LMFDB - Embedded newform 300.3.l.g.107.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [300,3,Mod(107,300)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(300, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 2, 1]))

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

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

chi := DirichletCharacter("300.107");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 300 = 2^{2} \cdot 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	300.l (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$8.17440793081$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$20$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 60)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			107.18
Character	$\chi$	$=$	300.107
Dual form			300.3.l.g.143.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.81610 - 0.837725i) q^{2} +(-2.69303 + 1.32197i) q^{3} +(2.59643 - 3.04278i) q^{4} +(-3.78336 + 4.65685i) q^{6} +(-3.54241 + 3.54241i) q^{7} +(2.16636 - 7.70110i) q^{8} +(5.50478 - 7.12021i) q^{9} +O(q^{10})$	\(q+(1.81610 - 0.837725i) q^{2} +(-2.69303 + 1.32197i) q^{3} +(2.59643 - 3.04278i) q^{4} +(-3.78336 + 4.65685i) q^{6} +(-3.54241 + 3.54241i) q^{7} +(2.16636 - 7.70110i) q^{8} +(5.50478 - 7.12021i) q^{9} +16.8337 q^{11} +(-2.96979 + 11.6267i) q^{12} +(8.64592 - 8.64592i) q^{13} +(-3.46580 + 9.40093i) q^{14} +(-2.51707 - 15.8008i) q^{16} +(9.72710 - 9.72710i) q^{17} +(4.03246 - 17.5425i) q^{18} -4.78419 q^{19} +(4.85684 - 14.2228i) q^{21} +(30.5716 - 14.1020i) q^{22} +(13.5716 - 13.5716i) q^{23} +(4.34655 + 23.6031i) q^{24} +(8.45895 - 22.9448i) q^{26} +(-5.41182 + 26.4521i) q^{27} +(1.58116 + 19.9764i) q^{28} +14.8741 q^{29} +14.0641i q^{31} +(-17.8080 - 26.5872i) q^{32} +(-45.3336 + 22.2536i) q^{33} +(9.51674 - 25.8140i) q^{34} +(-7.37245 - 35.2370i) q^{36} +(10.1182 + 10.1182i) q^{37} +(-8.68857 + 4.00784i) q^{38} +(-11.8540 + 34.7134i) q^{39} +6.08509i q^{41} +(-3.09427 - 29.8987i) q^{42} +(-57.2366 - 57.2366i) q^{43} +(43.7075 - 51.2213i) q^{44} +(13.2781 - 36.0167i) q^{46} +(17.6247 + 17.6247i) q^{47} +(27.6667 + 39.2244i) q^{48} +23.9027i q^{49} +(-13.3364 + 39.0543i) q^{51} +(-3.85911 - 48.7562i) q^{52} +(16.2015 + 16.2015i) q^{53} +(12.3312 + 52.5732i) q^{54} +(19.6063 + 34.9546i) q^{56} +(12.8840 - 6.32456i) q^{57} +(27.0128 - 12.4604i) q^{58} -4.37150i q^{59} +8.52269 q^{61} +(11.7818 + 25.5418i) q^{62} +(5.72249 + 44.7229i) q^{63} +(-54.6137 - 33.3667i) q^{64} +(-63.6878 + 78.3919i) q^{66} +(-53.9714 + 53.9714i) q^{67} +(-4.34170 - 54.8532i) q^{68} +(-18.6074 + 54.4900i) q^{69} +36.6679 q^{71} +(-42.9080 - 57.8178i) q^{72} +(12.6800 - 12.6800i) q^{73} +(26.8519 + 9.89937i) q^{74} +(-12.4218 + 14.5573i) q^{76} +(-59.6318 + 59.6318i) q^{77} +(7.55214 + 72.9733i) q^{78} -88.4346 q^{79} +(-20.3947 - 78.3904i) q^{81} +(5.09763 + 11.0511i) q^{82} +(-63.7372 + 63.7372i) q^{83} +(-30.6663 - 51.7068i) q^{84} +(-151.896 - 55.9988i) q^{86} +(-40.0563 + 19.6631i) q^{87} +(36.4679 - 129.638i) q^{88} -115.022 q^{89} +61.2548i q^{91} +(-6.05770 - 76.5332i) q^{92} +(-18.5923 - 37.8749i) q^{93} +(46.7728 + 17.2435i) q^{94} +(83.1047 + 48.0583i) q^{96} +(85.3544 + 85.3544i) q^{97} +(20.0239 + 43.4096i) q^{98} +(92.6658 - 119.859i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 4 q^{6}+O(q^{10}) $ 40 * q - 4 * q^6	$ 40 q - 4 q^{6} + 20 q^{12} + 8 q^{13} - 36 q^{16} + 24 q^{18} - 24 q^{21} + 76 q^{22} + 84 q^{28} + 40 q^{33} + 172 q^{36} + 40 q^{37} - 236 q^{42} + 240 q^{46} - 196 q^{48} - 304 q^{52} + 72 q^{57} - 180 q^{58} + 48 q^{61} - 552 q^{66} + 600 q^{72} - 104 q^{73} - 736 q^{76} + 408 q^{78} + 72 q^{81} + 720 q^{82} + 580 q^{88} - 368 q^{93} + 884 q^{96} - 72 q^{97}+O(q^{100}) $ 40 * q - 4 * q^6 + 20 * q^12 + 8 * q^13 - 36 * q^16 + 24 * q^18 - 24 * q^21 + 76 * q^22 + 84 * q^28 + 40 * q^33 + 172 * q^36 + 40 * q^37 - 236 * q^42 + 240 * q^46 - 196 * q^48 - 304 * q^52 + 72 * q^57 - 180 * q^58 + 48 * q^61 - 552 * q^66 + 600 * q^72 - 104 * q^73 - 736 * q^76 + 408 * q^78 + 72 * q^81 + 720 * q^82 + 580 * q^88 - 368 * q^93 + 884 * q^96 - 72 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/300\mathbb{Z}\right)^\times$.

$n$	$101$	$151$	$277$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$	1.81610	−	0.837725i	0.908050	−	0.418863i
$2$	1.81610	−	0.837725i	0.908050	−	0.418863i
$3$	−2.69303	+	1.32197i	−0.897676	+	0.440657i
$3$	−2.69303	+	1.32197i	−0.897676	+	0.440657i
$4$	2.59643	−	3.04278i	0.649108	−	0.760696i
$5$		0			0
$5$		0			0
$6$	−3.78336	+	4.65685i	−0.630559	+	0.776141i
$7$	−3.54241	+	3.54241i	−0.506059	+	0.506059i	−0.913314	−	0.407256i	$-0.866486\pi$
$7$	−3.54241	+	3.54241i	−0.506059	+	0.506059i	0.407256	+	0.913314i	$0.366486\pi$
$8$	2.16636	−	7.70110i	0.270795	−	0.962637i
$9$	5.50478	−	7.12021i	0.611643	−	0.791134i
$10$		0			0
$11$	16.8337			1.53034			0.765168	−	0.643831i	$-0.222656\pi$
$11$	16.8337			1.53034			0.765168	+	0.643831i	$0.222656\pi$
$12$	−2.96979	+	11.6267i	−0.247483	+	0.968892i
$13$	8.64592	−	8.64592i	0.665071	−	0.665071i	−0.291500	−	0.956571i	$-0.594154\pi$
$13$	8.64592	−	8.64592i	0.665071	−	0.665071i	0.956571	+	0.291500i	$0.0941543\pi$
$14$	−3.46580	+	9.40093i	−0.247557	+	0.671495i
$15$		0			0
$16$	−2.51707	−	15.8008i	−0.157317	−	0.987548i
$17$	9.72710	−	9.72710i	0.572182	−	0.572182i	−0.360556	−	0.932738i	$-0.617413\pi$
$17$	9.72710	−	9.72710i	0.572182	−	0.572182i	0.932738	+	0.360556i	$0.117413\pi$
$18$	4.03246	−	17.5425i	0.224025	−	0.974583i
$19$	−4.78419			−0.251800			−0.125900	−	0.992043i	$-0.540182\pi$
$19$	−4.78419			−0.251800			−0.125900	+	0.992043i	$0.540182\pi$
$20$		0			0
$21$	4.85684	−	14.2228i	0.231278	−	0.677275i
$22$	30.5716	−	14.1020i	1.38962	−	0.641000i
$23$	13.5716	−	13.5716i	0.590070	−	0.590070i	−0.347580	−	0.937650i	$-0.612997\pi$
$23$	13.5716	−	13.5716i	0.590070	−	0.590070i	0.937650	+	0.347580i	$0.112997\pi$
$24$	4.34655	+	23.6031i	0.181106	+	0.983464i
$25$		0			0
$26$	8.45895	−	22.9448i	0.325344	−	0.882491i
$27$	−5.41182	+	26.4521i	−0.200438	+	0.979706i
$28$	1.58116	+	19.9764i	0.0564699	+	0.713444i
$29$	14.8741			0.512899			0.256449	−	0.966558i	$-0.417447\pi$
$29$	14.8741			0.512899			0.256449	+	0.966558i	$0.417447\pi$
$30$		0			0
$31$			14.0641i			0.453680i	0.973932	+	0.226840i	$0.0728395\pi$
$31$			14.0641i			0.453680i	−0.973932	+	0.226840i	$0.927161\pi$
$32$	−17.8080	−	26.5872i	−0.556498	−	0.830849i
$33$	−45.3336	+	22.2536i	−1.37374	+	0.674353i
$34$	9.51674	−	25.8140i	0.279904	−	0.759235i
$35$		0			0
$36$	−7.37245	−	35.2370i	−0.204790	−	0.978806i
$37$	10.1182	+	10.1182i	0.273465	+	0.273465i	0.830493	−	0.557029i	$-0.188059\pi$
$37$	10.1182	+	10.1182i	0.273465	+	0.273465i	−0.557029	+	0.830493i	$0.688059\pi$
$38$	−8.68857	+	4.00784i	−0.228647	+	0.105469i
$39$	−11.8540	+	34.7134i	−0.303950	+	0.890086i
$40$		0			0
$41$			6.08509i			0.148417i	0.997243	+	0.0742084i	$0.0236430\pi$
$41$			6.08509i			0.148417i	−0.997243	+	0.0742084i	$0.976357\pi$
$42$	−3.09427	−	29.8987i	−0.0736730	−	0.711873i
$43$	−57.2366	−	57.2366i	−1.33108	−	1.33108i	−0.904401	−	0.426683i	$-0.859682\pi$
$43$	−57.2366	−	57.2366i	−1.33108	−	1.33108i	−0.426683	−	0.904401i	$-0.640318\pi$
$44$	43.7075	−	51.2213i	0.993353	−	1.16412i
$45$		0			0
$46$	13.2781	−	36.0167i	0.288654	−	0.782971i
$47$	17.6247	+	17.6247i	0.374993	+	0.374993i	0.869292	−	0.494299i	$-0.164575\pi$
$47$	17.6247	+	17.6247i	0.374993	+	0.374993i	−0.494299	+	0.869292i	$0.664575\pi$
$48$	27.6667	+	39.2244i	0.576390	+	0.817175i
$49$			23.9027i			0.487809i
$50$		0			0
$51$	−13.3364	+	39.0543i	−0.261498	+	0.765770i
$52$	−3.85911	−	48.7562i	−0.0742137	−	0.937620i
$53$	16.2015	+	16.2015i	0.305688	+	0.305688i	0.843234	−	0.537546i	$-0.180649\pi$
$53$	16.2015	+	16.2015i	0.305688	+	0.305688i	−0.537546	+	0.843234i	$0.680649\pi$
$54$	12.3312	+	52.5732i	0.228355	+	0.973578i
$55$		0			0
$56$	19.6063	+	34.9546i	0.350112	+	0.624189i
$57$	12.8840	−	6.32456i	0.226034	−	0.110957i
$58$	27.0128	−	12.4604i	0.465738	−	0.214834i
$59$		−	4.37150i		−	0.0740931i	−0.999314	−	0.0370466i	$-0.988205\pi$
$59$		−	4.37150i		−	0.0740931i	0.999314	−	0.0370466i	$-0.0117950\pi$
$60$		0			0
$61$	8.52269			0.139716			0.0698582	−	0.997557i	$-0.477745\pi$
$61$	8.52269			0.139716			0.0698582	+	0.997557i	$0.477745\pi$
$62$	11.7818	+	25.5418i	0.190030	+	0.411964i
$63$	5.72249	+	44.7229i	0.0908332	+	0.709887i
$64$	−54.6137	−	33.3667i	−0.853340	−	0.521355i
$65$		0			0
$66$	−63.6878	+	78.3919i	−0.964967	+	1.18776i
$67$	−53.9714	+	53.9714i	−0.805543	+	0.805543i	−0.983956	−	0.178413i	$-0.942904\pi$
$67$	−53.9714	+	53.9714i	−0.805543	+	0.805543i	0.178413	+	0.983956i	$0.442904\pi$
$68$	−4.34170	−	54.8532i	−0.0638485	−	0.806665i
$69$	−18.6074	+	54.4900i	−0.269673	+	0.789710i
$70$		0			0
$71$	36.6679			0.516449			0.258225	−	0.966085i	$-0.416863\pi$
$71$	36.6679			0.516449			0.258225	+	0.966085i	$0.416863\pi$
$72$	−42.9080	−	57.8178i	−0.595945	−	0.803025i
$73$	12.6800	−	12.6800i	0.173699	−	0.173699i	−0.614903	−	0.788602i	$-0.710805\pi$
$73$	12.6800	−	12.6800i	0.173699	−	0.173699i	0.788602	+	0.614903i	$0.210805\pi$
$74$	26.8519	+	9.89937i	0.362863	+	0.133775i
$75$		0			0
$76$	−12.4218	+	14.5573i	−0.163445	+	0.191543i
$77$	−59.6318	+	59.6318i	−0.774439	+	0.774439i
$78$	7.55214	+	72.9733i	0.0968223	+	0.935555i
$79$	−88.4346			−1.11943			−0.559713	−	0.828687i	$-0.689088\pi$
$79$	−88.4346			−1.11943			−0.559713	+	0.828687i	$0.689088\pi$
$80$		0			0
$81$	−20.3947	−	78.3904i	−0.251786	−	0.967783i
$82$	5.09763	+	11.0511i	0.0621663	+	0.134770i
$83$	−63.7372	+	63.7372i	−0.767918	+	0.767918i	−0.977740	−	0.209822i	$-0.932712\pi$
$83$	−63.7372	+	63.7372i	−0.767918	+	0.767918i	0.209822	+	0.977740i	$0.432712\pi$
$84$	−30.6663	−	51.7068i	−0.365076	−	0.615557i
$85$		0			0
$86$	−151.896	−	55.9988i	−1.76623	−	0.651149i
$87$	−40.0563	+	19.6631i	−0.460417	+	0.226013i
$88$	36.4679	−	129.638i	0.414408	−	1.47316i
$89$	−115.022			−1.29238			−0.646190	−	0.763177i	$-0.723639\pi$
$89$	−115.022			−1.29238			−0.646190	+	0.763177i	$0.723639\pi$
$90$		0			0
$91$			61.2548i			0.673130i
$92$	−6.05770	−	76.5332i	−0.0658445	−	0.831883i
$93$	−18.5923	−	37.8749i	−0.199917	−	0.407258i
$94$	46.7728	+	17.2435i	0.497583	+	0.183442i
$95$		0			0
$96$	83.1047	+	48.0583i	0.865674	+	0.500607i
$97$	85.3544	+	85.3544i	0.879942	+	0.879942i	0.993528	−	0.113586i	$-0.0362338\pi$
$97$	85.3544	+	85.3544i	0.879942	+	0.879942i	−0.113586	+	0.993528i	$0.536234\pi$
$98$	20.0239	+	43.4096i	0.204325	+	0.442955i
$99$	92.6658	−	119.859i	0.936018	−	1.21070i
$100$		0			0
$101$			158.917i			1.57343i	0.617313	+	0.786717i	$0.288221\pi$
$101$			158.917i			1.57343i	−0.617313	+	0.786717i	$0.711779\pi$
$102$	8.49654	+	82.0987i	0.0832994	+	0.804889i
$103$	28.6266	+	28.6266i	0.277928	+	0.277928i	0.832282	−	0.554353i	$-0.187034\pi$
$103$	28.6266	+	28.6266i	0.277928	+	0.277928i	−0.554353	+	0.832282i	$0.687034\pi$
$104$	−47.8529	−	85.3133i	−0.460124	−	0.820320i
$105$		0			0
$106$	42.9959	+	15.8511i	0.405622	+	0.149539i
$107$	−28.1808	−	28.1808i	−0.263372	−	0.263372i	0.563050	−	0.826423i	$-0.309628\pi$
$107$	−28.1808	−	28.1808i	−0.263372	−	0.263372i	−0.826423	+	0.563050i	$0.809628\pi$
$108$	66.4365	+	85.1480i	0.615153	+	0.788408i
$109$		−	159.944i		−	1.46737i	−0.679489	−	0.733686i	$-0.737798\pi$
$109$		−	159.944i		−	1.46737i	0.679489	−	0.733686i	$-0.262202\pi$
$110$		0			0
$111$	−40.6245	−	13.8726i	−0.365986	−	0.124978i
$112$	64.8893	+	47.0563i	0.579369	+	0.420146i
$113$	101.260	+	101.260i	0.896110	+	0.896110i	0.995089	−	0.0989792i	$-0.0315577\pi$
$113$	101.260	+	101.260i	0.896110	+	0.896110i	−0.0989792	+	0.995089i	$0.531558\pi$
$114$	18.1003	−	22.2793i	0.158775	−	0.195432i
$115$		0			0
$116$	38.6195	−	45.2586i	0.332927	−	0.390160i
$117$	−13.9668	−	109.155i	−0.119375	−	0.932946i
$118$	−3.66211	−	7.93907i	−0.0310348	−	0.0672803i
$119$			68.9147i			0.579115i
$120$		0			0
$121$	162.373			1.34193
$122$	15.4781	−	7.13968i	0.126869	−	0.0585219i
$123$	−8.04432	−	16.3873i	−0.0654009	−	0.133230i
$124$	42.7940	+	36.5165i	0.345113	+	0.294488i
$125$		0			0
$126$	47.8581	+	76.4273i	0.379826	+	0.606566i
$127$	94.0845	−	94.0845i	0.740823	−	0.740823i	−0.231914	−	0.972736i	$-0.574499\pi$
$127$	94.0845	−	94.0845i	0.740823	−	0.740823i	0.972736	+	0.231914i	$0.0744987\pi$
$128$	−127.136	−	14.8460i	−0.993251	−	0.115985i
$129$	229.805	+	78.4746i	1.78143	+	0.608330i
$130$		0			0
$131$	−145.148			−1.10800			−0.554002	−	0.832515i	$-0.686900\pi$
$131$	−145.148			−1.10800			−0.554002	+	0.832515i	$0.686900\pi$
$132$	−49.9925	+	195.720i	−0.378731	+	1.48273i
$133$	16.9476	−	16.9476i	0.127425	−	0.127425i
$134$	−52.8042	+	143.231i	−0.394061	+	1.06888i
$135$		0			0
$136$	−53.8369	−	95.9817i	−0.395859	−	0.705748i
$137$	60.1022	−	60.1022i	0.438702	−	0.438702i	−0.452873	−	0.891575i	$-0.649601\pi$
$137$	60.1022	−	60.1022i	0.438702	−	0.438702i	0.891575	+	0.452873i	$0.149601\pi$
$138$	11.8547	+	114.547i	0.0859035	+	0.830051i
$139$	12.5985			0.0906366			0.0453183	−	0.998973i	$-0.485570\pi$
$139$	12.5985			0.0906366			0.0453183	+	0.998973i	$0.485570\pi$
$140$		0			0
$141$	−70.7630	−	24.1644i	−0.501865	−	0.171379i
$142$	66.5925	−	30.7176i	0.468961	−	0.216321i
$143$	145.543	−	145.543i	1.01778	−	1.01778i
$144$	−126.361	−	69.0578i	−0.877505	−	0.479568i
$145$		0			0
$146$	12.4058	−	33.6506i	0.0849713	−	0.230483i
$147$	−31.5986	−	64.3705i	−0.214957	−	0.437895i
$148$	57.0587	−	4.51626i	0.385531	−	0.0305153i
$149$	−25.9233			−0.173982			−0.0869911	−	0.996209i	$-0.527725\pi$
$149$	−25.9233			−0.173982			−0.0869911	+	0.996209i	$0.527725\pi$
$150$		0			0
$151$		−	200.379i		−	1.32701i	−0.748171	−	0.663506i	$-0.769068\pi$
$151$		−	200.379i		−	1.32701i	0.748171	−	0.663506i	$-0.230932\pi$
$152$	−10.3643	+	36.8435i	−0.0681862	+	0.242392i
$153$	−15.7134	−	122.805i	−0.102702	−	0.802644i
$154$	−58.3422	+	158.252i	−0.378846	+	1.02761i
$155$		0			0
$156$	74.8470	+	126.200i	0.479789	+	0.808976i
$157$	−139.992	−	139.992i	−0.891666	−	0.891666i	0.103014	−	0.994680i	$-0.467151\pi$
$157$	−139.992	−	139.992i	−0.891666	−	0.891666i	−0.994680	+	0.103014i	$0.967151\pi$
$158$	−160.606	+	74.0839i	−1.01649	+	0.468885i
$159$	−65.0489	−	22.2131i	−0.409113	−	0.139705i
$160$		0			0
$161$			96.1524i			0.597220i
$162$	−102.708	−	125.280i	−0.634003	−	0.773331i
$163$	58.6324	+	58.6324i	0.359708	+	0.359708i	0.863705	−	0.503997i	$-0.168138\pi$
$163$	58.6324	+	58.6324i	0.359708	+	0.359708i	−0.503997	+	0.863705i	$0.668138\pi$
$164$	18.5156	+	15.7995i	0.112900	+	0.0963386i
$165$		0			0
$166$	−62.3588	+	169.147i	−0.375655	+	1.01896i
$167$	84.2556	+	84.2556i	0.504524	+	0.504524i	0.912841	−	0.408316i	$-0.133884\pi$
$167$	84.2556	+	84.2556i	0.504524	+	0.504524i	−0.408316	+	0.912841i	$0.633884\pi$
$168$	−99.0092	−	68.2147i	−0.589341	−	0.406040i
$169$			19.4961i			0.115361i
$170$		0			0
$171$	−26.3359	+	34.0644i	−0.154011	+	0.199207i
$172$	−322.770	+	25.5476i	−1.87657	+	0.148533i
$173$	−51.2341	−	51.2341i	−0.296151	−	0.296151i	0.543353	−	0.839504i	$-0.317154\pi$
$173$	−51.2341	−	51.2341i	−0.296151	−	0.296151i	−0.839504	+	0.543353i	$0.817154\pi$
$174$	−56.2739	+	69.2663i	−0.323413	+	0.398082i
$175$		0			0
$176$	−42.3716	−	265.985i	−0.240747	−	1.51128i
$177$	5.77899	+	11.7726i	0.0326497	+	0.0665116i
$178$	−208.891	+	96.3566i	−1.17354	+	0.541329i
$179$			27.2276i			0.152109i	0.997104	+	0.0760547i	$0.0242324\pi$
$179$			27.2276i			0.152109i	−0.997104	+	0.0760547i	$0.975768\pi$
$180$		0			0
$181$	−276.624			−1.52831			−0.764155	−	0.645033i	$-0.776844\pi$
$181$	−276.624			−1.52831			−0.764155	+	0.645033i	$0.776844\pi$
$182$	51.3147	+	111.245i	0.281949	+	0.611235i
$183$	−22.9518	+	11.2668i	−0.125420	+	0.0615670i
$184$	−75.1152	−	133.917i	−0.408235	−	0.727811i
$185$		0			0
$186$	−65.4943	−	53.2094i	−0.352120	−	0.286072i
$187$	163.743	−	163.743i	0.875630	−	0.875630i
$188$	99.3894	−	7.86679i	0.528667	−	0.0418446i
$189$	−74.5332	−	112.875i	−0.394356	−	0.597222i
$190$		0			0
$191$	340.010			1.78016			0.890078	−	0.455807i	$-0.150649\pi$
$191$	340.010			1.78016			0.890078	+	0.455807i	$0.150649\pi$
$192$	191.186	+	17.6597i	0.995761	+	0.0919779i
$193$	−100.981	+	100.981i	−0.523220	+	0.523220i	−0.918542	−	0.395322i	$-0.870633\pi$
$193$	−100.981	+	100.981i	−0.523220	+	0.523220i	0.395322	+	0.918542i	$0.370633\pi$
$194$	226.515	+	83.5085i	1.16761	+	0.430456i
$195$		0			0
$196$	72.7306	+	62.0617i	0.371075	+	0.316641i
$197$	−225.584	+	225.584i	−1.14510	+	1.14510i	−0.157595	+	0.987504i	$0.550374\pi$
$197$	−225.584	+	225.584i	−1.14510	+	1.14510i	−0.987504	+	0.157595i	$0.949626\pi$
$198$	67.8811	−	295.305i	0.342834	−	1.49144i
$199$	286.672			1.44056			0.720281	−	0.693682i	$-0.244013\pi$
$199$	286.672			1.44056			0.720281	+	0.693682i	$0.244013\pi$
$200$		0			0
$201$	73.9977	−	216.695i	0.368148	−	1.07808i
$202$	133.129	+	288.609i	0.659053	+	1.42876i
$203$	−52.6900	+	52.6900i	−0.259557	+	0.259557i
$204$	84.2067	+	141.982i	0.412778	+	0.695988i
$205$		0			0
$206$	75.9701	+	28.0076i	0.368787	+	0.135959i
$207$	−21.9239	−	171.341i	−0.105912	−	0.827736i
$208$	−158.375	−	114.850i	−0.761416	−	0.552163i
$209$	−80.5356			−0.385338
$210$		0			0
$211$		−	183.842i		−	0.871288i	−0.900119	−	0.435644i	$-0.856521\pi$
$211$		−	183.842i		−	0.871288i	0.900119	−	0.435644i	$-0.143479\pi$
$212$	91.3637	−	7.23155i	0.430961	−	0.0341111i
$213$	−98.7476	+	48.4739i	−0.463604	+	0.227577i
$214$	−74.7870	−	27.5714i	−0.349472	−	0.128838i
$215$		0			0
$216$	191.986	+	98.9818i	0.888824	+	0.458249i
$217$	−49.8207	−	49.8207i	−0.229589	−	0.229589i
$218$	−133.989	−	290.473i	−0.614627	−	1.33245i
$219$	−17.3850	+	50.9103i	−0.0793836	+	0.232467i
$220$		0			0
$221$		−	168.199i		−	0.761083i
$222$	−85.3995	+	8.83816i	−0.384683	+	0.0398115i
$223$	7.02165	+	7.02165i	0.0314872	+	0.0314872i	0.722675	−	0.691188i	$-0.242912\pi$
$223$	7.02165	+	7.02165i	0.0314872	+	0.0314872i	−0.691188	+	0.722675i	$0.742912\pi$
$224$	157.266	+	31.0995i	0.702079	+	0.138837i
$225$		0			0
$226$	268.727	+	99.0706i	1.18906	+	0.438366i
$227$	−36.6684	−	36.6684i	−0.161535	−	0.161535i	0.621711	−	0.783246i	$-0.286438\pi$
$227$	−36.6684	−	36.6684i	−0.161535	−	0.161535i	−0.783246	+	0.621711i	$0.786438\pi$
$228$	14.2081	−	55.6244i	0.0623160	−	0.243967i
$229$			270.126i			1.17959i	0.807554	+	0.589794i	$0.200791\pi$
$229$			270.126i			1.17959i	−0.807554	+	0.589794i	$0.799209\pi$
$230$		0			0
$231$	81.7585	−	239.422i	0.353933	−	1.03646i
$232$	32.2226	−	114.547i	0.138891	−	0.493735i
$233$	55.2135	+	55.2135i	0.236968	+	0.236968i	0.815593	−	0.578625i	$-0.196411\pi$
$233$	55.2135	+	55.2135i	0.236968	+	0.236968i	−0.578625	+	0.815593i	$0.696411\pi$
$234$	−116.807	−	186.535i	−0.499174	−	0.797160i
$235$		0			0
$236$	−13.3015	−	11.3503i	−0.0563624	−	0.0480945i
$237$	238.157	−	116.908i	1.00488	−	0.493283i
$238$	57.7316	+	125.156i	0.242570	+	0.525865i
$239$			46.1374i			0.193044i	0.995331	+	0.0965218i	$0.0307718\pi$
$239$			46.1374i			0.193044i	−0.995331	+	0.0965218i	$0.969228\pi$
$240$		0			0
$241$	−212.165			−0.880351			−0.440176	−	0.897912i	$-0.645084\pi$
$241$	−212.165			−0.880351			−0.440176	+	0.897912i	$0.645084\pi$
$242$	294.885	−	136.024i	1.21853	−	0.562082i
$243$	158.553	+	184.146i	0.652483	+	0.757803i
$244$	22.1286	−	25.9327i	0.0906910	−	0.106282i
$245$		0			0
$246$	−28.3373	−	23.0221i	−0.115192	−	0.0935856i
$247$	−41.3638	+	41.3638i	−0.167465	+	0.167465i
$248$	108.309	+	30.4679i	0.436729	+	0.122855i
$249$	87.3872	−	255.905i	0.350953	−	1.02773i
$250$		0			0
$251$	−159.687			−0.636203			−0.318101	−	0.948057i	$-0.603045\pi$
$251$	−159.687			−0.636203			−0.318101	+	0.948057i	$0.603045\pi$
$252$	150.940	+	98.7077i	0.598969	+	0.391697i
$253$	228.460	−	228.460i	0.903004	−	0.903004i
$254$	92.0498	−	249.684i	0.362401	−	0.983007i
$255$		0			0
$256$	−243.329	+	79.5433i	−0.950503	+	0.310716i
$257$	98.0877	−	98.0877i	0.381664	−	0.381664i	−0.490037	−	0.871701i	$-0.663017\pi$
$257$	98.0877	−	98.0877i	0.381664	−	0.381664i	0.871701	+	0.490037i	$0.163017\pi$
$258$	483.089	−	49.9957i	1.87244	−	0.193782i
$259$	−71.6855			−0.276778
$260$		0			0
$261$	81.8785	−	105.906i	0.313711	−	0.405772i
$262$	−263.604	+	121.595i	−1.00612	+	0.464101i
$263$	141.919	−	141.919i	0.539614	−	0.539614i	−0.383802	−	0.923416i	$-0.625385\pi$
$263$	141.919	−	141.919i	0.539614	−	0.539614i	0.923416	+	0.383802i	$0.125385\pi$
$264$	73.1685	+	397.328i	0.277153	+	1.50503i
$265$		0			0
$266$	16.5811	−	44.9759i	0.0623348	−	0.169082i
$267$	309.757	−	152.055i	1.16014	−	0.569496i
$268$	24.0902	+	304.356i	0.0898887	+	1.13566i
$269$	−0.543377			−0.00201999			−0.00100999	−	0.999999i	$-0.500321\pi$
$269$	−0.543377			−0.00201999			−0.00100999	+	0.999999i	$0.500321\pi$
$270$		0			0
$271$			362.830i			1.33886i	0.742877	+	0.669428i	$0.233461\pi$
$271$			362.830i			1.33886i	−0.742877	+	0.669428i	$0.766539\pi$
$272$	−178.179	−	129.212i	−0.655071	−	0.475044i
$273$	−80.9771	−	164.961i	−0.296619	−	0.604252i
$274$	58.8025	−	159.501i	0.214608	−	0.582120i
$275$		0			0
$276$	117.488	+	198.098i	0.425682	+	0.717746i
$277$	79.2266	+	79.2266i	0.286016	+	0.286016i	0.835503	−	0.549486i	$-0.185177\pi$
$277$	79.2266	+	79.2266i	0.286016	+	0.286016i	−0.549486	+	0.835503i	$0.685177\pi$
$278$	22.8801	−	10.5541i	0.0823025	−	0.0379643i
$279$	100.139	+	77.4197i	0.358922	+	0.277490i
$280$		0			0
$281$			318.753i			1.13435i	0.823597	+	0.567176i	$0.191964\pi$
$281$			318.753i			1.13435i	−0.823597	+	0.567176i	$0.808036\pi$
$282$	−148.756	+	15.3950i	−0.527503	+	0.0545922i
$283$	223.036	+	223.036i	0.788112	+	0.788112i	0.981185	−	0.193072i	$-0.0618451\pi$
$283$	223.036	+	223.036i	0.788112	+	0.788112i	−0.193072	+	0.981185i	$0.561845\pi$
$284$	95.2057	−	111.572i	0.335231	−	0.392861i
$285$		0			0
$286$	142.395	−	386.245i	0.497885	−	1.35051i
$287$	−21.5559	−	21.5559i	−0.0751076	−	0.0751076i
$288$	−287.335	−	19.5603i	−0.997691	−	0.0679176i
$289$			99.7672i			0.345215i
$290$		0			0
$291$	−342.698	−	117.026i	−1.17765	−	0.402150i
$292$	−5.65974	−	71.5054i	−0.0193827	−	0.244881i
$293$	−75.3066	−	75.3066i	−0.257019	−	0.257019i	0.566822	−	0.823841i	$-0.308173\pi$
$293$	−75.3066	−	75.3066i	−0.257019	−	0.257019i	−0.823841	+	0.566822i	$0.808173\pi$
$294$	−111.311	−	90.4323i	−0.378609	−	0.307593i
$295$		0			0
$296$	99.8408	−	56.0015i	0.337300	−	0.189194i
$297$	−91.1009	+	445.286i	−0.306737	+	1.49928i
$298$	−47.0794	+	21.7166i	−0.157984	+	0.0728746i
$299$		−	234.678i		−	0.784876i
$300$		0			0
$301$	405.511			1.34721
$302$	−167.862	−	363.908i	−0.555836	−	1.20499i
$303$	−210.084	−	427.967i	−0.693345	−	1.41243i
$304$	12.0421	+	75.5939i	0.0396123	+	0.248664i
$305$		0			0
$306$	−131.413	−	209.862i	−0.429456	−	0.685823i
$307$	−330.497	+	330.497i	−1.07654	+	1.07654i	−0.0797218	+	0.996817i	$0.525403\pi$
$307$	−330.497	+	330.497i	−1.07654	+	1.07654i	−0.996817	+	0.0797218i	$0.974597\pi$
$308$	26.6167	+	336.277i	0.0864179	+	1.09181i
$309$	−114.936	−	39.2487i	−0.371961	−	0.127018i
$310$		0			0
$311$	−26.5302			−0.0853063			−0.0426531	−	0.999090i	$-0.513581\pi$
$311$	−26.5302			−0.0853063			−0.0426531	+	0.999090i	$0.513581\pi$
$312$	241.651	+	166.491i	0.774522	+	0.533624i
$313$	−131.851	+	131.851i	−0.421248	+	0.421248i	−0.885633	−	0.464385i	$-0.846275\pi$
$313$	−131.851	+	131.851i	−0.421248	+	0.421248i	0.464385	+	0.885633i	$0.346275\pi$
$314$	−371.513	−	136.964i	−1.18316	−	0.436191i
$315$		0			0
$316$	−229.614	+	269.087i	−0.726628	+	0.851542i
$317$	66.6091	−	66.6091i	0.210123	−	0.210123i	−0.594197	−	0.804320i	$-0.702530\pi$
$317$	66.6091	−	66.6091i	0.210123	−	0.210123i	0.804320	+	0.594197i	$0.202530\pi$
$318$	−136.744	+	14.1519i	−0.430012	+	0.0445027i
$319$	250.385			0.784907
$320$		0			0
$321$	113.146	+	38.6375i	0.352480	+	0.120366i
$322$	80.5492	+	174.622i	0.250153	+	0.542305i
$323$	−46.5363	+	46.5363i	−0.144075	+	0.144075i
$324$	−291.479	−	141.479i	−0.899625	−	0.436663i
$325$		0			0
$326$	155.600	+	57.3644i	0.477301	+	0.175965i
$327$	211.441	+	430.732i	0.646608	+	1.31722i
$328$	46.8619	+	13.1825i	0.142872	+	0.0401906i
$329$	−124.868			−0.379537
$330$		0			0
$331$			284.948i			0.860871i	0.902621	+	0.430436i	$0.141640\pi$
$331$			284.948i			0.860871i	−0.902621	+	0.430436i	$0.858360\pi$
$332$	28.4491	+	359.428i	0.0856902	+	1.08261i
$333$	127.742	−	16.3452i	0.383610	−	0.0490845i
$334$	223.599	+	82.4335i	0.669460	+	0.246807i
$335$		0			0
$336$	−236.956	−	40.9421i	−0.705225	−	0.121852i
$337$	−294.164	−	294.164i	−0.872889	−	0.872889i	0.119897	−	0.992786i	$-0.461744\pi$
$337$	−294.164	−	294.164i	−0.872889	−	0.872889i	−0.992786	+	0.119897i	$0.961744\pi$
$338$	16.3324	+	35.4068i	0.0483206	+	0.104754i
$339$	−406.561	−	138.834i	−1.19929	−	0.409539i
$340$		0			0
$341$			236.750i			0.694283i
$342$	−19.2921	+	83.9267i	−0.0564095	+	0.245400i
$343$	−258.251	−	258.251i	−0.752919	−	0.752919i
$344$	−564.780	+	316.789i	−1.64180	+	0.920899i
$345$		0			0
$346$	−135.966	−	50.1262i	−0.392966	−	0.144873i
$347$	−274.053	−	274.053i	−0.789779	−	0.789779i	0.191679	−	0.981458i	$-0.438607\pi$
$347$	−274.053	−	274.053i	−0.789779	−	0.789779i	−0.981458	+	0.191679i	$0.938607\pi$
$348$	−44.1729	+	172.936i	−0.126934	+	0.496944i
$349$		−	129.175i		−	0.370128i	−0.982726	−	0.185064i	$-0.940751\pi$
$349$		−	129.175i		−	0.370128i	0.982726	−	0.185064i	$-0.0592492\pi$
$350$		0			0
$351$	181.912	+	275.493i	0.518269	+	0.784880i
$352$	−299.773	−	447.560i	−0.851629	−	1.27148i
$353$	381.746	+	381.746i	1.08143	+	1.08143i	0.996376	+	0.0850569i	$0.0271072\pi$
$353$	381.746	+	381.746i	1.08143	+	1.08143i	0.0850569	+	0.996376i	$0.472893\pi$
$354$	20.3574	+	16.5389i	0.0575067	+	0.0467201i
$355$		0			0
$356$	−298.646	+	349.986i	−0.838894	+	0.983108i
$357$	−91.1033	−	185.589i	−0.255191	−	0.519858i
$358$	22.8092	+	49.4480i	0.0637129	+	0.138123i
$359$			209.720i			0.584178i	0.956391	+	0.292089i	$0.0943503\pi$
$359$			209.720i			0.584178i	−0.956391	+	0.292089i	$0.905650\pi$
$360$		0			0
$361$	−338.112			−0.936597
$362$	−502.377	+	231.735i	−1.38778	+	0.640151i
$363$	−437.275	+	214.652i	−1.20461	+	0.591329i
$364$	186.385	+	159.044i	0.512047	+	0.436934i
$365$		0			0
$366$	−32.2444	+	39.6889i	−0.0880994	+	0.108440i
$367$	−4.27652	+	4.27652i	−0.0116527	+	0.0116527i	−0.712909	−	0.701256i	$-0.752623\pi$
$367$	−4.27652	+	4.27652i	−0.0116527	+	0.0116527i	0.701256	+	0.712909i	$0.252623\pi$
$368$	−248.602	−	180.281i	−0.675550	−	0.489894i
$369$	43.3271	+	33.4971i	0.117418	+	0.0907781i
$370$		0			0
$371$	−114.785			−0.309393
$372$	−163.519	−	41.7674i	−0.439567	−	0.112278i
$373$	−363.822	+	363.822i	−0.975394	+	0.975394i	−0.999704	−	0.0243109i	$-0.992261\pi$
$373$	−363.822	+	363.822i	−0.975394	+	0.975394i	0.0243109	+	0.999704i	$0.492261\pi$
$374$	160.202	−	434.545i	0.428347	−	1.16188i
$375$		0			0
$376$	173.911	−	97.5478i	0.462529	−	0.259436i
$377$	128.600	−	128.600i	0.341114	−	0.341114i
$378$	−229.918	−	142.554i	−0.608248	−	0.377127i
$379$	−732.379			−1.93240			−0.966199	−	0.257796i	$-0.917004\pi$
$379$	−732.379			−1.93240			−0.966199	+	0.257796i	$0.917004\pi$
$380$		0			0
$381$	−128.995	+	377.749i	−0.338570	+	0.991467i
$382$	617.492	−	284.835i	1.61647	−	0.745641i
$383$	−343.246	+	343.246i	−0.896203	+	0.896203i	−0.995098	−	0.0988948i	$-0.968469\pi$
$383$	−343.246	+	343.246i	−0.896203	+	0.896203i	0.0988948	+	0.995098i	$0.468469\pi$
$384$	362.007	−	128.090i	0.942727	−	0.333567i
$385$		0			0
$386$	−98.7977	+	267.987i	−0.255952	+	0.694267i
$387$	−722.612	+	92.4613i	−1.86721	+	0.238918i
$388$	481.332	−	38.0980i	1.24055	−	0.0981907i
$389$	600.575			1.54389			0.771947	−	0.635687i	$-0.219283\pi$
$389$	600.575			1.54389			0.771947	+	0.635687i	$0.219283\pi$
$390$		0			0
$391$		−	264.025i		−	0.675255i
$392$	184.077	+	51.7819i	0.469583	+	0.132097i
$393$	390.889	−	191.882i	0.994628	−	0.488250i
$394$	−220.706	+	598.662i	−0.560168	+	1.51945i
$395$		0			0
$396$	−124.105	−	593.169i	−0.313398	−	1.49790i
$397$	295.285	+	295.285i	0.743792	+	0.743792i	0.973306	−	0.229513i	$-0.0737135\pi$
$397$	295.285	+	295.285i	0.743792	+	0.743792i	−0.229513	+	0.973306i	$0.573713\pi$
$398$	520.625	−	240.152i	1.30810	−	0.603398i
$399$	−23.2361	+	68.0445i	−0.0582357	+	0.170537i
$400$		0			0
$401$		−	300.412i		−	0.749157i	−0.927195	−	0.374578i	$-0.877787\pi$
$401$		−	300.412i		−	0.749157i	0.927195	−	0.374578i	$-0.122213\pi$
$402$	−47.1436	−	455.529i	−0.117273	−	1.13316i
$403$	121.597	+	121.597i	0.301729	+	0.301729i
$404$	483.550	+	412.617i	1.19691	+	1.02133i
$405$		0			0
$406$	−51.5506	+	139.830i	−0.126972	+	0.344409i
$407$	170.326	+	170.326i	0.418492	+	0.418492i
$408$	271.869	+	187.311i	0.666346	+	0.459094i
$409$			53.8159i			0.131579i	0.997834	+	0.0657896i	$0.0209566\pi$
$409$			53.8159i			0.131579i	−0.997834	+	0.0657896i	$0.979043\pi$
$410$		0			0
$411$	−82.4035	+	241.310i	−0.200495	+	0.587130i
$412$	161.432	−	12.7775i	0.391825	−	0.0310134i
$413$	15.4856	+	15.4856i	0.0374955	+	0.0374955i
$414$	−183.353	−	292.807i	−0.442881	−	0.707263i
$415$		0			0
$416$	−383.837	−	75.9043i	−0.922684	−	0.182462i
$417$	−33.9281	+	16.6548i	−0.0813623	+	0.0399397i
$418$	−146.261	+	67.4667i	−0.349906	+	0.161404i
$419$		−	582.593i		−	1.39044i	−0.718799	−	0.695218i	$-0.755308\pi$
$419$		−	582.593i		−	1.39044i	0.718799	−	0.695218i	$-0.244692\pi$
$420$		0			0
$421$	486.678			1.15600			0.578002	−	0.816035i	$-0.303833\pi$
$421$	486.678			1.15600			0.578002	+	0.816035i	$0.303833\pi$
$422$	−154.009	−	333.875i	−0.364950	−	0.791173i
$423$	222.511	−	28.4713i	0.526032	−	0.0673080i
$424$	159.868	−	89.6709i	0.377046	−	0.211488i
$425$		0			0
$426$	−138.728	+	170.757i	−0.325652	+	0.400837i
$427$	−30.1909	+	30.1909i	−0.0707046	+	0.0707046i
$428$	−158.918	+	12.5785i	−0.371304	+	0.0293891i
$429$	−199.547	+	584.354i	−0.465145	+	1.36213i
$430$		0			0
$431$	554.639			1.28686			0.643432	−	0.765503i	$-0.277510\pi$
$431$	554.639			1.28686			0.643432	+	0.765503i	$0.277510\pi$
$432$	431.585	+	18.9292i	0.999040	+	0.0438177i
$433$	−152.907	+	152.907i	−0.353135	+	0.353135i	−0.861275	−	0.508140i	$-0.830333\pi$
$433$	−152.907	+	152.907i	−0.353135	+	0.353135i	0.508140	+	0.861275i	$0.330333\pi$
$434$	−132.216	−	48.7433i	−0.304644	−	0.112312i
$435$		0			0
$436$	−486.674	−	415.283i	−1.11622	−	0.952483i
$437$	−64.9292	+	64.9292i	−0.148579	+	0.148579i
$438$	11.0759	+	107.022i	0.0252874	+	0.244342i
$439$	218.824			0.498461			0.249231	−	0.968444i	$-0.419822\pi$
$439$	218.824			0.498461			0.249231	+	0.968444i	$0.419822\pi$
$440$		0			0
$441$	170.192	+	131.579i	0.385923	+	0.298365i
$442$	−140.905	−	305.467i	−0.318789	−	0.691101i
$443$	39.9964	−	39.9964i	0.0902853	−	0.0902853i	−0.660522	−	0.750807i	$-0.729665\pi$
$443$	39.9964	−	39.9964i	0.0902853	−	0.0902853i	0.750807	+	0.660522i	$0.229665\pi$
$444$	−147.690	+	87.5923i	−0.332635	+	0.197280i
$445$		0			0
$446$	18.6342	+	6.86980i	0.0417808	+	0.0154031i
$447$	69.8122	−	34.2699i	0.156180	−	0.0766665i
$448$	311.663	−	75.2655i	0.695676	−	0.168003i
$449$	−236.471			−0.526660			−0.263330	−	0.964706i	$-0.584821\pi$
$449$	−236.471			−0.526660			−0.263330	+	0.964706i	$0.584821\pi$
$450$		0			0
$451$			102.435i			0.227128i
$452$	571.030	−	45.1977i	1.26334	−	0.0999949i
$453$	264.895	+	539.626i	0.584757	+	1.19123i
$454$	−97.3115	−	35.8754i	−0.214343	−	0.0790208i
$455$		0			0
$456$	−20.7947	−	112.922i	−0.0456025	−	0.247636i
$457$	242.806	+	242.806i	0.531304	+	0.531304i	0.920960	−	0.389657i	$-0.127406\pi$
$457$	242.806	+	242.806i	0.531304	+	0.531304i	−0.389657	+	0.920960i	$0.627406\pi$
$458$	226.291	+	490.575i	0.494085	+	1.07112i
$459$	204.661	+	309.943i	0.445884	+	0.675257i
$460$		0			0
$461$		−	640.776i		−	1.38997i	−0.719024	−	0.694985i	$-0.755411\pi$
$461$		−	640.776i		−	1.38997i	0.719024	−	0.694985i	$-0.244589\pi$
$462$	−52.0879	−	503.305i	−0.112744	−	1.08940i
$463$	−162.780	−	162.780i	−0.351577	−	0.351577i	0.509119	−	0.860696i	$-0.329971\pi$
$463$	−162.780	−	162.780i	−0.351577	−	0.351577i	−0.860696	+	0.509119i	$0.829971\pi$
$464$	−37.4391	−	235.022i	−0.0806876	−	0.506512i
$465$		0			0
$466$	146.527	+	54.0195i	0.314436	+	0.115922i
$467$	424.962	+	424.962i	0.909984	+	0.909984i	0.996270	−	0.0862867i	$-0.0275001\pi$
$467$	424.962	+	424.962i	0.909984	+	0.909984i	−0.0862867	+	0.996270i	$0.527500\pi$
$468$	−368.398	−	240.915i	−0.787175	−	0.514775i
$469$		−	382.377i		−	0.815304i
$470$		0			0
$471$	562.066	+	191.936i	1.19335	+	0.407508i
$472$	−33.6653	−	9.47025i	−0.0713248	−	0.0200641i
$473$	−963.503	−	963.503i	−2.03700	−	2.03700i
$474$	334.579	−	411.826i	0.705864	−	0.868832i
$475$		0			0
$476$	209.693	+	178.932i	0.440531	+	0.375909i
$477$	204.544	−	26.1723i	0.428813	−	0.0548685i
$478$	38.6505	+	83.7902i	0.0808588	+	0.175293i
$479$			439.071i			0.916641i	0.888787	+	0.458321i	$0.151549\pi$
$479$			439.071i			0.916641i	−0.888787	+	0.458321i	$0.848451\pi$
$480$		0			0
$481$	174.962			0.363747
$482$	−385.312	+	177.736i	−0.799403	+	0.368746i
$483$	−127.111	−	258.941i	−0.263169	−	0.536109i
$484$	421.591	−	494.066i	0.871055	−	1.02080i
$485$		0			0
$486$	442.213	+	201.604i	0.909902	+	0.414823i
$487$	−308.231	+	308.231i	−0.632918	+	0.632918i	−0.948799	−	0.315881i	$-0.897700\pi$
$487$	−308.231	+	308.231i	−0.632918	+	0.632918i	0.315881	+	0.948799i	$0.397700\pi$
$488$	18.4633	−	65.6341i	0.0378345	−	0.134496i
$489$	−235.409	−	80.3883i	−0.481409	−	0.164393i
$490$		0			0
$491$	−751.660			−1.53088			−0.765438	−	0.643509i	$-0.777478\pi$
$491$	−751.660			−1.53088			−0.765438	+	0.643509i	$0.777478\pi$
$492$	−70.7496	−	18.0714i	−0.143800	−	0.0367306i
$493$	144.681	−	144.681i	0.293472	−	0.293472i
$494$	−40.4692	+	109.772i	−0.0819215	+	0.222211i
$495$		0			0
$496$	222.223	−	35.4003i	0.448031	−	0.0713715i
$497$	−129.893	+	129.893i	−0.261353	+	0.261353i
$498$	−55.6739	−	537.955i	−0.111795	−	1.08023i
$499$	304.485			0.610191			0.305096	−	0.952322i	$-0.401312\pi$
$499$	304.485			0.610191			0.305096	+	0.952322i	$0.401312\pi$
$500$		0			0
$501$	−338.286	−	115.519i	−0.675221	−	0.230577i
$502$	−290.007	+	133.774i	−0.577704	+	0.266481i
$503$	230.058	−	230.058i	0.457372	−	0.457372i	−0.440420	−	0.897792i	$-0.645170\pi$
$503$	230.058	−	230.058i	0.457372	−	0.457372i	0.897792	+	0.440420i	$0.145170\pi$
$504$	356.812	+	52.8166i	0.707961	+	0.104795i
$505$		0			0
$506$	223.519	−	606.293i	0.441738	−	1.19821i
$507$	−25.7733	−	52.5035i	−0.0508348	−	0.103557i
$508$	−41.9947	−	530.563i	−0.0826667	−	1.04442i
$509$	−98.9386			−0.194378			−0.0971892	−	0.995266i	$-0.530985\pi$
$509$	−98.9386			−0.194378			−0.0971892	+	0.995266i	$0.530985\pi$
$510$		0			0
$511$			89.8357i			0.175804i
$512$	−375.274	+	348.301i	−0.732956	+	0.680276i
$513$	25.8912	−	126.552i	0.0504702	−	0.246690i
$514$	95.9665	−	260.307i	0.186705	−	0.506435i
$515$		0			0
$516$	835.454	−	495.493i	1.61910	−	0.960257i
$517$	296.688	+	296.688i	0.573865	+	0.573865i
$518$	−130.188	+	60.0528i	−0.251328	+	0.115932i
$519$	205.705	+	70.2448i	0.396349	+	0.135346i
$520$		0			0
$521$		−	485.997i		−	0.932816i	−0.884570	−	0.466408i	$-0.845548\pi$
$521$		−	485.997i		−	0.932816i	0.884570	−	0.466408i	$-0.154452\pi$
$522$	59.9791	−	260.928i	0.114902	−	0.499863i
$523$	−303.922	−	303.922i	−0.581112	−	0.581112i	0.354096	−	0.935209i	$-0.384788\pi$
$523$	−303.922	−	303.922i	−0.581112	−	0.581112i	−0.935209	+	0.354096i	$0.884788\pi$
$524$	−376.868	+	441.655i	−0.719214	+	0.842854i
$525$		0			0
$526$	138.849	−	376.627i	0.263972	−	0.716021i
$527$	136.803	+	136.803i	0.259588	+	0.259588i
$528$	465.733	+	660.291i	0.882069	+	1.25055i
$529$			160.623i			0.303636i
$530$		0			0
$531$	−31.1260	−	24.0641i	−0.0586176	−	0.0453185i
$532$	−7.56456	−	95.5710i	−0.0142191	−	0.179645i
$533$	52.6112	+	52.6112i	0.0987077	+	0.0987077i
$534$	435.168	−	535.639i	0.814922	−	1.00307i
$535$		0			0
$536$	298.717	+	532.560i	0.557308	+	0.993583i
$537$	−35.9941	−	73.3246i	−0.0670281	−	0.136545i
$538$	−0.986826	+	0.455200i	−0.00183425	+	0.000846097i
$539$			402.370i			0.746512i
$540$		0			0
$541$	−388.275			−0.717700			−0.358850	−	0.933395i	$-0.616831\pi$
$541$	−388.275			−0.717700			−0.358850	+	0.933395i	$0.616831\pi$
$542$	303.952	+	658.936i	0.560797	+	1.21575i
$543$	744.956	−	365.689i	1.37193	−	0.673460i
$544$	−431.835	−	85.3962i	−0.793815	−	0.156978i
$545$		0			0
$546$	−285.254	−	231.749i	−0.522444	−	0.424448i
$547$	169.325	−	169.325i	0.309551	−	0.309551i	−0.535184	−	0.844735i	$-0.679758\pi$
$547$	169.325	−	169.325i	0.309551	−	0.309551i	0.844735	+	0.535184i	$0.179758\pi$
$548$	−26.8267	−	338.929i	−0.0489538	−	0.618484i
$549$	46.9156	−	60.6834i	0.0854565	−	0.110534i
$550$		0			0
$551$	−71.1604			−0.129148
$552$	379.322	+	261.343i	0.687177	+	0.473447i
$553$	313.272	−	313.272i	0.566495	−	0.566495i
$554$	210.253	+	77.5132i	0.379519	+	0.139916i
$555$		0			0
$556$	32.7111	−	38.3345i	0.0588330	−	0.0689469i
$557$	310.481	−	310.481i	0.557417	−	0.557417i	−0.371155	−	0.928571i	$-0.621038\pi$
$557$	310.481	−	310.481i	0.557417	−	0.557417i	0.928571	+	0.371155i	$0.121038\pi$
$558$	246.719	+	56.7128i	0.442149	+	0.101636i
$559$	−989.727			−1.77053
$560$		0			0
$561$	−224.501	+	657.427i	−0.400179	+	1.17188i
$562$	267.027	+	578.887i	0.475137	+	1.03005i
$563$	−234.187	+	234.187i	−0.415962	+	0.415962i	−0.883809	−	0.467847i	$-0.845030\pi$
$563$	−234.187	+	234.187i	−0.415962	+	0.415962i	0.467847	+	0.883809i	$0.345030\pi$
$564$	−257.259	+	152.575i	−0.456132	+	0.270524i
$565$		0			0
$566$	591.898	+	218.212i	1.04576	+	0.385534i
$567$	349.937	+	205.445i	0.617173	+	0.362336i
$568$	79.4360	−	282.383i	0.139852	−	0.497153i
$569$	386.708			0.679627			0.339813	−	0.940493i	$-0.389636\pi$
$569$	386.708			0.679627			0.339813	+	0.940493i	$0.389636\pi$
$570$		0			0
$571$			556.152i			0.973996i	0.873403	+	0.486998i	$0.161908\pi$
$571$			556.152i			0.973996i	−0.873403	+	0.486998i	$0.838092\pi$
$572$	−64.9631	−	820.747i	−0.113572	−	1.43487i
$573$	−915.656	+	449.483i	−1.59800	+	0.784439i
$574$	−57.2055	−	21.0897i	−0.0996612	−	0.0367417i
$575$		0			0
$576$	−538.215	+	205.184i	−0.934401	+	0.356223i
$577$	−695.792	−	695.792i	−1.20588	−	1.20588i	−0.972350	−	0.233530i	$-0.924972\pi$
$577$	−695.792	−	695.792i	−1.20588	−	1.20588i	−0.233530	−	0.972350i	$-0.575028\pi$
$578$	83.5775	+	181.187i	0.144598	+	0.313473i
$579$	138.451	−	405.440i	0.239121	−	0.700242i
$580$		0			0
$581$		−	451.566i		−	0.777223i
$582$	−720.408	+	74.5563i	−1.23781	+	0.128104i
$583$	272.731	+	272.731i	0.467806	+	0.467806i
$584$	−70.1805	−	125.120i	−0.120172	−	0.214246i
$585$		0			0
$586$	−199.850	−	73.6780i	−0.341042	−	0.125730i
$587$	−241.691	−	241.691i	−0.411740	−	0.411740i	0.470604	−	0.882344i	$-0.344036\pi$
$587$	−241.691	−	241.691i	−0.411740	−	0.411740i	−0.882344	+	0.470604i	$0.844036\pi$
$588$	−277.909	−	70.9859i	−0.472635	−	0.120724i
$589$		−	67.2853i		−	0.114236i
$590$		0			0
$591$	309.289	−	905.721i	0.523331	−	1.53252i
$592$	134.407	−	185.343i	0.227039	−	0.313080i
$593$	−109.471	−	109.471i	−0.184605	−	0.184605i	0.608754	−	0.793359i	$-0.291670\pi$
$593$	−109.471	−	109.471i	−0.184605	−	0.184605i	−0.793359	+	0.608754i	$0.791670\pi$
$594$	207.579	+	885.001i	0.349459	+	1.48990i
$595$		0			0
$596$	−67.3082	+	78.8791i	−0.112933	+	0.132348i
$597$	−772.015	+	378.972i	−1.29316	+	0.634794i
$598$	−196.596	−	426.199i	−0.328755	−	0.712707i
$599$			527.412i			0.880487i	0.897878	+	0.440243i	$0.145108\pi$
$599$			527.412i			0.880487i	−0.897878	+	0.440243i	$0.854892\pi$
$600$		0			0
$601$	−133.338			−0.221861			−0.110930	−	0.993828i	$-0.535383\pi$
$601$	−133.338			−0.221861			−0.110930	+	0.993828i	$0.535383\pi$
$602$	736.448	−	339.707i	1.22334	−	0.564297i
$603$	87.1866	+	681.388i	0.144588	+	1.13000i
$604$	−609.710	−	520.270i	−1.00945	−	0.861375i
$605$		0			0
$606$	−740.052	−	601.239i	−1.22121	−	0.992144i
$607$	401.515	−	401.515i	0.661475	−	0.661475i	−0.294253	−	0.955728i	$-0.595071\pi$
$607$	401.515	−	401.515i	0.661475	−	0.661475i	0.955728	+	0.294253i	$0.0950707\pi$
$608$	85.1967	+	127.198i	0.140126	+	0.209207i
$609$	72.2410	−	211.550i	0.118622	−	0.347373i
$610$		0			0
$611$	304.763			0.498794
$612$	−414.466	−	271.041i	−0.677233	−	0.442878i
$613$	604.618	−	604.618i	0.986326	−	0.986326i	−0.0135821	−	0.999908i	$-0.504323\pi$
$613$	604.618	−	604.618i	0.986326	−	0.986326i	0.999908	+	0.0135821i	$0.00432346\pi$
$614$	−323.350	+	877.082i	−0.526629	+	1.42847i
$615$		0			0
$616$	330.046	+	588.414i	0.535789	+	0.955218i
$617$	51.5846	−	51.5846i	0.0836055	−	0.0836055i	−0.664067	−	0.747673i	$-0.731171\pi$
$617$	51.5846	−	51.5846i	0.0836055	−	0.0836055i	0.747673	+	0.664067i	$0.231171\pi$
$618$	−241.615	+	25.0051i	−0.390962	+	0.0404614i
$619$	1063.63			1.71831			0.859155	−	0.511716i	$-0.170990\pi$
$619$	1063.63			1.71831			0.859155	+	0.511716i	$0.170990\pi$
$620$		0			0
$621$	285.550	+	432.444i	0.459823	+	0.696367i
$622$	−48.1816	+	22.2251i	−0.0774623	+	0.0357316i
$623$	407.454	−	407.454i	0.654020	−	0.654020i
$624$	578.335	+	99.9270i	0.926819	+	0.160139i
$625$		0			0
$626$	−128.999	+	349.908i	−0.206069	+	0.558959i
$627$	216.884	−	106.466i	0.345908	−	0.169802i
$628$	−789.443	+	62.4854i	−1.25707	+	0.0994990i
$629$	196.841			0.312943
$630$		0			0
$631$		−	834.260i		−	1.32212i	−0.750331	−	0.661062i	$-0.770106\pi$
$631$		−	834.260i		−	1.32212i	0.750331	−	0.661062i	$-0.229894\pi$
$632$	−191.581	+	681.043i	−0.303135	+	1.07760i
$633$	243.034	+	495.091i	0.383939	+	0.782134i
$634$	65.1686	−	176.769i	0.102790	−	0.278815i
$635$		0			0
$636$	−236.485	+	140.255i	−0.371832	+	0.220527i
$637$	206.661	+	206.661i	0.324428	+	0.324428i
$638$	454.725	−	209.754i	0.712735	−	0.328768i
$639$	201.849	−	261.083i	0.315882	−	0.408581i
$640$		0			0
$641$			104.566i			0.163130i	0.996668	+	0.0815648i	$0.0259918\pi$
$641$			104.566i			0.163130i	−0.996668	+	0.0815648i	$0.974008\pi$
$642$	237.852	−	24.6157i	0.370486	−	0.0383423i
$643$	−357.160	−	357.160i	−0.555459	−	0.555459i	0.372552	−	0.928011i	$-0.378483\pi$
$643$	−357.160	−	357.160i	−0.555459	−	0.555459i	−0.928011	+	0.372552i	$0.878483\pi$
$644$	292.571	+	249.653i	0.454303	+	0.387660i
$645$		0			0
$646$	−45.5299	+	123.499i	−0.0704797	+	0.191175i
$647$	−428.808	−	428.808i	−0.662764	−	0.662764i	0.293266	−	0.956031i	$-0.405258\pi$
$647$	−428.808	−	428.808i	−0.662764	−	0.662764i	−0.956031	+	0.293266i	$0.905258\pi$
$648$	−647.874	−	12.7606i	−0.999806	−	0.0196923i
$649$		−	73.5884i		−	0.113387i
$650$		0			0
$651$	200.030	+	68.3070i	0.307266	+	0.104926i
$652$	330.641	−	26.1706i	0.507118	−	0.0401390i
$653$	216.356	+	216.356i	0.331327	+	0.331327i	0.853090	−	0.521763i	$-0.174726\pi$
$653$	216.356	+	216.356i	0.331327	+	0.331327i	−0.521763	+	0.853090i	$0.674726\pi$
$654$	744.833	+	605.123i	1.13889	+	0.925265i
$655$		0			0
$656$	96.1491	−	15.3166i	0.146569	−	0.0233485i
$657$	−20.4836	−	160.085i	−0.0311775	−	0.243661i
$658$	−226.772	+	104.605i	−0.344638	+	0.158974i
$659$		−	862.678i		−	1.30907i	−0.756031	−	0.654535i	$-0.772864\pi$
$659$		−	862.678i		−	1.30907i	0.756031	−	0.654535i	$-0.227136\pi$
$660$		0			0
$661$	56.1770			0.0849879			0.0424939	−	0.999097i	$-0.486470\pi$
$661$	56.1770			0.0849879			0.0424939	+	0.999097i	$0.486470\pi$
$662$	238.708	+	517.494i	0.360587	+	0.781714i
$663$	222.355	+	452.966i	0.335377	+	0.683206i
$664$	352.768	+	628.924i	0.531277	+	0.947175i
$665$		0			0
$666$	218.299	−	136.697i	0.327777	−	0.205251i
$667$	201.865	−	201.865i	0.302646	−	0.302646i
$668$	475.135	−	37.6075i	0.711281	−	0.0562987i
$669$	−28.1919	−	9.62707i	−0.0421404	−	0.0143902i
$670$		0			0
$671$	143.468			0.213813
$672$	−464.633	+	124.149i	−0.691419	+	0.184745i
$673$	−236.472	+	236.472i	−0.351371	+	0.351371i	−0.860619	−	0.509249i	$-0.829923\pi$
$673$	−236.472	+	236.472i	−0.351371	+	0.351371i	0.509249	+	0.860619i	$0.329923\pi$
$674$	−780.659	−	287.802i	−1.15825	−	0.427006i
$675$		0			0
$676$	59.3223	+	50.6203i	0.0877550	+	0.0748820i
$677$	754.987	−	754.987i	1.11520	−	1.11520i	0.122759	−	0.992437i	$-0.460826\pi$
$677$	754.987	−	754.987i	1.11520	−	1.11520i	0.992437	−	0.122759i	$-0.0391742\pi$
$678$	−854.659	+	88.4502i	−1.26056	+	0.130458i
$679$	−604.720			−0.890604
$680$		0			0
$681$	147.224	+	50.2744i	0.216187	+	0.0738244i
$682$	198.332	+	429.962i	0.290809	+	0.630443i
$683$	−848.561	+	848.561i	−1.24240	+	1.24240i	−0.283401	+	0.959002i	$0.591463\pi$
$683$	−848.561	+	848.561i	−1.24240	+	1.24240i	−0.959002	+	0.283401i	$0.908537\pi$
$684$	35.2712	+	168.581i	0.0515661	+	0.246463i
$685$		0			0
$686$	−685.353	−	252.666i	−0.999057	−	0.368318i
$687$	−357.098	−	727.455i	−0.519794	−	1.05889i
$688$	−760.314	+	1048.45i	−1.10511	+	1.52391i
$689$	280.154			0.406609
$690$		0			0
$691$		−	973.366i		−	1.40863i	−0.709886	−	0.704317i	$-0.751253\pi$
$691$		−	973.366i		−	1.40863i	0.709886	−	0.704317i	$-0.248747\pi$
$692$	−288.920	+	22.8684i	−0.417515	+	0.0330468i
$693$	96.3306	+	752.851i	0.139005	+	1.08637i
$694$	−727.289	−	268.127i	−1.04797	−	0.386350i
$695$		0			0
$696$	64.6509	+	351.074i	0.0928892	+	0.504417i
$697$	59.1903	+	59.1903i	0.0849215	+	0.0849215i
$698$	−108.213	−	234.594i	−0.155033	−	0.336094i
$699$	−221.682	−	75.7008i	−0.317142	−	0.108299i
$700$		0			0
$701$		−	8.02635i		−	0.0114499i	−0.999984	−	0.00572493i	$-0.998178\pi$
$701$		−	8.02635i		−	0.0114499i	0.999984	−	0.00572493i	$-0.00182231\pi$
$702$	561.158	+	347.930i	0.799371	+	0.495626i
$703$	−48.4074	−	48.4074i	−0.0688583	−	0.0688583i
$704$	−919.350	−	561.685i	−1.30590	−	0.797848i
$705$		0			0
$706$	1013.09	+	373.490i	1.43497	+	0.529023i
$707$	−562.949	−	562.949i	−0.796250	−	0.796250i
$708$	50.8261	+	12.9824i	0.0717883	+	0.0183368i
$709$			378.225i			0.533463i	0.963771	+	0.266731i	$0.0859437\pi$
$709$			378.225i			0.533463i	−0.963771	+	0.266731i	$0.914056\pi$
$710$		0			0
$711$	−486.813	+	629.673i	−0.684688	+	0.885615i
$712$	−249.179	+	885.794i	−0.349970	+	1.24409i
$713$	190.872	+	190.872i	0.267703	+	0.267703i
$714$	−320.925	−	260.729i	−0.449475	−	0.365166i
$715$		0			0
$716$	82.8476	+	70.6946i	0.115709	+	0.0987354i
$717$	−60.9924	−	124.249i	−0.0850660	−	0.173291i
$718$	175.688	+	380.872i	0.244690	+	0.530463i
$719$		−	901.949i		−	1.25445i	−0.778838	−	0.627225i	$-0.784191\pi$
$719$		−	901.949i		−	1.25445i	0.778838	−	0.627225i	$-0.215809\pi$
$720$		0			0
$721$	−202.815			−0.281296
$722$	−614.044	+	283.245i	−0.850477	+	0.392305i
$723$	571.365	−	280.476i	0.790270	−	0.387933i
$724$	−718.236	+	841.707i	−0.992038	+	1.16258i
$725$		0			0
$726$	−614.315	+	756.146i	−0.846163	+	1.04152i
$727$	647.476	−	647.476i	0.890613	−	0.890613i	−0.103967	−	0.994581i	$-0.533154\pi$
$727$	647.476	−	647.476i	0.890613	−	0.890613i	0.994581	+	0.103967i	$0.0331537\pi$
$728$	471.729	+	132.700i	0.647979	+	0.182280i
$729$	−670.424	−	286.308i	−0.919649	−	0.392740i
$730$		0			0
$731$	−1113.49			−1.52325
$732$	−25.3106	+	99.0909i	−0.0345773	+	0.135370i
$733$	664.993	−	664.993i	0.907221	−	0.907221i	−0.0888262	−	0.996047i	$-0.528312\pi$
$733$	664.993	−	664.993i	0.907221	−	0.907221i	0.996047	+	0.0888262i	$0.0283116\pi$
$734$	−4.18404	+	11.3491i	−0.00570033	+	0.0154620i
$735$		0			0
$736$	−602.513	−	119.148i	−0.818631	−	0.161886i
$737$	−908.537	+	908.537i	−1.23275	+	1.23275i
$738$	106.748	+	24.5379i	0.144645	+	0.0332492i
$739$	605.307			0.819090			0.409545	−	0.912290i	$-0.365687\pi$
$739$	605.307			0.819090			0.409545	+	0.912290i	$0.365687\pi$
$740$		0			0
$741$	56.7120	−	166.075i	0.0765344	−	0.224123i
$742$	−208.460	+	96.1580i	−0.280944	+	0.129593i
$743$	149.548	−	149.548i	0.201275	−	0.201275i	−0.599271	−	0.800546i	$-0.704543\pi$
$743$	149.548	−	149.548i	0.201275	−	0.201275i	0.800546	+	0.599271i	$0.204543\pi$
$744$	−331.956	+	61.1303i	−0.446178	+	0.0821643i
$745$		0			0
$746$	−355.954	+	965.519i	−0.477150	+	1.29426i
$747$	102.963	+	804.681i	0.137835	+	1.07722i
$748$	−73.0868	−	923.382i	−0.0977096	−	1.23447i
$749$	199.656			0.266564
$750$		0			0
$751$		−	988.027i		−	1.31562i	−0.753186	−	0.657808i	$-0.771484\pi$
$751$		−	988.027i		−	1.31562i	0.753186	−	0.657808i	$-0.228516\pi$
$752$	234.121	−	322.846i	0.311331	−	0.429316i
$753$	430.041	−	211.101i	0.571103	−	0.280347i
$754$	125.819	−	341.282i	0.166869	−	0.452629i
$755$		0			0
$756$	−536.975	−	66.2839i	−0.710284	−	0.0876771i
$757$	−590.607	−	590.607i	−0.780195	−	0.780195i	0.199669	−	0.979863i	$-0.436013\pi$
$757$	−590.607	−	590.607i	−0.780195	−	0.780195i	−0.979863	+	0.199669i	$0.936013\pi$
$758$	−1330.07	+	613.532i	−1.75471	+	0.809410i
$759$	−313.231	+	917.267i	−0.412690	+	1.20852i
$760$		0			0
$761$			354.692i			0.466087i	0.972466	+	0.233043i	$0.0748684\pi$
$761$			354.692i			0.466087i	−0.972466	+	0.233043i	$0.925132\pi$
$762$	82.1820	+	794.092i	0.107850	+	1.04212i
$763$	566.586	+	566.586i	0.742576	+	0.742576i
$764$	882.813	−	1034.58i	1.15551	−	1.35416i
$765$		0			0
$766$	−335.823	+	910.914i	−0.438411	+	1.18918i
$767$	−37.7956	−	37.7956i	−0.0492772	−	0.0492772i
$768$	550.137	−	535.886i	0.716324	−	0.697768i
$769$		−	262.078i		−	0.340804i	−0.985375	−	0.170402i	$-0.945493\pi$
$769$		−	262.078i		−	0.340804i	0.985375	−	0.170402i	$-0.0545067\pi$
$770$		0			0
$771$	−134.484	+	393.822i	−0.174428	+	0.510794i
$772$	45.0732	+	569.456i	0.0583849	+	0.737638i
$773$	−616.984	−	616.984i	−0.798168	−	0.798168i	0.184639	−	0.982806i	$-0.440888\pi$
$773$	−616.984	−	616.984i	−0.798168	−	0.798168i	−0.982806	+	0.184639i	$0.940888\pi$
$774$	−1234.88	+	773.269i	−1.59545	+	0.999056i
$775$		0			0
$776$	842.231	−	472.413i	1.08535	−	0.608780i
$777$	193.051	−	94.7662i	0.248457	−	0.121964i
$778$	1090.70	−	503.117i	1.40193	−	0.646679i
$779$		−	29.1122i		−	0.0373713i
$780$		0			0
$781$	617.256			0.790340
$782$	−221.180	−	479.495i	−0.282839	−	0.613165i
$783$	−80.4958	+	393.450i	−0.102804	+	0.502490i
$784$	377.681	−	60.1647i	0.481735	−	0.0767407i
$785$		0			0
$786$	549.148	−	675.934i	0.698662	−	0.859967i
$787$	471.258	−	471.258i	0.598803	−	0.598803i	−0.341191	−	0.939994i	$-0.610830\pi$
$787$	471.258	−	471.258i	0.598803	−	0.598803i	0.939994	+	0.341191i	$0.110830\pi$
$788$	100.690	+	1272.12i	0.127779	+	1.61437i
$789$	−194.578	+	569.802i	−0.246614	+	0.722183i
$790$		0			0
$791$	−717.412			−0.906969
$792$	−722.300	−	973.287i	−0.911995	−	1.22890i
$793$	73.6865	−	73.6865i	0.0929212	−	0.0929212i
$794$	783.636	+	288.900i	0.986947	+	0.363853i
$795$		0			0
$796$	744.324	−	872.281i	0.935081	−	1.09583i
$797$	−485.701	+	485.701i	−0.609411	+	0.609411i	−0.942792	−	0.333381i	$-0.891811\pi$
$797$	−485.701	+	485.701i	−0.609411	+	0.609411i	0.333381	+	0.942792i	$0.391811\pi$
$798$	14.8036	+	143.041i	0.0185508	+	0.179249i
$799$	342.874			0.429129
$800$		0			0
$801$	−633.170	+	818.979i	−0.790474	+	1.02245i
$802$	−251.663	−	545.578i	−0.313794	−	0.680271i
$803$	213.451	−	213.451i	0.265818	−	0.265818i
$804$	−467.226	−	787.793i	−0.581127	−	0.979842i
$805$		0			0
$806$	322.697	+	118.967i	0.400368	+	0.147602i
$807$	1.46333	−	0.718328i	0.00181329	−	0.000890122i
$808$	1223.83	+	344.272i	1.51465	+	0.426079i
$809$	183.688			0.227056			0.113528	−	0.993535i	$-0.463785\pi$
$809$	183.688			0.227056			0.113528	+	0.993535i	$0.463785\pi$
$810$		0			0
$811$			1332.68i			1.64325i	0.570027	+	0.821626i	$0.306933\pi$
$811$			1332.68i			1.64325i	−0.570027	+	0.821626i	$0.693067\pi$
$812$	23.5182	+	297.131i	0.0289634	+	0.365924i
$813$	−479.651	−	977.111i	−0.589977	−	1.20186i
$814$	452.016	+	166.643i	0.555303	+	0.204721i
$815$		0			0
$816$	650.656	+	112.423i	0.797373	+	0.137773i
$817$	273.831	+	273.831i	0.335166	+	0.335166i
$818$	45.0829	+	97.7350i	0.0551136	+	0.119480i
$819$	436.147	+	337.194i	0.532536	+	0.411715i
$820$		0			0
$821$			1157.86i			1.41030i	0.709057	+	0.705152i	$0.249121\pi$
$821$			1157.86i			1.41030i	−0.709057	+	0.705152i	$0.750879\pi$
$822$	52.4988	+	507.275i	0.0638672	+	0.617123i
$823$	420.085	+	420.085i	0.510432	+	0.510432i	0.914659	−	0.404227i	$-0.132459\pi$
$823$	420.085	+	420.085i	0.510432	+	0.510432i	−0.404227	+	0.914659i	$0.632459\pi$
$824$	282.472	−	158.441i	0.342806	−	0.192282i
$825$		0			0
$826$	41.0961	+	15.1507i	0.0497532	+	0.0183423i
$827$	450.627	+	450.627i	0.544893	+	0.544893i	0.924959	−	0.380066i	$-0.124099\pi$
$827$	450.627	+	450.627i	0.544893	+	0.544893i	−0.380066	+	0.924959i	$0.624099\pi$
$828$	−578.279	−	378.167i	−0.698404	−	0.456723i
$829$		−	1059.56i		−	1.27812i	−0.769155	−	0.639062i	$-0.779323\pi$
$829$		−	1059.56i		−	1.27812i	0.769155	−	0.639062i	$-0.220677\pi$
$830$		0			0
$831$	−318.094	−	108.624i	−0.382785	−	0.130715i
$832$	−760.672	+	183.700i	−0.914270	+	0.220793i
$833$	232.504	+	232.504i	0.279116	+	0.279116i
$834$	−47.6646	+	58.6692i	−0.0571517	+	0.0703468i
$835$		0			0
$836$	−209.105	+	245.052i	−0.250126	+	0.293125i
$837$	−372.024	−	76.1123i	−0.444473	−	0.0909346i
$838$	−488.053	−	1058.05i	−0.582402	−	1.26259i
$839$		−	425.692i		−	0.507380i	−0.967286	−	0.253690i	$-0.918356\pi$
$839$		−	425.692i		−	0.507380i	0.967286	−	0.253690i	$-0.0816443\pi$
$840$		0			0
$841$	−619.762			−0.736935
$842$	883.855	−	407.702i	1.04971	−	0.484207i
$843$	−421.382	−	858.410i	−0.499860	−	1.01828i
$844$	−559.391	−	477.333i	−0.662786	−	0.565560i
$845$		0			0
$846$	380.252	−	238.110i	0.449470	−	0.281454i
$847$	−575.192	+	575.192i	−0.679093	+	0.679093i
$848$	215.216	−	296.776i	0.253792	−	0.349972i
$849$	−895.488	−	305.794i	−1.05476	−	0.360182i
$850$		0			0
$851$	274.640			0.322726
$852$	−108.896	+	426.327i	−0.127812	+	0.500384i
$853$	−533.860	+	533.860i	−0.625861	+	0.625861i	−0.947024	−	0.321163i	$-0.895926\pi$
$853$	−533.860	+	533.860i	−0.625861	+	0.625861i	0.321163	+	0.947024i	$0.395926\pi$
$854$	−29.5380	+	80.1213i	−0.0345878	+	0.0938188i
$855$		0			0
$856$	−278.073	+	155.973i	−0.324852	+	0.182212i
$857$	575.339	−	575.339i	0.671340	−	0.671340i	−0.286685	−	0.958025i	$-0.592553\pi$
$857$	575.339	−	575.339i	0.671340	−	0.671340i	0.958025	+	0.286685i	$0.0925532\pi$
$858$	127.130	+	1228.41i	0.148171	+	1.43171i
$859$	−730.948			−0.850929			−0.425465	−	0.904975i	$-0.639889\pi$
$859$	−730.948			−0.850929			−0.425465	+	0.904975i	$0.639889\pi$
$860$		0			0
$861$	86.5468	+	29.5543i	0.100519	+	0.0343256i
$862$	1007.28	−	464.635i	1.16854	−	0.539019i
$863$	503.710	−	503.710i	0.583673	−	0.583673i	−0.352238	−	0.935911i	$-0.614579\pi$
$863$	503.710	−	503.710i	0.583673	−	0.583673i	0.935911	+	0.352238i	$0.114579\pi$
$864$	799.659	−	327.172i	0.925531	−	0.378672i
$865$		0			0
$866$	−149.601	+	405.789i	−0.172749	+	0.468579i
$867$	−131.889	−	268.676i	−0.152122	−	0.309891i
$868$	−280.950	+	22.2375i	−0.323675	+	0.0256193i
$869$	−1488.68			−1.71310
$870$		0			0
$871$			933.264i			1.07149i
$872$	−1231.74	−	346.496i	−1.41255	−	0.397358i
$873$	1077.60	−	137.883i	1.23436	−	0.157942i
$874$	−63.5250	+	172.311i	−0.0726831	+	0.197152i
$875$		0			0
$876$	109.770	+	185.084i	0.125308	+	0.211283i
$877$	1002.77	+	1002.77i	1.14341	+	1.14341i	0.987822	+	0.155586i	$0.0497266\pi$
$877$	1002.77	+	1002.77i	1.14341	+	1.14341i	0.155586	+	0.987822i	$0.450273\pi$
$878$	397.407	−	183.315i	0.452627	−	0.208787i
$879$	302.356	+	103.249i	0.343977	+	0.117462i
$880$		0			0
$881$		−	1337.17i		−	1.51779i	−0.651213	−	0.758895i	$-0.725739\pi$
$881$		−	1337.17i		−	1.51779i	0.651213	−	0.758895i	$-0.274261\pi$
$882$	419.312	+	96.3865i	0.475411	+	0.109282i
$883$	−29.5709	−	29.5709i	−0.0334891	−	0.0334891i	0.690164	−	0.723653i	$-0.257538\pi$
$883$	−29.5709	−	29.5709i	−0.0334891	−	0.0334891i	−0.723653	+	0.690164i	$0.757538\pi$
$884$	−511.795	−	436.719i	−0.578953	−	0.494026i
$885$		0			0
$886$	39.1314	−	106.143i	0.0441664	−	0.119801i
$887$	815.068	+	815.068i	0.918904	+	0.918904i	0.996950	−	0.0780457i	$-0.0248680\pi$
$887$	815.068	+	815.068i	0.918904	+	0.918904i	−0.0780457	+	0.996950i	$0.524868\pi$
$888$	−194.842	+	282.800i	−0.219416	+	0.318469i
$889$			666.572i			0.749799i
$890$		0			0
$891$	−343.318	−	1319.60i	−0.385318	−	1.48103i
$892$	39.5966	−	3.13412i	0.0443908	−	0.00351359i
$893$	−84.3198	−	84.3198i	−0.0944231	−	0.0944231i
$894$	98.0772	−	120.721i	0.109706	−	0.135035i
$895$		0			0
$896$	502.959	−	397.778i	0.561338	−	0.443948i
$897$	310.238	+	631.994i	0.345861	+	0.704564i
$898$	−429.454	+	198.097i	−0.478234	+	0.220598i
$899$			209.190i			0.232692i
$900$		0			0
$901$	315.187			0.349819
$902$	85.8120	+	186.031i	0.0951352	+	0.206243i
$903$	−1092.05	+	536.074i	−1.20936	+	0.593659i
$904$	999.183	−	560.449i	1.10529	−	0.619966i
$905$		0			0
$906$	933.134	+	758.104i	1.02995	+	0.836760i
$907$	−551.789	+	551.789i	−0.608367	+	0.608367i	−0.942519	−	0.334152i	$-0.891550\pi$
$907$	−551.789	+	551.789i	−0.608367	+	0.608367i	0.334152	+	0.942519i	$0.391550\pi$
$908$	−206.781	+	16.3670i	−0.227733	+	0.0180253i
$909$	1131.52	+	874.803i	1.24480	+	0.962380i
$910$		0			0
$911$	1547.30			1.69846			0.849231	−	0.528022i	$-0.177066\pi$
$911$	1547.30			1.69846			0.849231	+	0.528022i	$0.177066\pi$
$912$	−132.363	−	187.657i	−0.145135	−	0.205764i
$913$	−1072.93	+	1072.93i	−1.17517	+	1.17517i
$914$	644.364	+	237.555i	0.704993	+	0.259907i
$915$		0			0
$916$	821.934	+	701.363i	0.897307	+	0.765680i
$917$	514.175	−	514.175i	0.560715	−	0.560715i
$918$	631.331	+	391.438i	0.687725	+	0.426403i
$919$	1012.94			1.10222			0.551109	−	0.834433i	$-0.314205\pi$
$919$	1012.94			1.10222			0.551109	+	0.834433i	$0.314205\pi$
$920$		0			0
$921$	453.130	−	1326.95i	0.491998	−	1.44077i
$922$	−536.794	−	1163.71i	−0.582207	−	1.26216i
$923$	317.028	−	317.028i	0.343475	−	0.343475i
$924$	−516.228	−	870.416i	−0.558688	−	0.942008i
$925$		0			0
$926$	−431.990	−	159.260i	−0.466512	−	0.171987i
$927$	361.411	−	46.2441i	0.389872	−	0.0498858i
$928$	−264.877	−	395.459i	−0.285427	−	0.426141i
$929$	1529.05			1.64591			0.822955	−	0.568106i	$-0.192324\pi$
$929$	1529.05			1.64591			0.822955	+	0.568106i	$0.192324\pi$
$930$		0			0
$931$		−	114.355i		−	0.122830i
$932$	311.361	−	24.6446i	0.334079	−	0.0264427i
$933$	71.4467	−	35.0722i	0.0765773	−	0.0375908i
$934$	1127.78	+	415.772i	1.20747	+	0.445152i
$935$		0			0
$936$	−870.868	−	128.909i	−0.930414	−	0.137723i
$937$	−662.561	−	662.561i	−0.707109	−	0.707109i	0.258818	−	0.965926i	$-0.416667\pi$
$937$	−662.561	−	662.561i	−0.707109	−	0.707109i	−0.965926	+	0.258818i	$0.916667\pi$
$938$	−320.327	−	694.435i	−0.341500	−	0.740336i
$939$	180.774	−	529.380i	0.192518	−	0.563769i
$940$		0			0
$941$		−	961.186i		−	1.02145i	−0.859744	−	0.510726i	$-0.829377\pi$
$941$		−	961.186i		−	1.02145i	0.859744	−	0.510726i	$-0.170623\pi$
$942$	1181.56	−	122.281i	1.25431	−	0.129811i
$943$	82.5844	+	82.5844i	0.0875763	+	0.0875763i
$944$	−69.0730	+	11.0034i	−0.0731706	+	0.0116561i
$945$		0			0
$946$	−2556.97	−	942.667i	−2.70293	−	0.996476i
$947$	−1259.29	−	1259.29i	−1.32977	−	1.32977i	−0.905568	−	0.424202i	$-0.860555\pi$
$947$	−1259.29	−	1259.29i	−1.32977	−	1.32977i	−0.424202	−	0.905568i	$-0.639445\pi$
$948$	262.632	−	1028.20i	0.277038	−	1.08460i
$949$		−	219.261i		−	0.231044i
$950$		0			0
$951$	−91.3247	+	267.435i	−0.0960302	+	0.281215i
$952$	530.719	+	149.294i	0.557478	+	0.156822i
$953$	−62.1880	−	62.1880i	−0.0652550	−	0.0652550i	0.673726	−	0.738981i	$-0.264693\pi$
$953$	−62.1880	−	62.1880i	−0.0652550	−	0.0652550i	−0.738981	+	0.673726i	$0.764693\pi$
$954$	349.546	−	218.883i	0.366401	−	0.229437i
$955$		0			0
$956$	140.386	+	119.793i	0.146848	+	0.125306i
$957$	−674.295	+	331.002i	−0.704592	+	0.345875i
$958$	367.821	+	797.397i	0.383947	+	0.832356i
$959$			425.813i			0.444018i
$960$		0			0
$961$	763.202			0.794174
$962$	317.749	−	146.570i	0.330300	−	0.152360i
$963$	−355.783	+	45.5240i	−0.369453	+	0.0472731i
$964$	−550.871	+	645.571i	−0.571443	+	0.669680i
$965$		0			0
$966$	−447.767	−	363.779i	−0.463527	−	0.376582i
$967$	1.17333	−	1.17333i	0.00121337	−	0.00121337i	−0.706500	−	0.707713i	$-0.749727\pi$
$967$	1.17333	−	1.17333i	0.00121337	−	0.00121337i	0.707713	+	0.706500i	$0.249727\pi$
$968$	351.759	−	1250.45i	0.363387	−	1.29179i
$969$	63.8038	−	186.843i	0.0658450	−	0.192821i
$970$		0			0
$971$	570.125			0.587153			0.293576	−	0.955936i	$-0.405154\pi$
$971$	570.125			0.587153			0.293576	+	0.955936i	$0.405154\pi$
$972$	971.990	−	4.32014i	0.999990	−	0.00444459i
$973$	−44.6290	+	44.6290i	−0.0458674	+	0.0458674i
$974$	−301.565	+	817.991i	−0.309615	+	0.839827i
$975$		0			0
$976$	−21.4522	−	134.665i	−0.0219797	−	0.137977i
$977$	−430.216	+	430.216i	−0.440344	+	0.440344i	−0.892128	−	0.451784i	$-0.850788\pi$
$977$	−430.216	+	430.216i	−0.440344	+	0.440344i	0.451784	+	0.892128i	$0.350788\pi$
$978$	−494.869	+	51.2149i	−0.506001	+	0.0523670i
$979$	−1936.24			−1.97777
$980$		0			0
$981$	−1138.83	−	880.455i	−1.16089	−	0.897507i
$982$	−1365.09	+	629.685i	−1.39011	+	0.641227i
$983$	−876.585	+	876.585i	−0.891745	+	0.891745i	−0.994687	−	0.102942i	$-0.967174\pi$
$983$	−876.585	+	876.585i	−0.891745	+	0.891745i	0.102942	+	0.994687i	$0.467174\pi$
$984$	−143.627	+	26.4492i	−0.145963	+	0.0268792i
$985$		0			0
$986$	141.553	−	383.959i	0.143563	−	0.389411i
$987$	336.272	−	165.071i	0.340701	−	0.167246i
$988$	18.4627	+	233.259i	0.0186870	+	0.236092i
$989$	−1553.59			−1.57086
$990$		0			0
$991$			183.991i			0.185662i	0.995682	+	0.0928310i	$0.0295916\pi$
$991$			183.991i			0.185662i	−0.995682	+	0.0928310i	$0.970408\pi$
$992$	373.924	−	250.453i	0.376939	−	0.252472i
$993$	−376.693	−	767.373i	−0.379349	−	0.772783i
$994$	−127.084	+	344.712i	−0.127851	+	0.346793i
$995$		0			0
$996$	−551.768	−	930.340i	−0.553983	−	0.934076i
$997$	−276.341	−	276.341i	−0.277172	−	0.277172i	0.554807	−	0.831979i	$-0.312792\pi$
$997$	−276.341	−	276.341i	−0.277172	−	0.277172i	−0.831979	+	0.554807i	$0.812792\pi$
$998$	552.976	−	255.075i	0.554084	−	0.255586i
$999$	−322.405	+	212.889i	−0.322728	+	0.213102i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	300.3.l.g.107.18		40
3.2	odd	2	inner	300.3.l.g.107.3		40
4.3	odd	2	inner	300.3.l.g.107.13		40
5.2	odd	4		60.3.l.a.23.13	yes	40
5.3	odd	4	inner	300.3.l.g.143.8		40
5.4	even	2		60.3.l.a.47.3	yes	40
12.11	even	2	inner	300.3.l.g.107.8		40
15.2	even	4		60.3.l.a.23.8	yes	40
15.8	even	4	inner	300.3.l.g.143.13		40
15.14	odd	2		60.3.l.a.47.18	yes	40
20.3	even	4	inner	300.3.l.g.143.3		40
20.7	even	4		60.3.l.a.23.18	yes	40
20.19	odd	2		60.3.l.a.47.8	yes	40
60.23	odd	4	inner	300.3.l.g.143.18		40
60.47	odd	4		60.3.l.a.23.3	✓	40
60.59	even	2		60.3.l.a.47.13	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
60.3.l.a.23.3	✓	40	60.47	odd	4
60.3.l.a.23.8	yes	40	15.2	even	4
60.3.l.a.23.13	yes	40	5.2	odd	4
60.3.l.a.23.18	yes	40	20.7	even	4
60.3.l.a.47.3	yes	40	5.4	even	2
60.3.l.a.47.8	yes	40	20.19	odd	2
60.3.l.a.47.13	yes	40	60.59	even	2
60.3.l.a.47.18	yes	40	15.14	odd	2
300.3.l.g.107.3		40	3.2	odd	2	inner
300.3.l.g.107.8		40	12.11	even	2	inner
300.3.l.g.107.13		40	4.3	odd	2	inner
300.3.l.g.107.18		40	1.1	even	1	trivial
300.3.l.g.143.3		40	20.3	even	4	inner
300.3.l.g.143.8		40	5.3	odd	4	inner
300.3.l.g.143.13		40	15.8	even	4	inner
300.3.l.g.143.18		40	60.23	odd	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 300 = 2^{2} \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	300.l (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.81610 - 0.837725i) q^{2} +(-2.69303 + 1.32197i) q^{3} +(2.59643 - 3.04278i) q^{4} +(-3.78336 + 4.65685i) q^{6} +(-3.54241 + 3.54241i) q^{7} +(2.16636 - 7.70110i) q^{8} +(5.50478 - 7.12021i) q^{9} +O(q^{10})\)	\(q+(1.81610 - 0.837725i) q^{2} +(-2.69303 + 1.32197i) q^{3} +(2.59643 - 3.04278i) q^{4} +(-3.78336 + 4.65685i) q^{6} +(-3.54241 + 3.54241i) q^{7} +(2.16636 - 7.70110i) q^{8} +(5.50478 - 7.12021i) q^{9} +16.8337 q^{11} +(-2.96979 + 11.6267i) q^{12} +(8.64592 - 8.64592i) q^{13} +(-3.46580 + 9.40093i) q^{14} +(-2.51707 - 15.8008i) q^{16} +(9.72710 - 9.72710i) q^{17} +(4.03246 - 17.5425i) q^{18} -4.78419 q^{19} +(4.85684 - 14.2228i) q^{21} +(30.5716 - 14.1020i) q^{22} +(13.5716 - 13.5716i) q^{23} +(4.34655 + 23.6031i) q^{24} +(8.45895 - 22.9448i) q^{26} +(-5.41182 + 26.4521i) q^{27} +(1.58116 + 19.9764i) q^{28} +14.8741 q^{29} +14.0641i q^{31} +(-17.8080 - 26.5872i) q^{32} +(-45.3336 + 22.2536i) q^{33} +(9.51674 - 25.8140i) q^{34} +(-7.37245 - 35.2370i) q^{36} +(10.1182 + 10.1182i) q^{37} +(-8.68857 + 4.00784i) q^{38} +(-11.8540 + 34.7134i) q^{39} +6.08509i q^{41} +(-3.09427 - 29.8987i) q^{42} +(-57.2366 - 57.2366i) q^{43} +(43.7075 - 51.2213i) q^{44} +(13.2781 - 36.0167i) q^{46} +(17.6247 + 17.6247i) q^{47} +(27.6667 + 39.2244i) q^{48} +23.9027i q^{49} +(-13.3364 + 39.0543i) q^{51} +(-3.85911 - 48.7562i) q^{52} +(16.2015 + 16.2015i) q^{53} +(12.3312 + 52.5732i) q^{54} +(19.6063 + 34.9546i) q^{56} +(12.8840 - 6.32456i) q^{57} +(27.0128 - 12.4604i) q^{58} -4.37150i q^{59} +8.52269 q^{61} +(11.7818 + 25.5418i) q^{62} +(5.72249 + 44.7229i) q^{63} +(-54.6137 - 33.3667i) q^{64} +(-63.6878 + 78.3919i) q^{66} +(-53.9714 + 53.9714i) q^{67} +(-4.34170 - 54.8532i) q^{68} +(-18.6074 + 54.4900i) q^{69} +36.6679 q^{71} +(-42.9080 - 57.8178i) q^{72} +(12.6800 - 12.6800i) q^{73} +(26.8519 + 9.89937i) q^{74} +(-12.4218 + 14.5573i) q^{76} +(-59.6318 + 59.6318i) q^{77} +(7.55214 + 72.9733i) q^{78} -88.4346 q^{79} +(-20.3947 - 78.3904i) q^{81} +(5.09763 + 11.0511i) q^{82} +(-63.7372 + 63.7372i) q^{83} +(-30.6663 - 51.7068i) q^{84} +(-151.896 - 55.9988i) q^{86} +(-40.0563 + 19.6631i) q^{87} +(36.4679 - 129.638i) q^{88} -115.022 q^{89} +61.2548i q^{91} +(-6.05770 - 76.5332i) q^{92} +(-18.5923 - 37.8749i) q^{93} +(46.7728 + 17.2435i) q^{94} +(83.1047 + 48.0583i) q^{96} +(85.3544 + 85.3544i) q^{97} +(20.0239 + 43.4096i) q^{98} +(92.6658 - 119.859i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 4 q^{6}+O(q^{10}) \) 40 * q - 4 * q^6	\( 40 q - 4 q^{6} + 20 q^{12} + 8 q^{13} - 36 q^{16} + 24 q^{18} - 24 q^{21} + 76 q^{22} + 84 q^{28} + 40 q^{33} + 172 q^{36} + 40 q^{37} - 236 q^{42} + 240 q^{46} - 196 q^{48} - 304 q^{52} + 72 q^{57} - 180 q^{58} + 48 q^{61} - 552 q^{66} + 600 q^{72} - 104 q^{73} - 736 q^{76} + 408 q^{78} + 72 q^{81} + 720 q^{82} + 580 q^{88} - 368 q^{93} + 884 q^{96} - 72 q^{97}+O(q^{100}) \) 40 * q - 4 * q^6 + 20 * q^12 + 8 * q^13 - 36 * q^16 + 24 * q^18 - 24 * q^21 + 76 * q^22 + 84 * q^28 + 40 * q^33 + 172 * q^36 + 40 * q^37 - 236 * q^42 + 240 * q^46 - 196 * q^48 - 304 * q^52 + 72 * q^57 - 180 * q^58 + 48 * q^61 - 552 * q^66 + 600 * q^72 - 104 * q^73 - 736 * q^76 + 408 * q^78 + 72 * q^81 + 720 * q^82 + 580 * q^88 - 368 * q^93 + 884 * q^96 - 72 * q^97

Introduction

L-functions

Modular forms

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