LMFDB - Embedded newform 15.6.e.a.2.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [15,6,Mod(2,15)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(15, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1]))

N = Newforms(chi, 6, names="a")

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

chi := DirichletCharacter("15.2");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 15 = 3 \cdot 5 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	15.e (of order $4$, degree $2$, 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:	$2.40575729719$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 10768x^{12} + 16341006x^{8} + 4217167600x^{4} + 50906640625 $ x^16 + 10768x^12 + 16341006x^8 + 4217167600*x^4 + 50906640625
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{9}\cdot 3^{10}\cdot 5^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			2.4
Root			$2.96509 + 2.96509i$ of defining polynomial
Character	$\chi$	$=$	15.2
Dual form			15.6.e.a.8.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.879873 + 0.879873i) q^{2} +(-15.5882 - 0.0935382i) q^{3} +30.4516i q^{4} +(-51.8842 + 20.8094i) q^{5} +(13.7979 - 13.6333i) q^{6} +(-11.3356 - 11.3356i) q^{7} +(-54.9495 - 54.9495i) q^{8} +(242.983 + 2.91618i) q^{9} +O(q^{10})$	\(q+(-0.879873 + 0.879873i) q^{2} +(-15.5882 - 0.0935382i) q^{3} +30.4516i q^{4} +(-51.8842 + 20.8094i) q^{5} +(13.7979 - 13.6333i) q^{6} +(-11.3356 - 11.3356i) q^{7} +(-54.9495 - 54.9495i) q^{8} +(242.983 + 2.91618i) q^{9} +(27.3419 - 63.9612i) q^{10} +359.671i q^{11} +(2.84839 - 474.686i) q^{12} +(370.007 - 370.007i) q^{13} +19.9477 q^{14} +(810.726 - 319.527i) q^{15} -877.755 q^{16} +(-1244.30 + 1244.30i) q^{17} +(-216.360 + 211.228i) q^{18} +2005.02i q^{19} +(-633.681 - 1579.96i) q^{20} +(175.640 + 177.761i) q^{21} +(-316.465 - 316.465i) q^{22} +(-245.087 - 245.087i) q^{23} +(851.423 + 861.703i) q^{24} +(2258.94 - 2159.36i) q^{25} +651.119i q^{26} +(-3787.38 - 68.1861i) q^{27} +(345.186 - 345.186i) q^{28} +7056.79 q^{29} +(-432.193 + 994.480i) q^{30} -3032.57 q^{31} +(2530.70 - 2530.70i) q^{32} +(33.6430 - 5606.61i) q^{33} -2189.65i q^{34} +(824.022 + 352.250i) q^{35} +(-88.8025 + 7399.22i) q^{36} +(2362.96 + 2362.96i) q^{37} +(-1764.17 - 1764.17i) q^{38} +(-5802.34 + 5733.13i) q^{39} +(3994.48 + 1707.55i) q^{40} -6435.18i q^{41} +(-310.948 - 1.86587i) q^{42} +(-9718.91 + 9718.91i) q^{43} -10952.6 q^{44} +(-12667.6 + 4905.02i) q^{45} +431.291 q^{46} +(-1492.86 + 1492.86i) q^{47} +(13682.6 + 82.1037i) q^{48} -16550.0i q^{49} +(-87.6175 + 3887.54i) q^{50} +(19512.8 - 19280.0i) q^{51} +(11267.3 + 11267.3i) q^{52} +(18730.5 + 18730.5i) q^{53} +(3392.41 - 3272.42i) q^{54} +(-7484.54 - 18661.2i) q^{55} +1245.77i q^{56} +(187.546 - 31254.6i) q^{57} +(-6209.09 + 6209.09i) q^{58} -21245.6 q^{59} +(9730.14 + 24688.0i) q^{60} -691.744 q^{61} +(2668.28 - 2668.28i) q^{62} +(-2721.29 - 2787.40i) q^{63} -23634.8i q^{64} +(-11497.9 + 26897.1i) q^{65} +(4903.51 + 4962.71i) q^{66} +(40533.4 + 40533.4i) q^{67} +(-37891.0 - 37891.0i) q^{68} +(3797.53 + 3843.38i) q^{69} +(-1034.97 + 415.100i) q^{70} +8449.81i q^{71} +(-13191.5 - 13512.0i) q^{72} +(-11657.9 + 11657.9i) q^{73} -4158.21 q^{74} +(-35414.7 + 33449.2i) q^{75} -61056.2 q^{76} +(4077.07 - 4077.07i) q^{77} +(60.9045 - 10149.8i) q^{78} +29899.1i q^{79} +(45541.6 - 18265.6i) q^{80} +(59032.0 + 1417.16i) q^{81} +(5662.15 + 5662.15i) q^{82} +(30668.9 + 30668.9i) q^{83} +(-5413.11 + 5348.54i) q^{84} +(38666.4 - 90452.7i) q^{85} -17102.8i q^{86} +(-110003. - 660.080i) q^{87} +(19763.8 - 19763.8i) q^{88} +106026. q^{89} +(6830.12 - 15461.7i) q^{90} -8388.47 q^{91} +(7463.29 - 7463.29i) q^{92} +(47272.3 + 283.661i) q^{93} -2627.06i q^{94} +(-41723.3 - 104029. i) q^{95} +(-39685.7 + 39212.3i) q^{96} +(-33142.7 - 33142.7i) q^{97} +(14561.9 + 14561.9i) q^{98} +(-1048.87 + 87393.7i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 84 q^{6} - 80 q^{7}+O(q^{10}) $ 16 * q - 84 * q^6 - 80 * q^7	$ 16 q - 84 q^{6} - 80 q^{7} + 1060 q^{10} + 420 q^{12} - 2120 q^{13} - 3000 q^{15} - 452 q^{16} + 6000 q^{18} + 1416 q^{21} + 3380 q^{22} + 9160 q^{25} - 12960 q^{27} - 10900 q^{28} - 13380 q^{30} - 21568 q^{31} + 5760 q^{33} + 61932 q^{36} + 55720 q^{37} + 21480 q^{40} - 103020 q^{42} - 23360 q^{43} - 21240 q^{45} - 151168 q^{46} + 74820 q^{48} + 138816 q^{51} + 204160 q^{52} + 89120 q^{55} - 163800 q^{57} - 163500 q^{58} - 217380 q^{60} - 175168 q^{61} + 143040 q^{63} + 263400 q^{66} + 140320 q^{67} + 385260 q^{70} - 328680 q^{72} - 240320 q^{73} - 199920 q^{75} - 271536 q^{76} + 429960 q^{78} + 326016 q^{81} + 431120 q^{82} + 2440 q^{85} - 331680 q^{87} - 401700 q^{88} - 348360 q^{90} - 487168 q^{91} - 22320 q^{93} + 311748 q^{96} + 440800 q^{97}+O(q^{100}) $ 16 * q - 84 * q^6 - 80 * q^7 + 1060 * q^10 + 420 * q^12 - 2120 * q^13 - 3000 * q^15 - 452 * q^16 + 6000 * q^18 + 1416 * q^21 + 3380 * q^22 + 9160 * q^25 - 12960 * q^27 - 10900 * q^28 - 13380 * q^30 - 21568 * q^31 + 5760 * q^33 + 61932 * q^36 + 55720 * q^37 + 21480 * q^40 - 103020 * q^42 - 23360 * q^43 - 21240 * q^45 - 151168 * q^46 + 74820 * q^48 + 138816 * q^51 + 204160 * q^52 + 89120 * q^55 - 163800 * q^57 - 163500 * q^58 - 217380 * q^60 - 175168 * q^61 + 143040 * q^63 + 263400 * q^66 + 140320 * q^67 + 385260 * q^70 - 328680 * q^72 - 240320 * q^73 - 199920 * q^75 - 271536 * q^76 + 429960 * q^78 + 326016 * q^81 + 431120 * q^82 + 2440 * q^85 - 331680 * q^87 - 401700 * q^88 - 348360 * q^90 - 487168 * q^91 - 22320 * q^93 + 311748 * q^96 + 440800 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/15\mathbb{Z}\right)^\times$.

$n$	$7$	$11$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$

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 $

$2$	−0.879873	+	0.879873i	−0.155541	+	0.155541i	−0.780588	−	0.625046i	$-0.785080\pi$
$2$	−0.879873	+	0.879873i	−0.155541	+	0.155541i	0.625046	+	0.780588i	$0.285080\pi$
$3$	−15.5882	−	0.0935382i	−0.999982	−	0.00600048i
$3$	−15.5882	−	0.0935382i	−0.999982	−	0.00600048i
$4$			30.4516i			0.951614i
$5$	−51.8842	+	20.8094i	−0.928133	+	0.372250i
$5$	−51.8842	+	20.8094i	−0.928133	+	0.372250i
$6$	13.7979	−	13.6333i	0.156472	−	0.154605i
$7$	−11.3356	−	11.3356i	−0.0874375	−	0.0874375i	0.662035	−	0.749473i	$-0.269693\pi$
$7$	−11.3356	−	11.3356i	−0.0874375	−	0.0874375i	−0.749473	+	0.662035i	$0.769693\pi$
$8$	−54.9495	−	54.9495i	−0.303556	−	0.303556i
$9$	242.983	+	2.91618i	0.999928	+	0.0120007i
$10$	27.3419	−	63.9612i	0.0864626	−	0.202263i
$11$			359.671i			0.896238i	0.893974	+	0.448119i	$0.147906\pi$
$11$			359.671i			0.896238i	−0.893974	+	0.448119i	$0.852094\pi$
$12$	2.84839	−	474.686i	0.00571014	−	0.951597i
$13$	370.007	−	370.007i	0.607228	−	0.607228i	−0.334993	−	0.942221i	$-0.608734\pi$
$13$	370.007	−	370.007i	0.607228	−	0.607228i	0.942221	+	0.334993i	$0.108734\pi$
$14$	19.9477			0.0272003
$15$	810.726	−	319.527i	0.930350	−	0.366674i
$16$	−877.755			−0.857183
$17$	−1244.30	+	1244.30i	−1.04425	+	1.04425i	−0.0452720	+	0.998975i	$0.514415\pi$
$17$	−1244.30	+	1244.30i	−1.04425	+	1.04425i	−0.998975	+	0.0452720i	$0.985585\pi$
$18$	−216.360	+	211.228i	−0.157397	+	0.153663i
$19$			2005.02i			1.27419i	0.770784	+	0.637096i	$0.219865\pi$
$19$			2005.02i			1.27419i	−0.770784	+	0.637096i	$0.780135\pi$
$20$	−633.681	−	1579.96i	−0.354238	−	0.883224i
$21$	175.640	+	177.761i	0.0869113	+	0.0879606i
$22$	−316.465	−	316.465i	−0.139402	−	0.139402i
$23$	−245.087	−	245.087i	−0.0966051	−	0.0966051i	0.657153	−	0.753758i	$-0.271761\pi$
$23$	−245.087	−	245.087i	−0.0966051	−	0.0966051i	−0.753758	+	0.657153i	$0.771761\pi$
$24$	851.423	+	861.703i	0.301729	+	0.305372i
$25$	2258.94	−	2159.36i	0.722860	−	0.690995i
$26$			651.119i			0.188898i
$27$	−3787.38	−	68.1861i	−0.999838	−	0.0180006i
$28$	345.186	−	345.186i	0.0832067	−	0.0832067i
$29$	7056.79			1.55816			0.779081	−	0.626924i	$-0.215686\pi$
$29$	7056.79			1.55816			0.779081	+	0.626924i	$0.215686\pi$
$30$	−432.193	+	994.480i	−0.0876747	+	0.201740i
$31$	−3032.57			−0.566770			−0.283385	−	0.959006i	$-0.591457\pi$
$31$	−3032.57			−0.566770			−0.283385	+	0.959006i	$0.591457\pi$
$32$	2530.70	−	2530.70i	0.436883	−	0.436883i
$33$	33.6430	−	5606.61i	0.00537786	−	0.896222i
$34$		−	2189.65i		−	0.324847i
$35$	824.022	+	352.250i	0.113702	+	0.0486050i
$36$	−88.8025	+	7399.22i	−0.0114201	+	0.951545i
$37$	2362.96	+	2362.96i	0.283761	+	0.283761i	0.834607	−	0.550846i	$-0.185695\pi$
$37$	2362.96	+	2362.96i	0.283761	+	0.283761i	−0.550846	+	0.834607i	$0.685695\pi$
$38$	−1764.17	−	1764.17i	−0.198189	−	0.198189i
$39$	−5802.34	+	5733.13i	−0.610860	+	0.603573i
$40$	3994.48	+	1707.55i	0.394739	+	0.168742i
$41$		−	6435.18i		−	0.597862i	−0.954275	−	0.298931i	$-0.903370\pi$
$41$		−	6435.18i		−	0.597862i	0.954275	−	0.298931i	$-0.0966301\pi$
$42$	−310.948	−	1.86587i	−0.0271998	−	0.000163215i
$43$	−9718.91	+	9718.91i	−0.801579	+	0.801579i	−0.983342	−	0.181763i	$-0.941820\pi$
$43$	−9718.91	+	9718.91i	−0.801579	+	0.801579i	0.181763	+	0.983342i	$0.441820\pi$
$44$	−10952.6			−0.852873
$45$	−12667.6	+	4905.02i	−0.932533	+	0.361085i
$46$	431.291			0.0300521
$47$	−1492.86	+	1492.86i	−0.0985767	+	0.0985767i	−0.754675	−	0.656099i	$-0.772206\pi$
$47$	−1492.86	+	1492.86i	−0.0985767	+	0.0985767i	0.656099	+	0.754675i	$0.272206\pi$
$48$	13682.6	+	82.1037i	0.857168	+	0.00514351i
$49$		−	16550.0i		−	0.984709i
$50$	−87.6175	+	3887.54i	−0.00495639	+	0.219913i
$51$	19512.8	−	19280.0i	1.05049	−	1.03796i
$52$	11267.3	+	11267.3i	0.577846	+	0.577846i
$53$	18730.5	+	18730.5i	0.915925	+	0.915925i	0.996730	−	0.0808054i	$-0.0257492\pi$
$53$	18730.5	+	18730.5i	0.915925	+	0.915925i	−0.0808054	+	0.996730i	$0.525749\pi$
$54$	3392.41	−	3272.42i	0.158316	−	0.152716i
$55$	−7484.54	−	18661.2i	−0.333625	−	0.831828i
$56$			1245.77i			0.0530844i
$57$	187.546	−	31254.6i	0.00764577	−	1.27417i
$58$	−6209.09	+	6209.09i	−0.242358	+	0.242358i
$59$	−21245.6			−0.794584			−0.397292	−	0.917692i	$-0.630050\pi$
$59$	−21245.6			−0.794584			−0.397292	+	0.917692i	$0.630050\pi$
$60$	9730.14	+	24688.0i	0.348932	+	0.885334i
$61$	−691.744			−0.0238024			−0.0119012	−	0.999929i	$-0.503788\pi$
$61$	−691.744			−0.0238024			−0.0119012	+	0.999929i	$0.503788\pi$
$62$	2668.28	−	2668.28i	0.0881560	−	0.0881560i
$63$	−2721.29	−	2787.40i	−0.0863819	−	0.0884805i
$64$		−	23634.8i		−	0.721276i
$65$	−11497.9	+	26897.1i	−0.337547	+	0.789628i
$66$	4903.51	+	4962.71i	0.138563	+	0.140236i
$67$	40533.4	+	40533.4i	1.10313	+	1.10313i	0.994031	+	0.109098i	$0.0347961\pi$
$67$	40533.4	+	40533.4i	1.10313	+	1.10313i	0.109098	+	0.994031i	$0.465204\pi$
$68$	−37891.0	−	37891.0i	−0.993720	−	0.993720i
$69$	3797.53	+	3843.38i	0.0960237	+	0.0971831i
$70$	−1034.97	+	415.100i	−0.0252454	+	0.0101253i
$71$			8449.81i			0.198930i	0.995041	+	0.0994652i	$0.0317132\pi$
$71$			8449.81i			0.198930i	−0.995041	+	0.0994652i	$0.968287\pi$
$72$	−13191.5	−	13512.0i	−0.299891	−	0.307177i
$73$	−11657.9	+	11657.9i	−0.256043	+	0.256043i	−0.823443	−	0.567399i	$-0.807950\pi$
$73$	−11657.9	+	11657.9i	−0.256043	+	0.256043i	0.567399	+	0.823443i	$0.307950\pi$
$74$	−4158.21			−0.0882729
$75$	−35414.7	+	33449.2i	−0.726993	+	0.686645i
$76$	−61056.2			−1.21254
$77$	4077.07	−	4077.07i	0.0783649	−	0.0783649i
$78$	60.9045	−	10149.8i	0.00113348	−	0.188894i
$79$			29899.1i			0.539002i	0.963000	+	0.269501i	$0.0868588\pi$
$79$			29899.1i			0.539002i	−0.963000	+	0.269501i	$0.913141\pi$
$80$	45541.6	−	18265.6i	0.795579	−	0.319086i
$81$	59032.0	+	1417.16i	0.999712	+	0.0239998i
$82$	5662.15	+	5662.15i	0.0929922	+	0.0929922i
$83$	30668.9	+	30668.9i	0.488656	+	0.488656i	0.907882	−	0.419226i	$-0.137699\pi$
$83$	30668.9	+	30668.9i	0.488656	+	0.488656i	−0.419226	+	0.907882i	$0.637699\pi$
$84$	−5413.11	+	5348.54i	−0.0837045	+	0.0827060i
$85$	38666.4	−	90452.7i	0.580479	−	1.35792i
$86$		−	17102.8i		−	0.249357i
$87$	−110003.	−	660.080i	−1.55813	−	0.00934972i
$88$	19763.8	−	19763.8i	0.272059	−	0.272059i
$89$	106026.			1.41886			0.709428	−	0.704778i	$-0.248953\pi$
$89$	106026.			1.41886			0.709428	+	0.704778i	$0.248953\pi$
$90$	6830.12	−	15461.7i	0.0888837	−	0.201211i
$91$	−8388.47			−0.106189
$92$	7463.29	−	7463.29i	0.0919308	−	0.0919308i
$93$	47272.3	+	283.661i	0.566760	+	0.00340089i
$94$		−	2627.06i		−	0.0306655i
$95$	−41723.3	−	104029.i	−0.474318	−	1.18262i
$96$	−39685.7	+	39212.3i	−0.439497	+	0.434254i
$97$	−33142.7	−	33142.7i	−0.357651	−	0.357651i	0.505296	−	0.862946i	$-0.331383\pi$
$97$	−33142.7	−	33142.7i	−0.357651	−	0.357651i	−0.862946	+	0.505296i	$0.831383\pi$
$98$	14561.9	+	14561.9i	0.153163	+	0.153163i
$99$	−1048.87	+	87393.7i	−0.0107555	+	0.896174i
$100$	65756.0	+	68788.4i	0.657560	+	0.687884i
$101$			13738.7i			0.134012i	0.997753	+	0.0670060i	$0.0213447\pi$
$101$			13738.7i			0.134012i	−0.997753	+	0.0670060i	$0.978655\pi$
$102$	−204.816	+	34132.7i	−0.00194924	+	0.324841i
$103$	−45415.8	+	45415.8i	−0.421807	+	0.421807i	−0.885825	−	0.464019i	$-0.846407\pi$
$103$	−45415.8	+	45415.8i	−0.421807	+	0.421807i	0.464019	+	0.885825i	$0.346407\pi$
$104$	−40663.4			−0.368656
$105$	−12812.1	−	5568.01i	−0.113408	−	0.0492864i
$106$	−32960.9			−0.284928
$107$	−47232.9	+	47232.9i	−0.398828	+	0.398828i	−0.877819	−	0.478992i	$-0.841002\pi$
$107$	−47232.9	+	47232.9i	−0.398828	+	0.398828i	0.478992	+	0.877819i	$0.341002\pi$
$108$	2076.38	−	115332.i	0.0171296	−	0.951460i
$109$			57758.8i			0.465642i	0.972520	+	0.232821i	$0.0747956\pi$
$109$			57758.8i			0.465642i	−0.972520	+	0.232821i	$0.925204\pi$
$110$	23005.0	+	9834.08i	0.181276	+	0.0774911i
$111$	−36613.2	−	37055.3i	−0.282053	−	0.285458i
$112$	9949.85	+	9949.85i	0.0749499	+	0.0749499i
$113$	−136180.	−	136180.i	−1.00327	−	1.00327i	−0.999995	−	0.00327423i	$-0.998958\pi$
$113$	−136180.	−	136180.i	−1.00327	−	1.00327i	−0.00327423	−	0.999995i	$-0.501042\pi$
$114$	27335.1	+	27665.1i	0.196997	+	0.199375i
$115$	17816.2	+	7616.02i	0.125624	+	0.0537011i
$116$			214891.i			1.48277i
$117$	90984.2	−	88826.2i	0.614471	−	0.599897i
$118$	18693.5	−	18693.5i	0.123590	−	0.123590i
$119$	28209.7			0.182613
$120$	−62106.9	−	26991.2i	−0.393720	−	0.171107i
$121$	31687.8			0.196757
$122$	608.647	−	608.647i	0.00370225	−	0.00370225i
$123$	−601.936	+	100313.i	−0.00358746	+	0.597852i
$124$		−	92346.8i		−	0.539346i
$125$	−72268.2	+	159044.i	−0.413687	+	0.910419i
$126$	4846.94	+	58.1711i	0.0271983	+	0.000326423i
$127$	−70532.8	−	70532.8i	−0.388044	−	0.388044i	0.485945	−	0.873989i	$-0.338476\pi$
$127$	−70532.8	−	70532.8i	−0.388044	−	0.388044i	−0.873989	+	0.485945i	$0.838476\pi$
$128$	101778.	+	101778.i	0.549072	+	0.549072i
$129$	152409.	−	150591.i	0.806375	−	0.796755i
$130$	−13549.4	−	33782.8i	−0.0703172	−	0.175322i
$131$		−	312818.i		−	1.59263i	−0.604884	−	0.796314i	$-0.706781\pi$
$131$		−	312818.i		−	1.59263i	0.604884	−	0.796314i	$-0.293219\pi$
$132$	170731.	+	1024.48i	0.852858	+	0.00511765i
$133$	22728.0	−	22728.0i	0.111412	−	0.111412i
$134$	−71328.6			−0.343164
$135$	197924.	−	75275.4i	0.934683	−	0.355483i
$136$	136748.			0.633975
$137$	−44151.7	+	44151.7i	−0.200977	+	0.200977i	−0.800418	−	0.599442i	$-0.795389\pi$
$137$	−44151.7	+	44151.7i	−0.200977	+	0.200977i	0.599442	+	0.800418i	$0.295389\pi$
$138$	−6723.03	−	40.3422i	−0.0300516	−	0.000180327i
$139$		−	10378.2i		−	0.0455600i	−0.999741	−	0.0227800i	$-0.992748\pi$
$139$		−	10378.2i		−	0.0455600i	0.999741	−	0.0227800i	$-0.00725173\pi$
$140$	−10726.6	+	25092.8i	−0.0462532	+	0.108201i
$141$	23410.6	−	23131.3i	0.0991665	−	0.0979834i
$142$	−7434.76	−	7434.76i	−0.0309419	−	0.0309419i
$143$	133081.	+	133081.i	0.544221	+	0.544221i
$144$	−213279.	−	2559.69i	−0.857121	−	0.0102868i
$145$	−366136.	+	146848.i	−1.44618	+	0.580025i
$146$		−	20515.0i		−	0.0796505i
$147$	−1548.06	+	257984.i	−0.00590873	+	0.984692i
$148$	−71956.1	+	71956.1i	−0.270031	+	0.270031i
$149$	−357728.			−1.32004			−0.660019	−	0.751249i	$-0.729452\pi$
$149$	−357728.			−1.32004			−0.660019	+	0.751249i	$0.729452\pi$
$150$	1729.43	−	60591.5i	0.00627589	−	0.219879i
$151$	181033.			0.646124			0.323062	−	0.946378i	$-0.395288\pi$
$151$	181033.			0.646124			0.323062	+	0.946378i	$0.395288\pi$
$152$	110175.	−	110175.i	0.386789	−	0.386789i
$153$	−305972.	+	298715.i	−1.05670	+	1.03164i
$154$			7174.61i			0.0243779i
$155$	157342.	−	63106.0i	0.526038	−	0.210980i
$156$	−174583.	−	176691.i	−0.574369	−	0.581303i
$157$	190153.	+	190153.i	0.615679	+	0.615679i	0.944420	−	0.328741i	$-0.106624\pi$
$157$	190153.	+	190153.i	0.615679	+	0.615679i	−0.328741	+	0.944420i	$0.606624\pi$
$158$	−26307.4	−	26307.4i	−0.0838370	−	0.0838370i
$159$	−290222.	−	293726.i	−0.910412	−	0.921404i
$160$	−78640.9	+	183966.i	−0.242856	+	0.568116i
$161$			5556.39i			0.0168938i
$162$	−53187.6	+	50693.8i	−0.159229	+	0.151763i
$163$	379306.	−	379306.i	1.11820	−	1.11820i	0.126198	−	0.992005i	$-0.459723\pi$
$163$	379306.	−	379306.i	1.11820	−	1.11820i	0.992005	−	0.126198i	$-0.0402773\pi$
$164$	195962.			0.568934
$165$	114925.	+	291595.i	0.328627	+	0.833815i
$166$	−53969.5			−0.152012
$167$	212126.	−	212126.i	0.588576	−	0.588576i	−0.348670	−	0.937246i	$-0.613367\pi$
$167$	212126.	−	212126.i	0.588576	−	0.588576i	0.937246	+	0.348670i	$0.113367\pi$
$168$	116.527	−	19419.2i	0.000318532	−	0.0530834i
$169$			97482.6i			0.262549i
$170$	45565.4	+	113608.i	0.120924	+	0.301501i
$171$	−5847.01	+	487185.i	−0.0152913	+	1.27410i
$172$	−295957.	−	295957.i	−0.762794	−	0.762794i
$173$	−52714.4	−	52714.4i	−0.133910	−	0.133910i	0.636974	−	0.770885i	$-0.280186\pi$
$173$	−52714.4	−	52714.4i	−0.133910	−	0.133910i	−0.770885	+	0.636974i	$0.780186\pi$
$174$	97369.1	−	96207.5i	0.243808	−	0.240900i
$175$	−50083.8	−	1128.79i	−0.123624	−	0.00278624i
$176$		−	315703.i		−	0.768240i
$177$	331181.	+	1987.28i	0.794569	+	0.00476788i
$178$	−93289.7	+	93289.7i	−0.220690	+	0.220690i
$179$	524394.			1.22328			0.611639	−	0.791137i	$-0.290510\pi$
$179$	524394.			1.22328			0.611639	+	0.791137i	$0.290510\pi$
$180$	−149366.	−	385750.i	−0.343613	−	0.887411i
$181$	163991.			0.372068			0.186034	−	0.982543i	$-0.440437\pi$
$181$	163991.			0.372068			0.186034	+	0.982543i	$0.440437\pi$
$182$	7380.79	−	7380.79i	0.0165167	−	0.0165167i
$183$	10783.0	+	64.7045i	0.0238020	+	0.000142826i
$184$			26934.8i			0.0586502i
$185$	−171772.	−	73428.5i	−0.368998	−	0.157738i
$186$	−41843.2	+	41344.0i	−0.0886834	+	0.0876255i
$187$	−447539.	−	447539.i	−0.935894	−	0.935894i
$188$	−45460.0	−	45460.0i	−0.0938070	−	0.0938070i
$189$	42159.1	+	43705.0i	0.0858494	+	0.0889973i
$190$	128244.	+	54821.1i	0.257722	+	0.110170i
$191$			559164.i			1.10906i	0.832163	+	0.554531i	$0.187102\pi$
$191$			559164.i			1.10906i	−0.832163	+	0.554531i	$0.812898\pi$
$192$	−2210.76	+	368423.i	−0.00432800	+	0.721263i
$193$	150013.	−	150013.i	0.289891	−	0.289891i	−0.547146	−	0.837037i	$-0.684286\pi$
$193$	150013.	−	150013.i	0.289891	−	0.289891i	0.837037	+	0.547146i	$0.184286\pi$
$194$	58322.8			0.111259
$195$	181747.	−	418202.i	0.342279	−	0.787589i
$196$	503975.			0.937063
$197$	−237011.	+	237011.i	−0.435113	+	0.435113i	−0.890363	−	0.455250i	$-0.849550\pi$
$197$	−237011.	+	237011.i	−0.435113	+	0.435113i	0.455250	+	0.890363i	$0.349550\pi$
$198$	−75972.6	−	77818.3i	−0.137719	−	0.141065i
$199$			602333.i			1.07821i	0.842238	+	0.539106i	$0.181238\pi$
$199$			602333.i			1.07821i	−0.842238	+	0.539106i	$0.818762\pi$
$200$	−242783.	−	5471.86i	−0.429184	−	0.00967297i
$201$	−628051.	−	635633.i	−1.09649	−	1.10973i
$202$	−12088.4	−	12088.4i	−0.0208444	−	0.0208444i
$203$	−79992.7	−	79992.7i	−0.136242	−	0.136242i
$204$	587107.	+	594196.i	0.987739	+	0.999665i
$205$	133912.	+	333884.i	0.222554	+	0.554896i
$206$		−	79920.3i		−	0.131217i
$207$	−58837.1	−	60266.5i	−0.0954388	−	0.0977575i
$208$	−324776.	+	324776.i	−0.520505	+	0.520505i
$209$	−721148.			−1.14198
$210$	16172.1	−	6373.84i	0.0253057	−	0.00997363i
$211$	−905177.			−1.39968			−0.699838	−	0.714302i	$-0.746744\pi$
$211$	−905177.			−1.39968			−0.699838	+	0.714302i	$0.746744\pi$
$212$	−570375.	+	570375.i	−0.871607	+	0.871607i
$213$	790.380	−	131717.i	0.00119368	−	0.198927i
$214$		−	83118.0i		−	0.124068i
$215$	302013.	−	706502.i	0.445584	−	1.04236i
$216$	204368.	+	211862.i	0.298043	+	0.308971i
$217$	34375.9	+	34375.9i	0.0495569	+	0.0495569i
$218$	−50820.5	−	50820.5i	−0.0724265	−	0.0724265i
$219$	182816.	−	180635.i	0.257575	−	0.254502i
$220$	568265.	−	227916.i	0.791579	−	0.317482i
$221$			920800.i			1.26819i
$222$	64819.0	+	388.952i	0.0882713	+	0.000529680i
$223$	325294.	−	325294.i	0.438040	−	0.438040i	−0.453312	−	0.891352i	$-0.649758\pi$
$223$	325294.	−	325294.i	0.438040	−	0.438040i	0.891352	+	0.453312i	$0.149758\pi$
$224$	−57373.8			−0.0764000
$225$	555179.	−	518099.i	0.731100	−	0.682270i
$226$	239642.			0.312099
$227$	71799.3	−	71799.3i	0.0924816	−	0.0924816i	−0.659352	−	0.751834i	$-0.729169\pi$
$227$	71799.3	−	71799.3i	0.0924816	−	0.0924816i	0.751834	+	0.659352i	$0.229169\pi$
$228$	951755.	+	5711.09i	1.21252	+	0.00727582i
$229$		−	278676.i		−	0.351165i	−0.984465	−	0.175583i	$-0.943819\pi$
$229$		−	278676.i		−	0.351165i	0.984465	−	0.175583i	$-0.0561809\pi$
$230$	−22377.2	+	8974.90i	−0.0278924	+	0.0111869i
$231$	−63935.4	+	63172.7i	−0.0788337	+	0.0778932i
$232$	−387768.	−	387768.i	−0.472990	−	0.472990i
$233$	−71640.1	−	71640.1i	−0.0864503	−	0.0864503i	0.662559	−	0.749010i	$-0.269470\pi$
$233$	−71640.1	−	71640.1i	−0.0864503	−	0.0864503i	−0.749010	+	0.662559i	$0.769470\pi$
$234$	−1898.78	+	158210.i	−0.00226691	+	0.188884i
$235$	46390.3	−	108521.i	0.0547971	−	0.128187i
$236$		−	646965.i		−	0.756137i
$237$	2796.71	−	466073.i	0.00323427	−	0.538993i
$238$	−24821.0	+	24821.0i	−0.0284038	+	0.0284038i
$239$	1.08062e6			1.22371			0.611854	−	0.790971i	$-0.290424\pi$
$239$	1.08062e6			1.22371			0.611854	+	0.790971i	$0.290424\pi$
$240$	−711619.	+	280467.i	−0.797480	+	0.314307i
$241$	−342370.			−0.379710			−0.189855	−	0.981812i	$-0.560802\pi$
$241$	−342370.			−0.379710			−0.189855	+	0.981812i	$0.560802\pi$
$242$	−27881.3	+	27881.3i	−0.0306037	+	0.0306037i
$243$	−920069.	−	27612.7i	−0.999550	−	0.0299981i
$244$		−	21064.7i		−	0.0226507i
$245$	344396.	+	858684.i	0.366558	+	0.913941i
$246$	−87732.9	−	88792.2i	−0.0924325	−	0.0935485i
$247$	741872.	+	741872.i	0.773725	+	0.773725i
$248$	166638.	+	166638.i	0.172047	+	0.172047i
$249$	−475203.	−	480941.i	−0.485715	−	0.491579i
$250$	−76351.4	−	203525.i	−0.0772622	−	0.205953i
$251$		−	195789.i		−	0.196157i	−0.995179	−	0.0980787i	$-0.968730\pi$
$251$		−	195789.i		−	0.196157i	0.995179	−	0.0980787i	$-0.0312697\pi$
$252$	84880.9	−	82867.6i	0.0841993	−	0.0822022i
$253$	88150.6	−	88150.6i	0.0865812	−	0.0865812i
$254$	124120.			0.120714
$255$	−611199.	+	1.40638e6i	−0.588616	+	1.35441i
$256$	577209.			0.550470
$257$	614221.	−	614221.i	0.580085	−	0.580085i	−0.354841	−	0.934927i	$-0.615465\pi$
$257$	614221.	−	614221.i	0.580085	−	0.580085i	0.934927	+	0.354841i	$0.115465\pi$
$258$	−1599.77	+	266602.i	−0.00149626	+	0.249353i
$259$		−	53571.0i		−	0.0496227i
$260$	−819062.	−	350130.i	−0.751421	−	0.321215i
$261$	1.71468e6	+	20578.9i	1.55805	+	0.0186991i
$262$	275241.	+	275241.i	0.247719	+	0.247719i
$263$	−398691.	−	398691.i	−0.355425	−	0.355425i	0.506699	−	0.862123i	$-0.330866\pi$
$263$	−398691.	−	398691.i	−0.355425	−	0.355425i	−0.862123	+	0.506699i	$0.830866\pi$
$264$	−309930.	+	306232.i	−0.273686	+	0.270421i
$265$	−1.36159e6	−	582046.i	−1.19105	−	0.509147i
$266$			39995.6i			0.0346584i
$267$	−1.65276e6	−	9917.51i	−1.41883	−	0.00851382i
$268$	−1.23431e6	+	1.23431e6i	−1.04975	+	1.04975i
$269$	−1.29261e6			−1.08915			−0.544575	−	0.838712i	$-0.683309\pi$
$269$	−1.29261e6			−1.08915			−0.544575	+	0.838712i	$0.683309\pi$
$270$	−107915.	+	240381.i	−0.0900894	+	0.200674i
$271$	−785610.			−0.649806			−0.324903	−	0.945747i	$-0.605332\pi$
$271$	−785610.			−0.649806			−0.324903	+	0.945747i	$0.605332\pi$
$272$	1.09219e6	−	1.09219e6i	0.895110	−	0.895110i
$273$	130761.	+	784.643i	0.106187	+	0.000637185i
$274$		−	77695.7i		−	0.0625203i
$275$	776658.	+	812474.i	0.619296	+	0.647855i
$276$	−117037.	+	115641.i	−0.0924808	+	0.0913775i
$277$	1.55247e6	+	1.55247e6i	1.21569	+	1.21569i	0.969127	+	0.246564i	$0.0793014\pi$
$277$	1.55247e6	+	1.55247e6i	1.21569	+	1.21569i	0.246564	+	0.969127i	$0.420699\pi$
$278$	9131.49	+	9131.49i	0.00708646	+	0.00708646i
$279$	−736862.	−	8843.53i	−0.566729	−	0.00680166i
$280$	−25923.7	−	64635.6i	−0.0197607	−	0.0492694i
$281$		−	1.24917e6i		−	0.943748i	−0.881666	−	0.471874i	$-0.843578\pi$
$281$		−	1.24917e6i		−	0.943748i	0.881666	−	0.471874i	$-0.156422\pi$
$282$	−245.730	+	40951.0i	−0.000184008	+	0.0306649i
$283$	564054.	−	564054.i	0.418654	−	0.418654i	−0.466086	−	0.884739i	$-0.654336\pi$
$283$	564054.	−	564054.i	0.418654	−	0.418654i	0.884739	+	0.466086i	$0.154336\pi$
$284$	−257311.			−0.189305
$285$	640660.	+	1.62552e6i	0.467213	+	1.18544i
$286$	−234188.			−0.169297
$287$	−72946.4	+	72946.4i	−0.0522756	+	0.0522756i
$288$	622296.	−	607536.i	0.442095	−	0.431609i
$289$		−	1.67671e6i		−	1.18090i
$290$	192946.	−	451361.i	0.134723	−	0.315158i
$291$	513535.	+	519735.i	0.355498	+	0.359790i
$292$	−355002.	−	355002.i	−0.243654	−	0.243654i
$293$	1.97297e6	+	1.97297e6i	1.34261	+	1.34261i	0.893449	+	0.449165i	$0.148279\pi$
$293$	1.97297e6	+	1.97297e6i	1.34261	+	1.34261i	0.449165	+	0.893449i	$0.351721\pi$
$294$	−225632.	−	228356.i	−0.152241	−	0.154079i
$295$	1.10231e6	−	442109.i	0.737479	−	0.295784i
$296$		−	259687.i		−	0.172275i
$297$	24524.6	−	1.36221e6i	0.0161328	−	0.896093i
$298$	314755.	−	314755.i	0.205320	−	0.205320i
$299$	−181368.			−0.117323
$300$	−1.01858e6	−	1.07844e6i	−0.653421	−	0.691817i
$301$	220339.			0.140176
$302$	−159286.	+	159286.i	−0.100499	+	0.100499i
$303$	1285.10	−	214162.i	0.000804136	−	0.134010i
$304$		−	1.75992e6i		−	1.09222i
$305$	35890.6	−	14394.8i	0.0220918	−	0.00886045i
$306$	6385.43	−	532048.i	0.00389840	−	0.324823i
$307$	712049.	+	712049.i	0.431185	+	0.431185i	0.889032	−	0.457846i	$-0.151379\pi$
$307$	712049.	+	712049.i	0.431185	+	0.431185i	−0.457846	+	0.889032i	$0.651379\pi$
$308$	124153.	+	124153.i	0.0745731	+	0.0745731i
$309$	712197.	−	703701.i	0.424330	−	0.419268i
$310$	−82916.2	+	193967.i	−0.0490044	+	0.114637i
$311$			801658.i			0.469990i	0.971997	+	0.234995i	$0.0755073\pi$
$311$			801658.i			0.469990i	−0.971997	+	0.234995i	$0.924493\pi$
$312$	633869.	+	3803.59i	0.368649	+	0.00221211i
$313$	−1.36383e6	+	1.36383e6i	−0.786862	+	0.786862i	−0.980978	−	0.194116i	$-0.937816\pi$
$313$	−1.36383e6	+	1.36383e6i	−0.786862	+	0.786862i	0.194116	+	0.980978i	$0.437816\pi$
$314$	−334621.			−0.191527
$315$	199196.	+	87993.6i	0.113111	+	0.0499660i
$316$	−910477.			−0.512922
$317$	−1.44550e6	+	1.44550e6i	−0.807925	+	0.807925i	−0.984320	−	0.176394i	$-0.943557\pi$
$317$	−1.44550e6	+	1.44550e6i	−0.807925	+	0.807925i	0.176394	+	0.984320i	$0.443557\pi$
$318$	513801.	+	3083.11i	0.284923	+	0.00170970i
$319$			2.53812e6i			1.39648i
$320$	491826.	+	1.22627e6i	0.268495	+	0.669440i
$321$	740693.	−	731857.i	0.401214	−	0.396428i
$322$	−4888.92	−	4888.92i	−0.00262768	−	0.00262768i
$323$	−2.49485e6	−	2.49485e6i	−1.33057	−	1.33057i
$324$	−43154.9	+	1.79762e6i	−0.0228385	+	0.951340i
$325$	36845.2	−	1.63480e6i	0.0193496	−	0.858532i
$326$			667482.i			0.347853i
$327$	5402.66	−	900355.i	0.00279408	−	0.465634i
$328$	−353610.	+	353610.i	−0.181485	+	0.181485i
$329$	33844.8			0.0172386
$330$	−357686.	−	155447.i	−0.180808	−	0.0785775i
$331$	−167596.			−0.0840801			−0.0420400	−	0.999116i	$-0.513386\pi$
$331$	−167596.			−0.0840801			−0.0420400	+	0.999116i	$0.513386\pi$
$332$	−933918.	+	933918.i	−0.465011	+	0.465011i
$333$	567267.	+	581049.i	0.280335	+	0.287146i
$334$			373288.i			0.183095i
$335$	−2.94652e6	−	1.25957e6i	−1.43449	−	0.613210i
$336$	−154169.	−	156031.i	−0.0744989	−	0.0753983i
$337$	−578695.	−	578695.i	−0.277571	−	0.277571i	0.554567	−	0.832139i	$-0.312884\pi$
$337$	−578695.	−	578695.i	−0.277571	−	0.277571i	−0.832139	+	0.554567i	$0.812884\pi$
$338$	−85772.3	−	85772.3i	−0.0408372	−	0.0408372i
$339$	2.11006e6	+	2.13554e6i	0.997231	+	1.00927i
$340$	2.75443e6	+	1.17745e6i	1.29222	+	0.552392i
$341$		−	1.09073e6i		−	0.507961i
$342$	−423517.	−	433806.i	−0.195797	−	0.200553i
$343$	−378120.	+	378120.i	−0.173538	+	0.173538i
$344$	1.06810e6			0.486649
$345$	−277010.	−	120386.i	−0.125299	−	0.0544539i
$346$	92764.1			0.0416572
$347$	55424.5	−	55424.5i	0.0247103	−	0.0247103i	−0.694644	−	0.719354i	$-0.744438\pi$
$347$	55424.5	−	55424.5i	0.0247103	−	0.0247103i	0.719354	+	0.694644i	$0.244438\pi$
$348$	20100.5	−	3.34976e6i	0.00889732	−	1.48274i
$349$		−	1.16783e6i		−	0.513234i	−0.966513	−	0.256617i	$-0.917392\pi$
$349$		−	1.16783e6i		−	0.513234i	0.966513	−	0.256617i	$-0.0826079\pi$
$350$	45060.6	−	43074.2i	0.0196620	−	0.0187952i
$351$	−1.42659e6	+	1.37613e6i	−0.618060	+	0.596199i
$352$	910219.	+	910219.i	0.391552	+	0.391552i
$353$	227606.	+	227606.i	0.0972182	+	0.0972182i	0.754043	−	0.656825i	$-0.228101\pi$
$353$	227606.	+	227606.i	0.0972182	+	0.0972182i	−0.656825	+	0.754043i	$0.728101\pi$
$354$	−293146.	+	289649.i	−0.124330	+	0.122847i
$355$	−175836.	−	438412.i	−0.0740518	−	0.184634i
$356$			3.22867e6i			1.35020i
$357$	−439738.	−	2638.68i	−0.182609	−	0.00109576i
$358$	−461401.	+	461401.i	−0.190270	+	0.190270i
$359$	3.03165e6			1.24149			0.620744	−	0.784014i	$-0.286831\pi$
$359$	3.03165e6			1.24149			0.620744	+	0.784014i	$0.286831\pi$
$360$	965609.	+	426552.i	0.392686	+	0.173467i
$361$	−1.54401e6			−0.623567
$362$	−144291.	+	144291.i	−0.0578719	+	0.0578719i
$363$	−493956.	−	2964.02i	−0.196753	−	0.00118063i
$364$		−	255443.i		−	0.101051i
$365$	362267.	−	847455.i	0.142330	−	0.332954i
$366$	−9544.63	+	9430.77i	−0.00372440	+	0.00367997i
$367$	−3.13626e6	−	3.13626e6i	−1.21548	−	1.21548i	−0.969200	−	0.246277i	$-0.920793\pi$
$367$	−3.13626e6	−	3.13626e6i	−1.21548	−	1.21548i	−0.246277	−	0.969200i	$-0.579207\pi$
$368$	215126.	+	215126.i	0.0828083	+	0.0828083i
$369$	18766.2	−	1.56364e6i	0.00717479	−	0.597819i
$370$	215746.	−	86530.0i	0.0819290	−	0.0328596i
$371$		−	424641.i		−	0.160172i
$372$	−8637.96	+	1.43952e6i	−0.00323634	+	0.539336i
$373$	3.09998e6	−	3.09998e6i	1.15368	−	1.15368i	0.167876	−	0.985808i	$-0.446309\pi$
$373$	3.09998e6	−	3.09998e6i	1.15368	−	1.15368i	0.985808	−	0.167876i	$-0.0536907\pi$
$374$	787555.			0.291140
$375$	1.14141e6	−	2.47244e6i	0.419143	−	0.907920i
$376$	164064.			0.0598472
$377$	2.61106e6	−	2.61106e6i	0.946159	−	0.946159i
$378$	−75549.6	−	1360.16i	−0.0271958	−	0.000489620i
$379$			3.76652e6i			1.34692i	0.739224	+	0.673460i	$0.235193\pi$
$379$			3.76652e6i			1.34692i	−0.739224	+	0.673460i	$0.764807\pi$
$380$	3.16785e6	−	1.27054e6i	1.12540	−	0.451368i
$381$	1.09288e6	+	1.10607e6i	0.385709	+	0.390366i
$382$	−491993.	−	491993.i	−0.172505	−	0.172505i
$383$	1.03003e6	+	1.03003e6i	0.358802	+	0.358802i	0.863371	−	0.504569i	$-0.168349\pi$
$383$	1.03003e6	+	1.03003e6i	0.358802	+	0.358802i	−0.504569	+	0.863371i	$0.668349\pi$
$384$	−1.57701e6	−	1.59605e6i	−0.545767	−	0.552356i
$385$	−126694.	+	296377.i	−0.0435617	+	0.101904i
$386$			263984.i			0.0901800i
$387$	−2.38987e6	+	2.33318e6i	−0.811141	+	0.791902i
$388$	1.00925e6	−	1.00925e6i	0.340345	−	0.340345i
$389$	−2.93288e6			−0.982698			−0.491349	−	0.870963i	$-0.663496\pi$
$389$	−2.93288e6			−0.982698			−0.491349	+	0.870963i	$0.663496\pi$
$390$	208050.	+	527879.i	0.0692639	+	0.175741i
$391$	609923.			0.201759
$392$	−909416.	+	909416.i	−0.298915	+	0.298915i
$393$	−29260.5	+	4.87627e6i	−0.00955653	+	1.59260i
$394$		−	417079.i		−	0.135356i
$395$	−622183.	−	1.55129e6i	−0.200644	−	0.500266i
$396$	−2.66128e6	−	31939.7i	−0.852812	−	0.0102351i
$397$	2.33959e6	+	2.33959e6i	0.745013	+	0.745013i	0.973538	−	0.228525i	$-0.0733902\pi$
$397$	2.33959e6	+	2.33959e6i	0.745013	+	0.745013i	−0.228525	+	0.973538i	$0.573390\pi$
$398$	−529977.	−	529977.i	−0.167706	−	0.167706i
$399$	−356415.	+	352163.i	−0.112079	+	0.110742i
$400$	−1.98279e6	+	1.89539e6i	−0.619623	+	0.592309i
$401$		−	3.56068e6i		−	1.10579i	−0.833251	−	0.552895i	$-0.813523\pi$
$401$		−	3.56068e6i		−	1.10579i	0.833251	−	0.552895i	$-0.186477\pi$
$402$	1.11188e6	+	6671.95i	0.343158	+	0.00205915i
$403$	−1.12207e6	+	1.12207e6i	−0.344158	+	0.344158i
$404$	−418367.			−0.127528
$405$	−3.09232e6	+	1.15489e6i	−0.936799	+	0.349868i
$406$	140767.			0.0423824
$407$	−849888.	+	849888.i	−0.254317	+	0.254317i
$408$	−2.13164e6	−	12791.1i	−0.633964	−	0.00380416i
$409$			2.99031e6i			0.883910i	0.897037	+	0.441955i	$0.145715\pi$
$409$			2.99031e6i			0.883910i	−0.897037	+	0.441955i	$0.854285\pi$
$410$	−411602.	−	175950.i	−0.120925	−	0.0516927i
$411$	692374.	−	684114.i	0.202179	−	0.199767i
$412$	−1.38298e6	−	1.38298e6i	−0.401397	−	0.401397i
$413$	240831.	+	240831.i	0.0694764	+	0.0694764i
$414$	104796.	+	1257.72i	0.0300500	+	0.000360648i
$415$	−2.22943e6	−	953029.i	−0.635439	−	0.271635i
$416$		−	1.87275e6i		−	0.530575i
$417$	−970.757	+	161777.i	−0.000273382	+	0.0455592i
$418$	634519.	−	634519.i	0.177625	−	0.177625i
$419$	552976.			0.153876			0.0769381	−	0.997036i	$-0.475486\pi$
$419$	552976.			0.153876			0.0769381	+	0.997036i	$0.475486\pi$
$420$	169555.	−	390148.i	0.0469016	−	0.107921i
$421$	5.56113e6			1.52918			0.764588	−	0.644519i	$-0.222942\pi$
$421$	5.56113e6			1.52918			0.764588	+	0.644519i	$0.222942\pi$
$422$	796441.	−	796441.i	0.217707	−	0.217707i
$423$	−367092.	+	358385.i	−0.0997526	+	0.0973866i
$424$		−	2.05846e6i		−	0.556069i
$425$	−123907.	+	5.49769e6i	−0.0332754	+	1.47641i
$426$	115199.	+	116590.i	0.0307556	+	0.0311270i
$427$	7841.31	+	7841.31i	0.00208122	+	0.00208122i
$428$	−1.43832e6	−	1.43832e6i	−0.379530	−	0.379530i
$429$	−2.06204e6	−	2.08693e6i	−0.540945	−	0.547477i
$430$	355900.	+	887366.i	0.0928231	+	0.231436i
$431$			3.18200e6i			0.825100i	0.910935	+	0.412550i	$0.135362\pi$
$431$			3.18200e6i			0.825100i	−0.910935	+	0.412550i	$0.864638\pi$
$432$	3.32439e6	+	59850.7i	0.857044	+	0.0154298i
$433$	−506874.	+	506874.i	−0.129921	+	0.129921i	−0.769077	−	0.639156i	$-0.779284\pi$
$433$	−506874.	+	506874.i	−0.129921	+	0.129921i	0.639156	+	0.769077i	$0.279284\pi$
$434$	−60492.9			−0.0154163
$435$	5.72113e6	−	2.25484e6i	1.44963	−	0.571337i
$436$	−1.75885e6			−0.443111
$437$	491404.	−	491404.i	0.123094	−	0.123094i
$438$	−1918.93	+	319791.i	−0.000477941	+	0.0796491i
$439$		−	4.28320e6i		−	1.06074i	−0.847767	−	0.530368i	$-0.822054\pi$
$439$		−	4.28320e6i		−	1.06074i	0.847767	−	0.530368i	$-0.177946\pi$
$440$	−614154.	+	1.43670e6i	−0.151233	+	0.353780i
$441$	48262.8	−	4.02136e6i	0.0118172	−	0.984638i
$442$	−810188.	−	810188.i	−0.197256	−	0.197256i
$443$	1.99417e6	+	1.99417e6i	0.482784	+	0.482784i	0.906020	−	0.423235i	$-0.139106\pi$
$443$	1.99417e6	+	1.99417e6i	0.482784	+	0.482784i	−0.423235	+	0.906020i	$0.639106\pi$
$444$	1.12839e6	−	1.11493e6i	0.271646	−	0.268406i
$445$	−5.50109e6	+	2.20634e6i	−1.31689	+	0.528169i
$446$			572435.i			0.136266i
$447$	5.57632e6	+	33461.2i	1.32002	+	0.00792087i
$448$	−267913.	+	267913.i	−0.0630666	+	0.0630666i
$449$	−524045.			−0.122674			−0.0613370	−	0.998117i	$-0.519536\pi$
$449$	−524045.			−0.122674			−0.0613370	+	0.998117i	$0.519536\pi$
$450$	−32626.3	+	944349.i	−0.00759515	+	0.219837i
$451$	2.31455e6			0.535827
$452$	4.14691e6	−	4.14691e6i	0.954725	−	0.954725i
$453$	−2.82198e6	−	16933.5i	−0.646113	−	0.00387706i
$454$			126349.i			0.0287694i
$455$	435229.	−	174559.i	0.0985574	−	0.0395288i
$456$	−1.72773e6	+	1.70712e6i	−0.389103	+	0.384461i
$457$	−782574.	−	782574.i	−0.175281	−	0.175281i	0.614014	−	0.789295i	$-0.289554\pi$
$457$	−782574.	−	782574.i	−0.175281	−	0.175281i	−0.789295	+	0.614014i	$0.789554\pi$
$458$	245200.	+	245200.i	0.0546206	+	0.0546206i
$459$	4.79749e6	−	4.62780e6i	1.06287	−	1.02528i
$460$	−231920.	+	542534.i	−0.0511027	+	0.119545i
$461$			1.72240e6i			0.377469i	0.982028	+	0.188734i	$0.0604385\pi$
$461$			1.72240e6i			0.377469i	−0.982028	+	0.188734i	$0.939562\pi$
$462$	671.100	−	111839.i	0.000146279	−	0.0243775i
$463$	4.87630e6	−	4.87630e6i	1.05715	−	1.05715i	0.0588893	−	0.998265i	$-0.481244\pi$
$463$	4.87630e6	−	4.87630e6i	1.05715	−	1.05715i	0.998265	−	0.0588893i	$-0.0187559\pi$
$464$	−6.19414e6			−1.33563
$465$	−2.45859e6	+	968990.i	−0.527294	+	0.207820i
$466$	126068.			0.0268931
$467$	−5.35029e6	+	5.35029e6i	−1.13523	+	1.13523i	−0.145940	+	0.989294i	$0.546620\pi$
$467$	−5.35029e6	+	5.35029e6i	−1.13523	+	1.13523i	−0.989294	+	0.145940i	$0.953380\pi$
$468$	2.70490e6	+	2.77062e6i	0.570870	+	0.584739i
$469$		−	918938.i		−	0.192910i
$470$	54667.5	+	136303.i	0.0114152	+	0.0284616i
$471$	−2.94635e6	−	2.98193e6i	−0.611973	−	0.619362i
$472$	1.16744e6	+	1.16744e6i	0.241201	+	0.241201i
$473$	−3.49561e6	−	3.49561e6i	−0.718406	−	0.718406i
$474$	407624.	+	412546.i	0.0833325	+	0.0843386i
$475$	4.32956e6	+	4.52922e6i	0.880460	+	0.921063i
$476$			859031.i			0.173777i
$477$	4.49656e6	+	4.60581e6i	0.904867	+	0.926850i
$478$	−950808.	+	950808.i	−0.190337	+	0.190337i
$479$	−2.68281e6			−0.534257			−0.267129	−	0.963661i	$-0.586075\pi$
$479$	−2.68281e6			−0.534257			−0.267129	+	0.963661i	$0.586075\pi$
$480$	1.24308e6	−	2.86033e6i	0.246260	−	0.566648i
$481$	1.74862e6			0.344615
$482$	301242.	−	301242.i	0.0590606	−	0.0590606i
$483$	519.735	−	86614.0i	0.000101371	−	0.0168935i
$484$			964947.i			0.187236i
$485$	2.40926e6	+	1.02990e6i	0.465082	+	0.198812i
$486$	833840.	−	785248.i	0.160137	−	0.150805i
$487$	−4.62946e6	−	4.62946e6i	−0.884521	−	0.884521i	0.109469	−	0.993990i	$-0.465085\pi$
$487$	−4.62946e6	−	4.62946e6i	−0.884521	−	0.884521i	−0.993990	+	0.109469i	$0.965085\pi$
$488$	38011.0	+	38011.0i	0.00722537	+	0.00722537i
$489$	−5.94817e6	+	5.87721e6i	−1.12489	+	1.11147i
$490$	−1.05856e6	−	452508.i	−0.199170	−	0.0851405i
$491$		−	5.60483e6i		−	1.04920i	−0.851349	−	0.524600i	$-0.824215\pi$
$491$		−	5.60483e6i		−	1.04920i	0.851349	−	0.524600i	$-0.175785\pi$
$492$	−3.05469e6	−	18329.9i	−0.568924	−	0.00341388i
$493$	−8.78078e6	+	8.78078e6i	−1.62710	+	1.62710i
$494$	−1.30551e6			−0.240692
$495$	−1.76419e6	−	4.55618e6i	−0.323618	−	0.835772i
$496$	2.66186e6			0.485826
$497$	95783.3	−	95783.3i	0.0173940	−	0.0173940i
$498$	841286.	+	5048.21i	0.152009	+	0.000912146i
$499$			4.52825e6i			0.814103i	0.913405	+	0.407052i	$0.133443\pi$
$499$			4.52825e6i			0.814103i	−0.913405	+	0.407052i	$0.866557\pi$
$500$	−4.84314e6	−	2.20069e6i	−0.866367	−	0.393671i
$501$	−3.32650e6	+	3.28681e6i	−0.592097	+	0.585033i
$502$	172270.	+	172270.i	0.0305105	+	0.0305105i
$503$	6.67659e6	+	6.67659e6i	1.17662	+	1.17662i	0.980601	+	0.196015i	$0.0628001\pi$
$503$	6.67659e6	+	6.67659e6i	1.17662	+	1.17662i	0.196015	+	0.980601i	$0.437200\pi$
$504$	−3632.88	+	302700.i	−0.000637052	+	0.0530806i
$505$	−285895.	−	712824.i	−0.0498859	−	0.124381i
$506$			155123.i			0.0269339i
$507$	9118.35	−	1.51958e6i	0.00157542	−	0.262544i
$508$	2.14784e6	−	2.14784e6i	0.369269	−	0.369269i
$509$	5.52619e6			0.945434			0.472717	−	0.881214i	$-0.343273\pi$
$509$	5.52619e6			0.945434			0.472717	+	0.881214i	$0.343273\pi$
$510$	−699655.	−	1.77521e6i	−0.119113	−	0.302221i
$511$	264298.			0.0447756
$512$	−3.76477e6	+	3.76477e6i	−0.634692	+	0.634692i
$513$	136715.	−	7.59378e6i	0.0229362	−	1.27399i
$514$			1.08087e6i			0.180454i
$515$	1.41129e6	−	3.30144e6i	0.234475	−	0.548510i
$516$	4.58574e6	+	4.64111e6i	0.758203	+	0.767357i
$517$	−536938.	−	536938.i	−0.0883483	−	0.0883483i
$518$	47135.7	+	47135.7i	0.00771836	+	0.00771836i
$519$	816791.	+	826653.i	0.133104	+	0.134712i
$520$	2.10979e6	−	846182.i	0.342161	−	0.137232i
$521$		−	619733.i		−	0.100025i	−0.998749	−	0.0500127i	$-0.984074\pi$
$521$		−	619733.i		−	0.100025i	0.998749	−	0.0500127i	$-0.0159262\pi$
$522$	−1.52681e6	+	1.49059e6i	−0.245249	+	0.239432i
$523$	6.44079e6	−	6.44079e6i	1.02964	−	1.02964i	0.0300909	−	0.999547i	$-0.490420\pi$
$523$	6.44079e6	−	6.44079e6i	1.02964	−	1.02964i	0.999547	−	0.0300909i	$-0.00957968\pi$
$524$	9.52584e6			1.51557
$525$	780610.	+	22280.5i	0.123605	+	0.00352799i
$526$	701596.			0.110566
$527$	3.77343e6	−	3.77343e6i	0.591848	−	0.591848i
$528$	−29530.3	+	4.92124e6i	−0.00460981	+	0.768227i
$529$		−	6.31621e6i		−	0.981335i
$530$	1.71015e6	−	685897.i	0.264451	−	0.106064i
$531$	−5.16232e6	−	61956.1i	−0.794527	−	0.00953560i
$532$	692106.	+	692106.i	0.106021	+	0.106021i
$533$	−2.38106e6	−	2.38106e6i	−0.363039	−	0.363039i
$534$	1.46294e6	−	1.44549e6i	0.222011	−	0.219362i
$535$	1.46775e6	−	3.43353e6i	0.221701	−	0.518629i
$536$		−	4.45459e6i		−	0.669723i
$537$	−8.17435e6	−	49050.9i	−1.22326	−	0.00734026i
$538$	1.13733e6	−	1.13733e6i	0.169408	−	0.169408i
$539$	5.95256e6			0.882534
$540$	2.29226e6	+	6.02711e6i	0.338282	+	0.889457i
$541$	−8.91778e6			−1.30998			−0.654988	−	0.755639i	$-0.727326\pi$
$541$	−8.91778e6			−1.30998			−0.654988	+	0.755639i	$0.727326\pi$
$542$	691237.	−	691237.i	0.101072	−	0.101072i
$543$	−2.55631e6	−	15339.4i	−0.372062	−	0.00223259i
$544$			6.29790e6i			0.912428i
$545$	−1.20193e6	−	2.99677e6i	−0.173335	−	0.432178i
$546$	−115743.	+	114363.i	−0.0166156	+	0.0164173i
$547$	−4.50080e6	−	4.50080e6i	−0.643164	−	0.643164i	0.308168	−	0.951332i	$-0.400284\pi$
$547$	−4.50080e6	−	4.50080e6i	−0.643164	−	0.643164i	−0.951332	+	0.308168i	$0.900284\pi$
$548$	−1.34449e6	−	1.34449e6i	−0.191252	−	0.191252i
$549$	−168082.	−	2017.25i	−0.0238007	−	0.000285647i
$550$	−1.39824e6	−	31513.5i	−0.197094	−	0.00444211i
$551$			1.41490e7i			1.98540i
$552$	2519.43	−	419865.i	0.000351929	−	0.0586491i
$553$	338923.	−	338923.i	0.0471290	−	0.0471290i
$554$	−2.73195e6			−0.378180
$555$	2.67075e6	+	1.16068e6i	0.368044	+	0.159949i
$556$	316033.			0.0433556
$557$	6.79813e6	−	6.79813e6i	0.928435	−	0.928435i	−0.0691698	−	0.997605i	$-0.522035\pi$
$557$	6.79813e6	−	6.79813e6i	0.928435	−	0.928435i	0.997605	+	0.0691698i	$0.0220350\pi$
$558$	656126.	−	640564.i	0.0892076	−	0.0870917i
$559$			7.19213e6i			0.973482i
$560$	−723290.	−	309189.i	−0.0974636	−	0.0416634i
$561$	6.93445e6	+	7.01818e6i	0.930261	+	0.941493i
$562$	1.09911e6	+	1.09911e6i	0.146792	+	0.146792i
$563$	−9.18684e6	−	9.18684e6i	−1.22150	−	1.22150i	−0.967097	−	0.254408i	$-0.918120\pi$
$563$	−9.18684e6	−	9.18684e6i	−1.22150	−	1.22150i	−0.254408	−	0.967097i	$-0.581880\pi$
$564$	704387.	+	712891.i	0.0932424	+	0.0943682i
$565$	9.89942e6	+	4.23177e6i	1.30463	+	0.557700i
$566$			992593.i			0.130236i
$567$	−653096.	−	685225.i	−0.0853138	−	0.0895108i
$568$	464313.	−	464313.i	0.0603866	−	0.0603866i
$569$	3.22815e6			0.417996			0.208998	−	0.977916i	$-0.432980\pi$
$569$	3.22815e6			0.417996			0.208998	+	0.977916i	$0.432980\pi$
$570$	−1.99395e6	−	866556.i	−0.257056	−	0.111714i
$571$	−9.43358e6			−1.21084			−0.605420	−	0.795907i	$-0.706995\pi$
$571$	−9.43358e6			−1.21084			−0.605420	+	0.795907i	$0.706995\pi$
$572$	−4.05253e6	+	4.05253e6i	−0.517888	+	0.517888i
$573$	52303.2	−	8.71634e6i	0.00665490	−	1.10904i
$574$		−	128367.i		−	0.0162620i
$575$	−1.08287e6	−	24405.7i	−0.136586	−	0.00307837i
$576$	68923.3	−	5.74284e6i	0.00865585	−	0.721224i
$577$	9.98594e6	+	9.98594e6i	1.24868	+	1.24868i	0.956305	+	0.292370i	$0.0944438\pi$
$577$	9.98594e6	+	9.98594e6i	1.24868	+	1.24868i	0.292370	+	0.956305i	$0.405556\pi$
$578$	1.47529e6	+	1.47529e6i	0.183679	+	0.183679i
$579$	−2.35246e6	+	2.32439e6i	−0.291625	+	0.288146i
$580$	−4.47175e6	−	1.11494e7i	−0.551960	−	1.37621i
$581$		−	695298.i		−	0.0854537i
$582$	−909146.	−	5455.41i	−0.111257	−	0.000667606i
$583$	−6.73682e6	+	6.73682e6i	−0.820887	+	0.820887i
$584$	1.28119e6			0.155447
$585$	−2.87222e6	+	6.50200e6i	−0.346999	+	0.785521i
$586$	−3.47193e6			−0.417663
$587$	−1.08667e7	+	1.08667e7i	−1.30168	+	1.30168i	−0.374419	+	0.927260i	$0.622158\pi$
$587$	−1.08667e7	+	1.08667e7i	−1.30168	+	1.30168i	−0.927260	+	0.374419i	$0.877842\pi$
$588$	−7.85605e6	−	47140.9i	−0.937046	−	0.00562283i
$589$		−	6.08037e6i		−	0.722174i
$590$	−580896.	+	1.35890e6i	−0.0687018	+	0.160715i
$591$	3.71673e6	−	3.67239e6i	0.437716	−	0.432494i
$592$	−2.07410e6	−	2.07410e6i	−0.243235	−	0.243235i
$593$	6.83953e6	+	6.83953e6i	0.798710	+	0.798710i	0.982892	−	0.184182i	$-0.0589636\pi$
$593$	6.83953e6	+	6.83953e6i	0.798710	+	0.798710i	−0.184182	+	0.982892i	$0.558964\pi$
$594$	1.17699e6	+	1.22015e6i	0.136870	+	0.141889i
$595$	−1.46364e6	+	587027.i	−0.169489	+	0.0679775i
$596$		−	1.08934e7i		−	1.25617i
$597$	56341.2	−	9.38928e6i	0.00646979	−	1.07819i
$598$	159581.	−	159581.i	0.0182485	−	0.0182485i
$599$	−1.22951e7			−1.40012			−0.700060	−	0.714084i	$-0.746844\pi$
$599$	−1.22951e7			−1.40012			−0.700060	+	0.714084i	$0.746844\pi$
$600$	3.78404e6	+	108006.i	0.429119	+	0.0122481i
$601$	5.35161e6			0.604364			0.302182	−	0.953250i	$-0.402285\pi$
$601$	5.35161e6			0.604364			0.302182	+	0.953250i	$0.402285\pi$
$602$	−193870.	+	193870.i	−0.0218032	+	0.0218032i
$603$	9.73071e6	+	9.96711e6i	1.08981	+	1.11629i
$604$			5.51276e6i			0.614861i
$605$	−1.64410e6	+	659405.i	−0.182616	+	0.0732426i
$606$	187305.	+	189566.i	0.0207189	+	0.0209691i
$607$	1.03013e7	+	1.03013e7i	1.13480	+	1.13480i	0.989368	+	0.145433i	$0.0464576\pi$
$607$	1.03013e7	+	1.03013e7i	1.13480	+	1.13480i	0.145433	+	0.989368i	$0.453542\pi$
$608$	5.07411e6	+	5.07411e6i	0.556674	+	0.556674i
$609$	1.23946e6	+	1.25442e6i	0.135422	+	0.137057i
$610$	−18913.6	+	44244.8i	−0.00205802	+	0.00481435i
$611$			1.10474e6i			0.119717i
$612$	−9.09636e6	−	9.31735e6i	−0.981723	−	1.00557i
$613$	4.89015e6	−	4.89015e6i	0.525619	−	0.525619i	−0.393644	−	0.919263i	$-0.628786\pi$
$613$	4.89015e6	−	4.89015e6i	0.525619	−	0.525619i	0.919263	+	0.393644i	$0.128786\pi$
$614$	−1.25303e6			−0.134134
$615$	−2.05622e6	−	5.21717e6i	−0.219221	−	0.556221i
$616$	−448066.			−0.0475763
$617$	833237.	−	833237.i	0.0881162	−	0.0881162i	−0.661675	−	0.749791i	$-0.730154\pi$
$617$	833237.	−	833237.i	0.0881162	−	0.0881162i	0.749791	+	0.661675i	$0.230154\pi$
$618$	−7475.60	+	1.24581e6i	−0.000787363	+	0.131214i
$619$		−	1.53788e7i		−	1.61323i	−0.591076	−	0.806616i	$-0.701297\pi$
$619$		−	1.53788e7i		−	1.61323i	0.591076	−	0.806616i	$-0.298703\pi$
$620$	1.92168e6	+	4.79134e6i	0.200772	+	0.500585i
$621$	911525.	+	944948.i	0.0948505	+	0.0983284i
$622$	−705358.	−	705358.i	−0.0731027	−	0.0731027i
$623$	−1.20187e6	−	1.20187e6i	−0.124061	−	0.124061i
$624$	5.09304e6	−	5.03228e6i	0.523619	−	0.517373i
$625$	439972.	−	9.75571e6i	0.0450532	−	0.998985i
$626$		−	2.39999e6i		−	0.244779i
$627$	1.12414e7	+	67454.9i	1.14196	+	0.00685243i
$628$	−5.79047e6	+	5.79047e6i	−0.585888	+	0.585888i
$629$	−5.88047e6			−0.592632
$630$	−252690.	+	97843.9i	−0.0253651	+	0.00982160i
$631$	6.50224e6			0.650114			0.325057	−	0.945694i	$-0.394617\pi$
$631$	6.50224e6			0.650114			0.325057	+	0.945694i	$0.394617\pi$
$632$	1.64294e6	−	1.64294e6i	0.163618	−	0.163618i
$633$	1.41101e7	+	84668.6i	1.39965	+	0.00839872i
$634$		−	2.54372e6i		−	0.251331i
$635$	5.12728e6	+	2.19179e6i	0.504606	+	0.215707i
$636$	8.94445e6	−	8.83775e6i	0.876821	−	0.866361i
$637$	−6.12362e6	−	6.12362e6i	−0.597943	−	0.597943i
$638$	−2.23323e6	−	2.23323e6i	−0.217211	−	0.217211i
$639$	−24641.2	+	2.05316e6i	−0.00238731	+	0.198916i
$640$	−7.39861e6	−	3.16273e6i	−0.714003	−	0.305219i
$641$			3.82299e6i			0.367501i	0.982973	+	0.183750i	$0.0588238\pi$
$641$			3.82299e6i			0.367501i	−0.982973	+	0.183750i	$0.941176\pi$
$642$	−7774.71	+	1.29566e6i	−0.000744469	+	0.124066i
$643$	−7.11939e6	+	7.11939e6i	−0.679071	+	0.679071i	−0.959790	−	0.280719i	$-0.909427\pi$
$643$	−7.11939e6	+	7.11939e6i	−0.679071	+	0.679071i	0.280719	+	0.959790i	$0.409427\pi$
$644$	−169201.			−0.0160764
$645$	−4.77392e6	+	1.09848e7i	−0.451831	+	1.03967i
$646$	4.39031e6			0.413917
$647$	6.21104e6	−	6.21104e6i	0.583316	−	0.583316i	−0.352497	−	0.935813i	$-0.614667\pi$
$647$	6.21104e6	−	6.21104e6i	0.583316	−	0.583316i	0.935813	+	0.352497i	$0.114667\pi$
$648$	−3.16591e6	−	3.32165e6i	−0.296184	−	0.310754i
$649$		−	7.64144e6i		−	0.712137i
$650$	1.40600e6	+	1.47084e6i	0.130527	+	0.136547i
$651$	−532642.	−	539073.i	−0.0492587	−	0.0498534i
$652$	1.15505e7	+	1.15505e7i	1.06410	+	1.06410i
$653$	−752240.	−	752240.i	−0.0690356	−	0.0690356i	0.671746	−	0.740782i	$-0.265545\pi$
$653$	−752240.	−	752240.i	−0.0690356	−	0.0690356i	−0.740782	+	0.671746i	$0.765545\pi$
$654$	787445.	+	796952.i	0.0719906	+	0.0728598i
$655$	6.50957e6	+	1.62303e7i	0.592855	+	1.47817i
$656$			5.64852e6i			0.512478i
$657$	−2.86666e6	+	2.79867e6i	−0.259097	+	0.252952i
$658$	−29779.1	+	29779.1i	−0.00268131	+	0.00268131i
$659$	−1.49063e7			−1.33707			−0.668536	−	0.743679i	$-0.733079\pi$
$659$	−1.49063e7			−1.33707			−0.668536	+	0.743679i	$0.733079\pi$
$660$	−8.87954e6	+	3.49965e6i	−0.793470	+	0.312726i
$661$	−1.55144e7			−1.38112			−0.690558	−	0.723277i	$-0.742635\pi$
$661$	−1.55144e7			−1.38112			−0.690558	+	0.723277i	$0.742635\pi$
$662$	147463.	−	147463.i	0.0130779	−	0.0130779i
$663$	86130.0	−	1.43536e7i	0.00760976	−	1.26817i
$664$		−	3.37048e6i		−	0.296669i
$665$	−706269.	+	1.65218e6i	−0.0619321	+	0.144878i
$666$	−1.01037e6	−	12126.1i	−0.0882666	−	0.00105934i
$667$	−1.72953e6	−	1.72953e6i	−0.150526	−	0.150526i
$668$	6.45958e6	+	6.45958e6i	0.560097	+	0.560097i
$669$	−5.10116e6	+	5.04031e6i	−0.440660	+	0.435403i
$670$	3.70082e6	−	1.48430e6i	0.318501	−	0.127743i
$671$		−	248800.i		−	0.0213326i
$672$	894352.	+	5366.64i	0.0763986	+	0.000458437i
$673$	−9.88243e6	+	9.88243e6i	−0.841058	+	0.841058i	−0.988997	−	0.147938i	$-0.952736\pi$
$673$	−9.88243e6	+	9.88243e6i	−0.841058	+	0.841058i	0.147938	+	0.988997i	$0.452736\pi$
$674$	1.01836e6			0.0863475
$675$	−8.70270e6	+	8.02428e6i	−0.735181	+	0.677871i
$676$	−2.96851e6			−0.249845
$677$	9.07764e6	−	9.07764e6i	0.761204	−	0.761204i	−0.215336	−	0.976540i	$-0.569085\pi$
$677$	9.07764e6	−	9.07764e6i	0.761204	−	0.761204i	0.976540	+	0.215336i	$0.0690847\pi$
$678$	−3.73559e6	−	22415.7i	−0.312094	−	0.00187274i
$679$			751382.i			0.0625441i
$680$	−7.09503e6	+	2.84563e6i	−0.588413	+	0.235997i
$681$	−1.12594e6	+	1.11250e6i	−0.0930349	+	0.0919250i
$682$	959702.	+	959702.i	0.0790088	+	0.0790088i
$683$	−1.17688e7	−	1.17688e7i	−0.965341	−	0.965341i	0.0340786	−	0.999419i	$-0.489150\pi$
$683$	−1.17688e7	−	1.17688e7i	−0.965341	−	0.965341i	−0.999419	+	0.0340786i	$0.989150\pi$
$684$	−1.48356e7	−	178051.i	−1.21245	−	0.0145514i
$685$	1.37200e6	−	3.20954e6i	0.111719	−	0.261347i
$686$		−	665396.i		−	0.0539846i
$687$	−26066.9	+	4.34405e6i	−0.00210716	+	0.351159i
$688$	8.53083e6	−	8.53083e6i	0.687100	−	0.687100i
$689$	1.38608e7			1.11235
$690$	349659.	−	137809.i	0.0279590	−	0.0110193i
$691$	1.13832e7			0.906920			0.453460	−	0.891277i	$-0.350189\pi$
$691$	1.13832e7			0.906920			0.453460	+	0.891277i	$0.350189\pi$
$692$	1.60524e6	−	1.60524e6i	0.127431	−	0.127431i
$693$	1.00255e6	−	978767.i	0.0792996	−	0.0774188i
$694$			97533.0i			0.00768693i
$695$	215964.	+	538463.i	0.0169597	+	0.0422858i
$696$	6.00832e6	+	6.08086e6i	0.470143	+	0.475819i
$697$	8.00730e6	+	8.00730e6i	0.624316	+	0.624316i
$698$	1.02754e6	+	1.02754e6i	0.0798290	+	0.0798290i
$699$	1.11004e6	+	1.12344e6i	0.0859300	+	0.0869674i
$700$	34373.5	−	1.52514e6i	0.00265142	−	0.117642i
$701$		−	1.43910e7i		−	1.10611i	−0.833146	−	0.553053i	$-0.813463\pi$
$701$		−	1.43910e7i		−	1.10611i	0.833146	−	0.553053i	$-0.186537\pi$
$702$	44397.2	−	2.46604e6i	0.00340027	−	0.188867i
$703$	−4.73779e6	+	4.73779e6i	−0.361566	+	0.361566i
$704$	8.50074e6			0.646436
$705$	−733291.	+	1.68731e6i	−0.0555653	+	0.127856i
$706$	−400530.			−0.0302429
$707$	155736.	−	155736.i	0.0117177	−	0.0117177i
$708$	−60515.9	+	1.00850e7i	−0.00453719	+	0.756123i
$709$		−	3.32746e6i		−	0.248598i	−0.992245	−	0.124299i	$-0.960332\pi$
$709$		−	3.32746e6i		−	0.248598i	0.992245	−	0.124299i	$-0.0396681\pi$
$710$	540460.	+	231034.i	0.0402362	+	0.0172000i
$711$	−87191.2	+	7.26496e6i	−0.00646843	+	0.538963i
$712$	−5.82609e6	−	5.82609e6i	−0.430703	−	0.430703i
$713$	743243.	+	743243.i	0.0547529	+	0.0547529i
$714$	389235.	−	384592.i	0.0285737	−	0.0282328i
$715$	−9.67412e6	−	4.13546e6i	−0.707695	−	0.302523i
$716$			1.59687e7i			1.16409i
$717$	−1.68449e7	−	101079.i	−1.22369	−	0.00734283i
$718$	−2.66746e6	+	2.66746e6i	−0.193102	+	0.193102i
$719$	4.31981e6			0.311632			0.155816	−	0.987786i	$-0.450199\pi$
$719$	4.31981e6			0.311632			0.155816	+	0.987786i	$0.450199\pi$
$720$	1.11191e7	−	4.30540e6i	0.799351	−	0.309516i
$721$	1.02963e6			0.0737635
$722$	1.35854e6	−	1.35854e6i	0.0969903	−	0.0969903i
$723$	5.33692e6	+	32024.6i	0.379704	+	0.00227845i
$724$			4.99378e6i			0.354065i
$725$	1.59409e7	−	1.52381e7i	1.12633	−	1.07668i
$726$	437226.	−	432011.i	0.0307868	−	0.0304195i
$727$	−1.03718e7	−	1.03718e7i	−0.727811	−	0.727811i	0.242373	−	0.970183i	$-0.422074\pi$
$727$	−1.03718e7	−	1.03718e7i	−0.727811	−	0.727811i	−0.970183	+	0.242373i	$0.922074\pi$
$728$	460943.	+	460943.i	0.0322343	+	0.0322343i
$729$	1.43396e7	+	516494.i	0.999352	+	0.0359953i
$730$	426904.	+	1.06440e6i	0.0296499	+	0.0739262i
$731$		−	2.41865e7i		−	1.67409i
$732$	−1970.36	+	328361.i	−0.000135915	+	0.0226503i
$733$	6.93586e6	−	6.93586e6i	0.476804	−	0.476804i	−0.427304	−	0.904108i	$-0.640537\pi$
$733$	6.93586e6	−	6.93586e6i	0.476804	−	0.476804i	0.904108	+	0.427304i	$0.140537\pi$
$734$	5.51902e6			0.378113
$735$	−5.28818e6	−	1.34175e7i	−0.361067	−	0.916124i
$736$	−1.24048e6			−0.0844104
$737$	−1.45787e7	+	1.45787e7i	−0.988666	+	0.988666i
$738$	1.35929e6	+	1.39231e6i	0.0918695	+	0.0941015i
$739$			5.27869e6i			0.355562i	0.984070	+	0.177781i	$0.0568919\pi$
$739$			5.27869e6i			0.355562i	−0.984070	+	0.177781i	$0.943108\pi$
$740$	2.23602e6	−	5.23074e6i	0.150105	−	0.351143i
$741$	−1.14950e7	−	1.16338e7i	−0.769068	−	0.778354i
$742$	373631.	+	373631.i	0.0249134	+	0.0249134i
$743$	1.42934e7	+	1.42934e7i	0.949871	+	0.949871i	0.998802	−	0.0489311i	$-0.0155815\pi$
$743$	1.42934e7	+	1.42934e7i	0.949871	+	0.949871i	−0.0489311	+	0.998802i	$0.515581\pi$
$744$	−2.58200e6	−	2.61318e6i	−0.171011	−	0.173076i
$745$	1.85604e7	−	7.44410e6i	1.22517	−	0.491384i
$746$			5.45518e6i			0.358891i
$747$	7.36257e6	+	7.54144e6i	0.482756	+	0.494485i
$748$	1.36283e7	−	1.36283e7i	0.890610	−	0.890610i
$749$	1.07082e6			0.0697450
$750$	1.17114e6	+	3.17973e6i	0.0760250	+	0.206413i
$751$	−4.87198e6			−0.315214			−0.157607	−	0.987502i	$-0.550378\pi$
$751$	−4.87198e6			−0.315214			−0.157607	+	0.987502i	$0.550378\pi$
$752$	1.31037e6	−	1.31037e6i	0.0844983	−	0.0844983i
$753$	−18313.8	+	3.05200e6i	−0.00117704	+	0.196154i
$754$			4.59481e6i			0.294333i
$755$	−9.39277e6	+	3.76719e6i	−0.599689	+	0.240520i
$756$	−1.33089e6	+	1.28382e6i	−0.0846910	+	0.0816955i
$757$	−4.56529e6	−	4.56529e6i	−0.289554	−	0.289554i	0.547350	−	0.836904i	$-0.315637\pi$
$757$	−4.56529e6	−	4.56529e6i	−0.289554	−	0.289554i	−0.836904	+	0.547350i	$0.815637\pi$
$758$	−3.31406e6	−	3.31406e6i	−0.209501	−	0.209501i
$759$	−1.38235e6	+	1.36586e6i	−0.0870992	+	0.0860601i
$760$	−3.42367e6	+	8.00902e6i	−0.215009	+	0.502974i
$761$			2.03979e7i			1.27680i	0.769703	+	0.638402i	$0.220404\pi$
$761$			2.03979e7i			1.27680i	−0.769703	+	0.638402i	$0.779596\pi$
$762$	−1.93480e6	−	11609.9i	−0.120712	−	0.000724341i
$763$	654729.	−	654729.i	0.0407146	−	0.0407146i
$764$	−1.70275e7			−1.05540
$765$	9.65903e6	−	2.18657e7i	0.596733	−	1.35086i
$766$	−1.81260e6			−0.111617
$767$	−7.86103e6	+	7.86103e6i	−0.482493	+	0.482493i
$768$	−8.99764e6	−	53991.2i	−0.550460	−	0.00330308i
$769$			2.14987e7i			1.31098i	0.755203	+	0.655490i	$0.227538\pi$
$769$			2.14987e7i			1.31098i	−0.755203	+	0.655490i	$0.772462\pi$
$770$	−149299.	−	372249.i	−0.00907468	−	0.0226259i
$771$	−9.63204e6	+	9.51713e6i	−0.583555	+	0.576594i
$772$	4.56813e6	+	4.56813e6i	0.275864	+	0.275864i
$773$	−1.03836e7	−	1.03836e7i	−0.625029	−	0.625029i	0.321784	−	0.946813i	$-0.395718\pi$
$773$	−1.03836e7	−	1.03836e7i	−0.625029	−	0.625029i	−0.946813	+	0.321784i	$0.895718\pi$
$774$	49874.9	−	4.15569e6i	0.00299247	−	0.249339i
$775$	−6.85039e6	+	6.54841e6i	−0.409695	+	0.391635i
$776$			3.64236e6i			0.217134i
$777$	−5010.93	+	835074.i	−0.000297760	+	0.0496218i
$778$	2.58056e6	−	2.58056e6i	0.152850	−	0.152850i
$779$	1.29027e7			0.761792
$780$	1.27349e7	+	5.53450e6i	0.749480	+	0.325718i
$781$	−3.03915e6			−0.178289
$782$	−536655.	+	536655.i	−0.0313818	+	0.0313818i
$783$	−2.67268e7	−	481175.i	−1.55791	−	0.0280478i
$784$			1.45269e7i			0.844076i
$785$	−1.38229e7	−	5.90896e6i	−0.800618	−	0.342245i
$786$	−4.26475e6	−	4.31625e6i	−0.246228	−	0.249201i
$787$	−6.79785e6	−	6.79785e6i	−0.391232	−	0.391232i	0.483894	−	0.875126i	$-0.339222\pi$
$787$	−6.79785e6	−	6.79785e6i	−0.391232	−	0.391232i	−0.875126	+	0.483894i	$0.839222\pi$
$788$	−7.21736e6	−	7.21736e6i	−0.414060	−	0.414060i
$789$	6.17758e6	+	6.25216e6i	0.353285	+	0.357551i
$790$	1.91238e6	+	817498.i	0.109020	+	0.0466035i
$791$			3.08735e6i			0.175447i
$792$	4.85988e6	−	4.74461e6i	0.275304	−	0.268774i
$793$	−255950.	+	255950.i	−0.0144535	+	0.0144535i
$794$	−4.11709e6			−0.231760
$795$	2.11702e7	+	9.20040e6i	1.18798	+	0.516284i
$796$	−1.83420e7			−1.02604
$797$	−1.32048e7	+	1.32048e7i	−0.736354	+	0.736354i	−0.971870	−	0.235516i	$-0.924322\pi$
$797$	−1.32048e7	+	1.32048e7i	−0.736354	+	0.736354i	0.235516	+	0.971870i	$0.424322\pi$
$798$	3741.12	−	623458.i	0.000207967	−	0.0346577i
$799$		−	3.71513e6i		−	0.205877i
$800$	252006.	−	1.11814e7i	0.0139215	−	0.617690i
$801$	2.57625e7	+	309192.i	1.41875	+	0.0170273i
$802$	3.13295e6	+	3.13295e6i	0.171996	+	0.171996i
$803$	−4.19301e6	−	4.19301e6i	−0.229476	−	0.229476i
$804$	1.93561e7	−	1.91252e7i	1.05603	−	1.04343i
$805$	−115625.	−	288289.i	−0.00628872	−	0.0156797i
$806$		−	1.97456e6i		−	0.107062i
$807$	2.01495e7	+	120909.i	1.08913	+	0.00653542i
$808$	754938.	−	754938.i	0.0406802	−	0.0406802i
$809$	−9.33642e6			−0.501544			−0.250772	−	0.968046i	$-0.580684\pi$
$809$	−9.33642e6			−0.501544			−0.250772	+	0.968046i	$0.580684\pi$
$810$	1.70469e6	−	3.73701e6i	0.0912920	−	0.200130i
$811$	2.41694e7			1.29037			0.645184	−	0.764028i	$-0.276781\pi$
$811$	2.41694e7			1.29037			0.645184	+	0.764028i	$0.276781\pi$
$812$	2.43591e6	−	2.43591e6i	0.129650	−	0.129650i
$813$	1.22462e7	+	73484.6i	0.649794	+	0.00389915i
$814$		−	1.49559e6i		−	0.0791136i
$815$	−1.17868e7	+	2.75731e7i	−0.621589	+	1.45409i
$816$	−1.71274e7	+	1.69231e7i	−0.900465	+	0.889723i
$817$	−1.94866e7	−	1.94866e7i	−1.02137	−	1.02137i
$818$	−2.63109e6	−	2.63109e6i	−0.137484	−	0.137484i
$819$	−2.03825e6	−	24462.3i	−0.106181	−	0.00127435i
$820$	−1.01673e7	+	4.07785e6i	−0.528046	+	0.211786i
$821$			2.01715e7i			1.04443i	0.852813	+	0.522217i	$0.174895\pi$
$821$			2.01715e7i			1.04443i	−0.852813	+	0.522217i	$0.825105\pi$
$822$	−7267.52	+	1.21114e6i	−0.000375152	+	0.0625191i
$823$	1.86980e7	−	1.86980e7i	0.962269	−	0.962269i	−0.0370443	−	0.999314i	$-0.511794\pi$
$823$	1.86980e7	−	1.86980e7i	0.962269	−	0.962269i	0.999314	+	0.0370443i	$0.0117943\pi$
$824$	4.99115e6			0.256084
$825$	−1.20307e7	−	1.27376e7i	−0.615397	−	0.651559i
$826$	−423802.			−0.0216129
$827$	2.18328e7	−	2.18328e7i	1.11006	−	1.11006i	0.116916	−	0.993142i	$-0.462699\pi$
$827$	2.18328e7	−	2.18328e7i	1.11006	−	1.11006i	0.993142	−	0.116916i	$-0.0373008\pi$
$828$	1.83521e6	−	1.79169e6i	0.0930274	−	0.0908209i
$829$			1.09016e7i			0.550941i	0.961310	+	0.275470i	$0.0888336\pi$
$829$			1.09016e7i			0.550941i	−0.961310	+	0.275470i	$0.911166\pi$
$830$	2.80016e6	−	1.12307e6i	0.141087	−	0.0565865i
$831$	−2.40549e7	−	2.43453e7i	−1.20837	−	1.22296i
$832$	−8.74504e6	−	8.74504e6i	−0.437979	−	0.437979i
$833$	2.05932e7	+	2.05932e7i	1.02828	+	1.02828i
$834$	−141489.	−	143197.i	−0.00704381	−	0.00712886i
$835$	−6.59176e6	+	1.54202e7i	−0.327179	+	0.765373i
$836$		−	2.19601e7i		−	1.08672i
$837$	1.14855e7	+	206779.i	0.566678	+	0.0102022i
$838$	−486549.	+	486549.i	−0.0239341	+	0.0239341i
$839$	2.66932e7			1.30917			0.654585	−	0.755989i	$-0.272844\pi$
$839$	2.66932e7			1.30917			0.654585	+	0.755989i	$0.272844\pi$
$840$	398057.	+	1.00998e6i	0.0194647	+	0.0493870i
$841$	2.92872e7			1.42787
$842$	−4.89309e6	+	4.89309e6i	−0.237850	+	0.237850i
$843$	−116845.	+	1.94723e7i	−0.00566294	+	0.943731i
$844$		−	2.75641e7i		−	1.33195i
$845$	−2.02855e6	−	5.05780e6i	−0.0977338	−	0.243680i
$846$	7660.97	−	638329.i	0.000368008	−	0.0306633i
$847$	−359199.	−	359199.i	−0.0172039	−	0.0172039i
$848$	−1.64408e7	−	1.64408e7i	−0.785115	−	0.785115i
$849$	−8.84534e6	+	8.73982e6i	−0.421158	+	0.416134i
$850$	−4.72825e6	−	4.94629e6i	−0.224467	−	0.234819i
$851$		−	1.15826e6i		−	0.0548255i
$852$	4.01100e6	+	24068.4i	0.189302	+	0.00113592i
$853$	−1.62298e7	+	1.62298e7i	−0.763729	+	0.763729i	−0.976994	−	0.213265i	$-0.931590\pi$
$853$	−1.62298e7	+	1.62298e7i	−0.763729	+	0.763729i	0.213265	+	0.976994i	$0.431590\pi$
$854$	−13798.7			−0.000647432
$855$	−9.83467e6	−	2.53989e7i	−0.460092	−	1.18823i
$856$	5.19086e6			0.242133
$857$	−1.20256e7	+	1.20256e7i	−0.559313	+	0.559313i	−0.929112	−	0.369799i	$-0.879427\pi$
$857$	−1.20256e7	+	1.20256e7i	−0.559313	+	0.559313i	0.369799	+	0.929112i	$0.379427\pi$
$858$	3.65057e6	+	21905.6i	0.169294	+	0.00101587i
$859$		−	8.22165e6i		−	0.380169i	−0.981768	−	0.190084i	$-0.939124\pi$
$859$		−	8.22165e6i		−	0.380169i	0.981768	−	0.190084i	$-0.0608761\pi$
$860$	2.15142e7	+	9.19679e6i	0.991924	+	0.424024i
$861$	1.14392e6	−	1.13028e6i	0.0525883	−	0.0519610i
$862$	−2.79975e6	−	2.79975e6i	−0.128337	−	0.128337i
$863$	1.99274e7	+	1.99274e7i	0.910803	+	0.910803i	0.996335	−	0.0855327i	$-0.0272592\pi$
$863$	1.99274e7	+	1.99274e7i	0.910803	+	0.910803i	−0.0855327	+	0.996335i	$0.527259\pi$
$864$	−9.75728e6	+	9.41216e6i	−0.444677	+	0.428948i
$865$	3.83200e6	+	1.63809e6i	0.174135	+	0.0744385i
$866$		−	891970.i		−	0.0404162i
$867$	−156837.	+	2.61369e7i	−0.00708598	+	1.18088i
$868$	−1.04680e6	+	1.04680e6i	−0.0471591	+	0.0471591i
$869$	−1.07538e7			−0.483075
$870$	−3.04990e6	+	7.01784e6i	−0.136611	+	0.314344i
$871$	2.99953e7			1.33970
$872$	3.17382e6	−	3.17382e6i	0.141349	−	0.141349i
$873$	−7.95645e6	−	8.14975e6i	−0.353333	−	0.361917i
$874$			864747.i			0.0382922i
$875$	2.62205e6	−	983648.i	0.115777	−	0.0434330i
$876$	5.50063e6	+	5.56704e6i	0.242188	+	0.245112i
$877$	6.32074e6	+	6.32074e6i	0.277504	+	0.277504i	0.832112	−	0.554608i	$-0.187132\pi$
$877$	6.32074e6	+	6.32074e6i	0.277504	+	0.277504i	−0.554608	+	0.832112i	$0.687132\pi$
$878$	3.76868e6	+	3.76868e6i	0.164988	+	0.164988i
$879$	−3.05704e7	−	3.09395e7i	−1.33453	−	1.35065i
$880$	6.56959e6	+	1.63800e7i	0.285977	+	0.713029i
$881$		−	3.32918e7i		−	1.44510i	−0.691319	−	0.722550i	$-0.742970\pi$
$881$		−	3.32918e7i		−	1.44510i	0.691319	−	0.722550i	$-0.257030\pi$
$882$	3.49583e6	+	3.58076e6i	0.151314	+	0.154990i
$883$	−5.57402e6	+	5.57402e6i	−0.240584	+	0.240584i	−0.817092	−	0.576508i	$-0.804415\pi$
$883$	−5.57402e6	+	5.57402e6i	−0.240584	+	0.240584i	0.576508	+	0.817092i	$0.304415\pi$
$884$	−2.80399e7			−1.20683
$885$	−1.72244e7	+	6.78856e6i	−0.739241	+	0.291353i
$886$	−3.50924e6			−0.150186
$887$	2.79973e7	−	2.79973e7i	1.19483	−	1.19483i	0.219141	−	0.975693i	$-0.429674\pi$
$887$	2.79973e7	−	2.79973e7i	1.19483	−	1.19483i	0.975693	−	0.219141i	$-0.0703256\pi$
$888$	−24290.7	+	4.04805e6i	−0.00103373	+	0.172272i
$889$			1.59906e6i			0.0678593i
$890$	2.89896e6	−	6.78156e6i	0.122678	−	0.286982i
$891$	−509712.	+	2.12321e7i	−0.0215095	+	0.895980i
$892$	9.90573e6	+	9.90573e6i	0.416845	+	0.416845i
$893$	−2.99322e6	−	2.99322e6i	−0.125606	−	0.125606i
$894$	−4.93590e6	+	4.87701e6i	−0.206549	+	0.204085i
$895$	−2.72078e7	+	1.09123e7i	−1.13536	+	0.455365i
$896$		−	2.30742e6i		−	0.0960189i
$897$	2.82719e6	+	16964.8i	0.117321	+	0.000703992i
$898$	461093.	−	461093.i	0.0190809	−	0.0190809i
$899$	−2.14002e7			−0.883119
$900$	1.57770e7	+	1.69061e7i	0.649258	+	0.695725i
$901$	−4.66128e7			−1.91290
$902$	−2.03651e6	+	2.03651e6i	−0.0833432	+	0.0833432i
$903$	−3.43468e6	−	20610.1i	−0.140174	−	0.000841124i
$904$			1.49661e7i			0.609097i
$905$	−8.50852e6	+	3.41255e6i	−0.345329	+	0.138502i
$906$	2.49788e6	−	2.46809e6i	0.101100	−	0.0998941i
$907$	−4.07896e6	−	4.07896e6i	−0.164638	−	0.164638i	0.619980	−	0.784618i	$-0.287141\pi$
$907$	−4.07896e6	−	4.07896e6i	−0.164638	−	0.164638i	−0.784618	+	0.619980i	$0.787141\pi$
$908$	2.18641e6	+	2.18641e6i	0.0880068	+	0.0880068i
$909$	−40064.7	+	3.33827e6i	−0.00160824	+	0.134002i
$910$	−229357.	+	536536.i	−0.00918137	+	0.0214781i
$911$		−	1.63280e7i		−	0.651833i	−0.945399	−	0.325917i	$-0.894327\pi$
$911$		−	1.63280e7i		−	0.651833i	0.945399	−	0.325917i	$-0.105673\pi$
$912$	−164620.	+	2.74339e7i	−0.00655382	+	1.09220i
$913$	−1.10307e7	+	1.10307e7i	−0.437952	+	0.437952i
$914$	1.37713e6			0.0545268
$915$	−560815.	+	221031.i	−0.0221446	+	0.00872772i
$916$	8.48615e6			0.334174
$917$	−3.54597e6	+	3.54597e6i	−0.139255	+	0.139255i
$918$	−149304.	+	8.29306e6i	−0.00584743	+	0.324794i
$919$		−	3.57465e7i		−	1.39619i	−0.716005	−	0.698095i	$-0.754031\pi$
$919$		−	3.57465e7i		−	1.39619i	0.716005	−	0.698095i	$-0.245969\pi$
$920$	−560497.	−	1.39749e6i	−0.0218325	−	0.0544351i
$921$	−1.10329e7	−	1.11662e7i	−0.428590	−	0.433765i
$922$	−1.51549e6	−	1.51549e6i	−0.0587119	−	0.0587119i
$923$	3.12649e6	+	3.12649e6i	0.120796	+	0.120796i
$924$	−1.92371e6	−	1.94694e6i	−0.0741243	−	0.0750192i
$925$	1.04403e7	+	235303.i	0.401196	+	0.00904218i
$926$			8.58106e6i			0.328862i
$927$	−1.11677e7	+	1.09028e7i	−0.426838	+	0.416714i
$928$	1.78586e7	−	1.78586e7i	0.680735	−	0.680735i
$929$	6.93935e6			0.263803			0.131901	−	0.991263i	$-0.457892\pi$
$929$	6.93935e6			0.263803			0.131901	+	0.991263i	$0.457892\pi$
$930$	1.31066e6	−	3.01583e6i	0.0496914	−	0.114340i
$931$	3.31831e7			1.25471
$932$	2.18156e6	−	2.18156e6i	0.0822673	−	0.0822673i
$933$	74985.7	−	1.24964e7i	0.00282016	−	0.469981i
$934$		−	9.41515e6i		−	0.353151i
$935$	3.25332e7	+	1.39072e7i	1.21702	+	0.520247i
$936$	−9.88050e6	−	118582.i	−0.368629	−	0.00442414i
$937$	1.00667e7	+	1.00667e7i	0.374575	+	0.374575i	0.869141	−	0.494565i	$-0.164673\pi$
$937$	1.00667e7	+	1.00667e7i	0.374575	+	0.374575i	−0.494565	+	0.869141i	$0.664673\pi$
$938$	808549.	+	808549.i	0.0300054	+	0.0300054i
$939$	2.13872e7	−	2.11320e7i	0.791569	−	0.782126i
$940$	3.30465e6	+	1.41266e6i	0.121985	+	0.0521457i
$941$			1.13958e7i			0.419536i	0.977751	+	0.209768i	$0.0672709\pi$
$941$			1.13958e7i			0.419536i	−0.977751	+	0.209768i	$0.932729\pi$
$942$	5.21613e6	+	31299.9i	0.191523	+	0.00114925i
$943$	−1.57718e6	+	1.57718e6i	−0.0577566	+	0.0577566i
$944$	1.86485e7			0.681104
$945$	−3.09687e6	−	1.39029e6i	−0.112809	−	0.0506438i
$946$	6.15139e6			0.223483
$947$	2.70855e7	−	2.70855e7i	0.981436	−	0.981436i	−0.0183949	−	0.999831i	$-0.505856\pi$
$947$	2.70855e7	−	2.70855e7i	0.981436	−	0.981436i	0.999831	+	0.0183949i	$0.00585562\pi$
$948$	1.41927e7	+	85164.4i	0.512913	+	0.00307778i
$949$			8.62701e6i			0.310953i
$950$	−7.79460e6	−	175675.i	−0.280211	−	0.00631540i
$951$	2.26680e7	−	2.23976e7i	0.812759	−	0.803063i
$952$	−1.55011e6	−	1.55011e6i	−0.0554332	−	0.0554332i
$953$	−1.31117e7	−	1.31117e7i	−0.467656	−	0.467656i	0.433498	−	0.901154i	$-0.357279\pi$
$953$	−1.31117e7	−	1.31117e7i	−0.467656	−	0.467656i	−0.901154	+	0.433498i	$0.857279\pi$
$954$	−8.00893e6	−	96120.1i	−0.284907	−	0.00341935i
$955$	−1.16359e7	−	2.90118e7i	−0.412848	−	1.02936i
$956$			3.29066e7i			1.16450i
$957$	237412.	−	3.95647e7i	0.00837958	−	1.39646i
$958$	2.36053e6	−	2.36053e6i	0.0830990	−	0.0830990i
$959$	1.00097e6			0.0351458
$960$	−7.55196e6	−	1.91613e7i	−0.264473	−	0.671039i
$961$	−1.94327e7			−0.678772
$962$	−1.53857e6	+	1.53857e6i	−0.0536018	+	0.0536018i
$963$	−1.16145e7	+	1.13390e7i	−0.403585	+	0.394013i
$964$		−	1.04257e7i		−	0.361338i
$965$	−4.66161e6	+	1.09050e7i	−0.161145	+	0.376969i
$966$	75752.0	+	76666.6i	0.00261187	+	0.00264340i
$967$	−1.94460e7	−	1.94460e7i	−0.668751	−	0.668751i	0.288676	−	0.957427i	$-0.406785\pi$
$967$	−1.94460e7	−	1.94460e7i	−0.668751	−	0.668751i	−0.957427	+	0.288676i	$0.906785\pi$
$968$	−1.74123e6	−	1.74123e6i	−0.0597267	−	0.0597267i
$969$	3.86568e7	+	3.91235e7i	1.32256	+	1.33853i
$970$	−3.02603e6	+	1.21366e6i	−0.103263	+	0.0414161i
$971$			1.06222e7i			0.361548i	0.983525	+	0.180774i	$0.0578603\pi$
$971$			1.06222e7i			0.361548i	−0.983525	+	0.180774i	$0.942140\pi$
$972$	840853.	−	2.80176e7i	0.0285466	−	0.951186i
$973$	−117642.	+	117642.i	−0.00398366	+	0.00398366i
$974$	8.14668e6			0.275159
$975$	−727265.	+	2.54801e7i	−0.0245009	+	0.858400i
$976$	607182.			0.0204030
$977$	−3.25074e7	+	3.25074e7i	−1.08955	+	1.08955i	−0.0939726	+	0.995575i	$0.529957\pi$
$977$	−3.25074e7	+	3.25074e7i	−1.08955	+	1.08955i	−0.995575	+	0.0939726i	$0.970043\pi$
$978$	62435.1	−	1.04048e7i	0.00208729	−	0.347847i
$979$			3.81346e7i			1.27163i
$980$	−2.61483e7	+	1.04874e7i	−0.869719	+	0.348822i
$981$	−168435.	+	1.40344e7i	−0.00558805	+	0.465609i
$982$	4.93154e6	+	4.93154e6i	0.163194	+	0.163194i
$983$	−342472.	−	342472.i	−0.0113042	−	0.0113042i	0.701432	−	0.712736i	$-0.252544\pi$
$983$	−342472.	−	342472.i	−0.0113042	−	0.0113042i	−0.712736	+	0.701432i	$0.752544\pi$
$984$	5.54522e6	−	5.47907e6i	0.182571	−	0.180393i
$985$	7.36505e6	−	1.72291e7i	0.241872	−	0.565813i
$986$		−	1.54519e7i		−	0.506163i
$987$	−527579.	−	3165.78i	−0.0172383	−	0.000103440i
$988$	−2.25912e7	+	2.25912e7i	−0.736288	+	0.736288i
$989$	4.76395e6			0.154873
$990$	5.56113e6	+	2.45660e6i	0.180333	+	0.0796610i
$991$	−2.24558e7			−0.726346			−0.363173	−	0.931722i	$-0.618307\pi$
$991$	−2.24558e7			−0.726346			−0.363173	+	0.931722i	$0.618307\pi$
$992$	−7.67453e6	+	7.67453e6i	−0.247612	+	0.247612i
$993$	2.61251e6	+	15676.6i	0.0840786	+	0.000504521i
$994$			168554.i			0.00541096i
$995$	−1.25342e7	−	3.12516e7i	−0.401364	−	1.00072i
$996$	1.46454e7	−	1.44707e7i	0.467793	−	0.462213i
$997$	2.66705e7	+	2.66705e7i	0.849755	+	0.849755i	0.990102	−	0.140347i	$-0.0448220\pi$
$997$	2.66705e7	+	2.66705e7i	0.849755	+	0.849755i	−0.140347	+	0.990102i	$0.544822\pi$
$998$	−3.98429e6	−	3.98429e6i	−0.126627	−	0.126627i
$999$	−8.78832e6	−	9.11056e6i	−0.278607	−	0.288823i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	15.6.e.a.2.4	✓	16
3.2	odd	2	inner	15.6.e.a.2.5	yes	16
5.2	odd	4		75.6.e.e.68.4		16
5.3	odd	4	inner	15.6.e.a.8.5	yes	16
5.4	even	2		75.6.e.e.32.5		16
15.2	even	4		75.6.e.e.68.5		16
15.8	even	4	inner	15.6.e.a.8.4	yes	16
15.14	odd	2		75.6.e.e.32.4		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
15.6.e.a.2.4	✓	16	1.1	even	1	trivial
15.6.e.a.2.5	yes	16	3.2	odd	2	inner
15.6.e.a.8.4	yes	16	15.8	even	4	inner
15.6.e.a.8.5	yes	16	5.3	odd	4	inner
75.6.e.e.32.4		16	15.14	odd	2
75.6.e.e.32.5		16	5.4	even	2
75.6.e.e.68.4		16	5.2	odd	4
75.6.e.e.68.5		16	15.2	even	4

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:	\( N \)	\(=\)	\( 15 = 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	15.e (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.879873 + 0.879873i) q^{2} +(-15.5882 - 0.0935382i) q^{3} +30.4516i q^{4} +(-51.8842 + 20.8094i) q^{5} +(13.7979 - 13.6333i) q^{6} +(-11.3356 - 11.3356i) q^{7} +(-54.9495 - 54.9495i) q^{8} +(242.983 + 2.91618i) q^{9} +O(q^{10})\)	\(q+(-0.879873 + 0.879873i) q^{2} +(-15.5882 - 0.0935382i) q^{3} +30.4516i q^{4} +(-51.8842 + 20.8094i) q^{5} +(13.7979 - 13.6333i) q^{6} +(-11.3356 - 11.3356i) q^{7} +(-54.9495 - 54.9495i) q^{8} +(242.983 + 2.91618i) q^{9} +(27.3419 - 63.9612i) q^{10} +359.671i q^{11} +(2.84839 - 474.686i) q^{12} +(370.007 - 370.007i) q^{13} +19.9477 q^{14} +(810.726 - 319.527i) q^{15} -877.755 q^{16} +(-1244.30 + 1244.30i) q^{17} +(-216.360 + 211.228i) q^{18} +2005.02i q^{19} +(-633.681 - 1579.96i) q^{20} +(175.640 + 177.761i) q^{21} +(-316.465 - 316.465i) q^{22} +(-245.087 - 245.087i) q^{23} +(851.423 + 861.703i) q^{24} +(2258.94 - 2159.36i) q^{25} +651.119i q^{26} +(-3787.38 - 68.1861i) q^{27} +(345.186 - 345.186i) q^{28} +7056.79 q^{29} +(-432.193 + 994.480i) q^{30} -3032.57 q^{31} +(2530.70 - 2530.70i) q^{32} +(33.6430 - 5606.61i) q^{33} -2189.65i q^{34} +(824.022 + 352.250i) q^{35} +(-88.8025 + 7399.22i) q^{36} +(2362.96 + 2362.96i) q^{37} +(-1764.17 - 1764.17i) q^{38} +(-5802.34 + 5733.13i) q^{39} +(3994.48 + 1707.55i) q^{40} -6435.18i q^{41} +(-310.948 - 1.86587i) q^{42} +(-9718.91 + 9718.91i) q^{43} -10952.6 q^{44} +(-12667.6 + 4905.02i) q^{45} +431.291 q^{46} +(-1492.86 + 1492.86i) q^{47} +(13682.6 + 82.1037i) q^{48} -16550.0i q^{49} +(-87.6175 + 3887.54i) q^{50} +(19512.8 - 19280.0i) q^{51} +(11267.3 + 11267.3i) q^{52} +(18730.5 + 18730.5i) q^{53} +(3392.41 - 3272.42i) q^{54} +(-7484.54 - 18661.2i) q^{55} +1245.77i q^{56} +(187.546 - 31254.6i) q^{57} +(-6209.09 + 6209.09i) q^{58} -21245.6 q^{59} +(9730.14 + 24688.0i) q^{60} -691.744 q^{61} +(2668.28 - 2668.28i) q^{62} +(-2721.29 - 2787.40i) q^{63} -23634.8i q^{64} +(-11497.9 + 26897.1i) q^{65} +(4903.51 + 4962.71i) q^{66} +(40533.4 + 40533.4i) q^{67} +(-37891.0 - 37891.0i) q^{68} +(3797.53 + 3843.38i) q^{69} +(-1034.97 + 415.100i) q^{70} +8449.81i q^{71} +(-13191.5 - 13512.0i) q^{72} +(-11657.9 + 11657.9i) q^{73} -4158.21 q^{74} +(-35414.7 + 33449.2i) q^{75} -61056.2 q^{76} +(4077.07 - 4077.07i) q^{77} +(60.9045 - 10149.8i) q^{78} +29899.1i q^{79} +(45541.6 - 18265.6i) q^{80} +(59032.0 + 1417.16i) q^{81} +(5662.15 + 5662.15i) q^{82} +(30668.9 + 30668.9i) q^{83} +(-5413.11 + 5348.54i) q^{84} +(38666.4 - 90452.7i) q^{85} -17102.8i q^{86} +(-110003. - 660.080i) q^{87} +(19763.8 - 19763.8i) q^{88} +106026. q^{89} +(6830.12 - 15461.7i) q^{90} -8388.47 q^{91} +(7463.29 - 7463.29i) q^{92} +(47272.3 + 283.661i) q^{93} -2627.06i q^{94} +(-41723.3 - 104029. i) q^{95} +(-39685.7 + 39212.3i) q^{96} +(-33142.7 - 33142.7i) q^{97} +(14561.9 + 14561.9i) q^{98} +(-1048.87 + 87393.7i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 84 q^{6} - 80 q^{7}+O(q^{10}) \) 16 * q - 84 * q^6 - 80 * q^7	\( 16 q - 84 q^{6} - 80 q^{7} + 1060 q^{10} + 420 q^{12} - 2120 q^{13} - 3000 q^{15} - 452 q^{16} + 6000 q^{18} + 1416 q^{21} + 3380 q^{22} + 9160 q^{25} - 12960 q^{27} - 10900 q^{28} - 13380 q^{30} - 21568 q^{31} + 5760 q^{33} + 61932 q^{36} + 55720 q^{37} + 21480 q^{40} - 103020 q^{42} - 23360 q^{43} - 21240 q^{45} - 151168 q^{46} + 74820 q^{48} + 138816 q^{51} + 204160 q^{52} + 89120 q^{55} - 163800 q^{57} - 163500 q^{58} - 217380 q^{60} - 175168 q^{61} + 143040 q^{63} + 263400 q^{66} + 140320 q^{67} + 385260 q^{70} - 328680 q^{72} - 240320 q^{73} - 199920 q^{75} - 271536 q^{76} + 429960 q^{78} + 326016 q^{81} + 431120 q^{82} + 2440 q^{85} - 331680 q^{87} - 401700 q^{88} - 348360 q^{90} - 487168 q^{91} - 22320 q^{93} + 311748 q^{96} + 440800 q^{97}+O(q^{100}) \) 16 * q - 84 * q^6 - 80 * q^7 + 1060 * q^10 + 420 * q^12 - 2120 * q^13 - 3000 * q^15 - 452 * q^16 + 6000 * q^18 + 1416 * q^21 + 3380 * q^22 + 9160 * q^25 - 12960 * q^27 - 10900 * q^28 - 13380 * q^30 - 21568 * q^31 + 5760 * q^33 + 61932 * q^36 + 55720 * q^37 + 21480 * q^40 - 103020 * q^42 - 23360 * q^43 - 21240 * q^45 - 151168 * q^46 + 74820 * q^48 + 138816 * q^51 + 204160 * q^52 + 89120 * q^55 - 163800 * q^57 - 163500 * q^58 - 217380 * q^60 - 175168 * q^61 + 143040 * q^63 + 263400 * q^66 + 140320 * q^67 + 385260 * q^70 - 328680 * q^72 - 240320 * q^73 - 199920 * q^75 - 271536 * q^76 + 429960 * q^78 + 326016 * q^81 + 431120 * q^82 + 2440 * q^85 - 331680 * q^87 - 401700 * q^88 - 348360 * q^90 - 487168 * q^91 - 22320 * q^93 + 311748 * q^96 + 440800 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more