LMFDB - Embedded newform 35.5.d.a.6.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [35,5,Mod(6,35)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(35, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 5, names="a")

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

chi := DirichletCharacter("35.6");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 35 = 5 \cdot 7 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	35.d (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.61794870793$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 6 x^{11} - 109 x^{10} + 570 x^{9} + 5814 x^{8} - 22512 x^{7} - 151120 x^{6} + 300288 x^{5} + \cdots + 205833600 $ x^12 - 6x^11 - 109x^10 + 570x^9 + 5814x^8 - 22512x^7 - 151120x^6 + 300288x^5 + 2661184x^4 - 1881600x^3 - 12922560x^2 + 25948800*x + 205833600
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{3}\cdot 5^{5} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			6.7
Root			$2.17355 - 2.23607i$ of defining polynomial
Character	$\chi$	$=$	35.6
Dual form			35.5.d.a.6.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.17355 q^{2} -9.10378i q^{3} -14.6228 q^{4} -11.1803i q^{5} -10.6837i q^{6} +(-40.5002 - 27.5814i) q^{7} -35.9373 q^{8} -1.87877 q^{9} +O(q^{10})$	\(q+1.17355 q^{2} -9.10378i q^{3} -14.6228 q^{4} -11.1803i q^{5} -10.6837i q^{6} +(-40.5002 - 27.5814i) q^{7} -35.9373 q^{8} -1.87877 q^{9} -13.1207i q^{10} +106.806 q^{11} +133.123i q^{12} -243.104i q^{13} +(-47.5290 - 32.3681i) q^{14} -101.783 q^{15} +191.790 q^{16} +148.252i q^{17} -2.20483 q^{18} +244.752i q^{19} +163.488i q^{20} +(-251.095 + 368.705i) q^{21} +125.342 q^{22} +621.143 q^{23} +327.166i q^{24} -125.000 q^{25} -285.294i q^{26} -720.302i q^{27} +(592.226 + 403.316i) q^{28} -774.981 q^{29} -119.448 q^{30} -403.109i q^{31} +800.073 q^{32} -972.334i q^{33} +173.981i q^{34} +(-308.369 + 452.806i) q^{35} +27.4729 q^{36} -1290.58 q^{37} +287.229i q^{38} -2213.16 q^{39} +401.792i q^{40} -2536.73i q^{41} +(-294.672 + 432.694i) q^{42} +2242.99 q^{43} -1561.79 q^{44} +21.0053i q^{45} +728.942 q^{46} -2494.61i q^{47} -1746.02i q^{48} +(879.536 + 2234.10i) q^{49} -146.694 q^{50} +1349.65 q^{51} +3554.85i q^{52} -281.688 q^{53} -845.310i q^{54} -1194.12i q^{55} +(1455.47 + 991.201i) q^{56} +2228.17 q^{57} -909.479 q^{58} +5822.15i q^{59} +1488.36 q^{60} +6268.19i q^{61} -473.068i q^{62} +(76.0908 + 51.8192i) q^{63} -2129.72 q^{64} -2717.98 q^{65} -1141.08i q^{66} +4128.43 q^{67} -2167.85i q^{68} -5654.74i q^{69} +(-361.886 + 531.390i) q^{70} -793.446 q^{71} +67.5182 q^{72} +1600.72i q^{73} -1514.56 q^{74} +1137.97i q^{75} -3578.96i q^{76} +(-4325.65 - 2945.84i) q^{77} -2597.25 q^{78} +9856.44 q^{79} -2144.28i q^{80} -6709.65 q^{81} -2976.98i q^{82} +617.012i q^{83} +(3671.70 - 5391.49i) q^{84} +1657.51 q^{85} +2632.26 q^{86} +7055.26i q^{87} -3838.31 q^{88} -7345.17i q^{89} +24.6508i q^{90} +(-6705.13 + 9845.75i) q^{91} -9082.83 q^{92} -3669.81 q^{93} -2927.55i q^{94} +2736.41 q^{95} -7283.69i q^{96} +67.6288i q^{97} +(1032.18 + 2621.83i) q^{98} -200.664 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 6 q^{2} + 122 q^{4} - 50 q^{7} - 186 q^{8} - 434 q^{9}+O(q^{10}) $ 12 * q - 6 * q^2 + 122 * q^4 - 50 * q^7 - 186 * q^8 - 434 * q^9	$ 12 q - 6 q^{2} + 122 q^{4} - 50 q^{7} - 186 q^{8} - 434 q^{9} + 126 q^{11} + 78 q^{14} + 50 q^{15} + 578 q^{16} + 734 q^{18} - 642 q^{21} + 2264 q^{22} - 756 q^{23} - 1500 q^{25} + 1414 q^{28} - 2190 q^{29} + 1600 q^{30} - 8682 q^{32} - 150 q^{35} - 3582 q^{36} + 5564 q^{37} + 8634 q^{39} + 5580 q^{42} + 3944 q^{43} - 11196 q^{44} + 7844 q^{46} - 8796 q^{49} + 750 q^{50} + 7206 q^{51} + 11760 q^{53} - 6606 q^{56} - 12900 q^{57} - 18496 q^{58} - 11700 q^{60} - 4310 q^{63} + 20146 q^{64} - 750 q^{65} - 24096 q^{67} + 14400 q^{70} - 5664 q^{71} + 39214 q^{72} + 17604 q^{74} + 26904 q^{77} + 20100 q^{78} - 1590 q^{79} - 11912 q^{81} - 43128 q^{84} + 1050 q^{85} + 17604 q^{86} - 7268 q^{88} - 7182 q^{91} - 60252 q^{92} - 70980 q^{93} - 3000 q^{95} + 57714 q^{98} + 23084 q^{99}+O(q^{100}) $ 12 * q - 6 * q^2 + 122 * q^4 - 50 * q^7 - 186 * q^8 - 434 * q^9 + 126 * q^11 + 78 * q^14 + 50 * q^15 + 578 * q^16 + 734 * q^18 - 642 * q^21 + 2264 * q^22 - 756 * q^23 - 1500 * q^25 + 1414 * q^28 - 2190 * q^29 + 1600 * q^30 - 8682 * q^32 - 150 * q^35 - 3582 * q^36 + 5564 * q^37 + 8634 * q^39 + 5580 * q^42 + 3944 * q^43 - 11196 * q^44 + 7844 * q^46 - 8796 * q^49 + 750 * q^50 + 7206 * q^51 + 11760 * q^53 - 6606 * q^56 - 12900 * q^57 - 18496 * q^58 - 11700 * q^60 - 4310 * q^63 + 20146 * q^64 - 750 * q^65 - 24096 * q^67 + 14400 * q^70 - 5664 * q^71 + 39214 * q^72 + 17604 * q^74 + 26904 * q^77 + 20100 * q^78 - 1590 * q^79 - 11912 * q^81 - 43128 * q^84 + 1050 * q^85 + 17604 * q^86 - 7268 * q^88 - 7182 * q^91 - 60252 * q^92 - 70980 * q^93 - 3000 * q^95 + 57714 * q^98 + 23084 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/35\mathbb{Z}\right)^\times$.

$n$	$22$	$31$
$\chi(n)$	$1$	$-1$

Coefficient data

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

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

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

$2$	1.17355			0.293387			0.146694	−	0.989182i	$-0.453137\pi$
$2$	1.17355			0.293387			0.146694	+	0.989182i	$0.453137\pi$
$3$		−	9.10378i		−	1.01153i	−0.862671	−	0.505765i	$-0.831210\pi$
$3$		−	9.10378i		−	1.01153i	0.862671	−	0.505765i	$-0.168790\pi$
$4$	−14.6228			−0.913924
$5$		−	11.1803i		−	0.447214i
$5$		−	11.1803i		−	0.447214i
$6$		−	10.6837i		−	0.296770i
$7$	−40.5002	−	27.5814i	−0.826535	−	0.562885i
$7$	−40.5002	−	27.5814i	−0.826535	−	0.562885i
$8$	−35.9373			−0.561521
$9$	−1.87877			−0.0231947
$10$		−	13.1207i		−	0.131207i
$11$	106.806			0.882690			0.441345	−	0.897337i	$-0.354501\pi$
$11$	106.806			0.882690			0.441345	+	0.897337i	$0.354501\pi$
$12$			133.123i			0.924462i
$13$		−	243.104i		−	1.43848i	−0.694760	−	0.719242i	$-0.744489\pi$
$13$		−	243.104i		−	1.43848i	0.694760	−	0.719242i	$-0.255511\pi$
$14$	−47.5290	−	32.3681i	−0.242495	−	0.165143i
$15$	−101.783			−0.452370
$16$	191.790			0.749181
$17$			148.252i			0.512982i	0.966547	+	0.256491i	$0.0825664\pi$
$17$			148.252i			0.512982i	−0.966547	+	0.256491i	$0.917434\pi$
$18$	−2.20483			−0.00680505
$19$			244.752i			0.677984i	0.940789	+	0.338992i	$0.110086\pi$
$19$			244.752i			0.677984i	−0.940789	+	0.338992i	$0.889914\pi$
$20$			163.488i			0.408719i
$21$	−251.095	+	368.705i	−0.569376	+	0.836066i
$22$	125.342			0.258970
$23$	621.143			1.17418			0.587091	−	0.809521i	$-0.300273\pi$
$23$	621.143			1.17418			0.587091	+	0.809521i	$0.300273\pi$
$24$			327.166i			0.567996i
$25$	−125.000			−0.200000
$26$		−	285.294i		−	0.422033i
$27$		−	720.302i		−	0.988069i
$28$	592.226	+	403.316i	0.755390	+	0.514434i
$29$	−774.981			−0.921500			−0.460750	−	0.887530i	$-0.652419\pi$
$29$	−774.981			−0.921500			−0.460750	+	0.887530i	$0.652419\pi$
$30$	−119.448			−0.132720
$31$		−	403.109i		−	0.419468i	−0.977759	−	0.209734i	$-0.932740\pi$
$31$		−	403.109i		−	0.419468i	0.977759	−	0.209734i	$-0.0672598\pi$
$32$	800.073			0.781321
$33$		−	972.334i		−	0.892869i
$34$			173.981i			0.150502i
$35$	−308.369	+	452.806i	−0.251730	+	0.369638i
$36$	27.4729			0.0211982
$37$	−1290.58			−0.942716			−0.471358	−	0.881942i	$-0.656236\pi$
$37$	−1290.58			−0.942716			−0.471358	+	0.881942i	$0.656236\pi$
$38$			287.229i			0.198912i
$39$	−2213.16			−1.45507
$40$			401.792i			0.251120i
$41$		−	2536.73i		−	1.50906i	−0.656264	−	0.754531i	$-0.727864\pi$
$41$		−	2536.73i		−	1.50906i	0.656264	−	0.754531i	$-0.272136\pi$
$42$	−294.672	+	432.694i	−0.167048	+	0.245291i
$43$	2242.99			1.21308			0.606542	−	0.795052i	$-0.292556\pi$
$43$	2242.99			1.21308			0.606542	+	0.795052i	$0.292556\pi$
$44$	−1561.79			−0.806712
$45$			21.0053i			0.0103730i
$46$	728.942			0.344490
$47$		−	2494.61i		−	1.12930i	−0.825332	−	0.564648i	$-0.809012\pi$
$47$		−	2494.61i		−	1.12930i	0.825332	−	0.564648i	$-0.190988\pi$
$48$		−	1746.02i		−	0.757819i
$49$	879.536	+	2234.10i	0.366321	+	0.930489i
$50$	−146.694			−0.0586775
$51$	1349.65			0.518897
$52$			3554.85i			1.31466i
$53$	−281.688			−0.100280			−0.0501402	−	0.998742i	$-0.515967\pi$
$53$	−281.688			−0.100280			−0.0501402	+	0.998742i	$0.515967\pi$
$54$		−	845.310i		−	0.289887i
$55$		−	1194.12i		−	0.394751i
$56$	1455.47	+	991.201i	0.464117	+	0.316072i
$57$	2228.17			0.685802
$58$	−909.479			−0.270356
$59$			5822.15i			1.67255i	0.548309	+	0.836276i	$0.315272\pi$
$59$			5822.15i			1.67255i	−0.548309	+	0.836276i	$0.684728\pi$
$60$	1488.36			0.413432
$61$			6268.19i			1.68454i	0.539053	+	0.842272i	$0.318782\pi$
$61$			6268.19i			1.68454i	−0.539053	+	0.842272i	$0.681218\pi$
$62$		−	473.068i		−	0.123067i
$63$	76.0908	+	51.8192i	0.0191713	+	0.0130560i
$64$	−2129.72			−0.519951
$65$	−2717.98			−0.643309
$66$		−	1141.08i		−	0.261956i
$67$	4128.43			0.919678			0.459839	−	0.888002i	$-0.347907\pi$
$67$	4128.43			0.919678			0.459839	+	0.888002i	$0.347907\pi$
$68$		−	2167.85i		−	0.468826i
$69$		−	5654.74i		−	1.18772i
$70$	−361.886	+	531.390i	−0.0738544	+	0.108447i
$71$	−793.446			−0.157399			−0.0786993	−	0.996898i	$-0.525077\pi$
$71$	−793.446			−0.157399			−0.0786993	+	0.996898i	$0.525077\pi$
$72$	67.5182			0.0130243
$73$			1600.72i			0.300380i	0.988657	+	0.150190i	$0.0479885\pi$
$73$			1600.72i			0.300380i	−0.988657	+	0.150190i	$0.952011\pi$
$74$	−1514.56			−0.276581
$75$			1137.97i			0.202306i
$76$		−	3578.96i		−	0.619626i
$77$	−4325.65	−	2945.84i	−0.729575	−	0.496853i
$78$	−2597.25			−0.426899
$79$	9856.44			1.57931			0.789653	−	0.613554i	$-0.210261\pi$
$79$	9856.44			1.57931			0.789653	+	0.613554i	$0.210261\pi$
$80$		−	2144.28i		−	0.335044i
$81$	−6709.65			−1.02266
$82$		−	2976.98i		−	0.442740i
$83$			617.012i			0.0895648i	0.998997	+	0.0447824i	$0.0142595\pi$
$83$			617.012i			0.0895648i	−0.998997	+	0.0447824i	$0.985741\pi$
$84$	3671.70	−	5391.49i	0.520366	−	0.764101i
$85$	1657.51			0.229413
$86$	2632.26			0.355903
$87$			7055.26i			0.932125i
$88$	−3838.31			−0.495649
$89$		−	7345.17i		−	0.927304i	−0.886018	−	0.463652i	$-0.846539\pi$
$89$		−	7345.17i		−	0.927304i	0.886018	−	0.463652i	$-0.153461\pi$
$90$			24.6508i			0.00304331i
$91$	−6705.13	+	9845.75i	−0.809701	+	1.18896i
$92$	−9082.83			−1.07311
$93$	−3669.81			−0.424305
$94$		−	2927.55i		−	0.331321i
$95$	2736.41			0.303204
$96$		−	7283.69i		−	0.790330i
$97$			67.6288i			0.00718767i	0.999994	+	0.00359383i	$0.00114396\pi$
$97$			67.6288i			0.00718767i	−0.999994	+	0.00359383i	$0.998856\pi$
$98$	1032.18	+	2621.83i	0.107474	+	0.272994i
$99$	−200.664			−0.0204738
$100$	1827.85			0.182785
$101$		−	14874.0i		−	1.45809i	−0.684466	−	0.729045i	$-0.739965\pi$
$101$		−	14874.0i		−	1.45809i	0.684466	−	0.729045i	$-0.260035\pi$
$102$	1583.88			0.152238
$103$			9948.88i			0.937778i	0.883257	+	0.468889i	$0.155346\pi$
$103$			9948.88i			0.937778i	−0.883257	+	0.468889i	$0.844654\pi$
$104$			8736.50i			0.807739i
$105$	4122.25	+	2807.32i	0.373900	+	0.254633i
$106$	−330.575			−0.0294210
$107$	2769.38			0.241888			0.120944	−	0.992659i	$-0.461408\pi$
$107$	2769.38			0.241888			0.120944	+	0.992659i	$0.461408\pi$
$108$			10532.8i			0.903020i
$109$	14013.8			1.17951			0.589755	−	0.807582i	$-0.299224\pi$
$109$	14013.8			1.17951			0.589755	+	0.807582i	$0.299224\pi$
$110$		−	1401.36i		−	0.115815i
$111$			11749.1i			0.953587i
$112$	−7767.55	−	5289.84i	−0.619224	−	0.421703i
$113$	9624.30			0.753724			0.376862	−	0.926269i	$-0.377003\pi$
$113$	9624.30			0.753724			0.376862	+	0.926269i	$0.377003\pi$
$114$	2614.87			0.201206
$115$		−	6944.59i		−	0.525110i
$116$	11332.4			0.842181
$117$			456.737i			0.0333653i
$118$			6832.59i			0.490706i
$119$	4088.99	−	6004.23i	0.288750	−	0.423998i
$120$	3657.82			0.254015
$121$	−3233.58			−0.220858
$122$			7356.03i			0.494224i
$123$	−23093.9			−1.52646
$124$			5894.57i			0.383362i
$125$			1397.54i			0.0894427i
$126$	89.2963	+	60.8124i	0.00562461	+	0.00383046i
$127$	9868.25			0.611833			0.305916	−	0.952058i	$-0.401037\pi$
$127$	9868.25			0.611833			0.305916	+	0.952058i	$0.401037\pi$
$128$	−15300.5			−0.933868
$129$		−	20419.7i		−	1.22707i
$130$	−3189.69			−0.188739
$131$			23662.2i			1.37884i	0.724363	+	0.689419i	$0.242134\pi$
$131$			23662.2i			1.37884i	−0.724363	+	0.689419i	$0.757866\pi$
$132$			14218.2i			0.816014i
$133$	6750.61	−	9912.53i	0.381627	−	0.560378i
$134$	4844.92			0.269822
$135$	−8053.22			−0.441878
$136$		−	5327.78i		−	0.288050i
$137$	−944.288			−0.0503111			−0.0251555	−	0.999684i	$-0.508008\pi$
$137$	−944.288			−0.0503111			−0.0251555	+	0.999684i	$0.508008\pi$
$138$		−	6636.12i		−	0.348463i
$139$			4891.95i			0.253193i	0.991954	+	0.126597i	$0.0404054\pi$
$139$			4891.95i			0.253193i	−0.991954	+	0.126597i	$0.959595\pi$
$140$	4509.21	−	6621.29i	0.230062	−	0.337821i
$141$	−22710.4			−1.14232
$142$	−931.149			−0.0461788
$143$		−	25964.8i		−	1.26974i
$144$	−360.331			−0.0173771
$145$			8664.55i			0.412107i
$146$			1878.53i			0.0881276i
$147$	20338.8	−	8007.10i	0.941218	−	0.370545i
$148$	18871.9			0.861571
$149$	−20464.1			−0.921764			−0.460882	−	0.887461i	$-0.652467\pi$
$149$	−20464.1			−0.921764			−0.460882	+	0.887461i	$0.652467\pi$
$150$			1335.47i			0.0593541i
$151$	1081.03			0.0474114			0.0237057	−	0.999719i	$-0.492454\pi$
$151$	1081.03			0.0474114			0.0237057	+	0.999719i	$0.492454\pi$
$152$		−	8795.75i		−	0.380702i
$153$		−	278.532i		−	0.0118985i
$154$	−5076.36	−	3457.09i	−0.214048	−	0.145770i
$155$	−4506.89			−0.187592
$156$	32362.6			1.32982
$157$		−	39342.0i		−	1.59609i	−0.602598	−	0.798045i	$-0.705868\pi$
$157$		−	39342.0i		−	1.59609i	0.602598	−	0.798045i	$-0.294132\pi$
$158$	11567.0			0.463348
$159$			2564.42i			0.101437i
$160$		−	8945.09i		−	0.349417i
$161$	−25156.4	−	17132.0i	−0.970503	−	0.660930i
$162$	−7874.11			−0.300035
$163$	−38468.4			−1.44787			−0.723935	−	0.689869i	$-0.757668\pi$
$163$	−38468.4			−1.44787			−0.723935	+	0.689869i	$0.757668\pi$
$164$			37094.1i			1.37917i
$165$	−10871.0			−0.399303
$166$			724.094i			0.0262772i
$167$			18181.1i			0.651908i	0.945386	+	0.325954i	$0.105686\pi$
$167$			18181.1i			0.651908i	−0.945386	+	0.325954i	$0.894314\pi$
$168$	9023.68	−	13250.3i	0.319716	−	0.469469i
$169$	−30538.4			−1.06923
$170$	1945.16			0.0673067
$171$		−	459.835i		−	0.0157257i
$172$	−32798.8			−1.10867
$173$			16735.0i			0.559157i	0.960123	+	0.279578i	$0.0901947\pi$
$173$			16735.0i			0.559157i	−0.960123	+	0.279578i	$0.909805\pi$
$174$			8279.69i			0.273474i
$175$	5062.53	+	3447.67i	0.165307	+	0.112577i
$176$	20484.3			0.661295
$177$	53003.6			1.69184
$178$		−	8619.92i		−	0.272059i
$179$	12395.3			0.386856			0.193428	−	0.981114i	$-0.438039\pi$
$179$	12395.3			0.386856			0.193428	+	0.981114i	$0.438039\pi$
$180$		−	307.156i		−	0.00948014i
$181$		−	5388.98i		−	0.164494i	−0.996612	−	0.0822469i	$-0.973790\pi$
$181$		−	5388.98i		−	0.164494i	0.996612	−	0.0822469i	$-0.0262096\pi$
$182$	−7868.80	+	11554.5i	−0.237556	+	0.348825i
$183$	57064.2			1.70397
$184$	−22322.2			−0.659328
$185$			14429.1i			0.421596i
$186$	−4306.70			−0.124486
$187$			15834.1i			0.452804i
$188$			36478.2i			1.03209i
$189$	−19866.9	+	29172.4i	−0.556169	+	0.816674i
$190$	3211.32			0.0889562
$191$	71584.2			1.96223			0.981116	−	0.193421i	$-0.0619582\pi$
$191$	71584.2			1.96223			0.981116	+	0.193421i	$0.0619582\pi$
$192$			19388.5i			0.525947i
$193$	49246.2			1.32208			0.661041	−	0.750350i	$-0.270115\pi$
$193$	49246.2			1.32208			0.661041	+	0.750350i	$0.270115\pi$
$194$			79.3657i			0.00210877i
$195$			24743.9i			0.650727i
$196$	−12861.3	−	32668.8i	−0.334789	−	0.850396i
$197$	−42979.5			−1.10746			−0.553731	−	0.832696i	$-0.686796\pi$
$197$	−42979.5			−1.10746			−0.553731	+	0.832696i	$0.686796\pi$
$198$	−235.489			−0.00600675
$199$		−	25661.8i		−	0.648010i	−0.946055	−	0.324005i	$-0.894971\pi$
$199$		−	25661.8i		−	0.648010i	0.946055	−	0.324005i	$-0.105029\pi$
$200$	4492.17			0.112304
$201$		−	37584.3i		−	0.930283i
$202$		−	17455.3i		−	0.427785i
$203$	31386.9	+	21375.0i	0.761652	+	0.518698i
$204$	−19735.7			−0.474232
$205$	−28361.5			−0.674873
$206$			11675.5i			0.275132i
$207$	−1166.99			−0.0272349
$208$		−	46624.9i		−	1.07768i
$209$			26140.9i			0.598450i
$210$	4837.66	+	3294.53i	0.109698	+	0.0747060i
$211$	−70893.9			−1.59237			−0.796185	−	0.605054i	$-0.793152\pi$
$211$	−70893.9			−1.59237			−0.796185	+	0.605054i	$0.793152\pi$
$212$	4119.06			0.0916487
$213$			7223.36i			0.159214i
$214$	3250.00			0.0709670
$215$		−	25077.4i		−	0.542508i
$216$			25885.7i			0.554821i
$217$	−11118.3	+	16326.0i	−0.236112	+	0.346705i
$218$	16445.8			0.346053
$219$	14572.6			0.303843
$220$			17461.4i			0.360773i
$221$	36040.6			0.737916
$222$			13788.2i			0.279770i
$223$		−	70941.4i		−	1.42656i	−0.700879	−	0.713280i	$-0.747209\pi$
$223$		−	70941.4i		−	1.42656i	0.700879	−	0.713280i	$-0.252791\pi$
$224$	−32403.1	−	22067.1i	−0.645789	−	0.439794i
$225$	234.847			0.00463895
$226$	11294.6			0.221133
$227$		−	34365.9i		−	0.666923i	−0.942764	−	0.333461i	$-0.891783\pi$
$227$		−	34365.9i		−	0.666923i	0.942764	−	0.333461i	$-0.108217\pi$
$228$	−32582.1			−0.626771
$229$			35773.0i			0.682157i	0.940035	+	0.341078i	$0.110792\pi$
$229$			35773.0i			0.682157i	−0.940035	+	0.341078i	$0.889208\pi$
$230$		−	8149.81i		−	0.154061i
$231$	−26818.3	+	39379.7i	−0.502582	+	0.737987i
$232$	27850.8			0.517441
$233$	−97169.7			−1.78986			−0.894930	−	0.446207i	$-0.852774\pi$
$233$	−97169.7			−1.78986			−0.894930	+	0.446207i	$0.852774\pi$
$234$			536.003i			0.00978894i
$235$	−27890.6			−0.505036
$236$		−	85136.1i		−	1.52859i
$237$		−	89730.9i		−	1.59752i
$238$	4798.63	−	7046.26i	0.0847156	−	0.124396i
$239$	27099.1			0.474415			0.237208	−	0.971459i	$-0.423768\pi$
$239$	27099.1			0.474415			0.237208	+	0.971459i	$0.423768\pi$
$240$	−19521.1			−0.338907
$241$			110921.i			1.90976i	0.296991	+	0.954880i	$0.404017\pi$
$241$			110921.i			1.90976i	−0.296991	+	0.954880i	$0.595983\pi$
$242$	−3794.76			−0.0647968
$243$			2738.70i			0.0463802i
$244$		−	91658.3i		−	1.53954i
$245$	24978.0	−	9833.51i	0.416127	−	0.163824i
$246$	−27101.8			−0.447845
$247$	59500.2			0.975269
$248$			14486.6i			0.235540i
$249$	5617.14			0.0905976
$250$			1640.09i			0.0262414i
$251$		−	41403.7i		−	0.657191i	−0.944471	−	0.328595i	$-0.893425\pi$
$251$		−	41403.7i		−	0.657191i	0.944471	−	0.328595i	$-0.106575\pi$
$252$	−1112.66	−	757.741i	−0.0175211	−	0.0119322i
$253$	66341.5			1.03644
$254$	11580.9			0.179504
$255$		−	15089.6i		−	0.232058i
$256$	16119.6			0.245966
$257$			73008.7i			1.10537i	0.833390	+	0.552686i	$0.186397\pi$
$257$			73008.7i			1.10537i	−0.833390	+	0.552686i	$0.813603\pi$
$258$		−	23963.5i		−	0.360007i
$259$	52268.7	+	35595.9i	0.779188	+	0.530641i
$260$	39744.5			0.587936
$261$	1456.02			0.0213740
$262$			27768.8i			0.404534i
$263$	−117673.			−1.70124			−0.850622	−	0.525778i	$-0.823774\pi$
$263$	−117673.			−1.70124			−0.850622	+	0.525778i	$0.823774\pi$
$264$			34943.1i			0.501365i
$265$			3149.37i			0.0448468i
$266$	7922.17	−	11632.8i	0.111965	−	0.164408i
$267$	−66868.8			−0.937996
$268$	−60369.2			−0.840516
$269$		−	30491.2i		−	0.421376i	−0.977553	−	0.210688i	$-0.932430\pi$
$269$		−	30491.2i		−	0.421376i	0.977553	−	0.210688i	$-0.0675704\pi$
$270$	−9450.85			−0.129641
$271$			70200.3i			0.955874i	0.878394	+	0.477937i	$0.158615\pi$
$271$			70200.3i			0.955874i	−0.878394	+	0.477937i	$0.841385\pi$
$272$			28433.2i			0.384316i
$273$	89633.5	+	61042.0i	1.20267	+	0.819037i
$274$	−1108.17			−0.0147606
$275$	−13350.7			−0.176538
$276$			82688.1i			1.08549i
$277$	77714.3			1.01284			0.506421	−	0.862286i	$-0.330968\pi$
$277$	77714.3			1.01284			0.506421	+	0.862286i	$0.330968\pi$
$278$			5740.95i			0.0742837i
$279$			757.350i			0.00972945i
$280$	11082.0	−	16272.7i	0.141352	−	0.207559i
$281$	40938.1			0.518459			0.259230	−	0.965816i	$-0.416531\pi$
$281$	40938.1			0.518459			0.259230	+	0.965816i	$0.416531\pi$
$282$	−26651.8			−0.335141
$283$			65881.7i			0.822606i	0.911499	+	0.411303i	$0.134926\pi$
$283$			65881.7i			0.822606i	−0.911499	+	0.411303i	$0.865074\pi$
$284$	11602.4			0.143850
$285$		−	24911.7i		−	0.306700i
$286$		−	30471.0i		−	0.372524i
$287$	−69966.6	+	102738.i	−0.849428	+	1.24729i
$288$	−1503.16			−0.0181225
$289$	61542.4			0.736850
$290$			10168.3i			0.120907i
$291$	615.677			0.00727055
$292$		−	23407.0i		−	0.274524i
$293$		−	10957.4i		−	0.127635i	−0.997962	−	0.0638176i	$-0.979672\pi$
$293$		−	10957.4i		−	0.127635i	0.997962	−	0.0638176i	$-0.0203276\pi$
$294$	23868.6	−	9396.73i	0.276141	−	0.108713i
$295$	65093.7			0.747988
$296$	46380.0			0.529355
$297$		−	76932.3i		−	0.872159i
$298$	−24015.6			−0.270434
$299$		−	151002.i		−	1.68904i
$300$		−	16640.3i		−	0.184892i
$301$	−90841.7	−	61864.8i	−1.00266	−	0.682827i
$302$	1268.64			0.0139099
$303$	−135409.			−1.47490
$304$			46941.1i			0.507933i
$305$	70080.5			0.753351
$306$		−	326.871i		−	0.00349087i
$307$		−	14692.2i		−	0.155887i	−0.996958	−	0.0779435i	$-0.975165\pi$
$307$		−	14692.2i		−	0.155887i	0.996958	−	0.0779435i	$-0.0248354\pi$
$308$	63253.0	+	43076.4i	0.666776	+	0.454086i
$309$	90572.4			0.948591
$310$	−5289.06			−0.0550370
$311$		−	101587.i		−	1.05031i	−0.851006	−	0.525156i	$-0.824007\pi$
$311$		−	101587.i		−	1.05031i	0.851006	−	0.525156i	$-0.175993\pi$
$312$	79535.2			0.817052
$313$			136196.i			1.39019i	0.718918	+	0.695095i	$0.244638\pi$
$313$			136196.i			1.39019i	−0.718918	+	0.695095i	$0.755362\pi$
$314$		−	46169.8i		−	0.468273i
$315$	579.356	−	850.721i	0.00583881	−	0.00857365i
$316$	−144129.			−1.44336
$317$	−50591.3			−0.503451			−0.251725	−	0.967799i	$-0.580998\pi$
$317$	−50591.3			−0.503451			−0.251725	+	0.967799i	$0.580998\pi$
$318$			3009.48i			0.0297603i
$319$	−82772.3			−0.813399
$320$			23811.0i			0.232529i
$321$		−	25211.8i		−	0.244678i
$322$	−29522.3	−	20105.2i	−0.284733	−	0.193908i
$323$	−36285.0			−0.347794
$324$	98113.8			0.934630
$325$			30388.0i			0.287697i
$326$	−45144.6			−0.424786
$327$		−	127578.i		−	1.19311i
$328$			91163.4i			0.847370i
$329$	−68804.9	+	101032.i	−0.635664	+	0.933402i
$330$	−12757.7			−0.117150
$331$	129218.			1.17942			0.589710	−	0.807615i	$-0.299242\pi$
$331$	129218.			1.17942			0.589710	+	0.807615i	$0.299242\pi$
$332$		−	9022.43i		−	0.0818554i
$333$	2424.71			0.0218661
$334$			21336.4i			0.191262i
$335$		−	46157.3i		−	0.411292i
$336$	−48157.5	+	70714.0i	−0.426565	+	0.626364i
$337$	407.464			0.00358781			0.00179391	−	0.999998i	$-0.499429\pi$
$337$	407.464			0.00358781			0.00179391	+	0.999998i	$0.499429\pi$
$338$	−35838.3			−0.313700
$339$		−	87617.5i		−	0.762415i
$340$	−24237.3			−0.209666
$341$		−	43054.2i		−	0.370260i
$342$		−	539.638i		−	0.00461371i
$343$	25998.2	−	114740.i	0.220981	−	0.975278i
$344$	−80607.2			−0.681172
$345$	−63222.0			−0.531165
$346$			19639.4i			0.164050i
$347$	−51626.2			−0.428757			−0.214379	−	0.976751i	$-0.568773\pi$
$347$	−51626.2			−0.428757			−0.214379	+	0.976751i	$0.568773\pi$
$348$		−	103167.i		−	0.851892i
$349$		−	30090.2i		−	0.247044i	−0.992342	−	0.123522i	$-0.960581\pi$
$349$		−	30090.2i		−	0.247044i	0.992342	−	0.123522i	$-0.0394189\pi$
$350$	5941.13	+	4046.01i	0.0484990	+	0.0330287i
$351$	−175108.			−1.42132
$352$	85452.2			0.689665
$353$		−	110850.i		−	0.889586i	−0.895633	−	0.444793i	$-0.853277\pi$
$353$		−	110850.i		−	0.889586i	0.895633	−	0.444793i	$-0.146723\pi$
$354$	62202.3			0.496364
$355$			8871.00i			0.0703908i
$356$			107407.i			0.847485i
$357$	−54661.2	−	37225.2i	−0.428887	−	0.292079i
$358$	14546.5			0.113499
$359$	69190.4			0.536855			0.268428	−	0.963300i	$-0.413496\pi$
$359$	69190.4			0.536855			0.268428	+	0.963300i	$0.413496\pi$
$360$		−	754.876i		−	0.00582466i
$361$	70417.3			0.540337
$362$		−	6324.24i		−	0.0482604i
$363$			29437.8i			0.223404i
$364$	98047.7	−	143972.i	0.740005	−	1.08662i
$365$	17896.6			0.134334
$366$	66967.6			0.499923
$367$			147407.i			1.09443i	0.836993	+	0.547214i	$0.184311\pi$
$367$			147407.i			1.09443i	−0.836993	+	0.547214i	$0.815689\pi$
$368$	119129.			0.879675
$369$			4765.95i			0.0350023i
$370$			16933.3i			0.123691i
$371$	11408.4	+	7769.34i	0.0828853	+	0.0564464i
$372$	53662.8			0.387782
$373$	−57675.4			−0.414546			−0.207273	−	0.978283i	$-0.566459\pi$
$373$	−57675.4			−0.414546			−0.207273	+	0.978283i	$0.566459\pi$
$374$			18582.1i			0.132847i
$375$	12722.9			0.0904741
$376$			89649.8i			0.634123i
$377$			188401.i			1.32556i
$378$	−23314.8	+	34235.2i	−0.163173	+	0.239602i
$379$	50676.3			0.352799			0.176399	−	0.984319i	$-0.443555\pi$
$379$	50676.3			0.352799			0.176399	+	0.984319i	$0.443555\pi$
$380$	−40014.0			−0.277105
$381$		−	89838.4i		−	0.618888i
$382$	84007.6			0.575694
$383$		−	23463.0i		−	0.159951i	−0.996797	−	0.0799754i	$-0.974516\pi$
$383$		−	23463.0i		−	0.159951i	0.996797	−	0.0799754i	$-0.0254842\pi$
$384$			139292.i			0.944637i
$385$	−32935.5	+	48362.2i	−0.222200	+	0.326276i
$386$	57792.9			0.387882
$387$	−4214.08			−0.0281372
$388$		−	988.921i		−	0.00656898i
$389$	−270049.			−1.78461			−0.892306	−	0.451430i	$-0.850914\pi$
$389$	−270049.			−1.78461			−0.892306	+	0.451430i	$0.850914\pi$
$390$			29038.2i			0.190915i
$391$			92085.5i			0.602335i
$392$	−31608.2	−	80287.7i	−0.205697	−	0.522489i
$393$	215416.			1.39474
$394$	−50438.6			−0.324915
$395$		−	110198.i		−	0.706287i
$396$	2934.26			0.0187115
$397$			234605.i			1.48853i	0.667886	+	0.744263i	$0.267199\pi$
$397$			234605.i			1.48853i	−0.667886	+	0.744263i	$0.732801\pi$
$398$		−	30115.4i		−	0.190118i
$399$	−90241.4	−	61456.0i	−0.566840	−	0.386028i
$400$	−23973.8			−0.149836
$401$	303695.			1.88864			0.944321	−	0.329026i	$-0.106721\pi$
$401$	303695.			1.88864			0.944321	+	0.329026i	$0.106721\pi$
$402$		−	44107.1i		−	0.272933i
$403$	−97997.1			−0.603397
$404$			217499.i			1.33258i
$405$			75016.2i			0.457346i
$406$	36834.1	+	25084.7i	0.223459	+	0.152180i
$407$	−137841.			−0.832127
$408$	−48502.9			−0.291372
$409$			207965.i			1.24321i	0.783332	+	0.621604i	$0.213519\pi$
$409$			207965.i			1.24321i	−0.783332	+	0.621604i	$0.786481\pi$
$410$	−33283.7			−0.197999
$411$			8596.59i			0.0508912i
$412$		−	145480.i		−	0.857058i
$413$	160583.	−	235799.i	0.941455	−	1.38242i
$414$	−1369.52			−0.00799037
$415$	6898.41			0.0400546
$416$		−	194501.i		−	1.12392i
$417$	44535.2			0.256113
$418$			30677.6i			0.175578i
$419$			200366.i			1.14129i	0.821196	+	0.570646i	$0.193307\pi$
$419$			200366.i			1.14129i	−0.821196	+	0.570646i	$0.806693\pi$
$420$	−60278.7	−	41050.9i	−0.341716	−	0.232715i
$421$	73619.2			0.415362			0.207681	−	0.978197i	$-0.433408\pi$
$421$	73619.2			0.415362			0.207681	+	0.978197i	$0.433408\pi$
$422$	−83197.5			−0.467181
$423$			4686.82i			0.0261937i
$424$	10123.1			0.0563096
$425$		−	18531.5i		−	0.102596i
$426$			8476.97i			0.0467112i
$427$	172885.	−	253863.i	0.948205	−	1.39233i
$428$	−40496.0			−0.221068
$429$	−236378.			−1.28438
$430$		−	29429.6i		−	0.159165i
$431$	128116.			0.689683			0.344841	−	0.938661i	$-0.387933\pi$
$431$	128116.			0.689683			0.344841	+	0.938661i	$0.387933\pi$
$432$		−	138147.i		−	0.740242i
$433$		−	84087.2i		−	0.448491i	−0.974533	−	0.224246i	$-0.928008\pi$
$433$		−	84087.2i		−	0.448491i	0.974533	−	0.224246i	$-0.0719918\pi$
$434$	−13047.9	+	19159.3i	−0.0692723	+	0.101719i
$435$	78880.2			0.416859
$436$	−204920.			−1.07798
$437$			152026.i			0.796078i
$438$	17101.7			0.0891438
$439$		−	99473.6i		−	0.516153i	−0.966124	−	0.258077i	$-0.916911\pi$
$439$		−	99473.6i		−	0.516153i	0.966124	−	0.258077i	$-0.0830887\pi$
$440$			42913.6i			0.221661i
$441$	−1652.45	−	4197.38i	−0.00849672	−	0.0215824i
$442$	42295.4			0.216495
$443$	56356.0			0.287166			0.143583	−	0.989638i	$-0.454138\pi$
$443$	56356.0			0.287166			0.143583	+	0.989638i	$0.454138\pi$
$444$		−	171805.i		−	0.871506i
$445$	−82121.5			−0.414703
$446$		−	83253.3i		−	0.418535i
$447$			186301.i			0.932393i
$448$	86254.1	+	58740.6i	0.429758	+	0.292673i
$449$	−156237.			−0.774982			−0.387491	−	0.921873i	$-0.626658\pi$
$449$	−156237.			−0.774982			−0.387491	+	0.921873i	$0.626658\pi$
$450$	275.604			0.00136101
$451$		−	270937.i		−	1.33203i
$452$	−140734.			−0.688846
$453$		−	9841.43i		−	0.0479581i
$454$		−	40330.0i		−	0.195667i
$455$	110079.	+	74965.7i	0.531718	+	0.362109i
$456$	−80074.6			−0.385092
$457$	−27368.9			−0.131046			−0.0655232	−	0.997851i	$-0.520872\pi$
$457$	−27368.9			−0.131046			−0.0655232	+	0.997851i	$0.520872\pi$
$458$			41981.4i			0.200136i
$459$	106786.			0.506861
$460$			101549.i			0.479911i
$461$		−	166565.i		−	0.783760i	−0.920016	−	0.391880i	$-0.871825\pi$
$461$		−	166565.i		−	0.783760i	0.920016	−	0.391880i	$-0.128175\pi$
$462$	−31472.6	+	46214.1i	−0.147451	+	0.216516i
$463$	103422.			0.482446			0.241223	−	0.970470i	$-0.422451\pi$
$463$	103422.			0.482446			0.241223	+	0.970470i	$0.422451\pi$
$464$	−148634.			−0.690370
$465$			41029.7i			0.189755i
$466$	−114033.			−0.525122
$467$		−	258020.i		−	1.18310i	−0.806270	−	0.591548i	$-0.798517\pi$
$467$		−	258020.i		−	1.18310i	0.806270	−	0.591548i	$-0.201483\pi$
$468$		−	6678.77i		−	0.0304933i
$469$	−167203.	−	113868.i	−0.760146	−	0.517673i
$470$	−32731.0			−0.148171
$471$	−358161.			−1.61449
$472$		−	209233.i		−	0.939173i
$473$	239564.			1.07078
$474$		−	105304.i		−	0.468691i
$475$		−	30594.0i		−	0.135597i
$476$	−59792.4	+	87798.6i	−0.263895	+	0.387502i
$477$	529.228			0.00232598
$478$	31802.1			0.139187
$479$			65308.6i			0.284642i	0.989821	+	0.142321i	$0.0454565\pi$
$479$			65308.6i			0.284642i	−0.989821	+	0.142321i	$0.954543\pi$
$480$	−81434.1			−0.353447
$481$			313744.i			1.35608i
$482$			130171.i			0.560300i
$483$	−155966.	+	229018.i	−0.668551	+	0.981694i
$484$	47283.9			0.201847
$485$	756.113			0.00321442
$486$			3214.01i			0.0136074i
$487$	−71073.0			−0.299672			−0.149836	−	0.988711i	$-0.547875\pi$
$487$	−71073.0			−0.299672			−0.149836	+	0.988711i	$0.547875\pi$
$488$		−	225262.i		−	0.945907i
$489$			350208.i			1.46456i
$490$	29313.0	−	11540.1i	0.122086	−	0.0480638i
$491$	247750.			1.02766			0.513831	−	0.857891i	$-0.328226\pi$
$491$	247750.			1.02766			0.513831	+	0.857891i	$0.328226\pi$
$492$	337696.			1.39507
$493$		−	114892.i		−	0.472713i
$494$	69826.4			0.286132
$495$			2243.49i			0.00915615i
$496$		−	77312.3i		−	0.314257i
$497$	32134.8	+	21884.3i	0.130095	+	0.0885973i
$498$	6591.99			0.0265802
$499$	252910.			1.01570			0.507850	−	0.861446i	$-0.330441\pi$
$499$	252910.			1.01570			0.507850	+	0.861446i	$0.330441\pi$
$500$		−	20436.0i		−	0.0817438i
$501$	165516.			0.659425
$502$		−	48589.2i		−	0.192811i
$503$			429828.i			1.69887i	0.527696	+	0.849433i	$0.323056\pi$
$503$			429828.i			1.69887i	−0.527696	+	0.849433i	$0.676944\pi$
$504$	−2734.50	−	1862.24i	−0.0107651	−	0.00733121i
$505$	−166296.			−0.652078
$506$	77855.0			0.304078
$507$			278015.i			1.08156i
$508$	−144301.			−0.559169
$509$		−	21329.0i		−	0.0823257i	−0.999152	−	0.0411629i	$-0.986894\pi$
$509$		−	21329.0i		−	0.0823257i	0.999152	−	0.0411629i	$-0.0131062\pi$
$510$		−	17708.3i		−	0.0680828i
$511$	44150.2	−	64829.7i	0.169079	−	0.248275i
$512$	263725.			1.00603
$513$	176296.			0.669895
$514$			85679.3i			0.324302i
$515$	111232.			0.419387
$516$			298593.i			1.12145i
$517$		−	266439.i		−	0.996818i
$518$	61339.9	+	41773.6i	0.228604	+	0.155683i
$519$	152352.			0.565604
$520$	97677.0			0.361232
$521$			175405.i			0.646198i	0.946365	+	0.323099i	$0.104725\pi$
$521$			175405.i			0.646198i	−0.946365	+	0.323099i	$0.895275\pi$
$522$	1708.71			0.00627085
$523$			204299.i			0.746901i	0.927650	+	0.373450i	$0.121825\pi$
$523$			204299.i			0.746901i	−0.927650	+	0.373450i	$0.878175\pi$
$524$		−	346008.i		−	1.26015i
$525$	31386.8	−	46088.1i	0.113875	−	0.167213i
$526$	−138095.			−0.499123
$527$	59761.6			0.215179
$528$		−	186484.i		−	0.668920i
$529$	105977.			0.378705
$530$			3695.94i			0.0131575i
$531$		−	10938.5i		−	0.0387944i
$532$	−98712.6	+	144949.i	−0.348778	+	0.512143i
$533$	−616689.			−2.17076
$534$	−78473.8			−0.275196
$535$		−	30962.6i		−	0.108176i
$536$	−148365.			−0.516418
$537$		−	112844.i		−	0.391317i
$538$		−	35782.9i		−	0.123626i
$539$	93939.3	+	238615.i	0.323348	+	0.821333i
$540$	117761.			0.403843
$541$	5119.20			0.0174907			0.00874535	−	0.999962i	$-0.497216\pi$
$541$	5119.20			0.0174907			0.00874535	+	0.999962i	$0.497216\pi$
$542$			82383.6i			0.280441i
$543$	−49060.1			−0.166391
$544$			118612.i			0.400804i
$545$		−	156678.i		−	0.527493i
$546$	105189.	+	71635.8i	0.352847	+	0.240295i
$547$	−499232.			−1.66851			−0.834253	−	0.551381i	$-0.814101\pi$
$547$	−499232.			−1.66851			−0.834253	+	0.551381i	$0.814101\pi$
$548$	13808.1			0.0459805
$549$		−	11776.5i		−	0.0390726i
$550$	−15667.7			−0.0517940
$551$		−	189679.i		−	0.624762i
$552$			203217.i			0.666931i
$553$	−399188.	−	271854.i	−1.30535	−	0.888967i
$554$	91201.6			0.297155
$555$	131359.			0.426457
$556$		−	71533.9i		−	0.231400i
$557$	−313721.			−1.01119			−0.505595	−	0.862771i	$-0.668727\pi$
$557$	−313721.			−1.01119			−0.505595	+	0.862771i	$0.668727\pi$
$558$			888.788i			0.00285450i
$559$		−	545280.i		−	1.74500i
$560$	−59142.2	+	86843.8i	−0.188591	+	0.276925i
$561$	144150.			0.458026
$562$	48042.8			0.152109
$563$			506466.i			1.59784i	0.601436	+	0.798921i	$0.294595\pi$
$563$			506466.i			1.59784i	−0.601436	+	0.798921i	$0.705405\pi$
$564$	332089.			1.04399
$565$		−	107603.i		−	0.337075i
$566$			77315.4i			0.241342i
$567$	271742.	+	185061.i	0.845262	+	0.575638i
$568$	28514.4			0.0883826
$569$	99722.7			0.308013			0.154007	−	0.988070i	$-0.450782\pi$
$569$	99722.7			0.308013			0.154007	+	0.988070i	$0.450782\pi$
$570$		−	29235.1i		−	0.0899819i
$571$	−101173.			−0.310308			−0.155154	−	0.987890i	$-0.549587\pi$
$571$	−101173.			−0.310308			−0.155154	+	0.987890i	$0.549587\pi$
$572$			379678.i			1.16044i
$573$		−	651686.i		−	1.98486i
$574$	−82109.2	+	120568.i	−0.249212	+	0.365940i
$575$	−77642.8			−0.234837
$576$	4001.26			0.0120601
$577$		−	70284.7i		−	0.211110i	−0.994413	−	0.105555i	$-0.966338\pi$
$577$		−	70284.7i		−	0.211110i	0.994413	−	0.105555i	$-0.0336619\pi$
$578$	72223.1			0.216182
$579$		−	448327.i		−	1.33733i
$580$		−	126700.i		−	0.376635i
$581$	17018.0	−	24989.1i	0.0504147	−	0.0740285i
$582$	722.528			0.00213309
$583$	−30085.8			−0.0885166
$584$		−	57525.8i		−	0.168670i
$585$	5106.47			0.0149214
$586$		−	12859.0i		−	0.0374466i
$587$		−	447428.i		−	1.29852i	−0.760569	−	0.649258i	$-0.775080\pi$
$587$		−	447428.i		−	1.29852i	0.760569	−	0.649258i	$-0.224920\pi$
$588$	−297410.	+	117086.i	−0.860202	+	0.338650i
$589$	98661.8			0.284393
$590$	76390.6			0.219450
$591$			391276.i			1.12023i
$592$	−247520.			−0.706265
$593$		−	168874.i		−	0.480234i	−0.970744	−	0.240117i	$-0.922814\pi$
$593$		−	168874.i		−	0.480234i	0.970744	−	0.240117i	$-0.0771858\pi$
$594$		−	90283.8i		−	0.255880i
$595$	−67129.3	−	45716.3i	−0.189618	−	0.129133i
$596$	299242.			0.842422
$597$	−233620.			−0.655482
$598$		−	177208.i		−	0.495544i
$599$	358762.			0.999892			0.499946	−	0.866057i	$-0.333353\pi$
$599$	358762.			0.999892			0.499946	+	0.866057i	$0.333353\pi$
$600$		−	40895.7i		−	0.113599i
$601$		−	259182.i		−	0.717555i	−0.933423	−	0.358778i	$-0.883194\pi$
$601$		−	259182.i		−	0.717555i	0.933423	−	0.358778i	$-0.116806\pi$
$602$	−106607.	−	72601.4i	−0.294167	−	0.200333i
$603$	−7756.40			−0.0213317
$604$	−15807.6			−0.0433304
$605$			36152.5i			0.0987705i
$606$	−158910.			−0.432718
$607$			263604.i			0.715442i	0.933829	+	0.357721i	$0.116446\pi$
$607$			263604.i			0.715442i	−0.933829	+	0.357721i	$0.883554\pi$
$608$			195820.i			0.529724i
$609$	194594.	−	285740.i	0.524680	−	0.770435i
$610$	82242.9			0.221024
$611$	−606450.			−1.62447
$612$			4072.91i			0.0108743i
$613$	1707.14			0.00454305			0.00227152	−	0.999997i	$-0.499277\pi$
$613$	1707.14			0.00454305			0.00227152	+	0.999997i	$0.499277\pi$
$614$		−	17242.0i		−	0.0457353i
$615$			258197.i			0.682655i
$616$	155452.	+	105866.i	0.409672	+	0.278994i
$617$	161392.			0.423947			0.211973	−	0.977275i	$-0.432011\pi$
$617$	161392.			0.423947			0.211973	+	0.977275i	$0.432011\pi$
$618$	106291.			0.278305
$619$			26905.1i			0.0702187i	0.999383	+	0.0351093i	$0.0111779\pi$
$619$			26905.1i			0.0702187i	−0.999383	+	0.0351093i	$0.988822\pi$
$620$	65903.3			0.171445
$621$		−	447410.i		−	1.16017i
$622$		−	119218.i		−	0.308148i
$623$	−202590.	+	297481.i	−0.521965	+	0.766449i
$624$	−424463.			−1.09011
$625$	15625.0			0.0400000
$626$			159832.i			0.407864i
$627$	237981.			0.605351
$628$			575290.i			1.45870i
$629$		−	191331.i		−	0.483597i
$630$	679.903	−	998.363i	0.00171303	−	0.00251540i
$631$	−173590.			−0.435978			−0.217989	−	0.975951i	$-0.569950\pi$
$631$	−173590.			−0.435978			−0.217989	+	0.975951i	$0.569950\pi$
$632$	−354214.			−0.886813
$633$			645402.i			1.61073i
$634$	−59371.3			−0.147706
$635$		−	110330.i		−	0.273620i
$636$		−	37499.0i		−	0.0927055i
$637$	543119.	−	213818.i	1.33849	−	0.526946i
$638$	−97137.4			−0.238641
$639$	1490.71			0.00365082
$640$			171065.i			0.417639i
$641$	−446618.			−1.08698			−0.543488	−	0.839417i	$-0.682897\pi$
$641$	−446618.			−1.08698			−0.543488	+	0.839417i	$0.682897\pi$
$642$		−	29587.3i		−	0.0717853i
$643$			42021.4i			0.101636i	0.998708	+	0.0508181i	$0.0161829\pi$
$643$			42021.4i			0.101636i	−0.998708	+	0.0508181i	$0.983817\pi$
$644$	367857.	+	250517.i	0.886966	+	0.604040i
$645$	−228299.			−0.548763
$646$	−42582.2			−0.102038
$647$		−	193276.i		−	0.461709i	−0.972988	−	0.230855i	$-0.925848\pi$
$647$		−	193276.i		−	0.461709i	0.972988	−	0.230855i	$-0.0741522\pi$
$648$	241127.			0.574243
$649$			621838.i			1.47635i
$650$			35661.8i			0.0844065i
$651$	148628.	+	101218.i	0.350703	+	0.238835i
$652$	562516.			1.32324
$653$	491628.			1.15295			0.576475	−	0.817115i	$-0.304428\pi$
$653$	491628.			1.15295			0.576475	+	0.817115i	$0.304428\pi$
$654$		−	149719.i		−	0.350043i
$655$	264552.			0.616635
$656$		−	486521.i		−	1.13056i
$657$		−	3007.40i		−	0.00696723i
$658$	−80745.9	+	118567.i	−0.186496	+	0.273848i
$659$	508474.			1.17084			0.585421	−	0.810730i	$-0.300929\pi$
$659$	508474.			1.17084			0.585421	+	0.810730i	$0.300929\pi$
$660$	158965.			0.364933
$661$			543970.i			1.24501i	0.782616	+	0.622504i	$0.213885\pi$
$661$			543970.i			1.24501i	−0.782616	+	0.622504i	$0.786115\pi$
$662$	151644.			0.346027
$663$		−	328105.i		−	0.746425i
$664$		−	22173.8i		−	0.0502925i
$665$	−110825.	−	75474.1i	−0.250609	−	0.170669i
$666$	2845.51			0.00641523
$667$	−481374.			−1.08201
$668$		−	265858.i		−	0.595795i
$669$	−645835.			−1.44301
$670$		−	54167.9i		−	0.120668i
$671$			669477.i			1.48693i
$672$	−200894.	+	294991.i	−0.444865	+	0.653236i
$673$	382196.			0.843832			0.421916	−	0.906635i	$-0.361358\pi$
$673$	382196.			0.843832			0.421916	+	0.906635i	$0.361358\pi$
$674$	478.179			0.00105262
$675$			90037.8i			0.197614i
$676$	446556.			0.977198
$677$		−	333305.i		−	0.727218i	−0.931552	−	0.363609i	$-0.881544\pi$
$677$		−	333305.i		−	0.727218i	0.931552	−	0.363609i	$-0.118456\pi$
$678$		−	102823.i		−	0.223683i
$679$	1865.29	−	2738.98i	0.00404583	−	0.00594086i
$680$	−59566.3			−0.128820
$681$	−312859.			−0.674613
$682$		−	50526.3i		−	0.108630i
$683$	−245601.			−0.526489			−0.263245	−	0.964729i	$-0.584793\pi$
$683$	−245601.			−0.526489			−0.263245	+	0.964729i	$0.584793\pi$
$684$			6724.06i			0.0143721i
$685$			10557.5i			0.0224998i
$686$	30510.2	−	134654.i	0.0648331	−	0.286134i
$687$	325669.			0.690023
$688$	430184.			0.908819
$689$			68479.3i			0.144252i
$690$	−74194.1			−0.155837
$691$		−	404072.i		−	0.846258i	−0.906069	−	0.423129i	$-0.860932\pi$
$691$		−	404072.i		−	0.846258i	0.906069	−	0.423129i	$-0.139068\pi$
$692$		−	244712.i		−	0.511027i
$693$	8126.92	+	5534.58i	0.0169223	+	0.0115244i
$694$	−60585.9			−0.125792
$695$	54693.7			0.113232
$696$		−	253547.i		−	0.523408i
$697$	376075.			0.774122
$698$		−	35312.3i		−	0.0724795i
$699$			884611.i			1.81050i
$700$	−74028.2	−	50414.5i	−0.151078	−	0.102887i
$701$	538983.			1.09683			0.548415	−	0.836206i	$-0.315232\pi$
$701$	538983.			1.09683			0.548415	+	0.836206i	$0.315232\pi$
$702$	−205498.			−0.416997
$703$		−	315872.i		−	0.639147i
$704$	−227466.			−0.458956
$705$			253910.i			0.510860i
$706$		−	130089.i		−	0.260993i
$707$	−410245.	+	602399.i	−0.820737	+	1.20516i
$708$	−775060.			−1.54621
$709$	−785804.			−1.56323			−0.781613	−	0.623763i	$-0.785603\pi$
$709$	−785804.			−1.56323			−0.781613	+	0.623763i	$0.785603\pi$
$710$			10410.6i			0.0206518i
$711$	−18518.0			−0.0366316
$712$			263966.i			0.520700i
$713$		−	250388.i		−	0.492532i
$714$	−64147.6	−	43685.6i	−0.125830	−	0.0856924i
$715$	−290295.			−0.567843
$716$	−181253.			−0.353557
$717$		−	246704.i		−	0.479886i
$718$	81198.4			0.157507
$719$		−	449412.i		−	0.869335i	−0.900591	−	0.434667i	$-0.856866\pi$
$719$		−	449412.i		−	0.869335i	0.900591	−	0.434667i	$-0.143134\pi$
$720$			4028.62i			0.00777126i
$721$	274404.	−	402932.i	0.527861	−	0.775106i
$722$	82638.1			0.158528
$723$	1.00980e6			1.93178
$724$			78801.9i			0.150335i
$725$	96872.7			0.184300
$726$			34546.7i			0.0655440i
$727$			421864.i			0.798185i	0.916911	+	0.399093i	$0.130675\pi$
$727$			421864.i			0.798185i	−0.916911	+	0.399093i	$0.869325\pi$
$728$	240965.	−	353830.i	0.454664	−	0.667624i
$729$	−518549.			−0.975742
$730$	21002.6			0.0394119
$731$			332528.i			0.622290i
$732$	−834437.			−1.55730
$733$		−	94838.7i		−	0.176513i	−0.996098	−	0.0882567i	$-0.971870\pi$
$733$		−	94838.7i		−	0.176513i	0.996098	−	0.0882567i	$-0.0281296\pi$
$734$			172990.i			0.321091i
$735$	−89522.1	−	227394.i	−0.165713	−	0.420925i
$736$	496959.			0.917414
$737$	440940.			0.811791
$738$			5593.08i			0.0102692i
$739$	−165402.			−0.302868			−0.151434	−	0.988467i	$-0.548389\pi$
$739$	−165402.			−0.302868			−0.151434	+	0.988467i	$0.548389\pi$
$740$		−	210994.i		−	0.385306i
$741$		−	541677.i		−	0.986515i
$742$	13388.3	+	9117.70i	0.0243175	+	0.0165607i
$743$	−504788.			−0.914391			−0.457195	−	0.889366i	$-0.651146\pi$
$743$	−504788.			−0.914391			−0.457195	+	0.889366i	$0.651146\pi$
$744$	131883.			0.238256
$745$			228795.i			0.412225i
$746$	−67684.9			−0.121623
$747$		−	1159.23i		−	0.00207743i
$748$		−	231539.i		−	0.413829i
$749$	−112160.	−	76383.3i	−0.199929	−	0.136155i
$750$	14931.0			0.0265439
$751$	−92962.3			−0.164826			−0.0824132	−	0.996598i	$-0.526263\pi$
$751$	−92962.3			−0.164826			−0.0824132	+	0.996598i	$0.526263\pi$
$752$		−	478443.i		−	0.846046i
$753$	−376930.			−0.664769
$754$			221098.i			0.388903i
$755$		−	12086.2i		−	0.0212030i
$756$	290510.	−	426582.i	0.508296	−	0.746377i
$757$	−337486.			−0.588931			−0.294466	−	0.955662i	$-0.595142\pi$
$757$	−337486.			−0.588931			−0.294466	+	0.955662i	$0.595142\pi$
$758$	59471.2			0.103507
$759$		−	603958.i		−	1.04839i
$760$	−98339.5			−0.170255
$761$			916721.i			1.58295i	0.611200	+	0.791476i	$0.290687\pi$
$761$			916721.i			1.58295i	−0.611200	+	0.791476i	$0.709313\pi$
$762$		−	105430.i		−	0.181574i
$763$	−567560.	−	386518.i	−0.974906	−	0.663928i
$764$	−1.04676e6			−1.79333
$765$	−3114.08			−0.00532117
$766$		−	27535.0i		−	0.0469275i
$767$	1.41539e6			2.40594
$768$		−	146749.i		−	0.248802i
$769$			9519.79i			0.0160981i	0.999968	+	0.00804905i	$0.00256212\pi$
$769$			9519.79i			0.0160981i	−0.999968	+	0.00804905i	$0.997438\pi$
$770$	−38651.5	+	56755.4i	−0.0651905	+	0.0957252i
$771$	664655.			1.11812
$772$	−720117.			−1.20828
$773$		−	992866.i		−	1.66162i	−0.556556	−	0.830810i	$-0.687877\pi$
$773$		−	992866.i		−	1.66162i	0.556556	−	0.830810i	$-0.312123\pi$
$774$	−4945.43			−0.00825509
$775$			50388.6i			0.0838935i
$776$		−	2430.40i		−	0.00403603i
$777$	324057.	−	475843.i	0.536760	−	0.788173i
$778$	−316916.			−0.523583
$779$	620871.			1.02312
$780$		−	361825.i		−	0.594715i
$781$	−84744.5			−0.138934
$782$			108067.i			0.176717i
$783$			558221.i			0.910505i
$784$	168686.	+	428479.i	0.274440	+	0.697104i
$785$	−439857.			−0.713793
$786$	252801.			0.409198
$787$		−	452522.i		−	0.730618i	−0.930886	−	0.365309i	$-0.880963\pi$
$787$		−	452522.i		−	0.730618i	0.930886	−	0.365309i	$-0.119037\pi$
$788$	628480.			1.01214
$789$			1.07127e6i			1.72086i
$790$		−	129323.i		−	0.207216i
$791$	−389786.	−	265451.i	−0.622979	−	0.424260i
$792$	7211.32			0.0114965
$793$	1.52382e6			2.42319
$794$			275321.i			0.436715i
$795$	28671.1			0.0453639
$796$			375248.i			0.592232i
$797$			688036.i			1.08316i	0.840648	+	0.541582i	$0.182175\pi$
$797$			688036.i			1.08316i	−0.840648	+	0.541582i	$0.817825\pi$
$798$	−105903.	−	72121.7i	−0.166304	−	0.113256i
$799$	369831.			0.579308
$800$	−100009.			−0.156264
$801$			13799.9i			0.0215086i
$802$	356402.			0.554103
$803$			170966.i			0.265142i
$804$			549588.i			0.850208i
$805$	−191541.	+	281257.i	−0.295577	+	0.434022i
$806$	−115004.			−0.177029
$807$	−277585.			−0.426235
$808$			534531.i			0.818748i
$809$	−879215.			−1.34338			−0.671688	−	0.740834i	$-0.734431\pi$
$809$	−879215.			−1.34338			−0.671688	+	0.740834i	$0.734431\pi$
$810$			88035.2i			0.134180i
$811$			1.19216e6i			1.81256i	0.422674	+	0.906282i	$0.361092\pi$
$811$			1.19216e6i			1.81256i	−0.422674	+	0.906282i	$0.638908\pi$
$812$	−458964.	−	312563.i	−0.696092	−	0.474051i
$813$	639088.			0.966896
$814$	−161763.			−0.244135
$815$			430090.i			0.647507i
$816$	258850.			0.388748
$817$			548978.i			0.822452i
$818$			244057.i			0.364741i
$819$	12597.4	−	18497.9i	0.0187808	−	0.0275776i
$820$	414725.			0.616783
$821$	−1.27851e6			−1.89679			−0.948395	−	0.317092i	$-0.897293\pi$
$821$	−1.27851e6			−1.89679			−0.948395	+	0.317092i	$0.897293\pi$
$822$			10088.5i			0.0149308i
$823$	287003.			0.423728			0.211864	−	0.977299i	$-0.432047\pi$
$823$	287003.			0.423728			0.211864	+	0.977299i	$0.432047\pi$
$824$		−	357537.i		−	0.526582i
$825$			121542.i			0.178574i
$826$	188452.	−	276721.i	0.276211	−	0.405585i
$827$	494589.			0.723158			0.361579	−	0.932341i	$-0.382238\pi$
$827$	494589.			0.723158			0.361579	+	0.932341i	$0.382238\pi$
$828$	17064.6			0.0248906
$829$			172405.i			0.250865i	0.992102	+	0.125433i	$0.0400319\pi$
$829$			172405.i			0.250865i	−0.992102	+	0.125433i	$0.959968\pi$
$830$	8095.62			0.0117515
$831$		−	707494.i		−	1.02452i
$832$			517743.i			0.747941i
$833$	−331210.	+	130393.i	−0.477324	+	0.187916i
$834$	52264.3			0.0751403
$835$	203271.			0.291542
$836$		−	382253.i		−	0.546938i
$837$	−290360.			−0.414463
$838$			235140.i			0.334841i
$839$		−	1.22445e6i		−	1.73947i	−0.493523	−	0.869733i	$-0.664291\pi$
$839$		−	1.22445e6i		−	1.73947i	0.493523	−	0.869733i	$-0.335709\pi$
$840$	−148143.	−	100888.i	−0.209953	−	0.142982i
$841$	−106685.			−0.150838
$842$	86395.8			0.121862
$843$		−	372691.i		−	0.524437i
$844$	1.03667e6			1.45530
$845$			341430.i			0.478176i
$846$			5500.21i			0.00768491i
$847$	130961.	+	89186.4i	0.182547	+	0.124317i
$848$	−54025.0			−0.0751282
$849$	599772.			0.832091
$850$		−	21747.6i		−	0.0301005i
$851$	−801634.			−1.10692
$852$		−	105626.i		−	0.145509i
$853$			1.05296e6i			1.44716i	0.690243	+	0.723578i	$0.257504\pi$
$853$			1.05296e6i			1.44716i	−0.690243	+	0.723578i	$0.742496\pi$
$854$	202889.	−	297921.i	0.278191	−	0.408493i
$855$	−5141.11			−0.00703274
$856$	−99524.2			−0.135825
$857$		−	48279.9i		−	0.0657362i	−0.999460	−	0.0328681i	$-0.989536\pi$
$857$		−	48279.9i		−	0.0657362i	0.999460	−	0.0328681i	$-0.0104641\pi$
$858$	−277401.			−0.376820
$859$		−	441680.i		−	0.598579i	−0.954162	−	0.299289i	$-0.903250\pi$
$859$		−	441680.i		−	0.598579i	0.954162	−	0.299289i	$-0.0967496\pi$
$860$			366702.i			0.495811i
$861$	935306.	+	636960.i	1.26168	+	0.859223i
$862$	150351.			0.202344
$863$	−445476.			−0.598139			−0.299070	−	0.954231i	$-0.596676\pi$
$863$	−445476.			−0.598139			−0.299070	+	0.954231i	$0.596676\pi$
$864$		−	576294.i		−	0.771999i
$865$	187103.			0.250062
$866$		−	98680.5i		−	0.131582i
$867$		−	560268.i		−	0.745346i
$868$	162580.	−	238731.i	0.215789	−	0.316862i
$869$	1.05272e6			1.39404
$870$	92569.8			0.122301
$871$		−	1.00364e6i		−	1.32294i
$872$	−503617.			−0.662319
$873$		−	127.059i		−	0.000166716i
$874$			178410.i			0.233559i
$875$	38546.1	−	56600.8i	0.0503460	−	0.0739276i
$876$	−213093.			−0.277690
$877$	182865.			0.237757			0.118878	−	0.992909i	$-0.462070\pi$
$877$	182865.			0.237757			0.118878	+	0.992909i	$0.462070\pi$
$878$		−	116737.i		−	0.151433i
$879$	−99753.3			−0.129107
$880$		−	229021.i		−	0.295740i
$881$		−	92699.7i		−	0.119434i	−0.998215	−	0.0597168i	$-0.980980\pi$
$881$		−	92699.7i		−	0.119434i	0.998215	−	0.0597168i	$-0.0190198\pi$
$882$	−1939.23	−	4925.83i	−0.00249283	−	0.00633202i
$883$	−767294.			−0.984103			−0.492052	−	0.870566i	$-0.663753\pi$
$883$	−767294.			−0.984103			−0.492052	+	0.870566i	$0.663753\pi$
$884$	−527013.			−0.674399
$885$		−	592598.i		−	0.756613i
$886$	66136.6			0.0842508
$887$		−	486927.i		−	0.618894i	−0.950917	−	0.309447i	$-0.899856\pi$
$887$		−	486927.i		−	0.618894i	0.950917	−	0.309447i	$-0.100144\pi$
$888$		−	422233.i		−	0.535459i
$889$	−399666.	−	272180.i	−0.505701	−	0.344392i
$890$	−96373.6			−0.121669
$891$	−716628.			−0.902689
$892$			1.03736e6i			1.30377i
$893$	610563.			0.765645
$894$			218633.i			0.273552i
$895$		−	138583.i		−	0.173007i
$896$	619674.	+	422009.i	0.771875	+	0.525660i
$897$	−1.37469e6			−1.70852
$898$	−183352.			−0.227370
$899$			312402.i			0.386539i
$900$	−3434.11			−0.00423965
$901$		−	41760.7i		−	0.0514421i
$902$		−	317958.i		−	0.390802i
$903$	−563203.	+	827002.i	−0.690700	+	1.01422i
$904$	−345872.			−0.423232
$905$	−60250.6			−0.0735639
$906$		−	11549.4i		−	0.0140703i
$907$	−1.24193e6			−1.50967			−0.754833	−	0.655917i	$-0.772282\pi$
$907$	−1.24193e6			−1.50967			−0.754833	+	0.655917i	$0.772282\pi$
$908$			502524.i			0.609517i
$909$			27944.8i			0.0338200i
$910$	129183.	+	87975.9i	0.155999	+	0.106238i
$911$	77748.2			0.0936814			0.0468407	−	0.998902i	$-0.485085\pi$
$911$	77748.2			0.0936814			0.0468407	+	0.998902i	$0.485085\pi$
$912$	427342.			0.513790
$913$			65900.3i			0.0790580i
$914$	−32118.7			−0.0384473
$915$		−	637997.i		−	0.762038i
$916$		−	523101.i		−	0.623440i
$917$	652637.	−	958326.i	0.776127	−	1.13966i
$918$	125319.			0.148707
$919$	−678961.			−0.803922			−0.401961	−	0.915657i	$-0.631671\pi$
$919$	−678961.			−0.803922			−0.401961	+	0.915657i	$0.631671\pi$
$920$			249570.i			0.294861i
$921$	−133754.			−0.157685
$922$		−	195473.i		−	0.229945i
$923$			192890.i			0.226415i
$924$	392158.	−	575841.i	0.459322	−	0.674464i
$925$	161322.			0.188543
$926$	121370.			0.141544
$927$		−	18691.7i		−	0.0217515i
$928$	−620042.			−0.719987
$929$		−	287085.i		−	0.332644i	−0.986072	−	0.166322i	$-0.946811\pi$
$929$		−	287085.i		−	0.332644i	0.986072	−	0.166322i	$-0.0531891\pi$
$930$			48150.4i			0.0556716i
$931$	−546802.	+	215269.i	−0.630857	+	0.248360i
$932$	1.42089e6			1.63580
$933$	−924827.			−1.06242
$934$		−	302799.i		−	0.347105i
$935$	177031.			0.202500
$936$		−	16413.9i		−	0.0187353i
$937$			43810.6i			0.0498999i	0.999689	+	0.0249500i	$0.00794265\pi$
$937$			43810.6i			0.0498999i	−0.999689	+	0.0249500i	$0.992057\pi$
$938$	−196220.	−	133630.i	−0.223017	−	0.151879i
$939$	1.23989e6			1.40622
$940$	407839.			0.461565
$941$		−	717811.i		−	0.810645i	−0.914174	−	0.405323i	$-0.867159\pi$
$941$		−	717811.i		−	0.810645i	0.914174	−	0.405323i	$-0.132841\pi$
$942$	−420320.			−0.473672
$943$		−	1.57567e6i		−	1.77191i
$944$			1.11663e6i			1.25304i
$945$	326157.	+	222119.i	0.365227	+	0.248726i
$946$	281140.			0.314153
$947$	−751406.			−0.837867			−0.418933	−	0.908017i	$-0.637596\pi$
$947$	−751406.			−0.837867			−0.418933	+	0.908017i	$0.637596\pi$
$948$			1.31211e6i			1.46001i
$949$	389142.			0.432091
$950$		−	35903.6i		−	0.0397824i
$951$			460572.i			0.509256i
$952$	−146947.	+	215776.i	−0.162139	+	0.238084i
$953$	−515132.			−0.567196			−0.283598	−	0.958943i	$-0.591528\pi$
$953$	−515132.			−0.567196			−0.283598	+	0.958943i	$0.591528\pi$
$954$	621.075			0.000682413
$955$		−	800335.i		−	0.877537i
$956$	−396264.			−0.433580
$957$			753541.i			0.822778i
$958$			76642.8i			0.0835104i
$959$	38243.9	+	26044.8i	0.0415839	+	0.0283193i
$960$	216770.			0.235210
$961$	761025.			0.824047
$962$			368195.i			0.397857i
$963$	−5203.04			−0.00561054
$964$		−	1.62197e6i		−	1.74538i
$965$		−	550589.i		−	0.591253i
$966$	−183033.	+	268764.i	−0.196144	+	0.288017i
$967$	−276226.			−0.295400			−0.147700	−	0.989032i	$-0.547187\pi$
$967$	−276226.			−0.295400			−0.147700	+	0.989032i	$0.547187\pi$
$968$	116206.			0.124016
$969$			330330.i			0.351804i
$970$	887.336			0.000943071
$971$			1.42162e6i			1.50781i	0.656986	+	0.753903i	$0.271831\pi$
$971$			1.42162e6i			1.50781i	−0.656986	+	0.753903i	$0.728169\pi$
$972$		−	40047.5i		−	0.0423880i
$973$	134927.	−	198125.i	0.142519	−	0.209273i
$974$	−83407.7			−0.0879201
$975$	276645.			0.291014
$976$			1.20218e6i			1.26203i
$977$	1.50221e6			1.57377			0.786885	−	0.617100i	$-0.211693\pi$
$977$	1.50221e6			1.57377			0.786885	+	0.617100i	$0.211693\pi$
$978$			410986.i			0.429685i
$979$		−	784505.i		−	0.818522i
$980$	−365248.	+	143793.i	−0.380309	+	0.149722i
$981$	−26328.7			−0.0273584
$982$	290747.			0.301503
$983$		−	94805.3i		−	0.0981128i	−0.998796	−	0.0490564i	$-0.984379\pi$
$983$		−	94805.3i		−	0.0981128i	0.998796	−	0.0490564i	$-0.0156214\pi$
$984$	829932.			0.857141
$985$			480525.i			0.495272i
$986$		−	134832.i		−	0.138688i
$987$	919777.	+	626384.i	0.944165	+	0.642993i
$988$	−870058.			−0.891322
$989$	1.39322e6			1.42438
$990$			2632.84i			0.00268630i
$991$	719358.			0.732484			0.366242	−	0.930520i	$-0.380644\pi$
$991$	719358.			0.732484			0.366242	+	0.930520i	$0.380644\pi$
$992$		−	322516.i		−	0.327739i
$993$		−	1.17638e6i		−	1.19302i
$994$	37711.7	+	25682.4i	0.0381684	+	0.0259933i
$995$	−286908.			−0.289799
$996$	−82138.2			−0.0827993
$997$			1.19572e6i			1.20292i	0.798901	+	0.601462i	$0.205415\pi$
$997$			1.19572e6i			1.20292i	−0.798901	+	0.601462i	$0.794585\pi$
$998$	296803.			0.297993
$999$			929607.i			0.931469i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	35.5.d.a.6.7	✓	12
3.2	odd	2		315.5.h.a.181.6		12
4.3	odd	2		560.5.f.b.321.9		12
5.2	odd	4		175.5.c.d.174.10		24
5.3	odd	4		175.5.c.d.174.15		24
5.4	even	2		175.5.d.i.76.6		12
7.6	odd	2	inner	35.5.d.a.6.8	yes	12
21.20	even	2		315.5.h.a.181.5		12
28.27	even	2		560.5.f.b.321.4		12
35.13	even	4		175.5.c.d.174.9		24
35.27	even	4		175.5.c.d.174.16		24
35.34	odd	2		175.5.d.i.76.5		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
35.5.d.a.6.7	✓	12	1.1	even	1	trivial
35.5.d.a.6.8	yes	12	7.6	odd	2	inner
175.5.c.d.174.9		24	35.13	even	4
175.5.c.d.174.10		24	5.2	odd	4
175.5.c.d.174.15		24	5.3	odd	4
175.5.c.d.174.16		24	35.27	even	4
175.5.d.i.76.5		12	35.34	odd	2
175.5.d.i.76.6		12	5.4	even	2
315.5.h.a.181.5		12	21.20	even	2
315.5.h.a.181.6		12	3.2	odd	2
560.5.f.b.321.4		12	28.27	even	2
560.5.f.b.321.9		12	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 35 = 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	35.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.17355 q^{2} -9.10378i q^{3} -14.6228 q^{4} -11.1803i q^{5} -10.6837i q^{6} +(-40.5002 - 27.5814i) q^{7} -35.9373 q^{8} -1.87877 q^{9} +O(q^{10})\)	\(q+1.17355 q^{2} -9.10378i q^{3} -14.6228 q^{4} -11.1803i q^{5} -10.6837i q^{6} +(-40.5002 - 27.5814i) q^{7} -35.9373 q^{8} -1.87877 q^{9} -13.1207i q^{10} +106.806 q^{11} +133.123i q^{12} -243.104i q^{13} +(-47.5290 - 32.3681i) q^{14} -101.783 q^{15} +191.790 q^{16} +148.252i q^{17} -2.20483 q^{18} +244.752i q^{19} +163.488i q^{20} +(-251.095 + 368.705i) q^{21} +125.342 q^{22} +621.143 q^{23} +327.166i q^{24} -125.000 q^{25} -285.294i q^{26} -720.302i q^{27} +(592.226 + 403.316i) q^{28} -774.981 q^{29} -119.448 q^{30} -403.109i q^{31} +800.073 q^{32} -972.334i q^{33} +173.981i q^{34} +(-308.369 + 452.806i) q^{35} +27.4729 q^{36} -1290.58 q^{37} +287.229i q^{38} -2213.16 q^{39} +401.792i q^{40} -2536.73i q^{41} +(-294.672 + 432.694i) q^{42} +2242.99 q^{43} -1561.79 q^{44} +21.0053i q^{45} +728.942 q^{46} -2494.61i q^{47} -1746.02i q^{48} +(879.536 + 2234.10i) q^{49} -146.694 q^{50} +1349.65 q^{51} +3554.85i q^{52} -281.688 q^{53} -845.310i q^{54} -1194.12i q^{55} +(1455.47 + 991.201i) q^{56} +2228.17 q^{57} -909.479 q^{58} +5822.15i q^{59} +1488.36 q^{60} +6268.19i q^{61} -473.068i q^{62} +(76.0908 + 51.8192i) q^{63} -2129.72 q^{64} -2717.98 q^{65} -1141.08i q^{66} +4128.43 q^{67} -2167.85i q^{68} -5654.74i q^{69} +(-361.886 + 531.390i) q^{70} -793.446 q^{71} +67.5182 q^{72} +1600.72i q^{73} -1514.56 q^{74} +1137.97i q^{75} -3578.96i q^{76} +(-4325.65 - 2945.84i) q^{77} -2597.25 q^{78} +9856.44 q^{79} -2144.28i q^{80} -6709.65 q^{81} -2976.98i q^{82} +617.012i q^{83} +(3671.70 - 5391.49i) q^{84} +1657.51 q^{85} +2632.26 q^{86} +7055.26i q^{87} -3838.31 q^{88} -7345.17i q^{89} +24.6508i q^{90} +(-6705.13 + 9845.75i) q^{91} -9082.83 q^{92} -3669.81 q^{93} -2927.55i q^{94} +2736.41 q^{95} -7283.69i q^{96} +67.6288i q^{97} +(1032.18 + 2621.83i) q^{98} -200.664 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 6 q^{2} + 122 q^{4} - 50 q^{7} - 186 q^{8} - 434 q^{9}+O(q^{10}) \) 12 * q - 6 * q^2 + 122 * q^4 - 50 * q^7 - 186 * q^8 - 434 * q^9	\( 12 q - 6 q^{2} + 122 q^{4} - 50 q^{7} - 186 q^{8} - 434 q^{9} + 126 q^{11} + 78 q^{14} + 50 q^{15} + 578 q^{16} + 734 q^{18} - 642 q^{21} + 2264 q^{22} - 756 q^{23} - 1500 q^{25} + 1414 q^{28} - 2190 q^{29} + 1600 q^{30} - 8682 q^{32} - 150 q^{35} - 3582 q^{36} + 5564 q^{37} + 8634 q^{39} + 5580 q^{42} + 3944 q^{43} - 11196 q^{44} + 7844 q^{46} - 8796 q^{49} + 750 q^{50} + 7206 q^{51} + 11760 q^{53} - 6606 q^{56} - 12900 q^{57} - 18496 q^{58} - 11700 q^{60} - 4310 q^{63} + 20146 q^{64} - 750 q^{65} - 24096 q^{67} + 14400 q^{70} - 5664 q^{71} + 39214 q^{72} + 17604 q^{74} + 26904 q^{77} + 20100 q^{78} - 1590 q^{79} - 11912 q^{81} - 43128 q^{84} + 1050 q^{85} + 17604 q^{86} - 7268 q^{88} - 7182 q^{91} - 60252 q^{92} - 70980 q^{93} - 3000 q^{95} + 57714 q^{98} + 23084 q^{99}+O(q^{100}) \) 12 * q - 6 * q^2 + 122 * q^4 - 50 * q^7 - 186 * q^8 - 434 * q^9 + 126 * q^11 + 78 * q^14 + 50 * q^15 + 578 * q^16 + 734 * q^18 - 642 * q^21 + 2264 * q^22 - 756 * q^23 - 1500 * q^25 + 1414 * q^28 - 2190 * q^29 + 1600 * q^30 - 8682 * q^32 - 150 * q^35 - 3582 * q^36 + 5564 * q^37 + 8634 * q^39 + 5580 * q^42 + 3944 * q^43 - 11196 * q^44 + 7844 * q^46 - 8796 * q^49 + 750 * q^50 + 7206 * q^51 + 11760 * q^53 - 6606 * q^56 - 12900 * q^57 - 18496 * q^58 - 11700 * q^60 - 4310 * q^63 + 20146 * q^64 - 750 * q^65 - 24096 * q^67 + 14400 * q^70 - 5664 * q^71 + 39214 * q^72 + 17604 * q^74 + 26904 * q^77 + 20100 * q^78 - 1590 * q^79 - 11912 * q^81 - 43128 * q^84 + 1050 * q^85 + 17604 * q^86 - 7268 * q^88 - 7182 * q^91 - 60252 * q^92 - 70980 * q^93 - 3000 * q^95 + 57714 * q^98 + 23084 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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