LMFDB - Embedded newform 275.3.x.j.101.10

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [275,3,Mod(51,275)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(275, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([0, 7])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("275.51"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 275 = 5^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	275.x (of order $10$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [40,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$7.49320726991$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$10$ over $\Q(\zeta_{10})$
Twist minimal:	no (minimal twist has level 55)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			101.10
Character	$\chi$	$=$	275.101
Dual form			275.3.x.j.226.10

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(3.37818 + 1.09764i) q^{2} +(-1.23390 + 0.896484i) q^{3} +(6.97124 + 5.06490i) q^{4} +(-5.15237 + 1.67411i) q^{6} +(-0.640839 + 0.882039i) q^{7} +(9.63938 + 13.2675i) q^{8} +(-2.06232 + 6.34716i) q^{9} +(3.85595 + 10.3020i) q^{11} -13.1425 q^{12} +(-0.831271 - 0.270096i) q^{13} +(-3.13303 + 2.27628i) q^{14} +(7.34959 + 22.6197i) q^{16} +(22.2122 - 7.21718i) q^{17} +(-13.9338 + 19.1782i) q^{18} +(-14.8922 - 20.4973i) q^{19} -1.66285i q^{21} +(1.71822 + 39.0346i) q^{22} +33.3562 q^{23} +(-23.7881 - 7.72924i) q^{24} +(-2.51172 - 1.82487i) q^{26} +(-7.38721 - 22.7355i) q^{27} +(-8.93489 + 2.90312i) q^{28} +(-9.90414 + 13.6319i) q^{29} +(-1.97870 + 6.08982i) q^{31} +18.8828i q^{32} +(-13.9935 - 9.25491i) q^{33} +82.9587 q^{34} +(-46.5246 + 33.8021i) q^{36} +(-53.0561 - 38.5475i) q^{37} +(-27.8099 - 85.5899i) q^{38} +(1.26785 - 0.411949i) q^{39} +(-22.7486 - 31.3107i) q^{41} +(1.82521 - 5.61743i) q^{42} -15.0656i q^{43} +(-25.2980 + 91.3479i) q^{44} +(112.683 + 36.6131i) q^{46} +(47.9712 - 34.8531i) q^{47} +(-29.3469 - 21.3218i) q^{48} +(14.7745 + 45.4713i) q^{49} +(-20.9376 + 28.8182i) q^{51} +(-4.42698 - 6.09322i) q^{52} +(7.31251 - 22.5056i) q^{53} -84.9132i q^{54} -17.8797 q^{56} +(36.7511 + 11.9411i) q^{57} +(-48.4209 + 35.1798i) q^{58} +(30.7715 + 22.3568i) q^{59} +(32.4198 - 10.5338i) q^{61} +(-13.3688 + 18.4006i) q^{62} +(-4.27683 - 5.88655i) q^{63} +(8.67190 - 26.6894i) q^{64} +(-37.1140 - 46.6246i) q^{66} +43.7033 q^{67} +(191.401 + 62.1899i) q^{68} +(-41.1584 + 29.9033i) q^{69} +(11.1969 + 34.4604i) q^{71} +(-104.090 + 33.8209i) q^{72} +(49.4053 - 68.0006i) q^{73} +(-136.922 - 188.457i) q^{74} -218.319i q^{76} +(-11.5578 - 3.20083i) q^{77} +4.73519 q^{78} +(-28.8577 - 9.37643i) q^{79} +(-19.0958 - 13.8739i) q^{81} +(-42.4810 - 130.743i) q^{82} +(-129.448 + 42.0601i) q^{83} +(8.42220 - 11.5922i) q^{84} +(16.5366 - 50.8943i) q^{86} -25.6994i q^{87} +(-99.5127 + 150.464i) q^{88} +8.46901 q^{89} +(0.770946 - 0.560125i) q^{91} +(232.534 + 168.946i) q^{92} +(-3.01790 - 9.28813i) q^{93} +(200.312 - 65.0852i) q^{94} +(-16.9281 - 23.2995i) q^{96} +(-20.5930 + 63.3788i) q^{97} +169.827i q^{98} +(-73.3407 + 3.22831i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 22 q^{4} - 10 q^{6} + 4 q^{9} - 16 q^{11} - 38 q^{14} - 138 q^{16} + 10 q^{19} - 30 q^{24} + 172 q^{26} + 10 q^{29} + 128 q^{31} + 112 q^{34} + 248 q^{36} + 170 q^{39} + 50 q^{41} - 422 q^{44} + 10 q^{46}+ \cdots - 882 q^{99}+O(q^{100}) $ 40 * q + 22 * q^4 - 10 * q^6 + 4 * q^9 - 16 * q^11 - 38 * q^14 - 138 * q^16 + 10 * q^19 - 30 * q^24 + 172 * q^26 + 10 * q^29 + 128 * q^31 + 112 * q^34 + 248 * q^36 + 170 * q^39 + 50 * q^41 - 422 * q^44 + 10 * q^46 - 18 * q^49 - 270 * q^51 + 144 * q^56 + 254 * q^59 - 300 * q^61 + 834 * q^64 - 1470 * q^66 - 246 * q^69 + 260 * q^71 - 620 * q^74 - 270 * q^79 + 606 * q^81 - 80 * q^84 + 602 * q^86 + 812 * q^89 + 582 * q^91 - 840 * q^94 + 1610 * q^96 - 882 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/275\mathbb{Z}\right)^\times$.

$n$	$101$	$177$
$\chi(n)$	$e\left(\frac{1}{10}\right)$	$1$

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 $

$2$	3.37818	+	1.09764i	1.68909	+	0.548819i	0.986640	−	0.162913i	$-0.0520890\pi$
$2$	3.37818	+	1.09764i	1.68909	+	0.548819i	0.702451	+	0.711732i	$0.252089\pi$
$3$	−1.23390	+	0.896484i	−0.411302	+	0.298828i	−0.774129	−	0.633028i	$-0.781812\pi$
$3$	−1.23390	+	0.896484i	−0.411302	+	0.298828i	0.362827	+	0.931857i	$0.381812\pi$
$4$	6.97124	+	5.06490i	1.74281	+	1.26623i
$5$		0			0
$5$		0			0
$6$	−5.15237	+	1.67411i	−0.858729	+	0.279018i
$7$	−0.640839	+	0.882039i	−0.0915484	+	0.126006i	−0.852334	−	0.522997i	$-0.824814\pi$
$7$	−0.640839	+	0.882039i	−0.0915484	+	0.126006i	0.760786	+	0.649003i	$0.224814\pi$
$8$	9.63938	+	13.2675i	1.20492	+	1.65843i
$9$	−2.06232	+	6.34716i	−0.229146	+	0.705239i
$10$		0			0
$11$	3.85595	+	10.3020i	0.350541	+	0.936547i
$11$	3.85595	+	10.3020i	0.350541	+	0.936547i
$12$	−13.1425			−1.09521
$13$	−0.831271	−	0.270096i	−0.0639440	−	0.0207766i	0.276870	−	0.960907i	$-0.410703\pi$
$13$	−0.831271	−	0.270096i	−0.0639440	−	0.0207766i	−0.340814	+	0.940131i	$0.610703\pi$
$14$	−3.13303	+	2.27628i	−0.223788	+	0.162591i
$15$		0			0
$16$	7.34959	+	22.6197i	0.459349	+	1.41373i
$17$	22.2122	−	7.21718i	1.30660	−	0.424540i	0.428727	−	0.903434i	$-0.358962\pi$
$17$	22.2122	−	7.21718i	1.30660	−	0.424540i	0.877873	+	0.478894i	$0.158962\pi$
$18$	−13.9338	+	19.1782i	−0.774098	+	1.06545i
$19$	−14.8922	−	20.4973i	−0.783799	−	1.07881i	−0.994853	−	0.101332i	$-0.967690\pi$
$19$	−14.8922	−	20.4973i	−0.783799	−	1.07881i	0.211054	−	0.977474i	$-0.432310\pi$
$20$		0			0
$21$		−	1.66285i		−	0.0791835i
$22$	1.71822	+	39.0346i	0.0781009	+	1.77430i
$23$	33.3562			1.45027			0.725135	−	0.688606i	$-0.241777\pi$
$23$	33.3562			1.45027			0.725135	+	0.688606i	$0.241777\pi$
$24$	−23.7881	−	7.72924i	−0.991173	−	0.322052i
$25$		0			0
$26$	−2.51172	−	1.82487i	−0.0966046	−	0.0701873i
$27$	−7.38721	−	22.7355i	−0.273600	−	0.842056i
$28$	−8.93489	+	2.90312i	−0.319103	+	0.103683i
$29$	−9.90414	+	13.6319i	−0.341522	+	0.470065i	−0.944885	−	0.327402i	$-0.893827\pi$
$29$	−9.90414	+	13.6319i	−0.341522	+	0.470065i	0.603363	+	0.797467i	$0.293827\pi$
$30$		0			0
$31$	−1.97870	+	6.08982i	−0.0638291	+	0.196446i	−0.977885	−	0.209142i	$-0.932933\pi$
$31$	−1.97870	+	6.08982i	−0.0638291	+	0.196446i	0.914056	+	0.405587i	$0.132933\pi$
$32$			18.8828i			0.590087i
$33$	−13.9935	−	9.25491i	−0.424045	−	0.280452i
$34$	82.9587			2.43996
$35$		0			0
$36$	−46.5246	+	33.8021i	−1.29235	+	0.938948i
$37$	−53.0561	−	38.5475i	−1.43395	−	1.04182i	−0.989264	−	0.146137i	$-0.953316\pi$
$37$	−53.0561	−	38.5475i	−1.43395	−	1.04182i	−0.444684	−	0.895687i	$-0.646684\pi$
$38$	−27.8099	−	85.5899i	−0.731838	−	2.25237i
$39$	1.26785	−	0.411949i	0.0325089	−	0.0105628i
$40$		0			0
$41$	−22.7486	−	31.3107i	−0.554843	−	0.763676i	0.435817	−	0.900036i	$-0.356460\pi$
$41$	−22.7486	−	31.3107i	−0.554843	−	0.763676i	−0.990659	+	0.136360i	$0.956460\pi$
$42$	1.82521	−	5.61743i	0.0434574	−	0.133748i
$43$		−	15.0656i		−	0.350362i	−0.984536	−	0.175181i	$-0.943949\pi$
$43$		−	15.0656i		−	0.350362i	0.984536	−	0.175181i	$-0.0560511\pi$
$44$	−25.2980	+	91.3479i	−0.574954	+	2.07609i
$45$		0			0
$46$	112.683	+	36.6131i	2.44964	+	0.795936i
$47$	47.9712	−	34.8531i	1.02066	−	0.741556i	0.0542457	−	0.998528i	$-0.482725\pi$
$47$	47.9712	−	34.8531i	1.02066	−	0.741556i	0.966419	+	0.256971i	$0.0827246\pi$
$48$	−29.3469	−	21.3218i	−0.611394	−	0.444204i
$49$	14.7745	+	45.4713i	0.301521	+	0.927985i
$50$		0			0
$51$	−20.9376	+	28.8182i	−0.410542	+	0.565063i
$52$	−4.42698	−	6.09322i	−0.0851343	−	0.117177i
$53$	7.31251	−	22.5056i	0.137972	−	0.424634i	−0.858069	−	0.513535i	$-0.828336\pi$
$53$	7.31251	−	22.5056i	0.137972	−	0.424634i	0.996040	+	0.0889014i	$0.0283356\pi$
$54$		−	84.9132i		−	1.57247i
$55$		0			0
$56$	−17.8797			−0.319280
$57$	36.7511	+	11.9411i	0.644755	+	0.209494i
$58$	−48.4209	+	35.1798i	−0.834843	+	0.606549i
$59$	30.7715	+	22.3568i	0.521550	+	0.378928i	0.817188	−	0.576372i	$-0.195532\pi$
$59$	30.7715	+	22.3568i	0.521550	+	0.378928i	−0.295637	+	0.955300i	$0.595532\pi$
$60$		0			0
$61$	32.4198	−	10.5338i	0.531472	−	0.172686i	−0.0309732	−	0.999520i	$-0.509861\pi$
$61$	32.4198	−	10.5338i	0.531472	−	0.172686i	0.562445	+	0.826834i	$0.309861\pi$
$62$	−13.3688	+	18.4006i	−0.215626	+	0.296784i
$63$	−4.27683	−	5.88655i	−0.0678861	−	0.0934372i
$64$	8.67190	−	26.6894i	0.135499	−	0.417022i
$65$		0			0
$66$	−37.1140	−	46.6246i	−0.562333	−	0.706433i
$67$	43.7033			0.652288			0.326144	−	0.945320i	$-0.394250\pi$
$67$	43.7033			0.652288			0.326144	+	0.945320i	$0.394250\pi$
$68$	191.401	+	62.1899i	2.81472	+	0.914558i
$69$	−41.1584	+	29.9033i	−0.596499	+	0.433382i
$70$		0			0
$71$	11.1969	+	34.4604i	0.157702	+	0.485358i	0.998425	−	0.0561087i	$-0.0178694\pi$
$71$	11.1969	+	34.4604i	0.157702	+	0.485358i	−0.840722	+	0.541466i	$0.817869\pi$
$72$	−104.090	+	33.8209i	−1.44570	+	0.469735i
$73$	49.4053	−	68.0006i	0.676785	−	0.931515i	−0.323105	−	0.946363i	$-0.604727\pi$
$73$	49.4053	−	68.0006i	0.676785	−	0.931515i	0.999890	+	0.0148485i	$0.00472661\pi$
$74$	−136.922	−	188.457i	−1.85030	−	2.54672i
$75$		0			0
$76$		−	218.319i		−	2.87262i
$77$	−11.5578	−	3.20083i	−0.150102	−	0.0415693i
$78$	4.73519			0.0607076
$79$	−28.8577	−	9.37643i	−0.365287	−	0.118689i	0.120621	−	0.992699i	$-0.461511\pi$
$79$	−28.8577	−	9.37643i	−0.365287	−	0.118689i	−0.485909	+	0.874010i	$0.661511\pi$
$80$		0			0
$81$	−19.0958	−	13.8739i	−0.235750	−	0.171283i
$82$	−42.4810	−	130.743i	−0.518061	−	1.59443i
$83$	−129.448	+	42.0601i	−1.55961	+	0.506748i	−0.956704	−	0.291064i	$-0.905991\pi$
$83$	−129.448	+	42.0601i	−1.55961	+	0.506748i	−0.602906	+	0.797812i	$0.705991\pi$
$84$	8.42220	−	11.5922i	0.100264	−	0.138002i
$85$		0			0
$86$	16.5366	−	50.8943i	0.192286	−	0.591794i
$87$		−	25.6994i		−	0.295395i
$88$	−99.5127	+	150.464i	−1.13083	+	1.70982i
$89$	8.46901			0.0951574			0.0475787	−	0.998867i	$-0.484850\pi$
$89$	8.46901			0.0951574			0.0475787	+	0.998867i	$0.484850\pi$
$90$		0			0
$91$	0.770946	−	0.560125i	0.00847194	−	0.00615522i
$92$	232.534	+	168.946i	2.52755	+	1.83637i
$93$	−3.01790	−	9.28813i	−0.0324505	−	0.0998724i
$94$	200.312	−	65.0852i	2.13098	−	0.692396i
$95$		0			0
$96$	−16.9281	−	23.2995i	−0.176335	−	0.242704i
$97$	−20.5930	+	63.3788i	−0.212299	+	0.653390i	0.787035	+	0.616908i	$0.211615\pi$
$97$	−20.5930	+	63.3788i	−0.212299	+	0.653390i	−0.999334	+	0.0364815i	$0.988385\pi$
$98$			169.827i			1.73293i
$99$	−73.3407	+	3.22831i	−0.740815	+	0.0326092i
$100$		0			0
$101$	−76.0831	−	24.7209i	−0.753298	−	0.244761i	−0.0928981	−	0.995676i	$-0.529613\pi$
$101$	−76.0831	−	24.7209i	−0.753298	−	0.244761i	−0.660400	+	0.750914i	$0.729613\pi$
$102$	−102.363	+	74.3712i	−1.00356	+	0.729129i
$103$	90.2154	+	65.5454i	0.875878	+	0.636363i	0.932158	−	0.362052i	$-0.117924\pi$
$103$	90.2154	+	65.5454i	0.875878	+	0.636363i	−0.0562796	+	0.998415i	$0.517924\pi$
$104$	−4.42944	−	13.6324i	−0.0425908	−	0.131081i
$105$		0			0
$106$	49.4060	−	68.0015i	0.466094	−	0.641524i
$107$	12.3479	+	16.9954i	0.115401	+	0.158836i	0.862810	−	0.505528i	$-0.168702\pi$
$107$	12.3479	+	16.9954i	0.115401	+	0.158836i	−0.747409	+	0.664364i	$0.768702\pi$
$108$	63.6551	−	195.910i	0.589399	−	1.81398i
$109$			118.493i			1.08710i	0.839378	+	0.543548i	$0.182919\pi$
$109$			118.493i			1.08710i	−0.839378	+	0.543548i	$0.817081\pi$
$110$		0			0
$111$	100.023			0.901112
$112$	−24.6614	−	8.01296i	−0.220191	−	0.0715443i
$113$	−86.2322	+	62.6514i	−0.763117	+	0.554437i	−0.899865	−	0.436169i	$-0.856335\pi$
$113$	−86.2322	+	62.6514i	−0.763117	+	0.554437i	0.136748	+	0.990606i	$0.456335\pi$
$114$	111.045	+	80.6787i	0.974077	+	0.707708i
$115$		0			0
$116$	−138.088	+	44.8676i	−1.19042	+	0.386790i
$117$	3.42869	−	4.71918i	0.0293050	−	0.0403349i
$118$	79.4120	+	109.301i	0.672983	+	0.926282i
$119$	−7.86860	+	24.2171i	−0.0661227	+	0.203505i
$120$		0			0
$121$	−91.2633	+	79.4482i	−0.754242	+	0.656597i
$122$	121.082			0.992479
$123$	56.1391	+	18.2407i	0.456416	+	0.148298i
$124$	−44.6384	+	32.4317i	−0.359987	+	0.261546i
$125$		0			0
$126$	−7.98660	−	24.5802i	−0.0633857	−	0.195081i
$127$	−121.986	+	39.6357i	−0.960520	+	0.312092i	−0.746983	−	0.664843i	$-0.768498\pi$
$127$	−121.986	+	39.6357i	−0.960520	+	0.312092i	−0.213537	+	0.976935i	$0.568498\pi$
$128$	102.987	−	141.749i	0.804583	−	1.10741i
$129$	13.5061	+	18.5895i	0.104698	+	0.144105i
$130$		0			0
$131$			15.3029i			0.116816i	0.998293	+	0.0584079i	$0.0186024\pi$
$131$			15.3029i			0.116816i	−0.998293	+	0.0584079i	$0.981398\pi$
$132$	−50.6767	−	135.394i	−0.383914	−	1.02571i
$133$	27.6229			0.207691
$134$	147.638	+	47.9704i	1.10177	+	0.357988i
$135$		0			0
$136$	309.865	+	225.130i	2.27842	+	1.65537i
$137$	−8.49047	−	26.1310i	−0.0619742	−	0.190737i	0.915276	−	0.402828i	$-0.131973\pi$
$137$	−8.49047	−	26.1310i	−0.0619742	−	0.190737i	−0.977250	+	0.212091i	$0.931973\pi$
$138$	−171.864	+	55.8419i	−1.24539	+	0.404651i
$139$	33.0584	−	45.5009i	0.237830	−	0.327345i	−0.673373	−	0.739303i	$-0.735155\pi$
$139$	33.0584	−	45.5009i	0.237830	−	0.327345i	0.911203	+	0.411958i	$0.135155\pi$
$140$		0			0
$141$	−27.9466	+	86.0109i	−0.198203	+	0.610007i
$142$			128.704i			0.906363i
$143$	−0.422803	−	9.60525i	−0.00295667	−	0.0671696i
$144$	−158.728			−1.10228
$145$		0			0
$146$	241.540	−	175.489i	1.65438	−	1.20198i
$147$	−58.9946	−	42.8621i	−0.401324	−	0.291579i
$148$	−174.627	−	537.448i	−1.17992	−	3.63141i
$149$	−225.598	+	73.3012i	−1.51408	+	0.491954i	−0.944087	−	0.329695i	$-0.893054\pi$
$149$	−225.598	+	73.3012i	−1.51408	+	0.491954i	−0.569993	+	0.821650i	$0.693054\pi$
$150$		0			0
$151$	−27.6455	−	38.0508i	−0.183083	−	0.251992i	0.707604	−	0.706609i	$-0.249776\pi$
$151$	−27.6455	−	38.0508i	−0.183083	−	0.251992i	−0.890687	+	0.454617i	$0.849776\pi$
$152$	128.396	−	395.163i	0.844712	−	2.59975i
$153$			155.868i			1.01875i
$154$	−35.5311	−	23.4993i	−0.230721	−	0.152593i
$155$		0			0
$156$	10.9250	+	3.54973i	0.0700317	+	0.0227547i
$157$	−118.090	+	85.7977i	−0.752168	+	0.546482i	−0.896498	−	0.443048i	$-0.853897\pi$
$157$	−118.090	+	85.7977i	−0.752168	+	0.546482i	0.144330	+	0.989530i	$0.453897\pi$
$158$	−87.1946	−	63.3506i	−0.551865	−	0.400953i
$159$	11.1530	+	34.3253i	0.0701444	+	0.215882i
$160$		0			0
$161$	−21.3760	+	29.4215i	−0.132770	+	0.182742i
$162$	−49.2805	−	67.8288i	−0.304201	−	0.418696i
$163$	24.8897	−	76.6025i	0.152697	−	0.469954i	−0.845223	−	0.534414i	$-0.820532\pi$
$163$	24.8897	−	76.6025i	0.152697	−	0.469954i	0.997920	+	0.0644598i	$0.0205324\pi$
$164$		−	333.494i		−	2.03350i
$165$		0			0
$166$	−483.465			−2.91244
$167$	106.633	+	34.6471i	0.638521	+	0.207468i	0.610346	−	0.792135i	$-0.291031\pi$
$167$	106.633	+	34.6471i	0.638521	+	0.207468i	0.0281747	+	0.999603i	$0.491031\pi$
$168$	22.0619	−	16.0289i	0.131321	−	0.0954100i
$169$	−136.106	−	98.8867i	−0.805360	−	0.585128i
$170$		0			0
$171$	160.812	−	52.2510i	0.940421	−	0.305561i
$172$	76.3057	−	105.026i	0.443638	−	0.610615i
$173$	−111.127	−	152.953i	−0.642351	−	0.884120i	0.356387	−	0.934338i	$-0.384008\pi$
$173$	−111.127	−	152.953i	−0.642351	−	0.884120i	−0.998738	+	0.0502182i	$0.984008\pi$
$174$	28.2086	−	86.8171i	0.162118	−	0.498949i
$175$		0			0
$176$	−204.689	+	162.936i	−1.16301	+	0.925774i
$177$	−58.0116			−0.327749
$178$	28.6099	+	9.29591i	0.160730	+	0.0522242i
$179$	185.169	−	134.533i	1.03446	−	0.751581i	0.0652651	−	0.997868i	$-0.479211\pi$
$179$	185.169	−	134.533i	1.03446	−	0.751581i	0.969197	+	0.246287i	$0.0792107\pi$
$180$		0			0
$181$	−3.84557	−	11.8355i	−0.0212463	−	0.0653893i	0.939871	−	0.341529i	$-0.110945\pi$
$181$	−3.84557	−	11.8355i	−0.0212463	−	0.0653893i	−0.961118	+	0.276140i	$0.910945\pi$
$182$	3.21921	−	1.04599i	0.0176880	−	0.00574718i
$183$	−30.5595	+	42.0616i	−0.166992	+	0.229845i
$184$	321.533	+	442.552i	1.74746	+	2.40518i
$185$		0			0
$186$		−	34.6896i		−	0.186503i
$187$	160.001	+	201.001i	0.855619	+	1.07487i
$188$	510.947			2.71780
$189$	24.7876	+	8.05398i	0.131151	+	0.0426137i
$190$		0			0
$191$	0.755326	+	0.548777i	0.00395459	+	0.00287318i	0.589761	−	0.807578i	$-0.299222\pi$
$191$	0.755326	+	0.548777i	0.00395459	+	0.00287318i	−0.585806	+	0.810451i	$0.699222\pi$
$192$	13.2263	+	40.7064i	0.0688870	+	0.212012i
$193$	−39.5768	+	12.8593i	−0.205061	+	0.0666284i	−0.409747	−	0.912199i	$-0.634383\pi$
$193$	−39.5768	+	12.8593i	−0.205061	+	0.0666284i	0.204685	+	0.978828i	$0.434383\pi$
$194$	−139.134	+	191.502i	−0.717186	+	0.987121i
$195$		0			0
$196$	−127.311	+	391.823i	−0.649546	+	1.99910i
$197$			85.8608i			0.435842i	0.975966	+	0.217921i	$0.0699274\pi$
$197$			85.8608i			0.435842i	−0.975966	+	0.217921i	$0.930073\pi$
$198$	−251.302	−	69.5958i	−1.26920	−	0.351494i
$199$	−78.5577			−0.394763			−0.197381	−	0.980327i	$-0.563244\pi$
$199$	−78.5577			−0.394763			−0.197381	+	0.980327i	$0.563244\pi$
$200$		0			0
$201$	−53.9258	+	39.1794i	−0.268287	+	0.194922i
$202$	−229.888	−	167.023i	−1.13806	−	0.826848i
$203$	−5.67689	−	17.4717i	−0.0279650	−	0.0860674i
$204$	−291.923	+	94.8515i	−1.43099	+	0.464958i
$205$		0			0
$206$	232.819	+	320.448i	1.13019	+	1.55557i
$207$	−68.7911	+	211.717i	−0.332324	+	1.02279i
$208$		−	20.7882i		−	0.0999433i
$209$	153.740	−	232.456i	0.735600	−	1.11223i
$210$		0			0
$211$	127.520	+	41.4339i	0.604362	+	0.196369i	0.595185	−	0.803589i	$-0.297079\pi$
$211$	127.520	+	41.4339i	0.604362	+	0.196369i	0.00917715	+	0.999958i	$0.497079\pi$
$212$	164.966	−	119.855i	0.778141	−	0.565353i
$213$	−44.7091	−	32.4830i	−0.209902	−	0.152503i
$214$	23.0586	+	70.9672i	0.107751	+	0.331622i
$215$		0			0
$216$	230.434	−	317.166i	1.06683	−	1.46836i
$217$	−4.10343	−	5.64788i	−0.0189098	−	0.0260271i
$218$	−130.063	+	400.293i	−0.596619	+	1.83620i
$219$			128.197i			0.585376i
$220$		0			0
$221$	−20.4137			−0.0923697
$222$	337.897	+	109.790i	1.52206	+	0.494547i
$223$	−162.389	+	117.983i	−0.728204	+	0.529071i	−0.888995	−	0.457917i	$-0.848596\pi$
$223$	−162.389	+	117.983i	−0.728204	+	0.529071i	0.160791	+	0.986988i	$0.448596\pi$
$224$	−16.6553	−	12.1008i	−0.0743542	−	0.0540215i
$225$		0			0
$226$	−360.077	+	116.996i	−1.59326	+	0.517681i
$227$	4.37724	−	6.02475i	0.0192830	−	0.0265408i	−0.799267	−	0.600977i	$-0.794778\pi$
$227$	4.37724	−	6.02475i	0.0192830	−	0.0265408i	0.818550	+	0.574436i	$0.194778\pi$
$228$	195.720	+	269.385i	0.858420	+	1.18151i
$229$	−57.4080	+	176.684i	−0.250690	+	0.771544i	0.743959	+	0.668226i	$0.232946\pi$
$229$	−57.4080	+	176.684i	−0.250690	+	0.771544i	−0.994648	+	0.103318i	$0.967054\pi$
$230$		0			0
$231$	17.1308	−	6.41189i	0.0741591	−	0.0277571i
$232$	−276.330			−1.19108
$233$	90.1691	+	29.2977i	0.386992	+	0.125741i	0.496050	−	0.868294i	$-0.334783\pi$
$233$	90.1691	+	29.2977i	0.386992	+	0.125741i	−0.109058	+	0.994035i	$0.534783\pi$
$234$	16.7627	−	12.1788i	0.0716354	−	0.0520462i
$235$		0			0
$236$	101.280	+	311.709i	0.429154	+	1.32080i
$237$	44.0135	−	14.3008i	0.185711	−	0.0603411i
$238$	−53.1632	+	73.1728i	−0.223375	+	0.307449i
$239$	232.413	+	319.889i	0.972439	+	1.33845i	0.940805	+	0.338948i	$0.110071\pi$
$239$	232.413	+	319.889i	0.972439	+	1.33845i	0.0316341	+	0.999500i	$0.489929\pi$
$240$		0			0
$241$			26.3347i			0.109273i	0.998506	+	0.0546364i	$0.0174000\pi$
$241$			26.3347i			0.109273i	−0.998506	+	0.0546364i	$0.982600\pi$
$242$	−395.509	+	168.217i	−1.63434	+	0.695110i
$243$	251.150			1.03354
$244$	279.359	+	90.7693i	1.14491	+	0.372005i
$245$		0			0
$246$	169.627	+	123.241i	0.689539	+	0.500979i
$247$	6.84319	+	21.0612i	0.0277052	+	0.0852679i
$248$	−99.8699	+	32.4497i	−0.402701	+	0.130846i
$249$	122.020	−	167.946i	0.490040	−	0.674482i
$250$		0			0
$251$	115.751	−	356.246i	0.461160	−	1.41931i	−0.402588	−	0.915381i	$-0.631889\pi$
$251$	115.751	−	356.246i	0.461160	−	1.41931i	0.863748	−	0.503924i	$-0.168111\pi$
$252$		−	62.6983i		−	0.248803i
$253$	128.620	+	343.637i	0.508379	+	1.35825i
$254$	−455.597			−1.79369
$255$		0			0
$256$	412.683	−	299.832i	1.61204	−	1.17122i
$257$	−206.714	−	150.186i	−0.804333	−	0.584382i	0.107849	−	0.994167i	$-0.465604\pi$
$257$	−206.714	−	150.186i	−0.804333	−	0.584382i	−0.912182	+	0.409785i	$0.865604\pi$
$258$	25.2214	+	77.6235i	0.0977574	+	0.300866i
$259$	68.0008	−	22.0948i	0.262551	−	0.0853081i
$260$		0			0
$261$	−66.0982	−	90.9764i	−0.253250	−	0.348569i
$262$	−16.7970	+	51.6959i	−0.0641107	+	0.197312i
$263$		−	288.916i		−	1.09854i	−0.835645	−	0.549270i	$-0.814906\pi$
$263$		−	288.916i		−	1.09854i	0.835645	−	0.549270i	$-0.185094\pi$
$264$	−12.0992	−	274.870i	−0.0458303	−	1.04117i
$265$		0			0
$266$	93.3153	+	30.3200i	0.350809	+	0.113985i
$267$	−10.4500	+	7.59233i	−0.0391384	+	0.0284357i
$268$	304.667	+	221.353i	1.13682	+	0.825945i
$269$	−66.9375	−	206.012i	−0.248838	−	0.765846i	−0.994981	−	0.100060i	$-0.968097\pi$
$269$	−66.9375	−	206.012i	−0.248838	−	0.765846i	0.746143	−	0.665786i	$-0.231903\pi$
$270$		0			0
$271$	30.9844	−	42.6464i	0.114334	−	0.157367i	−0.748015	−	0.663682i	$-0.768993\pi$
$271$	30.9844	−	42.6464i	0.114334	−	0.157367i	0.862348	+	0.506315i	$0.168993\pi$
$272$	326.501	+	449.390i	1.20037	+	1.65217i
$273$	−0.449131	+	1.38228i	−0.00164517	+	0.00506331i
$274$		−	97.5947i		−	0.356185i
$275$		0			0
$276$	−438.383			−1.58834
$277$	155.997	+	50.6866i	0.563167	+	0.182984i	0.576746	−	0.816924i	$-0.304322\pi$
$277$	155.997	+	50.6866i	0.563167	+	0.182984i	−0.0135787	+	0.999908i	$0.504322\pi$
$278$	161.621	−	117.424i	0.581370	−	0.422390i
$279$	−34.5723	−	25.1183i	−0.123915	−	0.0900296i
$280$		0			0
$281$	−486.240	+	157.989i	−1.73039	+	0.562239i	−0.993506	−	0.113778i	$-0.963705\pi$
$281$	−486.240	+	157.989i	−1.73039	+	0.562239i	−0.736887	+	0.676016i	$0.763705\pi$
$282$	−188.818	+	259.885i	−0.669567	+	0.921579i
$283$	104.898	+	144.379i	0.370664	+	0.510175i	0.953081	−	0.302715i	$-0.0978931\pi$
$283$	104.898	+	144.379i	0.370664	+	0.510175i	−0.582418	+	0.812890i	$0.697893\pi$
$284$	−96.4826	+	296.943i	−0.339727	+	1.04557i
$285$		0			0
$286$	9.11479	−	32.9124i	0.0318699	−	0.115078i
$287$	42.1954			0.147022
$288$	−119.852	−	38.9422i	−0.416152	−	0.135216i
$289$	207.488	−	150.749i	0.717951	−	0.521622i
$290$		0			0
$291$	−31.4083	−	96.6647i	−0.107932	−	0.332181i
$292$	688.833	−	223.815i	2.35902	−	0.766491i
$293$	33.4761	−	46.0759i	0.114253	−	0.157256i	−0.748061	−	0.663630i	$-0.769015\pi$
$293$	33.4761	−	46.0759i	0.114253	−	0.157256i	0.862313	+	0.506375i	$0.169015\pi$
$294$	−152.248	−	209.551i	−0.517849	−	0.712758i
$295$		0			0
$296$		−	1075.49i		−	3.63342i
$297$	205.737	−	163.770i	0.692717	−	0.551415i
$298$	−842.569			−2.82741
$299$	−27.7281	−	9.00940i	−0.0927360	−	0.0301318i
$300$		0			0
$301$	13.2884	+	9.65461i	0.0441476	+	0.0320751i
$302$	−51.6256	−	158.887i	−0.170946	−	0.526117i
$303$	116.041	−	37.7041i	0.382974	−	0.124436i
$304$	354.192	−	487.504i	1.16511	−	1.60363i
$305$		0			0
$306$	−171.087	+	526.552i	−0.559108	+	1.72076i
$307$		−	427.615i		−	1.39288i	−0.717613	−	0.696442i	$-0.754766\pi$
$307$		−	427.615i		−	1.39288i	0.717613	−	0.696442i	$-0.245234\pi$
$308$	−64.3605	−	80.8531i	−0.208963	−	0.262510i
$309$	−170.078			−0.550413
$310$		0			0
$311$	80.6811	−	58.6183i	0.259425	−	0.188483i	−0.450469	−	0.892792i	$-0.648743\pi$
$311$	80.6811	−	58.6183i	0.259425	−	0.188483i	0.709893	+	0.704309i	$0.248743\pi$
$312$	17.6868	+	12.8502i	0.0566884	+	0.0411865i
$313$	16.2938	+	50.1472i	0.0520569	+	0.160215i	0.973705	−	0.227812i	$-0.0731570\pi$
$313$	16.2938	+	50.1472i	0.0520569	+	0.160215i	−0.921648	+	0.388026i	$0.873157\pi$
$314$	−493.106	+	160.220i	−1.57040	+	0.510254i
$315$		0			0
$316$	−153.683	−	211.527i	−0.486339	−	0.669389i
$317$	−100.443	+	309.132i	−0.316855	+	0.975180i	0.658129	+	0.752905i	$0.271348\pi$
$317$	−100.443	+	309.132i	−0.316855	+	0.975180i	−0.974984	+	0.222275i	$0.928652\pi$
$318$			128.199i			0.403142i
$319$	−178.626	−	49.4688i	−0.559956	−	0.155075i
$320$		0			0
$321$	−30.4723	−	9.90104i	−0.0949292	−	0.0308444i
$322$	−104.506	+	75.9281i	−0.324553	+	0.235802i
$323$	−478.721	−	347.811i	−1.48211	−	1.07681i
$324$	−62.8513	−	193.437i	−0.193986	−	0.597026i
$325$		0			0
$326$	168.164	−	231.457i	0.515839	−	0.709992i
$327$	−106.228	−	146.210i	−0.324855	−	0.447124i
$328$	196.132	−	603.631i	0.597962	−	1.84034i
$329$			64.6477i			0.196498i
$330$		0			0
$331$	343.048			1.03640			0.518199	−	0.855260i	$-0.326603\pi$
$331$	343.048			1.03640			0.518199	+	0.855260i	$0.326603\pi$
$332$	−1115.44	−	362.429i	−3.35976	−	1.09165i
$333$	354.085	−	257.258i	1.06332	−	0.772547i
$334$	322.196	+	234.089i	0.964657	+	0.700865i
$335$		0			0
$336$	37.6133	−	12.2213i	0.111944	−	0.0363729i
$337$	367.738	−	506.148i	1.09121	−	1.50192i	0.244663	−	0.969608i	$-0.421323\pi$
$337$	367.738	−	506.148i	1.09121	−	1.50192i	0.846547	−	0.532313i	$-0.178677\pi$
$338$	−351.249	−	483.452i	−1.03920	−	1.43033i
$339$	50.2364	−	154.612i	0.148190	−	0.456082i
$340$		0			0
$341$	−70.3672	+	3.09742i	−0.206356	+	0.00908334i
$342$	600.605			1.75616
$343$	−100.384	−	32.6166i	−0.292663	−	0.0950921i
$344$	199.882	−	145.223i	0.581052	−	0.422159i
$345$		0			0
$346$	−207.519	−	638.679i	−0.599767	−	1.84589i
$347$	−453.741	+	147.429i	−1.30761	+	0.424868i	−0.878223	−	0.478252i	$-0.841271\pi$
$347$	−453.741	+	147.429i	−1.30761	+	0.424868i	−0.429388	+	0.903120i	$0.641271\pi$
$348$	130.165	−	179.156i	0.374037	−	0.514818i
$349$	108.085	+	148.766i	0.309699	+	0.426264i	0.935287	−	0.353890i	$-0.115141\pi$
$349$	108.085	+	148.766i	0.309699	+	0.426264i	−0.625589	+	0.780153i	$0.715141\pi$
$350$		0			0
$351$			20.8946i			0.0595289i
$352$	−194.531	+	72.8111i	−0.552644	+	0.206850i
$353$	−289.312			−0.819580			−0.409790	−	0.912180i	$-0.634398\pi$
$353$	−289.312			−0.819580			−0.409790	+	0.912180i	$0.634398\pi$
$354$	−195.974	−	63.6757i	−0.553598	−	0.179875i
$355$		0			0
$356$	59.0395	+	42.8947i	0.165841	+	0.120491i
$357$	−12.0011	−	36.9356i	−0.0336166	−	0.103461i
$358$	773.202	−	251.229i	2.15978	−	0.701756i
$359$	197.102	−	271.288i	0.549032	−	0.755677i	−0.440849	−	0.897581i	$-0.645322\pi$
$359$	197.102	−	271.288i	0.549032	−	0.755677i	0.989880	+	0.141904i	$0.0453225\pi$
$360$		0			0
$361$	−86.8081	+	267.168i	−0.240466	+	0.740078i
$362$		−	44.2034i		−	0.122109i
$363$	41.3861	−	179.848i	0.114011	−	0.495448i
$364$	8.21144			0.0225589
$365$		0			0
$366$	−149.404	+	108.548i	−0.408208	+	0.296581i
$367$	192.417	+	139.799i	0.524296	+	0.380924i	0.818220	−	0.574905i	$-0.194961\pi$
$367$	192.417	+	139.799i	0.524296	+	0.380924i	−0.293924	+	0.955829i	$0.594961\pi$
$368$	245.155	+	754.508i	0.666181	+	2.05029i
$369$	245.649	−	79.8161i	0.665714	−	0.216304i
$370$		0			0
$371$	15.1647	+	20.8724i	0.0408751	+	0.0562598i
$372$	26.0050	−	80.0352i	0.0699060	−	0.215148i
$373$		−	240.258i		−	0.644124i	−0.946719	−	0.322062i	$-0.895624\pi$
$373$		−	240.258i		−	0.644124i	0.946719	−	0.322062i	$-0.104376\pi$
$374$	319.885	+	854.642i	0.855307	+	2.28514i
$375$		0			0
$376$	924.826	+	300.494i	2.45964	+	0.799186i
$377$	11.9150	−	8.65672i	0.0316047	−	0.0229621i
$378$	74.8967	+	54.4157i	0.198139	+	0.143957i
$379$	81.0415	+	249.420i	0.213830	+	0.658101i	0.999235	+	0.0391181i	$0.0124549\pi$
$379$	81.0415	+	249.420i	0.213830	+	0.658101i	−0.785405	+	0.618983i	$0.787545\pi$
$380$		0			0
$381$	114.986	−	158.265i	0.301802	−	0.415394i
$382$	1.94927	+	2.68294i	0.00510281	+	0.00702341i
$383$	−105.890	+	325.896i	−0.276475	+	0.850904i	0.712350	+	0.701825i	$0.247631\pi$
$383$	−105.890	+	325.896i	−0.276475	+	0.850904i	−0.988825	+	0.149079i	$0.952369\pi$
$384$			267.231i			0.695913i
$385$		0			0
$386$	−147.813			−0.382934
$387$	95.6236	+	31.0700i	0.247089	+	0.0802842i
$388$	−464.567	+	337.527i	−1.19734	+	0.869916i
$389$	−511.645	−	371.732i	−1.31528	−	0.955608i	−0.999978	−	0.00661783i	$-0.997893\pi$
$389$	−511.645	−	371.732i	−1.31528	−	0.955608i	−0.315304	−	0.948991i	$-0.602107\pi$
$390$		0			0
$391$	740.915	−	240.738i	1.89492	−	0.615698i
$392$	−460.871	+	634.335i	−1.17569	+	1.61820i
$393$	−13.7188	−	18.8823i	−0.0349078	−	0.0480465i
$394$	−94.2441	+	290.053i	−0.239198	+	0.736176i
$395$		0			0
$396$	−527.627	−	348.958i	−1.33239	−	0.881208i
$397$	335.656			0.845482			0.422741	−	0.906251i	$-0.361068\pi$
$397$	335.656			0.845482			0.422741	+	0.906251i	$0.361068\pi$
$398$	−265.382	−	86.2280i	−0.666790	−	0.216653i
$399$	−34.0841	+	24.7635i	−0.0854237	+	0.0620639i
$400$		0			0
$401$	216.430	+	666.103i	0.539725	+	1.66110i	0.733211	+	0.680001i	$0.238021\pi$
$401$	216.430	+	666.103i	0.539725	+	1.66110i	−0.193486	+	0.981103i	$0.561979\pi$
$402$	−225.176	+	73.1641i	−0.560139	+	0.182000i
$403$	3.28968	−	4.52785i	0.00816297	−	0.0112354i
$404$	−405.185	−	557.689i	−1.00293	−	1.38042i
$405$		0			0
$406$		−	65.2537i		−	0.160723i
$407$	192.535	−	695.222i	0.473060	−	1.70816i
$408$	−584.170			−1.43179
$409$	17.4090	+	5.65652i	0.0425648	+	0.0138301i	0.330222	−	0.943903i	$-0.392876\pi$
$409$	17.4090	+	5.65652i	0.0425648	+	0.0138301i	−0.287657	+	0.957733i	$0.592876\pi$
$410$		0			0
$411$	33.9024	+	24.6316i	0.0824877	+	0.0599308i
$412$	296.933	+	913.865i	0.720711	+	2.21812i
$413$	−39.4391	+	12.8145i	−0.0954942	+	0.0310279i
$414$	−464.778	+	639.712i	−1.12265	+	1.54520i
$415$		0			0
$416$	5.10017	−	15.6967i	0.0122600	−	0.0377325i
$417$			85.7801i			0.205708i
$418$	774.516	−	616.528i	1.85291	−	1.47495i
$419$	420.944			1.00464			0.502320	−	0.864682i	$-0.332480\pi$
$419$	420.944			1.00464			0.502320	+	0.864682i	$0.332480\pi$
$420$		0			0
$421$	−377.591	+	274.336i	−0.896891	+	0.651629i	−0.937665	−	0.347539i	$-0.887017\pi$
$421$	−377.591	+	274.336i	−0.896891	+	0.651629i	0.0407749	+	0.999168i	$0.487017\pi$
$422$	385.308	+	279.943i	0.913052	+	0.663371i
$423$	122.286	+	376.359i	0.289093	+	0.889738i
$424$	369.080	−	119.921i	0.870472	−	0.282833i
$425$		0			0
$426$	−115.381	−	158.808i	−0.270847	−	0.372789i
$427$	−11.4846	+	35.3460i	−0.0268961	+	0.0827776i
$428$			181.020i			0.422944i
$429$	9.13266	+	11.4729i	0.0212883	+	0.0267434i
$430$		0			0
$431$	−227.136	−	73.8008i	−0.526997	−	0.171232i	0.0334216	−	0.999441i	$-0.489360\pi$
$431$	−227.136	−	73.8008i	−0.526997	−	0.171232i	−0.560418	+	0.828210i	$0.689360\pi$
$432$	459.977	−	334.193i	1.06476	−	0.773595i
$433$	−77.6015	−	56.3808i	−0.179218	−	0.130210i	0.494559	−	0.869144i	$-0.335329\pi$
$433$	−77.6015	−	56.3808i	−0.179218	−	0.130210i	−0.673778	+	0.738934i	$0.735329\pi$
$434$	−7.66280	−	23.5837i	−0.0176562	−	0.0543402i
$435$		0			0
$436$	−600.158	+	826.047i	−1.37651	+	1.89460i
$437$	−496.747	−	683.713i	−1.13672	−	1.56456i
$438$	−140.714	+	433.074i	−0.321266	+	0.988754i
$439$		−	749.426i		−	1.70712i	−0.520994	−	0.853560i	$-0.674439\pi$
$439$		−	749.426i		−	1.70712i	0.520994	−	0.853560i	$-0.325561\pi$
$440$		0			0
$441$	−319.083			−0.723544
$442$	−68.9612	−	22.4069i	−0.156021	−	0.0506942i
$443$	37.4905	−	27.2384i	0.0846286	−	0.0614863i	−0.544666	−	0.838653i	$-0.683344\pi$
$443$	37.4905	−	27.2384i	0.0846286	−	0.0614863i	0.629295	+	0.777166i	$0.283344\pi$
$444$	697.288	+	506.609i	1.57047	+	1.14101i
$445$		0			0
$446$	−678.084	+	220.323i	−1.52037	+	0.493997i
$447$	212.653	−	292.692i	0.475734	−	0.654791i
$448$	17.9838	+	24.7525i	0.0401424	+	0.0552512i
$449$	−15.0043	+	46.1784i	−0.0334171	+	0.102847i	−0.966374	−	0.257141i	$-0.917219\pi$
$449$	−15.0043	+	46.1784i	−0.0334171	+	0.102847i	0.932957	+	0.359989i	$0.117219\pi$
$450$		0			0
$451$	234.846	−	355.089i	0.520723	−	0.787336i
$452$	−918.469			−2.03201
$453$	68.2239	+	22.1673i	0.150605	+	0.0489344i
$454$	21.4001	−	15.5481i	0.0471368	−	0.0342469i
$455$		0			0
$456$	195.829	+	602.698i	0.429449	+	1.32171i
$457$	−395.176	+	128.400i	−0.864718	+	0.280964i	−0.707598	−	0.706616i	$-0.750221\pi$
$457$	−395.176	+	128.400i	−0.864718	+	0.280964i	−0.157120	+	0.987579i	$0.550221\pi$
$458$	−387.869	+	533.856i	−0.846876	+	1.16562i
$459$	−328.172	−	451.691i	−0.714972	−	0.984075i
$460$		0			0
$461$		−	704.025i		−	1.52717i	−0.645707	−	0.763585i	$-0.723437\pi$
$461$		−	704.025i		−	1.52717i	0.645707	−	0.763585i	$-0.276563\pi$
$462$	64.9088	−	2.85715i	0.140495	−	0.00618431i
$463$	506.506			1.09397			0.546983	−	0.837144i	$-0.315776\pi$
$463$	506.506			1.09397			0.546983	+	0.837144i	$0.315776\pi$
$464$	−381.141	−	123.840i	−0.821424	−	0.266897i
$465$		0			0
$466$	272.449	+	197.946i	0.584655	+	0.424777i
$467$	111.045	+	341.762i	0.237785	+	0.731825i	0.996740	+	0.0806828i	$0.0257101\pi$
$467$	111.045	+	341.762i	0.237785	+	0.731825i	−0.758955	+	0.651143i	$0.774290\pi$
$468$	47.8044	−	15.5326i	0.102146	−	0.0331893i
$469$	−28.0068	+	38.5480i	−0.0597160	+	0.0821920i
$470$		0			0
$471$	68.7960	−	211.732i	0.146064	−	0.449538i
$472$			623.765i			1.32154i
$473$	155.206	−	58.0922i	0.328131	−	0.122816i
$474$	164.383			0.346799
$475$		0			0
$476$	−177.511	+	128.969i	−0.372922	+	0.270944i
$477$	127.766	+	92.8272i	0.267853	+	0.194606i
$478$	434.011	+	1335.75i	0.907973	+	2.79445i
$479$	512.144	−	166.406i	1.06919	−	0.347402i	0.279020	−	0.960285i	$-0.409990\pi$
$479$	512.144	−	166.406i	1.06919	−	0.347402i	0.790173	+	0.612883i	$0.209990\pi$
$480$		0			0
$481$	33.6925	+	46.3737i	0.0700467	+	0.0964110i
$482$	−28.9060	+	88.9635i	−0.0599710	+	0.184572i
$483$		−	55.4665i		−	0.114838i
$484$	−1038.62	+	91.6129i	−2.14590	+	0.189283i
$485$		0			0
$486$	848.430	+	275.672i	1.74574	+	0.567226i
$487$	−534.918	+	388.640i	−1.09839	+	0.798029i	−0.980797	−	0.195032i	$-0.937519\pi$
$487$	−534.918	+	388.640i	−1.09839	+	0.798029i	−0.117596	+	0.993061i	$0.537519\pi$
$488$	452.264	+	328.589i	0.926770	+	0.673338i
$489$	37.9615	+	116.833i	0.0776308	+	0.238923i
$490$		0			0
$491$	39.8508	−	54.8499i	0.0811625	−	0.111711i	−0.766505	−	0.642238i	$-0.778006\pi$
$491$	39.8508	−	54.8499i	0.0811625	−	0.111711i	0.847668	+	0.530527i	$0.178006\pi$
$492$	298.972	+	411.500i	0.607667	+	0.836381i
$493$	−121.609	+	374.274i	−0.246671	+	0.759177i
$494$			78.6598i			0.159230i
$495$		0			0
$496$	−152.293			−0.307042
$497$	−37.5708	−	12.2075i	−0.0755951	−	0.0245624i
$498$	596.549	−	433.418i	1.19789	−	0.870318i
$499$	312.340	+	226.929i	0.625933	+	0.454767i	0.854989	−	0.518646i	$-0.173564\pi$
$499$	312.340	+	226.929i	0.625933	+	0.454767i	−0.229056	+	0.973413i	$0.573564\pi$
$500$		0			0
$501$	−162.636	+	52.8435i	−0.324622	+	0.105476i
$502$	782.058	−	1076.41i	1.55788	−	2.14424i
$503$	−152.395	−	209.753i	−0.302971	−	0.417004i	0.630202	−	0.776431i	$-0.282972\pi$
$503$	−152.395	−	209.753i	−0.302971	−	0.417004i	−0.933173	+	0.359427i	$0.882972\pi$
$504$	36.8736	−	113.485i	0.0731619	−	0.225169i
$505$		0			0
$506$	57.3133	+	1302.05i	0.113267	+	2.57321i
$507$	256.592			0.506099
$508$	−1051.14	−	341.538i	−2.06918	−	0.672318i
$509$	−653.416	+	474.735i	−1.28373	+	0.932681i	−0.999659	−	0.0261234i	$-0.991684\pi$
$509$	−653.416	+	474.735i	−1.28373	+	0.932681i	−0.284067	+	0.958805i	$0.591684\pi$
$510$		0			0
$511$	28.3183	+	87.1548i	0.0554174	+	0.170557i
$512$	1056.68	−	343.337i	2.06383	−	0.670581i
$513$	−356.005	+	489.999i	−0.693967	+	0.955164i
$514$	−533.466	−	734.253i	−1.03787	−	1.42851i
$515$		0			0
$516$			197.999i			0.383719i
$517$	544.033	+	359.809i	1.05229	+	0.695955i
$518$	253.971			0.490292
$519$	274.240	+	89.1058i	0.528400	+	0.171688i
$520$		0			0
$521$	−252.452	−	183.417i	−0.484553	−	0.352048i	0.318533	−	0.947912i	$-0.396810\pi$
$521$	−252.452	−	183.417i	−0.484553	−	0.352048i	−0.803086	+	0.595864i	$0.796810\pi$
$522$	−123.433	−	379.887i	−0.236461	−	0.727753i
$523$	70.0519	−	22.7612i	0.133942	−	0.0435205i	−0.241279	−	0.970456i	$-0.577567\pi$
$523$	70.0519	−	22.7612i	0.133942	−	0.0435205i	0.375221	+	0.926935i	$0.377567\pi$
$524$	−77.5075	+	106.680i	−0.147915	+	0.203588i
$525$		0			0
$526$	317.125	−	976.012i	0.602900	−	1.85554i
$527$			149.549i			0.283774i
$528$	106.497	−	384.548i	0.201699	−	0.728311i
$529$	583.638			1.10328
$530$		0			0
$531$	−205.362	+	149.205i	−0.386747	+	0.280988i
$532$	192.566	+	139.907i	0.361966	+	0.262984i
$533$	10.4533	+	32.1720i	0.0196122	+	0.0603602i
$534$	−43.6355	+	14.1780i	−0.0817144	+	0.0265506i
$535$		0			0
$536$	421.273	+	579.832i	0.785957	+	1.08178i
$537$	−107.874	+	332.002i	−0.200882	+	0.618253i
$538$		−	769.421i		−	1.43015i
$539$	−411.476	+	327.542i	−0.763407	+	0.607685i
$540$		0			0
$541$	39.3919	+	12.7992i	0.0728132	+	0.0236584i	0.345197	−	0.938530i	$-0.387812\pi$
$541$	39.3919	+	12.7992i	0.0728132	+	0.0236584i	−0.272384	+	0.962189i	$0.587812\pi$
$542$	151.481	−	110.058i	0.279486	−	0.203059i
$543$	15.3554	+	11.1563i	0.0282788	+	0.0205457i
$544$	136.280	+	419.428i	0.250515	+	0.771007i
$545$		0			0
$546$	−3.03449	+	4.17662i	−0.00555768	+	0.00764949i
$547$	−378.937	−	521.562i	−0.692755	−	0.953495i	−0.999998	−	0.00186448i	$-0.999407\pi$
$547$	−378.937	−	521.562i	−0.692755	−	0.953495i	0.307243	−	0.951631i	$-0.400593\pi$
$548$	73.1618	−	225.169i	0.133507	−	0.410892i
$549$			227.498i			0.414386i
$550$		0			0
$551$	426.911			0.774794
$552$	−793.483	−	257.818i	−1.43747	−	0.467062i
$553$	26.7635	−	19.4448i	0.0483969	−	0.0351624i
$554$	471.352	+	342.457i	0.850815	+	0.618154i
$555$		0			0
$556$	460.916	−	149.761i	0.828985	−	0.269354i
$557$	−263.713	+	362.970i	−0.473453	+	0.651652i	−0.977230	−	0.212181i	$-0.931943\pi$
$557$	−263.713	+	362.970i	−0.473453	+	0.651652i	0.503777	+	0.863834i	$0.331943\pi$
$558$	−89.2209	−	122.802i	−0.159894	−	0.220075i
$559$	−4.06916	+	12.5236i	−0.00727936	+	0.0224036i
$560$		0			0
$561$	−377.620	−	104.578i	−0.673120	−	0.186414i
$562$	−1816.02			−3.23136
$563$	−508.399	−	165.189i	−0.903018	−	0.293408i	−0.179536	−	0.983751i	$-0.557460\pi$
$563$	−508.399	−	165.189i	−0.903018	−	0.293408i	−0.723482	+	0.690343i	$0.757460\pi$
$564$	−630.460	+	458.056i	−1.11784	+	0.812156i
$565$		0			0
$566$	195.888	+	602.880i	0.346091	+	1.06516i
$567$	24.4746	−	7.95229i	0.0431651	−	0.0140252i
$568$	−349.271	+	480.731i	−0.614914	+	0.846357i
$569$	259.513	+	357.190i	0.456087	+	0.627750i	0.973692	−	0.227870i	$-0.0731762\pi$
$569$	259.513	+	357.190i	0.456087	+	0.627750i	−0.517605	+	0.855620i	$0.673176\pi$
$570$		0			0
$571$			935.409i			1.63819i	0.573655	+	0.819097i	$0.305525\pi$
$571$			935.409i			1.63819i	−0.573655	+	0.819097i	$0.694475\pi$
$572$	45.7022	−	69.1020i	0.0798990	−	0.120808i
$573$	−1.42397			−0.00248511
$574$	142.544	+	46.3153i	0.248334	+	0.0806887i
$575$		0			0
$576$	151.517	+	110.084i	0.263051	+	0.191118i
$577$	174.841	+	538.104i	0.303017	+	0.932590i	0.980410	+	0.196968i	$0.0631096\pi$
$577$	174.841	+	538.104i	0.303017	+	0.932590i	−0.677393	+	0.735621i	$0.736890\pi$
$578$	866.400	−	281.510i	1.49896	−	0.487042i
$579$	37.3059	−	51.3471i	0.0644316	−	0.0886825i
$580$		0			0
$581$	45.8564	−	141.132i	0.0789267	−	0.242911i
$582$		−	361.026i		−	0.620320i
$583$	260.050	−	11.4468i	0.446054	−	0.0196344i
$584$	1378.43			2.36033
$585$		0			0
$586$	163.663	−	118.908i	0.279289	−	0.202915i
$587$	−792.407	−	575.718i	−1.34993	−	0.980780i	−0.999015	−	0.0443714i	$-0.985872\pi$
$587$	−792.407	−	575.718i	−1.34993	−	0.980780i	−0.350912	−	0.936408i	$-0.614128\pi$
$588$	−194.173	−	597.604i	−0.330227	−	1.01633i
$589$	154.292	−	50.1326i	0.261956	−	0.0851147i
$590$		0			0
$591$	−76.9729	−	105.944i	−0.130242	−	0.179262i
$592$	481.993	−	1483.42i	0.814177	−	2.50578i
$593$		−	1106.21i		−	1.86544i	−0.360600	−	0.932720i	$-0.617428\pi$
$593$		−	1106.21i		−	1.86544i	0.360600	−	0.932720i	$-0.382572\pi$
$594$	874.777	−	327.421i	1.47269	−	0.551214i
$595$		0			0
$596$	−1943.96	−	631.632i	−3.26168	−	1.05978i
$597$	96.9328	−	70.4258i	0.162366	−	0.117966i
$598$	−83.7815	−	60.8708i	−0.140103	−	0.101791i
$599$	176.386	+	542.860i	0.294467	+	0.906276i	0.983400	+	0.181451i	$0.0580795\pi$
$599$	176.386	+	542.860i	0.294467	+	0.906276i	−0.688933	+	0.724825i	$0.741921\pi$
$600$		0			0
$601$	−98.4935	+	135.565i	−0.163883	+	0.225565i	−0.883058	−	0.469263i	$-0.844520\pi$
$601$	−98.4935	+	135.565i	−0.163883	+	0.225565i	0.719176	+	0.694828i	$0.244520\pi$
$602$	34.2935	+	47.2009i	0.0569659	+	0.0784068i
$603$	−90.1301	+	277.392i	−0.149469	+	0.460020i
$604$		−	405.283i		−	0.670999i
$605$		0			0
$606$	433.394			0.715171
$607$	801.915	+	260.558i	1.32111	+	0.429255i	0.882877	−	0.469605i	$-0.155604\pi$
$607$	801.915	+	260.558i	1.32111	+	0.429255i	0.438235	+	0.898860i	$0.355604\pi$
$608$	387.046	−	281.206i	0.636589	−	0.462509i
$609$	22.6678	+	16.4691i	0.0372214	+	0.0270429i
$610$		0			0
$611$	−49.2908	+	16.0156i	−0.0806724	+	0.0262120i
$612$	−789.458	+	1086.60i	−1.28996	+	1.77548i
$613$	−196.640	−	270.652i	−0.320783	−	0.441520i	0.617923	−	0.786239i	$-0.287974\pi$
$613$	−196.640	−	270.652i	−0.320783	−	0.441520i	−0.938706	+	0.344718i	$0.887974\pi$
$614$	469.367	−	1444.56i	0.764441	−	2.35271i
$615$		0			0
$616$	−68.9433	−	184.197i	−0.111921	−	0.299021i
$617$	916.072			1.48472			0.742360	−	0.670001i	$-0.233706\pi$
$617$	916.072			1.48472			0.742360	+	0.670001i	$0.233706\pi$
$618$	−574.554	−	186.684i	−0.929698	−	0.302077i
$619$	−563.143	+	409.147i	−0.909762	+	0.660981i	−0.940955	−	0.338532i	$-0.890070\pi$
$619$	−563.143	+	409.147i	−0.909762	+	0.660981i	0.0311923	+	0.999513i	$0.490070\pi$
$620$		0			0
$621$	−246.410	−	758.370i	−0.396795	−	1.22121i
$622$	336.897	−	109.465i	0.541635	−	0.175988i
$623$	−5.42727	+	7.46999i	−0.00871151	+	0.0119904i
$624$	18.6363	+	25.6507i	0.0298659	+	0.0411069i
$625$		0			0
$626$			187.291i			0.299187i
$627$	18.6924	+	424.655i	0.0298125	+	0.677280i
$628$	−1257.79			−2.00286
$629$	−1456.70	−	473.309i	−2.31589	−	0.752479i
$630$		0			0
$631$	355.498	+	258.284i	0.563388	+	0.409325i	0.832697	−	0.553728i	$-0.186795\pi$
$631$	355.498	+	258.284i	0.563388	+	0.409325i	−0.269309	+	0.963054i	$0.586795\pi$
$632$	−153.769	−	473.251i	−0.243305	−	0.748815i
$633$	−194.493	+	63.1946i	−0.307256	+	0.0998335i
$634$	−678.630	+	934.055i	−1.07039	+	1.47327i
$635$		0			0
$636$	−96.1043	+	295.779i	−0.151107	+	0.465061i
$637$		−	41.7895i		−	0.0656036i
$638$	−549.132	−	363.181i	−0.860708	−	0.569250i
$639$	−241.817			−0.378430
$640$		0			0
$641$	611.568	−	444.330i	0.954085	−	0.693183i	0.00231537	−	0.999997i	$-0.499263\pi$
$641$	611.568	−	444.330i	0.954085	−	0.693183i	0.951769	+	0.306814i	$0.0992630\pi$
$642$	−92.0732	−	66.8951i	−0.143416	−	0.104198i
$643$	−36.2624	−	111.604i	−0.0563957	−	0.173568i	0.918891	−	0.394512i	$-0.129086\pi$
$643$	−36.2624	−	111.604i	−0.0563957	−	0.173568i	−0.975287	+	0.220944i	$0.929086\pi$
$644$	−298.034	+	96.8371i	−0.462786	+	0.150368i
$645$		0			0
$646$	−1235.44	−	1700.43i	−1.91244	−	2.63225i
$647$	−324.099	+	997.473i	−0.500925	+	1.54169i	0.306590	+	0.951842i	$0.400812\pi$
$647$	−324.099	+	997.473i	−0.500925	+	1.54169i	−0.807515	+	0.589847i	$0.799188\pi$
$648$		−	387.088i		−	0.597358i
$649$	−111.667	+	403.215i	−0.172060	+	0.621286i
$650$		0			0
$651$	10.1265	+	3.29029i	0.0155553	+	0.00505421i
$652$	561.496	−	407.951i	0.861191	−	0.625692i
$653$	318.988	+	231.758i	0.488496	+	0.354913i	0.804606	−	0.593810i	$-0.202377\pi$
$653$	318.988	+	231.758i	0.488496	+	0.354913i	−0.316110	+	0.948723i	$0.602377\pi$
$654$	−198.371	−	610.522i	−0.303319	−	0.933521i
$655$		0			0
$656$	541.046	−	744.687i	0.824766	−	1.13519i
$657$	329.721	+	453.822i	0.501858	+	0.690749i
$658$	−70.9598	+	218.392i	−0.107842	+	0.331903i
$659$		−	894.004i		−	1.35661i	−0.734782	−	0.678303i	$-0.762715\pi$
$659$		−	894.004i		−	1.35661i	0.734782	−	0.678303i	$-0.237285\pi$
$660$		0			0
$661$	−1104.87			−1.67152			−0.835759	−	0.549097i	$-0.814972\pi$
$661$	−1104.87			−1.67152			−0.835759	+	0.549097i	$0.814972\pi$
$662$	1158.88	+	376.542i	1.75057	+	0.568795i
$663$	25.1886	−	18.3006i	0.0379918	−	0.0276027i
$664$	−1805.82	−	1312.01i	−2.71962	−	1.97592i
$665$		0			0
$666$	1478.54	−	480.407i	2.22003	−	0.721332i
$667$	−330.365	+	454.708i	−0.495300	+	0.681721i
$668$	567.880	+	781.619i	0.850119	+	1.17009i
$669$	94.6034	−	291.159i	0.141410	−	0.435216i
$670$		0			0
$671$	233.529	+	293.372i	0.348031	+	0.437215i
$672$	31.3993			0.0467251
$673$	992.653	+	322.533i	1.47497	+	0.479246i	0.932605	−	0.360899i	$-0.117530\pi$
$673$	992.653	+	322.533i	1.47497	+	0.479246i	0.542362	+	0.840145i	$0.317530\pi$
$674$	1797.85	−	1306.22i	2.66744	−	1.93801i
$675$		0			0
$676$	−447.975	−	1378.73i	−0.662685	−	2.03954i
$677$	−187.514	+	60.9269i	−0.276977	+	0.0899954i	−0.444212	−	0.895922i	$-0.646516\pi$
$677$	−187.514	+	60.9269i	−0.276977	+	0.0899954i	0.167235	+	0.985917i	$0.446516\pi$
$678$	339.415	−	467.165i	0.500613	−	0.689034i
$679$	−42.7058	−	58.7794i	−0.0628951	−	0.0865677i
$680$		0			0
$681$			11.3581i			0.0166786i
$682$	−241.113	−	66.7741i	−0.353538	−	0.0979092i
$683$	−779.498			−1.14129			−0.570643	−	0.821198i	$-0.693306\pi$
$683$	−779.498			−1.14129			−0.570643	+	0.821198i	$0.693306\pi$
$684$	1385.71	+	450.243i	2.02589	+	0.658250i
$685$		0			0
$686$	−303.313	−	220.370i	−0.442147	−	0.321239i
$687$	−87.5581	−	269.476i	−0.127450	−	0.392250i
$688$	340.779	−	110.726i	0.495318	−	0.160939i
$689$	−12.1574	+	16.7332i	−0.0176449	+	0.0242862i
$690$		0			0
$691$	−229.580	+	706.573i	−0.332242	+	1.02254i	0.635822	+	0.771836i	$0.280661\pi$
$691$	−229.580	+	706.573i	−0.332242	+	1.02254i	−0.968064	+	0.250701i	$0.919339\pi$
$692$		−	1629.12i		−	2.35422i
$693$	44.1521	−	66.7582i	0.0637115	−	0.0963322i
$694$	−1694.64			−2.44185
$695$		0			0
$696$	340.965	−	247.726i	0.489893	−	0.355928i
$697$	−731.270	−	531.299i	−1.04917	−	0.762265i
$698$	201.839	+	621.197i	0.289168	+	0.889967i
$699$	−137.525	+	44.6846i	−0.196745	+	0.0639265i
$700$		0			0
$701$	567.996	+	781.779i	0.810265	+	1.11523i	0.991282	+	0.131754i	$0.0420608\pi$
$701$	567.996	+	781.779i	0.810265	+	1.11523i	−0.181018	+	0.983480i	$0.557939\pi$
$702$	−22.9347	+	70.5859i	−0.0326706	+	0.100550i
$703$			1661.56i			2.36353i
$704$	308.393	−	13.5748i	0.438058	−	0.0192824i
$705$		0			0
$706$	−977.348	−	317.560i	−1.38435	−	0.449801i
$707$	70.5618	−	51.2661i	0.0998045	−	0.0725122i
$708$	−404.413	−	293.823i	−0.571204	−	0.415004i
$709$	109.834	+	338.035i	0.154914	+	0.476777i	0.998152	−	0.0607633i	$-0.0193535\pi$
$709$	109.834	+	338.035i	0.154914	+	0.476777i	−0.843238	+	0.537541i	$0.819353\pi$
$710$		0			0
$711$	119.027	−	163.827i	0.167408	−	0.230418i
$712$	81.6359	+	112.362i	0.114657	+	0.157812i
$713$	−66.0020	+	203.133i	−0.0925695	+	0.284900i
$714$		−	137.948i		−	0.193205i
$715$		0			0
$716$	1972.25			2.75454
$717$	−573.551	−	186.358i	−0.799932	−	0.259914i
$718$	963.624	−	700.114i	1.34210	−	0.975089i
$719$	201.778	+	146.600i	0.280636	+	0.203894i	0.719195	−	0.694808i	$-0.244511\pi$
$719$	201.778	+	146.600i	0.280636	+	0.203894i	−0.438558	+	0.898703i	$0.644511\pi$
$720$		0			0
$721$	−115.627	+	37.5695i	−0.160370	+	0.0521075i
$722$	−586.508	+	807.259i	−0.812337	+	1.11809i
$723$	−23.6087	−	32.4946i	−0.0326538	−	0.0449441i
$724$	33.1370	−	101.985i	0.0457694	−	0.140864i
$725$		0			0
$726$	337.218	−	562.131i	0.464487	−	0.774285i
$727$	−883.791			−1.21567			−0.607834	−	0.794064i	$-0.707961\pi$
$727$	−883.791			−1.21567			−0.607834	+	0.794064i	$0.707961\pi$
$728$	14.8629	+	4.82924i	0.0204161	+	0.00663358i
$729$	−138.033	+	100.287i	−0.189346	+	0.137568i
$730$		0			0
$731$	−108.731	−	334.640i	−0.148743	−	0.457783i
$732$	−426.076	+	138.440i	−0.582071	+	0.189126i
$733$	556.173	−	765.506i	0.758763	−	1.04435i	−0.238553	−	0.971129i	$-0.576673\pi$
$733$	556.173	−	765.506i	0.758763	−	1.04435i	0.997316	−	0.0732177i	$-0.0233268\pi$
$734$	496.570	+	683.471i	0.676527	+	0.931159i
$735$		0			0
$736$			629.858i			0.855785i
$737$	168.518	+	450.233i	0.228654	+	0.610899i
$738$	917.455			1.24316
$739$	450.994	+	146.537i	0.610277	+	0.198291i	0.597818	−	0.801632i	$-0.296034\pi$
$739$	450.994	+	146.537i	0.610277	+	0.198291i	0.0124581	+	0.999922i	$0.496034\pi$
$740$		0			0
$741$	−27.3248	−	19.8527i	−0.0368756	−	0.0267917i
$742$	28.3187	+	87.1560i	0.0381654	+	0.117461i
$743$	−229.097	+	74.4381i	−0.308340	+	0.100186i	−0.459100	−	0.888385i	$-0.651828\pi$
$743$	−229.097	+	74.4381i	−0.308340	+	0.100186i	0.150760	+	0.988570i	$0.451828\pi$
$744$	94.1393	−	129.572i	0.126531	−	0.174155i
$745$		0			0
$746$	263.716	−	811.636i	0.353507	−	1.08798i
$747$		−	908.365i		−	1.21602i
$748$	97.3508	+	2211.62i	0.130148	+	2.95671i
$749$	−22.9036			−0.0305790
$750$		0			0
$751$	−312.684	+	227.179i	−0.416357	+	0.302501i	−0.776171	−	0.630523i	$-0.782840\pi$
$751$	−312.684	+	227.179i	−0.416357	+	0.302501i	0.359813	+	0.933024i	$0.382840\pi$
$752$	1140.94	+	828.939i	1.51720	+	1.10231i
$753$	176.543	+	543.343i	0.234452	+	0.721570i
$754$	49.7528	−	16.1657i	0.0659852	−	0.0214399i
$755$		0			0
$756$	132.008	+	181.693i	0.174613	+	0.240335i
$757$	−240.706	+	740.817i	−0.317974	+	0.978622i	0.656540	+	0.754292i	$0.272020\pi$
$757$	−240.706	+	740.817i	−0.317974	+	0.978622i	−0.974513	+	0.224331i	$0.927980\pi$
$758$			931.541i			1.22895i
$759$	−466.770	−	308.709i	−0.614980	−	0.406731i
$760$		0			0
$761$	286.870	+	93.2098i	0.376965	+	0.122483i	0.491370	−	0.870951i	$-0.336496\pi$
$761$	286.870	+	93.2098i	0.376965	+	0.122483i	−0.114405	+	0.993434i	$0.536496\pi$
$762$	562.163	−	408.435i	0.737747	−	0.536004i
$763$	−104.516	−	75.9352i	−0.136980	−	0.0995219i
$764$	2.48606	+	7.65131i	0.00325401	+	0.0100148i
$765$		0			0
$766$	−715.432	+	984.708i	−0.933985	+	1.28552i
$767$	−19.5410	−	26.8958i	−0.0254771	−	0.0350662i
$768$	−240.417	+	739.928i	−0.313043	+	0.963448i
$769$			1335.43i			1.73658i	0.496054	+	0.868292i	$0.334782\pi$
$769$			1335.43i			1.73658i	−0.496054	+	0.868292i	$0.665218\pi$
$770$		0			0
$771$	389.705			0.505453
$772$	−341.031	−	110.808i	−0.441750	−	0.143533i
$773$	−347.748	+	252.654i	−0.449868	+	0.326848i	−0.789544	−	0.613695i	$-0.789683\pi$
$773$	−347.748	+	252.654i	−0.449868	+	0.326848i	0.339676	+	0.940543i	$0.389683\pi$
$774$	288.930	+	209.920i	0.373295	+	0.271215i
$775$		0			0
$776$	−1039.38	+	337.715i	−1.33941	+	0.435200i
$777$	−64.0989	+	88.2245i	−0.0824953	+	0.113545i
$778$	−1320.40	−	1817.38i	−1.69718	−	2.33596i
$779$	−303.010	+	932.569i	−0.388973	+	1.19714i
$780$		0			0
$781$	−311.837	+	248.228i	−0.399279	+	0.317833i
$782$	2767.19			3.53861
$783$	383.092	+	124.474i	0.489261	+	0.158971i
$784$	−919.961	+	668.390i	−1.17342	+	0.852539i
$785$		0			0
$786$	−25.6186	−	78.8460i	−0.0325937	−	0.100313i
$787$	973.345	−	316.259i	1.23678	−	0.401854i	0.383613	−	0.923494i	$-0.374680\pi$
$787$	973.345	−	316.259i	1.23678	−	0.401854i	0.853166	+	0.521640i	$0.174680\pi$
$788$	−434.877	+	598.556i	−0.551874	+	0.759589i
$789$	259.009	+	356.495i	0.328275	+	0.451832i
$790$		0			0
$791$		−	116.210i		−	0.146915i
$792$	−749.790	−	941.926i	−0.946705	−	1.18930i
$793$	−29.7948			−0.0375723
$794$	1133.91	+	368.429i	1.42810	+	0.464017i
$795$		0			0
$796$	−547.645	−	397.888i	−0.687996	−	0.499859i
$797$	−207.308	−	638.028i	−0.260110	−	0.800537i	−0.992780	−	0.119952i	$-0.961726\pi$
$797$	−207.308	−	638.028i	−0.260110	−	0.800537i	0.732669	−	0.680585i	$-0.238274\pi$
$798$	−142.324	+	46.2437i	−0.178350	+	0.0579495i
$799$	814.005	−	1120.38i	1.01878	−	1.40223i
$800$		0			0
$801$	−17.4658	+	53.7541i	−0.0218050	+	0.0671088i
$802$			2487.78i			3.10197i
$803$	891.048	+	246.768i	1.10965	+	0.307307i
$804$	−574.369			−0.714390
$805$		0			0
$806$	16.0831	−	11.6850i	0.0199542	−	0.0144976i
$807$	267.282	+	194.191i	0.331204	+	0.240634i
$808$	−405.410	−	1247.72i	−0.501745	−	1.54421i
$809$	369.452	−	120.042i	0.456677	−	0.148383i	−0.0716398	−	0.997431i	$-0.522823\pi$
$809$	369.452	−	120.042i	0.456677	−	0.148383i	0.528317	+	0.849047i	$0.322823\pi$
$810$		0			0
$811$	589.421	+	811.268i	0.726783	+	1.00033i	0.999271	+	0.0381716i	$0.0121534\pi$
$811$	589.421	+	811.268i	0.726783	+	1.00033i	−0.272488	+	0.962159i	$0.587847\pi$
$812$	48.9174	−	150.552i	0.0602431	−	0.185409i
$813$			80.3987i			0.0988914i
$814$	1413.52	−	2137.25i	1.73651	−	2.62562i
$815$		0			0
$816$	−805.742	−	261.802i	−0.987429	−	0.320835i
$817$	−308.804	+	224.359i	−0.377973	+	0.274614i
$818$	52.6019	+	38.2175i	0.0643055	+	0.0467207i
$819$	1.96527	+	6.04847i	0.00239959	+	0.00738519i
$820$		0			0
$821$	313.012	−	430.825i	0.381257	−	0.524756i	−0.574660	−	0.818393i	$-0.694866\pi$
$821$	313.012	−	430.825i	0.381257	−	0.524756i	0.955917	+	0.293637i	$0.0948656\pi$
$822$	87.4921	+	120.423i	0.106438	+	0.146499i
$823$	279.100	−	858.981i	0.339125	−	1.04372i	−0.625529	−	0.780201i	$-0.715117\pi$
$823$	279.100	−	858.981i	0.339125	−	1.04372i	0.964654	−	0.263519i	$-0.0848831\pi$
$824$			1828.75i			2.21935i
$825$		0			0
$826$	−147.298			−0.178327
$827$	1385.51	+	450.181i	1.67535	+	0.544354i	0.984000	−	0.178166i	$-0.0570165\pi$
$827$	1385.51	+	450.181i	1.67535	+	0.544354i	0.691349	+	0.722521i	$0.257017\pi$
$828$	−1551.89	+	1127.51i	−1.87426	+	1.36173i
$829$	−685.365	−	497.947i	−0.826737	−	0.600660i	0.0918972	−	0.995768i	$-0.470707\pi$
$829$	−685.365	−	497.947i	−0.826737	−	0.600660i	−0.918634	+	0.395109i	$0.870707\pi$
$830$		0			0
$831$	−237.926	+	77.3067i	−0.286312	+	0.0930285i
$832$	−14.4174	+	19.8439i	−0.0173286	+	0.0238508i
$833$	656.349	+	903.387i	0.787934	+	1.08450i
$834$	−94.1556	+	289.781i	−0.112896	+	0.347459i
$835$		0			0
$836$	2249.13	−	841.829i	2.69035	−	1.00697i
$837$	153.072			0.182882
$838$	1422.03	+	462.044i	1.69693	+	0.551365i
$839$	−773.960	+	562.315i	−0.922480	+	0.670221i	−0.944140	−	0.329545i	$-0.893105\pi$
$839$	−773.960	+	562.315i	−0.922480	+	0.670221i	0.0216603	+	0.999765i	$0.493105\pi$
$840$		0			0
$841$	172.147	+	529.814i	0.204693	+	0.629981i
$842$	−1576.69	+	512.299i	−1.87256	+	0.608431i
$843$	458.340	−	630.850i	0.543701	−	0.748340i
$844$	679.117	+	934.724i	0.804641	+	1.10749i
$845$		0			0
$846$			1405.64i			1.66151i
$847$	−11.5914	−	131.411i	−0.0136852	−	0.155149i
$848$	562.814			0.663695
$849$	−258.868	−	84.1112i	−0.304909	−	0.0990710i
$850$		0			0
$851$	−1769.75	−	1285.80i	−2.07961	−	1.51093i
$852$	−147.154	−	452.894i	−0.172716	−	0.531566i
$853$	−1191.15	+	387.028i	−1.39643	+	0.453726i	−0.908033	−	0.418898i	$-0.862416\pi$
$853$	−1191.15	+	387.028i	−1.39643	+	0.453726i	−0.488392	+	0.872624i	$0.662416\pi$
$854$	−77.5943	+	106.799i	−0.0908598	+	0.125058i
$855$		0			0
$856$	−106.460	+	327.651i	−0.124369	+	0.382769i
$857$		−	628.293i		−	0.733131i	−0.930392	−	0.366565i	$-0.880534\pi$
$857$		−	628.293i		−	0.733131i	0.930392	−	0.366565i	$-0.119466\pi$
$858$	18.2587	+	48.7820i	0.0212805	+	0.0568555i
$859$	−196.824			−0.229132			−0.114566	−	0.993416i	$-0.536548\pi$
$859$	−196.824			−0.229132			−0.114566	+	0.993416i	$0.536548\pi$
$860$		0			0
$861$	−52.0651	+	37.8275i	−0.0604705	+	0.0439344i
$862$	−686.299	−	498.625i	−0.796170	−	0.578452i
$863$	−251.616	−	774.393i	−0.291559	−	0.897327i	−0.984356	−	0.176194i	$-0.943622\pi$
$863$	−251.616	−	774.393i	−0.291559	−	0.897327i	0.692796	−	0.721133i	$-0.256378\pi$
$864$	429.309	−	139.491i	0.496886	−	0.161448i
$865$		0			0
$866$	−200.266	−	275.643i	−0.231254	−	0.318294i
$867$	−120.876	+	372.019i	−0.139419	+	0.429088i
$868$		−	60.1563i		−	0.0693044i
$869$	−14.6777	−	333.448i	−0.0168903	−	0.383714i
$870$		0			0
$871$	−36.3293	−	11.8041i	−0.0417099	−	0.0135524i
$872$	−1572.11	+	1142.20i	−1.80288	+	1.30987i
$873$	−359.806	−	261.414i	−0.412149	−	0.299444i
$874$	−927.632	−	2854.96i	−1.06136	−	3.26654i
$875$		0			0
$876$	−649.307	+	893.695i	−0.741218	+	1.02020i
$877$	−338.015	−	465.237i	−0.385422	−	0.530487i	0.571589	−	0.820540i	$-0.306327\pi$
$877$	−338.015	−	465.237i	−0.385422	−	0.530487i	−0.957011	+	0.290053i	$0.906327\pi$
$878$	822.598	−	2531.70i	0.936900	−	2.88348i
$879$			86.8641i			0.0988215i
$880$		0			0
$881$	513.793			0.583193			0.291596	−	0.956541i	$-0.405814\pi$
$881$	513.793			0.583193			0.291596	+	0.956541i	$0.405814\pi$
$882$	−1077.92	−	350.238i	−1.22213	−	0.397095i
$883$	−235.619	+	171.187i	−0.266839	+	0.193870i	−0.713156	−	0.701005i	$-0.752735\pi$
$883$	−235.619	+	171.187i	−0.266839	+	0.193870i	0.446318	+	0.894875i	$0.352735\pi$
$884$	−142.309	−	103.393i	−0.160983	−	0.116961i
$885$		0			0
$886$	156.548	−	50.8654i	0.176690	−	0.0574102i
$887$	683.839	−	941.224i	0.770958	−	1.06113i	−0.225265	−	0.974297i	$-0.572325\pi$
$887$	683.839	−	941.224i	0.770958	−	1.06113i	0.996223	−	0.0868346i	$-0.0276752\pi$
$888$	964.163	+	1327.06i	1.08577	+	1.49443i
$889$	43.2132	−	132.996i	0.0486087	−	0.149602i
$890$		0			0
$891$	69.2967	−	250.222i	0.0777741	−	0.280833i
$892$	−1729.63			−1.93905
$893$	−1428.79	−	464.243i	−1.59999	−	0.519869i
$894$	1039.65	−	755.350i	1.16292	−	0.844911i
$895$		0			0
$896$	59.0302	+	181.676i	0.0658820	+	0.202764i
$897$	42.2906	−	13.7410i	0.0471467	−	0.0153189i
$898$	−101.374	+	139.530i	−0.112889	+	0.155379i
$899$	−63.4184	−	87.2879i	−0.0705432	−	0.0970944i
$900$		0			0
$901$		−	552.674i		−	0.613401i
$902$	1183.11	−	941.778i	1.31165	−	1.04410i
$903$	−25.0519			−0.0277429
$904$	−1662.45	−	540.162i	−1.83899	−	0.597525i
$905$		0			0
$906$	206.141	+	149.770i	0.227529	+	0.165309i
$907$	−72.5322	−	223.231i	−0.0799694	−	0.246120i	0.903077	−	0.429479i	$-0.141303\pi$
$907$	−72.5322	−	223.231i	−0.0799694	−	0.246120i	−0.983046	+	0.183359i	$0.941303\pi$
$908$	61.0296	−	19.8297i	0.0672132	−	0.0218389i
$909$	313.815	−	431.929i	0.345231	−	0.475169i
$910$		0			0
$911$	−173.440	+	533.795i	−0.190385	+	0.585944i	−0.999999	−	0.00101779i	$-0.999676\pi$
$911$	−173.440	+	533.795i	−0.190385	+	0.585944i	0.809615	+	0.586962i	$0.199676\pi$
$912$			919.061i			1.00774i
$913$	−932.448	−	1171.39i	−1.02130	−	1.28301i
$914$	−1475.91			−1.61479
$915$		0			0
$916$	−1295.09	+	940.938i	−1.41385	+	1.02723i
$917$	−13.4977	−	9.80667i	−0.0147194	−	0.0106943i
$918$	−612.834	−	1886.11i	−0.667575	−	2.05458i
$919$	−761.551	+	247.443i	−0.828673	+	0.269252i	−0.692487	−	0.721431i	$-0.743485\pi$
$919$	−761.551	+	247.443i	−0.828673	+	0.269252i	−0.136187	+	0.990683i	$0.543485\pi$
$920$		0			0
$921$	383.350	+	527.636i	0.416233	+	0.572895i
$922$	772.765	−	2378.33i	0.838140	−	2.57953i
$923$		−	31.6702i		−	0.0343122i
$924$	151.898	+	42.0668i	0.164392	+	0.0455269i
$925$		0			0
$926$	1711.07	+	555.960i	1.84781	+	0.600389i
$927$	−602.079	+	437.436i	−0.649492	+	0.471884i
$928$	−257.408	−	187.018i	−0.277379	−	0.201528i
$929$	113.874	+	350.469i	0.122577	+	0.377254i	0.993452	−	0.114251i	$-0.0364469\pi$
$929$	113.874	+	350.469i	0.122577	+	0.377254i	−0.870875	+	0.491505i	$0.836447\pi$
$930$		0			0
$931$	712.015	−	980.004i	0.764785	−	1.05264i
$932$	480.201	+	660.939i	0.515237	+	0.709162i
$933$	−47.0025	+	144.659i	−0.0503778	+	0.155047i
$934$			1276.42i			1.36662i
$935$		0			0
$936$	95.6620			0.102203
$937$	−33.4113	−	10.8560i	−0.0356577	−	0.0115859i	0.291134	−	0.956682i	$-0.405968\pi$
$937$	−33.4113	−	10.8560i	−0.0356577	−	0.0115859i	−0.326792	+	0.945096i	$0.605968\pi$
$938$	−136.924	+	99.4810i	−0.145974	+	0.106057i
$939$	−65.0612	−	47.2697i	−0.0692877	−	0.0503405i
$940$		0			0
$941$	−897.547	+	291.631i	−0.953823	+	0.309916i	−0.744268	−	0.667881i	$-0.767201\pi$
$941$	−897.547	+	291.631i	−0.953823	+	0.309916i	−0.209555	+	0.977797i	$0.567201\pi$
$942$	464.811	−	639.757i	0.493430	−	0.679148i
$943$	−758.806	−	1044.41i	−0.804672	−	1.10754i
$944$	−279.546	+	860.355i	−0.296129	+	0.911393i
$945$		0			0
$946$	588.078	−	25.8860i	0.621647	−	0.0273636i
$947$	337.731			0.356633			0.178316	−	0.983973i	$-0.442935\pi$
$947$	337.731			0.356633			0.178316	+	0.983973i	$0.442935\pi$
$948$	379.261	+	123.229i	0.400064	+	0.129989i
$949$	−59.4359	+	43.1827i	−0.0626301	+	0.0455034i
$950$		0			0
$951$	−153.195	−	471.485i	−0.161088	−	0.495778i
$952$	−397.147	+	129.041i	−0.417172	+	0.135547i
$953$	619.393	−	852.521i	0.649940	−	0.894566i	−0.349156	−	0.937064i	$-0.613532\pi$
$953$	619.393	−	852.521i	0.649940	−	0.894566i	0.999097	+	0.0424986i	$0.0135318\pi$
$954$	329.725	+	453.828i	0.345624	+	0.475711i
$955$		0			0
$956$			3407.17i			3.56399i
$957$	264.755	−	99.0955i	0.276651	−	0.103548i
$958$	1912.77			1.99663
$959$	28.4896	+	9.25682i	0.0297076	+	0.00965257i
$960$		0			0
$961$	744.295	+	540.762i	0.774500	+	0.562707i
$962$	62.9178	+	193.641i	0.0654031	+	0.201290i
$963$	−133.338	+	43.3241i	−0.138461	+	0.0449887i
$964$	−133.383	+	183.586i	−0.138364	+	0.190442i
$965$		0			0
$966$	60.8822	−	187.376i	0.0630250	−	0.193971i
$967$			200.406i			0.207246i	0.994617	+	0.103623i	$0.0330435\pi$
$967$			200.406i			0.207246i	−0.994617	+	0.103623i	$0.966957\pi$
$968$	−1933.80	−	445.001i	−1.99772	−	0.459712i
$969$	902.503			0.931376
$970$		0			0
$971$	253.043	−	183.846i	0.260600	−	0.189337i	−0.449812	−	0.893124i	$-0.648509\pi$
$971$	253.043	−	183.846i	0.260600	−	0.189337i	0.710412	+	0.703787i	$0.248509\pi$
$972$	1750.83	+	1272.05i	1.80126	+	1.30869i
$973$	18.9485	+	58.3175i	0.0194743	+	0.0599358i
$974$	−2233.64	+	725.752i	−2.29326	+	0.745126i
$975$		0			0
$976$	476.545	+	655.907i	0.488263	+	0.672036i
$977$	151.887	−	467.459i	0.155462	−	0.478464i	−0.842745	−	0.538313i	$-0.819062\pi$
$977$	151.887	−	467.459i	0.155462	−	0.478464i	0.998207	+	0.0598491i	$0.0190620\pi$
$978$			436.353i			0.446168i
$979$	32.6561	+	87.2479i	0.0333566	+	0.0891194i
$980$		0			0
$981$	−752.096	−	244.371i	−0.766663	−	0.249104i
$982$	194.829	−	141.551i	0.198400	−	0.144146i
$983$	703.172	+	510.884i	0.715332	+	0.519719i	0.884889	−	0.465801i	$-0.154234\pi$
$983$	703.172	+	510.884i	0.715332	+	0.519719i	−0.169557	+	0.985520i	$0.554234\pi$
$984$	299.138	+	920.653i	0.304002	+	0.935623i
$985$		0			0
$986$	−821.635	+	1130.88i	−0.833301	+	1.14694i
$987$	−57.9557	−	79.7692i	−0.0587190	−	0.0808198i
$988$	−58.9673	+	181.483i	−0.0596835	+	0.183687i
$989$		−	502.531i		−	0.508120i
$990$		0			0
$991$	−901.175			−0.909360			−0.454680	−	0.890655i	$-0.650246\pi$
$991$	−901.175			−0.909360			−0.454680	+	0.890655i	$0.650246\pi$
$992$	−114.993	−	37.3634i	−0.115920	−	0.0376647i
$993$	−423.288	+	307.537i	−0.426272	+	0.309705i
$994$	−113.522	−	82.4783i	−0.114207	−	0.0829761i
$995$		0			0
$996$	1701.26	−	552.773i	1.70809	−	0.554993i
$997$	748.492	−	1030.21i	0.750744	−	1.03331i	−0.247184	−	0.968969i	$-0.579505\pi$
$997$	748.492	−	1030.21i	0.750744	−	1.03331i	0.997928	−	0.0643420i	$-0.0204949\pi$
$998$	806.058	+	1109.44i	0.807673	+	1.11167i
$999$	−484.460	+	1491.02i	−0.484945	+	1.49251i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	275.3.x.j.101.10		40
5.2	odd	4		55.3.h.a.24.1	✓	40
5.3	odd	4		55.3.h.a.24.10	yes	40
5.4	even	2	inner	275.3.x.j.101.1		40
11.6	odd	10	inner	275.3.x.j.226.10		40
55.7	even	20		605.3.d.b.604.38		40
55.17	even	20		55.3.h.a.39.10	yes	40
55.18	even	20		605.3.d.b.604.3		40
55.28	even	20		55.3.h.a.39.1	yes	40
55.37	odd	20		605.3.d.b.604.4		40
55.39	odd	10	inner	275.3.x.j.226.1		40
55.48	odd	20		605.3.d.b.604.37		40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
55.3.h.a.24.1	✓	40	5.2	odd	4
55.3.h.a.24.10	yes	40	5.3	odd	4
55.3.h.a.39.1	yes	40	55.28	even	20
55.3.h.a.39.10	yes	40	55.17	even	20
275.3.x.j.101.1		40	5.4	even	2	inner
275.3.x.j.101.10		40	1.1	even	1	trivial
275.3.x.j.226.1		40	55.39	odd	10	inner
275.3.x.j.226.10		40	11.6	odd	10	inner
605.3.d.b.604.3		40	55.18	even	20
605.3.d.b.604.4		40	55.37	odd	20
605.3.d.b.604.37		40	55.48	odd	20
605.3.d.b.604.38		40	55.7	even	20

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:	\( N \)	\(=\)	\( 275 = 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	275.x (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(3.37818 + 1.09764i) q^{2} +(-1.23390 + 0.896484i) q^{3} +(6.97124 + 5.06490i) q^{4} +(-5.15237 + 1.67411i) q^{6} +(-0.640839 + 0.882039i) q^{7} +(9.63938 + 13.2675i) q^{8} +(-2.06232 + 6.34716i) q^{9} +(3.85595 + 10.3020i) q^{11} -13.1425 q^{12} +(-0.831271 - 0.270096i) q^{13} +(-3.13303 + 2.27628i) q^{14} +(7.34959 + 22.6197i) q^{16} +(22.2122 - 7.21718i) q^{17} +(-13.9338 + 19.1782i) q^{18} +(-14.8922 - 20.4973i) q^{19} -1.66285i q^{21} +(1.71822 + 39.0346i) q^{22} +33.3562 q^{23} +(-23.7881 - 7.72924i) q^{24} +(-2.51172 - 1.82487i) q^{26} +(-7.38721 - 22.7355i) q^{27} +(-8.93489 + 2.90312i) q^{28} +(-9.90414 + 13.6319i) q^{29} +(-1.97870 + 6.08982i) q^{31} +18.8828i q^{32} +(-13.9935 - 9.25491i) q^{33} +82.9587 q^{34} +(-46.5246 + 33.8021i) q^{36} +(-53.0561 - 38.5475i) q^{37} +(-27.8099 - 85.5899i) q^{38} +(1.26785 - 0.411949i) q^{39} +(-22.7486 - 31.3107i) q^{41} +(1.82521 - 5.61743i) q^{42} -15.0656i q^{43} +(-25.2980 + 91.3479i) q^{44} +(112.683 + 36.6131i) q^{46} +(47.9712 - 34.8531i) q^{47} +(-29.3469 - 21.3218i) q^{48} +(14.7745 + 45.4713i) q^{49} +(-20.9376 + 28.8182i) q^{51} +(-4.42698 - 6.09322i) q^{52} +(7.31251 - 22.5056i) q^{53} -84.9132i q^{54} -17.8797 q^{56} +(36.7511 + 11.9411i) q^{57} +(-48.4209 + 35.1798i) q^{58} +(30.7715 + 22.3568i) q^{59} +(32.4198 - 10.5338i) q^{61} +(-13.3688 + 18.4006i) q^{62} +(-4.27683 - 5.88655i) q^{63} +(8.67190 - 26.6894i) q^{64} +(-37.1140 - 46.6246i) q^{66} +43.7033 q^{67} +(191.401 + 62.1899i) q^{68} +(-41.1584 + 29.9033i) q^{69} +(11.1969 + 34.4604i) q^{71} +(-104.090 + 33.8209i) q^{72} +(49.4053 - 68.0006i) q^{73} +(-136.922 - 188.457i) q^{74} -218.319i q^{76} +(-11.5578 - 3.20083i) q^{77} +4.73519 q^{78} +(-28.8577 - 9.37643i) q^{79} +(-19.0958 - 13.8739i) q^{81} +(-42.4810 - 130.743i) q^{82} +(-129.448 + 42.0601i) q^{83} +(8.42220 - 11.5922i) q^{84} +(16.5366 - 50.8943i) q^{86} -25.6994i q^{87} +(-99.5127 + 150.464i) q^{88} +8.46901 q^{89} +(0.770946 - 0.560125i) q^{91} +(232.534 + 168.946i) q^{92} +(-3.01790 - 9.28813i) q^{93} +(200.312 - 65.0852i) q^{94} +(-16.9281 - 23.2995i) q^{96} +(-20.5930 + 63.3788i) q^{97} +169.827i q^{98} +(-73.3407 + 3.22831i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 22 q^{4} - 10 q^{6} + 4 q^{9} - 16 q^{11} - 38 q^{14} - 138 q^{16} + 10 q^{19} - 30 q^{24} + 172 q^{26} + 10 q^{29} + 128 q^{31} + 112 q^{34} + 248 q^{36} + 170 q^{39} + 50 q^{41} - 422 q^{44} + 10 q^{46}+ \cdots - 882 q^{99}+O(q^{100}) \) 40 * q + 22 * q^4 - 10 * q^6 + 4 * q^9 - 16 * q^11 - 38 * q^14 - 138 * q^16 + 10 * q^19 - 30 * q^24 + 172 * q^26 + 10 * q^29 + 128 * q^31 + 112 * q^34 + 248 * q^36 + 170 * q^39 + 50 * q^41 - 422 * q^44 + 10 * q^46 - 18 * q^49 - 270 * q^51 + 144 * q^56 + 254 * q^59 - 300 * q^61 + 834 * q^64 - 1470 * q^66 - 246 * q^69 + 260 * q^71 - 620 * q^74 - 270 * q^79 + 606 * q^81 - 80 * q^84 + 602 * q^86 + 812 * q^89 + 582 * q^91 - 840 * q^94 + 1610 * q^96 - 882 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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