LMFDB - Embedded newform 300.2.w.a.67.7

Newspace parameters

Level:	$ N $	$=$	$ 300 = 2^{2} \cdot 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	300.w (of order $20$, degree $8$, minimal)

Newform invariants

Self dual:	no
Analytic conductor:	$2.39551206064$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$30$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			67.7
Character	$\chi$	$=$	300.67
Dual form			300.2.w.a.103.7

$q$-expansion

$f(q)$	$=$	$q+(-1.12003 - 0.863445i) q^{2} +(-0.987688 - 0.156434i) q^{3} +(0.508925 + 1.93417i) q^{4} +(-1.70279 + 1.44932i) q^{5} +(0.971166 + 1.02803i) q^{6} +(1.87554 - 1.87554i) q^{7} +(1.10004 - 2.60575i) q^{8} +(0.951057 + 0.309017i) q^{9} +O(q^{10})$	\(q+(-1.12003 - 0.863445i) q^{2} +(-0.987688 - 0.156434i) q^{3} +(0.508925 + 1.93417i) q^{4} +(-1.70279 + 1.44932i) q^{5} +(0.971166 + 1.02803i) q^{6} +(1.87554 - 1.87554i) q^{7} +(1.10004 - 2.60575i) q^{8} +(0.951057 + 0.309017i) q^{9} +(3.15857 - 0.153014i) q^{10} +(-2.91356 + 0.946674i) q^{11} +(-0.200089 - 1.98997i) q^{12} +(-1.26064 - 2.47414i) q^{13} +(-3.72009 + 0.481232i) q^{14} +(1.90854 - 1.16510i) q^{15} +(-3.48199 + 1.96869i) q^{16} +(-0.901092 - 5.68927i) q^{17} +(-0.798391 - 1.16729i) q^{18} +(-3.66420 - 2.66220i) q^{19} +(-3.66981 - 2.55588i) q^{20} +(-2.14585 + 1.55905i) q^{21} +(4.08067 + 1.45540i) q^{22} +(-3.07781 + 6.04055i) q^{23} +(-1.49412 + 2.40158i) q^{24} +(0.798959 - 4.93575i) q^{25} +(-0.724334 + 3.85959i) q^{26} +(-0.891007 - 0.453990i) q^{27} +(4.58212 + 2.67310i) q^{28} +(-4.48892 - 6.17846i) q^{29} +(-3.14362 - 0.342980i) q^{30} +(1.14385 - 1.57437i) q^{31} +(5.59978 + 0.801520i) q^{32} +(3.02578 - 0.479237i) q^{33} +(-3.90312 + 7.15018i) q^{34} +(-0.475391 + 5.91190i) q^{35} +(-0.113673 + 1.99677i) q^{36} +(-4.87556 + 2.48422i) q^{37} +(1.80534 + 6.14557i) q^{38} +(0.858075 + 2.64088i) q^{39} +(1.90343 + 6.03133i) q^{40} +(-1.46647 + 4.51334i) q^{41} +(3.74957 + 0.106643i) q^{42} +(-0.964168 - 0.964168i) q^{43} +(-3.31381 - 5.15353i) q^{44} +(-2.06731 + 0.852193i) q^{45} +(8.66292 - 4.10806i) q^{46} +(1.87467 - 11.8362i) q^{47} +(3.74709 - 1.39975i) q^{48} -0.0353135i q^{49} +(-5.15661 + 4.83832i) q^{50} +5.76019i q^{51} +(4.14382 - 3.69743i) q^{52} +(1.98116 - 12.5085i) q^{53} +(0.605956 + 1.27782i) q^{54} +(3.58914 - 5.83466i) q^{55} +(-2.82403 - 6.95035i) q^{56} +(3.20263 + 3.20263i) q^{57} +(-0.307052 + 10.7960i) q^{58} +(1.89101 - 5.81992i) q^{59} +(3.22480 + 3.09849i) q^{60} +(2.51370 + 7.73638i) q^{61} +(-2.64052 + 0.775690i) q^{62} +(2.36332 - 1.20417i) q^{63} +(-5.57984 - 5.73283i) q^{64} +(5.73240 + 2.38586i) q^{65} +(-3.80276 - 2.07584i) q^{66} +(-1.31873 + 0.208866i) q^{67} +(10.5454 - 4.63827i) q^{68} +(3.98487 - 5.48470i) q^{69} +(5.63705 - 6.21102i) q^{70} +(7.46718 + 10.2777i) q^{71} +(1.85142 - 2.13828i) q^{72} +(-3.04977 - 1.55394i) q^{73} +(7.60576 + 1.42738i) q^{74} +(-1.56124 + 4.75000i) q^{75} +(3.28432 - 8.44202i) q^{76} +(-3.68898 + 7.24004i) q^{77} +(1.31919 - 3.69876i) q^{78} +(-0.348097 + 0.252907i) q^{79} +(3.07583 - 8.39877i) q^{80} +(0.809017 + 0.587785i) q^{81} +(5.53951 - 3.78884i) q^{82} +(1.82263 + 11.5076i) q^{83} +(-4.10754 - 3.35699i) q^{84} +(9.77992 + 8.38164i) q^{85} +(0.247389 + 1.91240i) q^{86} +(3.46713 + 6.80462i) q^{87} +(-0.738228 + 8.63339i) q^{88} +(2.37328 - 0.771124i) q^{89} +(3.05127 + 0.830528i) q^{90} +(-7.00472 - 2.27597i) q^{91} +(-13.2498 - 2.87881i) q^{92} +(-1.37605 + 1.37605i) q^{93} +(-12.3196 + 11.6382i) q^{94} +(10.0977 - 0.777436i) q^{95} +(-5.40545 - 1.66765i) q^{96} +(-12.2095 - 1.93379i) q^{97} +(-0.0304912 + 0.0395521i) q^{98} -3.06350 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240q + 12q^{8} + O(q^{10}) $	$ 240q + 12q^{8} + 8q^{10} + 8q^{12} + 4q^{13} + 20q^{17} - 20q^{20} - 12q^{22} + 20q^{25} + 4q^{28} - 8q^{30} - 20q^{32} - 8q^{33} - 4q^{37} - 76q^{38} - 92q^{40} - 20q^{42} - 140q^{44} - 4q^{45} - 16q^{48} - 164q^{50} - 172q^{52} - 4q^{53} - 120q^{58} + 20q^{60} - 44q^{62} - 60q^{64} - 20q^{65} + 16q^{68} - 44q^{70} + 12q^{72} - 44q^{73} - 48q^{77} + 24q^{78} - 4q^{80} + 60q^{81} + 24q^{82} + 80q^{84} - 64q^{85} + 60q^{88} - 260q^{89} + 48q^{90} + 144q^{92} - 64q^{93} + 40q^{94} - 20q^{96} - 180q^{97} + 256q^{98} + O(q^{100}) $

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/300\mathbb{Z}\right)^\times$.

$n$	$101$	$151$	$277$
$\chi(n)$	$1$	$-1$	$e\left(\frac{13}{20}\right)$

Coefficient data

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

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

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

$2$	−1.12003	−	0.863445i	−0.791979	−	0.610548i
$2$	−1.12003	−	0.863445i	−0.791979	−	0.610548i
$3$	−0.987688	−	0.156434i	−0.570242	−	0.0903175i
$3$	−0.987688	−	0.156434i	−0.570242	−	0.0903175i
$4$	0.508925	+	1.93417i	0.254463	+	0.967083i
$5$	−1.70279	+	1.44932i	−0.761509	+	0.648154i
$5$	−1.70279	+	1.44932i	−0.761509	+	0.648154i
$6$	0.971166	+	1.02803i	0.396477	+	0.419690i
$7$	1.87554	−	1.87554i	0.708888	−	0.708888i	−0.257413	−	0.966301i	$-0.582870\pi$
$7$	1.87554	−	1.87554i	0.708888	−	0.708888i	0.966301	+	0.257413i	$0.0828702\pi$
$8$	1.10004	−	2.60575i	0.388921	−	0.921271i
$9$	0.951057	+	0.309017i	0.317019	+	0.103006i
$10$	3.15857	−	0.153014i	0.998829	−	0.0483872i
$11$	−2.91356	+	0.946674i	−0.878472	+	0.285433i	−0.713323	−	0.700836i	$-0.752811\pi$
$11$	−2.91356	+	0.946674i	−0.878472	+	0.285433i	−0.165149	+	0.986269i	$0.552811\pi$
$12$	−0.200089	−	1.98997i	−0.0577608	−	0.574454i
$13$	−1.26064	−	2.47414i	−0.349637	−	0.686202i	0.647479	−	0.762083i	$-0.275823\pi$
$13$	−1.26064	−	2.47414i	−0.349637	−	0.686202i	−0.997117	+	0.0758808i	$0.975823\pi$
$14$	−3.72009	+	0.481232i	−0.994235	+	0.128615i
$15$	1.90854	−	1.16510i	0.492784	−	0.300827i
$16$	−3.48199	+	1.96869i	−0.870498	+	0.492173i
$17$	−0.901092	−	5.68927i	−0.218547	−	1.37985i	−0.816049	−	0.577983i	$-0.803840\pi$
$17$	−0.901092	−	5.68927i	−0.218547	−	1.37985i	0.597502	−	0.801867i	$-0.296160\pi$
$18$	−0.798391	−	1.16729i	−0.188182	−	0.275134i
$19$	−3.66420	−	2.66220i	−0.840625	−	0.610750i	0.0819203	−	0.996639i	$-0.473895\pi$
$19$	−3.66420	−	2.66220i	−0.840625	−	0.610750i	−0.922545	+	0.385889i	$0.873895\pi$
$20$	−3.66981	−	2.55588i	−0.820594	−	0.571511i
$21$	−2.14585	+	1.55905i	−0.468263	+	0.340213i
$22$	4.08067	+	1.45540i	0.870002	+	0.310292i
$23$	−3.07781	+	6.04055i	−0.641768	+	1.25954i	0.309419	+	0.950926i	$0.399866\pi$
$23$	−3.07781	+	6.04055i	−0.641768	+	1.25954i	−0.951187	+	0.308615i	$0.900134\pi$
$24$	−1.49412	+	2.40158i	−0.304986	+	0.490221i
$25$	0.798959	−	4.93575i	0.159792	−	0.987151i
$26$	−0.724334	+	3.85959i	−0.142054	+	0.756928i
$27$	−0.891007	−	0.453990i	−0.171474	−	0.0873705i
$28$	4.58212	+	2.67310i	0.865939	+	0.505168i
$29$	−4.48892	−	6.17846i	−0.833571	−	1.14731i	−0.987248	−	0.159191i	$-0.949112\pi$
$29$	−4.48892	−	6.17846i	−0.833571	−	1.14731i	0.153677	−	0.988121i	$-0.450888\pi$
$30$	−3.14362	−	0.342980i	−0.573944	−	0.0626193i
$31$	1.14385	−	1.57437i	0.205441	−	0.282765i	−0.693847	−	0.720123i	$-0.744086\pi$
$31$	1.14385	−	1.57437i	0.205441	−	0.282765i	0.899288	+	0.437357i	$0.144086\pi$
$32$	5.59978	+	0.801520i	0.989911	+	0.141690i
$33$	3.02578	−	0.479237i	0.526721	−	0.0834245i
$34$	−3.90312	+	7.15018i	−0.669380	+	1.22625i
$35$	−0.475391	+	5.91190i	−0.0803557	+	0.999294i
$36$	−0.113673	+	1.99677i	−0.0189456	+	0.332794i
$37$	−4.87556	+	2.48422i	−0.801538	+	0.408404i	−0.806243	−	0.591585i	$-0.798502\pi$
$37$	−4.87556	+	2.48422i	−0.801538	+	0.408404i	0.00470480	+	0.999989i	$0.498502\pi$
$38$	1.80534	+	6.14557i	0.292866	+	0.996943i
$39$	0.858075	+	2.64088i	0.137402	+	0.422880i
$40$	1.90343	+	6.03133i	0.300959	+	0.953637i
$41$	−1.46647	+	4.51334i	−0.229024	+	0.704865i	0.768834	+	0.639449i	$0.220837\pi$
$41$	−1.46647	+	4.51334i	−0.229024	+	0.704865i	−0.997858	+	0.0654159i	$0.979163\pi$
$42$	3.74957	+	0.106643i	0.578571	+	0.0164553i
$43$	−0.964168	−	0.964168i	−0.147034	−	0.147034i	0.629758	−	0.776792i	$-0.283154\pi$
$43$	−0.964168	−	0.964168i	−0.147034	−	0.147034i	−0.776792	+	0.629758i	$0.783154\pi$
$44$	−3.31381	−	5.15353i	−0.499576	−	0.776923i
$45$	−2.06731	+	0.852193i	−0.308176	+	0.127037i
$46$	8.66292	−	4.10806i	1.27728	−	0.605700i
$47$	1.87467	−	11.8362i	0.273449	−	1.72649i	−0.343209	−	0.939259i	$-0.611514\pi$
$47$	1.87467	−	11.8362i	0.273449	−	1.72649i	0.616658	−	0.787231i	$-0.288486\pi$
$48$	3.74709	−	1.39975i	0.540846	−	0.202036i
$49$		−	0.0353135i		−	0.00504478i
$50$	−5.15661	+	4.83832i	−0.729255	+	0.684242i
$51$			5.76019i			0.806587i
$52$	4.14382	−	3.69743i	0.574644	−	0.512741i
$53$	1.98116	−	12.5085i	0.272133	−	1.71818i	−0.351266	−	0.936276i	$-0.614249\pi$
$53$	1.98116	−	12.5085i	0.272133	−	1.71818i	0.623399	−	0.781904i	$-0.285751\pi$
$54$	0.605956	+	1.27782i	0.0824602	+	0.173889i
$55$	3.58914	−	5.83466i	0.483960	−	0.786745i
$56$	−2.82403	−	6.95035i	−0.377376	−	0.928780i
$57$	3.20263	+	3.20263i	0.424198	+	0.424198i
$58$	−0.307052	+	10.7960i	−0.0403179	+	1.41758i
$59$	1.89101	−	5.81992i	0.246188	−	0.757690i	−0.749250	−	0.662287i	$-0.769586\pi$
$59$	1.89101	−	5.81992i	0.246188	−	0.757690i	0.995439	−	0.0954029i	$-0.0304139\pi$
$60$	3.22480	+	3.09849i	0.416320	+	0.400014i
$61$	2.51370	+	7.73638i	0.321846	+	0.990542i	0.972844	+	0.231462i	$0.0743508\pi$
$61$	2.51370	+	7.73638i	0.321846	+	0.990542i	−0.650998	+	0.759080i	$0.725649\pi$
$62$	−2.64052	+	0.775690i	−0.335347	+	0.0985127i
$63$	2.36332	−	1.20417i	0.297750	−	0.151711i
$64$	−5.57984	−	5.73283i	−0.697481	−	0.716604i
$65$	5.73240	+	2.38586i	0.711017	+	0.295930i
$66$	−3.80276	−	2.07584i	−0.468087	−	0.255518i
$67$	−1.31873	+	0.208866i	−0.161108	+	0.0255170i	−0.236467	−	0.971639i	$-0.575990\pi$
$67$	−1.31873	+	0.208866i	−0.161108	+	0.0255170i	0.0753593	+	0.997156i	$0.475990\pi$
$68$	10.5454	−	4.63827i	1.27882	−	0.562473i
$69$	3.98487	−	5.48470i	0.479722	−	0.660280i
$70$	5.63705	−	6.21102i	0.673757	−	0.742359i
$71$	7.46718	+	10.2777i	0.886192	+	1.21974i	0.974667	+	0.223660i	$0.0718005\pi$
$71$	7.46718	+	10.2777i	0.886192	+	1.21974i	−0.0884755	+	0.996078i	$0.528199\pi$
$72$	1.85142	−	2.13828i	0.218191	−	0.251999i
$73$	−3.04977	−	1.55394i	−0.356949	−	0.181874i	0.266315	−	0.963886i	$-0.414194\pi$
$73$	−3.04977	−	1.55394i	−0.356949	−	0.181874i	−0.623264	+	0.782012i	$0.714194\pi$
$74$	7.60576	+	1.42738i	0.884152	+	0.165930i
$75$	−1.56124	+	4.75000i	−0.180277	+	0.548483i
$76$	3.28432	−	8.44202i	0.376738	−	0.968367i
$77$	−3.68898	+	7.24004i	−0.420399	+	0.825079i
$78$	1.31919	−	3.69876i	0.149369	−	0.418802i
$79$	−0.348097	+	0.252907i	−0.0391640	+	0.0284543i	−0.607195	−	0.794553i	$-0.707705\pi$
$79$	−0.348097	+	0.252907i	−0.0391640	+	0.0284543i	0.568031	+	0.823007i	$0.307705\pi$
$80$	3.07583	−	8.39877i	0.343888	−	0.939011i
$81$	0.809017	+	0.587785i	0.0898908	+	0.0653095i
$82$	5.53951	−	3.78884i	0.611736	−	0.418408i
$83$	1.82263	+	11.5076i	0.200060	+	1.26313i	0.859408	+	0.511291i	$0.170832\pi$
$83$	1.82263	+	11.5076i	0.200060	+	1.26313i	−0.659348	+	0.751838i	$0.729168\pi$
$84$	−4.10754	−	3.35699i	−0.448169	−	0.366277i
$85$	9.77992	+	8.38164i	1.06078	+	0.909116i
$86$	0.247389	+	1.91240i	0.0266766	+	0.206219i
$87$	3.46713	+	6.80462i	0.371715	+	0.729531i
$88$	−0.738228	+	8.63339i	−0.0786954	+	0.920322i
$89$	2.37328	−	0.771124i	0.251567	−	0.0817390i	−0.180519	−	0.983571i	$-0.557778\pi$
$89$	2.37328	−	0.771124i	0.251567	−	0.0817390i	0.432086	+	0.901832i	$0.357778\pi$
$90$	3.05127	+	0.830528i	0.321632	+	0.0875454i
$91$	−7.00472	−	2.27597i	−0.734294	−	0.238587i
$92$	−13.2498	−	2.87881i	−1.38139	−	0.300137i
$93$	−1.37605	+	1.37605i	−0.142690	+	0.142690i
$94$	−12.3196	+	11.6382i	−1.27067	+	1.20039i
$95$	10.0977	−	0.777436i	1.03600	−	0.0797633i
$96$	−5.40545	−	1.66765i	−0.551692	−	0.170204i
$97$	−12.2095	−	1.93379i	−1.23968	−	0.196346i	−0.498047	−	0.867150i	$-0.665949\pi$
$97$	−12.2095	−	1.93379i	−1.23968	−	0.196346i	−0.741635	+	0.670804i	$0.765949\pi$
$98$	−0.0304912	+	0.0395521i	−0.00308008	+	0.00399536i
$99$	−3.06350			−0.307893
$100$	9.95317	−	0.966609i	0.995317	−	0.0966609i
$101$	5.29258			0.526631			0.263315	−	0.964710i	$-0.415184\pi$
$101$	5.29258			0.526631			0.263315	+	0.964710i	$0.415184\pi$
$102$	4.97361	−	6.45157i	0.492460	−	0.638801i
$103$	5.18961	+	0.821954i	0.511348	+	0.0809895i	0.406776	−	0.913528i	$-0.366653\pi$
$103$	5.18961	+	0.821954i	0.511348	+	0.0809895i	0.104572	+	0.994517i	$0.466653\pi$
$104$	−7.83372	+	0.563261i	−0.768159	+	0.0552323i
$105$	1.39436	−	5.76475i	0.136076	−	0.562582i
$106$	−13.0194	+	12.2993i	−1.26455	+	1.19461i
$107$	−3.87709	+	3.87709i	−0.374812	+	0.374812i	−0.869226	−	0.494414i	$-0.835383\pi$
$107$	−3.87709	+	3.87709i	−0.374812	+	0.374812i	0.494414	+	0.869226i	$0.335383\pi$
$108$	0.424637	−	1.95440i	0.0408607	−	0.188062i
$109$	13.2787	+	4.31450i	1.27186	+	0.413254i	0.865708	−	0.500550i	$-0.166869\pi$
$109$	13.2787	+	4.31450i	1.27186	+	0.413254i	0.406156	+	0.913804i	$0.366869\pi$
$110$	−9.05785	+	3.43595i	−0.863632	+	0.327605i
$111$	5.20416	−	1.69093i	0.493957	−	0.160496i
$112$	−2.83826	+	10.2230i	−0.268190	+	0.965981i
$113$	−0.889930	−	1.74659i	−0.0837175	−	0.164305i	0.845352	−	0.534209i	$-0.179391\pi$
$113$	−0.889930	−	1.74659i	−0.0837175	−	0.164305i	−0.929070	+	0.369904i	$0.879391\pi$
$114$	−0.821739	−	6.35232i	−0.0769629	−	0.594950i
$115$	−3.51381	−	14.7465i	−0.327665	−	1.37512i
$116$	9.66565	−	11.8267i	0.897433	−	1.09808i
$117$	−0.434385	−	2.74260i	−0.0401589	−	0.253554i
$118$	−7.14317	+	4.88570i	−0.657582	+	0.449765i
$119$	−12.3605	−	8.98043i	−1.13308	−	0.823234i
$120$	−0.936488	−	6.25484i	−0.0854893	−	0.570986i
$121$	−1.30653	+	0.949249i	−0.118775	+	0.0862954i
$122$	3.86452	−	10.8354i	0.349877	−	0.980991i
$123$	2.15446	−	4.22836i	0.194261	−	0.381259i
$124$	3.62722	+	1.41115i	0.325734	+	0.126725i
$125$	5.79302	+	9.56248i	0.518143	+	0.855294i
$126$	−3.68672	−	0.691891i	−0.328439	−	0.0616386i
$127$	−10.9630	−	5.58595i	−0.972812	−	0.495673i	−0.106032	−	0.994363i	$-0.533815\pi$
$127$	−10.9630	−	5.58595i	−0.972812	−	0.495673i	−0.866780	+	0.498690i	$0.833815\pi$
$128$	1.29960	+	11.2388i	0.114869	+	0.993381i
$129$	0.801468	+	1.10313i	0.0705653	+	0.0971249i
$130$	−4.36039	−	7.62185i	−0.382431	−	0.668480i
$131$	0.398490	−	0.548475i	0.0348163	−	0.0479205i	−0.791254	−	0.611488i	$-0.790571\pi$
$131$	0.398490	−	0.548475i	0.0348163	−	0.0479205i	0.826070	+	0.563567i	$0.190571\pi$
$132$	2.46682	+	5.60847i	0.214709	+	0.488155i
$133$	−11.8654	+	1.87930i	−1.02886	+	0.162956i
$134$	1.65735	+	0.904712i	0.143174	+	0.0781552i
$135$	2.17517	−	0.518303i	0.187209	−	0.0446084i
$136$	−15.8160	−	3.91038i	−1.35621	−	0.335312i
$137$	−17.7950	+	9.06702i	−1.52033	+	0.774648i	−0.996994	−	0.0774774i	$-0.975313\pi$
$137$	−17.7950	+	9.06702i	−1.52033	+	0.774648i	−0.523338	+	0.852125i	$0.675313\pi$
$138$	−9.19890	+	2.70230i	−0.783063	+	0.230035i
$139$	−0.0167604	−	0.0515832i	−0.00142160	−	0.00437523i	0.950343	−	0.311204i	$-0.100732\pi$
$139$	−0.0167604	−	0.0515832i	−0.00142160	−	0.00437523i	−0.951765	+	0.306829i	$0.900732\pi$
$140$	−11.6765	+	2.08923i	−0.986847	+	0.176572i
$141$	−3.70319	+	11.3972i	−0.311864	+	0.959820i
$142$	0.510773	−	17.9588i	0.0428631	−	1.50707i
$143$	6.01514	+	6.01514i	0.503011	+	0.503011i
$144$	−3.91993	+	0.796341i	−0.326661	+	0.0663618i
$145$	16.5982	+	4.01474i	1.37841	+	0.333406i
$146$	2.07409	+	4.37376i	0.171653	+	0.361975i
$147$	−0.00552424	+	0.0348787i	−0.000455632	+	0.00287675i
$148$	−7.28620	−	8.16586i	−0.598922	−	0.671230i
$149$			1.12997i			0.0925708i	0.998928	+	0.0462854i	$0.0147384\pi$
$149$			1.12997i			0.0925708i	−0.998928	+	0.0462854i	$0.985262\pi$
$150$	5.85000	−	3.97209i	0.477651	−	0.324319i
$151$		−	5.68829i		−	0.462907i	−0.972846	−	0.231453i	$-0.925652\pi$
$151$		−	5.68829i		−	0.462907i	0.972846	−	0.231453i	$-0.0743481\pi$
$152$	−10.9678	+	6.61947i	−0.889603	+	0.536910i
$153$	0.901092	−	5.68927i	0.0728489	−	0.459950i
$154$	10.3831	−	4.92381i	0.836697	−	0.396772i
$155$	0.334036	+	4.33861i	0.0268304	+	0.348486i
$156$	−4.67121	+	3.00367i	−0.373996	+	0.240486i
$157$	−6.65160	−	6.65160i	−0.530856	−	0.530856i	0.389971	−	0.920827i	$-0.372485\pi$
$157$	−6.65160	−	6.65160i	−0.530856	−	0.530856i	−0.920827	+	0.389971i	$0.872485\pi$
$158$	0.608250	+	0.0172994i	0.0483898	+	0.00137627i
$159$	−3.91353	+	12.0446i	−0.310363	+	0.955200i
$160$	−10.6969	+	6.75105i	−0.845663	+	0.533717i
$161$	5.55673	+	17.1019i	0.437932	+	1.34782i
$162$	−0.398601	−	1.35688i	−0.0313171	−	0.106606i
$163$	−7.61012	+	3.87755i	−0.596070	+	0.303713i	−0.725875	−	0.687827i	$-0.758565\pi$
$163$	−7.61012	+	3.87755i	−0.596070	+	0.303713i	0.129805	+	0.991540i	$0.458565\pi$
$164$	−9.47586	−	0.539449i	−0.739941	−	0.0421239i
$165$	−4.45770	+	5.20136i	−0.347031	+	0.404925i
$166$	7.89482	−	14.4626i	0.612757	−	1.12252i
$167$	16.7839	−	2.65830i	1.29877	−	0.205706i	0.531518	−	0.847047i	$-0.321622\pi$
$167$	16.7839	−	2.65830i	1.29877	−	0.205706i	0.767256	+	0.641342i	$0.221622\pi$
$168$	1.70198	+	7.30656i	0.131311	+	0.563713i
$169$	3.10906	−	4.27925i	0.239158	−	0.329173i
$170$	−3.71670	−	17.8321i	−0.285058	−	1.36766i
$171$	−2.66220	−	3.66420i	−0.203583	−	0.280208i
$172$	1.37417	−	2.35555i	0.104780	−	0.179609i
$173$	14.2524	+	7.26195i	1.08359	+	0.552116i	0.902210	−	0.431298i	$-0.141944\pi$
$173$	14.2524	+	7.26195i	1.08359	+	0.552116i	0.181378	+	0.983413i	$0.441944\pi$
$174$	1.99214	−	10.6150i	0.151023	−	0.804724i
$175$	−7.75873	−	10.7557i	−0.586505	−	0.813054i
$176$	8.28129	−	9.03221i	0.624226	−	0.680829i
$177$	−2.77816	+	5.45245i	−0.208820	+	0.409831i
$178$	−3.32396	−	1.18551i	−0.249141	−	0.0888580i
$179$	2.73419	−	1.98651i	0.204363	−	0.148479i	−0.480896	−	0.876777i	$-0.659689\pi$
$179$	2.73419	−	1.98651i	0.204363	−	0.148479i	0.685260	+	0.728299i	$0.259689\pi$
$180$	−2.70039	−	3.56482i	−0.201275	−	0.265706i
$181$	−6.86505	−	4.98775i	−0.510275	−	0.370736i	0.302653	−	0.953101i	$-0.402128\pi$
$181$	−6.86505	−	4.98775i	−0.510275	−	0.370736i	−0.812928	+	0.582364i	$0.802128\pi$
$182$	5.88031	+	8.59734i	0.435877	+	0.637278i
$183$	−1.27252	−	8.03436i	−0.0940672	−	0.593917i
$184$	12.3544	+	14.6648i	0.910781	+	1.08110i
$185$	4.70161	−	11.2963i	0.345669	−	0.830523i
$186$	2.72936	−	0.353071i	0.200126	−	0.0258884i
$187$	8.01127	+	15.7230i	0.585842	+	1.14978i
$188$	23.8473	−	2.39782i	1.73924	−	0.174879i
$189$	−2.52260	+	0.819642i	−0.183492	+	0.0596202i
$190$	−11.9810	−	7.84807i	−0.869193	−	0.569359i
$191$	−23.0771	−	7.49819i	−1.66980	−	0.542550i	−0.686908	−	0.726744i	$-0.741033\pi$
$191$	−23.0771	−	7.49819i	−1.66980	−	0.542550i	−0.982890	+	0.184194i	$0.941033\pi$
$192$	4.61434	+	6.53513i	0.333011	+	0.471632i
$193$	−17.1394	+	17.1394i	−1.23372	+	1.23372i	−0.271192	+	0.962525i	$0.587418\pi$
$193$	−17.1394	+	17.1394i	−1.23372	+	1.23372i	−0.962525	+	0.271192i	$0.912582\pi$
$194$	12.0052	+	12.7081i	0.861924	+	0.912388i
$195$	−5.28859	−	3.25324i	−0.378724	−	0.232969i
$196$	0.0683021	−	0.0179719i	0.00487872	−	0.00128371i
$197$	12.7478	+	2.01906i	0.908247	+	0.143852i	0.593042	−	0.805172i	$-0.297927\pi$
$197$	12.7478	+	2.01906i	0.908247	+	0.143852i	0.315205	+	0.949024i	$0.397927\pi$
$198$	3.43121	+	2.64517i	0.243845	+	0.187984i
$199$	15.5227			1.10038			0.550189	−	0.835040i	$-0.314556\pi$
$199$	15.5227			1.10038			0.550189	+	0.835040i	$0.314556\pi$
$200$	−11.9824	−	7.51139i	−0.847287	−	0.531135i
$201$	1.33516			0.0941752
$202$	−5.92783	−	4.56985i	−0.417081	−	0.321533i
$203$	−20.0071	−	3.16882i	−1.40422	−	0.222407i
$204$	−11.1412	+	2.93150i	−0.780037	+	0.205246i
$205$	−4.04417	−	9.81063i	−0.282457	−	0.685204i
$206$	−5.10280	−	5.40156i	−0.355529	−	0.376344i
$207$	−4.79380	+	4.79380i	−0.333192	+	0.333192i
$208$	9.26033	+	6.13312i	0.642088	+	0.425255i
$209$	13.1961	+	4.28767i	0.912794	+	0.296585i
$210$	−6.53927	+	5.25272i	−0.451252	+	0.362472i
$211$	−1.95961	+	0.636716i	−0.134905	+	0.0438334i	−0.375691	−	0.926745i	$-0.622595\pi$
$211$	−1.95961	+	0.636716i	−0.134905	+	0.0438334i	0.240786	+	0.970578i	$0.422595\pi$
$212$	25.2018	−	2.53402i	1.73087	−	0.174037i
$213$	−5.76746	−	11.3193i	−0.395180	−	0.775585i
$214$	7.69010	−	0.994794i	0.525684	−	0.0680027i
$215$	3.03916	+	0.244386i	0.207269	+	0.0166670i
$216$	−2.16312	+	1.82233i	−0.147182	+	0.123994i
$217$	−0.807464	−	5.09813i	−0.0548143	−	0.346084i
$218$	−11.1471	−	16.2977i	−0.754979	−	1.10382i
$219$	2.76913	+	2.01189i	0.187121	+	0.135951i
$220$	13.1118	+	3.97259i	0.883997	+	0.267832i
$221$	−12.9401	+	9.40152i	−0.870444	+	0.632415i
$222$	−7.28883	−	2.59961i	−0.489194	−	0.174474i
$223$	9.43662	−	18.5204i	0.631923	−	1.24022i	−0.323849	−	0.946109i	$-0.604977\pi$
$223$	9.43662	−	18.5204i	0.631923	−	1.24022i	0.955772	−	0.294110i	$-0.0950231\pi$
$224$	12.0059	−	8.99934i	0.802179	−	0.601294i
$225$	2.28509	−	4.44729i	0.152339	−	0.296486i
$226$	−0.511335	+	2.72463i	−0.0340135	+	0.181240i
$227$	4.30929	+	2.19569i	0.286018	+	0.145733i	0.591114	−	0.806588i	$-0.298688\pi$
$227$	4.30929	+	2.19569i	0.286018	+	0.145733i	−0.305096	+	0.952322i	$0.598688\pi$
$228$	−4.56451	+	7.82431i	−0.302292	+	0.518177i
$229$	5.84117	+	8.03968i	0.385996	+	0.531277i	0.957160	−	0.289558i	$-0.0935083\pi$
$229$	5.84117	+	8.03968i	0.385996	+	0.531277i	−0.571165	+	0.820835i	$0.693508\pi$
$230$	−8.79721	+	19.5505i	−0.580071	+	1.28912i
$231$	4.77616	−	6.57381i	0.314248	−	0.432525i
$232$	−21.0375	+	4.90046i	−1.38118	+	0.321731i
$233$	−8.00740	+	1.26825i	−0.524582	+	0.0830856i	−0.413109	−	0.910682i	$-0.635557\pi$
$233$	−8.00740	+	1.26825i	−0.524582	+	0.0830856i	−0.111473	+	0.993767i	$0.535557\pi$
$234$	−1.88156	+	3.44686i	−0.123002	+	0.225328i
$235$	13.9623	+	22.8715i	0.910798	+	1.49197i
$236$	12.2191	+	0.695617i	0.795394	+	0.0452808i
$237$	0.383375	−	0.195339i	0.0249029	−	0.0126886i
$238$	6.09000	+	20.7309i	0.394756	+	1.34379i
$239$	−7.34407	−	22.6027i	−0.475049	−	1.46205i	−0.845892	−	0.533354i	$-0.820931\pi$
$239$	−7.34407	−	22.6027i	−0.475049	−	1.46205i	0.370844	−	0.928695i	$-0.379069\pi$
$240$	−4.35182	+	7.81420i	−0.280908	+	0.504404i
$241$	7.36630	−	22.6712i	0.474505	−	1.46038i	−0.372118	−	0.928185i	$-0.621368\pi$
$241$	7.36630	−	22.6712i	0.474505	−	1.46038i	0.846624	−	0.532192i	$-0.178632\pi$
$242$	2.28297	+	0.0649309i	0.146755	+	0.00417391i
$243$	−0.707107	−	0.707107i	−0.0453609	−	0.0453609i
$244$	−13.6841	+	8.79915i	−0.876038	+	0.563308i
$245$	0.0511804	+	0.0601313i	0.00326980	+	0.00384165i
$246$	−6.06401	+	2.87563i	−0.386627	+	0.183343i
$247$	−1.96742	+	12.4218i	−0.125184	+	0.790379i
$248$	−2.84414	−	4.71244i	−0.180603	−	0.299240i
$249$		−	11.6511i		−	0.738358i
$250$	1.76833	−	15.7122i	0.111839	−	0.993726i
$251$		−	1.75011i		−	0.110466i	−0.998473	−	0.0552330i	$-0.982410\pi$
$251$		−	1.75011i		−	0.110466i	0.998473	−	0.0552330i	$-0.0175902\pi$
$252$	3.53182	+	3.95822i	0.222484	+	0.249344i
$253$	3.24897	−	20.5132i	0.204261	−	1.28965i
$254$	7.45575	+	15.7224i	0.467815	+	0.986511i
$255$	−8.34834	−	9.80836i	−0.522793	−	0.614224i
$256$	8.24852	−	13.7099i	0.515532	−	0.856870i
$257$	0.796610	+	0.796610i	0.0496912	+	0.0496912i	0.731516	−	0.681825i	$-0.238813\pi$
$257$	0.796610	+	0.796610i	0.0496912	+	0.0496912i	−0.681825	+	0.731516i	$0.738813\pi$
$258$	0.0548223	−	1.92756i	0.00341309	−	0.120004i
$259$	−4.48506	+	13.8036i	−0.278688	+	0.857713i
$260$	−1.69729	+	12.3016i	−0.105262	+	0.762915i
$261$	−2.35996	−	7.26322i	−0.146078	−	0.449582i
$262$	−0.919899	+	0.270233i	−0.0568315	+	0.0166950i
$263$	11.0232	−	5.61660i	0.679719	−	0.346334i	−0.0798075	−	0.996810i	$-0.525431\pi$
$263$	11.0232	−	5.61660i	0.679719	−	0.346334i	0.759527	+	0.650476i	$0.225431\pi$
$264$	2.07970	−	8.41161i	0.127997	−	0.517699i
$265$	14.7554	+	24.1707i	0.906414	+	1.48479i
$266$	14.9123	+	8.14027i	0.914330	+	0.499112i
$267$	−2.46469	+	0.390368i	−0.150836	+	0.0238901i
$268$	−1.07511	−	2.44434i	−0.0656730	−	0.149312i
$269$	15.0035	−	20.6506i	0.914780	−	1.25909i	−0.0507271	−	0.998713i	$-0.516154\pi$
$269$	15.0035	−	20.6506i	0.914780	−	1.25909i	0.965508	−	0.260375i	$-0.0838461\pi$
$270$	−2.88378	−	1.29763i	−0.175501	−	0.0789710i
$271$	10.3796	+	14.2864i	0.630519	+	0.867835i	0.998066	−	0.0621703i	$-0.0198022\pi$
$271$	10.3796	+	14.2864i	0.630519	+	0.867835i	−0.367547	+	0.930005i	$0.619802\pi$
$272$	14.3380	+	18.0360i	0.869369	+	1.09359i
$273$	6.56244	+	3.34373i	0.397177	+	0.202372i
$274$	27.7598	+	5.20972i	1.67703	+	0.314730i
$275$	2.34473	+	15.1370i	0.141393	+	0.912794i
$276$	12.6363	+	4.91609i	0.760617	+	0.295914i
$277$	5.69164	−	11.1705i	0.341977	−	0.671168i	−0.654406	−	0.756144i	$-0.727081\pi$
$277$	5.69164	−	11.1705i	0.341977	−	0.671168i	0.996383	+	0.0849753i	$0.0270811\pi$
$278$	−0.0257671	+	0.0722463i	−0.00154541	+	0.00433304i
$279$	1.57437	−	1.14385i	0.0942551	−	0.0684803i
$280$	14.8820	+	7.74205i	0.889368	+	0.462676i
$281$	−11.8374	−	8.60034i	−0.706157	−	0.513053i	0.175775	−	0.984430i	$-0.443757\pi$
$281$	−11.8374	−	8.60034i	−0.706157	−	0.513053i	−0.881932	+	0.471377i	$0.843757\pi$
$282$	13.9886	−	9.56772i	0.833006	−	0.569749i
$283$	−2.48745	−	15.7051i	−0.147864	−	0.933574i	−0.944356	−	0.328925i	$-0.893314\pi$
$283$	−2.48745	−	15.7051i	−0.147864	−	0.933574i	0.796492	−	0.604649i	$-0.206686\pi$
$284$	−16.0785	+	19.6733i	−0.954085	+	1.16740i
$285$	−10.0950	−	0.811765i	−0.597977	−	0.0480848i
$286$	−1.54338	−	11.9309i	−0.0912621	−	0.705487i
$287$	5.71452	+	11.2154i	0.337318	+	0.662023i
$288$	5.07803	+	2.49272i	0.299226	+	0.146885i
$289$	−15.3879	+	4.99982i	−0.905168	+	0.294107i
$290$	−15.1240	−	18.8283i	−0.888109	−	1.10563i
$291$	11.7566	+	3.81996i	0.689186	+	0.223930i
$292$	1.45346	−	6.68960i	0.0850575	−	0.391479i
$293$	6.91192	−	6.91192i	0.403799	−	0.403799i	−0.475771	−	0.879569i	$-0.657831\pi$
$293$	6.91192	−	6.91192i	0.403799	−	0.403799i	0.879569	+	0.475771i	$0.157831\pi$
$294$	0.0363031	−	0.0342952i	0.00211724	−	0.00200014i
$295$	5.21493	+	12.6508i	0.303625	+	0.736555i
$296$	1.10997	+	15.4372i	0.0645156	+	0.897271i
$297$	3.02578	+	0.479237i	0.175574	+	0.0278082i
$298$	0.975667	−	1.26560i	0.0565189	−	0.0733141i
$299$	18.8251			1.08869
$300$	−9.98184	−	0.602310i	−0.576302	−	0.0347744i
$301$	−3.61667			−0.208462
$302$	−4.91153	+	6.37105i	−0.282627	+	0.366613i
$303$	−5.22741	−	0.827941i	−0.300307	−	0.0475640i
$304$	17.9997	+	2.05607i	1.03236	+	0.117924i
$305$	−15.4928	−	9.53024i	−0.887113	−	0.545700i
$306$	−5.92162	+	5.59410i	−0.338516	+	0.319793i
$307$	−16.6157	+	16.6157i	−0.948310	+	0.948310i	−0.998728	−	0.0504178i	$-0.983945\pi$
$307$	−16.6157	+	16.6157i	−0.948310	+	0.948310i	0.0504178	+	0.998728i	$0.483945\pi$
$308$	−15.8808	−	3.45047i	−0.904895	−	0.196609i
$309$	−4.99714	−	1.62367i	−0.284277	−	0.0923673i
$310$	3.37202	−	5.14779i	0.191518	−	0.292375i
$311$	11.5934	−	3.76691i	0.657399	−	0.213602i	0.0387251	−	0.999250i	$-0.487670\pi$
$311$	11.5934	−	3.76691i	0.657399	−	0.213602i	0.618674	+	0.785648i	$0.287670\pi$
$312$	7.82539	+	0.669138i	0.443025	+	0.0378825i
$313$	−10.5644	−	20.7338i	−0.597135	−	1.17194i	−0.969783	−	0.243970i	$-0.921550\pi$
$313$	−10.5644	−	20.7338i	−0.597135	−	1.17194i	0.372648	−	0.927973i	$-0.378450\pi$
$314$	1.70669	+	13.1933i	0.0963139	+	0.744540i
$315$	−2.27900	+	5.47565i	−0.128407	+	0.308518i
$316$	−0.666320	−	0.544566i	−0.0374834	−	0.0306342i
$317$	−1.97013	−	12.4389i	−0.110653	−	0.698638i	−0.979180	−	0.202995i	$-0.934932\pi$
$317$	−1.97013	−	12.4389i	−0.110653	−	0.698638i	0.868526	−	0.495643i	$-0.165068\pi$
$318$	14.7831	−	10.1112i	0.828997	−	0.567007i
$319$	18.9277	+	13.7518i	1.05975	+	0.769953i
$320$	17.8100	+	1.67482i	0.995608	+	0.0936251i
$321$	4.43586	−	3.22284i	0.247586	−	0.179882i
$322$	8.54282	−	23.9525i	0.476073	−	1.33482i
$323$	−11.8442	+	23.2455i	−0.659027	+	1.29341i
$324$	−0.725145	+	1.86391i	−0.0402858	+	0.103551i
$325$	−13.2189	+	4.24545i	−0.733254	+	0.235495i
$326$	11.8716	+	2.22796i	0.657507	+	0.123395i
$327$	−12.4402	−	6.33862i	−0.687947	−	0.350526i
$328$	10.1474	+	8.78608i	0.560299	+	0.485130i
$329$	−18.6833	−	25.7153i	−1.03004	−	1.41773i
$330$	9.48383	−	1.97669i	0.522068	−	0.108813i
$331$	6.91545	−	9.51830i	0.380108	−	0.523173i	−0.575505	−	0.817798i	$-0.695195\pi$
$331$	6.91545	−	9.51830i	0.380108	−	0.523173i	0.955613	+	0.294625i	$0.0951946\pi$
$332$	−21.3301	+	9.38180i	−1.17064	+	0.514893i
$333$	−5.40460	+	0.856005i	−0.296171	+	0.0469088i
$334$	−21.0937	−	11.5146i	−1.15419	−	0.630049i
$335$	1.94280	−	2.26691i	0.106146	−	0.123854i
$336$	4.40254	−	9.65312i	0.240178	−	0.526621i
$337$	14.1885	−	7.22941i	0.772898	−	0.393811i	−0.0226179	−	0.999744i	$-0.507200\pi$
$337$	14.1885	−	7.22941i	0.772898	−	0.393811i	0.795516	+	0.605933i	$0.207200\pi$
$338$	−7.17713	+	2.10838i	−0.390384	+	0.114681i
$339$	0.605747	+	1.86430i	0.0328997	+	0.101255i
$340$	−11.2342	+	23.1816i	−0.609262	+	1.25720i
$341$	−1.84225	+	5.66988i	−0.0997637	+	0.307041i
$342$	−0.182100	+	6.40266i	−0.00984686	+	0.346216i
$343$	13.0626	+	13.0626i	0.705312	+	0.705312i
$344$	−3.57300	+	1.45176i	−0.192643	+	0.0782736i
$345$	1.16369	+	15.1146i	0.0626512	+	0.813743i
$346$	−9.69276	−	20.4397i	−0.521086	−	1.09885i
$347$	3.91892	−	24.7431i	0.210379	−	1.32828i	−0.625870	−	0.779928i	$-0.715256\pi$
$347$	3.91892	−	24.7431i	0.210379	−	1.32828i	0.836248	−	0.548351i	$-0.184744\pi$
$348$	−11.3967	+	10.1690i	−0.610930	+	0.545117i
$349$			3.77373i			0.202003i	0.994886	+	0.101002i	$0.0322047\pi$
$349$			3.77373i			0.202003i	−0.994886	+	0.101002i	$0.967795\pi$
$350$	−0.596956	+	18.7459i	−0.0319086	+	1.00201i
$351$			2.77679i			0.148214i
$352$	−17.0741	+	2.96589i	−0.910052	+	0.158082i
$353$	−2.35188	+	14.8492i	−0.125178	+	0.790341i	0.842601	+	0.538539i	$0.181023\pi$
$353$	−2.35188	+	14.8492i	−0.125178	+	0.790341i	−0.967779	+	0.251803i	$0.918977\pi$
$354$	7.81951	−	3.70811i	0.415602	−	0.197084i
$355$	−27.6107	−	6.67840i	−1.46542	−	0.354453i
$356$	2.69930	+	4.19786i	0.143063	+	0.222486i
$357$	10.8035	+	10.8035i	0.571780	+	0.571780i
$358$	−4.77761	−	0.135882i	−0.252505	−	0.00718157i
$359$	−8.66676	+	26.6735i	−0.457414	+	1.40778i	0.410864	+	0.911697i	$0.365227\pi$
$359$	−8.66676	+	26.6735i	−0.457414	+	1.40778i	−0.868278	+	0.496079i	$0.834773\pi$
$360$	−0.0535135	+	6.32433i	−0.00282041	+	0.333321i
$361$	0.467740	+	1.43956i	0.0246179	+	0.0757661i
$362$	3.38240	+	11.5140i	0.177775	+	0.605163i
$363$	1.43894	−	0.733176i	0.0755247	−	0.0384818i
$364$	0.837228	−	14.7066i	0.0438827	−	0.770835i
$365$	7.44525	−	1.77407i	0.389702	−	0.0928588i
$366$	−5.51197	+	10.0975i	−0.288115	+	0.527802i
$367$	−25.9476	+	4.10970i	−1.35445	+	0.214524i	−0.791098	−	0.611690i	$-0.790490\pi$
$367$	−25.9476	+	4.10970i	−1.35445	+	0.214524i	−0.563356	+	0.826214i	$0.690490\pi$
$368$	−1.17505	−	27.0924i	−0.0612538	−	1.41229i
$369$	−2.78940	+	3.83927i	−0.145210	+	0.199865i
$370$	−15.0197	+	8.59263i	−0.780837	+	0.446710i
$371$	−19.7445	−	27.1760i	−1.02509	−	1.41091i
$372$	−3.36181	−	1.96120i	−0.174302	−	0.101684i
$373$	22.7635	+	11.5986i	1.17865	+	0.600552i	0.929827	−	0.367997i	$-0.119956\pi$
$373$	22.7635	+	11.5986i	1.17865	+	0.600552i	0.248823	+	0.968549i	$0.419956\pi$
$374$	4.60310	−	24.5275i	0.238021	−	1.26829i
$375$	−4.22579	−	10.3510i	−0.218219	−	0.534522i
$376$	−28.7800	−	17.9052i	−1.48421	−	0.923389i
$377$	−9.62747	+	18.8950i	−0.495840	+	0.973141i
$378$	3.53310	+	1.26010i	0.181723	+	0.0648127i
$379$	−18.5839	+	13.5020i	−0.954593	+	0.693553i	−0.951889	−	0.306444i	$-0.900861\pi$
$379$	−18.5839	+	13.5020i	−0.954593	+	0.693553i	−0.00270450	+	0.999996i	$0.500861\pi$
$380$	6.64267	+	19.1350i	0.340762	+	0.981604i
$381$	9.95423	+	7.23217i	0.509971	+	0.370515i
$382$	19.3727	+	28.3240i	0.991193	+	1.44918i
$383$	−3.48028	−	21.9736i	−0.177834	−	1.12280i	−0.901541	−	0.432693i	$-0.857563\pi$
$383$	−3.48028	−	21.9736i	−0.177834	−	1.12280i	0.723707	−	0.690107i	$-0.242437\pi$
$384$	0.474541	−	11.3038i	0.0242163	−	0.576842i
$385$	−4.21156	−	17.6747i	−0.214641	−	0.900788i
$386$	33.9954	−	4.39766i	1.73032	−	0.223835i
$387$	−0.619034	−	1.21492i	−0.0314673	−	0.0617580i
$388$	−2.47343	−	24.5993i	−0.125569	−	1.24884i
$389$	−25.2281	+	8.19711i	−1.27912	+	0.415610i	−0.868269	−	0.496094i	$-0.834767\pi$
$389$	−25.2281	+	8.19711i	−1.27912	+	0.415610i	−0.410847	+	0.911704i	$0.634767\pi$
$390$	3.11438	+	8.21013i	0.157703	+	0.415736i
$391$	37.1397	+	12.0674i	1.87823	+	0.610275i
$392$	−0.0920180	−	0.0388461i	−0.00464761	−	0.00196202i
$393$	−0.479385	+	0.479385i	−0.0241818	+	0.0241818i
$394$	−12.5346	−	13.2685i	−0.631484	−	0.668456i
$395$	0.226192	−	0.935150i	0.0113809	−	0.0470525i
$396$	−1.55909	−	5.92532i	−0.0783474	−	0.297758i
$397$	−31.3701	−	4.96854i	−1.57442	−	0.249364i	−0.692732	−	0.721195i	$-0.743593\pi$
$397$	−31.3701	−	4.96854i	−1.57442	−	0.249364i	−0.881689	+	0.471831i	$0.843593\pi$
$398$	−17.3859	−	13.4030i	−0.871477	−	0.671833i
$399$	12.0133			0.601418
$400$	6.93500	+	18.7592i	0.346750	+	0.937958i
$401$	1.93725			0.0967417			0.0483708	−	0.998829i	$-0.484597\pi$
$401$	1.93725			0.0967417			0.0483708	+	0.998829i	$0.484597\pi$
$402$	−1.49542	−	1.15284i	−0.0745848	−	0.0574985i
$403$	−5.33718	−	0.845327i	−0.265864	−	0.0421087i
$404$	2.69352	+	10.2367i	0.134008	+	0.509296i
$405$	−2.22947	+	0.171650i	−0.110783	+	0.00852935i
$406$	19.6724	+	20.8242i	0.976326	+	1.03349i
$407$	11.8535	−	11.8535i	0.587557	−	0.587557i
$408$	15.0096	+	6.33641i	0.743086	+	0.313699i
$409$	11.2145	+	3.64381i	0.554520	+	0.180175i	0.572854	−	0.819657i	$-0.305836\pi$
$409$	11.2145	+	3.64381i	0.554520	+	0.180175i	−0.0183337	+	0.999832i	$0.505836\pi$
$410$	−3.94136	+	14.4801i	−0.194650	+	0.715121i
$411$	18.9943	−	6.17163i	0.936922	−	0.304424i
$412$	1.05133	+	10.4559i	0.0517953	+	0.515124i
$413$	−7.36885	−	14.4622i	−0.362597	−	0.711637i
$414$	9.50838	−	1.23001i	0.467312	−	0.0604516i
$415$	−19.7818	−	16.9535i	−0.971050	−	0.832214i
$416$	−5.07622	−	14.8651i	−0.248882	−	0.728819i
$417$	0.00848465	+	0.0535700i	0.000415495	+	0.00262333i
$418$	−11.0778	−	16.1964i	−0.541835	−	0.792193i
$419$	−24.8894	−	18.0832i	−1.21593	−	0.883421i	−0.220170	−	0.975462i	$-0.570661\pi$
$419$	−24.8894	−	18.0832i	−1.21593	−	0.883421i	−0.995755	+	0.0920401i	$0.970661\pi$
$420$	11.8596	−	0.236896i	0.578689	−	0.0115593i
$421$	13.5139	−	9.81844i	0.658628	−	0.478522i	−0.207571	−	0.978220i	$-0.566556\pi$
$421$	13.5139	−	9.81844i	0.658628	−	0.478522i	0.866199	+	0.499698i	$0.166556\pi$
$422$	2.74459	+	0.978877i	0.133604	+	0.0476510i
$423$	5.44051	−	10.6776i	0.264527	−	0.519163i
$424$	−30.4148	−	18.9222i	−1.47707	−	0.918945i
$425$	−28.8008	−	0.0979274i	−1.39704	−	0.00475017i
$426$	−3.31386	+	17.6578i	−0.160557	+	0.855524i
$427$	19.2244	+	9.79535i	0.930336	+	0.474030i
$428$	−9.47207	−	5.52578i	−0.457850	−	0.267099i
$429$	−5.00011	−	6.88206i	−0.241408	−	0.332269i
$430$	−3.19293	−	2.89786i	−0.153977	−	0.139747i
$431$	−10.2982	+	14.1742i	−0.496046	+	0.682749i	−0.981489	−	0.191519i	$-0.938658\pi$
$431$	−10.2982	+	14.1742i	−0.496046	+	0.682749i	0.485443	+	0.874269i	$0.338658\pi$
$432$	3.99624	−	0.173325i	0.192269	−	0.00833912i
$433$	21.0372	−	3.33196i	1.01098	−	0.160124i	0.371096	−	0.928594i	$-0.378982\pi$
$433$	21.0372	−	3.33196i	1.01098	−	0.160124i	0.639885	+	0.768471i	$0.278982\pi$
$434$	−3.49757	+	6.40725i	−0.167889	+	0.307558i
$435$	−15.7658	−	6.56184i	−0.755913	−	0.314616i
$436$	−1.58711	+	27.8789i	−0.0760087	+	1.33516i
$437$	27.3588	−	13.9400i	1.30875	−	0.666842i
$438$	−1.36435	−	4.64437i	−0.0651910	−	0.221917i
$439$	−3.66634	−	11.2838i	−0.174985	−	0.538547i	0.824648	−	0.565646i	$-0.191373\pi$
$439$	−3.66634	−	11.2838i	−0.174985	−	0.538547i	−0.999633	+	0.0270987i	$0.991373\pi$
$440$	−11.2555	−	15.7707i	−0.536583	−	0.751840i
$441$	0.0109125	−	0.0335851i	0.000519641	−	0.00159929i
$442$	22.6109	+	0.643086i	1.07549	+	0.0305885i
$443$	−4.55801	−	4.55801i	−0.216558	−	0.216558i	0.590488	−	0.807046i	$-0.298935\pi$
$443$	−4.55801	−	4.55801i	−0.216558	−	0.216558i	−0.807046	+	0.590488i	$0.798935\pi$
$444$	5.91907	+	9.20514i	0.280907	+	0.436857i
$445$	−2.92358	+	4.75269i	−0.138591	+	0.225299i
$446$	−26.5606	+	12.5954i	−1.25768	+	0.596408i
$447$	0.176766	−	1.11606i	0.00836076	−	0.0527877i
$448$	−21.2174	−	0.286929i	−1.00243	−	0.0135561i
$449$			15.7982i			0.745562i	0.927919	+	0.372781i	$0.121596\pi$
$449$			15.7982i			0.745562i	−0.927919	+	0.372781i	$0.878404\pi$
$450$	−6.39935	+	3.00804i	−0.301668	+	0.141800i
$451$		−	14.5382i		−	0.684575i
$452$	2.92528	−	2.61015i	0.137593	−	0.122771i
$453$	−0.889845	+	5.61826i	−0.0418086	+	0.263969i
$454$	−2.93067	−	6.18008i	−0.137543	−	0.290045i
$455$	15.2261	−	6.27657i	0.713813	−	0.294250i
$456$	11.8682	−	4.82224i	0.555781	−	0.225822i
$457$	29.8131	+	29.8131i	1.39460	+	1.39460i	0.814667	+	0.579929i	$0.196920\pi$
$457$	29.8131	+	29.8131i	1.39460	+	1.39460i	0.579929	+	0.814667i	$0.303080\pi$
$458$	0.399550	−	14.0482i	0.0186697	−	0.656429i
$459$	−1.78000	+	5.47826i	−0.0830831	+	0.255703i
$460$	26.7339	−	14.3011i	1.24647	−	0.666795i
$461$	−7.67255	−	23.6137i	−0.357346	−	1.09980i	−0.954636	−	0.297774i	$-0.903756\pi$
$461$	−7.67255	−	23.6137i	−0.357346	−	1.09980i	0.597290	−	0.802025i	$-0.296244\pi$
$462$	−11.0256	+	3.23891i	−0.512955	+	0.150688i
$463$	−7.34620	+	3.74307i	−0.341407	+	0.173955i	−0.616284	−	0.787524i	$-0.711363\pi$
$463$	−7.34620	+	3.74307i	−0.341407	+	0.173955i	0.274877	+	0.961479i	$0.411363\pi$
$464$	27.7938	+	12.6761i	1.29030	+	0.588471i
$465$	0.348786	−	4.33745i	0.0161745	−	0.201145i
$466$	10.0636	+	5.49348i	0.466186	+	0.254480i
$467$	11.4787	−	1.81805i	0.531172	−	0.0841294i	0.114913	−	0.993376i	$-0.463341\pi$
$467$	11.4787	−	1.81805i	0.531172	−	0.0841294i	0.416259	+	0.909246i	$0.363341\pi$
$468$	5.08358	−	2.23595i	0.234988	−	0.103357i
$469$	−2.08159	+	2.86506i	−0.0961189	+	0.132296i
$470$	4.11019	−	37.6724i	0.189589	−	1.73770i
$471$	5.52917	+	7.61025i	0.254771	+	0.350662i
$472$	−13.0851	−	11.3296i	−0.602290	−	0.521488i
$473$	3.72192	+	1.89641i	0.171134	+	0.0871971i
$474$	−0.598055	−	0.112238i	−0.0274696	−	0.00515525i
$475$	−16.0675	+	15.9586i	−0.737227	+	0.732231i
$476$	11.0791	−	28.4776i	0.507808	−	1.30527i
$477$	5.74954	−	11.2841i	0.263254	−	0.516664i
$478$	−11.2907	+	31.6569i	−0.516422	+	1.44795i
$479$	−2.26075	+	1.64253i	−0.103296	+	0.0750491i	−0.638234	−	0.769842i	$-0.720335\pi$
$479$	−2.26075	+	1.64253i	−0.103296	+	0.0750491i	0.534938	+	0.844891i	$0.320335\pi$
$480$	11.6213	−	4.99457i	0.530437	−	0.227970i
$481$	12.2926	+	8.93111i	0.560495	+	0.407224i
$482$	−27.8258	+	19.0319i	−1.26743	+	0.866880i
$483$	−2.81300	−	17.7606i	−0.127996	−	0.808134i
$484$	−2.50093	−	2.04395i	−0.113679	−	0.0929067i
$485$	23.5928	−	14.4025i	1.07129	−	0.653986i
$486$	0.181431	+	1.40253i	0.00822990	+	0.0636199i
$487$	−14.7690	−	28.9857i	−0.669245	−	1.31347i	−0.936780	−	0.349920i	$-0.886209\pi$
$487$	−14.7690	−	28.9857i	−0.669245	−	1.31347i	0.267534	−	0.963548i	$-0.413791\pi$
$488$	22.9242	+	1.96022i	1.03773	+	0.0887348i
$489$	8.12301	−	2.63932i	0.367335	−	0.119354i
$490$	−0.00540344	−	0.111540i	−0.000244103	−	0.00503887i
$491$	−15.9391	−	5.17893i	−0.719321	−	0.233722i	−0.0735925	−	0.997288i	$-0.523446\pi$
$491$	−15.9391	−	5.17893i	−0.719321	−	0.233722i	−0.645729	+	0.763567i	$0.723446\pi$
$492$	9.27481	+	2.01516i	0.418141	+	0.0908504i
$493$	−31.1060	+	31.1060i	−1.40094	+	1.40094i
$494$	12.9291	−	12.2140i	0.581707	−	0.549533i
$495$	5.21649	−	4.43999i	0.234464	−	0.199562i
$496$	−0.883417	+	7.73382i	−0.0396666	+	0.347259i
$497$	33.2813	+	5.27123i	1.49287	+	0.236447i
$498$	−10.0601	+	13.0495i	−0.450803	+	0.584764i
$499$	41.5528			1.86016			0.930079	−	0.367359i	$-0.119738\pi$
$499$	41.5528			1.86016			0.930079	+	0.367359i	$0.119738\pi$
$500$	−15.5472	+	16.0712i	−0.695292	+	0.718727i
$501$	−16.9931			−0.759194
$502$	−1.51112	+	1.96017i	−0.0674448	+	0.0874868i
$503$	8.35723	+	1.32366i	0.372630	+	0.0590189i	0.339941	−	0.940447i	$-0.389593\pi$
$503$	8.35723	+	1.32366i	0.372630	+	0.0590189i	0.0326893	+	0.999466i	$0.489593\pi$
$504$	−0.538033	−	7.48285i	−0.0239659	−	0.333313i
$505$	−9.01212	+	7.67062i	−0.401034	+	0.341338i
$506$	−21.3510	+	20.1700i	−0.949166	+	0.896668i
$507$	−3.74020	+	3.74020i	−0.166108	+	0.166108i
$508$	5.22478	−	24.0472i	0.231812	−	1.06692i
$509$	21.4866	+	6.98141i	0.952376	+	0.309446i	0.743681	−	0.668535i	$-0.233078\pi$
$509$	21.4866	+	6.98141i	0.952376	+	0.309446i	0.208695	+	0.977981i	$0.433078\pi$
$510$	0.881387	+	18.1940i	0.0390285	+	0.805643i
$511$	−8.63444	+	2.80550i	−0.381965	+	0.124108i
$512$	−21.0763	+	8.23335i	−0.931451	+	0.363866i
$513$	2.05621	+	4.03555i	0.0907840	+	0.178174i
$514$	−0.204396	−	1.58005i	−0.00901554	−	0.0696932i
$515$	−10.0281	+	6.12178i	−0.441890	+	0.269758i
$516$	−1.72574	+	2.11158i	−0.0759715	+	0.0929572i
$517$	5.74306	+	36.2603i	0.252580	+	1.59472i
$518$	16.9420	−	11.5878i	0.744390	−	0.509139i
$519$	−12.9409	−	9.40210i	−0.568042	−	0.412707i
$520$	12.5228	−	12.3127i	0.549161	−	0.539946i
$521$	−9.58644	+	6.96496i	−0.419990	+	0.305140i	−0.777634	−	0.628718i	$-0.783580\pi$
$521$	−9.58644	+	6.96496i	−0.419990	+	0.305140i	0.357644	+	0.933858i	$0.383580\pi$
$522$	−3.62817	+	10.1727i	−0.158801	+	0.445247i
$523$	−2.25878	+	4.43311i	−0.0987696	+	0.193846i	−0.935104	−	0.354373i	$-0.884694\pi$
$523$	−2.25878	+	4.43311i	−0.0987696	+	0.193846i	0.836334	+	0.548220i	$0.184694\pi$
$524$	1.26364	+	0.491614i	0.0552025	+	0.0214762i
$525$	5.98065	+	11.8370i	0.261017	+	0.516609i
$526$	−17.1959	−	3.22718i	−0.749777	−	0.140712i
$527$	−9.98773	−	5.08900i	−0.435072	−	0.221680i
$528$	−9.59228	+	7.62553i	−0.417451	+	0.331859i
$529$	−13.4962	−	18.5759i	−0.586792	−	0.807650i
$530$	4.34366	−	39.8123i	0.188676	−	1.72933i
$531$	3.59691	−	4.95072i	0.156093	−	0.214843i
$532$	−9.67348	−	21.9933i	−0.419399	−	0.953529i
$533$	13.0153	−	2.06142i	0.563755	−	0.0892900i
$534$	3.09758	+	1.69090i	0.134045	+	0.0731724i
$535$	0.982720	−	12.2210i	0.0424867	−	0.528359i
$536$	−0.906394	+	3.66603i	−0.0391503	+	0.158348i
$537$	−3.01129	+	1.53433i	−0.129947	+	0.0662111i
$538$	−34.6350	+	10.1745i	−1.49322	+	0.438654i
$539$	0.0334303	+	0.102888i	0.00143995	+	0.00443170i
$540$	2.10948	+	3.94336i	0.0907776	+	0.169695i
$541$	−2.92452	+	9.00075i	−0.125735	+	0.386973i	−0.994034	−	0.109068i	$-0.965213\pi$
$541$	−2.92452	+	9.00075i	−0.125735	+	0.386973i	0.868299	+	0.496041i	$0.165213\pi$
$542$	0.709992	−	24.9634i	0.0304968	−	1.07227i
$543$	6.00027	+	6.00027i	0.257496	+	0.257496i
$544$	−0.485856	−	32.5809i	−0.0208309	−	1.39690i
$545$	−28.8638	+	11.8983i	−1.23639	+	0.509668i
$546$	−4.46299	−	9.41138i	−0.190998	−	0.402770i
$547$	−2.16103	+	13.6442i	−0.0923989	+	0.583384i	0.897434	+	0.441149i	$0.145429\pi$
$547$	−2.16103	+	13.6442i	−0.0923989	+	0.583384i	−0.989833	+	0.142235i	$0.954571\pi$
$548$	−26.5935	−	29.8041i	−1.13602	−	1.27317i
$549$			8.13451i			0.347172i
$550$	10.4438	−	18.9784i	0.445325	−	0.809241i
$551$			34.5895i			1.47356i
$552$	−9.90825	−	16.4169i	−0.421723	−	0.698751i
$553$	−0.178532	+	1.12721i	−0.00759196	+	0.0479338i
$554$	−16.0199	+	7.59682i	−0.680619	+	0.322758i
$555$	−6.41087	+	10.4218i	−0.272126	+	0.442379i
$556$	0.0912406	−	0.0586693i	0.00386946	−	0.00248813i
$557$	−20.2567	−	20.2567i	−0.858304	−	0.858304i	0.132834	−	0.991138i	$-0.457592\pi$
$557$	−20.2567	−	20.2567i	−0.858304	−	0.858304i	−0.991138	+	0.132834i	$0.957592\pi$
$558$	−2.75099	−	0.0782418i	−0.116459	−	0.00331224i
$559$	−1.17002	+	3.60095i	−0.0494865	+	0.152304i
$560$	−9.98339	−	21.5211i	−0.421875	−	0.909432i
$561$	−5.45302	−	16.7827i	−0.230227	−	0.708565i
$562$	5.83224	+	19.8535i	0.246018	+	0.837470i
$563$	−18.7194	+	9.53800i	−0.788928	+	0.401979i	−0.801540	−	0.597942i	$-0.795985\pi$
$563$	−18.7194	+	9.53800i	−0.788928	+	0.401979i	0.0126118	+	0.999920i	$0.495985\pi$
$564$	−23.9288	−	1.36224i	−1.00758	−	0.0573605i
$565$	4.04672	+	1.68427i	0.170247	+	0.0708578i
$566$	−10.7745	+	19.7380i	−0.452887	+	0.829649i
$567$	2.61976	−	0.414929i	0.110020	−	0.0174254i
$568$	34.9953	−	8.15177i	1.46837	−	0.342041i
$569$	−22.8243	+	31.4149i	−0.956843	+	1.31698i	−0.00842243	+	0.999965i	$0.502681\pi$
$569$	−22.8243	+	31.4149i	−0.956843	+	1.31698i	−0.948420	+	0.317016i	$0.897319\pi$
$570$	10.6058	+	9.62569i	0.444227	+	0.403176i
$571$	4.66625	+	6.42254i	0.195276	+	0.268775i	0.895415	−	0.445232i	$-0.146879\pi$
$571$	4.66625	+	6.42254i	0.195276	+	0.268775i	−0.700139	+	0.714007i	$0.746879\pi$
$572$	−8.57302	+	14.6955i	−0.358456	+	0.614451i
$573$	21.6200	+	11.0159i	0.903187	+	0.460197i
$574$	3.28344	−	17.4957i	0.137048	−	0.730257i
$575$	27.3556	+	20.0175i	1.14081	+	0.834786i
$576$	−3.53521	−	7.17651i	−0.147300	−	0.299021i
$577$	9.74625	−	19.1281i	0.405742	−	0.796313i	−0.594226	−	0.804298i	$-0.702542\pi$
$577$	9.74625	−	19.1281i	0.405742	−	0.796313i	0.999968	+	0.00798495i	$0.00254172\pi$
$578$	21.5519	+	7.68663i	0.896441	+	0.319722i
$579$	19.6095	−	14.2472i	0.814944	−	0.592091i
$580$	0.682085	+	34.1469i	0.0283220	+	1.41787i
$581$	25.0015	+	18.1647i	1.03724	+	0.753597i
$582$	−9.86942	−	14.4297i	−0.409101	−	0.598129i
$583$	6.06928	+	38.3199i	0.251364	+	1.58705i
$584$	−7.40402	+	6.23755i	−0.306381	+	0.258112i
$585$	4.71456	+	4.04050i	0.194923	+	0.167054i
$586$	−13.7096	+	1.77348i	−0.566339	+	0.0732618i
$587$	11.3820	+	22.3385i	0.469787	+	0.922009i	0.997368	+	0.0725046i	$0.0230992\pi$
$587$	11.3820	+	22.3385i	0.469787	+	0.922009i	−0.527581	+	0.849505i	$0.676901\pi$
$588$	−0.0702726	+	0.00706584i	−0.00289799	+	0.000291390i
$589$	−8.38257	+	2.72366i	−0.345398	+	0.112226i
$590$	5.08236	−	18.6720i	0.209237	−	0.768714i
$591$	−12.2751	−	3.98841i	−0.504928	−	0.164061i
$592$	12.0860	−	18.2485i	0.496732	−	0.750010i
$593$	−28.1891	+	28.1891i	−1.15759	+	1.15759i	−0.172594	+	0.984993i	$0.555215\pi$
$593$	−28.1891	+	28.1891i	−1.15759	+	1.15759i	−0.984993	+	0.172594i	$0.944785\pi$
$594$	−2.97517	−	3.14936i	−0.122073	−	0.129220i
$595$	34.0628	−	2.62254i	1.39644	−	0.107514i
$596$	−2.18555	+	0.575070i	−0.0895236	+	0.0235558i
$597$	−15.3316	−	2.42829i	−0.627482	−	0.0993834i
$598$	−21.0847	−	16.2545i	−0.862217	−	0.664695i
$599$	11.5491			0.471885			0.235943	−	0.971767i	$-0.424182\pi$
$599$	11.5491			0.471885			0.235943	+	0.971767i	$0.424182\pi$
$600$	10.6599	+	9.29338i	0.435188	+	0.379401i
$601$	10.4058			0.424462			0.212231	−	0.977220i	$-0.431927\pi$
$601$	10.4058			0.424462			0.212231	+	0.977220i	$0.431927\pi$
$602$	4.05078	+	3.12280i	0.165097	+	0.127276i
$603$	−1.31873	−	0.208866i	−0.0537027	−	0.00850567i
$604$	11.0021	−	2.89492i	0.447669	−	0.117792i
$605$	0.848977	−	3.50994i	0.0345158	−	0.142700i
$606$	5.13997	+	5.44090i	0.208797	+	0.221022i
$607$	16.1166	−	16.1166i	0.654154	−	0.654154i	−0.299837	−	0.953991i	$-0.596932\pi$
$607$	16.1166	−	16.1166i	0.654154	−	0.654154i	0.953991	+	0.299837i	$0.0969322\pi$
$608$	−18.3849	−	17.8446i	−0.745607	−	0.723696i
$609$	19.2651	+	6.25960i	0.780660	+	0.253652i
$610$	9.12348	+	24.0513i	0.369399	+	0.973808i
$611$	−31.6477	+	10.2830i	−1.28033	+	0.416004i
$612$	11.4626	−	1.15255i	0.463347	−	0.0465891i
$613$	15.0439	+	29.5254i	0.607619	+	1.19252i	0.965903	+	0.258906i	$0.0833619\pi$
$613$	15.0439	+	29.5254i	0.607619	+	1.19252i	−0.358284	+	0.933613i	$0.616638\pi$
$614$	32.9569	−	4.26331i	1.33003	−	0.172053i
$615$	2.45966	+	10.3225i	0.0991830	+	0.416243i
$616$	14.8077	+	17.5769i	0.596619	+	0.708192i
$617$	−4.40691	−	27.8241i	−0.177415	−	1.12016i	−0.902243	−	0.431227i	$-0.858081\pi$
$617$	−4.40691	−	27.8241i	−0.177415	−	1.12016i	0.724828	−	0.688930i	$-0.241919\pi$
$618$	4.19499	+	6.13331i	0.168747	+	0.246718i
$619$	26.0513	+	18.9274i	1.04709	+	0.760756i	0.971657	−	0.236394i	$-0.0759657\pi$
$619$	26.0513	+	18.9274i	1.04709	+	0.760756i	0.0754341	+	0.997151i	$0.475966\pi$
$620$	−8.22160	+	2.85411i	−0.330187	+	0.114624i
$621$	5.48470	−	3.98487i	0.220093	−	0.159907i
$622$	−16.2374	−	5.79118i	−0.651060	−	0.232205i
$623$	3.00490	−	5.89745i	0.120389	−	0.236276i
$624$	−8.18689	−	7.50625i	−0.327738	−	0.300490i
$625$	−23.7233	−	7.88693i	−0.948933	−	0.315477i
$626$	−6.07007	+	32.3442i	−0.242609	+	1.29273i
$627$	−12.3629	−	6.29921i	−0.493727	−	0.251566i
$628$	9.48013	−	16.2505i	0.378298	−	0.648464i
$629$	18.5267	+	25.4999i	0.738710	+	1.01675i
$630$	7.28047	−	4.16509i	0.290061	−	0.165941i
$631$	−2.63098	+	3.62123i	−0.104738	+	0.144159i	−0.858168	−	0.513368i	$-0.828398\pi$
$631$	−2.63098	+	3.62123i	−0.104738	+	0.144159i	0.753431	+	0.657527i	$0.228398\pi$
$632$	0.276094	+	1.18526i	0.0109824	+	0.0471471i
$633$	2.03509	−	0.322326i	0.0808875	−	0.0128113i
$634$	−8.53371	+	15.6330i	−0.338917	+	0.620866i
$635$	26.7635	−	6.37725i	1.06208	−	0.253073i
$636$	−25.2880	−	1.43961i	−1.00273	−	0.0570844i
$637$	−0.0873703	+	0.0445174i	−0.00346174	+	0.00176384i
$638$	−9.32566	−	31.7455i	−0.369206	−	1.25681i
$639$	3.92573	+	12.0822i	0.155300	+	0.477963i
$640$	−18.5016	−	17.2538i	−0.731338	−	0.682015i
$641$	10.1109	−	31.1181i	0.399356	−	1.22909i	−0.526160	−	0.850385i	$-0.676369\pi$
$641$	10.1109	−	31.1181i	0.399356	−	1.22909i	0.925517	−	0.378707i	$-0.123631\pi$
$642$	−7.75104	−	0.220450i	−0.305909	−	0.00870047i
$643$	−20.7316	−	20.7316i	−0.817573	−	0.817573i	0.168183	−	0.985756i	$-0.446210\pi$
$643$	−20.7316	−	20.7316i	−0.817573	−	0.817573i	−0.985756	+	0.168183i	$0.946210\pi$
$644$	−30.2499	+	19.4512i	−1.19201	+	0.766485i
$645$	−2.96351	−	0.716806i	−0.116688	−	0.0282242i
$646$	33.3370	−	15.8088i	1.31163	−	0.621989i
$647$	1.54895	−	9.77971i	0.0608957	−	0.384480i	−0.938351	−	0.345683i	$-0.887647\pi$
$647$	1.54895	−	9.77971i	0.0608957	−	0.384480i	0.999247	−	0.0387973i	$-0.0123527\pi$
$648$	2.42157	−	1.46151i	0.0951282	−	0.0574135i
$649$			18.7469i			0.735880i
$650$	18.4713	+	6.65879i	0.724503	+	0.261179i
$651$			5.16168i			0.202302i
$652$	−11.3728	−	12.7458i	−0.445393	−	0.499166i
$653$	0.873916	−	5.51769i	0.0341990	−	0.215924i	−0.964671	−	0.263459i	$-0.915137\pi$
$653$	0.873916	−	5.51769i	0.0341990	−	0.215924i	0.998870	+	0.0475352i	$0.0151366\pi$
$654$	8.46036	+	17.8409i	0.330826	+	0.697634i
$655$	0.116370	+	1.51147i	0.00454697	+	0.0590582i
$656$	−3.77912	−	18.6024i	−0.147550	−	0.726303i
$657$	−2.42031	−	2.42031i	−0.0944253	−	0.0944253i
$658$	−1.27798	+	44.9339i	−0.0498209	+	1.75171i
$659$	11.9644	−	36.8226i	0.466066	−	1.43440i	−0.391570	−	0.920148i	$-0.628068\pi$
$659$	11.9644	−	36.8226i	0.466066	−	1.43440i	0.857636	−	0.514256i	$-0.171932\pi$
$660$	−12.3289	−	5.97482i	−0.479903	−	0.232570i
$661$	−9.93403	−	30.5738i	−0.386389	−	1.18918i	−0.935468	−	0.353412i	$-0.885021\pi$
$661$	−9.93403	−	30.5738i	−0.386389	−	1.18918i	0.549079	−	0.835771i	$-0.314979\pi$
$662$	−15.9640	+	4.68965i	−0.620460	+	0.182269i
$663$	14.2515	−	7.26150i	0.553482	−	0.282013i
$664$	31.9910	+	7.90950i	1.24149	+	0.306948i
$665$	17.4806	−	20.3968i	0.677867	−	0.790954i
$666$	6.79242	+	3.70783i	0.263201	+	0.143675i
$667$	51.1373	−	8.09936i	1.98005	−	0.313608i
$668$	13.6833	+	31.1099i	0.529423	+	1.20368i
$669$	−12.2177	+	16.8162i	−0.472362	+	0.650151i
$670$	−4.13333	+	0.861501i	−0.159685	+	0.0332827i
$671$	−14.6477	−	20.1608i	−0.565466	−	0.778298i
$672$	−13.2659	+	7.01041i	−0.511743	+	0.270432i
$673$	25.8524	+	13.1724i	0.996535	+	0.507760i	0.874635	−	0.484782i	$-0.161101\pi$
$673$	25.8524	+	13.1724i	0.996535	+	0.507760i	0.121900	+	0.992542i	$0.461101\pi$
$674$	−22.1337	−	4.15386i	−0.852559	−	0.160001i
$675$	−2.95266	+	4.03507i	−0.113648	+	0.155310i
$676$	9.85906	+	3.83561i	0.379195	+	0.147524i
$677$	2.17299	−	4.26473i	0.0835147	−	0.163907i	−0.845472	−	0.534019i	$-0.820681\pi$
$677$	2.17299	−	4.26473i	0.0835147	−	0.163907i	0.928987	+	0.370113i	$0.120681\pi$
$678$	0.931265	−	2.61109i	0.0357650	−	0.100278i
$679$	−26.5262	+	19.2724i	−1.01798	+	0.739608i
$680$	32.5987	−	16.2639i	1.25010	−	0.623693i
$681$	−3.91276	−	2.84278i	−0.149937	−	0.108936i
$682$	6.95900	−	4.75974i	0.266474	−	0.182260i
$683$	5.72483	+	36.1452i	0.219055	+	1.38306i	0.814734	+	0.579835i	$0.196883\pi$
$683$	5.72483	+	36.1452i	0.219055	+	1.38306i	−0.595679	+	0.803222i	$0.703117\pi$
$684$	5.73231	−	7.01393i	0.219180	−	0.268184i
$685$	17.1601	−	41.2298i	0.655655	−	1.57531i
$686$	−3.35163	−	25.9092i	−0.127966	−	0.989219i
$687$	−4.51157	−	8.85446i	−0.172127	−	0.337819i
$688$	5.25537	+	1.45908i	0.200359	+	0.0556267i
$689$	−33.4453	+	10.8671i	−1.27417	+	0.414002i
$690$	11.7473	−	17.9336i	0.447211	−	0.682719i
$691$	−3.63597	−	1.18140i	−0.138319	−	0.0449425i	0.239039	−	0.971010i	$-0.423167\pi$
$691$	−3.63597	−	1.18140i	−0.138319	−	0.0449425i	−0.377358	+	0.926067i	$0.623167\pi$
$692$	−6.79242	+	31.2622i	−0.258209	+	1.18841i
$693$	−5.74572	+	5.74572i	−0.218262	+	0.218262i
$694$	−25.7536	+	24.3292i	−0.977593	+	0.923523i
$695$	0.103300	+	0.0635440i	0.00391838	+	0.00241036i
$696$	21.5451	−	1.54914i	0.816664	−	0.0587199i
$697$	26.9990	+	4.27622i	1.02266	+	0.161973i
$698$	3.25841	−	4.22668i	0.123333	−	0.159982i
$699$	8.10721			0.306643
$700$	16.8547	−	20.4805i	0.637047	−	0.774090i
$701$	22.6934			0.857118			0.428559	−	0.903514i	$-0.359021\pi$
$701$	22.6934			0.857118			0.428559	+	0.903514i	$0.359021\pi$
$702$	2.39760	−	3.11008i	0.0904917	−	0.117382i
$703$	24.4785	+	3.87702i	0.923225	+	0.146224i
$704$	21.6843	+	11.4207i	0.817260	+	0.430433i
$705$	−10.2125	−	24.7741i	−0.384624	−	0.933048i
$706$	15.4556	−	14.6008i	0.581679	−	0.549507i
$707$	9.92645	−	9.92645i	0.373322	−	0.373322i
$708$	−11.9598	−	2.59854i	−0.449478	−	0.0976590i
$709$	−23.3358	−	7.58226i	−0.876394	−	0.284758i	−0.163935	−	0.986471i	$-0.552419\pi$
$709$	−23.3358	−	7.58226i	−0.876394	−	0.284758i	−0.712459	+	0.701714i	$0.752419\pi$
$710$	25.1583	+	31.3203i	0.944173	+	1.17543i
$711$	−0.409212	+	0.132961i	−0.0153467	+	0.00498643i
$712$	0.601332	−	7.03242i	0.0225359	−	0.263551i
$713$	5.98951	+	11.7551i	0.224309	+	0.440231i
$714$	−2.77198	−	21.4284i	−0.103739	−	0.801937i
$715$	−18.9603	−	1.52465i	−0.709077	−	0.0570187i
$716$	5.23373	+	4.27740i	0.195594	+	0.159854i
$717$	3.71781	+	23.4733i	0.138844	+	0.876627i
$718$	32.7381	−	22.3918i	1.22178	−	0.835656i
$719$	−30.8564	−	22.4185i	−1.15075	−	0.836068i	−0.162168	−	0.986763i	$-0.551849\pi$
$719$	−30.8564	−	22.4185i	−1.15075	−	0.836068i	−0.988580	+	0.150695i	$0.951849\pi$
$720$	5.52065	−	7.03722i	0.205742	−	0.262262i
$721$	11.2749	−	8.19173i	0.419901	−	0.305076i
$722$	0.719096	−	2.01621i	0.0267620	−	0.0750356i
$723$	−10.8222	+	21.2397i	−0.402481	+	0.789913i
$724$	6.15333	−	15.8165i	0.228687	−	0.587816i
$725$	−34.0818	+	17.2198i	−1.26577	+	0.639529i
$726$	−2.24471	−	0.421267i	−0.0833090	−	0.0156347i
$727$	−17.5691	−	8.95193i	−0.651603	−	0.332009i	0.0967500	−	0.995309i	$-0.469155\pi$
$727$	−17.5691	−	8.95193i	−0.651603	−	0.332009i	−0.748353	+	0.663300i	$0.769155\pi$
$728$	−13.6360	+	15.7489i	−0.505386	+	0.583693i
$729$	0.587785	+	0.809017i	0.0217698	+	0.0299636i
$730$	−9.87070	−	4.44156i	−0.365331	−	0.164390i
$731$	−4.61661	+	6.35421i	−0.170751	+	0.235019i
$732$	14.8922	−	6.55015i	0.550430	−	0.242100i
$733$	11.6075	−	1.83845i	0.428732	−	0.0679046i	0.0616607	−	0.998097i	$-0.480360\pi$
$733$	11.6075	−	1.83845i	0.428732	−	0.0679046i	0.367072	+	0.930193i	$0.380360\pi$
$734$	32.6105	+	17.8014i	1.20368	+	0.657060i
$735$	−0.0411437	−	0.0673973i	−0.00151761	−	0.00248599i
$736$	−22.0767	+	31.3588i	−0.813758	+	1.15590i
$737$	3.64446	−	1.85695i	0.134246	−	0.0684015i
$738$	6.43920	−	1.89160i	0.237030	−	0.0696309i
$739$	−11.7485	−	36.1581i	−0.432175	−	1.33010i	−0.895954	−	0.444147i	$-0.853507\pi$
$739$	−11.7485	−	36.1581i	−0.432175	−	1.33010i	0.463779	−	0.885951i	$-0.346493\pi$
$740$	24.2418	+	3.34471i	0.891145	+	0.122954i
$741$	3.88639	−	11.9611i	0.142770	−	0.439401i
$742$	−1.35057	+	47.4862i	−0.0495811	+	1.74327i
$743$	23.1808	+	23.1808i	0.850422	+	0.850422i	0.990185	−	0.139763i	$-0.0446339\pi$
$743$	23.1808	+	23.1808i	0.850422	+	0.850422i	−0.139763	+	0.990185i	$0.544634\pi$
$744$	2.07194	+	5.09934i	0.0759609	+	0.186951i
$745$	−1.63769	−	1.92410i	−0.0600001	−	0.0704935i
$746$	−15.4810	−	32.6458i	−0.566800	−	1.19525i
$747$	−1.82263	+	11.5076i	−0.0666866	+	0.421043i
$748$	−26.3338	+	23.4970i	−0.962857	+	0.859134i
$749$			14.5433i			0.531400i
$750$	−4.20449	+	15.2421i	−0.153526	+	0.556564i
$751$			6.42557i			0.234473i	0.993104	+	0.117236i	$0.0374035\pi$
$751$			6.42557i			0.234473i	−0.993104	+	0.117236i	$0.962597\pi$
$752$	16.7743	+	44.9043i	0.611694	+	1.63749i
$753$	−0.273778	+	1.72856i	−0.00997701	+	0.0629924i
$754$	27.0978	−	12.8501i	0.986844	−	0.467973i
$755$	8.24414	+	9.68595i	0.300035	+	0.352508i
$756$	−2.86914	−	4.46199i	−0.104349	−	0.162281i
$757$	−13.6083	−	13.6083i	−0.494602	−	0.494602i	0.415150	−	0.909753i	$-0.363729\pi$
$757$	−13.6083	−	13.6083i	−0.494602	−	0.494602i	−0.909753	+	0.415150i	$0.863729\pi$
$758$	32.4728	+	0.923570i	1.17947	+	0.0335456i
$759$	−6.41794	+	19.7524i	−0.232957	+	0.716966i
$760$	9.08204	−	27.1673i	0.329440	−	0.985462i
$761$	2.47261	+	7.60993i	0.0896322	+	0.275860i	0.985818	−	0.167820i	$-0.0536728\pi$
$761$	2.47261	+	7.60993i	0.0896322	+	0.275860i	−0.896185	+	0.443680i	$0.853673\pi$
$762$	−4.90443	−	16.6952i	−0.177669	−	0.604802i
$763$	32.9967	−	16.8126i	1.19456	−	0.608659i
$764$	2.75825	−	48.4509i	0.0997899	−	1.75289i
$765$	6.71119	+	10.9936i	0.242644	+	0.397474i
$766$	−15.0750	+	27.6161i	−0.544682	+	0.997810i
$767$	−16.7832	+	2.65819i	−0.606005	+	0.0959817i
$768$	−10.2917	+	12.2508i	−0.371369	+	0.442062i
$769$	21.7509	−	29.9376i	0.784358	−	1.07958i	−0.210430	−	0.977609i	$-0.567486\pi$
$769$	21.7509	−	29.9376i	0.784358	−	1.07958i	0.994788	−	0.101967i	$-0.0325137\pi$
$770$	−10.5441	+	23.4326i	−0.379983	+	0.844454i
$771$	−0.662185	−	0.911419i	−0.0238480	−	0.0328240i
$772$	−41.8730	−	24.4277i	−1.50704	−	0.879172i
$773$	44.7020	+	22.7768i	1.60782	+	0.819226i	0.999677	+	0.0253983i	$0.00808540\pi$
$773$	44.7020	+	22.7768i	1.60782	+	0.819226i

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:	\( N \)	\(=\)	\( 300 = 2^{2} \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	300.w (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.12003 - 0.863445i) q^{2} +(-0.987688 - 0.156434i) q^{3} +(0.508925 + 1.93417i) q^{4} +(-1.70279 + 1.44932i) q^{5} +(0.971166 + 1.02803i) q^{6} +(1.87554 - 1.87554i) q^{7} +(1.10004 - 2.60575i) q^{8} +(0.951057 + 0.309017i) q^{9} +O(q^{10})\)	\(q+(-1.12003 - 0.863445i) q^{2} +(-0.987688 - 0.156434i) q^{3} +(0.508925 + 1.93417i) q^{4} +(-1.70279 + 1.44932i) q^{5} +(0.971166 + 1.02803i) q^{6} +(1.87554 - 1.87554i) q^{7} +(1.10004 - 2.60575i) q^{8} +(0.951057 + 0.309017i) q^{9} +(3.15857 - 0.153014i) q^{10} +(-2.91356 + 0.946674i) q^{11} +(-0.200089 - 1.98997i) q^{12} +(-1.26064 - 2.47414i) q^{13} +(-3.72009 + 0.481232i) q^{14} +(1.90854 - 1.16510i) q^{15} +(-3.48199 + 1.96869i) q^{16} +(-0.901092 - 5.68927i) q^{17} +(-0.798391 - 1.16729i) q^{18} +(-3.66420 - 2.66220i) q^{19} +(-3.66981 - 2.55588i) q^{20} +(-2.14585 + 1.55905i) q^{21} +(4.08067 + 1.45540i) q^{22} +(-3.07781 + 6.04055i) q^{23} +(-1.49412 + 2.40158i) q^{24} +(0.798959 - 4.93575i) q^{25} +(-0.724334 + 3.85959i) q^{26} +(-0.891007 - 0.453990i) q^{27} +(4.58212 + 2.67310i) q^{28} +(-4.48892 - 6.17846i) q^{29} +(-3.14362 - 0.342980i) q^{30} +(1.14385 - 1.57437i) q^{31} +(5.59978 + 0.801520i) q^{32} +(3.02578 - 0.479237i) q^{33} +(-3.90312 + 7.15018i) q^{34} +(-0.475391 + 5.91190i) q^{35} +(-0.113673 + 1.99677i) q^{36} +(-4.87556 + 2.48422i) q^{37} +(1.80534 + 6.14557i) q^{38} +(0.858075 + 2.64088i) q^{39} +(1.90343 + 6.03133i) q^{40} +(-1.46647 + 4.51334i) q^{41} +(3.74957 + 0.106643i) q^{42} +(-0.964168 - 0.964168i) q^{43} +(-3.31381 - 5.15353i) q^{44} +(-2.06731 + 0.852193i) q^{45} +(8.66292 - 4.10806i) q^{46} +(1.87467 - 11.8362i) q^{47} +(3.74709 - 1.39975i) q^{48} -0.0353135i q^{49} +(-5.15661 + 4.83832i) q^{50} +5.76019i q^{51} +(4.14382 - 3.69743i) q^{52} +(1.98116 - 12.5085i) q^{53} +(0.605956 + 1.27782i) q^{54} +(3.58914 - 5.83466i) q^{55} +(-2.82403 - 6.95035i) q^{56} +(3.20263 + 3.20263i) q^{57} +(-0.307052 + 10.7960i) q^{58} +(1.89101 - 5.81992i) q^{59} +(3.22480 + 3.09849i) q^{60} +(2.51370 + 7.73638i) q^{61} +(-2.64052 + 0.775690i) q^{62} +(2.36332 - 1.20417i) q^{63} +(-5.57984 - 5.73283i) q^{64} +(5.73240 + 2.38586i) q^{65} +(-3.80276 - 2.07584i) q^{66} +(-1.31873 + 0.208866i) q^{67} +(10.5454 - 4.63827i) q^{68} +(3.98487 - 5.48470i) q^{69} +(5.63705 - 6.21102i) q^{70} +(7.46718 + 10.2777i) q^{71} +(1.85142 - 2.13828i) q^{72} +(-3.04977 - 1.55394i) q^{73} +(7.60576 + 1.42738i) q^{74} +(-1.56124 + 4.75000i) q^{75} +(3.28432 - 8.44202i) q^{76} +(-3.68898 + 7.24004i) q^{77} +(1.31919 - 3.69876i) q^{78} +(-0.348097 + 0.252907i) q^{79} +(3.07583 - 8.39877i) q^{80} +(0.809017 + 0.587785i) q^{81} +(5.53951 - 3.78884i) q^{82} +(1.82263 + 11.5076i) q^{83} +(-4.10754 - 3.35699i) q^{84} +(9.77992 + 8.38164i) q^{85} +(0.247389 + 1.91240i) q^{86} +(3.46713 + 6.80462i) q^{87} +(-0.738228 + 8.63339i) q^{88} +(2.37328 - 0.771124i) q^{89} +(3.05127 + 0.830528i) q^{90} +(-7.00472 - 2.27597i) q^{91} +(-13.2498 - 2.87881i) q^{92} +(-1.37605 + 1.37605i) q^{93} +(-12.3196 + 11.6382i) q^{94} +(10.0977 - 0.777436i) q^{95} +(-5.40545 - 1.66765i) q^{96} +(-12.2095 - 1.93379i) q^{97} +(-0.0304912 + 0.0395521i) q^{98} -3.06350 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240q + 12q^{8} + O(q^{10}) \)	\( 240q + 12q^{8} + 8q^{10} + 8q^{12} + 4q^{13} + 20q^{17} - 20q^{20} - 12q^{22} + 20q^{25} + 4q^{28} - 8q^{30} - 20q^{32} - 8q^{33} - 4q^{37} - 76q^{38} - 92q^{40} - 20q^{42} - 140q^{44} - 4q^{45} - 16q^{48} - 164q^{50} - 172q^{52} - 4q^{53} - 120q^{58} + 20q^{60} - 44q^{62} - 60q^{64} - 20q^{65} + 16q^{68} - 44q^{70} + 12q^{72} - 44q^{73} - 48q^{77} + 24q^{78} - 4q^{80} + 60q^{81} + 24q^{82} + 80q^{84} - 64q^{85} + 60q^{88} - 260q^{89} + 48q^{90} + 144q^{92} - 64q^{93} + 40q^{94} - 20q^{96} - 180q^{97} + 256q^{98} + O(q^{100}) \)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Properties

Related objects

Downloads

Learn more about