LMFDB - Embedded newform 600.3.p.b.499.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [600,3,Mod(499,600)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("600.499"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(600, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 1, 0, 1])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 600 = 2^{3} \cdot 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	600.p (of order $2$, degree $1$, not minimal)

Newform invariants

comment:select newform

sage:traces = [32,0,0,-28] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(4)] == traces)

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

Self dual:	no
Analytic conductor:	$16.3488158616$
Analytic rank:	$0$
Dimension:	$32$
Twist minimal:	no (minimal twist has level 120)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			499.6
Character	$\chi$	$=$	600.499
Dual form			600.3.p.b.499.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.64881 + 1.13200i) q^{2} +1.73205i q^{3} +(1.43715 - 3.73291i) q^{4} +(-1.96068 - 2.85582i) q^{6} -11.6935 q^{7} +(1.85607 + 7.78171i) q^{8} -3.00000 q^{9} +19.3398 q^{11} +(6.46559 + 2.48921i) q^{12} +12.9092 q^{13} +(19.2803 - 13.2370i) q^{14} +(-11.8692 - 10.7295i) q^{16} -3.08243i q^{17} +(4.94643 - 3.39600i) q^{18} +10.1462 q^{19} -20.2537i q^{21} +(-31.8876 + 21.8926i) q^{22} -12.5038 q^{23} +(-13.4783 + 3.21481i) q^{24} +(-21.2849 + 14.6133i) q^{26} -5.19615i q^{27} +(-16.8053 + 43.6507i) q^{28} +0.924932i q^{29} +32.5955i q^{31} +(31.7159 + 4.25493i) q^{32} +33.4975i q^{33} +(3.48931 + 5.08233i) q^{34} +(-4.31144 + 11.1987i) q^{36} +3.15307 q^{37} +(-16.7292 + 11.4855i) q^{38} +22.3595i q^{39} -68.9305 q^{41} +(22.9272 + 33.3945i) q^{42} +69.7882i q^{43} +(27.7941 - 72.1936i) q^{44} +(20.6164 - 14.1543i) q^{46} +46.2730 q^{47} +(18.5840 - 20.5581i) q^{48} +87.7376 q^{49} +5.33892 q^{51} +(18.5525 - 48.1890i) q^{52} +16.7503 q^{53} +(5.88205 + 8.56747i) q^{54} +(-21.7039 - 90.9953i) q^{56} +17.5737i q^{57} +(-1.04702 - 1.52504i) q^{58} -72.0926 q^{59} +37.8730i q^{61} +(-36.8981 - 53.7438i) q^{62} +35.0805 q^{63} +(-57.1100 + 28.8868i) q^{64} +(-37.9192 - 55.2310i) q^{66} +121.224i q^{67} +(-11.5064 - 4.42990i) q^{68} -21.6572i q^{69} +67.4107i q^{71} +(-5.56821 - 23.3451i) q^{72} -14.7754i q^{73} +(-5.19881 + 3.56928i) q^{74} +(14.5816 - 37.8748i) q^{76} -226.149 q^{77} +(-25.3109 - 36.8665i) q^{78} +132.433i q^{79} +9.00000 q^{81} +(113.653 - 78.0294i) q^{82} -33.3714i q^{83} +(-75.6052 - 29.1076i) q^{84} +(-79.0003 - 115.068i) q^{86} -1.60203 q^{87} +(35.8960 + 150.497i) q^{88} +60.3607 q^{89} -150.954 q^{91} +(-17.9698 + 46.6755i) q^{92} -56.4571 q^{93} +(-76.2953 + 52.3810i) q^{94} +(-7.36975 + 54.9335i) q^{96} +13.2188i q^{97} +(-144.663 + 99.3190i) q^{98} -58.0193 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 28 q^{4} + 12 q^{6} - 96 q^{9} + 128 q^{11} + 40 q^{14} - 28 q^{16} + 64 q^{19} + 108 q^{24} + 72 q^{26} + 144 q^{34} + 84 q^{36} + 200 q^{44} + 424 q^{46} + 160 q^{49} + 192 q^{51} - 36 q^{54} - 232 q^{56}+ \cdots - 384 q^{99}+O(q^{100}) $ 32 * q - 28 * q^4 + 12 * q^6 - 96 * q^9 + 128 * q^11 + 40 * q^14 - 28 * q^16 + 64 * q^19 + 108 * q^24 + 72 * q^26 + 144 * q^34 + 84 * q^36 + 200 * q^44 + 424 * q^46 + 160 * q^49 + 192 * q^51 - 36 * q^54 - 232 * q^56 - 256 * q^59 - 28 * q^64 - 360 * q^66 - 600 * q^74 + 840 * q^76 + 288 * q^81 - 360 * q^84 + 624 * q^86 - 384 * q^91 - 920 * q^94 - 372 * q^96 - 384 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/600\mathbb{Z}\right)^\times$.

$n$	$151$	$301$	$401$	$577$
$\chi(n)$	$-1$	$-1$	$1$	$-1$

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 $

$2$	−1.64881	+	1.13200i	−0.824405	+	0.566000i
$2$	−1.64881	+	1.13200i	−0.824405	+	0.566000i
$3$			1.73205i			0.577350i
$3$			1.73205i			0.577350i
$4$	1.43715	−	3.73291i	0.359287	−	0.933227i
$5$		0			0
$5$		0			0
$6$	−1.96068	−	2.85582i	−0.326780	−	0.475970i
$7$	−11.6935			−1.67050			−0.835249	−	0.549872i	$-0.814676\pi$
$7$	−11.6935			−1.67050			−0.835249	+	0.549872i	$0.814676\pi$
$8$	1.85607	+	7.78171i	0.232009	+	0.972714i
$9$	−3.00000			−0.333333
$10$		0			0
$11$	19.3398			1.75816			0.879081	−	0.476673i	$-0.158157\pi$
$11$	19.3398			1.75816			0.879081	+	0.476673i	$0.158157\pi$
$12$	6.46559	+	2.48921i	0.538799	+	0.207434i
$13$	12.9092			0.993019			0.496510	−	0.868031i	$-0.334615\pi$
$13$	12.9092			0.993019			0.496510	+	0.868031i	$0.334615\pi$
$14$	19.2803	−	13.2370i	1.37717	−	0.945502i
$15$		0			0
$16$	−11.8692	−	10.7295i	−0.741826	−	0.670593i
$17$		−	3.08243i		−	0.181319i	−0.995882	−	0.0906596i	$-0.971102\pi$
$17$		−	3.08243i		−	0.181319i	0.995882	−	0.0906596i	$-0.0288975\pi$
$18$	4.94643	−	3.39600i	0.274802	−	0.188667i
$19$	10.1462			0.534010			0.267005	−	0.963695i	$-0.413966\pi$
$19$	10.1462			0.534010			0.267005	+	0.963695i	$0.413966\pi$
$20$		0			0
$21$		−	20.2537i		−	0.964462i
$22$	−31.8876	+	21.8926i	−1.44944	+	0.995120i
$23$	−12.5038			−0.543643			−0.271821	−	0.962348i	$-0.587626\pi$
$23$	−12.5038			−0.543643			−0.271821	+	0.962348i	$0.587626\pi$
$24$	−13.4783	+	3.21481i	−0.561596	+	0.133950i
$25$		0			0
$26$	−21.2849	+	14.6133i	−0.818650	+	0.562049i
$27$		−	5.19615i		−	0.192450i
$28$	−16.8053	+	43.6507i	−0.600188	+	1.55895i
$29$			0.924932i			0.0318942i	0.999873	+	0.0159471i	$0.00507633\pi$
$29$			0.924932i			0.0318942i	−0.999873	+	0.0159471i	$0.994924\pi$
$30$		0			0
$31$			32.5955i			1.05147i	0.850649	+	0.525734i	$0.176209\pi$
$31$			32.5955i			1.05147i	−0.850649	+	0.525734i	$0.823791\pi$
$32$	31.7159	+	4.25493i	0.991121	+	0.132966i
$33$			33.4975i			1.01508i
$34$	3.48931	+	5.08233i	0.102627	+	0.149480i
$35$		0			0
$36$	−4.31144	+	11.1987i	−0.119762	+	0.311076i
$37$	3.15307			0.0852181			0.0426090	−	0.999092i	$-0.486433\pi$
$37$	3.15307			0.0852181			0.0426090	+	0.999092i	$0.486433\pi$
$38$	−16.7292	+	11.4855i	−0.440241	+	0.302250i
$39$			22.3595i			0.573320i
$40$		0			0
$41$	−68.9305			−1.68123			−0.840616	−	0.541631i	$-0.817807\pi$
$41$	−68.9305			−1.68123			−0.840616	+	0.541631i	$0.817807\pi$
$42$	22.9272	+	33.3945i	0.545886	+	0.795108i
$43$			69.7882i			1.62298i	0.584365	+	0.811491i	$0.301344\pi$
$43$			69.7882i			1.62298i	−0.584365	+	0.811491i	$0.698656\pi$
$44$	27.7941	−	72.1936i	0.631685	−	1.64076i
$45$		0			0
$46$	20.6164	−	14.1543i	0.448182	−	0.307702i
$47$	46.2730			0.984531			0.492265	−	0.870445i	$-0.336169\pi$
$47$	46.2730			0.984531			0.492265	+	0.870445i	$0.336169\pi$
$48$	18.5840	−	20.5581i	0.387167	−	0.428293i
$49$	87.7376			1.79056
$50$		0			0
$51$	5.33892			0.104685
$52$	18.5525	−	48.1890i	0.356779	−	0.926712i
$53$	16.7503			0.316043			0.158021	−	0.987436i	$-0.449488\pi$
$53$	16.7503			0.316043			0.158021	+	0.987436i	$0.449488\pi$
$54$	5.88205	+	8.56747i	0.108927	+	0.158657i
$55$		0			0
$56$	−21.7039	−	90.9953i	−0.387570	−	1.62492i
$57$			17.5737i			0.308311i
$58$	−1.04702	−	1.52504i	−0.0180521	−	0.0262937i
$59$	−72.0926			−1.22191			−0.610954	−	0.791666i	$-0.709214\pi$
$59$	−72.0926			−1.22191			−0.610954	+	0.791666i	$0.709214\pi$
$60$		0			0
$61$			37.8730i			0.620869i	0.950595	+	0.310434i	$0.100474\pi$
$61$			37.8730i			0.620869i	−0.950595	+	0.310434i	$0.899526\pi$
$62$	−36.8981	−	53.7438i	−0.595131	−	0.866835i
$63$	35.0805			0.556833
$64$	−57.1100	+	28.8868i	−0.892344	+	0.451356i
$65$		0			0
$66$	−37.9192	−	55.2310i	−0.574533	−	0.836833i
$67$			121.224i			1.80931i	0.426148	+	0.904654i	$0.359870\pi$
$67$			121.224i			1.80931i	−0.426148	+	0.904654i	$0.640130\pi$
$68$	−11.5064	−	4.42990i	−0.169212	−	0.0651456i
$69$		−	21.6572i		−	0.313872i
$70$		0			0
$71$			67.4107i			0.949447i	0.880135	+	0.474724i	$0.157452\pi$
$71$			67.4107i			0.949447i	−0.880135	+	0.474724i	$0.842548\pi$
$72$	−5.56821	−	23.3451i	−0.0773363	−	0.324238i
$73$		−	14.7754i		−	0.202402i	−0.994866	−	0.101201i	$-0.967731\pi$
$73$		−	14.7754i		−	0.202402i	0.994866	−	0.101201i	$-0.0322685\pi$
$74$	−5.19881	+	3.56928i	−0.0702542	+	0.0482335i
$75$		0			0
$76$	14.5816	−	37.8748i	0.191863	−	0.498353i
$77$	−226.149			−2.93701
$78$	−25.3109	−	36.8665i	−0.324499	−	0.472648i
$79$			132.433i			1.67637i	0.545390	+	0.838183i	$0.316382\pi$
$79$			132.433i			1.67637i	−0.545390	+	0.838183i	$0.683618\pi$
$80$		0			0
$81$	9.00000			0.111111
$82$	113.653	−	78.0294i	1.38602	−	0.951578i
$83$		−	33.3714i		−	0.402065i	−0.979585	−	0.201033i	$-0.935570\pi$
$83$		−	33.3714i		−	0.402065i	0.979585	−	0.201033i	$-0.0644297\pi$
$84$	−75.6052	−	29.1076i	−0.900062	−	0.346519i
$85$		0			0
$86$	−79.0003	−	115.068i	−0.918608	−	1.33799i
$87$	−1.60203			−0.0184141
$88$	35.8960	+	150.497i	0.407909	+	1.71019i
$89$	60.3607			0.678210			0.339105	−	0.940749i	$-0.389876\pi$
$89$	60.3607			0.678210			0.339105	+	0.940749i	$0.389876\pi$
$90$		0			0
$91$	−150.954			−1.65884
$92$	−17.9698	+	46.6755i	−0.195324	+	0.507342i
$93$	−56.4571			−0.607065
$94$	−76.2953	+	52.3810i	−0.811652	+	0.557245i
$95$		0			0
$96$	−7.36975	+	54.9335i	−0.0767682	+	0.572224i
$97$			13.2188i			0.136277i	0.997676	+	0.0681383i	$0.0217059\pi$
$97$			13.2188i			0.136277i	−0.997676	+	0.0681383i	$0.978294\pi$
$98$	−144.663	+	99.3190i	−1.47615	+	1.01346i
$99$	−58.0193			−0.586054
$100$		0			0
$101$			148.736i			1.47263i	0.676636	+	0.736317i	$0.263437\pi$
$101$			148.736i			1.47263i	−0.676636	+	0.736317i	$0.736563\pi$
$102$	−8.80286	+	6.04366i	−0.0863025	+	0.0592516i
$103$	−133.780			−1.29883			−0.649416	−	0.760434i	$-0.724986\pi$
$103$	−133.780			−1.29883			−0.649416	+	0.760434i	$0.724986\pi$
$104$	23.9605	+	100.456i	0.230389	+	0.965923i
$105$		0			0
$106$	−27.6180	+	18.9613i	−0.260547	+	0.178880i
$107$		−	55.2036i		−	0.515921i	−0.966155	−	0.257961i	$-0.916949\pi$
$107$		−	55.2036i		−	0.515921i	0.966155	−	0.257961i	$-0.0830505\pi$
$108$	−19.3968	−	7.46764i	−0.179600	−	0.0691448i
$109$		−	77.6680i		−	0.712550i	−0.934381	−	0.356275i	$-0.884047\pi$
$109$		−	77.6680i		−	0.712550i	0.934381	−	0.356275i	$-0.115953\pi$
$110$		0			0
$111$			5.46128i			0.0492007i
$112$	138.792	+	125.465i	1.23922	+	1.12022i
$113$		−	90.7924i		−	0.803472i	−0.915755	−	0.401736i	$-0.868407\pi$
$113$		−	90.7924i		−	0.803472i	0.915755	−	0.401736i	$-0.131593\pi$
$114$	−19.8935	−	28.9757i	−0.174504	−	0.254173i
$115$		0			0
$116$	3.45268	+	1.32926i	0.0297645	+	0.0114592i
$117$	−38.7277			−0.331006
$118$	118.867	−	81.6088i	1.00735	−	0.691600i
$119$			36.0443i			0.302893i
$120$		0			0
$121$	253.027			2.09113
$122$	−42.8723	−	62.4454i	−0.351412	−	0.511847i
$123$		−	119.391i		−	0.970660i
$124$	121.676	+	46.8446i	0.981258	+	0.377779i
$125$		0			0
$126$	−57.8410	+	39.7111i	−0.459056	+	0.315167i
$127$	−45.7755			−0.360437			−0.180219	−	0.983627i	$-0.557681\pi$
$127$	−45.7755			−0.360437			−0.180219	+	0.983627i	$0.557681\pi$
$128$	61.4636	−	112.277i	0.480185	−	0.877167i
$129$	−120.877			−0.937029
$130$		0			0
$131$	186.279			1.42197			0.710987	−	0.703205i	$-0.248248\pi$
$131$	186.279			1.42197			0.710987	+	0.703205i	$0.248248\pi$
$132$	125.043	+	48.1408i	0.947296	+	0.364703i
$133$	−118.644			−0.892063
$134$	−137.225	−	199.875i	−1.02407	−	1.49160i
$135$		0			0
$136$	23.9865	−	5.72120i	0.176372	−	0.0420677i
$137$		−	32.9523i		−	0.240528i	−0.992742	−	0.120264i	$-0.961626\pi$
$137$		−	32.9523i		−	0.240528i	0.992742	−	0.120264i	$-0.0383741\pi$
$138$	24.5160	+	35.7086i	0.177652	+	0.258758i
$139$	83.8571			0.603289			0.301644	−	0.953421i	$-0.402464\pi$
$139$	83.8571			0.603289			0.301644	+	0.953421i	$0.402464\pi$
$140$		0			0
$141$			80.1471i			0.568419i
$142$	−76.3090	−	111.148i	−0.537387	−	0.782729i
$143$	249.662			1.74589
$144$	35.6076	+	32.1885i	0.247275	+	0.223531i
$145$		0			0
$146$	16.7257	+	24.3618i	0.114560	+	0.166861i
$147$			151.966i			1.03378i
$148$	4.53143	−	11.7701i	0.0306178	−	0.0795278i
$149$		−	81.4421i		−	0.546591i	−0.961930	−	0.273296i	$-0.911886\pi$
$149$		−	81.4421i		−	0.546591i	0.961930	−	0.273296i	$-0.0881137\pi$
$150$		0			0
$151$		−	84.7219i		−	0.561072i	−0.959843	−	0.280536i	$-0.909488\pi$
$151$		−	84.7219i		−	0.561072i	0.959843	−	0.280536i	$-0.0905123\pi$
$152$	18.8321	+	78.9548i	0.123895	+	0.519439i
$153$			9.24728i			0.0604397i
$154$	372.877	−	256.001i	2.42128	−	1.66235i
$155$		0			0
$156$	83.4659	+	32.1339i	0.535038	+	0.205986i
$157$	−167.846			−1.06908			−0.534540	−	0.845143i	$-0.679515\pi$
$157$	−167.846			−1.06908			−0.534540	+	0.845143i	$0.679515\pi$
$158$	−149.914	−	218.357i	−0.948823	−	1.38200i
$159$			29.0123i			0.182467i
$160$		0			0
$161$	146.213			0.908154
$162$	−14.8393	+	10.1880i	−0.0916006	+	0.0628889i
$163$			82.8713i			0.508413i	0.967150	+	0.254206i	$0.0818142\pi$
$163$			82.8713i			0.508413i	−0.967150	+	0.254206i	$0.918186\pi$
$164$	−99.0634	+	257.311i	−0.604045	+	1.56897i
$165$		0			0
$166$	37.7765	+	55.0231i	0.227569	+	0.331464i
$167$	37.2973			0.223337			0.111669	−	0.993746i	$-0.464380\pi$
$167$	37.2973			0.223337			0.111669	+	0.993746i	$0.464380\pi$
$168$	157.608	−	37.5923i	0.938146	−	0.223764i
$169$	−2.35134			−0.0139132
$170$		0			0
$171$	−30.4386			−0.178003
$172$	260.513	+	100.296i	1.51461	+	0.583116i
$173$	211.828			1.22444			0.612218	−	0.790689i	$-0.290277\pi$
$173$	211.828			1.22444			0.612218	+	0.790689i	$0.290277\pi$
$174$	2.64144	−	1.81350i	0.0151807	−	0.0104224i
$175$		0			0
$176$	−229.548	−	207.506i	−1.30425	−	1.17901i
$177$		−	124.868i		−	0.705469i
$178$	−99.5233	+	68.3283i	−0.559120	+	0.383867i
$179$	−86.4715			−0.483081			−0.241540	−	0.970391i	$-0.577653\pi$
$179$	−86.4715			−0.483081			−0.241540	+	0.970391i	$0.577653\pi$
$180$		0			0
$181$			79.4036i			0.438694i	0.975647	+	0.219347i	$0.0703926\pi$
$181$			79.4036i			0.438694i	−0.975647	+	0.219347i	$0.929607\pi$
$182$	248.895	−	170.880i	1.36755	−	0.938902i
$183$	−65.5979			−0.358459
$184$	−23.2079	−	97.3008i	−0.126130	−	0.528809i
$185$		0			0
$186$	93.0870	−	63.9094i	0.500468	−	0.343599i
$187$		−	59.6134i		−	0.318788i
$188$	66.5011	−	172.733i	0.353729	−	0.918791i
$189$			60.7611i			0.321487i
$190$		0			0
$191$			290.341i			1.52011i	0.649858	+	0.760056i	$0.274828\pi$
$191$			290.341i			1.52011i	−0.649858	+	0.760056i	$0.725172\pi$
$192$	−50.0334	−	98.9174i	−0.260591	−	0.515195i
$193$			182.850i			0.947408i	0.880684	+	0.473704i	$0.157083\pi$
$193$			182.850i			0.947408i	−0.880684	+	0.473704i	$0.842917\pi$
$194$	−14.9637	−	21.7953i	−0.0771326	−	0.112347i
$195$		0			0
$196$	126.092	−	327.516i	0.643326	−	1.67100i
$197$	98.1640			0.498295			0.249147	−	0.968466i	$-0.419850\pi$
$197$	98.1640			0.498295			0.249147	+	0.968466i	$0.419850\pi$
$198$	95.6629	−	65.6779i	0.483146	−	0.331707i
$199$			225.355i			1.13244i	0.824255	+	0.566218i	$0.191594\pi$
$199$			225.355i			1.13244i	−0.824255	+	0.566218i	$0.808406\pi$
$200$		0			0
$201$	−209.965			−1.04460
$202$	−168.369	−	245.238i	−0.833512	−	1.21405i
$203$		−	10.8157i		−	0.0532792i
$204$	7.67282	−	19.9297i	0.0376118	−	0.0976946i
$205$		0			0
$206$	220.577	−	151.439i	1.07076	−	0.735139i
$207$	37.5113			0.181214
$208$	−153.223	−	138.510i	−0.736647	−	0.665911i
$209$	196.225			0.938877
$210$		0			0
$211$	302.658			1.43440			0.717199	−	0.696869i	$-0.245424\pi$
$211$	302.658			1.43440			0.717199	+	0.696869i	$0.245424\pi$
$212$	24.0726	−	62.5272i	0.113550	−	0.294940i
$213$	−116.759			−0.548164
$214$	62.4905	+	91.0202i	0.292012	+	0.425328i
$215$		0			0
$216$	40.4349	−	9.64443i	0.187199	−	0.0446501i
$217$		−	381.155i		−	1.75647i
$218$	87.9202	+	128.060i	0.403304	+	0.587430i
$219$	25.5917			0.116857
$220$		0			0
$221$		−	39.7918i		−	0.180053i
$222$	−6.18217	−	9.00460i	−0.0278476	−	0.0405613i
$223$	432.537			1.93963			0.969815	−	0.243842i	$-0.0784079\pi$
$223$	432.537			1.93963			0.969815	+	0.243842i	$0.0784079\pi$
$224$	−370.869	−	49.7549i	−1.65566	−	0.222120i
$225$		0			0
$226$	102.777	+	149.699i	0.454766	+	0.662387i
$227$			359.320i			1.58291i	0.611230	+	0.791453i	$0.290675\pi$
$227$			359.320i			1.58291i	−0.611230	+	0.791453i	$0.709325\pi$
$228$	65.6011	+	25.2561i	0.287724	+	0.110772i
$229$		−	212.212i		−	0.926688i	−0.886179	−	0.463344i	$-0.846649\pi$
$229$		−	212.212i		−	0.926688i	0.886179	−	0.463344i	$-0.153351\pi$
$230$		0			0
$231$		−	391.702i		−	1.69568i
$232$	−7.19755	+	1.71674i	−0.0310239	+	0.00739974i
$233$		−	276.656i		−	1.18736i	−0.804699	−	0.593682i	$-0.797674\pi$
$233$		−	276.656i		−	1.18736i	0.804699	−	0.593682i	$-0.202326\pi$
$234$	63.8547	−	43.8398i	0.272883	−	0.187350i
$235$		0			0
$236$	−103.608	+	269.115i	−0.439016	+	1.14032i
$237$	−229.380			−0.967850
$238$	−40.8022	−	59.4302i	−0.171438	−	0.249707i
$239$		−	27.9106i		−	0.116781i	−0.998294	−	0.0583904i	$-0.981403\pi$
$239$		−	27.9106i		−	0.116781i	0.998294	−	0.0583904i	$-0.0185968\pi$
$240$		0			0
$241$	−115.420			−0.478920			−0.239460	−	0.970906i	$-0.576970\pi$
$241$	−115.420			−0.478920			−0.239460	+	0.970906i	$0.576970\pi$
$242$	−417.194	+	286.427i	−1.72394	+	1.18358i
$243$			15.5885i			0.0641500i
$244$	141.376	+	54.4291i	0.579411	+	0.223070i
$245$		0			0
$246$	135.151	+	196.853i	0.549394	+	0.800217i
$247$	130.980			0.530282
$248$	−253.649	+	60.4996i	−1.02278	+	0.243950i
$249$	57.8010			0.232132
$250$		0			0
$251$	−26.6696			−0.106253			−0.0531267	−	0.998588i	$-0.516919\pi$
$251$	−26.6696			−0.106253			−0.0531267	+	0.998588i	$0.516919\pi$
$252$	50.4158	−	130.952i	0.200063	−	0.519651i
$253$	−241.820			−0.955812
$254$	75.4752	−	51.8179i	0.297146	−	0.204008i
$255$		0			0
$256$	25.7563	+	254.701i	0.100610	+	0.994926i
$257$		−	170.155i		−	0.662082i	−0.943616	−	0.331041i	$-0.892600\pi$
$257$		−	170.155i		−	0.662082i	0.943616	−	0.331041i	$-0.107400\pi$
$258$	199.303	−	136.833i	0.772491	−	0.530359i
$259$	−36.8704			−0.142357
$260$		0			0
$261$		−	2.77479i		−	0.0106314i
$262$	−307.138	+	210.868i	−1.17228	+	0.804838i
$263$	105.658			0.401741			0.200870	−	0.979618i	$-0.435623\pi$
$263$	105.658			0.401741			0.200870	+	0.979618i	$0.435623\pi$
$264$	−260.668	+	62.1737i	−0.987378	+	0.235506i
$265$		0			0
$266$	195.622	−	134.306i	0.735421	−	0.504908i
$267$			104.548i			0.391565i
$268$	452.517	+	174.216i	1.68849	+	0.650061i
$269$		−	206.889i		−	0.769103i	−0.923104	−	0.384551i	$-0.874356\pi$
$269$		−	206.889i		−	0.769103i	0.923104	−	0.384551i	$-0.125644\pi$
$270$		0			0
$271$			247.759i			0.914241i	0.889405	+	0.457120i	$0.151119\pi$
$271$			247.759i			0.914241i	−0.889405	+	0.457120i	$0.848881\pi$
$272$	−33.0728	+	36.5860i	−0.121591	+	0.134507i
$273$		−	261.460i		−	0.957729i
$274$	37.3020	+	54.3321i	0.136139	+	0.198292i
$275$		0			0
$276$	−80.8443	−	31.1246i	−0.292914	−	0.112770i
$277$	−26.9487			−0.0972879			−0.0486439	−	0.998816i	$-0.515490\pi$
$277$	−26.9487			−0.0972879			−0.0486439	+	0.998816i	$0.515490\pi$
$278$	−138.264	+	94.9264i	−0.497354	+	0.341462i
$279$		−	97.7865i		−	0.350489i
$280$		0			0
$281$	−289.489			−1.03021			−0.515106	−	0.857127i	$-0.672247\pi$
$281$	−289.489			−1.03021			−0.515106	+	0.857127i	$0.672247\pi$
$282$	−90.7266	−	132.147i	−0.321725	−	0.468608i
$283$			3.01272i			0.0106457i	0.999986	+	0.00532283i	$0.00169432\pi$
$283$			3.01272i			0.0106457i	−0.999986	+	0.00532283i	$0.998306\pi$
$284$	251.638	+	96.8792i	0.886050	+	0.341124i
$285$		0			0
$286$	−411.645	+	282.618i	−1.43932	+	0.988173i
$287$	806.038			2.80849
$288$	−95.1476	−	12.7648i	−0.330374	−	0.0443221i
$289$	279.499			0.967123
$290$		0			0
$291$	−22.8957			−0.0786794
$292$	−55.1551	−	21.2344i	−0.188887	−	0.0727205i
$293$	−95.1952			−0.324898			−0.162449	−	0.986717i	$-0.551939\pi$
$293$	−95.1952			−0.324898			−0.162449	+	0.986717i	$0.551939\pi$
$294$	−172.026	−	250.563i	−0.585121	−	0.852255i
$295$		0			0
$296$	5.85232	+	24.5363i	0.0197714	+	0.0828928i
$297$		−	100.492i		−	0.338358i
$298$	92.1925	+	134.282i	0.309371	+	0.450612i
$299$	−161.414			−0.539848
$300$		0			0
$301$		−	816.068i		−	2.71119i
$302$	95.9053	+	139.690i	0.317567	+	0.462551i
$303$	−257.618			−0.850226
$304$	−120.427	−	108.863i	−0.396143	−	0.358104i
$305$		0			0
$306$	−10.4679	−	15.2470i	−0.0342089	−	0.0498268i
$307$		−	167.348i		−	0.545108i	−0.962140	−	0.272554i	$-0.912132\pi$
$307$		−	167.348i		−	0.545108i	0.962140	−	0.272554i	$-0.0878684\pi$
$308$	−325.010	+	844.195i	−1.05523	+	2.74089i
$309$		−	231.713i		−	0.749881i
$310$		0			0
$311$		−	299.478i		−	0.962951i	−0.876460	−	0.481475i	$-0.840101\pi$
$311$		−	299.478i		−	0.962951i	0.876460	−	0.481475i	$-0.159899\pi$
$312$	−173.995	+	41.5008i	−0.557676	+	0.133015i
$313$		−	123.623i		−	0.394963i	−0.980307	−	0.197481i	$-0.936724\pi$
$313$		−	123.623i		−	0.394963i	0.980307	−	0.197481i	$-0.0632762\pi$
$314$	276.746	−	190.001i	0.881356	−	0.605100i
$315$		0			0
$316$	494.360	+	190.326i	1.56443	+	0.602296i
$317$	135.949			0.428862			0.214431	−	0.976739i	$-0.431210\pi$
$317$	135.949			0.428862			0.214431	+	0.976739i	$0.431210\pi$
$318$	−32.8420	−	47.8358i	−0.103277	−	0.150427i
$319$			17.8880i			0.0560752i
$320$		0			0
$321$	95.6154			0.297867
$322$	−241.077	+	165.513i	−0.748687	+	0.514016i
$323$		−	31.2749i		−	0.0968263i
$324$	12.9343	−	33.5962i	0.0399208	−	0.103692i
$325$		0			0
$326$	−93.8104	−	136.639i	−0.287762	−	0.419138i
$327$	134.525			0.411391
$328$	−127.940	−	536.397i	−0.390061	−	1.63536i
$329$	−541.092			−1.64466
$330$		0			0
$331$	−41.1886			−0.124437			−0.0622185	−	0.998063i	$-0.519818\pi$
$331$	−41.1886			−0.124437			−0.0622185	+	0.998063i	$0.519818\pi$
$332$	−124.572	−	47.9597i	−0.375218	−	0.144457i
$333$	−9.45921			−0.0284060
$334$	−61.4962	+	42.2206i	−0.184120	+	0.126409i
$335$		0			0
$336$	−217.312	+	240.396i	−0.646762	+	0.715463i
$337$			565.599i			1.67834i	0.543873	+	0.839168i	$0.316957\pi$
$337$			565.599i			1.67834i	−0.543873	+	0.839168i	$0.683043\pi$
$338$	3.87690	−	2.66171i	0.0114701	−	0.00787489i
$339$	157.257			0.463885
$340$		0			0
$341$			630.390i			1.84865i
$342$	50.1875	−	34.4565i	0.146747	−	0.100750i
$343$	−452.977			−1.32063
$344$	−543.072	+	129.532i	−1.57870	+	0.376546i
$345$		0			0
$346$	−349.263	+	239.789i	−1.00943	+	0.693032i
$347$		−	134.668i		−	0.388092i	−0.980992	−	0.194046i	$-0.937839\pi$
$347$		−	134.668i		−	0.388092i	0.980992	−	0.194046i	$-0.0621612\pi$
$348$	−2.30235	+	5.98023i	−0.00661596	+	0.0171846i
$349$			461.309i			1.32180i	0.750473	+	0.660901i	$0.229826\pi$
$349$			461.309i			1.32180i	−0.750473	+	0.660901i	$0.770174\pi$
$350$		0			0
$351$		−	67.0784i		−	0.191107i
$352$	613.378	+	82.2893i	1.74255	+	0.233777i
$353$		−	429.790i		−	1.21754i	−0.793349	−	0.608768i	$-0.791664\pi$
$353$		−	429.790i		−	1.21754i	0.793349	−	0.608768i	$-0.208336\pi$
$354$	141.351	+	205.884i	0.399296	+	0.581592i
$355$		0			0
$356$	86.7473	−	225.321i	0.243672	−	0.632924i
$357$	−62.4305			−0.174875
$358$	142.575	−	97.8858i	0.398254	−	0.273424i
$359$			312.402i			0.870200i	0.900382	+	0.435100i	$0.143287\pi$
$359$			312.402i			0.870200i	−0.900382	+	0.435100i	$0.856713\pi$
$360$		0			0
$361$	−258.055			−0.714833
$362$	−89.8849	−	130.921i	−0.248301	−	0.361661i
$363$			438.256i			1.20732i
$364$	−216.943	+	563.498i	−0.595998	+	1.54807i
$365$		0			0
$366$	108.159	−	74.2569i	0.295515	−	0.202888i
$367$	−138.931			−0.378558			−0.189279	−	0.981923i	$-0.560615\pi$
$367$	−138.931			−0.378558			−0.189279	+	0.981923i	$0.560615\pi$
$368$	148.410	+	134.159i	0.403288	+	0.364563i
$369$	206.792			0.560411
$370$		0			0
$371$	−195.869			−0.527949
$372$	−81.1372	+	210.749i	−0.218111	+	0.566530i
$373$	−422.559			−1.13287			−0.566433	−	0.824108i	$-0.691677\pi$
$373$	−422.559			−1.13287			−0.566433	+	0.824108i	$0.691677\pi$
$374$	67.4824	+	98.2912i	0.180434	+	0.262811i
$375$		0			0
$376$	85.8859	+	360.083i	0.228420	+	0.957667i
$377$			11.9402i			0.0316715i
$378$	−68.7816	−	100.184i	−0.181962	−	0.265036i
$379$	−419.245			−1.10619			−0.553094	−	0.833119i	$-0.686553\pi$
$379$	−419.245			−1.10619			−0.553094	+	0.833119i	$0.686553\pi$
$380$		0			0
$381$		−	79.2856i		−	0.208099i
$382$	−328.667	−	478.718i	−0.860384	−	1.25319i
$383$	306.762			0.800944			0.400472	−	0.916309i	$-0.368846\pi$
$383$	306.762			0.800944			0.400472	+	0.916309i	$0.368846\pi$
$384$	194.470	+	106.458i	0.506433	+	0.277235i
$385$		0			0
$386$	−206.986	−	301.485i	−0.536234	−	0.781048i
$387$		−	209.365i		−	0.540994i
$388$	49.3447	+	18.9974i	0.127177	+	0.0489624i
$389$			441.866i			1.13590i	0.823062	+	0.567951i	$0.192264\pi$
$389$			441.866i			1.13590i	−0.823062	+	0.567951i	$0.807736\pi$
$390$		0			0
$391$			38.5420i			0.0985728i
$392$	162.847	+	682.748i	0.415426	+	1.74170i
$393$			322.644i			0.820978i
$394$	−161.854	+	111.122i	−0.410797	+	0.282035i
$395$		0			0
$396$	−83.3824	+	216.581i	−0.210562	+	0.546921i
$397$	160.391			0.404007			0.202004	−	0.979385i	$-0.435255\pi$
$397$	160.391			0.404007			0.202004	+	0.979385i	$0.435255\pi$
$398$	−255.102	−	371.567i	−0.640960	−	0.933587i
$399$		−	205.498i		−	0.515033i
$400$		0			0
$401$	193.791			0.483270			0.241635	−	0.970367i	$-0.422316\pi$
$401$	193.791			0.483270			0.241635	+	0.970367i	$0.422316\pi$
$402$	346.193	−	237.681i	0.861177	−	0.591246i
$403$			420.783i			1.04413i
$404$	555.218	+	213.756i	1.37430	+	0.529099i
$405$		0			0
$406$	12.2434	+	17.8330i	0.0301560	+	0.0439236i
$407$	60.9797			0.149827
$408$	9.90941	+	41.5459i	0.0242878	+	0.101828i
$409$	459.509			1.12349			0.561747	−	0.827309i	$-0.310130\pi$
$409$	459.509			1.12349			0.561747	+	0.827309i	$0.310130\pi$
$410$		0			0
$411$	57.0751			0.138869
$412$	−192.261	+	499.387i	−0.466653	+	1.21210i
$413$	843.013			2.04119
$414$	−61.8491	+	42.4629i	−0.149394	+	0.102567i
$415$		0			0
$416$	409.428	+	54.9279i	0.984202	+	0.132038i
$417$			145.245i			0.348309i
$418$	−323.538	+	222.127i	−0.774015	+	0.531405i
$419$	−223.442			−0.533274			−0.266637	−	0.963797i	$-0.585912\pi$
$419$	−223.442			−0.533274			−0.266637	+	0.963797i	$0.585912\pi$
$420$		0			0
$421$		−	753.492i		−	1.78977i	−0.446299	−	0.894884i	$-0.647258\pi$
$421$		−	753.492i		−	1.78977i	0.446299	−	0.894884i	$-0.352742\pi$
$422$	−499.025	+	342.609i	−1.18252	+	0.811870i
$423$	−138.819			−0.328177
$424$	31.0897	+	130.346i	0.0733247	+	0.307419i
$425$		0			0
$426$	192.513	−	132.171i	0.451909	−	0.310261i
$427$		−	442.867i		−	1.03716i
$428$	−206.070	−	79.3357i	−0.481472	−	0.185364i
$429$			432.427i			1.00799i
$430$		0			0
$431$		−	801.595i		−	1.85985i	−0.367752	−	0.929924i	$-0.619872\pi$
$431$		−	801.595i		−	1.85985i	0.367752	−	0.929924i	$-0.380128\pi$
$432$	−55.7520	+	61.6742i	−0.129056	+	0.142764i
$433$			725.058i			1.67450i	0.546822	+	0.837249i	$0.315838\pi$
$433$			725.058i			1.67450i	−0.546822	+	0.837249i	$0.684162\pi$
$434$	431.468	+	628.452i	0.994165	+	1.44805i
$435$		0			0
$436$	−289.927	−	111.620i	−0.664971	−	0.256010i
$437$	−126.866			−0.290311
$438$	−42.1958	+	28.9698i	−0.0963374	+	0.0661411i
$439$		−	551.061i		−	1.25526i	−0.778510	−	0.627632i	$-0.784024\pi$
$439$		−	551.061i		−	1.25526i	0.778510	−	0.627632i	$-0.215976\pi$
$440$		0			0
$441$	−263.213			−0.596854
$442$	45.0443	+	65.6091i	0.101910	+	0.148437i
$443$			36.7779i			0.0830201i	0.999138	+	0.0415100i	$0.0132169\pi$
$443$			36.7779i			0.0830201i	−0.999138	+	0.0415100i	$0.986783\pi$
$444$	20.3864	+	7.84866i	0.0459154	+	0.0176772i
$445$		0			0
$446$	−713.172	+	489.633i	−1.59904	+	1.09783i
$447$	141.062			0.315574
$448$	667.815	−	337.787i	1.49066	−	0.753990i
$449$	−332.641			−0.740849			−0.370424	−	0.928863i	$-0.620788\pi$
$449$	−332.641			−0.740849			−0.370424	+	0.928863i	$0.620788\pi$
$450$		0			0
$451$	−1333.10			−2.95588
$452$	−338.920	−	130.482i	−0.749822	−	0.288677i
$453$	146.743			0.323935
$454$	−406.750	−	592.450i	−0.895926	−	1.30496i
$455$		0			0
$456$	−136.754	+	32.6181i	−0.299898	+	0.0715309i
$457$			343.279i			0.751158i	0.926790	+	0.375579i	$0.122556\pi$
$457$			343.279i			0.751158i	−0.926790	+	0.375579i	$0.877444\pi$
$458$	240.224	+	349.896i	0.524506	+	0.763966i
$459$	−16.0168			−0.0348949
$460$		0			0
$461$			208.768i			0.452859i	0.974028	+	0.226429i	$0.0727053\pi$
$461$			208.768i			0.452859i	−0.974028	+	0.226429i	$0.927295\pi$
$462$	443.407	+	645.843i	0.959756	+	1.39793i
$463$	−239.500			−0.517278			−0.258639	−	0.965974i	$-0.583274\pi$
$463$	−239.500			−0.517278			−0.258639	+	0.965974i	$0.583274\pi$
$464$	9.92404	−	10.9782i	0.0213880	−	0.0236599i
$465$		0			0
$466$	313.175	+	456.153i	0.672049	+	0.978869i
$467$			295.094i			0.631892i	0.948777	+	0.315946i	$0.102322\pi$
$467$			295.094i			0.631892i	−0.948777	+	0.315946i	$0.897678\pi$
$468$	−55.6575	+	144.567i	−0.118926	+	0.308904i
$469$		−	1417.53i		−	3.02244i
$470$		0			0
$471$		−	290.717i		−	0.617234i
$472$	−133.809	−	561.003i	−0.283493	−	1.18857i
$473$			1349.69i			2.85346i
$474$	378.205	−	259.659i	0.797900	−	0.547803i
$475$		0			0
$476$	134.550	+	51.8010i	0.282668	+	0.108826i
$477$	−50.2508			−0.105348
$478$	31.5948	+	46.0193i	0.0660979	+	0.0962746i
$479$		−	533.361i		−	1.11349i	−0.830684	−	0.556745i	$-0.812050\pi$
$479$		−	533.361i		−	1.11349i	0.830684	−	0.556745i	$-0.187950\pi$
$480$		0			0
$481$	40.7037			0.0846232
$482$	190.305	−	130.655i	0.394824	−	0.271069i
$483$			253.248i			0.524323i
$484$	363.637	−	944.527i	0.751317	−	1.95150i
$485$		0			0
$486$	−17.6461	−	25.7024i	−0.0363089	−	0.0528856i
$487$	−285.675			−0.586601			−0.293301	−	0.956020i	$-0.594754\pi$
$487$	−285.675			−0.586601			−0.293301	+	0.956020i	$0.594754\pi$
$488$	−294.717	+	70.2950i	−0.603927	+	0.144047i
$489$	−143.537			−0.293532
$490$		0			0
$491$	188.244			0.383388			0.191694	−	0.981455i	$-0.438602\pi$
$491$	188.244			0.383388			0.191694	+	0.981455i	$0.438602\pi$
$492$	−445.676	−	171.583i	−0.905846	−	0.348746i
$493$	2.85103			0.00578303
$494$	−215.961	+	148.269i	−0.437167	+	0.300140i
$495$		0			0
$496$	349.733	−	386.883i	0.705107	−	0.780006i
$497$		−	788.266i		−	1.58605i
$498$	−95.3028	+	65.4307i	−0.191371	+	0.131387i
$499$	−625.534			−1.25357			−0.626787	−	0.779190i	$-0.715631\pi$
$499$	−625.534			−1.25357			−0.626787	+	0.779190i	$0.715631\pi$
$500$		0			0
$501$			64.6008i			0.128944i
$502$	43.9731	−	30.1900i	0.0875959	−	0.0601395i
$503$	232.863			0.462949			0.231474	−	0.972841i	$-0.425645\pi$
$503$	232.863			0.462949			0.231474	+	0.972841i	$0.425645\pi$
$504$	65.1118	+	272.986i	0.129190	+	0.541639i
$505$		0			0
$506$	398.716	−	273.741i	0.787976	−	0.540990i
$507$		−	4.07263i		−	0.00803280i
$508$	−65.7862	+	170.876i	−0.129500	+	0.336370i
$509$		−	615.343i		−	1.20893i	−0.796633	−	0.604463i	$-0.793388\pi$
$509$		−	615.343i		−	1.20893i	0.796633	−	0.604463i	$-0.206612\pi$
$510$		0			0
$511$			172.775i			0.338112i
$512$	−330.789	−	390.797i	−0.646072	−	0.763276i
$513$		−	52.7212i		−	0.102770i
$514$	192.616	+	280.553i	0.374739	+	0.545823i
$515$		0			0
$516$	−173.718	+	451.222i	−0.336662	+	0.874461i
$517$	894.909			1.73096
$518$	60.7922	−	41.7373i	0.117359	−	0.0805739i
$519$			366.896i			0.706929i
$520$		0			0
$521$	132.731			0.254761			0.127381	−	0.991854i	$-0.459343\pi$
$521$	132.731			0.254761			0.127381	+	0.991854i	$0.459343\pi$
$522$	3.14107	+	4.57511i	0.00601738	+	0.00876458i
$523$		−	911.886i		−	1.74357i	−0.489890	−	0.871784i	$-0.662963\pi$
$523$		−	911.886i		−	1.74357i	0.489890	−	0.871784i	$-0.337037\pi$
$524$	267.710	−	695.361i	0.510897	−	1.32703i
$525$		0			0
$526$	−174.210	+	119.605i	−0.331197	+	0.227385i
$527$	100.473			0.190651
$528$	359.411	−	397.589i	0.680702	−	0.753009i
$529$	−372.655			−0.704453
$530$		0			0
$531$	216.278			0.407303
$532$	−170.510	+	442.889i	−0.320507	+	0.832497i
$533$	−889.841			−1.66950
$534$	−118.348	−	172.379i	−0.221626	−	0.322808i
$535$		0			0
$536$	−943.327	+	225.000i	−1.75994	+	0.419775i
$537$		−	149.773i		−	0.278907i
$538$	234.198	+	341.120i	0.435313	+	0.634052i
$539$	1696.83			3.14810
$540$		0			0
$541$		−	373.215i		−	0.689861i	−0.938628	−	0.344931i	$-0.887902\pi$
$541$		−	373.215i		−	0.689861i	0.938628	−	0.344931i	$-0.112098\pi$
$542$	−280.464	−	408.508i	−0.517461	−	0.753705i
$543$	−137.531			−0.253280
$544$	13.1155	−	97.7618i	0.0241094	−	0.179709i
$545$		0			0
$546$	295.973	+	431.098i	0.542075	+	0.789557i
$547$			175.297i			0.320469i	0.987079	+	0.160235i	$0.0512251\pi$
$547$			175.297i			0.320469i	−0.987079	+	0.160235i	$0.948775\pi$
$548$	−123.008	−	47.3573i	−0.224467	−	0.0864185i
$549$		−	113.619i		−	0.206956i
$550$		0			0
$551$			9.38454i			0.0170318i
$552$	168.530	−	40.1973i	0.305308	−	0.0728212i
$553$		−	1548.60i		−	2.80036i
$554$	44.4334	−	30.5060i	0.0802046	−	0.0550650i
$555$		0			0
$556$	120.515	−	313.031i	0.216754	−	0.563005i
$557$	−403.527			−0.724466			−0.362233	−	0.932088i	$-0.617985\pi$
$557$	−403.527			−0.724466			−0.362233	+	0.932088i	$0.617985\pi$
$558$	110.694	+	161.231i	0.198377	+	0.288945i
$559$			900.913i			1.61165i
$560$		0			0
$561$	103.253			0.184053
$562$	477.313	−	327.702i	0.849311	−	0.583100i
$563$		−	236.345i		−	0.419796i	−0.977723	−	0.209898i	$-0.932687\pi$
$563$		−	236.345i		−	0.419796i	0.977723	−	0.209898i	$-0.0673132\pi$
$564$	299.182	+	115.183i	0.530464	+	0.204226i
$565$		0			0
$566$	−3.41041	−	4.96741i	−0.00602545	−	0.00877634i
$567$	−105.241			−0.185611
$568$	−524.571	+	125.119i	−0.923540	+	0.220280i
$569$	757.837			1.33187			0.665937	−	0.746008i	$-0.268032\pi$
$569$	757.837			1.33187			0.665937	+	0.746008i	$0.268032\pi$
$570$		0			0
$571$	198.009			0.346775			0.173388	−	0.984854i	$-0.444529\pi$
$571$	198.009			0.346775			0.173388	+	0.984854i	$0.444529\pi$
$572$	358.801	−	931.965i	0.627275	−	1.62931i
$573$	−502.886			−0.877637
$574$	−1329.00	+	912.436i	−2.31534	+	1.58961i
$575$		0			0
$576$	171.330	−	86.6604i	0.297448	−	0.150452i
$577$			479.109i			0.830346i	0.909743	+	0.415173i	$0.136279\pi$
$577$			479.109i			0.830346i	−0.909743	+	0.415173i	$0.863721\pi$
$578$	−460.840	+	316.393i	−0.797301	+	0.547392i
$579$	−316.705			−0.546986
$580$		0			0
$581$			390.228i			0.671649i
$582$	37.7506	−	25.9179i	0.0648637	−	0.0445326i
$583$	323.947			0.555654
$584$	114.978	−	27.4241i	0.196879	−	0.0469591i
$585$		0			0
$586$	156.959	−	107.761i	0.267848	−	0.183893i
$587$			658.065i			1.12106i	0.828133	+	0.560532i	$0.189403\pi$
$587$			658.065i			1.12106i	−0.828133	+	0.560532i	$0.810597\pi$
$588$	567.275	+	218.398i	0.964753	+	0.371424i
$589$			330.720i			0.561495i
$590$		0			0
$591$			170.025i			0.287691i
$592$	−37.4244	−	33.8308i	−0.0632169	−	0.0571466i
$593$			202.971i			0.342279i	0.985247	+	0.171139i	$0.0547448\pi$
$593$			202.971i			0.342279i	−0.985247	+	0.171139i	$0.945255\pi$
$594$	113.758	+	165.693i	0.191511	+	0.278944i
$595$		0			0
$596$	−304.016	−	117.044i	−0.510094	−	0.196383i
$597$	−390.326			−0.653813
$598$	266.142	−	182.721i	0.445053	−	0.305554i
$599$			11.7767i			0.0196605i	0.999952	+	0.00983027i	$0.00312912\pi$
$599$			11.7767i			0.0196605i	−0.999952	+	0.00983027i	$0.996871\pi$
$600$		0			0
$601$	206.863			0.344198			0.172099	−	0.985080i	$-0.444945\pi$
$601$	206.863			0.344198			0.172099	+	0.985080i	$0.444945\pi$
$602$	923.789	+	1345.54i	1.53453	+	2.23512i
$603$		−	363.671i		−	0.603102i
$604$	−316.259	−	121.758i	−0.523608	−	0.201586i
$605$		0			0
$606$	424.764	−	291.624i	0.700931	−	0.481228i
$607$	−885.649			−1.45906			−0.729529	−	0.683950i	$-0.760261\pi$
$607$	−885.649			−1.45906			−0.729529	+	0.683950i	$0.760261\pi$
$608$	321.795	+	43.1713i	0.529269	+	0.0710055i
$609$	18.7333			0.0307607
$610$		0			0
$611$	597.349			0.977658
$612$	34.5192	+	13.2897i	0.0564040	+	0.0217152i
$613$	979.091			1.59721			0.798606	−	0.601855i	$-0.205571\pi$
$613$	979.091			1.59721			0.798606	+	0.601855i	$0.205571\pi$
$614$	189.438	+	275.925i	0.308531	+	0.449390i
$615$		0			0
$616$	−419.749	−	1759.83i	−0.681411	−	2.85687i
$617$		−	1064.97i		−	1.72604i	−0.505171	−	0.863019i	$-0.668571\pi$
$617$		−	1064.97i		−	1.72604i	0.505171	−	0.863019i	$-0.331429\pi$
$618$	262.299	+	382.051i	0.424433	+	0.618205i
$619$	658.875			1.06442			0.532209	−	0.846613i	$-0.321362\pi$
$619$	658.875			1.06442			0.532209	+	0.846613i	$0.321362\pi$
$620$		0			0
$621$			64.9716i			0.104624i
$622$	339.009	+	493.782i	0.545030	+	0.793861i
$623$	−705.827			−1.13295
$624$	239.906	−	265.389i	0.384464	−	0.425303i
$625$		0			0
$626$	139.942	+	203.831i	0.223549	+	0.325609i
$627$			339.872i			0.542061i
$628$	−241.219	+	626.553i	−0.384107	+	0.997695i
$629$		−	9.71910i		−	0.0154517i
$630$		0			0
$631$			1074.30i			1.70253i	0.524736	+	0.851265i	$0.324164\pi$
$631$			1074.30i			1.70253i	−0.524736	+	0.851265i	$0.675836\pi$
$632$	−1030.55	+	245.805i	−1.63062	+	0.388932i
$633$			524.219i			0.828150i
$634$	−224.154	+	153.895i	−0.353556	+	0.242736i
$635$		0			0
$636$	108.300	+	41.6950i	0.170284	+	0.0655582i
$637$	1132.63			1.77806
$638$	−20.2492	−	29.4939i	−0.0317386	−	0.0462286i
$639$		−	202.232i		−	0.316482i
$640$		0			0
$641$	170.402			0.265838			0.132919	−	0.991127i	$-0.457565\pi$
$641$	170.402			0.265838			0.132919	+	0.991127i	$0.457565\pi$
$642$	−157.652	+	108.237i	−0.245563	+	0.168593i
$643$		−	387.322i		−	0.602367i	−0.953566	−	0.301183i	$-0.902618\pi$
$643$		−	387.322i		−	0.602367i	0.953566	−	0.301183i	$-0.0973816\pi$
$644$	210.129	−	545.799i	0.326288	−	0.847514i
$645$		0			0
$646$	35.4032	+	51.5664i	0.0548037	+	0.0798241i
$647$	−1098.39			−1.69766			−0.848830	−	0.528665i	$-0.822693\pi$
$647$	−1098.39			−1.69766			−0.848830	+	0.528665i	$0.822693\pi$
$648$	16.7046	+	70.0354i	0.0257788	+	0.108079i
$649$	−1394.25			−2.14831
$650$		0			0
$651$	660.180			1.01410
$652$	309.351	+	119.098i	0.474465	+	0.182666i
$653$	801.196			1.22695			0.613473	−	0.789716i	$-0.289772\pi$
$653$	801.196			1.22695			0.613473	+	0.789716i	$0.289772\pi$
$654$	−221.806	+	152.282i	−0.339153	+	0.232848i
$655$		0			0
$656$	818.151	+	739.589i	1.24718	+	1.12742i
$657$			44.3261i			0.0674674i
$658$	892.158	−	612.517i	1.35586	−	0.930876i
$659$	204.225			0.309901			0.154950	−	0.987922i	$-0.450478\pi$
$659$	204.225			0.309901			0.154950	+	0.987922i	$0.450478\pi$
$660$		0			0
$661$		−	283.821i		−	0.429382i	−0.976682	−	0.214691i	$-0.931126\pi$
$661$		−	283.821i		−	0.429382i	0.976682	−	0.214691i	$-0.0688744\pi$
$662$	67.9122	−	46.6255i	0.102586	−	0.0704313i
$663$	68.9214			0.103954
$664$	259.687	−	61.9397i	0.391094	−	0.0932827i
$665$		0			0
$666$	15.5964	−	10.7078i	0.0234181	−	0.0160778i
$667$		−	11.5651i		−	0.0173390i
$668$	53.6018	−	139.227i	0.0802422	−	0.208424i
$669$			749.177i			1.11985i
$670$		0			0
$671$			732.455i			1.09159i
$672$	86.1780	−	642.364i	0.128241	−	0.955898i
$673$		−	371.454i		−	0.551937i	−0.961167	−	0.275969i	$-0.911001\pi$
$673$		−	371.454i		−	0.551937i	0.961167	−	0.275969i	$-0.0889986\pi$
$674$	−640.258	−	932.565i	−0.949938	−	1.38363i
$675$		0			0
$676$	−3.37922	+	8.77732i	−0.00499884	+	0.0129842i
$677$	1084.06			1.60127			0.800637	−	0.599150i	$-0.204495\pi$
$677$	1084.06			1.60127			0.800637	+	0.599150i	$0.204495\pi$
$678$	−259.287	+	178.015i	−0.382429	+	0.262559i
$679$		−	154.574i		−	0.227650i
$680$		0			0
$681$	−622.360			−0.913891
$682$	−713.602	−	1039.39i	−1.04634	−	1.52404i
$683$		−	580.301i		−	0.849636i	−0.905279	−	0.424818i	$-0.860338\pi$
$683$		−	580.301i		−	0.849636i	0.905279	−	0.424818i	$-0.139662\pi$
$684$	−43.7448	+	113.624i	−0.0639543	+	0.166118i
$685$		0			0
$686$	746.873	−	512.771i	1.08874	−	0.747479i
$687$	367.561			0.535023
$688$	748.792	−	828.331i	1.08836	−	1.20397i
$689$	216.233			0.313837
$690$		0			0
$691$	−438.911			−0.635183			−0.317592	−	0.948228i	$-0.602874\pi$
$691$	−438.911			−0.635183			−0.317592	+	0.948228i	$0.602874\pi$
$692$	304.428	−	790.733i	0.439924	−	1.14268i
$693$	678.448			0.979002
$694$	152.444	+	222.042i	0.219660	+	0.319945i
$695$		0			0
$696$	−2.97348	−	12.4665i	−0.00427224	−	0.0179117i
$697$			212.473i			0.304840i
$698$	−522.202	−	760.611i	−0.748141	−	1.08970i
$699$	479.182			0.685525
$700$		0			0
$701$		−	173.658i		−	0.247730i	−0.992299	−	0.123865i	$-0.960471\pi$
$701$		−	173.658i		−	0.247730i	0.992299	−	0.123865i	$-0.0395289\pi$
$702$	75.9328	+	110.600i	0.108166	+	0.157549i
$703$	31.9917			0.0455073
$704$	−1104.49	+	558.665i	−1.56888	+	0.793558i
$705$		0			0
$706$	486.523	+	708.642i	0.689125	+	1.00374i
$707$		−	1739.24i		−	2.46003i
$708$	−466.121	−	179.454i	−0.658363	−	0.253466i
$709$			1231.35i			1.73674i	0.495913	+	0.868372i	$0.334834\pi$
$709$			1231.35i			1.73674i	−0.495913	+	0.868372i	$0.665166\pi$
$710$		0			0
$711$		−	397.299i		−	0.558788i
$712$	112.034	+	469.709i	0.157351	+	0.659704i
$713$		−	407.567i		−	0.571623i
$714$	102.936	−	70.6714i	0.144168	−	0.0989796i
$715$		0			0
$716$	−124.272	+	322.790i	−0.173565	+	0.450824i
$717$	48.3426			0.0674234
$718$	−353.639	−	515.091i	−0.492533	−	0.717397i
$719$		−	327.782i		−	0.455885i	−0.973675	−	0.227943i	$-0.926800\pi$
$719$		−	327.782i		−	0.455885i	0.973675	−	0.227943i	$-0.0731999\pi$
$720$		0			0
$721$	1564.35			2.16970
$722$	425.483	−	292.118i	0.589312	−	0.404596i
$723$		−	199.913i		−	0.276505i
$724$	296.406	+	114.115i	0.409401	+	0.157617i
$725$		0			0
$726$	−496.106	−	722.600i	−0.683341	−	0.995317i
$727$	217.872			0.299686			0.149843	−	0.988710i	$-0.452123\pi$
$727$	217.872			0.299686			0.149843	+	0.988710i	$0.452123\pi$
$728$	−280.182	−	1174.68i	−0.384865	−	1.61357i
$729$	−27.0000			−0.0370370
$730$		0			0
$731$	215.117			0.294278
$732$	−94.2740	+	244.871i	−0.128790	+	0.334523i
$733$	154.099			0.210231			0.105115	−	0.994460i	$-0.466479\pi$
$733$	154.099			0.210231			0.105115	+	0.994460i	$0.466479\pi$
$734$	229.071	−	157.270i	0.312085	−	0.214264i
$735$		0			0
$736$	−396.568	−	53.2027i	−0.538815	−	0.0722862i
$737$			2344.44i			3.18106i
$738$	−340.960	+	234.088i	−0.462005	+	0.317193i
$739$	−497.686			−0.673459			−0.336729	−	0.941601i	$-0.609321\pi$
$739$	−497.686			−0.673459			−0.336729	+	0.941601i	$0.609321\pi$
$740$		0			0
$741$			226.864i			0.306159i
$742$	322.951	−	221.724i	0.435244	−	0.298819i
$743$	657.468			0.884883			0.442441	−	0.896797i	$-0.354112\pi$
$743$	657.468			0.884883			0.442441	+	0.896797i	$0.354112\pi$
$744$	−104.788	−	439.332i	−0.140845	−	0.590501i
$745$		0			0
$746$	696.720	−	478.337i	0.933940	−	0.641203i
$747$			100.114i			0.134022i
$748$	−222.531	−	85.6733i	−0.297502	−	0.114537i
$749$			645.522i			0.861846i
$750$		0			0
$751$		−	379.552i		−	0.505396i	−0.967545	−	0.252698i	$-0.918682\pi$
$751$		−	379.552i		−	0.505396i	0.967545	−	0.252698i	$-0.0813179\pi$
$752$	−549.223	−	496.485i	−0.730350	−	0.660219i
$753$		−	46.1931i		−	0.0613455i
$754$	−13.5163	−	19.6871i	−0.0179261	−	0.0261102i
$755$		0			0
$756$	226.816	+	87.3227i	0.300021	+	0.115506i
$757$	−195.966			−0.258872			−0.129436	−	0.991588i	$-0.541317\pi$
$757$	−195.966			−0.258872			−0.129436	+	0.991588i	$0.541317\pi$
$758$	691.255	−	474.586i	0.911946	−	0.626103i
$759$		−	418.845i		−	0.551838i
$760$		0			0
$761$	−963.030			−1.26548			−0.632740	−	0.774364i	$-0.718070\pi$
$761$	−963.030			−1.26548			−0.632740	+	0.774364i	$0.718070\pi$
$762$	89.7513	+	130.727i	0.117784	+	0.171557i
$763$			908.209i			1.19031i
$764$	1083.82	+	417.264i	1.41861	+	0.546156i
$765$		0			0
$766$	−505.792	+	347.254i	−0.660302	+	0.453335i
$767$	−930.661			−1.21338
$768$	−441.155	+	44.6112i	−0.574421	+	0.0580875i
$769$	−81.3670			−0.105809			−0.0529044	−	0.998600i	$-0.516848\pi$
$769$	−81.3670			−0.105809			−0.0529044	+	0.998600i	$0.516848\pi$
$770$		0			0
$771$	294.717			0.382253
$772$	682.562	+	262.782i	0.884147	+	0.340392i
$773$	−781.463			−1.01095			−0.505474	−	0.862842i	$-0.668682\pi$
$773$	−781.463			−1.01095			−0.505474	+	0.862842i	$0.668682\pi$
$774$	237.001	+	345.203i	0.306203	+	0.445998i
$775$		0			0
$776$	−102.865	+	24.5351i	−0.132558	+	0.0316174i
$777$		−	63.8613i		−	0.0821896i
$778$	−500.193	−	728.553i	−0.642921	−	0.936443i
$779$	−699.383			−0.897795
$780$		0			0
$781$			1303.71i			1.66928i
$782$	−43.6296	−	63.5484i	−0.0557923	−	0.0812639i
$783$	4.80609			0.00613804
$784$	−1041.38	−	941.379i	−1.32829	−	1.20074i
$785$		0			0
$786$	−365.234	−	531.979i	−0.464674	−	0.676818i
$787$		−	1030.41i		−	1.30929i	−0.755937	−	0.654644i	$-0.772818\pi$
$787$		−	1030.41i		−	1.30929i	0.755937	−	0.654644i	$-0.227182\pi$
$788$	141.076	−	366.437i	0.179031	−	0.465022i
$789$			183.005i			0.231945i
$790$		0			0
$791$			1061.68i			1.34220i
$792$	−107.688	−	451.490i	−0.135970	−	0.570063i
$793$			488.912i			0.616534i
$794$	−264.454	+	181.563i	−0.333066	+	0.228668i
$795$		0			0
$796$	841.229	+	323.868i	1.05682	+	0.406870i
$797$	85.4710			0.107241			0.0536205	−	0.998561i	$-0.482924\pi$
$797$	85.4710			0.107241			0.0536205	+	0.998561i	$0.482924\pi$
$798$	232.624	+	338.827i	0.291509	+	0.424596i
$799$		−	142.633i		−	0.178514i
$800$		0			0
$801$	−181.082			−0.226070
$802$	−319.525	+	219.372i	−0.398410	+	0.273531i
$803$		−	285.752i		−	0.355856i
$804$	−301.751	+	783.782i	−0.375313	+	0.974853i
$805$		0			0
$806$	−476.327	−	693.792i	−0.590977	−	0.860784i
$807$	358.342			0.444042
$808$	−1157.42	+	276.065i	−1.43245	+	0.341664i
$809$	−749.874			−0.926915			−0.463458	−	0.886119i	$-0.653391\pi$
$809$	−749.874			−0.926915			−0.463458	+	0.886119i	$0.653391\pi$
$810$		0			0
$811$	−454.606			−0.560550			−0.280275	−	0.959920i	$-0.590426\pi$
$811$	−454.606			−0.560550			−0.280275	+	0.959920i	$0.590426\pi$
$812$	−40.3739	−	15.5437i	−0.0497216	−	0.0191425i
$813$	−429.132			−0.527837
$814$	−100.544	+	69.0290i	−0.123518	+	0.0848022i
$815$		0			0
$816$	−63.3687	−	57.2838i	−0.0776578	−	0.0702008i
$817$			708.085i			0.866689i
$818$	−757.643	+	520.164i	−0.926214	+	0.635898i
$819$	452.862			0.552945
$820$		0			0
$821$		−	40.2949i		−	0.0490802i	−0.999699	−	0.0245401i	$-0.992188\pi$
$821$		−	40.2949i		−	0.0490802i	0.999699	−	0.0245401i	$-0.00781214\pi$
$822$	−94.1059	+	64.6090i	−0.114484	+	0.0785998i
$823$	−1109.53			−1.34815			−0.674076	−	0.738662i	$-0.735458\pi$
$823$	−1109.53			−1.34815			−0.674076	+	0.738662i	$0.735458\pi$
$824$	−248.305	−	1041.03i	−0.301340	−	1.26339i
$825$		0			0
$826$	−1389.97	+	954.292i	−1.68277	+	1.15532i
$827$		−	750.168i		−	0.907096i	−0.891232	−	0.453548i	$-0.850158\pi$
$827$		−	750.168i		−	0.907096i	0.891232	−	0.453548i	$-0.149842\pi$
$828$	53.9094	−	140.026i	0.0651079	−	0.169114i
$829$			182.949i			0.220687i	0.993894	+	0.110343i	$0.0351950\pi$
$829$			182.949i			0.220687i	−0.993894	+	0.110343i	$0.964805\pi$
$830$		0			0
$831$		−	46.6766i		−	0.0561692i
$832$	−737.247	+	372.907i	−0.886114	+	0.448206i
$833$		−	270.445i		−	0.324663i
$834$	−164.417	−	239.481i	−0.197143	−	0.287148i
$835$		0			0
$836$	282.005	−	732.491i	0.337326	−	0.876185i
$837$	169.371			0.202355
$838$	368.413	−	252.936i	0.439634	−	0.301833i
$839$		−	719.345i		−	0.857384i	−0.903451	−	0.428692i	$-0.858975\pi$
$839$		−	719.345i		−	0.857384i	0.903451	−	0.428692i	$-0.141025\pi$
$840$		0			0
$841$	840.145			0.998983
$842$	852.954	+	1242.37i	1.01301	+	1.47549i
$843$		−	501.410i		−	0.594793i
$844$	434.964	−	1129.79i	0.515360	−	1.33862i
$845$		0			0
$846$	228.886	−	157.143i	0.270551	−	0.185748i
$847$	−2958.77			−3.49323
$848$	−198.812	−	179.722i	−0.234449	−	0.211936i
$849$	−5.21819			−0.00614628
$850$		0			0
$851$	−39.4253			−0.0463282
$852$	−167.800	+	435.850i	−0.196948	+	0.511561i
$853$	593.155			0.695375			0.347688	−	0.937610i	$-0.386967\pi$
$853$	593.155			0.695375			0.347688	+	0.937610i	$0.386967\pi$
$854$	501.326	+	730.204i	0.587033	+	0.855040i
$855$		0			0
$856$	429.578	−	102.462i	0.501844	−	0.119698i
$857$			180.069i			0.210116i	0.994466	+	0.105058i	$0.0335028\pi$
$857$			180.069i			0.210116i	−0.994466	+	0.105058i	$0.966497\pi$
$858$	−489.508	−	712.990i	−0.570522	−	0.830991i
$859$	−509.587			−0.593232			−0.296616	−	0.954997i	$-0.595858\pi$
$859$	−509.587			−0.593232			−0.296616	+	0.954997i	$0.595858\pi$
$860$		0			0
$861$			1396.10i			1.62149i
$862$	907.406	+	1321.68i	1.05267	+	1.53327i
$863$	−1430.93			−1.65809			−0.829046	−	0.559181i	$-0.811116\pi$
$863$	−1430.93			−1.65809			−0.829046	+	0.559181i	$0.811116\pi$
$864$	22.1092	−	164.800i	0.0255894	−	0.190741i
$865$		0			0
$866$	−820.766	−	1195.48i	−0.947767	−	1.38046i
$867$			484.106i			0.558369i
$868$	−1422.82	−	547.776i	−1.63919	−	0.631079i
$869$			2561.22i			2.94732i
$870$		0			0
$871$			1564.91i			1.79668i
$872$	604.390	−	144.157i	0.693107	−	0.165318i
$873$		−	39.6565i		−	0.0454256i
$874$	209.178	−	143.612i	0.239334	−	0.164316i
$875$		0			0
$876$	36.7790	−	95.5313i	0.0419852	−	0.109054i
$877$	−905.426			−1.03241			−0.516207	−	0.856464i	$-0.672656\pi$
$877$	−905.426			−1.03241			−0.516207	+	0.856464i	$0.672656\pi$
$878$	623.802	+	908.595i	0.710480	+	1.03485i
$879$		−	164.883i		−	0.187580i
$880$		0			0
$881$	1479.51			1.67935			0.839677	−	0.543086i	$-0.182744\pi$
$881$	1479.51			1.67935			0.839677	+	0.543086i	$0.182744\pi$
$882$	433.988	−	297.957i	0.492050	−	0.337820i
$883$			360.404i			0.408158i	0.978954	+	0.204079i	$0.0654200\pi$
$883$			360.404i			0.408158i	−0.978954	+	0.204079i	$0.934580\pi$
$884$	−148.539	−	57.1867i	−0.168031	−	0.0646908i
$885$		0			0
$886$	−41.6326	−	60.6397i	−0.0469894	−	0.0684422i
$887$	1106.42			1.24738			0.623688	−	0.781674i	$-0.285634\pi$
$887$	1106.42			1.24738			0.623688	+	0.781674i	$0.285634\pi$
$888$	−42.4981	+	10.1365i	−0.0478582	+	0.0114150i
$889$	535.276			0.602110
$890$		0			0
$891$	174.058			0.195351
$892$	621.620	−	1614.62i	0.696884	−	1.81012i
$893$	469.494			0.525750
$894$	−232.584	+	159.682i	−0.260161	+	0.178615i
$895$		0			0
$896$	−718.724	+	1312.91i	−0.802147	+	1.46531i
$897$		−	279.578i		−	0.311681i
$898$	548.462	−	376.550i	0.610759	−	0.419321i
$899$	−30.1486			−0.0335357
$900$		0			0
$901$		−	51.6315i		−	0.0573046i
$902$	2198.03	−	1509.07i	2.43684	−	1.67303i
$903$	1413.47			1.56530
$904$	706.520	−	168.517i	0.781549	−	0.186413i
$905$		0			0
$906$	−241.951	+	166.113i	−0.267054	+	0.183347i
$907$		−	1467.30i		−	1.61775i	−0.587979	−	0.808876i	$-0.700076\pi$
$907$		−	1467.30i		−	1.61775i	0.587979	−	0.808876i	$-0.299924\pi$
$908$	1341.31	+	516.396i	1.47721	+	0.568718i
$909$		−	446.208i		−	0.490878i
$910$		0			0
$911$		−	1188.75i		−	1.30488i	−0.757840	−	0.652441i	$-0.773745\pi$
$911$		−	1188.75i		−	1.30488i	0.757840	−	0.652441i	$-0.226255\pi$
$912$	188.557	−	208.586i	0.206751	−	0.228713i
$913$		−	645.396i		−	0.706896i
$914$	−388.592	−	566.002i	−0.425156	−	0.619258i
$915$		0			0
$916$	−792.166	−	304.979i	−0.864810	−	0.332947i
$917$	−2178.25			−2.37541
$918$	26.4086	−	18.1310i	0.0287675	−	0.0197505i
$919$		−	917.844i		−	0.998743i	−0.866388	−	0.499371i	$-0.833564\pi$
$919$		−	917.844i		−	0.998743i	0.866388	−	0.499371i	$-0.166436\pi$
$920$		0			0
$921$	289.856			0.314718
$922$	−236.325	−	344.219i	−0.256318	−	0.373339i
$923$			870.222i			0.942819i
$924$	−1462.19	−	562.934i	−1.58246	−	0.609236i
$925$		0			0
$926$	394.889	−	271.114i	0.426447	−	0.292780i
$927$	401.339			0.432944
$928$	−3.93552	+	29.3350i	−0.00424086	+	0.0316110i
$929$	326.140			0.351066			0.175533	−	0.984474i	$-0.443835\pi$
$929$	326.140			0.351066			0.175533	+	0.984474i	$0.443835\pi$
$930$		0			0
$931$	890.203			0.956179
$932$	−1032.73	−	397.596i	−1.10808	−	0.426605i
$933$	518.710			0.555960
$934$	−334.046	−	486.553i	−0.357651	−	0.520935i
$935$		0			0
$936$	−71.8814	−	301.368i	−0.0767964	−	0.321974i
$937$		−	803.356i		−	0.857370i	−0.903454	−	0.428685i	$-0.858977\pi$
$937$		−	803.356i		−	0.857370i	0.903454	−	0.428685i	$-0.141023\pi$
$938$	1604.64	+	2337.23i	1.71070	+	2.49172i
$939$	214.122			0.228032
$940$		0			0
$941$		−	617.150i		−	0.655845i	−0.944705	−	0.327922i	$-0.893652\pi$
$941$		−	617.150i		−	0.655845i	0.944705	−	0.327922i	$-0.106348\pi$
$942$	329.092	+	479.338i	0.349355	+	0.508851i
$943$	861.892			0.913990
$944$	855.682	+	773.516i	0.906443	+	0.819403i
$945$		0			0
$946$	−1527.85	−	2225.38i	−1.61506	−	2.35241i
$947$			1372.28i			1.44908i	0.689231	+	0.724542i	$0.257948\pi$
$947$			1372.28i			1.44908i	−0.689231	+	0.724542i	$0.742052\pi$
$948$	−329.654	+	856.256i	−0.347736	+	0.903224i
$949$		−	190.739i		−	0.200989i
$950$		0			0
$951$			235.471i			0.247603i
$952$	−280.486	+	66.9008i	−0.294628	+	0.0702739i
$953$		−	313.823i		−	0.329300i	−0.986352	−	0.164650i	$-0.947351\pi$
$953$		−	313.823i		−	0.329300i	0.986352	−	0.164650i	$-0.0526495\pi$
$954$	82.8540	−	56.8840i	0.0868491	−	0.0596268i
$955$		0			0
$956$	−104.188	−	40.1117i	−0.108983	−	0.0419578i
$957$	−30.9829			−0.0323750
$958$	603.766	+	879.412i	0.630236	+	0.917966i
$959$			385.327i			0.401801i
$960$		0			0
$961$	−101.467			−0.105585
$962$	−67.1127	+	46.0767i	−0.0697638	+	0.0478967i
$963$			165.611i			0.171974i
$964$	−165.875	+	430.851i	−0.172070	+	0.446941i
$965$		0			0
$966$	−286.677	−	417.558i	−0.296767	−	0.432254i
$967$	−191.090			−0.197611			−0.0988055	−	0.995107i	$-0.531502\pi$
$967$	−191.090			−0.197611			−0.0988055	+	0.995107i	$0.531502\pi$
$968$	469.636	+	1968.98i	0.485161	+	2.03407i
$969$	54.1697			0.0559027
$970$		0			0
$971$	88.4914			0.0911343			0.0455671	−	0.998961i	$-0.485491\pi$
$971$	88.4914			0.0911343			0.0455671	+	0.998961i	$0.485491\pi$
$972$	58.1903	+	22.4029i	0.0598665	+	0.0230483i
$973$	−980.582			−1.00779
$974$	471.023	−	323.384i	0.483597	−	0.332016i
$975$		0			0
$976$	406.358	−	449.522i	0.416350	−	0.460576i
$977$			1367.80i			1.40000i	0.714142	+	0.700001i	$0.246817\pi$
$977$			1367.80i			1.40000i	−0.714142	+	0.700001i	$0.753183\pi$
$978$	236.666	−	162.484i	0.241989	−	0.166139i
$979$	1167.36			1.19240
$980$		0			0
$981$			233.004i			0.237517i
$982$	−310.378	+	213.092i	−0.316067	+	0.216998i
$983$	−266.437			−0.271045			−0.135522	−	0.990774i	$-0.543271\pi$
$983$	−266.437			−0.271045			−0.135522	+	0.990774i	$0.543271\pi$
$984$	929.067	−	221.598i	0.944174	−	0.225202i
$985$		0			0
$986$	−4.70081	+	3.22737i	−0.00476756	+	0.00327320i
$987$		−	937.199i		−	0.949543i
$988$	188.237	−	488.935i	0.190524	−	0.494874i
$989$		−	872.617i		−	0.882322i
$990$		0			0
$991$		−	842.673i		−	0.850326i	−0.905117	−	0.425163i	$-0.860217\pi$
$991$		−	842.673i		−	0.850326i	0.905117	−	0.425163i	$-0.139783\pi$
$992$	−138.691	+	1033.79i	−0.139810	+	1.04213i
$993$		−	71.3408i		−	0.0718437i
$994$	892.318	+	1299.70i	0.897705	+	1.30755i
$995$		0			0
$996$	83.0686	−	215.766i	0.0834022	−	0.216632i
$997$	1590.97			1.59576			0.797879	−	0.602817i	$-0.205955\pi$
$997$	1590.97			1.59576			0.797879	+	0.602817i	$0.205955\pi$
$998$	1031.39	−	708.105i	1.03345	−	0.709524i
$999$		−	16.3838i		−	0.0164002i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	600.3.p.b.499.6		32
4.3	odd	2		2400.3.p.b.1999.9		32
5.2	odd	4		120.3.g.a.91.7	✓	16
5.3	odd	4		600.3.g.d.451.10		16
5.4	even	2	inner	600.3.p.b.499.27		32
8.3	odd	2	inner	600.3.p.b.499.28		32
8.5	even	2		2400.3.p.b.1999.21		32
15.2	even	4		360.3.g.c.91.10		16
20.3	even	4		2400.3.g.b.751.9		16
20.7	even	4		480.3.g.a.271.8		16
20.19	odd	2		2400.3.p.b.1999.22		32
40.3	even	4		600.3.g.d.451.9		16
40.13	odd	4		2400.3.g.b.751.16		16
40.19	odd	2	inner	600.3.p.b.499.5		32
40.27	even	4		120.3.g.a.91.8	yes	16
40.29	even	2		2400.3.p.b.1999.10		32
40.37	odd	4		480.3.g.a.271.1		16
60.47	odd	4		1440.3.g.c.271.8		16
120.77	even	4		1440.3.g.c.271.9		16
120.107	odd	4		360.3.g.c.91.9		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
120.3.g.a.91.7	✓	16	5.2	odd	4
120.3.g.a.91.8	yes	16	40.27	even	4
360.3.g.c.91.9		16	120.107	odd	4
360.3.g.c.91.10		16	15.2	even	4
480.3.g.a.271.1		16	40.37	odd	4
480.3.g.a.271.8		16	20.7	even	4
600.3.g.d.451.9		16	40.3	even	4
600.3.g.d.451.10		16	5.3	odd	4
600.3.p.b.499.5		32	40.19	odd	2	inner
600.3.p.b.499.6		32	1.1	even	1	trivial
600.3.p.b.499.27		32	5.4	even	2	inner
600.3.p.b.499.28		32	8.3	odd	2	inner
1440.3.g.c.271.8		16	60.47	odd	4
1440.3.g.c.271.9		16	120.77	even	4
2400.3.g.b.751.9		16	20.3	even	4
2400.3.g.b.751.16		16	40.13	odd	4
2400.3.p.b.1999.9		32	4.3	odd	2
2400.3.p.b.1999.10		32	40.29	even	2
2400.3.p.b.1999.21		32	8.5	even	2
2400.3.p.b.1999.22		32	20.19	odd	2

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 600 = 2^{3} \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	600.p (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.64881 + 1.13200i) q^{2} +1.73205i q^{3} +(1.43715 - 3.73291i) q^{4} +(-1.96068 - 2.85582i) q^{6} -11.6935 q^{7} +(1.85607 + 7.78171i) q^{8} -3.00000 q^{9} +19.3398 q^{11} +(6.46559 + 2.48921i) q^{12} +12.9092 q^{13} +(19.2803 - 13.2370i) q^{14} +(-11.8692 - 10.7295i) q^{16} -3.08243i q^{17} +(4.94643 - 3.39600i) q^{18} +10.1462 q^{19} -20.2537i q^{21} +(-31.8876 + 21.8926i) q^{22} -12.5038 q^{23} +(-13.4783 + 3.21481i) q^{24} +(-21.2849 + 14.6133i) q^{26} -5.19615i q^{27} +(-16.8053 + 43.6507i) q^{28} +0.924932i q^{29} +32.5955i q^{31} +(31.7159 + 4.25493i) q^{32} +33.4975i q^{33} +(3.48931 + 5.08233i) q^{34} +(-4.31144 + 11.1987i) q^{36} +3.15307 q^{37} +(-16.7292 + 11.4855i) q^{38} +22.3595i q^{39} -68.9305 q^{41} +(22.9272 + 33.3945i) q^{42} +69.7882i q^{43} +(27.7941 - 72.1936i) q^{44} +(20.6164 - 14.1543i) q^{46} +46.2730 q^{47} +(18.5840 - 20.5581i) q^{48} +87.7376 q^{49} +5.33892 q^{51} +(18.5525 - 48.1890i) q^{52} +16.7503 q^{53} +(5.88205 + 8.56747i) q^{54} +(-21.7039 - 90.9953i) q^{56} +17.5737i q^{57} +(-1.04702 - 1.52504i) q^{58} -72.0926 q^{59} +37.8730i q^{61} +(-36.8981 - 53.7438i) q^{62} +35.0805 q^{63} +(-57.1100 + 28.8868i) q^{64} +(-37.9192 - 55.2310i) q^{66} +121.224i q^{67} +(-11.5064 - 4.42990i) q^{68} -21.6572i q^{69} +67.4107i q^{71} +(-5.56821 - 23.3451i) q^{72} -14.7754i q^{73} +(-5.19881 + 3.56928i) q^{74} +(14.5816 - 37.8748i) q^{76} -226.149 q^{77} +(-25.3109 - 36.8665i) q^{78} +132.433i q^{79} +9.00000 q^{81} +(113.653 - 78.0294i) q^{82} -33.3714i q^{83} +(-75.6052 - 29.1076i) q^{84} +(-79.0003 - 115.068i) q^{86} -1.60203 q^{87} +(35.8960 + 150.497i) q^{88} +60.3607 q^{89} -150.954 q^{91} +(-17.9698 + 46.6755i) q^{92} -56.4571 q^{93} +(-76.2953 + 52.3810i) q^{94} +(-7.36975 + 54.9335i) q^{96} +13.2188i q^{97} +(-144.663 + 99.3190i) q^{98} -58.0193 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 28 q^{4} + 12 q^{6} - 96 q^{9} + 128 q^{11} + 40 q^{14} - 28 q^{16} + 64 q^{19} + 108 q^{24} + 72 q^{26} + 144 q^{34} + 84 q^{36} + 200 q^{44} + 424 q^{46} + 160 q^{49} + 192 q^{51} - 36 q^{54} - 232 q^{56}+ \cdots - 384 q^{99}+O(q^{100}) \) 32 * q - 28 * q^4 + 12 * q^6 - 96 * q^9 + 128 * q^11 + 40 * q^14 - 28 * q^16 + 64 * q^19 + 108 * q^24 + 72 * q^26 + 144 * q^34 + 84 * q^36 + 200 * q^44 + 424 * q^46 + 160 * q^49 + 192 * q^51 - 36 * q^54 - 232 * q^56 - 256 * q^59 - 28 * q^64 - 360 * q^66 - 600 * q^74 + 840 * q^76 + 288 * q^81 - 360 * q^84 + 624 * q^86 - 384 * q^91 - 920 * q^94 - 372 * q^96 - 384 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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