LMFDB - Embedded newform 504.4.c.e.253.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [504,4,Mod(253,504)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(504, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1, 0, 0]))

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

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

chi := DirichletCharacter("504.253");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 504 = 2^{3} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	504.c (of order $2$, degree $1$, 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:	$29.7369626429$
Analytic rank:	$0$
Dimension:	$20$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 2 x^{19} - 5 x^{18} - 26 x^{17} + 122 x^{16} + 124 x^{15} - 276 x^{14} - 1376 x^{13} + \cdots + 1073741824 $ x^20 - 2x^19 - 5x^18 - 26x^17 + 122x^16 + 124x^15 - 276x^14 - 1376x^13 - 3344x^12 + 15424x^11 - 1920x^10 + 123392x^9 - 214016x^8 - 704512x^7 - 1130496x^6 + 4063232x^5 + 31981568x^4 - 54525952x^3 - 83886080x^2 - 268435456*x + 1073741824
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 2^{31}\cdot 3^{10} $
Twist minimal:	no (minimal twist has level 168)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			253.14
Root			$2.78865 - 0.472666i$ of defining polynomial
Character	$\chi$	$=$	504.253
Dual form			504.4.c.e.253.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.472666 + 2.78865i) q^{2} +(-7.55317 + 2.63620i) q^{4} -8.98099i q^{5} -7.00000 q^{7} +(-10.9216 - 19.8171i) q^{8} +O(q^{10})$	\(q+(0.472666 + 2.78865i) q^{2} +(-7.55317 + 2.63620i) q^{4} -8.98099i q^{5} -7.00000 q^{7} +(-10.9216 - 19.8171i) q^{8} +(25.0449 - 4.24501i) q^{10} +58.9468i q^{11} -54.8428i q^{13} +(-3.30866 - 19.5206i) q^{14} +(50.1009 - 39.8234i) q^{16} +111.971 q^{17} -38.6067i q^{19} +(23.6757 + 67.8350i) q^{20} +(-164.382 + 27.8621i) q^{22} -112.146 q^{23} +44.3418 q^{25} +(152.937 - 25.9223i) q^{26} +(52.8722 - 18.4534i) q^{28} +234.402i q^{29} -180.033 q^{31} +(134.735 + 120.891i) q^{32} +(52.9249 + 312.248i) q^{34} +62.8669i q^{35} +131.345i q^{37} +(107.661 - 18.2480i) q^{38} +(-177.978 + 98.0866i) q^{40} +500.500 q^{41} +495.083i q^{43} +(-155.396 - 445.235i) q^{44} +(-53.0077 - 312.737i) q^{46} -111.705 q^{47} +49.0000 q^{49} +(20.9588 + 123.654i) q^{50} +(144.577 + 414.237i) q^{52} +696.410i q^{53} +529.400 q^{55} +(76.4511 + 138.720i) q^{56} +(-653.666 + 110.794i) q^{58} +407.787i q^{59} -124.411i q^{61} +(-85.0952 - 502.048i) q^{62} +(-273.438 + 432.869i) q^{64} -492.542 q^{65} -143.848i q^{67} +(-845.736 + 295.178i) q^{68} +(-175.314 + 29.7151i) q^{70} -251.341 q^{71} -709.691 q^{73} +(-366.276 + 62.0823i) q^{74} +(101.775 + 291.603i) q^{76} -412.627i q^{77} +865.909 q^{79} +(-357.654 - 449.956i) q^{80} +(236.569 + 1395.72i) q^{82} -57.3886i q^{83} -1005.61i q^{85} +(-1380.61 + 234.009i) q^{86} +(1168.16 - 643.792i) q^{88} +765.447 q^{89} +383.899i q^{91} +(847.060 - 295.640i) q^{92} +(-52.7990 - 311.506i) q^{94} -346.726 q^{95} +370.748 q^{97} +(23.1606 + 136.644i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 4 q^{2} - 14 q^{4} - 140 q^{7} - 10 q^{8}+O(q^{10}) $ 20 * q - 4 * q^2 - 14 * q^4 - 140 * q^7 - 10 * q^8	$ 20 q - 4 q^{2} - 14 q^{4} - 140 q^{7} - 10 q^{8} - 84 q^{10} + 28 q^{14} - 134 q^{16} + 52 q^{17} + 8 q^{20} + 8 q^{22} + 244 q^{23} - 844 q^{25} + 332 q^{26} + 98 q^{28} + 264 q^{31} + 46 q^{32} - 612 q^{34} - 884 q^{38} - 964 q^{40} + 236 q^{41} - 576 q^{44} + 1356 q^{46} + 980 q^{49} + 2456 q^{50} + 1492 q^{52} + 72 q^{55} + 70 q^{56} - 1404 q^{58} - 4964 q^{62} - 1670 q^{64} - 1744 q^{65} - 3408 q^{68} + 588 q^{70} + 636 q^{71} - 2784 q^{73} + 4916 q^{74} + 2664 q^{76} + 2872 q^{79} + 1764 q^{80} + 2628 q^{82} - 3328 q^{86} - 2348 q^{88} - 220 q^{89} - 2580 q^{92} - 1704 q^{94} + 1240 q^{95} + 4400 q^{97} - 196 q^{98}+O(q^{100}) $ 20 * q - 4 * q^2 - 14 * q^4 - 140 * q^7 - 10 * q^8 - 84 * q^10 + 28 * q^14 - 134 * q^16 + 52 * q^17 + 8 * q^20 + 8 * q^22 + 244 * q^23 - 844 * q^25 + 332 * q^26 + 98 * q^28 + 264 * q^31 + 46 * q^32 - 612 * q^34 - 884 * q^38 - 964 * q^40 + 236 * q^41 - 576 * q^44 + 1356 * q^46 + 980 * q^49 + 2456 * q^50 + 1492 * q^52 + 72 * q^55 + 70 * q^56 - 1404 * q^58 - 4964 * q^62 - 1670 * q^64 - 1744 * q^65 - 3408 * q^68 + 588 * q^70 + 636 * q^71 - 2784 * q^73 + 4916 * q^74 + 2664 * q^76 + 2872 * q^79 + 1764 * q^80 + 2628 * q^82 - 3328 * q^86 - 2348 * q^88 - 220 * q^89 - 2580 * q^92 - 1704 * q^94 + 1240 * q^95 + 4400 * q^97 - 196 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/504\mathbb{Z}\right)^\times$.

$n$	$73$	$127$	$253$	$281$
$\chi(n)$	$1$	$1$	$-1$	$1$

Coefficient data

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

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

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

$2$	0.472666	+	2.78865i	0.167113	+	0.985938i
$2$	0.472666	+	2.78865i	0.167113	+	0.985938i
$3$		0			0
$3$		0			0
$4$	−7.55317	+	2.63620i	−0.944147	+	0.329525i
$5$		−	8.98099i		−	0.803284i	−0.915797	−	0.401642i	$-0.868440\pi$
$5$		−	8.98099i		−	0.803284i	0.915797	−	0.401642i	$-0.131560\pi$
$6$		0			0
$7$	−7.00000			−0.377964
$7$	−7.00000			−0.377964
$8$	−10.9216	−	19.8171i	−0.482670	−	0.875802i
$9$		0			0
$10$	25.0449	−	4.24501i	0.791988	−	0.134239i
$11$			58.9468i			1.61574i	0.589362	+	0.807869i	$0.299379\pi$
$11$			58.9468i			1.61574i	−0.589362	+	0.807869i	$0.700621\pi$
$12$		0			0
$13$		−	54.8428i		−	1.17005i	−0.811015	−	0.585025i	$-0.801085\pi$
$13$		−	54.8428i		−	1.17005i	0.811015	−	0.585025i	$-0.198915\pi$
$14$	−3.30866	−	19.5206i	−0.0631626	−	0.372649i
$15$		0			0
$16$	50.1009	−	39.8234i	0.782826	−	0.622240i
$17$	111.971			1.59747			0.798734	−	0.601684i	$-0.205503\pi$
$17$	111.971			1.59747			0.798734	+	0.601684i	$0.205503\pi$
$18$		0			0
$19$		−	38.6067i		−	0.466157i	−0.972458	−	0.233078i	$-0.925120\pi$
$19$		−	38.6067i		−	0.466157i	0.972458	−	0.233078i	$-0.0748798\pi$
$20$	23.6757	+	67.8350i	0.264703	+	0.758418i
$21$		0			0
$22$	−164.382	+	27.8621i	−1.59302	+	0.270010i
$23$	−112.146			−1.01670			−0.508350	−	0.861151i	$-0.669744\pi$
$23$	−112.146			−1.01670			−0.508350	+	0.861151i	$0.669744\pi$
$24$		0			0
$25$	44.3418			0.354734
$26$	152.937	−	25.9223i	1.15360	−	0.195530i
$27$		0			0
$28$	52.8722	−	18.4534i	0.356854	−	0.124549i
$29$			234.402i			1.50094i	0.660902	+	0.750472i	$0.270174\pi$
$29$			234.402i			1.50094i	−0.660902	+	0.750472i	$0.729826\pi$
$30$		0			0
$31$	−180.033			−1.04306			−0.521529	−	0.853234i	$-0.674638\pi$
$31$	−180.033			−1.04306			−0.521529	+	0.853234i	$0.674638\pi$
$32$	134.735	+	120.891i	0.744311	+	0.667834i
$33$		0			0
$34$	52.9249	+	312.248i	0.266957	+	1.57500i
$35$			62.8669i			0.303613i
$36$		0			0
$37$			131.345i			0.583594i	0.956480	+	0.291797i	$0.0942532\pi$
$37$			131.345i			0.583594i	−0.956480	+	0.291797i	$0.905747\pi$
$38$	107.661	−	18.2480i	0.459601	−	0.0779006i
$39$		0			0
$40$	−177.978	+	98.0866i	−0.703518	+	0.387721i
$41$	500.500			1.90646			0.953231	−	0.302242i	$-0.0977350\pi$
$41$	500.500			1.90646			0.953231	+	0.302242i	$0.0977350\pi$
$42$		0			0
$43$			495.083i			1.75580i	0.478844	+	0.877900i	$0.341056\pi$
$43$			495.083i			1.75580i	−0.478844	+	0.877900i	$0.658944\pi$
$44$	−155.396	−	445.235i	−0.532426	−	1.52549i
$45$		0			0
$46$	−53.0077	−	312.737i	−0.169903	−	1.00240i
$47$	−111.705			−0.346677			−0.173338	−	0.984862i	$-0.555455\pi$
$47$	−111.705			−0.346677			−0.173338	+	0.984862i	$0.555455\pi$
$48$		0			0
$49$	49.0000			0.142857
$50$	20.9588	+	123.654i	0.0592806	+	0.349746i
$51$		0			0
$52$	144.577	+	414.237i	0.385561	+	1.10470i
$53$			696.410i			1.80489i	0.430804	+	0.902445i	$0.358230\pi$
$53$			696.410i			1.80489i	−0.430804	+	0.902445i	$0.641770\pi$
$54$		0			0
$55$	529.400			1.29790
$56$	76.4511	+	138.720i	0.182432	+	0.331022i
$57$		0			0
$58$	−653.666	+	110.794i	−1.47984	+	0.250827i
$59$			407.787i			0.899819i	0.893074	+	0.449909i	$0.148544\pi$
$59$			407.787i			0.899819i	−0.893074	+	0.449909i	$0.851456\pi$
$60$		0			0
$61$		−	124.411i		−	0.261134i	−0.991440	−	0.130567i	$-0.958320\pi$
$61$		−	124.411i		−	0.261134i	0.991440	−	0.130567i	$-0.0416797\pi$
$62$	−85.0952	−	502.048i	−0.174308	−	1.02839i
$63$		0			0
$64$	−273.438	+	432.869i	−0.534059	+	0.845447i
$65$	−492.542			−0.939882
$66$		0			0
$67$		−	143.848i		−	0.262296i	−0.991363	−	0.131148i	$-0.958134\pi$
$67$		−	143.848i		−	0.262296i	0.991363	−	0.131148i	$-0.0418663\pi$
$68$	−845.736	+	295.178i	−1.50824	+	0.526406i
$69$		0			0
$70$	−175.314	+	29.7151i	−0.299343	+	0.0507376i
$71$	−251.341			−0.420122			−0.210061	−	0.977688i	$-0.567366\pi$
$71$	−251.341			−0.420122			−0.210061	+	0.977688i	$0.567366\pi$
$72$		0			0
$73$	−709.691			−1.13785			−0.568925	−	0.822390i	$-0.692640\pi$
$73$	−709.691			−1.13785			−0.568925	+	0.822390i	$0.692640\pi$
$74$	−366.276	+	62.0823i	−0.575387	+	0.0975259i
$75$		0			0
$76$	101.775	+	291.603i	0.153610	+	0.440120i
$77$		−	412.627i		−	0.610691i
$78$		0			0
$79$	865.909			1.23319			0.616597	−	0.787279i	$-0.288511\pi$
$79$	865.909			1.23319			0.616597	+	0.787279i	$0.288511\pi$
$80$	−357.654	−	449.956i	−0.499836	−	0.628832i
$81$		0			0
$82$	236.569	+	1395.72i	0.318594	+	1.87965i
$83$		−	57.3886i		−	0.0758942i	−0.999280	−	0.0379471i	$-0.987918\pi$
$83$		−	57.3886i		−	0.0758942i	0.999280	−	0.0379471i	$-0.0120818\pi$
$84$		0			0
$85$		−	1005.61i		−	1.28322i
$86$	−1380.61	+	234.009i	−1.73111	+	0.293416i
$87$		0			0
$88$	1168.16	−	643.792i	1.41507	−	0.779869i
$89$	765.447			0.911654			0.455827	−	0.890068i	$-0.349344\pi$
$89$	765.447			0.911654			0.455827	+	0.890068i	$0.349344\pi$
$90$		0			0
$91$			383.899i			0.442237i
$92$	847.060	−	295.640i	0.959914	−	0.335028i
$93$		0			0
$94$	−52.7990	−	311.506i	−0.0579340	−	0.341802i
$95$	−346.726			−0.374456
$96$		0			0
$97$	370.748			0.388080			0.194040	−	0.980994i	$-0.437841\pi$
$97$	370.748			0.388080			0.194040	+	0.980994i	$0.437841\pi$
$98$	23.1606	+	136.644i	0.0238732	+	0.140848i
$99$		0			0
$100$	−334.921	+	116.894i	−0.334921	+	0.116894i
$101$		−	621.424i		−	0.612218i	−0.951997	−	0.306109i	$-0.900973\pi$
$101$		−	621.424i		−	0.612218i	0.951997	−	0.306109i	$-0.0990272\pi$
$102$		0			0
$103$	433.871			0.415054			0.207527	−	0.978229i	$-0.433458\pi$
$103$	433.871			0.415054			0.207527	+	0.978229i	$0.433458\pi$
$104$	−1086.83	+	598.970i	−1.02473	+	0.564748i
$105$		0			0
$106$	−1942.04	+	329.169i	−1.77951	+	0.301620i
$107$			926.967i			0.837508i	0.908100	+	0.418754i	$0.137533\pi$
$107$			926.967i			0.837508i	−0.908100	+	0.418754i	$0.862467\pi$
$108$		0			0
$109$			1423.90i			1.25123i	0.780131	+	0.625617i	$0.215153\pi$
$109$			1423.90i			1.25123i	−0.780131	+	0.625617i	$0.784847\pi$
$110$	250.229	+	1476.31i	0.216895	+	1.27965i
$111$		0			0
$112$	−350.706	+	278.764i	−0.295880	+	0.235185i
$113$	2027.39			1.68779			0.843897	−	0.536505i	$-0.180256\pi$
$113$	2027.39			1.68779			0.843897	+	0.536505i	$0.180256\pi$
$114$		0			0
$115$			1007.18i			0.816699i
$116$	−617.931	−	1770.48i	−0.494599	−	1.41711i
$117$		0			0
$118$	−1137.18	+	192.747i	−0.887165	+	0.150371i
$119$	−783.797			−0.603786
$120$		0			0
$121$	−2143.72			−1.61061
$122$	346.938	−	58.8047i	0.257461	−	0.0436387i
$123$		0			0
$124$	1359.82	−	474.602i	0.984800	−	0.343714i
$125$		−	1520.86i		−	1.08824i
$126$		0			0
$127$	−482.735			−0.337290			−0.168645	−	0.985677i	$-0.553939\pi$
$127$	−482.735			−0.337290			−0.168645	+	0.985677i	$0.553939\pi$
$128$	−1336.37	−	557.922i	−0.922806	−	0.385264i
$129$		0			0
$130$	−232.808	−	1373.53i	−0.157066	−	0.926666i
$131$		−	1448.68i		−	0.966193i	−0.875567	−	0.483097i	$-0.839512\pi$
$131$		−	1448.68i		−	0.966193i	0.875567	−	0.483097i	$-0.160488\pi$
$132$		0			0
$133$			270.247i			0.176191i
$134$	401.142	−	67.9920i	0.258608	−	0.0438330i
$135$		0			0
$136$	−1222.90	−	2218.94i	−0.771050	−	1.39907i
$137$	1043.62			0.650823			0.325412	−	0.945572i	$-0.394497\pi$
$137$	1043.62			0.650823			0.325412	+	0.945572i	$0.394497\pi$
$138$		0			0
$139$		−	630.925i		−	0.384995i	−0.981297	−	0.192498i	$-0.938341\pi$
$139$		−	630.925i		−	0.384995i	0.981297	−	0.192498i	$-0.0616588\pi$
$140$	−165.730	−	474.845i	−0.100048	−	0.286655i
$141$		0			0
$142$	−118.800	−	700.903i	−0.0702077	−	0.414214i
$143$	3232.80			1.89049
$144$		0			0
$145$	2105.16			1.20568
$146$	−335.447	−	1979.08i	−0.190149	−	1.12185i
$147$		0			0
$148$	−346.252	−	992.071i	−0.192309	−	0.550998i
$149$			562.011i			0.309005i	0.987992	+	0.154502i	$0.0493775\pi$
$149$			562.011i			0.309005i	−0.987992	+	0.154502i	$0.950623\pi$
$150$		0			0
$151$	−466.027			−0.251157			−0.125579	−	0.992084i	$-0.540079\pi$
$151$	−466.027			−0.251157			−0.125579	+	0.992084i	$0.540079\pi$
$152$	−765.074	+	421.646i	−0.408261	+	0.225000i
$153$		0			0
$154$	1150.67	−	195.035i	0.602104	−	0.102054i
$155$			1616.87i			0.837872i
$156$		0			0
$157$			314.250i			0.159745i	0.996805	+	0.0798723i	$0.0254513\pi$
$157$			314.250i			0.159745i	−0.996805	+	0.0798723i	$0.974549\pi$
$158$	409.285	+	2414.72i	0.206082	+	1.21585i
$159$		0			0
$160$	1085.72	−	1210.05i	0.536460	−	0.597893i
$161$	785.023			0.384276
$162$		0			0
$163$			1926.67i			0.925820i	0.886405	+	0.462910i	$0.153195\pi$
$163$			1926.67i			0.925820i	−0.886405	+	0.462910i	$0.846805\pi$
$164$	−3780.36	+	1319.42i	−1.79998	+	0.628228i
$165$		0			0
$166$	160.037	−	27.1256i	0.0748270	−	0.0126829i
$167$	−1454.39			−0.673917			−0.336958	−	0.941520i	$-0.609398\pi$
$167$	−1454.39			−0.673917			−0.336958	+	0.941520i	$0.609398\pi$
$168$		0			0
$169$	−810.727			−0.369016
$170$	2804.30	−	475.318i	1.26518	−	0.214442i
$171$		0			0
$172$	−1305.14	−	3739.45i	−0.578581	−	1.65773i
$173$			3142.64i			1.38110i	0.723284	+	0.690550i	$0.242632\pi$
$173$			3142.64i			1.38110i	−0.723284	+	0.690550i	$0.757368\pi$
$174$		0			0
$175$	−310.392			−0.134077
$176$	2347.46	+	2953.28i	1.00538	+	1.26484i
$177$		0			0
$178$	361.801	+	2134.57i	0.152349	+	0.898834i
$179$		−	608.194i		−	0.253958i	−0.991905	−	0.126979i	$-0.959472\pi$
$179$		−	608.194i		−	0.253958i	0.991905	−	0.126979i	$-0.0405281\pi$
$180$		0			0
$181$		−	3075.47i		−	1.26297i	−0.775387	−	0.631486i	$-0.782445\pi$
$181$		−	3075.47i		−	1.26297i	0.775387	−	0.631486i	$-0.217555\pi$
$182$	−1070.56	+	181.456i	−0.436018	+	0.0739034i
$183$		0			0
$184$	1224.81	+	2222.42i	0.490731	+	0.890428i
$185$	1179.61			0.468792
$186$		0			0
$187$			6600.33i			2.58109i
$188$	843.725	−	294.476i	0.327314	−	0.114239i
$189$		0			0
$190$	−163.886	−	966.899i	−0.0625764	−	0.369191i
$191$	222.395			0.0842509			0.0421255	−	0.999112i	$-0.486587\pi$
$191$	222.395			0.0842509			0.0421255	+	0.999112i	$0.486587\pi$
$192$		0			0
$193$	2275.04			0.848502			0.424251	−	0.905545i	$-0.360537\pi$
$193$	2275.04			0.848502			0.424251	+	0.905545i	$0.360537\pi$
$194$	175.240	+	1033.89i	0.0648531	+	0.382623i
$195$		0			0
$196$	−370.106	+	129.174i	−0.134878	+	0.0470750i
$197$			140.119i			0.0506754i	0.999679	+	0.0253377i	$0.00806610\pi$
$197$			140.119i			0.0506754i	−0.999679	+	0.0253377i	$0.991934\pi$
$198$		0			0
$199$	1003.14			0.357342			0.178671	−	0.983909i	$-0.442820\pi$
$199$	1003.14			0.357342			0.178671	+	0.983909i	$0.442820\pi$
$200$	−484.282	−	878.727i	−0.171220	−	0.310677i
$201$		0			0
$202$	1732.94	−	293.726i	0.603609	−	0.102309i
$203$		−	1640.81i		−	0.567303i
$204$		0			0
$205$		−	4494.99i		−	1.53143i
$206$	205.076	+	1209.92i	0.0693608	+	0.409218i
$207$		0			0
$208$	−2184.02	−	2747.67i	−0.728052	−	0.915945i
$209$	2275.74			0.753187
$210$		0			0
$211$		−	2462.02i		−	0.803283i	−0.915797	−	0.401641i	$-0.868440\pi$
$211$		−	2462.02i		−	0.803283i	0.915797	−	0.401641i	$-0.131560\pi$
$212$	−1835.88	−	5260.10i	−0.594757	−	1.70408i
$213$		0			0
$214$	−2584.99	+	438.146i	−0.825730	+	0.139958i
$215$	4446.33			1.41041
$216$		0			0
$217$	1260.23			0.394239
$218$	−3970.75	+	673.027i	−1.23364	+	0.209097i
$219$		0			0
$220$	−3998.65	+	1395.61i	−1.22541	+	0.427690i
$221$		−	6140.80i		−	1.86912i
$222$		0			0
$223$	6458.67			1.93948			0.969741	−	0.244138i	$-0.0785050\pi$
$223$	6458.67			1.93948			0.969741	+	0.244138i	$0.0785050\pi$
$224$	−943.142	−	846.236i	−0.281323	−	0.252417i
$225$		0			0
$226$	958.278	+	5653.69i	0.282052	+	1.66406i
$227$			1776.16i			0.519329i	0.965699	+	0.259664i	$0.0836120\pi$
$227$			1776.16i			0.519329i	−0.965699	+	0.259664i	$0.916388\pi$
$228$		0			0
$229$			2046.20i			0.590466i	0.955425	+	0.295233i	$0.0953972\pi$
$229$			2046.20i			0.590466i	−0.955425	+	0.295233i	$0.904603\pi$
$230$	−2808.69	+	476.062i	−0.805215	+	0.136481i
$231$		0			0
$232$	4645.18	−	2560.04i	1.31453	−	0.724461i
$233$	−5827.32			−1.63846			−0.819229	−	0.573467i	$-0.805598\pi$
$233$	−5827.32			−1.63846			−0.819229	+	0.573467i	$0.805598\pi$
$234$		0			0
$235$			1003.22i			0.278480i
$236$	−1075.01	−	3080.08i	−0.296513	−	0.849561i
$237$		0			0
$238$	−370.474	−	2185.74i	−0.100900	−	0.595296i
$239$	5894.12			1.59523			0.797613	−	0.603169i	$-0.206096\pi$
$239$	5894.12			1.59523			0.797613	+	0.603169i	$0.206096\pi$
$240$		0			0
$241$	−2057.48			−0.549934			−0.274967	−	0.961454i	$-0.588667\pi$
$241$	−2057.48			−0.549934			−0.274967	+	0.961454i	$0.588667\pi$
$242$	−1013.26	−	5978.09i	−0.269153	−	1.58796i
$243$		0			0
$244$	327.972	+	939.695i	0.0860501	+	0.246548i
$245$		−	440.069i		−	0.114755i
$246$		0			0
$247$	−2117.30			−0.545426
$248$	1966.24	+	3567.73i	0.503453	+	0.913512i
$249$		0			0
$250$	4241.14	−	718.857i	1.07293	−	0.181858i
$251$			5593.16i			1.40652i	0.710932	+	0.703261i	$0.248273\pi$
$251$			5593.16i			1.40652i	−0.710932	+	0.703261i	$0.751727\pi$
$252$		0			0
$253$		−	6610.65i		−	1.64272i
$254$	−228.172	−	1346.18i	−0.0563654	−	0.332547i
$255$		0			0
$256$	924.195	−	3990.37i	0.225634	−	0.974212i
$257$	−1528.67			−0.371035			−0.185517	−	0.982641i	$-0.559396\pi$
$257$	−1528.67			−0.371035			−0.185517	+	0.982641i	$0.559396\pi$
$258$		0			0
$259$		−	919.415i		−	0.220578i
$260$	3720.26	−	1298.44i	0.887387	−	0.309715i
$261$		0			0
$262$	4039.85	−	684.739i	0.952607	−	0.161463i
$263$	2983.60			0.699530			0.349765	−	0.936837i	$-0.386261\pi$
$263$	2983.60			0.699530			0.349765	+	0.936837i	$0.386261\pi$
$264$		0			0
$265$	6254.45			1.44984
$266$	−753.624	+	127.736i	−0.173713	+	0.0294437i
$267$		0			0
$268$	379.212	+	1086.51i	0.0864332	+	0.247646i
$269$		−	5552.68i		−	1.25856i	−0.777178	−	0.629281i	$-0.783350\pi$
$269$		−	5552.68i		−	1.25856i	0.777178	−	0.629281i	$-0.216650\pi$
$270$		0			0
$271$	−4238.12			−0.949990			−0.474995	−	0.879988i	$-0.657550\pi$
$271$	−4238.12			−0.949990			−0.474995	+	0.879988i	$0.657550\pi$
$272$	5609.84	−	4459.06i	1.25054	−	0.994009i
$273$		0			0
$274$	493.285	+	2910.30i	0.108761	+	0.641671i
$275$			2613.80i			0.573157i
$276$		0			0
$277$		−	3761.88i		−	0.815990i	−0.912984	−	0.407995i	$-0.866228\pi$
$277$		−	3761.88i		−	0.815990i	0.912984	−	0.407995i	$-0.133772\pi$
$278$	1759.43	−	298.217i	0.379582	−	0.0643376i
$279$		0			0
$280$	1245.84	−	686.606i	0.265905	−	0.146545i
$281$	−1343.51			−0.285221			−0.142610	−	0.989779i	$-0.545550\pi$
$281$	−1343.51			−0.285221			−0.142610	+	0.989779i	$0.545550\pi$
$282$		0			0
$283$			2863.45i			0.601463i	0.953709	+	0.300732i	$0.0972309\pi$
$283$			2863.45i			0.601463i	−0.953709	+	0.300732i	$0.902769\pi$
$284$	1898.42	−	662.586i	0.396657	−	0.138441i
$285$		0			0
$286$	1528.04	+	9015.16i	0.315925	+	1.86391i
$287$	−3503.50			−0.720575
$288$		0			0
$289$	7624.50			1.55190
$290$	995.039	+	5870.57i	0.201485	+	1.18873i
$291$		0			0
$292$	5360.42	−	1870.89i	1.07430	−	0.374950i
$293$			3539.23i			0.705680i	0.935684	+	0.352840i	$0.114784\pi$
$293$			3539.23i			0.705680i	−0.935684	+	0.352840i	$0.885216\pi$
$294$		0			0
$295$	3662.33			0.722810
$296$	2602.88	−	1434.49i	0.511113	−	0.281683i
$297$		0			0
$298$	−1567.25	+	265.643i	−0.304660	+	0.0516386i
$299$			6150.41i			1.18959i
$300$		0			0
$301$		−	3465.58i		−	0.663630i
$302$	−220.275	−	1299.59i	−0.0419716	−	0.247626i
$303$		0			0
$304$	−1537.45	−	1934.23i	−0.290061	−	0.364920i
$305$	−1117.33			−0.209765
$306$		0			0
$307$		−	3008.84i		−	0.559360i	−0.960093	−	0.279680i	$-0.909772\pi$
$307$		−	3008.84i		−	0.559360i	0.960093	−	0.279680i	$-0.0902283\pi$
$308$	1087.77	+	3116.65i	0.201238	+	0.576582i
$309$		0			0
$310$	−4508.89	+	764.240i	−0.826090	+	0.140019i
$311$	−3951.63			−0.720503			−0.360252	−	0.932855i	$-0.617309\pi$
$311$	−3951.63			−0.720503			−0.360252	+	0.932855i	$0.617309\pi$
$312$		0			0
$313$	−262.745			−0.0474479			−0.0237240	−	0.999719i	$-0.507552\pi$
$313$	−262.745			−0.0474479			−0.0237240	+	0.999719i	$0.507552\pi$
$314$	−876.336	+	148.535i	−0.157498	+	0.0266954i
$315$		0			0
$316$	−6540.36	+	2282.71i	−1.16432	+	0.406369i
$317$			5155.26i			0.913401i	0.889621	+	0.456700i	$0.150969\pi$
$317$			5155.26i			0.913401i	−0.889621	+	0.456700i	$0.849031\pi$
$318$		0			0
$319$	−13817.2			−2.42513
$320$	3887.59	+	2455.75i	0.679135	+	0.429001i
$321$		0			0
$322$	371.054	+	2189.16i	0.0642174	+	0.378873i
$323$		−	4322.83i		−	0.744670i
$324$		0			0
$325$		−	2431.83i		−	0.415057i
$326$	−5372.82	+	910.673i	−0.912801	+	0.154716i
$327$		0			0
$328$	−5466.25	−	9918.48i	−0.920193	−	1.66968i
$329$	781.933			0.131031
$330$		0			0
$331$		−	6802.50i		−	1.12961i	−0.825226	−	0.564803i	$-0.808952\pi$
$331$		−	6802.50i		−	1.12961i	0.825226	−	0.564803i	$-0.191048\pi$
$332$	151.288	+	433.466i	0.0250091	+	0.0716553i
$333$		0			0
$334$	−687.440	−	4055.79i	−0.112620	−	0.664440i
$335$	−1291.90			−0.210698
$336$		0			0
$337$	433.772			0.0701159			0.0350580	−	0.999385i	$-0.488838\pi$
$337$	433.772			0.0701159			0.0350580	+	0.999385i	$0.488838\pi$
$338$	−383.203	−	2260.84i	−0.0616672	−	0.363826i
$339$		0			0
$340$	2650.99	+	7595.55i	0.422854	+	1.21155i
$341$		−	10612.3i		−	1.68531i
$342$		0			0
$343$	−343.000			−0.0539949
$344$	9811.12	−	5407.09i	1.53773	−	0.847473i
$345$		0			0
$346$	−8763.73	+	1485.42i	−1.36168	+	0.230799i
$347$			4388.13i			0.678867i	0.940630	+	0.339434i	$0.110235\pi$
$347$			4388.13i			0.678867i	−0.940630	+	0.339434i	$0.889765\pi$
$348$		0			0
$349$			1270.81i			0.194914i	0.995240	+	0.0974571i	$0.0310709\pi$
$349$			1270.81i			0.194914i	−0.995240	+	0.0974571i	$0.968929\pi$
$350$	−146.712	−	865.577i	−0.0224059	−	0.132192i
$351$		0			0
$352$	−7126.12	+	7942.17i	−1.07904	+	1.20261i
$353$	−12777.9			−1.92663			−0.963315	−	0.268375i	$-0.913514\pi$
$353$	−12777.9			−1.92663			−0.963315	+	0.268375i	$0.913514\pi$
$354$		0			0
$355$			2257.29i			0.337478i
$356$	−5781.55	+	2017.87i	−0.860735	+	0.300413i
$357$		0			0
$358$	1696.04	−	287.472i	0.250387	−	0.0424396i
$359$	−6124.58			−0.900399			−0.450199	−	0.892928i	$-0.648647\pi$
$359$	−6124.58			−0.900399			−0.450199	+	0.892928i	$0.648647\pi$
$360$		0			0
$361$	5368.53			0.782698
$362$	8576.43	−	1453.67i	1.24521	−	0.211059i
$363$		0			0
$364$	−1012.04	−	2899.66i	−0.145728	−	0.417537i
$365$			6373.73i			0.914017i
$366$		0			0
$367$	−3190.01			−0.453725			−0.226863	−	0.973927i	$-0.572847\pi$
$367$	−3190.01			−0.453725			−0.226863	+	0.973927i	$0.572847\pi$
$368$	−5618.62	+	4466.04i	−0.795899	+	0.632632i
$369$		0			0
$370$	557.560	+	3289.52i	0.0783410	+	0.462200i
$371$		−	4874.87i		−	0.682185i
$372$		0			0
$373$		−	8037.61i		−	1.11574i	−0.829928	−	0.557871i	$-0.811618\pi$
$373$		−	8037.61i		−	1.11574i	0.829928	−	0.557871i	$-0.188382\pi$
$374$	−18406.0	+	3119.75i	−2.54479	+	0.431333i
$375$		0			0
$376$	1219.99	+	2213.67i	0.167331	+	0.303620i
$377$	12855.3			1.75618
$378$		0			0
$379$			3762.31i			0.509913i	0.966953	+	0.254956i	$0.0820611\pi$
$379$			3762.31i			0.509913i	−0.966953	+	0.254956i	$0.917939\pi$
$380$	2618.88	−	914.040i	0.353542	−	0.123393i
$381$		0			0
$382$	105.118	+	620.182i	0.0140794	+	0.0830662i
$383$	−9479.32			−1.26468			−0.632338	−	0.774693i	$-0.717904\pi$
$383$	−9479.32			−1.26468			−0.632338	+	0.774693i	$0.717904\pi$
$384$		0			0
$385$	−3705.80			−0.490559
$386$	1075.33	+	6344.30i	0.141795	+	0.836571i
$387$		0			0
$388$	−2800.33	+	977.367i	−0.366405	+	0.127882i
$389$		−	6672.27i		−	0.869660i	−0.900513	−	0.434830i	$-0.856808\pi$
$389$		−	6672.27i		−	0.869660i	0.900513	−	0.434830i	$-0.143192\pi$
$390$		0			0
$391$	−12557.1			−1.62415
$392$	−535.158	−	971.040i	−0.0689529	−	0.125115i
$393$		0			0
$394$	−390.743	+	66.2294i	−0.0499628	+	0.00846850i
$395$		−	7776.72i		−	0.990606i
$396$		0			0
$397$			13824.8i			1.74772i	0.486178	+	0.873860i	$0.338391\pi$
$397$			13824.8i			1.74772i	−0.486178	+	0.873860i	$0.661609\pi$
$398$	474.152	+	2797.42i	0.0597163	+	0.352317i
$399$		0			0
$400$	2221.56	−	1765.84i	0.277695	−	0.220730i
$401$	137.695			0.0171475			0.00857377	−	0.999963i	$-0.497271\pi$
$401$	137.695			0.0171475			0.00857377	+	0.999963i	$0.497271\pi$
$402$		0			0
$403$			9873.48i			1.22043i
$404$	1638.20	+	4693.72i	0.201741	+	0.578023i
$405$		0			0
$406$	4575.66	−	775.557i	0.559326	−	0.0948036i
$407$	−7742.36			−0.942935
$408$		0			0
$409$	−12325.1			−1.49007			−0.745034	−	0.667027i	$-0.767567\pi$
$409$	−12325.1			−1.49007			−0.745034	+	0.667027i	$0.767567\pi$
$410$	12535.0	−	2124.63i	1.50990	−	0.255922i
$411$		0			0
$412$	−3277.10	+	1143.77i	−0.391872	+	0.136771i
$413$		−	2854.51i		−	0.340100i
$414$		0			0
$415$	−515.407			−0.0609646
$416$	6629.98	−	7389.22i	0.781398	−	0.870880i
$417$		0			0
$418$	1075.66	+	6346.24i	0.125867	+	0.742595i
$419$			3339.25i			0.389339i	0.980869	+	0.194670i	$0.0623635\pi$
$419$			3339.25i			0.389339i	−0.980869	+	0.194670i	$0.937637\pi$
$420$		0			0
$421$		−	3287.17i		−	0.380539i	−0.981732	−	0.190270i	$-0.939064\pi$
$421$		−	3287.17i		−	0.380539i	0.981732	−	0.190270i	$-0.0609362\pi$
$422$	6865.73	−	1163.71i	0.791987	−	0.134239i
$423$		0			0
$424$	13800.8	−	7605.89i	1.58073	−	0.871167i
$425$	4964.99			0.566677
$426$		0			0
$427$			870.874i			0.0986992i
$428$	−2443.67	−	7001.55i	−0.275980	−	0.790730i
$429$		0			0
$430$	2101.63	+	12399.3i	0.235697	+	1.39057i
$431$	12701.9			1.41955			0.709776	−	0.704427i	$-0.248796\pi$
$431$	12701.9			1.41955			0.709776	+	0.704427i	$0.248796\pi$
$432$		0			0
$433$	−11643.1			−1.29222			−0.646108	−	0.763246i	$-0.723604\pi$
$433$	−11643.1			−1.29222			−0.646108	+	0.763246i	$0.723604\pi$
$434$	595.667	+	3514.34i	0.0658823	+	0.388695i
$435$		0			0
$436$	−3753.68	−	10754.9i	−0.412313	−	1.18135i
$437$			4329.59i			0.473941i
$438$		0			0
$439$	−11073.2			−1.20386			−0.601930	−	0.798549i	$-0.705601\pi$
$439$	−11073.2			−1.20386			−0.601930	+	0.798549i	$0.705601\pi$
$440$	−5781.89	−	10491.2i	−0.626456	−	1.13670i
$441$		0			0
$442$	17124.6	−	2902.55i	1.84283	−	0.312353i
$443$			7274.35i			0.780168i	0.920779	+	0.390084i	$0.127554\pi$
$443$			7274.35i			0.780168i	−0.920779	+	0.390084i	$0.872446\pi$
$444$		0			0
$445$		−	6874.47i		−	0.732318i
$446$	3052.79	+	18011.0i	0.324112	+	1.91221i
$447$		0			0
$448$	1914.07	−	3030.08i	0.201855	−	0.319549i
$449$	−9735.36			−1.02325			−0.511626	−	0.859208i	$-0.670957\pi$
$449$	−9735.36			−1.02325			−0.511626	+	0.859208i	$0.670957\pi$
$450$		0			0
$451$			29502.8i			3.08034i
$452$	−15313.2	+	5344.61i	−1.59353	+	0.556171i
$453$		0			0
$454$	−4953.09	+	839.529i	−0.512026	+	0.0867864i
$455$	3447.80			0.355242
$456$		0			0
$457$	2155.33			0.220617			0.110309	−	0.993897i	$-0.464816\pi$
$457$	2155.33			0.220617			0.110309	+	0.993897i	$0.464816\pi$
$458$	−5706.14	+	967.168i	−0.582162	+	0.0986742i
$459$		0			0
$460$	−2655.14	−	7607.44i	−0.269123	−	0.771084i
$461$			3606.81i			0.364395i	0.983262	+	0.182197i	$0.0583209\pi$
$461$			3606.81i			0.364395i	−0.983262	+	0.182197i	$0.941679\pi$
$462$		0			0
$463$	8719.74			0.875250			0.437625	−	0.899158i	$-0.355820\pi$
$463$	8719.74			0.875250			0.437625	+	0.899158i	$0.355820\pi$
$464$	9334.68	+	11743.7i	0.933948	+	1.17498i
$465$		0			0
$466$	−2754.38	−	16250.4i	−0.273807	−	1.61542i
$467$		−	9661.28i		−	0.957325i	−0.877999	−	0.478662i	$-0.841122\pi$
$467$		−	9661.28i		−	0.957325i	0.877999	−	0.478662i	$-0.158878\pi$
$468$		0			0
$469$			1006.94i			0.0991386i
$470$	−2797.63	+	474.187i	−0.274564	+	0.0465375i
$471$		0			0
$472$	8081.17	−	4453.68i	0.788063	−	0.434316i
$473$	−29183.5			−2.83691
$474$		0			0
$475$		−	1711.89i		−	0.165362i
$476$	5920.15	−	2066.25i	0.570063	−	0.198963i
$477$		0			0
$478$	2785.95	+	16436.7i	0.266582	+	1.57279i
$479$	−7341.60			−0.700306			−0.350153	−	0.936693i	$-0.613870\pi$
$479$	−7341.60			−0.700306			−0.350153	+	0.936693i	$0.613870\pi$
$480$		0			0
$481$	7203.32			0.682834
$482$	−972.502	−	5737.61i	−0.0919010	−	0.542201i
$483$		0			0
$484$	16191.9	−	5651.28i	1.52065	−	0.530736i
$485$		−	3329.69i		−	0.311739i
$486$		0			0
$487$	14785.8			1.37579			0.687894	−	0.725811i	$-0.258535\pi$
$487$	14785.8			1.37579			0.687894	+	0.725811i	$0.258535\pi$
$488$	−2465.46	+	1358.76i	−0.228701	+	0.126041i
$489$		0			0
$490$	1227.20	−	208.005i	0.113141	−	0.0191770i
$491$			7352.33i			0.675776i	0.941186	+	0.337888i	$0.109712\pi$
$491$			7352.33i			0.675776i	−0.941186	+	0.337888i	$0.890288\pi$
$492$		0			0
$493$			26246.2i			2.39771i
$494$	−1000.77	−	5904.40i	−0.0911476	−	0.537756i
$495$		0			0
$496$	−9019.79	+	7169.51i	−0.816533	+	0.649033i
$497$	1759.39			0.158791
$498$		0			0
$499$			16803.9i			1.50751i	0.657157	+	0.753754i	$0.271759\pi$
$499$			16803.9i			1.50751i	−0.657157	+	0.753754i	$0.728241\pi$
$500$	4009.29	+	11487.3i	0.358602	+	1.02746i
$501$		0			0
$502$	−15597.4	+	2643.69i	−1.38674	+	0.235047i
$503$	−3372.87			−0.298984			−0.149492	−	0.988763i	$-0.547764\pi$
$503$	−3372.87			−0.298984			−0.149492	+	0.988763i	$0.547764\pi$
$504$		0			0
$505$	−5581.00			−0.491785
$506$	18434.8	−	3124.63i	1.61962	−	0.274519i
$507$		0			0
$508$	3646.18	−	1272.59i	0.318451	−	0.111146i
$509$			1413.69i			0.123106i	0.998104	+	0.0615530i	$0.0196053\pi$
$509$			1413.69i			0.123106i	−0.998104	+	0.0615530i	$0.980395\pi$
$510$		0			0
$511$	4967.83			0.430067
$512$	11564.6	+	691.147i	0.998219	+	0.0596575i
$513$		0			0
$514$	−722.551	−	4262.93i	−0.0620046	−	0.365817i
$515$		−	3896.59i		−	0.333407i
$516$		0			0
$517$		−	6584.63i		−	0.560139i
$518$	2563.93	−	434.576i	0.217476	−	0.0368613i
$519$		0			0
$520$	5379.34	+	9760.78i	0.453653	+	0.823151i
$521$	20868.7			1.75484			0.877422	−	0.479720i	$-0.159262\pi$
$521$	20868.7			1.75484			0.877422	+	0.479720i	$0.159262\pi$
$522$		0			0
$523$		−	17290.7i		−	1.44564i	−0.691035	−	0.722821i	$-0.742845\pi$
$523$		−	17290.7i		−	1.44564i	0.691035	−	0.722821i	$-0.257155\pi$
$524$	3819.00	+	10942.1i	0.318385	+	0.912228i
$525$		0			0
$526$	1410.24	+	8320.21i	0.116900	+	0.689693i
$527$	−20158.4			−1.66625
$528$		0			0
$529$	409.770			0.0336788
$530$	2956.26	+	17441.5i	0.242287	+	1.42945i
$531$		0			0
$532$	−712.425	−	2041.22i	−0.0580593	−	0.166350i
$533$		−	27448.8i		−	2.23066i
$534$		0			0
$535$	8325.09			0.672757
$536$	−2850.66	+	1571.05i	−0.229719	+	0.126602i
$537$		0			0
$538$	15484.5	−	2624.56i	1.24086	−	0.210321i
$539$			2888.39i			0.230820i
$540$		0			0
$541$		−	4714.93i		−	0.374696i	−0.982294	−	0.187348i	$-0.940011\pi$
$541$		−	4714.93i		−	0.374696i	0.982294	−	0.187348i	$-0.0599892\pi$
$542$	−2003.21	−	11818.6i	−0.158755	−	0.936631i
$543$		0			0
$544$	15086.4	+	13536.3i	1.18901	+	1.06684i
$545$	12788.0			1.00510
$546$		0			0
$547$		−	11384.3i		−	0.889868i	−0.895563	−	0.444934i	$-0.853227\pi$
$547$		−	11384.3i		−	0.889868i	0.895563	−	0.444934i	$-0.146773\pi$
$548$	−7882.67	+	2751.20i	−0.614473	+	0.214463i
$549$		0			0
$550$	−7288.99	+	1235.46i	−0.565098	+	0.0957818i
$551$	9049.48			0.699675
$552$		0			0
$553$	−6061.36			−0.466104
$554$	10490.6	−	1778.11i	0.804515	−	0.136362i
$555$		0			0
$556$	1663.25	+	4765.49i	0.126866	+	0.363492i
$557$		−	1616.13i		−	0.122940i	−0.998109	−	0.0614699i	$-0.980421\pi$
$557$		−	1616.13i		−	0.122940i	0.998109	−	0.0614699i	$-0.0195788\pi$
$558$		0			0
$559$	27151.7			2.05437
$560$	2503.57	+	3149.69i	0.188920	+	0.237676i
$561$		0			0
$562$	−635.031	−	3746.58i	−0.0476640	−	0.281210i
$563$		−	2529.62i		−	0.189362i	−0.995508	−	0.0946811i	$-0.969817\pi$
$563$		−	2529.62i		−	0.189362i	0.995508	−	0.0946811i	$-0.0301831\pi$
$564$		0			0
$565$		−	18208.0i		−	1.35578i
$566$	−7985.16	+	1353.45i	−0.593006	+	0.100512i
$567$		0			0
$568$	2745.04	+	4980.86i	0.202781	+	0.367944i
$569$	−5697.25			−0.419756			−0.209878	−	0.977728i	$-0.567307\pi$
$569$	−5697.25			−0.419756			−0.209878	+	0.977728i	$0.567307\pi$
$570$		0			0
$571$		−	15930.1i		−	1.16752i	−0.811926	−	0.583760i	$-0.801581\pi$
$571$		−	15930.1i		−	1.16752i	0.811926	−	0.583760i	$-0.198419\pi$
$572$	−24417.9	+	8522.32i	−1.78490	+	0.622965i
$573$		0			0
$574$	−1655.98	−	9770.05i	−0.120417	−	0.710442i
$575$	−4972.76			−0.360658
$576$		0			0
$577$	−9446.91			−0.681595			−0.340797	−	0.940137i	$-0.610697\pi$
$577$	−9446.91			−0.681595			−0.340797	+	0.940137i	$0.610697\pi$
$578$	3603.84	+	21262.1i	0.259343	+	1.53008i
$579$		0			0
$580$	−15900.7	+	5549.64i	−1.13834	+	0.397304i
$581$			401.720i			0.0286853i
$582$		0			0
$583$	−41051.1			−2.91623
$584$	7750.94	+	14064.0i	0.549206	+	0.996531i
$585$		0			0
$586$	−9869.69	+	1672.87i	−0.695756	+	0.117928i
$587$		−	17574.2i		−	1.23571i	−0.786290	−	0.617857i	$-0.788001\pi$
$587$		−	17574.2i		−	1.23571i	0.786290	−	0.617857i	$-0.211999\pi$
$588$		0			0
$589$			6950.45i			0.486228i
$590$	1731.06	+	10213.0i	0.120791	+	0.712646i
$591$		0			0
$592$	5230.60	+	6580.50i	0.363136	+	0.456853i
$593$	−6137.13			−0.424995			−0.212497	−	0.977162i	$-0.568160\pi$
$593$	−6137.13			−0.424995			−0.212497	+	0.977162i	$0.568160\pi$
$594$		0			0
$595$			7039.27i			0.485012i
$596$	−1481.57	−	4244.97i	−0.101825	−	0.291746i
$597$		0			0
$598$	−17151.3	+	2907.09i	−1.17286	+	0.198795i
$599$	26532.1			1.80980			0.904901	−	0.425622i	$-0.139945\pi$
$599$	26532.1			1.80980			0.904901	+	0.425622i	$0.139945\pi$
$600$		0			0
$601$	−6237.94			−0.423379			−0.211690	−	0.977337i	$-0.567897\pi$
$601$	−6237.94			−0.423379			−0.211690	+	0.977337i	$0.567897\pi$
$602$	9664.30	−	1638.06i	0.654298	−	0.110901i
$603$		0			0
$604$	3519.99	−	1228.54i	0.237130	−	0.0827627i
$605$			19252.7i			1.29378i
$606$		0			0
$607$	2650.63			0.177242			0.0886209	−	0.996065i	$-0.471754\pi$
$607$	2650.63			0.177242			0.0886209	+	0.996065i	$0.471754\pi$
$608$	4667.19	−	5201.65i	0.311315	−	0.346965i
$609$		0			0
$610$	−528.124	−	3115.85i	−0.0350543	−	0.206815i
$611$			6126.19i			0.405629i
$612$		0			0
$613$		−	2531.31i		−	0.166784i	−0.996517	−	0.0833921i	$-0.973425\pi$
$613$		−	2531.31i		−	0.166784i	0.996517	−	0.0833921i	$-0.0265754\pi$
$614$	8390.60	−	1422.17i	0.551494	−	0.0934760i
$615$		0			0
$616$	−8177.09	+	4506.54i	−0.534845	+	0.294763i
$617$	−22390.8			−1.46097			−0.730485	−	0.682928i	$-0.760706\pi$
$617$	−22390.8			−1.46097			−0.730485	+	0.682928i	$0.760706\pi$
$618$		0			0
$619$			4854.99i			0.315248i	0.987499	+	0.157624i	$0.0503834\pi$
$619$			4854.99i			0.315248i	−0.987499	+	0.157624i	$0.949617\pi$
$620$	−4262.40	−	12212.5i	−0.276100	−	0.791074i
$621$		0			0
$622$	−1867.80	−	11019.7i	−0.120405	−	0.710371i
$623$	−5358.13			−0.344573
$624$		0			0
$625$	−8116.08			−0.519429
$626$	−124.190	−	732.704i	−0.00792915	−	0.0467807i
$627$		0			0
$628$	−828.428	−	2373.59i	−0.0526399	−	0.150822i
$629$			14706.8i			0.932273i
$630$		0			0
$631$	23946.3			1.51076			0.755379	−	0.655289i	$-0.227453\pi$
$631$	23946.3			1.51076			0.755379	+	0.655289i	$0.227453\pi$
$632$	−9457.09	−	17159.8i	−0.595226	−	1.08003i
$633$		0			0
$634$	−14376.2	+	2436.71i	−0.900556	+	0.152641i
$635$			4335.44i			0.270940i
$636$		0			0
$637$		−	2687.29i		−	0.167150i
$638$	−6530.94	−	38531.5i	−0.405270	−	2.39103i
$639$		0			0
$640$	−5010.69	+	12001.9i	−0.309476	+	0.741276i
$641$	17358.0			1.06958			0.534790	−	0.844985i	$-0.320391\pi$
$641$	17358.0			1.06958			0.534790	+	0.844985i	$0.320391\pi$
$642$		0			0
$643$			11744.3i			0.720293i	0.932896	+	0.360146i	$0.117273\pi$
$643$			11744.3i			0.720293i	−0.932896	+	0.360146i	$0.882727\pi$
$644$	−5929.42	+	2069.48i	−0.362813	+	0.126629i
$645$		0			0
$646$	12054.9	−	2043.25i	0.734199	−	0.124444i
$647$	−23793.4			−1.44577			−0.722887	−	0.690967i	$-0.757185\pi$
$647$	−23793.4			−1.44577			−0.722887	+	0.690967i	$0.757185\pi$
$648$		0			0
$649$	−24037.7			−1.45387
$650$	6781.52	−	1149.44i	0.409220	−	0.0693612i
$651$		0			0
$652$	−5079.10	−	14552.5i	−0.305081	−	0.874110i
$653$			7027.81i			0.421163i	0.977576	+	0.210582i	$0.0675358\pi$
$653$			7027.81i			0.421163i	−0.977576	+	0.210582i	$0.932464\pi$
$654$		0			0
$655$	−13010.5			−0.776128
$656$	25075.5	−	19931.6i	1.49243	−	1.18628i
$657$		0			0
$658$	369.593	+	2180.54i	0.0218970	+	0.129189i
$659$		−	16588.1i		−	0.980547i	−0.871569	−	0.490273i	$-0.836897\pi$
$659$		−	16588.1i		−	0.980547i	0.871569	−	0.490273i	$-0.163103\pi$
$660$		0			0
$661$		−	5341.60i		−	0.314318i	−0.987573	−	0.157159i	$-0.949766\pi$
$661$		−	5341.60i		−	0.314318i	0.987573	−	0.157159i	$-0.0502335\pi$
$662$	18969.8	−	3215.31i	1.11372	−	0.188771i
$663$		0			0
$664$	−1137.28	+	626.774i	−0.0664683	+	0.0366319i
$665$	2427.08			0.141531
$666$		0			0
$667$		−	26287.3i		−	1.52601i
$668$	10985.3	−	3834.07i	0.636276	−	0.222073i
$669$		0			0
$670$	−610.636	−	3602.66i	−0.0352103	−	0.207735i
$671$	7333.60			0.421923
$672$		0			0
$673$	−10396.5			−0.595477			−0.297738	−	0.954648i	$-0.596232\pi$
$673$	−10396.5			−0.595477			−0.297738	+	0.954648i	$0.596232\pi$
$674$	205.029	+	1209.64i	0.0117173	+	0.0691300i
$675$		0			0
$676$	6123.56	−	2137.24i	0.348405	−	0.121600i
$677$			7689.12i			0.436510i	0.975892	+	0.218255i	$0.0700364\pi$
$677$			7689.12i			0.436510i	−0.975892	+	0.218255i	$0.929964\pi$
$678$		0			0
$679$	−2595.24			−0.146681
$680$	−19928.3	+	10982.9i	−1.12385	+	0.619373i
$681$		0			0
$682$	29594.1	−	5016.09i	1.66161	−	0.281636i
$683$			1703.19i			0.0954182i	0.998861	+	0.0477091i	$0.0151920\pi$
$683$			1703.19i			0.0954182i	−0.998861	+	0.0477091i	$0.984808\pi$
$684$		0			0
$685$		−	9372.78i		−	0.522796i
$686$	−162.124	−	956.508i	−0.00902323	−	0.0532356i
$687$		0			0
$688$	19715.9	+	24804.1i	1.09253	+	1.37449i
$689$	38193.0			2.11181
$690$		0			0
$691$		−	19314.7i		−	1.06334i	−0.846952	−	0.531669i	$-0.821565\pi$
$691$		−	19314.7i		−	1.06334i	0.846952	−	0.531669i	$-0.178435\pi$
$692$	−8284.63	−	23736.9i	−0.455108	−	1.30396i
$693$		0			0
$694$	−12237.0	+	2074.12i	−0.669321	+	0.113447i
$695$	−5666.33			−0.309261
$696$		0			0
$697$	56041.5			3.04551
$698$	−3543.86	+	600.670i	−0.192173	+	0.0325726i
$699$		0			0
$700$	2344.45	−	818.257i	0.126588	−	0.0441817i
$701$		−	8776.10i		−	0.472851i	−0.971650	−	0.236426i	$-0.924024\pi$
$701$		−	8776.10i		−	0.472851i	0.971650	−	0.236426i	$-0.0759760\pi$
$702$		0			0
$703$	5070.79			0.272046
$704$	−25516.2	−	16118.3i	−1.36602	−	0.862899i
$705$		0			0
$706$	−6039.69	−	35633.2i	−0.321964	−	1.89954i
$707$			4349.97i			0.231397i
$708$		0			0
$709$			15446.1i			0.818180i	0.912494	+	0.409090i	$0.134154\pi$
$709$			15446.1i			0.818180i	−0.912494	+	0.409090i	$0.865846\pi$
$710$	−6294.80	+	1066.94i	−0.332732	+	0.0563968i
$711$		0			0
$712$	−8359.89	−	15169.0i	−0.440028	−	0.798429i
$713$	20190.0			1.06048
$714$		0			0
$715$		−	29033.8i		−	1.51860i
$716$	1603.32	+	4593.79i	0.0836857	+	0.239774i
$717$		0			0
$718$	−2894.88	−	17079.3i	−0.150468	−	0.887737i
$719$	−1510.03			−0.0783237			−0.0391618	−	0.999233i	$-0.512469\pi$
$719$	−1510.03			−0.0783237			−0.0391618	+	0.999233i	$0.512469\pi$
$720$		0			0
$721$	−3037.10			−0.156876
$722$	2537.52	+	14971.0i	0.130799	+	0.771692i
$723$		0			0
$724$	8107.57	+	23229.6i	0.416181	+	1.19243i
$725$			10393.8i			0.532436i
$726$		0			0
$727$	32352.4			1.65046			0.825231	−	0.564795i	$-0.191045\pi$
$727$	32352.4			1.65046			0.825231	+	0.564795i	$0.191045\pi$
$728$	7607.79	−	4192.79i	0.387312	−	0.213455i
$729$		0			0
$730$	−17774.1	+	3012.64i	−0.901164	+	0.152744i
$731$			55434.9i			2.80483i
$732$		0			0
$733$			11397.7i			0.574327i	0.957882	+	0.287164i	$0.0927123\pi$
$733$			11397.7i			0.574327i	−0.957882	+	0.287164i	$0.907288\pi$
$734$	−1507.81	−	8895.84i	−0.0758232	−	0.447345i
$735$		0			0
$736$	−15110.0	−	13557.4i	−0.756740	−	0.678986i
$737$	8479.37			0.423802
$738$		0			0
$739$			5146.85i			0.256198i	0.991761	+	0.128099i	$0.0408875\pi$
$739$			5146.85i			0.256198i	−0.991761	+	0.128099i	$0.959113\pi$
$740$	−8909.78	+	3109.69i	−0.442608	+	0.154479i
$741$		0			0
$742$	13594.3	−	2304.18i	0.672592	−	0.114002i
$743$	−22350.2			−1.10357			−0.551783	−	0.833988i	$-0.686052\pi$
$743$	−22350.2			−1.10357			−0.551783	+	0.833988i	$0.686052\pi$
$744$		0			0
$745$	5047.42			0.248219
$746$	22414.1	−	3799.11i	1.10005	−	0.186455i
$747$		0			0
$748$	−17399.8	−	49853.4i	−0.850534	−	2.43693i
$749$		−	6488.77i		−	0.316548i
$750$		0			0
$751$	12773.8			0.620670			0.310335	−	0.950627i	$-0.399559\pi$
$751$	12773.8			0.620670			0.310335	+	0.950627i	$0.399559\pi$
$752$	−5596.50	+	4448.46i	−0.271388	+	0.215716i
$753$		0			0
$754$	6076.24	+	35848.8i	0.293480	+	1.73148i
$755$			4185.39i			0.201751i
$756$		0			0
$757$		−	1662.37i		−	0.0798149i	−0.999203	−	0.0399075i	$-0.987294\pi$
$757$		−	1662.37i		−	0.0798149i	0.999203	−	0.0399075i	$-0.0127063\pi$
$758$	−10491.8	+	1778.32i	−0.502742	+	0.0852129i
$759$		0			0
$760$	3786.80	+	6871.12i	0.180739	+	0.327950i
$761$	−36358.5			−1.73192			−0.865962	−	0.500109i	$-0.833293\pi$
$761$	−36358.5			−1.73192			−0.865962	+	0.500109i	$0.833293\pi$
$762$		0			0
$763$		−	9967.27i		−	0.472922i
$764$	−1679.79	+	586.278i	−0.0795452	+	0.0277628i
$765$		0			0
$766$	−4480.55	−	26434.5i	−0.211343	−	1.24689i
$767$	22364.1			1.05283
$768$		0			0
$769$	17531.9			0.822127			0.411063	−	0.911607i	$-0.365158\pi$
$769$	17531.9			0.822127			0.411063	+	0.911607i	$0.365158\pi$
$770$	−1751.61	−	10334.2i	−0.0819786	−	0.483661i
$771$		0			0
$772$	−17183.8	+	5997.47i	−0.801111	+	0.279603i
$773$		−	17860.7i		−	0.831054i	−0.909581	−	0.415527i	$-0.863597\pi$
$773$		−	17860.7i		−	0.831054i	0.909581	−	0.415527i	$-0.136403\pi$
$774$		0			0
$775$	−7982.96			−0.370008
$776$	−4049.16	−	7347.17i	−0.187315	−	0.339882i
$777$		0			0
$778$	18606.7	−	3153.76i	0.857431	−	0.145331i
$779$		−	19322.6i		−	0.888710i
$780$		0			0
$781$		−	14815.7i		−	0.678807i
$782$	−5935.32	−	35017.5i	−0.271415	−	1.60131i
$783$		0			0
$784$	2454.94	−	1951.35i	0.111832	−	0.0888915i
$785$	2822.28			0.128320
$786$		0			0
$787$		−	11778.6i		−	0.533496i	−0.963766	−	0.266748i	$-0.914051\pi$
$787$		−	11778.6i		−	0.533496i	0.963766	−	0.266748i	$-0.0859492\pi$
$788$	−369.382	−	1058.34i	−0.0166988	−	0.0478450i
$789$		0			0
$790$	21686.6	−	3675.79i	0.976675	−	0.165543i
$791$	−14191.7			−0.637926
$792$		0			0
$793$	−6823.02			−0.305539
$794$	−38552.5	+	6534.49i	−1.72314	+	0.292066i
$795$		0			0
$796$	−7576.93	+	2644.49i	−0.337383	+	0.117753i
$797$			9149.34i			0.406633i	0.979113	+	0.203316i	$0.0651720\pi$
$797$			9149.34i			0.406633i	−0.979113	+	0.203316i	$0.934828\pi$
$798$		0			0
$799$	−12507.7			−0.553805
$800$	5974.37	+	5360.51i	0.264032	+	0.236903i
$801$		0			0
$802$	65.0838	+	383.984i	0.00286557	+	0.0169064i
$803$		−	41834.0i		−	1.83847i
$804$		0			0
$805$		−	7050.29i		−	0.308683i
$806$	−27533.7	+	4666.86i	−1.20327	+	0.203949i
$807$		0			0
$808$	−12314.8	+	6786.93i	−0.536182	+	0.295499i
$809$	−11885.2			−0.516514			−0.258257	−	0.966076i	$-0.583148\pi$
$809$	−11885.2			−0.516514			−0.258257	+	0.966076i	$0.583148\pi$
$810$		0			0
$811$		−	22554.1i		−	0.976549i	−0.872690	−	0.488274i	$-0.837626\pi$
$811$		−	22554.1i		−	0.976549i	0.872690	−	0.488274i	$-0.162374\pi$
$812$	4325.52	+	12393.4i	0.186941	+	0.535618i
$813$		0			0
$814$	−3659.55	−	21590.8i	−0.157576	−	0.929675i
$815$	17303.4			0.743697
$816$		0			0
$817$	19113.5			0.818478
$818$	−5825.66	−	34370.5i	−0.249009	−	1.46911i
$819$		0			0
$820$	11849.7	+	33951.4i	0.504645	+	1.44590i
$821$		−	9016.04i		−	0.383267i	−0.981467	−	0.191633i	$-0.938622\pi$
$821$		−	9016.04i		−	0.383267i	0.981467	−	0.191633i	$-0.0613784\pi$
$822$		0			0
$823$	8909.42			0.377355			0.188677	−	0.982039i	$-0.439580\pi$
$823$	8909.42			0.377355			0.188677	+	0.982039i	$0.439580\pi$
$824$	−4738.56	−	8598.08i	−0.200334	−	0.363505i
$825$		0			0
$826$	7960.23	−	1349.23i	0.335317	−	0.0568349i
$827$		−	24206.8i		−	1.01784i	−0.860814	−	0.508920i	$-0.830045\pi$
$827$		−	24206.8i		−	1.01784i	0.860814	−	0.508920i	$-0.169955\pi$
$828$		0			0
$829$			498.801i			0.0208976i	0.999945	+	0.0104488i	$0.00332601\pi$
$829$			498.801i			0.0208976i	−0.999945	+	0.0104488i	$0.996674\pi$
$830$	−243.615	−	1437.29i	−0.0101880	−	0.0601073i
$831$		0			0
$832$	23739.7	+	14996.1i	0.989215	+	0.624875i
$833$	5486.58			0.228210
$834$		0			0
$835$			13061.9i			0.541347i
$836$	−17189.0	+	5999.30i	−0.711119	+	0.248194i
$837$		0			0
$838$	−9312.02	+	1578.35i	−0.383864	+	0.0650635i
$839$	23273.2			0.957666			0.478833	−	0.877906i	$-0.341060\pi$
$839$	23273.2			0.957666			0.478833	+	0.877906i	$0.341060\pi$
$840$		0			0
$841$	−30555.3			−1.25283
$842$	9166.79	−	1553.74i	0.375188	−	0.0635929i
$843$		0			0
$844$	6490.39	+	18596.1i	0.264702	+	0.758417i
$845$			7281.14i			0.296424i
$846$		0			0
$847$	15006.0			0.608753
$848$	27733.4	+	34890.7i	1.12308	+	1.41292i
$849$		0			0
$850$	2346.78	+	13845.6i	0.0946988	+	0.558708i
$851$		−	14729.8i		−	0.593340i
$852$		0			0
$853$			17701.4i			0.710531i	0.934765	+	0.355266i	$0.115610\pi$
$853$			17701.4i			0.710531i	−0.934765	+	0.355266i	$0.884390\pi$
$854$	−2428.57	+	411.633i	−0.0973113	+	0.0164939i
$855$		0			0
$856$	18369.8	−	10123.9i	0.733491	−	0.404240i
$857$	−13312.4			−0.530620			−0.265310	−	0.964163i	$-0.585474\pi$
$857$	−13312.4			−0.530620			−0.265310	+	0.964163i	$0.585474\pi$
$858$		0			0
$859$		−	6535.20i		−	0.259579i	−0.991542	−	0.129789i	$-0.958570\pi$
$859$		−	6535.20i		−	0.259579i	0.991542	−	0.129789i	$-0.0414301\pi$
$860$	−33583.9	+	11721.4i	−1.33163	+	0.464765i
$861$		0			0
$862$	6003.74	+	35421.1i	0.237225	+	1.39959i
$863$	32795.4			1.29359			0.646795	−	0.762664i	$-0.276109\pi$
$863$	32795.4			1.29359			0.646795	+	0.762664i	$0.276109\pi$
$864$		0			0
$865$	28224.0			1.10942
$866$	−5503.28	−	32468.4i	−0.215946	−	1.27404i
$867$		0			0
$868$	−9518.72	+	3322.22i	−0.372219	+	0.129912i
$869$			51042.5i			1.99252i
$870$		0			0
$871$	−7889.02			−0.306899
$872$	28217.5	−	15551.2i	1.09583	−	0.603933i
$873$		0			0
$874$	−12073.7	+	2046.45i	−0.467277	+	0.0792016i
$875$			10646.0i			0.411315i
$876$		0			0
$877$			47714.2i			1.83716i	0.395231	+	0.918582i	$0.370665\pi$
$877$			47714.2i			1.83716i	−0.395231	+	0.918582i	$0.629335\pi$
$878$	−5233.92	−	30879.3i	−0.201180	−	1.18693i
$879$		0			0
$880$	26523.4	−	21082.5i	1.01603	−	0.807604i
$881$	26128.4			0.999191			0.499595	−	0.866259i	$-0.333482\pi$
$881$	26128.4			0.999191			0.499595	+	0.866259i	$0.333482\pi$
$882$		0			0
$883$			26426.3i			1.00715i	0.863950	+	0.503577i	$0.167983\pi$
$883$			26426.3i			1.00715i	−0.863950	+	0.503577i	$0.832017\pi$
$884$	16188.4	+	46382.5i	0.615921	+	1.76472i
$885$		0			0
$886$	−20285.6	+	3438.34i	−0.769198	+	0.130376i
$887$	−11595.6			−0.438944			−0.219472	−	0.975619i	$-0.570433\pi$
$887$	−11595.6			−0.438944			−0.219472	+	0.975619i	$0.570433\pi$
$888$		0			0
$889$	3379.15			0.127484
$890$	19170.5	−	3249.33i	0.722020	−	0.122379i
$891$		0			0
$892$	−48783.4	+	17026.4i	−1.83115	+	0.639108i
$893$			4312.55i			0.161606i
$894$		0			0
$895$	−5462.18			−0.204001
$896$	9354.57	+	3905.45i	0.348788	+	0.145616i
$897$		0			0
$898$	−4601.57	−	27148.5i	−0.170998	−	1.00886i
$899$		−	42200.0i		−	1.56557i
$900$		0			0
$901$			77977.7i			2.88326i
$902$	−82273.2	+	13945.0i	−3.03703	+	0.514764i
$903$		0			0
$904$	−22142.3	−	40177.1i	−0.814648	−	1.47817i
$905$	−27620.8			−1.01453
$906$		0			0
$907$		−	42382.2i		−	1.55158i	−0.630994	−	0.775788i	$-0.717353\pi$
$907$		−	42382.2i		−	1.55158i	0.630994	−	0.775788i	$-0.282647\pi$
$908$	−4682.31	−	13415.6i	−0.171132	−	0.490323i
$909$		0			0
$910$	1629.66	+	9614.71i	0.0593654	+	0.350247i
$911$	8454.22			0.307465			0.153733	−	0.988112i	$-0.450871\pi$
$911$	8454.22			0.307465			0.153733	+	0.988112i	$0.450871\pi$
$912$		0			0
$913$	3382.87			0.122625
$914$	1018.75	+	6010.47i	0.0368680	+	0.217515i
$915$		0			0
$916$	−5394.19	−	15455.3i	−0.194573	−	0.557486i
$917$			10140.7i			0.365187i
$918$		0			0
$919$	36015.8			1.29277			0.646383	−	0.763014i	$-0.276281\pi$
$919$	36015.8			1.29277			0.646383	+	0.763014i	$0.276281\pi$
$920$	19959.5	−	11000.0i	0.715267	−	0.394196i
$921$		0			0
$922$	−10058.1	+	1704.82i	−0.359270	+	0.0608949i
$923$			13784.2i			0.491564i
$924$		0			0
$925$			5824.07i			0.207021i
$926$	4121.53	+	24316.3i	0.146265	+	0.862942i
$927$		0			0
$928$	−28337.1	+	31582.1i	−1.00238	+	1.11717i
$929$	−19664.5			−0.694481			−0.347240	−	0.937776i	$-0.612881\pi$
$929$	−19664.5			−0.694481			−0.347240	+	0.937776i	$0.612881\pi$
$930$		0			0
$931$		−	1891.73i		−	0.0665938i
$932$	44014.8	−	15362.0i	1.54694	−	0.539913i
$933$		0			0
$934$	26942.0	−	4566.56i	0.943863	−	0.159981i
$935$	59277.5			2.07335
$936$		0			0
$937$	20967.0			0.731017			0.365509	−	0.930808i	$-0.380895\pi$
$937$	20967.0			0.731017			0.365509	+	0.930808i	$0.380895\pi$
$938$	−2808.00	+	475.944i	−0.0977445	+	0.0165673i
$939$		0			0
$940$	−2644.69	−	7577.49i	−0.0917662	−	0.262926i
$941$			37124.0i			1.28609i	0.765829	+	0.643044i	$0.222329\pi$
$941$			37124.0i			1.28609i	−0.765829	+	0.643044i	$0.777671\pi$
$942$		0			0
$943$	−56129.2			−1.93830
$944$	16239.5	+	20430.5i	0.559904	+	0.704402i
$945$		0			0
$946$	−13794.1	−	81382.7i	−0.474084	−	2.79702i
$947$			28450.0i			0.976240i	0.872776	+	0.488120i	$0.162317\pi$
$947$			28450.0i			0.976240i	−0.872776	+	0.488120i	$0.837683\pi$
$948$		0			0
$949$			38921.4i			1.33134i
$950$	4773.86	−	809.151i	0.163036	−	0.0276340i
$951$		0			0
$952$	8560.30	+	15532.6i	0.291430	+	0.528797i
$953$	36489.4			1.24030			0.620151	−	0.784483i	$-0.287071\pi$
$953$	36489.4			1.24030			0.620151	+	0.784483i	$0.287071\pi$
$954$		0			0
$955$		−	1997.33i		−	0.0676774i
$956$	−44519.3	+	15538.1i	−1.50613	+	0.525667i
$957$		0			0
$958$	−3470.13	−	20473.2i	−0.117030	−	0.690458i
$959$	−7305.37			−0.245988
$960$		0			0
$961$	2620.72			0.0879700
$962$	3404.76	+	20087.6i	0.114110	+	0.673232i
$963$		0			0
$964$	15540.5	−	5423.94i	0.519219	−	0.181217i
$965$		−	20432.1i		−	0.681589i
$966$		0			0
$967$	−39597.5			−1.31682			−0.658412	−	0.752658i	$-0.728772\pi$
$967$	−39597.5			−1.31682			−0.658412	+	0.752658i	$0.728772\pi$
$968$	23412.8	+	42482.4i	0.777393	+	1.41057i
$969$		0			0
$970$	9285.34	−	1573.83i	0.307355	−	0.0520955i
$971$			6633.40i			0.219234i	0.993974	+	0.109617i	$0.0349624\pi$
$971$			6633.40i			0.219234i	−0.993974	+	0.109617i	$0.965038\pi$
$972$		0			0
$973$			4416.48i			0.145515i
$974$	6988.75	+	41232.5i	0.229912	+	1.35644i
$975$		0			0
$976$	−4954.45	−	6233.08i	−0.162488	−	0.204422i
$977$	24844.2			0.813549			0.406774	−	0.913529i	$-0.366654\pi$
$977$	24844.2			0.813549			0.406774	+	0.913529i	$0.366654\pi$
$978$		0			0
$979$			45120.6i			1.47299i
$980$	1160.11	+	3323.91i	0.0378146	+	0.108345i
$981$		0			0
$982$	−20503.1	+	3475.19i	−0.666273	+	0.112931i
$983$	7133.71			0.231465			0.115732	−	0.993280i	$-0.463078\pi$
$983$	7133.71			0.231465			0.115732	+	0.993280i	$0.463078\pi$
$984$		0			0
$985$	1258.41			0.0407068
$986$	−73191.6	+	12405.7i	−2.36399	+	0.400688i
$987$		0			0
$988$	15992.3	−	5581.62i	0.514962	−	0.179732i
$989$		−	55521.6i		−	1.78512i
$990$		0			0
$991$	−56431.1			−1.80887			−0.904436	−	0.426609i	$-0.859708\pi$
$991$	−56431.1			−1.80887			−0.904436	+	0.426609i	$0.859708\pi$
$992$	−24256.6	−	21764.3i	−0.776359	−	0.696589i
$993$		0			0
$994$	831.602	+	4906.32i	0.0265360	+	0.156558i
$995$		−	9009.23i		−	0.287047i
$996$		0			0
$997$		−	55825.3i		−	1.77333i	−0.462417	−	0.886663i	$-0.653018\pi$
$997$		−	55825.3i		−	1.77333i	0.462417	−	0.886663i	$-0.346982\pi$
$998$	−46860.3	+	7942.63i	−1.48631	+	0.251923i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	504.4.c.e.253.14		20
3.2	odd	2		168.4.c.b.85.7	✓	20
4.3	odd	2		2016.4.c.f.1009.6		20
8.3	odd	2		2016.4.c.f.1009.15		20
8.5	even	2	inner	504.4.c.e.253.13		20
12.11	even	2		672.4.c.b.337.7		20
24.5	odd	2		168.4.c.b.85.8	yes	20
24.11	even	2		672.4.c.b.337.14		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
168.4.c.b.85.7	✓	20	3.2	odd	2
168.4.c.b.85.8	yes	20	24.5	odd	2
504.4.c.e.253.13		20	8.5	even	2	inner
504.4.c.e.253.14		20	1.1	even	1	trivial
672.4.c.b.337.7		20	12.11	even	2
672.4.c.b.337.14		20	24.11	even	2
2016.4.c.f.1009.6		20	4.3	odd	2
2016.4.c.f.1009.15		20	8.3	odd	2

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:	\( N \)	\(=\)	\( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	504.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(0.472666 + 2.78865i) q^{2} +(-7.55317 + 2.63620i) q^{4} -8.98099i q^{5} -7.00000 q^{7} +(-10.9216 - 19.8171i) q^{8} +O(q^{10})\)	\(q+(0.472666 + 2.78865i) q^{2} +(-7.55317 + 2.63620i) q^{4} -8.98099i q^{5} -7.00000 q^{7} +(-10.9216 - 19.8171i) q^{8} +(25.0449 - 4.24501i) q^{10} +58.9468i q^{11} -54.8428i q^{13} +(-3.30866 - 19.5206i) q^{14} +(50.1009 - 39.8234i) q^{16} +111.971 q^{17} -38.6067i q^{19} +(23.6757 + 67.8350i) q^{20} +(-164.382 + 27.8621i) q^{22} -112.146 q^{23} +44.3418 q^{25} +(152.937 - 25.9223i) q^{26} +(52.8722 - 18.4534i) q^{28} +234.402i q^{29} -180.033 q^{31} +(134.735 + 120.891i) q^{32} +(52.9249 + 312.248i) q^{34} +62.8669i q^{35} +131.345i q^{37} +(107.661 - 18.2480i) q^{38} +(-177.978 + 98.0866i) q^{40} +500.500 q^{41} +495.083i q^{43} +(-155.396 - 445.235i) q^{44} +(-53.0077 - 312.737i) q^{46} -111.705 q^{47} +49.0000 q^{49} +(20.9588 + 123.654i) q^{50} +(144.577 + 414.237i) q^{52} +696.410i q^{53} +529.400 q^{55} +(76.4511 + 138.720i) q^{56} +(-653.666 + 110.794i) q^{58} +407.787i q^{59} -124.411i q^{61} +(-85.0952 - 502.048i) q^{62} +(-273.438 + 432.869i) q^{64} -492.542 q^{65} -143.848i q^{67} +(-845.736 + 295.178i) q^{68} +(-175.314 + 29.7151i) q^{70} -251.341 q^{71} -709.691 q^{73} +(-366.276 + 62.0823i) q^{74} +(101.775 + 291.603i) q^{76} -412.627i q^{77} +865.909 q^{79} +(-357.654 - 449.956i) q^{80} +(236.569 + 1395.72i) q^{82} -57.3886i q^{83} -1005.61i q^{85} +(-1380.61 + 234.009i) q^{86} +(1168.16 - 643.792i) q^{88} +765.447 q^{89} +383.899i q^{91} +(847.060 - 295.640i) q^{92} +(-52.7990 - 311.506i) q^{94} -346.726 q^{95} +370.748 q^{97} +(23.1606 + 136.644i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 4 q^{2} - 14 q^{4} - 140 q^{7} - 10 q^{8}+O(q^{10}) \) 20 * q - 4 * q^2 - 14 * q^4 - 140 * q^7 - 10 * q^8	\( 20 q - 4 q^{2} - 14 q^{4} - 140 q^{7} - 10 q^{8} - 84 q^{10} + 28 q^{14} - 134 q^{16} + 52 q^{17} + 8 q^{20} + 8 q^{22} + 244 q^{23} - 844 q^{25} + 332 q^{26} + 98 q^{28} + 264 q^{31} + 46 q^{32} - 612 q^{34} - 884 q^{38} - 964 q^{40} + 236 q^{41} - 576 q^{44} + 1356 q^{46} + 980 q^{49} + 2456 q^{50} + 1492 q^{52} + 72 q^{55} + 70 q^{56} - 1404 q^{58} - 4964 q^{62} - 1670 q^{64} - 1744 q^{65} - 3408 q^{68} + 588 q^{70} + 636 q^{71} - 2784 q^{73} + 4916 q^{74} + 2664 q^{76} + 2872 q^{79} + 1764 q^{80} + 2628 q^{82} - 3328 q^{86} - 2348 q^{88} - 220 q^{89} - 2580 q^{92} - 1704 q^{94} + 1240 q^{95} + 4400 q^{97} - 196 q^{98}+O(q^{100}) \) 20 * q - 4 * q^2 - 14 * q^4 - 140 * q^7 - 10 * q^8 - 84 * q^10 + 28 * q^14 - 134 * q^16 + 52 * q^17 + 8 * q^20 + 8 * q^22 + 244 * q^23 - 844 * q^25 + 332 * q^26 + 98 * q^28 + 264 * q^31 + 46 * q^32 - 612 * q^34 - 884 * q^38 - 964 * q^40 + 236 * q^41 - 576 * q^44 + 1356 * q^46 + 980 * q^49 + 2456 * q^50 + 1492 * q^52 + 72 * q^55 + 70 * q^56 - 1404 * q^58 - 4964 * q^62 - 1670 * q^64 - 1744 * q^65 - 3408 * q^68 + 588 * q^70 + 636 * q^71 - 2784 * q^73 + 4916 * q^74 + 2664 * q^76 + 2872 * q^79 + 1764 * q^80 + 2628 * q^82 - 3328 * q^86 - 2348 * q^88 - 220 * q^89 - 2580 * q^92 - 1704 * q^94 + 1240 * q^95 + 4400 * q^97 - 196 * q^98

Introduction

L-functions

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