LMFDB - Embedded newform 405.4.e.x.136.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [405,4,Mod(136,405)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(405, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 0]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("405.136");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 405 = 3^{4} \cdot 5 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	405.e (of order $3$, degree $2$, not 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:	$23.8957735523$
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} - 2 x^{11} + 2 x^{10} + 32 x^{9} + 583 x^{8} - 624 x^{7} + 594 x^{6} + 9450 x^{5} + 90513 x^{4} + \cdots + 746496 $ x^12 - 2x^11 + 2x^10 + 32x^9 + 583x^8 - 624x^7 + 594x^6 + 9450x^5 + 90513x^4 - 20304x^3 + 10368x^2 + 124416*x + 746496
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2}\cdot 3^{9} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			136.6
Root			$2.93142 - 2.93142i$ of defining polynomial
Character	$\chi$	$=$	405.136
Dual form			405.4.e.x.271.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.61668 - 4.53223i) q^{2} +(-9.69405 - 16.7906i) q^{4} +(2.50000 + 4.33013i) q^{5} +(-16.5090 + 28.5945i) q^{7} -59.5981 q^{8} +O(q^{10})$	\(q+(2.61668 - 4.53223i) q^{2} +(-9.69405 - 16.7906i) q^{4} +(2.50000 + 4.33013i) q^{5} +(-16.5090 + 28.5945i) q^{7} -59.5981 q^{8} +26.1668 q^{10} +(3.04155 - 5.26813i) q^{11} +(32.2254 + 55.8160i) q^{13} +(86.3977 + 149.645i) q^{14} +(-78.3969 + 135.787i) q^{16} +76.9845 q^{17} -118.716 q^{19} +(48.4703 - 83.9529i) q^{20} +(-15.9176 - 27.5700i) q^{22} +(38.8002 + 67.2039i) q^{23} +(-12.5000 + 21.6506i) q^{25} +337.294 q^{26} +640.157 q^{28} +(31.4075 - 54.3993i) q^{29} +(53.4569 + 92.5901i) q^{31} +(171.887 + 297.717i) q^{32} +(201.444 - 348.911i) q^{34} -165.090 q^{35} +108.268 q^{37} +(-310.642 + 538.048i) q^{38} +(-148.995 - 258.067i) q^{40} +(71.3830 + 123.639i) q^{41} +(-169.784 + 294.075i) q^{43} -117.940 q^{44} +406.111 q^{46} +(-299.173 + 518.182i) q^{47} +(-373.595 - 647.086i) q^{49} +(65.4171 + 113.306i) q^{50} +(624.789 - 1082.17i) q^{52} -488.041 q^{53} +30.4155 q^{55} +(983.906 - 1704.18i) q^{56} +(-164.367 - 284.691i) q^{58} +(121.413 + 210.294i) q^{59} +(249.669 - 432.440i) q^{61} +559.519 q^{62} +544.744 q^{64} +(-161.127 + 279.080i) q^{65} +(460.817 + 798.159i) q^{67} +(-746.292 - 1292.62i) q^{68} +(-431.989 + 748.226i) q^{70} +60.6882 q^{71} -338.439 q^{73} +(283.303 - 490.695i) q^{74} +(1150.84 + 1993.31i) q^{76} +(100.426 + 173.943i) q^{77} +(278.155 - 481.779i) q^{79} -783.969 q^{80} +747.147 q^{82} +(-32.4210 + 56.1548i) q^{83} +(192.461 + 333.353i) q^{85} +(888.542 + 1539.00i) q^{86} +(-181.271 + 313.970i) q^{88} -941.159 q^{89} -2128.04 q^{91} +(752.262 - 1302.96i) q^{92} +(1565.68 + 2711.84i) q^{94} +(-296.790 - 514.056i) q^{95} +(521.085 - 902.546i) q^{97} -3910.32 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 4 q^{2} - 34 q^{4} + 30 q^{5} - 40 q^{7} - 132 q^{8}+O(q^{10}) $ 12 * q + 4 * q^2 - 34 * q^4 + 30 * q^5 - 40 * q^7 - 132 * q^8	$ 12 q + 4 q^{2} - 34 q^{4} + 30 q^{5} - 40 q^{7} - 132 q^{8} + 40 q^{10} + 88 q^{11} - 20 q^{13} + 180 q^{14} - 58 q^{16} - 248 q^{17} - 92 q^{19} + 170 q^{20} + 74 q^{22} + 210 q^{23} - 150 q^{25} - 8 q^{26} + 704 q^{28} + 296 q^{29} + 104 q^{31} + 722 q^{32} + 428 q^{34} - 400 q^{35} - 408 q^{37} - 20 q^{38} - 330 q^{40} + 344 q^{41} - 512 q^{43} - 1432 q^{44} - 372 q^{46} + 238 q^{47} - 68 q^{49} + 100 q^{50} + 468 q^{52} - 1700 q^{53} + 880 q^{55} + 2316 q^{56} - 890 q^{58} + 1840 q^{59} + 364 q^{61} - 2076 q^{62} - 1980 q^{64} + 100 q^{65} - 88 q^{67} + 236 q^{68} - 900 q^{70} - 2728 q^{71} + 1672 q^{73} + 1316 q^{74} + 2106 q^{76} + 840 q^{77} + 680 q^{79} - 580 q^{80} + 3484 q^{82} + 2148 q^{83} - 620 q^{85} + 2872 q^{86} - 1296 q^{88} - 6000 q^{89} - 6116 q^{91} + 1002 q^{92} + 3662 q^{94} - 230 q^{95} + 612 q^{97} - 3964 q^{98}+O(q^{100}) $ 12 * q + 4 * q^2 - 34 * q^4 + 30 * q^5 - 40 * q^7 - 132 * q^8 + 40 * q^10 + 88 * q^11 - 20 * q^13 + 180 * q^14 - 58 * q^16 - 248 * q^17 - 92 * q^19 + 170 * q^20 + 74 * q^22 + 210 * q^23 - 150 * q^25 - 8 * q^26 + 704 * q^28 + 296 * q^29 + 104 * q^31 + 722 * q^32 + 428 * q^34 - 400 * q^35 - 408 * q^37 - 20 * q^38 - 330 * q^40 + 344 * q^41 - 512 * q^43 - 1432 * q^44 - 372 * q^46 + 238 * q^47 - 68 * q^49 + 100 * q^50 + 468 * q^52 - 1700 * q^53 + 880 * q^55 + 2316 * q^56 - 890 * q^58 + 1840 * q^59 + 364 * q^61 - 2076 * q^62 - 1980 * q^64 + 100 * q^65 - 88 * q^67 + 236 * q^68 - 900 * q^70 - 2728 * q^71 + 1672 * q^73 + 1316 * q^74 + 2106 * q^76 + 840 * q^77 + 680 * q^79 - 580 * q^80 + 3484 * q^82 + 2148 * q^83 - 620 * q^85 + 2872 * q^86 - 1296 * q^88 - 6000 * q^89 - 6116 * q^91 + 1002 * q^92 + 3662 * q^94 - 230 * q^95 + 612 * q^97 - 3964 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/405\mathbb{Z}\right)^\times$.

$n$	$82$	$326$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	2.61668	−	4.53223i	0.925137	−	1.60238i	0.133796	−	0.991009i	$-0.457283\pi$
$2$	2.61668	−	4.53223i	0.925137	−	1.60238i	0.791341	−	0.611375i	$-0.209383\pi$
$3$		0			0
$3$		0			0
$4$	−9.69405	−	16.7906i	−1.21176	−	2.09882i
$5$	2.50000	+	4.33013i	0.223607	+	0.387298i
$5$	2.50000	+	4.33013i	0.223607	+	0.387298i
$6$		0			0
$7$	−16.5090	+	28.5945i	−0.891403	+	1.54396i	−0.0532095	+	0.998583i	$0.516945\pi$
$7$	−16.5090	+	28.5945i	−0.891403	+	1.54396i	−0.838194	+	0.545372i	$0.816388\pi$
$8$	−59.5981			−2.63389
$9$		0			0
$10$	26.1668			0.827468
$11$	3.04155	−	5.26813i	0.0833694	−	0.144400i	−0.821326	−	0.570459i	$-0.806765\pi$
$11$	3.04155	−	5.26813i	0.0833694	−	0.144400i	0.904695	+	0.426059i	$0.140099\pi$
$12$		0			0
$13$	32.2254	+	55.8160i	0.687516	+	1.19081i	0.972639	+	0.232322i	$0.0746322\pi$
$13$	32.2254	+	55.8160i	0.687516	+	1.19081i	−0.285123	+	0.958491i	$0.592034\pi$
$14$	86.3977	+	149.645i	1.64934	+	2.85674i
$15$		0			0
$16$	−78.3969	+	135.787i	−1.22495	+	2.12168i
$17$	76.9845			1.09832			0.549162	−	0.835716i	$-0.314947\pi$
$17$	76.9845			1.09832			0.549162	+	0.835716i	$0.314947\pi$
$18$		0			0
$19$	−118.716			−1.43344			−0.716720	−	0.697361i	$-0.754357\pi$
$19$	−118.716			−1.43344			−0.716720	+	0.697361i	$0.754357\pi$
$20$	48.4703	−	83.9529i	0.541914	−	0.938623i
$21$		0			0
$22$	−15.9176	−	27.5700i	−0.154256	−	0.267179i
$23$	38.8002	+	67.2039i	0.351757	+	0.609260i	0.986557	−	0.163416i	$-0.0522511\pi$
$23$	38.8002	+	67.2039i	0.351757	+	0.609260i	−0.634801	+	0.772676i	$0.718918\pi$
$24$		0			0
$25$	−12.5000	+	21.6506i	−0.100000	+	0.173205i
$26$	337.294			2.54419
$27$		0			0
$28$	640.157			4.32065
$29$	31.4075	−	54.3993i	0.201111	−	0.348334i	−0.747776	−	0.663951i	$-0.768878\pi$
$29$	31.4075	−	54.3993i	0.201111	−	0.348334i	0.948887	+	0.315617i	$0.102211\pi$
$30$		0			0
$31$	53.4569	+	92.5901i	0.309714	+	0.536441i	0.978300	−	0.207194i	$-0.0664332\pi$
$31$	53.4569	+	92.5901i	0.309714	+	0.536441i	−0.668585	+	0.743635i	$0.733100\pi$
$32$	171.887	+	297.717i	0.949550	+	1.64467i
$33$		0			0
$34$	201.444	−	348.911i	1.01610	−	1.75994i
$35$	−165.090			−0.797295
$36$		0			0
$37$	108.268			0.481058			0.240529	−	0.970642i	$-0.422679\pi$
$37$	108.268			0.481058			0.240529	+	0.970642i	$0.422679\pi$
$38$	−310.642	+	538.048i	−1.32613	+	2.29692i
$39$		0			0
$40$	−148.995	−	258.067i	−0.588955	−	1.02010i
$41$	71.3830	+	123.639i	0.271906	+	0.470955i	0.969350	−	0.245684i	$-0.0790126\pi$
$41$	71.3830	+	123.639i	0.271906	+	0.470955i	−0.697444	+	0.716640i	$0.745679\pi$
$42$		0			0
$43$	−169.784	+	294.075i	−0.602136	+	1.04293i	0.390361	+	0.920662i	$0.372350\pi$
$43$	−169.784	+	294.075i	−0.602136	+	1.04293i	−0.992497	+	0.122268i	$0.960983\pi$
$44$	−117.940			−0.404093
$45$		0			0
$46$	406.111			1.30169
$47$	−299.173	+	518.182i	−0.928486	+	1.60818i	−0.142629	+	0.989776i	$0.545555\pi$
$47$	−299.173	+	518.182i	−0.928486	+	1.60818i	−0.785857	+	0.618408i	$0.787778\pi$
$48$		0			0
$49$	−373.595	−	647.086i	−1.08920	−	1.88655i
$50$	65.4171	+	113.306i	0.185027	+	0.320477i
$51$		0			0
$52$	624.789	−	1082.17i	1.66620	−	2.88595i
$53$	−488.041			−1.26486			−0.632431	−	0.774617i	$-0.717943\pi$
$53$	−488.041			−1.26486			−0.632431	+	0.774617i	$0.717943\pi$
$54$		0			0
$55$	30.4155			0.0745678
$56$	983.906	−	1704.18i	2.34786	−	4.06661i
$57$		0			0
$58$	−164.367	−	284.691i	−0.372110	−	0.644514i
$59$	121.413	+	210.294i	0.267909	+	0.464033i	0.968322	−	0.249706i	$-0.0803339\pi$
$59$	121.413	+	210.294i	0.267909	+	0.464033i	−0.700412	+	0.713738i	$0.747001\pi$
$60$		0			0
$61$	249.669	−	432.440i	0.524047	−	0.907676i	−0.475561	−	0.879683i	$-0.657755\pi$
$61$	249.669	−	432.440i	0.524047	−	0.907676i	0.999608	−	0.0279936i	$-0.00891181\pi$
$62$	559.519			1.14611
$63$		0			0
$64$	544.744			1.06395
$65$	−161.127	+	279.080i	−0.307466	+	0.532548i
$66$		0			0
$67$	460.817	+	798.159i	0.840266	+	1.45538i	0.889670	+	0.456604i	$0.150934\pi$
$67$	460.817	+	798.159i	0.840266	+	1.45538i	−0.0494046	+	0.998779i	$0.515732\pi$
$68$	−746.292	−	1292.62i	−1.33090	−	2.30519i
$69$		0			0
$70$	−431.989	+	748.226i	−0.737607	+	1.27757i
$71$	60.6882			0.101442			0.0507209	−	0.998713i	$-0.483848\pi$
$71$	60.6882			0.101442			0.0507209	+	0.998713i	$0.483848\pi$
$72$		0			0
$73$	−338.439			−0.542621			−0.271311	−	0.962492i	$-0.587457\pi$
$73$	−338.439			−0.542621			−0.271311	+	0.962492i	$0.587457\pi$
$74$	283.303	−	490.695i	0.445045	−	0.770840i
$75$		0			0
$76$	1150.84	+	1993.31i	1.73698	+	3.00854i
$77$	100.426	+	173.943i	0.148631	+	0.257437i
$78$		0			0
$79$	278.155	−	481.779i	0.396138	−	0.686131i	−0.597108	−	0.802161i	$-0.703683\pi$
$79$	278.155	−	481.779i	0.396138	−	0.686131i	0.993246	+	0.116030i	$0.0370168\pi$
$80$	−783.969			−1.09563
$81$		0			0
$82$	747.147			1.00620
$83$	−32.4210	+	56.1548i	−0.0428755	+	0.0742625i	−0.886667	−	0.462409i	$-0.846985\pi$
$83$	−32.4210	+	56.1548i	−0.0428755	+	0.0742625i	0.843791	+	0.536671i	$0.180319\pi$
$84$		0			0
$85$	192.461	+	333.353i	0.245592	+	0.425379i
$86$	888.542	+	1539.00i	1.11412	+	1.92971i
$87$		0			0
$88$	−181.271	+	313.970i	−0.219586	+	0.380333i
$89$	−941.159			−1.12093			−0.560465	−	0.828178i	$-0.689377\pi$
$89$	−941.159			−1.12093			−0.560465	+	0.828178i	$0.689377\pi$
$90$		0			0
$91$	−2128.04			−2.45142
$92$	752.262	−	1302.96i	0.852487	−	1.47655i
$93$		0			0
$94$	1565.68	+	2711.84i	1.71795	+	2.97558i
$95$	−296.790	−	514.056i	−0.320527	−	0.555169i
$96$		0			0
$97$	521.085	−	902.546i	0.545445	−	0.944738i	−0.453134	−	0.891442i	$-0.649694\pi$
$97$	521.085	−	902.546i	0.545445	−	0.944738i	0.998579	−	0.0532958i	$-0.0169726\pi$
$98$	−3910.32			−4.03064
$99$		0			0
$100$	484.703			0.484703
$101$	341.121	−	590.840i	0.336068	−	0.582086i	−0.647622	−	0.761962i	$-0.724236\pi$
$101$	341.121	−	590.840i	0.336068	−	0.582086i	0.983689	+	0.179876i	$0.0575696\pi$
$102$		0			0
$103$	−606.832	−	1051.06i	−0.580514	−	1.00548i	−0.995418	−	0.0956144i	$-0.969518\pi$
$103$	−606.832	−	1051.06i	−0.580514	−	1.00548i	0.414905	−	0.909865i	$-0.363815\pi$
$104$	−1920.57	−	3326.52i	−1.81084	−	3.13647i
$105$		0			0
$106$	−1277.05	+	2211.91i	−1.17017	+	2.02679i
$107$	1311.93			1.18532			0.592658	−	0.805454i	$-0.298079\pi$
$107$	1311.93			1.18532			0.592658	+	0.805454i	$0.298079\pi$
$108$		0			0
$109$	−294.780			−0.259035			−0.129518	−	0.991577i	$-0.541343\pi$
$109$	−294.780			−0.259035			−0.129518	+	0.991577i	$0.541343\pi$
$110$	79.5878	−	137.850i	0.0689854	−	0.119486i
$111$		0			0
$112$	−2588.51	−	4483.43i	−2.18385	−	3.78254i
$113$	792.562	+	1372.76i	0.659805	+	1.14282i	0.980666	+	0.195689i	$0.0626944\pi$
$113$	792.562	+	1372.76i	0.659805	+	1.14282i	−0.320861	+	0.947126i	$0.603972\pi$
$114$		0			0
$115$	−194.001	+	336.020i	−0.157310	+	0.272469i
$116$	−1217.86			−0.974790
$117$		0			0
$118$	1270.80			0.991412
$119$	−1270.94	+	2201.33i	−0.979049	+	1.69576i
$120$		0			0
$121$	646.998	+	1120.63i	0.486099	+	0.841948i
$122$	−1306.61	−	2263.12i	−0.969631	−	1.67945i
$123$		0			0
$124$	1036.43	−	1795.15i	0.750597	−	1.30007i
$125$	−125.000			−0.0894427
$126$		0			0
$127$	−149.176			−0.104230			−0.0521149	−	0.998641i	$-0.516596\pi$
$127$	−149.176			−0.104230			−0.0521149	+	0.998641i	$0.516596\pi$
$128$	50.3275	−	87.1698i	0.0347528	−	0.0601937i
$129$		0			0
$130$	843.235	+	1460.53i	0.568897	+	0.985359i
$131$	585.886	+	1014.78i	0.390757	+	0.676810i	0.992550	−	0.121842i	$-0.0388801\pi$
$131$	585.886	+	1014.78i	0.390757	+	0.676810i	−0.601793	+	0.798652i	$0.705547\pi$
$132$		0			0
$133$	1959.89	−	3394.62i	1.27777	−	2.21317i
$134$	4823.25			3.10944
$135$		0			0
$136$	−4588.13			−2.89286
$137$	−579.313	+	1003.40i	−0.361270	+	0.625739i	−0.988170	−	0.153361i	$-0.950990\pi$
$137$	−579.313	+	1003.40i	−0.361270	+	0.625739i	0.626900	+	0.779100i	$0.284324\pi$
$138$		0			0
$139$	−793.262	−	1373.97i	−0.484055	−	0.838408i	0.515777	−	0.856723i	$-0.327503\pi$
$139$	−793.262	−	1373.97i	−0.484055	−	0.838408i	−0.999832	+	0.0183149i	$0.994170\pi$
$140$	1600.39	+	2771.96i	0.966128	+	1.67338i
$141$		0			0
$142$	158.802	−	275.053i	0.0938475	−	0.162549i
$143$	392.061			0.229271
$144$		0			0
$145$	314.075			0.179879
$146$	−885.588	+	1533.88i	−0.501999	+	0.869487i
$147$		0			0
$148$	−1049.56	−	1817.88i	−0.582925	−	1.00966i
$149$	258.555	+	447.830i	0.142158	+	0.246226i	0.928309	−	0.371809i	$-0.121262\pi$
$149$	258.555	+	447.830i	0.142158	+	0.246226i	−0.786151	+	0.618035i	$0.787929\pi$
$150$		0			0
$151$	−277.793	+	481.151i	−0.149712	+	0.259308i	−0.931121	−	0.364711i	$-0.881168\pi$
$151$	−277.793	+	481.151i	−0.149712	+	0.259308i	0.781409	+	0.624019i	$0.214501\pi$
$152$	7075.25			3.77552
$153$		0			0
$154$	1051.13			0.550018
$155$	−267.285	+	462.950i	−0.138508	+	0.239904i
$156$		0			0
$157$	−527.016	−	912.818i	−0.267901	−	0.464018i	0.700419	−	0.713732i	$-0.252997\pi$
$157$	−527.016	−	912.818i	−0.267901	−	0.464018i	−0.968320	+	0.249714i	$0.919663\pi$
$158$	−1455.69	−	2521.33i	−0.732964	−	1.26953i
$159$		0			0
$160$	−859.435	+	1488.58i	−0.424652	+	0.735519i
$161$	−2562.21			−1.25423
$162$		0			0
$163$	−635.916			−0.305575			−0.152788	−	0.988259i	$-0.548825\pi$
$163$	−635.916			−0.305575			−0.152788	+	0.988259i	$0.548825\pi$
$164$	1383.98	−	2397.13i	0.658968	−	1.14137i
$165$		0			0
$166$	169.671	+	293.879i	0.0793314	+	0.137406i
$167$	682.557	+	1182.22i	0.316274	+	0.547803i	0.979708	−	0.200432i	$-0.0642346\pi$
$167$	682.557	+	1182.22i	0.316274	+	0.547803i	−0.663433	+	0.748236i	$0.730901\pi$
$168$		0			0
$169$	−978.448	+	1694.72i	−0.445356	+	0.771380i
$170$	2014.44			0.908827
$171$		0			0
$172$	6583.59			2.91857
$173$	567.465	−	982.878i	0.249385	−	0.431947i	−0.713970	−	0.700176i	$-0.753105\pi$
$173$	567.465	−	982.878i	0.249385	−	0.431947i	0.963355	+	0.268229i	$0.0864383\pi$
$174$		0			0
$175$	−412.726	−	714.862i	−0.178281	−	0.308791i
$176$	476.897	+	826.009i	0.204247	+	0.353766i
$177$		0			0
$178$	−2462.72	+	4265.55i	−1.03701	+	1.79616i
$179$	−1813.33			−0.757179			−0.378589	−	0.925565i	$-0.623591\pi$
$179$	−1813.33			−0.757179			−0.378589	+	0.925565i	$0.623591\pi$
$180$		0			0
$181$	2334.37			0.958634			0.479317	−	0.877642i	$-0.340884\pi$
$181$	2334.37			0.958634			0.479317	+	0.877642i	$0.340884\pi$
$182$	−5568.40	+	9644.74i	−2.26790	+	3.92811i
$183$		0			0
$184$	−2312.42	−	4005.23i	−0.926488	−	1.60472i
$185$	270.670	+	468.814i	0.107568	+	0.186313i
$186$		0			0
$187$	234.153	−	405.564i	0.0915665	−	0.158598i
$188$	11600.8			4.50039
$189$		0			0
$190$	−3106.42			−1.18612
$191$	221.322	−	383.341i	0.0838444	−	0.145223i	−0.821054	−	0.570851i	$-0.806613\pi$
$191$	221.322	−	383.341i	0.0838444	−	0.145223i	0.904898	+	0.425628i	$0.139947\pi$
$192$		0			0
$193$	1851.27	+	3206.49i	0.690452	+	1.19590i	0.971690	+	0.236261i	$0.0759219\pi$
$193$	1851.27	+	3206.49i	0.690452	+	1.19590i	−0.281237	+	0.959638i	$0.590745\pi$
$194$	−2727.03	−	4723.35i	−1.00922	−	1.74802i
$195$		0			0
$196$	−7243.31	+	12545.8i	−2.63969	+	4.57208i
$197$	−4491.92			−1.62455			−0.812274	−	0.583276i	$-0.801771\pi$
$197$	−4491.92			−1.62455			−0.812274	+	0.583276i	$0.801771\pi$
$198$		0			0
$199$	−2934.08			−1.04518			−0.522591	−	0.852584i	$-0.675034\pi$
$199$	−2934.08			−1.04518			−0.522591	+	0.852584i	$0.675034\pi$
$200$	744.976	−	1290.34i	0.263389	−	0.456203i
$201$		0			0
$202$	−1785.21	−	3092.08i	−0.621817	−	1.07702i
$203$	1037.01	+	1796.16i	0.358542	+	0.621013i
$204$		0			0
$205$	−356.915	+	618.195i	−0.121600	+	0.210618i
$206$	−6351.54			−2.14822
$207$		0			0
$208$	−10105.5			−3.36869
$209$	−361.082	+	625.412i	−0.119505	+	0.206989i
$210$		0			0
$211$	336.970	+	583.649i	0.109943	+	0.190427i	0.915747	−	0.401756i	$-0.131600\pi$
$211$	336.970	+	583.649i	0.109943	+	0.190427i	−0.805804	+	0.592182i	$0.798267\pi$
$212$	4731.10	+	8194.50i	1.53270	+	2.65472i
$213$		0			0
$214$	3432.90	−	5945.95i	1.09658	−	1.89933i
$215$	−1697.84			−0.538567
$216$		0			0
$217$	−3530.08			−1.10432
$218$	−771.347	+	1336.01i	−0.239643	+	0.415074i
$219$		0			0
$220$	−294.850	−	510.695i	−0.0903580	−	0.156505i
$221$	2480.85	+	4296.97i	0.755115	+	1.30790i
$222$		0			0
$223$	−89.2581	+	154.599i	−0.0268034	+	0.0464249i	−0.879116	−	0.476608i	$-0.841866\pi$
$223$	−89.2581	+	154.599i	−0.0268034	+	0.0464249i	0.852313	+	0.523033i	$0.175199\pi$
$224$	−11350.7			−3.38573
$225$		0			0
$226$	8295.53			2.44164
$227$	2526.05	−	4375.25i	0.738590	−	1.27928i	−0.214540	−	0.976715i	$-0.568825\pi$
$227$	2526.05	−	4375.25i	0.738590	−	1.27928i	0.953130	−	0.302561i	$-0.0978415\pi$
$228$		0			0
$229$	−654.484	−	1133.60i	−0.188863	−	0.327120i	0.756009	−	0.654562i	$-0.227147\pi$
$229$	−654.484	−	1133.60i	−0.188863	−	0.327120i	−0.944871	+	0.327442i	$0.893813\pi$
$230$	1015.28	+	1758.51i	0.291067	+	0.504143i
$231$		0			0
$232$	−1871.82	+	3242.10i	−0.529704	+	0.917474i
$233$	6591.30			1.85326			0.926632	−	0.375970i	$-0.122691\pi$
$233$	6591.30			1.85326			0.926632	+	0.375970i	$0.122691\pi$
$234$		0			0
$235$	−2991.73			−0.830463
$236$	2353.97	−	4077.20i	0.649282	−	1.12459i
$237$		0			0
$238$	6651.29	+	11520.4i	1.81151	+	3.13762i
$239$	792.252	+	1372.22i	0.214421	+	0.371387i	0.953093	−	0.302677i	$-0.0978803\pi$
$239$	792.252	+	1372.22i	0.214421	+	0.371387i	−0.738673	+	0.674064i	$0.764547\pi$
$240$		0			0
$241$	837.234	−	1450.13i	0.223780	−	0.387598i	−0.732173	−	0.681119i	$-0.761494\pi$
$241$	837.234	−	1450.13i	0.223780	−	0.387598i	0.955953	+	0.293521i	$0.0948269\pi$
$242$	6771.95			1.79883
$243$		0			0
$244$	−9681.23			−2.54007
$245$	1867.98	−	3235.43i	0.487105	−	0.843690i
$246$		0			0
$247$	−3825.67	−	6626.25i	−0.985512	−	1.70696i
$248$	−3185.93	−	5518.19i	−0.815753	−	1.41293i
$249$		0			0
$250$	−327.085	+	566.528i	−0.0827468	+	0.143322i
$251$	1200.75			0.301955			0.150978	−	0.988537i	$-0.451758\pi$
$251$	1200.75			0.301955			0.150978	+	0.988537i	$0.451758\pi$
$252$		0			0
$253$	472.052			0.117303
$254$	−390.345	+	676.098i	−0.0964269	+	0.167016i
$255$		0			0
$256$	1915.60	+	3317.91i	0.467675	+	0.810036i
$257$	−2603.34	−	4509.12i	−0.631876	−	1.09444i	−0.987168	−	0.159686i	$-0.948952\pi$
$257$	−2603.34	−	4509.12i	−0.631876	−	1.09444i	0.355292	−	0.934755i	$-0.384381\pi$
$258$		0			0
$259$	−1787.40	+	3095.87i	−0.428817	+	0.742733i
$260$	6247.89			1.49030
$261$		0			0
$262$	6132.31			1.44601
$263$	3841.78	−	6654.16i	0.900739	−	1.56012i	0.0742011	−	0.997243i	$-0.476359\pi$
$263$	3841.78	−	6654.16i	0.900739	−	1.56012i	0.826537	−	0.562882i	$-0.190307\pi$
$264$		0			0
$265$	−1220.10	−	2113.28i	−0.282832	−	0.489879i
$266$	−10256.8	−	17765.3i	−2.36423	−	4.09496i
$267$		0			0
$268$	8934.37	−	15474.8i	2.03639	−	3.52714i
$269$	624.277			0.141497			0.0707487	−	0.997494i	$-0.477461\pi$
$269$	624.277			0.141497			0.0707487	+	0.997494i	$0.477461\pi$
$270$		0			0
$271$	−1462.51			−0.327828			−0.163914	−	0.986475i	$-0.552412\pi$
$271$	−1462.51			−0.327828			−0.163914	+	0.986475i	$0.552412\pi$
$272$	−6035.35	+	10453.5i	−1.34539	+	2.33029i
$273$		0			0
$274$	3031.76	+	5251.15i	0.668449	+	1.15779i
$275$	76.0388	+	131.703i	0.0166739	+	0.0288800i
$276$		0			0
$277$	2949.02	−	5107.85i	0.639673	−	1.10795i	−0.345832	−	0.938297i	$-0.612403\pi$
$277$	2949.02	−	5107.85i	0.639673	−	1.10795i	0.985505	−	0.169649i	$-0.0542635\pi$
$278$	−8302.86			−1.79127
$279$		0			0
$280$	9839.06			2.09999
$281$	−2636.45	+	4566.47i	−0.559707	+	0.969441i	0.437813	+	0.899066i	$0.355753\pi$
$281$	−2636.45	+	4566.47i	−0.559707	+	0.969441i	−0.997521	+	0.0703753i	$0.977580\pi$
$282$		0			0
$283$	559.632	+	969.311i	0.117550	+	0.203603i	0.918796	−	0.394732i	$-0.129163\pi$
$283$	559.632	+	969.311i	0.117550	+	0.203603i	−0.801246	+	0.598335i	$0.795829\pi$
$284$	−588.315	−	1018.99i	−0.122923	−	0.212908i
$285$		0			0
$286$	1025.90	−	1776.91i	0.212107	−	0.367380i
$287$	−4713.86			−0.969513
$288$		0			0
$289$	1013.62			0.206313
$290$	821.833	−	1423.46i	0.166413	−	0.288235i
$291$		0			0
$292$	3280.85	+	5682.60i	0.657525	+	1.13887i
$293$	−470.370	−	814.705i	−0.0937860	−	0.162442i	0.815315	−	0.579017i	$-0.196564\pi$
$293$	−470.370	−	814.705i	−0.0937860	−	0.162442i	−0.909101	+	0.416575i	$0.863230\pi$
$294$		0			0
$295$	−607.066	+	1051.47i	−0.119813	+	0.207522i
$296$	−6452.57			−1.26705
$297$		0			0
$298$	2706.22			0.526064
$299$	−2500.70	+	4331.34i	−0.483676	+	0.837752i
$300$		0			0
$301$	−5605.94	−	9709.77i	−1.07349	−	1.85934i
$302$	1453.79	+	2518.04i	0.277008	+	0.479791i
$303$		0			0
$304$	9306.97	−	16120.1i	1.75589	−	3.04130i
$305$	2496.69			0.468722
$306$		0			0
$307$	1931.88			0.359148			0.179574	−	0.983744i	$-0.442528\pi$
$307$	1931.88			0.359148			0.179574	+	0.983744i	$0.442528\pi$
$308$	1947.07	−	3372.43i	0.360210	−	0.623902i
$309$		0			0
$310$	1398.80	+	2422.79i	0.256279	+	0.443888i
$311$	−3149.08	−	5454.37i	−0.574174	−	0.994498i	−0.996131	−	0.0878821i	$-0.971990\pi$
$311$	−3149.08	−	5454.37i	−0.574174	−	0.994498i	0.421957	−	0.906616i	$-0.361343\pi$
$312$		0			0
$313$	909.403	−	1575.13i	0.164225	−	0.284446i	−0.772155	−	0.635435i	$-0.780821\pi$
$313$	909.403	−	1575.13i	0.164225	−	0.284446i	0.936380	+	0.350988i	$0.114154\pi$
$314$	−5516.13			−0.991380
$315$		0			0
$316$	−10785.8			−1.92009
$317$	1579.32	−	2735.46i	0.279821	−	0.484665i	−0.691519	−	0.722358i	$-0.743058\pi$
$317$	1579.32	−	2735.46i	0.279821	−	0.484665i	0.971340	+	0.237694i	$0.0763914\pi$
$318$		0			0
$319$	−191.055	−	330.917i	−0.0335330	−	0.0580808i
$320$	1361.86	+	2358.81i	0.237907	+	0.412068i
$321$		0			0
$322$	−6704.50	+	11612.5i	−1.16033	+	2.00975i
$323$	−9139.31			−1.57438
$324$		0			0
$325$	−1611.27			−0.275006
$326$	−1663.99	+	2882.12i	−0.282699	+	0.489649i
$327$		0			0
$328$	−4254.29	−	7368.65i	−0.716171	−	1.24044i
$329$	−9878.10	−	17109.4i	−1.65531	−	2.86708i
$330$		0			0
$331$	476.545	−	825.400i	0.0791338	−	0.137064i	−0.823743	−	0.566964i	$-0.808118\pi$
$331$	476.545	−	825.400i	0.0791338	−	0.137064i	0.902876	+	0.429900i	$0.141451\pi$
$332$	1257.16			0.207819
$333$		0			0
$334$	7144.14			1.17039
$335$	−2304.09	+	3990.79i	−0.375778	+	0.650867i
$336$		0			0
$337$	284.447	+	492.676i	0.0459786	+	0.0796373i	0.888099	−	0.459653i	$-0.152026\pi$
$337$	284.447	+	492.676i	0.0459786	+	0.0796373i	−0.842120	+	0.539290i	$0.818693\pi$
$338$	5120.57	+	8869.09i	0.824031	+	1.42726i
$339$		0			0
$340$	3731.46	−	6463.08i	0.595197	−	1.03091i
$341$	650.368			0.103283
$342$		0			0
$343$	13345.6			2.10086
$344$	10118.8	−	17526.3i	1.58596	−	2.74696i
$345$		0			0
$346$	−2969.75	−	5143.76i	−0.461430	−	0.799220i
$347$	4213.28	+	7297.61i	0.651817	+	1.12898i	0.982682	+	0.185302i	$0.0593264\pi$
$347$	4213.28	+	7297.61i	0.651817	+	1.12898i	−0.330864	+	0.943678i	$0.607340\pi$
$348$		0			0
$349$	−3571.98	+	6186.85i	−0.547861	+	0.948924i	0.450559	+	0.892746i	$0.351225\pi$
$349$	−3571.98	+	6186.85i	−0.547861	+	0.948924i	−0.998421	+	0.0561773i	$0.982109\pi$
$350$	−4319.89			−0.659736
$351$		0			0
$352$	2091.21			0.316654
$353$	2650.35	−	4590.54i	0.399614	−	0.692152i	−0.594064	−	0.804418i	$-0.702478\pi$
$353$	2650.35	−	4590.54i	0.399614	−	0.692152i	0.993678	+	0.112266i	$0.0358108\pi$
$354$		0			0
$355$	151.720	+	262.788i	0.0226831	+	0.0392882i
$356$	9123.65	+	15802.6i	1.35829	+	2.35263i
$357$		0			0
$358$	−4744.92	+	8218.44i	−0.700494	+	1.21329i
$359$	9536.35			1.40198			0.700988	−	0.713173i	$-0.252743\pi$
$359$	9536.35			1.40198			0.700988	+	0.713173i	$0.252743\pi$
$360$		0			0
$361$	7234.52			1.05475
$362$	6108.32	−	10579.9i	0.886867	−	1.53610i
$363$		0			0
$364$	20629.3	+	35731.0i	2.97052	+	5.14509i
$365$	−846.098	−	1465.49i	−0.121334	−	0.210156i
$366$		0			0
$367$	365.104	−	632.379i	0.0519299	−	0.0899453i	−0.838892	−	0.544298i	$-0.816796\pi$
$367$	365.104	−	632.379i	0.0519299	−	0.0899453i	0.890822	+	0.454353i	$0.150129\pi$
$368$	−12167.3			−1.72354
$369$		0			0
$370$	2833.03			0.398060
$371$	8057.09	−	13955.3i	1.12750	−	1.95289i
$372$		0			0
$373$	−6434.47	−	11144.8i	−0.893201	−	1.54707i	−0.836015	−	0.548707i	$-0.815120\pi$
$373$	−6434.47	−	11144.8i	−0.893201	−	1.54707i	−0.0571863	−	0.998364i	$-0.518213\pi$
$374$	−1225.41	−	2122.47i	−0.169423	−	0.293449i
$375$		0			0
$376$	17830.1	−	30882.7i	2.44553	−	4.23578i
$377$	4048.47			0.553068
$378$		0			0
$379$	−4000.88			−0.542246			−0.271123	−	0.962545i	$-0.587395\pi$
$379$	−4000.88			−0.542246			−0.271123	+	0.962545i	$0.587395\pi$
$380$	−5754.20	+	9966.57i	−0.776801	+	1.34546i
$381$		0			0
$382$	−1158.26	−	2006.16i	−0.155135	−	0.268702i
$383$	−32.6599	−	56.5687i	−0.00435730	−	0.00754706i	0.863839	−	0.503769i	$-0.168054\pi$
$383$	−32.6599	−	56.5687i	−0.00435730	−	0.00754706i	−0.868196	+	0.496222i	$0.834720\pi$
$384$		0			0
$385$	−502.131	+	869.716i	−0.0664700	+	0.115129i
$386$	19376.7			2.55505
$387$		0			0
$388$	−20205.7			−2.64379
$389$	2959.89	−	5126.67i	0.385790	−	0.668207i	−0.606089	−	0.795397i	$-0.707262\pi$
$389$	2959.89	−	5126.67i	0.385790	−	0.668207i	0.991878	+	0.127190i	$0.0405957\pi$
$390$		0			0
$391$	2987.02	+	5173.66i	0.386342	+	0.669165i
$392$	22265.6	+	38565.1i	2.86883	+	4.96896i
$393$		0			0
$394$	−11753.9	+	20358.4i	−1.50293	+	2.60315i
$395$	2781.55			0.354317
$396$		0			0
$397$	−10228.7			−1.29310			−0.646551	−	0.762871i	$-0.723789\pi$
$397$	−10228.7			−1.29310			−0.646551	+	0.762871i	$0.723789\pi$
$398$	−7677.54	+	13297.9i	−0.966936	+	1.67478i
$399$		0			0
$400$	−1959.92	−	3394.68i	−0.244990	−	0.424335i
$401$	6122.56	+	10604.6i	0.762460	+	1.32062i	0.941579	+	0.336791i	$0.109342\pi$
$401$	6122.56	+	10604.6i	0.762460	+	1.32062i	−0.179120	+	0.983827i	$0.557325\pi$
$402$		0			0
$403$	−3445.34	+	5967.50i	−0.425867	+	0.737623i
$404$	−13227.4			−1.62893
$405$		0			0
$406$	10854.1			1.32680
$407$	329.303	−	570.370i	0.0401055	−	0.0694648i
$408$		0			0
$409$	−4916.47	−	8515.58i	−0.594386	−	1.02951i	−0.993633	−	0.112664i	$-0.964062\pi$
$409$	−4916.47	−	8515.58i	−0.594386	−	1.02951i	0.399247	−	0.916843i	$-0.369272\pi$
$410$	1867.87	+	3235.24i	0.224994	+	0.389700i
$411$		0			0
$412$	−11765.3	+	20378.1i	−1.40688	+	2.43679i
$413$	−8017.65			−0.955262
$414$		0			0
$415$	−324.210			−0.0383490
$416$	−11078.2	+	19188.1i	−1.30566	+	2.26147i
$417$		0			0
$418$	1889.67	+	3273.01i	0.221117	+	0.382986i
$419$	6157.57	+	10665.2i	0.717941	+	1.24351i	0.961814	+	0.273703i	$0.0882485\pi$
$419$	6157.57	+	10665.2i	0.717941	+	1.24351i	−0.243873	+	0.969807i	$0.578418\pi$
$420$		0			0
$421$	2159.21	−	3739.86i	0.249961	−	0.432945i	−0.713554	−	0.700600i	$-0.752916\pi$
$421$	2159.21	−	3739.86i	0.249961	−	0.432945i	0.963515	+	0.267656i	$0.0862489\pi$
$422$	3526.97			0.406849
$423$		0			0
$424$	29086.3			3.33150
$425$	−962.307	+	1666.76i	−0.109832	+	0.190235i
$426$		0			0
$427$	8243.59	+	14278.3i	0.934275	+	1.61821i
$428$	−12717.9	−	22028.0i	−1.43631	−	2.48777i
$429$		0			0
$430$	−4442.71	+	7695.00i	−0.498248	+	0.862991i
$431$	−5265.39			−0.588457			−0.294228	−	0.955735i	$-0.595063\pi$
$431$	−5265.39			−0.588457			−0.294228	+	0.955735i	$0.595063\pi$
$432$		0			0
$433$	5855.07			0.649831			0.324916	−	0.945743i	$-0.394664\pi$
$433$	5855.07			0.649831			0.324916	+	0.945743i	$0.394664\pi$
$434$	−9237.11	+	15999.1i	−1.02165	+	1.76955i
$435$		0			0
$436$	2857.62	+	4949.54i	0.313888	+	0.543669i
$437$	−4606.21	−	7978.19i	−0.504222	−	0.873338i
$438$		0			0
$439$	−2011.35	+	3483.76i	−0.218671	+	0.378748i	−0.954402	−	0.298525i	$-0.903505\pi$
$439$	−2011.35	+	3483.76i	−0.218671	+	0.378748i	0.735731	+	0.677274i	$0.236839\pi$
$440$	−1812.71			−0.196403
$441$		0			0
$442$	25966.4			2.79434
$443$	3751.11	−	6497.12i	0.402304	−	0.696811i	−0.591699	−	0.806159i	$-0.701543\pi$
$443$	3751.11	−	6497.12i	0.402304	−	0.696811i	0.994004	+	0.109347i	$0.0348761\pi$
$444$		0			0
$445$	−2352.90	−	4075.34i	−0.250647	−	0.434134i
$446$	467.120	+	809.076i	0.0495937	+	0.0858987i
$447$		0			0
$448$	−8993.20	+	15576.7i	−0.948412	+	1.64270i
$449$	18574.2			1.95227			0.976135	−	0.217166i	$-0.0696813\pi$
$449$	18574.2			1.95227			0.976135	+	0.217166i	$0.0696813\pi$
$450$		0			0
$451$	868.461			0.0906746
$452$	15366.3	−	26615.2i	1.59905	−	2.76963i
$453$		0			0
$454$	−13219.8	−	22897.3i	−1.36659	−	2.36701i
$455$	−5320.09	−	9214.67i	−0.548153	−	0.949429i
$456$		0			0
$457$	−7072.78	+	12250.4i	−0.723962	+	1.25394i	0.235438	+	0.971889i	$0.424347\pi$
$457$	−7072.78	+	12250.4i	−0.723962	+	1.25394i	−0.959400	+	0.282049i	$0.908986\pi$
$458$	−6850.31			−0.698895
$459$		0			0
$460$	7522.62			0.762487
$461$	−2455.37	+	4252.83i	−0.248066	+	0.429662i	−0.962989	−	0.269541i	$-0.913128\pi$
$461$	−2455.37	+	4252.83i	−0.248066	+	0.429662i	0.714923	+	0.699203i	$0.246462\pi$
$462$		0			0
$463$	−4627.72	−	8015.45i	−0.464511	−	0.804557i	0.534668	−	0.845062i	$-0.320437\pi$
$463$	−4627.72	−	8015.45i	−0.464511	−	0.804557i	−0.999179	+	0.0405054i	$0.987103\pi$
$464$	4924.49	+	8529.47i	0.492702	+	0.853385i
$465$		0			0
$466$	17247.3	−	29873.3i	1.71452	−	2.96964i
$467$	2825.10			0.279936			0.139968	−	0.990156i	$-0.455300\pi$
$467$	2825.10			0.279936			0.139968	+	0.990156i	$0.455300\pi$
$468$		0			0
$469$	−30430.6			−2.99606
$470$	−7828.40	+	13559.2i	−0.768292	+	1.33072i
$471$		0			0
$472$	−7236.00	−	12533.1i	−0.705644	−	1.22221i
$473$	1032.82	+	1788.89i	0.100399	+	0.173897i
$474$		0			0
$475$	1483.95	−	2570.28i	0.143344	−	0.248279i
$476$	49282.2			4.74547
$477$		0			0
$478$	8292.29			0.793474
$479$	4586.74	−	7944.47i	0.437523	−	0.757812i	−0.559975	−	0.828510i	$-0.689189\pi$
$479$	4586.74	−	7944.47i	0.437523	−	0.757812i	0.997498	+	0.0706977i	$0.0225226\pi$
$480$		0			0
$481$	3488.98	+	6043.08i	0.330735	+	0.572850i
$482$	−4381.55	−	7589.07i	−0.414054	−	0.717163i
$483$		0			0
$484$	12544.1	−	21727.0i	1.17807	−	2.04047i
$485$	5210.85			0.487861
$486$		0			0
$487$	13663.7			1.27138			0.635690	−	0.771945i	$-0.280716\pi$
$487$	13663.7			1.27138			0.635690	+	0.771945i	$0.280716\pi$
$488$	−14879.8	+	25772.6i	−1.38028	+	2.39072i
$489$		0			0
$490$	−9775.81	−	16932.2i	−0.901277	−	1.56106i
$491$	−2925.16	−	5066.52i	−0.268860	−	0.465680i	0.699707	−	0.714430i	$-0.253314\pi$
$491$	−2925.16	−	5066.52i	−0.268860	−	0.465680i	−0.968568	+	0.248750i	$0.919980\pi$
$492$		0			0
$493$	2417.89	−	4187.91i	0.220885	−	0.382584i
$494$	−40042.2			−3.64694
$495$		0			0
$496$	−16763.4			−1.51754
$497$	−1001.90	+	1735.35i	−0.0904255	+	0.156622i
$498$		0			0
$499$	−1921.49	−	3328.11i	−0.172380	−	0.298571i	0.766872	−	0.641801i	$-0.221812\pi$
$499$	−1921.49	−	3328.11i	−0.172380	−	0.298571i	−0.939251	+	0.343230i	$0.888479\pi$
$500$	1211.76	+	2098.82i	0.108383	+	0.187725i
$501$		0			0
$502$	3141.98	−	5442.08i	0.279350	−	0.483848i
$503$	−4242.88			−0.376104			−0.188052	−	0.982159i	$-0.560217\pi$
$503$	−4242.88			−0.376104			−0.188052	+	0.982159i	$0.560217\pi$
$504$		0			0
$505$	3411.21			0.300588
$506$	1235.21	−	2139.44i	0.108521	−	0.187964i
$507$		0			0
$508$	1446.12	+	2504.75i	0.126301	+	0.218760i
$509$	3682.80	+	6378.80i	0.320702	+	0.555472i	0.980633	−	0.195854i	$-0.0627479\pi$
$509$	3682.80	+	6378.80i	0.320702	+	0.555472i	−0.659931	+	0.751326i	$0.729415\pi$
$510$		0			0
$511$	5587.30	−	9677.49i	0.483694	−	0.837783i
$512$	20855.3			1.80016
$513$		0			0
$514$	−27248.5			−2.33829
$515$	3034.16	−	5255.32i	0.259614	−	0.449664i
$516$		0			0
$517$	1819.90	+	3152.16i	0.154815	+	0.268147i
$518$	9354.11	+	16201.8i	0.793429	+	1.37426i
$519$		0			0
$520$	9602.85	−	16632.6i	0.809832	−	1.40267i
$521$	8717.87			0.733084			0.366542	−	0.930401i	$-0.380542\pi$
$521$	8717.87			0.733084			0.366542	+	0.930401i	$0.380542\pi$
$522$		0			0
$523$	23515.4			1.96607			0.983037	−	0.183407i	$-0.0587127\pi$
$523$	23515.4			1.96607			0.983037	+	0.183407i	$0.0587127\pi$
$524$	11359.2	−	19674.7i	0.947004	−	1.64026i
$525$		0			0
$526$	−20105.4	−	34823.6i	−1.66661	−	2.88666i
$527$	4115.36	+	7128.00i	0.340166	+	0.589185i
$528$		0			0
$529$	3072.59	−	5321.88i	0.252535	−	0.437403i
$530$	−12770.5			−1.04663
$531$		0			0
$532$	−75997.0			−6.19340
$533$	−4600.69	+	7968.63i	−0.373880	+	0.647579i
$534$		0			0
$535$	3279.82	+	5680.81i	0.265045	+	0.459071i
$536$	−27463.8	−	47568.8i	−2.21317	−	3.83332i
$537$		0			0
$538$	1633.53	−	2829.36i	0.130905	−	0.226733i
$539$	−4545.24			−0.363224
$540$		0			0
$541$	3803.94			0.302300			0.151150	−	0.988511i	$-0.451702\pi$
$541$	3803.94			0.302300			0.151150	+	0.988511i	$0.451702\pi$
$542$	−3826.94	+	6628.45i	−0.303286	+	0.525307i
$543$		0			0
$544$	13232.6	+	22919.6i	1.04291	+	1.80638i
$545$	−736.951	−	1276.44i	−0.0579221	−	0.100324i
$546$		0			0
$547$	−8667.95	+	15013.3i	−0.677540	+	1.17353i	0.298179	+	0.954510i	$0.403621\pi$
$547$	−8667.95	+	15013.3i	−0.677540	+	1.17353i	−0.975719	+	0.219024i	$0.929713\pi$
$548$	22463.6			1.75109
$549$		0			0
$550$	795.878			0.0617025
$551$	−3728.57	+	6458.07i	−0.288280	+	0.499316i
$552$		0			0
$553$	9184.14	+	15907.4i	0.706238	+	1.22324i
$554$	−15433.3	−	26731.2i	−1.18357	−	2.05000i
$555$		0			0
$556$	−15379.9	+	26638.7i	−1.17311	+	2.03189i
$557$	−7797.62			−0.593170			−0.296585	−	0.955006i	$-0.595848\pi$
$557$	−7797.62			−0.593170			−0.296585	+	0.955006i	$0.595848\pi$
$558$		0			0
$559$	−21885.4			−1.65591
$560$	12942.6	−	22417.2i	0.976648	−	1.69160i
$561$		0			0
$562$	13797.5	+	23898.0i	1.03561	+	1.79373i
$563$	−5767.81	−	9990.14i	−0.431766	−	0.747840i	0.565260	−	0.824913i	$-0.308776\pi$
$563$	−5767.81	−	9990.14i	−0.431766	−	0.747840i	−0.997025	+	0.0770727i	$0.975443\pi$
$564$		0			0
$565$	−3962.81	+	6863.79i	−0.295074	+	0.511083i
$566$	5857.52			0.435000
$567$		0			0
$568$	−3616.90			−0.267186
$569$	−5038.86	+	8727.56i	−0.371248	+	0.643020i	−0.989758	−	0.142757i	$-0.954403\pi$
$569$	−5038.86	+	8727.56i	−0.371248	+	0.643020i	0.618510	+	0.785777i	$0.287737\pi$
$570$		0			0
$571$	8169.66	+	14150.3i	0.598756	+	1.03708i	0.993005	+	0.118072i	$0.0376714\pi$
$571$	8169.66	+	14150.3i	0.598756	+	1.03708i	−0.394249	+	0.919004i	$0.628995\pi$
$572$	−3800.66	−	6582.93i	−0.277821	−	0.481200i
$573$		0			0
$574$	−12334.7	+	21364.3i	−0.896932	+	1.55353i
$575$	−1940.01			−0.140703
$576$		0			0
$577$	18648.6			1.34550			0.672748	−	0.739871i	$-0.265114\pi$
$577$	18648.6			1.34550			0.672748	+	0.739871i	$0.265114\pi$
$578$	2652.32	−	4593.95i	0.190868	−	0.330593i
$579$		0			0
$580$	−3044.65	−	5273.50i	−0.217970	−	0.377535i
$581$	−1070.48	−	1854.12i	−0.0764387	−	0.132396i
$582$		0			0
$583$	−1484.40	+	2571.06i	−0.105451	+	0.182646i
$584$	20170.3			1.42920
$585$		0			0
$586$	−4923.24			−0.347060
$587$	−9048.54	+	15672.5i	−0.636241	+	1.10200i	0.350010	+	0.936746i	$0.386178\pi$
$587$	−9048.54	+	15672.5i	−0.636241	+	1.10200i	−0.986251	+	0.165255i	$0.947155\pi$
$588$		0			0
$589$	−6346.20	−	10991.9i	−0.443957	−	0.768956i
$590$	3177.00	+	5502.72i	0.221686	+	0.383972i
$591$		0			0
$592$	−8487.87	+	14701.4i	−0.589273	+	1.02065i
$593$	−27154.1			−1.88041			−0.940207	−	0.340602i	$-0.889369\pi$
$593$	−27154.1			−1.88041			−0.940207	+	0.340602i	$0.889369\pi$
$594$		0			0
$595$	−12709.4			−0.875688
$596$	5012.88	−	8682.57i	0.344523	−	0.596731i
$597$		0			0
$598$	13087.1	+	22667.5i	0.894934	+	1.55007i
$599$	1728.73	+	2994.25i	0.117920	+	0.204243i	0.918943	−	0.394390i	$-0.129044\pi$
$599$	1728.73	+	2994.25i	0.117920	+	0.204243i	−0.801023	+	0.598633i	$0.795711\pi$
$600$		0			0
$601$	1469.21	−	2544.75i	0.0997179	−	0.172717i	−0.811850	−	0.583866i	$-0.801539\pi$
$601$	1469.21	−	2544.75i	0.0997179	−	0.172717i	0.911568	+	0.411150i	$0.134873\pi$
$602$	−58675.9			−3.97251
$603$		0			0
$604$	10771.8			0.725656
$605$	−3234.99	+	5603.17i	−0.217390	+	0.376531i
$606$		0			0
$607$	3892.97	+	6742.82i	0.260314	+	0.450877i	0.966325	−	0.257323i	$-0.0828405\pi$
$607$	3892.97	+	6742.82i	0.260314	+	0.450877i	−0.706011	+	0.708201i	$0.749507\pi$
$608$	−20405.8	−	35343.8i	−1.36112	−	2.35753i
$609$		0			0
$610$	6533.05	−	11315.6i	0.433632	−	0.751073i
$611$	−38563.8			−2.55339
$612$		0			0
$613$	23893.4			1.57430			0.787151	−	0.616760i	$-0.211555\pi$
$613$	23893.4			1.57430			0.787151	+	0.616760i	$0.211555\pi$
$614$	5055.13	−	8755.74i	0.332261	−	0.575493i
$615$		0			0
$616$	−5985.21	−	10366.7i	−0.391479	−	0.678061i
$617$	−2440.23	−	4226.60i	−0.159222	−	0.275781i	0.775366	−	0.631512i	$-0.217565\pi$
$617$	−2440.23	−	4226.60i	−0.159222	−	0.275781i	−0.934588	+	0.355731i	$0.884232\pi$
$618$		0			0
$619$	−7941.77	+	13755.6i	−0.515681	+	0.893186i	0.484153	+	0.874983i	$0.339128\pi$
$619$	−7941.77	+	13755.6i	−0.515681	+	0.893186i	−0.999834	+	0.0182030i	$0.994205\pi$
$620$	10364.3			0.671354
$621$		0			0
$622$	−32960.6			−2.12476
$623$	15537.6	−	26911.9i	0.999200	−	1.73067i
$624$		0			0
$625$	−312.500	−	541.266i	−0.0200000	−	0.0346410i
$626$	−4759.24	−	8243.24i	−0.303862	−	0.526304i
$627$		0			0
$628$	−10217.8	+	17697.8i	−0.649261	+	1.12455i
$629$	8334.96			0.528357
$630$		0			0
$631$	−12862.4			−0.811479			−0.405740	−	0.913989i	$-0.632986\pi$
$631$	−12862.4			−0.811479			−0.405740	+	0.913989i	$0.632986\pi$
$632$	−16577.5	+	28713.1i	−1.04338	+	1.80719i
$633$		0			0
$634$	−8265.15	−	14315.7i	−0.517746	−	0.896763i
$635$	−372.939	−	645.949i	−0.0233065	−	0.0403680i
$636$		0			0
$637$	24078.5	−	41705.2i	1.49768	−	2.59407i
$638$	−1999.72			−0.124090
$639$		0			0
$640$	503.275			0.0310839
$641$	−14742.8	+	25535.3i	−0.908435	+	1.57346i	−0.0921970	+	0.995741i	$0.529389\pi$
$641$	−14742.8	+	25535.3i	−0.908435	+	1.57346i	−0.816238	+	0.577715i	$0.803944\pi$
$642$		0			0
$643$	7057.32	+	12223.6i	0.432836	+	0.749694i	0.997116	−	0.0758891i	$-0.0241795\pi$
$643$	7057.32	+	12223.6i	0.432836	+	0.749694i	−0.564280	+	0.825583i	$0.690846\pi$
$644$	24838.2	+	43021.1i	1.51982	+	2.63240i
$645$		0			0
$646$	−23914.7	+	41421.4i	−1.45652	+	2.52276i
$647$	13313.3			0.808962			0.404481	−	0.914546i	$-0.367452\pi$
$647$	13313.3			0.808962			0.404481	+	0.914546i	$0.367452\pi$
$648$		0			0
$649$	1477.14			0.0893418
$650$	−4216.18	+	7302.63i	−0.254419	+	0.440666i
$651$		0			0
$652$	6164.60	+	10677.4i	0.370283	+	0.641349i
$653$	5753.08	+	9964.62i	0.344771	+	0.597160i	0.985312	−	0.170763i	$-0.0546233\pi$
$653$	5753.08	+	9964.62i	0.344771	+	0.597160i	−0.640541	+	0.767924i	$0.721290\pi$
$654$		0			0
$655$	−2929.43	+	5073.92i	−0.174752	+	0.302679i
$656$	−22384.8			−1.33229
$657$		0			0
$658$	−103391.			−6.12556
$659$	−12885.8	+	22318.9i	−0.761699	+	1.31930i	0.180275	+	0.983616i	$0.442301\pi$
$659$	−12885.8	+	22318.9i	−0.761699	+	1.31930i	−0.941974	+	0.335686i	$0.891032\pi$
$660$		0			0
$661$	−3941.44	−	6826.77i	−0.231928	−	0.401710i	0.726448	−	0.687222i	$-0.241170\pi$
$661$	−3941.44	−	6826.77i	−0.231928	−	0.401710i	−0.958375	+	0.285511i	$0.907837\pi$
$662$	−2493.93	−	4319.62i	−0.146419	−	0.253605i
$663$		0			0
$664$	1932.23	−	3346.72i	0.112929	−	0.195599i
$665$	19598.9			1.14287
$666$		0			0
$667$	4874.46			0.282968
$668$	13233.5	−	22921.1i	0.766495	−	1.32761i
$669$		0			0
$670$	12058.1	+	20885.3i	0.695292	+	1.20428i
$671$	−1518.77	−	2630.58i	−0.0873790	−	0.151345i
$672$		0			0
$673$	9815.64	−	17001.2i	0.562207	−	0.973771i	−0.435097	−	0.900384i	$-0.643286\pi$
$673$	9815.64	−	17001.2i	0.562207	−	0.973771i	0.997304	−	0.0733871i	$-0.0233808\pi$
$674$	2977.23			0.170146
$675$		0			0
$676$	37940.5			2.15865
$677$	299.163	−	518.166i	0.0169834	−	0.0294161i	−0.857409	−	0.514636i	$-0.827927\pi$
$677$	299.163	−	518.166i	0.0169834	−	0.0294161i	0.874392	+	0.485220i	$0.161260\pi$
$678$		0			0
$679$	17205.2	+	29800.3i	0.972423	+	1.68429i
$680$	−11470.3	−	19867.2i	−0.646863	−	1.12040i
$681$		0			0
$682$	1701.81	−	2947.62i	0.0955507	−	0.165499i
$683$	19041.9			1.06679			0.533394	−	0.845867i	$-0.320916\pi$
$683$	19041.9			1.06679			0.533394	+	0.845867i	$0.320916\pi$
$684$		0			0
$685$	−5793.13			−0.323130
$686$	34921.2	−	60485.3i	1.94358	−	3.36638i
$687$		0			0
$688$	−26621.1	−	46109.1i	−1.47517	−	2.55508i
$689$	−15727.3	−	27240.5i	−0.869612	−	1.50621i
$690$		0			0
$691$	13585.4	−	23530.6i	0.747921	−	1.29544i	−0.200896	−	0.979613i	$-0.564385\pi$
$691$	13585.4	−	23530.6i	0.747921	−	1.29544i	0.948817	−	0.315825i	$-0.102281\pi$
$692$	−22004.1			−1.20877
$693$		0			0
$694$	44099.2			2.41208
$695$	3966.31	−	6869.85i	0.216476	−	0.374947i
$696$		0			0
$697$	5495.39	+	9518.29i	0.298641	+	0.517261i
$698$	18693.5	+	32378.0i	1.01369	+	1.75577i
$699$		0			0
$700$	−8001.96	+	13859.8i	−0.432065	+	0.748359i
$701$	27091.0			1.45965			0.729824	−	0.683635i	$-0.239602\pi$
$701$	27091.0			1.45965			0.729824	+	0.683635i	$0.239602\pi$
$702$		0			0
$703$	−12853.2			−0.689568
$704$	1656.87	−	2869.78i	0.0887012	−	0.153635i
$705$		0			0
$706$	−13870.2	−	24023.9i	−0.739395	−	1.28067i
$707$	11263.2	+	19508.4i	0.599144	+	1.03775i
$708$		0			0
$709$	2477.30	−	4290.81i	0.131223	−	0.227284i	−0.792925	−	0.609319i	$-0.791443\pi$
$709$	2477.30	−	4290.81i	0.131223	−	0.227284i	0.924148	+	0.382034i	$0.124776\pi$
$710$	1588.02			0.0839398
$711$		0			0
$712$	56091.3			2.95240
$713$	−4148.28	+	7185.03i	−0.217888	+	0.377393i
$714$		0			0
$715$	980.152	+	1697.67i	0.0512666	+	0.0887963i
$716$	17578.6	+	30447.0i	0.917516	+	1.58918i
$717$		0			0
$718$	24953.6	−	43220.9i	1.29702	−	2.24650i
$719$	23414.3			1.21447			0.607235	−	0.794522i	$-0.292279\pi$
$719$	23414.3			1.21447			0.607235	+	0.794522i	$0.292279\pi$
$720$		0			0
$721$	40072.8			2.06989
$722$	18930.4	−	32788.5i	0.975787	−	1.69011i
$723$		0			0
$724$	−22629.5	−	39195.5i	−1.16163	−	2.01200i
$725$	785.186	+	1359.98i	0.0402222	+	0.0696669i
$726$		0			0
$727$	−15477.8	+	26808.4i	−0.789603	+	1.36763i	0.136607	+	0.990625i	$0.456380\pi$
$727$	−15477.8	+	26808.4i	−0.789603	+	1.36763i	−0.926210	+	0.377007i	$0.876953\pi$
$728$	126827.			6.45676
$729$		0			0
$730$	−8855.88			−0.449001
$731$	−13070.8	+	22639.2i	−0.661340	+	1.14547i
$732$		0			0
$733$	−7786.36	−	13486.4i	−0.392354	−	0.679578i	0.600405	−	0.799696i	$-0.295006\pi$
$733$	−7786.36	−	13486.4i	−0.392354	−	0.679578i	−0.992760	+	0.120118i	$0.961673\pi$
$734$	−1910.72	−	3309.47i	−0.0960846	−	0.166423i
$735$		0			0
$736$	−13338.5	+	23103.0i	−0.668021	+	1.15705i
$737$	5606.40			0.280210
$738$		0			0
$739$	−30909.9			−1.53862			−0.769310	−	0.638876i	$-0.779400\pi$
$739$	−30909.9			−1.53862			−0.769310	+	0.638876i	$0.779400\pi$
$740$	5247.78	−	9089.42i	0.260692	−	0.451532i
$741$		0			0
$742$	−42165.7	−	73033.1i	−2.08619	−	3.61338i
$743$	17511.6	+	30331.0i	0.864656	+	1.49763i	0.867389	+	0.497631i	$0.165797\pi$
$743$	17511.6	+	30331.0i	0.864656	+	1.49763i	−0.00273301	+	0.999996i	$0.500870\pi$
$744$		0			0
$745$	−1292.77	+	2239.15i	−0.0635752	+	0.110115i
$746$	−67347.8			−3.30533
$747$		0			0
$748$	−9079.55			−0.443825
$749$	−21658.6	+	37513.8i	−1.05659	+	1.83007i
$750$		0			0
$751$	1805.39	+	3127.03i	0.0877226	+	0.151940i	0.906548	−	0.422102i	$-0.138708\pi$
$751$	1805.39	+	3127.03i	0.0877226	+	0.151940i	−0.818826	+	0.574043i	$0.805374\pi$
$752$	−46908.4	−	81247.7i	−2.27470	−	3.93989i
$753$		0			0
$754$	10593.5	−	18348.6i	0.511664	−	0.886227i
$755$	−2777.93			−0.133906
$756$		0			0
$757$	−19982.2			−0.959399			−0.479700	−	0.877433i	$-0.659254\pi$
$757$	−19982.2			−0.959399			−0.479700	+	0.877433i	$0.659254\pi$
$758$	−10469.0	+	18132.9i	−0.501652	+	0.868887i
$759$		0			0
$760$	17688.1	+	30636.8i	0.844232	+	1.46225i
$761$	17578.7	+	30447.1i	0.837354	+	1.45034i	0.892100	+	0.451839i	$0.149232\pi$
$761$	17578.7	+	30447.1i	0.837354	+	1.45034i	−0.0547461	+	0.998500i	$0.517435\pi$
$762$		0			0
$763$	4866.54	−	8429.09i	0.230905	−	0.399939i
$764$	−8582.02			−0.406396
$765$		0			0
$766$	−341.843			−0.0161244
$767$	−7825.17	+	13553.6i	−0.368384	+	0.638060i
$768$		0			0
$769$	19520.6	+	33810.6i	0.915384	+	1.58549i	0.806339	+	0.591454i	$0.201446\pi$
$769$	19520.6	+	33810.6i	0.915384	+	1.58549i	0.109045	+	0.994037i	$0.465221\pi$
$770$	2627.83	+	4551.54i	0.122988	+	0.213021i
$771$		0			0
$772$	35892.6	−	62167.8i	1.67332	−	2.89828i
$773$	18244.4			0.848907			0.424453	−	0.905450i	$-0.360466\pi$
$773$	18244.4			0.848907			0.424453	+	0.905450i	$0.360466\pi$
$774$		0			0
$775$	−2672.85			−0.123886
$776$	−31055.7	+	53790.0i	−1.43664	+	2.48834i
$777$		0			0
$778$	−15490.2	−	26829.7i	−0.713816	−	1.23637i
$779$	−8474.32	−	14677.9i	−0.389761	−	0.675086i
$780$		0			0
$781$	184.586	−	319.713i	0.00845713	−	0.0146482i
$782$	31264.3			1.42968
$783$		0			0
$784$	117155.			5.33686
$785$	2635.08	−	4564.09i	0.119809	−	0.207515i
$786$		0			0
$787$	−21444.1	−	37142.2i	−0.971282	−	1.68231i	−0.691695	−	0.722190i	$-0.743136\pi$
$787$	−21444.1	−	37142.2i	−0.971282	−	1.68231i	−0.279587	−	0.960120i	$-0.590198\pi$
$788$	43544.9	+	75422.0i	1.96856	+	3.40964i
$789$		0			0
$790$	7278.44	−	12606.6i	0.327791	−	0.567751i
$791$	−52337.7			−2.35261
$792$		0			0
$793$	32182.7			1.44116
$794$	−26765.1	+	46358.6i	−1.19630	+	2.07205i
$795$		0			0
$796$	28443.1	+	49264.9i	1.26651	+	2.19365i
$797$	−5736.57	−	9936.03i	−0.254956	−	0.441596i	0.709928	−	0.704274i	$-0.248728\pi$
$797$	−5736.57	−	9936.03i	−0.254956	−	0.441596i	−0.964883	+	0.262678i	$0.915394\pi$
$798$		0			0
$799$	−23031.7	+	39892.0i	−1.01978	+	1.76631i
$800$	−8594.35			−0.379820
$801$		0			0
$802$	64083.2			2.82152
$803$	−1029.38	+	1782.94i	−0.0452380	+	0.0783545i
$804$		0			0
$805$	−6405.53	−	11094.7i	−0.280454	−	0.485760i
$806$	18030.7	+	31230.1i	0.787971	+	1.36481i
$807$		0			0
$808$	−20330.2	+	35212.9i	−0.885165	+	1.53315i
$809$	−6454.45			−0.280502			−0.140251	−	0.990116i	$-0.544791\pi$
$809$	−6454.45			−0.280502			−0.140251	+	0.990116i	$0.544791\pi$
$810$		0			0
$811$	−11250.0			−0.487102			−0.243551	−	0.969888i	$-0.578312\pi$
$811$	−11250.0			−0.487102			−0.243551	+	0.969888i	$0.578312\pi$
$812$	20105.7	−	34824.1i	0.868931	−	1.50503i
$813$		0			0
$814$	−1723.36	−	2984.95i	−0.0742062	−	0.128529i
$815$	−1589.79	−	2753.60i	−0.0683288	−	0.118349i
$816$		0			0
$817$	20156.1	−	34911.4i	0.863125	−	1.49498i
$818$	−51459.4			−2.19955
$819$		0			0
$820$	13839.8			0.589399
$821$	266.219	−	461.105i	0.0113168	−	0.0196013i	−0.860312	−	0.509769i	$-0.829731\pi$
$821$	266.219	−	461.105i	0.0113168	−	0.0196013i	0.871628	+	0.490167i	$0.163064\pi$
$822$		0			0
$823$	16508.3	+	28593.3i	0.699204	+	1.21106i	0.968743	+	0.248067i	$0.0797953\pi$
$823$	16508.3	+	28593.3i	0.699204	+	1.21106i	−0.269539	+	0.962989i	$0.586871\pi$
$824$	36166.0	+	62641.4i	1.52901	+	2.64832i
$825$		0			0
$826$	−20979.7	+	36337.8i	−0.883748	+	1.53070i
$827$	−36231.3			−1.52344			−0.761720	−	0.647906i	$-0.775645\pi$
$827$	−36231.3			−1.52344			−0.761720	+	0.647906i	$0.775645\pi$
$828$		0			0
$829$	36588.3			1.53289			0.766445	−	0.642310i	$-0.222024\pi$
$829$	36588.3			1.53289			0.766445	+	0.642310i	$0.222024\pi$
$830$	−848.354	+	1469.39i	−0.0354781	+	0.0614498i
$831$		0			0
$832$	17554.6	+	30405.4i	0.731485	+	1.26697i
$833$	−28761.1	−	49815.6i	−1.19629	−	2.07204i
$834$		0			0
$835$	−3412.78	+	5911.12i	−0.141442	+	0.244985i
$836$	14001.4			0.579243
$837$		0			0
$838$	64449.7			2.65677
$839$	−7663.38	+	13273.4i	−0.315339	+	0.546183i	−0.979509	−	0.201398i	$-0.935451\pi$
$839$	−7663.38	+	13273.4i	−0.315339	+	0.546183i	0.664171	+	0.747581i	$0.268785\pi$
$840$		0			0
$841$	10221.6	+	17704.4i	0.419109	+	0.725918i
$842$	−11299.9	−	19572.1i	−0.462496	−	0.801066i
$843$		0			0
$844$	6533.21	−	11315.8i	0.266448	−	0.461502i
$845$	−9784.48			−0.398339
$846$		0			0
$847$	−42725.2			−1.73324
$848$	38260.9	−	66269.9i	1.54939	−	2.68363i
$849$		0			0
$850$	5036.10	+	8722.78i	0.203220	+	0.351987i
$851$	4200.82	+	7276.04i	0.169215	+	0.293090i
$852$		0			0
$853$	−2286.65	+	3960.59i	−0.0917859	+	0.158978i	−0.908263	−	0.418400i	$-0.862591\pi$
$853$	−2286.65	+	3960.59i	−0.0917859	+	0.158978i	0.816477	+	0.577378i	$0.195924\pi$
$854$	86283.4			3.45733
$855$		0			0
$856$	−78188.3			−3.12199
$857$	−9784.58	+	16947.4i	−0.390006	+	0.675509i	−0.992450	−	0.122652i	$-0.960860\pi$
$857$	−9784.58	+	16947.4i	−0.390006	+	0.675509i	0.602444	+	0.798161i	$0.294194\pi$
$858$		0			0
$859$	−10948.5	−	18963.3i	−0.434875	−	0.753226i	0.562410	−	0.826858i	$-0.309874\pi$
$859$	−10948.5	−	18963.3i	−0.434875	−	0.753226i	−0.997285	+	0.0736324i	$0.976541\pi$
$860$	16459.0	+	28507.8i	0.652612	+	1.13036i
$861$		0			0
$862$	−13777.9	+	23863.9i	−0.544403	+	0.942934i
$863$	13335.5			0.526008			0.263004	−	0.964795i	$-0.415287\pi$
$863$	13335.5			0.526008			0.263004	+	0.964795i	$0.415287\pi$
$864$		0			0
$865$	5674.65			0.223057
$866$	15320.9	−	26536.5i	0.601183	−	1.04128i
$867$		0			0
$868$	34220.8	+	59272.2i	1.33817	+	2.31778i
$869$	−1692.05	−	2930.71i	−0.0660516	−	0.114405i
$870$		0			0
$871$	−29700.0	+	51441.9i	−1.15539	+	2.00120i
$872$	17568.4			0.682270
$873$		0			0
$874$	−48211.9			−1.86590
$875$	2063.63	−	3574.31i	0.0797295	−	0.138096i
$876$		0			0
$877$	10905.9	+	18889.5i	0.419915	+	0.727314i	0.995931	−	0.0901245i	$-0.0287265\pi$
$877$	10905.9	+	18889.5i	0.419915	+	0.727314i	−0.576015	+	0.817439i	$0.695393\pi$
$878$	10526.1	+	18231.8i	0.404600	+	0.700788i
$879$		0			0
$880$	−2384.48	+	4130.05i	−0.0913419	+	0.158209i
$881$	3646.54			0.139450			0.0697248	−	0.997566i	$-0.477788\pi$
$881$	3646.54			0.139450			0.0697248	+	0.997566i	$0.477788\pi$
$882$		0			0
$883$	9019.80			0.343760			0.171880	−	0.985118i	$-0.445016\pi$
$883$	9019.80			0.343760			0.171880	+	0.985118i	$0.445016\pi$
$884$	48099.1	−	83310.0i	1.83003	−	3.16970i
$885$		0			0
$886$	−19630.9	−	34001.8i	−0.744373	−	1.28929i
$887$	9865.97	+	17088.4i	0.373469	+	0.646867i	0.990097	−	0.140388i	$-0.0448350\pi$
$887$	9865.97	+	17088.4i	0.373469	+	0.646867i	−0.616628	+	0.787255i	$0.711502\pi$
$888$		0			0
$889$	2462.74	−	4265.60i	0.0929108	−	0.160926i
$890$	−24627.2			−0.927533
$891$		0			0
$892$	3461.09			0.129917
$893$	35516.6	−	61516.6i	1.33093	−	2.30523i
$894$		0			0
$895$	−4533.34	−	7851.97i	−0.169310	−	0.293254i
$896$	1661.72	+	2878.18i	0.0619576	+	0.107314i
$897$		0			0
$898$	48602.7	−	84182.3i	1.80612	−	3.12829i
$899$	6715.78			0.249148
$900$		0			0
$901$	−37571.6			−1.38923
$902$	2272.49	−	3936.06i	0.0838864	−	0.145296i
$903$		0			0
$904$	−47235.2	−	81813.7i	−1.73785	−	3.01005i
$905$	5835.94	+	10108.1i	0.214357	+	0.371277i
$906$		0			0
$907$	−3853.07	+	6673.71i	−0.141057	+	0.244319i	−0.927895	−	0.372841i	$-0.878384\pi$
$907$	−3853.07	+	6673.71i	−0.141057	+	0.244319i	0.786838	+	0.617160i	$0.211717\pi$
$908$	−97950.7			−3.57997
$909$		0			0
$910$	−55684.0			−2.02847
$911$	12382.6	−	21447.2i	0.450332	−	0.779998i	−0.548074	−	0.836430i	$-0.684639\pi$
$911$	12382.6	−	21447.2i	0.450332	−	0.779998i	0.998406	+	0.0564313i	$0.0179722\pi$
$912$		0			0
$913$	197.220	+	341.596i	0.00714901	+	0.0123824i
$914$	37014.4	+	64110.8i	1.33953	+	2.32013i
$915$		0			0
$916$	−12689.2	+	21978.4i	−0.457711	+	0.792779i
$917$	−38689.6			−1.39329
$918$		0			0
$919$	−4899.44			−0.175862			−0.0879312	−	0.996127i	$-0.528026\pi$
$919$	−4899.44			−0.175862			−0.0879312	+	0.996127i	$0.528026\pi$
$920$	11562.1	−	20026.1i	0.414338	−	0.717654i
$921$		0			0
$922$	12849.9	+	22256.6i	0.458989	+	0.794993i
$923$	1955.70	+	3387.37i	0.0697428	+	0.120798i
$924$		0			0
$925$	−1353.35	+	2344.07i	−0.0481058	+	0.0833217i
$926$	−48437.1			−1.71894
$927$		0			0
$928$	21594.1			0.763860
$929$	6678.09	−	11566.8i	0.235846	−	0.408498i	−0.723672	−	0.690144i	$-0.757547\pi$
$929$	6678.09	−	11566.8i	0.235846	−	0.408498i	0.959518	+	0.281646i	$0.0908805\pi$
$930$		0			0
$931$	44351.8	+	76819.6i	1.56130	+	2.70425i
$932$	−63896.4	−	110672.i	−2.24570	−	3.88967i
$933$		0			0
$934$	7392.40	−	12804.0i	0.258979	−	0.448565i
$935$	2341.53			0.0818996
$936$		0			0
$937$	4960.13			0.172935			0.0864677	−	0.996255i	$-0.472442\pi$
$937$	4960.13			0.172935			0.0864677	+	0.996255i	$0.472442\pi$
$938$	−79627.1	+	137918.i	−2.77177	+	4.80084i
$939$		0			0
$940$	29002.0	+	50232.9i	1.00632	+	1.74300i
$941$	27787.2	+	48128.8i	0.962631	+	1.66733i	0.715850	+	0.698254i	$0.246039\pi$
$941$	27787.2	+	48128.8i	0.962631	+	1.66733i	0.246781	+	0.969071i	$0.420627\pi$
$942$		0			0
$943$	−5539.35	+	9594.44i	−0.191290	+	0.331323i
$944$	−38073.7			−1.31270
$945$		0			0
$946$	10810.2			0.371533
$947$	−10472.8	+	18139.4i	−0.359366	+	0.622440i	−0.987855	−	0.155378i	$-0.950340\pi$
$947$	−10472.8	+	18139.4i	−0.359366	+	0.622440i	0.628489	+	0.777818i	$0.283674\pi$
$948$		0			0
$949$	−10906.3	−	18890.3i	−0.373061	−	0.646160i
$950$	−7766.06	−	13451.2i	−0.265226	−	0.459384i
$951$		0			0
$952$	75745.6	−	131195.i	2.57871	−	4.46645i
$953$	26967.8			0.916656			0.458328	−	0.888783i	$-0.348449\pi$
$953$	26967.8			0.916656			0.458328	+	0.888783i	$0.348449\pi$
$954$		0			0
$955$	2213.22			0.0749927
$956$	15360.3	−	26604.8i	0.519651	−	0.900062i
$957$		0			0
$958$	−24004.1	−	41576.3i	−0.809537	−	1.40216i
$959$	−19127.8	−	33130.3i	−0.644075	−	1.11557i
$960$		0			0
$961$	9180.22	−	15900.6i	0.308154	−	0.533738i
$962$	36518.2			1.22390
$963$		0			0
$964$	−32464.8			−1.08467
$965$	−9256.35	+	16032.5i	−0.308780	+	0.534822i
$966$		0			0
$967$	9253.25	+	16027.1i	0.307719	+	0.532985i	0.977863	−	0.209246i	$-0.0671009\pi$
$967$	9253.25	+	16027.1i	0.307719	+	0.532985i	−0.670144	+	0.742231i	$0.733768\pi$
$968$	−38559.8	−	66787.6i	−1.28033	−	2.21760i
$969$		0			0
$970$	13635.1	−	23616.7i	0.451338	−	0.781740i
$971$	56274.4			1.85987			0.929934	−	0.367726i	$-0.119864\pi$
$971$	56274.4			1.85987			0.929934	+	0.367726i	$0.119864\pi$
$972$		0			0
$973$	52383.9			1.72595
$974$	35753.6	−	61927.0i	1.17620	−	2.03724i
$975$		0			0
$976$	39146.6	+	67803.9i	1.28386	+	2.22372i
$977$	11582.8	+	20062.1i	0.379292	+	0.656952i	0.990959	−	0.134162i	$-0.0428344\pi$
$977$	11582.8	+	20062.1i	0.379292	+	0.656952i	−0.611668	+	0.791115i	$0.709501\pi$
$978$		0			0
$979$	−2862.59	+	4958.15i	−0.0934512	+	0.161862i
$980$	−72433.1			−2.36101
$981$		0			0
$982$	−30616.8			−0.994931
$983$	1643.43	−	2846.50i	0.0533237	−	0.0923594i	−0.838131	−	0.545468i	$-0.816352\pi$
$983$	1643.43	−	2846.50i	0.0533237	−	0.0923594i	0.891455	+	0.453109i	$0.149685\pi$
$984$		0			0
$985$	−11229.8	−	19450.6i	−0.363260	−	0.629185i
$986$	−12653.7	−	21916.8i	−0.408697	−	0.707885i
$987$		0			0
$988$	−74172.5	+	128471.i	−2.38840	+	4.13683i
$989$	−26350.6			−0.847221
$990$		0			0
$991$	35155.7			1.12690			0.563450	−	0.826150i	$-0.309474\pi$
$991$	35155.7			1.12690			0.563450	+	0.826150i	$0.309474\pi$
$992$	−18377.1	+	31830.1i	−0.588179	+	1.01876i
$993$		0			0
$994$	5243.32	+	9081.70i	0.167312	+	0.289793i
$995$	−7335.19	−	12704.9i	−0.233710	−	0.404797i
$996$		0			0
$997$	6820.73	−	11813.9i	0.216665	−	0.375274i	−0.737122	−	0.675760i	$-0.763816\pi$
$997$	6820.73	−	11813.9i	0.216665	−	0.375274i	0.953786	+	0.300486i	$0.0971488\pi$
$998$	−20111.7			−0.637900
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	405.4.e.x.136.6		12
3.2	odd	2		405.4.e.w.136.1		12
9.2	odd	6		405.4.a.l.1.6	yes	6
9.4	even	3	inner	405.4.e.x.271.6		12
9.5	odd	6		405.4.e.w.271.1		12
9.7	even	3		405.4.a.k.1.1	✓	6
45.29	odd	6		2025.4.a.y.1.1		6
45.34	even	6		2025.4.a.z.1.6		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
405.4.a.k.1.1	✓	6	9.7	even	3
405.4.a.l.1.6	yes	6	9.2	odd	6
405.4.e.w.136.1		12	3.2	odd	2
405.4.e.w.271.1		12	9.5	odd	6
405.4.e.x.136.6		12	1.1	even	1	trivial
405.4.e.x.271.6		12	9.4	even	3	inner
2025.4.a.y.1.1		6	45.29	odd	6
2025.4.a.z.1.6		6	45.34	even	6

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:	\( N \)	\(=\)	\( 405 = 3^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	405.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(2.61668 - 4.53223i) q^{2} +(-9.69405 - 16.7906i) q^{4} +(2.50000 + 4.33013i) q^{5} +(-16.5090 + 28.5945i) q^{7} -59.5981 q^{8} +O(q^{10})\)	\(q+(2.61668 - 4.53223i) q^{2} +(-9.69405 - 16.7906i) q^{4} +(2.50000 + 4.33013i) q^{5} +(-16.5090 + 28.5945i) q^{7} -59.5981 q^{8} +26.1668 q^{10} +(3.04155 - 5.26813i) q^{11} +(32.2254 + 55.8160i) q^{13} +(86.3977 + 149.645i) q^{14} +(-78.3969 + 135.787i) q^{16} +76.9845 q^{17} -118.716 q^{19} +(48.4703 - 83.9529i) q^{20} +(-15.9176 - 27.5700i) q^{22} +(38.8002 + 67.2039i) q^{23} +(-12.5000 + 21.6506i) q^{25} +337.294 q^{26} +640.157 q^{28} +(31.4075 - 54.3993i) q^{29} +(53.4569 + 92.5901i) q^{31} +(171.887 + 297.717i) q^{32} +(201.444 - 348.911i) q^{34} -165.090 q^{35} +108.268 q^{37} +(-310.642 + 538.048i) q^{38} +(-148.995 - 258.067i) q^{40} +(71.3830 + 123.639i) q^{41} +(-169.784 + 294.075i) q^{43} -117.940 q^{44} +406.111 q^{46} +(-299.173 + 518.182i) q^{47} +(-373.595 - 647.086i) q^{49} +(65.4171 + 113.306i) q^{50} +(624.789 - 1082.17i) q^{52} -488.041 q^{53} +30.4155 q^{55} +(983.906 - 1704.18i) q^{56} +(-164.367 - 284.691i) q^{58} +(121.413 + 210.294i) q^{59} +(249.669 - 432.440i) q^{61} +559.519 q^{62} +544.744 q^{64} +(-161.127 + 279.080i) q^{65} +(460.817 + 798.159i) q^{67} +(-746.292 - 1292.62i) q^{68} +(-431.989 + 748.226i) q^{70} +60.6882 q^{71} -338.439 q^{73} +(283.303 - 490.695i) q^{74} +(1150.84 + 1993.31i) q^{76} +(100.426 + 173.943i) q^{77} +(278.155 - 481.779i) q^{79} -783.969 q^{80} +747.147 q^{82} +(-32.4210 + 56.1548i) q^{83} +(192.461 + 333.353i) q^{85} +(888.542 + 1539.00i) q^{86} +(-181.271 + 313.970i) q^{88} -941.159 q^{89} -2128.04 q^{91} +(752.262 - 1302.96i) q^{92} +(1565.68 + 2711.84i) q^{94} +(-296.790 - 514.056i) q^{95} +(521.085 - 902.546i) q^{97} -3910.32 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 4 q^{2} - 34 q^{4} + 30 q^{5} - 40 q^{7} - 132 q^{8}+O(q^{10}) \) 12 * q + 4 * q^2 - 34 * q^4 + 30 * q^5 - 40 * q^7 - 132 * q^8	\( 12 q + 4 q^{2} - 34 q^{4} + 30 q^{5} - 40 q^{7} - 132 q^{8} + 40 q^{10} + 88 q^{11} - 20 q^{13} + 180 q^{14} - 58 q^{16} - 248 q^{17} - 92 q^{19} + 170 q^{20} + 74 q^{22} + 210 q^{23} - 150 q^{25} - 8 q^{26} + 704 q^{28} + 296 q^{29} + 104 q^{31} + 722 q^{32} + 428 q^{34} - 400 q^{35} - 408 q^{37} - 20 q^{38} - 330 q^{40} + 344 q^{41} - 512 q^{43} - 1432 q^{44} - 372 q^{46} + 238 q^{47} - 68 q^{49} + 100 q^{50} + 468 q^{52} - 1700 q^{53} + 880 q^{55} + 2316 q^{56} - 890 q^{58} + 1840 q^{59} + 364 q^{61} - 2076 q^{62} - 1980 q^{64} + 100 q^{65} - 88 q^{67} + 236 q^{68} - 900 q^{70} - 2728 q^{71} + 1672 q^{73} + 1316 q^{74} + 2106 q^{76} + 840 q^{77} + 680 q^{79} - 580 q^{80} + 3484 q^{82} + 2148 q^{83} - 620 q^{85} + 2872 q^{86} - 1296 q^{88} - 6000 q^{89} - 6116 q^{91} + 1002 q^{92} + 3662 q^{94} - 230 q^{95} + 612 q^{97} - 3964 q^{98}+O(q^{100}) \) 12 * q + 4 * q^2 - 34 * q^4 + 30 * q^5 - 40 * q^7 - 132 * q^8 + 40 * q^10 + 88 * q^11 - 20 * q^13 + 180 * q^14 - 58 * q^16 - 248 * q^17 - 92 * q^19 + 170 * q^20 + 74 * q^22 + 210 * q^23 - 150 * q^25 - 8 * q^26 + 704 * q^28 + 296 * q^29 + 104 * q^31 + 722 * q^32 + 428 * q^34 - 400 * q^35 - 408 * q^37 - 20 * q^38 - 330 * q^40 + 344 * q^41 - 512 * q^43 - 1432 * q^44 - 372 * q^46 + 238 * q^47 - 68 * q^49 + 100 * q^50 + 468 * q^52 - 1700 * q^53 + 880 * q^55 + 2316 * q^56 - 890 * q^58 + 1840 * q^59 + 364 * q^61 - 2076 * q^62 - 1980 * q^64 + 100 * q^65 - 88 * q^67 + 236 * q^68 - 900 * q^70 - 2728 * q^71 + 1672 * q^73 + 1316 * q^74 + 2106 * q^76 + 840 * q^77 + 680 * q^79 - 580 * q^80 + 3484 * q^82 + 2148 * q^83 - 620 * q^85 + 2872 * q^86 - 1296 * q^88 - 6000 * q^89 - 6116 * q^91 + 1002 * q^92 + 3662 * q^94 - 230 * q^95 + 612 * q^97 - 3964 * q^98

Introduction

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