LMFDB - Embedded newform 476.3.s.a.341.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [476,3,Mod(341,476)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(476, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 5, 0]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("476.341");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 476 = 2^{2} \cdot 7 \cdot 17 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	476.s (of order $6$, degree $2$, 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:	$12.9700605836$
Analytic rank:	$0$
Dimension:	$44$
Relative dimension:	$22$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			341.16
Character	$\chi$	$=$	476.341
Dual form			476.3.s.a.409.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.37662 - 1.37214i) q^{3} +(-2.65296 - 1.53169i) q^{5} +(0.400909 + 6.98851i) q^{7} +(-0.734465 + 1.27213i) q^{9} +O(q^{10})$	\(q+(2.37662 - 1.37214i) q^{3} +(-2.65296 - 1.53169i) q^{5} +(0.400909 + 6.98851i) q^{7} +(-0.734465 + 1.27213i) q^{9} +(4.33786 + 7.51339i) q^{11} +5.66933i q^{13} -8.40677 q^{15} +(-3.57071 + 2.06155i) q^{17} +(19.0218 + 10.9823i) q^{19} +(10.5420 + 16.0589i) q^{21} +(-13.5826 + 23.5258i) q^{23} +(-7.80785 - 13.5236i) q^{25} +28.7297i q^{27} +26.3170 q^{29} +(1.36816 - 0.789908i) q^{31} +(20.6188 + 11.9043i) q^{33} +(9.64063 - 19.1543i) q^{35} +(17.0248 - 29.4878i) q^{37} +(7.77911 + 13.4738i) q^{39} +49.7950i q^{41} +67.9537 q^{43} +(3.89702 - 2.24994i) q^{45} +(-12.0328 - 6.94715i) q^{47} +(-48.6785 + 5.60351i) q^{49} +(-5.65748 + 9.79904i) q^{51} +(-7.94143 - 13.7550i) q^{53} -26.5770i q^{55} +60.2768 q^{57} +(-12.2086 + 7.04863i) q^{59} +(-43.0707 - 24.8669i) q^{61} +(-9.18475 - 4.62281i) q^{63} +(8.68365 - 15.0405i) q^{65} +(-7.75501 - 13.4321i) q^{67} +74.5491i q^{69} -29.1781 q^{71} +(90.4343 - 52.2123i) q^{73} +(-37.1125 - 21.4269i) q^{75} +(-50.7683 + 33.3274i) q^{77} +(-19.3045 + 33.4364i) q^{79} +(32.8109 + 56.8302i) q^{81} +67.7467i q^{83} +12.6306 q^{85} +(62.5454 - 36.1106i) q^{87} +(66.1837 + 38.2112i) q^{89} +(-39.6202 + 2.27288i) q^{91} +(2.16773 - 3.75462i) q^{93} +(-33.6428 - 58.2711i) q^{95} +133.750i q^{97} -12.7440 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q - 6 q^{3} + 22 q^{7} + 88 q^{9}+O(q^{10}) $ 44 * q - 6 * q^3 + 22 * q^7 + 88 * q^9	$ 44 q - 6 q^{3} + 22 q^{7} + 88 q^{9} + 8 q^{11} + 16 q^{15} - 54 q^{19} - 16 q^{21} - 52 q^{23} + 150 q^{25} + 8 q^{29} + 78 q^{31} - 6 q^{33} + 10 q^{35} - 34 q^{37} - 60 q^{39} - 76 q^{43} - 72 q^{45} - 6 q^{47} - 56 q^{49} - 172 q^{53} - 64 q^{57} + 30 q^{59} + 444 q^{61} + 206 q^{63} - 54 q^{65} - 56 q^{67} + 204 q^{71} - 48 q^{73} + 132 q^{75} - 494 q^{77} - 16 q^{79} - 342 q^{81} + 594 q^{87} - 252 q^{89} + 284 q^{91} - 146 q^{93} + 148 q^{95} - 180 q^{99}+O(q^{100}) $ 44 * q - 6 * q^3 + 22 * q^7 + 88 * q^9 + 8 * q^11 + 16 * q^15 - 54 * q^19 - 16 * q^21 - 52 * q^23 + 150 * q^25 + 8 * q^29 + 78 * q^31 - 6 * q^33 + 10 * q^35 - 34 * q^37 - 60 * q^39 - 76 * q^43 - 72 * q^45 - 6 * q^47 - 56 * q^49 - 172 * q^53 - 64 * q^57 + 30 * q^59 + 444 * q^61 + 206 * q^63 - 54 * q^65 - 56 * q^67 + 204 * q^71 - 48 * q^73 + 132 * q^75 - 494 * q^77 - 16 * q^79 - 342 * q^81 + 594 * q^87 - 252 * q^89 + 284 * q^91 - 146 * q^93 + 148 * q^95 - 180 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/476\mathbb{Z}\right)^\times$.

$n$	$239$	$309$	$409$
$\chi(n)$	$1$	$1$	$e\left(\frac{5}{6}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	2.37662	−	1.37214i	0.792205	−	0.457380i	−0.0485331	−	0.998822i	$-0.515455\pi$
$3$	2.37662	−	1.37214i	0.792205	−	0.457380i	0.840738	+	0.541442i	$0.182121\pi$
$4$		0			0
$5$	−2.65296	−	1.53169i	−0.530593	−	0.306338i	0.210665	−	0.977558i	$-0.432437\pi$
$5$	−2.65296	−	1.53169i	−0.530593	−	0.306338i	−0.741258	+	0.671220i	$0.765770\pi$
$6$		0			0
$7$	0.400909	+	6.98851i	0.0572727	+	0.998359i
$7$	0.400909	+	6.98851i	0.0572727	+	0.998359i
$8$		0			0
$9$	−0.734465	+	1.27213i	−0.0816072	+	0.141348i
$10$		0			0
$11$	4.33786	+	7.51339i	0.394351	+	0.683036i	0.993018	−	0.117962i	$-0.0376362\pi$
$11$	4.33786	+	7.51339i	0.394351	+	0.683036i	−0.598667	+	0.800998i	$0.704303\pi$
$12$		0			0
$13$			5.66933i			0.436102i	0.975937	+	0.218051i	$0.0699700\pi$
$13$			5.66933i			0.436102i	−0.975937	+	0.218051i	$0.930030\pi$
$14$		0			0
$15$	−8.40677			−0.560451
$16$		0			0
$17$	−3.57071	+	2.06155i	−0.210042	+	0.121268i
$17$	−3.57071	+	2.06155i	−0.210042	+	0.121268i
$18$		0			0
$19$	19.0218	+	10.9823i	1.00115	+	0.578013i	0.908588	−	0.417694i	$-0.137161\pi$
$19$	19.0218	+	10.9823i	1.00115	+	0.578013i	0.0925606	+	0.995707i	$0.470495\pi$
$20$		0			0
$21$	10.5420	+	16.0589i	0.502001	+	0.764710i
$22$		0			0
$23$	−13.5826	+	23.5258i	−0.590549	+	1.02286i	0.403609	+	0.914931i	$0.367755\pi$
$23$	−13.5826	+	23.5258i	−0.590549	+	1.02286i	−0.994159	+	0.107930i	$0.965578\pi$
$24$		0			0
$25$	−7.80785	−	13.5236i	−0.312314	−	0.540944i
$26$		0			0
$27$			28.7297i			1.06406i
$28$		0			0
$29$	26.3170			0.907482			0.453741	−	0.891133i	$-0.350089\pi$
$29$	26.3170			0.907482			0.453741	+	0.891133i	$0.350089\pi$
$30$		0			0
$31$	1.36816	−	0.789908i	0.0441342	−	0.0254809i	−0.477771	−	0.878485i	$-0.658555\pi$
$31$	1.36816	−	0.789908i	0.0441342	−	0.0254809i	0.521905	+	0.853004i	$0.325222\pi$
$32$		0			0
$33$	20.6188	+	11.9043i	0.624814	+	0.360736i
$34$		0			0
$35$	9.64063	−	19.1543i	0.275447	−	0.547267i
$36$		0			0
$37$	17.0248	−	29.4878i	0.460130	−	0.796968i	−0.538837	−	0.842410i	$-0.681136\pi$
$37$	17.0248	−	29.4878i	0.460130	−	0.796968i	0.998967	+	0.0454416i	$0.0144695\pi$
$38$		0			0
$39$	7.77911	+	13.4738i	0.199464	+	0.345483i
$40$		0			0
$41$			49.7950i			1.21451i	0.794506	+	0.607256i	$0.207730\pi$
$41$			49.7950i			1.21451i	−0.794506	+	0.607256i	$0.792270\pi$
$42$		0			0
$43$	67.9537			1.58032			0.790159	−	0.612902i	$-0.209998\pi$
$43$	67.9537			1.58032			0.790159	+	0.612902i	$0.209998\pi$
$44$		0			0
$45$	3.89702	−	2.24994i	0.0866004	−	0.0499988i
$46$		0			0
$47$	−12.0328	−	6.94715i	−0.256017	−	0.147812i	0.366499	−	0.930418i	$-0.380556\pi$
$47$	−12.0328	−	6.94715i	−0.256017	−	0.147812i	−0.622516	+	0.782607i	$0.713890\pi$
$48$		0			0
$49$	−48.6785	+	5.60351i	−0.993440	+	0.114357i
$50$		0			0
$51$	−5.65748	+	9.79904i	−0.110931	+	0.192138i
$52$		0			0
$53$	−7.94143	−	13.7550i	−0.149838	−	0.259527i	0.781329	−	0.624119i	$-0.214542\pi$
$53$	−7.94143	−	13.7550i	−0.149838	−	0.259527i	−0.931168	+	0.364592i	$0.881209\pi$
$54$		0			0
$55$		−	26.5770i		−	0.483218i
$56$		0			0
$57$	60.2768			1.05749
$58$		0			0
$59$	−12.2086	+	7.04863i	−0.206925	+	0.119468i	−0.599882	−	0.800089i	$-0.704786\pi$
$59$	−12.2086	+	7.04863i	−0.206925	+	0.119468i	0.392956	+	0.919557i	$0.371452\pi$
$60$		0			0
$61$	−43.0707	−	24.8669i	−0.706078	−	0.407654i	0.103529	−	0.994626i	$-0.466986\pi$
$61$	−43.0707	−	24.8669i	−0.706078	−	0.407654i	−0.809607	+	0.586972i	$0.800320\pi$
$62$		0			0
$63$	−9.18475	−	4.62281i	−0.145790	−	0.0733779i
$64$		0			0
$65$	8.68365	−	15.0405i	0.133595	−	0.231393i
$66$		0			0
$67$	−7.75501	−	13.4321i	−0.115746	−	0.200479i	0.802331	−	0.596879i	$-0.203593\pi$
$67$	−7.75501	−	13.4321i	−0.115746	−	0.200479i	−0.918078	+	0.396400i	$0.870259\pi$
$68$		0			0
$69$			74.5491i			1.08042i
$70$		0			0
$71$	−29.1781			−0.410959			−0.205480	−	0.978661i	$-0.565875\pi$
$71$	−29.1781			−0.410959			−0.205480	+	0.978661i	$0.565875\pi$
$72$		0			0
$73$	90.4343	−	52.2123i	1.23883	−	0.715237i	0.269972	−	0.962868i	$-0.412985\pi$
$73$	90.4343	−	52.2123i	1.23883	−	0.715237i	0.968854	+	0.247631i	$0.0796521\pi$
$74$		0			0
$75$	−37.1125	−	21.4269i	−0.494834	−	0.285692i
$76$		0			0
$77$	−50.7683	+	33.3274i	−0.659329	+	0.432823i
$78$		0			0
$79$	−19.3045	+	33.4364i	−0.244361	+	0.423245i	−0.961952	−	0.273220i	$-0.911911\pi$
$79$	−19.3045	+	33.4364i	−0.244361	+	0.423245i	0.717591	+	0.696465i	$0.245245\pi$
$80$		0			0
$81$	32.8109	+	56.8302i	0.405073	+	0.701608i
$82$		0			0
$83$			67.7467i			0.816225i	0.912932	+	0.408113i	$0.133813\pi$
$83$			67.7467i			0.816225i	−0.912932	+	0.408113i	$0.866187\pi$
$84$		0			0
$85$	12.6306			0.148596
$86$		0			0
$87$	62.5454	−	36.1106i	0.718912	−	0.415064i
$88$		0			0
$89$	66.1837	+	38.2112i	0.743637	+	0.429339i	0.823390	−	0.567476i	$-0.192080\pi$
$89$	66.1837	+	38.2112i	0.743637	+	0.429339i	−0.0797534	+	0.996815i	$0.525413\pi$
$90$		0			0
$91$	−39.6202	+	2.27288i	−0.435386	+	0.0249767i
$92$		0			0
$93$	2.16773	−	3.75462i	0.0233089	−	0.0403722i
$94$		0			0
$95$	−33.6428	−	58.2711i	−0.354135	−	0.613380i
$96$		0			0
$97$			133.750i			1.37887i	0.724347	+	0.689435i	$0.242141\pi$
$97$			133.750i			1.37887i	−0.724347	+	0.689435i	$0.757859\pi$
$98$		0			0
$99$	−12.7440			−0.128727
$100$		0			0
$101$	−70.8624	+	40.9125i	−0.701608	+	0.405074i	−0.807946	−	0.589256i	$-0.799421\pi$
$101$	−70.8624	+	40.9125i	−0.701608	+	0.405074i	0.106338	+	0.994330i	$0.466088\pi$
$102$		0			0
$103$	−107.940	−	62.3191i	−1.04796	−	0.605040i	−0.125882	−	0.992045i	$-0.540176\pi$
$103$	−107.940	−	62.3191i	−1.04796	−	0.605040i	−0.922078	+	0.387005i	$0.873510\pi$
$104$		0			0
$105$	−3.37035	−	58.7508i	−0.0320985	−	0.559531i
$106$		0			0
$107$	50.0307	−	86.6557i	0.467576	−	0.809866i	−0.531737	−	0.846909i	$-0.678461\pi$
$107$	50.0307	−	86.6557i	0.467576	−	0.809866i	0.999314	+	0.0370432i	$0.0117939\pi$
$108$		0			0
$109$	35.2524	+	61.0589i	0.323416	+	0.560173i	0.981191	−	0.193042i	$-0.0618353\pi$
$109$	35.2524	+	61.0589i	0.323416	+	0.560173i	−0.657774	+	0.753215i	$0.728502\pi$
$110$		0			0
$111$		−	93.4417i		−	0.841817i
$112$		0			0
$113$	−179.849			−1.59159			−0.795794	−	0.605568i	$-0.792946\pi$
$113$	−179.849			−1.59159			−0.795794	+	0.605568i	$0.792946\pi$
$114$		0			0
$115$	72.0685	−	41.6088i	0.626682	−	0.361815i
$116$		0			0
$117$	−7.21213	−	4.16392i	−0.0616421	−	0.0355891i
$118$		0			0
$119$	−15.8387	−	24.1275i	−0.133098	−	0.202752i
$120$		0			0
$121$	22.8660	−	39.6050i	0.188975	−	0.327314i
$122$		0			0
$123$	68.3257	+	118.344i	0.555494	+	0.962143i
$124$		0			0
$125$			124.421i			0.995371i
$126$		0			0
$127$	165.734			1.30499			0.652494	−	0.757794i	$-0.273723\pi$
$127$	165.734			1.30499			0.652494	+	0.757794i	$0.273723\pi$
$128$		0			0
$129$	161.500	−	93.2420i	1.25194	−	0.722806i
$130$		0			0
$131$	56.0304	+	32.3491i	0.427713	+	0.246940i	0.698372	−	0.715735i	$-0.253908\pi$
$131$	56.0304	+	32.3491i	0.427713	+	0.246940i	−0.270659	+	0.962675i	$0.587242\pi$
$132$		0			0
$133$	−69.1236	+	137.337i	−0.519726	+	1.03261i
$134$		0			0
$135$	44.0049	−	76.2188i	0.325963	−	0.564584i
$136$		0			0
$137$	−95.4983	−	165.408i	−0.697068	−	1.20736i	−0.969479	−	0.245176i	$-0.921154\pi$
$137$	−95.4983	−	165.408i	−0.697068	−	1.20736i	0.272411	−	0.962181i	$-0.412179\pi$
$138$		0			0
$139$		−	194.770i		−	1.40122i	−0.713543	−	0.700611i	$-0.752911\pi$
$139$		−	194.770i		−	1.40122i	0.713543	−	0.700611i	$-0.247089\pi$
$140$		0			0
$141$	−38.1298			−0.270424
$142$		0			0
$143$	−42.5959	+	24.5927i	−0.297873	+	0.171977i
$144$		0			0
$145$	−69.8180	−	40.3095i	−0.481504	−	0.277996i
$146$		0			0
$147$	−108.001	+	80.1112i	−0.734703	+	0.544974i
$148$		0			0
$149$	−38.7666	+	67.1457i	−0.260178	+	0.450642i	−0.966289	−	0.257459i	$-0.917115\pi$
$149$	−38.7666	+	67.1457i	−0.260178	+	0.450642i	0.706111	+	0.708101i	$0.250448\pi$
$150$		0			0
$151$	−78.9321	−	136.714i	−0.522729	−	0.905393i	−0.999650	−	0.0264470i	$-0.991581\pi$
$151$	−78.9321	−	136.714i	−0.522729	−	0.905393i	0.476921	−	0.878946i	$-0.341753\pi$
$152$		0			0
$153$		−	6.05655i		−	0.0395853i
$154$		0			0
$155$	−4.83958			−0.0312231
$156$		0			0
$157$	−93.4730	+	53.9667i	−0.595369	+	0.343737i	−0.767218	−	0.641387i	$-0.778359\pi$
$157$	−93.4730	+	53.9667i	−0.595369	+	0.343737i	0.171848	+	0.985123i	$0.445026\pi$
$158$		0			0
$159$	−37.7474	−	21.7935i	−0.237405	−	0.137066i
$160$		0			0
$161$	−169.856	−	85.4907i	−1.05500	−	0.530998i
$162$		0			0
$163$	30.9548	−	53.6153i	0.189907	−	0.328928i	−0.755312	−	0.655365i	$-0.772515\pi$
$163$	30.9548	−	53.6153i	0.189907	−	0.328928i	0.945219	+	0.326437i	$0.105848\pi$
$164$		0			0
$165$	−36.4674	−	63.1634i	−0.221014	−	0.382808i
$166$		0			0
$167$		−	228.870i		−	1.37048i	−0.728318	−	0.685240i	$-0.759697\pi$
$167$		−	228.870i		−	1.37048i	0.728318	−	0.685240i	$-0.240303\pi$
$168$		0			0
$169$	136.859			0.809815
$170$		0			0
$171$	−27.9417	+	16.1322i	−0.163402	+	0.0943401i
$172$		0			0
$173$	−280.073	−	161.700i	−1.61892	−	0.934682i	−0.987201	−	0.159483i	$-0.949017\pi$
$173$	−280.073	−	161.700i	−1.61892	−	0.934682i	−0.631717	−	0.775199i	$-0.717649\pi$
$174$		0			0
$175$	91.3796	−	59.9870i	0.522169	−	0.342783i
$176$		0			0
$177$	−19.3434	+	33.5038i	−0.109285	+	0.189287i
$178$		0			0
$179$	−52.5859	−	91.0815i	−0.293776	−	0.508835i	0.680923	−	0.732355i	$-0.261579\pi$
$179$	−52.5859	−	91.0815i	−0.293776	−	0.508835i	−0.974699	+	0.223519i	$0.928245\pi$
$180$		0			0
$181$		−	126.817i		−	0.700644i	−0.936629	−	0.350322i	$-0.886072\pi$
$181$		−	126.817i		−	0.700644i	0.936629	−	0.350322i	$-0.113928\pi$
$182$		0			0
$183$	−136.483			−0.745811
$184$		0			0
$185$	−90.3324	+	52.1535i	−0.488283	+	0.281911i
$186$		0			0
$187$	−30.9785	−	17.8854i	−0.165660	−	0.0956441i
$188$		0			0
$189$	−200.778	+	11.5180i	−1.06232	+	0.0609417i
$190$		0			0
$191$	104.265	−	180.593i	0.545892	−	0.945512i	−0.452659	−	0.891684i	$-0.649524\pi$
$191$	104.265	−	180.593i	0.545892	−	0.945512i	0.998550	−	0.0538281i	$-0.0171423\pi$
$192$		0			0
$193$	157.217	+	272.307i	0.814594	+	1.41092i	0.909619	+	0.415443i	$0.136374\pi$
$193$	157.217	+	272.307i	0.814594	+	1.41092i	−0.0950249	+	0.995475i	$0.530293\pi$
$194$		0			0
$195$		−	47.6608i		−	0.244414i
$196$		0			0
$197$	−2.83175			−0.0143744			−0.00718719	−	0.999974i	$-0.502288\pi$
$197$	−2.83175			−0.0143744			−0.00718719	+	0.999974i	$0.502288\pi$
$198$		0			0
$199$	192.063	−	110.887i	0.965139	−	0.557223i	0.0673879	−	0.997727i	$-0.478533\pi$
$199$	192.063	−	110.887i	0.965139	−	0.557223i	0.897751	+	0.440504i	$0.145200\pi$
$200$		0			0
$201$	−36.8614	−	21.2819i	−0.183390	−	0.105880i
$202$		0			0
$203$	10.5507	+	183.917i	0.0519739	+	0.905993i
$204$		0			0
$205$	76.2705	−	132.104i	0.372051	−	0.644412i
$206$		0			0
$207$	−19.9519	−	34.5578i	−0.0963861	−	0.166946i
$208$		0			0
$209$			190.558i			0.911760i
$210$		0			0
$211$	98.6658			0.467610			0.233805	−	0.972283i	$-0.424882\pi$
$211$	98.6658			0.467610			0.233805	+	0.972283i	$0.424882\pi$
$212$		0			0
$213$	−69.3452	+	40.0365i	−0.325564	+	0.187965i
$214$		0			0
$215$	−180.279	−	104.084i	−0.838506	−	0.484112i
$216$		0			0
$217$	6.06879	+	9.24473i	0.0279668	+	0.0426024i
$218$		0			0
$219$	143.285	−	248.177i	0.654270	−	1.13323i
$220$		0			0
$221$	−11.6876	−	20.2436i	−0.0528852	−	0.0915998i
$222$		0			0
$223$			46.2291i			0.207305i	0.994614	+	0.103653i	$0.0330530\pi$
$223$			46.2291i			0.207305i	−0.994614	+	0.103653i	$0.966947\pi$
$224$		0			0
$225$	22.9384			0.101948
$226$		0			0
$227$	295.544	−	170.632i	1.30195	−	0.751684i	0.321215	−	0.947006i	$-0.395909\pi$
$227$	295.544	−	170.632i	1.30195	−	0.751684i	0.980739	+	0.195322i	$0.0625753\pi$
$228$		0			0
$229$	−6.72996	−	3.88554i	−0.0293885	−	0.0169674i	0.485234	−	0.874384i	$-0.338734\pi$
$229$	−6.72996	−	3.88554i	−0.0293885	−	0.0169674i	−0.514622	+	0.857417i	$0.672068\pi$
$230$		0			0
$231$	−74.9270	+	148.868i	−0.324359	+	0.644448i
$232$		0			0
$233$	123.791	−	214.412i	0.531290	−	0.920221i	−0.468043	−	0.883706i	$-0.655041\pi$
$233$	123.791	−	214.412i	0.531290	−	0.920221i	0.999333	−	0.0365157i	$-0.0116259\pi$
$234$		0			0
$235$	21.2817	+	36.8611i	0.0905606	+	0.156856i
$236$		0			0
$237$			105.954i			0.447063i
$238$		0			0
$239$	259.517			1.08584			0.542922	−	0.839783i	$-0.317318\pi$
$239$	259.517			1.08584			0.542922	+	0.839783i	$0.317318\pi$
$240$		0			0
$241$	−165.701	+	95.6674i	−0.687555	+	0.396960i	−0.802696	−	0.596389i	$-0.796602\pi$
$241$	−165.701	+	95.6674i	−0.687555	+	0.396960i	0.115140	+	0.993349i	$0.463268\pi$
$242$		0			0
$243$	−67.9676	−	39.2411i	−0.279702	−	0.161486i
$244$		0			0
$245$	137.725	+	59.6945i	0.562144	+	0.243651i
$246$		0			0
$247$	−62.2620	+	107.841i	−0.252073	+	0.436603i
$248$		0			0
$249$	92.9580	+	161.008i	0.373325	+	0.646618i
$250$		0			0
$251$			244.819i			0.975374i	0.873019	+	0.487687i	$0.162159\pi$
$251$			244.819i			0.975374i	−0.873019	+	0.487687i	$0.837841\pi$
$252$		0			0
$253$	−235.678			−0.931534
$254$		0			0
$255$	30.0182	−	17.3310i	0.117718	−	0.0679647i
$256$		0			0
$257$	119.764	+	69.1456i	0.466007	+	0.269049i	0.714567	−	0.699567i	$-0.246624\pi$
$257$	119.764	+	69.1456i	0.466007	+	0.269049i	−0.248560	+	0.968617i	$0.579957\pi$
$258$		0			0
$259$	212.901	+	107.156i	0.822013	+	0.413730i
$260$		0			0
$261$	−19.3289	+	33.4786i	−0.0740571	+	0.128271i
$262$		0			0
$263$	146.477	+	253.706i	0.556948	+	0.964662i	0.997749	+	0.0670571i	$0.0213610\pi$
$263$	146.477	+	253.706i	0.556948	+	0.964662i	−0.440801	+	0.897605i	$0.645306\pi$
$264$		0			0
$265$			48.6552i			0.183605i
$266$		0			0
$267$	209.724			0.785484
$268$		0			0
$269$	28.6207	−	16.5242i	0.106397	−	0.0614281i	−0.445857	−	0.895104i	$-0.647101\pi$
$269$	28.6207	−	16.5242i	0.106397	−	0.0614281i	0.552254	+	0.833676i	$0.313768\pi$
$270$		0			0
$271$	−198.947	−	114.862i	−0.734123	−	0.423846i	0.0858056	−	0.996312i	$-0.472654\pi$
$271$	−198.947	−	114.862i	−0.734123	−	0.423846i	−0.819929	+	0.572466i	$0.805987\pi$
$272$		0			0
$273$	−91.0432	+	59.7662i	−0.333492	+	0.218924i
$274$		0			0
$275$	67.7387	−	117.327i	0.246323	−	0.426643i
$276$		0			0
$277$	214.356	+	371.276i	0.773849	+	1.34035i	0.935439	+	0.353488i	$0.115004\pi$
$277$	214.356	+	371.276i	0.773849	+	1.34035i	−0.161590	+	0.986858i	$0.551662\pi$
$278$		0			0
$279$			2.32064i			0.00831770i
$280$		0			0
$281$	−53.0141			−0.188662			−0.0943312	−	0.995541i	$-0.530071\pi$
$281$	−53.0141			−0.188662			−0.0943312	+	0.995541i	$0.530071\pi$
$282$		0			0
$283$	12.9793	−	7.49361i	0.0458633	−	0.0264792i	−0.476893	−	0.878961i	$-0.658237\pi$
$283$	12.9793	−	7.49361i	0.0458633	−	0.0264792i	0.522756	+	0.852482i	$0.324904\pi$
$284$		0			0
$285$	−159.912	−	92.3253i	−0.561095	−	0.323948i
$286$		0			0
$287$	−347.993	+	19.9633i	−1.21252	+	0.0695584i
$288$		0			0
$289$	8.50000	−	14.7224i	0.0294118	−	0.0509427i
$290$		0			0
$291$	183.524	+	317.873i	0.630668	+	1.09235i
$292$		0			0
$293$			141.143i			0.481717i	0.970560	+	0.240859i	$0.0774290\pi$
$293$			141.143i			0.481717i	−0.970560	+	0.240859i	$0.922571\pi$
$294$		0			0
$295$	43.1853			0.146391
$296$		0			0
$297$	−215.857	+	124.625i	−0.726792	+	0.419614i
$298$		0			0
$299$	−133.376	−	77.0044i	−0.446072	−	0.257540i
$300$		0			0
$301$	27.2432	+	474.895i	0.0905090	+	1.57772i
$302$		0			0
$303$	−112.275	+	194.466i	−0.370545	+	0.641803i
$304$		0			0
$305$	76.1768	+	131.942i	0.249760	+	0.432597i
$306$		0			0
$307$		−	90.2924i		−	0.294112i	−0.989128	−	0.147056i	$-0.953020\pi$
$307$		−	90.2924i		−	0.294112i	0.989128	−	0.147056i	$-0.0469798\pi$
$308$		0			0
$309$	−342.042			−1.10693
$310$		0			0
$311$	−220.863	+	127.515i	−0.710170	+	0.410017i	−0.811124	−	0.584874i	$-0.801144\pi$
$311$	−220.863	+	127.515i	−0.710170	+	0.410017i	0.100954	+	0.994891i	$0.467811\pi$
$312$		0			0
$313$	457.688	+	264.246i	1.46226	+	0.844237i	0.999116	−	0.0420453i	$-0.0133874\pi$
$313$	457.688	+	264.246i	1.46226	+	0.844237i	0.463146	+	0.886282i	$0.346721\pi$
$314$		0			0
$315$	17.2861	+	26.3323i	0.0548765	+	0.0835947i
$316$		0			0
$317$	240.830	−	417.129i	0.759715	−	1.31587i	−0.183280	−	0.983061i	$-0.558672\pi$
$317$	240.830	−	417.129i	0.759715	−	1.31587i	0.942996	−	0.332805i	$-0.107995\pi$
$318$		0			0
$319$	114.159	+	197.730i	0.357866	+	0.619843i
$320$		0			0
$321$		−	274.596i		−	0.855440i
$322$		0			0
$323$	−90.5620			−0.280378
$324$		0			0
$325$	76.6697	−	44.2653i	0.235907	−	0.136201i
$326$		0			0
$327$	167.563	+	96.7423i	0.512424	+	0.295848i
$328$		0			0
$329$	43.7261	−	86.8766i	0.132906	−	0.264063i
$330$		0			0
$331$	79.5012	−	137.700i	0.240185	−	0.416012i	−0.720582	−	0.693370i	$-0.756125\pi$
$331$	79.5012	−	137.700i	0.240185	−	0.416012i	0.960767	+	0.277357i	$0.0894586\pi$
$332$		0			0
$333$	25.0082	+	43.3156i	0.0750998	+	0.130077i
$334$		0			0
$335$			47.5131i			0.141830i
$336$		0			0
$337$	544.256			1.61500			0.807502	−	0.589865i	$-0.200819\pi$
$337$	544.256			1.61500			0.807502	+	0.589865i	$0.200819\pi$
$338$		0			0
$339$	−427.433	+	246.778i	−1.26086	+	0.727960i
$340$		0			0
$341$	11.8698	+	6.85302i	0.0348087	+	0.0200968i
$342$		0			0
$343$	−58.6758	−	337.944i	−0.171067	−	0.985259i
$344$		0			0
$345$	114.186	−	197.776i	0.330974	−	0.573264i
$346$		0			0
$347$	211.885	+	366.995i	0.610618	+	1.05762i	0.991136	+	0.132849i	$0.0424124\pi$
$347$	211.885	+	366.995i	0.610618	+	1.05762i	−0.380518	+	0.924774i	$0.624254\pi$
$348$		0			0
$349$			197.582i			0.566137i	0.959100	+	0.283069i	$0.0913525\pi$
$349$			197.582i			0.566137i	−0.959100	+	0.283069i	$0.908648\pi$
$350$		0			0
$351$	−162.878			−0.464040
$352$		0			0
$353$	42.8058	−	24.7139i	0.121263	−	0.0700111i	−0.438142	−	0.898906i	$-0.644363\pi$
$353$	42.8058	−	24.7139i	0.121263	−	0.0700111i	0.559404	+	0.828895i	$0.311030\pi$
$354$		0			0
$355$	77.4085	+	44.6918i	0.218052	+	0.125892i
$356$		0			0
$357$	−70.7488	−	35.6088i	−0.198176	−	0.0997446i
$358$		0			0
$359$	−121.905	+	211.145i	−0.339568	+	0.588149i	−0.984351	−	0.176216i	$-0.943614\pi$
$359$	−121.905	+	211.145i	−0.339568	+	0.588149i	0.644784	+	0.764365i	$0.276948\pi$
$360$		0			0
$361$	60.7198	+	105.170i	0.168199	+	0.291329i
$362$		0			0
$363$		−	125.501i		−	0.345733i
$364$		0			0
$365$	−319.892			−0.876417
$366$		0			0
$367$	88.5960	−	51.1509i	0.241406	−	0.139376i	−0.374417	−	0.927261i	$-0.622157\pi$
$367$	88.5960	−	51.1509i	0.241406	−	0.139376i	0.615823	+	0.787885i	$0.288824\pi$
$368$		0			0
$369$	−63.3458	−	36.5727i	−0.171669	−	0.0991130i
$370$		0			0
$371$	92.9428	−	61.0132i	0.250520	−	0.164456i
$372$		0			0
$373$	97.4633	−	168.811i	0.261296	−	0.452578i	−0.705291	−	0.708918i	$-0.749184\pi$
$373$	97.4633	−	168.811i	0.261296	−	0.452578i	0.966587	+	0.256341i	$0.0825169\pi$
$374$		0			0
$375$	170.723	+	295.702i	0.455263	+	0.788538i
$376$		0			0
$377$			149.200i			0.395755i
$378$		0			0
$379$	656.951			1.73338			0.866690	−	0.498847i	$-0.166243\pi$
$379$	656.951			1.73338			0.866690	+	0.498847i	$0.166243\pi$
$380$		0			0
$381$	393.885	−	227.410i	1.03382	−	0.596876i
$382$		0			0
$383$	−643.794	−	371.694i	−1.68092	−	0.970481i	−0.961050	−	0.276376i	$-0.910866\pi$
$383$	−643.794	−	371.694i	−1.68092	−	0.970481i	−0.719874	−	0.694105i	$-0.755800\pi$
$384$		0			0
$385$	185.734	−	10.6550i	0.482425	−	0.0276752i
$386$		0			0
$387$	−49.9096	+	86.4460i	−0.128965	+	0.223375i
$388$		0			0
$389$	110.203	+	190.878i	0.283299	+	0.490689i	0.972195	−	0.234171i	$-0.0752377\pi$
$389$	110.203	+	190.878i	0.283299	+	0.490689i	−0.688896	+	0.724860i	$0.741904\pi$
$390$		0			0
$391$		−	112.005i		−	0.286458i
$392$		0			0
$393$	177.550			0.451782
$394$		0			0
$395$	102.428	−	59.1370i	0.259312	−	0.149714i
$396$		0			0
$397$	−190.283	−	109.860i	−0.479301	−	0.276725i	0.240824	−	0.970569i	$-0.422582\pi$
$397$	−190.283	−	109.860i	−0.479301	−	0.276725i	−0.720125	+	0.693844i	$0.755916\pi$
$398$		0			0
$399$	24.1655	+	421.245i	0.0605651	+	1.05575i
$400$		0			0
$401$	48.3936	−	83.8201i	0.120682	−	0.209028i	−0.799355	−	0.600859i	$-0.794825\pi$
$401$	48.3936	−	83.8201i	0.120682	−	0.209028i	0.920037	+	0.391832i	$0.128158\pi$
$402$		0			0
$403$	4.47825	+	7.75655i	0.0111123	+	0.0192470i
$404$		0			0
$405$		−	201.025i		−	0.496357i
$406$		0			0
$407$	295.405			0.725810
$408$		0			0
$409$	305.899	−	176.611i	0.747920	−	0.431812i	−0.0770217	−	0.997029i	$-0.524541\pi$
$409$	305.899	−	176.611i	0.747920	−	0.431812i	0.824942	+	0.565217i	$0.191208\pi$
$410$		0			0
$411$	−453.925	−	262.074i	−1.10444	−	0.637650i
$412$		0			0
$413$	−54.1539	−	82.4940i	−0.131123	−	0.199743i
$414$		0			0
$415$	103.767	−	179.730i	0.250041	−	0.433083i
$416$		0			0
$417$	−267.251	−	462.893i	−0.640891	−	1.11006i
$418$		0			0
$419$		−	324.252i		−	0.773870i	−0.922107	−	0.386935i	$-0.873534\pi$
$419$		−	324.252i		−	0.773870i	0.922107	−	0.386935i	$-0.126466\pi$
$420$		0			0
$421$	112.726			0.267758			0.133879	−	0.990998i	$-0.457257\pi$
$421$	112.726			0.267758			0.133879	+	0.990998i	$0.457257\pi$
$422$		0			0
$423$	17.6754	−	10.2049i	0.0417857	−	0.0241250i
$424$		0			0
$425$	55.7592	+	32.1926i	0.131198	+	0.0757473i
$426$		0			0
$427$	156.515	−	310.970i	0.366546	−	0.728266i
$428$		0			0
$429$	−67.4894	+	116.895i	−0.157318	+	0.272483i
$430$		0			0
$431$	315.615	+	546.661i	0.732285	+	1.26835i	0.955905	+	0.293678i	$0.0948792\pi$
$431$	315.615	+	546.661i	0.732285	+	1.26835i	−0.223620	+	0.974676i	$0.571787\pi$
$432$		0			0
$433$			464.547i			1.07286i	0.843946	+	0.536428i	$0.180227\pi$
$433$			464.547i			1.07286i	−0.843946	+	0.536428i	$0.819773\pi$
$434$		0			0
$435$	−221.241			−0.508600
$436$		0			0
$437$	−516.733	+	298.336i	−1.18245	+	0.682691i
$438$		0			0
$439$	−300.010	−	173.211i	−0.683394	−	0.394558i	0.117739	−	0.993045i	$-0.462436\pi$
$439$	−300.010	−	173.211i	−0.683394	−	0.394558i	−0.801133	+	0.598487i	$0.795769\pi$
$440$		0			0
$441$	28.6243	−	66.0410i	0.0649077	−	0.149753i
$442$		0			0
$443$	−261.085	+	452.213i	−0.589357	+	1.02080i	0.404959	+	0.914335i	$0.367286\pi$
$443$	−261.085	+	452.213i	−0.589357	+	1.02080i	−0.994317	+	0.106462i	$0.966048\pi$
$444$		0			0
$445$	−117.055	−	202.746i	−0.263046	−	0.455608i
$446$		0			0
$447$			212.773i			0.476002i
$448$		0			0
$449$	−99.2420			−0.221029			−0.110514	−	0.993875i	$-0.535250\pi$
$449$	−99.2420			−0.221029			−0.110514	+	0.993875i	$0.535250\pi$
$450$		0			0
$451$	−374.129	+	216.004i	−0.829555	+	0.478944i
$452$		0			0
$453$	−375.182	−	216.612i	−0.828217	−	0.478171i
$454$		0			0
$455$	108.592	+	54.6559i	0.238664	+	0.120123i
$456$		0			0
$457$	401.581	−	695.558i	0.878732	−	1.52201i	0.0259986	−	0.999662i	$-0.491723\pi$
$457$	401.581	−	695.558i	0.878732	−	1.52201i	0.852733	−	0.522346i	$-0.174943\pi$
$458$		0			0
$459$	−59.2277	−	102.585i	−0.129036	−	0.223498i
$460$		0			0
$461$			573.998i			1.24512i	0.782574	+	0.622558i	$0.213906\pi$
$461$			573.998i			1.24512i	−0.782574	+	0.622558i	$0.786094\pi$
$462$		0			0
$463$	680.397			1.46954			0.734770	−	0.678317i	$-0.237290\pi$
$463$	680.397			1.46954			0.734770	+	0.678317i	$0.237290\pi$
$464$		0			0
$465$	−11.5018	+	6.64058i	−0.0247351	+	0.0142808i
$466$		0			0
$467$	−667.318	−	385.276i	−1.42895	−	0.825002i	−0.431908	−	0.901918i	$-0.642160\pi$
$467$	−667.318	−	385.276i	−1.42895	−	0.825002i	−0.997038	+	0.0769153i	$0.975493\pi$
$468$		0			0
$469$	90.7611	−	59.5810i	0.193520	−	0.127038i
$470$		0			0
$471$	−148.100	+	256.516i	−0.314437	+	0.544620i
$472$		0			0
$473$	294.774	+	510.563i	0.623200	+	1.07941i
$474$		0			0
$475$		−	342.991i		−	0.722087i
$476$		0			0
$477$	23.3308			0.0489115
$478$		0			0
$479$	−84.5488	+	48.8143i	−0.176511	+	0.101909i	−0.585652	−	0.810562i	$-0.699162\pi$
$479$	−84.5488	+	48.8143i	−0.176511	+	0.101909i	0.409141	+	0.912471i	$0.365828\pi$
$480$		0			0
$481$	167.176	+	96.5192i	0.347560	+	0.200664i
$482$		0			0
$483$	−520.987	+	29.8874i	−1.07865	+	0.0618786i
$484$		0			0
$485$	204.864	−	354.835i	0.422401	−	0.731619i
$486$		0			0
$487$	−363.466	−	629.542i	−0.746337	−	1.29269i	−0.949568	−	0.313562i	$-0.898478\pi$
$487$	−363.466	−	629.542i	−0.746337	−	1.29269i	0.203231	−	0.979131i	$-0.434856\pi$
$488$		0			0
$489$		−	169.897i		−	0.347438i
$490$		0			0
$491$	35.9677			0.0732540			0.0366270	−	0.999329i	$-0.488339\pi$
$491$	35.9677			0.0732540			0.0366270	+	0.999329i	$0.488339\pi$
$492$		0			0
$493$	−93.9705	+	54.2539i	−0.190609	+	0.110048i
$494$		0			0
$495$	33.8094	+	19.5199i	0.0683019	+	0.0394341i
$496$		0			0
$497$	−11.6978	−	203.912i	−0.0235367	−	0.410285i
$498$		0			0
$499$	112.731	−	195.256i	0.225915	−	0.391295i	−0.730679	−	0.682721i	$-0.760796\pi$
$499$	112.731	−	195.256i	0.225915	−	0.391295i	0.956593	+	0.291426i	$0.0941297\pi$
$500$		0			0
$501$	−314.042	−	543.936i	−0.626830	−	1.08570i
$502$		0			0
$503$			158.285i			0.314682i	0.987544	+	0.157341i	$0.0502922\pi$
$503$			158.285i			0.314682i	−0.987544	+	0.157341i	$0.949708\pi$
$504$		0			0
$505$	250.661			0.496358
$506$		0			0
$507$	325.261	−	187.789i	0.641540	−	0.370393i
$508$		0			0
$509$	259.917	+	150.063i	0.510643	+	0.294820i	0.733098	−	0.680123i	$-0.238074\pi$
$509$	259.917	+	150.063i	0.510643	+	0.294820i	−0.222455	+	0.974943i	$0.571407\pi$
$510$		0			0
$511$	401.142	+	611.069i	0.785014	+	1.19583i
$512$		0			0
$513$	−315.517	+	546.491i	−0.615042	+	1.06528i
$514$		0			0
$515$	190.907	+	330.661i	0.370693	+	0.642060i
$516$		0			0
$517$		−	120.543i		−	0.233159i
$518$		0			0
$519$	−887.500			−1.71002
$520$		0			0
$521$	−34.1957	+	19.7429i	−0.0656347	+	0.0378942i	−0.532458	−	0.846456i	$-0.678732\pi$
$521$	−34.1957	+	19.7429i	−0.0656347	+	0.0378942i	0.466824	+	0.884350i	$0.345398\pi$
$522$		0			0
$523$	−50.9476	−	29.4146i	−0.0974142	−	0.0562421i	0.450501	−	0.892776i	$-0.351245\pi$
$523$	−50.9476	−	29.4146i	−0.0974142	−	0.0562421i	−0.547916	+	0.836534i	$0.684579\pi$
$524$		0			0
$525$	134.864	−	267.952i	0.256883	−	0.510384i
$526$		0			0
$527$	−3.25687	+	5.64107i	−0.00618003	+	0.0107041i
$528$		0			0
$529$	−104.476	−	180.957i	−0.197497	−	0.342074i
$530$		0			0
$531$		−	20.7079i		−	0.0389979i
$532$		0			0
$533$	−282.304			−0.529652
$534$		0			0
$535$	−265.459	+	153.263i	−0.496186	+	0.286473i
$536$		0			0
$537$	−249.953	−	144.311i	−0.465462	−	0.268735i
$538$		0			0
$539$	−253.262	−	341.434i	−0.469874	−	0.633458i
$540$		0			0
$541$	274.999	−	476.311i	0.508315	−	0.880428i	−0.491638	−	0.870799i	$-0.663602\pi$
$541$	274.999	−	476.311i	0.508315	−	0.880428i	0.999954	−	0.00962829i	$-0.00306483\pi$
$542$		0			0
$543$	−174.010	−	301.394i	−0.320460	−	0.555054i
$544$		0			0
$545$		−	215.983i		−	0.396299i
$546$		0			0
$547$	−441.457			−0.807052			−0.403526	−	0.914968i	$-0.632215\pi$
$547$	−441.457			−0.807052			−0.403526	+	0.914968i	$0.632215\pi$
$548$		0			0
$549$	63.2679	−	36.5277i	0.115242	−	0.0665350i
$550$		0			0
$551$	500.597	+	289.020i	0.908525	+	0.524537i
$552$		0			0
$553$	−241.410	−	121.505i	−0.436545	−	0.219719i
$554$		0			0
$555$	−143.124	+	247.897i	−0.257880	+	0.446662i
$556$		0			0
$557$	−449.788	−	779.056i	−0.807519	−	1.39866i	−0.914577	−	0.404411i	$-0.867476\pi$
$557$	−449.788	−	779.056i	−0.807519	−	1.39866i	0.107058	−	0.994253i	$-0.465857\pi$
$558$		0			0
$559$			385.252i			0.689180i
$560$		0			0
$561$	−98.1653			−0.174983
$562$		0			0
$563$	−336.762	+	194.430i	−0.598157	+	0.345346i	−0.768316	−	0.640071i	$-0.778905\pi$
$563$	−336.762	+	194.430i	−0.598157	+	0.345346i	0.170159	+	0.985417i	$0.445572\pi$
$564$		0			0
$565$	477.134	+	275.473i	0.844485	+	0.487564i
$566$		0			0
$567$	−384.004	+	252.083i	−0.677256	+	0.444591i
$568$		0			0
$569$	278.062	−	481.618i	0.488686	−	0.846429i	−0.511229	−	0.859444i	$-0.670810\pi$
$569$	278.062	−	481.618i	0.488686	−	0.846429i	0.999915	+	0.0130154i	$0.00414303\pi$
$570$		0			0
$571$	465.580	+	806.408i	0.815376	+	1.41227i	0.909058	+	0.416671i	$0.136803\pi$
$571$	465.580	+	806.408i	0.815376	+	1.41227i	−0.0936814	+	0.995602i	$0.529864\pi$
$572$		0			0
$573$		−	572.266i		−	0.998719i
$574$		0			0
$575$	424.205			0.737747
$576$		0			0
$577$	187.868	−	108.465i	0.325594	−	0.187982i	−0.328289	−	0.944577i	$-0.606472\pi$
$577$	187.868	−	108.465i	0.325594	−	0.187982i	0.653883	+	0.756596i	$0.273139\pi$
$578$		0			0
$579$	747.287	+	431.446i	1.29065	+	0.745158i
$580$		0			0
$581$	−473.449	+	27.1602i	−0.814886	+	0.0467474i
$582$		0			0
$583$	68.8976	−	119.334i	0.118178	−	0.204690i
$584$		0			0
$585$	12.7557	+	22.0935i	0.0218046	+	0.0377666i
$586$		0			0
$587$		−	169.733i		−	0.289154i	−0.989494	−	0.144577i	$-0.953818\pi$
$587$		−	169.733i		−	0.289154i	0.989494	−	0.144577i	$-0.0461821\pi$
$588$		0			0
$589$	34.6999			0.0589132
$590$		0			0
$591$	−6.72999	+	3.88556i	−0.0113875	+	0.00657455i
$592$		0			0
$593$	−731.182	−	422.148i	−1.23302	−	0.711885i	−0.265363	−	0.964149i	$-0.585492\pi$
$593$	−731.182	−	422.148i	−1.23302	−	0.711885i	−0.967659	+	0.252264i	$0.918825\pi$
$594$		0			0
$595$	5.06373	+	88.2693i	0.00851047	+	0.148352i
$596$		0			0
$597$	304.306	−	527.073i	0.509725	−	0.882870i
$598$		0			0
$599$	−340.508	−	589.778i	−0.568461	−	0.984604i	−0.996718	−	0.0809471i	$-0.974206\pi$
$599$	−340.508	−	589.778i	−0.568461	−	0.984604i	0.428257	−	0.903657i	$-0.359128\pi$
$600$		0			0
$601$		−	50.8834i		−	0.0846645i	−0.999104	−	0.0423323i	$-0.986521\pi$
$601$		−	50.8834i		−	0.0846645i	0.999104	−	0.0423323i	$-0.0134788\pi$
$602$		0			0
$603$	22.7831			0.0377830
$604$		0			0
$605$	−121.325	+	70.0471i	−0.200538	+	0.115780i
$606$		0			0
$607$	−392.632	−	226.686i	−0.646841	−	0.373454i	0.140404	−	0.990094i	$-0.455160\pi$
$607$	−392.632	−	226.686i	−0.646841	−	0.373454i	−0.787245	+	0.616641i	$0.788493\pi$
$608$		0			0
$609$	277.434	+	422.622i	0.455557	+	0.693960i
$610$		0			0
$611$	39.3857	−	68.2180i	0.0644610	−	0.111650i
$612$		0			0
$613$	−101.103	−	175.115i	−0.164931	−	0.285669i	0.771700	−	0.635987i	$-0.219407\pi$
$613$	−101.103	−	175.115i	−0.164931	−	0.285669i	−0.936631	+	0.350318i	$0.886073\pi$
$614$		0			0
$615$		−	418.615i		−	0.680675i
$616$		0			0
$617$	457.762			0.741916			0.370958	−	0.928650i	$-0.379029\pi$
$617$	457.762			0.741916			0.370958	+	0.928650i	$0.379029\pi$
$618$		0			0
$619$	−66.2799	+	38.2667i	−0.107076	+	0.0618203i	−0.552582	−	0.833459i	$-0.686357\pi$
$619$	−66.2799	+	38.2667i	−0.107076	+	0.0618203i	0.445506	+	0.895279i	$0.353024\pi$
$620$		0			0
$621$	−675.889	−	390.224i	−1.08839	−	0.628381i
$622$		0			0
$623$	−240.505	+	477.844i	−0.386044	+	0.767006i
$624$		0			0
$625$	−4.62142	+	8.00453i	−0.00739426	+	0.0128072i
$626$		0			0
$627$	261.472	+	452.883i	0.417021	+	0.722301i
$628$		0			0
$629$			140.390i			0.223196i
$630$		0			0
$631$	492.996			0.781294			0.390647	−	0.920541i	$-0.372251\pi$
$631$	492.996			0.781294			0.390647	+	0.920541i	$0.372251\pi$
$632$		0			0
$633$	234.491	−	135.383i	0.370443	−	0.213876i
$634$		0			0
$635$	−439.685	−	253.852i	−0.692418	−	0.399768i
$636$		0			0
$637$	−31.7681	−	275.975i	−0.0498715	−	0.433241i
$638$		0			0
$639$	21.4303	−	37.1184i	0.0335372	−	0.0580882i
$640$		0			0
$641$	2.07396	+	3.59220i	0.00323550	+	0.00560406i	0.867639	−	0.497195i	$-0.165637\pi$
$641$	2.07396	+	3.59220i	0.00323550	+	0.00560406i	−0.864403	+	0.502799i	$0.832303\pi$
$642$		0			0
$643$			507.975i			0.790008i	0.918679	+	0.395004i	$0.129257\pi$
$643$			507.975i			0.790008i	−0.918679	+	0.395004i	$0.870743\pi$
$644$		0			0
$645$	−571.271			−0.885692
$646$		0			0
$647$	407.421	−	235.224i	0.629707	−	0.363562i	−0.150931	−	0.988544i	$-0.548227\pi$
$647$	407.421	−	235.224i	0.629707	−	0.363562i	0.780639	+	0.624983i	$0.214894\pi$
$648$		0			0
$649$	−105.918	−	61.1519i	−0.163202	−	0.0942248i
$650$		0			0
$651$	27.1082	+	13.6439i	0.0416409	+	0.0209584i
$652$		0			0
$653$	−219.471	+	380.135i	−0.336096	+	0.582136i	−0.983695	−	0.179846i	$-0.942440\pi$
$653$	−219.471	+	380.135i	−0.336096	+	0.582136i	0.647598	+	0.761982i	$0.275773\pi$
$654$		0			0
$655$	−99.0977	−	171.642i	−0.151294	−	0.262049i
$656$		0			0
$657$			153.392i			0.233474i
$658$		0			0
$659$	−752.565			−1.14198			−0.570990	−	0.820957i	$-0.693441\pi$
$659$	−752.565			−1.14198			−0.570990	+	0.820957i	$0.693441\pi$
$660$		0			0
$661$	−83.5775	+	48.2535i	−0.126441	+	0.0730008i	−0.561886	−	0.827214i	$-0.689924\pi$
$661$	−83.5775	+	48.2535i	−0.126441	+	0.0730008i	0.435445	+	0.900215i	$0.356591\pi$
$662$		0			0
$663$	−55.5540	−	32.0741i	−0.0837918	−	0.0483772i
$664$		0			0
$665$	393.740	−	258.475i	0.592091	−	0.388683i
$666$		0			0
$667$	−357.454	+	619.128i	−0.535913	+	0.928229i
$668$		0			0
$669$	63.4328	+	109.869i	0.0948173	+	0.164228i
$670$		0			0
$671$		−	431.477i		−	0.643035i
$672$		0			0
$673$	983.437			1.46127			0.730637	−	0.682767i	$-0.239223\pi$
$673$	983.437			1.46127			0.730637	+	0.682767i	$0.239223\pi$
$674$		0			0
$675$	388.528	−	224.317i	0.575598	−	0.332322i
$676$		0			0
$677$	841.850	+	486.042i	1.24350	+	0.717936i	0.969805	−	0.243881i	$-0.0784205\pi$
$677$	841.850	+	486.042i	1.24350	+	0.717936i	0.273696	+	0.961816i	$0.411754\pi$
$678$		0			0
$679$	−934.717	+	53.6217i	−1.37661	+	0.0789716i
$680$		0			0
$681$	468.262	−	811.054i	0.687610	−	1.19098i
$682$		0			0
$683$	−368.113	−	637.590i	−0.538965	−	0.933514i	−0.998960	−	0.0455928i	$-0.985482\pi$
$683$	−368.113	−	637.590i	−0.538965	−	0.933514i	0.459995	−	0.887921i	$-0.347851\pi$
$684$		0			0
$685$			585.095i			0.854153i
$686$		0			0
$687$	−21.3260			−0.0310423
$688$		0			0
$689$	77.9814	−	45.0226i	0.113180	−	0.0653448i
$690$		0			0
$691$	538.733	+	311.038i	0.779643	+	0.450127i	0.836304	−	0.548266i	$-0.184712\pi$
$691$	538.733	+	311.038i	0.779643	+	0.450127i	−0.0566608	+	0.998393i	$0.518045\pi$
$692$		0			0
$693$	−5.10919	−	89.0617i	−0.00737256	−	0.128516i
$694$		0			0
$695$	−298.327	+	516.718i	−0.429248	+	0.743479i
$696$		0			0
$697$	−102.655	−	177.804i	−0.147281	−	0.255099i
$698$		0			0
$699$		−	679.432i		−	0.972006i
$700$		0			0
$701$	−1107.89			−1.58045			−0.790224	−	0.612818i	$-0.790036\pi$
$701$	−1107.89			−1.58045			−0.790224	+	0.612818i	$0.790036\pi$
$702$		0			0
$703$	647.686	−	373.942i	0.921317	−	0.531923i
$704$		0			0
$705$	101.157	+	58.4031i	0.143485	+	0.0828412i
$706$		0			0
$707$	−314.326	−	478.821i	−0.444592	−	0.677257i
$708$		0			0
$709$	−512.932	+	888.424i	−0.723459	+	1.25307i	0.236147	+	0.971717i	$0.424115\pi$
$709$	−512.932	+	888.424i	−0.723459	+	1.25307i	−0.959605	+	0.281350i	$0.909218\pi$
$710$		0			0
$711$	−28.3569	−	49.1157i	−0.0398832	−	0.0690797i
$712$		0			0
$713$			42.9161i			0.0601909i
$714$		0			0
$715$	150.674			0.210733
$716$		0			0
$717$	616.772	−	356.093i	0.860212	−	0.496643i
$718$		0			0
$719$	1133.72	+	654.551i	1.57680	+	0.910364i	0.995303	+	0.0968124i	$0.0308647\pi$
$719$	1133.72	+	654.551i	1.57680	+	0.910364i	0.581493	+	0.813551i	$0.302469\pi$
$720$		0			0
$721$	392.244	−	779.323i	0.544027	−	1.08089i
$722$		0			0
$723$	−262.538	+	454.729i	−0.363123	+	0.628948i
$724$		0			0
$725$	−205.479	−	355.900i	−0.283420	−	0.490897i
$726$		0			0
$727$		−	1417.52i		−	1.94982i	−0.222589	−	0.974912i	$-0.571451\pi$
$727$		−	1417.52i		−	1.94982i	0.222589	−	0.974912i	$-0.428549\pi$
$728$		0			0
$729$	−805.974			−1.10559
$730$		0			0
$731$	−242.643	+	140.090i	−0.331933	+	0.191642i
$732$		0			0
$733$	144.026	+	83.1536i	0.196489	+	0.113443i	0.595017	−	0.803713i	$-0.297145\pi$
$733$	144.026	+	83.1536i	0.196489	+	0.113443i	−0.398528	+	0.917156i	$0.630479\pi$
$734$		0			0
$735$	409.229	−	47.1074i	0.556775	−	0.0640917i
$736$		0			0
$737$	67.2803	−	116.533i	0.0912894	−	0.158118i
$738$		0			0
$739$	−493.042	−	853.973i	−0.667174	−	1.15558i	−0.978691	−	0.205339i	$-0.934170\pi$
$739$	−493.042	−	853.973i	−0.667174	−	1.15558i	0.311517	−	0.950241i	$-0.399163\pi$
$740$		0			0
$741$			341.729i			0.461172i
$742$		0			0
$743$	1089.52			1.46637			0.733187	−	0.680027i	$-0.238032\pi$
$743$	1089.52			1.46637			0.733187	+	0.680027i	$0.238032\pi$
$744$		0			0
$745$	205.693	−	118.757i	0.276098	−	0.159405i
$746$		0			0
$747$	−86.1827	−	49.7576i	−0.115372	−	0.0666099i
$748$		0			0
$749$	625.652	+	314.899i	0.835316	+	0.420426i
$750$		0			0
$751$	−202.064	+	349.986i	−0.269060	+	0.466026i	−0.968619	−	0.248548i	$-0.920046\pi$
$751$	−202.064	+	349.986i	−0.269060	+	0.466026i	0.699559	+	0.714575i	$0.253380\pi$
$752$		0			0
$753$	335.926	+	581.840i	0.446116	+	0.772696i
$754$		0			0
$755$			483.598i			0.640527i
$756$		0			0
$757$	−1288.98			−1.70274			−0.851372	−	0.524562i	$-0.824229\pi$
$757$	−1288.98			−1.70274			−0.851372	+	0.524562i	$0.824229\pi$
$758$		0			0
$759$	−560.116	+	323.383i	−0.737966	+	0.426065i
$760$		0			0
$761$	−528.667	−	305.226i	−0.694700	−	0.401085i	0.110670	−	0.993857i	$-0.464700\pi$
$761$	−528.667	−	305.226i	−0.694700	−	0.401085i	−0.805370	+	0.592772i	$0.798034\pi$
$762$		0			0
$763$	−412.578	+	270.841i	−0.540731	+	0.354968i
$764$		0			0
$765$	−9.27676	+	16.0678i	−0.0121265	+	0.0210037i
$766$		0			0
$767$	−39.9610	−	69.2145i	−0.0521004	−	0.0902405i
$768$		0			0
$769$			1235.09i			1.60609i	0.595915	+	0.803047i	$0.296789\pi$
$769$			1235.09i			1.60609i	−0.595915	+	0.803047i	$0.703211\pi$
$770$		0			0
$771$	379.510			0.492231
$772$		0			0
$773$	4.22997	−	2.44217i	0.00547215	−	0.00315935i	−0.497261	−	0.867601i	$-0.665661\pi$
$773$	4.22997	−	2.44217i	0.00547215	−	0.00315935i	0.502734	+	0.864441i	$0.332328\pi$
$774$		0			0
$775$	−21.3648	−	12.3350i	−0.0275675	−	0.0159161i
$776$		0			0
$777$	653.018	−	37.4616i	0.840435	−	0.0482131i
$778$		0			0
$779$	−546.861	+	947.192i	−0.702004	+	1.21591i
$780$		0			0
$781$	−126.571	−	219.227i	−0.162062	−	0.280700i
$782$		0			0
$783$			756.078i			0.965617i
$784$		0			0
$785$	330.641			0.421198
$786$		0			0
$787$	685.446	−	395.742i	0.870961	−	0.502849i	0.00329336	−	0.999995i	$-0.498952\pi$
$787$	685.446	−	395.742i	0.870961	−	0.502849i	0.867667	+	0.497145i	$0.165618\pi$
$788$		0			0
$789$	696.240	+	401.975i	0.882434	+	0.509473i
$790$		0			0
$791$	−72.1032	−	1256.88i	−0.0911544	−	1.58897i
$792$		0			0
$793$	140.979	−	244.182i	0.177779	−	0.307922i
$794$		0			0
$795$	66.7617	+	115.635i	0.0839770	+	0.145452i
$796$		0			0
$797$		−	373.825i		−	0.469041i	−0.972111	−	0.234520i	$-0.924648\pi$
$797$		−	373.825i		−	0.469041i	0.972111	−	0.234520i	$-0.0753519\pi$
$798$		0			0
$799$	57.2876			0.0716992
$800$		0			0
$801$	−97.2192	+	56.1295i	−0.121372	+	0.0700743i
$802$		0			0
$803$	784.583	+	452.979i	0.977065	+	0.564108i
$804$		0			0
$805$	319.676	+	486.970i	0.397113	+	0.604932i
$806$		0			0
$807$	45.3469	−	78.5431i	0.0561919	−	0.0973273i
$808$		0			0
$809$	−188.448	−	326.402i	−0.232940	−	0.403463i	0.725732	−	0.687977i	$-0.241501\pi$
$809$	−188.448	−	326.402i	−0.232940	−	0.403463i	−0.958672	+	0.284514i	$0.908168\pi$
$810$		0			0
$811$			531.465i			0.655320i	0.944796	+	0.327660i	$0.106260\pi$
$811$			531.465i			0.655320i	−0.944796	+	0.327660i	$0.893740\pi$
$812$		0			0
$813$	−630.429			−0.775435
$814$		0			0
$815$	−164.244	+	94.8264i	−0.201526	+	0.116351i
$816$		0			0
$817$	1292.60	+	746.285i	1.58213	+	0.913445i
$818$		0			0
$819$	26.2082	−	52.0714i	0.0320003	−	0.0635792i
$820$		0			0
$821$	270.881	−	469.179i	0.329940	−	0.571473i	−0.652560	−	0.757737i	$-0.726305\pi$
$821$	270.881	−	469.179i	0.329940	−	0.571473i	0.982500	+	0.186264i	$0.0596381\pi$
$822$		0			0
$823$	−114.700	−	198.667i	−0.139369	−	0.241393i	0.787889	−	0.615817i	$-0.211174\pi$
$823$	−114.700	−	198.667i	−0.139369	−	0.241393i	−0.927258	+	0.374424i	$0.877841\pi$
$824$		0			0
$825$		−	371.788i		−	0.450652i
$826$		0			0
$827$	−267.027			−0.322887			−0.161443	−	0.986882i	$-0.551615\pi$
$827$	−267.027			−0.322887			−0.161443	+	0.986882i	$0.551615\pi$
$828$		0			0
$829$	−85.8913	+	49.5894i	−0.103608	+	0.0598183i	−0.550909	−	0.834565i	$-0.685719\pi$
$829$	−85.8913	+	49.5894i	−0.103608	+	0.0598183i	0.447300	+	0.894384i	$0.352385\pi$
$830$		0			0
$831$	1018.88	+	588.253i	1.22609	+	0.707886i
$832$		0			0
$833$	162.265	−	120.362i	0.194796	−	0.144492i
$834$		0			0
$835$	−350.558	+	607.184i	−0.419830	+	0.727167i
$836$		0			0
$837$	22.6938	+	39.3068i	0.0271133	+	0.0469615i
$838$		0			0
$839$			748.747i			0.892427i	0.894926	+	0.446214i	$0.147228\pi$
$839$			748.747i			0.892427i	−0.894926	+	0.446214i	$0.852772\pi$
$840$		0			0
$841$	−148.416			−0.176476
$842$		0			0
$843$	−125.994	+	72.7428i	−0.149459	+	0.0862904i
$844$		0			0
$845$	−363.081	−	209.625i	−0.429682	−	0.248077i
$846$		0			0
$847$	285.947	+	143.921i	0.337600	+	0.169919i
$848$		0			0
$849$	20.5646	−	35.6188i	0.0242221	−	0.0419539i
$850$		0			0
$851$	462.483	+	801.045i	0.543459	+	0.941298i
$852$		0			0
$853$			685.267i			0.803361i	0.915780	+	0.401680i	$0.131574\pi$
$853$			685.267i			0.803361i	−0.915780	+	0.401680i	$0.868426\pi$
$854$		0			0
$855$	98.8379			0.115600
$856$		0			0
$857$	1154.27	−	666.416i	1.34687	−	0.777615i	0.359065	−	0.933313i	$-0.383096\pi$
$857$	1154.27	−	666.416i	1.34687	−	0.777615i	0.987805	+	0.155697i	$0.0497624\pi$
$858$		0			0
$859$	235.469	+	135.948i	0.274120	+	0.158263i	0.630758	−	0.775979i	$-0.282744\pi$
$859$	235.469	+	135.948i	0.274120	+	0.158263i	−0.356638	+	0.934242i	$0.616077\pi$
$860$		0			0
$861$	−799.653	+	524.940i	−0.928749	+	0.609686i
$862$		0			0
$863$	−592.609	+	1026.43i	−0.686685	+	1.18937i	0.286219	+	0.958164i	$0.407602\pi$
$863$	−592.609	+	1026.43i	−0.686685	+	1.18937i	−0.972904	+	0.231209i	$0.925732\pi$
$864$		0			0
$865$	495.349	+	857.969i	0.572657	+	0.991872i
$866$		0			0
$867$		−	46.6528i		−	0.0538094i
$868$		0			0
$869$	−334.961			−0.385455
$870$		0			0
$871$	76.1508	−	43.9657i	0.0874292	−	0.0504773i
$872$		0			0
$873$	−170.148	−	98.2350i	−0.194900	−	0.112526i
$874$		0			0
$875$	−869.520	+	49.8816i	−0.993737	+	0.0570075i
$876$		0			0
$877$	215.642	−	373.503i	0.245886	−	0.425887i	−0.716494	−	0.697593i	$-0.754254\pi$
$877$	215.642	−	373.503i	0.245886	−	0.425887i	0.962380	+	0.271706i	$0.0875878\pi$
$878$		0			0
$879$	193.668	+	335.443i	0.220328	+	0.381619i
$880$		0			0
$881$			1175.07i			1.33379i	0.745151	+	0.666895i	$0.232377\pi$
$881$			1175.07i			1.33379i	−0.745151	+	0.666895i	$0.767623\pi$
$882$		0			0
$883$	409.593			0.463866			0.231933	−	0.972732i	$-0.425495\pi$
$883$	409.593			0.463866			0.231933	+	0.972732i	$0.425495\pi$
$884$		0			0
$885$	102.635	−	59.2562i	0.115971	−	0.0669562i
$886$		0			0
$887$	1075.31	+	620.829i	1.21230	+	0.699920i	0.963259	−	0.268574i	$-0.0865525\pi$
$887$	1075.31	+	620.829i	1.21230	+	0.699920i	0.249037	+	0.968494i	$0.419886\pi$
$888$		0			0
$889$	66.4440	+	1158.23i	0.0747402	+	1.30285i
$890$		0			0
$891$	−284.658	+	493.043i	−0.319482	+	0.553359i
$892$		0			0
$893$	−152.591	−	264.295i	−0.170874	−	0.295963i
$894$		0			0
$895$			322.181i			0.359979i
$896$		0			0
$897$	−422.643			−0.471174
$898$		0			0
$899$	36.0059	−	20.7880i	0.0400510	−	0.0231235i
$900$		0			0
$901$	56.7131	+	32.7433i	0.0629446	+	0.0363411i
$902$		0			0
$903$	716.369	+	1091.26i	0.793321	+	1.20848i
$904$		0			0
$905$	−194.244	+	336.440i	−0.214634	+	0.371757i
$906$		0			0
$907$	−726.193	−	1257.80i	−0.800654	−	1.38677i	−0.919186	−	0.393823i	$-0.871152\pi$
$907$	−726.193	−	1257.80i	−0.800654	−	1.38677i	0.118532	−	0.992950i	$-0.462181\pi$
$908$		0			0
$909$		−	120.195i		−	0.132228i
$910$		0			0
$911$	884.067			0.970436			0.485218	−	0.874393i	$-0.338740\pi$
$911$	884.067			0.970436			0.485218	+	0.874393i	$0.338740\pi$
$912$		0			0
$913$	−509.008	+	293.876i	−0.557511	+	0.321879i
$914$		0			0
$915$	362.086	+	209.050i	0.395722	+	0.228470i
$916$		0			0
$917$	−203.609	+	404.538i	−0.222038	+	0.441153i
$918$		0			0
$919$	−577.016	+	999.421i	−0.627874	+	1.08751i	0.360104	+	0.932912i	$0.382741\pi$
$919$	−577.016	+	999.421i	−0.627874	+	1.08751i	−0.987978	+	0.154597i	$0.950592\pi$
$920$		0			0
$921$	−123.894	−	214.590i	−0.134521	−	0.232997i
$922$		0			0
$923$		−	165.420i		−	0.179220i
$924$		0			0
$925$	−531.709			−0.574820
$926$		0			0
$927$	158.556	−	91.5424i	0.171042	−	0.0987512i
$928$		0			0
$929$	−590.399	−	340.867i	−0.635521	−	0.366918i	0.147366	−	0.989082i	$-0.452920\pi$
$929$	−590.399	−	340.867i	−0.635521	−	0.366918i	−0.782887	+	0.622164i	$0.786254\pi$
$930$		0			0
$931$	−987.494	−	428.011i	−1.06068	−	0.459733i
$932$		0			0
$933$	−349.938	+	606.110i	−0.375067	+	0.649635i
$934$		0			0
$935$	54.7899	+	94.8989i	0.0585988	+	0.101496i
$936$		0			0
$937$		−	1338.67i		−	1.42868i	−0.699799	−	0.714340i	$-0.746727\pi$
$937$		−	1338.67i		−	1.42868i	0.699799	−	0.714340i	$-0.253273\pi$
$938$		0			0
$939$	1450.33			1.54455
$940$		0			0
$941$	−504.163	+	291.079i	−0.535774	+	0.309329i	−0.743364	−	0.668887i	$-0.766771\pi$
$941$	−504.163	+	291.079i	−0.535774	+	0.309329i	0.207591	+	0.978216i	$0.433438\pi$
$942$		0			0
$943$	−1171.47	−	676.347i	−1.24228	−	0.717229i
$944$		0			0
$945$	550.298	+	276.972i	0.582326	+	0.293092i
$946$		0			0
$947$	763.859	−	1323.04i	0.806609	−	1.39709i	−0.108591	−	0.994087i	$-0.534634\pi$
$947$	763.859	−	1323.04i	0.806609	−	1.39709i	0.915200	−	0.403001i	$-0.132033\pi$
$948$		0			0
$949$	296.009	+	512.702i	0.311916	+	0.540255i
$950$		0			0
$951$		−	1321.81i		−	1.38991i
$952$		0			0
$953$	541.283			0.567978			0.283989	−	0.958827i	$-0.408342\pi$
$953$	541.283			0.567978			0.283989	+	0.958827i	$0.408342\pi$
$954$		0			0
$955$	−553.224	+	319.404i	−0.579292	+	0.334455i
$956$		0			0
$957$	542.626	+	313.285i	0.567007	+	0.327362i
$958$		0			0
$959$	1117.67	−	733.704i	1.16545	−	0.765072i
$960$		0			0
$961$	−479.252	+	830.089i	−0.498701	+	0.863776i
$962$		0			0
$963$	73.4916	+	127.291i	0.0763152	+	0.132182i
$964$		0			0
$965$		−	963.229i		−	0.998164i
$966$		0			0
$967$	−496.836			−0.513791			−0.256896	−	0.966439i	$-0.582700\pi$
$967$	−496.836			−0.513791			−0.256896	+	0.966439i	$0.582700\pi$
$968$		0			0
$969$	−215.231	+	124.264i	−0.222117	+	0.128239i
$970$		0			0
$971$	1294.20	+	747.205i	1.33285	+	0.769521i	0.985736	−	0.168301i	$-0.0538281\pi$
$971$	1294.20	+	747.205i	1.33285	+	0.769521i	0.347115	+	0.937823i	$0.387161\pi$
$972$		0			0
$973$	1361.15	−	78.0849i	1.39892	−	0.0802517i
$974$		0			0
$975$	121.476	−	210.403i	0.124591	−	0.215798i
$976$		0			0
$977$	72.0563	+	124.805i	0.0737526	+	0.127743i	0.900543	−	0.434767i	$-0.143169\pi$
$977$	72.0563	+	124.805i	0.0737526	+	0.127743i	−0.826791	+	0.562510i	$0.809836\pi$
$978$		0			0
$979$			663.018i			0.677241i
$980$		0			0
$981$	−103.566			−0.105572
$982$		0			0
$983$	846.665	−	488.822i	0.861308	−	0.497276i	−0.00314239	−	0.999995i	$-0.501000\pi$
$983$	846.665	−	488.822i	0.861308	−	0.497276i	0.864450	+	0.502719i	$0.167667\pi$
$984$		0			0
$985$	7.51254	+	4.33737i	0.00762694	+	0.00440342i
$986$		0			0
$987$	−15.2866	−	266.471i	−0.0154879	−	0.269980i
$988$		0			0
$989$	−922.990	+	1598.67i	−0.933256	+	1.61645i
$990$		0			0
$991$	−251.842	−	436.203i	−0.254129	−	0.440164i	0.710530	−	0.703667i	$-0.248455\pi$
$991$	−251.842	−	436.203i	−0.254129	−	0.440164i	−0.964659	+	0.263503i	$0.915122\pi$
$992$		0			0
$993$		−	436.347i		−	0.439423i
$994$		0			0
$995$	−679.380			−0.682794
$996$		0			0
$997$	−1068.75	+	617.045i	−1.07197	+	0.618902i	−0.928719	−	0.370784i	$-0.879089\pi$
$997$	−1068.75	+	617.045i	−1.07197	+	0.618902i	−0.143251	+	0.989686i	$0.545756\pi$
$998$		0			0
$999$	847.176	+	489.117i	0.848024	+	0.489607i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	476.3.s.a.341.16	✓	44
7.3	odd	6	inner	476.3.s.a.409.16	yes	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
476.3.s.a.341.16	✓	44	1.1	even	1	trivial
476.3.s.a.409.16	yes	44	7.3	odd	6	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:	\( N \)	\(=\)	\( 476 = 2^{2} \cdot 7 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	476.s (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(2.37662 - 1.37214i) q^{3} +(-2.65296 - 1.53169i) q^{5} +(0.400909 + 6.98851i) q^{7} +(-0.734465 + 1.27213i) q^{9} +O(q^{10})\)	\(q+(2.37662 - 1.37214i) q^{3} +(-2.65296 - 1.53169i) q^{5} +(0.400909 + 6.98851i) q^{7} +(-0.734465 + 1.27213i) q^{9} +(4.33786 + 7.51339i) q^{11} +5.66933i q^{13} -8.40677 q^{15} +(-3.57071 + 2.06155i) q^{17} +(19.0218 + 10.9823i) q^{19} +(10.5420 + 16.0589i) q^{21} +(-13.5826 + 23.5258i) q^{23} +(-7.80785 - 13.5236i) q^{25} +28.7297i q^{27} +26.3170 q^{29} +(1.36816 - 0.789908i) q^{31} +(20.6188 + 11.9043i) q^{33} +(9.64063 - 19.1543i) q^{35} +(17.0248 - 29.4878i) q^{37} +(7.77911 + 13.4738i) q^{39} +49.7950i q^{41} +67.9537 q^{43} +(3.89702 - 2.24994i) q^{45} +(-12.0328 - 6.94715i) q^{47} +(-48.6785 + 5.60351i) q^{49} +(-5.65748 + 9.79904i) q^{51} +(-7.94143 - 13.7550i) q^{53} -26.5770i q^{55} +60.2768 q^{57} +(-12.2086 + 7.04863i) q^{59} +(-43.0707 - 24.8669i) q^{61} +(-9.18475 - 4.62281i) q^{63} +(8.68365 - 15.0405i) q^{65} +(-7.75501 - 13.4321i) q^{67} +74.5491i q^{69} -29.1781 q^{71} +(90.4343 - 52.2123i) q^{73} +(-37.1125 - 21.4269i) q^{75} +(-50.7683 + 33.3274i) q^{77} +(-19.3045 + 33.4364i) q^{79} +(32.8109 + 56.8302i) q^{81} +67.7467i q^{83} +12.6306 q^{85} +(62.5454 - 36.1106i) q^{87} +(66.1837 + 38.2112i) q^{89} +(-39.6202 + 2.27288i) q^{91} +(2.16773 - 3.75462i) q^{93} +(-33.6428 - 58.2711i) q^{95} +133.750i q^{97} -12.7440 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q - 6 q^{3} + 22 q^{7} + 88 q^{9}+O(q^{10}) \) 44 * q - 6 * q^3 + 22 * q^7 + 88 * q^9	\( 44 q - 6 q^{3} + 22 q^{7} + 88 q^{9} + 8 q^{11} + 16 q^{15} - 54 q^{19} - 16 q^{21} - 52 q^{23} + 150 q^{25} + 8 q^{29} + 78 q^{31} - 6 q^{33} + 10 q^{35} - 34 q^{37} - 60 q^{39} - 76 q^{43} - 72 q^{45} - 6 q^{47} - 56 q^{49} - 172 q^{53} - 64 q^{57} + 30 q^{59} + 444 q^{61} + 206 q^{63} - 54 q^{65} - 56 q^{67} + 204 q^{71} - 48 q^{73} + 132 q^{75} - 494 q^{77} - 16 q^{79} - 342 q^{81} + 594 q^{87} - 252 q^{89} + 284 q^{91} - 146 q^{93} + 148 q^{95} - 180 q^{99}+O(q^{100}) \) 44 * q - 6 * q^3 + 22 * q^7 + 88 * q^9 + 8 * q^11 + 16 * q^15 - 54 * q^19 - 16 * q^21 - 52 * q^23 + 150 * q^25 + 8 * q^29 + 78 * q^31 - 6 * q^33 + 10 * q^35 - 34 * q^37 - 60 * q^39 - 76 * q^43 - 72 * q^45 - 6 * q^47 - 56 * q^49 - 172 * q^53 - 64 * q^57 + 30 * q^59 + 444 * q^61 + 206 * q^63 - 54 * q^65 - 56 * q^67 + 204 * q^71 - 48 * q^73 + 132 * q^75 - 494 * q^77 - 16 * q^79 - 342 * q^81 + 594 * q^87 - 252 * q^89 + 284 * q^91 - 146 * q^93 + 148 * q^95 - 180 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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