LMFDB - Embedded newform 483.2.d.d.461.1

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			461.1
Character	$\chi$	$=$	483.461
Dual form			483.2.d.d.461.43

$q$-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} +(-3.97387 + 2.28217i) 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} +(6.14405 + 10.6984i) 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} +(0.654997 - 7.91018i) 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} +(20.8544 - 11.9766i) 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	$-0.830950\pi$
$5$	−3.85613			−1.72451			−0.862257	+	0.506471i	$0.830950\pi$
$6$	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	$-0.938620\pi$
$13$		−	1.38191i		−	0.383273i	0.981466	−	0.191637i	$-0.0613795\pi$
$14$	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	$-0.264316\pi$
$17$	5.56290			1.34920			0.674601	+	0.738182i	$0.264316\pi$
$18$	−7.55039	+	2.86750i	−1.77964	+	0.675877i
$19$		−	1.06769i		−	0.244945i	−0.992472	−	0.122472i	$-0.960918\pi$
$19$		−	1.06769i		−	0.244945i	0.992472	−	0.122472i	$-0.0390823\pi$
$20$	20.2365			4.52502
$21$	−3.97387	+	2.28217i	−0.867170	+	0.498011i
$22$	−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	$-0.974202\pi$
$31$		−	0.901500i		−	0.161914i	0.996718	−	0.0809571i	$-0.0257977\pi$
$32$		−	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	$-0.562898\pi$
$41$	−2.51407			−0.392632			−0.196316	+	0.980541i	$0.562898\pi$
$42$	6.14405	+	10.6984i	0.948047	+	1.65080i
$43$	−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	$-0.256684\pi$
$47$	9.48964			1.38421			0.692103	+	0.721799i	$0.256684\pi$
$48$	−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	$-0.513007\pi$
$59$	−0.627554			−0.0817006			−0.0408503	+	0.999165i	$0.513007\pi$
$60$	−19.9043	+	28.8508i	−2.56964	+	3.72462i
$61$		−	2.29561i		−	0.293923i	−0.989142	−	0.146961i	$-0.953051\pi$
$61$		−	2.29561i		−	0.293923i	0.989142	−	0.146961i	$-0.0469493\pi$
$62$	−2.42701			−0.308230
$63$	0.654997	−	7.91018i	0.0825219	−	0.996589i
$64$	−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	$0.0177397\pi$
$73$			0.951840i			0.111404i	−0.998447	+	0.0557022i	$0.982260\pi$
$74$		−	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	$-0.580476\pi$
$83$	−4.55771			−0.500273			−0.250137	+	0.968211i	$0.580476\pi$
$84$	20.8544	−	11.9766i	2.27540	−	1.30675i
$85$	−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	$-0.223195\pi$
$89$	14.4166			1.52815			0.764076	+	0.645126i	$0.223195\pi$
$90$	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	$0.105226\pi$
$97$			6.39369i			0.649181i	−0.945855	+	0.324590i	$0.894774\pi$
$98$	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	$-0.229748\pi$
$101$	15.0876			1.50127			0.750634	+	0.660719i	$0.229748\pi$
$102$	21.3515	+	14.7306i	2.11412	+	1.45854i
$103$			10.5198i			1.03655i	0.855215	+	0.518273i	$0.173425\pi$
$103$			10.5198i			1.03655i	−0.855215	+	0.518273i	$0.826575\pi$
$104$	12.0833			1.18487
$105$	15.3238	−	8.80037i	1.49545	−	0.858828i
$106$	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
$126$	−21.2957	−	1.76338i	−1.89717	−	0.157094i
$127$	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	$-0.756642\pi$
$131$	−16.5206			−1.44341			−0.721707	+	0.692198i	$0.756642\pi$
$132$	−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	$0.142567\pi$
$139$			10.2114i			0.866123i	−0.901364	+	0.433061i	$0.857433\pi$
$140$	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
$147$	−12.0896	+	0.917321i	−0.997134	+	0.0756594i
$148$	−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	$0.0649007\pi$
$157$			5.07418i			0.404964i	−0.979286	+	0.202482i	$0.935099\pi$
$158$			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	$-0.681925\pi$
$167$	−13.9806			−1.08185			−0.540924	+	0.841071i	$0.681925\pi$
$168$	−19.9551	−	34.7472i	−1.53957	−	2.68080i
$169$	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	$-0.288011\pi$
$173$	16.2527			1.23567			0.617833	+	0.786309i	$0.288011\pi$
$174$	−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	$-0.846433\pi$
$181$		−	12.4835i		−	0.927892i	0.885863	−	0.463946i	$-0.153567\pi$
$182$	−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
$189$	10.6331	+	8.71416i	0.773446	+	0.633862i
$190$	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	$0.291337\pi$
$199$			22.3655i			1.58545i	−0.609582	+	0.792723i	$0.708663\pi$
$200$			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
$210$	−23.6922	−	41.2545i	−1.63492	−	2.84683i
$211$	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	$-0.923600\pi$
$223$		−	7.09986i		−	0.475442i	0.971333	−	0.237721i	$-0.0764004\pi$
$224$	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	$-0.647133\pi$
$227$	−13.4377			−0.891893			−0.445946	+	0.895060i	$0.647133\pi$
$228$	−7.98822	−	5.51113i	−0.529033	−	0.364984i
$229$		−	25.2317i		−	1.66736i	−0.552251	−	0.833678i	$-0.686231\pi$
$229$		−	25.2317i		−	1.66736i	0.552251	−	0.833678i	$-0.313769\pi$
$230$	−10.3814			−0.684531
$231$	0.744899	+	1.29707i	0.0490107	+	0.0853407i
$232$	−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	$-0.970748\pi$
$241$		−	2.84930i		−	0.183539i	0.995780	−	0.0917696i	$-0.0292523\pi$
$242$		−	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	$-0.335908\pi$
$251$	15.6205			0.985958			0.492979	+	0.870041i	$0.335908\pi$
$252$	−3.43735	+	41.5117i	−0.216533	+	2.61499i
$253$	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	$-0.541551\pi$
$257$	−4.17343			−0.260331			−0.130166	+	0.991492i	$0.541551\pi$
$258$	−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	$-0.208853\pi$
$269$	25.9913			1.58472			0.792359	+	0.610055i	$0.208853\pi$
$270$	−12.8730	+	52.3850i	−0.783425	+	3.18805i
$271$			14.5849i			0.885972i	0.896529	+	0.442986i	$0.146081\pi$
$271$			14.5849i			0.885972i	−0.896529	+	0.442986i	$0.853919\pi$
$272$	72.5653			4.39992
$273$	3.15376	+	5.49154i	0.190874	+	0.332363i
$274$	−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	$0.392999\pi$
$283$			31.7621i			1.88806i	−0.329860	+	0.944030i	$0.607001\pi$
$284$			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	$-0.672462\pi$
$293$	−17.6542			−1.03137			−0.515684	+	0.856779i	$0.672462\pi$
$294$	2.46960	+	32.5475i	0.144030	+	1.89821i
$295$	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	$-0.605055\pi$
$307$		−	33.1515i		−	1.89206i	0.324082	−	0.946029i	$-0.394945\pi$
$308$	−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	$-0.337377\pi$
$311$	17.2458			0.977919			0.488959	+	0.872307i	$0.337377\pi$
$312$	−11.8850	+	17.2269i	−0.672854	+	0.975282i
$313$		−	0.501419i		−	0.0283419i	−0.999900	−	0.0141709i	$-0.995489\pi$
$313$		−	0.501419i		−	0.0283419i	0.999900	−	0.0141709i	$-0.00451090\pi$
$314$	13.6607			0.770915
$315$	−2.52576	+	30.5027i	−0.142310	+	1.71863i
$316$	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
$336$	−51.8372	+	29.7698i	−2.82795	+	1.62408i
$337$	−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	$0.225662\pi$
$349$			24.3244i			1.30205i	−0.759054	+	0.651027i	$0.774338\pi$
$350$	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	$-0.440104\pi$
$353$	7.02910			0.374121			0.187061	+	0.982348i	$0.440104\pi$
$354$	−2.40868	−	1.66176i	−0.128020	−	0.0883217i
$355$			28.9656i			1.53733i
$356$	−75.6564			−4.00978
$357$	−22.1063	+	12.6955i	−1.16999	+	0.671918i
$358$	−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	$0.0188733\pi$
$367$			2.27041i			0.118515i	−0.998243	+	0.0592573i	$0.981127\pi$
$368$			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
$378$	23.4602	−	28.6264i	1.20666	−	1.47238i
$379$	−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	$-0.432853\pi$
$383$	8.19559			0.418775			0.209388	+	0.977833i	$0.432853\pi$
$384$	−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	$-0.826008\pi$
$397$		−	20.7137i		−	1.03959i	0.854290	−	0.519797i	$-0.173992\pi$
$398$	60.2121			3.01816
$399$	2.43665	+	4.24286i	0.121985	+	0.212409i
$400$	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	$0.0734246\pi$
$409$			9.24751i			0.457260i	−0.973513	+	0.228630i	$0.926575\pi$
$410$		−	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	$-0.602660\pi$
$419$	−12.9758			−0.633908			−0.316954	+	0.948441i	$0.602660\pi$
$420$	−80.4174	+	46.1833i	−3.92397	+	2.25351i
$421$	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	$0.0280127\pi$
$433$			3.65778i			0.175782i	−0.996130	+	0.0878908i	$0.971987\pi$
$434$	−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	$-0.753833\pi$
$439$		−	29.2721i		−	1.39708i	0.715570	−	0.698541i	$-0.246167\pi$
$440$	−11.0054			−0.524662
$441$	10.5834	−	18.1382i	0.503969	−	0.863722i
$442$	−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	$-0.281191\pi$
$461$	27.2481			1.26907			0.634536	+	0.772894i	$0.281191\pi$
$462$	3.49195	−	2.00541i	0.162460	−	0.0933000i
$463$	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	$-0.349657\pi$
$467$	19.6632			0.909903			0.454951	+	0.890516i	$0.349657\pi$
$468$	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	$-0.412762\pi$
$479$	11.8469			0.541297			0.270649	+	0.962678i	$0.412762\pi$
$480$	−96.9251	−	66.8693i	−4.42400	−	3.05215i
$481$		−	4.60015i		−	0.209749i
$482$	−7.67084			−0.349397
$483$	−2.28217	−	3.97387i	−0.103843	−	0.180818i
$484$	−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	$-0.825577\pi$
$503$	−38.2879			−1.70717			−0.853586	+	0.520952i	$0.825577\pi$
$504$	69.1659	+	5.72724i	3.08089	+	0.255111i
$505$	−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	$-0.371832\pi$
$509$	17.6815			0.783719			0.391860	+	0.920025i	$0.371832\pi$
$510$	−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	$-0.403783\pi$
$521$	13.5900			0.595387			0.297694	+	0.954661i	$0.403783\pi$
$522$	−28.6690	−	75.4881i	−1.25481	−	3.30402i
$523$		−	7.66195i		−	0.335033i	−0.985869	−	0.167517i	$-0.946425\pi$
$523$		−	7.66195i		−	0.335033i	0.985869	−	0.167517i	$-0.0535748\pi$
$524$	86.6983			3.78743
$525$	−39.2211	+	22.5245i	−1.71175	+	0.983049i
$526$	−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
$546$	14.7843	−	8.49053i	0.632708	−	0.363361i
$547$	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	$-0.525900\pi$
$563$	−3.85701			−0.162553			−0.0812767	+	0.996692i	$0.525900\pi$
$564$	48.9831	−	70.9995i	2.06256	−	2.98962i
$565$			31.3319i			1.31814i
$566$	85.5095			3.59423
$567$	−22.8822	+	6.58831i	−0.960961	+	0.276683i
$568$	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	$-0.933456\pi$
$577$		−	9.97035i		−	0.415071i	0.978227	−	0.207535i	$-0.0665442\pi$
$578$		−	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	$-0.712577\pi$
$587$	−30.0082			−1.23857			−0.619285	+	0.785167i	$0.712577\pi$
$588$	63.4448	−	4.81399i	2.61642	−	0.198526i
$589$	−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	$-0.539116\pi$
$593$	−5.96994			−0.245156			−0.122578	+	0.992459i	$0.539116\pi$
$594$	−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	$-0.819649\pi$
$601$		−	26.3175i		−	1.07352i	0.843737	−	0.536758i	$-0.180351\pi$
$602$	−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	$-0.956079\pi$
$607$		−	6.77740i		−	0.275086i	0.990496	−	0.137543i	$-0.0439205\pi$
$608$	−18.8238			−0.763406
$609$	−22.8170	−	39.7304i	−0.924590	−	1.60996i
$610$	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	$0.222755\pi$
$619$			32.0484i			1.28814i	−0.764968	+	0.644068i	$0.777245\pi$
$620$		−	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
$630$	82.1190	+	6.79981i	3.27170	+	0.270911i
$631$	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	$-0.933630\pi$
$643$		−	10.4980i		−	0.414000i	0.978341	−	0.207000i	$-0.0663700\pi$
$644$	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	$-0.367580\pi$
$647$	20.5582			0.808225			0.404113	+	0.914709i	$0.367580\pi$
$648$	−52.2393	−	58.8556i	−2.05215	−	2.31207i
$649$			0.204833i			0.00804039i
$650$	−36.7191			−1.44024
$651$	2.05738	+	3.58245i	0.0806351	+	0.140407i
$652$	−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	$0.161433\pi$
$661$			24.9742i			0.971386i	−0.874130	+	0.485693i	$0.838567\pi$
$662$			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
$672$	40.2357	+	70.0611i	1.55213	+	2.70266i
$673$	−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	$-0.781893\pi$
$677$	−40.2929			−1.54858			−0.774291	+	0.632830i	$0.781893\pi$
$678$	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	$-0.822690\pi$
$691$		−	27.7943i		−	1.05734i	0.848826	−	0.528672i	$-0.177310\pi$
$692$	−85.2920			−3.24232
$693$	−2.58187	−	0.213790i	−0.0980772	−	0.00812122i
$694$	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
$714$	34.1787	+	59.5143i	1.27911	+	2.22727i
$715$	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	$-0.935756\pi$
$719$	−52.5398			−1.95940			−0.979702	+	0.200461i	$0.935756\pi$
$720$	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	$0.149332\pi$
$727$			24.3809i			0.904239i	−0.891957	+	0.452120i	$0.850668\pi$
$728$	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	$-0.762686\pi$
$733$		−	36.7324i		−	1.35674i	0.734719	−	0.678371i	$-0.237314\pi$
$734$	6.11239			0.225612
$735$	46.6191	−	3.53731i	1.71957	−	0.130476i
$736$	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
$756$	−55.8014	−	45.7309i	−2.02948	−	1.66322i
$757$	−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	$-0.452090\pi$
$761$	8.27288			0.299892			0.149946	+	0.988694i	$0.452090\pi$
$762$	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	$-0.973077\pi$
$769$		−	4.68540i		−	0.168960i	0.996425	−	0.0844800i	$-0.0269229\pi$
$770$	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	$-0.470452\pi$
$773$	5.15437			0.185390			0.0926949	+	0.995695i	$0.470452\pi$
$774$	8.81249	−	3.34683i	0.316759	−	0.120299i
$775$		−	8.89758i		−	0.319610i
$776$	−55.9058			−2.00690
$777$	−13.2284	+	7.59698i	−0.474565	+	0.272540i
$778$	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	$-0.821449\pi$
$787$		−	29.8477i		−	1.06396i	0.846758	−	0.531978i	$-0.178551\pi$
$788$		−	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	$-0.590007\pi$
$797$	−15.7537			−0.558023			−0.279012	+	0.960288i	$0.590007\pi$
$798$	11.4226	−	6.55993i	0.404355	−	0.232219i
$799$	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	$-0.955016\pi$
$811$		−	8.02230i		−	0.281701i	0.990031	−	0.140850i	$-0.0449837\pi$
$812$	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
$819$	−10.9312	−	0.905148i	−0.381966	−	0.0316284i
$820$	−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	$-0.996587\pi$
$829$		−	0.617412i		−	0.0214436i	0.999943	−	0.0107218i	$-0.00341292\pi$
$830$		−	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	$-0.507516\pi$
$839$	−1.36766			−0.0472169			−0.0236085	+	0.999721i	$0.507516\pi$
$840$	76.9496	+	133.990i	2.65501	+	4.62309i
$841$	−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	$0.357305\pi$
$853$			52.6406i			1.80238i	−0.433426	+	0.901189i	$0.642695\pi$
$854$	−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	$-0.708957\pi$
$857$	−35.7334			−1.22063			−0.610315	+	0.792159i	$0.708957\pi$
$858$	−1.73123	−	1.19439i	−0.0591033	−	0.0407758i
$859$			24.9261i			0.850468i	0.905083	+	0.425234i	$0.139808\pi$
$859$			24.9261i			0.850468i	−0.905083	+	0.425234i	$0.860192\pi$
$860$	−23.6192			−0.805408
$861$	9.99061	−	5.73755i	0.340479	−	0.195535i
$862$	−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	$-0.603807\pi$
$881$	−19.0181			−0.640737			−0.320368	+	0.947293i	$0.603807\pi$
$882$	−48.8313	−	28.4924i	−1.64424	−	0.959389i
$883$	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	$-0.588465\pi$
$887$	−16.3421			−0.548712			−0.274356	+	0.961628i	$0.588465\pi$
$888$	−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
$903$	4.63814	−	2.66366i	0.154348	−	0.0886410i
$904$	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
$924$	−3.90914	−	6.80685i	−0.128601	−	0.223929i
$925$	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	$-0.280958\pi$
$929$	38.7152			1.27020			0.635102	+	0.772428i	$0.280958\pi$
$930$	−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	$-0.979134\pi$
$937$		−	4.01037i		−	0.131013i	0.997852	−	0.0655065i	$-0.0208663\pi$
$938$	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	$-0.730774\pi$
$941$	−40.6842			−1.32627			−0.663133	+	0.748501i	$0.730774\pi$
$942$	−13.4364	+	19.4757i	−0.437782	+	0.634553i
$943$		−	2.51407i		−	0.0818694i
$944$	−8.18613			−0.266436
$945$	−41.0027	−	33.6029i	−1.33382	−	1.09310i
$946$	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
$966$	−10.6984	+	6.14405i	−0.344216	+	0.197681i
$967$	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	$-0.923734\pi$
$971$	−60.5415			−1.94287			−0.971434	+	0.237310i	$0.923734\pi$
$972$	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	$-0.705922\pi$
$983$	−37.7949			−1.20547			−0.602735	+	0.797941i	$0.705922\pi$
$984$	31.3404	+	21.6220i	0.999096	+	0.689284i
$985$		−	17.5427i		−	0.558957i
$986$	149.733			4.76845
$987$	−37.7106	+	21.6570i	−1.20034	+	0.689351i
$988$	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	$-0.697656\pi$
$997$		−	51.3618i		−	1.62665i	0.581813	−	0.813323i	$-0.302344\pi$
$998$			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.461.1	✓	44
3.2	odd	2	inner	483.2.d.d.461.44	yes	44
7.6	odd	2	inner	483.2.d.d.461.2	yes	44
21.20	even	2	inner	483.2.d.d.461.43	yes	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
483.2.d.d.461.1	✓	44	1.1	even	1	trivial
483.2.d.d.461.2	yes	44	7.6	odd	2	inner
483.2.d.d.461.43	yes	44	21.20	even	2	inner
483.2.d.d.461.44	yes	44	3.2	odd	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} +(-3.97387 + 2.28217i) 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} +(6.14405 + 10.6984i) 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} +(0.654997 - 7.91018i) 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} +(20.8544 - 11.9766i) 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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