LMFDB - Embedded newform 50.6.e.a.29.7

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			29.7
Character	$\chi$	$=$	50.29
Dual form			50.6.e.a.19.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(3.80423 + 1.23607i) q^{2} +(-16.9585 + 23.3414i) q^{3} +(12.9443 + 9.40456i) q^{4} +(-8.25144 + 55.2894i) q^{5} +(-93.3657 + 67.8341i) q^{6} -138.453i q^{7} +(37.6183 + 51.7771i) q^{8} +(-182.139 - 560.566i) q^{9} +O(q^{10})$	\(q+(3.80423 + 1.23607i) q^{2} +(-16.9585 + 23.3414i) q^{3} +(12.9443 + 9.40456i) q^{4} +(-8.25144 + 55.2894i) q^{5} +(-93.3657 + 67.8341i) q^{6} -138.453i q^{7} +(37.6183 + 51.7771i) q^{8} +(-182.139 - 560.566i) q^{9} +(-99.7318 + 200.134i) q^{10} +(-71.4074 + 219.769i) q^{11} +(-439.032 + 142.650i) q^{12} +(-251.878 + 81.8400i) q^{13} +(171.137 - 526.707i) q^{14} +(-1150.60 - 1130.23i) q^{15} +(79.1084 + 243.470i) q^{16} +(323.609 + 445.410i) q^{17} -2357.66i q^{18} +(-1503.87 + 1092.63i) q^{19} +(-626.781 + 638.079i) q^{20} +(3231.69 + 2347.96i) q^{21} +(-543.300 + 747.788i) q^{22} +(3180.04 + 1033.26i) q^{23} -1846.50 q^{24} +(-2988.83 - 912.434i) q^{25} -1059.36 q^{26} +(9505.42 + 3088.50i) q^{27} +(1302.09 - 1792.18i) q^{28} +(-3656.43 - 2656.55i) q^{29} +(-2980.11 - 5721.86i) q^{30} +(-8606.44 + 6252.94i) q^{31} +1024.00i q^{32} +(-3918.76 - 5393.72i) q^{33} +(680.526 + 2094.44i) q^{34} +(7654.99 + 1142.44i) q^{35} +(2914.22 - 8969.05i) q^{36} +(12117.1 - 3937.07i) q^{37} +(-7071.64 + 2297.71i) q^{38} +(2361.21 - 7267.07i) q^{39} +(-3173.13 + 1652.65i) q^{40} +(2161.21 + 6651.52i) q^{41} +(9391.85 + 12926.8i) q^{42} +14511.7i q^{43} +(-2991.15 + 2173.20i) q^{44} +(32496.2 - 5444.87i) q^{45} +(10820.4 + 7861.50i) q^{46} +(-9939.24 + 13680.2i) q^{47} +(-7024.51 - 2282.40i) q^{48} -2362.27 q^{49} +(-10242.3 - 7165.50i) q^{50} -15884.4 q^{51} +(-4030.04 - 1309.44i) q^{52} +(7607.08 - 10470.2i) q^{53} +(32343.2 + 23498.7i) q^{54} +(-11561.7 - 5761.48i) q^{55} +(7168.70 - 5208.37i) q^{56} -53631.9i q^{57} +(-10626.2 - 14625.7i) q^{58} +(7688.01 + 23661.3i) q^{59} +(-4264.39 - 25450.9i) q^{60} +(6872.86 - 21152.5i) q^{61} +(-40469.9 + 13149.5i) q^{62} +(-77612.1 + 25217.7i) q^{63} +(-1265.73 + 3895.53i) q^{64} +(-2446.53 - 14601.5i) q^{65} +(-8240.87 - 25362.8i) q^{66} +(8845.67 + 12175.0i) q^{67} +8808.92i q^{68} +(-78046.6 + 56704.2i) q^{69} +(27709.2 + 13808.2i) q^{70} +(-37184.7 - 27016.3i) q^{71} +(22172.7 - 30518.1i) q^{72} +(-27613.5 - 8972.17i) q^{73} +50962.5 q^{74} +(71983.6 - 54289.9i) q^{75} -29742.2 q^{76} +(30427.8 + 9886.58i) q^{77} +(17965.2 - 24727.0i) q^{78} +(20275.5 + 14731.0i) q^{79} +(-14114.1 + 2364.87i) q^{80} +(-117414. + 85306.5i) q^{81} +27975.3i q^{82} +(40339.0 + 55521.9i) q^{83} +(19750.4 + 60785.3i) q^{84} +(-27296.7 + 14216.9i) q^{85} +(-17937.5 + 55206.0i) q^{86} +(124015. - 40295.0i) q^{87} +(-14065.2 + 4570.07i) q^{88} +(8330.04 - 25637.2i) q^{89} +(130353. + 19454.1i) q^{90} +(11331.0 + 34873.3i) q^{91} +(31446.0 + 43281.7i) q^{92} -306927. i q^{93} +(-54720.7 + 39756.9i) q^{94} +(-48001.6 - 92164.0i) q^{95} +(-23901.6 - 17365.5i) q^{96} +(-26055.6 + 35862.5i) q^{97} +(-8986.62 - 2919.93i) q^{98} +136201. 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 $\left(\mathbb{Z}/50\mathbb{Z}\right)^\times$.

$n$	$27$
$\chi(n)$	$e\left(\frac{1}{10}\right)$

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 $

$2$	3.80423	+	1.23607i	0.672499	+	0.218508i
$2$	3.80423	+	1.23607i	0.672499	+	0.218508i
$3$	−16.9585	+	23.3414i	−1.08789	+	1.49735i	−0.237364	+	0.971421i	$0.576283\pi$
$3$	−16.9585	+	23.3414i	−1.08789	+	1.49735i	−0.850527	+	0.525932i	$0.823717\pi$
$4$	12.9443	+	9.40456i	0.404508	+	0.293893i
$5$	−8.25144	+	55.2894i	−0.147606	+	0.989046i
$5$	−8.25144	+	55.2894i	−0.147606	+	0.989046i
$6$	−93.3657	+	67.8341i	−1.05879	+	0.769255i
$7$		−	138.453i		−	1.06797i	−0.845495	−	0.533983i	$-0.820694\pi$
$7$		−	138.453i		−	1.06797i	0.845495	−	0.533983i	$-0.179306\pi$
$8$	37.6183	+	51.7771i	0.207813	+	0.286031i
$9$	−182.139	−	560.566i	−0.749543	−	2.30686i
$10$	−99.7318	+	200.134i	−0.315379	+	0.632879i
$11$	−71.4074	+	219.769i	−0.177935	+	0.547628i	−0.999755	−	0.0221190i	$-0.992959\pi$
$11$	−71.4074	+	219.769i	−0.177935	+	0.547628i	0.821820	+	0.569747i	$0.192959\pi$
$12$	−439.032	+	142.650i	−0.880122	+	0.285969i
$13$	−251.878	+	81.8400i	−0.413363	+	0.134310i	−0.508313	−	0.861172i	$-0.669731\pi$
$13$	−251.878	+	81.8400i	−0.413363	+	0.134310i	0.0949504	+	0.995482i	$0.469731\pi$
$14$	171.137	−	526.707i	0.233359	−	0.718206i
$15$	−1150.60	−	1130.23i	−1.32037	−	1.29699i
$16$	79.1084	+	243.470i	0.0772542	+	0.237764i
$17$	323.609	+	445.410i	0.271581	+	0.373799i	0.922923	−	0.384986i	$-0.125794\pi$
$17$	323.609	+	445.410i	0.271581	+	0.373799i	−0.651342	+	0.758784i	$0.725794\pi$
$18$		−	2357.66i		−	1.71514i
$19$	−1503.87	+	1092.63i	−0.955713	+	0.694366i	−0.952151	−	0.305628i	$-0.901134\pi$
$19$	−1503.87	+	1092.63i	−0.955713	+	0.694366i	−0.00356161	+	0.999994i	$0.501134\pi$
$20$	−626.781	+	638.079i	−0.350381	+	0.356697i
$21$	3231.69	+	2347.96i	1.59912	+	1.16183i
$22$	−543.300	+	747.788i	−0.239322	+	0.329399i
$23$	3180.04	+	1033.26i	1.25347	+	0.407277i	0.859163	−	0.511702i	$-0.170985\pi$
$23$	3180.04	+	1033.26i	1.25347	+	0.407277i	0.394306	+	0.918979i	$0.370985\pi$
$24$	−1846.50			−0.654367
$25$	−2988.83	−	912.434i	−0.956425	−	0.291979i
$26$	−1059.36			−0.307334
$27$	9505.42	+	3088.50i	2.50935	+	0.815338i
$28$	1302.09	−	1792.18i	0.313868	−	0.432002i
$29$	−3656.43	−	2656.55i	−0.807350	−	0.586574i	0.105711	−	0.994397i	$-0.466288\pi$
$29$	−3656.43	−	2656.55i	−0.807350	−	0.586574i	−0.913061	+	0.407823i	$0.866288\pi$
$30$	−2980.11	−	5721.86i	−0.604545	−	1.16074i
$31$	−8606.44	+	6252.94i	−1.60849	+	1.16864i	−0.740508	+	0.672047i	$0.765415\pi$
$31$	−8606.44	+	6252.94i	−1.60849	+	1.16864i	−0.867984	+	0.496591i	$0.834585\pi$
$32$			1024.00i			0.176777i
$33$	−3918.76	−	5393.72i	−0.626418	−	0.862191i
$34$	680.526	+	2094.44i	0.100960	+	0.310722i
$35$	7654.99	+	1142.44i	1.05627	+	0.157639i
$36$	2914.22	−	8969.05i	0.374771	−	1.15343i
$37$	12117.1	−	3937.07i	1.45510	−	0.472790i	0.528530	−	0.848915i	$-0.322743\pi$
$37$	12117.1	−	3937.07i	1.45510	−	0.472790i	0.926569	+	0.376124i	$0.122743\pi$
$38$	−7071.64	+	2297.71i	−0.794440	+	0.258129i
$39$	2361.21	−	7267.07i	0.248584	−	0.765064i
$40$	−3173.13	+	1652.65i	−0.313572	+	0.163317i
$41$	2161.21	+	6651.52i	0.200788	+	0.617961i	0.999860	+	0.0167264i	$0.00532442\pi$
$41$	2161.21	+	6651.52i	0.200788	+	0.617961i	−0.799072	+	0.601235i	$0.794676\pi$
$42$	9391.85	+	12926.8i	0.821538	+	1.13075i
$43$			14511.7i			1.19687i	0.801170	+	0.598437i	$0.204211\pi$
$43$			14511.7i			1.19687i	−0.801170	+	0.598437i	$0.795789\pi$
$44$	−2991.15	+	2173.20i	−0.232920	+	0.169226i
$45$	32496.2	−	5444.87i	2.39222	−	0.400826i
$46$	10820.4	+	7861.50i	0.753963	+	0.547786i
$47$	−9939.24	+	13680.2i	−0.656309	+	0.903332i	−0.999352	−	0.0359878i	$-0.988542\pi$
$47$	−9939.24	+	13680.2i	−0.656309	+	0.903332i	0.343043	+	0.939320i	$0.388542\pi$
$48$	−7024.51	−	2282.40i	−0.440061	−	0.142984i
$49$	−2362.27			−0.140553
$50$	−10242.3	−	7165.50i	−0.579395	−	0.405342i
$51$	−15884.4			−0.855159
$52$	−4030.04	−	1309.44i	−0.206681	−	0.0671548i
$53$	7607.08	−	10470.2i	0.371987	−	0.511997i	−0.581452	−	0.813580i	$-0.697515\pi$
$53$	7607.08	−	10470.2i	0.371987	−	0.511997i	0.953440	+	0.301584i	$0.0975153\pi$
$54$	32343.2	+	23498.7i	1.50938	+	1.09663i
$55$	−11561.7	−	5761.48i	−0.515365	−	0.256819i
$56$	7168.70	−	5208.37i	0.305471	−	0.221938i
$57$		−	53631.9i		−	2.18643i
$58$	−10626.2	−	14625.7i	−0.414771	−	0.570883i
$59$	7688.01	+	23661.3i	0.287530	+	0.884928i	0.985629	+	0.168926i	$0.0540298\pi$
$59$	7688.01	+	23661.3i	0.287530	+	0.884928i	−0.698098	+	0.716002i	$0.745970\pi$
$60$	−4264.39	−	25450.9i	−0.152925	−	0.912692i
$61$	6872.86	−	21152.5i	0.236490	−	0.727842i	−0.760430	−	0.649420i	$-0.775012\pi$
$61$	6872.86	−	21152.5i	0.236490	−	0.727842i	0.996920	−	0.0784221i	$-0.0249882\pi$
$62$	−40469.9	+	13149.5i	−1.33707	+	0.434439i
$63$	−77612.1	+	25217.7i	−2.46364	+	0.800487i
$64$	−1265.73	+	3895.53i	−0.0386271	+	0.118882i
$65$	−2446.53	−	14601.5i	−0.0718236	−	0.428660i
$66$	−8240.87	−	25362.8i	−0.232870	−	0.716699i
$67$	8845.67	+	12175.0i	0.240738	+	0.331347i	0.912240	−	0.409655i	$-0.134351\pi$
$67$	8845.67	+	12175.0i	0.240738	+	0.331347i	−0.671503	+	0.741002i	$0.734351\pi$
$68$			8808.92i			0.231020i
$69$	−78046.6	+	56704.2i	−1.97347	+	1.43381i
$70$	27709.2	+	13808.2i	0.675894	+	0.336815i
$71$	−37184.7	−	27016.3i	−0.875425	−	0.636033i	0.0566123	−	0.998396i	$-0.481970\pi$
$71$	−37184.7	−	27016.3i	−0.875425	−	0.636033i	−0.932037	+	0.362363i	$0.881970\pi$
$72$	22172.7	−	30518.1i	0.504066	−	0.693788i
$73$	−27613.5	−	8972.17i	−0.606477	−	0.197056i	−0.0103500	−	0.999946i	$-0.503295\pi$
$73$	−27613.5	−	8972.17i	−0.606477	−	0.197056i	−0.596127	+	0.802890i	$0.703295\pi$
$74$	50962.5			1.08186
$75$	71983.6	−	54289.9i	1.47768	−	1.11446i
$76$	−29742.2			−0.590663
$77$	30427.8	+	9886.58i	0.584848	+	0.190029i
$78$	17965.2	−	24727.0i	0.334345	−	0.460187i
$79$	20275.5	+	14731.0i	0.365515	+	0.265562i	0.755348	−	0.655323i	$-0.227468\pi$
$79$	20275.5	+	14731.0i	0.365515	+	0.265562i	−0.389834	+	0.920885i	$0.627468\pi$
$80$	−14114.1	+	2364.87i	−0.246563	+	0.0413126i
$81$	−117414.	+	85306.5i	−1.98842	+	1.44467i
$82$			27975.3i			0.459452i
$83$	40339.0	+	55521.9i	0.642732	+	0.884645i	0.998758	−	0.0498311i	$-0.0158683\pi$
$83$	40339.0	+	55521.9i	0.642732	+	0.884645i	−0.356025	+	0.934476i	$0.615868\pi$
$84$	19750.4	+	60785.3i	0.305405	+	0.939941i
$85$	−27296.7	+	14216.9i	−0.409791	+	0.213431i
$86$	−17937.5	+	55206.0i	−0.261527	+	0.804896i
$87$	124015.	−	40295.0i	1.75662	−	0.570760i
$88$	−14065.2	+	4570.07i	−0.193616	+	0.0629095i
$89$	8330.04	−	25637.2i	0.111474	−	0.343080i	−0.879722	−	0.475489i	$-0.842271\pi$
$89$	8330.04	−	25637.2i	0.111474	−	0.343080i	0.991195	+	0.132409i	$0.0422711\pi$
$90$	130353.	+	19454.1i	1.69635	+	0.253165i
$91$	11331.0	+	34873.3i	0.143438	+	0.441458i
$92$	31446.0	+	43281.7i	0.387343	+	0.533132i
$93$		−	306927.i		−	3.67983i
$94$	−54720.7	+	39756.9i	−0.638752	+	0.464080i
$95$	−48001.6	−	92164.0i	−0.545691	−	1.04774i
$96$	−23901.6	−	17365.5i	−0.264697	−	0.192314i
$97$	−26055.6	+	35862.5i	−0.281172	+	0.387000i	−0.926122	−	0.377225i	$-0.876878\pi$
$97$	−26055.6	+	35862.5i	−0.281172	+	0.387000i	0.644950	+	0.764225i	$0.276878\pi$
$98$	−8986.62	−	2919.93i	−0.0945216	−	0.0307119i
$99$	136201.			1.39667
$100$	−30107.2	−	39919.4i	−0.301072	−	0.399194i
$101$	146396.			1.42800			0.713998	−	0.700148i	$-0.246883\pi$
$101$	146396.			1.42800			0.713998	+	0.700148i	$0.246883\pi$
$102$	−60428.0	−	19634.3i	−0.575093	−	0.186859i
$103$	110565.	−	152180.i	1.02689	−	1.41339i	0.119634	−	0.992818i	$-0.461828\pi$
$103$	110565.	−	152180.i	1.02689	−	1.41339i	0.907257	−	0.420577i	$-0.138172\pi$
$104$	−13712.6	−	9962.81i	−0.124319	−	0.0903231i
$105$	−156483.	+	159304.i	−1.38514	+	1.41011i
$106$	41881.0	−	30428.3i	0.362036	−	0.263035i
$107$		−	66810.0i		−	0.564133i	−0.959395	−	0.282067i	$-0.908980\pi$
$107$		−	66810.0i		−	0.564133i	0.959395	−	0.282067i	$-0.0910199\pi$
$108$	93994.7	+	129373.i	0.775433	+	1.06729i
$109$	31183.7	+	95973.5i	0.251397	+	0.773722i	0.994518	+	0.104564i	$0.0333448\pi$
$109$	31183.7	+	95973.5i	0.251397	+	0.773722i	−0.743121	+	0.669157i	$0.766655\pi$
$110$	−36861.7	−	36209.0i	−0.290465	−	0.285322i
$111$	−113591.	+	349596.i	−0.875055	+	2.69314i
$112$	33709.3	−	10952.8i	0.253924	−	0.0825050i
$113$	−1425.97	+	463.325i	−0.0105054	+	0.00341342i	−0.314265	−	0.949335i	$-0.601758\pi$
$113$	−1425.97	+	463.325i	−0.0105054	+	0.00341342i	0.303760	+	0.952749i	$0.401758\pi$
$114$	66292.7	−	204028.i	0.477753	−	1.47037i
$115$	−83368.2	+	167297.i	−0.587835	+	1.17962i
$116$	−22346.1	−	68774.2i	−0.154190	−	0.474549i
$117$	91753.4	+	126288.i	0.619666	+	0.852897i
$118$			99515.7i			0.657940i
$119$	61668.4	−	44804.7i	0.399205	−	0.290039i
$120$	15236.3	−	102092.i	0.0965887	−	0.647199i
$121$	87093.4	+	63277.1i	0.540782	+	0.392901i
$122$	52291.9	−	71973.6i	0.318079	−	0.437798i
$123$	−191907.	−	62354.3i	−1.14374	−	0.371624i
$124$	−170210.			−0.994103
$125$	75110.0	−	157721.i	0.429955	−	0.902850i
$126$	−326425.			−1.83171
$127$	243787.	+	79211.0i	1.34122	+	0.435789i	0.889730	−	0.456487i	$-0.150892\pi$
$127$	243787.	+	79211.0i	1.34122	+	0.435789i	0.451491	+	0.892276i	$0.350892\pi$
$128$	−9630.27	+	13254.9i	−0.0519534	+	0.0715077i
$129$	−338725.	−	246098.i	−1.79214	−	1.30207i
$130$	8741.24	−	58571.3i	0.0453644	−	0.303967i
$131$	196367.	−	142669.i	0.999750	−	0.726361i	0.0377151	−	0.999289i	$-0.487992\pi$
$131$	196367.	−	142669.i	0.999750	−	0.726361i	0.962034	+	0.272928i	$0.0879921\pi$
$132$		−	106672.i		−	0.532863i
$133$	151278.	+	208216.i	0.741560	+	1.02067i
$134$	18601.8	+	57250.4i	0.0894937	+	0.275433i
$135$	−249194.	+	500064.i	−1.17680	+	2.36152i
$136$	−10888.4	+	33511.1i	−0.0504798	+	0.155361i
$137$	−204139.	+	66328.7i	−0.929231	+	0.301925i	−0.734248	−	0.678881i	$-0.762465\pi$
$137$	−204139.	+	66328.7i	−0.929231	+	0.301925i	−0.194983	+	0.980807i	$0.562465\pi$
$138$	−366997.	+	119245.i	−1.64046	+	0.533017i
$139$	−22526.5	+	69329.5i	−0.0988911	+	0.304356i	−0.988248	−	0.152858i	$-0.951152\pi$
$139$	−22526.5	+	69329.5i	−0.0988911	+	0.304356i	0.889357	+	0.457213i	$0.151152\pi$
$140$	88344.1	+	86779.8i	0.380941	+	0.374196i
$141$	−150760.	−	463992.i	−0.638614	−	1.96545i
$142$	−108065.	−	148739.i	−0.449743	−	0.619019i
$143$		−	61199.0i		−	0.250267i
$144$	122073.	−	88690.9i	0.490582	−	0.356429i
$145$	177050.	−	180241.i	0.699319	−	0.711925i
$146$	−93957.8	−	68264.4i	−0.364797	−	0.265040i
$147$	40060.7	−	55138.8i	0.152906	−	0.210457i
$148$	193873.	+	62993.1i	0.727550	+	0.236395i
$149$	−94088.2			−0.347192			−0.173596	−	0.984817i	$-0.555539\pi$
$149$	−94088.2			−0.347192			−0.173596	+	0.984817i	$0.555539\pi$
$150$	340948.	−	117555.i	1.23726	−	0.426591i
$151$	199612.			0.712432			0.356216	−	0.934404i	$-0.384067\pi$
$151$	199612.			0.712432			0.356216	+	0.934404i	$0.384067\pi$
$152$	−113146.	−	36763.4i	−0.397220	−	0.129065i
$153$	190740.	−	262531.i	0.658738	−	0.906675i
$154$	103534.	+	75221.6i	0.351787	+	0.255588i
$155$	−274706.	−	527440.i	−0.918414	−	1.76337i
$156$	98907.8	−	71860.7i	0.325401	−	0.236418i
$157$			281118.i			0.910206i	0.890439	+	0.455103i	$0.150398\pi$
$157$			281118.i			0.910206i	−0.890439	+	0.455103i	$0.849602\pi$
$158$	58924.2	+	81102.1i	0.187781	+	0.258458i
$159$	115385.	+	355120.i	0.361958	+	1.11399i
$160$	−56616.3	−	8449.47i	−0.174840	−	0.0260933i
$161$	143058.	−	440287.i	0.434958	−	1.33866i
$162$	−552115.	+	179393.i	−1.65288	+	0.537054i
$163$	−531412.	+	172666.i	−1.56662	+	0.509024i	−0.958565	−	0.284874i	$-0.908048\pi$
$163$	−531412.	+	172666.i	−1.56662	+	0.509024i	−0.608051	+	0.793898i	$0.708048\pi$
$164$	−34579.4	+	106424.i	−0.100394	+	0.308981i
$165$	330551.	−	172160.i	0.945209	−	0.492292i
$166$	84829.9	+	261080.i	0.238935	+	0.735365i
$167$	−50656.9	−	69723.2i	−0.140555	−	0.193458i	0.732936	−	0.680298i	$-0.238150\pi$
$167$	−50656.9	−	69723.2i	−0.140555	−	0.193458i	−0.873491	+	0.486840i	$0.838150\pi$
$168$			255654.i			0.698842i
$169$	−243638.	+	177013.i	−0.656187	+	0.476748i
$170$	−121416.	+	20343.7i	−0.322220	+	0.0539892i
$171$	886404.	+	644010.i	2.31815	+	1.68423i
$172$	−136477.	+	187844.i	−0.351752	+	0.484146i
$173$	134035.	+	43550.6i	0.340489	+	0.110632i	0.474270	−	0.880379i	$-0.342712\pi$
$173$	134035.	+	43550.6i	0.340489	+	0.110632i	−0.133781	+	0.991011i	$0.542712\pi$
$174$	521590.			1.30604
$175$	−126329.	+	413813.i	−0.311824	+	1.02143i
$176$	−59156.3			−0.143952
$177$	−682665.	−	221811.i	−1.63785	−	0.532170i
$178$	63378.7	−	87233.3i	0.149932	−	0.206363i
$179$	−335547.	−	243789.i	−0.782746	−	0.568699i	0.123056	−	0.992400i	$-0.460731\pi$
$179$	−335547.	−	243789.i	−0.782746	−	0.568699i	−0.905802	+	0.423701i	$0.860731\pi$
$180$	471847.	+	235133.i	1.08547	+	0.540919i
$181$	120640.	−	87650.4i	0.273714	−	0.198865i	−0.442457	−	0.896790i	$-0.645893\pi$
$181$	120640.	−	87650.4i	0.273714	−	0.198865i	0.716171	+	0.697925i	$0.245893\pi$
$182$			146672.i			0.328222i
$183$	377176.	+	519138.i	0.832561	+	1.14592i
$184$	66128.6	+	203523.i	0.143994	+	0.443168i
$185$	117695.	+	702431.i	0.252830	+	1.50895i
$186$	379383.	−	1.16762e6i	0.804073	−	2.47468i
$187$	−120996.	+	39313.9i	−0.253026	+	0.0822132i
$188$	−257312.	+	83605.8i	−0.530965	+	0.172521i
$189$	427612.	−	1.31605e6i	0.870754	−	2.67991i
$190$	−68688.0	−	409946.i	−0.138037	−	0.823839i
$191$	−4523.64	−	13922.3i	−0.00897231	−	0.0276139i	0.946470	−	0.322791i	$-0.104621\pi$
$191$	−4523.64	−	13922.3i	−0.00897231	−	0.0276139i	−0.955442	+	0.295177i	$0.904621\pi$
$192$	−69462.2	−	95606.5i	−0.135986	−	0.187169i
$193$			189528.i			0.366251i	0.983090	+	0.183126i	$0.0586215\pi$
$193$			189528.i			0.366251i	−0.983090	+	0.183126i	$0.941378\pi$
$194$	−143450.	+	104222.i	−0.273650	+	0.198819i
$195$	382308.	+	190514.i	0.719991	+	0.358790i
$196$	−30577.9	−	22216.1i	−0.0568548	−	0.0413074i
$197$	158987.	−	218827.i	0.291875	−	0.401731i	−0.637747	−	0.770246i	$-0.720134\pi$
$197$	158987.	−	218827.i	0.291875	−	0.401731i	0.929622	+	0.368515i	$0.120134\pi$
$198$	518140.	+	168354.i	0.939257	+	0.305183i
$199$	−736825.			−1.31896			−0.659480	−	0.751722i	$-0.729223\pi$
$199$	−736825.			−1.31896			−0.659480	+	0.751722i	$0.729223\pi$
$200$	−65191.3	−	189077.i	−0.115243	−	0.334244i
$201$	−434192.			−0.758039
$202$	556925.	+	180956.i	0.960325	+	0.312029i
$203$	−367808.	+	506244.i	−0.626442	+	0.862223i
$204$	−205613.	−	149386.i	−0.345919	−	0.251325i
$205$	−385591.	+	64607.3i	−0.640830	+	0.107373i
$206$	608718.	−	442260.i	0.999421	−	0.726122i
$207$		−	1.97082e6i		−	3.19684i
$208$	−39851.3	−	54850.6i	−0.0638681	−	0.0879068i
$209$	−132738.	−	408527.i	−0.210199	−	0.646927i
$210$	−792209.	+	412605.i	−1.23963	+	0.645634i
$211$	−245320.	+	755017.i	−0.379338	+	1.16748i	0.561167	+	0.827703i	$0.310353\pi$
$211$	−245320.	+	755017.i	−0.379338	+	1.16748i	−0.940505	+	0.339780i	$0.889647\pi$
$212$	196936.	−	63988.4i	0.300944	−	0.0977826i
$213$	1.26120e6	−	409788.i	1.90473	−	0.618885i
$214$	82581.6	−	254160.i	0.123268	−	0.379379i
$215$	−802345.	−	119743.i	−1.18376	−	0.176666i
$216$	197664.	+	608347.i	0.288266	+	0.887190i
$217$	865739.	+	1.19159e6i	1.24807	+	1.71782i
$218$			403650.i			0.575259i
$219$	677708.	−	492384.i	0.954844	−	0.693735i
$220$	−95473.5	−	183311.i	−0.132992	−	0.255347i
$221$	−117962.	−	85704.7i	−0.162466	−	0.118039i
$222$	−864249.	+	1.18954e6i	−1.17695	+	1.61993i
$223$	246370.	+	80050.4i	0.331761	+	0.107796i	0.470161	−	0.882581i	$-0.344196\pi$
$223$	246370.	+	80050.4i	0.331761	+	0.107796i	−0.138400	+	0.990376i	$0.544196\pi$
$224$	141776.			0.188792
$225$	32902.5	+	1.84162e6i	0.0433284	+	2.42518i
$226$	−5997.41			−0.00781075
$227$	201151.	+	65358.1i	0.259095	+	0.0841850i	0.435684	−	0.900100i	$-0.356506\pi$
$227$	201151.	+	65358.1i	0.259095	+	0.0841850i	−0.176589	+	0.984285i	$0.556506\pi$
$228$	504385.	−	694226.i	0.642577	−	0.884431i
$229$	−216130.	−	157028.i	−0.272349	−	0.197873i	0.443224	−	0.896411i	$-0.353835\pi$
$229$	−216130.	−	157028.i	−0.272349	−	0.197873i	−0.715573	+	0.698537i	$0.753835\pi$
$230$	−523942.	+	533386.i	−0.653075	+	0.664847i
$231$	−746777.	+	542565.i	−0.920791	+	0.668994i
$232$		−	289254.i		−	0.352825i
$233$	−275836.	−	379656.i	−0.332860	−	0.458142i	0.609479	−	0.792802i	$-0.291379\pi$
$233$	−275836.	−	379656.i	−0.332860	−	0.458142i	−0.942339	+	0.334660i	$0.891379\pi$
$234$	192951.	+	593841.i	0.230360	+	0.708974i
$235$	−674356.	−	662415.i	−0.796562	−	0.782457i
$236$	−123008.	+	378580.i	−0.143765	+	0.442464i
$237$	−687687.	+	223443.i	−0.795280	+	0.258402i
$238$	289982.	−	94221.0i	0.331840	−	0.107821i
$239$	−88917.4	+	273660.i	−0.100691	+	0.309896i	−0.988695	−	0.149940i	$-0.952092\pi$
$239$	−88917.4	+	273660.i	−0.100691	+	0.309896i	0.888004	+	0.459836i	$0.152092\pi$
$240$	184155.	−	369548.i	0.206374	−	0.414135i
$241$	−244885.	−	753678.i	−0.271594	−	0.835879i	−0.990101	−	0.140359i	$-0.955174\pi$
$241$	−244885.	−	753678.i	−0.271594	−	0.835879i	0.718507	−	0.695520i	$-0.244826\pi$
$242$	253108.	+	348374.i	0.277823	+	0.382390i
$243$		−	1.75861e6i		−	1.91053i
$244$	287894.	−	209167.i	0.309570	−	0.224916i
$245$	19492.1	−	130608.i	0.0207465	−	0.139013i
$246$	−652983.	−	474420.i	−0.687961	−	0.499833i
$247$	289372.	−	398286.i	0.301796	−	0.415386i
$248$	−647518.	−	210391.i	−0.668533	−	0.217220i
$249$	−1.98005e6			−2.02385
$250$	480690.	−	507167.i	0.486424	−	0.513217i
$251$	1.16215e6			1.16433			0.582166	−	0.813070i	$-0.302205\pi$
$251$	1.16215e6			1.16433			0.582166	+	0.813070i	$0.302205\pi$
$252$	−1.24179e6	−	403483.i	−1.23182	−	0.400243i
$253$	−454157.	+	625094.i	−0.446072	+	0.613966i
$254$	829509.	+	602673.i	0.806746	+	0.586135i
$255$	131070.	−	878241.i	0.126227	−	0.845791i
$256$	−53019.7	+	38521.1i	−0.0505636	+	0.0367366i
$257$		−	190013.i		−	0.179453i	−0.995966	−	0.0897266i	$-0.971401\pi$
$257$		−	190013.i		−	0.179453i	0.995966	−	0.0897266i	$-0.0285993\pi$
$258$	−984392.	−	1.35490e6i	−0.920701	−	1.26724i
$259$	−545100.	−	1.67764e6i	−0.504924	−	1.55400i
$260$	105652.	−	212014.i	0.0969267	−	0.194505i
$261$	−823194.	+	2.53353e6i	−0.747999	+	2.30210i
$262$	923375.	−	300023.i	0.831046	−	0.270023i
$263$	1.40413e6	−	456229.i	1.25175	−	0.406718i	0.393201	−	0.919452i	$-0.371368\pi$
$263$	1.40413e6	−	456229.i	1.25175	−	0.406718i	0.858547	+	0.512735i	$0.171368\pi$
$264$	131854.	−	405804.i	0.116435	−	0.358350i
$265$	516124.	+	506985.i	0.451481	+	0.443486i
$266$	318126.	+	979090.i	0.275673	+	0.848435i
$267$	457144.	+	629205.i	0.392441	+	0.540149i
$268$			240787.i			0.204784i
$269$	−855905.	+	621851.i	−0.721182	+	0.523969i	−0.886762	−	0.462227i	$-0.847051\pi$
$269$	−855905.	+	621851.i	−0.721182	+	0.523969i	0.165580	+	0.986196i	$0.447051\pi$
$270$	−1.56611e6	+	1.59434e6i	−1.30741	+	1.33098i
$271$	−1.86399e6	−	1.35427e6i	−1.54177	−	1.12016i	−0.949213	−	0.314633i	$-0.898119\pi$
$271$	−1.86399e6	−	1.35427e6i	−1.54177	−	1.12016i	−0.592557	−	0.805529i	$-0.701881\pi$
$272$	−82844.0	+	114025.i	−0.0678952	+	0.0934497i
$273$	−1.00615e6	−	326918.i	−0.817063	−	0.265480i
$274$	−858576.			−0.690880
$275$	413949.	−	591698.i	0.330077	−	0.471811i
$276$	−1.54354e6			−1.21967
$277$	537798.	+	174741.i	0.421133	+	0.136835i	0.511915	−	0.859036i	$-0.328936\pi$
$277$	537798.	+	174741.i	0.421133	+	0.136835i	−0.0907813	+	0.995871i	$0.528936\pi$
$278$	−171392.	+	235901.i	−0.133008	+	0.183070i
$279$	5.07275e6	+	3.68557e6i	3.90151	+	2.83462i
$280$	228815.	+	439329.i	0.174417	+	0.334885i
$281$	968392.	−	703578.i	0.731620	−	0.531553i	−0.158456	−	0.987366i	$-0.550652\pi$
$281$	968392.	−	703578.i	0.731620	−	0.531553i	0.890075	+	0.455813i	$0.150652\pi$
$282$		−	1.95148e6i		−	1.46131i
$283$	763974.	+	1.05152e6i	0.567038	+	0.780461i	0.992200	−	0.124656i	$-0.0397828\pi$
$283$	763974.	+	1.05152e6i	0.567038	+	0.780461i	−0.425162	+	0.905117i	$0.639783\pi$
$284$	−227253.	−	699412.i	−0.167191	−	0.514562i
$285$	2.96527e6	+	442541.i	2.16248	+	0.322731i
$286$	75646.1	−	232815.i	0.0546854	−	0.168304i
$287$	920924.	−	299226.i	0.659962	−	0.214435i
$288$	574019.	−	186510.i	0.407798	−	0.132502i
$289$	345093.	−	1.06209e6i	0.243048	−	0.748024i
$290$	896328.	−	466833.i	0.625852	−	0.325961i
$291$	−395216.	−	1.21635e6i	−0.273591	−	0.842027i
$292$	−273057.	−	375831.i	−0.187412	−	0.257950i
$293$			1.18136e6i			0.803920i	0.915657	+	0.401960i	$0.131671\pi$
$293$			1.18136e6i			0.803920i	−0.915657	+	0.401960i	$0.868329\pi$
$294$	220555.	−	160243.i	0.148816	−	0.108121i
$295$	−1.37165e6	+	229826.i	−0.917676	+	0.153760i
$296$	659672.	+	479280.i	0.437622	+	0.317951i
$297$	−1.35751e6	+	1.86846e6i	−0.893004	+	1.22911i
$298$	−357933.	−	116299.i	−0.233486	−	0.0758642i
$299$	−885544.			−0.572839
$300$	1.44235e6	−	25769.1i	0.925267	−	0.0165309i
$301$	2.00920e6			1.27822
$302$	759368.	+	246734.i	0.479110	+	0.155672i
$303$	−2.48267e6	+	3.41710e6i	−1.55350	+	2.13821i
$304$	−384992.	−	279713.i	−0.238928	−	0.173591i
$305$	1.11280e6	+	554535.i	0.684962	+	0.341334i
$306$	1.05012e6	−	762959.i	0.641116	−	0.465798i
$307$		−	836844.i		−	0.506755i	−0.967367	−	0.253378i	$-0.918458\pi$
$307$		−	836844.i		−	0.506755i	0.967367	−	0.253378i	$-0.0815415\pi$
$308$	300886.	+	414134.i	0.180728	+	0.248751i
$309$	1.67707e6	+	5.16149e6i	0.999205	+	3.07524i
$310$	−393091.	−	2.34606e6i	−0.232321	−	1.38655i
$311$	435337.	−	1.33983e6i	0.255226	−	0.785505i	−0.738559	−	0.674189i	$-0.764493\pi$
$311$	435337.	−	1.33983e6i	0.255226	−	0.785505i	0.993785	−	0.111316i	$-0.0355066\pi$
$312$	465092.	−	151118.i	0.270491	−	0.0878879i
$313$	1.97042e6	−	640227.i	1.13683	−	0.369380i	0.320665	−	0.947193i	$-0.396094\pi$
$313$	1.97042e6	−	640227.i	1.13683	−	0.369380i	0.816169	+	0.577813i	$0.196094\pi$
$314$	−347481.	+	1.06944e6i	−0.198887	+	0.612112i
$315$	−753859.	−	4.49921e6i	−0.428069	−	2.55482i
$316$	123913.	+	381365.i	0.0698071	+	0.214844i
$317$	−333279.	−	458720.i	−0.186277	−	0.256389i	0.705657	−	0.708554i	$-0.250652\pi$
$317$	−333279.	−	458720.i	−0.186277	−	0.256389i	−0.891934	+	0.452165i	$0.850652\pi$
$318$			1.49358e6i			0.828249i
$319$	844924.	−	613873.i	0.464880	−	0.337755i
$320$	−204937.	−	102125.i	−0.111878	−	0.0557517i
$321$	1.55944e6	+	1.13300e6i	0.844707	+	0.613715i
$322$	1.08845e6	−	1.49812e6i	0.585017	−	0.805207i
$323$	−973335.	−	316256.i	−0.519106	−	0.168668i
$324$	−2.32211e6			−1.22891
$325$	827493.	−	14784.0i	0.434566	−	0.00776397i
$326$	−2.23504e6			−1.16477
$327$	−2.76899e6	−	899698.i	−1.43203	−	0.465294i
$328$	−263095.	+	362120.i	−0.135030	+	0.185852i
$329$	1.89406e6	+	1.37612e6i	0.964728	+	0.700916i
$330$	1.47029e6	−	246353.i	0.743222	−	0.124530i
$331$	−977021.	+	709848.i	−0.490156	+	0.356119i	−0.805244	−	0.592943i	$-0.797966\pi$
$331$	−977021.	+	709848.i	−0.490156	+	0.356119i	0.315088	+	0.949062i	$0.397966\pi$
$332$			1.09806e6i			0.546741i
$333$	−4.41397e6	−	6.07531e6i	−2.18132	−	3.00233i
$334$	−106528.	−	327858.i	−0.0522512	−	0.160813i
$335$	−746139.	+	388610.i	−0.363252	+	0.189192i
$336$	−316006.	+	972565.i	−0.152703	+	0.469970i
$337$	1.31618e6	−	427652.i	0.631306	−	0.205124i	0.0241523	−	0.999708i	$-0.492311\pi$
$337$	1.31618e6	−	427652.i	0.631306	−	0.205124i	0.607153	+	0.794585i	$0.292311\pi$
$338$	−1.14565e6	+	372245.i	−0.545458	+	0.177230i
$339$	13367.7	−	41141.4i	0.00631766	−	0.0194438i
$340$	−487039.	−	72686.2i	−0.228490	−	0.0341000i
$341$	−759642.	−	2.33794e6i	−0.353772	−	1.08880i
$342$	2.57604e6	+	3.54562e6i	1.19093	+	1.63918i
$343$		−	1.99992e6i		−	0.917861i
$344$	−751376.	+	545906.i	−0.342343	+	0.248727i
$345$	−2.49114e6	−	4.78304e6i	−1.12681	−	2.16350i
$346$	456068.	+	331353.i	0.204804	+	0.148799i
$347$	−1.98980e6	+	2.73873e6i	−0.887128	+	1.22103i	0.0872672	+	0.996185i	$0.472187\pi$
$347$	−1.98980e6	+	2.73873e6i	−0.887128	+	1.22103i	−0.974395	+	0.224842i	$0.927813\pi$
$348$	1.98424e6	+	644720.i	0.878309	+	0.285380i
$349$	−2.65903e6			−1.16858			−0.584292	−	0.811544i	$-0.698628\pi$
$349$	−2.65903e6			−1.16858			−0.584292	+	0.811544i	$0.698628\pi$
$350$	−992086.	+	1.41808e6i	−0.432892	+	0.618774i
$351$	−2.64697e6			−1.14678
$352$	−225044.	−	73121.2i	−0.0968078	−	0.0314548i
$353$	−687258.	+	945929.i	−0.293551	+	0.404038i	−0.930163	−	0.367146i	$-0.880335\pi$
$353$	−687258.	+	945929.i	−0.293551	+	0.404038i	0.636613	+	0.771184i	$0.280335\pi$
$354$	−2.32284e6	−	1.68764e6i	−0.985169	−	0.715767i
$355$	1.80054e6	−	1.83300e6i	0.758284	−	0.771953i
$356$	348933.	−	253515.i	0.145921	−	0.106018i
$357$			2.19925e6i			0.913281i
$358$	−975157.	−	1.34219e6i	−0.402131	−	0.553485i
$359$	670533.	+	2.06369e6i	0.274590	+	0.845100i	0.989328	+	0.145708i	$0.0465459\pi$
$359$	670533.	+	2.06369e6i	0.274590	+	0.845100i	−0.714738	+	0.699392i	$0.753454\pi$
$360$	1.50437e6	+	1.47773e6i	0.611785	+	0.600952i
$361$	302643.	−	931439.i	0.122226	−	0.376172i
$362$	567285.	−	184322.i	0.227526	−	0.0739275i
$363$	−2.95395e6	+	959798.i	−1.17662	+	0.382308i
$364$	−181296.	+	557972.i	−0.0717191	+	0.220729i
$365$	723917.	−	1.45270e6i	0.284418	−	0.570747i
$366$	793172.	+	2.44113e6i	0.309503	+	0.952552i
$367$	680084.	+	936055.i	0.263571	+	0.362774i	0.920206	−	0.391434i	$-0.128021\pi$
$367$	680084.	+	936055.i	0.263571	+	0.362774i	−0.656635	+	0.754208i	$0.728021\pi$
$368$			855986.i			0.329494i
$369$	3.33498e6	−	2.42300e6i	1.27505	−	0.926377i
$370$	−420514.	+	2.81768e6i	−0.159689	+	1.07001i
$371$	−1.44964e6	−	1.05322e6i	−0.546795	−	0.397270i
$372$	2.88652e6	−	3.97295e6i	1.08148	−	1.48852i
$373$	−377330.	−	122602.i	−0.140427	−	0.0456274i	0.237960	−	0.971275i	$-0.423521\pi$
$373$	−377330.	−	122602.i	−0.140427	−	0.0456274i	−0.378387	+	0.925647i	$0.623521\pi$
$374$	−508889.			−0.188124
$375$	2.40769e6	+	4.42790e6i	0.884142	+	1.62600i
$376$	−1.08222e6			−0.394770
$377$	1.13838e6	+	369884.i	0.412511	+	0.134033i
$378$	3.25347e6	−	4.47801e6i	1.17116	−	1.61197i
$379$	−1.15107e6	−	836300.i	−0.411626	−	0.299064i	0.362633	−	0.931932i	$-0.381878\pi$
$379$	−1.15107e6	−	836300.i	−0.411626	−	0.299064i	−0.774260	+	0.632868i	$0.781878\pi$
$380$	245416.	−	1.64443e6i	0.0871855	−	0.584193i
$381$	−5.98316e6	+	4.34702e6i	−2.11163	+	1.53419i
$382$		−	58555.2i		−	0.0205308i
$383$	−290477.	−	399807.i	−0.101185	−	0.139269i	0.755422	−	0.655238i	$-0.227432\pi$
$383$	−290477.	−	399807.i	−0.101185	−	0.139269i	−0.856607	+	0.515970i	$0.827432\pi$
$384$	−146074.	−	449569.i	−0.0505526	−	0.155585i
$385$	−797695.	+	1.60075e6i	−0.274274	+	0.550392i
$386$	−234269.	+	721006.i	−0.0800288	+	0.246303i
$387$	8.13479e6	−	2.64315e6i	2.76102	−	0.897108i
$388$	−674542.	+	219172.i	−0.227473	+	0.0739104i
$389$	243560.	−	749601.i	0.0816079	−	0.251163i	−0.901925	−	0.431893i	$-0.857846\pi$
$389$	243560.	−	749601.i	0.0816079	−	0.251163i	0.983533	+	0.180729i	$0.0578459\pi$
$390$	1.21890e6	+	1.19732e6i	0.405795	+	0.398609i
$391$	568868.	+	1.75080e6i	0.188178	+	0.579154i
$392$	−88864.5	−	122312.i	−0.0292088	−	0.0402024i
$393$			7.00296e6i			2.28718i
$394$	875308.	−	635948.i	0.284067	−	0.206387i
$395$	−981772.	+	999469.i	−0.316605	+	0.322312i
$396$	1.76303e6	+	1.28091e6i	0.564964	+	0.410470i
$397$	−1.09738e6	+	1.51042e6i	−0.349448	+	0.480974i	−0.947171	−	0.320729i	$-0.896072\pi$
$397$	−1.09738e6	+	1.51042e6i	−0.349448	+	0.480974i	0.597723	+	0.801703i	$0.296072\pi$
$398$	−2.80305e6	−	910765.i	−0.886998	−	0.288203i
$399$	−7.42551e6			−2.33504
$400$	−14290.5	−	799872.i	−0.00446580	−	0.249960i
$401$	2.45781e6			0.763285			0.381643	−	0.924310i	$-0.375359\pi$
$401$	2.45781e6			0.763285			0.381643	+	0.924310i	$0.375359\pi$
$402$	−1.65176e6	−	536691.i	−0.509780	−	0.165638i
$403$	1.65603e6	−	2.27933e6i	0.507932	−	0.699108i
$404$	1.89500e6	+	1.37679e6i	0.577637	+	0.419678i
$405$	−3.74771e6	−	7.19567e6i	−1.13535	−	2.17988i
$406$	−2.02498e6	+	1.47123e6i	−0.609684	+	0.442961i
$407$			2.94409e6i			0.880979i
$408$	−597545.	−	822450.i	−0.177713	−	0.244602i
$409$	−1.83554e6	−	5.64921e6i	−0.542570	−	1.66986i	−0.726699	−	0.686956i	$-0.758947\pi$
$409$	−1.83554e6	−	5.64921e6i	−0.542570	−	1.66986i	0.184130	−	0.982902i	$-0.441053\pi$
$410$	−1.54674e6	−	230836.i	−0.454419	−	0.0678180i
$411$	1.91369e6	−	5.88972e6i	0.558813	−	1.71985i
$412$	2.86237e6	−	930039.i	0.830772	−	0.269934i
$413$	3.27597e6	−	1.06443e6i	0.945073	−	0.307073i
$414$	2.43607e6	−	7.49745e6i	0.698536	−	2.14987i
$415$	−3.40263e6	+	1.77218e6i	−0.969826	+	0.505113i
$416$	−83804.2	−	257923.i	−0.0237428	−	0.0730729i
$417$	−1.23623e6	−	1.70153e6i	−0.348145	−	0.479181i
$418$		−	1.71820e6i		−	0.480988i
$419$	2.33836e6	−	1.69892e6i	0.650692	−	0.472756i	−0.212815	−	0.977093i	$-0.568263\pi$
$419$	2.33836e6	−	1.69892e6i	0.650692	−	0.472756i	0.863507	+	0.504337i	$0.168263\pi$
$420$	−3.52375e6	+	590418.i	−0.974725	+	0.163319i
$421$	3.67779e6	+	2.67207e6i	1.01130	+	0.734754i	0.964482	−	0.264149i	$-0.0850910\pi$
$421$	3.67779e6	+	2.67207e6i	1.01130	+	0.734754i	0.0468208	+	0.998903i	$0.485091\pi$
$422$	−1.86650e6	+	2.56902e6i	−0.510209	+	0.702242i
$423$	9.47897e6	+	3.07990e6i	2.57579	+	0.836924i
$424$	828284.			0.223751
$425$	−560805.	−	1.62653e6i	−0.150605	−	0.436806i
$426$	5.30441e6			1.41616
$427$	−2.92863e6	−	951570.i	−0.777311	−	0.252564i
$428$	628319.	−	864806.i	0.165795	−	0.228197i
$429$	1.42847e6	+	1.03785e6i	0.374738	+	0.272263i
$430$	−2.90429e6	−	1.44728e6i	−0.757476	−	0.377470i
$431$	2.48007e6	−	1.80187e6i	0.643088	−	0.467231i	−0.217822	−	0.975989i	$-0.569895\pi$
$431$	2.48007e6	−	1.80187e6i	0.643088	−	0.467231i	0.860910	+	0.508758i	$0.169895\pi$
$432$			2.55861e6i			0.659623i
$433$	1.89347e6	+	2.60614e6i	0.485331	+	0.668001i	0.979518	−	0.201354i	$-0.0645343\pi$
$433$	1.89347e6	+	2.60614e6i	0.485331	+	0.668001i	−0.494187	+	0.869355i	$0.664534\pi$
$434$	1.82058e6	+	5.60318e6i	0.463966	+	1.42794i
$435$	1.20458e6	+	7.18922e6i	0.305220	+	1.82162i
$436$	−498939.	+	1.53558e6i	−0.125699	+	0.386861i
$437$	−5.91135e6	+	1.92072e6i	−1.48076	+	0.481127i
$438$	3.18677e6	−	1.03545e6i	0.793718	−	0.257894i
$439$	−1.66160e6	+	5.11389e6i	−0.411497	+	1.26646i	0.503851	+	0.863791i	$0.331916\pi$
$439$	−1.66160e6	+	5.11389e6i	−0.411497	+	1.26646i	−0.915347	+	0.402665i	$0.868084\pi$
$440$	−136618.	−	815368.i	−0.0336416	−	0.200781i
$441$	430262.	+	1.32421e6i	0.105350	+	0.324235i
$442$	−342819.	−	471849.i	−0.0834659	−	0.114881i
$443$		−	5.74971e6i		−	1.39199i	−0.718046	−	0.695996i	$-0.754963\pi$
$443$		−	5.74971e6i		−	1.39199i	0.718046	−	0.695996i	$-0.245037\pi$
$444$	−4.75815e6	+	3.45700e6i	−1.14546	+	0.832227i
$445$	1.34873e6	+	672106.i	0.322868	+	0.160893i
$446$	838298.	+	609059.i	0.199554	+	0.144985i
$447$	1.59560e6	−	2.19615e6i	0.377707	−	0.519869i
$448$	539348.	+	175245.i	0.126962	+	0.0412525i
$449$	6.99766e6			1.63809			0.819043	−	0.573732i	$-0.194505\pi$
$449$	6.99766e6			1.63809			0.819043	+	0.573732i	$0.194505\pi$
$450$	−2.15120e6	+	7.04663e6i	−0.500784	+	1.64040i
$451$	−1.61613e6			−0.374140
$452$	−22815.5	−	7413.20i	−0.00525271	−	0.00170671i
$453$	−3.38512e6	+	4.65922e6i	−0.775048	+	1.06676i
$454$	684439.	+	497274.i	0.155846	+	0.113229i
$455$	−2.02162e6	+	338730.i	−0.457794	+	0.0767052i
$456$	2.77690e6	−	2.01754e6i	0.625387	−	0.454370i
$457$		−	7.32140e6i		−	1.63985i	−0.572473	−	0.819924i	$-0.694016\pi$
$457$		−	7.32140e6i		−	1.63985i	0.572473	−	0.819924i	$-0.305984\pi$
$458$	−628110.	−	864520.i	−0.139918	−	0.192580i
$459$	1.70039e6	+	5.23328e6i	0.376719	+	1.15942i
$460$	−2.65249e6	+	1.38149e6i	−0.584467	+	0.304407i
$461$	−504051.	+	1.55131e6i	−0.110464	+	0.339974i	−0.990974	−	0.134054i	$-0.957200\pi$
$461$	−504051.	+	1.55131e6i	−0.110464	+	0.339974i	0.880510	+	0.474028i	$0.157200\pi$
$462$	−3.51156e6	+	1.14097e6i	−0.765411	+	0.248697i
$463$	−678051.	+	220312.i	−0.146998	+	0.0477624i	−0.381592	−	0.924331i	$-0.624624\pi$
$463$	−678051.	+	220312.i	−0.146998	+	0.0477624i	0.234594	+	0.972093i	$0.424624\pi$
$464$	357538.	−	1.10039e6i	0.0770951	−	0.237274i
$465$	1.69698e7	+	2.53259e6i	3.63952	+	0.543166i
$466$	−580063.	−	1.78525e6i	−0.123740	−	0.380833i
$467$	−994781.	−	1.36920e6i	−0.211074	−	0.290519i	0.690332	−	0.723492i	$-0.257464\pi$
$467$	−994781.	−	1.36920e6i	−0.211074	−	0.290519i	−0.901407	+	0.432974i	$0.857464\pi$
$468$			2.49760e6i			0.527119i
$469$	1.68567e6	−	1.22471e6i	0.353867	−	0.257100i
$470$	−1.74661e6	−	3.35353e6i	−0.364713	−	0.700256i
$471$	−6.56170e6	−	4.76735e6i	−1.36290	−	0.990204i
$472$	−935901.	+	1.28816e6i	−0.193364	+	0.266142i
$473$	−3.18924e6	−	1.03625e6i	−0.655441	−	0.212966i
$474$	−2.89231e6			−0.591287
$475$	5.49177e6	−	1.89349e6i	1.11681	−	0.385061i
$476$	1.21962e6			0.246722
$477$	−7.25480e6	−	2.35723e6i	−1.45992	−	0.474358i
$478$	−676524.	+	931155.i	−0.135430	+	0.186403i
$479$	−4.39195e6	−	3.19094e6i	−0.874618	−	0.635447i	0.0572039	−	0.998363i	$-0.481781\pi$
$479$	−4.39195e6	−	3.19094e6i	−0.874618	−	0.635447i	−0.931822	+	0.362915i	$0.881781\pi$
$480$	1.15735e6	−	1.17821e6i	0.229278	−	0.233411i
$481$	−2.72981e6	+	1.98332e6i	−0.537984	+	0.390868i
$482$		−	3.16986e6i		−	0.621473i
$483$	7.85087e6	+	1.08058e7i	1.53126	+	2.10760i
$484$	532268.	+	1.63815e6i	0.103280	+	0.317864i
$485$	−1.76782e6	−	1.73651e6i	−0.341258	−	0.335216i
$486$	2.17376e6	−	6.69014e6i	0.417465	−	1.28483i
$487$	−2.16686e6	+	704055.i	−0.414008	+	0.134519i	−0.508612	−	0.860996i	$-0.669841\pi$
$487$	−2.16686e6	+	704055.i	−0.414008	+	0.134519i	0.0946047	+	0.995515i	$0.469841\pi$
$488$	1.35376e6	−	439863.i	0.257331	−	0.0836119i
$489$	4.98169e6	−	1.53321e7i	0.942117	−	2.89954i
$490$	235594.	−	472771.i	0.0443275	−	0.0889529i
$491$	−1.26777e6	−	3.90180e6i	−0.237322	−	0.730401i	−0.996805	−	0.0798742i	$-0.974548\pi$
$491$	−1.26777e6	−	3.90180e6i	−0.237322	−	0.730401i	0.759483	−	0.650527i	$-0.225452\pi$
$492$	−1.89768e6	−	2.61193e6i	−0.353435	−	0.486462i
$493$		−	2.48829e6i		−	0.461089i
$494$	1.59314e6	−	1.15749e6i	0.293723	−	0.213402i
$495$	−1.12386e6	+	7.53048e6i	−0.206157	+	1.38137i
$496$	−2.20325e6	−	1.60075e6i	−0.402123	−	0.292160i
$497$	−3.74049e6	+	5.14834e6i	−0.679262	+	0.934924i
$498$	−7.53256e6	−	2.44748e6i	−1.36104	−	0.442227i
$499$	−1.98306e6			−0.356521			−0.178261	−	0.983983i	$-0.557047\pi$
$499$	−1.98306e6			−0.356521			−0.178261	+	0.983983i	$0.557047\pi$
$500$	2.45555e6	−	1.33521e6i	0.439261	−	0.238850i
$501$	2.48651e6			0.442583
$502$	4.42107e6	+	1.43649e6i	0.783011	+	0.254416i
$503$	1.69852e6	−	2.33781e6i	0.299331	−	0.411993i	−0.632686	−	0.774408i	$-0.718048\pi$
$503$	1.69852e6	−	2.33781e6i	0.299331	−	0.411993i	0.932017	+	0.362415i	$0.118048\pi$
$504$	−4.22533e6	−	3.06988e6i	−0.740942	−	0.538326i
$505$	−1.20798e6	+	8.09417e6i	−0.210781	+	1.41235i
$506$	−2.50038e6	+	1.81663e6i	−0.434139	+	0.315421i
$507$		−	8.68874e6i		−	1.50119i
$508$	2.41069e6	+	3.31804e6i	0.414460	+	0.570455i
$509$	2.45078e6	+	7.54274e6i	0.419286	+	1.29043i	0.908360	+	0.418188i	$0.137335\pi$
$509$	2.45078e6	+	7.54274e6i	0.419286	+	1.29043i	−0.489074	+	0.872242i	$0.662665\pi$
$510$	1.58418e6	−	3.17902e6i	0.269699	−	0.541212i
$511$	−1.24223e6	+	3.82318e6i	−0.210450	+	0.647697i
$512$	−249314.	+	81007.0i	−0.0420312	+	0.0136568i
$513$	−1.76695e7	+	5.74118e6i	−2.96436	+	0.963180i
$514$	234869.	−	722854.i	0.0392120	−	0.120682i
$515$	7.50159e6	+	7.36877e6i	1.24634	+	1.22427i
$516$	−2.07010e6	−	6.37112e6i	−0.342269	−	1.05340i
$517$	−2.29675e6	−	3.16121e6i	−0.377909	−	0.520147i
$518$		−	7.05592e6i		−	1.15539i
$519$	−3.28957e6	+	2.39001e6i	−0.536069	+	0.389477i
$520$	663987.	−	675955.i	0.107684	−	0.109625i
$521$	−4.46955e6	−	3.24732e6i	−0.721390	−	0.524120i	0.165438	−	0.986220i	$-0.447096\pi$
$521$	−4.46955e6	−	3.24732e6i	−0.721390	−	0.524120i	−0.886828	+	0.462100i	$0.847096\pi$
$522$	−6.26323e6	+	8.62060e6i	−1.00606	+	1.38472i
$523$	8.63270e6	+	2.80493e6i	1.38004	+	0.448403i	0.902683	−	0.430306i	$-0.141594\pi$
$523$	8.63270e6	+	2.80493e6i	1.38004	+	0.448403i	0.477359	+	0.878709i	$0.341594\pi$
$524$	3.88358e6			0.617879
$525$	−7.51661e6	−	9.96636e6i	−1.19021	−	1.57811i
$526$	5.90555e6			0.930670
$527$	−5.57025e6	−	1.80988e6i	−0.873671	−	0.283873i
$528$	1.00320e6	−	1.38079e6i	0.156605	−	0.215548i
$529$	3.83795e6	+	2.78843e6i	0.596293	+	0.433232i
$530$	1.33678e6	+	2.56665e6i	0.206715	+	0.396896i
$531$	1.18634e7	−	8.61927e6i	1.82588	−	1.32658i
$532$			4.11791e6i			0.630808i
$533$	−1.08872e6	−	1.49850e6i	−0.165996	−	0.228474i
$534$	961339.	+	2.95870e6i	0.145889	+	0.449001i
$535$	3.69388e6	+	551278.i	0.557954	+	0.0832696i
$536$	−297628.	+	916006.i	−0.0447469	+	0.137717i
$537$	1.13808e7	−	3.69784e6i	1.70308	−	0.553366i
$538$	−4.02471e6	+	1.30771e6i	−0.599485	+	0.194785i
$539$	168684.	−	519155.i	0.0250093	−	0.0769706i
$540$	−7.92852e6	+	4.12940e6i	−1.17006	+	0.609400i
$541$	3.63236e6	+	1.11793e7i	0.533575	+	1.64218i	0.746708	+	0.665152i	$0.231633\pi$
$541$	3.63236e6	+	1.11793e7i	0.533575	+	1.64218i	−0.213132	+	0.977023i	$0.568367\pi$
$542$	−5.41706e6	−	7.45595e6i	−0.792074	−	1.09020i
$543$			4.30234e6i			0.626189i
$544$	−456100.	+	331376.i	−0.0660789	+	0.0480091i
$545$	−5.56362e6	+	932206.i	−0.802355	+	0.134438i
$546$	−3.42352e6	−	2.48734e6i	−0.491464	−	0.357070i
$547$	−4.46079e6	+	6.13975e6i	−0.637446	+	0.877369i	−0.998476	−	0.0551853i	$-0.982425\pi$
$547$	−4.46079e6	+	6.13975e6i	−0.637446	+	0.877369i	0.361030	+	0.932554i	$0.382425\pi$
$548$	−3.26622e6	−	1.06126e6i	−0.464616	−	0.150963i
$549$	−1.31092e7			−1.85629
$550$	2.30614e6	−	1.73928e6i	0.325071	−	0.245168i
$551$	8.40143e6			1.17889
$552$	−5.87196e6	−	1.90791e6i	−0.820229	−	0.266509i
$553$	2.03956e6	−	2.80721e6i	0.283611	−	0.390357i
$554$	1.82991e6	+	1.32951e6i	0.253312	+	0.184042i
$555$	−1.83917e7	−	9.16503e6i	−2.53448	−	1.26299i
$556$	−943604.	+	685568.i	−0.129450	+	0.0940511i
$557$			7.36653e6i			1.00606i	0.864268	+	0.503031i	$0.167782\pi$
$557$			7.36653e6i			1.00606i	−0.864268	+	0.503031i	$0.832218\pi$
$558$	1.47423e7	+	2.02910e7i	2.00438	+	2.75879i
$559$	−1.18764e6	−	3.65518e6i	−0.160752	−	0.494743i
$560$	327423.	+	1.95414e6i	0.0441204	+	0.263321i
$561$	1.13427e6	−	3.49091e6i	0.152163	−	0.468309i
$562$	4.55365e6	−	1.47957e6i	0.608162	−	0.197604i
$563$	6.71298e6	−	2.18118e6i	0.892574	−	0.290015i	0.173405	−	0.984851i	$-0.444523\pi$
$563$	6.71298e6	−	2.18118e6i	0.892574	−	0.290015i	0.719169	+	0.694836i	$0.244523\pi$
$564$	2.41216e6	−	7.42387e6i	0.319307	−	0.982726i
$565$	−13850.7	−	82664.0i	−0.00182536	−	0.0108942i
$566$	1.60658e6	+	4.94454e6i	0.210795	+	0.648761i
$567$	1.18110e7	+	1.62564e7i	1.54286	+	2.12357i
$568$		−	2.94162e6i		−	0.382575i
$569$	−4.51226e6	+	3.27835e6i	−0.584270	+	0.424497i	−0.840261	−	0.542182i	$-0.817598\pi$
$569$	−4.51226e6	+	3.27835e6i	−0.584270	+	0.424497i	0.255991	+	0.966679i	$0.417598\pi$
$570$	1.07336e7	+	5.34881e6i	1.38375	+	0.689556i
$571$	−4.87338e6	−	3.54072e6i	−0.625518	−	0.454465i	0.229327	−	0.973350i	$-0.426348\pi$
$571$	−4.87338e6	−	3.54072e6i	−0.625518	−	0.454465i	−0.854845	+	0.518884i	$0.826348\pi$
$572$	575550.	−	792176.i	0.0735517	−	0.101235i
$573$	401681.	+	130514.i	0.0511087	+	0.0166062i
$574$	3.87327e6			0.490679
$575$	−8.56182e6	−	5.98981e6i	−1.07993	−	0.755516i
$576$	2.41424e6			0.303196
$577$	−3.09945e6	−	1.00707e6i	−0.387565	−	0.125928i	0.108752	−	0.994069i	$-0.465315\pi$
$577$	−3.09945e6	−	1.00707e6i	−0.387565	−	0.125928i	−0.496317	+	0.868141i	$0.665315\pi$
$578$	2.62562e6	−	3.61386e6i	0.326898	−	0.449937i
$579$	−4.42384e6	−	3.21411e6i	−0.548407	−	0.398441i
$580$	3.98687e6	−	668015.i	0.492110	−	0.0824549i
$581$	7.68718e6	−	5.58507e6i	0.944772	−	0.686417i
$582$		−	5.11578e6i		−	0.626044i
$583$	1.75784e6	+	2.41945e6i	0.214194	+	0.294813i
$584$	−574219.	−	1.76726e6i	−0.0696700	−	0.214422i
$585$	−7.73947e6	+	4.03093e6i	−0.935021	+	0.486985i
$586$	−1.46024e6	+	4.49416e6i	−0.175663	+	0.540635i
$587$	−251079.	+	81580.6i	−0.0300757	+	0.00977219i	−0.324016	−	0.946052i	$-0.605033\pi$
$587$	−251079.	+	81580.6i	−0.0300757	+	0.00977219i	0.293941	+	0.955824i	$0.405033\pi$
$588$	1.03711e6	−	336978.i	0.123704	−	0.0401937i
$589$	6.11085e6	−	1.88073e7i	0.725794	−	2.23377i
$590$	−5.50216e6	−	821147.i	−0.650733	−	0.0971161i
$591$	2.41154e6	+	7.42197e6i	0.284005	+	0.874079i
$592$	1.91712e6	+	2.63869e6i	0.224825	+	0.309445i
$593$		−	1.10427e7i		−	1.28955i	−0.764371	−	0.644777i	$-0.776950\pi$
$593$		−	1.10427e7i		−	1.28955i	0.764371	−	0.644777i	$-0.223050\pi$
$594$	−7.47383e6	+	5.43006e6i	−0.869115	+	0.631449i
$595$	1.96837e6	+	3.77931e6i	0.227937	+	0.437643i
$596$	−1.21790e6	−	884859.i	−0.140442	−	0.102037i
$597$	1.24955e7	−	1.71985e7i	1.43488	−	1.97495i
$598$	−3.36881e6	−	1.09459e6i	−0.385233	−	0.125170i
$599$	4.30541e6			0.490284			0.245142	−	0.969487i	$-0.421165\pi$
$599$	4.30541e6			0.490284			0.245142	+	0.969487i	$0.421165\pi$
$600$	5.51887e6	+	1.68481e6i	0.625853	+	0.191061i
$601$	−8.55823e6			−0.966491			−0.483245	−	0.875485i	$-0.660542\pi$
$601$	−8.55823e6			−0.966491			−0.483245	+	0.875485i	$0.660542\pi$
$602$	7.64344e6	+	2.48350e6i	0.859602	+	0.279302i
$603$	5.21376e6	−	7.17613e6i	0.583926	−	0.803705i
$604$	2.58383e6	+	1.87726e6i	0.288185	+	0.209379i
$605$	−4.21720e6	+	4.29321e6i	−0.468420	+	0.476864i
$606$	−1.36684e7	+	9.93068e6i	−1.51195	+	1.09849i
$607$			6.04896e6i			0.666360i	0.942863	+	0.333180i	$0.108122\pi$
$607$			6.04896e6i			0.666360i	−0.942863	+	0.333180i	$0.891878\pi$
$608$	−1.11885e6	−	1.53997e6i	−0.122748	−	0.168948i
$609$	−5.57897e6	−	1.71703e7i	−0.609552	−	1.87601i
$610$	3.54789e6	+	3.48507e6i	0.386052	+	0.379216i
$611$	1.38389e6	−	4.25916e6i	0.149967	−	0.461552i
$612$	4.93798e6	−	1.60445e6i	0.532930	−	0.173160i
$613$	−8.54468e6	+	2.77633e6i	−0.918427	+	0.298415i	−0.729821	−	0.683638i	$-0.760397\pi$
$613$	−8.54468e6	+	2.77633e6i	−0.918427	+	0.298415i	−0.188605	+	0.982053i	$0.560397\pi$
$614$	1.03440e6	−	3.18354e6i	0.110730	−	0.340792i
$615$	5.03104e6	−	1.00959e7i	0.536377	−	1.07636i
$616$	632741.	+	1.94738e6i	0.0671853	+	0.206775i
$617$	5.99492e6	+	8.25130e6i	0.633972	+	0.872588i	0.998276	−	0.0586919i	$-0.0186930\pi$
$617$	5.99492e6	+	8.25130e6i	0.633972	+	0.872588i	−0.364304	+	0.931280i	$0.618693\pi$
$618$			2.17084e7i			2.28643i
$619$	−4.72558e6	+	3.43333e6i	−0.495711	+	0.360155i	−0.807376	−	0.590037i	$-0.799113\pi$
$619$	−4.72558e6	+	3.43333e6i	−0.495711	+	0.360155i	0.311665	+	0.950192i	$0.399113\pi$
$620$	1.40448e6	−	9.41082e6i	0.146736	−	0.983214i
$621$	2.70364e7	+	1.96431e7i	2.81333	+	2.04400i
$622$	3.31224e6	−	4.55891e6i	0.343278	−	0.472482i
$623$	−3.54955e6	−	1.15332e6i	−0.366398	−	0.119050i
$624$	1.95611e6			0.201109
$625$	8.10055e6	+	5.45421e6i	0.829497	+	0.558512i
$626$	8.28728e6			0.845232
$627$	1.17867e7	+	3.82972e6i	1.19735	+	0.389043i
$628$	−2.64379e6	+	3.63887e6i	−0.267503	+	0.368186i
$629$	5.67480e6	+	4.12299e6i	0.571905	+	0.415514i
$630$	2.69347e6	−	1.80478e7i	0.270372	−	1.81165i
$631$	410115.	−	297966.i	0.0410046	−	0.0297916i	−0.567094	−	0.823653i	$-0.691932\pi$
$631$	410115.	−	297966.i	0.0410046	−	0.0297916i	0.608099	+	0.793861i	$0.291932\pi$
$632$			1.60396e6i			0.159736i
$633$	−1.34629e7	−	1.85301e7i	−1.33546	−	1.83810i
$634$	−700861.	−	2.15703e6i	−0.0692483	−	0.213124i
$635$	−6.39112e6	+	1.28252e7i	−0.628988	+	1.26220i
$636$	−1.84617e6	+	5.68192e6i	−0.180979	+	0.556996i
$637$	595004.	−	193328.i	0.0580993	−	0.0188776i
$638$	3.97307e6	−	1.29093e6i	0.386433	−	0.125560i
$639$	−8.37162e6	+	2.57652e7i	−0.811069	+	2.49621i
$640$	−653393.	−	641824.i	−0.0630558	−	0.0619393i
$641$	2.99730e6	+	9.22474e6i	0.288128	+	0.886766i	0.985444	+	0.170002i	$0.0543775\pi$
$641$	2.99730e6	+	9.22474e6i	0.288128	+	0.886766i	−0.697316	+	0.716764i	$0.745622\pi$
$642$	4.53200e6	+	6.23776e6i	0.433962	+	0.597298i
$643$		−	1.22370e7i		−	1.16720i	−0.812041	−	0.583601i	$-0.801643\pi$
$643$		−	1.22370e7i		−	1.16720i	0.812041	−	0.583601i	$-0.198357\pi$
$644$	5.99249e6	−	4.35380e6i	0.569367	−	0.413670i
$645$	1.64016e7	−	1.66972e7i	1.55234	−	1.58032i
$646$	−3.31187e6	−	2.40622e6i	−0.312243	−	0.226858i
$647$	−4.33856e6	+	5.97151e6i	−0.407460	+	0.560820i	−0.962597	−	0.270939i	$-0.912666\pi$
$647$	−4.33856e6	+	5.97151e6i	−0.407460	+	0.560820i	0.555137	+	0.831759i	$0.312666\pi$
$648$	−8.83385e6	−	2.87029e6i	−0.826442	−	0.268527i
$649$	−5.74900e6			−0.535773
$650$	3.16624e6	+	966595.i	0.293941	+	0.0897349i
$651$	−4.24950e7			−3.92994
$652$	−8.50259e6	−	2.76266e6i	−0.783308	−	0.254512i
$653$	9.14649e6	−	1.25891e7i	0.839405	−	1.15534i	−0.146693	−	0.989182i	$-0.546863\pi$
$653$	9.14649e6	−	1.25891e7i	0.839405	−	1.15534i	0.986099	−	0.166160i	$-0.0531369\pi$
$654$	−9.42176e6	−	6.84531e6i	−0.861366	−	0.625819i
$655$	6.26778e6	+	1.20343e7i	0.570835	+	1.09601i
$656$	−1.44848e6	+	1.05238e6i	−0.131417	+	0.0954803i
$657$			1.71134e7i			1.54676i
$658$	5.50447e6	+	7.57626e6i	0.495623	+	0.682166i
$659$	5.29948e6	+	1.63101e7i	0.475356	+	1.46300i	0.845476	+	0.534013i	$0.179317\pi$
$659$	5.29948e6	+	1.63101e7i	0.475356	+	1.46300i	−0.370120	+	0.928984i	$0.620683\pi$
$660$	5.89783e6	+	880198.i	0.527026	+	0.0786539i
$661$	−1.53976e6	+	4.73890e6i	−0.137072	+	0.421865i	−0.995907	−	0.0903882i	$-0.971189\pi$
$661$	−1.53976e6	+	4.73890e6i	−0.137072	+	0.421865i	0.858834	+	0.512254i	$0.171189\pi$
$662$	−4.59423e6	+	1.49276e6i	−0.407444	+	0.132387i
$663$	4.00094e6	−	1.29998e6i	0.353491	−	0.114856i
$664$	−1.35728e6	+	4.17727e6i	−0.119467	+	0.367682i
$665$	−1.27604e7	+	6.64597e6i	−1.11895	+	0.582780i
$666$	−9.28225e6	−	2.85678e7i	−0.810901	−	2.49570i
$667$	−8.88270e6	−	1.22260e7i	−0.773090	−	1.06407i
$668$		−	1.37892e6i		−	0.119564i
$669$	−6.04656e6	+	4.39308e6i	−0.522328	+	0.379493i
$670$	−3.31883e6	+	556082.i	−0.285626	+	0.0478577i
$671$	4.15790e6	+	3.02089e6i	0.356507	+	0.259017i
$672$	−2.40431e6	+	3.30925e6i	−0.205385	+	0.282688i
$673$	6.94021e6	+	2.25501e6i	0.590656	+	0.191916i	0.589069	−	0.808083i	$-0.299495\pi$
$673$	6.94021e6	+	2.25501e6i	0.590656	+	0.191916i	0.00158737	+	0.999999i	$0.499495\pi$
$674$	5.53564e6			0.469373
$675$	−2.55920e7	−	1.79040e7i	−2.16195	−	1.51249i
$676$	−4.81845e6			−0.405546
$677$	−1.71605e6	−	557578.i	−0.143899	−	0.0467556i	0.236182	−	0.971709i	$-0.424104\pi$
$677$	−1.71605e6	−	557578.i	−0.143899	−	0.0467556i	−0.380081	+	0.924953i	$0.624104\pi$
$678$	101707.	−	139988.i	0.00849724	−	0.0116954i
$679$	4.96527e6	+	3.60748e6i	0.413303	+	0.300282i
$680$	−1.76296e6	−	878529.i	−0.146208	−	0.0728591i
$681$	−4.93679e6	+	3.58678e6i	−0.407921	+	0.296372i
$682$		−	9.83301e6i		−	0.809516i
$683$	−6.91368e6	−	9.51587e6i	−0.567097	−	0.780543i	0.425110	−	0.905142i	$-0.360235\pi$
$683$	−6.91368e6	−	9.51587e6i	−0.567097	−	0.780543i	−0.992207	+	0.124599i	$0.960235\pi$
$684$	5.41722e6	+	1.66725e7i	0.442727	+	1.36257i
$685$	−1.98283e6	−	1.18340e7i	−0.161458	−	0.963619i
$686$	2.47203e6	−	7.60814e6i	0.200560	−	0.617260i
$687$	7.33049e6	−	2.38182e6i	0.592572	−	0.192538i
$688$	−3.53318e6	+	1.14800e6i	−0.284574	+	0.0924636i
$689$	−1.05917e6	+	3.25978e6i	−0.0849996	+	0.261602i
$690$	−3.56470e6	−	2.12750e7i	−0.285037	−	1.70117i
$691$	−879577.	−	2.70706e6i	−0.0700776	−	0.215677i	0.909884	−	0.414862i	$-0.136170\pi$
$691$	−879577.	−	2.70706e6i	−0.0700776	−	0.215677i	−0.979962	+	0.199186i	$0.936170\pi$
$692$	1.32541e6	+	1.82427e6i	0.105217	+	0.144819i
$693$		−	1.88575e7i		−	1.49159i
$694$	−1.09549e7	+	7.95921e6i	−0.863396	+	0.627294i
$695$	−3.64731e6	−	1.81755e6i	−0.286425	−	0.142733i
$696$	6.75160e6	+	4.90532e6i	0.528304	+	0.383835i
$697$	−2.26327e6	+	3.11512e6i	−0.176463	+	0.242881i
$698$	−1.01156e7	−	3.28674e6i	−0.785871	−	0.255345i
$699$	1.35395e7			1.04812
$700$	−5.52697e6	+	4.16843e6i	−0.426326	+	0.321534i
$701$	1.26859e7			0.975052			0.487526	−	0.873109i	$-0.337900\pi$
$701$	1.26859e7			0.975052			0.487526	+	0.873109i	$0.337900\pi$
$702$	−1.00697e7	−	3.27183e6i	−0.771208	−	0.250581i
$703$	−1.39208e7	+	1.91603e7i	−1.06237	+	1.46222i
$704$	−765735.	−	556339.i	−0.0582300	−	0.0423066i
$705$	2.68978e7	−	4.50683e6i	2.03819	−	0.341506i
$706$	−3.78372e6	+	2.74903e6i	−0.285698	+	0.207572i
$707$		−	2.02690e7i		−	1.52505i
$708$	−6.75056e6	−	9.29135e6i	−0.506124	−	0.696619i
$709$	1.40277e6	+	4.31730e6i	0.104803	+	0.322549i	0.989684	−	0.143267i	$-0.0457607\pi$
$709$	1.40277e6	+	4.31730e6i	0.104803	+	0.322549i	−0.884881	+	0.465816i	$0.845761\pi$
$710$	9.11537e6	−	4.74754e6i	0.678623	−	0.353446i
$711$	4.56475e6	−	1.40489e7i	0.338644	−	1.04224i
$712$	1.64078e6	−	533122.i	0.121297	−	0.0394119i
$713$	−3.38298e7	+	1.09920e7i	−2.49216	+	0.809750i
$714$	−2.71842e6	+	8.36645e6i	−0.199559	+	0.614180i
$715$	3.38365e6	+	504980.i	0.247526	+	0.0369410i
$716$	−2.05068e6	−	6.31135e6i	−0.149491	−	0.460087i
$717$	−4.87970e6	−	6.71633e6i	−0.354483	−	0.487903i
$718$			8.67956e6i			0.628328i
$719$	1.33839e7	−	9.72398e6i	0.965519	−	0.701491i	0.0110929	−	0.999938i	$-0.496469\pi$
$719$	1.33839e7	−	9.72398e6i	0.965519	−	0.701491i	0.954426	+	0.298448i	$0.0964689\pi$
$720$	3.89639e6	+	7.48114e6i	0.280112	+	0.537819i
$721$	−2.10697e7	−	1.53081e7i	−1.50946	−	1.09669i
$722$	2.30264e6	−	3.16932e6i	0.164393	−	0.226268i
$723$	2.17448e7	+	7.06532e6i	1.54707	+	0.502674i
$724$	2.38592e6			0.169164
$725$	8.50451e6	+	1.12762e7i	0.600903	+	0.796743i
$726$	−1.24239e7			−0.874814
$727$	6.79406e6	+	2.20752e6i	0.476753	+	0.154906i	0.537530	−	0.843245i	$-0.319358\pi$
$727$	6.79406e6	+	2.20752e6i	0.476753	+	0.154906i	−0.0607764	+	0.998151i	$0.519358\pi$
$728$	−1.37938e6	+	1.89856e6i	−0.0964620	+	0.132769i
$729$	1.25167e7	+	9.09391e6i	0.872309	+	0.633770i
$730$	4.54958e6	−	4.63159e6i	0.315983	−	0.321679i
$731$	−6.46368e6	+	4.69614e6i	−0.447390	+	0.325048i
$732$			1.02670e7i			0.708219i
$733$	1.69972e6	+	2.33946e6i	0.116847	+	0.160826i	0.863434	−	0.504462i	$-0.168309\pi$
$733$	1.69972e6	+	2.33946e6i	0.116847	+	0.160826i	−0.746587	+	0.665288i	$0.768309\pi$
$734$	1.43016e6	+	4.40159e6i	0.0979819	+	0.301557i
$735$	2.71803e6	+	2.66990e6i	0.185582	+	0.182296i
$736$	−1.05806e6	+	3.25637e6i	−0.0719970	+	0.221584i
$737$	−3.30734e6	+	1.07462e6i	−0.224290	+	0.0728763i
$738$	1.56820e7	−	5.09539e6i	1.05989	−	0.344379i
$739$	−4.58568e6	+	1.41133e7i	−0.308882	+	0.950642i	0.669318	+	0.742976i	$0.266587\pi$
$739$	−4.58568e6	+	1.41133e7i	−0.308882	+	0.950642i	−0.978200	+	0.207666i	$0.933413\pi$
$740$	−5.08258e6	+	1.01993e7i	−0.341197	+	0.684687i
$741$	4.38924e6	+	1.35087e7i	0.293659	+	0.903790i
$742$	−4.21289e6	−	5.79855e6i	−0.280912	−	0.386643i
$743$			1.97032e7i			1.30938i	0.755899	+	0.654688i	$0.227200\pi$
$743$			1.97032e7i			1.30938i	−0.755899	+	0.654688i	$0.772800\pi$
$744$	1.58918e7	−	1.15461e7i	1.05254	−	0.764719i
$745$	776363.	−	5.20208e6i	0.0512477	−	0.343389i
$746$	−1.28391e6	−	932812.i	−0.0844668	−	0.0613687i
$747$	2.37764e7	−	3.27254e7i	1.55899	−	2.14577i
$748$	−1.93593e6	−	629022.i	−0.126513	−	0.0411066i
$749$	−9.25005e6			−0.602476
$750$	3.68620e6	+	1.98208e7i	0.239291	+	1.28667i
$751$	2.35954e6			0.152661			0.0763304	−	0.997083i	$-0.475680\pi$
$751$	2.35954e6			0.152661			0.0763304	+	0.997083i	$0.475680\pi$
$752$	−4.11700e6	−	1.33769e6i	−0.265483	−	0.0862605i
$753$	−1.97083e7	+	2.71262e7i	−1.26667	+	1.74342i
$754$	3.87347e6	+	2.81424e6i	0.248126	+	0.180274i
$755$	−1.64708e6	+	1.10364e7i	−0.105159	+	0.704628i
$756$	1.79121e7	−	1.30139e7i	1.13983	−	0.828136i
$757$			2.12249e6i			0.134619i	0.997732	+	0.0673093i	$0.0214414\pi$
$757$			2.12249e6i			0.134619i	−0.997732	+	0.0673093i	$0.978559\pi$
$758$	−3.34520e6	−	4.60428e6i	−0.211470	−	0.291064i
$759$	−6.88874e6	−	2.12014e7i	−0.434046	−	1.33585i
$760$	2.96625e6	−	5.95243e6i	0.186283	−	0.373818i
$761$	−3.13591e6	+	9.65133e6i	−0.196292	+	0.604123i	0.803668	+	0.595079i	$0.202879\pi$
$761$	−3.13591e6	+	9.65133e6i	−0.196292	+	0.604123i	−0.999959	+	0.00904479i	$0.997121\pi$
$762$	−2.81345e7	+	9.14146e6i	−1.75530	+	0.570332i
$763$	1.32878e7	−	4.31748e6i	0.826309	−	0.268484i
$764$	72378.2	−	222757.i	0.00448615	−	0.0138070i
$765$	1.29413e7	+	1.27121e7i	0.799510	+	0.785354i
$766$	−610851.	−	1.88001e6i	−0.0376152	−	0.115768i
$767$	−3.87288e6	−	5.33056e6i	−0.237709	−	0.327178i
$768$		−	1.89082e6i		−	0.115677i
$769$	1.88713e7	−	1.37108e7i	1.15077	−	0.836081i	0.162184	−	0.986761i	$-0.448146\pi$
$769$	1.88713e7	−	1.37108e7i	1.15077	−	0.836081i	0.988583	+	0.150680i	$0.0481463\pi$
$770$	−5.01325e6	+	5.10362e6i	−0.304714	+	0.310207i
$771$	4.43518e6	+	3.22235e6i	0.268705	+	0.195225i
$772$	−1.78242e6	+	2.45330e6i	−0.107639	+	0.148152i
$773$	2.23078e7	+	7.24824e6i	1.34279	+	0.436299i	0.890261	−	0.455451i	$-0.150522\pi$
$773$	2.23078e7	+	7.24824e6i	1.34279	+	0.436299i	0.452529	+	0.891750i	$0.350522\pi$
$774$	3.42137e7			2.05280
$775$	3.14285e7	−	1.08362e7i	1.87962	−	0.648069i
$776$	−2.83702e6			−0.169125
$777$	4.84027e7	+	1.57270e7i	2.87619	+	0.934529i
$778$	1.85312e6	−	2.55060e6i	0.109762	−	0.151075i
$779$	−1.05178e7	−	7.64165e6i	−0.620987	−	0.451173i
$780$	3.15700e6	+	6.06151e6i	0.185797	+	0.356734i
$781$	8.59262e6	−	6.24290e6i	0.504078	−	0.366234i
$782$			7.36359e6i			0.430598i
$783$	−2.65511e7	−	3.65445e7i	−1.54767	−	2.13019i
$784$	−186875.	−	575143.i	−0.0108583	−	0.0334184i
$785$	−1.55428e7	−	2.31963e6i	−0.900236	−	0.134352i
$786$	−8.65613e6	+	2.66408e7i	−0.499767	+	1.53812i
$787$	1.13700e7	−	3.69433e6i	0.654369	−	0.212617i	0.0370295	−	0.999314i	$-0.488210\pi$
$787$	1.13700e7	−	3.69433e6i	0.654369	−	0.212617i	0.617340	+	0.786697i	$0.288210\pi$
$788$	4.11594e6	−	1.33735e6i	0.236132	−	0.0767238i
$789$	−1.31629e7	+	4.05113e7i	−0.752765	+	2.31677i
$790$	−4.97030e6	+	2.58867e6i	−0.283344	+	0.147574i
$791$	64148.8	+	197430.i	0.00364542	+	0.0112194i
$792$	5.12365e6	+	7.05210e6i	0.290246	+	0.399490i
$793$			5.89032e6i			0.332626i
$794$	−6.04168e6	+	4.38954e6i	−0.340100	+	0.247097i
$795$	−2.05865e7	+	3.44934e6i	−1.15522	+	0.193561i
$796$	−9.53766e6	−	6.92951e6i	−0.533530	−	0.387632i
$797$	−1.84258e7	+	2.53609e7i	−1.02750	+	1.41423i	−0.120685	+	0.992691i	$0.538509\pi$
$797$	−1.84258e7	+	2.53609e7i	−1.02750	+	1.41423i	−0.906811	+	0.421536i	$0.861491\pi$
$798$	−2.82483e7	−	9.17843e6i	−1.57031	−	0.510224i
$799$	−9.30972e6			−0.515905
$800$	934332.	−	3.06056e6i	0.0516150	−	0.169074i
$801$	−1.58886e7			−0.874991
$802$	9.35005e6	+	3.03802e6i	0.513308	+	0.166784i
$803$	3.94362e6	−	5.42792e6i	0.215827	−	0.297060i
$804$	−5.62030e6	−	4.08339e6i	−0.306633	−	0.222782i
$805$	2.31628e7	+	1.15426e7i	1.25980	+	0.627789i
$806$	9.11731e6	−	6.62411e6i	0.494344	−	0.359162i
$807$		−	3.05237e7i		−	1.64989i
$808$	5.50718e6	+	7.57998e6i	0.296757	+	0.408451i
$809$	−5.94660e6	−	1.83018e7i	−0.319446	−	0.983154i	−0.973886	−	0.227040i	$-0.927095\pi$
$809$	−5.94660e6	−	1.83018e7i	−0.319446	−	0.983154i	0.654439	−	0.756114i	$-0.272905\pi$
$810$	−5.36279e6	−	3.20064e7i	−0.287196	−	1.71405i
$811$	−7.27218e6	+	2.23815e7i	−0.388251	+	1.19491i	0.545843	+	0.837887i	$0.316209\pi$
$811$	−7.27218e6	+	2.23815e7i	−0.388251	+	1.19491i	−0.934094	+	0.357026i	$0.883791\pi$
$812$	−9.52201e6	+	3.09389e6i	−0.506802	+	0.164670i
$813$	6.32210e7	−	2.05417e7i	3.35455	−	1.08996i
$814$	−3.63910e6	+	1.12000e7i	−0.192501	+	0.592457i
$815$	−5.16169e6	−	3.08062e7i	−0.272206	−	1.62459i
$816$	−1.25659e6	−	3.86739e6i	−0.0660646	−	0.203326i
$817$	−1.58559e7	−	2.18238e7i	−0.831069	−	1.14387i
$818$		−	2.37597e7i		−	1.24153i
$819$	1.74849e7	−	1.27036e7i	0.910866	−	0.661783i
$820$	−5.59880e6	−	2.79002e6i	−0.290777	−	0.144902i
$821$	−1.80240e7	−	1.30952e7i	−0.933241	−	0.678039i	0.0135435	−	0.999908i	$-0.495689\pi$
$821$	−1.80240e7	−	1.30952e7i	−0.933241	−	0.678039i	−0.946784	+	0.321869i	$0.895689\pi$
$822$	1.45602e7	−	2.00404e7i	0.751601	−	1.03449i
$823$	−3.37960e7	−	1.09810e7i	−1.73927	−	0.565122i	−0.744530	−	0.667589i	$-0.767326\pi$
$823$	−3.37960e7	−	1.09810e7i	−1.73927	−	0.565122i	−0.994736	+	0.102467i	$0.967326\pi$
$824$	1.20387e7			0.617676
$825$	6.79110e6	+	1.96965e7i	0.347380	+	1.00752i
$826$	1.37783e7			0.702658
$827$	2.46597e7	+	8.01242e6i	1.25379	+	0.407380i	0.859277	−	0.511511i	$-0.170914\pi$
$827$	2.46597e7	+	8.01242e6i	1.25379	+	0.407380i	0.394510	+	0.918891i	$0.370914\pi$
$828$	1.85347e7	−	2.55108e7i	0.939529	−	1.29315i
$829$	2.18045e6	+	1.58419e6i	0.110194	+	0.0800609i	0.641518	−	0.767108i	$-0.278305\pi$
$829$	2.18045e6	+	1.58419e6i	0.110194	+	0.0800609i	−0.531323	+	0.847169i	$0.678305\pi$
$830$	−1.51349e7	+	2.53591e6i	−0.762578	+	0.127773i
$831$	−1.31990e7	+	9.58961e6i	−0.663036	+	0.481724i
$832$		−	1.08478e6i		−	0.0543294i
$833$	−764453.	−	1.05218e6i	−0.0381714	−	0.0525385i
$834$	−2.59970e6	−	8.00107e6i	−0.129422	−	0.398321i
$835$	4.27295e6	−	2.22547e6i	0.212086	−	0.110460i
$836$	2.12382e6	−	6.53643e6i	0.105100	−	0.323463i
$837$	−1.01120e8	+	3.28559e7i	−4.98911	+	1.62106i
$838$	1.09956e7	−	3.57269e6i	0.540890	−	0.175746i
$839$	−4.65770e6	+	1.43349e7i	−0.228437	+	0.703057i	0.769487	+	0.638662i	$0.220512\pi$
$839$	−4.65770e6	+	1.43349e7i	−0.228437	+	0.703057i	−0.997924	+	0.0643950i	$0.979488\pi$
$840$	−1.41349e7	−	2.10951e6i	−0.691187	−	0.103153i
$841$	−26089.8	−	80296.0i	−0.00127198	−	0.00391475i
$842$	1.06883e7	+	1.47111e7i	0.519550	+	0.715099i
$843$			3.45353e7i			1.67376i
$844$	−1.02761e7	+	7.46602e6i	−0.496560	+	0.360772i
$845$	−7.77658e6	−	1.49312e7i	−0.374668	−	0.719371i
$846$	3.22532e7	+	2.34333e7i	1.54934	+	1.12566i
$847$	8.76091e6	−	1.20584e7i	0.419605	−	0.577537i
$848$	3.15098e6	+	1.02381e6i	0.150472	+	0.0488913i
$849$	−3.74998e7			−1.78550
$850$	−122934.	−	6.88087e6i	−0.00583612	−	0.326660i
$851$	4.26008e7			2.01648
$852$	2.01792e7	+	6.55661e6i	0.952366	+	0.309443i
$853$	−3.31419e6	+	4.56159e6i	−0.155957	+	0.214656i	−0.879845	−	0.475262i	$-0.842353\pi$
$853$	−3.31419e6	+	4.56159e6i	−0.155957	+	0.214656i	0.723888	+	0.689918i	$0.242353\pi$
$854$	−9.96497e6	−	7.23997e6i	−0.467553	−	0.339697i
$855$	−4.29210e7	+	4.36947e7i	−2.00796	+	2.04415i
$856$	3.45923e6	−	2.51327e6i	0.161359	−	0.117235i
$857$			4.16633e7i			1.93777i	0.247516	+	0.968884i	$0.420386\pi$
$857$			4.16633e7i			1.93777i	−0.247516	+	0.968884i	$0.579614\pi$
$858$	4.15138e6	+	5.71388e6i	0.192519	+	0.264980i
$859$	−8.66770e6	−	2.66764e7i	−0.400794	−	1.23352i	−0.924357	−	0.381530i	$-0.875397\pi$
$859$	−8.66770e6	−	2.66764e7i	−0.400794	−	1.23352i	0.523563	−	0.851987i	$-0.324603\pi$
$860$	−9.25964e6	−	9.09569e6i	−0.426922	−	0.419362i
$861$	−8.63315e6	+	2.65701e7i	−0.396882	+	1.22148i
$862$	1.16620e7	−	3.78920e6i	0.534569	−	0.173692i
$863$	3.31143e7	−	1.07595e7i	1.51352	−	0.491773i	0.569595	−	0.821925i	$-0.307100\pi$
$863$	3.31143e7	−	1.07595e7i	1.51352	−	0.491773i	0.943928	+	0.330152i	$0.107100\pi$
$864$	−3.16262e6	+	9.73355e6i	−0.144133	+	0.443595i
$865$	−3.51387e6	+	7.05135e6i	−0.159678	+	0.320429i
$866$	3.98182e6	+	1.22548e7i	0.180421	+	0.555279i
$867$	1.89383e7	+	2.60664e7i	0.855646	+	1.17770i
$868$			2.35661e7i			1.06167i
$869$	−4.68525e6	+	3.40404e6i	−0.210467	+	0.152913i
$870$	−4.30387e6	+	2.88384e7i	−0.192779	+	1.29173i
$871$	−3.22443e6	−	2.34269e6i	−0.144015	−	0.104633i
$872$	−3.79615e6	+	5.22495e6i	−0.169064	+	0.232697i
$873$	2.48490e7	+	8.07393e6i	1.10350	+	0.358550i
$874$	−2.48623e7			−1.10094
$875$	−2.18370e7	−	1.03992e7i	−0.964214	−	0.459177i
$876$	1.34031e7			0.590126
$877$	7.55208e6	+	2.45382e6i	0.331564	+	0.107732i	0.470068	−	0.882630i	$-0.344229\pi$
$877$	7.55208e6	+	2.45382e6i	0.331564	+	0.107732i	−0.138504	+	0.990362i	$0.544229\pi$
$878$	−1.26422e7	+	1.74005e7i	−0.553462	+	0.761775i
$879$	−2.75746e7	−	2.00341e7i	−1.20375	−	0.874577i
$880$	488124.	−	3.27071e6i	0.0212483	−	0.142376i
$881$	943959.	−	685826.i	0.0409745	−	0.0297697i	−0.567110	−	0.823642i	$-0.691938\pi$
$881$	943959.	−	685826.i	0.0409745	−	0.0297697i	0.608084	+	0.793873i	$0.291938\pi$
$882$			5.56942e6i			0.241068i
$883$	−1.25300e7	−	1.72461e7i	−0.540816	−	0.744369i	0.447915	−	0.894076i	$-0.352167\pi$
$883$	−1.25300e7	−	1.72461e7i	−0.540816	−	0.744369i	−0.988730	+	0.149707i	$0.952167\pi$
$884$	−720922.	−	2.21877e6i	−0.0310283	−	0.0954952i
$885$	1.78968e7	−	3.59138e7i	0.768098	−	1.54136i
$886$	7.10703e6	−	2.18732e7i	0.304161	−	0.936112i
$887$	3.56547e7	−	1.15849e7i	1.52162	−	0.494405i	0.575387	−	0.817881i	$-0.304851\pi$
$887$	3.56547e7	−	1.15849e7i	1.52162	−	0.494405i	0.946236	+	0.323476i	$0.104851\pi$
$888$	−2.23742e7	+	7.26980e6i	−0.952169	+	0.309379i
$889$	1.09670e7	−	3.37530e7i	0.465408	−	1.43238i
$890$	4.30011e6	+	4.22397e6i	0.181972	+	0.178750i
$891$	−1.03635e7	−	3.18956e7i	−0.437333	−	1.34597i
$892$	2.43624e6	+	3.35319e6i	0.102520	+	0.141106i
$893$		−	3.14332e7i		−	1.31904i
$894$	8.78461e6	−	6.38239e6i	0.367603	−	0.267079i
$895$	1.62477e7	−	1.65406e7i	0.678007	−	0.690229i
$896$	1.83519e6	+	1.33334e6i	0.0763678	+	0.0554845i
$897$	1.50175e7	−	2.06699e7i	0.623186	−	0.857742i
$898$	2.66207e7	+	8.64958e6i	1.10161	+	0.357935i
$899$	4.80801e7			1.98411
$900$	−1.68938e7	+	2.41479e7i	−0.695217	+	0.993742i
$901$	7.12527e6			0.292408
$902$	−6.14811e6	−	1.99764e6i	−0.251609	−	0.0817526i
$903$	−3.40730e7	+	4.68975e7i	−1.39057	+	1.91395i
$904$	−77632.1	−	56403.0i	−0.00315951	−	0.00229552i
$905$	3.85068e6	+	7.39338e6i	0.156284	+	0.300069i
$906$	−1.86369e7	+	1.35405e7i	−0.754315	+	0.548042i
$907$		−	3.08263e7i		−	1.24424i	−0.782924	−	0.622118i	$-0.786272\pi$
$907$		−	3.08263e7i		−	1.24424i	0.782924	−	0.622118i	$-0.213728\pi$
$908$	1.98910e6	+	2.73775e6i	0.0800647	+	0.110200i
$909$	−2.66645e7	−	8.20648e7i	−1.07034	−	3.29418i
$910$	−8.10938e6	−	1.21025e6i	−0.324627	−	0.0484476i
$911$	9.30698e6	−	2.86439e7i	0.371546	−	1.14350i	−0.574233	−	0.818692i	$-0.694700\pi$
$911$	9.30698e6	−	2.86439e7i	0.371546	−	1.14350i	0.945779	−	0.324810i	$-0.105300\pi$
$912$	1.30578e7	−	4.24273e6i	0.519855	−	0.168911i
$913$	−1.50825e7	+	4.90061e6i	−0.598821	+	0.194569i
$914$	9.04975e6	−	2.78523e7i	0.358320	−	1.10280i
$915$	−3.18150e7	+	1.65702e7i	−1.25626	+	0.654296i
$916$	−1.32087e6	−	4.06522e6i	−0.0520141	−	0.160083i
$917$	−1.97530e7	−	2.71877e7i	−0.775729	−	1.06770i
$918$			2.20104e7i			0.862027i
$919$	−5.75705e6	+	4.18274e6i	−0.224859	+	0.163370i	−0.694511	−	0.719482i	$-0.744379\pi$
$919$	−5.75705e6	+	4.18274e6i	−0.224859	+	0.163370i	0.469652	+	0.882852i	$0.344379\pi$
$920$	−1.17983e7	+	1.97685e6i	−0.459568	+	0.0770024i
$921$	1.95331e7	+	1.41916e7i	0.758792	+	0.551294i
$922$	−3.83504e6	+	5.27849e6i	−0.148574	+	0.204495i
$923$	1.15770e7	+	3.76160e6i	0.447293	+	0.145334i
$924$	−1.47691e7			−0.569080
$925$	−3.98081e7	+	711213.i	−1.52974	+	0.0273304i
$926$	−2.85178e6			−0.109292
$927$	−1.05445e8	−	3.42611e7i	−4.03020	−	1.30949i
$928$	2.72031e6	−	3.74418e6i	0.103693	−	0.142721i
$929$	2.24212e7	+	1.62900e7i	0.852353	+	0.619271i	0.925794	−	0.378029i	$-0.123398\pi$
$929$	2.24212e7	+	1.62900e7i	0.852353	+	0.619271i	−0.0734407	+	0.997300i	$0.523398\pi$
$930$	6.14265e7	+	3.06104e7i	2.32889	+	1.16054i
$931$	3.55256e6	−	2.58108e6i	0.134328	−	0.0975951i
$932$		−	7.50849e6i		−	0.283148i
$933$	2.38909e7	+	3.28830e7i	0.898520	+	1.23671i
$934$	−2.09195e6	−	6.43836e6i	−0.0784664	−	0.241495i
$935$	−1.17525e6	−	7.01417e6i	−0.0439644	−	0.262390i
$936$	−3.08721e6	+	9.50145e6i	−0.115180	+	0.354487i
$937$	−4.14082e6	+	1.34544e6i	−0.154077	+	0.0500626i	−0.385040	−	0.922900i	$-0.625812\pi$
$937$	−4.14082e6	+	1.34544e6i	−0.154077	+	0.0500626i	0.230963	+	0.972963i	$0.425812\pi$
$938$	7.92650e6	−	2.57547e6i	0.294154	−	0.0955763i
$939$	−1.84716e7	+	5.68497e7i	−0.683660	+	2.10409i
$940$	−2.49932e6	−	1.49165e7i	−0.0922575	−	0.550614i
$941$	−1.00030e7	−	3.07859e7i	−0.368260	−	1.13339i	−0.947914	−	0.318525i	$-0.896812\pi$
$941$	−1.00030e7	−	3.07859e7i	−0.368260	−	1.13339i	0.579654	−	0.814862i	$-0.303188\pi$
$942$	−1.90694e7	−	2.62468e7i	−0.700180	−	0.963715i
$943$			2.33852e7i			0.856372i
$944$	−5.15263e6	+	3.74361e6i	−0.188191	+	0.136729i
$945$	6.92354e7	+	3.45018e7i	2.52202	+	1.25679i
$946$	−1.08517e7	−	7.88423e6i	−0.394249	−	0.286438i
$947$	−2.84927e7	+	3.92169e7i	−1.03243	+	1.42101i	−0.129316	+	0.991603i	$0.541278\pi$
$947$	−2.84927e7	+	3.92169e7i	−1.03243	+	1.42101i	−0.903110	+	0.429409i	$0.858722\pi$
$948$	−1.10030e7	−	3.57509e6i	−0.397640	−	0.129201i
$949$	7.68951e6			0.277162
$950$	2.32324e7	−	415071.i	0.835190	−	0.0149215i
$951$	1.63591e7			0.586554
$952$	4.63972e6	+	1.50754e6i	0.165920	+	0.0539107i
$953$	−1.03544e7	+	1.42516e7i	−0.369312	+	0.508314i	−0.952714	−	0.303870i	$-0.901721\pi$
$953$	−1.03544e7	+	1.42516e7i	−0.369312	+	0.508314i	0.583402	+	0.812184i	$0.301721\pi$
$954$	−2.46852e7	−	1.79349e7i	−0.878145	−	0.638009i
$955$	807083.	−	135230.i	0.0286358	−	0.00479804i
$956$	−3.72462e6	+	2.70610e6i	−0.131807	+	0.0957632i
$957$			3.01321e7i			1.06353i
$958$	−1.27638e7	−	1.75678e7i	−0.449329	−	0.618448i
$959$	9.18341e6	+	2.82636e7i	0.322446	+	0.992388i
$960$	5.85918e6	−	3.05163e6i	0.205191	−	0.106869i
$961$	2.61246e7	−	8.04032e7i	0.912516	−	2.80844i
$962$	−1.28363e7	+	4.17077e6i	−0.447201	+	0.145304i
$963$	−3.74514e7	+	1.21687e7i	−1.30137	+	0.422842i
$964$	3.91816e6	−	1.20589e7i	0.135797	−	0.417940i
$965$	−1.04789e7	−	1.56388e6i	−0.362239	−	0.0540610i
$966$	1.65098e7	+	5.08119e7i	0.569245	+	1.75195i
$967$	1.44724e7	+	1.99196e7i	0.497709	+	0.685038i	0.981787	−	0.189987i	$-0.0608447\pi$
$967$	1.44724e7	+	1.99196e7i	0.497709	+	0.685038i	−0.484078	+	0.875025i	$0.660845\pi$
$968$			6.88982e6i			0.236330i
$969$	2.38882e7	−	1.73558e7i	0.817286	−	0.593793i
$970$	−4.57872e6	−	8.79124e6i	−0.156248	−	0.300000i
$971$	2.56121e7	+	1.86083e7i	0.871761	+	0.633371i	0.931059	−	0.364869i	$-0.118886\pi$
$971$	2.56121e7	+	1.86083e7i	0.871761	+	0.633371i	−0.0592982	+	0.998240i	$0.518886\pi$
$972$	1.65389e7	−	2.27639e7i	0.561490	−	0.772824i
$973$	9.59889e6	+	3.11887e6i	0.325042	+	0.105612i
$974$	−9.11348e6			−0.307813
$975$	−1.36880e7	+	1.95656e7i	−0.461135	+	0.659145i
$976$	5.69371e6			0.191325
$977$	4.67637e7	+	1.51944e7i	1.56737	+	0.509270i	0.958765	−	0.284201i	$-0.0917285\pi$
$977$	4.67637e7	+	1.51944e7i	1.56737	+	0.509270i	0.608607	+	0.793472i	$0.291728\pi$
$978$	3.79030e7	−	5.21690e7i	1.26714	−	1.74408i
$979$	5.03945e6	+	3.66137e6i	0.168045	+	0.122092i
$980$	1.48063e6	−	1.50732e6i	0.0492471	−	0.0501348i
$981$	4.81197e7	−	3.49610e7i	1.59643	−	1.15988i
$982$		−	1.64104e7i		−	0.543050i
$983$	1.68647e7	+	2.32122e7i	0.556665	+	0.766184i	0.990898	−	0.134617i	$-0.0429804\pi$
$983$	1.68647e7	+	2.32122e7i	0.556665	+	0.766184i	−0.434232	+	0.900801i	$0.642980\pi$
$984$	−3.99068e6	−	1.22820e7i	−0.131389	−	0.404374i
$985$	1.07869e7	+	1.05959e7i	0.354248	+	0.347975i
$986$	3.07570e6	−	9.46604e6i	0.100752	−	0.310081i
$987$	−6.42411e7	+	2.08732e7i	−2.09904	+	0.682019i
$988$	7.49141e6	−	2.43411e6i	0.244158	−	0.0793318i
$989$	−1.49944e7	+	4.61480e7i	−0.487459	+	1.50024i
$990$	−1.35836e7	+	2.72585e7i	−0.440480	+	0.883922i
$991$	38963.9	+	119919.i	0.00126031	+	0.00387885i	0.951685	−	0.307077i	$-0.0993509\pi$
$991$	38963.9	+	119919.i	0.00126031	+	0.00387885i	−0.950424	+	0.310956i	$0.899351\pi$
$992$	−6.40301e6	−	8.81299e6i	−0.206588	−	0.284344i
$993$		−	3.48430e7i		−	1.12135i
$994$	−2.05934e7	+	1.49620e7i	−0.661091	+	0.480311i
$995$	6.07986e6	−	4.07386e7i	0.194687	−	1.30451i
$996$	−2.56303e7	−	1.86215e7i	−0.818664	−	0.594794i
$997$	−1.93637e7	+	2.66519e7i	−0.616952	+	0.849161i	−0.997127	−	0.0757534i	$-0.975864\pi$
$997$	−1.93637e7	+	2.66519e7i	−0.616952	+	0.849161i	0.380175	+	0.924915i	$0.375864\pi$
$998$	−7.54402e6	−	2.45120e6i	−0.239760	−	0.0779028i
$999$	1.27337e8			4.03684

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	50.6.e.a.29.7	yes	48
25.19	even	10	inner	50.6.e.a.19.7	✓	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
50.6.e.a.19.7	✓	48	25.19	even	10	inner
50.6.e.a.29.7	yes	48	1.1	even	1	trivial

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)

\(f(q)\)	\(=\)	\(q+(3.80423 + 1.23607i) q^{2} +(-16.9585 + 23.3414i) q^{3} +(12.9443 + 9.40456i) q^{4} +(-8.25144 + 55.2894i) q^{5} +(-93.3657 + 67.8341i) q^{6} -138.453i q^{7} +(37.6183 + 51.7771i) q^{8} +(-182.139 - 560.566i) q^{9} +O(q^{10})\)	\(q+(3.80423 + 1.23607i) q^{2} +(-16.9585 + 23.3414i) q^{3} +(12.9443 + 9.40456i) q^{4} +(-8.25144 + 55.2894i) q^{5} +(-93.3657 + 67.8341i) q^{6} -138.453i q^{7} +(37.6183 + 51.7771i) q^{8} +(-182.139 - 560.566i) q^{9} +(-99.7318 + 200.134i) q^{10} +(-71.4074 + 219.769i) q^{11} +(-439.032 + 142.650i) q^{12} +(-251.878 + 81.8400i) q^{13} +(171.137 - 526.707i) q^{14} +(-1150.60 - 1130.23i) q^{15} +(79.1084 + 243.470i) q^{16} +(323.609 + 445.410i) q^{17} -2357.66i q^{18} +(-1503.87 + 1092.63i) q^{19} +(-626.781 + 638.079i) q^{20} +(3231.69 + 2347.96i) q^{21} +(-543.300 + 747.788i) q^{22} +(3180.04 + 1033.26i) q^{23} -1846.50 q^{24} +(-2988.83 - 912.434i) q^{25} -1059.36 q^{26} +(9505.42 + 3088.50i) q^{27} +(1302.09 - 1792.18i) q^{28} +(-3656.43 - 2656.55i) q^{29} +(-2980.11 - 5721.86i) q^{30} +(-8606.44 + 6252.94i) q^{31} +1024.00i q^{32} +(-3918.76 - 5393.72i) q^{33} +(680.526 + 2094.44i) q^{34} +(7654.99 + 1142.44i) q^{35} +(2914.22 - 8969.05i) q^{36} +(12117.1 - 3937.07i) q^{37} +(-7071.64 + 2297.71i) q^{38} +(2361.21 - 7267.07i) q^{39} +(-3173.13 + 1652.65i) q^{40} +(2161.21 + 6651.52i) q^{41} +(9391.85 + 12926.8i) q^{42} +14511.7i q^{43} +(-2991.15 + 2173.20i) q^{44} +(32496.2 - 5444.87i) q^{45} +(10820.4 + 7861.50i) q^{46} +(-9939.24 + 13680.2i) q^{47} +(-7024.51 - 2282.40i) q^{48} -2362.27 q^{49} +(-10242.3 - 7165.50i) q^{50} -15884.4 q^{51} +(-4030.04 - 1309.44i) q^{52} +(7607.08 - 10470.2i) q^{53} +(32343.2 + 23498.7i) q^{54} +(-11561.7 - 5761.48i) q^{55} +(7168.70 - 5208.37i) q^{56} -53631.9i q^{57} +(-10626.2 - 14625.7i) q^{58} +(7688.01 + 23661.3i) q^{59} +(-4264.39 - 25450.9i) q^{60} +(6872.86 - 21152.5i) q^{61} +(-40469.9 + 13149.5i) q^{62} +(-77612.1 + 25217.7i) q^{63} +(-1265.73 + 3895.53i) q^{64} +(-2446.53 - 14601.5i) q^{65} +(-8240.87 - 25362.8i) q^{66} +(8845.67 + 12175.0i) q^{67} +8808.92i q^{68} +(-78046.6 + 56704.2i) q^{69} +(27709.2 + 13808.2i) q^{70} +(-37184.7 - 27016.3i) q^{71} +(22172.7 - 30518.1i) q^{72} +(-27613.5 - 8972.17i) q^{73} +50962.5 q^{74} +(71983.6 - 54289.9i) q^{75} -29742.2 q^{76} +(30427.8 + 9886.58i) q^{77} +(17965.2 - 24727.0i) q^{78} +(20275.5 + 14731.0i) q^{79} +(-14114.1 + 2364.87i) q^{80} +(-117414. + 85306.5i) q^{81} +27975.3i q^{82} +(40339.0 + 55521.9i) q^{83} +(19750.4 + 60785.3i) q^{84} +(-27296.7 + 14216.9i) q^{85} +(-17937.5 + 55206.0i) q^{86} +(124015. - 40295.0i) q^{87} +(-14065.2 + 4570.07i) q^{88} +(8330.04 - 25637.2i) q^{89} +(130353. + 19454.1i) q^{90} +(11331.0 + 34873.3i) q^{91} +(31446.0 + 43281.7i) q^{92} -306927. i q^{93} +(-54720.7 + 39756.9i) q^{94} +(-48001.6 - 92164.0i) q^{95} +(-23901.6 - 17365.5i) q^{96} +(-26055.6 + 35862.5i) q^{97} +(-8986.62 - 2919.93i) q^{98} +136201. 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

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