LMFDB - Embedded newform 1098.2.bd.b.467.7

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			467.7
Character	$\chi$	$=$	1098.467
Dual form			1098.2.bd.b.395.7

$q$-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	$-0.471929\pi$
$5$	2.02743	−	3.51162i	0.906696	−	1.57044i	0.818624	−	0.574330i	$-0.194737\pi$
$6$		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	−0.947151	−	0.320789i	$-0.896052\pi$
$11$	−2.07741	+	2.07741i	−0.626362	+	0.626362i	0.320789	+	0.947151i	$0.396052\pi$
$12$		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	0.527112	−	0.849796i	$-0.323275\pi$
$17$	2.30360	+	0.617248i	0.558706	+	0.149705i	0.0315941	+	0.999501i	$0.489942\pi$
$18$		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	0.999943	−	0.0106987i	$-0.00340556\pi$
$23$	4.74425	+	4.74425i	0.989244	+	0.989244i	−0.0106987	+	0.999943i	$0.503406\pi$
$24$		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	−0.329326	−	0.944216i	$-0.606822\pi$
$29$	−5.85173	−	1.56797i	−1.08664	−	0.291164i	−0.757313	+	0.653052i	$0.773488\pi$
$30$		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	$-0.864742\pi$
$41$	−11.6674			−1.82214			−0.911070	+	0.412253i	$0.864742\pi$
$42$		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	−0.331413	−	0.943486i	$-0.607525\pi$
$47$	2.19356	−	1.26645i	0.319963	−	0.184731i	0.651376	+	0.758755i	$0.274192\pi$
$48$		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	0.569670	−	0.821874i	$-0.307071\pi$
$53$	−1.83607	−	1.83607i	−0.252204	−	0.252204i	−0.821874	+	0.569670i	$0.807071\pi$
$54$		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	$0.225137\pi$
$59$	3.27774	+	12.2327i	0.426725	+	1.59256i	−0.333401	+	0.942785i	$0.608196\pi$
$60$		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	0.744207	−	0.667949i	$-0.232828\pi$
$71$	8.88735	+	2.38136i	1.05473	+	0.282615i	0.310528	+	0.950564i	$0.399494\pi$
$72$		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	0.309856	−	0.950783i	$-0.399719\pi$
$83$	−3.26716	−	1.88630i	−0.358618	−	0.207048i	−0.668474	+	0.743735i	$0.733052\pi$
$84$		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	$0.727622\pi$
$89$	−13.3087	+	13.3087i	−1.41072	+	1.41072i	−0.755031	+	0.655689i	$0.772378\pi$
$90$		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	−0.257056	−	0.966397i	$-0.582752\pi$
$101$	0.0354365	−	0.00949519i	0.00352607	−	0.000944807i	0.260582	+	0.965452i	$0.416086\pi$
$102$		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	−0.549682	−	0.835374i	$-0.685251\pi$
$107$	4.64050	−	8.03759i	0.448614	−	0.777023i	0.998296	+	0.0583512i	$0.0185843\pi$
$108$		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	$-0.139318\pi$
$113$	19.2563			1.81148			0.905738	+	0.423838i	$0.139318\pi$
$114$		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	$-0.900729\pi$
$131$		−	7.02383i		−	0.613675i	0.951762	−	0.306837i	$-0.0992708\pi$
$132$		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	0.364602	−	0.931163i	$-0.381205\pi$
$137$	−3.03746	−	1.75368i	−0.259508	−	0.149827i	−0.624110	+	0.781337i	$0.714538\pi$
$138$		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	$-0.410549\pi$
$149$	6.77062			0.554671			0.277336	+	0.960773i	$0.410549\pi$
$150$		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	$0.618556\pi$
$167$	−12.7755	+	22.1279i	−0.988600	+	1.71230i	−0.624696	+	0.780868i	$0.714777\pi$
$168$		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	$0.184993\pi$
$173$	−2.13766	+	7.97784i	−0.162523	+	0.606544i	−0.998343	+	0.0575406i	$0.981674\pi$
$174$		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	−0.293915	−	0.955831i	$-0.594958\pi$
$179$	5.17639	−	2.98859i	0.386902	−	0.223378i	0.680817	+	0.732454i	$0.261625\pi$
$180$		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	−0.875161	−	0.483832i	$-0.839245\pi$
$191$	−5.40828	+	5.40828i	−0.391329	+	0.391329i	0.483832	+	0.875161i	$0.339245\pi$
$192$		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	$0.0886731\pi$
$197$	10.0898	+	17.4761i	0.718869	+	1.24512i	−0.242580	+	0.970131i	$0.577994\pi$
$198$		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	$0.395335\pi$
$227$	−6.47784	+	24.1756i	−0.429949	+	1.60459i	−0.752871	+	0.658168i	$0.771332\pi$
$228$		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	0.897442	−	0.441133i	$-0.145423\pi$
$233$	6.96525	+	6.96525i	0.456309	+	0.456309i	−0.441133	+	0.897442i	$0.645423\pi$
$234$		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	0.773910	−	0.633295i	$-0.218298\pi$
$239$	9.46772	+	5.46619i	0.612416	+	0.353579i	−0.161494	+	0.986874i	$0.551631\pi$
$240$		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	$0.834832\pi$
$251$	−29.6004	+	7.93140i	−1.86836	+	0.500625i	−0.999989	+	0.00470968i	$0.998501\pi$
$252$		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	0.0884912	−	0.996077i	$-0.471795\pi$
$257$	−11.7010	−	6.75560i	−0.729891	−	0.421403i	−0.818382	+	0.574674i	$0.805129\pi$
$258$		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	0.838920	−	0.544256i	$-0.183188\pi$
$263$	−0.841342	−	1.45725i	−0.0518794	−	0.0898577i	−0.890799	+	0.454398i	$0.849854\pi$
$264$		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	−0.234841	−	0.972034i	$-0.575457\pi$
$269$	8.02914	−	4.63562i	0.489545	−	0.282639i	0.724386	+	0.689395i	$0.242123\pi$
$270$		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	−0.880676	−	0.473718i	$-0.842911\pi$
$281$	−6.82186	+	6.82186i	−0.406958	+	0.406958i	0.473718	+	0.880676i	$0.342911\pi$
$282$		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	$0.0231189\pi$
$293$	9.61178	+	16.6481i	0.561526	+	0.972592i	−0.435837	+	0.900025i	$0.643548\pi$
$294$		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	$-0.819376\pi$
$311$	−6.73167	−	25.1229i	−0.381718	−	1.42459i	0.461558	−	0.887110i	$-0.347291\pi$
$312$		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	0.0887767	−	0.996052i	$-0.471704\pi$
$317$	17.7292	−	10.2360i	0.995771	−	0.574909i	0.906994	+	0.421143i	$0.138371\pi$
$318$		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	0.0359360	−	0.999354i	$-0.488559\pi$
$347$	17.1260	−	9.88768i	0.919370	−	0.530799i	0.883434	+	0.468556i	$0.155225\pi$
$348$		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	−0.587719	−	0.809065i	$-0.699974\pi$
$353$	7.64329	−	13.2386i	0.406811	−	0.704618i	0.994530	+	0.104447i	$0.0333073\pi$
$354$		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	0.981093	−	0.193535i	$-0.0619952\pi$
$359$	0.656984	+	2.45190i	0.0346743	+	0.129406i	−0.946419	+	0.322941i	$0.895329\pi$
$360$		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	0.985576	−	0.169236i	$-0.0541299\pi$
$383$	34.3361	+	9.20032i	1.75449	+	0.470115i	0.768916	+	0.639350i	$0.220797\pi$
$384$		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	0.0496000	−	0.998769i	$-0.484205\pi$
$389$	−18.7205	−	18.7205i	−0.949169	−	0.949169i	−0.998769	+	0.0496000i	$0.984205\pi$
$390$		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	0.500551	−	0.865707i	$-0.333131\pi$
$401$	10.0363	+	2.68921i	0.501187	+	0.134293i	0.000636069		1.00000i	$0.499798\pi$
$402$		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	0.943289	−	0.331972i	$-0.107714\pi$
$419$	12.5133	+	12.5133i	0.611317	+	0.611317i	−0.331972	+	0.943289i	$0.607714\pi$
$420$		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	$-0.904957\pi$
$431$	−15.2099	−	26.3443i	−0.732636	−	1.26896i	0.223117	−	0.974792i	$-0.428377\pi$
$432$		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	0.662802	−	0.748795i	$-0.269367\pi$
$443$	7.27672	+	4.20122i	0.345727	+	0.199606i	−0.317074	+	0.948401i	$0.602701\pi$
$444$		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	0.0215399	−	0.999768i	$-0.493143\pi$
$449$	−17.6619	−	10.1971i	−0.833515	−	0.481230i	−0.855055	+	0.518538i	$0.826476\pi$
$450$		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	$0.0240805\pi$
$461$			3.24549i			0.151158i	−0.997140	+	0.0755789i	$0.975920\pi$
$462$		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	−0.970745	−	0.240112i	$-0.922816\pi$
$467$	−36.5510	+	9.79382i	−1.69138	+	0.453204i	−0.720634	+	0.693315i	$0.756149\pi$
$468$		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	$-0.704350\pi$
$479$	−26.2102			−1.19757			−0.598786	+	0.800909i	$0.704350\pi$
$480$		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	$-0.470825\pi$
$491$	4.05628			0.183058			0.0915288	+	0.995802i	$0.470825\pi$
$492$		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	$-0.984302\pi$
$503$	−34.5581	−	19.9521i	−1.54087	−	0.889621i	−0.542085	−	0.840324i	$-0.682365\pi$
$504$		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	$-0.822101\pi$
$509$	−8.54412	−	31.8871i	−0.378711	−	1.41337i	0.469134	−	0.883127i	$-0.344566\pi$
$510$		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	$0.0257045\pi$
$521$	24.5923	+	24.5923i	1.07741	+	1.07741i	0.0806652	+	0.996741i	$0.474296\pi$
$522$		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	−0.992359	−	0.123384i	$-0.960625\pi$
$557$	−20.5085	+	20.5085i	−0.868975	+	0.868975i	0.123384	+	0.992359i	$0.460625\pi$
$558$		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	$0.121824\pi$
$563$	18.6794	+	32.3536i	0.787241	+	1.36354i	−0.140411	+	0.990093i	$0.544842\pi$
$564$		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	$0.214915\pi$
$569$			29.8188i			1.25007i	−0.780597	+	0.625034i	$0.785085\pi$
$570$		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	−0.908655	−	0.417547i	$-0.862890\pi$
$587$	−11.8986	+	11.8986i	−0.491108	+	0.491108i	0.417547	+	0.908655i	$0.362890\pi$
$588$		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	$-0.654667\pi$
$593$	9.24291	−	34.4950i	0.379561	−	1.41654i	0.846565	−	0.532285i	$-0.178667\pi$
$594$		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	$0.00327006\pi$
$599$	24.7246	+	24.7246i	1.01022	+	1.01022i	0.0102730	+	0.999947i	$0.496730\pi$
$600$		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	−0.523311	−	0.852142i	$-0.675303\pi$
$617$	−13.6727	+	3.66358i	−0.550440	+	0.147490i	−0.0271296	+	0.999632i	$0.508637\pi$
$618$		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	0.132460	−	0.991188i	$-0.457712\pi$
$641$	−6.28949	−	1.68526i	−0.248420	−	0.0665640i	−0.380880	+	0.924624i	$0.624379\pi$
$642$		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	−0.553763	−	0.832674i	$-0.686809\pi$
$647$	7.09443	−	7.09443i	0.278911	−	0.278911i	0.832674	+	0.553763i	$0.186809\pi$
$648$		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	$-0.796986\pi$
$653$	−10.3582	−	38.6573i	−0.405347	−	1.51278i	0.398068	−	0.917356i	$-0.369681\pi$
$654$		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	$0.00750434\pi$
$659$	13.3560	+	23.1333i	0.520276	+	0.901145i	−0.479446	+	0.877571i	$0.659162\pi$
$660$		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	$-0.809239\pi$
$677$	−10.2166	−	38.1290i	−0.392657	−	1.46542i	0.433077	−	0.901357i	$-0.357428\pi$
$678$		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	−0.863454	−	0.504428i	$-0.831703\pi$
$683$	−22.4319	+	12.9511i	−0.858333	+	0.495559i	0.00512049	+	0.999987i	$0.498370\pi$
$684$		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	$-0.586022\pi$
$701$	11.8107	−	44.0783i	0.446085	−	1.66481i	0.713055	−	0.701108i	$-0.247311\pi$
$702$		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	−0.991584	−	0.129467i	$-0.958673\pi$
$719$	−10.2878	+	17.8190i	−0.383670	+	0.664537i	0.607913	+	0.794003i	$0.292007\pi$
$720$		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	−0.380998	−	0.924576i	$-0.624420\pi$
$743$	14.8169	−	14.8169i	0.543578	−	0.543578i	0.924576	+	0.380998i	$0.124420\pi$
$744$		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	−0.653130	−	0.757246i	$-0.726545\pi$
$761$	−44.0657	−	11.8074i	−1.59738	−	0.428017i	−0.944250	+	0.329229i	$0.893211\pi$
$762$		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	$-0.658468\pi$
$773$	−26.5534			−0.955059			−0.477529	+	0.878616i	$0.658468\pi$
$774$		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	0.997107	−	0.0760147i	$-0.0242196\pi$
$797$	12.2163	+	21.1592i	0.432723	+	0.749498i	−0.564384	+	0.825512i	$0.690886\pi$
$798$		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	−0.283185	−	0.959065i	$-0.591391\pi$
$809$	−35.7059	−	20.6148i	−1.25535	−	0.724778i	−0.972167	+	0.234287i	$0.924724\pi$
$810$		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	−0.268653	−	0.963237i	$-0.586579\pi$
$821$	19.9020	−	19.9020i	0.694584	−	0.694584i	0.963237	+	0.268653i	$0.0865785\pi$
$822$		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	$0.0539500\pi$
$827$			9.70158i			0.337357i	−0.985671	+	0.168679i	$0.946050\pi$
$828$		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	−0.645195	−	0.764018i	$-0.723224\pi$
$839$	9.82107	−	17.0106i	0.339061	−	0.587271i	0.984256	+	0.176747i	$0.0565574\pi$
$840$		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	$-0.833649\pi$
$857$	−50.7340			−1.73304			−0.866521	+	0.499141i	$0.833649\pi$
$858$		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	$0.0363669\pi$
$863$			6.69803i			0.228003i	−0.993481	+	0.114002i	$0.963633\pi$
$864$		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	$-0.556520\pi$
$881$	−10.4855			−0.353265			−0.176633	+	0.984277i	$0.556520\pi$
$882$		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	$-0.966127\pi$
$887$	−32.7774	−	32.7774i	−1.10056	−	1.10056i	−0.106214	−	0.994343i	$-0.533873\pi$
$888$		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	−0.936246	−	0.351346i	$-0.885724\pi$
$911$	−33.2039	+	19.1703i	−1.10009	+	0.635139i	−0.163848	+	0.986486i	$0.552391\pi$
$912$		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	$0.135537\pi$
$929$	24.7818	+	42.9234i	0.813066	+	1.40827i	−0.0976422	+	0.995222i	$0.531130\pi$
$930$		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	$-0.734554\pi$
$941$	8.59715	−	32.0850i	0.280259	−	1.04594i	0.952235	−	0.305368i	$-0.0987793\pi$
$942$		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	$-0.830836\pi$
$947$	4.24346	−	15.8368i	0.137894	−	0.514627i	0.999969	−	0.00784671i	$-0.00249771\pi$
$948$		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	−0.108260	−	0.994123i	$-0.534528\pi$
$953$	27.3472	−	27.3472i	0.885863	−	0.885863i	0.994123	+	0.108260i	$0.0345279\pi$
$954$		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	−0.162210	−	0.986756i	$-0.551862\pi$
$971$	−34.2106	−	19.7515i	−1.09787	−	0.633856i	−0.935661	+	0.352900i	$0.885195\pi$
$972$		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	$0.157002\pi$
$977$			29.5991i			0.946958i	−0.880805	+	0.473479i	$0.842998\pi$
$978$		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	−0.616458	−	0.787388i	$-0.711433\pi$
$983$	−23.7226	+	6.35645i	−0.756633	+	0.202739i	−0.140175	+	0.990127i	$0.544766\pi$
$984$		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.467.7	yes	48
3.2	odd	2	inner	1098.2.bd.b.467.6	yes	48
61.29	odd	12	inner	1098.2.bd.b.395.6	✓	48
183.29	even	12	inner	1098.2.bd.b.395.7	yes	48

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

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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