LMFDB - Embedded newform 585.2.bt.b.571.30

Newspace parameters

Level:	$ N $	$=$	$ 585 = 3^{2} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	585.bt (of order $6$, degree $2$, minimal)

Newform invariants

Self dual:	no
Analytic conductor:	$4.67124851824$
Analytic rank:	$0$
Dimension:	$108$
Relative dimension:	$54$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			571.30
Character	$\chi$	$=$	585.571
Dual form			585.2.bt.b.376.30

$q$-expansion

$f(q)$	$=$	$q+(0.231678 - 0.133759i) q^{2} +(1.70348 + 0.313309i) q^{3} +(-0.964217 + 1.67007i) q^{4} +(-0.866025 - 0.500000i) q^{5} +(0.436567 - 0.155269i) q^{6} +(-3.30805 + 1.90990i) q^{7} +1.05093i q^{8} +(2.80367 + 1.06743i) q^{9} +O(q^{10})$	\(q+(0.231678 - 0.133759i) q^{2} +(1.70348 + 0.313309i) q^{3} +(-0.964217 + 1.67007i) q^{4} +(-0.866025 - 0.500000i) q^{5} +(0.436567 - 0.155269i) q^{6} +(-3.30805 + 1.90990i) q^{7} +1.05093i q^{8} +(2.80367 + 1.06743i) q^{9} -0.267519 q^{10} +(-4.13207 + 2.38565i) q^{11} +(-2.16577 + 2.54283i) q^{12} +(3.37175 - 1.27721i) q^{13} +(-0.510935 + 0.884965i) q^{14} +(-1.31860 - 1.12307i) q^{15} +(-1.78786 - 3.09667i) q^{16} -4.49245 q^{17} +(0.792329 - 0.127717i) q^{18} -0.832616i q^{19} +(1.67007 - 0.964217i) q^{20} +(-6.23357 + 2.21703i) q^{21} +(-0.638207 + 1.10541i) q^{22} +(-2.95117 + 5.11158i) q^{23} +(-0.329266 + 1.79024i) q^{24} +(0.500000 + 0.866025i) q^{25} +(0.610322 - 0.746907i) q^{26} +(4.44156 + 2.69676i) q^{27} -7.36623i q^{28} +(1.72114 + 2.98110i) q^{29} +(-0.455713 - 0.0838162i) q^{30} +(4.11935 + 2.37831i) q^{31} +(-2.64868 - 1.52922i) q^{32} +(-7.78634 + 2.76929i) q^{33} +(-1.04080 + 0.600908i) q^{34} +3.81980 q^{35} +(-4.48604 + 3.65310i) q^{36} +1.42971i q^{37} +(-0.111370 - 0.192899i) q^{38} +(6.14387 - 1.11931i) q^{39} +(0.525465 - 0.910132i) q^{40} +(-1.22492 - 0.707206i) q^{41} +(-1.14763 + 1.34744i) q^{42} +(4.57220 + 7.91929i) q^{43} -9.20114i q^{44} +(-1.89434 - 2.32626i) q^{45} +1.57899i q^{46} +(11.2552 - 6.49820i) q^{47} +(-2.07537 - 5.83526i) q^{48} +(3.79544 - 6.57390i) q^{49} +(0.231678 + 0.133759i) q^{50} +(-7.65279 - 1.40753i) q^{51} +(-1.11806 + 6.86258i) q^{52} -8.34571 q^{53} +(1.38973 + 0.0306803i) q^{54} +4.77130 q^{55} +(-2.00717 - 3.47652i) q^{56} +(0.260866 - 1.41834i) q^{57} +(0.797502 + 0.460438i) q^{58} +(0.991497 + 0.572441i) q^{59} +(3.14703 - 1.11927i) q^{60} +(-5.08702 - 8.81097i) q^{61} +1.27248 q^{62} +(-11.3134 + 1.82363i) q^{63} +6.33326 q^{64} +(-3.55863 - 0.579777i) q^{65} +(-1.43351 + 1.68308i) q^{66} +(10.5335 + 6.08150i) q^{67} +(4.33170 - 7.50272i) q^{68} +(-6.62876 + 7.78283i) q^{69} +(0.884965 - 0.510935i) q^{70} +1.12258i q^{71} +(-1.12180 + 2.94647i) q^{72} +6.20857i q^{73} +(0.191238 + 0.331233i) q^{74} +(0.580405 + 1.63191i) q^{75} +(1.39053 + 0.802822i) q^{76} +(9.11272 - 15.7837i) q^{77} +(1.27368 - 1.08112i) q^{78} +(7.21565 + 12.4979i) q^{79} +3.57572i q^{80} +(6.72118 + 5.98546i) q^{81} -0.378382 q^{82} +(7.32055 - 4.22652i) q^{83} +(2.30791 - 12.5482i) q^{84} +(3.89058 + 2.24622i) q^{85} +(2.11856 + 1.22315i) q^{86} +(1.99792 + 5.61750i) q^{87} +(-2.50715 - 4.34252i) q^{88} -5.87702i q^{89} +(-0.750036 - 0.285558i) q^{90} +(-8.71456 + 10.6648i) q^{91} +(-5.69113 - 9.85733i) q^{92} +(6.27207 + 5.34202i) q^{93} +(1.73839 - 3.01098i) q^{94} +(-0.416308 + 0.721066i) q^{95} +(-4.03285 - 3.43484i) q^{96} +(-12.3612 + 7.13676i) q^{97} -2.03070i q^{98} +(-14.1315 + 2.27789i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 108 q - 6 q^{3} + 52 q^{4} - 14 q^{9}+O(q^{10}) $ 108 * q - 6 * q^3 + 52 * q^4 - 14 * q^9	$ 108 q - 6 q^{3} + 52 q^{4} - 14 q^{9} - 8 q^{10} - 36 q^{12} - 4 q^{13} - 8 q^{14} - 64 q^{16} + 36 q^{17} + 24 q^{22} - 22 q^{23} + 54 q^{25} + 40 q^{26} + 48 q^{27} - 16 q^{29} + 20 q^{30} - 40 q^{35} - 76 q^{36} - 12 q^{38} + 26 q^{39} - 52 q^{42} - 6 q^{43} - 68 q^{48} + 58 q^{49} + 34 q^{51} + 22 q^{52} - 116 q^{53} + 24 q^{55} + 40 q^{56} + 18 q^{61} + 152 q^{62} - 216 q^{64} + 2 q^{65} - 72 q^{66} - 134 q^{69} + 32 q^{74} + 40 q^{77} - 34 q^{78} + 18 q^{79} + 34 q^{81} + 88 q^{82} + 60 q^{87} + 8 q^{90} + 16 q^{91} + 176 q^{92} - 76 q^{94} - 56 q^{95}+O(q^{100}) $ 108 * q - 6 * q^3 + 52 * q^4 - 14 * q^9 - 8 * q^10 - 36 * q^12 - 4 * q^13 - 8 * q^14 - 64 * q^16 + 36 * q^17 + 24 * q^22 - 22 * q^23 + 54 * q^25 + 40 * q^26 + 48 * q^27 - 16 * q^29 + 20 * q^30 - 40 * q^35 - 76 * q^36 - 12 * q^38 + 26 * q^39 - 52 * q^42 - 6 * q^43 - 68 * q^48 + 58 * q^49 + 34 * q^51 + 22 * q^52 - 116 * q^53 + 24 * q^55 + 40 * q^56 + 18 * q^61 + 152 * q^62 - 216 * q^64 + 2 * q^65 - 72 * q^66 - 134 * q^69 + 32 * q^74 + 40 * q^77 - 34 * q^78 + 18 * q^79 + 34 * q^81 + 88 * q^82 + 60 * q^87 + 8 * q^90 + 16 * q^91 + 176 * q^92 - 76 * q^94 - 56 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/585\mathbb{Z}\right)^\times$.

$n$	$326$	$352$	$496$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$-1$

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 $

$2$	0.231678	−	0.133759i	0.163821	−	0.0945822i	−0.415848	−	0.909434i	$-0.636515\pi$
$2$	0.231678	−	0.133759i	0.163821	−	0.0945822i	0.579669	+	0.814852i	$0.303182\pi$
$3$	1.70348	+	0.313309i	0.983503	+	0.180889i
$3$	1.70348	+	0.313309i	0.983503	+	0.180889i
$4$	−0.964217	+	1.67007i	−0.482108	+	0.835036i
$5$	−0.866025	−	0.500000i	−0.387298	−	0.223607i
$5$	−0.866025	−	0.500000i	−0.387298	−	0.223607i
$6$	0.436567	−	0.155269i	0.178228	−	0.0633884i
$7$	−3.30805	+	1.90990i	−1.25032	+	0.721875i	−0.971174	−	0.238373i	$-0.923386\pi$
$7$	−3.30805	+	1.90990i	−1.25032	+	0.721875i	−0.279150	+	0.960248i	$0.590053\pi$
$8$			1.05093i			0.371560i
$9$	2.80367	+	1.06743i	0.934558	+	0.355810i
$10$	−0.267519			−0.0845969
$11$	−4.13207	+	2.38565i	−1.24587	+	0.719301i	−0.970282	−	0.241976i	$-0.922205\pi$
$11$	−4.13207	+	2.38565i	−1.24587	+	0.719301i	−0.275584	+	0.961277i	$0.588871\pi$
$12$	−2.16577	+	2.54283i	−0.625204	+	0.734053i
$13$	3.37175	−	1.27721i	0.935156	−	0.354236i
$13$	3.37175	−	1.27721i	0.935156	−	0.354236i
$14$	−0.510935	+	0.884965i	−0.136553	+	0.236517i
$15$	−1.31860	−	1.12307i	−0.340461	−	0.289976i
$16$	−1.78786	−	3.09667i	−0.446965	−	0.774167i
$17$	−4.49245			−1.08958			−0.544790	−	0.838573i	$-0.683390\pi$
$17$	−4.49245			−1.08958			−0.544790	+	0.838573i	$0.683390\pi$
$18$	0.792329	−	0.127717i	0.186754	−	0.0301033i
$19$		−	0.832616i		−	0.191015i	−0.995429	−	0.0955076i	$-0.969553\pi$
$19$		−	0.832616i		−	0.191015i	0.995429	−	0.0955076i	$-0.0304474\pi$
$20$	1.67007	−	0.964217i	0.373440	−	0.215605i
$21$	−6.23357	+	2.21703i	−1.36028	+	0.483796i
$22$	−0.638207	+	1.10541i	−0.136066	+	0.235674i
$23$	−2.95117	+	5.11158i	−0.615361	+	1.06584i	0.374960	+	0.927041i	$0.377657\pi$
$23$	−2.95117	+	5.11158i	−0.615361	+	1.06584i	−0.990321	+	0.138796i	$0.955677\pi$
$24$	−0.329266	+	1.79024i	−0.0672112	+	0.365431i
$25$	0.500000	+	0.866025i	0.100000	+	0.173205i
$26$	0.610322	−	0.746907i	0.119694	−	0.146480i
$27$	4.44156	+	2.69676i	0.854779	+	0.518992i
$28$		−	7.36623i		−	1.39209i
$29$	1.72114	+	2.98110i	0.319608	+	0.553577i	0.980406	−	0.196986i	$-0.0631154\pi$
$29$	1.72114	+	2.98110i	0.319608	+	0.553577i	−0.660798	+	0.750564i	$0.729782\pi$
$30$	−0.455713	−	0.0838162i	−0.0832014	−	0.0153027i
$31$	4.11935	+	2.37831i	0.739857	+	0.427157i	0.822017	−	0.569463i	$-0.192849\pi$
$31$	4.11935	+	2.37831i	0.739857	+	0.427157i	−0.0821605	+	0.996619i	$0.526182\pi$
$32$	−2.64868	−	1.52922i	−0.468225	−	0.270330i
$33$	−7.78634	+	2.76929i	−1.35543	+	0.482071i
$34$	−1.04080	+	0.600908i	−0.178496	+	0.103055i
$35$	3.81980			0.645664
$36$	−4.48604	+	3.65310i	−0.747673	+	0.608851i
$37$			1.42971i			0.235043i	0.993070	+	0.117522i	$0.0374950\pi$
$37$			1.42971i			0.235043i	−0.993070	+	0.117522i	$0.962505\pi$
$38$	−0.111370	−	0.192899i	−0.0180666	−	0.0312923i
$39$	6.14387	−	1.11931i	0.983807	−	0.179232i
$40$	0.525465	−	0.910132i	0.0830833	−	0.143905i
$41$	−1.22492	−	0.707206i	−0.191300	−	0.110447i	0.401291	−	0.915951i	$-0.368562\pi$
$41$	−1.22492	−	0.707206i	−0.191300	−	0.110447i	−0.592591	+	0.805504i	$0.701895\pi$
$42$	−1.14763	+	1.34744i	−0.177084	+	0.207914i
$43$	4.57220	+	7.91929i	0.697255	+	1.20768i	0.969415	+	0.245429i	$0.0789287\pi$
$43$	4.57220	+	7.91929i	0.697255	+	1.20768i	−0.272160	+	0.962252i	$0.587738\pi$
$44$		−	9.20114i		−	1.38712i
$45$	−1.89434	−	2.32626i	−0.282391	−	0.346778i
$46$			1.57899i			0.232809i
$47$	11.2552	−	6.49820i	1.64174	−	0.947860i	0.661528	−	0.749920i	$-0.269908\pi$
$47$	11.2552	−	6.49820i	1.64174	−	0.947860i	0.980214	−	0.197940i	$-0.0634253\pi$
$48$	−2.07537	−	5.83526i	−0.299554	−	0.842247i
$49$	3.79544	−	6.57390i	0.542206	−	0.939128i
$50$	0.231678	+	0.133759i	0.0327642	+	0.0189164i
$51$	−7.65279	−	1.40753i	−1.07160	−	0.197093i
$52$	−1.11806	+	6.86258i	−0.155047	+	0.951669i
$53$	−8.34571			−1.14637			−0.573185	−	0.819426i	$-0.694293\pi$
$53$	−8.34571			−1.14637			−0.573185	+	0.819426i	$0.694293\pi$
$54$	1.38973	+	0.0306803i	0.189118	+	0.00417506i
$55$	4.77130			0.643363
$56$	−2.00717	−	3.47652i	−0.268220	−	0.464570i
$57$	0.260866	−	1.41834i	0.0345526	−	0.187864i
$58$	0.797502	+	0.460438i	0.104717	+	0.0604585i
$59$	0.991497	+	0.572441i	0.129082	+	0.0745255i	0.563151	−	0.826354i	$-0.309589\pi$
$59$	0.991497	+	0.572441i	0.129082	+	0.0745255i	−0.434069	+	0.900880i	$0.642922\pi$
$60$	3.14703	−	1.11927i	0.406280	−	0.144497i
$61$	−5.08702	−	8.81097i	−0.651326	−	1.12813i	−0.982801	−	0.184666i	$-0.940880\pi$
$61$	−5.08702	−	8.81097i	−0.651326	−	1.12813i	0.331476	−	0.943464i	$-0.392454\pi$
$62$	1.27248			0.161606
$63$	−11.3134	+	1.82363i	−1.42535	+	0.229756i
$64$	6.33326			0.791657
$65$	−3.55863	−	0.579777i	−0.441394	−	0.0719124i
$66$	−1.43351	+	1.68308i	−0.176452	+	0.207173i
$67$	10.5335	+	6.08150i	1.28687	+	0.742974i	0.978094	−	0.208162i	$-0.0667480\pi$
$67$	10.5335	+	6.08150i	1.28687	+	0.742974i	0.308774	+	0.951135i	$0.400081\pi$
$68$	4.33170	−	7.50272i	0.525295	−	0.909838i
$69$	−6.62876	+	7.78283i	−0.798008	+	0.936942i
$70$	0.884965	−	0.510935i	0.105774	−	0.0610684i
$71$			1.12258i			0.133226i	0.997779	+	0.0666131i	$0.0212193\pi$
$71$			1.12258i			0.133226i	−0.997779	+	0.0666131i	$0.978781\pi$
$72$	−1.12180	+	2.94647i	−0.132205	+	0.347244i
$73$			6.20857i			0.726658i	0.931661	+	0.363329i	$0.118360\pi$
$73$			6.20857i			0.726658i	−0.931661	+	0.363329i	$0.881640\pi$
$74$	0.191238	+	0.331233i	0.0222309	+	0.0385051i
$75$	0.580405	+	1.63191i	0.0670194	+	0.188437i
$76$	1.39053	+	0.802822i	0.159505	+	0.0920900i
$77$	9.11272	−	15.7837i	1.03849	−	1.79872i
$78$	1.27368	−	1.08112i	0.144216	−	0.122413i
$79$	7.21565	+	12.4979i	0.811824	+	1.40612i	0.911586	+	0.411109i	$0.134858\pi$
$79$	7.21565	+	12.4979i	0.811824	+	1.40612i	−0.0997625	+	0.995011i	$0.531808\pi$
$80$			3.57572i			0.399778i
$81$	6.72118	+	5.98546i	0.746798	+	0.665051i
$82$	−0.378382			−0.0417853
$83$	7.32055	−	4.22652i	0.803535	−	0.463921i	−0.0411708	−	0.999152i	$-0.513109\pi$
$83$	7.32055	−	4.22652i	0.803535	−	0.463921i	0.844706	+	0.535231i	$0.179775\pi$
$84$	2.30791	−	12.5482i	0.251814	−	1.36912i
$85$	3.89058	+	2.24622i	0.421992	+	0.243637i
$86$	2.11856	+	1.22315i	0.228450	+	0.131896i
$87$	1.99792	+	5.61750i	0.214199	+	0.602259i
$88$	−2.50715	−	4.34252i	−0.267264	−	0.462914i
$89$		−	5.87702i		−	0.622963i	−0.950252	−	0.311481i	$-0.899175\pi$
$89$		−	5.87702i		−	0.622963i	0.950252	−	0.311481i	$-0.100825\pi$
$90$	−0.750036	−	0.285558i	−0.0790607	−	0.0301005i
$91$	−8.71456	+	10.6648i	−0.913534	+	1.11797i
$92$	−5.69113	−	9.85733i	−0.593342	−	1.02770i
$93$	6.27207	+	5.34202i	0.650384	+	0.553942i
$94$	1.73839	−	3.01098i	0.179301	−	0.310559i
$95$	−0.416308	+	0.721066i	−0.0427123	+	0.0739799i
$96$	−4.03285	−	3.43484i	−0.411601	−	0.350567i
$97$	−12.3612	+	7.13676i	−1.25509	+	0.724629i	−0.972117	−	0.234498i	$-0.924655\pi$
$97$	−12.3612	+	7.13676i	−1.25509	+	0.724629i	−0.282977	+	0.959127i	$0.591322\pi$
$98$		−	2.03070i		−	0.205132i
$99$	−14.1315	+	2.27789i	−1.42027	+	0.228937i
$100$	−1.92843			−0.192843
$101$	4.23325	+	7.33220i	0.421224	+	0.729581i	0.996059	−	0.0886877i	$-0.0282673\pi$
$101$	4.23325	+	7.33220i	0.421224	+	0.729581i	−0.574836	+	0.818269i	$0.694934\pi$
$102$	−1.96125	+	0.697540i	−0.194193	+	0.0690667i
$103$	6.17393	−	10.6936i	0.608336	−	1.05367i	−0.383179	−	0.923674i	$-0.625171\pi$
$103$	6.17393	−	10.6936i	0.608336	−	1.05367i	0.991515	−	0.129994i	$-0.0414959\pi$
$104$	1.34226	+	3.54348i	0.131620	+	0.347467i
$105$	6.50695	+	1.19678i	0.635013	+	0.116794i
$106$	−1.93352	+	1.11632i	−0.187800	+	0.108426i
$107$	−9.80820			−0.948195			−0.474097	−	0.880472i	$-0.657226\pi$
$107$	−9.80820			−0.948195			−0.474097	+	0.880472i	$0.657226\pi$
$108$	−8.78642	+	4.81747i	−0.845473	+	0.463561i
$109$		−	14.7105i		−	1.40901i	−0.709701	−	0.704503i	$-0.751170\pi$
$109$		−	14.7105i		−	1.40901i	0.709701	−	0.704503i	$-0.248830\pi$
$110$	1.10541	−	0.638207i	0.105396	−	0.0608507i
$111$	−0.447942	+	2.43548i	−0.0425168	+	0.231166i
$112$	11.8287	+	6.82928i	1.11770	+	0.645306i
$113$	−7.17072	+	12.4201i	−0.674565	+	1.16838i	0.302031	+	0.953298i	$0.402335\pi$
$113$	−7.17072	+	12.4201i	−0.674565	+	1.16838i	−0.976596	+	0.215082i	$0.930998\pi$
$114$	−0.129280	−	0.363492i	−0.0121082	−	0.0340442i
$115$	5.11158	−	2.95117i	0.476657	−	0.275198i
$116$	−6.63821			−0.616343
$117$	10.8166	+	0.0182210i	0.999999	+	0.00168454i
$118$	0.306278			0.0281951
$119$	14.8612	−	8.58013i	1.36233	−	0.786540i
$120$	1.18027	−	1.38576i	0.107744	−	0.126502i
$121$	5.88267	−	10.1891i	0.534788	−	0.926281i
$122$	−2.35710	−	1.36087i	−0.213402	−	0.123208i
$123$	−1.86504	−	1.58849i	−0.168165	−	0.143229i
$124$	−7.94389	+	4.58641i	−0.713382	+	0.411871i
$125$		−	1.00000i		−	0.0894427i
$126$	−2.37713	+	1.93577i	−0.211772	+	0.172452i
$127$	−8.48951			−0.753322			−0.376661	−	0.926351i	$-0.622928\pi$
$127$	−8.48951			−0.753322			−0.376661	+	0.926351i	$0.622928\pi$
$128$	6.76464	−	3.90557i	0.597915	−	0.345207i
$129$	5.30746	+	14.9229i	0.467296	+	1.31388i
$130$	−0.902008	+	0.341679i	−0.0791113	+	0.0299672i
$131$	4.78570	−	8.28908i	0.418129	−	0.724220i	−0.577622	−	0.816304i	$-0.696019\pi$
$131$	4.78570	−	8.28908i	0.418129	−	0.724220i	0.995751	+	0.0920836i	$0.0293527\pi$
$132$	2.88280	−	15.6739i	0.250916	−	1.36424i
$133$	1.59021	+	2.75433i	0.137889	+	0.238831i
$134$	3.25383			0.281088
$135$	−2.49812	−	4.55625i	−0.215004	−	0.392139i
$136$		−	4.72125i		−	0.404844i
$137$	−10.3403	+	5.96997i	−0.883431	+	0.510049i	−0.871788	−	0.489883i	$-0.837039\pi$
$137$	−10.3403	+	5.96997i	−0.883431	+	0.510049i	−0.0116427	+	0.999932i	$0.503706\pi$
$138$	−0.494711	+	2.68977i	−0.0421126	+	0.228968i
$139$	5.93993	−	10.2883i	0.503819	−	0.872639i	−0.496172	−	0.868224i	$-0.665261\pi$
$139$	5.93993	−	10.2883i	0.503819	−	0.872639i	0.999990	−	0.00441494i	$-0.00140532\pi$
$140$	−3.68312	+	6.37935i	−0.311280	+	0.539153i
$141$	21.2090	−	7.54318i	1.78612	−	0.635251i
$142$	0.150156	+	0.260078i	0.0126008	+	0.0218253i
$143$	−10.8853	+	13.3214i	−0.910277	+	1.11399i
$144$	−1.70710	−	10.5905i	−0.142259	−	0.882539i
$145$		−	3.44228i		−	0.285866i
$146$	0.830454	+	1.43839i	0.0687289	+	0.119042i
$147$	8.52511	−	10.0093i	0.703140	−	0.825557i
$148$	−2.38772	−	1.37855i	−0.196270	−	0.113316i
$149$	11.4392	+	6.60442i	0.937136	+	0.541056i	0.889061	−	0.457788i	$-0.151358\pi$
$149$	11.4392	+	6.60442i	0.937136	+	0.541056i	0.0480744	+	0.998844i	$0.484692\pi$
$150$	0.352751	+	0.300443i	0.0288020	+	0.0245311i
$151$	−1.58329	+	0.914115i	−0.128847	+	0.0743896i	−0.563038	−	0.826431i	$-0.690368\pi$
$151$	−1.58329	+	0.914115i	−0.128847	+	0.0743896i	0.434191	+	0.900821i	$0.357034\pi$
$152$	0.875021			0.0709736
$153$	−12.5954	−	4.79538i	−1.01828	−	0.387684i
$154$		−	4.87565i		−	0.392891i
$155$	−2.37831	−	4.11935i	−0.191030	−	0.330874i
$156$	−4.05470	+	11.3400i	−0.324636	+	0.907924i
$157$	2.72779	−	4.72466i	0.217701	−	0.377069i	−0.736404	−	0.676542i	$-0.763478\pi$
$157$	2.72779	−	4.72466i	0.217701	−	0.377069i	0.954105	+	0.299473i	$0.0968109\pi$
$158$	3.34342	+	1.93032i	0.265988	+	0.153568i
$159$	−14.2167	−	2.61479i	−1.12746	−	0.207366i
$160$	1.52922	+	2.64868i	0.120895	+	0.209397i
$161$		−	22.5458i		−	1.77685i
$162$	2.35776	+	0.487679i	0.185243	+	0.0383157i
$163$			20.0027i			1.56673i	0.621562	+	0.783365i	$0.286498\pi$
$163$			20.0027i			1.56673i	−0.621562	+	0.783365i	$0.713502\pi$
$164$	2.36217	−	1.36380i	0.184454	−	0.106495i
$165$	8.12781	+	1.49489i	0.632749	+	0.116377i
$166$	1.13067	−	1.95839i	0.0877574	−	0.152000i
$167$	−15.8612	−	9.15745i	−1.22737	−	0.708625i	−0.260894	−	0.965367i	$-0.584017\pi$
$167$	−15.8612	−	9.15745i	−1.22737	−	0.708625i	−0.966480	+	0.256743i	$0.917351\pi$
$168$	−2.32995	−	6.55105i	−0.179759	−	0.505424i
$169$	9.73745	−	8.61291i	0.749034	−	0.662531i
$170$	1.20182			0.0921750
$171$	0.888760	−	2.33438i	0.0679652	−	0.178515i
$172$	−17.6344			−1.34461
$173$	−8.48559	−	14.6975i	−0.645148	−	1.11743i	−0.984267	−	0.176685i	$-0.943463\pi$
$173$	−8.48559	−	14.6975i	−0.645148	−	1.11743i	0.339120	−	0.940743i	$-0.389871\pi$
$174$	1.21427	+	1.03421i	0.0920534	+	0.0784033i
$175$	−3.30805	−	1.90990i	−0.250065	−	0.144375i
$176$	14.7751	+	8.53043i	1.11372	+	0.643006i
$177$	1.50964	+	1.28579i	0.113472	+	0.0966456i
$178$	−0.786107	−	1.36158i	−0.0589212	−	0.102054i
$179$	8.16369			0.610183			0.305091	−	0.952323i	$-0.401313\pi$
$179$	8.16369			0.610183			0.305091	+	0.952323i	$0.401313\pi$
$180$	5.71157	−	0.920663i	0.425716	−	0.0686221i
$181$	8.83681			0.656835			0.328417	−	0.944533i	$-0.393485\pi$
$181$	8.83681			0.656835			0.328417	+	0.944533i	$0.393485\pi$
$182$	−0.592456	+	3.63646i	−0.0439157	+	0.269552i
$183$	−5.90506	−	16.6031i	−0.436515	−	1.22734i
$184$	−5.37191	−	3.10147i	−0.396022	−	0.228644i
$185$	0.714856	−	1.23817i	0.0525573	−	0.0910319i
$186$	2.16765	+	0.398681i	0.158940	+	0.0292327i
$187$	18.5631	−	10.7174i	1.35747	−	0.783736i
$188$			25.0627i			1.82789i
$189$	−19.8434	−	0.438072i	−1.44340	−	0.0318651i
$190$			0.222740i			0.0161593i
$191$	−3.11255	−	5.39110i	−0.225217	−	0.390086i	0.731168	−	0.682198i	$-0.238976\pi$
$191$	−3.11255	−	5.39110i	−0.225217	−	0.390086i	−0.956384	+	0.292111i	$0.905642\pi$
$192$	10.7886	+	1.98427i	0.778598	+	0.143202i
$193$	3.50344	+	2.02271i	0.252183	+	0.145598i	0.620764	−	0.783998i	$-0.286823\pi$
$193$	3.50344	+	2.02271i	0.252183	+	0.145598i	−0.368580	+	0.929596i	$0.620156\pi$
$194$	−1.90922	+	3.30687i	−0.137074	+	0.237419i
$195$	−5.88040	−	2.10259i	−0.421104	−	0.150570i
$196$	7.31926	+	12.6773i	0.522804	+	0.905523i
$197$			0.284920i			0.0202997i	0.999948	+	0.0101498i	$0.00323085\pi$
$197$			0.284920i			0.0202997i	−0.999948	+	0.0101498i	$0.996769\pi$
$198$	−2.96927	+	2.41796i	−0.211017	+	0.171837i
$199$	10.3617			0.734520			0.367260	−	0.930118i	$-0.380296\pi$
$199$	10.3617			0.734520			0.367260	+	0.930118i	$0.380296\pi$
$200$	−0.910132	+	0.525465i	−0.0643561	+	0.0371560i
$201$	16.0381	+	13.6599i	1.13124	+	0.963498i
$202$	1.96150	+	1.13247i	0.138011	+	0.0796806i
$203$	−11.3872	−	6.57442i	−0.799227	−	0.461434i
$204$	9.72962	−	11.4236i	0.681210	−	0.799809i
$205$	0.707206	+	1.22492i	0.0493934	+	0.0855519i
$206$		−	3.30329i		−	0.230151i
$207$	−13.7304	+	11.1810i	−0.954327	+	0.777135i
$208$	−9.98334	−	8.15772i	−0.692220	−	0.565636i
$209$	1.98633	+	3.44043i	0.137397	+	0.237979i
$210$	1.66760	−	0.593098i	0.115075	−	0.0409277i
$211$	−8.61115	+	14.9149i	−0.592816	+	1.02679i	0.401035	+	0.916063i	$0.368650\pi$
$211$	−8.61115	+	14.9149i	−0.592816	+	1.02679i	−0.993851	+	0.110724i	$0.964683\pi$
$212$	8.04707	−	13.9379i	0.552675	−	0.957261i
$213$	−0.351716	+	1.91230i	−0.0240992	+	0.131029i
$214$	−2.27235	+	1.31194i	−0.155334	+	0.0896824i
$215$		−	9.14441i		−	0.623644i
$216$	−2.83411	+	4.66777i	−0.192837	+	0.317602i
$217$	−18.1693			−1.23341
$218$	−1.96766	−	3.40809i	−0.133267	−	0.230825i
$219$	−1.94520	+	10.5762i	−0.131445	+	0.714670i
$220$	−4.60057	+	7.96842i	−0.310170	+	0.537231i
$221$	−15.1474	+	5.73782i	−1.01893	+	0.385968i
$222$	0.221991	+	0.624165i	0.0148990	+	0.0418912i
$223$	−4.17729	+	2.41176i	−0.279732	+	0.161503i	−0.633302	−	0.773905i	$-0.718301\pi$
$223$	−4.17729	+	2.41176i	−0.279732	+	0.161503i	0.353570	+	0.935408i	$0.384968\pi$
$224$	11.6826			0.780577
$225$	0.477415	+	2.96177i	0.0318276	+	0.197451i
$226$			3.83661i			0.255207i
$227$	−22.5056	+	12.9936i	−1.49375	+	0.862415i	−0.999974	−	0.00717601i	$-0.997716\pi$
$227$	−22.5056	+	12.9936i	−1.49375	+	0.862415i	−0.493773	+	0.869591i	$0.664382\pi$
$228$	2.11720	+	1.80326i	0.140215	+	0.119424i
$229$	17.5404	+	10.1269i	1.15910	+	0.669207i	0.951088	−	0.308919i	$-0.0999673\pi$
$229$	17.5404	+	10.1269i	1.15910	+	0.669207i	0.208012	+	0.978126i	$0.433301\pi$
$230$	0.789494	−	1.36744i	0.0520577	−	0.0901665i
$231$	20.4685	−	24.0321i	1.34673	−	1.58119i
$232$	−3.13293	+	1.80880i	−0.205687	+	0.118754i
$233$	4.52185			0.296237			0.148118	−	0.988970i	$-0.452678\pi$
$233$	4.52185			0.296237			0.148118	+	0.988970i	$0.452678\pi$
$234$	2.50842	−	1.44261i	0.163980	−	0.0943061i
$235$	−12.9964			−0.847792
$236$	−1.91204	+	1.10391i	−0.124463	+	0.0718587i
$237$	8.37600	+	23.5506i	0.544080	+	1.52977i
$238$	2.29535	−	3.97566i	0.148785	−	0.257704i
$239$	4.86344	+	2.80791i	0.314590	+	0.181628i	0.648978	−	0.760807i	$-0.275197\pi$
$239$	4.86344	+	2.80791i	0.314590	+	0.181628i	−0.334389	+	0.942435i	$0.608530\pi$
$240$	−1.12031	+	6.09117i	−0.0723156	+	0.393183i
$241$	12.8454	−	7.41628i	0.827443	−	0.477724i	−0.0255335	−	0.999674i	$-0.508128\pi$
$241$	12.8454	−	7.41628i	0.827443	−	0.477724i	0.852976	+	0.521950i	$0.174795\pi$
$242$		−	3.14745i		−	0.202326i
$243$	9.57408	+	12.3019i	0.614178	+	0.789168i
$244$	19.6199			1.25604
$245$	−6.57390	+	3.79544i	−0.419991	+	0.242482i
$246$	−0.644565	−	0.118551i	−0.0410960	−	0.00755851i
$247$	−1.06343	−	2.80738i	−0.0676644	−	0.178629i
$248$	−2.49943	+	4.32915i	−0.158714	+	0.274901i
$249$	13.7946	−	4.90619i	0.874198	−	0.310917i
$250$	−0.133759	−	0.231678i	−0.00845969	−	0.0146526i
$251$	17.6935			1.11681			0.558403	−	0.829570i	$-0.311414\pi$
$251$	17.6935			1.11681			0.558403	+	0.829570i	$0.311414\pi$
$252$	7.86295	−	20.6525i	0.495319	−	1.30099i
$253$		−	28.1619i		−	1.77052i
$254$	−1.96683	+	1.13555i	−0.123410	+	0.0712509i
$255$	5.92375	+	5.04535i	0.370959	+	0.315952i
$256$	−5.28844	+	9.15986i	−0.330528	+	0.572491i
$257$	−4.10102	+	7.10317i	−0.255814	+	0.443084i	−0.965116	−	0.261821i	$-0.915677\pi$
$257$	−4.10102	+	7.10317i	−0.255814	+	0.443084i	0.709302	+	0.704905i	$0.249010\pi$
$258$	3.22570	+	2.74738i	0.200823	+	0.171044i
$259$	−2.73061	−	4.72955i	−0.169672	−	0.293880i
$260$	4.39956	−	5.38414i	0.272849	−	0.333910i
$261$	1.64340	+	10.1952i	0.101724	+	0.631070i
$262$		−	2.56053i		−	0.158190i
$263$	1.42875	+	2.47467i	0.0881004	+	0.152594i	0.906708	−	0.421759i	$-0.138587\pi$
$263$	1.42875	+	2.47467i	0.0881004	+	0.152594i	−0.818608	+	0.574353i	$0.805254\pi$
$264$	−2.91033	−	8.18290i	−0.179118	−	0.503623i
$265$	7.22759	+	4.17285i	0.443988	+	0.256336i
$266$	0.736836	+	0.425412i	0.0451783	+	0.0260837i
$267$	1.84132	−	10.0114i	0.112687	−	0.612686i
$268$	−20.3131	+	11.7278i	−1.24082	+	0.716388i
$269$	3.93682			0.240032			0.120016	−	0.992772i	$-0.461705\pi$
$269$	3.93682			0.240032			0.120016	+	0.992772i	$0.461705\pi$
$270$	−1.18820	−	0.721435i	−0.0723117	−	0.0439051i
$271$		−	22.1080i		−	1.34296i	−0.741021	−	0.671482i	$-0.765658\pi$
$271$		−	22.1080i		−	1.34296i	0.741021	−	0.671482i	$-0.234342\pi$
$272$	8.03188	+	13.9116i	0.487004	+	0.843516i
$273$	−18.1864	+	15.4369i	−1.10069	+	0.934283i
$274$	−1.59708	+	2.76622i	−0.0964831	+	0.167114i
$275$	−4.13207	−	2.38565i	−0.249173	−	0.143860i
$276$	−6.60633	−	18.5748i	−0.397654	−	1.11807i
$277$	4.77717	+	8.27430i	0.287032	+	0.497154i	0.973100	−	0.230383i	$-0.0739980\pi$
$277$	4.77717	+	8.27430i	0.287032	+	0.497154i	−0.686068	+	0.727538i	$0.740665\pi$
$278$		−	3.17809i		−	0.190609i
$279$	9.01063	+	11.0651i	0.539452	+	0.662451i
$280$			4.01435i			0.239903i
$281$	−22.5837	+	13.0387i	−1.34723	+	0.777823i	−0.987856	−	0.155371i	$-0.950343\pi$
$281$	−22.5837	+	13.0387i	−1.34723	+	0.777823i	−0.359373	+	0.933194i	$0.617009\pi$
$282$	3.90468	−	4.58449i	0.232520	−	0.273002i
$283$	−11.6980	+	20.2616i	−0.695376	+	1.20443i	0.274678	+	0.961536i	$0.411429\pi$
$283$	−11.6980	+	20.2616i	−0.695376	+	1.20443i	−0.970054	+	0.242890i	$0.921905\pi$
$284$	−1.87480	−	1.08241i	−0.111249	−	0.0642295i
$285$	−0.935088	+	1.09789i	−0.0553898	+	0.0650333i
$286$	−0.740035	+	4.54229i	−0.0437592	+	0.268591i
$287$	5.40277			0.318915
$288$	−5.79371	−	7.11471i	−0.341397	−	0.419238i
$289$	3.18211			0.187183
$290$	−0.460438	−	0.797502i	−0.0270378	−	0.0468309i
$291$	−23.2931	+	8.28443i	−1.36547	+	0.485642i
$292$	−10.3688	−	5.98640i	−0.606786	−	0.350328i
$293$	−8.06287	−	4.65510i	−0.471038	−	0.271954i	0.245636	−	0.969362i	$-0.421003\pi$
$293$	−8.06287	−	4.65510i	−0.471038	−	0.271954i	−0.716674	+	0.697408i	$0.754337\pi$
$294$	0.636239	−	3.45926i	0.0371062	−	0.201748i
$295$	−0.572441	−	0.991497i	−0.0333288	−	0.0577272i
$296$	−1.50253			−0.0873327
$297$	−24.7864	−	0.547195i	−1.43825	−	0.0317515i
$298$	3.53362			0.204697
$299$	−3.42204	+	21.0042i	−0.197902	+	1.21471i
$300$	−3.28504	−	0.604196i	−0.189662	−	0.0348833i
$301$	−30.2501	−	17.4649i	−1.74359	−	1.00666i
$302$	−0.244543	+	0.423561i	−0.0140719	+	0.0243732i
$303$	4.91400	+	13.8166i	0.282302	+	0.793741i
$304$	−2.57833	+	1.48860i	−0.147878	+	0.0853772i
$305$			10.1740i			0.582563i
$306$	−3.55950	+	0.573764i	−0.203483	+	0.0327999i
$307$			23.3836i			1.33458i	0.744800	+	0.667288i	$0.232545\pi$
$307$			23.3836i			1.33458i	−0.744800	+	0.667288i	$0.767455\pi$
$308$	17.5733	+	30.4378i	1.00133	+	1.73435i
$309$	13.8676	−	16.2819i	0.788898	−	0.926245i
$310$	−1.10200	−	0.636242i	−0.0625896	−	0.0361361i
$311$	−0.686243	+	1.18861i	−0.0389133	+	0.0673998i	−0.884826	−	0.465921i	$-0.845723\pi$
$311$	−0.686243	+	1.18861i	−0.0389133	+	0.0673998i	0.845913	+	0.533321i	$0.179056\pi$
$312$	1.17631	+	6.45678i	0.0665955	+	0.365543i
$313$	−5.56238	−	9.63433i	−0.314405	−	0.544565i	0.664906	−	0.746927i	$-0.268471\pi$
$313$	−5.56238	−	9.63433i	−0.314405	−	0.544565i	−0.979311	+	0.202362i	$0.935138\pi$
$314$		−	1.45947i		−	0.0823626i
$315$	10.7095	+	4.07738i	0.603411	+	0.229734i
$316$	−27.8298			−1.56555
$317$	−0.868084	+	0.501188i	−0.0487564	+	0.0281495i	−0.524180	−	0.851607i	$-0.675628\pi$
$317$	−0.868084	+	0.501188i	−0.0487564	+	0.0281495i	0.475424	+	0.879757i	$0.342295\pi$
$318$	−3.64346	+	1.29583i	−0.204315	+	0.0726667i
$319$	−14.2238	−	8.21209i	−0.796378	−	0.459789i
$320$	−5.48476	−	3.16663i	−0.306608	−	0.177020i
$321$	−16.7081	−	3.07300i	−0.932553	−	0.171518i
$322$	−3.01571	−	5.22336i	−0.168059	−	0.291087i
$323$			3.74048i			0.208126i
$324$	−16.4768	+	5.45358i	−0.915379	+	0.302977i
$325$	2.79198	+	2.28142i	0.154871	+	0.126550i
$326$	2.67555	+	4.63418i	0.148185	+	0.256664i
$327$	4.60892	−	25.0589i	0.254874	−	1.38576i
$328$	0.743224	−	1.28730i	0.0410377	−	0.0710793i
$329$	−24.8218	+	42.9927i	−1.36847	+	2.37026i
$330$	2.08299	−	0.740837i	0.114665	−	0.0407818i
$331$	−28.8372	+	16.6492i	−1.58504	+	0.915122i	−0.590930	+	0.806723i	$0.701239\pi$
$331$	−28.8372	+	16.6492i	−1.58504	+	0.915122i	−0.994107	+	0.108399i	$0.965427\pi$
$332$			16.3011i			0.894641i
$333$	−1.52612	+	4.00845i	−0.0836309	+	0.219662i
$334$	−4.89958			−0.268093
$335$	−6.08150	−	10.5335i	−0.332268	−	0.575505i
$336$	18.0102	+	15.3396i	0.982536	+	0.836841i
$337$	−14.2103	+	24.6130i	−0.774085	+	1.34075i	0.161223	+	0.986918i	$0.448456\pi$
$337$	−14.2103	+	24.6130i	−0.774085	+	1.34075i	−0.935308	+	0.353836i	$0.884877\pi$
$338$	1.10390	−	3.29790i	0.0600440	−	0.179382i
$339$	−16.1065	+	18.9106i	−0.874784	+	1.02708i
$340$	−7.50272	+	4.33170i	−0.406892	+	0.234919i
$341$	−22.6953			−1.22902
$342$	−0.106340	−	0.659706i	−0.00575019	−	0.0356728i
$343$			2.25706i			0.121870i
$344$	−8.32262	+	4.80507i	−0.448726	+	0.259072i
$345$	9.63208	−	3.42575i	0.518574	−	0.184436i
$346$	−3.93185	−	2.27006i	−0.211378	−	0.122039i
$347$	14.4761	−	25.0733i	0.777115	−	1.34600i	−0.156483	−	0.987681i	$-0.550016\pi$
$347$	14.4761	−	25.0733i	0.777115	−	1.34600i	0.933598	−	0.358322i	$-0.116651\pi$
$348$	−11.3081	−	2.07981i	−0.606175	−	0.111490i
$349$	2.19739	−	1.26867i	0.117624	−	0.0679101i	−0.440034	−	0.897981i	$-0.645034\pi$
$349$	2.19739	−	1.26867i	0.117624	−	0.0679101i	0.557658	+	0.830071i	$0.311700\pi$
$350$	−1.02187			−0.0546212
$351$	18.4202	+	3.41999i	0.983197	+	0.182546i
$352$	14.5927			0.777795
$353$	4.46674	−	2.57887i	0.237741	−	0.137260i	−0.376397	−	0.926458i	$-0.622837\pi$
$353$	4.46674	−	2.57887i	0.237741	−	0.137260i	0.614138	+	0.789199i	$0.289504\pi$
$354$	0.521737	+	0.0959596i	0.0277300	+	0.00510020i
$355$	0.561292	−	0.972187i	0.0297903	−	0.0515983i
$356$	9.81505	+	5.66672i	0.520196	+	0.300336i
$357$	28.0040	−	9.95991i	1.48213	−	0.527134i
$358$	1.89135	−	1.09197i	0.0999609	−	0.0577124i
$359$			11.9673i			0.631610i	0.948824	+	0.315805i	$0.102274\pi$
$359$			11.9673i			0.631610i	−0.948824	+	0.315805i	$0.897726\pi$
$360$	2.44474	−	1.99082i	0.128849	−	0.104925i
$361$	18.3068			0.963513
$362$	2.04730	−	1.18201i	0.107603	−	0.0621249i
$363$	13.2133	−	15.5138i	0.693520	−	0.814263i
$364$	−9.40826	−	24.8371i	−0.493127	−	1.30182i
$365$	3.10428	−	5.37678i	0.162486	−	0.281433i
$366$	−3.58890	−	3.05672i	−0.187595	−	0.159777i
$367$	−8.68972	−	15.0510i	−0.453600	−	0.785658i	0.545007	−	0.838432i	$-0.316527\pi$
$367$	−8.68972	−	15.0510i	−0.453600	−	0.785658i	−0.998606	+	0.0527738i	$0.983194\pi$
$368$	21.1051			1.10018
$369$	−2.67937	−	3.29029i	−0.139483	−	0.171286i
$370$		−	0.382475i		−	0.0198839i
$371$	27.6080	−	15.9395i	1.43333	−	0.827536i
$372$	−14.9692	+	5.32395i	−0.776117	+	0.276034i
$373$	5.21095	−	9.02562i	0.269813	−	0.467329i	−0.699001	−	0.715121i	$-0.746372\pi$
$373$	5.21095	−	9.02562i	0.269813	−	0.467329i	0.968813	+	0.247792i	$0.0797049\pi$
$374$	2.86711	−	4.96599i	0.148255	−	0.256785i
$375$	0.313309	−	1.70348i	0.0161792	−	0.0879672i
$376$	6.82916	+	11.8285i	0.352187	+	0.610006i
$377$	9.61078	+	7.85328i	0.494980	+	0.404465i
$378$	−4.65589	+	2.55276i	−0.239473	+	0.131300i
$379$		−	21.9098i		−	1.12543i	−0.826651	−	0.562715i	$-0.809757\pi$
$379$		−	21.9098i		−	1.12543i	0.826651	−	0.562715i	$-0.190243\pi$
$380$	−0.802822	−	1.39053i	−0.0411839	−	0.0713326i
$381$	−14.4617	−	2.65984i	−0.740895	−	0.136268i
$382$	−1.44222	−	0.832667i	−0.0737905	−	0.0426030i
$383$	27.7328	+	16.0115i	1.41708	+	0.818150i	0.996041	−	0.0888937i	$-0.0283331\pi$
$383$	27.7328	+	16.0115i	1.41708	+	0.818150i	0.421036	+	0.907044i	$0.361666\pi$
$384$	12.7471	−	4.53362i	0.650496	−	0.231355i
$385$	−15.7837	+	9.11272i	−0.804411	+	0.464427i
$386$	1.08223			0.0550840
$387$	4.36568	+	27.0836i	0.221920	+	1.37674i
$388$		−	27.5256i		−	1.39740i
$389$	4.45126	+	7.70981i	0.225688	+	0.390903i	0.956526	−	0.291648i	$-0.0942037\pi$
$389$	4.45126	+	7.70981i	0.225688	+	0.390903i	−0.730838	+	0.682551i	$0.760870\pi$
$390$	−1.64360	+	0.299435i	−0.0832270	+	0.0151625i
$391$	13.2580	−	22.9635i	0.670485	−	1.16131i
$392$	6.90871	+	3.98874i	0.348942	+	0.201462i
$393$	10.7494	−	12.6209i	0.542235	−	0.636638i
$394$	0.0381107	+	0.0660097i	0.00191999	+	0.00332552i
$395$		−	14.4313i		−	0.726117i
$396$	9.82159	−	25.7970i	0.493553	−	1.29635i
$397$		−	8.79341i		−	0.441328i	−0.975350	−	0.220664i	$-0.929178\pi$
$397$		−	8.79341i		−	0.441328i	0.975350	−	0.220664i	$-0.0708225\pi$
$398$	2.40058	−	1.38597i	0.120330	−	0.0694726i
$399$	1.84594	+	5.19017i	0.0924124	+	0.259834i
$400$	1.78786	−	3.09667i	0.0893931	−	0.154833i
$401$	−2.80491	−	1.61941i	−0.140070	−	0.0808697i	0.428327	−	0.903624i	$-0.359103\pi$
$401$	−2.80491	−	1.61941i	−0.140070	−	0.0808697i	−0.568398	+	0.822754i	$0.692436\pi$
$402$	5.54283	+	1.01946i	0.276451	+	0.0508459i
$403$	16.9270	+	2.75777i	0.843196	+	0.137374i
$404$	−16.3271			−0.812302
$405$	−2.82798	−	8.54415i	−0.140524	−	0.424562i
$406$	−3.51756			−0.174574
$407$	−3.41080	−	5.90767i	−0.169067	−	0.292833i
$408$	1.47921	−	8.04255i	0.0732319	−	0.398165i
$409$	−16.0582	−	9.27123i	−0.794029	−	0.458433i	0.0473500	−	0.998878i	$-0.484922\pi$
$409$	−16.0582	−	9.27123i	−0.794029	−	0.458433i	−0.841379	+	0.540446i	$0.818256\pi$
$410$	0.327688	+	0.189191i	0.0161834	+	0.00934347i
$411$	−19.4849	+	6.93000i	−0.961120	+	0.341832i
$412$	11.9060	+	20.6218i	0.586568	+	1.01596i
$413$	−4.37322			−0.215192
$414$	−1.68546	+	4.42697i	−0.0828358	+	0.217574i
$415$	−8.45305			−0.414944
$416$	−10.8838	−	1.77321i	−0.533624	−	0.0869387i
$417$	13.3420	−	15.6648i	0.653358	−	0.767108i
$418$	0.920379	+	0.531381i	0.0450172	+	0.0259907i
$419$	1.51665	−	2.62692i	0.0740934	−	0.128334i	−0.826598	−	0.562792i	$-0.809727\pi$
$419$	1.51665	−	2.62692i	0.0740934	−	0.128334i	0.900692	+	0.434459i	$0.143060\pi$
$420$	−8.27282	+	9.71312i	−0.403672	+	0.473952i
$421$	15.2998	−	8.83336i	0.745668	−	0.430512i	−0.0784584	−	0.996917i	$-0.525000\pi$
$421$	15.2998	−	8.83336i	0.745668	−	0.430512i	0.824127	+	0.566406i	$0.191666\pi$
$422$			4.60729i			0.224279i
$423$	38.4924	−	6.20468i	1.87156	−	0.301682i
$424$		−	8.77076i		−	0.425946i
$425$	−2.24622	−	3.89058i	−0.108958	−	0.188721i
$426$	0.174303	+	0.490083i	0.00844501	+	0.0237446i
$427$	33.6562	+	19.4314i	1.62874	+	0.940351i
$428$	9.45723	−	16.3804i	0.457133	−	0.791777i
$429$	−22.7166	+	19.2822i	−1.09677	+	0.930953i
$430$	−1.22315	−	2.11856i	−0.0589856	−	0.102166i
$431$			18.4289i			0.887690i	0.896104	+	0.443845i	$0.146386\pi$
$431$			18.4289i			0.887690i	−0.896104	+	0.443845i	$0.853614\pi$
$432$	0.410080	−	18.5755i	0.0197300	−	0.893713i
$433$	−4.84859			−0.233008			−0.116504	−	0.993190i	$-0.537169\pi$
$433$	−4.84859			−0.233008			−0.116504	+	0.993190i	$0.537169\pi$
$434$	−4.20943	+	2.43032i	−0.202059	+	0.116659i
$435$	1.07850	−	5.86385i	0.0517101	−	0.281150i
$436$	24.5675	+	14.1841i	1.17657	+	0.679294i
$437$	4.25598	+	2.45719i	0.203591	+	0.117543i
$438$	0.964000	+	2.71045i	0.0460617	+	0.129510i
$439$	−7.77071	−	13.4593i	−0.370876	−	0.642376i	0.618825	−	0.785529i	$-0.287609\pi$
$439$	−7.77071	−	13.4593i	−0.370876	−	0.642376i	−0.989701	+	0.143153i	$0.954276\pi$
$440$			5.01431i			0.239048i
$441$	17.6584	−	14.3797i	0.840875	−	0.684747i
$442$	−2.74184	+	3.35544i	−0.130416	+	0.159602i
$443$	16.7839	+	29.0706i	0.797427	+	1.38118i	0.921287	+	0.388884i	$0.127139\pi$
$443$	16.7839	+	29.0706i	0.797427	+	1.38118i	−0.123860	+	0.992300i	$0.539527\pi$
$444$	−3.63552	−	3.09643i	−0.172534	−	0.146950i
$445$	−2.93851	+	5.08965i	−0.139299	+	0.241272i
$446$	−0.645191	+	1.11750i	−0.0305507	+	0.0529153i
$447$	17.4172	+	14.8345i	0.823805	+	0.701648i
$448$	−20.9507	+	12.0959i	−0.989828	+	0.571477i
$449$		−	4.17757i		−	0.197152i	−0.995130	−	0.0985760i	$-0.968571\pi$
$449$		−	4.17757i		−	0.197152i	0.995130	−	0.0985760i	$-0.0314287\pi$
$450$	0.506771	+	0.622318i	0.0238894	+	0.0293364i
$451$	6.74859			0.317779
$452$	−13.8283	−	23.9512i	−0.650427	−	1.12657i
$453$	−2.98351	+	1.06111i	−0.140177	+	0.0498555i
$454$	−3.47603	+	6.02066i	−0.163138	+	0.282564i
$455$	12.8794	−	4.87871i	0.603797	−	0.228717i
$456$	1.49058	+	0.274152i	0.0698028	+	0.0128384i
$457$	−6.76599	+	3.90635i	−0.316500	+	0.182731i	−0.649831	−	0.760078i	$-0.725160\pi$
$457$	−6.76599	+	3.90635i	−0.316500	+	0.182731i	0.333332	+	0.942810i	$0.391827\pi$
$458$	5.41829			0.253180
$459$	−19.9535	−	12.1151i	−0.931349	−	0.565483i
$460$			11.3823i			0.530701i
$461$	−1.48368	+	0.856604i	−0.0691019	+	0.0398960i	−0.534153	−	0.845388i	$-0.679369\pi$
$461$	−1.48368	+	0.856604i	−0.0691019	+	0.0398960i	0.465051	+	0.885284i	$0.346036\pi$
$462$	1.52759	−	8.30556i	0.0710698	−	0.386410i
$463$	19.1053	+	11.0304i	0.887897	+	0.512627i	0.873254	−	0.487265i	$-0.162006\pi$
$463$	19.1053	+	11.0304i	0.887897	+	0.512627i	0.0146429	+	0.999893i	$0.495339\pi$
$464$	6.15433	−	10.6596i	0.285707	−	0.494860i
$465$	−2.76076	−	7.76236i	−0.128027	−	0.359971i
$466$	1.04761	−	0.604841i	0.0485298	−	0.0280187i
$467$	−23.5518			−1.08985			−0.544923	−	0.838486i	$-0.683441\pi$
$467$	−23.5518			−1.08985			−0.544923	+	0.838486i	$0.683441\pi$
$468$	−10.4600	+	18.0470i	−0.483514	+	0.834223i
$469$	−46.4603			−2.14534
$470$	−3.01098	+	1.73839i	−0.138886	+	0.0801861i
$471$	6.12700	−	7.19372i	0.282317	−	0.331469i
$472$	−0.601596	+	1.04199i	−0.0276907	+	0.0479617i
$473$	−37.7853	−	21.8154i	−1.73737	−	1.00307i
$474$	5.09065	+	4.33579i	0.233821	+	0.199149i
$475$	0.721066	−	0.416308i	0.0330848	−	0.0191015i
$476$			33.0924i			1.51679i
$477$	−23.3986	−	8.90847i	−1.07135	−	0.407891i
$478$	1.50234			0.0687153
$479$	31.9463	−	18.4442i	1.45966	−	0.842736i	0.460667	−	0.887573i	$-0.347610\pi$
$479$	31.9463	−	18.4442i	1.45966	−	0.842736i	0.998994	+	0.0448367i	$0.0142767\pi$
$480$	1.77513	+	4.99109i	0.0810233	+	0.227811i
$481$	1.82605	+	4.82064i	0.0832607	+	0.219802i
$482$	1.98399	−	3.43638i	0.0903685	−	0.156523i
$483$	7.06380	−	38.4062i	0.321414	−	1.74754i
$484$	11.3443	+	19.6490i	0.515652	+	0.893135i
$485$	14.2735			0.648128
$486$	3.86360	+	1.56946i	0.175257	+	0.0711921i
$487$			20.6923i			0.937657i	0.883289	+	0.468829i	$0.155324\pi$
$487$			20.6923i			0.937657i	−0.883289	+	0.468829i	$0.844676\pi$
$488$	9.25972	−	5.34610i	0.419168	−	0.242007i
$489$	−6.26702	+	34.0741i	−0.283405	+	1.54088i
$490$	−1.01535	+	1.75864i	−0.0458689	+	0.0794473i
$491$	−4.33370	+	7.50620i	−0.195577	+	0.338750i	−0.947090	−	0.320969i	$-0.895991\pi$
$491$	−4.33370	+	7.50620i	−0.195577	+	0.338750i	0.751512	+	0.659719i	$0.229325\pi$
$492$	4.45120	−	1.58311i	0.200675	−	0.0713722i
$493$	−7.73214	−	13.3925i	−0.348238	−	0.603166i
$494$	−0.621886	−	0.508164i	−0.0279800	−	0.0228634i
$495$	13.3772	+	5.09304i	0.601260	+	0.228915i
$496$		−	17.0083i		−	0.763697i
$497$	−2.14403	−	3.71356i	−0.0961727	−	0.166576i
$498$	2.53966	−	2.98182i	0.113805	−	0.133618i
$499$	1.92096	+	1.10907i	0.0859941	+	0.0496487i	0.542380	−	0.840133i	$-0.317523\pi$
$499$	1.92096	+	1.10907i	0.0859941	+	0.0496487i	−0.456386	+	0.889782i	$0.650856\pi$
$500$	1.67007	+	0.964217i	0.0746879	+	0.0431211i
$501$	−24.1500	−	20.5690i	−1.07894	−	0.918954i
$502$	4.09921	−	2.36668i	0.182957	−	0.105630i
$503$	8.41584			0.375244			0.187622	−	0.982241i	$-0.439922\pi$
$503$	8.41584			0.375244			0.187622	+	0.982241i	$0.439922\pi$
$504$	−1.91651	−	11.8896i	−0.0853680	−	0.529603i
$505$		−	8.46650i		−	0.376754i
$506$	−3.76691	−	6.52449i	−0.167460	−	0.290049i
$507$	19.2860	−	11.6211i	0.856523	−	0.516110i
$508$	8.18573	−	14.1781i	0.363183	−	0.629051i
$509$	8.71784	+	5.03325i	0.386412	+	0.223095i	0.680604	−	0.732651i	$-0.261717\pi$
$509$	8.71784	+	5.03325i	0.386412	+	0.223095i	−0.294193	+	0.955746i	$0.595051\pi$
$510$	2.04727	+	0.376540i	0.0906545	+	0.0166735i
$511$	−11.8577	−	20.5382i	−0.524556	−	0.908557i
$512$			18.4518i			0.815462i
$513$	2.24537	−	3.69811i	0.0991354	−	0.163276i
$514$			2.19420i			0.0967820i
$515$	−10.6936	+	6.17393i	−0.471215	+	0.272056i
$516$	−30.0398	−	5.52502i	−1.32243	−	0.243225i
$517$	−31.0049	+	53.7021i	−1.36359	+	2.36181i
$518$	−1.26525	−	0.730490i	−0.0555917	−	0.0320959i
$519$	−9.85016	−	27.6954i	−0.432374	−	1.21569i
$520$	0.609305	−	3.73987i	0.0267198	−	0.164004i
$521$	13.2577			0.580832			0.290416	−	0.956900i	$-0.406206\pi$
$521$	13.2577			0.580832			0.290416	+	0.956900i	$0.406206\pi$
$522$	1.74445	+	2.14220i	0.0763525	+	0.0937614i
$523$	27.9447			1.22193			0.610967	−	0.791656i	$-0.290781\pi$
$523$	27.9447			1.22193			0.610967	+	0.791656i	$0.290781\pi$
$524$	9.22891	+	15.9849i	0.403167	+	0.698306i
$525$	−5.03679	−	4.28992i	−0.219824	−	0.187227i
$526$	0.662020	+	0.382217i	0.0288654	+	0.0166655i
$527$	−18.5060	−	10.6844i	−0.806133	−	0.465421i
$528$	22.4965	+	19.1606i	0.979033	+	0.833858i
$529$	−5.91880	−	10.2517i	−0.257339	−	0.445724i
$530$	2.23263			0.0969794
$531$	2.16879	+	2.66329i	0.0941176	+	0.115577i
$532$	−6.13324			−0.265910
$533$	−5.03337	−	0.820043i	−0.218019	−	0.0355200i
$534$	−0.912521	−	2.56571i	−0.0394886	−	0.111029i
$535$	8.49415	+	4.90410i	0.367234	+	0.212023i
$536$	−6.39124	+	11.0699i	−0.276059	+	0.478149i
$537$	13.9067	+	2.55776i	0.600117	+	0.110376i
$538$	0.912076	−	0.526588i	0.0393224	−	0.0227028i
$539$			36.2184i			1.56004i
$540$	10.0180	+	0.221162i	0.431106	+	0.00951728i
$541$		−	37.7179i		−	1.62162i	−0.585310	−	0.810810i	$-0.699027\pi$
$541$		−	37.7179i		−	1.62162i	0.585310	−	0.810810i	$-0.300973\pi$
$542$	−2.95715	−	5.12194i	−0.127021	−	0.220006i
$543$	15.0533	+	2.76866i	0.645999	+	0.118814i
$544$	11.8991	+	6.86993i	0.510168	+	0.294546i
$545$	−7.35523	+	12.7396i	−0.315063	+	0.545706i
$546$	−2.14857	+	6.00900i	−0.0919503	+	0.257161i
$547$	7.56197	+	13.0977i	0.323326	+	0.560018i	0.981172	−	0.193135i	$-0.0618655\pi$
$547$	7.56197	+	13.0977i	0.323326	+	0.560018i	−0.657846	+	0.753153i	$0.728532\pi$
$548$		−	23.0254i		−	0.983596i
$549$	−4.85723	−	30.1331i	−0.207302	−	1.28605i
$550$	−1.27641			−0.0544265
$551$	2.48212	−	1.43305i	0.105742	−	0.0610500i
$552$	−8.17921	−	6.96636i	−0.348130	−	0.296508i
$553$	−47.7394	−	27.5623i	−2.03008	−	1.17207i
$554$	2.21353	+	1.27798i	0.0940439	+	0.0542963i
$555$	1.60567	−	1.88522i	0.0681570	−	0.0800231i
$556$	11.4548	+	19.8402i	0.485790	+	0.841414i
$557$		−	29.0794i		−	1.23213i	−0.787694	−	0.616066i	$-0.788725\pi$
$557$		−	29.0794i		−	1.23213i	0.787694	−	0.616066i	$-0.211275\pi$
$558$	3.56763	+	1.35829i	0.151030	+	0.0575010i
$559$	25.5310	+	20.8622i	1.07985	+	0.882378i
$560$	−6.82928	−	11.8287i	−0.288590	−	0.499852i
$561$	34.9797	−	12.4409i	1.47685	−	0.525255i
$562$	−3.48810	+	6.04156i	−0.147136	+	0.254848i
$563$	7.70300	−	13.3420i	0.324643	−	0.562298i	−0.656797	−	0.754067i	$-0.728089\pi$
$563$	7.70300	−	13.3420i	0.324643	−	0.562298i	0.981440	+	0.191770i	$0.0614226\pi$
$564$	−7.85238	+	42.6938i	−0.330645	+	1.79773i
$565$	12.4201	−	7.17072i	0.522516	−	0.301674i
$566$			6.25889i			0.263081i
$567$	−33.6656	−	6.96338i	−1.41382	−	0.292435i
$568$	−1.17976			−0.0495016
$569$	−3.04754	−	5.27850i	−0.127760	−	0.221286i	0.795049	−	0.606546i	$-0.207445\pi$
$569$	−3.04754	−	5.27850i	−0.127760	−	0.221286i	−0.922808	+	0.385260i	$0.874112\pi$
$570$	−0.0697867	+	0.379434i	−0.00292304	+	0.0158927i
$571$	7.94152	−	13.7551i	0.332342	−	0.575634i	−0.650628	−	0.759396i	$-0.725494\pi$
$571$	7.94152	−	13.7551i	0.332342	−	0.575634i	0.982971	+	0.183762i	$0.0588277\pi$
$572$	−11.7518	−	31.0240i	−0.491369	−	1.29718i
$573$	−3.61308	−	10.1588i	−0.150939	−	0.424391i
$574$	1.25170	−	0.722672i	0.0522451	−	0.0301637i
$575$	−5.90234			−0.246145
$576$	17.7564	+	6.76032i	0.739850	+	0.281680i
$577$		−	11.4920i		−	0.478418i	−0.970968	−	0.239209i	$-0.923112\pi$
$577$		−	11.4920i		−	0.478418i	0.970968	−	0.239209i	$-0.0768882\pi$
$578$	0.737224	−	0.425637i	0.0306645	−	0.0177042i
$579$	5.33430	+	4.54331i	0.221686	+	0.188813i
$580$	5.74886	+	3.31911i	0.238709	+	0.137818i
$581$	−16.1445	+	27.9631i	−0.669786	+	1.16010i
$582$	−4.28839	+	5.03500i	−0.177759	+	0.208707i
$583$	34.4851	−	19.9100i	1.42822	−	0.824586i
$584$	−6.52477			−0.269997
$585$	−9.35837	−	5.42410i	−0.386921	−	0.224259i
$586$	−2.49066			−0.102888
$587$	10.1519	−	5.86119i	0.419013	−	0.241917i	−0.275642	−	0.961260i	$-0.588890\pi$
$587$	10.1519	−	5.86119i	0.419013	−	0.241917i	0.694655	+	0.719343i	$0.255557\pi$
$588$	8.49627	+	23.8887i	0.350380	+	0.985155i
$589$	1.98022	−	3.42983i	0.0815934	−	0.141324i
$590$	−0.265244	−	0.153139i	−0.0109199	−	0.00630462i
$591$	−0.0892681	+	0.485355i	−0.00367200	+	0.0199648i
$592$	4.42734	−	2.55613i	0.181963	−	0.105056i
$593$		−	45.8759i		−	1.88390i	−0.335758	−	0.941948i	$-0.608992\pi$
$593$		−	45.8759i		−	1.88390i	0.335758	−	0.941948i	$-0.391008\pi$
$594$	−5.81566	+	3.18864i	−0.238619	+	0.130831i
$595$	−17.1603			−0.703502
$596$	−22.0597	+	12.7362i	−0.903602	+	0.521695i
$597$	17.6509	+	3.24641i	0.722403	+	0.132867i
$598$	2.01671	+	5.32396i	0.0824692	+	0.217713i
$599$	4.04403	−	7.00446i	0.165234	−	0.286194i	−0.771504	−	0.636224i	$-0.780495\pi$
$599$	4.04403	−	7.00446i	0.165234	−	0.286194i	0.936738	+	0.350030i	$0.113829\pi$
$600$	−1.71502	+	0.609965i	−0.0700155	+	0.0249017i
$601$	−0.350315	−	0.606763i	−0.0142896	−	0.0247504i	0.858792	−	0.512324i	$-0.171215\pi$
$601$	−0.350315	−	0.606763i	−0.0142896	−	0.0247504i	−0.873082	+	0.487574i	$0.837882\pi$
$602$	−9.34439			−0.380849
$603$	23.0408	+	28.2943i	0.938296	+	1.15223i
$604$		−	3.52562i		−	0.143455i
$605$	−10.1891	+	5.88267i	−0.414245	+	0.239165i
$606$	2.98656	+	2.54370i	0.121321	+	0.103331i
$607$	9.23783	−	16.0004i	0.374952	−	0.649436i	−0.615368	−	0.788240i	$-0.710993\pi$
$607$	9.23783	−	16.0004i	0.374952	−	0.649436i	0.990320	+	0.138804i	$0.0443258\pi$
$608$	−1.27325	+	2.20533i	−0.0516371	+	0.0894381i
$609$	−17.3381	−	14.7671i	−0.702574	−	0.598393i
$610$	1.36087	+	2.35710i	0.0551001	+	0.0954363i
$611$	29.6502	−	36.2857i	1.19952	−	1.46796i
$612$	20.1533	−	16.4114i	0.814649	−	0.663391i
$613$		−	14.1482i		−	0.571442i	−0.958313	−	0.285721i	$-0.907767\pi$
$613$		−	14.1482i		−	0.571442i	0.958313	−	0.285721i	$-0.0922331\pi$
$614$	3.12778	+	5.41748i	0.126227	+	0.218632i
$615$	0.820932	+	2.30819i	0.0331032	+	0.0930753i
$616$	16.5876	+	9.57683i	0.668332	+	0.385862i
$617$	21.1972	+	12.2382i	0.853365	+	0.492691i	0.861785	−	0.507274i	$-0.169347\pi$
$617$	21.1972	+	12.2382i	0.853365	+	0.492691i	−0.00841953	+	0.999965i	$0.502680\pi$
$618$	1.03495	−	5.62708i	0.0416318	−	0.226354i
$619$	−21.2194	+	12.2510i	−0.852879	+	0.492410i	−0.861621	−	0.507552i	$-0.830551\pi$
$619$	−21.2194	+	12.2510i	−0.852879	+	0.492410i	0.00874197	+	0.999962i	$0.497217\pi$
$620$	9.17281			0.368389
$621$	−26.8925	+	14.7448i	−1.07916	+	0.591687i
$622$			0.367166i			0.0147220i
$623$	11.2245	+	19.4414i	0.449701	+	0.778905i
$624$	−14.4505	−	17.0244i	−0.578483	−	0.681520i
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	−2.57737	−	1.48804i	−0.103012	−	0.0594742i
$627$	2.30575	+	6.48303i	0.0920830	+	0.258907i
$628$	5.26035	+	9.11120i	0.209911	+	0.363576i
$629$		−	6.42291i		−	0.256098i
$630$	3.02654	−	0.487855i	0.120580	−	0.0194366i
$631$		−	9.58282i		−	0.381486i	−0.981640	−	0.190743i	$-0.938910\pi$
$631$		−	9.58282i		−	0.381486i	0.981640	−	0.190743i	$-0.0610897\pi$
$632$	−13.1344	+	7.58314i	−0.522458	+	0.301641i
$633$	−19.3419	+	22.7093i	−0.768771	+	0.902614i
$634$	−0.134077	+	0.232229i	−0.00532489	+	0.00922298i
$635$	7.35213	+	4.24475i	0.291760	+	0.168448i
$636$	18.0749	−	21.2217i	0.716716	−	0.841497i
$637$	4.40102	−	27.0132i	0.174375	−	1.07030i
$638$	−4.39378			−0.173951
$639$	−1.19828	+	3.14736i	−0.0474033	+	0.124508i
$640$	−7.81113			−0.308762
$641$	10.9001	+	18.8796i	0.430529	+	0.745698i	0.996919	−	0.0784393i	$-0.0249937\pi$
$641$	10.9001	+	18.8796i	0.430529	+	0.745698i	−0.566390	+	0.824137i	$0.691660\pi$
$642$	−4.28194	+	1.52291i	−0.168994	+	0.0601046i
$643$	−10.1778	−	5.87618i	−0.401375	−	0.231734i	0.285702	−	0.958318i	$-0.407773\pi$
$643$	−10.1778	−	5.87618i	−0.401375	−	0.231734i	−0.687077	+	0.726585i	$0.741107\pi$
$644$	37.6531	+	21.7390i	1.48374	+	0.856637i
$645$	2.86503	−	15.5773i	0.112810	−	0.613356i
$646$	0.500325	+	0.866589i	0.0196850	+	0.0340955i
$647$	−14.5742			−0.572970			−0.286485	−	0.958085i	$-0.592487\pi$
$647$	−14.5742			−0.572970			−0.286485	+	0.958085i	$0.592487\pi$
$648$	−6.29030	+	7.06349i	−0.247106	+	0.277480i
$649$	−5.46258			−0.214425
$650$	0.952001	+	0.155101i	0.0373406	+	0.00608357i
$651$	−30.9510	−	5.69262i	−1.21307	−	0.223111i
$652$	−33.4059	−	19.2869i	−1.30828	−	0.755334i
$653$	11.0634	−	19.1624i	0.432944	−	0.749881i	−0.564181	−	0.825651i	$-0.690808\pi$
$653$	11.0634	−	19.1624i	0.432944	−	0.749881i	0.997125	+	0.0757697i	$0.0241414\pi$
$654$	−2.28408	−	6.42209i	−0.0893147	−	0.251124i
$655$	−8.28908	+	4.78570i	−0.323881	+	0.186993i
$656$			5.05754i			0.197464i
$657$	−6.62722	+	17.4068i	−0.258552	+	0.679104i
$658$			13.2806i			0.517733i
$659$	−16.5680	−	28.6966i	−0.645397	−	1.11786i	−0.984210	−	0.177006i	$-0.943359\pi$
$659$	−16.5680	−	28.6966i	−0.645397	−	1.11786i	0.338813	−	0.940854i	$-0.389975\pi$
$660$	−10.3336	+	12.1326i	−0.402233	+	0.472262i
$661$	12.5256	+	7.23168i	0.487191	+	0.281280i	0.723408	−	0.690421i	$-0.242574\pi$
$661$	12.5256	+	7.23168i	0.487191	+	0.281280i	−0.236218	+	0.971700i	$0.575908\pi$
$662$	−4.45397	+	7.71451i	−0.173109	+	0.299833i
$663$	−27.6010	+	5.02842i	−1.07194	+	0.195288i
$664$	4.44178	+	7.69339i	0.172375	+	0.298561i
$665$		−	3.18043i		−	0.123332i
$666$	0.182599	+	1.13280i	0.00707558	+	0.0438952i
$667$	−20.3175			−0.786698
$668$	30.5872	−	17.6595i	1.18345	−	0.683268i
$669$	−7.87155	+	2.79959i	−0.304332	+	0.108239i
$670$	−2.81790	−	1.62692i	−0.108865	−	0.0628533i
$671$	42.0398	+	24.2717i	1.62293	+	0.936999i
$672$	19.9011	+	3.66027i	0.767701	+	0.141198i
$673$	−5.87759	−	10.1803i	−0.226565	−	0.392421i	0.730223	−	0.683209i	$-0.239416\pi$
$673$	−5.87759	−	10.1803i	−0.226565	−	0.392421i	−0.956788	+	0.290787i	$0.906083\pi$
$674$			7.60305i			0.292859i
$675$	−0.114685	+	5.19489i	−0.00441421	+	0.199951i
$676$	4.99517	+	24.5669i	0.192122	+	0.944883i
$677$	5.78307	+	10.0166i	0.222262	+	0.384968i	0.955494	−	0.295009i	$-0.0953228\pi$
$677$	5.78307	+	10.0166i	0.222262	+	0.384968i	−0.733233	+	0.679978i	$0.761989\pi$
$678$	−1.20204	+	6.53557i	−0.0461643	+	0.250997i
$679$	27.2610	−	47.2175i	1.04618	−	1.81204i
$680$	−2.36063	+	4.08872i	−0.0905259	+	0.156795i
$681$	−42.4087	+	15.0831i	−1.62511	+	0.577986i
$682$	−5.25799	+	3.03570i	−0.201339	+	0.116243i
$683$		−	8.58495i		−	0.328494i	−0.986419	−	0.164247i	$-0.947481\pi$
$683$		−	8.58495i		−	0.328494i	0.986419	−	0.164247i	$-0.0525194\pi$
$684$	3.04163	+	3.73515i	0.116300	+	0.142817i
$685$	11.9399			0.456202
$686$	0.301903	+	0.522911i	0.0115267	+	0.0199648i
$687$	26.7068	+	22.7466i	1.01893	+	0.867836i
$688$	16.3489	−	28.3172i	0.623298	−	1.07958i
$689$	−28.1397	+	10.6593i	−1.07204	+	0.406085i
$690$	1.77332	−	2.08205i	0.0675090	−	0.0792624i
$691$	11.7004	−	6.75524i	0.445105	−	0.256981i	−0.260656	−	0.965432i	$-0.583939\pi$
$691$	11.7004	−	6.75524i	0.445105	−	0.256981i	0.705761	+	0.708450i	$0.250605\pi$
$692$	32.7278			1.24412
$693$	42.3971	−	34.5251i	1.61053	−	1.31150i
$694$		−	7.74524i		−	0.294005i
$695$	−10.2883	+	5.93993i	−0.390256	+	0.225315i
$696$	−5.90360	+	2.09967i	−0.223775	+	0.0795879i
$697$	5.50288	+	3.17709i	0.208436	+	0.120341i
$698$	0.339392	−	0.587844i	0.0128462	−	0.0222502i
$699$	7.70288	+	1.41674i	0.291350	+	0.0535860i
$700$	6.37935	−	3.68312i	0.241117	−	0.139209i
$701$	31.6071			1.19378			0.596892	−	0.802321i	$-0.296402\pi$
$701$	31.6071			1.19378			0.596892	+	0.802321i	$0.296402\pi$
$702$	4.72501	−	1.67154i	0.178334	−	0.0630881i
$703$	1.19040			0.0448968
$704$	−26.1695	+	15.1090i	−0.986299	+	0.569440i
$705$	−22.1391	−	4.07190i	−0.833807	−	0.153356i
$706$	0.689897	−	1.19494i	0.0259646	−	0.0449721i
$707$	−28.0076	−	16.1702i	−1.05333	−	0.608142i
$708$	−3.60298	+	1.28144i	−0.135408	+	0.0481593i
$709$	21.4899	−	12.4072i	0.807069	−	0.465962i	−0.0388678	−	0.999244i	$-0.512375\pi$
$709$	21.4899	−	12.4072i	0.807069	−	0.465962i	0.845937	+	0.533283i	$0.179042\pi$
$710$		−	0.300313i		−	0.0112705i
$711$	6.88971	+	42.7422i	0.258384	+	1.60296i
$712$	6.17634			0.231468
$713$	−24.3138	+	14.0376i	−0.910559	+	0.525711i
$714$	5.15569	−	6.05329i	0.192947	−	0.226539i
$715$	16.0877	−	6.09398i	0.601644	−	0.227902i
$716$	−7.87157	+	13.6340i	−0.294174	+	0.509525i
$717$	7.40502	+	6.30697i	0.276545	+	0.235538i
$718$	1.60074	+	2.77256i	0.0597390	+	0.103471i
$719$	−52.7117			−1.96582			−0.982908	−	0.184097i	$-0.941064\pi$
$719$	−52.7117			−1.96582			−0.982908	+	0.184097i	$0.941064\pi$
$720$	−3.81684	+	10.0252i	−0.142245	+	0.373616i
$721$			47.1664i			1.75657i
$722$	4.24127	−	2.44870i	0.157844	−	0.0911312i
$723$	24.2054	−	8.60889i	0.900208	−	0.320168i
$724$	−8.52060	+	14.7581i	−0.316666	+	0.548481i
$725$	−1.72114	+	2.98110i	−0.0639216	+	0.110715i
$726$	0.986126	−	5.36162i	0.0365986	−	0.198988i
$727$	−23.5424	−	40.7766i	−0.873140	−	1.51232i	−0.858732	−	0.512426i	$-0.828747\pi$
$727$	−23.5424	−	40.7766i	−0.873140	−	1.51232i	−0.0144080	−	0.999896i	$-0.504586\pi$
$728$	−11.2080	−	9.15840i	−0.415395	−	0.339433i
$729$	12.4549	+	23.9557i	0.461294	+	0.887247i
$730$		−	1.66091i		−	0.0614730i
$731$	−20.5404	−	35.5770i	−0.759714	−	1.31586i
$732$	33.4222	+	6.14711i	1.23532	+	0.227204i
$733$	26.6295	+	15.3746i	0.983585	+	0.567873i	0.903350	−	0.428903i	$-0.141100\pi$
$733$	26.6295	+	15.3746i	0.983585	+	0.567873i	0.0802342	+	0.996776i	$0.474433\pi$
$734$	−4.02644	−	2.32466i	−0.148619	−	0.0858049i
$735$	−12.3876	+	4.40579i	−0.456925	+	0.162510i
$736$	15.6334	−	9.02596i	0.576255	−	0.332701i
$737$	−58.0334			−2.13769
$738$	−1.06086	−	0.403897i	−0.0390508	−	0.0148676i
$739$			26.2948i			0.967271i	0.875269	+	0.483636i	$0.160684\pi$
$739$			26.2948i			0.967271i	−0.875269	+	0.483636i	$0.839316\pi$
$740$	1.37855	+	2.38772i	0.0506766	+	0.0877745i
$741$	−0.931951	−	5.11548i	−0.0342361	−	0.187922i
$742$	4.26411	−	7.38566i	0.156540	−	0.271136i
$743$	40.9295	+	23.6307i	1.50156	+	0.866926i	0.999998	+	0.00180359i	$0.000574101\pi$
$743$	40.9295	+	23.6307i	1.50156	+	0.866926i	0.501561	+	0.865122i	$0.332759\pi$
$744$	−5.61409	+	6.59151i	−0.205823	+	0.241657i
$745$	−6.60442	−	11.4392i	−0.241967	−	0.419100i
$746$		−	2.78805i		−	0.102078i
$747$	25.0360	−	4.03561i	0.916018	−	0.147655i
$748$			41.3357i			1.51138i
$749$	32.4460	−	18.7327i	1.18555	−	0.684478i
$750$	−0.155269	−	0.436567i	−0.00566963	−	0.0159412i
$751$	4.66988	−	8.08847i	0.170406	−	0.295153i	−0.768156	−	0.640263i	$-0.778825\pi$
$751$	4.66988	−	8.08847i	0.170406	−	0.295153i	0.938562	+	0.345111i	$0.112159\pi$
$752$	−40.2456	−	23.2358i	−1.46760	−	0.847322i
$753$	30.1406	+	5.54355i	1.09838	+	0.202018i
$754$	3.27706	+	0.533902i	0.119343	+	0.0194436i
$755$	1.82823			0.0665361
$756$	19.8650	−	32.7176i	0.722483	−	1.18993i
$757$	6.34739			0.230700			0.115350	−	0.993325i	$-0.463201\pi$
$757$	6.34739			0.230700			0.115350	+	0.993325i	$0.463201\pi$
$758$	−2.93064	−	5.07602i	−0.106446	−	0.184369i
$759$	8.82337	−	47.9731i	0.320268	−	1.74131i
$760$	−0.757791	−	0.437511i	−0.0274880	−	0.0158702i
$761$	−3.37436	−	1.94819i	−0.122321	−	0.0706218i	0.437591	−	0.899174i	$-0.355832\pi$
$761$	−3.37436	−	1.94819i	−0.122321	−	0.0706218i	−0.559912	+	0.828552i	$0.689165\pi$
$762$	−3.70624	+	1.31816i	−0.134263	+	0.0477519i
$763$	28.0955	+	48.6628i	1.01713	+	1.76171i
$764$	12.0047			0.434315
$765$	8.51022	+	10.4506i	0.307688	+	0.377842i
$766$	8.56676			0.309530
$767$	4.07421	+	0.663776i	0.147111	+	0.0239676i
$768$	−11.8786	+	13.9467i	−0.428633	+	0.503258i
$769$	−16.9967	−	9.81305i	−0.612916	−	0.353867i	0.161190	−	0.986923i	$-0.448467\pi$
$769$	−16.9967	−	9.81305i	−0.612916	−	0.353867i	−0.774106	+	0.633056i	$0.781800\pi$
$770$	−2.43782	+	4.22244i	−0.0878531	+	0.152166i
$771$	−9.21148	+	10.8152i	−0.331743	+	0.389500i
$772$	−6.75615	+	3.90067i	−0.243159	+	0.140388i
$773$			41.6088i			1.49656i	0.663381	+	0.748282i	$0.269121\pi$
$773$			41.6088i			1.49656i	−0.663381	+	0.748282i	$0.730879\pi$
$774$	4.63412	+	5.69074i	0.166570	+	0.204549i

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:	\( N \)	\(=\)	\( 585 = 3^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	585.bt (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.231678 - 0.133759i) q^{2} +(1.70348 + 0.313309i) q^{3} +(-0.964217 + 1.67007i) q^{4} +(-0.866025 - 0.500000i) q^{5} +(0.436567 - 0.155269i) q^{6} +(-3.30805 + 1.90990i) q^{7} +1.05093i q^{8} +(2.80367 + 1.06743i) q^{9} +O(q^{10})\)	\(q+(0.231678 - 0.133759i) q^{2} +(1.70348 + 0.313309i) q^{3} +(-0.964217 + 1.67007i) q^{4} +(-0.866025 - 0.500000i) q^{5} +(0.436567 - 0.155269i) q^{6} +(-3.30805 + 1.90990i) q^{7} +1.05093i q^{8} +(2.80367 + 1.06743i) q^{9} -0.267519 q^{10} +(-4.13207 + 2.38565i) q^{11} +(-2.16577 + 2.54283i) q^{12} +(3.37175 - 1.27721i) q^{13} +(-0.510935 + 0.884965i) q^{14} +(-1.31860 - 1.12307i) q^{15} +(-1.78786 - 3.09667i) q^{16} -4.49245 q^{17} +(0.792329 - 0.127717i) q^{18} -0.832616i q^{19} +(1.67007 - 0.964217i) q^{20} +(-6.23357 + 2.21703i) q^{21} +(-0.638207 + 1.10541i) q^{22} +(-2.95117 + 5.11158i) q^{23} +(-0.329266 + 1.79024i) q^{24} +(0.500000 + 0.866025i) q^{25} +(0.610322 - 0.746907i) q^{26} +(4.44156 + 2.69676i) q^{27} -7.36623i q^{28} +(1.72114 + 2.98110i) q^{29} +(-0.455713 - 0.0838162i) q^{30} +(4.11935 + 2.37831i) q^{31} +(-2.64868 - 1.52922i) q^{32} +(-7.78634 + 2.76929i) q^{33} +(-1.04080 + 0.600908i) q^{34} +3.81980 q^{35} +(-4.48604 + 3.65310i) q^{36} +1.42971i q^{37} +(-0.111370 - 0.192899i) q^{38} +(6.14387 - 1.11931i) q^{39} +(0.525465 - 0.910132i) q^{40} +(-1.22492 - 0.707206i) q^{41} +(-1.14763 + 1.34744i) q^{42} +(4.57220 + 7.91929i) q^{43} -9.20114i q^{44} +(-1.89434 - 2.32626i) q^{45} +1.57899i q^{46} +(11.2552 - 6.49820i) q^{47} +(-2.07537 - 5.83526i) q^{48} +(3.79544 - 6.57390i) q^{49} +(0.231678 + 0.133759i) q^{50} +(-7.65279 - 1.40753i) q^{51} +(-1.11806 + 6.86258i) q^{52} -8.34571 q^{53} +(1.38973 + 0.0306803i) q^{54} +4.77130 q^{55} +(-2.00717 - 3.47652i) q^{56} +(0.260866 - 1.41834i) q^{57} +(0.797502 + 0.460438i) q^{58} +(0.991497 + 0.572441i) q^{59} +(3.14703 - 1.11927i) q^{60} +(-5.08702 - 8.81097i) q^{61} +1.27248 q^{62} +(-11.3134 + 1.82363i) q^{63} +6.33326 q^{64} +(-3.55863 - 0.579777i) q^{65} +(-1.43351 + 1.68308i) q^{66} +(10.5335 + 6.08150i) q^{67} +(4.33170 - 7.50272i) q^{68} +(-6.62876 + 7.78283i) q^{69} +(0.884965 - 0.510935i) q^{70} +1.12258i q^{71} +(-1.12180 + 2.94647i) q^{72} +6.20857i q^{73} +(0.191238 + 0.331233i) q^{74} +(0.580405 + 1.63191i) q^{75} +(1.39053 + 0.802822i) q^{76} +(9.11272 - 15.7837i) q^{77} +(1.27368 - 1.08112i) q^{78} +(7.21565 + 12.4979i) q^{79} +3.57572i q^{80} +(6.72118 + 5.98546i) q^{81} -0.378382 q^{82} +(7.32055 - 4.22652i) q^{83} +(2.30791 - 12.5482i) q^{84} +(3.89058 + 2.24622i) q^{85} +(2.11856 + 1.22315i) q^{86} +(1.99792 + 5.61750i) q^{87} +(-2.50715 - 4.34252i) q^{88} -5.87702i q^{89} +(-0.750036 - 0.285558i) q^{90} +(-8.71456 + 10.6648i) q^{91} +(-5.69113 - 9.85733i) q^{92} +(6.27207 + 5.34202i) q^{93} +(1.73839 - 3.01098i) q^{94} +(-0.416308 + 0.721066i) q^{95} +(-4.03285 - 3.43484i) q^{96} +(-12.3612 + 7.13676i) q^{97} -2.03070i q^{98} +(-14.1315 + 2.27789i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 108 q - 6 q^{3} + 52 q^{4} - 14 q^{9}+O(q^{10}) \) 108 * q - 6 * q^3 + 52 * q^4 - 14 * q^9	\( 108 q - 6 q^{3} + 52 q^{4} - 14 q^{9} - 8 q^{10} - 36 q^{12} - 4 q^{13} - 8 q^{14} - 64 q^{16} + 36 q^{17} + 24 q^{22} - 22 q^{23} + 54 q^{25} + 40 q^{26} + 48 q^{27} - 16 q^{29} + 20 q^{30} - 40 q^{35} - 76 q^{36} - 12 q^{38} + 26 q^{39} - 52 q^{42} - 6 q^{43} - 68 q^{48} + 58 q^{49} + 34 q^{51} + 22 q^{52} - 116 q^{53} + 24 q^{55} + 40 q^{56} + 18 q^{61} + 152 q^{62} - 216 q^{64} + 2 q^{65} - 72 q^{66} - 134 q^{69} + 32 q^{74} + 40 q^{77} - 34 q^{78} + 18 q^{79} + 34 q^{81} + 88 q^{82} + 60 q^{87} + 8 q^{90} + 16 q^{91} + 176 q^{92} - 76 q^{94} - 56 q^{95}+O(q^{100}) \) 108 * q - 6 * q^3 + 52 * q^4 - 14 * q^9 - 8 * q^10 - 36 * q^12 - 4 * q^13 - 8 * q^14 - 64 * q^16 + 36 * q^17 + 24 * q^22 - 22 * q^23 + 54 * q^25 + 40 * q^26 + 48 * q^27 - 16 * q^29 + 20 * q^30 - 40 * q^35 - 76 * q^36 - 12 * q^38 + 26 * q^39 - 52 * q^42 - 6 * q^43 - 68 * q^48 + 58 * q^49 + 34 * q^51 + 22 * q^52 - 116 * q^53 + 24 * q^55 + 40 * q^56 + 18 * q^61 + 152 * q^62 - 216 * q^64 + 2 * q^65 - 72 * q^66 - 134 * q^69 + 32 * q^74 + 40 * q^77 - 34 * q^78 + 18 * q^79 + 34 * q^81 + 88 * q^82 + 60 * q^87 + 8 * q^90 + 16 * q^91 + 176 * q^92 - 76 * q^94 - 56 * q^95

Introduction

L-functions

Modular forms

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