LMFDB - Embedded newform 208.4.w.d.49.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [208,4,Mod(17,208)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(208, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("208.17");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 208 = 2^{4} \cdot 13 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	208.w (of order $6$, 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:	$12.2723972812$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 122x^{6} + 5305x^{4} + 97056x^{2} + 627264 $ x^8 + 122x^6 + 5305x^4 + 97056*x^2 + 627264
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{4}\cdot 3^{2} $
Twist minimal:	no (minimal twist has level 26)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			49.1
Root			$-5.87513i$ of defining polynomial
Character	$\chi$	$=$	208.49
Dual form			208.4.w.d.17.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.43757 - 4.22199i) q^{3} -0.110135i q^{5} +(14.0246 + 8.09712i) q^{7} +(1.61655 - 2.79994i) q^{9} +O(q^{10})$	\(q+(-2.43757 - 4.22199i) q^{3} -0.110135i q^{5} +(14.0246 + 8.09712i) q^{7} +(1.61655 - 2.79994i) q^{9} +(33.6077 - 19.4034i) q^{11} +(-23.6233 + 40.4838i) q^{13} +(-0.464989 + 0.268462i) q^{15} +(47.2228 - 81.7923i) q^{17} +(-33.5104 - 19.3472i) q^{19} -78.9491i q^{21} +(-46.2232 - 80.0610i) q^{23} +124.988 q^{25} -147.390 q^{27} +(-96.2678 - 166.741i) q^{29} -158.597i q^{31} +(-163.842 - 94.5942i) q^{33} +(0.891778 - 1.54460i) q^{35} +(-248.280 + 143.344i) q^{37} +(228.506 + 1.05553i) q^{39} +(202.882 - 117.134i) q^{41} +(262.935 - 455.417i) q^{43} +(-0.308372 - 0.178039i) q^{45} +320.423i q^{47} +(-40.3733 - 69.9286i) q^{49} -460.435 q^{51} +414.352 q^{53} +(-2.13700 - 3.70139i) q^{55} +188.641i q^{57} +(223.006 + 128.753i) q^{59} +(-71.6545 + 124.109i) q^{61} +(45.3429 - 26.1787i) q^{63} +(4.45869 + 2.60176i) q^{65} +(-392.729 + 226.742i) q^{67} +(-225.344 + 390.308i) q^{69} +(654.631 + 377.952i) q^{71} -641.108i q^{73} +(-304.666 - 527.697i) q^{75} +628.447 q^{77} +588.290 q^{79} +(315.627 + 546.682i) q^{81} +744.654i q^{83} +(-9.00822 - 5.20090i) q^{85} +(-469.318 + 812.883i) q^{87} +(-1081.79 + 624.570i) q^{89} +(-659.111 + 376.489i) q^{91} +(-669.593 + 386.590i) q^{93} +(-2.13081 + 3.69067i) q^{95} +(1043.14 + 602.258i) q^{97} -125.466i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 6 q^{3} - 18 q^{7} - 22 q^{9}+O(q^{10}) $ 8 * q + 6 * q^3 - 18 * q^7 - 22 * q^9	$ 8 q + 6 q^{3} - 18 q^{7} - 22 q^{9} + 18 q^{11} - 130 q^{13} + 192 q^{15} + 112 q^{17} - 594 q^{19} + 230 q^{23} - 180 q^{25} - 468 q^{27} + 32 q^{29} - 42 q^{33} + 128 q^{35} - 768 q^{37} + 230 q^{39} - 564 q^{41} + 114 q^{43} + 630 q^{45} - 110 q^{49} - 1300 q^{51} + 36 q^{53} - 1248 q^{55} + 1110 q^{59} + 900 q^{61} + 1980 q^{63} + 1870 q^{65} - 510 q^{67} - 2402 q^{69} + 1470 q^{71} + 862 q^{75} + 2340 q^{77} - 784 q^{79} + 1868 q^{81} - 2898 q^{85} - 1598 q^{87} - 4434 q^{89} + 886 q^{91} + 3108 q^{93} + 816 q^{95} + 1854 q^{97}+O(q^{100}) $ 8 * q + 6 * q^3 - 18 * q^7 - 22 * q^9 + 18 * q^11 - 130 * q^13 + 192 * q^15 + 112 * q^17 - 594 * q^19 + 230 * q^23 - 180 * q^25 - 468 * q^27 + 32 * q^29 - 42 * q^33 + 128 * q^35 - 768 * q^37 + 230 * q^39 - 564 * q^41 + 114 * q^43 + 630 * q^45 - 110 * q^49 - 1300 * q^51 + 36 * q^53 - 1248 * q^55 + 1110 * q^59 + 900 * q^61 + 1980 * q^63 + 1870 * q^65 - 510 * q^67 - 2402 * q^69 + 1470 * q^71 + 862 * q^75 + 2340 * q^77 - 784 * q^79 + 1868 * q^81 - 2898 * q^85 - 1598 * q^87 - 4434 * q^89 + 886 * q^91 + 3108 * q^93 + 816 * q^95 + 1854 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/208\mathbb{Z}\right)^\times$.

$n$	$53$	$79$	$145$
$\chi(n)$	$1$	$1$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−2.43757	−	4.22199i	−0.469110	−	0.812522i	0.530267	−	0.847831i	$-0.322092\pi$
$3$	−2.43757	−	4.22199i	−0.469110	−	0.812522i	−0.999376	+	0.0353090i	$0.988758\pi$
$4$		0			0
$5$		−	0.110135i		−	0.00985079i	−0.999988	−	0.00492540i	$-0.998432\pi$
$5$		−	0.110135i		−	0.00985079i	0.999988	−	0.00492540i	$-0.00156781\pi$
$6$		0			0
$7$	14.0246	+	8.09712i	0.757258	+	0.437203i	0.828311	−	0.560269i	$-0.189302\pi$
$7$	14.0246	+	8.09712i	0.757258	+	0.437203i	−0.0710521	+	0.997473i	$0.522636\pi$
$8$		0			0
$9$	1.61655	−	2.79994i	0.0598720	−	0.103701i
$10$		0			0
$11$	33.6077	−	19.4034i	0.921191	−	0.531850i	0.0371760	−	0.999309i	$-0.488164\pi$
$11$	33.6077	−	19.4034i	0.921191	−	0.531850i	0.884015	+	0.467459i	$0.154830\pi$
$12$		0			0
$13$	−23.6233	+	40.4838i	−0.503995	+	0.863707i
$13$	−23.6233	+	40.4838i	−0.503995	+	0.863707i
$14$		0			0
$15$	−0.464989	+	0.268462i	−0.00800398	+	0.00462110i
$16$		0			0
$17$	47.2228	−	81.7923i	0.673719	−	1.16692i	−0.303123	−	0.952951i	$-0.598029\pi$
$17$	47.2228	−	81.7923i	0.673719	−	1.16692i	0.976842	−	0.213964i	$-0.0686374\pi$
$18$		0			0
$19$	−33.5104	−	19.3472i	−0.404622	−	0.233608i	0.283855	−	0.958867i	$-0.408387\pi$
$19$	−33.5104	−	19.3472i	−0.404622	−	0.233608i	−0.688476	+	0.725259i	$0.741720\pi$
$20$		0			0
$21$		−	78.9491i		−	0.820385i
$22$		0			0
$23$	−46.2232	−	80.0610i	−0.419053	−	0.725820i	0.576792	−	0.816891i	$-0.304304\pi$
$23$	−46.2232	−	80.0610i	−0.419053	−	0.725820i	−0.995844	+	0.0910708i	$0.970971\pi$
$24$		0			0
$25$	124.988			0.999903
$26$		0			0
$27$	−147.390			−1.05057
$28$		0			0
$29$	−96.2678	−	166.741i	−0.616431	−	1.06769i	−0.990132	−	0.140140i	$-0.955245\pi$
$29$	−96.2678	−	166.741i	−0.616431	−	1.06769i	0.373701	−	0.927549i	$-0.378089\pi$
$30$		0			0
$31$		−	158.597i		−	0.918865i	−0.888213	−	0.459432i	$-0.848053\pi$
$31$		−	158.597i		−	0.918865i	0.888213	−	0.459432i	$-0.151947\pi$
$32$		0			0
$33$	−163.842	−	94.5942i	−0.864279	−	0.498992i
$34$		0			0
$35$	0.891778	−	1.54460i	0.00430680	−	0.00745959i
$36$		0			0
$37$	−248.280	+	143.344i	−1.10316	+	0.636910i	−0.937049	−	0.349197i	$-0.886454\pi$
$37$	−248.280	+	143.344i	−1.10316	+	0.636910i	−0.166111	+	0.986107i	$0.553121\pi$
$38$		0			0
$39$	228.506	+	1.05553i	0.938210	+	0.00433383i
$40$		0			0
$41$	202.882	−	117.134i	0.772800	−	0.446176i	−0.0610728	−	0.998133i	$-0.519452\pi$
$41$	202.882	−	117.134i	0.772800	−	0.446176i	0.833872	+	0.551957i	$0.186119\pi$
$42$		0			0
$43$	262.935	−	455.417i	0.932494	−	1.61513i	0.153450	−	0.988156i	$-0.450961\pi$
$43$	262.935	−	455.417i	0.932494	−	1.61513i	0.779043	−	0.626970i	$-0.215705\pi$
$44$		0			0
$45$	−0.308372	−	0.178039i	−0.00102154	−	0.000589787i
$46$		0			0
$47$			320.423i			0.994437i	0.867625	+	0.497219i	$0.165645\pi$
$47$			320.423i			0.994437i	−0.867625	+	0.497219i	$0.834355\pi$
$48$		0			0
$49$	−40.3733	−	69.9286i	−0.117706	−	0.203874i
$50$		0			0
$51$	−460.435			−1.26419
$52$		0			0
$53$	414.352			1.07388			0.536940	−	0.843620i	$-0.319580\pi$
$53$	414.352			1.07388			0.536940	+	0.843620i	$0.319580\pi$
$54$		0			0
$55$	−2.13700	−	3.70139i	−0.00523914	−	0.00907446i
$56$		0			0
$57$			188.641i			0.438352i
$58$		0			0
$59$	223.006	+	128.753i	0.492084	+	0.284105i	0.725438	−	0.688287i	$-0.241637\pi$
$59$	223.006	+	128.753i	0.492084	+	0.284105i	−0.233355	+	0.972392i	$0.574970\pi$
$60$		0			0
$61$	−71.6545	+	124.109i	−0.150400	+	0.260501i	−0.931375	−	0.364062i	$-0.881390\pi$
$61$	−71.6545	+	124.109i	−0.150400	+	0.260501i	0.780974	+	0.624563i	$0.214723\pi$
$62$		0			0
$63$	45.3429	−	26.1787i	0.0906772	−	0.0523525i
$64$		0			0
$65$	4.45869	+	2.60176i	0.00850819	+	0.00496475i
$66$		0			0
$67$	−392.729	+	226.742i	−0.716111	+	0.413447i	−0.813320	−	0.581817i	$-0.802342\pi$
$67$	−392.729	+	226.742i	−0.716111	+	0.413447i	0.0972086	+	0.995264i	$0.469009\pi$
$68$		0			0
$69$	−225.344	+	390.308i	−0.393163	+	0.680979i
$70$		0			0
$71$	654.631	+	377.952i	1.09423	+	0.631755i	0.934700	−	0.355438i	$-0.115668\pi$
$71$	654.631	+	377.952i	1.09423	+	0.631755i	0.159532	+	0.987193i	$0.449002\pi$
$72$		0			0
$73$		−	641.108i		−	1.02789i	−0.857823	−	0.513945i	$-0.828183\pi$
$73$		−	641.108i		−	1.02789i	0.857823	−	0.513945i	$-0.171817\pi$
$74$		0			0
$75$	−304.666	−	527.697i	−0.469064	−	0.812443i
$76$		0			0
$77$	628.447			0.930106
$78$		0			0
$79$	588.290			0.837820			0.418910	−	0.908028i	$-0.362412\pi$
$79$	588.290			0.837820			0.418910	+	0.908028i	$0.362412\pi$
$80$		0			0
$81$	315.627	+	546.682i	0.432959	+	0.749906i
$82$		0			0
$83$			744.654i			0.984776i	0.870376	+	0.492388i	$0.163876\pi$
$83$			744.654i			0.984776i	−0.870376	+	0.492388i	$0.836124\pi$
$84$		0			0
$85$	−9.00822	−	5.20090i	−0.0114950	−	0.00663666i
$86$		0			0
$87$	−469.318	+	812.883i	−0.578347	+	1.00173i
$88$		0			0
$89$	−1081.79	+	624.570i	−1.28842	+	0.743869i	−0.978372	−	0.206853i	$-0.933678\pi$
$89$	−1081.79	+	624.570i	−1.28842	+	0.743869i	−0.310046	+	0.950721i	$0.600345\pi$
$90$		0			0
$91$	−659.111	+	376.489i	−0.759270	+	0.433701i
$92$		0			0
$93$	−669.593	+	386.590i	−0.746598	+	0.431048i
$94$		0			0
$95$	−2.13081	+	3.69067i	−0.00230123	+	0.00398584i
$96$		0			0
$97$	1043.14	+	602.258i	1.09191	+	0.630412i	0.934083	−	0.357055i	$-0.116219\pi$
$97$	1043.14	+	602.258i	1.09191	+	0.630412i	0.157823	+	0.987467i	$0.449552\pi$
$98$		0			0
$99$		−	125.466i		−	0.127372i
$100$		0			0
$101$	−313.860	−	543.622i	−0.309210	−	0.535568i	0.668979	−	0.743281i	$-0.266731\pi$
$101$	−313.860	−	543.622i	−0.309210	−	0.535568i	−0.978190	+	0.207713i	$0.933398\pi$
$102$		0			0
$103$	−532.283			−0.509198			−0.254599	−	0.967047i	$-0.581943\pi$
$103$	−532.283			−0.509198			−0.254599	+	0.967047i	$0.581943\pi$
$104$		0			0
$105$	−8.69507			−0.00808145
$106$		0			0
$107$	−741.335	−	1284.03i	−0.669790	−	1.16011i	−0.977963	−	0.208780i	$-0.933051\pi$
$107$	−741.335	−	1284.03i	−0.669790	−	1.16011i	0.308173	−	0.951330i	$-0.400283\pi$
$108$		0			0
$109$		−	72.2452i		−	0.0634847i	−0.999496	−	0.0317424i	$-0.989894\pi$
$109$		−	72.2452i		−	0.0634847i	0.999496	−	0.0317424i	$-0.0101056\pi$
$110$		0			0
$111$	1210.40	+	698.823i	1.03501	+	0.597561i
$112$		0			0
$113$	−293.899	+	509.048i	−0.244670	+	0.423781i	−0.962039	−	0.272913i	$-0.912013\pi$
$113$	−293.899	+	509.048i	−0.244670	+	0.423781i	0.717369	+	0.696694i	$0.245346\pi$
$114$		0			0
$115$	−8.81753	+	5.09080i	−0.00714990	+	0.00412800i
$116$		0			0
$117$	75.1639	+	131.588i	0.0593924	+	0.103977i
$118$		0			0
$119$	1324.56	−	764.738i	1.02036	−	0.589104i
$120$		0			0
$121$	87.4844	−	151.527i	0.0657283	−	0.113845i
$122$		0			0
$123$	−989.075	−	571.042i	−0.725056	−	0.418611i
$124$		0			0
$125$		−	27.5325i		−	0.0197006i
$126$		0			0
$127$	1126.21	+	1950.65i	0.786888	+	1.36293i	0.927864	+	0.372918i	$0.121643\pi$
$127$	1126.21	+	1950.65i	0.786888	+	1.36293i	−0.140976	+	0.990013i	$0.545024\pi$
$128$		0			0
$129$	−2563.69			−1.74977
$130$		0			0
$131$	201.795			0.134587			0.0672935	−	0.997733i	$-0.478564\pi$
$131$	201.795			0.134587			0.0672935	+	0.997733i	$0.478564\pi$
$132$		0			0
$133$	−313.314	−	542.675i	−0.204269	−	0.353804i
$134$		0			0
$135$			16.2329i			0.0103489i
$136$		0			0
$137$	1663.44	+	960.387i	1.03735	+	0.598915i	0.919082	−	0.394066i	$-0.128932\pi$
$137$	1663.44	+	960.387i	1.03735	+	0.598915i	0.118269	+	0.992982i	$0.462265\pi$
$138$		0			0
$139$	−112.070	+	194.110i	−0.0683857	+	0.118448i	−0.898191	−	0.439606i	$-0.855118\pi$
$139$	−112.070	+	194.110i	−0.0683857	+	0.118448i	0.829805	+	0.558053i	$0.188452\pi$
$140$		0			0
$141$	1352.82	−	781.053i	0.808002	−	0.466500i
$142$		0			0
$143$	−8.40215	+	1818.94i	−0.00491345	+	1.06369i
$144$		0			0
$145$	−18.3640	+	10.6025i	−0.0105176	+	0.00607233i
$146$		0			0
$147$	−196.825	+	340.911i	−0.110434	+	0.191278i
$148$		0			0
$149$	2008.37	+	1159.53i	1.10424	+	0.637533i	0.937331	−	0.348439i	$-0.113288\pi$
$149$	2008.37	+	1159.53i	1.10424	+	0.637533i	0.166909	+	0.985972i	$0.446621\pi$
$150$		0			0
$151$		−	1961.99i		−	1.05738i	−0.848815	−	0.528690i	$-0.822684\pi$
$151$		−	1961.99i		−	1.05738i	0.848815	−	0.528690i	$-0.177316\pi$
$152$		0			0
$153$	−152.676	−	264.442i	−0.0806738	−	0.139731i
$154$		0			0
$155$	−17.4671			−0.00905154
$156$		0			0
$157$	2499.22			1.27044			0.635221	−	0.772330i	$-0.280909\pi$
$157$	2499.22			1.27044			0.635221	+	0.772330i	$0.280909\pi$
$158$		0			0
$159$	−1010.01	−	1749.39i	−0.503768	−	0.872551i
$160$		0			0
$161$		−	1497.10i		−	0.732845i
$162$		0			0
$163$	−2288.75	−	1321.41i	−1.09981	−	0.634975i	−0.163638	−	0.986520i	$-0.552323\pi$
$163$	−2288.75	−	1321.41i	−1.09981	−	0.634975i	−0.936171	+	0.351545i	$0.885656\pi$
$164$		0			0
$165$	−10.4181	+	18.0448i	−0.00491546	+	0.00851383i
$166$		0			0
$167$	743.976	−	429.535i	0.344734	−	0.199032i	−0.317629	−	0.948215i	$-0.602887\pi$
$167$	743.976	−	429.535i	0.344734	−	0.199032i	0.662364	+	0.749183i	$0.269553\pi$
$168$		0			0
$169$	−1080.88	−	1912.72i	−0.491978	−	0.870608i
$170$		0			0
$171$	−108.342	+	62.5513i	−0.0484510	+	0.0279732i
$172$		0			0
$173$	1056.57	−	1830.03i	0.464331	−	0.804244i	−0.534840	−	0.844953i	$-0.679628\pi$
$173$	1056.57	−	1830.03i	0.464331	−	0.804244i	0.999171	+	0.0407087i	$0.0129616\pi$
$174$		0			0
$175$	1752.91	+	1012.04i	0.757185	+	0.437161i
$176$		0			0
$177$		−	1255.37i		−	0.533105i
$178$		0			0
$179$	104.764	+	181.456i	0.0437453	+	0.0757691i	0.887069	−	0.461637i	$-0.152738\pi$
$179$	104.764	+	181.456i	0.0437453	+	0.0757691i	−0.843324	+	0.537406i	$0.819404\pi$
$180$		0			0
$181$	−4500.28			−1.84808			−0.924041	−	0.382293i	$-0.875135\pi$
$181$	−4500.28			−1.84808			−0.924041	+	0.382293i	$0.875135\pi$
$182$		0			0
$183$	698.650			0.282217
$184$		0			0
$185$	15.7873	+	27.3443i	0.00627407	+	0.0108670i
$186$		0			0
$187$		−	3665.14i		−	1.43327i
$188$		0			0
$189$	−2067.09	−	1193.44i	−0.795550	−	0.459311i
$190$		0			0
$191$	−32.2122	+	55.7932i	−0.0122031	+	0.0211364i	−0.872062	−	0.489395i	$-0.837218\pi$
$191$	−32.2122	+	55.7932i	−0.0122031	+	0.0211364i	0.859859	+	0.510531i	$0.170551\pi$
$192$		0			0
$193$	−1893.47	+	1093.19i	−0.706190	+	0.407719i	−0.809649	−	0.586915i	$-0.800342\pi$
$193$	−1893.47	+	1093.19i	−0.706190	+	0.407719i	0.103459	+	0.994634i	$0.467009\pi$
$194$		0			0
$195$	0.116250	−	25.1665i	4.26916e−5	−	0.00924211i
$196$		0			0
$197$	−1173.25	+	677.376i	−0.424318	+	0.244980i	−0.696923	−	0.717146i	$-0.745448\pi$
$197$	−1173.25	+	677.376i	−0.424318	+	0.244980i	0.272605	+	0.962126i	$0.412115\pi$
$198$		0			0
$199$	703.491	−	1218.48i	0.250599	−	0.434050i	−0.713092	−	0.701071i	$-0.752706\pi$
$199$	703.491	−	1218.48i	0.250599	−	0.434050i	0.963691	+	0.267020i	$0.0860391\pi$
$200$		0			0
$201$	1914.60	+	1105.40i	0.671869	+	0.387904i
$202$		0			0
$203$		−	3117.97i		−	1.07802i
$204$		0			0
$205$	−12.9005	−	22.3444i	−0.00439519	−	0.00761269i
$206$		0			0
$207$	−298.888			−0.100358
$208$		0			0
$209$	−1501.61			−0.496978
$210$		0			0
$211$	−204.037	−	353.402i	−0.0665709	−	0.115304i	0.830819	−	0.556543i	$-0.187873\pi$
$211$	−204.037	−	353.402i	−0.0665709	−	0.115304i	−0.897390	+	0.441239i	$0.854539\pi$
$212$		0			0
$213$		−	3685.13i		−	1.18545i
$214$		0			0
$215$	−50.1574	−	28.9584i	−0.0159103	−	0.00918580i
$216$		0			0
$217$	1284.18	−	2224.26i	0.401731	−	0.695818i
$218$		0			0
$219$	−2706.75	+	1562.74i	−0.835184	+	0.482194i
$220$		0			0
$221$	2195.70	+	3843.97i	0.668321	+	1.17001i
$222$		0			0
$223$	−2246.35	+	1296.93i	−0.674560	+	0.389457i	−0.797802	−	0.602919i	$-0.794004\pi$
$223$	−2246.35	+	1296.93i	−0.674560	+	0.389457i	0.123242	+	0.992377i	$0.460671\pi$
$224$		0			0
$225$	202.049	−	349.958i	0.0598662	−	0.103691i
$226$		0			0
$227$	4509.90	+	2603.79i	1.31865	+	0.761320i	0.983511	−	0.180850i	$-0.0578849\pi$
$227$	4509.90	+	2603.79i	1.31865	+	0.761320i	0.335135	+	0.942170i	$0.391218\pi$
$228$		0			0
$229$			2454.17i			0.708193i	0.935209	+	0.354097i	$0.115212\pi$
$229$			2454.17i			0.708193i	−0.935209	+	0.354097i	$0.884788\pi$
$230$		0			0
$231$	−1531.88	−	2653.30i	−0.436322	−	0.755732i
$232$		0			0
$233$	4251.72			1.19545			0.597724	−	0.801702i	$-0.296072\pi$
$233$	4251.72			1.19545			0.597724	+	0.801702i	$0.296072\pi$
$234$		0			0
$235$	35.2899			0.00979599
$236$		0			0
$237$	−1434.00	−	2483.75i	−0.393029	−	0.680747i
$238$		0			0
$239$			302.969i			0.0819977i	0.999159	+	0.0409988i	$0.0130540\pi$
$239$			302.969i			0.0819977i	−0.999159	+	0.0409988i	$0.986946\pi$
$240$		0			0
$241$	−874.074	−	504.647i	−0.233627	−	0.134884i	0.378617	−	0.925553i	$-0.376400\pi$
$241$	−874.074	−	504.647i	−0.233627	−	0.134884i	−0.612244	+	0.790669i	$0.709733\pi$
$242$		0			0
$243$	−451.047	+	781.236i	−0.119073	+	0.206240i
$244$		0			0
$245$	−7.70160	+	4.44652i	−0.00200832	+	0.00115950i
$246$		0			0
$247$	1574.88	−	899.582i	0.405696	−	0.231737i
$248$		0			0
$249$	3143.92	−	1815.14i	0.800152	−	0.461968i
$250$		0			0
$251$	−1661.62	+	2878.02i	−0.417852	+	0.723741i	−0.995723	−	0.0923872i	$-0.970550\pi$
$251$	−1661.62	+	2878.02i	−0.417852	+	0.723741i	0.577871	+	0.816128i	$0.303884\pi$
$252$		0			0
$253$	−3106.91	−	1793.78i	−0.772055	−	0.445746i
$254$		0			0
$255$			50.7101i			0.0124533i
$256$		0			0
$257$	3204.14	+	5549.73i	0.777698	+	1.34701i	0.933265	+	0.359188i	$0.116946\pi$
$257$	3204.14	+	5549.73i	0.777698	+	1.34701i	−0.155567	+	0.987825i	$0.549720\pi$
$258$		0			0
$259$	−4642.70			−1.11384
$260$		0			0
$261$	−622.485			−0.147628
$262$		0			0
$263$	2142.32	+	3710.61i	0.502286	+	0.869985i	0.999997	+	0.00264167i	$0.000840872\pi$
$263$	2142.32	+	3710.61i	0.502286	+	0.869985i	−0.497710	+	0.867343i	$0.665826\pi$
$264$		0			0
$265$		−	45.6348i		−	0.0105786i
$266$		0			0
$267$	5273.86	+	3044.86i	1.20882	+	0.697912i
$268$		0			0
$269$	−2840.56	+	4920.00i	−0.643837	+	1.11516i	0.340732	+	0.940160i	$0.389325\pi$
$269$	−2840.56	+	4920.00i	−0.643837	+	1.11516i	−0.984569	+	0.174997i	$0.944008\pi$
$270$		0			0
$271$	−4255.71	+	2457.03i	−0.953933	+	0.550753i	−0.894300	−	0.447467i	$-0.852326\pi$
$271$	−4255.71	+	2457.03i	−0.953933	+	0.550753i	−0.0596325	+	0.998220i	$0.518993\pi$
$272$		0			0
$273$	3196.16	+	1865.04i	0.708572	+	0.413470i
$274$		0			0
$275$	4200.55	−	2425.19i	0.921101	−	0.531798i
$276$		0			0
$277$	−3869.67	+	6702.46i	−0.839371	+	1.45383i	0.0510496	+	0.998696i	$0.483743\pi$
$277$	−3869.67	+	6702.46i	−0.839371	+	1.45383i	−0.890421	+	0.455138i	$0.849590\pi$
$278$		0			0
$279$	−444.061	−	256.379i	−0.0952876	−	0.0550143i
$280$		0			0
$281$		−	4205.91i		−	0.892895i	−0.894810	−	0.446447i	$-0.852689\pi$
$281$		−	4205.91i		−	0.892895i	0.894810	−	0.446447i	$-0.147311\pi$
$282$		0			0
$283$	1672.67	+	2897.15i	0.351343	+	0.608543i	0.986485	−	0.163852i	$-0.0523919\pi$
$283$	1672.67	+	2897.15i	0.351343	+	0.608543i	−0.635142	+	0.772395i	$0.719059\pi$
$284$		0			0
$285$	20.7760			0.00431811
$286$		0			0
$287$	3793.78			0.780279
$288$		0			0
$289$	−2003.49	−	3470.15i	−0.407794	−	0.706320i
$290$		0			0
$291$		−	5872.17i		−	1.18293i
$292$		0			0
$293$	4787.46	+	2764.04i	0.954561	+	0.551116i	0.894495	−	0.447078i	$-0.147535\pi$
$293$	4787.46	+	2764.04i	0.954561	+	0.551116i	0.0600664	+	0.998194i	$0.480869\pi$
$294$		0			0
$295$	14.1802	−	24.5608i	0.00279865	−	0.00484741i
$296$		0			0
$297$	−4953.45	+	2859.87i	−0.967772	+	0.558743i
$298$		0			0
$299$	4333.12	+	20.0158i	0.838096	+	0.00387138i
$300$		0			0
$301$	7375.13	−	4258.03i	1.41228	−	0.815379i
$302$		0			0
$303$	−1530.11	+	2650.23i	−0.290107	+	0.502480i
$304$		0			0
$305$	13.6688	+	7.89168i	0.00256614	+	0.00148156i
$306$		0			0
$307$			10085.6i			1.87497i	0.348030	+	0.937484i	$0.386851\pi$
$307$			10085.6i			1.87497i	−0.348030	+	0.937484i	$0.613149\pi$
$308$		0			0
$309$	1297.47	+	2247.29i	0.238870	+	0.413734i
$310$		0			0
$311$	−6397.41			−1.16644			−0.583222	−	0.812313i	$-0.698208\pi$
$311$	−6397.41			−1.16644			−0.583222	+	0.812313i	$0.698208\pi$
$312$		0			0
$313$	2987.39			0.539480			0.269740	−	0.962933i	$-0.413062\pi$
$313$	2987.39			0.539480			0.269740	+	0.962933i	$0.413062\pi$
$314$		0			0
$315$	−2.88320	−	4.99385i	−0.000515714	−	0.000893242i
$316$		0			0
$317$		−	841.335i		−	0.149067i	−0.997219	−	0.0745333i	$-0.976253\pi$
$317$		−	841.335i		−	0.149067i	0.997219	−	0.0745333i	$-0.0237467\pi$
$318$		0			0
$319$	−6470.68	−	3735.85i	−1.13570	−	0.655697i
$320$		0			0
$321$	−3614.10	+	6259.81i	−0.628410	+	1.08844i
$322$		0			0
$323$	−3164.91	+	1827.26i	−0.545202	+	0.314773i
$324$		0			0
$325$	−2952.63	+	5059.98i	−0.503946	+	0.863623i
$326$		0			0
$327$	−305.018	+	176.102i	−0.0515827	+	0.0297813i
$328$		0			0
$329$	−2594.51	+	4493.82i	−0.434771	+	0.753046i
$330$		0			0
$331$	2586.21	+	1493.15i	0.429459	+	0.247948i	0.699116	−	0.715008i	$-0.253577\pi$
$331$	2586.21	+	1493.15i	0.429459	+	0.247948i	−0.269657	+	0.962956i	$0.586910\pi$
$332$		0			0
$333$			926.890i			0.152532i
$334$		0			0
$335$	24.9723	+	43.2532i	0.00407278	+	0.00705426i
$336$		0			0
$337$	−8483.23			−1.37125			−0.685625	−	0.727955i	$-0.740471\pi$
$337$	−8483.23			−1.37125			−0.685625	+	0.727955i	$0.740471\pi$
$338$		0			0
$339$	2865.59			0.459108
$340$		0			0
$341$	−3077.32	−	5330.07i	−0.488698	−	0.846450i
$342$		0			0
$343$		−	6862.25i		−	1.08025i
$344$		0			0
$345$	42.9866	+	24.8183i	0.00670818	+	0.00387297i
$346$		0			0
$347$	−1054.36	+	1826.21i	−0.163115	+	0.282524i	−0.935984	−	0.352041i	$-0.885488\pi$
$347$	−1054.36	+	1826.21i	−0.163115	+	0.282524i	0.772869	+	0.634566i	$0.218821\pi$
$348$		0			0
$349$	7978.73	−	4606.52i	1.22376	−	0.706537i	0.258042	−	0.966134i	$-0.416923\pi$
$349$	7978.73	−	4606.52i	1.22376	−	0.706537i	0.965717	+	0.259596i	$0.0835895\pi$
$350$		0			0
$351$	3481.85	−	5966.92i	0.529480	−	0.907381i
$352$		0			0
$353$	347.274	−	200.499i	0.0523613	−	0.0302308i	−0.473591	−	0.880745i	$-0.657042\pi$
$353$	347.274	−	200.499i	0.0523613	−	0.0302308i	0.525952	+	0.850514i	$0.323709\pi$
$354$		0			0
$355$	41.6258	−	72.0980i	0.00622329	−	0.0107790i
$356$		0			0
$357$	−6457.43	−	3728.20i	−0.957320	−	0.552709i
$358$		0			0
$359$			2709.95i			0.398400i	0.979959	+	0.199200i	$0.0638344\pi$
$359$			2709.95i			0.398400i	−0.979959	+	0.199200i	$0.936166\pi$
$360$		0			0
$361$	−2680.87	−	4643.40i	−0.390854	−	0.676979i
$362$		0			0
$363$	−852.996			−0.123335
$364$		0			0
$365$	−70.6086			−0.0101255
$366$		0			0
$367$	−183.562	−	317.939i	−0.0261087	−	0.0452215i	0.852676	−	0.522440i	$-0.174978\pi$
$367$	−183.562	−	317.939i	−0.0261087	−	0.0452215i	−0.878785	+	0.477219i	$0.841645\pi$
$368$		0			0
$369$		−	757.408i		−	0.106854i
$370$		0			0
$371$	5811.13	+	3355.06i	0.813205	+	0.469504i
$372$		0			0
$373$	−1399.02	+	2423.17i	−0.194205	+	0.336373i	−0.946640	−	0.322294i	$-0.895546\pi$
$373$	−1399.02	+	2423.17i	−0.194205	+	0.336373i	0.752435	+	0.658667i	$0.228879\pi$
$374$		0			0
$375$	−116.242	+	67.1122i	−0.0160072	+	0.00924176i
$376$		0			0
$377$	9024.47	+	41.6863i	1.23285	+	0.00569484i
$378$		0			0
$379$	3786.81	−	2186.32i	0.513234	−	0.296316i	−0.220928	−	0.975290i	$-0.570909\pi$
$379$	3786.81	−	2186.32i	0.513234	−	0.296316i	0.734162	+	0.678975i	$0.237575\pi$
$380$		0			0
$381$	5490.41	−	9509.68i	0.738274	−	1.27873i
$382$		0			0
$383$	−8471.57	−	4891.06i	−1.13023	−	0.652537i	−0.186235	−	0.982505i	$-0.559629\pi$
$383$	−8471.57	−	4891.06i	−1.13023	−	0.652537i	−0.943992	+	0.329968i	$0.892962\pi$
$384$		0			0
$385$		−	69.2141i		−	0.00916228i
$386$		0			0
$387$	−850.093	−	1472.40i	−0.111661	−	0.193402i
$388$		0			0
$389$	−1150.89			−0.150007			−0.0750033	−	0.997183i	$-0.523897\pi$
$389$	−1150.89			−0.150007			−0.0750033	+	0.997183i	$0.523897\pi$
$390$		0			0
$391$	−8731.17			−1.12929
$392$		0			0
$393$	−491.888	−	851.975i	−0.0631361	−	0.109355i
$394$		0			0
$395$		−	64.7914i		−	0.00825319i
$396$		0			0
$397$	8339.28	+	4814.69i	1.05425	+	0.608671i	0.923836	−	0.382789i	$-0.125036\pi$
$397$	8339.28	+	4814.69i	1.05425	+	0.608671i	0.130413	+	0.991460i	$0.458370\pi$
$398$		0			0
$399$	−1527.45	+	2645.61i	−0.191649	+	0.331946i
$400$		0			0
$401$	−5373.63	+	3102.47i	−0.669192	+	0.386358i	−0.795771	−	0.605598i	$-0.792934\pi$
$401$	−5373.63	+	3102.47i	−0.669192	+	0.386358i	0.126578	+	0.991957i	$0.459601\pi$
$402$		0			0
$403$	6420.60	+	3746.58i	0.793630	+	0.463103i
$404$		0			0
$405$	60.2089	−	34.7616i	0.00738717	−	0.00426499i
$406$		0			0
$407$	−5562.74	+	9634.94i	−0.677481	+	1.17343i
$408$		0			0
$409$	4901.86	+	2830.09i	0.592619	+	0.342149i	0.766132	−	0.642683i	$-0.222179\pi$
$409$	4901.86	+	2830.09i	0.592619	+	0.342149i	−0.173513	+	0.984832i	$0.555512\pi$
$410$		0			0
$411$		−	9364.02i		−	1.12383i
$412$		0			0
$413$	2085.05	+	3611.41i	0.248423	+	0.430281i
$414$		0			0
$415$	82.0127			0.00970083
$416$		0			0
$417$	1092.71			0.128322
$418$		0			0
$419$	−1834.51	−	3177.47i	−0.213895	−	0.370477i	0.739035	−	0.673667i	$-0.235282\pi$
$419$	−1834.51	−	3177.47i	−0.213895	−	0.370477i	−0.952930	+	0.303190i	$0.901948\pi$
$420$		0			0
$421$		−	13716.5i		−	1.58789i	−0.607991	−	0.793944i	$-0.708024\pi$
$421$		−	13716.5i		−	1.58789i	0.607991	−	0.793944i	$-0.291976\pi$
$422$		0			0
$423$	897.166	+	517.979i	0.103125	+	0.0595390i
$424$		0			0
$425$	5902.28	−	10223.1i	0.673653	−	1.16680i
$426$		0			0
$427$	−2009.86	+	1160.39i	−0.227784	+	0.131511i
$428$		0			0
$429$	7700.02	−	4398.31i	0.866575	−	0.494994i
$430$		0			0
$431$	13180.5	−	7609.74i	1.47304	−	0.850460i	0.473500	−	0.880794i	$-0.342990\pi$
$431$	13180.5	−	7609.74i	1.47304	−	0.850460i	0.999540	+	0.0303334i	$0.00965690\pi$
$432$		0			0
$433$	−8097.51	+	14025.3i	−0.898710	+	1.55661i	−0.0695656	+	0.997577i	$0.522161\pi$
$433$	−8097.51	+	14025.3i	−0.898710	+	1.55661i	−0.829145	+	0.559034i	$0.811172\pi$
$434$		0			0
$435$	89.5270	+	51.6885i	0.00986780	+	0.00569718i
$436$		0			0
$437$			3577.17i			0.391577i
$438$		0			0
$439$	1136.17	+	1967.90i	0.123522	+	0.213947i	0.921154	−	0.389197i	$-0.127248\pi$
$439$	1136.17	+	1967.90i	0.123522	+	0.213947i	−0.797632	+	0.603144i	$0.793914\pi$
$440$		0			0
$441$	−261.061			−0.0281893
$442$		0			0
$443$	13195.8			1.41524			0.707622	−	0.706591i	$-0.249768\pi$
$443$	13195.8			1.41524			0.707622	+	0.706591i	$0.249768\pi$
$444$		0			0
$445$	68.7872	+	119.143i	0.00732770	+	0.0126919i
$446$		0			0
$447$		−	11305.7i		−	1.19629i
$448$		0			0
$449$	−12667.8	−	7313.74i	−1.33147	−	0.768724i	−0.345944	−	0.938255i	$-0.612441\pi$
$449$	−12667.8	−	7313.74i	−1.33147	−	0.768724i	−0.985525	+	0.169532i	$0.945775\pi$
$450$		0			0
$451$	4545.59	−	7873.19i	0.474597	−	0.822027i
$452$		0			0
$453$	−8283.49	+	4782.47i	−0.859144	+	0.496027i
$454$		0			0
$455$	41.4647	+	72.5913i	0.00427230	+	0.00747941i
$456$		0			0
$457$	2790.63	−	1611.17i	0.285646	−	0.164918i	−0.350331	−	0.936626i	$-0.613931\pi$
$457$	2790.63	−	1611.17i	0.285646	−	0.164918i	0.635977	+	0.771708i	$0.280598\pi$
$458$		0			0
$459$	−6960.19	+	12055.4i	−0.707786	+	1.22592i
$460$		0			0
$461$	1134.40	+	654.948i	0.114608	+	0.0661691i	0.556208	−	0.831043i	$-0.312256\pi$
$461$	1134.40	+	654.948i	0.114608	+	0.0661691i	−0.441600	+	0.897212i	$0.645589\pi$
$462$		0			0
$463$		−	16084.0i		−	1.61444i	−0.590249	−	0.807221i	$-0.700970\pi$
$463$		−	16084.0i		−	1.61444i	0.590249	−	0.807221i	$-0.299030\pi$
$464$		0			0
$465$	42.5772	+	73.7458i	0.00424617	+	0.00735458i
$466$		0			0
$467$	10100.7			1.00087			0.500435	−	0.865774i	$-0.333173\pi$
$467$	10100.7			1.00087			0.500435	+	0.865774i	$0.333173\pi$
$468$		0			0
$469$	−7343.83			−0.723042
$470$		0			0
$471$	−6092.01	−	10551.7i	−0.595977	−	1.03226i
$472$		0			0
$473$		−	20407.3i		−	1.98379i
$474$		0			0
$475$	−4188.39	−	2418.17i	−0.404582	−	0.233586i
$476$		0			0
$477$	669.819	−	1160.16i	0.0642954	−	0.111363i
$478$		0			0
$479$	−7343.90	+	4240.00i	−0.700525	+	0.404448i	−0.807543	−	0.589809i	$-0.799203\pi$
$479$	−7343.90	+	4240.00i	−0.700525	+	0.404448i	0.107018	+	0.994257i	$0.465870\pi$
$480$		0			0
$481$	62.0716	−	13437.6i	0.00588404	−	1.27381i
$482$		0			0
$483$	−6320.74	+	3649.28i	−0.595453	+	0.343785i
$484$		0			0
$485$	66.3298	−	114.887i	0.00621006	−	0.0107561i
$486$		0			0
$487$	5865.01	+	3386.17i	0.545727	+	0.315076i	0.747397	−	0.664378i	$-0.231303\pi$
$487$	5865.01	+	3386.17i	0.545727	+	0.315076i	−0.201670	+	0.979454i	$0.564637\pi$
$488$		0			0
$489$			12884.1i			1.19149i
$490$		0			0
$491$	4212.80	+	7296.79i	0.387212	+	0.670671i	0.992073	−	0.125660i	$-0.0401047\pi$
$491$	4212.80	+	7296.79i	0.387212	+	0.670671i	−0.604861	+	0.796331i	$0.706771\pi$
$492$		0			0
$493$	−18184.2			−1.66120
$494$		0			0
$495$	−13.8182			−0.00125471
$496$		0			0
$497$	6120.64	+	10601.3i	0.552411	+	0.956804i
$498$		0			0
$499$		−	12421.7i		−	1.11437i	−0.830388	−	0.557186i	$-0.811881\pi$
$499$		−	12421.7i		−	1.11437i	0.830388	−	0.557186i	$-0.188119\pi$
$500$		0			0
$501$	−3626.98	−	2094.04i	−0.323436	−	0.186736i
$502$		0			0
$503$	−5642.87	+	9773.74i	−0.500205	+	0.866381i	0.499795	+	0.866144i	$0.333409\pi$
$503$	−5642.87	+	9773.74i	−0.500205	+	0.866381i	−1.00000		0.000236966i	$0.999925\pi$
$504$		0			0
$505$	−59.8719	+	34.5670i	−0.00527577	+	0.00304597i
$506$		0			0
$507$	−5440.80	+	9225.84i	−0.476596	+	0.808154i
$508$		0			0
$509$	9718.44	−	5610.95i	0.846292	−	0.488607i	−0.0131062	−	0.999914i	$-0.504172\pi$
$509$	9718.44	−	5610.95i	0.846292	−	0.488607i	0.859398	+	0.511307i	$0.170839\pi$
$510$		0			0
$511$	5191.13	−	8991.30i	0.449397	−	0.778379i
$512$		0			0
$513$	4939.11	+	2851.59i	0.425082	+	0.245421i
$514$		0			0
$515$			58.6230i			0.00501600i
$516$		0			0
$517$	6217.31	+	10768.7i	0.528891	+	0.916067i
$518$		0			0
$519$	−10301.8			−0.871288
$520$		0			0
$521$	9592.88			0.806664			0.403332	−	0.915054i	$-0.367852\pi$
$521$	9592.88			0.806664			0.403332	+	0.915054i	$0.367852\pi$
$522$		0			0
$523$	−265.667	−	460.149i	−0.0222119	−	0.0384721i	0.854706	−	0.519113i	$-0.173738\pi$
$523$	−265.667	−	460.149i	−0.0222119	−	0.0384721i	−0.876918	+	0.480641i	$0.840404\pi$
$524$		0			0
$525$		−	9867.67i		−	0.820306i
$526$		0			0
$527$	−12972.0	−	7489.39i	−1.07224	−	0.619056i
$528$		0			0
$529$	1810.33	−	3135.58i	0.148790	−	0.257712i
$530$		0			0
$531$	720.999	−	416.269i	0.0589241	−	0.0340198i
$532$		0			0
$533$	−50.7218	+	10980.5i	−0.00412196	+	0.892343i
$534$		0			0
$535$	−141.417	+	81.6470i	−0.0114280	+	0.00659796i
$536$		0			0
$537$	510.737	−	884.623i	0.0410427	−	0.0710881i
$538$		0			0
$539$	−2713.71	−	1566.76i	−0.216860	−	0.125204i
$540$		0			0
$541$		−	3385.98i		−	0.269085i	−0.990908	−	0.134542i	$-0.957044\pi$
$541$		−	3385.98i		−	0.269085i	0.990908	−	0.134542i	$-0.0429564\pi$
$542$		0			0
$543$	10969.7	+	19000.1i	0.866954	+	1.50161i
$544$		0			0
$545$	−7.95674			−0.000625375
$546$		0			0
$547$	−21727.3			−1.69834			−0.849169	−	0.528121i	$-0.822897\pi$
$547$	−21727.3			−1.69834			−0.849169	+	0.528121i	$0.822897\pi$
$548$		0			0
$549$	231.666	+	401.256i	0.0180096	+	0.0311935i
$550$		0			0
$551$			7450.06i			0.576013i
$552$		0			0
$553$	8250.54	+	4763.45i	0.634446	+	0.366298i
$554$		0			0
$555$	76.9650	−	133.307i	0.00588645	−	0.0101956i
$556$		0			0
$557$	2201.34	−	1270.94i	0.167457	−	0.0966816i	−0.413929	−	0.910309i	$-0.635844\pi$
$557$	2201.34	−	1270.94i	0.167457	−	0.0966816i	0.581386	+	0.813628i	$0.302510\pi$
$558$		0			0
$559$	12225.6	+	21403.1i	0.925023	+	1.61942i
$560$		0			0
$561$	−15474.2	+	8934.01i	−1.16456	+	0.672360i
$562$		0			0
$563$	4573.52	−	7921.57i	0.342364	−	0.592992i	−0.642507	−	0.766280i	$-0.722106\pi$
$563$	4573.52	−	7921.57i	0.342364	−	0.592992i	0.984871	+	0.173288i	$0.0554391\pi$
$564$		0			0
$565$	56.0641	+	32.3686i	0.00417457	+	0.00241019i
$566$		0			0
$567$			10222.7i			0.757164i
$568$		0			0
$569$	−4178.43	−	7237.25i	−0.307854	−	0.533219i	0.670039	−	0.742326i	$-0.266278\pi$
$569$	−4178.43	−	7237.25i	−0.307854	−	0.533219i	−0.977893	+	0.209107i	$0.932944\pi$
$570$		0			0
$571$	1254.50			0.0919427			0.0459713	−	0.998943i	$-0.485362\pi$
$571$	1254.50			0.0919427			0.0459713	+	0.998943i	$0.485362\pi$
$572$		0			0
$573$	314.078			0.0228984
$574$		0			0
$575$	−5777.34	−	10006.7i	−0.419012	−	0.725750i
$576$		0			0
$577$			8182.68i			0.590381i	0.955438	+	0.295190i	$0.0953830\pi$
$577$			8182.68i			0.590381i	−0.955438	+	0.295190i	$0.904617\pi$
$578$		0			0
$579$	9230.90	+	5329.46i	0.662561	+	0.382530i
$580$		0			0
$581$	−6029.56	+	10443.5i	−0.430548	+	0.745730i
$582$		0			0
$583$	13925.4	−	8039.85i	0.989249	−	0.571143i
$584$		0			0
$585$	14.4924	−	8.27820i	0.00102425	−	0.000585062i
$586$		0			0
$587$	8583.51	−	4955.69i	0.603543	−	0.348455i	−0.166891	−	0.985975i	$-0.553373\pi$
$587$	8583.51	−	4955.69i	0.603543	−	0.348455i	0.770434	+	0.637520i	$0.220040\pi$
$588$		0			0
$589$	−3068.41	+	5314.64i	−0.214655	+	0.371793i
$590$		0			0
$591$	5719.75	+	3302.30i	0.398103	+	0.229845i
$592$		0			0
$593$		−	16356.5i		−	1.13268i	−0.824170	−	0.566342i	$-0.808358\pi$
$593$		−	16356.5i		−	1.13268i	0.824170	−	0.566342i	$-0.191642\pi$
$594$		0			0
$595$	−84.2246	−	145.881i	−0.00580314	−	0.0100513i
$596$		0			0
$597$	−6859.23			−0.470234
$598$		0			0
$599$	20073.9			1.36928			0.684640	−	0.728881i	$-0.259959\pi$
$599$	20073.9			1.36928			0.684640	+	0.728881i	$0.259959\pi$
$600$		0			0
$601$	3286.93	+	5693.13i	0.223089	+	0.386402i	0.955745	−	0.294198i	$-0.0950525\pi$
$601$	3286.93	+	5693.13i	0.223089	+	0.386402i	−0.732655	+	0.680600i	$0.761719\pi$
$602$		0			0
$603$			1466.15i			0.0990157i
$604$		0			0
$605$	−16.6885	−	9.63511i	−0.00112146	−	0.000647476i
$606$		0			0
$607$	−7187.22	+	12448.6i	−0.480593	+	0.832412i	−0.999752	−	0.0222657i	$-0.992912\pi$
$607$	−7187.22	+	12448.6i	−0.480593	+	0.832412i	0.519159	+	0.854678i	$0.326245\pi$
$608$		0			0
$609$	−13164.0	+	7600.25i	−0.875917	+	0.505711i
$610$		0			0
$611$	−12972.0	−	7569.47i	−0.858902	−	0.501191i
$612$		0			0
$613$	1095.61	−	632.550i	0.0721879	−	0.0416777i	−0.463472	−	0.886112i	$-0.653396\pi$
$613$	1095.61	−	632.550i	0.0721879	−	0.0416777i	0.535660	+	0.844434i	$0.320063\pi$
$614$		0			0
$615$	−62.8919	+	108.932i	−0.00412365	+	0.00714237i
$616$		0			0
$617$	16903.7	+	9759.33i	1.10294	+	0.636784i	0.936992	−	0.349350i	$-0.113598\pi$
$617$	16903.7	+	9759.33i	1.10294	+	0.636784i	0.165950	+	0.986134i	$0.446931\pi$
$618$		0			0
$619$			16094.2i			1.04504i	0.852626	+	0.522521i	$0.175008\pi$
$619$			16094.2i			1.04504i	−0.852626	+	0.522521i	$0.824992\pi$
$620$		0			0
$621$	6812.86	+	11800.2i	0.440242	+	0.762522i
$622$		0			0
$623$	−20228.9			−1.30089
$624$		0			0
$625$	15620.5			0.999709
$626$		0			0
$627$	3660.27	+	6339.77i	0.233137	+	0.403806i
$628$		0			0
$629$			27076.5i			1.71639i
$630$		0			0
$631$	14480.6	+	8360.35i	0.913569	+	0.527449i	0.881578	−	0.472039i	$-0.156482\pi$
$631$	14480.6	+	8360.35i	0.913569	+	0.527449i	0.0319910	+	0.999488i	$0.489815\pi$
$632$		0			0
$633$	−994.706	+	1722.88i	−0.0624581	+	0.108181i
$634$		0			0
$635$	214.835	−	124.035i	0.0134259	−	0.00775147i
$636$		0			0
$637$	3784.73	+	17.4826i	0.235410	+	0.00108742i
$638$		0			0
$639$	2116.48	−	1221.95i	0.131028	−	0.0756489i
$640$		0			0
$641$	−4882.19	+	8456.20i	−0.300834	+	0.521060i	−0.976325	−	0.216308i	$-0.930598\pi$
$641$	−4882.19	+	8456.20i	−0.300834	+	0.521060i	0.675491	+	0.737368i	$0.263932\pi$
$642$		0			0
$643$	−3455.26	−	1994.90i	−0.211916	−	0.122350i	0.390285	−	0.920694i	$-0.372376\pi$
$643$	−3455.26	−	1994.90i	−0.211916	−	0.122350i	−0.602202	+	0.798344i	$0.705710\pi$
$644$		0			0
$645$			282.352i			0.0172366i
$646$		0			0
$647$	193.788	+	335.650i	0.0117752	+	0.0203953i	0.871853	−	0.489768i	$-0.162918\pi$
$647$	193.788	+	335.650i	0.0117752	+	0.0203953i	−0.860078	+	0.510163i	$0.829585\pi$
$648$		0			0
$649$	9992.96			0.604404
$650$		0			0
$651$	−12521.1			−0.753823
$652$		0			0
$653$	−7564.69	−	13102.4i	−0.453337	−	0.785203i	0.545254	−	0.838271i	$-0.316433\pi$
$653$	−7564.69	−	13102.4i	−0.453337	−	0.785203i	−0.998591	+	0.0530682i	$0.983100\pi$
$654$		0			0
$655$		−	22.2247i		−	0.00132579i
$656$		0			0
$657$	−1795.06	−	1036.38i	−0.106594	−	0.0615419i
$658$		0			0
$659$	4997.61	−	8656.12i	0.295416	−	0.511676i	−0.679665	−	0.733522i	$-0.737875\pi$
$659$	4997.61	−	8656.12i	0.295416	−	0.511676i	0.975082	+	0.221846i	$0.0712083\pi$
$660$		0			0
$661$	4915.76	−	2838.11i	0.289260	−	0.167004i	−0.348348	−	0.937365i	$-0.613257\pi$
$661$	4915.76	−	2838.11i	0.289260	−	0.167004i	0.637608	+	0.770361i	$0.279924\pi$
$662$		0			0
$663$	10877.0	−	18640.2i	0.637147	−	1.09189i
$664$		0			0
$665$	−59.7676	+	34.5069i	−0.00348525	+	0.00201221i
$666$		0			0
$667$	−8899.62	+	15414.6i	−0.516634	+	0.894836i
$668$		0			0
$669$	10951.3	+	6322.71i	0.632885	+	0.365397i
$670$		0			0
$671$			5561.37i			0.319962i
$672$		0			0
$673$	−4590.03	−	7950.17i	−0.262901	−	0.455359i	0.704110	−	0.710091i	$-0.251346\pi$
$673$	−4590.03	−	7950.17i	−0.262901	−	0.455359i	−0.967012	+	0.254732i	$0.918013\pi$
$674$		0			0
$675$	−18422.0			−1.05046
$676$		0			0
$677$	−25308.1			−1.43673			−0.718366	−	0.695665i	$-0.755110\pi$
$677$	−25308.1			−1.43673			−0.718366	+	0.695665i	$0.755110\pi$
$678$		0			0
$679$	9753.11	+	16892.9i	0.551237	+	0.954770i
$680$		0			0
$681$		−	25387.7i		−	1.42857i
$682$		0			0
$683$	13192.5	+	7616.72i	0.739090	+	0.426714i	0.821738	−	0.569865i	$-0.193004\pi$
$683$	13192.5	+	7616.72i	0.739090	+	0.426714i	−0.0826483	+	0.996579i	$0.526338\pi$
$684$		0			0
$685$	105.772	−	183.203i	0.00589979	−	0.0102187i
$686$		0			0
$687$	10361.5	−	5982.20i	0.575422	−	0.332220i
$688$		0			0
$689$	−9788.38	+	16774.6i	−0.541230	+	0.927518i
$690$		0			0
$691$	−10818.4	+	6246.03i	−0.595590	+	0.343864i	−0.767305	−	0.641283i	$-0.778403\pi$
$691$	−10818.4	+	6246.03i	−0.595590	+	0.343864i	0.171715	+	0.985147i	$0.445069\pi$
$692$		0			0
$693$	1015.91	−	1759.61i	0.0556874	−	0.0964533i
$694$		0			0
$695$	21.3784	+	12.3428i	0.00116680	+	0.000673654i
$696$		0			0
$697$		−	22125.5i		−	1.20239i
$698$		0			0
$699$	−10363.9	−	17950.7i	−0.560797	−	0.971328i
$700$		0			0
$701$	11945.1			0.643597			0.321799	−	0.946808i	$-0.395713\pi$
$701$	11945.1			0.643597			0.321799	+	0.946808i	$0.395713\pi$
$702$		0			0
$703$	11093.3			0.595150
$704$		0			0
$705$	−86.0214	−	148.993i	−0.00459540	−	0.00795946i
$706$		0			0
$707$		−	10165.5i		−	0.540751i
$708$		0			0
$709$	3204.65	+	1850.20i	0.169750	+	0.0980054i	0.582468	−	0.812854i	$-0.302087\pi$
$709$	3204.65	+	1850.20i	0.169750	+	0.0980054i	−0.412718	+	0.910859i	$0.635420\pi$
$710$		0			0
$711$	950.997	−	1647.18i	0.0501620	−	0.0868831i
$712$		0			0
$713$	−12697.4	+	7330.85i	−0.666931	+	0.385053i
$714$		0			0
$715$	200.329	+	0.925372i	0.0104782	+	4.84013e-5i
$716$		0			0
$717$	1279.13	−	738.507i	0.0666249	−	0.0384659i
$718$		0			0
$719$	1756.18	−	3041.79i	0.0910910	−	0.157774i	−0.816879	−	0.576808i	$-0.804298\pi$
$719$	1756.18	−	3041.79i	0.0910910	−	0.157774i	0.907970	+	0.419034i	$0.137631\pi$
$720$		0			0
$721$	−7465.06	−	4309.96i	−0.385594	−	0.222623i
$722$		0			0
$723$			4920.44i			0.253102i
$724$		0			0
$725$	−12032.3	−	20840.6i	−0.616371	−	1.06759i
$726$		0			0
$727$	−9484.80			−0.483868			−0.241934	−	0.970293i	$-0.577782\pi$
$727$	−9484.80			−0.483868			−0.241934	+	0.970293i	$0.577782\pi$
$728$		0			0
$729$	21441.7			1.08935
$730$		0			0
$731$	−24833.1	−	43012.2i	−1.25648	−	2.17628i
$732$		0			0
$733$			11063.5i			0.557490i	0.960365	+	0.278745i	$0.0899184\pi$
$733$			11063.5i			0.557490i	−0.960365	+	0.278745i	$0.910082\pi$
$734$		0			0
$735$	37.5463	+	21.6774i	0.00188424	+	0.00108787i
$736$		0			0
$737$	−8799.14	+	15240.5i	−0.439783	+	0.761727i
$738$		0			0
$739$	−7104.94	+	4102.04i	−0.353666	+	0.204189i	−0.666299	−	0.745685i	$-0.732122\pi$
$739$	−7104.94	+	4102.04i	−0.353666	+	0.204189i	0.312633	+	0.949874i	$0.398789\pi$
$740$		0			0
$741$	−7636.89	−	4456.32i	−0.378607	−	0.220927i
$742$		0			0
$743$	−7119.87	+	4110.66i	−0.351552	+	0.202968i	−0.665368	−	0.746515i	$-0.731726\pi$
$743$	−7119.87	+	4110.66i	−0.351552	+	0.202968i	0.313817	+	0.949484i	$0.398392\pi$
$744$		0			0
$745$	127.705	−	221.192i	0.00628021	−	0.0108776i
$746$		0			0
$747$	2084.99	+	1203.77i	0.102123	+	0.0589606i
$748$		0			0
$749$		−	24010.7i		−	1.17134i
$750$		0			0
$751$	−6732.53	−	11661.1i	−0.327129	−	0.566603i	0.654812	−	0.755792i	$-0.272748\pi$
$751$	−6732.53	−	11661.1i	−0.327129	−	0.566603i	−0.981941	+	0.189188i	$0.939414\pi$
$752$		0			0
$753$	16201.3			0.784074
$754$		0			0
$755$	−216.084			−0.0104160
$756$		0			0
$757$	−12027.9	−	20832.9i	−0.577491	−	1.00024i	−0.995766	−	0.0919236i	$-0.970698\pi$
$757$	−12027.9	−	20832.9i	−0.577491	−	1.00024i	0.418275	−	0.908321i	$-0.362635\pi$
$758$		0			0
$759$			17489.8i			0.836415i
$760$		0			0
$761$	−21161.7	−	12217.7i	−1.00803	−	0.581987i	−0.0974168	−	0.995244i	$-0.531058\pi$
$761$	−21161.7	−	12217.7i	−1.00803	−	0.581987i	−0.910615	+	0.413256i	$0.864391\pi$
$762$		0			0
$763$	584.978	−	1013.21i	0.0277557	−	0.0480743i
$764$		0			0
$765$	−29.1244	+	16.8150i	−0.00137646	+	0.000794701i
$766$		0			0
$767$	−10480.5	+	5986.57i	−0.493391	+	0.281828i
$768$		0			0
$769$	12584.3	−	7265.54i	0.590118	−	0.340705i	−0.175026	−	0.984564i	$-0.556001\pi$
$769$	12584.3	−	7265.54i	0.590118	−	0.340705i	0.765144	+	0.643859i	$0.222668\pi$
$770$		0			0
$771$	15620.6	−	27055.6i	0.729652	−	1.26379i
$772$		0			0
$773$	−5022.43	−	2899.70i	−0.233692	−	0.134922i	0.378582	−	0.925568i	$-0.376412\pi$
$773$	−5022.43	−	2899.70i	−0.233692	−	0.134922i	−0.612274	+	0.790645i	$0.709745\pi$
$774$		0			0
$775$		−	19822.7i		−	0.918776i
$776$		0			0
$777$	11316.9	+	19601.4i	0.522512	+	0.905017i
$778$		0			0
$779$	−9064.86			−0.416922
$780$		0			0
$781$	29334.2			1.34400
$782$		0			0
$783$	14188.9	+	24576.0i	0.647601	+	1.12168i
$784$		0			0
$785$		−	275.252i		−	0.0125149i
$786$		0			0
$787$	−4078.30	−	2354.61i	−0.184722	−	0.106649i	0.404788	−	0.914411i	$-0.367345\pi$
$787$	−4078.30	−	2354.61i	−0.184722	−	0.106649i	−0.589509	+	0.807762i	$0.700679\pi$
$788$		0			0
$789$	10444.1	−	18089.7i	0.471255	−	0.816237i
$790$		0			0
$791$	−8243.65	+	4759.47i	−0.370557	+	0.213941i
$792$		0			0
$793$	−3331.70	−	5832.72i	−0.149195	−	0.261193i
$794$		0			0
$795$	−192.669	+	111.238i	−0.00859532	+	0.00496251i
$796$		0			0
$797$	2892.14	−	5009.34i	0.128538	−	0.222635i	−0.794572	−	0.607170i	$-0.792305\pi$
$797$	2892.14	−	5009.34i	0.128538	−	0.222635i	0.923110	+	0.384535i	$0.125638\pi$
$798$		0			0
$799$	26208.2	+	15131.3i	1.16042	+	0.669971i
$800$		0			0
$801$			4038.58i			0.178148i
$802$		0			0
$803$	−12439.7	−	21546.2i	−0.546683	−	0.946884i
$804$		0			0
$805$	−164.883			−0.00721910
$806$		0			0
$807$	27696.2			1.20812
$808$		0			0
$809$	4513.56	+	7817.71i	0.196154	+	0.339748i	0.947278	−	0.320413i	$-0.103822\pi$
$809$	4513.56	+	7817.71i	0.196154	+	0.339748i	−0.751125	+	0.660161i	$0.770488\pi$
$810$		0			0
$811$		−	8982.87i		−	0.388941i	−0.980908	−	0.194471i	$-0.937701\pi$
$811$		−	8982.87i		−	0.388941i	0.980908	−	0.194471i	$-0.0622989\pi$
$812$		0			0
$813$	20747.1	+	11978.4i	0.894999	+	0.516728i
$814$		0			0
$815$	−145.534	+	252.072i	−0.00625501	+	0.0108340i
$816$		0			0
$817$	−17622.1	+	10174.1i	−0.754614	+	0.435677i
$818$		0			0
$819$	−11.3360	+	2454.08i	−0.000483654	+	0.104704i
$820$		0			0
$821$	4440.94	−	2563.98i	0.188782	−	0.108993i	−0.402630	−	0.915363i	$-0.631904\pi$
$821$	4440.94	−	2563.98i	0.188782	−	0.108993i	0.591412	+	0.806369i	$0.298571\pi$
$822$		0			0
$823$	18012.0	−	31197.7i	0.762890	−	1.32136i	−0.178465	−	0.983946i	$-0.557113\pi$
$823$	18012.0	−	31197.7i	0.762890	−	1.32136i	0.941355	−	0.337418i	$-0.109553\pi$
$824$		0			0
$825$	−20478.3	−	11823.1i	−0.864195	−	0.498943i
$826$		0			0
$827$		−	11728.0i		−	0.493136i	−0.969126	−	0.246568i	$-0.920697\pi$
$827$		−	11728.0i		−	0.493136i	0.969126	−	0.246568i	$-0.0793028\pi$
$828$		0			0
$829$	−7543.28	−	13065.3i	−0.316030	−	0.547380i	0.663626	−	0.748065i	$-0.269017\pi$
$829$	−7543.28	−	13065.3i	−0.316030	−	0.547380i	−0.979656	+	0.200684i	$0.935683\pi$
$830$		0			0
$831$	37730.3			1.57503
$832$		0			0
$833$	−7626.17			−0.317204
$834$		0			0
$835$	−47.3069	−	81.9380i	−0.00196063	−	0.00339590i
$836$		0			0
$837$			23375.6i			0.965328i
$838$		0			0
$839$	−23716.0	−	13692.5i	−0.975886	−	0.563428i	−0.0748602	−	0.997194i	$-0.523851\pi$
$839$	−23716.0	−	13692.5i	−0.975886	−	0.563428i	−0.901025	+	0.433766i	$0.857184\pi$
$840$		0			0
$841$	−6340.49	+	10982.0i	−0.259973	+	0.450287i
$842$		0			0
$843$	−17757.3	+	10252.2i	−0.725497	+	0.418866i
$844$		0			0
$845$	−210.658	+	119.042i	−0.00857617	+	0.00484637i
$846$		0			0
$847$	2453.87	−	1416.74i	0.0995467	−	0.0574733i
$848$		0			0
$849$	8154.49	−	14124.0i	0.329636	−	0.570947i
$850$		0			0
$851$	22952.6	+	13251.7i	0.924564	+	0.533797i
$852$		0			0
$853$			30583.1i			1.22760i	0.789460	+	0.613802i	$0.210361\pi$
$853$			30583.1i			1.22760i	−0.789460	+	0.613802i	$0.789639\pi$
$854$		0			0
$855$	6.88910	+	11.9323i	0.000275558	+	0.000477281i
$856$		0			0
$857$	−19542.8			−0.778962			−0.389481	−	0.921035i	$-0.627346\pi$
$857$	−19542.8			−0.778962			−0.389481	+	0.921035i	$0.627346\pi$
$858$		0			0
$859$	3593.03			0.142716			0.0713578	−	0.997451i	$-0.477267\pi$
$859$	3593.03			0.142716			0.0713578	+	0.997451i	$0.477267\pi$
$860$		0			0
$861$	−9247.60	−	16017.3i	−0.366036	−	0.633994i
$862$		0			0
$863$			22652.3i			0.893501i	0.894658	+	0.446751i	$0.147419\pi$
$863$			22652.3i			0.893501i	−0.894658	+	0.446751i	$0.852581\pi$
$864$		0			0
$865$	−201.550	−	116.365i	−0.00792244	−	0.00457402i
$866$		0			0
$867$	−9767.29	+	16917.4i	−0.382600	+	0.662683i
$868$		0			0
$869$	19771.1	−	11414.8i	0.771792	−	0.445594i
$870$		0			0
$871$	98.1848	−	21255.6i	0.00381959	−	0.826885i
$872$		0			0
$873$	3372.57	−	1947.15i	0.130749	−	0.0754882i
$874$		0			0
$875$	222.934	−	386.132i	0.00861318	−	0.0149185i
$876$		0			0
$877$	3379.00	+	1950.86i	0.130103	+	0.0751152i	0.563639	−	0.826021i	$-0.309401\pi$
$877$	3379.00	+	1950.86i	0.130103	+	0.0751152i	−0.433536	+	0.901136i	$0.642734\pi$
$878$		0			0
$879$		−	26950.1i		−	1.03414i
$880$		0			0
$881$	−18576.6	−	32175.6i	−0.710398	−	1.23044i	−0.964708	−	0.263322i	$-0.915182\pi$
$881$	−18576.6	−	32175.6i	−0.710398	−	1.23044i	0.254310	−	0.967123i	$-0.418152\pi$
$882$		0			0
$883$	32883.2			1.25324			0.626618	−	0.779326i	$-0.284439\pi$
$883$	32883.2			1.25324			0.626618	+	0.779326i	$0.284439\pi$
$884$		0			0
$885$	−138.261			−0.00525150
$886$		0			0
$887$	12940.4	+	22413.5i	0.489850	+	0.848445i	0.999932	−	0.0116807i	$-0.00371817\pi$
$887$	12940.4	+	22413.5i	0.489850	+	0.848445i	−0.510082	+	0.860126i	$0.670385\pi$
$888$		0			0
$889$			36476.2i			1.37612i
$890$		0			0
$891$	21215.0	+	12248.5i	0.797675	+	0.460538i
$892$		0			0
$893$	6199.31	−	10737.5i	0.232309	−	0.402371i
$894$		0			0
$895$	19.9847	−	11.5382i	0.000746386	−	0.000430926i
$896$		0			0
$897$	−10477.8	−	18343.2i	−0.390014	−	0.682788i
$898$		0			0
$899$	−26444.5	+	15267.8i	−0.981062	+	0.566416i
$900$		0			0
$901$	19566.9	−	33890.8i	0.723493	−	1.25313i
$902$		0			0
$903$	−35954.7	−	20758.5i	−1.32503	−	0.765004i
$904$		0			0
$905$			495.639i			0.0182051i
$906$		0			0
$907$	−11049.2	−	19137.8i	−0.404502	−	0.700617i	0.589762	−	0.807577i	$-0.299222\pi$
$907$	−11049.2	−	19137.8i	−0.404502	−	0.700617i	−0.994263	+	0.106960i	$0.965888\pi$
$908$		0			0
$909$	−2029.48			−0.0740522
$910$		0			0
$911$	−43509.4			−1.58236			−0.791180	−	0.611583i	$-0.790533\pi$
$911$	−43509.4			−1.58236			−0.791180	+	0.611583i	$0.790533\pi$
$912$		0			0
$913$	14448.8	+	25026.1i	0.523753	+	0.907167i
$914$		0			0
$915$		−	76.9460i		−	0.00278006i
$916$		0			0
$917$	2830.10	+	1633.96i	0.101917	+	0.0588419i
$918$		0			0
$919$	−6442.74	+	11159.2i	−0.231258	+	0.400551i	−0.958179	−	0.286170i	$-0.907618\pi$
$919$	−6442.74	+	11159.2i	−0.231258	+	0.400551i	0.726920	+	0.686722i	$0.240951\pi$
$920$		0			0
$921$	42581.2	−	24584.3i	1.52345	−	0.879565i
$922$		0			0
$923$	−30765.5	+	17573.5i	−1.09714	+	0.626694i
$924$		0			0
$925$	−31031.9	+	17916.3i	−1.10305	+	0.636848i
$926$		0			0
$927$	−860.459	+	1490.36i	−0.0304867	+	0.0528045i
$928$		0			0
$929$	9246.24	+	5338.32i	0.326544	+	0.188530i	0.654306	−	0.756230i	$-0.272961\pi$
$929$	9246.24	+	5338.32i	0.326544	+	0.188530i	−0.327762	+	0.944760i	$0.606294\pi$
$930$		0			0
$931$			3124.45i			0.109989i
$932$		0			0
$933$	15594.1	+	27009.8i	0.547190	+	0.947761i
$934$		0			0
$935$	−403.660			−0.0141188
$936$		0			0
$937$	−39125.1			−1.36410			−0.682050	−	0.731306i	$-0.738911\pi$
$937$	−39125.1			−1.36410			−0.682050	+	0.731306i	$0.738911\pi$
$938$		0			0
$939$	−7281.95	−	12612.7i	−0.253075	−	0.438339i
$940$		0			0
$941$		−	22571.0i		−	0.781926i	−0.920406	−	0.390963i	$-0.872142\pi$
$941$		−	22571.0i		−	0.781926i	0.920406	−	0.390963i	$-0.127858\pi$
$942$		0			0
$943$	−18755.7	−	10828.6i	−0.647687	−	0.373942i
$944$		0			0
$945$	−131.439	+	227.660i	−0.00452458	+	0.00783680i
$946$		0			0
$947$	−4052.60	+	2339.77i	−0.139062	+	0.0802874i	−0.567917	−	0.823086i	$-0.692250\pi$
$947$	−4052.60	+	2339.77i	−0.139062	+	0.0802874i	0.428855	+	0.903373i	$0.358917\pi$
$948$		0			0
$949$	25954.5	+	15145.1i	0.887796	+	0.518052i
$950$		0			0
$951$	−3552.11	+	2050.81i	−0.121120	+	0.0699286i
$952$		0			0
$953$	16683.0	−	28895.9i	0.567069	−	0.982192i	−0.429785	−	0.902931i	$-0.641411\pi$
$953$	16683.0	−	28895.9i	0.567069	−	0.982192i	0.996854	−	0.0792605i	$-0.0252559\pi$
$954$		0			0
$955$	6.14479	+	3.54770i	0.000208210	+	0.000120210i
$956$		0			0
$957$			36425.5i			1.23038i
$958$		0			0
$959$	15552.7	+	26938.1i	0.523695	+	0.907067i
$960$		0			0
$961$	4638.09			0.155688
$962$		0			0
$963$	−4793.60			−0.160407
$964$		0			0
$965$	120.399	+	208.537i	0.00401635	+	0.00695653i
$966$		0			0
$967$			56075.3i			1.86480i	0.361431	+	0.932399i	$0.382288\pi$
$967$			56075.3i			1.86480i	−0.361431	+	0.932399i	$0.617712\pi$
$968$		0			0
$969$	15429.4	+	8908.14i	0.511519	+	0.295326i
$970$		0			0
$971$	25273.7	−	43775.3i	0.835294	−	1.44677i	−0.0584964	−	0.998288i	$-0.518631\pi$
$971$	25273.7	−	43775.3i	0.835294	−	1.44677i	0.893791	−	0.448484i	$-0.148036\pi$
$972$		0			0
$973$	−3143.47	+	1814.88i	−0.103571	+	0.0597969i
$974$		0			0
$975$	28560.4	+	131.928i	0.938118	+	0.00433341i
$976$		0			0
$977$	−27148.1	+	15673.9i	−0.888990	+	0.513259i	−0.873612	−	0.486623i	$-0.838229\pi$
$977$	−27148.1	+	15673.9i	−0.888990	+	0.513259i	−0.0153782	+	0.999882i	$0.504895\pi$
$978$		0			0
$979$	−24237.6	+	41980.7i	−0.791253	+	1.37049i
$980$		0			0
$981$	−202.282	−	116.788i	−0.00658345	−	0.00380096i
$982$		0			0
$983$			6770.66i			0.219685i	0.993949	+	0.109843i	$0.0350346\pi$
$983$			6770.66i			0.219685i	−0.993949	+	0.109843i	$0.964965\pi$
$984$		0			0
$985$	74.6030	+	129.216i	0.00241325	+	0.00417987i
$986$		0			0
$987$	25297.1			0.815822
$988$		0			0
$989$	−48614.8			−1.56306
$990$		0			0
$991$	−3421.43	−	5926.09i	−0.109672	−	0.189958i	0.805965	−	0.591963i	$-0.201647\pi$
$991$	−3421.43	−	5926.09i	−0.109672	−	0.189958i	−0.915638	+	0.402005i	$0.868314\pi$
$992$		0			0
$993$		−	14558.6i		−	0.465259i
$994$		0			0
$995$	−134.198	−	77.4792i	−0.00427574	−	0.00246860i
$996$		0			0
$997$	−11882.5	+	20581.1i	−0.377455	+	0.653771i	−0.990691	−	0.136129i	$-0.956534\pi$
$997$	−11882.5	+	20581.1i	−0.377455	+	0.653771i	0.613237	+	0.789899i	$0.289867\pi$
$998$		0			0
$999$	36594.0	−	21127.6i	1.15894	−	0.669116i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	208.4.w.d.49.1		8
4.3	odd	2		26.4.e.a.23.4	yes	8
12.11	even	2		234.4.l.b.127.2		8
13.4	even	6	inner	208.4.w.d.17.1		8
52.3	odd	6		338.4.b.g.337.5		8
52.7	even	12		338.4.c.n.191.4		8
52.11	even	12		338.4.a.l.1.1		4
52.15	even	12		338.4.a.m.1.1		4
52.19	even	12		338.4.c.m.191.4		8
52.23	odd	6		338.4.b.g.337.1		8
52.31	even	4		338.4.c.m.315.4		8
52.35	odd	6		338.4.e.e.147.2		8
52.43	odd	6		26.4.e.a.17.4	✓	8
52.47	even	4		338.4.c.n.315.4		8
52.51	odd	2		338.4.e.e.23.2		8
156.95	even	6		234.4.l.b.199.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
26.4.e.a.17.4	✓	8	52.43	odd	6
26.4.e.a.23.4	yes	8	4.3	odd	2
208.4.w.d.17.1		8	13.4	even	6	inner
208.4.w.d.49.1		8	1.1	even	1	trivial
234.4.l.b.127.2		8	12.11	even	2
234.4.l.b.199.1		8	156.95	even	6
338.4.a.l.1.1		4	52.11	even	12
338.4.a.m.1.1		4	52.15	even	12
338.4.b.g.337.1		8	52.23	odd	6
338.4.b.g.337.5		8	52.3	odd	6
338.4.c.m.191.4		8	52.19	even	12
338.4.c.m.315.4		8	52.31	even	4
338.4.c.n.191.4		8	52.7	even	12
338.4.c.n.315.4		8	52.47	even	4
338.4.e.e.23.2		8	52.51	odd	2
338.4.e.e.147.2		8	52.35	odd	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:	\( N \)	\(=\)	\( 208 = 2^{4} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	208.w (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-2.43757 - 4.22199i) q^{3} -0.110135i q^{5} +(14.0246 + 8.09712i) q^{7} +(1.61655 - 2.79994i) q^{9} +O(q^{10})\)	\(q+(-2.43757 - 4.22199i) q^{3} -0.110135i q^{5} +(14.0246 + 8.09712i) q^{7} +(1.61655 - 2.79994i) q^{9} +(33.6077 - 19.4034i) q^{11} +(-23.6233 + 40.4838i) q^{13} +(-0.464989 + 0.268462i) q^{15} +(47.2228 - 81.7923i) q^{17} +(-33.5104 - 19.3472i) q^{19} -78.9491i q^{21} +(-46.2232 - 80.0610i) q^{23} +124.988 q^{25} -147.390 q^{27} +(-96.2678 - 166.741i) q^{29} -158.597i q^{31} +(-163.842 - 94.5942i) q^{33} +(0.891778 - 1.54460i) q^{35} +(-248.280 + 143.344i) q^{37} +(228.506 + 1.05553i) q^{39} +(202.882 - 117.134i) q^{41} +(262.935 - 455.417i) q^{43} +(-0.308372 - 0.178039i) q^{45} +320.423i q^{47} +(-40.3733 - 69.9286i) q^{49} -460.435 q^{51} +414.352 q^{53} +(-2.13700 - 3.70139i) q^{55} +188.641i q^{57} +(223.006 + 128.753i) q^{59} +(-71.6545 + 124.109i) q^{61} +(45.3429 - 26.1787i) q^{63} +(4.45869 + 2.60176i) q^{65} +(-392.729 + 226.742i) q^{67} +(-225.344 + 390.308i) q^{69} +(654.631 + 377.952i) q^{71} -641.108i q^{73} +(-304.666 - 527.697i) q^{75} +628.447 q^{77} +588.290 q^{79} +(315.627 + 546.682i) q^{81} +744.654i q^{83} +(-9.00822 - 5.20090i) q^{85} +(-469.318 + 812.883i) q^{87} +(-1081.79 + 624.570i) q^{89} +(-659.111 + 376.489i) q^{91} +(-669.593 + 386.590i) q^{93} +(-2.13081 + 3.69067i) q^{95} +(1043.14 + 602.258i) q^{97} -125.466i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 6 q^{3} - 18 q^{7} - 22 q^{9}+O(q^{10}) \) 8 * q + 6 * q^3 - 18 * q^7 - 22 * q^9	\( 8 q + 6 q^{3} - 18 q^{7} - 22 q^{9} + 18 q^{11} - 130 q^{13} + 192 q^{15} + 112 q^{17} - 594 q^{19} + 230 q^{23} - 180 q^{25} - 468 q^{27} + 32 q^{29} - 42 q^{33} + 128 q^{35} - 768 q^{37} + 230 q^{39} - 564 q^{41} + 114 q^{43} + 630 q^{45} - 110 q^{49} - 1300 q^{51} + 36 q^{53} - 1248 q^{55} + 1110 q^{59} + 900 q^{61} + 1980 q^{63} + 1870 q^{65} - 510 q^{67} - 2402 q^{69} + 1470 q^{71} + 862 q^{75} + 2340 q^{77} - 784 q^{79} + 1868 q^{81} - 2898 q^{85} - 1598 q^{87} - 4434 q^{89} + 886 q^{91} + 3108 q^{93} + 816 q^{95} + 1854 q^{97}+O(q^{100}) \) 8 * q + 6 * q^3 - 18 * q^7 - 22 * q^9 + 18 * q^11 - 130 * q^13 + 192 * q^15 + 112 * q^17 - 594 * q^19 + 230 * q^23 - 180 * q^25 - 468 * q^27 + 32 * q^29 - 42 * q^33 + 128 * q^35 - 768 * q^37 + 230 * q^39 - 564 * q^41 + 114 * q^43 + 630 * q^45 - 110 * q^49 - 1300 * q^51 + 36 * q^53 - 1248 * q^55 + 1110 * q^59 + 900 * q^61 + 1980 * q^63 + 1870 * q^65 - 510 * q^67 - 2402 * q^69 + 1470 * q^71 + 862 * q^75 + 2340 * q^77 - 784 * q^79 + 1868 * q^81 - 2898 * q^85 - 1598 * q^87 - 4434 * q^89 + 886 * q^91 + 3108 * q^93 + 816 * q^95 + 1854 * q^97

Introduction

L-functions

Modular forms

Varieties

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