LMFDB - Embedded newform 350.2.o.a.257.2

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			257.2
Root			$-0.258819 - 0.965926i$ of defining polynomial
Character	$\chi$	$=$	350.257
Dual form			350.2.o.a.143.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.965926 - 0.258819i) q^{2} +(0.707107 - 2.63896i) q^{3} +(0.866025 - 0.500000i) q^{4} -2.73205i q^{6} +(-2.19067 - 1.48356i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-3.86603 - 2.23205i) q^{9} +O(q^{10})$	\(q+(0.965926 - 0.258819i) q^{2} +(0.707107 - 2.63896i) q^{3} +(0.866025 - 0.500000i) q^{4} -2.73205i q^{6} +(-2.19067 - 1.48356i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-3.86603 - 2.23205i) q^{9} +(2.36603 + 4.09808i) q^{11} +(-0.707107 - 2.63896i) q^{12} +(-2.96713 - 2.96713i) q^{13} +(-2.50000 - 0.866025i) q^{14} +(0.500000 - 0.866025i) q^{16} +(6.24384 + 1.67303i) q^{17} +(-4.31199 - 1.15539i) q^{18} +(-5.46410 + 4.73205i) q^{21} +(3.34607 + 3.34607i) q^{22} +(1.34486 + 5.01910i) q^{23} +(-1.36603 - 2.36603i) q^{24} +(-3.63397 - 2.09808i) q^{26} +(-2.82843 + 2.82843i) q^{27} +(-2.63896 - 0.189469i) q^{28} -3.46410i q^{29} +(-1.50000 + 0.866025i) q^{31} +(0.258819 - 0.965926i) q^{32} +(12.4877 - 3.34607i) q^{33} +6.46410 q^{34} -4.46410 q^{36} +(6.69213 - 1.79315i) q^{37} +(-9.92820 + 5.73205i) q^{39} -0.803848i q^{41} +(-4.05317 + 5.98502i) q^{42} +(-5.13922 + 5.13922i) q^{43} +(4.09808 + 2.36603i) q^{44} +(2.59808 + 4.50000i) q^{46} +(-2.56961 - 9.58991i) q^{47} +(-1.93185 - 1.93185i) q^{48} +(2.59808 + 6.50000i) q^{49} +(8.83013 - 15.2942i) q^{51} +(-4.05317 - 1.08604i) q^{52} +(-2.12132 - 0.568406i) q^{53} +(-2.00000 + 3.46410i) q^{54} +(-2.59808 + 0.500000i) q^{56} +(-0.896575 - 3.34607i) q^{58} +(1.90192 + 3.29423i) q^{59} +(9.29423 + 5.36603i) q^{61} +(-1.22474 + 1.22474i) q^{62} +(5.15780 + 10.6252i) q^{63} -1.00000i q^{64} +(11.1962 - 6.46410i) q^{66} +(-3.67423 + 13.7124i) q^{67} +(6.24384 - 1.67303i) q^{68} +14.1962 q^{69} -7.39230 q^{71} +(-4.31199 + 1.15539i) q^{72} +(2.07055 - 7.72741i) q^{73} +(6.00000 - 3.46410i) q^{74} +(0.896575 - 12.4877i) q^{77} +(-8.10634 + 8.10634i) q^{78} +(8.13397 + 4.69615i) q^{79} +(-1.23205 - 2.13397i) q^{81} +(-0.208051 - 0.776457i) q^{82} +(4.24264 + 4.24264i) q^{83} +(-2.36603 + 6.83013i) q^{84} +(-3.63397 + 6.29423i) q^{86} +(-9.14162 - 2.44949i) q^{87} +(4.57081 + 1.22474i) q^{88} +(-0.401924 + 0.696152i) q^{89} +(2.09808 + 10.9019i) q^{91} +(3.67423 + 3.67423i) q^{92} +(1.22474 + 4.57081i) q^{93} +(-4.96410 - 8.59808i) q^{94} +(-2.36603 - 1.36603i) q^{96} +(-6.64136 + 6.64136i) q^{97} +(4.19187 + 5.60609i) 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 $\left(\mathbb{Z}/350\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{4}\right)$

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 $

$2$	0.965926	−	0.258819i	0.683013	−	0.183013i
$2$	0.965926	−	0.258819i	0.683013	−	0.183013i
$3$	0.707107	−	2.63896i	0.408248	−	1.52360i	−0.389737	−	0.920926i	$-0.627434\pi$
$3$	0.707107	−	2.63896i	0.408248	−	1.52360i	0.797985	−	0.602677i	$-0.205899\pi$
$4$	0.866025	−	0.500000i	0.433013	−	0.250000i
$5$		0			0
$5$		0			0
$6$		−	2.73205i		−	1.11536i
$7$	−2.19067	−	1.48356i	−0.827996	−	0.560734i
$7$	−2.19067	−	1.48356i	−0.827996	−	0.560734i
$8$	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	0.963580	+	0.267421i	$0.0861715\pi$
$11$	2.36603	+	4.09808i	0.713384	+	1.23562i	−0.250196	+	0.968195i	$0.580495\pi$
$12$	−0.707107	−	2.63896i	−0.204124	−	0.761802i
$13$	−2.96713	−	2.96713i	−0.822933	−	0.822933i	0.163594	−	0.986528i	$-0.447691\pi$
$13$	−2.96713	−	2.96713i	−0.822933	−	0.822933i	−0.986528	+	0.163594i	$0.947691\pi$
$14$	−2.50000	−	0.866025i	−0.668153	−	0.231455i
$15$		0			0
$16$	0.500000	−	0.866025i	0.125000	−	0.216506i
$17$	6.24384	+	1.67303i	1.51435	+	0.405770i	0.917879	−	0.396861i	$-0.129901\pi$
$17$	6.24384	+	1.67303i	1.51435	+	0.405770i	0.596476	+	0.802631i	$0.296567\pi$
$18$	−4.31199	−	1.15539i	−1.01635	−	0.272329i
$19$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$19$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$20$		0			0
$21$	−5.46410	+	4.73205i	−1.19236	+	1.03262i
$22$	3.34607	+	3.34607i	0.713384	+	0.713384i
$23$	1.34486	+	5.01910i	0.280423	+	1.04655i	0.952119	+	0.305727i	$0.0988995\pi$
$23$	1.34486	+	5.01910i	0.280423	+	1.04655i	−0.671696	+	0.740827i	$0.734434\pi$
$24$	−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
$28$	−2.63896	−	0.189469i	−0.498716	−	0.0358062i
$29$		−	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	−0.628619	−	0.777714i	$-0.716379\pi$
$31$	−1.50000	+	0.866025i	−0.269408	+	0.155543i	0.359211	+	0.933257i	$0.383046\pi$
$32$	0.258819	−	0.965926i	0.0457532	−	0.170753i
$33$	12.4877	−	3.34607i	2.17383	−	0.582475i
$34$	6.46410			1.10858
$35$		0			0
$36$	−4.46410			−0.744017
$37$	6.69213	−	1.79315i	1.10018	−	0.294792i	0.337342	−	0.941382i	$-0.390472\pi$
$37$	6.69213	−	1.79315i	1.10018	−	0.294792i	0.762838	+	0.646590i	$0.223806\pi$
$38$		0			0
$39$	−9.92820	+	5.73205i	−1.58978	+	0.917863i
$40$		0			0
$41$		−	0.803848i		−	0.125540i	−0.998028	−	0.0627700i	$-0.980007\pi$
$41$		−	0.803848i		−	0.125540i	0.998028	−	0.0627700i	$-0.0199934\pi$
$42$	−4.05317	+	5.98502i	−0.625418	+	0.923509i
$43$	−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
$47$	−2.56961	−	9.58991i	−0.374816	−	1.39883i	−0.853614	−	0.520907i	$-0.825594\pi$
$47$	−2.56961	−	9.58991i	−0.374816	−	1.39883i	0.478798	−	0.877925i	$-0.341073\pi$
$48$	−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
$52$	−4.05317	−	1.08604i	−0.562074	−	0.150607i
$53$	−2.12132	−	0.568406i	−0.291386	−	0.0780766i	0.110165	−	0.993913i	$-0.464862\pi$
$53$	−2.12132	−	0.568406i	−0.291386	−	0.0780766i	−0.401551	+	0.915837i	$0.631529\pi$
$54$	−2.00000	+	3.46410i	−0.272166	+	0.471405i
$55$		0			0
$56$	−2.59808	+	0.500000i	−0.347183	+	0.0668153i
$57$		0			0
$58$	−0.896575	−	3.34607i	−0.117726	−	0.439360i
$59$	1.90192	+	3.29423i	0.247609	+	0.428872i	0.962862	−	0.269994i	$-0.0870217\pi$
$59$	1.90192	+	3.29423i	0.247609	+	0.428872i	−0.715253	+	0.698866i	$0.753688\pi$
$60$		0			0
$61$	9.29423	+	5.36603i	1.19000	+	0.687049i	0.958307	−	0.285739i	$-0.0922390\pi$
$61$	9.29423	+	5.36603i	1.19000	+	0.687049i	0.231697	+	0.972788i	$0.425572\pi$
$62$	−1.22474	+	1.22474i	−0.155543	+	0.155543i
$63$	5.15780	+	10.6252i	0.649822	+	1.33865i
$64$		−	1.00000i		−	0.125000i
$65$		0			0
$66$	11.1962	−	6.46410i	1.37815	−	0.795676i
$67$	−3.67423	+	13.7124i	−0.448879	+	1.67524i	0.256607	+	0.966516i	$0.417396\pi$
$67$	−3.67423	+	13.7124i	−0.448879	+	1.67524i	−0.705486	+	0.708724i	$0.749271\pi$
$68$	6.24384	−	1.67303i	0.757177	−	0.202885i
$69$	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	$0.644544\pi$
$72$	−4.31199	+	1.15539i	−0.508173	+	0.136165i
$73$	2.07055	−	7.72741i	0.242340	−	0.904425i	−0.732362	−	0.680915i	$-0.761582\pi$
$73$	2.07055	−	7.72741i	0.242340	−	0.904425i	0.974702	−	0.223509i	$-0.0717512\pi$
$74$	6.00000	−	3.46410i	0.697486	−	0.402694i
$75$		0			0
$76$		0			0
$77$	0.896575	−	12.4877i	0.102174	−	1.42310i
$78$	−8.10634	+	8.10634i	−0.917863	+	0.917863i
$79$	8.13397	+	4.69615i	0.915144	+	0.528358i	0.882083	−	0.471095i	$-0.156141\pi$
$79$	8.13397	+	4.69615i	0.915144	+	0.528358i	0.0330611	+	0.999453i	$0.489474\pi$
$80$		0			0
$81$	−1.23205	−	2.13397i	−0.136895	−	0.237108i
$82$	−0.208051	−	0.776457i	−0.0229754	−	0.0857453i
$83$	4.24264	+	4.24264i	0.465690	+	0.465690i	0.900515	−	0.434825i	$-0.143190\pi$
$83$	4.24264	+	4.24264i	0.465690	+	0.465690i	−0.434825	+	0.900515i	$0.643190\pi$
$84$	−2.36603	+	6.83013i	−0.258155	+	0.745228i
$85$		0			0
$86$	−3.63397	+	6.29423i	−0.391862	+	0.678724i
$87$	−9.14162	−	2.44949i	−0.980085	−	0.262613i
$88$	4.57081	+	1.22474i	0.487250	+	0.130558i
$89$	−0.401924	+	0.696152i	−0.0426038	+	0.0737920i	−0.886541	−	0.462650i	$-0.846899\pi$
$89$	−0.401924	+	0.696152i	−0.0426038	+	0.0737920i	0.843937	+	0.536442i	$0.180232\pi$
$90$		0			0
$91$	2.09808	+	10.9019i	0.219938	+	1.14283i
$92$	3.67423	+	3.67423i	0.383065	+	0.383065i
$93$	1.22474	+	4.57081i	0.127000	+	0.473971i
$94$	−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	−0.958711	−	0.284383i	$-0.908211\pi$
$97$	−6.64136	+	6.64136i	−0.674328	+	0.674328i	0.284383	+	0.958711i	$0.408211\pi$
$98$	4.19187	+	5.60609i	0.423443	+	0.566300i
$99$		−	21.1244i		−	2.12308i
$100$		0			0
$101$	−3.80385	+	2.19615i	−0.378497	+	0.218525i	−0.677164	−	0.735832i	$-0.736791\pi$
$101$	−3.80385	+	2.19615i	−0.378497	+	0.218525i	0.298667	+	0.954357i	$0.403458\pi$
$102$	4.57081	−	17.0585i	0.452578	−	1.68904i
$103$	−12.5570	+	3.36465i	−1.23728	+	0.331529i	−0.817411	−	0.576055i	$-0.804591\pi$
$103$	−12.5570	+	3.36465i	−1.23728	+	0.331529i	−0.419871	+	0.907584i	$0.637925\pi$
$104$	−4.19615			−0.411467
$105$		0			0
$106$	−2.19615			−0.213309
$107$	−7.91688	+	2.12132i	−0.765353	+	0.205076i	−0.620318	−	0.784351i	$-0.712996\pi$
$107$	−7.91688	+	2.12132i	−0.765353	+	0.205076i	−0.145036	+	0.989426i	$0.546330\pi$
$108$	−1.03528	+	3.86370i	−0.0996195	+	0.371785i
$109$	−0.169873	+	0.0980762i	−0.0162709	+	0.00939400i	−0.508113	−	0.861290i	$-0.669657\pi$
$109$	−0.169873	+	0.0980762i	−0.0162709	+	0.00939400i	0.491842	+	0.870684i	$0.336324\pi$
$110$		0			0
$111$		−	18.9282i		−	1.79659i
$112$	−2.38014	+	1.15539i	−0.224902	+	0.109175i
$113$	−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
$117$	4.84821	+	18.0938i	0.448217	+	1.67277i
$118$	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
$122$	10.3664	+	2.77766i	0.938527	+	0.251477i
$123$	−2.12132	−	0.568406i	−0.191273	−	0.0512514i
$124$	−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	$0.849455\pi$
$128$	−0.258819	−	0.965926i	−0.0228766	−	0.0853766i
$129$	9.92820	+	17.1962i	0.874130	+	1.51404i
$130$		0			0
$131$	7.09808	+	4.09808i	0.620162	+	0.358051i	0.776932	−	0.629585i	$-0.216775\pi$
$131$	7.09808	+	4.09808i	0.620162	+	0.358051i	−0.156770	+	0.987635i	$0.550108\pi$
$132$	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
$137$	2.89778	−	10.8147i	0.247574	−	0.923958i	−0.724498	−	0.689276i	$-0.757929\pi$
$137$	2.89778	−	10.8147i	0.247574	−	0.923958i	0.972072	−	0.234682i	$-0.0754048\pi$
$138$	13.7124	−	3.67423i	1.16728	−	0.312772i
$139$	−3.46410			−0.293821			−0.146911	−	0.989150i	$-0.546933\pi$
$139$	−3.46410			−0.293821			−0.146911	+	0.989150i	$0.546933\pi$
$140$		0			0
$141$	−27.1244			−2.28428
$142$	−7.14042	+	1.91327i	−0.599211	+	0.160558i
$143$	5.13922	−	19.1798i	0.429763	−	1.60390i
$144$	−3.86603	+	2.23205i	−0.322169	+	0.186004i
$145$		0			0
$146$		−	8.00000i		−	0.662085i
$147$	18.9903	−	2.26002i	1.56630	−	0.186403i
$148$	4.89898	−	4.89898i	0.402694	−	0.402694i
$149$	−1.90192	−	1.09808i	−0.155812	−	0.0899579i	0.420067	−	0.907493i	$-0.362007\pi$
$149$	−1.90192	−	1.09808i	−0.155812	−	0.0899579i	−0.575879	+	0.817535i	$0.695340\pi$
$150$		0			0
$151$	1.19615	+	2.07180i	0.0973415	+	0.168600i	0.910583	−	0.413325i	$-0.135633\pi$
$151$	1.19615	+	2.07180i	0.0973415	+	0.168600i	−0.813242	+	0.581926i	$0.802299\pi$
$152$		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
$157$	1.93185	+	0.517638i	0.154179	+	0.0413120i	0.335083	−	0.942189i	$-0.391236\pi$
$157$	1.93185	+	0.517638i	0.154179	+	0.0413120i	−0.180904	+	0.983501i	$0.557902\pi$
$158$	9.07227	+	2.43091i	0.721751	+	0.193393i
$159$	−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
$163$	−5.55532	−	20.7327i	−0.435126	−	1.62391i	−0.740764	−	0.671765i	$-0.765536\pi$
$163$	−5.55532	−	20.7327i	−0.435126	−	1.62391i	0.305638	−	0.952148i	$-0.401130\pi$
$164$	−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	−0.832117	−	0.554600i	$-0.812871\pi$
$167$	−3.58630	+	3.58630i	−0.277516	+	0.277516i	0.554600	+	0.832117i	$0.312871\pi$
$168$	−0.517638	+	7.20977i	−0.0399366	+	0.556246i
$169$			4.60770i			0.354438i
$170$		0			0
$171$		0			0
$172$	−1.88108	+	7.02030i	−0.143431	+	0.535293i
$173$	−0.328169	+	0.0879327i	−0.0249503	+	0.00668540i	−0.271273	−	0.962503i	$-0.587444\pi$
$173$	−0.328169	+	0.0879327i	−0.0249503	+	0.00668540i	0.246322	+	0.969188i	$0.420778\pi$
$174$	−9.46410			−0.717472
$175$		0			0
$176$	4.73205			0.356692
$177$	10.0382	−	2.68973i	0.754517	−	0.202172i
$178$	−0.208051	+	0.776457i	−0.0155941	+	0.0581979i
$179$	−1.90192	+	1.09808i	−0.142156	+	0.0820741i	−0.569391	−	0.822067i	$-0.692821\pi$
$179$	−1.90192	+	1.09808i	−0.142156	+	0.0820741i	0.427235	+	0.904141i	$0.359488\pi$
$180$		0			0
$181$		−	10.7321i		−	0.797707i	−0.917015	−	0.398854i	$-0.869408\pi$
$181$		−	10.7321i		−	0.797707i	0.917015	−	0.398854i	$-0.130592\pi$
$182$	4.84821	+	9.98743i	0.359373	+	0.740317i
$183$	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
$187$	7.91688	+	29.5462i	0.578939	+	2.16063i
$188$	−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	−0.547509	−	0.836800i	$-0.684424\pi$
$191$	6.23205	−	10.7942i	0.450935	−	0.781043i	0.998444	+	0.0557568i	$0.0177572\pi$
$192$	−2.63896	−	0.707107i	−0.190450	−	0.0510310i
$193$	11.7112	+	3.13801i	0.842993	+	0.225879i	0.654374	−	0.756171i	$-0.272932\pi$
$193$	11.7112	+	3.13801i	0.842993	+	0.225879i	0.188619	+	0.982050i	$0.439599\pi$
$194$	−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	$0.774928\pi$
$198$	−5.46739	−	20.4046i	−0.388550	−	1.45009i
$199$	−8.13397	−	14.0885i	−0.576602	−	0.998704i	−0.995866	−	0.0908396i	$-0.971045\pi$
$199$	−8.13397	−	14.0885i	−0.576602	−	0.998704i	0.419263	−	0.907865i	$-0.362288\pi$
$200$		0			0
$201$	33.5885	+	19.3923i	2.36915	+	1.36783i
$202$	−3.10583	+	3.10583i	−0.218525	+	0.218525i
$203$	−5.13922	+	7.58871i	−0.360702	+	0.532623i
$204$		−	17.6603i		−	1.23647i
$205$		0			0
$206$	−11.2583	+	6.50000i	−0.784405	+	0.452876i
$207$	6.00361	−	22.4058i	0.417279	−	1.55731i
$208$	−4.05317	+	1.08604i	−0.281037	+	0.0753036i
$209$		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	$0.497851\pi$
$212$	−2.12132	+	0.568406i	−0.145693	+	0.0390383i
$213$	−5.22715	+	19.5080i	−0.358158	+	1.33667i
$214$	−7.09808	+	4.09808i	−0.485215	+	0.280139i
$215$		0			0
$216$			4.00000i			0.272166i
$217$	4.57081	+	0.328169i	0.310287	+	0.0222776i
$218$	−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
$222$	−4.89898	−	18.2832i	−0.328798	−	1.22709i
$223$	−8.05558	−	8.05558i	−0.539441	−	0.539441i	0.383924	−	0.923365i	$-0.374573\pi$
$223$	−8.05558	−	8.05558i	−0.539441	−	0.539441i	−0.923365	+	0.383924i	$0.874573\pi$
$224$	−2.00000	+	1.73205i	−0.133631	+	0.115728i
$225$		0			0
$226$	−8.59808	+	14.8923i	−0.571936	+	0.990621i
$227$	−19.8362	−	5.31508i	−1.31657	−	0.352774i	−0.468879	−	0.883262i	$-0.655342\pi$
$227$	−19.8362	−	5.31508i	−1.31657	−	0.352774i	−0.847693	+	0.530488i	$0.822009\pi$
$228$		0			0
$229$	−1.90192	+	3.29423i	−0.125683	+	0.217689i	−0.922000	−	0.387191i	$-0.873445\pi$
$229$	−1.90192	+	3.29423i	−0.125683	+	0.217689i	0.796317	+	0.604880i	$0.206779\pi$
$230$		0			0
$231$	−32.3205	−	11.1962i	−2.12653	−	0.736653i
$232$	−2.44949	−	2.44949i	−0.160817	−	0.160817i
$233$	1.55291	+	5.79555i	0.101735	+	0.379679i	0.997954	−	0.0639315i	$-0.0203639\pi$
$233$	1.55291	+	5.79555i	0.101735	+	0.379679i	−0.896219	+	0.443611i	$0.853697\pi$
$234$	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
$238$	−14.1607	−	9.58991i	−0.917903	−	0.621621i
$239$			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	−0.593502	−	0.804833i	$-0.702255\pi$
$241$	−3.00000	+	1.73205i	−0.193247	+	0.111571i	0.400255	+	0.916404i	$0.368922\pi$
$242$	−2.94855	+	11.0041i	−0.189540	+	0.707372i
$243$	−18.0938	+	4.84821i	−1.16072	+	0.311013i
$244$	10.7321			0.687049
$245$		0			0
$246$	−2.19615			−0.140022
$247$		0			0
$248$	−0.448288	+	1.67303i	−0.0284663	+	0.106238i
$249$	14.1962	−	8.19615i	0.899645	−	0.519410i
$250$		0			0
$251$			16.3923i			1.03467i	0.855782	+	0.517337i	$0.173076\pi$
$251$			16.3923i			1.03467i	−0.855782	+	0.517337i	$0.826924\pi$
$252$	9.77938	+	6.62278i	0.616043	+	0.417196i
$253$	−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
$257$	−4.24264	−	15.8338i	−0.264649	−	0.987682i	−0.962465	−	0.271406i	$-0.912512\pi$
$257$	−4.24264	−	15.8338i	−0.264649	−	0.987682i	0.697816	−	0.716277i	$-0.254155\pi$
$258$	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
$262$	7.91688	+	2.12132i	0.489106	+	0.131056i
$263$	26.6484	+	7.14042i	1.64321	+	0.440297i	0.957701	−	0.287766i	$-0.0929125\pi$
$263$	26.6484	+	7.14042i	1.64321	+	0.440297i	0.685510	+	0.728063i	$0.259579\pi$
$264$	6.46410	−	11.1962i	0.397838	−	0.689076i
$265$		0			0
$266$		0			0
$267$	1.55291	+	1.55291i	0.0950368	+	0.0950368i
$268$	3.67423	+	13.7124i	0.224440	+	0.837620i
$269$	−9.29423	−	16.0981i	−0.566679	−	0.981517i	−0.996891	−	0.0787892i	$-0.974895\pi$
$269$	−9.29423	−	16.0981i	−0.566679	−	0.981517i	0.430212	−	0.902728i	$-0.358439\pi$
$270$		0			0
$271$	−11.0885	−	6.40192i	−0.673576	−	0.388889i	0.123854	−	0.992300i	$-0.460474\pi$
$271$	−11.0885	−	6.40192i	−0.673576	−	0.388889i	−0.797430	+	0.603411i	$0.793808\pi$
$272$	4.57081	−	4.57081i	0.277146	−	0.277146i
$273$	30.2533	+	2.17209i	1.83101	+	0.131461i
$274$		−	11.1962i		−	0.676384i
$275$		0			0
$276$	12.2942	−	7.09808i	0.740026	−	0.427254i
$277$	−6.36396	+	23.7506i	−0.382373	+	1.42704i	0.459893	+	0.887975i	$0.347888\pi$
$277$	−6.36396	+	23.7506i	−0.382373	+	1.42704i	−0.842266	+	0.539062i	$0.818779\pi$
$278$	−3.34607	+	0.896575i	−0.200684	+	0.0537730i
$279$	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	$0.324793\pi$
$282$	−26.2001	+	7.02030i	−1.56019	+	0.418053i
$283$	−4.76028	+	17.7656i	−0.282969	+	1.05606i	0.667341	+	0.744752i	$0.267432\pi$
$283$	−4.76028	+	17.7656i	−0.282969	+	1.05606i	−0.950311	+	0.311303i	$0.899234\pi$
$284$	−6.40192	+	3.69615i	−0.379884	+	0.219326i
$285$		0			0
$286$		−	19.8564i		−	1.17413i
$287$	−1.19256	+	1.76097i	−0.0703945	+	0.103946i
$288$	−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
$292$	−2.07055	−	7.72741i	−0.121170	−	0.452212i
$293$	−2.92996	−	2.92996i	−0.171170	−	0.171170i	0.616323	−	0.787493i	$-0.288622\pi$
$293$	−2.92996	−	2.92996i	−0.171170	−	0.171170i	−0.787493	+	0.616323i	$0.788622\pi$
$294$	17.7583	−	7.09808i	1.03569	−	0.413968i
$295$		0			0
$296$	3.46410	−	6.00000i	0.201347	−	0.348743i
$297$	−18.2832	−	4.89898i	−1.06090	−	0.284268i
$298$	−2.12132	−	0.568406i	−0.122885	−	0.0329269i
$299$	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
$303$	3.10583	+	11.5911i	0.178425	+	0.665892i
$304$		0			0
$305$		0			0
$306$	−24.9904	−	14.4282i	−1.42860	−	0.824805i
$307$	−5.93426	+	5.93426i	−0.338686	+	0.338686i	−0.855873	−	0.517187i	$-0.826979\pi$
$307$	−5.93426	+	5.93426i	−0.338686	+	0.338686i	0.517187	+	0.855873i	$0.326979\pi$
$308$	−5.46739	−	11.2629i	−0.311533	−	0.641766i
$309$			35.5167i			2.02047i
$310$		0			0
$311$	9.69615	−	5.59808i	0.549818	−	0.317438i	−0.199230	−	0.979953i	$-0.563844\pi$
$311$	9.69615	−	5.59808i	0.549818	−	0.317438i	0.749049	+	0.662515i	$0.230511\pi$
$312$	−2.96713	+	11.0735i	−0.167981	+	0.626912i
$313$	18.3526	−	4.91756i	1.03735	−	0.277957i	0.300335	−	0.953834i	$-0.402902\pi$
$313$	18.3526	−	4.91756i	1.03735	−	0.277957i	0.737015	+	0.675877i	$0.236235\pi$
$314$	2.00000			0.112867
$315$		0			0
$316$	9.39230			0.528358
$317$	4.24264	−	1.13681i	0.238290	−	0.0638497i	−0.137697	−	0.990474i	$-0.543970\pi$
$317$	4.24264	−	1.13681i	0.238290	−	0.0638497i	0.375988	+	0.926625i	$0.377303\pi$
$318$	−1.55291	+	5.79555i	−0.0870831	+	0.324999i
$319$	14.1962	−	8.19615i	0.794832	−	0.458896i
$320$		0			0
$321$			22.3923i			1.24982i
$322$	0.984508	−	13.7124i	0.0548645	−	0.764164i
$323$		0			0
$324$	−2.13397	−	1.23205i	−0.118554	−	0.0684473i
$325$		0			0
$326$	−10.7321	−	18.5885i	−0.594393	−	1.02952i
$327$	0.138701	+	0.517638i	0.00767017	+	0.0286255i
$328$	−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	−0.606980	−	0.794717i	$-0.707619\pi$
$331$	7.00000	−	12.1244i	0.384755	−	0.666415i	0.991735	+	0.128302i	$0.0409527\pi$
$332$	5.79555	+	1.55291i	0.318072	+	0.0852272i
$333$	−29.8744	−	8.00481i	−1.63710	−	0.438661i
$334$	−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	$0.825796\pi$
$338$	1.19256	+	4.45069i	0.0648667	+	0.242086i
$339$	23.4904	+	40.6865i	1.27582	+	2.20979i
$340$		0			0
$341$	−7.09808	−	4.09808i	−0.384382	−	0.221923i
$342$		0			0
$343$	3.95164	−	18.0938i	0.213368	−	0.976972i
$344$			7.26795i			0.391862i
$345$		0			0
$346$	−0.294229	+	0.169873i	−0.0158178	+	0.00913243i
$347$	−1.55291	+	5.79555i	−0.0833648	+	0.311122i	−0.995000	−	0.0998797i	$-0.968154\pi$
$347$	−1.55291	+	5.79555i	−0.0833648	+	0.311122i	0.911635	+	0.411001i	$0.134821\pi$
$348$	−9.14162	+	2.44949i	−0.490042	+	0.131306i
$349$	−34.9808			−1.87248			−0.936239	−	0.351365i	$-0.885718\pi$
$349$	−34.9808			−1.87248			−0.936239	+	0.351365i	$0.885718\pi$
$350$		0			0
$351$	16.7846			0.895896
$352$	4.57081	−	1.22474i	0.243625	−	0.0652791i
$353$	7.88469	−	29.4261i	0.419660	−	1.56619i	−0.355656	−	0.934617i	$-0.615742\pi$
$353$	7.88469	−	29.4261i	0.419660	−	1.56619i	0.775315	−	0.631574i	$-0.217591\pi$
$354$	9.00000	−	5.19615i	0.478345	−	0.276172i
$355$		0			0
$356$			0.803848i			0.0426038i
$357$	−42.0339	+	20.4046i	−2.22467	+	1.07992i
$358$	−1.55291	+	1.55291i	−0.0820741	+	0.0820741i
$359$	9.00000	+	5.19615i	0.475002	+	0.274242i	0.718331	−	0.695701i	$-0.244906\pi$
$359$	9.00000	+	5.19615i	0.475002	+	0.274242i	−0.243329	+	0.969944i	$0.578240\pi$
$360$		0			0
$361$	9.50000	+	16.4545i	0.500000	+	0.866025i
$362$	−2.77766	−	10.3664i	−0.145991	−	0.544844i
$363$	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
$367$	−2.31079	−	0.619174i	−0.120622	−	0.0323206i	0.198003	−	0.980201i	$-0.436554\pi$
$367$	−2.31079	−	0.619174i	−0.120622	−	0.0323206i	−0.318625	+	0.947881i	$0.603221\pi$
$368$	5.01910	+	1.34486i	0.261639	+	0.0701058i
$369$	−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
$373$	9.05369	+	33.7888i	0.468782	+	1.74952i	0.644036	+	0.764996i	$0.277259\pi$
$373$	9.05369	+	33.7888i	0.468782	+	1.74952i	−0.175253	+	0.984523i	$0.556074\pi$
$374$	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
$378$	9.52056	−	4.62158i	0.489685	−	0.237708i
$379$			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
$382$	3.22595	−	12.0394i	0.165054	−	0.615989i
$383$	−17.1786	+	4.60300i	−0.877786	+	0.235202i	−0.669452	−	0.742856i	$-0.733471\pi$
$383$	−17.1786	+	4.60300i	−0.877786	+	0.235202i	−0.208334	+	0.978058i	$0.566804\pi$
$384$	−2.73205			−0.139419
$385$		0			0
$386$	12.1244			0.617113
$387$	31.3393	−	8.39735i	1.59307	−	0.426861i
$388$	−2.43091	+	9.07227i	−0.123411	+	0.460575i
$389$	29.4904	−	17.0263i	1.49522	−	0.863267i	0.495237	−	0.868758i	$-0.335081\pi$
$389$	29.4904	−	17.0263i	1.49522	−	0.863267i	0.999985	+	0.00549142i	$0.00174798\pi$
$390$		0			0
$391$			33.5885i			1.69864i
$392$	6.43331	+	2.75908i	0.324931	+	0.139354i
$393$	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
$397$	0.517638	+	1.93185i	0.0259795	+	0.0969569i	0.977698	−	0.210014i	$-0.0673511\pi$
$397$	0.517638	+	1.93185i	0.0259795	+	0.0969569i	−0.951719	+	0.306971i	$0.900684\pi$
$398$	−11.5032	−	11.5032i	−0.576602	−	0.576602i
$399$		0			0
$400$		0			0
$401$	12.4641	−	21.5885i	0.622428	−	1.07808i	−0.366605	−	0.930377i	$-0.619480\pi$
$401$	12.4641	−	21.5885i	0.622428	−	1.07808i	0.989032	−	0.147699i	$-0.0471868\pi$
$402$	37.4631	+	10.0382i	1.86849	+	0.500660i
$403$	7.02030	+	1.88108i	0.349706	+	0.0937035i
$404$	−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
$408$	−4.57081	−	17.0585i	−0.226289	−	0.844521i
$409$	−11.5981	−	20.0885i	−0.573488	−	0.993310i	−0.996204	−	0.0870481i	$-0.972257\pi$
$409$	−11.5981	−	20.0885i	−0.573488	−	0.993310i	0.422716	−	0.906262i	$-0.361077\pi$
$410$		0			0
$411$	−26.4904	−	15.2942i	−1.30667	−	0.754409i
$412$	−9.19239	+	9.19239i	−0.452876	+	0.452876i
$413$	0.720710	−	10.0382i	0.0354638	−	0.493947i
$414$		−	23.1962i		−	1.14003i
$415$		0			0
$416$	−3.63397	+	2.09808i	−0.178170	+	0.102867i
$417$	−2.44949	+	9.14162i	−0.119952	+	0.447667i
$418$		0			0
$419$	22.9808			1.12268			0.561342	−	0.827584i	$-0.310285\pi$
$419$	22.9808			1.12268			0.561342	+	0.827584i	$0.310285\pi$
$420$		0			0
$421$	−36.3923			−1.77365			−0.886826	−	0.462103i	$-0.847095\pi$
$421$	−36.3923			−1.77365			−0.886826	+	0.462103i	$0.847095\pi$
$422$	0.189469	−	0.0507680i	0.00922319	−	0.00247135i
$423$	−11.4710	+	42.8103i	−0.557739	+	2.08151i
$424$	−1.90192	+	1.09808i	−0.0923656	+	0.0533273i
$425$		0			0
$426$			20.1962i			0.978507i
$427$	−12.3998	−	25.5438i	−0.600066	−	1.23615i
$428$	−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	0.994338	+	0.106265i	$0.0338892\pi$
$431$	12.2321	+	21.1865i	0.589197	+	1.02052i	−0.405141	+	0.914254i	$0.632777\pi$
$432$	1.03528	+	3.86370i	0.0498097	+	0.185893i
$433$	21.3383	+	21.3383i	1.02545	+	1.02545i	0.999667	+	0.0257858i	$0.00820879\pi$
$433$	21.3383	+	21.3383i	1.02545	+	1.02545i	0.0257858	+	0.999667i	$0.491791\pi$
$434$	4.50000	−	0.866025i	0.216007	−	0.0415705i
$435$		0			0
$436$	−0.0980762	+	0.169873i	−0.00469700	+	0.00813544i
$437$		0			0
$438$	−21.1117	−	5.65685i	−1.00875	−	0.270295i
$439$	−15.0622	+	26.0885i	−0.718879	+	1.24513i	0.242566	+	0.970135i	$0.422011\pi$
$439$	−15.0622	+	26.0885i	−0.718879	+	1.24513i	−0.961444	+	0.274999i	$0.911322\pi$
$440$		0			0
$441$	4.46410	−	30.9282i	0.212576	−	1.47277i
$442$	−19.1798	−	19.1798i	−0.912291	−	0.912291i
$443$	−3.10583	−	11.5911i	−0.147562	−	0.550710i	−0.999628	−	0.0272752i	$-0.991317\pi$
$443$	−3.10583	−	11.5911i	−0.147562	−	0.550710i	0.852066	−	0.523435i	$-0.175350\pi$
$444$	−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
$448$	−1.48356	+	2.19067i	−0.0700918	+	0.103499i
$449$		−	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
$452$	−4.45069	+	16.6102i	−0.209343	+	0.781278i
$453$	6.31319	−	1.69161i	0.296620	−	0.0794790i
$454$	−20.5359			−0.963797
$455$		0			0
$456$		0			0
$457$	38.1194	−	10.2141i	1.78315	−	0.477794i	0.791998	−	0.610524i	$-0.209041\pi$
$457$	38.1194	−	10.2141i	1.78315	−	0.477794i	0.991152	+	0.132730i	$0.0423744\pi$
$458$	−0.984508	+	3.67423i	−0.0460030	+	0.171686i
$459$	−22.3923	+	12.9282i	−1.04518	+	0.603437i
$460$		0			0
$461$			24.0000i			1.11779i	0.829238	+	0.558896i	$0.188775\pi$
$461$			24.0000i			1.11779i	−0.829238	+	0.558896i	$0.811225\pi$
$462$	−34.1170	−	2.44949i	−1.58727	−	0.113961i
$463$	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
$467$	−9.55772	−	35.6699i	−0.442279	−	1.65061i	−0.723023	−	0.690824i	$-0.757248\pi$
$467$	−9.55772	−	35.6699i	−0.442279	−	1.65061i	0.280744	−	0.959783i	$-0.409419\pi$
$468$	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
$472$	3.67423	+	0.984508i	0.169120	+	0.0453157i
$473$	−33.2204	−	8.90138i	−1.52748	−	0.409286i
$474$	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
$478$	1.25693	+	4.69093i	0.0574907	+	0.214558i
$479$	−11.5981	−	20.0885i	−0.529930	−	0.917865i	−0.999390	−	0.0349117i	$-0.988885\pi$
$479$	−11.5981	−	20.0885i	−0.529930	−	0.917865i	0.469461	−	0.882953i	$-0.344448\pi$
$480$		0			0
$481$	−25.1769	−	14.5359i	−1.14797	−	0.662780i
$482$	−2.44949	+	2.44949i	−0.111571	+	0.111571i
$483$	−31.0991	−	21.0609i	−1.41506	−	0.958304i
$484$			11.3923i			0.517832i
$485$		0			0
$486$	−16.2224	+	9.36603i	−0.735864	+	0.424852i
$487$	6.90018	−	25.7518i	0.312677	−	1.16693i	−0.613456	−	0.789729i	$-0.710221\pi$
$487$	6.90018	−	25.7518i	0.312677	−	1.16693i	0.926133	−	0.377198i	$-0.123112\pi$
$488$	10.3664	−	2.77766i	0.469263	−	0.125739i
$489$	−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	$0.334211\pi$
$492$	−2.12132	+	0.568406i	−0.0956365	+	0.0256257i
$493$	5.79555	−	21.6293i	0.261019	−	0.974135i
$494$		0			0
$495$		0			0
$496$			1.73205i			0.0777714i
$497$	16.1941	+	10.9670i	0.726405	+	0.491935i
$498$	11.5911	−	11.5911i	0.519410	−	0.519410i
$499$	33.2487	+	19.1962i	1.48842	+	0.859338i	0.999913	−	0.0132238i	$-0.00420938\pi$
$499$	33.2487	+	19.1962i	1.48842	+	0.859338i	0.488504	+	0.872562i	$0.337543\pi$
$500$		0			0
$501$	6.92820	+	12.0000i	0.309529	+	0.536120i
$502$	4.24264	+	15.8338i	0.189358	+	0.706695i
$503$	17.6269	+	17.6269i	0.785945	+	0.785945i	0.980827	−	0.194882i	$-0.0624324\pi$
$503$	17.6269	+	17.6269i	0.785945	+	0.785945i	−0.194882	+	0.980827i	$0.562432\pi$
$504$	11.1603	+	3.86603i	0.497117	+	0.172206i
$505$		0			0
$506$	−12.2942	+	21.2942i	−0.546545	+	0.946644i
$507$	12.1595	+	3.25813i	0.540023	+	0.144699i
$508$	−6.69213	−	1.79315i	−0.296915	−	0.0795582i
$509$	8.49038	−	14.7058i	0.376330	−	0.651822i	−0.614196	−	0.789154i	$-0.710519\pi$
$509$	8.49038	−	14.7058i	0.376330	−	0.651822i	0.990525	+	0.137332i	$0.0438527\pi$
$510$		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
$518$	−18.2832	−	1.31268i	−0.803319	−	0.0576757i
$519$			0.928203i			0.0407436i
$520$		0			0
$521$	−2.08846	+	1.20577i	−0.0914970	+	0.0528258i	−0.545050	−	0.838403i	$-0.683489\pi$
$521$	−2.08846	+	1.20577i	−0.0914970	+	0.0528258i	0.453553	+	0.891229i	$0.350156\pi$
$522$	−4.00240	+	14.9372i	−0.175180	+	0.653782i
$523$	−9.65926	+	2.58819i	−0.422370	+	0.113174i	−0.463742	−	0.885970i	$-0.653494\pi$
$523$	−9.65926	+	2.58819i	−0.422370	+	0.113174i	0.0413724	+	0.999144i	$0.486827\pi$
$524$	8.19615			0.358051
$525$		0			0
$526$	27.5885			1.20291
$527$	−10.8147	+	2.89778i	−0.471094	+	0.126229i
$528$	3.34607	−	12.4877i	0.145619	−	0.543457i
$529$	−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
$537$	1.55291	+	5.79555i	0.0670132	+	0.250097i
$538$	−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	−0.769874	−	0.638196i	$-0.779681\pi$
$541$	3.90192	−	6.75833i	0.167757	−	0.290563i	0.937631	+	0.347633i	$0.113014\pi$
$542$	−12.3676	−	3.31388i	−0.531232	−	0.142343i
$543$	−28.3214	−	7.58871i	−1.21539	−	0.325663i
$544$	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	$0.802001\pi$
$548$	−2.89778	−	10.8147i	−0.123787	−	0.461979i
$549$	−23.9545	−	41.4904i	−1.02235	−	1.77077i
$550$		0			0
$551$		0			0
$552$	10.0382	−	10.0382i	0.427254	−	0.427254i
$553$	−10.8518	−	22.3550i	−0.461466	−	0.950631i
$554$			24.5885i			1.04466i
$555$		0			0
$556$	−3.00000	+	1.73205i	−0.127228	+	0.0734553i
$557$	−2.12132	+	7.91688i	−0.0898832	+	0.335449i	−0.996194	−	0.0871629i	$-0.972220\pi$
$557$	−2.12132	+	7.91688i	−0.0898832	+	0.335449i	0.906311	+	0.422612i	$0.138887\pi$
$558$	7.46859	−	2.00120i	0.316171	−	0.0847176i
$559$	30.4974			1.28990
$560$		0			0
$561$	83.5692			3.52830
$562$	16.9384	−	4.53862i	0.714502	−	0.191450i
$563$	−0.152304	+	0.568406i	−0.00641885	+	0.0239555i	−0.969061	−	0.246821i	$-0.920614\pi$
$563$	−0.152304	+	0.568406i	−0.00641885	+	0.0239555i	0.962642	+	0.270777i	$0.0872806\pi$
$564$	−23.4904	+	13.5622i	−0.989123	+	0.571071i
$565$		0			0
$566$			18.3923i			0.773086i
$567$	−0.466870	+	6.50266i	−0.0196067	+	0.273086i
$568$	−5.22715	+	5.22715i	−0.219326	+	0.219326i
$569$	−15.4019	−	8.89230i	−0.645682	−	0.372785i	0.141118	−	0.989993i	$-0.454930\pi$
$569$	−15.4019	−	8.89230i	−0.645682	−	0.372785i	−0.786800	+	0.617208i	$0.788264\pi$
$570$		0			0
$571$	−22.5885	−	39.1244i	−0.945298	−	1.63730i	−0.755154	−	0.655547i	$-0.772438\pi$
$571$	−22.5885	−	39.1244i	−0.945298	−	1.63730i	−0.190143	−	0.981756i	$-0.560895\pi$
$572$	−5.13922	−	19.1798i	−0.214881	−	0.801948i
$573$	−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
$577$	−11.9700	−	3.20736i	−0.498320	−	0.133524i	0.000900421	−	1.00000i	$-0.499713\pi$
$577$	−11.9700	−	3.20736i	−0.498320	−	0.133524i	−0.499220	+	0.866475i	$0.666380\pi$
$578$	23.9401	+	6.41473i	0.995777	+	0.266818i
$579$	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
$583$	−2.68973	−	10.0382i	−0.111397	−	0.415740i
$584$	−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	−0.883241	−	0.468920i	$-0.844643\pi$
$587$	−10.0382	+	10.0382i	−0.414321	+	0.414321i	0.468920	+	0.883241i	$0.344643\pi$
$588$	15.3161	−	11.4524i	0.631626	−	0.472289i
$589$		0			0
$590$		0			0
$591$	−5.19615	+	3.00000i	−0.213741	+	0.123404i
$592$	1.79315	−	6.69213i	0.0736980	−	0.275045i
$593$	19.3879	−	5.19496i	0.796164	−	0.213332i	0.162265	−	0.986747i	$-0.448120\pi$
$593$	19.3879	−	5.19496i	0.796164	−	0.213332i	0.633899	+	0.773416i	$0.281453\pi$
$594$	−18.9282			−0.776634
$595$		0			0
$596$	−2.19615			−0.0899579
$597$	−42.9304	+	11.5032i	−1.75703	+	0.470794i
$598$	5.64325	−	21.0609i	0.230770	−	0.861244i
$599$	−12.1865	+	7.03590i	−0.497928	+	0.287479i	−0.727858	−	0.685728i	$-0.759484\pi$
$599$	−12.1865	+	7.03590i	−0.497928	+	0.287479i	0.229929	+	0.973207i	$0.426150\pi$
$600$		0			0
$601$		−	38.7846i		−	1.58206i	−0.611779	−	0.791029i	$-0.709546\pi$
$601$		−	38.7846i		−	1.58206i	0.611779	−	0.791029i	$-0.290454\pi$
$602$	17.2987	−	8.39735i	0.705044	−	0.342250i
$603$	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
$607$	9.36327	+	34.9442i	0.380044	+	1.41834i	0.845834	+	0.533447i	$0.179104\pi$
$607$	9.36327	+	34.9442i	0.380044	+	1.41834i	−0.465790	+	0.884895i	$0.654230\pi$
$608$		0			0
$609$	16.3923	+	18.9282i	0.664250	+	0.767010i
$610$		0			0
$611$	−20.8301	+	36.0788i	−0.842697	+	1.45959i
$612$	−27.8731	−	7.46859i	−1.12671	−	0.301900i
$613$	17.3867	+	4.65874i	0.702241	+	0.188165i	0.592234	−	0.805766i	$-0.298246\pi$
$613$	17.3867	+	4.65874i	0.702241	+	0.188165i	0.110007	+	0.993931i	$0.464913\pi$
$614$	−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	$-0.543521\pi$
$618$	9.19239	+	34.3065i	0.369772	+	1.38001i
$619$	−5.53590	−	9.58846i	−0.222507	−	0.385393i	0.733062	−	0.680162i	$-0.238091\pi$
$619$	−5.53590	−	9.58846i	−0.222507	−	0.385393i	−0.955568	+	0.294769i	$0.904757\pi$
$620$		0			0
$621$	−18.0000	−	10.3923i	−0.722315	−	0.417029i
$622$	7.91688	−	7.91688i	0.317438	−	0.317438i
$623$	1.91327	−	0.928761i	0.0766535	−	0.0372100i
$624$			11.4641i			0.458931i
$625$		0			0
$626$	16.4545	−	9.50000i	0.657653	−	0.379696i
$627$		0			0
$628$	1.93185	−	0.517638i	0.0770893	−	0.0206560i
$629$	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	$0.478490\pi$
$632$	9.07227	−	2.43091i	0.360876	−	0.0966963i
$633$	0.138701	−	0.517638i	0.00551286	−	0.0205743i
$634$	3.80385	−	2.19615i	0.151070	−	0.0872204i
$635$		0			0
$636$			6.00000i			0.237915i
$637$	11.5775	−	26.9952i	0.458718	−	1.06959i
$638$	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	−0.999247	−	0.0387913i	$-0.987649\pi$
$641$	−13.5000	−	23.3827i	−0.533218	−	0.923561i	0.466029	−	0.884769i	$-0.345684\pi$
$642$	5.79555	+	21.6293i	0.228732	+	0.853641i
$643$	21.9067	+	21.9067i	0.863916	+	0.863916i	0.991790	−	0.127874i	$-0.0408154\pi$
$643$	21.9067	+	21.9067i	0.863916	+	0.863916i	−0.127874	+	0.991790i	$0.540815\pi$
$644$	−2.59808	−	13.5000i	−0.102379	−	0.531975i
$645$		0			0
$646$		0			0
$647$	44.8115	+	12.0072i	1.76172	+	0.472052i	0.987064	−	0.160327i	$-0.0512549\pi$
$647$	44.8115	+	12.0072i	1.76172	+	0.472052i	0.774659	+	0.632379i	$0.217922\pi$
$648$	−2.38014	−	0.637756i	−0.0935007	−	0.0250534i
$649$	−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
$653$	2.53742	+	9.46979i	0.0992970	+	0.370582i	0.997636	−	0.0687217i	$-0.0218921\pi$
$653$	2.53742	+	9.46979i	0.0992970	+	0.370582i	−0.898339	+	0.439303i	$0.855225\pi$
$654$	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
$658$	−1.88108	+	26.2001i	−0.0733323	+	1.02139i
$659$			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	−0.308237	−	0.951310i	$-0.599739\pi$
$661$	9.29423	−	5.36603i	0.361504	−	0.208714i	0.669740	+	0.742596i	$0.266405\pi$
$662$	3.62347	−	13.5230i	0.140830	−	0.525585i
$663$	−71.5800	+	19.1798i	−2.77994	+	0.744882i
$664$	6.00000			0.232845
$665$		0			0
$666$	−30.9282			−1.19844
$667$	17.3867	−	4.65874i	0.673214	−	0.180387i
$668$	−1.31268	+	4.89898i	−0.0507890	+	0.189547i
$669$	−26.9545	+	15.5622i	−1.04212	+	0.601669i
$670$		0			0
$671$			50.7846i			1.96052i
$672$	3.15660	+	6.50266i	0.121768	+	0.250846i
$673$	−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
$677$	10.6945	+	39.9125i	0.411024	+	1.53396i	0.792668	+	0.609654i	$0.208692\pi$
$677$	10.6945	+	39.9125i	0.411024	+	1.53396i	−0.381643	+	0.924310i	$0.624642\pi$
$678$	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
$682$	−7.91688	−	2.12132i	−0.303153	−	0.0812296i
$683$	−25.8719	−	6.93237i	−0.989963	−	0.265260i	−0.272728	−	0.962091i	$-0.587926\pi$
$683$	−25.8719	−	6.93237i	−0.989963	−	0.265260i	−0.717235	+	0.696832i	$0.754592\pi$
$684$		0			0
$685$		0			0
$686$	−0.866025	−	18.5000i	−0.0330650	−	0.706333i
$687$	7.34847	+	7.34847i	0.280362	+	0.280362i
$688$	1.88108	+	7.02030i	0.0717156	+	0.267646i
$689$	4.60770	+	7.98076i	0.175539	+	0.304043i
$690$		0			0
$691$	−9.58846	−	5.53590i	−0.364762	−	0.210595i	0.306406	−	0.951901i	$-0.400874\pi$
$691$	−9.58846	−	5.53590i	−0.364762	−	0.210595i	−0.671168	+	0.741306i	$0.734207\pi$
$692$	−0.240237	+	0.240237i	−0.00913243	+	0.00913243i
$693$	−31.3393	+	46.2765i	−1.19048	+	1.75790i
$694$			6.00000i			0.227757i
$695$		0			0
$696$	−8.19615	+	4.73205i	−0.310674	+	0.179368i
$697$	1.34486	−	5.01910i	0.0509403	−	0.190112i
$698$	−33.7888	+	9.05369i	−1.27893	+	0.342687i
$699$	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	$0.561354\pi$
$702$	16.2127	−	4.34418i	0.611908	−	0.163960i
$703$		0			0
$704$	4.09808	−	2.36603i	0.154452	−	0.0891729i
$705$		0			0
$706$		−	30.4641i		−	1.14653i
$707$	11.5911	+	0.832204i	0.435929	+	0.0312983i
$708$	7.34847	−	7.34847i	0.276172	−	0.276172i
$709$	−18.5429	−	10.7058i	−0.696395	−	0.402064i	0.109608	−	0.993975i	$-0.465040\pi$
$709$	−18.5429	−	10.7058i	−0.696395	−	0.402064i	−0.806003	+	0.591911i	$0.798374\pi$
$710$		0			0
$711$	−20.9641	−	36.3109i	−0.786215	−	1.36176i
$712$	0.208051	+	0.776457i	0.00779704	+	0.0290990i
$713$	−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
$717$	12.8159	+	3.43400i	0.478617	+	0.128245i
$718$	10.0382	+	2.68973i	0.374622	+	0.100380i
$719$	4.20577	−	7.28461i	0.156849	−	0.271670i	−0.776882	−	0.629646i	$-0.783200\pi$
$719$	4.20577	−	7.28461i	0.156849	−	0.271670i	0.933731	+	0.357976i	$0.116533\pi$
$720$		0			0
$721$	32.5000	+	11.2583i	1.21036	+	0.419282i
$722$	13.4350	+	13.4350i	0.500000	+	0.500000i
$723$	2.44949	+	9.14162i	0.0910975	+	0.339981i
$724$	−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	−0.910902	−	0.412624i	$-0.864612\pi$
$727$	−13.4350	+	13.4350i	−0.498278	+	0.498278i	0.412624	+	0.910902i	$0.364612\pi$
$728$	9.19239	+	6.22526i	0.340693	+	0.230723i
$729$			43.7846i			1.62165i
$730$		0			0
$731$	−40.6865	+	23.4904i	−1.50485	+	0.868823i
$732$	7.58871	−	28.3214i	0.280487	−	1.04679i
$733$	−13.5230	+	3.62347i	−0.499482	+	0.133836i	−0.499760	−	0.866164i	$-0.666578\pi$
$733$	−13.5230	+	3.62347i	−0.499482	+	0.133836i	0.000277595		1.00000i	$0.499912\pi$
$734$	−2.39230			−0.0883016
$735$		0			0
$736$	5.19615			0.191533
$737$	−64.8879	+	17.3867i	−2.39018	+	0.640446i
$738$	−0.928761	+	3.46618i	−0.0341882	+	0.127592i
$739$	17.3205	−	10.0000i	0.637145	−	0.367856i	−0.146369	−	0.989230i	$-0.546759\pi$
$739$	17.3205	−	10.0000i	0.637145	−	0.367856i	0.783514	+	0.621374i	$0.213425\pi$
$740$		0			0
$741$		0			0
$742$	4.81105	+	3.25813i	0.176619	+	0.119610i
$743$	−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
$747$	−6.93237	−	25.8719i	−0.253642	−	0.946605i
$748$	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	−0.965013	−	0.262201i	$-0.915552\pi$
$751$	−7.00000	+	12.1244i	−0.255434	+	0.442424i	0.709580	+	0.704625i	$0.248885\pi$
$752$	−9.58991	−	2.56961i	−0.349708	−	0.0937040i
$753$	43.2586	+	11.5911i	1.57643	+	0.422404i
$754$	−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	$0.875415\pi$
$758$	5.84632	+	21.8188i	0.212348	+	0.792494i
$759$	33.5885	+	58.1769i	1.21918	+	2.11169i
$760$		0			0
$761$	7.28461	+	4.20577i	0.264067	+	0.152459i	0.626188	−	0.779672i	$-0.284614\pi$
$761$	7.28461	+	4.20577i	0.264067	+	0.152459i	−0.362121	+	0.932131i	$0.617947\pi$
$762$	−13.3843	+	13.3843i	−0.484861	+	0.484861i
$763$	0.517638	+	0.0371647i	0.0187398	+	0.00134545i
$764$		−	12.4641i		−	0.450935i
$765$		0			0
$766$	−15.4019	+	8.89230i	−0.556494	+	0.321292i
$767$	4.13115	−	15.4176i	0.149167	−	0.556699i
$768$	−2.63896	+	0.707107i	−0.0952252	+	0.0255155i
$769$	−45.7128			−1.64845			−0.824223	−	0.566265i	$-0.808388\pi$
$769$	−45.7128			−1.64845			−0.824223	+	0.566265i	$0.808388\pi$
$770$		0			0
$771$	−44.7846			−1.61288
$772$	11.7112	−	3.13801i	0.421496	−	0.112940i
$773$	−7.82894	+	29.2180i	−0.281587	+	1.05090i	0.669710	+	0.742623i	$0.266419\pi$
$773$	−7.82894	+	29.2180i	−0.281587	+	1.05090i	−0.951297	+	0.308276i	$0.900248\pi$
$774$	28.0981	−	16.2224i	1.00996	−	0.583103i
$775$		0			0
$776$			9.39230i			0.337164i
$777$	−28.0812	+	41.4655i	−1.00741	+	1.48757i
$778$	24.0788	−	24.0788i	0.863267	−	0.863267i
$779$		0			0
$780$		0			0
$781$	−17.4904	−	30.2942i	−0.625855	−	1.08401i
$782$	8.69333	+	32.4440i	0.310873	+	1.16019i
$783$	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
$787$	−16.2127	−	4.34418i	−0.577920	−	0.154853i	−0.0419935	−	0.999118i	$-0.513371\pi$
$787$	−16.2127	−	4.34418i	−0.577920	−	0.154853i	−0.535926	+	0.844265i	$0.680038\pi$
$788$	−2.12132	−	0.568406i	−0.0755689	−	0.0202486i
$789$	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
$793$	−11.6555	−	43.4988i	−0.413898	−	1.54469i
$794$	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	−0.583544	−	0.812082i	$-0.698334\pi$
$797$	6.45189	−	6.45189i	0.228538	−	0.228538i	0.812082	+	0.583544i	$0.198334\pi$
$798$		0			0
$799$		−	64.1769i		−	2.27042i
$800$		0			0
$801$	3.10770	−	1.79423i	0.109805	−	0.0633960i
$802$	6.45189	−	24.0788i	0.227824	−	0.850252i
$803$	36.5665	−	9.79796i	1.29040	−	0.345762i
$804$	38.7846			1.36783
$805$		0			0
$806$	7.26795			0.256003
$807$	−49.0542	+	13.1440i	−1.72679	+	0.462692i
$808$	−1.13681	+	4.24264i	−0.0399929	+	0.149256i
$809$	−4.39230	+	2.53590i	−0.154425	+	0.0891574i	−0.575221	−	0.817998i	$-0.695084\pi$
$809$	−4.39230	+	2.53590i	−0.154425	+	0.0891574i	0.420796	+	0.907155i	$0.361751\pi$
$810$		0			0
$811$		−	41.9090i		−	1.47162i	−0.677187	−	0.735811i	$-0.736801\pi$
$811$		−	41.9090i		−	1.47162i	0.677187	−	0.735811i	$-0.263199\pi$
$812$	−0.656339	+	9.14162i	−0.0230330	+	0.320808i
$813$	−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	−0.168119	−	0.985767i	$-0.553769\pi$
$821$	22.0526	−	38.1962i	0.769640	−	1.33305i	0.937758	−	0.347288i	$-0.112897\pi$
$822$	−29.5462	−	7.91688i	−1.03054	−	0.276133i
$823$	3.34607	+	0.896575i	0.116637	+	0.0312527i	0.316665	−	0.948537i	$-0.397437\pi$
$823$	3.34607	+	0.896575i	0.116637	+	0.0312527i	−0.200029	+	0.979790i	$0.564104\pi$
$824$	−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	$0.692168\pi$
$828$	−6.00361	−	22.4058i	−0.208640	−	0.778654i
$829$	8.83013	+	15.2942i	0.306683	+	0.531191i	0.977635	−	0.210311i	$-0.0674475\pi$
$829$	8.83013	+	15.2942i	0.306683	+	0.531191i	−0.670952	+	0.741501i	$0.734114\pi$
$830$		0			0
$831$	58.1769	+	33.5885i	2.01813	+	1.16517i
$832$	−2.96713	+	2.96713i	−0.102867	+	0.102867i
$833$	5.34727	+	44.9316i	0.185272	+	1.55679i
$834$			9.46410i			0.327715i
$835$		0			0
$836$		0			0
$837$	1.79315	−	6.69213i	0.0619804	−	0.231314i
$838$	22.1977	−	5.94786i	0.766807	−	0.205465i
$839$	−55.9808			−1.93267			−0.966335	−	0.257286i	$-0.917172\pi$
$839$	−55.9808			−1.93267			−0.966335	+	0.257286i	$0.917172\pi$
$840$		0			0
$841$	17.0000			0.586207
$842$	−35.1523	+	9.41902i	−1.21143	+	0.324601i
$843$	12.3998	−	46.2765i	0.427070	−	1.59385i
$844$	0.169873	−	0.0980762i	0.00584727	−	0.00337592i
$845$		0			0
$846$			44.3205i			1.52377i
$847$	27.1153	−	13.1626i	0.931692	−	0.452273i
$848$	−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
$852$	5.22715	+	19.5080i	0.179079	+	0.668333i
$853$	20.2151	+	20.2151i	0.692152	+	0.692152i	0.962705	−	0.270553i	$-0.0872067\pi$
$853$	20.2151	+	20.2151i	0.692152	+	0.692152i	−0.270553	+	0.962705i	$0.587207\pi$
$854$	−18.5885	−	21.4641i	−0.636084	−	0.734486i
$855$		0			0
$856$	−4.09808	+	7.09808i	−0.140069	+	0.242607i
$857$	45.9483	+	12.3118i	1.56957	+	0.420564i	0.935676	−	0.352860i	$-0.114791\pi$
$857$	45.9483	+	12.3118i	1.56957	+	0.420564i	0.633889	+	0.773424i	$0.281458\pi$
$858$	−52.4002	−	14.0406i	−1.78891	−	0.479338i
$859$	−26.4904	+	45.8827i	−0.903840	+	1.56550i	−0.0813735	+	0.996684i	$0.525931\pi$
$859$	−26.4904	+	45.8827i	−0.903840	+	1.56550i	−0.822467	+	0.568813i	$0.807403\pi$
$860$		0			0
$861$	3.80385	+	4.39230i	0.129635	+	0.149689i
$862$	17.2987	+	17.2987i	0.589197	+	0.589197i
$863$	−3.31388	−	12.3676i	−0.112806	−	0.420997i	0.886308	−	0.463097i	$-0.153262\pi$
$863$	−3.31388	−	12.3676i	−0.112806	−	0.420997i	−0.999113	+	0.0421001i	$0.986595\pi$
$864$	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
$868$	4.12252	−	2.00120i	0.139928	−	0.0679252i
$869$			44.4449i			1.50769i
$870$		0			0
$871$	51.5885	−	29.7846i	1.74801	−	1.00921i
$872$	−0.0507680	+	0.189469i	−0.00171922	+	0.00641622i
$873$	40.4995	−	10.8518i	1.37070	−	0.367278i
$874$		0			0
$875$		0			0
$876$	−21.8564			−0.738460
$877$	−23.0943	+	6.18810i	−0.779839	+	0.208957i	−0.626714	−	0.779250i	$-0.715600\pi$
$877$	−23.0943	+	6.18810i	−0.779839	+	0.208957i	−0.153125	+	0.988207i	$0.548934\pi$
$878$	−7.79676	+	29.0979i	−0.263128	+	0.982006i
$879$	−9.80385	+	5.66025i	−0.330676	+	0.190916i
$880$		0			0
$881$		−	27.5885i		−	0.929479i	−0.885448	−	0.464739i	$-0.846148\pi$
$881$		−	27.5885i		−	0.929479i	0.885448	−	0.464739i	$-0.153852\pi$
$882$	−3.69282	−	31.0297i	−0.124344	−	1.04483i
$883$	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
$887$	−2.68973	−	10.0382i	−0.0903122	−	0.337050i	0.905955	−	0.423374i	$-0.139154\pi$
$887$	−2.68973	−	10.0382i	−0.0903122	−	0.337050i	−0.996267	+	0.0863246i	$0.972488\pi$
$888$	−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
$892$	−11.0041	−	2.94855i	−0.368445	−	0.0987246i
$893$		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
$898$	−6.81225	−	25.4237i	−0.227328	−	0.848398i
$899$	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
$903$	3.76217	−	52.4002i	0.125197	−	1.74377i
$904$			17.1962i			0.571936i
$905$		0			0
$906$	5.66025	−	3.26795i	0.188049	−	0.108570i
$907$	1.16037	−	4.33057i	0.0385296	−	0.143794i	−0.943982	−	0.329998i	$-0.892952\pi$
$907$	1.16037	−	4.33057i	0.0385296	−	0.143794i	0.982511	+	0.186204i	$0.0596185\pi$
$908$	−19.8362	+	5.31508i	−0.658286	+	0.176387i
$909$	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
$913$	−7.34847	+	27.4249i	−0.243199	+	0.907630i
$914$	34.1769	−	19.7321i	1.13047	−	0.652678i
$915$		0			0
$916$			3.80385i			0.125683i
$917$	−9.46979	−	19.5080i	−0.312720	−	0.644210i
$918$	−18.2832	+	18.2832i	−0.603437	+	0.603437i
$919$	−6.06218	−	3.50000i	−0.199973	−	0.115454i	0.396670	−	0.917961i	$-0.370166\pi$
$919$	−6.06218	−	3.50000i	−0.199973	−	0.115454i	−0.596643	+	0.802507i	$0.703499\pi$
$920$		0			0
$921$	11.4641	+	19.8564i	0.377755	+	0.654291i
$922$	6.21166	+	23.1822i	0.204570	+	0.763466i
$923$	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
$927$	56.0559	+	15.0201i	1.84112	+	0.493326i
$928$	−3.34607	−	0.896575i	−0.109840	−	0.0294315i
$929$	22.3923	−	38.7846i	0.734668	−	1.27248i	−0.220201	−	0.975454i	$-0.570671\pi$
$929$	22.3923	−	38.7846i	0.734668	−	1.27248i	0.954869	−	0.297027i	$-0.0959952\pi$
$930$		0			0
$931$		0			0
$932$	4.24264	+	4.24264i	0.138972	+	0.138972i
$933$	−7.91688	−	29.5462i	−0.259187	−	0.967299i
$934$	−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	−0.537797	−	0.843075i	$-0.680743\pi$
$937$	9.34469	−	9.34469i	0.305278	−	0.305278i	0.843075	+	0.537797i	$0.180743\pi$
$938$	21.0609	−	31.0991i	0.687663	−	1.01542i
$939$		−	51.9090i		−	1.69399i
$940$		0			0
$941$	−30.2942	+	17.4904i	−0.987564	+	0.570170i	−0.904545	−	0.426378i	$-0.859789\pi$
$941$	−30.2942	+	17.4904i	−0.987564	+	0.570170i	−0.0830185	+	0.996548i	$0.526456\pi$
$942$	1.41421	−	5.27792i	0.0460776	−	0.171964i
$943$	4.03459	−	1.08107i	0.131384	−	0.0352043i
$944$	3.80385			0.123805
$945$		0			0
$946$	−34.3923			−1.11819
$947$	−20.0764	+	5.37945i	−0.652395	+	0.174809i	−0.569812	−	0.821775i	$-0.692984\pi$
$947$	−20.0764	+	5.37945i	−0.652395	+	0.174809i	−0.0825835	+	0.996584i	$0.526317\pi$
$948$	6.64136	−	24.7859i	0.215701	−	0.805009i
$949$	−29.0718	+	16.7846i	−0.943710	+	0.544851i
$950$		0			0
$951$		−	12.0000i		−	0.389127i
$952$	−17.0585	−	1.22474i	−0.552869	−	0.0396942i
$953$	−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
$957$	−11.5911	−	43.2586i	−0.374687	−	1.39835i
$958$	−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
$962$	−28.0812	−	7.52433i	−0.905374	−	0.242594i
$963$	35.3417	+	9.46979i	1.13887	+	0.305160i
$964$	−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	$0.632079\pi$
$968$	2.94855	+	11.0041i	0.0947698	+	0.353686i
$969$		0			0
$970$		0			0
$971$	−16.6077	−	9.58846i	−0.532966	−	0.307708i	0.209257	−	0.977861i	$-0.432895\pi$
$971$	−16.6077	−	9.58846i	−0.532966	−	0.307708i	−0.742224	+	0.670152i	$0.766229\pi$
$972$	−13.2456	+	13.2456i	−0.424852	+	0.424852i
$973$	7.58871	+	5.13922i	0.243283	+	0.164756i
$974$		−	26.6603i		−	0.854250i
$975$		0			0
$976$	9.29423	−	5.36603i	0.297501	−	0.171762i
$977$	2.17707	−	8.12493i	0.0696506	−	0.259939i	−0.922317	−	0.386435i	$-0.873706\pi$
$977$	2.17707	−	8.12493i	0.0696506	−	0.259939i	0.991967	+	0.126496i	$0.0403730\pi$
$978$	−56.6429	+	15.1774i	−1.81124	+	0.485320i
$979$	−3.80385			−0.121571
$980$		0			0
$981$	0.875644			0.0279572
$982$	21.3011	−	5.70762i	0.679747	−	0.182138i
$983$	10.9991	−	41.0494i	0.350818	−	1.30927i	−0.534848	−	0.844948i	$-0.679631\pi$
$983$	10.9991	−	41.0494i	0.350818	−	1.30927i	0.885666	−	0.464323i	$-0.153702\pi$
$984$	−1.90192	+	1.09808i	−0.0606311	+	0.0350054i
$985$		0			0
$986$		−	22.3923i		−	0.713116i
$987$	59.4205	+	40.2407i	1.89138	+	1.28088i
$988$		0			0
$989$	−32.7058	−	18.8827i	−1.03998	−	0.600434i
$990$		0			0
$991$	−9.50000	−	16.4545i	−0.301777	−	0.522694i	0.674761	−	0.738036i	$-0.264247\pi$
$991$	−9.50000	−	16.4545i	−0.301777	−	0.522694i	−0.976539	+	0.215342i	$0.930913\pi$
$992$	0.448288	+	1.67303i	0.0142331	+	0.0531188i
$993$	−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
$997$	−39.7738	−	10.6574i	−1.25965	−	0.337522i	−0.433593	−	0.901109i	$-0.642755\pi$
$997$	−39.7738	−	10.6574i	−1.25965	−	0.337522i	−0.826057	+	0.563586i	$0.809421\pi$
$998$	37.0841	+	9.93666i	1.17388	+	0.314539i
$999$	−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.a.257.2	yes	8
5.2	odd	4		350.2.o.b.243.2	yes	8
5.3	odd	4		350.2.o.b.243.1	yes	8
5.4	even	2	inner	350.2.o.a.257.1	yes	8
7.3	odd	6		350.2.o.b.157.1	yes	8
35.3	even	12	inner	350.2.o.a.143.2	yes	8
35.17	even	12	inner	350.2.o.a.143.1	✓	8
35.24	odd	6		350.2.o.b.157.2	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
350.2.o.a.143.1	✓	8	35.17	even	12	inner
350.2.o.a.143.2	yes	8	35.3	even	12	inner
350.2.o.a.257.1	yes	8	5.4	even	2	inner
350.2.o.a.257.2	yes	8	1.1	even	1	trivial
350.2.o.b.157.1	yes	8	7.3	odd	6
350.2.o.b.157.2	yes	8	35.24	odd	6
350.2.o.b.243.1	yes	8	5.3	odd	4
350.2.o.b.243.2	yes	8	5.2	odd	4

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)

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