LMFDB - Embedded newform 350.2.o.b.157.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [350,2,Mod(143,350)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(350, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([9, 2]))

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

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

chi := DirichletCharacter("350.143");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 350 = 2 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	350.o (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:	$2.79476407074$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{12})$
Coefficient field:	$\Q(\zeta_{24})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{4} + 1 $ x^8 - x^4 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			157.1
Root			$0.965926 + 0.258819i$ of defining polynomial
Character	$\chi$	$=$	350.157
Dual form			350.2.o.b.243.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.258819 + 0.965926i) q^{2} +(2.63896 - 0.707107i) q^{3} +(-0.866025 - 0.500000i) q^{4} +2.73205i q^{6} +(-1.48356 - 2.19067i) q^{7} +(0.707107 - 0.707107i) q^{8} +(3.86603 - 2.23205i) q^{9} +O(q^{10})$	\(q+(-0.258819 + 0.965926i) q^{2} +(2.63896 - 0.707107i) q^{3} +(-0.866025 - 0.500000i) q^{4} +2.73205i q^{6} +(-1.48356 - 2.19067i) q^{7} +(0.707107 - 0.707107i) q^{8} +(3.86603 - 2.23205i) q^{9} +(2.36603 - 4.09808i) q^{11} +(-2.63896 - 0.707107i) q^{12} +(2.96713 + 2.96713i) q^{13} +(2.50000 - 0.866025i) q^{14} +(0.500000 + 0.866025i) q^{16} +(1.67303 + 6.24384i) q^{17} +(1.15539 + 4.31199i) q^{18} +(-5.46410 - 4.73205i) q^{21} +(3.34607 + 3.34607i) q^{22} +(-5.01910 - 1.34486i) q^{23} +(1.36603 - 2.36603i) q^{24} +(-3.63397 + 2.09808i) q^{26} +(2.82843 - 2.82843i) q^{27} +(0.189469 + 2.63896i) q^{28} -3.46410i q^{29} +(-1.50000 - 0.866025i) q^{31} +(-0.965926 + 0.258819i) q^{32} +(3.34607 - 12.4877i) q^{33} -6.46410 q^{34} -4.46410 q^{36} +(-1.79315 + 6.69213i) q^{37} +(9.92820 + 5.73205i) q^{39} +0.803848i q^{41} +(5.98502 - 4.05317i) q^{42} +(-5.13922 + 5.13922i) q^{43} +(-4.09808 + 2.36603i) q^{44} +(2.59808 - 4.50000i) q^{46} +(-9.58991 - 2.56961i) q^{47} +(1.93185 + 1.93185i) q^{48} +(-2.59808 + 6.50000i) q^{49} +(8.83013 + 15.2942i) q^{51} +(-1.08604 - 4.05317i) q^{52} +(0.568406 + 2.12132i) q^{53} +(2.00000 + 3.46410i) q^{54} +(-2.59808 - 0.500000i) q^{56} +(3.34607 + 0.896575i) q^{58} +(-1.90192 + 3.29423i) q^{59} +(9.29423 - 5.36603i) q^{61} +(1.22474 - 1.22474i) q^{62} +(-10.6252 - 5.15780i) q^{63} -1.00000i q^{64} +(11.1962 + 6.46410i) q^{66} +(13.7124 - 3.67423i) q^{67} +(1.67303 - 6.24384i) q^{68} -14.1962 q^{69} -7.39230 q^{71} +(1.15539 - 4.31199i) q^{72} +(7.72741 - 2.07055i) q^{73} +(-6.00000 - 3.46410i) q^{74} +(-12.4877 + 0.896575i) q^{77} +(-8.10634 + 8.10634i) q^{78} +(-8.13397 + 4.69615i) q^{79} +(-1.23205 + 2.13397i) q^{81} +(-0.776457 - 0.208051i) q^{82} +(-4.24264 - 4.24264i) q^{83} +(2.36603 + 6.83013i) q^{84} +(-3.63397 - 6.29423i) q^{86} +(-2.44949 - 9.14162i) q^{87} +(-1.22474 - 4.57081i) q^{88} +(0.401924 + 0.696152i) q^{89} +(2.09808 - 10.9019i) q^{91} +(3.67423 + 3.67423i) q^{92} +(-4.57081 - 1.22474i) q^{93} +(4.96410 - 8.59808i) q^{94} +(-2.36603 + 1.36603i) q^{96} +(6.64136 - 6.64136i) q^{97} +(-5.60609 - 4.19187i) q^{98} -21.1244i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 24 q^{9}+O(q^{10}) $ 8 * q + 24 * q^9	$ 8 q + 24 q^{9} + 12 q^{11} + 20 q^{14} + 4 q^{16} - 16 q^{21} + 4 q^{24} - 36 q^{26} - 12 q^{31} - 24 q^{34} - 8 q^{36} + 24 q^{39} - 12 q^{44} + 36 q^{51} + 16 q^{54} - 36 q^{59} + 12 q^{61} + 48 q^{66} - 72 q^{69} + 24 q^{71} - 48 q^{74} - 72 q^{79} + 4 q^{81} + 12 q^{84} - 36 q^{86} + 24 q^{89} - 4 q^{91} + 12 q^{94} - 12 q^{96}+O(q^{100}) $ 8 * q + 24 * q^9 + 12 * q^11 + 20 * q^14 + 4 * q^16 - 16 * q^21 + 4 * q^24 - 36 * q^26 - 12 * q^31 - 24 * q^34 - 8 * q^36 + 24 * q^39 - 12 * q^44 + 36 * q^51 + 16 * q^54 - 36 * q^59 + 12 * q^61 + 48 * q^66 - 72 * q^69 + 24 * q^71 - 48 * q^74 - 72 * q^79 + 4 * q^81 + 12 * q^84 - 36 * q^86 + 24 * q^89 - 4 * q^91 + 12 * q^94 - 12 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/350\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{4}\right)$

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 $

$2$	−0.258819	+	0.965926i	−0.183013	+	0.683013i
$2$	−0.258819	+	0.965926i	−0.183013	+	0.683013i
$3$	2.63896	−	0.707107i	1.52360	−	0.408248i	0.602677	−	0.797985i	$-0.294101\pi$
$3$	2.63896	−	0.707107i	1.52360	−	0.408248i	0.920926	+	0.389737i	$0.127434\pi$
$4$	−0.866025	−	0.500000i	−0.433013	−	0.250000i
$5$		0			0
$5$		0			0
$6$			2.73205i			1.11536i
$7$	−1.48356	−	2.19067i	−0.560734	−	0.827996i
$7$	−1.48356	−	2.19067i	−0.560734	−	0.827996i
$8$	0.707107	−	0.707107i	0.250000	−	0.250000i
$9$	3.86603	−	2.23205i	1.28868	−	0.744017i
$10$		0			0
$11$	2.36603	−	4.09808i	0.713384	−	1.23562i	−0.250196	−	0.968195i	$-0.580495\pi$
$11$	2.36603	−	4.09808i	0.713384	−	1.23562i	0.963580	−	0.267421i	$-0.0861715\pi$
$12$	−2.63896	−	0.707107i	−0.761802	−	0.204124i
$13$	2.96713	+	2.96713i	0.822933	+	0.822933i	0.986528	−	0.163594i	$-0.0523089\pi$
$13$	2.96713	+	2.96713i	0.822933	+	0.822933i	−0.163594	+	0.986528i	$0.552309\pi$
$14$	2.50000	−	0.866025i	0.668153	−	0.231455i
$15$		0			0
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$	1.67303	+	6.24384i	0.405770	+	1.51435i	0.802631	+	0.596476i	$0.203433\pi$
$17$	1.67303	+	6.24384i	0.405770	+	1.51435i	−0.396861	+	0.917879i	$0.629901\pi$
$18$	1.15539	+	4.31199i	0.272329	+	1.01635i
$19$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$19$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$20$		0			0
$21$	−5.46410	−	4.73205i	−1.19236	−	1.03262i
$22$	3.34607	+	3.34607i	0.713384	+	0.713384i
$23$	−5.01910	−	1.34486i	−1.04655	−	0.280423i	−0.305727	−	0.952119i	$-0.598900\pi$
$23$	−5.01910	−	1.34486i	−1.04655	−	0.280423i	−0.740827	+	0.671696i	$0.765566\pi$
$24$	1.36603	−	2.36603i	0.278839	−	0.482963i
$25$		0			0
$26$	−3.63397	+	2.09808i	−0.712681	+	0.411467i
$27$	2.82843	−	2.82843i	0.544331	−	0.544331i
$28$	0.189469	+	2.63896i	0.0358062	+	0.498716i
$29$		−	3.46410i		−	0.643268i	−0.946864	−	0.321634i	$-0.895768\pi$
$29$		−	3.46410i		−	0.643268i	0.946864	−	0.321634i	$-0.104232\pi$
$30$		0			0
$31$	−1.50000	−	0.866025i	−0.269408	−	0.155543i	0.359211	−	0.933257i	$-0.383046\pi$
$31$	−1.50000	−	0.866025i	−0.269408	−	0.155543i	−0.628619	+	0.777714i	$0.716379\pi$
$32$	−0.965926	+	0.258819i	−0.170753	+	0.0457532i
$33$	3.34607	−	12.4877i	0.582475	−	2.17383i
$34$	−6.46410			−1.10858
$35$		0			0
$36$	−4.46410			−0.744017
$37$	−1.79315	+	6.69213i	−0.294792	+	1.10018i	0.646590	+	0.762838i	$0.276194\pi$
$37$	−1.79315	+	6.69213i	−0.294792	+	1.10018i	−0.941382	+	0.337342i	$0.890472\pi$
$38$		0			0
$39$	9.92820	+	5.73205i	1.58978	+	0.917863i
$40$		0			0
$41$			0.803848i			0.125540i	0.998028	+	0.0627700i	$0.0199934\pi$
$41$			0.803848i			0.125540i	−0.998028	+	0.0627700i	$0.980007\pi$
$42$	5.98502	−	4.05317i	0.923509	−	0.625418i
$43$	−5.13922	+	5.13922i	−0.783723	+	0.783723i	−0.980457	−	0.196734i	$-0.936967\pi$
$43$	−5.13922	+	5.13922i	−0.783723	+	0.783723i	0.196734	+	0.980457i	$0.436967\pi$
$44$	−4.09808	+	2.36603i	−0.617808	+	0.356692i
$45$		0			0
$46$	2.59808	−	4.50000i	0.383065	−	0.663489i
$47$	−9.58991	−	2.56961i	−1.39883	−	0.374816i	−0.520907	−	0.853614i	$-0.674406\pi$
$47$	−9.58991	−	2.56961i	−1.39883	−	0.374816i	−0.877925	+	0.478798i	$0.841073\pi$
$48$	1.93185	+	1.93185i	0.278839	+	0.278839i
$49$	−2.59808	+	6.50000i	−0.371154	+	0.928571i
$50$		0			0
$51$	8.83013	+	15.2942i	1.23647	+	2.14162i
$52$	−1.08604	−	4.05317i	−0.150607	−	0.562074i
$53$	0.568406	+	2.12132i	0.0780766	+	0.291386i	0.993913	−	0.110165i	$-0.0351380\pi$
$53$	0.568406	+	2.12132i	0.0780766	+	0.291386i	−0.915837	+	0.401551i	$0.868471\pi$
$54$	2.00000	+	3.46410i	0.272166	+	0.471405i
$55$		0			0
$56$	−2.59808	−	0.500000i	−0.347183	−	0.0668153i
$57$		0			0
$58$	3.34607	+	0.896575i	0.439360	+	0.117726i
$59$	−1.90192	+	3.29423i	−0.247609	+	0.428872i	−0.962862	−	0.269994i	$-0.912978\pi$
$59$	−1.90192	+	3.29423i	−0.247609	+	0.428872i	0.715253	+	0.698866i	$0.246312\pi$
$60$		0			0
$61$	9.29423	−	5.36603i	1.19000	−	0.687049i	0.231697	−	0.972788i	$-0.425572\pi$
$61$	9.29423	−	5.36603i	1.19000	−	0.687049i	0.958307	+	0.285739i	$0.0922390\pi$
$62$	1.22474	−	1.22474i	0.155543	−	0.155543i
$63$	−10.6252	−	5.15780i	−1.33865	−	0.649822i
$64$		−	1.00000i		−	0.125000i
$65$		0			0
$66$	11.1962	+	6.46410i	1.37815	+	0.795676i
$67$	13.7124	−	3.67423i	1.67524	−	0.448879i	0.708724	−	0.705486i	$-0.249271\pi$
$67$	13.7124	−	3.67423i	1.67524	−	0.448879i	0.966516	+	0.256607i	$0.0826045\pi$
$68$	1.67303	−	6.24384i	0.202885	−	0.757177i
$69$	−14.1962			−1.70902
$70$		0			0
$71$	−7.39230			−0.877305			−0.438653	−	0.898657i	$-0.644544\pi$
$71$	−7.39230			−0.877305			−0.438653	+	0.898657i	$0.644544\pi$
$72$	1.15539	−	4.31199i	0.136165	−	0.508173i
$73$	7.72741	−	2.07055i	0.904425	−	0.242340i	0.223509	−	0.974702i	$-0.428249\pi$
$73$	7.72741	−	2.07055i	0.904425	−	0.242340i	0.680915	+	0.732362i	$0.261582\pi$
$74$	−6.00000	−	3.46410i	−0.697486	−	0.402694i
$75$		0			0
$76$		0			0
$77$	−12.4877	+	0.896575i	−1.42310	+	0.102174i
$78$	−8.10634	+	8.10634i	−0.917863	+	0.917863i
$79$	−8.13397	+	4.69615i	−0.915144	+	0.528358i	−0.882083	−	0.471095i	$-0.843859\pi$
$79$	−8.13397	+	4.69615i	−0.915144	+	0.528358i	−0.0330611	+	0.999453i	$0.510526\pi$
$80$		0			0
$81$	−1.23205	+	2.13397i	−0.136895	+	0.237108i
$82$	−0.776457	−	0.208051i	−0.0857453	−	0.0229754i
$83$	−4.24264	−	4.24264i	−0.465690	−	0.465690i	0.434825	−	0.900515i	$-0.356810\pi$
$83$	−4.24264	−	4.24264i	−0.465690	−	0.465690i	−0.900515	+	0.434825i	$0.856810\pi$
$84$	2.36603	+	6.83013i	0.258155	+	0.745228i
$85$		0			0
$86$	−3.63397	−	6.29423i	−0.391862	−	0.678724i
$87$	−2.44949	−	9.14162i	−0.262613	−	0.980085i
$88$	−1.22474	−	4.57081i	−0.130558	−	0.487250i
$89$	0.401924	+	0.696152i	0.0426038	+	0.0737920i	0.886541	−	0.462650i	$-0.153101\pi$
$89$	0.401924	+	0.696152i	0.0426038	+	0.0737920i	−0.843937	+	0.536442i	$0.819768\pi$
$90$		0			0
$91$	2.09808	−	10.9019i	0.219938	−	1.14283i
$92$	3.67423	+	3.67423i	0.383065	+	0.383065i
$93$	−4.57081	−	1.22474i	−0.473971	−	0.127000i
$94$	4.96410	−	8.59808i	0.512008	−	0.886824i
$95$		0			0
$96$	−2.36603	+	1.36603i	−0.241481	+	0.139419i
$97$	6.64136	−	6.64136i	0.674328	−	0.674328i	−0.284383	−	0.958711i	$-0.591789\pi$
$97$	6.64136	−	6.64136i	0.674328	−	0.674328i	0.958711	+	0.284383i	$0.0917886\pi$
$98$	−5.60609	−	4.19187i	−0.566300	−	0.423443i
$99$		−	21.1244i		−	2.12308i
$100$		0			0
$101$	−3.80385	−	2.19615i	−0.378497	−	0.218525i	0.298667	−	0.954357i	$-0.403458\pi$
$101$	−3.80385	−	2.19615i	−0.378497	−	0.218525i	−0.677164	+	0.735832i	$0.736791\pi$
$102$	−17.0585	+	4.57081i	−1.68904	+	0.452578i
$103$	−3.36465	+	12.5570i	−0.331529	+	1.23728i	0.576055	+	0.817411i	$0.304591\pi$
$103$	−3.36465	+	12.5570i	−0.331529	+	1.23728i	−0.907584	+	0.419871i	$0.862075\pi$
$104$	4.19615			0.411467
$105$		0			0
$106$	−2.19615			−0.213309
$107$	2.12132	−	7.91688i	0.205076	−	0.765353i	−0.784351	−	0.620318i	$-0.787004\pi$
$107$	2.12132	−	7.91688i	0.205076	−	0.765353i	0.989426	−	0.145036i	$-0.0463297\pi$
$108$	−3.86370	+	1.03528i	−0.371785	+	0.0996195i
$109$	0.169873	+	0.0980762i	0.0162709	+	0.00939400i	0.508113	−	0.861290i	$-0.330343\pi$
$109$	0.169873	+	0.0980762i	0.0162709	+	0.00939400i	−0.491842	+	0.870684i	$0.663676\pi$
$110$		0			0
$111$			18.9282i			1.79659i
$112$	1.15539	−	2.38014i	0.109175	−	0.224902i
$113$	−12.1595	+	12.1595i	−1.14387	+	1.14387i	−0.156135	+	0.987736i	$0.549904\pi$
$113$	−12.1595	+	12.1595i	−1.14387	+	1.14387i	−0.987736	+	0.156135i	$0.950096\pi$
$114$		0			0
$115$		0			0
$116$	−1.73205	+	3.00000i	−0.160817	+	0.278543i
$117$	18.0938	+	4.84821i	1.67277	+	0.448217i
$118$	−2.68973	−	2.68973i	−0.247609	−	0.247609i
$119$	11.1962	−	12.9282i	1.02635	−	1.18513i
$120$		0			0
$121$	−5.69615	−	9.86603i	−0.517832	−	0.896911i
$122$	2.77766	+	10.3664i	0.251477	+	0.938527i
$123$	0.568406	+	2.12132i	0.0512514	+	0.191273i
$124$	0.866025	+	1.50000i	0.0777714	+	0.134704i
$125$		0			0
$126$	7.73205	−	8.92820i	0.688826	−	0.795388i
$127$	−4.89898	−	4.89898i	−0.434714	−	0.434714i	0.455514	−	0.890228i	$-0.349455\pi$
$127$	−4.89898	−	4.89898i	−0.434714	−	0.434714i	−0.890228	+	0.455514i	$0.849455\pi$
$128$	0.965926	+	0.258819i	0.0853766	+	0.0228766i
$129$	−9.92820	+	17.1962i	−0.874130	+	1.51404i
$130$		0			0
$131$	7.09808	−	4.09808i	0.620162	−	0.358051i	−0.156770	−	0.987635i	$-0.550108\pi$
$131$	7.09808	−	4.09808i	0.620162	−	0.358051i	0.776932	+	0.629585i	$0.216775\pi$
$132$	−9.14162	+	9.14162i	−0.795676	+	0.795676i
$133$		0			0
$134$			14.1962i			1.22636i
$135$		0			0
$136$	5.59808	+	3.23205i	0.480031	+	0.277146i
$137$	−10.8147	+	2.89778i	−0.923958	+	0.247574i	−0.689276	−	0.724498i	$-0.742071\pi$
$137$	−10.8147	+	2.89778i	−0.923958	+	0.247574i	−0.234682	+	0.972072i	$0.575405\pi$
$138$	3.67423	−	13.7124i	0.312772	−	1.16728i
$139$	3.46410			0.293821			0.146911	−	0.989150i	$-0.453067\pi$
$139$	3.46410			0.293821			0.146911	+	0.989150i	$0.453067\pi$
$140$		0			0
$141$	−27.1244			−2.28428
$142$	1.91327	−	7.14042i	0.160558	−	0.599211i
$143$	19.1798	−	5.13922i	1.60390	−	0.429763i
$144$	3.86603	+	2.23205i	0.322169	+	0.186004i
$145$		0			0
$146$			8.00000i			0.662085i
$147$	−2.26002	+	18.9903i	−0.186403	+	1.56630i
$148$	4.89898	−	4.89898i	0.402694	−	0.402694i
$149$	1.90192	−	1.09808i	0.155812	−	0.0899579i	−0.420067	−	0.907493i	$-0.637993\pi$
$149$	1.90192	−	1.09808i	0.155812	−	0.0899579i	0.575879	+	0.817535i	$0.304660\pi$
$150$		0			0
$151$	1.19615	−	2.07180i	0.0973415	−	0.168600i	−0.813242	−	0.581926i	$-0.802299\pi$
$151$	1.19615	−	2.07180i	0.0973415	−	0.168600i	0.910583	+	0.413325i	$0.135633\pi$
$152$		0			0
$153$	20.4046	+	20.4046i	1.64961	+	1.64961i
$154$	2.36603	−	12.2942i	0.190660	−	0.990697i
$155$		0			0
$156$	−5.73205	−	9.92820i	−0.458931	−	0.794892i
$157$	0.517638	+	1.93185i	0.0413120	+	0.154179i	0.983501	−	0.180904i	$-0.0579024\pi$
$157$	0.517638	+	1.93185i	0.0413120	+	0.154179i	−0.942189	+	0.335083i	$0.891236\pi$
$158$	−2.43091	−	9.07227i	−0.193393	−	0.721751i
$159$	3.00000	+	5.19615i	0.237915	+	0.412082i
$160$		0			0
$161$	4.50000	+	12.9904i	0.354650	+	1.02379i
$162$	−1.74238	−	1.74238i	−0.136895	−	0.136895i
$163$	20.7327	+	5.55532i	1.62391	+	0.435126i	0.952148	−	0.305638i	$-0.0988698\pi$
$163$	20.7327	+	5.55532i	1.62391	+	0.435126i	0.671765	+	0.740764i	$0.265536\pi$
$164$	0.401924	−	0.696152i	0.0313850	−	0.0543604i
$165$		0			0
$166$	5.19615	−	3.00000i	0.403300	−	0.232845i
$167$	3.58630	−	3.58630i	0.277516	−	0.277516i	−0.554600	−	0.832117i	$-0.687129\pi$
$167$	3.58630	−	3.58630i	0.277516	−	0.277516i	0.832117	+	0.554600i	$0.187129\pi$
$168$	−7.20977	+	0.517638i	−0.556246	+	0.0399366i
$169$			4.60770i			0.354438i
$170$		0			0
$171$		0			0
$172$	7.02030	−	1.88108i	0.535293	−	0.143431i
$173$	−0.0879327	+	0.328169i	−0.00668540	+	0.0249503i	−0.969188	−	0.246322i	$-0.920778\pi$
$173$	−0.0879327	+	0.328169i	−0.00668540	+	0.0249503i	0.962503	+	0.271273i	$0.0874445\pi$
$174$	9.46410			0.717472
$175$		0			0
$176$	4.73205			0.356692
$177$	−2.68973	+	10.0382i	−0.202172	+	0.754517i
$178$	−0.776457	+	0.208051i	−0.0581979	+	0.0155941i
$179$	1.90192	+	1.09808i	0.142156	+	0.0820741i	0.569391	−	0.822067i	$-0.307179\pi$
$179$	1.90192	+	1.09808i	0.142156	+	0.0820741i	−0.427235	+	0.904141i	$0.640512\pi$
$180$		0			0
$181$			10.7321i			0.797707i	0.917015	+	0.398854i	$0.130592\pi$
$181$			10.7321i			0.797707i	−0.917015	+	0.398854i	$0.869408\pi$
$182$	9.98743	+	4.84821i	0.740317	+	0.359373i
$183$	20.7327	−	20.7327i	1.53261	−	1.53261i
$184$	−4.50000	+	2.59808i	−0.331744	+	0.191533i
$185$		0			0
$186$	2.36603	−	4.09808i	0.173485	−	0.300486i
$187$	29.5462	+	7.91688i	2.16063	+	0.578939i
$188$	7.02030	+	7.02030i	0.512008	+	0.512008i
$189$	−10.3923	−	2.00000i	−0.755929	−	0.145479i
$190$		0			0
$191$	6.23205	+	10.7942i	0.450935	+	0.781043i	0.998444	−	0.0557568i	$-0.0177572\pi$
$191$	6.23205	+	10.7942i	0.450935	+	0.781043i	−0.547509	+	0.836800i	$0.684424\pi$
$192$	−0.707107	−	2.63896i	−0.0510310	−	0.190450i
$193$	−3.13801	−	11.7112i	−0.225879	−	0.842993i	−0.982050	−	0.188619i	$-0.939599\pi$
$193$	−3.13801	−	11.7112i	−0.225879	−	0.842993i	0.756171	−	0.654374i	$-0.227068\pi$
$194$	4.69615	+	8.13397i	0.337164	+	0.583985i
$195$		0			0
$196$	5.50000	−	4.33013i	0.392857	−	0.309295i
$197$	−1.55291	−	1.55291i	−0.110641	−	0.110641i	0.649619	−	0.760260i	$-0.274928\pi$
$197$	−1.55291	−	1.55291i	−0.110641	−	0.110641i	−0.760260	+	0.649619i	$0.774928\pi$
$198$	20.4046	+	5.46739i	1.45009	+	0.388550i
$199$	8.13397	−	14.0885i	0.576602	−	0.998704i	−0.419263	−	0.907865i	$-0.637712\pi$
$199$	8.13397	−	14.0885i	0.576602	−	0.998704i	0.995866	−	0.0908396i	$-0.0289551\pi$
$200$		0			0
$201$	33.5885	−	19.3923i	2.36915	−	1.36783i
$202$	3.10583	−	3.10583i	0.218525	−	0.218525i
$203$	−7.58871	+	5.13922i	−0.532623	+	0.360702i
$204$		−	17.6603i		−	1.23647i
$205$		0			0
$206$	−11.2583	−	6.50000i	−0.784405	−	0.452876i
$207$	−22.4058	+	6.00361i	−1.55731	+	0.417279i
$208$	−1.08604	+	4.05317i	−0.0753036	+	0.281037i
$209$		0			0
$210$		0			0
$211$	0.196152			0.0135037			0.00675184	−	0.999977i	$-0.497851\pi$
$211$	0.196152			0.0135037			0.00675184	+	0.999977i	$0.497851\pi$
$212$	0.568406	−	2.12132i	0.0390383	−	0.145693i
$213$	−19.5080	+	5.22715i	−1.33667	+	0.358158i
$214$	7.09808	+	4.09808i	0.485215	+	0.280139i
$215$		0			0
$216$		−	4.00000i		−	0.272166i
$217$	0.328169	+	4.57081i	0.0222776	+	0.310287i
$218$	−0.138701	+	0.138701i	−0.00939400	+	0.00939400i
$219$	18.9282	−	10.9282i	1.27905	−	0.738460i
$220$		0			0
$221$	−13.5622	+	23.4904i	−0.912291	+	1.58013i
$222$	−18.2832	−	4.89898i	−1.22709	−	0.328798i
$223$	8.05558	+	8.05558i	0.539441	+	0.539441i	0.923365	−	0.383924i	$-0.125427\pi$
$223$	8.05558	+	8.05558i	0.539441	+	0.539441i	−0.383924	+	0.923365i	$0.625427\pi$
$224$	2.00000	+	1.73205i	0.133631	+	0.115728i
$225$		0			0
$226$	−8.59808	−	14.8923i	−0.571936	−	0.990621i
$227$	−5.31508	−	19.8362i	−0.352774	−	1.31657i	−0.883262	−	0.468879i	$-0.844658\pi$
$227$	−5.31508	−	19.8362i	−0.352774	−	1.31657i	0.530488	−	0.847693i	$-0.322009\pi$
$228$		0			0
$229$	1.90192	+	3.29423i	0.125683	+	0.217689i	0.922000	−	0.387191i	$-0.126555\pi$
$229$	1.90192	+	3.29423i	0.125683	+	0.217689i	−0.796317	+	0.604880i	$0.793221\pi$
$230$		0			0
$231$	−32.3205	+	11.1962i	−2.12653	+	0.736653i
$232$	−2.44949	−	2.44949i	−0.160817	−	0.160817i
$233$	−5.79555	−	1.55291i	−0.379679	−	0.101735i	0.0639315	−	0.997954i	$-0.479636\pi$
$233$	−5.79555	−	1.55291i	−0.379679	−	0.101735i	−0.443611	+	0.896219i	$0.646303\pi$
$234$	−9.36603	+	16.2224i	−0.612276	+	1.06049i
$235$		0			0
$236$	3.29423	−	1.90192i	0.214436	−	0.123805i
$237$	−18.1445	+	18.1445i	−1.17861	+	1.17861i
$238$	9.58991	+	14.1607i	0.621621	+	0.917903i
$239$			4.85641i			0.314135i	0.987588	+	0.157067i	$0.0502040\pi$
$239$			4.85641i			0.314135i	−0.987588	+	0.157067i	$0.949796\pi$
$240$		0			0
$241$	−3.00000	−	1.73205i	−0.193247	−	0.111571i	0.400255	−	0.916404i	$-0.368922\pi$
$241$	−3.00000	−	1.73205i	−0.193247	−	0.111571i	−0.593502	+	0.804833i	$0.702255\pi$
$242$	11.0041	−	2.94855i	0.707372	−	0.189540i
$243$	−4.84821	+	18.0938i	−0.311013	+	1.16072i
$244$	−10.7321			−0.687049
$245$		0			0
$246$	−2.19615			−0.140022
$247$		0			0
$248$	−1.67303	+	0.448288i	−0.106238	+	0.0284663i
$249$	−14.1962	−	8.19615i	−0.899645	−	0.519410i
$250$		0			0
$251$		−	16.3923i		−	1.03467i	−0.855782	−	0.517337i	$-0.826924\pi$
$251$		−	16.3923i		−	1.03467i	0.855782	−	0.517337i	$-0.173076\pi$
$252$	6.62278	+	9.77938i	0.417196	+	0.616043i
$253$	−17.3867	+	17.3867i	−1.09309	+	1.09309i
$254$	6.00000	−	3.46410i	0.376473	−	0.217357i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−15.8338	−	4.24264i	−0.987682	−	0.264649i	−0.271406	−	0.962465i	$-0.587488\pi$
$257$	−15.8338	−	4.24264i	−0.987682	−	0.264649i	−0.716277	+	0.697816i	$0.754155\pi$
$258$	−14.0406	−	14.0406i	−0.874130	−	0.874130i
$259$	17.3205	−	6.00000i	1.07624	−	0.372822i
$260$		0			0
$261$	−7.73205	−	13.3923i	−0.478602	−	0.828963i
$262$	2.12132	+	7.91688i	0.131056	+	0.489106i
$263$	−7.14042	−	26.6484i	−0.440297	−	1.64321i	−0.728063	−	0.685510i	$-0.759579\pi$
$263$	−7.14042	−	26.6484i	−0.440297	−	1.64321i	0.287766	−	0.957701i	$-0.407087\pi$
$264$	−6.46410	−	11.1962i	−0.397838	−	0.689076i
$265$		0			0
$266$		0			0
$267$	1.55291	+	1.55291i	0.0950368	+	0.0950368i
$268$	−13.7124	−	3.67423i	−0.837620	−	0.224440i
$269$	9.29423	−	16.0981i	0.566679	−	0.981517i	−0.430212	−	0.902728i	$-0.641561\pi$
$269$	9.29423	−	16.0981i	0.566679	−	0.981517i	0.996891	−	0.0787892i	$-0.0251054\pi$
$270$		0			0
$271$	−11.0885	+	6.40192i	−0.673576	+	0.388889i	−0.797430	−	0.603411i	$-0.793808\pi$
$271$	−11.0885	+	6.40192i	−0.673576	+	0.388889i	0.123854	+	0.992300i	$0.460474\pi$
$272$	−4.57081	+	4.57081i	−0.277146	+	0.277146i
$273$	−2.17209	−	30.2533i	−0.131461	−	1.83101i
$274$		−	11.1962i		−	0.676384i
$275$		0			0
$276$	12.2942	+	7.09808i	0.740026	+	0.427254i
$277$	23.7506	−	6.36396i	1.42704	−	0.382373i	0.539062	−	0.842266i	$-0.318779\pi$
$277$	23.7506	−	6.36396i	1.42704	−	0.382373i	0.887975	+	0.459893i	$0.152112\pi$
$278$	−0.896575	+	3.34607i	−0.0537730	+	0.200684i
$279$	−7.73205			−0.462906
$280$		0			0
$281$	17.5359			1.04610			0.523052	−	0.852301i	$-0.324793\pi$
$281$	17.5359			1.04610			0.523052	+	0.852301i	$0.324793\pi$
$282$	7.02030	−	26.2001i	0.418053	−	1.56019i
$283$	−17.7656	+	4.76028i	−1.05606	+	0.282969i	−0.744752	−	0.667341i	$-0.767432\pi$
$283$	−17.7656	+	4.76028i	−1.05606	+	0.282969i	−0.311303	+	0.950311i	$0.600766\pi$
$284$	6.40192	+	3.69615i	0.379884	+	0.219326i
$285$		0			0
$286$			19.8564i			1.17413i
$287$	1.76097	−	1.19256i	0.103946	−	0.0703945i
$288$	−3.15660	+	3.15660i	−0.186004	+	0.186004i
$289$	−21.4641	+	12.3923i	−1.26259	+	0.728959i
$290$		0			0
$291$	12.8301	−	22.2224i	0.752115	−	1.30270i
$292$	−7.72741	−	2.07055i	−0.452212	−	0.121170i
$293$	2.92996	+	2.92996i	0.171170	+	0.171170i	0.787493	−	0.616323i	$-0.211378\pi$
$293$	2.92996	+	2.92996i	0.171170	+	0.171170i	−0.616323	+	0.787493i	$0.711378\pi$
$294$	−17.7583	−	7.09808i	−1.03569	−	0.413968i
$295$		0			0
$296$	3.46410	+	6.00000i	0.201347	+	0.348743i
$297$	−4.89898	−	18.2832i	−0.284268	−	1.06090i
$298$	0.568406	+	2.12132i	0.0329269	+	0.122885i
$299$	−10.9019	−	18.8827i	−0.630475	−	1.09201i
$300$		0			0
$301$	18.8827	+	3.63397i	1.08838	+	0.209459i
$302$	1.69161	+	1.69161i	0.0973415	+	0.0973415i
$303$	−11.5911	−	3.10583i	−0.665892	−	0.178425i
$304$		0			0
$305$		0			0
$306$	−24.9904	+	14.4282i	−1.42860	+	0.824805i
$307$	5.93426	−	5.93426i	0.338686	−	0.338686i	−0.517187	−	0.855873i	$-0.673021\pi$
$307$	5.93426	−	5.93426i	0.338686	−	0.338686i	0.855873	+	0.517187i	$0.173021\pi$
$308$	11.2629	+	5.46739i	0.641766	+	0.311533i
$309$			35.5167i			2.02047i
$310$		0			0
$311$	9.69615	+	5.59808i	0.549818	+	0.317438i	0.749049	−	0.662515i	$-0.230511\pi$
$311$	9.69615	+	5.59808i	0.549818	+	0.317438i	−0.199230	+	0.979953i	$0.563844\pi$
$312$	11.0735	−	2.96713i	0.626912	−	0.167981i
$313$	4.91756	−	18.3526i	0.277957	−	1.03735i	−0.675877	−	0.737015i	$-0.736235\pi$
$313$	4.91756	−	18.3526i	0.277957	−	1.03735i	0.953834	−	0.300335i	$-0.0970985\pi$
$314$	−2.00000			−0.112867
$315$		0			0
$316$	9.39230			0.528358
$317$	−1.13681	+	4.24264i	−0.0638497	+	0.238290i	−0.990474	−	0.137697i	$-0.956030\pi$
$317$	−1.13681	+	4.24264i	−0.0638497	+	0.238290i	0.926625	+	0.375988i	$0.122697\pi$
$318$	−5.79555	+	1.55291i	−0.324999	+	0.0870831i
$319$	−14.1962	−	8.19615i	−0.794832	−	0.458896i
$320$		0			0
$321$		−	22.3923i		−	1.24982i
$322$	−13.7124	+	0.984508i	−0.764164	+	0.0548645i
$323$		0			0
$324$	2.13397	−	1.23205i	0.118554	−	0.0684473i
$325$		0			0
$326$	−10.7321	+	18.5885i	−0.594393	+	1.02952i
$327$	0.517638	+	0.138701i	0.0286255	+	0.00767017i
$328$	0.568406	+	0.568406i	0.0313850	+	0.0313850i
$329$	8.59808	+	24.8205i	0.474027	+	1.36840i
$330$		0			0
$331$	7.00000	+	12.1244i	0.384755	+	0.666415i	0.991735	−	0.128302i	$-0.0409527\pi$
$331$	7.00000	+	12.1244i	0.384755	+	0.666415i	−0.606980	+	0.794717i	$0.707619\pi$
$332$	1.55291	+	5.79555i	0.0852272	+	0.318072i
$333$	8.00481	+	29.8744i	0.438661	+	1.63710i
$334$	2.53590	+	4.39230i	0.138758	+	0.240336i
$335$		0			0
$336$	1.36603	−	7.09808i	0.0745228	−	0.387232i
$337$	−6.12372	−	6.12372i	−0.333581	−	0.333581i	0.520364	−	0.853945i	$-0.325796\pi$
$337$	−6.12372	−	6.12372i	−0.333581	−	0.333581i	−0.853945	+	0.520364i	$0.825796\pi$
$338$	−4.45069	−	1.19256i	−0.242086	−	0.0648667i
$339$	−23.4904	+	40.6865i	−1.27582	+	2.20979i
$340$		0			0
$341$	−7.09808	+	4.09808i	−0.384382	+	0.221923i
$342$		0			0
$343$	18.0938	−	3.95164i	0.976972	−	0.213368i
$344$			7.26795i			0.391862i
$345$		0			0
$346$	−0.294229	−	0.169873i	−0.0158178	−	0.00913243i
$347$	5.79555	−	1.55291i	0.311122	−	0.0833648i	−0.0998797	−	0.995000i	$-0.531846\pi$
$347$	5.79555	−	1.55291i	0.311122	−	0.0833648i	0.411001	+	0.911635i	$0.365179\pi$
$348$	−2.44949	+	9.14162i	−0.131306	+	0.490042i
$349$	34.9808			1.87248			0.936239	−	0.351365i	$-0.114282\pi$
$349$	34.9808			1.87248			0.936239	+	0.351365i	$0.114282\pi$
$350$		0			0
$351$	16.7846			0.895896
$352$	−1.22474	+	4.57081i	−0.0652791	+	0.243625i
$353$	29.4261	−	7.88469i	1.56619	−	0.419660i	0.631574	−	0.775315i	$-0.282409\pi$
$353$	29.4261	−	7.88469i	1.56619	−	0.419660i	0.934617	+	0.355656i	$0.115742\pi$
$354$	−9.00000	−	5.19615i	−0.478345	−	0.276172i
$355$		0			0
$356$		−	0.803848i		−	0.0426038i
$357$	20.4046	−	42.0339i	1.07992	−	2.22467i
$358$	−1.55291	+	1.55291i	−0.0820741	+	0.0820741i
$359$	−9.00000	+	5.19615i	−0.475002	+	0.274242i	−0.718331	−	0.695701i	$-0.755094\pi$
$359$	−9.00000	+	5.19615i	−0.475002	+	0.274242i	0.243329	+	0.969944i	$0.421760\pi$
$360$		0			0
$361$	9.50000	−	16.4545i	0.500000	−	0.866025i
$362$	−10.3664	−	2.77766i	−0.544844	−	0.145991i
$363$	−22.0082	−	22.0082i	−1.15513	−	1.15513i
$364$	−7.26795	+	8.39230i	−0.380944	+	0.439876i
$365$		0			0
$366$	14.6603	+	25.3923i	0.766304	+	1.32728i
$367$	−0.619174	−	2.31079i	−0.0323206	−	0.120622i	0.947881	−	0.318625i	$-0.103221\pi$
$367$	−0.619174	−	2.31079i	−0.0323206	−	0.120622i	−0.980201	+	0.198003i	$0.936554\pi$
$368$	−1.34486	−	5.01910i	−0.0701058	−	0.261639i
$369$	1.79423	+	3.10770i	0.0934038	+	0.161780i
$370$		0			0
$371$	3.80385	−	4.39230i	0.197486	−	0.228037i
$372$	3.34607	+	3.34607i	0.173485	+	0.173485i
$373$	−33.7888	−	9.05369i	−1.74952	−	0.468782i	−0.764996	−	0.644036i	$-0.777259\pi$
$373$	−33.7888	−	9.05369i	−1.74952	−	0.468782i	−0.984523	+	0.175253i	$0.943926\pi$
$374$	−15.2942	+	26.4904i	−0.790846	+	1.36978i
$375$		0			0
$376$	−8.59808	+	4.96410i	−0.443412	+	0.256004i
$377$	10.2784	−	10.2784i	0.529366	−	0.529366i
$378$	4.62158	−	9.52056i	0.237708	−	0.489685i
$379$			22.5885i			1.16029i	0.814513	+	0.580146i	$0.197004\pi$
$379$			22.5885i			1.16029i	−0.814513	+	0.580146i	$0.802996\pi$
$380$		0			0
$381$	−16.3923	−	9.46410i	−0.839803	−	0.484861i
$382$	−12.0394	+	3.22595i	−0.615989	+	0.165054i
$383$	−4.60300	+	17.1786i	−0.235202	+	0.877786i	0.742856	+	0.669452i	$0.233471\pi$
$383$	−4.60300	+	17.1786i	−0.235202	+	0.877786i	−0.978058	+	0.208334i	$0.933196\pi$
$384$	2.73205			0.139419
$385$		0			0
$386$	12.1244			0.617113
$387$	−8.39735	+	31.3393i	−0.426861	+	1.59307i
$388$	−9.07227	+	2.43091i	−0.460575	+	0.123411i
$389$	−29.4904	−	17.0263i	−1.49522	−	0.863267i	−0.495237	−	0.868758i	$-0.664919\pi$
$389$	−29.4904	−	17.0263i	−1.49522	−	0.863267i	−0.999985	+	0.00549142i	$0.998252\pi$
$390$		0			0
$391$		−	33.5885i		−	1.69864i
$392$	2.75908	+	6.43331i	0.139354	+	0.324931i
$393$	15.8338	−	15.8338i	0.798707	−	0.798707i
$394$	1.90192	−	1.09808i	0.0958175	−	0.0553203i
$395$		0			0
$396$	−10.5622	+	18.2942i	−0.530769	+	0.919320i
$397$	1.93185	+	0.517638i	0.0969569	+	0.0259795i	0.306971	−	0.951719i	$-0.400684\pi$
$397$	1.93185	+	0.517638i	0.0969569	+	0.0259795i	−0.210014	+	0.977698i	$0.567351\pi$
$398$	11.5032	+	11.5032i	0.576602	+	0.576602i
$399$		0			0
$400$		0			0
$401$	12.4641	+	21.5885i	0.622428	+	1.07808i	0.989032	+	0.147699i	$0.0471868\pi$
$401$	12.4641	+	21.5885i	0.622428	+	1.07808i	−0.366605	+	0.930377i	$0.619480\pi$
$402$	10.0382	+	37.4631i	0.500660	+	1.86849i
$403$	−1.88108	−	7.02030i	−0.0937035	−	0.349706i
$404$	2.19615	+	3.80385i	0.109263	+	0.189248i
$405$		0			0
$406$	−3.00000	−	8.66025i	−0.148888	−	0.429801i
$407$	23.1822	+	23.1822i	1.14910	+	1.14910i
$408$	17.0585	+	4.57081i	0.844521	+	0.226289i
$409$	11.5981	−	20.0885i	0.573488	−	0.993310i	−0.422716	−	0.906262i	$-0.638923\pi$
$409$	11.5981	−	20.0885i	0.573488	−	0.993310i	0.996204	−	0.0870481i	$-0.0277434\pi$
$410$		0			0
$411$	−26.4904	+	15.2942i	−1.30667	+	0.754409i
$412$	9.19239	−	9.19239i	0.452876	−	0.452876i
$413$	10.0382	−	0.720710i	0.493947	−	0.0354638i
$414$		−	23.1962i		−	1.14003i
$415$		0			0
$416$	−3.63397	−	2.09808i	−0.178170	−	0.102867i
$417$	9.14162	−	2.44949i	0.447667	−	0.119952i
$418$		0			0
$419$	−22.9808			−1.12268			−0.561342	−	0.827584i	$-0.689715\pi$
$419$	−22.9808			−1.12268			−0.561342	+	0.827584i	$0.689715\pi$
$420$		0			0
$421$	−36.3923			−1.77365			−0.886826	−	0.462103i	$-0.847095\pi$
$421$	−36.3923			−1.77365			−0.886826	+	0.462103i	$0.847095\pi$
$422$	−0.0507680	+	0.189469i	−0.00247135	+	0.00922319i
$423$	−42.8103	+	11.4710i	−2.08151	+	0.557739i
$424$	1.90192	+	1.09808i	0.0923656	+	0.0533273i
$425$		0			0
$426$		−	20.1962i		−	0.978507i
$427$	−25.5438	−	12.3998i	−1.23615	−	0.600066i
$428$	−5.79555	+	5.79555i	−0.280139	+	0.280139i
$429$	46.9808	−	27.1244i	2.26825	−	1.30958i
$430$		0			0
$431$	12.2321	−	21.1865i	0.589197	−	1.02052i	−0.405141	−	0.914254i	$-0.632777\pi$
$431$	12.2321	−	21.1865i	0.589197	−	1.02052i	0.994338	−	0.106265i	$-0.0338892\pi$
$432$	3.86370	+	1.03528i	0.185893	+	0.0498097i
$433$	−21.3383	−	21.3383i	−1.02545	−	1.02545i	−0.999667	−	0.0257858i	$-0.991791\pi$
$433$	−21.3383	−	21.3383i	−1.02545	−	1.02545i	−0.0257858	−	0.999667i	$-0.508209\pi$
$434$	−4.50000	−	0.866025i	−0.216007	−	0.0415705i
$435$		0			0
$436$	−0.0980762	−	0.169873i	−0.00469700	−	0.00813544i
$437$		0			0
$438$	5.65685	+	21.1117i	0.270295	+	1.00875i
$439$	15.0622	+	26.0885i	0.718879	+	1.24513i	0.961444	+	0.274999i	$0.0886776\pi$
$439$	15.0622	+	26.0885i	0.718879	+	1.24513i	−0.242566	+	0.970135i	$0.577989\pi$
$440$		0			0
$441$	4.46410	+	30.9282i	0.212576	+	1.47277i
$442$	−19.1798	−	19.1798i	−0.912291	−	0.912291i
$443$	11.5911	+	3.10583i	0.550710	+	0.147562i	0.523435	−	0.852066i	$-0.324650\pi$
$443$	11.5911	+	3.10583i	0.550710	+	0.147562i	0.0272752	+	0.999628i	$0.491317\pi$
$444$	9.46410	−	16.3923i	0.449146	−	0.777944i
$445$		0			0
$446$	−9.86603	+	5.69615i	−0.467170	+	0.269721i
$447$	4.24264	−	4.24264i	0.200670	−	0.200670i
$448$	−2.19067	+	1.48356i	−0.103499	+	0.0700918i
$449$		−	26.3205i		−	1.24214i	−0.783754	−	0.621071i	$-0.786698\pi$
$449$		−	26.3205i		−	1.24214i	0.783754	−	0.621071i	$-0.213302\pi$
$450$		0			0
$451$	3.29423	+	1.90192i	0.155119	+	0.0895581i
$452$	16.6102	−	4.45069i	0.781278	−	0.209343i
$453$	1.69161	−	6.31319i	0.0794790	−	0.296620i
$454$	20.5359			0.963797
$455$		0			0
$456$		0			0
$457$	−10.2141	+	38.1194i	−0.477794	+	1.78315i	0.132730	+	0.991152i	$0.457626\pi$
$457$	−10.2141	+	38.1194i	−0.477794	+	1.78315i	−0.610524	+	0.791998i	$0.709041\pi$
$458$	−3.67423	+	0.984508i	−0.171686	+	0.0460030i
$459$	22.3923	+	12.9282i	1.04518	+	0.603437i
$460$		0			0
$461$		−	24.0000i		−	1.11779i	−0.829238	−	0.558896i	$-0.811225\pi$
$461$		−	24.0000i		−	1.11779i	0.829238	−	0.558896i	$-0.188775\pi$
$462$	−2.44949	−	34.1170i	−0.113961	−	1.58727i
$463$	18.8516	−	18.8516i	0.876110	−	0.876110i	−0.117019	−	0.993130i	$-0.537334\pi$
$463$	18.8516	−	18.8516i	0.876110	−	0.876110i	0.993130	+	0.117019i	$0.0373339\pi$
$464$	3.00000	−	1.73205i	0.139272	−	0.0804084i
$465$		0			0
$466$	3.00000	−	5.19615i	0.138972	−	0.240707i
$467$	−35.6699	−	9.55772i	−1.65061	−	0.442279i	−0.690824	−	0.723023i	$-0.742752\pi$
$467$	−35.6699	−	9.55772i	−1.65061	−	0.442279i	−0.959783	+	0.280744i	$0.909419\pi$
$468$	−13.2456	−	13.2456i	−0.612276	−	0.612276i
$469$	−28.3923	−	24.5885i	−1.31103	−	1.13539i
$470$		0			0
$471$	2.73205	+	4.73205i	0.125886	+	0.218041i
$472$	0.984508	+	3.67423i	0.0453157	+	0.169120i
$473$	8.90138	+	33.2204i	0.409286	+	1.52748i
$474$	−12.8301	−	22.2224i	−0.589307	−	1.02071i
$475$		0			0
$476$	−16.1603	+	5.59808i	−0.740704	+	0.256587i
$477$	6.93237	+	6.93237i	0.317411	+	0.317411i
$478$	−4.69093	−	1.25693i	−0.214558	−	0.0574907i
$479$	11.5981	−	20.0885i	0.529930	−	0.917865i	−0.469461	−	0.882953i	$-0.655552\pi$
$479$	11.5981	−	20.0885i	0.529930	−	0.917865i	0.999390	−	0.0349117i	$-0.0111150\pi$
$480$		0			0
$481$	−25.1769	+	14.5359i	−1.14797	+	0.662780i
$482$	2.44949	−	2.44949i	0.111571	−	0.111571i
$483$	21.0609	+	31.0991i	0.958304	+	1.41506i
$484$			11.3923i			0.517832i
$485$		0			0
$486$	−16.2224	−	9.36603i	−0.735864	−	0.424852i
$487$	−25.7518	+	6.90018i	−1.16693	+	0.312677i	−0.789729	−	0.613456i	$-0.789779\pi$
$487$	−25.7518	+	6.90018i	−1.16693	+	0.312677i	−0.377198	+	0.926133i	$0.623112\pi$
$488$	2.77766	−	10.3664i	0.125739	−	0.469263i
$489$	58.6410			2.65184
$490$		0			0
$491$	22.0526			0.995218			0.497609	−	0.867401i	$-0.334211\pi$
$491$	22.0526			0.995218			0.497609	+	0.867401i	$0.334211\pi$
$492$	0.568406	−	2.12132i	0.0256257	−	0.0956365i
$493$	21.6293	−	5.79555i	0.974135	−	0.261019i
$494$		0			0
$495$		0			0
$496$		−	1.73205i		−	0.0777714i
$497$	10.9670	+	16.1941i	0.491935	+	0.726405i
$498$	11.5911	−	11.5911i	0.519410	−	0.519410i
$499$	−33.2487	+	19.1962i	−1.48842	+	0.859338i	−0.999913	−	0.0132238i	$-0.995791\pi$
$499$	−33.2487	+	19.1962i	−1.48842	+	0.859338i	−0.488504	+	0.872562i	$0.662457\pi$
$500$		0			0
$501$	6.92820	−	12.0000i	0.309529	−	0.536120i
$502$	15.8338	+	4.24264i	0.706695	+	0.189358i
$503$	−17.6269	−	17.6269i	−0.785945	−	0.785945i	0.194882	−	0.980827i	$-0.437568\pi$
$503$	−17.6269	−	17.6269i	−0.785945	−	0.785945i	−0.980827	+	0.194882i	$0.937568\pi$
$504$	−11.1603	+	3.86603i	−0.497117	+	0.172206i
$505$		0			0
$506$	−12.2942	−	21.2942i	−0.546545	−	0.946644i
$507$	3.25813	+	12.1595i	0.144699	+	0.540023i
$508$	1.79315	+	6.69213i	0.0795582	+	0.296915i
$509$	−8.49038	−	14.7058i	−0.376330	−	0.651822i	0.614196	−	0.789154i	$-0.289481\pi$
$509$	−8.49038	−	14.7058i	−0.376330	−	0.651822i	−0.990525	+	0.137332i	$0.956147\pi$
$510$		0			0
$511$	−16.0000	−	13.8564i	−0.707798	−	0.612971i
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$		0			0
$514$	8.19615	−	14.1962i	0.361517	−	0.626165i
$515$		0			0
$516$	17.1962	−	9.92820i	0.757018	−	0.437065i
$517$	−33.2204	+	33.2204i	−1.46103	+	1.46103i
$518$	1.31268	+	18.2832i	0.0576757	+	0.803319i
$519$			0.928203i			0.0407436i
$520$		0			0
$521$	−2.08846	−	1.20577i	−0.0914970	−	0.0528258i	0.453553	−	0.891229i	$-0.350156\pi$
$521$	−2.08846	−	1.20577i	−0.0914970	−	0.0528258i	−0.545050	+	0.838403i	$0.683489\pi$
$522$	14.9372	−	4.00240i	0.653782	−	0.175180i
$523$	−2.58819	+	9.65926i	−0.113174	+	0.422370i	−0.999144	−	0.0413724i	$-0.986827\pi$
$523$	−2.58819	+	9.65926i	−0.113174	+	0.422370i	0.885970	+	0.463742i	$0.153494\pi$
$524$	−8.19615			−0.358051
$525$		0			0
$526$	27.5885			1.20291
$527$	2.89778	−	10.8147i	0.126229	−	0.471094i
$528$	12.4877	−	3.34607i	0.543457	−	0.145619i
$529$	3.46410	+	2.00000i	0.150613	+	0.0869565i
$530$		0			0
$531$			16.9808i			0.736902i
$532$		0			0
$533$	−2.38512	+	2.38512i	−0.103311	+	0.103311i
$534$	−1.90192	+	1.09808i	−0.0823043	+	0.0475184i
$535$		0			0
$536$	7.09808	−	12.2942i	0.306590	−	0.531030i
$537$	5.79555	+	1.55291i	0.250097	+	0.0670132i
$538$	13.1440	+	13.1440i	0.566679	+	0.566679i
$539$	20.4904	+	26.0263i	0.882583	+	1.12103i
$540$		0			0
$541$	3.90192	+	6.75833i	0.167757	+	0.290563i	0.937631	−	0.347633i	$-0.113014\pi$
$541$	3.90192	+	6.75833i	0.167757	+	0.290563i	−0.769874	+	0.638196i	$0.779681\pi$
$542$	−3.31388	−	12.3676i	−0.142343	−	0.531232i
$543$	7.58871	+	28.3214i	0.325663	+	1.21539i
$544$	−3.23205	−	5.59808i	−0.138573	−	0.240016i
$545$		0			0
$546$	29.7846	+	5.73205i	1.27466	+	0.245309i
$547$	−5.37945	−	5.37945i	−0.230009	−	0.230009i	0.582688	−	0.812696i	$-0.302001\pi$
$547$	−5.37945	−	5.37945i	−0.230009	−	0.230009i	−0.812696	+	0.582688i	$0.802001\pi$
$548$	10.8147	+	2.89778i	0.461979	+	0.123787i
$549$	23.9545	−	41.4904i	1.02235	−	1.77077i
$550$		0			0
$551$		0			0
$552$	−10.0382	+	10.0382i	−0.427254	+	0.427254i
$553$	22.3550	+	10.8518i	0.950631	+	0.461466i
$554$			24.5885i			1.04466i
$555$		0			0
$556$	−3.00000	−	1.73205i	−0.127228	−	0.0734553i
$557$	7.91688	−	2.12132i	0.335449	−	0.0898832i	−0.0871629	−	0.996194i	$-0.527780\pi$
$557$	7.91688	−	2.12132i	0.335449	−	0.0898832i	0.422612	+	0.906311i	$0.361113\pi$
$558$	2.00120	−	7.46859i	0.0847176	−	0.316171i
$559$	−30.4974			−1.28990
$560$		0			0
$561$	83.5692			3.52830
$562$	−4.53862	+	16.9384i	−0.191450	+	0.714502i
$563$	−0.568406	+	0.152304i	−0.0239555	+	0.00641885i	−0.270777	−	0.962642i	$-0.587281\pi$
$563$	−0.568406	+	0.152304i	−0.0239555	+	0.00641885i	0.246821	+	0.969061i	$0.420614\pi$
$564$	23.4904	+	13.5622i	0.989123	+	0.571071i
$565$		0			0
$566$		−	18.3923i		−	0.773086i
$567$	6.50266	−	0.466870i	0.273086	−	0.0196067i
$568$	−5.22715	+	5.22715i	−0.219326	+	0.219326i
$569$	15.4019	−	8.89230i	0.645682	−	0.372785i	−0.141118	−	0.989993i	$-0.545070\pi$
$569$	15.4019	−	8.89230i	0.645682	−	0.372785i	0.786800	+	0.617208i	$0.211736\pi$
$570$		0			0
$571$	−22.5885	+	39.1244i	−0.945298	+	1.63730i	−0.190143	+	0.981756i	$0.560895\pi$
$571$	−22.5885	+	39.1244i	−0.945298	+	1.63730i	−0.755154	+	0.655547i	$0.772438\pi$
$572$	−19.1798	−	5.13922i	−0.801948	−	0.214881i
$573$	24.0788	+	24.0788i	1.00591	+	1.00591i
$574$	0.696152	+	2.00962i	0.0290568	+	0.0838799i
$575$		0			0
$576$	−2.23205	−	3.86603i	−0.0930021	−	0.161084i
$577$	−3.20736	−	11.9700i	−0.133524	−	0.498320i	0.866475	−	0.499220i	$-0.166380\pi$
$577$	−3.20736	−	11.9700i	−0.133524	−	0.498320i	−1.00000		0.000900421i	$0.999713\pi$
$578$	−6.41473	−	23.9401i	−0.266818	−	0.995777i
$579$	−16.5622	−	28.6865i	−0.688301	−	1.19217i
$580$		0			0
$581$	−3.00000	+	15.5885i	−0.124461	+	0.646718i
$582$	18.1445	+	18.1445i	0.752115	+	0.752115i
$583$	10.0382	+	2.68973i	0.415740	+	0.111397i
$584$	4.00000	−	6.92820i	0.165521	−	0.286691i
$585$		0			0
$586$	−3.58846	+	2.07180i	−0.148238	+	0.0855851i
$587$	10.0382	−	10.0382i	0.414321	−	0.414321i	−0.468920	−	0.883241i	$-0.655357\pi$
$587$	10.0382	−	10.0382i	0.414321	−	0.414321i	0.883241	+	0.468920i	$0.155357\pi$
$588$	11.4524	−	15.3161i	0.472289	−	0.631626i
$589$		0			0
$590$		0			0
$591$	−5.19615	−	3.00000i	−0.213741	−	0.123404i
$592$	−6.69213	+	1.79315i	−0.275045	+	0.0736980i
$593$	5.19496	−	19.3879i	0.213332	−	0.796164i	−0.773416	−	0.633899i	$-0.781453\pi$
$593$	5.19496	−	19.3879i	0.213332	−	0.796164i	0.986747	−	0.162265i	$-0.0518799\pi$
$594$	18.9282			0.776634
$595$		0			0
$596$	−2.19615			−0.0899579
$597$	11.5032	−	42.9304i	0.470794	−	1.75703i
$598$	21.0609	−	5.64325i	0.861244	−	0.230770i
$599$	12.1865	+	7.03590i	0.497928	+	0.287479i	0.727858	−	0.685728i	$-0.240516\pi$
$599$	12.1865	+	7.03590i	0.497928	+	0.287479i	−0.229929	+	0.973207i	$0.573850\pi$
$600$		0			0
$601$			38.7846i			1.58206i	0.611779	+	0.791029i	$0.290454\pi$
$601$			38.7846i			1.58206i	−0.611779	+	0.791029i	$0.709546\pi$
$602$	−8.39735	+	17.2987i	−0.342250	+	0.705044i
$603$	44.8115	−	44.8115i	1.82487	−	1.82487i
$604$	−2.07180	+	1.19615i	−0.0843002	+	0.0486708i
$605$		0			0
$606$	6.00000	−	10.3923i	0.243733	−	0.422159i
$607$	34.9442	+	9.36327i	1.41834	+	0.380044i	0.884895	−	0.465790i	$-0.154230\pi$
$607$	34.9442	+	9.36327i	1.41834	+	0.380044i	0.533447	+	0.845834i	$0.320896\pi$
$608$		0			0
$609$	−16.3923	+	18.9282i	−0.664250	+	0.767010i
$610$		0			0
$611$	−20.8301	−	36.0788i	−0.842697	−	1.45959i
$612$	−7.46859	−	27.8731i	−0.301900	−	1.12671i
$613$	−4.65874	−	17.3867i	−0.188165	−	0.702241i	−0.993931	−	0.110007i	$-0.964913\pi$
$613$	−4.65874	−	17.3867i	−0.188165	−	0.702241i	0.805766	−	0.592234i	$-0.201754\pi$
$614$	4.19615	+	7.26795i	0.169343	+	0.293311i
$615$		0			0
$616$	−8.19615	+	9.46410i	−0.330232	+	0.381320i
$617$	−27.9933	−	27.9933i	−1.12697	−	1.12697i	−0.990668	−	0.136299i	$-0.956479\pi$
$617$	−27.9933	−	27.9933i	−1.12697	−	1.12697i	−0.136299	−	0.990668i	$-0.543521\pi$
$618$	−34.3065	−	9.19239i	−1.38001	−	0.369772i
$619$	5.53590	−	9.58846i	0.222507	−	0.385393i	−0.733062	−	0.680162i	$-0.761909\pi$
$619$	5.53590	−	9.58846i	0.222507	−	0.385393i	0.955568	+	0.294769i	$0.0952428\pi$
$620$		0			0
$621$	−18.0000	+	10.3923i	−0.722315	+	0.417029i
$622$	−7.91688	+	7.91688i	−0.317438	+	0.317438i
$623$	0.928761	−	1.91327i	0.0372100	−	0.0766535i
$624$			11.4641i			0.458931i
$625$		0			0
$626$	16.4545	+	9.50000i	0.657653	+	0.379696i
$627$		0			0
$628$	0.517638	−	1.93185i	0.0206560	−	0.0770893i
$629$	−44.7846			−1.78568
$630$		0			0
$631$	3.39230			0.135046			0.0675228	−	0.997718i	$-0.478490\pi$
$631$	3.39230			0.135046			0.0675228	+	0.997718i	$0.478490\pi$
$632$	−2.43091	+	9.07227i	−0.0966963	+	0.360876i
$633$	0.517638	−	0.138701i	0.0205743	−	0.00551286i
$634$	−3.80385	−	2.19615i	−0.151070	−	0.0872204i
$635$		0			0
$636$		−	6.00000i		−	0.237915i
$637$	−26.9952	+	11.5775i	−1.06959	+	0.458718i
$638$	11.5911	−	11.5911i	0.458896	−	0.458896i
$639$	−28.5788	+	16.5000i	−1.13056	+	0.652730i
$640$		0			0
$641$	−13.5000	+	23.3827i	−0.533218	+	0.923561i	0.466029	+	0.884769i	$0.345684\pi$
$641$	−13.5000	+	23.3827i	−0.533218	+	0.923561i	−0.999247	+	0.0387913i	$0.987649\pi$
$642$	21.6293	+	5.79555i	0.853641	+	0.228732i
$643$	−21.9067	−	21.9067i	−0.863916	−	0.863916i	0.127874	−	0.991790i	$-0.459185\pi$
$643$	−21.9067	−	21.9067i	−0.863916	−	0.863916i	−0.991790	+	0.127874i	$0.959185\pi$
$644$	2.59808	−	13.5000i	0.102379	−	0.531975i
$645$		0			0
$646$		0			0
$647$	12.0072	+	44.8115i	0.472052	+	1.76172i	0.632379	+	0.774659i	$0.282078\pi$
$647$	12.0072	+	44.8115i	0.472052	+	1.76172i	−0.160327	+	0.987064i	$0.551255\pi$
$648$	0.637756	+	2.38014i	0.0250534	+	0.0935007i
$649$	9.00000	+	15.5885i	0.353281	+	0.611900i
$650$		0			0
$651$	4.09808	+	11.8301i	0.160616	+	0.463659i
$652$	−15.1774	−	15.1774i	−0.594393	−	0.594393i
$653$	−9.46979	−	2.53742i	−0.370582	−	0.0992970i	0.0687217	−	0.997636i	$-0.478108\pi$
$653$	−9.46979	−	2.53742i	−0.370582	−	0.0992970i	−0.439303	+	0.898339i	$0.644775\pi$
$654$	−0.267949	+	0.464102i	−0.0104776	+	0.0181478i
$655$		0			0
$656$	−0.696152	+	0.401924i	−0.0271802	+	0.0156925i
$657$	25.2528	−	25.2528i	0.985204	−	0.985204i
$658$	−26.2001	+	1.88108i	−1.02139	+	0.0733323i
$659$			5.32051i			0.207258i	0.994616	+	0.103629i	$0.0330454\pi$
$659$			5.32051i			0.207258i	−0.994616	+	0.103629i	$0.966955\pi$
$660$		0			0
$661$	9.29423	+	5.36603i	0.361504	+	0.208714i	0.669740	−	0.742596i	$-0.266405\pi$
$661$	9.29423	+	5.36603i	0.361504	+	0.208714i	−0.308237	+	0.951310i	$0.599739\pi$
$662$	−13.5230	+	3.62347i	−0.525585	+	0.140830i
$663$	−19.1798	+	71.5800i	−0.744882	+	2.77994i
$664$	−6.00000			−0.232845
$665$		0			0
$666$	−30.9282			−1.19844
$667$	−4.65874	+	17.3867i	−0.180387	+	0.673214i
$668$	−4.89898	+	1.31268i	−0.189547	+	0.0507890i
$669$	26.9545	+	15.5622i	1.04212	+	0.601669i
$670$		0			0
$671$		−	50.7846i		−	1.96052i
$672$	6.50266	+	3.15660i	0.250846	+	0.121768i
$673$	−6.12372	+	6.12372i	−0.236052	+	0.236052i	−0.815213	−	0.579161i	$-0.803380\pi$
$673$	−6.12372	+	6.12372i	−0.236052	+	0.236052i	0.579161	+	0.815213i	$0.303380\pi$
$674$	7.50000	−	4.33013i	0.288889	−	0.166790i
$675$		0			0
$676$	2.30385	−	3.99038i	0.0886095	−	0.153476i
$677$	39.9125	+	10.6945i	1.53396	+	0.411024i	0.924310	−	0.381643i	$-0.124642\pi$
$677$	39.9125	+	10.6945i	1.53396	+	0.411024i	0.609654	+	0.792668i	$0.291308\pi$
$678$	−33.2204	−	33.2204i	−1.27582	−	1.27582i
$679$	−24.4019	−	4.69615i	−0.936460	−	0.180222i
$680$		0			0
$681$	−28.0526	−	48.5885i	−1.07498	−	1.86191i
$682$	−2.12132	−	7.91688i	−0.0812296	−	0.303153i
$683$	6.93237	+	25.8719i	0.265260	+	0.989963i	0.962091	+	0.272728i	$0.0879258\pi$
$683$	6.93237	+	25.8719i	0.265260	+	0.989963i	−0.696832	+	0.717235i	$0.745408\pi$
$684$		0			0
$685$		0			0
$686$	−0.866025	+	18.5000i	−0.0330650	+	0.706333i
$687$	7.34847	+	7.34847i	0.280362	+	0.280362i
$688$	−7.02030	−	1.88108i	−0.267646	−	0.0717156i
$689$	−4.60770	+	7.98076i	−0.175539	+	0.304043i
$690$		0			0
$691$	−9.58846	+	5.53590i	−0.364762	+	0.210595i	−0.671168	−	0.741306i	$-0.734207\pi$
$691$	−9.58846	+	5.53590i	−0.364762	+	0.210595i	0.306406	+	0.951901i	$0.400874\pi$
$692$	0.240237	−	0.240237i	0.00913243	−	0.00913243i
$693$	−46.2765	+	31.3393i	−1.75790	+	1.19048i
$694$			6.00000i			0.227757i
$695$		0			0
$696$	−8.19615	−	4.73205i	−0.310674	−	0.179368i
$697$	−5.01910	+	1.34486i	−0.190112	+	0.0509403i
$698$	−9.05369	+	33.7888i	−0.342687	+	1.27893i
$699$	−16.3923			−0.620014
$700$		0			0
$701$	−10.1436			−0.383118			−0.191559	−	0.981481i	$-0.561354\pi$
$701$	−10.1436			−0.383118			−0.191559	+	0.981481i	$0.561354\pi$
$702$	−4.34418	+	16.2127i	−0.163960	+	0.611908i
$703$		0			0
$704$	−4.09808	−	2.36603i	−0.154452	−	0.0891729i
$705$		0			0
$706$			30.4641i			1.14653i
$707$	0.832204	+	11.5911i	0.0312983	+	0.435929i
$708$	7.34847	−	7.34847i	0.276172	−	0.276172i
$709$	18.5429	−	10.7058i	0.696395	−	0.402064i	−0.109608	−	0.993975i	$-0.534960\pi$
$709$	18.5429	−	10.7058i	0.696395	−	0.402064i	0.806003	+	0.591911i	$0.201626\pi$
$710$		0			0
$711$	−20.9641	+	36.3109i	−0.786215	+	1.36176i
$712$	0.776457	+	0.208051i	0.0290990	+	0.00779704i
$713$	6.36396	+	6.36396i	0.238332	+	0.238332i
$714$	35.3205	+	30.5885i	1.32184	+	1.14474i
$715$		0			0
$716$	−1.09808	−	1.90192i	−0.0410370	−	0.0710782i
$717$	3.43400	+	12.8159i	0.128245	+	0.478617i
$718$	−2.68973	−	10.0382i	−0.100380	−	0.374622i
$719$	−4.20577	−	7.28461i	−0.156849	−	0.271670i	0.776882	−	0.629646i	$-0.216800\pi$
$719$	−4.20577	−	7.28461i	−0.156849	−	0.271670i	−0.933731	+	0.357976i	$0.883467\pi$
$720$		0			0
$721$	32.5000	−	11.2583i	1.21036	−	0.419282i
$722$	13.4350	+	13.4350i	0.500000	+	0.500000i
$723$	−9.14162	−	2.44949i	−0.339981	−	0.0910975i
$724$	5.36603	−	9.29423i	0.199427	−	0.345417i
$725$		0			0
$726$	26.9545	−	15.5622i	1.00037	−	0.577567i
$727$	13.4350	−	13.4350i	0.498278	−	0.498278i	−0.412624	−	0.910902i	$-0.635388\pi$
$727$	13.4350	−	13.4350i	0.498278	−	0.498278i	0.910902	+	0.412624i	$0.135388\pi$
$728$	−6.22526	−	9.19239i	−0.230723	−	0.340693i
$729$			43.7846i			1.62165i
$730$		0			0
$731$	−40.6865	−	23.4904i	−1.50485	−	0.868823i
$732$	−28.3214	+	7.58871i	−1.04679	+	0.280487i
$733$	−3.62347	+	13.5230i	−0.133836	+	0.499482i	−1.00000		0.000277595i	$-0.999912\pi$
$733$	−3.62347	+	13.5230i	−0.133836	+	0.499482i	0.866164	+	0.499760i	$0.166578\pi$
$734$	2.39230			0.0883016
$735$		0			0
$736$	5.19615			0.191533
$737$	17.3867	−	64.8879i	0.640446	−	2.39018i
$738$	−3.46618	+	0.928761i	−0.127592	+	0.0341882i
$739$	−17.3205	−	10.0000i	−0.637145	−	0.367856i	0.146369	−	0.989230i	$-0.453241\pi$
$739$	−17.3205	−	10.0000i	−0.637145	−	0.367856i	−0.783514	+	0.621374i	$0.786575\pi$
$740$		0			0
$741$		0			0
$742$	3.25813	+	4.81105i	0.119610	+	0.176619i
$743$	−17.5390	+	17.5390i	−0.643442	+	0.643442i	−0.951400	−	0.307958i	$-0.900354\pi$
$743$	−17.5390	+	17.5390i	−0.643442	+	0.643442i	0.307958	+	0.951400i	$0.400354\pi$
$744$	−4.09808	+	2.36603i	−0.150243	+	0.0867427i
$745$		0			0
$746$	17.4904	−	30.2942i	0.640368	−	1.10915i
$747$	−25.8719	−	6.93237i	−0.946605	−	0.253642i
$748$	−21.6293	−	21.6293i	−0.790846	−	0.790846i
$749$	−20.4904	+	7.09808i	−0.748702	+	0.259358i
$750$		0			0
$751$	−7.00000	−	12.1244i	−0.255434	−	0.442424i	0.709580	−	0.704625i	$-0.248885\pi$
$751$	−7.00000	−	12.1244i	−0.255434	−	0.442424i	−0.965013	+	0.262201i	$0.915552\pi$
$752$	−2.56961	−	9.58991i	−0.0937040	−	0.349708i
$753$	−11.5911	−	43.2586i	−0.422404	−	1.57643i
$754$	7.26795	+	12.5885i	0.264683	+	0.458445i
$755$		0			0
$756$	8.00000	+	6.92820i	0.290957	+	0.251976i
$757$	−14.9372	−	14.9372i	−0.542901	−	0.542901i	0.381477	−	0.924378i	$-0.375415\pi$
$757$	−14.9372	−	14.9372i	−0.542901	−	0.542901i	−0.924378	+	0.381477i	$0.875415\pi$
$758$	−21.8188	−	5.84632i	−0.792494	−	0.212348i
$759$	−33.5885	+	58.1769i	−1.21918	+	2.11169i
$760$		0			0
$761$	7.28461	−	4.20577i	0.264067	−	0.152459i	−0.362121	−	0.932131i	$-0.617947\pi$
$761$	7.28461	−	4.20577i	0.264067	−	0.152459i	0.626188	+	0.779672i	$0.284614\pi$
$762$	13.3843	−	13.3843i	0.484861	−	0.484861i
$763$	−0.0371647	−	0.517638i	−0.00134545	−	0.0187398i
$764$		−	12.4641i		−	0.450935i
$765$		0			0
$766$	−15.4019	−	8.89230i	−0.556494	−	0.321292i
$767$	−15.4176	+	4.13115i	−0.556699	+	0.149167i
$768$	−0.707107	+	2.63896i	−0.0255155	+	0.0952252i
$769$	45.7128			1.64845			0.824223	−	0.566265i	$-0.191612\pi$
$769$	45.7128			1.64845			0.824223	+	0.566265i	$0.191612\pi$
$770$		0			0
$771$	−44.7846			−1.61288
$772$	−3.13801	+	11.7112i	−0.112940	+	0.421496i
$773$	−29.2180	+	7.82894i	−1.05090	+	0.281587i	−0.742623	−	0.669710i	$-0.766419\pi$
$773$	−29.2180	+	7.82894i	−1.05090	+	0.281587i	−0.308276	+	0.951297i	$0.599752\pi$
$774$	−28.0981	−	16.2224i	−1.00996	−	0.583103i
$775$		0			0
$776$		−	9.39230i		−	0.337164i
$777$	41.4655	−	28.0812i	1.48757	−	1.00741i
$778$	24.0788	−	24.0788i	0.863267	−	0.863267i
$779$		0			0
$780$		0			0
$781$	−17.4904	+	30.2942i	−0.625855	+	1.08401i
$782$	32.4440	+	8.69333i	1.16019	+	0.310873i
$783$	−9.79796	−	9.79796i	−0.350150	−	0.350150i
$784$	−6.92820	+	1.00000i	−0.247436	+	0.0357143i
$785$		0			0
$786$	11.1962	+	19.3923i	0.399354	+	0.691701i
$787$	−4.34418	−	16.2127i	−0.154853	−	0.577920i	−0.999118	−	0.0419935i	$-0.986629\pi$
$787$	−4.34418	−	16.2127i	−0.154853	−	0.577920i	0.844265	−	0.535926i	$-0.180038\pi$
$788$	0.568406	+	2.12132i	0.0202486	+	0.0755689i
$789$	−37.6865	−	65.2750i	−1.34168	−	2.32385i
$790$		0			0
$791$	44.6769	+	8.59808i	1.58853	+	0.305712i
$792$	−14.9372	−	14.9372i	−0.530769	−	0.530769i
$793$	43.4988	+	11.6555i	1.54469	+	0.413898i
$794$	−1.00000	+	1.73205i	−0.0354887	+	0.0614682i
$795$		0			0
$796$	−14.0885	+	8.13397i	−0.499352	+	0.288301i
$797$	−6.45189	+	6.45189i	−0.228538	+	0.228538i	−0.812082	−	0.583544i	$-0.801666\pi$
$797$	−6.45189	+	6.45189i	−0.228538	+	0.228538i	0.583544	+	0.812082i	$0.301666\pi$
$798$		0			0
$799$		−	64.1769i		−	2.27042i
$800$		0			0
$801$	3.10770	+	1.79423i	0.109805	+	0.0633960i
$802$	−24.0788	+	6.45189i	−0.850252	+	0.227824i
$803$	9.79796	−	36.5665i	0.345762	−	1.29040i
$804$	−38.7846			−1.36783
$805$		0			0
$806$	7.26795			0.256003
$807$	13.1440	−	49.0542i	0.462692	−	1.72679i
$808$	−4.24264	+	1.13681i	−0.149256	+	0.0399929i
$809$	4.39230	+	2.53590i	0.154425	+	0.0891574i	0.575221	−	0.817998i	$-0.304916\pi$
$809$	4.39230	+	2.53590i	0.154425	+	0.0891574i	−0.420796	+	0.907155i	$0.638249\pi$
$810$		0			0
$811$			41.9090i			1.47162i	0.677187	+	0.735811i	$0.263199\pi$
$811$			41.9090i			1.47162i	−0.677187	+	0.735811i	$0.736801\pi$
$812$	9.14162	−	0.656339i	0.320808	−	0.0230330i
$813$	−24.7351	+	24.7351i	−0.867499	+	0.867499i
$814$	−28.3923	+	16.3923i	−0.995150	+	0.574550i
$815$		0			0
$816$	−8.83013	+	15.2942i	−0.309116	+	0.535405i
$817$		0			0
$818$	16.4022	+	16.4022i	0.573488	+	0.573488i
$819$	−16.2224	−	46.8301i	−0.566858	−	1.63638i
$820$		0			0
$821$	22.0526	+	38.1962i	0.769640	+	1.33305i	0.937758	+	0.347288i	$0.112897\pi$
$821$	22.0526	+	38.1962i	0.769640	+	1.33305i	−0.168119	+	0.985767i	$0.553769\pi$
$822$	−7.91688	−	29.5462i	−0.276133	−	1.03054i
$823$	−0.896575	−	3.34607i	−0.0312527	−	0.116637i	0.948537	−	0.316665i	$-0.102563\pi$
$823$	−0.896575	−	3.34607i	−0.0312527	−	0.116637i	−0.979790	+	0.200029i	$0.935896\pi$
$824$	6.50000	+	11.2583i	0.226438	+	0.392203i
$825$		0			0
$826$	−1.90192	+	9.88269i	−0.0661764	+	0.343863i
$827$	7.34847	+	7.34847i	0.255531	+	0.255531i	0.823234	−	0.567702i	$-0.192168\pi$
$827$	7.34847	+	7.34847i	0.255531	+	0.255531i	−0.567702	+	0.823234i	$0.692168\pi$
$828$	22.4058	+	6.00361i	0.778654	+	0.208640i
$829$	−8.83013	+	15.2942i	−0.306683	+	0.531191i	−0.977635	−	0.210311i	$-0.932552\pi$
$829$	−8.83013	+	15.2942i	−0.306683	+	0.531191i	0.670952	+	0.741501i	$0.265886\pi$
$830$		0			0
$831$	58.1769	−	33.5885i	2.01813	−	1.16517i
$832$	2.96713	−	2.96713i	0.102867	−	0.102867i
$833$	−44.9316	−	5.34727i	−1.55679	−	0.185272i
$834$			9.46410i			0.327715i
$835$		0			0
$836$		0			0
$837$	−6.69213	+	1.79315i	−0.231314	+	0.0619804i
$838$	5.94786	−	22.1977i	0.205465	−	0.766807i
$839$	55.9808			1.93267			0.966335	−	0.257286i	$-0.0828283\pi$
$839$	55.9808			1.93267			0.966335	+	0.257286i	$0.0828283\pi$
$840$		0			0
$841$	17.0000			0.586207
$842$	9.41902	−	35.1523i	0.324601	−	1.21143i
$843$	46.2765	−	12.3998i	1.59385	−	0.427070i
$844$	−0.169873	−	0.0980762i	−0.00584727	−	0.00337592i
$845$		0			0
$846$		−	44.3205i		−	1.52377i
$847$	−13.1626	+	27.1153i	−0.452273	+	0.931692i
$848$	−1.55291	+	1.55291i	−0.0533273	+	0.0533273i
$849$	−43.5167	+	25.1244i	−1.49349	+	0.862266i
$850$		0			0
$851$	18.0000	−	31.1769i	0.617032	−	1.06873i
$852$	19.5080	+	5.22715i	0.668333	+	0.179079i
$853$	−20.2151	−	20.2151i	−0.692152	−	0.692152i	0.270553	−	0.962705i	$-0.412793\pi$
$853$	−20.2151	−	20.2151i	−0.692152	−	0.692152i	−0.962705	+	0.270553i	$0.912793\pi$
$854$	18.5885	−	21.4641i	0.636084	−	0.734486i
$855$		0			0
$856$	−4.09808	−	7.09808i	−0.140069	−	0.242607i
$857$	12.3118	+	45.9483i	0.420564	+	1.56957i	0.773424	+	0.633889i	$0.218542\pi$
$857$	12.3118	+	45.9483i	0.420564	+	1.56957i	−0.352860	+	0.935676i	$0.614791\pi$
$858$	14.0406	+	52.4002i	0.479338	+	1.78891i
$859$	26.4904	+	45.8827i	0.903840	+	1.56550i	0.822467	+	0.568813i	$0.192597\pi$
$859$	26.4904	+	45.8827i	0.903840	+	1.56550i	0.0813735	+	0.996684i	$0.474069\pi$
$860$		0			0
$861$	3.80385	−	4.39230i	0.129635	−	0.149689i
$862$	17.2987	+	17.2987i	0.589197	+	0.589197i
$863$	12.3676	+	3.31388i	0.420997	+	0.112806i	0.463097	−	0.886308i	$-0.346738\pi$
$863$	12.3676	+	3.31388i	0.420997	+	0.112806i	−0.0421001	+	0.999113i	$0.513405\pi$
$864$	−2.00000	+	3.46410i	−0.0680414	+	0.117851i
$865$		0			0
$866$	26.1340	−	15.0885i	0.888069	−	0.512727i
$867$	−47.8802	+	47.8802i	−1.62610	+	1.62610i
$868$	2.00120	−	4.12252i	0.0679252	−	0.139928i
$869$			44.4449i			1.50769i
$870$		0			0
$871$	51.5885	+	29.7846i	1.74801	+	1.00921i
$872$	0.189469	−	0.0507680i	0.00641622	−	0.00171922i
$873$	10.8518	−	40.4995i	0.367278	−	1.37070i
$874$		0			0
$875$		0			0
$876$	−21.8564			−0.738460
$877$	6.18810	−	23.0943i	0.208957	−	0.779839i	−0.779250	−	0.626714i	$-0.784400\pi$
$877$	6.18810	−	23.0943i	0.208957	−	0.779839i	0.988207	−	0.153125i	$-0.0489337\pi$
$878$	−29.0979	+	7.79676i	−0.982006	+	0.263128i
$879$	9.80385	+	5.66025i	0.330676	+	0.190916i
$880$		0			0
$881$			27.5885i			0.929479i	0.885448	+	0.464739i	$0.153852\pi$
$881$			27.5885i			0.929479i	−0.885448	+	0.464739i	$0.846148\pi$
$882$	−31.0297	−	3.69282i	−1.04483	−	0.124344i
$883$	1.96902	−	1.96902i	0.0662627	−	0.0662627i	−0.673199	−	0.739462i	$-0.735080\pi$
$883$	1.96902	−	1.96902i	0.0662627	−	0.0662627i	0.739462	+	0.673199i	$0.235080\pi$
$884$	23.4904	−	13.5622i	0.790067	−	0.456145i
$885$		0			0
$886$	−6.00000	+	10.3923i	−0.201574	+	0.349136i
$887$	−10.0382	−	2.68973i	−0.337050	−	0.0903122i	0.0863246	−	0.996267i	$-0.472488\pi$
$887$	−10.0382	−	2.68973i	−0.337050	−	0.0903122i	−0.423374	+	0.905955i	$0.639154\pi$
$888$	13.3843	+	13.3843i	0.449146	+	0.449146i
$889$	−3.46410	+	18.0000i	−0.116182	+	0.603701i
$890$		0			0
$891$	5.83013	+	10.0981i	0.195317	+	0.338298i
$892$	−2.94855	−	11.0041i	−0.0987246	−	0.368445i
$893$		0			0
$894$	3.00000	+	5.19615i	0.100335	+	0.173785i
$895$		0			0
$896$	−0.866025	−	2.50000i	−0.0289319	−	0.0835191i
$897$	−42.1218	−	42.1218i	−1.40641	−	1.40641i
$898$	25.4237	+	6.81225i	0.848398	+	0.227328i
$899$	−3.00000	+	5.19615i	−0.100056	+	0.173301i
$900$		0			0
$901$	−12.2942	+	7.09808i	−0.409580	+	0.236471i
$902$	−2.68973	+	2.68973i	−0.0895581	+	0.0895581i
$903$	52.4002	−	3.76217i	1.74377	−	0.125197i
$904$			17.1962i			0.571936i
$905$		0			0
$906$	5.66025	+	3.26795i	0.188049	+	0.108570i
$907$	−4.33057	+	1.16037i	−0.143794	+	0.0385296i	−0.329998	−	0.943982i	$-0.607048\pi$
$907$	−4.33057	+	1.16037i	−0.143794	+	0.0385296i	0.186204	+	0.982511i	$0.440381\pi$
$908$	−5.31508	+	19.8362i	−0.176387	+	0.658286i
$909$	−19.6077			−0.650346
$910$		0			0
$911$	−10.1769			−0.337176			−0.168588	−	0.985687i	$-0.553921\pi$
$911$	−10.1769			−0.337176			−0.168588	+	0.985687i	$0.553921\pi$
$912$		0			0
$913$	−27.4249	+	7.34847i	−0.907630	+	0.243199i
$914$	−34.1769	−	19.7321i	−1.13047	−	0.652678i
$915$		0			0
$916$		−	3.80385i		−	0.125683i
$917$	−19.5080	−	9.46979i	−0.644210	−	0.312720i
$918$	−18.2832	+	18.2832i	−0.603437	+	0.603437i
$919$	6.06218	−	3.50000i	0.199973	−	0.115454i	−0.396670	−	0.917961i	$-0.629834\pi$
$919$	6.06218	−	3.50000i	0.199973	−	0.115454i	0.596643	+	0.802507i	$0.296501\pi$
$920$		0			0
$921$	11.4641	−	19.8564i	0.377755	−	0.654291i
$922$	23.1822	+	6.21166i	0.763466	+	0.204570i
$923$	−21.9339	−	21.9339i	−0.721964	−	0.721964i
$924$	33.5885	+	6.46410i	1.10498	+	0.212653i
$925$		0			0
$926$	13.3301	+	23.0885i	0.438055	+	0.758734i
$927$	15.0201	+	56.0559i	0.493326	+	1.84112i
$928$	0.896575	+	3.34607i	0.0294315	+	0.109840i
$929$	−22.3923	−	38.7846i	−0.734668	−	1.27248i	−0.954869	−	0.297027i	$-0.904005\pi$
$929$	−22.3923	−	38.7846i	−0.734668	−	1.27248i	0.220201	−	0.975454i	$-0.429329\pi$
$930$		0			0
$931$		0			0
$932$	4.24264	+	4.24264i	0.138972	+	0.138972i
$933$	29.5462	+	7.91688i	0.967299	+	0.259187i
$934$	18.4641	−	31.9808i	0.604164	−	1.04644i
$935$		0			0
$936$	16.2224	−	9.36603i	0.530247	−	0.306138i
$937$	−9.34469	+	9.34469i	−0.305278	+	0.305278i	−0.843075	−	0.537797i	$-0.819257\pi$
$937$	−9.34469	+	9.34469i	−0.305278	+	0.305278i	0.537797	+	0.843075i	$0.319257\pi$
$938$	31.0991	−	21.0609i	1.01542	−	0.687663i
$939$		−	51.9090i		−	1.69399i
$940$		0			0
$941$	−30.2942	−	17.4904i	−0.987564	−	0.570170i	−0.0830185	−	0.996548i	$-0.526456\pi$
$941$	−30.2942	−	17.4904i	−0.987564	−	0.570170i	−0.904545	+	0.426378i	$0.859789\pi$
$942$	−5.27792	+	1.41421i	−0.171964	+	0.0460776i
$943$	1.08107	−	4.03459i	0.0352043	−	0.131384i
$944$	−3.80385			−0.123805
$945$		0			0
$946$	−34.3923			−1.11819
$947$	5.37945	−	20.0764i	0.174809	−	0.652395i	−0.821775	−	0.569812i	$-0.807016\pi$
$947$	5.37945	−	20.0764i	0.174809	−	0.652395i	0.996584	−	0.0825835i	$-0.0263171\pi$
$948$	24.7859	−	6.64136i	0.805009	−	0.215701i
$949$	29.0718	+	16.7846i	0.943710	+	0.544851i
$950$		0			0
$951$			12.0000i			0.389127i
$952$	−1.22474	−	17.0585i	−0.0396942	−	0.552869i
$953$	−23.1822	+	23.1822i	−0.750946	+	0.750946i	−0.974656	−	0.223710i	$-0.928183\pi$
$953$	−23.1822	+	23.1822i	−0.750946	+	0.750946i	0.223710	+	0.974656i	$0.428183\pi$
$954$	−8.49038	+	4.90192i	−0.274886	+	0.158706i
$955$		0			0
$956$	2.42820	−	4.20577i	0.0785337	−	0.136024i
$957$	−43.2586	−	11.5911i	−1.39835	−	0.374687i
$958$	16.4022	+	16.4022i	0.529930	+	0.529930i
$959$	22.3923	+	19.3923i	0.723085	+	0.626210i
$960$		0			0
$961$	−14.0000	−	24.2487i	−0.451613	−	0.782216i
$962$	−7.52433	−	28.0812i	−0.242594	−	0.905374i
$963$	−9.46979	−	35.3417i	−0.305160	−	1.13887i
$964$	1.73205	+	3.00000i	0.0557856	+	0.0966235i
$965$		0			0
$966$	−35.4904	+	12.2942i	−1.14188	+	0.395560i
$967$	15.9217	+	15.9217i	0.512007	+	0.512007i	0.915141	−	0.403134i	$-0.132079\pi$
$967$	15.9217	+	15.9217i	0.512007	+	0.512007i	−0.403134	+	0.915141i	$0.632079\pi$
$968$	−11.0041	−	2.94855i	−0.353686	−	0.0947698i
$969$		0			0
$970$		0			0
$971$	−16.6077	+	9.58846i	−0.532966	+	0.307708i	−0.742224	−	0.670152i	$-0.766229\pi$
$971$	−16.6077	+	9.58846i	−0.532966	+	0.307708i	0.209257	+	0.977861i	$0.432895\pi$
$972$	13.2456	−	13.2456i	0.424852	−	0.424852i
$973$	−5.13922	−	7.58871i	−0.164756	−	0.243283i
$974$		−	26.6603i		−	0.854250i
$975$		0			0
$976$	9.29423	+	5.36603i	0.297501	+	0.171762i
$977$	−8.12493	+	2.17707i	−0.259939	+	0.0696506i	−0.386435	−	0.922317i	$-0.626294\pi$
$977$	−8.12493	+	2.17707i	−0.259939	+	0.0696506i	0.126496	+	0.991967i	$0.459627\pi$
$978$	−15.1774	+	56.6429i	−0.485320	+	1.81124i
$979$	3.80385			0.121571
$980$		0			0
$981$	0.875644			0.0279572
$982$	−5.70762	+	21.3011i	−0.182138	+	0.679747i
$983$	41.0494	−	10.9991i	1.30927	−	0.350818i	0.464323	−	0.885666i	$-0.346298\pi$
$983$	41.0494	−	10.9991i	1.30927	−	0.350818i	0.844948	+	0.534848i	$0.179631\pi$
$984$	1.90192	+	1.09808i	0.0606311	+	0.0350054i
$985$		0			0
$986$			22.3923i			0.713116i
$987$	40.2407	+	59.4205i	1.28088	+	1.89138i
$988$		0			0
$989$	32.7058	−	18.8827i	1.03998	−	0.600434i
$990$		0			0
$991$	−9.50000	+	16.4545i	−0.301777	+	0.522694i	−0.976539	−	0.215342i	$-0.930913\pi$
$991$	−9.50000	+	16.4545i	−0.301777	+	0.522694i	0.674761	+	0.738036i	$0.264247\pi$
$992$	1.67303	+	0.448288i	0.0531188	+	0.0142331i
$993$	27.0459	+	27.0459i	0.858276	+	0.858276i
$994$	−18.4808	+	6.40192i	−0.586174	+	0.203057i
$995$		0			0
$996$	8.19615	+	14.1962i	0.259705	+	0.449822i
$997$	−10.6574	−	39.7738i	−0.337522	−	1.25965i	−0.901109	−	0.433593i	$-0.857245\pi$
$997$	−10.6574	−	39.7738i	−0.337522	−	1.25965i	0.563586	−	0.826057i	$-0.309421\pi$
$998$	−9.93666	−	37.0841i	−0.314539	−	1.17388i
$999$	13.8564	+	24.0000i	0.438397	+	0.759326i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	350.2.o.b.157.1	yes	8
5.2	odd	4		350.2.o.a.143.1	✓	8
5.3	odd	4		350.2.o.a.143.2	yes	8
5.4	even	2	inner	350.2.o.b.157.2	yes	8
7.5	odd	6		350.2.o.a.257.2	yes	8
35.12	even	12	inner	350.2.o.b.243.2	yes	8
35.19	odd	6		350.2.o.a.257.1	yes	8
35.33	even	12	inner	350.2.o.b.243.1	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
350.2.o.a.143.1	✓	8	5.2	odd	4
350.2.o.a.143.2	yes	8	5.3	odd	4
350.2.o.a.257.1	yes	8	35.19	odd	6
350.2.o.a.257.2	yes	8	7.5	odd	6
350.2.o.b.157.1	yes	8	1.1	even	1	trivial
350.2.o.b.157.2	yes	8	5.4	even	2	inner
350.2.o.b.243.1	yes	8	35.33	even	12	inner
350.2.o.b.243.2	yes	8	35.12	even	12	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:	\( N \)	\(=\)	\( 350 = 2 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	350.o (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.258819 + 0.965926i) q^{2} +(2.63896 - 0.707107i) q^{3} +(-0.866025 - 0.500000i) q^{4} +2.73205i q^{6} +(-1.48356 - 2.19067i) q^{7} +(0.707107 - 0.707107i) q^{8} +(3.86603 - 2.23205i) q^{9} +O(q^{10})\)	\(q+(-0.258819 + 0.965926i) q^{2} +(2.63896 - 0.707107i) q^{3} +(-0.866025 - 0.500000i) q^{4} +2.73205i q^{6} +(-1.48356 - 2.19067i) q^{7} +(0.707107 - 0.707107i) q^{8} +(3.86603 - 2.23205i) q^{9} +(2.36603 - 4.09808i) q^{11} +(-2.63896 - 0.707107i) q^{12} +(2.96713 + 2.96713i) q^{13} +(2.50000 - 0.866025i) q^{14} +(0.500000 + 0.866025i) q^{16} +(1.67303 + 6.24384i) q^{17} +(1.15539 + 4.31199i) q^{18} +(-5.46410 - 4.73205i) q^{21} +(3.34607 + 3.34607i) q^{22} +(-5.01910 - 1.34486i) q^{23} +(1.36603 - 2.36603i) q^{24} +(-3.63397 + 2.09808i) q^{26} +(2.82843 - 2.82843i) q^{27} +(0.189469 + 2.63896i) q^{28} -3.46410i q^{29} +(-1.50000 - 0.866025i) q^{31} +(-0.965926 + 0.258819i) q^{32} +(3.34607 - 12.4877i) q^{33} -6.46410 q^{34} -4.46410 q^{36} +(-1.79315 + 6.69213i) q^{37} +(9.92820 + 5.73205i) q^{39} +0.803848i q^{41} +(5.98502 - 4.05317i) q^{42} +(-5.13922 + 5.13922i) q^{43} +(-4.09808 + 2.36603i) q^{44} +(2.59808 - 4.50000i) q^{46} +(-9.58991 - 2.56961i) q^{47} +(1.93185 + 1.93185i) q^{48} +(-2.59808 + 6.50000i) q^{49} +(8.83013 + 15.2942i) q^{51} +(-1.08604 - 4.05317i) q^{52} +(0.568406 + 2.12132i) q^{53} +(2.00000 + 3.46410i) q^{54} +(-2.59808 - 0.500000i) q^{56} +(3.34607 + 0.896575i) q^{58} +(-1.90192 + 3.29423i) q^{59} +(9.29423 - 5.36603i) q^{61} +(1.22474 - 1.22474i) q^{62} +(-10.6252 - 5.15780i) q^{63} -1.00000i q^{64} +(11.1962 + 6.46410i) q^{66} +(13.7124 - 3.67423i) q^{67} +(1.67303 - 6.24384i) q^{68} -14.1962 q^{69} -7.39230 q^{71} +(1.15539 - 4.31199i) q^{72} +(7.72741 - 2.07055i) q^{73} +(-6.00000 - 3.46410i) q^{74} +(-12.4877 + 0.896575i) q^{77} +(-8.10634 + 8.10634i) q^{78} +(-8.13397 + 4.69615i) q^{79} +(-1.23205 + 2.13397i) q^{81} +(-0.776457 - 0.208051i) q^{82} +(-4.24264 - 4.24264i) q^{83} +(2.36603 + 6.83013i) q^{84} +(-3.63397 - 6.29423i) q^{86} +(-2.44949 - 9.14162i) q^{87} +(-1.22474 - 4.57081i) q^{88} +(0.401924 + 0.696152i) q^{89} +(2.09808 - 10.9019i) q^{91} +(3.67423 + 3.67423i) q^{92} +(-4.57081 - 1.22474i) q^{93} +(4.96410 - 8.59808i) q^{94} +(-2.36603 + 1.36603i) q^{96} +(6.64136 - 6.64136i) q^{97} +(-5.60609 - 4.19187i) q^{98} -21.1244i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 24 q^{9}+O(q^{10}) \) 8 * q + 24 * q^9	\( 8 q + 24 q^{9} + 12 q^{11} + 20 q^{14} + 4 q^{16} - 16 q^{21} + 4 q^{24} - 36 q^{26} - 12 q^{31} - 24 q^{34} - 8 q^{36} + 24 q^{39} - 12 q^{44} + 36 q^{51} + 16 q^{54} - 36 q^{59} + 12 q^{61} + 48 q^{66} - 72 q^{69} + 24 q^{71} - 48 q^{74} - 72 q^{79} + 4 q^{81} + 12 q^{84} - 36 q^{86} + 24 q^{89} - 4 q^{91} + 12 q^{94} - 12 q^{96}+O(q^{100}) \) 8 * q + 24 * q^9 + 12 * q^11 + 20 * q^14 + 4 * q^16 - 16 * q^21 + 4 * q^24 - 36 * q^26 - 12 * q^31 - 24 * q^34 - 8 * q^36 + 24 * q^39 - 12 * q^44 + 36 * q^51 + 16 * q^54 - 36 * q^59 + 12 * q^61 + 48 * q^66 - 72 * q^69 + 24 * q^71 - 48 * q^74 - 72 * q^79 + 4 * q^81 + 12 * q^84 - 36 * q^86 + 24 * q^89 - 4 * q^91 + 12 * q^94 - 12 * q^96

Introduction

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