LMFDB - Embedded newform 441.2.bg.a.395.17

Newspace parameters

Level:	$ N $	$=$	$ 441 = 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	441.bg (of order $42$, degree $12$, minimal)

Newform invariants

Self dual:	no
Analytic conductor:	$3.52140272914$
Analytic rank:	$0$
Dimension:	$216$
Relative dimension:	$18$ over $\Q(\zeta_{42})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{42}]$

Embedding invariants

Embedding label			395.17
Character	$\chi$	$=$	441.395
Dual form			441.2.bg.a.278.17

$q$-expansion

$f(q)$	$=$	$q+(2.21867 + 0.870763i) q^{2} +(2.69816 + 2.50352i) q^{4} +(1.55712 + 1.06163i) q^{5} +(0.00333353 - 2.64575i) q^{7} +(1.73808 + 3.60916i) q^{8} +O(q^{10})$	\(q+(2.21867 + 0.870763i) q^{2} +(2.69816 + 2.50352i) q^{4} +(1.55712 + 1.06163i) q^{5} +(0.00333353 - 2.64575i) q^{7} +(1.73808 + 3.60916i) q^{8} +(2.53032 + 3.71129i) q^{10} +(0.0972657 + 0.645316i) q^{11} +(0.531850 - 0.424136i) q^{13} +(2.31122 - 5.86714i) q^{14} +(0.163378 + 2.18013i) q^{16} +(-5.58077 - 1.72144i) q^{17} +(-5.58665 + 3.22545i) q^{19} +(1.54355 + 6.76274i) q^{20} +(-0.346117 + 1.51644i) q^{22} +(2.20835 + 7.15930i) q^{23} +(-0.529125 - 1.34819i) q^{25} +(1.54932 - 0.477902i) q^{26} +(6.63269 - 7.13030i) q^{28} +(4.23402 - 0.966388i) q^{29} +(-2.43240 - 1.40435i) q^{31} +(0.825605 - 2.67654i) q^{32} +(-10.8829 - 8.67884i) q^{34} +(2.81400 - 4.11622i) q^{35} +(-2.42947 + 2.25422i) q^{37} +(-15.2035 + 2.29156i) q^{38} +(-1.12518 + 7.46510i) q^{40} +(3.48592 - 1.67873i) q^{41} +(-2.03931 - 0.982079i) q^{43} +(-1.35313 + 1.98467i) q^{44} +(-1.33445 + 17.8071i) q^{46} +(1.26639 - 3.22670i) q^{47} +(-6.99998 - 0.0176394i) q^{49} -3.45192i q^{50} +(2.49685 + 0.187113i) q^{52} +(6.96046 - 7.50159i) q^{53} +(-0.533632 + 1.10810i) q^{55} +(9.55472 - 4.58649i) q^{56} +(10.2354 + 1.54274i) q^{58} +(-1.50981 + 1.02937i) q^{59} +(-6.85694 - 7.39003i) q^{61} +(-4.17384 - 5.23382i) q^{62} +(6.88858 - 8.63800i) q^{64} +(1.27843 - 0.0958053i) q^{65} +(-5.80262 + 10.0504i) q^{67} +(-10.7481 - 18.6163i) q^{68} +(9.82758 - 6.68221i) q^{70} +(15.2200 + 3.47387i) q^{71} +(8.21602 - 3.22455i) q^{73} +(-7.35308 + 2.88587i) q^{74} +(-23.1486 - 5.28353i) q^{76} +(1.70767 - 0.255190i) q^{77} +(4.60480 + 7.97575i) q^{79} +(-2.06009 + 3.56818i) q^{80} +(9.19589 - 0.689136i) q^{82} +(-5.98518 + 7.50517i) q^{83} +(-6.86243 - 8.60521i) q^{85} +(-3.66939 - 3.95466i) q^{86} +(-2.15999 + 1.47266i) q^{88} +(-4.81648 - 0.725967i) q^{89} +(-1.12039 - 1.40856i) q^{91} +(-11.9650 + 24.8456i) q^{92} +(5.61939 - 6.05626i) q^{94} +(-12.1233 - 0.908519i) q^{95} -8.08055i q^{97} +(-15.5153 - 6.13446i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 216 q - 16 q^{4} + 2 q^{7}+O(q^{10}) $ 216 * q - 16 * q^4 + 2 * q^7	$ 216 q - 16 q^{4} + 2 q^{7} + 12 q^{10} + 12 q^{16} - 6 q^{19} + 44 q^{22} + 26 q^{25} + 84 q^{28} - 6 q^{31} - 112 q^{34} + 60 q^{37} - 304 q^{40} + 20 q^{43} - 20 q^{46} - 86 q^{49} - 168 q^{52} - 84 q^{55} - 120 q^{58} - 2 q^{61} + 32 q^{64} + 22 q^{67} - 136 q^{70} - 6 q^{73} + 84 q^{76} + 2 q^{79} - 104 q^{82} + 96 q^{85} - 12 q^{88} + 58 q^{91} + 52 q^{94}+O(q^{100}) $ 216 * q - 16 * q^4 + 2 * q^7 + 12 * q^10 + 12 * q^16 - 6 * q^19 + 44 * q^22 + 26 * q^25 + 84 * q^28 - 6 * q^31 - 112 * q^34 + 60 * q^37 - 304 * q^40 + 20 * q^43 - 20 * q^46 - 86 * q^49 - 168 * q^52 - 84 * q^55 - 120 * q^58 - 2 * q^61 + 32 * q^64 + 22 * q^67 - 136 * q^70 - 6 * q^73 + 84 * q^76 + 2 * q^79 - 104 * q^82 + 96 * q^85 - 12 * q^88 + 58 * q^91 + 52 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/441\mathbb{Z}\right)^\times$.

$n$	$199$	$344$
$\chi(n)$	$e\left(\frac{1}{42}\right)$	$-1$

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 $

$2$	2.21867	+	0.870763i	1.56884	+	0.615722i	0.981129	−	0.193352i	$-0.0619360\pi$
$2$	2.21867	+	0.870763i	1.56884	+	0.615722i	0.587706	+	0.809075i	$0.300031\pi$
$3$		0			0
$3$		0			0
$4$	2.69816	+	2.50352i	1.34908	+	1.25176i
$5$	1.55712	+	1.06163i	0.696367	+	0.474775i	0.859042	−	0.511904i	$-0.171060\pi$
$5$	1.55712	+	1.06163i	0.696367	+	0.474775i	−0.162675	+	0.986680i	$0.552012\pi$
$6$		0			0
$7$	0.00333353	−	2.64575i	0.00125996	−	0.999999i
$7$	0.00333353	−	2.64575i	0.00125996	−	0.999999i
$8$	1.73808	+	3.60916i	0.614503	+	1.27603i
$9$		0			0
$10$	2.53032	+	3.71129i	0.800156	+	1.17361i
$11$	0.0972657	+	0.645316i	0.0293267	+	0.194570i	0.998697	−	0.0510342i	$-0.0162517\pi$
$11$	0.0972657	+	0.645316i	0.0293267	+	0.194570i	−0.969370	+	0.245604i	$0.921014\pi$
$12$		0			0
$13$	0.531850	−	0.424136i	0.147509	−	0.117634i	−0.546955	−	0.837162i	$-0.684213\pi$
$13$	0.531850	−	0.424136i	0.147509	−	0.117634i	0.694464	+	0.719528i	$0.255642\pi$
$14$	2.31122	−	5.86714i	0.617699	−	1.56806i
$15$		0			0
$16$	0.163378	+	2.18013i	0.0408445	+	0.545032i
$17$	−5.58077	−	1.72144i	−1.35354	−	0.417511i	−0.468677	−	0.883369i	$-0.655269\pi$
$17$	−5.58077	−	1.72144i	−1.35354	−	0.417511i	−0.884859	+	0.465859i	$0.845746\pi$
$18$		0			0
$19$	−5.58665	+	3.22545i	−1.28167	+	0.739970i	−0.977153	−	0.212539i	$-0.931827\pi$
$19$	−5.58665	+	3.22545i	−1.28167	+	0.739970i	−0.304513	+	0.952508i	$0.598494\pi$
$20$	1.54355	+	6.76274i	0.345149	+	1.51219i
$21$		0			0
$22$	−0.346117	+	1.51644i	−0.0737924	+	0.323305i
$23$	2.20835	+	7.15930i	0.460473	+	1.49282i	0.826889	+	0.562366i	$0.190109\pi$
$23$	2.20835	+	7.15930i	0.460473	+	1.49282i	−0.366415	+	0.930451i	$0.619415\pi$
$24$		0			0
$25$	−0.529125	−	1.34819i	−0.105825	−	0.269638i
$26$	1.54932	−	0.477902i	0.303847	−	0.0937244i
$27$		0			0
$28$	6.63269	−	7.13030i	1.25346	−	1.34750i
$29$	4.23402	−	0.966388i	0.786239	−	0.179454i	0.189491	−	0.981883i	$-0.439316\pi$
$29$	4.23402	−	0.966388i	0.786239	−	0.179454i	0.596748	+	0.802429i	$0.296459\pi$
$30$		0			0
$31$	−2.43240	−	1.40435i	−0.436872	−	0.252228i	0.265398	−	0.964139i	$-0.414497\pi$
$31$	−2.43240	−	1.40435i	−0.436872	−	0.252228i	−0.702270	+	0.711911i	$0.747830\pi$
$32$	0.825605	−	2.67654i	0.145948	−	0.473151i
$33$		0			0
$34$	−10.8829	−	8.67884i	−1.86641	−	1.48841i
$35$	2.81400	−	4.11622i	0.475652	−	0.695769i
$36$		0			0
$37$	−2.42947	+	2.25422i	−0.399403	+	0.370592i	−0.854148	−	0.520030i	$-0.825921\pi$
$37$	−2.42947	+	2.25422i	−0.399403	+	0.370592i	0.454745	+	0.890622i	$0.349730\pi$
$38$	−15.2035	+	2.29156i	−2.46634	+	0.371741i
$39$		0			0
$40$	−1.12518	+	7.46510i	−0.177907	+	1.18034i
$41$	3.48592	−	1.67873i	0.544410	−	0.262174i	−0.141403	−	0.989952i	$-0.545161\pi$
$41$	3.48592	−	1.67873i	0.544410	−	0.262174i	0.685813	+	0.727778i	$0.259447\pi$
$42$		0			0
$43$	−2.03931	−	0.982079i	−0.310991	−	0.149766i	0.271877	−	0.962332i	$-0.412356\pi$
$43$	−2.03931	−	0.982079i	−0.310991	−	0.149766i	−0.582869	+	0.812566i	$0.698070\pi$
$44$	−1.35313	+	1.98467i	−0.203991	+	0.299200i
$45$		0			0
$46$	−1.33445	+	17.8071i	−0.196755	+	2.62551i
$47$	1.26639	−	3.22670i	0.184722	−	0.470663i	−0.808275	−	0.588805i	$-0.799599\pi$
$47$	1.26639	−	3.22670i	0.184722	−	0.470663i	0.992997	+	0.118142i	$0.0376938\pi$
$48$		0			0
$49$	−6.99998	−	0.0176394i	−0.999997	−	0.00251991i
$50$		−	3.45192i		−	0.488176i
$51$		0			0
$52$	2.49685	+	0.187113i	0.346251	+	0.0259479i
$53$	6.96046	−	7.50159i	0.956093	−	1.03042i	−0.0434150	−	0.999057i	$-0.513824\pi$
$53$	6.96046	−	7.50159i	0.956093	−	1.03042i	0.999508	−	0.0313660i	$-0.00998575\pi$
$54$		0			0
$55$	−0.533632	+	1.10810i	−0.0719549	+	0.149416i
$56$	9.55472	−	4.58649i	1.27680	−	0.612895i
$57$		0			0
$58$	10.2354	+	1.54274i	1.34397	+	0.202571i
$59$	−1.50981	+	1.02937i	−0.196561	+	0.134013i	−0.657601	−	0.753366i	$-0.728429\pi$
$59$	−1.50981	+	1.02937i	−0.196561	+	0.134013i	0.461040	+	0.887379i	$0.347476\pi$
$60$		0			0
$61$	−6.85694	−	7.39003i	−0.877942	−	0.946196i	0.120978	−	0.992655i	$-0.461397\pi$
$61$	−6.85694	−	7.39003i	−0.877942	−	0.946196i	−0.998920	+	0.0464590i	$0.985206\pi$
$62$	−4.17384	−	5.23382i	−0.530078	−	0.664696i
$63$		0			0
$64$	6.88858	−	8.63800i	0.861072	−	1.07975i
$65$	1.27843	−	0.0958053i	0.158570	−	0.0118832i
$66$		0			0
$67$	−5.80262	+	10.0504i	−0.708903	+	1.22786i	0.256361	+	0.966581i	$0.417476\pi$
$67$	−5.80262	+	10.0504i	−0.708903	+	1.22786i	−0.965264	+	0.261275i	$0.915857\pi$
$68$	−10.7481	−	18.6163i	−1.30340	−	2.25756i
$69$		0			0
$70$	9.82758	−	6.68221i	1.17462	−	0.798677i
$71$	15.2200	+	3.47387i	1.80628	+	0.412272i	0.986948	−	0.161042i	$-0.0514855\pi$
$71$	15.2200	+	3.47387i	1.80628	+	0.412272i	0.819335	+	0.573314i	$0.194343\pi$
$72$		0			0
$73$	8.21602	−	3.22455i	0.961612	−	0.377405i	0.167971	−	0.985792i	$-0.446278\pi$
$73$	8.21602	−	3.22455i	0.961612	−	0.377405i	0.793641	+	0.608387i	$0.208183\pi$
$74$	−7.35308	+	2.88587i	−0.854779	+	0.335476i
$75$		0			0
$76$	−23.1486	−	5.28353i	−2.65533	−	0.606062i
$77$	1.70767	−	0.255190i	0.194607	−	0.0290815i
$78$		0			0
$79$	4.60480	+	7.97575i	0.518080	+	0.897342i	0.999779	+	0.0210049i	$0.00668657\pi$
$79$	4.60480	+	7.97575i	0.518080	+	0.897342i	−0.481699	+	0.876337i	$0.659980\pi$
$80$	−2.06009	+	3.56818i	−0.230325	+	0.398934i
$81$		0			0
$82$	9.19589	−	0.689136i	1.01552	−	0.0761024i
$83$	−5.98518	+	7.50517i	−0.656959	+	0.823800i	−0.993008	−	0.118044i	$-0.962338\pi$
$83$	−5.98518	+	7.50517i	−0.656959	+	0.823800i	0.336050	+	0.941844i	$0.390909\pi$
$84$		0			0
$85$	−6.86243	−	8.60521i	−0.744335	−	0.933367i
$86$	−3.66939	−	3.95466i	−0.395680	−	0.426442i
$87$		0			0
$88$	−2.15999	+	1.47266i	−0.230256	+	0.156986i
$89$	−4.81648	−	0.725967i	−0.510545	−	0.0769524i	−0.111283	−	0.993789i	$-0.535496\pi$
$89$	−4.81648	−	0.725967i	−0.510545	−	0.0769524i	−0.399263	+	0.916836i	$0.630734\pi$
$90$		0			0
$91$	−1.12039	−	1.40856i	−0.117448	−	0.147657i
$92$	−11.9650	+	24.8456i	−1.24744	+	2.59033i
$93$		0			0
$94$	5.61939	−	6.05626i	0.579596	−	0.624656i
$95$	−12.1233	−	0.908519i	−1.24383	−	0.0932121i
$96$		0			0
$97$		−	8.08055i		−	0.820455i	−0.911983	−	0.410228i	$-0.865449\pi$
$97$		−	8.08055i		−	0.820455i	0.911983	−	0.410228i	$-0.134551\pi$
$98$	−15.5153	−	6.13446i	−1.56728	−	0.619674i
$99$		0			0
$100$	1.94756	−	4.96230i	0.194756	−	0.496230i
$101$	−1.39058	+	18.5561i	−0.138368	+	1.84640i	0.307803	+	0.951450i	$0.400406\pi$
$101$	−1.39058	+	18.5561i	−0.138368	+	1.84640i	−0.446172	+	0.894947i	$0.647213\pi$
$102$		0			0
$103$	5.51061	−	8.08258i	0.542977	−	0.796400i	−0.452464	−	0.891783i	$-0.649455\pi$
$103$	5.51061	−	8.08258i	0.542977	−	0.796400i	0.995441	+	0.0953822i	$0.0304073\pi$
$104$	2.45517	+	1.18235i	0.240749	+	0.115939i
$105$		0			0
$106$	21.9751	−	10.5826i	2.13441	−	1.02788i
$107$	−1.47113	+	9.76031i	−0.142220	+	0.943565i	0.797917	+	0.602767i	$0.205935\pi$
$107$	−1.47113	+	9.76031i	−0.142220	+	0.943565i	−0.940137	+	0.340798i	$0.889303\pi$
$108$		0			0
$109$	−6.35767	+	0.958265i	−0.608955	+	0.0917852i	−0.446278	−	0.894894i	$-0.647251\pi$
$109$	−6.35767	+	0.958265i	−0.608955	+	0.0917852i	−0.162677	+	0.986679i	$0.552013\pi$
$110$	−2.14884	+	1.99383i	−0.204884	+	0.190105i
$111$		0			0
$112$	5.76861	−	0.424989i	0.545083	−	0.0401577i
$113$	−10.0205	−	7.99108i	−0.942649	−	0.751737i	0.0261316	−	0.999659i	$-0.491681\pi$
$113$	−10.0205	−	7.99108i	−0.942649	−	0.751737i	−0.968780	+	0.247921i	$0.920253\pi$
$114$		0			0
$115$	−4.16185	+	13.4924i	−0.388094	+	1.25817i
$116$	13.8434	+	7.99251i	1.28533	+	0.742086i
$117$		0			0
$118$	−4.24611	+	0.969146i	−0.390886	+	0.0892171i
$119$	−4.57310	+	14.7596i	−0.419216	+	1.35301i
$120$		0			0
$121$	10.1043	−	3.11677i	0.918575	−	0.283343i
$122$	−8.77832	−	22.3668i	−0.794752	−	2.02499i
$123$		0			0
$124$	−3.04718	−	9.87872i	−0.273645	−	0.887135i
$125$	2.70417	−	11.8478i	0.241868	−	1.05970i
$126$		0			0
$127$	−1.96619	−	8.61442i	−0.174471	−	0.764406i	−0.984122	−	0.177495i	$-0.943201\pi$
$127$	−1.96619	−	8.61442i	−0.174471	−	0.764406i	0.809651	−	0.586912i	$-0.199656\pi$
$128$	17.9537	−	10.3656i	1.58689	−	0.916194i
$129$		0			0
$130$	2.91984	+	0.900652i	0.256087	+	0.0789924i
$131$	−0.225403	−	3.00779i	−0.0196935	−	0.262792i	−0.998356	−	0.0573173i	$-0.981745\pi$
$131$	−0.225403	−	3.00779i	−0.0196935	−	0.262792i	0.978663	−	0.205474i	$-0.0658737\pi$
$132$		0			0
$133$	8.51512	+	14.7916i	0.738354	+	1.28260i
$134$	−21.6256	+	17.2459i	−1.86817	+	1.48982i
$135$		0			0
$136$	−3.48687	−	23.1339i	−0.298997	−	1.98371i
$137$	1.34187	+	1.96816i	0.114644	+	0.168151i	0.879272	−	0.476320i	$-0.158030\pi$
$137$	1.34187	+	1.96816i	0.114644	+	0.168151i	−0.764628	+	0.644472i	$0.777077\pi$
$138$		0			0
$139$	9.71304	+	20.1693i	0.823849	+	1.71074i	0.694921	+	0.719086i	$0.255439\pi$
$139$	9.71304	+	20.1693i	0.823849	+	1.71074i	0.128928	+	0.991654i	$0.458846\pi$
$140$	17.8977	−	4.06131i	1.51263	−	0.343243i
$141$		0			0
$142$	30.7432	+	20.9604i	2.57992	+	1.75896i
$143$	0.325433	+	0.301957i	0.0272141	+	0.0252510i
$144$		0			0
$145$	7.61885	+	2.99018i	0.632711	+	0.248321i
$146$	21.0364			1.74099
$147$		0			0
$148$	−12.1986			−1.00272
$149$	11.0236	+	4.32645i	0.903089	+	0.354436i	0.771025	−	0.636805i	$-0.219744\pi$
$149$	11.0236	+	4.32645i	0.903089	+	0.354436i	0.132064	+	0.991241i	$0.457839\pi$
$150$		0			0
$151$	−15.9225	−	14.7740i	−1.29576	−	1.20229i	−0.966094	−	0.258190i	$-0.916874\pi$
$151$	−15.9225	−	14.7740i	−1.29576	−	1.20229i	−0.329664	−	0.944098i	$-0.606936\pi$
$152$	−21.3512	−	14.5570i	−1.73181	−	1.18073i
$153$		0			0
$154$	4.01096	+	0.920794i	0.323212	+	0.0741997i
$155$	−2.29665	−	4.76905i	−0.184472	−	0.383060i
$156$		0			0
$157$	13.5566	+	19.8839i	1.08194	+	1.58691i	0.771401	+	0.636350i	$0.219556\pi$
$157$	13.5566	+	19.8839i	1.08194	+	1.58691i	0.310537	+	0.950561i	$0.399491\pi$
$158$	3.27154	+	21.7052i	0.260269	+	1.72678i
$159$		0			0
$160$	4.12707	−	3.29123i	0.326273	−	0.260194i
$161$	18.9491	−	5.81888i	1.49340	−	0.458592i
$162$		0			0
$163$	−1.41529	−	18.8857i	−0.110854	−	1.47924i	−0.724289	−	0.689497i	$-0.757832\pi$
$163$	−1.41529	−	18.8857i	−0.110854	−	1.47924i	0.613435	−	0.789745i	$-0.289787\pi$
$164$	13.6083	+	4.19761i	1.06263	+	0.327778i
$165$		0			0
$166$	−19.8144	+	11.4398i	−1.53789	+	0.887902i
$167$	3.44716	+	15.1030i	0.266749	+	1.16870i	0.913770	+	0.406231i	$0.133157\pi$
$167$	3.44716	+	15.1030i	0.266749	+	1.16870i	−0.647021	+	0.762472i	$0.723986\pi$
$168$		0			0
$169$	−2.78980	+	12.2229i	−0.214600	+	0.940224i
$170$	−7.73235	−	25.0677i	−0.593044	−	1.92260i
$171$		0			0
$172$	−3.04371	−	7.75525i	−0.232081	−	0.591332i
$173$	−2.35855	+	0.727517i	−0.179318	+	0.0553121i	−0.383114	−	0.923701i	$-0.625148\pi$
$173$	−2.35855	+	0.727517i	−0.179318	+	0.0553121i	0.203796	+	0.979013i	$0.434672\pi$
$174$		0			0
$175$	−3.56873	+	1.39544i	−0.269771	+	0.105485i
$176$	−1.39098	+	0.317482i	−0.104849	+	0.0239311i
$177$		0			0
$178$	−10.0540	−	5.80469i	−0.753580	−	0.435080i
$179$	−0.843671	+	2.73511i	−0.0630589	+	0.204432i	−0.981620	−	0.190848i	$-0.938876\pi$
$179$	−0.843671	+	2.73511i	−0.0630589	+	0.204432i	0.918561	+	0.395280i	$0.129352\pi$
$180$		0			0
$181$	11.8568	+	9.45547i	0.881308	+	0.702819i	0.955679	−	0.294411i	$-0.0951235\pi$
$181$	11.8568	+	9.45547i	0.881308	+	0.702819i	−0.0743711	+	0.997231i	$0.523695\pi$
$182$	−1.25925	−	4.10071i	−0.0933415	−	0.303965i
$183$		0			0
$184$	−22.0007	+	20.4137i	−1.62192	+	1.50492i
$185$	−6.17614	+	0.930903i	−0.454079	+	0.0684414i
$186$		0			0
$187$	0.568055	−	3.76880i	0.0415403	−	0.275602i
$188$	11.4950	−	5.53572i	0.838362	−	0.403734i
$189$		0			0
$190$	−26.1066	−	12.5723i	−1.89397	−	0.912088i
$191$	−3.80774	+	5.58493i	−0.275518	+	0.404111i	−0.938911	−	0.344160i	$-0.888164\pi$
$191$	−3.80774	+	5.58493i	−0.275518	+	0.404111i	0.663393	+	0.748272i	$0.269116\pi$
$192$		0			0
$193$	0.511397	−	6.82411i	0.0368111	−	0.491210i	−0.948080	−	0.318033i	$-0.896978\pi$
$193$	0.511397	−	6.82411i	0.0368111	−	0.491210i	0.984891	−	0.173177i	$-0.0554033\pi$
$194$	7.03624	−	17.9281i	0.505173	−	1.28716i
$195$		0			0
$196$	−18.8429	−	17.5722i	−1.34592	−	1.25516i
$197$			4.55093i			0.324240i	0.986771	+	0.162120i	$0.0518332\pi$
$197$			4.55093i			0.324240i	−0.986771	+	0.162120i	$0.948167\pi$
$198$		0			0
$199$	−5.37432	−	0.402750i	−0.380975	−	0.0285502i	−0.117134	−	0.993116i	$-0.537371\pi$
$199$	−5.37432	−	0.402750i	−0.380975	−	0.0285502i	−0.263842	+	0.964566i	$0.584990\pi$
$200$	3.94616	−	4.25295i	0.279036	−	0.300729i
$201$		0			0
$202$	−19.2432	+	39.9589i	−1.35395	+	2.81150i
$203$	−2.54271	−	11.2054i	−0.178463	−	0.786464i
$204$		0			0
$205$	7.21021	+	1.08676i	0.503583	+	0.0759029i
$206$	19.2642	−	13.1341i	1.34220	−	0.915098i
$207$		0			0
$208$	1.01156	+	1.09021i	0.0701393	+	0.0755922i
$209$	−2.62483	−	3.29143i	−0.181563	−	0.227673i
$210$		0			0
$211$	−3.02491	+	3.79311i	−0.208243	+	0.261129i	−0.874974	−	0.484170i	$-0.839122\pi$
$211$	−3.02491	+	3.79311i	−0.208243	+	0.261129i	0.666731	+	0.745299i	$0.267693\pi$
$212$	37.5608	−	2.81479i	2.57969	−	0.193321i
$213$		0			0
$214$	−11.7629	+	20.3739i	−0.804093	+	1.39273i
$215$	−2.13285	−	3.69421i	−0.145459	−	0.251943i
$216$		0			0
$217$	−3.72366	+	6.43084i	−0.252778	+	0.436554i
$218$	−14.9400	−	3.40996i	−1.01186	−	0.230951i
$219$		0			0
$220$	−4.21397	+	1.65386i	−0.284106	+	0.111503i
$221$	−3.69826	+	1.45146i	−0.248772	+	0.0976358i
$222$		0			0
$223$	8.69380	+	1.98430i	0.582180	+	0.132879i	0.503461	−	0.864018i	$-0.332060\pi$
$223$	8.69380	+	1.98430i	0.582180	+	0.132879i	0.0787193	+	0.996897i	$0.474917\pi$
$224$	−7.07871	−	2.19327i	−0.472966	−	0.146544i
$225$		0			0
$226$	−15.2738	−	26.4550i	−1.01600	−	1.75976i
$227$	−7.04102	+	12.1954i	−0.467329	+	0.809437i	−0.999303	−	0.0373231i	$-0.988117\pi$
$227$	−7.04102	+	12.1954i	−0.467329	+	0.809437i	0.531974	+	0.846760i	$0.321450\pi$
$228$		0			0
$229$	18.1348	−	1.35902i	1.19838	−	0.0898063i	0.539456	−	0.842014i	$-0.318630\pi$
$229$	18.1348	−	1.35902i	1.19838	−	0.0898063i	0.658926	+	0.752208i	$0.271011\pi$
$230$	−20.9824	+	26.3111i	−1.38354	+	1.73490i
$231$		0			0
$232$	10.8469	+	13.6016i	0.712135	+	0.892989i
$233$	−7.25919	−	7.82354i	−0.475565	−	0.512537i	0.449015	−	0.893524i	$-0.351775\pi$
$233$	−7.25919	−	7.82354i	−0.475565	−	0.512537i	−0.924581	+	0.380987i	$0.875584\pi$
$234$		0			0
$235$	5.39749	−	3.67995i	0.352093	−	0.240053i
$236$	−6.65076	−	1.00244i	−0.432928	−	0.0652533i
$237$		0			0
$238$	−22.9983	+	28.7645i	−1.49076	+	1.86453i
$239$	−9.07961	+	18.8540i	−0.587311	+	1.21956i	0.369602	+	0.929190i	$0.379494\pi$
$239$	−9.07961	+	18.8540i	−0.587311	+	1.21956i	−0.956913	+	0.290374i	$0.906220\pi$
$240$		0			0
$241$	−14.5707	+	15.7035i	−0.938582	+	1.01155i	0.0613279	+	0.998118i	$0.480466\pi$
$241$	−14.5707	+	15.7035i	−0.938582	+	1.01155i	−0.999910	+	0.0134331i	$0.995724\pi$
$242$	25.1321	+	1.88339i	1.61555	+	0.121069i
$243$		0			0
$244$		−	37.1060i		−	2.37547i
$245$	−10.8811	−	7.45885i	−0.695169	−	0.476529i
$246$		0			0
$247$	−1.60323	+	4.08496i	−0.102011	+	0.259920i
$248$	0.840806	−	11.2198i	0.0533913	−	0.712457i
$249$		0			0
$250$	16.3162	−	23.9315i	1.03193	−	1.51356i
$251$	3.25960	+	1.56974i	0.205744	+	0.0990812i	0.533918	−	0.845536i	$-0.320719\pi$
$251$	3.25960	+	1.56974i	0.205744	+	0.0990812i	−0.328174	+	0.944617i	$0.606433\pi$
$252$		0			0
$253$	−4.40521	+	2.12144i	−0.276953	+	0.133374i
$254$	3.13881	−	20.8246i	0.196946	−	1.30665i
$255$		0			0
$256$	27.0091	−	4.07097i	1.68807	−	0.254436i
$257$	7.50781	−	6.96623i	0.468324	−	0.434542i	−0.410375	−	0.911917i	$-0.634602\pi$
$257$	7.50781	−	6.96623i	0.468324	−	0.434542i	0.878700	+	0.477375i	$0.158412\pi$
$258$		0			0
$259$	5.95600	+	6.43529i	0.370088	+	0.399869i
$260$	3.68926	+	2.94209i	0.228798	+	0.182461i
$261$		0			0
$262$	2.11898	−	6.86956i	0.130911	−	0.424403i
$263$	−3.46319	−	1.99947i	−0.213549	−	0.123293i	0.389411	−	0.921064i	$-0.372679\pi$
$263$	−3.46319	−	1.99947i	−0.213549	−	0.123293i	−0.602960	+	0.797772i	$0.706012\pi$
$264$		0			0
$265$	18.8022	−	4.29148i	1.15501	−	0.263624i
$266$	6.01222	+	40.2324i	0.368633	+	2.46680i
$267$		0			0
$268$	−40.8179	+	12.5906i	−2.49335	+	0.769096i
$269$	−2.48226	−	6.32470i	−0.151346	−	0.385624i	0.835013	−	0.550230i	$-0.185460\pi$
$269$	−2.48226	−	6.32470i	−0.151346	−	0.385624i	−0.986359	+	0.164606i	$0.947365\pi$
$270$		0			0
$271$	−6.74647	−	21.8715i	−0.409819	−	1.32860i	−0.891805	−	0.452421i	$-0.850561\pi$
$271$	−6.74647	−	21.8715i	−0.409819	−	1.32860i	0.481986	−	0.876179i	$-0.339916\pi$
$272$	2.84118	−	12.4480i	0.172272	−	0.754773i
$273$		0			0
$274$	1.26336	+	5.53515i	0.0763225	+	0.334391i
$275$	0.818542	−	0.472585i	0.0493599	−	0.0284980i
$276$		0			0
$277$	−8.19644	−	2.52827i	−0.492476	−	0.151909i	0.0385627	−	0.999256i	$-0.487722\pi$
$277$	−8.19644	−	2.52827i	−0.492476	−	0.151909i	−0.531039	+	0.847347i	$0.678198\pi$
$278$	3.98730	+	53.2068i	0.239142	+	3.19113i
$279$		0			0
$280$	19.7470	+	3.00184i	1.18011	+	0.179394i
$281$	13.5840	−	10.8329i	0.810356	−	0.646238i	−0.128051	−	0.991768i	$-0.540872\pi$
$281$	13.5840	−	10.8329i	0.810356	−	0.646238i	0.938408	+	0.345530i	$0.112301\pi$
$282$		0			0
$283$	−4.82901	−	32.0384i	−0.287055	−	1.90449i	−0.410024	−	0.912075i	$-0.634480\pi$
$283$	−4.82901	−	32.0384i	−0.287055	−	1.90449i	0.122969	−	0.992411i	$-0.460758\pi$
$284$	32.3691	+	47.4767i	1.92075	+	2.81722i
$285$		0			0
$286$	0.459094	+	0.953318i	0.0271468	+	0.0563709i
$287$	−4.42988	−	9.22848i	−0.261488	−	0.544740i
$288$		0			0
$289$	14.1356	+	9.63750i	0.831507	+	0.566912i
$290$	14.3000	+	13.2684i	0.839723	+	0.779149i
$291$		0			0
$292$	30.2408	+	11.8686i	1.76971	+	0.694560i
$293$	−14.5324			−0.848993			−0.424496	−	0.905430i	$-0.639549\pi$
$293$	−14.5324			−0.848993			−0.424496	+	0.905430i	$0.639549\pi$
$294$		0			0
$295$	−3.44377			−0.200504
$296$	−12.3584	−	4.85033i	−0.718320	−	0.281920i
$297$		0			0
$298$	20.6904	+	19.1979i	1.19856	+	1.11210i
$299$	4.21103	+	2.87103i	0.243530	+	0.166036i
$300$		0			0
$301$	−2.60513	+	5.39222i	−0.150157	+	0.310802i
$302$	−22.4622	−	46.6433i	−1.29256	−	2.68402i
$303$		0			0
$304$	−7.94463	−	11.6526i	−0.455656	−	0.668324i
$305$	−2.83164	−	18.7867i	−0.162139	−	1.07573i
$306$		0			0
$307$	4.07997	−	3.25367i	0.232856	−	0.185697i	−0.500109	−	0.865962i	$-0.666707\pi$
$307$	4.07997	−	3.25367i	0.232856	−	0.185697i	0.732966	+	0.680265i	$0.238135\pi$
$308$	5.24643	+	3.58665i	0.298943	+	0.204368i
$309$		0			0
$310$	−0.942800	−	12.5808i	−0.0535474	−	0.714541i
$311$	−2.72915	−	0.841833i	−0.154756	−	0.0477359i	0.216409	−	0.976303i	$-0.430565\pi$
$311$	−2.72915	−	0.841833i	−0.154756	−	0.0477359i	−0.371165	+	0.928567i	$0.621042\pi$
$312$		0			0
$313$	15.4116	−	8.89791i	0.871117	−	0.502940i	0.00339768	−	0.999994i	$-0.498918\pi$
$313$	15.4116	−	8.89791i	0.871117	−	0.502940i	0.867719	+	0.497055i	$0.165585\pi$
$314$	12.7635	+	55.9205i	0.720285	+	3.15578i
$315$		0			0
$316$	−7.54300	+	33.0480i	−0.424327	+	1.85910i
$317$	−0.955904	−	3.09897i	−0.0536889	−	0.174055i	0.924757	−	0.380558i	$-0.124268\pi$
$317$	−0.955904	−	3.09897i	−0.0536889	−	0.174055i	−0.978446	+	0.206503i	$0.933792\pi$
$318$		0			0
$319$	1.03545	+	2.63829i	0.0579741	+	0.147716i
$320$	19.8967	−	6.13733i	1.11226	−	0.343087i
$321$		0			0
$322$	47.1086	+	3.58999i	2.62526	+	0.200062i
$323$	36.7303	−	8.38344i	2.04373	−	0.466467i
$324$		0			0
$325$	−0.853231	−	0.492613i	−0.0473287	−	0.0273253i
$326$	13.3049	−	43.1335i	0.736891	−	2.38894i
$327$		0			0
$328$	12.1176	+	9.66348i	0.669083	+	0.533576i
$329$	−8.53283	−	3.36130i	−0.470430	−	0.185315i
$330$		0			0
$331$	−13.3975	+	12.4310i	−0.736392	+	0.683272i	−0.956346	−	0.292238i	$-0.905600\pi$
$331$	−13.3975	+	12.4310i	−0.736392	+	0.683272i	0.219953	+	0.975510i	$0.429409\pi$
$332$	−34.9383	+	5.26610i	−1.91749	+	0.289015i
$333$		0			0
$334$	−5.50302	+	36.5101i	−0.301112	+	1.99775i
$335$	−19.7053	+	9.48955i	−1.07661	+	0.518470i
$336$		0			0
$337$	−12.9190	−	6.22147i	−0.703743	−	0.338905i	0.0475542	−	0.998869i	$-0.484857\pi$
$337$	−12.9190	−	6.22147i	−0.703743	−	0.338905i	−0.751297	+	0.659964i	$0.770572\pi$
$338$	−16.8329	+	24.6893i	−0.915589	+	1.34292i
$339$		0			0
$340$	3.02745	−	40.3985i	0.164186	−	2.19091i
$341$	0.669658	−	1.70626i	0.0362640	−	0.0923992i
$342$		0			0
$343$	−0.0700040	+	18.5201i	−0.00377986	+	0.999993i
$344$		−	9.06711i		−	0.488866i
$345$		0			0
$346$	−5.86634	−	0.439622i	−0.315377	−	0.0236342i
$347$	−8.48613	+	9.14588i	−0.455560	+	0.490976i	−0.918504	−	0.395411i	$-0.870602\pi$
$347$	−8.48613	+	9.14588i	−0.455560	+	0.490976i	0.462945	+	0.886387i	$0.346793\pi$
$348$		0			0
$349$	−5.62020	+	11.6705i	−0.300843	+	0.624706i	−0.995513	−	0.0946218i	$-0.969836\pi$
$349$	−5.62020	+	11.6705i	−0.300843	+	0.624706i	0.694671	+	0.719328i	$0.255550\pi$
$350$	−9.13293	−	0.0115071i	−0.488176	−	0.000615081i
$351$		0			0
$352$	1.80752	+	0.272440i	0.0963411	+	0.0145211i
$353$	21.8743	−	14.9136i	1.16425	−	0.793773i	0.182363	−	0.983231i	$-0.441626\pi$
$353$	21.8743	−	14.9136i	1.16425	−	0.793773i	0.981889	+	0.189458i	$0.0606732\pi$
$354$		0			0
$355$	20.0115	+	21.5673i	1.06210	+	1.14467i
$356$	−11.1781	−	14.0169i	−0.592440	−	0.742896i
$357$		0			0
$358$	−4.25346	+	5.33367i	−0.224802	+	0.281893i
$359$	8.44775	−	0.633071i	0.445855	−	0.0334122i	0.150089	−	0.988673i	$-0.452044\pi$
$359$	8.44775	−	0.633071i	0.445855	−	0.0334122i	0.295766	+	0.955260i	$0.404425\pi$
$360$		0			0
$361$	11.3071	−	19.5845i	0.595111	−	1.03076i
$362$	18.0728	+	31.3030i	0.949885	+	1.64525i
$363$		0			0
$364$	0.503378	−	6.60542i	0.0263842	−	0.346218i
$365$	16.2166	+	3.70134i	0.848818	+	0.193737i
$366$		0			0
$367$	4.17842	−	1.63991i	0.218112	−	0.0856025i	−0.253769	−	0.967265i	$-0.581670\pi$
$367$	4.17842	−	1.63991i	0.218112	−	0.0856025i	0.471881	+	0.881662i	$0.343575\pi$
$368$	−15.2474	+	5.98416i	−0.794825	+	0.311946i
$369$		0			0
$370$	−14.5134	−	3.31259i	−0.754516	−	0.172213i
$371$	−19.8241	−	18.4406i	−1.02922	−	0.957390i
$372$		0			0
$373$	−13.0224	−	22.5554i	−0.674274	−	1.16788i	−0.976681	−	0.214697i	$-0.931123\pi$
$373$	−13.0224	−	22.5554i	−0.674274	−	1.16788i	0.302407	−	0.953179i	$-0.402210\pi$
$374$	4.54206	−	7.86707i	0.234864	−	0.406797i
$375$		0			0
$376$	13.8468	−	1.03767i	0.714092	−	0.0535138i
$377$	1.84199	−	2.30978i	0.0948671	−	0.118960i
$378$		0			0
$379$	−10.1826	−	12.7685i	−0.523044	−	0.655876i	0.448209	−	0.893929i	$-0.352062\pi$
$379$	−10.1826	−	12.7685i	−0.523044	−	0.655876i	−0.971252	+	0.238053i	$0.923491\pi$
$380$	−30.4362	−	32.8024i	−1.56134	−	1.68273i
$381$		0			0
$382$	−13.3113	+	9.07546i	−0.681063	+	0.464341i
$383$	19.4310	+	2.92875i	0.992878	+	0.149652i	0.625337	−	0.780355i	$-0.284962\pi$
$383$	19.4310	+	2.92875i	0.992878	+	0.149652i	0.367541	+	0.930007i	$0.380200\pi$
$384$		0			0
$385$	2.92997	+	1.41555i	0.149325	+	0.0721431i
$386$	7.07680	−	14.6951i	0.360200	−	0.747963i
$387$		0			0
$388$	20.2298	−	21.8026i	1.02701	−	1.10686i
$389$	−7.09818	−	0.531935i	−0.359892	−	0.0269702i	−0.106443	−	0.994319i	$-0.533946\pi$
$389$	−7.09818	−	0.531935i	−0.359892	−	0.0269702i	−0.253449	+	0.967349i	$0.581565\pi$
$390$		0			0
$391$		−	43.7560i		−	2.21283i
$392$	−12.1028	−	25.2947i	−0.611286	−	1.27757i
$393$		0			0
$394$	−3.96278	+	10.0970i	−0.199642	+	0.508679i
$395$	−1.29704	+	17.3078i	−0.0652613	+	0.870851i
$396$		0			0
$397$	14.4992	−	21.2664i	0.727693	−	1.06733i	−0.266925	−	0.963717i	$-0.586008\pi$
$397$	14.4992	−	21.2664i	0.727693	−	1.06733i	0.994618	−	0.103612i	$-0.0330399\pi$
$398$	−11.5731	−	5.57333i	−0.580109	−	0.279366i
$399$		0			0
$400$	2.85277	−	1.37382i	0.142639	−	0.0686912i
$401$	−5.73624	+	38.0575i	−0.286454	+	1.90050i	0.130291	+	0.991476i	$0.458409\pi$
$401$	−5.73624	+	38.0575i	−0.286454	+	1.90050i	−0.416745	+	0.909023i	$0.636829\pi$
$402$		0			0
$403$	−1.88931	+	0.284767i	−0.0941131	+	0.0141853i
$404$	−50.2075	+	46.5858i	−2.49792	+	2.31773i
$405$		0			0
$406$	4.11581	−	27.0751i	0.204264	−	1.34372i
$407$	−1.69099	−	1.34852i	−0.0838192	−	0.0668436i
$408$		0			0
$409$	7.66146	−	24.8378i	0.378835	−	1.22815i	−0.542724	−	0.839911i	$-0.682607\pi$
$409$	7.66146	−	24.8378i	0.378835	−	1.22815i	0.921558	−	0.388240i	$-0.126917\pi$
$410$	15.0508	+	8.68956i	0.743304	+	0.429147i
$411$		0			0
$412$	35.1034	−	8.01213i	1.72942	−	0.394729i
$413$	2.71843	+	3.99801i	0.133765	+	0.196729i
$414$		0			0
$415$	−17.2874	+	5.33245i	−0.848604	+	0.261760i
$416$	−0.696122	−	1.77369i	−0.0341302	−	0.0869623i
$417$		0			0
$418$	−2.95756	−	9.58819i	−0.144659	−	0.468974i
$419$	2.78683	−	12.2099i	0.136146	−	0.596493i	−0.860115	−	0.510099i	$-0.829609\pi$
$419$	2.78683	−	12.2099i	0.136146	−	0.596493i	0.996261	−	0.0863937i	$-0.0275343\pi$
$420$		0			0
$421$	0.571227	+	2.50271i	0.0278399	+	0.121975i	0.986938	−	0.161098i	$-0.0515035\pi$
$421$	0.571227	+	2.50271i	0.0278399	+	0.121975i	−0.959099	+	0.283072i	$0.908646\pi$
$422$	−10.0142	+	5.78168i	−0.487482	+	0.281448i
$423$		0			0
$424$	39.1723	+	12.0830i	1.90237	+	0.586804i
$425$	0.632100	+	8.43479i	0.0306614	+	0.409147i
$426$		0			0
$427$	−19.5750	+	18.1171i	−0.947302	+	0.876749i
$428$	−28.4045	+	22.6518i	−1.37298	+	1.09492i
$429$		0			0
$430$	−1.51531	−	10.0534i	−0.0730748	−	0.484819i
$431$	−22.5961	−	33.1424i	−1.08842	−	1.59641i	−0.757601	−	0.652718i	$-0.773629\pi$
$431$	−22.5961	−	33.1424i	−1.08842	−	1.59641i	−0.330816	−	0.943695i	$-0.607324\pi$
$432$		0			0
$433$	11.9382	+	24.7899i	0.573713	+	1.19133i	0.962822	+	0.270135i	$0.0870684\pi$
$433$	11.9382	+	24.7899i	0.573713	+	1.19133i	−0.389110	+	0.921191i	$0.627217\pi$
$434$	−13.8613	+	11.0255i	−0.665364	+	0.529240i
$435$		0			0
$436$	−19.5530	−	13.3310i	−0.936421	−	0.638441i
$437$	−35.4293	−	32.8736i	−1.69481	−	1.57256i
$438$		0			0
$439$	−37.4380	−	14.6933i	−1.78682	−	0.701274i	−0.996013	−	0.0892056i	$-0.971567\pi$
$439$	−37.4380	−	14.6933i	−1.78682	−	0.701274i	−0.790805	−	0.612069i	$-0.790338\pi$
$440$	−4.92679			−0.234876
$441$		0			0
$442$	−9.46909			−0.450399
$443$	13.1010	+	5.14177i	0.622448	+	0.244293i	0.655541	−	0.755159i	$-0.272441\pi$
$443$	13.1010	+	5.14177i	0.622448	+	0.244293i	−0.0330932	+	0.999452i	$0.510536\pi$
$444$		0			0
$445$	−6.72915	−	6.24374i	−0.318992	−	0.295981i
$446$	17.5608	+	11.9728i	0.831528	+	0.566926i
$447$		0			0
$448$	−22.8310	−	18.2542i	−1.07866	−	0.862432i
$449$	−4.22605	−	8.77548i	−0.199439	−	0.414140i	0.777131	−	0.629339i	$-0.216674\pi$
$449$	−4.22605	−	8.77548i	−0.199439	−	0.414140i	−0.976570	+	0.215199i	$0.930960\pi$
$450$		0			0
$451$	1.42237	+	2.08624i	0.0669770	+	0.0982372i
$452$	−7.03101	−	46.6477i	−0.330711	−	2.19412i
$453$		0			0
$454$	−26.2410	+	20.9265i	−1.23155	+	0.982129i
$455$	−0.249215	−	3.38273i	−0.0116834	−	0.158585i
$456$		0			0
$457$	−1.07114	−	14.2933i	−0.0501057	−	0.668614i	−0.964550	−	0.263901i	$-0.914991\pi$
$457$	−1.07114	−	14.2933i	−0.0501057	−	0.668614i	0.914444	−	0.404712i	$-0.132628\pi$
$458$	41.4185	+	12.7759i	1.93536	+	0.596979i
$459$		0			0
$460$	−45.0078	+	25.9853i	−2.09850	+	1.21157i
$461$	−5.71927	−	25.0577i	−0.266373	−	1.16706i	−0.914198	−	0.405267i	$-0.867179\pi$
$461$	−5.71927	−	25.0577i	−0.266373	−	1.16706i	0.647826	−	0.761789i	$-0.275679\pi$
$462$		0			0
$463$	−1.45321	+	6.36694i	−0.0675365	+	0.295897i	−0.997405	−	0.0719954i	$-0.977063\pi$
$463$	−1.45321	+	6.36694i	−0.0675365	+	0.295897i	0.929868	+	0.367892i	$0.119920\pi$
$464$	2.79860	+	9.07282i	0.129922	+	0.421195i
$465$		0			0
$466$	−9.29327	−	23.6789i	−0.430503	−	1.09690i
$467$	15.0319	−	4.63672i	0.695592	−	0.214562i	0.0732575	−	0.997313i	$-0.476660\pi$
$467$	15.0319	−	4.63672i	0.695592	−	0.214562i	0.622335	+	0.782751i	$0.286184\pi$
$468$		0			0
$469$	26.5716	+	15.3858i	1.22696	+	0.710450i
$470$	15.1796	−	3.46464i	0.700183	−	0.159812i
$471$		0			0
$472$	−6.33933	−	3.66001i	−0.291791	−	0.168466i
$473$	0.435396	−	1.41152i	0.0200195	−	0.0649018i
$474$		0			0
$475$	7.30455	+	5.82519i	0.335156	+	0.267278i
$476$	−49.2899	+	28.3748i	−2.25920	+	1.30056i
$477$		0			0
$478$	−36.5620	+	33.9246i	−1.67231	+	1.55168i
$479$	−28.4563	+	4.28910i	−1.30020	+	0.195974i	−0.762406	−	0.647100i	$-0.775982\pi$
$479$	−28.4563	+	4.28910i	−1.30020	+	0.195974i	−0.537798	+	0.843074i	$0.680744\pi$
$480$		0			0
$481$	−0.336018	+	2.22934i	−0.0153211	+	0.101649i
$482$	−46.0016	+	22.1532i	−2.09531	+	1.00905i
$483$		0			0
$484$	35.0660	+	16.8869i	1.59391	+	0.767585i
$485$	8.57855	−	12.5824i	0.389532	−	0.571338i
$486$		0			0
$487$	0.958609	−	12.7918i	0.0434387	−	0.579650i	−0.932438	−	0.361329i	$-0.882323\pi$
$487$	0.958609	−	12.7918i	0.0434387	−	0.579650i	0.975877	−	0.218321i	$-0.0700579\pi$
$488$	14.7539	−	37.5922i	0.667876	−	1.70172i
$489$		0			0
$490$	−17.6467	−	26.0236i	−0.797196	−	1.17563i
$491$		−	13.5607i		−	0.611987i	−0.952034	−	0.305994i	$-0.901011\pi$
$491$		−	13.5607i		−	0.611987i	0.952034	−	0.305994i	$-0.0989886\pi$
$492$		0			0
$493$	−25.2927	−	1.89543i	−1.13913	−	0.0853657i
$494$	−7.11406	+	7.66714i	−0.320077	+	0.344961i
$495$		0			0
$496$	2.66425	−	5.53238i	0.119629	−	0.248411i
$497$	9.24172	−	40.2568i	0.414548	−	1.80576i
$498$		0			0
$499$	−6.55494	−	0.987999i	−0.293440	−	0.0442289i	0.000672682	−	1.00000i	$-0.499786\pi$
$499$	−6.55494	−	0.987999i	−0.293440	−	0.0442289i	−0.294112	+	0.955771i	$0.595024\pi$
$500$	36.9574	−	25.1971i	1.65278	−	1.12685i
$501$		0			0
$502$	5.86510	+	6.32108i	0.261772	+	0.282123i
$503$	14.0917	+	17.6704i	0.628316	+	0.787883i	0.989488	−	0.144616i	$-0.0461948\pi$
$503$	14.0917	+	17.6704i	0.628316	+	0.787883i	−0.361172	+	0.932499i	$0.617623\pi$
$504$		0			0
$505$	−21.8650	+	27.4178i	−0.972979	+	1.22008i
$506$	−11.6210	+	0.870872i	−0.516615	+	0.0387150i
$507$		0			0
$508$	16.2613	−	28.1654i	0.721480	−	1.24964i
$509$	−8.18340	−	14.1741i	−0.362723	−	0.628254i	0.625685	−	0.780076i	$-0.284819\pi$
$509$	−8.18340	−	14.1741i	−0.362723	−	0.628254i	−0.988408	+	0.151821i	$0.951486\pi$
$510$		0			0
$511$	−8.50396	−	21.7483i	−0.376193	−	0.962087i
$512$	23.0465	+	5.26021i	1.01852	+	0.232471i
$513$		0			0
$514$	22.7233	−	8.91823i	1.00228	−	0.393366i
$515$	17.1614	−	6.73536i	0.756222	−	0.296795i
$516$		0			0
$517$	2.20542	+	0.503373i	0.0969943	+	0.0221383i
$518$	7.61078	+	19.4640i	0.334399	+	0.855201i
$519$		0			0
$520$	2.56779	+	4.44755i	0.112605	+	0.195038i
$521$	−4.55691	+	7.89280i	−0.199642	+	0.345790i	−0.948412	−	0.317040i	$-0.897311\pi$
$521$	−4.55691	+	7.89280i	−0.199642	+	0.345790i	0.748770	+	0.662829i	$0.230645\pi$
$522$		0			0
$523$	−1.57530	+	0.118053i	−0.0688831	+	0.00516208i	−0.109127	−	0.994028i	$-0.534806\pi$
$523$	−1.57530	+	0.118053i	−0.0688831	+	0.00516208i	0.0402439	+	0.999190i	$0.487186\pi$
$524$	6.92189	−	8.67978i	0.302384	−	0.379178i
$525$		0			0
$526$	−5.94259	−	7.45178i	−0.259109	−	0.324913i
$527$	11.1572	+	12.0246i	0.486014	+	0.523799i
$528$		0			0
$529$	−27.3753	+	18.6641i	−1.19023	+	0.811484i
$530$	45.4528	+	6.85090i	1.97434	+	0.297584i
$531$		0			0
$532$	−14.0561	+	61.2279i	−0.609407	+	2.65457i
$533$	1.14198	−	2.37134i	0.0494646	−	0.102714i
$534$		0			0
$535$	−12.6526	+	13.6362i	−0.547019	+	0.589546i
$536$	−46.3590	−	3.47413i	−2.00240	−	0.150059i
$537$		0			0
$538$		−	16.1939i		−	0.698167i
$539$	−0.669475	−	4.51891i	−0.0288363	−	0.194643i
$540$		0			0
$541$	13.8278	−	35.2327i	0.594505	−	1.51477i	−0.243942	−	0.969790i	$-0.578441\pi$
$541$	13.8278	−	35.2327i	0.594505	−	1.51477i	0.838446	−	0.544984i	$-0.183464\pi$
$542$	4.07673	−	54.4002i	0.175111	−	2.33669i
$543$		0			0
$544$	−9.21503	+	13.5160i	−0.395091	+	0.579492i
$545$	−10.9170	−	5.25736i	−0.467634	−	0.225200i
$546$		0			0
$547$	24.3589	−	11.7306i	1.04151	−	0.501566i	0.166690	−	0.986009i	$-0.446692\pi$
$547$	24.3589	−	11.7306i	1.04151	−	0.501566i	0.874823	+	0.484443i	$0.160978\pi$
$548$	−1.30676	+	8.66981i	−0.0558222	+	0.370356i
$549$		0			0
$550$	2.22758	−	0.335754i	0.0949844	−	0.0143166i
$551$	−20.5370	+	19.0555i	−0.874904	+	0.811793i
$552$		0			0
$553$	21.1172	−	12.1566i	0.897994	−	0.516949i
$554$	−15.9837	−	12.7465i	−0.679080	−	0.541549i
$555$		0			0
$556$	−24.2871	+	78.7368i	−1.03000	+	3.33918i
$557$	17.8120	+	10.2837i	0.754717	+	0.435736i	0.827396	−	0.561620i	$-0.189822\pi$
$557$	17.8120	+	10.2837i	0.754717	+	0.435736i	−0.0726790	+	0.997355i	$0.523155\pi$
$558$		0			0
$559$	−1.50114	+	0.342626i	−0.0634915	+	0.0144915i
$560$	9.43363	+	5.46237i	0.398644	+	0.230827i
$561$		0			0
$562$	39.5714	−	12.2062i	1.66922	−	0.514886i
$563$	8.44139	+	21.5083i	0.355762	+	0.906468i	0.990965	+	0.134122i	$0.0428214\pi$
$563$	8.44139	+	21.5083i	0.355762	+	0.906468i	−0.635203	+	0.772346i	$0.719083\pi$
$564$		0			0
$565$	−7.11959	−	23.0812i	−0.299524	−	0.971032i
$566$	17.1839	−	75.2875i	0.722292	−	3.16457i
$567$		0			0
$568$	13.9158	+	60.9693i	0.583895	+	2.55821i
$569$	12.6638	−	7.31147i	0.530895	−	0.306513i	−0.210486	−	0.977597i	$-0.567505\pi$
$569$	12.6638	−	7.31147i	0.530895	−	0.306513i	0.741381	+	0.671084i	$0.234171\pi$
$570$		0			0
$571$	24.5887	+	7.58460i	1.02900	+	0.317406i	0.762885	−	0.646535i	$-0.223782\pi$
$571$	24.5887	+	7.58460i	1.02900	+	0.317406i	0.266119	+	0.963940i	$0.414259\pi$
$572$	0.122111	+	1.62946i	0.00510571	+	0.0681310i
$573$		0			0
$574$	−1.79263	−	24.3323i	−0.0748228	−	1.01561i
$575$	8.48359	−	6.76544i	0.353790	−	0.282138i
$576$		0			0
$577$	5.85704	+	38.8589i	0.243832	+	1.61772i	0.690717	+	0.723126i	$0.257295\pi$
$577$	5.85704	+	38.8589i	0.243832	+	1.61772i	−0.446885	+	0.894591i	$0.647467\pi$
$578$	22.9703	+	33.6912i	0.955437	+	1.40137i
$579$		0			0
$580$	13.0709	+	27.1419i	0.542738	+	1.12701i
$581$	19.8369	+	15.8603i	0.822972	+	0.657996i
$582$		0			0
$583$	5.51791	+	3.76205i	0.228529	+	0.155808i
$584$	25.9180	+	24.0484i	1.07249	+	0.995129i
$585$		0			0
$586$	−32.2426	−	12.6543i	−1.33193	−	0.522744i
$587$	28.0801			1.15899			0.579495	−	0.814976i	$-0.303250\pi$
$587$	28.0801			1.15899			0.579495	+	0.814976i	$0.303250\pi$
$588$		0			0
$589$	18.1186			0.746565
$590$	−7.64059	−	2.99871i	−0.314558	−	0.123455i
$591$		0			0
$592$	−5.31141	−	4.92827i	−0.218297	−	0.202550i
$593$	−21.7849	−	14.8527i	−0.894598	−	0.609927i	0.0263324	−	0.999653i	$-0.491617\pi$
$593$	−21.7849	−	14.8527i	−0.894598	−	0.609927i	−0.920931	+	0.389727i	$0.872570\pi$
$594$		0			0
$595$	−22.7901	+	18.1276i	−0.934304	+	0.743158i
$596$	18.9121	+	39.2713i	0.774668	+	1.60861i
$597$		0			0
$598$	6.84289	+	10.0367i	0.279827	+	0.410430i
$599$	2.15673	+	14.3089i	0.0881215	+	0.584648i	0.988695	+	0.149943i	$0.0479091\pi$
$599$	2.15673	+	14.3089i	0.0881215	+	0.584648i	−0.900573	+	0.434704i	$0.856853\pi$
$600$		0			0
$601$	17.2316	−	13.7417i	0.702890	−	0.560536i	−0.205502	−	0.978657i	$-0.565883\pi$
$601$	17.2316	−	13.7417i	0.702890	−	0.560536i	0.908391	+	0.418121i	$0.137311\pi$
$602$	−10.4753	+	9.69510i	−0.426940	+	0.395143i
$603$		0			0
$604$	−5.97456	−	79.7249i	−0.243101	−	3.24396i
$605$	19.0426	+	5.87385i	0.774190	+	0.238806i
$606$		0			0
$607$	20.0654	−	11.5848i	0.814429	−	0.470211i	−0.0340628	−	0.999420i	$-0.510845\pi$
$607$	20.0654	−	11.5848i	0.814429	−	0.470211i	0.848491	+	0.529209i	$0.177511\pi$
$608$	4.02071	+	17.6159i	0.163061	+	0.714418i
$609$		0			0
$610$	10.0763	−	44.1472i	0.407978	−	1.78747i
$611$	−0.695034	−	2.25324i	−0.0281181	−	0.0911565i
$612$		0			0
$613$	1.46128	+	3.72327i	0.0590204	+	0.150381i	0.957342	−	0.288957i	$-0.0933083\pi$
$613$	1.46128	+	3.72327i	0.0590204	+	0.150381i	−0.898322	+	0.439338i	$0.855213\pi$
$614$	11.8853	−	3.66612i	0.479651	−	0.147953i
$615$		0			0
$616$	3.88908	+	5.71970i	0.156696	+	0.230453i
$617$	−15.7453	+	3.59377i	−0.633884	+	0.144680i	−0.527376	−	0.849632i	$-0.676824\pi$
$617$	−15.7453	+	3.59377i	−0.633884	+	0.144680i	−0.106508	+	0.994312i	$0.533967\pi$
$618$		0			0
$619$	−18.0870	−	10.4425i	−0.726977	−	0.419720i	0.0903385	−	0.995911i	$-0.471205\pi$
$619$	−18.0870	−	10.4425i	−0.726977	−	0.419720i	−0.817315	+	0.576191i	$0.804538\pi$
$620$	5.74270	−	18.6174i	0.230632	−	0.747692i
$621$		0			0
$622$	−5.32205	−	4.24419i	−0.213395	−	0.170177i
$623$	−1.93678	+	12.7408i	−0.0775956	+	0.510448i
$624$		0			0
$625$	11.4802	−	10.6521i	0.459210	−	0.426085i
$626$	41.9413	−	6.32163i	1.67631	−	0.252663i
$627$		0			0
$628$	−13.2020	+	87.5893i	−0.526816	+	3.49519i
$629$	17.4388	−	8.39810i	0.695332	−	0.334854i
$630$		0			0
$631$	31.5757	+	15.2061i	1.25701	+	0.605343i	0.939382	−	0.342872i	$-0.111400\pi$
$631$	31.5757	+	15.2061i	1.25701	+	0.605343i	0.317627	+	0.948216i	$0.397114\pi$
$632$	−20.7822	+	30.4819i	−0.826672	+	1.21251i
$633$		0			0
$634$	0.577630	−	7.70794i	0.0229406	−	0.306122i
$635$	6.08373	−	15.5011i	0.241426	−	0.615142i
$636$		0			0
$637$	−3.73042	+	2.95956i	−0.147805	+	0.117262i
$638$			6.75512i			0.267438i
$639$		0			0
$640$	38.9605	+	2.91968i	1.54005	+	0.115411i
$641$	−18.0974	+	19.5044i	−0.714806	+	0.770377i	−0.981097	−	0.193515i	$-0.938011\pi$
$641$	−18.0974	+	19.5044i	−0.714806	+	0.770377i	0.266292	+	0.963892i	$0.414202\pi$
$642$		0			0
$643$	−5.79296	+	12.0292i	−0.228452	+	0.474386i	−0.983412	−	0.181385i	$-0.941942\pi$
$643$	−5.79296	+	12.0292i	−0.228452	+	0.474386i	0.754960	+	0.655771i	$0.227656\pi$
$644$	65.6952	+	31.7392i	2.58876	+	1.25070i
$645$		0			0
$646$	88.7922	+	13.3833i	3.49348	+	0.526558i
$647$	−39.3133	+	26.8034i	−1.54557	+	1.05375i	−0.573454	+	0.819238i	$0.694397\pi$
$647$	−39.3133	+	26.8034i	−1.54557	+	1.05375i	−0.972113	+	0.234512i	$0.924651\pi$
$648$		0			0
$649$	−0.811122	−	0.874182i	−0.0318393	−	0.0343147i
$650$	−1.46409	−	1.83591i	−0.0574262	−	0.0720102i
$651$		0			0
$652$	43.4621	−	54.4998i	1.70211	−	2.13438i
$653$	3.16428	−	0.237130i	0.123828	−	0.00927961i	−0.0126721	−	0.999920i	$-0.504034\pi$
$653$	3.16428	−	0.237130i	0.123828	−	0.00927961i	0.136500	+	0.990640i	$0.456415\pi$
$654$		0			0
$655$	2.84218	−	4.92280i	0.111053	−	0.192350i
$656$	4.22937	+	7.32549i	0.165129	+	0.286012i
$657$		0			0
$658$	−16.0046	−	14.8877i	−0.623925	−	0.580382i
$659$	−22.7243	−	5.18667i	−0.885213	−	0.202044i	−0.244338	−	0.969690i	$-0.578571\pi$
$659$	−22.7243	−	5.18667i	−0.885213	−	0.202044i	−0.640874	+	0.767646i	$0.721428\pi$
$660$		0			0
$661$	−2.60493	+	1.02236i	−0.101320	+	0.0397652i	−0.415460	−	0.909612i	$-0.636379\pi$
$661$	−2.60493	+	1.02236i	−0.101320	+	0.0397652i	0.314140	+	0.949377i	$0.398284\pi$
$662$	−40.5491	+	15.9143i	−1.57598	+	0.618528i
$663$		0			0
$664$	−37.4901	−	8.55686i	−1.45490	−	0.332071i
$665$	−2.44413	+	32.0723i	−0.0947792	+	1.24371i
$666$		0			0
$667$	16.2689	+	28.1785i	0.629933	+	1.09108i
$668$	−28.5097	+	49.3802i	−1.10307	+	1.91058i
$669$		0			0
$670$	−51.9826	+	3.89555i	−2.00826	+	0.150498i
$671$	4.10196	−	5.14369i	0.158354	−	0.198570i
$672$		0			0
$673$	−2.74477	−	3.44183i	−0.105803	−	0.132673i	0.726111	−	0.687578i	$-0.241326\pi$
$673$	−2.74477	−	3.44183i	−0.105803	−	0.132673i	−0.831914	+	0.554905i	$0.812755\pi$
$674$	−23.2456	−	25.0528i	−0.895386	−	0.964996i
$675$		0			0
$676$	−38.1276	+	25.9950i	−1.46645	+	0.999807i
$677$	−36.6933	−	5.53062i	−1.41024	−	0.212559i	−0.600628	−	0.799529i	$-0.705083\pi$
$677$	−36.6933	−	5.53062i	−1.41024	−	0.212559i	−0.809609	+	0.586970i	$0.800321\pi$
$678$		0			0
$679$	−21.3791	−	0.0269368i	−0.820455	−	0.00103374i
$680$	19.1301	−	39.7241i	0.733607	−	1.52335i
$681$		0			0
$682$	2.97150	−	3.20251i	0.113785	−	0.122631i
$683$	−18.0839	−	1.35520i	−0.691961	−	0.0518553i	−0.275892	−	0.961189i	$-0.588973\pi$
$683$	−18.0839	−	1.35520i	−0.691961	−	0.0518553i	−0.416069	+	0.909333i	$0.636592\pi$
$684$		0			0
$685$			4.48924i			0.171525i
$686$	−16.2820	+	41.0291i	−0.621648	+	1.56650i
$687$		0			0
$688$	1.80788	−	4.60640i	0.0689247	−	0.175617i
$689$	0.520224	−	6.94191i	0.0198190	−	0.264466i
$690$		0			0
$691$	3.01327	−	4.41965i	0.114630	−	0.168131i	−0.764636	−	0.644462i	$-0.777081\pi$
$691$	3.01327	−	4.41965i	0.114630	−	0.168131i	0.879266	+	0.476331i	$0.158034\pi$
$692$	−8.18510	−	3.94174i	−0.311151	−	0.149842i
$693$		0			0
$694$	−26.7918	+	12.9023i	−1.01700	+	0.489763i
$695$	−6.28795	+	41.7178i	−0.238515	+	1.58245i
$696$		0			0
$697$	−22.3440	+	3.36782i	−0.846339	+	0.127565i
$698$	−22.6316	+	20.9990i	−0.856618	+	0.794825i
$699$		0			0
$700$	−13.1225	−	5.16929i	−0.495984	−	0.195381i
$701$	21.0842	+	16.8141i	0.796338	+	0.635059i	0.934746	−	0.355317i	$-0.115627\pi$
$701$	21.0842	+	16.8141i	0.796338	+	0.635059i	−0.138408	+	0.990375i	$0.544198\pi$
$702$		0			0
$703$	6.30172	−	20.4297i	0.237674	−	0.770520i
$704$	6.24426	+	3.60513i	0.235339	+	0.135873i
$705$		0			0
$706$	61.5181	−	14.0411i	2.31526	−	0.528444i
$707$	49.0901	+	3.74100i	1.84622	+	0.140695i
$708$		0			0
$709$	−31.3445	+	9.66851i	−1.17717	+	0.363108i	−0.820788	−	0.571233i	$-0.806465\pi$
$709$	−31.3445	+	9.66851i	−1.17717	+	0.363108i	−0.356380	+	0.934341i	$0.615989\pi$
$710$	25.6189	+	65.2759i	0.961460	+	2.44976i
$711$		0			0
$712$	−5.75128	−	18.6452i	−0.215538	−	0.698759i
$713$	4.68255	−	20.5156i	0.175363	−	0.768314i
$714$		0			0
$715$	0.186172	+	0.815675i	0.00696245	+	0.0305045i
$716$	−9.12377	+	5.26761i	−0.340971	+	0.196860i
$717$		0			0
$718$	19.2940	+	5.95141i	0.720046	+	0.222105i
$719$	−0.716547	−	9.56166i	−0.0267227	−	0.356590i	−0.994497	−	0.104769i	$-0.966590\pi$
$719$	−0.716547	−	9.56166i	−0.0267227	−	0.356590i	0.967774	−	0.251821i	$-0.0810293\pi$
$720$		0			0
$721$	−21.3661	−	14.6066i	−0.795716	−	0.543980i
$722$	42.1401	−	33.6056i	1.56829	−	1.25067i
$723$		0			0
$724$	8.31947	+	55.1961i	0.309191	+	2.05135i
$725$	−3.54320	−	5.19692i	−0.131591	−	0.193009i
$726$		0			0
$727$	6.28579	+	13.0526i	0.233127	+	0.484093i	0.984410	−	0.175887i	$-0.0562792\pi$
$727$	6.28579	+	13.0526i	0.233127	+	0.484093i	−0.751284	+	0.659980i	$0.770565\pi$
$728$	3.13638	−	6.49183i	0.116242	−	0.240603i
$729$		0			0
$730$	32.7563	+	22.3329i	1.21237	+	0.826578i
$731$	9.69032	+	8.99130i	0.358410	+	0.332555i
$732$		0			0
$733$	8.26480	+	3.24370i	0.305267	+	0.119809i	0.513030	−	0.858371i	$-0.328523\pi$
$733$	8.26480	+	3.24370i	0.305267	+	0.119809i	−0.207763	+	0.978179i	$0.566618\pi$
$734$	10.6985			0.394889
$735$		0			0
$736$	20.9854			0.773532
$737$	−7.05010	−	2.76696i	−0.259694	−	0.101922i
$738$		0			0
$739$	12.6949	+	11.7791i	0.466988	+	0.433302i	0.878240	−	0.478220i	$-0.158718\pi$
$739$	12.6949	+	11.7791i	0.466988	+	0.433302i	−0.411252	+	0.911522i	$0.634908\pi$
$740$	−18.9947	−	12.9504i	−0.698260	−	0.476066i
$741$		0			0
$742$	−27.9257	−	58.1758i	−1.02519	−	2.13570i
$743$	8.23846	+	17.1073i	0.302240	+	0.627608i	0.995674	−	0.0929122i	$-0.0296176\pi$
$743$	8.23846	+	17.1073i	0.302240	+	0.627608i	−0.693434	+	0.720520i	$0.743903\pi$
$744$		0			0
$745$	12.5721	+	18.4398i	0.460604	+	0.675583i
$746$	−9.25192	−	61.3824i	−0.338737	−	2.24737i
$747$		0			0
$748$	10.9680	−	8.74667i	0.401029	−	0.319810i
$749$	25.8184	+	3.92478i	0.943385	+	0.143408i
$750$		0			0
$751$	0.437249	+	5.83469i	0.0159555	+	0.212911i	0.999483	+	0.0321523i	$0.0102362\pi$
$751$	0.437249	+	5.83469i	0.0159555	+	0.212911i	−0.983528	+	0.180758i	$0.942145\pi$
$752$	7.24152	+	2.23371i	0.264071	+	0.0814552i
$753$		0			0
$754$	6.09803	−	3.52070i	0.222077	−	0.128216i
$755$	−9.10891	−	39.9088i	−0.331507	−	1.45243i
$756$		0			0
$757$	7.60558	−	33.3222i	0.276429	−	1.21112i	−0.625843	−	0.779949i	$-0.715245\pi$
$757$	7.60558	−	33.3222i	0.276429	−	1.21112i	0.902272	−	0.431167i	$-0.141898\pi$
$758$	−11.4734	−	37.1958i	−0.416732	−	1.35101i
$759$		0			0
$760$	−17.7923	−	45.3341i	−0.645396	−	1.64444i
$761$	7.35231	−	2.26789i	0.266521	−	0.0822108i	−0.158614	−	0.987341i	$-0.550703\pi$
$761$	7.35231	−	2.26789i	0.266521	−	0.0822108i	0.425135	+	0.905130i	$0.360226\pi$
$762$		0			0
$763$	2.51414	+	16.8240i	0.0910178	+	0.609070i
$764$	−24.2559	+	5.53624i	−0.877546	+	0.200294i
$765$		0			0
$766$	40.5607	+	23.4177i	1.46552	+	0.846117i
$767$	−0.366399	+	1.18784i	−0.0132299	+	0.0428903i
$768$		0			0
$769$	−19.9737	−	15.9285i	−0.720272	−	0.574397i	0.193269	−	0.981146i	$-0.438091\pi$
$769$	−19.9737	−	15.9285i	−0.720272	−	0.574397i	−0.913540	+	0.406749i	$0.866663\pi$
$770$	5.26802	+	5.69194i	0.189846	+	0.205123i
$771$		0			0
$772$	18.4642	−	17.1322i	0.664539	−	0.616602i
$773$	37.6301	−	5.67182i	1.35346	−	0.204001i	0.568058	−	0.822988i	$-0.307695\pi$
$773$	37.6301	−	5.67182i	1.35346	−	0.204001i	0.785401	+	0.618987i	$0.212457\pi$
$774$		0			0
$775$	−0.606281	+	4.02241i	−0.0217782	+	0.144489i
$776$	29.1640	−	14.0446i	1.04693	−	0.504173i
$777$		0			0
$778$	−15.2853	−	7.36102i	−0.548005	−	0.263905i
$779$	−14.0600	+	20.6222i	−0.503750	+	0.738866i
$780$		0			0
$781$	−0.761357	+	10.1596i	−0.0272435	+	0.363539i
$782$	38.1011	−	97.0800i	1.36249	−	3.47157i
$783$		0			0
$784$	−1.10519	−	15.2637i	−0.0394709	−	0.545133i
$785$			45.3539i			1.61875i
$786$		0			0
$787$	13.7268	+	1.02868i	0.489307	+	0.0366685i

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:	\( N \)	\(=\)	\( 441 = 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	441.bg (of order \(42\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(2.21867 + 0.870763i) q^{2} +(2.69816 + 2.50352i) q^{4} +(1.55712 + 1.06163i) q^{5} +(0.00333353 - 2.64575i) q^{7} +(1.73808 + 3.60916i) q^{8} +O(q^{10})\)	\(q+(2.21867 + 0.870763i) q^{2} +(2.69816 + 2.50352i) q^{4} +(1.55712 + 1.06163i) q^{5} +(0.00333353 - 2.64575i) q^{7} +(1.73808 + 3.60916i) q^{8} +(2.53032 + 3.71129i) q^{10} +(0.0972657 + 0.645316i) q^{11} +(0.531850 - 0.424136i) q^{13} +(2.31122 - 5.86714i) q^{14} +(0.163378 + 2.18013i) q^{16} +(-5.58077 - 1.72144i) q^{17} +(-5.58665 + 3.22545i) q^{19} +(1.54355 + 6.76274i) q^{20} +(-0.346117 + 1.51644i) q^{22} +(2.20835 + 7.15930i) q^{23} +(-0.529125 - 1.34819i) q^{25} +(1.54932 - 0.477902i) q^{26} +(6.63269 - 7.13030i) q^{28} +(4.23402 - 0.966388i) q^{29} +(-2.43240 - 1.40435i) q^{31} +(0.825605 - 2.67654i) q^{32} +(-10.8829 - 8.67884i) q^{34} +(2.81400 - 4.11622i) q^{35} +(-2.42947 + 2.25422i) q^{37} +(-15.2035 + 2.29156i) q^{38} +(-1.12518 + 7.46510i) q^{40} +(3.48592 - 1.67873i) q^{41} +(-2.03931 - 0.982079i) q^{43} +(-1.35313 + 1.98467i) q^{44} +(-1.33445 + 17.8071i) q^{46} +(1.26639 - 3.22670i) q^{47} +(-6.99998 - 0.0176394i) q^{49} -3.45192i q^{50} +(2.49685 + 0.187113i) q^{52} +(6.96046 - 7.50159i) q^{53} +(-0.533632 + 1.10810i) q^{55} +(9.55472 - 4.58649i) q^{56} +(10.2354 + 1.54274i) q^{58} +(-1.50981 + 1.02937i) q^{59} +(-6.85694 - 7.39003i) q^{61} +(-4.17384 - 5.23382i) q^{62} +(6.88858 - 8.63800i) q^{64} +(1.27843 - 0.0958053i) q^{65} +(-5.80262 + 10.0504i) q^{67} +(-10.7481 - 18.6163i) q^{68} +(9.82758 - 6.68221i) q^{70} +(15.2200 + 3.47387i) q^{71} +(8.21602 - 3.22455i) q^{73} +(-7.35308 + 2.88587i) q^{74} +(-23.1486 - 5.28353i) q^{76} +(1.70767 - 0.255190i) q^{77} +(4.60480 + 7.97575i) q^{79} +(-2.06009 + 3.56818i) q^{80} +(9.19589 - 0.689136i) q^{82} +(-5.98518 + 7.50517i) q^{83} +(-6.86243 - 8.60521i) q^{85} +(-3.66939 - 3.95466i) q^{86} +(-2.15999 + 1.47266i) q^{88} +(-4.81648 - 0.725967i) q^{89} +(-1.12039 - 1.40856i) q^{91} +(-11.9650 + 24.8456i) q^{92} +(5.61939 - 6.05626i) q^{94} +(-12.1233 - 0.908519i) q^{95} -8.08055i q^{97} +(-15.5153 - 6.13446i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 216 q - 16 q^{4} + 2 q^{7}+O(q^{10}) \) 216 * q - 16 * q^4 + 2 * q^7	\( 216 q - 16 q^{4} + 2 q^{7} + 12 q^{10} + 12 q^{16} - 6 q^{19} + 44 q^{22} + 26 q^{25} + 84 q^{28} - 6 q^{31} - 112 q^{34} + 60 q^{37} - 304 q^{40} + 20 q^{43} - 20 q^{46} - 86 q^{49} - 168 q^{52} - 84 q^{55} - 120 q^{58} - 2 q^{61} + 32 q^{64} + 22 q^{67} - 136 q^{70} - 6 q^{73} + 84 q^{76} + 2 q^{79} - 104 q^{82} + 96 q^{85} - 12 q^{88} + 58 q^{91} + 52 q^{94}+O(q^{100}) \) 216 * q - 16 * q^4 + 2 * q^7 + 12 * q^10 + 12 * q^16 - 6 * q^19 + 44 * q^22 + 26 * q^25 + 84 * q^28 - 6 * q^31 - 112 * q^34 + 60 * q^37 - 304 * q^40 + 20 * q^43 - 20 * q^46 - 86 * q^49 - 168 * q^52 - 84 * q^55 - 120 * q^58 - 2 * q^61 + 32 * q^64 + 22 * q^67 - 136 * q^70 - 6 * q^73 + 84 * q^76 + 2 * q^79 - 104 * q^82 + 96 * q^85 - 12 * q^88 + 58 * q^91 + 52 * q^94

Introduction

L-functions

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