LMFDB - Embedded newform 405.4.e.x.136.5

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			136.5
Root			$-1.16241 - 1.16241i$ of defining polynomial
Character	$\chi$	$=$	405.136
Dual form			405.4.e.x.271.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.26722 - 3.92694i) q^{2} +(-6.28058 - 10.8783i) q^{4} +(2.50000 + 4.33013i) q^{5} +(1.31809 - 2.28300i) q^{7} -20.6823 q^{8} +O(q^{10})$	\(q+(2.26722 - 3.92694i) q^{2} +(-6.28058 - 10.8783i) q^{4} +(2.50000 + 4.33013i) q^{5} +(1.31809 - 2.28300i) q^{7} -20.6823 q^{8} +22.6722 q^{10} +(10.4655 - 18.1268i) q^{11} +(-30.4725 - 52.7800i) q^{13} +(-5.97680 - 10.3521i) q^{14} +(3.35333 - 5.80814i) q^{16} -86.8178 q^{17} +41.8063 q^{19} +(31.4029 - 54.3914i) q^{20} +(-47.4552 - 82.1949i) q^{22} +(-48.6593 - 84.2804i) q^{23} +(-12.5000 + 21.6506i) q^{25} -276.352 q^{26} -33.1135 q^{28} +(78.5350 - 136.027i) q^{29} +(-47.6980 - 82.6154i) q^{31} +(-97.9346 - 169.628i) q^{32} +(-196.835 + 340.928i) q^{34} +13.1809 q^{35} -160.833 q^{37} +(94.7841 - 164.171i) q^{38} +(-51.7057 - 89.5569i) q^{40} +(-116.595 - 201.948i) q^{41} +(-243.847 + 422.355i) q^{43} -262.918 q^{44} -441.285 q^{46} +(-12.1540 + 21.0513i) q^{47} +(168.025 + 291.028i) q^{49} +(56.6805 + 98.1735i) q^{50} +(-382.770 + 662.977i) q^{52} +709.828 q^{53} +104.655 q^{55} +(-27.2611 + 47.2176i) q^{56} +(-356.112 - 616.805i) q^{58} +(95.9990 + 166.275i) q^{59} +(372.317 - 644.871i) q^{61} -432.568 q^{62} -834.504 q^{64} +(152.363 - 263.900i) q^{65} +(411.783 + 713.230i) q^{67} +(545.266 + 944.428i) q^{68} +(29.8840 - 51.7606i) q^{70} -1068.85 q^{71} -132.416 q^{73} +(-364.645 + 631.583i) q^{74} +(-262.568 - 454.780i) q^{76} +(-27.5890 - 47.7855i) q^{77} +(352.288 - 610.181i) q^{79} +33.5333 q^{80} -1057.38 q^{82} +(709.881 - 1229.55i) q^{83} +(-217.044 - 375.932i) q^{85} +(1105.71 + 1915.14i) q^{86} +(-216.451 + 374.903i) q^{88} +401.847 q^{89} -160.662 q^{91} +(-611.217 + 1058.66i) q^{92} +(55.1114 + 95.4558i) q^{94} +(104.516 + 181.027i) q^{95} +(-265.440 + 459.756i) q^{97} +1523.80 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	2.26722	−	3.92694i	0.801583	−	1.38838i	−0.116990	−	0.993133i	$-0.537325\pi$
$2$	2.26722	−	3.92694i	0.801583	−	1.38838i	0.918574	−	0.395250i	$-0.129342\pi$
$3$		0			0
$3$		0			0
$4$	−6.28058	−	10.8783i	−0.785072	−	1.35978i
$5$	2.50000	+	4.33013i	0.223607	+	0.387298i
$5$	2.50000	+	4.33013i	0.223607	+	0.387298i
$6$		0			0
$7$	1.31809	−	2.28300i	0.0711702	−	0.123270i	−0.828244	−	0.560367i	$-0.810660\pi$
$7$	1.31809	−	2.28300i	0.0711702	−	0.123270i	0.899414	+	0.437097i	$0.143993\pi$
$8$	−20.6823			−0.914036
$9$		0			0
$10$	22.6722			0.716958
$11$	10.4655	−	18.1268i	0.286861	−	0.496858i	−0.686198	−	0.727415i	$-0.740722\pi$
$11$	10.4655	−	18.1268i	0.286861	−	0.496858i	0.973059	+	0.230557i	$0.0740549\pi$
$12$		0			0
$13$	−30.4725	−	52.7800i	−0.650120	−	1.12604i	−0.983093	−	0.183105i	$-0.941385\pi$
$13$	−30.4725	−	52.7800i	−0.650120	−	1.12604i	0.332974	−	0.942936i	$-0.391948\pi$
$14$	−5.97680	−	10.3521i	−0.114098	−	0.197623i
$15$		0			0
$16$	3.35333	−	5.80814i	0.0523958	−	0.0907522i
$17$	−86.8178			−1.23861			−0.619306	−	0.785150i	$-0.712586\pi$
$17$	−86.8178			−1.23861			−0.619306	+	0.785150i	$0.712586\pi$
$18$		0			0
$19$	41.8063			0.504791			0.252395	−	0.967624i	$-0.418782\pi$
$19$	41.8063			0.504791			0.252395	+	0.967624i	$0.418782\pi$
$20$	31.4029	−	54.3914i	0.351095	−	0.608114i
$21$		0			0
$22$	−47.4552	−	82.1949i	−0.459886	−	0.796546i
$23$	−48.6593	−	84.2804i	−0.441138	−	0.764073i	0.556637	−	0.830756i	$-0.312092\pi$
$23$	−48.6593	−	84.2804i	−0.441138	−	0.764073i	−0.997774	+	0.0666833i	$0.978758\pi$
$24$		0			0
$25$	−12.5000	+	21.6506i	−0.100000	+	0.173205i
$26$	−276.352			−2.08450
$27$		0			0
$28$	−33.1135			−0.223495
$29$	78.5350	−	136.027i	0.502882	−	0.871018i	−0.497112	−	0.867686i	$-0.665606\pi$
$29$	78.5350	−	136.027i	0.502882	−	0.871018i	0.999994	−	0.00333147i	$-0.00106044\pi$
$30$		0			0
$31$	−47.6980	−	82.6154i	−0.276349	−	0.478651i	0.694126	−	0.719854i	$-0.255791\pi$
$31$	−47.6980	−	82.6154i	−0.276349	−	0.478651i	−0.970475	+	0.241203i	$0.922458\pi$
$32$	−97.9346	−	169.628i	−0.541017	−	0.937069i
$33$		0			0
$34$	−196.835	+	340.928i	−0.992851	+	1.71967i
$35$	13.1809			0.0636566
$36$		0			0
$37$	−160.833			−0.714617			−0.357309	−	0.933986i	$-0.616306\pi$
$37$	−160.833			−0.714617			−0.357309	+	0.933986i	$0.616306\pi$
$38$	94.7841	−	164.171i	0.404632	−	0.700843i
$39$		0			0
$40$	−51.7057	−	89.5569i	−0.204385	−	0.354005i
$41$	−116.595	−	201.948i	−0.444123	−	0.769243i	0.553868	−	0.832604i	$-0.313151\pi$
$41$	−116.595	−	201.948i	−0.444123	−	0.769243i	−0.997991	+	0.0633617i	$0.979818\pi$
$42$		0			0
$43$	−243.847	+	422.355i	−0.864798	+	1.49787i	0.00245045	+	0.999997i	$0.499220\pi$
$43$	−243.847	+	422.355i	−0.864798	+	1.49787i	−0.867248	+	0.497876i	$0.834113\pi$
$44$	−262.918			−0.900826
$45$		0			0
$46$	−441.285			−1.41443
$47$	−12.1540	+	21.0513i	−0.0377200	+	0.0653329i	−0.884269	−	0.466978i	$-0.845343\pi$
$47$	−12.1540	+	21.0513i	−0.0377200	+	0.0653329i	0.846549	+	0.532311i	$0.178676\pi$
$48$		0			0
$49$	168.025	+	291.028i	0.489870	+	0.848479i
$50$	56.6805	+	98.1735i	0.160317	+	0.277677i
$51$		0			0
$52$	−382.770	+	662.977i	−1.02078	+	1.76805i
$53$	709.828			1.83967			0.919834	−	0.392308i	$-0.128323\pi$
$53$	709.828			1.83967			0.919834	+	0.392308i	$0.128323\pi$
$54$		0			0
$55$	104.655			0.256576
$56$	−27.2611	+	47.2176i	−0.0650521	+	0.112674i
$57$		0			0
$58$	−356.112	−	616.805i	−0.806204	−	1.39639i
$59$	95.9990	+	166.275i	0.211831	+	0.366901i	0.952287	−	0.305202i	$-0.0987241\pi$
$59$	95.9990	+	166.275i	0.211831	+	0.366901i	−0.740457	+	0.672104i	$0.765391\pi$
$60$		0			0
$61$	372.317	−	644.871i	0.781480	−	1.35356i	−0.149600	−	0.988747i	$-0.547799\pi$
$61$	372.317	−	644.871i	0.781480	−	1.35356i	0.931080	−	0.364816i	$-0.118868\pi$
$62$	−432.568			−0.886067
$63$		0			0
$64$	−834.504			−1.62989
$65$	152.363	−	263.900i	0.290742	−	0.503581i
$66$		0			0
$67$	411.783	+	713.230i	0.750856	+	1.30052i	0.947408	+	0.320027i	$0.103692\pi$
$67$	411.783	+	713.230i	0.750856	+	1.30052i	−0.196552	+	0.980493i	$0.562975\pi$
$68$	545.266	+	944.428i	0.972399	+	1.68425i
$69$		0			0
$70$	29.8840	−	51.7606i	0.0510261	−	0.0883797i
$71$	−1068.85			−1.78661			−0.893304	−	0.449452i	$-0.851619\pi$
$71$	−1068.85			−1.78661			−0.893304	+	0.449452i	$0.851619\pi$
$72$		0			0
$73$	−132.416			−0.212302			−0.106151	−	0.994350i	$-0.533853\pi$
$73$	−132.416			−0.212302			−0.106151	+	0.994350i	$0.533853\pi$
$74$	−364.645	+	631.583i	−0.572825	+	0.992163i
$75$		0			0
$76$	−262.568	−	454.780i	−0.396297	−	0.686406i
$77$	−27.5890	−	47.7855i	−0.0408319	−	0.0707229i
$78$		0			0
$79$	352.288	−	610.181i	0.501716	−	0.868997i	−0.498282	−	0.867015i	$-0.666036\pi$
$79$	352.288	−	610.181i	0.501716	−	0.868997i	0.999998	−	0.00198212i	$-0.000630930\pi$
$80$	33.5333			0.0468642
$81$		0			0
$82$	−1057.38			−1.42401
$83$	709.881	−	1229.55i	0.938790	−	1.62603i	0.171059	−	0.985261i	$-0.445281\pi$
$83$	709.881	−	1229.55i	0.938790	−	1.62603i	0.767731	−	0.640772i	$-0.221386\pi$
$84$		0			0
$85$	−217.044	−	375.932i	−0.276962	−	0.479712i
$86$	1105.71	+	1915.14i	1.38641	+	2.40134i
$87$		0			0
$88$	−216.451	+	374.903i	−0.262201	+	0.454146i
$89$	401.847			0.478604			0.239302	−	0.970945i	$-0.423081\pi$
$89$	401.847			0.478604			0.239302	+	0.970945i	$0.423081\pi$
$90$		0			0
$91$	−160.662			−0.185077
$92$	−611.217	+	1058.66i	−0.692650	+	1.19970i
$93$		0			0
$94$	55.1114	+	95.4558i	0.0604714	+	0.104740i
$95$	104.516	+	181.027i	0.112875	+	0.195505i
$96$		0			0
$97$	−265.440	+	459.756i	−0.277849	+	0.481249i	−0.970850	−	0.239688i	$-0.922955\pi$
$97$	−265.440	+	459.756i	−0.277849	+	0.481249i	0.693001	+	0.720937i	$0.256288\pi$
$98$	1523.80			1.57069
$99$		0			0
$100$	314.029			0.314029
$101$	499.231	−	864.694i	0.491835	−	0.851884i	−0.508120	−	0.861286i	$-0.669659\pi$
$101$	499.231	−	864.694i	0.491835	−	0.851884i	0.999956	+	0.00940212i	$0.00299283\pi$
$102$		0			0
$103$	418.736	+	725.273i	0.400576	+	0.693818i	0.993795	−	0.111223i	$-0.0354767\pi$
$103$	418.736	+	725.273i	0.400576	+	0.693818i	−0.593220	+	0.805041i	$0.702143\pi$
$104$	630.241	+	1091.61i	0.594233	+	1.02924i
$105$		0			0
$106$	1609.34	−	2787.45i	1.47465	−	2.55416i
$107$	1109.39			1.00233			0.501163	−	0.865353i	$-0.332906\pi$
$107$	1109.39			1.00233			0.501163	+	0.865353i	$0.332906\pi$
$108$		0			0
$109$	−1071.73			−0.941769			−0.470885	−	0.882195i	$-0.656065\pi$
$109$	−1071.73			−0.941769			−0.470885	+	0.882195i	$0.656065\pi$
$110$	237.276	−	410.974i	0.205667	−	0.356226i
$111$		0			0
$112$	−8.83999	−	15.3113i	−0.00745804	−	0.0129177i
$113$	544.749	+	943.533i	0.453501	+	0.785487i	0.998601	−	0.0528841i	$-0.0168414\pi$
$113$	544.749	+	943.533i	0.453501	+	0.785487i	−0.545099	+	0.838371i	$0.683508\pi$
$114$		0			0
$115$	243.296	−	421.402i	0.197283	−	0.341704i
$116$	−1972.98			−1.57920
$117$		0			0
$118$	870.604			0.679200
$119$	−114.434	+	198.205i	−0.0881523	+	0.152684i
$120$		0			0
$121$	446.446	+	773.268i	0.335422	+	0.580967i
$122$	−1688.25	−	2924.13i	−1.25284	−	2.16999i
$123$		0			0
$124$	−599.142	+	1037.75i	−0.433908	+	0.751550i
$125$	−125.000			−0.0894427
$126$		0			0
$127$	−371.442			−0.259529			−0.129764	−	0.991545i	$-0.541422\pi$
$127$	−371.442			−0.259529			−0.129764	+	0.991545i	$0.541422\pi$
$128$	−1108.53	+	1920.03i	−0.765476	+	1.32584i
$129$		0			0
$130$	−690.879	−	1196.64i	−0.466109	−	0.807324i
$131$	−132.633	−	229.727i	−0.0884597	−	0.153217i	0.818401	−	0.574648i	$-0.194861\pi$
$131$	−132.633	−	229.727i	−0.0884597	−	0.153217i	−0.906860	+	0.421432i	$0.861528\pi$
$132$		0			0
$133$	55.1045	−	95.4438i	0.0359260	−	0.0622257i
$134$	3734.42			2.40749
$135$		0			0
$136$	1795.59			1.13214
$137$	135.361	−	234.451i	0.0844134	−	0.146208i	−0.820728	−	0.571320i	$-0.806432\pi$
$137$	135.361	−	234.451i	0.0844134	−	0.146208i	0.905141	+	0.425111i	$0.139765\pi$
$138$		0			0
$139$	606.045	+	1049.70i	0.369814	+	0.640536i	0.989536	−	0.144285i	$-0.0460882\pi$
$139$	606.045	+	1049.70i	0.369814	+	0.640536i	−0.619723	+	0.784821i	$0.712755\pi$
$140$	−82.7837	−	143.386i	−0.0499750	−	0.0865592i
$141$		0			0
$142$	−2423.32	+	4197.31i	−1.43212	+	2.48050i
$143$	−1275.64			−0.745976
$144$		0			0
$145$	785.350			0.449792
$146$	−300.215	+	519.988i	−0.170178	+	0.294757i
$147$		0			0
$148$	1010.13	+	1749.59i	0.561026	+	0.971726i
$149$	−1206.67	−	2090.01i	−0.663450	−	1.14913i	−0.979703	−	0.200454i	$-0.935758\pi$
$149$	−1206.67	−	2090.01i	−0.663450	−	1.14913i	0.316253	−	0.948675i	$-0.397575\pi$
$150$		0			0
$151$	584.594	−	1012.55i	0.315057	−	0.545695i	−0.664393	−	0.747384i	$-0.731310\pi$
$151$	584.594	−	1012.55i	0.315057	−	0.545695i	0.979450	+	0.201689i	$0.0646430\pi$
$152$	−864.649			−0.461397
$153$		0			0
$154$	−250.201			−0.130921
$155$	238.490	−	413.077i	0.123587	−	0.214059i
$156$		0			0
$157$	1464.12	+	2535.92i	0.744262	+	1.28910i	0.950539	+	0.310606i	$0.100532\pi$
$157$	1464.12	+	2535.92i	0.744262	+	1.28910i	−0.206277	+	0.978494i	$0.566135\pi$
$158$	−1597.43	−	2766.83i	−0.804334	−	1.39315i
$159$		0			0
$160$	489.673	−	848.138i	0.241950	−	0.419070i
$161$	−256.549			−0.125583
$162$		0			0
$163$	−936.208			−0.449874			−0.224937	−	0.974373i	$-0.572218\pi$
$163$	−936.208			−0.449874			−0.224937	+	0.974373i	$0.572218\pi$
$164$	−1464.56	+	2536.70i	−0.697336	+	1.20782i
$165$		0			0
$166$	−3218.92	−	5575.32i	−1.50504	−	2.60680i
$167$	−1566.52	−	2713.30i	−0.725876	−	1.25725i	−0.958613	−	0.284714i	$-0.908102\pi$
$167$	−1566.52	−	2713.30i	−0.725876	−	1.25725i	0.232737	−	0.972540i	$-0.425232\pi$
$168$		0			0
$169$	−758.650	+	1314.02i	−0.345312	+	0.598098i
$170$	−1968.35			−0.888033
$171$		0			0
$172$	6125.99			2.71571
$173$	−119.633	+	207.210i	−0.0525751	+	0.0910628i	−0.891115	−	0.453777i	$-0.850076\pi$
$173$	−119.633	+	207.210i	−0.0525751	+	0.0910628i	0.838540	+	0.544840i	$0.183410\pi$
$174$		0			0
$175$	32.9523	+	57.0750i	0.0142340	+	0.0246541i
$176$	−70.1887	−	121.570i	−0.0300606	−	0.0520665i
$177$		0			0
$178$	911.077	−	1578.03i	0.383641	−	0.664485i
$179$	332.030			0.138643			0.0693215	−	0.997594i	$-0.477917\pi$
$179$	332.030			0.138643			0.0693215	+	0.997594i	$0.477917\pi$
$180$		0			0
$181$	3405.54			1.39852			0.699259	−	0.714869i	$-0.253514\pi$
$181$	3405.54			1.39852			0.699259	+	0.714869i	$0.253514\pi$
$182$	−364.257	+	630.911i	−0.148354	+	0.256957i
$183$		0			0
$184$	1006.39	+	1743.11i	0.403216	+	0.698390i
$185$	−402.083	−	696.429i	−0.159793	−	0.276770i
$186$		0			0
$187$	−908.592	+	1573.73i	−0.355309	+	0.615414i
$188$	305.336			0.118452
$189$		0			0
$190$	947.841			0.361914
$191$	2630.86	−	4556.78i	0.996661	−	1.72627i	0.427622	−	0.903957i	$-0.359351\pi$
$191$	2630.86	−	4556.78i	0.996661	−	1.72627i	0.569039	−	0.822311i	$-0.307315\pi$
$192$		0			0
$193$	−204.487	−	354.181i	−0.0762656	−	0.132096i	0.825370	−	0.564592i	$-0.190966\pi$
$193$	−204.487	−	354.181i	−0.0762656	−	0.132096i	−0.901636	+	0.432496i	$0.857633\pi$
$194$	1203.62	+	2084.74i	0.445438	+	0.771522i
$195$		0			0
$196$	2110.59	−	3655.65i	0.769166	−	1.33223i
$197$	−946.927			−0.342466			−0.171233	−	0.985231i	$-0.554775\pi$
$197$	−946.927			−0.342466			−0.171233	+	0.985231i	$0.554775\pi$
$198$		0			0
$199$	4917.06			1.75156			0.875782	−	0.482707i	$-0.160346\pi$
$199$	4917.06			1.75156			0.875782	+	0.482707i	$0.160346\pi$
$200$	258.528	−	447.784i	0.0914036	−	0.158316i
$201$		0			0
$202$	−2263.74	−	3920.90i	−0.788494	−	1.36571i
$203$	−207.033	−	358.591i	−0.0715805	−	0.123981i
$204$		0			0
$205$	582.973	−	1009.74i	0.198618	−	0.344016i
$206$	3797.47			1.28438
$207$		0			0
$208$	−408.738			−0.136254
$209$	437.524	−	757.814i	0.144805	−	0.250809i
$210$		0			0
$211$	−1224.70	−	2121.24i	−0.399582	−	0.692096i	0.594093	−	0.804397i	$-0.297511\pi$
$211$	−1224.70	−	2121.24i	−0.399582	−	0.692096i	−0.993674	+	0.112301i	$0.964178\pi$
$212$	−4458.13	−	7721.71i	−1.44427	−	2.50155i
$213$		0			0
$214$	2515.24	−	4356.52i	0.803449	−	1.39161i
$215$	−2438.47			−0.773498
$216$		0			0
$217$	−251.481			−0.0786713
$218$	−2429.84	+	4208.61i	−0.754907	+	1.30754i
$219$		0			0
$220$	−657.294	−	1138.47i	−0.201431	−	0.348888i
$221$	2645.56	+	4582.24i	0.805246	+	1.39473i
$222$		0			0
$223$	503.222	−	871.607i	0.151113	−	0.261736i	−0.780524	−	0.625126i	$-0.785048\pi$
$223$	503.222	−	871.607i	0.151113	−	0.261736i	0.931637	+	0.363390i	$0.118381\pi$
$224$	−516.347			−0.154017
$225$		0			0
$226$	4940.26			1.45408
$227$	1012.02	−	1752.87i	0.295903	−	0.512520i	−0.679291	−	0.733869i	$-0.737713\pi$
$227$	1012.02	−	1752.87i	0.295903	−	0.512520i	0.975195	+	0.221349i	$0.0710460\pi$
$228$		0			0
$229$	3393.96	+	5878.51i	0.979385	+	1.69634i	0.664633	+	0.747170i	$0.268588\pi$
$229$	3393.96	+	5878.51i	0.979385	+	1.69634i	0.314752	+	0.949174i	$0.398079\pi$
$230$	−1103.21	−	1910.82i	−0.316277	−	0.547808i
$231$		0			0
$232$	−1624.28	+	2813.34i	−0.459653	+	0.796142i
$233$	−4129.88			−1.16119			−0.580595	−	0.814193i	$-0.697180\pi$
$233$	−4129.88			−1.16119			−0.580595	+	0.814193i	$0.697180\pi$
$234$		0			0
$235$	−121.540			−0.0337378
$236$	1205.86	−	2088.61i	0.332605	−	0.576088i
$237$		0			0
$238$	518.893	+	898.749i	0.141323	+	0.244778i
$239$	1489.37	+	2579.66i	0.403093	+	0.698177i	0.994097	−	0.108491i	$-0.0346019\pi$
$239$	1489.37	+	2579.66i	0.403093	+	0.698177i	−0.591005	+	0.806668i	$0.701269\pi$
$240$		0			0
$241$	921.971	−	1596.90i	0.246429	−	0.426827i	−0.716103	−	0.697994i	$-0.754076\pi$
$241$	921.971	−	1596.90i	0.246429	−	0.426827i	0.962532	+	0.271167i	$0.0874095\pi$
$242$	4048.77			1.07547
$243$		0			0
$244$	−9353.45			−2.45407
$245$	−840.126	+	1455.14i	−0.219076	+	0.379451i
$246$		0			0
$247$	−1273.94	−	2206.53i	−0.328174	−	0.568415i
$248$	986.504	+	1708.68i	0.252593	+	0.437504i
$249$		0			0
$250$	−283.403	+	490.868i	−0.0716958	+	0.124181i
$251$	2360.72			0.593656			0.296828	−	0.954931i	$-0.404071\pi$
$251$	2360.72			0.593656			0.296828	+	0.954931i	$0.404071\pi$
$252$		0			0
$253$	−2036.98			−0.506181
$254$	−842.142	+	1458.63i	−0.208034	+	0.360326i
$255$		0			0
$256$	1688.54	+	2924.63i	0.412240	+	0.714021i
$257$	1236.32	+	2141.37i	0.300076	+	0.519746i	0.976153	−	0.217085i	$-0.0696547\pi$
$257$	1236.32	+	2141.37i	0.300076	+	0.519746i	−0.676077	+	0.736831i	$0.736321\pi$
$258$		0			0
$259$	−211.993	+	367.183i	−0.0508595	+	0.0880912i
$260$	−3827.70			−0.913015
$261$		0			0
$262$	−1202.83			−0.283631
$263$	−1083.59	+	1876.83i	−0.254056	+	0.440038i	−0.964639	−	0.263576i	$-0.915098\pi$
$263$	−1083.59	+	1876.83i	−0.254056	+	0.440038i	0.710583	+	0.703614i	$0.248431\pi$
$264$		0			0
$265$	1774.57	+	3073.65i	0.411362	+	0.712500i
$266$	−249.868	−	432.784i	−0.0575954	−	0.0997582i
$267$		0			0
$268$	5172.47	−	8958.99i	1.17895	−	2.04200i
$269$	4346.79			0.985236			0.492618	−	0.870246i	$-0.336040\pi$
$269$	4346.79			0.985236			0.492618	+	0.870246i	$0.336040\pi$
$270$		0			0
$271$	−3923.45			−0.879456			−0.439728	−	0.898131i	$-0.644925\pi$
$271$	−3923.45			−0.879456			−0.439728	+	0.898131i	$0.644925\pi$
$272$	−291.129	+	504.250i	−0.0648981	+	0.112407i
$273$		0			0
$274$	−613.784	−	1063.11i	−0.135329	−	0.234396i
$275$	261.638	+	453.170i	0.0573722	+	0.0993715i
$276$		0			0
$277$	−3017.95	+	5227.24i	−0.654624	+	1.13384i	0.327364	+	0.944898i	$0.393840\pi$
$277$	−3017.95	+	5227.24i	−0.654624	+	1.13384i	−0.981988	+	0.188943i	$0.939494\pi$
$278$	5496.15			1.18575
$279$		0			0
$280$	−272.611			−0.0581844
$281$	−1148.46	+	1989.19i	−0.243813	+	0.422296i	−0.961797	−	0.273763i	$-0.911732\pi$
$281$	−1148.46	+	1989.19i	−0.243813	+	0.422296i	0.717984	+	0.696059i	$0.245065\pi$
$282$		0			0
$283$	2748.31	+	4760.21i	0.577279	+	0.999876i	0.995790	+	0.0916644i	$0.0292187\pi$
$283$	2748.31	+	4760.21i	0.577279	+	0.999876i	−0.418511	+	0.908212i	$0.637448\pi$
$284$	6713.00	+	11627.3i	1.40262	+	2.42940i
$285$		0			0
$286$	−2892.16	+	5009.37i	−0.597962	+	1.03570i
$287$	−614.729			−0.126433
$288$		0			0
$289$	2624.32			0.534159
$290$	1780.56	−	3084.02i	0.360546	−	0.624483i
$291$		0			0
$292$	831.646	+	1440.45i	0.166673	+	0.288685i
$293$	2047.49	+	3546.36i	0.408245	+	0.707101i	0.994693	−	0.102886i	$-0.0328077\pi$
$293$	2047.49	+	3546.36i	0.408245	+	0.707101i	−0.586448	+	0.809987i	$0.699474\pi$
$294$		0			0
$295$	−479.995	+	831.376i	−0.0947335	+	0.164083i
$296$	3326.40			0.653186
$297$		0			0
$298$	−10943.1			−2.12724
$299$	−2965.54	+	5136.47i	−0.573585	+	0.993478i
$300$		0			0
$301$	642.825	+	1113.40i	0.123096	+	0.213208i
$302$	−2650.81	−	4591.34i	−0.505089	−	0.874840i
$303$		0			0
$304$	140.190	−	242.817i	0.0264489	−	0.0458109i
$305$	3723.17			0.698977
$306$		0			0
$307$	7535.90			1.40097			0.700483	−	0.713669i	$-0.252968\pi$
$307$	7535.90			1.40097			0.700483	+	0.713669i	$0.252968\pi$
$308$	−346.549	+	600.241i	−0.0641120	+	0.111045i
$309$		0			0
$310$	−1081.42	−	1873.07i	−0.198131	−	0.343172i
$311$	3165.45	+	5482.72i	0.577158	+	0.999666i	0.995804	+	0.0915168i	$0.0291715\pi$
$311$	3165.45	+	5482.72i	0.577158	+	0.999666i	−0.418646	+	0.908150i	$0.637495\pi$
$312$		0			0
$313$	−4490.98	+	7778.61i	−0.811008	+	1.40471i	0.101152	+	0.994871i	$0.467747\pi$
$313$	−4490.98	+	7778.61i	−0.811008	+	1.40471i	−0.912160	+	0.409835i	$0.865586\pi$
$314$	13277.9			2.38635
$315$		0			0
$316$	−8850.29			−1.57553
$317$	1618.24	−	2802.88i	0.286718	−	0.496609i	−0.686307	−	0.727312i	$-0.740769\pi$
$317$	1618.24	−	2802.88i	0.286718	−	0.496609i	0.973024	+	0.230703i	$0.0741026\pi$
$318$		0			0
$319$	−1643.82	−	2847.18i	−0.288515	−	0.499722i
$320$	−2086.26	−	3613.51i	−0.364455	−	0.631254i
$321$		0			0
$322$	−581.654	+	1007.45i	−0.100666	+	0.174358i
$323$	−3629.53			−0.625240
$324$		0			0
$325$	1523.63			0.260048
$326$	−2122.59	+	3676.43i	−0.360612	+	0.624598i
$327$		0			0
$328$	2411.44	+	4176.74i	0.405944	+	0.703116i
$329$	32.0401	+	55.4950i	0.00536907	+	0.00929951i
$330$		0			0
$331$	−3307.79	+	5729.27i	−0.549283	+	0.951387i	0.449040	+	0.893511i	$0.351766\pi$
$331$	−3307.79	+	5729.27i	−0.549283	+	0.951387i	−0.998324	+	0.0578753i	$0.981567\pi$
$332$	−17833.9			−2.94807
$333$		0			0
$334$	−14206.6			−2.32740
$335$	−2058.92	+	3566.15i	−0.335793	+	0.581611i
$336$		0			0
$337$	−1014.15	−	1756.55i	−0.163929	−	0.283933i	0.772346	−	0.635203i	$-0.219083\pi$
$337$	−1014.15	−	1756.55i	−0.163929	−	0.283933i	−0.936274	+	0.351270i	$0.885750\pi$
$338$	3440.05	+	5958.35i	0.553592	+	0.958850i
$339$		0			0
$340$	−2726.33	+	4722.14i	−0.434870	+	0.753217i
$341$	−1996.74			−0.317095
$342$		0			0
$343$	1790.10			0.281797
$344$	5043.31	−	8735.27i	0.790456	−	1.36911i
$345$		0			0
$346$	542.467	+	939.580i	0.0842867	+	0.145989i
$347$	1611.69	+	2791.53i	0.249337	+	0.431865i	0.963342	−	0.268276i	$-0.0864538\pi$
$347$	1611.69	+	2791.53i	0.249337	+	0.431865i	−0.714005	+	0.700141i	$0.753121\pi$
$348$		0			0
$349$	4814.26	−	8338.54i	0.738399	−	1.27895i	−0.214816	−	0.976654i	$-0.568915\pi$
$349$	4814.26	−	8338.54i	0.738399	−	1.27895i	0.953216	−	0.302291i	$-0.0977513\pi$
$350$	298.840			0.0456391
$351$		0			0
$352$	−4099.74			−0.620787
$353$	−1176.16	+	2037.16i	−0.177339	+	0.307159i	−0.940968	−	0.338495i	$-0.890082\pi$
$353$	−1176.16	+	2037.16i	−0.177339	+	0.307159i	0.763630	+	0.645655i	$0.223415\pi$
$354$		0			0
$355$	−2672.13	−	4628.26i	−0.399498	−	0.691951i
$356$	−2523.83	−	4371.41i	−0.375738	−	0.650798i
$357$		0			0
$358$	752.785	−	1303.86i	0.111134	−	0.192490i
$359$	−6464.01			−0.950299			−0.475150	−	0.879905i	$-0.657606\pi$
$359$	−6464.01			−0.950299			−0.475150	+	0.879905i	$0.657606\pi$
$360$		0			0
$361$	−5111.23			−0.745187
$362$	7721.10	−	13373.3i	1.12103	−	1.94168i
$363$		0			0
$364$	1009.05	+	1747.73i	0.145299	+	0.251664i
$365$	−331.039	−	573.376i	−0.0474722	−	0.0822243i
$366$		0			0
$367$	4578.37	−	7929.97i	0.651196	−	1.12790i	−0.331637	−	0.943407i	$-0.607601\pi$
$367$	4578.37	−	7929.97i	0.651196	−	1.12790i	0.982833	−	0.184497i	$-0.0590658\pi$
$368$	−652.683			−0.0924551
$369$		0			0
$370$	−3646.45			−0.512351
$371$	935.618	−	1620.54i	0.130930	−	0.226777i
$372$		0			0
$373$	−3964.82	−	6867.28i	−0.550377	−	0.953282i	−0.998247	−	0.0591828i	$-0.981151\pi$
$373$	−3964.82	−	6867.28i	−0.550377	−	0.953282i	0.447870	−	0.894099i	$-0.352183\pi$
$374$	4119.96	+	7135.97i	0.569620	+	0.986611i
$375$		0			0
$376$	251.372	−	435.389i	0.0344774	−	0.0597166i
$377$	−9572.64			−1.30774
$378$		0			0
$379$	9302.25			1.26075			0.630375	−	0.776290i	$-0.282901\pi$
$379$	9302.25			1.26075			0.630375	+	0.776290i	$0.282901\pi$
$380$	1312.84	−	2273.90i	0.177229	−	0.306970i
$381$		0			0
$382$	−11929.5	−	20662.5i	−1.59781	−	2.76750i
$383$	5217.94	+	9037.73i	0.696146	+	1.20576i	0.969793	+	0.243931i	$0.0784369\pi$
$383$	5217.94	+	9037.73i	0.696146	+	1.20576i	−0.273646	+	0.961830i	$0.588230\pi$
$384$		0			0
$385$	137.945	−	238.928i	0.0182606	−	0.0316283i
$386$	−1854.47			−0.244533
$387$		0			0
$388$	6668.47			0.872526
$389$	−1680.41	+	2910.55i	−0.219023	+	0.379359i	−0.954510	−	0.298180i	$-0.903620\pi$
$389$	−1680.41	+	2910.55i	−0.219023	+	0.379359i	0.735487	+	0.677539i	$0.236954\pi$
$390$		0			0
$391$	4224.49	+	7317.03i	0.546398	+	0.946390i
$392$	−3475.15	−	6019.13i	−0.447759	−	0.775540i
$393$		0			0
$394$	−2146.89	+	3718.53i	−0.274515	+	0.475474i
$395$	3522.88			0.448748
$396$		0			0
$397$	−1324.66			−0.167463			−0.0837314	−	0.996488i	$-0.526684\pi$
$397$	−1324.66			−0.167463			−0.0837314	+	0.996488i	$0.526684\pi$
$398$	11148.1	−	19309.0i	1.40402	−	2.43184i
$399$		0			0
$400$	83.8333	+	145.204i	0.0104792	+	0.0181504i
$401$	−7005.40	−	12133.7i	−0.872402	−	1.51104i	−0.859505	−	0.511128i	$-0.829228\pi$
$401$	−7005.40	−	12133.7i	−0.872402	−	1.51104i	−0.0128971	−	0.999917i	$-0.504105\pi$
$402$		0			0
$403$	−2906.96	+	5035.00i	−0.359320	+	0.622361i
$404$	−12541.8			−1.54450
$405$		0			0
$406$	−1877.55			−0.229511
$407$	−1683.20	+	2915.39i	−0.204996	+	0.355063i
$408$		0			0
$409$	−1808.01	−	3131.56i	−0.218582	−	0.378596i	0.735792	−	0.677207i	$-0.236810\pi$
$409$	−1808.01	−	3131.56i	−0.218582	−	0.378596i	−0.954375	+	0.298611i	$0.903477\pi$
$410$	−2643.46	−	4578.60i	−0.318417	−	0.551515i
$411$		0			0
$412$	5259.81	−	9110.26i	0.628962	−	1.08939i
$413$	506.142			0.0603041
$414$		0			0
$415$	7098.81			0.839680
$416$	−5968.63	+	10338.0i	−0.703452	+	1.21842i
$417$		0			0
$418$	−1983.93	−	3436.26i	−0.232146	−	0.402089i
$419$	−408.033	−	706.733i	−0.0475745	−	0.0824014i	0.841258	−	0.540635i	$-0.181816\pi$
$419$	−408.033	−	706.733i	−0.0475745	−	0.0824014i	−0.888832	+	0.458233i	$0.848482\pi$
$420$		0			0
$421$	−7482.86	+	12960.7i	−0.866252	+	1.50039i	−0.000453478		1.00000i	$0.500144\pi$
$421$	−7482.86	+	12960.7i	−0.866252	+	1.50039i	−0.865799	+	0.500393i	$0.833189\pi$
$422$	−11106.6			−1.28119
$423$		0			0
$424$	−14680.9			−1.68152
$425$	1085.22	−	1879.66i	0.123861	−	0.214534i
$426$		0			0
$427$	−981.494	−	1700.00i	−0.111236	−	0.192667i
$428$	−6967.62	−	12068.3i	−0.786899	−	1.36295i
$429$		0			0
$430$	−5528.55	+	9575.72i	−0.620024	+	1.07391i
$431$	−9752.30			−1.08991			−0.544955	−	0.838465i	$-0.683453\pi$
$431$	−9752.30			−1.08991			−0.544955	+	0.838465i	$0.683453\pi$
$432$		0			0
$433$	4546.03			0.504545			0.252273	−	0.967656i	$-0.418822\pi$
$433$	4546.03			0.504545			0.252273	+	0.967656i	$0.418822\pi$
$434$	−570.164	+	987.553i	−0.0630616	+	0.109226i
$435$		0			0
$436$	6731.07	+	11658.5i	0.739357	+	1.28060i
$437$	−2034.26	−	3523.45i	−0.222682	−	0.385697i
$438$		0			0
$439$	4309.32	−	7463.95i	0.468502	−	0.811469i	−0.530850	−	0.847466i	$-0.678127\pi$
$439$	4309.32	−	7463.95i	0.468502	−	0.811469i	0.999352	+	0.0359966i	$0.0114605\pi$
$440$	−2164.51			−0.234520
$441$		0			0
$442$	23992.2			2.58189
$443$	6134.92	−	10626.0i	0.657966	−	1.13963i	−0.323175	−	0.946339i	$-0.604750\pi$
$443$	6134.92	−	10626.0i	0.657966	−	1.13963i	0.981141	−	0.193292i	$-0.0619163\pi$
$444$		0			0
$445$	1004.62	+	1740.05i	0.107019	+	0.185362i
$446$	−2281.83	−	3952.25i	−0.242260	−	0.419606i
$447$		0			0
$448$	−1099.95	+	1905.17i	−0.116000	+	0.200917i
$449$	7617.88			0.800690			0.400345	−	0.916364i	$-0.368890\pi$
$449$	7617.88			0.800690			0.400345	+	0.916364i	$0.368890\pi$
$450$		0			0
$451$	−4880.89			−0.509606
$452$	6842.67	−	11851.9i	0.712062	−	1.23333i
$453$		0			0
$454$	−4588.94	−	7948.28i	−0.474383	−	0.821655i
$455$	−401.656	−	695.688i	−0.0413844	−	0.0716799i
$456$		0			0
$457$	−3031.03	+	5249.89i	−0.310253	+	0.537373i	−0.978417	−	0.206640i	$-0.933747\pi$
$457$	−3031.03	+	5249.89i	−0.310253	+	0.537373i	0.668164	+	0.744014i	$0.267080\pi$
$458$	30779.4			3.14023
$459$		0			0
$460$	−6112.17			−0.619525
$461$	−6909.75	+	11968.0i	−0.698090	+	1.20913i	0.271038	+	0.962569i	$0.412633\pi$
$461$	−6909.75	+	11968.0i	−0.698090	+	1.20913i	−0.969128	+	0.246558i	$0.920700\pi$
$462$		0			0
$463$	−8422.51	−	14588.2i	−0.845415	−	1.46430i	−0.885260	−	0.465096i	$-0.846020\pi$
$463$	−8422.51	−	14588.2i	−0.845415	−	1.46430i	0.0398452	−	0.999206i	$-0.487314\pi$
$464$	−526.708	−	912.285i	−0.0526979	−	0.0912754i
$465$		0			0
$466$	−9363.34	+	16217.8i	−0.930790	+	1.61218i
$467$	−8573.64			−0.849552			−0.424776	−	0.905299i	$-0.639647\pi$
$467$	−8573.64			−0.849552			−0.424776	+	0.905299i	$0.639647\pi$
$468$		0			0
$469$	2171.07			0.213754
$470$	−275.557	+	477.279i	−0.0270436	+	0.0468409i
$471$		0			0
$472$	−1985.48	−	3438.95i	−0.193621	−	0.335361i
$473$	5103.96	+	8840.32i	0.496153	+	0.859363i
$474$		0			0
$475$	−522.579	+	905.133i	−0.0504791	+	0.0874323i
$476$	2874.84			0.276823
$477$		0			0
$478$	13506.9			1.29245
$479$	148.677	−	257.516i	0.0141821	−	0.0245641i	−0.858847	−	0.512232i	$-0.828819\pi$
$479$	148.677	−	257.516i	0.0141821	−	0.0245641i	0.873029	+	0.487668i	$0.162152\pi$
$480$		0			0
$481$	4901.00	+	8488.78i	0.464587	+	0.804688i
$482$	−4180.62	−	7241.05i	−0.395067	−	0.684276i
$483$		0			0
$484$	5607.88	−	9713.13i	0.526660	−	0.912202i
$485$	−2654.40			−0.248516
$486$		0			0
$487$	−6827.58			−0.635292			−0.317646	−	0.948209i	$-0.602892\pi$
$487$	−6827.58			−0.635292			−0.317646	+	0.948209i	$0.602892\pi$
$488$	−7700.36	+	13337.4i	−0.714301	+	1.23720i
$489$		0			0
$490$	3809.50	+	6598.25i	0.351216	+	0.608324i
$491$	−2585.38	−	4478.00i	−0.237630	−	0.411587i	0.722404	−	0.691472i	$-0.243037\pi$
$491$	−2585.38	−	4478.00i	−0.237630	−	0.411587i	−0.960034	+	0.279884i	$0.909704\pi$
$492$		0			0
$493$	−6818.24	+	11809.5i	−0.622876	+	1.07885i
$494$	−11553.2			−1.05224
$495$		0			0
$496$	−639.790			−0.0579181
$497$	−1408.84	+	2440.19i	−0.127153	+	0.220236i
$498$		0			0
$499$	5376.99	+	9313.21i	0.482379	+	0.835504i	0.999795	−	0.0202292i	$-0.00643958\pi$
$499$	5376.99	+	9313.21i	0.482379	+	0.835504i	−0.517417	+	0.855734i	$0.673106\pi$
$500$	785.072	+	1359.78i	0.0702190	+	0.121623i
$501$		0			0
$502$	5352.28	−	9270.43i	0.475865	−	0.824222i
$503$	2141.00			0.189786			0.0948930	−	0.995487i	$-0.469749\pi$
$503$	2141.00			0.189786			0.0948930	+	0.995487i	$0.469749\pi$
$504$		0			0
$505$	4992.31			0.439911
$506$	−4618.28	+	7999.09i	−0.405746	+	0.702773i
$507$		0			0
$508$	2332.87	+	4040.65i	0.203749	+	0.352903i
$509$	−3030.25	−	5248.55i	−0.263877	−	0.457049i	0.703392	−	0.710803i	$-0.251668\pi$
$509$	−3030.25	−	5248.55i	−0.263877	−	0.457049i	−0.967269	+	0.253754i	$0.918335\pi$
$510$		0			0
$511$	−174.536	+	302.305i	−0.0151096	+	0.0261706i
$512$	−2423.30			−0.209172
$513$		0			0
$514$	11212.0			0.962143
$515$	−2093.68	+	3626.36i	−0.179143	+	0.310285i
$516$		0			0
$517$	254.395	+	440.625i	0.0216408	+	0.0374829i
$518$	961.269	+	1664.97i	0.0815362	+	0.141225i
$519$		0			0
$520$	−3151.21	+	5458.05i	−0.265749	+	0.460291i
$521$	8685.61			0.730371			0.365186	−	0.930935i	$-0.381006\pi$
$521$	8685.61			0.730371			0.365186	+	0.930935i	$0.381006\pi$
$522$		0			0
$523$	−20944.4			−1.75112			−0.875561	−	0.483108i	$-0.839508\pi$
$523$	−20944.4			−1.75112			−0.875561	+	0.483108i	$0.839508\pi$
$524$	−1666.03	+	2885.64i	−0.138894	+	0.240572i
$525$		0			0
$526$	4913.46	+	8510.36i	0.407295	+	0.705455i
$527$	4141.04	+	7172.49i	0.342289	+	0.592862i
$528$		0			0
$529$	1348.05	−	2334.88i	0.110795	−	0.191903i
$530$	16093.4			1.31896
$531$		0			0
$532$	−1384.35			−0.112818
$533$	−7105.87	+	12307.7i	−0.577466	+	1.00020i
$534$		0			0
$535$	2773.48	+	4803.81i	0.224127	+	0.388199i
$536$	−8516.62	−	14751.2i	−0.686310	−	1.18872i
$537$		0			0
$538$	9855.13	−	17069.6i	0.789749	−	1.36789i
$539$	7033.88			0.562098
$540$		0			0
$541$	−17178.0			−1.36513			−0.682567	−	0.730823i	$-0.739137\pi$
$541$	−17178.0			−1.36513			−0.682567	+	0.730823i	$0.739137\pi$
$542$	−8895.33	+	15407.2i	−0.704958	+	1.22102i
$543$		0			0
$544$	8502.46	+	14726.7i	0.670110	+	1.16067i
$545$	−2679.32	−	4640.72i	−0.210586	−	0.364746i
$546$		0			0
$547$	11146.8	−	19306.8i	0.871300	−	1.50914i	0.0106469	−	0.999943i	$-0.496611\pi$
$547$	11146.8	−	19306.8i	0.871300	−	1.50914i	0.860653	−	0.509192i	$-0.170056\pi$
$548$	−3400.57			−0.265082
$549$		0			0
$550$	2372.76			0.183954
$551$	3283.26	−	5686.77i	0.253850	−	0.439682i
$552$		0			0
$553$	−928.696	−	1608.55i	−0.0714144	−	0.123693i
$554$	13684.7	+	23702.6i	1.04947	+	1.81774i
$555$		0			0
$556$	7612.63	−	13185.5i	0.580661	−	1.00573i
$557$	10050.0			0.764512			0.382256	−	0.924056i	$-0.375147\pi$
$557$	10050.0			0.764512			0.382256	+	0.924056i	$0.375147\pi$
$558$		0			0
$559$	29722.5			2.24889
$560$	44.2000	−	76.5566i	0.00333534	−	0.00577698i
$561$		0			0
$562$	5207.62	+	9019.87i	0.390873	+	0.677011i
$563$	1234.70	+	2138.56i	0.0924269	+	0.160088i	0.908532	−	0.417816i	$-0.137204\pi$
$563$	1234.70	+	2138.56i	0.0924269	+	0.160088i	−0.816105	+	0.577904i	$0.803871\pi$
$564$		0			0
$565$	−2723.74	+	4717.66i	−0.202812	+	0.351281i
$566$	24924.1			1.85095
$567$		0			0
$568$	22106.3			1.63303
$569$	−867.365	+	1502.32i	−0.0639048	+	0.110686i	−0.896208	−	0.443635i	$-0.853689\pi$
$569$	−867.365	+	1502.32i	−0.0639048	+	0.110686i	0.832303	+	0.554321i	$0.187022\pi$
$570$		0			0
$571$	−2582.27	−	4472.61i	−0.189255	−	0.327799i	0.755747	−	0.654863i	$-0.227274\pi$
$571$	−2582.27	−	4472.61i	−0.189255	−	0.327799i	−0.945002	+	0.327065i	$0.893941\pi$
$572$	8011.77	+	13876.8i	0.585645	+	1.01437i
$573$		0			0
$574$	−1393.73	+	2414.01i	−0.101347	+	0.175538i
$575$	2432.96			0.176455
$576$		0			0
$577$	−3796.17			−0.273894			−0.136947	−	0.990578i	$-0.543729\pi$
$577$	−3796.17			−0.273894			−0.136947	+	0.990578i	$0.543729\pi$
$578$	5949.92	−	10305.6i	0.428173	−	0.741618i
$579$		0			0
$580$	−4932.45	−	8543.26i	−0.353119	−	0.611620i
$581$	−1871.38	−	3241.32i	−0.133628	−	0.231450i
$582$		0			0
$583$	7428.71	−	12866.9i	0.527729	−	0.914053i
$584$	2738.66			0.194052
$585$		0			0
$586$	18568.5			1.30897
$587$	6801.62	−	11780.8i	0.478250	−	0.828354i	−0.521439	−	0.853289i	$-0.674605\pi$
$587$	6801.62	−	11780.8i	0.478250	−	0.828354i	0.999689	+	0.0249349i	$0.00793784\pi$
$588$		0			0
$589$	−1994.08	−	3453.84i	−0.139498	−	0.241618i
$590$	2176.51	+	3769.82i	0.151874	+	0.263053i
$591$		0			0
$592$	−539.328	+	934.143i	−0.0374430	+	0.0648531i
$593$	82.8252			0.00573562			0.00286781	−	0.999996i	$-0.499087\pi$
$593$	82.8252			0.00573562			0.00286781	+	0.999996i	$0.499087\pi$
$594$		0			0
$595$	−1144.34			−0.0788458
$596$	−15157.1	+	26252.9i	−1.04171	+	1.80430i
$597$		0			0
$598$	13447.1	+	23291.0i	0.919552	+	1.59271i
$599$	565.521	+	979.511i	0.0385752	+	0.0668142i	0.884668	−	0.466221i	$-0.154385\pi$
$599$	565.521	+	979.511i	0.0385752	+	0.0668142i	−0.846093	+	0.533035i	$0.821051\pi$
$600$		0			0
$601$	1361.33	−	2357.90i	0.0923960	−	0.160035i	−0.816123	−	0.577878i	$-0.803881\pi$
$601$	1361.33	−	2357.90i	0.0923960	−	0.160035i	0.908519	+	0.417844i	$0.137214\pi$
$602$	5829.70			0.394686
$603$		0			0
$604$	−14686.4			−0.989370
$605$	−2232.23	+	3866.34i	−0.150005	+	0.259817i
$606$		0			0
$607$	−5508.87	−	9541.65i	−0.368366	−	0.638029i	0.620944	−	0.783855i	$-0.286749\pi$
$607$	−5508.87	−	9541.65i	−0.368366	−	0.638029i	−0.989310	+	0.145826i	$0.953416\pi$
$608$	−4094.28	−	7091.50i	−0.273100	−	0.473024i
$609$		0			0
$610$	8441.24	−	14620.7i	0.560288	−	0.970447i
$611$	1481.45			0.0980900
$612$		0			0
$613$	−12198.6			−0.803750			−0.401875	−	0.915695i	$-0.631641\pi$
$613$	−12198.6			−0.803750			−0.401875	+	0.915695i	$0.631641\pi$
$614$	17085.6	−	29593.1i	1.12299	−	1.94508i
$615$		0			0
$616$	570.603	+	988.313i	0.0373218	+	0.0646433i
$617$	−447.122	−	774.437i	−0.0291741	−	0.0505311i	0.851070	−	0.525053i	$-0.175954\pi$
$617$	−447.122	−	774.437i	−0.0291741	−	0.0505311i	−0.880244	+	0.474522i	$0.842621\pi$
$618$		0			0
$619$	13835.5	−	23963.9i	0.898381	−	1.55604i	0.0688163	−	0.997629i	$-0.478078\pi$
$619$	13835.5	−	23963.9i	0.898381	−	1.55604i	0.829564	−	0.558411i	$-0.188589\pi$
$620$	−5991.42			−0.388099
$621$		0			0
$622$	28707.1			1.85056
$623$	529.671	−	917.418i	0.0340623	−	0.0589977i
$624$		0			0
$625$	−312.500	−	541.266i	−0.0200000	−	0.0346410i
$626$	20364.1	+	35271.6i	1.30018	+	2.25198i
$627$		0			0
$628$	18391.0	−	31854.1i	1.16860	−	2.02407i
$629$	13963.2			0.885133
$630$		0			0
$631$	−4377.81			−0.276193			−0.138097	−	0.990419i	$-0.544098\pi$
$631$	−4377.81			−0.276193			−0.138097	+	0.990419i	$0.544098\pi$
$632$	−7286.12	+	12619.9i	−0.458586	+	0.794295i
$633$		0			0
$634$	−7337.82	−	12709.5i	−0.459656	−	0.796148i
$635$	−928.606	−	1608.39i	−0.0580324	−	0.100515i
$636$		0			0
$637$	10240.3	−	17736.7i	0.636948	−	1.10323i
$638$	−14907.6			−0.925074
$639$		0			0
$640$	−11085.3			−0.684662
$641$	12457.8	−	21577.5i	0.767633	−	1.32958i	−0.171211	−	0.985234i	$-0.554768\pi$
$641$	12457.8	−	21577.5i	0.767633	−	1.32958i	0.938843	−	0.344344i	$-0.111899\pi$
$642$		0			0
$643$	−5386.52	−	9329.73i	−0.330363	−	0.572206i	0.652220	−	0.758030i	$-0.273838\pi$
$643$	−5386.52	−	9329.73i	−0.330363	−	0.572206i	−0.982583	+	0.185824i	$0.940505\pi$
$644$	1611.28	+	2790.82i	0.0985920	+	0.170766i
$645$		0			0
$646$	−8228.94	+	14252.9i	−0.501182	+	0.868072i
$647$	19872.6			1.20753			0.603766	−	0.797162i	$-0.293666\pi$
$647$	19872.6			1.20753			0.603766	+	0.797162i	$0.293666\pi$
$648$		0			0
$649$	4018.71			0.243064
$650$	3454.40	−	5983.19i	0.208450	−	0.361046i
$651$		0			0
$652$	5879.93	+	10184.3i	0.353184	+	0.611732i
$653$	2066.09	+	3578.58i	0.123817	+	0.214457i	0.921270	−	0.388924i	$-0.127153\pi$
$653$	2066.09	+	3578.58i	0.123817	+	0.214457i	−0.797453	+	0.603381i	$0.793820\pi$
$654$		0			0
$655$	663.166	−	1148.64i	0.0395604	−	0.0685206i
$656$	−1563.92			−0.0930807
$657$		0			0
$658$	290.567			0.0172150
$659$	−11630.1	+	20143.8i	−0.687470	+	1.19073i	0.285184	+	0.958473i	$0.407945\pi$
$659$	−11630.1	+	20143.8i	−0.687470	+	1.19073i	−0.972654	+	0.232260i	$0.925388\pi$
$660$		0			0
$661$	−5658.24	−	9800.35i	−0.332950	−	0.576686i	0.650139	−	0.759815i	$-0.274711\pi$
$661$	−5658.24	−	9800.35i	−0.332950	−	0.576686i	−0.983089	+	0.183129i	$0.941377\pi$
$662$	14999.0	+	25979.0i	0.880593	+	1.52523i
$663$		0			0
$664$	−14682.0	+	25429.9i	−0.858088	+	1.48625i
$665$	551.045			0.0321332
$666$		0			0
$667$	−15285.8			−0.887361
$668$	−19677.3	+	34082.1i	−1.13973	+	1.97407i
$669$		0			0
$670$	9336.04	+	16170.5i	0.538332	+	0.932419i
$671$	−7792.97	−	13497.8i	−0.448352	−	0.776568i
$672$		0			0
$673$	−13036.1	+	22579.1i	−0.746662	+	1.29326i	0.202752	+	0.979230i	$0.435012\pi$
$673$	−13036.1	+	22579.1i	−0.746662	+	1.29326i	−0.949414	+	0.314027i	$0.898322\pi$
$674$	−9197.16			−0.525611
$675$		0			0
$676$	19059.0			1.08438
$677$	7625.96	−	13208.6i	0.432924	−	0.749846i	−0.564200	−	0.825638i	$-0.690815\pi$
$677$	7625.96	−	13208.6i	0.432924	−	0.749846i	0.997124	+	0.0757921i	$0.0241485\pi$
$678$		0			0
$679$	699.748	+	1212.00i	0.0395491	+	0.0685011i
$680$	4488.97	+	7775.13i	0.253153	+	0.438474i
$681$		0			0
$682$	−4527.04	+	7841.07i	−0.254178	+	0.440249i
$683$	−33196.1			−1.85976			−0.929878	−	0.367867i	$-0.880088\pi$
$683$	−33196.1			−1.85976			−0.929878	+	0.367867i	$0.880088\pi$
$684$		0			0
$685$	1353.61			0.0755016
$686$	4058.55	−	7029.62i	0.225884	−	0.391242i
$687$		0			0
$688$	1635.40	+	2832.59i	0.0906236	+	0.156965i
$689$	−21630.3	−	37464.7i	−1.19600	−	2.07154i
$690$		0			0
$691$	15663.7	−	27130.3i	0.862337	−	1.49361i	−0.00732930	−	0.999973i	$-0.502333\pi$
$691$	15663.7	−	27130.3i	0.862337	−	1.49361i	0.869667	−	0.493639i	$-0.164334\pi$
$692$	3005.45			0.165101
$693$		0			0
$694$	14616.2			0.799459
$695$	−3030.23	+	5248.51i	−0.165386	+	0.286456i
$696$		0			0
$697$	10122.5	+	17532.7i	0.550095	+	0.952793i
$698$	−21830.0	−	37810.6i	−1.18378	−	2.05036i
$699$		0			0
$700$	413.918	−	716.928i	0.0223495	−	0.0387105i
$701$	21416.8			1.15392			0.576962	−	0.816771i	$-0.304238\pi$
$701$	21416.8			1.15392			0.576962	+	0.816771i	$0.304238\pi$
$702$		0			0
$703$	−6723.85			−0.360732
$704$	−8733.51	+	15126.9i	−0.467552	+	0.809823i
$705$		0			0
$706$	5333.21	+	9237.40i	0.284303	+	0.492428i
$707$	−1316.06	−	2279.49i	−0.0700081	−	0.121258i
$708$		0			0
$709$	−3339.29	+	5783.82i	−0.176883	+	0.306370i	−0.940811	−	0.338931i	$-0.889935\pi$
$709$	−3339.29	+	5783.82i	−0.176883	+	0.306370i	0.763929	+	0.645301i	$0.223268\pi$
$710$	−24233.2			−1.28092
$711$		0			0
$712$	−8311.12			−0.437461
$713$	−4641.91	+	8040.02i	−0.243816	+	0.422302i
$714$		0			0
$715$	−3189.11	−	5523.69i	−0.166805	−	0.288915i
$716$	−2085.34	−	3611.92i	−0.108845	−	0.188525i
$717$		0			0
$718$	−14655.3	+	25383.8i	−0.761744	+	1.31938i
$719$	25245.9			1.30947			0.654737	−	0.755857i	$-0.272779\pi$
$719$	25245.9			1.30947			0.654737	+	0.755857i	$0.272779\pi$
$720$		0			0
$721$	2207.73			0.114036
$722$	−11588.3	+	20071.5i	−0.597329	+	1.03460i
$723$		0			0
$724$	−21388.7	−	37046.4i	−1.09794	−	1.90168i
$725$	1963.38	+	3400.67i	0.100576	+	0.174204i
$726$		0			0
$727$	−17593.4	+	30472.6i	−0.897527	+	1.55456i	−0.0668810	+	0.997761i	$0.521305\pi$
$727$	−17593.4	+	30472.6i	−0.897527	+	1.55456i	−0.830646	+	0.556801i	$0.812029\pi$
$728$	3322.86			0.169167
$729$		0			0
$730$	−3002.15			−0.152212
$731$	21170.2	−	36667.9i	1.07115	−	1.85528i
$732$		0			0
$733$	8534.31	+	14781.9i	0.430043	+	0.744857i	0.996877	−	0.0789756i	$-0.0251649\pi$
$733$	8534.31	+	14781.9i	0.430043	+	0.744857i	−0.566833	+	0.823833i	$0.691832\pi$
$734$	−20760.3	−	35958.0i	−1.04398	−	1.80822i
$735$		0			0
$736$	−9530.86	+	16507.9i	−0.477326	+	0.826753i
$737$	17238.1			0.861565
$738$		0			0
$739$	−38144.8			−1.89875			−0.949376	−	0.314141i	$-0.898283\pi$
$739$	−38144.8			−1.89875			−0.949376	+	0.314141i	$0.898283\pi$
$740$	−5050.63	+	8747.95i	−0.250898	+	0.434569i
$741$		0			0
$742$	−4242.50	−	7348.23i	−0.209902	−	0.363561i
$743$	2573.87	+	4458.07i	0.127087	+	0.220122i	0.922547	−	0.385885i	$-0.126104\pi$
$743$	2573.87	+	4458.07i	0.127087	+	0.220122i	−0.795460	+	0.606007i	$0.792770\pi$
$744$		0			0
$745$	6033.34	−	10450.0i	0.296704	−	0.513906i
$746$	−35956.5			−1.76469
$747$		0			0
$748$	22825.9			1.11577
$749$	1462.28	−	2532.74i	0.0713358	−	0.123557i
$750$		0			0
$751$	−11798.9	−	20436.3i	−0.573300	−	0.992984i	−0.996224	−	0.0868191i	$-0.972330\pi$
$751$	−11798.9	−	20436.3i	−0.573300	−	0.992984i	0.422924	−	0.906165i	$-0.361004\pi$
$752$	81.5126	+	141.184i	0.00395274	+	0.00684634i
$753$		0			0
$754$	−21703.3	+	37591.2i	−1.04826	+	1.81564i
$755$	5845.94			0.281796
$756$		0			0
$757$	1343.38			0.0644995			0.0322497	−	0.999480i	$-0.489733\pi$
$757$	1343.38			0.0644995			0.0322497	+	0.999480i	$0.489733\pi$
$758$	21090.3	−	36529.4i	1.01060	−	1.75041i
$759$		0			0
$760$	−2161.62	−	3744.04i	−0.103171	−	0.178698i
$761$	4008.19	+	6942.39i	0.190929	+	0.330698i	0.945558	−	0.325453i	$-0.105517\pi$
$761$	4008.19	+	6942.39i	0.190929	+	0.330698i	−0.754629	+	0.656151i	$0.772183\pi$
$762$		0			0
$763$	−1412.63	+	2446.75i	−0.0670259	+	0.116092i
$764$	−66093.3			−3.12980
$765$		0			0
$766$	47320.8			2.23208
$767$	5850.67	−	10133.7i	0.275431	−	0.477060i
$768$		0			0
$769$	11522.0	+	19956.7i	0.540305	+	0.935836i	0.998886	+	0.0471833i	$0.0150245\pi$
$769$	11522.0	+	19956.7i	0.540305	+	0.935836i	−0.458581	+	0.888653i	$0.651642\pi$
$770$	−625.503	−	1083.40i	−0.0292748	−	0.0507054i
$771$		0			0
$772$	−2568.59	+	4448.92i	−0.119748	+	0.207410i
$773$	−31884.9			−1.48359			−0.741797	−	0.670624i	$-0.766026\pi$
$773$	−31884.9			−1.48359			−0.741797	+	0.670624i	$0.766026\pi$
$774$		0			0
$775$	2384.90			0.110540
$776$	5489.91	−	9508.80i	0.253964	−	0.439879i
$777$		0			0
$778$	7619.70	+	13197.7i	0.351130	+	0.608176i
$779$	−4874.39	−	8442.69i	−0.224189	−	0.388306i
$780$		0			0
$781$	−11186.1	+	19374.8i	−0.512508	+	0.887690i
$782$	38311.4			1.75194
$783$		0			0
$784$	2253.78			0.102668
$785$	−7320.58	+	12679.6i	−0.332844	+	0.576503i
$786$		0			0
$787$	−8516.51	−	14751.0i	−0.385744	−	0.668129i	0.606128	−	0.795367i	$-0.292722\pi$
$787$	−8516.51	−	14751.0i	−0.385744	−	0.668129i	−0.991872	+	0.127239i	$0.959389\pi$
$788$	5947.25	+	10300.9i	0.268860	+	0.465680i
$789$		0			0
$790$	7987.15	−	13834.2i	0.359709	−	0.623034i
$791$	2872.11			0.129103
$792$		0			0
$793$	−45381.7			−2.03222
$794$	−3003.29	+	5201.86i	−0.134235	+	0.232503i
$795$		0			0
$796$	−30882.0	−	53489.2i	−1.37510	−	2.38175i
$797$	−20875.0	−	36156.6i	−0.927767	−	1.60694i	−0.787049	−	0.616891i	$-0.788392\pi$
$797$	−20875.0	−	36156.6i	−0.927767	−	1.60694i	−0.140718	−	0.990050i	$-0.544941\pi$
$798$		0			0
$799$	1055.18	−	1827.63i	0.0467204	−	0.0809221i
$800$	4896.73			0.216407
$801$		0			0
$802$	−63531.2			−2.79721
$803$	−1385.80	+	2400.27i	−0.0609012	+	0.105484i
$804$		0			0
$805$	−641.374	−	1110.89i	−0.0280813	−	0.0486383i
$806$	13181.4	+	22830.9i	0.576050	+	0.997748i
$807$		0			0
$808$	−10325.2	+	17883.8i	−0.449555	+	0.778653i
$809$	163.059			0.00708636			0.00354318	−	0.999994i	$-0.498872\pi$
$809$	163.059			0.00708636			0.00354318	+	0.999994i	$0.498872\pi$
$810$		0			0
$811$	9958.10			0.431167			0.215583	−	0.976485i	$-0.430835\pi$
$811$	9958.10			0.431167			0.215583	+	0.976485i	$0.430835\pi$
$812$	−2600.57	+	4504.32i	−0.112392	+	0.194668i
$813$		0			0
$814$	7632.38	+	13219.7i	0.328642	+	0.569225i
$815$	−2340.52	−	4053.90i	−0.100595	−	0.174235i
$816$		0			0
$817$	−10194.3	+	17657.1i	−0.436542	+	0.756112i
$818$	−16396.6			−0.700848
$819$		0			0
$820$	−14645.6			−0.623717
$821$	16136.6	−	27949.4i	0.685957	−	1.18811i	−0.287178	−	0.957877i	$-0.592717\pi$
$821$	16136.6	−	27949.4i	0.685957	−	1.18811i	0.973135	−	0.230235i	$-0.0739494\pi$
$822$		0			0
$823$	−16355.3	−	28328.2i	−0.692722	−	1.19983i	−0.970943	−	0.239313i	$-0.923078\pi$
$823$	−16355.3	−	28328.2i	−0.692722	−	1.19983i	0.278220	−	0.960517i	$-0.410255\pi$
$824$	−8660.42	−	15000.3i	−0.366141	−	0.634175i
$825$		0			0
$826$	1147.53	−	1987.59i	0.0483388	−	0.0837252i
$827$	−9763.68			−0.410540			−0.205270	−	0.978705i	$-0.565807\pi$
$827$	−9763.68			−0.410540			−0.205270	+	0.978705i	$0.565807\pi$
$828$		0			0
$829$	34886.9			1.46160			0.730802	−	0.682589i	$-0.239146\pi$
$829$	34886.9			1.46160			0.730802	+	0.682589i	$0.239146\pi$
$830$	16094.6	−	27876.6i	0.673073	−	1.16580i
$831$		0			0
$832$	25429.4	+	44045.1i	1.05962	+	1.83532i
$833$	−14587.6	−	25266.4i	−0.606758	−	1.05094i
$834$		0			0
$835$	7832.62	−	13566.5i	0.324621	−	0.562261i
$836$	−10991.6			−0.454728
$837$		0			0
$838$	−3700.40			−0.152540
$839$	12821.0	−	22206.7i	0.527570	−	0.913778i	−0.471914	−	0.881645i	$-0.656437\pi$
$839$	12821.0	−	22206.7i	0.527570	−	0.913778i	0.999484	−	0.0321330i	$-0.0102300\pi$
$840$		0			0
$841$	−141.001	−	244.221i	−0.00578135	−	0.0100136i
$842$	33930.6	+	58769.5i	1.38875	+	2.40538i
$843$		0			0
$844$	−15383.6	+	26645.2i	−0.627401	+	1.08669i
$845$	−7586.50			−0.308856
$846$		0			0
$847$	2353.83			0.0954881
$848$	2380.29	−	4122.78i	0.0963909	−	0.166954i
$849$		0			0
$850$	−4920.87	−	8523.21i	−0.198570	−	0.343934i
$851$	7826.04	+	13555.1i	0.315245	+	0.546020i
$852$		0			0
$853$	2251.36	−	3899.47i	0.0903694	−	0.156524i	−0.817297	−	0.576216i	$-0.804529\pi$
$853$	2251.36	−	3899.47i	0.0903694	−	0.156524i	0.907667	+	0.419692i	$0.137862\pi$
$854$	−8901.05			−0.356660
$855$		0			0
$856$	−22944.8			−0.916163
$857$	−13719.6	+	23763.0i	−0.546851	+	0.947174i	0.451637	+	0.892202i	$0.350840\pi$
$857$	−13719.6	+	23763.0i	−0.546851	+	0.947174i	−0.998488	+	0.0549717i	$0.982493\pi$
$858$		0			0
$859$	−13373.3	−	23163.3i	−0.531190	−	0.920048i	−0.999337	−	0.0363974i	$-0.988412\pi$
$859$	−13373.3	−	23163.3i	−0.531190	−	0.920048i	0.468148	−	0.883650i	$-0.344922\pi$
$860$	15315.0	+	26526.3i	0.607252	+	1.05179i
$861$		0			0
$862$	−22110.6	+	38296.7i	−0.873655	+	1.51321i
$863$	−4198.80			−0.165618			−0.0828092	−	0.996565i	$-0.526389\pi$
$863$	−4198.80			−0.165618			−0.0828092	+	0.996565i	$0.526389\pi$
$864$		0			0
$865$	−1196.33			−0.0470246
$866$	10306.8	−	17852.0i	0.404435	−	0.700502i
$867$		0			0
$868$	1579.45	+	2735.68i	0.0617626	+	0.106976i
$869$	−7373.75	−	12771.7i	−0.287845	−	0.498562i
$870$		0			0
$871$	25096.2	−	43467.8i	0.976293	−	1.69099i
$872$	22165.8			0.860811
$873$		0			0
$874$	−18448.5			−0.713993
$875$	−164.761	+	285.375i	−0.00636566	+	0.0110256i
$876$		0			0
$877$	9702.32	+	16804.9i	0.373574	+	0.647049i	0.990112	−	0.140276i	$-0.0447990\pi$
$877$	9702.32	+	16804.9i	0.373574	+	0.647049i	−0.616539	+	0.787325i	$0.711466\pi$
$878$	−19540.3	−	33844.9i	−0.751087	−	1.30092i
$879$		0			0
$880$	350.943	−	607.852i	0.0134435	−	0.0232849i
$881$	−8562.17			−0.327431			−0.163716	−	0.986508i	$-0.552348\pi$
$881$	−8562.17			−0.327431			−0.163716	+	0.986508i	$0.552348\pi$
$882$		0			0
$883$	44660.0			1.70207			0.851036	−	0.525107i	$-0.175975\pi$
$883$	44660.0			1.70207			0.851036	+	0.525107i	$0.175975\pi$
$884$	33231.2	−	57558.2i	1.26435	−	2.18992i
$885$		0			0
$886$	−27818.4	−	48183.0i	−1.05483	−	1.82702i
$887$	−4089.93	−	7083.97i	−0.154821	−	0.268158i	0.778173	−	0.628050i	$-0.216147\pi$
$887$	−4089.93	−	7083.97i	−0.154821	−	0.268158i	−0.932994	+	0.359892i	$0.882814\pi$
$888$		0			0
$889$	−489.595	+	848.003i	−0.0184707	+	0.0319922i
$890$	9110.77			0.343139
$891$		0			0
$892$	−12642.1			−0.474539
$893$	−508.112	+	880.076i	−0.0190407	+	0.0329794i
$894$		0			0
$895$	830.075	+	1437.73i	0.0310015	+	0.0536962i
$896$	2922.28	+	5061.54i	0.108958	+	0.188721i
$897$		0			0
$898$	17271.4	−	29915.0i	0.641820	−	1.11166i
$899$	−14983.9			−0.555884
$900$		0			0
$901$	−61625.7			−2.27863
$902$	−11066.1	+	19167.0i	−0.408491	+	0.707528i
$903$		0			0
$904$	−11266.6	−	19514.4i	−0.414517	−	0.717964i
$905$	8513.84	+	14746.4i	0.312718	+	0.541643i
$906$		0			0
$907$	16754.5	−	29019.6i	0.613366	−	1.06238i	−0.377302	−	0.926090i	$-0.623148\pi$
$907$	16754.5	−	29019.6i	0.613366	−	1.06238i	0.990669	−	0.136292i	$-0.0435184\pi$
$908$	−25424.3			−0.929222
$909$		0			0
$910$	−3642.57			−0.132692
$911$	−22332.6	+	38681.2i	−0.812198	+	1.40677i	0.0991249	+	0.995075i	$0.468396\pi$
$911$	−22332.6	+	38681.2i	−0.812198	+	1.40677i	−0.911323	+	0.411693i	$0.864938\pi$
$912$		0			0
$913$	−14858.5	−	25735.7i	−0.538605	−	0.932890i
$914$	13744.0	+	23805.3i	0.497387	+	0.861499i
$915$		0			0
$916$	42632.0	−	73840.8i	1.53778	−	2.66350i
$917$	−699.290			−0.0251828
$918$		0			0
$919$	13156.3			0.472237			0.236118	−	0.971724i	$-0.424125\pi$
$919$	13156.3			0.472237			0.236118	+	0.971724i	$0.424125\pi$
$920$	−5031.93	+	8715.55i	−0.180324	+	0.312330i
$921$		0			0
$922$	31331.9	+	54268.4i	1.11915	+	1.93843i
$923$	32570.6	+	56413.9i	1.16151	+	2.01179i
$924$		0			0
$925$	2010.42	−	3482.14i	0.0714617	−	0.123775i
$926$	−76382.7			−2.71068
$927$		0			0
$928$	−30765.2			−1.08827
$929$	−18833.9	+	32621.3i	−0.665146	+	1.15207i	0.314100	+	0.949390i	$0.398297\pi$
$929$	−18833.9	+	32621.3i	−0.665146	+	1.15207i	−0.979246	+	0.202676i	$0.935036\pi$
$930$		0			0
$931$	7024.51	+	12166.8i	0.247282	+	0.428304i
$932$	25938.0	+	44925.9i	0.911617	+	1.57897i
$933$		0			0
$934$	−19438.3	+	33668.2i	−0.680987	+	1.17950i
$935$	−9085.92			−0.317798
$936$		0			0
$937$	−37999.6			−1.32486			−0.662429	−	0.749125i	$-0.730474\pi$
$937$	−37999.6			−1.32486			−0.662429	+	0.749125i	$0.730474\pi$
$938$	4922.30	−	8525.67i	0.171342	−	0.296773i
$939$		0			0
$940$	763.339	+	1322.14i	0.0264866	+	0.0458761i
$941$	−5119.31	−	8866.90i	−0.177348	−	0.307176i	0.763623	−	0.645662i	$-0.223419\pi$
$941$	−5119.31	−	8866.90i	−0.177348	−	0.307176i	−0.940971	+	0.338486i	$0.890085\pi$
$942$		0			0
$943$	−11346.8	+	19653.3i	−0.391838	+	0.678684i
$944$	1287.67			0.0443962
$945$		0			0
$946$	46287.2			1.59083
$947$	5188.62	−	8986.96i	0.178044	−	0.308381i	−0.763167	−	0.646202i	$-0.776356\pi$
$947$	5188.62	−	8986.96i	0.178044	−	0.308381i	0.941210	+	0.337821i	$0.109690\pi$
$948$		0			0
$949$	4035.04	+	6988.89i	0.138022	+	0.239061i
$950$	2369.60	+	4104.27i	0.0809263	+	0.140169i
$951$		0			0
$952$	2366.75	−	4099.33i	0.0805743	−	0.139559i
$953$	54309.6			1.84602			0.923012	−	0.384772i	$-0.125720\pi$
$953$	54309.6			1.84602			0.923012	+	0.384772i	$0.125720\pi$
$954$		0			0
$955$	26308.6			0.891441
$956$	18708.2	−	32403.5i	0.632913	−	1.09624i
$957$		0			0
$958$	−674.167	−	1167.69i	−0.0227363	−	0.0393804i
$959$	−356.835	−	618.056i	−0.0120154	−	0.0208113i
$960$		0			0
$961$	10345.3	−	17918.6i	0.347262	−	0.601476i
$962$	44446.6			1.48962
$963$		0			0
$964$	−23162.0			−0.773858
$965$	1022.43	−	1770.91i	0.0341070	−	0.0590751i
$966$		0			0
$967$	6350.67	+	10999.7i	0.211193	+	0.365797i	0.952088	−	0.305824i	$-0.0989318\pi$
$967$	6350.67	+	10999.7i	0.211193	+	0.365797i	−0.740895	+	0.671621i	$0.765598\pi$
$968$	−9233.52	−	15992.9i	−0.306588	−	0.531025i
$969$		0			0
$970$	−6018.11	+	10423.7i	−0.199206	+	0.345035i
$971$	−3767.34			−0.124511			−0.0622553	−	0.998060i	$-0.519829\pi$
$971$	−3767.34			−0.124511			−0.0622553	+	0.998060i	$0.519829\pi$
$972$		0			0
$973$	3195.29			0.105279
$974$	−15479.6	+	26811.5i	−0.509239	+	0.882028i
$975$		0			0
$976$	−2497.00	−	4324.94i	−0.0818925	−	0.141842i
$977$	6679.93	+	11570.0i	0.218741	+	0.378871i	0.954423	−	0.298456i	$-0.0964717\pi$
$977$	6679.93	+	11570.0i	0.218741	+	0.378871i	−0.735682	+	0.677327i	$0.763138\pi$
$978$		0			0
$979$	4205.54	−	7284.20i	0.137293	−	0.237798i
$980$	21105.9			0.687963
$981$		0			0
$982$	−23446.5			−0.761921
$983$	−15853.5	+	27459.1i	−0.514394	+	0.890956i	0.485467	+	0.874255i	$0.338650\pi$
$983$	−15853.5	+	27459.1i	−0.514394	+	0.890956i	−0.999861	+	0.0167012i	$0.994684\pi$
$984$		0			0
$985$	−2367.32	−	4100.31i	−0.0765777	−	0.132636i
$986$	30916.9	+	53549.6i	0.998574	+	1.72958i
$987$		0			0
$988$	−16002.2	+	27716.6i	−0.515281	+	0.892493i
$989$	47461.7			1.52598
$990$		0			0
$991$	−19393.7			−0.621657			−0.310829	−	0.950466i	$-0.600606\pi$
$991$	−19393.7			−0.621657			−0.310829	+	0.950466i	$0.600606\pi$
$992$	−9342.58	+	16181.8i	−0.299019	+	0.517917i
$993$		0			0
$994$	6388.31	+	11064.9i	0.203848	+	0.353075i
$995$	12292.7	+	21291.5i	0.391662	+	0.678378i
$996$		0			0
$997$	−20771.5	+	35977.4i	−0.659821	+	1.14284i	0.320841	+	0.947133i	$0.396034\pi$
$997$	−20771.5	+	35977.4i	−0.659821	+	1.14284i	−0.980662	+	0.195710i	$0.937299\pi$
$998$	48763.3			1.54667
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	405.4.e.x.136.5		12
3.2	odd	2		405.4.e.w.136.2		12
9.2	odd	6		405.4.a.l.1.5	yes	6
9.4	even	3	inner	405.4.e.x.271.5		12
9.5	odd	6		405.4.e.w.271.2		12
9.7	even	3		405.4.a.k.1.2	✓	6
45.29	odd	6		2025.4.a.y.1.2		6
45.34	even	6		2025.4.a.z.1.5		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
405.4.a.k.1.2	✓	6	9.7	even	3
405.4.a.l.1.5	yes	6	9.2	odd	6
405.4.e.w.136.2		12	3.2	odd	2
405.4.e.w.271.2		12	9.5	odd	6
405.4.e.x.136.5		12	1.1	even	1	trivial
405.4.e.x.271.5		12	9.4	even	3	inner
2025.4.a.y.1.2		6	45.29	odd	6
2025.4.a.z.1.5		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)

\(f(q)\)	\(=\)	\(q+(2.26722 - 3.92694i) q^{2} +(-6.28058 - 10.8783i) q^{4} +(2.50000 + 4.33013i) q^{5} +(1.31809 - 2.28300i) q^{7} -20.6823 q^{8} +O(q^{10})\)	\(q+(2.26722 - 3.92694i) q^{2} +(-6.28058 - 10.8783i) q^{4} +(2.50000 + 4.33013i) q^{5} +(1.31809 - 2.28300i) q^{7} -20.6823 q^{8} +22.6722 q^{10} +(10.4655 - 18.1268i) q^{11} +(-30.4725 - 52.7800i) q^{13} +(-5.97680 - 10.3521i) q^{14} +(3.35333 - 5.80814i) q^{16} -86.8178 q^{17} +41.8063 q^{19} +(31.4029 - 54.3914i) q^{20} +(-47.4552 - 82.1949i) q^{22} +(-48.6593 - 84.2804i) q^{23} +(-12.5000 + 21.6506i) q^{25} -276.352 q^{26} -33.1135 q^{28} +(78.5350 - 136.027i) q^{29} +(-47.6980 - 82.6154i) q^{31} +(-97.9346 - 169.628i) q^{32} +(-196.835 + 340.928i) q^{34} +13.1809 q^{35} -160.833 q^{37} +(94.7841 - 164.171i) q^{38} +(-51.7057 - 89.5569i) q^{40} +(-116.595 - 201.948i) q^{41} +(-243.847 + 422.355i) q^{43} -262.918 q^{44} -441.285 q^{46} +(-12.1540 + 21.0513i) q^{47} +(168.025 + 291.028i) q^{49} +(56.6805 + 98.1735i) q^{50} +(-382.770 + 662.977i) q^{52} +709.828 q^{53} +104.655 q^{55} +(-27.2611 + 47.2176i) q^{56} +(-356.112 - 616.805i) q^{58} +(95.9990 + 166.275i) q^{59} +(372.317 - 644.871i) q^{61} -432.568 q^{62} -834.504 q^{64} +(152.363 - 263.900i) q^{65} +(411.783 + 713.230i) q^{67} +(545.266 + 944.428i) q^{68} +(29.8840 - 51.7606i) q^{70} -1068.85 q^{71} -132.416 q^{73} +(-364.645 + 631.583i) q^{74} +(-262.568 - 454.780i) q^{76} +(-27.5890 - 47.7855i) q^{77} +(352.288 - 610.181i) q^{79} +33.5333 q^{80} -1057.38 q^{82} +(709.881 - 1229.55i) q^{83} +(-217.044 - 375.932i) q^{85} +(1105.71 + 1915.14i) q^{86} +(-216.451 + 374.903i) q^{88} +401.847 q^{89} -160.662 q^{91} +(-611.217 + 1058.66i) q^{92} +(55.1114 + 95.4558i) q^{94} +(104.516 + 181.027i) q^{95} +(-265.440 + 459.756i) q^{97} +1523.80 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 4 q^{2} - 34 q^{4} + 30 q^{5} - 40 q^{7} - 132 q^{8}+O(q^{10}) \) 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

L-functions

Modular forms

Varieties

Fields

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