LMFDB - Embedded newform 1098.2.bd.b.467.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1098,2,Mod(143,1098)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1098, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 11]))

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

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

chi := DirichletCharacter("1098.143");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1098 = 2 \cdot 3^{2} \cdot 61 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1098.bd (of order $12$, 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:	$8.76757414194$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$12$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			467.6
Character	$\chi$	$=$	1098.467
Dual form			1098.2.bd.b.395.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.965926 + 0.258819i) q^{2} +(0.866025 - 0.500000i) q^{4} +(-2.02743 + 3.51162i) q^{5} +(-0.376882 - 1.40654i) q^{7} +(-0.707107 + 0.707107i) q^{8} +O(q^{10})$	\(q+(-0.965926 + 0.258819i) q^{2} +(0.866025 - 0.500000i) q^{4} +(-2.02743 + 3.51162i) q^{5} +(-0.376882 - 1.40654i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(1.04948 - 3.91670i) q^{10} +(2.07741 - 2.07741i) q^{11} +(2.10707 - 3.64954i) q^{13} +(0.728080 + 1.26107i) q^{14} +(0.500000 - 0.866025i) q^{16} +(-2.30360 - 0.617248i) q^{17} +(-3.11899 + 1.80075i) q^{19} +4.05487i q^{20} +(-1.46895 + 2.54429i) q^{22} +(-4.74425 - 4.74425i) q^{23} +(-5.72098 - 9.90904i) q^{25} +(-1.09070 + 4.07054i) q^{26} +(-1.02966 - 1.02966i) q^{28} +(5.85173 + 1.56797i) q^{29} +(-0.0233460 + 0.0871284i) q^{31} +(-0.258819 + 0.965926i) q^{32} +2.38486 q^{34} +(5.70335 + 1.52821i) q^{35} +(2.07988 + 2.07988i) q^{37} +(2.54665 - 2.54665i) q^{38} +(-1.04948 - 3.91670i) q^{40} +11.6674 q^{41} +(4.34096 - 1.16316i) q^{43} +(0.760384 - 2.83779i) q^{44} +(5.81049 + 3.35469i) q^{46} +(-2.19356 + 1.26645i) q^{47} +(4.22586 - 2.43980i) q^{49} +(8.09069 + 8.09069i) q^{50} -4.21413i q^{52} +(1.83607 + 1.83607i) q^{53} +(3.08326 + 11.5069i) q^{55} +(1.26107 + 0.728080i) q^{56} -6.05816 q^{58} +(-3.27774 - 12.2327i) q^{59} +(7.31406 + 2.73945i) q^{61} -0.0902019i q^{62} -1.00000i q^{64} +(8.54388 + 14.7984i) q^{65} +(5.71065 - 1.53017i) q^{67} +(-2.30360 + 0.617248i) q^{68} -5.90454 q^{70} +(-8.88735 - 2.38136i) q^{71} +(-0.863448 - 1.49554i) q^{73} +(-2.54732 - 1.47070i) q^{74} +(-1.80075 + 3.11899i) q^{76} +(-3.70490 - 2.13902i) q^{77} +(-1.68178 - 6.27650i) q^{79} +(2.02743 + 3.51162i) q^{80} +(-11.2698 + 3.01974i) q^{82} +(3.26716 + 1.88630i) q^{83} +(6.83795 - 6.83795i) q^{85} +(-3.89200 + 2.24705i) q^{86} +2.93790i q^{88} +(13.3087 - 13.3087i) q^{89} +(-5.92735 - 1.58823i) q^{91} +(-6.48076 - 1.73652i) q^{92} +(1.79103 - 1.79103i) q^{94} -14.6036i q^{95} +(9.18303 - 5.30182i) q^{97} +(-3.45040 + 3.45040i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 4 q^{7}+O(q^{10}) $ 48 * q + 4 * q^7	$ 48 q + 4 q^{7} + 4 q^{10} - 12 q^{13} + 24 q^{16} - 36 q^{19} - 4 q^{22} - 48 q^{25} - 8 q^{28} - 20 q^{31} - 16 q^{34} + 8 q^{37} - 4 q^{40} + 20 q^{43} + 12 q^{46} + 72 q^{49} - 52 q^{55} + 32 q^{58} + 8 q^{61} + 28 q^{67} - 8 q^{70} + 16 q^{73} - 28 q^{76} + 32 q^{79} - 48 q^{82} + 120 q^{85} - 92 q^{91} + 8 q^{94} + 72 q^{97}+O(q^{100}) $ 48 * q + 4 * q^7 + 4 * q^10 - 12 * q^13 + 24 * q^16 - 36 * q^19 - 4 * q^22 - 48 * q^25 - 8 * q^28 - 20 * q^31 - 16 * q^34 + 8 * q^37 - 4 * q^40 + 20 * q^43 + 12 * q^46 + 72 * q^49 - 52 * q^55 + 32 * q^58 + 8 * q^61 + 28 * q^67 - 8 * q^70 + 16 * q^73 - 28 * q^76 + 32 * q^79 - 48 * q^82 + 120 * q^85 - 92 * q^91 + 8 * q^94 + 72 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1098\mathbb{Z}\right)^\times$.

$n$	$245$	$307$
$\chi(n)$	$-1$	$e\left(\frac{5}{12}\right)$

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 $

$2$	−0.965926	+	0.258819i	−0.683013	+	0.183013i
$2$	−0.965926	+	0.258819i	−0.683013	+	0.183013i
$3$		0			0
$3$		0			0
$4$	0.866025	−	0.500000i	0.433013	−	0.250000i
$5$	−2.02743	+	3.51162i	−0.906696	+	1.57044i	−0.0880728	+	0.996114i	$0.528071\pi$
$5$	−2.02743	+	3.51162i	−0.906696	+	1.57044i	−0.818624	+	0.574330i	$0.805263\pi$
$6$		0			0
$7$	−0.376882	−	1.40654i	−0.142448	−	0.531623i	−0.999856	−	0.0169854i	$-0.994593\pi$
$7$	−0.376882	−	1.40654i	−0.142448	−	0.531623i	0.857408	−	0.514638i	$-0.172074\pi$
$8$	−0.707107	+	0.707107i	−0.250000	+	0.250000i
$9$		0			0
$10$	1.04948	−	3.91670i	0.331874	−	1.23857i
$11$	2.07741	−	2.07741i	0.626362	−	0.626362i	−0.320789	−	0.947151i	$-0.603948\pi$
$11$	2.07741	−	2.07741i	0.626362	−	0.626362i	0.947151	+	0.320789i	$0.103948\pi$
$12$		0			0
$13$	2.10707	−	3.64954i	0.584395	−	1.01220i	−0.410556	−	0.911835i	$-0.634665\pi$
$13$	2.10707	−	3.64954i	0.584395	−	1.01220i	0.994951	−	0.100366i	$-0.0320014\pi$
$14$	0.728080	+	1.26107i	0.194588	+	0.337035i
$15$		0			0
$16$	0.500000	−	0.866025i	0.125000	−	0.216506i
$17$	−2.30360	−	0.617248i	−0.558706	−	0.149705i	−0.0315941	−	0.999501i	$-0.510058\pi$
$17$	−2.30360	−	0.617248i	−0.558706	−	0.149705i	−0.527112	+	0.849796i	$0.676725\pi$
$18$		0			0
$19$	−3.11899	+	1.80075i	−0.715547	+	0.413121i	−0.813111	−	0.582108i	$-0.802228\pi$
$19$	−3.11899	+	1.80075i	−0.715547	+	0.413121i	0.0975648	+	0.995229i	$0.468895\pi$
$20$			4.05487i			0.906696i
$21$		0			0
$22$	−1.46895	+	2.54429i	−0.313181	+	0.542445i
$23$	−4.74425	−	4.74425i	−0.989244	−	0.989244i	0.0106987	−	0.999943i	$-0.496594\pi$
$23$	−4.74425	−	4.74425i	−0.989244	−	0.989244i	−0.999943	+	0.0106987i	$0.996594\pi$
$24$		0			0
$25$	−5.72098	−	9.90904i	−1.14420	−	1.98181i
$26$	−1.09070	+	4.07054i	−0.213903	+	0.798298i
$27$		0			0
$28$	−1.02966	−	1.02966i	−0.194588	−	0.194588i
$29$	5.85173	+	1.56797i	1.08664	+	0.291164i	0.757313	−	0.653052i	$-0.226512\pi$
$29$	5.85173	+	1.56797i	1.08664	+	0.291164i	0.329326	+	0.944216i	$0.393178\pi$
$30$		0			0
$31$	−0.0233460	+	0.0871284i	−0.00419306	+	0.0156487i	−0.967991	−	0.250986i	$-0.919245\pi$
$31$	−0.0233460	+	0.0871284i	−0.00419306	+	0.0156487i	0.963798	+	0.266635i	$0.0859118\pi$
$32$	−0.258819	+	0.965926i	−0.0457532	+	0.170753i
$33$		0			0
$34$	2.38486			0.409001
$35$	5.70335	+	1.52821i	0.964041	+	0.258314i
$36$		0			0
$37$	2.07988	+	2.07988i	0.341930	+	0.341930i	0.857093	−	0.515162i	$-0.172268\pi$
$37$	2.07988	+	2.07988i	0.341930	+	0.341930i	−0.515162	+	0.857093i	$0.672268\pi$
$38$	2.54665	−	2.54665i	0.413121	−	0.413121i
$39$		0			0
$40$	−1.04948	−	3.91670i	−0.165937	−	0.619285i
$41$	11.6674			1.82214			0.911070	−	0.412253i	$-0.135258\pi$
$41$	11.6674			1.82214			0.911070	+	0.412253i	$0.135258\pi$
$42$		0			0
$43$	4.34096	−	1.16316i	0.661991	−	0.177380i	0.0878465	−	0.996134i	$-0.472001\pi$
$43$	4.34096	−	1.16316i	0.661991	−	0.177380i	0.574144	+	0.818754i	$0.305335\pi$
$44$	0.760384	−	2.83779i	0.114632	−	0.427813i
$45$		0			0
$46$	5.81049	+	3.35469i	0.856711	+	0.494622i
$47$	−2.19356	+	1.26645i	−0.319963	+	0.184731i	−0.651376	−	0.758755i	$-0.725808\pi$
$47$	−2.19356	+	1.26645i	−0.319963	+	0.184731i	0.331413	+	0.943486i	$0.392475\pi$
$48$		0			0
$49$	4.22586	−	2.43980i	0.603694	−	0.348543i
$50$	8.09069	+	8.09069i	1.14420	+	1.14420i
$51$		0			0
$52$		−	4.21413i		−	0.584395i
$53$	1.83607	+	1.83607i	0.252204	+	0.252204i	0.821874	−	0.569670i	$-0.192929\pi$
$53$	1.83607	+	1.83607i	0.252204	+	0.252204i	−0.569670	+	0.821874i	$0.692929\pi$
$54$		0			0
$55$	3.08326	+	11.5069i	0.415747	+	1.55159i
$56$	1.26107	+	0.728080i	0.168518	+	0.0972938i
$57$		0			0
$58$	−6.05816			−0.795475
$59$	−3.27774	−	12.2327i	−0.426725	−	1.59256i	−0.760126	−	0.649775i	$-0.774863\pi$
$59$	−3.27774	−	12.2327i	−0.426725	−	1.59256i	0.333401	−	0.942785i	$-0.391804\pi$
$60$		0			0
$61$	7.31406	+	2.73945i	0.936469	+	0.350751i
$61$	7.31406	+	2.73945i	0.936469	+	0.350751i
$62$		−	0.0902019i		−	0.0114557i
$63$		0			0
$64$		−	1.00000i		−	0.125000i
$65$	8.54388	+	14.7984i	1.05974	+	1.83552i
$66$		0			0
$67$	5.71065	−	1.53017i	0.697667	−	0.186939i	0.107482	−	0.994207i	$-0.465721\pi$
$67$	5.71065	−	1.53017i	0.697667	−	0.186939i	0.590186	+	0.807268i	$0.299055\pi$
$68$	−2.30360	+	0.617248i	−0.279353	+	0.0748524i
$69$		0			0
$70$	−5.90454			−0.705727
$71$	−8.88735	−	2.38136i	−1.05473	−	0.282615i	−0.310528	−	0.950564i	$-0.600506\pi$
$71$	−8.88735	−	2.38136i	−1.05473	−	0.282615i	−0.744207	+	0.667949i	$0.767172\pi$
$72$		0			0
$73$	−0.863448	−	1.49554i	−0.101059	−	0.175039i	0.811062	−	0.584960i	$-0.198890\pi$
$73$	−0.863448	−	1.49554i	−0.101059	−	0.175039i	−0.912121	+	0.409921i	$0.865556\pi$
$74$	−2.54732	−	1.47070i	−0.296120	−	0.170965i
$75$		0			0
$76$	−1.80075	+	3.11899i	−0.206560	+	0.357773i
$77$	−3.70490	−	2.13902i	−0.422213	−	0.243765i
$78$		0			0
$79$	−1.68178	−	6.27650i	−0.189215	−	0.706162i	−0.993689	−	0.112173i	$-0.964219\pi$
$79$	−1.68178	−	6.27650i	−0.189215	−	0.706162i	0.804473	−	0.593989i	$-0.202448\pi$
$80$	2.02743	+	3.51162i	0.226674	+	0.392611i
$81$		0			0
$82$	−11.2698	+	3.01974i	−1.24454	+	0.333475i
$83$	3.26716	+	1.88630i	0.358618	+	0.207048i	0.668474	−	0.743735i	$-0.266948\pi$
$83$	3.26716	+	1.88630i	0.358618	+	0.207048i	−0.309856	+	0.950783i	$0.600281\pi$
$84$		0			0
$85$	6.83795	−	6.83795i	0.741679	−	0.741679i
$86$	−3.89200	+	2.24705i	−0.419685	+	0.242305i
$87$		0			0
$88$			2.93790i			0.313181i
$89$	13.3087	−	13.3087i	1.41072	−	1.41072i	0.655689	−	0.755031i	$-0.272378\pi$
$89$	13.3087	−	13.3087i	1.41072	−	1.41072i	0.755031	−	0.655689i	$-0.227622\pi$
$90$		0			0
$91$	−5.92735	−	1.58823i	−0.621355	−	0.166492i
$92$	−6.48076	−	1.73652i	−0.675666	−	0.181044i
$93$		0			0
$94$	1.79103	−	1.79103i	0.184731	−	0.184731i
$95$		−	14.6036i		−	1.49830i
$96$		0			0
$97$	9.18303	−	5.30182i	0.932395	−	0.538319i	0.0448270	−	0.998995i	$-0.485726\pi$
$97$	9.18303	−	5.30182i	0.932395	−	0.538319i	0.887568	+	0.460676i	$0.152393\pi$
$98$	−3.45040	+	3.45040i	−0.348543	+	0.348543i
$99$		0			0
$100$	−9.90904	−	5.72098i	−0.990904	−	0.572098i
$101$	−0.0354365	+	0.00949519i	−0.00352607	+	0.000944807i	−0.260582	−	0.965452i	$-0.583914\pi$
$101$	−0.0354365	+	0.00949519i	−0.00352607	+	0.000944807i	0.257056	+	0.966397i	$0.417248\pi$
$102$		0			0
$103$	−6.56634	−	11.3732i	−0.647001	−	1.12064i	−0.983835	−	0.179075i	$-0.942690\pi$
$103$	−6.56634	−	11.3732i	−0.647001	−	1.12064i	0.336835	−	0.941564i	$-0.390644\pi$
$104$	1.09070	+	4.07054i	0.106952	+	0.399149i
$105$		0			0
$106$	−2.24872	−	1.29830i	−0.218415	−	0.126102i
$107$	−4.64050	+	8.03759i	−0.448614	+	0.777023i	−0.998296	−	0.0583512i	$-0.981416\pi$
$107$	−4.64050	+	8.03759i	−0.448614	+	0.777023i	0.549682	+	0.835374i	$0.314749\pi$
$108$		0			0
$109$	4.90172	+	2.83001i	0.469499	+	0.271066i	0.716030	−	0.698069i	$-0.245957\pi$
$109$	4.90172	+	2.83001i	0.469499	+	0.271066i	−0.246531	+	0.969135i	$0.579291\pi$
$110$	−5.95640	−	10.3168i	−0.567920	−	0.983667i
$111$		0			0
$112$	−1.40654	−	0.376882i	−0.132906	−	0.0356120i
$113$	−19.2563			−1.81148			−0.905738	−	0.423838i	$-0.860682\pi$
$113$	−19.2563			−1.81148			−0.905738	+	0.423838i	$0.860682\pi$
$114$		0			0
$115$	26.2787	−	7.04134i	2.45050	−	0.656609i
$116$	5.85173	−	1.56797i	0.543319	−	0.145582i
$117$		0			0
$118$	6.33210	+	10.9675i	0.582917	+	1.00964i
$119$			3.47274i			0.318346i
$120$		0			0
$121$			2.36875i			0.215341i
$122$	−7.77386	−	0.753091i	−0.703812	−	0.0681816i
$123$		0			0
$124$	0.0233460	+	0.0871284i	0.00209653	+	0.00782436i
$125$	26.1213			2.33636
$126$		0			0
$127$	10.3724	+	5.98850i	0.920401	+	0.531394i	0.883763	−	0.467935i	$-0.155002\pi$
$127$	10.3724	+	5.98850i	0.920401	+	0.531394i	0.0366379	+	0.999329i	$0.488335\pi$
$128$	0.258819	+	0.965926i	0.0228766	+	0.0853766i
$129$		0			0
$130$	−12.0829	−	12.0829i	−1.05974	−	1.05974i
$131$			7.02383i			0.613675i	0.951762	+	0.306837i	$0.0992708\pi$
$131$			7.02383i			0.613675i	−0.951762	+	0.306837i	$0.900729\pi$
$132$		0			0
$133$	3.70833	+	3.70833i	0.321553	+	0.321553i
$134$	−5.12003	+	2.95605i	−0.442303	+	0.255364i
$135$		0			0
$136$	2.06535	−	1.19243i	0.177103	−	0.102250i
$137$	3.03746	+	1.75368i	0.259508	+	0.149827i	0.624110	−	0.781337i	$-0.285462\pi$
$137$	3.03746	+	1.75368i	0.259508	+	0.149827i	−0.364602	+	0.931163i	$0.618795\pi$
$138$		0			0
$139$	−2.52060	+	9.40701i	−0.213795	+	0.797893i	0.772793	+	0.634659i	$0.218859\pi$
$139$	−2.52060	+	9.40701i	−0.213795	+	0.797893i	−0.986587	+	0.163234i	$0.947807\pi$
$140$	5.70335	−	1.52821i	0.482021	−	0.129157i
$141$		0			0
$142$	9.20087			0.772120
$143$	−3.20436	−	11.9588i	−0.267962	−	1.00005i
$144$		0			0
$145$	−17.3701	+	17.3701i	−1.44251	+	1.44251i
$146$	1.22110	+	1.22110i	0.101059	+	0.101059i
$147$		0			0
$148$	2.84117	+	0.761289i	0.233543	+	0.0625776i
$149$	−6.77062			−0.554671			−0.277336	−	0.960773i	$-0.589451\pi$
$149$	−6.77062			−0.554671			−0.277336	+	0.960773i	$0.589451\pi$
$150$		0			0
$151$	−2.27333	+	8.48419i	−0.185001	+	0.690434i	0.809629	+	0.586942i	$0.199668\pi$
$151$	−2.27333	+	8.48419i	−0.185001	+	0.690434i	−0.994630	+	0.103492i	$0.966998\pi$
$152$	0.932138	−	3.47879i	0.0756064	−	0.282167i
$153$		0			0
$154$	4.13228	+	1.10724i	0.332989	+	0.0892240i
$155$	−0.258629	−	0.258629i	−0.0207736	−	0.0207736i
$156$		0			0
$157$	−0.595606	+	2.22283i	−0.0475346	+	0.177401i	−0.985612	−	0.169025i	$-0.945938\pi$
$157$	−0.595606	+	2.22283i	−0.0475346	+	0.177401i	0.938077	+	0.346426i	$0.112605\pi$
$158$	3.24896	+	5.62736i	0.258473	+	0.447689i
$159$		0			0
$160$	−2.86723	−	2.86723i	−0.226674	−	0.226674i
$161$	−4.88496	+	8.46101i	−0.384989	+	0.666821i
$162$		0			0
$163$		−	20.9856i		−	1.64372i	−0.569688	−	0.821861i	$-0.692936\pi$
$163$		−	20.9856i		−	1.64372i	0.569688	−	0.821861i	$-0.307064\pi$
$164$	10.1043	−	5.83369i	0.789009	−	0.455535i
$165$		0			0
$166$	−3.64405	−	0.976420i	−0.282833	−	0.0757849i
$167$	12.7755	−	22.1279i	0.988600	−	1.71230i	0.363904	−	0.931436i	$-0.381444\pi$
$167$	12.7755	−	22.1279i	0.988600	−	1.71230i	0.624696	−	0.780868i	$-0.285223\pi$
$168$		0			0
$169$	−2.37945	−	4.12132i	−0.183034	−	0.317025i
$170$	−4.83516	+	8.37474i	−0.370840	+	0.642313i
$171$		0			0
$172$	3.17781	−	3.17781i	0.242305	−	0.242305i
$173$	2.13766	−	7.97784i	0.162523	−	0.606544i	−0.835820	−	0.549003i	$-0.815007\pi$
$173$	2.13766	−	7.97784i	0.162523	−	0.606544i	0.998343	−	0.0575406i	$-0.0183259\pi$
$174$		0			0
$175$	−11.7813	+	11.7813i	−0.890586	+	0.890586i
$176$	−0.760384	−	2.83779i	−0.0573161	−	0.213907i
$177$		0			0
$178$	−9.41068	+	16.2998i	−0.705360	+	1.22172i
$179$	−5.17639	+	2.98859i	−0.386902	+	0.223378i	−0.680817	−	0.732454i	$-0.738375\pi$
$179$	−5.17639	+	2.98859i	−0.386902	+	0.223378i	0.293915	+	0.955831i	$0.405042\pi$
$180$		0			0
$181$	16.4850	−	4.41713i	1.22532	−	0.328323i	0.412563	−	0.910929i	$-0.364634\pi$
$181$	16.4850	−	4.41713i	1.22532	−	0.328323i	0.812755	+	0.582606i	$0.197967\pi$
$182$	6.13645			0.454864
$183$		0			0
$184$	6.70938			0.494622
$185$	−11.5206	+	3.08693i	−0.847009	+	0.226955i
$186$		0			0
$187$	−6.06780	+	3.50325i	−0.443721	+	0.256183i
$188$	−1.26645	+	2.19356i	−0.0923654	+	0.159982i
$189$		0			0
$190$	3.77970	+	14.1060i	0.274208	+	1.02336i
$191$	5.40828	−	5.40828i	0.391329	−	0.391329i	−0.483832	−	0.875161i	$-0.660755\pi$
$191$	5.40828	−	5.40828i	0.391329	−	0.391329i	0.875161	+	0.483832i	$0.160755\pi$
$192$		0			0
$193$	0.666012	−	2.48559i	0.0479406	−	0.178917i	−0.937804	−	0.347165i	$-0.887144\pi$
$193$	0.666012	−	2.48559i	0.0479406	−	0.178917i	0.985745	+	0.168248i	$0.0538110\pi$
$194$	−7.49791	+	7.49791i	−0.538319	+	0.538319i
$195$		0			0
$196$	2.43980	−	4.22586i	0.174271	−	0.301847i
$197$	−10.0898	−	17.4761i	−0.718869	−	1.24512i	−0.961448	−	0.274986i	$-0.911327\pi$
$197$	−10.0898	−	17.4761i	−0.718869	−	1.24512i	0.242580	−	0.970131i	$-0.422006\pi$
$198$		0			0
$199$	−10.9158	+	18.9067i	−0.773800	+	1.34026i	0.161666	+	0.986845i	$0.448313\pi$
$199$	−10.9158	+	18.9067i	−0.773800	+	1.34026i	−0.935466	+	0.353416i	$0.885020\pi$
$200$	11.0521	+	2.96140i	0.781501	+	0.209403i
$201$		0			0
$202$	0.0317715	−	0.0183433i	0.00223544	−	0.00129063i
$203$		−	8.82164i		−	0.619158i
$204$		0			0
$205$	−23.6549	+	40.9714i	−1.65213	+	2.86157i
$206$	9.28621	+	9.28621i	0.647001	+	0.647001i
$207$		0			0
$208$	−2.10707	−	3.64954i	−0.146099	−	0.253050i
$209$	−2.73853	+	10.2203i	−0.189428	+	0.706955i
$210$		0			0
$211$	−7.93187	−	7.93187i	−0.546053	−	0.546053i	0.379244	−	0.925297i	$-0.376184\pi$
$211$	−7.93187	−	7.93187i	−0.546053	−	0.546053i	−0.925297	+	0.379244i	$0.876184\pi$
$212$	2.50812	+	0.672048i	0.172258	+	0.0461564i
$213$		0			0
$214$	2.40210	−	8.96477i	0.164204	−	0.612819i
$215$	−4.71645	+	17.6020i	−0.321659	+	1.20045i
$216$		0			0
$217$	0.131348			0.00891651
$218$	−5.46715	−	1.46492i	−0.370282	−	0.0992169i
$219$		0			0
$220$	8.42362	+	8.42362i	0.567920	+	0.567920i
$221$	−7.10652	+	7.10652i	−0.478036	+	0.478036i
$222$		0			0
$223$	5.53766	+	20.6668i	0.370829	+	1.38395i	0.859344	+	0.511398i	$0.170872\pi$
$223$	5.53766	+	20.6668i	0.370829	+	1.38395i	−0.488515	+	0.872556i	$0.662461\pi$
$224$	1.45616			0.0972938
$225$		0			0
$226$	18.6001	−	4.98388i	1.23726	−	0.331523i
$227$	6.47784	−	24.1756i	0.429949	−	1.60459i	−0.322922	−	0.946426i	$-0.604665\pi$
$227$	6.47784	−	24.1756i	0.429949	−	1.60459i	0.752871	−	0.658168i	$-0.228668\pi$
$228$		0			0
$229$	−13.2013	−	7.62177i	−0.872367	−	0.503661i	−0.00423259	−	0.999991i	$-0.501347\pi$
$229$	−13.2013	−	7.62177i	−0.872367	−	0.503661i	−0.868134	+	0.496330i	$0.834681\pi$
$230$	−23.5608	+	13.6028i	−1.55355	+	0.896944i
$231$		0			0
$232$	−5.24652	+	3.02908i	−0.344451	+	0.198869i
$233$	−6.96525	−	6.96525i	−0.456309	−	0.456309i	0.441133	−	0.897442i	$-0.354577\pi$
$233$	−6.96525	−	6.96525i	−0.456309	−	0.456309i	−0.897442	+	0.441133i	$0.854577\pi$
$234$		0			0
$235$		−	10.2706i		−	0.669979i
$236$	−8.95495	−	8.95495i	−0.582917	−	0.582917i
$237$		0			0
$238$	−0.898812	−	3.35441i	−0.0582613	−	0.217434i
$239$	−9.46772	−	5.46619i	−0.612416	−	0.353579i	0.161494	−	0.986874i	$-0.448369\pi$
$239$	−9.46772	−	5.46619i	−0.612416	−	0.353579i	−0.773910	+	0.633295i	$0.781702\pi$
$240$		0			0
$241$	−6.02409			−0.388046			−0.194023	−	0.980997i	$-0.562154\pi$
$241$	−6.02409			−0.388046			−0.194023	+	0.980997i	$0.562154\pi$
$242$	−0.613078	−	2.28804i	−0.0394101	−	0.147081i
$243$		0			0
$244$	7.70388	−	1.28459i	0.493191	−	0.0822376i
$245$			19.7861i			1.26409i
$246$		0			0
$247$			15.1772i			0.965703i
$248$	−0.0451010	−	0.0781172i	−0.00286391	−	0.00496045i
$249$		0			0
$250$	−25.2313	+	6.76070i	−1.59577	+	0.427584i
$251$	29.6004	−	7.93140i	1.86836	−	0.500625i	0.868371	−	0.495916i	$-0.165168\pi$
$251$	29.6004	−	7.93140i	1.86836	−	0.500625i	0.999989	−	0.00470968i	$-0.00149914\pi$
$252$		0			0
$253$	−19.7115			−1.23925
$254$	−11.5689	−	3.09988i	−0.725897	−	0.194504i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	11.7010	+	6.75560i	0.729891	+	0.421403i	0.818382	−	0.574674i	$-0.194871\pi$
$257$	11.7010	+	6.75560i	0.729891	+	0.421403i	−0.0884912	+	0.996077i	$0.528205\pi$
$258$		0			0
$259$	2.14157	−	3.70931i	0.133071	−	0.230485i
$260$	14.7984	+	8.54388i	0.917759	+	0.529869i
$261$		0			0
$262$	−1.81790	−	6.78450i	−0.112310	−	0.419148i
$263$	0.841342	+	1.45725i	0.0518794	+	0.0898577i	0.890799	−	0.454398i	$-0.150146\pi$
$263$	0.841342	+	1.45725i	0.0518794	+	0.0898577i	−0.838920	+	0.544256i	$0.816812\pi$
$264$		0			0
$265$	−10.1701	+	2.72507i	−0.624744	+	0.167400i
$266$	−4.54175	−	2.62218i	−0.278473	−	0.160776i
$267$		0			0
$268$	4.18049	−	4.18049i	0.255364	−	0.255364i
$269$	−8.02914	+	4.63562i	−0.489545	+	0.282639i	−0.724386	−	0.689395i	$-0.757877\pi$
$269$	−8.02914	+	4.63562i	−0.489545	+	0.282639i	0.234841	+	0.972034i	$0.424543\pi$
$270$		0			0
$271$		−	1.35553i		−	0.0823425i	−0.999152	−	0.0411713i	$-0.986891\pi$
$271$		−	1.35553i		−	0.0823425i	0.999152	−	0.0411713i	$-0.0131089\pi$
$272$	−1.68635	+	1.68635i	−0.102250	+	0.102250i
$273$		0			0
$274$	−3.38785	−	0.907770i	−0.204667	−	0.0548404i
$275$	−32.4699	−	8.70029i	−1.95801	−	0.524647i
$276$		0			0
$277$	−14.9286	+	14.9286i	−0.896975	+	0.896975i	−0.995167	−	0.0981923i	$-0.968694\pi$
$277$	−14.9286	+	14.9286i	−0.896975	+	0.896975i	0.0981923	+	0.995167i	$0.468694\pi$
$278$		−	9.73886i		−	0.584098i
$279$		0			0
$280$	−5.11348	+	2.95227i	−0.305589	+	0.176432i
$281$	6.82186	−	6.82186i	0.406958	−	0.406958i	−0.473718	−	0.880676i	$-0.657089\pi$
$281$	6.82186	−	6.82186i	0.406958	−	0.406958i	0.880676	+	0.473718i	$0.157089\pi$
$282$		0			0
$283$	1.52318	+	0.879409i	0.0905437	+	0.0522755i	0.544588	−	0.838704i	$-0.316686\pi$
$283$	1.52318	+	0.879409i	0.0905437	+	0.0522755i	−0.454044	+	0.890979i	$0.650019\pi$
$284$	−8.88735	+	2.38136i	−0.527367	+	0.141308i
$285$		0			0
$286$	6.19034	+	10.7220i	0.366043	+	0.634005i
$287$	−4.39723	−	16.4107i	−0.259560	−	0.968691i
$288$		0			0
$289$	−9.79684	−	5.65621i	−0.576285	−	0.332718i
$290$	12.2825	−	21.2739i	0.721254	−	1.24925i
$291$		0			0
$292$	−1.49554	−	0.863448i	−0.0875196	−	0.0505295i
$293$	−9.61178	−	16.6481i	−0.561526	−	0.972592i	−0.997364	−	0.0725664i	$-0.976881\pi$
$293$	−9.61178	−	16.6481i	−0.561526	−	0.972592i	0.435837	−	0.900025i	$-0.356452\pi$
$294$		0			0
$295$	49.6020	+	13.2908i	2.88794	+	0.773820i
$296$	−2.94140			−0.170965
$297$		0			0
$298$	6.53992	−	1.75237i	0.378847	−	0.101512i
$299$	−27.3108	+	7.31790i	−1.57942	+	0.423205i
$300$		0			0
$301$	−3.27206	−	5.66738i	−0.188598	−	0.326662i
$302$		−	8.78348i		−	0.505433i
$303$		0			0
$304$			3.60151i			0.206560i
$305$	−24.4487	+	20.1301i	−1.39993	+	1.15265i
$306$		0			0
$307$	−8.38942	−	31.3097i	−0.478810	−	1.78694i	−0.606451	−	0.795121i	$-0.707407\pi$
$307$	−8.38942	−	31.3097i	−0.478810	−	1.78694i	0.127641	−	0.991820i	$-0.459259\pi$
$308$	−4.27805			−0.243765
$309$		0			0
$310$	0.316755	+	0.182879i	0.0179905	+	0.0103868i
$311$	6.73167	+	25.1229i	0.381718	+	1.42459i	0.843276	+	0.537481i	$0.180624\pi$
$311$	6.73167	+	25.1229i	0.381718	+	1.42459i	−0.461558	+	0.887110i	$0.652709\pi$
$312$		0			0
$313$	13.3053	+	13.3053i	0.752062	+	0.752062i	0.974864	−	0.222802i	$-0.0715203\pi$
$313$	13.3053	+	13.3053i	0.752062	+	0.752062i	−0.222802	+	0.974864i	$0.571520\pi$
$314$		−	2.30125i		−	0.129867i
$315$		0			0
$316$	−4.59472	−	4.59472i	−0.258473	−	0.258473i
$317$	−17.7292	+	10.2360i	−0.995771	+	0.574909i	−0.906994	−	0.421143i	$-0.861629\pi$
$317$	−17.7292	+	10.2360i	−0.995771	+	0.574909i	−0.0887767	+	0.996052i	$0.528296\pi$
$318$		0			0
$319$	15.4137	−	8.89912i	0.863004	−	0.498255i
$320$	3.51162	+	2.02743i	0.196306	+	0.113337i
$321$		0			0
$322$	2.52864	−	9.43703i	0.140916	−	0.525905i
$323$	8.29644	−	2.22302i	0.461626	−	0.123692i
$324$		0			0
$325$	−48.2180			−2.67465
$326$	5.43148	+	20.2706i	0.300822	+	1.12268i
$327$		0			0
$328$	−8.25009	+	8.25009i	−0.455535	+	0.455535i
$329$	2.60803	+	2.60803i	0.143785	+	0.143785i
$330$		0			0
$331$	−3.53702	−	0.947742i	−0.194412	−	0.0520926i	0.160299	−	0.987068i	$-0.448754\pi$
$331$	−3.53702	−	0.947742i	−0.194412	−	0.0520926i	−0.354711	+	0.934976i	$0.615421\pi$
$332$	3.77260			0.207048
$333$		0			0
$334$	−6.61310	+	24.6804i	−0.361853	+	1.35045i
$335$	−6.20462	+	23.1560i	−0.338995	+	1.26515i
$336$		0			0
$337$	−11.7792	−	3.15622i	−0.641652	−	0.171930i	−0.0767005	−	0.997054i	$-0.524439\pi$
$337$	−11.7792	−	3.15622i	−0.641652	−	0.171930i	−0.564952	+	0.825124i	$0.691105\pi$
$338$	3.36505	+	3.36505i	0.183034	+	0.183034i
$339$		0			0
$340$	2.50286	−	9.34081i	0.135737	−	0.506576i
$341$	0.132502	+	0.229500i	0.00717539	+	0.0124281i
$342$		0			0
$343$	−12.2320	−	12.2320i	−0.660463	−	0.660463i
$344$	−2.24705	+	3.89200i	−0.121153	+	0.209843i
$345$		0			0
$346$			8.25927i			0.444021i
$347$	−17.1260	+	9.88768i	−0.919370	+	0.530799i	−0.883434	−	0.468556i	$-0.844775\pi$
$347$	−17.1260	+	9.88768i	−0.919370	+	0.530799i	−0.0359360	+	0.999354i	$0.511441\pi$
$348$		0			0
$349$	4.74826	+	1.27229i	0.254169	+	0.0681043i	0.383654	−	0.923477i	$-0.374666\pi$
$349$	4.74826	+	1.27229i	0.254169	+	0.0681043i	−0.129485	+	0.991581i	$0.541332\pi$
$350$	8.33067	−	14.4291i	0.445293	−	0.771270i
$351$		0			0
$352$	1.46895	+	2.54429i	0.0782953	+	0.135611i
$353$	−7.64329	+	13.2386i	−0.406811	+	0.704618i	−0.994530	−	0.104447i	$-0.966693\pi$
$353$	−7.64329	+	13.2386i	−0.406811	+	0.704618i	0.587719	+	0.809065i	$0.300026\pi$
$354$		0			0
$355$	26.3810	−	26.3810i	1.40016	−	1.40016i
$356$	4.87132	−	18.1800i	0.258180	−	0.963540i
$357$		0			0
$358$	4.22650	−	4.22650i	0.223378	−	0.223378i
$359$	−0.656984	−	2.45190i	−0.0346743	−	0.129406i	0.946419	−	0.322941i	$-0.104671\pi$
$359$	−0.656984	−	2.45190i	−0.0346743	−	0.129406i	−0.981093	+	0.193535i	$0.938005\pi$
$360$		0			0
$361$	−3.01458	+	5.22141i	−0.158662	+	0.274811i
$362$	−14.7800	+	8.53325i	−0.776820	+	0.448497i
$363$		0			0
$364$	−5.92735	+	1.58823i	−0.310678	+	0.0832458i
$365$	7.00234			0.366519
$366$		0			0
$367$	−4.36643			−0.227926			−0.113963	−	0.993485i	$-0.536355\pi$
$367$	−4.36643			−0.227926			−0.113963	+	0.993485i	$0.536355\pi$
$368$	−6.48076	+	1.73652i	−0.337833	+	0.0905221i
$369$		0			0
$370$	10.3291	−	5.96349i	0.536982	−	0.310027i
$371$	1.89053	−	3.27449i	0.0981513	−	0.170003i
$372$		0			0
$373$	−7.47703	−	27.9047i	−0.387146	−	1.44485i	−0.834756	−	0.550620i	$-0.814391\pi$
$373$	−7.47703	−	27.9047i	−0.387146	−	1.44485i	0.447610	−	0.894229i	$-0.352275\pi$
$374$	4.95434	−	4.95434i	0.256183	−	0.256183i
$375$		0			0
$376$	0.655563	−	2.44660i	0.0338081	−	0.126174i
$377$	18.0523	−	18.0523i	0.929743	−	0.929743i
$378$		0			0
$379$	8.21964	−	14.2368i	0.422215	−	0.731297i	−0.573941	−	0.818897i	$-0.694586\pi$
$379$	8.21964	−	14.2368i	0.422215	−	0.731297i	0.996156	+	0.0875993i	$0.0279195\pi$
$380$	−7.30182	−	12.6471i	−0.374575	−	0.648784i
$381$		0			0
$382$	−3.82423	+	6.62376i	−0.195665	+	0.338901i
$383$	−34.3361	−	9.20032i	−1.75449	−	0.470115i	−0.768916	−	0.639350i	$-0.779203\pi$
$383$	−34.3361	−	9.20032i	−1.75449	−	0.470115i	−0.985576	+	0.169236i	$0.945870\pi$
$384$		0			0
$385$	15.0229	−	8.67347i	0.765637	−	0.442041i
$386$			2.57327i			0.130976i
$387$		0			0
$388$	5.30182	−	9.18303i	0.269159	−	0.466198i
$389$	18.7205	+	18.7205i	0.949169	+	0.949169i	0.998769	−	0.0496000i	$-0.0157946\pi$
$389$	18.7205	+	18.7205i	0.949169	+	0.949169i	−0.0496000	+	0.998769i	$0.515795\pi$
$390$		0			0
$391$	8.00048	+	13.8572i	0.404602	+	0.700791i
$392$	−1.26293	+	4.71333i	−0.0637878	+	0.238059i
$393$		0			0
$394$	14.2691	+	14.2691i	0.718869	+	0.718869i
$395$	25.4504	+	6.81941i	1.28055	+	0.343122i
$396$		0			0
$397$	2.70784	−	10.1058i	0.135903	−	0.507195i	−0.864090	−	0.503337i	$-0.832105\pi$
$397$	2.70784	−	10.1058i	0.135903	−	0.507195i	0.999993	−	0.00385797i	$-0.00122803\pi$
$398$	5.65043	−	21.0877i	0.283230	−	1.05703i
$399$		0			0
$400$	−11.4420			−0.572098
$401$	−10.0363	−	2.68921i	−0.501187	−	0.134293i	−0.000636069	−	1.00000i	$-0.500202\pi$
$401$	−10.0363	−	2.68921i	−0.501187	−	0.134293i	−0.500551	+	0.865707i	$0.666869\pi$
$402$		0			0
$403$	0.268787	+	0.268787i	0.0133893	+	0.0133893i
$404$	−0.0259413	+	0.0259413i	−0.00129063	+	0.00129063i
$405$		0			0
$406$	2.28321	+	8.52105i	0.113314	+	0.422893i
$407$	8.64152			0.428344
$408$		0			0
$409$	11.4777	−	3.07544i	0.567535	−	0.152071i	0.0363693	−	0.999338i	$-0.488421\pi$
$409$	11.4777	−	3.07544i	0.567535	−	0.152071i	0.531166	+	0.847268i	$0.321754\pi$
$410$	12.2447	−	45.6977i	0.604720	−	2.25685i
$411$		0			0
$412$	−11.3732	−	6.56634i	−0.560319	−	0.323500i
$413$	−15.9705	+	9.22056i	−0.785855	+	0.453714i
$414$		0			0
$415$	−13.2479	+	7.64869i	−0.650315	+	0.375460i
$416$	2.97984	+	2.97984i	0.146099	+	0.146099i
$417$		0			0
$418$		−	10.5809i		−	0.517527i
$419$	−12.5133	−	12.5133i	−0.611317	−	0.611317i	0.331972	−	0.943289i	$-0.392286\pi$
$419$	−12.5133	−	12.5133i	−0.611317	−	0.611317i	−0.943289	+	0.331972i	$0.892286\pi$
$420$		0			0
$421$	−1.35888	−	5.07140i	−0.0662277	−	0.247165i	0.924874	−	0.380274i	$-0.124170\pi$
$421$	−1.35888	−	5.07140i	−0.0662277	−	0.247165i	−0.991101	+	0.133109i	$0.957504\pi$
$422$	9.71452	+	5.60868i	0.472895	+	0.273026i
$423$		0			0
$424$	−2.59659			−0.126102
$425$	7.06254	+	26.3578i	0.342583	+	1.27854i
$426$		0			0
$427$	1.09662	−	11.3200i	0.0530692	−	0.547812i
$428$			9.28101i			0.448614i
$429$		0			0
$430$		−	18.2230i		−	0.878790i
$431$	15.2099	+	26.3443i	0.732636	+	1.26896i	0.955753	+	0.294171i	$0.0950434\pi$
$431$	15.2099	+	26.3443i	0.732636	+	1.26896i	−0.223117	+	0.974792i	$0.571623\pi$
$432$		0			0
$433$	5.62304	−	1.50669i	0.270226	−	0.0724069i	−0.121161	−	0.992633i	$-0.538662\pi$
$433$	5.62304	−	1.50669i	0.270226	−	0.0724069i	0.391388	+	0.920226i	$0.371995\pi$
$434$	−0.126873	+	0.0339955i	−0.00609009	+	0.00163184i
$435$		0			0
$436$	5.66001			0.271066
$437$	23.3405	+	6.25407i	1.11653	+	0.299173i
$438$		0			0
$439$	−0.406454	−	0.703998i	−0.0193990	−	0.0336000i	0.856163	−	0.516706i	$-0.172842\pi$
$439$	−0.406454	−	0.703998i	−0.0193990	−	0.0336000i	−0.875562	+	0.483106i	$0.839509\pi$
$440$	−10.3168	−	5.95640i	−0.491833	−	0.283960i
$441$		0			0
$442$	5.02507	−	8.70367i	0.239018	−	0.413991i
$443$	−7.27672	−	4.20122i	−0.345727	−	0.199606i	0.317074	−	0.948401i	$-0.397299\pi$
$443$	−7.27672	−	4.20122i	−0.345727	−	0.199606i	−0.662802	+	0.748795i	$0.730633\pi$
$444$		0			0
$445$	19.7526	+	73.7177i	0.936362	+	3.49455i
$446$	−10.6979	−	18.5294i	−0.506562	−	0.877391i
$447$		0			0
$448$	−1.40654	+	0.376882i	−0.0664529	+	0.0178060i
$449$	17.6619	+	10.1971i	0.833515	+	0.481230i	0.855055	−	0.518538i	$-0.173524\pi$
$449$	17.6619	+	10.1971i	0.833515	+	0.481230i	−0.0215399	+	0.999768i	$0.506857\pi$
$450$		0			0
$451$	24.2379	−	24.2379i	1.14132	−	1.14132i
$452$	−16.6764	+	9.62813i	−0.784392	+	0.452869i
$453$		0			0
$454$			25.0285i			1.17464i
$455$	17.5946	−	17.5946i	0.824847	−	0.824847i
$456$		0			0
$457$	−26.0019	−	6.96720i	−1.21632	−	0.325912i	−0.407081	−	0.913392i	$-0.633453\pi$
$457$	−26.0019	−	6.96720i	−1.21632	−	0.325912i	−0.809238	+	0.587480i	$0.800120\pi$
$458$	14.7241	+	3.94532i	0.688014	+	0.184353i
$459$		0			0
$460$	19.2373	−	19.2373i	0.896944	−	0.896944i
$461$		−	3.24549i		−	0.151158i	−0.997140	−	0.0755789i	$-0.975920\pi$
$461$		−	3.24549i		−	0.151158i	0.997140	−	0.0755789i	$-0.0240805\pi$
$462$		0			0
$463$	−27.4759	+	15.8632i	−1.27691	+	0.737225i	−0.976279	−	0.216515i	$-0.930531\pi$
$463$	−27.4759	+	15.8632i	−1.27691	+	0.737225i	−0.300632	+	0.953740i	$0.597198\pi$
$464$	4.28376	−	4.28376i	0.198869	−	0.198869i
$465$		0			0
$466$	8.53066	+	4.92518i	0.395175	+	0.228154i
$467$	36.5510	−	9.79382i	1.69138	−	0.453204i	0.720634	−	0.693315i	$-0.243851\pi$
$467$	36.5510	−	9.79382i	1.69138	−	0.453204i	0.970745	+	0.240112i	$0.0771841\pi$
$468$		0			0
$469$	−4.30448	−	7.45558i	−0.198763	−	0.344267i
$470$	2.65822	+	9.92063i	0.122615	+	0.457604i
$471$		0			0
$472$	10.9675	+	6.33210i	0.504821	+	0.291459i
$473$	6.60160	−	11.4343i	0.303542	−	0.525750i
$474$		0			0
$475$	35.6874	+	20.6042i	1.63745	+	0.945384i
$476$	1.73637	+	3.00748i	0.0795865	+	0.137848i
$477$		0			0
$478$	10.5599	+	2.82951i	0.482997	+	0.129419i
$479$	26.2102			1.19757			0.598786	−	0.800909i	$-0.295650\pi$
$479$	26.2102			1.19757			0.598786	+	0.800909i	$0.295650\pi$
$480$		0			0
$481$	11.9731	−	3.20817i	0.545924	−	0.146280i
$482$	5.81882	−	1.55915i	0.265040	−	0.0710173i
$483$		0			0
$484$	1.18438	+	2.05140i	0.0538353	+	0.0932454i
$485$			42.9964i			1.95237i
$486$		0			0
$487$			36.9998i			1.67662i	0.545194	+	0.838310i	$0.316456\pi$
$487$			36.9998i			1.67662i	−0.545194	+	0.838310i	$0.683544\pi$
$488$	−7.10890	+	3.23473i	−0.321805	+	0.146429i
$489$		0			0
$490$	−5.12103	−	19.1119i	−0.231345	−	0.863390i
$491$	−4.05628			−0.183058			−0.0915288	−	0.995802i	$-0.529175\pi$
$491$	−4.05628			−0.183058			−0.0915288	+	0.995802i	$0.529175\pi$
$492$		0			0
$493$	−12.5122	−	7.22394i	−0.563523	−	0.325350i
$494$	−3.92815	−	14.6601i	−0.176736	−	0.659587i
$495$		0			0
$496$	0.0637824	+	0.0637824i	0.00286391	+	0.00286391i
$497$			13.3979i			0.600979i
$498$		0			0
$499$	17.5333	+	17.5333i	0.784900	+	0.784900i	0.980653	−	0.195753i	$-0.0627150\pi$
$499$	17.5333	+	17.5333i	0.784900	+	0.784900i	−0.195753	+	0.980653i	$0.562715\pi$
$500$	22.6218	−	13.0607i	1.01168	−	0.584091i
$501$		0			0
$502$	−26.5390	+	15.3223i	−1.18449	+	0.683867i
$503$	34.5581	+	19.9521i	1.54087	+	0.889621i	0.998784	+	0.0492975i	$0.0156983\pi$
$503$	34.5581	+	19.9521i	1.54087	+	0.889621i	0.542085	+	0.840324i	$0.317635\pi$
$504$		0			0
$505$	0.0385018	−	0.143691i	0.00171331	−	0.00639414i
$506$	19.0398	−	5.10171i	0.846424	−	0.226798i
$507$		0			0
$508$	11.9770			0.531394
$509$	8.54412	+	31.8871i	0.378711	+	1.41337i	0.847845	+	0.530243i	$0.177899\pi$
$509$	8.54412	+	31.8871i	0.378711	+	1.41337i	−0.469134	+	0.883127i	$0.655434\pi$
$510$		0			0
$511$	−1.77812	+	1.77812i	−0.0786592	+	0.0786592i
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$		0			0
$514$	−13.0508	−	3.49696i	−0.575647	−	0.154244i
$515$	53.2513			2.34653
$516$		0			0
$517$	−1.92598	+	7.18785i	−0.0847045	+	0.316121i
$518$	−1.10856	+	4.13720i	−0.0487073	+	0.181778i
$519$		0			0
$520$	−16.5055	−	4.42264i	−0.723814	−	0.193945i
$521$	−24.5923	−	24.5923i	−1.07741	−	1.07741i	−0.996741	−	0.0806652i	$-0.974296\pi$
$521$	−24.5923	−	24.5923i	−1.07741	−	1.07741i	−0.0806652	−	0.996741i	$-0.525704\pi$
$522$		0			0
$523$	10.1873	−	38.0195i	0.445459	−	1.66248i	−0.269262	−	0.963067i	$-0.586780\pi$
$523$	10.1873	−	38.0195i	0.445459	−	1.66248i	0.714721	−	0.699410i	$-0.246554\pi$
$524$	3.51191	+	6.08281i	0.153419	+	0.265729i
$525$		0			0
$526$	−1.18984	−	1.18984i	−0.0518794	−	0.0518794i
$527$	0.107560	−	0.186299i	0.00468538	−	0.00811531i
$528$		0			0
$529$			22.0158i			0.957208i
$530$	9.11825	−	5.26443i	0.396072	−	0.228672i
$531$		0			0
$532$	5.06567	+	1.35734i	0.219625	+	0.0588482i
$533$	24.5839	−	42.5806i	1.06485	−	1.84437i
$534$		0			0
$535$	−18.8166	−	32.5914i	−0.813514	−	1.40905i
$536$	−2.95605	+	5.12003i	−0.127682	+	0.221152i
$537$		0			0
$538$	6.55576	−	6.55576i	0.282639	−	0.282639i
$539$	3.71037	−	13.8473i	0.159817	−	0.596445i
$540$		0			0
$541$	1.23366	−	1.23366i	0.0530392	−	0.0530392i	−0.680090	−	0.733129i	$-0.738059\pi$
$541$	1.23366	−	1.23366i	0.0530392	−	0.0530392i	0.733129	+	0.680090i	$0.238059\pi$
$542$	0.350837	+	1.30934i	0.0150697	+	0.0562410i
$543$		0			0
$544$	1.19243	−	2.06535i	0.0511251	−	0.0885513i
$545$	−19.8758	+	11.4753i	−0.851387	+	0.491548i
$546$		0			0
$547$	−6.01803	+	1.61253i	−0.257312	+	0.0689467i	−0.385169	−	0.922846i	$-0.625857\pi$
$547$	−6.01803	+	1.61253i	−0.257312	+	0.0689467i	0.127857	+	0.991793i	$0.459190\pi$
$548$	3.50736			0.149827
$549$		0			0
$550$	33.6153			1.43336
$551$	−21.0750	+	5.64704i	−0.897827	+	0.240572i
$552$		0			0
$553$	−8.19433	+	4.73100i	−0.348458	+	0.201183i
$554$	10.5561	−	18.2838i	0.448488	−	0.776803i
$555$		0			0
$556$	2.52060	+	9.40701i	0.106897	+	0.398946i
$557$	20.5085	−	20.5085i	0.868975	−	0.868975i	−0.123384	−	0.992359i	$-0.539375\pi$
$557$	20.5085	−	20.5085i	0.868975	−	0.868975i	0.992359	+	0.123384i	$0.0393747\pi$
$558$		0			0
$559$	4.90170	−	18.2934i	0.207320	−	0.773728i
$560$	4.17514	−	4.17514i	0.176432	−	0.176432i
$561$		0			0
$562$	−4.82378	+	8.35503i	−0.203479	+	0.352436i
$563$	−18.6794	−	32.3536i	−0.787241	−	1.36354i	−0.927651	−	0.373448i	$-0.878176\pi$
$563$	−18.6794	−	32.3536i	−0.787241	−	1.36354i	0.140411	−	0.990093i	$-0.455158\pi$
$564$		0			0
$565$	39.0408	−	67.6206i	1.64246	−	2.84482i
$566$	−1.69889	−	0.455216i	−0.0714096	−	0.0191341i
$567$		0			0
$568$	7.96818	−	4.60043i	0.334338	−	0.193030i
$569$		−	29.8188i		−	1.25007i	−0.780597	−	0.625034i	$-0.785085\pi$
$569$		−	29.8188i		−	1.25007i	0.780597	−	0.625034i	$-0.214915\pi$
$570$		0			0
$571$	19.6377	−	34.0135i	0.821812	−	1.42342i	−0.0825193	−	0.996589i	$-0.526297\pi$
$571$	19.6377	−	34.0135i	0.821812	−	1.42342i	0.904331	−	0.426831i	$-0.140370\pi$
$572$	−8.75447	−	8.75447i	−0.366043	−	0.366043i
$573$		0			0
$574$	8.49479	+	14.7134i	0.354566	+	0.614126i
$575$	−19.8692	+	74.1527i	−0.828601	+	3.09238i
$576$		0			0
$577$	2.30399	+	2.30399i	0.0959162	+	0.0959162i	0.753437	−	0.657520i	$-0.228395\pi$
$577$	2.30399	+	2.30399i	0.0959162	+	0.0959162i	−0.657520	+	0.753437i	$0.728395\pi$
$578$	10.9270	+	2.92787i	0.454502	+	0.121783i
$579$		0			0
$580$	−6.35790	+	23.7280i	−0.263997	+	0.985252i
$581$	1.42182	−	5.30632i	0.0589872	−	0.220143i
$582$		0			0
$583$	7.62853			0.315941
$584$	1.66805	+	0.446954i	0.0690245	+	0.0184951i
$585$		0			0
$586$	13.5931	+	13.5931i	0.561526	+	0.561526i
$587$	11.8986	−	11.8986i	0.491108	−	0.491108i	−0.417547	−	0.908655i	$-0.637110\pi$
$587$	11.8986	−	11.8986i	0.491108	−	0.491108i	0.908655	+	0.417547i	$0.137110\pi$
$588$		0			0
$589$	−0.0840807	−	0.313793i	−0.00346448	−	0.0129296i
$590$	−51.3517			−2.11412
$591$		0			0
$592$	2.84117	−	0.761289i	0.116771	−	0.0312888i
$593$	−9.24291	+	34.4950i	−0.379561	+	1.41654i	0.467004	+	0.884255i	$0.345333\pi$
$593$	−9.24291	+	34.4950i	−0.379561	+	1.41654i	−0.846565	+	0.532285i	$0.821333\pi$
$594$		0			0
$595$	−12.1950	−	7.04076i	−0.499945	−	0.288643i
$596$	−5.86353	+	3.38531i	−0.240180	+	0.138668i
$597$		0			0
$598$	24.4862	−	14.1371i	1.00131	−	0.578109i
$599$	−24.7246	−	24.7246i	−1.01022	−	1.01022i	−0.999947	−	0.0102730i	$-0.996730\pi$
$599$	−24.7246	−	24.7246i	−1.01022	−	1.01022i	−0.0102730	−	0.999947i	$-0.503270\pi$
$600$		0			0
$601$			1.47465i			0.0601521i	0.999548	+	0.0300760i	$0.00957494\pi$
$601$			1.47465i			0.0601521i	−0.999548	+	0.0300760i	$0.990425\pi$
$602$	4.62739	+	4.62739i	0.188598	+	0.188598i
$603$		0			0
$604$	2.27333	+	8.48419i	0.0925006	+	0.345217i
$605$	−8.31815	−	4.80249i	−0.338181	−	0.195249i
$606$		0			0
$607$	−30.6155			−1.24264			−0.621322	−	0.783555i	$-0.713404\pi$
$607$	−30.6155			−1.24264			−0.621322	+	0.783555i	$0.713404\pi$
$608$	−0.932138	−	3.47879i	−0.0378032	−	0.141083i
$609$		0			0
$610$	18.4056	−	25.7720i	0.745219	−	1.04348i
$611$			10.6740i			0.431823i
$612$		0			0
$613$			4.74081i			0.191479i	0.995406	+	0.0957397i	$0.0305216\pi$
$613$			4.74081i			0.191479i	−0.995406	+	0.0957397i	$0.969478\pi$
$614$	16.2071	+	28.0716i	0.654066	+	1.13288i
$615$		0			0
$616$	4.13228	−	1.10724i	0.166494	−	0.0446120i
$617$	13.6727	−	3.66358i	0.550440	−	0.147490i	0.0271296	−	0.999632i	$-0.491363\pi$
$617$	13.6727	−	3.66358i	0.550440	−	0.147490i	0.523311	+	0.852142i	$0.324697\pi$
$618$		0			0
$619$	−33.6609			−1.35294			−0.676472	−	0.736468i	$-0.736492\pi$
$619$	−33.6609			−1.35294			−0.676472	+	0.736468i	$0.736492\pi$
$620$	−0.353294	−	0.0946649i	−0.0141886	−	0.00380183i
$621$		0			0
$622$	−13.0046	−	22.5246i	−0.521436	−	0.903154i
$623$	−23.7351	−	13.7034i	−0.950925	−	0.549017i
$624$		0			0
$625$	−24.3544	+	42.1831i	−0.974177	+	1.68732i
$626$	−16.2956	−	9.40829i	−0.651305	−	0.376031i
$627$		0			0
$628$	0.595606	+	2.22283i	0.0237673	+	0.0887007i
$629$	−3.50741	−	6.07502i	−0.139850	−	0.242227i
$630$		0			0
$631$	36.1853	−	9.69583i	1.44051	−	0.385985i	0.547801	−	0.836609i	$-0.315465\pi$
$631$	36.1853	−	9.69583i	1.44051	−	0.385985i	0.892714	+	0.450624i	$0.148798\pi$
$632$	5.62736	+	3.24896i	0.223844	+	0.129237i
$633$		0			0
$634$	14.4758	−	14.4758i	0.574909	−	0.574909i
$635$	−42.0587	+	24.2826i	−1.66905	+	0.963625i
$636$		0			0
$637$		−	20.5633i		−	0.814746i
$638$	−12.5853	+	12.5853i	−0.498255	+	0.498255i
$639$		0			0
$640$	−3.91670	−	1.04948i	−0.154821	−	0.0414842i
$641$	6.28949	+	1.68526i	0.248420	+	0.0665640i	0.380880	−	0.924624i	$-0.375621\pi$
$641$	6.28949	+	1.68526i	0.248420	+	0.0665640i	−0.132460	+	0.991188i	$0.542288\pi$
$642$		0			0
$643$	−5.53411	+	5.53411i	−0.218244	+	0.218244i	−0.807758	−	0.589514i	$-0.799319\pi$
$643$	−5.53411	+	5.53411i	−0.218244	+	0.218244i	0.589514	+	0.807758i	$0.299319\pi$
$644$			9.76993i			0.384989i
$645$		0			0
$646$	−7.43838	+	4.29455i	−0.292659	+	0.168967i
$647$	−7.09443	+	7.09443i	−0.278911	+	0.278911i	−0.832674	−	0.553763i	$-0.813191\pi$
$647$	−7.09443	+	7.09443i	−0.278911	+	0.278911i	0.553763	+	0.832674i	$0.313191\pi$
$648$		0			0
$649$	−32.2215	−	18.6031i	−1.26480	−	0.730235i
$650$	46.5750	−	12.4797i	1.82682	−	0.489495i
$651$		0			0
$652$	−10.4928	−	18.1741i	−0.410931	−	0.711753i
$653$	10.3582	+	38.6573i	0.405347	+	1.51278i	0.803415	+	0.595420i	$0.203014\pi$
$653$	10.3582	+	38.6573i	0.405347	+	1.51278i	−0.398068	+	0.917356i	$0.630319\pi$
$654$		0			0
$655$	−24.6650	−	14.2404i	−0.963742	−	0.556417i
$656$	5.83369	−	10.1043i	0.227767	−	0.394505i
$657$		0			0
$658$	−3.19417	−	1.84416i	−0.124522	−	0.0718927i
$659$	−13.3560	−	23.1333i	−0.520276	−	0.901145i	−0.999722	−	0.0235734i	$-0.992496\pi$
$659$	−13.3560	−	23.1333i	−0.520276	−	0.901145i	0.479446	−	0.877571i	$-0.340838\pi$
$660$		0			0
$661$	29.2498	+	7.83747i	1.13769	+	0.304842i	0.778021	−	0.628239i	$-0.216224\pi$
$661$	29.2498	+	7.83747i	1.13769	+	0.304842i	0.359666	+	0.933081i	$0.382891\pi$
$662$	3.66179			0.142320
$663$		0			0
$664$	−3.64405	+	0.976420i	−0.141416	+	0.0378924i
$665$	−20.5406	+	5.50385i	−0.796531	+	0.213430i
$666$		0			0
$667$	−20.3232	−	35.2009i	−0.786919	−	1.36298i
$668$		−	25.5510i		−	0.988600i
$669$		0			0
$670$		−	23.9728i		−	0.926151i
$671$	20.8852	−	9.50332i	0.806266	−	0.366872i
$672$		0			0
$673$	−2.83993	−	10.5988i	−0.109471	−	0.408552i	0.889343	−	0.457241i	$-0.151162\pi$
$673$	−2.83993	−	10.5988i	−0.109471	−	0.408552i	−0.998814	+	0.0486891i	$0.984496\pi$
$674$	12.1947			0.469722
$675$		0			0
$676$	−4.12132	−	2.37945i	−0.158512	−	0.0915172i
$677$	10.2166	+	38.1290i	0.392657	+	1.46542i	0.825734	+	0.564059i	$0.190761\pi$
$677$	10.2166	+	38.1290i	0.392657	+	1.46542i	−0.433077	+	0.901357i	$0.642572\pi$
$678$		0			0
$679$	−10.9182	−	10.9182i	−0.419000	−	0.419000i
$680$			9.67032i			0.370840i
$681$		0			0
$682$	−0.187386	−	0.187386i	−0.00717539	−	0.00717539i
$683$	22.4319	−	12.9511i	0.858333	−	0.495559i	−0.00512049	−	0.999987i	$-0.501630\pi$
$683$	22.4319	−	12.9511i	0.858333	−	0.495559i	0.863454	+	0.504428i	$0.168297\pi$
$684$		0			0
$685$	−12.3165	+	7.11093i	−0.470589	+	0.271695i
$686$	14.9810	+	8.64930i	0.571978	+	0.330232i
$687$		0			0
$688$	1.16316	−	4.34096i	0.0443450	−	0.165498i
$689$	10.5695	−	2.83210i	0.402667	−	0.107894i
$690$		0			0
$691$	−2.31781			−0.0881735			−0.0440868	−	0.999028i	$-0.514038\pi$
$691$	−2.31781			−0.0881735			−0.0440868	+	0.999028i	$0.514038\pi$
$692$	−2.13766	−	7.97784i	−0.0812615	−	0.303272i
$693$		0			0
$694$	13.9833	−	13.9833i	0.530799	−	0.530799i
$695$	−27.9235	−	27.9235i	−1.05920	−	1.05920i
$696$		0			0
$697$	−26.8770	−	7.20167i	−1.01804	−	0.272783i
$698$	−4.91576			−0.186064
$699$		0			0
$700$	−4.31227	+	16.0936i	−0.162989	+	0.608281i
$701$	−11.8107	+	44.0783i	−0.446085	+	1.66481i	0.266969	+	0.963705i	$0.413978\pi$
$701$	−11.8107	+	44.0783i	−0.446085	+	1.66481i	−0.713055	+	0.701108i	$0.752689\pi$
$702$		0			0
$703$	−10.2325	−	2.74179i	−0.385926	−	0.103408i
$704$	−2.07741	−	2.07741i	−0.0782953	−	0.0782953i
$705$		0			0
$706$	3.95646	−	14.7657i	0.148903	−	0.555715i
$707$	0.0267108	+	0.0462644i	0.00100456	+	0.00173995i
$708$		0			0
$709$	6.53631	+	6.53631i	0.245476	+	0.245476i	0.819111	−	0.573635i	$-0.194467\pi$
$709$	6.53631	+	6.53631i	0.245476	+	0.245476i	−0.573635	+	0.819111i	$0.694467\pi$
$710$	−18.6542	+	32.3099i	−0.700078	+	1.21257i
$711$		0			0
$712$			18.8214i			0.705360i
$713$	0.524118	−	0.302600i	0.0196284	−	0.0113324i
$714$		0			0
$715$	48.4915	+	12.9933i	1.81348	+	0.485920i
$716$	−2.98859	+	5.17639i	−0.111689	+	0.193451i
$717$		0			0
$718$	1.26920	+	2.19831i	0.0473660	+	0.0820403i
$719$	10.2878	−	17.8190i	0.383670	−	0.664537i	−0.607913	−	0.794003i	$-0.707993\pi$
$719$	10.2878	−	17.8190i	0.383670	−	0.664537i	0.991584	+	0.129467i	$0.0413265\pi$
$720$		0			0
$721$	−13.5222	+	13.5222i	−0.503593	+	0.503593i
$722$	1.56046	−	5.82372i	0.0580744	−	0.216736i
$723$		0			0
$724$	12.0678	−	12.0678i	0.448497	−	0.448497i
$725$	−17.9406	−	66.9553i	−0.666298	−	2.48666i
$726$		0			0
$727$	−11.9330	+	20.6685i	−0.442569	+	0.766551i	−0.997879	−	0.0650916i	$-0.979266\pi$
$727$	−11.9330	+	20.6685i	−0.442569	+	0.766551i	0.555311	+	0.831643i	$0.312599\pi$
$728$	5.31432	−	3.06822i	0.196962	−	0.113716i
$729$		0			0
$730$	−6.76374	+	1.81234i	−0.250337	+	0.0670777i
$731$	−10.7178			−0.396413
$732$		0			0
$733$	21.2153			0.783603			0.391802	−	0.920050i	$-0.371852\pi$
$733$	21.2153			0.783603			0.391802	+	0.920050i	$0.371852\pi$
$734$	4.21765	−	1.13012i	0.155676	−	0.0417133i
$735$		0			0
$736$	5.81049	−	3.35469i	0.214178	−	0.123656i
$737$	8.68458	−	15.0421i	0.319901	−	0.554084i
$738$		0			0
$739$	−3.61140	−	13.4779i	−0.132848	−	0.495794i	0.867150	−	0.498047i	$-0.165949\pi$
$739$	−3.61140	−	13.4779i	−0.132848	−	0.495794i	−0.999997	+	0.00225326i	$0.999283\pi$
$740$	−8.43364	+	8.43364i	−0.310027	+	0.310027i
$741$		0			0
$742$	−0.978609	+	3.65222i	−0.0359259	+	0.134077i
$743$	−14.8169	+	14.8169i	−0.543578	+	0.543578i	−0.924576	−	0.380998i	$-0.875580\pi$
$743$	−14.8169	+	14.8169i	−0.543578	+	0.543578i	0.380998	+	0.924576i	$0.375580\pi$
$744$		0			0
$745$	13.7270	−	23.7759i	0.502918	−	0.871080i
$746$	14.4445	+	25.0186i	0.528851	+	0.915997i
$747$		0			0
$748$	−3.50325	+	6.06780i	−0.128091	+	0.221861i
$749$	13.0541	+	3.49784i	0.476988	+	0.127808i
$750$		0			0
$751$	13.0819	−	7.55286i	0.477367	−	0.275608i	−0.241952	−	0.970288i	$-0.577788\pi$
$751$	13.0819	−	7.55286i	0.477367	−	0.275608i	0.719318	+	0.694680i	$0.244454\pi$
$752$			2.53290i			0.0923654i
$753$		0			0
$754$	−12.7649	+	22.1095i	−0.464871	+	0.805181i
$755$	−25.1842	−	25.1842i	−0.916548	−	0.916548i
$756$		0			0
$757$	−0.101825	−	0.176366i	−0.00370089	−	0.00641012i	0.864169	−	0.503202i	$-0.167845\pi$
$757$	−0.101825	−	0.176366i	−0.00370089	−	0.00641012i	−0.867870	+	0.496792i	$0.834511\pi$
$758$	−4.25480	+	15.8791i	−0.154541	+	0.576756i
$759$		0			0
$760$	10.3263	+	10.3263i	0.374575	+	0.374575i
$761$	44.0657	+	11.8074i	1.59738	+	0.428017i	0.944250	−	0.329229i	$-0.106789\pi$
$761$	44.0657	+	11.8074i	1.59738	+	0.428017i	0.653130	+	0.757246i	$0.273455\pi$
$762$		0			0
$763$	2.13316	−	7.96105i	0.0772255	−	0.288209i
$764$	1.97957	−	7.38785i	0.0716183	−	0.267283i
$765$		0			0
$766$	35.5473			1.28438
$767$	−51.5501	−	13.8128i	−1.86137	−	0.498752i
$768$		0			0
$769$	0.720583	+	0.720583i	0.0259849	+	0.0259849i	0.719980	−	0.693995i	$-0.244151\pi$
$769$	0.720583	+	0.720583i	0.0259849	+	0.0259849i	−0.693995	+	0.719980i	$0.744151\pi$
$770$	−12.2661	+	12.2661i	−0.442041	+	0.442041i
$771$		0			0
$772$	−0.666012	−	2.48559i	−0.0239703	−	0.0894583i
$773$	26.5534			0.955059			0.477529	−	0.878616i	$-0.341532\pi$
$773$	26.5534			0.955059			0.477529	+	0.878616i	$0.341532\pi$
$774$		0			0
$775$	0.996920	−	0.267124i	0.0358104	−	0.00959538i
$776$	−2.74443	+	10.2423i	−0.0985192	+	0.367678i
$777$		0			0
$778$	−22.9279	−	13.2374i	−0.822005	−	0.474585i
$779$	−36.3905	+	21.0101i	−1.30383	+	0.752764i
$780$		0			0
$781$	−23.4097	+	13.5156i	−0.837666	+	0.483626i
$782$	−11.3144	−	11.3144i	−0.404602	−	0.404602i
$783$		0			0
$784$		−	4.87960i		−	0.174271i
$785$	−6.59819	−	6.59819i	−0.235500	−	0.235500i
$786$		0			0
$787$	9.99894	+	37.3166i	0.356424	+	1.33019i	0.878683	+	0.477405i	$0.158423\pi$
$787$	9.99894	+	37.3166i	0.356424	+	1.33019i	−0.522260	+	0.852787i	$0.674911\pi$
$788$	−17.4761	−	10.0898i	−0.622559	−	0.359434i
$789$		0			0
$790$	−26.3482			−0.937427
$791$	7.25733	+	27.0847i	0.258041	+	0.963022i
$792$		0			0
$793$	25.4089	−	20.9208i	0.902298	−	0.742918i
$794$			10.4623i			0.371293i
$795$		0			0
$796$			21.8316i			0.773800i
$797$	−12.2163	−	21.1592i	−0.432723	−	0.749498i	0.564384	−	0.825512i	$-0.309114\pi$
$797$	−12.2163	−	21.1592i	−0.432723	−	0.749498i	−0.997107	+	0.0760147i	$0.975780\pi$
$798$		0			0
$799$	5.83480	−	1.56343i	0.206420	−	0.0553102i
$800$	11.0521	−	2.96140i	0.390751	−	0.104701i
$801$		0			0
$802$	10.3903			0.366894
$803$	−4.90057	−	1.31310i	−0.172937	−	0.0463384i
$804$		0			0
$805$	−19.8079	−	34.3083i	−0.698137	−	1.20921i
$806$	−0.329196	−	0.190061i	−0.0115954	−	0.00669463i
$807$		0			0
$808$	0.0183433	−	0.0317715i	0.000645315	−	0.00111772i
$809$	35.7059	+	20.6148i	1.25535	+	0.724778i	0.972167	−	0.234287i	$-0.0752757\pi$
$809$	35.7059	+	20.6148i	1.25535	+	0.724778i	0.283185	+	0.959065i	$0.408609\pi$
$810$		0			0
$811$	14.4349	+	53.8717i	0.506877	+	1.89169i	0.449371	+	0.893345i	$0.351648\pi$
$811$	14.4349	+	53.8717i	0.506877	+	1.89169i	0.0575061	+	0.998345i	$0.481685\pi$
$812$	−4.41082	−	7.63977i	−0.154789	−	0.268103i
$813$		0			0
$814$	−8.34707	+	2.23659i	−0.292565	+	0.0783924i
$815$	73.6936	+	42.5470i	2.58137	+	1.49036i
$816$		0			0
$817$	−11.4449	+	11.4449i	−0.400406	+	0.400406i
$818$	−10.2906	+	5.94129i	−0.359803	+	0.207732i
$819$		0			0
$820$			47.3097i			1.65213i
$821$	−19.9020	+	19.9020i	−0.694584	+	0.694584i	−0.963237	−	0.268653i	$-0.913421\pi$
$821$	−19.9020	+	19.9020i	−0.694584	+	0.694584i	0.268653	+	0.963237i	$0.413421\pi$
$822$		0			0
$823$	−3.40602	−	0.912641i	−0.118726	−	0.0318127i	0.198967	−	0.980006i	$-0.436241\pi$
$823$	−3.40602	−	0.912641i	−0.118726	−	0.0318127i	−0.317693	+	0.948194i	$0.602908\pi$
$824$	12.6852	+	3.39899i	0.441910	+	0.118409i
$825$		0			0
$826$	13.0398	−	13.0398i	0.453714	−	0.453714i
$827$		−	9.70158i		−	0.337357i	−0.985671	−	0.168679i	$-0.946050\pi$
$827$		−	9.70158i		−	0.337357i	0.985671	−	0.168679i	$-0.0539500\pi$
$828$		0			0
$829$	−2.80627	+	1.62020i	−0.0974659	+	0.0562720i	−0.547941	−	0.836517i	$-0.684588\pi$
$829$	−2.80627	+	1.62020i	−0.0974659	+	0.0562720i	0.450475	+	0.892789i	$0.351255\pi$
$830$	10.8169	−	10.8169i	0.375460	−	0.375460i
$831$		0			0
$832$	−3.64954	−	2.10707i	−0.126525	−	0.0730493i
$833$	−11.2407	+	3.01192i	−0.389466	+	0.104357i
$834$		0			0
$835$	51.8031	+	89.7256i	1.79272	+	3.10508i
$836$	2.73853	+	10.2203i	0.0947140	+	0.353477i
$837$		0			0
$838$	15.3257	+	8.84827i	0.529416	+	0.305658i
$839$	−9.82107	+	17.0106i	−0.339061	+	0.587271i	−0.984256	−	0.176747i	$-0.943443\pi$
$839$	−9.82107	+	17.0106i	−0.339061	+	0.587271i	0.645195	+	0.764018i	$0.276776\pi$
$840$		0			0
$841$	6.66948	+	3.85063i	0.229982	+	0.132780i
$842$	2.62515	+	4.54689i	0.0904687	+	0.156696i
$843$		0			0
$844$	−10.8351	−	2.90327i	−0.372961	−	0.0999346i
$845$	19.2967			0.663827
$846$		0			0
$847$	3.33175	−	0.892739i	0.114480	−	0.0306749i
$848$	2.50812	−	0.672048i	0.0861291	−	0.0230782i
$849$		0			0
$850$	−13.6438	−	23.6317i	−0.467978	−	0.810561i
$851$		−	19.7349i		−	0.676505i
$852$		0			0
$853$		−	10.9333i		−	0.374348i	−0.982327	−	0.187174i	$-0.940067\pi$
$853$		−	10.9333i		−	0.374348i	0.982327	−	0.187174i	$-0.0599329\pi$
$854$	1.87057	+	11.2181i	0.0640097	+	0.383875i
$855$		0			0
$856$	−2.40210	−	8.96477i	−0.0821021	−	0.306409i
$857$	50.7340			1.73304			0.866521	−	0.499141i	$-0.166351\pi$
$857$	50.7340			1.73304			0.866521	+	0.499141i	$0.166351\pi$
$858$		0			0
$859$	−18.3966	−	10.6213i	−0.627683	−	0.362393i	0.152172	−	0.988354i	$-0.451373\pi$
$859$	−18.3966	−	10.6213i	−0.627683	−	0.362393i	−0.779854	+	0.625961i	$0.784707\pi$
$860$	4.71645	+	17.6020i	0.160830	+	0.600225i
$861$		0			0
$862$	−21.5101	−	21.5101i	−0.732636	−	0.732636i
$863$		−	6.69803i		−	0.228003i	−0.993481	−	0.114002i	$-0.963633\pi$
$863$		−	6.69803i		−	0.228003i	0.993481	−	0.114002i	$-0.0363669\pi$
$864$		0			0
$865$	23.6812	+	23.6812i	0.805184	+	0.805184i
$866$	−5.04148	+	2.91070i	−0.171316	+	0.0989096i
$867$		0			0
$868$	0.113751	−	0.0656742i	0.00386096	−	0.00222913i
$869$	−16.5326	−	9.54511i	−0.560830	−	0.323796i
$870$		0			0
$871$	6.44832	−	24.0654i	0.218493	−	0.815426i
$872$	−5.46715	+	1.46492i	−0.185141	+	0.0496084i
$873$		0			0
$874$	−24.1639			−0.817355
$875$	−9.84466	−	36.7408i	−0.332810	−	1.24207i
$876$		0			0
$877$	−18.1296	+	18.1296i	−0.612194	+	0.612194i	−0.943517	−	0.331323i	$-0.892505\pi$
$877$	−18.1296	+	18.1296i	−0.612194	+	0.612194i	0.331323	+	0.943517i	$0.392505\pi$
$878$	0.574812	+	0.574812i	0.0193990	+	0.0193990i
$879$		0			0
$880$	11.5069	+	3.08326i	0.387897	+	0.103937i
$881$	10.4855			0.353265			0.176633	−	0.984277i	$-0.443480\pi$
$881$	10.4855			0.353265			0.176633	+	0.984277i	$0.443480\pi$
$882$		0			0
$883$	−6.26109	+	23.3667i	−0.210702	+	0.786352i	0.776933	+	0.629583i	$0.216774\pi$
$883$	−6.26109	+	23.3667i	−0.210702	+	0.786352i	−0.987635	+	0.156769i	$0.949892\pi$
$884$	−2.60117	+	9.70768i	−0.0874867	+	0.326505i
$885$		0			0
$886$	8.11613	+	2.17471i	0.272667	+	0.0730608i
$887$	32.7774	+	32.7774i	1.10056	+	1.10056i	0.994343	+	0.106214i	$0.0338730\pi$
$887$	32.7774	+	32.7774i	1.10056	+	1.10056i	0.106214	+	0.994343i	$0.466127\pi$
$888$		0			0
$889$	4.51392	−	16.8462i	0.151392	−	0.565002i
$890$	−38.1591	−	66.0934i	−1.27909	−	2.21546i
$891$		0			0
$892$	15.1292	+	15.1292i	0.506562	+	0.506562i
$893$	4.56113	−	7.90011i	0.152632	−	0.264367i
$894$		0			0
$895$		−	24.2367i		−	0.810143i
$896$	1.26107	−	0.728080i	0.0421294	−	0.0243234i
$897$		0			0
$898$	−19.6992	−	5.27840i	−0.657372	−	0.176142i
$899$	−0.273229	+	0.473246i	−0.00911269	+	0.0157836i
$900$		0			0
$901$	−3.09626	−	5.36289i	−0.103151	−	0.178664i
$902$	−17.1388	+	29.6853i	−0.570659	+	0.988411i
$903$		0			0
$904$	13.6162	−	13.6162i	0.452869	−	0.452869i
$905$	−17.9109	+	66.8444i	−0.595378	+	2.22198i
$906$		0			0
$907$	13.1955	−	13.1955i	0.438149	−	0.438149i	−0.453240	−	0.891389i	$-0.649732\pi$
$907$	13.1955	−	13.1955i	0.438149	−	0.438149i	0.891389	+	0.453240i	$0.149732\pi$
$908$	−6.47784	−	24.1756i	−0.214975	−	0.802297i
$909$		0			0
$910$	−12.4412	+	21.5489i	−0.412423	+	0.714338i
$911$	33.2039	−	19.1703i	1.10009	−	0.635139i	0.163848	−	0.986486i	$-0.447609\pi$
$911$	33.2039	−	19.1703i	1.10009	−	0.635139i	0.936246	+	0.351346i	$0.114276\pi$
$912$		0			0
$913$	10.7058	−	2.86862i	0.354312	−	0.0949375i
$914$	26.9192			0.890408
$915$		0			0
$916$	−15.2435			−0.503661
$917$	9.87931	−	2.64715i	0.326244	−	0.0874167i
$918$		0			0
$919$	−45.6447	+	26.3530i	−1.50568	+	0.869305i	−0.505703	+	0.862708i	$0.668767\pi$
$919$	−45.6447	+	26.3530i	−1.50568	+	0.869305i	−0.999978	+	0.00659738i	$0.997900\pi$
$920$	−13.6028	+	23.5608i	−0.448472	+	0.776776i
$921$		0			0
$922$	0.839996	+	3.13491i	0.0276638	+	0.103243i
$923$	−27.4171	+	27.4171i	−0.902445	+	0.902445i
$924$		0			0
$925$	8.71065	−	32.5086i	0.286404	−	1.06888i
$926$	22.4340	−	22.4340i	0.737225	−	0.737225i
$927$		0			0
$928$	−3.02908	+	5.24652i	−0.0994344	+	0.172225i
$929$	−24.7818	−	42.9234i	−0.813066	−	1.40827i	−0.910708	−	0.413050i	$-0.864463\pi$
$929$	−24.7818	−	42.9234i	−0.813066	−	1.40827i	0.0976422	−	0.995222i	$-0.468870\pi$
$930$		0			0
$931$	−8.78695	+	15.2194i	−0.287981	+	0.498797i
$932$	−9.51471	−	2.54946i	−0.311665	−	0.0835103i
$933$		0			0
$934$	−32.7707	+	18.9202i	−1.07229	+	0.619088i
$935$		−	28.4104i		−	0.929120i
$936$		0			0
$937$	−21.5170	+	37.2686i	−0.702931	+	1.21751i	0.264502	+	0.964385i	$0.414792\pi$
$937$	−21.5170	+	37.2686i	−0.702931	+	1.21751i	−0.967433	+	0.253127i	$0.918541\pi$
$938$	6.08746	+	6.08746i	0.198763	+	0.198763i
$939$		0			0
$940$	−5.13529	−	8.89459i	−0.167495	−	0.290110i
$941$	−8.59715	+	32.0850i	−0.280259	+	1.04594i	0.671976	+	0.740573i	$0.265446\pi$
$941$	−8.59715	+	32.0850i	−0.280259	+	1.04594i	−0.952235	+	0.305368i	$0.901221\pi$
$942$		0			0
$943$	−55.3530	−	55.3530i	−1.80254	−	1.80254i
$944$	−12.2327	−	3.27774i	−0.398140	−	0.106681i
$945$		0			0
$946$	−3.41724	+	12.7533i	−0.111104	+	0.414646i
$947$	−4.24346	+	15.8368i	−0.137894	+	0.514627i	0.862075	+	0.506780i	$0.169164\pi$
$947$	−4.24346	+	15.8368i	−0.137894	+	0.514627i	−0.999969	+	0.00784671i	$0.997502\pi$
$948$		0			0
$949$	−7.27736			−0.236233
$950$	−39.8042	−	10.6655i	−1.29142	−	0.346034i
$951$		0			0
$952$	−2.45560	−	2.45560i	−0.0795865	−	0.0795865i
$953$	−27.3472	+	27.3472i	−0.885863	+	0.885863i	−0.994123	−	0.108260i	$-0.965472\pi$
$953$	−27.3472	+	27.3472i	−0.885863	+	0.885863i	0.108260	+	0.994123i	$0.465472\pi$
$954$		0			0
$955$	8.02689	+	29.9568i	0.259744	+	0.969378i
$956$	−10.9324			−0.353579
$957$		0			0
$958$	−25.3171	+	6.78369i	−0.817957	+	0.219171i
$959$	1.32186	−	4.93324i	0.0426850	−	0.159303i
$960$		0			0
$961$	26.8397	+	15.4959i	0.865798	+	0.499869i
$962$	−10.7348	+	6.19771i	−0.346102	+	0.199822i
$963$		0			0
$964$	−5.21701	+	3.01204i	−0.168029	+	0.0970114i
$965$	7.37815	+	7.37815i	0.237511	+	0.237511i
$966$		0			0
$967$			30.3191i			0.974997i	0.873124	+	0.487498i	$0.162090\pi$
$967$			30.3191i			0.974997i	−0.873124	+	0.487498i	$0.837910\pi$
$968$	−1.67496	−	1.67496i	−0.0538353	−	0.0538353i
$969$		0			0
$970$	−11.1283	−	41.5313i	−0.357308	−	1.33349i
$971$	34.2106	+	19.7515i	1.09787	+	0.633856i	0.935661	−	0.352900i	$-0.114805\pi$
$971$	34.2106	+	19.7515i	1.09787	+	0.633856i	0.162210	+	0.986756i	$0.448138\pi$
$972$		0			0
$973$	14.1813			0.454633
$974$	−9.57624	−	35.7390i	−0.306843	−	1.14515i
$975$		0			0
$976$	6.02946	−	4.96443i	0.192998	−	0.158908i
$977$		−	29.5991i		−	0.946958i	−0.880805	−	0.473479i	$-0.842998\pi$
$977$		−	29.5991i		−	0.946958i	0.880805	−	0.473479i	$-0.157002\pi$
$978$		0			0
$979$		−	55.2952i		−	1.76724i
$980$	9.89307	+	17.1353i	0.316023	+	0.547367i
$981$		0			0
$982$	3.91807	−	1.04984i	0.125031	−	0.0335019i
$983$	23.7226	−	6.35645i	0.756633	−	0.202739i	0.140175	−	0.990127i	$-0.455234\pi$
$983$	23.7226	−	6.35645i	0.756633	−	0.202739i	0.616458	+	0.787388i	$0.288567\pi$
$984$		0			0
$985$	81.8257			2.60718
$986$	13.9556	+	3.73939i	0.444436	+	0.119086i
$987$		0			0
$988$	7.58861	+	13.1439i	0.241426	+	0.418162i
$989$	−26.1129	−	15.0763i	−0.830343	−	0.479399i
$990$		0			0
$991$	−28.2419	+	48.9165i	−0.897134	+	1.55388i	−0.0659937	+	0.997820i	$0.521022\pi$
$991$	−28.2419	+	48.9165i	−0.897134	+	1.55388i	−0.831141	+	0.556062i	$0.812312\pi$
$992$	−0.0781172	−	0.0451010i	−0.00248022	−	0.00143196i
$993$		0			0
$994$	−3.46764	−	12.9414i	−0.109987	−	0.410476i
$995$	−44.2621	−	76.6642i	−1.40320	−	2.43042i
$996$		0			0
$997$	26.1330	−	7.00232i	0.827641	−	0.221766i	0.179957	−	0.983675i	$-0.442404\pi$
$997$	26.1330	−	7.00232i	0.827641	−	0.221766i	0.647684	+	0.761909i	$0.275738\pi$
$998$	−21.4739	−	12.3979i	−0.679744	−	0.392450i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1098.2.bd.b.467.6	yes	48
3.2	odd	2	inner	1098.2.bd.b.467.7	yes	48
61.29	odd	12	inner	1098.2.bd.b.395.7	yes	48
183.29	even	12	inner	1098.2.bd.b.395.6	✓	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1098.2.bd.b.395.6	✓	48	183.29	even	12	inner
1098.2.bd.b.395.7	yes	48	61.29	odd	12	inner
1098.2.bd.b.467.6	yes	48	1.1	even	1	trivial
1098.2.bd.b.467.7	yes	48	3.2	odd	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:	\( N \)	\(=\)	\( 1098 = 2 \cdot 3^{2} \cdot 61 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1098.bd (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.965926 + 0.258819i) q^{2} +(0.866025 - 0.500000i) q^{4} +(-2.02743 + 3.51162i) q^{5} +(-0.376882 - 1.40654i) q^{7} +(-0.707107 + 0.707107i) q^{8} +O(q^{10})\)	\(q+(-0.965926 + 0.258819i) q^{2} +(0.866025 - 0.500000i) q^{4} +(-2.02743 + 3.51162i) q^{5} +(-0.376882 - 1.40654i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(1.04948 - 3.91670i) q^{10} +(2.07741 - 2.07741i) q^{11} +(2.10707 - 3.64954i) q^{13} +(0.728080 + 1.26107i) q^{14} +(0.500000 - 0.866025i) q^{16} +(-2.30360 - 0.617248i) q^{17} +(-3.11899 + 1.80075i) q^{19} +4.05487i q^{20} +(-1.46895 + 2.54429i) q^{22} +(-4.74425 - 4.74425i) q^{23} +(-5.72098 - 9.90904i) q^{25} +(-1.09070 + 4.07054i) q^{26} +(-1.02966 - 1.02966i) q^{28} +(5.85173 + 1.56797i) q^{29} +(-0.0233460 + 0.0871284i) q^{31} +(-0.258819 + 0.965926i) q^{32} +2.38486 q^{34} +(5.70335 + 1.52821i) q^{35} +(2.07988 + 2.07988i) q^{37} +(2.54665 - 2.54665i) q^{38} +(-1.04948 - 3.91670i) q^{40} +11.6674 q^{41} +(4.34096 - 1.16316i) q^{43} +(0.760384 - 2.83779i) q^{44} +(5.81049 + 3.35469i) q^{46} +(-2.19356 + 1.26645i) q^{47} +(4.22586 - 2.43980i) q^{49} +(8.09069 + 8.09069i) q^{50} -4.21413i q^{52} +(1.83607 + 1.83607i) q^{53} +(3.08326 + 11.5069i) q^{55} +(1.26107 + 0.728080i) q^{56} -6.05816 q^{58} +(-3.27774 - 12.2327i) q^{59} +(7.31406 + 2.73945i) q^{61} -0.0902019i q^{62} -1.00000i q^{64} +(8.54388 + 14.7984i) q^{65} +(5.71065 - 1.53017i) q^{67} +(-2.30360 + 0.617248i) q^{68} -5.90454 q^{70} +(-8.88735 - 2.38136i) q^{71} +(-0.863448 - 1.49554i) q^{73} +(-2.54732 - 1.47070i) q^{74} +(-1.80075 + 3.11899i) q^{76} +(-3.70490 - 2.13902i) q^{77} +(-1.68178 - 6.27650i) q^{79} +(2.02743 + 3.51162i) q^{80} +(-11.2698 + 3.01974i) q^{82} +(3.26716 + 1.88630i) q^{83} +(6.83795 - 6.83795i) q^{85} +(-3.89200 + 2.24705i) q^{86} +2.93790i q^{88} +(13.3087 - 13.3087i) q^{89} +(-5.92735 - 1.58823i) q^{91} +(-6.48076 - 1.73652i) q^{92} +(1.79103 - 1.79103i) q^{94} -14.6036i q^{95} +(9.18303 - 5.30182i) q^{97} +(-3.45040 + 3.45040i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 4 q^{7}+O(q^{10}) \) 48 * q + 4 * q^7	\( 48 q + 4 q^{7} + 4 q^{10} - 12 q^{13} + 24 q^{16} - 36 q^{19} - 4 q^{22} - 48 q^{25} - 8 q^{28} - 20 q^{31} - 16 q^{34} + 8 q^{37} - 4 q^{40} + 20 q^{43} + 12 q^{46} + 72 q^{49} - 52 q^{55} + 32 q^{58} + 8 q^{61} + 28 q^{67} - 8 q^{70} + 16 q^{73} - 28 q^{76} + 32 q^{79} - 48 q^{82} + 120 q^{85} - 92 q^{91} + 8 q^{94} + 72 q^{97}+O(q^{100}) \) 48 * q + 4 * q^7 + 4 * q^10 - 12 * q^13 + 24 * q^16 - 36 * q^19 - 4 * q^22 - 48 * q^25 - 8 * q^28 - 20 * q^31 - 16 * q^34 + 8 * q^37 - 4 * q^40 + 20 * q^43 + 12 * q^46 + 72 * q^49 - 52 * q^55 + 32 * q^58 + 8 * q^61 + 28 * q^67 - 8 * q^70 + 16 * q^73 - 28 * q^76 + 32 * q^79 - 48 * q^82 + 120 * q^85 - 92 * q^91 + 8 * q^94 + 72 * q^97

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