LMFDB - Embedded newform 448.4.i.b.193.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [448,4,Mod(65,448)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(448, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 2]))

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

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

chi := DirichletCharacter("448.65");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 448 = 2^{6} \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	448.i (of order $3$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$26.4328556826$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 14)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			193.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	448.193
Dual form			448.4.i.b.65.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.50000 + 4.33013i) q^{3} +(-4.50000 - 7.79423i) q^{5} +(-14.0000 + 12.1244i) q^{7} +(1.00000 + 1.73205i) q^{9} +O(q^{10})$	\(q+(-2.50000 + 4.33013i) q^{3} +(-4.50000 - 7.79423i) q^{5} +(-14.0000 + 12.1244i) q^{7} +(1.00000 + 1.73205i) q^{9} +(-28.5000 + 49.3634i) q^{11} +70.0000 q^{13} +45.0000 q^{15} +(-25.5000 + 44.1673i) q^{17} +(2.50000 + 4.33013i) q^{19} +(-17.5000 - 90.9327i) q^{21} +(-34.5000 - 59.7558i) q^{23} +(22.0000 - 38.1051i) q^{25} -145.000 q^{27} -114.000 q^{29} +(-11.5000 + 19.9186i) q^{31} +(-142.500 - 246.817i) q^{33} +(157.500 + 54.5596i) q^{35} +(-126.500 - 219.104i) q^{37} +(-175.000 + 303.109i) q^{39} -42.0000 q^{41} +124.000 q^{43} +(9.00000 - 15.5885i) q^{45} +(-100.500 - 174.071i) q^{47} +(49.0000 - 339.482i) q^{49} +(-127.500 - 220.836i) q^{51} +(-196.500 + 340.348i) q^{53} +513.000 q^{55} -25.0000 q^{57} +(109.500 - 189.660i) q^{59} +(-354.500 - 614.012i) q^{61} +(-35.0000 - 12.1244i) q^{63} +(-315.000 - 545.596i) q^{65} +(209.500 - 362.865i) q^{67} +345.000 q^{69} -96.0000 q^{71} +(156.500 - 271.066i) q^{73} +(110.000 + 190.526i) q^{75} +(-199.500 - 1036.63i) q^{77} +(-230.500 - 399.238i) q^{79} +(335.500 - 581.103i) q^{81} +588.000 q^{83} +459.000 q^{85} +(285.000 - 493.634i) q^{87} +(508.500 + 880.748i) q^{89} +(-980.000 + 848.705i) q^{91} +(-57.5000 - 99.5929i) q^{93} +(22.5000 - 38.9711i) q^{95} -1834.00 q^{97} -114.000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 5 q^{3} - 9 q^{5} - 28 q^{7} + 2 q^{9}+O(q^{10}) $ 2 * q - 5 * q^3 - 9 * q^5 - 28 * q^7 + 2 * q^9	$ 2 q - 5 q^{3} - 9 q^{5} - 28 q^{7} + 2 q^{9} - 57 q^{11} + 140 q^{13} + 90 q^{15} - 51 q^{17} + 5 q^{19} - 35 q^{21} - 69 q^{23} + 44 q^{25} - 290 q^{27} - 228 q^{29} - 23 q^{31} - 285 q^{33} + 315 q^{35} - 253 q^{37} - 350 q^{39} - 84 q^{41} + 248 q^{43} + 18 q^{45} - 201 q^{47} + 98 q^{49} - 255 q^{51} - 393 q^{53} + 1026 q^{55} - 50 q^{57} + 219 q^{59} - 709 q^{61} - 70 q^{63} - 630 q^{65} + 419 q^{67} + 690 q^{69} - 192 q^{71} + 313 q^{73} + 220 q^{75} - 399 q^{77} - 461 q^{79} + 671 q^{81} + 1176 q^{83} + 918 q^{85} + 570 q^{87} + 1017 q^{89} - 1960 q^{91} - 115 q^{93} + 45 q^{95} - 3668 q^{97} - 228 q^{99}+O(q^{100}) $ 2 * q - 5 * q^3 - 9 * q^5 - 28 * q^7 + 2 * q^9 - 57 * q^11 + 140 * q^13 + 90 * q^15 - 51 * q^17 + 5 * q^19 - 35 * q^21 - 69 * q^23 + 44 * q^25 - 290 * q^27 - 228 * q^29 - 23 * q^31 - 285 * q^33 + 315 * q^35 - 253 * q^37 - 350 * q^39 - 84 * q^41 + 248 * q^43 + 18 * q^45 - 201 * q^47 + 98 * q^49 - 255 * q^51 - 393 * q^53 + 1026 * q^55 - 50 * q^57 + 219 * q^59 - 709 * q^61 - 70 * q^63 - 630 * q^65 + 419 * q^67 + 690 * q^69 - 192 * q^71 + 313 * q^73 + 220 * q^75 - 399 * q^77 - 461 * q^79 + 671 * q^81 + 1176 * q^83 + 918 * q^85 + 570 * q^87 + 1017 * q^89 - 1960 * q^91 - 115 * q^93 + 45 * q^95 - 3668 * q^97 - 228 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/448\mathbb{Z}\right)^\times$.

$n$	$127$	$129$	$197$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$1$

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			0
$2$		0			0
$3$	−2.50000	+	4.33013i	−0.481125	+	0.833333i	−0.999765	−	0.0216593i	$-0.993105\pi$
$3$	−2.50000	+	4.33013i	−0.481125	+	0.833333i	0.518640	+	0.854993i	$0.326438\pi$
$4$		0			0
$5$	−4.50000	−	7.79423i	−0.402492	−	0.697137i	0.591534	−	0.806280i	$-0.298523\pi$
$5$	−4.50000	−	7.79423i	−0.402492	−	0.697137i	−0.994026	+	0.109143i	$0.965189\pi$
$6$		0			0
$7$	−14.0000	+	12.1244i	−0.755929	+	0.654654i
$7$	−14.0000	+	12.1244i	−0.755929	+	0.654654i
$8$		0			0
$9$	1.00000	+	1.73205i	0.0370370	+	0.0641500i
$10$		0			0
$11$	−28.5000	+	49.3634i	−0.781188	+	1.35306i	0.150061	+	0.988677i	$0.452053\pi$
$11$	−28.5000	+	49.3634i	−0.781188	+	1.35306i	−0.931250	+	0.364381i	$0.881280\pi$
$12$		0			0
$13$	70.0000			1.49342			0.746712	−	0.665148i	$-0.231631\pi$
$13$	70.0000			1.49342			0.746712	+	0.665148i	$0.231631\pi$
$14$		0			0
$15$	45.0000			0.774597
$16$		0			0
$17$	−25.5000	+	44.1673i	−0.363803	+	0.630126i	−0.988583	−	0.150675i	$-0.951855\pi$
$17$	−25.5000	+	44.1673i	−0.363803	+	0.630126i	0.624780	+	0.780801i	$0.285189\pi$
$18$		0			0
$19$	2.50000	+	4.33013i	0.0301863	+	0.0522842i	0.880724	−	0.473630i	$-0.157057\pi$
$19$	2.50000	+	4.33013i	0.0301863	+	0.0522842i	−0.850538	+	0.525914i	$0.823723\pi$
$20$		0			0
$21$	−17.5000	−	90.9327i	−0.181848	−	0.944911i
$22$		0			0
$23$	−34.5000	−	59.7558i	−0.312772	−	0.541736i	0.666190	−	0.745782i	$-0.267924\pi$
$23$	−34.5000	−	59.7558i	−0.312772	−	0.541736i	−0.978961	+	0.204046i	$0.934591\pi$
$24$		0			0
$25$	22.0000	−	38.1051i	0.176000	−	0.304841i
$26$		0			0
$27$	−145.000			−1.03353
$28$		0			0
$29$	−114.000			−0.729975			−0.364987	−	0.931012i	$-0.618927\pi$
$29$	−114.000			−0.729975			−0.364987	+	0.931012i	$0.618927\pi$
$30$		0			0
$31$	−11.5000	+	19.9186i	−0.0666278	+	0.115403i	−0.897415	−	0.441188i	$-0.854557\pi$
$31$	−11.5000	+	19.9186i	−0.0666278	+	0.115403i	0.830787	+	0.556590i	$0.187891\pi$
$32$		0			0
$33$	−142.500	−	246.817i	−0.751699	−	1.30198i
$34$		0			0
$35$	157.500	+	54.5596i	0.760639	+	0.263493i
$36$		0			0
$37$	−126.500	−	219.104i	−0.562067	−	0.973528i	−0.997316	−	0.0732182i	$-0.976673\pi$
$37$	−126.500	−	219.104i	−0.562067	−	0.973528i	0.435249	−	0.900310i	$-0.356660\pi$
$38$		0			0
$39$	−175.000	+	303.109i	−0.718524	+	1.24452i
$40$		0			0
$41$	−42.0000			−0.159983			−0.0799914	−	0.996796i	$-0.525489\pi$
$41$	−42.0000			−0.159983			−0.0799914	+	0.996796i	$0.525489\pi$
$42$		0			0
$43$	124.000			0.439763			0.219882	−	0.975527i	$-0.429433\pi$
$43$	124.000			0.439763			0.219882	+	0.975527i	$0.429433\pi$
$44$		0			0
$45$	9.00000	−	15.5885i	0.0298142	−	0.0516398i
$46$		0			0
$47$	−100.500	−	174.071i	−0.311903	−	0.540231i	0.666871	−	0.745173i	$-0.267633\pi$
$47$	−100.500	−	174.071i	−0.311903	−	0.540231i	−0.978774	+	0.204941i	$0.934300\pi$
$48$		0			0
$49$	49.0000	−	339.482i	0.142857	−	0.989743i
$50$		0			0
$51$	−127.500	−	220.836i	−0.350070	−	0.606339i
$52$		0			0
$53$	−196.500	+	340.348i	−0.509271	+	0.882083i	0.490672	+	0.871345i	$0.336751\pi$
$53$	−196.500	+	340.348i	−0.509271	+	0.882083i	−0.999942	+	0.0107383i	$0.996582\pi$
$54$		0			0
$55$	513.000			1.25769
$56$		0			0
$57$	−25.0000			−0.0580935
$58$		0			0
$59$	109.500	−	189.660i	0.241622	−	0.418501i	−0.719555	−	0.694436i	$-0.755654\pi$
$59$	109.500	−	189.660i	0.241622	−	0.418501i	0.961176	+	0.275935i	$0.0889873\pi$
$60$		0			0
$61$	−354.500	−	614.012i	−0.744083	−	1.28879i	−0.950622	−	0.310351i	$-0.899553\pi$
$61$	−354.500	−	614.012i	−0.744083	−	1.28879i	0.206539	−	0.978438i	$-0.433780\pi$
$62$		0			0
$63$	−35.0000	−	12.1244i	−0.0699934	−	0.0242464i
$64$		0			0
$65$	−315.000	−	545.596i	−0.601091	−	1.04112i
$66$		0			0
$67$	209.500	−	362.865i	0.382007	−	0.661656i	−0.609342	−	0.792908i	$-0.708566\pi$
$67$	209.500	−	362.865i	0.382007	−	0.661656i	0.991349	+	0.131251i	$0.0418995\pi$
$68$		0			0
$69$	345.000			0.601929
$70$		0			0
$71$	−96.0000			−0.160466			−0.0802331	−	0.996776i	$-0.525566\pi$
$71$	−96.0000			−0.160466			−0.0802331	+	0.996776i	$0.525566\pi$
$72$		0			0
$73$	156.500	−	271.066i	0.250917	−	0.434601i	−0.712862	−	0.701305i	$-0.752601\pi$
$73$	156.500	−	271.066i	0.250917	−	0.434601i	0.963779	+	0.266704i	$0.0859346\pi$
$74$		0			0
$75$	110.000	+	190.526i	0.169356	+	0.293333i
$76$		0			0
$77$	−199.500	−	1036.63i	−0.295261	−	1.53422i
$78$		0			0
$79$	−230.500	−	399.238i	−0.328269	−	0.568579i	0.653899	−	0.756582i	$-0.273132\pi$
$79$	−230.500	−	399.238i	−0.328269	−	0.568579i	−0.982169	+	0.188003i	$0.939799\pi$
$80$		0			0
$81$	335.500	−	581.103i	0.460219	−	0.797124i
$82$		0			0
$83$	588.000			0.777607			0.388804	−	0.921321i	$-0.372888\pi$
$83$	588.000			0.777607			0.388804	+	0.921321i	$0.372888\pi$
$84$		0			0
$85$	459.000			0.585712
$86$		0			0
$87$	285.000	−	493.634i	0.351209	−	0.608312i
$88$		0			0
$89$	508.500	+	880.748i	0.605628	+	1.04898i	0.991952	+	0.126615i	$0.0404114\pi$
$89$	508.500	+	880.748i	0.605628	+	1.04898i	−0.386324	+	0.922363i	$0.626255\pi$
$90$		0			0
$91$	−980.000	+	848.705i	−1.12892	+	0.977675i
$92$		0			0
$93$	−57.5000	−	99.5929i	−0.0641126	−	0.111046i
$94$		0			0
$95$	22.5000	−	38.9711i	0.0242995	−	0.0420879i
$96$		0			0
$97$	−1834.00			−1.91974			−0.959868	−	0.280451i	$-0.909516\pi$
$97$	−1834.00			−1.91974			−0.959868	+	0.280451i	$0.909516\pi$
$98$		0			0
$99$	−114.000			−0.115732
$100$		0			0
$101$	−142.500	+	246.817i	−0.140389	+	0.243161i	−0.927643	−	0.373468i	$-0.878169\pi$
$101$	−142.500	+	246.817i	−0.140389	+	0.243161i	0.787254	+	0.616629i	$0.211502\pi$
$102$		0			0
$103$	249.500	+	432.147i	0.238679	+	0.413405i	0.960336	−	0.278847i	$-0.0899522\pi$
$103$	249.500	+	432.147i	0.238679	+	0.413405i	−0.721656	+	0.692252i	$0.756619\pi$
$104$		0			0
$105$	−630.000	+	545.596i	−0.585540	+	0.507093i
$106$		0			0
$107$	−553.500	−	958.690i	−0.500083	−	0.866169i	−1.00000		9.56665e-5i	$-0.999970\pi$
$107$	−553.500	−	958.690i	−0.500083	−	0.866169i	0.499917	−	0.866073i	$-0.333364\pi$
$108$		0			0
$109$	461.500	−	799.341i	0.405538	−	0.702413i	−0.588846	−	0.808246i	$-0.700417\pi$
$109$	461.500	−	799.341i	0.405538	−	0.702413i	0.994384	+	0.105832i	$0.0337507\pi$
$110$		0			0
$111$	1265.00			1.08170
$112$		0			0
$113$	1542.00			1.28371			0.641855	−	0.766826i	$-0.278165\pi$
$113$	1542.00			1.28371			0.641855	+	0.766826i	$0.278165\pi$
$114$		0			0
$115$	−310.500	+	537.802i	−0.251776	+	0.436089i
$116$		0			0
$117$	70.0000	+	121.244i	0.0553120	+	0.0958032i
$118$		0			0
$119$	−178.500	−	927.513i	−0.137505	−	0.714496i
$120$		0			0
$121$	−959.000	−	1661.04i	−0.720511	−	1.24796i
$122$		0			0
$123$	105.000	−	181.865i	0.0769718	−	0.133319i
$124$		0			0
$125$	−1521.00			−1.08834
$126$		0			0
$127$	−2056.00			−1.43654			−0.718270	−	0.695765i	$-0.755066\pi$
$127$	−2056.00			−1.43654			−0.718270	+	0.695765i	$0.755066\pi$
$128$		0			0
$129$	−310.000	+	536.936i	−0.211581	+	0.366469i
$130$		0			0
$131$	1024.50	+	1774.49i	0.683290	+	1.18349i	0.973971	+	0.226673i	$0.0727848\pi$
$131$	1024.50	+	1774.49i	0.683290	+	1.18349i	−0.290681	+	0.956820i	$0.593882\pi$
$132$		0			0
$133$	−87.5000	−	30.3109i	−0.0570467	−	0.0197616i
$134$		0			0
$135$	652.500	+	1130.16i	0.415987	+	0.720511i
$136$		0			0
$137$	70.5000	−	122.110i	0.0439651	−	0.0761498i	−0.843205	−	0.537591i	$-0.819334\pi$
$137$	70.5000	−	122.110i	0.0439651	−	0.0761498i	0.887171	+	0.461442i	$0.152668\pi$
$138$		0			0
$139$	−1484.00			−0.905548			−0.452774	−	0.891625i	$-0.649566\pi$
$139$	−1484.00			−0.905548			−0.452774	+	0.891625i	$0.649566\pi$
$140$		0			0
$141$	1005.00			0.600257
$142$		0			0
$143$	−1995.00	+	3455.44i	−1.16665	+	2.02069i
$144$		0			0
$145$	513.000	+	888.542i	0.293809	+	0.508892i
$146$		0			0
$147$	1347.50	+	1060.88i	0.756054	+	0.595238i
$148$		0			0
$149$	−28.5000	−	49.3634i	−0.0156699	−	0.0271410i	0.858084	−	0.513509i	$-0.171655\pi$
$149$	−28.5000	−	49.3634i	−0.0156699	−	0.0271410i	−0.873754	+	0.486368i	$0.838321\pi$
$150$		0			0
$151$	−419.500	+	726.595i	−0.226082	+	0.391586i	−0.956644	−	0.291261i	$-0.905925\pi$
$151$	−419.500	+	726.595i	−0.226082	+	0.391586i	0.730561	+	0.682847i	$0.239258\pi$
$152$		0			0
$153$	−102.000			−0.0538968
$154$		0			0
$155$	207.000			0.107269
$156$		0			0
$157$	−1416.50	+	2453.45i	−0.720057	+	1.24718i	0.240919	+	0.970545i	$0.422551\pi$
$157$	−1416.50	+	2453.45i	−0.720057	+	1.24718i	−0.960976	+	0.276631i	$0.910782\pi$
$158$		0			0
$159$	−982.500	−	1701.74i	−0.490046	−	0.848785i
$160$		0			0
$161$	1207.50	+	418.290i	0.591083	+	0.204757i
$162$		0			0
$163$	−1155.50	−	2001.38i	−0.555250	−	0.961721i	−0.997884	−	0.0650188i	$-0.979289\pi$
$163$	−1155.50	−	2001.38i	−0.555250	−	0.961721i	0.442634	−	0.896702i	$-0.354044\pi$
$164$		0			0
$165$	−1282.50	+	2221.36i	−0.605106	+	1.04807i
$166$		0			0
$167$	1260.00			0.583843			0.291921	−	0.956442i	$-0.405705\pi$
$167$	1260.00			0.583843			0.291921	+	0.956442i	$0.405705\pi$
$168$		0			0
$169$	2703.00			1.23031
$170$		0			0
$171$	−5.00000	+	8.66025i	−0.00223602	+	0.00387290i
$172$		0			0
$173$	1633.50	+	2829.30i	0.717877	+	1.24340i	0.961839	+	0.273615i	$0.0882193\pi$
$173$	1633.50	+	2829.30i	0.717877	+	1.24340i	−0.243962	+	0.969785i	$0.578447\pi$
$174$		0			0
$175$	154.000	+	800.207i	0.0665217	+	0.345657i
$176$		0			0
$177$	547.500	+	948.298i	0.232501	+	0.402703i
$178$		0			0
$179$	643.500	−	1114.57i	0.268701	−	0.465403i	−0.699826	−	0.714314i	$-0.746739\pi$
$179$	643.500	−	1114.57i	0.268701	−	0.465403i	0.968527	+	0.248910i	$0.0800724\pi$
$180$		0			0
$181$	2674.00			1.09810			0.549052	−	0.835788i	$-0.314989\pi$
$181$	2674.00			1.09810			0.549052	+	0.835788i	$0.314989\pi$
$182$		0			0
$183$	3545.00			1.43199
$184$		0			0
$185$	−1138.50	+	1971.94i	−0.452455	+	0.783675i
$186$		0			0
$187$	−1453.50	−	2517.54i	−0.568398	−	0.984494i
$188$		0			0
$189$	2030.00	−	1758.03i	0.781274	−	0.676603i
$190$		0			0
$191$	−2092.50	−	3624.32i	−0.792712	−	1.37302i	−0.924282	−	0.381711i	$-0.875335\pi$
$191$	−2092.50	−	3624.32i	−0.792712	−	1.37302i	0.131570	−	0.991307i	$-0.457998\pi$
$192$		0			0
$193$	42.5000	−	73.6122i	0.0158509	−	0.0274545i	−0.857991	−	0.513664i	$-0.828288\pi$
$193$	42.5000	−	73.6122i	0.0158509	−	0.0274545i	0.873842	+	0.486210i	$0.161621\pi$
$194$		0			0
$195$	3150.00			1.15680
$196$		0			0
$197$	390.000			0.141047			0.0705237	−	0.997510i	$-0.477533\pi$
$197$	390.000			0.141047			0.0705237	+	0.997510i	$0.477533\pi$
$198$		0			0
$199$	1416.50	−	2453.45i	0.504588	−	0.873972i	−0.495398	−	0.868666i	$-0.664978\pi$
$199$	1416.50	−	2453.45i	0.504588	−	0.873972i	0.999986	−	0.00530596i	$-0.00168895\pi$
$200$		0			0
$201$	1047.50	+	1814.32i	0.367587	+	0.636679i
$202$		0			0
$203$	1596.00	−	1382.18i	0.551809	−	0.477881i
$204$		0			0
$205$	189.000	+	327.358i	0.0643919	+	0.111530i
$206$		0			0
$207$	69.0000	−	119.512i	0.0231683	−	0.0401286i
$208$		0			0
$209$	−285.000			−0.0943247
$210$		0			0
$211$	124.000			0.0404574			0.0202287	−	0.999795i	$-0.493561\pi$
$211$	124.000			0.0404574			0.0202287	+	0.999795i	$0.493561\pi$
$212$		0			0
$213$	240.000	−	415.692i	0.0772044	−	0.133722i
$214$		0			0
$215$	−558.000	−	966.484i	−0.177001	−	0.306575i
$216$		0			0
$217$	−80.5000	−	418.290i	−0.0251829	−	0.130854i
$218$		0			0
$219$	782.500	+	1355.33i	0.241445	+	0.418195i
$220$		0			0
$221$	−1785.00	+	3091.71i	−0.543313	+	0.941045i
$222$		0			0
$223$	56.0000			0.0168163			0.00840816	−	0.999965i	$-0.497324\pi$
$223$	56.0000			0.0168163			0.00840816	+	0.999965i	$0.497324\pi$
$224$		0			0
$225$	88.0000			0.0260741
$226$		0			0
$227$	−1528.50	+	2647.44i	−0.446917	+	0.774083i	−0.998184	−	0.0602465i	$-0.980811\pi$
$227$	−1528.50	+	2647.44i	−0.446917	+	0.774083i	0.551267	+	0.834329i	$0.314145\pi$
$228$		0			0
$229$	−480.500	−	832.250i	−0.138656	−	0.240160i	0.788332	−	0.615250i	$-0.210945\pi$
$229$	−480.500	−	832.250i	−0.138656	−	0.240160i	−0.926988	+	0.375090i	$0.877612\pi$
$230$		0			0
$231$	4987.50	+	1727.72i	1.42058	+	0.492102i
$232$		0			0
$233$	1414.50	+	2449.99i	0.397712	+	0.688858i	0.993443	−	0.114326i	$-0.0364709\pi$
$233$	1414.50	+	2449.99i	0.397712	+	0.688858i	−0.595731	+	0.803184i	$0.703138\pi$
$234$		0			0
$235$	−904.500	+	1566.64i	−0.251077	+	0.434878i
$236$		0			0
$237$	2305.00			0.631755
$238$		0			0
$239$	−3540.00			−0.958090			−0.479045	−	0.877790i	$-0.659017\pi$
$239$	−3540.00			−0.958090			−0.479045	+	0.877790i	$0.659017\pi$
$240$		0			0
$241$	−2615.50	+	4530.18i	−0.699084	+	1.21085i	0.269701	+	0.962944i	$0.413075\pi$
$241$	−2615.50	+	4530.18i	−0.699084	+	1.21085i	−0.968785	+	0.247904i	$0.920258\pi$
$242$		0			0
$243$	−280.000	−	484.974i	−0.0739177	−	0.128029i
$244$		0			0
$245$	−2866.50	+	1145.75i	−0.747486	+	0.298773i
$246$		0			0
$247$	175.000	+	303.109i	0.0450809	+	0.0780824i
$248$		0			0
$249$	−1470.00	+	2546.11i	−0.374126	+	0.648006i
$250$		0			0
$251$	−5040.00			−1.26742			−0.633709	−	0.773571i	$-0.718468\pi$
$251$	−5040.00			−1.26742			−0.633709	+	0.773571i	$0.718468\pi$
$252$		0			0
$253$	3933.00			0.977334
$254$		0			0
$255$	−1147.50	+	1987.53i	−0.281801	+	0.488094i
$256$		0			0
$257$	718.500	+	1244.48i	0.174392	+	0.302056i	0.939951	−	0.341310i	$-0.110871\pi$
$257$	718.500	+	1244.48i	0.174392	+	0.302056i	−0.765559	+	0.643366i	$0.777537\pi$
$258$		0			0
$259$	4427.50	+	1533.73i	1.06221	+	0.367959i
$260$		0			0
$261$	−114.000	−	197.454i	−0.0270361	−	0.0468279i
$262$		0			0
$263$	1162.50	−	2013.51i	0.272558	−	0.472085i	−0.696958	−	0.717112i	$-0.745464\pi$
$263$	1162.50	−	2013.51i	0.272558	−	0.472085i	0.969516	+	0.245027i	$0.0787969\pi$
$264$		0			0
$265$	3537.00			0.819910
$266$		0			0
$267$	−5085.00			−1.16553
$268$		0			0
$269$	−1192.50	+	2065.47i	−0.270290	+	0.468156i	−0.968936	−	0.247311i	$-0.920453\pi$
$269$	−1192.50	+	2065.47i	−0.270290	+	0.468156i	0.698646	+	0.715467i	$0.253786\pi$
$270$		0			0
$271$	165.500	+	286.654i	0.0370975	+	0.0642547i	0.883978	−	0.467528i	$-0.154855\pi$
$271$	165.500	+	286.654i	0.0370975	+	0.0642547i	−0.846881	+	0.531783i	$0.821522\pi$
$272$		0			0
$273$	−1225.00	−	6365.29i	−0.271576	−	1.41115i
$274$		0			0
$275$	1254.00	+	2171.99i	0.274978	+	0.476276i
$276$		0			0
$277$	2435.50	−	4218.41i	0.528285	−	0.915017i	−0.471171	−	0.882042i	$-0.656169\pi$
$277$	2435.50	−	4218.41i	0.528285	−	0.915017i	0.999456	−	0.0329750i	$-0.0104982\pi$
$278$		0			0
$279$	−46.0000			−0.00987078
$280$		0			0
$281$	−7026.00			−1.49159			−0.745794	−	0.666177i	$-0.767930\pi$
$281$	−7026.00			−1.49159			−0.745794	+	0.666177i	$0.767930\pi$
$282$		0			0
$283$	−2676.50	+	4635.83i	−0.562196	+	0.973752i	0.435109	+	0.900378i	$0.356710\pi$
$283$	−2676.50	+	4635.83i	−0.562196	+	0.973752i	−0.997305	+	0.0733738i	$0.976623\pi$
$284$		0			0
$285$	112.500	+	194.856i	0.0233822	+	0.0404991i
$286$		0			0
$287$	588.000	−	509.223i	0.120936	−	0.104733i
$288$		0			0
$289$	1156.00	+	2002.25i	0.235294	+	0.407541i
$290$		0			0
$291$	4585.00	−	7941.45i	0.923634	−	1.59978i
$292$		0			0
$293$	−4158.00			−0.829054			−0.414527	−	0.910037i	$-0.636053\pi$
$293$	−4158.00			−0.829054			−0.414527	+	0.910037i	$0.636053\pi$
$294$		0			0
$295$	−1971.00			−0.389004
$296$		0			0
$297$	4132.50	−	7157.70i	0.807380	−	1.39842i
$298$		0			0
$299$	−2415.00	−	4182.90i	−0.467101	−	0.809042i
$300$		0			0
$301$	−1736.00	+	1503.42i	−0.332430	+	0.287893i
$302$		0			0
$303$	−712.500	−	1234.09i	−0.135089	−	0.233982i
$304$		0			0
$305$	−3190.50	+	5526.11i	−0.598975	+	1.03746i
$306$		0			0
$307$	9604.00			1.78544			0.892719	−	0.450615i	$-0.148795\pi$
$307$	9604.00			1.78544			0.892719	+	0.450615i	$0.148795\pi$
$308$		0			0
$309$	−2495.00			−0.459338
$310$		0			0
$311$	−5065.50	+	8773.70i	−0.923595	+	1.59971i	−0.129791	+	0.991541i	$0.541430\pi$
$311$	−5065.50	+	8773.70i	−0.923595	+	1.59971i	−0.793805	+	0.608173i	$0.791903\pi$
$312$		0			0
$313$	−5399.50	−	9352.21i	−0.975073	−	1.68888i	−0.679695	−	0.733495i	$-0.737888\pi$
$313$	−5399.50	−	9352.21i	−0.975073	−	1.68888i	−0.295378	−	0.955380i	$-0.595446\pi$
$314$		0			0
$315$	63.0000	+	327.358i	0.0112687	+	0.0585540i
$316$		0			0
$317$	265.500	+	459.859i	0.0470409	+	0.0814772i	0.888587	−	0.458708i	$-0.151688\pi$
$317$	265.500	+	459.859i	0.0470409	+	0.0814772i	−0.841546	+	0.540185i	$0.818354\pi$
$318$		0			0
$319$	3249.00	−	5627.43i	0.570248	−	0.987698i
$320$		0			0
$321$	5535.00			0.962410
$322$		0			0
$323$	−255.000			−0.0439275
$324$		0			0
$325$	1540.00	−	2667.36i	0.262843	−	0.455257i
$326$		0			0
$327$	2307.50	+	3996.71i	0.390229	+	0.675897i
$328$		0			0
$329$	3517.50	+	1218.50i	0.589441	+	0.204188i
$330$		0			0
$331$	−3507.50	−	6075.17i	−0.582446	−	1.00883i	−0.995189	−	0.0979784i	$-0.968762\pi$
$331$	−3507.50	−	6075.17i	−0.582446	−	1.00883i	0.412743	−	0.910848i	$-0.364571\pi$
$332$		0			0
$333$	253.000	−	438.209i	0.0416346	−	0.0721132i
$334$		0			0
$335$	−3771.00			−0.615020
$336$		0			0
$337$	8990.00			1.45316			0.726582	−	0.687079i	$-0.241108\pi$
$337$	8990.00			1.45316			0.726582	+	0.687079i	$0.241108\pi$
$338$		0			0
$339$	−3855.00	+	6677.06i	−0.617625	+	1.06976i
$340$		0			0
$341$	−655.500	−	1135.36i	−0.104098	−	0.180303i
$342$		0			0
$343$	3430.00	+	5346.84i	0.539949	+	0.841698i
$344$		0			0
$345$	−1552.50	−	2689.01i	−0.242272	−	0.419627i
$346$		0			0
$347$	−4354.50	+	7542.22i	−0.673665	+	1.16682i	0.303192	+	0.952929i	$0.401948\pi$
$347$	−4354.50	+	7542.22i	−0.673665	+	1.16682i	−0.976857	+	0.213893i	$0.931386\pi$
$348$		0			0
$349$	−6482.00			−0.994193			−0.497097	−	0.867695i	$-0.665601\pi$
$349$	−6482.00			−0.994193			−0.497097	+	0.867695i	$0.665601\pi$
$350$		0			0
$351$	−10150.0			−1.54350
$352$		0			0
$353$	1066.50	−	1847.23i	0.160805	−	0.278522i	−0.774353	−	0.632754i	$-0.781924\pi$
$353$	1066.50	−	1847.23i	0.160805	−	0.278522i	0.935158	+	0.354232i	$0.115258\pi$
$354$		0			0
$355$	432.000	+	748.246i	0.0645864	+	0.111867i
$356$		0			0
$357$	4462.50	+	1545.86i	0.661570	+	0.229175i
$358$		0			0
$359$	−1924.50	−	3333.33i	−0.282928	−	0.490046i	0.689176	−	0.724594i	$-0.257972\pi$
$359$	−1924.50	−	3333.33i	−0.282928	−	0.490046i	−0.972105	+	0.234548i	$0.924639\pi$
$360$		0			0
$361$	3417.00	−	5918.42i	0.498178	−	0.862869i
$362$		0			0
$363$	9590.00			1.38662
$364$		0			0
$365$	−2817.00			−0.403969
$366$		0			0
$367$	−3245.50	+	5621.37i	−0.461618	+	0.799545i	−0.999042	−	0.0437668i	$-0.986064\pi$
$367$	−3245.50	+	5621.37i	−0.461618	+	0.799545i	0.537424	+	0.843312i	$0.319397\pi$
$368$		0			0
$369$	−42.0000	−	72.7461i	−0.00592529	−	0.0102629i
$370$		0			0
$371$	−1375.50	−	7147.31i	−0.192486	−	1.00019i
$372$		0			0
$373$	461.500	+	799.341i	0.0640632	+	0.110961i	0.896278	−	0.443493i	$-0.146261\pi$
$373$	461.500	+	799.341i	0.0640632	+	0.110961i	−0.832215	+	0.554453i	$0.812927\pi$
$374$		0			0
$375$	3802.50	−	6586.12i	0.523627	−	0.906949i
$376$		0			0
$377$	−7980.00			−1.09016
$378$		0			0
$379$	−6344.00			−0.859814			−0.429907	−	0.902873i	$-0.641454\pi$
$379$	−6344.00			−0.859814			−0.429907	+	0.902873i	$0.641454\pi$
$380$		0			0
$381$	5140.00	−	8902.74i	0.691155	−	1.19712i
$382$		0			0
$383$	2503.50	+	4336.19i	0.334002	+	0.578509i	0.983293	−	0.182032i	$-0.0582673\pi$
$383$	2503.50	+	4336.19i	0.334002	+	0.578509i	−0.649290	+	0.760541i	$0.724934\pi$
$384$		0			0
$385$	−7182.00	+	6219.79i	−0.950724	+	0.823351i
$386$		0			0
$387$	124.000	+	214.774i	0.0162875	+	0.0282108i
$388$		0			0
$389$	6145.50	−	10644.3i	0.801001	−	1.38737i	−0.117958	−	0.993019i	$-0.537635\pi$
$389$	6145.50	−	10644.3i	0.801001	−	1.38737i	0.918958	−	0.394355i	$-0.129032\pi$
$390$		0			0
$391$	3519.00			0.455150
$392$		0			0
$393$	−10245.0			−1.31499
$394$		0			0
$395$	−2074.50	+	3593.14i	−0.264252	+	0.457697i
$396$		0			0
$397$	443.500	+	768.165i	0.0560671	+	0.0971110i	0.892697	−	0.450658i	$-0.148811\pi$
$397$	443.500	+	768.165i	0.0560671	+	0.0971110i	−0.836630	+	0.547769i	$0.815477\pi$
$398$		0			0
$399$	350.000	−	303.109i	0.0439146	−	0.0380311i
$400$		0			0
$401$	−5977.50	−	10353.3i	−0.744394	−	1.28933i	−0.950477	−	0.310794i	$-0.899405\pi$
$401$	−5977.50	−	10353.3i	−0.744394	−	1.28933i	0.206083	−	0.978535i	$-0.433928\pi$
$402$		0			0
$403$	−805.000	+	1394.30i	−0.0995035	+	0.172345i
$404$		0			0
$405$	−6039.00			−0.740939
$406$		0			0
$407$	14421.0			1.75632
$408$		0			0
$409$	1710.50	−	2962.67i	0.206794	−	0.358178i	−0.743909	−	0.668281i	$-0.767030\pi$
$409$	1710.50	−	2962.67i	0.206794	−	0.358178i	0.950703	+	0.310103i	$0.100364\pi$
$410$		0			0
$411$	352.500	+	610.548i	0.0423055	+	0.0732752i
$412$		0			0
$413$	766.500	+	3982.85i	0.0913245	+	0.474536i
$414$		0			0
$415$	−2646.00	−	4583.01i	−0.312981	−	0.542099i
$416$		0			0
$417$	3710.00	−	6425.91i	0.435682	−	0.754624i
$418$		0			0
$419$	5460.00			0.636607			0.318304	−	0.947989i	$-0.396887\pi$
$419$	5460.00			0.636607			0.318304	+	0.947989i	$0.396887\pi$
$420$		0			0
$421$	−7730.00			−0.894863			−0.447431	−	0.894318i	$-0.647661\pi$
$421$	−7730.00			−0.894863			−0.447431	+	0.894318i	$0.647661\pi$
$422$		0			0
$423$	201.000	−	348.142i	0.0231039	−	0.0400171i
$424$		0			0
$425$	1122.00	+	1943.36i	0.128059	+	0.221804i
$426$		0			0
$427$	12407.5	+	4298.08i	1.40619	+	0.487117i
$428$		0			0
$429$	−9975.00	−	17277.2i	−1.12260	−	1.94441i
$430$		0			0
$431$	5656.50	−	9797.35i	0.632167	−	1.09495i	−0.354941	−	0.934889i	$-0.615499\pi$
$431$	5656.50	−	9797.35i	0.632167	−	1.09495i	0.987108	−	0.160057i	$-0.0511677\pi$
$432$		0			0
$433$	4214.00			0.467695			0.233847	−	0.972273i	$-0.424868\pi$
$433$	4214.00			0.467695			0.233847	+	0.972273i	$0.424868\pi$
$434$		0			0
$435$	−5130.00			−0.565436
$436$		0			0
$437$	172.500	−	298.779i	0.0188828	−	0.0327060i
$438$		0			0
$439$	−8276.50	−	14335.3i	−0.899808	−	1.55851i	−0.827739	−	0.561114i	$-0.810373\pi$
$439$	−8276.50	−	14335.3i	−0.899808	−	1.55851i	−0.0720696	−	0.997400i	$-0.522960\pi$
$440$		0			0
$441$	637.000	−	254.611i	0.0687831	−	0.0274929i
$442$		0			0
$443$	−8197.50	−	14198.5i	−0.879176	−	1.52278i	−0.852247	−	0.523140i	$-0.824760\pi$
$443$	−8197.50	−	14198.5i	−0.879176	−	1.52278i	−0.0269294	−	0.999637i	$-0.508573\pi$
$444$		0			0
$445$	4576.50	−	7926.73i	0.487521	−	0.844411i
$446$		0			0
$447$	285.000			0.0301567
$448$		0			0
$449$	−15090.0			−1.58606			−0.793030	−	0.609182i	$-0.791498\pi$
$449$	−15090.0			−1.58606			−0.793030	+	0.609182i	$0.791498\pi$
$450$		0			0
$451$	1197.00	−	2073.26i	0.124977	−	0.216466i
$452$		0			0
$453$	−2097.50	−	3632.98i	−0.217548	−	0.376804i
$454$		0			0
$455$	11025.0	+	3819.17i	1.13596	+	0.393507i
$456$		0			0
$457$	7392.50	+	12804.2i	0.756688	+	1.31062i	0.944531	+	0.328423i	$0.106517\pi$
$457$	7392.50	+	12804.2i	0.756688	+	1.31062i	−0.187842	+	0.982199i	$0.560149\pi$
$458$		0			0
$459$	3697.50	−	6404.26i	0.376001	−	0.651253i
$460$		0			0
$461$	−2898.00			−0.292784			−0.146392	−	0.989227i	$-0.546766\pi$
$461$	−2898.00			−0.292784			−0.146392	+	0.989227i	$0.546766\pi$
$462$		0			0
$463$	464.000			0.0465743			0.0232872	−	0.999729i	$-0.492587\pi$
$463$	464.000			0.0465743			0.0232872	+	0.999729i	$0.492587\pi$
$464$		0			0
$465$	−517.500	+	896.336i	−0.0516097	+	0.0893905i
$466$		0			0
$467$	2116.50	+	3665.89i	0.209721	+	0.363248i	0.951627	−	0.307256i	$-0.0994109\pi$
$467$	2116.50	+	3665.89i	0.209721	+	0.363248i	−0.741905	+	0.670505i	$0.766078\pi$
$468$		0			0
$469$	1466.50	+	7620.16i	0.144385	+	0.750248i
$470$		0			0
$471$	−7082.50	−	12267.2i	−0.692876	−	1.20010i
$472$		0			0
$473$	−3534.00	+	6121.07i	−0.343538	+	0.595025i
$474$		0			0
$475$	220.000			0.0212511
$476$		0			0
$477$	−786.000			−0.0754475
$478$		0			0
$479$	−1369.50	+	2372.04i	−0.130635	+	0.226266i	−0.923921	−	0.382582i	$-0.875035\pi$
$479$	−1369.50	+	2372.04i	−0.130635	+	0.226266i	0.793287	+	0.608848i	$0.208368\pi$
$480$		0			0
$481$	−8855.00	−	15337.3i	−0.839404	−	1.45389i
$482$		0			0
$483$	−4830.00	+	4182.90i	−0.455016	+	0.394055i
$484$		0			0
$485$	8253.00	+	14294.6i	0.772679	+	1.33832i
$486$		0			0
$487$	−8525.50	+	14766.6i	−0.793280	+	1.37400i	0.130646	+	0.991429i	$0.458295\pi$
$487$	−8525.50	+	14766.6i	−0.793280	+	1.37400i	−0.923926	+	0.382572i	$0.875038\pi$
$488$		0			0
$489$	11555.0			1.06858
$490$		0			0
$491$	4296.00			0.394859			0.197429	−	0.980317i	$-0.436741\pi$
$491$	4296.00			0.394859			0.197429	+	0.980317i	$0.436741\pi$
$492$		0			0
$493$	2907.00	−	5035.07i	0.265567	−	0.459976i
$494$		0			0
$495$	513.000	+	888.542i	0.0465811	+	0.0806808i
$496$		0			0
$497$	1344.00	−	1163.94i	0.121301	−	0.105050i
$498$		0			0
$499$	1700.50	+	2945.35i	0.152555	+	0.264233i	0.932166	−	0.362031i	$-0.117917\pi$
$499$	1700.50	+	2945.35i	0.152555	+	0.264233i	−0.779611	+	0.626264i	$0.784583\pi$
$500$		0			0
$501$	−3150.00	+	5455.96i	−0.280901	+	0.486536i
$502$		0			0
$503$	16800.0			1.48921			0.744607	−	0.667503i	$-0.232637\pi$
$503$	16800.0			1.48921			0.744607	+	0.667503i	$0.232637\pi$
$504$		0			0
$505$	2565.00			0.226022
$506$		0			0
$507$	−6757.50	+	11704.3i	−0.591935	+	1.02526i
$508$		0			0
$509$	919.500	+	1592.62i	0.0800710	+	0.138687i	0.903280	−	0.429051i	$-0.141152\pi$
$509$	919.500	+	1592.62i	0.0800710	+	0.138687i	−0.823209	+	0.567738i	$0.807819\pi$
$510$		0			0
$511$	1095.50	+	5692.38i	0.0948377	+	0.492791i
$512$		0			0
$513$	−362.500	−	627.868i	−0.0311984	−	0.0540372i
$514$		0			0
$515$	2245.50	−	3889.32i	0.192133	−	0.332784i
$516$		0			0
$517$	11457.0			0.974620
$518$		0			0
$519$	−16335.0			−1.38155
$520$		0			0
$521$	−151.500	+	262.406i	−0.0127396	+	0.0220656i	−0.872325	−	0.488927i	$-0.837389\pi$
$521$	−151.500	+	262.406i	−0.0127396	+	0.0220656i	0.859585	+	0.510992i	$0.170722\pi$
$522$		0			0
$523$	−10833.5	−	18764.2i	−0.905767	−	1.56883i	−0.819885	−	0.572528i	$-0.805963\pi$
$523$	−10833.5	−	18764.2i	−0.905767	−	1.56883i	−0.0858815	−	0.996305i	$-0.527371\pi$
$524$		0			0
$525$	−3850.00	−	1333.68i	−0.320053	−	0.110870i
$526$		0			0
$527$	−586.500	−	1015.85i	−0.0484788	−	0.0839678i
$528$		0			0
$529$	3703.00	−	6413.78i	0.304348	−	0.527146i
$530$		0			0
$531$	438.000			0.0357958
$532$		0			0
$533$	−2940.00			−0.238922
$534$		0			0
$535$	−4981.50	+	8628.21i	−0.402559	+	0.697253i
$536$		0			0
$537$	3217.50	+	5572.87i	0.258557	+	0.447835i
$538$		0			0
$539$	15361.5	+	12094.0i	1.22758	+	0.966470i
$540$		0			0
$541$	2519.50	+	4363.90i	0.200225	+	0.346800i	0.948601	−	0.316475i	$-0.102499\pi$
$541$	2519.50	+	4363.90i	0.200225	+	0.346800i	−0.748376	+	0.663275i	$0.769166\pi$
$542$		0			0
$543$	−6685.00	+	11578.8i	−0.528326	+	0.915087i
$544$		0			0
$545$	−8307.00			−0.652904
$546$		0			0
$547$	2392.00			0.186974			0.0934868	−	0.995621i	$-0.470199\pi$
$547$	2392.00			0.186974			0.0934868	+	0.995621i	$0.470199\pi$
$548$		0			0
$549$	709.000	−	1228.02i	0.0551173	−	0.0954659i
$550$		0			0
$551$	−285.000	−	493.634i	−0.0220352	−	0.0381661i
$552$		0			0
$553$	8067.50	+	2794.66i	0.620371	+	0.214903i
$554$		0			0
$555$	−5692.50	−	9859.70i	−0.435375	−	0.754092i
$556$		0			0
$557$	−11074.5	+	19181.6i	−0.842445	+	1.45916i	0.0453775	+	0.998970i	$0.485551\pi$
$557$	−11074.5	+	19181.6i	−0.842445	+	1.45916i	−0.887822	+	0.460187i	$0.847782\pi$
$558$		0			0
$559$	8680.00			0.656753
$560$		0			0
$561$	14535.0			1.09388
$562$		0			0
$563$	−4174.50	+	7230.45i	−0.312494	+	0.541256i	−0.978902	−	0.204332i	$-0.934498\pi$
$563$	−4174.50	+	7230.45i	−0.312494	+	0.541256i	0.666408	+	0.745588i	$0.267831\pi$
$564$		0			0
$565$	−6939.00	−	12018.7i	−0.516683	−	0.894921i
$566$		0			0
$567$	2348.50	+	12203.2i	0.173947	+	0.903853i
$568$		0			0
$569$	7672.50	+	13289.2i	0.565286	+	0.979105i	0.997023	+	0.0771050i	$0.0245677\pi$
$569$	7672.50	+	13289.2i	0.565286	+	0.979105i	−0.431737	+	0.902000i	$0.642099\pi$
$570$		0			0
$571$	−5796.50	+	10039.8i	−0.424827	+	0.735821i	−0.996404	−	0.0847268i	$-0.972998\pi$
$571$	−5796.50	+	10039.8i	−0.424827	+	0.735821i	0.571578	+	0.820548i	$0.306332\pi$
$572$		0			0
$573$	20925.0			1.52557
$574$		0			0
$575$	−3036.00			−0.220191
$576$		0			0
$577$	7296.50	−	12637.9i	0.526442	−	0.911825i	−0.473083	−	0.881018i	$-0.656859\pi$
$577$	7296.50	−	12637.9i	0.526442	−	0.911825i	0.999525	−	0.0308071i	$-0.00980776\pi$
$578$		0			0
$579$	212.500	+	368.061i	0.0152525	+	0.0264181i
$580$		0			0
$581$	−8232.00	+	7129.12i	−0.587816	+	0.509063i
$582$		0			0
$583$	−11200.5	−	19399.8i	−0.795673	−	1.37815i
$584$		0			0
$585$	630.000	−	1091.19i	0.0445253	−	0.0771201i
$586$		0			0
$587$	15372.0			1.08087			0.540435	−	0.841386i	$-0.318260\pi$
$587$	15372.0			1.08087			0.540435	+	0.841386i	$0.318260\pi$
$588$		0			0
$589$	−115.000			−0.00804498
$590$		0			0
$591$	−975.000	+	1688.75i	−0.0678615	+	0.117540i
$592$		0			0
$593$	7186.50	+	12447.4i	0.497663	+	0.861978i	0.999996	−	0.00269639i	$-0.000858288\pi$
$593$	7186.50	+	12447.4i	0.497663	+	0.861978i	−0.502333	+	0.864674i	$0.667525\pi$
$594$		0			0
$595$	−6426.00	+	5565.08i	−0.442757	+	0.383439i
$596$		0			0
$597$	7082.50	+	12267.2i	0.485540	+	0.840980i
$598$		0			0
$599$	−1273.50	+	2205.77i	−0.0868678	+	0.150459i	−0.906186	−	0.422880i	$-0.861019\pi$
$599$	−1273.50	+	2205.77i	−0.0868678	+	0.150459i	0.819318	+	0.573340i	$0.194352\pi$
$600$		0			0
$601$	−7042.00			−0.477952			−0.238976	−	0.971025i	$-0.576812\pi$
$601$	−7042.00			−0.477952			−0.238976	+	0.971025i	$0.576812\pi$
$602$		0			0
$603$	838.000			0.0565937
$604$		0			0
$605$	−8631.00	+	14949.3i	−0.580000	+	1.00459i
$606$		0			0
$607$	11295.5	+	19564.4i	0.755305	+	1.30823i	0.945223	+	0.326427i	$0.105845\pi$
$607$	11295.5	+	19564.4i	0.755305	+	1.30823i	−0.189917	+	0.981800i	$0.560822\pi$
$608$		0			0
$609$	1995.00	+	10366.3i	0.132745	+	0.689761i
$610$		0			0
$611$	−7035.00	−	12185.0i	−0.465803	−	0.806794i
$612$		0			0
$613$	−4242.50	+	7348.23i	−0.279532	+	0.484163i	−0.971268	−	0.237987i	$-0.923513\pi$
$613$	−4242.50	+	7348.23i	−0.279532	+	0.484163i	0.691737	+	0.722150i	$0.256846\pi$
$614$		0			0
$615$	−1890.00			−0.123922
$616$		0			0
$617$	−18282.0			−1.19288			−0.596439	−	0.802658i	$-0.703418\pi$
$617$	−18282.0			−1.19288			−0.596439	+	0.802658i	$0.703418\pi$
$618$		0			0
$619$	1145.50	−	1984.06i	0.0743805	−	0.128831i	−0.826436	−	0.563030i	$-0.809635\pi$
$619$	1145.50	−	1984.06i	0.0743805	−	0.128831i	0.900817	+	0.434200i	$0.142969\pi$
$620$		0			0
$621$	5002.50	+	8664.58i	0.323258	+	0.559900i
$622$		0			0
$623$	−17797.5	−	6165.23i	−1.14453	−	0.396477i
$624$		0			0
$625$	4094.50	+	7091.88i	0.262048	+	0.453880i
$626$		0			0
$627$	712.500	−	1234.09i	0.0453820	−	0.0786039i
$628$		0			0
$629$	12903.0			0.817927
$630$		0			0
$631$	−6928.00			−0.437083			−0.218541	−	0.975828i	$-0.570130\pi$
$631$	−6928.00			−0.437083			−0.218541	+	0.975828i	$0.570130\pi$
$632$		0			0
$633$	−310.000	+	536.936i	−0.0194651	+	0.0337145i
$634$		0			0
$635$	9252.00	+	16024.9i	0.578196	+	1.00146i
$636$		0			0
$637$	3430.00	−	23763.7i	0.213346	−	1.47811i
$638$		0			0
$639$	−96.0000	−	166.277i	−0.00594319	−	0.0102939i
$640$		0			0
$641$	−12487.5	+	21629.0i	−0.769464	+	1.33275i	0.168390	+	0.985721i	$0.446143\pi$
$641$	−12487.5	+	21629.0i	−0.769464	+	1.33275i	−0.937854	+	0.347031i	$0.887190\pi$
$642$		0			0
$643$	−9548.00			−0.585593			−0.292797	−	0.956175i	$-0.594586\pi$
$643$	−9548.00			−0.585593			−0.292797	+	0.956175i	$0.594586\pi$
$644$		0			0
$645$	5580.00			0.340639
$646$		0			0
$647$	−5065.50	+	8773.70i	−0.307798	+	0.533122i	−0.977880	−	0.209165i	$-0.932925\pi$
$647$	−5065.50	+	8773.70i	−0.307798	+	0.533122i	0.670082	+	0.742287i	$0.266259\pi$
$648$		0			0
$649$	6241.50	+	10810.6i	0.377504	+	0.653857i
$650$		0			0
$651$	2012.50	+	697.150i	0.121161	+	0.0419716i
$652$		0			0
$653$	8329.50	+	14427.1i	0.499171	+	0.864589i	1.00000		0.000957229i	$-0.000304695\pi$
$653$	8329.50	+	14427.1i	0.499171	+	0.864589i	−0.500829	+	0.865546i	$0.666971\pi$
$654$		0			0
$655$	9220.50	−	15970.4i	0.550038	−	0.952693i
$656$		0			0
$657$	626.000			0.0371729
$658$		0			0
$659$	−29556.0			−1.74710			−0.873550	−	0.486735i	$-0.838188\pi$
$659$	−29556.0			−1.74710			−0.873550	+	0.486735i	$0.838188\pi$
$660$		0			0
$661$	95.5000	−	165.411i	0.00561955	−	0.00973334i	−0.863202	−	0.504859i	$-0.831545\pi$
$661$	95.5000	−	165.411i	0.00561955	−	0.00973334i	0.868822	+	0.495125i	$0.164878\pi$
$662$		0			0
$663$	−8925.00	−	15458.6i	−0.522803	−	0.905521i
$664$		0			0
$665$	157.500	+	818.394i	0.00918434	+	0.0477232i
$666$		0			0
$667$	3933.00	+	6812.16i	0.228315	+	0.395454i
$668$		0			0
$669$	−140.000	+	242.487i	−0.00809075	+	0.0140136i
$670$		0			0
$671$	40413.0			2.32508
$672$		0			0
$673$	2606.00			0.149263			0.0746314	−	0.997211i	$-0.476222\pi$
$673$	2606.00			0.149263			0.0746314	+	0.997211i	$0.476222\pi$
$674$		0			0
$675$	−3190.00	+	5525.24i	−0.181901	+	0.315062i
$676$		0			0
$677$	−2104.50	−	3645.10i	−0.119472	−	0.206931i	0.800087	−	0.599885i	$-0.204787\pi$
$677$	−2104.50	−	3645.10i	−0.119472	−	0.206931i	−0.919559	+	0.392953i	$0.871453\pi$
$678$		0			0
$679$	25676.0	−	22236.1i	1.45118	−	1.25676i
$680$		0			0
$681$	−7642.50	−	13237.2i	−0.430046	−	0.744861i
$682$		0			0
$683$	12151.5	−	21047.0i	0.680768	−	1.17912i	−0.293979	−	0.955812i	$-0.594980\pi$
$683$	12151.5	−	21047.0i	0.680768	−	1.17912i	0.974747	−	0.223312i	$-0.0716869\pi$
$684$		0			0
$685$	−1269.00			−0.0707825
$686$		0			0
$687$	4805.00			0.266845
$688$		0			0
$689$	−13755.0	+	23824.4i	−0.760557	+	1.31732i
$690$		0			0
$691$	7520.50	+	13025.9i	0.414028	+	0.717117i	0.995326	−	0.0965734i	$-0.0307882\pi$
$691$	7520.50	+	13025.9i	0.414028	+	0.717117i	−0.581298	+	0.813691i	$0.697455\pi$
$692$		0			0
$693$	1596.00	−	1382.18i	0.0874849	−	0.0757641i
$694$		0			0
$695$	6678.00	+	11566.6i	0.364476	+	0.631291i
$696$		0			0
$697$	1071.00	−	1855.03i	0.0582023	−	0.100809i
$698$		0			0
$699$	−14145.0			−0.765398
$700$		0			0
$701$	−24726.0			−1.33222			−0.666111	−	0.745852i	$-0.732042\pi$
$701$	−24726.0			−1.33222			−0.666111	+	0.745852i	$0.732042\pi$
$702$		0			0
$703$	632.500	−	1095.52i	0.0339334	−	0.0587744i
$704$		0			0
$705$	−4522.50	−	7833.20i	−0.241599	−	0.418462i
$706$		0			0
$707$	−997.500	−	5183.16i	−0.0530620	−	0.275718i
$708$		0			0
$709$	−2478.50	−	4292.89i	−0.131286	−	0.227395i	0.792886	−	0.609370i	$-0.208577\pi$
$709$	−2478.50	−	4292.89i	−0.131286	−	0.227395i	−0.924173	+	0.381975i	$0.875244\pi$
$710$		0			0
$711$	461.000	−	798.475i	0.0243162	−	0.0421170i
$712$		0			0
$713$	1587.00			0.0833571
$714$		0			0
$715$	35910.0			1.87826
$716$		0			0
$717$	8850.00	−	15328.6i	0.460961	−	0.798409i
$718$		0			0
$719$	−13834.5	−	23962.1i	−0.717580	−	1.24288i	−0.961956	−	0.273204i	$-0.911917\pi$
$719$	−13834.5	−	23962.1i	−0.717580	−	1.24288i	0.244376	−	0.969680i	$-0.421417\pi$
$720$		0			0
$721$	−8732.50	−	3025.03i	−0.451061	−	0.156252i
$722$		0			0
$723$	−13077.5	−	22650.9i	−0.672694	−	1.16514i
$724$		0			0
$725$	−2508.00	+	4343.98i	−0.128476	+	0.222526i
$726$		0			0
$727$	−13888.0			−0.708497			−0.354249	−	0.935151i	$-0.615263\pi$
$727$	−13888.0			−0.708497			−0.354249	+	0.935151i	$0.615263\pi$
$728$		0			0
$729$	20917.0			1.06269
$730$		0			0
$731$	−3162.00	+	5476.74i	−0.159987	+	0.277106i
$732$		0			0
$733$	7121.50	+	12334.8i	0.358852	+	0.621550i	0.987769	−	0.155922i	$-0.0498349\pi$
$733$	7121.50	+	12334.8i	0.358852	+	0.621550i	−0.628917	+	0.777472i	$0.716502\pi$
$734$		0			0
$735$	2205.00	−	15276.7i	0.110657	−	0.766652i
$736$		0			0
$737$	11941.5	+	20683.3i	0.596840	+	1.03376i
$738$		0			0
$739$	18479.5	−	32007.4i	0.919864	−	1.59325i	0.120244	−	0.992744i	$-0.461632\pi$
$739$	18479.5	−	32007.4i	0.919864	−	1.59325i	0.799620	−	0.600507i	$-0.205034\pi$
$740$		0			0
$741$	−1750.00			−0.0867582
$742$		0			0
$743$	−12528.0			−0.618584			−0.309292	−	0.950967i	$-0.600092\pi$
$743$	−12528.0			−0.618584			−0.309292	+	0.950967i	$0.600092\pi$
$744$		0			0
$745$	−256.500	+	444.271i	−0.0126140	+	0.0218481i
$746$		0			0
$747$	588.000	+	1018.45i	0.0288003	+	0.0498835i
$748$		0			0
$749$	19372.5	+	6710.83i	0.945068	+	0.327381i
$750$		0			0
$751$	8883.50	+	15386.7i	0.431643	+	0.747627i	0.997015	−	0.0772090i	$-0.0246009\pi$
$751$	8883.50	+	15386.7i	0.431643	+	0.747627i	−0.565372	+	0.824836i	$0.691268\pi$
$752$		0			0
$753$	12600.0	−	21823.8i	0.609787	−	1.05618i
$754$		0			0
$755$	7551.00			0.363985
$756$		0			0
$757$	28726.0			1.37921			0.689606	−	0.724184i	$-0.257784\pi$
$757$	28726.0			1.37921			0.689606	+	0.724184i	$0.257784\pi$
$758$		0			0
$759$	−9832.50	+	17030.4i	−0.470220	+	0.814445i
$760$		0			0
$761$	13234.5	+	22922.8i	0.630421	+	1.09192i	0.987466	+	0.157834i	$0.0504510\pi$
$761$	13234.5	+	22922.8i	0.630421	+	1.09192i	−0.357045	+	0.934087i	$0.616216\pi$
$762$		0			0
$763$	3230.50	+	16786.2i	0.153279	+	0.796462i
$764$		0			0
$765$	459.000	+	795.011i	0.0216930	+	0.0375735i
$766$		0			0
$767$	7665.00	−	13276.2i	0.360844	−	0.625000i
$768$		0			0
$769$	5054.00			0.236999			0.118499	−	0.992954i	$-0.462192\pi$
$769$	5054.00			0.236999			0.118499	+	0.992954i	$0.462192\pi$
$770$		0			0
$771$	−7185.00			−0.335618
$772$		0			0
$773$	−17782.5	+	30800.2i	−0.827415	+	1.43313i	0.0726439	+	0.997358i	$0.476856\pi$
$773$	−17782.5	+	30800.2i	−0.827415	+	1.43313i	−0.900059	+	0.435767i	$0.856477\pi$
$774$		0			0
$775$	506.000	+	876.418i	0.0234530	+	0.0406217i
$776$		0			0
$777$	−17710.0	+	15337.3i	−0.817687	+	0.708138i
$778$		0			0
$779$	−105.000	−	181.865i	−0.00482929	−	0.00836457i
$780$		0			0
$781$	2736.00	−	4738.89i	0.125354	−	0.217120i
$782$		0			0
$783$	16530.0			0.754450
$784$		0			0
$785$	25497.0			1.15927
$786$		0			0
$787$	−4314.50	+	7472.93i	−0.195420	+	0.338477i	−0.947038	−	0.321121i	$-0.895940\pi$
$787$	−4314.50	+	7472.93i	−0.195420	+	0.338477i	0.751618	+	0.659598i	$0.229274\pi$
$788$		0			0
$789$	5812.50	+	10067.5i	0.262269	+	0.454264i
$790$		0			0
$791$	−21588.0	+	18695.8i	−0.970393	+	0.840385i
$792$		0			0
$793$	−24815.0	−	42980.8i	−1.11123	−	1.92471i
$794$		0			0
$795$	−8842.50	+	15315.7i	−0.394479	+	0.683258i
$796$		0			0
$797$	−20706.0			−0.920256			−0.460128	−	0.887853i	$-0.652197\pi$
$797$	−20706.0			−0.920256			−0.460128	+	0.887853i	$0.652197\pi$
$798$		0			0
$799$	10251.0			0.453885
$800$		0			0
$801$	−1017.00	+	1761.50i	−0.0448613	+	0.0777021i
$802$		0			0
$803$	8920.50	+	15450.8i	0.392027	+	0.679011i
$804$		0			0
$805$	−2173.50	−	11293.8i	−0.0951625	−	0.494479i
$806$		0			0
$807$	−5962.50	−	10327.4i	−0.260087	−	0.450483i
$808$		0			0
$809$	8092.50	−	14016.6i	0.351690	−	0.609145i	−0.634856	−	0.772631i	$-0.718940\pi$
$809$	8092.50	−	14016.6i	0.351690	−	0.609145i	0.986546	+	0.163486i	$0.0522738\pi$
$810$		0			0
$811$	11788.0			0.510398			0.255199	−	0.966889i	$-0.417859\pi$
$811$	11788.0			0.510398			0.255199	+	0.966889i	$0.417859\pi$
$812$		0			0
$813$	−1655.00			−0.0713941
$814$		0			0
$815$	−10399.5	+	18012.5i	−0.446968	+	0.774171i
$816$		0			0
$817$	310.000	+	536.936i	0.0132748	+	0.0229927i
$818$		0			0
$819$	−2450.00	−	848.705i	−0.104530	−	0.0362102i
$820$		0			0
$821$	−14896.5	−	25801.5i	−0.633242	−	1.09681i	−0.986885	−	0.161426i	$-0.948391\pi$
$821$	−14896.5	−	25801.5i	−0.633242	−	1.09681i	0.353643	−	0.935380i	$-0.384943\pi$
$822$		0			0
$823$	−15161.5	+	26260.5i	−0.642159	+	1.11225i	0.342791	+	0.939412i	$0.388628\pi$
$823$	−15161.5	+	26260.5i	−0.642159	+	1.11225i	−0.984950	+	0.172840i	$0.944706\pi$
$824$		0			0
$825$	−12540.0			−0.529196
$826$		0			0
$827$	−21156.0			−0.889560			−0.444780	−	0.895640i	$-0.646718\pi$
$827$	−21156.0			−0.889560			−0.444780	+	0.895640i	$0.646718\pi$
$828$		0			0
$829$	−2634.50	+	4563.09i	−0.110374	+	0.191173i	−0.915921	−	0.401358i	$-0.868538\pi$
$829$	−2634.50	+	4563.09i	−0.110374	+	0.191173i	0.805547	+	0.592532i	$0.201871\pi$
$830$		0			0
$831$	12177.5	+	21092.0i	0.508343	+	0.880475i
$832$		0			0
$833$	13744.5	+	10821.0i	0.571691	+	0.450090i
$834$		0			0
$835$	−5670.00	−	9820.73i	−0.234992	−	0.407018i
$836$		0			0
$837$	1667.50	−	2888.19i	0.0688617	−	0.119272i
$838$		0			0
$839$	−39816.0			−1.63838			−0.819190	−	0.573522i	$-0.805577\pi$
$839$	−39816.0			−1.63838			−0.819190	+	0.573522i	$0.805577\pi$
$840$		0			0
$841$	−11393.0			−0.467137
$842$		0			0
$843$	17565.0	−	30423.5i	0.717640	−	1.24299i
$844$		0			0
$845$	−12163.5	−	21067.8i	−0.495192	−	0.857697i
$846$		0			0
$847$	33565.0	+	11627.3i	1.36164	+	0.471685i
$848$		0			0
$849$	−13382.5	−	23179.2i	−0.540973	−	0.936993i
$850$		0			0
$851$	−8728.50	+	15118.2i	−0.351597	+	0.608984i
$852$		0			0
$853$	−14546.0			−0.583875			−0.291938	−	0.956437i	$-0.594300\pi$
$853$	−14546.0			−0.583875			−0.291938	+	0.956437i	$0.594300\pi$
$854$		0			0
$855$	90.0000			0.00359992
$856$		0			0
$857$	15724.5	−	27235.6i	0.626766	−	1.08559i	−0.361430	−	0.932399i	$-0.617711\pi$
$857$	15724.5	−	27235.6i	0.626766	−	1.08559i	0.988196	−	0.153192i	$-0.0489552\pi$
$858$		0			0
$859$	−12261.5	−	21237.5i	−0.487028	−	0.843557i	0.512861	−	0.858472i	$-0.328586\pi$
$859$	−12261.5	−	21237.5i	−0.487028	−	0.843557i	−0.999889	+	0.0149147i	$0.995252\pi$
$860$		0			0
$861$	735.000	+	3819.17i	0.0290926	+	0.151170i
$862$		0			0
$863$	4081.50	+	7069.37i	0.160992	+	0.278846i	0.935225	−	0.354055i	$-0.115197\pi$
$863$	4081.50	+	7069.37i	0.160992	+	0.278846i	−0.774233	+	0.632901i	$0.781864\pi$
$864$		0			0
$865$	14701.5	−	25463.7i	0.577880	−	1.00092i
$866$		0			0
$867$	−11560.0			−0.452824
$868$		0			0
$869$	26277.0			1.02576
$870$		0			0
$871$	14665.0	−	25400.5i	0.570499	−	0.988133i
$872$		0			0
$873$	−1834.00	−	3176.58i	−0.0711014	−	0.123151i
$874$		0			0
$875$	21294.0	−	18441.1i	0.822707	−	0.712485i
$876$		0			0
$877$	2183.50	+	3781.93i	0.0840725	+	0.145618i	0.904996	−	0.425421i	$-0.139874\pi$
$877$	2183.50	+	3781.93i	0.0840725	+	0.145618i	−0.820923	+	0.571039i	$0.806541\pi$
$878$		0			0
$879$	10395.0	−	18004.7i	0.398879	−	0.690879i
$880$		0			0
$881$	−50190.0			−1.91935			−0.959673	−	0.281118i	$-0.909295\pi$
$881$	−50190.0			−1.91935			−0.959673	+	0.281118i	$0.909295\pi$
$882$		0			0
$883$	−12308.0			−0.469079			−0.234540	−	0.972107i	$-0.575358\pi$
$883$	−12308.0			−0.469079			−0.234540	+	0.972107i	$0.575358\pi$
$884$		0			0
$885$	4927.50	−	8534.68i	0.187159	−	0.324170i
$886$		0			0
$887$	−15808.5	−	27381.1i	−0.598419	−	1.03649i	−0.993055	−	0.117654i	$-0.962463\pi$
$887$	−15808.5	−	27381.1i	−0.598419	−	1.03649i	0.394636	−	0.918838i	$-0.370871\pi$
$888$		0			0
$889$	28784.0	−	24927.7i	1.08592	−	0.940436i
$890$		0			0
$891$	19123.5	+	33122.9i	0.719036	+	1.24541i
$892$		0			0
$893$	502.500	−	870.356i	0.0188304	−	0.0326152i
$894$		0			0
$895$	−11583.0			−0.432600
$896$		0			0
$897$	24150.0			0.898935
$898$		0			0
$899$	1311.00	−	2270.72i	0.0486366	−	0.0842411i
$900$		0			0
$901$	−10021.5	−	17357.7i	−0.370549	−	0.641810i
$902$		0			0
$903$	−2170.00	−	11275.7i	−0.0799702	−	0.415537i
$904$		0			0
$905$	−12033.0	−	20841.8i	−0.441978	−	0.765529i
$906$		0			0
$907$	−6762.50	+	11713.0i	−0.247569	+	0.428802i	−0.962851	−	0.270034i	$-0.912965\pi$
$907$	−6762.50	+	11713.0i	−0.247569	+	0.428802i	0.715282	+	0.698836i	$0.246298\pi$
$908$		0			0
$909$	−570.000			−0.0207984
$910$		0			0
$911$	−19248.0			−0.700016			−0.350008	−	0.936747i	$-0.613821\pi$
$911$	−19248.0			−0.700016			−0.350008	+	0.936747i	$0.613821\pi$
$912$		0			0
$913$	−16758.0	+	29025.7i	−0.607458	+	1.05215i
$914$		0			0
$915$	−15952.5	−	27630.5i	−0.576364	−	0.998292i
$916$		0			0
$917$	−35857.5	−	12421.4i	−1.29130	−	0.447318i
$918$		0			0
$919$	4347.50	+	7530.09i	0.156051	+	0.270288i	0.933441	−	0.358730i	$-0.116790\pi$
$919$	4347.50	+	7530.09i	0.156051	+	0.270288i	−0.777390	+	0.629019i	$0.783457\pi$
$920$		0			0
$921$	−24010.0	+	41586.5i	−0.859019	+	1.48786i
$922$		0			0
$923$	−6720.00			−0.239644
$924$		0			0
$925$	−11132.0			−0.395695
$926$		0			0
$927$	−499.000	+	864.293i	−0.0176799	+	0.0306226i
$928$		0			0
$929$	−9739.50	−	16869.3i	−0.343964	−	0.595763i	0.641201	−	0.767373i	$-0.278437\pi$
$929$	−9739.50	−	16869.3i	−0.343964	−	0.595763i	−0.985165	+	0.171610i	$0.945103\pi$
$930$		0			0
$931$	1592.50	−	636.529i	0.0560602	−	0.0224075i
$932$		0			0
$933$	−25327.5	−	43868.5i	−0.888730	−	1.53933i
$934$		0			0
$935$	−13081.5	+	22657.8i	−0.457552	+	0.792503i
$936$		0			0
$937$	−12502.0			−0.435883			−0.217942	−	0.975962i	$-0.569934\pi$
$937$	−12502.0			−0.435883			−0.217942	+	0.975962i	$0.569934\pi$
$938$		0			0
$939$	53995.0			1.87653
$940$		0			0
$941$	−7996.50	+	13850.3i	−0.277023	+	0.479818i	−0.970643	−	0.240523i	$-0.922681\pi$
$941$	−7996.50	+	13850.3i	−0.277023	+	0.479818i	0.693621	+	0.720340i	$0.256014\pi$
$942$		0			0
$943$	1449.00	+	2509.74i	0.0500381	+	0.0866685i
$944$		0			0
$945$	−22837.5	−	7911.14i	−0.786142	−	0.272327i
$946$		0			0
$947$	22000.5	+	38106.0i	0.754932	+	1.30758i	0.945408	+	0.325888i	$0.105663\pi$
$947$	22000.5	+	38106.0i	0.754932	+	1.30758i	−0.190477	+	0.981692i	$0.561003\pi$
$948$		0			0
$949$	10955.0	−	18974.6i	0.374725	−	0.649043i
$950$		0			0
$951$	−2655.00			−0.0905303
$952$		0			0
$953$	−4002.00			−0.136031			−0.0680155	−	0.997684i	$-0.521667\pi$
$953$	−4002.00			−0.136031			−0.0680155	+	0.997684i	$0.521667\pi$
$954$		0			0
$955$	−18832.5	+	32618.8i	−0.638121	+	1.10526i
$956$		0			0
$957$	16245.0	+	28137.2i	0.548721	+	0.950413i
$958$		0			0
$959$	493.500	+	2564.30i	0.0166173	+	0.0863458i
$960$		0			0
$961$	14631.0	+	25341.6i	0.491121	+	0.850647i
$962$		0			0
$963$	1107.00	−	1917.38i	0.0370432	−	0.0641607i
$964$		0			0
$965$	−765.000			−0.0255194
$966$		0			0
$967$	10544.0			0.350643			0.175322	−	0.984511i	$-0.443903\pi$
$967$	10544.0			0.350643			0.175322	+	0.984511i	$0.443903\pi$
$968$		0			0
$969$	637.500	−	1104.18i	0.0211346	−	0.0366062i
$970$		0			0
$971$	−3091.50	−	5354.64i	−0.102174	−	0.176971i	0.810406	−	0.585869i	$-0.199247\pi$
$971$	−3091.50	−	5354.64i	−0.102174	−	0.176971i	−0.912580	+	0.408898i	$0.865913\pi$
$972$		0			0
$973$	20776.0	−	17992.5i	0.684530	−	0.592821i
$974$		0			0
$975$	7700.00	+	13336.8i	0.252920	+	0.438071i
$976$		0			0
$977$	−1861.50	+	3224.21i	−0.0609567	+	0.105580i	−0.894893	−	0.446280i	$-0.852748\pi$
$977$	−1861.50	+	3224.21i	−0.0609567	+	0.105580i	0.833937	+	0.551860i	$0.186082\pi$
$978$		0			0
$979$	−57969.0			−1.89244
$980$		0			0
$981$	1846.00			0.0600798
$982$		0			0
$983$	22948.5	−	39748.0i	0.744602	−	1.28969i	−0.205779	−	0.978599i	$-0.565973\pi$
$983$	22948.5	−	39748.0i	0.744602	−	1.28969i	0.950381	−	0.311089i	$-0.100694\pi$
$984$		0			0
$985$	−1755.00	−	3039.75i	−0.0567705	−	0.0983294i
$986$		0			0
$987$	−14070.0	+	12185.0i	−0.453752	+	0.392961i
$988$		0			0
$989$	−4278.00	−	7409.71i	−0.137545	−	0.238236i
$990$		0			0
$991$	−3233.50	+	5600.59i	−0.103648	+	0.179524i	−0.913185	−	0.407545i	$-0.866385\pi$
$991$	−3233.50	+	5600.59i	−0.103648	+	0.179524i	0.809537	+	0.587069i	$0.199718\pi$
$992$		0			0
$993$	35075.0			1.12092
$994$		0			0
$995$	−25497.0			−0.812371
$996$		0			0
$997$	11519.5	−	19952.4i	0.365924	−	0.633799i	−0.623000	−	0.782222i	$-0.714086\pi$
$997$	11519.5	−	19952.4i	0.365924	−	0.633799i	0.988924	+	0.148423i	$0.0474197\pi$
$998$		0			0
$999$	18342.5	+	31770.1i	0.580912	+	1.00617i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	448.4.i.b.193.1		2
4.3	odd	2		448.4.i.e.193.1		2
7.2	even	3	inner	448.4.i.b.65.1		2
8.3	odd	2		112.4.i.a.81.1		2
8.5	even	2		14.4.c.a.11.1	yes	2
24.5	odd	2		126.4.g.d.109.1		2
28.23	odd	6		448.4.i.e.65.1		2
40.13	odd	4		350.4.j.b.249.1		4
40.29	even	2		350.4.e.e.151.1		2
40.37	odd	4		350.4.j.b.249.2		4
56.3	even	6		784.4.a.c.1.1		1
56.5	odd	6		98.4.c.a.79.1		2
56.11	odd	6		784.4.a.p.1.1		1
56.13	odd	2		98.4.c.a.67.1		2
56.37	even	6		14.4.c.a.9.1	✓	2
56.45	odd	6		98.4.a.f.1.1		1
56.51	odd	6		112.4.i.a.65.1		2
56.53	even	6		98.4.a.d.1.1		1
168.5	even	6		882.4.g.u.667.1		2
168.53	odd	6		882.4.a.f.1.1		1
168.101	even	6		882.4.a.c.1.1		1
168.125	even	2		882.4.g.u.361.1		2
168.149	odd	6		126.4.g.d.37.1		2
280.37	odd	12		350.4.j.b.149.1		4
280.93	odd	12		350.4.j.b.149.2		4
280.109	even	6		2450.4.a.q.1.1		1
280.149	even	6		350.4.e.e.51.1		2
280.269	odd	6		2450.4.a.d.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
14.4.c.a.9.1	✓	2	56.37	even	6
14.4.c.a.11.1	yes	2	8.5	even	2
98.4.a.d.1.1		1	56.53	even	6
98.4.a.f.1.1		1	56.45	odd	6
98.4.c.a.67.1		2	56.13	odd	2
98.4.c.a.79.1		2	56.5	odd	6
112.4.i.a.65.1		2	56.51	odd	6
112.4.i.a.81.1		2	8.3	odd	2
126.4.g.d.37.1		2	168.149	odd	6
126.4.g.d.109.1		2	24.5	odd	2
350.4.e.e.51.1		2	280.149	even	6
350.4.e.e.151.1		2	40.29	even	2
350.4.j.b.149.1		4	280.37	odd	12
350.4.j.b.149.2		4	280.93	odd	12
350.4.j.b.249.1		4	40.13	odd	4
350.4.j.b.249.2		4	40.37	odd	4
448.4.i.b.65.1		2	7.2	even	3	inner
448.4.i.b.193.1		2	1.1	even	1	trivial
448.4.i.e.65.1		2	28.23	odd	6
448.4.i.e.193.1		2	4.3	odd	2
784.4.a.c.1.1		1	56.3	even	6
784.4.a.p.1.1		1	56.11	odd	6
882.4.a.c.1.1		1	168.101	even	6
882.4.a.f.1.1		1	168.53	odd	6
882.4.g.u.361.1		2	168.125	even	2
882.4.g.u.667.1		2	168.5	even	6
2450.4.a.d.1.1		1	280.269	odd	6
2450.4.a.q.1.1		1	280.109	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 448 = 2^{6} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	448.i (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-2.50000 + 4.33013i) q^{3} +(-4.50000 - 7.79423i) q^{5} +(-14.0000 + 12.1244i) q^{7} +(1.00000 + 1.73205i) q^{9} +O(q^{10})\)	\(q+(-2.50000 + 4.33013i) q^{3} +(-4.50000 - 7.79423i) q^{5} +(-14.0000 + 12.1244i) q^{7} +(1.00000 + 1.73205i) q^{9} +(-28.5000 + 49.3634i) q^{11} +70.0000 q^{13} +45.0000 q^{15} +(-25.5000 + 44.1673i) q^{17} +(2.50000 + 4.33013i) q^{19} +(-17.5000 - 90.9327i) q^{21} +(-34.5000 - 59.7558i) q^{23} +(22.0000 - 38.1051i) q^{25} -145.000 q^{27} -114.000 q^{29} +(-11.5000 + 19.9186i) q^{31} +(-142.500 - 246.817i) q^{33} +(157.500 + 54.5596i) q^{35} +(-126.500 - 219.104i) q^{37} +(-175.000 + 303.109i) q^{39} -42.0000 q^{41} +124.000 q^{43} +(9.00000 - 15.5885i) q^{45} +(-100.500 - 174.071i) q^{47} +(49.0000 - 339.482i) q^{49} +(-127.500 - 220.836i) q^{51} +(-196.500 + 340.348i) q^{53} +513.000 q^{55} -25.0000 q^{57} +(109.500 - 189.660i) q^{59} +(-354.500 - 614.012i) q^{61} +(-35.0000 - 12.1244i) q^{63} +(-315.000 - 545.596i) q^{65} +(209.500 - 362.865i) q^{67} +345.000 q^{69} -96.0000 q^{71} +(156.500 - 271.066i) q^{73} +(110.000 + 190.526i) q^{75} +(-199.500 - 1036.63i) q^{77} +(-230.500 - 399.238i) q^{79} +(335.500 - 581.103i) q^{81} +588.000 q^{83} +459.000 q^{85} +(285.000 - 493.634i) q^{87} +(508.500 + 880.748i) q^{89} +(-980.000 + 848.705i) q^{91} +(-57.5000 - 99.5929i) q^{93} +(22.5000 - 38.9711i) q^{95} -1834.00 q^{97} -114.000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 5 q^{3} - 9 q^{5} - 28 q^{7} + 2 q^{9}+O(q^{10}) \) 2 * q - 5 * q^3 - 9 * q^5 - 28 * q^7 + 2 * q^9	\( 2 q - 5 q^{3} - 9 q^{5} - 28 q^{7} + 2 q^{9} - 57 q^{11} + 140 q^{13} + 90 q^{15} - 51 q^{17} + 5 q^{19} - 35 q^{21} - 69 q^{23} + 44 q^{25} - 290 q^{27} - 228 q^{29} - 23 q^{31} - 285 q^{33} + 315 q^{35} - 253 q^{37} - 350 q^{39} - 84 q^{41} + 248 q^{43} + 18 q^{45} - 201 q^{47} + 98 q^{49} - 255 q^{51} - 393 q^{53} + 1026 q^{55} - 50 q^{57} + 219 q^{59} - 709 q^{61} - 70 q^{63} - 630 q^{65} + 419 q^{67} + 690 q^{69} - 192 q^{71} + 313 q^{73} + 220 q^{75} - 399 q^{77} - 461 q^{79} + 671 q^{81} + 1176 q^{83} + 918 q^{85} + 570 q^{87} + 1017 q^{89} - 1960 q^{91} - 115 q^{93} + 45 q^{95} - 3668 q^{97} - 228 q^{99}+O(q^{100}) \) 2 * q - 5 * q^3 - 9 * q^5 - 28 * q^7 + 2 * q^9 - 57 * q^11 + 140 * q^13 + 90 * q^15 - 51 * q^17 + 5 * q^19 - 35 * q^21 - 69 * q^23 + 44 * q^25 - 290 * q^27 - 228 * q^29 - 23 * q^31 - 285 * q^33 + 315 * q^35 - 253 * q^37 - 350 * q^39 - 84 * q^41 + 248 * q^43 + 18 * q^45 - 201 * q^47 + 98 * q^49 - 255 * q^51 - 393 * q^53 + 1026 * q^55 - 50 * q^57 + 219 * q^59 - 709 * q^61 - 70 * q^63 - 630 * q^65 + 419 * q^67 + 690 * q^69 - 192 * q^71 + 313 * q^73 + 220 * q^75 - 399 * q^77 - 461 * q^79 + 671 * q^81 + 1176 * q^83 + 918 * q^85 + 570 * q^87 + 1017 * q^89 - 1960 * q^91 - 115 * q^93 + 45 * q^95 - 3668 * q^97 - 228 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more