LMFDB - Embedded newform 300.3.l.g.143.8

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			143.8
Character	$\chi$	$=$	300.143
Dual form			300.3.l.g.107.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.837725 - 1.81610i) q^{2} +(-1.32197 - 2.69303i) q^{3} +(-2.59643 + 3.04278i) q^{4} +(-3.78336 + 4.65685i) q^{6} +(3.54241 + 3.54241i) q^{7} +(7.70110 + 2.16636i) q^{8} +(-5.50478 + 7.12021i) q^{9} +O(q^{10})$	\(q+(-0.837725 - 1.81610i) q^{2} +(-1.32197 - 2.69303i) q^{3} +(-2.59643 + 3.04278i) q^{4} +(-3.78336 + 4.65685i) q^{6} +(3.54241 + 3.54241i) q^{7} +(7.70110 + 2.16636i) q^{8} +(-5.50478 + 7.12021i) q^{9} +16.8337 q^{11} +(11.6267 + 2.96979i) 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} +(17.5425 + 4.03246i) q^{18} +4.78419 q^{19} +(4.85684 - 14.2228i) q^{21} +(-14.1020 - 30.5716i) q^{22} +(13.5716 + 13.5716i) q^{23} +(-4.34655 - 23.6031i) q^{24} +(8.45895 - 22.9448i) q^{26} +(26.4521 + 5.41182i) q^{27} +(-19.9764 + 1.58116i) q^{28} -14.8741 q^{29} +14.0641i q^{31} +(-26.5872 + 17.8080i) q^{32} +(-22.2536 - 45.3336i) q^{33} +(-9.51674 + 25.8140i) q^{34} +(-7.37245 - 35.2370i) q^{36} +(10.1182 - 10.1182i) q^{37} +(-4.00784 - 8.68857i) q^{38} +(11.8540 - 34.7134i) q^{39} +6.08509i q^{41} +(-29.8987 + 3.09427i) 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} +(-39.2244 + 27.6667i) q^{48} -23.9027i q^{49} +(-13.3364 + 39.0543i) q^{51} +(-48.7562 + 3.85911i) q^{52} +(-16.2015 + 16.2015i) q^{53} +(-12.3312 - 52.5732i) q^{54} +(19.6063 + 34.9546i) q^{56} +(-6.32456 - 12.8840i) q^{57} +(12.4604 + 27.0128i) q^{58} +4.37150i q^{59} +8.52269 q^{61} +(25.5418 - 11.7818i) q^{62} +(-44.7229 + 5.72249i) q^{63} +(54.6137 + 33.3667i) q^{64} +(-63.6878 + 78.3919i) q^{66} +(53.9714 + 53.9714i) q^{67} +(54.8532 - 4.34170i) q^{68} +(18.6074 - 54.4900i) q^{69} +36.6679 q^{71} +(-57.8178 + 42.9080i) 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} +(-72.9733 + 7.55214i) q^{78} +88.4346 q^{79} +(-20.3947 - 78.3904i) q^{81} +(11.0511 - 5.09763i) q^{82} +(-63.7372 - 63.7372i) q^{83} +(30.6663 + 51.7068i) q^{84} +(-151.896 - 55.9988i) q^{86} +(19.6631 + 40.0563i) q^{87} +(129.638 + 36.4679i) q^{88} +115.022 q^{89} +61.2548i q^{91} +(-76.5332 + 6.05770i) q^{92} +(37.8749 - 18.5923i) q^{93} +(-46.7728 - 17.2435i) q^{94} +(83.1047 + 48.0583i) q^{96} +(85.3544 - 85.3544i) q^{97} +(-43.4096 + 20.0239i) 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 $\left(\mathbb{Z}/300\mathbb{Z}\right)^\times$.

$n$	$101$	$151$	$277$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−0.837725	−	1.81610i	−0.418863	−	0.908050i
$2$	−0.837725	−	1.81610i	−0.418863	−	0.908050i
$3$	−1.32197	−	2.69303i	−0.440657	−	0.897676i
$3$	−1.32197	−	2.69303i	−0.440657	−	0.897676i
$4$	−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	$-0.133514\pi$
$7$	3.54241	+	3.54241i	0.506059	+	0.506059i	−0.407256	+	0.913314i	$0.633514\pi$
$8$	7.70110	+	2.16636i	0.962637	+	0.270795i
$9$	−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	$0.222656\pi$
$12$	11.6267	+	2.96979i	0.968892	+	0.247483i
$13$	8.64592	+	8.64592i	0.665071	+	0.665071i	0.956571	−	0.291500i	$-0.0941543\pi$
$13$	8.64592	+	8.64592i	0.665071	+	0.665071i	−0.291500	+	0.956571i	$0.594154\pi$
$14$	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	$-0.382587\pi$
$17$	−9.72710	−	9.72710i	−0.572182	−	0.572182i	−0.932738	+	0.360556i	$0.882587\pi$
$18$	17.5425	+	4.03246i	0.974583	+	0.224025i
$19$	4.78419			0.251800			0.125900	−	0.992043i	$-0.459818\pi$
$19$	4.78419			0.251800			0.125900	+	0.992043i	$0.459818\pi$
$20$		0			0
$21$	4.85684	−	14.2228i	0.231278	−	0.677275i
$22$	−14.1020	−	30.5716i	−0.641000	−	1.38962i
$23$	13.5716	+	13.5716i	0.590070	+	0.590070i	0.937650	−	0.347580i	$-0.112997\pi$
$23$	13.5716	+	13.5716i	0.590070	+	0.590070i	−0.347580	+	0.937650i	$0.612997\pi$
$24$	−4.34655	−	23.6031i	−0.181106	−	0.983464i
$25$		0			0
$26$	8.45895	−	22.9448i	0.325344	−	0.882491i
$27$	26.4521	+	5.41182i	0.979706	+	0.200438i
$28$	−19.9764	+	1.58116i	−0.713444	+	0.0564699i
$29$	−14.8741			−0.512899			−0.256449	−	0.966558i	$-0.582553\pi$
$29$	−14.8741			−0.512899			−0.256449	+	0.966558i	$0.582553\pi$
$30$		0			0
$31$			14.0641i			0.453680i	0.973932	+	0.226840i	$0.0728395\pi$
$31$			14.0641i			0.453680i	−0.973932	+	0.226840i	$0.927161\pi$
$32$	−26.5872	+	17.8080i	−0.830849	+	0.556498i
$33$	−22.2536	−	45.3336i	−0.674353	−	1.37374i
$34$	−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	−0.557029	−	0.830493i	$-0.688059\pi$
$37$	10.1182	−	10.1182i	0.273465	−	0.273465i	0.830493	+	0.557029i	$0.188059\pi$
$38$	−4.00784	−	8.68857i	−0.105469	−	0.228647i
$39$	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	$0.976357\pi$
$42$	−29.8987	+	3.09427i	−0.711873	+	0.0736730i
$43$	57.2366	−	57.2366i	1.33108	−	1.33108i	0.426683	−	0.904401i	$-0.359682\pi$
$43$	57.2366	−	57.2366i	1.33108	−	1.33108i	0.904401	−	0.426683i	$-0.140318\pi$
$44$	−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	−0.494299	−	0.869292i	$-0.664575\pi$
$47$	17.6247	−	17.6247i	0.374993	−	0.374993i	0.869292	+	0.494299i	$0.164575\pi$
$48$	−39.2244	+	27.6667i	−0.817175	+	0.576390i
$49$		−	23.9027i		−	0.487809i
$50$		0			0
$51$	−13.3364	+	39.0543i	−0.261498	+	0.765770i
$52$	−48.7562	+	3.85911i	−0.937620	+	0.0742137i
$53$	−16.2015	+	16.2015i	−0.305688	+	0.305688i	−0.843234	−	0.537546i	$-0.819351\pi$
$53$	−16.2015	+	16.2015i	−0.305688	+	0.305688i	0.537546	+	0.843234i	$0.319351\pi$
$54$	−12.3312	−	52.5732i	−0.228355	−	0.973578i
$55$		0			0
$56$	19.6063	+	34.9546i	0.350112	+	0.624189i
$57$	−6.32456	−	12.8840i	−0.110957	−	0.226034i
$58$	12.4604	+	27.0128i	0.214834	+	0.465738i
$59$			4.37150i			0.0740931i	0.999314	+	0.0370466i	$0.0117950\pi$
$59$			4.37150i			0.0740931i	−0.999314	+	0.0370466i	$0.988205\pi$
$60$		0			0
$61$	8.52269			0.139716			0.0698582	−	0.997557i	$-0.477745\pi$
$61$	8.52269			0.139716			0.0698582	+	0.997557i	$0.477745\pi$
$62$	25.5418	−	11.7818i	0.411964	−	0.190030i
$63$	−44.7229	+	5.72249i	−0.709887	+	0.0908332i
$64$	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	$-0.0570963\pi$
$67$	53.9714	+	53.9714i	0.805543	+	0.805543i	−0.178413	+	0.983956i	$0.557096\pi$
$68$	54.8532	−	4.34170i	0.806665	−	0.0638485i
$69$	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	$0.416863\pi$
$72$	−57.8178	+	42.9080i	−0.803025	+	0.595945i
$73$	12.6800	+	12.6800i	0.173699	+	0.173699i	0.788602	−	0.614903i	$-0.210805\pi$
$73$	12.6800	+	12.6800i	0.173699	+	0.173699i	−0.614903	+	0.788602i	$0.710805\pi$
$74$	−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
$78$	−72.9733	+	7.55214i	−0.935555	+	0.0968223i
$79$	88.4346			1.11943			0.559713	−	0.828687i	$-0.310912\pi$
$79$	88.4346			1.11943			0.559713	+	0.828687i	$0.310912\pi$
$80$		0			0
$81$	−20.3947	−	78.3904i	−0.251786	−	0.967783i
$82$	11.0511	−	5.09763i	0.134770	−	0.0621663i
$83$	−63.7372	−	63.7372i	−0.767918	−	0.767918i	0.209822	−	0.977740i	$-0.432712\pi$
$83$	−63.7372	−	63.7372i	−0.767918	−	0.767918i	−0.977740	+	0.209822i	$0.932712\pi$
$84$	30.6663	+	51.7068i	0.365076	+	0.615557i
$85$		0			0
$86$	−151.896	−	55.9988i	−1.76623	−	0.651149i
$87$	19.6631	+	40.0563i	0.226013	+	0.460417i
$88$	129.638	+	36.4679i	1.47316	+	0.414408i
$89$	115.022			1.29238			0.646190	−	0.763177i	$-0.276361\pi$
$89$	115.022			1.29238			0.646190	+	0.763177i	$0.276361\pi$
$90$		0			0
$91$			61.2548i			0.673130i
$92$	−76.5332	+	6.05770i	−0.831883	+	0.0658445i
$93$	37.8749	−	18.5923i	0.407258	−	0.199917i
$94$	−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	−0.113586	−	0.993528i	$-0.536234\pi$
$97$	85.3544	−	85.3544i	0.879942	−	0.879942i	0.993528	+	0.113586i	$0.0362338\pi$
$98$	−43.4096	+	20.0239i	−0.442955	+	0.204325i
$99$	−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	$0.711779\pi$
$102$	82.0987	−	8.49654i	0.804889	−	0.0832994i
$103$	−28.6266	+	28.6266i	−0.277928	+	0.277928i	−0.832282	−	0.554353i	$-0.812966\pi$
$103$	−28.6266	+	28.6266i	−0.277928	+	0.277928i	0.554353	+	0.832282i	$0.312966\pi$
$104$	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	−0.826423	−	0.563050i	$-0.809628\pi$
$107$	−28.1808	+	28.1808i	−0.263372	+	0.263372i	0.563050	+	0.826423i	$0.309628\pi$
$108$	−85.1480	+	66.4365i	−0.788408	+	0.615153i
$109$			159.944i			1.46737i	0.679489	+	0.733686i	$0.262202\pi$
$109$			159.944i			1.46737i	−0.679489	+	0.733686i	$0.737798\pi$
$110$		0			0
$111$	−40.6245	−	13.8726i	−0.365986	−	0.124978i
$112$	47.0563	−	64.8893i	0.420146	−	0.579369i
$113$	−101.260	+	101.260i	−0.896110	+	0.896110i	−0.995089	−	0.0989792i	$-0.968442\pi$
$113$	−101.260	+	101.260i	−0.896110	+	0.896110i	0.0989792	+	0.995089i	$0.468442\pi$
$114$	−18.1003	+	22.2793i	−0.158775	+	0.195432i
$115$		0			0
$116$	38.6195	−	45.2586i	0.332927	−	0.390160i
$117$	−109.155	+	13.9668i	−0.932946	+	0.119375i
$118$	7.93907	−	3.66211i	0.0672803	−	0.0310348i
$119$		−	68.9147i		−	0.579115i
$120$		0			0
$121$	162.373			1.34193
$122$	−7.13968	−	15.4781i	−0.0585219	−	0.126869i
$123$	16.3873	−	8.04432i	0.133230	−	0.0654009i
$124$	−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	$-0.425501\pi$
$127$	−94.0845	−	94.0845i	−0.740823	−	0.740823i	−0.972736	+	0.231914i	$0.925501\pi$
$128$	14.8460	−	127.136i	0.115985	−	0.993251i
$129$	−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	$0.686900\pi$
$132$	195.720	+	49.9925i	1.48273	+	0.378731i
$133$	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	$-0.350399\pi$
$137$	−60.1022	−	60.1022i	−0.438702	−	0.438702i	−0.891575	+	0.452873i	$0.850399\pi$
$138$	−114.547	+	11.8547i	−0.830051	+	0.0859035i
$139$	−12.5985			−0.0906366			−0.0453183	−	0.998973i	$-0.514430\pi$
$139$	−12.5985			−0.0906366			−0.0453183	+	0.998973i	$0.514430\pi$
$140$		0			0
$141$	−70.7630	−	24.1644i	−0.501865	−	0.171379i
$142$	−30.7176	−	66.5925i	−0.216321	−	0.468961i
$143$	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
$147$	−64.3705	+	31.5986i	−0.437895	+	0.214957i
$148$	4.51626	+	57.0587i	0.0305153	+	0.385531i
$149$	25.9233			0.173982			0.0869911	−	0.996209i	$-0.472275\pi$
$149$	25.9233			0.173982			0.0869911	+	0.996209i	$0.472275\pi$
$150$		0			0
$151$		−	200.379i		−	1.32701i	−0.748171	−	0.663506i	$-0.769068\pi$
$151$		−	200.379i		−	1.32701i	0.748171	−	0.663506i	$-0.230932\pi$
$152$	36.8435	+	10.3643i	0.242392	+	0.0681862i
$153$	122.805	−	15.7134i	0.802644	−	0.102702i
$154$	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	−0.994680	−	0.103014i	$-0.967151\pi$
$157$	−139.992	+	139.992i	−0.891666	+	0.891666i	0.103014	+	0.994680i	$0.467151\pi$
$158$	−74.0839	−	160.606i	−0.468885	−	1.01649i
$159$	65.0489	+	22.2131i	0.409113	+	0.139705i
$160$		0			0
$161$			96.1524i			0.597220i
$162$	−125.280	+	102.708i	−0.773331	+	0.634003i
$163$	−58.6324	+	58.6324i	−0.359708	+	0.359708i	−0.863705	−	0.503997i	$-0.831862\pi$
$163$	−58.6324	+	58.6324i	−0.359708	+	0.359708i	0.503997	+	0.863705i	$0.331862\pi$
$164$	−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	−0.408316	−	0.912841i	$-0.633884\pi$
$167$	84.2556	−	84.2556i	0.504524	−	0.504524i	0.912841	+	0.408316i	$0.133884\pi$
$168$	68.2147	−	99.0092i	0.406040	−	0.589341i
$169$		−	19.4961i		−	0.115361i
$170$		0			0
$171$	−26.3359	+	34.0644i	−0.154011	+	0.199207i
$172$	25.5476	+	322.770i	0.148533	+	1.87657i
$173$	51.2341	−	51.2341i	0.296151	−	0.296151i	−0.543353	−	0.839504i	$-0.682846\pi$
$173$	51.2341	−	51.2341i	0.296151	−	0.296151i	0.839504	+	0.543353i	$0.182846\pi$
$174$	56.2739	−	69.2663i	0.323413	−	0.398082i
$175$		0			0
$176$	−42.3716	−	265.985i	−0.240747	−	1.51128i
$177$	11.7726	−	5.77899i	0.0665116	−	0.0326497i
$178$	−96.3566	−	208.891i	−0.541329	−	1.17354i
$179$		−	27.2276i		−	0.152109i	−0.997104	−	0.0760547i	$-0.975768\pi$
$179$		−	27.2276i		−	0.152109i	0.997104	−	0.0760547i	$-0.0242324\pi$
$180$		0			0
$181$	−276.624			−1.52831			−0.764155	−	0.645033i	$-0.776844\pi$
$181$	−276.624			−1.52831			−0.764155	+	0.645033i	$0.776844\pi$
$182$	111.245	−	51.3147i	0.611235	−	0.281949i
$183$	−11.2668	−	22.9518i	−0.0615670	−	0.125420i
$184$	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
$188$	7.86679	+	99.3894i	0.0418446	+	0.528667i
$189$	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	$0.150649\pi$
$192$	17.6597	−	191.186i	0.0919779	−	0.995761i
$193$	−100.981	−	100.981i	−0.523220	−	0.523220i	0.395322	−	0.918542i	$-0.370633\pi$
$193$	−100.981	−	100.981i	−0.523220	−	0.523220i	−0.918542	+	0.395322i	$0.870633\pi$
$194$	−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	0.987504	+	0.157595i	$0.0503741\pi$
$197$	225.584	+	225.584i	1.14510	+	1.14510i	0.157595	+	0.987504i	$0.449626\pi$
$198$	295.305	+	67.8811i	1.49144	+	0.342834i
$199$	−286.672			−1.44056			−0.720281	−	0.693682i	$-0.755987\pi$
$199$	−286.672			−1.44056			−0.720281	+	0.693682i	$0.755987\pi$
$200$		0			0
$201$	73.9977	−	216.695i	0.368148	−	1.07808i
$202$	288.609	−	133.129i	1.42876	−	0.659053i
$203$	−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
$207$	−171.341	+	21.9239i	−0.827736	+	0.105912i
$208$	114.850	−	158.375i	0.552163	−	0.761416i
$209$	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	$-0.143479\pi$
$212$	−7.23155	−	91.3637i	−0.0341111	−	0.430961i
$213$	−48.4739	−	98.7476i	−0.227577	−	0.463604i
$214$	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
$218$	290.473	−	133.989i	1.33245	−	0.614627i
$219$	17.3850	−	50.9103i	0.0793836	−	0.232467i
$220$		0			0
$221$		−	168.199i		−	0.761083i
$222$	8.83816	+	85.3995i	0.0398115	+	0.384683i
$223$	−7.02165	+	7.02165i	−0.0314872	+	0.0314872i	−0.722675	−	0.691188i	$-0.757088\pi$
$223$	−7.02165	+	7.02165i	−0.0314872	+	0.0314872i	0.691188	+	0.722675i	$0.257088\pi$
$224$	−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	−0.783246	−	0.621711i	$-0.786438\pi$
$227$	−36.6684	+	36.6684i	−0.161535	+	0.161535i	0.621711	+	0.783246i	$0.286438\pi$
$228$	55.6244	+	14.2081i	0.243967	+	0.0623160i
$229$		−	270.126i		−	1.17959i	−0.807554	−	0.589794i	$-0.799209\pi$
$229$		−	270.126i		−	1.17959i	0.807554	−	0.589794i	$-0.200791\pi$
$230$		0			0
$231$	81.7585	−	239.422i	0.353933	−	1.03646i
$232$	−114.547	−	32.2226i	−0.493735	−	0.138891i
$233$	−55.2135	+	55.2135i	−0.236968	+	0.236968i	−0.815593	−	0.578625i	$-0.803589\pi$
$233$	−55.2135	+	55.2135i	−0.236968	+	0.236968i	0.578625	+	0.815593i	$0.303589\pi$
$234$	116.807	+	186.535i	0.499174	+	0.797160i
$235$		0			0
$236$	−13.3015	−	11.3503i	−0.0563624	−	0.0480945i
$237$	−116.908	−	238.157i	−0.493283	−	1.00488i
$238$	−125.156	+	57.7316i	−0.525865	+	0.242570i
$239$		−	46.1374i		−	0.193044i	−0.995331	−	0.0965218i	$-0.969228\pi$
$239$		−	46.1374i		−	0.193044i	0.995331	−	0.0965218i	$-0.0307718\pi$
$240$		0			0
$241$	−212.165			−0.880351			−0.440176	−	0.897912i	$-0.645084\pi$
$241$	−212.165			−0.880351			−0.440176	+	0.897912i	$0.645084\pi$
$242$	−136.024	−	294.885i	−0.562082	−	1.21853i
$243$	−184.146	+	158.553i	−0.757803	+	0.652483i
$244$	−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
$248$	−30.4679	+	108.309i	−0.122855	+	0.436729i
$249$	−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	$0.603045\pi$
$252$	98.7077	−	150.940i	0.391697	−	0.598969i
$253$	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	$-0.336983\pi$
$257$	−98.0877	−	98.0877i	−0.381664	−	0.381664i	−0.871701	+	0.490037i	$0.836983\pi$
$258$	49.9957	+	483.089i	0.193782	+	1.87244i
$259$	71.6855			0.276778
$260$		0			0
$261$	81.8785	−	105.906i	0.313711	−	0.405772i
$262$	121.595	+	263.604i	0.464101	+	1.00612i
$263$	141.919	+	141.919i	0.539614	+	0.539614i	0.923416	−	0.383802i	$-0.125385\pi$
$263$	141.919	+	141.919i	0.539614	+	0.539614i	−0.383802	+	0.923416i	$0.625385\pi$
$264$	−73.1685	−	397.328i	−0.277153	−	1.50503i
$265$		0			0
$266$	16.5811	−	44.9759i	0.0623348	−	0.169082i
$267$	−152.055	−	309.757i	−0.569496	−	1.16014i
$268$	−304.356	+	24.0902i	−1.13566	+	0.0898887i
$269$	0.543377			0.00201999			0.00100999	−	0.999999i	$-0.499679\pi$
$269$	0.543377			0.00201999			0.00100999	+	0.999999i	$0.499679\pi$
$270$		0			0
$271$			362.830i			1.33886i	0.742877	+	0.669428i	$0.233461\pi$
$271$			362.830i			1.33886i	−0.742877	+	0.669428i	$0.766539\pi$
$272$	−129.212	+	178.179i	−0.475044	+	0.655071i
$273$	164.961	−	80.9771i	0.604252	−	0.296619i
$274$	−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	−0.549486	−	0.835503i	$-0.685177\pi$
$277$	79.2266	−	79.2266i	0.286016	−	0.286016i	0.835503	+	0.549486i	$0.185177\pi$
$278$	10.5541	+	22.8801i	0.0379643	+	0.0823025i
$279$	−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	$0.808036\pi$
$282$	15.3950	+	148.756i	0.0545922	+	0.527503i
$283$	−223.036	+	223.036i	−0.788112	+	0.788112i	−0.981185	−	0.193072i	$-0.938155\pi$
$283$	−223.036	+	223.036i	−0.788112	+	0.788112i	0.193072	+	0.981185i	$0.438155\pi$
$284$	−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
$288$	19.5603	−	287.335i	0.0679176	−	0.997691i
$289$		−	99.7672i		−	0.345215i
$290$		0			0
$291$	−342.698	−	117.026i	−1.17765	−	0.402150i
$292$	−71.5054	+	5.65974i	−0.244881	+	0.0193827i
$293$	75.3066	−	75.3066i	0.257019	−	0.257019i	−0.566822	−	0.823841i	$-0.691827\pi$
$293$	75.3066	−	75.3066i	0.257019	−	0.257019i	0.823841	+	0.566822i	$0.191827\pi$
$294$	111.311	+	90.4323i	0.378609	+	0.307593i
$295$		0			0
$296$	99.8408	−	56.0015i	0.337300	−	0.189194i
$297$	445.286	+	91.1009i	1.49928	+	0.306737i
$298$	−21.7166	−	47.0794i	−0.0728746	−	0.157984i
$299$			234.678i			0.784876i
$300$		0			0
$301$	405.511			1.34721
$302$	−363.908	+	167.862i	−1.20499	+	0.555836i
$303$	427.967	−	210.084i	1.41243	−	0.693345i
$304$	−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	0.996817	+	0.0797218i	$0.0254032\pi$
$307$	330.497	+	330.497i	1.07654	+	1.07654i	0.0797218	+	0.996817i	$0.474597\pi$
$308$	−336.277	+	26.6167i	−1.09181	+	0.0864179i
$309$	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	$0.513581\pi$
$312$	166.491	−	241.651i	0.533624	−	0.774522i
$313$	−131.851	−	131.851i	−0.421248	−	0.421248i	0.464385	−	0.885633i	$-0.346275\pi$
$313$	−131.851	−	131.851i	−0.421248	−	0.421248i	−0.885633	+	0.464385i	$0.846275\pi$
$314$	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	$-0.297470\pi$
$317$	−66.6091	−	66.6091i	−0.210123	−	0.210123i	−0.804320	+	0.594197i	$0.797470\pi$
$318$	−14.1519	−	136.744i	−0.0445027	−	0.430012i
$319$	−250.385			−0.784907
$320$		0			0
$321$	113.146	+	38.6375i	0.352480	+	0.120366i
$322$	174.622	−	80.5492i	0.542305	−	0.250153i
$323$	−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
$327$	430.732	−	211.441i	1.31722	−	0.646608i
$328$	−13.1825	+	46.8619i	−0.0401906	+	0.142872i
$329$	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	$0.858360\pi$
$332$	359.428	−	28.4491i	1.08261	−	0.0856902i
$333$	16.3452	+	127.742i	0.0490845	+	0.383610i
$334$	−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	−0.992786	−	0.119897i	$-0.961744\pi$
$337$	−294.164	+	294.164i	−0.872889	+	0.872889i	0.119897	+	0.992786i	$0.461744\pi$
$338$	−35.4068	+	16.3324i	−0.104754	+	0.0483206i
$339$	406.561	+	138.834i	1.19929	+	0.409539i
$340$		0			0
$341$			236.750i			0.694283i
$342$	83.9267	+	19.2921i	0.245400	+	0.0564095i
$343$	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	−0.981458	−	0.191679i	$-0.938607\pi$
$347$	−274.053	+	274.053i	−0.789779	+	0.789779i	0.191679	+	0.981458i	$0.438607\pi$
$348$	−172.936	−	44.1729i	−0.496944	−	0.126934i
$349$			129.175i			0.370128i	0.982726	+	0.185064i	$0.0592492\pi$
$349$			129.175i			0.370128i	−0.982726	+	0.185064i	$0.940751\pi$
$350$		0			0
$351$	181.912	+	275.493i	0.518269	+	0.784880i
$352$	−447.560	+	299.773i	−1.27148	+	0.851629i
$353$	−381.746	+	381.746i	−1.08143	+	1.08143i	−0.0850569	+	0.996376i	$0.527107\pi$
$353$	−381.746	+	381.746i	−1.08143	+	1.08143i	−0.996376	+	0.0850569i	$0.972893\pi$
$354$	−20.3574	−	16.5389i	−0.0575067	−	0.0467201i
$355$		0			0
$356$	−298.646	+	349.986i	−0.838894	+	0.983108i
$357$	−185.589	+	91.1033i	−0.519858	+	0.255191i
$358$	−49.4480	+	22.8092i	−0.138123	+	0.0637129i
$359$		−	209.720i		−	0.584178i	−0.956391	−	0.292089i	$-0.905650\pi$
$359$		−	209.720i		−	0.584178i	0.956391	−	0.292089i	$-0.0943503\pi$
$360$		0			0
$361$	−338.112			−0.936597
$362$	231.735	+	502.377i	0.640151	+	1.38778i
$363$	−214.652	−	437.275i	−0.591329	−	1.20461i
$364$	−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	$-0.247377\pi$
$367$	4.27652	+	4.27652i	0.0116527	+	0.0116527i	−0.701256	+	0.712909i	$0.747377\pi$
$368$	180.281	−	248.602i	0.489894	−	0.675550i
$369$	−43.3271	−	33.4971i	−0.117418	−	0.0907781i
$370$		0			0
$371$	−114.785			−0.309393
$372$	−41.7674	+	163.519i	−0.112278	+	0.439567i
$373$	−363.822	−	363.822i	−0.975394	−	0.975394i	0.0243109	−	0.999704i	$-0.492261\pi$
$373$	−363.822	−	363.822i	−0.975394	−	0.975394i	−0.999704	+	0.0243109i	$0.992261\pi$
$374$	−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
$378$	142.554	−	229.918i	0.377127	−	0.608248i
$379$	732.379			1.93240			0.966199	−	0.257796i	$-0.0829962\pi$
$379$	732.379			1.93240			0.966199	+	0.257796i	$0.0829962\pi$
$380$		0			0
$381$	−128.995	+	377.749i	−0.338570	+	0.991467i
$382$	−284.835	−	617.492i	−0.745641	−	1.61647i
$383$	−343.246	−	343.246i	−0.896203	−	0.896203i	0.0988948	−	0.995098i	$-0.468469\pi$
$383$	−343.246	−	343.246i	−0.896203	−	0.896203i	−0.995098	+	0.0988948i	$0.968469\pi$
$384$	−362.007	+	128.090i	−0.942727	+	0.333567i
$385$		0			0
$386$	−98.7977	+	267.987i	−0.255952	+	0.694267i
$387$	92.4613	+	722.612i	0.238918	+	1.86721i
$388$	38.0980	+	481.332i	0.0981907	+	1.24055i
$389$	−600.575			−1.54389			−0.771947	−	0.635687i	$-0.780717\pi$
$389$	−600.575			−1.54389			−0.771947	+	0.635687i	$0.780717\pi$
$390$		0			0
$391$		−	264.025i		−	0.675255i
$392$	51.7819	−	184.077i	0.132097	−	0.469583i
$393$	191.882	+	390.889i	0.488250	+	0.994628i
$394$	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	−0.229513	−	0.973306i	$-0.573713\pi$
$397$	295.285	−	295.285i	0.743792	−	0.743792i	0.973306	+	0.229513i	$0.0737135\pi$
$398$	240.152	+	520.625i	0.603398	+	1.30810i
$399$	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	$-0.122213\pi$
$402$	−455.529	+	47.1436i	−1.13316	+	0.117273i
$403$	−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
$408$	−187.311	+	271.869i	−0.459094	+	0.666346i
$409$		−	53.8159i		−	0.131579i	−0.997834	−	0.0657896i	$-0.979043\pi$
$409$		−	53.8159i		−	0.131579i	0.997834	−	0.0657896i	$-0.0209566\pi$
$410$		0			0
$411$	−82.4035	+	241.310i	−0.200495	+	0.587130i
$412$	−12.7775	−	161.432i	−0.0310134	−	0.391825i
$413$	−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
$417$	16.6548	+	33.9281i	0.0399397	+	0.0813623i
$418$	−67.4667	−	146.261i	−0.161404	−	0.349906i
$419$			582.593i			1.39044i	0.718799	+	0.695218i	$0.244692\pi$
$419$			582.593i			1.39044i	−0.718799	+	0.695218i	$0.755308\pi$
$420$		0			0
$421$	486.678			1.15600			0.578002	−	0.816035i	$-0.303833\pi$
$421$	486.678			1.15600			0.578002	+	0.816035i	$0.303833\pi$
$422$	−333.875	+	154.009i	−0.791173	+	0.364950i
$423$	28.4713	+	222.511i	0.0673080	+	0.526032i
$424$	−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
$428$	−12.5785	−	158.918i	−0.0293891	−	0.371304i
$429$	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	$0.277510\pi$
$432$	18.9292	−	431.585i	0.0438177	−	0.999040i
$433$	−152.907	−	152.907i	−0.353135	−	0.353135i	0.508140	−	0.861275i	$-0.330333\pi$
$433$	−152.907	−	152.907i	−0.353135	−	0.353135i	−0.861275	+	0.508140i	$0.830333\pi$
$434$	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
$438$	−107.022	+	11.0759i	−0.244342	+	0.0252874i
$439$	−218.824			−0.498461			−0.249231	−	0.968444i	$-0.580178\pi$
$439$	−218.824			−0.498461			−0.249231	+	0.968444i	$0.580178\pi$
$440$		0			0
$441$	170.192	+	131.579i	0.385923	+	0.298365i
$442$	−305.467	+	140.905i	−0.691101	+	0.318789i
$443$	39.9964	+	39.9964i	0.0902853	+	0.0902853i	0.750807	−	0.660522i	$-0.229665\pi$
$443$	39.9964	+	39.9964i	0.0902853	+	0.0902853i	−0.660522	+	0.750807i	$0.729665\pi$
$444$	147.690	−	87.5923i	0.332635	−	0.197280i
$445$		0			0
$446$	18.6342	+	6.86980i	0.0417808	+	0.0154031i
$447$	−34.2699	−	69.8122i	−0.0766665	−	0.156180i
$448$	75.2655	+	311.663i	0.168003	+	0.695676i
$449$	236.471			0.526660			0.263330	−	0.964706i	$-0.415179\pi$
$449$	236.471			0.526660			0.263330	+	0.964706i	$0.415179\pi$
$450$		0			0
$451$			102.435i			0.227128i
$452$	−45.1977	−	571.030i	−0.0999949	−	1.26334i
$453$	−539.626	+	264.895i	−1.19123	+	0.584757i
$454$	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	−0.389657	−	0.920960i	$-0.627406\pi$
$457$	242.806	−	242.806i	0.531304	−	0.531304i	0.920960	+	0.389657i	$0.127406\pi$
$458$	−490.575	+	226.291i	−1.07112	+	0.494085i
$459$	−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	$-0.244589\pi$
$462$	−503.305	+	52.0879i	−1.08940	+	0.112744i
$463$	162.780	−	162.780i	0.351577	−	0.351577i	−0.509119	−	0.860696i	$-0.670029\pi$
$463$	162.780	−	162.780i	0.351577	−	0.351577i	0.860696	+	0.509119i	$0.170029\pi$
$464$	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	−0.0862867	−	0.996270i	$-0.527500\pi$
$467$	424.962	−	424.962i	0.909984	−	0.909984i	0.996270	+	0.0862867i	$0.0275001\pi$
$468$	240.915	−	368.398i	0.514775	−	0.787175i
$469$			382.377i			0.815304i
$470$		0			0
$471$	562.066	+	191.936i	1.19335	+	0.407508i
$472$	−9.47025	+	33.6653i	−0.0200641	+	0.0713248i
$473$	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
$477$	−26.1723	−	204.544i	−0.0548685	−	0.428813i
$478$	−83.7902	+	38.6505i	−0.175293	+	0.0808588i
$479$		−	439.071i		−	0.916641i	−0.888787	−	0.458321i	$-0.848451\pi$
$479$		−	439.071i		−	0.916641i	0.888787	−	0.458321i	$-0.151549\pi$
$480$		0			0
$481$	174.962			0.363747
$482$	177.736	+	385.312i	0.368746	+	0.799403i
$483$	258.941	−	127.111i	0.536109	−	0.263169i
$484$	−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	$-0.102300\pi$
$487$	308.231	+	308.231i	0.632918	+	0.632918i	−0.315881	+	0.948799i	$0.602300\pi$
$488$	65.6341	+	18.4633i	0.134496	+	0.0378345i
$489$	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	$0.777478\pi$
$492$	−18.0714	+	70.7496i	−0.0367306	+	0.143800i
$493$	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
$498$	537.955	−	55.6739i	1.08023	−	0.111795i
$499$	−304.485			−0.610191			−0.305096	−	0.952322i	$-0.598688\pi$
$499$	−304.485			−0.610191			−0.305096	+	0.952322i	$0.598688\pi$
$500$		0			0
$501$	−338.286	−	115.519i	−0.675221	−	0.230577i
$502$	133.774	+	290.007i	0.266481	+	0.577704i
$503$	230.058	+	230.058i	0.457372	+	0.457372i	0.897792	−	0.440420i	$-0.145170\pi$
$503$	230.058	+	230.058i	0.457372	+	0.457372i	−0.440420	+	0.897792i	$0.645170\pi$
$504$	−356.812	−	52.8166i	−0.707961	−	0.104795i
$505$		0			0
$506$	223.519	−	606.293i	0.441738	−	1.19821i
$507$	−52.5035	+	25.7733i	−0.103557	+	0.0508348i
$508$	530.563	−	41.9947i	1.04442	−	0.0826667i
$509$	98.9386			0.194378			0.0971892	−	0.995266i	$-0.469015\pi$
$509$	98.9386			0.194378			0.0971892	+	0.995266i	$0.469015\pi$
$510$		0			0
$511$			89.8357i			0.175804i
$512$	348.301	+	375.274i	0.680276	+	0.732956i
$513$	126.552	+	25.8912i	0.246690	+	0.0504702i
$514$	−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
$518$	−60.0528	−	130.188i	−0.115932	−	0.251328i
$519$	−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	$-0.154452\pi$
$522$	−260.928	−	59.9791i	−0.499863	−	0.114902i
$523$	303.922	−	303.922i	0.581112	−	0.581112i	−0.354096	−	0.935209i	$-0.615212\pi$
$523$	303.922	−	303.922i	0.581112	−	0.581112i	0.935209	+	0.354096i	$0.115212\pi$
$524$	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
$528$	−660.291	+	465.733i	−1.25055	+	0.882069i
$529$		−	160.623i		−	0.303636i
$530$		0			0
$531$	−31.1260	−	24.0641i	−0.0586176	−	0.0453185i
$532$	−95.5710	+	7.56456i	−0.179645	+	0.0142191i
$533$	−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
$537$	−73.3246	+	35.9941i	−0.136545	+	0.0670281i
$538$	−0.455200	−	0.986826i	−0.000846097	−	0.00183425i
$539$		−	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	$0.616831\pi$
$542$	658.936	−	303.952i	1.21575	−	0.560797i
$543$	365.689	+	744.956i	0.673460	+	1.37193i
$544$	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	$-0.320242\pi$
$547$	−169.325	−	169.325i	−0.309551	−	0.309551i	−0.844735	+	0.535184i	$0.820242\pi$
$548$	338.929	−	26.8267i	0.618484	−	0.0489538i
$549$	−46.9156	+	60.6834i	−0.0854565	+	0.110534i
$550$		0			0
$551$	−71.1604			−0.129148
$552$	261.343	−	379.322i	0.473447	−	0.687177i
$553$	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	$-0.378962\pi$
$557$	−310.481	−	310.481i	−0.557417	−	0.557417i	−0.928571	+	0.371155i	$0.878962\pi$
$558$	−56.7128	+	246.719i	−0.101636	+	0.442149i
$559$	989.727			1.77053
$560$		0			0
$561$	−224.501	+	657.427i	−0.400179	+	1.17188i
$562$	578.887	−	267.027i	1.03005	−	0.475137i
$563$	−234.187	−	234.187i	−0.415962	−	0.415962i	0.467847	−	0.883809i	$-0.345030\pi$
$563$	−234.187	−	234.187i	−0.415962	−	0.415962i	−0.883809	+	0.467847i	$0.845030\pi$
$564$	257.259	−	152.575i	0.456132	−	0.270524i
$565$		0			0
$566$	591.898	+	218.212i	1.04576	+	0.385534i
$567$	205.445	−	349.937i	0.362336	−	0.617173i
$568$	282.383	+	79.4360i	0.497153	+	0.139852i
$569$	−386.708			−0.679627			−0.339813	−	0.940493i	$-0.610364\pi$
$569$	−386.708			−0.679627			−0.339813	+	0.940493i	$0.610364\pi$
$570$		0			0
$571$			556.152i			0.973996i	0.873403	+	0.486998i	$0.161908\pi$
$571$			556.152i			0.973996i	−0.873403	+	0.486998i	$0.838092\pi$
$572$	−820.747	+	64.9631i	−1.43487	+	0.113572i
$573$	−449.483	−	915.656i	−0.784439	−	1.59800i
$574$	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	−0.233530	+	0.972350i	$0.575028\pi$
$577$	−695.792	+	695.792i	−1.20588	+	1.20588i	−0.972350	+	0.233530i	$0.924972\pi$
$578$	−181.187	+	83.5775i	−0.313473	+	0.144598i
$579$	−138.451	+	405.440i	−0.239121	+	0.700242i
$580$		0			0
$581$		−	451.566i		−	0.777223i
$582$	74.5563	+	720.408i	0.128104	+	1.23781i
$583$	−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	−0.882344	−	0.470604i	$-0.844036\pi$
$587$	−241.691	+	241.691i	−0.411740	+	0.411740i	0.470604	+	0.882344i	$0.344036\pi$
$588$	70.9859	−	277.909i	0.120724	−	0.472635i
$589$			67.2853i			0.114236i
$590$		0			0
$591$	309.289	−	905.721i	0.523331	−	1.53252i
$592$	−185.343	−	134.407i	−0.313080	−	0.227039i
$593$	109.471	−	109.471i	0.184605	−	0.184605i	−0.608754	−	0.793359i	$-0.708330\pi$
$593$	109.471	−	109.471i	0.184605	−	0.184605i	0.793359	+	0.608754i	$0.208330\pi$
$594$	−207.579	−	885.001i	−0.349459	−	1.48990i
$595$		0			0
$596$	−67.3082	+	78.8791i	−0.112933	+	0.132348i
$597$	378.972	+	772.015i	0.634794	+	1.29316i
$598$	426.199	−	196.596i	0.712707	−	0.328755i
$599$		−	527.412i		−	0.880487i	−0.897878	−	0.440243i	$-0.854892\pi$
$599$		−	527.412i		−	0.880487i	0.897878	−	0.440243i	$-0.145108\pi$
$600$		0			0
$601$	−133.338			−0.221861			−0.110930	−	0.993828i	$-0.535383\pi$
$601$	−133.338			−0.221861			−0.110930	+	0.993828i	$0.535383\pi$
$602$	−339.707	−	736.448i	−0.564297	−	1.22334i
$603$	−681.388	+	87.1866i	−1.13000	+	0.144588i
$604$	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	$-0.404929\pi$
$607$	−401.515	−	401.515i	−0.661475	−	0.661475i	−0.955728	+	0.294253i	$0.904929\pi$
$608$	−127.198	+	85.1967i	−0.209207	+	0.140126i
$609$	−72.2410	+	211.550i	−0.118622	+	0.347373i
$610$		0			0
$611$	304.763			0.498794
$612$	−271.041	+	414.466i	−0.442878	+	0.677233i
$613$	604.618	+	604.618i	0.986326	+	0.986326i	0.999908	−	0.0135821i	$-0.00432346\pi$
$613$	604.618	+	604.618i	0.986326	+	0.986326i	−0.0135821	+	0.999908i	$0.504323\pi$
$614$	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	$-0.268829\pi$
$617$	−51.5846	−	51.5846i	−0.0836055	−	0.0836055i	−0.747673	+	0.664067i	$0.768829\pi$
$618$	−25.0051	−	241.615i	−0.0404614	−	0.390962i
$619$	−1063.63			−1.71831			−0.859155	−	0.511716i	$-0.829010\pi$
$619$	−1063.63			−1.71831			−0.859155	+	0.511716i	$0.829010\pi$
$620$		0			0
$621$	285.550	+	432.444i	0.459823	+	0.696367i
$622$	22.2251	+	48.1816i	0.0357316	+	0.0774623i
$623$	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
$627$	−106.466	−	216.884i	−0.169802	−	0.345908i
$628$	−62.4854	−	789.443i	−0.0994990	−	1.25707i
$629$	−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	$-0.229894\pi$
$632$	681.043	+	191.581i	1.07760	+	0.303135i
$633$	−495.091	+	243.034i	−0.782134	+	0.383939i
$634$	−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
$638$	209.754	+	454.725i	0.328768	+	0.712735i
$639$	−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	$0.974008\pi$
$642$	−24.6157	−	237.852i	−0.0383423	−	0.370486i
$643$	357.160	−	357.160i	0.555459	−	0.555459i	−0.372552	−	0.928011i	$-0.621517\pi$
$643$	357.160	−	357.160i	0.555459	−	0.555459i	0.928011	+	0.372552i	$0.121517\pi$
$644$	−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	−0.956031	−	0.293266i	$-0.905258\pi$
$647$	−428.808	+	428.808i	−0.662764	+	0.662764i	0.293266	+	0.956031i	$0.405258\pi$
$648$	12.7606	−	647.874i	0.0196923	−	0.999806i
$649$			73.5884i			0.113387i
$650$		0			0
$651$	200.030	+	68.3070i	0.307266	+	0.104926i
$652$	−26.1706	−	330.641i	−0.0401390	−	0.507118i
$653$	−216.356	+	216.356i	−0.331327	+	0.331327i	−0.853090	−	0.521763i	$-0.825274\pi$
$653$	−216.356	+	216.356i	−0.331327	+	0.331327i	0.521763	+	0.853090i	$0.325274\pi$
$654$	−744.833	−	605.123i	−1.13889	−	0.925265i
$655$		0			0
$656$	96.1491	−	15.3166i	0.146569	−	0.0233485i
$657$	−160.085	+	20.4836i	−0.243661	+	0.0311775i
$658$	−104.605	−	226.772i	−0.158974	−	0.344638i
$659$			862.678i			1.30907i	0.756031	+	0.654535i	$0.227136\pi$
$659$			862.678i			1.30907i	−0.756031	+	0.654535i	$0.772864\pi$
$660$		0			0
$661$	56.1770			0.0849879			0.0424939	−	0.999097i	$-0.486470\pi$
$661$	56.1770			0.0849879			0.0424939	+	0.999097i	$0.486470\pi$
$662$	517.494	−	238.708i	0.781714	−	0.360587i
$663$	−452.966	+	222.355i	−0.683206	+	0.335377i
$664$	−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
$668$	37.6075	+	475.135i	0.0562987	+	0.711281i
$669$	28.1919	+	9.62707i	0.0421404	+	0.0143902i
$670$		0			0
$671$	143.468			0.213813
$672$	124.149	+	464.633i	0.184745	+	0.691419i
$673$	−236.472	−	236.472i	−0.351371	−	0.351371i	0.509249	−	0.860619i	$-0.329923\pi$
$673$	−236.472	−	236.472i	−0.351371	−	0.351371i	−0.860619	+	0.509249i	$0.829923\pi$
$674$	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	−0.992437	−	0.122759i	$-0.960826\pi$
$677$	−754.987	−	754.987i	−1.11520	−	1.11520i	−0.122759	−	0.992437i	$-0.539174\pi$
$678$	−88.4502	−	854.659i	−0.130458	−	1.26056i
$679$	604.720			0.890604
$680$		0			0
$681$	147.224	+	50.2744i	0.216187	+	0.0738244i
$682$	429.962	−	198.332i	0.630443	−	0.290809i
$683$	−848.561	−	848.561i	−1.24240	−	1.24240i	−0.959002	−	0.283401i	$-0.908537\pi$
$683$	−848.561	−	848.561i	−1.24240	−	1.24240i	−0.283401	−	0.959002i	$-0.591463\pi$
$684$	−35.2712	−	168.581i	−0.0515661	−	0.246463i
$685$		0			0
$686$	−685.353	−	252.666i	−0.999057	−	0.368318i
$687$	−727.455	+	357.098i	−1.05889	+	0.519794i
$688$	−1048.45	−	760.314i	−1.52391	−	1.10511i
$689$	−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	$-0.248747\pi$
$692$	22.8684	+	288.920i	0.0330468	+	0.417515i
$693$	−752.851	+	96.3306i	−1.08637	+	0.139005i
$694$	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
$698$	234.594	−	108.213i	0.336094	−	0.155033i
$699$	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	$-0.00182231\pi$
$702$	347.930	−	561.158i	0.495626	−	0.799371i
$703$	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
$708$	−12.9824	+	50.8261i	−0.0183368	+	0.0717883i
$709$		−	378.225i		−	0.533463i	−0.963771	−	0.266731i	$-0.914056\pi$
$709$		−	378.225i		−	0.533463i	0.963771	−	0.266731i	$-0.0859437\pi$
$710$		0			0
$711$	−486.813	+	629.673i	−0.684688	+	0.885615i
$712$	885.794	+	249.179i	1.24409	+	0.349970i
$713$	−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
$717$	−124.249	+	60.9924i	−0.173291	+	0.0850660i
$718$	−380.872	+	175.688i	−0.530463	+	0.244690i
$719$			901.949i			1.25445i	0.778838	+	0.627225i	$0.215809\pi$
$719$			901.949i			1.25445i	−0.778838	+	0.627225i	$0.784191\pi$
$720$		0			0
$721$	−202.815			−0.281296
$722$	283.245	+	614.044i	0.392305	+	0.850477i
$723$	280.476	+	571.365i	0.387933	+	0.790270i
$724$	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	$-0.466846\pi$
$727$	−647.476	−	647.476i	−0.890613	−	0.890613i	−0.994581	+	0.103967i	$0.966846\pi$
$728$	−132.700	+	471.729i	−0.182280	+	0.647979i
$729$	670.424	+	286.308i	0.919649	+	0.392740i
$730$		0			0
$731$	−1113.49			−1.52325
$732$	99.0909	+	25.3106i	0.135370	+	0.0345773i
$733$	664.993	+	664.993i	0.907221	+	0.907221i	0.996047	−	0.0888262i	$-0.0283116\pi$
$733$	664.993	+	664.993i	0.907221	+	0.907221i	−0.0888262	+	0.996047i	$0.528312\pi$
$734$	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
$738$	−24.5379	+	106.748i	−0.0332492	+	0.144645i
$739$	−605.307			−0.819090			−0.409545	−	0.912290i	$-0.634313\pi$
$739$	−605.307			−0.819090			−0.409545	+	0.912290i	$0.634313\pi$
$740$		0			0
$741$	56.7120	−	166.075i	0.0765344	−	0.224123i
$742$	96.1580	+	208.460i	0.129593	+	0.280944i
$743$	149.548	+	149.548i	0.201275	+	0.201275i	0.800546	−	0.599271i	$-0.204543\pi$
$743$	149.548	+	149.548i	0.201275	+	0.201275i	−0.599271	+	0.800546i	$0.704543\pi$
$744$	331.956	−	61.1303i	0.446178	−	0.0821643i
$745$		0			0
$746$	−355.954	+	965.519i	−0.477150	+	1.29426i
$747$	804.681	−	102.963i	1.07722	−	0.137835i
$748$	923.382	−	73.0868i	1.23447	−	0.0977096i
$749$	−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	$-0.228516\pi$
$752$	−322.846	−	234.121i	−0.429316	−	0.311331i
$753$	211.101	+	430.041i	0.280347	+	0.571103i
$754$	−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	−0.979863	−	0.199669i	$-0.936013\pi$
$757$	−590.607	+	590.607i	−0.780195	+	0.780195i	0.199669	+	0.979863i	$0.436013\pi$
$758$	−613.532	−	1330.07i	−0.809410	−	1.75471i
$759$	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	$0.925132\pi$
$762$	794.092	−	82.1820i	1.04212	−	0.107850i
$763$	−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
$768$	535.886	+	550.137i	0.697768	+	0.716324i
$769$			262.078i			0.340804i	0.985375	+	0.170402i	$0.0545067\pi$
$769$			262.078i			0.340804i	−0.985375	+	0.170402i	$0.945493\pi$
$770$		0			0
$771$	−134.484	+	393.822i	−0.174428	+	0.510794i
$772$	569.456	−	45.0732i	0.737638	−	0.0583849i
$773$	616.984	−	616.984i	0.798168	−	0.798168i	−0.184639	−	0.982806i	$-0.559112\pi$
$773$	616.984	−	616.984i	0.798168	−	0.798168i	0.982806	+	0.184639i	$0.0591115\pi$
$774$	1234.88	−	773.269i	1.59545	−	0.999056i
$775$		0			0
$776$	842.231	−	472.413i	1.08535	−	0.608780i
$777$	−94.7662	−	193.051i	−0.121964	−	0.248457i
$778$	503.117	+	1090.70i	0.646679	+	1.40193i
$779$			29.1122i			0.0373713i
$780$		0			0
$781$	617.256			0.790340
$782$	−479.495	+	221.180i	−0.613165	+	0.282839i
$783$	−393.450	−	80.4958i	−0.502490	−	0.102804i
$784$	−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	$-0.389170\pi$
$787$	−471.258	−	471.258i	−0.598803	−	0.598803i	−0.939994	+	0.341191i	$0.889170\pi$
$788$	−1272.12	+	100.690i	−1.61437	+	0.127779i
$789$	194.578	−	569.802i	0.246614	−	0.722183i
$790$		0			0
$791$	−717.412			−0.906969
$792$	−973.287	+	722.300i	−1.22890	+	0.911995i
$793$	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	$-0.108189\pi$
$797$	485.701	+	485.701i	0.609411	+	0.609411i	−0.333381	+	0.942792i	$0.608189\pi$
$798$	−143.041	+	14.8036i	−0.179249	+	0.0185508i
$799$	−342.874			−0.429129
$800$		0			0
$801$	−633.170	+	818.979i	−0.790474	+	1.02245i
$802$	−545.578	+	251.663i	−0.680271	+	0.313794i
$803$	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
$807$	−0.718328	−	1.46333i	−0.000890122	−	0.00181329i
$808$	−344.272	+	1223.83i	−0.426079	+	1.51465i
$809$	−183.688			−0.227056			−0.113528	−	0.993535i	$-0.536215\pi$
$809$	−183.688			−0.227056			−0.113528	+	0.993535i	$0.536215\pi$
$810$		0			0
$811$			1332.68i			1.64325i	0.570027	+	0.821626i	$0.306933\pi$
$811$			1332.68i			1.64325i	−0.570027	+	0.821626i	$0.693067\pi$
$812$	297.131	−	23.5182i	0.365924	−	0.0289634i
$813$	977.111	−	479.651i	1.20186	−	0.589977i
$814$	−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
$818$	−97.7350	+	45.0829i	−0.119480	+	0.0551136i
$819$	−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	$0.750879\pi$
$822$	507.275	−	52.4988i	0.617123	−	0.0638672i
$823$	−420.085	+	420.085i	−0.510432	+	0.510432i	−0.914659	−	0.404227i	$-0.867541\pi$
$823$	−420.085	+	420.085i	−0.510432	+	0.510432i	0.404227	+	0.914659i	$0.367541\pi$
$824$	−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	−0.380066	−	0.924959i	$-0.624099\pi$
$827$	450.627	−	450.627i	0.544893	−	0.544893i	0.924959	+	0.380066i	$0.124099\pi$
$828$	378.167	−	578.279i	0.456723	−	0.698404i
$829$			1059.56i			1.27812i	0.769155	+	0.639062i	$0.220677\pi$
$829$			1059.56i			1.27812i	−0.769155	+	0.639062i	$0.779323\pi$
$830$		0			0
$831$	−318.094	−	108.624i	−0.382785	−	0.130715i
$832$	183.700	+	760.672i	0.220793	+	0.914270i
$833$	−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
$837$	−76.1123	+	372.024i	−0.0909346	+	0.444473i
$838$	1058.05	−	488.053i	1.26259	−	0.582402i
$839$			425.692i			0.507380i	0.967286	+	0.253690i	$0.0816443\pi$
$839$			425.692i			0.507380i	−0.967286	+	0.253690i	$0.918356\pi$
$840$		0			0
$841$	−619.762			−0.736935
$842$	−407.702	−	883.855i	−0.484207	−	1.04971i
$843$	858.410	−	421.382i	1.01828	−	0.499860i
$844$	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
$848$	296.776	+	215.216i	0.349972	+	0.253792i
$849$	895.488	+	305.794i	1.05476	+	0.360182i
$850$		0			0
$851$	274.640			0.322726
$852$	426.327	+	108.896i	0.500384	+	0.127812i
$853$	−533.860	−	533.860i	−0.625861	−	0.625861i	0.321163	−	0.947024i	$-0.395926\pi$
$853$	−533.860	−	533.860i	−0.625861	−	0.625861i	−0.947024	+	0.321163i	$0.895926\pi$
$854$	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	$-0.407447\pi$
$857$	−575.339	−	575.339i	−0.671340	−	0.671340i	−0.958025	+	0.286685i	$0.907447\pi$
$858$	−1228.41	+	127.130i	−1.43171	+	0.148171i
$859$	730.948			0.850929			0.425465	−	0.904975i	$-0.360111\pi$
$859$	730.948			0.850929			0.425465	+	0.904975i	$0.360111\pi$
$860$		0			0
$861$	86.5468	+	29.5543i	0.100519	+	0.0343256i
$862$	−464.635	−	1007.28i	−0.539019	−	1.16854i
$863$	503.710	+	503.710i	0.583673	+	0.583673i	0.935911	−	0.352238i	$-0.114579\pi$
$863$	503.710	+	503.710i	0.583673	+	0.583673i	−0.352238	+	0.935911i	$0.614579\pi$
$864$	−799.659	+	327.172i	−0.925531	+	0.378672i
$865$		0			0
$866$	−149.601	+	405.789i	−0.172749	+	0.468579i
$867$	−268.676	+	131.889i	−0.309891	+	0.152122i
$868$	−22.2375	−	280.950i	−0.0256193	−	0.323675i
$869$	1488.68			1.71310
$870$		0			0
$871$			933.264i			1.07149i
$872$	−346.496	+	1231.74i	−0.397358	+	1.41255i
$873$	137.883	+	1077.60i	0.157942	+	1.23436i
$874$	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	0.155586	−	0.987822i	$-0.450273\pi$
$877$	1002.77	−	1002.77i	1.14341	−	1.14341i	0.987822	−	0.155586i	$-0.0497266\pi$
$878$	183.315	+	397.407i	0.208787	+	0.452627i
$879$	−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	$-0.274261\pi$
$882$	96.3865	−	419.312i	0.109282	−	0.475411i
$883$	29.5709	−	29.5709i	0.0334891	−	0.0334891i	−0.690164	−	0.723653i	$-0.742462\pi$
$883$	29.5709	−	29.5709i	0.0334891	−	0.0334891i	0.723653	+	0.690164i	$0.242462\pi$
$884$	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	−0.0780457	−	0.996950i	$-0.524868\pi$
$887$	815.068	−	815.068i	0.918904	−	0.918904i	0.996950	+	0.0780457i	$0.0248680\pi$
$888$	−282.800	−	194.842i	−0.318469	−	0.219416i
$889$		−	666.572i		−	0.749799i
$890$		0			0
$891$	−343.318	−	1319.60i	−0.385318	−	1.48103i
$892$	−3.13412	−	39.5966i	−0.00351359	−	0.0443908i
$893$	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
$897$	631.994	−	310.238i	0.704564	−	0.345861i
$898$	−198.097	−	429.454i	−0.220598	−	0.478234i
$899$		−	209.190i		−	0.232692i
$900$		0			0
$901$	315.187			0.349819
$902$	186.031	−	85.8120i	0.206243	−	0.0951352i
$903$	−536.074	−	1092.05i	−0.593659	−	1.20936i
$904$	−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	$-0.108450\pi$
$907$	551.789	+	551.789i	0.608367	+	0.608367i	−0.334152	+	0.942519i	$0.608450\pi$
$908$	−16.3670	−	206.781i	−0.0180253	−	0.227733i
$909$	−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	$0.177066\pi$
$912$	−187.657	+	132.363i	−0.205764	+	0.145135i
$913$	−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
$918$	−391.438	+	631.331i	−0.426403	+	0.687725i
$919$	−1012.94			−1.10222			−0.551109	−	0.834433i	$-0.685795\pi$
$919$	−1012.94			−1.10222			−0.551109	+	0.834433i	$0.685795\pi$
$920$		0			0
$921$	453.130	−	1326.95i	0.491998	−	1.44077i
$922$	−1163.71	+	536.794i	−1.26216	+	0.582207i
$923$	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
$927$	−46.2441	−	361.411i	−0.0498858	−	0.389872i
$928$	395.459	−	264.877i	0.426141	−	0.285427i
$929$	−1529.05			−1.64591			−0.822955	−	0.568106i	$-0.807676\pi$
$929$	−1529.05			−1.64591			−0.822955	+	0.568106i	$0.807676\pi$
$930$		0			0
$931$		−	114.355i		−	0.122830i
$932$	−24.6446	−	311.361i	−0.0264427	−	0.334079i
$933$	35.0722	+	71.4467i	0.0375908	+	0.0765773i
$934$	−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	−0.965926	−	0.258818i	$-0.916667\pi$
$937$	−662.561	+	662.561i	−0.707109	+	0.707109i	0.258818	+	0.965926i	$0.416667\pi$
$938$	694.435	−	320.327i	0.740336	−	0.341500i
$939$	−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	$-0.170623\pi$
$942$	−122.281	−	1181.56i	−0.129811	−	1.25431i
$943$	−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	−0.424202	+	0.905568i	$0.639445\pi$
$947$	−1259.29	+	1259.29i	−1.32977	+	1.32977i	−0.905568	+	0.424202i	$0.860555\pi$
$948$	1028.20	+	262.632i	1.08460	+	0.277038i
$949$			219.261i			0.231044i
$950$		0			0
$951$	−91.3247	+	267.435i	−0.0960302	+	0.281215i
$952$	149.294	−	530.719i	0.156822	−	0.557478i
$953$	62.1880	−	62.1880i	0.0652550	−	0.0652550i	−0.673726	−	0.738981i	$-0.735307\pi$
$953$	62.1880	−	62.1880i	0.0652550	−	0.0652550i	0.738981	+	0.673726i	$0.235307\pi$
$954$	−349.546	+	218.883i	−0.366401	+	0.229437i
$955$		0			0
$956$	140.386	+	119.793i	0.146848	+	0.125306i
$957$	331.002	+	674.295i	0.345875	+	0.704592i
$958$	−797.397	+	367.821i	−0.832356	+	0.383947i
$959$		−	425.813i		−	0.444018i
$960$		0			0
$961$	763.202			0.794174
$962$	−146.570	−	317.749i	−0.152360	−	0.330300i
$963$	−45.5240	−	355.783i	−0.0472731	−	0.369453i
$964$	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	$-0.250273\pi$
$967$	−1.17333	−	1.17333i	−0.00121337	−	0.00121337i	−0.707713	+	0.706500i	$0.750273\pi$
$968$	1250.45	+	351.759i	1.29179	+	0.363387i
$969$	−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	$0.405154\pi$
$972$	−4.32014	−	971.990i	−0.00444459	−	0.999990i
$973$	−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	$-0.149212\pi$
$977$	430.216	+	430.216i	0.440344	+	0.440344i	−0.451784	+	0.892128i	$0.649212\pi$
$978$	−51.2149	−	494.869i	−0.0523670	−	0.506001i
$979$	1936.24			1.97777
$980$		0			0
$981$	−1138.83	−	880.455i	−1.16089	−	0.897507i
$982$	629.685	+	1365.09i	0.641227	+	1.39011i
$983$	−876.585	−	876.585i	−0.891745	−	0.891745i	0.102942	−	0.994687i	$-0.467174\pi$
$983$	−876.585	−	876.585i	−0.891745	−	0.891745i	−0.994687	+	0.102942i	$0.967174\pi$
$984$	143.627	−	26.4492i	0.145963	−	0.0268792i
$985$		0			0
$986$	141.553	−	383.959i	0.143563	−	0.389411i
$987$	−165.071	−	336.272i	−0.167246	−	0.340701i
$988$	−233.259	+	18.4627i	−0.236092	+	0.0186870i
$989$	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	$0.970408\pi$
$992$	−250.453	−	373.924i	−0.252472	−	0.376939i
$993$	767.373	−	376.693i	0.772783	−	0.379349i
$994$	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	−0.831979	−	0.554807i	$-0.812792\pi$
$997$	−276.341	+	276.341i	−0.277172	+	0.277172i	0.554807	+	0.831979i	$0.312792\pi$
$998$	255.075	+	552.976i	0.255586	+	0.554084i
$999$	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.143.8		40
3.2	odd	2	inner	300.3.l.g.143.13		40
4.3	odd	2	inner	300.3.l.g.143.3		40
5.2	odd	4	inner	300.3.l.g.107.18		40
5.3	odd	4		60.3.l.a.47.3	yes	40
5.4	even	2		60.3.l.a.23.13	yes	40
12.11	even	2	inner	300.3.l.g.143.18		40
15.2	even	4	inner	300.3.l.g.107.3		40
15.8	even	4		60.3.l.a.47.18	yes	40
15.14	odd	2		60.3.l.a.23.8	yes	40
20.3	even	4		60.3.l.a.47.8	yes	40
20.7	even	4	inner	300.3.l.g.107.13		40
20.19	odd	2		60.3.l.a.23.18	yes	40
60.23	odd	4		60.3.l.a.47.13	yes	40
60.47	odd	4	inner	300.3.l.g.107.8		40
60.59	even	2		60.3.l.a.23.3	✓	40

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.837725 - 1.81610i) q^{2} +(-1.32197 - 2.69303i) q^{3} +(-2.59643 + 3.04278i) q^{4} +(-3.78336 + 4.65685i) q^{6} +(3.54241 + 3.54241i) q^{7} +(7.70110 + 2.16636i) q^{8} +(-5.50478 + 7.12021i) q^{9} +O(q^{10})\)	\(q+(-0.837725 - 1.81610i) q^{2} +(-1.32197 - 2.69303i) q^{3} +(-2.59643 + 3.04278i) q^{4} +(-3.78336 + 4.65685i) q^{6} +(3.54241 + 3.54241i) q^{7} +(7.70110 + 2.16636i) q^{8} +(-5.50478 + 7.12021i) q^{9} +16.8337 q^{11} +(11.6267 + 2.96979i) 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} +(17.5425 + 4.03246i) q^{18} +4.78419 q^{19} +(4.85684 - 14.2228i) q^{21} +(-14.1020 - 30.5716i) q^{22} +(13.5716 + 13.5716i) q^{23} +(-4.34655 - 23.6031i) q^{24} +(8.45895 - 22.9448i) q^{26} +(26.4521 + 5.41182i) q^{27} +(-19.9764 + 1.58116i) q^{28} -14.8741 q^{29} +14.0641i q^{31} +(-26.5872 + 17.8080i) q^{32} +(-22.2536 - 45.3336i) q^{33} +(-9.51674 + 25.8140i) q^{34} +(-7.37245 - 35.2370i) q^{36} +(10.1182 - 10.1182i) q^{37} +(-4.00784 - 8.68857i) q^{38} +(11.8540 - 34.7134i) q^{39} +6.08509i q^{41} +(-29.8987 + 3.09427i) 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} +(-39.2244 + 27.6667i) q^{48} -23.9027i q^{49} +(-13.3364 + 39.0543i) q^{51} +(-48.7562 + 3.85911i) q^{52} +(-16.2015 + 16.2015i) q^{53} +(-12.3312 - 52.5732i) q^{54} +(19.6063 + 34.9546i) q^{56} +(-6.32456 - 12.8840i) q^{57} +(12.4604 + 27.0128i) q^{58} +4.37150i q^{59} +8.52269 q^{61} +(25.5418 - 11.7818i) q^{62} +(-44.7229 + 5.72249i) q^{63} +(54.6137 + 33.3667i) q^{64} +(-63.6878 + 78.3919i) q^{66} +(53.9714 + 53.9714i) q^{67} +(54.8532 - 4.34170i) q^{68} +(18.6074 - 54.4900i) q^{69} +36.6679 q^{71} +(-57.8178 + 42.9080i) 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} +(-72.9733 + 7.55214i) q^{78} +88.4346 q^{79} +(-20.3947 - 78.3904i) q^{81} +(11.0511 - 5.09763i) q^{82} +(-63.7372 - 63.7372i) q^{83} +(30.6663 + 51.7068i) q^{84} +(-151.896 - 55.9988i) q^{86} +(19.6631 + 40.0563i) q^{87} +(129.638 + 36.4679i) q^{88} +115.022 q^{89} +61.2548i q^{91} +(-76.5332 + 6.05770i) q^{92} +(37.8749 - 18.5923i) q^{93} +(-46.7728 - 17.2435i) q^{94} +(83.1047 + 48.0583i) q^{96} +(85.3544 - 85.3544i) q^{97} +(-43.4096 + 20.0239i) 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

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more