LMFDB - Embedded newform 867.2.h.m.688.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [867,2,Mod(688,867)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("867.688"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(867, base_ring=CyclotomicField(8)) chi = DirichletCharacter(H, H._module([0, 5])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 867 = 3 \cdot 17^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	867.h (of order $8$, degree $4$, not minimal)

Newform invariants

comment:select newform

sage:traces = [48,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-120] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(16)] == traces)

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

Self dual:	no
Analytic conductor:	$6.92302985525$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$12$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			688.3
Character	$\chi$	$=$	867.688
Dual form			867.2.h.m.712.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.72814 + 1.72814i) q^{2} +(-0.382683 + 0.923880i) q^{3} -3.97290i q^{4} +(-2.65475 - 1.09964i) q^{5} +(-0.935260 - 2.25792i) q^{6} +(1.44358 - 0.597950i) q^{7} +(3.40944 + 3.40944i) q^{8} +(-0.707107 - 0.707107i) q^{9} +(6.48809 - 2.68746i) q^{10} +(-2.42716 - 5.85969i) q^{11} +(3.67048 + 1.52036i) q^{12} +0.803928i q^{13} +(-1.46136 + 3.52804i) q^{14} +(2.03186 - 2.03186i) q^{15} -3.83815 q^{16} +2.44395 q^{18} +(-2.29932 + 2.29932i) q^{19} +(-4.36874 + 10.5471i) q^{20} +1.56252i q^{21} +(14.3208 + 5.93187i) q^{22} +(2.36264 + 5.70393i) q^{23} +(-4.45465 + 1.84518i) q^{24} +(2.30299 + 2.30299i) q^{25} +(-1.38930 - 1.38930i) q^{26} +(0.923880 - 0.382683i) q^{27} +(-2.37560 - 5.73519i) q^{28} +(-1.41257 - 0.585104i) q^{29} +7.02266i q^{30} +(0.831623 - 2.00771i) q^{31} +(-0.186048 + 0.186048i) q^{32} +6.34249 q^{33} -4.48987 q^{35} +(-2.80927 + 2.80927i) q^{36} +(-0.243477 + 0.587805i) q^{37} -7.94707i q^{38} +(-0.742733 - 0.307650i) q^{39} +(-5.30209 - 12.8004i) q^{40} +(-5.18831 + 2.14907i) q^{41} +(-2.70024 - 2.70024i) q^{42} +(7.79523 + 7.79523i) q^{43} +(-23.2800 + 9.64289i) q^{44} +(1.09964 + 2.65475i) q^{45} +(-13.9401 - 5.77419i) q^{46} +7.46399i q^{47} +(1.46879 - 3.54598i) q^{48} +(-3.22337 + 3.22337i) q^{49} -7.95975 q^{50} +3.19393 q^{52} +(-0.952419 + 0.952419i) q^{53} +(-0.935260 + 2.25792i) q^{54} +18.2250i q^{55} +(6.96047 + 2.88312i) q^{56} +(-1.24438 - 3.00421i) q^{57} +(3.45224 - 1.42997i) q^{58} +(2.85255 + 2.85255i) q^{59} +(-8.07238 - 8.07238i) q^{60} +(7.73119 - 3.20237i) q^{61} +(2.03245 + 4.90676i) q^{62} +(-1.44358 - 0.597950i) q^{63} -8.31932i q^{64} +(0.884028 - 2.13423i) q^{65} +(-10.9607 + 10.9607i) q^{66} -7.75709 q^{67} -6.17389 q^{69} +(7.75911 - 7.75911i) q^{70} +(1.72877 - 4.17362i) q^{71} -4.82168i q^{72} +(-7.65058 - 3.16897i) q^{73} +(-0.595046 - 1.43657i) q^{74} +(-3.00900 + 1.24637i) q^{75} +(9.13498 + 9.13498i) q^{76} +(-7.00760 - 7.00760i) q^{77} +(1.81520 - 0.751882i) q^{78} +(0.576780 + 1.39247i) q^{79} +(10.1893 + 4.22056i) q^{80} +1.00000i q^{81} +(5.25222 - 12.6800i) q^{82} +(5.32113 - 5.32113i) q^{83} +6.20773 q^{84} -26.9424 q^{86} +(1.08113 - 1.08113i) q^{87} +(11.7030 - 28.2536i) q^{88} +6.12748i q^{89} +(-6.48809 - 2.68746i) q^{90} +(0.480709 + 1.16053i) q^{91} +(22.6611 - 9.38655i) q^{92} +(1.53664 + 1.53664i) q^{93} +(-12.8988 - 12.8988i) q^{94} +(8.63255 - 3.57572i) q^{95} +(-0.100689 - 0.243084i) q^{96} +(4.47303 + 1.85279i) q^{97} -11.1408i q^{98} +(-2.42716 + 5.85969i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 120 q^{16} + 24 q^{18} + 72 q^{33} - 96 q^{50} - 144 q^{52} + 48 q^{67} - 72 q^{69} + 120 q^{84} + 48 q^{86}+O(q^{100}) $ 48 * q - 120 * q^16 + 24 * q^18 + 72 * q^33 - 96 * q^50 - 144 * q^52 + 48 * q^67 - 72 * q^69 + 120 * q^84 + 48 * q^86

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/867\mathbb{Z}\right)^\times$.

$n$	$290$	$292$
$\chi(n)$	$1$	$e\left(\frac{5}{8}\right)$

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 $

$2$	−1.72814	+	1.72814i	−1.22198	+	1.22198i	−0.255048	+	0.966929i	$0.582091\pi$
$2$	−1.72814	+	1.72814i	−1.22198	+	1.22198i	−0.966929	+	0.255048i	$0.917909\pi$
$3$	−0.382683	+	0.923880i	−0.220942	+	0.533402i
$3$	−0.382683	+	0.923880i	−0.220942	+	0.533402i
$4$		−	3.97290i		−	1.98645i
$5$	−2.65475	−	1.09964i	−1.18724	−	0.491772i	−0.300386	−	0.953818i	$-0.597116\pi$
$5$	−2.65475	−	1.09964i	−1.18724	−	0.491772i	−0.886856	+	0.462046i	$0.847116\pi$
$6$	−0.935260	−	2.25792i	−0.381818	−	0.921791i
$7$	1.44358	−	0.597950i	0.545621	−	0.226004i	−0.0928083	−	0.995684i	$-0.529584\pi$
$7$	1.44358	−	0.597950i	0.545621	−	0.226004i	0.638430	+	0.769680i	$0.279584\pi$
$8$	3.40944	+	3.40944i	1.20542	+	1.20542i
$9$	−0.707107	−	0.707107i	−0.235702	−	0.235702i
$10$	6.48809	−	2.68746i	2.05172	−	0.849848i
$11$	−2.42716	−	5.85969i	−0.731818	−	1.76676i	−0.636444	−	0.771323i	$-0.719596\pi$
$11$	−2.42716	−	5.85969i	−0.731818	−	1.76676i	−0.0953733	−	0.995442i	$-0.530404\pi$
$12$	3.67048	+	1.52036i	1.05958	+	0.438891i
$13$			0.803928i			0.222970i	0.993766	+	0.111485i	$0.0355606\pi$
$13$			0.803928i			0.222970i	−0.993766	+	0.111485i	$0.964439\pi$
$14$	−1.46136	+	3.52804i	−0.390565	+	0.942907i
$15$	2.03186	−	2.03186i	0.524624	−	0.524624i
$16$	−3.83815			−0.959536
$17$		0			0
$17$		0			0
$18$	2.44395			0.576045
$19$	−2.29932	+	2.29932i	−0.527500	+	0.527500i	−0.919826	−	0.392326i	$-0.871671\pi$
$19$	−2.29932	+	2.29932i	−0.527500	+	0.527500i	0.392326	+	0.919826i	$0.371671\pi$
$20$	−4.36874	+	10.5471i	−0.976881	+	2.35840i
$21$			1.56252i			0.340969i
$22$	14.3208	+	5.93187i	3.05321	+	1.26468i
$23$	2.36264	+	5.70393i	0.492645	+	1.18935i	0.953369	+	0.301807i	$0.0975899\pi$
$23$	2.36264	+	5.70393i	0.492645	+	1.18935i	−0.460724	+	0.887544i	$0.652410\pi$
$24$	−4.45465	+	1.84518i	−0.909301	+	0.376645i
$25$	2.30299	+	2.30299i	0.460598	+	0.460598i
$26$	−1.38930	−	1.38930i	−0.272463	−	0.272463i
$27$	0.923880	−	0.382683i	0.177801	−	0.0736475i
$28$	−2.37560	−	5.73519i	−0.448945	−	1.08385i
$29$	−1.41257	−	0.585104i	−0.262307	−	0.108651i	0.247654	−	0.968848i	$-0.420340\pi$
$29$	−1.41257	−	0.585104i	−0.262307	−	0.108651i	−0.509961	+	0.860197i	$0.670340\pi$
$30$			7.02266i			1.28216i
$31$	0.831623	−	2.00771i	0.149364	−	0.360596i	−0.831434	−	0.555624i	$-0.812480\pi$
$31$	0.831623	−	2.00771i	0.149364	−	0.360596i	0.980798	+	0.195027i	$0.0624796\pi$
$32$	−0.186048	+	0.186048i	−0.0328890	+	0.0328890i
$33$	6.34249			1.10409
$34$		0			0
$35$	−4.48987			−0.758927
$36$	−2.80927	+	2.80927i	−0.468211	+	0.468211i
$37$	−0.243477	+	0.587805i	−0.0400274	+	0.0966346i	−0.942629	−	0.333842i	$-0.891655\pi$
$37$	−0.243477	+	0.587805i	−0.0400274	+	0.0966346i	0.902602	+	0.430477i	$0.141655\pi$
$38$		−	7.94707i		−	1.28919i
$39$	−0.742733	−	0.307650i	−0.118932	−	0.0492634i
$40$	−5.30209	−	12.8004i	−0.838334	−	2.02392i
$41$	−5.18831	+	2.14907i	−0.810278	+	0.335628i	−0.749065	−	0.662496i	$-0.769497\pi$
$41$	−5.18831	+	2.14907i	−0.810278	+	0.335628i	−0.0612132	+	0.998125i	$0.519497\pi$
$42$	−2.70024	−	2.70024i	−0.416656	−	0.416656i
$43$	7.79523	+	7.79523i	1.18876	+	1.18876i	0.977410	+	0.211352i	$0.0677865\pi$
$43$	7.79523	+	7.79523i	1.18876	+	1.18876i	0.211352	+	0.977410i	$0.432213\pi$
$44$	−23.2800	+	9.64289i	−3.50959	+	1.45372i
$45$	1.09964	+	2.65475i	0.163924	+	0.395747i
$46$	−13.9401	−	5.77419i	−2.05536	−	0.851358i
$47$			7.46399i			1.08874i	0.838847	+	0.544368i	$0.183230\pi$
$47$			7.46399i			1.08874i	−0.838847	+	0.544368i	$0.816770\pi$
$48$	1.46879	−	3.54598i	0.212002	−	0.511819i
$49$	−3.22337	+	3.22337i	−0.460482	+	0.460482i
$50$	−7.95975			−1.12568
$51$		0			0
$52$	3.19393			0.442918
$53$	−0.952419	+	0.952419i	−0.130825	+	0.130825i	−0.769487	−	0.638662i	$-0.779488\pi$
$53$	−0.952419	+	0.952419i	−0.130825	+	0.130825i	0.638662	+	0.769487i	$0.279488\pi$
$54$	−0.935260	+	2.25792i	−0.127273	+	0.307264i
$55$			18.2250i			2.45746i
$56$	6.96047	+	2.88312i	0.930132	+	0.385273i
$57$	−1.24438	−	3.00421i	−0.164823	−	0.397917i
$58$	3.45224	−	1.42997i	0.453302	−	0.187764i
$59$	2.85255	+	2.85255i	0.371371	+	0.371371i	0.867976	−	0.496605i	$-0.165420\pi$
$59$	2.85255	+	2.85255i	0.371371	+	0.371371i	−0.496605	+	0.867976i	$0.665420\pi$
$60$	−8.07238	−	8.07238i	−1.04214	−	1.04214i
$61$	7.73119	−	3.20237i	0.989878	−	0.410021i	0.171802	−	0.985131i	$-0.445041\pi$
$61$	7.73119	−	3.20237i	0.989878	−	0.410021i	0.818076	+	0.575111i	$0.195041\pi$
$62$	2.03245	+	4.90676i	0.258121	+	0.623159i
$63$	−1.44358	−	0.597950i	−0.181874	−	0.0753346i
$64$		−	8.31932i		−	1.03992i
$65$	0.884028	−	2.13423i	0.109650	−	0.264719i
$66$	−10.9607	+	10.9607i	−1.34917	+	1.34917i
$67$	−7.75709			−0.947680			−0.473840	−	0.880611i	$-0.657132\pi$
$67$	−7.75709			−0.947680			−0.473840	+	0.880611i	$0.657132\pi$
$68$		0			0
$69$	−6.17389			−0.743248
$70$	7.75911	−	7.75911i	0.927391	−	0.927391i
$71$	1.72877	−	4.17362i	0.205167	−	0.495317i	−0.787483	−	0.616336i	$-0.788616\pi$
$71$	1.72877	−	4.17362i	0.205167	−	0.495317i	0.992650	+	0.121019i	$0.0386162\pi$
$72$		−	4.82168i		−	0.568240i
$73$	−7.65058	−	3.16897i	−0.895433	−	0.370900i	−0.112970	−	0.993598i	$-0.536037\pi$
$73$	−7.65058	−	3.16897i	−0.895433	−	0.370900i	−0.782462	+	0.622698i	$0.786037\pi$
$74$	−0.595046	−	1.43657i	−0.0691727	−	0.166998i
$75$	−3.00900	+	1.24637i	−0.347449	+	0.143918i
$76$	9.13498	+	9.13498i	1.04785	+	1.04785i
$77$	−7.00760	−	7.00760i	−0.798591	−	0.798591i
$78$	1.81520	−	0.751882i	0.205531	−	0.0851338i
$79$	0.576780	+	1.39247i	0.0648928	+	0.156665i	0.952999	−	0.302973i	$-0.0979792\pi$
$79$	0.576780	+	1.39247i	0.0648928	+	0.156665i	−0.888106	+	0.459638i	$0.847979\pi$
$80$	10.1893	+	4.22056i	1.13920	+	0.471873i
$81$			1.00000i			0.111111i
$82$	5.25222	−	12.6800i	0.580011	−	1.40027i
$83$	5.32113	−	5.32113i	0.584070	−	0.584070i	−0.351949	−	0.936019i	$-0.614481\pi$
$83$	5.32113	−	5.32113i	0.584070	−	0.584070i	0.936019	+	0.351949i	$0.114481\pi$
$84$	6.20773			0.677319
$85$		0			0
$86$	−26.9424			−2.90528
$87$	1.08113	−	1.08113i	0.115909	−	0.115909i
$88$	11.7030	−	28.2536i	1.24754	−	3.01184i
$89$			6.12748i			0.649511i	0.945798	+	0.324756i	$0.105282\pi$
$89$			6.12748i			0.649511i	−0.945798	+	0.324756i	$0.894718\pi$
$90$	−6.48809	−	2.68746i	−0.683905	−	0.283283i
$91$	0.480709	+	1.16053i	0.0503919	+	0.121657i
$92$	22.6611	−	9.38655i	2.36259	−	0.978616i
$93$	1.53664	+	1.53664i	0.159342	+	0.159342i
$94$	−12.8988	−	12.8988i	−1.33041	−	1.33041i
$95$	8.63255	−	3.57572i	0.885681	−	0.366861i
$96$	−0.100689	−	0.243084i	−0.0102765	−	0.0248097i
$97$	4.47303	+	1.85279i	0.454168	+	0.188122i	0.598027	−	0.801476i	$-0.295951\pi$
$97$	4.47303	+	1.85279i	0.454168	+	0.188122i	−0.143860	+	0.989598i	$0.545951\pi$
$98$		−	11.1408i		−	1.12540i
$99$	−2.42716	+	5.85969i	−0.243939	+	0.588921i
$100$	9.14955	−	9.14955i	0.914955	−	0.914955i
$101$	15.8161			1.57376			0.786882	−	0.617104i	$-0.211694\pi$
$101$	15.8161			1.57376			0.786882	+	0.617104i	$0.211694\pi$
$102$		0			0
$103$	−7.19272			−0.708720			−0.354360	−	0.935109i	$-0.615301\pi$
$103$	−7.19272			−0.708720			−0.354360	+	0.935109i	$0.615301\pi$
$104$	−2.74094	+	2.74094i	−0.268772	+	0.268772i
$105$	1.71820	−	4.14810i	0.167679	−	0.404813i
$106$		−	3.29182i		−	0.319730i
$107$	−3.39774	−	1.40739i	−0.328472	−	0.136057i	0.212352	−	0.977193i	$-0.431888\pi$
$107$	−3.39774	−	1.40739i	−0.328472	−	0.136057i	−0.540824	+	0.841136i	$0.681888\pi$
$108$	−1.52036	−	3.67048i	−0.146297	−	0.353192i
$109$	−9.50083	+	3.93537i	−0.910014	+	0.376940i	−0.788062	−	0.615596i	$-0.788915\pi$
$109$	−9.50083	+	3.93537i	−0.910014	+	0.376940i	−0.121952	+	0.992536i	$0.538915\pi$
$110$	−31.4953	−	31.4953i	−3.00296	−	3.00296i
$111$	−0.449887	−	0.449887i	−0.0427014	−	0.0427014i
$112$	−5.54066	+	2.29502i	−0.523543	+	0.216859i
$113$	5.33089	+	12.8699i	0.501488	+	1.21070i	0.948673	+	0.316258i	$0.102427\pi$
$113$	5.33089	+	12.8699i	0.501488	+	1.21070i	−0.447185	+	0.894442i	$0.647573\pi$
$114$	7.34214	+	3.04121i	0.687654	+	0.284836i
$115$		−	17.7406i		−	1.65432i
$116$	−2.32456	+	5.61198i	−0.215830	+	0.521060i
$117$	0.568463	−	0.568463i	0.0525544	−	0.0525544i
$118$	−9.85920			−0.907613
$119$		0			0
$120$	13.8550			1.26478
$121$	−20.6667	+	20.6667i	−1.87879	+	1.87879i
$122$	−7.82643	+	18.8947i	−0.708572	+	1.71064i
$123$		−	5.61579i		−	0.506359i
$124$	−7.97645	−	3.30395i	−0.716307	−	0.296704i
$125$	1.91675	+	4.62745i	0.171440	+	0.413892i
$126$	3.52804	−	1.46136i	0.314302	−	0.130188i
$127$	1.53967	+	1.53967i	0.136624	+	0.136624i	0.772111	−	0.635487i	$-0.219201\pi$
$127$	1.53967	+	1.53967i	0.136624	+	0.136624i	−0.635487	+	0.772111i	$0.719201\pi$
$128$	14.0048	+	14.0048i	1.23786	+	1.23786i
$129$	−10.1850	+	4.21875i	−0.896736	+	0.371440i
$130$	2.16052	+	5.21596i	0.189490	+	0.457470i
$131$	−4.07304	−	1.68711i	−0.355863	−	0.147403i	0.197588	−	0.980285i	$-0.436689\pi$
$131$	−4.07304	−	1.68711i	−0.355863	−	0.147403i	−0.553451	+	0.832882i	$0.686689\pi$
$132$		−	25.1981i		−	2.19321i
$133$	−1.94437	+	4.69413i	−0.168598	+	0.407033i
$134$	13.4053	−	13.4053i	1.15804	−	1.15804i
$135$	−2.87349			−0.247310
$136$		0			0
$137$	0.311499			0.0266131			0.0133066	−	0.999911i	$-0.495764\pi$
$137$	0.311499			0.0266131			0.0133066	+	0.999911i	$0.495764\pi$
$138$	10.6693	−	10.6693i	0.908232	−	0.908232i
$139$	4.13671	−	9.98691i	0.350871	−	0.847078i	−0.645642	−	0.763641i	$-0.723410\pi$
$139$	4.13671	−	9.98691i	0.350871	−	0.847078i	0.996513	−	0.0834378i	$-0.0265900\pi$
$140$			17.8378i			1.50757i
$141$	−6.89583	−	2.85635i	−0.580734	−	0.240548i
$142$	4.22503	+	10.2001i	0.354556	+	0.855975i
$143$	4.71077	−	1.95127i	0.393935	−	0.163173i
$144$	2.71398	+	2.71398i	0.226165	+	0.226165i
$145$	3.10661	+	3.10661i	0.257990	+	0.257990i
$146$	18.6977	−	7.74482i	1.54743	−	0.640966i
$147$	−1.74448	−	4.21154i	−0.143882	−	0.347362i
$148$	2.33529	+	0.967310i	0.191960	+	0.0795124i
$149$			17.7269i			1.45225i	0.687565	+	0.726123i	$0.258680\pi$
$149$			17.7269i			1.45225i	−0.687565	+	0.726123i	$0.741320\pi$
$150$	3.04607	−	7.35385i	0.248710	−	0.600440i
$151$	−11.4017	+	11.4017i	−0.927856	+	0.927856i	−0.997567	−	0.0697111i	$-0.977792\pi$
$151$	−11.4017	+	11.4017i	−0.927856	+	0.927856i	0.0697111	+	0.997567i	$0.477792\pi$
$152$	−15.6788			−1.27172
$153$		0			0
$154$	24.2202			1.95172
$155$	−4.41551	+	4.41551i	−0.354662	+	0.354662i
$156$	−1.22226	+	2.95080i	−0.0978594	+	0.236253i
$157$		−	19.6347i		−	1.56702i	−0.621380	−	0.783510i	$-0.713428\pi$
$157$		−	19.6347i		−	1.56702i	0.621380	−	0.783510i	$-0.286572\pi$
$158$	−3.40313	−	1.40962i	−0.270738	−	0.112144i
$159$	−0.515446	−	1.24440i	−0.0408775	−	0.0986870i
$160$	0.698499	−	0.289328i	0.0552212	−	0.0228734i
$161$	6.82132	+	6.82132i	0.537595	+	0.537595i
$162$	−1.72814	−	1.72814i	−0.135775	−	0.135775i
$163$	−10.0496	+	4.16269i	−0.787147	+	0.326047i	−0.739796	−	0.672831i	$-0.765078\pi$
$163$	−10.0496	+	4.16269i	−0.787147	+	0.326047i	−0.0473511	+	0.998878i	$0.515078\pi$
$164$	8.53804	+	20.6127i	0.666709	+	1.60958i
$165$	−16.8377	−	6.97442i	−1.31082	−	0.542958i
$166$			18.3913i			1.42744i
$167$	−4.02356	+	9.71373i	−0.311352	+	0.751671i	0.688303	+	0.725423i	$0.258356\pi$
$167$	−4.02356	+	9.71373i	−0.311352	+	0.751671i	−0.999655	+	0.0262480i	$0.991644\pi$
$168$	−5.32731	+	5.32731i	−0.411011	+	0.411011i
$169$	12.3537			0.950285
$170$		0			0
$171$	3.25173			0.248666
$172$	30.9697	−	30.9697i	2.36142	−	2.36142i
$173$	2.96520	−	7.15863i	0.225440	−	0.544261i	−0.770172	−	0.637836i	$-0.779830\pi$
$173$	2.96520	−	7.15863i	0.225440	−	0.544261i	0.995612	+	0.0935754i	$0.0298296\pi$
$174$			3.73668i			0.283277i
$175$	4.70162	+	1.94747i	0.355409	+	0.147215i
$176$	9.31581	+	22.4904i	0.702206	+	1.69527i
$177$	−3.72704	+	1.54379i	−0.280142	+	0.116038i
$178$	−10.5891	−	10.5891i	−0.793687	−	0.793687i
$179$	8.44819	+	8.44819i	0.631447	+	0.631447i	0.948431	−	0.316984i	$-0.102670\pi$
$179$	8.44819	+	8.44819i	0.631447	+	0.631447i	−0.316984	+	0.948431i	$0.602670\pi$
$180$	10.5471	−	4.36874i	0.786133	−	0.325627i
$181$	−0.670892	−	1.61968i	−0.0498670	−	0.120390i	0.896983	−	0.442065i	$-0.145754\pi$
$181$	−0.670892	−	1.61968i	−0.0498670	−	0.120390i	−0.946850	+	0.321676i	$0.895754\pi$
$182$	−2.83629	−	1.17483i	−0.210240	−	0.0870841i
$183$			8.36818i			0.618594i
$184$	−11.3919	+	27.5025i	−0.839822	+	2.02751i
$185$	1.29274	−	1.29274i	0.0950444	−	0.0950444i
$186$	−5.31104			−0.389424
$187$		0			0
$188$	29.6537			2.16272
$189$	1.10487	−	1.10487i	0.0803672	−	0.0803672i
$190$	−8.73888	+	21.0975i	−0.633985	+	1.53058i
$191$			22.3232i			1.61525i	0.589694	+	0.807627i	$0.299248\pi$
$191$			22.3232i			1.61525i	−0.589694	+	0.807627i	$0.700752\pi$
$192$	7.68605	+	3.18367i	0.554693	+	0.229761i
$193$	10.0101	+	24.1665i	0.720543	+	1.73954i	0.671799	+	0.740733i	$0.265522\pi$
$193$	10.0101	+	24.1665i	0.720543	+	1.73954i	0.0487439	+	0.998811i	$0.484478\pi$
$194$	−10.9319	+	4.52813i	−0.784863	+	0.325101i
$195$	1.63347	+	1.63347i	0.116975	+	0.116975i
$196$	12.8061	+	12.8061i	0.914725	+	0.914725i
$197$	−16.4414	+	6.81025i	−1.17140	+	0.485210i	−0.881655	−	0.471894i	$-0.843571\pi$
$197$	−16.4414	+	6.81025i	−1.17140	+	0.485210i	−0.289745	+	0.957104i	$0.593571\pi$
$198$	−5.93187	−	14.3208i	−0.421560	−	1.01774i
$199$	20.9296	+	8.66932i	1.48366	+	0.614552i	0.969927	−	0.243398i	$-0.0782620\pi$
$199$	20.9296	+	8.66932i	1.48366	+	0.614552i	0.513733	+	0.857950i	$0.328262\pi$
$200$			15.7038i			1.11043i
$201$	2.96851	−	7.16662i	0.209383	−	0.505494i
$202$	−27.3324	+	27.3324i	−1.92310	+	1.92310i
$203$	−2.38901			−0.167676
$204$		0			0
$205$	16.1369			1.12705
$206$	12.4300	−	12.4300i	0.866039	−	0.866039i
$207$	2.36264	−	5.70393i	0.164215	−	0.396450i
$208$		−	3.08559i		−	0.213947i
$209$	19.0541	+	7.89249i	1.31800	+	0.545935i
$210$	4.19920	+	10.1378i	0.289772	+	0.699572i
$211$	−20.9956	+	8.69668i	−1.44540	+	0.598704i	−0.961101	−	0.276198i	$-0.910925\pi$
$211$	−20.9956	+	8.69668i	−1.44540	+	0.598704i	−0.484299	+	0.874903i	$0.660925\pi$
$212$	3.78387	+	3.78387i	0.259877	+	0.259877i
$213$	3.19435	+	3.19435i	0.218873	+	0.218873i
$214$	8.30391	−	3.43959i	0.567644	−	0.235126i
$215$	−12.1225	−	29.2663i	−0.826749	−	1.99595i
$216$	4.45465	+	1.84518i	0.303100	+	0.125548i
$217$		−	3.39556i		−	0.230506i
$218$	9.61786	−	23.2196i	0.651404	−	1.57263i
$219$	5.85550	−	5.85550i	0.395678	−	0.395678i
$220$	72.4063			4.88163
$221$		0			0
$222$	1.55493			0.104360
$223$	−0.420543	+	0.420543i	−0.0281616	+	0.0281616i	−0.721047	−	0.692886i	$-0.756339\pi$
$223$	−0.420543	+	0.420543i	−0.0281616	+	0.0281616i	0.692886	+	0.721047i	$0.256339\pi$
$224$	−0.157328	+	0.379823i	−0.0105119	+	0.0253780i
$225$		−	3.25692i		−	0.217128i
$226$	−31.4535	−	13.0284i	−2.09225	−	0.866640i
$227$	−7.67010	−	18.5173i	−0.509082	−	1.22903i	−0.944413	−	0.328763i	$-0.893368\pi$
$227$	−7.67010	−	18.5173i	−0.509082	−	1.22903i	0.435330	−	0.900271i	$-0.356632\pi$
$228$	−11.9354	+	4.94381i	−0.790443	+	0.327412i
$229$	1.37160	+	1.37160i	0.0906382	+	0.0906382i	0.750972	−	0.660334i	$-0.229585\pi$
$229$	1.37160	+	1.37160i	0.0906382	+	0.0906382i	−0.660334	+	0.750972i	$0.729585\pi$
$230$	30.6581	+	30.6581i	2.02154	+	2.02154i
$231$	9.15588	−	3.79249i	0.602412	−	0.249527i
$232$	−2.82118	−	6.81093i	−0.185220	−	0.447160i
$233$	7.80008	+	3.23090i	0.511000	+	0.211663i	0.623259	−	0.782016i	$-0.285808\pi$
$233$	7.80008	+	3.23090i	0.511000	+	0.211663i	−0.112258	+	0.993679i	$0.535808\pi$
$234$			1.96476i			0.128440i
$235$	8.20767	−	19.8151i	0.535409	−	1.29259i
$236$	11.3329	−	11.3329i	0.737710	−	0.737710i
$237$	−1.50720			−0.0979031
$238$		0			0
$239$	15.5030			1.00281			0.501403	−	0.865214i	$-0.332817\pi$
$239$	15.5030			1.00281			0.501403	+	0.865214i	$0.332817\pi$
$240$	−7.79858	+	7.79858i	−0.503396	+	0.503396i
$241$	−11.4008	+	27.5240i	−0.734391	+	1.77298i	−0.107017	+	0.994257i	$0.534130\pi$
$241$	−11.4008	+	27.5240i	−0.734391	+	1.77298i	−0.627374	+	0.778718i	$0.715870\pi$
$242$		−	71.4297i		−	4.59168i
$243$	−0.923880	−	0.382683i	−0.0592669	−	0.0245492i
$244$	−12.7227	−	30.7153i	−0.814486	−	1.96634i
$245$	12.1018	−	5.01273i	0.773156	−	0.320252i
$246$	9.70484	+	9.70484i	0.618758	+	0.618758i
$247$	−1.84849	−	1.84849i	−0.117617	−	0.117617i
$248$	9.68055	−	4.00982i	0.614716	−	0.254624i
$249$	2.87977	+	6.95239i	0.182498	+	0.440590i
$250$	−11.3093	−	4.68445i	−0.715261	−	0.296271i
$251$		−	4.59133i		−	0.289802i	−0.989446	−	0.144901i	$-0.953714\pi$
$251$		−	4.59133i		−	0.289802i	0.989446	−	0.144901i	$-0.0462864\pi$
$252$	−2.37560	+	5.73519i	−0.149648	+	0.361283i
$253$	27.6887	−	27.6887i	1.74078	−	1.74078i
$254$	−5.32152			−0.333902
$255$		0			0
$256$	−31.7658			−1.98536
$257$	20.5578	−	20.5578i	1.28236	−	1.28236i	0.343037	−	0.939322i	$-0.388544\pi$
$257$	20.5578	−	20.5578i	1.28236	−	1.28236i	0.939322	−	0.343037i	$-0.111456\pi$
$258$	10.3104	−	24.8916i	0.641899	−	1.54968i
$259$			0.994130i			0.0617722i
$260$	−8.47909	−	3.51215i	−0.525851	−	0.217815i
$261$	0.585104	+	1.41257i	0.0362170	+	0.0874356i
$262$	9.95432	−	4.12321i	0.614980	−	0.254733i
$263$	−0.759845	−	0.759845i	−0.0468541	−	0.0468541i	0.683292	−	0.730146i	$-0.260548\pi$
$263$	−0.759845	−	0.759845i	−0.0468541	−	0.0468541i	−0.730146	+	0.683292i	$0.760548\pi$
$264$	21.6243	+	21.6243i	1.33089	+	1.33089i
$265$	3.57575	−	1.48113i	0.219657	−	0.0909848i
$266$	−4.75195	−	11.4722i	−0.291361	−	0.703407i
$267$	−5.66105	−	2.34488i	−0.346451	−	0.143505i
$268$			30.8182i			1.88252i
$269$	−9.68912	+	23.3916i	−0.590756	+	1.42621i	0.292018	+	0.956413i	$0.405673\pi$
$269$	−9.68912	+	23.3916i	−0.590756	+	1.42621i	−0.882774	+	0.469798i	$0.844327\pi$
$270$	4.96577	−	4.96577i	0.302207	−	0.302207i
$271$	−19.4812			−1.18340			−0.591699	−	0.806159i	$-0.701542\pi$
$271$	−19.4812			−1.18340			−0.591699	+	0.806159i	$0.701542\pi$
$272$		0			0
$273$	−1.25615			−0.0760258
$274$	−0.538312	+	0.538312i	−0.0325206	+	0.0325206i
$275$	7.90508	−	19.0845i	0.476694	−	1.15084i
$276$			24.5282i			1.47643i
$277$	8.77975	+	3.63669i	0.527524	+	0.218508i	0.630518	−	0.776174i	$-0.282842\pi$
$277$	8.77975	+	3.63669i	0.527524	+	0.218508i	−0.102994	+	0.994682i	$0.532842\pi$
$278$	10.1099	+	24.4075i	0.606353	+	1.46387i
$279$	−2.00771	+	0.831623i	−0.120199	+	0.0497879i
$280$	−15.3080	−	15.3080i	−0.914825	−	0.914825i
$281$	−10.1977	−	10.1977i	−0.608344	−	0.608344i	0.334169	−	0.942513i	$-0.391544\pi$
$281$	−10.1977	−	10.1977i	−0.608344	−	0.608344i	−0.942513	+	0.334169i	$0.891544\pi$
$282$	16.8531	−	6.98077i	1.00359	−	0.415699i
$283$	7.42822	+	17.9333i	0.441562	+	1.06602i	0.975401	+	0.220439i	$0.0707488\pi$
$283$	7.42822	+	17.9333i	0.441562	+	1.06602i	−0.533839	+	0.845586i	$0.679251\pi$
$284$	−16.5814	−	6.86823i	−0.983923	−	0.407554i
$285$			9.34380i			0.553479i
$286$	−4.76880	+	11.5129i	−0.281985	+	0.680772i
$287$	−6.20470	+	6.20470i	−0.366252	+	0.366252i
$288$	0.263112			0.0155040
$289$		0			0
$290$	−10.7373			−0.630516
$291$	−3.42351	+	3.42351i	−0.200690	+	0.200690i
$292$	−12.5900	+	30.3950i	−0.736775	+	1.77873i
$293$			1.07338i			0.0627076i	0.999508	+	0.0313538i	$0.00998186\pi$
$293$			1.07338i			0.0627076i	−0.999508	+	0.0313538i	$0.990018\pi$
$294$	10.2928	+	4.26342i	0.600288	+	0.248648i
$295$	−4.43606	−	10.7096i	−0.258278	−	0.623537i
$296$	−2.83421	+	1.17397i	−0.164735	+	0.0682355i
$297$	−4.48482	−	4.48482i	−0.260235	−	0.260235i
$298$	−30.6345	−	30.6345i	−1.77461	−	1.77461i
$299$	−4.58555	+	1.89940i	−0.265189	+	0.109845i
$300$	4.95170	+	11.9545i	0.285887	+	0.690191i
$301$	15.9142	+	6.59187i	0.917278	+	0.379949i
$302$		−	39.4073i		−	2.26764i
$303$	−6.05257	+	14.6122i	−0.347711	+	0.839448i
$304$	8.82513	−	8.82513i	0.506156	−	0.506156i
$305$	−24.0459			−1.37686
$306$		0			0
$307$	14.5796			0.832104			0.416052	−	0.909341i	$-0.363413\pi$
$307$	14.5796			0.832104			0.416052	+	0.909341i	$0.363413\pi$
$308$	−27.8405	+	27.8405i	−1.58636	+	1.58636i
$309$	2.75254	−	6.64521i	0.156586	−	0.378033i
$310$		−	15.2612i		−	0.866777i
$311$	−13.2530	−	5.48957i	−0.751509	−	0.311285i	−0.0261519	−	0.999658i	$-0.508325\pi$
$311$	−13.2530	−	5.48957i	−0.751509	−	0.311285i	−0.725357	+	0.688373i	$0.758325\pi$
$312$	−1.48339	−	3.58122i	−0.0839803	−	0.202746i
$313$	10.4569	−	4.33139i	0.591059	−	0.244825i	−0.0670473	−	0.997750i	$-0.521358\pi$
$313$	10.4569	−	4.33139i	0.591059	−	0.244825i	0.658106	+	0.752925i	$0.271358\pi$
$314$	33.9314	+	33.9314i	1.91486	+	1.91486i
$315$	3.17482	+	3.17482i	0.178881	+	0.178881i
$316$	5.53215	−	2.29149i	0.311208	−	0.128906i
$317$	4.50122	+	10.8669i	0.252814	+	0.610347i	0.998429	−	0.0560300i	$-0.0178442\pi$
$317$	4.50122	+	10.8669i	0.252814	+	0.610347i	−0.745615	+	0.666377i	$0.767844\pi$
$318$	3.04124	+	1.25972i	0.170544	+	0.0706418i
$319$			9.69734i			0.542947i
$320$	−9.14822	+	22.0858i	−0.511401	+	1.23463i
$321$	2.60052	−	2.60052i	0.145147	−	0.145147i
$322$	−23.5763			−1.31386
$323$		0			0
$324$	3.97290			0.220717
$325$	−1.85144	+	1.85144i	−0.102699	+	0.102699i
$326$	10.1734	−	24.5608i	0.563453	−	1.36030i
$327$		−	10.2836i		−	0.568686i
$328$	−25.0164	−	10.3621i	−1.38130	−	0.572152i
$329$	4.46309	+	10.7749i	0.246058	+	0.594037i
$330$	41.1506	−	17.0452i	2.26527	−	0.938305i
$331$	−14.2895	−	14.2895i	−0.785420	−	0.785420i	0.195320	−	0.980740i	$-0.437426\pi$
$331$	−14.2895	−	14.2895i	−0.785420	−	0.785420i	−0.980740	+	0.195320i	$0.937426\pi$
$332$	−21.1403	−	21.1403i	−1.16023	−	1.16023i
$333$	0.587805	−	0.243477i	0.0322115	−	0.0133425i
$334$	−9.83339	−	23.7399i	−0.538059	−	1.29899i
$335$	20.5932	+	8.52997i	1.12513	+	0.466042i
$336$		−	5.99717i		−	0.327172i
$337$	2.45224	−	5.92023i	0.133582	−	0.322496i	−0.842908	−	0.538057i	$-0.819158\pi$
$337$	2.45224	−	5.92023i	0.133582	−	0.322496i	0.976490	+	0.215562i	$0.0691583\pi$
$338$	−21.3489	+	21.3489i	−1.16123	+	1.16123i
$339$	−13.9303			−0.756590
$340$		0			0
$341$	−13.7831			−0.746395
$342$	−5.61943	+	5.61943i	−0.303864	+	0.303864i
$343$	−6.91142	+	16.6857i	−0.373182	+	0.900941i
$344$			53.1548i			2.86591i
$345$	16.3901	+	6.78902i	0.882416	+	0.365509i
$346$	7.24681	+	17.4954i	0.389591	+	0.940556i
$347$	10.8362	−	4.48851i	0.581719	−	0.240956i	−0.0723643	−	0.997378i	$-0.523054\pi$
$347$	10.8362	−	4.48851i	0.581719	−	0.240956i	0.654084	+	0.756422i	$0.273054\pi$
$348$	−4.29523	−	4.29523i	−0.230248	−	0.230248i
$349$	−18.2298	−	18.2298i	−0.975817	−	0.975817i	0.0238972	−	0.999714i	$-0.492393\pi$
$349$	−18.2298	−	18.2298i	−0.975817	−	0.975817i	−0.999714	+	0.0238972i	$0.992393\pi$
$350$	−11.4905	+	4.75953i	−0.614195	+	0.254408i
$351$	0.307650	+	0.742733i	0.0164211	+	0.0396441i
$352$	1.54176	+	0.638617i	0.0821759	+	0.0340384i
$353$		−	3.96309i		−	0.210934i	−0.994423	−	0.105467i	$-0.966366\pi$
$353$		−	3.96309i		−	0.210934i	0.994423	−	0.105467i	$-0.0336337\pi$
$354$	3.77295	−	9.10871i	0.200530	−	0.484123i
$355$	−9.17891	+	9.17891i	−0.487166	+	0.487166i
$356$	24.3439			1.29022
$357$		0			0
$358$	−29.1992			−1.54323
$359$	7.94943	−	7.94943i	0.419555	−	0.419555i	−0.465495	−	0.885050i	$-0.654124\pi$
$359$	7.94943	−	7.94943i	0.419555	−	0.419555i	0.885050	+	0.465495i	$0.154124\pi$
$360$	−5.30209	+	12.8004i	−0.279445	+	0.674639i
$361$			8.42625i			0.443487i
$362$	3.95841	+	1.63963i	0.208049	+	0.0861769i
$363$	−11.1847	−	27.0024i	−0.587047	−	1.41726i
$364$	4.61068	−	1.90981i	0.241665	−	0.100101i
$365$	16.8257	+	16.8257i	0.880697	+	0.880697i
$366$	−14.4614	−	14.4614i	−0.755907	−	0.755907i
$367$	−14.2769	+	5.91367i	−0.745246	+	0.308691i	−0.722800	−	0.691057i	$-0.757145\pi$
$367$	−14.2769	+	5.91367i	−0.745246	+	0.308691i	−0.0224459	+	0.999748i	$0.507145\pi$
$368$	−9.06817	−	21.8925i	−0.472711	−	1.14123i
$369$	5.18831	+	2.14907i	0.270093	+	0.111876i
$370$			4.46807i			0.232284i
$371$	−0.805393	+	1.94439i	−0.0418139	+	0.100948i
$372$	6.10491	−	6.10491i	0.316525	−	0.316525i
$373$	5.14892			0.266601			0.133300	−	0.991076i	$-0.457442\pi$
$373$	5.14892			0.266601			0.133300	+	0.991076i	$0.457442\pi$
$374$		0			0
$375$	−5.00872			−0.258649
$376$	−25.4480	+	25.4480i	−1.31238	+	1.31238i
$377$	0.470381	−	1.13560i	0.0242259	−	0.0584864i
$378$			3.81872i			0.196414i
$379$	−10.9450	−	4.53358i	−0.562209	−	0.232875i	0.0834349	−	0.996513i	$-0.473411\pi$
$379$	−10.9450	−	4.53358i	−0.562209	−	0.232875i	−0.645644	+	0.763639i	$0.723411\pi$
$380$	−14.2060	−	34.2963i	−0.728751	−	1.75936i
$381$	−2.01168	+	0.833264i	−0.103061	+	0.0426894i
$382$	−38.5776	−	38.5776i	−1.97380	−	1.97380i
$383$	−21.7327	−	21.7327i	−1.11049	−	1.11049i	−0.993084	−	0.117404i	$-0.962543\pi$
$383$	−21.7327	−	21.7327i	−1.11049	−	1.11049i	−0.117404	−	0.993084i	$-0.537457\pi$
$384$	−18.2982	+	7.57935i	−0.933775	+	0.386782i
$385$	10.8977	+	26.3093i	0.555396	+	1.34084i
$386$	−59.0618	−	24.4642i	−3.00617	−	1.24520i
$387$		−	11.0241i		−	0.560388i
$388$	7.36096	−	17.7709i	0.373696	−	0.902182i
$389$	13.6827	−	13.6827i	0.693741	−	0.693741i	−0.269312	−	0.963053i	$-0.586796\pi$
$389$	13.6827	−	13.6827i	0.693741	−	0.693741i	0.963053	+	0.269312i	$0.0867962\pi$
$390$	−5.64571			−0.285882
$391$		0			0
$392$	−21.9798			−1.11015
$393$	3.11737	−	3.11737i	0.157251	−	0.157251i
$394$	16.6439	−	40.1820i	0.838508	−	2.02434i
$395$		−	4.33091i		−	0.217912i
$396$	23.2800	+	9.64289i	1.16986	+	0.484573i
$397$	−5.18251	−	12.5117i	−0.260103	−	0.627944i	0.738842	−	0.673879i	$-0.235373\pi$
$397$	−5.18251	−	12.5117i	−0.260103	−	0.627944i	−0.998944	+	0.0459354i	$0.985373\pi$
$398$	−51.1509	+	21.1874i	−2.56397	+	1.06203i
$399$	−3.59273	−	3.59273i	−0.179861	−	0.179861i
$400$	−8.83921	−	8.83921i	−0.441960	−	0.441960i
$401$	−7.99625	+	3.31215i	−0.399314	+	0.165401i	−0.573297	−	0.819347i	$-0.694336\pi$
$401$	−7.99625	+	3.31215i	−0.399314	+	0.165401i	0.173984	+	0.984749i	$0.444336\pi$
$402$	7.25490	+	17.5149i	0.361841	+	0.873563i
$403$	1.61406	+	0.668565i	0.0804019	+	0.0333036i
$404$		−	62.8359i		−	3.12620i
$405$	1.09964	−	2.65475i	0.0546413	−	0.131916i
$406$	4.12853	−	4.12853i	0.204896	−	0.204896i
$407$	4.03532			0.200023
$408$		0			0
$409$	20.2269			1.00015			0.500077	−	0.865981i	$-0.333305\pi$
$409$	20.2269			1.00015			0.500077	+	0.865981i	$0.333305\pi$
$410$	−27.8867	+	27.8867i	−1.37723	+	1.37723i
$411$	−0.119205	+	0.287787i	−0.00587997	+	0.0141955i
$412$			28.5760i			1.40784i
$413$	5.82357	+	2.41220i	0.286559	+	0.118697i
$414$	5.77419	+	13.9401i	0.283786	+	0.685120i
$415$	−19.9776	+	8.27499i	−0.980661	+	0.406203i
$416$	−0.149570	−	0.149570i	−0.00733325	−	0.00733325i
$417$	7.64365	+	7.64365i	0.374311	+	0.374311i
$418$	−46.5674	+	19.2889i	−2.27769	+	0.943449i
$419$	−10.6641	−	25.7455i	−0.520977	−	1.25775i	−0.937297	−	0.348532i	$-0.886680\pi$
$419$	−10.6641	−	25.7455i	−0.520977	−	1.25775i	0.416320	−	0.909218i	$-0.363320\pi$
$420$	−16.4800	−	6.82624i	−0.804142	−	0.333086i
$421$		−	30.5071i		−	1.48682i	−0.668834	−	0.743411i	$-0.733206\pi$
$421$		−	30.5071i		−	1.48682i	0.668834	−	0.743411i	$-0.266794\pi$
$422$	21.2543	−	51.3123i	1.03464	−	2.49785i
$423$	5.27784	−	5.27784i	0.256617	−	0.256617i
$424$	−6.49443			−0.315398
$425$		0			0
$426$	−11.0405			−0.534915
$427$	9.24573	−	9.24573i	0.447432	−	0.447432i
$428$	−5.59142	+	13.4989i	−0.270272	+	0.652493i
$429$			5.09890i			0.246177i
$430$	71.5255	+	29.6268i	3.44927	+	1.42873i
$431$	4.52968	+	10.9356i	0.218187	+	0.526751i	0.994637	−	0.103429i	$-0.0329814\pi$
$431$	4.52968	+	10.9356i	0.218187	+	0.526751i	−0.776450	+	0.630179i	$0.782981\pi$
$432$	−3.54598	+	1.46879i	−0.170606	+	0.0706674i
$433$	17.6378	+	17.6378i	0.847617	+	0.847617i	0.989835	−	0.142219i	$-0.0454236\pi$
$433$	17.6378	+	17.6378i	0.847617	+	0.847617i	−0.142219	+	0.989835i	$0.545424\pi$
$434$	5.86799	+	5.86799i	0.281672	+	0.281672i
$435$	−4.05899	+	1.68129i	−0.194613	+	0.0806115i
$436$	15.6348	+	37.7459i	0.748773	+	1.80770i
$437$	−18.5476	−	7.68268i	−0.887254	−	0.367512i
$438$			20.2382i			0.967018i
$439$	5.46645	−	13.1972i	0.260899	−	0.629867i	−0.738095	−	0.674697i	$-0.764274\pi$
$439$	5.46645	−	13.1972i	0.260899	−	0.629867i	0.998995	+	0.0448296i	$0.0142745\pi$
$440$	−62.1372	+	62.1372i	−2.96228	+	2.96228i
$441$	4.55854			0.217073
$442$		0			0
$443$	3.36806			0.160021			0.0800107	−	0.996794i	$-0.474505\pi$
$443$	3.36806			0.160021			0.0800107	+	0.996794i	$0.474505\pi$
$444$	−1.78736	+	1.78736i	−0.0848242	+	0.0848242i
$445$	6.73799	−	16.2669i	0.319411	−	0.771127i
$446$		−	1.45351i		−	0.0688257i
$447$	−16.3775	−	6.78380i	−0.774631	−	0.320863i
$448$	−4.97454	−	12.0096i	−0.235025	−	0.567400i
$449$	3.63649	−	1.50628i	0.171616	−	0.0710858i	−0.295221	−	0.955429i	$-0.595393\pi$
$449$	3.63649	−	1.50628i	0.171616	−	0.0710858i	0.466837	+	0.884343i	$0.345393\pi$
$450$	5.62840	+	5.62840i	0.265325	+	0.265325i
$451$	25.1858	+	25.1858i	1.18595	+	1.18595i
$452$	51.1309	−	21.1791i	2.40500	−	0.996182i
$453$	−6.17055	−	14.8970i	−0.289918	−	0.699923i
$454$	45.2553	+	18.7454i	2.12394	+	0.879763i
$455$		−	3.60953i		−	0.169218i
$456$	6.00002	−	14.4853i	0.280976	−	0.678337i
$457$	−10.4775	+	10.4775i	−0.490119	+	0.490119i	−0.908344	−	0.418225i	$-0.862652\pi$
$457$	−10.4775	+	10.4775i	−0.490119	+	0.490119i	0.418225	+	0.908344i	$0.362652\pi$
$458$	−4.74064			−0.221515
$459$		0			0
$460$	−70.4815			−3.28622
$461$	23.5353	−	23.5353i	1.09615	−	1.09615i	0.101290	−	0.994857i	$-0.467703\pi$
$461$	23.5353	−	23.5353i	1.09615	−	1.09615i	0.994857	−	0.101290i	$-0.0322970\pi$
$462$	−9.26866	+	22.3765i	−0.431217	+	1.04105i
$463$		−	19.1509i		−	0.890018i	−0.895526	−	0.445009i	$-0.853201\pi$
$463$		−	19.1509i		−	0.890018i	0.895526	−	0.445009i	$-0.146799\pi$
$464$	5.42163	+	2.24571i	0.251693	+	0.104255i
$465$	−2.38966	−	5.76914i	−0.110818	−	0.267537i
$466$	−19.0630	+	7.89617i	−0.883078	+	0.365783i
$467$	−26.7499	−	26.7499i	−1.23784	−	1.23784i	−0.960882	−	0.276958i	$-0.910674\pi$
$467$	−26.7499	−	26.7499i	−1.23784	−	1.23784i	−0.276958	−	0.960882i	$-0.589326\pi$
$468$	−2.25845	−	2.25845i	−0.104397	−	0.104397i
$469$	−11.1980	+	4.63835i	−0.517074	+	0.214179i
$470$	20.0592	+	48.4271i	0.925260	+	2.23377i
$471$	18.1401	+	7.51387i	0.835851	+	0.346221i
$472$			19.4512i			0.895315i
$473$	26.7574	−	64.5980i	1.23030	−	2.97022i
$474$	2.60464	−	2.60464i	0.119635	−	0.119635i
$475$	−10.5906			−0.485931
$476$		0			0
$477$	1.34692			0.0616714
$478$	−26.7913	+	26.7913i	−1.22540	+	1.22540i
$479$	−0.164358	+	0.396795i	−0.00750971	+	0.0181300i	−0.927590	−	0.373600i	$-0.878123\pi$
$479$	−0.164358	+	0.396795i	−0.00750971	+	0.0181300i	0.920080	+	0.391730i	$0.128123\pi$
$480$			0.756049i			0.0345088i
$481$	−0.472553	−	0.195738i	−0.0215466	−	0.00892488i
$482$	−27.8630	−	67.2673i	−1.26913	−	3.06394i
$483$	−8.91249	+	3.69167i	−0.405532	+	0.167977i
$484$	82.1068	+	82.1068i	3.73213	+	3.73213i
$485$	−9.83741	−	9.83741i	−0.446694	−	0.446694i
$486$	2.25792	−	0.935260i	0.102421	−	0.0424243i
$487$	−0.0748629	−	0.180735i	−0.00339236	−	0.00818988i	0.922174	−	0.386775i	$-0.126411\pi$
$487$	−0.0748629	−	0.180735i	−0.00339236	−	0.00818988i	−0.925567	+	0.378585i	$0.876411\pi$
$488$	37.2773	+	15.4408i	1.68747	+	0.698971i
$489$		−	10.8776i		−	0.491903i
$490$	−12.2509	+	29.5762i	−0.553438	+	1.33612i
$491$	−6.59593	+	6.59593i	−0.297670	+	0.297670i	−0.840101	−	0.542431i	$-0.817504\pi$
$491$	−6.59593	+	6.59593i	−0.297670	+	0.297670i	0.542431	+	0.840101i	$0.317504\pi$
$492$	−22.3110			−1.00586
$493$		0			0
$494$	6.38888			0.287449
$495$	12.8871	−	12.8871i	0.579230	−	0.579230i
$496$	−3.19189	+	7.70590i	−0.143320	+	0.346005i
$497$		−	7.05866i		−	0.316624i
$498$	−16.9913	−	7.03803i	−0.761399	−	0.315382i
$499$	−3.14331	−	7.58862i	−0.140714	−	0.339713i	0.837774	−	0.546017i	$-0.183857\pi$
$499$	−3.14331	−	7.58862i	−0.140714	−	0.339713i	−0.978488	+	0.206304i	$0.933857\pi$
$500$	18.3844	−	7.61507i	0.822176	−	0.340556i
$501$	−7.43457	−	7.43457i	−0.332152	−	0.332152i
$502$	7.93444	+	7.93444i	0.354132	+	0.354132i
$503$	−27.6542	+	11.4547i	−1.23304	+	0.510742i	−0.901533	−	0.432711i	$-0.857557\pi$
$503$	−27.6542	+	11.4547i	−1.23304	+	0.510742i	−0.331507	+	0.943453i	$0.607557\pi$
$504$	−2.88312	−	6.96047i	−0.128424	−	0.310044i
$505$	−41.9879	−	17.3920i	−1.86844	−	0.773932i
$506$			95.6998i			4.25437i
$507$	−4.72756	+	11.4133i	−0.209958	+	0.506884i
$508$	6.11696	−	6.11696i	0.271396	−	0.271396i
$509$	−2.71603			−0.120386			−0.0601929	−	0.998187i	$-0.519172\pi$
$509$	−2.71603			−0.120386			−0.0601929	+	0.998187i	$0.519172\pi$
$510$		0			0
$511$	−12.9391			−0.572392
$512$	26.8859	−	26.8859i	1.18820	−	1.18820i
$513$	−1.24438	+	3.00421i	−0.0549409	+	0.132639i
$514$			71.0532i			3.13402i
$515$	19.0949	+	7.90937i	0.841423	+	0.348529i
$516$	16.7607	+	40.4639i	0.737848	+	1.78132i
$517$	43.7367	−	18.1163i	1.92354	−	0.796756i
$518$	−1.71799	−	1.71799i	−0.0754842	−	0.0754842i
$519$	5.47898	+	5.47898i	0.240501	+	0.240501i
$520$	10.2906	−	4.26250i	0.451272	−	0.186923i
$521$	−0.794026	−	1.91695i	−0.0347869	−	0.0839831i	0.905531	−	0.424279i	$-0.139473\pi$
$521$	−0.794026	−	1.91695i	−0.0347869	−	0.0839831i	−0.940318	+	0.340296i	$0.889473\pi$
$522$	−3.45224	−	1.42997i	−0.151101	−	0.0625879i
$523$			17.2333i			0.753558i	0.926303	+	0.376779i	$0.122968\pi$
$523$			17.2333i			0.753558i	−0.926303	+	0.376779i	$0.877032\pi$
$524$	−6.70272	+	16.1818i	−0.292810	+	0.706905i
$525$	−3.59846	+	3.59846i	−0.157050	+	0.157050i
$526$	2.62623			0.114509
$527$		0			0
$528$	−24.3434			−1.05941
$529$	−10.6892	+	10.6892i	−0.464749	+	0.464749i
$530$	−3.61980	+	8.73897i	−0.157234	+	0.379597i
$531$		−	4.03412i		−	0.175066i
$532$	18.6493	+	7.72480i	0.808550	+	0.334912i
$533$	−1.72770	−	4.17103i	−0.0748349	−	0.180667i
$534$	13.8353	−	5.73078i	0.598713	−	0.247995i
$535$	7.47255	+	7.47255i	0.323066	+	0.323066i
$536$	−26.4474	−	26.4474i	−1.14235	−	1.14235i
$537$	−11.0381	+	4.57213i	−0.476329	+	0.197302i
$538$	−23.6797	−	57.1680i	−1.02091	−	2.46469i
$539$	26.7116	+	11.0643i	1.15055	+	0.476574i
$540$			11.4161i			0.491270i
$541$	−1.35311	+	3.26669i	−0.0581746	+	0.140446i	−0.950294	−	0.311353i	$-0.899218\pi$
$541$	−1.35311	+	3.26669i	−0.0581746	+	0.140446i	0.892120	+	0.451799i	$0.149218\pi$
$542$	33.6661	−	33.6661i	1.44608	−	1.44608i
$543$	1.75313			0.0752338
$544$		0			0
$545$	29.5498			1.26578
$546$	2.17080	−	2.17080i	0.0929017	−	0.0929017i
$547$	−7.48924	+	18.0806i	−0.320217	+	0.773071i	0.679024	+	0.734116i	$0.262403\pi$
$547$	−7.48924	+	18.0806i	−0.320217	+	0.773071i	−0.999241	+	0.0389555i	$0.987597\pi$
$548$		−	1.23755i		−	0.0528657i
$549$	−7.73119	−	3.20237i	−0.329959	−	0.136674i
$550$	19.3196	+	46.6417i	0.823792	+	1.98881i
$551$	4.59328	−	1.90260i	0.195680	−	0.0810535i
$552$	−21.0495	−	21.0495i	−0.895926	−	0.895926i
$553$	1.66525	+	1.66525i	0.0708138	+	0.0708138i
$554$	−21.4573	+	8.88790i	−0.911632	+	0.377611i
$555$	0.699628	+	1.68905i	0.0296975	+	0.0716962i
$556$	−39.6770	−	16.4347i	−1.68268	−	0.696989i
$557$			15.0835i			0.639110i	0.947568	+	0.319555i	$0.103533\pi$
$557$			15.0835i			0.639110i	−0.947568	+	0.319555i	$0.896467\pi$
$558$	2.03245	−	4.90676i	0.0860403	−	0.207720i
$559$	−6.26681	+	6.26681i	−0.265058	+	0.265058i
$560$	17.2328			0.728218
$561$		0			0
$562$	35.2460			1.48676
$563$	−27.3301	+	27.3301i	−1.15183	+	1.15183i	−0.165643	+	0.986186i	$0.552970\pi$
$563$	−27.3301	+	27.3301i	−1.15183	+	1.15183i	−0.986186	+	0.165643i	$0.947030\pi$
$564$	−11.3480	+	27.3965i	−0.477836	+	1.15360i
$565$		−	40.0285i		−	1.68401i
$566$	−43.8282	−	18.1542i	−1.84223	−	0.763079i
$567$	0.597950	+	1.44358i	0.0251115	+	0.0606246i
$568$	20.1238	−	8.33556i	0.844377	−	0.349752i
$569$	−2.25813	−	2.25813i	−0.0946659	−	0.0946659i	0.658188	−	0.752854i	$-0.271323\pi$
$569$	−2.25813	−	2.25813i	−0.0946659	−	0.0946659i	−0.752854	+	0.658188i	$0.771323\pi$
$570$	−16.1474	−	16.1474i	−0.676338	−	0.676338i
$571$	4.91635	−	2.03642i	0.205743	−	0.0852216i	−0.277432	−	0.960745i	$-0.589483\pi$
$571$	4.91635	−	2.03642i	0.205743	−	0.0852216i	0.483175	+	0.875524i	$0.339483\pi$
$572$	−7.75219	−	18.7154i	−0.324135	−	0.782532i
$573$	−20.6240	−	8.54273i	−0.861579	−	0.356878i
$574$		−	21.4451i		−	0.895102i
$575$	−7.69494	+	18.5772i	−0.320901	+	0.774724i
$576$	−5.88265	+	5.88265i	−0.245110	+	0.245110i
$577$	10.4307			0.434236			0.217118	−	0.976145i	$-0.430334\pi$
$577$	10.4307			0.434236			0.217118	+	0.976145i	$0.430334\pi$
$578$		0			0
$579$	−26.1577			−1.08708
$580$	12.3423	−	12.3423i	0.512485	−	0.512485i
$581$	4.49970	−	10.8632i	0.186679	−	0.450683i
$582$		−	11.8326i		−	0.490476i
$583$	7.89256	+	3.26921i	0.326877	+	0.135397i
$584$	−15.2798	−	36.8886i	−0.632281	−	1.52646i
$585$	−2.13423	+	0.884028i	−0.0882396	+	0.0365500i
$586$	−1.85495	−	1.85495i	−0.0766272	−	0.0766272i
$587$	13.2502	+	13.2502i	0.546896	+	0.546896i	0.925542	−	0.378646i	$-0.123610\pi$
$587$	13.2502	+	13.2502i	0.546896	+	0.546896i	−0.378646	+	0.925542i	$0.623610\pi$
$588$	−16.7320	+	6.93064i	−0.690017	+	0.285815i
$589$	2.70421	+	6.52855i	0.111425	+	0.269004i
$590$	26.1738	+	10.8415i	1.07756	+	0.446338i
$591$		−	17.7960i		−	0.732031i
$592$	0.934500	−	2.25608i	0.0384077	−	0.0927244i
$593$	−5.15770	+	5.15770i	−0.211802	+	0.211802i	−0.805032	−	0.593231i	$-0.797852\pi$
$593$	−5.15770	+	5.15770i	−0.211802	+	0.211802i	0.593231	+	0.805032i	$0.297852\pi$
$594$	15.5007			0.636003
$595$		0			0
$596$	70.4273			2.88482
$597$	−16.0188	+	16.0188i	−0.655607	+	0.655607i
$598$	4.64203	−	11.2069i	0.189827	−	0.458282i
$599$		−	31.8625i		−	1.30187i	−0.759135	−	0.650933i	$-0.774378\pi$
$599$		−	31.8625i		−	1.30187i	0.759135	−	0.650933i	$-0.225622\pi$
$600$	−14.5084	−	6.00959i	−0.592304	−	0.245340i
$601$	0.200589	+	0.484264i	0.00818219	+	0.0197535i	0.927918	−	0.372785i	$-0.121597\pi$
$601$	0.200589	+	0.484264i	0.00818219	+	0.0197535i	−0.919736	+	0.392538i	$0.871597\pi$
$602$	−38.8935	+	16.1102i	−1.58518	+	0.656603i
$603$	5.48509	+	5.48509i	0.223370	+	0.223370i
$604$	45.2978	+	45.2978i	1.84314	+	1.84314i
$605$	77.5909	−	32.1392i	3.15452	−	1.30664i
$606$	−14.7922	−	35.7115i	−0.600891	−	1.45068i
$607$	−0.876879	−	0.363215i	−0.0355914	−	0.0147424i	0.364817	−	0.931079i	$-0.381132\pi$
$607$	−0.876879	−	0.363215i	−0.0355914	−	0.0147424i	−0.400408	+	0.916337i	$0.631132\pi$
$608$		−	0.855570i		−	0.0346980i
$609$	0.914235	−	2.20716i	0.0370467	−	0.0894386i
$610$	41.5545	−	41.5545i	1.68249	−	1.68249i
$611$	−6.00051			−0.242755
$612$		0			0
$613$	3.89703			0.157399			0.0786997	−	0.996898i	$-0.474923\pi$
$613$	3.89703			0.157399			0.0786997	+	0.996898i	$0.474923\pi$
$614$	−25.1956	+	25.1956i	−1.01681	+	1.01681i
$615$	−6.17532	+	14.9085i	−0.249013	+	0.601170i
$616$		−	47.7840i		−	1.92527i
$617$	17.8779	+	7.40526i	0.719736	+	0.298125i	0.712327	−	0.701848i	$-0.247641\pi$
$617$	17.8779	+	7.40526i	0.719736	+	0.298125i	0.00740953	+	0.999973i	$0.497641\pi$
$618$	6.72707	+	16.2406i	0.270602	+	0.653292i
$619$	18.1773	−	7.52927i	0.730606	−	0.302627i	0.0138051	−	0.999905i	$-0.495606\pi$
$619$	18.1773	−	7.52927i	0.730606	−	0.302627i	0.716801	+	0.697278i	$0.245606\pi$
$620$	17.5424	+	17.5424i	0.704519	+	0.704519i
$621$	4.36560	+	4.36560i	0.175185	+	0.175185i
$622$	32.3897	−	13.4163i	1.29871	−	0.537943i
$623$	3.66392	+	8.84549i	0.146792	+	0.354387i
$624$	2.85072	+	1.18081i	0.114120	+	0.0472700i
$625$		−	30.6771i		−	1.22708i
$626$	−10.5857	+	25.5562i	−0.423090	+	1.02143i
$627$	−14.5834	+	14.5834i	−0.582405	+	0.582405i
$628$	−78.0067			−3.11281
$629$		0			0
$630$	−10.9730			−0.437176
$631$	1.96458	−	1.96458i	0.0782088	−	0.0782088i	−0.666920	−	0.745129i	$-0.732388\pi$
$631$	1.96458	−	1.96458i	0.0782088	−	0.0782088i	0.745129	+	0.666920i	$0.232388\pi$
$632$	−2.78105	+	6.71404i	−0.110624	+	0.267070i
$633$		−	22.7255i		−	0.903258i
$634$	−26.5582	−	11.0008i	−1.05476	−	0.436897i
$635$	−2.39437	−	5.78053i	−0.0950178	−	0.229393i
$636$	−4.94386	+	2.04781i	−0.196037	+	0.0812011i
$637$	−2.59136	−	2.59136i	−0.102673	−	0.102673i
$638$	−16.7583	−	16.7583i	−0.663468	−	0.663468i
$639$	−4.17362	+	1.72877i	−0.165106	+	0.0683890i
$640$	−21.7792	−	52.5795i	−0.860897	−	2.07839i
$641$	19.8788	+	8.23405i	0.785164	+	0.325225i	0.738997	−	0.673708i	$-0.235300\pi$
$641$	19.8788	+	8.23405i	0.785164	+	0.325225i	0.0461663	+	0.998934i	$0.485300\pi$
$642$			8.98809i			0.354732i
$643$	−17.0048	+	41.0533i	−0.670605	+	1.61898i	0.109979	+	0.993934i	$0.464922\pi$
$643$	−17.0048	+	41.0533i	−0.670605	+	1.61898i	−0.780585	+	0.625050i	$0.785078\pi$
$644$	27.1004	−	27.1004i	1.06791	−	1.06791i
$645$	31.6777			1.24731
$646$		0			0
$647$	−43.8840			−1.72526			−0.862629	−	0.505838i	$-0.831183\pi$
$647$	−43.8840			−1.72526			−0.862629	+	0.505838i	$0.831183\pi$
$648$	−3.40944	+	3.40944i	−0.133935	+	0.133935i
$649$	9.79148	−	23.6387i	0.384349	−	0.927901i
$650$		−	6.39907i		−	0.250992i
$651$	3.13709	+	1.29943i	0.122952	+	0.0509285i
$652$	16.5380	+	39.9262i	0.647676	+	1.56363i
$653$	−7.89762	+	3.27130i	−0.309058	+	0.128016i	−0.531821	−	0.846857i	$-0.678492\pi$
$653$	−7.89762	+	3.27130i	−0.309058	+	0.128016i	0.222764	+	0.974873i	$0.428492\pi$
$654$	17.7715	+	17.7715i	0.694920	+	0.694920i
$655$	8.95772	+	8.95772i	0.350007	+	0.350007i
$656$	19.9135	−	8.24844i	0.777491	−	0.322047i
$657$	3.16897	+	7.65058i	0.123633	+	0.298478i
$658$	−26.3332	−	10.9076i	−1.02658	−	0.425222i
$659$			36.1408i			1.40785i	0.710276	+	0.703924i	$0.248570\pi$
$659$			36.1408i			1.40785i	−0.710276	+	0.703924i	$0.751430\pi$
$660$	−27.7087	+	66.8947i	−1.07856	+	2.60387i
$661$	32.8241	−	32.8241i	1.27671	−	1.27671i	0.334213	−	0.942497i	$-0.391529\pi$
$661$	32.8241	−	32.8241i	1.27671	−	1.27671i	0.942497	−	0.334213i	$-0.108471\pi$
$662$	49.3882			1.91953
$663$		0			0
$664$	36.2841			1.40810
$665$	10.3237	−	10.3237i	0.400334	−	0.400334i
$666$	−0.595046	+	1.43657i	−0.0230576	+	0.0556659i
$667$		−	9.43956i		−	0.365501i
$668$	38.5917	+	15.9852i	1.49316	+	0.618486i
$669$	−0.227596	−	0.549466i	−0.00879938	−	0.0212436i
$670$	−50.3287	+	20.8468i	−1.94437	+	0.805384i
$671$	−37.5298	−	37.5298i	−1.44882	−	1.44882i
$672$	−0.290704	−	0.290704i	−0.0112142	−	0.0112142i
$673$	41.6953	−	17.2708i	1.60724	−	0.665739i	0.614820	−	0.788668i	$-0.289229\pi$
$673$	41.6953	−	17.2708i	1.60724	−	0.665739i	0.992415	+	0.122929i	$0.0392288\pi$
$674$	5.99316	+	14.4688i	0.230848	+	0.557316i
$675$	3.00900	+	1.24637i	0.115816	+	0.0479728i
$676$		−	49.0800i		−	1.88769i
$677$	−13.8668	+	33.4774i	−0.532944	+	1.28664i	0.396622	+	0.917982i	$0.370182\pi$
$677$	−13.8668	+	33.4774i	−0.532944	+	1.28664i	−0.929565	+	0.368657i	$0.879818\pi$
$678$	24.0734	−	24.0734i	0.924535	−	0.924535i
$679$	7.56505			0.290320
$680$		0			0
$681$	20.0429			0.768047
$682$	23.8190	−	23.8190i	0.912077	−	0.912077i
$683$	−9.31054	+	22.4776i	−0.356258	+	0.860083i	0.639561	+	0.768740i	$0.279116\pi$
$683$	−9.31054	+	22.4776i	−0.356258	+	0.860083i	−0.995819	+	0.0913431i	$0.970884\pi$
$684$		−	12.9188i		−	0.493963i
$685$	−0.826952	−	0.342535i	−0.0315962	−	0.0130876i
$686$	−16.8912	−	40.7789i	−0.644909	−	1.55695i
$687$	−1.79209	+	0.742307i	−0.0683724	+	0.0283208i
$688$	−29.9192	−	29.9192i	−1.14066	−	1.14066i
$689$	−0.765676	−	0.765676i	−0.0291699	−	0.0291699i
$690$	−40.0567	+	16.5920i	−1.52493	+	0.631648i
$691$	−8.18512	−	19.7606i	−0.311377	−	0.751729i	−0.999655	−	0.0262825i	$-0.991633\pi$
$691$	−8.18512	−	19.7606i	−0.311377	−	0.751729i	0.688278	−	0.725447i	$-0.258367\pi$
$692$	−28.4406	−	11.7805i	−1.08115	−	0.447826i
$693$			9.91025i			0.376459i
$694$	−10.9697	+	26.4832i	−0.416405	+	1.00529i
$695$	−21.9639	+	21.9639i	−0.833139	+	0.833139i
$696$	7.37210			0.279439
$697$		0			0
$698$	63.0070			2.38485
$699$	−5.96993	+	5.96993i	−0.225803	+	0.225803i
$700$	7.73712	−	18.6791i	0.292436	−	0.706002i
$701$			15.3315i			0.579063i	0.957168	+	0.289532i	$0.0934995\pi$
$701$			15.3315i			0.579063i	−0.957168	+	0.289532i	$0.906500\pi$
$702$	−1.81520	−	0.751882i	−0.0685104	−	0.0283779i
$703$	−0.791722	−	1.91139i	−0.0298603	−	0.0720893i
$704$	−48.7487	+	20.1924i	−1.83729	+	0.761029i
$705$	15.1658	+	15.1658i	0.571177	+	0.571177i
$706$	6.84875	+	6.84875i	0.257756	+	0.257756i
$707$	22.8318	−	9.45725i	0.858679	−	0.355676i
$708$	6.13333	+	14.8072i	0.230505	+	0.556488i
$709$	−35.5706	−	14.7338i	−1.33588	−	0.553340i	−0.403555	−	0.914956i	$-0.632225\pi$
$709$	−35.5706	−	14.7338i	−1.33588	−	0.553340i	−0.932327	+	0.361615i	$0.882225\pi$
$710$		−	31.7248i		−	1.19061i
$711$	0.576780	−	1.39247i	0.0216309	−	0.0522217i
$712$	−20.8913	+	20.8913i	−0.782933	+	0.782933i
$713$	13.4167			0.502459
$714$		0			0
$715$	−14.6516			−0.547940
$716$	33.5638	−	33.5638i	1.25434	−	1.25434i
$717$	−5.93274	+	14.3229i	−0.221562	+	0.534899i
$718$			27.4754i			1.02537i
$719$	−14.0718	−	5.82873i	−0.524789	−	0.217375i	0.104530	−	0.994522i	$-0.466666\pi$
$719$	−14.0718	−	5.82873i	−0.524789	−	0.217375i	−0.629319	+	0.777147i	$0.716666\pi$
$720$	−4.22056	−	10.1893i	−0.157291	−	0.379734i
$721$	−10.3833	+	4.30089i	−0.386693	+	0.160173i
$722$	−14.5617	−	14.5617i	−0.541930	−	0.541930i
$723$	−21.0659	−	21.0659i	−0.783451	−	0.783451i
$724$	−6.43482	+	2.66539i	−0.239148	+	0.0990584i
$725$	−1.90564	−	4.60061i	−0.0707735	−	0.170862i
$726$	65.9925	+	27.3350i	2.44921	+	1.01450i
$727$			11.2839i			0.418495i	0.977863	+	0.209248i	$0.0671015\pi$
$727$			11.2839i			0.418495i	−0.977863	+	0.209248i	$0.932899\pi$
$728$	−2.31782	+	5.59572i	−0.0859042	+	0.207391i
$729$	0.707107	−	0.707107i	0.0261891	−	0.0261891i
$730$	−58.1542			−2.15238
$731$		0			0
$732$	33.2460			1.22881
$733$	18.7534	−	18.7534i	0.692671	−	0.692671i	−0.270148	−	0.962819i	$-0.587073\pi$
$733$	18.7534	−	18.7534i	0.692671	−	0.692671i	0.962819	+	0.270148i	$0.0870725\pi$
$734$	14.4527	−	34.8920i	0.533460	−	1.28789i
$735$			13.0989i			0.483160i
$736$	−1.50077	−	0.621641i	−0.0553192	−	0.0229140i
$737$	18.8277	+	45.4542i	0.693529	+	1.67433i
$738$	−12.6800	+	5.25222i	−0.466757	+	0.193337i
$739$	0.609301	+	0.609301i	0.0224135	+	0.0224135i	0.718225	−	0.695811i	$-0.244955\pi$
$739$	0.609301	+	0.609301i	0.0224135	+	0.0224135i	−0.695811	+	0.718225i	$0.744955\pi$
$740$	−5.13594	−	5.13594i	−0.188801	−	0.188801i
$741$	2.41517	−	1.00039i	0.0887234	−	0.0367504i
$742$	−1.96834	−	4.75200i	−0.0722601	−	0.174451i
$743$	4.00679	+	1.65967i	0.146995	+	0.0608873i	0.454968	−	0.890508i	$-0.349651\pi$
$743$	4.00679	+	1.65967i	0.146995	+	0.0608873i	−0.307973	+	0.951395i	$0.599651\pi$
$744$			10.4782i			0.384148i
$745$	19.4932	−	47.0606i	0.714174	−	1.72417i
$746$	−8.89802	+	8.89802i	−0.325780	+	0.325780i
$747$	−7.52521			−0.275333
$748$		0			0
$749$	−5.74645			−0.209971
$750$	8.65574	−	8.65574i	0.316063	−	0.316063i
$751$	−13.0476	+	31.4996i	−0.476113	+	1.14944i	0.485305	+	0.874345i	$0.338709\pi$
$751$	−13.0476	+	31.4996i	−0.476113	+	1.14944i	−0.961418	+	0.275093i	$0.911291\pi$
$752$		−	28.6479i		−	1.04468i
$753$	4.24184	+	1.75703i	0.154581	+	0.0640296i
$754$	1.14959	+	2.77535i	0.0418656	+	0.101072i
$755$	42.8064	−	17.7310i	1.55788	−	0.645296i
$756$	−4.38953	−	4.38953i	−0.159646	−	0.159646i
$757$	−25.3076	−	25.3076i	−0.919822	−	0.919822i	0.0771942	−	0.997016i	$-0.475404\pi$
$757$	−25.3076	−	25.3076i	−0.919822	−	0.919822i	−0.997016	+	0.0771942i	$0.975404\pi$
$758$	26.7492	−	11.0799i	0.971573	−	0.402439i
$759$	14.9850	+	36.1771i	0.543922	+	1.31314i
$760$	41.6234	+	17.2410i	1.50984	+	0.625395i
$761$			24.8283i			0.900025i	0.893022	+	0.450013i	$0.148580\pi$
$761$			24.8283i			0.900025i	−0.893022	+	0.450013i	$0.851420\pi$
$762$	2.03646	−	4.91644i	0.0737731	−	0.178104i
$763$	−11.3620	+	11.3620i	−0.411333	+	0.411333i
$764$	88.6880			3.20862
$765$		0			0
$766$	75.1140			2.71398
$767$	−2.29325	+	2.29325i	−0.0828044	+	0.0828044i
$768$	12.1562	−	29.3478i	0.438651	−	1.05900i
$769$			47.0234i			1.69571i	0.530230	+	0.847854i	$0.322106\pi$
$769$			47.0234i			1.69571i	−0.530230	+	0.847854i	$0.677894\pi$
$770$	−64.2986	−	26.6334i	−2.31716	−	0.959800i
$771$	11.1258	+	26.8600i	0.400686	+	0.967341i
$772$	96.0112	−	39.7692i	3.45552	−	1.43132i
$773$	29.5210	+	29.5210i	1.06180	+	1.06180i	0.997960	+	0.0638366i	$0.0203337\pi$
$773$	29.5210	+	29.5210i	1.06180	+	1.06180i	0.0638366	+	0.997960i	$0.479666\pi$
$774$	19.0512	+	19.0512i	0.684780	+	0.684780i
$775$	6.53896	−	2.70853i	0.234886	−	0.0972932i
$776$	8.93356	+	21.5675i	0.320696	+	0.774229i
$777$	−0.918457	−	0.380437i	−0.0329494	−	0.0136481i
$778$			47.2912i			1.69547i
$779$	6.98819	−	16.8710i	0.250378	−	0.604466i
$780$	6.48962	−	6.48962i	0.232366	−	0.232366i
$781$	−28.6521			−1.02525
$782$		0			0
$783$	−1.52895			−0.0546402
$784$	12.3718	−	12.3718i	0.441849	−	0.441849i
$785$	−21.5910	+	52.1253i	−0.770616	+	1.86043i
$786$			10.7745i			0.384313i
$787$	−2.19942	−	0.911029i	−0.0784008	−	0.0324747i	0.343138	−	0.939285i	$-0.388510\pi$
$787$	−2.19942	−	0.911029i	−0.0784008	−	0.0324747i	−0.421539	+	0.906810i	$0.638510\pi$
$788$	27.0564	+	65.3200i	0.963846	+	2.32693i
$789$	0.992786	−	0.411225i	0.0353441	−	0.0146400i
$790$	7.48440	+	7.48440i	0.266283	+	0.266283i
$791$	15.3911	+	15.3911i	0.547245	+	0.547245i
$792$	−28.2536	+	11.7030i	−1.00395	+	0.415848i
$793$	2.57447	+	6.21532i	0.0914222	+	0.220713i
$794$	30.5780	+	12.6658i	1.08517	+	0.449493i
$795$			3.87037i			0.137268i
$796$	34.4424	−	83.1512i	1.22078	−	2.94722i
$797$	−27.1747	+	27.1747i	−0.962577	+	0.962577i	−0.999325	−	0.0367476i	$-0.988300\pi$
$797$	−27.1747	+	27.1747i	−0.962577	+	0.962577i	0.0367476	+	0.999325i	$0.488300\pi$
$798$	12.4174			0.439573
$799$		0			0
$800$	−0.856935			−0.0302972
$801$	4.33278	−	4.33278i	0.153091	−	0.153091i
$802$	8.09475	−	19.5424i	0.285835	−	0.690068i
$803$			52.5217i			1.85345i
$804$	−28.4723	−	11.7936i	−1.00414	−	0.415928i
$805$	−10.6080	−	25.6099i	−0.373882	−	0.902630i
$806$	−3.94468	+	1.63394i	−0.138945	+	0.0575531i
$807$	−17.9032	−	17.9032i	−0.630221	−	0.630221i
$808$	53.9241	+	53.9241i	1.89704	+	1.89704i
$809$	−13.4708	+	5.57979i	−0.473609	+	0.196175i	−0.606704	−	0.794928i	$-0.707508\pi$
$809$	−13.4708	+	5.57979i	−0.473609	+	0.196175i	0.133095	+	0.991103i	$0.457508\pi$
$810$	2.68746	+	6.48809i	0.0944276	+	0.227968i
$811$	0.256997	+	0.106452i	0.00902439	+	0.00373802i	0.387191	−	0.922000i	$-0.373445\pi$
$811$	0.256997	+	0.106452i	0.00902439	+	0.00373802i	−0.378167	+	0.925738i	$0.623445\pi$
$812$			9.49131i			0.333080i
$813$	7.45512	−	17.9983i	0.261463	−	0.631227i
$814$	−6.97358	+	6.97358i	−0.244424	+	0.244424i
$815$	31.2567			1.09487
$816$		0			0
$817$	−35.8475			−1.25414
$818$	−34.9548	+	34.9548i	−1.22216	+	1.22216i
$819$	0.480709	−	1.16053i	0.0167973	−	0.0405523i
$820$		−	64.1103i		−	2.23883i
$821$	−11.5019	−	4.76424i	−0.401418	−	0.166273i	0.172835	−	0.984951i	$-0.444707\pi$
$821$	−11.5019	−	4.76424i	−0.401418	−	0.166273i	−0.574253	+	0.818678i	$0.694707\pi$
$822$	−0.291332	−	0.703338i	−0.0101614	−	0.0245317i
$823$	−19.3390	+	8.01049i	−0.674117	+	0.279228i	−0.693365	−	0.720586i	$-0.743873\pi$
$823$	−19.3390	+	8.01049i	−0.674117	+	0.279228i	0.0192484	+	0.999815i	$0.493873\pi$
$824$	−24.5232	−	24.5232i	−0.854305	−	0.854305i
$825$	14.6067	+	14.6067i	0.508539	+	0.508539i
$826$	−14.2325	+	5.89530i	−0.495213	+	0.205124i
$827$	−11.8383	−	28.5803i	−0.411660	−	0.993834i	−0.984692	−	0.174302i	$-0.944233\pi$
$827$	−11.8383	−	28.5803i	−0.411660	−	0.993834i	0.573033	−	0.819532i	$-0.305767\pi$
$828$	−22.6611	−	9.38655i	−0.787529	−	0.326205i
$829$			5.04799i			0.175324i	0.996150	+	0.0876620i	$0.0279395\pi$
$829$			5.04799i			0.175324i	−0.996150	+	0.0876620i	$0.972060\pi$
$830$	20.2237	−	48.8243i	0.701974	−	1.69472i
$831$	−6.71973	+	6.71973i	−0.233105	+	0.233105i
$832$	6.68814			0.231869
$833$		0			0
$834$	−26.4185			−0.914798
$835$	21.3631	−	21.3631i	0.739302	−	0.739302i
$836$	31.3561	−	75.7003i	1.08447	−	2.61815i
$837$		−	2.17313i		−	0.0751145i
$838$	62.9208	+	26.0626i	2.17356	+	0.900319i
$839$	−4.19651	−	10.1313i	−0.144880	−	0.349770i	0.834736	−	0.550650i	$-0.185620\pi$
$839$	−4.19651	−	10.1313i	−0.144880	−	0.349770i	−0.979616	+	0.200880i	$0.935620\pi$
$840$	20.0008	−	8.28461i	0.690093	−	0.285846i
$841$	−18.8531	−	18.8531i	−0.650107	−	0.650107i
$842$	52.7203	+	52.7203i	1.81686	+	1.81686i
$843$	13.3239	−	5.51896i	0.458901	−	0.190083i
$844$	34.5511	+	83.4136i	1.18930	+	2.87122i
$845$	−32.7960	−	13.5846i	−1.12822	−	0.467323i
$846$			18.2416i			0.627161i
$847$	−17.4764	+	42.1917i	−0.600495	+	1.44972i
$848$	3.65552	−	3.65552i	0.125531	−	0.125531i
$849$	−19.4109			−0.666180
$850$		0			0
$851$	−3.92805			−0.134652
$852$	12.6908	−	12.6908i	0.434781	−	0.434781i
$853$	10.1911	−	24.6036i	0.348938	−	0.842411i	−0.647808	−	0.761804i	$-0.724314\pi$
$853$	10.1911	−	24.6036i	0.348938	−	0.842411i	0.996746	−	0.0806072i	$-0.0256859\pi$
$854$			31.9557i			1.09350i
$855$	−8.63255	−	3.57572i	−0.295227	−	0.122287i
$856$	−6.78598	−	16.3828i	−0.231940	−	0.559953i
$857$	−1.23266	+	0.510585i	−0.0421069	+	0.0174413i	−0.403638	−	0.914919i	$-0.632254\pi$
$857$	−1.23266	+	0.510585i	−0.0421069	+	0.0174413i	0.361531	+	0.932360i	$0.382254\pi$
$858$	−8.81159	−	8.81159i	−0.300823	−	0.300823i
$859$	17.3140	+	17.3140i	0.590746	+	0.590746i	0.937833	−	0.347087i	$-0.112829\pi$
$859$	17.3140	+	17.3140i	0.590746	+	0.590746i	−0.347087	+	0.937833i	$0.612829\pi$
$860$	−116.272	+	48.1616i	−3.96485	+	1.64230i
$861$	−3.35796	−	8.10683i	−0.114439	−	0.276280i
$862$	−26.7261	−	11.0703i	−0.910296	−	0.377057i
$863$		−	39.3336i		−	1.33893i	−0.742843	−	0.669465i	$-0.766523\pi$
$863$		−	39.3336i		−	1.33893i	0.742843	−	0.669465i	$-0.233477\pi$
$864$	−0.100689	+	0.243084i	−0.00342550	+	0.00826989i
$865$	−15.7438	+	15.7438i	−0.535304	+	0.535304i
$866$	−60.9609			−2.07153
$867$		0			0
$868$	−13.4902			−0.457888
$869$	6.75951	−	6.75951i	0.229301	−	0.229301i
$870$	4.10899	−	9.91997i	0.139308	−	0.336318i
$871$		−	6.23614i		−	0.211304i
$872$	−45.8099	−	18.9751i	−1.55132	−	0.642578i
$873$	−1.85279	−	4.47303i	−0.0627075	−	0.151389i
$874$	45.3295	−	18.7761i	1.53329	−	0.635111i
$875$	5.53397	+	5.53397i	0.187082	+	0.187082i
$876$	−23.2633	−	23.2633i	−0.785995	−	0.785995i
$877$	−3.57285	+	1.47992i	−0.120646	+	0.0499734i	−0.442190	−	0.896921i	$-0.645798\pi$
$877$	−3.57285	+	1.47992i	−0.120646	+	0.0499734i	0.321544	+	0.946895i	$0.395798\pi$
$878$	13.3597	+	32.2533i	0.450869	+	1.08850i
$879$	−0.991675	−	0.410765i	−0.0334484	−	0.0138548i
$880$		−	69.9504i		−	2.35803i
$881$	−6.25489	+	15.1006i	−0.210732	+	0.508753i	−0.993536	−	0.113515i	$-0.963789\pi$
$881$	−6.25489	+	15.1006i	−0.210732	+	0.508753i	0.782804	+	0.622269i	$0.213789\pi$
$882$	−7.87777	+	7.87777i	−0.265258	+	0.265258i
$883$	33.5409			1.12874			0.564370	−	0.825522i	$-0.309119\pi$
$883$	33.5409			1.12874			0.564370	+	0.825522i	$0.309119\pi$
$884$		0			0
$885$	11.5920			0.389660
$886$	−5.82047	+	5.82047i	−0.195542	+	0.195542i
$887$	9.63849	−	23.2694i	0.323629	−	0.781309i	−0.675409	−	0.737444i	$-0.736033\pi$
$887$	9.63849	−	23.2694i	0.323629	−	0.781309i	0.999037	−	0.0438654i	$-0.0139673\pi$
$888$		−	3.06772i		−	0.102946i
$889$	3.14328	+	1.30199i	0.105422	+	0.0436673i
$890$	16.4673	+	39.7556i	0.551986	+	1.33261i
$891$	5.85969	−	2.42716i	0.196307	−	0.0813131i
$892$	1.67078	+	1.67078i	0.0559417	+	0.0559417i
$893$	−17.1621	−	17.1621i	−0.574308	−	0.574308i
$894$	40.0259	−	16.5793i	1.33867	−	0.554494i
$895$	−13.1379	−	31.7178i	−0.439153	−	1.06021i
$896$	28.5912	+	11.8429i	0.955166	+	0.395643i
$897$		−	4.96336i		−	0.165722i
$898$	−3.68128	+	8.88740i	−0.122846	+	0.296576i
$899$	−2.34944	+	2.34944i	−0.0783583	+	0.0783583i
$900$	−12.9394			−0.431314
$901$		0			0
$902$	−87.0488			−2.89841
$903$	−12.1802	+	12.1802i	−0.405331	+	0.405331i
$904$	−25.7039	+	62.0546i	−0.854897	+	2.06390i
$905$			5.03758i			0.167455i
$906$	36.4076	+	15.0805i	1.20956	+	0.501017i
$907$	17.2464	+	41.6366i	0.572659	+	1.38252i	0.899284	+	0.437366i	$0.144089\pi$
$907$	17.2464	+	41.6366i	0.572659	+	1.38252i	−0.326625	+	0.945154i	$0.605911\pi$
$908$	−73.5672	+	30.4725i	−2.44141	+	1.01127i
$909$	−11.1837	−	11.1837i	−0.370940	−	0.370940i
$910$	6.23776	+	6.23776i	0.206780	+	0.206780i
$911$	−41.6045	+	17.2332i	−1.37842	+	0.570960i	−0.944058	−	0.329779i	$-0.893026\pi$
$911$	−41.6045	+	17.2332i	−1.37842	+	0.570960i	−0.434361	+	0.900739i	$0.643026\pi$
$912$	4.77612	+	11.5306i	0.158153	+	0.381816i
$913$	−44.0954	−	18.2649i	−1.45935	−	0.604481i
$914$		−	36.2132i		−	1.19783i
$915$	9.20195	−	22.2155i	0.304207	−	0.734421i
$916$	5.44925	−	5.44925i	0.180048	−	0.180048i
$917$	−6.88856			−0.227480
$918$		0			0
$919$	−56.5601			−1.86574			−0.932872	−	0.360208i	$-0.882706\pi$
$919$	−56.5601			−1.86574			−0.932872	+	0.360208i	$0.882706\pi$
$920$	60.4854	−	60.4854i	1.99415	−	1.99415i
$921$	−5.57938	+	13.4698i	−0.183847	+	0.443846i
$922$			81.3443i			2.67893i
$923$	3.35529	+	1.38981i	0.110441	+	0.0457460i
$924$	−15.0672	−	36.3754i	−0.495674	−	1.19666i
$925$	−1.91443	+	0.792985i	−0.0629462	+	0.0260732i
$926$	33.0953	+	33.0953i	1.08758	+	1.08758i
$927$	5.08602	+	5.08602i	0.167047	+	0.167047i
$928$	0.371663	−	0.153948i	0.0122004	−	0.00505359i
$929$	12.8659	+	31.0610i	0.422116	+	1.01908i	0.981722	+	0.190319i	$0.0609521\pi$
$929$	12.8659	+	31.0610i	0.422116	+	1.01908i	−0.559607	+	0.828758i	$0.689048\pi$
$930$	14.0995	+	5.84020i	0.462341	+	0.191508i
$931$		−	14.8231i		−	0.485809i
$932$	12.8360	−	30.9890i	0.420459	−	1.01508i
$933$	10.1434	−	10.1434i	0.332080	−	0.332080i
$934$	92.4550			3.02522
$935$		0			0
$936$	3.87628			0.126700
$937$	1.47162	−	1.47162i	0.0480756	−	0.0480756i	−0.682660	−	0.730736i	$-0.739177\pi$
$937$	1.47162	−	1.47162i	0.0480756	−	0.0480756i	0.730736	+	0.682660i	$0.239177\pi$
$938$	11.3359	−	27.3673i	0.370131	−	0.893574i
$939$			11.3185i			0.369364i
$940$	−78.7233	−	32.6083i	−2.56767	−	1.06356i
$941$	2.20641	+	5.32674i	0.0719268	+	0.173647i	0.955754	−	0.294166i	$-0.0950420\pi$
$941$	2.20641	+	5.32674i	0.0719268	+	0.173647i	−0.883827	+	0.467813i	$0.845042\pi$
$942$	−44.3335	+	18.3635i	−1.44446	+	0.598317i
$943$	−24.5163	−	24.5163i	−0.798359	−	0.798359i
$944$	−10.9485	−	10.9485i	−0.356344	−	0.356344i
$945$	−4.14810	+	1.71820i	−0.134938	+	0.0558930i
$946$	65.3937	+	157.874i	2.12613	+	5.13294i
$947$	−22.6586	−	9.38550i	−0.736305	−	0.304988i	−0.0171652	−	0.999853i	$-0.505464\pi$
$947$	−22.6586	−	9.38550i	−0.736305	−	0.304988i	−0.719140	+	0.694865i	$0.755464\pi$
$948$			5.98795i			0.194480i
$949$	2.54763	−	6.15052i	0.0826995	−	0.199654i
$950$	18.3020	−	18.3020i	0.593796	−	0.593796i
$951$	−11.7623			−0.381418
$952$		0			0
$953$	13.3063			0.431033			0.215517	−	0.976500i	$-0.430856\pi$
$953$	13.3063			0.431033			0.215517	+	0.976500i	$0.430856\pi$
$954$	−2.32767	+	2.32767i	−0.0753610	+	0.0753610i
$955$	24.5474	−	59.2627i	0.794336	−	1.91770i
$956$		−	61.5919i		−	1.99202i
$957$	−8.95918	−	3.71101i	−0.289609	−	0.119960i
$958$	−0.401683	−	0.969749i	−0.0129778	−	0.0313312i
$959$	0.449673	−	0.186261i	0.0145207	−	0.00601467i
$960$	−16.9037	−	16.9037i	−0.545565	−	0.545565i
$961$	18.5810	+	18.5810i	0.599387	+	0.599387i
$962$	1.15490	−	0.478374i	0.0372354	−	0.0154234i
$963$	1.40739	+	3.39774i	0.0453525	+	0.109491i
$964$	109.350	+	45.2943i	3.52193	+	1.45883i
$965$		−	75.1637i		−	2.41960i
$966$	9.02227	−	21.7817i	0.290287	−	0.700814i
$967$	−12.7983	+	12.7983i	−0.411567	+	0.411567i	−0.882284	−	0.470717i	$-0.843995\pi$
$967$	−12.7983	+	12.7983i	−0.411567	+	0.411567i	0.470717	+	0.882284i	$0.343995\pi$
$968$	−140.924			−4.52946
$969$		0			0
$970$	34.0008			1.09170
$971$	−1.69960	+	1.69960i	−0.0545428	+	0.0545428i	−0.733852	−	0.679309i	$-0.762279\pi$
$971$	−1.69960	+	1.69960i	−0.0545428	+	0.0545428i	0.679309	+	0.733852i	$0.262279\pi$
$972$	−1.52036	+	3.67048i	−0.0487657	+	0.117731i
$973$		−	16.8904i		−	0.541482i
$974$	0.441707	+	0.182961i	0.0141532	+	0.00586246i
$975$	−1.00199	−	2.41902i	−0.0320894	−	0.0774706i
$976$	−29.6734	+	12.2911i	−0.949824	+	0.393430i
$977$	29.3032	+	29.3032i	0.937492	+	0.937492i	0.998158	−	0.0606656i	$-0.0193223\pi$
$977$	29.3032	+	29.3032i	0.937492	+	0.937492i	−0.0606656	+	0.998158i	$0.519322\pi$
$978$	18.7980	+	18.7980i	0.601094	+	0.601094i
$979$	35.9051	−	14.8724i	1.14753	−	0.475324i
$980$	−19.9151	−	48.0793i	−0.636164	−	1.53584i
$981$	9.50083	+	3.93537i	0.303338	+	0.125647i
$982$		−	22.7973i		−	0.727491i
$983$	14.5023	−	35.0116i	0.462551	−	1.11670i	−0.504796	−	0.863239i	$-0.668432\pi$
$983$	14.5023	−	35.0116i	0.462551	−	1.11670i	0.967347	−	0.253457i	$-0.0815678\pi$
$984$	19.1467	−	19.1467i	0.610374	−	0.610374i
$985$	51.1366			1.62935
$986$		0			0
$987$	−11.6626			−0.371225
$988$	−7.34386	+	7.34386i	−0.233639	+	0.233639i
$989$	−26.0461	+	62.8808i	−0.828217	+	1.99949i
$990$			44.5411i			1.41561i
$991$	23.4162	+	9.69931i	0.743840	+	0.308109i	0.722226	−	0.691658i	$-0.243119\pi$
$991$	23.4162	+	9.69931i	0.743840	+	0.308109i	0.0216147	+	0.999766i	$0.493119\pi$
$992$	0.218810	+	0.528254i	0.00694723	+	0.0167721i
$993$	18.6701	−	7.73340i	0.592477	−	0.245412i
$994$	12.1983	+	12.1983i	0.386907	+	0.386907i
$995$	−46.0299	−	46.0299i	−1.45924	−	1.45924i
$996$	27.6212	−	11.4411i	0.875210	−	0.362524i
$997$	−12.9343	−	31.2262i	−0.409634	−	0.988945i	−0.985234	−	0.171213i	$-0.945231\pi$
$997$	−12.9343	−	31.2262i	−0.409634	−	0.988945i	0.575600	−	0.817732i	$-0.304769\pi$
$998$	18.5462	+	7.68210i	0.587070	+	0.243173i
$999$			0.636236i			0.0201296i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	867.2.h.m.688.3		48
17.2	even	8	inner	867.2.h.m.712.4		48
17.3	odd	16		867.2.e.k.616.9		24
17.4	even	4	inner	867.2.h.m.757.10		48
17.5	odd	16		867.2.e.k.829.3		24
17.6	odd	16		867.2.d.g.577.4		12
17.7	odd	16		867.2.a.p.1.5	yes	6
17.8	even	8	inner	867.2.h.m.733.10		48
17.9	even	8	inner	867.2.h.m.733.9		48
17.10	odd	16		867.2.a.o.1.5	✓	6
17.11	odd	16		867.2.d.g.577.3		12
17.12	odd	16		867.2.e.k.829.4		24
17.13	even	4	inner	867.2.h.m.757.9		48
17.14	odd	16		867.2.e.k.616.10		24
17.15	even	8	inner	867.2.h.m.712.3		48
17.16	even	2	inner	867.2.h.m.688.4		48
51.41	even	16		2601.2.a.bi.1.2		6
51.44	even	16		2601.2.a.bh.1.2		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
867.2.a.o.1.5	✓	6	17.10	odd	16
867.2.a.p.1.5	yes	6	17.7	odd	16
867.2.d.g.577.3		12	17.11	odd	16
867.2.d.g.577.4		12	17.6	odd	16
867.2.e.k.616.9		24	17.3	odd	16
867.2.e.k.616.10		24	17.14	odd	16
867.2.e.k.829.3		24	17.5	odd	16
867.2.e.k.829.4		24	17.12	odd	16
867.2.h.m.688.3		48	1.1	even	1	trivial
867.2.h.m.688.4		48	17.16	even	2	inner
867.2.h.m.712.3		48	17.15	even	8	inner
867.2.h.m.712.4		48	17.2	even	8	inner
867.2.h.m.733.9		48	17.9	even	8	inner
867.2.h.m.733.10		48	17.8	even	8	inner
867.2.h.m.757.9		48	17.13	even	4	inner
867.2.h.m.757.10		48	17.4	even	4	inner
2601.2.a.bh.1.2		6	51.44	even	16
2601.2.a.bi.1.2		6	51.41	even	16

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 867 = 3 \cdot 17^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	867.h (of order \(8\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.72814 + 1.72814i) q^{2} +(-0.382683 + 0.923880i) q^{3} -3.97290i q^{4} +(-2.65475 - 1.09964i) q^{5} +(-0.935260 - 2.25792i) q^{6} +(1.44358 - 0.597950i) q^{7} +(3.40944 + 3.40944i) q^{8} +(-0.707107 - 0.707107i) q^{9} +(6.48809 - 2.68746i) q^{10} +(-2.42716 - 5.85969i) q^{11} +(3.67048 + 1.52036i) q^{12} +0.803928i q^{13} +(-1.46136 + 3.52804i) q^{14} +(2.03186 - 2.03186i) q^{15} -3.83815 q^{16} +2.44395 q^{18} +(-2.29932 + 2.29932i) q^{19} +(-4.36874 + 10.5471i) q^{20} +1.56252i q^{21} +(14.3208 + 5.93187i) q^{22} +(2.36264 + 5.70393i) q^{23} +(-4.45465 + 1.84518i) q^{24} +(2.30299 + 2.30299i) q^{25} +(-1.38930 - 1.38930i) q^{26} +(0.923880 - 0.382683i) q^{27} +(-2.37560 - 5.73519i) q^{28} +(-1.41257 - 0.585104i) q^{29} +7.02266i q^{30} +(0.831623 - 2.00771i) q^{31} +(-0.186048 + 0.186048i) q^{32} +6.34249 q^{33} -4.48987 q^{35} +(-2.80927 + 2.80927i) q^{36} +(-0.243477 + 0.587805i) q^{37} -7.94707i q^{38} +(-0.742733 - 0.307650i) q^{39} +(-5.30209 - 12.8004i) q^{40} +(-5.18831 + 2.14907i) q^{41} +(-2.70024 - 2.70024i) q^{42} +(7.79523 + 7.79523i) q^{43} +(-23.2800 + 9.64289i) q^{44} +(1.09964 + 2.65475i) q^{45} +(-13.9401 - 5.77419i) q^{46} +7.46399i q^{47} +(1.46879 - 3.54598i) q^{48} +(-3.22337 + 3.22337i) q^{49} -7.95975 q^{50} +3.19393 q^{52} +(-0.952419 + 0.952419i) q^{53} +(-0.935260 + 2.25792i) q^{54} +18.2250i q^{55} +(6.96047 + 2.88312i) q^{56} +(-1.24438 - 3.00421i) q^{57} +(3.45224 - 1.42997i) q^{58} +(2.85255 + 2.85255i) q^{59} +(-8.07238 - 8.07238i) q^{60} +(7.73119 - 3.20237i) q^{61} +(2.03245 + 4.90676i) q^{62} +(-1.44358 - 0.597950i) q^{63} -8.31932i q^{64} +(0.884028 - 2.13423i) q^{65} +(-10.9607 + 10.9607i) q^{66} -7.75709 q^{67} -6.17389 q^{69} +(7.75911 - 7.75911i) q^{70} +(1.72877 - 4.17362i) q^{71} -4.82168i q^{72} +(-7.65058 - 3.16897i) q^{73} +(-0.595046 - 1.43657i) q^{74} +(-3.00900 + 1.24637i) q^{75} +(9.13498 + 9.13498i) q^{76} +(-7.00760 - 7.00760i) q^{77} +(1.81520 - 0.751882i) q^{78} +(0.576780 + 1.39247i) q^{79} +(10.1893 + 4.22056i) q^{80} +1.00000i q^{81} +(5.25222 - 12.6800i) q^{82} +(5.32113 - 5.32113i) q^{83} +6.20773 q^{84} -26.9424 q^{86} +(1.08113 - 1.08113i) q^{87} +(11.7030 - 28.2536i) q^{88} +6.12748i q^{89} +(-6.48809 - 2.68746i) q^{90} +(0.480709 + 1.16053i) q^{91} +(22.6611 - 9.38655i) q^{92} +(1.53664 + 1.53664i) q^{93} +(-12.8988 - 12.8988i) q^{94} +(8.63255 - 3.57572i) q^{95} +(-0.100689 - 0.243084i) q^{96} +(4.47303 + 1.85279i) q^{97} -11.1408i q^{98} +(-2.42716 + 5.85969i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 120 q^{16} + 24 q^{18} + 72 q^{33} - 96 q^{50} - 144 q^{52} + 48 q^{67} - 72 q^{69} + 120 q^{84} + 48 q^{86}+O(q^{100}) \) 48 * q - 120 * q^16 + 24 * q^18 + 72 * q^33 - 96 * q^50 - 144 * q^52 + 48 * q^67 - 72 * q^69 + 120 * q^84 + 48 * q^86

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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