LMFDB - Embedded newform 448.4.i.e.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:	$0$
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.e.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	−0.518640	−	0.854993i	$-0.673562\pi$
$3$	2.50000	−	4.33013i	0.481125	−	0.833333i	0.999765	+	0.0216593i	$0.00689490\pi$
$4$		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	$-0.547947\pi$
$11$	28.5000	−	49.3634i	0.781188	−	1.35306i	0.931250	−	0.364381i	$-0.118720\pi$
$12$		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	0.850538	−	0.525914i	$-0.176277\pi$
$19$	−2.50000	−	4.33013i	−0.0301863	−	0.0522842i	−0.880724	+	0.473630i	$0.842943\pi$
$20$		0			0
$21$	−17.5000	−	90.9327i	−0.181848	−	0.944911i
$22$		0			0
$23$	34.5000	+	59.7558i	0.312772	+	0.541736i	0.978961	−	0.204046i	$-0.0654092\pi$
$23$	34.5000	+	59.7558i	0.312772	+	0.541736i	−0.666190	+	0.745782i	$0.732076\pi$
$24$		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	−0.830787	−	0.556590i	$-0.812109\pi$
$31$	11.5000	−	19.9186i	0.0666278	−	0.115403i	0.897415	+	0.441188i	$0.145443\pi$
$32$		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	$-0.570567\pi$
$43$	−124.000			−0.439763			−0.219882	+	0.975527i	$0.570567\pi$
$44$		0			0
$45$	9.00000	−	15.5885i	0.0298142	−	0.0516398i
$46$		0			0
$47$	100.500	+	174.071i	0.311903	+	0.540231i	0.978774	−	0.204941i	$-0.0657003\pi$
$47$	100.500	+	174.071i	0.311903	+	0.540231i	−0.666871	+	0.745173i	$0.732367\pi$
$48$		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	−0.961176	−	0.275935i	$-0.911013\pi$
$59$	−109.500	+	189.660i	−0.241622	+	0.418501i	0.719555	+	0.694436i	$0.244346\pi$
$60$		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	−0.991349	−	0.131251i	$-0.958100\pi$
$67$	−209.500	+	362.865i	−0.382007	+	0.661656i	0.609342	+	0.792908i	$0.291434\pi$
$68$		0			0
$69$	345.000			0.601929
$70$		0			0
$71$	96.0000			0.160466			0.0802331	−	0.996776i	$-0.474434\pi$
$71$	96.0000			0.160466			0.0802331	+	0.996776i	$0.474434\pi$
$72$		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	0.982169	−	0.188003i	$-0.0602013\pi$
$79$	230.500	+	399.238i	0.328269	+	0.568579i	−0.653899	+	0.756582i	$0.726868\pi$
$80$		0			0
$81$	335.500	−	581.103i	0.460219	−	0.797124i
$82$		0			0
$83$	−588.000			−0.777607			−0.388804	−	0.921321i	$-0.627112\pi$
$83$	−588.000			−0.777607			−0.388804	+	0.921321i	$0.627112\pi$
$84$		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	0.721656	−	0.692252i	$-0.243381\pi$
$103$	−249.500	−	432.147i	−0.238679	−	0.413405i	−0.960336	+	0.278847i	$0.910048\pi$
$104$		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	$3.04516e-5\pi$
$107$	553.500	+	958.690i	0.500083	+	0.866169i	−0.499917	+	0.866073i	$0.666636\pi$
$108$		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	$-0.244934\pi$
$127$	2056.00			1.43654			0.718270	+	0.695765i	$0.244934\pi$
$128$		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	$-0.927215\pi$
$131$	−1024.50	−	1774.49i	−0.683290	−	1.18349i	0.290681	−	0.956820i	$-0.406118\pi$
$132$		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	$-0.350434\pi$
$139$	1484.00			0.905548			0.452774	+	0.891625i	$0.350434\pi$
$140$		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	−0.730561	−	0.682847i	$-0.760742\pi$
$151$	419.500	−	726.595i	0.226082	−	0.391586i	0.956644	+	0.291261i	$0.0940748\pi$
$152$		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	$0.0207107\pi$
$163$	1155.50	+	2001.38i	0.555250	+	0.961721i	−0.442634	+	0.896702i	$0.645956\pi$
$164$		0			0
$165$	−1282.50	+	2221.36i	−0.605106	+	1.04807i
$166$		0			0
$167$	−1260.00			−0.583843			−0.291921	−	0.956442i	$-0.594295\pi$
$167$	−1260.00			−0.583843			−0.291921	+	0.956442i	$0.594295\pi$
$168$		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	−0.968527	−	0.248910i	$-0.919928\pi$
$179$	−643.500	+	1114.57i	−0.268701	+	0.465403i	0.699826	+	0.714314i	$0.253261\pi$
$180$		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	$0.124665\pi$
$191$	2092.50	+	3624.32i	0.792712	+	1.37302i	−0.131570	+	0.991307i	$0.542002\pi$
$192$		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	$0.335022\pi$
$199$	−1416.50	+	2453.45i	−0.504588	+	0.873972i	−0.999986	+	0.00530596i	$0.998311\pi$
$200$		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	$-0.506439\pi$
$211$	−124.000			−0.0404574			−0.0202287	+	0.999795i	$0.506439\pi$
$212$		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	$-0.502676\pi$
$223$	−56.0000			−0.0168163			−0.00840816	+	0.999965i	$0.502676\pi$
$224$		0			0
$225$	88.0000			0.0260741
$226$		0			0
$227$	1528.50	−	2647.44i	0.446917	−	0.774083i	−0.551267	−	0.834329i	$-0.685855\pi$
$227$	1528.50	−	2647.44i	0.446917	−	0.774083i	0.998184	+	0.0602465i	$0.0191887\pi$
$228$		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	$-0.340983\pi$
$239$	3540.00			0.958090			0.479045	+	0.877790i	$0.340983\pi$
$240$		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	$-0.281532\pi$
$251$	5040.00			1.26742			0.633709	+	0.773571i	$0.281532\pi$
$252$		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	−0.969516	−	0.245027i	$-0.921203\pi$
$263$	−1162.50	+	2013.51i	−0.272558	+	0.472085i	0.696958	+	0.717112i	$0.254536\pi$
$264$		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	0.846881	−	0.531783i	$-0.178478\pi$
$271$	−165.500	−	286.654i	−0.0370975	−	0.0642547i	−0.883978	+	0.467528i	$0.845145\pi$
$272$		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	$-0.643290\pi$
$283$	2676.50	−	4635.83i	0.562196	−	0.973752i	0.997305	−	0.0733738i	$-0.0233766\pi$
$284$		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	$-0.851205\pi$
$307$	−9604.00			−1.78544			−0.892719	+	0.450615i	$0.851205\pi$
$308$		0			0
$309$	−2495.00			−0.459338
$310$		0			0
$311$	5065.50	−	8773.70i	0.923595	−	1.59971i	0.129791	−	0.991541i	$-0.458570\pi$
$311$	5065.50	−	8773.70i	0.923595	−	1.59971i	0.793805	−	0.608173i	$-0.208097\pi$
$312$		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	$0.0312376\pi$
$331$	3507.50	+	6075.17i	0.582446	+	1.00883i	−0.412743	+	0.910848i	$0.635429\pi$
$332$		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	$-0.598052\pi$
$347$	4354.50	−	7542.22i	0.673665	−	1.16682i	0.976857	−	0.213893i	$-0.0686143\pi$
$348$		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	0.972105	−	0.234548i	$-0.0753608\pi$
$359$	1924.50	+	3333.33i	0.282928	+	0.490046i	−0.689176	+	0.724594i	$0.742028\pi$
$360$		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	−0.537424	−	0.843312i	$-0.680603\pi$
$367$	3245.50	−	5621.37i	0.461618	−	0.799545i	0.999042	+	0.0437668i	$0.0139358\pi$
$368$		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	$-0.358546\pi$
$379$	6344.00			0.859814			0.429907	+	0.902873i	$0.358546\pi$
$380$		0			0
$381$	5140.00	−	8902.74i	0.691155	−	1.19712i
$382$		0			0
$383$	−2503.50	−	4336.19i	−0.334002	−	0.578509i	0.649290	−	0.760541i	$-0.275066\pi$
$383$	−2503.50	−	4336.19i	−0.334002	−	0.578509i	−0.983293	+	0.182032i	$0.941733\pi$
$384$		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	$-0.603113\pi$
$419$	−5460.00			−0.636607			−0.318304	+	0.947989i	$0.603113\pi$
$420$		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	$0.384501\pi$
$431$	−5656.50	+	9797.35i	−0.632167	+	1.09495i	−0.987108	+	0.160057i	$0.948832\pi$
$432$		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	$0.189627\pi$
$439$	8276.50	+	14335.3i	0.899808	+	1.55851i	0.0720696	+	0.997400i	$0.477040\pi$
$440$		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	$0.175240\pi$
$443$	8197.50	+	14198.5i	0.879176	+	1.52278i	0.0269294	+	0.999637i	$0.491427\pi$
$444$		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	$-0.507413\pi$
$463$	−464.000			−0.0465743			−0.0232872	+	0.999729i	$0.507413\pi$
$464$		0			0
$465$	−517.500	+	896.336i	−0.0516097	+	0.0893905i
$466$		0			0
$467$	−2116.50	−	3665.89i	−0.209721	−	0.363248i	0.741905	−	0.670505i	$-0.233922\pi$
$467$	−2116.50	−	3665.89i	−0.209721	−	0.363248i	−0.951627	+	0.307256i	$0.900589\pi$
$468$		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	−0.793287	−	0.608848i	$-0.791632\pi$
$479$	1369.50	−	2372.04i	0.130635	−	0.226266i	0.923921	+	0.382582i	$0.124965\pi$
$480$		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	$-0.541705\pi$
$487$	8525.50	−	14766.6i	0.793280	−	1.37400i	0.923926	−	0.382572i	$-0.124962\pi$
$488$		0			0
$489$	11555.0			1.06858
$490$		0			0
$491$	−4296.00			−0.394859			−0.197429	−	0.980317i	$-0.563259\pi$
$491$	−4296.00			−0.394859			−0.197429	+	0.980317i	$0.563259\pi$
$492$		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	0.779611	−	0.626264i	$-0.215417\pi$
$499$	−1700.50	−	2945.35i	−0.152555	−	0.264233i	−0.932166	+	0.362031i	$0.882083\pi$
$500$		0			0
$501$	−3150.00	+	5455.96i	−0.280901	+	0.486536i
$502$		0			0
$503$	−16800.0			−1.48921			−0.744607	−	0.667503i	$-0.767363\pi$
$503$	−16800.0			−1.48921			−0.744607	+	0.667503i	$0.767363\pi$
$504$		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	$0.194037\pi$
$523$	10833.5	+	18764.2i	0.905767	+	1.56883i	0.0858815	+	0.996305i	$0.472629\pi$
$524$		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	$-0.529801\pi$
$547$	−2392.00			−0.186974			−0.0934868	+	0.995621i	$0.529801\pi$
$548$		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	−0.666408	−	0.745588i	$-0.732169\pi$
$563$	4174.50	−	7230.45i	0.312494	−	0.541256i	0.978902	+	0.204332i	$0.0655022\pi$
$564$		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	−0.571578	−	0.820548i	$-0.693668\pi$
$571$	5796.50	−	10039.8i	0.424827	−	0.735821i	0.996404	+	0.0847268i	$0.0270017\pi$
$572$		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	$-0.681740\pi$
$587$	−15372.0			−1.08087			−0.540435	+	0.841386i	$0.681740\pi$
$588$		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	−0.819318	−	0.573340i	$-0.805648\pi$
$599$	1273.50	−	2205.77i	0.0868678	−	0.150459i	0.906186	+	0.422880i	$0.138981\pi$
$600$		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	$-0.894155\pi$
$607$	−11295.5	−	19564.4i	−0.755305	−	1.30823i	0.189917	−	0.981800i	$-0.439178\pi$
$608$		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	−0.900817	−	0.434200i	$-0.857031\pi$
$619$	−1145.50	+	1984.06i	−0.0743805	+	0.128831i	0.826436	+	0.563030i	$0.190365\pi$
$620$		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	$-0.429870\pi$
$631$	6928.00			0.437083			0.218541	+	0.975828i	$0.429870\pi$
$632$		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	$-0.405414\pi$
$643$	9548.00			0.585593			0.292797	+	0.956175i	$0.405414\pi$
$644$		0			0
$645$	5580.00			0.340639
$646$		0			0
$647$	5065.50	−	8773.70i	0.307798	−	0.533122i	−0.670082	−	0.742287i	$-0.733741\pi$
$647$	5065.50	−	8773.70i	0.307798	−	0.533122i	0.977880	+	0.209165i	$0.0670745\pi$
$648$		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	$-0.161812\pi$
$659$	29556.0			1.74710			0.873550	+	0.486735i	$0.161812\pi$
$660$		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	$0.405020\pi$
$683$	−12151.5	+	21047.0i	−0.680768	+	1.17912i	−0.974747	+	0.223312i	$0.928313\pi$
$684$		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	0.581298	−	0.813691i	$-0.302545\pi$
$691$	−7520.50	−	13025.9i	−0.414028	−	0.717117i	−0.995326	+	0.0965734i	$0.969212\pi$
$692$		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	$0.0880834\pi$
$719$	13834.5	+	23962.1i	0.717580	+	1.24288i	−0.244376	+	0.969680i	$0.578583\pi$
$720$		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	$-0.384737\pi$
$727$	13888.0			0.708497			0.354249	+	0.935151i	$0.384737\pi$
$728$		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	$0.538368\pi$
$739$	−18479.5	+	32007.4i	−0.919864	+	1.59325i	−0.799620	+	0.600507i	$0.794966\pi$
$740$		0			0
$741$	−1750.00			−0.0867582
$742$		0			0
$743$	12528.0			0.618584			0.309292	−	0.950967i	$-0.399908\pi$
$743$	12528.0			0.618584			0.309292	+	0.950967i	$0.399908\pi$
$744$		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	0.565372	−	0.824836i	$-0.308732\pi$
$751$	−8883.50	−	15386.7i	−0.431643	−	0.747627i	−0.997015	+	0.0772090i	$0.975399\pi$
$752$		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	−0.751618	−	0.659598i	$-0.770726\pi$
$787$	4314.50	−	7472.93i	0.195420	−	0.338477i	0.947038	+	0.321121i	$0.104060\pi$
$788$		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	$-0.582141\pi$
$811$	−11788.0			−0.510398			−0.255199	+	0.966889i	$0.582141\pi$
$812$		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	$-0.611372\pi$
$823$	15161.5	−	26260.5i	0.642159	−	1.11225i	0.984950	−	0.172840i	$-0.0552943\pi$
$824$		0			0
$825$	−12540.0			−0.529196
$826$		0			0
$827$	21156.0			0.889560			0.444780	−	0.895640i	$-0.353282\pi$
$827$	21156.0			0.889560			0.444780	+	0.895640i	$0.353282\pi$
$828$		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	$-0.194423\pi$
$839$	39816.0			1.63838			0.819190	+	0.573522i	$0.194423\pi$
$840$		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	0.999889	−	0.0149147i	$-0.00474766\pi$
$859$	12261.5	+	21237.5i	0.487028	+	0.843557i	−0.512861	+	0.858472i	$0.671414\pi$
$860$		0			0
$861$	735.000	+	3819.17i	0.0290926	+	0.151170i
$862$		0			0
$863$	−4081.50	−	7069.37i	−0.160992	−	0.278846i	0.774233	−	0.632901i	$-0.218136\pi$
$863$	−4081.50	−	7069.37i	−0.160992	−	0.278846i	−0.935225	+	0.354055i	$0.884803\pi$
$864$		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	$-0.424642\pi$
$883$	12308.0			0.469079			0.234540	+	0.972107i	$0.424642\pi$
$884$		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	$0.0375374\pi$
$887$	15808.5	+	27381.1i	0.598419	+	1.03649i	−0.394636	+	0.918838i	$0.629129\pi$
$888$		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	−0.715282	−	0.698836i	$-0.753702\pi$
$907$	6762.50	−	11713.0i	0.247569	−	0.428802i	0.962851	+	0.270034i	$0.0870350\pi$
$908$		0			0
$909$	−570.000			−0.0207984
$910$		0			0
$911$	19248.0			0.700016			0.350008	−	0.936747i	$-0.386179\pi$
$911$	19248.0			0.700016			0.350008	+	0.936747i	$0.386179\pi$
$912$		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	0.777390	−	0.629019i	$-0.216543\pi$
$919$	−4347.50	−	7530.09i	−0.156051	−	0.270288i	−0.933441	+	0.358730i	$0.883210\pi$
$920$		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	$-0.894337\pi$
$947$	−22000.5	−	38106.0i	−0.754932	−	1.30758i	0.190477	−	0.981692i	$-0.438997\pi$
$948$		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	$-0.556097\pi$
$967$	−10544.0			−0.350643			−0.175322	+	0.984511i	$0.556097\pi$
$968$		0			0
$969$	637.500	−	1104.18i	0.0211346	−	0.0366062i
$970$		0			0
$971$	3091.50	+	5354.64i	0.102174	+	0.176971i	0.912580	−	0.408898i	$-0.134087\pi$
$971$	3091.50	+	5354.64i	0.102174	+	0.176971i	−0.810406	+	0.585869i	$0.800753\pi$
$972$		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	$0.434027\pi$
$983$	−22948.5	+	39748.0i	−0.744602	+	1.28969i	−0.950381	+	0.311089i	$0.899306\pi$
$984$		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	−0.809537	−	0.587069i	$-0.800282\pi$
$991$	3233.50	−	5600.59i	0.103648	−	0.179524i	0.913185	+	0.407545i	$0.133615\pi$
$992$		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.e.193.1		2
4.3	odd	2		448.4.i.b.193.1		2
7.2	even	3	inner	448.4.i.e.65.1		2
8.3	odd	2		14.4.c.a.11.1	yes	2
8.5	even	2		112.4.i.a.81.1		2
24.11	even	2		126.4.g.d.109.1		2
28.23	odd	6		448.4.i.b.65.1		2
40.3	even	4		350.4.j.b.249.1		4
40.19	odd	2		350.4.e.e.151.1		2
40.27	even	4		350.4.j.b.249.2		4
56.3	even	6		98.4.a.f.1.1		1
56.11	odd	6		98.4.a.d.1.1		1
56.19	even	6		98.4.c.a.79.1		2
56.27	even	2		98.4.c.a.67.1		2
56.37	even	6		112.4.i.a.65.1		2
56.45	odd	6		784.4.a.c.1.1		1
56.51	odd	6		14.4.c.a.9.1	✓	2
56.53	even	6		784.4.a.p.1.1		1
168.11	even	6		882.4.a.f.1.1		1
168.59	odd	6		882.4.a.c.1.1		1
168.83	odd	2		882.4.g.u.361.1		2
168.107	even	6		126.4.g.d.37.1		2
168.131	odd	6		882.4.g.u.667.1		2
280.59	even	6		2450.4.a.d.1.1		1
280.107	even	12		350.4.j.b.149.1		4
280.163	even	12		350.4.j.b.149.2		4
280.179	odd	6		2450.4.a.q.1.1		1
280.219	odd	6		350.4.e.e.51.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
14.4.c.a.9.1	✓	2	56.51	odd	6
14.4.c.a.11.1	yes	2	8.3	odd	2
98.4.a.d.1.1		1	56.11	odd	6
98.4.a.f.1.1		1	56.3	even	6
98.4.c.a.67.1		2	56.27	even	2
98.4.c.a.79.1		2	56.19	even	6
112.4.i.a.65.1		2	56.37	even	6
112.4.i.a.81.1		2	8.5	even	2
126.4.g.d.37.1		2	168.107	even	6
126.4.g.d.109.1		2	24.11	even	2
350.4.e.e.51.1		2	280.219	odd	6
350.4.e.e.151.1		2	40.19	odd	2
350.4.j.b.149.1		4	280.107	even	12
350.4.j.b.149.2		4	280.163	even	12
350.4.j.b.249.1		4	40.3	even	4
350.4.j.b.249.2		4	40.27	even	4
448.4.i.b.65.1		2	28.23	odd	6
448.4.i.b.193.1		2	4.3	odd	2
448.4.i.e.65.1		2	7.2	even	3	inner
448.4.i.e.193.1		2	1.1	even	1	trivial
784.4.a.c.1.1		1	56.45	odd	6
784.4.a.p.1.1		1	56.53	even	6
882.4.a.c.1.1		1	168.59	odd	6
882.4.a.f.1.1		1	168.11	even	6
882.4.g.u.361.1		2	168.83	odd	2
882.4.g.u.667.1		2	168.131	odd	6
2450.4.a.d.1.1		1	280.59	even	6
2450.4.a.q.1.1		1	280.179	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:	\( N \)	\(=\)	\( 448 = 2^{6} \cdot 7 \)
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