LMFDB - Embedded newform 442.2.m.b.373.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [442,2,Mod(237,442)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(442, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 3]))

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

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

chi := DirichletCharacter("442.237");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 442 = 2 \cdot 13 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	442.m (of order $6$, degree $2$, 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:	$3.52938776934$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			373.2
Character	$\chi$	$=$	442.373
Dual form			442.2.m.b.237.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{2} +(-2.19681 - 1.26833i) q^{3} +(-0.500000 - 0.866025i) q^{4} -3.07158i q^{5} +(-2.19681 + 1.26833i) q^{6} +(-2.78270 + 1.60659i) q^{7} -1.00000 q^{8} +(1.71730 + 2.97445i) q^{9} +O(q^{10})$	\(q+(0.500000 - 0.866025i) q^{2} +(-2.19681 - 1.26833i) q^{3} +(-0.500000 - 0.866025i) q^{4} -3.07158i q^{5} +(-2.19681 + 1.26833i) q^{6} +(-2.78270 + 1.60659i) q^{7} -1.00000 q^{8} +(1.71730 + 2.97445i) q^{9} +(-2.66007 - 1.53579i) q^{10} +(0.916260 + 0.529003i) q^{11} +2.53665i q^{12} +(-2.59136 - 2.50696i) q^{13} +3.21319i q^{14} +(-3.89576 + 6.74766i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(4.04828 + 0.781925i) q^{17} +3.43460 q^{18} +(0.357890 + 0.619883i) q^{19} +(-2.66007 + 1.53579i) q^{20} +8.15074 q^{21} +(0.916260 - 0.529003i) q^{22} +(1.54064 + 0.889487i) q^{23} +(2.19681 + 1.26833i) q^{24} -4.43460 q^{25} +(-3.46677 + 0.990709i) q^{26} -1.10244i q^{27} +(2.78270 + 1.60659i) q^{28} +(-6.98341 - 4.03187i) q^{29} +(3.89576 + 6.74766i) q^{30} +8.58052i q^{31} +(0.500000 + 0.866025i) q^{32} +(-1.34190 - 2.32423i) q^{33} +(2.70131 - 3.11495i) q^{34} +(4.93478 + 8.54729i) q^{35} +(1.71730 - 2.97445i) q^{36} +(-6.96769 - 4.02279i) q^{37} +0.715779 q^{38} +(2.51308 + 8.79399i) q^{39} +3.07158i q^{40} +(5.81161 + 3.35534i) q^{41} +(4.07537 - 7.05875i) q^{42} +(-6.22167 - 10.7762i) q^{43} -1.05801i q^{44} +(9.13627 - 5.27483i) q^{45} +(1.54064 - 0.889487i) q^{46} -5.10774 q^{47} +(2.19681 - 1.26833i) q^{48} +(1.66229 - 2.87917i) q^{49} +(-2.21730 + 3.84048i) q^{50} +(-7.90155 - 6.85228i) q^{51} +(-0.875406 + 3.49767i) q^{52} -8.33560 q^{53} +(-0.954739 - 0.551219i) q^{54} +(1.62487 - 2.81436i) q^{55} +(2.78270 - 1.60659i) q^{56} -1.81568i q^{57} +(-6.98341 + 4.03187i) q^{58} +(-2.60888 - 4.51871i) q^{59} +7.79153 q^{60} +(0.903276 - 0.521506i) q^{61} +(7.43095 + 4.29026i) q^{62} +(-9.55748 - 5.51801i) q^{63} +1.00000 q^{64} +(-7.70032 + 7.95958i) q^{65} -2.68379 q^{66} +(0.928995 - 1.60907i) q^{67} +(-1.34697 - 3.89688i) q^{68} +(-2.25632 - 3.90806i) q^{69} +9.86957 q^{70} +(-4.72397 + 2.72739i) q^{71} +(-1.71730 - 2.97445i) q^{72} -3.73101i q^{73} +(-6.96769 + 4.02279i) q^{74} +(9.74196 + 5.62452i) q^{75} +(0.357890 - 0.619883i) q^{76} -3.39957 q^{77} +(8.87236 + 2.22060i) q^{78} -13.2724i q^{79} +(2.66007 + 1.53579i) q^{80} +(3.75365 - 6.50152i) q^{81} +(5.81161 - 3.35534i) q^{82} +9.75954 q^{83} +(-4.07537 - 7.05875i) q^{84} +(2.40174 - 12.4346i) q^{85} -12.4433 q^{86} +(10.2275 + 17.7145i) q^{87} +(-0.916260 - 0.529003i) q^{88} +(4.20007 - 7.27473i) q^{89} -10.5497i q^{90} +(11.2387 + 2.81284i) q^{91} -1.77897i q^{92} +(10.8829 - 18.8497i) q^{93} +(-2.55387 + 4.42343i) q^{94} +(1.90402 - 1.09929i) q^{95} -2.53665i q^{96} +(4.06325 - 2.34592i) q^{97} +(-1.66229 - 2.87917i) q^{98} +3.63383i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 12 q^{2} - 12 q^{4} - 24 q^{8} + 12 q^{9}+O(q^{10}) $ 24 * q + 12 * q^2 - 12 * q^4 - 24 * q^8 + 12 * q^9	$ 24 q + 12 q^{2} - 12 q^{4} - 24 q^{8} + 12 q^{9} + 12 q^{13} - 12 q^{16} + 5 q^{17} + 24 q^{18} + 8 q^{19} - 4 q^{21} - 48 q^{25} - 6 q^{26} + 12 q^{32} - 6 q^{33} + 10 q^{34} - 10 q^{35} + 12 q^{36} + 16 q^{38} - 2 q^{42} - 4 q^{43} + 12 q^{47} + 20 q^{49} - 24 q^{50} + 16 q^{51} - 18 q^{52} - 44 q^{53} - 12 q^{55} + 14 q^{59} + 24 q^{64} - 12 q^{66} + 6 q^{67} + 5 q^{68} + 10 q^{69} - 20 q^{70} - 12 q^{72} + 8 q^{76} - 28 q^{77} - 4 q^{81} - 4 q^{83} + 2 q^{84} + 13 q^{85} - 8 q^{86} - 12 q^{87} + 20 q^{89} + 6 q^{94} - 20 q^{98}+O(q^{100}) $ 24 * q + 12 * q^2 - 12 * q^4 - 24 * q^8 + 12 * q^9 + 12 * q^13 - 12 * q^16 + 5 * q^17 + 24 * q^18 + 8 * q^19 - 4 * q^21 - 48 * q^25 - 6 * q^26 + 12 * q^32 - 6 * q^33 + 10 * q^34 - 10 * q^35 + 12 * q^36 + 16 * q^38 - 2 * q^42 - 4 * q^43 + 12 * q^47 + 20 * q^49 - 24 * q^50 + 16 * q^51 - 18 * q^52 - 44 * q^53 - 12 * q^55 + 14 * q^59 + 24 * q^64 - 12 * q^66 + 6 * q^67 + 5 * q^68 + 10 * q^69 - 20 * q^70 - 12 * q^72 + 8 * q^76 - 28 * q^77 - 4 * q^81 - 4 * q^83 + 2 * q^84 + 13 * q^85 - 8 * q^86 - 12 * q^87 + 20 * q^89 + 6 * q^94 - 20 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/442\mathbb{Z}\right)^\times$.

$n$	$105$	$171$
$\chi(n)$	$-1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$3$	−2.19681	−	1.26833i	−1.26833	−	0.732268i	−0.293655	−	0.955911i	$-0.594872\pi$
$3$	−2.19681	−	1.26833i	−1.26833	−	0.732268i	−0.974671	+	0.223643i	$0.928205\pi$
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$		−	3.07158i		−	1.37365i	−0.726822	−	0.686826i	$-0.759003\pi$
$5$		−	3.07158i		−	1.37365i	0.726822	−	0.686826i	$-0.240997\pi$
$6$	−2.19681	+	1.26833i	−0.896842	+	0.517792i
$7$	−2.78270	+	1.60659i	−1.05176	+	0.607236i	−0.923142	−	0.384458i	$-0.874388\pi$
$7$	−2.78270	+	1.60659i	−1.05176	+	0.607236i	−0.128620	+	0.991694i	$0.541055\pi$
$8$	−1.00000			−0.353553
$9$	1.71730	+	2.97445i	0.572434	+	0.991485i
$10$	−2.66007	−	1.53579i	−0.841187	−	0.485659i
$11$	0.916260	+	0.529003i	0.276263	+	0.159500i	0.631730	−	0.775188i	$-0.282345\pi$
$11$	0.916260	+	0.529003i	0.276263	+	0.159500i	−0.355468	+	0.934689i	$0.615678\pi$
$12$			2.53665i			0.732268i
$13$	−2.59136	−	2.50696i	−0.718715	−	0.695305i
$13$	−2.59136	−	2.50696i	−0.718715	−	0.695305i
$14$			3.21319i			0.858761i
$15$	−3.89576	+	6.74766i	−1.00588	+	1.74224i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	4.04828	+	0.781925i	0.981853	+	0.189645i
$17$	4.04828	+	0.781925i	0.981853	+	0.189645i
$18$	3.43460			0.809544
$19$	0.357890	+	0.619883i	0.0821055	+	0.142211i	0.904154	−	0.427206i	$-0.140502\pi$
$19$	0.357890	+	0.619883i	0.0821055	+	0.142211i	−0.822049	+	0.569417i	$0.807169\pi$
$20$	−2.66007	+	1.53579i	−0.594809	+	0.343413i
$21$	8.15074			1.77864
$22$	0.916260	−	0.529003i	0.195347	−	0.112784i
$23$	1.54064	+	0.889487i	0.321245	+	0.185471i	0.651947	−	0.758264i	$-0.273952\pi$
$23$	1.54064	+	0.889487i	0.321245	+	0.185471i	−0.330702	+	0.943735i	$0.607286\pi$
$24$	2.19681	+	1.26833i	0.448421	+	0.258896i
$25$	−4.43460			−0.886921
$26$	−3.46677	+	0.990709i	−0.679890	+	0.194294i
$27$		−	1.10244i		−	0.212164i
$28$	2.78270	+	1.60659i	0.525881	+	0.303618i
$29$	−6.98341	−	4.03187i	−1.29679	−	0.748700i	−0.316938	−	0.948446i	$-0.602655\pi$
$29$	−6.98341	−	4.03187i	−1.29679	−	0.748700i	−0.979848	+	0.199746i	$0.935988\pi$
$30$	3.89576	+	6.74766i	0.711266	+	1.23195i
$31$			8.58052i			1.54111i	0.637376	+	0.770553i	$0.280020\pi$
$31$			8.58052i			1.54111i	−0.637376	+	0.770553i	$0.719980\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$	−1.34190	−	2.32423i	−0.233594	−	0.404597i
$34$	2.70131	−	3.11495i	0.463271	−	0.534210i
$35$	4.93478	+	8.54729i	0.834131	+	1.44476i
$36$	1.71730	−	2.97445i	0.286217	−	0.495742i
$37$	−6.96769	−	4.02279i	−1.14548	−	0.661343i	−0.197699	−	0.980263i	$-0.563347\pi$
$37$	−6.96769	−	4.02279i	−1.14548	−	0.661343i	−0.947782	+	0.318919i	$0.896680\pi$
$38$	0.715779			0.116115
$39$	2.51308	+	8.79399i	0.402416	+	1.40817i
$40$			3.07158i			0.485659i
$41$	5.81161	+	3.35534i	0.907621	+	0.524015i	0.879665	−	0.475594i	$-0.157767\pi$
$41$	5.81161	+	3.35534i	0.907621	+	0.524015i	0.0279561	+	0.999609i	$0.491100\pi$
$42$	4.07537	−	7.05875i	0.628843	−	1.08919i
$43$	−6.22167	−	10.7762i	−0.948795	−	1.64336i	−0.747968	−	0.663735i	$-0.768970\pi$
$43$	−6.22167	−	10.7762i	−0.948795	−	1.64336i	−0.200828	−	0.979627i	$-0.564363\pi$
$44$		−	1.05801i		−	0.159500i
$45$	9.13627	−	5.27483i	1.36196	−	0.786325i
$46$	1.54064	−	0.889487i	0.227155	−	0.131148i
$47$	−5.10774			−0.745040			−0.372520	−	0.928024i	$-0.621506\pi$
$47$	−5.10774			−0.745040			−0.372520	+	0.928024i	$0.621506\pi$
$48$	2.19681	−	1.26833i	0.317082	−	0.183067i
$49$	1.66229	−	2.87917i	0.237470	−	0.411310i
$50$	−2.21730	+	3.84048i	−0.313574	+	0.543126i
$51$	−7.90155	−	6.85228i	−1.10644	−	0.959511i
$52$	−0.875406	+	3.49767i	−0.121397	+	0.485039i
$53$	−8.33560			−1.14498			−0.572491	−	0.819911i	$-0.694023\pi$
$53$	−8.33560			−1.14498			−0.572491	+	0.819911i	$0.694023\pi$
$54$	−0.954739	−	0.551219i	−0.129924	−	0.0750114i
$55$	1.62487	−	2.81436i	0.219098	−	0.379489i
$56$	2.78270	−	1.60659i	0.371854	−	0.214690i
$57$		−	1.81568i		−	0.240493i
$58$	−6.98341	+	4.03187i	−0.916966	+	0.529411i
$59$	−2.60888	−	4.51871i	−0.339647	−	0.588286i	0.644719	−	0.764420i	$-0.276974\pi$
$59$	−2.60888	−	4.51871i	−0.339647	−	0.588286i	−0.984366	+	0.176133i	$0.943641\pi$
$60$	7.79153			1.00588
$61$	0.903276	−	0.521506i	0.115653	−	0.0667721i	−0.441058	−	0.897479i	$-0.645397\pi$
$61$	0.903276	−	0.521506i	0.115653	−	0.0667721i	0.556710	+	0.830707i	$0.312063\pi$
$62$	7.43095	+	4.29026i	0.943731	+	0.544863i
$63$	−9.55748	−	5.51801i	−1.20413	−	0.695204i
$64$	1.00000			0.125000
$65$	−7.70032	+	7.95958i	−0.955107	+	0.987265i
$66$	−2.68379			−0.330352
$67$	0.928995	−	1.60907i	0.113495	−	0.196579i	−0.803682	−	0.595059i	$-0.797129\pi$
$67$	0.928995	−	1.60907i	0.113495	−	0.196579i	0.917177	+	0.398480i	$0.130462\pi$
$68$	−1.34697	−	3.89688i	−0.163345	−	0.472566i
$69$	−2.25632	−	3.90806i	−0.271629	−	0.470475i
$70$	9.86957			1.17964
$71$	−4.72397	+	2.72739i	−0.560632	+	0.323681i	−0.753399	−	0.657563i	$-0.771587\pi$
$71$	−4.72397	+	2.72739i	−0.560632	+	0.323681i	0.192767	+	0.981245i	$0.438254\pi$
$72$	−1.71730	−	2.97445i	−0.202386	−	0.350543i
$73$		−	3.73101i		−	0.436681i	−0.975873	−	0.218341i	$-0.929936\pi$
$73$		−	3.73101i		−	0.436681i	0.975873	−	0.218341i	$-0.0700644\pi$
$74$	−6.96769	+	4.02279i	−0.809977	+	0.467640i
$75$	9.74196	+	5.62452i	1.12490	+	0.649464i
$76$	0.357890	−	0.619883i	0.0410528	−	0.0711055i
$77$	−3.39957			−0.387417
$78$	8.87236	+	2.22060i	1.00460	+	0.251433i
$79$		−	13.2724i		−	1.49326i	−0.665242	−	0.746628i	$-0.731671\pi$
$79$		−	13.2724i		−	1.49326i	0.665242	−	0.746628i	$-0.268329\pi$
$80$	2.66007	+	1.53579i	0.297404	+	0.171707i
$81$	3.75365	−	6.50152i	0.417073	−	0.722391i
$82$	5.81161	−	3.35534i	0.641785	−	0.370535i
$83$	9.75954			1.07125			0.535624	−	0.844456i	$-0.320076\pi$
$83$	9.75954			1.07125			0.535624	+	0.844456i	$0.320076\pi$
$84$	−4.07537	−	7.05875i	−0.444659	−	0.770173i
$85$	2.40174	−	12.4346i	0.260506	−	1.34872i
$86$	−12.4433			−1.34180
$87$	10.2275	+	17.7145i	1.09650	+	1.89919i
$88$	−0.916260	−	0.529003i	−0.0976736	−	0.0563919i
$89$	4.20007	−	7.27473i	0.445206	−	0.771120i	−0.552860	−	0.833274i	$-0.686464\pi$
$89$	4.20007	−	7.27473i	0.445206	−	0.771120i	0.998067	+	0.0621543i	$0.0197971\pi$
$90$		−	10.5497i		−	1.11203i
$91$	11.2387	+	2.81284i	1.17813	+	0.294866i
$92$		−	1.77897i		−	0.185471i
$93$	10.8829	−	18.8497i	1.12850	−	1.95463i
$94$	−2.55387	+	4.42343i	−0.263411	+	0.456242i
$95$	1.90402	−	1.09929i	0.195348	−	0.112784i
$96$		−	2.53665i		−	0.258896i
$97$	4.06325	−	2.34592i	0.412560	−	0.238192i	−0.279329	−	0.960195i	$-0.590112\pi$
$97$	4.06325	−	2.34592i	0.412560	−	0.238192i	0.691889	+	0.722004i	$0.256779\pi$
$98$	−1.66229	−	2.87917i	−0.167917	−	0.290840i
$99$			3.63383i			0.365214i
$100$	2.21730	+	3.84048i	0.221730	+	0.384048i
$101$	−8.93773	+	15.4806i	−0.889337	+	1.54038i	−0.0486764	+	0.998815i	$0.515500\pi$
$101$	−8.93773	+	15.4806i	−0.889337	+	1.54038i	−0.840661	+	0.541562i	$0.817833\pi$
$102$	−9.88502	+	3.41681i	−0.978763	+	0.338314i
$103$	−0.715779			−0.0705278			−0.0352639	−	0.999378i	$-0.511227\pi$
$103$	−0.715779			−0.0705278			−0.0352639	+	0.999378i	$0.511227\pi$
$104$	2.59136	+	2.50696i	0.254104	+	0.245827i
$105$		−	25.0357i		−	2.44323i
$106$	−4.16780	+	7.21884i	−0.404812	+	0.701156i
$107$	−10.9468	−	6.32012i	−1.05826	−	0.610989i	−0.133313	−	0.991074i	$-0.542562\pi$
$107$	−10.9468	−	6.32012i	−1.05826	−	0.610989i	−0.924952	+	0.380084i	$0.875895\pi$
$108$	−0.954739	+	0.551219i	−0.0918698	+	0.0530411i
$109$			9.30149i			0.890921i	0.895302	+	0.445460i	$0.146960\pi$
$109$			9.30149i			0.890921i	−0.895302	+	0.445460i	$0.853040\pi$
$110$	−1.62487	−	2.81436i	−0.154926	−	0.268339i
$111$	10.2044	+	17.6746i	0.968562	+	1.67760i
$112$		−	3.21319i		−	0.303618i
$113$	5.82064	−	3.36055i	0.547560	−	0.316134i	−0.200577	−	0.979678i	$-0.564282\pi$
$113$	5.82064	−	3.36055i	0.547560	−	0.316134i	0.748137	+	0.663544i	$0.230948\pi$
$114$	−1.57243	−	0.907842i	−0.147271	−	0.0850271i
$115$	2.73213	−	4.73219i	0.254773	−	0.441279i
$116$			8.06374i			0.748700i
$117$	3.00667	−	12.0131i	0.277967	−	1.11061i
$118$	−5.21776			−0.480334
$119$	−12.5214	+	4.32808i	−1.14784	+	0.396755i
$120$	3.89576	−	6.74766i	0.355633	−	0.615975i
$121$	−4.94031	−	8.55687i	−0.449119	−	0.777897i
$122$		−	1.04301i		−	0.0944299i
$123$	−8.51132	−	14.7420i	−0.767440	−	1.32924i
$124$	7.43095	−	4.29026i	0.667319	−	0.385277i
$125$		−	1.73666i		−	0.155332i
$126$	−9.55748	+	5.51801i	−0.851448	+	0.491584i
$127$	−9.40165	+	16.2841i	−0.834262	+	1.44498i	0.0603683	+	0.998176i	$0.480772\pi$
$127$	−9.40165	+	16.2841i	−0.834262	+	1.44498i	−0.894630	+	0.446808i	$0.852561\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$			31.5644i			2.77909i
$130$	3.04304	+	10.6485i	0.266892	+	0.933932i
$131$			3.58023i			0.312806i	0.987693	+	0.156403i	$0.0499899\pi$
$131$			3.58023i			0.312806i	−0.987693	+	0.156403i	$0.950010\pi$
$132$	−1.34190	+	2.32423i	−0.116797	+	0.202298i
$133$	−1.99180	−	1.14997i	−0.172711	−	0.0997148i
$134$	−0.928995	−	1.60907i	−0.0802529	−	0.139002i
$135$	−3.38623			−0.291440
$136$	−4.04828	−	0.781925i	−0.347137	−	0.0670495i
$137$	−8.64676	−	14.9766i	−0.738742	−	1.27954i	−0.953062	−	0.302775i	$-0.902087\pi$
$137$	−8.64676	−	14.9766i	−0.738742	−	1.27954i	0.214320	−	0.976764i	$-0.431247\pi$
$138$	−4.51264			−0.384141
$139$	5.53148	−	3.19360i	0.469174	−	0.270878i	−0.246720	−	0.969087i	$-0.579353\pi$
$139$	5.53148	−	3.19360i	0.469174	−	0.270878i	0.715894	+	0.698209i	$0.246019\pi$
$140$	4.93478	−	8.54729i	0.417065	−	0.722378i
$141$	11.2207	+	6.47828i	0.944954	+	0.545569i
$142$			5.45477i			0.457754i
$143$	−1.04818	−	3.66786i	−0.0876529	−	0.306722i
$144$	−3.43460			−0.286217
$145$	−12.3842	+	21.4501i	−1.02845	+	1.78133i
$146$	−3.23115	−	1.86550i	−0.267412	−	0.154390i
$147$	−7.30346	+	4.21665i	−0.602379	+	0.347784i
$148$			8.04559i			0.661343i
$149$	2.64630	+	4.58352i	0.216793	+	0.375497i	0.953826	−	0.300361i	$-0.0971070\pi$
$149$	2.64630	+	4.58352i	0.216793	+	0.375497i	−0.737033	+	0.675857i	$0.763774\pi$
$150$	9.74196	−	5.62452i	0.795428	−	0.459240i
$151$	−7.39957			−0.602169			−0.301084	−	0.953598i	$-0.597349\pi$
$151$	−7.39957			−0.602169			−0.301084	+	0.953598i	$0.597349\pi$
$152$	−0.357890	−	0.619883i	−0.0290287	−	0.0502792i
$153$	4.62632	+	13.3842i	0.374016	+	1.08205i
$154$	−1.69979	+	2.94411i	−0.136973	+	0.237244i
$155$	26.3557			2.11694
$156$	6.35928	−	6.57339i	0.509150	−	0.526292i
$157$	15.8294			1.26332			0.631660	−	0.775245i	$-0.282374\pi$
$157$	15.8294			1.26332			0.631660	+	0.775245i	$0.282374\pi$
$158$	−11.4942	−	6.63618i	−0.914429	−	0.527946i
$159$	18.3117	+	10.5723i	1.45221	+	0.838434i
$160$	2.66007	−	1.53579i	0.210297	−	0.121415i
$161$	−5.71618			−0.450498
$162$	−3.75365	−	6.50152i	−0.294915	−	0.510808i
$163$	−9.30740	+	5.37363i	−0.729012	+	0.420895i	−0.818061	−	0.575132i	$-0.804951\pi$
$163$	−9.30740	+	5.37363i	−0.729012	+	0.420895i	0.0890485	+	0.996027i	$0.471617\pi$
$164$		−	6.71067i		−	0.524015i
$165$	−7.13906	+	4.12174i	−0.555775	+	0.320877i
$166$	4.87977	−	8.45201i	0.378744	−	0.656003i
$167$	−14.9975	−	8.65883i	−1.16054	−	0.670040i	−0.209109	−	0.977892i	$-0.567056\pi$
$167$	−14.9975	−	8.65883i	−1.16054	−	0.670040i	−0.951434	+	0.307852i	$0.900390\pi$
$168$	−8.15074			−0.628843
$169$	0.430338	+	12.9929i	0.0331029	+	0.999452i
$170$	−9.56783	−	8.29728i	−0.733819	−	0.636373i
$171$	−1.22921	+	2.12905i	−0.0940000	+	0.162813i
$172$	−6.22167	+	10.7762i	−0.474398	+	0.821681i
$173$	−0.432074	+	0.249458i	−0.0328500	+	0.0189660i	−0.516335	−	0.856387i	$-0.672704\pi$
$173$	−0.432074	+	0.249458i	−0.0328500	+	0.0189660i	0.483485	+	0.875353i	$0.339371\pi$
$174$	20.4549			1.55068
$175$	12.3402	−	7.12461i	0.932830	−	0.538570i
$176$	−0.916260	+	0.529003i	−0.0690657	+	0.0398751i
$177$			13.2356i			0.994852i
$178$	−4.20007	−	7.27473i	−0.314808	−	0.545264i
$179$	−3.52064	+	6.09793i	−0.263145	+	0.455780i	−0.967076	−	0.254488i	$-0.918093\pi$
$179$	−3.52064	+	6.09793i	−0.263145	+	0.455780i	0.703931	+	0.710268i	$0.251426\pi$
$180$	−9.13627	−	5.27483i	−0.680978	−	0.393163i
$181$		−	15.1538i		−	1.12637i	−0.826331	−	0.563185i	$-0.809576\pi$
$181$		−	15.1538i		−	1.12637i	0.826331	−	0.563185i	$-0.190424\pi$
$182$	8.05532	−	8.32654i	0.597100	−	0.617204i
$183$	−2.64576			−0.195580
$184$	−1.54064	−	0.889487i	−0.113577	−	0.0655739i
$185$	−12.3563	+	21.4018i	−0.908456	+	1.57349i
$186$	−10.8829	−	18.8497i	−0.797973	−	1.38213i
$187$	3.29564	+	2.85800i	0.241001	+	0.208998i
$188$	2.55387	+	4.42343i	0.186260	+	0.322612i
$189$	1.77117	+	3.06776i	0.128834	+	0.223147i
$190$		−	2.19857i		−	0.159501i
$191$	3.60222	+	6.23923i	0.260648	+	0.451455i	0.966414	−	0.256989i	$-0.0827306\pi$
$191$	3.60222	+	6.23923i	0.260648	+	0.451455i	−0.705767	+	0.708445i	$0.749397\pi$
$192$	−2.19681	−	1.26833i	−0.158541	−	0.0915335i
$193$	7.69503	+	4.44273i	0.553900	+	0.319794i	0.750694	−	0.660651i	$-0.229720\pi$
$193$	7.69503	+	4.44273i	0.553900	+	0.319794i	−0.196793	+	0.980445i	$0.563053\pi$
$194$		−	4.69184i		−	0.336854i
$195$	27.0114	−	7.71914i	1.93433	−	0.552779i
$196$	−3.32458			−0.237470
$197$	8.13105	+	4.69447i	0.579314	+	0.334467i	0.760861	−	0.648915i	$-0.224777\pi$
$197$	8.13105	+	4.69447i	0.579314	+	0.334467i	−0.181547	+	0.983382i	$0.558110\pi$
$198$	3.14699	+	1.81691i	0.223647	+	0.129123i
$199$	8.23969	−	4.75719i	0.584096	−	0.337228i	−0.178664	−	0.983910i	$-0.557177\pi$
$199$	8.23969	−	4.75719i	0.584096	−	0.337228i	0.762759	+	0.646682i	$0.223844\pi$
$200$	4.43460			0.313574
$201$	−4.08164	+	2.35654i	−0.287897	+	0.166217i
$202$	8.93773	+	15.4806i	0.628856	+	1.08921i
$203$	25.9103			1.81855
$204$	−1.98347	+	10.2691i	−0.138871	+	0.718980i
$205$	10.3062	−	17.8508i	0.719815	−	1.24676i
$206$	−0.357890	+	0.619883i	−0.0249354	+	0.0431893i
$207$			6.11007i			0.424679i
$208$	3.46677	−	0.990709i	0.240377	−	0.0686933i
$209$			0.757298i			0.0523834i
$210$	−21.6815	−	12.5178i	−1.49617	−	0.863812i
$211$	1.86066	+	1.07425i	0.128093	+	0.0739545i	0.562677	−	0.826677i	$-0.309771\pi$
$211$	1.86066	+	1.07425i	0.128093	+	0.0739545i	−0.434584	+	0.900631i	$0.643105\pi$
$212$	4.16780	+	7.21884i	0.286246	+	0.495792i
$213$	13.8369			0.948086
$214$	−10.9468	+	6.32012i	−0.748306	+	0.432035i
$215$	−33.1001	+	19.1103i	−2.25741	+	1.30331i
$216$			1.10244i			0.0750114i
$217$	−13.7854	−	23.8770i	−0.935815	−	1.62088i
$218$	8.05532	+	4.65074i	0.545575	+	0.314988i
$219$	−4.73213	+	8.19629i	−0.319768	+	0.553854i
$220$	−3.24975			−0.219098
$221$	−8.53032	−	12.1751i	−0.573812	−	0.818987i
$222$	20.4089			1.36975
$223$	13.9016	−	24.0782i	0.930917	−	1.61240i	0.149159	−	0.988813i	$-0.452343\pi$
$223$	13.9016	−	24.0782i	0.930917	−	1.61240i	0.781758	−	0.623582i	$-0.214323\pi$
$224$	−2.78270	−	1.60659i	−0.185927	−	0.107345i
$225$	−7.61555	−	13.1905i	−0.507704	−	0.879368i
$226$		−	6.72110i		−	0.447081i
$227$	−0.874127	+	0.504677i	−0.0580178	+	0.0334966i	−0.528728	−	0.848791i	$-0.677331\pi$
$227$	−0.874127	+	0.504677i	−0.0580178	+	0.0334966i	0.470711	+	0.882288i	$0.343998\pi$
$228$	−1.57243	+	0.907842i	−0.104137	+	0.0601233i
$229$	27.4722			1.81542			0.907708	−	0.419603i	$-0.137831\pi$
$229$	27.4722			1.81542			0.907708	+	0.419603i	$0.137831\pi$
$230$	−2.73213	−	4.73219i	−0.180151	−	0.312031i
$231$	7.46820	+	4.31176i	0.491371	+	0.283693i
$232$	6.98341	+	4.03187i	0.458483	+	0.264705i
$233$		−	11.3158i		−	0.741320i	−0.928769	−	0.370660i	$-0.879132\pi$
$233$		−	11.3158i		−	0.741320i	0.928769	−	0.370660i	$-0.120868\pi$
$234$	−8.90031	−	8.61040i	−0.581831	−	0.562880i
$235$			15.6888i			1.02343i
$236$	−2.60888	+	4.51871i	−0.169824	+	0.294143i
$237$	−16.8337	+	29.1568i	−1.09346	+	1.89394i
$238$	−2.51247	+	13.0079i	−0.162859	+	0.843177i
$239$	21.7764			1.40860			0.704301	−	0.709902i	$-0.251261\pi$
$239$	21.7764			1.40860			0.704301	+	0.709902i	$0.251261\pi$
$240$	−3.89576	−	6.74766i	−0.251471	−	0.435560i
$241$	19.4311	−	11.2186i	1.25167	−	0.722651i	0.280227	−	0.959934i	$-0.409590\pi$
$241$	19.4311	−	11.2186i	1.25167	−	0.722651i	0.971441	+	0.237283i	$0.0762569\pi$
$242$	−9.88062			−0.635151
$243$	−19.3563	+	11.1754i	−1.24171	+	0.716900i
$244$	−0.903276	−	0.521506i	−0.0578263	−	0.0333860i
$245$	−8.84360	−	5.10586i	−0.564997	−	0.326201i
$246$	−17.0226			−1.08532
$247$	0.626597	−	2.50356i	0.0398694	−	0.159297i
$248$		−	8.58052i		−	0.544863i
$249$	−21.4398	−	12.3783i	−1.35869	−	0.784442i
$250$	−1.50399	−	0.868330i	−0.0951208	−	0.0549180i
$251$	−6.00579	−	10.4023i	−0.379082	−	0.656589i	0.611847	−	0.790976i	$-0.290427\pi$
$251$	−6.00579	−	10.4023i	−0.379082	−	0.656589i	−0.990929	+	0.134387i	$0.957094\pi$
$252$			11.0360i			0.695204i
$253$	0.941082	+	1.63000i	0.0591653	+	0.102477i
$254$	9.40165	+	16.2841i	0.589912	+	1.02176i
$255$	−21.0473	+	24.2703i	−1.31803	+	1.51986i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−6.75231	+	11.6953i	−0.421198	+	0.729536i	−0.996057	−	0.0887166i	$-0.971723\pi$
$257$	−6.75231	+	11.6953i	−0.421198	+	0.729536i	0.574859	+	0.818252i	$0.305057\pi$
$258$	27.3356	+	15.7822i	1.70184	+	0.982557i
$259$	25.8520			1.60636
$260$	10.7434	+	2.68888i	0.666275	+	0.166757i
$261$		−	27.6958i		−	1.71432i
$262$	3.10057	+	1.79011i	0.191554	+	0.110594i
$263$	5.65686	−	9.79797i	0.348817	−	0.604169i	−0.637223	−	0.770680i	$-0.719917\pi$
$263$	5.65686	−	9.79797i	0.348817	−	0.604169i	0.986040	+	0.166511i	$0.0532501\pi$
$264$	1.34190	+	2.32423i	0.0825880	+	0.143047i
$265$			25.6035i			1.57281i
$266$	−1.99180	+	1.14997i	−0.122125	+	0.0705090i
$267$	−18.4535	+	10.6541i	−1.12933	+	0.652021i
$268$	−1.85799			−0.113495
$269$	−15.2450	+	8.80173i	−0.929506	+	0.536651i	−0.886655	−	0.462431i	$-0.846977\pi$
$269$	−15.2450	+	8.80173i	−0.929506	+	0.536651i	−0.0428508	+	0.999081i	$0.513644\pi$
$270$	−1.69311	+	2.93256i	−0.103040	+	0.178470i
$271$	−10.4941	+	18.1763i	−0.637470	+	1.10413i	0.348516	+	0.937303i	$0.386686\pi$
$271$	−10.4941	+	18.1763i	−0.637470	+	1.10413i	−0.985986	+	0.166828i	$0.946648\pi$
$272$	−2.70131	+	3.11495i	−0.163791	+	0.188872i
$273$	−21.1215	−	20.4336i	−1.27833	−	1.23669i
$274$	−17.2935			−1.04474
$275$	−4.06325	−	2.34592i	−0.245023	−	0.141464i
$276$	−2.25632	+	3.90806i	−0.135814	+	0.235238i
$277$	1.70969	−	0.987092i	0.102726	−	0.0593086i	−0.447757	−	0.894155i	$-0.647777\pi$
$277$	1.70969	−	0.987092i	0.102726	−	0.0593086i	0.550483	+	0.834847i	$0.314444\pi$
$278$		−	6.38721i		−	0.383079i
$279$	−25.5224	+	14.7353i	−1.52798	+	0.882182i
$280$	−4.93478	−	8.54729i	−0.294910	−	0.510799i
$281$	10.8376			0.646516			0.323258	−	0.946311i	$-0.395222\pi$
$281$	10.8376			0.646516			0.323258	+	0.946311i	$0.395222\pi$
$282$	11.2207	−	6.47828i	0.668183	−	0.385776i
$283$	−25.3026	−	14.6085i	−1.50408	−	0.868383i	−0.999989	−	0.00473542i	$-0.998493\pi$
$283$	−25.3026	−	14.6085i	−1.50408	−	0.868383i	−0.504095	−	0.863648i	$-0.668174\pi$
$284$	4.72397	+	2.72739i	0.280316	+	0.161841i
$285$	−5.57702			−0.330354
$286$	−3.70055	−	0.926184i	−0.218818	−	0.0547664i
$287$	−21.5626			−1.27280
$288$	−1.71730	+	2.97445i	−0.101193	+	0.175271i
$289$	15.7772	+	6.33090i	0.928070	+	0.372406i
$290$	12.3842	+	21.4501i	0.727226	+	1.25959i
$291$	−11.9016			−0.697681
$292$	−3.23115	+	1.86550i	−0.189088	+	0.109170i
$293$	9.83293	+	17.0311i	0.574446	+	0.994970i	0.996102	+	0.0882137i	$0.0281158\pi$
$293$	9.83293	+	17.0311i	0.574446	+	0.994970i	−0.421656	+	0.906756i	$0.638551\pi$
$294$			8.43330i			0.491840i
$295$	−13.8796	+	8.01339i	−0.808101	+	0.466557i
$296$	6.96769	+	4.02279i	0.404988	+	0.233820i
$297$	0.583193	−	1.01012i	0.0338403	−	0.0586131i
$298$	5.29259			0.306592
$299$	−1.76245	−	6.16730i	−0.101925	−	0.356664i
$300$		−	11.2490i		−	0.649464i
$301$	34.6261	+	19.9914i	1.99582	+	1.15228i
$302$	−3.69979	+	6.40822i	−0.212899	+	0.368751i
$303$	39.2689	−	22.6719i	2.25594	−	1.30247i
$304$	−0.715779			−0.0410528
$305$	−1.60185	−	2.77448i	−0.0917216	−	0.158866i
$306$	13.9042	+	2.68560i	0.794853	+	0.153526i
$307$	−6.38947			−0.364667			−0.182333	−	0.983237i	$-0.558365\pi$
$307$	−6.38947			−0.364667			−0.182333	+	0.983237i	$0.558365\pi$
$308$	1.69979	+	2.94411i	0.0968543	+	0.167757i
$309$	1.57243	+	0.907842i	0.0894523	+	0.0516453i
$310$	13.1779	−	22.8247i	0.748453	−	1.29636i
$311$		−	33.2913i		−	1.88778i	−0.330262	−	0.943889i	$-0.607137\pi$
$311$		−	33.2913i		−	1.88778i	0.330262	−	0.943889i	$-0.392863\pi$
$312$	−2.51308	−	8.79399i	−0.142275	−	0.497862i
$313$		−	26.4346i		−	1.49417i	−0.664727	−	0.747086i	$-0.731452\pi$
$313$		−	26.4346i		−	1.49417i	0.664727	−	0.747086i	$-0.268548\pi$
$314$	7.91468	−	13.7086i	0.446651	−	0.773623i
$315$	−16.9490	+	29.3566i	−0.954969	+	1.65406i
$316$	−11.4942	+	6.63618i	−0.646599	+	0.373314i
$317$			21.3715i			1.20034i	0.799872	+	0.600171i	$0.204901\pi$
$317$			21.3715i			1.20034i	−0.799872	+	0.600171i	$0.795099\pi$
$318$	18.3117	−	10.5723i	1.02687	−	0.592863i
$319$	−4.26574	−	7.38848i	−0.238836	−	0.413676i
$320$		−	3.07158i		−	0.171707i
$321$	16.0320	+	27.7682i	0.894817	+	1.54987i
$322$	−2.85809	+	4.95036i	−0.159275	+	0.275873i
$323$	0.964137	+	2.78930i	0.0536460	+	0.155201i
$324$	−7.50731			−0.417073
$325$	11.4917	+	11.1174i	0.637443	+	0.616680i
$326$			10.7473i			0.595236i
$327$	11.7973	−	20.4336i	0.652393	−	1.12998i
$328$	−5.81161	−	3.35534i	−0.320893	−	0.185267i
$329$	14.2133	−	8.20606i	0.783606	−	0.452415i
$330$			8.24348i			0.453789i
$331$	−9.03586	−	15.6506i	−0.496656	−	0.860233i	0.503337	−	0.864090i	$-0.332106\pi$
$331$	−9.03586	−	15.6506i	−0.496656	−	0.860233i	−0.999993	+	0.00385711i	$0.998772\pi$
$332$	−4.87977	−	8.45201i	−0.267812	−	0.463864i
$333$		−	27.6334i		−	1.51430i
$334$	−14.9975	+	8.65883i	−0.820628	+	0.473790i
$335$	−4.94237	−	2.85348i	−0.270031	−	0.155902i
$336$	−4.07537	+	7.05875i	−0.222330	+	0.385086i
$337$			4.61590i			0.251444i	0.992066	+	0.125722i	$0.0401247\pi$
$337$			4.61590i			0.251444i	−0.992066	+	0.125722i	$0.959875\pi$
$338$	11.4673	+	6.12375i	0.623740	+	0.333088i
$339$	−17.0491			−0.925979
$340$	−11.9696	+	4.13734i	−0.649141	+	0.224379i
$341$	−4.53912	+	7.86198i	−0.245807	+	0.425750i
$342$	1.22921	+	2.12905i	0.0664680	+	0.115126i
$343$		−	11.8098i		−	0.637670i
$344$	6.22167	+	10.7762i	0.335450	+	0.581016i
$345$	−12.0039	+	6.93047i	−0.646269	+	0.373124i
$346$			0.498917i			0.0268219i
$347$	7.79523	−	4.50058i	0.418470	−	0.241604i	−0.275953	−	0.961171i	$-0.588993\pi$
$347$	7.79523	−	4.50058i	0.418470	−	0.241604i	0.694422	+	0.719568i	$0.255660\pi$
$348$	10.2275	−	17.7145i	0.548249	−	0.949595i
$349$	1.34448	−	2.32871i	0.0719685	−	0.124653i	−0.827795	−	0.561030i	$-0.810405\pi$
$349$	1.34448	−	2.32871i	0.0719685	−	0.124653i	0.899764	+	0.436377i	$0.143739\pi$
$350$		−	14.2492i		−	0.761653i
$351$	−2.76376	+	2.85682i	−0.147519	+	0.152486i
$352$			1.05801i			0.0563919i
$353$	−12.7974	+	22.1658i	−0.681138	+	1.17977i	0.293496	+	0.955960i	$0.405181\pi$
$353$	−12.7974	+	22.1658i	−0.681138	+	1.17977i	−0.974634	+	0.223805i	$0.928152\pi$
$354$	11.4624	+	6.61782i	0.609220	+	0.351733i
$355$	8.37739	+	14.5101i	0.444625	+	0.770114i
$356$	−8.40013			−0.445206
$357$	32.9965	+	6.37327i	1.74636	+	0.337309i
$358$	3.52064	+	6.09793i	0.186072	+	0.322285i
$359$	−20.9295			−1.10462			−0.552309	−	0.833640i	$-0.686253\pi$
$359$	−20.9295			−1.10462			−0.552309	+	0.833640i	$0.686253\pi$
$360$	−9.13627	+	5.27483i	−0.481524	+	0.278008i
$361$	9.24383	−	16.0108i	0.486517	−	0.842673i
$362$	−13.1235	−	7.57688i	−0.689758	−	0.398232i
$363$			25.0637i			1.31550i
$364$	−3.18333	−	11.1394i	−0.166852	−	0.583862i
$365$	−11.4601			−0.599848
$366$	−1.32288	+	2.29130i	−0.0691481	+	0.119768i
$367$	−15.2087	−	8.78074i	−0.793887	−	0.458351i	0.0474421	−	0.998874i	$-0.484893\pi$
$367$	−15.2087	−	8.78074i	−0.793887	−	0.458351i	−0.841329	+	0.540523i	$0.818226\pi$
$368$	−1.54064	+	0.889487i	−0.0803113	+	0.0463677i
$369$			23.0485i			1.19986i
$370$	12.3563	+	21.4018i	0.642375	+	1.11263i
$371$	23.1955	−	13.3919i	1.20425	−	0.695274i
$372$	−21.7658			−1.12850
$373$	−16.8835	−	29.2432i	−0.874197	−	1.51415i	−0.857616	−	0.514291i	$-0.828055\pi$
$373$	−16.8835	−	29.2432i	−0.874197	−	1.51415i	−0.0165811	−	0.999863i	$-0.505278\pi$
$374$	4.12292	−	1.42511i	0.213191	−	0.0736905i
$375$	−2.20265	+	3.81510i	−0.113744	+	0.197011i
$376$	5.10774			0.263411
$377$	7.98882	+	27.9551i	0.411445	+	1.43976i
$378$	3.54234			0.182198
$379$	−2.23984	−	1.29317i	−0.115053	−	0.0664258i	0.441369	−	0.897326i	$-0.354493\pi$
$379$	−2.23984	−	1.29317i	−0.115053	−	0.0664258i	−0.556422	+	0.830900i	$0.687826\pi$
$380$	−1.90402	−	1.09929i	−0.0976742	−	0.0563922i
$381$	41.3072	−	23.8487i	2.11623	−	1.22181i
$382$	7.20445			0.368611
$383$	1.29897	+	2.24989i	0.0663744	+	0.114964i	0.897303	−	0.441416i	$-0.145524\pi$
$383$	1.29897	+	2.24989i	0.0663744	+	0.114964i	−0.830928	+	0.556379i	$0.812190\pi$
$384$	−2.19681	+	1.26833i	−0.112105	+	0.0647240i
$385$			10.4421i			0.532176i
$386$	7.69503	−	4.44273i	0.391667	−	0.226129i
$387$	21.3690	−	37.0121i	1.08625	−	1.88143i
$388$	−4.06325	−	2.34592i	−0.206280	−	0.119096i
$389$	−1.34246			−0.0680656			−0.0340328	−	0.999421i	$-0.510835\pi$
$389$	−1.34246			−0.0680656			−0.0340328	+	0.999421i	$0.510835\pi$
$390$	6.82075	−	27.2522i	0.345382	−	1.37997i
$391$	5.54142	+	4.80556i	0.280242	+	0.243028i
$392$	−1.66229	+	2.87917i	−0.0839583	+	0.145420i
$393$	4.54090	−	7.86506i	0.229058	−	0.396740i
$394$	8.13105	−	4.69447i	0.409637	−	0.236504i
$395$	−40.7671			−2.05122
$396$	3.14699	−	1.81691i	0.158142	−	0.0913034i
$397$	2.82209	−	1.62933i	0.141636	−	0.0817738i	−0.427507	−	0.904012i	$-0.640608\pi$
$397$	2.82209	−	1.62933i	0.141636	−	0.0817738i	0.569144	+	0.822238i	$0.307275\pi$
$398$		−	9.51437i		−	0.476912i
$399$	2.91707	+	5.05251i	0.146036	+	0.252942i
$400$	2.21730	−	3.84048i	0.110865	−	0.192024i
$401$	−14.6607	−	8.46437i	−0.732121	−	0.422690i	0.0870764	−	0.996202i	$-0.472248\pi$
$401$	−14.6607	−	8.46437i	−0.732121	−	0.422690i	−0.819198	+	0.573511i	$0.805581\pi$
$402$			4.71307i			0.235067i
$403$	21.5110	−	22.2352i	1.07154	−	1.10762i
$404$	17.8755			0.889337
$405$	−19.9699	−	11.5296i	−0.992314	−	0.572913i
$406$	12.9552	−	22.4390i	0.642954	−	1.11363i
$407$	−4.25614	−	7.37185i	−0.210969	−	0.365409i
$408$	7.90155	+	6.85228i	0.391185	+	0.339238i
$409$	−1.53778	−	2.66351i	−0.0760381	−	0.131702i	0.825499	−	0.564403i	$-0.190894\pi$
$409$	−1.53778	−	2.66351i	−0.0760381	−	0.131702i	−0.901537	+	0.432702i	$0.857560\pi$
$410$	−10.3062	−	17.8508i	−0.508986	−	0.881590i
$411$			43.8676i			2.16383i
$412$	0.357890	+	0.619883i	0.0176320	+	0.0305394i
$413$	14.5195	+	8.38282i	0.714457	+	0.412492i
$414$	5.29148	+	3.05504i	0.260062	+	0.150147i
$415$		−	29.9772i		−	1.47152i
$416$	0.875406	−	3.49767i	0.0429203	−	0.171487i
$417$	−16.2021			−0.793421
$418$	0.655840	+	0.378649i	0.0320782	+	0.0185203i
$419$	−1.37321	−	0.792823i	−0.0670857	−	0.0387320i	0.466082	−	0.884742i	$-0.345665\pi$
$419$	−1.37321	−	0.792823i	−0.0670857	−	0.0387320i	−0.533168	+	0.846010i	$0.678999\pi$
$420$	−21.6815	+	12.5178i	−1.05795	+	0.610807i
$421$	25.9851			1.26644			0.633219	−	0.773973i	$-0.281733\pi$
$421$	25.9851			1.26644			0.633219	+	0.773973i	$0.281733\pi$
$422$	1.86066	−	1.07425i	0.0905753	−	0.0522937i
$423$	−8.77153	−	15.1927i	−0.426486	−	0.738696i
$424$	8.33560			0.404812
$425$	−17.9525	−	3.46753i	−0.870826	−	0.168200i
$426$	6.91843	−	11.9831i	0.335199	−	0.580582i
$427$	−1.67570	+	2.90239i	−0.0810927	+	0.140457i
$428$			12.6402i			0.610989i
$429$	−2.34941	+	9.38701i	−0.113430	+	0.453209i
$430$			38.2207i			1.84317i
$431$	1.89152	+	1.09207i	0.0911115	+	0.0526033i	0.544864	−	0.838525i	$-0.316581\pi$
$431$	1.89152	+	1.09207i	0.0911115	+	0.0526033i	−0.453752	+	0.891128i	$0.649915\pi$
$432$	0.954739	+	0.551219i	0.0459349	+	0.0265205i
$433$	−12.7814	−	22.1381i	−0.614236	−	1.06389i	−0.990518	−	0.137383i	$-0.956131\pi$
$433$	−12.7814	−	22.1381i	−0.614236	−	1.06389i	0.376282	−	0.926505i	$-0.377202\pi$
$434$	−27.5708			−1.32344
$435$	54.4114	−	31.4144i	2.60883	−	1.50621i
$436$	8.05532	−	4.65074i	0.385780	−	0.222730i
$437$			1.27335i			0.0609127i
$438$	4.73213	+	8.19629i	0.226110	+	0.391634i
$439$	−33.3028	−	19.2274i	−1.58946	−	0.917674i	−0.993396	−	0.114736i	$-0.963398\pi$
$439$	−33.3028	−	19.2274i	−1.58946	−	0.917674i	−0.596062	−	0.802938i	$-0.703269\pi$
$440$	−1.62487	+	2.81436i	−0.0774628	+	0.134170i
$441$	11.4186			0.543744
$442$	−14.8091	+	1.29992i	−0.704398	+	0.0618308i
$443$	−28.4718			−1.35274			−0.676368	−	0.736564i	$-0.736447\pi$
$443$	−28.4718			−1.35274			−0.676368	+	0.736564i	$0.736447\pi$
$444$	10.2044	−	17.6746i	0.484281	−	0.838799i
$445$	−22.3449	−	12.9008i	−1.05925	−	0.611558i
$446$	−13.9016	−	24.0782i	−0.658258	−	1.14014i
$447$		−	13.4255i		−	0.635003i
$448$	−2.78270	+	1.60659i	−0.131470	+	0.0759044i
$449$	−5.05556	+	2.91883i	−0.238587	+	0.137748i	−0.614527	−	0.788896i	$-0.710653\pi$
$449$	−5.05556	+	2.91883i	−0.238587	+	0.137748i	0.375940	+	0.926644i	$0.377320\pi$
$450$	−15.2311			−0.718001
$451$	3.54996	+	6.14872i	0.167161	+	0.289532i
$452$	−5.82064	−	3.36055i	−0.273780	−	0.158067i
$453$	16.2554	+	9.38507i	0.763746	+	0.440949i
$454$			1.00935i			0.0473714i
$455$	8.63988	−	34.5204i	0.405044	−	1.61834i
$456$			1.81568i			0.0850271i
$457$	−9.58525	+	16.6021i	−0.448379	+	0.776615i	−0.998281	−	0.0586143i	$-0.981332\pi$
$457$	−9.58525	+	16.6021i	−0.448379	+	0.776615i	0.549902	+	0.835229i	$0.314665\pi$
$458$	13.7361	−	23.7916i	0.641846	−	1.11171i
$459$	0.862024	−	4.46298i	0.0402358	−	0.208314i
$460$	−5.46426			−0.254773
$461$	6.95542	+	12.0471i	0.323946	+	0.561091i	0.981299	−	0.192492i	$-0.0616570\pi$
$461$	6.95542	+	12.0471i	0.323946	+	0.561091i	−0.657352	+	0.753583i	$0.728324\pi$
$462$	7.46820	−	4.31176i	0.347452	−	0.200601i
$463$	10.6704			0.495898			0.247949	−	0.968773i	$-0.420243\pi$
$463$	10.6704			0.495898			0.247949	+	0.968773i	$0.420243\pi$
$464$	6.98341	−	4.03187i	0.324196	−	0.187175i
$465$	−57.8984	−	33.4277i	−2.68498	−	1.55017i
$466$	−9.79973	−	5.65788i	−0.453964	−	0.262096i
$467$	33.2557			1.53889			0.769446	−	0.638712i	$-0.220532\pi$
$467$	33.2557			1.53889			0.769446	+	0.638712i	$0.220532\pi$
$468$	−11.9070	+	3.40269i	−0.550400	+	0.157290i
$469$			5.97007i			0.275672i
$470$	13.5869	+	7.84441i	0.626718	+	0.361836i
$471$	−34.7740	−	20.0768i	−1.60230	−	0.925090i
$472$	2.60888	+	4.51871i	0.120083	+	0.207991i
$473$		−	13.1651i		−	0.605333i
$474$	16.8337	+	29.1568i	0.773196	+	1.33921i
$475$	−1.58710	−	2.74894i	−0.0728211	−	0.126130i
$476$	10.0089	+	8.67981i	0.458759	+	0.397839i
$477$	−14.3147	−	24.7938i	−0.655427	−	1.13523i
$478$	10.8882	−	18.8590i	0.498016	−	0.862589i
$479$	23.1255	+	13.3515i	1.05663	+	0.610047i	0.924499	−	0.381184i	$-0.124484\pi$
$479$	23.1255	+	13.3515i	1.05663	+	0.610047i	0.132134	+	0.991232i	$0.457817\pi$
$480$	−7.79153			−0.355633
$481$	7.97084	+	27.8922i	0.363439	+	1.27178i
$482$		−	22.4371i		−	1.02198i
$483$	12.5573	+	7.24998i	0.571379	+	0.329886i
$484$	−4.94031	+	8.55687i	−0.224560	+	0.388949i
$485$	−7.20567	−	12.4806i	−0.327193	−	0.566715i
$486$			22.3507i			1.01385i
$487$	6.43782	−	3.71688i	0.291726	−	0.168428i	−0.346994	−	0.937867i	$-0.612798\pi$
$487$	6.43782	−	3.71688i	0.291726	−	0.168428i	0.638720	+	0.769439i	$0.279464\pi$
$488$	−0.903276	+	0.521506i	−0.0408894	+	0.0236075i
$489$	27.2621			1.23283
$490$	−8.84360	+	5.10586i	−0.399513	+	0.230659i
$491$	14.7520	−	25.5512i	0.665748	−	1.15311i	−0.313333	−	0.949643i	$-0.601446\pi$
$491$	14.7520	−	25.5512i	0.665748	−	1.15311i	0.979082	−	0.203467i	$-0.0652209\pi$
$492$	−8.51132	+	14.7420i	−0.383720	+	0.664622i
$493$	−25.1182	−	21.7827i	−1.13127	−	0.981041i
$494$	−1.85484	−	1.79443i	−0.0834534	−	0.0807351i
$495$	11.1616			0.501677
$496$	−7.43095	−	4.29026i	−0.333659	−	0.192638i
$497$	8.76361	−	15.1790i	0.393102	−	0.680872i
$498$	−21.4398	+	12.3783i	−0.960741	+	0.554684i
$499$			24.3021i			1.08791i	0.839114	+	0.543955i	$0.183074\pi$
$499$			24.3021i			1.08791i	−0.839114	+	0.543955i	$0.816926\pi$
$500$	−1.50399	+	0.868330i	−0.0672606	+	0.0388329i
$501$	21.9644	+	38.0435i	0.981298	+	1.69966i
$502$	−12.0116			−0.536103
$503$	30.4257	−	17.5663i	1.35661	−	0.783242i	0.367449	−	0.930044i	$-0.380231\pi$
$503$	30.4257	−	17.5663i	1.35661	−	0.783242i	0.989166	+	0.146802i	$0.0468980\pi$
$504$	9.55748	+	5.51801i	0.425724	+	0.245792i
$505$	47.5499	+	27.4529i	2.11594	+	1.22164i
$506$	1.88216			0.0836724
$507$	15.5338	−	29.0886i	0.689882	−	1.29187i
$508$	18.8033			0.834262
$509$	2.01219	−	3.48521i	0.0891886	−	0.154479i	−0.817980	−	0.575247i	$-0.804906\pi$
$509$	2.01219	−	3.48521i	0.0891886	−	0.154479i	0.907168	+	0.420768i	$0.138239\pi$
$510$	10.4950	+	30.3626i	0.464726	+	1.34448i
$511$	5.99421	+	10.3823i	0.265168	+	0.459285i
$512$	−1.00000			−0.0441942
$513$	0.683383	−	0.394551i	0.0301721	−	0.0174199i
$514$	6.75231	+	11.6953i	0.297832	+	0.515860i
$515$			2.19857i			0.0968807i
$516$	27.3356	−	15.7822i	1.20338	−	0.694773i
$517$	−4.68001	−	2.70201i	−0.205827	−	0.118834i
$518$	12.9260	−	22.3885i	0.567936	−	0.983694i
$519$	1.26558			0.0555527
$520$	7.70032	−	7.95958i	0.337681	−	0.349051i
$521$			9.23392i			0.404545i	0.979329	+	0.202273i	$0.0648327\pi$
$521$			9.23392i			0.404545i	−0.979329	+	0.202273i	$0.935167\pi$
$522$	−23.9852	−	13.8479i	−1.04981	−	0.606105i
$523$	7.67110	−	13.2867i	0.335434	−	0.580988i	−0.648134	−	0.761526i	$-0.724450\pi$
$523$	7.67110	−	13.2867i	0.335434	−	0.580988i	0.983568	+	0.180538i	$0.0577838\pi$
$524$	3.10057	−	1.79011i	0.135449	−	0.0782015i
$525$	−36.1453			−1.57751
$526$	−5.65686	−	9.79797i	−0.246651	−	0.427212i
$527$	−6.70932	+	34.7364i	−0.292263	+	1.51314i
$528$	2.68379			0.116797
$529$	−9.91762	−	17.1778i	−0.431201	−	0.746862i
$530$	22.1732	+	12.8017i	0.963144	+	0.556071i
$531$	8.96047	−	15.5200i	0.388851	−	0.673510i
$532$			2.29993i			0.0997148i
$533$	−6.64832	−	23.2644i	−0.287971	−	1.00769i
$534$			21.3082i			0.922096i
$535$	−19.4128	+	33.6239i	−0.839287	+	1.45369i
$536$	−0.928995	+	1.60907i	−0.0401265	+	0.0695011i
$537$	15.4683	−	8.93064i	0.667507	−	0.385385i
$538$			17.6035i			0.758939i
$539$	3.04618	−	1.75871i	0.131208	−	0.0757531i
$540$	1.69311	+	2.93256i	0.0728600	+	0.126197i
$541$		−	9.15033i		−	0.393403i	−0.980463	−	0.196702i	$-0.936977\pi$
$541$		−	9.15033i		−	0.393403i	0.980463	−	0.196702i	$-0.0630231\pi$
$542$	10.4941	+	18.1763i	0.450759	+	0.780738i
$543$	−19.2199	+	33.2899i	−0.824805	+	1.42860i
$544$	1.34697	+	3.89688i	0.0577511	+	0.167077i
$545$	28.5703			1.22382
$546$	−28.2567	+	8.07501i	−1.20928	+	0.345579i
$547$			17.5894i			0.752068i	0.926606	+	0.376034i	$0.122712\pi$
$547$			17.5894i			0.752068i	−0.926606	+	0.376034i	$0.877288\pi$
$548$	−8.64676	+	14.9766i	−0.369371	+	0.639770i
$549$	3.10239	+	1.79117i	0.132407	+	0.0764452i
$550$	−4.06325	+	2.34592i	−0.173257	+	0.100030i
$551$		−	5.77186i		−	0.245890i
$552$	2.25632	+	3.90806i	0.0960353	+	0.166338i
$553$	21.3233	+	36.9330i	0.906758	+	1.57055i
$554$		−	1.97418i		−	0.0838750i
$555$	54.2889	−	31.3437i	2.30444	−	1.33047i
$556$	−5.53148	−	3.19360i	−0.234587	−	0.135439i
$557$	−8.78335	+	15.2132i	−0.372163	+	0.644604i	−0.989898	−	0.141782i	$-0.954717\pi$
$557$	−8.78335	+	15.2132i	−0.372163	+	0.644604i	0.617735	+	0.786386i	$0.288050\pi$
$558$			29.4707i			1.24759i
$559$	−10.8930	+	43.5226i	−0.460723	+	1.84081i
$560$	−9.86957			−0.417065
$561$	−3.61500	−	10.4584i	−0.152625	−	0.441554i
$562$	5.41879	−	9.38562i	0.228578	−	0.395908i
$563$	9.76536	+	16.9141i	0.411561	+	0.712844i	0.995061	−	0.0992689i	$-0.0316504\pi$
$563$	9.76536	+	16.9141i	0.411561	+	0.712844i	−0.583500	+	0.812113i	$0.698317\pi$
$564$		−	12.9566i		−	0.545569i
$565$	−10.3222	−	17.8786i	−0.434258	−	0.752157i
$566$	−25.3026	+	14.6085i	−1.06355	+	0.614040i
$567$			24.1224i			1.01305i
$568$	4.72397	−	2.72739i	0.198213	−	0.114439i
$569$	10.2611	−	17.7728i	0.430170	−	0.745076i	−0.566718	−	0.823912i	$-0.691787\pi$
$569$	10.2611	−	17.7728i	0.430170	−	0.745076i	0.996888	+	0.0788363i	$0.0251204\pi$
$570$	−2.78851	+	4.82984i	−0.116798	+	0.202300i
$571$			30.3351i			1.26948i	0.772724	+	0.634742i	$0.218894\pi$
$571$			30.3351i			1.26948i	−0.772724	+	0.634742i	$0.781106\pi$
$572$	−2.65237	+	2.74168i	−0.110901	+	0.114635i
$573$		−	18.2752i		−	0.763456i
$574$	−10.7813	+	18.6738i	−0.450004	+	0.779429i
$575$	−6.83212	−	3.94452i	−0.284919	−	0.164498i
$576$	1.71730	+	2.97445i	0.0715542	+	0.123936i
$577$	15.8462			0.659684			0.329842	−	0.944036i	$-0.393005\pi$
$577$	15.8462			0.659684			0.329842	+	0.944036i	$0.393005\pi$
$578$	13.3713	−	10.4980i	0.556174	−	0.436659i
$579$	−11.2696	−	19.5196i	−0.468351	−	0.811207i
$580$	24.7684			1.02845
$581$	−27.1579	+	15.6796i	−1.12670	+	0.650500i
$582$	−5.95078	+	10.3070i	−0.246668	+	0.427241i
$583$	−7.63757	−	4.40955i	−0.316316	−	0.182625i
$584$			3.73101i			0.154390i
$585$	−36.8992	−	9.23523i	−1.52559	−	0.381830i
$586$	19.6659			0.812389
$587$	−3.20723	+	5.55508i	−0.132376	+	0.229283i	−0.924592	−	0.380958i	$-0.875594\pi$
$587$	−3.20723	+	5.55508i	−0.132376	+	0.229283i	0.792216	+	0.610241i	$0.208927\pi$
$588$	7.30346	+	4.21665i	0.301189	+	0.173892i
$589$	−5.31892	+	3.07088i	−0.219162	+	0.126533i
$590$			16.0268i			0.659812i
$591$	−11.9082	−	20.6257i	−0.489839	−	0.848426i
$592$	6.96769	−	4.02279i	0.286370	−	0.165336i
$593$	−45.7372			−1.87820			−0.939101	−	0.343641i	$-0.888340\pi$
$593$	−45.7372			−1.87820			−0.939101	+	0.343641i	$0.888340\pi$
$594$	−0.583193	−	1.01012i	−0.0239287	−	0.0414457i
$595$	13.2941	+	38.4605i	0.545003	+	1.57673i
$596$	2.64630	−	4.58352i	0.108397	−	0.187748i
$597$	−24.1346			−0.987765
$598$	−6.22226	−	1.55732i	−0.254447	−	0.0636837i
$599$	−21.2002			−0.866216			−0.433108	−	0.901342i	$-0.642583\pi$
$599$	−21.2002			−0.866216			−0.433108	+	0.901342i	$0.642583\pi$
$600$	−9.74196	−	5.62452i	−0.397714	−	0.229620i
$601$	−7.26214	−	4.19280i	−0.296229	−	0.171028i	0.344519	−	0.938780i	$-0.388042\pi$
$601$	−7.26214	−	4.19280i	−0.296229	−	0.171028i	−0.640748	+	0.767752i	$0.721376\pi$
$602$	34.6261	−	19.9914i	1.41125	−	0.814788i
$603$	6.38146			0.259873
$604$	3.69979	+	6.40822i	0.150542	+	0.260747i
$605$	−26.2831	+	15.1746i	−1.06856	+	0.616934i
$606$		−	45.3438i		−	1.84197i
$607$	7.60147	−	4.38871i	0.308534	−	0.178132i	−0.337736	−	0.941241i	$-0.609661\pi$
$607$	7.60147	−	4.38871i	0.308534	−	0.178132i	0.646270	+	0.763108i	$0.276328\pi$
$608$	−0.357890	+	0.619883i	−0.0145143	+	0.0251396i
$609$	−56.9199	−	32.8627i	−2.30651	−	1.33167i
$610$	−3.20370			−0.129714
$611$	13.2360	+	12.8049i	0.535472	+	0.518030i
$612$	9.27792	−	10.6986i	0.375038	−	0.432466i
$613$	−9.83303	+	17.0313i	−0.397152	+	0.687888i	−0.993373	−	0.114932i	$-0.963335\pi$
$613$	−9.83303	+	17.0313i	−0.397152	+	0.687888i	0.596221	+	0.802820i	$0.296668\pi$
$614$	−3.19474	+	5.53345i	−0.128929	+	0.223312i
$615$	−45.2813	+	26.1432i	−1.82592	+	1.05420i
$616$	3.39957			0.136973
$617$	25.0961	−	14.4892i	1.01033	−	0.583315i	0.0990422	−	0.995083i	$-0.468422\pi$
$617$	25.0961	−	14.4892i	1.01033	−	0.583315i	0.911288	+	0.411769i	$0.135089\pi$
$618$	1.57243	−	0.907842i	0.0632523	−	0.0365187i
$619$			1.87403i			0.0753237i	0.999291	+	0.0376619i	$0.0119910\pi$
$619$			1.87403i			0.0753237i	−0.999291	+	0.0376619i	$0.988009\pi$
$620$	−13.1779	−	22.8247i	−0.529236	−	0.916664i
$621$	0.980605	−	1.69846i	0.0393503	−	0.0681567i
$622$	−28.8311	−	16.6457i	−1.15602	−	0.667430i
$623$			26.9912i			1.08138i
$624$	−8.87236	−	2.22060i	−0.355179	−	0.0888951i
$625$	−27.5073			−1.10029
$626$	−22.8930	−	13.2173i	−0.914990	−	0.528270i
$627$	0.960501	−	1.66364i	0.0383587	−	0.0664393i
$628$	−7.91468	−	13.7086i	−0.315830	−	0.547034i
$629$	−25.0616	−	21.7336i	−0.999273	−	0.866576i
$630$	16.9490	+	29.3566i	0.675265	+	1.16959i
$631$	−8.35523	−	14.4717i	−0.332616	−	0.576108i	0.650408	−	0.759585i	$-0.274598\pi$
$631$	−8.35523	−	14.4717i	−0.332616	−	0.576108i	−0.983024	+	0.183477i	$0.941265\pi$
$632$			13.2724i			0.527946i
$633$	−2.72500	−	4.71984i	−0.108309	−	0.187597i
$634$	18.5082	+	10.6857i	0.735056	+	0.424385i
$635$	50.0180	+	28.8779i	1.98491	+	1.14599i
$636$		−	21.1445i		−	0.838434i
$637$	−11.5256	+	3.29369i	−0.456659	+	0.130501i
$638$	−8.53148			−0.337765
$639$	−16.2250	−	9.36749i	−0.641850	−	0.370572i
$640$	−2.66007	−	1.53579i	−0.105148	−	0.0607074i
$641$	−41.3270	+	23.8602i	−1.63232	+	0.942420i	−0.648943	+	0.760837i	$0.724789\pi$
$641$	−41.3270	+	23.8602i	−1.63232	+	0.942420i	−0.983376	+	0.181582i	$0.941878\pi$
$642$	32.0639			1.26546
$643$	8.15137	−	4.70620i	0.321459	−	0.185594i	−0.330584	−	0.943777i	$-0.607246\pi$
$643$	8.15137	−	4.70620i	0.321459	−	0.185594i	0.652043	+	0.758182i	$0.273912\pi$
$644$	2.85809	+	4.95036i	0.112625	+	0.195071i
$645$	96.9526			3.81751
$646$	2.89768	+	0.559686i	0.114008	+	0.0220205i
$647$	15.2350	−	26.3878i	0.598950	−	1.03741i	−0.394027	−	0.919099i	$-0.628918\pi$
$647$	15.2350	−	26.3878i	0.598950	−	1.03741i	0.992976	−	0.118312i	$-0.0377483\pi$
$648$	−3.75365	+	6.50152i	−0.147457	+	0.255404i
$649$		−	5.52042i		−	0.216695i
$650$	15.3738	−	4.39340i	0.603008	−	0.172323i
$651$			69.9376i			2.74107i
$652$	9.30740	+	5.37363i	0.364506	+	0.210448i
$653$	18.7879	+	10.8472i	0.735228	+	0.424484i	0.820332	−	0.571888i	$-0.193789\pi$
$653$	18.7879	+	10.8472i	0.735228	+	0.424484i	−0.0851035	+	0.996372i	$0.527122\pi$
$654$	−11.7973	−	20.4336i	−0.461312	−	0.799015i
$655$	10.9970			0.429687
$656$	−5.81161	+	3.35534i	−0.226905	+	0.131004i
$657$	11.0977	−	6.40726i	0.432963	−	0.249971i
$658$		−	16.4121i		−	0.639811i
$659$	11.3059	+	19.5824i	0.440415	+	0.762822i	0.997720	−	0.0674862i	$-0.0214979\pi$
$659$	11.3059	+	19.5824i	0.440415	+	0.762822i	−0.557305	+	0.830308i	$0.688165\pi$
$660$	7.13906	+	4.12174i	0.277888	+	0.160439i
$661$	7.73537	−	13.3981i	0.300871	−	0.521124i	−0.675462	−	0.737394i	$-0.736056\pi$
$661$	7.73537	−	13.3981i	0.300871	−	0.521124i	0.976333	+	0.216270i	$0.0693893\pi$
$662$	−18.0717			−0.702378
$663$	3.29744	+	37.5656i	0.128062	+	1.45893i
$664$	−9.75954			−0.378744
$665$	−3.53222	+	6.11798i	−0.136973	+	0.237245i
$666$	−23.9312	−	13.8167i	−0.927317	−	0.535386i
$667$	−7.17260	−	12.4233i	−0.277724	−	0.481032i
$668$			17.3177i			0.670040i
$669$	−61.0780	+	35.2634i	−2.36141	+	1.36336i
$670$	−4.94237	+	2.85348i	−0.190941	+	0.110240i
$671$	1.10351			0.0426007
$672$	4.07537	+	7.05875i	0.157211	+	0.272297i
$673$	18.8851	+	10.9033i	0.727968	+	0.420292i	0.817678	−	0.575676i	$-0.195261\pi$
$673$	18.8851	+	10.9033i	0.727968	+	0.420292i	−0.0897106	+	0.995968i	$0.528594\pi$
$674$	3.99748	+	2.30795i	0.153977	+	0.0888988i
$675$			4.88888i			0.188173i
$676$	11.0370	−	6.86912i	0.424500	−	0.264197i
$677$			44.8027i			1.72191i	0.508684	+	0.860953i	$0.330132\pi$
$677$			44.8027i			1.72191i	−0.508684	+	0.860953i	$0.669868\pi$
$678$	−8.52455	+	14.7649i	−0.327383	+	0.567044i
$679$	−7.53788	+	13.0560i	−0.289277	+	0.501043i
$680$	−2.40174	+	12.4346i	−0.0921027	+	0.476846i
$681$	2.56038			0.0981140
$682$	4.53912	+	7.86198i	0.173812	+	0.301051i
$683$	24.8479	−	14.3459i	0.950779	−	0.548932i	0.0574561	−	0.998348i	$-0.481701\pi$
$683$	24.8479	−	14.3459i	0.950779	−	0.548932i	0.893323	+	0.449416i	$0.148368\pi$
$684$	2.45842			0.0940000
$685$	−46.0019	+	26.5592i	−1.75764	+	1.01477i
$686$	−10.2276	−	5.90491i	−0.390492	−	0.225450i
$687$	−60.3511	−	34.8437i	−2.30254	−	1.32937i
$688$	12.4433			0.474398
$689$	21.6006	+	20.8970i	0.822916	+	0.796111i
$690$			13.8609i			0.527677i
$691$	−5.39818	−	3.11664i	−0.205357	−	0.118563i	0.393795	−	0.919198i	$-0.371162\pi$
$691$	−5.39818	−	3.11664i	−0.205357	−	0.118563i	−0.599152	+	0.800636i	$0.704495\pi$
$692$	0.432074	+	0.249458i	0.0164250	+	0.00948298i
$693$	−5.83809	−	10.1119i	−0.221771	−	0.384118i
$694$		−	9.00116i		−	0.341679i
$695$	−9.80941	−	16.9904i	−0.372092	−	0.644482i
$696$	−10.2275	−	17.7145i	−0.387671	−	0.671465i
$697$	20.9034	+	18.1276i	0.791774	+	0.686631i
$698$	−1.34448	−	2.32871i	−0.0508894	−	0.0881430i
$699$	−14.3521	+	24.8585i	−0.542845	+	0.940235i
$700$	−12.3402	−	7.12461i	−0.466415	−	0.269285i
$701$	10.8371			0.409310			0.204655	−	0.978834i	$-0.434393\pi$
$701$	10.8371			0.409310			0.204655	+	0.978834i	$0.434393\pi$
$702$	1.09220	+	3.82190i	0.0412223	+	0.144248i
$703$		−	5.75887i		−	0.217200i
$704$	0.916260	+	0.529003i	0.0345328	+	0.0199375i
$705$	19.8985	−	34.4653i	0.749423	−	1.29804i
$706$	12.7974	+	22.1658i	0.481637	+	0.834220i
$707$		−	57.4372i		−	2.16015i
$708$	11.4624	−	6.61782i	0.430784	−	0.248713i
$709$	−32.2973	+	18.6469i	−1.21295	+	0.700297i	−0.963401	−	0.268065i	$-0.913616\pi$
$709$	−32.2973	+	18.6469i	−1.21295	+	0.700297i	−0.249550	+	0.968362i	$0.580283\pi$
$710$	16.7548			0.628795
$711$	39.4780	−	22.7926i	1.48054	−	0.854791i
$712$	−4.20007	+	7.27473i	−0.157404	+	0.272632i
$713$	−7.63226	+	13.2195i	−0.285830	+	0.495073i
$714$	22.0177	−	25.3892i	0.823990	−	0.950166i
$715$	−11.2661	+	3.21956i	−0.421329	+	0.120405i
$716$	7.04128			0.263145
$717$	−47.8386	−	27.6196i	−1.78657	−	1.03147i
$718$	−10.4648	+	18.1255i	−0.390541	+	0.676437i
$719$	5.11190	−	2.95136i	0.190642	−	0.110067i	−0.401641	−	0.915797i	$-0.631560\pi$
$719$	5.11190	−	2.95136i	0.190642	−	0.110067i	0.592283	+	0.805730i	$0.298227\pi$
$720$			10.5497i			0.393163i
$721$	1.99180	−	1.14997i	0.0741785	−	0.0428270i
$722$	−9.24383	−	16.0108i	−0.344020	−	0.595860i
$723$	−56.9151			−2.11670
$724$	−13.1235	+	7.57688i	−0.487733	+	0.281593i
$725$	30.9686	+	17.8798i	1.15015	+	0.664037i
$726$	21.7058	+	12.5319i	0.805578	+	0.465101i
$727$	−43.1857			−1.60167			−0.800835	−	0.598885i	$-0.795610\pi$
$727$	−43.1857			−1.60167			−0.800835	+	0.598885i	$0.795610\pi$
$728$	−11.2387	−	2.81284i	−0.416532	−	0.104251i
$729$	34.1741			1.26571
$730$	−5.73004	+	9.92472i	−0.212078	+	0.367330i
$731$	−16.7609	−	48.4902i	−0.619923	−	1.79347i
$732$	1.32288	+	2.29130i	0.0488951	+	0.0846887i
$733$	−35.8086			−1.32262			−0.661311	−	0.750112i	$-0.730000\pi$
$733$	−35.8086			−1.32262			−0.661311	+	0.750112i	$0.730000\pi$
$734$	−15.2087	+	8.78074i	−0.561363	+	0.324103i
$735$	12.9518	+	22.4331i	0.477734	+	0.827459i
$736$			1.77897i			0.0655739i
$737$	1.70240	−	0.982881i	0.0627087	−	0.0362049i
$738$	19.9606	+	11.5242i	0.734759	+	0.424213i
$739$	3.78260	−	6.55165i	0.139145	−	0.241006i	−0.788028	−	0.615639i	$-0.788898\pi$
$739$	3.78260	−	6.55165i	0.139145	−	0.241006i	0.927173	+	0.374633i	$0.122231\pi$
$740$	24.7127			0.908456
$741$	−4.55184	+	4.70510i	−0.167216	+	0.172846i
$742$		−	26.7838i		−	0.983266i
$743$	20.5446	+	11.8614i	0.753707	+	0.435153i	0.827032	−	0.562155i	$-0.190028\pi$
$743$	20.5446	+	11.8614i	0.753707	+	0.435153i	−0.0733248	+	0.997308i	$0.523361\pi$
$744$	−10.8829	+	18.8497i	−0.398986	+	0.691064i
$745$	14.0786	−	8.12831i	0.515802	−	0.297798i
$746$	−33.7671			−1.23630
$747$	16.7601	+	29.0293i	0.613219	+	1.06213i
$748$	0.827281	−	4.28311i	0.0302484	−	0.156606i
$749$	40.6155			1.48406
$750$	2.20265	+	3.81510i	0.0804295	+	0.139308i
$751$	−12.7818	−	7.37956i	−0.466414	−	0.269284i	0.248324	−	0.968677i	$-0.420120\pi$
$751$	−12.7818	−	7.37956i	−0.466414	−	0.269284i	−0.714737	+	0.699393i	$0.753454\pi$
$752$	2.55387	−	4.42343i	0.0931300	−	0.161306i
$753$			30.4692i			1.11036i
$754$	28.2043	+	7.05905i	1.02714	+	0.257075i
$755$			22.7284i			0.827170i
$756$	1.77117	−	3.06776i	0.0644169	−	0.111573i
$757$	15.8890	−	27.5205i	0.577494	−	1.00025i	−0.418272	−	0.908322i	$-0.637364\pi$
$757$	15.8890	−	27.5205i	0.577494	−	1.00025i	0.995766	−	0.0919271i	$-0.0293027\pi$
$758$	−2.23984	+	1.29317i	−0.0813547	+	0.0469701i
$759$		−	4.77440i		−	0.173300i
$760$	−1.90402	+	1.09929i	−0.0690661	+	0.0398753i
$761$	−9.54176	−	16.5268i	−0.345889	−	0.599096i	0.639626	−	0.768686i	$-0.279089\pi$
$761$	−9.54176	−	16.5268i	−0.345889	−	0.599096i	−0.985515	+	0.169590i	$0.945756\pi$
$762$		−	47.6974i		−	1.72790i
$763$	−14.9437	−	25.8833i	−0.540999	−	0.937037i
$764$	3.60222	−	6.23923i	0.130324	−	0.225728i
$765$	41.1107	−	14.2101i	1.48636	−	0.513768i
$766$	2.59794			0.0938675
$767$	−4.56766	+	18.2500i	−0.164929	+	0.658969i
$768$			2.53665i			0.0915335i
$769$	4.59659	−	7.96153i	0.165757	−	0.287100i	−0.771167	−	0.636633i	$-0.780326\pi$
$769$	4.59659	−	7.96153i	0.165757	−	0.287100i	0.936924	+	0.349533i	$0.113660\pi$
$770$	9.04308	+	5.22103i	0.325890	+	0.188153i
$771$	29.6670	−	17.1283i	1.06843	−	0.616859i
$772$		−	8.88545i		−	0.319794i
$773$	19.5502	+	33.8620i	0.703173	+	1.21793i	0.967347	+	0.253456i	$0.0815674\pi$
$773$	19.5502	+	33.8620i	0.703173	+	1.21793i	−0.264174	+	0.964475i	$0.585099\pi$
$774$	−21.3690	−	37.0121i	−0.768091	−	1.33037i
$775$		−	38.0512i		−	1.36684i
$776$	−4.06325	+	2.34592i	−0.145862	+	0.0842135i
$777$	−56.7918	−	32.7888i	−2.03739	−	1.17629i
$778$	−0.671232	+	1.16261i	−0.0240648	+	0.0416815i
$779$			4.80336i			0.172098i
$780$	−20.1907	−	19.5330i	−0.722943	−	0.699395i
$781$	−5.77118			−0.206509
$782$	6.93245	−	2.39623i	0.247904	−	0.0856891i
$783$	−4.44489	+	7.69877i	−0.158847	+	0.275132i
$784$	1.66229	+	2.87917i	0.0593675	+	0.102828i
$785$		−	48.6212i		−	1.73536i
$786$	−4.54090	−	7.86506i	−0.161968	−	0.280538i
$787$	42.2096	−	24.3697i	1.50461	−	0.868688i	0.504625	−	0.863338i	$-0.331631\pi$
$787$	42.2096	−	24.3697i	1.50461	−	0.868688i	0.999986	−	0.00534931i	$-0.00170275\pi$
$788$		−	9.38893i		−	0.334467i
$789$	−24.8540	+	14.3495i	−0.884827	+	0.510855i
$790$	−20.3835	+	35.3053i	−0.725214	+	1.25611i
$791$	−10.7981	+	18.7028i	−0.383936	+	0.664996i
$792$		−	3.63383i		−	0.129123i
$793$	−3.64811	−	0.913060i	−0.129548	−	0.0324237i
$794$		−	3.25866i		−	0.115646i
$795$	32.4735	−	56.2458i	1.15172	−	1.99483i
$796$	−8.23969	−	4.75719i	−0.292048	−	0.168614i
$797$	−15.3052	−	26.5094i	−0.542138	−	0.939011i	−0.998781	−	0.0493610i	$-0.984282\pi$
$797$	−15.3052	−	26.5094i	−0.542138	−	0.939011i	0.456643	−	0.889650i	$-0.349052\pi$
$798$	5.83413			0.206526
$799$	−20.6776	−	3.99387i	−0.731520	−	0.141293i
$800$	−2.21730	−	3.84048i	−0.0783935	−	0.135781i
$801$	28.8511			1.01940
$802$	−14.6607	+	8.46437i	−0.517688	+	0.298887i
$803$	1.97371	−	3.41857i	0.0696508	−	0.120639i
$804$	4.08164	+	2.35654i	0.143948	+	0.0831086i
$805$			17.5577i			0.618828i
$806$	−8.50080	−	29.7467i	−0.299428	−	1.04778i
$807$	44.6538			1.57189
$808$	8.93773	−	15.4806i	0.314428	−	0.544605i
$809$	−1.08095	−	0.624086i	−0.0380042	−	0.0219417i	0.480878	−	0.876788i	$-0.340318\pi$
$809$	−1.08095	−	0.624086i	−0.0380042	−	0.0219417i	−0.518882	+	0.854846i	$0.673651\pi$
$810$	−19.9699	+	11.5296i	−0.701672	+	0.405111i
$811$			9.53048i			0.334660i	0.985901	+	0.167330i	$0.0535146\pi$
$811$			9.53048i			0.334660i	−0.985901	+	0.167330i	$0.946485\pi$
$812$	−12.9552	−	22.4390i	−0.454637	−	0.787455i
$813$	46.1069	−	26.6198i	1.61704	−	0.933598i
$814$	−8.51228			−0.298355
$815$	16.5055	+	28.5884i	0.578164	+	1.00141i
$816$	9.88502	−	3.41681i	0.346045	−	0.119612i
$817$	4.45334	−	7.71341i	0.155803	−	0.269858i
$818$	−3.07555			−0.107534
$819$	10.9335	+	38.2594i	0.382047	+	1.33689i
$820$	−20.6124			−0.719815
$821$	24.7368	+	14.2818i	0.863320	+	0.498438i	0.865123	−	0.501560i	$-0.167240\pi$
$821$	24.7368	+	14.2818i	0.863320	+	0.498438i	−0.00180243	+	0.999998i	$0.500574\pi$
$822$	37.9905	+	21.9338i	1.32507	+	0.765029i
$823$	6.59889	−	3.80987i	0.230023	−	0.132804i	−0.380560	−	0.924756i	$-0.624269\pi$
$823$	6.59889	−	3.80987i	0.230023	−	0.132804i	0.610583	+	0.791953i	$0.290935\pi$
$824$	0.715779			0.0249354
$825$	5.95078	+	10.3070i	0.207179	+	0.358845i
$826$	14.5195	−	8.38282i	0.505197	−	0.291676i
$827$			33.8231i			1.17615i	0.808808	+	0.588073i	$0.200113\pi$
$827$			33.8231i			1.17615i	−0.808808	+	0.588073i	$0.799887\pi$
$828$	5.29148	−	3.05504i	0.183892	−	0.106170i
$829$	−24.3656	+	42.2025i	−0.846253	+	1.46575i	0.0382752	+	0.999267i	$0.487814\pi$
$829$	−24.3656	+	42.2025i	−0.846253	+	1.46575i	−0.884528	+	0.466486i	$0.845520\pi$
$830$	−25.9610	−	14.9886i	−0.901120	−	0.520262i
$831$	−5.00782			−0.173719
$832$	−2.59136	−	2.50696i	−0.0898394	−	0.0869131i
$833$	8.98072	−	10.3559i	0.311163	−	0.358811i
$834$	−8.10106	+	14.0314i	−0.280517	+	0.485869i
$835$	−26.5963	+	46.0661i	−0.920402	+	1.59418i
$836$	0.655840	−	0.378649i	0.0226827	−	0.0130959i
$837$	9.45949			0.326968
$838$	−1.37321	+	0.792823i	−0.0474368	+	0.0273876i
$839$	−5.61148	+	3.23979i	−0.193730	+	0.111850i	−0.593727	−	0.804666i	$-0.702344\pi$
$839$	−5.61148	+	3.23979i	−0.193730	+	0.111850i	0.399998	+	0.916516i	$0.369011\pi$
$840$			25.0357i			0.863812i
$841$	18.0120	+	31.1977i	0.621103	+	1.07578i
$842$	12.9926	−	22.5038i	0.447753	−	0.775531i
$843$	−23.8080	−	13.7456i	−0.819993	−	0.473423i
$844$		−	2.14850i		−	0.0739545i
$845$	39.9087	−	1.32182i	1.37290	−	0.0454719i
$846$	−17.5431			−0.603143
$847$	27.4948	+	15.8742i	0.944734	+	0.545442i
$848$	4.16780	−	7.21884i	0.143123	−	0.247896i
$849$	37.0566	+	64.1839i	1.27178	+	2.20279i
$850$	−11.9792	+	13.8136i	−0.410884	+	0.473802i
$851$	−7.15645	−	12.3953i	−0.245320	−	0.424907i
$852$	−6.91843	−	11.9831i	−0.237022	−	0.410533i
$853$			16.2592i			0.556703i	0.960479	+	0.278352i	$0.0897881\pi$
$853$			16.2592i			0.556703i	−0.960479	+	0.278352i	$0.910212\pi$
$854$	1.67570	+	2.90239i	0.0573412	+	0.0993179i
$855$	6.53956	+	3.77561i	0.223648	+	0.129123i
$856$	10.9468	+	6.32012i	0.374153	+	0.216017i
$857$			1.41238i			0.0482461i	0.999709	+	0.0241230i	$0.00767935\pi$
$857$			1.41238i			0.0482461i	−0.999709	+	0.0241230i	$0.992321\pi$
$858$	6.95468	+	6.72815i	0.237429	+	0.229695i
$859$	33.7666			1.15210			0.576050	−	0.817414i	$-0.304593\pi$
$859$	33.7666			1.15210			0.576050	+	0.817414i	$0.304593\pi$
$860$	33.1001	+	19.1103i	1.12870	+	0.651657i
$861$	47.3689	+	27.3485i	1.61433	+	0.932033i
$862$	1.89152	−	1.09207i	0.0644256	−	0.0371961i
$863$	15.2765			0.520019			0.260009	−	0.965606i	$-0.416274\pi$
$863$	15.2765			0.520019			0.260009	+	0.965606i	$0.416274\pi$
$864$	0.954739	−	0.551219i	0.0324809	−	0.0187529i
$865$	0.766231	+	1.32715i	0.0260526	+	0.0451245i
$866$	−25.5628			−0.868661
$867$	−26.6298	−	33.9184i	−0.904394	−	1.15193i
$868$	−13.7854	+	23.8770i	−0.467907	+	0.810439i
$869$	7.02111	−	12.1609i	0.238175	−	0.412531i
$870$		−	62.8289i		−	2.13010i
$871$	−6.44122	+	1.84073i	−0.218252	+	0.0623706i
$872$		−	9.30149i		−	0.314988i
$873$	13.9556	+	8.05730i	0.472327	+	0.272698i
$874$	1.10276	+	0.636677i	0.0373013	+	0.0215359i
$875$	2.79011	+	4.83261i	0.0943229	+	0.163372i
$876$	9.46426			0.319768
$877$	−26.9962	+	15.5863i	−0.911597	+	0.526311i	−0.880945	−	0.473219i	$-0.843092\pi$
$877$	−26.9962	+	15.5863i	−0.911597	+	0.526311i	−0.0306526	+	0.999530i	$0.509759\pi$
$878$	−33.3028	+	19.2274i	−1.12392	+	0.648894i
$879$		−	49.8855i		−	1.68259i
$880$	1.62487	+	2.81436i	0.0547745	+	0.0948722i
$881$	40.6831	+	23.4884i	1.37065	+	0.791345i	0.991010	−	0.133789i	$-0.0427145\pi$
$881$	40.6831	+	23.4884i	1.37065	+	0.791345i	0.379640	+	0.925134i	$0.376048\pi$
$882$	5.70931	−	9.88881i	0.192242	−	0.332974i
$883$	−4.88347			−0.164342			−0.0821709	−	0.996618i	$-0.526185\pi$
$883$	−4.88347			−0.164342			−0.0821709	+	0.996618i	$0.526185\pi$
$884$	−6.27880	+	13.4750i	−0.211179	+	0.453215i
$885$	40.6543			1.36658
$886$	−14.2359	+	24.6573i	−0.478265	+	0.828379i
$887$	31.2935	+	18.0673i	1.05073	+	0.606640i	0.922854	−	0.385150i	$-0.125850\pi$
$887$	31.2935	+	18.0673i	1.05073	+	0.606640i	0.127878	+	0.991790i	$0.459184\pi$
$888$	−10.2044	−	17.6746i	−0.342438	−	0.593121i
$889$		−	60.4186i		−	2.02637i
$890$	−22.3449	+	12.9008i	−0.749003	+	0.432437i
$891$	6.87864	−	3.97139i	0.230443	−	0.133046i
$892$	−27.8031			−0.930917
$893$	−1.82801	−	3.16620i	−0.0611719	−	0.105953i
$894$	−11.6268	−	6.71273i	−0.388858	−	0.224507i
$895$	18.7303	+	10.8139i	0.626084	+	0.361470i
$896$			3.21319i			0.107345i
$897$	−3.95039	+	15.7837i	−0.131900	+	0.527003i
$898$			5.83766i			0.194805i
$899$	34.5955	−	59.9212i	1.15383	−	1.99849i
$900$	−7.61555	+	13.1905i	−0.253852	+	0.439684i
$901$	−33.7449	−	6.51781i	−1.12420	−	0.217140i
$902$	7.09993			0.236402
$903$	−50.7112	−	87.8344i	−1.68756	−	2.92294i
$904$	−5.82064	+	3.36055i	−0.193592	+	0.111770i
$905$	−46.5460			−1.54724
$906$	16.2554	−	9.38507i	0.540050	−	0.311798i
$907$	−6.97925	−	4.02947i	−0.231742	−	0.133796i	0.379633	−	0.925137i	$-0.376050\pi$
$907$	−6.97925	−	4.02947i	−0.231742	−	0.133796i	−0.611376	+	0.791341i	$0.709383\pi$
$908$	0.874127	+	0.504677i	0.0290089	+	0.0167483i
$909$	−61.3951			−2.03635
$910$	−25.5756	−	24.7426i	−0.847824	−	0.820208i
$911$			10.9449i			0.362620i	0.983426	+	0.181310i	$0.0580337\pi$
$911$			10.9449i			0.362620i	−0.983426	+	0.181310i	$0.941966\pi$
$912$	1.57243	+	0.907842i	0.0520683	+	0.0300616i
$913$	8.94227	+	5.16282i	0.295946	+	0.170865i
$914$	9.58525	+	16.6021i	0.317052	+	0.549150i
$915$			8.12667i			0.268659i
$916$	−13.7361	−	23.7916i	−0.453854	−	0.786098i
$917$	−5.75197	−	9.96271i	−0.189947	−	0.328998i
$918$	−3.43404	−	2.97802i	−0.113340	−	0.0982895i
$919$	−12.4606	−	21.5823i	−0.411036	−	0.711936i	0.583967	−	0.811777i	$-0.301500\pi$
$919$	−12.4606	−	21.5823i	−0.411036	−	0.711936i	−0.995003	+	0.0998416i	$0.968166\pi$
$920$	−2.73213	+	4.73219i	−0.0900757	+	0.156016i
$921$	14.0364	+	8.10394i	0.462516	+	0.267034i
$922$	13.9108			0.458129
$923$	19.0790	+	4.77514i	0.627992	+	0.157176i
$924$		−	8.62353i		−	0.283693i
$925$	30.8989	+	17.8395i	1.01595	+	0.586559i
$926$	5.33522	−	9.24088i	0.175326	−	0.303674i
$927$	−1.22921	−	2.12905i	−0.0403725	−	0.0699273i
$928$		−	8.06374i		−	0.264705i
$929$	−8.61108	+	4.97161i	−0.282520	+	0.163113i	−0.634564	−	0.772870i	$-0.718820\pi$
$929$	−8.61108	+	4.97161i	−0.282520	+	0.163113i	0.352044	+	0.935984i	$0.385487\pi$
$930$	−57.8984	+	33.4277i	−1.89856	+	1.09614i
$931$	2.37967			0.0779904
$932$	−9.79973	+	5.65788i	−0.321001	+	0.185330i
$933$	−42.2243	+	73.1346i	−1.38236	+	2.39432i
$934$	16.6279	−	28.8003i	0.544080	−	0.942375i
$935$	8.77857	−	10.1228i	0.287090	−	0.331051i
$936$	−3.00667	+	12.0131i	−0.0982762	+	0.392660i
$937$	44.5742			1.45618			0.728088	−	0.685483i	$-0.240409\pi$
$937$	44.5742			1.45618			0.728088	+	0.685483i	$0.240409\pi$
$938$	5.17023	+	2.98503i	0.168814	+	0.0974648i
$939$	−33.5277	+	58.0717i	−1.09413	+	1.89510i
$940$	13.5869	−	7.84441i	0.443157	−	0.255857i
$941$		−	49.2595i		−	1.60581i	−0.596105	−	0.802906i	$-0.703286\pi$
$941$		−	49.2595i		−	1.60581i	0.596105	−	0.802906i	$-0.296714\pi$
$942$	−34.7740	+	20.0768i	−1.13300	+	0.654137i
$943$	5.96906	+	10.3387i	0.194379	+	0.336675i
$944$	5.21776			0.169824
$945$	9.42286	−	5.44029i	0.306526	−	0.176973i
$946$	−11.4013	−	6.58256i	−0.370689	−	0.214017i
$947$	25.0913	+	14.4865i	0.815358	+	0.470747i	0.848813	−	0.528693i	$-0.177318\pi$
$947$	25.0913	+	14.4865i	0.815358	+	0.470747i	−0.0334553	+	0.999440i	$0.510651\pi$
$948$	33.6673			1.09346
$949$	−9.35347	+	9.66839i	−0.303626	+	0.313849i
$950$	−3.17420			−0.102985
$951$	27.1060	−	46.9490i	0.878972	−	1.52242i
$952$	12.5214	−	4.32808i	0.405821	−	0.140274i
$953$	15.8594	+	27.4693i	0.513737	+	0.889818i	0.999873	+	0.0159351i	$0.00507253\pi$
$953$	15.8594	+	27.4693i	0.513737	+	0.889818i	−0.486136	+	0.873883i	$0.661594\pi$
$954$	−28.6295			−0.926913
$955$	19.1643	−	11.0645i	0.620142	−	0.358039i
$956$	−10.8882	−	18.8590i	−0.352150	−	0.609942i
$957$			21.6414i			0.699567i
$958$	23.1255	−	13.3515i	0.747152	−	0.431369i
$959$	48.1227	+	27.7837i	1.55396	+	0.897181i
$960$	−3.89576	+	6.74766i	−0.125735	+	0.217780i
$961$	−42.6253			−1.37501
$962$	28.1408	+	7.04316i	0.907295	+	0.227080i
$963$		−	43.4142i		−	1.39900i
$964$	−19.4311	−	11.2186i	−0.625834	−	0.361325i
$965$	13.6462	−	23.6359i	0.439286	−	0.760866i
$966$	12.5573	−	7.24998i	0.404026	−	0.233264i
$967$	60.1258			1.93352			0.966758	−	0.255692i	$-0.0823032\pi$
$967$	60.1258			1.93352			0.966758	+	0.255692i	$0.0823032\pi$
$968$	4.94031	+	8.55687i	0.158788	+	0.275028i
$969$	1.41973	−	7.35040i	0.0456082	−	0.236129i
$970$	−14.4113			−0.462720
$971$	−14.6322	−	25.3436i	−0.469568	−	0.813316i	0.529826	−	0.848106i	$-0.322257\pi$
$971$	−14.6322	−	25.3436i	−0.469568	−	0.813316i	−0.999395	+	0.0347899i	$0.988924\pi$
$972$	19.3563	+	11.1754i	0.620854	+	0.358450i
$973$	−10.2616	+	17.7737i	−0.328973	+	0.569798i
$974$		−	7.43376i		−	0.238193i
$975$	−11.1445	−	38.9979i	−0.356911	−	1.24893i
$976$			1.04301i			0.0333860i
$977$	−8.68804	+	15.0481i	−0.277955	+	0.481432i	−0.970876	−	0.239581i	$-0.922990\pi$
$977$	−8.68804	+	15.0481i	−0.277955	+	0.481432i	0.692921	+	0.721013i	$0.256323\pi$
$978$	13.6310	−	23.6096i	0.435872	−	0.754953i
$979$	7.69670	−	4.44369i	0.245988	−	0.142021i
$980$			10.2117i			0.326201i
$981$	−27.6668	+	15.9735i	−0.883334	+	0.509993i
$982$	−14.7520	−	25.5512i	−0.470755	−	0.815372i
$983$			61.9018i			1.97436i	0.159610	+	0.987180i	$0.448976\pi$
$983$			61.9018i			1.97436i	−0.159610	+	0.987180i	$0.551024\pi$
$984$	8.51132	+	14.7420i	0.271331	+	0.469959i
$985$	14.4194	−	24.9752i	0.459441	−	0.795775i
$986$	−31.4234	+	10.8617i	−1.00073	+	0.345906i
$987$	−41.6318			−1.32516
$988$	−2.48144	+	0.709129i	−0.0789452	+	0.0225604i
$989$		−	22.1364i		−	0.703896i
$990$	5.58080	−	9.66623i	0.177369	−	0.307213i
$991$	−44.3045	−	25.5792i	−1.40738	−	0.812550i	−0.412243	−	0.911074i	$-0.635255\pi$
$991$	−44.3045	−	25.5792i	−1.40738	−	0.812550i	−0.995135	+	0.0985235i	$0.968588\pi$
$992$	−7.43095	+	4.29026i	−0.235933	+	0.136216i
$993$			45.8417i			1.45474i
$994$	−8.76361	−	15.1790i	−0.277965	−	0.481449i
$995$	−14.6121	−	25.3089i	−0.463234	−	0.802345i
$996$			24.7566i			0.784442i
$997$	12.3083	−	7.10618i	0.389807	−	0.225055i	−0.292270	−	0.956336i	$-0.594410\pi$
$997$	12.3083	−	7.10618i	0.389807	−	0.225055i	0.682076	+	0.731281i	$0.261077\pi$
$998$	21.0462	+	12.1510i	0.666206	+	0.384634i
$999$	−4.43488	+	7.68144i	−0.140313	+	0.243030i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	442.2.m.b.373.2	yes	24
13.3	even	3	inner	442.2.m.b.237.11	yes	24
17.16	even	2	inner	442.2.m.b.373.11	yes	24
221.16	even	6	inner	442.2.m.b.237.2	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
442.2.m.b.237.2	✓	24	221.16	even	6	inner
442.2.m.b.237.11	yes	24	13.3	even	3	inner
442.2.m.b.373.2	yes	24	1.1	even	1	trivial
442.2.m.b.373.11	yes	24	17.16	even	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 442 = 2 \cdot 13 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	442.m (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(-2.19681 - 1.26833i) q^{3} +(-0.500000 - 0.866025i) q^{4} -3.07158i q^{5} +(-2.19681 + 1.26833i) q^{6} +(-2.78270 + 1.60659i) q^{7} -1.00000 q^{8} +(1.71730 + 2.97445i) q^{9} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{2} +(-2.19681 - 1.26833i) q^{3} +(-0.500000 - 0.866025i) q^{4} -3.07158i q^{5} +(-2.19681 + 1.26833i) q^{6} +(-2.78270 + 1.60659i) q^{7} -1.00000 q^{8} +(1.71730 + 2.97445i) q^{9} +(-2.66007 - 1.53579i) q^{10} +(0.916260 + 0.529003i) q^{11} +2.53665i q^{12} +(-2.59136 - 2.50696i) q^{13} +3.21319i q^{14} +(-3.89576 + 6.74766i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(4.04828 + 0.781925i) q^{17} +3.43460 q^{18} +(0.357890 + 0.619883i) q^{19} +(-2.66007 + 1.53579i) q^{20} +8.15074 q^{21} +(0.916260 - 0.529003i) q^{22} +(1.54064 + 0.889487i) q^{23} +(2.19681 + 1.26833i) q^{24} -4.43460 q^{25} +(-3.46677 + 0.990709i) q^{26} -1.10244i q^{27} +(2.78270 + 1.60659i) q^{28} +(-6.98341 - 4.03187i) q^{29} +(3.89576 + 6.74766i) q^{30} +8.58052i q^{31} +(0.500000 + 0.866025i) q^{32} +(-1.34190 - 2.32423i) q^{33} +(2.70131 - 3.11495i) q^{34} +(4.93478 + 8.54729i) q^{35} +(1.71730 - 2.97445i) q^{36} +(-6.96769 - 4.02279i) q^{37} +0.715779 q^{38} +(2.51308 + 8.79399i) q^{39} +3.07158i q^{40} +(5.81161 + 3.35534i) q^{41} +(4.07537 - 7.05875i) q^{42} +(-6.22167 - 10.7762i) q^{43} -1.05801i q^{44} +(9.13627 - 5.27483i) q^{45} +(1.54064 - 0.889487i) q^{46} -5.10774 q^{47} +(2.19681 - 1.26833i) q^{48} +(1.66229 - 2.87917i) q^{49} +(-2.21730 + 3.84048i) q^{50} +(-7.90155 - 6.85228i) q^{51} +(-0.875406 + 3.49767i) q^{52} -8.33560 q^{53} +(-0.954739 - 0.551219i) q^{54} +(1.62487 - 2.81436i) q^{55} +(2.78270 - 1.60659i) q^{56} -1.81568i q^{57} +(-6.98341 + 4.03187i) q^{58} +(-2.60888 - 4.51871i) q^{59} +7.79153 q^{60} +(0.903276 - 0.521506i) q^{61} +(7.43095 + 4.29026i) q^{62} +(-9.55748 - 5.51801i) q^{63} +1.00000 q^{64} +(-7.70032 + 7.95958i) q^{65} -2.68379 q^{66} +(0.928995 - 1.60907i) q^{67} +(-1.34697 - 3.89688i) q^{68} +(-2.25632 - 3.90806i) q^{69} +9.86957 q^{70} +(-4.72397 + 2.72739i) q^{71} +(-1.71730 - 2.97445i) q^{72} -3.73101i q^{73} +(-6.96769 + 4.02279i) q^{74} +(9.74196 + 5.62452i) q^{75} +(0.357890 - 0.619883i) q^{76} -3.39957 q^{77} +(8.87236 + 2.22060i) q^{78} -13.2724i q^{79} +(2.66007 + 1.53579i) q^{80} +(3.75365 - 6.50152i) q^{81} +(5.81161 - 3.35534i) q^{82} +9.75954 q^{83} +(-4.07537 - 7.05875i) q^{84} +(2.40174 - 12.4346i) q^{85} -12.4433 q^{86} +(10.2275 + 17.7145i) q^{87} +(-0.916260 - 0.529003i) q^{88} +(4.20007 - 7.27473i) q^{89} -10.5497i q^{90} +(11.2387 + 2.81284i) q^{91} -1.77897i q^{92} +(10.8829 - 18.8497i) q^{93} +(-2.55387 + 4.42343i) q^{94} +(1.90402 - 1.09929i) q^{95} -2.53665i q^{96} +(4.06325 - 2.34592i) q^{97} +(-1.66229 - 2.87917i) q^{98} +3.63383i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 12 q^{2} - 12 q^{4} - 24 q^{8} + 12 q^{9}+O(q^{10}) \) 24 * q + 12 * q^2 - 12 * q^4 - 24 * q^8 + 12 * q^9	\( 24 q + 12 q^{2} - 12 q^{4} - 24 q^{8} + 12 q^{9} + 12 q^{13} - 12 q^{16} + 5 q^{17} + 24 q^{18} + 8 q^{19} - 4 q^{21} - 48 q^{25} - 6 q^{26} + 12 q^{32} - 6 q^{33} + 10 q^{34} - 10 q^{35} + 12 q^{36} + 16 q^{38} - 2 q^{42} - 4 q^{43} + 12 q^{47} + 20 q^{49} - 24 q^{50} + 16 q^{51} - 18 q^{52} - 44 q^{53} - 12 q^{55} + 14 q^{59} + 24 q^{64} - 12 q^{66} + 6 q^{67} + 5 q^{68} + 10 q^{69} - 20 q^{70} - 12 q^{72} + 8 q^{76} - 28 q^{77} - 4 q^{81} - 4 q^{83} + 2 q^{84} + 13 q^{85} - 8 q^{86} - 12 q^{87} + 20 q^{89} + 6 q^{94} - 20 q^{98}+O(q^{100}) \) 24 * q + 12 * q^2 - 12 * q^4 - 24 * q^8 + 12 * q^9 + 12 * q^13 - 12 * q^16 + 5 * q^17 + 24 * q^18 + 8 * q^19 - 4 * q^21 - 48 * q^25 - 6 * q^26 + 12 * q^32 - 6 * q^33 + 10 * q^34 - 10 * q^35 + 12 * q^36 + 16 * q^38 - 2 * q^42 - 4 * q^43 + 12 * q^47 + 20 * q^49 - 24 * q^50 + 16 * q^51 - 18 * q^52 - 44 * q^53 - 12 * q^55 + 14 * q^59 + 24 * q^64 - 12 * q^66 + 6 * q^67 + 5 * q^68 + 10 * q^69 - 20 * q^70 - 12 * q^72 + 8 * q^76 - 28 * q^77 - 4 * q^81 - 4 * q^83 + 2 * q^84 + 13 * q^85 - 8 * q^86 - 12 * q^87 + 20 * q^89 + 6 * q^94 - 20 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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