LMFDB - Embedded newform 240.2.bl.a.109.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [240,2,Mod(109,240)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(240, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 3, 0, 2]))

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

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

chi := DirichletCharacter("240.109");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 240 = 2^{4} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	240.bl (of order $4$, 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:	$1.91640964851$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			109.17
Character	$\chi$	$=$	240.109
Dual form			240.2.bl.a.229.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.750333 + 1.19875i) q^{2} +(0.707107 - 0.707107i) q^{3} +(-0.874002 + 1.79892i) q^{4} +(1.95942 - 1.07735i) q^{5} +(1.37821 + 0.317079i) q^{6} +1.22137 q^{7} +(-2.81225 + 0.302081i) q^{8} -1.00000i q^{9} +O(q^{10})$	\(q+(0.750333 + 1.19875i) q^{2} +(0.707107 - 0.707107i) q^{3} +(-0.874002 + 1.79892i) q^{4} +(1.95942 - 1.07735i) q^{5} +(1.37821 + 0.317079i) q^{6} +1.22137 q^{7} +(-2.81225 + 0.302081i) q^{8} -1.00000i q^{9} +(2.76169 + 1.54047i) q^{10} +(1.38208 - 1.38208i) q^{11} +(0.654018 + 1.89004i) q^{12} +(-2.12237 + 2.12237i) q^{13} +(0.916431 + 1.46411i) q^{14} +(0.623711 - 2.14732i) q^{15} +(-2.47224 - 3.14452i) q^{16} +6.00218i q^{17} +(1.19875 - 0.750333i) q^{18} +(-3.06223 - 3.06223i) q^{19} +(0.225545 + 4.46644i) q^{20} +(0.863636 - 0.863636i) q^{21} +(2.69379 + 0.619748i) q^{22} -2.90813 q^{23} +(-1.77496 + 2.20216i) q^{24} +(2.67861 - 4.22197i) q^{25} +(-4.13668 - 0.951709i) q^{26} +(-0.707107 - 0.707107i) q^{27} +(-1.06748 + 2.19714i) q^{28} +(3.18392 + 3.18392i) q^{29} +(3.04209 - 0.863531i) q^{30} -3.88079 q^{31} +(1.91449 - 5.32304i) q^{32} -1.95456i q^{33} +(-7.19511 + 4.50363i) q^{34} +(2.39316 - 1.31584i) q^{35} +(1.79892 + 0.874002i) q^{36} +(-2.44376 - 2.44376i) q^{37} +(1.37316 - 5.96855i) q^{38} +3.00149i q^{39} +(-5.18492 + 3.62169i) q^{40} -2.38396i q^{41} +(1.68330 + 0.387269i) q^{42} +(-9.00811 - 9.00811i) q^{43} +(1.27831 + 3.69420i) q^{44} +(-1.07735 - 1.95942i) q^{45} +(-2.18206 - 3.48612i) q^{46} +0.586179i q^{47} +(-3.97165 - 0.475374i) q^{48} -5.50826 q^{49} +(7.07094 + 0.0431074i) q^{50} +(4.24418 + 4.24418i) q^{51} +(-1.96303 - 5.67295i) q^{52} +(2.36822 + 2.36822i) q^{53} +(0.317079 - 1.37821i) q^{54} +(1.21908 - 4.19706i) q^{55} +(-3.43479 + 0.368951i) q^{56} -4.33065 q^{57} +(-1.42772 + 6.20572i) q^{58} +(8.43447 - 8.43447i) q^{59} +(3.31774 + 2.99877i) q^{60} +(9.98062 + 9.98062i) q^{61} +(-2.91189 - 4.65210i) q^{62} -1.22137i q^{63} +(7.81749 - 1.69905i) q^{64} +(-1.87206 + 6.44516i) q^{65} +(2.34302 - 1.46657i) q^{66} +(3.82203 - 3.82203i) q^{67} +(-10.7974 - 5.24591i) q^{68} +(-2.05636 + 2.05636i) q^{69} +(3.37304 + 1.88148i) q^{70} +11.5314i q^{71} +(0.302081 + 2.81225i) q^{72} -1.31108 q^{73} +(1.09583 - 4.76310i) q^{74} +(-1.09132 - 4.87945i) q^{75} +(8.18512 - 2.83232i) q^{76} +(1.68803 - 1.68803i) q^{77} +(-3.59804 + 2.25212i) q^{78} -12.5967 q^{79} +(-8.23191 - 3.49794i) q^{80} -1.00000 q^{81} +(2.85777 - 1.78876i) q^{82} +(2.91633 - 2.91633i) q^{83} +(0.798795 + 2.30843i) q^{84} +(6.46647 + 11.7608i) q^{85} +(4.03939 - 17.5575i) q^{86} +4.50274 q^{87} +(-3.46926 + 4.30426i) q^{88} -9.58659i q^{89} +(1.54047 - 2.76169i) q^{90} +(-2.59220 + 2.59220i) q^{91} +(2.54171 - 5.23150i) q^{92} +(-2.74413 + 2.74413i) q^{93} +(-0.702682 + 0.439829i) q^{94} +(-9.29930 - 2.70108i) q^{95} +(-2.41021 - 5.11770i) q^{96} -9.45309i q^{97} +(-4.13303 - 6.60303i) q^{98} +(-1.38208 - 1.38208i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q+O(q^{10}) $ 48 * q	$ 48 q + 12 q^{10} - 16 q^{14} - 4 q^{16} + 8 q^{19} - 4 q^{24} - 40 q^{26} - 8 q^{30} - 48 q^{31} - 28 q^{34} + 24 q^{35} - 4 q^{36} - 16 q^{40} - 40 q^{44} - 4 q^{46} + 48 q^{49} - 32 q^{50} + 8 q^{51} - 4 q^{54} + 48 q^{56} - 32 q^{59} - 24 q^{60} + 16 q^{61} + 48 q^{64} + 16 q^{65} + 24 q^{66} - 16 q^{69} + 40 q^{74} - 16 q^{75} + 60 q^{76} - 96 q^{79} + 72 q^{80} - 48 q^{81} + 16 q^{86} + 8 q^{90} - 32 q^{91} + 44 q^{94} - 48 q^{95} - 40 q^{96}+O(q^{100}) $ 48 * q + 12 * q^10 - 16 * q^14 - 4 * q^16 + 8 * q^19 - 4 * q^24 - 40 * q^26 - 8 * q^30 - 48 * q^31 - 28 * q^34 + 24 * q^35 - 4 * q^36 - 16 * q^40 - 40 * q^44 - 4 * q^46 + 48 * q^49 - 32 * q^50 + 8 * q^51 - 4 * q^54 + 48 * q^56 - 32 * q^59 - 24 * q^60 + 16 * q^61 + 48 * q^64 + 16 * q^65 + 24 * q^66 - 16 * q^69 + 40 * q^74 - 16 * q^75 + 60 * q^76 - 96 * q^79 + 72 * q^80 - 48 * q^81 + 16 * q^86 + 8 * q^90 - 32 * q^91 + 44 * q^94 - 48 * q^95 - 40 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/240\mathbb{Z}\right)^\times$.

$n$	$31$	$97$	$161$	$181$
$\chi(n)$	$1$	$-1$	$1$	$e\left(\frac{3}{4}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.750333	+	1.19875i	0.530565	+	0.847644i
$2$	0.750333	+	1.19875i	0.530565	+	0.847644i
$3$	0.707107	−	0.707107i	0.408248	−	0.408248i
$3$	0.707107	−	0.707107i	0.408248	−	0.408248i
$4$	−0.874002	+	1.79892i	−0.437001	+	0.899461i
$5$	1.95942	−	1.07735i	0.876277	−	0.481808i
$5$	1.95942	−	1.07735i	0.876277	−	0.481808i
$6$	1.37821	+	0.317079i	0.562652	+	0.129447i
$7$	1.22137			0.461633			0.230817	−	0.972997i	$-0.425860\pi$
$7$	1.22137			0.461633			0.230817	+	0.972997i	$0.425860\pi$
$8$	−2.81225	+	0.302081i	−0.994280	+	0.106802i
$9$		−	1.00000i		−	0.333333i
$10$	2.76169	+	1.54047i	0.873324	+	0.487141i
$11$	1.38208	−	1.38208i	0.416713	−	0.416713i	−0.467356	−	0.884069i	$-0.654793\pi$
$11$	1.38208	−	1.38208i	0.416713	−	0.416713i	0.884069	+	0.467356i	$0.154793\pi$
$12$	0.654018	+	1.89004i	0.188799	+	0.545608i
$13$	−2.12237	+	2.12237i	−0.588641	+	0.588641i	−0.937263	−	0.348622i	$-0.886650\pi$
$13$	−2.12237	+	2.12237i	−0.588641	+	0.588641i	0.348622	+	0.937263i	$0.386650\pi$
$14$	0.916431	+	1.46411i	0.244926	+	0.391300i
$15$	0.623711	−	2.14732i	0.161042	−	0.554436i
$16$	−2.47224	−	3.14452i	−0.618061	−	0.786130i
$17$			6.00218i			1.45574i	0.685714	+	0.727871i	$0.259490\pi$
$17$			6.00218i			1.45574i	−0.685714	+	0.727871i	$0.740510\pi$
$18$	1.19875	−	0.750333i	0.282548	−	0.176855i
$19$	−3.06223	−	3.06223i	−0.702525	−	0.702525i	0.262427	−	0.964952i	$-0.415477\pi$
$19$	−3.06223	−	3.06223i	−0.702525	−	0.702525i	−0.964952	+	0.262427i	$0.915477\pi$
$20$	0.225545	+	4.46644i	0.0504333	+	0.998727i
$21$	0.863636	−	0.863636i	0.188461	−	0.188461i
$22$	2.69379	+	0.619748i	0.574318	+	0.132131i
$23$	−2.90813			−0.606387			−0.303193	−	0.952929i	$-0.598053\pi$
$23$	−2.90813			−0.606387			−0.303193	+	0.952929i	$0.598053\pi$
$24$	−1.77496	+	2.20216i	−0.362312	+	0.449515i
$25$	2.67861	−	4.22197i	0.535723	−	0.844394i
$26$	−4.13668	−	0.951709i	−0.811270	−	0.186645i
$27$	−0.707107	−	0.707107i	−0.136083	−	0.136083i
$28$	−1.06748	+	2.19714i	−0.201734	+	0.415221i
$29$	3.18392	+	3.18392i	0.591239	+	0.591239i	0.937966	−	0.346727i	$-0.112707\pi$
$29$	3.18392	+	3.18392i	0.591239	+	0.591239i	−0.346727	+	0.937966i	$0.612707\pi$
$30$	3.04209	−	0.863531i	0.555407	−	0.157659i
$31$	−3.88079			−0.697011			−0.348505	−	0.937307i	$-0.613311\pi$
$31$	−3.88079			−0.697011			−0.348505	+	0.937307i	$0.613311\pi$
$32$	1.91449	−	5.32304i	0.338437	−	0.940989i
$33$		−	1.95456i		−	0.340245i
$34$	−7.19511	+	4.50363i	−1.23395	+	0.772366i
$35$	2.39316	−	1.31584i	0.404518	−	0.222418i
$36$	1.79892	+	0.874002i	0.299820	+	0.145667i
$37$	−2.44376	−	2.44376i	−0.401752	−	0.401752i	0.477098	−	0.878850i	$-0.341689\pi$
$37$	−2.44376	−	2.44376i	−0.401752	−	0.401752i	−0.878850	+	0.477098i	$0.841689\pi$
$38$	1.37316	−	5.96855i	0.222756	−	0.968226i
$39$			3.00149i			0.480623i
$40$	−5.18492	+	3.62169i	−0.819807	+	0.572640i
$41$		−	2.38396i		−	0.372312i	−0.982520	−	0.186156i	$-0.940397\pi$
$41$		−	2.38396i		−	0.372312i	0.982520	−	0.186156i	$-0.0596029\pi$
$42$	1.68330	+	0.387269i	0.259739	+	0.0597569i
$43$	−9.00811	−	9.00811i	−1.37372	−	1.37372i	−0.854852	−	0.518871i	$-0.826352\pi$
$43$	−9.00811	−	9.00811i	−1.37372	−	1.37372i	−0.518871	−	0.854852i	$-0.673648\pi$
$44$	1.27831	+	3.69420i	0.192713	+	0.556921i
$45$	−1.07735	−	1.95942i	−0.160603	−	0.292092i
$46$	−2.18206	−	3.48612i	−0.321728	−	0.514000i
$47$			0.586179i			0.0855030i	0.999086	+	0.0427515i	$0.0136124\pi$
$47$			0.586179i			0.0855030i	−0.999086	+	0.0427515i	$0.986388\pi$
$48$	−3.97165	−	0.475374i	−0.573259	−	0.0686143i
$49$	−5.50826			−0.786895
$50$	7.07094	+	0.0431074i	0.999981	+	0.00609631i
$51$	4.24418	+	4.24418i	0.594304	+	0.594304i
$52$	−1.96303	−	5.67295i	−0.272223	−	0.786696i
$53$	2.36822	+	2.36822i	0.325300	+	0.325300i	0.850796	−	0.525496i	$-0.176120\pi$
$53$	2.36822	+	2.36822i	0.325300	+	0.325300i	−0.525496	+	0.850796i	$0.676120\pi$
$54$	0.317079	−	1.37821i	0.0431489	−	0.187551i
$55$	1.21908	−	4.19706i	0.164381	−	0.565931i
$56$	−3.43479	+	0.368951i	−0.458993	+	0.0493032i
$57$	−4.33065			−0.573609
$58$	−1.42772	+	6.20572i	−0.187469	+	0.814851i
$59$	8.43447	−	8.43447i	1.09807	−	1.09807i	0.103438	−	0.994636i	$-0.467016\pi$
$59$	8.43447	−	8.43447i	1.09807	−	1.09807i	0.994636	−	0.103438i	$-0.0329844\pi$
$60$	3.31774	+	2.99877i	0.428318	+	0.387139i
$61$	9.98062	+	9.98062i	1.27789	+	1.27789i	0.941848	+	0.336040i	$0.109088\pi$
$61$	9.98062	+	9.98062i	1.27789	+	1.27789i	0.336040	+	0.941848i	$0.390912\pi$
$62$	−2.91189	−	4.65210i	−0.369810	−	0.590817i
$63$		−	1.22137i		−	0.153878i
$64$	7.81749	−	1.69905i	0.977187	−	0.212382i
$65$	−1.87206	+	6.44516i	−0.232201	+	0.799424i
$66$	2.34302	−	1.46657i	0.288406	−	0.180522i
$67$	3.82203	−	3.82203i	0.466936	−	0.466936i	−0.433985	−	0.900920i	$-0.642893\pi$
$67$	3.82203	−	3.82203i	0.466936	−	0.466936i	0.900920	+	0.433985i	$0.142893\pi$
$68$	−10.7974	−	5.24591i	−1.30938	−	0.636160i
$69$	−2.05636	+	2.05636i	−0.247556	+	0.247556i
$70$	3.37304	+	1.88148i	0.403155	+	0.224880i
$71$			11.5314i			1.36852i	0.729238	+	0.684260i	$0.239875\pi$
$71$			11.5314i			1.36852i	−0.729238	+	0.684260i	$0.760125\pi$
$72$	0.302081	+	2.81225i	0.0356006	+	0.331427i
$73$	−1.31108			−0.153450			−0.0767250	−	0.997052i	$-0.524446\pi$
$73$	−1.31108			−0.153450			−0.0767250	+	0.997052i	$0.524446\pi$
$74$	1.09583	−	4.76310i	0.127387	−	0.553699i
$75$	−1.09132	−	4.87945i	−0.126014	−	0.563430i
$76$	8.18512	−	2.83232i	0.938897	−	0.324890i
$77$	1.68803	−	1.68803i	0.192368	−	0.192368i
$78$	−3.59804	+	2.25212i	−0.407397	+	0.255002i
$79$	−12.5967			−1.41724			−0.708619	−	0.705592i	$-0.750681\pi$
$79$	−12.5967			−1.41724			−0.708619	+	0.705592i	$0.750681\pi$
$80$	−8.23191	−	3.49794i	−0.920356	−	0.391082i
$81$	−1.00000			−0.111111
$82$	2.85777	−	1.78876i	0.315588	−	0.197536i
$83$	2.91633	−	2.91633i	0.320108	−	0.320108i	−0.528700	−	0.848809i	$-0.677320\pi$
$83$	2.91633	−	2.91633i	0.320108	−	0.320108i	0.848809	+	0.528700i	$0.177320\pi$
$84$	0.798795	+	2.30843i	0.0871557	+	0.251871i
$85$	6.46647	+	11.7608i	0.701387	+	1.27563i
$86$	4.03939	−	17.5575i	0.435578	−	1.89328i
$87$	4.50274			0.482744
$88$	−3.46926	+	4.30426i	−0.369824	+	0.458835i
$89$		−	9.58659i		−	1.01618i	−0.861305	−	0.508088i	$-0.830352\pi$
$89$		−	9.58659i		−	1.01618i	0.861305	−	0.508088i	$-0.169648\pi$
$90$	1.54047	−	2.76169i	0.162380	−	0.291108i
$91$	−2.59220	+	2.59220i	−0.271736	+	0.271736i
$92$	2.54171	−	5.23150i	0.264991	−	0.545421i
$93$	−2.74413	+	2.74413i	−0.284553	+	0.284553i
$94$	−0.702682	+	0.439829i	−0.0724761	+	0.0453649i
$95$	−9.29930	−	2.70108i	−0.954088	−	0.277125i
$96$	−2.41021	−	5.11770i	−0.245991	−	0.522324i
$97$		−	9.45309i		−	0.959816i	−0.877319	−	0.479908i	$-0.840670\pi$
$97$		−	9.45309i		−	0.959816i	0.877319	−	0.479908i	$-0.159330\pi$
$98$	−4.13303	−	6.60303i	−0.417499	−	0.667007i
$99$	−1.38208	−	1.38208i	−0.138904	−	0.138904i
$100$	5.25388	+	8.50863i	0.525388	+	0.850863i
$101$	−11.6519	+	11.6519i	−1.15940	+	1.15940i	−0.174798	+	0.984604i	$0.555927\pi$
$101$	−11.6519	+	11.6519i	−1.15940	+	1.15940i	−0.984604	+	0.174798i	$0.944073\pi$
$102$	−1.90316	+	8.27226i	−0.188441	+	0.819075i
$103$	2.15006			0.211852			0.105926	−	0.994374i	$-0.466219\pi$
$103$	2.15006			0.211852			0.105926	+	0.994374i	$0.466219\pi$
$104$	5.32752	−	6.60978i	0.522406	−	0.648142i
$105$	0.761780	−	2.62266i	0.0743421	−	0.255946i
$106$	−1.06195	+	4.61585i	−0.103146	+	0.448331i
$107$	13.4992	+	13.4992i	1.30501	+	1.30501i	0.924967	+	0.380048i	$0.124092\pi$
$107$	13.4992	+	13.4992i	1.30501	+	1.30501i	0.380048	+	0.924967i	$0.375908\pi$
$108$	1.89004	−	0.654018i	0.181869	−	0.0629329i
$109$	10.7618	+	10.7618i	1.03079	+	1.03079i	0.999511	+	0.0312781i	$0.00995775\pi$
$109$	10.7618	+	10.7618i	1.03079	+	1.03079i	0.0312781	+	0.999511i	$0.490042\pi$
$110$	5.94594	−	1.68782i	0.566923	−	0.160927i
$111$	−3.45601			−0.328029
$112$	−3.01951	−	3.84061i	−0.285317	−	0.362904i
$113$			12.6206i			1.18725i	0.804742	+	0.593624i	$0.202304\pi$
$113$			12.6206i			1.18725i	−0.804742	+	0.593624i	$0.797696\pi$
$114$	−3.24943	−	5.19137i	−0.304337	−	0.486216i
$115$	−5.69823	+	3.13308i	−0.531363	+	0.292162i
$116$	−8.51037	+	2.94487i	−0.790168	+	0.273424i
$117$	2.12237	+	2.12237i	0.196214	+	0.196214i
$118$	16.4395	+	3.78216i	1.51338	+	0.348176i
$119$			7.33086i			0.672018i
$120$	−1.10537	+	6.22721i	−0.100906	+	0.568464i
$121$			7.17971i			0.652701i
$122$	−4.47548	+	19.4531i	−0.405191	+	1.76120i
$123$	−1.68571	−	1.68571i	−0.151996	−	0.151996i
$124$	3.39182	−	6.98124i	0.304594	−	0.626934i
$125$	0.699962	−	11.1584i	0.0626065	−	0.998038i
$126$	1.46411	−	0.916431i	0.130433	−	0.0816422i
$127$			9.66786i			0.857883i	0.903332	+	0.428942i	$0.141113\pi$
$127$			9.66786i			0.857883i	−0.903332	+	0.428942i	$0.858887\pi$
$128$	7.90246	+	8.09636i	0.698486	+	0.715624i
$129$	−12.7394			−1.12164
$130$	−9.13081	+	2.59188i	−0.800825	+	0.227323i
$131$	10.5362	+	10.5362i	0.920553	+	0.920553i	0.997068	−	0.0765154i	$-0.0243794\pi$
$131$	10.5362	+	10.5362i	0.920553	+	0.920553i	−0.0765154	+	0.997068i	$0.524379\pi$
$132$	3.51610	+	1.70829i	0.306037	+	0.148687i
$133$	−3.74011	−	3.74011i	−0.324309	−	0.324309i
$134$	7.44946	+	1.71386i	0.643535	+	0.148055i
$135$	−2.14732	−	0.623711i	−0.184812	−	0.0536805i
$136$	−1.81314	−	16.8796i	−0.155476	−	1.44742i
$137$	−12.9189			−1.10374			−0.551869	−	0.833931i	$-0.686085\pi$
$137$	−12.9189			−1.10374			−0.551869	+	0.833931i	$0.686085\pi$
$138$	−4.00801	−	0.922106i	−0.341184	−	0.0784948i
$139$	11.5153	−	11.5153i	0.976718	−	0.976718i	−0.0230167	−	0.999735i	$-0.507327\pi$
$139$	11.5153	−	11.5153i	0.976718	−	0.976718i	0.999735	+	0.0230167i	$0.00732710\pi$
$140$	0.275473	+	5.45516i	0.0232817	+	0.461046i
$141$	0.414491	+	0.414491i	0.0349064	+	0.0349064i
$142$	−13.8232	+	8.65235i	−1.16002	+	0.726089i
$143$			5.86659i			0.490589i
$144$	−3.14452	+	2.47224i	−0.262043	+	0.206020i
$145$	9.66882	+	2.80841i	0.802952	+	0.233226i
$146$	−0.983744	−	1.57165i	−0.0814153	−	0.130071i
$147$	−3.89493	+	3.89493i	−0.321249	+	0.321249i
$148$	6.53200	−	2.26029i	0.536927	−	0.185795i
$149$	11.8344	−	11.8344i	0.969513	−	0.969513i	−0.0300356	−	0.999549i	$-0.509562\pi$
$149$	11.8344	−	11.8344i	0.969513	−	0.969513i	0.999549	+	0.0300356i	$0.00956208\pi$
$150$	5.03039	−	4.96943i	0.410730	−	0.405752i
$151$			0.240930i			0.0196066i	0.999952	+	0.00980330i	$0.00312054\pi$
$151$			0.240930i			0.0196066i	−0.999952	+	0.00980330i	$0.996879\pi$
$152$	9.53681	+	7.68672i	0.773537	+	0.623476i
$153$	6.00218			0.485247
$154$	3.29010	+	0.756940i	0.265124	+	0.0609959i
$155$	−7.60408	+	4.18099i	−0.610775	+	0.335825i
$156$	−5.39945	−	2.62331i	−0.432302	−	0.210033i
$157$	7.19573	−	7.19573i	0.574282	−	0.574282i	−0.359040	−	0.933322i	$-0.616896\pi$
$157$	7.19573	−	7.19573i	0.574282	−	0.574282i	0.933322	+	0.359040i	$0.116896\pi$
$158$	−9.45170	−	15.1003i	−0.751937	−	1.20131i
$159$	3.34917			0.265606
$160$	−1.98352	−	12.4926i	−0.156811	−	0.987629i
$161$	−3.55189			−0.279928
$162$	−0.750333	−	1.19875i	−0.0589517	−	0.0941827i
$163$	−11.7446	+	11.7446i	−0.919910	+	0.919910i	−0.997022	−	0.0771120i	$-0.975430\pi$
$163$	−11.7446	+	11.7446i	−0.919910	+	0.919910i	0.0771120	+	0.997022i	$0.475430\pi$
$164$	4.28855	+	2.08358i	0.334880	+	0.162700i
$165$	−2.10575	−	3.82979i	−0.163932	−	0.298149i
$166$	5.68416	+	1.30773i	0.441176	+	0.101500i
$167$	0.213418			0.0165148			0.00825739	−	0.999966i	$-0.497372\pi$
$167$	0.213418			0.0165148			0.00825739	+	0.999966i	$0.497372\pi$
$168$	−2.16787	+	2.68965i	−0.167255	+	0.207511i
$169$			3.99105i			0.307004i
$170$	−9.24620	+	16.5762i	−0.709151	+	1.27133i
$171$	−3.06223	+	3.06223i	−0.234175	+	0.234175i
$172$	24.0780	−	8.33178i	1.83593	−	0.635293i
$173$	6.36918	−	6.36918i	0.484240	−	0.484240i	−0.422243	−	0.906483i	$-0.638757\pi$
$173$	6.36918	−	6.36918i	0.484240	−	0.484240i	0.906483	+	0.422243i	$0.138757\pi$
$174$	3.37855	+	5.39766i	0.256127	+	0.409195i
$175$	3.27157	−	5.15657i	0.247307	−	0.389800i
$176$	−7.76282	−	0.929145i	−0.585145	−	0.0700369i
$177$		−	11.9281i		−	0.896574i
$178$	11.4919	−	7.19313i	0.861356	−	0.539148i
$179$	−6.53473	−	6.53473i	−0.488428	−	0.488428i	0.419382	−	0.907810i	$-0.362247\pi$
$179$	−6.53473	−	6.53473i	−0.488428	−	0.488428i	−0.907810	+	0.419382i	$0.862247\pi$
$180$	4.46644	−	0.225545i	0.332909	−	0.0168111i
$181$	5.23014	−	5.23014i	0.388753	−	0.388753i	−0.485490	−	0.874242i	$-0.661359\pi$
$181$	5.23014	−	5.23014i	0.388753	−	0.388753i	0.874242	+	0.485490i	$0.161359\pi$
$182$	−5.05241	−	1.16239i	−0.374509	−	0.0861617i
$183$	14.1147			1.04339
$184$	8.17838	−	0.878490i	0.602918	−	0.0647632i
$185$	−7.42115	−	2.15555i	−0.545614	−	0.158479i
$186$	−5.34854	−	1.23052i	−0.392174	−	0.0902258i
$187$	8.29549	+	8.29549i	0.606626	+	0.606626i
$188$	−1.05449	−	0.512321i	−0.0769066	−	0.0373649i
$189$	−0.863636	−	0.863636i	−0.0628203	−	0.0628203i
$190$	−3.73965	−	13.1742i	−0.271303	−	0.955760i
$191$	13.1318			0.950181			0.475090	−	0.879937i	$-0.342415\pi$
$191$	13.1318			0.950181			0.475090	+	0.879937i	$0.342415\pi$
$192$	4.32639	−	6.72922i	0.312230	−	0.485639i
$193$		−	20.0131i		−	1.44057i	−0.693676	−	0.720287i	$-0.744010\pi$
$193$		−	20.0131i		−	1.44057i	0.693676	−	0.720287i	$-0.255990\pi$
$194$	11.3319	−	7.09296i	0.813582	−	0.509245i
$195$	3.23367	+	5.88117i	0.231568	+	0.421159i
$196$	4.81423	−	9.90894i	0.343874	−	0.707781i
$197$	−19.2424	−	19.2424i	−1.37096	−	1.37096i	−0.859021	−	0.511941i	$-0.828927\pi$
$197$	−19.2424	−	19.2424i	−1.37096	−	1.37096i	−0.511941	−	0.859021i	$-0.671073\pi$
$198$	0.619748	−	2.69379i	0.0440436	−	0.191439i
$199$			5.18227i			0.367361i	0.982986	+	0.183681i	$0.0588012\pi$
$199$			5.18227i			0.367361i	−0.982986	+	0.183681i	$0.941199\pi$
$200$	−6.25756	+	12.6824i	−0.442476	+	0.896780i
$201$		−	5.40517i		−	0.381251i
$202$	−22.7104	−	5.22489i	−1.59790	−	0.367622i
$203$	3.88873	+	3.88873i	0.272935	+	0.272935i
$204$	−11.3444	+	3.92553i	−0.794265	+	0.274842i
$205$	−2.56837	−	4.67116i	−0.179383	−	0.326248i
$206$	1.61326	+	2.57738i	0.112401	+	0.179575i
$207$			2.90813i			0.202129i
$208$	11.9209	+	1.42683i	0.826564	+	0.0989328i
$209$	−8.46451			−0.585502
$210$	3.71551	−	1.05469i	0.256394	−	0.0727804i
$211$	−5.53295	−	5.53295i	−0.380904	−	0.380904i	0.490524	−	0.871428i	$-0.336805\pi$
$211$	−5.53295	−	5.53295i	−0.380904	−	0.380904i	−0.871428	+	0.490524i	$0.836805\pi$
$212$	−6.33007	+	2.19041i	−0.434751	+	0.150438i
$213$	8.15390	+	8.15390i	0.558696	+	0.558696i
$214$	−6.05326	+	26.3110i	−0.413792	+	1.79858i
$215$	−27.3555	−	7.94570i	−1.86563	−	0.541892i
$216$	2.20216	+	1.77496i	0.149838	+	0.120771i
$217$	−4.73987			−0.321763
$218$	−4.82575	+	20.9755i	−0.326841	+	1.42064i
$219$	−0.927072	+	0.927072i	−0.0626457	+	0.0626457i
$220$	6.48471	+	5.86127i	0.437199	+	0.395166i
$221$	−12.7389	−	12.7389i	−0.856909	−	0.856909i
$222$	−2.59315	−	4.14289i	−0.174041	−	0.278052i
$223$		−	0.639576i		−	0.0428292i	−0.999771	−	0.0214146i	$-0.993183\pi$
$223$		−	0.639576i		−	0.0428292i	0.999771	−	0.0214146i	$-0.00681700\pi$
$224$	2.33829	−	6.50138i	0.156234	−	0.434392i
$225$	−4.22197	−	2.67861i	−0.281465	−	0.178574i
$226$	−15.1290	+	9.46967i	−1.00636	+	0.629913i
$227$	0.272194	−	0.272194i	0.0180662	−	0.0180662i	−0.698016	−	0.716082i	$-0.745934\pi$
$227$	0.272194	−	0.272194i	0.0180662	−	0.0180662i	0.716082	+	0.698016i	$0.245934\pi$
$228$	3.78500	−	7.79051i	0.250668	−	0.515939i
$229$	4.80055	−	4.80055i	0.317229	−	0.317229i	−0.530473	−	0.847702i	$-0.677986\pi$
$229$	4.80055	−	4.80055i	0.317229	−	0.317229i	0.847702	+	0.530473i	$0.177986\pi$
$230$	−8.03135	−	4.47990i	−0.529572	−	0.295396i
$231$		−	2.38723i		−	0.157068i
$232$	−9.91577	−	7.99217i	−0.651002	−	0.524712i
$233$	21.8025			1.42833			0.714166	−	0.699977i	$-0.246806\pi$
$233$	21.8025			1.42833			0.714166	+	0.699977i	$0.246806\pi$
$234$	−0.951709	+	4.13668i	−0.0622152	+	0.270423i
$235$	0.631522	+	1.14857i	0.0411960	+	0.0749243i
$236$	7.80121	+	22.5447i	0.507816	+	1.46753i
$237$	−8.90720	+	8.90720i	−0.578585	+	0.578585i
$238$	−8.78786	+	5.50058i	−0.569632	+	0.356550i
$239$	2.01781			0.130521			0.0652606	−	0.997868i	$-0.479212\pi$
$239$	2.01781			0.130521			0.0652606	+	0.997868i	$0.479212\pi$
$240$	−8.29426	+	3.34742i	−0.535392	+	0.216075i
$241$	15.4653			0.996209			0.498105	−	0.867117i	$-0.334030\pi$
$241$	15.4653			0.996209			0.498105	+	0.867117i	$0.334030\pi$
$242$	−8.60667	+	5.38717i	−0.553258	+	0.346300i
$243$	−0.707107	+	0.707107i	−0.0453609	+	0.0453609i
$244$	−26.6774	+	9.23128i	−1.70785	+	0.590972i
$245$	−10.7930	+	5.93435i	−0.689538	+	0.379132i
$246$	0.755902	−	3.28559i	0.0481946	−	0.209482i
$247$	12.9984			0.827069
$248$	10.9138	−	1.17231i	0.693024	−	0.0744420i
$249$		−	4.12431i		−	0.261367i
$250$	13.9013	−	7.53344i	0.879198	−	0.476457i
$251$	3.43023	−	3.43023i	0.216514	−	0.216514i	−0.590514	−	0.807028i	$-0.701075\pi$
$251$	3.43023	−	3.43023i	0.216514	−	0.216514i	0.807028	+	0.590514i	$0.201075\pi$
$252$	2.19714	+	1.06748i	0.138407	+	0.0672447i
$253$	−4.01927	+	4.01927i	−0.252689	+	0.252689i
$254$	−11.5893	+	7.25411i	−0.727180	+	0.455163i
$255$	12.8886	+	3.74362i	0.807115	+	0.234435i
$256$	−3.77604	+	15.5480i	−0.236002	+	0.971752i
$257$		−	19.3076i		−	1.20437i	−0.798355	−	0.602187i	$-0.794296\pi$
$257$		−	19.3076i		−	1.20437i	0.798355	−	0.602187i	$-0.205704\pi$
$258$	−9.55878	−	15.2713i	−0.595104	−	0.950752i
$259$	−2.98473	−	2.98473i	−0.185462	−	0.185462i
$260$	−9.95816	−	9.00078i	−0.617579	−	0.558205i
$261$	3.18392	−	3.18392i	0.197080	−	0.197080i
$262$	−4.72462	+	20.5359i	−0.291888	+	1.26871i
$263$	−9.26068			−0.571038			−0.285519	−	0.958373i	$-0.592166\pi$
$263$	−9.26068			−0.571038			−0.285519	+	0.958373i	$0.592166\pi$
$264$	0.590434	+	5.49670i	0.0363387	+	0.338299i
$265$	7.19173	+	2.08891i	0.441785	+	0.128321i
$266$	1.67713	−	7.28978i	0.102831	−	0.446965i
$267$	−6.77874	−	6.77874i	−0.414852	−	0.414852i
$268$	3.53508	+	10.2160i	0.215939	+	0.624042i
$269$	5.68909	+	5.68909i	0.346870	+	0.346870i	0.858942	−	0.512073i	$-0.171122\pi$
$269$	5.68909	+	5.68909i	0.346870	+	0.346870i	−0.512073	+	0.858942i	$0.671122\pi$
$270$	−0.863531	−	3.04209i	−0.0525528	−	0.185136i
$271$	1.56587			0.0951199			0.0475599	−	0.998868i	$-0.484855\pi$
$271$	1.56587			0.0951199			0.0475599	+	0.998868i	$0.484855\pi$
$272$	18.8740	−	14.8388i	1.14440	−	0.899736i
$273$			3.66592i			0.221872i
$274$	−9.69350	−	15.4866i	−0.585606	−	0.935578i
$275$	−2.13304	−	9.53716i	−0.128627	−	0.575113i
$276$	−1.90197	−	5.49649i	−0.114485	−	0.330850i
$277$	−11.2915	−	11.2915i	−0.678441	−	0.678441i	0.281206	−	0.959647i	$-0.409266\pi$
$277$	−11.2915	−	11.2915i	−0.678441	−	0.678441i	−0.959647	+	0.281206i	$0.909266\pi$
$278$	22.4443	+	5.16367i	1.34612	+	0.309697i
$279$			3.88079i			0.232337i
$280$	−6.33268	+	4.42341i	−0.378450	+	0.264349i
$281$			15.8017i			0.942653i	0.881959	+	0.471326i	$0.156225\pi$
$281$			15.8017i			0.942653i	−0.881959	+	0.471326i	$0.843775\pi$
$282$	−0.185865	+	0.807877i	−0.0110681	+	0.0481084i
$283$	−2.32452	−	2.32452i	−0.138178	−	0.138178i	0.634634	−	0.772813i	$-0.281151\pi$
$283$	−2.32452	−	2.32452i	−0.138178	−	0.138178i	−0.772813	+	0.634634i	$0.781151\pi$
$284$	−20.7440	−	10.0784i	−1.23093	−	0.598044i
$285$	−8.48555	+	4.66565i	−0.502640	+	0.276369i
$286$	−7.03257	+	4.40189i	−0.415845	+	0.260289i
$287$		−	2.91169i		−	0.171871i
$288$	−5.32304	−	1.91449i	−0.313663	−	0.112812i
$289$	−19.0261			−1.11918
$290$	3.88826	+	13.6977i	0.228326	+	0.804359i
$291$	−6.68434	−	6.68434i	−0.391843	−	0.391843i
$292$	1.14588	−	2.35853i	0.0670578	−	0.138022i
$293$	−7.44154	−	7.44154i	−0.434739	−	0.434739i	0.455498	−	0.890237i	$-0.349461\pi$
$293$	−7.44154	−	7.44154i	−0.434739	−	0.434739i	−0.890237	+	0.455498i	$0.849461\pi$
$294$	−7.59154	−	1.74655i	−0.442748	−	0.101861i
$295$	7.43971	−	25.6135i	0.433157	−	1.49128i
$296$	7.61069	+	6.13426i	0.442362	+	0.356547i
$297$	−1.95456			−0.113415
$298$	23.0663	+	5.30675i	1.33619	+	0.307412i
$299$	6.17214	−	6.17214i	0.356944	−	0.356944i
$300$	9.73156	+	2.30145i	0.561852	+	0.132875i
$301$	−11.0022	−	11.0022i	−0.634156	−	0.634156i
$302$	−0.288815	+	0.180778i	−0.0166194	+	0.0104026i
$303$			16.4782i			0.946648i
$304$	−2.05868	+	17.1998i	−0.118073	+	0.986479i
$305$	30.3088	+	8.80351i	1.73548	+	0.504088i
$306$	4.50363	+	7.19511i	0.257455	+	0.411317i
$307$	−3.28621	+	3.28621i	−0.187554	+	0.187554i	−0.794638	−	0.607084i	$-0.792339\pi$
$307$	−3.28621	+	3.28621i	−0.187554	+	0.187554i	0.607084	+	0.794638i	$0.292339\pi$
$308$	1.56129	+	4.51197i	0.0889628	+	0.257093i
$309$	1.52032	−	1.52032i	0.0864881	−	0.0864881i
$310$	−10.7176	−	5.97826i	−0.608716	−	0.339542i
$311$		−	29.0235i		−	1.64577i	−0.568206	−	0.822886i	$-0.692362\pi$
$311$		−	29.0235i		−	1.64577i	0.568206	−	0.822886i	$-0.307638\pi$
$312$	−0.906693	−	8.44094i	−0.0513314	−	0.477874i
$313$	−5.50831			−0.311348			−0.155674	−	0.987808i	$-0.549755\pi$
$313$	−5.50831			−0.311348			−0.155674	+	0.987808i	$0.549755\pi$
$314$	14.0251	+	3.22669i	0.791480	+	0.182092i
$315$	−1.31584	−	2.39316i	−0.0741394	−	0.134839i
$316$	11.0095	−	22.6605i	0.619334	−	1.27475i
$317$	10.6401	−	10.6401i	0.597609	−	0.597609i	−0.342067	−	0.939676i	$-0.611127\pi$
$317$	10.6401	−	10.6401i	0.597609	−	0.597609i	0.939676	+	0.342067i	$0.111127\pi$
$318$	2.51299	+	4.01481i	0.140921	+	0.225139i
$319$	8.80086			0.492754
$320$	13.4872	−	11.7514i	0.753959	−	0.656921i
$321$	19.0907			1.06554
$322$	−2.66510	−	4.25783i	−0.148520	−	0.237279i
$323$	18.3801	−	18.3801i	1.02269	−	1.02269i
$324$	0.874002	−	1.79892i	0.0485556	−	0.0999401i
$325$	3.27558	+	14.6456i	0.181696	+	0.812393i
$326$	−22.8913	−	5.26649i	−1.26783	−	0.291684i
$327$	15.2194			0.841636
$328$	0.720148	+	6.70428i	0.0397635	+	0.370182i
$329$			0.715939i			0.0394710i
$330$	3.01094	−	5.39788i	0.165747	−	0.297144i
$331$	−8.08181	+	8.08181i	−0.444217	+	0.444217i	−0.893426	−	0.449210i	$-0.851706\pi$
$331$	−8.08181	+	8.08181i	−0.444217	+	0.444217i	0.449210	+	0.893426i	$0.351706\pi$
$332$	2.69737	+	7.79512i	0.148037	+	0.427813i
$333$	−2.44376	+	2.44376i	−0.133917	+	0.133917i
$334$	0.160135	+	0.255835i	0.00876217	+	0.0139987i
$335$	3.37126	−	11.6066i	0.184192	−	0.634138i
$336$	−4.85084	−	0.580605i	−0.264635	−	0.0316746i
$337$			24.4098i			1.32969i	0.746983	+	0.664843i	$0.231502\pi$
$337$			24.4098i			1.32969i	−0.746983	+	0.664843i	$0.768498\pi$
$338$	−4.78427	+	2.99461i	−0.260230	+	0.162886i
$339$	8.92413	+	8.92413i	0.484692	+	0.484692i
$340$	−26.8084	+	1.35376i	−1.45389	+	0.0734179i
$341$	−5.36357	+	5.36357i	−0.290453	+	0.290453i
$342$	−5.96855	−	1.37316i	−0.322742	−	0.0742519i
$343$	−15.2772			−0.824890
$344$	28.0542	+	22.6119i	1.51258	+	1.21915i
$345$	−1.81383	+	6.24468i	−0.0976534	+	0.336202i
$346$	12.4141	+	2.85605i	0.667384	+	0.153542i
$347$	−1.40907	−	1.40907i	−0.0756427	−	0.0756427i	0.668273	−	0.743916i	$-0.267034\pi$
$347$	−1.40907	−	1.40907i	−0.0756427	−	0.0756427i	−0.743916	+	0.668273i	$0.767034\pi$
$348$	−3.93540	+	8.10008i	−0.210960	+	0.434210i
$349$	−6.11269	−	6.11269i	−0.327205	−	0.327205i	0.524318	−	0.851523i	$-0.324320\pi$
$349$	−6.11269	−	6.11269i	−0.327205	−	0.327205i	−0.851523	+	0.524318i	$0.824320\pi$
$350$	8.63620	+	0.0526499i	0.461624	+	0.00281426i
$351$	3.00149			0.160208
$352$	−4.71089	−	10.0028i	−0.251091	−	0.533154i
$353$			10.7150i			0.570304i	0.958482	+	0.285152i	$0.0920441\pi$
$353$			10.7150i			0.570304i	−0.958482	+	0.285152i	$0.907956\pi$
$354$	14.2989	−	8.95007i	0.759975	−	0.475691i
$355$	12.4234	+	22.5947i	0.659363	+	1.19920i
$356$	17.2455	+	8.37870i	0.914011	+	0.444070i
$357$	5.18370	+	5.18370i	0.274350	+	0.274350i
$358$	2.93028	−	12.7367i	0.154870	−	0.673157i
$359$			31.7234i			1.67430i	0.546975	+	0.837149i	$0.315779\pi$
$359$			31.7234i			1.67430i	−0.546975	+	0.837149i	$0.684221\pi$
$360$	3.62169	+	5.18492i	0.190880	+	0.273269i
$361$		−	0.245451i		−	0.0129185i
$362$	10.1940	+	2.34528i	0.535783	+	0.123265i
$363$	5.07682	+	5.07682i	0.266464	+	0.266464i
$364$	−2.39758	−	6.92875i	−0.125667	−	0.363165i
$365$	−2.56895	+	1.41250i	−0.134465	+	0.0739334i
$366$	10.5907	+	16.9200i	0.553587	+	0.884424i
$367$			31.8025i			1.66008i	0.557707	+	0.830038i	$0.311681\pi$
$367$			31.8025i			1.66008i	−0.557707	+	0.830038i	$0.688319\pi$
$368$	7.18960	+	9.14467i	0.374784	+	0.476699i
$369$	−2.38396			−0.124104
$370$	−2.98437	−	10.5135i	−0.155150	−	0.546570i
$371$	2.89246	+	2.89246i	0.150169	+	0.150169i
$372$	−2.53811	−	7.33486i	−0.131595	−	0.380295i
$373$	17.3861	+	17.3861i	0.900220	+	0.900220i	0.995455	−	0.0952347i	$-0.0303602\pi$
$373$	17.3861	+	17.3861i	0.900220	+	0.900220i	−0.0952347	+	0.995455i	$0.530360\pi$
$374$	−3.71984	+	16.1686i	−0.192348	+	0.836058i
$375$	−7.39524	−	8.38513i	−0.381888	−	0.433006i
$376$	−0.177073	−	1.64848i	−0.00913187	−	0.0850139i
$377$	−13.5149			−0.696054
$378$	0.387269	−	1.68330i	0.0199190	−	0.0865795i
$379$	−16.4215	+	16.4215i	−0.843513	+	0.843513i	−0.989314	−	0.145801i	$-0.953424\pi$
$379$	−16.4215	+	16.4215i	−0.843513	+	0.843513i	0.145801	+	0.989314i	$0.453424\pi$
$380$	12.9866	−	14.3680i	0.666200	−	0.737061i
$381$	6.83621	+	6.83621i	0.350229	+	0.350229i
$382$	9.85319	+	15.7417i	0.504133	+	0.805415i
$383$		−	9.00561i		−	0.460165i	−0.973171	−	0.230083i	$-0.926100\pi$
$383$		−	9.00561i		−	0.460165i	0.973171	−	0.230083i	$-0.0738997\pi$
$384$	11.3129	+	0.137109i	0.577308	+	0.00699679i
$385$	1.48894	−	5.12615i	0.0758835	−	0.261253i
$386$	23.9907	−	15.0165i	1.22109	−	0.764318i
$387$	−9.00811	+	9.00811i	−0.457908	+	0.457908i
$388$	17.0054	+	8.26201i	0.863317	+	0.419440i
$389$	1.84497	−	1.84497i	0.0935438	−	0.0935438i	−0.658786	−	0.752330i	$-0.728930\pi$
$389$	1.84497	−	1.84497i	0.0935438	−	0.0935438i	0.752330	+	0.658786i	$0.228930\pi$
$390$	−4.62372	+	8.28919i	−0.234131	+	0.419740i
$391$		−	17.4551i		−	0.882742i
$392$	15.4906	−	1.66394i	0.782394	−	0.0840418i
$393$	14.9005			0.751628
$394$	8.62860	−	37.5050i	0.434703	−	1.88947i
$395$	−24.6821	+	13.5711i	−1.24189	+	0.682836i
$396$	3.69420	−	1.27831i	0.185640	−	0.0642377i
$397$	−24.0894	+	24.0894i	−1.20901	+	1.20901i	−0.237663	+	0.971348i	$0.576381\pi$
$397$	−24.0894	+	24.0894i	−1.20901	+	1.20901i	−0.971348	+	0.237663i	$0.923619\pi$
$398$	−6.21224	+	3.88843i	−0.311392	+	0.194909i
$399$	−5.28931			−0.264797
$400$	−19.8983	+	2.01477i	−0.994913	+	0.100738i
$401$	−10.4494			−0.521817			−0.260909	−	0.965364i	$-0.584022\pi$
$401$	−10.4494			−0.521817			−0.260909	+	0.965364i	$0.584022\pi$
$402$	6.47945	−	4.05568i	0.323165	−	0.202279i
$403$	8.23650	−	8.23650i	0.410289	−	0.410289i
$404$	−10.7770	−	31.1445i	−0.536178	−	1.54950i
$405$	−1.95942	+	1.07735i	−0.0973641	+	0.0535342i
$406$	−1.74377	+	7.57945i	−0.0865420	+	0.376162i
$407$	−6.75496			−0.334831
$408$	−13.2178	−	10.6536i	−0.654378	−	0.527432i
$409$		−	6.67465i		−	0.330040i	−0.986290	−	0.165020i	$-0.947231\pi$
$409$		−	6.67465i		−	0.330040i	0.986290	−	0.165020i	$-0.0527689\pi$
$410$	3.67242	−	6.58376i	0.181368	−	0.325149i
$411$	−9.13506	+	9.13506i	−0.450599	+	0.450599i
$412$	−1.87916	+	3.86779i	−0.0925793	+	0.190552i
$413$	10.3016	−	10.3016i	0.506907	−	0.506907i
$414$	−3.48612	+	2.18206i	−0.171333	+	0.107243i
$415$	2.57238	−	8.85621i	0.126273	−	0.434734i
$416$	7.23421	+	15.3607i	0.354687	+	0.753123i
$417$		−	16.2851i		−	0.797487i
$418$	−6.35120	−	10.1468i	−0.310647	−	0.496297i
$419$	−15.8121	−	15.8121i	−0.772472	−	0.772472i	0.206066	−	0.978538i	$-0.433934\pi$
$419$	−15.8121	−	15.8121i	−0.772472	−	0.772472i	−0.978538	+	0.206066i	$0.933934\pi$
$420$	4.05217	+	3.66260i	0.197726	+	0.178716i
$421$	−1.69730	+	1.69730i	−0.0827211	+	0.0827211i	−0.747257	−	0.664536i	$-0.768629\pi$
$421$	−1.69730	+	1.69730i	−0.0827211	+	0.0827211i	0.664536	+	0.747257i	$0.268629\pi$
$422$	2.48107	−	10.7842i	0.120776	−	0.524965i
$423$	0.586179			0.0285010
$424$	−7.37541	−	5.94463i	−0.358182	−	0.288697i
$425$	25.3410	+	16.0775i	1.22922	+	0.779874i
$426$	−3.65635	+	15.8926i	−0.177151	+	0.770000i
$427$	12.1900	+	12.1900i	0.589915	+	0.589915i
$428$	−36.0823	+	12.4857i	−1.74410	+	0.603517i
$429$	4.14830	+	4.14830i	0.200282	+	0.200282i
$430$	−11.0009	−	38.7544i	−0.530509	−	1.86890i
$431$	7.28686			0.350996			0.175498	−	0.984480i	$-0.443847\pi$
$431$	7.28686			0.350996			0.175498	+	0.984480i	$0.443847\pi$
$432$	−0.475374	+	3.97165i	−0.0228714	+	0.191086i
$433$		−	2.13785i		−	0.102738i	−0.998680	−	0.0513692i	$-0.983641\pi$
$433$		−	2.13785i		−	0.102738i	0.998680	−	0.0513692i	$-0.0163585\pi$
$434$	−3.55648	−	5.68192i	−0.170716	−	0.272741i
$435$	8.82274	−	4.85105i	0.423018	−	0.232590i
$436$	−28.7653	+	9.95376i	−1.37761	+	0.476699i
$437$	8.90537	+	8.90537i	0.426002	+	0.426002i
$438$	−1.80694	−	0.415715i	−0.0863389	−	0.0198636i
$439$			33.2103i			1.58504i	0.609846	+	0.792520i	$0.291231\pi$
$439$			33.2103i			1.58504i	−0.609846	+	0.792520i	$0.708769\pi$
$440$	−2.16050	+	12.1714i	−0.102998	+	0.580251i
$441$			5.50826i			0.262298i
$442$	5.71233	−	24.8291i	0.271708	−	1.18100i
$443$	12.4343	+	12.4343i	0.590771	+	0.590771i	0.937840	−	0.347068i	$-0.112823\pi$
$443$	12.4343	+	12.4343i	0.590771	+	0.590771i	−0.347068	+	0.937840i	$0.612823\pi$
$444$	3.02055	−	6.21708i	0.143349	−	0.295050i
$445$	−10.3282	−	18.7841i	−0.489602	−	0.890452i
$446$	0.766691	−	0.479895i	0.0363039	−	0.0227237i
$447$		−	16.7364i		−	0.791604i
$448$	9.54802	−	2.07517i	0.451102	−	0.0980424i
$449$	10.8408			0.511607			0.255803	−	0.966729i	$-0.417660\pi$
$449$	10.8408			0.511607			0.255803	+	0.966729i	$0.417660\pi$
$450$	0.0431074	−	7.07094i	0.00203210	−	0.333327i
$451$	−3.29482	−	3.29482i	−0.155147	−	0.155147i
$452$	−22.7035	−	11.0304i	−1.06788	−	0.518829i
$453$	0.170363	+	0.170363i	0.00800436	+	0.00800436i
$454$	0.530529	+	0.122057i	0.0248990	+	0.00572840i
$455$	−2.28648	+	7.87190i	−0.107192	+	0.369041i
$456$	12.1789	−	1.30821i	0.570328	−	0.0612624i
$457$	32.6178			1.52580			0.762899	−	0.646518i	$-0.223776\pi$
$457$	32.6178			1.52580			0.762899	+	0.646518i	$0.223776\pi$
$458$	9.35667	+	2.15265i	0.437209	+	0.100587i
$459$	4.24418	−	4.24418i	0.198101	−	0.198101i
$460$	−0.655913	−	12.9890i	−0.0305821	−	0.605615i
$461$	−18.9449	−	18.9449i	−0.882353	−	0.882353i	0.111421	−	0.993773i	$-0.464460\pi$
$461$	−18.9449	−	18.9449i	−0.882353	−	0.882353i	−0.993773	+	0.111421i	$0.964460\pi$
$462$	2.86169	−	1.79122i	0.133138	−	0.0833349i
$463$		−	37.7663i		−	1.75515i	−0.479441	−	0.877574i	$-0.659160\pi$
$463$		−	37.7663i		−	1.75515i	0.479441	−	0.877574i	$-0.340840\pi$
$464$	2.14048	−	17.8833i	0.0993694	−	0.830212i
$465$	−2.42049	+	8.33330i	−0.112248	+	0.386448i
$466$	16.3592	+	26.1358i	0.757823	+	1.21072i
$467$	3.10601	−	3.10601i	0.143729	−	0.143729i	−0.631581	−	0.775310i	$-0.717594\pi$
$467$	3.10601	−	3.10601i	0.143729	−	0.143729i	0.775310	+	0.631581i	$0.217594\pi$
$468$	−5.67295	+	1.96303i	−0.262232	+	0.0907410i
$469$	4.66810	−	4.66810i	0.215553	−	0.215553i
$470$	−0.902993	+	1.61884i	−0.0416520	+	0.0746717i
$471$		−	10.1763i		−	0.468899i
$472$	−21.1719	+	26.2677i	−0.974517	+	1.20907i
$473$	−24.8999			−1.14490
$474$	−17.3609	−	3.99414i	−0.797411	−	0.183457i
$475$	−21.1312	+	4.72611i	−0.969566	+	0.216849i
$476$	−13.1876	−	6.40718i	−0.604454	−	0.293673i
$477$	2.36822	−	2.36822i	0.108433	−	0.108433i
$478$	1.51403	+	2.41885i	0.0692500	+	0.110635i
$479$	−8.23987			−0.376489			−0.188245	−	0.982122i	$-0.560280\pi$
$479$	−8.23987			−0.376489			−0.188245	+	0.982122i	$0.560280\pi$
$480$	−10.2362	−	7.43106i	−0.467215	−	0.339180i
$481$	10.3732			0.472976
$482$	11.6041	+	18.5391i	0.528554	+	0.844431i
$483$	−2.51157	+	2.51157i	−0.114280	+	0.114280i
$484$	−12.9157	−	6.27508i	−0.587079	−	0.285231i
$485$	−10.1843	−	18.5225i	−0.462446	−	0.841064i
$486$	−1.37821	−	0.317079i	−0.0625168	−	0.0143830i
$487$	−15.7527			−0.713822			−0.356911	−	0.934138i	$-0.616170\pi$
$487$	−15.7527			−0.713822			−0.356911	+	0.934138i	$0.616170\pi$
$488$	−31.0830	−	25.0530i	−1.40706	−	1.13410i
$489$			16.6094i			0.751104i
$490$	−15.2121	−	8.48534i	−0.687214	−	0.383329i
$491$	−9.14298	+	9.14298i	−0.412617	+	0.412617i	−0.882649	−	0.470032i	$-0.844242\pi$
$491$	−9.14298	+	9.14298i	−0.412617	+	0.412617i	0.470032	+	0.882649i	$0.344242\pi$
$492$	4.50578	−	1.55915i	0.203136	−	0.0702919i
$493$	−19.1104	+	19.1104i	−0.860691	+	0.860691i
$494$	9.75314	+	15.5818i	0.438814	+	0.701060i
$495$	−4.19706	−	1.21908i	−0.188644	−	0.0547935i
$496$	9.59426	+	12.2032i	0.430795	+	0.547941i
$497$			14.0840i			0.631754i
$498$	4.94401	−	3.09460i	0.221546	−	0.138672i
$499$	−5.93929	−	5.93929i	−0.265879	−	0.265879i	0.561558	−	0.827437i	$-0.310202\pi$
$499$	−5.93929	−	5.93929i	−0.265879	−	0.265879i	−0.827437	+	0.561558i	$0.810202\pi$
$500$	19.4613	+	11.0116i	0.870338	+	0.492456i
$501$	0.150909	−	0.150909i	0.00674213	−	0.00674213i
$502$	6.68580	+	1.53817i	0.298402	+	0.0686521i
$503$	−3.53406			−0.157576			−0.0787879	−	0.996891i	$-0.525105\pi$
$503$	−3.53406			−0.157576			−0.0787879	+	0.996891i	$0.525105\pi$
$504$	0.368951	+	3.43479i	0.0164344	+	0.152998i
$505$	−10.2776	+	35.3840i	−0.457349	+	1.57457i
$506$	−7.83388	−	1.80231i	−0.348259	−	0.0801224i
$507$	2.82210	+	2.82210i	0.125334	+	0.125334i
$508$	−17.3917	−	8.44972i	−0.771633	−	0.374896i
$509$	8.43955	+	8.43955i	0.374076	+	0.374076i	0.868960	−	0.494883i	$-0.164789\pi$
$509$	8.43955	+	8.43955i	0.374076	+	0.374076i	−0.494883	+	0.868960i	$0.664789\pi$
$510$	5.18307	+	18.2592i	0.229510	+	0.808529i
$511$	−1.60131			−0.0708376
$512$	−21.4715	+	7.13968i	−0.948915	+	0.315532i
$513$			4.33065i			0.191203i
$514$	23.1450	−	14.4871i	1.02088	−	0.638999i
$515$	4.21286	−	2.31638i	0.185641	−	0.102072i
$516$	11.1342	−	22.9172i	0.490158	−	1.00887i
$517$	0.810146	+	0.810146i	0.0356302	+	0.0356302i
$518$	1.33840	−	5.81749i	0.0588061	−	0.255606i
$519$		−	9.00739i		−	0.395380i
$520$	3.31775	−	18.6909i	0.145493	−	0.819651i
$521$		−	9.64810i		−	0.422691i	−0.977411	−	0.211345i	$-0.932216\pi$
$521$		−	9.64810i		−	0.422691i	0.977411	−	0.211345i	$-0.0677845\pi$
$522$	6.20572	+	1.42772i	0.271617	+	0.0624897i
$523$	−25.7409	−	25.7409i	−1.12557	−	1.12557i	−0.990889	−	0.134683i	$-0.956998\pi$
$523$	−25.7409	−	25.7409i	−1.12557	−	1.12557i	−0.134683	−	0.990889i	$-0.543002\pi$
$524$	−28.1625	+	9.74516i	−1.23028	+	0.425719i
$525$	−1.33290	−	5.95959i	−0.0581724	−	0.260098i
$526$	−6.94859	−	11.1012i	−0.302973	−	0.484037i
$527$		−	23.2932i		−	1.01467i
$528$	−6.14615	+	4.83214i	−0.267477	+	0.210292i
$529$	−14.5428			−0.632295
$530$	2.89211	+	10.1885i	0.125625	+	0.442559i
$531$	−8.43447	−	8.43447i	−0.366025	−	0.366025i
$532$	9.99703	−	3.45930i	0.433426	−	0.149980i
$533$	5.05965	+	5.05965i	0.219158	+	0.219158i
$534$	3.03970	−	13.2123i	0.131541	−	0.571753i
$535$	40.9939	+	11.9071i	1.77232	+	0.514788i
$536$	−9.59395	+	11.9031i	−0.414395	+	0.514134i
$537$	−9.24150			−0.398800
$538$	−2.55108	+	11.0885i	−0.109985	+	0.478059i
$539$	−7.61287	+	7.61287i	−0.327909	+	0.327909i
$540$	2.99877	−	3.31774i	0.129046	−	0.142773i
$541$	−19.2087	−	19.2087i	−0.825846	−	0.825846i	0.161093	−	0.986939i	$-0.448498\pi$
$541$	−19.2087	−	19.2087i	−0.825846	−	0.825846i	−0.986939	+	0.161093i	$0.948498\pi$
$542$	1.17492	+	1.87709i	0.0504673	+	0.0806278i
$543$		−	7.39653i		−	0.317415i
$544$	31.9498	+	11.4911i	1.36984	+	0.492677i
$545$	32.6810	+	9.49252i	1.39990	+	0.406615i
$546$	−4.39452	+	2.75066i	−0.188068	+	0.117717i
$547$	27.9722	−	27.9722i	1.19600	−	1.19600i	0.220652	−	0.975353i	$-0.429181\pi$
$547$	27.9722	−	27.9722i	1.19600	−	1.19600i	0.975353	−	0.220652i	$-0.0708185\pi$
$548$	11.2912	−	23.2402i	0.482335	−	0.992770i
$549$	9.98062	−	9.98062i	0.425963	−	0.425963i
$550$	9.83218	−	9.71303i	0.419246	−	0.414165i
$551$		−	19.4998i		−	0.830719i
$552$	5.16180	−	6.40418i	0.219701	−	0.272580i
$553$	−15.3852			−0.654244
$554$	5.06331	−	22.0081i	0.215119	−	0.935034i
$555$	−6.77175	+	3.72334i	−0.287445	+	0.158047i
$556$	10.6508	+	30.7796i	0.451693	+	1.30535i
$557$	−15.4266	+	15.4266i	−0.653647	+	0.653647i	−0.953869	−	0.300222i	$-0.902939\pi$
$557$	−15.4266	+	15.4266i	−0.653647	+	0.653647i	0.300222	+	0.953869i	$0.402939\pi$
$558$	−4.65210	+	2.91189i	−0.196939	+	0.123270i
$559$	38.2372			1.61726
$560$	−10.0542	−	4.27227i	−0.424867	−	0.180536i
$561$	11.7316			0.495308
$562$	−18.9423	+	11.8566i	−0.799034	+	0.500139i
$563$	−18.2389	+	18.2389i	−0.768676	+	0.768676i	−0.977874	−	0.209197i	$-0.932915\pi$
$563$	−18.2389	+	18.2389i	−0.768676	+	0.768676i	0.209197	+	0.977874i	$0.432915\pi$
$564$	−1.10790	+	0.383371i	−0.0466511	+	0.0161428i
$565$	13.5969	+	24.7290i	0.572025	+	1.04036i
$566$	1.04235	−	4.53067i	0.0438133	−	0.190438i
$567$	−1.22137			−0.0512926
$568$	−3.48340	−	32.4291i	−0.146160	−	1.36069i
$569$			34.0254i			1.42642i	0.700950	+	0.713210i	$0.252760\pi$
$569$			34.0254i			1.42642i	−0.700950	+	0.713210i	$0.747240\pi$
$570$	−11.9599	−	6.67126i	−0.500946	−	0.279428i
$571$	−17.9297	+	17.9297i	−0.750335	+	0.750335i	−0.974542	−	0.224207i	$-0.928021\pi$
$571$	−17.9297	+	17.9297i	−0.750335	+	0.750335i	0.224207	+	0.974542i	$0.428021\pi$
$572$	−10.5535	−	5.12741i	−0.441265	−	0.214388i
$573$	9.28556	−	9.28556i	0.387910	−	0.387910i
$574$	3.49038	−	2.18473i	0.145686	−	0.0911890i
$575$	−7.78976	+	12.2780i	−0.324855	+	0.512029i
$576$	−1.69905	−	7.81749i	−0.0707939	−	0.325729i
$577$			0.122769i			0.00511093i	0.999997	+	0.00255547i	$0.000813431\pi$
$577$			0.122769i			0.00511093i	−0.999997	+	0.00255547i	$0.999187\pi$
$578$	−14.2759	−	22.8076i	−0.593800	−	0.948669i
$579$	−14.1514	−	14.1514i	−0.588112	−	0.588112i
$580$	−13.5027	+	14.9389i	−0.560668	+	0.620304i
$581$	3.56190	−	3.56190i	0.147773	−	0.147773i
$582$	2.99737	−	13.0283i	0.124245	−	0.540042i
$583$	6.54614			0.271113
$584$	3.68708	−	0.396052i	0.152572	−	0.0163887i
$585$	6.44516	+	1.87206i	0.266475	+	0.0774003i
$586$	3.33691	−	14.5042i	0.137847	−	0.599162i
$587$	−6.93139	−	6.93139i	−0.286089	−	0.286089i	0.549443	−	0.835531i	$-0.314840\pi$
$587$	−6.93139	−	6.93139i	−0.286089	−	0.286089i	−0.835531	+	0.549443i	$0.814840\pi$
$588$	−3.60250	−	10.4109i	−0.148565	−	0.429336i
$589$	11.8839	+	11.8839i	0.489667	+	0.489667i
$590$	36.2865	−	10.3003i	1.49389	−	0.424057i
$591$	−27.2128			−1.11939
$592$	−1.64289	+	13.7261i	−0.0675225	+	0.564137i
$593$			21.4611i			0.881303i	0.897678	+	0.440652i	$0.145253\pi$
$593$			21.4611i			0.881303i	−0.897678	+	0.440652i	$0.854747\pi$
$594$	−1.46657	−	2.34302i	−0.0601740	−	0.0961355i
$595$	7.89793	+	14.3642i	0.323784	+	0.588874i
$596$	10.9459	+	31.6325i	0.448361	+	1.29572i
$597$	3.66442	+	3.66442i	0.149975	+	0.149975i
$598$	12.0300	+	2.76769i	0.491944	+	0.113179i
$599$			4.94482i			0.202040i	0.994884	+	0.101020i	$0.0322106\pi$
$599$			4.94482i			0.202040i	−0.994884	+	0.101020i	$0.967789\pi$
$600$	4.54304	+	13.3926i	0.185469	+	0.546749i
$601$		−	20.1862i		−	0.823414i	−0.911316	−	0.411707i	$-0.864933\pi$
$601$		−	20.1862i		−	0.823414i	0.911316	−	0.411707i	$-0.135067\pi$
$602$	4.93357	−	21.4442i	0.201077	−	0.874000i
$603$	−3.82203	−	3.82203i	−0.155645	−	0.155645i
$604$	−0.433414	−	0.210573i	−0.0176354	−	0.00856810i
$605$	7.73509	+	14.0680i	0.314476	+	0.571947i
$606$	−19.7532	+	12.3641i	−0.802421	+	0.502259i
$607$		−	23.8529i		−	0.968161i	−0.875024	−	0.484080i	$-0.839154\pi$
$607$		−	23.8529i		−	0.968161i	0.875024	−	0.484080i	$-0.160846\pi$
$608$	−22.1630	+	10.4378i	−0.898828	+	0.423307i
$609$	5.49949			0.222851
$610$	12.1885	+	42.9383i	0.493498	+	1.73852i
$611$	−1.24409	−	1.24409i	−0.0503305	−	0.0503305i
$612$	−5.24591	+	10.7974i	−0.212053	+	0.436461i
$613$	−24.1159	−	24.1159i	−0.974031	−	0.974031i	0.0256404	−	0.999671i	$-0.491838\pi$
$613$	−24.1159	−	24.1159i	−0.974031	−	0.974031i	−0.999671	+	0.0256404i	$0.991838\pi$
$614$	−6.40509	−	1.47359i	−0.258488	−	0.0594693i
$615$	−5.11912	−	1.48690i	−0.206423	−	0.0599576i
$616$	−4.23723	+	5.25707i	−0.170723	+	0.211813i
$617$	8.63876			0.347783			0.173892	−	0.984765i	$-0.444366\pi$
$617$	8.63876			0.347783			0.173892	+	0.984765i	$0.444366\pi$
$618$	2.96323	+	0.681738i	0.119199	+	0.0274235i
$619$	32.3601	−	32.3601i	1.30066	−	1.30066i	0.372716	−	0.927945i	$-0.378427\pi$
$619$	32.3601	−	32.3601i	1.30066	−	1.30066i	0.927945	−	0.372716i	$-0.121573\pi$
$620$	−0.875292	−	17.3333i	−0.0351526	−	0.696124i
$621$	2.05636	+	2.05636i	0.0825188	+	0.0825188i
$622$	34.7919	−	21.7773i	1.39503	−	0.873190i
$623$		−	11.7087i		−	0.469101i
$624$	9.43826	−	7.42041i	0.377833	−	0.297054i
$625$	−10.6500	−	22.6181i	−0.426002	−	0.904722i
$626$	−4.13306	−	6.60308i	−0.165190	−	0.263912i
$627$	−5.98531	+	5.98531i	−0.239030	+	0.239030i
$628$	6.65548	+	19.2336i	0.265582	+	0.767506i
$629$	14.6679	−	14.6679i	0.584848	−	0.584848i
$630$	1.88148	−	3.37304i	0.0749601	−	0.134385i
$631$		−	11.3652i		−	0.452443i	−0.974076	−	0.226222i	$-0.927363\pi$
$631$		−	11.3652i		−	0.452443i	0.974076	−	0.226222i	$-0.0726373\pi$
$632$	35.4250	−	3.80522i	1.40913	−	0.151363i
$633$	−7.82477			−0.311007
$634$	20.7385	+	4.77121i	0.823630	+	0.189489i
$635$	10.4157	+	18.9433i	0.413335	+	0.751744i
$636$	−2.92718	+	6.02489i	−0.116070	+	0.238902i
$637$	11.6906	−	11.6906i	0.463199	−	0.463199i
$638$	6.60357	+	10.5500i	0.261438	+	0.417680i
$639$	11.5314			0.456173
$640$	24.2069	+	7.35038i	0.956860	+	0.290549i
$641$	−13.9081			−0.549336			−0.274668	−	0.961539i	$-0.588568\pi$
$641$	−13.9081			−0.549336			−0.274668	+	0.961539i	$0.588568\pi$
$642$	14.3244	+	22.8850i	0.565339	+	0.903199i
$643$	−18.4850	+	18.4850i	−0.728977	+	0.728977i	−0.970416	−	0.241439i	$-0.922381\pi$
$643$	−18.4850	+	18.4850i	−0.728977	+	0.728977i	0.241439	+	0.970416i	$0.422381\pi$
$644$	3.10436	−	6.38957i	0.122329	−	0.251784i
$645$	−24.9618	+	13.7248i	−0.982868	+	0.540415i
$646$	35.8243	+	8.24193i	1.40949	+	0.324275i
$647$	−1.15900			−0.0455649			−0.0227825	−	0.999740i	$-0.507253\pi$
$647$	−1.15900			−0.0455649			−0.0227825	+	0.999740i	$0.507253\pi$
$648$	2.81225	−	0.302081i	0.110476	−	0.0118669i
$649$		−	23.3142i		−	0.915163i
$650$	−15.0987	+	14.9157i	−0.592219	+	0.585041i
$651$	−3.35159	+	3.35159i	−0.131359	+	0.131359i
$652$	−10.8629	−	31.3925i	−0.425422	−	1.22943i
$653$	−11.8412	+	11.8412i	−0.463383	+	0.463383i	−0.899763	−	0.436380i	$-0.856260\pi$
$653$	−11.8412	+	11.8412i	−0.463383	+	0.463383i	0.436380	+	0.899763i	$0.356260\pi$
$654$	11.4196	+	18.2443i	0.446543	+	0.713407i
$655$	31.9960	+	9.29358i	1.25019	+	0.363130i
$656$	−7.49641	+	5.89372i	−0.292686	+	0.230111i
$657$			1.31108i			0.0511500i
$658$	−0.858232	+	0.537192i	−0.0334573	+	0.0209419i
$659$	−1.22941	−	1.22941i	−0.0478909	−	0.0478909i	0.682756	−	0.730647i	$-0.260781\pi$
$659$	−1.22941	−	1.22941i	−0.0478909	−	0.0478909i	−0.730647	+	0.682756i	$0.760781\pi$
$660$	8.72992	−	0.440840i	0.339812	−	0.0171597i
$661$	13.2100	−	13.2100i	0.513810	−	0.513810i	−0.401882	−	0.915692i	$-0.631644\pi$
$661$	13.2100	−	13.2100i	0.513810	−	0.513810i	0.915692	+	0.401882i	$0.131644\pi$
$662$	−15.7521	−	3.62402i	−0.612223	−	0.140852i
$663$	−18.0155			−0.699663
$664$	−7.32047	+	9.08240i	−0.284089	+	0.352466i
$665$	−11.3578	−	3.29900i	−0.440438	−	0.127930i
$666$	−4.76310	−	1.09583i	−0.184566	−	0.0424624i
$667$	−9.25924	−	9.25924i	−0.358519	−	0.358519i
$668$	−0.186528	+	0.383922i	−0.00721697	+	0.0148544i
$669$	−0.452248	−	0.452248i	−0.0174849	−	0.0174849i
$670$	16.4430	−	4.66753i	0.635249	−	0.180323i
$671$	27.5880			1.06502
$672$	−2.94374	−	6.25059i	−0.113557	−	0.241122i
$673$		−	4.69175i		−	0.180854i	−0.995903	−	0.0904268i	$-0.971177\pi$
$673$		−	4.69175i		−	0.180854i	0.995903	−	0.0904268i	$-0.0288231\pi$
$674$	−29.2612	+	18.3155i	−1.12710	+	0.705486i
$675$	−4.87945	+	1.09132i	−0.187810	+	0.0420048i
$676$	−7.17959	−	3.48818i	−0.276138	−	0.134161i
$677$	36.1893	+	36.1893i	1.39087	+	1.39087i	0.823385	+	0.567483i	$0.192083\pi$
$677$	36.1893	+	36.1893i	1.39087	+	1.39087i	0.567483	+	0.823385i	$0.307917\pi$
$678$	−4.00173	+	17.3939i	−0.153686	+	0.668007i
$679$		−	11.5457i		−	0.443083i
$680$	−21.7380	−	31.1208i	−0.833615	−	1.19343i
$681$		−	0.384941i		−	0.0147510i
$682$	−10.4540	−	2.40511i	−0.400306	−	0.0920966i
$683$	18.7839	+	18.7839i	0.718744	+	0.718744i	0.968348	−	0.249604i	$-0.0803004\pi$
$683$	18.7839	+	18.7839i	0.718744	+	0.718744i	−0.249604	+	0.968348i	$0.580300\pi$
$684$	−2.83232	−	8.18512i	−0.108297	−	0.312966i
$685$	−25.3135	+	13.9183i	−0.967181	+	0.531790i
$686$	−11.4630	−	18.3135i	−0.437658	−	0.699213i
$687$		−	6.78901i		−	0.259017i
$688$	−6.05597	+	50.5964i	−0.230882	+	1.92897i
$689$	−10.0525			−0.382969
$690$	−8.84679	+	2.51126i	−0.336792	+	0.0956020i
$691$	12.0077	+	12.0077i	0.456795	+	0.456795i	0.897602	−	0.440807i	$-0.145308\pi$
$691$	12.0077	+	12.0077i	0.456795	+	0.456795i	−0.440807	+	0.897602i	$0.645308\pi$
$692$	5.89099	+	17.0243i	0.223942	+	0.647168i
$693$	−1.68803	−	1.68803i	−0.0641228	−	0.0641228i
$694$	0.631850	−	2.74639i	0.0239847	−	0.104251i
$695$	10.1572	−	34.9694i	0.385286	−	1.32647i
$696$	−12.6628	+	1.36019i	−0.479983	+	0.0515579i
$697$	14.3089			0.541990
$698$	2.74104	−	11.9141i	0.103750	−	0.450957i
$699$	15.4167	−	15.4167i	0.583114	−	0.583114i
$700$	6.41691	+	10.3922i	0.242536	+	0.392786i
$701$	−18.6671	−	18.6671i	−0.705046	−	0.705046i	0.260443	−	0.965489i	$-0.416131\pi$
$701$	−18.6671	−	18.6671i	−0.705046	−	0.705046i	−0.965489	+	0.260443i	$0.916131\pi$
$702$	2.25212	+	3.59804i	0.0850007	+	0.135799i
$703$			14.9668i			0.564482i
$704$	8.45618	−	13.1526i	0.318704	−	0.495709i
$705$	1.25871	+	0.365606i	0.0474059	+	0.0137695i
$706$	−12.8447	+	8.03985i	−0.483415	+	0.302584i
$707$	−14.2312	+	14.2312i	−0.535219	+	0.535219i
$708$	21.4578	+	10.4252i	0.806433	+	0.391803i
$709$	−0.320563	+	0.320563i	−0.0120390	+	0.0120390i	−0.713101	−	0.701062i	$-0.752710\pi$
$709$	−0.320563	+	0.320563i	−0.0120390	+	0.0120390i	0.701062	+	0.713101i	$0.252710\pi$
$710$	−17.7638	+	31.8460i	−0.666662	+	1.19516i
$711$			12.5967i			0.472413i
$712$	2.89593	+	26.9599i	0.108529	+	1.01036i
$713$	11.2858			0.422658
$714$	−2.32446	+	10.1035i	−0.0869907	+	0.378112i
$715$	6.32039	+	11.4951i	0.236369	+	0.429892i
$716$	17.4668	−	6.04410i	0.652766	−	0.225879i
$717$	1.42681	−	1.42681i	0.0532850	−	0.0532850i
$718$	−38.0284	+	23.8031i	−1.41921	+	0.888324i
$719$	−48.8907			−1.82332			−0.911658	−	0.410951i	$-0.865197\pi$
$719$	−48.8907			−1.82332			−0.911658	+	0.410951i	$0.865197\pi$
$720$	−3.49794	+	8.23191i	−0.130361	+	0.306785i
$721$	2.62601			0.0977977
$722$	0.294234	−	0.184170i	0.0109503	−	0.00685409i
$723$	10.9356	−	10.9356i	0.406701	−	0.406701i
$724$	4.83746	+	13.9798i	0.179783	+	0.519554i
$725$	21.9709	−	4.91391i	0.815978	−	0.182498i
$726$	−2.27653	+	9.89514i	−0.0844900	+	0.367243i
$727$	−24.5201			−0.909401			−0.454700	−	0.890644i	$-0.650254\pi$
$727$	−24.5201			−0.909401			−0.454700	+	0.890644i	$0.650254\pi$
$728$	6.50685	−	8.07296i	0.241160	−	0.299204i
$729$			1.00000i			0.0370370i
$730$	−3.62079	−	2.01968i	−0.134012	−	0.0747517i
$731$	54.0683	−	54.0683i	1.99979	−	1.99979i
$732$	−12.3363	+	25.3913i	−0.455963	+	0.938489i
$733$	27.3958	−	27.3958i	1.01189	−	1.01189i	0.0119594	−	0.999928i	$-0.496193\pi$
$733$	27.3958	−	27.3958i	1.01189	−	1.01189i	0.999928	−	0.0119594i	$-0.00380688\pi$
$734$	−38.1232	+	23.8624i	−1.40715	+	0.880779i
$735$	−3.43557	+	11.8280i	−0.126723	+	0.436283i
$736$	−5.56758	+	15.4801i	−0.205224	+	0.570603i
$737$		−	10.5647i		−	0.389156i
$738$	−1.78876	−	2.85777i	−0.0658452	−	0.105196i
$739$	19.1011	+	19.1011i	0.702644	+	0.702644i	0.964977	−	0.262333i	$-0.0844919\pi$
$739$	19.1011	+	19.1011i	0.702644	+	0.702644i	−0.262333	+	0.964977i	$0.584492\pi$
$740$	10.3638	−	11.4661i	0.380979	−	0.421503i
$741$	9.19127	−	9.19127i	0.337650	−	0.337650i
$742$	−1.29703	+	5.63765i	−0.0476154	+	0.206964i
$743$	−0.305994			−0.0112258			−0.00561291	−	0.999984i	$-0.501787\pi$
$743$	−0.305994			−0.0112258			−0.00561291	+	0.999984i	$0.501787\pi$
$744$	6.88824	−	8.54614i	0.252535	−	0.313317i
$745$	10.4387	−	35.9384i	0.382443	−	1.31668i
$746$	−7.79624	+	33.8870i	−0.285441	+	1.24069i
$747$	−2.91633	−	2.91633i	−0.106703	−	0.106703i
$748$	−22.1732	+	7.67267i	−0.810733	+	0.280541i
$749$	16.4874	+	16.4874i	0.602438	+	0.602438i
$750$	4.50279	−	15.1567i	0.164419	−	0.553444i
$751$	−7.13631			−0.260408			−0.130204	−	0.991487i	$-0.541563\pi$
$751$	−7.13631			−0.260408			−0.130204	+	0.991487i	$0.541563\pi$
$752$	1.84325	−	1.44918i	0.0672165	−	0.0528460i
$753$		−	4.85108i		−	0.176783i
$754$	−10.1407	−	16.2010i	−0.369302	−	0.590006i
$755$	0.259567	+	0.472082i	0.00944660	+	0.0171808i
$756$	2.30843	−	0.798795i	0.0839569	−	0.0290519i
$757$	−25.8469	−	25.8469i	−0.939422	−	0.939422i	0.0588455	−	0.998267i	$-0.481258\pi$
$757$	−25.8469	−	25.8469i	−0.939422	−	0.939422i	−0.998267	+	0.0588455i	$0.981258\pi$
$758$	−32.0068	−	7.36366i	−1.16254	−	0.267460i
$759$			5.68410i			0.206320i
$760$	26.9679	+	4.78696i	0.978228	+	0.173641i
$761$		−	11.9718i		−	0.433979i	−0.976174	−	0.216989i	$-0.930376\pi$
$761$		−	11.9718i		−	0.433979i	0.976174	−	0.216989i	$-0.0696237\pi$
$762$	−3.06547	+	13.3243i	−0.111050	+	0.482690i
$763$	13.1440	+	13.1440i	0.475846	+	0.475846i
$764$	−11.4772	+	23.6230i	−0.415230	+	0.854651i
$765$	11.7608	−	6.46647i	0.425211	−	0.233796i
$766$	10.7955	−	6.75721i	0.390056	−	0.244148i
$767$			35.8022i			1.29274i
$768$	8.32406	+	13.6642i	0.300369	+	0.493064i
$769$	−27.2266			−0.981816			−0.490908	−	0.871211i	$-0.663335\pi$
$769$	−27.2266			−0.981816			−0.490908	+	0.871211i	$0.663335\pi$
$770$	7.26217	−	2.06145i	0.261710	−	0.0742894i
$771$	−13.6525	−	13.6525i	−0.491684	−	0.491684i
$772$	36.0020	+	17.4915i	1.29574	+	0.629532i
$773$	−8.83729	−	8.83729i	−0.317855	−	0.317855i	0.530088	−	0.847943i	$-0.322159\pi$
$773$	−8.83729	−	8.83729i	−0.317855	−	0.317855i	−0.847943	+	0.530088i	$0.822159\pi$
$774$	−17.5575	−	4.03939i	−0.631093	−	0.145193i
$775$	−10.3951	+	16.3846i	−0.373405	+	0.588552i
$776$	2.85560	+	26.5844i	0.102510	+	0.954326i
$777$	−4.22105			−0.151429
$778$	3.59600	+	0.827316i	0.128923	+	0.0296607i
$779$	−7.30024	+	7.30024i	−0.261558	+	0.261558i
$780$	−13.4060	+	0.676971i	−0.480012	+	0.0242394i
$781$	15.9373	+	15.9373i	0.570280	+	0.570280i
$782$	20.9243	−	13.0971i	0.748251	−	0.468352i
$783$		−	4.50274i		−	0.160915i
$784$	13.6178	+	17.3209i	0.486349	+	0.618602i
$785$	6.34707	−	21.8518i	0.226537	−	0.779923i
$786$	11.1803	+	17.8619i	0.398788	+	0.637113i
$787$	21.7150	−	21.7150i	0.774058	−	0.774058i	−0.204755	−	0.978813i	$-0.565640\pi$
$787$	21.7150	−	21.7150i	0.774058	−	0.774058i	0.978813	+	0.204755i	$0.0656399\pi$
$788$	51.4334	−	17.7977i	1.83224	−	0.634015i
$789$	−6.54829	+	6.54829i	−0.233125	+	0.233125i
$790$	−34.7882	−	19.4049i	−1.23771	−	0.690394i
$791$			15.4144i			0.548073i
$792$	4.30426	+	3.46926i	0.152945	+	0.123275i
$793$	−42.3652			−1.50443
$794$	−46.9522	−	10.8021i	−1.66627	−	0.383352i
$795$	6.56241	−	3.60824i	0.232745	−	0.127971i
$796$	−9.32250	−	4.52931i	−0.330427	−	0.160537i
$797$	28.4134	−	28.4134i	1.00645	−	1.00645i	0.00647582	−	0.999979i	$-0.497939\pi$
$797$	28.4134	−	28.4134i	1.00645	−	1.00645i	0.999979	−	0.00647582i	$-0.00206133\pi$
$798$	−3.96874	−	6.34056i	−0.140492	−	0.224453i
$799$	−3.51835			−0.124470
$800$	−17.3455	−	22.3413i	−0.613257	−	0.789884i
$801$	−9.58659			−0.338726
$802$	−7.84051	−	12.5262i	−0.276858	−	0.442315i
$803$	−1.81201	+	1.81201i	−0.0639446	+	0.0639446i
$804$	9.72348	+	4.72413i	0.342921	+	0.166607i
$805$	−6.95963	+	3.82664i	−0.245295	+	0.134871i
$806$	16.0536	+	3.69338i	0.565464	+	0.130094i
$807$	8.04558			0.283218
$808$	29.2481	−	36.2877i	1.02894	−	1.27660i
$809$		−	26.4356i		−	0.929426i	−0.885461	−	0.464713i	$-0.846158\pi$
$809$		−	26.4356i		−	0.929426i	0.885461	−	0.464713i	$-0.153842\pi$
$810$	−2.76169	−	1.54047i	−0.0970359	−	0.0541267i
$811$	15.0962	−	15.0962i	0.530100	−	0.530100i	−0.390502	−	0.920602i	$-0.627699\pi$
$811$	15.0962	−	15.0962i	0.530100	−	0.530100i	0.920602	+	0.390502i	$0.127699\pi$
$812$	−10.3943	+	3.59677i	−0.364768	+	0.126222i
$813$	1.10724	−	1.10724i	0.0388325	−	0.0388325i
$814$	−5.06847	−	8.09751i	−0.177650	−	0.283817i
$815$	−10.3595	+	35.6657i	−0.362877	+	1.24932i
$816$	2.85328	−	23.8386i	0.0998846	−	0.834516i
$817$			55.1699i			1.93015i
$818$	8.00123	−	5.00821i	0.279757	−	0.175108i
$819$	2.59220	+	2.59220i	0.0905787	+	0.0905787i
$820$	10.6478	−	0.537689i	0.371838	−	0.0187769i
$821$	−29.4997	+	29.4997i	−1.02955	+	1.02955i	−0.0299962	+	0.999550i	$0.509550\pi$
$821$	−29.4997	+	29.4997i	−1.02955	+	1.02955i	−0.999550	+	0.0299962i	$0.990450\pi$
$822$	−17.8050	−	4.09632i	−0.621020	−	0.142875i
$823$	21.2908			0.742152			0.371076	−	0.928602i	$-0.378989\pi$
$823$	21.2908			0.742152			0.371076	+	0.928602i	$0.378989\pi$
$824$	−6.04650	+	0.649492i	−0.210640	+	0.0226261i
$825$	−8.25208	−	5.23551i	−0.287301	−	0.182277i
$826$	20.0786	+	4.61940i	0.698624	+	0.160729i
$827$	−14.4619	−	14.4619i	−0.502888	−	0.502888i	0.409446	−	0.912334i	$-0.365722\pi$
$827$	−14.4619	−	14.4619i	−0.502888	−	0.502888i	−0.912334	+	0.409446i	$0.865722\pi$
$828$	−5.23150	−	2.54171i	−0.181807	−	0.0883305i
$829$	5.64651	+	5.64651i	0.196111	+	0.196111i	0.798331	−	0.602219i	$-0.205717\pi$
$829$	5.64651	+	5.64651i	0.196111	+	0.196111i	−0.602219	+	0.798331i	$0.705717\pi$
$830$	12.5465	−	3.56147i	0.435496	−	0.123620i
$831$	−15.9686			−0.553945
$832$	−12.9856	+	20.1977i	−0.450196	+	0.700229i
$833$		−	33.0616i		−	1.14552i
$834$	19.5218	−	12.2193i	0.675985	−	0.423119i
$835$	0.418175	−	0.229927i	0.0144715	−	0.00795695i
$836$	7.39799	−	15.2270i	0.255865	−	0.526636i
$837$	2.74413	+	2.74413i	0.0948512	+	0.0948512i
$838$	7.09042	−	30.8191i	0.244934	−	1.06463i
$839$		−	21.4686i		−	0.741178i	−0.928797	−	0.370589i	$-0.879156\pi$
$839$		−	21.4686i		−	0.741178i	0.928797	−	0.370589i	$-0.120844\pi$
$840$	−1.35006	+	7.60571i	−0.0465814	+	0.262422i
$841$		−	8.72534i		−	0.300874i
$842$	−3.30817	−	0.761096i	−0.114007	−	0.0262291i
$843$	11.1735	+	11.1735i	0.384836	+	0.384836i
$844$	14.7891	−	5.11754i	0.509063	−	0.176153i
$845$	4.29977	+	7.82012i	0.147917	+	0.269020i
$846$	0.439829	+	0.702682i	0.0151216	+	0.0241587i
$847$			8.76905i			0.301308i
$848$	1.59210	−	13.3017i	0.0546731	−	0.456783i
$849$	−3.28736			−0.112822
$850$	−0.258738	+	42.4410i	−0.00887465	+	1.45571i
$851$	7.10678	+	7.10678i	0.243617	+	0.243617i
$852$	−21.7948	+	7.54171i	−0.746676	+	0.258375i
$853$	5.10917	+	5.10917i	0.174935	+	0.174935i	0.789143	−	0.614209i	$-0.210525\pi$
$853$	5.10917	+	5.10917i	0.174935	+	0.174935i	−0.614209	+	0.789143i	$0.710525\pi$
$854$	−5.46620	+	23.7593i	−0.187050	+	0.813027i
$855$	−2.70108	+	9.29930i	−0.0923748	+	0.318029i
$856$	−42.0409	−	33.8852i	−1.43693	−	1.15817i
$857$	7.14205			0.243968			0.121984	−	0.992532i	$-0.461074\pi$
$857$	7.14205			0.243968			0.121984	+	0.992532i	$0.461074\pi$
$858$	−1.86017	+	8.08538i	−0.0635051	+	0.276030i
$859$	12.9070	−	12.9070i	0.440381	−	0.440381i	−0.451759	−	0.892140i	$-0.649203\pi$
$859$	12.9070	−	12.9070i	0.440381	−	0.440381i	0.892140	+	0.451759i	$0.149203\pi$
$860$	38.2025	−	42.2660i	1.30269	−	1.44126i
$861$	−2.05887	−	2.05887i	−0.0701662	−	0.0701662i
$862$	5.46757	+	8.73512i	0.186226	+	0.297519i
$863$			34.4382i			1.17229i	0.810206	+	0.586145i	$0.199355\pi$
$863$			34.4382i			1.17229i	−0.810206	+	0.586145i	$0.800645\pi$
$864$	−5.11770	+	2.41021i	−0.174108	+	0.0819969i
$865$	5.61801	−	19.3417i	0.191018	−	0.657639i
$866$	2.56274	−	1.60410i	0.0870856	−	0.0545094i
$867$	−13.4535	+	13.4535i	−0.456905	+	0.456905i
$868$	4.14265	−	8.52665i	0.140611	−	0.289413i
$869$	−17.4096	+	17.4096i	−0.590581	+	0.590581i
$870$	12.4352	+	6.93635i	0.421592	+	0.235164i
$871$			16.2236i			0.549715i
$872$	−33.5156	−	27.0138i	−1.13498	−	0.914803i
$873$	−9.45309			−0.319939
$874$	−3.99332	+	17.3573i	−0.135076	+	0.587119i
$875$	0.854909	−	13.6285i	0.0289012	−	0.460727i
$876$	−0.857468	−	2.47799i	−0.0289712	−	0.0837236i
$877$	20.5999	−	20.5999i	0.695609	−	0.695609i	−0.267851	−	0.963460i	$-0.586314\pi$
$877$	20.5999	−	20.5999i	0.695609	−	0.695609i	0.963460	+	0.267851i	$0.0863136\pi$
$878$	−39.8108	+	24.9187i	−1.34355	+	0.840967i
$879$	−10.5239			−0.354963
$880$	−16.2116	+	6.54273i	−0.546493	+	0.220555i
$881$	22.0289			0.742171			0.371086	−	0.928599i	$-0.378986\pi$
$881$	22.0289			0.742171			0.371086	+	0.928599i	$0.378986\pi$
$882$	−6.60303	+	4.13303i	−0.222336	+	0.139166i
$883$	−15.2149	+	15.2149i	−0.512022	+	0.512022i	−0.915146	−	0.403123i	$-0.867925\pi$
$883$	−15.2149	+	15.2149i	−0.512022	+	0.512022i	0.403123	+	0.915146i	$0.367925\pi$
$884$	34.0500	−	11.7824i	1.14523	−	0.396286i
$885$	−12.8508	−	23.3722i	−0.431976	−	0.785647i
$886$	−5.57575	+	24.2355i	−0.187321	+	0.814207i
$887$	41.6823			1.39956			0.699778	−	0.714361i	$-0.253282\pi$
$887$	41.6823			1.39956			0.699778	+	0.714361i	$0.253282\pi$
$888$	9.71915	−	1.04399i	0.326153	−	0.0350341i
$889$			11.8080i			0.396027i
$890$	14.7679	−	26.4752i	0.495021	−	0.887451i
$891$	−1.38208	+	1.38208i	−0.0463014	+	0.0463014i
$892$	1.15055	+	0.558990i	0.0385232	+	0.0187164i
$893$	1.79502	−	1.79502i	0.0600679	−	0.0600679i
$894$	20.0627	−	12.5579i	0.670999	−	0.419998i
$895$	−19.8445	−	5.76403i	−0.663327	−	0.192670i
$896$	9.65180	+	9.88862i	0.322444	+	0.330356i
$897$		−	8.72872i		−	0.291444i
$898$	8.13417	+	12.9953i	0.271441	+	0.433660i
$899$	−12.3561	−	12.3561i	−0.412100	−	0.412100i
$900$	8.50863	−	5.25388i	0.283621	−	0.175129i
$901$	−14.2145	+	14.2145i	−0.473552	+	0.473552i
$902$	1.47745	−	6.42188i	0.0491938	−	0.213825i
$903$	−15.5595			−0.517786
$904$	−3.81245	−	35.4924i	−0.126800	−	1.18046i
$905$	4.61330	−	15.8827i	0.153351	−	0.527959i
$906$	−0.0763937	+	0.332052i	−0.00253801	+	0.0110317i
$907$	−27.7322	−	27.7322i	−0.920834	−	0.920834i	0.0762544	−	0.997088i	$-0.475704\pi$
$907$	−27.7322	−	27.7322i	−0.920834	−	0.920834i	−0.997088	+	0.0762544i	$0.975704\pi$
$908$	0.251758	+	0.727555i	0.00835489	+	0.0241448i
$909$	11.6519	+	11.6519i	0.386468	+	0.386468i
$910$	−11.1521	+	3.16564i	−0.369687	+	0.104940i
$911$	32.3043			1.07029			0.535145	−	0.844760i	$-0.320257\pi$
$911$	32.3043			1.07029			0.535145	+	0.844760i	$0.320257\pi$
$912$	10.7064	+	13.6178i	0.354525	+	0.450931i
$913$		−	8.06119i		−	0.266787i
$914$	24.4742	+	39.1006i	0.809535	+	1.29333i
$915$	27.6566	−	15.2066i	0.914299	−	0.502714i
$916$	4.44013	+	12.8315i	0.146706	+	0.423965i
$917$	12.8686	+	12.8686i	0.424958	+	0.424958i
$918$	8.27226	+	1.90316i	0.273025	+	0.0628137i
$919$			54.5387i			1.79907i	0.436853	+	0.899533i	$0.356093\pi$
$919$			54.5387i			1.79907i	−0.436853	+	0.899533i	$0.643907\pi$
$920$	15.0784	−	10.5323i	0.497120	−	0.347241i
$921$			4.64740i			0.153137i
$922$	8.49522	−	36.9252i	0.279775	−	1.21607i
$923$	−24.4739	−	24.4739i	−0.805567	−	0.805567i
$924$	4.29444	+	2.08644i	0.141277	+	0.0686389i
$925$	−16.8634	+	3.77159i	−0.554465	+	0.124009i
$926$	45.2723	−	28.3373i	1.48774	−	0.931221i
$927$		−	2.15006i		−	0.0706172i
$928$	23.0437	−	10.8525i	0.756446	−	0.356252i
$929$	−41.8714			−1.37375			−0.686877	−	0.726773i	$-0.741019\pi$
$929$	−41.8714			−1.37375			−0.686877	+	0.726773i	$0.741019\pi$
$930$	−11.8057	+	3.35119i	−0.387125	+	0.109890i
$931$	16.8676	+	16.8676i	0.552813	+	0.552813i
$932$	−19.0555	+	39.2211i	−0.624182	+	1.28473i
$933$	−20.5227	−	20.5227i	−0.671884	−	0.671884i
$934$	6.05387	+	1.39279i	0.198089	+	0.0455734i
$935$	25.1915	+	7.31713i	0.823850	+	0.239296i
$936$	−6.60978	−	5.32752i	−0.216047	−	0.174135i
$937$	12.5314			0.409384			0.204692	−	0.978826i	$-0.434381\pi$
$937$	12.5314			0.409384			0.204692	+	0.978826i	$0.434381\pi$
$938$	9.09851	+	2.09326i	0.297077	+	0.0683472i
$939$	−3.89496	+	3.89496i	−0.127107	+	0.127107i
$940$	−2.61814	+	0.132210i	−0.0853941	+	0.00431220i
$941$	40.1881	+	40.1881i	1.31009	+	1.31009i	0.921343	+	0.388751i	$0.127093\pi$
$941$	40.1881	+	40.1881i	1.31009	+	1.31009i	0.388751	+	0.921343i	$0.372907\pi$
$942$	12.1988	−	7.63561i	0.397459	−	0.248782i
$943$			6.93285i			0.225765i
$944$	−47.3744	−	5.67032i	−1.54191	−	0.184553i
$945$	−2.62266	−	0.761780i	−0.0853153	−	0.0247807i
$946$	−18.6832	−	29.8487i	−0.607443	−	0.970465i
$947$	−26.2243	+	26.2243i	−0.852174	+	0.852174i	−0.990401	−	0.138227i	$-0.955860\pi$
$947$	−26.2243	+	26.2243i	−0.852174	+	0.852174i	0.138227	+	0.990401i	$0.455860\pi$
$948$	−8.23845	−	23.8083i	−0.267572	−	0.773257i
$949$	2.78260	−	2.78260i	0.0903270	−	0.0903270i
$950$	−21.5209	−	21.7849i	−0.698229	−	0.706794i
$951$		−	15.0474i		−	0.487945i
$952$	−2.21451	−	20.6162i	−0.0717727	−	0.668175i
$953$	2.51475			0.0814607			0.0407304	−	0.999170i	$-0.487032\pi$
$953$	2.51475			0.0814607			0.0407304	+	0.999170i	$0.487032\pi$
$954$	4.61585	+	1.06195i	0.149444	+	0.0343819i
$955$	25.7306	−	14.1476i	0.832622	−	0.457804i
$956$	−1.76357	+	3.62988i	−0.0570378	+	0.117399i
$957$	6.22315	−	6.22315i	0.201166	−	0.201166i
$958$	−6.18264	−	9.87754i	−0.199752	−	0.319129i
$959$	−15.7787			−0.509522
$960$	1.22744	−	17.8464i	0.0396156	−	0.575990i
$961$	−15.9395			−0.514176
$962$	7.78333	+	12.4348i	0.250945	+	0.400915i
$963$	13.4992	−	13.4992i	0.435005	−	0.435005i
$964$	−13.5167	+	27.8209i	−0.435344	+	0.896051i
$965$	−21.5612	−	39.2139i	−0.694079	−	1.26234i
$966$	−4.89525	−	1.12623i	−0.157502	−	0.0362358i
$967$	−51.5088			−1.65641			−0.828205	−	0.560425i	$-0.810638\pi$
$967$	−51.5088			−1.65641			−0.828205	+	0.560425i	$0.810638\pi$
$968$	−2.16885	−	20.1911i	−0.0697096	−	0.648967i
$969$		−	25.9933i		−	0.835026i
$970$	14.5622	−	26.1065i	0.467565	−	0.838230i
$971$	−26.0586	+	26.0586i	−0.836259	+	0.836259i	−0.988364	−	0.152105i	$-0.951395\pi$
$971$	−26.0586	+	26.0586i	−0.836259	+	0.836259i	0.152105	+	0.988364i	$0.451395\pi$
$972$	−0.654018	−	1.89004i	−0.0209776	−	0.0606231i
$973$	14.0644	−	14.0644i	0.450885	−	0.450885i
$974$	−11.8198	−	18.8835i	−0.378729	−	0.605067i
$975$	12.6722	+	8.03984i	0.405835	+	0.257481i
$976$	6.70977	−	56.0588i	0.214774	−	1.79440i
$977$		−	17.6258i		−	0.563899i	−0.959429	−	0.281950i	$-0.909019\pi$
$977$		−	17.6258i		−	0.563899i	0.959429	−	0.281950i	$-0.0909811\pi$
$978$	−19.9105	+	12.4626i	−0.636669	+	0.398510i
$979$	−13.2494	−	13.2494i	−0.423454	−	0.423454i
$980$	−1.24236	−	24.6024i	−0.0396857	−	0.785894i
$981$	10.7618	−	10.7618i	0.343596	−	0.343596i
$982$	−17.8204	−	4.09987i	−0.568672	−	0.130832i
$983$	−1.64257			−0.0523899			−0.0261949	−	0.999657i	$-0.508339\pi$
$983$	−1.64257			−0.0523899			−0.0261949	+	0.999657i	$0.508339\pi$
$984$	5.24987	+	4.23142i	0.167360	+	0.134893i
$985$	−58.4346	−	16.9729i	−1.86188	−	0.540803i
$986$	−37.2478	−	8.56944i	−1.18621	−	0.272907i
$987$	0.506245	+	0.506245i	0.0161140	+	0.0161140i
$988$	−11.3606	+	23.3831i	−0.361430	+	0.743917i
$989$	26.1967	+	26.1967i	0.833008	+	0.833008i
$990$	−1.68782	−	5.94594i	−0.0536425	−	0.188974i
$991$	−62.3434			−1.98040			−0.990202	−	0.139642i	$-0.955405\pi$
$991$	−62.3434			−1.98040			−0.990202	+	0.139642i	$0.955405\pi$
$992$	−7.42974	+	20.6576i	−0.235894	+	0.655879i
$993$			11.4294i			0.362701i
$994$	−16.8832	+	10.5677i	−0.535503	+	0.335187i
$995$	5.58314	+	10.1542i	0.176997	+	0.321910i
$996$	7.41931	+	3.60465i	0.235090	+	0.114218i
$997$	−30.0563	−	30.0563i	−0.951891	−	0.951891i	0.0470037	−	0.998895i	$-0.485033\pi$
$997$	−30.0563	−	30.0563i	−0.951891	−	0.951891i	−0.998895	+	0.0470037i	$0.985033\pi$
$998$	2.66328	−	11.5762i	0.0843047	−	0.366437i
$999$			3.45601i			0.109343i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	240.2.bl.a.109.17	yes	48
3.2	odd	2		720.2.bm.h.109.8		48
4.3	odd	2		960.2.bl.a.529.11		48
5.4	even	2	inner	240.2.bl.a.109.8	✓	48
8.3	odd	2		1920.2.bl.b.289.17		48
8.5	even	2		1920.2.bl.a.289.8		48
15.14	odd	2		720.2.bm.h.109.17		48
16.3	odd	4		1920.2.bl.b.1249.8		48
16.5	even	4	inner	240.2.bl.a.229.8	yes	48
16.11	odd	4		960.2.bl.a.49.20		48
16.13	even	4		1920.2.bl.a.1249.17		48
20.19	odd	2		960.2.bl.a.529.20		48
40.19	odd	2		1920.2.bl.b.289.8		48
40.29	even	2		1920.2.bl.a.289.17		48
48.5	odd	4		720.2.bm.h.469.17		48
80.19	odd	4		1920.2.bl.b.1249.17		48
80.29	even	4		1920.2.bl.a.1249.8		48
80.59	odd	4		960.2.bl.a.49.11		48
80.69	even	4	inner	240.2.bl.a.229.17	yes	48
240.149	odd	4		720.2.bm.h.469.8		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
240.2.bl.a.109.8	✓	48	5.4	even	2	inner
240.2.bl.a.109.17	yes	48	1.1	even	1	trivial
240.2.bl.a.229.8	yes	48	16.5	even	4	inner
240.2.bl.a.229.17	yes	48	80.69	even	4	inner
720.2.bm.h.109.8		48	3.2	odd	2
720.2.bm.h.109.17		48	15.14	odd	2
720.2.bm.h.469.8		48	240.149	odd	4
720.2.bm.h.469.17		48	48.5	odd	4
960.2.bl.a.49.11		48	80.59	odd	4
960.2.bl.a.49.20		48	16.11	odd	4
960.2.bl.a.529.11		48	4.3	odd	2
960.2.bl.a.529.20		48	20.19	odd	2
1920.2.bl.a.289.8		48	8.5	even	2
1920.2.bl.a.289.17		48	40.29	even	2
1920.2.bl.a.1249.8		48	80.29	even	4
1920.2.bl.a.1249.17		48	16.13	even	4
1920.2.bl.b.289.8		48	40.19	odd	2
1920.2.bl.b.289.17		48	8.3	odd	2
1920.2.bl.b.1249.8		48	16.3	odd	4
1920.2.bl.b.1249.17		48	80.19	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 240 = 2^{4} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	240.bl (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.750333 + 1.19875i) q^{2} +(0.707107 - 0.707107i) q^{3} +(-0.874002 + 1.79892i) q^{4} +(1.95942 - 1.07735i) q^{5} +(1.37821 + 0.317079i) q^{6} +1.22137 q^{7} +(-2.81225 + 0.302081i) q^{8} -1.00000i q^{9} +O(q^{10})\)	\(q+(0.750333 + 1.19875i) q^{2} +(0.707107 - 0.707107i) q^{3} +(-0.874002 + 1.79892i) q^{4} +(1.95942 - 1.07735i) q^{5} +(1.37821 + 0.317079i) q^{6} +1.22137 q^{7} +(-2.81225 + 0.302081i) q^{8} -1.00000i q^{9} +(2.76169 + 1.54047i) q^{10} +(1.38208 - 1.38208i) q^{11} +(0.654018 + 1.89004i) q^{12} +(-2.12237 + 2.12237i) q^{13} +(0.916431 + 1.46411i) q^{14} +(0.623711 - 2.14732i) q^{15} +(-2.47224 - 3.14452i) q^{16} +6.00218i q^{17} +(1.19875 - 0.750333i) q^{18} +(-3.06223 - 3.06223i) q^{19} +(0.225545 + 4.46644i) q^{20} +(0.863636 - 0.863636i) q^{21} +(2.69379 + 0.619748i) q^{22} -2.90813 q^{23} +(-1.77496 + 2.20216i) q^{24} +(2.67861 - 4.22197i) q^{25} +(-4.13668 - 0.951709i) q^{26} +(-0.707107 - 0.707107i) q^{27} +(-1.06748 + 2.19714i) q^{28} +(3.18392 + 3.18392i) q^{29} +(3.04209 - 0.863531i) q^{30} -3.88079 q^{31} +(1.91449 - 5.32304i) q^{32} -1.95456i q^{33} +(-7.19511 + 4.50363i) q^{34} +(2.39316 - 1.31584i) q^{35} +(1.79892 + 0.874002i) q^{36} +(-2.44376 - 2.44376i) q^{37} +(1.37316 - 5.96855i) q^{38} +3.00149i q^{39} +(-5.18492 + 3.62169i) q^{40} -2.38396i q^{41} +(1.68330 + 0.387269i) q^{42} +(-9.00811 - 9.00811i) q^{43} +(1.27831 + 3.69420i) q^{44} +(-1.07735 - 1.95942i) q^{45} +(-2.18206 - 3.48612i) q^{46} +0.586179i q^{47} +(-3.97165 - 0.475374i) q^{48} -5.50826 q^{49} +(7.07094 + 0.0431074i) q^{50} +(4.24418 + 4.24418i) q^{51} +(-1.96303 - 5.67295i) q^{52} +(2.36822 + 2.36822i) q^{53} +(0.317079 - 1.37821i) q^{54} +(1.21908 - 4.19706i) q^{55} +(-3.43479 + 0.368951i) q^{56} -4.33065 q^{57} +(-1.42772 + 6.20572i) q^{58} +(8.43447 - 8.43447i) q^{59} +(3.31774 + 2.99877i) q^{60} +(9.98062 + 9.98062i) q^{61} +(-2.91189 - 4.65210i) q^{62} -1.22137i q^{63} +(7.81749 - 1.69905i) q^{64} +(-1.87206 + 6.44516i) q^{65} +(2.34302 - 1.46657i) q^{66} +(3.82203 - 3.82203i) q^{67} +(-10.7974 - 5.24591i) q^{68} +(-2.05636 + 2.05636i) q^{69} +(3.37304 + 1.88148i) q^{70} +11.5314i q^{71} +(0.302081 + 2.81225i) q^{72} -1.31108 q^{73} +(1.09583 - 4.76310i) q^{74} +(-1.09132 - 4.87945i) q^{75} +(8.18512 - 2.83232i) q^{76} +(1.68803 - 1.68803i) q^{77} +(-3.59804 + 2.25212i) q^{78} -12.5967 q^{79} +(-8.23191 - 3.49794i) q^{80} -1.00000 q^{81} +(2.85777 - 1.78876i) q^{82} +(2.91633 - 2.91633i) q^{83} +(0.798795 + 2.30843i) q^{84} +(6.46647 + 11.7608i) q^{85} +(4.03939 - 17.5575i) q^{86} +4.50274 q^{87} +(-3.46926 + 4.30426i) q^{88} -9.58659i q^{89} +(1.54047 - 2.76169i) q^{90} +(-2.59220 + 2.59220i) q^{91} +(2.54171 - 5.23150i) q^{92} +(-2.74413 + 2.74413i) q^{93} +(-0.702682 + 0.439829i) q^{94} +(-9.29930 - 2.70108i) q^{95} +(-2.41021 - 5.11770i) q^{96} -9.45309i q^{97} +(-4.13303 - 6.60303i) q^{98} +(-1.38208 - 1.38208i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q+O(q^{10}) \) 48 * q	\( 48 q + 12 q^{10} - 16 q^{14} - 4 q^{16} + 8 q^{19} - 4 q^{24} - 40 q^{26} - 8 q^{30} - 48 q^{31} - 28 q^{34} + 24 q^{35} - 4 q^{36} - 16 q^{40} - 40 q^{44} - 4 q^{46} + 48 q^{49} - 32 q^{50} + 8 q^{51} - 4 q^{54} + 48 q^{56} - 32 q^{59} - 24 q^{60} + 16 q^{61} + 48 q^{64} + 16 q^{65} + 24 q^{66} - 16 q^{69} + 40 q^{74} - 16 q^{75} + 60 q^{76} - 96 q^{79} + 72 q^{80} - 48 q^{81} + 16 q^{86} + 8 q^{90} - 32 q^{91} + 44 q^{94} - 48 q^{95} - 40 q^{96}+O(q^{100}) \) 48 * q + 12 * q^10 - 16 * q^14 - 4 * q^16 + 8 * q^19 - 4 * q^24 - 40 * q^26 - 8 * q^30 - 48 * q^31 - 28 * q^34 + 24 * q^35 - 4 * q^36 - 16 * q^40 - 40 * q^44 - 4 * q^46 + 48 * q^49 - 32 * q^50 + 8 * q^51 - 4 * q^54 + 48 * q^56 - 32 * q^59 - 24 * q^60 + 16 * q^61 + 48 * q^64 + 16 * q^65 + 24 * q^66 - 16 * q^69 + 40 * q^74 - 16 * q^75 + 60 * q^76 - 96 * q^79 + 72 * q^80 - 48 * q^81 + 16 * q^86 + 8 * q^90 - 32 * q^91 + 44 * q^94 - 48 * q^95 - 40 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more