LMFDB - Embedded newform 280.4.q.c.81.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [280,4,Mod(81,280)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("280.81"); S:= CuspForms(chi, 4); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(280, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 0, 4])) N = Newforms(chi, 4, names="a")

Level:	$ N $	$=$	$ 280 = 2^{3} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	280.q (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [12,0,-7] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$16.5205348016$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - x^{11} + 97 x^{10} + 136 x^{9} + 6932 x^{8} + 7120 x^{7} + 190192 x^{6} + 97856 x^{5} + \cdots + 199148544 $ x^12 - x^11 + 97x^10 + 136x^9 + 6932x^8 + 7120x^7 + 190192x^6 + 97856x^5 + 3784384x^4 + 956928x^3 + 32401152x^2 - 9483264x + 199148544
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{14} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			81.1
Root			$4.47849 + 7.75697i$ of defining polynomial
Character	$\chi$	$=$	280.81
Dual form			280.4.q.c.121.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-4.97849 + 8.62300i) q^{3} +(2.50000 + 4.33013i) q^{5} +(-14.6186 + 11.3709i) q^{7} +(-36.0707 - 62.4763i) q^{9} +(15.1914 - 26.3123i) q^{11} -55.7969 q^{13} -49.7849 q^{15} +(5.96029 - 10.3235i) q^{17} +(0.763290 + 1.32206i) q^{19} +(-25.2724 - 182.666i) q^{21} +(81.2906 + 140.800i) q^{23} +(-12.5000 + 21.6506i) q^{25} +449.472 q^{27} -127.122 q^{29} +(27.4919 - 47.6174i) q^{31} +(151.261 + 261.991i) q^{33} +(-85.7838 - 34.8732i) q^{35} +(-195.695 - 338.954i) q^{37} +(277.784 - 481.136i) q^{39} +353.749 q^{41} -277.674 q^{43} +(180.354 - 312.382i) q^{45} +(208.852 + 361.742i) q^{47} +(84.4069 - 332.452i) q^{49} +(59.3465 + 102.791i) q^{51} +(262.824 - 455.225i) q^{53} +151.914 q^{55} -15.2001 q^{57} +(250.925 - 434.614i) q^{59} +(250.034 + 433.072i) q^{61} +(1237.71 + 503.161i) q^{63} +(-139.492 - 241.608i) q^{65} +(-33.8545 + 58.6377i) q^{67} -1618.82 q^{69} -911.524 q^{71} +(31.2672 - 54.1565i) q^{73} +(-124.462 - 215.575i) q^{75} +(77.1164 + 557.389i) q^{77} +(-305.767 - 529.604i) q^{79} +(-1263.78 + 2188.94i) q^{81} -1000.22 q^{83} +59.6029 q^{85} +(632.876 - 1096.17i) q^{87} +(-581.616 - 1007.39i) q^{89} +(815.672 - 634.459i) q^{91} +(273.737 + 474.126i) q^{93} +(-3.81645 + 6.61029i) q^{95} -1156.69 q^{97} -2191.86 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 7 q^{3} + 30 q^{5} - q^{7} - 39 q^{9} + 51 q^{11} - 54 q^{13} - 70 q^{15} - 6 q^{17} - 9 q^{19} + 123 q^{21} + 72 q^{23} - 150 q^{25} + 1118 q^{27} - 242 q^{29} - 132 q^{31} + 156 q^{33} - 115 q^{35}+ \cdots - 6978 q^{99}+O(q^{100}) $ 12 * q - 7 * q^3 + 30 * q^5 - q^7 - 39 * q^9 + 51 * q^11 - 54 * q^13 - 70 * q^15 - 6 * q^17 - 9 * q^19 + 123 * q^21 + 72 * q^23 - 150 * q^25 + 1118 * q^27 - 242 * q^29 - 132 * q^31 + 156 * q^33 - 115 * q^35 - 523 * q^37 + 358 * q^39 + 928 * q^41 - 1202 * q^43 + 195 * q^45 + 73 * q^47 + 753 * q^49 + 28 * q^51 + 999 * q^53 + 510 * q^55 - 1080 * q^57 - 98 * q^59 + 111 * q^61 + 3011 * q^63 - 135 * q^65 - 289 * q^67 - 1794 * q^69 - 3668 * q^71 + 332 * q^73 - 175 * q^75 + 285 * q^77 + 1368 * q^79 - 498 * q^81 + 1678 * q^83 - 60 * q^85 + 1075 * q^87 - 1035 * q^89 + 2368 * q^91 - 448 * q^93 + 45 * q^95 + 8 * q^97 - 6978 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/280\mathbb{Z}\right)^\times$.

$n$	$57$	$71$	$141$	$241$
$\chi(n)$	$1$	$1$	$1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−4.97849	+	8.62300i	−0.958111	+	1.65950i	−0.231027	+	0.972947i	$0.574209\pi$
$3$	−4.97849	+	8.62300i	−0.958111	+	1.65950i	−0.727083	+	0.686549i	$0.759125\pi$
$4$		0			0
$5$	2.50000	+	4.33013i	0.223607	+	0.387298i
$5$	2.50000	+	4.33013i	0.223607	+	0.387298i
$6$		0			0
$7$	−14.6186	+	11.3709i	−0.789330	+	0.613969i
$7$	−14.6186	+	11.3709i	−0.789330	+	0.613969i
$8$		0			0
$9$	−36.0707	−	62.4763i	−1.33595	−	2.31394i
$10$		0			0
$11$	15.1914	−	26.3123i	0.416399	−	0.721224i	−0.579175	−	0.815203i	$-0.696625\pi$
$11$	15.1914	−	26.3123i	0.416399	−	0.721224i	0.995574	+	0.0939792i	$0.0299587\pi$
$12$		0			0
$13$	−55.7969			−1.19041			−0.595203	−	0.803576i	$-0.702928\pi$
$13$	−55.7969			−1.19041			−0.595203	+	0.803576i	$0.702928\pi$
$14$		0			0
$15$	−49.7849			−0.856960
$16$		0			0
$17$	5.96029	−	10.3235i	0.0850343	−	0.147284i	−0.820372	−	0.571831i	$-0.806233\pi$
$17$	5.96029	−	10.3235i	0.0850343	−	0.147284i	0.905406	+	0.424547i	$0.139567\pi$
$18$		0			0
$19$	0.763290	+	1.32206i	0.00921636	+	0.0159632i	0.870597	−	0.491997i	$-0.163733\pi$
$19$	0.763290	+	1.32206i	0.00921636	+	0.0159632i	−0.861380	+	0.507960i	$0.830400\pi$
$20$		0			0
$21$	−25.2724	−	182.666i	−0.262614	−	1.89814i
$22$		0			0
$23$	81.2906	+	140.800i	0.736968	+	1.27647i	0.953854	+	0.300270i	$0.0970767\pi$
$23$	81.2906	+	140.800i	0.736968	+	1.27647i	−0.216886	+	0.976197i	$0.569590\pi$
$24$		0			0
$25$	−12.5000	+	21.6506i	−0.100000	+	0.173205i
$26$		0			0
$27$	449.472			3.20374
$28$		0			0
$29$	−127.122			−0.813999			−0.407000	−	0.913428i	$-0.633425\pi$
$29$	−127.122			−0.813999			−0.407000	+	0.913428i	$0.633425\pi$
$30$		0			0
$31$	27.4919	−	47.6174i	0.159281	−	0.275882i	−0.775329	−	0.631558i	$-0.782416\pi$
$31$	27.4919	−	47.6174i	0.159281	−	0.275882i	0.934609	+	0.355676i	$0.115749\pi$
$32$		0			0
$33$	151.261	+	261.991i	0.797912	+	1.38202i
$34$		0			0
$35$	−85.7838	−	34.8732i	−0.414289	−	0.168419i
$36$		0			0
$37$	−195.695	−	338.954i	−0.869515	−	1.50604i	−0.862493	−	0.506068i	$-0.831098\pi$
$37$	−195.695	−	338.954i	−0.869515	−	1.50604i	−0.00702125	−	0.999975i	$-0.502235\pi$
$38$		0			0
$39$	277.784	−	481.136i	1.14054	−	1.97547i
$40$		0			0
$41$	353.749			1.34747			0.673736	−	0.738973i	$-0.264689\pi$
$41$	353.749			1.34747			0.673736	+	0.738973i	$0.264689\pi$
$42$		0			0
$43$	−277.674			−0.984765			−0.492382	−	0.870379i	$-0.663874\pi$
$43$	−277.674			−0.984765			−0.492382	+	0.870379i	$0.663874\pi$
$44$		0			0
$45$	180.354	−	312.382i	0.597456	−	1.03482i
$46$		0			0
$47$	208.852	+	361.742i	0.648174	+	1.12267i	0.983559	+	0.180589i	$0.0578002\pi$
$47$	208.852	+	361.742i	0.648174	+	1.12267i	−0.335385	+	0.942081i	$0.608866\pi$
$48$		0			0
$49$	84.4069	−	332.452i	0.246084	−	0.969248i
$50$		0			0
$51$	59.3465	+	102.791i	0.162945	+	0.282228i
$52$		0			0
$53$	262.824	−	455.225i	0.681164	−	1.17981i	−0.293462	−	0.955971i	$-0.594808\pi$
$53$	262.824	−	455.225i	0.681164	−	1.17981i	0.974626	−	0.223840i	$-0.0718592\pi$
$54$		0			0
$55$	151.914			0.372438
$56$		0			0
$57$	−15.2001			−0.0353212
$58$		0			0
$59$	250.925	−	434.614i	0.553688	−	0.959016i	−0.444316	−	0.895870i	$-0.646553\pi$
$59$	250.925	−	434.614i	0.553688	−	0.959016i	0.998004	−	0.0631458i	$-0.0201133\pi$
$60$		0			0
$61$	250.034	+	433.072i	0.524813	+	0.909003i	0.999583	+	0.0288929i	$0.00919816\pi$
$61$	250.034	+	433.072i	0.524813	+	0.909003i	−0.474769	+	0.880110i	$0.657469\pi$
$62$		0			0
$63$	1237.71	+	503.161i	2.47519	+	1.00623i
$64$		0			0
$65$	−139.492	−	241.608i	−0.266183	−	0.461042i
$66$		0			0
$67$	−33.8545	+	58.6377i	−0.0617311	+	0.106921i	−0.895239	−	0.445586i	$-0.852995\pi$
$67$	−33.8545	+	58.6377i	−0.0617311	+	0.106921i	0.833508	+	0.552507i	$0.186329\pi$
$68$		0			0
$69$	−1618.82			−2.82439
$70$		0			0
$71$	−911.524			−1.52363			−0.761817	−	0.647793i	$-0.775692\pi$
$71$	−911.524			−1.52363			−0.761817	+	0.647793i	$0.775692\pi$
$72$		0			0
$73$	31.2672	−	54.1565i	0.0501309	−	0.0868292i	−0.839871	−	0.542786i	$-0.817369\pi$
$73$	31.2672	−	54.1565i	0.0501309	−	0.0868292i	0.890002	+	0.455957i	$0.150703\pi$
$74$		0			0
$75$	−124.462	−	215.575i	−0.191622	−	0.331899i
$76$		0			0
$77$	77.1164	+	557.389i	0.114133	+	0.824940i
$78$		0			0
$79$	−305.767	−	529.604i	−0.435462	−	0.754243i	0.561871	−	0.827225i	$-0.310082\pi$
$79$	−305.767	−	529.604i	−0.435462	−	0.754243i	−0.997333	+	0.0729823i	$0.976748\pi$
$80$		0			0
$81$	−1263.78	+	2188.94i	−1.73359	+	3.00266i
$82$		0			0
$83$	−1000.22			−1.32275			−0.661376	−	0.750055i	$-0.730027\pi$
$83$	−1000.22			−1.32275			−0.661376	+	0.750055i	$0.730027\pi$
$84$		0			0
$85$	59.6029			0.0760570
$86$		0			0
$87$	632.876	−	1096.17i	0.779902	−	1.35083i
$88$		0			0
$89$	−581.616	−	1007.39i	−0.692710	−	1.19981i	−0.970947	−	0.239296i	$-0.923083\pi$
$89$	−581.616	−	1007.39i	−0.692710	−	1.19981i	0.278237	−	0.960513i	$-0.410250\pi$
$90$		0			0
$91$	815.672	−	634.459i	0.939623	−	0.730872i
$92$		0			0
$93$	273.737	+	474.126i	0.305217	+	0.528651i
$94$		0			0
$95$	−3.81645	+	6.61029i	−0.00412168	+	0.00713896i
$96$		0			0
$97$	−1156.69			−1.21077			−0.605383	−	0.795934i	$-0.706980\pi$
$97$	−1156.69			−1.21077			−0.605383	+	0.795934i	$0.706980\pi$
$98$		0			0
$99$	−2191.86			−2.22516
$100$		0			0
$101$	−34.8155	+	60.3023i	−0.0342998	+	0.0594089i	−0.882666	−	0.470001i	$-0.844253\pi$
$101$	−34.8155	+	60.3023i	−0.0342998	+	0.0594089i	0.848366	+	0.529410i	$0.177587\pi$
$102$		0			0
$103$	133.433	+	231.112i	0.127646	+	0.221089i	0.922764	−	0.385365i	$-0.125925\pi$
$103$	133.433	+	231.112i	0.127646	+	0.221089i	−0.795118	+	0.606454i	$0.792591\pi$
$104$		0			0
$105$	727.785	−	566.097i	0.676425	−	0.526147i
$106$		0			0
$107$	−279.224	−	483.630i	−0.252277	−	0.436956i	0.711876	−	0.702306i	$-0.247846\pi$
$107$	−279.224	−	483.630i	−0.252277	−	0.436956i	−0.964152	+	0.265350i	$0.914513\pi$
$108$		0			0
$109$	−726.096	+	1257.64i	−0.638049	+	1.10513i	0.347811	+	0.937565i	$0.386925\pi$
$109$	−726.096	+	1257.64i	−0.638049	+	1.10513i	−0.985860	+	0.167569i	$0.946408\pi$
$110$		0			0
$111$	3897.06			3.33237
$112$		0			0
$113$	−222.168			−0.184954			−0.0924769	−	0.995715i	$-0.529478\pi$
$113$	−222.168			−0.184954			−0.0924769	+	0.995715i	$0.529478\pi$
$114$		0			0
$115$	−406.453	+	703.998i	−0.329582	+	0.570853i
$116$		0			0
$117$	2012.63	+	3485.98i	1.59033	+	2.75452i
$118$		0			0
$119$	30.2563	+	218.689i	0.0233075	+	0.168464i
$120$		0			0
$121$	203.941	+	353.237i	0.153224	+	0.265392i
$122$		0			0
$123$	−1761.14	+	3050.38i	−1.29103	+	2.23612i
$124$		0			0
$125$	−125.000			−0.0894427
$126$		0			0
$127$	1150.70			0.804002			0.402001	−	0.915639i	$-0.368315\pi$
$127$	1150.70			0.804002			0.402001	+	0.915639i	$0.368315\pi$
$128$		0			0
$129$	1382.40	−	2394.38i	0.943514	−	1.63421i
$130$		0			0
$131$	−785.481	−	1360.49i	−0.523877	−	0.907381i	−0.999614	−	0.0277934i	$-0.991152\pi$
$131$	−785.481	−	1360.49i	−0.523877	−	0.907381i	0.475737	−	0.879588i	$-0.342181\pi$
$132$		0			0
$133$	−26.1912	−	10.6474i	−0.0170757	−	0.00694168i
$134$		0			0
$135$	1123.68	+	1946.27i	0.716378	+	1.24080i
$136$		0			0
$137$	1324.19	−	2293.57i	0.825792	−	1.43031i	−0.0755201	−	0.997144i	$-0.524062\pi$
$137$	1324.19	−	2293.57i	0.825792	−	1.43031i	0.901312	−	0.433170i	$-0.142605\pi$
$138$		0			0
$139$	−792.411			−0.483536			−0.241768	−	0.970334i	$-0.577727\pi$
$139$	−792.411			−0.483536			−0.241768	+	0.970334i	$0.577727\pi$
$140$		0			0
$141$	−4159.07			−2.48409
$142$		0			0
$143$	−847.634	+	1468.15i	−0.495683	+	0.858549i
$144$		0			0
$145$	−317.805	−	550.455i	−0.182016	−	0.315261i
$146$		0			0
$147$	2446.52	+	2382.95i	1.37269	+	1.33702i
$148$		0			0
$149$	28.5451	+	49.4416i	0.0156947	+	0.0271840i	0.873766	−	0.486346i	$-0.161671\pi$
$149$	28.5451	+	49.4416i	0.0156947	+	0.0271840i	−0.858071	+	0.513530i	$0.828337\pi$
$150$		0			0
$151$	827.925	−	1434.01i	0.446196	−	0.772834i	−0.551939	−	0.833885i	$-0.686112\pi$
$151$	827.925	−	1434.01i	0.446196	−	0.772834i	0.998135	+	0.0610507i	$0.0194451\pi$
$152$		0			0
$153$	−859.968			−0.454407
$154$		0			0
$155$	274.919			0.142465
$156$		0			0
$157$	1620.35	−	2806.53i	0.823682	−	1.42666i	−0.0792397	−	0.996856i	$-0.525249\pi$
$157$	1620.35	−	2806.53i	0.823682	−	1.42666i	0.902922	−	0.429804i	$-0.141417\pi$
$158$		0			0
$159$	2616.93	+	4532.66i	1.30526	+	2.26078i
$160$		0			0
$161$	−2789.37	−	1133.95i	−1.36542	−	0.555078i
$162$		0			0
$163$	−1427.90	−	2473.20i	−0.686146	−	1.18844i	−0.973075	−	0.230488i	$-0.925968\pi$
$163$	−1427.90	−	2473.20i	−0.686146	−	1.18844i	0.286929	−	0.957952i	$-0.407366\pi$
$164$		0			0
$165$	−756.303	+	1309.96i	−0.356837	+	0.618060i
$166$		0			0
$167$	−1995.53			−0.924664			−0.462332	−	0.886707i	$-0.652987\pi$
$167$	−1995.53			−0.924664			−0.462332	+	0.886707i	$0.652987\pi$
$168$		0			0
$169$	916.292			0.417065
$170$		0			0
$171$	55.0649	−	95.3751i	0.0246252	−	0.0426522i
$172$		0			0
$173$	−1126.54	−	1951.22i	−0.495081	−	0.857505i	0.504903	−	0.863176i	$-0.331528\pi$
$173$	−1126.54	−	1951.22i	−0.495081	−	0.857505i	−0.999984	+	0.00567069i	$0.998195\pi$
$174$		0			0
$175$	−63.4539	−	458.638i	−0.0274095	−	0.198113i
$176$		0			0
$177$	2498.45	+	4327.44i	1.06099	+	1.83769i
$178$		0			0
$179$	−948.530	+	1642.90i	−0.396070	+	0.686013i	−0.993237	−	0.116104i	$-0.962959\pi$
$179$	−948.530	+	1642.90i	−0.396070	+	0.686013i	0.597167	+	0.802117i	$0.296293\pi$
$180$		0			0
$181$	2780.22			1.14173			0.570863	−	0.821045i	$-0.306609\pi$
$181$	2780.22			1.14173			0.570863	+	0.821045i	$0.306609\pi$
$182$		0			0
$183$	−4979.17			−2.01132
$184$		0			0
$185$	978.474	−	1694.77i	0.388859	−	0.673523i
$186$		0			0
$187$	−181.091	−	313.658i	−0.0708164	−	0.122658i
$188$		0			0
$189$	−6570.66	+	5110.89i	−2.52881	+	1.96700i
$190$		0			0
$191$	−87.3933	−	151.370i	−0.0331076	−	0.0573441i	0.848997	−	0.528398i	$-0.177207\pi$
$191$	−87.3933	−	151.370i	−0.0331076	−	0.0573441i	−0.882104	+	0.471054i	$0.843874\pi$
$192$		0			0
$193$	978.642	−	1695.06i	0.364996	−	0.632191i	−0.623780	−	0.781600i	$-0.714404\pi$
$193$	978.642	−	1695.06i	0.364996	−	0.632191i	0.988775	+	0.149409i	$0.0477371\pi$
$194$		0			0
$195$	2777.84			1.02013
$196$		0			0
$197$	−3545.05			−1.28210			−0.641051	−	0.767498i	$-0.721501\pi$
$197$	−3545.05			−1.28210			−0.641051	+	0.767498i	$0.721501\pi$
$198$		0			0
$199$	−1386.75	+	2401.92i	−0.493990	+	0.855616i	−0.999976	−	0.00692602i	$-0.997795\pi$
$199$	−1386.75	+	2401.92i	−0.493990	+	0.855616i	0.505986	+	0.862542i	$0.331129\pi$
$200$		0			0
$201$	−337.088	−	583.854i	−0.118290	−	0.204885i
$202$		0			0
$203$	1858.35	−	1445.49i	0.642514	−	0.499770i
$204$		0			0
$205$	884.373	+	1531.78i	0.301304	+	0.521873i
$206$		0			0
$207$	5864.42	−	10157.5i	1.96911	−	3.41060i
$208$		0			0
$209$	46.3819			0.0153507
$210$		0			0
$211$	−4157.59			−1.35650			−0.678248	−	0.734833i	$-0.737260\pi$
$211$	−4157.59			−1.35650			−0.678248	+	0.734833i	$0.737260\pi$
$212$		0			0
$213$	4538.01	−	7860.07i	1.45981	−	2.52846i
$214$		0			0
$215$	−694.185	−	1202.36i	−0.220200	−	0.381398i
$216$		0			0
$217$	139.558	+	1008.71i	0.0436580	+	0.315555i
$218$		0			0
$219$	311.327	+	539.235i	0.0960619	+	0.166384i
$220$		0			0
$221$	−332.566	+	576.021i	−0.101225	+	0.175327i
$222$		0			0
$223$	−395.045			−0.118629			−0.0593143	−	0.998239i	$-0.518891\pi$
$223$	−395.045			−0.118629			−0.0593143	+	0.998239i	$0.518891\pi$
$224$		0			0
$225$	1803.54			0.534381
$226$		0			0
$227$	−2774.03	+	4804.77i	−0.811097	+	1.40486i	0.101000	+	0.994886i	$0.467796\pi$
$227$	−2774.03	+	4804.77i	−0.811097	+	1.40486i	−0.912097	+	0.409975i	$0.865538\pi$
$228$		0			0
$229$	−1197.02	−	2073.29i	−0.345420	−	0.598284i	0.640010	−	0.768366i	$-0.278930\pi$
$229$	−1197.02	−	2073.29i	−0.345420	−	0.598284i	−0.985430	+	0.170082i	$0.945597\pi$
$230$		0			0
$231$	−5190.28	−	2109.98i	−1.47834	−	0.600980i
$232$		0			0
$233$	−90.7583	−	157.198i	−0.0255183	−	0.0441991i	0.852984	−	0.521937i	$-0.174790\pi$
$233$	−90.7583	−	157.198i	−0.0255183	−	0.0441991i	−0.878503	+	0.477738i	$0.841457\pi$
$234$		0			0
$235$	−1044.26	+	1808.71i	−0.289872	+	0.502073i
$236$		0			0
$237$	6089.04			1.66888
$238$		0			0
$239$	−1950.99			−0.528029			−0.264015	−	0.964519i	$-0.585047\pi$
$239$	−1950.99			−0.528029			−0.264015	+	0.964519i	$0.585047\pi$
$240$		0			0
$241$	686.491	−	1189.04i	0.183489	−	0.317812i	−0.759577	−	0.650417i	$-0.774594\pi$
$241$	686.491	−	1189.04i	0.183489	−	0.317812i	0.943066	+	0.332605i	$0.107928\pi$
$242$		0			0
$243$	−6515.59	−	11285.3i	−1.72006	−	2.97924i
$244$		0			0
$245$	1650.58	−	465.638i	0.430414	−	0.121422i
$246$		0			0
$247$	−42.5892	−	73.7667i	−0.0109712	−	0.0190027i
$248$		0			0
$249$	4979.58	−	8624.89i	1.26734	−	2.19510i
$250$		0			0
$251$	−1123.75			−0.282590			−0.141295	−	0.989968i	$-0.545127\pi$
$251$	−1123.75			−0.282590			−0.141295	+	0.989968i	$0.545127\pi$
$252$		0			0
$253$	4939.68			1.22749
$254$		0			0
$255$	−296.733	+	513.956i	−0.0728710	+	0.126216i
$256$		0			0
$257$	2058.81	+	3565.97i	0.499709	+	0.865522i	1.00000		0.000335900i	$-0.000106920\pi$
$257$	2058.81	+	3565.97i	0.499709	+	0.865522i	−0.500291	+	0.865857i	$0.666774\pi$
$258$		0			0
$259$	6714.98	+	2729.81i	1.61100	+	0.654911i
$260$		0			0
$261$	4585.39	+	7942.12i	1.08746	+	1.88354i
$262$		0			0
$263$	740.525	−	1282.63i	0.173622	−	0.300723i	−0.766061	−	0.642768i	$-0.777786\pi$
$263$	740.525	−	1282.63i	0.173622	−	0.300723i	0.939684	+	0.342045i	$0.111119\pi$
$264$		0			0
$265$	2628.24			0.609251
$266$		0			0
$267$	11582.3			2.65477
$268$		0			0
$269$	−2123.18	+	3677.45i	−0.481236	+	0.833526i	−0.999768	−	0.0215327i	$-0.993145\pi$
$269$	−2123.18	+	3677.45i	−0.481236	+	0.833526i	0.518532	+	0.855058i	$0.326479\pi$
$270$		0			0
$271$	−723.730	−	1253.54i	−0.162227	−	0.280985i	0.773440	−	0.633869i	$-0.218534\pi$
$271$	−723.730	−	1253.54i	−0.162227	−	0.280985i	−0.935667	+	0.352884i	$0.885201\pi$
$272$		0			0
$273$	1410.12	+	10192.2i	0.312617	+	2.25956i
$274$		0			0
$275$	379.786	+	657.808i	0.0832797	+	0.144245i
$276$		0			0
$277$	−2170.34	+	3759.14i	−0.470770	+	0.815397i	−0.999441	−	0.0334294i	$-0.989357\pi$
$277$	−2170.34	+	3759.14i	−0.470770	+	0.815397i	0.528671	+	0.848827i	$0.322690\pi$
$278$		0			0
$279$	−3966.62			−0.851165
$280$		0			0
$281$	7100.71			1.50745			0.753724	−	0.657191i	$-0.228256\pi$
$281$	7100.71			1.50745			0.753724	+	0.657191i	$0.228256\pi$
$282$		0			0
$283$	1225.40	−	2122.45i	0.257393	−	0.445818i	−0.708150	−	0.706062i	$-0.750470\pi$
$283$	1225.40	−	2122.45i	0.257393	−	0.445818i	0.965543	+	0.260244i	$0.0838031\pi$
$284$		0			0
$285$	−38.0003	−	65.8185i	−0.00789805	−	0.0136798i
$286$		0			0
$287$	−5171.32	+	4022.43i	−1.06360	+	0.827305i
$288$		0			0
$289$	2385.45	+	4131.72i	0.485538	+	0.840977i
$290$		0			0
$291$	5758.58	−	9974.16i	1.16005	−	2.00926i
$292$		0			0
$293$	−3817.63			−0.761188			−0.380594	−	0.924742i	$-0.624280\pi$
$293$	−3817.63			−0.761188			−0.380594	+	0.924742i	$0.624280\pi$
$294$		0			0
$295$	2509.25			0.495234
$296$		0			0
$297$	6828.12	−	11826.7i	1.33403	−	2.31061i
$298$		0			0
$299$	−4535.76	−	7856.18i	−0.877291	−	1.51951i
$300$		0			0
$301$	4059.20	−	3157.39i	0.777305	−	0.604615i
$302$		0			0
$303$	−346.658	−	600.429i	−0.0657259	−	0.113841i
$304$		0			0
$305$	−1250.17	+	2165.36i	−0.234704	+	0.406519i
$306$		0			0
$307$	6749.01			1.25468			0.627339	−	0.778746i	$-0.284144\pi$
$307$	6749.01			1.25468			0.627339	+	0.778746i	$0.284144\pi$
$308$		0			0
$309$	−2657.17			−0.489195
$310$		0			0
$311$	−1357.38	+	2351.05i	−0.247491	+	0.428668i	−0.962829	−	0.270111i	$-0.912940\pi$
$311$	−1357.38	+	2351.05i	−0.247491	+	0.428668i	0.715338	+	0.698779i	$0.246273\pi$
$312$		0			0
$313$	−4065.03	−	7040.83i	−0.734086	−	1.27147i	−0.955123	−	0.296208i	$-0.904278\pi$
$313$	−4065.03	−	7040.83i	−0.734086	−	1.27147i	0.221038	−	0.975265i	$-0.429056\pi$
$314$		0			0
$315$	915.531	+	6617.36i	0.163760	+	1.18364i
$316$		0			0
$317$	−3539.48	−	6130.56i	−0.627120	−	1.08620i	−0.988127	−	0.153641i	$-0.950900\pi$
$317$	−3539.48	−	6130.56i	−0.627120	−	1.08620i	0.361007	−	0.932563i	$-0.382433\pi$
$318$		0			0
$319$	−1931.17	+	3344.88i	−0.338948	+	0.587076i
$320$		0			0
$321$	5560.46			0.966836
$322$		0			0
$323$	18.1977			0.00313483
$324$		0			0
$325$	697.461	−	1208.04i	0.119041	−	0.206184i
$326$		0			0
$327$	−7229.72	−	12522.2i	−1.22264	−	2.11768i
$328$		0			0
$329$	−7166.44	−	2913.33i	−1.20091	−	0.488199i
$330$		0			0
$331$	2049.92	+	3550.57i	0.340405	+	0.589599i	0.984508	−	0.175340i	$-0.0561025\pi$
$331$	2049.92	+	3550.57i	0.340405	+	0.589599i	−0.644103	+	0.764939i	$0.722769\pi$
$332$		0			0
$333$	−14117.7	+	24452.6i	−2.32326	+	4.02401i
$334$		0			0
$335$	−338.545			−0.0552140
$336$		0			0
$337$	−4437.71			−0.717322			−0.358661	−	0.933468i	$-0.616767\pi$
$337$	−4437.71			−0.717322			−0.358661	+	0.933468i	$0.616767\pi$
$338$		0			0
$339$	1106.06	−	1915.75i	0.177206	−	0.306930i
$340$		0			0
$341$	−835.283	−	1446.75i	−0.132648	−	0.229754i
$342$		0			0
$343$	2546.36	+	5819.77i	0.400847	+	0.916145i
$344$		0			0
$345$	−4047.05	−	7009.69i	−0.631553	−	1.09388i
$346$		0			0
$347$	−2223.43	+	3851.09i	−0.343976	+	0.595784i	−0.985167	−	0.171597i	$-0.945107\pi$
$347$	−2223.43	+	3851.09i	−0.343976	+	0.595784i	0.641191	+	0.767381i	$0.278441\pi$
$348$		0			0
$349$	3197.13			0.490368			0.245184	−	0.969477i	$-0.421152\pi$
$349$	3197.13			0.490368			0.245184	+	0.969477i	$0.421152\pi$
$350$		0			0
$351$	−25079.2			−3.81375
$352$		0			0
$353$	−4381.97	+	7589.79i	−0.660704	+	1.14437i	0.319727	+	0.947510i	$0.396409\pi$
$353$	−4381.97	+	7589.79i	−0.660704	+	1.14437i	−0.980431	+	0.196863i	$0.936924\pi$
$354$		0			0
$355$	−2278.81	−	3947.01i	−0.340695	−	0.590101i
$356$		0			0
$357$	−2036.39	−	827.842i	−0.301897	−	0.122728i
$358$		0			0
$359$	5970.87	+	10341.9i	0.877801	+	1.52040i	0.853748	+	0.520686i	$0.174324\pi$
$359$	5970.87	+	10341.9i	0.877801	+	1.52040i	0.0240532	+	0.999711i	$0.492343\pi$
$360$		0			0
$361$	3428.33	−	5938.05i	0.499830	−	0.865731i
$362$		0			0
$363$	−4061.28			−0.587223
$364$		0			0
$365$	312.672			0.0448384
$366$		0			0
$367$	−5205.05	+	9015.40i	−0.740330	+	1.28229i	0.212015	+	0.977266i	$0.431997\pi$
$367$	−5205.05	+	9015.40i	−0.740330	+	1.28229i	−0.952345	+	0.305023i	$0.901336\pi$
$368$		0			0
$369$	−12760.0	−	22100.9i	−1.80016	−	3.11796i
$370$		0			0
$371$	1334.18	+	9643.29i	0.186704	+	1.34947i
$372$		0			0
$373$	2188.64	+	3790.84i	0.303817	+	0.526226i	0.976997	−	0.213252i	$-0.0684056\pi$
$373$	2188.64	+	3790.84i	0.303817	+	0.526226i	−0.673180	+	0.739478i	$0.735072\pi$
$374$		0			0
$375$	622.311	−	1077.87i	0.0856960	−	0.148430i
$376$		0			0
$377$	7093.02			0.968989
$378$		0			0
$379$	−6769.37			−0.917466			−0.458733	−	0.888574i	$-0.651696\pi$
$379$	−6769.37			−0.917466			−0.458733	+	0.888574i	$0.651696\pi$
$380$		0			0
$381$	−5728.75	+	9922.49i	−0.770323	+	1.33424i
$382$		0			0
$383$	3168.12	+	5487.34i	0.422671	+	0.732088i	0.996200	−	0.0870974i	$-0.0277591\pi$
$383$	3168.12	+	5487.34i	0.422671	+	0.732088i	−0.573528	+	0.819186i	$0.694426\pi$
$384$		0			0
$385$	−2220.77	+	1727.40i	−0.293977	+	0.228666i
$386$		0			0
$387$	10015.9	+	17348.0i	1.31560	+	2.27868i
$388$		0			0
$389$	4113.64	−	7125.04i	0.536169	−	0.928673i	−0.462936	−	0.886392i	$-0.653204\pi$
$389$	4113.64	−	7125.04i	0.536169	−	0.928673i	0.999106	−	0.0422812i	$-0.0134625\pi$
$390$		0			0
$391$	1938.06			0.250670
$392$		0			0
$393$	15642.0			2.00773
$394$		0			0
$395$	1528.84	−	2648.02i	0.194745	−	0.337308i
$396$		0			0
$397$	6927.43	+	11998.7i	0.875762	+	1.51686i	0.855949	+	0.517061i	$0.172974\pi$
$397$	6927.43	+	11998.7i	0.875762	+	1.51686i	0.0198135	+	0.999804i	$0.493693\pi$
$398$		0			0
$399$	222.205	−	172.839i	0.0278801	−	0.0216861i
$400$		0			0
$401$	−6372.45	−	11037.4i	−0.793578	−	1.37452i	−0.923738	−	0.383025i	$-0.874882\pi$
$401$	−6372.45	−	11037.4i	−0.793578	−	1.37452i	0.130160	−	0.991493i	$-0.458451\pi$
$402$		0			0
$403$	−1533.96	+	2656.90i	−0.189609	+	0.328412i
$404$		0			0
$405$	−12637.8			−1.55057
$406$		0			0
$407$	−11891.5			−1.44826
$408$		0			0
$409$	−3879.64	+	6719.73i	−0.469036	+	0.812395i	−0.999374	−	0.0353922i	$-0.988732\pi$
$409$	−3879.64	+	6719.73i	−0.469036	+	0.812395i	0.530337	+	0.847787i	$0.322065\pi$
$410$		0			0
$411$	13185.0	+	22837.0i	1.58240	+	2.74080i
$412$		0			0
$413$	1273.77	+	9206.68i	0.151763	+	1.09693i
$414$		0			0
$415$	−2500.55	−	4331.08i	−0.295776	−	0.512299i
$416$		0			0
$417$	3945.01	−	6832.96i	0.463281	−	0.802426i
$418$		0			0
$419$	1712.84			0.199709			0.0998544	−	0.995002i	$-0.468162\pi$
$419$	1712.84			0.199709			0.0998544	+	0.995002i	$0.468162\pi$
$420$		0			0
$421$	1553.04			0.179788			0.0898939	−	0.995951i	$-0.471347\pi$
$421$	1553.04			0.179788			0.0898939	+	0.995951i	$0.471347\pi$
$422$		0			0
$423$	15066.9	−	26096.6i	1.73186	−	2.99967i
$424$		0			0
$425$	149.007	+	258.088i	0.0170069	+	0.0294568i
$426$		0			0
$427$	−8579.55	−	3487.80i	−0.972351	−	0.395285i
$428$		0			0
$429$	−8439.87	−	14618.3i	−0.949839	−	1.64517i
$430$		0			0
$431$	7469.97	−	12938.4i	0.834839	−	1.44598i	−0.0593219	−	0.998239i	$-0.518894\pi$
$431$	7469.97	−	12938.4i	0.834839	−	1.44598i	0.894161	−	0.447745i	$-0.147773\pi$
$432$		0			0
$433$	2455.23			0.272496			0.136248	−	0.990675i	$-0.456496\pi$
$433$	2455.23			0.272496			0.136248	+	0.990675i	$0.456496\pi$
$434$		0			0
$435$	6328.76			0.697565
$436$		0			0
$437$	−124.097	+	214.942i	−0.0135843	+	0.0235288i
$438$		0			0
$439$	6273.79	+	10866.5i	0.682077	+	1.18139i	0.974346	+	0.225056i	$0.0722563\pi$
$439$	6273.79	+	10866.5i	0.682077	+	1.18139i	−0.292269	+	0.956336i	$0.594410\pi$
$440$		0			0
$441$	−23815.0	+	6718.36i	−2.57154	+	0.725446i
$442$		0			0
$443$	−269.287	−	466.419i	−0.0288809	−	0.0500231i	0.851224	−	0.524803i	$-0.175861\pi$
$443$	−269.287	−	466.419i	−0.0288809	−	0.0500231i	−0.880105	+	0.474780i	$0.842528\pi$
$444$		0			0
$445$	2908.08	−	5036.94i	0.309789	−	0.536571i
$446$		0			0
$447$	−568.447			−0.0601490
$448$		0			0
$449$	−9933.89			−1.04412			−0.522059	−	0.852909i	$-0.674836\pi$
$449$	−9933.89			−1.04412			−0.522059	+	0.852909i	$0.674836\pi$
$450$		0			0
$451$	5373.95	−	9307.96i	0.561085	−	0.971828i
$452$		0			0
$453$	8243.63	+	14278.4i	0.855010	+	1.48092i
$454$		0			0
$455$	4786.47	+	1945.82i	0.493172	+	0.200486i
$456$		0			0
$457$	6948.68	+	12035.5i	0.711260	+	1.23194i	0.964385	+	0.264504i	$0.0852083\pi$
$457$	6948.68	+	12035.5i	0.711260	+	1.23194i	−0.253125	+	0.967434i	$0.581458\pi$
$458$		0			0
$459$	2678.99	−	4640.14i	0.272428	−	0.471859i
$460$		0			0
$461$	−6849.65			−0.692018			−0.346009	−	0.938231i	$-0.612463\pi$
$461$	−6849.65			−0.692018			−0.346009	+	0.938231i	$0.612463\pi$
$462$		0			0
$463$	8062.80			0.809309			0.404654	−	0.914470i	$-0.367392\pi$
$463$	8062.80			0.809309			0.404654	+	0.914470i	$0.367392\pi$
$464$		0			0
$465$	−1368.68	+	2370.63i	−0.136497	+	0.236420i
$466$		0			0
$467$	2442.23	+	4230.06i	0.241997	+	0.419152i	0.961283	−	0.275563i	$-0.0888641\pi$
$467$	2442.23	+	4230.06i	0.241997	+	0.419152i	−0.719286	+	0.694714i	$0.755531\pi$
$468$		0			0
$469$	−171.856	−	1242.16i	−0.0169202	−	0.122297i
$470$		0			0
$471$	16133.8	+	27944.6i	1.57836	+	2.73380i
$472$		0			0
$473$	−4218.26	+	7306.24i	−0.410055	+	0.710236i
$474$		0			0
$475$	−38.1645			−0.00368654
$476$		0			0
$477$	−37921.0			−3.64001
$478$		0			0
$479$	−4024.76	+	6971.09i	−0.383916	+	0.664963i	−0.991618	−	0.129202i	$-0.958758\pi$
$479$	−4024.76	+	6971.09i	−0.383916	+	0.664963i	0.607702	+	0.794165i	$0.292092\pi$
$480$		0			0
$481$	10919.2	+	18912.5i	1.03508	+	1.79280i
$482$		0			0
$483$	23664.9	−	18407.4i	2.22938	−	1.73409i
$484$		0			0
$485$	−2891.73	−	5008.63i	−0.270736	−	0.468928i
$486$		0			0
$487$	1555.23	−	2693.74i	0.144711	−	0.250647i	−0.784554	−	0.620060i	$-0.787108\pi$
$487$	1555.23	−	2693.74i	0.144711	−	0.250647i	0.929265	+	0.369413i	$0.120441\pi$
$488$		0			0
$489$	28435.2			2.62962
$490$		0			0
$491$	−5273.36			−0.484692			−0.242346	−	0.970190i	$-0.577917\pi$
$491$	−5273.36			−0.484692			−0.242346	+	0.970190i	$0.577917\pi$
$492$		0			0
$493$	−757.685	+	1312.35i	−0.0692179	+	0.119889i
$494$		0			0
$495$	−5479.65	−	9491.04i	−0.497560	−	0.861799i
$496$		0			0
$497$	13325.2	−	10364.8i	1.20265	−	0.935464i
$498$		0			0
$499$	−6757.87	−	11705.0i	−0.606260	−	1.05007i	−0.991851	−	0.127403i	$-0.959336\pi$
$499$	−6757.87	−	11705.0i	−0.606260	−	1.05007i	0.385591	−	0.922670i	$-0.373997\pi$
$500$		0			0
$501$	9934.73	−	17207.5i	0.885930	−	1.53448i
$502$		0			0
$503$	−9240.34			−0.819098			−0.409549	−	0.912288i	$-0.634314\pi$
$503$	−9240.34			−0.819098			−0.409549	+	0.912288i	$0.634314\pi$
$504$		0			0
$505$	−348.155			−0.0306786
$506$		0			0
$507$	−4561.75	+	7901.19i	−0.399595	+	0.692118i
$508$		0			0
$509$	2060.04	+	3568.10i	0.179391	+	0.310714i	0.941672	−	0.336532i	$-0.109254\pi$
$509$	2060.04	+	3568.10i	0.179391	+	0.310714i	−0.762281	+	0.647246i	$0.775921\pi$
$510$		0			0
$511$	158.722	+	1147.23i	0.0137406	+	0.0993157i
$512$		0			0
$513$	343.078	+	594.228i	0.0295268	+	0.0511420i
$514$		0			0
$515$	−667.163	+	1155.56i	−0.0570849	+	0.0988740i
$516$		0			0
$517$	12691.0			1.07959
$518$		0			0
$519$	22433.8			1.89737
$520$		0			0
$521$	903.297	−	1564.56i	0.0759581	−	0.131563i	−0.825544	−	0.564337i	$-0.809132\pi$
$521$	903.297	−	1564.56i	0.0759581	−	0.131563i	0.901503	+	0.432774i	$0.142465\pi$
$522$		0			0
$523$	−9072.68	−	15714.3i	−0.758548	−	1.31384i	−0.943591	−	0.331113i	$-0.892576\pi$
$523$	−9072.68	−	15714.3i	−0.758548	−	1.31384i	0.185044	−	0.982730i	$-0.440757\pi$
$524$		0			0
$525$	4270.74	+	1736.16i	0.355029	+	0.144328i
$526$		0			0
$527$	−327.720	−	567.628i	−0.0270886	−	0.0469189i
$528$		0			0
$529$	−7132.84	+	12354.4i	−0.586245	+	1.01541i
$530$		0			0
$531$	−36204.1			−2.95880
$532$		0			0
$533$	−19738.1			−1.60404
$534$		0			0
$535$	1396.12	−	2418.15i	0.112822	−	0.195413i
$536$		0			0
$537$	−9444.49	−	16358.3i	−0.758957	−	1.31455i
$538$		0			0
$539$	−7465.33	−	7271.36i	−0.596576	−	0.581076i
$540$		0			0
$541$	−9626.80	−	16674.1i	−0.765043	−	1.32509i	−0.940224	−	0.340557i	$-0.889384\pi$
$541$	−9626.80	−	16674.1i	−0.765043	−	1.32509i	0.175181	−	0.984536i	$-0.443949\pi$
$542$		0			0
$543$	−13841.3	+	23973.9i	−1.09390	+	1.89469i
$544$		0			0
$545$	−7260.96			−0.570689
$546$		0			0
$547$	−1410.94			−0.110288			−0.0551438	−	0.998478i	$-0.517562\pi$
$547$	−1410.94			−0.110288			−0.0551438	+	0.998478i	$0.517562\pi$
$548$		0			0
$549$	18037.8	−	31242.4i	1.40225	−	2.42877i
$550$		0			0
$551$	−97.0311	−	168.063i	−0.00750211	−	0.0129940i
$552$		0			0
$553$	10491.9	+	4265.24i	0.806805	+	0.327986i
$554$		0			0
$555$	9742.65	+	16874.8i	0.745140	+	1.29062i
$556$		0			0
$557$	−11247.9	+	19481.9i	−0.855635	+	1.48200i	0.0204195	+	0.999792i	$0.493500\pi$
$557$	−11247.9	+	19481.9i	−0.855635	+	1.48200i	−0.876055	+	0.482212i	$0.839834\pi$
$558$		0			0
$559$	15493.3			1.17227
$560$		0			0
$561$	3606.23			0.271400
$562$		0			0
$563$	1081.38	−	1873.01i	0.0809499	−	0.140209i	−0.822708	−	0.568464i	$-0.807538\pi$
$563$	1081.38	−	1873.01i	0.0809499	−	0.140209i	0.903658	+	0.428254i	$0.140871\pi$
$564$		0			0
$565$	−555.419	−	962.014i	−0.0413569	−	0.0716323i
$566$		0			0
$567$	−6415.36	−	46369.5i	−0.475167	−	3.43446i
$568$		0			0
$569$	−2013.53	−	3487.53i	−0.148351	−	0.256951i	0.782267	−	0.622943i	$-0.214063\pi$
$569$	−2013.53	−	3487.53i	−0.148351	−	0.256951i	−0.930618	+	0.365992i	$0.880730\pi$
$570$		0			0
$571$	8380.85	−	14516.1i	0.614234	−	1.06388i	−0.376284	−	0.926504i	$-0.622798\pi$
$571$	8380.85	−	14516.1i	0.614234	−	1.06388i	0.990518	−	0.137380i	$-0.0438682\pi$
$572$		0			0
$573$	1740.35			0.126883
$574$		0			0
$575$	−4064.53			−0.294787
$576$		0			0
$577$	−5304.65	+	9187.92i	−0.382730	+	0.662909i	−0.991451	−	0.130476i	$-0.958350\pi$
$577$	−5304.65	+	9187.92i	−0.382730	+	0.662909i	0.608721	+	0.793384i	$0.291683\pi$
$578$		0			0
$579$	9744.32	+	16877.7i	0.699413	+	1.21142i
$580$		0			0
$581$	14621.8	−	11373.4i	1.04409	−	0.812128i
$582$		0			0
$583$	−7985.35	−	13831.0i	−0.567271	−	0.982543i
$584$		0			0
$585$	−10063.2	+	17429.9i	−0.711215	+	1.23186i
$586$		0			0
$587$	−15740.8			−1.10680			−0.553402	−	0.832914i	$-0.686671\pi$
$587$	−15740.8			−1.10680			−0.553402	+	0.832914i	$0.686671\pi$
$588$		0			0
$589$	83.9374			0.00587195
$590$		0			0
$591$	17649.0	−	30568.9i	1.22840	−	2.12764i
$592$		0			0
$593$	−8409.07	−	14564.9i	−0.582326	−	1.00862i	−0.995203	−	0.0978313i	$-0.968809\pi$
$593$	−8409.07	−	14564.9i	−0.582326	−	1.00862i	0.412877	−	0.910787i	$-0.364524\pi$
$594$		0			0
$595$	−871.311	+	677.737i	−0.0600341	+	0.0466966i
$596$		0			0
$597$	−13807.8	−	23915.9i	−0.946594	−	1.63955i
$598$		0			0
$599$	−1172.11	+	2030.15i	−0.0799517	+	0.138480i	−0.903229	−	0.429159i	$-0.858810\pi$
$599$	−1172.11	+	2030.15i	−0.0799517	+	0.138480i	0.823277	+	0.567640i	$0.192143\pi$
$600$		0			0
$601$	17128.4			1.16253			0.581265	−	0.813714i	$-0.302558\pi$
$601$	17128.4			1.16253			0.581265	+	0.813714i	$0.302558\pi$
$602$		0			0
$603$	4884.62			0.329879
$604$		0			0
$605$	−1019.71	+	1766.18i	−0.0685239	+	0.118687i
$606$		0			0
$607$	−262.862	−	455.291i	−0.0175770	−	0.0304443i	0.857103	−	0.515145i	$-0.172262\pi$
$607$	−262.862	−	455.291i	−0.0175770	−	0.0304443i	−0.874680	+	0.484701i	$0.838929\pi$
$608$		0			0
$609$	3212.68	+	23220.9i	0.213767	+	1.54509i
$610$		0			0
$611$	−11653.3	−	20184.1i	−0.771589	−	1.33643i
$612$		0			0
$613$	−10194.9	+	17658.0i	−0.671723	+	1.16346i	0.305692	+	0.952130i	$0.401112\pi$
$613$	−10194.9	+	17658.0i	−0.671723	+	1.16346i	−0.977415	+	0.211328i	$0.932221\pi$
$614$		0			0
$615$	−17611.4			−1.15473
$616$		0			0
$617$	−16815.3			−1.09718			−0.548589	−	0.836092i	$-0.684835\pi$
$617$	−16815.3			−1.09718			−0.548589	+	0.836092i	$0.684835\pi$
$618$		0			0
$619$	−1552.53	+	2689.05i	−0.100810	+	0.174608i	−0.912019	−	0.410149i	$-0.865477\pi$
$619$	−1552.53	+	2689.05i	−0.100810	+	0.174608i	0.811209	+	0.584757i	$0.198810\pi$
$620$		0			0
$621$	36537.9	+	63285.5i	2.36105	+	4.08947i
$622$		0			0
$623$	19957.3	+	8113.13i	1.28342	+	0.521743i
$624$		0			0
$625$	−312.500	−	541.266i	−0.0200000	−	0.0346410i
$626$		0			0
$627$	−230.912	+	399.951i	−0.0147077	+	0.0254745i
$628$		0			0
$629$	−4665.60			−0.295754
$630$		0			0
$631$	6729.19			0.424540			0.212270	−	0.977211i	$-0.431914\pi$
$631$	6729.19			0.424540			0.212270	+	0.977211i	$0.431914\pi$
$632$		0			0
$633$	20698.5	−	35850.9i	1.29967	−	2.25110i
$634$		0			0
$635$	2876.75	+	4982.68i	0.179780	+	0.311388i
$636$		0			0
$637$	−4709.64	+	18549.8i	−0.292940	+	1.15380i
$638$		0			0
$639$	32879.3	+	56948.6i	2.03550	+	3.52559i
$640$		0			0
$641$	13038.4	−	22583.1i	0.803407	−	1.39154i	−0.113954	−	0.993486i	$-0.536352\pi$
$641$	13038.4	−	22583.1i	0.803407	−	1.39154i	0.917361	−	0.398056i	$-0.130315\pi$
$642$		0			0
$643$	−13703.7			−0.840471			−0.420236	−	0.907415i	$-0.638053\pi$
$643$	−13703.7			−0.840471			−0.420236	+	0.907415i	$0.638053\pi$
$644$		0			0
$645$	13824.0			0.843904
$646$		0			0
$647$	6863.09	−	11887.2i	0.417026	−	0.722311i	−0.578613	−	0.815603i	$-0.696406\pi$
$647$	6863.09	−	11887.2i	0.417026	−	0.722311i	0.995639	+	0.0932918i	$0.0297390\pi$
$648$		0			0
$649$	−7623.80	−	13204.8i	−0.461110	−	0.798666i
$650$		0			0
$651$	−9392.87	−	3818.43i	−0.565492	−	0.229887i
$652$		0			0
$653$	−4348.59	−	7531.97i	−0.260602	−	0.451376i	0.705800	−	0.708411i	$-0.250588\pi$
$653$	−4348.59	−	7531.97i	−0.260602	−	0.451376i	−0.966402	+	0.257035i	$0.917254\pi$
$654$		0			0
$655$	3927.41	−	6802.47i	0.234285	−	0.405793i
$656$		0			0
$657$	−4511.33			−0.267890
$658$		0			0
$659$	21355.0			1.26233			0.631164	−	0.775650i	$-0.282578\pi$
$659$	21355.0			1.26233			0.631164	+	0.775650i	$0.282578\pi$
$660$		0			0
$661$	−6789.56	+	11759.9i	−0.399521	+	0.691990i	−0.993667	−	0.112367i	$-0.964157\pi$
$661$	−6789.56	+	11759.9i	−0.399521	+	0.691990i	0.594146	+	0.804357i	$0.297490\pi$
$662$		0			0
$663$	−3311.35	−	5735.43i	−0.193970	−	0.335966i
$664$		0			0
$665$	−19.3735	−	140.030i	−0.00112973	−	0.00816558i
$666$		0			0
$667$	−10333.8	−	17898.7i	−0.599892	−	1.03904i
$668$		0			0
$669$	1966.73	−	3406.47i	0.113659	−	0.196864i
$670$		0			0
$671$	15193.5			0.874126
$672$		0			0
$673$	1852.25			0.106090			0.0530452	−	0.998592i	$-0.483107\pi$
$673$	1852.25			0.106090			0.0530452	+	0.998592i	$0.483107\pi$
$674$		0			0
$675$	−5618.40	+	9731.36i	−0.320374	+	0.554904i
$676$		0			0
$677$	−4420.00	−	7655.67i	−0.250922	−	0.434611i	0.712858	−	0.701309i	$-0.247401\pi$
$677$	−4420.00	−	7655.67i	−0.250922	−	0.434611i	−0.963780	+	0.266698i	$0.914067\pi$
$678$		0			0
$679$	16909.2	−	13152.6i	0.955695	−	0.743373i
$680$		0			0
$681$	−27621.0	−	47840.9i	−1.55424	−	2.69203i
$682$		0			0
$683$	−3155.10	+	5464.79i	−0.176759	+	0.306156i	−0.940769	−	0.339049i	$-0.889895\pi$
$683$	−3155.10	+	5464.79i	−0.176759	+	0.306156i	0.764009	+	0.645205i	$0.223228\pi$
$684$		0			0
$685$	13241.9			0.738611
$686$		0			0
$687$	23837.3			1.32380
$688$		0			0
$689$	−14664.8	+	25400.1i	−0.810861	+	1.40445i
$690$		0			0
$691$	−8729.90	−	15120.6i	−0.480609	−	0.832440i	0.519143	−	0.854687i	$-0.326251\pi$
$691$	−8729.90	−	15120.6i	−0.480609	−	0.832440i	−0.999752	+	0.0222474i	$0.992918\pi$
$692$		0			0
$693$	32041.9	−	24923.4i	1.75638	−	1.36618i
$694$		0			0
$695$	−1981.03	−	3431.24i	−0.108122	−	0.187273i
$696$		0			0
$697$	2108.45	−	3651.94i	0.114581	−	0.198461i
$698$		0			0
$699$	1807.36			0.0977976
$700$		0			0
$701$	−12737.6			−0.686292			−0.343146	−	0.939282i	$-0.611493\pi$
$701$	−12737.6			−0.686292			−0.343146	+	0.939282i	$0.611493\pi$
$702$		0			0
$703$	298.744	−	517.440i	0.0160275	−	0.0277605i
$704$		0			0
$705$	−10397.7	−	18009.3i	−0.555459	−	0.962083i
$706$		0			0
$707$	−176.735	−	1277.42i	−0.00940140	−	0.0679522i
$708$		0			0
$709$	7097.12	+	12292.6i	0.375935	+	0.651139i	0.990467	−	0.137754i	$-0.0439882\pi$
$709$	7097.12	+	12292.6i	0.375935	+	0.651139i	−0.614531	+	0.788892i	$0.710655\pi$
$710$		0			0
$711$	−22058.5	+	38206.4i	−1.16351	+	2.01526i
$712$		0			0
$713$	8939.35			0.469539
$714$		0			0
$715$	−8476.34			−0.443353
$716$		0			0
$717$	9712.98	−	16823.4i	0.505911	−	0.876263i
$718$		0			0
$719$	4809.44	+	8330.20i	0.249460	+	0.432078i	0.963376	−	0.268154i	$-0.0864135\pi$
$719$	4809.44	+	8330.20i	0.249460	+	0.432078i	−0.713916	+	0.700231i	$0.753080\pi$
$720$		0			0
$721$	−4578.54	−	1861.29i	−0.236496	−	0.0961416i
$722$		0			0
$723$	6835.38	+	11839.2i	0.351605	+	0.608998i
$724$		0			0
$725$	1589.03	−	2752.27i	0.0813999	−	0.140989i
$726$		0			0
$727$	−16970.9			−0.865773			−0.432886	−	0.901448i	$-0.642505\pi$
$727$	−16970.9			−0.865773			−0.432886	+	0.901448i	$0.642505\pi$
$728$		0			0
$729$	61506.9			3.12487
$730$		0			0
$731$	−1655.02	+	2866.58i	−0.0837388	+	0.145040i
$732$		0			0
$733$	−4651.74	−	8057.05i	−0.234401	−	0.405995i	0.724697	−	0.689067i	$-0.241980\pi$
$733$	−4651.74	−	8057.05i	−0.234401	−	0.405995i	−0.959098	+	0.283073i	$0.908646\pi$
$734$		0			0
$735$	−4202.19	+	16551.1i	−0.210884	+	0.830607i
$736$		0			0
$737$	1028.60	+	1781.58i	0.0514095	+	0.0890439i
$738$		0			0
$739$	8779.86	−	15207.2i	0.437040	−	0.756975i	−0.560420	−	0.828209i	$-0.689360\pi$
$739$	8779.86	−	15207.2i	0.437040	−	0.756975i	0.997460	+	0.0712338i	$0.0226936\pi$
$740$		0			0
$741$	848.120			0.0420465
$742$		0			0
$743$	14823.5			0.731926			0.365963	−	0.930629i	$-0.380740\pi$
$743$	14823.5			0.731926			0.365963	+	0.930629i	$0.380740\pi$
$744$		0			0
$745$	−142.726	+	247.208i	−0.00701888	+	0.0121571i
$746$		0			0
$747$	36078.6	+	62490.0i	1.76713	+	3.06076i
$748$		0			0
$749$	9581.16	+	3894.98i	0.467407	+	0.190013i
$750$		0			0
$751$	4566.94	+	7910.18i	0.221904	+	0.384349i	0.955386	−	0.295360i	$-0.0954394\pi$
$751$	4566.94	+	7910.18i	0.221904	+	0.384349i	−0.733482	+	0.679709i	$0.762106\pi$
$752$		0			0
$753$	5594.55	−	9690.05i	0.270753	−	0.468958i
$754$		0			0
$755$	8279.25			0.399090
$756$		0			0
$757$	−10791.4			−0.518125			−0.259063	−	0.965861i	$-0.583414\pi$
$757$	−10791.4			−0.518125			−0.259063	+	0.965861i	$0.583414\pi$
$758$		0			0
$759$	−24592.2	+	42594.9i	−1.17607	+	2.03702i
$760$		0			0
$761$	2078.00	+	3599.20i	0.0989848	+	0.171447i	0.911265	−	0.411821i	$-0.135107\pi$
$761$	2078.00	+	3599.20i	0.0989848	+	0.171447i	−0.812280	+	0.583268i	$0.801774\pi$
$762$		0			0
$763$	−3685.89	−	26641.2i	−0.174886	−	1.26406i
$764$		0			0
$765$	−2149.92	−	3723.77i	−0.101609	−	0.175991i
$766$		0			0
$767$	−14000.8	+	24250.1i	−0.659113	+	1.14162i
$768$		0			0
$769$	−7697.15			−0.360944			−0.180472	−	0.983580i	$-0.557763\pi$
$769$	−7697.15			−0.360944			−0.180472	+	0.983580i	$0.557763\pi$
$770$		0			0
$771$	−40999.1			−1.91511
$772$		0			0
$773$	1409.10	−	2440.64i	0.0655652	−	0.113562i	−0.831379	−	0.555705i	$-0.812448\pi$
$773$	1409.10	−	2440.64i	0.0655652	−	0.113562i	0.896945	+	0.442143i	$0.145782\pi$
$774$		0			0
$775$	687.299	+	1190.44i	0.0318561	+	0.0551764i
$776$		0			0
$777$	−56969.6	+	44312.9i	−2.63034	+	2.04597i
$778$		0			0
$779$	270.013	+	467.677i	0.0124188	+	0.0215100i
$780$		0			0
$781$	−13847.3	+	23984.3i	−0.634439	+	1.09888i
$782$		0			0
$783$	−57137.9			−2.60784
$784$		0			0
$785$	16203.5			0.736724
$786$		0			0
$787$	−19968.2	+	34585.9i	−0.904432	+	1.56652i	−0.0827540	+	0.996570i	$0.526372\pi$
$787$	−19968.2	+	34585.9i	−0.904432	+	1.56652i	−0.821678	+	0.569952i	$0.806962\pi$
$788$		0			0
$789$	7373.39	+	12771.1i	0.332699	+	0.576252i
$790$		0			0
$791$	3247.78	−	2526.24i	0.145990	−	0.113556i
$792$		0			0
$793$	−13951.1	−	24164.1i	−0.624741	−	1.08208i
$794$		0			0
$795$	−13084.7	+	22663.3i	−0.583730	+	1.01105i
$796$		0			0
$797$	11023.4			0.489925			0.244962	−	0.969533i	$-0.421224\pi$
$797$	11023.4			0.489925			0.244962	+	0.969533i	$0.421224\pi$
$798$		0			0
$799$	4979.27			0.220468
$800$		0			0
$801$	−41958.6	+	72674.5i	−1.85086	+	3.20578i
$802$		0			0
$803$	−949.988	−	1645.43i	−0.0417489	−	0.0723112i
$804$		0			0
$805$	−2063.28	−	14913.2i	−0.0903369	−	0.652945i
$806$		0			0
$807$	−21140.5	−	36616.3i	−0.922155	−	1.59722i
$808$		0			0
$809$	7017.19	−	12154.1i	0.304958	−	0.528203i	−0.672294	−	0.740284i	$-0.734691\pi$
$809$	7017.19	−	12154.1i	0.304958	−	0.528203i	0.977252	+	0.212081i	$0.0680241\pi$
$810$		0			0
$811$	38981.9			1.68784			0.843920	−	0.536469i	$-0.180242\pi$
$811$	38981.9			1.68784			0.843920	+	0.536469i	$0.180242\pi$
$812$		0			0
$813$	14412.3			0.621725
$814$		0			0
$815$	7139.50	−	12366.0i	0.306854	−	0.531487i
$816$		0			0
$817$	−211.946	−	367.101i	−0.00907595	−	0.0157200i
$818$		0			0
$819$	−69060.5	−	28074.8i	−2.94648	−	1.19782i
$820$		0			0
$821$	9448.98	+	16366.1i	0.401671	+	0.695714i	0.993928	−	0.110035i	$-0.0350964\pi$
$821$	9448.98	+	16366.1i	0.401671	+	0.695714i	−0.592257	+	0.805749i	$0.701763\pi$
$822$		0			0
$823$	13962.0	−	24182.9i	0.591355	−	1.02426i	−0.402695	−	0.915334i	$-0.631926\pi$
$823$	13962.0	−	24182.9i	0.591355	−	1.02426i	0.994050	−	0.108923i	$-0.0347403\pi$
$824$		0			0
$825$	−7563.03			−0.319165
$826$		0			0
$827$	−13984.6			−0.588019			−0.294010	−	0.955802i	$-0.594990\pi$
$827$	−13984.6			−0.588019			−0.294010	+	0.955802i	$0.594990\pi$
$828$		0			0
$829$	−145.549	+	252.098i	−0.00609785	+	0.0105618i	−0.869058	−	0.494710i	$-0.835274\pi$
$829$	−145.549	+	252.098i	−0.00609785	+	0.0105618i	0.862960	+	0.505272i	$0.168608\pi$
$830$		0			0
$831$	−21610.1	−	37429.7i	−0.902099	−	1.56248i
$832$		0			0
$833$	−2928.99	−	2852.89i	−0.121829	−	0.118664i
$834$		0			0
$835$	−4988.83	−	8640.90i	−0.206761	−	0.358121i
$836$		0			0
$837$	12356.9	−	21402.7i	0.510294	−	0.883854i
$838$		0			0
$839$	−18467.2			−0.759902			−0.379951	−	0.925007i	$-0.624059\pi$
$839$	−18467.2			−0.759902			−0.379951	+	0.925007i	$0.624059\pi$
$840$		0			0
$841$	−8228.97			−0.337405
$842$		0			0
$843$	−35350.8	+	61229.4i	−1.44430	+	2.50160i
$844$		0			0
$845$	2290.73	+	3967.66i	0.0932586	+	0.161529i
$846$		0			0
$847$	−6997.95	−	2844.84i	−0.283887	−	0.115407i
$848$		0			0
$849$	12201.2	+	21133.2i	0.493222	+	0.854286i
$850$		0			0
$851$	31816.3	−	55107.5i	1.28161	−	2.21981i
$852$		0			0
$853$	8251.96			0.331233			0.165617	−	0.986190i	$-0.447039\pi$
$853$	8251.96			0.331233			0.165617	+	0.986190i	$0.447039\pi$
$854$		0			0
$855$	550.649			0.0220255
$856$		0			0
$857$	−14493.7	+	25103.9i	−0.577709	+	1.00062i	0.418032	+	0.908432i	$0.362720\pi$
$857$	−14493.7	+	25103.9i	−0.577709	+	1.00062i	−0.995741	+	0.0921899i	$0.970613\pi$
$858$		0			0
$859$	−17131.3	−	29672.3i	−0.680457	−	1.17859i	−0.974842	−	0.222899i	$-0.928448\pi$
$859$	−17131.3	−	29672.3i	−0.680457	−	1.17859i	0.294385	−	0.955687i	$-0.404885\pi$
$860$		0			0
$861$	−8940.08	−	64617.9i	−0.353864	−	2.55769i
$862$		0			0
$863$	−1975.41	−	3421.51i	−0.0779186	−	0.134959i	0.824433	−	0.565959i	$-0.191494\pi$
$863$	−1975.41	−	3421.51i	−0.0779186	−	0.134959i	−0.902352	+	0.431000i	$0.858161\pi$
$864$		0			0
$865$	5632.68	−	9756.10i	0.221407	−	0.383488i
$866$		0			0
$867$	−47503.7			−1.86080
$868$		0			0
$869$	−18580.2			−0.725304
$870$		0			0
$871$	1888.97	−	3271.80i	0.0734850	−	0.127280i
$872$		0			0
$873$	41722.7	+	72265.9i	1.61753	+	2.80164i
$874$		0			0
$875$	1827.32	−	1421.36i	0.0705998	−	0.0549151i
$876$		0			0
$877$	1133.83	+	1963.84i	0.0436563	+	0.0756149i	0.887028	−	0.461716i	$-0.152766\pi$
$877$	1133.83	+	1963.84i	0.0436563	+	0.0756149i	−0.843372	+	0.537331i	$0.819433\pi$
$878$		0			0
$879$	19006.0	−	32919.4i	0.729302	−	1.26319i
$880$		0			0
$881$	−13145.9			−0.502721			−0.251360	−	0.967894i	$-0.580878\pi$
$881$	−13145.9			−0.502721			−0.251360	+	0.967894i	$0.580878\pi$
$882$		0			0
$883$	−36041.0			−1.37359			−0.686793	−	0.726853i	$-0.740982\pi$
$883$	−36041.0			−1.37359			−0.686793	+	0.726853i	$0.740982\pi$
$884$		0			0
$885$	−12492.3	+	21637.2i	−0.474489	+	0.821838i
$886$		0			0
$887$	−7798.12	−	13506.7i	−0.295192	−	0.511287i	0.679838	−	0.733363i	$-0.262050\pi$
$887$	−7798.12	−	13506.7i	−0.295192	−	0.511287i	−0.975030	+	0.222075i	$0.928717\pi$
$888$		0			0
$889$	−16821.6	+	13084.5i	−0.634623	+	0.493632i
$890$		0			0
$891$	38397.3	+	66506.1i	1.44373	+	2.50061i
$892$		0			0
$893$	−318.829	+	552.228i	−0.0119476	+	0.0206939i
$894$		0			0
$895$	−9485.30			−0.354255
$896$		0			0
$897$	90325.0			3.36217
$898$		0			0
$899$	−3494.83	+	6053.23i	−0.129654	+	0.224568i
$900$		0			0
$901$	−3133.02	−	5426.55i	−0.115845	−	0.200649i
$902$		0			0
$903$	7017.48	+	50721.6i	0.258613	+	1.86922i
$904$		0			0
$905$	6950.56	+	12038.7i	0.255298	+	0.442189i
$906$		0			0
$907$	27180.6	−	47078.2i	0.995059	−	1.72349i	0.411543	−	0.911390i	$-0.364990\pi$
$907$	27180.6	−	47078.2i	0.995059	−	1.72349i	0.583516	−	0.812102i	$-0.301677\pi$
$908$		0			0
$909$	5023.29			0.183291
$910$		0			0
$911$	1049.62			0.0381730			0.0190865	−	0.999818i	$-0.493924\pi$
$911$	1049.62			0.0381730			0.0190865	+	0.999818i	$0.493924\pi$
$912$		0			0
$913$	−15194.8	+	26318.1i	−0.550792	+	0.953999i
$914$		0			0
$915$	−12447.9	−	21560.4i	−0.449744	−	0.778980i
$916$		0			0
$917$	26952.6	+	10956.9i	0.970615	+	0.394579i
$918$		0			0
$919$	−19859.6	−	34397.8i	−0.712848	−	1.23469i	−0.963784	−	0.266685i	$-0.914072\pi$
$919$	−19859.6	−	34397.8i	−0.712848	−	1.23469i	0.250936	−	0.968004i	$-0.419262\pi$
$920$		0			0
$921$	−33599.9	+	58196.7i	−1.20212	+	2.08213i
$922$		0			0
$923$	50860.2			1.81374
$924$		0			0
$925$	9784.74			0.347806
$926$		0			0
$927$	9626.02	−	16672.8i	0.341057	−	0.590729i
$928$		0			0
$929$	−5717.94	−	9903.76i	−0.201937	−	0.349765i	0.747215	−	0.664582i	$-0.231390\pi$
$929$	−5717.94	−	9903.76i	−0.201937	−	0.349765i	−0.949153	+	0.314817i	$0.898057\pi$
$930$		0			0
$931$	503.948	−	142.167i	0.0177403	−	0.00500465i
$932$		0			0
$933$	−13515.4	−	23409.3i	−0.474248	−	0.821422i
$934$		0			0
$935$	905.453	−	1568.29i	0.0316700	−	0.0548541i
$936$		0			0
$937$	30599.3			1.06685			0.533423	−	0.845849i	$-0.320905\pi$
$937$	30599.3			1.06685			0.533423	+	0.845849i	$0.320905\pi$
$938$		0			0
$939$	80950.7			2.81334
$940$		0			0
$941$	9674.35	−	16756.5i	0.335149	−	0.580494i	−0.648365	−	0.761330i	$-0.724547\pi$
$941$	9674.35	−	16756.5i	0.335149	−	0.580494i	0.983513	+	0.180836i	$0.0578802\pi$
$942$		0			0
$943$	28756.5	+	49807.7i	0.993044	+	1.72000i
$944$		0			0
$945$	−38557.4	−	15674.6i	−1.32727	−	0.539570i
$946$		0			0
$947$	4276.02	+	7406.29i	0.146729	+	0.254142i	0.930017	−	0.367518i	$-0.119792\pi$
$947$	4276.02	+	7406.29i	0.146729	+	0.254142i	−0.783288	+	0.621659i	$0.786459\pi$
$948$		0			0
$949$	−1744.61	+	3021.76i	−0.0596761	+	0.103362i
$950$		0			0
$951$	70485.1			2.40340
$952$		0			0
$953$	40243.0			1.36789			0.683944	−	0.729534i	$-0.260263\pi$
$953$	40243.0			1.36789			0.683944	+	0.729534i	$0.260263\pi$
$954$		0			0
$955$	436.966	−	756.848i	0.0148062	−	0.0256450i
$956$		0			0
$957$	−19228.6	−	33304.9i	−0.649500	−	1.12497i
$958$		0			0
$959$	6722.02	+	48586.0i	0.226346	+	1.63600i
$960$		0			0
$961$	13383.9	+	23181.6i	0.449259	+	0.778140i
$962$		0			0
$963$	−20143.6	+	34889.8i	−0.674059	+	1.16751i
$964$		0			0
$965$	9786.42			0.326462
$966$		0			0
$967$	−38460.8			−1.27903			−0.639513	−	0.768781i	$-0.720864\pi$
$967$	−38460.8			−1.27903			−0.639513	+	0.768781i	$0.720864\pi$
$968$		0			0
$969$	−90.5973	+	156.919i	−0.00300351	+	0.00520224i
$970$		0			0
$971$	−6941.57	−	12023.2i	−0.229419	−	0.397365i	0.728217	−	0.685346i	$-0.240349\pi$
$971$	−6941.57	−	12023.2i	−0.229419	−	0.397365i	−0.957636	+	0.287981i	$0.907016\pi$
$972$		0			0
$973$	11583.9	−	9010.40i	0.381669	−	0.296876i
$974$		0			0
$975$	6944.60	+	12028.4i	0.228108	+	0.395095i
$976$		0			0
$977$	14458.4	−	25042.7i	0.473454	−	0.820047i	−0.526084	−	0.850433i	$-0.676340\pi$
$977$	14458.4	−	25042.7i	0.473454	−	0.820047i	0.999538	+	0.0303858i	$0.00967360\pi$
$978$		0			0
$979$	−35342.3			−1.15377
$980$		0			0
$981$	104763.			3.40961
$982$		0			0
$983$	−25591.6	+	44325.9i	−0.830360	+	1.43823i	0.0673927	+	0.997727i	$0.478532\pi$
$983$	−25591.6	+	44325.9i	−0.830360	+	1.43823i	−0.897753	+	0.440499i	$0.854801\pi$
$984$		0			0
$985$	−8862.61	−	15350.5i	−0.286687	−	0.496556i
$986$		0			0
$987$	60799.7	−	47292.2i	1.96077	−	1.52515i
$988$		0			0
$989$	−22572.3	−	39096.4i	−0.725740	−	1.25702i
$990$		0			0
$991$	−22318.0	+	38655.9i	−0.715393	+	1.23910i	0.247414	+	0.968910i	$0.420419\pi$
$991$	−22318.0	+	38655.9i	−0.715393	+	1.23910i	−0.962808	+	0.270188i	$0.912914\pi$
$992$		0			0
$993$	−40822.1			−1.30458
$994$		0			0
$995$	−13867.5			−0.441838
$996$		0			0
$997$	−7104.48	+	12305.3i	−0.225678	+	0.390886i	−0.956523	−	0.291658i	$-0.905793\pi$
$997$	−7104.48	+	12305.3i	−0.225678	+	0.390886i	0.730845	+	0.682544i	$0.239126\pi$
$998$		0			0
$999$	−87959.4	−	152350.i	−2.78570	−	4.82497i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	280.4.q.c.81.1	✓	12
4.3	odd	2		560.4.q.r.81.6		12
7.2	even	3	inner	280.4.q.c.121.1	yes	12
7.3	odd	6		1960.4.a.x.1.1		6
7.4	even	3		1960.4.a.ba.1.6		6
28.23	odd	6		560.4.q.r.401.6		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
280.4.q.c.81.1	✓	12	1.1	even	1	trivial
280.4.q.c.121.1	yes	12	7.2	even	3	inner
560.4.q.r.81.6		12	4.3	odd	2
560.4.q.r.401.6		12	28.23	odd	6
1960.4.a.x.1.1		6	7.3	odd	6
1960.4.a.ba.1.6		6	7.4	even	3

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 280 = 2^{3} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	280.q (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-4.97849 + 8.62300i) q^{3} +(2.50000 + 4.33013i) q^{5} +(-14.6186 + 11.3709i) q^{7} +(-36.0707 - 62.4763i) q^{9} +(15.1914 - 26.3123i) q^{11} -55.7969 q^{13} -49.7849 q^{15} +(5.96029 - 10.3235i) q^{17} +(0.763290 + 1.32206i) q^{19} +(-25.2724 - 182.666i) q^{21} +(81.2906 + 140.800i) q^{23} +(-12.5000 + 21.6506i) q^{25} +449.472 q^{27} -127.122 q^{29} +(27.4919 - 47.6174i) q^{31} +(151.261 + 261.991i) q^{33} +(-85.7838 - 34.8732i) q^{35} +(-195.695 - 338.954i) q^{37} +(277.784 - 481.136i) q^{39} +353.749 q^{41} -277.674 q^{43} +(180.354 - 312.382i) q^{45} +(208.852 + 361.742i) q^{47} +(84.4069 - 332.452i) q^{49} +(59.3465 + 102.791i) q^{51} +(262.824 - 455.225i) q^{53} +151.914 q^{55} -15.2001 q^{57} +(250.925 - 434.614i) q^{59} +(250.034 + 433.072i) q^{61} +(1237.71 + 503.161i) q^{63} +(-139.492 - 241.608i) q^{65} +(-33.8545 + 58.6377i) q^{67} -1618.82 q^{69} -911.524 q^{71} +(31.2672 - 54.1565i) q^{73} +(-124.462 - 215.575i) q^{75} +(77.1164 + 557.389i) q^{77} +(-305.767 - 529.604i) q^{79} +(-1263.78 + 2188.94i) q^{81} -1000.22 q^{83} +59.6029 q^{85} +(632.876 - 1096.17i) q^{87} +(-581.616 - 1007.39i) q^{89} +(815.672 - 634.459i) q^{91} +(273.737 + 474.126i) q^{93} +(-3.81645 + 6.61029i) q^{95} -1156.69 q^{97} -2191.86 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 7 q^{3} + 30 q^{5} - q^{7} - 39 q^{9} + 51 q^{11} - 54 q^{13} - 70 q^{15} - 6 q^{17} - 9 q^{19} + 123 q^{21} + 72 q^{23} - 150 q^{25} + 1118 q^{27} - 242 q^{29} - 132 q^{31} + 156 q^{33} - 115 q^{35}+ \cdots - 6978 q^{99}+O(q^{100}) \) 12 * q - 7 * q^3 + 30 * q^5 - q^7 - 39 * q^9 + 51 * q^11 - 54 * q^13 - 70 * q^15 - 6 * q^17 - 9 * q^19 + 123 * q^21 + 72 * q^23 - 150 * q^25 + 1118 * q^27 - 242 * q^29 - 132 * q^31 + 156 * q^33 - 115 * q^35 - 523 * q^37 + 358 * q^39 + 928 * q^41 - 1202 * q^43 + 195 * q^45 + 73 * q^47 + 753 * q^49 + 28 * q^51 + 999 * q^53 + 510 * q^55 - 1080 * q^57 - 98 * q^59 + 111 * q^61 + 3011 * q^63 - 135 * q^65 - 289 * q^67 - 1794 * q^69 - 3668 * q^71 + 332 * q^73 - 175 * q^75 + 285 * q^77 + 1368 * q^79 - 498 * q^81 + 1678 * q^83 - 60 * q^85 + 1075 * q^87 - 1035 * q^89 + 2368 * q^91 - 448 * q^93 + 45 * q^95 + 8 * q^97 - 6978 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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