LMFDB - Embedded newform 273.2.u.c.251.15

Newspace parameters

Level:	$ N $	$=$	$ 273 = 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	273.u (of order $6$, degree $2$, minimal)

Newform invariants

Self dual:	no
Analytic conductor:	$2.17991597518$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$32$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			251.15
Character	$\chi$	$=$	273.251
Dual form			273.2.u.c.62.15

$q$-expansion

$f(q)$	$=$	$q+(-0.230023 + 0.398412i) q^{2} +(-0.688459 + 1.58935i) q^{3} +(0.894179 + 1.54876i) q^{4} +2.35202i q^{5} +(-0.474854 - 0.639877i) q^{6} +(1.77437 + 1.96255i) q^{7} -1.74282 q^{8} +(-2.05205 - 2.18840i) q^{9} +O(q^{10})$	\(q+(-0.230023 + 0.398412i) q^{2} +(-0.688459 + 1.58935i) q^{3} +(0.894179 + 1.54876i) q^{4} +2.35202i q^{5} +(-0.474854 - 0.639877i) q^{6} +(1.77437 + 1.96255i) q^{7} -1.74282 q^{8} +(-2.05205 - 2.18840i) q^{9} +(-0.937075 - 0.541020i) q^{10} +(1.89523 - 3.28263i) q^{11} +(-3.07713 + 0.354901i) q^{12} +(-0.259976 - 3.59617i) q^{13} +(-1.19005 + 0.255498i) q^{14} +(-3.73818 - 1.61927i) q^{15} +(-1.38747 + 2.40316i) q^{16} +(-0.112205 - 0.194344i) q^{17} +(1.34390 - 0.314178i) q^{18} +(0.495455 + 0.858154i) q^{19} +(-3.64273 + 2.10313i) q^{20} +(-4.34076 + 1.46895i) q^{21} +(0.871892 + 1.51016i) q^{22} +(5.19329 + 2.99835i) q^{23} +(1.19986 - 2.76995i) q^{24} -0.532016 q^{25} +(1.49256 + 0.723624i) q^{26} +(4.89088 - 1.75480i) q^{27} +(-1.45292 + 4.50295i) q^{28} +(-3.01682 - 1.74176i) q^{29} +(1.50501 - 1.11687i) q^{30} -8.13560 q^{31} +(-2.38112 - 4.12422i) q^{32} +(3.91245 + 5.27212i) q^{33} +0.103239 q^{34} +(-4.61597 + 4.17336i) q^{35} +(1.55441 - 5.13496i) q^{36} +(5.67975 + 3.27921i) q^{37} -0.455865 q^{38} +(5.89454 + 2.06262i) q^{39} -4.09916i q^{40} +(1.81328 + 1.04690i) q^{41} +(0.413226 - 2.06730i) q^{42} +(-0.647431 - 1.12138i) q^{43} +6.77868 q^{44} +(5.14717 - 4.82647i) q^{45} +(-2.38916 + 1.37938i) q^{46} -7.64729i q^{47} +(-2.86425 - 3.85965i) q^{48} +(-0.703223 + 6.96459i) q^{49} +(0.122376 - 0.211962i) q^{50} +(0.386129 - 0.0445343i) q^{51} +(5.33714 - 3.61826i) q^{52} +7.19458i q^{53} +(-0.425883 + 2.35223i) q^{54} +(7.72082 + 4.45762i) q^{55} +(-3.09241 - 3.42038i) q^{56} +(-1.70500 + 0.196647i) q^{57} +(1.38788 - 0.801293i) q^{58} +(6.86061 - 3.96098i) q^{59} +(-0.834737 - 7.23748i) q^{60} +(-1.77043 + 1.02216i) q^{61} +(1.87138 - 3.24132i) q^{62} +(0.653753 - 7.91028i) q^{63} -3.35902 q^{64} +(8.45827 - 0.611471i) q^{65} +(-3.00043 + 0.346056i) q^{66} +(9.58594 + 5.53444i) q^{67} +(0.200662 - 0.347557i) q^{68} +(-8.34078 + 6.18970i) q^{69} +(-0.600936 - 2.79903i) q^{70} +(-5.36792 - 9.29750i) q^{71} +(3.57635 + 3.81399i) q^{72} +1.05464 q^{73} +(-2.61295 + 1.50859i) q^{74} +(0.366271 - 0.845558i) q^{75} +(-0.886051 + 1.53469i) q^{76} +(9.80516 - 2.10512i) q^{77} +(-2.17765 + 1.87401i) q^{78} -8.02255 q^{79} +(-5.65230 - 3.26336i) q^{80} +(-0.578184 + 8.98141i) q^{81} +(-0.834193 + 0.481621i) q^{82} -8.85334i q^{83} +(-6.15647 - 5.40930i) q^{84} +(0.457103 - 0.263908i) q^{85} +0.595696 q^{86} +(4.84523 - 3.59565i) q^{87} +(-3.30304 + 5.72103i) q^{88} +(8.09262 + 4.67228i) q^{89} +(0.738955 + 3.16089i) q^{90} +(6.59637 - 6.89115i) q^{91} +10.7242i q^{92} +(5.60103 - 12.9303i) q^{93} +(3.04677 + 1.75906i) q^{94} +(-2.01840 + 1.16532i) q^{95} +(8.19412 - 0.945072i) q^{96} +(-1.92049 - 3.32639i) q^{97} +(-2.61302 - 1.88219i) q^{98} +(-11.0728 + 2.58860i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q - 40 q^{4} - 6 q^{9}+O(q^{10}) $ 64 * q - 40 * q^4 - 6 * q^9	$ 64 q - 40 q^{4} - 6 q^{9} + 18 q^{15} - 32 q^{16} + 24 q^{22} - 80 q^{25} + 12 q^{28} + 20 q^{30} + 50 q^{36} - 36 q^{37} - 60 q^{39} + 48 q^{43} - 84 q^{46} - 16 q^{49} + 52 q^{51} - 48 q^{58} - 36 q^{63} + 176 q^{64} + 60 q^{67} - 66 q^{72} + 166 q^{78} - 104 q^{79} - 30 q^{81} + 60 q^{84} + 132 q^{85} - 8 q^{91} - 162 q^{93}+O(q^{100}) $ 64 * q - 40 * q^4 - 6 * q^9 + 18 * q^15 - 32 * q^16 + 24 * q^22 - 80 * q^25 + 12 * q^28 + 20 * q^30 + 50 * q^36 - 36 * q^37 - 60 * q^39 + 48 * q^43 - 84 * q^46 - 16 * q^49 + 52 * q^51 - 48 * q^58 - 36 * q^63 + 176 * q^64 + 60 * q^67 - 66 * q^72 + 166 * q^78 - 104 * q^79 - 30 * q^81 + 60 * q^84 + 132 * q^85 - 8 * q^91 - 162 * q^93

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/273\mathbb{Z}\right)^\times$.

$n$	$92$	$106$	$157$
$\chi(n)$	$-1$	$e\left(\frac{1}{6}\right)$	$-1$

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 $

$2$	−0.230023	+	0.398412i	−0.162651	+	0.281720i	−0.935819	−	0.352482i	$-0.885338\pi$
$2$	−0.230023	+	0.398412i	−0.162651	+	0.281720i	0.773168	+	0.634202i	$0.218671\pi$
$3$	−0.688459	+	1.58935i	−0.397482	+	0.917610i
$3$	−0.688459	+	1.58935i	−0.397482	+	0.917610i
$4$	0.894179	+	1.54876i	0.447089	+	0.774381i
$5$			2.35202i			1.05186i	0.850529	+	0.525929i	$0.176282\pi$
$5$			2.35202i			1.05186i	−0.850529	+	0.525929i	$0.823718\pi$
$6$	−0.474854	−	0.639877i	−0.193858	−	0.261229i
$7$	1.77437	+	1.96255i	0.670649	+	0.741775i
$7$	1.77437	+	1.96255i	0.670649	+	0.741775i
$8$	−1.74282			−0.616180
$9$	−2.05205	−	2.18840i	−0.684017	−	0.729466i
$10$	−0.937075	−	0.541020i	−0.296329	−	0.171086i
$11$	1.89523	−	3.28263i	0.571432	−	0.989749i	−0.424987	−	0.905199i	$-0.639721\pi$
$11$	1.89523	−	3.28263i	0.571432	−	0.989749i	0.996419	−	0.0845500i	$-0.0269453\pi$
$12$	−3.07713	+	0.354901i	−0.888290	+	0.102451i
$13$	−0.259976	−	3.59617i	−0.0721045	−	0.997397i
$13$	−0.259976	−	3.59617i	−0.0721045	−	0.997397i
$14$	−1.19005	+	0.255498i	−0.318054	+	0.0682846i
$15$	−3.73818	−	1.61927i	−0.965195	−	0.418094i
$16$	−1.38747	+	2.40316i	−0.346867	+	0.600791i
$17$	−0.112205	−	0.194344i	−0.0272137	−	0.0471355i	0.852098	−	0.523383i	$-0.175330\pi$
$17$	−0.112205	−	0.194344i	−0.0272137	−	0.0471355i	−0.879311	+	0.476247i	$0.841997\pi$
$18$	1.34390	−	0.314178i	0.316761	−	0.0740526i
$19$	0.495455	+	0.858154i	0.113665	+	0.196874i	0.917245	−	0.398323i	$-0.130408\pi$
$19$	0.495455	+	0.858154i	0.113665	+	0.196874i	−0.803580	+	0.595197i	$0.797074\pi$
$20$	−3.64273	+	2.10313i	−0.814538	+	0.470274i
$21$	−4.34076	+	1.46895i	−0.947231	+	0.320552i
$22$	0.871892	+	1.51016i	0.185888	+	0.321967i
$23$	5.19329	+	2.99835i	1.08288	+	0.625199i	0.931671	−	0.363304i	$-0.118351\pi$
$23$	5.19329	+	2.99835i	1.08288	+	0.625199i	0.151205	+	0.988502i	$0.451685\pi$
$24$	1.19986	−	2.76995i	0.244920	−	0.565413i
$25$	−0.532016			−0.106403
$26$	1.49256	+	0.723624i	0.292714	+	0.141914i
$27$	4.89088	−	1.75480i	0.941250	−	0.337711i
$28$	−1.45292	+	4.50295i	−0.274577	+	0.850978i
$29$	−3.01682	−	1.74176i	−0.560210	−	0.323438i	0.193020	−	0.981195i	$-0.438172\pi$
$29$	−3.01682	−	1.74176i	−0.560210	−	0.323438i	−0.753230	+	0.657757i	$0.771505\pi$
$30$	1.50501	−	1.11687i	0.274775	−	0.203911i
$31$	−8.13560			−1.46120			−0.730599	−	0.682807i	$-0.760759\pi$
$31$	−8.13560			−1.46120			−0.730599	+	0.682807i	$0.760759\pi$
$32$	−2.38112	−	4.12422i	−0.420927	−	0.729066i
$33$	3.91245	+	5.27212i	0.681070	+	0.917759i
$34$	0.103239			0.0177053
$35$	−4.61597	+	4.17336i	−0.780241	+	0.705427i
$36$	1.55441	−	5.13496i	0.259069	−	0.855826i
$37$	5.67975	+	3.27921i	0.933746	+	0.539098i	0.887994	−	0.459855i	$-0.152098\pi$
$37$	5.67975	+	3.27921i	0.933746	+	0.539098i	0.0457513	+	0.998953i	$0.485432\pi$
$38$	−0.455865			−0.0739511
$39$	5.89454	+	2.06262i	0.943882	+	0.330283i
$40$		−	4.09916i		−	0.648133i
$41$	1.81328	+	1.04690i	0.283187	+	0.163498i	0.634865	−	0.772623i	$-0.281056\pi$
$41$	1.81328	+	1.04690i	0.283187	+	0.163498i	−0.351679	+	0.936121i	$0.614389\pi$
$42$	0.413226	−	2.06730i	0.0637622	−	0.318992i
$43$	−0.647431	−	1.12138i	−0.0987322	−	0.171009i	0.812428	−	0.583062i	$-0.198145\pi$
$43$	−0.647431	−	1.12138i	−0.0987322	−	0.171009i	−0.911160	+	0.412052i	$0.864812\pi$
$44$	6.77868			1.02192
$45$	5.14717	−	4.82647i	0.767294	−	0.719488i
$46$	−2.38916	+	1.37938i	−0.352262	+	0.203378i
$47$		−	7.64729i		−	1.11547i	−0.830018	−	0.557736i	$-0.811670\pi$
$47$		−	7.64729i		−	1.11547i	0.830018	−	0.557736i	$-0.188330\pi$
$48$	−2.86425	−	3.85965i	−0.413419	−	0.557092i
$49$	−0.703223	+	6.96459i	−0.100460	+	0.994941i
$50$	0.122376	−	0.211962i	0.0173066	−	0.0299759i
$51$	0.386129	−	0.0445343i	0.0540689	−	0.00623605i
$52$	5.33714	−	3.61826i	0.740129	−	0.501762i
$53$			7.19458i			0.988252i	0.869390	+	0.494126i	$0.164512\pi$
$53$			7.19458i			0.988252i	−0.869390	+	0.494126i	$0.835488\pi$
$54$	−0.425883	+	2.35223i	−0.0579554	+	0.320098i
$55$	7.72082	+	4.45762i	1.04107	+	0.601065i
$56$	−3.09241	−	3.42038i	−0.413241	−	0.457067i
$57$	−1.70500	+	0.196647i	−0.225833	+	0.0260466i
$58$	1.38788	−	0.801293i	0.182238	−	0.105215i
$59$	6.86061	−	3.96098i	0.893176	−	0.515675i	0.0181958	−	0.999834i	$-0.494208\pi$
$59$	6.86061	−	3.96098i	0.893176	−	0.515675i	0.874980	+	0.484159i	$0.160874\pi$
$60$	−0.834737	−	7.23748i	−0.107764	−	0.934354i
$61$	−1.77043	+	1.02216i	−0.226680	+	0.130874i	−0.609040	−	0.793140i	$-0.708445\pi$
$61$	−1.77043	+	1.02216i	−0.226680	+	0.130874i	0.382359	+	0.924014i	$0.375112\pi$
$62$	1.87138	−	3.24132i	0.237665	−	0.411648i
$63$	0.653753	−	7.91028i	0.0823651	−	0.996602i
$64$	−3.35902			−0.419877
$65$	8.45827	−	0.611471i	1.04912	−	0.0758436i
$66$	−3.00043	+	0.346056i	−0.369328	+	0.0425965i
$67$	9.58594	+	5.53444i	1.17111	+	0.676140i	0.953941	−	0.299994i	$-0.0969848\pi$
$67$	9.58594	+	5.53444i	1.17111	+	0.676140i	0.217168	+	0.976134i	$0.430318\pi$
$68$	0.200662	−	0.347557i	0.0243339	−	0.0421475i
$69$	−8.34078	+	6.18970i	−1.00411	+	0.745153i
$70$	−0.600936	−	2.79903i	−0.0718256	−	0.334548i
$71$	−5.36792	−	9.29750i	−0.637054	−	1.10341i	−0.986076	−	0.166296i	$-0.946819\pi$
$71$	−5.36792	−	9.29750i	−0.637054	−	1.10341i	0.349021	−	0.937115i	$-0.386514\pi$
$72$	3.57635	+	3.81399i	0.421477	+	0.449483i
$73$	1.05464			0.123437			0.0617183	−	0.998094i	$-0.480342\pi$
$73$	1.05464			0.123437			0.0617183	+	0.998094i	$0.480342\pi$
$74$	−2.61295	+	1.50859i	−0.303749	+	0.175370i
$75$	0.366271	−	0.845558i	0.0422933	−	0.0976366i
$76$	−0.886051	+	1.53469i	−0.101637	+	0.176040i
$77$	9.80516	−	2.10512i	1.11740	−	0.239900i
$78$	−2.17765	+	1.87401i	−0.246571	+	0.212189i
$79$	−8.02255			−0.902608			−0.451304	−	0.892370i	$-0.649041\pi$
$79$	−8.02255			−0.902608			−0.451304	+	0.892370i	$0.649041\pi$
$80$	−5.65230	−	3.26336i	−0.631946	−	0.364854i
$81$	−0.578184	+	8.98141i	−0.0642426	+	0.997934i
$82$	−0.834193	+	0.481621i	−0.0921212	+	0.0531862i
$83$		−	8.85334i		−	0.971780i	−0.874020	−	0.485890i	$-0.838495\pi$
$83$		−	8.85334i		−	0.971780i	0.874020	−	0.485890i	$-0.161505\pi$
$84$	−6.15647	−	5.40930i	−0.671726	−	0.590203i
$85$	0.457103	−	0.263908i	0.0495798	−	0.0286249i
$86$	0.595696			0.0642356
$87$	4.84523	−	3.59565i	0.519463	−	0.385494i
$88$	−3.30304	+	5.72103i	−0.352105	+	0.609864i
$89$	8.09262	+	4.67228i	0.857816	+	0.495261i	0.863280	−	0.504725i	$-0.168406\pi$
$89$	8.09262	+	4.67228i	0.857816	+	0.495261i	−0.00546401	+	0.999985i	$0.501739\pi$
$90$	0.738955	+	3.16089i	0.0778927	+	0.333187i
$91$	6.59637	−	6.89115i	0.691487	−	0.722388i
$92$			10.7242i			1.11808i
$93$	5.60103	−	12.9303i	0.580799	−	1.34081i
$94$	3.04677	+	1.75906i	0.314251	+	0.181433i
$95$	−2.01840	+	1.16532i	−0.207083	+	0.119560i
$96$	8.19412	−	0.945072i	0.836309	−	0.0964560i
$97$	−1.92049	−	3.32639i	−0.194997	−	0.337744i	0.751903	−	0.659274i	$-0.229136\pi$
$97$	−1.92049	−	3.32639i	−0.194997	−	0.337744i	−0.946899	+	0.321530i	$0.895803\pi$
$98$	−2.61302	−	1.88219i	−0.263955	−	0.190130i
$99$	−11.0728	+	2.58860i	−1.11286	+	0.260164i
$100$	−0.475717	−	0.823966i	−0.0475717	−	0.0823966i
$101$	−6.18926	+	10.7201i	−0.615854	+	1.06669i	0.374380	+	0.927276i	$0.377856\pi$
$101$	−6.18926	+	10.7201i	−0.615854	+	1.06669i	−0.990234	+	0.139416i	$0.955478\pi$
$102$	−0.0710757	+	0.164082i	−0.00703754	+	0.0162466i
$103$		−	3.71736i		−	0.366283i	−0.983087	−	0.183141i	$-0.941373\pi$
$103$		−	3.71736i		−	0.366283i	0.983087	−	0.183141i	$-0.0586266\pi$
$104$	0.453092	+	6.26747i	0.0444294	+	0.614576i
$105$	−3.45502	−	10.2096i	−0.337175	−	0.996351i
$106$	−2.86641	−	1.65492i	−0.278410	−	0.160740i
$107$	14.5306	+	8.38925i	1.40473	+	0.811019i	0.994873	−	0.101132i	$-0.0322466\pi$
$107$	14.5306	+	8.38925i	1.40473	+	0.811019i	0.409853	+	0.912151i	$0.365580\pi$
$108$	7.09108	+	6.00571i	0.682340	+	0.577899i
$109$		−	9.13097i		−	0.874588i	−0.899319	−	0.437294i	$-0.855937\pi$
$109$		−	9.13097i		−	0.874588i	0.899319	−	0.437294i	$-0.144063\pi$
$110$	−3.55194	+	2.05071i	−0.338664	+	0.195528i
$111$	−9.12207	+	6.76950i	−0.865829	+	0.642533i
$112$	−7.17822	+	1.54113i	−0.678278	+	0.145623i
$113$	−17.6645	+	10.1986i	−1.66174	+	0.959404i	−0.689851	+	0.723952i	$0.742324\pi$
$113$	−17.6645	+	10.1986i	−1.66174	+	0.959404i	−0.971886	+	0.235453i	$0.924343\pi$
$114$	0.313844	−	0.724528i	0.0293942	−	0.0678583i
$115$	−7.05219	+	12.2147i	−0.657620	+	1.13903i
$116$		−	6.22979i		−	0.578422i
$117$	−7.33636	+	7.94844i	−0.678247	+	0.734834i
$118$			3.64447i			0.335500i
$119$	0.182318	−	0.565047i	0.0167131	−	0.0517978i
$120$	6.51498	+	2.82210i	0.594734	+	0.257621i
$121$	−1.68376	−	2.91636i	−0.153069	−	0.265124i
$122$		−	0.940481i		−	0.0851471i
$123$	−2.91225	+	2.16118i	−0.262589	+	0.194867i
$124$	−7.27468	−	12.6001i	−0.653286	−	1.13152i
$125$			10.5088i			0.939936i
$126$	3.00117	+	2.08001i	0.267366	+	0.185302i
$127$	9.42915	−	16.3318i	0.836702	−	1.44921i	−0.0559355	−	0.998434i	$-0.517814\pi$
$127$	9.42915	−	16.3318i	0.836702	−	1.44921i	0.892637	−	0.450776i	$-0.148853\pi$
$128$	5.53489	−	9.58672i	0.489220	−	0.847354i
$129$	2.22800	−	0.256967i	0.196164	−	0.0226246i
$130$	−1.70198	+	3.51053i	−0.149274	+	0.307894i
$131$	−12.9891			−1.13486			−0.567431	−	0.823421i	$-0.692063\pi$
$131$	−12.9891			−1.13486			−0.567431	+	0.823421i	$0.692063\pi$
$132$	−4.66684	+	10.7737i	−0.406196	+	0.937728i
$133$	−0.805051	+	2.49504i	−0.0698067	+	0.216347i
$134$	−4.40998	+	2.54610i	−0.380964	+	0.219950i
$135$	4.12733	+	11.5035i	0.355224	+	0.990060i
$136$	0.195553	+	0.338708i	0.0167685	+	0.0290439i
$137$	3.09348	+	5.35807i	0.264294	+	0.457771i	0.967378	−	0.253336i	$-0.0815278\pi$
$137$	3.09348	+	5.35807i	0.264294	+	0.457771i	−0.703084	+	0.711106i	$0.748194\pi$
$138$	−0.547479	−	4.74684i	−0.0466045	−	0.404078i
$139$	12.1887	−	7.03717i	1.03384	−	0.596885i	0.115754	−	0.993278i	$-0.463071\pi$
$139$	12.1887	−	7.03717i	1.03384	−	0.596885i	0.918081	+	0.396393i	$0.129738\pi$
$140$	−10.5910	−	3.41731i	−0.895107	−	0.288816i
$141$	12.1542	+	5.26484i	1.02357	+	0.443380i
$142$	4.93898			0.414470
$143$	−12.2976	−	5.96214i	−1.02838	−	0.498579i
$144$	8.10624	−	1.89508i	0.675520	−	0.157923i
$145$	4.09667	−	7.09564i	0.340210	−	0.589261i
$146$	−0.242592	+	0.420182i	−0.0200771	+	0.0347745i
$147$	−10.5850	−	5.91249i	−0.873037	−	0.487654i
$148$			11.7288i			0.964100i
$149$	−4.54225	−	7.86740i	−0.372115	−	0.644523i	0.617775	−	0.786355i	$-0.288034\pi$
$149$	−4.54225	−	7.86740i	−0.372115	−	0.644523i	−0.989891	+	0.141832i	$0.954701\pi$
$150$	0.252630	+	0.340425i	0.0206271	+	0.0277956i
$151$		−	15.9114i		−	1.29485i	−0.762130	−	0.647424i	$-0.775846\pi$
$151$		−	15.9114i		−	1.29485i	0.762130	−	0.647424i	$-0.224154\pi$
$152$	−0.863490	−	1.49561i	−0.0700383	−	0.121310i
$153$	−0.195053	+	0.644353i	−0.0157691	+	0.0520929i
$154$	−1.41671	+	4.39072i	−0.114162	+	0.353814i
$155$		−	19.1351i		−	1.53697i
$156$	2.07626	+	10.9736i	0.166234	+	0.878591i
$157$			20.1836i			1.61082i	0.592716	+	0.805411i	$0.298056\pi$
$157$			20.1836i			1.61082i	−0.592716	+	0.805411i	$0.701944\pi$
$158$	1.84537	−	3.19628i	0.146810	−	0.254283i
$159$	−11.4347	−	4.95317i	−0.906830	−	0.392812i
$160$	9.70027	−	5.60045i	0.766873	−	0.442755i
$161$	3.33040	+	15.5123i	0.262473	+	1.22254i
$162$	−3.44531	−	2.29629i	−0.270689	−	0.180413i
$163$	4.43944	−	2.56311i	0.347724	−	0.200758i	−0.315959	−	0.948773i	$-0.602326\pi$
$163$	4.43944	−	2.56311i	0.347724	−	0.200758i	0.663682	+	0.748015i	$0.268993\pi$
$164$			3.74445i			0.292392i
$165$	−12.4002	+	9.20218i	−0.965351	+	0.716388i
$166$	3.52728	+	2.03647i	0.273770	+	0.158061i
$167$	−8.25075	−	4.76358i	−0.638463	−	0.368617i	0.145559	−	0.989350i	$-0.453502\pi$
$167$	−8.25075	−	4.76358i	−0.638463	−	0.368617i	−0.784022	+	0.620733i	$0.786835\pi$
$168$	7.56516	−	2.56012i	0.583665	−	0.197518i
$169$	−12.8648	+	1.86984i	−0.989602	+	0.143834i
$170$			0.242820i			0.0186235i
$171$	0.861284	−	2.84523i	0.0658641	−	0.217580i
$172$	1.15784	−	2.00543i	0.0882843	−	0.152913i
$173$	2.96590	+	5.13709i	0.225493	+	0.390566i	0.956467	−	0.291840i	$-0.0942674\pi$
$173$	2.96590	+	5.13709i	0.225493	+	0.390566i	−0.730974	+	0.682405i	$0.760934\pi$
$174$	0.318035	+	2.75748i	0.0241102	+	0.209044i
$175$	−0.943993	−	1.04411i	−0.0713592	−	0.0789272i
$176$	5.25913	+	9.10908i	0.396422	+	0.686623i
$177$	1.57212	+	13.6309i	0.118168	+	1.02456i
$178$	−3.72298	+	2.14947i	−0.279049	+	0.161109i
$179$	12.2143	+	7.05191i	0.912937	+	0.527084i	0.881375	−	0.472418i	$-0.156619\pi$
$179$	12.2143	+	7.05191i	0.912937	+	0.527084i	0.0315618	+	0.999502i	$0.489952\pi$
$180$	12.0775	+	3.65602i	0.900207	+	0.272503i
$181$		−	18.8153i		−	1.39853i	−0.714861	−	0.699267i	$-0.753510\pi$
$181$		−	18.8153i		−	1.39853i	0.714861	−	0.699267i	$-0.246490\pi$
$182$	1.22820	+	4.21320i	0.0910400	+	0.312303i
$183$	−0.405697	−	3.51754i	−0.0299900	−	0.260024i
$184$	−9.05098	−	5.22558i	−0.667247	−	0.385235i
$185$	−7.71277	+	13.3589i	−0.567054	+	0.982167i
$186$	3.86322	+	5.20579i	0.283265	+	0.381707i
$187$	−0.850614			−0.0622030
$188$	11.8438	−	6.83805i	0.863801	−	0.498716i
$189$	12.1221	+	6.48494i	0.881754	+	0.471710i
$190$		−	1.07221i		−	0.0777860i
$191$	−12.5467	+	7.24383i	−0.907846	+	0.524145i	−0.879737	−	0.475460i	$-0.842282\pi$
$191$	−12.5467	+	7.24383i	−0.907846	+	0.524145i	−0.0281084	+	0.999605i	$0.508948\pi$
$192$	2.31254	−	5.33865i	0.166894	−	0.385284i
$193$	−22.6818	−	13.0954i	−1.63267	−	0.942624i	−0.983264	−	0.182184i	$-0.941683\pi$
$193$	−22.6818	−	13.0954i	−1.63267	−	0.942624i	−0.649408	−	0.760440i	$-0.724983\pi$
$194$	1.76703			0.126866
$195$	−4.85133	+	13.8641i	−0.347411	+	0.992829i
$196$	−11.4153	+	5.13846i	−0.815379	+	0.367033i
$197$	8.78580	−	15.2175i	0.625963	−	1.08420i	−0.362391	−	0.932026i	$-0.618040\pi$
$197$	8.78580	−	15.2175i	0.625963	−	1.08420i	0.988354	−	0.152173i	$-0.0486271\pi$
$198$	1.51567	−	5.00697i	0.107714	−	0.355830i
$199$	0.680378	−	0.392816i	0.0482307	−	0.0278460i	−0.475691	−	0.879613i	$-0.657802\pi$
$199$	0.680378	−	0.392816i	0.0482307	−	0.0278460i	0.523921	+	0.851767i	$0.324469\pi$
$200$	0.927208			0.0655635
$201$	−15.3957	+	11.4252i	−1.08593	+	0.805868i
$202$	−2.84735	−	4.93175i	−0.200339	−	0.346997i
$203$	−1.93466	−	9.01121i	−0.135786	−	0.632463i
$204$	0.414242	+	0.558201i	0.0290027	+	0.0390819i
$205$	−2.46233	+	4.26487i	−0.171976	+	0.297872i
$206$	1.48104	+	0.855080i	0.103189	+	0.0595762i
$207$	−4.09531	−	17.5178i	−0.284644	−	1.21757i
$208$	9.00289	+	4.36480i	0.624238	+	0.302644i
$209$	3.75600			0.259808
$210$	4.86235	+	0.971918i	0.335534	+	0.0670687i
$211$	−4.51799	+	7.82538i	−0.311031	+	0.538722i	−0.978586	−	0.205839i	$-0.934008\pi$
$211$	−4.51799	+	7.82538i	−0.311031	+	0.538722i	0.667555	+	0.744561i	$0.267341\pi$
$212$	−11.1427	+	6.43324i	−0.765284	+	0.441837i
$213$	18.4726	−	2.13054i	1.26572	−	0.145982i
$214$	−6.68475	+	3.85944i	−0.456960	+	0.263826i
$215$	2.63752	−	1.52277i	0.179877	−	0.103852i
$216$	−8.52392	+	3.05830i	−0.579980	+	0.208091i
$217$	−14.4356	−	15.9665i	−0.979951	−	1.08388i
$218$	3.63789	+	2.10034i	0.246389	+	0.142253i
$219$	−0.726078	+	1.67619i	−0.0490638	+	0.113267i
$220$			15.9436i			1.07492i
$221$	−0.669724	+	0.454032i	−0.0450505	+	0.0305415i
$222$	−0.598762	−	5.19149i	−0.0401863	−	0.348430i
$223$	10.0659	−	17.4347i	0.674064	−	1.16751i	−0.302678	−	0.953093i	$-0.597881\pi$
$223$	10.0659	−	17.4347i	0.674064	−	1.16751i	0.976742	−	0.214420i	$-0.0687860\pi$
$224$	3.86901	−	11.9910i	0.258509	−	0.801180i
$225$	1.09172	+	1.16426i	0.0727815	+	0.0776175i
$226$		−	9.38367i		−	0.624192i
$227$	16.1076	−	9.29975i	1.06910	−	0.617246i	0.141166	−	0.989986i	$-0.454915\pi$
$227$	16.1076	−	9.29975i	1.06910	−	0.617246i	0.927936	+	0.372740i	$0.121582\pi$
$228$	−1.82914	−	2.46481i	−0.121138	−	0.163236i
$229$	13.1082			0.866217			0.433108	−	0.901342i	$-0.357417\pi$
$229$	13.1082			0.866217			0.433108	+	0.901342i	$0.357417\pi$
$230$	−3.24433	−	5.61935i	−0.213925	−	0.370529i
$231$	−3.40469	+	17.0331i	−0.224012	+	1.12069i
$232$	5.25778	+	3.03558i	0.345190	+	0.199296i
$233$		−	11.6644i		−	0.764163i	−0.924129	−	0.382082i	$-0.875207\pi$
$233$		−	11.6644i		−	0.764163i	0.924129	−	0.382082i	$-0.124793\pi$
$234$	−1.47922	−	4.75122i	−0.0966997	−	0.310597i
$235$	17.9866			1.17332
$236$	12.2692	+	7.08364i	0.798659	+	0.461106i
$237$	5.52320	−	12.7506i	0.358770	−	0.828242i
$238$	0.183184	+	0.202612i	0.0118741	+	0.0131334i
$239$	8.52575			0.551485			0.275742	−	0.961232i	$-0.411076\pi$
$239$	8.52575			0.551485			0.275742	+	0.961232i	$0.411076\pi$
$240$	9.07798	−	6.73678i	0.585981	−	0.434857i
$241$	−4.92539	−	8.53103i	−0.317272	−	0.549532i	0.662646	−	0.748933i	$-0.269434\pi$
$241$	−4.92539	−	8.53103i	−0.317272	−	0.549532i	−0.979918	+	0.199401i	$0.936100\pi$
$242$	1.54922			0.0995874
$243$	−13.8765	−	7.10226i	−0.890179	−	0.455610i
$244$	−3.16616	−	1.82798i	−0.202693	−	0.117025i
$245$	−16.3809	−	1.65400i	−1.04654	−	0.105670i
$246$	−0.191157	−	1.65740i	−0.0121877	−	0.105672i
$247$	2.95726	−	2.00484i	0.188166	−	0.127565i
$248$	14.1789			0.900361
$249$	14.0710	+	6.09516i	0.891716	+	0.386265i
$250$	−4.18683	−	2.41727i	−0.264799	−	0.152882i
$251$	−2.43053	−	4.20980i	−0.153414	−	0.265720i	0.779067	−	0.626941i	$-0.215693\pi$
$251$	−2.43053	−	4.20980i	−0.153414	−	0.265720i	−0.932480	+	0.361221i	$0.882360\pi$
$252$	12.8357	−	6.06070i	0.808575	−	0.381788i
$253$	19.6849	−	11.3651i	1.23758	−	0.714517i
$254$	4.33785	+	7.51337i	0.272181	+	0.471431i
$255$	0.104746	+	0.908185i	0.00655944	+	0.0568728i
$256$	−0.812710	−	1.40765i	−0.0507943	−	0.0879784i
$257$	12.4841	−	21.6231i	0.778736	−	1.34881i	−0.153935	−	0.988081i	$-0.549195\pi$
$257$	12.4841	−	21.6231i	0.778736	−	1.34881i	0.932671	−	0.360729i	$-0.117472\pi$
$258$	−0.410112	+	0.946769i	−0.0255325	+	0.0589432i
$259$	3.64237	+	16.9653i	0.226326	+	1.05417i
$260$	8.51023	+	12.5531i	0.527782	+	0.778509i
$261$	2.37900	+	10.1762i	0.147256	+	0.629891i
$262$	2.98779	−	5.17501i	0.184587	−	0.319713i
$263$	4.44691	+	2.56742i	0.274208	+	0.158314i	0.630799	−	0.775947i	$-0.282727\pi$
$263$	4.44691	+	2.56742i	0.274208	+	0.158314i	−0.356590	+	0.934261i	$0.616061\pi$
$264$	−6.81870	−	9.18837i	−0.419662	−	0.565505i
$265$	−16.9218			−1.03950
$266$	−0.808873	−	0.894659i	−0.0495952	−	0.0548551i
$267$	−12.9973	+	9.64532i	−0.795422	+	0.590284i
$268$			19.7951i			1.20918i
$269$	−7.38606	−	12.7930i	−0.450336	−	0.780004i	0.548071	−	0.836432i	$-0.315362\pi$
$269$	−7.38606	−	12.7930i	−0.450336	−	0.780004i	−0.998407	+	0.0564275i	$0.982029\pi$
$270$	−5.53250	−	1.00169i	−0.336697	−	0.0609608i
$271$	−8.16316	+	14.1390i	−0.495877	+	0.858884i	−0.999989	−	0.00475467i	$-0.998487\pi$
$271$	−8.16316	+	14.1390i	−0.495877	+	0.858884i	0.504112	+	0.863638i	$0.331820\pi$
$272$	0.622722			0.0377581
$273$	6.41110	+	15.2282i	0.388017	+	0.921652i
$274$	−2.84629			−0.171951
$275$	−1.00829	+	1.74641i	−0.0608022	+	0.105312i
$276$	−17.0445	−	7.38319i	−1.02596	−	0.444416i
$277$	9.21864	+	15.9671i	0.553894	+	0.959373i	0.997989	+	0.0633928i	$0.0201921\pi$
$277$	9.21864	+	15.9671i	0.553894	+	0.959373i	−0.444095	+	0.895980i	$0.646475\pi$
$278$			6.47486i			0.388336i
$279$	16.6947	+	17.8040i	0.999483	+	1.06589i
$280$	8.04481	−	7.27342i	0.480769	−	0.434670i
$281$	−0.680410			−0.0405899			−0.0202949	−	0.999794i	$-0.506461\pi$
$281$	−0.680410			−0.0405899			−0.0202949	+	0.999794i	$0.506461\pi$
$282$	−4.89333	+	3.63135i	−0.291393	+	0.216243i
$283$	−11.9377	−	6.89223i	−0.709622	−	0.409701i	0.101299	−	0.994856i	$-0.467700\pi$
$283$	−11.9377	−	6.89223i	−0.709622	−	0.409701i	−0.810921	+	0.585155i	$0.801034\pi$
$284$	9.59975	−	16.6273i	0.569640	−	0.986646i
$285$	−0.462519	−	4.01021i	−0.0273973	−	0.237544i
$286$	5.20412	−	3.52808i	0.307726	−	0.208619i
$287$	1.16284	+	5.41624i	0.0686401	+	0.319710i
$288$	−4.13927	+	13.6740i	−0.243909	+	0.805745i
$289$	8.47482	−	14.6788i	0.498519	−	0.863460i
$290$	1.88466	+	3.26433i	0.110671	+	0.191688i
$291$	6.60897	−	0.762248i	0.387425	−	0.0446838i
$292$	0.943039	+	1.63339i	0.0551872	+	0.0955870i
$293$	2.79809	−	1.61548i	0.163466	−	0.0943771i	−0.416035	−	0.909348i	$-0.636581\pi$
$293$	2.79809	−	1.61548i	0.163466	−	0.0943771i	0.579501	+	0.814971i	$0.303247\pi$
$294$	4.79041	−	2.85718i	0.279382	−	0.166634i
$295$	9.31631	+	16.1363i	0.542417	+	0.939493i
$296$	−9.89879	−	5.71507i	−0.575355	−	0.332182i
$297$	3.50897	−	19.3807i	0.203611	−	1.12458i
$298$	4.17929			0.242100
$299$	9.43242	−	19.4554i	0.545491	−	1.12514i
$300$	1.63708	−	0.188813i	0.0945169	−	0.0109011i
$301$	1.05199	−	3.26036i	0.0606357	−	0.187924i
$302$	6.33928	+	3.65998i	0.364785	+	0.210608i
$303$	−12.7769	−	17.2172i	−0.734016	−	0.989104i
$304$	−2.74971			−0.157707
$305$	−2.40414	−	4.16409i	−0.137661	−	0.238435i
$306$	−0.211851	−	0.225928i	−0.0121107	−	0.0129154i
$307$	21.1154			1.20512			0.602559	−	0.798074i	$-0.294148\pi$
$307$	21.1154			1.20512			0.602559	+	0.798074i	$0.294148\pi$
$308$	12.0279	+	13.3035i	0.685353	+	0.758038i
$309$	5.90818	+	2.55925i	0.336105	+	0.145591i
$310$	7.62367	+	4.40153i	0.432995	+	0.249990i
$311$	−18.4685			−1.04725			−0.523627	−	0.851948i	$-0.675421\pi$
$311$	−18.4685			−1.04725			−0.523627	+	0.851948i	$0.675421\pi$
$312$	−10.2731	−	3.59477i	−0.581601	−	0.203514i
$313$			25.4208i			1.43687i	0.695595	+	0.718434i	$0.255141\pi$
$313$			25.4208i			1.43687i	−0.695595	+	0.718434i	$0.744859\pi$
$314$	−8.04137	−	4.64269i	−0.453801	−	0.262002i
$315$	18.6052	+	1.53764i	1.04828	+	0.0866363i
$316$	−7.17360	−	12.4250i	−0.403546	−	0.698963i
$317$	−24.4218			−1.37167			−0.685833	−	0.727759i	$-0.740562\pi$
$317$	−24.4218			−1.37167			−0.685833	+	0.727759i	$0.740562\pi$
$318$	4.60365	−	3.41637i	0.258160	−	0.191581i
$319$	−11.4351	+	6.60207i	−0.640244	+	0.369645i
$320$		−	7.90049i		−	0.441651i
$321$	−23.3371	+	17.3185i	−1.30255	+	0.966626i
$322$	−6.94635	−	2.24131i	−0.387105	−	0.124903i
$323$	0.111185	−	0.192578i	0.00618650	−	0.0107153i
$324$	−14.4271	+	7.13551i	−0.801504	+	0.396417i
$325$	0.138312	+	1.91322i	0.00767215	+	0.106126i
$326$			2.35830i			0.130614i
$327$	14.5123	+	6.28629i	0.802531	+	0.347633i
$328$	−3.16022	−	1.82455i	−0.174494	−	0.100744i
$329$	15.0082	−	13.5691i	0.827430	−	0.748090i
$330$	−0.813932	−	7.05709i	−0.0448055	−	0.388480i
$331$	−11.3311	+	6.54203i	−0.622815	+	0.359583i	−0.777964	−	0.628309i	$-0.783748\pi$
$331$	−11.3311	+	6.54203i	−0.622815	+	0.359583i	0.155149	+	0.987891i	$0.450414\pi$
$332$	13.7117	−	7.91647i	0.752529	−	0.434473i
$333$	−4.47892	−	19.1587i	−0.245443	−	1.04989i
$334$	3.79573	−	2.19147i	0.207693	−	0.119912i
$335$	−13.0171	+	22.5464i	−0.711203	+	1.23184i
$336$	2.49252	−	12.4697i	0.135978	−	0.680277i
$337$	−12.6677			−0.690053			−0.345027	−	0.938593i	$-0.612130\pi$
$337$	−12.6677			−0.690053			−0.345027	+	0.938593i	$0.612130\pi$
$338$	2.21424	−	5.55561i	0.120439	−	0.302185i
$339$	−4.04785	−	35.0963i	−0.219849	−	1.90617i
$340$	0.817463	+	0.471962i	0.0443332	+	0.0255958i
$341$	−15.4188	+	26.7062i	−0.834975	+	1.44622i
$342$	0.935458	+	0.997615i	0.0505838	+	0.0539448i
$343$	−14.9161	+	10.9776i	−0.805396	+	0.592737i
$344$	1.12836	+	1.95437i	0.0608368	+	0.105373i
$345$	−14.5583	−	19.6177i	−0.783794	−	1.05618i
$346$	−2.72890			−0.146707
$347$	−0.557421	+	0.321827i	−0.0299239	+	0.0172766i	−0.514887	−	0.857258i	$-0.672166\pi$
$347$	−0.557421	+	0.321827i	−0.0299239	+	0.0172766i	0.484963	+	0.874534i	$0.338833\pi$
$348$	9.90131	+	4.28895i	0.530766	+	0.229912i
$349$	2.81297	−	4.87221i	0.150575	−	0.260803i	−0.780864	−	0.624701i	$-0.785221\pi$
$349$	2.81297	−	4.87221i	0.150575	−	0.260803i	0.931439	+	0.363898i	$0.118554\pi$
$350$	0.633126	−	0.135929i	0.0338420	−	0.00726570i
$351$	−7.58206	−	17.1322i	−0.404700	−	0.914449i
$352$	−18.0510			−0.962124
$353$	13.2511	+	7.65053i	0.705285	+	0.407197i	0.809313	−	0.587378i	$-0.199840\pi$
$353$	13.2511	+	7.65053i	0.705285	+	0.407197i	−0.104028	+	0.994574i	$0.533173\pi$
$354$	−5.79233	−	2.50906i	−0.307859	−	0.133355i
$355$	21.8679	−	12.6255i	1.16063	−	0.670090i
$356$			16.7114i			0.885703i
$357$	0.772537	+	0.678778i	0.0408870	+	0.0359248i
$358$	−5.61913	+	3.24421i	−0.296980	+	0.171462i
$359$	−35.6728			−1.88274			−0.941368	−	0.337380i	$-0.890459\pi$
$359$	−35.6728			−1.88274			−0.941368	+	0.337380i	$0.890459\pi$
$360$	−8.97059	+	8.41167i	−0.472792	+	0.443334i
$361$	9.00905	−	15.6041i	0.474160	−	0.821270i
$362$	7.49626	+	4.32797i	0.393995	+	0.227473i
$363$	5.79431	−	0.668288i	0.304122	−	0.0350760i
$364$	16.5711	+	4.05430i	0.868561	+	0.212503i
$365$			2.48055i			0.129838i
$366$	1.49475	+	0.647482i	0.0781319	+	0.0338444i
$367$	−9.30509	−	5.37229i	−0.485722	−	0.280431i	0.237076	−	0.971491i	$-0.423811\pi$
$367$	−9.30509	−	5.37229i	−0.485722	−	0.280431i	−0.722798	+	0.691060i	$0.757144\pi$
$368$	−14.4110	+	8.32022i	−0.751228	+	0.433722i
$369$	−1.42991	−	6.11646i	−0.0744381	−	0.318410i
$370$	−3.54823	−	6.14572i	−0.184464	−	0.319501i
$371$	−14.1197	+	12.7659i	−0.733061	+	0.662770i
$372$	25.0343	−	2.88734i	1.29797	−	0.149701i
$373$	2.09900	+	3.63557i	0.108682	+	0.188243i	0.915237	−	0.402917i	$-0.132004\pi$
$373$	2.09900	+	3.63557i	0.108682	+	0.188243i	−0.806555	+	0.591160i	$0.798670\pi$
$374$	0.195661	−	0.338895i	0.0101174	−	0.0175238i
$375$	−16.7021	−	7.23488i	−0.862495	−	0.373607i
$376$			13.3279i			0.687332i
$377$	−5.47937	+	11.3018i	−0.282202	+	0.582073i
$378$	−5.37205	+	3.33791i	−0.276308	+	0.171683i
$379$	9.29657	+	5.36738i	0.477533	+	0.275704i	0.719388	−	0.694609i	$-0.244422\pi$
$379$	9.29657	+	5.36738i	0.477533	+	0.275704i	−0.241855	+	0.970312i	$0.577756\pi$
$380$	−3.60962	−	2.08401i	−0.185169	−	0.106908i
$381$	19.4653	+	26.2299i	0.997236	+	1.34380i
$382$		−	6.66500i		−	0.341011i
$383$	−31.0766	+	17.9421i	−1.58794	+	0.916798i	−0.594294	+	0.804248i	$0.702568\pi$
$383$	−31.0766	+	17.9421i	−1.58794	+	0.916798i	−0.993646	+	0.112549i	$0.964098\pi$
$384$	11.4261	+	15.3969i	0.583085	+	0.785721i
$385$	4.95128	+	23.0620i	0.252341	+	1.17535i
$386$	10.4347	−	6.02447i	0.531112	−	0.306638i
$387$	−1.12547	+	3.71797i	−0.0572110	+	0.188995i
$388$	3.43453	−	5.94878i	0.174362	−	0.302003i
$389$			20.6088i			1.04491i	0.852668	+	0.522454i	$0.174983\pi$
$389$			20.6088i			1.04491i	−0.852668	+	0.522454i	$0.825017\pi$
$390$	−4.40771	−	5.12189i	−0.223193	−	0.259357i
$391$		−	1.34572i		−	0.0680558i
$392$	1.22559	−	12.1380i	0.0619017	−	0.613063i
$393$	8.94245	−	20.6442i	0.451087	−	1.04136i
$394$	4.04188	+	7.00074i	0.203627	+	0.352692i
$395$		−	18.8692i		−	0.949414i
$396$	−13.9102	−	14.8345i	−0.699013	−	0.745460i
$397$	10.1975	+	17.6625i	0.511796	+	0.886457i	0.999906	+	0.0136748i	$0.00435296\pi$
$397$	10.1975	+	17.6625i	0.511796	+	0.886457i	−0.488111	+	0.872782i	$0.662314\pi$
$398$			0.361427i			0.0181167i
$399$	−3.41124	−	2.99724i	−0.170776	−	0.150049i
$400$	0.738155	−	1.27852i	0.0369077	−	0.0639261i
$401$	−10.1356	+	17.5554i	−0.506149	+	0.876675i	0.493826	+	0.869561i	$0.335598\pi$
$401$	−10.1356	+	17.5554i	−0.506149	+	0.876675i	−0.999975	+	0.00711434i	$0.997735\pi$
$402$	−1.01055	−	8.76187i	−0.0504018	−	0.437003i
$403$	2.11507	+	29.2570i	0.105359	+	1.45739i
$404$	−22.1372			−1.10137
$405$	−21.1245	−	1.35990i	−1.04968	−	0.0675741i
$406$	4.03519	+	1.30200i	0.200263	+	0.0646170i
$407$	21.5288	−	12.4297i	1.06714	−	0.616116i
$408$	−0.672954	+	0.0776154i	−0.0333162	+	0.00384253i
$409$	−1.23396	−	2.13729i	−0.0610156	−	0.105682i	0.833904	−	0.551909i	$-0.186101\pi$
$409$	−1.23396	−	2.13729i	−0.0610156	−	0.105682i	−0.894920	+	0.446227i	$0.852767\pi$
$410$	−1.13278	−	1.96204i	−0.0559442	−	0.0968983i
$411$	−10.6456	+	1.22781i	−0.525107	+	0.0605634i
$412$	5.75731	−	3.32399i	0.283642	−	0.163761i
$413$	19.9469	+	6.43607i	0.981522	+	0.316698i
$414$	7.92130	+	2.39787i	0.389311	+	0.117849i
$415$	20.8233			1.02217
$416$	−14.2124	+	9.63511i	−0.696818	+	0.472400i
$417$	2.79307	+	24.2169i	0.136777	+	1.18591i
$418$	−0.863967	+	1.49644i	−0.0422580	+	0.0731930i
$419$	13.9311	−	24.1294i	0.680580	−	1.17880i	−0.294224	−	0.955736i	$-0.595061\pi$
$419$	13.9311	−	24.1294i	0.680580	−	1.17880i	0.974804	−	0.223062i	$-0.0716054\pi$
$420$	12.7228	−	14.4802i	0.620809	−	0.706560i
$421$			10.7361i			0.523244i	0.965170	+	0.261622i	$0.0842574\pi$
$421$			10.7361i			0.523244i	−0.965170	+	0.261622i	$0.915743\pi$
$422$	−2.07848	−	3.60004i	−0.101179	−	0.175247i
$423$	−16.7353	+	15.6926i	−0.813700	+	0.763002i
$424$		−	12.5389i		−	0.608941i
$425$	0.0596947	+	0.103394i	0.00289562	+	0.00501536i
$426$	−3.40028	+	7.84976i	−0.164744	+	0.380322i
$427$	−5.14744	−	1.66087i	−0.249102	−	0.0803753i
$428$			30.0059i			1.45039i
$429$	17.9423	−	15.4405i	0.866262	−	0.745472i
$430$			1.40109i			0.0675667i
$431$	−6.94810	+	12.0345i	−0.334678	+	0.579680i	−0.983423	−	0.181326i	$-0.941961\pi$
$431$	−6.94810	+	12.0345i	−0.334678	+	0.579680i	0.648745	+	0.761006i	$0.275294\pi$
$432$	−2.56887	+	14.1883i	−0.123595	+	0.682635i
$433$	−12.0000	+	6.92818i	−0.576681	+	0.332947i	−0.759813	−	0.650141i	$-0.774710\pi$
$433$	−12.0000	+	6.92818i	−0.576681	+	0.332947i	0.183132	+	0.983088i	$0.441376\pi$
$434$	9.68178	−	2.07863i	0.464740	−	0.0997773i
$435$	8.45705	+	11.3961i	0.405485	+	0.546401i
$436$	14.1417	−	8.16472i	0.677265	−	0.391019i
$437$			5.94219i			0.284253i
$438$	−0.500801	−	0.674842i	−0.0239292	−	0.0322452i
$439$	−30.1089	−	17.3834i	−1.43702	−	0.829664i	−0.439378	−	0.898302i	$-0.644801\pi$
$439$	−30.1089	−	17.3834i	−1.43702	−	0.829664i	−0.997642	+	0.0686384i	$0.978135\pi$
$440$	−13.4560	−	7.76883i	−0.641490	−	0.370364i
$441$	16.6843	−	12.7527i	0.794493	−	0.607274i
$442$	−0.0268397	−	0.371264i	−0.00127663	−	0.0176592i
$443$		−	28.7921i		−	1.36796i	−0.729502	−	0.683978i	$-0.760248\pi$
$443$		−	28.7921i		−	1.36796i	0.729502	−	0.683978i	$-0.239752\pi$
$444$	−18.6411	−	8.07478i	−0.884668	−	0.383212i
$445$	−10.9893	+	19.0340i	−0.520943	+	0.902300i
$446$	4.63079	+	8.02076i	0.219274	+	0.379794i
$447$	15.6312	−	1.80283i	0.739330	−	0.0852708i
$448$	−5.96014	−	6.59225i	−0.281590	−	0.311454i
$449$	−10.4960	−	18.1797i	−0.495339	−	0.857952i	0.504647	−	0.863326i	$-0.331623\pi$
$449$	−10.4960	−	18.1797i	−0.495339	−	0.857952i	−0.999986	+	0.00537424i	$0.998289\pi$
$450$	−0.714978	+	0.167148i	−0.0337044	+	0.00787943i
$451$	6.87314	−	3.96821i	0.323644	−	0.186856i
$452$	−31.5904	−	18.2387i	−1.48589	−	0.857879i
$453$	25.2887	+	10.9543i	1.18817	+	0.514679i
$454$			8.55664i			0.401583i
$455$	16.2081	+	15.5148i	0.759849	+	0.727346i
$456$	2.97152	−	0.342721i	0.139154	−	0.0160494i
$457$	−13.4844	−	7.78524i	−0.630775	−	0.364178i	0.150277	−	0.988644i	$-0.451983\pi$
$457$	−13.4844	−	7.78524i	−0.630775	−	0.364178i	−0.781052	+	0.624466i	$0.785317\pi$
$458$	−3.01520	+	5.22248i	−0.140891	+	0.244031i
$459$	−0.889815	−	0.753618i	−0.0415330	−	0.0351759i
$460$	−25.2237			−1.17606
$461$	9.70023	−	5.60043i	0.451785	−	0.260838i	−0.256799	−	0.966465i	$-0.582668\pi$
$461$	9.70023	−	5.60043i	0.451785	−	0.260838i	0.708584	+	0.705627i	$0.249334\pi$
$462$	−6.00303	−	5.27447i	−0.279286	−	0.245391i
$463$			3.98299i			0.185105i	0.995708	+	0.0925527i	$0.0295027\pi$
$463$			3.98299i			0.185105i	−0.995708	+	0.0925527i	$0.970497\pi$
$464$	8.37149	−	4.83328i	0.388637	−	0.224380i
$465$	30.4124	+	13.1737i	1.41034	+	0.610918i
$466$	4.64726	+	2.68309i	0.215280	+	0.124292i
$467$	6.52375			0.301883			0.150942	−	0.988543i	$-0.451769\pi$
$467$	6.52375			0.301883			0.150942	+	0.988543i	$0.451769\pi$
$468$	−18.8703	−	4.25496i	−0.872279	−	0.196685i
$469$	6.14737	+	28.6331i	0.283859	+	1.32215i
$470$	−4.13734	+	7.16608i	−0.190841	+	0.330547i
$471$	−32.0787	−	13.8955i	−1.47811	−	0.640273i
$472$	−11.9568	+	6.90327i	−0.550357	+	0.317749i
$473$	−4.90811			−0.225675
$474$	3.80954	+	5.13345i	0.174978	+	0.235787i
$475$	−0.263590	−	0.456551i	−0.0120943	−	0.0209480i
$476$	1.03815	−	0.222885i	0.0475835	−	0.0102159i
$477$	15.7446	−	14.7636i	0.720897	−	0.675981i
$478$	−1.96112	+	3.39676i	−0.0896996	+	0.155364i
$479$	20.1576	+	11.6380i	0.921023	+	0.531753i	0.883961	−	0.467560i	$-0.154867\pi$
$479$	20.1576	+	11.6380i	0.921023	+	0.531753i	0.0370614	+	0.999313i	$0.488200\pi$
$480$	2.22283	+	19.2728i	0.101458	+	0.879678i
$481$	10.3160	−	21.2779i	0.470368	−	0.970186i
$482$	4.53182			0.206419
$483$	−26.9473	−	5.38639i	−1.22614	−	0.245089i
$484$	3.01117	−	5.21549i	0.136871	−	0.237068i
$485$	7.82375	−	4.51705i	0.355258	−	0.205108i
$486$	6.02155	−	3.89489i	0.273143	−	0.176676i
$487$	−3.92467	+	2.26591i	−0.177844	+	0.102678i	−0.586279	−	0.810109i	$-0.699408\pi$
$487$	−3.92467	+	2.26591i	−0.177844	+	0.102678i	0.408435	+	0.912787i	$0.366075\pi$
$488$	3.08554	−	1.78144i	0.139676	−	0.0806419i
$489$	1.01730	+	8.82040i	0.0460041	+	0.398872i
$490$	4.42695	−	6.14588i	0.199989	−	0.277643i
$491$	1.54789	+	0.893673i	0.0698551	+	0.0403309i	0.534521	−	0.845155i	$-0.320492\pi$
$491$	1.54789	+	0.893673i	0.0698551	+	0.0403309i	−0.464666	+	0.885486i	$0.653825\pi$
$492$	−5.95123	−	2.57790i	−0.268302	−	0.116221i
$493$			0.781738i			0.0352077i
$494$	0.118514	+	1.63937i	0.00533220	+	0.0737586i
$495$	−6.08846	−	26.0435i	−0.273656	−	1.17057i
$496$	11.2879	−	19.5512i	0.506841	−	0.877875i
$497$	8.72217	−	27.0320i	0.391243	−	1.21255i
$498$	−5.66505	+	4.20404i	−0.253857	+	0.188388i
$499$			4.39239i			0.196630i	0.995155	+	0.0983151i	$0.0313453\pi$
$499$			4.39239i			0.196630i	−0.995155	+	0.0983151i	$0.968655\pi$
$500$	−16.2756	+	9.39675i	−0.727869	+	0.420235i
$501$	13.2513	−	9.83379i	0.592023	−	0.439341i
$502$	2.23631			0.0998115
$503$	17.0936	+	29.6071i	0.762168	+	1.32011i	0.941731	+	0.336367i	$0.109198\pi$
$503$	17.0936	+	29.6071i	0.762168	+	1.32011i	−0.179563	+	0.983746i	$0.557468\pi$
$504$	−1.13937	+	13.7862i	−0.0507517	+	0.614087i
$505$	−25.2140	−	14.5573i	−1.12201	−	0.647791i
$506$			10.4569i			0.464868i
$507$	5.88508	−	21.7340i	0.261365	−	0.965240i
$508$	33.7254			1.49632
$509$	−6.70134	−	3.86902i	−0.297032	−	0.171491i	0.344077	−	0.938941i	$-0.388192\pi$
$509$	−6.70134	−	3.86902i	−0.297032	−	0.171491i	−0.641109	+	0.767450i	$0.721525\pi$
$510$	−0.385926	−	0.167172i	−0.0170891	−	0.00740249i
$511$	1.87133	+	2.06979i	0.0827826	+	0.0915622i
$512$	22.8873			1.01149
$513$	3.92910	+	3.32770i	0.173474	+	0.146922i
$514$	5.74326	+	9.94762i	0.253324	+	0.438771i
$515$	8.74332			0.385277
$516$	2.39021	+	3.22086i	0.105223	+	0.141791i
$517$	−25.1032	−	14.4933i	−1.10404	−	0.637417i
$518$	−7.59702	−	2.45126i	−0.333794	−	0.107702i
$519$	−10.2065	+	1.17717i	−0.448016	+	0.0516721i
$520$	−14.7412	+	1.06568i	−0.646446	+	0.0467333i
$521$	16.4592			0.721092			0.360546	−	0.932741i	$-0.382590\pi$
$521$	16.4592			0.721092			0.360546	+	0.932741i	$0.382590\pi$
$522$	−4.60155	−	1.39294i	−0.201404	−	0.0609674i
$523$	31.5959	+	18.2419i	1.38159	+	0.797663i	0.992348	−	0.123472i	$-0.0394029\pi$
$523$	31.5959	+	18.2419i	1.38159	+	0.797663i	0.389244	+	0.921135i	$0.372736\pi$
$524$	−11.6146	−	20.1170i	−0.507385	−	0.878816i
$525$	2.30935	−	0.781507i	0.100788	−	0.0341078i
$526$	−2.04579	+	1.18113i	−0.0892005	+	0.0514999i
$527$	0.912854	+	1.58111i	0.0397645	+	0.0688742i
$528$	−18.0982	+	2.08736i	−0.787622	+	0.0908407i
$529$	6.48018	+	11.2240i	0.281747	+	0.488000i
$530$	3.89242	−	6.74186i	0.169076	−	0.292848i
$531$	−22.7465	−	6.88564i	−0.987115	−	0.298811i
$532$	−4.58408	+	0.984178i	−0.198745	+	0.0426695i
$533$	3.29341	−	6.79302i	0.142653	−	0.294238i
$534$	−0.853128	−	7.39693i	−0.0369184	−	0.320097i
$535$	−19.7317	+	34.1763i	−0.853076	+	1.47757i
$536$	−16.7066	−	9.64554i	−0.721614	−	0.416624i
$537$	−19.6169	+	14.5578i	−0.846533	+	0.628214i
$538$	6.79586			0.292990
$539$	21.5294	+	15.5079i	0.927336	+	0.667972i
$540$	−14.1256	+	16.6784i	−0.607868	+	0.717724i
$541$		−	5.50520i		−	0.236687i	−0.992973	−	0.118344i	$-0.962242\pi$
$541$		−	5.50520i		−	0.236687i	0.992973	−	0.118344i	$-0.0377584\pi$
$542$	−3.75543	−	6.50460i	−0.161310	−	0.279397i
$543$	29.9041	+	12.9536i	1.28331	+	0.555891i
$544$	−0.534346	+	0.925515i	−0.0229099	+	0.0396811i
$545$	21.4763			0.919942
$546$	−7.54180	−	0.948580i	−0.322759	−	0.0405955i
$547$	2.43948			0.104304			0.0521522	−	0.998639i	$-0.483392\pi$
$547$	2.43948			0.104304			0.0521522	+	0.998639i	$0.483392\pi$
$548$	−5.53225	+	9.58214i	−0.236326	+	0.409329i
$549$	5.86990	+	1.77689i	0.250521	+	0.0758357i
$550$	−0.463860	−	0.803430i	−0.0197791	−	0.0342584i
$551$		−	3.45187i		−	0.147054i
$552$	14.5365	−	10.7875i	0.618714	−	0.459148i
$553$	−14.2350	−	15.7447i	−0.605333	−	0.669532i
$554$	−8.48200			−0.360366
$555$	−15.9220	−	21.4553i	−0.675852	−	0.910728i
$556$	21.7978	+	12.5850i	0.924434	+	0.533722i
$557$	−18.3528	+	31.7879i	−0.777632	+	1.34690i	0.155671	+	0.987809i	$0.450246\pi$
$557$	−18.3528	+	31.7879i	−0.777632	+	1.34690i	−0.933303	+	0.359089i	$0.883087\pi$
$558$	−10.9335	+	2.55603i	−0.462851	+	0.108205i
$559$	−3.86436	+	2.61980i	−0.163445	+	0.110806i
$560$	−3.62476	−	16.8833i	−0.153174	−	0.713451i
$561$	0.585612	−	1.35192i	0.0247246	−	0.0570781i
$562$	0.156510	−	0.271084i	0.00660198	−	0.0114350i
$563$	−5.26528	−	9.11974i	−0.221905	−	0.384351i	0.733481	−	0.679710i	$-0.237894\pi$
$563$	−5.26528	−	9.11974i	−0.221905	−	0.384351i	−0.955386	+	0.295359i	$0.904561\pi$
$564$	2.71404	+	23.5317i	0.114282	+	0.990863i
$565$	−23.9874	−	41.5473i	−1.00916	−	1.74791i
$566$	5.49190	−	3.17075i	0.230842	−	0.133276i
$567$	−18.6524	+	14.8016i	−0.783327	+	0.621610i
$568$	9.35532	+	16.2039i	0.392540	+	0.679900i
$569$	9.38052	+	5.41585i	0.393252	+	0.227044i	0.683568	−	0.729887i	$-0.260427\pi$
$569$	9.38052	+	5.41585i	0.393252	+	0.227044i	−0.290316	+	0.956931i	$0.593761\pi$
$570$	1.70411	+	0.738169i	0.0713772	+	0.0309185i
$571$	−19.3339			−0.809098			−0.404549	−	0.914516i	$-0.632572\pi$
$571$	−19.3339			−0.809098			−0.404549	+	0.914516i	$0.632572\pi$
$572$	−1.76230	−	24.3773i	−0.0736853	−	1.01926i
$573$	−2.87509	−	24.9281i	−0.120109	−	1.04139i
$574$	−2.42537	−	0.782572i	−0.101233	−	0.0326639i
$575$	−2.76291	−	1.59517i	−0.115221	−	0.0665231i
$576$	6.89287	+	7.35087i	0.287203	+	0.306286i
$577$	5.49588			0.228796			0.114398	−	0.993435i	$-0.463506\pi$
$577$	5.49588			0.228796			0.114398	+	0.993435i	$0.463506\pi$
$578$	3.89881	+	6.75294i	0.162169	+	0.280885i
$579$	36.4286	−	27.0337i	1.51392	−	1.12348i
$580$	14.6526			0.608417
$581$	17.3751	−	15.7091i	0.720842	−	0.651723i
$582$	−1.21653	+	2.80843i	−0.0504267	+	0.116413i
$583$	23.6171	+	13.6354i	0.978122	+	0.564719i
$584$	−1.83805			−0.0760592
$585$	−18.6949	−	17.2553i	−0.772940	−	0.713419i
$586$			1.48639i			0.0614021i
$587$	−2.85249	−	1.64688i	−0.117735	−	0.0679742i	0.439976	−	0.898009i	$-0.354987\pi$
$587$	−2.85249	−	1.64688i	−0.117735	−	0.0679742i	−0.557711	+	0.830035i	$0.688320\pi$
$588$	−0.307837	−	21.6805i	−0.0126950	−	0.894088i
$589$	−4.03083	−	6.98160i	−0.166087	−	0.287672i
$590$	−8.57188			−0.352899
$591$	18.1372	+	24.4403i	0.746063	+	1.00534i
$592$	−15.7609	+	9.09959i	−0.647771	+	0.373991i
$593$		−	43.9998i		−	1.80686i	−0.428740	−	0.903428i	$-0.641042\pi$
$593$		−	43.9998i		−	1.80686i	0.428740	−	0.903428i	$-0.358958\pi$
$594$	6.91435	+	5.85602i	0.283699	+	0.240275i
$595$	1.32900	+	0.428817i	0.0544838	+	0.0175798i
$596$	8.12316	−	14.0697i	0.332738	−	0.576318i
$597$	0.155910	+	1.35179i	0.00638096	+	0.0553252i
$598$	5.58160	+	8.23320i	0.228249	+	0.336680i
$599$		−	37.9227i		−	1.54948i	−0.632281	−	0.774739i	$-0.717881\pi$
$599$		−	37.9227i		−	1.54948i	0.632281	−	0.774739i	$-0.282119\pi$
$600$	−0.638344	+	1.47366i	−0.0260603	+	0.0601618i
$601$	29.5468	+	17.0589i	1.20524	+	0.695846i	0.961716	−	0.274049i	$-0.0883631\pi$
$601$	29.5468	+	17.0589i	1.20524	+	0.695846i	0.243524	+	0.969895i	$0.421696\pi$
$602$	1.05699	+	1.16909i	0.0430795	+	0.0476484i
$603$	−7.55925	−	32.3348i	−0.307836	−	1.31678i
$604$	24.6429	−	14.2276i	1.00271	−	0.578913i
$605$	6.85935	−	3.96025i	0.278872	−	0.161007i
$606$	9.79855	−	1.13012i	0.398039	−	0.0459079i
$607$	35.8778	−	20.7141i	1.45624	−	0.840759i	0.457413	−	0.889254i	$-0.348776\pi$
$607$	35.8778	−	20.7141i	1.45624	−	0.840759i	0.998823	+	0.0484954i	$0.0154426\pi$
$608$	2.35948	−	4.08674i	0.0956895	−	0.165739i
$609$	15.6539	+	3.12900i	0.634327	+	0.126793i
$610$	2.21203			0.0895626
$611$	−27.5009	+	1.98812i	−1.11257	+	0.0804306i
$612$	−1.17236	+	0.274076i	−0.0473900	+	0.0110788i
$613$	3.76362	+	2.17293i	0.152011	+	0.0877636i	0.574076	−	0.818802i	$-0.305361\pi$
$613$	3.76362	+	2.17293i	0.152011	+	0.0877636i	−0.422065	+	0.906566i	$0.638695\pi$
$614$	−4.85703	+	8.41262i	−0.196014	+	0.339506i
$615$	−5.08316	−	6.84968i	−0.204973	−	0.276206i
$616$	−17.0886	+	3.66884i	−0.688521	+	0.147822i
$617$	9.10939	+	15.7779i	0.366730	+	0.635195i	0.989052	−	0.147566i	$-0.0471439\pi$
$617$	9.10939	+	15.7779i	0.366730	+	0.635195i	−0.622322	+	0.782761i	$0.713811\pi$
$618$	−2.37865	+	1.76520i	−0.0956835	+	0.0710069i
$619$	−27.0696			−1.08802			−0.544009	−	0.839079i	$-0.683094\pi$
$619$	−27.0696			−1.08802			−0.544009	+	0.839079i	$0.683094\pi$
$620$	29.6358	−	17.1102i	1.19020	−	0.687163i
$621$	30.6612	+	5.55138i	1.23039	+	0.222769i
$622$	4.24819	−	7.35808i	0.170337	−	0.295032i
$623$	5.18972	+	24.1725i	0.207922	+	0.968453i
$624$	−13.1353	+	11.3037i	−0.525833	+	0.452512i
$625$	−27.3770			−1.09508
$626$	−10.1280	−	5.84738i	−0.404794	−	0.233708i
$627$	−2.58585	+	5.96959i	−0.103269	+	0.238402i
$628$	−31.2595	+	18.0477i	−1.24739	+	0.720182i
$629$		−	1.47177i		−	0.0586834i
$630$	−4.89224	+	7.05883i	−0.194911	+	0.281231i
$631$	26.5893	−	15.3513i	1.05850	−	0.611128i	0.133486	−	0.991051i	$-0.457383\pi$
$631$	26.5893	−	15.3513i	1.05850	−	0.611128i	0.925018	+	0.379923i	$0.124050\pi$
$632$	13.9819			0.556169
$633$	−9.32681	−	12.5681i	−0.370707	−	0.499537i
$634$	5.61758	−	9.72994i	0.223103	−	0.386425i
$635$	38.4127	+	22.1776i	1.52436	+	0.880091i
$636$	−2.55337	−	22.1386i	−0.101248	−	0.877854i
$637$	25.2286	+	0.718277i	0.999595	+	0.0284592i
$638$		−	6.07452i		−	0.240493i
$639$	−9.33142	+	30.8261i	−0.369145	+	1.21946i
$640$	22.5482	+	13.0182i	0.891295	+	0.514590i
$641$	13.6801	−	7.89820i	0.540331	−	0.311960i	−0.204882	−	0.978787i	$-0.565681\pi$
$641$	13.6801	−	7.89820i	0.540331	−	0.311960i	0.745213	+	0.666827i	$0.232348\pi$
$642$	−1.53182	−	13.2815i	−0.0604562	−	0.524177i
$643$	2.03677	+	3.52779i	0.0803225	+	0.139123i	0.903388	−	0.428823i	$-0.141072\pi$
$643$	2.03677	+	3.52779i	0.0803225	+	0.139123i	−0.823066	+	0.567946i	$0.807738\pi$
$644$	−21.0469	+	19.0288i	−0.829363	+	0.749838i
$645$	0.604392	+	5.24030i	0.0237979	+	0.206337i
$646$	0.0511503	+	0.0885948i	0.00201248	+	0.00348572i
$647$	−4.46688	+	7.73687i	−0.175611	+	0.304168i	−0.940373	−	0.340146i	$-0.889524\pi$
$647$	−4.46688	+	7.73687i	−0.175611	+	0.304168i	0.764761	+	0.644314i	$0.222857\pi$
$648$	1.00767	−	15.6530i	0.0395850	−	0.614907i
$649$		−	30.0278i		−	1.17869i
$650$	−0.794064	−	0.384980i	−0.0311457	−	0.0151001i
$651$	35.3147	−	11.9508i	1.38409	−	0.468390i
$652$	7.93930	+	4.58376i	0.310927	+	0.179514i
$653$	1.14833	+	0.662991i	0.0449378	+	0.0259448i	0.522301	−	0.852761i	$-0.325074\pi$
$653$	1.14833	+	0.662991i	0.0449378	+	0.0259448i	−0.477363	+	0.878706i	$0.658407\pi$
$654$	−5.84270	+	4.33587i	−0.228468	+	0.169546i
$655$		−	30.5507i		−	1.19371i
$656$	−5.03173	+	2.90507i	−0.196456	+	0.113424i
$657$	−2.16418	−	2.30798i	−0.0844327	−	0.0900429i
$658$	1.95387	+	9.10067i	0.0761696	+	0.354781i
$659$	−6.38195	+	3.68462i	−0.248605	+	0.143532i	−0.619125	−	0.785292i	$-0.712513\pi$
$659$	−6.38195	+	3.68462i	−0.248605	+	0.143532i	0.370520	+	0.928824i	$0.379179\pi$
$660$	−25.3399	−	10.9765i	−0.986356	−	0.427260i
$661$	−0.786536	+	1.36232i	−0.0305927	+	0.0529881i	−0.880916	−	0.473272i	$-0.843073\pi$
$661$	−0.786536	+	1.36232i	−0.0305927	+	0.0529881i	0.850324	+	0.526260i	$0.176406\pi$
$662$		−	6.01928i		−	0.233946i
$663$	−0.260537	−	1.37701i	−0.0101184	−	0.0534785i
$664$			15.4298i			0.598792i
$665$	−5.86839	−	1.89350i	−0.227566	−	0.0734267i
$666$	8.66330	+	2.62248i	0.335696	+	0.101619i
$667$	−10.4448	−	18.0910i	−0.404426	−	0.700486i
$668$		−	17.0379i		−	0.659218i
$669$	20.7798	+	28.0013i	0.803393	+	1.08259i
$670$	−5.98849	−	10.3724i	−0.231356	−	0.400720i
$671$			7.74888i			0.299142i
$672$	16.3942	+	14.4045i	0.632418	+	0.555665i
$673$	−14.4046	+	24.9496i	−0.555258	+	0.961735i	0.442625	+	0.896707i	$0.354047\pi$
$673$	−14.4046	+	24.9496i	−0.555258	+	0.961735i	−0.997883	+	0.0650286i	$0.979286\pi$
$674$	2.91386	−	5.04696i	0.112238	−	0.194402i
$675$	−2.60202	+	0.933580i	−0.100152	+	0.0359335i
$676$	−14.3994	−	18.2526i	−0.553822	−	0.702023i
$677$	−21.6929			−0.833725			−0.416862	−	0.908970i	$-0.636870\pi$
$677$	−21.6929			−0.833725			−0.416862	+	0.908970i	$0.636870\pi$
$678$	14.9139	+	6.46027i	0.572765	+	0.248105i
$679$	3.12055	−	9.67132i	0.119756	−	0.371151i
$680$	−0.796648	+	0.459945i	−0.0305501	+	0.0176381i
$681$	3.69109	+	32.0031i	0.141443	+	1.22636i
$682$	−7.09337	−	12.2861i	−0.271619	−	0.470458i
$683$	−14.5351	−	25.1755i	−0.556168	−	0.963312i	−0.997812	−	0.0661211i	$-0.978938\pi$
$683$	−14.5351	−	25.1755i	−0.556168	−	0.963312i	0.441643	−	0.897191i	$-0.354396\pi$
$684$	5.17673	−	1.21022i	0.197937	−	0.0462738i
$685$	−12.6023	+	7.27594i	−0.481509	+	0.277999i
$686$	−0.942565	−	8.46788i	−0.0359873	−	0.323305i
$687$	−9.02448	+	20.8335i	−0.344305	+	0.794849i
$688$	3.59316			0.136988
$689$	25.8729	−	1.87042i	0.985680	−	0.0712574i
$690$	11.1647	−	1.28768i	0.425032	−	0.0490213i
$691$	−12.9355	+	22.4049i	−0.492090	+	0.852324i	−0.999959	−	0.00911016i	$-0.997100\pi$
$691$	−12.9355	+	22.4049i	−0.492090	+	0.852324i	0.507869	+	0.861434i	$0.330433\pi$
$692$	−5.30409	+	9.18695i	−0.201631	+	0.349235i
$693$	−24.7275	−	17.1378i	−0.939320	−	0.651011i
$694$		−	0.296111i		−	0.0112402i
$695$	16.5516	+	28.6682i	0.627838	+	1.08745i
$696$	−8.44436	+	6.26657i	−0.320083	+	0.237534i
$697$		−	0.469867i		−	0.0177975i
$698$	1.29410	+	2.24144i	0.0489823	+	0.0848399i
$699$	18.5389	+	8.03049i	0.701204	+	0.303741i
$700$	0.772979	−	2.39564i	0.0292158	−	0.0905467i
$701$		−	5.11584i		−	0.193223i	−0.995322	−	0.0966113i	$-0.969200\pi$
$701$		−	5.11584i		−	0.193223i	0.995322	−	0.0966113i	$-0.0308004\pi$
$702$	8.56973	+	0.920023i	0.323443	+	0.0347240i
$703$			6.49880i			0.245107i
$704$	−6.36610	+	11.0264i	−0.239931	+	0.415573i
$705$	−12.3830	+	28.5870i	−0.466372	+	1.07665i
$706$	−6.09612	+	3.51960i	−0.229431	+	0.132462i
$707$	−32.0208	+	6.87470i	−1.20427	+	0.258550i
$708$	−19.7052	+	14.6233i	−0.740568	+	0.549576i
$709$	−12.3564	+	7.13397i	−0.464054	+	0.267922i	−0.713748	−	0.700403i	$-0.753004\pi$
$709$	−12.3564	+	7.13397i	−0.464054	+	0.267922i	0.249693	+	0.968325i	$0.419670\pi$
$710$			11.6166i			0.435963i
$711$	16.4627	+	17.5566i	0.617399	+	0.658422i
$712$	−14.1040	−	8.14294i	−0.528570	−	0.305170i
$713$	−42.2506	−	24.3934i	−1.58230	−	0.913539i
$714$	−0.448135	+	0.151653i	−0.0167710	+	0.00567548i
$715$	14.0231	−	28.9242i	0.524434	−	1.08170i
$716$			25.2227i			0.942615i
$717$	−5.86962	+	13.5504i	−0.219205	+	0.506048i
$718$	8.20557	−	14.2125i	0.306229	−	0.530404i
$719$	23.4338	+	40.5885i	0.873932	+	1.51369i	0.857896	+	0.513823i	$0.171771\pi$
$719$	23.4338	+	40.5885i	0.873932	+	1.51369i	0.0160360	+	0.999871i	$0.494895\pi$
$720$	4.45727	+	19.0661i	0.166113	+	0.710550i
$721$	7.29552	−	6.59598i	0.271699	−	0.245647i
$722$	4.14458	+	7.17863i	0.154245	+	0.267161i
$723$	16.9497	−	1.95490i	0.630366	−	0.0727034i
$724$	29.1405	−	16.8243i	1.08300	−	0.625269i
$725$	1.60500	+	0.926646i	0.0596082	+	0.0344148i
$726$	−1.06657	+	2.46224i	−0.0395842	+	0.0913824i
$727$			17.6742i			0.655498i	0.944765	+	0.327749i	$0.106290\pi$
$727$			17.6742i			0.655498i	−0.944765	+	0.327749i	$0.893710\pi$
$728$	−11.4963	+	12.0100i	−0.426081	+	0.445121i
$729$	20.8414	−	17.1650i	0.771903	−	0.635741i
$730$	−0.988279	−	0.570583i	−0.0365779	−	0.0211182i
$731$	−0.145290	+	0.251649i	−0.00537373	+	0.00930758i
$732$	5.08507	−	3.77364i	0.187950	−	0.139478i
$733$	4.65518			0.171943			0.0859714	−	0.996298i	$-0.472601\pi$
$733$	4.65518			0.171943			0.0859714	+	0.996298i	$0.472601\pi$
$734$	4.28077	−	2.47151i	0.158006	−	0.0912249i
$735$	13.9063	−	24.8962i	0.512943	−	0.918310i
$736$		−	28.5577i		−	1.05265i
$737$	36.3350	−	20.9780i	1.33842	−	0.772736i
$738$	2.76578	+	0.837236i	0.101810	+	0.0308191i
$739$	11.8187	+	6.82354i	0.434759	+	0.251008i	0.701372	−	0.712796i	$-0.252571\pi$
$739$	11.8187	+	6.82354i	0.434759	+	0.251008i	−0.266613	+	0.963804i	$0.585905\pi$
$740$	−27.5864			−1.01410
$741$	1.15044	+	6.08036i	0.0422624	+	0.223368i
$742$	−1.83820	−	8.56192i	−0.0674824	−	0.314318i
$743$	1.06718	−	1.84841i	0.0391511	−	0.0678118i	−0.845786	−	0.533523i	$-0.820868\pi$
$743$	1.06718	−	1.84841i	0.0391511	−	0.0678118i	0.884937	+	0.465711i	$0.154201\pi$
$744$	−9.76158	+	22.5352i	−0.357877	+	0.826180i
$745$	18.5043	−	10.6835i	0.677946	−	0.391412i
$746$	−1.93127			−0.0707089
$747$	−19.3746	+	18.1675i	−0.708881	+	0.664714i
$748$	−0.760601	−	1.31740i	−0.0278103	−	0.0481689i
$749$	9.31833	+	43.4027i	0.340484	+	1.58590i
$750$	6.72434	−	4.99014i	0.245538	−	0.182214i
$751$	−11.8515	+	20.5273i	−0.432466	+	0.749053i	−0.997085	−	0.0762988i	$-0.975690\pi$
$751$	−11.8515	+	20.5273i	−0.432466	+	0.749053i	0.564619	+	0.825352i	$0.309023\pi$
$752$	18.3777	+	10.6104i	0.670166	+	0.386921i
$753$	8.36415	−	0.964682i	0.304806	−	0.0351550i
$754$	−3.24240	−	4.78273i	−0.118081	−	0.174177i
$755$	37.4239			1.36200
$756$	0.795691	+	24.5730i	0.0289390	+	0.893710i
$757$	−21.5472	+	37.3209i	−0.783147	+	1.35645i	0.146953	+	0.989143i	$0.453053\pi$
$757$	−21.5472	+	37.3209i	−0.783147	+	1.35645i	−0.930100	+	0.367306i	$0.880280\pi$
$758$	−4.27686	+	2.46924i	−0.155342	+	0.0896870i
$759$	4.51083	+	39.1106i	0.163733	+	1.41962i
$760$	3.51771	−	2.03095i	0.127601	−	0.0736702i
$761$	13.4926	−	7.78996i	0.489107	−	0.282386i	−0.235097	−	0.971972i	$-0.575541\pi$
$761$	13.4926	−	7.78996i	0.489107	−	0.282386i	0.724204	+	0.689586i	$0.242207\pi$
$762$	−14.9278	+	1.72170i	−0.540777	+	0.0623707i
$763$	17.9200	−	16.2017i	0.648748	−	0.586542i
$764$	−22.4379	−	12.9546i	−0.811776	−	0.468679i
$765$	−1.51553	−	0.458770i	−0.0547943	−	0.0165869i
$766$		−	16.5084i		−	0.596472i
$767$	−16.0279	−	23.6421i	−0.578735	−	0.853668i
$768$	2.79677	−	0.322566i	0.100920	−	0.0116396i
$769$	−9.20985	+	15.9519i	−0.332116	+	0.575241i	−0.982926	−	0.183999i	$-0.941096\pi$
$769$	−9.20985	+	15.9519i	−0.332116	+	0.575241i	0.650811	+	0.759240i	$0.274429\pi$
$770$	−10.3271	−	3.33214i	−0.372162	−	0.120082i
$771$	25.7718	+	34.7281i	0.928149	+	1.25070i
$772$		−	46.8383i		−	1.68575i
$773$	−18.5377	+	10.7027i	−0.666754	+	0.384951i	−0.794846	−	0.606812i	$-0.792448\pi$
$773$	−18.5377	+	10.7027i	−0.666754	+	0.384951i	0.128091	+	0.991762i	$0.459115\pi$
$774$	−1.22240	−	1.30362i	−0.0439382

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:	\( N \)	\(=\)	\( 273 = 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	273.u (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.230023 + 0.398412i) q^{2} +(-0.688459 + 1.58935i) q^{3} +(0.894179 + 1.54876i) q^{4} +2.35202i q^{5} +(-0.474854 - 0.639877i) q^{6} +(1.77437 + 1.96255i) q^{7} -1.74282 q^{8} +(-2.05205 - 2.18840i) q^{9} +O(q^{10})\)	\(q+(-0.230023 + 0.398412i) q^{2} +(-0.688459 + 1.58935i) q^{3} +(0.894179 + 1.54876i) q^{4} +2.35202i q^{5} +(-0.474854 - 0.639877i) q^{6} +(1.77437 + 1.96255i) q^{7} -1.74282 q^{8} +(-2.05205 - 2.18840i) q^{9} +(-0.937075 - 0.541020i) q^{10} +(1.89523 - 3.28263i) q^{11} +(-3.07713 + 0.354901i) q^{12} +(-0.259976 - 3.59617i) q^{13} +(-1.19005 + 0.255498i) q^{14} +(-3.73818 - 1.61927i) q^{15} +(-1.38747 + 2.40316i) q^{16} +(-0.112205 - 0.194344i) q^{17} +(1.34390 - 0.314178i) q^{18} +(0.495455 + 0.858154i) q^{19} +(-3.64273 + 2.10313i) q^{20} +(-4.34076 + 1.46895i) q^{21} +(0.871892 + 1.51016i) q^{22} +(5.19329 + 2.99835i) q^{23} +(1.19986 - 2.76995i) q^{24} -0.532016 q^{25} +(1.49256 + 0.723624i) q^{26} +(4.89088 - 1.75480i) q^{27} +(-1.45292 + 4.50295i) q^{28} +(-3.01682 - 1.74176i) q^{29} +(1.50501 - 1.11687i) q^{30} -8.13560 q^{31} +(-2.38112 - 4.12422i) q^{32} +(3.91245 + 5.27212i) q^{33} +0.103239 q^{34} +(-4.61597 + 4.17336i) q^{35} +(1.55441 - 5.13496i) q^{36} +(5.67975 + 3.27921i) q^{37} -0.455865 q^{38} +(5.89454 + 2.06262i) q^{39} -4.09916i q^{40} +(1.81328 + 1.04690i) q^{41} +(0.413226 - 2.06730i) q^{42} +(-0.647431 - 1.12138i) q^{43} +6.77868 q^{44} +(5.14717 - 4.82647i) q^{45} +(-2.38916 + 1.37938i) q^{46} -7.64729i q^{47} +(-2.86425 - 3.85965i) q^{48} +(-0.703223 + 6.96459i) q^{49} +(0.122376 - 0.211962i) q^{50} +(0.386129 - 0.0445343i) q^{51} +(5.33714 - 3.61826i) q^{52} +7.19458i q^{53} +(-0.425883 + 2.35223i) q^{54} +(7.72082 + 4.45762i) q^{55} +(-3.09241 - 3.42038i) q^{56} +(-1.70500 + 0.196647i) q^{57} +(1.38788 - 0.801293i) q^{58} +(6.86061 - 3.96098i) q^{59} +(-0.834737 - 7.23748i) q^{60} +(-1.77043 + 1.02216i) q^{61} +(1.87138 - 3.24132i) q^{62} +(0.653753 - 7.91028i) q^{63} -3.35902 q^{64} +(8.45827 - 0.611471i) q^{65} +(-3.00043 + 0.346056i) q^{66} +(9.58594 + 5.53444i) q^{67} +(0.200662 - 0.347557i) q^{68} +(-8.34078 + 6.18970i) q^{69} +(-0.600936 - 2.79903i) q^{70} +(-5.36792 - 9.29750i) q^{71} +(3.57635 + 3.81399i) q^{72} +1.05464 q^{73} +(-2.61295 + 1.50859i) q^{74} +(0.366271 - 0.845558i) q^{75} +(-0.886051 + 1.53469i) q^{76} +(9.80516 - 2.10512i) q^{77} +(-2.17765 + 1.87401i) q^{78} -8.02255 q^{79} +(-5.65230 - 3.26336i) q^{80} +(-0.578184 + 8.98141i) q^{81} +(-0.834193 + 0.481621i) q^{82} -8.85334i q^{83} +(-6.15647 - 5.40930i) q^{84} +(0.457103 - 0.263908i) q^{85} +0.595696 q^{86} +(4.84523 - 3.59565i) q^{87} +(-3.30304 + 5.72103i) q^{88} +(8.09262 + 4.67228i) q^{89} +(0.738955 + 3.16089i) q^{90} +(6.59637 - 6.89115i) q^{91} +10.7242i q^{92} +(5.60103 - 12.9303i) q^{93} +(3.04677 + 1.75906i) q^{94} +(-2.01840 + 1.16532i) q^{95} +(8.19412 - 0.945072i) q^{96} +(-1.92049 - 3.32639i) q^{97} +(-2.61302 - 1.88219i) q^{98} +(-11.0728 + 2.58860i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q - 40 q^{4} - 6 q^{9}+O(q^{10}) \) 64 * q - 40 * q^4 - 6 * q^9	\( 64 q - 40 q^{4} - 6 q^{9} + 18 q^{15} - 32 q^{16} + 24 q^{22} - 80 q^{25} + 12 q^{28} + 20 q^{30} + 50 q^{36} - 36 q^{37} - 60 q^{39} + 48 q^{43} - 84 q^{46} - 16 q^{49} + 52 q^{51} - 48 q^{58} - 36 q^{63} + 176 q^{64} + 60 q^{67} - 66 q^{72} + 166 q^{78} - 104 q^{79} - 30 q^{81} + 60 q^{84} + 132 q^{85} - 8 q^{91} - 162 q^{93}+O(q^{100}) \) 64 * q - 40 * q^4 - 6 * q^9 + 18 * q^15 - 32 * q^16 + 24 * q^22 - 80 * q^25 + 12 * q^28 + 20 * q^30 + 50 * q^36 - 36 * q^37 - 60 * q^39 + 48 * q^43 - 84 * q^46 - 16 * q^49 + 52 * q^51 - 48 * q^58 - 36 * q^63 + 176 * q^64 + 60 * q^67 - 66 * q^72 + 166 * q^78 - 104 * q^79 - 30 * q^81 + 60 * q^84 + 132 * q^85 - 8 * q^91 - 162 * q^93

Introduction

L-functions

Modular forms

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