LMFDB - Embedded newform 50.6.e.a.9.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [50,6,Mod(9,50)]

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([7]))

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

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

chi := DirichletCharacter("50.9");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 50 = 2 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	50.e (of order $10$, 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:	$48$
Relative dimension:	$12$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			9.6
Character	$\chi$	$=$	50.9
Dual form			50.6.e.a.39.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.35114 + 3.23607i) q^{2} +(25.8671 - 8.40474i) q^{3} +(-4.94427 - 15.2169i) q^{4} +(52.0281 + 20.4469i) q^{5} +(-33.6189 + 103.468i) q^{6} -51.8294i q^{7} +(60.8676 + 19.7771i) q^{8} +(401.877 - 291.981i) q^{9} +O(q^{10})$	\(q+(-2.35114 + 3.23607i) q^{2} +(25.8671 - 8.40474i) q^{3} +(-4.94427 - 15.2169i) q^{4} +(52.0281 + 20.4469i) q^{5} +(-33.6189 + 103.468i) q^{6} -51.8294i q^{7} +(60.8676 + 19.7771i) q^{8} +(401.877 - 291.981i) q^{9} +(-188.493 + 120.293i) q^{10} +(-441.763 - 320.960i) q^{11} +(-255.788 - 352.062i) q^{12} +(144.241 + 198.530i) q^{13} +(167.723 + 121.858i) q^{14} +(1517.67 + 91.6186i) q^{15} +(-207.108 + 150.473i) q^{16} +(1807.71 + 587.359i) q^{17} +1986.99i q^{18} +(-261.142 + 803.711i) q^{19} +(53.8967 - 892.802i) q^{20} +(-435.612 - 1340.68i) q^{21} +(2077.30 - 674.954i) q^{22} +(-1021.67 + 1406.21i) q^{23} +1740.69 q^{24} +(2288.85 + 2127.62i) q^{25} -981.587 q^{26} +(4056.60 - 5583.43i) q^{27} +(-788.682 + 256.258i) q^{28} +(-2244.77 - 6908.69i) q^{29} +(-3864.74 + 4695.87i) q^{30} +(-2438.99 + 7506.43i) q^{31} -1024.00i q^{32} +(-14124.7 - 4589.40i) q^{33} +(-6150.91 + 4468.90i) q^{34} +(1059.75 - 2696.58i) q^{35} +(-6430.03 - 4671.69i) q^{36} +(-6378.23 - 8778.88i) q^{37} +(-1986.88 - 2734.71i) q^{38} +(5399.68 + 3923.10i) q^{39} +(2762.45 + 2273.52i) q^{40} +(-3541.23 + 2572.85i) q^{41} +(5362.70 + 1742.45i) q^{42} +5774.34i q^{43} +(-2699.82 + 8309.18i) q^{44} +(26879.0 - 6974.09i) q^{45} +(-2148.50 - 6612.40i) q^{46} +(-12724.1 + 4134.32i) q^{47} +(-4092.61 + 5632.99i) q^{48} +14120.7 q^{49} +(-12266.5 + 2404.54i) q^{50} +51696.8 q^{51} +(2307.85 - 3176.48i) q^{52} +(-25282.4 + 8214.75i) q^{53} +(8530.72 + 26254.9i) q^{54} +(-16421.5 - 25731.6i) q^{55} +(1025.03 - 3154.73i) q^{56} +22984.5i q^{57} +(27634.8 + 8979.08i) q^{58} +(-17544.6 + 12746.9i) q^{59} +(-6109.61 - 23547.2i) q^{60} +(-9283.57 - 6744.91i) q^{61} +(-18556.9 - 25541.4i) q^{62} +(-15133.2 - 20829.0i) q^{63} +(3313.73 + 2407.57i) q^{64} +(3445.25 + 13278.4i) q^{65} +(48060.8 - 34918.2i) q^{66} +(-41118.8 - 13360.3i) q^{67} -30411.8i q^{68} +(-14608.9 + 44961.5i) q^{69} +(6234.71 + 9769.46i) q^{70} +(10520.8 + 32379.7i) q^{71} +(30235.8 - 9824.22i) q^{72} +(37283.5 - 51316.4i) q^{73} +43405.1 q^{74} +(77088.1 + 35798.3i) q^{75} +13521.2 q^{76} +(-16635.1 + 22896.3i) q^{77} +(-25390.8 + 8249.98i) q^{78} +(26801.3 + 82485.9i) q^{79} +(-13852.2 + 3594.11i) q^{80} +(20703.9 - 63720.2i) q^{81} -17508.8i q^{82} +(-53524.1 - 17391.0i) q^{83} +(-18247.2 + 13257.3i) q^{84} +(82041.9 + 67521.1i) q^{85} +(-18686.1 - 13576.3i) q^{86} +(-116131. - 159841. i) q^{87} +(-20541.4 - 28272.8i) q^{88} +(-59140.1 - 42967.8i) q^{89} +(-40627.7 + 103379. i) q^{90} +(10289.7 - 7475.89i) q^{91} +(26449.6 + 8593.99i) q^{92} +214669. i q^{93} +(16537.3 - 50896.5i) q^{94} +(-30020.1 + 36476.1i) q^{95} +(-8606.45 - 26487.9i) q^{96} +(122033. - 39650.8i) q^{97} +(-33199.8 + 45695.6i) q^{98} -271249. q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 192 q^{4} + 180 q^{5} + 72 q^{6} + 686 q^{9}+O(q^{10}) $ 48 * q + 192 * q^4 + 180 * q^5 + 72 * q^6 + 686 * q^9	\( 48 q + 192 q^{4} + 180 q^{5} + 72 q^{6} + 686 q^{9} + 80 q^{10} + 716 q^{11} - 160 q^{12} - 784 q^{14} - 940 q^{15} - 3072 q^{16} + 1910 q^{17} - 5990 q^{19} - 640 q^{20} - 4344 q^{21} + 4720 q^{22} + 12410 q^{23} + 4608 q^{24} + 23660 q^{25} - 15248 q^{26} + 27600 q^{27} - 3040 q^{28} - 17170 q^{29} - 14720 q^{30} - 18834 q^{31} - 56930 q^{33} + 11696 q^{34} + 28450 q^{35} - 10976 q^{36} + 3540 q^{37} + 13432 q^{39} - 1280 q^{40} + 37146 q^{41} - 43560 q^{42} + 1184 q^{44} + 75240 q^{45} + 28672 q^{46} - 17830 q^{47} - 2560 q^{48} - 54656 q^{49} + 8800 q^{50} - 85984 q^{51} + 22350 q^{53} + 16080 q^{54} - 64730 q^{55} + 12544 q^{56} + 18000 q^{59} + 78720 q^{60} + 67086 q^{61} - 159600 q^{62} + 132820 q^{63} + 49152 q^{64} - 195820 q^{65} - 52256 q^{66} - 90790 q^{67} - 212608 q^{69} + 180080 q^{70} - 122874 q^{71} + 121200 q^{73} + 281456 q^{74} + 672810 q^{75} - 102400 q^{76} + 434040 q^{77} + 170720 q^{78} + 113600 q^{79} - 28160 q^{80} + 115878 q^{81} - 582750 q^{83} - 174816 q^{84} + 107770 q^{85} - 26888 q^{86} - 911580 q^{87} - 56960 q^{88} - 357730 q^{89} - 282920 q^{90} - 216324 q^{91} + 451040 q^{92} + 79136 q^{94} + 135000 q^{95} + 18432 q^{96} - 123520 q^{97} - 206240 q^{98} + 235252 q^{99}+O(q^{100}) \) 48 * q + 192 * q^4 + 180 * q^5 + 72 * q^6 + 686 * q^9 + 80 * q^10 + 716 * q^11 - 160 * q^12 - 784 * q^14 - 940 * q^15 - 3072 * q^16 + 1910 * q^17 - 5990 * q^19 - 640 * q^20 - 4344 * q^21 + 4720 * q^22 + 12410 * q^23 + 4608 * q^24 + 23660 * q^25 - 15248 * q^26 + 27600 * q^27 - 3040 * q^28 - 17170 * q^29 - 14720 * q^30 - 18834 * q^31 - 56930 * q^33 + 11696 * q^34 + 28450 * q^35 - 10976 * q^36 + 3540 * q^37 + 13432 * q^39 - 1280 * q^40 + 37146 * q^41 - 43560 * q^42 + 1184 * q^44 + 75240 * q^45 + 28672 * q^46 - 17830 * q^47 - 2560 * q^48 - 54656 * q^49 + 8800 * q^50 - 85984 * q^51 + 22350 * q^53 + 16080 * q^54 - 64730 * q^55 + 12544 * q^56 + 18000 * q^59 + 78720 * q^60 + 67086 * q^61 - 159600 * q^62 + 132820 * q^63 + 49152 * q^64 - 195820 * q^65 - 52256 * q^66 - 90790 * q^67 - 212608 * q^69 + 180080 * q^70 - 122874 * q^71 + 121200 * q^73 + 281456 * q^74 + 672810 * q^75 - 102400 * q^76 + 434040 * q^77 + 170720 * q^78 + 113600 * q^79 - 28160 * q^80 + 115878 * q^81 - 582750 * q^83 - 174816 * q^84 + 107770 * q^85 - 26888 * q^86 - 911580 * q^87 - 56960 * q^88 - 357730 * q^89 - 282920 * q^90 - 216324 * q^91 + 451040 * q^92 + 79136 * q^94 + 135000 * q^95 + 18432 * q^96 - 123520 * q^97 - 206240 * q^98 + 235252 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$27$
$\chi(n)$	$e\left(\frac{7}{10}\right)$

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 $

$2$	−2.35114	+	3.23607i	−0.415627	+	0.572061i
$2$	−2.35114	+	3.23607i	−0.415627	+	0.572061i
$3$	25.8671	−	8.40474i	1.65938	−	0.539164i	0.678635	−	0.734476i	$-0.262572\pi$
$3$	25.8671	−	8.40474i	1.65938	−	0.539164i	0.980741	+	0.195311i	$0.0625718\pi$
$4$	−4.94427	−	15.2169i	−0.154508	−	0.475528i
$5$	52.0281	+	20.4469i	0.930707	+	0.365764i
$5$	52.0281	+	20.4469i	0.930707	+	0.365764i
$6$	−33.6189	+	103.468i	−0.381247	+	1.17336i
$7$		−	51.8294i		−	0.399789i	−0.979817	−	0.199894i	$-0.935940\pi$
$7$		−	51.8294i		−	0.399789i	0.979817	−	0.199894i	$-0.0640599\pi$
$8$	60.8676	+	19.7771i	0.336249	+	0.109254i
$9$	401.877	−	291.981i	1.65382	−	1.20157i
$10$	−188.493	+	120.293i	−0.596067	+	0.380400i
$11$	−441.763	−	320.960i	−1.10080	−	0.799777i	−0.119608	−	0.992821i	$-0.538164\pi$
$11$	−441.763	−	320.960i	−1.10080	−	0.799777i	−0.981190	+	0.193044i	$0.938164\pi$
$12$	−255.788	−	352.062i	−0.512776	−	0.705775i
$13$	144.241	+	198.530i	0.236717	+	0.325813i	0.910804	−	0.412839i	$-0.135463\pi$
$13$	144.241	+	198.530i	0.236717	+	0.325813i	−0.674087	+	0.738652i	$0.735463\pi$
$14$	167.723	+	121.858i	0.228704	+	0.166163i
$15$	1517.67	+	91.6186i	1.74160	+	0.105137i
$16$	−207.108	+	150.473i	−0.202254	+	0.146946i
$17$	1807.71	+	587.359i	1.51707	+	0.492926i	0.944942	−	0.327238i	$-0.106118\pi$
$17$	1807.71	+	587.359i	1.51707	+	0.492926i	0.572128	+	0.820164i	$0.306118\pi$
$18$			1986.99i			1.44549i
$19$	−261.142	+	803.711i	−0.165956	+	0.510759i	−0.999105	−	0.0422884i	$-0.986535\pi$
$19$	−261.142	+	803.711i	−0.165956	+	0.510759i	0.833150	+	0.553047i	$0.186535\pi$
$20$	53.8967	−	892.802i	0.0301291	−	0.499091i
$21$	−435.612	−	1340.68i	−0.215552	−	0.663400i
$22$	2077.30	−	674.954i	0.915043	−	0.297315i
$23$	−1021.67	+	1406.21i	−0.402709	+	0.554282i	−0.961421	−	0.275080i	$-0.911296\pi$
$23$	−1021.67	+	1406.21i	−0.402709	+	0.554282i	0.558712	+	0.829362i	$0.311296\pi$
$24$	1740.69			0.616870
$25$	2288.85	+	2127.62i	0.732433	+	0.680839i
$26$	−981.587			−0.284771
$27$	4056.60	−	5583.43i	1.07091	−	1.47398i
$28$	−788.682	+	256.258i	−0.190111	+	0.0617708i
$29$	−2244.77	−	6908.69i	−0.495652	−	1.52546i	−0.815938	−	0.578139i	$-0.803779\pi$
$29$	−2244.77	−	6908.69i	−0.495652	−	1.52546i	0.320286	−	0.947321i	$-0.396221\pi$
$30$	−3864.74	+	4695.87i	−0.784001	+	0.952605i
$31$	−2438.99	+	7506.43i	−0.455833	+	1.40291i	0.414322	+	0.910130i	$0.364019\pi$
$31$	−2438.99	+	7506.43i	−0.455833	+	1.40291i	−0.870155	+	0.492778i	$0.835981\pi$
$32$		−	1024.00i		−	0.176777i
$33$	−14124.7	−	4589.40i	−2.25785	−	0.733620i
$34$	−6150.91	+	4468.90i	−0.912519	+	0.662984i
$35$	1059.75	−	2696.58i	0.146229	−	0.372086i
$36$	−6430.03	−	4671.69i	−0.826908	−	0.600784i
$37$	−6378.23	−	8778.88i	−0.765942	−	1.05423i	−0.996697	−	0.0812162i	$-0.974120\pi$
$37$	−6378.23	−	8778.88i	−0.765942	−	1.05423i	0.230755	−	0.973012i	$-0.425880\pi$
$38$	−1986.88	−	2734.71i	−0.223210	−	0.307222i
$39$	5399.68	+	3923.10i	0.568469	+	0.413017i
$40$	2762.45	+	2273.52i	0.272988	+	0.224672i
$41$	−3541.23	+	2572.85i	−0.328999	+	0.239031i	−0.740006	−	0.672601i	$-0.765177\pi$
$41$	−3541.23	+	2572.85i	−0.328999	+	0.239031i	0.411007	+	0.911632i	$0.365177\pi$
$42$	5362.70	+	1742.45i	0.469095	+	0.152418i
$43$			5774.34i			0.476245i	0.971235	+	0.238123i	$0.0765321\pi$
$43$			5774.34i			0.476245i	−0.971235	+	0.238123i	$0.923468\pi$
$44$	−2699.82	+	8309.18i	−0.210234	+	0.647033i
$45$	26879.0	−	6974.09i	1.97871	−	0.513401i
$46$	−2148.50	−	6612.40i	−0.149706	−	0.460749i
$47$	−12724.1	+	4134.32i	−0.840202	+	0.272998i	−0.697336	−	0.716744i	$-0.745632\pi$
$47$	−12724.1	+	4134.32i	−0.840202	+	0.272998i	−0.142865	+	0.989742i	$0.545632\pi$
$48$	−4092.61	+	5632.99i	−0.256388	+	0.352887i
$49$	14120.7			0.840169
$50$	−12266.5	+	2404.54i	−0.693901	+	0.136021i
$51$	51696.8			2.78316
$52$	2307.85	−	3176.48i	0.118358	−	0.162906i
$53$	−25282.4	+	8214.75i	−1.23631	+	0.401703i	−0.852998	−	0.521915i	$-0.825218\pi$
$53$	−25282.4	+	8214.75i	−1.23631	+	0.401703i	−0.383316	+	0.923617i	$0.625218\pi$
$54$	8530.72	+	26254.9i	0.398108	+	1.22525i
$55$	−16421.5	−	25731.6i	−0.731991	−	1.14699i
$56$	1025.03	−	3154.73i	0.0436785	−	0.134429i
$57$			22984.5i			0.937019i
$58$	27634.8	+	8979.08i	1.07866	+	0.350479i
$59$	−17544.6	+	12746.9i	−0.656166	+	0.476733i	−0.865366	−	0.501140i	$-0.832914\pi$
$59$	−17544.6	+	12746.9i	−0.656166	+	0.476733i	0.209200	+	0.977873i	$0.432914\pi$
$60$	−6109.61	−	23547.2i	−0.219097	−	0.844425i
$61$	−9283.57	−	6744.91i	−0.319441	−	0.232087i	0.416496	−	0.909138i	$-0.363258\pi$
$61$	−9283.57	−	6744.91i	−0.319441	−	0.232087i	−0.735937	+	0.677050i	$0.763258\pi$
$62$	−18556.9	−	25541.4i	−0.613094	−	0.843851i
$63$	−15133.2	−	20829.0i	−0.480373	−	0.661177i
$64$	3313.73	+	2407.57i	0.101127	+	0.0734732i
$65$	3445.25	+	13278.4i	0.101143	+	0.389819i
$66$	48060.8	−	34918.2i	1.35810	−	0.986717i
$67$	−41118.8	−	13360.3i	−1.11906	−	0.363605i	−0.309652	−	0.950850i	$-0.600213\pi$
$67$	−41118.8	−	13360.3i	−1.11906	−	0.363605i	−0.809409	+	0.587245i	$0.800213\pi$
$68$		−	30411.8i		−	0.797571i
$69$	−14608.9	+	44961.5i	−0.369398	+	1.13689i
$70$	6234.71	+	9769.46i	0.152080	+	0.238301i
$71$	10520.8	+	32379.7i	0.247687	+	0.762302i	0.995183	+	0.0980356i	$0.0312559\pi$
$71$	10520.8	+	32379.7i	0.247687	+	0.762302i	−0.747496	+	0.664266i	$0.768744\pi$
$72$	30235.8	−	9824.22i	0.687370	−	0.223340i
$73$	37283.5	−	51316.4i	0.818861	−	1.12707i	−0.171034	−	0.985265i	$-0.554711\pi$
$73$	37283.5	−	51316.4i	0.818861	−	1.12707i	0.989895	−	0.141800i	$-0.0452890\pi$
$74$	43405.1			0.921429
$75$	77088.1	+	35798.3i	1.58247	+	0.734868i
$76$	13521.2			0.268522
$77$	−16635.1	+	22896.3i	−0.319742	+	0.440087i
$78$	−25390.8	+	8249.98i	−0.472542	+	0.153538i
$79$	26801.3	+	82485.9i	0.483156	+	1.48700i	0.834633	+	0.550806i	$0.185680\pi$
$79$	26801.3	+	82485.9i	0.483156	+	1.48700i	−0.351477	+	0.936197i	$0.614320\pi$
$80$	−13852.2	+	3594.11i	−0.241987	+	0.0627866i
$81$	20703.9	−	63720.2i	0.350623	−	1.07911i
$82$		−	17508.8i		−	0.287555i
$83$	−53524.1	−	17391.0i	−0.852814	−	0.277096i	−0.150190	−	0.988657i	$-0.547988\pi$
$83$	−53524.1	−	17391.0i	−0.852814	−	0.277096i	−0.702624	+	0.711561i	$0.747988\pi$
$84$	−18247.2	+	13257.3i	−0.282161	+	0.205002i
$85$	82041.9	+	67521.1i	1.23165	+	1.01366i
$86$	−18686.1	−	13576.3i	−0.272442	−	0.197940i
$87$	−116131.	−	159841.i	−1.64495	−	2.26407i
$88$	−20541.4	−	28272.8i	−0.282764	−	0.389191i
$89$	−59140.1	−	42967.8i	−0.791419	−	0.575000i	0.116965	−	0.993136i	$-0.462684\pi$
$89$	−59140.1	−	42967.8i	−0.791419	−	0.575000i	−0.908384	+	0.418136i	$0.862684\pi$
$90$	−40627.7	+	103379.i	−0.528708	+	1.34533i
$91$	10289.7	−	7475.89i	0.130256	−	0.0946367i
$92$	26449.6	+	8593.99i	0.325799	+	0.105858i
$93$			214669.i			2.57372i
$94$	16537.3	−	50896.5i	0.193039	−	0.594112i
$95$	−30020.1	+	36476.1i	−0.341274	+	0.414667i
$96$	−8606.45	−	26487.9i	−0.0953116	−	0.293339i
$97$	122033.	−	39650.8i	1.31688	−	0.427881i	0.435458	−	0.900209i	$-0.356586\pi$
$97$	122033.	−	39650.8i	1.31688	−	0.427881i	0.881423	+	0.472328i	$0.156586\pi$
$98$	−33199.8	+	45695.6i	−0.349197	+	0.480628i
$99$	−271249.			−2.78150
$100$	21059.1	−	45348.8i	0.210591	−	0.453488i
$101$	42557.5			0.415119			0.207559	−	0.978222i	$-0.433448\pi$
$101$	42557.5			0.415119			0.207559	+	0.978222i	$0.433448\pi$
$102$	−121546.	+	167294.i	−1.15676	+	1.59214i
$103$	5315.47	−	1727.10i	0.0493683	−	0.0160407i	−0.284229	−	0.958756i	$-0.591738\pi$
$103$	5315.47	−	1727.10i	0.0493683	−	0.0160407i	0.333597	+	0.942716i	$0.391738\pi$
$104$	4853.23	+	14936.7i	0.0439995	+	0.135417i
$105$	4748.53	−	78659.8i	0.0420326	−	0.696273i
$106$	32859.0	−	101130.i	0.284047	−	0.874206i
$107$		−	107007.i		−	0.903553i	−0.892131	−	0.451776i	$-0.850791\pi$
$107$		−	107007.i		−	0.903553i	0.892131	−	0.451776i	$-0.149209\pi$
$108$	−105019.	−	34122.9i	−0.866384	−	0.281505i
$109$	143678.	−	104388.i	1.15831	−	0.841562i	0.168747	−	0.985659i	$-0.446028\pi$
$109$	143678.	−	104388.i	1.15831	−	0.841562i	0.989563	+	0.144098i	$0.0460279\pi$
$110$	121878.	+	7357.56i	0.960385	+	0.0579765i
$111$	−238770.	−	173477.i	−1.83939	−	1.33639i
$112$	7798.92	+	10734.3i	0.0587475	+	0.0808590i
$113$	93836.2	+	129154.i	0.691312	+	0.951510i	1.00000		0.000346302i	$0.000110231\pi$
$113$	93836.2	+	129154.i	0.691312	+	0.951510i	−0.308688	+	0.951163i	$0.599890\pi$
$114$	−74379.5	−	54039.9i	−0.536032	−	0.389450i
$115$	−81908.2	+	52272.5i	−0.577541	+	0.368578i
$116$	−94030.2	+	68316.9i	−0.648817	+	0.471393i
$117$	115934.	+	37669.2i	0.782972	+	0.254403i
$118$		−	86745.3i		−	0.573510i
$119$	30442.5	−	93692.3i	0.197066	−	0.606508i
$120$	90564.9	+	35591.7i	0.574125	+	0.225629i
$121$	42372.1	+	130408.i	0.263097	+	0.809730i
$122$	43653.9	−	14184.0i	0.265536	−	0.0862780i
$123$	−69977.2	+	96315.3i	−0.417055	+	0.574027i
$124$	126284.			0.737553
$125$	75581.5	+	157496.i	0.432654	+	0.901560i
$126$	102984.			0.577890
$127$	11488.0	−	15811.9i	0.0632026	−	0.0869910i	−0.776246	−	0.630431i	$-0.782878\pi$
$127$	11488.0	−	15811.9i	0.0632026	−	0.0869910i	0.839448	+	0.543440i	$0.182878\pi$
$128$	−15582.1	+	5062.93i	−0.0840623	+	0.0273135i
$129$	48531.8	+	149365.i	0.256774	+	0.790271i
$130$	−51070.1	−	20070.4i	−0.265038	−	0.104159i
$131$	27075.1	−	83328.4i	0.137845	−	0.424243i	−0.858177	−	0.513354i	$-0.828403\pi$
$131$	27075.1	−	83328.4i	0.137845	−	0.424243i	0.996022	+	0.0891111i	$0.0284026\pi$
$132$			237626.i			1.18702i
$133$	41655.8	+	13534.8i	0.204196	+	0.0663472i
$134$	139911.	−	101651.i	0.673116	−	0.489048i
$135$	325221.	−	207551.i	1.53583	−	0.980143i
$136$	98414.5	+	71502.3i	0.456260	+	0.331492i
$137$	−195914.	−	269653.i	−0.891794	−	1.22745i	−0.973012	−	0.230753i	$-0.925881\pi$
$137$	−195914.	−	269653.i	−0.891794	−	1.22745i	0.0812179	−	0.996696i	$-0.474119\pi$
$138$	−111151.	−	152986.i	−0.496839	−	0.683840i
$139$	61145.6	+	44424.9i	0.268428	+	0.195025i	0.713854	−	0.700294i	$-0.246948\pi$
$139$	61145.6	+	44424.9i	0.268428	+	0.195025i	−0.445426	+	0.895319i	$0.646948\pi$
$140$	−46273.3	−	2793.43i	−0.199531	−	0.0120453i
$141$	−294389.	+	213886.i	−1.24702	+	0.906013i
$142$	−129519.	−	42083.2i	−0.539029	−	0.175141i
$143$		−	133999.i		−	0.547975i
$144$	−39296.9	+	120943.i	−0.157925	+	0.486044i
$145$	24469.9	−	405345.i	0.0966521	−	1.60105i
$146$	78404.5	+	241304.i	0.304410	+	0.936877i
$147$	365262.	−	118681.i	1.39416	−	0.452989i
$148$	−102052.	+	140462.i	−0.382971	+	0.527114i
$149$	61501.7			0.226945			0.113473	−	0.993541i	$-0.463803\pi$
$149$	61501.7			0.226945			0.113473	+	0.993541i	$0.463803\pi$
$150$	−297091.	+	165296.i	−1.07810	+	0.599837i
$151$	241334.			0.861344			0.430672	−	0.902509i	$-0.358277\pi$
$151$	241334.			0.861344			0.430672	+	0.902509i	$0.358277\pi$
$152$	−31790.1	+	43755.4i	−0.111605	+	0.153611i
$153$	897973.	−	291769.i	3.10124	−	1.00765i
$154$	−34982.4	−	107665.i	−0.118863	−	0.365824i
$155$	−280379.	+	340676.i	−0.937381	+	1.13897i
$156$	32999.9	−	101563.i	0.108568	−	0.334138i
$157$			277592.i			0.898790i	0.893333	+	0.449395i	$0.148360\pi$
$157$			277592.i			0.898790i	−0.893333	+	0.449395i	$0.851640\pi$
$158$	−329943.	−	107205.i	−1.05147	−	0.341643i
$159$	−584940.	+	424984.i	−1.83493	+	1.33315i
$160$	20937.6	−	53276.8i	0.0646586	−	0.164527i
$161$	72883.0	+	52952.6i	0.221596	+	0.160999i
$162$	157525.	+	216814.i	0.471587	+	0.649084i
$163$	18918.3	+	26038.8i	0.0557716	+	0.0767630i	0.835992	−	0.548742i	$-0.184893\pi$
$163$	18918.3	+	26038.8i	0.0557716	+	0.0767630i	−0.780220	+	0.625505i	$0.784893\pi$
$164$	56659.6	+	41165.6i	0.164499	+	0.119516i
$165$	−641044.	−	527584.i	−1.83307	−	1.50863i
$166$	182121.	−	132319.i	0.512968	−	0.372693i
$167$	466484.	+	151570.i	1.29433	+	0.420554i	0.873606	−	0.486634i	$-0.161775\pi$
$167$	466484.	+	151570.i	1.29433	+	0.420554i	0.420726	+	0.907188i	$0.361775\pi$
$168$		−	90218.9i		−	0.246618i
$169$	96127.0	−	295848.i	0.258898	−	0.796806i
$170$	−411395.	+	106742.i	−1.09178	+	0.283277i
$171$	129721.	+	399242.i	0.339251	+	1.04411i
$172$	87867.5	−	28549.9i	0.226468	−	0.0735840i
$173$	38085.1	−	52419.6i	0.0967474	−	0.133161i	−0.757899	−	0.652372i	$-0.773774\pi$
$173$	38085.1	−	52419.6i	0.0967474	−	0.133161i	0.854646	+	0.519211i	$0.173774\pi$
$174$	790299.			1.97887
$175$	110273.	−	118630.i	0.272192	−	0.292818i
$176$	139789.			0.340165
$177$	−346694.	+	477184.i	−0.831789	+	1.14486i
$178$	278093.	−	90358.0i	0.657871	−	0.213755i
$179$	−2642.26	−	8132.04i	−0.00616372	−	0.0189700i	0.947927	−	0.318487i	$-0.103175\pi$
$179$	−2642.26	−	8132.04i	−0.00616372	−	0.0189700i	−0.954091	+	0.299517i	$0.903175\pi$
$180$	−239021.	−	374533.i	−0.549864	−	0.861607i
$181$	−192844.	+	593513.i	−0.437532	+	1.34658i	0.452938	+	0.891542i	$0.350376\pi$
$181$	−192844.	+	593513.i	−0.437532	+	1.34658i	−0.890470	+	0.455043i	$0.849624\pi$
$182$			50875.0i			0.113848i
$183$	−296828.	−	96445.4i	−0.655206	−	0.212889i
$184$	−89997.5	+	65387.0i	−0.195968	+	0.142379i
$185$	−152347.	−	587163.i	−0.327268	−	1.26133i
$186$	−694683.	−	504717.i	−1.47233	−	1.06971i
$187$	−610059.	−	839675.i	−1.27576	−	1.75593i
$188$	125823.	+	173181.i	0.259637	+	0.357359i
$189$	−289385.	−	210251.i	−0.589281	−	0.428137i
$190$	−47457.6	−	182907.i	−0.0953722	−	0.367576i
$191$	−383886.	+	278910.i	−0.761411	+	0.553197i	−0.899343	−	0.437244i	$-0.855955\pi$
$191$	−383886.	+	278910.i	−0.761411	+	0.553197i	0.137932	+	0.990442i	$0.455955\pi$
$192$	105952.	+	34425.8i	0.207422	+	0.0673955i
$193$			60544.4i			0.116999i	0.998287	+	0.0584993i	$0.0186316\pi$
$193$			60544.4i			0.116999i	−0.998287	+	0.0584993i	$0.981368\pi$
$194$	−158603.	+	488130.i	−0.302557	+	0.931175i
$195$	200720.	+	314518.i	0.378011	+	0.592323i
$196$	−69816.7	−	214874.i	−0.129813	−	0.399524i
$197$	−662320.	+	215201.i	−1.21591	+	0.395074i	−0.845592	−	0.533830i	$-0.820752\pi$
$197$	−662320.	+	215201.i	−1.21591	+	0.395074i	−0.370320	+	0.928904i	$0.620752\pi$
$198$	637744.	−	877779.i	1.15607	−	1.59119i
$199$	278810.			0.499087			0.249543	−	0.968364i	$-0.419720\pi$
$199$	278810.			0.499087			0.249543	+	0.968364i	$0.419720\pi$
$200$	97238.8	+	174770.i	0.171895	+	0.308953i
$201$	−1.17592e6			−2.05299
$202$	−100059.	+	137719.i	−0.172535	+	0.237474i
$203$	−358073.	+	116345.i	−0.609862	+	0.198156i
$204$	−255603.	−	786665.i	−0.430022	−	1.32347i
$205$	−236850.	+	61453.7i	−0.393631	+	0.102132i
$206$	−6908.40	+	21261.9i	−0.0113425	+	0.0349087i
$207$			863432.i			1.40056i
$208$	−59746.9	−	19412.9i	−0.0957539	−	0.0311123i
$209$	373322.	−	271234.i	0.591177	−	0.429515i
$210$	243384.	+	200307.i	0.380841	+	0.313435i
$211$	300797.	+	218542.i	0.465122	+	0.337931i	0.795537	−	0.605905i	$-0.207189\pi$
$211$	300797.	+	218542.i	0.465122	+	0.337931i	−0.330415	+	0.943836i	$0.607189\pi$
$212$	250006.	+	344104.i	0.382042	+	0.525836i
$213$	544286.	+	749145.i	0.822012	+	1.13140i
$214$	346282.	+	251589.i	0.516888	+	0.375541i
$215$	−118067.	+	300428.i	−0.174194	+	0.443245i
$216$	357339.	−	259622.i	0.521131	−	0.378623i
$217$	389054.	+	126411.i	0.560867	+	0.182237i
$218$			710385.i			1.01240i
$219$	533117.	−	1.64077e6i	0.751125	−	2.31173i
$220$	−310363.	+	377108.i	−0.432328	+	0.525302i
$221$	144136.	+	443605.i	0.198514	+	0.610964i
$222$	1.12277e6	−	364809.i	1.52900	−	0.496802i
$223$	−343770.	+	473159.i	−0.462920	+	0.637154i	−0.975111	−	0.221717i	$-0.928834\pi$
$223$	−343770.	+	473159.i	−0.462920	+	0.637154i	0.512191	+	0.858871i	$0.328834\pi$
$224$	−53073.3			−0.0706733
$225$	1.54106e6	+	186742.i	2.02938	+	0.245916i
$226$	−638575.			−0.831650
$227$	828782.	−	1.14072e6i	1.06752	−	1.46931i	0.194956	−	0.980812i	$-0.437544\pi$
$227$	828782.	−	1.14072e6i	1.06752	−	1.46931i	0.872563	−	0.488501i	$-0.162456\pi$
$228$	349753.	−	113642.i	0.445579	−	0.144777i
$229$	−146755.	−	451665.i	−0.184928	−	0.569151i	0.815019	−	0.579435i	$-0.196727\pi$
$229$	−146755.	−	451665.i	−0.184928	−	0.569151i	−0.999947	+	0.0102836i	$0.996727\pi$
$230$	23420.4	−	387961.i	0.0291927	−	0.483580i
$231$	−237866.	+	732075.i	−0.293293	+	0.902663i
$232$		−	464911.i		−	0.567087i
$233$	124256.	+	40373.2i	0.149943	+	0.0487195i	0.383027	−	0.923737i	$-0.374882\pi$
$233$	124256.	+	40373.2i	0.149943	+	0.0487195i	−0.233084	+	0.972457i	$0.574882\pi$
$234$	−394477.	+	286604.i	−0.470958	+	0.342171i
$235$	−746547.	−	45067.5i	−0.881835	−	0.0532346i
$236$	280714.	+	203951.i	0.328083	+	0.238366i
$237$	1.38654e6	+	1.90841e6i	1.60348	+	2.20700i
$238$	231620.	+	318798.i	0.265054	+	0.364815i
$239$	−984711.	−	715435.i	−1.11510	−	0.810168i	−0.131642	−	0.991297i	$-0.542025\pi$
$239$	−984711.	−	715435.i	−1.11510	−	0.810168i	−0.983459	+	0.181129i	$0.942025\pi$
$240$	−328108.	+	209393.i	−0.367696	+	0.234657i
$241$	1.22764e6	−	891930.i	1.36153	−	0.989209i	0.363183	−	0.931718i	$-0.381690\pi$
$241$	1.22764e6	−	891930.i	1.36153	−	0.989209i	0.998346	−	0.0574911i	$-0.0183101\pi$
$242$	−521631.	−	169488.i	−0.572565	−	0.186038i
$243$		−	145204.i		−	0.157748i
$244$	−56736.1	+	174616.i	−0.0610078	+	0.187763i
$245$	734675.	+	288724.i	0.781951	+	0.307304i
$246$	−147157.	−	452902.i	−0.155040	−	0.477163i
$247$	−197228.	+	64083.3i	−0.205696	+	0.0668348i
$248$	−296911.	+	408663.i	−0.306547	+	0.421925i
$249$	−1.53068e6			−1.56454
$250$	−687371.	−	125709.i	−0.695570	−	0.127208i
$251$	1.76112e6			1.76444			0.882218	−	0.470842i	$-0.156050\pi$
$251$	1.76112e6			1.76444			0.882218	+	0.470842i	$0.156050\pi$
$252$	−242131.	+	333264.i	−0.240187	+	0.330588i
$253$	902674.	−	293297.i	0.886604	−	0.288075i
$254$	24158.4	+	74351.9i	0.0234955	+	0.0723116i
$255$	2.68969e6	+	1.05704e6i	2.59031	+	1.01798i
$256$	20251.7	−	62328.4i	0.0193136	−	0.0594410i
$257$		−	1.34210e6i		−	1.26751i	−0.773532	−	0.633757i	$-0.781512\pi$
$257$		−	1.34210e6i		−	1.26751i	0.773532	−	0.633757i	$-0.218488\pi$
$258$	−597462.	−	194127.i	−0.558806	−	0.181567i
$259$	−455003.	+	330579.i	−0.421469	+	0.306215i
$260$	185022.	−	118078.i	0.169742	−	0.108327i
$261$	−2.91933e6	−	2.12102e6i	−2.65266	−	1.92727i
$262$	205999.	+	283534.i	0.185401	+	0.255183i
$263$	−736143.	−	1.01321e6i	−0.656256	−	0.903258i	0.343095	−	0.939301i	$-0.388525\pi$
$263$	−736143.	−	1.01321e6i	−0.656256	−	0.903258i	−0.999350	+	0.0360426i	$0.988525\pi$
$264$	−768973.	−	558692.i	−0.679049	−	0.493358i
$265$	−1.48336e6	−	89547.6i	−1.29757	−	0.0783320i
$266$	−141738.	+	102979.i	−0.122824	+	0.0892368i
$267$	−1.89092e6	−	614396.i	−1.62328	−	0.527436i
$268$			691758.i			0.588325i
$269$	551426.	−	1.69711e6i	0.464629	−	1.42998i	−0.394819	−	0.918759i	$-0.629193\pi$
$269$	551426.	−	1.69711e6i	0.464629	−	1.42998i	0.859448	−	0.511222i	$-0.170807\pi$
$270$	−92991.9	+	1.54042e6i	−0.0776311	+	1.28596i
$271$	117787.	+	362510.i	0.0974256	+	0.299845i	0.987878	−	0.155231i	$-0.0496121\pi$
$271$	117787.	+	362510.i	0.0974256	+	0.299845i	−0.890453	+	0.455076i	$0.849612\pi$
$272$	−462773.	+	150364.i	−0.379267	+	0.123231i
$273$	203332.	−	279862.i	0.165119	−	0.227267i
$274$	1.33324e6			1.07283
$275$	−328249.	−	1.67454e6i	−0.261741	−	1.33525i
$276$	756405.			0.597698
$277$	−68252.5	+	93941.6i	−0.0534465	+	0.0735628i	−0.834904	−	0.550396i	$-0.814477\pi$
$277$	−68252.5	+	93941.6i	−0.0534465	+	0.0735628i	0.781457	+	0.623959i	$0.214477\pi$
$278$	−287524.	+	93422.2i	−0.223132	+	0.0725000i
$279$	1.21156e6	+	3.72880e6i	0.931826	+	2.86786i
$280$	117835.	−	143176.i	0.0898212	−	0.109138i
$281$	−464707.	+	1.43022e6i	−0.351086	+	1.08053i	0.607158	+	0.794581i	$0.292310\pi$
$281$	−464707.	+	1.43022e6i	−0.351086	+	1.08053i	−0.958244	+	0.285951i	$0.907690\pi$
$282$		−	1.45554e6i		−	1.08994i
$283$	−274415.	−	89163.0i	−0.203677	−	0.0661787i	0.205402	−	0.978678i	$-0.434150\pi$
$283$	−274415.	−	89163.0i	−0.203677	−	0.0661787i	−0.409079	+	0.912499i	$0.634150\pi$
$284$	440701.	−	320188.i	0.324226	−	0.235564i
$285$	−469961.	+	1.19584e6i	−0.342728	+	0.872090i
$286$	433629.	+	315050.i	0.313475	+	0.227753i
$287$	133349.	+	183539.i	0.0955621	+	0.131530i
$288$	−298988.	−	411522.i	−0.212409	−	0.292356i
$289$	1.77412e6	+	1.28898e6i	1.24951	+	0.907821i
$290$	1.25419e6	+	1.03221e6i	0.875727	+	0.720730i
$291$	2.82338e6	−	2.05130e6i	1.95450	−	1.42003i
$292$	−965217.	−	313618.i	−0.662472	−	0.215250i
$293$			250644.i			0.170564i	0.996357	+	0.0852821i	$0.0271791\pi$
$293$			250644.i			0.170564i	−0.996357	+	0.0852821i	$0.972821\pi$
$294$	−474724.	+	1.46105e6i	−0.320312	+	0.985817i
$295$	−1.17345e6	+	304466.i	−0.785071	+	0.203696i
$296$	−214607.	−	660492.i	−0.142369	−	0.438166i
$297$	−3.58411e6	+	1.16455e6i	−2.35771	+	0.766066i
$298$	−144599.	+	199024.i	−0.0943246	+	0.129827i
$299$	−426542.			−0.275920
$300$	163594.	−	1.35004e6i	0.104946	−	0.866050i
$301$	299280.			0.190398
$302$	−567411.	+	780974.i	−0.357998	+	0.492741i
$303$	1.10084e6	−	357684.i	0.688839	−	0.223817i
$304$	−66852.3	−	205750.i	−0.0414889	−	0.127690i
$305$	−345094.	−	540745.i	−0.212417	−	0.332845i
$306$	−1.16708e6	+	3.59189e6i	−0.712518	+	2.19291i
$307$		−	584488.i		−	0.353940i	−0.984216	−	0.176970i	$-0.943370\pi$
$307$		−	584488.i		−	0.353940i	0.984216	−	0.176970i	$-0.0566295\pi$
$308$	430659.	+	139930.i	0.258677	+	0.0840491i
$309$	122980.	−	89350.2i	0.0732720	−	0.0532352i
$310$	−443240.	−	1.70830e6i	−0.261960	−	1.00963i
$311$	−458499.	−	333119.i	−0.268805	−	0.195298i	0.445215	−	0.895424i	$-0.353127\pi$
$311$	−458499.	−	333119.i	−0.268805	−	0.195298i	−0.714020	+	0.700126i	$0.753127\pi$
$312$	251078.	+	345580.i	0.146023	+	0.200984i
$313$	103249.	+	142110.i	0.0595696	+	0.0819905i	0.837762	−	0.546035i	$-0.183863\pi$
$313$	103249.	+	142110.i	0.0595696	+	0.0819905i	−0.778193	+	0.628025i	$0.783863\pi$
$314$	−898308.	−	652659.i	−0.514163	−	0.373561i
$315$	−361463.	−	1.39312e6i	−0.205252	−	0.791066i
$316$	1.12267e6	−	815665.i	0.632460	−	0.459509i
$317$	1.39165e6	+	452175.i	0.777825	+	0.252731i	0.670911	−	0.741538i	$-0.265903\pi$
$317$	1.39165e6	+	452175.i	0.777825	+	0.252731i	0.106914	+	0.994268i	$0.465903\pi$
$318$		−	2.89210e6i		−	1.60378i
$319$	−1.22576e6	+	3.77249e6i	−0.674415	+	2.07564i
$320$	123180.	+	193017.i	0.0672459	+	0.105371i
$321$	−899367.	−	2.76797e6i	−0.487163	−	1.49933i
$322$	−342716.	+	111355.i	−0.184202	+	0.0598510i
$323$	−944135.	+	1.29949e6i	−0.503533	+	0.693053i
$324$	−1.07199e6			−0.567320
$325$	−92252.0	+	761296.i	−0.0484470	+	0.399802i
$326$	−128743.			−0.0670933
$327$	2.83919e6	−	3.90781e6i	1.46833	−	2.02099i
$328$	−266430.	+	86568.2i	−0.136741	+	0.0444297i
$329$	214279.	+	659484.i	0.109142	+	0.335903i
$330$	3.21448e6	−	834037.i	1.62490	−	0.421600i
$331$	−196355.	+	604317.i	−0.0985079	+	0.303176i	−0.988152	−	0.153478i	$-0.950952\pi$
$331$	−196355.	+	604317.i	−0.0985079	+	0.303176i	0.889644	+	0.456655i	$0.150952\pi$
$332$			900458.i			0.448351i
$333$	−5.12653e6	−	1.66571e6i	−2.53345	−	0.823168i
$334$	−1.58726e6	+	1.15321e6i	−0.778542	+	0.565644i
$335$	−1.86616e6	−	1.53586e6i	−0.908525	−	0.747723i
$336$	291954.	+	212117.i	0.141080	+	0.102501i
$337$	445502.	+	613180.i	0.213685	+	0.294112i	0.902382	−	0.430937i	$-0.141817\pi$
$337$	445502.	+	613180.i	0.213685	+	0.294112i	−0.688697	+	0.725049i	$0.741817\pi$
$338$	731378.	+	1.00665e6i	0.348217	+	0.479279i
$339$	3.51278e6	+	2.55218e6i	1.66017	+	1.20618i
$340$	621825.	−	1.58227e6i	0.291723	−	0.742305i
$341$	3.48672e6	−	2.53325e6i	1.62379	−	1.17976i
$342$	−1.59697e6	−	518886.i	−0.738296	−	0.239887i
$343$		−	1.60296e6i		−	0.735679i
$344$	−114200.	+	351470.i	−0.0520317	+	0.160137i
$345$	−1.67939e6	+	2.04056e6i	−0.759635	+	0.922998i
$346$	80090.0	+	246492.i	0.0359657	+	0.110691i
$347$	−700168.	+	227498.i	−0.312161	+	0.101427i	−0.460908	−	0.887448i	$-0.652476\pi$
$347$	−700168.	+	227498.i	−0.312161	+	0.101427i	0.148747	+	0.988875i	$0.452476\pi$
$348$	−1.85810e6	+	2.55746e6i	−0.822473	+	1.13204i
$349$	−1.31298e6			−0.577024			−0.288512	−	0.957476i	$-0.593160\pi$
$349$	−1.31298e6			−0.577024			−0.288512	+	0.957476i	$0.593160\pi$
$350$	124626.	+	635767.i	0.0543798	+	0.277414i
$351$	1.69360e6			0.733743
$352$	−328663.	+	452365.i	−0.141382	+	0.194596i
$353$	−1.17860e6	+	382952.i	−0.503421	+	0.163571i	−0.549708	−	0.835357i	$-0.685261\pi$
$353$	−1.17860e6	+	382952.i	−0.503421	+	0.163571i	0.0462872	+	0.998928i	$0.485261\pi$
$354$	−729072.	−	2.24385e6i	−0.309216	−	0.951669i
$355$	−114685.	+	1.89977e6i	−0.0482989	+	0.800075i
$356$	−361432.	+	1.11237e6i	−0.151148	+	0.465185i
$357$		−	2.67941e6i		−	1.11268i
$358$	32528.1	+	10569.0i	0.0134138	+	0.00435841i
$359$	2.49897e6	−	1.81560e6i	1.02335	−	0.743507i	0.0563829	−	0.998409i	$-0.482043\pi$
$359$	2.49897e6	−	1.81560e6i	1.02335	−	0.743507i	0.966967	+	0.254902i	$0.0820432\pi$
$360$	1.77399e6	+	107092.i	0.721430	+	0.0435513i
$361$	1.42545e6	+	1.03565e6i	0.575683	+	0.418259i
$362$	−1.46724e6	−	2.01949e6i	−0.588479	−	0.809972i
$363$	2.19209e6	+	3.01715e6i	0.873154	+	1.20179i
$364$	−164635.	−	119614.i	−0.0651281	−	0.0473184i
$365$	2.98905e6	−	1.90756e6i	1.17436	−	0.749458i
$366$	1.00999e6	−	733800.i	0.394107	−	0.286335i
$367$	1.64927e6	+	535882.i	0.639187	+	0.207684i	0.610640	−	0.791908i	$-0.290912\pi$
$367$	1.64927e6	+	535882.i	0.639187	+	0.207684i	0.0285464	+	0.999592i	$0.490912\pi$
$368$		−	444972.i		−	0.171283i
$369$	−671914.	+	2.06794e6i	−0.256891	+	0.790628i
$370$	2.25829e6	+	887499.i	0.857581	+	0.337026i
$371$	425765.	+	1.31037e6i	0.160596	+	0.494264i
$372$	3.26660e6	−	1.06138e6i	1.22388	−	0.397662i
$373$	−285895.	+	393500.i	−0.106398	+	0.146444i	−0.858896	−	0.512151i	$-0.828849\pi$
$373$	−285895.	+	393500.i	−0.106398	+	0.146444i	0.752498	+	0.658595i	$0.228849\pi$
$374$	4.15158e6			1.53474
$375$	3.27879e6	+	3.43873e6i	1.20402	+	1.26276i
$376$	−856253.			−0.312343
$377$	1.04780e6	−	1.44217e6i	0.379685	−	0.522592i
$378$	1.36077e6	−	442142.i	0.489842	−	0.159159i
$379$	−403712.	−	1.24250e6i	−0.144369	−	0.444321i	0.852561	−	0.522628i	$-0.175048\pi$
$379$	−403712.	−	1.24250e6i	−0.144369	−	0.444321i	−0.996929	+	0.0783072i	$0.975048\pi$
$380$	703480.	+	276465.i	0.249915	+	0.0982158i
$381$	164267.	−	505561.i	0.0579745	−	0.178427i
$382$		−	1.89804e6i		−	0.665498i
$383$	−2.46195e6	−	799937.i	−0.857597	−	0.278650i	−0.152972	−	0.988231i	$-0.548884\pi$
$383$	−2.46195e6	−	799937.i	−0.857597	−	0.278650i	−0.704624	+	0.709581i	$0.748884\pi$
$384$	−360512.	+	261927.i	−0.124765	+	0.0906468i
$385$	−1.33365e6	+	851115.i	−0.458554	+	0.292642i
$386$	−195926.	−	142349.i	−0.0669304	−	0.0486278i
$387$	1.68599e6	+	2.32057e6i	0.572241	+	0.787622i
$388$	−1.20672e6	−	1.66091e6i	−0.406939	−	0.560103i
$389$	−1.20721e6	−	877091.i	−0.404492	−	0.293880i	0.366876	−	0.930270i	$-0.380427\pi$
$389$	−1.20721e6	−	877091.i	−0.404492	−	0.293880i	−0.771368	+	0.636389i	$0.780427\pi$
$390$	−1.48972e6	−	89931.6i	−0.495957	−	0.0299399i
$391$	−2.67283e6	+	1.94193e6i	−0.884158	+	0.642379i
$392$	859494.	+	279267.i	0.282506	+	0.0917918i
$393$		−	2.38303e6i		−	0.778300i
$394$	860803.	−	2.64928e6i	0.279359	−	0.859780i
$395$	−292156.	+	4.83959e6i	−0.0942155	+	1.56069i
$396$	1.34113e6	+	4.12756e6i	0.429766	+	1.32268i
$397$	−3.94057e6	+	1.28037e6i	−1.25483	+	0.407717i	−0.859648	−	0.510887i	$-0.829317\pi$
$397$	−3.94057e6	+	1.28037e6i	−1.25483	+	0.407717i	−0.395178	+	0.918605i	$0.629317\pi$
$398$	−655522.	+	902248.i	−0.207434	+	0.285508i
$399$	1.19127e6			0.374610
$400$	−794190.	−	96238.1i	−0.248184	−	0.0300744i
$401$	−5.05642e6			−1.57030			−0.785150	−	0.619306i	$-0.787414\pi$
$401$	−5.05642e6			−1.57030			−0.785150	+	0.619306i	$0.787414\pi$
$402$	2.76474e6	−	3.80534e6i	0.853276	−	1.17443i
$403$	−1.84205e6	+	598520.i	−0.564989	+	0.183576i
$404$	−210416.	−	647593.i	−0.0641394	−	0.197401i
$405$	2.38006e6	−	2.89191e6i	0.721026	−	0.876087i
$406$	465380.	−	1.43229e6i	0.140118	−	0.431238i
$407$			5.92534e6i			1.77308i
$408$	3.14666e6	+	1.02241e6i	0.935835	+	0.304071i
$409$	−3.34034e6	+	2.42690e6i	−0.987375	+	0.717370i	−0.959345	−	0.282237i	$-0.908923\pi$
$409$	−3.34034e6	+	2.42690e6i	−0.987375	+	0.717370i	−0.0280301	+	0.999607i	$0.508923\pi$
$410$	358000.	−	910949.i	0.105178	−	0.267630i
$411$	−7.33410e6	−	5.32854e6i	−2.14162	−	1.55598i
$412$	−52562.2	−	72345.7i	−0.0152556	−	0.0209976i
$413$	660664.	+	909326.i	0.190592	+	0.262328i
$414$	−2.79413e6	−	2.03005e6i	−0.801208	−	0.582111i
$415$	−2.42917e6	−	1.99922e6i	−0.692368	−	0.569824i
$416$	203295.	−	147702.i	0.0575961	−	0.0418460i
$417$	1.95504e6	+	635231.i	0.550574	+	0.178892i
$418$			1.84580e6i			0.516708i
$419$	1.70789e6	−	5.25635e6i	0.475253	−	1.46268i	−0.370363	−	0.928887i	$-0.620767\pi$
$419$	1.70789e6	−	5.25635e6i	0.475253	−	1.46268i	0.845616	−	0.533791i	$-0.179233\pi$
$420$	−1.22044e6	+	316657.i	−0.337592	+	0.0875924i
$421$	168483.	+	518538.i	0.0463288	+	0.142585i	0.971545	−	0.236855i	$-0.0761166\pi$
$421$	168483.	+	518538.i	0.0463288	+	0.142585i	−0.925216	+	0.379440i	$0.876117\pi$
$422$	−1.41443e6	+	459576.i	−0.386634	+	0.125625i
$423$	−3.90640e6	+	5.37669e6i	−1.06151	+	1.46105i
$424$	−1.70134e6			−0.459597
$425$	2.88789e6	+	5.19050e6i	0.775548	+	1.39392i
$426$	−3.70398e6			−0.988882
$427$	−349584.	+	481161.i	−0.0927859	+	0.127709i
$428$	−1.62832e6	+	529073.i	−0.429665	+	0.139607i
$429$	−1.12622e6	−	3.46616e6i	−0.295448	−	0.909296i
$430$	−694613.	−	1.08842e6i	−0.181164	−	0.283874i
$431$	−272759.	+	839466.i	−0.0707271	+	0.217676i	−0.980172	−	0.198149i	$-0.936507\pi$
$431$	−272759.	+	839466.i	−0.0707271	+	0.217676i	0.909445	+	0.415825i	$0.136507\pi$
$432$			1.76678e6i			0.455485i
$433$	2.68604e6	+	872747.i	0.688482	+	0.223701i	0.632305	−	0.774720i	$-0.282109\pi$
$433$	2.68604e6	+	872747.i	0.688482	+	0.223701i	0.0561767	+	0.998421i	$0.482109\pi$
$434$	−1.32379e6	+	961793.i	−0.337362	+	0.245108i
$435$	−2.77385e6	−	1.06908e7i	−0.702846	−	2.70885i
$436$	−2.29885e6	−	1.67021e6i	−0.579155	−	0.420781i
$437$	−863386.	−	1.18835e6i	−0.216273	−	0.297674i
$438$	4.05620e6	+	5.58288e6i	1.01026	+	1.39051i
$439$	−882654.	−	641286.i	−0.218589	−	0.158814i	0.473102	−	0.881008i	$-0.343134\pi$
$439$	−882654.	−	641286.i	−0.218589	−	0.158814i	−0.691691	+	0.722193i	$0.743134\pi$
$440$	−490641.	−	1.89099e6i	−0.120818	−	0.465648i
$441$	5.67479e6	−	4.12298e6i	1.38948	−	1.00952i
$442$	−1.77442e6	−	576544.i	−0.432017	−	0.140371i
$443$		−	5.60202e6i		−	1.35624i	−0.734953	−	0.678118i	$-0.762796\pi$
$443$		−	5.60202e6i		−	1.35624i	0.734953	−	0.678118i	$-0.237204\pi$
$444$	−1.45924e6	+	4.49106e6i	−0.351292	+	1.08116i
$445$	−2.19839e6	−	3.44476e6i	−0.526265	−	0.824630i
$446$	−722922.	−	2.22493e6i	−0.172089	−	0.529637i
$447$	1.59087e6	−	516905.i	0.376588	−	0.122361i
$448$	124783.	−	171749.i	0.0293737	−	0.0404295i
$449$	−728723.			−0.170587			−0.0852936	−	0.996356i	$-0.527183\pi$
$449$	−728723.			−0.170587			−0.0852936	+	0.996356i	$0.527183\pi$
$450$	−4.22757e6	+	4.54793e6i	−0.984145	+	1.05872i
$451$	2.39017e6			0.553333
$452$	1.50138e6	−	2.06647e6i	0.345656	−	0.475755i
$453$	6.24262e6	−	2.02835e6i	1.42929	−	0.464406i
$454$	1.74287e6	+	5.36399e6i	0.396848	+	1.22137i
$455$	688212.	−	178565.i	0.155845	−	0.0404360i
$456$	−454567.	+	1.39901e6i	−0.102373	+	0.315072i
$457$			1.79105e6i			0.401160i	0.979677	+	0.200580i	$0.0642827\pi$
$457$			1.79105e6i			0.401160i	−0.979677	+	0.200580i	$0.935717\pi$
$458$	1.80666e6	+	587019.i	0.402451	+	0.130764i
$459$	1.06126e7	−	7.71052e6i	2.35121	−	1.70825i
$460$	1.20040e6	+	987940.i	0.264504	+	0.217689i
$461$	2.98220e6	+	2.16670e6i	0.653559	+	0.474838i	0.864482	−	0.502664i	$-0.167647\pi$
$461$	2.98220e6	+	2.16670e6i	0.653559	+	0.474838i	−0.210923	+	0.977503i	$0.567647\pi$
$462$	−1.80979e6	−	2.49096e6i	−0.394478	−	0.542953i
$463$	−593079.	−	816303.i	−0.128576	−	0.176970i	0.739876	−	0.672744i	$-0.234884\pi$
$463$	−593079.	−	816303.i	−0.128576	−	0.176970i	−0.868451	+	0.495774i	$0.834884\pi$
$464$	1.50448e6	+	1.09307e6i	0.324408	+	0.235697i
$465$	−4.38930e6	+	1.11688e7i	−0.941376	+	2.39538i
$466$	−422793.	+	307177.i	−0.0901911	+	0.0655276i
$467$	−2.14399e6	−	696625.i	−0.454915	−	0.147811i	0.0725914	−	0.997362i	$-0.476873\pi$
$467$	−2.14399e6	−	696625.i	−0.454915	−	0.147811i	−0.527507	+	0.849551i	$0.676873\pi$
$468$		−	1.95040e6i		−	0.411633i
$469$	−692457.	+	2.13116e6i	−0.145365	+	0.447388i
$470$	1.90108e6	−	2.30992e6i	0.396968	−	0.482338i
$471$	2.33309e6	+	7.18051e6i	0.484595	+	1.49143i
$472$	−1.32000e6	+	428893.i	−0.272720	+	0.0886122i
$473$	1.85333e6	−	2.55089e6i	0.380890	−	0.524250i
$474$	−9.43572e6			−1.92899
$475$	−2.30771e6	+	1.28397e6i	−0.469296	+	0.261107i
$476$	−1.57622e6			−0.318860
$477$	−7.76187e6	+	1.06833e7i	−1.56196	+	2.14986i
$478$	4.63039e6	−	1.50451e6i	0.926932	−	0.301178i
$479$	−1.21544e6	−	3.74075e6i	−0.242045	−	0.744938i	−0.996108	−	0.0881366i	$-0.971909\pi$
$479$	−1.21544e6	−	3.74075e6i	−0.242045	−	0.744938i	0.754063	−	0.656802i	$-0.228091\pi$
$480$	93817.4	−	1.55409e6i	0.0185858	−	0.307874i
$481$	822872.	−	2.53254e6i	0.162170	−	0.499107i
$482$			6.06977e6i			1.19002i
$483$	2.33032e6	+	757168.i	0.454515	+	0.147681i
$484$	1.77490e6	−	1.28954e6i	0.344399	−	0.250220i
$485$	7.15986e6	+	432226.i	1.38213	+	0.0834367i
$486$	469891.	+	341396.i	0.0902416	+	0.0655644i
$487$	249002.	+	342722.i	0.0475751	+	0.0654816i	0.832142	−	0.554563i	$-0.187115\pi$
$487$	249002.	+	342722.i	0.0475751	+	0.0654816i	−0.784567	+	0.620044i	$0.787115\pi$
$488$	−431674.	−	594148.i	−0.0820552	−	0.112939i
$489$	708211.	+	514545.i	0.133934	+	0.0973087i
$490$	−2.66165e6	+	1.69863e6i	−0.500797	+	0.319600i
$491$	−5.83779e6	+	4.24141e6i	−1.09281	+	0.793974i	−0.979872	−	0.199628i	$-0.936027\pi$
$491$	−5.83779e6	+	4.24141e6i	−1.09281	+	0.793974i	−0.112939	+	0.993602i	$0.536027\pi$
$492$	1.81161e6	+	588627.i	0.337405	+	0.109629i
$493$		−	1.38074e7i		−	2.55855i
$494$	256333.	−	788912.i	0.0472593	−	0.145449i
$495$	−1.41126e7	−	5.54618e6i	−2.58877	−	1.01737i
$496$	−624381.	−	1.92165e6i	−0.113958	−	0.350727i
$497$	1.67822e6	−	545286.i	0.304760	−	0.0990225i
$498$	3.59885e6	−	4.95339e6i	0.650265	−	0.895013i
$499$	3.67087e6			0.659961			0.329980	−	0.943988i	$-0.392958\pi$
$499$	3.67087e6			0.659961			0.329980	+	0.943988i	$0.392958\pi$
$500$	2.02291e6	−	1.92882e6i	0.361869	−	0.345038i
$501$	1.33405e7			2.37453
$502$	−4.14065e6	+	5.69912e6i	−0.733347	+	1.00937i
$503$	717887.	−	233256.i	0.126513	−	0.0411067i	−0.245076	−	0.969504i	$-0.578813\pi$
$503$	717887.	−	233256.i	0.126513	−	0.0411067i	0.371589	+	0.928397i	$0.378813\pi$
$504$	−509183.	−	1.56710e6i	−0.0892889	−	0.274803i
$505$	2.21419e6	+	870167.i	0.386354	+	0.151836i
$506$	−1.17319e6	+	3.61070e6i	−0.203700	+	0.626924i
$507$		−	8.46067e6i		−	1.46179i
$508$	−297408.	−	96633.6i	−0.0511320	−	0.0166138i
$509$	−2.68345e6	+	1.94964e6i	−0.459091	+	0.333549i	−0.793175	−	0.608994i	$-0.791573\pi$
$509$	−2.68345e6	+	1.94964e6i	−0.459091	+	0.333549i	0.334084	+	0.942543i	$0.391573\pi$
$510$	−9.74447e6	+	6.21876e6i	−1.65895	+	1.05871i
$511$	−2.65970e6	−	1.93238e6i	−0.450588	−	0.327371i
$512$	154084.	+	212079.i	0.0259767	+	0.0357538i
$513$	3.42812e6	+	4.71840e6i	0.575125	+	0.791592i
$514$	4.34313e6	+	3.15547e6i	0.725096	+	0.526813i
$515$	311867.	+	18826.8i	0.0518146	+	0.00312794i
$516$	2.03292e6	−	1.47701e6i	0.336122	−	0.244207i
$517$	6.94801e6	+	2.25754e6i	1.14323	+	0.371458i
$518$		−	2.24966e6i		−	0.368377i
$519$	544578.	−	1.67604e6i	0.0887446	−	0.273128i
$520$	−52904.2	+	876363.i	−0.00857990	+	0.142127i
$521$	2.43292e6	+	7.48776e6i	0.392676	+	1.20853i	0.930757	+	0.365638i	$0.119149\pi$
$521$	2.43292e6	+	7.48776e6i	0.392676	+	1.20853i	−0.538081	+	0.842893i	$0.680851\pi$
$522$	1.37275e7	−	4.46034e6i	2.20503	−	0.716459i
$523$	3.64369e6	−	5.01511e6i	0.582488	−	0.801726i	−0.411477	−	0.911420i	$-0.634987\pi$
$523$	3.64369e6	−	5.01511e6i	0.582488	−	0.801726i	0.993965	+	0.109694i	$0.0349870\pi$
$524$	−1.40187e6			−0.223038
$525$	1.85540e6	−	3.99543e6i	0.293792	−	0.632652i
$526$	5.00961e6			0.789477
$527$	−8.81795e6	+	1.21369e7i	−1.38306	+	1.90362i
$528$	3.61593e6	−	1.17489e6i	0.564462	−	0.183405i
$529$	1.05532e6	+	3.24796e6i	0.163963	+	0.504627i
$530$	3.77737e6	−	4.58972e6i	0.584118	−	0.709736i
$531$	−3.32893e6	+	1.02454e7i	−0.512351	+	1.57686i
$532$		−	700793.i		−	0.107352i
$533$	−1.02158e6	−	331930.i	−0.155759	−	0.0506092i
$534$	6.43404e6	−	4.67460e6i	0.976406	−	0.709400i
$535$	2.18796e6	−	5.56738e6i	0.330487	−	0.840943i
$536$	−2.23858e6	−	1.62642e6i	−0.336558	−	0.244524i
$537$	−136695.	−	188145.i	−0.0204559	−	0.0281551i
$538$	4.19550e6	+	5.77461e6i	0.624925	+	0.860135i
$539$	−6.23801e6	−	4.53218e6i	−0.924857	−	0.671948i
$540$	−4.76626e6	−	3.92267e6i	−0.703385	−	0.578891i
$541$	2.06000e6	−	1.49668e6i	0.302603	−	0.219854i	−0.426113	−	0.904670i	$-0.640117\pi$
$541$	2.06000e6	−	1.49668e6i	0.302603	−	0.219854i	0.728716	+	0.684816i	$0.240117\pi$
$542$	−1.45004e6	−	471147.i	−0.212023	−	0.0688903i
$543$			1.69733e7i			2.47039i
$544$	601456.	−	1.85109e6i	0.0871378	−	0.268183i
$545$	9.60973e6	−	2.49336e6i	1.38586	−	0.359579i
$546$	427591.	+	1.31599e6i	0.0613828	+	0.188917i
$547$	8.74074e6	−	2.84004e6i	1.24905	−	0.405841i	0.391470	−	0.920191i	$-0.371967\pi$
$547$	8.74074e6	−	2.84004e6i	1.24905	−	0.405841i	0.857580	+	0.514350i	$0.171967\pi$
$548$	−3.13463e6	+	4.31445e6i	−0.445897	+	0.613725i
$549$	−5.70024e6			−0.807164
$550$	6.19067e6	+	2.87483e6i	0.872631	+	0.405234i
$551$	6.13880e6			0.861399
$552$	−1.77841e6	+	2.44778e6i	−0.248419	+	0.341920i
$553$	4.27519e6	−	1.38909e6i	0.594487	−	0.193161i
$554$	−143530.	−	441740.i	−0.0198686	−	0.0611494i
$555$	−8.87572e6	−	1.39078e7i	−1.22313	−	1.91657i
$556$	373689.	−	1.15010e6i	0.0512652	−	0.157778i
$557$			5.62765e6i			0.768579i	0.923213	+	0.384290i	$0.125554\pi$
$557$			5.62765e6i			0.768579i	−0.923213	+	0.384290i	$0.874446\pi$
$558$	−1.49152e7	−	4.84624e6i	−2.02789	−	0.658900i
$559$	−1.14638e6	+	832893.i	−0.155167	+	0.112735i
$560$	186281.	+	717948.i	0.0251014	+	0.0967438i
$561$	−2.28377e7	−	1.65926e7i	−3.06370	−	2.22591i
$562$	−3.53570e6	−	4.86648e6i	−0.472210	−	0.649941i
$563$	−2.78009e6	−	3.82646e6i	−0.369647	−	0.508776i	0.583158	−	0.812359i	$-0.301817\pi$
$563$	−2.78009e6	−	3.82646e6i	−0.369647	−	0.508776i	−0.952805	+	0.303583i	$0.901817\pi$
$564$	4.71022e6	+	3.42218e6i	0.623510	+	0.453007i
$565$	2.24132e6	+	8.63832e6i	0.295381	+	1.13843i
$566$	933727.	−	678392.i	0.122512	−	0.0890102i
$567$	−3.30257e6	−	1.07307e6i	−0.431415	−	0.140175i
$568$			2.17895e6i			0.283384i
$569$	−451620.	+	1.38994e6i	−0.0584780	+	0.179977i	−0.976029	−	0.217642i	$-0.930163\pi$
$569$	−451620.	+	1.38994e6i	−0.0584780	+	0.179977i	0.917551	+	0.397619i	$0.130163\pi$
$570$	−2.76488e6	−	4.33242e6i	−0.356442	−	0.558526i
$571$	−1.17143e6	−	3.60529e6i	−0.150358	−	0.462754i	0.847303	−	0.531110i	$-0.178225\pi$
$571$	−1.17143e6	−	3.60529e6i	−0.150358	−	0.462754i	−0.997661	+	0.0683555i	$0.978225\pi$
$572$	−2.03905e6	+	662526.i	−0.260577	+	0.0846667i
$573$	−7.58587e6	+	1.04411e7i	−0.965203	+	1.32849i
$574$	−907469.			−0.114961
$575$	−5.33034e6	+	1.04488e6i	−0.672335	+	0.131794i
$576$	2.03468e6			0.255528
$577$	7.93203e6	−	1.09175e7i	0.991847	−	1.36516i	0.0616514	−	0.998098i	$-0.480363\pi$
$577$	7.93203e6	−	1.09175e7i	0.991847	−	1.36516i	0.930196	−	0.367063i	$-0.119637\pi$
$578$	−8.34243e6	+	2.71062e6i	−1.03866	+	0.337481i
$579$	508860.	+	1.56611e6i	0.0630815	+	0.194145i
$580$	−6.28908e6	+	1.63178e6i	−0.776278	+	0.201415i
$581$	−901366.	+	2.77412e6i	−0.110780	+	0.340946i
$582$			1.39595e7i			1.70830i
$583$	1.38054e7	+	4.48566e6i	1.68220	+	0.546581i
$584$	3.28425e6	−	2.38615e6i	0.398478	−	0.289511i
$585$	5.26161e6	+	4.33034e6i	0.635666	+	0.523158i
$586$	−811100.	−	589299.i	−0.0975732	−	0.0708911i
$587$	817430.	+	1.12510e6i	0.0979164	+	0.134770i	0.855164	−	0.518358i	$-0.173456\pi$
$587$	817430.	+	1.12510e6i	0.0979164	+	0.134770i	−0.757248	+	0.653128i	$0.773456\pi$
$588$	−3.61191e6	−	4.97137e6i	−0.430818	−	0.592970i
$589$	−5.39608e6	−	3.92048e6i	−0.640900	−	0.465641i
$590$	1.77367e6	−	4.51320e6i	0.209770	−	0.533770i
$591$	−1.53236e7	+	1.11332e7i	−1.80465	+	1.31115i
$592$	2.64197e6	+	858427.i	0.309830	+	0.100670i
$593$		−	9.54853e6i		−	1.11506i	−0.830155	−	0.557532i	$-0.811748\pi$
$593$		−	9.54853e6i		−	1.11506i	0.830155	−	0.557532i	$-0.188252\pi$
$594$	4.65819e6	−	1.43364e7i	0.541691	−	1.66715i
$595$	3.49958e6	−	4.25218e6i	0.405250	−	0.492401i
$596$	−304081.	−	935865.i	−0.0350650	−	0.107919i
$597$	7.21201e6	−	2.34333e6i	0.828172	−	0.269090i
$598$	1.00286e6	−	1.38032e6i	0.114680	−	0.157843i
$599$	1.22015e7			1.38946			0.694731	−	0.719270i	$-0.255523\pi$
$599$	1.22015e7			1.38946			0.694731	+	0.719270i	$0.255523\pi$
$600$	3.98418e6	+	3.70353e6i	0.451816	+	0.419989i
$601$	−1.11390e7			−1.25794			−0.628972	−	0.777428i	$-0.716524\pi$
$601$	−1.11390e7			−1.25794			−0.628972	+	0.777428i	$0.716524\pi$
$602$	−703650.	+	968491.i	−0.0791344	+	0.108919i
$603$	−2.04257e7	+	6.63670e6i	−2.28762	+	0.743292i
$604$	−1.19322e6	−	3.67236e6i	−0.133085	−	0.409593i
$605$	−461891.	+	7.65125e6i	−0.0513039	+	0.849853i
$606$	−1.43074e6	+	4.40336e6i	−0.158263	+	0.487082i
$607$		−	1.31175e7i		−	1.44504i	−0.691349	−	0.722521i	$-0.742983\pi$
$607$		−	1.31175e7i		−	1.44504i	0.691349	−	0.722521i	$-0.257017\pi$
$608$	823000.	+	267409.i	0.0902903	+	0.0293371i
$609$	−8.28447e6	+	6.01902e6i	−0.905152	+	0.657631i
$610$	2.56125e6	+	154618.i	0.278694	+	0.0168242i
$611$	−2.65612e6	−	1.92979e6i	−0.287836	−	0.209125i
$612$	−8.87965e6	−	1.22218e7i	−0.958335	−	1.31903i
$613$	1.52831e6	+	2.10354e6i	0.164271	+	0.226100i	0.883215	−	0.468968i	$-0.155374\pi$
$613$	1.52831e6	+	2.10354e6i	0.164271	+	0.226100i	−0.718944	+	0.695068i	$0.755374\pi$
$614$	1.89144e6	+	1.37421e6i	0.202475	+	0.147107i
$615$	−5.61013e6	+	3.58029e6i	−0.598115	+	0.381708i
$616$	−1.46536e6	+	1.06465e6i	−0.155594	+	0.113046i
$617$	−5.73619e6	−	1.86380e6i	−0.606611	−	0.197100i	−0.0104243	−	0.999946i	$-0.503318\pi$
$617$	−5.73619e6	−	1.86380e6i	−0.606611	−	0.197100i	−0.596187	+	0.802846i	$0.703318\pi$
$618$			608046.i			0.0640421i
$619$	−3.94532e6	+	1.21424e7i	−0.413862	+	1.27374i	0.499403	+	0.866370i	$0.333553\pi$
$619$	−3.94532e6	+	1.21424e7i	−0.413862	+	1.27374i	−0.913265	+	0.407366i	$0.866447\pi$
$620$	6.57030e6	+	2.58210e6i	0.686446	+	0.269771i
$621$	3.70696e6	+	1.14089e7i	0.385735	+	1.18717i
$622$	2.15599e6	−	700524.i	0.223445	−	0.0726018i
$623$	−2.22699e6	+	3.06519e6i	−0.229879	+	0.316401i
$624$	−1.70864e6			−0.175666
$625$	712063.	+	9.73963e6i	0.0729152	+	0.997338i
$626$	−702630.			−0.0716623
$627$	7.37711e6	−	1.01537e7i	0.749406	−	1.03147i
$628$	4.22410e6	−	1.37249e6i	0.427400	−	0.138871i
$629$	−6.37361e6	−	1.96159e7i	−0.642331	−	1.97689i
$630$	5.35808e6	+	2.10571e6i	0.537846	+	0.211372i
$631$	1.16920e6	−	3.59842e6i	0.116900	−	0.359781i	−0.875439	−	0.483329i	$-0.839427\pi$
$631$	1.16920e6	−	3.59842e6i	0.116900	−	0.359781i	0.992339	+	0.123548i	$0.0394274\pi$
$632$			5.55077e6i			0.552790i
$633$	9.61753e6	+	3.12492e6i	0.954013	+	0.309977i
$634$	−4.73523e6	+	3.44035e6i	−0.467863	+	0.339922i
$635$	921002.	−	587769.i	0.0906414	−	0.0578458i
$636$	9.35904e6	+	6.79974e6i	0.917463	+	0.666576i
$637$	2.03678e6	+	2.80339e6i	0.198882	+	0.273738i
$638$	−9.32610e6	−	1.28363e7i	−0.907086	−	1.24850i
$639$	1.36823e7	+	9.94079e6i	1.32559	+	0.963094i
$640$	−914229.	−	55190.2i	−0.0882277	−	0.00532613i
$641$	2.52759e6	−	1.83640e6i	0.242975	−	0.176532i	−0.459633	−	0.888109i	$-0.652019\pi$
$641$	2.52759e6	−	1.83640e6i	0.242975	−	0.176532i	0.702608	+	0.711578i	$0.252019\pi$
$642$	1.10719e7	+	3.59747e6i	1.06019	+	0.344476i
$643$		−	1.18472e6i		−	0.113002i	−0.998403	−	0.0565012i	$-0.982006\pi$
$643$		−	1.18472e6i		−	0.113002i	0.998403	−	0.0565012i	$-0.0179945\pi$
$644$	445421.	−	1.37087e6i	0.0423210	−	0.130251i
$645$	−529036.	+	8.76352e6i	−0.0500710	+	0.829430i
$646$	−1.98544e6	−	6.11057e6i	−0.187187	−	0.576103i
$647$	−5.83563e6	+	1.89611e6i	−0.548059	+	0.178075i	−0.569941	−	0.821685i	$-0.693034\pi$
$647$	−5.83563e6	+	1.89611e6i	−0.548059	+	0.178075i	0.0218824	+	0.999761i	$0.493034\pi$
$648$	2.52040e6	−	3.46903e6i	0.235793	−	0.324542i
$649$	1.18418e7			1.10359
$650$	−2.24671e6	−	2.08845e6i	−0.208575	−	0.193883i
$651$	1.11261e7			1.02895
$652$	302693.	−	416621.i	0.0278858	−	0.0383815i
$653$	458102.	−	148846.i	0.0420416	−	0.0136601i	−0.287921	−	0.957654i	$-0.592964\pi$
$653$	458102.	−	148846.i	0.0420416	−	0.0136601i	0.329962	+	0.943994i	$0.392964\pi$
$654$	5.97060e6	+	1.83756e7i	0.545850	+	1.67995i
$655$	3.11247e6	−	3.78182e6i	0.283467	−	0.344428i
$656$	346273.	−	1.06572e6i	0.0314166	−	0.0966903i
$657$		−	3.15090e7i		−	2.84787i
$658$	−2.63793e6	−	857117.i	−0.237520	−	0.0771748i
$659$	−1.76209e7	+	1.28023e7i	−1.58057	+	1.14835i	−0.664538	+	0.747255i	$0.731371\pi$
$659$	−1.76209e7	+	1.28023e7i	−1.58057	+	1.14835i	−0.916035	+	0.401098i	$0.868629\pi$
$660$	−4.85870e6	+	1.23632e7i	−0.434170	+	1.10477i
$661$	−6.81967e6	−	4.95478e6i	−0.607099	−	0.441083i	0.241293	−	0.970452i	$-0.422429\pi$
$661$	−6.81967e6	−	4.95478e6i	−0.607099	−	0.441083i	−0.848392	+	0.529369i	$0.822429\pi$
$662$	−1.49395e6	−	2.05625e6i	−0.132493	−	0.182361i
$663$	7.45677e6	+	1.02634e7i	0.658820	+	0.906788i
$664$	−2.91394e6	−	2.11710e6i	−0.256484	−	0.186347i
$665$	1.89053e6	+	1.55592e6i	0.165779	+	0.136437i
$666$	1.74435e7	−	1.26735e7i	1.52387	−	1.10716i
$667$	1.20085e7	+	3.90180e6i	1.04514	+	0.339586i
$668$		−	7.84785e6i		−	0.680470i
$669$	−4.91556e6	+	1.51285e7i	−0.424627	+	1.30687i
$670$	9.35776e6	−	2.42799e6i	0.805351	−	0.208958i
$671$	1.93629e6	+	5.95930e6i	0.166022	+	0.510963i
$672$	−1.37285e6	+	446067.i	−0.117274	+	0.0381045i
$673$	−7.09494e6	+	9.76534e6i	−0.603825	+	0.831093i	−0.996052	−	0.0887752i	$-0.971705\pi$
$673$	−7.09494e6	+	9.76534e6i	−0.603825	+	0.831093i	0.392227	+	0.919868i	$0.371705\pi$
$674$	−3.03173e6			−0.257064
$675$	2.11644e7	−	4.14873e6i	1.78791	−	0.350474i
$676$	−4.97718e6			−0.418906
$677$	−5.60291e6	+	7.71174e6i	−0.469831	+	0.646667i	−0.976511	−	0.215467i	$-0.930873\pi$
$677$	−5.60291e6	+	7.71174e6i	−0.469831	+	0.646667i	0.506680	+	0.862134i	$0.330873\pi$
$678$	−1.65181e7	+	5.36705e6i	−1.38002	+	0.448396i
$679$	−2.05507e6	−	6.32487e6i	−0.171062	−	0.526474i
$680$	3.65833e6	+	5.73240e6i	0.303396	+	0.475406i
$681$	1.18507e7	−	3.64728e7i	0.979214	−	3.01371i
$682$			1.72393e7i			1.41925i
$683$	−1.07317e7	−	3.48693e6i	−0.880270	−	0.286017i	−0.166200	−	0.986092i	$-0.553150\pi$
$683$	−1.07317e7	−	3.48693e6i	−0.880270	−	0.286017i	−0.714069	+	0.700075i	$0.753150\pi$
$684$	5.43384e6	−	3.94792e6i	0.444086	−	0.322647i
$685$	−4.67950e6	−	1.80354e7i	−0.381042	−	1.46858i
$686$	5.18730e6	+	3.76879e6i	0.420854	+	0.305768i
$687$	−7.59225e6	−	1.04498e7i	−0.613732	−	0.844729i
$688$	−868882.	−	1.19591e6i	−0.0699825	−	0.0963227i
$689$	−5.27762e6	−	3.83442e6i	−0.423536	−	0.307717i
$690$	−2.65489e6	−	1.02323e7i	−0.212287	−	0.818181i
$691$	2.82119e6	−	2.04972e6i	0.224770	−	0.163305i	−0.469701	−	0.882825i	$-0.655638\pi$
$691$	2.82119e6	−	2.04972e6i	0.224770	−	0.163305i	0.694471	+	0.719521i	$0.255638\pi$
$692$	−985967.	−	320360.i	−0.0782703	−	0.0254316i
$693$			1.40586e7i			1.11201i
$694$	909993.	−	2.80067e6i	0.0717199	−	0.220731i
$695$	2.27294e6	+	3.56158e6i	0.178495	+	0.279692i
$696$	−3.90745e6	−	1.20259e7i	−0.305753	−	0.941010i
$697$	−7.91269e6	+	2.57099e6i	−0.616939	+	0.200456i
$698$	3.08700e6	−	4.24889e6i	0.239827	−	0.330093i
$699$	3.55347e6			0.275080
$700$	−2.35040e6	−	1.09148e6i	−0.181299	−	0.0841921i
$701$	1.24022e7			0.953245			0.476623	−	0.879108i	$-0.341861\pi$
$701$	1.24022e7			0.953245			0.476623	+	0.879108i	$0.341861\pi$
$702$	−3.98190e6	+	5.48062e6i	−0.304964	+	0.419746i
$703$	8.72130e6	−	2.83372e6i	0.665569	−	0.216256i
$704$	−691153.	−	2.12715e6i	−0.0525584	−	0.161758i
$705$	−1.96898e7	+	5.10876e6i	−1.49200	+	0.387118i
$706$	1.53181e6	−	4.71442e6i	0.115662	−	0.355972i
$707$		−	2.20573e6i		−	0.165960i
$708$	8.97541e6	+	2.91629e6i	0.672932	+	0.218649i
$709$	−9.88872e6	+	7.18458e6i	−0.738796	+	0.536767i	−0.892334	−	0.451376i	$-0.850933\pi$
$709$	−9.88872e6	+	7.18458e6i	−0.738796	+	0.536767i	0.153538	+	0.988143i	$0.450933\pi$
$710$	−5.87815e6	−	4.83776e6i	−0.437618	−	0.360163i
$711$	3.48551e7	+	2.53237e7i	2.58578	+	1.87868i
$712$	−2.74994e6	−	3.78496e6i	−0.203293	−	0.279809i
$713$	−8.06378e6	−	1.10988e7i	−0.594039	−	0.817624i
$714$	8.67075e6	+	6.29967e6i	0.636519	+	0.462458i
$715$	2.73985e6	−	6.97170e6i	0.200430	−	0.510004i
$716$	−110680.	+	80414.0i	−0.00806841	+	0.00586204i
$717$	−3.14847e7	−	1.02300e7i	−2.28719	−	0.743152i
$718$			1.23556e7i			0.894441i
$719$	−2.84973e6	+	8.77058e6i	−0.205581	+	0.632712i	0.794109	+	0.607776i	$0.207938\pi$
$719$	−2.84973e6	+	8.77058e6i	−0.205581	+	0.632712i	−0.999689	+	0.0249358i	$0.992062\pi$
$720$	−4.51745e6	+	5.48896e6i	−0.324760	+	0.394601i
$721$	−89514.4	−	275497.i	−0.00641291	−	0.0197369i
$722$	−6.70286e6	+	2.17789e6i	−0.478539	+	0.155487i
$723$	2.42590e7	−	3.33896e7i	1.72594	−	2.37556i
$724$	9.98490e6			0.707942
$725$	9.56115e6	−	2.05890e7i	0.675562	−	1.45476i
$726$	−1.49176e7			−1.05041
$727$	9.17610e6	−	1.26298e7i	0.643905	−	0.886260i	−0.354911	−	0.934900i	$-0.615489\pi$
$727$	9.17610e6	−	1.26298e7i	0.643905	−	0.886260i	0.998816	+	0.0486405i	$0.0154889\pi$
$728$	774160.	−	251540.i	0.0541380	−	0.0175905i
$729$	3.81065e6	+	1.17280e7i	0.265571	+	0.817343i
$730$	−854674.	+	1.41577e7i	−0.0593599	+	0.983301i
$731$	−3.39161e6	+	1.04383e7i	−0.234754	+	0.722498i
$732$			4.99366e6i			0.344462i
$733$	−1.57437e7	−	5.11544e6i	−1.08230	−	0.351660i	−0.287032	−	0.957921i	$-0.592669\pi$
$733$	−1.57437e7	−	5.11544e6i	−1.08230	−	0.351660i	−0.795266	+	0.606261i	$0.792669\pi$
$734$	−5.61183e6	+	4.07723e6i	−0.384471	+	0.279335i
$735$	2.14306e7	+	1.29372e6i	1.46324	+	0.0883328i
$736$	1.43996e6	+	1.04619e6i	0.0979841	+	0.0711896i
$737$	1.38767e7	+	1.90996e7i	0.941058	+	1.29526i
$738$	−5.11223e6	−	7.03638e6i	−0.345517	−	0.475563i
$739$	4.66218e6	+	3.38727e6i	0.314035	+	0.228160i	0.733626	−	0.679554i	$-0.237827\pi$
$739$	4.66218e6	+	3.38727e6i	0.314035	+	0.228160i	−0.419591	+	0.907713i	$0.637827\pi$
$740$	−8.18156e6	+	5.22134e6i	−0.549233	+	0.350512i
$741$	−4.56312e6	+	3.31530e6i	−0.305293	+	0.221808i
$742$	−5.24148e6	−	1.70306e6i	−0.349498	−	0.113559i
$743$			1.95776e7i			1.30103i	0.759492	+	0.650516i	$0.225447\pi$
$743$			1.95776e7i			1.30103i	−0.759492	+	0.650516i	$0.774553\pi$
$744$	−4.24552e6	+	1.30664e7i	−0.281189	+	0.865412i
$745$	3.19982e6	+	1.25752e6i	0.211220	+	0.0830085i
$746$	−601215.	−	1.85035e6i	−0.0395533	−	0.121733i
$747$	−2.65880e7	+	8.63895e6i	−1.74335	+	0.566448i
$748$	−9.76095e6	+	1.34348e7i	−0.637879	+	0.877965i
$749$	−5.54611e6			−0.361230
$750$	−1.88368e7	+	2.52545e6i	−1.22280	+	0.163940i
$751$	−1.00031e7			−0.647197			−0.323599	−	0.946194i	$-0.604893\pi$
$751$	−1.00031e7			−0.647197			−0.323599	+	0.946194i	$0.604893\pi$
$752$	2.01317e6	−	2.77089e6i	0.129818	−	0.178680i
$753$	4.55552e7	−	1.48018e7i	2.92786	−	0.951320i
$754$	2.20344e6	+	6.78148e6i	0.141147	+	0.434406i
$755$	1.25562e7	+	4.93453e6i	0.801659	+	0.315049i
$756$	−1.76857e6	+	5.44309e6i	−0.112543	+	0.346370i
$757$			2.25859e7i			1.43251i	0.697838	+	0.716255i	$0.254145\pi$
$757$			2.25859e7i			1.43251i	−0.697838	+	0.716255i	$0.745855\pi$
$758$	4.96999e6	+	1.61485e6i	0.314183	+	0.102084i
$759$	2.08845e7	−	1.51735e7i	1.31589	−	0.956050i
$760$	−2.54864e6	+	1.62650e6i	−0.160057	+	0.102146i
$761$	1.18271e7	+	8.59287e6i	0.740313	+	0.537869i	0.892809	−	0.450435i	$-0.148731\pi$
$761$	1.18271e7	+	8.59287e6i	0.740313	+	0.537869i	−0.152496	+	0.988304i	$0.548731\pi$
$762$	1.24982e6	+	1.72022e6i	0.0779756	+	0.107324i
$763$	−5.41038e6	−	7.44675e6i	−0.336447	−	0.463080i
$764$	6.14218e6	+	4.46256e6i	0.380706	+	0.276599i
$765$	5.26856e7	+	3.18053e6i	3.25491	+	0.196492i
$766$	8.37705e6	−	6.08629e6i	0.515845	−	0.374783i
$767$	−5.06129e6	−	1.64451e6i	−0.310651	−	0.100937i
$768$		−	1.78247e6i		−	0.109048i
$769$	3.37485e6	−	1.03867e7i	0.205797	−	0.633378i	−0.793883	−	0.608071i	$-0.791944\pi$
$769$	3.37485e6	−	1.03867e7i	0.205797	−	0.633378i	0.999680	−	0.0253070i	$-0.00805632\pi$
$770$	381337.	−	6.31688e6i	0.0231784	−	0.383951i
$771$	−1.12800e7	−	3.47163e7i	−0.683398	−	2.10328i
$772$	921299.	−	299348.i	0.0556362	−	0.0180773i
$773$	−2.26027e6	+	3.11100e6i	−0.136054	+	0.187263i	−0.871608	−	0.490204i	$-0.836922\pi$
$773$	−2.26027e6	+	3.11100e6i	−0.136054	+	0.187263i	0.735553	+	0.677467i	$0.236922\pi$
$774$	−1.14735e7			−0.688407
$775$	−2.15533e7	+	1.19919e7i	−1.28902	+	0.717187i
$776$	8.21201e6			0.489548
$777$	−8.99120e6	+	1.23753e7i	−0.534275	+	0.735367i
$778$	5.67665e6	−	1.84446e6i	0.336235	−	0.109249i
$779$	−1.14307e6	−	3.51800e6i	−0.0674883	−	0.207708i
$780$	3.79357e6	−	4.60940e6i	0.223261	−	0.271274i
$781$	5.74488e6	−	1.76809e7i	0.337018	−	1.03724i
$782$		−	1.32152e7i		−	0.772783i
$783$	−4.76803e7	−	1.54923e7i	−2.77930	−	0.903048i
$784$	−2.92452e6	+	2.12479e6i	−0.169928	+	0.123460i
$785$	−5.67589e6	+	1.44426e7i	−0.328746	+	0.836511i
$786$	7.71163e6	+	5.60283e6i	0.445236	+	0.323483i
$787$	6.44946e6	+	8.87692e6i	0.371182	+	0.510888i	0.953222	−	0.302273i	$-0.0977453\pi$
$787$	6.44946e6	+	8.87692e6i	0.371182	+	0.510888i	−0.582040	+	0.813160i	$0.697745\pi$
$788$	6.54938e6	+	9.01445e6i	0.375737	+	0.517158i
$789$	−2.75577e7	−	2.00218e7i	−1.57598	−	1.14502i
$790$	−1.49743e7	−	1.23240e7i	−0.853650	−	0.702560i
$791$	6.69399e6	−	4.86347e6i	0.380403	−	0.276379i
$792$	−1.65103e7	−	5.36451e6i	−0.935278	−	0.303890i
$793$		−	2.81596e6i		−	0.159017i
$794$	5.12148e6	−	1.57623e7i	0.288300	−	0.887296i
$795$	−3.91229e7	+	1.01509e7i	−2.19540	+	0.569624i
$796$	−1.37851e6	−	4.24263e6i	−0.0771131	−	0.237330i
$797$	−2.81051e7	+	9.13191e6i	−1.56726	+	0.509232i	−0.958734	−	0.284305i	$-0.908237\pi$
$797$	−2.81051e7	+	9.13191e6i	−1.56726	+	0.509232i	−0.608521	+	0.793538i	$0.708237\pi$
$798$	−2.80085e6	+	3.85504e6i	−0.155698	+	0.214300i
$799$	−2.54298e7			−1.40921
$800$	2.17869e6	−	2.34378e6i	0.120357	−	0.129477i
$801$	−3.63128e7			−1.99976
$802$	1.18884e7	−	1.63629e7i	0.652659	−	0.898307i
$803$	−3.29410e7	+	1.07032e7i	−1.80280	+	0.585766i
$804$	5.81405e6	+	1.78938e7i	0.317204	+	0.976253i
$805$	2.70925e6	+	4.24525e6i	0.147353	+	0.230895i
$806$	2.39408e6	−	7.36822e6i	0.129808	−	0.399507i
$807$		−	4.85340e7i		−	2.62339i
$808$	2.59037e6	+	841663.i	0.139583	+	0.0453534i
$809$	9.98142e6	−	7.25192e6i	0.536193	−	0.389567i	−0.286476	−	0.958087i	$-0.592484\pi$
$809$	9.98142e6	−	7.25192e6i	0.536193	−	0.389567i	0.822669	+	0.568521i	$0.192484\pi$
$810$	3.76255e6	+	1.45013e7i	0.201498	+	0.776597i
$811$	1.20687e7	+	8.76843e6i	0.644330	+	0.468133i	0.861335	−	0.508037i	$-0.169629\pi$
$811$	1.20687e7	+	8.76843e6i	0.644330	+	0.468133i	−0.217005	+	0.976171i	$0.569629\pi$
$812$	3.54082e6	+	4.87352e6i	0.188458	+	0.259390i
$813$	6.09361e6	+	8.38713e6i	0.323332	+	0.445028i
$814$	−1.91748e7	−	1.39313e7i	−1.01431	−	0.736938i
$815$	451872.	+	1.74157e6i	0.0238298	+	0.0918432i
$816$	−1.07068e7	+	7.77897e6i	−0.562906	+	0.408975i
$817$	−4.64090e6	−	1.50792e6i	−0.243247	−	0.0790356i
$818$		−	1.65155e7i		−	0.862997i
$819$	1.95237e6	−	6.00878e6i	0.101707	−	0.313023i
$820$	2.10619e6	+	3.30028e6i	0.109386	+	0.171402i
$821$	7.67458e6	+	2.36199e7i	0.397371	+	1.22298i	0.927099	+	0.374816i	$0.122294\pi$
$821$	7.67458e6	+	2.36199e7i	0.397371	+	1.22298i	−0.529728	+	0.848168i	$0.677706\pi$
$822$	3.44870e7	−	1.12055e7i	1.78023	−	0.578432i
$823$	−1.61448e7	+	2.22214e7i	−0.830870	+	1.14359i	0.156891	+	0.987616i	$0.449853\pi$
$823$	−1.61448e7	+	2.22214e7i	−0.830870	+	1.14359i	−0.987760	+	0.155978i	$0.950147\pi$
$824$	357697.			0.0183526
$825$	−2.25649e7	−	4.05565e7i	−1.15425	−	2.07456i
$826$	−4.49595e6			−0.229283
$827$	1.63105e7	−	2.24494e7i	0.829283	−	1.14141i	−0.158773	−	0.987315i	$-0.550754\pi$
$827$	1.63105e7	−	2.24494e7i	0.829283	−	1.14141i	0.988056	−	0.154095i	$-0.0492463\pi$
$828$	1.31388e7	−	4.26904e6i	0.666007	−	0.216399i
$829$	3.67777e6	+	1.13190e7i	0.185865	+	0.572034i	0.999962	−	0.00869487i	$-0.00276770\pi$
$829$	3.67777e6	+	1.13190e7i	0.185865	+	0.572034i	−0.814097	+	0.580729i	$0.802768\pi$
$830$	1.21809e7	−	3.16050e6i	0.613742	−	0.159243i
$831$	−975942.	+	3.00364e6i	−0.0490255	+	0.150885i
$832$			1.00514e6i			0.0503408i
$833$	2.55261e7	+	8.29394e6i	1.27459	+	0.414141i
$834$	−6.65223e6	+	4.83313e6i	−0.331171	+	0.240610i
$835$	2.11712e7	+	1.74240e7i	1.05082	+	0.864833i
$836$	−5.97315e6	−	4.33975e6i	−0.295589	−	0.214758i
$837$	3.20176e7	+	4.40685e7i	1.57970	+	2.17428i
$838$	1.29944e7	+	1.78853e7i	0.639214	+	0.879803i
$839$	3.44722e6	+	2.50455e6i	0.169069	+	0.122836i	0.669102	−	0.743171i	$-0.266679\pi$
$839$	3.44722e6	+	2.50455e6i	0.169069	+	0.122836i	−0.500033	+	0.866006i	$0.666679\pi$
$840$	1.84469e6	−	4.69392e6i	0.0902040	−	0.229529i
$841$	−2.60972e7	+	1.89607e7i	−1.27234	+	0.924410i
$842$	−2.07415e6	−	673932.i	−0.100823	−	0.0327594i
$843$			4.09015e7i			1.98230i
$844$	1.83831e6	−	5.65772e6i	0.0888304	−	0.273392i
$845$	1.10505e7	−	1.34269e7i	0.532402	−	0.646897i
$846$	−8.21485e6	−	2.52827e7i	−0.394615	−	1.21450i
$847$	6.75895e6	−	2.19612e6i	0.323721	−	0.105183i
$848$	4.00010e6	−	5.50566e6i	0.191021	−	0.262918i
$849$	−7.84773e6			−0.373658
$850$	−2.35866e7	−	2.85817e6i	−1.11974	−	0.135688i
$851$	1.88614e7			0.892791
$852$	8.70857e6	−	1.19863e7i	0.411006	−	0.565701i
$853$	−3.13316e7	+	1.01802e7i	−1.47438	+	0.479055i	−0.932429	−	0.361355i	$-0.882314\pi$
$853$	−3.13316e7	+	1.01802e7i	−1.47438	+	0.479055i	−0.541952	+	0.840410i	$0.682314\pi$
$854$	−735149.	−	2.26256e6i	−0.0344930	−	0.106158i
$855$	−1.41407e6	+	2.34242e7i	−0.0661540	+	1.09585i
$856$	2.11629e6	−	6.51327e6i	0.0987167	−	0.303819i
$857$		−	7.49930e6i		−	0.348794i	−0.984675	−	0.174397i	$-0.944202\pi$
$857$		−	7.49930e6i		−	0.348794i	0.984675	−	0.174397i	$-0.0557976\pi$
$858$	1.38646e7	+	4.50490e6i	0.642970	+	0.208913i
$859$	3.11748e6	−	2.26498e6i	0.144152	−	0.104733i	−0.513372	−	0.858166i	$-0.671604\pi$
$859$	3.11748e6	−	2.26498e6i	0.144152	−	0.104733i	0.657524	+	0.753434i	$0.271604\pi$
$860$	5.15534e6	+	311217.i	0.237690	+	0.0143489i
$861$	4.99196e6	+	3.62687e6i	0.229490	+	0.166734i
$862$	−2.07527e6	−	2.85637e6i	−0.0951277	−	0.130932i
$863$	−1.64573e7	−	2.26515e7i	−0.752195	−	1.03531i	−0.997823	−	0.0659440i	$-0.978994\pi$
$863$	−1.64573e7	−	2.26515e7i	−0.752195	−	1.03531i	0.245628	−	0.969364i	$-0.421006\pi$
$864$	−5.71743e6	−	4.15396e6i	−0.260565	−	0.189312i
$865$	3.05331e6	−	1.94857e6i	0.138749	−	0.0885475i
$866$	−9.13952e6	+	6.64025e6i	−0.414122	+	0.300877i
$867$	5.67250e7	+	1.84311e7i	2.56287	+	0.832727i
$868$		−	6.54520e6i		−	0.294865i
$869$	1.46348e7	−	4.50413e7i	0.657413	−	2.02331i
$870$	4.11178e7	+	1.61591e7i	1.84175	+	0.723802i
$871$	−3.27858e6	−	1.00904e7i	−0.146433	−	0.450676i
$872$	1.08099e7	−	3.51233e6i	0.481425	−	0.156424i
$873$	3.74648e7	−	5.15659e7i	1.66375	−	2.28996i
$874$	5.87552e6			0.260176
$875$	8.16292e6	−	3.91734e6i	0.360434	−	0.172970i
$876$	−2.76033e7			−1.21535
$877$	4.87718e6	−	6.71286e6i	0.214126	−	0.294719i	−0.688420	−	0.725312i	$-0.741695\pi$
$877$	4.87718e6	−	6.71286e6i	0.214126	−	0.294719i	0.902546	+	0.430593i	$0.141695\pi$
$878$	4.15049e6	−	1.34857e6i	0.181703	−	0.0590390i
$879$	2.10659e6	+	6.48343e6i	0.0919621	+	0.283030i
$880$	7.27294e6	+	2.85824e6i	0.316594	+	0.124420i
$881$	−9.02815e6	+	2.77858e7i	−0.391885	+	1.20610i	0.539476	+	0.842001i	$0.318622\pi$
$881$	−9.02815e6	+	2.77858e7i	−0.391885	+	1.20610i	−0.931361	+	0.364097i	$0.881378\pi$
$882$			2.80577e7i			1.21445i
$883$	3.69357e7	+	1.20011e7i	1.59420	+	0.517989i	0.965665	−	0.259789i	$-0.0836531\pi$
$883$	3.69357e7	+	1.20011e7i	1.59420	+	0.517989i	0.628539	+	0.777778i	$0.283653\pi$
$884$	6.03765e6	−	4.38661e6i	0.259859	−	0.188798i
$885$	−2.77948e7	+	1.77382e7i	−1.19290	+	0.761291i
$886$	1.81285e7	+	1.31711e7i	0.775850	+	0.563688i
$887$	2.01146e7	+	2.76853e7i	0.858423	+	1.18152i	0.981943	+	0.189176i	$0.0605817\pi$
$887$	2.01146e7	+	2.76853e7i	0.858423	+	1.18152i	−0.123520	+	0.992342i	$0.539418\pi$
$888$	−1.11025e7	−	1.52813e7i	−0.472486	−	0.650322i
$889$	−819519.	−	595416.i	−0.0347780	−	0.0252677i
$890$	1.63162e7	+	984977.i	0.690469	+	0.0416822i
$891$	−2.95978e7	+	2.15041e7i	−1.24901	+	0.907459i
$892$	8.89970e6	+	2.89169e6i	0.374510	+	0.121686i
$893$		−	1.13062e7i		−	0.474446i
$894$	−2.06762e6	+	6.36348e6i	−0.0865221	+	0.266288i
$895$	28802.8	−	477120.i	0.00120192	−	0.0199100i
$896$	262409.	+	807611.i	0.0109196	+	0.0336072i
$897$	−1.10334e7	+	3.58497e6i	−0.457855	+	0.148766i
$898$	1.71333e6	−	2.35820e6i	0.0709007	−	0.0975864i
$899$	5.73346e7			2.36602
$900$	−4.77779e6	−	2.43735e7i	−0.196617	−	1.00302i
$901$	−5.05282e7			−2.07358
$902$	−5.61962e6	+	7.73474e6i	−0.229980	+	0.316540i
$903$	7.74151e6	−	2.51537e6i	0.315941	−	0.102656i
$904$	3.15729e6	+	9.71713e6i	0.128497	+	0.395473i
$905$	−2.21688e7	+	2.69363e7i	−0.899747	+	1.09324i
$906$	−8.11340e6	+	2.49705e7i	−0.328384	+	1.01066i
$907$		−	2.45292e7i		−	0.990069i	−0.868873	−	0.495034i	$-0.835155\pi$
$907$		−	2.45292e7i		−	0.990069i	0.868873	−	0.495034i	$-0.164845\pi$
$908$	−2.14560e7	−	6.97146e6i	−0.863641	−	0.280614i
$909$	1.71029e7	−	1.24260e7i	0.686530	−	0.498793i
$910$	−1.04023e6	+	2.64693e6i	−0.0416416	+	0.105959i
$911$	2.04467e7	+	1.48554e7i	0.816257	+	0.593045i	0.915638	−	0.402004i	$-0.131686\pi$
$911$	2.04467e7	+	1.48554e7i	0.816257	+	0.593045i	−0.0993808	+	0.995049i	$0.531686\pi$
$912$	−3.45855e6	−	4.76029e6i	−0.137691	−	0.189516i
$913$	1.80632e7	+	2.48618e7i	0.717161	+	0.987088i
$914$	−5.79596e6	−	4.21101e6i	−0.229488	−	0.166733i
$915$	−1.34714e7	−	1.10871e7i	−0.531937	−	0.437788i
$916$	−6.14734e6	+	4.46631e6i	−0.242074	+	0.175877i
$917$	−4.31886e6	−	1.40328e6i	−0.169608	−	0.0551089i
$918$			5.24717e7i			2.05503i
$919$	2.33341e6	−	7.18151e6i	0.0911387	−	0.280496i	−0.895089	−	0.445887i	$-0.852888\pi$
$919$	2.33341e6	−	7.18151e6i	0.0911387	−	0.280496i	0.986228	+	0.165391i	$0.0528885\pi$
$920$	−6.01936e6	+	1.56180e6i	−0.234466	+	0.0608352i
$921$	−4.91246e6	−	1.51190e7i	−0.190832	−	0.587319i
$922$	−1.40232e7	+	4.55640e6i	−0.543273	+	0.176520i
$923$	−4.91082e6	+	6.75916e6i	−0.189736	+	0.261149i
$924$	1.23160e7			0.474558
$925$	4.07932e6	−	3.36640e7i	0.156759	−	1.29363i
$926$	4.03602e6			0.154677
$927$	1.63188e6	−	2.24610e6i	0.0623720	−	0.0858477i
$928$	−7.07450e6	+	2.29864e6i	−0.269666	+	0.0876197i
$929$	4.34173e6	+	1.33625e7i	0.165053	+	0.507981i	0.999040	−	0.0438030i	$-0.0139474\pi$
$929$	4.34173e6	+	1.33625e7i	0.165053	+	0.507981i	−0.833987	+	0.551784i	$0.813947\pi$
$930$	−2.58232e7	−	4.04635e7i	−0.979044	−	1.53411i
$931$	−3.68751e6	+	1.13490e7i	−0.139431	+	0.429124i
$932$		−	2.09041e6i		−	0.0788299i
$933$	−1.46598e7	−	4.76327e6i	−0.551347	−	0.179143i
$934$	7.29515e6	−	5.30024e6i	0.273632	−	0.198805i
$935$	−1.45715e7	−	5.61605e7i	−0.545100	−	2.10088i
$936$	6.31164e6	+	4.58567e6i	0.235479	+	0.171086i
$937$	−2.50340e7	−	3.44563e7i	−0.931495	−	1.28209i	−0.959274	−	0.282479i	$-0.908843\pi$
$937$	−2.50340e7	−	3.44563e7i	−0.931495	−	1.28209i	0.0277786	−	0.999614i	$-0.491157\pi$
$938$	−5.26852e6	−	7.25150e6i	−0.195516	−	0.269104i
$939$	3.86515e6	+	2.80819e6i	0.143055	+	0.103935i
$940$	3.00534e6	+	1.15830e7i	0.110936	+	0.427563i
$941$	2.38133e7	−	1.73013e7i	0.876687	−	0.636951i	−0.0556856	−	0.998448i	$-0.517734\pi$
$941$	2.38133e7	−	1.73013e7i	0.876687	−	0.636951i	0.932373	+	0.361498i	$0.117734\pi$
$942$	−2.87221e7	−	9.33236e6i	−1.05460	−	0.342661i
$943$		−	7.60832e6i		−	0.278618i
$944$	1.71557e6	−	5.27998e6i	0.0626583	−	0.192842i
$945$	−1.07572e7	−	1.68560e7i	−0.391850	−	0.614009i
$946$	3.89741e6	+	1.19950e7i	0.141595	+	0.435785i
$947$	−4.77893e7	+	1.55277e7i	−1.73163	+	0.562641i	−0.993684	−	0.112215i	$-0.964205\pi$
$947$	−4.77893e7	+	1.55277e7i	−1.73163	+	0.562641i	−0.737949	+	0.674857i	$0.764205\pi$
$948$	2.21847e7	−	3.05346e7i	0.801738	−	1.10350i
$949$	1.55657e7			0.561050
$950$	1.27075e6	−	1.04867e7i	0.0456827	−	0.376990i
$951$	3.97984e7			1.42697
$952$	3.70592e6	−	5.10076e6i	0.132527	−	0.182407i
$953$	2.00847e7	−	6.52593e6i	0.716364	−	0.232761i	0.0719180	−	0.997411i	$-0.477088\pi$
$953$	2.00847e7	−	6.52593e6i	0.716364	−	0.232761i	0.644446	+	0.764650i	$0.277088\pi$
$954$	−1.63226e7	−	5.02359e7i	−0.580656	−	1.78708i
$955$	−2.56757e7	+	6.66188e6i	−0.910991	+	0.236368i
$956$	−6.01802e6	+	1.85216e7i	−0.212965	+	0.655440i
$957$			1.07886e8i			3.80788i
$958$	1.49630e7	+	4.86178e6i	0.526751	+	0.171152i
$959$	−1.39759e7	+	1.01541e7i	−0.490721	+	0.356529i
$960$	4.80857e6	+	3.95749e6i	0.168398	+	0.138593i
$961$	−2.72364e7	−	1.97884e7i	−0.951352	−	0.691198i
$962$	6.26078e6	+	8.61723e6i	0.218118	+	0.300213i
$963$	−3.12440e7	−	4.30037e7i	−1.08568	−	1.49431i
$964$	−1.96422e7	−	1.42709e7i	−0.680765	−	0.494604i
$965$	−1.23794e6	+	3.15001e6i	−0.0427940	+	0.108892i
$966$	−7.92917e6	+	5.76088e6i	−0.273391	+	0.198631i
$967$	1.80966e7	+	5.87995e6i	0.622345	+	0.202212i	0.603181	−	0.797604i	$-0.293900\pi$
$967$	1.80966e7	+	5.87995e6i	0.622345	+	0.202212i	0.0191638	+	0.999816i	$0.493900\pi$
$968$			8.77561e6i			0.301015i
$969$	−1.35002e7	+	4.15493e7i	−0.461881	+	1.42152i
$970$	−1.82326e7	+	2.21536e7i	−0.622183	+	0.755987i
$971$	−7.83883e6	−	2.41254e7i	−0.266811	−	0.821159i	−0.991271	−	0.131842i	$-0.957911\pi$
$971$	−7.83883e6	−	2.41254e7i	−0.266811	−	0.821159i	0.724460	−	0.689317i	$-0.242089\pi$
$972$	−2.20956e6	+	717930.i	−0.0750137	+	0.0243734i
$973$	2.30251e6	−	3.16914e6i	0.0779687	−	0.107315i
$974$	−1.69451e6			−0.0572330
$975$	4.01220e6	+	2.04679e7i	0.135167	+	0.689543i
$976$	2.93763e6			0.0987126
$977$	−1.42059e6	+	1.95528e6i	−0.0476139	+	0.0655349i	−0.832160	−	0.554535i	$-0.812896\pi$
$977$	−1.42059e6	+	1.95528e6i	−0.0476139	+	0.0655349i	0.784546	+	0.620070i	$0.212896\pi$
$978$	−3.33021e6	+	1.08205e6i	−0.111333	+	0.0361743i
$979$	1.23350e7	+	3.79632e7i	0.411322	+	1.26592i
$980$	761059.	−	1.26070e7i	0.0253136	−	0.419321i
$981$	2.72616e7	−	8.39026e7i	0.904438	−	2.78358i
$982$		−	2.88636e7i		−	0.955152i
$983$	3.96406e7	+	1.28800e7i	1.30845	+	0.425140i	0.878512	−	0.477720i	$-0.158537\pi$
$983$	3.96406e7	+	1.28800e7i	1.30845	+	0.425140i	0.429935	+	0.902860i	$0.358537\pi$
$984$	−6.16418e6	+	4.47854e6i	−0.202949	+	0.147451i
$985$	−3.88594e7	−	2.34587e6i	−1.27616	−	0.0770394i
$986$	4.46816e7	+	3.24631e7i	1.46365	+	1.06340i
$987$	1.10856e7	+	1.52580e7i	0.362214	+	0.498545i
$988$	1.95030e6	+	2.68436e6i	0.0635636	+	0.0874879i
$989$	−8.11993e6	−	5.89947e6i	−0.263974	−	0.191789i
$990$	5.11284e7	−	3.26293e7i	1.65796	−	1.05808i
$991$	−2.44177e7	+	1.77405e7i	−0.789805	+	0.573827i	−0.907906	−	0.419175i	$-0.862319\pi$
$991$	−2.44177e7	+	1.77405e7i	−0.789805	+	0.573827i	0.118101	+	0.993002i	$0.462319\pi$
$992$	7.68659e6	+	2.49752e6i	0.248002	+	0.0805806i
$993$			1.72823e7i			0.556195i
$994$	−2.18115e6	+	6.71288e6i	−0.0700195	+	0.215498i
$995$	1.45060e7	+	5.70079e6i	0.464504	+	0.182548i
$996$	7.56811e6	+	2.32922e7i	0.241735	+	0.743983i
$997$	2.50621e7	−	8.14318e6i	0.798509	−	0.259451i	0.118786	−	0.992920i	$-0.462100\pi$
$997$	2.50621e7	−	8.14318e6i	0.798509	−	0.259451i	0.679723	+	0.733469i	$0.262100\pi$
$998$	−8.63074e6	+	1.18792e7i	−0.274297	+	0.377538i
$999$	−7.48901e7			−2.37416

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	50.6.e.a.9.6	✓	48
25.14	even	10	inner	50.6.e.a.39.6	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
50.6.e.a.9.6	✓	48	1.1	even	1	trivial
50.6.e.a.39.6	yes	48	25.14	even	10	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.e (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.35114 + 3.23607i) q^{2} +(25.8671 - 8.40474i) q^{3} +(-4.94427 - 15.2169i) q^{4} +(52.0281 + 20.4469i) q^{5} +(-33.6189 + 103.468i) q^{6} -51.8294i q^{7} +(60.8676 + 19.7771i) q^{8} +(401.877 - 291.981i) q^{9} +O(q^{10})\)	\(q+(-2.35114 + 3.23607i) q^{2} +(25.8671 - 8.40474i) q^{3} +(-4.94427 - 15.2169i) q^{4} +(52.0281 + 20.4469i) q^{5} +(-33.6189 + 103.468i) q^{6} -51.8294i q^{7} +(60.8676 + 19.7771i) q^{8} +(401.877 - 291.981i) q^{9} +(-188.493 + 120.293i) q^{10} +(-441.763 - 320.960i) q^{11} +(-255.788 - 352.062i) q^{12} +(144.241 + 198.530i) q^{13} +(167.723 + 121.858i) q^{14} +(1517.67 + 91.6186i) q^{15} +(-207.108 + 150.473i) q^{16} +(1807.71 + 587.359i) q^{17} +1986.99i q^{18} +(-261.142 + 803.711i) q^{19} +(53.8967 - 892.802i) q^{20} +(-435.612 - 1340.68i) q^{21} +(2077.30 - 674.954i) q^{22} +(-1021.67 + 1406.21i) q^{23} +1740.69 q^{24} +(2288.85 + 2127.62i) q^{25} -981.587 q^{26} +(4056.60 - 5583.43i) q^{27} +(-788.682 + 256.258i) q^{28} +(-2244.77 - 6908.69i) q^{29} +(-3864.74 + 4695.87i) q^{30} +(-2438.99 + 7506.43i) q^{31} -1024.00i q^{32} +(-14124.7 - 4589.40i) q^{33} +(-6150.91 + 4468.90i) q^{34} +(1059.75 - 2696.58i) q^{35} +(-6430.03 - 4671.69i) q^{36} +(-6378.23 - 8778.88i) q^{37} +(-1986.88 - 2734.71i) q^{38} +(5399.68 + 3923.10i) q^{39} +(2762.45 + 2273.52i) q^{40} +(-3541.23 + 2572.85i) q^{41} +(5362.70 + 1742.45i) q^{42} +5774.34i q^{43} +(-2699.82 + 8309.18i) q^{44} +(26879.0 - 6974.09i) q^{45} +(-2148.50 - 6612.40i) q^{46} +(-12724.1 + 4134.32i) q^{47} +(-4092.61 + 5632.99i) q^{48} +14120.7 q^{49} +(-12266.5 + 2404.54i) q^{50} +51696.8 q^{51} +(2307.85 - 3176.48i) q^{52} +(-25282.4 + 8214.75i) q^{53} +(8530.72 + 26254.9i) q^{54} +(-16421.5 - 25731.6i) q^{55} +(1025.03 - 3154.73i) q^{56} +22984.5i q^{57} +(27634.8 + 8979.08i) q^{58} +(-17544.6 + 12746.9i) q^{59} +(-6109.61 - 23547.2i) q^{60} +(-9283.57 - 6744.91i) q^{61} +(-18556.9 - 25541.4i) q^{62} +(-15133.2 - 20829.0i) q^{63} +(3313.73 + 2407.57i) q^{64} +(3445.25 + 13278.4i) q^{65} +(48060.8 - 34918.2i) q^{66} +(-41118.8 - 13360.3i) q^{67} -30411.8i q^{68} +(-14608.9 + 44961.5i) q^{69} +(6234.71 + 9769.46i) q^{70} +(10520.8 + 32379.7i) q^{71} +(30235.8 - 9824.22i) q^{72} +(37283.5 - 51316.4i) q^{73} +43405.1 q^{74} +(77088.1 + 35798.3i) q^{75} +13521.2 q^{76} +(-16635.1 + 22896.3i) q^{77} +(-25390.8 + 8249.98i) q^{78} +(26801.3 + 82485.9i) q^{79} +(-13852.2 + 3594.11i) q^{80} +(20703.9 - 63720.2i) q^{81} -17508.8i q^{82} +(-53524.1 - 17391.0i) q^{83} +(-18247.2 + 13257.3i) q^{84} +(82041.9 + 67521.1i) q^{85} +(-18686.1 - 13576.3i) q^{86} +(-116131. - 159841. i) q^{87} +(-20541.4 - 28272.8i) q^{88} +(-59140.1 - 42967.8i) q^{89} +(-40627.7 + 103379. i) q^{90} +(10289.7 - 7475.89i) q^{91} +(26449.6 + 8593.99i) q^{92} +214669. i q^{93} +(16537.3 - 50896.5i) q^{94} +(-30020.1 + 36476.1i) q^{95} +(-8606.45 - 26487.9i) q^{96} +(122033. - 39650.8i) q^{97} +(-33199.8 + 45695.6i) q^{98} -271249. q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 192 q^{4} + 180 q^{5} + 72 q^{6} + 686 q^{9}+O(q^{10}) \) 48 * q + 192 * q^4 + 180 * q^5 + 72 * q^6 + 686 * q^9	\( 48 q + 192 q^{4} + 180 q^{5} + 72 q^{6} + 686 q^{9} + 80 q^{10} + 716 q^{11} - 160 q^{12} - 784 q^{14} - 940 q^{15} - 3072 q^{16} + 1910 q^{17} - 5990 q^{19} - 640 q^{20} - 4344 q^{21} + 4720 q^{22} + 12410 q^{23} + 4608 q^{24} + 23660 q^{25} - 15248 q^{26} + 27600 q^{27} - 3040 q^{28} - 17170 q^{29} - 14720 q^{30} - 18834 q^{31} - 56930 q^{33} + 11696 q^{34} + 28450 q^{35} - 10976 q^{36} + 3540 q^{37} + 13432 q^{39} - 1280 q^{40} + 37146 q^{41} - 43560 q^{42} + 1184 q^{44} + 75240 q^{45} + 28672 q^{46} - 17830 q^{47} - 2560 q^{48} - 54656 q^{49} + 8800 q^{50} - 85984 q^{51} + 22350 q^{53} + 16080 q^{54} - 64730 q^{55} + 12544 q^{56} + 18000 q^{59} + 78720 q^{60} + 67086 q^{61} - 159600 q^{62} + 132820 q^{63} + 49152 q^{64} - 195820 q^{65} - 52256 q^{66} - 90790 q^{67} - 212608 q^{69} + 180080 q^{70} - 122874 q^{71} + 121200 q^{73} + 281456 q^{74} + 672810 q^{75} - 102400 q^{76} + 434040 q^{77} + 170720 q^{78} + 113600 q^{79} - 28160 q^{80} + 115878 q^{81} - 582750 q^{83} - 174816 q^{84} + 107770 q^{85} - 26888 q^{86} - 911580 q^{87} - 56960 q^{88} - 357730 q^{89} - 282920 q^{90} - 216324 q^{91} + 451040 q^{92} + 79136 q^{94} + 135000 q^{95} + 18432 q^{96} - 123520 q^{97} - 206240 q^{98} + 235252 q^{99}+O(q^{100}) \) 48 * q + 192 * q^4 + 180 * q^5 + 72 * q^6 + 686 * q^9 + 80 * q^10 + 716 * q^11 - 160 * q^12 - 784 * q^14 - 940 * q^15 - 3072 * q^16 + 1910 * q^17 - 5990 * q^19 - 640 * q^20 - 4344 * q^21 + 4720 * q^22 + 12410 * q^23 + 4608 * q^24 + 23660 * q^25 - 15248 * q^26 + 27600 * q^27 - 3040 * q^28 - 17170 * q^29 - 14720 * q^30 - 18834 * q^31 - 56930 * q^33 + 11696 * q^34 + 28450 * q^35 - 10976 * q^36 + 3540 * q^37 + 13432 * q^39 - 1280 * q^40 + 37146 * q^41 - 43560 * q^42 + 1184 * q^44 + 75240 * q^45 + 28672 * q^46 - 17830 * q^47 - 2560 * q^48 - 54656 * q^49 + 8800 * q^50 - 85984 * q^51 + 22350 * q^53 + 16080 * q^54 - 64730 * q^55 + 12544 * q^56 + 18000 * q^59 + 78720 * q^60 + 67086 * q^61 - 159600 * q^62 + 132820 * q^63 + 49152 * q^64 - 195820 * q^65 - 52256 * q^66 - 90790 * q^67 - 212608 * q^69 + 180080 * q^70 - 122874 * q^71 + 121200 * q^73 + 281456 * q^74 + 672810 * q^75 - 102400 * q^76 + 434040 * q^77 + 170720 * q^78 + 113600 * q^79 - 28160 * q^80 + 115878 * q^81 - 582750 * q^83 - 174816 * q^84 + 107770 * q^85 - 26888 * q^86 - 911580 * q^87 - 56960 * q^88 - 357730 * q^89 - 282920 * q^90 - 216324 * q^91 + 451040 * q^92 + 79136 * q^94 + 135000 * q^95 + 18432 * q^96 - 123520 * q^97 - 206240 * q^98 + 235252 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more