LMFDB - Embedded newform 50.6.d.a.11.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [50,6,Mod(11,50)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(50, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([8]))

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

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

chi := DirichletCharacter("50.11");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 50 = 2 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	50.d (of order $5$, degree $4$, 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:	$8.01919099065$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$6$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			11.5
Character	$\chi$	$=$	50.11
Dual form			50.6.d.a.41.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-3.23607 + 2.35114i) q^{2} +(5.67913 - 17.4786i) q^{3} +(4.94427 - 15.2169i) q^{4} +(6.69834 - 55.4989i) q^{5} +(22.7165 + 69.9143i) q^{6} -86.1311 q^{7} +(19.7771 + 60.8676i) q^{8} +(-76.6568 - 55.6945i) q^{9} +O(q^{10})$	\(q+(-3.23607 + 2.35114i) q^{2} +(5.67913 - 17.4786i) q^{3} +(4.94427 - 15.2169i) q^{4} +(6.69834 - 55.4989i) q^{5} +(22.7165 + 69.9143i) q^{6} -86.1311 q^{7} +(19.7771 + 60.8676i) q^{8} +(-76.6568 - 55.6945i) q^{9} +(108.810 + 195.347i) q^{10} +(-370.519 + 269.198i) q^{11} +(-237.891 - 172.838i) q^{12} +(-147.354 - 107.059i) q^{13} +(278.726 - 202.506i) q^{14} +(-932.002 - 432.263i) q^{15} +(-207.108 - 150.473i) q^{16} +(-394.287 - 1213.49i) q^{17} +379.012 q^{18} +(-338.184 - 1040.82i) q^{19} +(-811.404 - 376.330i) q^{20} +(-489.150 + 1505.45i) q^{21} +(566.103 - 1742.29i) q^{22} +(-1138.15 + 826.914i) q^{23} +1176.20 q^{24} +(-3035.26 - 743.501i) q^{25} +728.559 q^{26} +(2204.16 - 1601.42i) q^{27} +(-425.855 + 1310.65i) q^{28} +(252.462 - 776.999i) q^{29} +(4032.33 - 792.434i) q^{30} +(1769.12 + 5444.80i) q^{31} +1024.00 q^{32} +(2600.97 + 8004.96i) q^{33} +(4129.02 + 2999.91i) q^{34} +(-576.935 + 4780.18i) q^{35} +(-1226.51 + 891.111i) q^{36} +(-1524.38 - 1107.53i) q^{37} +(3541.51 + 2573.05i) q^{38} +(-2708.08 + 1967.54i) q^{39} +(3510.56 - 689.896i) q^{40} +(-4470.31 - 3247.87i) q^{41} +(-1956.60 - 6021.79i) q^{42} +16377.6 q^{43} +(2264.41 + 6969.14i) q^{44} +(-3604.46 + 3881.31i) q^{45} +(1738.94 - 5351.90i) q^{46} +(8617.72 - 26522.6i) q^{47} +(-3806.25 + 2765.40i) q^{48} -9388.44 q^{49} +(11570.4 - 4730.32i) q^{50} -23449.3 q^{51} +(-2357.67 + 1712.95i) q^{52} +(12317.4 - 37909.1i) q^{53} +(-3367.66 + 10364.6i) q^{54} +(12458.3 + 22366.6i) q^{55} +(-1703.42 - 5242.59i) q^{56} -20112.7 q^{57} +(1009.85 + 3108.00i) q^{58} +(4421.59 + 3212.47i) q^{59} +(-11185.8 + 12045.0i) q^{60} +(-29357.2 + 21329.2i) q^{61} +(-18526.5 - 13460.3i) q^{62} +(6602.54 + 4797.02i) q^{63} +(-3313.73 + 2407.57i) q^{64} +(-6928.69 + 7460.89i) q^{65} +(-27237.7 - 19789.3i) q^{66} +(11469.3 + 35298.8i) q^{67} -20415.0 q^{68} +(7989.57 + 24589.4i) q^{69} +(-9371.88 - 16825.5i) q^{70} +(17440.2 - 53675.5i) q^{71} +(1873.94 - 5767.39i) q^{72} +(69985.6 - 50847.5i) q^{73} +7536.95 q^{74} +(-30233.0 + 48829.7i) q^{75} -17510.2 q^{76} +(31913.2 - 23186.3i) q^{77} +(4137.59 - 12734.2i) q^{78} +(-6465.63 + 19899.2i) q^{79} +(-9738.37 + 10486.4i) q^{80} +(-22587.9 - 69518.3i) q^{81} +22102.4 q^{82} +(10204.4 + 31405.9i) q^{83} +(20489.8 + 14886.7i) q^{84} +(-69988.4 + 13754.1i) q^{85} +(-52999.0 + 38506.0i) q^{86} +(-12147.1 - 8825.36i) q^{87} +(-23713.2 - 17228.7i) q^{88} +(53042.2 - 38537.4i) q^{89} +(2538.75 - 21034.8i) q^{90} +(12691.8 + 9221.12i) q^{91} +(6955.75 + 21407.6i) q^{92} +105214. q^{93} +(34470.9 + 106090. i) q^{94} +(-60029.8 + 11797.1i) q^{95} +(5815.43 - 17898.1i) q^{96} +(26173.2 - 80552.8i) q^{97} +(30381.6 - 22073.5i) q^{98} +43395.7 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 24 q^{2} - 11 q^{3} - 96 q^{4} - 120 q^{5} - 44 q^{6} + 548 q^{7} - 384 q^{8} - 893 q^{9}+O(q^{10}) $ 24 * q - 24 * q^2 - 11 * q^3 - 96 * q^4 - 120 * q^5 - 44 * q^6 + 548 * q^7 - 384 * q^8 - 893 * q^9	\( 24 q - 24 q^{2} - 11 q^{3} - 96 q^{4} - 120 q^{5} - 44 q^{6} + 548 q^{7} - 384 q^{8} - 893 q^{9} + 320 q^{10} - 327 q^{11} - 96 q^{12} - 1161 q^{13} - 948 q^{14} + 760 q^{15} - 1536 q^{16} + 83 q^{17} + 7368 q^{18} - 6250 q^{19} + 2320 q^{20} + 6193 q^{21} + 852 q^{22} + 2069 q^{23} + 2176 q^{24} - 14380 q^{25} + 15976 q^{26} - 18935 q^{27} - 592 q^{28} - 11775 q^{29} - 9840 q^{30} + 2103 q^{31} + 24576 q^{32} - 11747 q^{33} + 972 q^{34} + 33235 q^{35} - 14288 q^{36} + 4148 q^{37} + 14260 q^{38} - 12576 q^{39} + 1600 q^{40} - 26427 q^{41} + 24772 q^{42} + 13024 q^{43} + 3408 q^{44} - 65535 q^{45} - 16964 q^{46} + 29803 q^{47} - 1536 q^{48} + 38368 q^{49} - 14020 q^{50} + 194058 q^{51} - 18576 q^{52} - 29011 q^{53} + 11820 q^{54} - 4185 q^{55} - 2368 q^{56} - 78040 q^{57} - 47100 q^{58} + 31430 q^{59} + 28160 q^{60} - 18362 q^{61} - 15828 q^{62} - 95886 q^{63} - 24576 q^{64} - 193280 q^{65} + 28992 q^{66} - 71657 q^{67} - 10432 q^{68} + 245919 q^{69} - 107460 q^{70} - 153827 q^{71} - 1792 q^{72} + 108264 q^{73} - 27648 q^{74} + 126020 q^{75} + 85920 q^{76} + 96141 q^{77} - 55724 q^{78} + 66670 q^{79} - 33280 q^{80} + 17709 q^{81} - 42408 q^{82} - 30621 q^{83} - 140352 q^{84} - 64895 q^{85} - 94444 q^{86} - 265360 q^{87} - 20928 q^{88} + 351835 q^{89} - 101720 q^{90} + 19323 q^{91} - 67856 q^{92} + 707998 q^{93} + 119212 q^{94} + 158570 q^{95} - 11264 q^{96} + 11058 q^{97} + 18532 q^{98} - 455966 q^{99}+O(q^{100}) \) 24 * q - 24 * q^2 - 11 * q^3 - 96 * q^4 - 120 * q^5 - 44 * q^6 + 548 * q^7 - 384 * q^8 - 893 * q^9 + 320 * q^10 - 327 * q^11 - 96 * q^12 - 1161 * q^13 - 948 * q^14 + 760 * q^15 - 1536 * q^16 + 83 * q^17 + 7368 * q^18 - 6250 * q^19 + 2320 * q^20 + 6193 * q^21 + 852 * q^22 + 2069 * q^23 + 2176 * q^24 - 14380 * q^25 + 15976 * q^26 - 18935 * q^27 - 592 * q^28 - 11775 * q^29 - 9840 * q^30 + 2103 * q^31 + 24576 * q^32 - 11747 * q^33 + 972 * q^34 + 33235 * q^35 - 14288 * q^36 + 4148 * q^37 + 14260 * q^38 - 12576 * q^39 + 1600 * q^40 - 26427 * q^41 + 24772 * q^42 + 13024 * q^43 + 3408 * q^44 - 65535 * q^45 - 16964 * q^46 + 29803 * q^47 - 1536 * q^48 + 38368 * q^49 - 14020 * q^50 + 194058 * q^51 - 18576 * q^52 - 29011 * q^53 + 11820 * q^54 - 4185 * q^55 - 2368 * q^56 - 78040 * q^57 - 47100 * q^58 + 31430 * q^59 + 28160 * q^60 - 18362 * q^61 - 15828 * q^62 - 95886 * q^63 - 24576 * q^64 - 193280 * q^65 + 28992 * q^66 - 71657 * q^67 - 10432 * q^68 + 245919 * q^69 - 107460 * q^70 - 153827 * q^71 - 1792 * q^72 + 108264 * q^73 - 27648 * q^74 + 126020 * q^75 + 85920 * q^76 + 96141 * q^77 - 55724 * q^78 + 66670 * q^79 - 33280 * q^80 + 17709 * q^81 - 42408 * q^82 - 30621 * q^83 - 140352 * q^84 - 64895 * q^85 - 94444 * q^86 - 265360 * q^87 - 20928 * q^88 + 351835 * q^89 - 101720 * q^90 + 19323 * q^91 - 67856 * q^92 + 707998 * q^93 + 119212 * q^94 + 158570 * q^95 - 11264 * q^96 + 11058 * q^97 + 18532 * q^98 - 455966 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/50\mathbb{Z}\right)^\times$.

$n$	$27$
$\chi(n)$	$e\left(\frac{4}{5}\right)$

Coefficient data

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

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

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

$2$	−3.23607	+	2.35114i	−0.572061	+	0.415627i
$2$	−3.23607	+	2.35114i	−0.572061	+	0.415627i
$3$	5.67913	−	17.4786i	0.364317	−	1.12125i	−0.586091	−	0.810245i	$-0.699334\pi$
$3$	5.67913	−	17.4786i	0.364317	−	1.12125i	0.950408	−	0.311006i	$-0.100666\pi$
$4$	4.94427	−	15.2169i	0.154508	−	0.475528i
$5$	6.69834	−	55.4989i	0.119823	−	0.992795i
$5$	6.69834	−	55.4989i	0.119823	−	0.992795i
$6$	22.7165	+	69.9143i	0.257611	+	0.792844i
$7$	−86.1311			−0.664377			−0.332189	−	0.943213i	$-0.607787\pi$
$7$	−86.1311			−0.664377			−0.332189	+	0.943213i	$0.607787\pi$
$8$	19.7771	+	60.8676i	0.109254	+	0.336249i
$9$	−76.6568	−	55.6945i	−0.315460	−	0.229195i
$10$	108.810	+	195.347i	0.344086	+	0.617742i
$11$	−370.519	+	269.198i	−0.923270	+	0.670795i	−0.944336	−	0.328983i	$-0.893294\pi$
$11$	−370.519	+	269.198i	−0.923270	+	0.670795i	0.0210655	+	0.999778i	$0.493294\pi$
$12$	−237.891	−	172.838i	−0.476897	−	0.346486i
$13$	−147.354	−	107.059i	−0.241827	−	0.175697i	0.460270	−	0.887779i	$-0.347753\pi$
$13$	−147.354	−	107.059i	−0.241827	−	0.175697i	−0.702097	+	0.712082i	$0.747753\pi$
$14$	278.726	−	202.506i	0.380065	−	0.276133i
$15$	−932.002	−	432.263i	−1.06952	−	0.496044i
$16$	−207.108	−	150.473i	−0.202254	−	0.146946i
$17$	−394.287	−	1213.49i	−0.330895	−	1.01839i	−0.968709	−	0.248199i	$-0.920161\pi$
$17$	−394.287	−	1213.49i	−0.330895	−	1.01839i	0.637814	−	0.770190i	$-0.279839\pi$
$18$	379.012			0.275722
$19$	−338.184	−	1040.82i	−0.214916	−	0.661443i	−0.999160	−	0.0409903i	$-0.986949\pi$
$19$	−338.184	−	1040.82i	−0.214916	−	0.661443i	0.784244	−	0.620453i	$-0.213051\pi$
$20$	−811.404	−	376.330i	−0.453588	−	0.210375i
$21$	−489.150	+	1505.45i	−0.242044	+	0.744934i
$22$	566.103	−	1742.29i	0.249367	−	0.767472i
$23$	−1138.15	+	826.914i	−0.448621	+	0.325942i	−0.789051	−	0.614328i	$-0.789427\pi$
$23$	−1138.15	+	826.914i	−0.448621	+	0.325942i	0.340430	+	0.940270i	$0.389427\pi$
$24$	1176.20			0.416823
$25$	−3035.26	−	743.501i	−0.971285	−	0.237920i
$26$	728.559			0.211364
$27$	2204.16	−	1601.42i	0.581880	−	0.422761i
$28$	−425.855	+	1310.65i	−0.102652	+	0.315930i
$29$	252.462	−	776.999i	0.0557445	−	0.171564i	−0.919308	−	0.393539i	$-0.871251\pi$
$29$	252.462	−	776.999i	0.0557445	−	0.171564i	0.975052	+	0.221976i	$0.0712505\pi$
$30$	4032.33	−	792.434i	0.818000	−	0.160753i
$31$	1769.12	+	5444.80i	0.330639	+	1.01760i	0.968831	+	0.247724i	$0.0796825\pi$
$31$	1769.12	+	5444.80i	0.330639	+	1.01760i	−0.638192	+	0.769877i	$0.720317\pi$
$32$	1024.00			0.176777
$33$	2600.97	+	8004.96i	0.415767	+	1.27960i
$34$	4129.02	+	2999.91i	0.612562	+	0.445052i
$35$	−576.935	+	4780.18i	−0.0796080	+	0.659591i
$36$	−1226.51	+	891.111i	−0.157730	+	0.114598i
$37$	−1524.38	−	1107.53i	−0.183058	−	0.133000i	0.492482	−	0.870322i	$-0.336090\pi$
$37$	−1524.38	−	1107.53i	−0.183058	−	0.133000i	−0.675540	+	0.737323i	$0.736090\pi$
$38$	3541.51	+	2573.05i	0.397859	+	0.289061i
$39$	−2708.08	+	1967.54i	−0.285102	+	0.207139i
$40$	3510.56	−	689.896i	0.346918	−	0.0681763i
$41$	−4470.31	−	3247.87i	−0.415315	−	0.301744i	0.360435	−	0.932784i	$-0.382628\pi$
$41$	−4470.31	−	3247.87i	−0.415315	−	0.301744i	−0.775750	+	0.631040i	$0.782628\pi$
$42$	−1956.60	−	6021.79i	−0.171151	−	0.526748i
$43$	16377.6			1.35076			0.675381	−	0.737469i	$-0.263979\pi$
$43$	16377.6			1.35076			0.675381	+	0.737469i	$0.263979\pi$
$44$	2264.41	+	6969.14i	0.176329	+	0.542685i
$45$	−3604.46	+	3881.31i	−0.265344	+	0.285724i
$46$	1738.94	−	5351.90i	0.121168	−	0.372918i
$47$	8617.72	−	26522.6i	0.569047	−	1.75135i	−0.0865645	−	0.996246i	$-0.527589\pi$
$47$	8617.72	−	26522.6i	0.569047	−	1.75135i	0.655611	−	0.755099i	$-0.272411\pi$
$48$	−3806.25	+	2765.40i	−0.238448	+	0.173243i
$49$	−9388.44			−0.558603
$50$	11570.4	−	4730.32i	0.654521	−	0.267587i
$51$	−23449.3			−1.26242
$52$	−2357.67	+	1712.95i	−0.120913	+	0.0878487i
$53$	12317.4	−	37909.1i	0.602324	−	1.85376i	0.0880905	−	0.996112i	$-0.471924\pi$
$53$	12317.4	−	37909.1i	0.602324	−	1.85376i	0.514234	−	0.857650i	$-0.328076\pi$
$54$	−3367.66	+	10364.6i	−0.157160	+	0.483690i
$55$	12458.3	+	22366.6i	0.555333	+	0.996995i
$56$	−1703.42	−	5242.59i	−0.0725859	−	0.223396i
$57$	−20112.7			−0.819942
$58$	1009.85	+	3108.00i	0.0394173	+	0.121314i
$59$	4421.59	+	3212.47i	0.165367	+	0.120146i	0.667391	−	0.744708i	$-0.267411\pi$
$59$	4421.59	+	3212.47i	0.165367	+	0.120146i	−0.502024	+	0.864854i	$0.667411\pi$
$60$	−11185.8	+	12045.0i	−0.401133	+	0.431943i
$61$	−29357.2	+	21329.2i	−1.01016	+	0.733923i	−0.964242	−	0.265022i	$-0.914621\pi$
$61$	−29357.2	+	21329.2i	−1.01016	+	0.733923i	−0.0459160	+	0.998945i	$0.514621\pi$
$62$	−18526.5	−	13460.3i	−0.612088	−	0.444708i
$63$	6602.54	+	4797.02i	0.209585	+	0.152272i
$64$	−3313.73	+	2407.57i	−0.101127	+	0.0734732i
$65$	−6928.69	+	7460.89i	−0.203408	+	0.219032i
$66$	−27237.7	−	19789.3i	−0.769680	−	0.559205i
$67$	11469.3	+	35298.8i	0.312139	+	0.960666i	0.976916	+	0.213624i	$0.0685268\pi$
$67$	11469.3	+	35298.8i	0.312139	+	0.960666i	−0.664776	+	0.747042i	$0.731473\pi$
$68$	−20415.0			−0.535399
$69$	7989.57	+	24589.4i	0.202023	+	0.621763i
$70$	−9371.88	−	16825.5i	−0.228603	−	0.410414i
$71$	17440.2	−	53675.5i	0.410588	−	1.26366i	−0.505550	−	0.862797i	$-0.668710\pi$
$71$	17440.2	−	53675.5i	0.410588	−	1.26366i	0.916138	−	0.400863i	$-0.131290\pi$
$72$	1873.94	−	5767.39i	0.0426015	−	0.131114i
$73$	69985.6	−	50847.5i	1.53710	−	1.11677i	0.584975	−	0.811051i	$-0.301104\pi$
$73$	69985.6	−	50847.5i	1.53710	−	1.11677i	0.952123	−	0.305716i	$-0.0988958\pi$
$74$	7536.95			0.159999
$75$	−30233.0	+	48829.7i	−0.620623	+	1.00238i
$76$	−17510.2			−0.347741
$77$	31913.2	−	23186.3i	0.613400	−	0.445661i
$78$	4137.59	−	12734.2i	0.0770035	−	0.236992i
$79$	−6465.63	+	19899.2i	−0.116558	+	0.358730i	−0.992269	−	0.124107i	$-0.960393\pi$
$79$	−6465.63	+	19899.2i	−0.116558	+	0.358730i	0.875711	+	0.482837i	$0.160393\pi$
$80$	−9738.37	+	10486.4i	−0.170122	+	0.183189i
$81$	−22587.9	−	69518.3i	−0.382527	−	1.17730i
$82$	22102.4			0.362999
$83$	10204.4	+	31405.9i	0.162590	+	0.500399i	0.998851	−	0.0479324i	$-0.0152632\pi$
$83$	10204.4	+	31405.9i	0.162590	+	0.500399i	−0.836261	+	0.548331i	$0.815263\pi$
$84$	20489.8	+	14886.7i	0.316839	+	0.230197i
$85$	−69988.4	+	13754.1i	−1.05070	+	0.206484i
$86$	−52999.0	+	38506.0i	−0.772719	+	0.561413i
$87$	−12147.1	−	8825.36i	−0.172057	−	0.125007i
$88$	−23713.2	−	17228.7i	−0.326425	−	0.237162i
$89$	53042.2	−	38537.4i	0.709817	−	0.515712i	−0.173298	−	0.984870i	$-0.555442\pi$
$89$	53042.2	−	38537.4i	0.709817	−	0.515712i	0.883115	+	0.469157i	$0.155442\pi$
$90$	2538.75	−	21034.8i	0.0330380	−	0.273736i
$91$	12691.8	+	9221.12i	0.160664	+	0.116729i
$92$	6955.75	+	21407.6i	0.0856790	+	0.263693i
$93$	105214.			1.26144
$94$	34470.9	+	106090.i	0.402377	+	1.23839i
$95$	−60029.8	+	11797.1i	−0.682430	+	0.134111i
$96$	5815.43	−	17898.1i	0.0644027	−	0.198211i
$97$	26173.2	−	80552.8i	0.282441	−	0.869263i	−0.704713	−	0.709492i	$-0.748924\pi$
$97$	26173.2	−	80552.8i	0.282441	−	0.869263i	0.987154	−	0.159771i	$-0.0510756\pi$
$98$	30381.6	−	22073.5i	0.319555	−	0.232170i
$99$	43395.7			0.444998
$100$	−26321.0	+	42511.3i	−0.263210	+	0.425113i
$101$	102368.			0.998532			0.499266	−	0.866449i	$-0.333603\pi$
$101$	102368.			0.998532			0.499266	+	0.866449i	$0.333603\pi$
$102$	75883.4	−	55132.5i	0.722182	−	0.524696i
$103$	−31058.2	+	95587.4i	−0.288459	+	0.887785i	0.696882	+	0.717186i	$0.254570\pi$
$103$	−31058.2	+	95587.4i	−0.288459	+	0.887785i	−0.985341	+	0.170599i	$0.945430\pi$
$104$	3602.20	−	11086.4i	0.0326576	−	0.100510i
$105$	80274.3	+	37231.3i	0.710564	+	0.329560i
$106$	49269.7	+	151637.i	0.425907	+	1.31081i
$107$	−210035.			−1.77350			−0.886752	−	0.462245i	$-0.847044\pi$
$107$	−210035.			−1.77350			−0.886752	+	0.462245i	$0.847044\pi$
$108$	−13470.6	−	41458.3i	−0.111129	−	0.342021i
$109$	92005.6	+	66846.0i	0.741734	+	0.538901i	0.893254	−	0.449553i	$-0.148417\pi$
$109$	92005.6	+	66846.0i	0.741734	+	0.538901i	−0.151520	+	0.988454i	$0.548417\pi$
$110$	−92903.0	−	43088.5i	−0.732063	−	0.339531i
$111$	−28015.2	+	20354.2i	−0.215817	+	0.156800i
$112$	17838.5	+	12960.4i	0.134373	+	0.0976278i
$113$	−85889.9	−	62402.6i	−0.632770	−	0.459734i	0.224589	−	0.974454i	$-0.427896\pi$
$113$	−85889.9	−	62402.6i	−0.632770	−	0.459734i	−0.857359	+	0.514719i	$0.827896\pi$
$114$	65086.0	−	47287.8i	0.469057	−	0.340790i
$115$	38269.1	+	68705.0i	0.269839	+	0.484444i
$116$	−10575.3	−	7683.39i	−0.0729704	−	0.0530161i
$117$	5333.11	+	16413.6i	0.0360177	+	0.110851i
$118$	−21861.6			−0.144536
$119$	33960.3	+	104519.i	0.219839	+	0.676594i
$120$	7878.55	−	65277.6i	0.0499452	−	0.413820i
$121$	15049.4	−	46317.3i	0.0934450	−	0.287594i
$122$	44853.7	−	138046.i	0.272834	−	0.839698i
$123$	−82155.6	+	59689.5i	−0.489637	+	0.355742i
$124$	91600.0			0.534984
$125$	−61594.7	+	163474.i	−0.352589	+	0.935778i
$126$	−32644.7			−0.183184
$127$	7754.52	−	5633.99i	0.0426624	−	0.0309961i	−0.566250	−	0.824234i	$-0.691606\pi$
$127$	7754.52	−	5633.99i	0.0426624	−	0.0309961i	0.608912	+	0.793238i	$0.291606\pi$
$128$	5062.93	−	15582.1i	0.0273135	−	0.0840623i
$129$	93010.6	−	286257.i	0.492105	−	1.51454i
$130$	4880.13	−	40434.3i	0.0253264	−	0.209841i
$131$	−20971.2	−	64542.7i	−0.106769	−	0.328601i	0.883373	−	0.468671i	$-0.155267\pi$
$131$	−20971.2	−	64542.7i	−0.106769	−	0.328601i	−0.990142	+	0.140070i	$0.955267\pi$
$132$	134671.			0.672725
$133$	29128.1	+	89647.2i	0.142785	+	0.439448i
$134$	−120108.	−	87263.4i	−0.577842	−	0.419827i
$135$	−74112.7	−	133055.i	−0.349992	−	0.628345i
$136$	66064.4	−	47998.6i	0.306281	−	0.222526i
$137$	−230235.	−	167275.i	−1.04802	−	0.761431i	−0.0761849	−	0.997094i	$-0.524274\pi$
$137$	−230235.	−	167275.i	−1.04802	−	0.761431i	−0.971835	+	0.235663i	$0.924274\pi$
$138$	−83667.9	−	60788.3i	−0.373991	−	0.271720i
$139$	−328409.	+	238603.i	−1.44171	+	1.04746i	−0.454028	+	0.890987i	$0.650013\pi$
$139$	−328409.	+	238603.i	−1.44171	+	1.04746i	−0.987682	+	0.156476i	$0.949987\pi$
$140$	69887.1	+	32413.7i	0.301354	+	0.139768i
$141$	−414636.	−	301251.i	−1.75638	−	1.27609i
$142$	69760.9	+	214702.i	0.290330	+	0.893543i
$143$	83417.6			0.341128
$144$	7495.76	+	23069.6i	0.0301238	+	0.0927114i
$145$	−41431.6	−	19216.0i	−0.163648	−	0.0759002i
$146$	−106928.	+	329092.i	−0.415156	+	1.27772i
$147$	−53318.2	+	164097.i	−0.203508	+	0.626334i
$148$	−24390.1	+	17720.4i	−0.0915291	+	0.0664998i
$149$	−180605.			−0.666444			−0.333222	−	0.942848i	$-0.608136\pi$
$149$	−180605.			−0.666444			−0.333222	+	0.942848i	$0.608136\pi$
$150$	−16969.3	−	229098.i	−0.0615796	−	0.831368i
$151$	547956.			1.95570			0.977852	−	0.209295i	$-0.0671170\pi$
$151$	547956.			1.95570			0.977852	+	0.209295i	$0.0671170\pi$
$152$	56664.1	−	41168.9i	0.198929	−	0.144531i
$153$	−37359.9	+	114982.i	−0.129026	+	0.397101i
$154$	−48759.0	+	150065.i	−0.165674	+	0.509891i
$155$	314031.	−	61713.3i	1.04989	−	0.206324i
$156$	16550.3	+	50936.7i	0.0544497	+	0.167579i
$157$	−391840.			−1.26870			−0.634351	−	0.773045i	$-0.718733\pi$
$157$	−391840.			−1.26870			−0.634351	+	0.773045i	$0.718733\pi$
$158$	−25862.5	−	79596.7i	−0.0824192	−	0.253660i
$159$	−592645.	−	430582.i	−1.85910	−	1.35071i
$160$	6859.10	−	56830.9i	0.0211820	−	0.175503i
$161$	98030.0	−	71223.0i	0.298054	−	0.216549i
$162$	236543.	+	171859.i	0.708146	+	0.514498i
$163$	−19353.8	−	14061.4i	−0.0570555	−	0.0414532i	0.558892	−	0.829240i	$-0.311227\pi$
$163$	−19353.8	−	14061.4i	−0.0570555	−	0.0414532i	−0.615947	+	0.787787i	$0.711227\pi$
$164$	−71524.9	+	51965.9i	−0.207658	+	0.150872i
$165$	461689.	−	90731.1i	1.32020	−	0.259446i
$166$	−106862.	−	77639.7i	−0.300990	−	0.218682i
$167$	180893.	+	556732.i	0.501916	+	1.54474i	0.805894	+	0.592060i	$0.201685\pi$
$167$	180893.	+	556732.i	0.501916	+	1.54474i	−0.303978	+	0.952679i	$0.598315\pi$
$168$	−101307.			−0.276928
$169$	−104484.	−	321569.i	−0.281406	−	0.866080i
$170$	194149.	−	209062.i	0.515245	−	0.554821i
$171$	−32043.9	+	98621.1i	−0.0838023	+	0.257917i
$172$	80975.3	−	249216.i	0.208704	−	0.642326i
$173$	399113.	−	289973.i	1.01387	−	0.736617i	0.0488497	−	0.998806i	$-0.484444\pi$
$173$	399113.	−	289973.i	1.01387	−	0.736617i	0.965016	+	0.262189i	$0.0844445\pi$
$174$	60058.4			0.150384
$175$	261431.	+	64038.5i	0.645299	+	0.158069i
$176$	117245.			0.285306
$177$	81260.3	−	59039.0i	0.194960	−	0.141647i
$178$	−81041.3	+	249419.i	−0.191715	+	0.590038i
$179$	134322.	−	413402.i	0.313340	−	0.964362i	−0.663092	−	0.748538i	$-0.730756\pi$
$179$	134322.	−	413402.i	0.313340	−	0.964362i	0.976432	−	0.215824i	$-0.0692438\pi$
$180$	41240.2	+	74038.9i	0.0948722	+	0.170325i
$181$	129592.	+	398842.i	0.294022	+	0.904908i	0.983548	+	0.180647i	$0.0578190\pi$
$181$	129592.	+	398842.i	0.294022	+	0.904908i	−0.689526	+	0.724261i	$0.742181\pi$
$182$	−62751.6			−0.140426
$183$	206081.	+	634253.i	0.454894	+	1.40002i
$184$	−72841.5	−	52922.5i	−0.158611	−	0.115238i
$185$	−71677.4	+	77182.9i	−0.153976	+	0.165803i
$186$	−340481.	+	247374.i	−0.721623	+	0.524290i
$187$	472760.	+	343480.i	0.988636	+	0.718286i
$188$	−360984.	−	262270.i	−0.744892	−	0.541195i
$189$	−189847.	+	137932.i	−0.386588	+	0.280873i
$190$	166524.	−	179315.i	0.334652	−	0.360356i
$191$	254511.	+	184913.i	0.504804	+	0.366761i	0.810849	−	0.585256i	$-0.199006\pi$
$191$	254511.	+	184913.i	0.504804	+	0.366761i	−0.306045	+	0.952017i	$0.599006\pi$
$192$	23261.7	+	71592.2i	0.0455396	+	0.140156i
$193$	177800.			0.343589			0.171795	−	0.985133i	$-0.445043\pi$
$193$	177800.			0.343589			0.171795	+	0.985133i	$0.445043\pi$
$194$	104693.	+	322211.i	0.199716	+	0.614662i
$195$	91056.7	+	163475.i	0.171485	+	0.307868i
$196$	−46419.0	+	142863.i	−0.0863089	+	0.265631i
$197$	−184644.	+	568275.i	−0.338976	+	1.04326i	0.625755	+	0.780020i	$0.284791\pi$
$197$	−184644.	+	568275.i	−0.338976	+	1.04326i	−0.964730	+	0.263240i	$0.915209\pi$
$198$	−140431.	+	102029.i	−0.254566	+	0.184953i
$199$	159142.			0.284874			0.142437	−	0.989804i	$-0.454506\pi$
$199$	159142.			0.284874			0.142437	+	0.989804i	$0.454506\pi$
$200$	−14773.6	−	199454.i	−0.0261162	−	0.352587i
$201$	682108.			1.19087
$202$	−331271.	+	240682.i	−0.571222	+	0.415017i
$203$	−21744.9	+	66923.8i	−0.0370353	+	0.113983i
$204$	−115940.	+	356825.i	−0.195055	+	0.600316i
$205$	−210197.	+	226342.i	−0.349335	+	0.376167i
$206$	−124233.	−	382350.i	−0.203971	−	0.627759i
$207$	133301.			0.216227
$208$	14408.8	+	44345.7i	0.0230924	+	0.0710711i
$209$	405491.	+	294606.i	0.642119	+	0.466526i
$210$	−347309.	+	68253.2i	−0.543460	+	0.106801i
$211$	286493.	−	208149.i	0.443004	−	0.321861i	−0.343823	−	0.939034i	$-0.611722\pi$
$211$	286493.	−	208149.i	0.443004	−	0.321861i	0.786827	+	0.617173i	$0.211722\pi$
$212$	−515959.	−	374866.i	−0.788452	−	0.572844i
$213$	−839126.	−	609661.i	−1.26730	−	0.920745i
$214$	679688.	−	493822.i	1.01455	−	0.737116i
$215$	109703.	−	908939.i	0.161853	−	1.34103i
$216$	141066.	+	102491.i	0.205726	+	0.149468i
$217$	−152376.	−	468966.i	−0.219669	−	0.676071i
$218$	−454901.			−0.648299
$219$	−491285.	−	1.51202e6i	−0.692186	−	2.13033i
$220$	401948.	−	78990.8i	0.559903	−	0.110032i
$221$	−71815.3	+	221025.i	−0.0989091	+	0.304411i
$222$	42803.4	−	131735.i	0.0582902	−	0.179399i
$223$	−429131.	+	311782.i	−0.577867	+	0.419845i	−0.837954	−	0.545740i	$-0.816249\pi$
$223$	−429131.	+	311782.i	−0.577867	+	0.419845i	0.260088	+	0.965585i	$0.416249\pi$
$224$	−88198.2			−0.117446
$225$	191265.	+	226042.i	0.251872	+	0.297668i
$226$	424663.			0.553061
$227$	32414.5	−	23550.5i	0.0417517	−	0.0303344i	−0.566714	−	0.823915i	$-0.691785\pi$
$227$	32414.5	−	23550.5i	0.0417517	−	0.0303344i	0.608465	+	0.793580i	$0.291785\pi$
$228$	−99442.6	+	306053.i	−0.126688	+	0.389905i
$229$	104349.	−	321152.i	0.131492	−	0.404690i	−0.863536	−	0.504287i	$-0.831755\pi$
$229$	104349.	−	321152.i	0.131492	−	0.404690i	0.995028	+	0.0995970i	$0.0317554\pi$
$230$	−285377.	−	132358.i	−0.355712	−	0.164980i
$231$	−224024.	−	689475.i	−0.276226	−	0.850137i
$232$	52287.1			0.0637785
$233$	32185.6	+	99057.2i	0.0388394	+	0.119535i	0.968596	−	0.248639i	$-0.0799831\pi$
$233$	32185.6	+	99057.2i	0.0388394	+	0.119535i	−0.929757	+	0.368174i	$0.879983\pi$
$234$	−55849.1	−	40576.7i	−0.0666770	−	0.0484437i
$235$	−1.41425e6	−	655932.i	−1.67054	−	0.774799i
$236$	70745.5	−	51399.6i	0.0826835	−	0.0600730i
$237$	311090.	+	226020.i	0.359762	+	0.261382i
$238$	−355637.	−	258386.i	−0.406972	−	0.295683i
$239$	−622311.	+	452135.i	−0.704714	+	0.512004i	−0.881464	−	0.472251i	$-0.843442\pi$
$239$	−622311.	+	452135.i	−0.704714	+	0.512004i	0.176750	+	0.984256i	$0.443442\pi$
$240$	127981.	+	229766.i	0.143423	+	0.257489i
$241$	621042.	+	451214.i	0.688777	+	0.500426i	0.876258	−	0.481843i	$-0.160032\pi$
$241$	621042.	+	451214.i	0.688777	+	0.500426i	−0.187481	+	0.982268i	$0.560032\pi$
$242$	60197.6	+	185269.i	0.0660756	+	0.203360i
$243$	−681309.			−0.740164
$244$	179415.	+	552183.i	0.192923	+	0.593756i
$245$	−62886.9	+	521048.i	−0.0669337	+	0.554578i
$246$	125523.	−	386319.i	0.132246	−	0.407013i
$247$	−61596.7	+	189575.i	−0.0642414	+	0.197715i
$248$	−296424.	+	215364.i	−0.306044	+	0.222354i
$249$	606883.			0.620307
$250$	−185025.	−	673830.i	−0.187232	−	0.681868i
$251$	280145.			0.280671			0.140336	−	0.990104i	$-0.455182\pi$
$251$	280145.			0.280671			0.140336	+	0.990104i	$0.455182\pi$
$252$	105641.	−	76752.4i	0.104792	−	0.0761361i
$253$	199103.	−	612775.i	0.195558	−	0.601866i
$254$	−11847.8	+	36463.9i	−0.0115227	+	0.0354633i
$255$	−157071.	+	1.30141e6i	−0.151268	+	1.25332i
$256$	20251.7	+	62328.4i	0.0193136	+	0.0594410i
$257$	−708311.			−0.668946			−0.334473	−	0.942405i	$-0.608558\pi$
$257$	−708311.			−0.668946			−0.334473	+	0.942405i	$0.608558\pi$
$258$	372042.	+	1.14503e6i	0.347971	+	1.07094i
$259$	131297.	+	95392.5i	0.121620	+	0.0883619i
$260$	79274.2	+	142322.i	0.0727275	+	0.130569i
$261$	−62627.5	+	45501.6i	−0.0569068	+	0.0413452i
$262$	219613.	+	159558.i	0.197654	+	0.143604i
$263$	−3831.02	−	2783.40i	−0.00341527	−	0.00248134i	0.586076	−	0.810256i	$-0.300672\pi$
$263$	−3831.02	−	2783.40i	−0.00341527	−	0.00248134i	−0.589492	+	0.807775i	$0.700672\pi$
$264$	−435803.	+	316629.i	−0.384840	+	0.279603i
$265$	−2.02141e6	−	937532.i	−1.76823	−	0.820109i
$266$	−305034.	−	221620.i	−0.264328	−	0.192046i
$267$	−372345.	−	1.14596e6i	−0.319645	−	0.983766i
$268$	593845.			0.505052
$269$	644521.	+	1.98363e6i	0.543071	+	1.67140i	0.725533	+	0.688187i	$0.241593\pi$
$269$	644521.	+	1.98363e6i	0.543071	+	1.67140i	−0.182462	+	0.983213i	$0.558407\pi$
$270$	552665.	+	256327.i	0.461374	+	0.213986i
$271$	−503302.	+	1.54900e6i	−0.416299	+	1.28124i	0.494784	+	0.869016i	$0.335247\pi$
$271$	−503302.	+	1.54900e6i	−0.416299	+	1.28124i	−0.911084	+	0.412222i	$0.864753\pi$
$272$	−100937.	+	310653.i	−0.0827237	+	0.254597i
$273$	233250.	−	169466.i	0.189415	−	0.137618i
$274$	1.13834e6			0.916003
$275$	1.32477e6	−	541605.i	1.05635	−	0.431868i
$276$	413677.			0.326880
$277$	137653.	−	100010.i	0.107792	−	0.0783152i	−0.532584	−	0.846377i	$-0.678779\pi$
$277$	137653.	−	100010.i	0.107792	−	0.0783152i	0.640375	+	0.768062i	$0.278779\pi$
$278$	501764.	−	1.54427e6i	0.389392	−	1.19843i
$279$	167630.	−	515911.i	0.128926	−	0.396793i
$280$	−302368.	+	59421.5i	−0.230484	+	0.0452948i
$281$	−614849.	−	1.89231e6i	−0.464518	−	1.42964i	−0.859588	−	0.510988i	$-0.829280\pi$
$281$	−614849.	−	1.89231e6i	−0.464518	−	1.42964i	0.395070	−	0.918651i	$-0.370720\pi$
$282$	2.05007e6			1.53514
$283$	253693.	+	780788.i	0.188297	+	0.579518i	0.999990	−	0.00456663i	$-0.00145361\pi$
$283$	253693.	+	780788.i	0.188297	+	0.579518i	−0.811693	+	0.584085i	$0.801454\pi$
$284$	−730546.	−	530773.i	−0.537467	−	0.390493i
$285$	−134721.	+	1.11623e6i	−0.0982482	+	0.814034i
$286$	−269945.	+	196127.i	−0.195146	+	0.141782i
$287$	385032.	+	279742.i	0.275926	+	0.200472i
$288$	−78496.6	−	57031.1i	−0.0557660	−	0.0405164i
$289$	−168406.	+	122354.i	−0.118608	+	0.0861738i
$290$	179255.	−	35227.2i	0.125163	−	0.0245970i
$291$	−1.25931e6	−	914940.i	−0.871765	−	0.633374i
$292$	−427714.	−	1.31637e6i	−0.293560	−	0.903484i
$293$	2.47023e6			1.68100			0.840501	−	0.541810i	$-0.182261\pi$
$293$	2.47023e6			1.68100			0.840501	+	0.541810i	$0.182261\pi$
$294$	−213273.	−	656386.i	−0.143902	−	0.442885i
$295$	207906.	−	223875.i	0.139095	−	0.149779i
$296$	37264.7	−	114689.i	0.0247212	−	0.0760839i
$297$	−385585.	+	1.18671e6i	−0.253647	+	0.780645i
$298$	584449.	−	424627.i	0.381247	−	0.276992i
$299$	256240.			0.165756
$300$	593556.	+	701480.i	0.380766	+	0.450000i
$301$	−1.41062e6			−0.897416
$302$	−1.77322e6	+	1.28832e6i	−1.11878	+	0.812844i
$303$	581363.	−	1.78925e6i	0.363782	−	1.11961i
$304$	−86575.0	+	266451.i	−0.0537290	+	0.165361i
$305$	987105.	+	1.77216e6i	0.607595	+	1.09082i
$306$	−149439.	−	459927.i	−0.0912351	−	0.280793i
$307$	756859.			0.458320			0.229160	−	0.973389i	$-0.426402\pi$
$307$	756859.			0.458320			0.229160	+	0.973389i	$0.426402\pi$
$308$	−195036.	−	600260.i	−0.117149	−	0.360547i
$309$	1.49435e6	+	1.08571e6i	0.890339	+	0.646869i
$310$	−871128.	+	938039.i	−0.514846	+	0.554391i
$311$	418554.	−	304097.i	0.245386	−	0.178284i	−0.458293	−	0.888801i	$-0.651539\pi$
$311$	418554.	−	304097.i	0.245386	−	0.178284i	0.703680	+	0.710517i	$0.251539\pi$
$312$	−173317.	−	125922.i	−0.100799	−	0.0732347i
$313$	−1.31095e6	−	952462.i	−0.756355	−	0.549524i	0.141435	−	0.989948i	$-0.454828\pi$
$313$	−1.31095e6	−	952462.i	−0.756355	−	0.549524i	−0.897790	+	0.440423i	$0.854828\pi$
$314$	1.26802e6	−	921271.i	0.725775	−	0.527307i
$315$	310456.	−	334302.i	0.176288	−	0.189829i
$316$	270836.	+	196774.i	0.152577	+	0.110854i
$317$	−203657.	−	626793.i	−0.113829	−	0.350329i	0.877872	−	0.478895i	$-0.158963\pi$
$317$	−203657.	−	626793.i	−0.113829	−	0.350329i	−0.991701	+	0.128566i	$0.958963\pi$
$318$	2.93020e6			1.62491
$319$	115624.	+	355855.i	0.0636170	+	0.195793i
$320$	111421.	+	200035.i	0.0608264	+	0.109202i
$321$	−1.19282e6	+	3.67111e6i	−0.646117	+	1.98854i
$322$	−149777.	+	460965.i	−0.0805015	+	0.247758i
$323$	−1.12969e6	+	820765.i	−0.602492	+	0.437736i
$324$	−1.16953e6			−0.618942
$325$	367661.	+	434511.i	0.193081	+	0.228188i
$326$	95690.5			0.0498683
$327$	1.69088e6	−	1.22850e6i	0.874469	−	0.635339i
$328$	109280.	−	336330.i	0.0560864	−	0.172616i
$329$	−742253.	+	2.28442e6i	−0.378062	+	1.16355i
$330$	−1.28073e6	+	1.37911e6i	−0.647402	+	0.697129i
$331$	−938614.	−	2.88876e6i	−0.470887	−	1.44924i	−0.851425	−	0.524476i	$-0.824261\pi$
$331$	−938614.	−	2.88876e6i	−0.470887	−	1.44924i	0.380538	−	0.924765i	$-0.375739\pi$
$332$	528354.			0.263075
$333$	55171.1	+	169799.i	0.0272647	+	0.0839121i
$334$	−1.89434e6	−	1.37632e6i	−0.929162	−	0.675076i
$335$	2.03587e6	−	400089.i	0.991147	−	0.194780i
$336$	327836.	−	238187.i	0.158420	−	0.115099i
$337$	−1.38759e6	−	1.00814e6i	−0.665560	−	0.483557i	0.202976	−	0.979184i	$-0.434939\pi$
$337$	−1.38759e6	−	1.00814e6i	−0.665560	−	0.483557i	−0.868536	+	0.495626i	$0.834939\pi$
$338$	1.09417e6	+	794963.i	0.520948	+	0.378491i
$339$	−1.57849e6	+	1.14684e6i	−0.746006	+	0.542005i
$340$	−136747.	+	1.13301e6i	−0.0641533	+	0.531541i
$341$	−2.12122e6	−	1.54116e6i	−0.987870	−	0.717730i
$342$	−128176.	−	394485.i	−0.0592571	−	0.182375i
$343$	2.25624e6			1.03550
$344$	323901.	+	996865.i	0.147576	+	0.454193i
$345$	1.41820e6	−	278705.i	0.641490	−	0.126066i
$346$	−609790.	+	1.87674e6i	−0.273836	+	0.842780i
$347$	665479.	−	2.04813e6i	0.296695	−	0.913135i	−0.685951	−	0.727648i	$-0.740614\pi$
$347$	665479.	−	2.04813e6i	0.296695	−	0.913135i	0.982647	−	0.185487i	$-0.0593863\pi$
$348$	−194353.	+	141206.i	−0.0860287	+	0.0625035i
$349$	−181303.			−0.0796785			−0.0398393	−	0.999206i	$-0.512685\pi$
$349$	−181303.			−0.0796785			−0.0398393	+	0.999206i	$0.512685\pi$
$350$	−996571.	+	407427.i	−0.434849	+	0.177779i
$351$	−496238.			−0.214992
$352$	−379412.	+	275659.i	−0.163213	+	0.118581i
$353$	−454047.	+	1.39741e6i	−0.193939	+	0.596882i	0.806049	+	0.591849i	$0.201602\pi$
$353$	−454047.	+	1.39741e6i	−0.193939	+	0.596882i	−0.999987	+	0.00503250i	$0.998398\pi$
$354$	−124155.	+	382109.i	−0.0526568	+	0.162061i
$355$	−2.86211e6	−	1.32745e6i	−1.20536	−	0.559046i
$356$	−324165.	−	997677.i	−0.135563	−	0.417220i
$357$	2.01971e6			0.838723
$358$	537290.	+	1.65361e6i	0.221565	+	0.681907i
$359$	1.91266e6	+	1.38963e6i	0.783252	+	0.569066i	0.905953	−	0.423378i	$-0.139156\pi$
$359$	1.91266e6	+	1.38963e6i	0.783252	+	0.569066i	−0.122701	+	0.992444i	$0.539156\pi$
$360$	−307532.	−	142634.i	−0.125064	−	0.0580050i
$361$	1.03426e6	−	751436.i	0.417698	−	0.303476i
$362$	−1.35710e6	−	985991.i	−0.544303	−	0.395459i
$363$	−724093.	−	526084.i	−0.288422	−	0.209550i
$364$	203068.	−	147538.i	0.0803321	−	0.0583647i
$365$	−2.35320e6	−	4.22472e6i	−0.924541	−	1.65984i
$366$	−2.15811e6	−	1.56796e6i	−0.842114	−	0.611832i
$367$	−1.47129e6	−	4.52817e6i	−0.570209	−	1.75492i	−0.651944	−	0.758267i	$-0.726046\pi$
$367$	−1.47129e6	−	4.52817e6i	−0.570209	−	1.75492i	0.0817353	−	0.996654i	$-0.473954\pi$
$368$	360148.			0.138632
$369$	161791.	+	497943.i	0.0618571	+	0.190377i
$370$	50485.0	−	418293.i	0.0191716	−	0.158846i
$371$	−1.06091e6	+	3.26515e6i	−0.400170	+	1.23160i
$372$	520208.	−	1.60104e6i	0.194904	−	0.599852i
$373$	−1.05940e6	+	769701.i	−0.394266	+	0.286451i	−0.767201	−	0.641406i	$-0.778351\pi$
$373$	−1.05940e6	+	769701.i	−0.394266	+	0.286451i	0.372936	+	0.927857i	$0.378351\pi$
$374$	−2.33745e6			−0.864099
$375$	2.50748e6	+	2.00498e6i	0.920788	+	0.736260i
$376$	1.78480e6			0.651059
$377$	−120386.	+	87465.7i	−0.0436238	+	0.0316945i
$378$	290060.	−	892712.i	0.104414	−	0.321353i
$379$	346960.	−	1.06783e6i	0.124074	−	0.381861i	−0.869657	−	0.493656i	$-0.835660\pi$
$379$	346960.	−	1.06783e6i	0.124074	−	0.381861i	0.993731	+	0.111795i	$0.0356601\pi$
$380$	−117289.	+	971796.i	−0.0416676	+	0.345236i
$381$	−54435.1	−	167534.i	−0.0192117	−	0.0591277i
$382$	−1.25837e6			−0.441214
$383$	743572.	+	2.28848e6i	0.259016	+	0.797168i	0.993012	+	0.118015i	$0.0376530\pi$
$383$	743572.	+	2.28848e6i	0.259016	+	0.797168i	−0.733996	+	0.679154i	$0.762347\pi$
$384$	−243600.	−	176986.i	−0.0843042	−	0.0612506i
$385$	−1.07305e6	−	1.92646e6i	−0.368950	−	0.662381i
$386$	−575374.	+	418034.i	−0.196554	+	0.142805i
$387$	−1.25546e6	−	912142.i	−0.426112	−	0.309588i
$388$	−1.09636e6	−	796550.i	−0.369720	−	0.268617i
$389$	1.51874e6	−	1.10343e6i	0.508874	−	0.369719i	−0.303522	−	0.952824i	$-0.598163\pi$
$389$	1.51874e6	−	1.10343e6i	0.508874	−	0.369719i	0.812396	+	0.583106i	$0.198163\pi$
$390$	−679018.	−	314929.i	−0.226058	−	0.104846i
$391$	1.45221e6	+	1.05509e6i	0.480382	+	0.349018i
$392$	−185676.	−	571452.i	−0.0610296	−	0.187830i
$393$	−1.24721e6			−0.407342
$394$	−738574.	−	2.27310e6i	−0.239692	−	0.737696i
$395$	1.06107e6	+	492127.i	0.342179	+	0.158703i
$396$	214560.	−	660348.i	0.0687560	−	0.211609i
$397$	725251.	−	2.23209e6i	0.230947	−	0.710782i	−0.766686	−	0.642022i	$-0.778096\pi$
$397$	725251.	−	2.23209e6i	0.230947	−	0.710782i	0.997633	−	0.0687598i	$-0.0219042\pi$
$398$	−514995.	+	374166.i	−0.162965	+	0.118401i
$399$	1.73233e6			0.544750
$400$	516752.	+	610711.i	0.161485	+	0.190847i
$401$	5.94822e6			1.84725			0.923626	−	0.383295i	$-0.125211\pi$
$401$	5.94822e6			1.84725			0.923626	+	0.383295i	$0.125211\pi$
$402$	−2.20735e6	+	1.60373e6i	−0.681248	+	0.494956i
$403$	322228.	−	991714.i	0.0988326	−	0.304175i
$404$	506137.	−	1.55773e6i	0.154282	−	0.474830i
$405$	−4.00949e6	+	787946.i	−1.21465	+	0.238703i
$406$	−86979.4	−	267695.i	−0.0261879	−	0.0805982i
$407$	862956.			0.258228
$408$	−463758.	−	1.42730e6i	−0.137924	−	0.424488i
$409$	2.50530e6	+	1.82021e6i	0.740546	+	0.538038i	0.892882	−	0.450291i	$-0.148680\pi$
$409$	2.50530e6	+	1.82021e6i	0.740546	+	0.538038i	−0.152336	+	0.988329i	$0.548680\pi$
$410$	148049.	−	1.22666e6i	0.0434958	−	0.360383i
$411$	−4.23127e6	+	3.07420e6i	−1.23557	+	0.897691i
$412$	1.30098e6	+	945220.i	0.377597	+	0.274341i
$413$	−380836.	−	276694.i	−0.109866	−	0.0798223i
$414$	−431373.	+	313410.i	−0.123695	+	0.0898696i
$415$	1.81135e6	−	355966.i	0.516276	−	0.101459i
$416$	−150891.	−	109629.i	−0.0427493	−	0.0310592i
$417$	2.30536e6	+	7.09518e6i	0.649231	+	1.99813i
$418$	−2.00486e6			−0.561232
$419$	443962.	+	1.36637e6i	0.123541	+	0.380219i	0.993632	−	0.112671i	$-0.0359405\pi$
$419$	443962.	+	1.36637e6i	0.123541	+	0.380219i	−0.870092	+	0.492890i	$0.835940\pi$
$420$	963443.	−	1.03744e6i	0.266503	−	0.286973i
$421$	−1.29546e6	+	3.98702e6i	−0.356221	+	1.09634i	0.599077	+	0.800691i	$0.295534\pi$
$421$	−1.29546e6	+	3.98702e6i	−0.356221	+	1.09634i	−0.955298	+	0.295644i	$0.904466\pi$
$422$	−437722.	+	1.34717e6i	−0.119651	+	0.368249i
$423$	−2.13777e6	+	1.55318e6i	−0.580912	+	0.422057i
$424$	2.55104e6			0.689133
$425$	294534.	+	3.97641e6i	0.0790975	+	1.06787i
$426$	4.14887e6			1.10766
$427$	2.52856e6	−	1.83711e6i	0.671126	−	0.487602i
$428$	−1.03847e6	+	3.19608e6i	−0.274022	+	0.843352i
$429$	473740.	−	1.45802e6i	0.124279	−	0.382490i
$430$	1.78204e6	+	3.19932e6i	0.464779	+	0.834423i
$431$	−785164.	−	2.41649e6i	−0.203595	−	0.626601i	−0.999768	−	0.0215320i	$-0.993146\pi$
$431$	−785164.	−	2.41649e6i	−0.203595	−	0.626601i	0.796173	−	0.605069i	$-0.206854\pi$
$432$	−697470.			−0.179811
$433$	−870904.	−	2.68037e6i	−0.223229	−	0.687028i	−0.998467	−	0.0553585i	$-0.982370\pi$
$433$	−870904.	−	2.68037e6i	−0.223229	−	0.687028i	0.775238	−	0.631670i	$-0.217630\pi$
$434$	1.59571e6	+	1.15935e6i	0.406657	+	0.295454i
$435$	−571164.	+	615034.i	−0.144723	+	0.155839i
$436$	1.47209e6	−	1.06954e6i	0.370867	−	0.269451i
$437$	1.24557e6	+	904963.i	0.312008	+	0.226687i
$438$	5.14480e6	+	3.73791e6i	1.28140	+	0.930988i
$439$	3.20044e6	−	2.32526e6i	0.792589	−	0.575850i	−0.116141	−	0.993233i	$-0.537053\pi$
$439$	3.20044e6	−	2.32526e6i	0.792589	−	0.575850i	0.908731	+	0.417383i	$0.137053\pi$
$440$	−1.11501e6	+	1.20066e6i	−0.274567	+	0.295656i
$441$	719688.	+	522884.i	0.176217	+	0.128029i
$442$	−287261.	−	884099.i	−0.0699393	−	0.215251i
$443$	−1.62430e6			−0.393238			−0.196619	−	0.980480i	$-0.562996\pi$
$443$	−1.62430e6			−0.393238			−0.196619	+	0.980480i	$0.562996\pi$
$444$	171213.	+	526941.i	0.0412174	+	0.126854i
$445$	−1.78349e6	−	3.20192e6i	−0.426944	−	0.766497i
$446$	655654.	−	2.01789e6i	0.156076	−	0.480354i
$447$	−1.02568e6	+	3.15671e6i	−0.242797	+	0.747251i
$448$	285415.	−	207366.i	0.0671866	−	0.0488139i
$449$	−3.69504e6			−0.864975			−0.432487	−	0.901640i	$-0.642364\pi$
$449$	−3.69504e6			−0.864975			−0.432487	+	0.901640i	$0.642364\pi$
$450$	−1.15040e6	−	281796.i	−0.267805	−	0.0656000i
$451$	2.53065e6			0.585857
$452$	−1.37424e6	+	998442.i	−0.316385	+	0.229867i
$453$	3.11191e6	−	9.57749e6i	0.712496	−	2.19284i
$454$	−49524.9	+	152422.i	−0.0112768	+	0.0347063i
$455$	596776.	−	642614.i	0.135140	−	0.145520i
$456$	−397770.	−	1.22421e6i	−0.0895819	−	0.275705i
$457$	676967.			0.151627			0.0758136	−	0.997122i	$-0.475845\pi$
$457$	676967.			0.151627			0.0758136	+	0.997122i	$0.475845\pi$
$458$	417395.	+	1.28461e6i	0.0929787	+	0.286159i
$459$	−2.81237e6	−	2.04331e6i	−0.623076	−	0.452691i
$460$	1.23469e6	−	242641.i	0.272059	−	0.0534651i
$461$	4.27473e6	−	3.10578e6i	0.936821	−	0.680640i	−0.0108323	−	0.999941i	$-0.503448\pi$
$461$	4.27473e6	−	3.10578e6i	0.936821	−	0.680640i	0.947653	+	0.319301i	$0.103448\pi$
$462$	2.34601e6	+	1.70448e6i	0.511358	+	0.371523i
$463$	87866.7	+	63838.9i	0.0190490	+	0.0138399i	0.597269	−	0.802041i	$-0.296252\pi$
$463$	87866.7	+	63838.9i	0.0190490	+	0.0138399i	−0.578220	+	0.815881i	$0.696252\pi$
$464$	−169205.	+	122934.i	−0.0364852	+	0.0265081i
$465$	704761.	−	5.83928e6i	0.151150	−	1.25235i
$466$	−337052.	−	244883.i	−0.0719006	−	0.0522389i
$467$	1.35301e6	+	4.16413e6i	0.287084	+	0.883553i	0.985766	+	0.168121i	$0.0537700\pi$
$467$	1.35301e6	+	4.16413e6i	0.287084	+	0.883553i	−0.698683	+	0.715432i	$0.746230\pi$
$468$	276133.			0.0582779
$469$	−987860.	−	3.04032e6i	−0.207378	−	0.638245i
$470$	6.11881e6	−	1.20247e6i	1.27768	−	0.251090i
$471$	−2.22531e6	+	6.84880e6i	−0.462209	+	1.42253i
$472$	−108089.	+	332665.i	−0.0223320	+	0.0687309i
$473$	−6.06821e6	+	4.40881e6i	−1.24712	+	0.906085i
$474$	−1.53811e6			−0.314443
$475$	252625.	+	3.41061e6i	0.0513738	+	0.693583i
$476$	1.75837e6			0.355707
$477$	−3.05554e6	+	2.21998e6i	−0.614883	+	0.446739i
$478$	950807.	−	2.92628e6i	0.190337	−	0.585796i
$479$	−1.05465e6	+	3.24589e6i	−0.210025	+	0.646391i	0.789444	+	0.613822i	$0.210369\pi$
$479$	−1.05465e6	+	3.24589e6i	−0.210025	+	0.646391i	−0.999469	+	0.0325689i	$0.989631\pi$
$480$	−954370.	−	442638.i	−0.189066	−	0.0876890i
$481$	106053.	+	326398.i	0.0209007	+	0.0643257i
$482$	−3.07060e6			−0.602013
$483$	−688150.	−	2.11791e6i	−0.134219	−	0.413085i
$484$	−630398.	−	458011.i	−0.122321	−	0.0888714i
$485$	−4.29528e6	−	1.99215e6i	−0.829158	−	0.384564i
$486$	2.20476e6	−	1.60185e6i	0.423419	−	0.307632i
$487$	3.98339e6	+	2.89410e6i	0.761079	+	0.552957i	0.899241	−	0.437453i	$-0.144119\pi$
$487$	3.98339e6	+	2.89410e6i	0.761079	+	0.552957i	−0.138162	+	0.990410i	$0.544119\pi$
$488$	−1.87886e6	−	1.36507e6i	−0.357145	−	0.259481i
$489$	−355685.	+	258421.i	−0.0672657	+	0.0488714i
$490$	−1.02155e6	−	1.83400e6i	−0.192207	−	0.345072i
$491$	−7.52274e6	−	5.46559e6i	−1.40823	−	1.02314i	−0.993577	−	0.113154i	$-0.963905\pi$
$491$	−7.52274e6	−	5.46559e6i	−1.40823	−	1.02314i	−0.414648	−	0.909982i	$-0.636095\pi$
$492$	502090.	+	1.54527e6i	0.0935124	+	0.287801i
$493$	−1.04242e6			−0.193164
$494$	−246387.	−	758301.i	−0.0454256	−	0.139805i
$495$	290679.	−	2.40841e6i	0.0533212	−	0.441792i
$496$	452895.	−	1.39387e6i	0.0826596	−	0.254400i
$497$	−1.50215e6	+	4.62313e6i	−0.272785	+	0.839547i
$498$	−1.96391e6	+	1.42687e6i	−0.354854	+	0.257816i
$499$	−9.74945e6			−1.75279			−0.876393	−	0.481597i	$-0.840057\pi$
$499$	−9.74945e6			−1.75279			−0.876393	+	0.481597i	$0.840057\pi$
$500$	2.18302e6	+	1.74554e6i	0.390511	+	0.312252i
$501$	1.07582e7			1.91490
$502$	−906568.	+	658660.i	−0.160561	+	0.116655i
$503$	−365559.	+	1.12507e6i	−0.0644224	+	0.198272i	−0.978087	−	0.208198i	$-0.933240\pi$
$503$	−365559.	+	1.12507e6i	−0.0644224	+	0.198272i	0.913664	+	0.406470i	$0.133240\pi$
$504$	−161404.	+	496752.i	−0.0283034	+	0.0871090i
$505$	685697.	−	5.68133e6i	0.119648	−	0.991338i
$506$	796410.	+	2.45110e6i	0.138280	+	0.425583i
$507$	−6.21395e6			−1.07361
$508$	−47391.4	−	145856.i	−0.00814780	−	0.0250763i
$509$	−5.15191e6	−	3.74308e6i	−0.881401	−	0.640375i	0.0522207	−	0.998636i	$-0.483370\pi$
$509$	−5.15191e6	−	3.74308e6i	−0.881401	−	0.640375i	−0.933622	+	0.358260i	$0.883370\pi$
$510$	−2.55151e6	−	4.58075e6i	−0.434381	−	0.779850i
$511$	−6.02793e6	+	4.37955e6i	−1.02121	+	0.741955i
$512$	−212079.	−	154084.i	−0.0357538	−	0.0259767i
$513$	−2.41220e6	−	1.75257e6i	−0.404688	−	0.294023i
$514$	2.29214e6	−	1.66534e6i	0.382678	−	0.278032i
$515$	5.09696e6	+	2.36398e6i	0.846824	+	0.392758i
$516$	−3.89608e6	−	2.83067e6i	−0.644174	−	0.468020i
$517$	3.94680e6	+	1.21470e7i	0.649410	+	1.99868i
$518$	−649166.			−0.106300
$519$	−2.80169e6	−	8.62272e6i	−0.456564	−	1.40516i
$520$	−591156.	−	274179.i	−0.0958724	−	0.0444657i
$521$	3.59243e6	−	1.10564e7i	0.579822	−	1.78451i	−0.0393181	−	0.999227i	$-0.512519\pi$
$521$	3.59243e6	−	1.10564e7i	0.579822	−	1.78451i	0.619140	−	0.785281i	$-0.287481\pi$
$522$	95686.3	−	294492.i	0.0153700	−	0.0473040i
$523$	−7.51200e6	+	5.45779e6i	−1.20088	+	0.872494i	−0.994371	−	0.105950i	$-0.966212\pi$
$523$	−7.51200e6	+	5.45779e6i	−1.20088	+	0.872494i	−0.206513	+	0.978444i	$0.566212\pi$
$524$	−1.08583e6			−0.172756
$525$	2.60400e6	−	4.20575e6i	0.412328	−	0.665956i
$526$	18941.6			0.00298505
$527$	5.90966e6	−	4.29362e6i	0.926907	−	0.673437i
$528$	665848.	−	2.04927e6i	0.103942	−	0.319900i
$529$	−1.37734e6	+	4.23902e6i	−0.213995	+	0.658607i
$530$	8.74569e6	−	1.71870e6i	1.35240	−	0.265773i
$531$	−160028.	−	492516.i	−0.0246298	−	0.0758026i
$532$	1.50817e6			0.231031
$533$	311005.	+	957174.i	0.0474186	+	0.145940i
$534$	3.89925e6	+	2.83297e6i	0.591736	+	0.429921i
$535$	−1.40689e6	+	1.16567e7i	−0.212507	+	1.76073i
$536$	−1.92172e6	+	1.39621e6i	−0.288921	+	0.209913i
$537$	−6.46284e6	−	4.69553e6i	−0.967137	−	0.702666i
$538$	−6.74951e6	−	4.90381e6i	−1.00535	−	0.730429i
$539$	3.47860e6	−	2.52735e6i	0.515741	−	0.374708i
$540$	−2.39112e6	+	469904.i	−0.352872	+	0.0693465i
$541$	5.67506e6	+	4.12317e6i	0.833637	+	0.605673i	0.920586	−	0.390540i	$-0.127712\pi$
$541$	5.67506e6	+	4.12317e6i	0.833637	+	0.605673i	−0.0869486	+	0.996213i	$0.527712\pi$
$542$	−2.01321e6	−	6.19602e6i	−0.294368	−	0.905972i
$543$	7.70715e6			1.12175
$544$	−403750.	−	1.24261e6i	−0.0584945	−	0.180027i
$545$	4.32617e6	−	4.65846e6i	0.623896	−	0.671817i
$546$	−356375.	+	1.09681e6i	−0.0511594	+	0.157452i
$547$	1.73451e6	−	5.33827e6i	0.247861	−	0.762838i	−0.747292	−	0.664496i	$-0.768646\pi$
$547$	1.73451e6	−	5.33827e6i	0.247861	−	0.762838i	0.995153	−	0.0983417i	$-0.0313538\pi$
$548$	−3.68376e6	+	2.67641e6i	−0.524010	+	0.380715i
$549$	3.43835e6			0.486876
$550$	−3.01366e6	+	4.86740e6i	−0.424803	+	0.686104i
$551$	−894097.			−0.125460
$552$	−1.33869e6	+	972612.i	−0.186995	+	0.135860i
$553$	556892.	−	1.71394e6i	0.0774387	−	0.238332i
$554$	−210314.	+	647281.i	−0.0291135	+	0.0896022i
$555$	941982.	+	1.69115e6i	0.129811	+	0.233050i
$556$	2.00706e6	+	6.17708e6i	0.275342	+	0.847416i
$557$	−1.00468e7			−1.37212			−0.686059	−	0.727546i	$-0.740661\pi$
$557$	−1.00468e7			−1.37212			−0.686059	+	0.727546i	$0.740661\pi$
$558$	670519.	+	2.06364e6i	0.0911644	+	0.280575i
$559$	−2.41331e6	−	1.75337e6i	−0.326650	−	0.237325i
$560$	838777.	−	903203.i	0.113025	−	0.121707i
$561$	8.68840e6	−	6.31249e6i	1.16556	−	0.846825i
$562$	6.43878e6	+	4.67805e6i	0.859929	+	0.624775i
$563$	−513807.	−	373302.i	−0.0683170	−	0.0496352i	0.553103	−	0.833113i	$-0.313444\pi$
$563$	−513807.	−	373302.i	−0.0683170	−	0.0496352i	−0.621420	+	0.783478i	$0.713444\pi$
$564$	−6.63418e6	+	4.82001e6i	−0.878192	+	0.638044i
$565$	−4.03860e6	+	4.34880e6i	−0.532243	+	0.573124i
$566$	−2.65671e6	−	1.93021e6i	−0.348581	−	0.253259i
$567$	1.94552e6	+	5.98768e6i	0.254142	+	0.782170i
$568$	3.61202e6			0.469763
$569$	2.77281e6	+	8.53382e6i	0.359037	+	1.10500i	0.953632	+	0.300976i	$0.0973125\pi$
$569$	2.77281e6	+	8.53382e6i	0.359037	+	1.10500i	−0.594595	+	0.804026i	$0.702687\pi$
$570$	−2.18845e6	−	3.92895e6i	−0.282130	−	0.506512i
$571$	−2.74162e6	+	8.43785e6i	−0.351899	+	1.08303i	0.605887	+	0.795550i	$0.292818\pi$
$571$	−2.74162e6	+	8.43785e6i	−0.351899	+	1.08303i	−0.957786	+	0.287482i	$0.907182\pi$
$572$	412439.	−	1.26936e6i	0.0527072	−	0.162216i
$573$	4.67741e6	−	3.39834e6i	0.595140	−	0.432394i
$574$	−1.90370e6			−0.241168
$575$	4.06940e6	−	1.66369e6i	0.513287	−	0.209847i
$576$	388109.			0.0487413
$577$	5.89394e6	−	4.28220e6i	0.736997	−	0.535460i	−0.154772	−	0.987950i	$-0.549464\pi$
$577$	5.89394e6	−	4.28220e6i	0.736997	−	0.535460i	0.891769	+	0.452490i	$0.149464\pi$
$578$	257302.	−	791894.i	0.0320349	−	0.0985934i
$579$	1.00975e6	−	3.10770e6i	0.125175	−	0.385250i
$580$	−497257.	+	535451.i	−0.0613777	+	0.0660921i
$581$	−878916.	−	2.70503e6i	−0.108021	−	0.332454i
$582$	6.22636e6			0.761950
$583$	5.64122e6	+	1.73619e7i	0.687387	+	2.11556i
$584$	4.47908e6	+	3.25424e6i	0.543446	+	0.394837i
$585$	946662.	−	186038.i	0.114368	−	0.0224756i
$586$	−7.99383e6	+	5.80786e6i	−0.961636	+	0.698670i
$587$	−1.17619e7	−	8.54553e6i	−1.40891	−	1.02363i	−0.993480	−	0.114005i	$-0.963632\pi$
$587$	−1.17619e7	−	8.54553e6i	−1.40891	−	1.02363i	−0.415428	−	0.909626i	$-0.636368\pi$
$588$	2.23342e6	+	1.62268e6i	0.266396	+	0.193548i
$589$	5.06878e6	−	3.68268e6i	0.602026	−	0.437397i
$590$	−146436.	+	1.21329e6i	−0.0173188	+	0.143495i
$591$	8.88401e6	+	6.45461e6i	1.04626	+	0.760154i
$592$	149059.	+	458756.i	0.0174805	+	0.0537994i
$593$	−7.76606e6			−0.906910			−0.453455	−	0.891279i	$-0.649809\pi$
$593$	−7.76606e6			−0.906910			−0.453455	+	0.891279i	$0.649809\pi$
$594$	−1.54234e6	−	4.74684e6i	−0.179355	−	0.551999i
$595$	6.02818e6	−	1.18466e6i	0.698062	−	0.137183i
$596$	−892959.	+	2.74825e6i	−0.102971	+	0.316913i
$597$	903790.	−	2.78158e6i	0.103784	−	0.319415i
$598$	−829209.	+	602456.i	−0.0948224	+	0.0688925i
$599$	1.17150e7			1.33406			0.667028	−	0.745032i	$-0.267566\pi$
$599$	1.17150e7			1.33406			0.667028	+	0.745032i	$0.267566\pi$
$600$	−3.57007e6	−	874503.i	−0.404854	−	0.0991706i
$601$	−1.04748e6			−0.118294			−0.0591468	−	0.998249i	$-0.518838\pi$
$601$	−1.04748e6			−0.118294			−0.0591468	+	0.998249i	$0.518838\pi$
$602$	4.56486e6	−	3.31657e6i	0.513377	−	0.372990i
$603$	1.08675e6	−	3.34467e6i	0.121713	−	0.374593i
$604$	2.70924e6	−	8.33819e6i	0.302173	−	0.929993i
$605$	−2.46976e6	−	1.14547e6i	−0.274325	−	0.127232i
$606$	2.32545e6	+	7.15701e6i	0.257233	+	0.791680i
$607$	−3.04989e6			−0.335979			−0.167990	−	0.985789i	$-0.553727\pi$
$607$	−3.04989e6			−0.335979			−0.167990	+	0.985789i	$0.553727\pi$
$608$	−346300.	−	1.06580e6i	−0.0379921	−	0.116928i
$609$	1.04624e6	+	760138.i	0.114311	+	0.0830518i
$610$	−7.36094e6	−	3.41401e6i	−0.800956	−	0.371484i
$611$	−4.10935e6	+	2.98561e6i	−0.445317	+	0.323542i
$612$	1.56495e6	+	1.13700e6i	0.168897	+	0.122711i
$613$	1.04227e7	+	7.57253e6i	1.12029	+	0.813936i	0.984252	−	0.176769i	$-0.0565644\pi$
$613$	1.04227e7	+	7.57253e6i	1.12029	+	0.813936i	0.136034	+	0.990704i	$0.456564\pi$
$614$	−2.44925e6	+	1.77948e6i	−0.262187	+	0.190490i
$615$	2.76240e6	+	4.95937e6i	0.294509	+	0.528736i
$616$	2.04245e6	+	1.48392e6i	0.216870	+	0.157565i
$617$	−819459.	−	2.52204e6i	−0.0866591	−	0.266709i	0.898331	−	0.439319i	$-0.144780\pi$
$617$	−819459.	−	2.52204e6i	−0.0866591	−	0.266709i	−0.984990	+	0.172609i	$0.944780\pi$
$618$	−7.38846e6			−0.778185
$619$	−1.98001e6	−	6.09384e6i	−0.207702	−	0.639240i	−0.999592	−	0.0285764i	$-0.990903\pi$
$619$	−1.98001e6	−	6.09384e6i	−0.207702	−	0.639240i	0.791890	−	0.610664i	$-0.209097\pi$
$620$	613567.	−	5.08370e6i	0.0641037	−	0.531130i
$621$	−1.18443e6	+	3.64530e6i	−0.123248	+	0.379319i
$622$	−639493.	+	1.96816e6i	−0.0662765	+	0.203978i
$623$	−4.56858e6	+	3.31927e6i	−0.471586	+	0.342627i
$624$	856928.			0.0881015
$625$	8.66004e6	+	4.51344e6i	0.886788	+	0.462177i
$626$	6.48170e6			0.661079
$627$	7.45213e6	−	5.41429e6i	0.757028	−	0.550013i
$628$	−1.93736e6	+	5.96259e6i	−0.196025	+	0.603304i
$629$	−742930.	+	2.28650e6i	−0.0748723	+	0.230433i
$630$	−218665.	+	1.81175e6i	−0.0219497	+	0.181864i
$631$	−2.14964e6	−	6.61593e6i	−0.214928	−	0.661481i	−0.999159	−	0.0410112i	$-0.986942\pi$
$631$	−2.14964e6	−	6.61593e6i	−0.214928	−	0.661481i	0.784231	−	0.620470i	$-0.213058\pi$
$632$	−1.33909e6			−0.133357
$633$	−2.01112e6	−	6.18960e6i	−0.199494	−	0.613978i
$634$	2.13273e6	+	1.54952e6i	0.210723	+	0.153099i
$635$	−260738.	−	468106.i	−0.0256608	−	0.0460691i
$636$	−9.48232e6	+	6.88931e6i	−0.929548	+	0.675356i
$637$	1.38343e6	+	1.00512e6i	0.135085	+	0.0981451i
$638$	−1.21083e6	−	879723.i	−0.117770	−	0.0855646i
$639$	−4.32634e6	+	3.14327e6i	−0.419149	+	0.304530i
$640$	−830877.	−	385362.i	−0.0801839	−	0.0371894i
$641$	−8.21878e6	−	5.97129e6i	−0.790064	−	0.574015i	0.117919	−	0.993023i	$-0.462378\pi$
$641$	−8.21878e6	−	5.97129e6i	−0.790064	−	0.574015i	−0.907982	+	0.419008i	$0.862378\pi$
$642$	−4.77127e6	−	1.46845e7i	−0.456874	−	1.40611i
$643$	1.83468e7			1.74998			0.874988	−	0.484144i	$-0.160869\pi$
$643$	1.83468e7			1.74998			0.874988	+	0.484144i	$0.160869\pi$
$644$	−599106.	−	1.84386e6i	−0.0569232	−	0.175191i
$645$	−1.52639e7	−	7.07943e6i	−1.44467	−	0.670038i
$646$	1.72601e6	−	5.31210e6i	0.162728	−	0.500824i
$647$	4.40698e6	−	1.35633e7i	0.413886	−	1.27381i	−0.499358	−	0.866396i	$-0.666431\pi$
$647$	4.40698e6	−	1.35633e7i	0.413886	−	1.27381i	0.913244	−	0.407414i	$-0.133569\pi$
$648$	3.78469e6	−	2.74974e6i	0.354073	−	0.257249i
$649$	−2.50308e6			−0.233272
$650$	−2.21137e6	−	541685.i	−0.205295	−	0.0502879i
$651$	−9.06222e6			−0.838074
$652$	−309661.	+	224982.i	−0.0285277	+	0.0207266i
$653$	−3.49440e6	+	1.07547e7i	−0.320693	+	0.986992i	0.652654	+	0.757656i	$0.273655\pi$
$653$	−3.49440e6	+	1.07547e7i	−0.320693	+	0.986992i	−0.973347	+	0.229336i	$0.926345\pi$
$654$	−2.58344e6	+	7.95102e6i	−0.236186	+	0.726906i
$655$	−3.72252e6	+	731550.i	−0.339027	+	0.0666256i
$656$	437121.	+	1.34532e6i	0.0396591	+	0.122058i
$657$	−8.19680e6			−0.740851
$658$	−2.96901e6	−	9.13769e6i	−0.267330	−	0.822757i
$659$	−1.78109e6	−	1.29404e6i	−0.159762	−	0.116074i	0.505032	−	0.863101i	$-0.331481\pi$
$659$	−1.78109e6	−	1.29404e6i	−0.159762	−	0.116074i	−0.664794	+	0.747027i	$0.731481\pi$
$660$	902068.	−	7.47407e6i	0.0806083	−	0.667878i
$661$	6.23262e6	−	4.52826e6i	0.554839	−	0.403114i	−0.274728	−	0.961522i	$-0.588588\pi$
$661$	6.23262e6	−	4.52826e6i	0.554839	−	0.403114i	0.829566	+	0.558408i	$0.188588\pi$
$662$	9.82929e6	+	7.14140e6i	0.871720	+	0.633342i
$663$	3.45535e6	+	2.51046e6i	0.305287	+	0.221804i
$664$	−1.70979e6	+	1.24224e6i	−0.150495	+	0.109341i
$665$	5.17043e6	−	1.01609e6i	0.453391	−	0.0891004i
$666$	−577759.	−	419766.i	−0.0504732	−	0.0366710i
$667$	355172.	+	1.09311e6i	0.0309118	+	0.0951366i
$668$	9.36613e6			0.812117
$669$	3.01241e6	+	9.27125e6i	0.260225	+	0.800890i
$670$	−5.64755e6	+	6.08133e6i	−0.486041	+	0.523373i
$671$	5.13561e6	−	1.58058e7i	0.440337	−	1.35522i
$672$	−500889.	+	1.54158e6i	−0.0427877	+	0.131687i
$673$	1.66493e7	−	1.20964e7i	1.41696	−	1.02948i	0.424696	−	0.905336i	$-0.360381\pi$
$673$	1.66493e7	−	1.20964e7i	1.41696	−	1.02948i	0.992264	−	0.124146i	$-0.0396192\pi$
$674$	6.86063e6			0.581720
$675$	−7.88086e6	+	3.22193e6i	−0.665755	+	0.272180i
$676$	−5.40989e6			−0.455325
$677$	−8.41654e6	+	6.11497e6i	−0.705768	+	0.512770i	−0.881806	−	0.471613i	$-0.843672\pi$
$677$	−8.41654e6	+	6.11497e6i	−0.705768	+	0.512770i	0.176038	+	0.984383i	$0.443672\pi$
$678$	2.41172e6	−	7.42250e6i	0.201489	−	0.620120i
$679$	−2.25433e6	+	6.93810e6i	−0.187647	+	0.577519i
$680$	−2.22135e6	−	3.98801e6i	−0.184223	−	0.330738i
$681$	−227543.	−	700305.i	−0.0188016	−	0.0578655i
$682$	1.04879e7			0.863430
$683$	−161911.	−	498312.i	−0.0132808	−	0.0408742i	0.944196	−	0.329383i	$-0.106841\pi$
$683$	−161911.	−	498312.i	−0.0132808	−	0.0408742i	−0.957477	+	0.288509i	$0.906841\pi$
$684$	1.34227e6	+	975219.i	0.109699	+	0.0797007i
$685$	−1.08258e7	+	1.16573e7i	−0.881522	+	0.949232i
$686$	−7.30135e6	+	5.30474e6i	−0.592370	+	0.430382i
$687$	−5.02068e6	−	3.64773e6i	−0.405855	−	0.294871i
$688$	−3.39194e6	−	2.46439e6i	−0.273198	−	0.198490i
$689$	−5.87354e6	+	4.26738e6i	−0.471359	+	0.342463i
$690$	−3.93412e6	+	4.23630e6i	−0.314576	+	0.338738i
$691$	−1.90033e6	−	1.38067e6i	−0.151403	−	0.110001i	0.509505	−	0.860468i	$-0.329829\pi$
$691$	−1.90033e6	−	1.38067e6i	−0.151403	−	0.110001i	−0.660908	+	0.750467i	$0.729829\pi$
$692$	−2.43916e6	−	7.50697e6i	−0.193631	−	0.595936i
$693$	−3.73771e6			−0.295647
$694$	2.66192e6	+	8.19254e6i	0.209795	+	0.645684i
$695$	1.10424e7	+	1.98246e7i	0.867166	+	1.55683i
$696$	296945.	−	913903.i	0.0232356	−	0.0715117i
$697$	−2.17867e6	+	6.70526e6i	−0.169867	+	0.522798i
$698$	586709.	−	426269.i	0.0455810	−	0.0331165i
$699$	1.91417e6			0.148179
$700$	2.26705e6	−	3.66154e6i	0.174870	−	0.282435i
$701$	−2.14123e7			−1.64577			−0.822884	−	0.568209i	$-0.807637\pi$
$701$	−2.14123e7			−1.64577			−0.822884	+	0.568209i	$0.807637\pi$
$702$	1.60586e6	−	1.16673e6i	0.122989	−	0.0893565i
$703$	−637219.	+	1.96116e6i	−0.0486295	+	0.149666i
$704$	579689.	−	1.78410e6i	0.0440822	−	0.135671i
$705$	−1.94965e7	+	2.09940e7i	−1.47735	+	1.59082i
$706$	−1.81619e6	−	5.58966e6i	−0.137135	−	0.422059i
$707$	−8.81709e6			−0.663402
$708$	−496619.	−	1.52843e6i	−0.0372340	−	0.114595i
$709$	−7.01553e6	−	5.09708e6i	−0.524137	−	0.380808i	0.294023	−	0.955798i	$-0.405006\pi$
$709$	−7.01553e6	−	5.09708e6i	−0.524137	−	0.380808i	−0.818160	+	0.574990i	$0.805006\pi$
$710$	1.23830e7	−	2.43351e6i	0.921894	−	0.181171i
$711$	1.60391e6	−	1.16531e6i	0.118989	−	0.0864504i
$712$	3.39470e6	+	2.46639e6i	0.250958	+	0.182332i
$713$	−6.51590e6	−	4.73408e6i	−0.480010	−	0.348748i
$714$	−6.53592e6	+	4.74862e6i	−0.479801	+	0.348596i
$715$	558759.	−	4.62959e6i	0.0408752	−	0.338671i
$716$	−5.62657e6	−	4.08794e6i	−0.410168	−	0.298004i
$717$	4.36850e6	+	1.34448e7i	0.317347	+	0.976693i
$718$	−9.45671e6			−0.684588
$719$	−1.10110e6	−	3.38884e6i	−0.0794336	−	0.244472i	0.903452	−	0.428690i	$-0.141025\pi$
$719$	−1.10110e6	−	3.38884e6i	−0.0794336	−	0.244472i	−0.982885	+	0.184218i	$0.941025\pi$
$720$	1.33055e6	−	261479.i	0.0956530	−	0.0187977i
$721$	2.67508e6	−	8.23305e6i	0.191645	−	0.589824i
$722$	−1.58021e6	+	4.86340e6i	−0.112817	+	0.347213i
$723$	1.14136e7	−	8.29243e6i	0.812036	−	0.589978i
$724$	6.70987e6			0.475738
$725$	−1.34399e6	+	2.17069e6i	−0.0949622	+	0.153375i
$726$	3.58011e6			0.252090
$727$	−5.38732e6	+	3.91412e6i	−0.378039	+	0.274661i	−0.760537	−	0.649295i	$-0.775064\pi$
$727$	−5.38732e6	+	3.91412e6i	−0.378039	+	0.274661i	0.382498	+	0.923957i	$0.375064\pi$
$728$	−310261.	+	954885.i	−0.0216969	+	0.0667763i
$729$	1.61961e6	−	4.98464e6i	0.112873	−	0.347388i
$730$	1.75480e7	+	8.13879e6i	1.21877	+	0.565266i
$731$	−6.45747e6	−	1.98740e7i	−0.446960	−	1.37560i
$732$	1.06703e7			0.736035
$733$	−6.24810e6	−	1.92297e7i	−0.429525	−	1.32194i	−0.898594	−	0.438780i	$-0.855411\pi$
$733$	−6.24810e6	−	1.92297e7i	−0.429525	−	1.32194i	0.469070	−	0.883161i	$-0.344589\pi$
$734$	1.54076e7	+	1.11943e7i	1.05559	+	0.766929i
$735$	8.75004e6	+	4.05828e6i	0.597436	+	0.277092i
$736$	−1.16546e6	+	846760.i	−0.0793057	+	0.0576190i
$737$	−1.37519e7	−	9.99137e6i	−0.932599	−	0.677573i
$738$	−1.69430e6	−	1.23098e6i	−0.114512	−	0.0831976i
$739$	3.88012e6	−	2.81907e6i	0.261357	−	0.189887i	−0.449388	−	0.893337i	$-0.648358\pi$
$739$	3.88012e6	−	2.81907e6i	0.261357	−	0.189887i	0.710745	+	0.703450i	$0.248358\pi$
$740$	820093.	+	1.47232e6i	0.0550533	+	0.0988379i
$741$	2.96369e6	+	2.15325e6i	0.198284	+	0.144062i
$742$	−4.24365e6	−	1.30606e7i	−0.282963	−	0.870871i
$743$	2.22311e6			0.147737			0.0738685	−	0.997268i	$-0.476465\pi$
$743$	2.22311e6			0.147737			0.0738685	+	0.997268i	$0.476465\pi$
$744$	2.08083e6	+	6.40415e6i	0.137818	+	0.424159i
$745$	−1.20975e6	+	1.00234e7i	−0.0798556	+	0.661642i
$746$	1.61862e6	−	4.98161e6i	0.106488	−	0.327735i
$747$	966899.	−	2.97581e6i	0.0633986	−	0.195121i
$748$	7.56415e6	−	5.49568e6i	0.494318	−	0.359143i
$749$	1.80905e7			1.17828
$750$	−1.28284e7	−	592796.i	−0.832757	−	0.0384815i
$751$	−1.38644e7			−0.897018			−0.448509	−	0.893778i	$-0.648045\pi$
$751$	−1.38644e7			−0.897018			−0.448509	+	0.893778i	$0.648045\pi$
$752$	−5.77574e6	+	4.19632e6i	−0.372446	+	0.270598i
$753$	1.59098e6	−	4.89653e6i	0.102253	−	0.314703i
$754$	183934.	−	566090.i	0.0117824	−	0.0362625i
$755$	3.67039e6	−	3.04110e7i	0.234339	−	1.94161i
$756$	1.16024e6	+	3.57085e6i	0.0738317	+	0.227231i
$757$	1.11924e7			0.709876			0.354938	−	0.934890i	$-0.384502\pi$
$757$	1.11924e7			0.709876			0.354938	+	0.934890i	$0.384502\pi$
$758$	1.38784e6	+	4.27133e6i	0.0877337	+	0.270017i
$759$	−9.57970e6	−	6.96006e6i	−0.603597	−	0.438539i
$760$	−1.90527e6	−	3.42056e6i	−0.119653	−	0.214814i
$761$	2.20345e7	−	1.60090e7i	1.37925	−	1.00208i	0.382296	−	0.924040i	$-0.375134\pi$
$761$	2.20345e7	−	1.60090e7i	1.37925	−	1.00208i	0.996950	−	0.0780406i	$-0.0248664\pi$
$762$	570052.	+	414167.i	0.0355653	+	0.0258397i
$763$	−7.92454e6	−	5.75752e6i	−0.492791	−	0.358034i
$764$	4.07217e6	−	2.95860e6i	0.252402	−	0.183381i
$765$	6.13112e6	+	2.84362e6i	0.378779	+	0.175678i
$766$	−7.78679e6	−	5.65743e6i	−0.479497	−	0.348375i
$767$	−307616.	−	946743.i	−0.0188808	−	0.0581091i
$768$	1.20442e6			0.0736846
$769$	6.72932e6	+	2.07107e7i	0.410351	+	1.26293i	0.916344	+	0.400392i	$0.131126\pi$
$769$	6.72932e6	+	2.07107e7i	0.410351	+	1.26293i	−0.505993	+	0.862537i	$0.668874\pi$
$770$	8.00184e6	+	3.71126e6i	0.486366	+	0.225577i
$771$	−4.02259e6	+	1.23803e7i	−0.243708	+	0.750056i
$772$	879093.	−	2.70557e6i	0.0530874	−	0.163386i
$773$	1.78943e7	−	1.30010e7i	1.07712	−	0.782577i	0.0999456	−	0.994993i	$-0.468133\pi$
$773$	1.78943e7	−	1.30010e7i	1.07712	−	0.782577i	0.977179	+	0.212416i	$0.0681331\pi$
$774$	6.20731e6			0.372436
$775$	−1.32154e6	−	1.78417e7i	−0.0790362	−	1.06705i
$776$	5.42069e6			0.323147
$777$	2.41298e6	−	1.75313e6i	0.143384	−	0.104174i
$778$	−2.32043e6	+	7.14156e6i	−0.137442	+	0.423004i
$779$	−1.86867e6	+	5.75117e6i	−0.110329	+	0.339557i
$780$	2.93779e6	−	577335.i	0.172896	−	0.0339775i
$781$	7.98740e6	+	2.45827e7i	0.468574	+	1.44212i
$782$	−7.18011e6			−0.419870
$783$	−687831.	−	2.11693e6i	−0.0400938	−	0.123396i
$784$	1.94442e6	+	1.41271e6i	0.112980	+	0.0820846i
$785$	−2.62468e6	+	2.17467e7i	−0.152020	+	1.25956i
$786$	4.03606e6	−	2.93237e6i	0.233025	−	0.169302i
$787$	5.58552e6	+	4.05812e6i	0.321460	+	0.233554i	0.736798	−	0.676113i	$-0.236337\pi$
$787$	5.58552e6	+	4.05812e6i	0.321460	+	0.233554i	−0.415338	+	0.909667i	$0.636337\pi$
$788$	7.73445e6	+	5.61941e6i	0.443725	+	0.322385i
$789$	−70406.7	+	51153.4i	−0.00402644	+	0.00292538i
$790$	−4.59077e6	+	902178.i	−0.261708	+	0.0514309i
$791$	7.39779e6	+	5.37481e6i	0.420398	+	0.305437i
$792$	858240.	+	2.64139e6i	0.0486178	+	0.149630i
$793$	6.60939e6			0.373232
$794$	2.90101e6	+	8.92838e6i	0.163304	+	0.502599i
$795$	−2.78666e7	+	3.00070e7i	−1.56374	+	1.68386i
$796$	786842.	−	2.42165e6i	0.0440154	−	0.135466i
$797$	−7.04956e6	+	2.16963e7i	−0.393112	+	1.20987i	0.537311	+	0.843384i	$0.319440\pi$
$797$	−7.04956e6	+	2.16963e7i	−0.393112	+	1.20987i	−0.930422	+	0.366489i	$0.880560\pi$
$798$	−5.60593e6	+	4.07294e6i	−0.311631	+	0.226413i
$799$	−3.55828e7			−1.97185
$800$	−3.10811e6	−	761345.i	−0.171700	−	0.0420588i
$801$	−6.21237e6			−0.342118
$802$	−1.92488e7	+	1.39851e7i	−1.05674	+	0.767768i
$803$	−1.22430e7	+	3.76800e7i	−0.670035	+	2.06216i
$804$	3.37253e6	−	1.03796e7i	0.183999	−	0.566290i
$805$	−3.29616e6	−	5.91764e6i	−0.179275	−	0.321854i
$806$	1.28891e6	+	3.96686e6i	0.0698852	+	0.215084i
$807$	3.83314e7			2.07191
$808$	2.02455e6	+	6.23091e6i	0.109094	+	0.335756i
$809$	2.24955e7	+	1.63439e7i	1.20844	+	0.877982i	0.995088	−	0.0989943i	$-0.0315626\pi$
$809$	2.24955e7	+	1.63439e7i	1.20844	+	0.877982i	0.213350	+	0.976976i	$0.431563\pi$
$810$	1.11224e7	−	1.19767e7i	0.595644	−	0.641395i
$811$	3.53083e6	−	2.56530e6i	0.188506	−	0.136957i	−0.489530	−	0.871987i	$-0.662832\pi$
$811$	3.53083e6	−	2.56530e6i	0.188506	−	0.136957i	0.678035	+	0.735029i	$0.262832\pi$
$812$	910860.	+	661779.i	0.0484799	+	0.0352227i
$813$	2.42161e7	+	1.75940e7i	1.28492	+	0.933552i
$814$	−2.79258e6	+	2.02893e6i	−0.147722	+	0.107326i
$815$	−910029.	+	979928.i	−0.0479912	+	0.0516773i
$816$	4.85654e6	+	3.52848e6i	0.255330	+	0.185508i
$817$	−5.53864e6	−	1.70462e7i	−0.290301	−	0.893453i
$818$	−1.23869e7			−0.647261
$819$	−459347.	−	1.41372e6i	−0.0239293	−	0.0736469i
$820$	2.40495e6	+	4.31764e6i	0.124903	+	0.224239i
$821$	−8.05568e6	+	2.47928e7i	−0.417104	+	1.28371i	0.493252	+	0.869887i	$0.335808\pi$
$821$	−8.05568e6	+	2.47928e7i	−0.417104	+	1.28371i	−0.910356	+	0.413827i	$0.864192\pi$
$822$	6.46480e6	−	1.98966e7i	0.333715	−	1.02707i
$823$	7.33710e6	−	5.33072e6i	0.377594	−	0.274338i	−0.382759	−	0.923848i	$-0.625026\pi$
$823$	7.33710e6	−	5.33072e6i	0.377594	−	0.274338i	0.760353	+	0.649510i	$0.225026\pi$
$824$	−6.43242e6			−0.330032
$825$	−1.94293e6	−	2.62310e7i	−0.0993855	−	1.34177i
$826$	1.88296e6			0.0960264
$827$	1.97859e7	−	1.43753e7i	1.00599	−	0.730892i	0.0426234	−	0.999091i	$-0.486428\pi$
$827$	1.97859e7	−	1.43753e7i	1.00599	−	0.730892i	0.963364	+	0.268199i	$0.0864284\pi$
$828$	659079.	−	2.02844e6i	0.0334088	−	0.102822i
$829$	2.82274e6	−	8.68751e6i	0.142654	−	0.439045i	−0.854048	−	0.520195i	$-0.825859\pi$
$829$	2.82274e6	−	8.68751e6i	0.142654	−	0.439045i	0.996702	+	0.0811499i	$0.0258593\pi$
$830$	−5.02472e6	+	5.41067e6i	−0.253173	+	0.272619i
$831$	−966293.	−	2.97394e6i	−0.0485407	−	0.149393i
$832$	746045.			0.0373643
$833$	3.70174e6	+	1.13928e7i	0.184839	+	0.568875i
$834$	−2.41421e7	−	1.75402e7i	−1.20188	−	0.873213i
$835$	3.21097e7	−	6.31020e6i	1.59375	−	0.313204i
$836$	6.48785e6	−	4.71370e6i	0.321059	−	0.233263i
$837$	1.26188e7	+	9.16810e6i	0.622594	+	0.452341i
$838$	−4.64923e6	−	3.37786e6i	−0.228702	−	0.166162i
$839$	1.68106e7	−	1.22136e7i	0.824477	−	0.599018i	−0.0935142	−	0.995618i	$-0.529810\pi$
$839$	1.68106e7	−	1.22136e7i	0.824477	−	0.599018i	0.917991	+	0.396600i	$0.129810\pi$
$840$	−678588.	+	5.62243e6i	−0.0331824	+	0.274932i
$841$	1.60539e7	+	1.16638e7i	0.782690	+	0.568658i
$842$	−5.18185e6	−	1.59481e7i	−0.251886	−	0.775226i
$843$	−3.65667e7			−1.77222
$844$	−1.75089e6	−	5.38868e6i	−0.0846063	−	0.260391i
$845$	−1.85466e7	+	3.64478e6i	−0.893559	+	0.175602i
$846$	3.26622e6	−	1.00524e7i	0.156899	−	0.482885i
$847$	−1.29622e6	+	3.98936e6i	−0.0620827	+	0.191071i
$848$	−8.25534e6	+	5.99786e6i	−0.394226	+	0.286422i
$849$	1.50878e7			0.718385
$850$	−1.03022e7	−	1.21755e7i	−0.489085	−	0.578013i
$851$	2.65080e6			0.125474
$852$	−1.34260e7	+	9.75457e6i	−0.633648	+	0.460372i
$853$	7.60050e6	−	2.33919e7i	0.357659	−	1.10076i	−0.596792	−	0.802396i	$-0.703558\pi$
$853$	7.60050e6	−	2.33919e7i	0.357659	−	1.10076i	0.954451	−	0.298366i	$-0.0964417\pi$
$854$	−3.86330e6	+	1.18900e7i	−0.181265	+	0.557876i
$855$	5.25873e6	+	2.43900e6i	0.246017	+	0.114103i
$856$	−4.15388e6	−	1.27843e7i	−0.193763	−	0.596340i
$857$	−1.83109e7			−0.851643			−0.425822	−	0.904807i	$-0.640015\pi$
$857$	−1.83109e7			−0.851643			−0.425822	+	0.904807i	$0.640015\pi$
$858$	1.89496e6	+	5.83209e6i	0.0878783	+	0.270462i
$859$	−2.61471e7	−	1.89970e7i	−1.20904	−	0.878419i	−0.213897	−	0.976856i	$-0.568616\pi$
$859$	−2.61471e7	−	1.89970e7i	−1.20904	−	0.878419i	−0.995143	+	0.0984373i	$0.968616\pi$
$860$	−1.32888e7	−	6.16338e6i	−0.612690	−	0.284166i
$861$	7.07615e6	−	5.14112e6i	0.325304	−	0.236347i
$862$	8.22234e6	+	5.97388e6i	0.376901	+	0.273835i
$863$	−1.46449e7	−	1.06402e7i	−0.669361	−	0.486319i	0.200450	−	0.979704i	$-0.435759\pi$
$863$	−1.46449e7	−	1.06402e7i	−0.669361	−	0.486319i	−0.869811	+	0.493385i	$0.835759\pi$
$864$	2.25706e6	−	1.63985e6i	0.102863	−	0.0747342i
$865$	−1.34198e7	−	2.40927e7i	−0.609825	−	1.09483i
$866$	9.12023e6	+	6.62623e6i	0.413248	+	0.300242i
$867$	1.18218e6	+	3.63837e6i	0.0534116	+	0.164384i
$868$	−7.88960e6			−0.355431
$869$	−2.96118e6	−	9.11356e6i	−0.133019	−	0.409391i
$870$	402291.	−	3.33318e6i	0.0180195	−	0.149300i
$871$	2.08901e6	−	6.42931e6i	0.0933029	−	0.287157i
$872$	−2.24915e6	+	6.92218e6i	−0.100168	+	0.308285i
$873$	−6.49270e6	+	4.71722e6i	−0.288330	+	0.209484i
$874$	−6.15846e6			−0.272705
$875$	5.30522e6	−	1.40802e7i	0.234252	−	0.621710i
$876$	−2.54373e7			−1.11998
$877$	−6.38133e6	+	4.63630e6i	−0.280164	+	0.203551i	−0.718989	−	0.695022i	$-0.755395\pi$
$877$	−6.38133e6	+	4.63630e6i	−0.280164	+	0.203551i	0.438825	+	0.898573i	$0.355395\pi$
$878$	−4.88984e6	+	1.50494e7i	−0.214071	+	0.658843i
$879$	1.40288e7	−	4.31761e7i	0.612417	−	1.88483i
$880$	785344.	−	6.50695e6i	0.0341864	−	0.283251i
$881$	5.56272e6	+	1.71203e7i	0.241461	+	0.743141i	0.996198	+	0.0871140i	$0.0277644\pi$
$881$	5.56272e6	+	1.71203e7i	0.241461	+	0.743141i	−0.754737	+	0.656027i	$0.772236\pi$
$882$	−3.55833e6			−0.154019
$883$	580053.	+	1.78522e6i	0.0250361	+	0.0770531i	0.962794	−	0.270237i	$-0.0871020\pi$
$883$	580053.	+	1.78522e6i	0.0250361	+	0.0770531i	−0.937758	+	0.347290i	$0.887102\pi$
$884$	3.00824e6	+	2.18561e6i	0.129474	+	0.0940682i
$885$	−2.73230e6	−	4.90532e6i	−0.117265	−	0.210528i
$886$	5.25633e6	−	3.81895e6i	0.224956	−	0.163440i
$887$	−2.61073e7	−	1.89681e7i	−1.11417	−	0.809495i	−0.130858	−	0.991401i	$-0.541773\pi$
$887$	−2.61073e7	−	1.89681e7i	−1.11417	−	0.809495i	−0.983316	+	0.181907i	$0.941773\pi$
$888$	−1.79297e6	−	1.30267e6i	−0.0763028	−	0.0554373i
$889$	−667905.	+	485261.i	−0.0283439	+	0.0205931i
$890$	1.32997e7	+	6.16840e6i	0.562815	+	0.261034i
$891$	2.70834e7	+	1.96772e7i	1.14290	+	0.830367i
$892$	2.62261e6	+	8.07158e6i	0.110363	+	0.339661i
$893$	−3.05197e7			−1.28071
$894$	−4.10271e6	−	1.26269e7i	−0.171683	−	0.528386i
$895$	−2.20436e7	−	1.02239e7i	−0.919868	−	0.426636i
$896$	−436076.	+	1.34210e6i	−0.0181465	+	0.0558491i
$897$	1.45522e6	−	4.47870e6i	0.0603875	−	0.185854i
$898$	1.19574e7	−	8.68756e6i	0.494819	−	0.359507i
$899$	4.67724e6			0.193015
$900$	4.38532e6	−	1.79285e6i	0.180466	−	0.0737797i
$901$	−5.08589e7			−2.08716
$902$	−8.18937e6	+	5.94992e6i	−0.335146	+	0.243498i
$903$	−8.01110e6	+	2.46556e7i	−0.326944	+	1.00623i
$904$	2.09965e6	−	6.46205e6i	0.0854526	−	0.262996i
$905$	2.30033e7	−	4.52062e6i	0.933619	−	0.183475i
$906$	1.24477e7	+	3.83100e7i	0.503810	+	1.55057i
$907$	2.32799e7			0.939641			0.469821	−	0.882762i	$-0.344319\pi$
$907$	2.32799e7			0.939641			0.469821	+	0.882762i	$0.344319\pi$
$908$	−198100.	−	609688.i	−0.00797387	−	0.0245410i
$909$	−7.84723e6	−	5.70135e6i	−0.314997	−	0.228859i
$910$	−420331.	+	3.48265e6i	−0.0168263	+	0.139414i
$911$	−6.43583e6	+	4.67590e6i	−0.256926	+	0.186668i	−0.708791	−	0.705419i	$-0.750759\pi$
$911$	−6.43583e6	+	4.67590e6i	−0.256926	+	0.186668i	0.451865	+	0.892087i	$0.350759\pi$
$912$	4.16550e6	+	3.02642e6i	0.165837	+	0.120487i
$913$	−1.22353e7	−	8.88949e6i	−0.485779	−	0.352939i
$914$	−2.19071e6	+	1.59165e6i	−0.0867401	+	0.0630204i
$915$	3.65808e7	−	7.18885e6i	1.44444	−	0.283862i
$916$	−4.37102e6	−	3.17573e6i	−0.172125	−	0.125056i
$917$	1.80627e6	+	5.55913e6i	0.0709348	+	0.218315i
$918$	1.39051e7			0.544588
$919$	−5.59027e6	−	1.72051e7i	−0.218345	−	0.671998i	−0.998899	−	0.0469095i	$-0.985063\pi$
$919$	−5.59027e6	−	1.72051e7i	−0.218345	−	0.671998i	0.780554	−	0.625089i	$-0.214937\pi$
$920$	−3.42506e6	+	3.68814e6i	−0.133413	+	0.143660i
$921$	4.29830e6	−	1.32288e7i	0.166974	−	0.513892i
$922$	−6.53121e6	+	2.01010e7i	−0.253027	+	0.778736i
$923$	−8.31635e6	+	6.04218e6i	−0.321313	+	0.233448i
$924$	−1.15993e7			−0.446943
$925$	3.80345e6	+	4.49502e6i	0.146158	+	0.172734i
$926$	−434437.			−0.0166494
$927$	7.70452e6	−	5.59766e6i	0.294473	−	0.213947i
$928$	258521.	−	795647.i	0.00985432	−	0.0303285i
$929$	−7.69949e6	+	2.36966e7i	−0.292700	+	0.900838i	0.691284	+	0.722583i	$0.257045\pi$
$929$	−7.69949e6	+	2.36966e7i	−0.292700	+	0.900838i	−0.983984	+	0.178255i	$0.942955\pi$
$930$	1.14483e7	+	2.05533e7i	0.434045	+	0.779246i
$931$	3.17502e6	+	9.77170e6i	0.120053	+	0.369484i
$932$	1.66648e6			0.0628435
$933$	−2.93816e6	−	9.04273e6i	−0.110502	−	0.340091i
$934$	−1.41689e7	−	1.02943e7i	−0.531458	−	0.386127i
$935$	2.22295e7	−	2.39369e7i	0.831573	−	0.895445i
$936$	−893585.	+	649227.i	−0.0333385	+	0.0242218i
$937$	−2.04191e7	−	1.48354e7i	−0.759780	−	0.552013i	0.139063	−	0.990284i	$-0.455591\pi$
$937$	−2.04191e7	−	1.48354e7i	−0.759780	−	0.552013i	−0.898843	+	0.438271i	$0.855591\pi$
$938$	1.03450e7	+	7.51609e6i	0.383905	+	0.278923i
$939$	−2.40927e7	+	1.75044e7i	−0.891707	+	0.647863i
$940$	−1.69737e7	+	1.82774e7i	−0.626552	+	0.674677i
$941$	2.30954e7	+	1.67798e7i	0.850260	+	0.617750i	0.925218	−	0.379437i	$-0.123882\pi$
$941$	2.30954e7	+	1.67798e7i	0.850260	+	0.617750i	−0.0749579	+	0.997187i	$0.523882\pi$
$942$	−8.90125e6	−	2.73952e7i	−0.326831	−	1.00588i
$943$	7.77358e6			0.284670
$944$	−432358.	−	1.33066e6i	−0.0157911	−	0.0486001i
$945$	6.38340e6	+	1.14602e7i	0.232527	+	0.417458i
$946$	9.27140e6	−	2.85344e7i	0.336835	−	1.03667i
$947$	−6.99431e6	+	2.15263e7i	−0.253437	+	0.779998i	0.740697	+	0.671839i	$0.234496\pi$
$947$	−6.99431e6	+	2.15263e7i	−0.253437	+	0.779998i	−0.994134	+	0.108159i	$0.965504\pi$
$948$	4.97744e6	−	3.61632e6i	0.179881	−	0.130691i
$949$	−1.57564e7			−0.567924
$950$	−8.83634e6	−	1.04430e7i	−0.317661	−	0.375420i
$951$	−1.21121e7			−0.434277
$952$	−5.69020e6	+	4.13417e6i	−0.203486	+	0.147841i
$953$	−1.16880e7	+	3.59718e7i	−0.416875	+	1.28301i	0.493687	+	0.869639i	$0.335649\pi$
$953$	−1.16880e7	+	3.59718e7i	−0.416875	+	1.28301i	−0.910563	+	0.413371i	$0.864351\pi$
$954$	4.66845e6	−	1.43680e7i	0.166074	−	0.511124i
$955$	1.19673e7	−	1.28865e7i	0.424606	−	0.457220i
$956$	3.80323e6	+	1.17051e7i	0.134588	+	0.414220i
$957$	6.87649e6			0.242710
$958$	−4.21862e6	−	1.29836e7i	−0.148510	−	0.457068i
$959$	1.98304e7	+	1.44076e7i	0.696281	+	0.505877i
$960$	4.12911e6	−	811452.i	0.144603	−	0.0284174i
$961$	−3.35455e6	+	2.43722e6i	−0.117172	+	0.0851308i
$962$	−1.11060e6	−	806899.i	−0.0386920	−	0.0281114i
$963$	1.61006e7	+	1.16978e7i	0.559470	+	0.406479i
$964$	9.93668e6	−	7.21942e6i	0.344388	−	0.250213i
$965$	1.19097e6	−	9.86773e6i	0.0411700	−	0.341114i
$966$	7.20640e6	+	5.23576e6i	0.248471	+	0.180525i
$967$	9.01934e6	+	2.77587e7i	0.310176	+	0.954625i	0.977695	+	0.210031i	$0.0673566\pi$
$967$	9.01934e6	+	2.77587e7i	0.310176	+	0.954625i	−0.667518	+	0.744593i	$0.732643\pi$
$968$	3.11686e6			0.106913
$969$	7.93016e6	+	2.44065e7i	0.271314	+	0.835019i
$970$	1.85837e7	−	3.65206e6i	0.634164	−	0.124626i
$971$	1.29925e7	−	3.99869e7i	0.442227	−	1.36104i	−0.443268	−	0.896389i	$-0.646181\pi$
$971$	1.29925e7	−	3.99869e7i	0.442227	−	1.36104i	0.885496	−	0.464647i	$-0.153819\pi$
$972$	−3.36858e6	+	1.03674e7i	−0.114362	+	0.351969i
$973$	2.82862e7	−	2.05511e7i	0.957839	−	0.695911i
$974$	−1.96949e7			−0.665208
$975$	9.68262e6	−	3.95854e6i	0.326198	−	0.133359i
$976$	9.28959e6			0.312156
$977$	8.54145e6	−	6.20573e6i	0.286283	−	0.207997i	−0.435370	−	0.900251i	$-0.643383\pi$
$977$	8.54145e6	−	6.20573e6i	0.286283	−	0.207997i	0.721653	+	0.692255i	$0.243383\pi$
$978$	543439.	−	1.67253e6i	0.0181679	−	0.0559149i
$979$	−9.27896e6	+	2.85577e7i	−0.309416	+	0.952284i
$980$	7.61781e6	+	3.53315e6i	0.253376	+	0.117516i
$981$	−3.32991e6	−	1.02484e7i	−0.110474	−	0.340004i
$982$	3.71945e7			1.23083
$983$	2.81677e6	+	8.66912e6i	0.0929752	+	0.286148i	0.986721	−	0.162426i	$-0.0519319\pi$
$983$	2.81677e6	+	8.66912e6i	0.0929752	+	0.286148i	−0.893745	+	0.448574i	$0.851932\pi$
$984$	−5.25796e6	−	3.82013e6i	−0.173113	−	0.125774i
$985$	3.03018e7	+	1.40540e7i	0.995127	+	0.461541i
$986$	3.37335e6	−	2.45088e6i	0.110502	−	0.0802843i
$987$	3.57131e7	+	2.59471e7i	1.16690	+	0.847804i
$988$	2.58020e6	+	1.87462e6i	0.0840931	+	0.0610972i
$989$	−1.86402e7	+	1.35429e7i	−0.605981	+	0.440271i
$990$	4.72186e6	+	8.47721e6i	0.153118	+	0.274894i
$991$	4.73485e7	+	3.44007e7i	1.53152	+	1.11271i	0.955388	+	0.295355i	$0.0954379\pi$
$991$	4.73485e7	+	3.44007e7i	1.53152	+	1.11271i	0.576130	+	0.817358i	$0.304562\pi$
$992$	1.81158e6	+	5.57547e6i	0.0584492	+	0.179888i
$993$	−5.58218e7			−1.79652
$994$	−6.00858e6	−	1.84925e7i	−0.192888	−	0.593650i
$995$	1.06599e6	−	8.83222e6i	0.0341346	−	0.282821i
$996$	3.00059e6	−	9.23488e6i	0.0958427	−	0.294973i
$997$	−3.71493e6	+	1.14334e7i	−0.118362	+	0.364281i	−0.992633	−	0.121156i	$-0.961340\pi$
$997$	−3.71493e6	+	1.14334e7i	−0.118362	+	0.364281i	0.874271	+	0.485438i	$0.161340\pi$
$998$	3.15499e7	−	2.29223e7i	1.00270	−	0.728505i
$999$	−5.13359e6			−0.162745

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	50.6.d.a.11.5	✓	24
25.16	even	5	inner	50.6.d.a.41.5	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
50.6.d.a.11.5	✓	24	1.1	even	1	trivial
50.6.d.a.41.5	yes	24	25.16	even	5	inner

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:	\( N \)	\(=\)	\( 50 = 2 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	50.d (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-3.23607 + 2.35114i) q^{2} +(5.67913 - 17.4786i) q^{3} +(4.94427 - 15.2169i) q^{4} +(6.69834 - 55.4989i) q^{5} +(22.7165 + 69.9143i) q^{6} -86.1311 q^{7} +(19.7771 + 60.8676i) q^{8} +(-76.6568 - 55.6945i) q^{9} +O(q^{10})\)	\(q+(-3.23607 + 2.35114i) q^{2} +(5.67913 - 17.4786i) q^{3} +(4.94427 - 15.2169i) q^{4} +(6.69834 - 55.4989i) q^{5} +(22.7165 + 69.9143i) q^{6} -86.1311 q^{7} +(19.7771 + 60.8676i) q^{8} +(-76.6568 - 55.6945i) q^{9} +(108.810 + 195.347i) q^{10} +(-370.519 + 269.198i) q^{11} +(-237.891 - 172.838i) q^{12} +(-147.354 - 107.059i) q^{13} +(278.726 - 202.506i) q^{14} +(-932.002 - 432.263i) q^{15} +(-207.108 - 150.473i) q^{16} +(-394.287 - 1213.49i) q^{17} +379.012 q^{18} +(-338.184 - 1040.82i) q^{19} +(-811.404 - 376.330i) q^{20} +(-489.150 + 1505.45i) q^{21} +(566.103 - 1742.29i) q^{22} +(-1138.15 + 826.914i) q^{23} +1176.20 q^{24} +(-3035.26 - 743.501i) q^{25} +728.559 q^{26} +(2204.16 - 1601.42i) q^{27} +(-425.855 + 1310.65i) q^{28} +(252.462 - 776.999i) q^{29} +(4032.33 - 792.434i) q^{30} +(1769.12 + 5444.80i) q^{31} +1024.00 q^{32} +(2600.97 + 8004.96i) q^{33} +(4129.02 + 2999.91i) q^{34} +(-576.935 + 4780.18i) q^{35} +(-1226.51 + 891.111i) q^{36} +(-1524.38 - 1107.53i) q^{37} +(3541.51 + 2573.05i) q^{38} +(-2708.08 + 1967.54i) q^{39} +(3510.56 - 689.896i) q^{40} +(-4470.31 - 3247.87i) q^{41} +(-1956.60 - 6021.79i) q^{42} +16377.6 q^{43} +(2264.41 + 6969.14i) q^{44} +(-3604.46 + 3881.31i) q^{45} +(1738.94 - 5351.90i) q^{46} +(8617.72 - 26522.6i) q^{47} +(-3806.25 + 2765.40i) q^{48} -9388.44 q^{49} +(11570.4 - 4730.32i) q^{50} -23449.3 q^{51} +(-2357.67 + 1712.95i) q^{52} +(12317.4 - 37909.1i) q^{53} +(-3367.66 + 10364.6i) q^{54} +(12458.3 + 22366.6i) q^{55} +(-1703.42 - 5242.59i) q^{56} -20112.7 q^{57} +(1009.85 + 3108.00i) q^{58} +(4421.59 + 3212.47i) q^{59} +(-11185.8 + 12045.0i) q^{60} +(-29357.2 + 21329.2i) q^{61} +(-18526.5 - 13460.3i) q^{62} +(6602.54 + 4797.02i) q^{63} +(-3313.73 + 2407.57i) q^{64} +(-6928.69 + 7460.89i) q^{65} +(-27237.7 - 19789.3i) q^{66} +(11469.3 + 35298.8i) q^{67} -20415.0 q^{68} +(7989.57 + 24589.4i) q^{69} +(-9371.88 - 16825.5i) q^{70} +(17440.2 - 53675.5i) q^{71} +(1873.94 - 5767.39i) q^{72} +(69985.6 - 50847.5i) q^{73} +7536.95 q^{74} +(-30233.0 + 48829.7i) q^{75} -17510.2 q^{76} +(31913.2 - 23186.3i) q^{77} +(4137.59 - 12734.2i) q^{78} +(-6465.63 + 19899.2i) q^{79} +(-9738.37 + 10486.4i) q^{80} +(-22587.9 - 69518.3i) q^{81} +22102.4 q^{82} +(10204.4 + 31405.9i) q^{83} +(20489.8 + 14886.7i) q^{84} +(-69988.4 + 13754.1i) q^{85} +(-52999.0 + 38506.0i) q^{86} +(-12147.1 - 8825.36i) q^{87} +(-23713.2 - 17228.7i) q^{88} +(53042.2 - 38537.4i) q^{89} +(2538.75 - 21034.8i) q^{90} +(12691.8 + 9221.12i) q^{91} +(6955.75 + 21407.6i) q^{92} +105214. q^{93} +(34470.9 + 106090. i) q^{94} +(-60029.8 + 11797.1i) q^{95} +(5815.43 - 17898.1i) q^{96} +(26173.2 - 80552.8i) q^{97} +(30381.6 - 22073.5i) q^{98} +43395.7 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 24 q^{2} - 11 q^{3} - 96 q^{4} - 120 q^{5} - 44 q^{6} + 548 q^{7} - 384 q^{8} - 893 q^{9}+O(q^{10}) \) 24 * q - 24 * q^2 - 11 * q^3 - 96 * q^4 - 120 * q^5 - 44 * q^6 + 548 * q^7 - 384 * q^8 - 893 * q^9	\( 24 q - 24 q^{2} - 11 q^{3} - 96 q^{4} - 120 q^{5} - 44 q^{6} + 548 q^{7} - 384 q^{8} - 893 q^{9} + 320 q^{10} - 327 q^{11} - 96 q^{12} - 1161 q^{13} - 948 q^{14} + 760 q^{15} - 1536 q^{16} + 83 q^{17} + 7368 q^{18} - 6250 q^{19} + 2320 q^{20} + 6193 q^{21} + 852 q^{22} + 2069 q^{23} + 2176 q^{24} - 14380 q^{25} + 15976 q^{26} - 18935 q^{27} - 592 q^{28} - 11775 q^{29} - 9840 q^{30} + 2103 q^{31} + 24576 q^{32} - 11747 q^{33} + 972 q^{34} + 33235 q^{35} - 14288 q^{36} + 4148 q^{37} + 14260 q^{38} - 12576 q^{39} + 1600 q^{40} - 26427 q^{41} + 24772 q^{42} + 13024 q^{43} + 3408 q^{44} - 65535 q^{45} - 16964 q^{46} + 29803 q^{47} - 1536 q^{48} + 38368 q^{49} - 14020 q^{50} + 194058 q^{51} - 18576 q^{52} - 29011 q^{53} + 11820 q^{54} - 4185 q^{55} - 2368 q^{56} - 78040 q^{57} - 47100 q^{58} + 31430 q^{59} + 28160 q^{60} - 18362 q^{61} - 15828 q^{62} - 95886 q^{63} - 24576 q^{64} - 193280 q^{65} + 28992 q^{66} - 71657 q^{67} - 10432 q^{68} + 245919 q^{69} - 107460 q^{70} - 153827 q^{71} - 1792 q^{72} + 108264 q^{73} - 27648 q^{74} + 126020 q^{75} + 85920 q^{76} + 96141 q^{77} - 55724 q^{78} + 66670 q^{79} - 33280 q^{80} + 17709 q^{81} - 42408 q^{82} - 30621 q^{83} - 140352 q^{84} - 64895 q^{85} - 94444 q^{86} - 265360 q^{87} - 20928 q^{88} + 351835 q^{89} - 101720 q^{90} + 19323 q^{91} - 67856 q^{92} + 707998 q^{93} + 119212 q^{94} + 158570 q^{95} - 11264 q^{96} + 11058 q^{97} + 18532 q^{98} - 455966 q^{99}+O(q^{100}) \) 24 * q - 24 * q^2 - 11 * q^3 - 96 * q^4 - 120 * q^5 - 44 * q^6 + 548 * q^7 - 384 * q^8 - 893 * q^9 + 320 * q^10 - 327 * q^11 - 96 * q^12 - 1161 * q^13 - 948 * q^14 + 760 * q^15 - 1536 * q^16 + 83 * q^17 + 7368 * q^18 - 6250 * q^19 + 2320 * q^20 + 6193 * q^21 + 852 * q^22 + 2069 * q^23 + 2176 * q^24 - 14380 * q^25 + 15976 * q^26 - 18935 * q^27 - 592 * q^28 - 11775 * q^29 - 9840 * q^30 + 2103 * q^31 + 24576 * q^32 - 11747 * q^33 + 972 * q^34 + 33235 * q^35 - 14288 * q^36 + 4148 * q^37 + 14260 * q^38 - 12576 * q^39 + 1600 * q^40 - 26427 * q^41 + 24772 * q^42 + 13024 * q^43 + 3408 * q^44 - 65535 * q^45 - 16964 * q^46 + 29803 * q^47 - 1536 * q^48 + 38368 * q^49 - 14020 * q^50 + 194058 * q^51 - 18576 * q^52 - 29011 * q^53 + 11820 * q^54 - 4185 * q^55 - 2368 * q^56 - 78040 * q^57 - 47100 * q^58 + 31430 * q^59 + 28160 * q^60 - 18362 * q^61 - 15828 * q^62 - 95886 * q^63 - 24576 * q^64 - 193280 * q^65 + 28992 * q^66 - 71657 * q^67 - 10432 * q^68 + 245919 * q^69 - 107460 * q^70 - 153827 * q^71 - 1792 * q^72 + 108264 * q^73 - 27648 * q^74 + 126020 * q^75 + 85920 * q^76 + 96141 * q^77 - 55724 * q^78 + 66670 * q^79 - 33280 * q^80 + 17709 * q^81 - 42408 * q^82 - 30621 * q^83 - 140352 * q^84 - 64895 * q^85 - 94444 * q^86 - 265360 * q^87 - 20928 * q^88 + 351835 * q^89 - 101720 * q^90 + 19323 * q^91 - 67856 * q^92 + 707998 * q^93 + 119212 * q^94 + 158570 * q^95 - 11264 * q^96 + 11058 * q^97 + 18532 * q^98 - 455966 * q^99

Introduction

L-functions

Modular forms

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