
$660$	−39.5641	+	4.15671i	−1.54003	+	0.161800i
$661$			22.0683i			0.858356i	0.903220	+	0.429178i	$0.141197\pi$
$661$			22.0683i			0.858356i	−0.903220	+	0.429178i	$0.858803\pi$
$662$	−11.1669	+	12.4016i	−0.434016	+	0.482003i
$663$			8.59385i			0.333757i
$664$	−14.1865	+	19.5235i	−0.550544	+	0.757660i
$665$	21.3334			0.827275
$666$	5.45009	−	6.05269i	0.211187	−	0.234537i
$667$		−	10.7093i		−	0.414665i
$668$	−24.6970	+	2.59473i	−0.955555	+	0.100393i
$669$		−	20.5887i		−	0.796005i
$670$	9.24092	+	50.4321i	0.357008	+	1.94836i
$671$			43.3902i			1.67506i
$672$	−7.97061	+	13.8022i	−0.307473	+	0.532432i
$673$			32.4767i			1.25188i	0.779870	+	0.625942i	$0.215285\pi$
$673$			32.4767i			1.25188i	−0.779870	+	0.625942i	$0.784715\pi$
$674$	28.1457	+	25.3435i	1.08413	+	0.976195i
$675$	−14.6179			−0.562643
$676$	5.96906	+	56.8143i	0.229579	+	2.18516i
$677$			28.8665i			1.10943i	0.832040	+	0.554715i	$0.187173\pi$
$677$			28.8665i			1.10943i	−0.832040	+	0.554715i	$0.812827\pi$
$678$	−12.3648	−	11.1338i	−0.474867	−	0.427590i
$679$		−	37.2792i		−	1.43065i
$680$	−9.81654	+	13.5096i	−0.376447	+	0.518068i
$681$			8.99211i			0.344578i
$682$	−35.9222	+	39.8940i	−1.37553	+	1.52762i
$683$	17.2983			0.661901			0.330951	−	0.943648i	$-0.392631\pi$
$683$	17.2983			0.661901			0.330951	+	0.943648i	$0.392631\pi$
$684$	3.40026	−	0.357240i	0.130012	−	0.0136594i
$685$	−30.5233			−1.16623
$686$	−16.1616	+	17.9486i	−0.617054	+	0.685279i
$687$		−	2.72243i		−	0.103867i
$688$	4.16681	−	0.885326i	0.158858	−	0.0337527i
$689$	−29.8912			−1.13877
$690$	14.3054	−	15.8871i	0.544596	−	0.604810i
$691$		−	28.2517i		−	1.07475i	−0.843345	−	0.537373i	$-0.819417\pi$
$691$		−	28.2517i		−	1.07475i	0.843345	−	0.537373i	$-0.180583\pi$
$692$	−3.92498	−	37.3585i	−0.149205	−	1.42016i
$693$	12.6531			0.480653
$694$	−10.8723	+	12.0744i	−0.412707	+	0.458338i
$695$		−	14.6866i		−	0.557095i
$696$	7.17971	+	5.21704i	0.272146	+	0.197751i
$697$			6.86560i			0.260053i
$698$	−15.5771	+	17.2994i	−0.589602	+	0.654793i
$699$		−	18.8884i		−	0.714423i
$700$	8.60693	+	81.9219i	0.325311	+	3.09636i
$701$		−	19.9558i		−	0.753719i	−0.926270	−	0.376860i	$-0.877004\pi$
$701$		−	19.9558i		−	0.753719i	0.926270	−	0.376860i	$-0.122996\pi$
$702$	6.77542	+	6.10087i	0.255722	+	0.230262i
$703$			9.84540i			0.371326i
$704$	11.0978	+	34.1698i	0.418264	+	1.28782i
$705$	20.0597			0.755492
$706$	4.09603	+	3.68823i	0.154156	+	0.138808i
$707$			12.4075i			0.466631i
$708$	−20.4514	+	2.14868i	−0.768612	+	0.0807525i
$709$	2.92170			0.109727			0.0548633	−	0.998494i	$-0.482528\pi$
$709$	2.92170			0.109727			0.0548633	+	0.998494i	$0.482528\pi$
$710$	−2.00934	+	2.23151i	−0.0754093	+	0.0837470i
$711$	9.91224			0.371738
$712$	26.7429	+	19.4324i	1.00223	+	0.728259i
$713$		−	28.8493i		−	1.08041i
$714$	3.55416	−	3.94713i	0.133011	−	0.147718i
$715$	128.236			4.79577
$716$	−0.105040	−	0.999789i	−0.00392555	−	0.0373639i
$717$	26.7279			0.998171
$718$	−31.3594	−	28.2373i	−1.17032	−	1.05381i
$719$			16.4667i			0.614103i	0.951693	+	0.307051i	$0.0993424\pi$
$719$			16.4667i			0.614103i	−0.951693	+	0.307051i	$0.900658\pi$
$720$	3.68211	+	17.3300i	0.137224	+	0.645850i
$721$			24.3199i			0.905722i
$722$	15.2145	−	16.8968i	0.566226	−	0.628832i
$723$	12.0626			0.448614
$724$	3.22355	+	30.6822i	0.119802	+	1.14029i
$725$	45.8678			1.70349
$726$	8.67560	−	9.63483i	0.321982	−	0.357582i
$727$	−0.181194			−0.00672011			−0.00336006	−	0.999994i	$-0.501070\pi$
$727$	−0.181194			−0.00672011			−0.00336006	+	0.999994i	$0.501070\pi$
$728$	30.2013	−	41.5631i	1.11933	−	1.54043i
$729$	1.00000			0.0370370
$730$	−17.1391	−	15.4327i	−0.634346	−	0.571191i
$731$	−1.41959			−0.0525056
$732$	19.2180	−	2.01910i	0.710319	−	0.0746280i
$733$			18.0519i			0.666764i	0.942792	+	0.333382i	$0.108190\pi$
$733$			18.0519i			0.666764i	−0.942792	+	0.333382i	$0.891810\pi$
$734$	35.1585	−	39.0458i	1.29772	−	1.44121i
$735$		−	4.15682i		−	0.153327i
$736$	−16.7193	−	9.65516i	−0.616280	−	0.355894i
$737$	−29.1179	−	22.4363i	−1.07257	−	0.826452i
$738$	5.41286	+	4.87397i	0.199250	+	0.179413i
$739$	9.27764			0.341284			0.170642	−	0.985333i	$-0.445416\pi$
$739$	9.27764			0.341284			0.170642	+	0.985333i	$0.445416\pi$
$740$	−50.7388	+	5.33076i	−1.86520	+	0.195962i
$741$	−11.0210			−0.404867
$742$	13.7290	+	12.3621i	0.504006	+	0.453828i
$743$		−	1.38908i		−	0.0509605i	−0.999675	−	0.0254802i	$-0.991889\pi$
$743$		−	1.38908i		−	0.0509605i	0.999675	−	0.0254802i	$-0.00811149\pi$
$744$	19.3411	+	14.0540i	0.709079	+	0.515243i
$745$			85.1825i			3.12084i
$746$	33.3134	+	29.9968i	1.21969	+	1.09826i
$747$		−	8.53248i		−	0.312187i
$748$	−1.25099	−	11.9071i	−0.0457409	−	0.435368i
$749$		−	14.0256i		−	0.512485i
$750$	44.7699	+	40.3126i	1.63476	+	1.47201i
$751$			23.9459i			0.873799i	0.899510	+	0.436900i	$0.143924\pi$
$751$			23.9459i			0.873799i	−0.899510	+	0.436900i	$0.856076\pi$
$752$	−3.76504	−	17.7203i	−0.137297	−	0.646192i
$753$	25.4913			0.928955
$754$	−21.2598	−	19.1432i	−0.774237	−	0.697155i
$755$	−49.3467			−1.79591
$756$	−0.588795	−	5.60422i	−0.0214143	−	0.203824i
$757$		−	11.8148i		−	0.429418i	−0.976678	−	0.214709i	$-0.931120\pi$
$757$		−	11.8148i		−	0.429418i	0.976678	−	0.214709i	$-0.0688803\pi$
$758$	−30.1700	+	33.5058i	−1.09582	+	1.21699i
$759$			15.3273i			0.556346i
$760$	−17.3251	−	12.5890i	−0.628446	−	0.456652i
$761$	22.1353			0.802405			0.401202	−	0.915989i	$-0.368592\pi$
$761$	22.1353			0.802405			0.401202	+	0.915989i	$0.368592\pi$
$762$	−7.05042	−	6.34849i	−0.255410	−	0.229982i
$763$			17.0992i			0.619033i
$764$	−1.38244	−	13.1583i	−0.0500151	−	0.476050i
$765$		−	5.90416i		−	0.213465i
$766$	−28.3151	+	31.4458i	−1.02307	+	1.13618i
$767$	66.2878			2.39351
$768$	14.6178	−	6.50538i	0.527474	−	0.234743i
$769$		−	27.5107i		−	0.992062i	−0.868305	−	0.496031i	$-0.834790\pi$
$769$		−	27.5107i		−	0.992062i	0.868305	−	0.496031i	$-0.165210\pi$
$770$	−58.8986	−	53.0347i	−2.12256	−	1.91124i
$771$	12.9570			0.466635
$772$	1.58327	+	15.0698i	0.0569832	+	0.542373i
$773$	−12.8342			−0.461613			−0.230806	−	0.973000i	$-0.574136\pi$
$773$	−12.8342			−0.461613			−0.230806	+	0.973000i	$0.574136\pi$
$774$	−1.00779	+	1.11921i	−0.0362241	+	0.0402293i
$775$	123.561			4.43845
$776$	−21.9988	+	30.2748i	−0.789709	+	1.08680i
$777$	16.2270			0.582139
$778$	27.0714	−	30.0646i	0.970556	−	1.07787i
$779$	−8.80465			−0.315459
$780$	−5.96728	−	56.7974i	−0.213663	−	2.03367i
$781$		−	2.15289i		−	0.0770363i
$782$	4.78134	+	4.30531i	0.170980	+	0.153958i
$783$	−3.13779			−0.112135
$784$	−3.67204	+	0.780200i	−0.131144	+	0.0278643i
$785$			48.0269i			1.71415i
$786$	3.10090	+	2.79218i	0.110606	+	0.0995938i
$787$	−14.0936			−0.502383			−0.251191	−	0.967937i	$-0.580822\pi$
$787$	−14.0936			−0.502383			−0.251191	+	0.967937i	$0.580822\pi$
$788$	15.5289	−	1.63150i	0.553192	−	0.0581199i
$789$		−	1.56509i		−	0.0557186i
$790$	−46.1401	−	41.5464i	−1.64159	−	1.47816i
$791$		−	33.1494i		−	1.17866i
$792$	−10.2757	−	7.46671i	−0.365132	−	0.265318i
$793$	−62.2901			−2.21199
$794$	−24.6819	+	27.4108i	−0.875926	+	0.972774i
$795$	20.5359			0.728334
$796$	−12.7520	+	1.33975i	−0.451981	+	0.0474864i
$797$	0.0454042			0.00160830			0.000804149	−	1.00000i	$-0.499744\pi$
$797$	0.0454042			0.00160830			0.000804149		1.00000i	$0.499744\pi$
$798$	5.06192	+	4.55796i	0.179190	+	0.161350i
$799$			6.03713i			0.213578i
$800$	41.3530	−	71.6085i	1.46205	−	2.53174i
$801$	−11.6876			−0.412961
$802$	−1.71960	−	1.54840i	−0.0607212	−	0.0546759i
$803$	16.5352			0.583515
$804$	−8.58235	+	13.9407i	−0.302676	+	0.491651i
$805$	42.5924			1.50119
$806$	−57.2710	−	51.5691i	−2.01728	−	1.81645i
$807$	6.01649			0.211790
$808$	7.32174	−	10.0762i	0.257578	−	0.354480i
$809$			50.0032i			1.75802i	0.476804	+	0.879010i	$0.341795\pi$
$809$			50.0032i			1.75802i	−0.476804	+	0.879010i	$0.658205\pi$
$810$	−4.65486	−	4.19143i	−0.163555	−	0.147272i
$811$	−20.2892			−0.712450			−0.356225	−	0.934400i	$-0.615936\pi$
$811$	−20.2892			−0.712450			−0.356225	+	0.934400i	$0.615936\pi$
$812$	1.84751	+	17.5849i	0.0648350	+	0.617108i
$813$	25.6297			0.898872
$814$	24.4756	−	27.1818i	0.857868	−	0.952720i
$815$	−76.5276			−2.68065
$816$	−5.21559	+	1.10816i	−0.182582	+	0.0387934i
$817$		−	1.82053i		−	0.0636922i
$818$	−1.06428	−	0.958326i	−0.0372119	−	0.0335071i
$819$			18.1646i			0.634722i
$820$	−4.76725	−	45.3753i	−0.166479	−	1.58457i
$821$	29.0883			1.01519			0.507594	−	0.861597i	$-0.330535\pi$
$821$	29.0883			1.01519			0.507594	+	0.861597i	$0.330535\pi$
$822$	−7.24245	−	6.52140i	−0.252609	−	0.227460i
$823$		−	37.9961i		−	1.32446i	−0.749300	−	0.662231i	$-0.769610\pi$
$823$		−	37.9961i		−	1.32446i	0.749300	−	0.662231i	$-0.230390\pi$
$824$	14.3514	−	19.7504i	0.499954	−	0.688039i
$825$	−65.6468			−2.28553
$826$	−30.4458	−	27.4147i	−1.05934	−	0.953878i
$827$			15.8924i			0.552634i	0.961067	+	0.276317i	$0.0891140\pi$
$827$			15.8924i			0.552634i	−0.961067	+	0.276317i	$0.910886\pi$
$828$	6.78865	−	0.713234i	0.235922	−	0.0247866i
$829$	31.9818			1.11077			0.555386	−	0.831593i	$-0.312570\pi$
$829$	31.9818			1.11077			0.555386	+	0.831593i	$0.312570\pi$
$830$	−35.7633	+	39.7175i	−1.24136	+	1.37861i
$831$	5.21072			0.180758
$832$	−49.0535	+	15.9317i	−1.70062	+	0.552334i
$833$	1.25103			0.0433455
$834$	3.13784	−	3.48479i	0.108655	−	0.120668i
$835$	−54.9951			−1.90318
$836$	15.2701	−	1.60431i	0.528126	−	0.0554863i
$837$	−8.45275			−0.292170
$838$	10.1111	+	9.10444i	0.349282	+	0.314508i
$839$			29.9516i			1.03404i	0.855972	+	0.517022i	$0.172960\pi$
$839$			29.9516i			1.03404i	−0.855972	+	0.517022i	$0.827040\pi$
$840$	−20.7489	+	28.5548i	−0.715906	+	0.985233i
$841$	−19.1543			−0.660493
$842$	9.71601	−	10.7903i	0.334836	−	0.371858i
$843$		−	24.6197i		−	0.847947i
$844$	19.0483	−	2.00127i	0.655670	−	0.0688864i
$845$			126.514i			4.35220i
$846$	4.75969	+	4.28582i	0.163642	+	0.147350i
$847$	25.8305			0.887547
$848$	−3.85442	−	18.1409i	−0.132361	−	0.622963i
$849$		−	8.75201i		−	0.300368i
$850$	−18.4396	+	20.4784i	−0.632474	+	0.702404i
$851$			19.6565i			0.673815i
$852$	−0.953539	+	0.100181i	−0.0326677	+	0.00343216i
$853$	44.7101			1.53084			0.765422	−	0.643529i	$-0.222530\pi$
$853$	44.7101			1.53084			0.765422	+	0.643529i	$0.222530\pi$
$854$	28.6097	+	25.7613i	0.979002	+	0.881534i
$855$	7.57166			0.258945
$856$	−8.27662	+	11.3903i	−0.282889	+	0.389313i
$857$		−	27.1676i		−	0.928028i	−0.885828	−	0.464014i	$-0.846409\pi$
$857$		−	27.1676i		−	0.928028i	0.885828	−	0.464014i	$-0.153591\pi$
$858$	30.4274	+	27.3981i	1.03878	+	0.935356i
$859$			27.5620i			0.940403i	0.882559	+	0.470201i	$0.155819\pi$
$859$			27.5620i			0.940403i	−0.882559	+	0.470201i	$0.844181\pi$
$860$	9.38220	−	0.985719i	0.319930	−	0.0336127i
$861$			14.5116i			0.494555i
$862$	−6.82108	−	6.14198i	−0.232327	−	0.209197i
$863$		−	36.0347i		−	1.22663i	−0.789837	−	0.613317i	$-0.789835\pi$
$863$		−	36.0347i		−	1.22663i	0.789837	−	0.613317i	$-0.210165\pi$
$864$	−2.82893	+	4.89869i	−0.0962422	+	0.166657i
$865$		−	83.1896i		−	2.82853i
$866$	25.8178	+	23.2474i	0.877325	+	0.789979i
$867$	−15.2231			−0.517004
$868$	4.97694	+	47.3711i	0.168928	+	1.60788i
$869$	44.5144			1.51005
$870$	14.6060	+	13.1518i	0.495188	+	0.445888i
$871$	32.2091	−	41.8011i	1.09136	−	1.41637i
$872$	10.0904	−	13.8864i	0.341703	−	0.470253i
$873$		−	13.2311i		−	0.447807i
$874$	−5.52126	+	6.13173i	−0.186759	+	0.207409i
$875$			120.026i			4.05761i
$876$	−0.769442	−	7.32364i	−0.0259970	−	0.247443i
$877$	−56.3692			−1.90345			−0.951726	−	0.306948i	$-0.900692\pi$
$877$	−56.3692			−1.90345			−0.951726	+	0.306948i	$0.900692\pi$
$878$	10.9668	+	9.87494i	0.370111	+	0.333263i
$879$	−12.2547			−0.413342
$880$	16.5358	+	77.8264i	0.557423	+	2.62353i
$881$	28.0003			0.943353			0.471677	−	0.881772i	$-0.343649\pi$
$881$	28.0003			0.943353			0.471677	+	0.881772i	$0.343649\pi$
$882$	0.888118	−	0.986314i	0.0299045	−	0.0332109i
$883$	−52.9765			−1.78280			−0.891400	−	0.453217i	$-0.850276\pi$
$883$	−52.9765			−1.78280			−0.891400	+	0.453217i	$0.850276\pi$
$884$	17.0936	−	1.79590i	0.574920	−	0.0604027i
$885$	−45.5411			−1.53085
$886$	2.51368	−	2.79161i	0.0844486	−	0.0937858i
$887$			19.9943i			0.671344i	0.941979	+	0.335672i	$0.108963\pi$
$887$			19.9943i			0.671344i	−0.941979	+	0.335672i	$0.891037\pi$
$888$	−13.1781	−	9.57566i	−0.442227	−	0.321338i
$889$		−	18.9018i		−	0.633947i
$890$	54.4041	+	48.9877i	1.82363	+	1.64207i
$891$	4.49085			0.150449
$892$	−40.9520	+	4.30253i	−1.37117	+	0.144059i
$893$	−7.74219			−0.259082
$894$	−18.1995	+	20.2118i	−0.608683	+	0.675983i
$895$		−	2.22632i		−	0.0744177i
$896$	29.1190	+	12.9696i	0.972798	+	0.433285i
$897$	−22.0036			−0.734678
$898$	−9.56609	+	10.6238i	−0.319225	+	0.354520i
$899$	26.5229			0.884590
$900$	3.05477	+	29.0757i	0.101826	+	0.969191i
$901$			6.18044i			0.205900i
$902$	24.3084	+	21.8883i	0.809381	+	0.728800i
$903$	−3.00055			−0.0998522
$904$	−19.5617	+	26.9209i	−0.650613	+	0.895376i
$905$			68.3229i			2.27113i
$906$	−11.7088	−	10.5431i	−0.388999	−	0.350270i
$907$			35.9873i			1.19494i	0.801892	+	0.597469i	$0.203827\pi$
$907$			35.9873i			1.19494i	−0.801892	+	0.597469i	$0.796173\pi$
$908$	17.8858	−	1.87913i	0.593561	−	0.0623611i
$909$			4.40366i			0.146060i
$910$	76.1355	−	84.5535i	2.52387	−	2.80292i
$911$		−	41.2271i		−	1.36592i	−0.730458	−	0.682958i	$-0.760693\pi$
$911$		−	41.2271i		−	1.36592i	0.730458	−	0.682958i	$-0.239307\pi$
$912$	−1.42114	−	6.68863i	−0.0470586	−	0.221483i
$913$		−	38.3181i		−	1.26814i
$914$	9.00610	−	10.0019i	0.297895	−	0.330833i
$915$	42.7946			1.41475
$916$	−5.41505	+	0.568919i	−0.178918	+	0.0187976i
$917$			8.31337i			0.274532i
$918$	1.26144	−	1.40092i	0.0416338	−	0.0462371i
$919$	6.94070			0.228952			0.114476	−	0.993426i	$-0.463481\pi$
$919$	6.94070			0.228952			0.114476	+	0.993426i	$0.463481\pi$
$920$	−34.5897	−	25.1341i	−1.14039	−	0.828647i
$921$			20.6834i			0.681541i
$922$	−36.3433	+	40.3616i	−1.19690	+	1.32924i
$923$	3.09064			0.101730
$924$	−2.64419	−	25.1678i	−0.0869875	−	0.827958i
$925$	−84.1884			−2.76810
$926$	−14.3258	+	15.9098i	−0.470777	+	0.522829i
$927$			8.63164i			0.283500i
$928$	8.87658	−	15.3710i	0.291388	−	0.504579i
$929$			26.8342i			0.880400i	0.897900	+	0.440200i	$0.145092\pi$
$929$			26.8342i			0.880400i	−0.897900	+	0.440200i	$0.854908\pi$
$930$	39.3464	+	35.4291i	1.29022	+	1.16177i
$931$			1.60435i			0.0525806i
$932$	−37.5699	+	3.94720i	−1.23064	+	0.129295i
$933$	6.74222			0.220730
$934$	32.4530	+	29.2221i	1.06190	+	0.956175i
$935$		−	26.5147i		−	0.867123i
$936$	10.7191	−	14.7516i	0.350363	−	0.482171i
$937$		−	35.3256i		−	1.15404i	−0.816731	−	0.577019i	$-0.804216\pi$
$937$		−	35.3256i		−	1.15404i	0.816731	−	0.577019i	$-0.195784\pi$
$938$	−32.0812	+	5.87839i	−1.04749	+	0.191936i
$939$		−	6.93434i		−	0.226294i
$940$	−4.19198	−	39.8998i	−0.136727	−	1.30139i
$941$		−	4.39946i		−	0.143418i	−0.997426	−	0.0717091i	$-0.977155\pi$
$941$		−	4.39946i		−	0.143418i	0.997426	−	0.0717091i	$-0.0228453\pi$
$942$	−10.2611	+	11.3957i	−0.334325	+	0.371290i
$943$	−17.5786			−0.572437
$944$	8.54769	+	40.2300i	0.278203	+	1.30937i
$945$		−	12.4794i		−	0.405956i
$946$	−4.52582	+	5.02622i	−0.147147	+	0.163417i
$947$		−	49.4127i		−	1.60570i	−0.596183	−	0.802848i	$-0.703317\pi$
$947$		−	49.4127i		−	1.60570i	0.596183	−	0.802848i	$-0.296683\pi$
$948$	−2.07141	−	19.7160i	−0.0672763	−	0.640345i
$949$			23.7376i			0.770555i
$950$	−26.2621	−	23.6475i	−0.852056	−	0.767227i
$951$	−17.2122			−0.558143
$952$	−8.59378	−	6.24456i	−0.278526	−	0.202387i
$953$	−29.3374			−0.950333			−0.475166	−	0.879896i	$-0.657612\pi$
$953$	−29.3374			−0.950333			−0.475166	+	0.879896i	$0.657612\pi$
$954$	4.87268	+	4.38757i	0.157759	+	0.142053i
$955$		−	29.3008i		−	0.948151i
$956$	−5.58546	−	53.1631i	−0.180647	−	1.71942i
$957$	−14.0913			−0.455508
$958$	−26.8868	−	24.2100i	−0.868675	−	0.782190i
$959$		−	19.4166i		−	0.626996i
$960$	33.7008	−	10.9454i	1.08769	−	0.353263i
$961$	40.4490			1.30481
$962$	39.0215	+	35.1366i	1.25811	+	1.13285i
$963$		−	4.97798i		−	0.160413i
$964$	−2.52079	−	23.9932i	−0.0811892	−	0.772769i
$965$			33.5573i			1.08025i
$966$	10.1062	+	9.10002i	0.325161	+	0.292788i
$967$			2.15484i			0.0692951i	0.999400	+	0.0346476i	$0.0110309\pi$
$967$			2.15484i			0.0692951i	−0.999400	+	0.0346476i	$0.988969\pi$
$968$	−20.9772	−	15.2428i	−0.674232	−	0.489922i
$969$			2.27875i			0.0732041i
$970$	−55.4574	+	61.5891i	−1.78063	+	1.97751i
$971$			27.3862i			0.878864i	0.898276	+	0.439432i	$0.144820\pi$
$971$			27.3862i			0.878864i	−0.898276	+	0.439432i	$0.855180\pi$
$972$	−0.208975	−	1.98905i	−0.00670288	−	0.0637989i
$973$	9.34254			0.299508
$974$	−20.6274	+	22.9081i	−0.660945	+	0.734024i
$975$		−	94.2411i		−	3.01813i
$976$	−8.03219	−	37.8037i	−0.257104	−	1.21007i
$977$	24.2286			0.775140			0.387570	−	0.921840i	$-0.373315\pi$
$977$	24.2286			0.775140			0.387570	+	0.921840i	$0.373315\pi$
$978$	−18.1582	−	16.3504i	−0.580635	−	0.522828i
$979$	−52.4873			−1.67750
$980$	−8.26813	+	0.868672i	−0.264116	+	0.0277487i
$981$			6.06886i			0.193764i
$982$	−31.2249	−	28.1162i	−0.996426	−	0.897223i
$983$	16.3688			0.522083			0.261041	−	0.965328i	$-0.415934\pi$
$983$	16.3688			0.522083			0.261041	+	0.965328i	$0.415934\pi$
$984$	8.56342	−	11.7850i	0.272992	−	0.375692i
$985$	34.5795			1.10180
$986$	−3.95814	+	4.39578i	−0.126053	+	0.139990i
$987$			12.7605i			0.406171i
$988$	2.30312	+	21.9214i	0.0732719	+	0.697411i
$989$		−	3.63471i		−	0.115577i
$990$	−20.9043	−	18.8231i	−0.664382	−	0.598237i
$991$	38.1245			1.21106			0.605532	−	0.795821i	$-0.292961\pi$
$991$	38.1245			1.21106			0.605532	+	0.795821i	$0.292961\pi$
$992$	23.9123	−	41.4074i	0.759215	−	1.31469i
$993$	−11.8004			−0.374476
$994$	−1.41952	−	1.27820i	−0.0450245	−	0.0405419i
$995$	−28.3960			−0.900213
$996$	−16.9716	+	1.78308i	−0.537764	+	0.0564989i
$997$	48.6222			1.53988			0.769940	−	0.638116i	$-0.220286\pi$
$997$	48.6222			1.53988			0.769940	+	0.638116i	$0.220286\pi$
$998$	12.3266	−	13.6895i	0.390193	−	0.433335i
$999$	5.75928			0.182216

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	804.2.e.b.535.25	yes	34
4.3	odd	2		804.2.e.a.535.9	✓	34
67.66	odd	2		804.2.e.a.535.10	yes	34
268.267	even	2	inner	804.2.e.b.535.26	yes	34

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
804.2.e.a.535.9	✓	34	4.3	odd	2
804.2.e.a.535.10	yes	34	67.66	odd	2
804.2.e.b.535.25	yes	34	1.1	even	1	trivial
804.2.e.b.535.26	yes	34	268.267	even	2	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:	\( N \)	\(=\)	\( 804 = 2^{2} \cdot 3 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	804.e (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(0.946315 - 1.05095i) q^{2} +1.00000 q^{3} +(-0.208975 - 1.98905i) q^{4} -4.42921i q^{5} +(0.946315 - 1.05095i) q^{6} +2.81753 q^{7} +(-2.28814 - 1.66265i) q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+(0.946315 - 1.05095i) q^{2} +1.00000 q^{3} +(-0.208975 - 1.98905i) q^{4} -4.42921i q^{5} +(0.946315 - 1.05095i) q^{6} +2.81753 q^{7} +(-2.28814 - 1.66265i) q^{8} +1.00000 q^{9} +(-4.65486 - 4.19143i) q^{10} +4.49085 q^{11} +(-0.208975 - 1.98905i) q^{12} +6.44697i q^{13} +(2.66628 - 2.96108i) q^{14} -4.42921i q^{15} +(-3.91266 + 0.831325i) q^{16} +1.33300 q^{17} +(0.946315 - 1.05095i) q^{18} +1.70948i q^{19} +(-8.80993 + 0.925594i) q^{20} +2.81753 q^{21} +(4.24976 - 4.71965i) q^{22} +3.41301i q^{23} +(-2.28814 - 1.66265i) q^{24} -14.6179 q^{25} +(6.77542 + 6.10087i) q^{26} +1.00000 q^{27} +(-0.588795 - 5.60422i) q^{28} -3.13779 q^{29} +(-4.65486 - 4.19143i) q^{30} -8.45275 q^{31} +(-2.82893 + 4.89869i) q^{32} +4.49085 q^{33} +(1.26144 - 1.40092i) q^{34} -12.4794i q^{35} +(-0.208975 - 1.98905i) q^{36} +5.75928 q^{37} +(1.79658 + 1.61771i) q^{38} +6.44697i q^{39} +(-7.36422 + 10.1347i) q^{40} +5.15047i q^{41} +(2.66628 - 2.96108i) q^{42} -1.06496 q^{43} +(-0.938477 - 8.93254i) q^{44} -4.42921i q^{45} +(3.58689 + 3.22978i) q^{46} +4.52896i q^{47} +(-3.91266 + 0.831325i) q^{48} +0.938501 q^{49} +(-13.8331 + 15.3626i) q^{50} +1.33300 q^{51} +(12.8234 - 1.34726i) q^{52} +4.63647i q^{53} +(0.946315 - 1.05095i) q^{54} -19.8909i q^{55} +(-6.44692 - 4.68457i) q^{56} +1.70948i q^{57} +(-2.96934 + 3.29764i) q^{58} -10.2820i q^{59} +(-8.80993 + 0.925594i) q^{60} +9.66191i q^{61} +(-7.99897 + 8.88339i) q^{62} +2.81753 q^{63} +(2.47120 + 7.60876i) q^{64} +28.5550 q^{65} +(4.24976 - 4.71965i) q^{66} +(-6.48382 - 4.99600i) q^{67} +(-0.278565 - 2.65142i) q^{68} +3.41301i q^{69} +(-13.1152 - 11.8095i) q^{70} -0.479394i q^{71} +(-2.28814 - 1.66265i) q^{72} +3.68198 q^{73} +(5.45009 - 6.05269i) q^{74} -14.6179 q^{75} +(3.40026 - 0.357240i) q^{76} +12.6531 q^{77} +(6.77542 + 6.10087i) q^{78} +9.91224 q^{79} +(3.68211 + 17.3300i) q^{80} +1.00000 q^{81} +(5.41286 + 4.87397i) q^{82} -8.53248i q^{83} +(-0.588795 - 5.60422i) q^{84} -5.90416i q^{85} +(-1.00779 + 1.11921i) q^{86} -3.13779 q^{87} +(-10.2757 - 7.46671i) q^{88} -11.6876 q^{89} +(-4.65486 - 4.19143i) q^{90} +18.1646i q^{91} +(6.78865 - 0.713234i) q^{92} -8.45275 q^{93} +(4.75969 + 4.28582i) q^{94} +7.57166 q^{95} +(-2.82893 + 4.89869i) q^{96} -13.2311i q^{97} +(0.888118 - 0.986314i) q^{98} +4.49085 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 34 q + 34 q^{3} + 2 q^{4} + 4 q^{7} - 6 q^{8} + 34 q^{9}+O(q^{10}) \) 34 * q + 34 * q^3 + 2 * q^4 + 4 * q^7 - 6 * q^8 + 34 * q^9	\( 34 q + 34 q^{3} + 2 q^{4} + 4 q^{7} - 6 q^{8} + 34 q^{9} - 6 q^{10} + 2 q^{12} - 4 q^{14} + 2 q^{16} - 12 q^{20} + 4 q^{21} - 8 q^{22} - 6 q^{24} - 34 q^{25} + 10 q^{26} + 34 q^{27} - 8 q^{28} - 16 q^{29} - 6 q^{30} - 4 q^{31} + 2 q^{36} + 12 q^{37} + 26 q^{38} - 18 q^{40} - 4 q^{42} - 4 q^{43} + 26 q^{44} - 4 q^{46} + 2 q^{48} + 46 q^{49} - 18 q^{50} + 32 q^{52} + 14 q^{56} + 4 q^{58} - 12 q^{60} - 2 q^{62} + 4 q^{63} + 26 q^{64} - 8 q^{66} - 18 q^{67} - 34 q^{68} + 56 q^{70} - 6 q^{72} + 12 q^{73} + 22 q^{74} - 34 q^{75} - 32 q^{76} - 8 q^{77} + 10 q^{78} - 12 q^{79} - 2 q^{80} + 34 q^{81} + 26 q^{82} - 8 q^{84} + 6 q^{86} - 16 q^{87} - 28 q^{88} - 6 q^{90} - 46 q^{92} - 4 q^{93} + 32 q^{94} - 40 q^{95} - 40 q^{98}+O(q^{100}) \) 34 * q + 34 * q^3 + 2 * q^4 + 4 * q^7 - 6 * q^8 + 34 * q^9 - 6 * q^10 + 2 * q^12 - 4 * q^14 + 2 * q^16 - 12 * q^20 + 4 * q^21 - 8 * q^22 - 6 * q^24 - 34 * q^25 + 10 * q^26 + 34 * q^27 - 8 * q^28 - 16 * q^29 - 6 * q^30 - 4 * q^31 + 2 * q^36 + 12 * q^37 + 26 * q^38 - 18 * q^40 - 4 * q^42 - 4 * q^43 + 26 * q^44 - 4 * q^46 + 2 * q^48 + 46 * q^49 - 18 * q^50 + 32 * q^52 + 14 * q^56 + 4 * q^58 - 12 * q^60 - 2 * q^62 + 4 * q^63 + 26 * q^64 - 8 * q^66 - 18 * q^67 - 34 * q^68 + 56 * q^70 - 6 * q^72 + 12 * q^73 + 22 * q^74 - 34 * q^75 - 32 * q^76 - 8 * q^77 + 10 * q^78 - 12 * q^79 - 2 * q^80 + 34 * q^81 + 26 * q^82 - 8 * q^84 + 6 * q^86 - 16 * q^87 - 28 * q^88 - 6 * q^90 - 46 * q^92 - 4 * q^93 + 32 * q^94 - 40 * q^95 - 40 * q^98

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