LMFDB - Embedded newform 483.2.d.d.461.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [483,2,Mod(461,483)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(483, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1, 0]))

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

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

chi := DirichletCharacter("483.461");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 483 = 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	483.d (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$3.85677441763$
Analytic rank:	$0$
Dimension:	$44$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			461.2
Character	$\chi$	$=$	483.461
Dual form			483.2.d.d.461.44

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.69219i q^{2} +(0.983586 - 1.42568i) q^{3} -5.24788 q^{4} +3.85613 q^{5} +(-3.83820 - 2.64800i) q^{6} +(2.38743 - 1.14025i) q^{7} +8.74391i q^{8} +(-1.06512 - 2.80455i) q^{9} +O(q^{10})$	\(q-2.69219i q^{2} +(0.983586 - 1.42568i) q^{3} -5.24788 q^{4} +3.85613 q^{5} +(-3.83820 - 2.64800i) q^{6} +(2.38743 - 1.14025i) q^{7} +8.74391i q^{8} +(-1.06512 - 2.80455i) q^{9} -10.3814i q^{10} -0.326399i q^{11} +(-5.16174 + 7.48179i) q^{12} +1.38191i q^{13} +(-3.06977 - 6.42742i) q^{14} +(3.79283 - 5.49760i) q^{15} +13.0445 q^{16} -5.56290 q^{17} +(-7.55039 + 2.86750i) q^{18} +1.06769i q^{19} -20.2365 q^{20} +(0.722611 - 4.52524i) q^{21} -0.878727 q^{22} +1.00000i q^{23} +(12.4660 + 8.60038i) q^{24} +9.86975 q^{25} +3.72037 q^{26} +(-5.04603 - 1.24000i) q^{27} +(-12.5290 + 5.98390i) q^{28} +9.99790i q^{29} +(-14.8006 - 10.2110i) q^{30} +0.901500i q^{31} -17.6304i q^{32} +(-0.465339 - 0.321041i) q^{33} +14.9764i q^{34} +(9.20625 - 4.39696i) q^{35} +(5.58962 + 14.7180i) q^{36} +3.32883 q^{37} +2.87442 q^{38} +(1.97016 + 1.35923i) q^{39} +33.7177i q^{40} +2.51407 q^{41} +(-12.1828 - 1.94541i) q^{42} -1.16716 q^{43} +1.71290i q^{44} +(-4.10724 - 10.8147i) q^{45} +2.69219 q^{46} -9.48964 q^{47} +(12.8304 - 18.5973i) q^{48} +(4.39965 - 5.44454i) q^{49} -26.5712i q^{50} +(-5.47159 + 7.93091i) q^{51} -7.25211i q^{52} +9.04306i q^{53} +(-3.33832 + 13.5849i) q^{54} -1.25864i q^{55} +(9.97025 + 20.8755i) q^{56} +(1.52218 + 1.05016i) q^{57} +26.9162 q^{58} +0.627554 q^{59} +(-19.9043 + 28.8508i) q^{60} +2.29561i q^{61} +2.42701 q^{62} +(-5.74079 - 5.48118i) q^{63} -21.3754 q^{64} +5.32883i q^{65} +(-0.864303 + 1.25278i) q^{66} +8.95895 q^{67} +29.1935 q^{68} +(1.42568 + 0.983586i) q^{69} +(-11.8374 - 24.7850i) q^{70} -7.51156i q^{71} +(24.5228 - 9.31330i) q^{72} -0.951840i q^{73} -8.96185i q^{74} +(9.70774 - 14.0711i) q^{75} -5.60310i q^{76} +(-0.372176 - 0.779254i) q^{77} +(3.65930 - 5.30405i) q^{78} -6.01142 q^{79} +50.3013 q^{80} +(-6.73104 + 5.97437i) q^{81} -6.76836i q^{82} +4.55771 q^{83} +(-3.79218 + 23.7479i) q^{84} -21.4513 q^{85} +3.14221i q^{86} +(14.2538 + 9.83379i) q^{87} +2.85400 q^{88} -14.4166 q^{89} +(-29.1153 + 11.0575i) q^{90} +(1.57573 + 3.29922i) q^{91} -5.24788i q^{92} +(1.28525 + 0.886702i) q^{93} +25.5479i q^{94} +4.11715i q^{95} +(-25.1353 - 17.3410i) q^{96} -6.39369i q^{97} +(-14.6577 - 11.8447i) q^{98} +(-0.915402 + 0.347653i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q - 76 q^{4} - 8 q^{7} + 20 q^{9}+O(q^{10}) $ 44 * q - 76 * q^4 - 8 * q^7 + 20 * q^9	$ 44 q - 76 q^{4} - 8 q^{7} + 20 q^{9} + 4 q^{15} + 92 q^{16} + 4 q^{18} - 22 q^{21} + 12 q^{22} + 16 q^{25} + 16 q^{28} - 32 q^{30} - 112 q^{37} + 4 q^{39} - 12 q^{42} - 68 q^{43} + 4 q^{46} + 44 q^{49} + 32 q^{51} + 16 q^{57} + 28 q^{58} - 44 q^{60} - 10 q^{63} - 16 q^{64} + 108 q^{67} - 60 q^{70} + 112 q^{72} - 48 q^{78} + 40 q^{79} - 4 q^{81} - 26 q^{84} - 108 q^{85} + 8 q^{88} + 24 q^{91} + 4 q^{93} + 4 q^{99}+O(q^{100}) $ 44 * q - 76 * q^4 - 8 * q^7 + 20 * q^9 + 4 * q^15 + 92 * q^16 + 4 * q^18 - 22 * q^21 + 12 * q^22 + 16 * q^25 + 16 * q^28 - 32 * q^30 - 112 * q^37 + 4 * q^39 - 12 * q^42 - 68 * q^43 + 4 * q^46 + 44 * q^49 + 32 * q^51 + 16 * q^57 + 28 * q^58 - 44 * q^60 - 10 * q^63 - 16 * q^64 + 108 * q^67 - 60 * q^70 + 112 * q^72 - 48 * q^78 + 40 * q^79 - 4 * q^81 - 26 * q^84 - 108 * q^85 + 8 * q^88 + 24 * q^91 + 4 * q^93 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/483\mathbb{Z}\right)^\times$.

$n$	$323$	$346$	$442$
$\chi(n)$	$-1$	$-1$	$1$

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 $

$2$		−	2.69219i		−	1.90367i	−0.306618	−	0.951833i	$-0.599198\pi$
$2$		−	2.69219i		−	1.90367i	0.306618	−	0.951833i	$-0.400802\pi$
$3$	0.983586	−	1.42568i	0.567873	−	0.823116i
$3$	0.983586	−	1.42568i	0.567873	−	0.823116i
$4$	−5.24788			−2.62394
$5$	3.85613			1.72451			0.862257	−	0.506471i	$-0.169050\pi$
$5$	3.85613			1.72451			0.862257	+	0.506471i	$0.169050\pi$
$6$	−3.83820	−	2.64800i	−1.56694	−	1.08104i
$7$	2.38743	−	1.14025i	0.902364	−	0.430974i
$7$	2.38743	−	1.14025i	0.902364	−	0.430974i
$8$			8.74391i			3.09144i
$9$	−1.06512	−	2.80455i	−0.355040	−	0.934851i
$10$		−	10.3814i		−	3.28290i
$11$		−	0.326399i		−	0.0984129i	−0.998789	−	0.0492064i	$-0.984331\pi$
$11$		−	0.326399i		−	0.0984129i	0.998789	−	0.0492064i	$-0.0156692\pi$
$12$	−5.16174	+	7.48179i	−1.49007	+	2.15981i
$13$			1.38191i			0.383273i	0.981466	+	0.191637i	$0.0613795\pi$
$13$			1.38191i			0.383273i	−0.981466	+	0.191637i	$0.938620\pi$
$14$	−3.06977	−	6.42742i	−0.820431	−	1.71780i
$15$	3.79283	−	5.49760i	0.979306	−	1.41948i
$16$	13.0445			3.26112
$17$	−5.56290			−1.34920			−0.674601	−	0.738182i	$-0.735684\pi$
$17$	−5.56290			−1.34920			−0.674601	+	0.738182i	$0.735684\pi$
$18$	−7.55039	+	2.86750i	−1.77964	+	0.675877i
$19$			1.06769i			0.244945i	0.992472	+	0.122472i	$0.0390823\pi$
$19$			1.06769i			0.244945i	−0.992472	+	0.122472i	$0.960918\pi$
$20$	−20.2365			−4.52502
$21$	0.722611	−	4.52524i	0.157687	−	0.987489i
$22$	−0.878727			−0.187345
$23$			1.00000i			0.208514i
$23$			1.00000i			0.208514i
$24$	12.4660	+	8.60038i	2.54461	+	1.75555i
$25$	9.86975			1.97395
$26$	3.72037			0.729624
$27$	−5.04603	−	1.24000i	−0.971109	−	0.238638i
$28$	−12.5290	+	5.98390i	−2.36775	+	1.13085i
$29$			9.99790i			1.85656i	0.371877	+	0.928282i	$0.378714\pi$
$29$			9.99790i			1.85656i	−0.371877	+	0.928282i	$0.621286\pi$
$30$	−14.8006	−	10.2110i	−2.70221	−	1.86427i
$31$			0.901500i			0.161914i	0.996718	+	0.0809571i	$0.0257977\pi$
$31$			0.901500i			0.161914i	−0.996718	+	0.0809571i	$0.974202\pi$
$32$		−	17.6304i		−	3.11665i
$33$	−0.465339	−	0.321041i	−0.0810052	−	0.0558861i
$34$			14.9764i			2.56843i
$35$	9.20625	−	4.39696i	1.55614	−	0.743222i
$36$	5.58962	+	14.7180i	0.931603	+	2.45299i
$37$	3.32883			0.547257			0.273628	−	0.961835i	$-0.411776\pi$
$37$	3.32883			0.547257			0.273628	+	0.961835i	$0.411776\pi$
$38$	2.87442			0.466292
$39$	1.97016	+	1.35923i	0.315478	+	0.217651i
$40$			33.7177i			5.33123i
$41$	2.51407			0.392632			0.196316	−	0.980541i	$-0.437102\pi$
$41$	2.51407			0.392632			0.196316	+	0.980541i	$0.437102\pi$
$42$	−12.1828	−	1.94541i	−1.87985	−	0.300183i
$43$	−1.16716			−0.177990			−0.0889949	−	0.996032i	$-0.528365\pi$
$43$	−1.16716			−0.177990			−0.0889949	+	0.996032i	$0.528365\pi$
$44$			1.71290i			0.258230i
$45$	−4.10724	−	10.8147i	−0.612271	−	1.61216i
$46$	2.69219			0.396942
$47$	−9.48964			−1.38421			−0.692103	−	0.721799i	$-0.743316\pi$
$47$	−9.48964			−1.38421			−0.692103	+	0.721799i	$0.743316\pi$
$48$	12.8304	−	18.5973i	1.85191	−	2.68428i
$49$	4.39965	−	5.44454i	0.628522	−	0.777792i
$50$		−	26.5712i		−	3.75774i
$51$	−5.47159	+	7.93091i	−0.766176	+	1.11055i
$52$		−	7.25211i		−	1.00569i
$53$			9.04306i			1.24216i	0.783747	+	0.621080i	$0.213306\pi$
$53$			9.04306i			1.24216i	−0.783747	+	0.621080i	$0.786694\pi$
$54$	−3.33832	+	13.5849i	−0.454287	+	1.84867i
$55$		−	1.25864i		−	0.169714i
$56$	9.97025	+	20.8755i	1.33233	+	2.78960i
$57$	1.52218	+	1.05016i	0.201618	+	0.139098i
$58$	26.9162			3.53428
$59$	0.627554			0.0817006			0.0408503	−	0.999165i	$-0.486993\pi$
$59$	0.627554			0.0817006			0.0408503	+	0.999165i	$0.486993\pi$
$60$	−19.9043	+	28.8508i	−2.56964	+	3.72462i
$61$			2.29561i			0.293923i	0.989142	+	0.146961i	$0.0469493\pi$
$61$			2.29561i			0.293923i	−0.989142	+	0.146961i	$0.953051\pi$
$62$	2.42701			0.308230
$63$	−5.74079	−	5.48118i	−0.723272	−	0.690563i
$64$	−21.3754			−2.67193
$65$			5.32883i			0.660960i
$66$	−0.864303	+	1.25278i	−0.106388	+	0.154207i
$67$	8.95895			1.09451			0.547255	−	0.836966i	$-0.315673\pi$
$67$	8.95895			1.09451			0.547255	+	0.836966i	$0.315673\pi$
$68$	29.1935			3.54023
$69$	1.42568	+	0.983586i	0.171632	+	0.118410i
$70$	−11.8374	−	24.7850i	−1.41484	−	2.96237i
$71$		−	7.51156i		−	0.891458i	−0.895168	−	0.445729i	$-0.852944\pi$
$71$		−	7.51156i		−	0.891458i	0.895168	−	0.445729i	$-0.147056\pi$
$72$	24.5228	−	9.31330i	2.89004	−	1.09758i
$73$		−	0.951840i		−	0.111404i	−0.998447	−	0.0557022i	$-0.982260\pi$
$73$		−	0.951840i		−	0.111404i	0.998447	−	0.0557022i	$-0.0177397\pi$
$74$		−	8.96185i		−	1.04179i
$75$	9.70774	−	14.0711i	1.12095	−	1.62479i
$76$		−	5.60310i		−	0.642720i
$77$	−0.372176	−	0.779254i	−0.0424134	−	0.0888042i
$78$	3.65930	−	5.30405i	0.414334	−	0.600565i
$79$	−6.01142			−0.676337			−0.338169	−	0.941086i	$-0.609807\pi$
$79$	−6.01142			−0.676337			−0.338169	+	0.941086i	$0.609807\pi$
$80$	50.3013			5.62385
$81$	−6.73104	+	5.97437i	−0.747894	+	0.663819i
$82$		−	6.76836i		−	0.747440i
$83$	4.55771			0.500273			0.250137	−	0.968211i	$-0.419524\pi$
$83$	4.55771			0.500273			0.250137	+	0.968211i	$0.419524\pi$
$84$	−3.79218	+	23.7479i	−0.413760	+	2.59111i
$85$	−21.4513			−2.32672
$86$			3.14221i			0.338833i
$87$	14.2538	+	9.83379i	1.52817	+	1.05429i
$88$	2.85400			0.304237
$89$	−14.4166			−1.52815			−0.764076	−	0.645126i	$-0.776805\pi$
$89$	−14.4166			−1.52815			−0.764076	+	0.645126i	$0.776805\pi$
$90$	−29.1153	+	11.0575i	−3.06902	+	1.16556i
$91$	1.57573	+	3.29922i	0.165181	+	0.345852i
$92$		−	5.24788i		−	0.547129i
$93$	1.28525	+	0.886702i	0.133274	+	0.0919468i
$94$			25.5479i			2.63507i
$95$			4.11715i			0.422410i
$96$	−25.1353	−	17.3410i	−2.56536	−	1.76986i
$97$		−	6.39369i		−	0.649181i	−0.945855	−	0.324590i	$-0.894774\pi$
$97$		−	6.39369i		−	0.649181i	0.945855	−	0.324590i	$-0.105226\pi$
$98$	−14.6577	−	11.8447i	−1.48065	−	1.19650i
$99$	−0.915402	+	0.347653i	−0.0920014	+	0.0349405i
$100$	−51.7953			−5.17953
$101$	−15.0876			−1.50127			−0.750634	−	0.660719i	$-0.770252\pi$
$101$	−15.0876			−1.50127			−0.750634	+	0.660719i	$0.770252\pi$
$102$	21.3515	+	14.7306i	2.11412	+	1.45854i
$103$		−	10.5198i		−	1.03655i	−0.855215	−	0.518273i	$-0.826575\pi$
$103$		−	10.5198i		−	1.03655i	0.855215	−	0.518273i	$-0.173425\pi$
$104$	−12.0833			−1.18487
$105$	2.78648	−	17.4499i	0.271933	−	1.70294i
$106$	24.3456			2.36466
$107$			3.05655i			0.295487i	0.989026	+	0.147744i	$0.0472011\pi$
$107$			3.05655i			0.295487i	−0.989026	+	0.147744i	$0.952799\pi$
$108$	26.4810	+	6.50738i	2.54813	+	0.626173i
$109$	−12.0190			−1.15121			−0.575606	−	0.817727i	$-0.695234\pi$
$109$	−12.0190			−1.15121			−0.575606	+	0.817727i	$0.695234\pi$
$110$	−3.38849			−0.323079
$111$	3.27419	−	4.74585i	0.310773	−	0.450456i
$112$	31.1428	−	14.8740i	2.94272	−	1.40546i
$113$		−	8.12521i		−	0.764355i	−0.924089	−	0.382178i	$-0.875174\pi$
$113$		−	8.12521i		−	0.764355i	0.924089	−	0.382178i	$-0.124826\pi$
$114$	2.82724	−	4.09800i	0.264795	−	0.383813i
$115$			3.85613i			0.359586i
$116$		−	52.4678i		−	4.87151i
$117$	3.87565	−	1.47190i	0.358304	−	0.136077i
$118$		−	1.68949i		−	0.155531i
$119$	−13.2811	+	6.34311i	−1.21747	+	0.581472i
$120$	48.0705	+	33.1642i	4.38822	+	3.02746i
$121$	10.8935			0.990315
$122$	6.18021			0.559530
$123$	2.47280	−	3.58426i	0.222965	−	0.323182i
$124$		−	4.73096i		−	0.424853i
$125$	18.7784			1.67959
$126$	−14.7564	+	15.4553i	−1.31460	+	1.37687i
$127$	0.467510			0.0414848			0.0207424	−	0.999785i	$-0.493397\pi$
$127$	0.467510			0.0414848			0.0207424	+	0.999785i	$0.493397\pi$
$128$			22.2859i			1.96981i
$129$	−1.14800	+	1.66399i	−0.101076	+	0.146506i
$130$	14.3462			1.25825
$131$	16.5206			1.44341			0.721707	−	0.692198i	$-0.243358\pi$
$131$	16.5206			1.44341			0.721707	+	0.692198i	$0.243358\pi$
$132$	2.44205	+	1.68478i	0.212553	+	0.146642i
$133$	1.21743	+	2.54903i	0.105565	+	0.221029i
$134$		−	24.1192i		−	2.08358i
$135$	−19.4581	−	4.78161i	−1.67469	−	0.411535i
$136$		−	48.6415i		−	4.17098i
$137$		−	16.3534i		−	1.39717i	−0.715529	−	0.698583i	$-0.753814\pi$
$137$		−	16.3534i		−	1.39717i	0.715529	−	0.698583i	$-0.246186\pi$
$138$	2.64800	−	3.83820i	0.225413	−	0.326729i
$139$		−	10.2114i		−	0.866123i	−0.901364	−	0.433061i	$-0.857433\pi$
$139$		−	10.2114i		−	0.866123i	0.901364	−	0.433061i	$-0.142567\pi$
$140$	−48.3133	+	23.0747i	−4.08322	+	1.95017i
$141$	−9.33387	+	13.5292i	−0.786054	+	1.13936i
$142$	−20.2225			−1.69704
$143$	0.451054			0.0377190
$144$	−13.8939	−	36.5840i	−1.15783	−	3.04867i
$145$			38.5532i			3.20167i
$146$	−2.56253			−0.212077
$147$	−3.43473	−	11.6277i	−0.283292	−	0.959034i
$148$	−17.4693			−1.43597
$149$			11.6763i			0.956562i	0.878207	+	0.478281i	$0.158740\pi$
$149$			11.6763i			0.956562i	−0.878207	+	0.478281i	$0.841260\pi$
$150$	−37.8820	−	26.1351i	−3.09305	−	2.13392i
$151$	7.66343			0.623641			0.311820	−	0.950141i	$-0.399061\pi$
$151$	7.66343			0.623641			0.311820	+	0.950141i	$0.399061\pi$
$152$	−9.33577			−0.757231
$153$	5.92516	+	15.6015i	0.479020	+	1.26130i
$154$	−2.09790	+	1.00197i	−0.169054	+	0.0807410i
$155$			3.47630i			0.279223i
$156$	−10.3392	−	7.13307i	−0.827797	−	0.571103i
$157$		−	5.07418i		−	0.404964i	−0.979286	−	0.202482i	$-0.935099\pi$
$157$		−	5.07418i		−	0.404964i	0.979286	−	0.202482i	$-0.0649007\pi$
$158$			16.1839i			1.28752i
$159$	12.8925	+	8.89463i	1.02244	+	0.705390i
$160$		−	67.9852i		−	5.37470i
$161$	1.14025	+	2.38743i	0.0898644	+	0.188156i
$162$	16.0841	+	18.1212i	1.26369	+	1.42374i
$163$	9.44778			0.740007			0.370004	−	0.929030i	$-0.379356\pi$
$163$	9.44778			0.740007			0.370004	+	0.929030i	$0.379356\pi$
$164$	−13.1935			−1.03024
$165$	−1.79441	−	1.23798i	−0.139695	−	0.0963763i
$166$		−	12.2702i		−	0.952353i
$167$	13.9806			1.08185			0.540924	−	0.841071i	$-0.318075\pi$
$167$	13.9806			1.08185			0.540924	+	0.841071i	$0.318075\pi$
$168$	39.5683	+	6.31845i	3.05276	+	0.487479i
$169$	11.0903			0.853102
$170$			57.7509i			4.42929i
$171$	2.99439	−	1.13722i	0.228987	−	0.0869650i
$172$	6.12510			0.467035
$173$	−16.2527			−1.23567			−0.617833	−	0.786309i	$-0.711989\pi$
$173$	−16.2527			−1.23567			−0.617833	+	0.786309i	$0.711989\pi$
$174$	26.4744	−	38.3739i	2.00702	−	2.90912i
$175$	23.5633	−	11.2540i	1.78122	−	0.850722i
$176$		−	4.25770i		−	0.320937i
$177$	0.617253	−	0.894690i	0.0463956	−	0.0672491i
$178$			38.8121i			2.90909i
$179$		−	7.00290i		−	0.523421i	−0.965146	−	0.261711i	$-0.915713\pi$
$179$		−	7.00290i		−	0.523421i	0.965146	−	0.261711i	$-0.0842866\pi$
$180$	21.5543	+	56.7544i	1.60656	+	4.23022i
$181$			12.4835i			0.927892i	0.885863	+	0.463946i	$0.153567\pi$
$181$			12.4835i			0.927892i	−0.885863	+	0.463946i	$0.846433\pi$
$182$	8.88212	−	4.24215i	0.658387	−	0.314449i
$183$	3.27280	+	2.25793i	0.241932	+	0.166911i
$184$	−8.74391			−0.644610
$185$	12.8364			0.943752
$186$	2.38717	−	3.46013i	0.175036	−	0.253709i
$187$			1.81572i			0.132779i
$188$	49.8005			3.63208
$189$	−13.4610	+	2.79332i	−0.979141	+	0.203184i
$190$	11.0841			0.804128
$191$			10.7879i			0.780587i	0.920690	+	0.390294i	$0.127627\pi$
$191$			10.7879i			0.780587i	−0.920690	+	0.390294i	$0.872373\pi$
$192$	−21.0246	+	30.4745i	−1.51732	+	2.19931i
$193$	−12.6908			−0.913501			−0.456750	−	0.889595i	$-0.650987\pi$
$193$	−12.6908			−0.913501			−0.456750	+	0.889595i	$0.650987\pi$
$194$	−17.2130			−1.23582
$195$	7.59720	+	5.24136i	0.544047	+	0.375342i
$196$	−23.0889	+	28.5723i	−1.64920	+	2.04088i
$197$			4.54930i			0.324124i	0.986781	+	0.162062i	$0.0518145\pi$
$197$			4.54930i			0.324124i	−0.986781	+	0.162062i	$0.948185\pi$
$198$	0.935948	+	2.46444i	0.0665150	+	0.175140i
$199$		−	22.3655i		−	1.58545i	−0.609582	−	0.792723i	$-0.708663\pi$
$199$		−	22.3655i		−	1.58545i	0.609582	−	0.792723i	$-0.291337\pi$
$200$			86.3002i			6.10234i
$201$	8.81189	−	12.7726i	0.621543	−	0.900909i
$202$			40.6185i			2.85791i
$203$	11.4001	+	23.8693i	0.800132	+	1.67530i
$204$	28.7143	−	41.6205i	2.01040	−	2.91402i
$205$	9.69459			0.677100
$206$	−28.3213			−1.97324
$207$	2.80455	−	1.06512i	0.194930	−	0.0740309i
$208$			18.0263i			1.24990i
$209$	0.348492			0.0241057
$210$	−46.9785	−	7.50174i	−3.24183	−	0.517669i
$211$	13.0272			0.896826			0.448413	−	0.893826i	$-0.351989\pi$
$211$	13.0272			0.896826			0.448413	+	0.893826i	$0.351989\pi$
$212$		−	47.4569i		−	3.25935i
$213$	−10.7091	−	7.38826i	−0.733773	−	0.506235i
$214$	8.22880			0.562509
$215$	−4.50071			−0.306946
$216$	10.8425	−	44.1220i	0.737736	−	3.00212i
$217$	1.02794	+	2.15227i	0.0697809	+	0.146106i
$218$			32.3574i			2.19152i
$219$	−1.35702	−	0.936216i	−0.0916988	−	0.0632636i
$220$			6.60517i			0.445320i
$221$		−	7.68744i		−	0.517113i
$222$	−12.7767	−	8.81474i	−0.857517	−	0.591607i
$223$			7.09986i			0.475442i	0.971333	+	0.237721i	$0.0764004\pi$
$223$			7.09986i			0.475442i	−0.971333	+	0.237721i	$0.923600\pi$
$224$	−20.1031	−	42.0914i	−1.34320	−	2.81235i
$225$	−10.5125	−	27.6802i	−0.700830	−	1.84535i
$226$	−21.8746			−1.45508
$227$	13.4377			0.891893			0.445946	−	0.895060i	$-0.352867\pi$
$227$	13.4377			0.891893			0.445946	+	0.895060i	$0.352867\pi$
$228$	−7.98822	−	5.51113i	−0.529033	−	0.364984i
$229$			25.2317i			1.66736i	0.552251	+	0.833678i	$0.313769\pi$
$229$			25.2317i			1.66736i	−0.552251	+	0.833678i	$0.686231\pi$
$230$	10.3814			0.684531
$231$	−1.47703	−	0.235859i	−0.0971817	−	0.0155184i
$232$	−87.4208			−5.73945
$233$		−	11.6543i		−	0.763497i	−0.924266	−	0.381748i	$-0.875322\pi$
$233$		−	11.6543i		−	0.763497i	0.924266	−	0.381748i	$-0.124678\pi$
$234$	−3.96263	−	10.4340i	−0.259045	−	0.682090i
$235$	−36.5933			−2.38708
$236$	−3.29333			−0.214377
$237$	−5.91274	+	8.57035i	−0.384074	+	0.556704i
$238$	17.0768	+	35.7551i	1.10693	+	2.31766i
$239$			4.12366i			0.266737i	0.991067	+	0.133369i	$0.0425794\pi$
$239$			4.12366i			0.266737i	−0.991067	+	0.133369i	$0.957421\pi$
$240$	49.4756	−	71.7135i	3.19364	−	4.62908i
$241$			2.84930i			0.183539i	0.995780	+	0.0917696i	$0.0292523\pi$
$241$			2.84930i			0.183539i	−0.995780	+	0.0917696i	$0.970748\pi$
$242$		−	29.3273i		−	1.88523i
$243$	1.89697	+	15.4726i	0.121691	+	0.992568i
$244$		−	12.0471i		−	0.771235i
$245$	16.9656	−	20.9949i	1.08390	−	1.34131i
$246$	−9.64950	−	6.65726i	−0.615230	−	0.424451i
$247$	−1.47545			−0.0938807
$248$	−7.88263			−0.500548
$249$	4.48289	−	6.49782i	0.284092	−	0.411783i
$250$		−	50.5550i		−	3.19738i
$251$	−15.6205			−0.985958			−0.492979	−	0.870041i	$-0.664092\pi$
$251$	−15.6205			−0.985958			−0.492979	+	0.870041i	$0.664092\pi$
$252$	30.1270	+	28.7646i	1.89782	+	1.81200i
$253$	0.326399			0.0205205
$254$		−	1.25863i		−	0.0789732i
$255$	−21.0992	+	30.5826i	−1.32128	+	1.91516i
$256$	17.2469			1.07793
$257$	4.17343			0.260331			0.130166	−	0.991492i	$-0.458449\pi$
$257$	4.17343			0.260331			0.130166	+	0.991492i	$0.458449\pi$
$258$	4.47978	+	3.09063i	0.278899	+	0.192414i
$259$	7.94736	−	3.79571i	0.493825	−	0.235854i
$260$		−	27.9651i		−	1.73432i
$261$	28.0397	−	10.6490i	1.73561	−	0.659154i
$262$		−	44.4767i		−	2.74778i
$263$		−	0.516839i		−	0.0318696i	−0.999873	−	0.0159348i	$-0.994928\pi$
$263$		−	0.516839i		−	0.0318696i	0.999873	−	0.0159348i	$-0.00507242\pi$
$264$	2.80715	−	4.06889i	0.172768	−	0.250423i
$265$			34.8712i			2.14212i
$266$	6.86248	−	3.27756i	0.420766	−	0.200960i
$267$	−14.1799	+	20.5534i	−0.867797	+	1.25785i
$268$	−47.0155			−2.87193
$269$	−25.9913			−1.58472			−0.792359	−	0.610055i	$-0.791147\pi$
$269$	−25.9913			−1.58472			−0.792359	+	0.610055i	$0.791147\pi$
$270$	−12.8730	+	52.3850i	−0.783425	+	3.18805i
$271$		−	14.5849i		−	0.885972i	−0.896529	−	0.442986i	$-0.853919\pi$
$271$		−	14.5849i		−	0.885972i	0.896529	−	0.442986i	$-0.146081\pi$
$272$	−72.5653			−4.39992
$273$	6.25349	+	0.998585i	0.378478	+	0.0604371i
$274$	−44.0264			−2.65973
$275$		−	3.22147i		−	0.194262i
$276$	−7.48179	−	5.16174i	−0.450351	−	0.310700i
$277$	−17.8114			−1.07018			−0.535092	−	0.844794i	$-0.679723\pi$
$277$	−17.8114			−1.07018			−0.535092	+	0.844794i	$0.679723\pi$
$278$	−27.4911			−1.64881
$279$	2.52831	−	0.960205i	0.151366	−	0.0574860i
$280$	38.4466	+	80.4986i	2.29762	+	4.81071i
$281$			20.4949i			1.22262i	0.791391	+	0.611310i	$0.209357\pi$
$281$			20.4949i			1.22262i	−0.791391	+	0.611310i	$0.790643\pi$
$282$	36.4231	+	25.1286i	2.16896	+	1.49638i
$283$		−	31.7621i		−	1.88806i	−0.329860	−	0.944030i	$-0.607001\pi$
$283$		−	31.7621i		−	1.88806i	0.329860	−	0.944030i	$-0.392999\pi$
$284$			39.4198i			2.33913i
$285$	5.86973	+	4.04957i	0.347693	+	0.239876i
$286$		−	1.21432i		−	0.0718044i
$287$	6.00217	−	2.86667i	0.354297	−	0.169214i
$288$	−49.4455	+	18.7785i	−2.91360	+	1.10653i
$289$	13.9459			0.820348
$290$	103.793			6.09491
$291$	−9.11535	−	6.28874i	−0.534351	−	0.368653i
$292$			4.99514i			0.292319i
$293$	17.6542			1.03137			0.515684	−	0.856779i	$-0.327538\pi$
$293$	17.6542			1.03137			0.515684	+	0.856779i	$0.327538\pi$
$294$	−31.3039	+	9.24694i	−1.82568	+	0.539293i
$295$	2.41993			0.140894
$296$			29.1070i			1.69181i
$297$	−0.404735	+	1.64702i	−0.0234851	+	0.0955696i
$298$	31.4349			1.82097
$299$	−1.38191			−0.0799180
$300$	−50.9451	+	73.8434i	−2.94131	+	4.26335i
$301$	−2.78651	+	1.33085i	−0.160612	+	0.0767091i
$302$		−	20.6314i		−	1.18720i
$303$	−14.8399	+	21.5100i	−0.852530	+	1.23572i
$304$			13.9275i			0.798795i
$305$			8.85217i			0.506874i
$306$	42.0021	−	15.9516i	2.40110	−	0.911894i
$307$			33.1515i			1.89206i	0.324082	+	0.946029i	$0.394945\pi$
$307$			33.1515i			1.89206i	−0.324082	+	0.946029i	$0.605055\pi$
$308$	1.95314	+	4.08943i	0.111290	+	0.233017i
$309$	−14.9978	−	10.3471i	−0.853197	−	0.588627i
$310$	9.35886			0.531548
$311$	−17.2458			−0.977919			−0.488959	−	0.872307i	$-0.662623\pi$
$311$	−17.2458			−0.977919			−0.488959	+	0.872307i	$0.662623\pi$
$312$	−11.8850	+	17.2269i	−0.672854	+	0.975282i
$313$			0.501419i			0.0283419i	0.999900	+	0.0141709i	$0.00451090\pi$
$313$			0.501419i			0.0283419i	−0.999900	+	0.0141709i	$0.995489\pi$
$314$	−13.6607			−0.770915
$315$	−22.1373	−	21.1361i	−1.24729	−	1.19089i
$316$	31.5472			1.77467
$317$			2.32057i			0.130336i	0.997874	+	0.0651681i	$0.0207583\pi$
$317$			2.32057i			0.130336i	−0.997874	+	0.0651681i	$0.979242\pi$
$318$	23.9460	−	34.7091i	1.34283	−	1.94639i
$319$	3.26330			0.182710
$320$	−82.4265			−4.60778
$321$	4.35765	+	3.00637i	0.243220	+	0.167799i
$322$	6.42742	−	3.06977i	0.358186	−	0.171072i
$323$		−	5.93945i		−	0.330480i
$324$	35.3237	−	31.3528i	1.96243	−	1.74182i
$325$			13.6391i			0.756562i
$326$		−	25.4352i		−	1.40873i
$327$	−11.8217	+	17.1352i	−0.653743	+	0.947581i
$328$			21.9828i			1.21380i
$329$	−22.6559	+	10.8206i	−1.24906	+	0.596558i
$330$	−3.33286	+	4.83089i	−0.183468	+	0.265932i
$331$	−19.6963			−1.08261			−0.541304	−	0.840827i	$-0.682069\pi$
$331$	−19.6963			−1.08261			−0.541304	+	0.840827i	$0.682069\pi$
$332$	−23.9183			−1.31269
$333$	−3.54560	−	9.33589i	−0.194298	−	0.511604i
$334$		−	37.6383i		−	2.05948i
$335$	34.5469			1.88750
$336$	9.42610	−	59.0295i	0.514236	−	3.22032i
$337$	−13.6736			−0.744848			−0.372424	−	0.928063i	$-0.621473\pi$
$337$	−13.6736			−0.744848			−0.372424	+	0.928063i	$0.621473\pi$
$338$		−	29.8572i		−	1.62402i
$339$	−11.5839	−	7.99184i	−0.629153	−	0.434057i
$340$	112.574			6.10517
$341$	0.294248			0.0159344
$342$	−3.06160	−	8.06146i	−0.165552	−	0.435914i
$343$	4.29573	−	18.0152i	0.231947	−	0.972728i
$344$		−	10.2055i		−	0.550245i
$345$	5.49760	+	3.79283i	0.295981	+	0.204199i
$346$			43.7552i			2.35230i
$347$			2.00654i			0.107717i	0.998549	+	0.0538584i	$0.0171520\pi$
$347$			2.00654i			0.107717i	−0.998549	+	0.0538584i	$0.982848\pi$
$348$	−74.8022	−	51.6066i	−4.00982	−	2.76640i
$349$		−	24.3244i		−	1.30205i	−0.759054	−	0.651027i	$-0.774338\pi$
$349$		−	24.3244i		−	1.30205i	0.759054	−	0.651027i	$-0.225662\pi$
$350$	−30.2979	−	63.4370i	−1.61949	−	3.39085i
$351$	1.71357	−	6.97316i	0.0914637	−	0.372200i
$352$	−5.75454			−0.306718
$353$	−7.02910			−0.374121			−0.187061	−	0.982348i	$-0.559896\pi$
$353$	−7.02910			−0.374121			−0.187061	+	0.982348i	$0.559896\pi$
$354$	−2.40868	−	1.66176i	−0.128020	−	0.0883217i
$355$		−	28.9656i		−	1.53733i
$356$	75.6564			4.00978
$357$	−4.01982	+	25.1735i	−0.212751	+	1.33232i
$358$	−18.8531			−0.996419
$359$			21.8537i			1.15339i	0.816958	+	0.576697i	$0.195659\pi$
$359$			21.8537i			1.15339i	−0.816958	+	0.576697i	$0.804341\pi$
$360$	94.5630	−	35.9133i	4.98391	−	1.89280i
$361$	17.8600			0.940002
$362$	33.6080			1.76640
$363$	10.7147	−	15.5306i	0.562373	−	0.815144i
$364$	−8.26922	−	17.3139i	−0.433425	−	0.907495i
$365$		−	3.67042i		−	0.192119i
$366$	6.07877	−	8.81100i	0.317742	−	0.460558i
$367$		−	2.27041i		−	0.118515i	−0.998243	−	0.0592573i	$-0.981127\pi$
$367$		−	2.27041i		−	0.118515i	0.998243	−	0.0592573i	$-0.0188733\pi$
$368$			13.0445i			0.679991i
$369$	−2.67779	−	7.05085i	−0.139400	−	0.367053i
$370$		−	34.5581i		−	1.79659i
$371$	10.3114	+	21.5897i	0.535339	+	1.12088i
$372$	−6.74484	−	4.65331i	−0.349703	−	0.241263i
$373$	11.8146			0.611736			0.305868	−	0.952074i	$-0.401053\pi$
$373$	11.8146			0.611736			0.305868	+	0.952074i	$0.401053\pi$
$374$	4.88827			0.252767
$375$	18.4701	−	26.7719i	0.953794	−	1.38250i
$376$		−	82.9766i		−	4.27919i
$377$	−13.8162			−0.711572
$378$	7.52015	+	36.2394i	0.386795	+	1.86396i
$379$	−20.4503			−1.05046			−0.525231	−	0.850960i	$-0.676021\pi$
$379$	−20.4503			−1.05046			−0.525231	+	0.850960i	$0.676021\pi$
$380$		−	21.6063i		−	1.10838i
$381$	0.459836	−	0.666519i	0.0235581	−	0.0341468i
$382$	29.0432			1.48598
$383$	−8.19559			−0.418775			−0.209388	−	0.977833i	$-0.567147\pi$
$383$	−8.19559			−0.418775			−0.209388	+	0.977833i	$0.567147\pi$
$384$	31.7725	+	21.9201i	1.62138	+	1.11860i
$385$	−1.43516	−	3.00491i	−0.0731426	−	0.153144i
$386$			34.1659i			1.73900i
$387$	1.24316	+	3.27336i	0.0631935	+	0.166394i
$388$			33.5533i			1.70341i
$389$			24.7438i			1.25456i	0.778794	+	0.627280i	$0.215832\pi$
$389$			24.7438i			1.25456i	−0.778794	+	0.627280i	$0.784168\pi$
$390$	14.1107	−	20.4531i	0.714525	−	1.03568i
$391$		−	5.56290i		−	0.281328i
$392$	47.6066	+	38.4702i	2.40450	+	1.94304i
$393$	16.2495	−	23.5531i	0.819677	−	1.18810i
$394$	12.2476			0.617024
$395$	−23.1808			−1.16635
$396$	4.80392	−	1.82444i	0.241406	−	0.0916817i
$397$			20.7137i			1.03959i	0.854290	+	0.519797i	$0.173992\pi$
$397$			20.7137i			1.03959i	−0.854290	+	0.519797i	$0.826008\pi$
$398$	−60.2121			−3.01816
$399$	4.83155	+	0.771524i	0.241880	+	0.0386245i
$400$	128.746			6.43729
$401$		−	2.37671i		−	0.118687i	−0.998238	−	0.0593437i	$-0.981099\pi$
$401$		−	2.37671i		−	0.118687i	0.998238	−	0.0593437i	$-0.0189008\pi$
$402$	−34.3862	−	23.7233i	−1.71503	−	1.18321i
$403$	−1.24579			−0.0620574
$404$	79.1777			3.93924
$405$	−25.9558	+	23.0379i	−1.28975	+	1.14476i
$406$	64.2607	−	30.6913i	3.18920	−	1.52318i
$407$		−	1.08653i		−	0.0538571i
$408$	−69.3472	−	47.8431i	−3.43320	−	2.36859i
$409$		−	9.24751i		−	0.457260i	−0.973513	−	0.228630i	$-0.926575\pi$
$409$		−	9.24751i		−	0.457260i	0.973513	−	0.228630i	$-0.0734246\pi$
$410$		−	26.0997i		−	1.28897i
$411$	−23.3147	−	16.0850i	−1.15003	−	0.793413i
$412$			55.2066i			2.71983i
$413$	1.49824	−	0.715569i	0.0737237	−	0.0352109i
$414$	−2.86750	−	7.55039i	−0.140930	−	0.371081i
$415$	17.5751			0.862728
$416$	24.3637			1.19453
$417$	−14.5582	−	10.0438i	−0.712919	−	0.491848i
$418$		−	0.938207i		−	0.0458892i
$419$	12.9758			0.633908			0.316954	−	0.948441i	$-0.397340\pi$
$419$	12.9758			0.633908			0.316954	+	0.948441i	$0.397340\pi$
$420$	−14.6231	+	91.5752i	−0.713536	+	4.46841i
$421$	32.9201			1.60443			0.802213	−	0.597038i	$-0.203656\pi$
$421$	32.9201			1.60443			0.802213	+	0.597038i	$0.203656\pi$
$422$		−	35.0716i		−	1.70726i
$423$	10.1076	+	26.6142i	0.491448	+	1.29403i
$424$	−79.0717			−3.84006
$425$	−54.9045			−2.66326
$426$	−19.8906	+	28.8308i	−0.963703	+	1.39686i
$427$	2.61757	+	5.48061i	0.126673	+	0.265225i
$428$		−	16.0404i		−	0.775342i
$429$	0.443650	−	0.643058i	0.0214196	−	0.0310471i
$430$			12.1168i			0.584322i
$431$		−	9.74992i		−	0.469637i	−0.972039	−	0.234819i	$-0.924550\pi$
$431$		−	9.74992i		−	0.469637i	0.972039	−	0.234819i	$-0.0754496\pi$
$432$	−65.8229	−	16.1752i	−3.16690	−	0.778229i
$433$		−	3.65778i		−	0.175782i	−0.996130	−	0.0878908i	$-0.971987\pi$
$433$		−	3.65778i		−	0.175782i	0.996130	−	0.0878908i	$-0.0280127\pi$
$434$	5.79432	−	2.76740i	0.278136	−	0.132839i
$435$	54.9645	+	37.9204i	2.63535	+	1.81814i
$436$	63.0743			3.02071
$437$	−1.06769			−0.0510745
$438$	−2.52047	+	3.65335i	−0.120433	+	0.174564i
$439$			29.2721i			1.39708i	0.715570	+	0.698541i	$0.246167\pi$
$439$			29.2721i			1.39708i	−0.715570	+	0.698541i	$0.753833\pi$
$440$	11.0054			0.524662
$441$	−19.9557	−	6.53998i	−0.950270	−	0.311428i
$442$	−20.6960			−0.984411
$443$		−	25.5008i		−	1.21158i	−0.795624	−	0.605791i	$-0.792857\pi$
$443$		−	25.5008i		−	1.21158i	0.795624	−	0.605791i	$-0.207143\pi$
$444$	−17.1826	+	24.9056i	−0.815449	+	1.18197i
$445$	−55.5921			−2.63532
$446$	19.1142			0.905082
$447$	16.6467	+	11.4847i	0.787362	+	0.543206i
$448$	−51.0324	+	24.3734i	−2.41105	+	1.15153i
$449$		−	18.4483i		−	0.870627i	−0.900279	−	0.435313i	$-0.856638\pi$
$449$		−	18.4483i		−	0.870627i	0.900279	−	0.435313i	$-0.143362\pi$
$450$	−74.5204	+	28.3015i	−3.51293	+	1.33415i
$451$		−	0.820589i		−	0.0386400i
$452$			42.6401i			2.00562i
$453$	7.53763	−	10.9256i	0.354149	−	0.513329i
$454$		−	36.1769i		−	1.69787i
$455$	6.07621	+	12.7222i	0.284857	+	0.596427i
$456$	−9.18253	+	13.3098i	−0.430011	+	0.623289i
$457$	0.613108			0.0286800			0.0143400	−	0.999897i	$-0.495435\pi$
$457$	0.613108			0.0286800			0.0143400	+	0.999897i	$0.495435\pi$
$458$	67.9284			3.17409
$459$	28.0706	+	6.89801i	1.31022	+	0.321971i
$460$		−	20.2365i		−	0.943532i
$461$	−27.2481			−1.26907			−0.634536	−	0.772894i	$-0.718809\pi$
$461$	−27.2481			−1.26907			−0.634536	+	0.772894i	$0.718809\pi$
$462$	−0.634978	+	3.97645i	−0.0295418	+	0.185001i
$463$	5.67918			0.263934			0.131967	−	0.991254i	$-0.457871\pi$
$463$	5.67918			0.263934			0.131967	+	0.991254i	$0.457871\pi$
$464$			130.418i			6.05448i
$465$	4.95609	+	3.41924i	0.229833	+	0.158563i
$466$	−31.3755			−1.45344
$467$	−19.6632			−0.909903			−0.454951	−	0.890516i	$-0.650343\pi$
$467$	−19.6632			−0.909903			−0.454951	+	0.890516i	$0.650343\pi$
$468$	−20.3389	+	7.72436i	−0.940167	+	0.357059i
$469$	21.3889	−	10.2155i	0.987646	−	0.471706i
$470$			98.5161i			4.54421i
$471$	−7.23415	−	4.99089i	−0.333332	−	0.229968i
$472$			5.48728i			0.252572i
$473$			0.380959i			0.0175165i
$474$	23.0730	+	15.9182i	1.05978	+	0.731148i
$475$			10.5378i			0.483508i
$476$	69.6974	−	33.2879i	3.19457	−	1.52575i
$477$	25.3618	−	9.63194i	1.16124	−	0.441016i
$478$	11.1017			0.507778
$479$	−11.8469			−0.541297			−0.270649	−	0.962678i	$-0.587238\pi$
$479$	−11.8469			−0.541297			−0.270649	+	0.962678i	$0.587238\pi$
$480$	−96.9251	−	66.8693i	−4.42400	−	3.05215i
$481$			4.60015i			0.209749i
$482$	7.67084			0.349397
$483$	4.52524	+	0.722611i	0.205906	+	0.0328799i
$484$	−57.1676			−2.59853
$485$		−	24.6549i		−	1.11952i
$486$	41.6552	−	5.10700i	1.88952	−	0.231658i
$487$	11.6067			0.525951			0.262975	−	0.964803i	$-0.415296\pi$
$487$	11.6067			0.525951			0.262975	+	0.964803i	$0.415296\pi$
$488$	−20.0726			−0.908644
$489$	9.29270	−	13.4695i	0.420231	−	0.609112i
$490$	−56.5221	−	45.6747i	−2.55341	−	2.06337i
$491$		−	35.1027i		−	1.58416i	−0.610416	−	0.792081i	$-0.708998\pi$
$491$		−	35.1027i		−	1.58416i	0.610416	−	0.792081i	$-0.291002\pi$
$492$	−12.9770	+	18.8098i	−0.585048	+	0.848010i
$493$		−	55.6174i		−	2.50488i
$494$			3.97219i			0.178717i
$495$	−3.52991	+	1.34060i	−0.158658	+	0.0602553i
$496$			11.7596i			0.528022i
$497$	−8.56506	−	17.9333i	−0.384196	−	0.804420i
$498$	−17.4934	−	12.0688i	−0.783897	−	0.540816i
$499$	−9.73833			−0.435947			−0.217974	−	0.975955i	$-0.569945\pi$
$499$	−9.73833			−0.435947			−0.217974	+	0.975955i	$0.569945\pi$
$500$	−98.5467			−4.40714
$501$	13.7511	−	19.9318i	0.614353	−	0.890487i
$502$			42.0534i			1.87693i
$503$	38.2879			1.70717			0.853586	−	0.520952i	$-0.174423\pi$
$503$	38.2879			1.70717			0.853586	+	0.520952i	$0.174423\pi$
$504$	47.9269	−	50.1970i	2.13483	−	2.23595i
$505$	−58.1796			−2.58896
$506$		−	0.878727i		−	0.0390642i
$507$	10.9083	−	15.8112i	0.484454	−	0.702201i
$508$	−2.45344			−0.108854
$509$	−17.6815			−0.783719			−0.391860	−	0.920025i	$-0.628168\pi$
$509$	−17.6815			−0.783719			−0.391860	+	0.920025i	$0.628168\pi$
$510$	82.3343	+	56.8030i	3.64582	+	2.51528i
$511$	−1.08534	−	2.27245i	−0.0480125	−	0.100527i
$512$		−	1.86019i		−	0.0822095i
$513$	1.32394	−	5.38759i	0.0584532	−	0.237868i
$514$		−	11.2357i		−	0.495584i
$515$		−	40.5657i		−	1.78754i
$516$	6.02456	−	8.73243i	0.265217	−	0.384424i
$517$			3.09741i			0.136224i
$518$	−10.2188	−	21.3958i	−0.448986	−	0.940077i
$519$	−15.9859	+	23.1711i	−0.701702	+	1.01710i
$520$	−46.5948			−2.04332
$521$	−13.5900			−0.595387			−0.297694	−	0.954661i	$-0.596217\pi$
$521$	−13.5900			−0.595387			−0.297694	+	0.954661i	$0.596217\pi$
$522$	−28.6690	−	75.4881i	−1.25481	−	3.30402i
$523$			7.66195i			0.335033i	0.985869	+	0.167517i	$0.0535748\pi$
$523$			7.66195i			0.335033i	−0.985869	+	0.167517i	$0.946425\pi$
$524$	−86.6983			−3.78743
$525$	7.13199	−	44.6630i	0.311266	−	1.94925i
$526$	−1.39143			−0.0606691
$527$		−	5.01496i		−	0.218455i
$528$	−6.07012	−	4.18782i	−0.264168	−	0.182251i
$529$	−1.00000			−0.0434783
$530$	93.8800			4.07788
$531$	−0.668420	−	1.76001i	−0.0290069	−	0.0763779i
$532$	−6.38894	−	13.3770i	−0.276996	−	0.579968i
$533$			3.47423i			0.150485i
$534$	55.3336	+	38.1750i	2.39452	+	1.65199i
$535$			11.7864i			0.509572i
$536$			78.3362i			3.38361i
$537$	−9.98389	−	6.88795i	−0.430837	−	0.297237i
$538$			69.9735i			3.01677i
$539$	−1.77709	−	1.43604i	−0.0765447	−	0.0618547i
$540$	102.114	+	25.0933i	4.39429	+	1.07984i
$541$	2.85315			0.122667			0.0613333	−	0.998117i	$-0.480465\pi$
$541$	2.85315			0.122667			0.0613333	+	0.998117i	$0.480465\pi$
$542$	−39.2654			−1.68659
$543$	17.7975	+	12.2786i	0.763763	+	0.526925i
$544$			98.0764i			4.20499i
$545$	−46.3469			−1.98528
$546$	2.68838	−	16.8356i	0.115052	−	0.720496i
$547$	6.61189			0.282704			0.141352	−	0.989959i	$-0.454855\pi$
$547$	6.61189			0.282704			0.141352	+	0.989959i	$0.454855\pi$
$548$			85.8207i			3.66608i
$549$	6.43816	−	2.44510i	0.274774	−	0.104354i
$550$	−8.67281			−0.369810
$551$	−10.6746			−0.454755
$552$	−8.60038	+	12.4660i	−0.366057	+	0.530588i
$553$	−14.3518	+	6.85452i	−0.610302	+	0.291484i
$554$			47.9517i			2.03727i
$555$	12.6257	−	18.3006i	0.535932	−	0.776817i
$556$			53.5884i			2.27265i
$557$			41.0064i			1.73750i	0.495253	+	0.868749i	$0.335075\pi$
$557$			41.0064i			1.73750i	−0.495253	+	0.868749i	$0.664925\pi$
$558$	−2.58505	−	6.80668i	−0.109434	−	0.288150i
$559$		−	1.61291i		−	0.0682188i
$560$	120.091	−	57.3561i	5.07476	−	2.42374i
$561$	2.58864	+	1.78592i	0.109292	+	0.0754016i
$562$	55.1760			2.32746
$563$	3.85701			0.162553			0.0812767	−	0.996692i	$-0.474100\pi$
$563$	3.85701			0.162553			0.0812767	+	0.996692i	$0.474100\pi$
$564$	48.9831	−	70.9995i	2.06256	−	2.98962i
$565$		−	31.3319i		−	1.31814i
$566$	−85.5095			−3.59423
$567$	−9.25762	+	21.9385i	−0.388784	+	0.921329i
$568$	65.6804			2.75589
$569$		−	12.5403i		−	0.525715i	−0.964835	−	0.262858i	$-0.915335\pi$
$569$		−	12.5403i		−	0.525715i	0.964835	−	0.262858i	$-0.0846649\pi$
$570$	10.9022	−	15.8024i	0.456643	−	0.661891i
$571$	−8.07060			−0.337744			−0.168872	−	0.985638i	$-0.554012\pi$
$571$	−8.07060			−0.337744			−0.168872	+	0.985638i	$0.554012\pi$
$572$	−2.36708			−0.0989725
$573$	15.3801	+	10.6109i	0.642514	+	0.443275i
$574$	−7.71763	−	16.1590i	−0.322127	−	0.674463i
$575$			9.86975i			0.411597i
$576$	22.7674	+	59.9486i	0.948641	+	2.49786i
$577$			9.97035i			0.415071i	0.978227	+	0.207535i	$0.0665442\pi$
$577$			9.97035i			0.415071i	−0.978227	+	0.207535i	$0.933456\pi$
$578$		−	37.5450i		−	1.56167i
$579$	−12.4824	+	18.0929i	−0.518753	+	0.751917i
$580$		−	202.323i		−	8.40100i
$581$	10.8812	−	5.19693i	0.451429	−	0.215605i
$582$	−16.9305	+	24.5402i	−0.701791	+	1.01723i
$583$	2.95164			0.122245
$584$	8.32280			0.344400
$585$	14.9450	−	5.67584i	0.617900	−	0.234667i
$586$		−	47.5284i		−	1.96338i
$587$	30.0082			1.23857			0.619285	−	0.785167i	$-0.287423\pi$
$587$	30.0082			1.23857			0.619285	+	0.785167i	$0.287423\pi$
$588$	18.0251	+	61.0206i	0.743341	+	2.51645i
$589$	−0.962521			−0.0396600
$590$		−	6.51491i		−	0.268215i
$591$	6.48584	+	4.47463i	0.266792	+	0.184062i
$592$	43.4229			1.78467
$593$	5.96994			0.245156			0.122578	−	0.992459i	$-0.460884\pi$
$593$	5.96994			0.245156			0.122578	+	0.992459i	$0.460884\pi$
$594$	4.43408	+	1.08962i	0.181932	+	0.0447077i
$595$	−51.2135	+	24.4599i	−2.09955	+	1.00276i
$596$		−	61.2760i		−	2.50996i
$597$	−31.8860	−	21.9983i	−1.30501	−	0.900332i
$598$			3.72037i			0.152137i
$599$			16.8239i			0.687405i	0.939079	+	0.343703i	$0.111681\pi$
$599$			16.8239i			0.687405i	−0.939079	+	0.343703i	$0.888319\pi$
$600$	123.036	+	84.8836i	5.02294	+	3.46536i
$601$			26.3175i			1.07352i	0.843737	+	0.536758i	$0.180351\pi$
$601$			26.3175i			1.07352i	−0.843737	+	0.536758i	$0.819649\pi$
$602$	3.58291	+	7.50181i	0.146028	+	0.305751i
$603$	−9.54235	−	25.1259i	−0.388594	−	1.02320i
$604$	−40.2167			−1.63640
$605$	42.0066			1.70781
$606$	57.9090	+	39.9518i	2.35239	+	1.62293i
$607$			6.77740i			0.275086i	0.990496	+	0.137543i	$0.0439205\pi$
$607$			6.77740i			0.275086i	−0.990496	+	0.137543i	$0.956079\pi$
$608$	18.8238			0.763406
$609$	45.2430	+	7.22460i	1.83334	+	0.292755i
$610$	23.8317			0.964918
$611$		−	13.1138i		−	0.530529i
$612$	−31.0945	−	81.8746i	−1.25692	−	3.30959i
$613$	−24.0058			−0.969587			−0.484793	−	0.874629i	$-0.661105\pi$
$613$	−24.0058			−0.969587			−0.484793	+	0.874629i	$0.661105\pi$
$614$	89.2502			3.60185
$615$	9.53546	−	13.8214i	0.384507	−	0.557331i
$616$	6.81373	−	3.25428i	0.274533	−	0.131119i
$617$			25.3374i			1.02005i	0.860161	+	0.510023i	$0.170363\pi$
$617$			25.3374i			1.02005i	−0.860161	+	0.510023i	$0.829637\pi$
$618$	−27.8564	+	40.3770i	−1.12055	+	1.62420i
$619$		−	32.0484i		−	1.28814i	−0.764968	−	0.644068i	$-0.777245\pi$
$619$		−	32.0484i		−	1.28814i	0.764968	−	0.644068i	$-0.222755\pi$
$620$		−	18.2432i		−	0.732665i
$621$	1.24000	−	5.04603i	0.0497595	−	0.202490i
$622$			46.4289i			1.86163i
$623$	−34.4185	+	16.4385i	−1.37895	+	0.658595i
$624$	25.6998	+	17.7304i	1.02881	+	0.709786i
$625$	23.0632			0.922527
$626$	1.34992			0.0539535
$627$	0.342772	−	0.496838i	0.0136890	−	0.0198418i
$628$			26.6287i			1.06260i
$629$	−18.5180			−0.738360
$630$	−56.9025	+	59.5977i	−2.26705	+	2.37443i
$631$	8.02052			0.319292			0.159646	−	0.987174i	$-0.448965\pi$
$631$	8.02052			0.319292			0.159646	+	0.987174i	$0.448965\pi$
$632$		−	52.5633i		−	2.09086i
$633$	12.8133	−	18.5725i	0.509284	−	0.738192i
$634$	6.24741			0.248116
$635$	1.80278			0.0715412
$636$	−67.6583	−	46.6779i	−2.68283	−	1.85090i
$637$	7.52388	+	6.07993i	0.298107	+	0.240896i
$638$		−	8.78542i		−	0.347818i
$639$	−21.0666	+	8.00071i	−0.833381	+	0.316503i
$640$			85.9373i			3.39697i
$641$		−	8.09499i		−	0.319733i	−0.987139	−	0.159866i	$-0.948894\pi$
$641$		−	8.09499i		−	0.319733i	0.987139	−	0.159866i	$-0.0511063\pi$
$642$	8.09373	−	11.7316i	0.319434	−	0.463010i
$643$			10.4980i			0.414000i	0.978341	+	0.207000i	$0.0663700\pi$
$643$			10.4980i			0.414000i	−0.978341	+	0.207000i	$0.933630\pi$
$644$	−5.98390	−	12.5290i	−0.235799	−	0.493710i
$645$	−4.42684	+	6.41657i	−0.174306	+	0.252652i
$646$	−15.9901			−0.629123
$647$	−20.5582			−0.808225			−0.404113	−	0.914709i	$-0.632420\pi$
$647$	−20.5582			−0.808225			−0.404113	+	0.914709i	$0.632420\pi$
$648$	−52.2393	−	58.8556i	−2.05215	−	2.31207i
$649$		−	0.204833i		−	0.00804039i
$650$	36.7191			1.44024
$651$	4.07951	+	0.651434i	0.159889	+	0.0255317i
$652$	−49.5808			−1.94174
$653$		−	36.8024i		−	1.44019i	−0.693876	−	0.720094i	$-0.744098\pi$
$653$		−	36.8024i		−	1.44019i	0.693876	−	0.720094i	$-0.255902\pi$
$654$	46.1313	+	31.8263i	1.80388	+	1.24451i
$655$	63.7057			2.48919
$656$	32.7948			1.28042
$657$	−2.66949	+	1.01382i	−0.104147	+	0.0395530i
$658$	29.1310	+	60.9939i	1.13565	+	2.37779i
$659$		−	32.4144i		−	1.26268i	−0.775505	−	0.631342i	$-0.782504\pi$
$659$		−	32.4144i		−	1.26268i	0.775505	−	0.631342i	$-0.217496\pi$
$660$	9.41685	+	6.49675i	0.366550	+	0.252886i
$661$		−	24.9742i		−	0.971386i	−0.874130	−	0.485693i	$-0.838567\pi$
$661$		−	24.9742i		−	0.971386i	0.874130	−	0.485693i	$-0.161433\pi$
$662$			53.0263i			2.06092i
$663$	−10.9598	−	7.56126i	−0.425644	−	0.293655i
$664$			39.8522i			1.54656i
$665$	4.69458	+	9.82941i	0.182048	+	0.381168i
$666$	−25.1340	+	9.54543i	−0.973922	+	0.369878i
$667$	−9.99790			−0.387120
$668$	−73.3683			−2.83871
$669$	10.1221	+	6.98332i	0.391344	+	0.269991i
$670$		−	93.0067i		−	3.59316i
$671$	0.749283			0.0289258
$672$	−79.7820	−	12.7399i	−3.07766	−	0.491454i
$673$	−18.4995			−0.713105			−0.356553	−	0.934275i	$-0.616048\pi$
$673$	−18.4995			−0.713105			−0.356553	+	0.934275i	$0.616048\pi$
$674$			36.8119i			1.41794i
$675$	−49.8030	−	12.2385i	−1.91692	−	0.471060i
$676$	−58.2007			−2.23849
$677$	40.2929			1.54858			0.774291	−	0.632830i	$-0.218107\pi$
$677$	40.2929			1.54858			0.774291	+	0.632830i	$0.218107\pi$
$678$	−21.5155	+	31.1861i	−0.826299	+	1.19770i
$679$	−7.29041	−	15.2645i	−0.279780	−	0.585798i
$680$		−	187.568i		−	7.19291i
$681$	13.2171	−	19.1579i	0.506482	−	0.734131i
$682$		−	0.792172i		−	0.0303338i
$683$			5.23283i			0.200229i	0.994976	+	0.100114i	$0.0319209\pi$
$683$			5.23283i			0.200229i	−0.994976	+	0.100114i	$0.968079\pi$
$684$	−15.7142	+	5.96797i	−0.600848	+	0.228191i
$685$		−	63.0609i		−	2.40943i
$686$	−48.5003	−	11.5649i	−1.85175	−	0.441550i
$687$	35.9723	+	24.8175i	1.37243	+	0.946847i
$688$	−15.2250			−0.580447
$689$	−12.4967			−0.476087
$690$	10.2110	−	14.8006i	0.388727	−	0.563449i
$691$			27.7943i			1.05734i	0.848826	+	0.528672i	$0.177310\pi$
$691$			27.7943i			1.05734i	−0.848826	+	0.528672i	$0.822690\pi$
$692$	85.2920			3.24232
$693$	−1.78905	+	1.87379i	−0.0679603	+	0.0711793i
$694$	5.40199			0.205057
$695$		−	39.3766i		−	1.49364i
$696$	−85.9858	+	124.634i	−3.25928	+	4.72424i
$697$	−13.9855			−0.529740
$698$	−65.4858			−2.47868
$699$	−16.6152	−	11.4630i	−0.628446	−	0.433569i
$700$	−123.658	+	59.0596i	−4.67382	+	2.23224i
$701$			9.88870i			0.373491i	0.982408	+	0.186746i	$0.0597940\pi$
$701$			9.88870i			0.373491i	−0.982408	+	0.186746i	$0.940206\pi$
$702$	−18.7731	−	4.61326i	−0.708544	−	0.174116i
$703$			3.55416i			0.134048i
$704$			6.97691i			0.262952i
$705$	−35.9926	+	52.1703i	−1.35556	+	1.96485i
$706$			18.9237i			0.712201i
$707$	−36.0205	+	17.2036i	−1.35469	+	0.647008i
$708$	−3.23927	+	4.69523i	−0.121739	+	0.176458i
$709$	2.16888			0.0814540			0.0407270	−	0.999170i	$-0.487033\pi$
$709$	2.16888			0.0814540			0.0407270	+	0.999170i	$0.487033\pi$
$710$	−77.9808			−2.92657
$711$	6.40287	+	16.8593i	0.240127	+	0.632275i
$712$		−	126.057i		−	4.72419i
$713$	−0.901500			−0.0337614
$714$	67.7718	+	10.8221i	2.53630	+	0.405007i
$715$	1.73932			0.0650470
$716$			36.7504i			1.37343i
$717$	5.87901	+	4.05597i	0.219556	+	0.151473i
$718$	58.8343			2.19568
$719$	52.5398			1.95940			0.979702	−	0.200461i	$-0.0642439\pi$
$719$	52.5398			1.95940			0.979702	+	0.200461i	$0.0642439\pi$
$720$	−53.5768	−	141.073i	−1.99669	−	5.25747i
$721$	−11.9952	−	25.1153i	−0.446725	−	0.935342i
$722$		−	48.0826i		−	1.78945i
$723$	4.06218	+	2.80253i	0.151074	+	0.104227i
$724$		−	65.5120i		−	2.43473i
$725$			98.6768i			3.66476i
$726$	−41.8113	−	28.8459i	−1.55176	−	1.07057i
$727$		−	24.3809i		−	0.904239i	−0.891957	−	0.452120i	$-0.850668\pi$
$727$		−	24.3809i		−	0.904239i	0.891957	−	0.452120i	$-0.149332\pi$
$728$	−28.8481	+	13.7780i	−1.06918	+	0.510647i
$729$	23.9248	+	12.5142i	0.886103	+	0.463487i
$730$	−9.88146			−0.365729
$731$	6.49279			0.240144
$732$	−17.1753	−	11.8493i	−0.634816	−	0.437964i
$733$			36.7324i			1.35674i	0.734719	+	0.678371i	$0.237314\pi$
$733$			36.7324i			1.35674i	−0.734719	+	0.678371i	$0.762686\pi$
$734$	−6.11239			−0.225612
$735$	−13.2448	−	44.8378i	−0.488541	−	1.65387i
$736$	17.6304			0.649866
$737$		−	2.92419i		−	0.107714i
$738$	−18.9822	+	7.20910i	−0.698745	+	0.265371i
$739$	−21.2821			−0.782874			−0.391437	−	0.920205i	$-0.628022\pi$
$739$	−21.2821			−0.782874			−0.391437	+	0.920205i	$0.628022\pi$
$740$	−67.3640			−2.47635
$741$	−1.45123	+	2.10352i	−0.0533124	+	0.0772747i
$742$	58.1235	−	27.7601i	2.13378	−	1.01911i
$743$			1.48666i			0.0545404i	0.999628	+	0.0272702i	$0.00868145\pi$
$743$			1.48666i			0.0545404i	−0.999628	+	0.0272702i	$0.991319\pi$
$744$	−7.75325	+	11.2381i	−0.284248	+	0.412009i
$745$			45.0255i			1.64961i
$746$		−	31.8071i		−	1.16454i
$747$	−4.85450	−	12.7823i	−0.177617	−	0.467681i
$748$		−	9.52870i		−	0.348404i
$749$	3.48523	+	7.29729i	0.127348	+	0.266637i
$750$	−72.0751	−	49.7251i	−2.63181	−	1.81570i
$751$	−21.4334			−0.782115			−0.391057	−	0.920366i	$-0.627891\pi$
$751$	−21.4334			−0.782115			−0.391057	+	0.920366i	$0.627891\pi$
$752$	−123.788			−4.51407
$753$	−15.3641	+	22.2698i	−0.559899	+	0.811558i
$754$			37.1959i			1.35459i
$755$	29.5512			1.07548
$756$	70.6415	−	14.6590i	2.56921	−	0.533143i
$757$	−16.0762			−0.584300			−0.292150	−	0.956372i	$-0.594371\pi$
$757$	−16.0762			−0.584300			−0.292150	+	0.956372i	$0.594371\pi$
$758$			55.0561i			1.99973i
$759$	0.321041	−	0.465339i	0.0116530	−	0.0168908i
$760$	−36.0000			−1.30586
$761$	−8.27288			−0.299892			−0.149946	−	0.988694i	$-0.547910\pi$
$761$	−8.27288			−0.299892			−0.149946	+	0.988694i	$0.547910\pi$
$762$	−1.79440	−	1.23797i	−0.0650041	−	0.0448468i
$763$	−28.6945	+	13.7047i	−1.03881	+	0.496143i
$764$		−	56.6138i		−	2.04821i
$765$	22.8482	+	60.1613i	0.826078	+	2.17514i
$766$			22.0641i			0.797207i
$767$			0.867224i			0.0313137i
$768$	16.9638	−	24.5886i	0.612129	−	0.887263i
$769$			4.68540i			0.168960i	0.996425	+	0.0844800i	$0.0269229\pi$
$769$			4.68540i			0.168960i	−0.996425	+	0.0844800i	$0.973077\pi$
$770$	−8.08977	+	3.86372i	−0.291535	+	0.139239i
$771$	4.10493	−	5.94997i	0.147835	−	0.214283i
$772$	66.5996			2.39697
$773$	−5.15437			−0.185390			−0.0926949	−	0.995695i	$-0.529548\pi$
$773$	−5.15437			−0.185390			−0.0926949	+	0.995695i	$0.529548\pi$
$774$	8.81249	−	3.34683i	0.316759	−	0.120299i
$775$			8.89758i			0.319610i
$776$	55.9058			2.00690
$777$	2.40545	−	15.0638i	0.0862951	−	0.540410i
$778$	66.6149			2.38826
$779$			2.68425i			0.0961731i
$780$	−39.8692	−	27.5060i	−1.42755	−	0.984874i
$781$	−2.45176			−0.0877310
$782$	−14.9764			−0.535555
$783$	12.3974	−	50.4497i	0.443047	−	1.80293i
$784$	57.3913	−	71.0213i	2.04969	−	2.53647i
$785$		−	19.5667i		−	0.698366i
$786$	−63.4095	−	43.7466i	−2.26174	−	1.56039i
$787$			29.8477i			1.06396i	0.846758	+	0.531978i	$0.178551\pi$
$787$			29.8477i			1.06396i	−0.846758	+	0.531978i	$0.821449\pi$
$788$		−	23.8742i		−	0.850483i
$789$	−0.736846	−	0.508355i	−0.0262324	−	0.0180979i
$790$			62.4071i			2.22035i
$791$	−9.26478	−	19.3984i	−0.329418	−	0.689727i
$792$	−3.03985	−	8.00420i	−0.108016	−	0.284417i
$793$	−3.17233			−0.112653
$794$	55.7653			1.97904
$795$	49.7152	+	34.2988i	1.76322	+	1.21645i
$796$			117.371i			4.16012i
$797$	15.7537			0.558023			0.279012	−	0.960288i	$-0.409993\pi$
$797$	15.7537			0.558023			0.279012	+	0.960288i	$0.409993\pi$
$798$	2.07709	−	13.0075i	0.0735281	−	0.460459i
$799$	52.7900			1.86757
$800$		−	174.008i		−	6.15210i
$801$	15.3554	+	40.4320i	0.542555	+	1.42860i
$802$	−6.39856			−0.225941
$803$	−0.310679			−0.0109636
$804$	−46.2438	+	67.0290i	−1.63089	+	2.36393i
$805$	4.39696	+	9.20625i	0.154972	+	0.324478i
$806$			3.35391i			0.118136i
$807$	−25.5647	+	37.0552i	−0.899919	+	1.30441i
$808$		−	131.924i		−	4.64108i
$809$			27.2659i			0.958619i	0.877646	+	0.479309i	$0.159113\pi$
$809$			27.2659i			0.958619i	−0.877646	+	0.479309i	$0.840887\pi$
$810$	62.0225	+	69.8779i	2.17925	+	2.45526i
$811$			8.02230i			0.281701i	0.990031	+	0.140850i	$0.0449837\pi$
$811$			8.02230i			0.281701i	−0.990031	+	0.140850i	$0.955016\pi$
$812$	−59.8265	−	125.263i	−2.09950	−	4.39588i
$813$	−20.7934	−	14.3455i	−0.729258	−	0.503120i
$814$	−2.92513			−0.102526
$815$	36.4319			1.27615
$816$	−71.3742	+	103.455i	−2.49860	+	3.62164i
$817$		−	1.24616i		−	0.0435977i
$818$	−24.8961			−0.870470
$819$	7.57450	−	7.93327i	0.264674	−	0.277211i
$820$	−50.8761			−1.77667
$821$			21.1405i			0.737810i	0.929467	+	0.368905i	$0.120267\pi$
$821$			21.1405i			0.737810i	−0.929467	+	0.368905i	$0.879733\pi$
$822$	−43.3038	+	62.7676i	−1.51039	+	2.18927i
$823$	−32.0465			−1.11707			−0.558535	−	0.829481i	$-0.688637\pi$
$823$	−32.0465			−1.11707			−0.558535	+	0.829481i	$0.688637\pi$
$824$	91.9841			3.20442
$825$	−4.59278	−	3.16859i	−0.159900	−	0.110316i
$826$	−1.92645	−	4.03355i	−0.0670297	−	0.140345i
$827$			52.0577i			1.81022i	0.425174	+	0.905112i	$0.360213\pi$
$827$			52.0577i			1.81022i	−0.425174	+	0.905112i	$0.639787\pi$
$828$	−14.7180	+	5.58962i	−0.511485	+	0.194253i
$829$			0.617412i			0.0214436i	0.999943	+	0.0107218i	$0.00341292\pi$
$829$			0.617412i			0.0214436i	−0.999943	+	0.0107218i	$0.996587\pi$
$830$		−	47.3155i		−	1.64235i
$831$	−17.5191	+	25.3934i	−0.607729	+	0.880886i
$832$		−	29.5390i		−	1.02408i
$833$	−24.4749	+	30.2875i	−0.848004	+	1.04940i
$834$	−27.0399	+	39.1935i	−0.936314	+	1.35716i
$835$	53.9109			1.86566
$836$	−1.82885			−0.0632519
$837$	1.11786	−	4.54899i	0.0386389	−	0.157236i
$838$		−	34.9332i		−	1.20675i
$839$	1.36766			0.0472169			0.0236085	−	0.999721i	$-0.492484\pi$
$839$	1.36766			0.0472169			0.0236085	+	0.999721i	$0.492484\pi$
$840$	152.581	+	24.3648i	5.26453	+	0.840664i
$841$	−70.9581			−2.44683
$842$		−	88.6270i		−	3.05429i
$843$	29.2191	+	20.1584i	1.00636	+	0.694294i
$844$	−68.3649			−2.35322
$845$	42.7657			1.47119
$846$	71.6505	−	27.2116i	2.46339	−	0.935553i
$847$	26.0074	−	12.4213i	0.893625	−	0.426800i
$848$			117.962i			4.05084i
$849$	−45.2825	−	31.2407i	−1.55409	−	1.07218i
$850$			147.813i			5.06995i
$851$			3.32883i			0.114111i
$852$	56.1999	+	38.7727i	1.92538	+	1.32833i
$853$		−	52.6406i		−	1.80238i	−0.433426	−	0.901189i	$-0.642695\pi$
$853$		−	52.6406i		−	1.80238i	0.433426	−	0.901189i	$-0.357305\pi$
$854$	14.7548	−	7.04699i	0.504900	−	0.241143i
$855$	11.5468	−	4.38525i	0.394891	−	0.149972i
$856$	−26.7262			−0.913481
$857$	35.7334			1.22063			0.610315	−	0.792159i	$-0.291043\pi$
$857$	35.7334			1.22063			0.610315	+	0.792159i	$0.291043\pi$
$858$	−1.73123	−	1.19439i	−0.0591033	−	0.0407758i
$859$		−	24.9261i		−	0.850468i	−0.905083	−	0.425234i	$-0.860192\pi$
$859$		−	24.9261i		−	0.850468i	0.905083	−	0.425234i	$-0.139808\pi$
$860$	23.6192			0.805408
$861$	1.81670	−	11.3768i	0.0619128	−	0.387720i
$862$	−26.2486			−0.894032
$863$		−	44.6107i		−	1.51857i	−0.650761	−	0.759283i	$-0.725550\pi$
$863$		−	44.6107i		−	1.51857i	0.650761	−	0.759283i	$-0.274450\pi$
$864$	−21.8617	+	88.9636i	−0.743752	+	3.02660i
$865$	−62.6724			−2.13092
$866$	−9.84743			−0.334629
$867$	13.7170	−	19.8824i	0.465854	−	0.675241i
$868$	−5.39449	−	11.2949i	−0.183101	−	0.383372i
$869$			1.96212i			0.0665603i
$870$	102.089	−	147.975i	3.46114	−	5.01682i
$871$			12.3805i			0.419496i
$872$		−	105.093i		−	3.55890i
$873$	−17.9314	+	6.81004i	−0.606888	+	0.230485i
$874$			2.87442i			0.0972287i
$875$	44.8321	−	21.4121i	1.51560	−	0.723860i
$876$	7.12147	+	4.91315i	0.240612	+	0.166000i
$877$	−8.37605			−0.282839			−0.141420	−	0.989950i	$-0.545167\pi$
$877$	−8.37605			−0.282839			−0.141420	+	0.989950i	$0.545167\pi$
$878$	78.8060			2.65957
$879$	17.3644	−	25.1692i	0.585686	−	0.848935i
$880$		−	16.4183i		−	0.553460i
$881$	19.0181			0.640737			0.320368	−	0.947293i	$-0.396193\pi$
$881$	19.0181			0.640737			0.320368	+	0.947293i	$0.396193\pi$
$882$	−17.6069	+	53.7244i	−0.592854	+	1.80900i
$883$	10.9039			0.366945			0.183473	−	0.983025i	$-0.441266\pi$
$883$	10.9039			0.366945			0.183473	+	0.983025i	$0.441266\pi$
$884$			40.3428i			1.35687i
$885$	2.38021	−	3.45004i	0.0800099	−	0.115972i
$886$	−68.6531			−2.30645
$887$	16.3421			0.548712			0.274356	−	0.961628i	$-0.411535\pi$
$887$	16.3421			0.548712			0.274356	+	0.961628i	$0.411535\pi$
$888$	41.4972	+	28.6292i	1.39256	+	0.960734i
$889$	1.11615	−	0.533079i	0.0374344	−	0.0178789i
$890$			149.665i			5.01677i
$891$	1.95002	+	2.19700i	0.0653283	+	0.0736024i
$892$		−	37.2592i		−	1.24753i
$893$		−	10.1320i		−	0.339054i
$894$	30.9189	−	44.8160i	1.03408	−	1.49887i
$895$		−	27.0041i		−	0.902648i
$896$	25.4115	+	53.2060i	0.848938	+	1.77749i
$897$	−1.35923	+	1.97016i	−0.0453833	+	0.0657818i
$898$	−49.6662			−1.65738
$899$	−9.01311			−0.300604
$900$	55.1681	+	145.263i	1.83894	+	4.84209i
$901$		−	50.3057i		−	1.67593i
$902$	−2.20918			−0.0735577
$903$	−0.843401	+	5.28167i	−0.0280666	+	0.175763i
$904$	71.0461			2.36296
$905$			48.1381i			1.60016i
$906$	−29.4137	−	20.2927i	−0.977206	−	0.674181i
$907$	15.4118			0.511740			0.255870	−	0.966711i	$-0.417638\pi$
$907$	15.4118			0.511740			0.255870	+	0.966711i	$0.417638\pi$
$908$	−70.5196			−2.34027
$909$	16.0700	+	42.3138i	0.533009	+	1.40346i
$910$	34.2506	−	16.3583i	1.13540	−	0.542272i
$911$			12.1077i			0.401147i	0.979679	+	0.200574i	$0.0642806\pi$
$911$			12.1077i			0.401147i	−0.979679	+	0.200574i	$0.935719\pi$
$912$	19.8561	+	13.6988i	0.657501	+	0.453614i
$913$		−	1.48763i		−	0.0492333i
$914$		−	1.65060i		−	0.0545971i
$915$	12.6203	+	8.70686i	0.417216	+	0.287840i
$916$		−	132.413i		−	4.37504i
$917$	39.4419	−	18.8377i	1.30249	−	0.622075i
$918$	18.5707	−	75.5713i	0.612926	−	2.49422i
$919$	−48.9319			−1.61412			−0.807058	−	0.590472i	$-0.798941\pi$
$919$	−48.9319			−1.61412			−0.807058	+	0.590472i	$0.798941\pi$
$920$	−33.7177			−1.11164
$921$	47.2634	+	32.6074i	1.55738	+	1.07445i
$922$			73.3571i			2.41589i
$923$	10.3803			0.341672
$924$	7.75129	+	1.23776i	0.254999	+	0.0407194i
$925$	32.8547			1.08026
$926$		−	15.2894i		−	0.502441i
$927$	−29.5033	+	11.2048i	−0.969016	+	0.368015i
$928$	176.267			5.78626
$929$	−38.7152			−1.27020			−0.635102	−	0.772428i	$-0.719042\pi$
$929$	−38.7152			−1.27020			−0.635102	+	0.772428i	$0.719042\pi$
$930$	9.20524	−	13.3427i	0.301852	−	0.437525i
$931$	5.81308	+	4.69746i	0.190516	+	0.153953i
$932$			61.1602i			2.00337i
$933$	−16.9627	+	24.5869i	−0.555334	+	0.804940i
$934$			52.9369i			1.73215i
$935$			7.00167i			0.228979i
$936$	12.8702	+	33.8883i	0.420674	+	1.10767i
$937$			4.01037i			0.131013i	0.997852	+	0.0655065i	$0.0208663\pi$
$937$			4.01037i			0.131013i	−0.997852	+	0.0655065i	$0.979134\pi$
$938$	−27.5019	−	57.5829i	−0.897970	−	1.88015i
$939$	0.714863	+	0.493189i	0.0233287	+	0.0160946i
$940$	192.037			6.26357
$941$	40.6842			1.32627			0.663133	−	0.748501i	$-0.269226\pi$
$941$	40.6842			1.32627			0.663133	+	0.748501i	$0.269226\pi$
$942$	−13.4364	+	19.4757i	−0.437782	+	0.634553i
$943$			2.51407i			0.0818694i
$944$	8.18613			0.266436
$945$	−51.9072	+	10.7714i	−1.68854	+	0.350394i
$946$	1.02561			0.0333455
$947$		−	29.7098i		−	0.965438i	−0.875775	−	0.482719i	$-0.839649\pi$
$947$		−	29.7098i		−	0.965438i	0.875775	−	0.482719i	$-0.160351\pi$
$948$	31.0294	−	44.9762i	1.00779	−	1.46076i
$949$	1.31536			0.0426983
$950$	28.3698			0.920438
$951$	3.30838	+	2.28248i	0.107282	+	0.0740144i
$952$	−55.4636	−	116.128i	−1.79758	−	3.76374i
$953$		−	12.8297i		−	0.415596i	−0.978172	−	0.207798i	$-0.933370\pi$
$953$		−	12.8297i		−	0.415596i	0.978172	−	0.207798i	$-0.0666297\pi$
$954$	−25.9310	−	68.2786i	−0.839547	−	2.21060i
$955$			41.5997i			1.34613i
$956$		−	21.6405i		−	0.699903i
$957$	3.20974	−	4.65242i	0.103756	−	0.150391i
$958$			31.8940i			1.03045i
$959$	−18.6470	−	39.0426i	−0.602143	−	1.26075i
$960$	−81.0735	+	117.514i	−2.61664	+	3.79274i
$961$	30.1873			0.973784
$962$	12.3845			0.399292
$963$	8.57225	−	3.25559i	0.276237	−	0.104910i
$964$		−	14.9528i		−	0.481596i
$965$	−48.9372			−1.57535
$966$	1.94541	−	12.1828i	0.0625924	−	0.391976i
$967$	3.36706			0.108277			0.0541387	−	0.998533i	$-0.482759\pi$
$967$	3.36706			0.108277			0.0541387	+	0.998533i	$0.482759\pi$
$968$			95.2515i			3.06150i
$969$	−8.46775	−	5.84196i	−0.272023	−	0.187671i
$970$	−66.3757			−2.13119
$971$	60.5415			1.94287			0.971434	−	0.237310i	$-0.0762658\pi$
$971$	60.5415			1.94287			0.971434	+	0.237310i	$0.0762658\pi$
$972$	−9.95507	−	81.1984i	−0.319309	−	2.60444i
$973$	−11.6436	−	24.3791i	−0.373277	−	0.781558i
$974$		−	31.2475i		−	1.00123i
$975$	19.4450	+	13.4152i	0.622738	+	0.429632i
$976$			29.9451i			0.958518i
$977$		−	36.0087i		−	1.15202i	−0.817443	−	0.576009i	$-0.804609\pi$
$977$		−	36.0087i		−	1.15202i	0.817443	−	0.576009i	$-0.195391\pi$
$978$	−36.2624	−	25.0177i	−1.15954	−	0.799978i
$979$			4.70554i			0.150390i
$980$	−89.0337	+	110.179i	−2.84408	+	3.51953i
$981$	12.8017	+	33.7079i	0.408726	+	1.07621i
$982$	−94.5030			−3.01571
$983$	37.7949			1.20547			0.602735	−	0.797941i	$-0.294078\pi$
$983$	37.7949			1.20547			0.602735	+	0.797941i	$0.294078\pi$
$984$	31.3404	+	21.6220i	0.999096	+	0.689284i
$985$			17.5427i			0.558957i
$986$	−149.733			−4.76845
$987$	−6.85732	+	42.9429i	−0.218271	+	1.36689i
$988$	7.74299			0.246337
$989$		−	1.16716i		−	0.0371135i
$990$	3.60914	+	9.50319i	0.114706	+	0.302031i
$991$	−45.6984			−1.45166			−0.725828	−	0.687876i	$-0.758543\pi$
$991$	−45.6984			−1.45166			−0.725828	+	0.687876i	$0.758543\pi$
$992$	15.8938			0.504629
$993$	−19.3730	+	28.0806i	−0.614785	+	0.891112i
$994$	−48.2799	+	23.0588i	−1.53135	+	0.731380i
$995$		−	86.2442i		−	2.73412i
$996$	−23.5257	+	34.0998i	−0.745440	+	1.08049i
$997$			51.3618i			1.62665i	0.581813	+	0.813323i	$0.302344\pi$
$997$			51.3618i			1.62665i	−0.581813	+	0.813323i	$0.697656\pi$
$998$			26.2174i			0.829898i
$999$	−16.7974	−	4.12776i	−0.531446	−	0.130596i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	483.2.d.d.461.2	yes	44
3.2	odd	2	inner	483.2.d.d.461.43	yes	44
7.6	odd	2	inner	483.2.d.d.461.1	✓	44
21.20	even	2	inner	483.2.d.d.461.44	yes	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
483.2.d.d.461.1	✓	44	7.6	odd	2	inner
483.2.d.d.461.2	yes	44	1.1	even	1	trivial
483.2.d.d.461.43	yes	44	3.2	odd	2	inner
483.2.d.d.461.44	yes	44	21.20	even	2	inner

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:	\( N \)	\(=\)	\( 483 = 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	483.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-2.69219i q^{2} +(0.983586 - 1.42568i) q^{3} -5.24788 q^{4} +3.85613 q^{5} +(-3.83820 - 2.64800i) q^{6} +(2.38743 - 1.14025i) q^{7} +8.74391i q^{8} +(-1.06512 - 2.80455i) q^{9} +O(q^{10})\)	\(q-2.69219i q^{2} +(0.983586 - 1.42568i) q^{3} -5.24788 q^{4} +3.85613 q^{5} +(-3.83820 - 2.64800i) q^{6} +(2.38743 - 1.14025i) q^{7} +8.74391i q^{8} +(-1.06512 - 2.80455i) q^{9} -10.3814i q^{10} -0.326399i q^{11} +(-5.16174 + 7.48179i) q^{12} +1.38191i q^{13} +(-3.06977 - 6.42742i) q^{14} +(3.79283 - 5.49760i) q^{15} +13.0445 q^{16} -5.56290 q^{17} +(-7.55039 + 2.86750i) q^{18} +1.06769i q^{19} -20.2365 q^{20} +(0.722611 - 4.52524i) q^{21} -0.878727 q^{22} +1.00000i q^{23} +(12.4660 + 8.60038i) q^{24} +9.86975 q^{25} +3.72037 q^{26} +(-5.04603 - 1.24000i) q^{27} +(-12.5290 + 5.98390i) q^{28} +9.99790i q^{29} +(-14.8006 - 10.2110i) q^{30} +0.901500i q^{31} -17.6304i q^{32} +(-0.465339 - 0.321041i) q^{33} +14.9764i q^{34} +(9.20625 - 4.39696i) q^{35} +(5.58962 + 14.7180i) q^{36} +3.32883 q^{37} +2.87442 q^{38} +(1.97016 + 1.35923i) q^{39} +33.7177i q^{40} +2.51407 q^{41} +(-12.1828 - 1.94541i) q^{42} -1.16716 q^{43} +1.71290i q^{44} +(-4.10724 - 10.8147i) q^{45} +2.69219 q^{46} -9.48964 q^{47} +(12.8304 - 18.5973i) q^{48} +(4.39965 - 5.44454i) q^{49} -26.5712i q^{50} +(-5.47159 + 7.93091i) q^{51} -7.25211i q^{52} +9.04306i q^{53} +(-3.33832 + 13.5849i) q^{54} -1.25864i q^{55} +(9.97025 + 20.8755i) q^{56} +(1.52218 + 1.05016i) q^{57} +26.9162 q^{58} +0.627554 q^{59} +(-19.9043 + 28.8508i) q^{60} +2.29561i q^{61} +2.42701 q^{62} +(-5.74079 - 5.48118i) q^{63} -21.3754 q^{64} +5.32883i q^{65} +(-0.864303 + 1.25278i) q^{66} +8.95895 q^{67} +29.1935 q^{68} +(1.42568 + 0.983586i) q^{69} +(-11.8374 - 24.7850i) q^{70} -7.51156i q^{71} +(24.5228 - 9.31330i) q^{72} -0.951840i q^{73} -8.96185i q^{74} +(9.70774 - 14.0711i) q^{75} -5.60310i q^{76} +(-0.372176 - 0.779254i) q^{77} +(3.65930 - 5.30405i) q^{78} -6.01142 q^{79} +50.3013 q^{80} +(-6.73104 + 5.97437i) q^{81} -6.76836i q^{82} +4.55771 q^{83} +(-3.79218 + 23.7479i) q^{84} -21.4513 q^{85} +3.14221i q^{86} +(14.2538 + 9.83379i) q^{87} +2.85400 q^{88} -14.4166 q^{89} +(-29.1153 + 11.0575i) q^{90} +(1.57573 + 3.29922i) q^{91} -5.24788i q^{92} +(1.28525 + 0.886702i) q^{93} +25.5479i q^{94} +4.11715i q^{95} +(-25.1353 - 17.3410i) q^{96} -6.39369i q^{97} +(-14.6577 - 11.8447i) q^{98} +(-0.915402 + 0.347653i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q - 76 q^{4} - 8 q^{7} + 20 q^{9}+O(q^{10}) \) 44 * q - 76 * q^4 - 8 * q^7 + 20 * q^9	\( 44 q - 76 q^{4} - 8 q^{7} + 20 q^{9} + 4 q^{15} + 92 q^{16} + 4 q^{18} - 22 q^{21} + 12 q^{22} + 16 q^{25} + 16 q^{28} - 32 q^{30} - 112 q^{37} + 4 q^{39} - 12 q^{42} - 68 q^{43} + 4 q^{46} + 44 q^{49} + 32 q^{51} + 16 q^{57} + 28 q^{58} - 44 q^{60} - 10 q^{63} - 16 q^{64} + 108 q^{67} - 60 q^{70} + 112 q^{72} - 48 q^{78} + 40 q^{79} - 4 q^{81} - 26 q^{84} - 108 q^{85} + 8 q^{88} + 24 q^{91} + 4 q^{93} + 4 q^{99}+O(q^{100}) \) 44 * q - 76 * q^4 - 8 * q^7 + 20 * q^9 + 4 * q^15 + 92 * q^16 + 4 * q^18 - 22 * q^21 + 12 * q^22 + 16 * q^25 + 16 * q^28 - 32 * q^30 - 112 * q^37 + 4 * q^39 - 12 * q^42 - 68 * q^43 + 4 * q^46 + 44 * q^49 + 32 * q^51 + 16 * q^57 + 28 * q^58 - 44 * q^60 - 10 * q^63 - 16 * q^64 + 108 * q^67 - 60 * q^70 + 112 * q^72 - 48 * q^78 + 40 * q^79 - 4 * q^81 - 26 * q^84 - 108 * q^85 + 8 * q^88 + 24 * q^91 + 4 * q^93 + 4 * q^99

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